LMFDB - Embedded newform 950.2.u.h.199.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [950,2,Mod(99,950)]

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([9, 2]))

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

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

chi := DirichletCharacter("950.99");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 950 = 2 \cdot 5^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	950.u (of order $18$, degree $6$, 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:	$7.58578819202$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$8$ over $\Q(\zeta_{18})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			199.2
Character	$\chi$	$=$	950.199
Dual form			950.2.u.h.549.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.984808 + 0.173648i) q^{2} +(-0.536848 - 0.639791i) q^{3} +(0.939693 - 0.342020i) q^{4} +(0.639791 + 0.536848i) q^{6} +(-3.62467 - 2.09271i) q^{7} +(-0.866025 + 0.500000i) q^{8} +(0.399818 - 2.26748i) q^{9} +O(q^{10})$	\(q+(-0.984808 + 0.173648i) q^{2} +(-0.536848 - 0.639791i) q^{3} +(0.939693 - 0.342020i) q^{4} +(0.639791 + 0.536848i) q^{6} +(-3.62467 - 2.09271i) q^{7} +(-0.866025 + 0.500000i) q^{8} +(0.399818 - 2.26748i) q^{9} +(-2.69402 - 4.66617i) q^{11} +(-0.723294 - 0.417594i) q^{12} +(-2.52674 + 3.01125i) q^{13} +(3.93300 + 1.43150i) q^{14} +(0.766044 - 0.642788i) q^{16} +(2.10829 - 0.371748i) q^{17} +2.30246i q^{18} +(2.92715 + 3.22983i) q^{19} +(0.607005 + 3.44250i) q^{21} +(3.46336 + 4.12747i) q^{22} +(0.976988 + 2.68425i) q^{23} +(0.784820 + 0.285651i) q^{24} +(1.96545 - 3.40427i) q^{26} +(-3.83524 + 2.21428i) q^{27} +(-4.12183 - 0.726789i) q^{28} +(-1.34929 + 7.65218i) q^{29} +(-2.86692 + 4.96565i) q^{31} +(-0.642788 + 0.766044i) q^{32} +(-1.53910 + 4.22863i) q^{33} +(-2.01170 + 0.732201i) q^{34} +(-0.399818 - 2.26748i) q^{36} -1.84763i q^{37} +(-3.44353 - 2.67247i) q^{38} +3.28305 q^{39} +(4.67266 - 3.92083i) q^{41} +(-1.19557 - 3.28479i) q^{42} +(4.31289 - 11.8496i) q^{43} +(-4.12747 - 3.46336i) q^{44} +(-1.42826 - 2.47382i) q^{46} +(-4.31400 - 0.760675i) q^{47} +(-0.822499 - 0.145029i) q^{48} +(5.25884 + 9.10858i) q^{49} +(-1.36967 - 1.14929i) q^{51} +(-1.34445 + 3.69385i) q^{52} +(4.44050 + 12.2002i) q^{53} +(3.39247 - 2.84662i) q^{54} +4.18541 q^{56} +(0.494982 - 3.60669i) q^{57} -7.77023i q^{58} +(1.36789 + 7.75770i) q^{59} +(-10.3018 + 3.74954i) q^{61} +(1.96109 - 5.38804i) q^{62} +(-6.19439 + 7.38218i) q^{63} +(0.500000 - 0.866025i) q^{64} +(0.781420 - 4.43165i) q^{66} +(-10.3287 - 1.82123i) q^{67} +(1.85400 - 1.07041i) q^{68} +(1.19287 - 2.06610i) q^{69} +(-12.6676 - 4.61063i) q^{71} +(0.787488 + 2.16361i) q^{72} +(2.16499 + 2.58013i) q^{73} +(0.320837 + 1.81956i) q^{74} +(3.85529 + 2.03391i) q^{76} +22.5511i q^{77} +(-3.23317 + 0.570095i) q^{78} +(3.96546 - 3.32742i) q^{79} +(-3.01521 - 1.09745i) q^{81} +(-3.92083 + 4.67266i) q^{82} +(7.56326 + 4.36665i) q^{83} +(1.74780 + 3.02728i) q^{84} +(-2.18971 + 12.4185i) q^{86} +(5.62016 - 3.24480i) q^{87} +(4.66617 + 2.69402i) q^{88} +(2.52982 + 2.12277i) q^{89} +(15.4603 - 5.62708i) q^{91} +(1.83614 + 2.18822i) q^{92} +(4.71607 - 0.831571i) q^{93} +4.38055 q^{94} +0.835188 q^{96} +(0.851757 - 0.150188i) q^{97} +(-6.76064 - 8.05701i) q^{98} +(-11.6576 + 4.24301i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q+O(q^{10}) $ 48 * q	$ 48 q - 12 q^{11} + 30 q^{14} + 30 q^{19} - 36 q^{21} - 18 q^{26} + 24 q^{29} + 18 q^{31} + 18 q^{34} - 132 q^{39} + 36 q^{41} - 6 q^{46} + 54 q^{49} - 6 q^{51} - 54 q^{54} - 12 q^{56} - 72 q^{59} + 24 q^{61} + 24 q^{64} + 96 q^{66} - 42 q^{69} - 78 q^{71} - 36 q^{74} + 12 q^{76} + 84 q^{79} - 72 q^{81} - 18 q^{84} - 78 q^{86} + 72 q^{89} + 24 q^{91} - 24 q^{94} + 12 q^{96} - 102 q^{99}+O(q^{100}) $ 48 * q - 12 * q^11 + 30 * q^14 + 30 * q^19 - 36 * q^21 - 18 * q^26 + 24 * q^29 + 18 * q^31 + 18 * q^34 - 132 * q^39 + 36 * q^41 - 6 * q^46 + 54 * q^49 - 6 * q^51 - 54 * q^54 - 12 * q^56 - 72 * q^59 + 24 * q^61 + 24 * q^64 + 96 * q^66 - 42 * q^69 - 78 * q^71 - 36 * q^74 + 12 * q^76 + 84 * q^79 - 72 * q^81 - 18 * q^84 - 78 * q^86 + 72 * q^89 + 24 * q^91 - 24 * q^94 + 12 * q^96 - 102 * 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 $

