LMFDB - Embedded newform 950.2.l.k.351.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [950,2,Mod(101,950)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(950, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([0, 14]))

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

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

chi := DirichletCharacter("950.101");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 950 = 2 \cdot 5^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	950.l (of order $9$, degree $6$, 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:	$7.58578819202$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$4$ over $\Q(\zeta_{9})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			351.3
Character	$\chi$	$=$	950.351
Dual form			950.2.l.k.701.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.173648 + 0.984808i) q^{2} +(0.639791 - 0.536848i) q^{3} +(-0.939693 + 0.342020i) q^{4} +(0.639791 + 0.536848i) q^{6} +(-2.09271 + 3.62467i) q^{7} +(-0.500000 - 0.866025i) q^{8} +(-0.399818 + 2.26748i) q^{9} +O(q^{10})$	\(q+(0.173648 + 0.984808i) q^{2} +(0.639791 - 0.536848i) q^{3} +(-0.939693 + 0.342020i) q^{4} +(0.639791 + 0.536848i) q^{6} +(-2.09271 + 3.62467i) q^{7} +(-0.500000 - 0.866025i) q^{8} +(-0.399818 + 2.26748i) q^{9} +(-2.69402 - 4.66617i) q^{11} +(-0.417594 + 0.723294i) q^{12} +(-3.01125 - 2.52674i) q^{13} +(-3.93300 - 1.43150i) q^{14} +(0.766044 - 0.642788i) q^{16} +(-0.371748 - 2.10829i) q^{17} -2.30246 q^{18} +(-2.92715 - 3.22983i) q^{19} +(0.607005 + 3.44250i) q^{21} +(4.12747 - 3.46336i) q^{22} +(-2.68425 + 0.976988i) q^{23} +(-0.784820 - 0.285651i) q^{24} +(1.96545 - 3.40427i) q^{26} +(2.21428 + 3.83524i) q^{27} +(0.726789 - 4.12183i) q^{28} +(1.34929 - 7.65218i) q^{29} +(-2.86692 + 4.96565i) q^{31} +(0.766044 + 0.642788i) q^{32} +(-4.22863 - 1.53910i) q^{33} +(2.01170 - 0.732201i) q^{34} +(-0.399818 - 2.26748i) q^{36} -1.84763 q^{37} +(2.67247 - 3.44353i) q^{38} -3.28305 q^{39} +(4.67266 - 3.92083i) q^{41} +(-3.28479 + 1.19557i) q^{42} +(11.8496 + 4.31289i) q^{43} +(4.12747 + 3.46336i) q^{44} +(-1.42826 - 2.47382i) q^{46} +(-0.760675 + 4.31400i) q^{47} +(0.145029 - 0.822499i) q^{48} +(-5.25884 - 9.10858i) q^{49} +(-1.36967 - 1.14929i) q^{51} +(3.69385 + 1.34445i) q^{52} +(-12.2002 + 4.44050i) q^{53} +(-3.39247 + 2.84662i) q^{54} +4.18541 q^{56} +(-3.60669 - 0.494982i) q^{57} +7.77023 q^{58} +(-1.36789 - 7.75770i) q^{59} +(-10.3018 + 3.74954i) q^{61} +(-5.38804 - 1.96109i) q^{62} +(-7.38218 - 6.19439i) q^{63} +(-0.500000 + 0.866025i) q^{64} +(0.781420 - 4.43165i) q^{66} +(-1.82123 + 10.3287i) q^{67} +(1.07041 + 1.85400i) q^{68} +(-1.19287 + 2.06610i) q^{69} +(-12.6676 - 4.61063i) q^{71} +(2.16361 - 0.787488i) q^{72} +(-2.58013 + 2.16499i) q^{73} +(-0.320837 - 1.81956i) q^{74} +(3.85529 + 2.03391i) q^{76} +22.5511 q^{77} +(-0.570095 - 3.23317i) q^{78} +(-3.96546 + 3.32742i) q^{79} +(-3.01521 - 1.09745i) q^{81} +(4.67266 + 3.92083i) q^{82} +(-4.36665 + 7.56326i) q^{83} +(-1.74780 - 3.02728i) q^{84} +(-2.18971 + 12.4185i) q^{86} +(-3.24480 - 5.62016i) q^{87} +(-2.69402 + 4.66617i) q^{88} +(-2.52982 - 2.12277i) q^{89} +(15.4603 - 5.62708i) q^{91} +(2.18822 - 1.83614i) q^{92} +(0.831571 + 4.71607i) q^{93} -4.38055 q^{94} +0.835188 q^{96} +(-0.150188 - 0.851757i) q^{97} +(8.05701 - 6.76064i) q^{98} +(11.6576 - 4.24301i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 3 q^{7} - 12 q^{8}+O(q^{10}) $ 24 * q + 3 * q^7 - 12 * q^8	$ 24 q + 3 q^{7} - 12 q^{8} - 6 q^{11} - 3 q^{12} + 24 q^{13} - 15 q^{14} - 9 q^{17} + 30 q^{18} - 15 q^{19} - 18 q^{21} + 12 q^{23} - 9 q^{26} - 21 q^{27} + 12 q^{28} - 12 q^{29} + 9 q^{31} - 42 q^{33} - 9 q^{34} + 66 q^{37} + 6 q^{38} + 66 q^{39} + 18 q^{41} + 9 q^{42} - 3 q^{43} - 3 q^{46} - 12 q^{47} - 27 q^{49} - 3 q^{51} - 12 q^{52} - 45 q^{53} + 27 q^{54} - 6 q^{56} - 27 q^{57} - 18 q^{58} + 36 q^{59} + 12 q^{61} - 24 q^{62} - 63 q^{63} - 12 q^{64} + 48 q^{66} - 54 q^{67} + 3 q^{68} + 21 q^{69} - 39 q^{71} + 48 q^{73} + 18 q^{74} + 6 q^{76} + 48 q^{77} - 12 q^{78} - 42 q^{79} - 36 q^{81} + 18 q^{82} - 3 q^{83} + 9 q^{84} - 39 q^{86} - 24 q^{87} - 6 q^{88} - 36 q^{89} + 12 q^{91} - 15 q^{92} - 6 q^{93} + 12 q^{94} + 6 q^{96} - 54 q^{97} + 3 q^{98} + 51 q^{99}+O(q^{100}) $ 24 * q + 3 * q^7 - 12 * q^8 - 6 * q^11 - 3 * q^12 + 24 * q^13 - 15 * q^14 - 9 * q^17 + 30 * q^18 - 15 * q^19 - 18 * q^21 + 12 * q^23 - 9 * q^26 - 21 * q^27 + 12 * q^28 - 12 * q^29 + 9 * q^31 - 42 * q^33 - 9 * q^34 + 66 * q^37 + 6 * q^38 + 66 * q^39 + 18 * q^41 + 9 * q^42 - 3 * q^43 - 3 * q^46 - 12 * q^47 - 27 * q^49 - 3 * q^51 - 12 * q^52 - 45 * q^53 + 27 * q^54 - 6 * q^56 - 27 * q^57 - 18 * q^58 + 36 * q^59 + 12 * q^61 - 24 * q^62 - 63 * q^63 - 12 * q^64 + 48 * q^66 - 54 * q^67 + 3 * q^68 + 21 * q^69 - 39 * q^71 + 48 * q^73 + 18 * q^74 + 6 * q^76 + 48 * q^77 - 12 * q^78 - 42 * q^79 - 36 * q^81 + 18 * q^82 - 3 * q^83 + 9 * q^84 - 39 * q^86 - 24 * q^87 - 6 * q^88 - 36 * q^89 + 12 * q^91 - 15 * q^92 - 6 * q^93 + 12 * q^94 + 6 * q^96 - 54 * q^97 + 3 * q^98 + 51 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/950\mathbb{Z}\right)^\times$.

$n$	$77$	$401$
$\chi(n)$	$1$	$e\left(\frac{4}{9}\right)$

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 $

$2$	0.173648	+	0.984808i	0.122788	+	0.696364i
$2$	0.173648	+	0.984808i	0.122788	+	0.696364i
$3$	0.639791	−	0.536848i	0.369383	−	0.309949i	−0.439134	−	0.898421i	$-0.644715\pi$
$3$	0.639791	−	0.536848i	0.369383	−	0.309949i	0.808518	+	0.588472i	$0.200270\pi$
$4$	−0.939693	+	0.342020i	−0.469846	+	0.171010i
$5$		0			0
$5$		0			0
$6$	0.639791	+	0.536848i	0.261194	+	0.219167i
$7$	−2.09271	+	3.62467i	−0.790969	+	1.37000i	0.134399	+	0.990927i	$0.457090\pi$
$7$	−2.09271	+	3.62467i	−0.790969	+	1.37000i	−0.925368	+	0.379071i	$0.876244\pi$
$8$	−0.500000	−	0.866025i	−0.176777	−	0.306186i
$9$	−0.399818	+	2.26748i	−0.133273	+	0.755827i
$10$		0			0
$11$	−2.69402	−	4.66617i	−0.812276	−	1.40690i	−0.911267	−	0.411816i	$-0.864895\pi$
$11$	−2.69402	−	4.66617i	−0.812276	−	1.40690i	0.0989909	−	0.995088i	$-0.468439\pi$
$12$	−0.417594	+	0.723294i	−0.120549	+	0.208797i
$13$	−3.01125	−	2.52674i	−0.835171	−	0.700791i	0.121301	−	0.992616i	$-0.461293\pi$
$13$	−3.01125	−	2.52674i	−0.835171	−	0.700791i	−0.956472	+	0.291824i	$0.905738\pi$
$14$	−3.93300	−	1.43150i	−1.05114	−	0.382583i
$15$		0			0
$16$	0.766044	−	0.642788i	0.191511	−	0.160697i
$17$	−0.371748	−	2.10829i	−0.0901621	−	0.511335i	−0.996123	−	0.0879731i	$-0.971961\pi$
$17$	−0.371748	−	2.10829i	−0.0901621	−	0.511335i	0.905961	−	0.423362i	$-0.139150\pi$
$18$	−2.30246			−0.542695
$19$	−2.92715	−	3.22983i	−0.671534	−	0.740974i
$19$	−2.92715	−	3.22983i	−0.671534	−	0.740974i
$20$		0			0
$21$	0.607005	+	3.44250i	0.132459	+	0.751215i
$22$	4.12747	−	3.46336i	0.879980	−	0.738391i
$23$	−2.68425	+	0.976988i	−0.559705	+	0.203716i	−0.606353	−	0.795195i	$-0.707368\pi$
$23$	−2.68425	+	0.976988i	−0.559705	+	0.203716i	0.0466481	+	0.998911i	$0.485146\pi$
$24$	−0.784820	−	0.285651i	−0.160201	−	0.0583083i
$25$		0			0
$26$	1.96545	−	3.40427i	0.385457	−	0.667632i
$27$	2.21428	+	3.83524i	0.426137	+	0.738092i
$28$	0.726789	−	4.12183i	0.137350	−	0.778952i
$29$	1.34929	−	7.65218i	0.250556	−	1.42097i	−0.556671	−	0.830733i	$-0.687922\pi$
$29$	1.34929	−	7.65218i	0.250556	−	1.42097i	0.807227	−	0.590241i	$-0.200967\pi$
$30$		0			0
$31$	−2.86692	+	4.96565i	−0.514913	+	0.891856i	0.484937	+	0.874549i	$0.338843\pi$
$31$	−2.86692	+	4.96565i	−0.514913	+	0.891856i	−0.999850	+	0.0173071i	$0.994491\pi$
$32$	0.766044	+	0.642788i	0.135419	+	0.113630i
$33$	−4.22863	−	1.53910i	−0.736111	−	0.267922i
$34$	2.01170	−	0.732201i	0.345004	−	0.125571i
$35$		0			0
$36$	−0.399818	−	2.26748i	−0.0666364	−	0.377914i
$37$	−1.84763			−0.303748			−0.151874	−	0.988400i	$-0.548531\pi$
$37$	−1.84763			−0.303748			−0.151874	+	0.988400i	$0.548531\pi$
$38$	2.67247	−	3.44353i	0.433532	−	0.558615i
$39$	−3.28305			−0.525708
$40$		0			0
$41$	4.67266	−	3.92083i	0.729748	−	0.612331i	−0.200315	−	0.979732i	$-0.564197\pi$
$41$	4.67266	−	3.92083i	0.729748	−	0.612331i	0.930063	+	0.367401i	$0.119752\pi$
$42$	−3.28479	+	1.19557i	−0.506855	+	0.184480i
$43$	11.8496	+	4.31289i	1.80704	+	0.657710i	0.997501	+	0.0706461i	$0.0225061\pi$
$43$	11.8496	+	4.31289i	1.80704	+	0.657710i	0.809541	+	0.587063i	$0.199716\pi$
$44$	4.12747	+	3.46336i	0.622240	+	0.522121i
$45$		0			0
$46$	−1.42826	−	2.47382i	−0.210586	−	0.364745i
$47$	−0.760675	+	4.31400i	−0.110956	+	0.629262i	0.877718	+	0.479178i	$0.159065\pi$
$47$	−0.760675	+	4.31400i	−0.110956	+	0.629262i	−0.988673	+	0.150083i	$0.952046\pi$
$48$	0.145029	−	0.822499i	0.0209331	−	0.118718i
