LMFDB - Embedded newform 784.2.x.m.165.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [784,2,Mod(165,784)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(784, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([0, 3, 8]))

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

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

chi := DirichletCharacter("784.165");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 784 = 2^{4} \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	784.x (of order $12$, degree $4$, 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:	$6.26027151847$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$6$ over $\Q(\zeta_{12})$
Twist minimal:	no (minimal twist has level 112)
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			165.3
Character	$\chi$	$=$	784.165
Dual form			784.2.x.m.765.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.329210 - 1.37536i) q^{2} +(-0.231031 - 0.862219i) q^{3} +(-1.78324 + 0.905566i) q^{4} +(0.857449 - 3.20004i) q^{5} +(-1.10981 + 0.601602i) q^{6} +(1.83254 + 2.15448i) q^{8} +(1.90803 - 1.10160i) q^{9} +O(q^{10})$	\(q+(-0.329210 - 1.37536i) q^{2} +(-0.231031 - 0.862219i) q^{3} +(-1.78324 + 0.905566i) q^{4} +(0.857449 - 3.20004i) q^{5} +(-1.10981 + 0.601602i) q^{6} +(1.83254 + 2.15448i) q^{8} +(1.90803 - 1.10160i) q^{9} +(-4.68350 - 0.125816i) q^{10} +(2.98217 - 0.799070i) q^{11} +(1.19278 + 1.32833i) q^{12} +(4.03390 - 4.03390i) q^{13} -2.95723 q^{15} +(2.35990 - 3.22969i) q^{16} +(0.173966 - 0.301317i) q^{17} +(-2.14324 - 2.26157i) q^{18} +(5.82380 + 1.56048i) q^{19} +(1.36881 + 6.48293i) q^{20} +(-2.08077 - 3.83850i) q^{22} +(-5.40216 + 3.11894i) q^{23} +(1.43426 - 2.07780i) q^{24} +(-5.17494 - 2.98775i) q^{25} +(-6.87607 - 4.22007i) q^{26} +(-3.28420 - 3.28420i) q^{27} +(1.21961 - 1.21961i) q^{29} +(0.973551 + 4.06727i) q^{30} +(-0.631188 + 1.09325i) q^{31} +(-5.21889 - 2.18247i) q^{32} +(-1.37795 - 2.38667i) q^{33} +(-0.471692 - 0.140069i) q^{34} +(-2.40491 + 3.69227i) q^{36} +(-2.35091 + 8.77373i) q^{37} +(0.228975 - 8.52356i) q^{38} +(-4.41005 - 2.54615i) q^{39} +(8.46575 - 4.01686i) q^{40} -2.68519i q^{41} +(4.05478 + 4.05478i) q^{43} +(-4.59432 + 4.12548i) q^{44} +(-1.88914 - 7.05035i) q^{45} +(6.06811 + 6.40314i) q^{46} +(2.32249 + 4.02267i) q^{47} +(-3.32990 - 1.28859i) q^{48} +(-2.40560 + 8.10101i) q^{50} +(-0.299993 - 0.0803829i) q^{51} +(-3.54045 + 10.8464i) q^{52} +(-11.5307 + 3.08965i) q^{53} +(-3.43577 + 5.59815i) q^{54} -10.2282i q^{55} -5.38191i q^{57} +(-2.07891 - 1.27590i) q^{58} +(-7.07295 + 1.89519i) q^{59} +(5.27346 - 2.67797i) q^{60} +(-0.00728993 - 0.00195333i) q^{61} +(1.71141 + 0.508203i) q^{62} +(-1.28358 + 7.89636i) q^{64} +(-9.44979 - 16.3675i) q^{65} +(-2.82890 + 2.68089i) q^{66} +(1.10544 + 4.12554i) q^{67} +(-0.0373600 + 0.694859i) q^{68} +(3.93727 + 3.93727i) q^{69} -0.828913i q^{71} +(5.86993 + 2.09208i) q^{72} +(5.41415 + 3.12586i) q^{73} +(12.8410 + 0.344957i) q^{74} +(-1.38052 + 5.15219i) q^{75} +(-11.7984 + 2.49112i) q^{76} +(-2.05004 + 6.90364i) q^{78} +(0.377945 + 0.654620i) q^{79} +(-8.31164 - 10.3211i) q^{80} +(1.23186 - 2.13364i) q^{81} +(-3.69311 + 0.883991i) q^{82} +(3.66586 - 3.66586i) q^{83} +(-0.815062 - 0.815062i) q^{85} +(4.24191 - 6.91166i) q^{86} +(-1.33334 - 0.769803i) q^{87} +(7.18653 + 4.96070i) q^{88} +(5.40799 - 3.12231i) q^{89} +(-9.07486 + 4.91929i) q^{90} +(6.80895 - 10.4538i) q^{92} +(1.08844 + 0.291648i) q^{93} +(4.76804 - 4.51857i) q^{94} +(9.98723 - 17.2984i) q^{95} +(-0.676044 + 5.00404i) q^{96} -2.18393 q^{97} +(4.80981 - 4.80981i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q - 2 q^{2} + 4 q^{3} + 6 q^{4} + 4 q^{5} - 8 q^{6} - 8 q^{8}+O(q^{10}) $ 24 * q - 2 * q^2 + 4 * q^3 + 6 * q^4 + 4 * q^5 - 8 * q^6 - 8 * q^8	$ 24 q - 2 q^{2} + 4 q^{3} + 6 q^{4} + 4 q^{5} - 8 q^{6} - 8 q^{8} - 4 q^{10} + 8 q^{12} - 48 q^{15} - 10 q^{16} - 8 q^{17} + 40 q^{20} + 28 q^{22} - 8 q^{24} - 20 q^{26} - 8 q^{27} - 8 q^{29} + 28 q^{30} - 8 q^{31} - 12 q^{32} - 16 q^{34} - 32 q^{36} + 20 q^{37} + 16 q^{38} - 8 q^{40} + 32 q^{43} - 14 q^{44} + 40 q^{45} + 28 q^{46} + 16 q^{47} - 32 q^{48} + 88 q^{50} + 16 q^{51} - 16 q^{52} - 4 q^{53} + 64 q^{54} - 14 q^{58} - 16 q^{59} - 60 q^{60} - 20 q^{61} - 16 q^{62} - 36 q^{64} - 32 q^{65} + 12 q^{66} - 24 q^{67} - 28 q^{68} + 8 q^{69} - 6 q^{72} + 38 q^{74} - 40 q^{75} - 96 q^{76} - 152 q^{78} - 24 q^{79} + 24 q^{80} + 44 q^{81} - 16 q^{82} + 40 q^{83} - 16 q^{85} - 38 q^{86} + 14 q^{88} + 80 q^{90} + 64 q^{92} + 48 q^{93} - 24 q^{94} - 16 q^{96} - 96 q^{97} + 64 q^{99}+O(q^{100}) $ 24 * q - 2 * q^2 + 4 * q^3 + 6 * q^4 + 4 * q^5 - 8 * q^6 - 8 * q^8 - 4 * q^10 + 8 * q^12 - 48 * q^15 - 10 * q^16 - 8 * q^17 + 40 * q^20 + 28 * q^22 - 8 * q^24 - 20 * q^26 - 8 * q^27 - 8 * q^29 + 28 * q^30 - 8 * q^31 - 12 * q^32 - 16 * q^34 - 32 * q^36 + 20 * q^37 + 16 * q^38 - 8 * q^40 + 32 * q^43 - 14 * q^44 + 40 * q^45 + 28 * q^46 + 16 * q^47 - 32 * q^48 + 88 * q^50 + 16 * q^51 - 16 * q^52 - 4 * q^53 + 64 * q^54 - 14 * q^58 - 16 * q^59 - 60 * q^60 - 20 * q^61 - 16 * q^62 - 36 * q^64 - 32 * q^65 + 12 * q^66 - 24 * q^67 - 28 * q^68 + 8 * q^69 - 6 * q^72 + 38 * q^74 - 40 * q^75 - 96 * q^76 - 152 * q^78 - 24 * q^79 + 24 * q^80 + 44 * q^81 - 16 * q^82 + 40 * q^83 - 16 * q^85 - 38 * q^86 + 14 * q^88 + 80 * q^90 + 64 * q^92 + 48 * q^93 - 24 * q^94 - 16 * q^96 - 96 * q^97 + 64 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/784\mathbb{Z}\right)^\times$.

$n$	$197$	$687$	$689$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$1$	$e\left(\frac{2}{3}\right)$

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 $

$2$	−0.329210	−	1.37536i	−0.232787	−	0.972528i
$2$	−0.329210	−	1.37536i	−0.232787	−	0.972528i
$3$	−0.231031	−	0.862219i	−0.133386	−	0.497802i	0.866614	−	0.498980i	$-0.166292\pi$
$3$	−0.231031	−	0.862219i	−0.133386	−	0.497802i	−0.999999	+	0.00117766i	$0.999625\pi$
$4$	−1.78324	+	0.905566i	−0.891621	+	0.452783i
$5$	0.857449	−	3.20004i	0.383463	−	1.43110i	−0.457113	−	0.889409i	$-0.651116\pi$
$5$	0.857449	−	3.20004i	0.383463	−	1.43110i	0.840576	−	0.541694i	$-0.182217\pi$
$6$	−1.10981	+	0.601602i	−0.453076	+	0.245603i
$7$		0			0
$7$		0			0
$8$	1.83254	+	2.15448i	0.647902	+	0.761724i
$9$	1.90803	−	1.10160i	0.636010	−	0.367201i
$10$	−4.68350	−	0.125816i	−1.48105	−	0.0397866i
$11$	2.98217	−	0.799070i	0.899158	−	0.240929i	0.220503	−	0.975386i	$-0.429230\pi$
$11$	2.98217	−	0.799070i	0.899158	−	0.240929i	0.678654	+	0.734458i	$0.262563\pi$
$12$	1.19278	+	1.32833i	0.344326	+	0.383456i
$13$	4.03390	−	4.03390i	1.11880	−	1.11880i	0.126884	−	0.991918i	$-0.459502\pi$
$13$	4.03390	−	4.03390i	1.11880	−	1.11880i	0.991918	−	0.126884i	$-0.0404976\pi$
$14$		0			0
$15$	−2.95723			−0.763555
$16$	2.35990	−	3.22969i	0.589975	−	0.807421i
$17$	0.173966	−	0.301317i	0.0421929	−	0.0730802i	−0.844158	−	0.536095i	$-0.819899\pi$
$17$	0.173966	−	0.301317i	0.0421929	−	0.0730802i	0.886351	+	0.463015i	$0.153232\pi$
$18$	−2.14324	−	2.26157i	−0.505168	−	0.533058i
$19$	5.82380	+	1.56048i	1.33607	+	0.357999i	0.854975	−	0.518669i	$-0.173572\pi$
$19$	5.82380	+	1.56048i	1.33607	+	0.357999i	0.481096	+	0.876668i	$0.340239\pi$
$20$	1.36881	+	6.48293i	0.306076	+	1.44963i
$21$		0			0
$22$	−2.08077	−	3.83850i	−0.443622	−	0.818371i
$23$	−5.40216	+	3.11894i	−1.12643	+	0.650344i	−0.943034	−	0.332696i	$-0.892042\pi$
$23$	−5.40216	+	3.11894i	−1.12643	+	0.650344i	−0.183394	+	0.983040i	$0.558708\pi$
$24$	1.43426	−	2.07780i	0.292767	−	0.424130i
$25$	−5.17494	−	2.98775i	−1.03499	−	0.597550i
$26$	−6.87607	−	4.22007i	−1.34851	−	0.827624i
$27$	−3.28420	−	3.28420i	−0.632044	−	0.632044i
$28$		0			0
$29$	1.21961	−	1.21961i	0.226476	−	0.226476i	−0.584743	−	0.811219i	$-0.698805\pi$
$29$	1.21961	−	1.21961i	0.226476	−	0.226476i	0.811219	+	0.584743i	$0.198805\pi$
$30$	0.973551	+	4.06727i	0.177745	+	0.742578i
$31$	−0.631188	+	1.09325i	−0.113365	+	0.196353i	−0.917125	−	0.398600i	$-0.869496\pi$
$31$	−0.631188	+	1.09325i	−0.113365	+	0.196353i	0.803760	+	0.594953i	$0.202830\pi$
$32$	−5.21889	−	2.18247i	−0.922578	−	0.385810i
$33$	−1.37795	−	2.38667i	−0.239869	−	0.415466i
$34$	−0.471692	−	0.140069i	−0.0808945	−	0.0240216i
$35$		0			0
$36$	−2.40491	+	3.69227i	−0.400818	+	0.615378i
$37$	−2.35091	+	8.77373i	−0.386488	+	1.44239i	0.449321	+	0.893371i	$0.351666\pi$
$37$	−2.35091	+	8.77373i	−0.386488	+	1.44239i	−0.835808	+	0.549021i	$0.815001\pi$
$38$	0.228975	−	8.52356i	0.0371446	−	1.38270i
$39$	−4.41005	−	2.54615i	−0.706174	−	0.407710i
$40$	8.46575	−	4.01686i	1.33855	−	0.635121i
$41$		−	2.68519i		−	0.419356i	−0.977770	−	0.209678i	$-0.932758\pi$
$41$		−	2.68519i		−	0.419356i	0.977770	−	0.209678i	$-0.0672416\pi$
$42$		0			0
$43$	4.05478	+	4.05478i	0.618348	+	0.618348i	0.945107	−	0.326760i	$-0.105957\pi$
$43$	4.05478	+	4.05478i	0.618348	+	0.618348i	−0.326760	+	0.945107i	$0.605957\pi$
$44$	−4.59432	+	4.12548i	−0.692619	+	0.621940i
$45$	−1.88914	−	7.05035i	−0.281616	−	1.05100i
$46$	6.06811	+	6.40314i	0.894695	+	0.944091i
$47$	2.32249	+	4.02267i	0.338770	+	0.586767i	0.984202	−	0.177051i	$-0.0566558\pi$
$47$	2.32249	+	4.02267i	0.338770	+	0.586767i	−0.645432	+	0.763818i	$0.723323\pi$