$2$	−0.984808	+	0.173648i	−0.696364	+	0.122788i
$2$	−0.984808	+	0.173648i	−0.696364	+	0.122788i
$3$	−0.536848	−	0.639791i	−0.309949	−	0.369383i	0.588472	−	0.808518i	$-0.299730\pi$
$3$	−0.536848	−	0.639791i	−0.309949	−	0.369383i	−0.898421	+	0.439134i	$0.855285\pi$
$4$	0.939693	−	0.342020i	0.469846	−	0.171010i
$5$		0			0
$5$		0			0
$6$	0.639791	+	0.536848i	0.261194	+	0.219167i
$7$	−3.62467	−	2.09271i	−1.37000	−	0.790969i	−0.379071	−	0.925368i	$-0.623756\pi$
$7$	−3.62467	−	2.09271i	−1.37000	−	0.790969i	−0.990927	+	0.134399i	$0.957090\pi$
$8$	−0.866025	+	0.500000i	−0.306186	+	0.176777i
$9$	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	$-0.468439\pi$
$12$	−0.723294	−	0.417594i	−0.208797	−	0.120549i
$13$	−2.52674	+	3.01125i	−0.700791	+	0.835171i	−0.992616	−	0.121301i	$-0.961293\pi$
$13$	−2.52674	+	3.01125i	−0.700791	+	0.835171i	0.291824	+	0.956472i	$0.405738\pi$
$14$	3.93300	+	1.43150i	1.05114	+	0.382583i
$15$		0			0
$16$	0.766044	−	0.642788i	0.191511	−	0.160697i
$17$	2.10829	−	0.371748i	0.511335	−	0.0901621i	0.0879731	−	0.996123i	$-0.471961\pi$
$17$	2.10829	−	0.371748i	0.511335	−	0.0901621i	0.423362	+	0.905961i	$0.360850\pi$
$18$			2.30246i			0.542695i
$19$	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
$22$	3.46336	+	4.12747i	0.738391	+	0.879980i
$23$	0.976988	+	2.68425i	0.203716	+	0.559705i	0.998911	−	0.0466481i	$-0.0148540\pi$
$23$	0.976988	+	2.68425i	0.203716	+	0.559705i	−0.795195	+	0.606353i	$0.792632\pi$
$24$	0.784820	+	0.285651i	0.160201	+	0.0583083i
$25$		0			0
$26$	1.96545	−	3.40427i	0.385457	−	0.667632i
$27$	−3.83524	+	2.21428i	−0.738092	+	0.426137i
$28$	−4.12183	−	0.726789i	−0.778952	−	0.137350i
$29$	−1.34929	+	7.65218i	−0.250556	+	1.42097i	0.556671	+	0.830733i	$0.312078\pi$
$29$	−1.34929	+	7.65218i	−0.250556	+	1.42097i	−0.807227	+	0.590241i	$0.799033\pi$
$30$		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	$0.994491\pi$
$32$	−0.642788	+	0.766044i	−0.113630	+	0.135419i
$33$	−1.53910	+	4.22863i	−0.267922	+	0.736111i
$34$	−2.01170	+	0.732201i	−0.345004	+	0.125571i
$35$		0			0
$36$	−0.399818	−	2.26748i	−0.0666364	−	0.377914i
$37$		−	1.84763i		−	0.303748i	−0.988400	−	0.151874i	$-0.951469\pi$
$37$		−	1.84763i		−	0.303748i	0.988400	−	0.151874i	$-0.0485308\pi$
$38$	−3.44353	−	2.67247i	−0.558615	−	0.433532i
$39$	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	$0.119752\pi$
$42$	−1.19557	−	3.28479i	−0.184480	−	0.506855i
$43$	4.31289	−	11.8496i	0.657710	−	1.80704i	0.0706461	−	0.997501i	$-0.477494\pi$
$43$	4.31289	−	11.8496i	0.657710	−	1.80704i	0.587063	−	0.809541i	$-0.300284\pi$
$44$	−4.12747	−	3.46336i	−0.622240	−	0.522121i
$45$		0			0
$46$	−1.42826	−	2.47382i	−0.210586	−	0.364745i
$47$	−4.31400	−	0.760675i	−0.629262	−	0.110956i	−0.150083	−	0.988673i	$-0.547954\pi$
$47$	−4.31400	−	0.760675i	−0.629262	−	0.110956i	−0.479178	+	0.877718i	$0.659065\pi$
$48$	−0.822499	−	0.145029i	−0.118718	−	0.0209331i
$49$	5.25884	+	9.10858i	0.751263	+	1.30123i
$50$		0			0
$51$	−1.36967	−	1.14929i	−0.191792	−	0.160933i
$52$	−1.34445	+	3.69385i	−0.186442	+	0.512244i
$53$	4.44050	+	12.2002i	0.609949	+	1.67582i	0.730330	+	0.683094i	$0.239366\pi$
$53$	4.44050	+	12.2002i	0.609949	+	1.67582i	−0.120381	+	0.992728i	$0.538412\pi$
$54$	3.39247	−	2.84662i	0.461656	−	0.387376i
$55$		0			0
$56$	4.18541			0.559299
$57$	0.494982	−	3.60669i	0.0655620	−	0.477718i
$58$		−	7.77023i		−	1.02028i
$59$	1.36789	+	7.75770i	0.178084	+	1.00997i	0.934523	+	0.355902i	$0.115826\pi$
$59$	1.36789	+	7.75770i	0.178084	+	1.00997i	−0.756439	+	0.654065i	$0.773062\pi$
$60$		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	$0.636522\pi$
$62$	1.96109	−	5.38804i	0.249058	−	0.684282i
$63$	−6.19439	+	7.38218i	−0.780419	+	0.930068i
$64$	0.500000	−	0.866025i	0.0625000	−	0.108253i
$65$		0			0
$66$	0.781420	−	4.43165i	0.0961861	−	0.545499i
$67$	−10.3287	−	1.82123i	−1.26185	−	0.222498i	−0.497593	−	0.867411i	$-0.665783\pi$
$67$	−10.3287	−	1.82123i	−1.26185	−	0.222498i	−0.764256	+	0.644913i	$0.776894\pi$
$68$	1.85400	−	1.07041i	0.224830	−	0.129806i
$69$	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	$0.906239\pi$
$72$	0.787488	+	2.16361i	0.0928064	+	0.254983i