$49$	−5.25884	−	9.10858i	−0.751263	−	1.30123i
$50$		0			0
$51$	−1.36967	−	1.14929i	−0.191792	−	0.160933i
$52$	3.69385	+	1.34445i	0.512244	+	0.186442i
$53$	−12.2002	+	4.44050i	−1.67582	+	0.609949i	−0.992728	−	0.120381i	$-0.961588\pi$
$53$	−12.2002	+	4.44050i	−1.67582	+	0.609949i	−0.683094	+	0.730330i	$0.739366\pi$
$54$	−3.39247	+	2.84662i	−0.461656	+	0.387376i
$55$		0			0
$56$	4.18541			0.559299
$57$	−3.60669	−	0.494982i	−0.477718	−	0.0655620i
$58$	7.77023			1.02028
$59$	−1.36789	−	7.75770i	−0.178084	−	1.00997i	−0.934523	−	0.355902i	$-0.884174\pi$
$59$	−1.36789	−	7.75770i	−0.178084	−	1.00997i	0.756439	−	0.654065i	$-0.226938\pi$
$60$		0			0
$61$	−10.3018	+	3.74954i	−1.31901	+	0.480080i	−0.903140	−	0.429345i	$-0.858744\pi$
$61$	−10.3018	+	3.74954i	−1.31901	+	0.480080i	−0.415868	+	0.909425i	$0.636522\pi$
$62$	−5.38804	−	1.96109i	−0.684282	−	0.249058i
$63$	−7.38218	−	6.19439i	−0.930068	−	0.780419i
$64$	−0.500000	+	0.866025i	−0.0625000	+	0.108253i
$65$		0			0
$66$	0.781420	−	4.43165i	0.0961861	−	0.545499i
$67$	−1.82123	+	10.3287i	−0.222498	+	1.26185i	0.644913	+	0.764256i	$0.276894\pi$
$67$	−1.82123	+	10.3287i	−0.222498	+	1.26185i	−0.867411	+	0.497593i	$0.834217\pi$
$68$	1.07041	+	1.85400i	0.129806	+	0.224830i
$69$	−1.19287	+	2.06610i	−0.143604	+	0.248730i
$70$		0			0
$71$	−12.6676	−	4.61063i	−1.50337	−	0.547181i	−0.546437	−	0.837500i	$-0.684016\pi$
$71$	−12.6676	−	4.61063i	−1.50337	−	0.547181i	−0.956930	+	0.290319i	$0.906239\pi$
$72$	2.16361	−	0.787488i	0.254983	−	0.0928064i
$73$	−2.58013	+	2.16499i	−0.301982	+	0.253393i	−0.781169	−	0.624320i	$-0.785376\pi$
$73$	−2.58013	+	2.16499i	−0.301982	+	0.253393i	0.479187	+	0.877713i	$0.340932\pi$
$74$	−0.320837	−	1.81956i	−0.0372966	−	0.211519i
$75$		0			0
$76$	3.85529	+	2.03391i	0.442232	+	0.233305i
$77$	22.5511			2.56994
$78$	−0.570095	−	3.23317i	−0.0645505	−	0.366084i
$79$	−3.96546	+	3.32742i	−0.446149	+	0.374364i	−0.838005	−	0.545663i	$-0.816278\pi$
$79$	−3.96546	+	3.32742i	−0.446149	+	0.374364i	0.391855	+	0.920027i	$0.371833\pi$
$80$		0			0
$81$	−3.01521	−	1.09745i	−0.335023	−	0.121938i
$82$	4.67266	+	3.92083i	0.516009	+	0.432983i
$83$	−4.36665	+	7.56326i	−0.479302	+	0.830175i	−0.999718	−	0.0237373i	$-0.992443\pi$
$83$	−4.36665	+	7.56326i	−0.479302	+	0.830175i	0.520416	+	0.853913i	$0.325777\pi$
$84$	−1.74780	−	3.02728i	−0.190701	−	0.330304i
$85$		0			0
$86$	−2.18971	+	12.4185i	−0.236123	+	1.33912i
$87$	−3.24480	−	5.62016i	−0.347879	−	0.602544i
$88$	−2.69402	+	4.66617i	−0.287183	+	0.497416i
$89$	−2.52982	−	2.12277i	−0.268160	−	0.225013i	0.498785	−	0.866726i	$-0.333780\pi$
$89$	−2.52982	−	2.12277i	−0.268160	−	0.225013i	−0.766945	+	0.641713i	$0.778224\pi$
$90$		0			0
$91$	15.4603	−	5.62708i	1.62068	−	0.589878i
$92$	2.18822	−	1.83614i	0.228138	−	0.191430i
$93$	0.831571	+	4.71607i	0.0862299	+	0.489034i
$94$	−4.38055			−0.451819
$95$		0			0
$96$	0.835188			0.0852410
$97$	−0.150188	−	0.851757i	−0.0152492	−	0.0864828i	0.976233	−	0.216722i	$-0.0695365\pi$
$97$	−0.150188	−	0.851757i	−0.0152492	−	0.0864828i	−0.991483	+	0.130239i	$0.958425\pi$
$98$	8.05701	−	6.76064i	0.813881	−	0.682928i
$99$	11.6576	−	4.24301i	1.17163	−	0.426439i
$100$		0			0
$101$	3.02817	+	2.54093i	0.301314	+	0.252832i	0.780891	−	0.624667i	$-0.214765\pi$
$101$	3.02817	+	2.54093i	0.301314	+	0.252832i	−0.479577	+	0.877500i	$0.659210\pi$
$102$	0.893989	−	1.54844i	0.0885181	−	0.153318i
$103$	−4.23376	−	7.33309i	−0.417165	−	0.722551i	0.578488	−	0.815691i	$-0.303643\pi$
$103$	−4.23376	−	7.33309i	−0.417165	−	0.722551i	−0.995653	+	0.0931401i	$0.970310\pi$
$104$	−0.682595	+	3.87119i	−0.0669340	+	0.379601i
$105$		0			0
$106$	−6.49157	−	11.2437i	−0.630517	−	1.09209i
$107$	−1.42206	+	2.46307i	−0.137475	+	0.238114i	−0.926540	−	0.376196i	$-0.877232\pi$
$107$	−1.42206	+	2.46307i	−0.137475	+	0.238114i	0.789065	+	0.614310i	$0.210565\pi$
$108$	−3.39247	−	2.84662i	−0.326440	−	0.273916i
$109$	11.2867	+	4.10804i	1.08107	+	0.393479i	0.820307	−	0.571923i	$-0.193802\pi$
$109$	11.2867	+	4.10804i	1.08107	+	0.393479i	0.260767	+	0.965402i	$0.416025\pi$
$110$		0			0
$111$	−1.18210	+	0.991896i	−0.112200	+	0.0941466i
$112$	0.726789	+	4.12183i	0.0686751	+	0.389476i
$113$	5.10799			0.480519			0.240260	−	0.970709i	$-0.422767\pi$
$113$	5.10799			0.480519			0.240260	+	0.970709i	$0.422767\pi$
$114$	−0.138833	−	3.63785i	−0.0130029	−	0.340716i
$115$		0			0
$116$	1.34929	+	7.65218i	0.125278	+	0.710487i
$117$	6.93329	−	5.81772i	0.640983	−	0.537848i
$118$	7.40232	−	2.69422i	0.681438	−	0.248023i
$119$	8.41982	+	3.06456i	0.771843	+	0.280928i
$120$		0			0
$121$	−9.01544	+	15.6152i	−0.819586	+	1.41956i
$122$	−5.48146	−	9.49417i	−0.496268	−	0.859562i
$123$	0.884637	−	5.01702i	0.0797650	−	0.452370i
$124$	0.995670	−	5.64672i	0.0894138	−	0.507091i
$125$		0			0
$126$	4.81838	−	8.34567i	0.429255	−	0.743492i
$127$	−8.44006	−	7.08205i	−0.748934	−	0.628430i	0.186287	−	0.982495i	$-0.440355\pi$
$127$	−8.44006	−	7.08205i	−0.748934	−	0.628430i	−0.935221	+	0.354065i	$0.884799\pi$
$128$	−0.939693	−	0.342020i	−0.0830579	−	0.0302306i
$129$	9.89661	−	3.60207i	0.871348	−	0.317145i
$130$		0			0
$131$	3.64801	+	20.6889i	0.318728	+	1.80759i	0.550512	+	0.834828i	$0.314433\pi$
$131$	3.64801	+	20.6889i	0.318728	+	1.80759i	−0.231784	+	0.972767i	$0.574456\pi$
$132$	4.50002			0.391676
$133$	17.8327	−	3.85087i	1.54630	−	0.333912i
$134$	−10.4880			−0.906027
$135$		0			0
$136$	−1.63996	+	1.37609i	−0.140625	+	0.117998i
$137$	3.59013	−	1.30670i	0.306725	−	0.111639i	−0.184072	−	0.982913i	$-0.558928\pi$
$137$	3.59013	−	1.30670i	0.306725	−	0.111639i	0.490797	+	0.871274i	$0.336706\pi$
$138$	−2.24185	−	0.815968i	−0.190839	−	0.0694598i
$139$	11.1485	+	9.35471i	0.945605	+	0.793457i	0.978552	−	0.206001i	$-0.0660449\pi$
$139$	11.1485	+	9.35471i	0.945605	+	0.793457i	−0.0329472	+	0.999457i	$0.510489\pi$
$140$		0			0
$141$	1.82929	+	3.16842i	0.154054	+	0.266829i
$142$	2.34088	−	13.2758i	0.196442	−	1.11408i
$143$	−3.67784	+	20.8581i	−0.307557	+	1.74424i
$144$	1.15123	+	1.99399i	0.0959359	+	0.166166i
$145$		0			0
$146$	−2.58013	−	2.16499i	−0.213533	−	0.179176i
$147$	−8.25449	−	3.00439i	−0.680819	−	0.247798i
$148$	1.73620	−	0.631926i	0.142715	−	0.0519440i
$149$	9.12001	−	7.65259i	0.747140	−	0.626925i	−0.187605	−	0.982245i	$-0.560072\pi$
$149$	9.12001	−	7.65259i	0.747140	−	0.626925i	0.934745	+	0.355320i	$0.115628\pi$
$150$		0			0
$151$	−5.21314			−0.424239			−0.212120	−	0.977244i	$-0.568037\pi$
$151$	−5.21314			−0.424239			−0.212120	+	0.977244i	$0.568037\pi$
$152$	−1.33354	+	4.14990i	−0.108165	+	0.336601i
$153$	4.92914			0.398497
$154$	3.91596	+	22.2085i	0.315557	+	1.78961i
$155$		0			0
$156$	3.08505	−	1.12287i	0.247002	−	0.0899014i
$157$	−3.83971	−	1.39754i	−0.306442	−	0.111536i	0.184222	−	0.982885i	$-0.441023\pi$
$157$	−3.83971	−	1.39754i	−0.306442	−	0.111536i	−0.490664	+	0.871349i	$0.663246\pi$
$158$	−3.96546	−	3.32742i	−0.315475	−	0.264715i
$159$	−5.42168	+	9.39063i	−0.429967	+	0.744725i
$160$		0			0
$161$	2.07609	−	11.7741i	0.163619	−	0.927928i
$162$	0.557188	−	3.15997i	0.0437768	−	0.248270i
$163$	−2.41120	−	4.17632i	−0.188860	−	0.327115i	0.756011	−	0.654559i	$-0.227146\pi$
$163$	−2.41120	−	4.17632i	−0.188860	−	0.327115i	−0.944870	+	0.327445i	$0.893813\pi$
$164$	−3.04987	+	5.28252i	−0.238154	+	0.412496i
$165$		0			0
$166$	−8.20662	−	2.98696i	−0.636957	−	0.231833i
$167$	4.84712	−	1.76421i	0.375082	−	0.136519i	−0.147599	−	0.989047i	$-0.547154\pi$
$167$	4.84712	−	1.76421i	0.375082	−	0.136519i	0.522680	+	0.852529i	$0.324932\pi$
$168$	2.67779	−	2.24693i	0.206596	−	0.173355i
$169$	0.425793	+	2.41479i	0.0327533	+	0.185753i
$170$		0			0
$171$	8.49391	−	5.34591i	0.649546	−	0.408812i
$172$	−12.6100			−0.961507
$173$	−1.45277	−	8.23908i	−0.110452	−	0.626406i	−0.988902	−	0.148571i	$-0.952533\pi$
$173$	−1.45277	−	8.23908i	−0.110452	−	0.626406i	0.878450	−	0.477835i	$-0.158578\pi$
$174$	4.97132	−	4.17143i	0.376875	−	0.316236i
$175$		0			0
$176$	−5.06309	−	1.84282i	−0.381645	−	0.138907i
$177$	−5.03987	−	4.22896i	−0.378820	−	0.317868i
$178$	1.65122	−	2.86000i	0.123764	−	0.214366i
$179$	2.56041	+	4.43476i	0.191374	+	0.331469i	0.945706	−	0.325024i	$-0.105372\pi$
$179$	2.56041	+	4.43476i	0.191374	+	0.331469i	−0.754332	+	0.656493i	$0.772039\pi$
$180$		0			0
$181$	−0.326411	+	1.85117i	−0.0242620	+	0.137596i	−0.994533	−	0.104426i	$-0.966700\pi$
$181$	−0.326411	+	1.85117i	−0.0242620	+	0.137596i	0.970271	+	0.242022i	$0.0778107\pi$
$182$	8.22624	+	14.2483i	0.609769	+	1.05615i
$183$	−4.57805	+	7.92942i	−0.338419	+	0.586159i
$184$	2.18822	+	1.83614i	0.161318	+	0.135362i
$185$		0			0
$186$	−4.50003	+	1.63788i	−0.329958	+	0.120095i
$187$	−8.83614	+	7.41440i	−0.646162	+	0.542195i