$48$	−3.32990	−	1.28859i	−0.480630	−	0.185992i
$49$		0			0
$50$	−2.40560	+	8.10101i	−0.340203	+	1.14566i
$51$	−0.299993	−	0.0803829i	−0.0420074	−	0.0112559i
$52$	−3.54045	+	10.8464i	−0.490972	+	1.50412i
$53$	−11.5307	+	3.08965i	−1.58387	+	0.424396i	−0.940120	−	0.340842i	$-0.889288\pi$
$53$	−11.5307	+	3.08965i	−1.58387	+	0.424396i	−0.643747	+	0.765238i	$0.722621\pi$
$54$	−3.43577	+	5.59815i	−0.467549	+	0.761812i
$55$		−	10.2282i		−	1.37917i
$56$		0			0
$57$		−	5.38191i		−	0.712851i
$58$	−2.07891	−	1.27590i	−0.272975	−	0.167534i
$59$	−7.07295	+	1.89519i	−0.920820	+	0.246733i	−0.687936	−	0.725771i	$-0.741483\pi$
$59$	−7.07295	+	1.89519i	−0.920820	+	0.246733i	−0.232884	+	0.972504i	$0.574816\pi$
$60$	5.27346	−	2.67797i	0.680801	−	0.345725i
$61$	−0.00728993	−	0.00195333i	−0.000933379	−	0.000250098i	0.258352	−	0.966051i	$-0.416820\pi$
$61$	−0.00728993	−	0.00195333i	−0.000933379	−	0.000250098i	−0.259286	+	0.965801i	$0.583487\pi$
$62$	1.71141	+	0.508203i	0.217349	+	0.0645419i
$63$		0			0
$64$	−1.28358	+	7.89636i	−0.160447	+	0.987044i
$65$	−9.44979	−	16.3675i	−1.17210	−	2.03014i
$66$	−2.82890	+	2.68089i	−0.348214	+	0.329995i
$67$	1.10544	+	4.12554i	0.135050	+	0.504015i	0.999998	+	0.00215224i	$0.000685080\pi$
$67$	1.10544	+	4.12554i	0.135050	+	0.504015i	−0.864947	+	0.501863i	$0.832648\pi$
$68$	−0.0373600	+	0.694859i	−0.00453057	+	0.0842640i
$69$	3.93727	+	3.93727i	0.473992	+	0.473992i
$70$		0			0
$71$		−	0.828913i		−	0.0983739i	−0.998790	−	0.0491869i	$-0.984337\pi$
$71$		−	0.828913i		−	0.0983739i	0.998790	−	0.0491869i	$-0.0156630\pi$
$72$	5.86993	+	2.09208i	0.691778	+	0.246554i
$73$	5.41415	+	3.12586i	0.633679	+	0.365855i	0.782175	−	0.623058i	$-0.214110\pi$
$73$	5.41415	+	3.12586i	0.633679	+	0.365855i	−0.148497	+	0.988913i	$0.547443\pi$
$74$	12.8410	+	0.344957i	1.49274	+	0.0401005i
$75$	−1.38052	+	5.15219i	−0.159409	+	0.594923i
$76$	−11.7984	+	2.49112i	−1.35337	+	0.285751i
$77$		0			0
$78$	−2.05004	+	6.90364i	−0.232121	+	0.781683i
$79$	0.377945	+	0.654620i	0.0425222	+	0.0736506i	0.886503	−	0.462722i	$-0.153127\pi$
$79$	0.377945	+	0.654620i	0.0425222	+	0.0736506i	−0.843981	+	0.536373i	$0.819794\pi$
$80$	−8.31164	−	10.3211i	−0.929270	−	1.15393i
$81$	1.23186	−	2.13364i	0.136873	−	0.237072i
$82$	−3.69311	+	0.883991i	−0.407836	+	0.0976205i
$83$	3.66586	−	3.66586i	0.402380	−	0.402380i	−0.476691	−	0.879071i	$-0.658164\pi$
$83$	3.66586	−	3.66586i	0.402380	−	0.402380i	0.879071	+	0.476691i	$0.158164\pi$
$84$		0			0
$85$	−0.815062	−	0.815062i	−0.0884059	−	0.0884059i
$86$	4.24191	−	6.91166i	0.457417	−	0.745304i
$87$	−1.33334	−	0.769803i	−0.142949	−	0.0825315i
$88$	7.18653	+	4.96070i	0.766087	+	0.528812i
$89$	5.40799	−	3.12231i	0.573246	−	0.330964i	−0.185199	−	0.982701i	$-0.559293\pi$
$89$	5.40799	−	3.12231i	0.573246	−	0.330964i	0.758445	+	0.651737i	$0.225960\pi$
$90$	−9.07486	+	4.91929i	−0.956574	+	0.518539i
$91$		0			0
$92$	6.80895	−	10.4538i	0.709882	−	1.08989i
$93$	1.08844	+	0.291648i	0.112866	+	0.0302424i
$94$	4.76804	−	4.51857i	0.491786	−	0.466055i
$95$	9.98723	−	17.2984i	1.02467	−	1.77478i
$96$	−0.676044	+	5.00404i	−0.0689984	+	0.510723i
$97$	−2.18393			−0.221745			−0.110872	−	0.993835i	$-0.535365\pi$
$97$	−2.18393			−0.221745			−0.110872	+	0.993835i	$0.535365\pi$
$98$		0			0
$99$	4.80981	−	4.80981i	0.483404	−	0.483404i
$100$	11.9338	+	0.641635i	1.19338	+	0.0641635i
$101$	−6.49307	+	1.73981i	−0.646084	+	0.173118i	−0.566958	−	0.823747i	$-0.691880\pi$
$101$	−6.49307	+	1.73981i	−0.646084	+	0.173118i	−0.0791265	+	0.996865i	$0.525213\pi$
$102$	−0.0117948	+	0.439062i	−0.00116786	+	0.0434736i
$103$	−13.6190	+	7.86295i	−1.34192	+	0.774760i	−0.987089	−	0.160170i	$-0.948796\pi$
$103$	−13.6190	+	7.86295i	−1.34192	+	0.774760i	−0.354834	+	0.934929i	$0.615462\pi$
$104$	16.0832	+	1.29867i	1.57709	+	0.127345i
$105$		0			0
$106$	8.04542	+	14.8418i	0.781440	+	1.44156i
$107$	−2.44534	+	9.12614i	−0.236400	+	0.882257i	0.741113	+	0.671381i	$0.234298\pi$
$107$	−2.44534	+	9.12614i	−0.236400	+	0.882257i	−0.977513	+	0.210876i	$0.932368\pi$
$108$	8.83058	+	2.88246i	0.849723	+	0.277365i
$109$	−0.297398	−	1.10991i	−0.0284856	−	0.106310i	0.950219	−	0.311582i	$-0.100859\pi$
$109$	−0.297398	−	1.10991i	−0.0284856	−	0.106310i	−0.978705	+	0.205272i	$0.934192\pi$
$110$	−14.0675	+	3.36724i	−1.34129	+	0.321053i
$111$	8.10800			0.769578
$112$		0			0
$113$	−18.5170			−1.74193			−0.870966	−	0.491343i	$-0.836506\pi$
$113$	−18.5170			−1.74193			−0.870966	+	0.491343i	$0.836506\pi$
$114$	−7.40207	+	1.77178i	−0.693268	+	0.165942i
$115$	5.34866	+	19.9615i	0.498765	+	1.86142i
$116$	−1.07042	+	3.27930i	−0.0993862	+	0.304475i
$117$	3.25305	−	12.1405i	0.300745	−	1.12239i
$118$	4.93506	+	9.10396i	0.454309	+	0.838087i
$119$		0			0
$120$	−5.41926	−	6.37131i	−0.494708	−	0.581618i
$121$	−1.27146	+	0.734080i	−0.115588	+	0.0667345i
$122$	−0.000286619		0.0106693i	−2.59492e−5		0.000965957i
$123$	−2.31522	+	0.620361i	−0.208756	+	0.0559361i
$124$	0.135551	−	2.52111i	0.0121728	−	0.226402i
$125$	−2.28520	+	2.28520i	−0.204395	+	0.204395i
$126$		0			0
$127$	13.7063			1.21624			0.608121	−	0.793845i	$-0.291924\pi$
$127$	13.7063			1.21624			0.608121	+	0.793845i	$0.291924\pi$
$128$	11.2829	−	0.834175i	0.997278	−	0.0737313i
$129$	2.55933	−	4.43288i	0.225336	−	0.390294i
$130$	−19.4003	+	18.3852i	−1.70152	+	1.61249i
$131$	−4.82105	−	1.29180i	−0.421217	−	0.112865i	0.0419836	−	0.999118i	$-0.486632\pi$
$131$	−4.82105	−	1.29180i	−0.421217	−	0.112865i	−0.463200	+	0.886254i	$0.653299\pi$
$132$	4.61850	+	3.00819i	0.401989	+	0.261829i
$133$		0			0
$134$	5.31019	−	2.87854i	0.458731	−	0.248668i
$135$	−13.3256	+	7.69355i	−1.14689	+	0.662155i
$136$	0.967982	−	0.177371i	0.0830038	−	0.0152094i
$137$	13.5567	+	7.82698i	1.15823	+	0.668704i	0.950879	−	0.309563i	$-0.100183\pi$
$137$	13.5567	+	7.82698i	1.15823	+	0.668704i	0.207350	+	0.978267i	$0.433516\pi$
$138$	4.11898	−	6.71136i	0.350631	−	0.571309i
$139$	−1.52569	−	1.52569i	−0.129408	−	0.129408i	0.639436	−	0.768844i	$-0.279168\pi$
$139$	−1.52569	−	1.52569i	−0.129408	−	0.129408i	−0.768844	+	0.639436i	$0.779168\pi$
$140$		0			0
$141$	2.93185	−	2.93185i	0.246907	−	0.246907i
$142$	−1.14006	+	0.272887i	−0.0956713	+	0.0229001i
$143$	8.80639	−	15.2531i	0.736428	−	1.27553i
$144$	0.944934	−	8.76201i	0.0787445	−	0.730168i
$145$	−2.85705	−	4.94856i	−0.237265	−	0.410955i
$146$	2.51680	−	8.47549i	0.208292	−	0.701436i
$147$		0			0
$148$	−3.75294	−	17.7746i	−0.308490	−	1.46106i
$149$	3.38130	−	12.6192i	0.277007	−	1.03380i	−0.677478	−	0.735543i	$-0.736927\pi$
$149$	3.38130	−	12.6192i	0.277007	−	1.03380i	0.954485	−	0.298260i	$-0.0964062\pi$
$150$	7.54061	+	0.202569i	0.615688	+	0.0165397i
$151$	10.1555	+	5.86330i	0.826445	+	0.477149i	0.852634	−	0.522508i	$-0.175004\pi$
$151$	10.1555	+	5.86330i	0.826445	+	0.477149i	−0.0261886	+	0.999657i	$0.508337\pi$
$152$	7.31033	+	15.4069i	0.592946	+	1.24967i
$153$		−	0.766564i		−	0.0619730i
$154$		0			0
$155$	2.95723	+	2.95723i	0.237531	+	0.237531i
$156$	10.1699	+	0.546798i	0.814243	+	0.0437789i
$157$	3.80001	+	14.1818i	0.303274	+	1.13183i	0.934421	+	0.356171i	$0.115918\pi$
$157$	3.80001	+	14.1818i	0.303274	+	1.13183i	−0.631147	+	0.775663i	$0.717415\pi$
$158$	0.775917	−	0.735319i	0.0617286	−	0.0584989i
$159$	5.32791	+	9.22821i	0.422530	+	0.731844i
$160$	−11.4589	+	14.8293i	−0.905909	+	1.17236i
$161$		0			0
$162$	−3.34007	−	0.991836i	−0.262421	−	0.0779260i
$163$	21.3857	+	5.73029i	1.67506	+	0.448831i	0.966468	−	0.256788i	$-0.0826642\pi$
$163$	21.3857	+	5.73029i	1.67506	+	0.448831i	0.708592	+	0.705619i	$0.249331\pi$
$164$	2.43162	+	4.78834i	0.189877	+	0.373907i
$165$	−8.81897	+	2.36304i	−0.686556	+	0.183962i
$166$	−6.24872	−	3.83505i	−0.484995	−	0.297657i
$167$			2.12023i			0.164068i	0.996630	+	0.0820341i	$0.0261416\pi$
$167$			2.12023i			0.164068i	−0.996630	+	0.0820341i	$0.973858\pi$
$168$		0			0
$169$		−	19.5446i		−	1.50343i
$170$	−0.852679	+	1.38933i	−0.0653975	+	0.106557i
$171$	12.8310	−	3.43806i	0.981213	−	0.262915i
$172$	−10.9025	−	3.55878i	−0.831309	−	0.271354i
$173$	2.90491	+	0.778368i	0.220856	+	0.0591782i	0.367550	−	0.930004i	$-0.380197\pi$
$173$	2.90491	+	0.778368i	0.220856	+	0.0591782i	−0.146694	+	0.989182i	$0.546863\pi$
$174$	−0.619810	+	2.08725i	−0.0469876	+	0.158234i
$175$		0			0
$176$	4.45688	−	11.5172i	0.335950	−	0.868141i
$177$	3.26814	+	5.66059i	0.245648	+	0.425476i
$178$	−6.07467	−	6.41005i	−0.455316	−	0.480454i
$179$	0.519432	+	1.93855i	0.0388242	+	0.144894i	0.982617	−	0.185643i	$-0.0594368\pi$
$179$	0.519432	+	1.93855i	0.0388242	+	0.144894i	−0.943793	+	0.330537i	$0.892770\pi$
$180$	9.75334	+	10.8617i	0.726971	+	0.809586i
$181$	−14.3191	−	14.3191i	−1.06433	−	1.06433i	−0.997783	−	0.0665470i	$-0.978802\pi$
$181$	−14.3191	−	14.3191i	−1.06433	−	1.06433i	−0.0665470	−	0.997783i	$-0.521198\pi$
$182$		0			0
$183$			0.00673679i			0.000497998i
$184$	−16.6194	−	5.92326i	−1.22520	−	0.436669i
$185$	26.0605	+	15.0461i	1.91601	+	1.10621i
$186$	0.0427944	−	1.59302i	0.00313784	−	0.116806i
$187$	0.278021	−	1.03759i	0.0203309	−	0.0758761i
$188$	−7.78435	−	5.07022i	−0.567732	−	0.369784i
$189$		0			0
$190$	−27.0794	−	8.04125i	−1.96455	−	0.583374i
$191$	−3.11139	−	5.38909i	−0.225133	−	0.389941i	0.731227	−	0.682135i	$-0.238948\pi$