$73$	2.16499	+	2.58013i	0.253393	+	0.301982i	0.877713	−	0.479187i	$-0.159068\pi$
$73$	2.16499	+	2.58013i	0.253393	+	0.301982i	−0.624320	+	0.781169i	$0.714624\pi$
$74$	0.320837	+	1.81956i	0.0372966	+	0.211519i
$75$		0			0
$76$	3.85529	+	2.03391i	0.442232	+	0.233305i
$77$			22.5511i			2.56994i
$78$	−3.23317	+	0.570095i	−0.366084	+	0.0645505i
$79$	3.96546	−	3.32742i	0.446149	−	0.374364i	−0.391855	−	0.920027i	$-0.628167\pi$
$79$	3.96546	−	3.32742i	0.446149	−	0.374364i	0.838005	+	0.545663i	$0.183722\pi$
$80$		0			0
$81$	−3.01521	−	1.09745i	−0.335023	−	0.121938i
$82$	−3.92083	+	4.67266i	−0.432983	+	0.516009i
$83$	7.56326	+	4.36665i	0.830175	+	0.479302i	0.853913	−	0.520416i	$-0.174223\pi$
$83$	7.56326	+	4.36665i	0.830175	+	0.479302i	−0.0237373	+	0.999718i	$0.507557\pi$
$84$	1.74780	+	3.02728i	0.190701	+	0.330304i
$85$		0			0
$86$	−2.18971	+	12.4185i	−0.236123	+	1.33912i
$87$	5.62016	−	3.24480i	0.602544	−	0.347879i
$88$	4.66617	+	2.69402i	0.497416	+	0.287183i
$89$	2.52982	+	2.12277i	0.268160	+	0.225013i	0.766945	−	0.641713i	$-0.221776\pi$
$89$	2.52982	+	2.12277i	0.268160	+	0.225013i	−0.498785	+	0.866726i	$0.666220\pi$
$90$		0			0
$91$	15.4603	−	5.62708i	1.62068	−	0.589878i
$92$	1.83614	+	2.18822i	0.191430	+	0.228138i
$93$	4.71607	−	0.831571i	0.489034	−	0.0862299i
$94$	4.38055			0.451819
$95$		0			0
$96$	0.835188			0.0852410
$97$	0.851757	−	0.150188i	0.0864828	−	0.0152492i	−0.130239	−	0.991483i	$-0.541575\pi$
$97$	0.851757	−	0.150188i	0.0864828	−	0.0152492i	0.216722	+	0.976233i	$0.430463\pi$
$98$	−6.76064	−	8.05701i	−0.682928	−	0.813881i
$99$	−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	$0.659210\pi$
$102$	1.54844	+	0.893989i	0.153318	+	0.0885181i
$103$	−7.33309	+	4.23376i	−0.722551	+	0.417165i	−0.815691	−	0.578488i	$-0.803643\pi$
$103$	−7.33309	+	4.23376i	−0.722551	+	0.417165i	0.0931401	+	0.995653i	$0.470310\pi$
$104$	0.682595	−	3.87119i	0.0669340	−	0.379601i
$105$		0			0
$106$	−6.49157	−	11.2437i	−0.630517	−	1.09209i
$107$	−2.46307	−	1.42206i	−0.238114	−	0.137475i	0.376196	−	0.926540i	$-0.377232\pi$
$107$	−2.46307	−	1.42206i	−0.238114	−	0.137475i	−0.614310	+	0.789065i	$0.710565\pi$
$108$	−2.84662	+	3.39247i	−0.273916	+	0.326440i
$109$	−11.2867	−	4.10804i	−1.08107	−	0.393479i	−0.260767	−	0.965402i	$-0.583975\pi$
$109$	−11.2867	−	4.10804i	−1.08107	−	0.393479i	−0.820307	+	0.571923i	$0.806198\pi$
$110$		0			0
$111$	−1.18210	+	0.991896i	−0.112200	+	0.0941466i
$112$	−4.12183	+	0.726789i	−0.389476	+	0.0686751i
$113$		−	5.10799i		−	0.480519i	−0.970709	−	0.240260i	$-0.922767\pi$
$113$		−	5.10799i		−	0.480519i	0.970709	−	0.240260i	$-0.0772326\pi$
$114$	0.138833	+	3.63785i	0.0130029	+	0.340716i
$115$		0			0
$116$	1.34929	+	7.65218i	0.125278	+	0.710487i
$117$	5.81772	+	6.93329i	0.537848	+	0.640983i
$118$	−2.69422	−	7.40232i	−0.248023	−	0.681438i
$119$	−8.41982	−	3.06456i	−0.771843	−	0.280928i
$120$		0			0
$121$	−9.01544	+	15.6152i	−0.819586	+	1.41956i
$122$	9.49417	−	5.48146i	0.859562	−	0.496268i
$123$	−5.01702	−	0.884637i	−0.452370	−	0.0797650i
$124$	−0.995670	+	5.64672i	−0.0894138	+	0.507091i
$125$		0			0
$126$	4.81838	−	8.34567i	0.429255	−	0.743492i
$127$	7.08205	−	8.44006i	0.628430	−	0.748934i	−0.354065	−	0.935221i	$-0.615201\pi$
$127$	7.08205	−	8.44006i	0.628430	−	0.748934i	0.982495	+	0.186287i	$0.0596453\pi$
$128$	−0.342020	+	0.939693i	−0.0302306	+	0.0830579i
$129$	−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	$0.574456\pi$
$132$			4.50002i			0.391676i
$133$	−3.85087	−	17.8327i	−0.333912	−	1.54630i
$134$	10.4880			0.906027
$135$		0			0
$136$	−1.63996	+	1.37609i	−0.140625	+	0.117998i
$137$	1.30670	+	3.59013i	0.111639	+	0.306725i	0.982913	−	0.184072i	$-0.0589279\pi$
$137$	1.30670	+	3.59013i	0.111639	+	0.306725i	−0.871274	+	0.490797i	$0.836706\pi$
$138$	−0.815968	+	2.24185i	−0.0694598	+	0.190839i
$139$	−11.1485	−	9.35471i	−0.945605	−	0.793457i	0.0329472	−	0.999457i	$-0.489511\pi$
$139$	−11.1485	−	9.35471i	−0.945605	−	0.793457i	−0.978552	+	0.206001i	$0.933955\pi$
$140$		0			0
$141$	1.82929	+	3.16842i	0.154054	+	0.266829i
$142$	13.2758	+	2.34088i	1.11408	+	0.196442i
$143$	20.8581	+	3.67784i	1.74424	+	0.307557i
$144$	−1.15123	−	1.99399i	−0.0959359	−	0.166166i
$145$		0			0