$188$	−0.760675	−	4.31400i	−0.0554779	−	0.314631i
$189$	−18.5353			−1.34825
$190$		0			0
$191$	16.2208			1.17370			0.586849	−	0.809696i	$-0.300368\pi$
$191$	16.2208			1.17370			0.586849	+	0.809696i	$0.300368\pi$
$192$	0.145029	+	0.822499i	0.0104666	+	0.0593588i
$193$	−4.09336	+	3.43474i	−0.294647	+	0.247238i	−0.778112	−	0.628126i	$-0.783822\pi$
$193$	−4.09336	+	3.43474i	−0.294647	+	0.247238i	0.483465	+	0.875364i	$0.339378\pi$
$194$	0.812737	−	0.295812i	0.0583511	−	0.0212381i
$195$		0			0
$196$	8.05701	+	6.76064i	0.575501	+	0.482903i
$197$	−6.98903	+	12.1054i	−0.497948	+	0.862471i	−0.999997	−	0.00236780i	$-0.999246\pi$
$197$	−6.98903	+	12.1054i	−0.497948	+	0.862471i	0.502049	+	0.864839i	$0.332580\pi$
$198$	6.20287	+	10.7437i	0.440819	+	0.763520i
$199$	−1.93501	+	10.9740i	−0.137169	+	0.777923i	0.836156	+	0.548492i	$0.184798\pi$
$199$	−1.93501	+	10.9740i	−0.137169	+	0.777923i	−0.973325	+	0.229432i	$0.926313\pi$
$200$		0			0
$201$	4.37973	+	7.58592i	0.308922	+	0.535069i
$202$	−1.97649	+	3.42339i	−0.139066	+	0.240869i
$203$	24.9130	+	20.9045i	1.74855	+	1.46721i
$204$	1.68015	+	0.611525i	0.117634	+	0.0428153i
$205$		0			0
$206$	6.48650	−	5.44282i	0.451936	−	0.379219i
$207$	−1.14209	−	6.47711i	−0.0793807	−	0.450190i
$208$	−3.93091			−0.272559
$209$	−7.18517	+	22.3598i	−0.497008	+	1.54666i
$210$		0			0
$211$	−2.88244	−	16.3471i	−0.198435	−	1.12538i	−0.907441	−	0.420179i	$-0.861967\pi$
$211$	−2.88244	−	16.3471i	−0.198435	−	1.12538i	0.709006	−	0.705202i	$-0.249144\pi$
$212$	9.94567	−	8.34541i	0.683071	−	0.573165i
$213$	−10.5798	+	3.85074i	−0.724917	+	0.263848i
$214$	−2.67259	−	0.972743i	−0.182694	−	0.0664954i
$215$		0			0
$216$	2.21428	−	3.83524i	0.150662	−	0.260955i
$217$	−11.9992	−	20.7833i	−0.814561	−	1.41086i
$218$	−2.08571	+	11.8286i	−0.141262	+	0.801135i
$219$	−0.488475	+	2.77028i	−0.0330081	+	0.187198i
$220$		0			0
$221$	−4.20767	+	7.28789i	−0.283038	+	0.490237i
$222$	−1.18210	−	0.991896i	−0.0793370	−	0.0665717i
$223$	−18.2133	−	6.62909i	−1.21965	−	0.443917i	−0.349610	−	0.936895i	$-0.613686\pi$
$223$	−18.2133	−	6.62909i	−1.21965	−	0.443917i	−0.870041	+	0.492979i	$0.835908\pi$
$224$	−3.93300	+	1.43150i	−0.262785	+	0.0956458i
$225$		0			0
$226$	0.886993	+	5.03039i	0.0590019	+	0.334616i
$227$	2.70146			0.179302			0.0896512	−	0.995973i	$-0.471425\pi$
$227$	2.70146			0.179302			0.0896512	+	0.995973i	$0.471425\pi$
$228$	3.55847	−	0.768430i	0.235666	−	0.0508905i
$229$	1.21719			0.0804343			0.0402172	−	0.999191i	$-0.487195\pi$
$229$	1.21719			0.0804343			0.0402172	+	0.999191i	$0.487195\pi$
$230$		0			0
$231$	14.4280	−	12.1065i	0.949294	−	0.796552i
$232$	−7.30163	+	2.65757i	−0.479375	+	0.174478i
$233$	7.59685	+	2.76503i	0.497686	+	0.181143i	0.578653	−	0.815574i	$-0.303579\pi$
$233$	7.59685	+	2.76503i	0.497686	+	0.181143i	−0.0809667	+	0.996717i	$0.525801\pi$
$234$	6.93329	+	5.81772i	0.453243	+	0.380316i
$235$		0			0
$236$	3.93869	+	6.82201i	0.256387	+	0.444075i
$237$	−0.750747	+	4.25770i	−0.0487663	+	0.276567i
$238$	−1.55592	+	8.82405i	−0.100855	+	0.571979i
$239$	3.20276	+	5.54735i	0.207170	+	0.358828i	0.950822	−	0.309738i	$-0.100241\pi$
$239$	3.20276	+	5.54735i	0.207170	+	0.358828i	−0.743652	+	0.668567i	$0.766908\pi$
$240$		0			0
$241$	−19.8037	−	16.6173i	−1.27567	−	1.07041i	−0.993826	−	0.110954i	$-0.964609\pi$
$241$	−19.8037	−	16.6173i	−1.27567	−	1.07041i	−0.281845	−	0.959460i	$-0.590946\pi$
$242$	−16.9435	−	6.16693i	−1.08917	−	0.396425i
$243$	−15.0027	+	5.46053i	−0.962423	+	0.350293i
$244$	8.39809	−	7.04683i	0.537633	−	0.451127i
$245$		0			0
$246$	5.09442			0.324808
$247$	0.653433	+	17.1220i	0.0415769	+	1.08944i
$248$	5.73383			0.364099
$249$	1.26658	+	7.18313i	0.0802662	+	0.455212i
$250$		0			0
$251$	17.7178	−	6.44874i	1.11834	−	0.407041i	0.284291	−	0.958738i	$-0.408242\pi$
$251$	17.7178	−	6.44874i	1.11834	−	0.407041i	0.834044	+	0.551697i	$0.186020\pi$
$252$	9.05559	+	3.29596i	0.570448	+	0.207626i
$253$	11.7902	+	9.89316i	0.741244	+	0.621978i
$254$	5.50886	−	9.54162i	0.345657	−	0.598695i
$255$		0			0
$256$	0.173648	−	0.984808i	0.0108530	−	0.0615505i
$257$	2.66512	−	15.1146i	0.166246	−	0.942825i	−0.781525	−	0.623874i	$-0.785558\pi$
$257$	2.66512	−	15.1146i	0.166246	−	0.942825i	0.947771	−	0.318952i	$-0.103331\pi$
$258$	5.26588	+	9.12077i	0.327839	+	0.567834i
$259$	3.86654	−	6.69705i	0.240255	−	0.416134i
$260$		0			0
$261$	16.8117	+	6.11896i	1.04062	+	0.378754i
$262$	−19.7411	+	7.18517i	−1.21961	+	0.443901i
$263$	7.12267	−	5.97663i	0.439202	−	0.368535i	−0.396208	−	0.918161i	$-0.629674\pi$
$263$	7.12267	−	5.97663i	0.439202	−	0.368535i	0.835411	+	0.549626i	$0.185230\pi$
$264$	0.781420	+	4.43165i	0.0480931	+	0.272749i
$265$		0			0
$266$	6.88899	+	16.8931i	0.422391	+	1.03578i
$267$	−2.75816			−0.168797
$268$	−1.82123	−	10.3287i	−0.111249	−	0.630925i
$269$	7.43644	−	6.23991i	0.453408	−	0.380454i	−0.387291	−	0.921958i	$-0.626589\pi$
$269$	7.43644	−	6.23991i	0.453408	−	0.380454i	0.840699	+	0.541503i	$0.182145\pi$
$270$		0			0
$271$	−14.7919	−	5.38380i	−0.898541	−	0.327042i	−0.148873	−	0.988856i	$-0.547565\pi$
$271$	−14.7919	−	5.38380i	−0.898541	−	0.327042i	−0.749668	+	0.661814i	$0.769787\pi$
$272$	−1.63996	−	1.37609i	−0.0994370	−	0.0834375i
$273$	6.87045	−	11.9000i	0.415819	−	0.720219i
$274$	1.91027	+	3.30868i	0.115403	+	0.199885i
$275$		0			0
$276$	0.414278	−	2.34949i	0.0249366	−	0.141422i
$277$	−14.7692	−	25.5809i	−0.887392	−	1.53701i	−0.842947	−	0.537997i	$-0.819181\pi$
$277$	−14.7692	−	25.5809i	−0.887392	−	1.53701i	−0.0444457	−	0.999012i	$-0.514152\pi$
$278$	−7.27668	+	12.6036i	−0.436426	+	0.755912i
$279$	−10.1133	−	8.48604i	−0.605465	−	0.508046i
$280$		0			0
$281$	2.00483	−	0.729699i	0.119598	−	0.0435302i	−0.281528	−	0.959553i	$-0.590841\pi$
$281$	2.00483	−	0.729699i	0.119598	−	0.0435302i	0.401126	+	0.916023i	$0.368619\pi$
$282$	−2.80264	+	2.35169i	−0.166895	+	0.140041i
$283$	−3.32317	−	18.8466i	−0.197542	−	1.12032i	−0.908752	−	0.417336i	$-0.862964\pi$
$283$	−3.32317	−	18.8466i	−0.197542	−	1.12032i	0.711210	−	0.702979i	$-0.248147\pi$
$284$	13.4806			0.799925
$285$		0			0
$286$	−21.1799			−1.25239
$287$	4.43322	+	25.1420i	0.261685	+	1.48409i
$288$	−1.76379	+	1.47999i	−0.103932	+	0.0872095i
$289$	11.6681	−	4.24684i	0.686359	−	0.249814i
$290$		0			0
$291$	−0.553353	−	0.464318i	−0.0324381	−	0.0272188i
$292$	1.68406	−	2.91688i	0.0985523	−	0.170698i
$293$	9.35413	+	16.2018i	0.546474	+	0.946521i	0.998513	+	0.0545223i	$0.0173636\pi$
$293$	9.35413	+	16.2018i	0.546474	+	0.946521i	−0.452039	+	0.891998i	$0.649303\pi$
$294$	1.52537	−	8.65079i	0.0889612	−	0.504524i
$295$		0			0
$296$	0.923814	+	1.60009i	0.0536956	+	0.0930035i
$297$	11.9306	−	20.6644i	0.692283	−	1.19907i
$298$	9.12001	+	7.65259i	0.528308	+	0.443303i
$299$	10.5515	+	3.84045i	0.610212	+	0.222099i
$300$		0			0
$301$	−40.4305	+	33.9252i	−2.33038	+	1.95542i
$302$	−0.905252	−	5.13394i	−0.0520914	−	0.295425i
$303$	3.30149			0.189666
$304$	−4.31842	−	0.592660i	−0.247678	−	0.0339914i
$305$		0			0
$306$	0.855935	+	4.85425i	0.0489306	+	0.277499i
$307$	−11.7379	+	9.84929i	−0.669919	+	0.562129i	−0.913041	−	0.407867i	$-0.866273\pi$
$307$	−11.7379	+	9.84929i	−0.669919	+	0.562129i	0.243123	+	0.969996i	$0.421828\pi$
$308$	−21.1911	+	7.71294i	−1.20748	+	0.439486i
$309$	−6.64548	−	2.41876i	−0.378048	−	0.137598i
$310$		0			0
$311$	−9.59523	+	16.6194i	−0.544095	+	0.942401i	0.454568	+	0.890712i	$0.349794\pi$
$311$	−9.59523	+	16.6194i	−0.544095	+	0.942401i	−0.998663	+	0.0516889i	$0.983540\pi$
$312$	1.64152	+	2.84320i	0.0929329	+	0.160965i
$313$	4.60930	−	26.1407i	0.260533	−	1.47756i	−0.520926	−	0.853602i	$-0.674413\pi$
$313$	4.60930	−	26.1407i	0.260533	−	1.47756i	0.781460	−	0.623956i	$-0.214476\pi$
$314$	0.709549	−	4.02405i	0.0400422	−	0.227090i
$315$		0			0
$316$	2.58827	−	4.48301i	0.145602	−	0.252189i
$317$	−6.88064	−	5.77354i	−0.386455	−	0.324274i	0.428775	−	0.903411i	$-0.358945\pi$
$317$	−6.88064	−	5.77354i	−0.386455	−	0.324274i	−0.815230	+	0.579137i	$0.803390\pi$
$318$	−10.1894	−	3.70865i	−0.571395	−	0.207971i
$319$	−39.3414	+	14.3191i	−2.20269	+	0.801715i
$320$		0			0
$321$	0.412478	+	2.33928i	0.0230223	+	0.130566i
$322$	11.9557			0.666266
$323$	−5.72125	+	7.37195i	−0.318339	+	0.410186i
$324$	3.20871			0.178262
$325$		0			0
$326$	3.69418	−	3.09978i	0.204601	−	0.171681i
$327$	9.42655	−	3.43098i	0.521289	−	0.189734i
$328$	−5.73187	−	2.08623i	−0.316490	−	0.115193i
$329$	−14.0450	−	11.7851i	−0.774325	−	0.649736i
$330$		0			0
$331$	12.3448	+	21.3818i	0.678532	+	1.17525i	0.975423	+	0.220341i	$0.0707170\pi$
$331$	12.3448	+	21.3818i	0.678532	+	1.17525i	−0.296891	+	0.954911i	$0.595950\pi$
$332$	1.51652	−	8.60062i	0.0832299	−	0.472020i
$333$	0.738715	−	4.18946i	0.0404814	−	0.229581i