$191$	−3.11139	−	5.38909i	−0.225133	−	0.389941i	−0.956359	+	0.292194i	$0.905615\pi$
$192$	7.10493	−	0.717576i	0.512754	−	0.0517866i
$193$	−0.788091	+	1.36501i	−0.0567280	+	0.0982558i	−0.892995	−	0.450067i	$-0.851400\pi$
$193$	−0.788091	+	1.36501i	−0.0567280	+	0.0982558i	0.836267	+	0.548323i	$0.184733\pi$
$194$	0.718973	+	3.00370i	0.0516193	+	0.215653i
$195$	−11.9292	+	11.9292i	−0.854266	+	0.854266i
$196$		0			0
$197$	10.7183	+	10.7183i	0.763648	+	0.763648i	0.976980	−	0.213332i	$-0.0684315\pi$
$197$	10.7183	+	10.7183i	0.763648	+	0.763648i	−0.213332	+	0.976980i	$0.568432\pi$
$198$	−8.19867	−	5.03179i	−0.582654	−	0.357594i
$199$	−22.1151	−	12.7681i	−1.56769	−	0.905109i	−0.996437	−	0.0843377i	$-0.973123\pi$
$199$	−22.1151	−	12.7681i	−1.56769	−	0.905109i	−0.571257	−	0.820771i	$-0.693544\pi$
$200$	−3.04624	−	16.6245i	−0.215401	−	1.17553i
$201$	3.30173	−	1.90625i	0.232886	−	0.134457i
$202$	4.53045	+	8.35755i	0.318762	+	0.588035i
$203$		0			0
$204$	0.607752	−	0.128321i	0.0425511	−	0.00898429i
$205$	−8.59272	−	2.30241i	−0.600142	−	0.160808i
$206$	15.2979	+	16.1425i	1.06586	+	1.12470i
$207$	−6.87166	+	11.9021i	−0.477613	+	0.827250i
$208$	−3.50863	−	22.5478i	−0.243279	−	1.56341i
$209$	18.6145			1.28759
$210$		0			0
$211$	9.19881	−	9.19881i	0.633272	−	0.633272i	−0.315615	−	0.948887i	$-0.602211\pi$
$211$	9.19881	−	9.19881i	0.633272	−	0.633272i	0.948887	+	0.315615i	$0.102211\pi$
$212$	17.7642	−	15.9514i	1.22005	−	1.09555i
$213$	−0.714704	+	0.191504i	−0.0489707	+	0.0131217i
$214$	13.3568	+	0.358813i	0.913050	+	0.0245280i
$215$	16.4522	−	9.49870i	1.12203	−	0.647806i
$216$	1.05731	−	13.0942i	0.0719409	−	0.890946i
$217$		0			0
$218$	−1.42862	+	0.774422i	−0.0967580	+	0.0524505i
$219$	1.44434	−	5.39036i	0.0975995	−	0.364246i
$220$	9.26234	+	18.2394i	0.624467	+	1.22970i
$221$	−0.513724	−	1.91724i	−0.0345568	−	0.128968i
$222$	−2.66924	−	11.1514i	−0.179147	−	0.748436i
$223$	−12.7530			−0.854003			−0.427001	−	0.904251i	$-0.640430\pi$
$223$	−12.7530			−0.854003			−0.427001	+	0.904251i	$0.640430\pi$
$224$		0			0
$225$	−13.1652			−0.877683
$226$	6.09598	+	25.4676i	0.405499	+	1.69408i
$227$	4.48200	+	16.7271i	0.297481	+	1.11021i	0.939227	+	0.343296i	$0.111544\pi$
$227$	4.48200	+	16.7271i	0.297481	+	1.11021i	−0.641746	+	0.766917i	$0.721790\pi$
$228$	4.87367	+	9.59724i	0.322767	+	0.635593i
$229$	3.63534	−	13.5673i	0.240230	−	0.896551i	−0.735491	−	0.677534i	$-0.763049\pi$
$229$	3.63534	−	13.5673i	0.240230	−	0.896551i	0.975721	−	0.219016i	$-0.0702848\pi$
$230$	25.6934	−	13.9279i	1.69417	−	0.918376i
$231$		0			0
$232$	4.86261	+	0.392640i	0.319246	+	0.0257781i
$233$	15.8606	−	9.15715i	1.03907	−	0.599905i	0.119497	−	0.992835i	$-0.461872\pi$
$233$	15.8606	−	9.15715i	1.03907	−	0.599905i	0.919568	+	0.392930i	$0.128539\pi$
$234$	−17.7686	−	0.477331i	−1.16157	−	0.0312041i
$235$	14.8641	−	3.98283i	0.969629	−	0.259811i
$236$	10.8966	−	9.78461i	0.709306	−	0.636924i
$237$	0.477109	−	0.477109i	0.0309916	−	0.0309916i
$238$		0			0
$239$	−18.3443			−1.18660			−0.593298	−	0.804983i	$-0.702174\pi$
$239$	−18.3443			−1.18660			−0.593298	+	0.804983i	$0.702174\pi$
$240$	−6.97878	+	9.55094i	−0.450478	+	0.616510i
$241$	12.7073	−	22.0098i	0.818552	−	1.41777i	−0.0881977	−	0.996103i	$-0.528111\pi$
$241$	12.7073	−	22.0098i	0.818552	−	1.41777i	0.906749	−	0.421670i	$-0.138556\pi$
$242$	1.42820	+	1.50706i	0.0918084	+	0.0968772i
$243$	−15.5832	−	4.17550i	−0.999660	−	0.267858i
$244$	0.0147686	−	0.00311825i	0.000945461	−	0.000199626i
$245$		0			0
$246$	1.61542	+	2.98004i	0.102995	+	0.190000i
$247$	29.7874	−	17.1978i	1.89533	−	1.09427i
$248$	−3.51206	+	0.643543i	−0.223016	+	0.0408650i
$249$	−4.00770	−	2.31385i	−0.253978	−	0.146634i
$250$	3.89529	+	2.39067i	0.246360	+	0.151199i
$251$	10.9301	+	10.9301i	0.689903	+	0.689903i	0.962210	−	0.272307i	$-0.0877867\pi$
$251$	10.9301	+	10.9301i	0.689903	+	0.689903i	−0.272307	+	0.962210i	$0.587787\pi$
$252$		0			0
$253$	−13.6179	+	13.6179i	−0.856150	+	0.856150i
$254$	−4.51227	−	18.8512i	−0.283125	−	1.18283i
$255$	−0.514457	+	0.891066i	−0.0322166	+	0.0558007i
$256$	−4.86174	−	15.2435i	−0.303859	−	0.952717i
$257$	1.14826	+	1.98884i	0.0716265	+	0.124061i	0.899614	−	0.436685i	$-0.143848\pi$
$257$	1.14826	+	1.98884i	0.0716265	+	0.124061i	−0.827988	+	0.560746i	$0.810514\pi$
$258$	−6.93937	−	2.06065i	−0.432027	−	0.128290i
$259$		0			0
$260$	31.6731	+	20.6298i	1.96428	+	1.27941i
$261$	0.983528	−	3.67058i	0.0608789	−	0.227203i
$262$	−0.189549	+	7.05596i	−0.0117104	+	0.435918i
$263$	−10.2631	−	5.92538i	−0.632848	−	0.365375i	0.149007	−	0.988836i	$-0.452392\pi$
$263$	−10.2631	−	5.92538i	−0.632848	−	0.365375i	−0.781854	+	0.623462i	$0.785726\pi$
$264$	2.61690	−	7.34243i	0.161059	−	0.451896i
$265$			39.5481i			2.42942i
$266$		0			0
$267$	−3.94152	−	3.94152i	−0.241217	−	0.241217i
$268$	−5.70721	−	6.35579i	−0.348623	−	0.388242i
$269$	−2.08924	−	7.79715i	−0.127383	−	0.475401i	0.872530	−	0.488560i	$-0.162478\pi$
$269$	−2.08924	−	7.79715i	−0.127383	−	0.475401i	−0.999913	+	0.0131596i	$0.995811\pi$
$270$	14.9683	+	15.7948i	0.910944	+	0.961238i
$271$	13.0617	+	22.6235i	0.793441	+	1.37428i	0.923825	+	0.382816i	$0.125046\pi$
$271$	13.0617	+	22.6235i	0.793441	+	1.37428i	−0.130384	+	0.991464i	$0.541621\pi$
$272$	−0.562619	−	1.27293i	−0.0341138	−	0.0771829i
$273$		0			0
$274$	6.30192	−	21.2221i	0.380713	−	1.28208i
$275$	−17.8199	−	4.77484i	−1.07458	−	0.287934i
$276$	−10.5866	−	3.45565i	−0.637236	−	0.208005i
$277$	−2.70847	+	0.725732i	−0.162736	+	0.0436050i	−0.339267	−	0.940690i	$-0.610179\pi$
$277$	−2.70847	+	0.725732i	−0.162736	+	0.0436050i	0.176531	+	0.984295i	$0.443512\pi$
$278$	−1.59611	+	2.60065i	−0.0957282	+	0.155977i
$279$			2.78127i			0.166510i
$280$		0			0
$281$			6.52475i			0.389234i	0.980879	+	0.194617i	$0.0623464\pi$
$281$			6.52475i			0.389234i	−0.980879	+	0.194617i	$0.937654\pi$
$282$	−4.99756	−	3.06717i	−0.297600	−	0.182647i
$283$	−19.0667	+	5.10891i	−1.13340	+	0.303693i	−0.776294	−	0.630371i	$-0.782903\pi$
$283$	−19.0667	+	5.10891i	−1.13340	+	0.303693i	−0.357104	+	0.934064i	$0.616236\pi$
$284$	0.750636	+	1.47815i	0.0445420	+	0.0877122i
$285$	−17.2223	−	4.61471i	−1.02016	−	0.273352i
$286$	−23.8777	−	7.09050i	−1.41192	−	0.419270i
$287$		0			0
$288$	−12.3620	+	1.58492i	−0.728439	+	0.0933921i
$289$	8.43947	+	14.6176i	0.496440	+	0.859858i
$290$	−5.86549	+	5.55860i	−0.344433	+	0.326412i
$291$	0.504556	+	1.88303i	0.0295776	+	0.110385i
$292$	−12.4854	−	0.671295i	−0.730654	−	0.0392846i
$293$	2.57087	+	2.57087i	0.150192	+	0.150192i	0.778204	−	0.628012i	$-0.216131\pi$
$293$	2.57087	+	2.57087i	0.150192	+	0.150192i	−0.628012	+	0.778204i	$0.716131\pi$
$294$		0			0
$295$			24.2588i			1.41240i
$296$	−23.2110	+	11.0132i	−1.34911	+	0.640131i
$297$	−12.4183	−	7.16973i	−0.720585	−	0.416030i
$298$	−18.4691	−	0.496149i	−1.06989	−	0.0287411i
$299$	−9.21028	+	34.3732i	−0.532644	+	1.98785i
$300$	−2.20384	−	10.4378i	−0.127239	−	0.602624i
$301$		0			0
$302$	4.72086	−	15.8978i	0.271655	−	0.914815i
$303$	3.00020	+	5.19649i	0.172357	+	0.298531i
$304$	18.7835	−	15.1265i	1.07731	−	0.867562i
$305$	−0.0125015	+	0.0216532i	−0.000715833	+	0.00123986i
$306$	−1.05430	+	0.252361i	−0.0602705	+	0.0144265i
$307$	−18.8253	+	18.8253i	−1.07441	+	1.07441i	−0.0774148	+	0.996999i	$0.524667\pi$
$307$	−18.8253	+	18.8253i	−1.07441	+	1.07441i	−0.996999	+	0.0774148i	$0.975333\pi$
$308$		0			0
$309$	9.92600	+	9.92600i	0.564670	+	0.564670i
$310$	3.09372	−	5.04082i	0.175711	−	0.286299i
$311$	−20.6909	−	11.9459i	−1.17327	−	0.677389i	−0.218824	−	0.975764i	$-0.570222\pi$
$311$	−20.6909	−	11.9459i	−1.17327	−	0.677389i	−0.954449	+	0.298375i	$0.903555\pi$
$312$	−2.59599	−	14.1673i	−0.146969	−	0.802065i
$313$	−15.6650	+	9.04419i	−0.885438	+	0.511208i	−0.872448	−	0.488708i	$-0.837468\pi$
$313$	−15.6650	+	9.04419i	−0.885438	+	0.511208i	−0.0129904	+	0.999916i	$0.504135\pi$
$314$	18.2542	−	9.89520i	1.03014	−	0.558418i
$315$		0			0
$316$	−1.26677	−	0.825092i	−0.0712614	−	0.0464150i
$317$	7.32824	+	1.96360i	0.411595	+	0.110287i	0.458674	−	0.888605i	$-0.348325\pi$
$317$	7.32824	+	1.96360i	0.411595	+	0.110287i	−0.0470789	+	0.998891i	$0.514991\pi$
$318$	10.9381	−	10.3658i	0.613379	−	0.581286i
$319$	2.66253	−	4.61164i	0.149073	−	0.258202i
$320$	24.1681	+	10.8782i	1.35104	+	0.608112i
$321$	8.43367			0.470722
$322$		0			0
$323$	1.48334	−	1.48334i	0.0825354	−	0.0825354i
$324$	−0.264548	+	4.92033i	−0.0146971	+	0.273352i
$325$	−32.9274	+	8.82288i	−1.82649	+	0.489405i
$326$	0.840824	−	31.2996i	0.0465690	−	1.73352i
$327$	−0.888273	+	0.512845i	−0.0491216	+	0.0283604i
$328$	5.78519	−	4.92072i	0.319434	−	0.271701i
$329$		0			0
$330$	6.15332	+	11.3513i	0.338729	+	0.624871i
$331$	−8.18298	+	30.5393i	−0.449777	+	1.67859i	0.253228	+	0.967407i	$0.418508\pi$
$331$	−8.18298	+	30.5393i	−0.449777	+	1.67859i	−0.703005	+	0.711185i	$0.748159\pi$
$332$	−3.21744	+	9.85679i	−0.176580	+	0.540962i
$333$	5.17954	+	19.3303i	0.283837	+	1.05929i
$334$	2.91608	−	0.698000i	0.159561	−	0.0381929i
$335$	14.1498			0.773084
$336$		0			0
$337$	11.5086			0.626914			0.313457	−	0.949602i	$-0.398513\pi$
$337$	11.5086			0.626914			0.313457	+	0.949602i	$0.398513\pi$
$338$	−26.8810	+	6.43429i	−1.46213	+	0.349979i