$146$	−2.58013	−	2.16499i	−0.213533	−	0.179176i
$147$	3.00439	−	8.25449i	0.247798	−	0.680819i
$148$	−0.631926	−	1.73620i	−0.0519440	−	0.142715i
$149$	−9.12001	+	7.65259i	−0.747140	+	0.626925i	−0.934745	−	0.355320i	$-0.884372\pi$
$149$	−9.12001	+	7.65259i	−0.747140	+	0.626925i	0.187605	+	0.982245i	$0.439928\pi$
$150$		0			0
$151$	−5.21314			−0.424239			−0.212120	−	0.977244i	$-0.568037\pi$
$151$	−5.21314			−0.424239			−0.212120	+	0.977244i	$0.568037\pi$
$152$	−4.14990	−	1.33354i	−0.336601	−	0.108165i
$153$		−	4.92914i		−	0.398497i
$154$	−3.91596	−	22.2085i	−0.315557	−	1.78961i
$155$		0			0
$156$	3.08505	−	1.12287i	0.247002	−	0.0899014i
$157$	1.39754	−	3.83971i	0.111536	−	0.306442i	−0.871349	−	0.490664i	$-0.836754\pi$
$157$	1.39754	−	3.83971i	0.111536	−	0.306442i	0.982885	+	0.184222i	$0.0589765\pi$
$158$	−3.32742	+	3.96546i	−0.264715	+	0.315475i
$159$	5.42168	−	9.39063i	0.429967	−	0.744725i
$160$		0			0
$161$	2.07609	−	11.7741i	0.163619	−	0.927928i
$162$	3.15997	+	0.557188i	0.248270	+	0.0437768i
$163$	−4.17632	+	2.41120i	−0.327115	+	0.188860i	−0.654559	−	0.756011i	$-0.727146\pi$
$163$	−4.17632	+	2.41120i	−0.327115	+	0.188860i	0.327445	+	0.944870i	$0.393813\pi$
$164$	3.04987	−	5.28252i	0.238154	−	0.412496i
$165$		0			0
$166$	−8.20662	−	2.98696i	−0.636957	−	0.231833i
$167$	1.76421	+	4.84712i	0.136519	+	0.375082i	0.989047	−	0.147599i	$-0.0471544\pi$
$167$	1.76421	+	4.84712i	0.136519	+	0.375082i	−0.852529	+	0.522680i	$0.824932\pi$
$168$	−2.24693	−	2.67779i	−0.173355	−	0.206596i
$169$	−0.425793	−	2.41479i	−0.0327533	−	0.185753i
$170$		0			0
$171$	8.49391	−	5.34591i	0.649546	−	0.408812i
$172$		−	12.6100i		−	0.961507i
$173$	−8.23908	+	1.45277i	−0.626406	+	0.110452i	−0.477835	−	0.878450i	$-0.658578\pi$
$173$	−8.23908	+	1.45277i	−0.626406	+	0.110452i	−0.148571	+	0.988902i	$0.547467\pi$
$174$	−4.97132	+	4.17143i	−0.376875	+	0.316236i
$175$		0			0
$176$	−5.06309	−	1.84282i	−0.381645	−	0.138907i
$177$	4.22896	−	5.03987i	0.317868	−	0.378820i
$178$	−2.86000	−	1.65122i	−0.214366	−	0.123764i
$179$	−2.56041	−	4.43476i	−0.191374	−	0.331469i	0.754332	−	0.656493i	$-0.227961\pi$
$179$	−2.56041	−	4.43476i	−0.191374	−	0.331469i	−0.945706	+	0.325024i	$0.894628\pi$
$180$		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	$0.0778107\pi$
$182$	−14.2483	+	8.22624i	−1.05615	+	0.609769i
$183$	7.92942	+	4.57805i	0.586159	+	0.338419i
$184$	−2.18822	−	1.83614i	−0.161318	−	0.135362i
$185$		0			0
$186$	−4.50003	+	1.63788i	−0.329958	+	0.120095i
$187$	−7.41440	−	8.83614i	−0.542195	−	0.646162i
$188$	−4.31400	+	0.760675i	−0.314631	+	0.0554779i
$189$	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	$0.300368\pi$
$192$	−0.822499	+	0.145029i	−0.0593588	+	0.0104666i
$193$	3.43474	+	4.09336i	0.247238	+	0.294647i	0.875364	−	0.483465i	$-0.160622\pi$
$193$	3.43474	+	4.09336i	0.247238	+	0.294647i	−0.628126	+	0.778112i	$0.716178\pi$
$194$	−0.812737	+	0.295812i	−0.0583511	+	0.0212381i
$195$		0			0
$196$	8.05701	+	6.76064i	0.575501	+	0.482903i
$197$	−12.1054	−	6.98903i	−0.862471	−	0.497948i	0.00236780	−	0.999997i	$-0.499246\pi$
$197$	−12.1054	−	6.98903i	−0.862471	−	0.497948i	−0.864839	+	0.502049i	$0.832580\pi$
$198$	10.7437	−	6.20287i	0.763520	−	0.440819i
$199$	1.93501	−	10.9740i	0.137169	−	0.777923i	−0.836156	−	0.548492i	$-0.815202\pi$
$199$	1.93501	−	10.9740i	0.137169	−	0.777923i	0.973325	−	0.229432i	$-0.0736867\pi$
$200$		0			0
$201$	4.37973	+	7.58592i	0.308922	+	0.535069i
$202$	−3.42339	−	1.97649i	−0.240869	−	0.139066i
$203$	20.9045	−	24.9130i	1.46721	−	1.74855i
$204$	−1.68015	−	0.611525i	−0.117634	−	0.0428153i
$205$		0			0
$206$	6.48650	−	5.44282i	0.451936	−	0.379219i
$207$	6.47711	−	1.14209i	0.450190	−	0.0793807i
$208$			3.93091i			0.272559i
$209$	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	$-0.249144\pi$
$212$	8.34541	+	9.94567i	0.573165	+	0.683071i
$213$	3.85074	+	10.5798i	0.263848	+	0.724917i
$214$	2.67259	+	0.972743i	0.182694	+	0.0664954i
$215$		0			0
$216$	2.21428	−	3.83524i	0.150662	−	0.260955i
$217$	20.7833	−	11.9992i	1.41086	−	0.814561i
$218$	11.8286	+	2.08571i	0.801135	+	0.141262i
$219$	0.488475	−	2.77028i	0.0330081	−	0.187198i
$220$		0			0
$221$	−4.20767	+	7.28789i	−0.283038	+	0.490237i