$334$	2.57910	+	4.46713i	0.141122	+	0.244431i
$335$		0			0
$336$	2.67779	+	2.24693i	0.146085	+	0.122580i
$337$	26.8096	+	9.75791i	1.46041	+	0.531547i	0.945479	−	0.325682i	$-0.105594\pi$
$337$	26.8096	+	9.75791i	1.46041	+	0.531547i	0.514935	+	0.857229i	$0.327816\pi$
$338$	−2.30417	+	0.838648i	−0.125330	+	0.0456164i
$339$	3.26805	−	2.74222i	0.177496	−	0.148937i
$340$		0			0
$341$	30.8941			1.67301
$342$	6.73964	+	7.43656i	0.364438	+	0.402123i
$343$	14.7230			0.794966
$344$	−2.18971	−	12.4185i	−0.118061	−	0.669559i
$345$		0			0
$346$	7.86164	−	2.86140i	0.422644	−	0.153830i
$347$	4.00560	+	1.45792i	0.215032	+	0.0782653i	0.447290	−	0.894389i	$-0.352389\pi$
$347$	4.00560	+	1.45792i	0.215032	+	0.0782653i	−0.232258	+	0.972654i	$0.574611\pi$
$348$	4.97132	+	4.17143i	0.266491	+	0.223612i
$349$	−5.74459	+	9.94993i	−0.307501	+	0.532608i	−0.977815	−	0.209470i	$-0.932826\pi$
$349$	−5.74459	+	9.94993i	−0.307501	+	0.532608i	0.670314	+	0.742078i	$0.266159\pi$
$350$		0			0
$351$	3.02291	−	17.1438i	0.161351	−	0.915066i
$352$	0.935622	−	5.30618i	0.0498688	−	0.282820i
$353$	−12.8991	−	22.3419i	−0.686549	−	1.18914i	−0.972947	−	0.231027i	$-0.925792\pi$
$353$	−12.8991	−	22.3419i	−0.686549	−	1.18914i	0.286399	−	0.958111i	$-0.407542\pi$
$354$	3.28954	−	5.69766i	0.174837	−	0.302827i
$355$		0			0
$356$	3.10328	+	1.12950i	0.164474	+	0.0598635i
$357$	7.03213	−	2.55948i	0.372180	−	0.135462i
$358$	−3.92277	+	3.29160i	−0.207325	+	0.173966i
$359$	4.09930	+	23.2483i	0.216353	+	1.22700i	0.878544	+	0.477662i	$0.158515\pi$
$359$	4.09930	+	23.2483i	0.216353	+	1.22700i	−0.662191	+	0.749335i	$0.730373\pi$
$360$		0			0
$361$	−1.86362	+	18.9084i	−0.0980852	+	0.995178i
$362$	−1.87973			−0.0987963
$363$	2.61500	+	14.8304i	0.137252	+	0.778394i
$364$	−12.6033	+	10.5754i	−0.660594	+	0.554304i
$365$		0			0
$366$	−8.60392	−	3.13157i	−0.449734	−	0.163690i
$367$	15.6569	+	13.1377i	0.817284	+	0.685782i	0.952334	−	0.305056i	$-0.0986753\pi$
$367$	15.6569	+	13.1377i	0.817284	+	0.685782i	−0.135051	+	0.990839i	$0.543120\pi$
$368$	−1.42826	+	2.47382i	−0.0744532	+	0.128957i
$369$	7.02220	+	12.1628i	0.365561	+	0.633170i
$370$		0			0
$371$	9.43602	−	53.5143i	0.489894	−	2.77832i
$372$	−2.39441	−	4.14725i	−0.124145	−	0.215025i
$373$	2.54628	−	4.41029i	0.131841	−	0.228356i	−0.792545	−	0.609813i	$-0.791244\pi$
$373$	2.54628	−	4.41029i	0.131841	−	0.228356i	0.924386	+	0.381457i	$0.124578\pi$
$374$	−8.83614	−	7.41440i	−0.456906	−	0.383389i
$375$		0			0
$376$	4.11637	−	1.49824i	0.212286	−	0.0772657i
$377$	−23.3981	+	19.6333i	−1.20506	+	1.01117i
$378$	−3.21862	−	18.2537i	−0.165548	−	0.938870i
$379$	8.24487			0.423511			0.211755	−	0.977323i	$-0.432082\pi$
$379$	8.24487			0.423511			0.211755	+	0.977323i	$0.432082\pi$
$380$		0			0
$381$	−9.20186			−0.471426
$382$	2.81672	+	15.9744i	0.144116	+	0.817322i
$383$	1.07800	−	0.904546i	0.0550830	−	0.0462201i	−0.614831	−	0.788659i	$-0.710776\pi$
$383$	1.07800	−	0.904546i	0.0550830	−	0.0462201i	0.669914	+	0.742439i	$0.266331\pi$
$384$	−0.784820	+	0.285651i	−0.0400502	+	0.0145771i
$385$		0			0
$386$	−4.09336	−	3.43474i	−0.208347	−	0.174824i
$387$	−14.5171	+	25.1443i	−0.737944	+	1.27816i
$388$	0.432448	+	0.749022i	0.0219542	+	0.0380258i
$389$	6.81569	−	38.6537i	0.345569	−	1.95982i	0.0746916	−	0.997207i	$-0.476203\pi$
$389$	6.81569	−	38.6537i	0.345569	−	1.95982i	0.270878	−	0.962614i	$-0.412686\pi$
$390$		0			0
$391$	3.05764	+	5.29598i	0.154631	+	0.267829i
$392$	−5.25884	+	9.10858i	−0.265612	+	0.460053i
$393$	13.4407	+	11.2781i	0.677996	+	0.568906i
$394$	−13.1351	−	4.78078i	−0.661736	−	0.240852i
$395$		0			0
$396$	−9.50335	+	7.97425i	−0.477561	+	0.400721i
$397$	−1.01418	−	5.75169i	−0.0509001	−	0.288669i	0.948723	−	0.316107i	$-0.102376\pi$
$397$	−1.01418	−	5.75169i	−0.0509001	−	0.288669i	−0.999623	+	0.0274386i	$0.991265\pi$
$398$	−11.1433			−0.558561
$399$	9.34190	−	12.0372i	0.467680	−	0.602615i
$400$		0			0
$401$	−3.15559	−	17.8963i	−0.157583	−	0.893697i	−0.956386	−	0.292105i	$-0.905644\pi$
$401$	−3.15559	−	17.8963i	−0.157583	−	0.893697i	0.798803	−	0.601592i	$-0.205467\pi$
$402$	−6.71014	+	5.63047i	−0.334671	+	0.280822i
$403$	21.1799	−	7.70885i	1.05505	−	0.384005i
$404$	−3.71460	−	1.35200i	−0.184808	−	0.0672646i
$405$		0			0
$406$	−16.2608	+	28.1645i	−0.807010	+	1.39778i
$407$	4.97754	+	8.62135i	0.246727	+	0.427344i
$408$	−0.310479	+	1.76082i	−0.0153710	+	0.0871734i
$409$	2.08439	−	11.8212i	0.103066	−	0.584518i	−0.888909	−	0.458085i	$-0.848536\pi$
$409$	2.08439	−	11.8212i	0.103066	−	0.584518i	0.991975	−	0.126434i	$-0.0403532\pi$
$410$		0			0
$411$	1.59543	−	2.76337i	0.0786968	−	0.136307i
$412$	6.48650	+	5.44282i	0.319567	+	0.268148i
$413$	30.9817	+	11.2764i	1.52451	+	0.554877i
$414$	6.18039	−	2.24948i	0.303749	−	0.110556i
$415$		0			0
$416$	−0.682595	−	3.87119i	−0.0334670	−	0.189801i
$417$	12.1548			0.595222
$418$	−23.2678	−	3.19327i	−1.13806	−	0.156188i
$419$	−22.3338			−1.09108			−0.545539	−	0.838086i	$-0.683675\pi$
$419$	−22.3338			−1.09108			−0.545539	+	0.838086i	$0.683675\pi$
$420$		0			0
$421$	10.0243	−	8.41142i	0.488556	−	0.409947i	−0.364952	−	0.931026i	$-0.618915\pi$
$421$	10.0243	−	8.41142i	0.488556	−	0.409947i	0.853509	+	0.521079i	$0.174470\pi$
$422$	15.5982	−	5.67729i	0.759310	−	0.276366i
$423$	−9.47779	−	3.44963i	−0.460826	−	0.167727i
$424$	9.94567	+	8.34541i	0.483004	+	0.405289i
$425$		0			0
$426$	−5.62941	−	9.75042i	−0.272746	−	0.472409i
$427$	7.96774	−	45.1873i	0.385586	−	2.18677i
$428$	0.493875	−	2.80090i	0.0238723	−	0.135387i
$429$	8.84458	+	15.3193i	0.427020	+	0.739621i
$430$		0			0
$431$	−6.52872	−	5.47824i	−0.314477	−	0.263878i	0.471862	−	0.881672i	$-0.343582\pi$
$431$	−6.52872	−	5.47824i	−0.314477	−	0.263878i	−0.786340	+	0.617794i	$0.788026\pi$
$432$	4.16148	+	1.51465i	0.200219	+	0.0728738i
$433$	−15.8778	+	5.77906i	−0.763040	+	0.277724i	−0.694082	−	0.719896i	$-0.744190\pi$
$433$	−15.8778	+	5.77906i	−0.763040	+	0.277724i	−0.0689576	+	0.997620i	$0.521967\pi$
$434$	18.3839	−	15.4259i	0.882455	−	0.740468i
$435$		0			0
$436$	−12.0111			−0.575227
$437$	11.0127	+	5.80989i	0.526809	+	0.277925i
$438$	−2.81301			−0.134411
$439$	3.47186	+	19.6899i	0.165703	+	0.939749i	0.948337	+	0.317266i	$0.102765\pi$
$439$	3.47186	+	19.6899i	0.165703	+	0.939749i	−0.782634	+	0.622483i	$0.786124\pi$
$440$		0			0
$441$	22.7561	−	8.28255i	1.08363	−	0.394407i
$442$	−7.90783	−	2.87821i	−0.376137	−	0.136903i
$443$	−15.4915	−	12.9989i	−0.736024	−	0.617598i	0.195742	−	0.980655i	$-0.437288\pi$
$443$	−15.4915	−	12.9989i	−0.736024	−	0.617598i	−0.931767	+	0.363058i	$0.881733\pi$
$444$	0.771558	−	1.33638i	0.0366165	−	0.0634217i
$445$		0			0
$446$	3.36568	−	19.0877i	0.159369	−	0.903829i
$447$	1.72661	−	9.79212i	0.0816661	−	0.463151i
$448$	−2.09271	−	3.62467i	−0.0988711	−	0.171250i
$449$	9.05817	−	15.6892i	0.427481	−	0.740420i	−0.569167	−	0.822222i	$-0.692734\pi$
$449$	9.05817	−	15.6892i	0.427481	−	0.740420i	0.996649	+	0.0818023i	$0.0260676\pi$
$450$		0			0
$451$	−30.8835	−	11.2407i	−1.45425	−	0.529303i
$452$	−4.79994	+	1.74704i	−0.225770	+	0.0821736i
$453$	−3.33532	+	2.79866i	−0.156707	+	0.131493i
$454$	0.469104	+	2.66042i	0.0220161	+	0.124860i
$455$		0			0
$456$	1.37468	+	3.37098i	0.0643752	+	0.157860i
$457$	−14.5742			−0.681750			−0.340875	−	0.940109i	$-0.610723\pi$
$457$	−14.5742			−0.681750			−0.340875	+	0.940109i	$0.610723\pi$
$458$	0.211363	+	1.19870i	0.00987635	+	0.0560116i
$459$	7.26263	−	6.09407i	0.338991	−	0.284447i
$460$		0			0
$461$	−15.4115	−	5.60932i	−0.717784	−	0.261252i	−0.0427992	−	0.999084i	$-0.513628\pi$
$461$	−15.4115	−	5.60932i	−0.717784	−	0.261252i	−0.674985	+	0.737832i	$0.735850\pi$
$462$	14.4280	+	12.1065i	0.671252	+	0.563247i
$463$	16.3647	−	28.3445i	0.760533	−	1.31728i	−0.182043	−	0.983291i	$-0.558271\pi$
$463$	16.3647	−	28.3445i	0.760533	−	1.31728i	0.942576	−	0.333991i	$-0.108396\pi$
$464$	−3.88511	−	6.72921i	−0.180362	−	0.312396i
$465$		0			0
$466$	−1.40384	+	7.96158i	−0.0650317	+	0.368813i
$467$	6.93817	+	12.0173i	0.321060	+	0.556093i	0.980707	−	0.195483i	$-0.0626274\pi$
$467$	6.93817	+	12.0173i	0.321060	+	0.556093i	−0.659647	+	0.751576i	$0.729294\pi$
$468$	−4.52538	+	7.83819i	−0.209186	+	0.362321i
$469$	−33.6268	−	28.2162i	−1.55274	−	1.30291i
$470$		0			0
$471$	−3.20688	+	1.16721i	−0.147765	+	0.0537821i
$472$	−6.03442	+	5.06348i	−0.277757	+	0.233066i
$473$	−11.7982	−	66.9111i	−0.542484	−	3.07658i
$474$	−4.32338			−0.198579
$475$		0			0
$476$	−8.96018			−0.410689
$477$	−5.19090	−	29.4391i	−0.237675	−	1.34792i
$478$	−4.90692	+	4.11739i	−0.224437	+	0.188325i
$479$	−8.93600	+	3.25244i	−0.408296	+	0.148608i	−0.538000	−	0.842945i	$-0.680820\pi$
$479$	−8.93600	+	3.25244i	−0.408296	+	0.148608i	0.129703	+	0.991553i	$0.458598\pi$