$339$	4.27799	+	15.9657i	0.232349	+	0.867137i
$340$	2.19155	+	0.715360i	0.118853	+	0.0387958i
$341$	−1.00873	+	3.76462i	−0.0546256	+	0.203865i
$342$	−8.95268	−	16.5155i	−0.484106	−	0.893053i
$343$		0			0
$344$	−1.30539	+	16.1665i	−0.0703820	+	0.871639i
$345$	15.9755	−	9.22343i	0.860089	−	0.496573i
$346$	0.114213	−	4.25155i	0.00614011	−	0.228565i
$347$	−16.8281	+	4.50907i	−0.903379	+	0.242060i	−0.680467	−	0.732779i	$-0.738223\pi$
$347$	−16.8281	+	4.50907i	−0.903379	+	0.242060i	−0.222912	+	0.974839i	$0.571556\pi$
$348$	3.07477	+	0.165319i	0.164825	+	0.00886203i
$349$	−0.251501	+	0.251501i	−0.0134625	+	0.0134625i	−0.713806	−	0.700343i	$-0.753030\pi$
$349$	−0.251501	+	0.251501i	−0.0134625	+	0.0134625i	0.700343	+	0.713806i	$0.253030\pi$
$350$		0			0
$351$	−26.4962			−1.41426
$352$	−17.3076	−	2.33824i	−0.922496	−	0.124629i
$353$	8.34440	−	14.4529i	0.444128	−	0.769251i	−0.553863	−	0.832608i	$-0.686847\pi$
$353$	8.34440	−	14.4529i	0.444128	−	0.769251i	0.997991	+	0.0633560i	$0.0201804\pi$
$354$	6.70945	−	6.35840i	0.356603	−	0.337945i
$355$	−2.65256	−	0.710751i	−0.140783	−	0.0377227i
$356$	−6.81630	+	10.4651i	−0.361263	+	0.554650i
$357$		0			0
$358$	2.49520	−	1.35260i	0.131876	−	0.0714869i
$359$	−15.5695	+	8.98907i	−0.821728	+	0.474425i	−0.851012	−	0.525146i	$-0.824011\pi$
$359$	−15.5695	+	8.98907i	−0.821728	+	0.474425i	0.0292842	+	0.999571i	$0.490677\pi$
$360$	11.7279	−	16.9902i	0.618116	−	0.895461i
$361$	15.0271	+	8.67588i	0.790898	+	0.456625i
$362$	−14.9800	+	24.4079i	−0.787329	+	1.28285i
$363$	0.926684	+	0.926684i	0.0486383	+	0.0486383i
$364$		0			0
$365$	14.6453	−	14.6453i	0.766568	−	0.766568i
$366$	0.00926552	−	0.00221782i	0.000484317	−	0.000115927i
$367$	10.8135	−	18.7296i	0.564461	−	0.977675i	−0.432639	−	0.901567i	$-0.642418\pi$
$367$	10.8135	−	18.7296i	0.564461	−	0.977675i	0.997100	−	0.0761073i	$-0.0242492\pi$
$368$	−2.67537	+	24.8077i	−0.139463	+	1.29319i
$369$	−2.95801	−	5.12342i	−0.153988	−	0.266715i
$370$	12.1144	−	40.7960i	0.629797	−	2.12088i
$371$		0			0
$372$	−2.20506	+	0.465580i	−0.114327	+	0.0241392i
$373$	−4.43346	+	16.5459i	−0.229556	+	0.856715i	0.750972	+	0.660334i	$0.229585\pi$
$373$	−4.43346	+	16.5459i	−0.229556	+	0.856715i	−0.980528	+	0.196380i	$0.937081\pi$
$374$	−1.51859	−	0.0407950i	−0.0785244	−	0.00210946i
$375$	2.49830	+	1.44239i	0.129011	+	0.0744848i
$376$	−4.41071	+	12.3755i	−0.227465	+	0.638216i
$377$		−	9.83956i		−	0.506763i
$378$		0			0
$379$	4.34251	+	4.34251i	0.223060	+	0.223060i	0.809786	−	0.586726i	$-0.199583\pi$
$379$	4.34251	+	4.34251i	0.223060	+	0.223060i	−0.586726	+	0.809786i	$0.699583\pi$
$380$	−2.14481	+	39.8913i	−0.110026	+	2.04638i
$381$	−3.16659	−	11.8179i	−0.162229	−	0.605448i
$382$	−6.38765	+	6.05344i	−0.326821	+	0.309721i
$383$	−16.4121	−	28.4266i	−0.838619	−	1.45253i	−0.891049	−	0.453907i	$-0.850030\pi$
$383$	−16.4121	−	28.4266i	−0.838619	−	1.45253i	0.0524297	−	0.998625i	$-0.483303\pi$
$384$	−3.32594	−	9.53562i	−0.169726	−	0.486612i
$385$		0			0
$386$	2.13684	+	0.634534i	0.108762	+	0.0322969i
$387$	12.2034	+	3.26989i	0.620333	+	0.166218i
$388$	3.89448	−	1.97770i	0.197712	−	0.100402i
$389$	−0.320999	+	0.0860114i	−0.0162753	+	0.00436095i	−0.266948	−	0.963711i	$-0.586015\pi$
$389$	−0.320999	+	0.0860114i	−0.0162753	+	0.00436095i	0.250672	+	0.968072i	$0.419348\pi$
$390$	20.3341	+	12.4797i	1.02966	+	0.631936i
$391$			2.17035i			0.109759i
$392$		0			0
$393$			4.45524i			0.224737i
$394$	11.2130	−	18.2701i	0.564902	−	0.920436i
$395$	2.41888	−	0.648138i	0.121707	−	0.0326114i
$396$	−4.22145	+	12.9327i	−0.212136	+	0.649891i
$397$	2.70450	+	0.724669i	0.135735	+	0.0363701i	0.326047	−	0.945354i	$-0.394283\pi$
$397$	2.70450	+	0.724669i	0.135735	+	0.0363701i	−0.190312	+	0.981724i	$0.560950\pi$
$398$	−10.2803	+	34.6196i	−0.515305	+	1.73532i
$399$		0			0
$400$	−21.8618	+	9.66262i	−1.09309	+	0.483131i
$401$	2.57522	+	4.46041i	0.128600	+	0.222742i	0.923134	−	0.384477i	$-0.125618\pi$
$401$	2.57522	+	4.46041i	0.128600	+	0.222742i	−0.794534	+	0.607219i	$0.792285\pi$
$402$	−3.70875	−	3.91351i	−0.184976	−	0.195188i
$403$	1.86391	+	6.95620i	0.0928479	+	0.346513i
$404$	10.0032	−	8.98241i	0.497677	−	0.446891i
$405$	−5.77150	−	5.77150i	−0.286788	−	0.286788i
$406$		0			0
$407$			28.0433i			1.39005i
$408$	−0.376566	−	0.793634i	−0.0186428	−	0.0392907i
$409$	−0.0631364	−	0.0364518i	−0.00312189	−	0.00180243i	0.498438	−	0.866925i	$-0.333907\pi$
$409$	−0.0631364	−	0.0364518i	−0.00312189	−	0.00180243i	−0.501560	+	0.865123i	$0.667240\pi$
$410$	−0.337841	+	12.5761i	−0.0166848	+	0.621089i
$411$	3.61654	−	13.4971i	0.178391	−	0.665764i
$412$	17.1656	−	26.3545i	0.845688	−	1.29839i
$413$		0			0
$414$	18.6319	+	5.53274i	0.915706	+	0.271919i
$415$	−8.58762	−	14.8742i	−0.421550	−	0.730146i
$416$	−29.8563	+	12.2486i	−1.46383	+	0.600537i
$417$	−0.962999	+	1.66796i	−0.0471583	+	0.0816805i
$418$	−6.12808	−	25.6017i	−0.299734	−	1.25222i
$419$	13.7426	−	13.7426i	0.671370	−	0.671370i	−0.286662	−	0.958032i	$-0.592546\pi$
$419$	13.7426	−	13.7426i	0.671370	−	0.671370i	0.958032	+	0.286662i	$0.0925456\pi$
$420$		0			0
$421$	3.88097	+	3.88097i	0.189147	+	0.189147i	0.795327	−	0.606180i	$-0.207299\pi$
$421$	3.88097	+	3.88097i	0.189147	+	0.189147i	−0.606180	+	0.795327i	$0.707299\pi$
$422$	−15.6800	−	9.62335i	−0.763292	−	0.468457i
$423$	8.86276	+	5.11692i	0.430922	+	0.248793i
$424$	−27.7871	−	19.1808i	−1.34946	−	0.931503i
$425$	−1.80052	+	1.03953i	−0.0873382	+	0.0504247i
$426$	0.498676	+	0.919932i	0.0241609	+	0.0445708i
$427$		0			0
$428$	−3.90369	−	18.4885i	−0.188692	−	0.893676i
$429$	−15.1861	−	4.06910i	−0.733191	−	0.196458i
$430$	−18.4804	−	19.5007i	−0.891204	−	0.940408i
$431$	16.9017	−	29.2746i	0.814125	−	1.41011i	−0.0958298	−	0.995398i	$-0.530550\pi$
$431$	16.9017	−	29.2746i	0.814125	−	1.41011i	0.909955	−	0.414708i	$-0.136116\pi$
$432$	−18.3573	+	2.85655i	−0.883217	+	0.137436i
$433$	−18.6931			−0.898334			−0.449167	−	0.893448i	$-0.648279\pi$
$433$	−18.6931			−0.898334			−0.449167	+	0.893448i	$0.648279\pi$
$434$		0			0
$435$	−3.60667	+	3.60667i	−0.172927	+	0.172927i
$436$	1.53543	+	1.70992i	0.0735335	+	0.0818901i
$437$	−36.3281	+	9.73410i	−1.73781	+	0.465645i
$438$	−7.88918	−	0.211933i	−0.376960	−	0.0101266i
$439$	5.22336	−	3.01571i	0.249298	−	0.143932i	−0.370145	−	0.928974i	$-0.620692\pi$
$439$	5.22336	−	3.01571i	0.249298	−	0.143932i	0.619443	+	0.785042i	$0.287359\pi$
$440$	22.0365	−	18.7437i	1.05055	−	0.893569i
$441$		0			0
$442$	−2.46778	+	1.33773i	−0.117380	+	0.0636294i
$443$	9.11980	−	34.0356i	0.433295	−	1.61708i	−0.311819	−	0.950141i	$-0.600938\pi$
$443$	9.11980	−	34.0356i	0.433295	−	1.61708i	0.745114	−	0.666937i	$-0.232395\pi$
$444$	−14.4585	+	7.34233i	−0.686171	+	0.348452i
$445$	−5.35444	−	19.9830i	−0.253825	−	0.947287i
$446$	4.19841	+	17.5400i	0.198800	+	0.830542i
$447$	−11.6617			−0.551578
$448$		0			0
$449$	21.9883			1.03769			0.518846	−	0.854868i	$-0.326362\pi$
$449$	21.9883			1.03769			0.518846	+	0.854868i	$0.326362\pi$
$450$	4.33413	+	18.1070i	0.204313	+	0.853571i
$451$	−2.14565	−	8.00769i	−0.101035	−	0.377067i
$452$	33.0203	−	16.7684i	1.55314	−	0.788717i
$453$	2.70921	−	10.1109i	0.127290	−	0.475051i
$454$	21.5302	−	11.6711i	1.01046	−	0.547751i
$455$		0			0
$456$	11.5952	−	9.86257i	0.542996	−	0.461857i
$457$	−23.1559	+	13.3691i	−1.08319	+	0.625378i	−0.931754	−	0.363090i	$-0.881722\pi$
$457$	−23.1559	+	13.3691i	−1.08319	+	0.625378i	−0.151432	+	0.988468i	$0.548389\pi$
$458$	−19.8567	−	0.533426i	−0.927843	−	0.0249253i
$459$	−1.56092	+	0.418248i	−0.0728577	+	0.0195222i
$460$	−27.6144	−	30.7526i	−1.28753	−	1.43385i
$461$	−23.5563	+	23.5563i	−1.09713	+	1.09713i	−0.102381	+	0.994745i	$0.532646\pi$
$461$	−23.5563	+	23.5563i	−1.09713	+	1.09713i	−0.994745	+	0.102381i	$0.967354\pi$
$462$		0			0
$463$	−9.83629			−0.457131			−0.228566	−	0.973529i	$-0.573404\pi$
$463$	−9.83629			−0.457131			−0.228566	+	0.973529i	$0.573404\pi$
$464$	−1.06080	−	6.81712i	−0.0492464	−	0.316477i
$465$	1.86657	−	3.23299i	0.0865601	−	0.149927i
$466$	−17.8159	−	18.7995i	−0.825304	−	0.870870i
$467$	2.68552	+	0.719583i	0.124271	+	0.0332983i	0.320419	−	0.947276i	$-0.396176\pi$
$467$	2.68552	+	0.719583i	0.124271	+	0.0332983i	−0.196147	+	0.980574i	$0.562843\pi$
$468$	5.19309	+	24.5954i	0.240051	+	1.13692i
$469$		0			0
$470$	−10.3713	−	19.1324i	−0.478391	−	0.882511i
$471$	11.3499	−	6.55288i	0.522977	−	0.301941i
$472$	−17.0446	−	11.7655i	−0.784543	−	0.541552i
$473$	15.3321	+	8.85198i	0.704970	+	0.407014i
$474$	−0.813267	−	0.499128i	−0.0373546	−	0.0229257i
$475$	−25.4755	−	25.4755i	−1.16889	−	1.16889i
$476$		0			0
$477$	−18.5974	+	18.5974i	−0.851517	+	0.851517i
$478$	6.03914	+	25.2301i	0.276224	+	1.15400i
$479$	1.89344	−	3.27954i	0.0865136	−	0.149846i	−0.819522	−	0.573048i	$-0.805761\pi$
$479$	1.89344	−	3.27954i	0.0865136	−	0.149846i	0.906035	+	0.423202i	$0.139094\pi$
$480$	15.4335	+	6.45408i	0.704439	+	0.294587i
$481$	25.9090	+	44.8756i	1.18135	+	2.04615i
$482$	−34.4548	−	10.2314i	−1.56937	−	0.466026i
$483$		0			0
$484$	1.60257	−	2.46044i	0.0728440	−	0.111838i
$485$	−1.87261	+	6.98868i	−0.0850309	+	0.317340i
$486$	−0.612684	+	22.8071i	−0.0277919	+	1.03455i
$487$	−14.5665	−	8.40999i	−0.660073	−	0.381093i	0.132232	−	0.991219i	$-0.457786\pi$