$222$	0.991896	−	1.18210i	0.0665717	−	0.0793370i
$223$	−6.62909	+	18.2133i	−0.443917	+	1.21965i	0.492979	+	0.870041i	$0.335908\pi$
$223$	−6.62909	+	18.2133i	−0.443917	+	1.21965i	−0.936895	+	0.349610i	$0.886314\pi$
$224$	3.93300	−	1.43150i	0.262785	−	0.0956458i
$225$		0			0
$226$	0.886993	+	5.03039i	0.0590019	+	0.334616i
$227$			2.70146i			0.179302i	0.995973	+	0.0896512i	$0.0285752\pi$
$227$			2.70146i			0.179302i	−0.995973	+	0.0896512i	$0.971425\pi$
$228$	−0.768430	−	3.55847i	−0.0508905	−	0.235666i
$229$	−1.21719			−0.0804343			−0.0402172	−	0.999191i	$-0.512805\pi$
$229$	−1.21719			−0.0804343			−0.0402172	+	0.999191i	$0.512805\pi$
$230$		0			0
$231$	14.4280	−	12.1065i	0.949294	−	0.796552i
$232$	−2.65757	−	7.30163i	−0.174478	−	0.479375i
$233$	2.76503	−	7.59685i	0.181143	−	0.497686i	−0.815574	−	0.578653i	$-0.803579\pi$
$233$	2.76503	−	7.59685i	0.181143	−	0.497686i	0.996717	+	0.0809667i	$0.0258007\pi$
$234$	−6.93329	−	5.81772i	−0.453243	−	0.380316i
$235$		0			0
$236$	3.93869	+	6.82201i	0.256387	+	0.444075i
$237$	−4.25770	−	0.750747i	−0.276567	−	0.0487663i
$238$	8.82405	+	1.55592i	0.571979	+	0.100855i
$239$	−3.20276	−	5.54735i	−0.207170	−	0.358828i	0.743652	−	0.668567i	$-0.233092\pi$
$239$	−3.20276	−	5.54735i	−0.207170	−	0.358828i	−0.950822	+	0.309738i	$0.899759\pi$
$240$		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	$-0.590946\pi$
$242$	6.16693	−	16.9435i	0.396425	−	1.08917i
$243$	5.46053	+	15.0027i	0.350293	+	0.962423i
$244$	−8.39809	+	7.04683i	−0.537633	+	0.451127i
$245$		0			0
$246$	5.09442			0.324808
$247$	−17.1220	+	0.653433i	−1.08944	+	0.0415769i
$248$		−	5.73383i		−	0.364099i
$249$	−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	$0.186020\pi$
$252$	−3.29596	+	9.05559i	−0.207626	+	0.570448i
$253$	9.89316	−	11.7902i	0.621978	−	0.741244i
$254$	−5.50886	+	9.54162i	−0.345657	+	0.598695i
$255$		0			0
$256$	0.173648	−	0.984808i	0.0108530	−	0.0615505i
$257$	15.1146	+	2.66512i	0.942825	+	0.166246i	0.623874	−	0.781525i	$-0.285558\pi$
$257$	15.1146	+	2.66512i	0.942825	+	0.166246i	0.318952	+	0.947771i	$0.396669\pi$
$258$	9.12077	−	5.26588i	0.567834	−	0.327839i
$259$	−3.86654	+	6.69705i	−0.240255	+	0.416134i
$260$		0			0
$261$	16.8117	+	6.11896i	1.04062	+	0.378754i
$262$	−7.18517	−	19.7411i	−0.443901	−	1.21961i
$263$	−5.97663	−	7.12267i	−0.368535	−	0.439202i	0.549626	−	0.835411i	$-0.314770\pi$
$263$	−5.97663	−	7.12267i	−0.368535	−	0.439202i	−0.918161	+	0.396208i	$0.870326\pi$
$264$	−0.781420	−	4.43165i	−0.0480931	−	0.272749i
$265$		0			0
$266$	6.88899	+	16.8931i	0.422391	+	1.03578i
$267$		−	2.75816i		−	0.168797i
$268$	−10.3287	+	1.82123i	−0.630925	+	0.111249i
$269$	−7.43644	+	6.23991i	−0.453408	+	0.380454i	−0.840699	−	0.541503i	$-0.817855\pi$
$269$	−7.43644	+	6.23991i	−0.453408	+	0.380454i	0.387291	+	0.921958i	$0.373411\pi$
$270$		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	$0.769787\pi$
$272$	1.37609	−	1.63996i	0.0834375	−	0.0994370i
$273$	−11.9000	−	6.87045i	−0.720219	−	0.415819i
$274$	−1.91027	−	3.30868i	−0.115403	−	0.199885i
$275$		0			0
$276$	0.414278	−	2.34949i	0.0249366	−	0.141422i
$277$	25.5809	−	14.7692i	1.53701	−	0.887392i	0.537997	−	0.842947i	$-0.319181\pi$
$277$	25.5809	−	14.7692i	1.53701	−	0.887392i	0.999012	−	0.0444457i	$-0.0141522\pi$
$278$	12.6036	+	7.27668i	0.755912	+	0.436426i
$279$	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	$0.368619\pi$
$282$	−2.35169	−	2.80264i	−0.140041	−	0.166895i
$283$	−18.8466	+	3.32317i	−1.12032	+	0.197542i	−0.702979	−	0.711210i	$-0.748147\pi$
$283$	−18.8466	+	3.32317i	−1.12032	+	0.197542i	−0.417336	+	0.908752i	$0.637036\pi$
$284$	−13.4806			−0.799925
$285$		0			0
$286$	−21.1799			−1.25239
$287$	−25.1420	+	4.43322i	−1.48409	+	0.261685i
$288$	1.47999	+	1.76379i	0.0872095	+	0.103932i
$289$	−11.6681	+	4.24684i	−0.686359	+	0.249814i
$290$		0			0
$291$	−0.553353	−	0.464318i	−0.0324381	−	0.0272188i
$292$	2.91688	+	1.68406i	0.170698	+	0.0985523i
$293$	16.2018	−	9.35413i	0.946521	−	0.546474i	0.0545223	−	0.998513i	$-0.482636\pi$
$293$	16.2018	−	9.35413i	0.946521	−	0.546474i	0.891998	+	0.452039i	$0.149303\pi$
$294$	−1.52537	+	8.65079i	−0.0889612	+	0.504524i
$295$		0			0
$296$	0.923814	+	1.60009i	0.0536956	+	0.0930035i