$480$		0			0
$481$	5.56367	+	4.66847i	0.253682	+	0.212864i
$482$	12.9260	−	22.3884i	0.588762	−	1.01976i
$483$	−4.99264	−	8.64750i	−0.227173	−	0.393475i
$484$	3.13103	−	17.7570i	0.142320	−	0.807134i
$485$		0			0
$486$	−7.98276	−	13.8266i	−0.362106	−	0.627185i
$487$	−18.8925	+	32.7228i	−0.856102	+	1.48281i	0.0195172	+	0.999810i	$0.493787\pi$
$487$	−18.8925	+	32.7228i	−0.856102	+	1.48281i	−0.875619	+	0.483002i	$0.839546\pi$
$488$	8.39809	+	7.04683i	0.380164	+	0.318995i
$489$	−3.78472	−	1.37752i	−0.171151	−	0.0622938i
$490$		0			0
$491$	−12.1540	+	10.1984i	−0.548504	+	0.460249i	−0.874434	−	0.485145i	$-0.838767\pi$
$491$	−12.1540	+	10.1984i	−0.548504	+	0.460249i	0.325930	+	0.945394i	$0.394323\pi$
$492$	0.884637	+	5.01702i	0.0398825	+	0.226185i
$493$	−16.6346			−0.749184
$494$	−16.7484	+	3.61670i	−0.753545	+	0.162723i
$495$		0			0
$496$	0.995670	+	5.64672i	0.0447069	+	0.253545i
$497$	43.2216	−	36.2672i	1.93875	−	1.62681i
$498$	−6.85406	+	2.49468i	−0.307138	+	0.111789i
$499$	−33.2604	−	12.1058i	−1.48894	−	0.541930i	−0.535769	−	0.844364i	$-0.679978\pi$
$499$	−33.2604	−	12.1058i	−1.48894	−	0.541930i	−0.953170	+	0.302435i	$0.902201\pi$
$500$		0			0
$501$	2.15403	−	3.73089i	0.0962351	−	0.166684i
$502$	9.42743	+	16.3288i	0.420767	+	0.728789i
$503$	−5.79148	+	32.8451i	−0.258229	+	1.46449i	0.529416	+	0.848363i	$0.322411\pi$
$503$	−5.79148	+	32.8451i	−0.258229	+	1.46449i	−0.787645	+	0.616129i	$0.788700\pi$
$504$	−1.67340	+	9.49035i	−0.0745394	+	0.422734i
$505$		0			0
$506$	−7.69551	+	13.3290i	−0.342107	+	0.592547i
$507$	1.56879	+	1.31637i	0.0696726	+	0.0584623i
$508$	10.3533	+	3.76828i	0.459352	+	0.167190i
$509$	40.4293	−	14.7151i	1.79200	−	0.652234i	0.792918	−	0.609328i	$-0.208561\pi$
$509$	40.4293	−	14.7151i	1.79200	−	0.652234i	0.999079	−	0.0429055i	$-0.0136615\pi$
$510$		0			0
$511$	−2.44792	−	13.8828i	−0.108289	−	0.614140i
$512$	1.00000			0.0441942
$513$	5.90566	−	18.3780i	0.260741	−	0.811410i
$514$	15.3478			0.676963
$515$		0			0
$516$	−8.06779	+	6.76968i	−0.355165	+	0.298019i
$517$	22.1791	−	8.07255i	0.975437	−	0.355030i
$518$	7.26672	+	2.64487i	0.319282	+	0.116209i
$519$	−5.35261	−	4.49137i	−0.234953	−	0.197149i
$520$		0			0
$521$	6.76680	+	11.7204i	0.296459	+	0.513482i	0.975323	−	0.220782i	$-0.0708609\pi$
$521$	6.76680	+	11.7204i	0.296459	+	0.513482i	−0.678864	+	0.734264i	$0.737528\pi$
$522$	−3.10668	+	17.6189i	−0.135976	+	0.771156i
$523$	6.10706	−	34.6349i	0.267043	−	1.51448i	−0.496110	−	0.868260i	$-0.665239\pi$
$523$	6.10706	−	34.6349i	0.267043	−	1.51448i	0.763153	−	0.646218i	$-0.223650\pi$
$524$	−10.5040	−	18.1935i	−0.458870	−	0.794786i
$525$		0			0
$526$	7.12267	+	5.97663i	0.310563	+	0.260593i
$527$	11.5348	+	4.19832i	0.502463	+	0.182882i
$528$	−4.22863	+	1.53910i	−0.184028	+	0.0669806i
$529$	−11.3683	+	9.53915i	−0.494275	+	0.414746i
$530$		0			0
$531$	18.1374			0.787095
$532$	−15.4402	+	9.71779i	−0.669419	+	0.421320i
$533$	−23.9775			−1.03858
$534$	−0.478949	−	2.71626i	−0.0207262	−	0.117544i
$535$		0			0
$536$	9.85551	−	3.58711i	0.425693	−	0.154940i
$537$	4.01892	+	1.46277i	0.173429	+	0.0631230i
$538$	7.43644	+	6.23991i	0.320608	+	0.269022i
$539$	−28.3348	+	49.0773i	−1.22047	+	2.11391i
$540$		0			0
$541$	1.47256	−	8.35128i	0.0633101	−	0.359050i	−0.936651	−	0.350263i	$-0.886092\pi$
$541$	1.47256	−	8.35128i	0.0633101	−	0.359050i	0.999961	−	0.00878628i	$-0.00279680\pi$
$542$	2.73342	−	15.5020i	0.117411	−	0.665869i
$543$	0.784963	+	1.35960i	0.0336860	+	0.0583458i
$544$	1.07041	−	1.85400i	0.0458933	−	0.0794895i
$545$		0			0
$546$	12.9122	+	4.69967i	0.552592	+	0.201127i
$547$	23.0411	−	8.38627i	0.985166	−	0.358571i	0.201320	−	0.979526i	$-0.435477\pi$
$547$	23.0411	−	8.38627i	0.985166	−	0.358571i	0.783847	+	0.620954i	$0.213255\pi$
$548$	−2.92670	+	2.45579i	−0.125022	+	0.104906i
$549$	−4.38318	−	24.8582i	−0.187070	−	1.06092i
$550$		0			0
$551$	−28.6648	+	18.0411i	−1.22116	+	0.768576i
$552$	2.38573			0.101543
$553$	−3.76225	−	21.3368i	−0.159987	−	0.907333i
$554$	22.6277	−	18.9869i	0.961357	−	0.806674i
$555$		0			0
$556$	−13.6757	−	4.97754i	−0.579978	−	0.211095i
$557$	12.9962	+	10.9051i	0.550666	+	0.462063i	0.875166	−	0.483822i	$-0.160752\pi$
$557$	12.9962	+	10.9051i	0.550666	+	0.462063i	−0.324501	+	0.945885i	$0.605196\pi$
$558$	6.60097	−	11.4332i	0.279441	−	0.484006i
$559$	−24.7845	−	42.9280i	−1.04827	−	1.81566i
$560$		0			0
$561$	−1.67287	+	9.48733i	−0.0706287	+	0.400555i
$562$	1.06675	+	1.84766i	0.0449981	+	0.0779390i
$563$	−1.37047	+	2.37372i	−0.0577582	+	0.100040i	−0.893459	−	0.449145i	$-0.851729\pi$
$563$	−1.37047	+	2.37372i	−0.0577582	+	0.100040i	0.835701	+	0.549185i	$0.185062\pi$
$564$	−2.80264	−	2.35169i	−0.118012	−	0.0990241i
$565$		0			0
$566$	17.9832	−	6.54537i	0.755892	−	0.275122i
$567$	10.2878	−	8.63251i	0.432048	−	0.362531i
$568$	2.34088	+	13.2758i	0.0982210	+	0.557039i
$569$	−19.0648			−0.799238			−0.399619	−	0.916681i	$-0.630857\pi$
$569$	−19.0648			−0.799238			−0.399619	+	0.916681i	$0.630857\pi$
$570$		0			0
$571$	−8.52486			−0.356754			−0.178377	−	0.983962i	$-0.557085\pi$
$571$	−8.52486			−0.356754			−0.178377	+	0.983962i	$0.557085\pi$
$572$	−3.67784	−	20.8581i	−0.153778	−	0.872121i
$573$	10.3779	−	8.70813i	0.433545	−	0.363787i
$574$	−23.9903	+	8.73174i	−1.00133	+	0.364456i
$575$		0			0
$576$	−1.76379	−	1.47999i	−0.0734912	−	0.0616664i
$577$	−12.9129	+	22.3658i	−0.537571	+	0.931099i	0.461464	+	0.887159i	$0.347324\pi$
$577$	−12.9129	+	22.3658i	−0.537571	+	0.931099i	−0.999034	+	0.0439404i	$0.986009\pi$
$578$	6.20846	+	10.7534i	0.258238	+	0.447281i
$579$	−0.774962	+	4.39503i	−0.0322063	+	0.182651i
$580$		0			0
$581$	−18.2762	−	31.6554i	−0.758226	−	1.31329i
$582$	0.361175	−	0.625574i	0.0149712	−	0.0259309i
$583$	53.5876	+	44.9653i	2.21937	+	1.86227i
$584$	3.16500	+	1.15197i	0.130969	+	0.0476687i
$585$		0			0
$586$	−14.3314	+	12.0254i	−0.592023	+	0.496766i
$587$	−3.34088	−	18.9471i	−0.137893	−	0.782030i	−0.972801	−	0.231641i	$-0.925591\pi$
$587$	−3.34088	−	18.9471i	−0.137893	−	0.782030i	0.834908	−	0.550389i	$-0.185521\pi$
$588$	8.78424			0.362256
$589$	24.4301	−	5.27552i	1.00662	−	0.217374i
$590$		0			0
$591$	2.02722	+	11.4969i	0.0833888	+	0.472921i
$592$	−1.41537	+	1.18763i	−0.0581711	+	0.0488114i
$593$	−13.0331	+	4.74367i	−0.535206	+	0.194799i	−0.595462	−	0.803384i	$-0.703031\pi$
$593$	−13.0331	+	4.74367i	−0.535206	+	0.194799i	0.0602552	+	0.998183i	$0.480809\pi$
$594$	22.4222	+	8.16100i	0.919993	+	0.334850i
$595$		0			0
$596$	−5.95266	+	10.3103i	−0.243831	+	0.422327i
$597$	4.65335	+	8.05984i	0.190449	+	0.329867i
$598$	−1.94985	+	11.0581i	−0.0797352	+	0.452201i
$599$	−2.41256	+	13.6823i	−0.0985745	+	0.559044i	0.895019	+	0.446029i	$0.147162\pi$
$599$	−2.41256	+	13.6823i	−0.0985745	+	0.559044i	−0.993593	+	0.113015i	$0.963949\pi$
$600$		0			0
$601$	9.29949	−	16.1072i	0.379334	−	0.657026i	−0.611631	−	0.791143i	$-0.709486\pi$
$601$	9.29949	−	16.1072i	0.379334	−	0.657026i	0.990966	+	0.134117i	$0.0428198\pi$
$602$	−40.4305	−	33.9252i	−1.64782	−	1.38269i
$603$	−22.6919	−	8.25919i	−0.924087	−	0.336340i
$604$	4.89875	−	1.78300i	0.199327	−	0.0725491i
$605$		0			0
$606$	0.573297	+	3.25133i	0.0232886	+	0.132076i
$607$	−19.4066			−0.787689			−0.393844	−	0.919177i	$-0.628855\pi$
$607$	−19.4066			−0.787689			−0.393844	+	0.919177i	$0.628855\pi$
$608$	−0.166229	−	4.35573i	−0.00674149	−	0.176648i
$609$	27.1616			1.10065
$610$		0			0
$611$	13.1909	−	11.0685i	0.533648	−	0.447784i
$612$	−4.63187	+	1.68586i	−0.187232	+	0.0681470i
$613$	−9.63208	−	3.50579i	−0.389036	−	0.141598i	0.140094	−	0.990138i	$-0.455259\pi$
$613$	−9.63208	−	3.50579i	−0.389036	−	0.141598i	−0.529130	+	0.848541i	$0.677482\pi$
$614$	−11.7379	−	9.84929i	−0.473704	−	0.397485i
$615$		0			0
$616$	−11.2756	−	19.5299i	−0.454306	−	0.786880i
$617$	−4.44187	+	25.1911i	−0.178823	+	1.01416i	0.754815	+	0.655937i	$0.227727\pi$
$617$	−4.44187	+	25.1911i	−0.178823	+	1.01416i	−0.933638	+	0.358218i	$0.883385\pi$
$618$	1.22803	−	6.96453i	0.0493988	−	0.280154i
$619$	−6.47023	−	11.2068i	−0.260061	−	0.450438i	0.706197	−	0.708015i	$-0.250409\pi$
$619$	−6.47023	−	11.2068i	−0.260061	−	0.450438i	−0.966258	+	0.257577i	$0.917076\pi$
$620$		0			0
$621$	−9.69065	−	8.13142i	−0.388872	−	0.326303i
$622$	−18.0331	−	6.56352i	−0.723063	−	0.263173i
$623$	12.9885	−	4.72743i	0.520374	−	0.189401i
$624$	−2.51496	+	2.11030i	−0.100679	+	0.0844797i
$625$		0			0
$626$	26.5439			1.06091
$627$	7.40681	+	18.1629i	0.295799	+	0.725358i
$628$	4.08613			0.163054
$629$	0.686852	+	3.89533i	0.0273866	+	0.155317i
$630$		0			0
$631$	29.5627	−	10.7599i	1.17687	−	0.428347i	0.321776	−	0.946816i	$-0.395720\pi$
$631$	29.5627	−	10.7599i	1.17687	−	0.428347i	0.855096	+	0.518469i	$0.173498\pi$