$487$	−14.5665	−	8.40999i	−0.660073	−	0.381093i	−0.792305	+	0.610126i	$0.791119\pi$
$488$	−0.00915069	−	0.0192856i	−0.000414232	−	0.000873017i
$489$		−	19.7630i		−	0.893716i
$490$		0			0
$491$	−6.41618	−	6.41618i	−0.289558	−	0.289558i	0.547347	−	0.836906i	$-0.315638\pi$
$491$	−6.41618	−	6.41618i	−0.289558	−	0.289558i	−0.836906	+	0.547347i	$0.815638\pi$
$492$	3.56682	−	3.20284i	0.160805	−	0.144395i
$493$	−0.155319	−	0.579660i	−0.00699524	−	0.0261066i
$494$	−33.4595	−	35.3068i	−1.50541	−	1.58853i
$495$	−11.2674	−	19.5158i	−0.506434	−	0.877169i
$496$	2.04131	+	4.61850i	0.0916576	+	0.207377i
$497$		0			0
$498$	−1.86300	+	6.27378i	−0.0834831	+	0.281135i
$499$	6.41078	+	1.71776i	0.286986	+	0.0768977i	0.399440	−	0.916759i	$-0.369204\pi$
$499$	6.41078	+	1.71776i	0.286986	+	0.0768977i	−0.112454	+	0.993657i	$0.535871\pi$
$500$	2.00567	−	6.14447i	0.0896961	−	0.274789i
$501$	1.82810	−	0.489838i	0.0816735	−	0.0218843i
$502$	11.4346	−	18.6312i	0.510350	−	0.831550i
$503$		−	4.37360i		−	0.195009i	−0.995235	−	0.0975045i	$-0.968914\pi$
$503$		−	4.37360i		−	0.195009i	0.995235	−	0.0975045i	$-0.0310860\pi$
$504$		0			0
$505$			22.2699i			0.990998i
$506$	23.2127	+	14.2464i	1.03193	+	0.633329i
$507$	−16.8518	+	4.51541i	−0.748413	+	0.200537i
$508$	−24.4417	+	12.4120i	−1.08443	+	0.550693i
$509$	2.64488	+	0.708694i	0.117232	+	0.0314123i	0.316958	−	0.948440i	$-0.397339\pi$
$509$	2.64488	+	0.708694i	0.117232	+	0.0314123i	−0.199726	+	0.979852i	$0.564005\pi$
$510$	1.39490	+	0.414217i	0.0617674	+	0.0183418i
$511$		0			0
$512$	−19.3648	+	11.7050i	−0.855810	+	0.517291i
$513$	−14.0016	−	24.2515i	−0.618185	−	1.07073i
$514$	2.35736	−	2.23402i	0.103979	−	0.0985384i
$515$	13.4842	+	50.3236i	0.594183	+	2.21752i
$516$	−0.549628	+	10.2225i	−0.0241960	+	0.450022i
$517$	10.1404	+	10.1404i	0.445976	+	0.445976i
$518$		0			0
$519$		−	2.68449i		−	0.117836i
$520$	17.9464	−	50.3535i	0.787000	−	2.20815i
$521$	30.5966	+	17.6650i	1.34046	+	0.773917i	0.986875	−	0.161485i	$-0.0516282\pi$
$521$	30.5966	+	17.6650i	1.34046	+	0.773917i	0.353588	+	0.935401i	$0.384962\pi$
$522$	−5.37216	−	0.144316i	−0.235133	−	0.00631656i
$523$	8.55965	−	31.9451i	0.374287	−	1.39686i	−0.480096	−	0.877216i	$-0.659398\pi$
$523$	8.55965	−	31.9451i	0.374287	−	1.39686i	0.854383	−	0.519644i	$-0.173935\pi$
$524$	9.76690	−	2.06219i	0.426669	−	0.0900873i
$525$		0			0
$526$	−4.77084	+	16.0661i	−0.208019	+	0.700516i
$527$	0.219610	+	0.380376i	0.00956636	+	0.0165694i
$528$	−10.9600	−	1.18198i	−0.476973	−	0.0514389i
$529$	7.95555	−	13.7794i	0.345893	−	0.599105i
$530$	54.3929	−	13.0196i	2.36268	−	0.565536i
$531$	−11.4077	+	11.4077i	−0.495051	+	0.495051i
$532$		0			0
$533$	−10.8318	−	10.8318i	−0.469176	−	0.469176i
$534$	−4.12343	+	6.71861i	−0.178438	+	0.290743i
$535$	27.1073	+	15.6504i	1.17195	+	0.676626i
$536$	−6.86264	+	9.94187i	−0.296421	+	0.429423i
$537$	1.55145	−	0.895728i	0.0669499	−	0.0386535i
$538$	−10.0361	+	5.44036i	−0.432687	+	0.234551i
$539$		0			0
$540$	16.7958	−	25.7867i	0.722775	−	1.10968i
$541$	7.01011	+	1.87835i	0.301388	+	0.0807567i	0.406344	−	0.913720i	$-0.366803\pi$
$541$	7.01011	+	1.87835i	0.301388	+	0.0807567i	−0.104956	+	0.994477i	$0.533470\pi$
$542$	26.8155	−	25.4124i	1.15182	−	1.09156i
$543$	−9.03804	+	15.6543i	−0.387859	+	0.671792i
$544$	−1.56552	+	1.19287i	−0.0671213	+	0.0511438i
$545$	−3.80675			−0.163063
$546$		0			0
$547$	16.8157	−	16.8157i	0.718989	−	0.718989i	−0.249409	−	0.968398i	$-0.580236\pi$
$547$	16.8157	−	16.8157i	0.718989	−	0.718989i	0.968398	+	0.249409i	$0.0802365\pi$
$548$	−31.2628	−	1.68088i	−1.33548	−	0.0718038i
$549$	−0.0160612	+	0.00430358i	−0.000685475	+	0.000183672i
$550$	−0.700628	+	26.0808i	−0.0298749	+	1.11209i
$551$	9.00595	−	5.19959i	0.383666	−	0.221510i
$552$	−1.26756	+	15.6980i	−0.0539510	+	0.668151i
$553$		0			0
$554$	1.88980	+	3.48621i	0.0802899	+	0.148115i
$555$	6.95220	−	25.9460i	0.295105	−	1.10135i
$556$	4.10230	+	1.33906i	0.173976	+	0.0567890i
$557$	−4.05828	−	15.1457i	−0.171955	−	0.641744i	−0.997050	−	0.0767505i	$-0.975546\pi$
$557$	−4.05828	−	15.1457i	−0.171955	−	0.641744i	0.825096	−	0.564993i	$-0.191121\pi$
$558$	3.82525	−	0.915622i	0.161936	−	0.0387614i
$559$	32.7131			1.38362
$560$		0			0
$561$	−0.958861			−0.0404831
$562$	8.97390	−	2.14801i	0.378541	−	0.0906085i
$563$	−8.12783	−	30.3335i	−0.342547	−	1.27840i	−0.895451	−	0.445159i	$-0.853147\pi$
$563$	−8.12783	−	30.3335i	−0.342547	−	1.27840i	0.552904	−	0.833245i	$-0.313520\pi$
$564$	−2.57322	+	7.88319i	−0.108352	+	0.331942i
$565$	−15.8774	+	59.2552i	−0.667966	+	2.49288i
$566$	13.3036	+	24.5417i	0.559190	+	1.03157i
$567$		0			0
$568$	1.78588	−	1.51902i	0.0749338	−	0.0637366i
$569$	0.274678	−	0.158585i	0.0115151	−	0.00664825i	−0.494231	−	0.869330i	$-0.664550\pi$
$569$	0.274678	−	0.158585i	0.0115151	−	0.00664825i	0.505746	+	0.862682i	$0.331217\pi$
$570$	−0.677132	+	25.2062i	−0.0283620	+	1.05577i
$571$	10.6599	−	2.85631i	0.446102	−	0.119533i	−0.0287727	−	0.999586i	$-0.509160\pi$
$571$	10.6599	−	2.85631i	0.446102	−	0.119533i	0.474875	+	0.880053i	$0.342493\pi$
$572$	−1.89122	+	35.1748i	−0.0790758	+	1.47073i
$573$	−3.92775	+	3.92775i	−0.164084	+	0.164084i
$574$		0			0
$575$	37.2744			1.55445
$576$	6.24953	+	16.4805i	0.260397	+	0.686687i
$577$	−5.13494	+	8.89397i	−0.213770	+	0.370261i	−0.952891	−	0.303312i	$-0.901908\pi$
$577$	−5.13494	+	8.89397i	−0.213770	+	0.370261i	0.739121	+	0.673572i	$0.235241\pi$
$578$	17.3261	−	16.4196i	0.720672	−	0.682965i
$579$	1.35901	+	0.364147i	0.0564787	+	0.0151334i
$580$	9.57606	+	6.23723i	0.397624	+	0.258987i
$581$		0			0
$582$	2.42374	−	1.31386i	0.100467	−	0.0544612i
$583$	−31.9177	+	18.4277i	−1.32190	+	0.763198i
$584$	3.18705	+	17.3930i	0.131881	+	0.719726i
$585$	−36.0610	−	20.8198i	−1.49094	−	0.860793i
$586$	2.68952	−	4.38224i	0.111103	−	0.181029i
$587$	27.9965	+	27.9965i	1.15554	+	1.15554i	0.985425	+	0.170113i	$0.0544133\pi$
$587$	27.9965	+	27.9965i	1.15554	+	1.15554i	0.170113	+	0.985425i	$0.445587\pi$
$588$		0			0
$589$	−5.38191	+	5.38191i	−0.221758	+	0.221758i
$590$	33.3646	−	7.98624i	1.37360	−	0.328788i
$591$	6.76527	−	11.7178i	0.278286	−	0.482005i
$592$	22.7885	+	28.2978i	0.936600	+	1.16303i
$593$	−17.2951	−	29.9560i	−0.710225	−	1.23015i	−0.964772	−	0.263086i	$-0.915260\pi$
$593$	−17.2951	−	29.9560i	−0.710225	−	1.23015i	0.254547	−	0.967060i	$-0.418074\pi$
$594$	−5.77273	+	19.4401i	−0.236858	+	0.797635i
$595$		0			0
$596$	5.39783	+	25.5650i	0.221104	+	1.04718i
$597$	−5.89966	+	22.0178i	−0.241457	+	0.901130i
$598$	50.3077	+	1.35146i	2.05724	+	0.0552651i
$599$	−12.1993	−	7.04329i	−0.498452	−	0.287781i	0.229622	−	0.973280i	$-0.426251\pi$
$599$	−12.1993	−	7.04329i	−0.498452	−	0.287781i	−0.728074	+	0.685499i	$0.759584\pi$
$600$	−13.6302	+	6.46729i	−0.556449	+	0.264026i
$601$			7.07501i			0.288595i	0.989534	+	0.144298i	$0.0460923\pi$
$601$			7.07501i			0.288595i	−0.989534	+	0.144298i	$0.953908\pi$
$602$		0			0
$603$	6.65391	+	6.65391i	0.270968	+	0.270968i
$604$	−23.4194	−	1.25917i	−0.952921	−	0.0512350i
$605$	1.25887	+	4.69817i	0.0511804	+	0.191008i
$606$	6.15936	−	5.83709i	0.250207	−	0.237116i
$607$	2.99647	+	5.19003i	0.121623	+	0.210657i	0.920408	−	0.390960i	$-0.127857\pi$
$607$	2.99647	+	5.19003i	0.121623	+	0.210657i	−0.798785	+	0.601617i	$0.794523\pi$
$608$	−26.9881	−	20.8543i	−1.09451	−	0.845752i
$609$		0			0
$610$	0.0338966	+	0.0100656i	0.00137243	+	0.000407545i
$611$	25.5957	+	6.85835i	1.03549	+	0.277459i
$612$	0.694174	+	1.36697i	0.0280603	+	0.0552564i
$613$	16.8248	−	4.50820i	0.679549	−	0.182084i	0.0974963	−	0.995236i	$-0.468917\pi$
$613$	16.8248	−	4.50820i	0.679549	−	0.182084i	0.582052	+	0.813151i	$0.302250\pi$
$614$	32.0890	+	19.6941i	1.29501	+	0.794788i
$615$			7.94074i			0.320201i
$616$		0			0
$617$		−	40.3690i		−	1.62519i	−0.582827	−	0.812596i	$-0.698053\pi$
$617$		−	40.3690i		−	1.62519i	0.582827	−	0.812596i	$-0.301947\pi$
$618$	10.3841	−	16.9196i	0.417710	−	0.680605i
$619$	42.2614	−	11.3239i	1.69863	−	0.455147i	0.726036	−	0.687656i	$-0.241360\pi$
$619$	42.2614	−	11.3239i	1.69863	−	0.455147i	0.972594	+	0.232510i	$0.0746937\pi$
$620$	−7.95143	−	2.59549i	−0.319337	−	0.104237i
$621$	27.9850	+	7.49855i	1.12300	+	0.300907i
$622$	−9.61828	+	32.3902i	−0.385658	+	1.29873i
$623$		0			0
$624$	−18.6305	+	8.23444i	−0.745819	+	0.329641i
$625$	−9.58545	−	16.6025i	−0.383418	−	0.664099i
$626$	17.5961	+	18.5676i	0.703282	+	0.742111i
$627$	−4.30052	−	16.0498i	−0.171746	−	0.640966i
$628$	−19.6189	−	21.8485i	−0.782881	−	0.871849i
$629$	2.23470	+	2.23470i	0.0891033	+	0.0891033i
$630$		0			0
$631$		−	23.7329i		−	0.944792i	−0.881386	−	0.472396i	$-0.843389\pi$
$631$		−	23.7329i		−	0.944792i	0.881386	−	0.472396i	$-0.156611\pi$
$632$	−0.717767	+	2.01390i	−0.0285512	+	0.0801085i
$633$	−10.0566	−	5.80618i	−0.399714	−	0.230775i
$634$	0.288125	−	10.7254i	0.0114429	−	0.425961i
$635$	11.7525	−	43.8609i	0.466384	−	1.74057i
$636$	−17.8577	−	11.6313i	−0.708104	−	0.461213i
$637$		0			0
$638$	−7.21920	−	2.14374i	−0.285811	−	0.0848717i
$639$	−0.913132	−	1.58159i	−0.0361230	−	0.0625668i
$640$	7.00513	−	36.8211i	0.276902	−	1.45548i
$641$	7.49413	−	12.9802i	0.296000	−	0.512687i	−0.679217	−	0.733938i	$-0.737680\pi$