$297$	20.6644	+	11.9306i	1.19907	+	0.692283i
$298$	7.65259	−	9.12001i	0.443303	−	0.528308i
$299$	−10.5515	−	3.84045i	−0.610212	−	0.222099i
$300$		0			0
$301$	−40.4305	+	33.9252i	−2.33038	+	1.95542i
$302$	5.13394	−	0.905252i	0.295425	−	0.0520914i
$303$		−	3.30149i		−	0.189666i
$304$	4.31842	+	0.592660i	0.247678	+	0.0339914i
$305$		0			0
$306$	0.855935	+	4.85425i	0.0489306	+	0.277499i
$307$	−9.84929	−	11.7379i	−0.562129	−	0.669919i	0.407867	−	0.913041i	$-0.366273\pi$
$307$	−9.84929	−	11.7379i	−0.562129	−	0.669919i	−0.969996	+	0.243123i	$0.921828\pi$
$308$	7.71294	+	21.1911i	0.439486	+	1.20748i
$309$	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	$0.983540\pi$
$312$	−2.84320	+	1.64152i	−0.160965	+	0.0929329i
$313$	−26.1407	−	4.60930i	−1.47756	−	0.260533i	−0.623956	−	0.781460i	$-0.714476\pi$
$313$	−26.1407	−	4.60930i	−1.47756	−	0.260533i	−0.853602	+	0.520926i	$0.825587\pi$
$314$	−0.709549	+	4.02405i	−0.0400422	+	0.227090i
$315$		0			0
$316$	2.58827	−	4.48301i	0.145602	−	0.252189i
$317$	5.77354	−	6.88064i	0.324274	−	0.386455i	−0.579137	−	0.815230i	$-0.696610\pi$
$317$	5.77354	−	6.88064i	0.324274	−	0.386455i	0.903411	+	0.428775i	$0.141055\pi$
$318$	−3.70865	+	10.1894i	−0.207971	+	0.571395i
$319$	39.3414	−	14.3191i	2.20269	−	0.801715i
$320$		0			0
$321$	0.412478	+	2.33928i	0.0230223	+	0.130566i
$322$			11.9557i			0.666266i
$323$	7.37195	+	5.72125i	0.410186	+	0.318339i
$324$	−3.20871			−0.178262
$325$		0			0
$326$	3.69418	−	3.09978i	0.204601	−	0.171681i
$327$	3.43098	+	9.42655i	0.189734	+	0.521289i
$328$	−2.08623	+	5.73187i	−0.115193	+	0.316490i
$329$	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	$0.595950\pi$
$332$	8.60062	+	1.51652i	0.472020	+	0.0832299i
$333$	−4.18946	−	0.738715i	−0.229581	−	0.0404814i
$334$	−2.57910	−	4.46713i	−0.141122	−	0.244431i
$335$		0			0
$336$	2.67779	+	2.24693i	0.146085	+	0.122580i
$337$	−9.75791	+	26.8096i	−0.531547	+	1.46041i	0.325682	+	0.945479i	$0.394406\pi$
$337$	−9.75791	+	26.8096i	−0.531547	+	1.46041i	−0.857229	+	0.514935i	$0.827816\pi$
$338$	0.838648	+	2.30417i	0.0456164	+	0.125330i
$339$	−3.26805	+	2.74222i	−0.177496	+	0.148937i
$340$		0			0
$341$	30.8941			1.67301
$342$	−7.43656	+	6.73964i	−0.402123	+	0.364438i
$343$		−	14.7230i		−	0.794966i
$344$	2.18971	+	12.4185i	0.118061	+	0.669559i
$345$		0			0
$346$	7.86164	−	2.86140i	0.422644	−	0.153830i
$347$	−1.45792	+	4.00560i	−0.0782653	+	0.215032i	−0.972654	−	0.232258i	$-0.925389\pi$
$347$	−1.45792	+	4.00560i	−0.0782653	+	0.215032i	0.894389	+	0.447290i	$0.147611\pi$
$348$	4.17143	−	4.97132i	0.223612	−	0.266491i
$349$	5.74459	−	9.94993i	0.307501	−	0.532608i	−0.670314	−	0.742078i	$-0.733841\pi$
$349$	5.74459	−	9.94993i	0.307501	−	0.532608i	0.977815	+	0.209470i	$0.0671739\pi$
$350$		0			0
$351$	3.02291	−	17.1438i	0.161351	−	0.915066i
$352$	5.30618	+	0.935622i	0.282820	+	0.0498688i
$353$	−22.3419	+	12.8991i	−1.18914	+	0.686549i	−0.958111	−	0.286399i	$-0.907542\pi$
$353$	−22.3419	+	12.8991i	−1.18914	+	0.686549i	−0.231027	+	0.972947i	$0.574208\pi$
$354$	−3.28954	+	5.69766i	−0.174837	+	0.302827i
$355$		0			0
$356$	3.10328	+	1.12950i	0.164474	+	0.0598635i
$357$	2.55948	+	7.03213i	0.135462	+	0.372180i
$358$	3.29160	+	3.92277i	0.173966	+	0.207325i
$359$	−4.09930	−	23.2483i	−0.216353	−	1.22700i	−0.878544	−	0.477662i	$-0.841485\pi$
$359$	−4.09930	−	23.2483i	−0.216353	−	1.22700i	0.662191	−	0.749335i	$-0.269627\pi$
$360$		0			0
$361$	−1.86362	+	18.9084i	−0.0980852	+	0.995178i
$362$		−	1.87973i		−	0.0987963i
$363$	14.8304	−	2.61500i	0.778394	−	0.137252i
$364$	12.6033	−	10.5754i	0.660594	−	0.554304i
$365$		0			0
$366$	−8.60392	−	3.13157i	−0.449734	−	0.163690i
$367$	−13.1377	+	15.6569i	−0.685782	+	0.817284i	−0.990839	−	0.135051i	$-0.956880\pi$
$367$	−13.1377	+	15.6569i	−0.685782	+	0.817284i	0.305056	+	0.952334i	$0.401325\pi$
$368$	2.47382	+	1.42826i	0.128957	+	0.0744532i
$369$	−7.02220	−	12.1628i	−0.365561	−	0.633170i
$370$		0			0
$371$	9.43602	−	53.5143i	0.489894	−	2.77832i
$372$	4.14725	−	2.39441i	0.215025	−	0.124145i
$373$	−4.41029	−	2.54628i	−0.228356	−	0.131841i	0.381457	−	0.924386i	$-0.375422\pi$
$373$	−4.41029	−	2.54628i	−0.228356	−	0.131841i	−0.609813	+	0.792545i	$0.708756\pi$