$632$	4.86436	+	1.77048i	0.193494	+	0.0704259i
$633$	−10.6201	−	8.91130i	−0.422110	−	0.354192i
$634$	4.49102	−	7.77867i	0.178361	−	0.308931i
$635$		0			0
$636$	1.88293	−	10.6786i	0.0746631	−	0.423435i
$637$	−7.17932	+	40.7160i	−0.284455	+	1.61322i
$638$	−20.9331	−	36.2572i	−0.828750	−	1.43544i
$639$	15.5193	−	26.8801i	0.613932	−	1.06336i
$640$		0			0
$641$	0.312857	+	0.113871i	0.0123571	+	0.00449762i	0.348191	−	0.937423i	$-0.386796\pi$
$641$	0.312857	+	0.113871i	0.0123571	+	0.00449762i	−0.335834	+	0.941921i	$0.609018\pi$
$642$	−2.23211	+	0.812423i	−0.0880945	+	0.0320638i
$643$	−34.6571	+	29.0808i	−1.36674	+	1.14683i	−0.392907	+	0.919578i	$0.628531\pi$
$643$	−34.6571	+	29.0808i	−1.36674	+	1.14683i	−0.973835	+	0.227255i	$0.927025\pi$
$644$	2.07609	+	11.7741i	0.0818094	+	0.463964i
$645$		0			0
$646$	−8.25344	−	4.35421i	−0.324727	−	0.171314i
$647$	−31.3588			−1.23284			−0.616420	−	0.787417i	$-0.711418\pi$
$647$	−31.3588			−1.23284			−0.616420	+	0.787417i	$0.711418\pi$
$648$	0.557188	+	3.15997i	0.0218884	+	0.124135i
$649$	−32.5137	+	27.2822i	−1.27627	+	1.07092i
$650$		0			0
$651$	−18.8345	−	6.85519i	−0.738181	−	0.268676i
$652$	3.69418	+	3.09978i	0.144675	+	0.121397i
$653$	−3.89705	+	6.74989i	−0.152503	+	0.264143i	−0.932147	−	0.362080i	$-0.882067\pi$
$653$	−3.89705	+	6.74989i	−0.152503	+	0.264143i	0.779644	+	0.626223i	$0.215400\pi$
$654$	5.01576	+	8.68755i	0.196132	+	0.339710i
$655$		0			0
$656$	1.05921	−	6.00706i	0.0413551	−	0.234536i
$657$	−3.87749	−	6.71601i	−0.151275	−	0.262016i
$658$	9.16721	−	15.8781i	0.357375	−	0.618992i
$659$	5.73729	+	4.81416i	0.223493	+	0.187533i	0.747658	−	0.664084i	$-0.231178\pi$
$659$	5.73729	+	4.81416i	0.223493	+	0.187533i	−0.524165	+	0.851617i	$0.675623\pi$
$660$		0			0
$661$	32.6923	−	11.8990i	1.27158	−	0.462819i	0.383944	−	0.923357i	$-0.374566\pi$
$661$	32.6923	−	11.8990i	1.27158	−	0.462819i	0.887640	+	0.460538i	$0.152343\pi$
$662$	−18.9133	+	15.8702i	−0.735088	+	0.616812i
$663$	1.22047	+	6.92161i	0.0473990	+	0.268813i
$664$	8.73330			0.338918
$665$		0			0
$666$	4.25409			0.164843
$667$	3.85426	+	21.8586i	0.149238	+	0.846369i
$668$	−3.95141	+	3.31563i	−0.152885	+	0.128285i
$669$	−15.2115	+	5.53653i	−0.588111	+	0.214055i
$670$		0			0
$671$	45.2492	+	37.9686i	1.74683	+	1.46576i
$672$	−1.74780	+	3.02728i	−0.0674230	+	0.116780i
$673$	18.8289	+	32.6126i	0.725801	+	1.25712i	0.958644	+	0.284610i	$0.0918640\pi$
$673$	18.8289	+	32.6126i	0.725801	+	1.25712i	−0.232843	+	0.972514i	$0.574803\pi$
$674$	−4.95422	+	28.0968i	−0.190830	+	1.08225i
$675$		0			0
$676$	−1.22602	−	2.12353i	−0.0471547	−	0.0816743i
$677$	−5.06823	+	8.77843i	−0.194788	+	0.337383i	−0.946831	−	0.321731i	$-0.895735\pi$
$677$	−5.06823	+	8.77843i	−0.194788	+	0.337383i	0.752043	+	0.659114i	$0.229069\pi$
$678$	3.26805	+	2.74222i	0.125509	+	0.105314i
$679$	3.40164	+	1.23810i	0.130543	+	0.0475137i
$680$		0			0
$681$	1.72837	−	1.45028i	0.0662313	−	0.0555747i
$682$	5.36470	+	30.4247i	0.205425	+	1.16502i
$683$	−16.0866			−0.615537			−0.307769	−	0.951461i	$-0.599582\pi$
$683$	−16.0866			−0.615537			−0.307769	+	0.951461i	$0.599582\pi$
$684$	−6.15326	+	7.92860i	−0.235276	+	0.303158i
$685$		0			0
$686$	2.55662	+	14.4993i	0.0976121	+	0.553586i
$687$	0.778748	−	0.653447i	0.0297111	−	0.0249306i
$688$	11.8496	−	4.31289i	0.451761	−	0.164427i
$689$	47.9578	+	17.4552i	1.82704	+	0.664990i
$690$		0			0
$691$	−20.6155	+	35.7070i	−0.784249	+	1.35836i	0.145197	+	0.989403i	$0.453618\pi$
$691$	−20.6155	+	35.7070i	−0.784249	+	1.35836i	−0.929446	+	0.368957i	$0.879715\pi$
$692$	4.18309	+	7.24533i	0.159017	+	0.275426i
$693$	−9.01636	+	51.1343i	−0.342503	+	1.94243i
$694$	−0.740206	+	4.19791i	−0.0280978	+	0.159351i
$695$		0			0
$696$	−3.24480	+	5.62016i	−0.122994	+	0.213031i
$697$	−10.0033	−	8.39376i	−0.378902	−	0.317936i
$698$	−10.7963	−	3.92953i	−0.408646	−	0.148735i
$699$	6.34480	−	2.30932i	0.239982	−	0.0873464i
$700$		0			0
$701$	3.64987	+	20.6994i	0.137854	+	0.781806i	0.972830	+	0.231521i	$0.0743701\pi$
$701$	3.64987	+	20.6994i	0.137854	+	0.781806i	−0.834976	+	0.550286i	$0.814519\pi$
$702$	17.4082			0.657031
$703$	5.40828	+	5.96753i	0.203977	+	0.225070i
$704$	5.38803			0.203069
$705$		0			0
$706$	19.7625	−	16.5827i	0.743773	−	0.624099i
$707$	−15.5471	+	5.65869i	−0.584710	+	0.212817i
$708$	6.18232	+	2.25018i	0.232346	+	0.0845670i
$709$	−4.92868	−	4.13565i	−0.185101	−	0.155318i	0.545529	−	0.838092i	$-0.316329\pi$
$709$	−4.92868	−	4.13565i	−0.185101	−	0.155318i	−0.730629	+	0.682774i	$0.760773\pi$
$710$		0			0
$711$	−5.95939	−	10.3220i	−0.223495	−	0.387104i
$712$	−0.573463	+	3.25227i	−0.0214914	+	0.121884i
$713$	2.84415	−	16.1300i	0.106514	−	0.604073i
$714$	3.74172	+	6.48084i	0.140030	+	0.242539i
$715$		0			0
$716$	−3.92277	−	3.29160i	−0.146601	−	0.123013i
$717$	5.02718	+	1.82975i	0.187744	+	0.0683331i
$718$	−22.1832	+	8.07404i	−0.827871	+	0.301320i
$719$	−10.5258	+	8.83217i	−0.392545	+	0.329384i	−0.817604	−	0.575782i	$-0.804698\pi$
$719$	−10.5258	+	8.83217i	−0.392545	+	0.329384i	0.425059	+	0.905166i	$0.360253\pi$
$720$		0			0
$721$	35.4401			1.31986
$722$	−18.9447	+	1.44810i	−0.705050	+	0.0538927i
$723$	−21.5912			−0.802986
$724$	−0.326411	−	1.85117i	−0.0121310	−	0.0687982i
$725$		0			0
$726$	−14.1510	+	5.15054i	−0.525193	+	0.191154i
$727$	−44.0426	−	16.0302i	−1.63345	−	0.594527i	−0.647573	−	0.762003i	$-0.724216\pi$
$727$	−44.0426	−	16.0302i	−1.63345	−	0.594527i	−0.985876	+	0.167477i	$0.946438\pi$
$728$	−12.6033	−	10.5754i	−0.467110	−	0.391952i
$729$	−1.85403	+	3.21128i	−0.0686679	+	0.118936i
$730$		0			0
$731$	4.68776	−	26.5856i	0.173383	−	0.983304i
$732$	1.58994	−	9.01700i	0.0587659	−	0.333278i
$733$	20.8968	+	36.1943i	0.771840	+	1.33687i	0.936553	+	0.350525i	$0.113997\pi$
$733$	20.8968	+	36.1943i	0.771840	+	1.33687i	−0.164713	+	0.986341i	$0.552670\pi$
$734$	−10.2193	+	17.7004i	−0.377202	+	0.653333i
$735$		0			0
$736$	−2.68425	−	0.976988i	−0.0989428	−	0.0360122i
$737$	53.1018	−	19.3275i	1.95603	−	0.711937i
$738$	−10.7586	+	9.02756i	−0.396031	+	0.332309i
$739$	2.10661	+	11.9472i	0.0774930	+	0.439484i	0.998725	+	0.0504720i	$0.0160726\pi$
$739$	2.10661	+	11.9472i	0.0774930	+	0.439484i	−0.921233	+	0.389012i	$0.872816\pi$
$740$		0			0
$741$	9.60996	+	10.6037i	0.353031	+	0.389536i
$742$	54.3398			1.99488
$743$	−7.56669	−	42.9128i	−0.277595	−	1.57432i	−0.730596	−	0.682810i	$-0.760758\pi$
$743$	−7.56669	−	42.9128i	−0.277595	−	1.57432i	0.453001	−	0.891510i	$-0.350353\pi$
$744$	3.66845	−	3.07820i	0.134492	−	0.112852i
$745$		0			0
$746$	4.78544	+	1.74176i	0.175207	+	0.0637703i
$747$	−15.4037	−	12.9252i	−0.563591	−	0.472909i
$748$	5.76738	−	9.98939i	0.210876	−	0.365248i
$749$	−5.95189	−	10.3090i	−0.217477	−	0.376682i
$750$		0			0
$751$	−2.33304	+	13.2313i	−0.0851338	+	0.482818i	0.912194	+	0.409759i	$0.134387\pi$
$751$	−2.33304	+	13.2313i	−0.0851338	+	0.482818i	−0.997328	+	0.0730589i	$0.976724\pi$
$752$	2.19028	+	3.79367i	0.0798711	+	0.138341i
$753$	7.87367	−	13.6376i	0.286932	−	0.496982i
$754$	−23.3981	−	19.6333i	−0.852109	−	0.715004i
$755$		0			0
$756$	17.4175	−	6.33945i	0.633468	−	0.230564i
$757$	−7.05698	+	5.92151i	−0.256490	+	0.215221i	−0.761961	−	0.647623i	$-0.775763\pi$
$757$	−7.05698	+	5.92151i	−0.256490	+	0.215221i	0.505471	+	0.862844i	$0.331319\pi$
$758$	1.43171	+	8.11961i	0.0520019	+	0.294918i
$759$	12.8544			0.466585
$760$		0			0
$761$	−38.8696			−1.40902			−0.704512	−	0.709692i	$-0.748834\pi$
$761$	−38.8696			−1.40902			−0.704512	+	0.709692i	$0.748834\pi$
$762$	−1.59789	−	9.06206i	−0.0578853	−	0.328284i
$763$	−38.5101	+	32.3138i	−1.39416	+	1.16984i
$764$	−15.2426	+	5.54785i	−0.551458	+	0.200714i
$765$		0			0
$766$	1.07800	+	0.904546i	0.0389496	+	0.0326826i
$767$	−15.4826	+	26.8167i	−0.559045	+	0.968295i
$768$	−0.417594	−	0.723294i	−0.0150686	−	0.0260996i
$769$	1.08826	−	6.17181i	0.0392435	−	0.222561i	−0.958879	−	0.283817i	$-0.908399\pi$
$769$	1.08826	−	6.17181i	0.0392435	−	0.222561i	0.998122	+	0.0612554i	$0.0195104\pi$
$770$		0			0
$771$	−6.40915	−	11.1010i	−0.230820	−	0.399792i
$772$	2.67175	−	4.62761i	0.0961585	−	0.166551i
$773$	9.48900	+	7.96222i	0.341296	+	0.286381i	0.797284	−	0.603605i	$-0.206270\pi$
$773$	9.48900	+	7.96222i	0.341296	+	0.286381i	−0.455988	+	0.889986i	$0.650714\pi$
$774$	−27.2832	−	9.93027i	−0.980674	−	0.356936i
$775$		0			0
$776$	−0.662549	+	0.555945i	−0.0237841	+	0.0199573i
$777$	−1.12152	−	6.36046i	−0.0402343	−	0.228180i
$778$	39.2500			1.40718
$779$	−26.3412	−	3.61507i	−0.943771	−	0.129523i
$780$		0			0
$781$	12.6127	+	71.5303i	0.451319	+	2.55956i
$782$	−4.68457	+	3.93082i	−0.167520	+	0.140566i
$783$	32.3356	−	11.7692i	1.15558	−	0.420597i
$784$	−9.88339	−	3.59726i	−0.352978	−	0.128474i