$641$	7.49413	−	12.9802i	0.296000	−	0.512687i	0.975217	+	0.221250i	$0.0710138\pi$
$642$	−2.77645	−	11.5994i	−0.109578	−	0.457790i
$643$	11.8452	−	11.8452i	0.467130	−	0.467130i	−0.433854	−	0.900983i	$-0.642847\pi$
$643$	11.8452	−	11.8452i	0.467130	−	0.467130i	0.900983	+	0.433854i	$0.142847\pi$
$644$		0			0
$645$	−11.9909	−	11.9909i	−0.472142	−	0.472142i
$646$	−2.52846	−	1.55180i	−0.0994811	−	0.0610548i
$647$	−3.57210	−	2.06235i	−0.140434	−	0.0810795i	0.428137	−	0.903714i	$-0.359170\pi$
$647$	−3.57210	−	2.06235i	−0.140434	−	0.0810795i	−0.568571	+	0.822634i	$0.692503\pi$
$648$	6.85433	−	1.25597i	0.269264	−	0.0493393i
$649$	−19.5784	+	11.3036i	−0.768518	+	0.443704i
$650$	22.9747	+	42.3826i	0.901142	+	1.66238i
$651$		0			0
$652$	−43.3251	+	9.14770i	−1.69674	+	0.358252i
$653$	34.7675	+	9.31592i	1.36056	+	0.364560i	0.864021	−	0.503456i	$-0.167938\pi$
$653$	34.7675	+	9.31592i	1.36056	+	0.364560i	0.496536	+	0.868016i	$0.334605\pi$
$654$	0.997775	+	1.05286i	0.0390161	+	0.0411702i
$655$	−8.26760	+	14.3199i	−0.323042	+	0.559525i
$656$	−8.67232	−	6.33678i	−0.338597	−	0.247410i
$657$	13.7738			0.537368
$658$		0			0
$659$	7.38409	−	7.38409i	0.287643	−	0.287643i	−0.548504	−	0.836148i	$-0.684803\pi$
$659$	7.38409	−	7.38409i	0.287643	−	0.287643i	0.836148	+	0.548504i	$0.184803\pi$
$660$	13.5865	−	12.2000i	0.528853	−	0.474885i
$661$	19.2505	−	5.15817i	0.748759	−	0.200629i	0.135792	−	0.990737i	$-0.456642\pi$
$661$	19.2505	−	5.15817i	0.748759	−	0.200629i	0.612968	+	0.790108i	$0.289976\pi$
$662$	44.6965	+	1.20072i	1.73718	+	0.0466672i
$663$	−1.53440	+	0.885884i	−0.0595910	+	0.0344049i
$664$	14.6159	+	1.18018i	0.567206	+	0.0458000i
$665$		0			0
$666$	24.8810	−	13.4875i	0.964120	−	0.522629i
$667$	−2.78464	+	10.3924i	−0.107822	+	0.402396i
$668$	−1.92001	−	3.78088i	−0.0742873	−	0.146287i
$669$	2.94633	+	10.9959i	0.113912	+	0.425124i
$670$	−4.65825	−	19.4610i	−0.179964	−	0.751846i
$671$	−0.0233006			−0.000899511
$672$		0			0
$673$	−35.0089			−1.34949			−0.674746	−	0.738050i	$-0.735747\pi$
$673$	−35.0089			−1.34949			−0.674746	+	0.738050i	$0.735747\pi$
$674$	−3.78875	−	15.8285i	−0.145937	−	0.609692i
$675$	7.18315	+	26.8079i	0.276480	+	1.03184i
$676$	17.6990	+	34.8528i	0.680729	+	1.34049i
$677$	−4.13095	+	15.4169i	−0.158765	+	0.592521i	0.839988	+	0.542605i	$0.182562\pi$
$677$	−4.13095	+	15.4169i	−0.158765	+	0.592521i	−0.998753	+	0.0499158i	$0.984105\pi$
$678$	20.5502	−	11.1399i	0.789228	−	0.427824i
$679$		0			0
$680$	0.262400	−	3.24967i	0.0100626	−	0.124619i
$681$	13.3869	−	7.72893i	0.512987	−	0.296173i
$682$	5.50979	+	0.148014i	0.210981	+	0.00566774i
$683$	−45.6621	+	12.2351i	−1.74721	+	0.468164i	−0.984028	−	0.178016i	$-0.943032\pi$
$683$	−45.6621	+	12.2351i	−1.74721	+	0.468164i	−0.763185	+	0.646180i	$0.776366\pi$
$684$	−19.7674	+	17.7502i	−0.755826	+	0.678697i
$685$	36.6709	−	36.6709i	1.40112	−	1.40112i
$686$		0			0
$687$	−12.5378			−0.478348
$688$	22.6645	−	3.52679i	0.864077	−	0.134457i
$689$	−34.0504	+	58.9771i	−1.29722	+	2.24685i
$690$	−17.9448	−	18.9356i	−0.683148	−	0.720865i
$691$	−6.88067	−	1.84367i	−0.261753	−	0.0701365i	0.125556	−	0.992087i	$-0.459929\pi$
$691$	−6.88067	−	1.84367i	−0.261753	−	0.0701365i	−0.387309	+	0.921950i	$0.626595\pi$
$692$	−5.88502	+	1.24257i	−0.223715	+	0.0472354i
$693$		0			0
$694$	11.7416	+	21.6603i	0.445704	+	0.822213i
$695$	−6.19049	+	3.57408i	−0.234819	+	0.135573i
$696$	−0.784872	−	4.28335i	−0.0297505	−	0.162360i
$697$	−0.809094	−	0.467131i	−0.0306466	−	0.0176938i
$698$	0.428701	+	0.263108i	0.0162266	+	0.00995879i
$699$	−11.5598	−	11.5598i	−0.437230	−	0.437230i
$700$		0			0
$701$	1.77330	−	1.77330i	0.0669766	−	0.0669766i	−0.672825	−	0.739802i	$-0.734919\pi$
$701$	1.77330	−	1.77330i	0.0669766	−	0.0669766i	0.739802	+	0.672825i	$0.234919\pi$
$702$	8.72283	+	36.4419i	0.329222	+	1.37541i
$703$	−27.3825	+	47.4279i	−1.03275	+	1.78878i
$704$	2.48189	+	24.5739i	0.0935398	+	0.926165i
$705$	−6.86815	−	11.8960i	−0.258669	−	0.448028i
$706$	−22.6251	−	6.71852i	−0.851505	−	0.252855i
$707$		0			0
$708$	−10.9539	−	7.13467i	−0.411673	−	0.268137i
$709$	−3.23852	+	12.0863i	−0.121625	+	0.453912i	−0.999697	−	0.0246175i	$-0.992163\pi$
$709$	−3.23852	+	12.0863i	−0.121625	+	0.453912i	0.878072	+	0.478529i	$0.158830\pi$
$710$	−0.104291	+	3.88221i	−0.00391397	+	0.145697i
$711$	1.44226	+	0.832691i	0.0540891	+	0.0312283i
$712$	16.6373	+	5.92966i	0.623510	+	0.222223i
$713$		−	7.87454i		−	0.294904i
$714$		0			0
$715$	−41.2596	−	41.2596i	−1.54302	−	1.54302i
$716$	−2.68176	−	2.98652i	−0.100222	−	0.111611i
$717$	4.23810	+	15.8168i	0.158275	+	0.590690i
$718$	17.4889	+	18.4544i	0.652679	+	0.688713i
$719$	−5.91286	−	10.2414i	−0.220512	−	0.381939i	0.734451	−	0.678661i	$-0.237440\pi$
$719$	−5.91286	−	10.2414i	−0.220512	−	0.381939i	−0.954964	+	0.296723i	$0.904106\pi$
$720$	−27.2286	−	10.5368i	−1.01475	−	0.392684i
$721$		0			0
$722$	6.98542	−	23.5238i	0.259970	−	0.875467i
$723$	−21.9130	−	5.87157i	−0.814953	−	0.218366i
$724$	38.5013	+	12.5675i	1.43089	+	0.467068i
$725$	−9.95529	+	2.66751i	−0.369730	+	0.0990689i
$726$	0.969453	−	1.57960i	0.0359798	−	0.0586245i
$727$			27.7703i			1.02994i	0.857207	+	0.514972i	$0.172198\pi$
$727$			27.7703i			1.02994i	−0.857207	+	0.514972i	$0.827802\pi$
$728$		0			0
$729$			7.00960i			0.259615i
$730$	−24.9639	−	15.3212i	−0.923956	−	0.567062i
$731$	1.92717	−	0.516383i	0.0712789	−	0.0190991i
$732$	−0.00610061	−	0.0120133i	−0.000225485	−	0.000444025i
$733$	48.9673	+	13.1208i	1.80865	+	0.484626i	0.995273	−	0.0971120i	$-0.0309605\pi$
$733$	48.9673	+	13.1208i	1.80865	+	0.484626i	0.813376	+	0.581738i	$0.197627\pi$
$734$	−29.3198	−	8.70654i	−1.08221	−	0.321364i
$735$		0			0
$736$	35.0003	−	4.48733i	1.29013	−	0.165405i
$737$	6.59319	+	11.4197i	0.242863	+	0.420651i
$738$	−6.07276	+	5.75502i	−0.223541	+	0.211845i
$739$	−3.70009	−	13.8089i	−0.136110	−	0.507970i	−0.999991	−	0.00427340i	$-0.998640\pi$
$739$	−3.70009	−	13.8089i	−0.136110	−	0.507970i	0.863881	−	0.503696i	$-0.168027\pi$
$740$	−60.0974	−	3.23122i	−2.20922	−	0.118782i
$741$	−21.7101	−	21.7101i	−0.797539	−	0.797539i
$742$		0			0
$743$		−	31.4037i		−	1.15209i	−0.817418	−	0.576045i	$-0.804595\pi$
$743$		−	31.4037i		−	1.15209i	0.817418	−	0.576045i	$-0.195405\pi$
$744$	1.36627	+	2.87949i	0.0500899	+	0.105567i
$745$	−37.4826	−	21.6406i	−1.37326	−	0.792850i
$746$	24.2162	+	0.650537i	0.886616	+	0.0238178i
$747$	2.95625	−	11.0329i	0.108164	−	0.403672i
$748$	0.443827	+	2.10204i	0.0162279	+	0.0768582i
$749$		0			0
$750$	1.16135	−	3.91091i	0.0424064	−	0.142806i
$751$	−6.32654	−	10.9579i	−0.230859	−	0.399859i	0.727202	−	0.686423i	$-0.240820\pi$
$751$	−6.32654	−	10.9579i	−0.230859	−	0.399859i	−0.958061	+	0.286564i	$0.907487\pi$
$752$	18.4728	+	1.99219i	0.673634	+	0.0726476i
$753$	6.89896	−	11.9493i	0.251412	−	0.435458i
$754$	−13.5330	+	3.23928i	−0.492841	+	0.117968i
$755$	27.4707	−	27.4707i	0.999760	−	0.999760i
$756$		0			0
$757$	19.6555	+	19.6555i	0.714391	+	0.714391i	0.967451	−	0.253060i	$-0.0814370\pi$
$757$	19.6555	+	19.6555i	0.714391	+	0.714391i	−0.253060	+	0.967451i	$0.581437\pi$
$758$	4.54292	−	7.40212i	0.165006	−	0.268857i
$759$	14.8878	+	8.59545i	0.540391	+	0.311995i
$760$	55.5711	−	10.1827i	2.01577	−	0.369366i
$761$	−10.6308	+	6.13772i	−0.385368	+	0.222492i	−0.680151	−	0.733072i	$-0.738086\pi$
$761$	−10.6308	+	6.13772i	−0.385368	+	0.222492i	0.294783	+	0.955564i	$0.404752\pi$
$762$	−15.2114	+	8.24576i	−0.551050	+	0.298713i
$763$		0			0
$764$	10.4285	+	6.79248i	0.377292	+	0.245743i
$765$	−2.45304	−	0.657290i	−0.0886898	−	0.0237644i
$766$	−33.6938	+	31.9309i	−1.21741	+	1.15371i
$767$	−20.8866	+	36.1766i	−0.754170	+	1.30626i
$768$	−12.0200	+	7.71359i	−0.433734	+	0.278340i
$769$	−44.0633			−1.58896			−0.794481	−	0.607289i	$-0.792257\pi$
$769$	−44.0633			−1.58896			−0.794481	+	0.607289i	$0.792257\pi$
$770$		0			0
$771$	1.44954	−	1.44954i	0.0522037	−	0.0522037i
$772$	0.169247	−	3.14782i	0.00609132	−	0.113292i
$773$	42.2358	−	11.3171i	1.51912	−	0.407046i	0.599666	−	0.800251i	$-0.295300\pi$
$773$	42.2358	−	11.3171i	1.51912	−	0.407046i	0.919451	+	0.393205i	$0.128634\pi$
$774$	0.479802	−	17.8606i	0.0172461	−	0.641985i
$775$	6.53271	−	3.77166i	0.234662	−	0.135482i
$776$	−4.00215	−	4.70524i	−0.143669	−	0.168908i
$777$		0			0
$778$	0.223973	+	0.413174i	0.00802982	+	0.0148130i
$779$	4.19019	−	15.6380i	0.150129	−	0.560290i
$780$	10.4699	−	32.0753i	0.374884	−	1.14848i
$781$	−0.662359	−	2.47196i	−0.0237011	−	0.0884536i
$782$	2.98502	−	0.714502i	0.106744	−	0.0255505i
$783$	−8.01088			−0.286286
$784$		0			0
$785$	48.6408			1.73607
$786$	6.12757	−	1.46671i	0.218563	−	0.0523158i
$787$	−4.90453	−	18.3040i	−0.174828	−	0.652465i	−0.996581	−	0.0826221i	$-0.973671\pi$
$787$	−4.90453	−	18.3040i	−0.174828	−	0.652465i	0.821753	−	0.569843i	$-0.192996\pi$
$788$	−28.8195	−	9.40720i	−1.02665	−	0.335118i
$789$	−2.73789	+	10.2179i	−0.0974715	+	0.363769i
$790$	−1.68774	−	3.11347i	−0.0600473	−	0.110772i
$791$		0			0
$792$	19.1768	+	1.54847i	0.681419	+	0.0550223i
$793$	−0.0372863	+	0.0215273i	−0.00132408	+	0.000764456i
$794$	0.106333	−	3.95824i	0.00377362	−	0.140473i
$795$	34.0991	−	9.13682i	1.20937	−	0.324050i
$796$	50.9989	+	2.74202i	1.80761	+	0.0971883i
$797$	16.1055	−	16.1055i	0.570485	−	0.570485i	−0.361779	−	0.932264i	$-0.617831\pi$