$374$	8.83614	+	7.41440i	0.456906	+	0.383389i
$375$		0			0
$376$	4.11637	−	1.49824i	0.212286	−	0.0772657i
$377$	−19.6333	−	23.3981i	−1.01117	−	1.20506i
$378$	−18.2537	+	3.21862i	−0.938870	+	0.165548i
$379$	−8.24487			−0.423511			−0.211755	−	0.977323i	$-0.567918\pi$
$379$	−8.24487			−0.423511			−0.211755	+	0.977323i	$0.567918\pi$
$380$		0			0
$381$	−9.20186			−0.471426
$382$	−15.9744	+	2.81672i	−0.817322	+	0.144116i
$383$	−0.904546	−	1.07800i	−0.0462201	−	0.0550830i	0.742439	−	0.669914i	$-0.233669\pi$
$383$	−0.904546	−	1.07800i	−0.0462201	−	0.0550830i	−0.788659	+	0.614831i	$0.789224\pi$
$384$	0.784820	−	0.285651i	0.0400502	−	0.0145771i
$385$		0			0
$386$	−4.09336	−	3.43474i	−0.208347	−	0.174824i
$387$	−25.1443	−	14.5171i	−1.27816	−	0.737944i
$388$	0.749022	−	0.432448i	0.0380258	−	0.0219542i
$389$	−6.81569	+	38.6537i	−0.345569	+	1.95982i	−0.0746916	+	0.997207i	$0.523797\pi$
$389$	−6.81569	+	38.6537i	−0.345569	+	1.95982i	−0.270878	+	0.962614i	$0.587314\pi$
$390$		0			0
$391$	3.05764	+	5.29598i	0.154631	+	0.267829i
$392$	−9.10858	−	5.25884i	−0.460053	−	0.265612i
$393$	11.2781	−	13.4407i	0.568906	−	0.677996i
$394$	13.1351	+	4.78078i	0.661736	+	0.240852i
$395$		0			0
$396$	−9.50335	+	7.97425i	−0.477561	+	0.400721i
$397$	5.75169	−	1.01418i	0.288669	−	0.0509001i	−0.0274386	−	0.999623i	$-0.508735\pi$
$397$	5.75169	−	1.01418i	0.288669	−	0.0509001i	0.316107	+	0.948723i	$0.397624\pi$
$398$			11.1433i			0.558561i
$399$	−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	$-0.205467\pi$
$402$	−5.63047	−	6.71014i	−0.280822	−	0.334671i
$403$	−7.70885	−	21.1799i	−0.384005	−	1.05505i
$404$	3.71460	+	1.35200i	0.184808	+	0.0672646i
$405$		0			0
$406$	−16.2608	+	28.1645i	−0.807010	+	1.39778i
$407$	−8.62135	+	4.97754i	−0.427344	+	0.246727i
$408$	1.76082	+	0.310479i	0.0871734	+	0.0153710i
$409$	−2.08439	+	11.8212i	−0.103066	+	0.584518i	0.888909	+	0.458085i	$0.151464\pi$
$409$	−2.08439	+	11.8212i	−0.103066	+	0.584518i	−0.991975	+	0.126434i	$0.959647\pi$
$410$		0			0
$411$	1.59543	−	2.76337i	0.0786968	−	0.136307i
$412$	−5.44282	+	6.48650i	−0.268148	+	0.319567i
$413$	11.2764	−	30.9817i	0.554877	−	1.52451i
$414$	−6.18039	+	2.24948i	−0.303749	+	0.110556i
$415$		0			0
$416$	−0.682595	−	3.87119i	−0.0334670	−	0.189801i
$417$			12.1548i			0.595222i
$418$	−3.19327	+	23.2678i	−0.156188	+	1.13806i
$419$	22.3338			1.09108			0.545539	−	0.838086i	$-0.316325\pi$
$419$	22.3338			1.09108			0.545539	+	0.838086i	$0.316325\pi$
$420$		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	$0.174470\pi$
$422$	5.67729	+	15.5982i	0.276366	+	0.759310i
$423$	−3.44963	+	9.47779i	−0.167727	+	0.460826i
$424$	−9.94567	−	8.34541i	−0.483004	−	0.405289i
$425$		0			0
$426$	−5.62941	−	9.75042i	−0.272746	−	0.472409i
$427$	45.1873	+	7.96774i	2.18677	+	0.385586i
$428$	−2.80090	−	0.493875i	−0.135387	−	0.0238723i
$429$	−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	$0.788026\pi$
$432$	−1.51465	+	4.16148i	−0.0728738	+	0.200219i
$433$	5.77906	+	15.8778i	0.277724	+	0.763040i	0.997620	+	0.0689576i	$0.0219673\pi$
$433$	5.77906	+	15.8778i	0.277724	+	0.763040i	−0.719896	+	0.694082i	$0.755810\pi$
$434$	−18.3839	+	15.4259i	−0.882455	+	0.740468i
$435$		0			0
$436$	−12.0111			−0.575227
$437$	−5.80989	+	11.0127i	−0.277925	+	0.526809i
$438$			2.81301i			0.134411i
$439$	−3.47186	−	19.6899i	−0.165703	−	0.939749i	−0.948337	−	0.317266i	$-0.897235\pi$
$439$	−3.47186	−	19.6899i	−0.165703	−	0.939749i	0.782634	−	0.622483i	$-0.213876\pi$
$440$		0			0
$441$	22.7561	−	8.28255i	1.08363	−	0.394407i
$442$	2.87821	−	7.90783i	0.136903	−	0.376137i
$443$	−12.9989	+	15.4915i	−0.617598	+	0.736024i	−0.980655	−	0.195742i	$-0.937288\pi$
$443$	−12.9989	+	15.4915i	−0.617598	+	0.736024i	0.363058	+	0.931767i	$0.381733\pi$
$444$	−0.771558	+	1.33638i	−0.0366165	+	0.0634217i
$445$		0			0
$446$	3.36568	−	19.0877i	0.159369	−	0.903829i
$447$	9.79212	+	1.72661i	0.463151	+	0.0816661i
$448$	−3.62467	+	2.09271i	−0.171250	+	0.0988711i
$449$	−9.05817	+	15.6892i	−0.427481	+	0.740420i	−0.996649	−	0.0818023i	$-0.973932\pi$
$449$	−9.05817	+	15.6892i	−0.427481	+	0.740420i	0.569167	+	0.822222i	$0.307266\pi$
$450$		0			0
$451$	−30.8835	−	11.2407i	−1.45425	−	0.529303i
$452$	−1.74704	−	4.79994i	−0.0821736	−	0.225770i