$785$		0			0
$786$	−8.77282	+	15.1950i	−0.312916	+	0.541987i
$787$	−0.266681	−	0.461905i	−0.00950616	−	0.0164652i	0.861233	−	0.508210i	$-0.169693\pi$
$787$	−0.266681	−	0.461905i	−0.00950616	−	0.0164652i	−0.870739	+	0.491745i	$0.836359\pi$
$788$	2.42727	−	13.7657i	0.0864678	−	0.490383i
$789$	1.34847	−	7.64758i	0.0480070	−	0.272261i
$790$		0			0
$791$	−10.6895	+	18.5148i	−0.380076	+	0.658311i
$792$	−9.50335	−	7.97425i	−0.337687	−	0.283353i
$793$	40.4954	+	14.7391i	1.43803	+	0.523401i
$794$	5.48819	−	1.99754i	0.194769	−	0.0708900i
$795$		0			0
$796$	−1.93501	−	10.9740i	−0.0685844	−	0.388962i
$797$	2.72969			0.0966907			0.0483453	−	0.998831i	$-0.484605\pi$
$797$	2.72969			0.0966907			0.0483453	+	0.998831i	$0.484605\pi$
$798$	13.4766	+	7.10973i	0.477065	+	0.251682i
$799$	9.37793			0.331767
$800$		0			0
$801$	5.82481	−	4.88759i	0.205809	−	0.172695i
$802$	17.0764	−	6.21531i	0.602989	−	0.219470i
$803$	17.0531	+	6.20683i	0.601792	+	0.219034i
$804$	−6.71014	−	5.63047i	−0.236648	−	0.198571i
$805$		0			0
$806$	11.2696	+	19.5195i	0.396954	+	0.687545i
$807$	1.40788	−	7.98448i	0.0495597	−	0.281067i
$808$	0.686429	−	3.89294i	0.0241485	−	0.136953i
$809$	14.7742	+	25.5896i	0.519433	+	0.899684i	0.999745	+	0.0225862i	$0.00719003\pi$
$809$	14.7742	+	25.5896i	0.519433	+	0.899684i	−0.480312	+	0.877098i	$0.659477\pi$
$810$		0			0
$811$	−23.2042	−	19.4706i	−0.814810	−	0.683707i	0.136941	−	0.990579i	$-0.456273\pi$
$811$	−23.2042	−	19.4706i	−0.814810	−	0.683707i	−0.951751	+	0.306872i	$0.900717\pi$
$812$	−30.5603	−	11.1230i	−1.07246	−	0.390342i
$813$	−12.3540	+	4.49648i	−0.433273	+	0.157698i
$814$	−7.62603	+	6.39900i	−0.267292	+	0.224285i
$815$		0			0
$816$	−1.78798			−0.0625918
$817$	−20.7555	−	50.8966i	−0.726144	−	1.78065i
$818$	12.0035			0.419693
$819$	6.57800	+	37.3057i	0.229854	+	1.30357i
$820$		0			0
$821$	−26.9586	+	9.81211i	−0.940860	+	0.342445i	−0.766505	−	0.642238i	$-0.778006\pi$
$821$	−26.9586	+	9.81211i	−0.940860	+	0.342445i	−0.174355	+	0.984683i	$0.555784\pi$
$822$	2.99843	+	1.09134i	0.104582	+	0.0380648i
$823$	−22.9178	−	19.2303i	−0.798864	−	0.670327i	0.149058	−	0.988828i	$-0.452376\pi$
$823$	−22.9178	−	19.2303i	−0.798864	−	0.670327i	−0.947922	+	0.318502i	$0.896820\pi$
$824$	−4.23376	+	7.33309i	−0.147490	+	0.255460i
$825$		0			0
$826$	−5.72520	+	32.4692i	−0.199205	+	1.12975i
$827$	2.76402	−	15.6755i	0.0961144	−	0.545092i	−0.898286	−	0.439412i	$-0.855187\pi$
$827$	2.76402	−	15.6755i	0.0961144	−	0.545092i	0.994400	−	0.105680i	$-0.0337019\pi$
$828$	3.28852	+	5.69588i	0.114284	+	0.197945i
$829$	−16.9348	+	29.3319i	−0.588169	+	1.01874i	0.406304	+	0.913738i	$0.366818\pi$
$829$	−16.9348	+	29.3319i	−0.588169	+	1.01874i	−0.994472	+	0.105000i	$0.966516\pi$
$830$		0			0
$831$	−23.1822	−	8.43765i	−0.804183	−	0.292699i
$832$	3.69385	−	1.34445i	0.128061	−	0.0466104i
$833$	−17.2485	+	14.4732i	−0.597627	+	0.501468i
$834$	2.11066	+	11.9701i	0.0730860	+	0.414491i
$835$		0			0
$836$	−0.895650	−	23.4688i	−0.0309767	−	0.811685i
$837$	−25.3926			−0.877696
$838$	−3.87822	−	21.9945i	−0.133971	−	0.759788i
$839$	23.5861	−	19.7911i	0.814284	−	0.683265i	−0.137343	−	0.990524i	$-0.543856\pi$
$839$	23.5861	−	19.7911i	0.814284	−	0.683265i	0.951626	+	0.307259i	$0.0994117\pi$
$840$		0			0
$841$	−29.4842	−	10.7314i	−1.01670	−	0.370047i
$842$	10.0243	+	8.41142i	0.345462	+	0.289877i
$843$	0.890936	−	1.54315i	0.0306855	−	0.0531488i
$844$	8.29965	+	14.3754i	0.285686	+	0.494822i
$845$		0			0
$846$	1.75142	−	9.93282i	0.0602152	−	0.341497i
$847$	−37.7334	−	65.3561i	−1.29653	−	2.24566i
$848$	−6.49157	+	11.2437i	−0.222922	+	0.386112i
$849$	−12.2439	−	10.2739i	−0.420210	−	0.352598i
$850$		0			0
$851$	4.95950	−	1.80511i	0.170009	−	0.0618784i
$852$	8.62475	−	7.23702i	0.295479	−	0.247936i
$853$	−1.14530	−	6.49532i	−0.0392143	−	0.222396i	0.958903	−	0.283735i	$-0.0915738\pi$
$853$	−1.14530	−	6.49532i	−0.0392143	−	0.222396i	−0.998117	+	0.0613399i	$0.980463\pi$
$854$	45.8844			1.57013
$855$		0			0
$856$	2.84411			0.0972097
$857$	6.13734	+	34.8066i	0.209647	+	1.18897i	0.889957	+	0.456045i	$0.150734\pi$
$857$	6.13734	+	34.8066i	0.209647	+	1.18897i	−0.680309	+	0.732925i	$0.738155\pi$
$858$	−13.5507	+	11.3704i	−0.462613	+	0.388178i
$859$	47.8371	−	17.4113i	1.63218	−	0.594065i	0.646534	−	0.762885i	$-0.276218\pi$
$859$	47.8371	−	17.4113i	1.63218	−	0.594065i	0.985647	+	0.168820i	$0.0539956\pi$
$860$		0			0
$861$	16.3338	+	13.7057i	0.556654	+	0.467088i
$862$	4.26132	−	7.38082i	0.145141	−	0.251392i
$863$	−18.7712	−	32.5126i	−0.638978	−	1.10674i	−0.985657	−	0.168759i	$-0.946024\pi$
$863$	−18.7712	−	32.5126i	−0.638978	−	1.10674i	0.346679	−	0.937984i	$-0.387309\pi$
$864$	−0.769010	+	4.36127i	−0.0261622	+	0.148373i
$865$		0			0
$866$	−8.44842	−	14.6331i	−0.287089	−	0.497252i
$867$	5.18523	−	8.98108i	0.176100	−	0.305014i
$868$	18.3839	+	15.4259i	0.623990	+	0.523590i
$869$	26.2093	+	9.53941i	0.889090	+	0.323602i
$870$		0			0
$871$	31.5820	−	26.5005i	1.07012	−	0.897935i
$872$	−2.08571	−	11.8286i	−0.0706309	−	0.400568i
$873$	1.99139			0.0673984
$874$	−3.80929	+	11.8543i	−0.128851	+	0.400977i
$875$		0			0
$876$	−0.488475	−	2.77028i	−0.0165040	−	0.0935990i
$877$	−14.1043	+	11.8349i	−0.476269	+	0.399637i	−0.849075	−	0.528272i	$-0.822840\pi$
$877$	−14.1043	+	11.8349i	−0.476269	+	0.399637i	0.372806	+	0.927909i	$0.378396\pi$
$878$	−18.7879	+	6.83824i	−0.634061	+	0.230779i
$879$	14.6826	+	5.34403i	0.495232	+	0.180250i
$880$		0			0
$881$	27.7203	−	48.0130i	0.933921	−	1.61760i	0.157374	−	0.987539i	$-0.449697\pi$
$881$	27.7203	−	48.0130i	0.933921	−	1.61760i	0.776547	−	0.630059i	$-0.216969\pi$
$882$	12.1083	+	20.9722i	0.407707	+	0.706169i
$883$	3.47349	−	19.6991i	0.116892	−	0.662929i	−0.868904	−	0.494981i	$-0.835175\pi$
$883$	3.47349	−	19.6991i	0.116892	−	0.662929i	0.985796	−	0.167948i	$-0.0537140\pi$
$884$	1.46131	−	8.28749i	0.0491491	−	0.278738i
$885$		0			0
$886$	10.1114	−	17.5134i	0.339698	−	0.588375i
$887$	18.8918	+	15.8521i	0.634325	+	0.532262i	0.902270	−	0.431172i	$-0.141900\pi$
$887$	18.8918	+	15.8521i	0.634325	+	0.532262i	−0.267944	+	0.963434i	$0.586344\pi$
$888$	1.45005	+	0.527777i	0.0486606	+	0.0177110i
$889$	43.3327	−	15.7718i	1.45333	−	0.528970i
$890$		0			0
$891$	3.00214	+	17.0260i	0.100576	+	0.570393i
$892$	19.3822			0.648963
$893$	16.1601	−	10.1709i	0.540777	−	0.340355i
$894$	9.94318			0.332550
$895$		0			0
$896$	3.20621	−	2.69033i	0.107112	−	0.0898777i
$897$	8.81252	−	3.20750i	0.294242	−	0.107095i
$898$	17.0238	+	6.19615i	0.568091	+	0.206768i
$899$	34.1297	+	28.6382i	1.13829	+	0.955139i
$900$		0			0
$901$	13.8972	+	24.0707i	0.462984	+	0.801912i
$902$	5.70704	−	32.3662i	0.190024	−	1.07768i
$903$	−7.65437	+	43.4101i	−0.254721	+	1.44460i
$904$	−2.55400	−	4.42365i	−0.0849446	−	0.147128i
$905$		0			0
$906$	−3.33532	−	2.79866i	−0.110808	−	0.0929794i
$907$	24.7114	+	8.99422i	0.820529	+	0.298648i	0.717966	−	0.696078i	$-0.245073\pi$
$907$	24.7114	+	8.99422i	0.820529	+	0.298648i	0.102563	+	0.994727i	$0.467296\pi$
$908$	−2.53854	+	0.923955i	−0.0842446	+	0.0306625i
$909$	−6.97224	+	5.85040i	−0.231254	+	0.194046i
$910$		0			0
$911$	31.3631			1.03910			0.519552	−	0.854439i	$-0.326099\pi$
$911$	31.3631			1.03910			0.519552	+	0.854439i	$0.326099\pi$
$912$	−3.08105	+	1.93916i	−0.102024	+	0.0642119i
$913$	47.0553			1.55730
$914$	−2.53077	−	14.3527i	−0.0837106	−	0.474746i
$915$		0			0
$916$	−1.14379	+	0.416304i	−0.0377918	+	0.0137551i
$917$	−82.6246	−	30.0729i	−2.72851	−	0.993095i
$918$	7.26263	+	6.09407i	0.239703	+	0.201134i
$919$	7.75554	−	13.4330i	0.255832	−	0.443113i	−0.709289	−	0.704917i	$-0.750984\pi$
$919$	7.75554	−	13.4330i	0.255832	−	0.443113i	0.965121	+	0.261804i	$0.0843174\pi$
$920$		0			0
$921$	−2.22224	+	12.6030i	−0.0732254	+	0.415282i
$922$	2.84793	−	16.1514i	0.0937914	−	0.531918i
$923$	26.4955	+	45.8915i	0.872109	+	1.51054i
$924$	−9.41722	+	16.3111i	−0.309804	+	0.536596i
$925$		0			0
$926$	30.7556	+	11.1941i	1.01069	+	0.367862i
$927$	18.3204	−	6.66807i	0.601720	−	0.219008i
$928$	5.95234	−	4.99461i	0.195395	−	0.163956i
$929$	5.96023	+	33.8021i	0.195549	+	1.10901i	0.911635	+	0.411000i	$0.134820\pi$
$929$	5.96023	+	33.8021i	0.195549	+	1.10901i	−0.716087	+	0.698011i	$0.754068\pi$
$930$		0			0
$931$	−14.0258	+	43.6473i	−0.459676	+	1.43048i
$932$	−8.08440			−0.264813
$933$	2.78317	+	15.7841i	0.0911169	+	0.516749i
$934$	−10.6299	+	8.91954i	−0.347821	+	0.291856i
$935$		0			0
$936$	−8.50494	−	3.09554i	−0.277993	−	0.101181i
$937$	−11.0745	−	9.29262i	−0.361789	−	0.303577i	0.443715	−	0.896168i	$-0.353660\pi$
$937$	−11.0745	−	9.29262i	−0.361789	−	0.303577i	−0.805503	+	0.592592i	$0.798105\pi$
$938$	21.9483	−	38.0156i	0.716639	−	1.24125i