$797$	16.1055	−	16.1055i	0.570485	−	0.570485i	0.932264	+	0.361779i	$0.117831\pi$
$798$		0			0
$799$	1.61613			0.0571747
$800$	20.4867	+	26.8869i	0.724316	+	0.950595i
$801$	6.87908	−	11.9149i	0.243060	−	0.420993i
$802$	5.28689	−	5.01027i	0.186687	−	0.176919i
$803$	18.6437	+	4.99557i	0.657922	+	0.176290i
$804$	−4.16154	+	6.38924i	−0.146766	+	0.225331i
$805$		0			0
$806$	8.95368	−	4.85360i	0.315380	−	0.170961i
$807$	−6.24017	+	3.60276i	−0.219664	+	0.126823i
$808$	−15.6472	−	10.8009i	−0.550467	−	0.379975i
$809$	32.5667	+	18.8024i	1.14498	+	0.661056i	0.947660	−	0.319282i	$-0.103442\pi$
$809$	32.5667	+	18.8024i	1.14498	+	0.661056i	0.197323	+	0.980339i	$0.436775\pi$
$810$	−6.03786	+	9.83793i	−0.212149	+	0.345670i
$811$	−7.00106	−	7.00106i	−0.245841	−	0.245841i	0.573421	−	0.819261i	$-0.305616\pi$
$811$	−7.00106	−	7.00106i	−0.245841	−	0.245841i	−0.819261	+	0.573421i	$0.805616\pi$
$812$		0			0
$813$	16.4887	−	16.4887i	0.578286	−	0.578286i
$814$	38.5697	−	9.23213i	1.35187	−	0.323586i
$815$	36.6744	−	63.5218i	1.28465	−	2.22507i
$816$	−0.967565	+	0.779187i	−0.0338715	+	0.0272770i
$817$	17.2868	+	29.9416i	0.604789	+	1.04752i
$818$	−0.0293493	+	0.0988357i	−0.00102617	+	0.00345571i
$819$		0			0
$820$	17.4079	−	3.67552i	0.607910	−	0.128355i
$821$	0.260570	−	0.972462i	0.00909397	−	0.0339392i	−0.961230	−	0.275749i	$-0.911074\pi$
$821$	0.260570	−	0.972462i	0.00909397	−	0.0339392i	0.970324	+	0.241810i	$0.0777409\pi$
$822$	−19.7540	−	0.530668i	−0.689001	−	0.0185092i
$823$	10.4164	+	6.01390i	0.363092	+	0.209631i	0.670436	−	0.741967i	$-0.266107\pi$
$823$	10.4164	+	6.01390i	0.363092	+	0.209631i	−0.307344	+	0.951598i	$0.599440\pi$
$824$	−41.8980	−	14.9328i	−1.45959	−	0.520207i
$825$			16.4678i			0.573336i
$826$		0			0
$827$	16.1838	+	16.1838i	0.562764	+	0.562764i	0.930092	−	0.367328i	$-0.119727\pi$
$827$	16.1838	+	16.1838i	0.562764	+	0.562764i	−0.367328	+	0.930092i	$0.619727\pi$
$828$	1.47572	−	27.4470i	0.0512849	−	0.953849i
$829$	−1.21363	−	4.52931i	−0.0421510	−	0.157310i	0.941643	−	0.336614i	$-0.109282\pi$
$829$	−1.21363	−	4.52931i	−0.0421510	−	0.157310i	−0.983794	+	0.179305i	$0.942615\pi$
$830$	−17.6303	+	16.7078i	−0.611956	+	0.579937i
$831$	1.25148	+	2.16763i	0.0434134	+	0.0751941i
$832$	26.6753	+	37.0309i	0.924798	+	1.28382i
$833$		0			0
$834$	2.61108	+	0.775362i	0.0904144	+	0.0268486i
$835$	6.78482	+	1.81799i	0.234798	+	0.0629141i
$836$	−33.1941	+	16.8566i	−1.14804	+	0.582999i
$837$	5.66339	−	1.51750i	0.195756	−	0.0524525i
$838$	−23.4253	−	14.3769i	−0.809212	−	0.496640i
$839$		−	47.4324i		−	1.63755i	−0.574116	−	0.818774i	$-0.694654\pi$
$839$		−	47.4324i		−	1.63755i	0.574116	−	0.818774i	$-0.305346\pi$
$840$		0			0
$841$			26.0251i			0.897417i
$842$	4.06009	−	6.61539i	0.139920	−	0.227982i
$843$	5.62576	−	1.50742i	0.193762	−	0.0519182i
$844$	−8.07357	+	24.7338i	−0.277904	+	0.851373i
$845$	−62.5437	−	16.7585i	−2.15157	−	0.576511i
$846$	4.11990	−	13.8740i	0.141645	−	0.477000i
$847$		0			0
$848$	−17.2328	+	44.5319i	−0.591776	+	1.52923i
$849$	8.80999	+	15.2594i	0.302358	+	0.523700i
$850$	2.02248	+	2.13415i	0.0693706	+	0.0732006i
$851$	−14.6647	−	54.7294i	−0.502700	−	1.87610i
$852$	1.10107	−	0.988711i	0.0377220	−	0.0338727i
$853$	−3.99601	−	3.99601i	−0.136821	−	0.136821i	0.635379	−	0.772200i	$-0.280844\pi$
$853$	−3.99601	−	3.99601i	−0.136821	−	0.136821i	−0.772200	+	0.635379i	$0.780844\pi$
$854$		0			0
$855$		−	44.0078i		−	1.50503i
$856$	−24.1433	+	11.4556i	−0.825200	+	0.391544i
$857$	9.68683	+	5.59270i	0.330896	+	0.191043i	0.656239	−	0.754553i	$-0.272146\pi$
$857$	9.68683	+	5.59270i	0.330896	+	0.191043i	−0.325343	+	0.945596i	$0.605480\pi$
$858$	−0.597072	+	22.2259i	−0.0203837	+	0.758781i
$859$	−5.51627	+	20.5870i	−0.188213	+	0.702420i	0.805707	+	0.592314i	$0.201786\pi$
$859$	−5.51627	+	20.5870i	−0.188213	+	0.702420i	−0.993920	+	0.110106i	$0.964881\pi$
$860$	−20.7366	+	31.8371i	−0.707112	+	1.08563i
$861$		0			0
$862$	−45.8273	−	13.6084i	−1.56088	−	0.463505i
$863$	−14.8376	−	25.6994i	−0.505076	−	0.874818i	−0.999983	−	0.00587153i	$-0.998131\pi$
$863$	−14.8376	−	25.6994i	−0.505076	−	0.874818i	0.494906	−	0.868946i	$-0.335202\pi$
$864$	9.97220	+	24.3075i	0.339261	+	0.826959i
$865$	4.98163	−	8.62843i	0.169380	−	0.293375i
$866$	6.15396	+	25.7098i	0.209120	+	0.873655i
$867$	10.6538	−	10.6538i	0.361821	−	0.361821i
$868$		0			0
$869$	1.65018	+	1.65018i	0.0559787	+	0.0559787i
$870$	6.14783	+	3.77313i	0.208431	+	0.127921i
$871$	21.1012	+	12.1828i	0.714987	+	0.412798i
$872$	1.84628	−	2.67469i	0.0625228	−	0.0905763i
$873$	−4.16701	+	2.40583i	−0.141032	+	0.0814249i
$874$	25.3475	+	46.7598i	0.857392	+	1.58167i
$875$		0			0
$876$	2.30571	+	10.9203i	0.0779028	+	0.368961i
$877$	−3.89460	−	1.04356i	−0.131511	−	0.0352384i	0.192463	−	0.981304i	$-0.438352\pi$
$877$	−3.89460	−	1.04356i	−0.131511	−	0.0352384i	−0.323974	+	0.946066i	$0.605019\pi$
$878$	−5.86728	−	6.19121i	−0.198011	−	0.208943i
$879$	1.62270	−	2.81060i	0.0547324	−	0.0947993i
$880$	−33.0340	−	24.1376i	−1.11358	−	0.813679i
$881$	23.4719			0.790789			0.395394	−	0.918511i	$-0.370608\pi$
$881$	23.4719			0.790789			0.395394	+	0.918511i	$0.370608\pi$
$882$		0			0
$883$	−22.0401	+	22.0401i	−0.741710	+	0.741710i	−0.972907	−	0.231197i	$-0.925736\pi$
$883$	−22.0401	+	22.0401i	−0.741710	+	0.741710i	0.231197	+	0.972907i	$0.425736\pi$
$884$	2.65228	+	2.95370i	0.0892059	+	0.0993436i
$885$	20.9164	−	5.60453i	0.703097	−	0.188394i
$886$	−49.8136	−	1.33818i	−1.67352	−	0.0449570i
$887$	−16.1626	+	9.33146i	−0.542686	+	0.313320i	−0.746167	−	0.665759i	$-0.768108\pi$
$887$	−16.1626	+	9.33146i	−0.542686	+	0.313320i	0.203481	+	0.979079i	$0.434775\pi$
$888$	14.8583	+	17.4685i	0.498611	+	0.586206i
$889$		0			0
$890$	−25.7212	+	13.9429i	−0.862176	+	0.467367i
$891$	1.96868	−	7.34723i	0.0659534	−	0.246141i
$892$	22.7416	−	11.5487i	0.761447	−	0.386678i
$893$	7.24841	+	27.0514i	0.242559	+	0.905242i
$894$	3.83914	+	16.0390i	0.128400	+	0.536425i
$895$	6.64882			0.222246
$896$		0			0
$897$	31.7651			1.06061
$898$	−7.23877	−	30.2419i	−0.241561	−	1.00918i
$899$	0.563535	+	2.10314i	0.0187949	+	0.0701437i
$900$	23.4768	−	11.9220i	0.782560	−	0.397400i
$901$	−1.07499	+	4.01190i	−0.0358130	+	0.133656i
$902$	−10.3071	+	5.58726i	−0.343189	+	0.186035i
$903$		0			0
$904$	−33.9332	−	39.8945i	−1.12860	−	1.32687i
$905$	−58.0996	+	33.5438i	−1.93130	+	1.11504i
$906$	−14.7980	−	0.397531i	−0.491632	−	0.0132071i
$907$	4.03036	−	1.07993i	0.133826	−	0.0358585i	−0.191284	−	0.981535i	$-0.561265\pi$
$907$	4.03036	−	1.07993i	0.133826	−	0.0358585i	0.325110	+	0.945676i	$0.394599\pi$
$908$	−23.1399	−	25.7696i	−0.767926	−	0.855195i
$909$	−10.4724	+	10.4724i	−0.347347	+	0.347347i
$910$		0			0
$911$	−26.5648			−0.880132			−0.440066	−	0.897965i	$-0.645045\pi$
$911$	−26.5648			−0.880132			−0.440066	+	0.897965i	$0.645045\pi$
$912$	−17.3819	−	12.7008i	−0.575571	−	0.420564i
$913$	8.00293	−	13.8615i	0.264858	−	0.458748i
$914$	26.0104	+	27.4465i	0.860349	+	0.907849i
$915$	0.0215580	+	0.00577645i	0.000712686	+	0.000190964i
$916$	5.80337	+	27.4858i	0.191749	+	0.908155i
$917$		0			0
$918$	1.08911	+	2.00914i	0.0359461	+	0.0663116i
$919$	19.0369	−	10.9909i	0.627969	−	0.362558i	−0.151996	−	0.988381i	$-0.548570\pi$
$919$	19.0369	−	10.9909i	0.627969	−	0.362558i	0.779965	+	0.625823i	$0.215237\pi$
$920$	−33.2050	+	48.1038i	−1.09474	+	1.58594i
$921$	20.5807	+	11.8823i	0.678157	+	0.391534i
$922$	40.1534	+	24.6435i	1.32238	+	0.811590i
$923$	−3.34375	−	3.34375i	−0.110061	−	0.110061i
$924$		0			0
$925$	38.3795	−	38.3795i	1.26191	−	1.26191i
$926$	3.23820	+	13.5285i	0.106414	+	0.444573i
$927$	−17.3237	+	30.0055i	−0.568985	+	0.985510i
$928$	−9.02678	+	3.70325i	−0.296318	+	0.121565i
$929$	7.02800	+	12.1729i	0.230581	+	0.399379i	0.957979	−	0.286837i	$-0.0926039\pi$
$929$	7.02800	+	12.1729i	0.230581	+	0.399379i	−0.727398	+	0.686216i	$0.759271\pi$
$930$	−5.06103	−	1.50288i	−0.165958	−	0.0492812i
$931$		0			0
$932$	−19.9910	+	30.6923i	−0.654825	+	1.00536i
$933$	−5.51974	+	20.5999i	−0.180708	+	0.674412i
$934$	0.105587	−	3.93046i	0.00345491	−	0.128608i
$935$	−3.08194	−	1.77936i	−0.100790	−	0.0581913i
$936$	32.1179	−	15.2394i	1.04981	−	0.498116i
$937$		−	57.9965i		−	1.89466i	−0.320256	−	0.947331i	$-0.603769\pi$
$937$		−	57.9965i		−	1.89466i	0.320256	−	0.947331i	$-0.396231\pi$
$938$		0			0
$939$	11.4172	+	11.4172i	0.372585	+	0.372585i
$940$	−22.8996	+	20.5628i	−0.746904	+	0.670685i
$941$	5.66139	+	21.1286i	0.184556	+	0.688773i	0.994725	+	0.102576i	$0.0327086\pi$
$941$	5.66139	+	21.1286i	0.184556	+	0.688773i	−0.810169	+	0.586196i	$0.800625\pi$
$942$	−12.7491	−	13.4530i	−0.415388	−	0.438322i
$943$	8.37494	+	14.5058i	0.272726	+	0.472375i
$944$	−10.5706	+	27.3159i	−0.344043	+	0.889056i
$945$		0			0
$946$	7.12720	−	24.0013i	0.231725	−	0.780350i
$947$	−25.8773	−	6.93379i	−0.840898	−	0.225318i	−0.187436	−	0.982277i	$-0.560018\pi$
$947$	−25.8773	−	6.93379i	−0.840898	−	0.225318i	−0.653463	+	0.756959i	$0.726684\pi$
$948$	−0.418747	+	1.28285i	−0.0136003	+	0.0416652i
$949$	34.4495	−	9.23073i	1.11828	−	0.299642i
$950$	−26.6512	+	43.4248i	−0.864679	+	1.40889i
$951$		−	6.77220i		−	0.219604i
$952$		0			0
$953$		−	20.2198i		−	0.654983i	−0.944854	−	0.327491i	$-0.893797\pi$