$939$	−11.0846	−	19.1991i	−0.361732	−	0.626537i
$940$		0			0
$941$	−1.69085	+	9.58931i	−0.0551202	+	0.312602i	−0.999885	−	0.0151459i	$-0.995179\pi$
$941$	−1.69085	+	9.58931i	−0.0551202	+	0.312602i	0.944765	+	0.327748i	$0.106290\pi$
$942$	−1.70634	−	2.95547i	−0.0555957	−	0.0962945i
$943$	−8.71200	+	15.0896i	−0.283702	+	0.491386i
$944$	−6.03442	−	5.06348i	−0.196404	−	0.164802i
$945$		0			0
$946$	63.8459	−	23.2380i	2.07581	−	0.755532i
$947$	33.9731	−	28.5068i	1.10398	−	0.926348i	0.106292	−	0.994335i	$-0.466102\pi$
$947$	33.9731	−	28.5068i	1.10398	−	0.926348i	0.997686	+	0.0679874i	$0.0216578\pi$
$948$	−0.750747	−	4.25770i	−0.0243831	−	0.138284i
$949$	13.2398			0.429782
$950$		0			0
$951$	−7.50169			−0.243259
$952$	−1.55592	−	8.82405i	−0.0504276	−	0.285989i
$953$	3.28938	−	2.76012i	0.106553	−	0.0894089i	−0.587954	−	0.808894i	$-0.700067\pi$
$953$	3.28938	−	2.76012i	0.106553	−	0.0894089i	0.694508	+	0.719485i	$0.255622\pi$
$954$	28.0904	−	10.2241i	0.909461	−	0.331017i
$955$		0			0
$956$	−4.90692	−	4.11739i	−0.158701	−	0.133166i
$957$	−17.4831	+	30.2816i	−0.565148	+	0.978864i
$958$	−4.75475	−	8.23546i	−0.153619	−	0.266076i
$959$	−2.77672	+	15.7476i	−0.0896650	+	0.508516i
$960$		0			0
$961$	−0.938425	−	1.62540i	−0.0302718	−	0.0524323i
$962$	−3.63143	+	6.28982i	−0.117082	+	0.202792i
$963$	−5.01641	−	4.20927i	−0.161652	−	0.135642i
$964$	24.2929	+	8.84188i	0.782421	+	0.284778i
$965$		0			0
$966$	7.64916	−	6.41841i	0.246108	−	0.206509i
$967$	5.70593	+	32.3599i	0.183490	+	1.04063i	0.927880	+	0.372879i	$0.121629\pi$
$967$	5.70593	+	32.3599i	0.183490	+	1.04063i	−0.744390	+	0.667746i	$0.767259\pi$
$968$	18.0309			0.579535
$969$	0.297215	+	7.78795i	0.00954791	+	0.250185i
$970$		0			0
$971$	−1.81722	−	10.3060i	−0.0583174	−	0.330734i	0.941666	−	0.336550i	$-0.109260\pi$
$971$	−1.81722	−	10.3060i	−0.0583174	−	0.330734i	−0.999983	+	0.00581535i	$0.998149\pi$
$972$	12.2303	−	10.2624i	0.392287	−	0.329168i
$973$	−57.2384	+	20.8331i	−1.83498	+	0.667877i
$974$	−35.5063	−	12.9232i	−1.13770	−	0.414087i
$975$		0			0
$976$	−5.48146	+	9.49417i	−0.175457	+	0.303901i
$977$	−8.97886	−	15.5518i	−0.287259	−	0.497548i	0.685895	−	0.727700i	$-0.259411\pi$
$977$	−8.97886	−	15.5518i	−0.287259	−	0.497548i	−0.973155	+	0.230153i	$0.926077\pi$
$978$	0.699387	−	3.96642i	0.0223639	−	0.126832i
$979$	−3.08984	+	17.5233i	−0.0987516	+	0.560048i
$980$		0			0
$981$	−13.8275	+	23.9500i	−0.441480	+	0.764665i
$982$	−12.1540	−	10.1984i	−0.387851	−	0.325445i
$983$	16.3898	+	5.96541i	0.522755	+	0.190267i	0.589900	−	0.807476i	$-0.299167\pi$
$983$	16.3898	+	5.96541i	0.522755	+	0.190267i	−0.0671457	+	0.997743i	$0.521389\pi$
$984$	−4.78719	+	1.74239i	−0.152610	+	0.0555455i
$985$		0			0
$986$	−2.88857	−	16.3819i	−0.0919907	−	0.521705i
$987$	−15.3127			−0.487408
$988$	−6.47008	−	15.8659i	−0.205841	−	0.504762i
$989$	−36.0209			−1.14540
$990$		0			0
$991$	−15.3841	+	12.9088i	−0.488693	+	0.410062i	−0.853558	−	0.520998i	$-0.825560\pi$
$991$	−15.3841	+	12.9088i	−0.488693	+	0.410062i	0.364865	+	0.931061i	$0.381115\pi$
$992$	−5.38804	+	1.96109i	−0.171070	+	0.0622646i
$993$	19.3769	+	7.05262i	0.614907	+	0.223808i
$994$	43.2216	+	36.2672i	1.37091	+	1.15033i
$995$		0			0
$996$	−3.64697	−	6.31674i	−0.115559	−	0.200154i
$997$	6.68890	−	37.9346i	0.211840	−	1.20140i	−0.674467	−	0.738305i	$-0.735627\pi$
$997$	6.68890	−	37.9346i	0.211840	−	1.20140i	0.886307	−	0.463098i	$-0.153262\pi$
$998$	6.14627	−	34.8572i	0.194557	−	1.10339i
$999$	−4.09116	−	7.08609i	−0.129438	−	0.224194i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	950.2.l.k.351.3	yes	24
5.2	odd	4		950.2.u.h.199.2		48
5.3	odd	4		950.2.u.h.199.7		48
5.4	even	2		950.2.l.j.351.2	✓	24
19.17	even	9	inner	950.2.l.k.701.3	yes	24
95.17	odd	36		950.2.u.h.549.7		48
95.74	even	18		950.2.l.j.701.2	yes	24
95.93	odd	36		950.2.u.h.549.2		48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
950.2.l.j.351.2	✓	24	5.4	even	2
950.2.l.j.701.2	yes	24	95.74	even	18
950.2.l.k.351.3	yes	24	1.1	even	1	trivial
950.2.l.k.701.3	yes	24	19.17	even	9	inner
950.2.u.h.199.2		48	5.2	odd	4
950.2.u.h.199.7		48	5.3	odd	4
950.2.u.h.549.2		48	95.93	odd	36
950.2.u.h.549.7		48	95.17	odd	36

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:	\( N \)	\(=\)	\( 950 = 2 \cdot 5^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	950.l (of order \(9\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(0.173648 + 0.984808i) q^{2} +(0.639791 - 0.536848i) q^{3} +(-0.939693 + 0.342020i) q^{4} +(0.639791 + 0.536848i) q^{6} +(-2.09271 + 3.62467i) q^{7} +(-0.500000 - 0.866025i) q^{8} +(-0.399818 + 2.26748i) q^{9} +O(q^{10})\)	\(q+(0.173648 + 0.984808i) q^{2} +(0.639791 - 0.536848i) q^{3} +(-0.939693 + 0.342020i) q^{4} +(0.639791 + 0.536848i) q^{6} +(-2.09271 + 3.62467i) q^{7} +(-0.500000 - 0.866025i) q^{8} +(-0.399818 + 2.26748i) q^{9} +(-2.69402 - 4.66617i) q^{11} +(-0.417594 + 0.723294i) q^{12} +(-3.01125 - 2.52674i) q^{13} +(-3.93300 - 1.43150i) q^{14} +(0.766044 - 0.642788i) q^{16} +(-0.371748 - 2.10829i) q^{17} -2.30246 q^{18} +(-2.92715 - 3.22983i) q^{19} +(0.607005 + 3.44250i) q^{21} +(4.12747 - 3.46336i) q^{22} +(-2.68425 + 0.976988i) q^{23} +(-0.784820 - 0.285651i) q^{24} +(1.96545 - 3.40427i) q^{26} +(2.21428 + 3.83524i) q^{27} +(0.726789 - 4.12183i) q^{28} +(1.34929 - 7.65218i) q^{29} +(-2.86692 + 4.96565i) q^{31} +(0.766044 + 0.642788i) q^{32} +(-4.22863 - 1.53910i) q^{33} +(2.01170 - 0.732201i) q^{34} +(-0.399818 - 2.26748i) q^{36} -1.84763 q^{37} +(2.67247 - 3.44353i) q^{38} -3.28305 q^{39} +(4.67266 - 3.92083i) q^{41} +(-3.28479 + 1.19557i) q^{42} +(11.8496 + 4.31289i) q^{43} +(4.12747 + 3.46336i) q^{44} +(-1.42826 - 2.47382i) q^{46} +(-0.760675 + 4.31400i) q^{47} +(0.145029 - 0.822499i) q^{48} +(-5.25884 - 9.10858i) q^{49} +(-1.36967 - 1.14929i) q^{51} +(3.69385 + 1.34445i) q^{52} +(-12.2002 + 4.44050i) q^{53} +(-3.39247 + 2.84662i) q^{54} +4.18541 q^{56} +(-3.60669 - 0.494982i) q^{57} +7.77023 q^{58} +(-1.36789 - 7.75770i) q^{59} +(-10.3018 + 3.74954i) q^{61} +(-5.38804 - 1.96109i) q^{62} +(-7.38218 - 6.19439i) q^{63} +(-0.500000 + 0.866025i) q^{64} +(0.781420 - 4.43165i) q^{66} +(-1.82123 + 10.3287i) q^{67} +(1.07041 + 1.85400i) q^{68} +(-1.19287 + 2.06610i) q^{69} +(-12.6676 - 4.61063i) q^{71} +(2.16361 - 0.787488i) q^{72} +(-2.58013 + 2.16499i) q^{73} +(-0.320837 - 1.81956i) q^{74} +(3.85529 + 2.03391i) q^{76} +22.5511 q^{77} +(-0.570095 - 3.23317i) q^{78} +(-3.96546 + 3.32742i) q^{79} +(-3.01521 - 1.09745i) q^{81} +(4.67266 + 3.92083i) q^{82} +(-4.36665 + 7.56326i) q^{83} +(-1.74780 - 3.02728i) q^{84} +(-2.18971 + 12.4185i) q^{86} +(-3.24480 - 5.62016i) q^{87} +(-2.69402 + 4.66617i) q^{88} +(-2.52982 - 2.12277i) q^{89} +(15.4603 - 5.62708i) q^{91} +(2.18822 - 1.83614i) q^{92} +(0.831571 + 4.71607i) q^{93} -4.38055 q^{94} +0.835188 q^{96} +(-0.150188 - 0.851757i) q^{97} +(8.05701 - 6.76064i) q^{98} +(11.6576 - 4.24301i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 3 q^{7} - 12 q^{8}+O(q^{10}) \) 24 * q + 3 * q^7 - 12 * q^8	\( 24 q + 3 q^{7} - 12 q^{8} - 6 q^{11} - 3 q^{12} + 24 q^{13} - 15 q^{14} - 9 q^{17} + 30 q^{18} - 15 q^{19} - 18 q^{21} + 12 q^{23} - 9 q^{26} - 21 q^{27} + 12 q^{28} - 12 q^{29} + 9 q^{31} - 42 q^{33} - 9 q^{34} + 66 q^{37} + 6 q^{38} + 66 q^{39} + 18 q^{41} + 9 q^{42} - 3 q^{43} - 3 q^{46} - 12 q^{47} - 27 q^{49} - 3 q^{51} - 12 q^{52} - 45 q^{53} + 27 q^{54} - 6 q^{56} - 27 q^{57} - 18 q^{58} + 36 q^{59} + 12 q^{61} - 24 q^{62} - 63 q^{63} - 12 q^{64} + 48 q^{66} - 54 q^{67} + 3 q^{68} + 21 q^{69} - 39 q^{71} + 48 q^{73} + 18 q^{74} + 6 q^{76} + 48 q^{77} - 12 q^{78} - 42 q^{79} - 36 q^{81} + 18 q^{82} - 3 q^{83} + 9 q^{84} - 39 q^{86} - 24 q^{87} - 6 q^{88} - 36 q^{89} + 12 q^{91} - 15 q^{92} - 6 q^{93} + 12 q^{94} + 6 q^{96} - 54 q^{97} + 3 q^{98} + 51 q^{99}+O(q^{100}) \) 24 * q + 3 * q^7 - 12 * q^8 - 6 * q^11 - 3 * q^12 + 24 * q^13 - 15 * q^14 - 9 * q^17 + 30 * q^18 - 15 * q^19 - 18 * q^21 + 12 * q^23 - 9 * q^26 - 21 * q^27 + 12 * q^28 - 12 * q^29 + 9 * q^31 - 42 * q^33 - 9 * q^34 + 66 * q^37 + 6 * q^38 + 66 * q^39 + 18 * q^41 + 9 * q^42 - 3 * q^43 - 3 * q^46 - 12 * q^47 - 27 * q^49 - 3 * q^51 - 12 * q^52 - 45 * q^53 + 27 * q^54 - 6 * q^56 - 27 * q^57 - 18 * q^58 + 36 * q^59 + 12 * q^61 - 24 * q^62 - 63 * q^63 - 12 * q^64 + 48 * q^66 - 54 * q^67 + 3 * q^68 + 21 * q^69 - 39 * q^71 + 48 * q^73 + 18 * q^74 + 6 * q^76 + 48 * q^77 - 12 * q^78 - 42 * q^79 - 36 * q^81 + 18 * q^82 - 3 * q^83 + 9 * q^84 - 39 * q^86 - 24 * q^87 - 6 * q^88 - 36 * q^89 + 12 * q^91 - 15 * q^92 - 6 * q^93 + 12 * q^94 + 6 * q^96 - 54 * q^97 + 3 * q^98 + 51 * q^99

Introduction

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