$953$		−	20.2198i		−	0.654983i	0.944854	−	0.327491i	$-0.106203\pi$
$954$	31.7006	+	19.4557i	1.02635	+	0.629902i
$955$	−19.9132	+	5.33572i	−0.644376	+	0.172660i
$956$	32.7124	−	16.6120i	1.05799	−	0.537271i
$957$	−4.59136	−	1.23025i	−0.148418	−	0.0397684i
$958$	−5.13389	−	1.52451i	−0.165869	−	0.0492547i
$959$		0			0
$960$	3.79584	−	23.3514i	0.122510	−	0.753662i
$961$	14.7032	+	25.4667i	0.474297	+	0.821506i
$962$	53.1908	−	50.4077i	1.71494	−	1.62521i
$963$	5.38758	+	20.1067i	0.173612	+	0.647931i
$964$	−2.72897	+	50.7560i	−0.0878941	+	1.63474i
$965$	3.69236	+	3.69236i	0.118861	+	0.118861i
$966$		0			0
$967$			33.3933i			1.07385i	0.843628	+	0.536927i	$0.180415\pi$
$967$			33.3933i			1.07385i	−0.843628	+	0.536927i	$0.819585\pi$
$968$	−3.91157	−	1.39411i	−0.125723	−	0.0448085i
$969$	−1.62166	−	0.936267i	−0.0520953	−	0.0300772i
$970$	10.2285	+	0.274775i	0.328416	+	0.00882248i
$971$	−2.75325	+	10.2753i	−0.0883560	+	0.329749i	−0.995929	−	0.0901463i	$-0.971267\pi$
$971$	−2.75325	+	10.2753i	−0.0883560	+	0.329749i	0.907573	+	0.419895i	$0.137933\pi$
$972$	31.5697	−	6.66567i	1.01260	−	0.213801i
$973$		0			0
$974$	−6.77134	+	22.8029i	−0.216968	+	0.730653i
$975$	15.2145	+	26.3523i	0.487254	+	0.843949i
$976$	−0.0235121	+	0.0189345i	−0.000752605	+	0.000606079i
$977$	−14.1382	+	24.4881i	−0.452321	+	0.783442i	−0.998530	−	0.0542066i	$-0.982737\pi$
$977$	−14.1382	+	24.4881i	−0.452321	+	0.783442i	0.546209	+	0.837649i	$0.316070\pi$
$978$	−27.1813	+	6.50619i	−0.869163	+	0.208045i
$979$	13.6326	−	13.6326i	0.435700	−	0.435700i
$980$		0			0
$981$	−1.79012	−	1.79012i	−0.0571541	−	0.0571541i
$982$	−6.71230	+	10.9368i	−0.214198	+	0.349009i
$983$	−1.68335	−	0.971882i	−0.0536905	−	0.0309982i	0.472914	−	0.881108i	$-0.343202\pi$
$983$	−1.68335	−	0.971882i	−0.0536905	−	0.0309982i	−0.526605	+	0.850110i	$0.676535\pi$
$984$	−5.57930	−	3.85126i	−0.177861	−	0.122774i
$985$	43.4895	−	25.1087i	1.38569	−	0.800028i
$986$	−0.746110	+	0.404450i	−0.0237610	+	0.0128803i
$987$		0			0
$988$	−37.5445	+	57.6423i	−1.19445	+	1.83385i
$989$	−34.5512	−	9.25795i	−1.09866	−	0.294386i
$990$	−23.1319	+	21.9216i	−0.735180	+	0.696714i
$991$	4.30271	−	7.45251i	0.136680	−	0.236737i	−0.789558	−	0.613676i	$-0.789690\pi$
$991$	4.30271	−	7.45251i	0.136680	−	0.236737i	0.926238	+	0.376939i	$0.123023\pi$
$992$	5.68009	−	4.32800i	0.180343	−	0.137414i
$993$	28.2221			0.895600
$994$		0			0
$995$	−59.8211	+	59.8211i	−1.89646	+	1.89646i
$996$	9.24204	+	0.496910i	0.292845	+	0.0157452i
$997$	10.6324	−	2.84895i	0.336732	−	0.0902272i	−0.0864907	−	0.996253i	$-0.527565\pi$
$997$	10.6324	−	2.84895i	0.336732	−	0.0902272i	0.423223	+	0.906025i	$0.360899\pi$
$998$	0.252053	−	9.38265i	0.00797861	−	0.297003i
$999$	36.5355	−	21.0938i	1.15593	−	0.667378i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	784.2.x.m.165.3		24
7.2	even	3	inner	784.2.x.m.373.2		24
7.3	odd	6		112.2.m.d.85.6	yes	12
7.4	even	3		784.2.m.h.197.6		12
7.5	odd	6		784.2.x.l.373.2		24
7.6	odd	2		784.2.x.l.165.3		24
16.13	even	4	inner	784.2.x.m.557.2		24
28.3	even	6		448.2.m.d.113.3		12
56.3	even	6		896.2.m.h.225.4		12
56.45	odd	6		896.2.m.g.225.3		12
112.3	even	12		448.2.m.d.337.3		12
112.13	odd	4		784.2.x.l.557.2		24
112.45	odd	12		112.2.m.d.29.6	✓	12
112.59	even	12		896.2.m.h.673.4		12
112.61	odd	12		784.2.x.l.765.3		24
112.93	even	12	inner	784.2.x.m.765.3		24
112.101	odd	12		896.2.m.g.673.3		12
112.109	even	12		784.2.m.h.589.6		12
224.3	even	24		7168.2.a.bi.1.4		12
224.45	odd	24		7168.2.a.bj.1.4		12
224.115	even	24		7168.2.a.bi.1.9		12
224.157	odd	24		7168.2.a.bj.1.9		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
112.2.m.d.29.6	✓	12	112.45	odd	12
112.2.m.d.85.6	yes	12	7.3	odd	6
448.2.m.d.113.3		12	28.3	even	6
448.2.m.d.337.3		12	112.3	even	12
784.2.m.h.197.6		12	7.4	even	3
784.2.m.h.589.6		12	112.109	even	12
784.2.x.l.165.3		24	7.6	odd	2
784.2.x.l.373.2		24	7.5	odd	6
784.2.x.l.557.2		24	112.13	odd	4
784.2.x.l.765.3		24	112.61	odd	12
784.2.x.m.165.3		24	1.1	even	1	trivial
784.2.x.m.373.2		24	7.2	even	3	inner
784.2.x.m.557.2		24	16.13	even	4	inner
784.2.x.m.765.3		24	112.93	even	12	inner
896.2.m.g.225.3		12	56.45	odd	6
896.2.m.g.673.3		12	112.101	odd	12
896.2.m.h.225.4		12	56.3	even	6
896.2.m.h.673.4		12	112.59	even	12
7168.2.a.bi.1.4		12	224.3	even	24
7168.2.a.bi.1.9		12	224.115	even	24
7168.2.a.bj.1.4		12	224.45	odd	24
7168.2.a.bj.1.9		12	224.157	odd	24

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:	\( N \)	\(=\)	\( 784 = 2^{4} \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	784.x (of order \(12\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.329210 - 1.37536i) q^{2} +(-0.231031 - 0.862219i) q^{3} +(-1.78324 + 0.905566i) q^{4} +(0.857449 - 3.20004i) q^{5} +(-1.10981 + 0.601602i) q^{6} +(1.83254 + 2.15448i) q^{8} +(1.90803 - 1.10160i) q^{9} +O(q^{10})\)	\(q+(-0.329210 - 1.37536i) q^{2} +(-0.231031 - 0.862219i) q^{3} +(-1.78324 + 0.905566i) q^{4} +(0.857449 - 3.20004i) q^{5} +(-1.10981 + 0.601602i) q^{6} +(1.83254 + 2.15448i) q^{8} +(1.90803 - 1.10160i) q^{9} +(-4.68350 - 0.125816i) q^{10} +(2.98217 - 0.799070i) q^{11} +(1.19278 + 1.32833i) q^{12} +(4.03390 - 4.03390i) q^{13} -2.95723 q^{15} +(2.35990 - 3.22969i) q^{16} +(0.173966 - 0.301317i) q^{17} +(-2.14324 - 2.26157i) q^{18} +(5.82380 + 1.56048i) q^{19} +(1.36881 + 6.48293i) q^{20} +(-2.08077 - 3.83850i) q^{22} +(-5.40216 + 3.11894i) q^{23} +(1.43426 - 2.07780i) q^{24} +(-5.17494 - 2.98775i) q^{25} +(-6.87607 - 4.22007i) q^{26} +(-3.28420 - 3.28420i) q^{27} +(1.21961 - 1.21961i) q^{29} +(0.973551 + 4.06727i) q^{30} +(-0.631188 + 1.09325i) q^{31} +(-5.21889 - 2.18247i) q^{32} +(-1.37795 - 2.38667i) q^{33} +(-0.471692 - 0.140069i) q^{34} +(-2.40491 + 3.69227i) q^{36} +(-2.35091 + 8.77373i) q^{37} +(0.228975 - 8.52356i) q^{38} +(-4.41005 - 2.54615i) q^{39} +(8.46575 - 4.01686i) q^{40} -2.68519i q^{41} +(4.05478 + 4.05478i) q^{43} +(-4.59432 + 4.12548i) q^{44} +(-1.88914 - 7.05035i) q^{45} +(6.06811 + 6.40314i) q^{46} +(2.32249 + 4.02267i) q^{47} +(-3.32990 - 1.28859i) q^{48} +(-2.40560 + 8.10101i) q^{50} +(-0.299993 - 0.0803829i) q^{51} +(-3.54045 + 10.8464i) q^{52} +(-11.5307 + 3.08965i) q^{53} +(-3.43577 + 5.59815i) q^{54} -10.2282i q^{55} -5.38191i q^{57} +(-2.07891 - 1.27590i) q^{58} +(-7.07295 + 1.89519i) q^{59} +(5.27346 - 2.67797i) q^{60} +(-0.00728993 - 0.00195333i) q^{61} +(1.71141 + 0.508203i) q^{62} +(-1.28358 + 7.89636i) q^{64} +(-9.44979 - 16.3675i) q^{65} +(-2.82890 + 2.68089i) q^{66} +(1.10544 + 4.12554i) q^{67} +(-0.0373600 + 0.694859i) q^{68} +(3.93727 + 3.93727i) q^{69} -0.828913i q^{71} +(5.86993 + 2.09208i) q^{72} +(5.41415 + 3.12586i) q^{73} +(12.8410 + 0.344957i) q^{74} +(-1.38052 + 5.15219i) q^{75} +(-11.7984 + 2.49112i) q^{76} +(-2.05004 + 6.90364i) q^{78} +(0.377945 + 0.654620i) q^{79} +(-8.31164 - 10.3211i) q^{80} +(1.23186 - 2.13364i) q^{81} +(-3.69311 + 0.883991i) q^{82} +(3.66586 - 3.66586i) q^{83} +(-0.815062 - 0.815062i) q^{85} +(4.24191 - 6.91166i) q^{86} +(-1.33334 - 0.769803i) q^{87} +(7.18653 + 4.96070i) q^{88} +(5.40799 - 3.12231i) q^{89} +(-9.07486 + 4.91929i) q^{90} +(6.80895 - 10.4538i) q^{92} +(1.08844 + 0.291648i) q^{93} +(4.76804 - 4.51857i) q^{94} +(9.98723 - 17.2984i) q^{95} +(-0.676044 + 5.00404i) q^{96} -2.18393 q^{97} +(4.80981 - 4.80981i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - 2 q^{2} + 4 q^{3} + 6 q^{4} + 4 q^{5} - 8 q^{6} - 8 q^{8}+O(q^{10}) \) 24 * q - 2 * q^2 + 4 * q^3 + 6 * q^4 + 4 * q^5 - 8 * q^6 - 8 * q^8	\( 24 q - 2 q^{2} + 4 q^{3} + 6 q^{4} + 4 q^{5} - 8 q^{6} - 8 q^{8} - 4 q^{10} + 8 q^{12} - 48 q^{15} - 10 q^{16} - 8 q^{17} + 40 q^{20} + 28 q^{22} - 8 q^{24} - 20 q^{26} - 8 q^{27} - 8 q^{29} + 28 q^{30} - 8 q^{31} - 12 q^{32} - 16 q^{34} - 32 q^{36} + 20 q^{37} + 16 q^{38} - 8 q^{40} + 32 q^{43} - 14 q^{44} + 40 q^{45} + 28 q^{46} + 16 q^{47} - 32 q^{48} + 88 q^{50} + 16 q^{51} - 16 q^{52} - 4 q^{53} + 64 q^{54} - 14 q^{58} - 16 q^{59} - 60 q^{60} - 20 q^{61} - 16 q^{62} - 36 q^{64} - 32 q^{65} + 12 q^{66} - 24 q^{67} - 28 q^{68} + 8 q^{69} - 6 q^{72} + 38 q^{74} - 40 q^{75} - 96 q^{76} - 152 q^{78} - 24 q^{79} + 24 q^{80} + 44 q^{81} - 16 q^{82} + 40 q^{83} - 16 q^{85} - 38 q^{86} + 14 q^{88} + 80 q^{90} + 64 q^{92} + 48 q^{93} - 24 q^{94} - 16 q^{96} - 96 q^{97} + 64 q^{99}+O(q^{100}) \) 24 * q - 2 * q^2 + 4 * q^3 + 6 * q^4 + 4 * q^5 - 8 * q^6 - 8 * q^8 - 4 * q^10 + 8 * q^12 - 48 * q^15 - 10 * q^16 - 8 * q^17 + 40 * q^20 + 28 * q^22 - 8 * q^24 - 20 * q^26 - 8 * q^27 - 8 * q^29 + 28 * q^30 - 8 * q^31 - 12 * q^32 - 16 * q^34 - 32 * q^36 + 20 * q^37 + 16 * q^38 - 8 * q^40 + 32 * q^43 - 14 * q^44 + 40 * q^45 + 28 * q^46 + 16 * q^47 - 32 * q^48 + 88 * q^50 + 16 * q^51 - 16 * q^52 - 4 * q^53 + 64 * q^54 - 14 * q^58 - 16 * q^59 - 60 * q^60 - 20 * q^61 - 16 * q^62 - 36 * q^64 - 32 * q^65 + 12 * q^66 - 24 * q^67 - 28 * q^68 + 8 * q^69 - 6 * q^72 + 38 * q^74 - 40 * q^75 - 96 * q^76 - 152 * q^78 - 24 * q^79 + 24 * q^80 + 44 * q^81 - 16 * q^82 + 40 * q^83 - 16 * q^85 - 38 * q^86 + 14 * q^88 + 80 * q^90 + 64 * q^92 + 48 * q^93 - 24 * q^94 - 16 * q^96 - 96 * q^97 + 64 * q^99

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