$453$	2.79866	+	3.33532i	0.131493	+	0.156707i
$454$	−0.469104	−	2.66042i	−0.0220161	−	0.124860i
$455$		0			0
$456$	1.37468	+	3.37098i	0.0643752	+	0.157860i
$457$		−	14.5742i		−	0.681750i	−0.940109	−	0.340875i	$-0.889277\pi$
$457$		−	14.5742i		−	0.681750i	0.940109	−	0.340875i	$-0.110723\pi$
$458$	1.19870	−	0.211363i	0.0560116	−	0.00987635i
$459$	−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	$0.735850\pi$
$462$	−12.1065	+	14.4280i	−0.563247	+	0.671252i
$463$	−28.3445	−	16.3647i	−1.31728	−	0.760533i	−0.333991	−	0.942576i	$-0.608396\pi$
$463$	−28.3445	−	16.3647i	−1.31728	−	0.760533i	−0.983291	+	0.182043i	$0.941729\pi$
$464$	3.88511	+	6.72921i	0.180362	+	0.312396i
$465$		0			0
$466$	−1.40384	+	7.96158i	−0.0650317	+	0.368813i
$467$	−12.0173	+	6.93817i	−0.556093	+	0.321060i	−0.751576	−	0.659647i	$-0.770706\pi$
$467$	−12.0173	+	6.93817i	−0.556093	+	0.321060i	0.195483	+	0.980707i	$0.437373\pi$
$468$	7.83819	+	4.52538i	0.362321	+	0.209186i
$469$	33.6268	+	28.2162i	1.55274	+	1.30291i
$470$		0			0
$471$	−3.20688	+	1.16721i	−0.147765	+	0.0537821i
$472$	−5.06348	−	6.03442i	−0.233066	−	0.277757i
$473$	−66.9111	+	11.7982i	−3.07658	+	0.542484i
$474$	4.32338			0.198579
$475$		0			0
$476$	−8.96018			−0.410689
$477$	29.4391	−	5.19090i	1.34792	−	0.237675i
$478$	4.11739	+	4.90692i	0.188325	+	0.224437i
$479$	8.93600	−	3.25244i	0.408296	−	0.148608i	−0.129703	−	0.991553i	$-0.541402\pi$
$479$	8.93600	−	3.25244i	0.408296	−	0.148608i	0.538000	+	0.842945i	$0.319180\pi$
$480$		0			0
$481$	5.56367	+	4.66847i	0.253682	+	0.212864i
$482$	22.3884	+	12.9260i	1.01976	+	0.588762i
$483$	−8.64750	+	4.99264i	−0.393475	+	0.227173i
$484$	−3.13103	+	17.7570i	−0.142320	+	0.807134i
$485$		0			0
$486$	−7.98276	−	13.8266i	−0.362106	−	0.627185i
$487$	−32.7228	−	18.8925i	−1.48281	−	0.856102i	−0.483002	−	0.875619i	$-0.660454\pi$
$487$	−32.7228	−	18.8925i	−1.48281	−	0.856102i	−0.999810	+	0.0195172i	$0.993787\pi$
$488$	7.04683	−	8.39809i	0.318995	−	0.380164i
$489$	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	$0.394323\pi$
$492$	−5.01702	+	0.884637i	−0.226185	+	0.0398825i
$493$			16.6346i			0.749184i
$494$	16.7484	−	3.61670i	0.753545	−	0.162723i
$495$		0			0
$496$	0.995670	+	5.64672i	0.0447069	+	0.253545i
$497$	36.2672	+	43.2216i	1.62681	+	1.93875i
$498$	2.49468	+	6.85406i	0.111789	+	0.307138i
$499$	33.2604	+	12.1058i	1.48894	+	0.541930i	0.953170	−	0.302435i	$-0.0977995\pi$
$499$	33.2604	+	12.1058i	1.48894	+	0.541930i	0.535769	+	0.844364i	$0.320022\pi$
$500$		0			0
$501$	2.15403	−	3.73089i	0.0962351	−	0.166684i
$502$	−16.3288	+	9.42743i	−0.728789	+	0.420767i
$503$	32.8451	+	5.79148i	1.46449	+	0.258229i	0.848363	−	0.529416i	$-0.177589\pi$
$503$	32.8451	+	5.79148i	1.46449	+	0.258229i	0.616129	+	0.787645i	$0.288700\pi$
$504$	1.67340	−	9.49035i	0.0745394	−	0.422734i
$505$		0			0
$506$	−7.69551	+	13.3290i	−0.342107	+	0.592547i
$507$	−1.31637	+	1.56879i	−0.0584623	+	0.0696726i
$508$	3.76828	−	10.3533i	0.167190	−	0.459352i
$509$	−40.4293	+	14.7151i	−1.79200	+	0.652234i	−0.792918	+	0.609328i	$0.791439\pi$
$509$	−40.4293	+	14.7151i	−1.79200	+	0.652234i	−0.999079	+	0.0429055i	$0.986339\pi$
$510$		0			0
$511$	−2.44792	−	13.8828i	−0.108289	−	0.614140i
$512$			1.00000i			0.0441942i
$513$	−18.3780	−	5.90566i	−0.811410	−	0.260741i
$514$	−15.3478			−0.676963
$515$		0			0
$516$	−8.06779	+	6.76968i	−0.355165	+	0.298019i
$517$	8.07255	+	22.1791i	0.355030	+	0.975437i
$518$	2.64487	−	7.26672i	0.116209	−	0.319282i
$519$	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	$0.737528\pi$
$522$	−17.6189	−	3.10668i	−0.771156	−	0.135976i
$523$	−34.6349	−	6.10706i	−1.51448	−	0.267043i	−0.646218	−	0.763153i	$-0.723650\pi$
$523$	−34.6349	−	6.10706i	−1.51448	−	0.267043i	−0.868260	+	0.496110i	$0.834761\pi$
$524$	10.5040	+	18.1935i	0.458870	+	0.794786i
$525$		0			0
$526$	7.12267	+	5.97663i	0.310563	+	0.260593i
$527$	−4.19832	+	11.5348i	−0.182882	+	0.502463i
$528$	1.53910	+	4.22863i	0.0669806	+	0.184028i
$529$	11.3683	−	9.53915i	0.494275	−	0.414746i
$530$		0			0
$531$	18.1374			0.787095
$532$	−9.71779	−	15.4402i	−0.421320	−	0.669419i
$533$			23.9775i			1.03858i
$534$	0.478949	+	2.71626i	0.0207262	+	0.117544i
$535$		0			0
$536$	9.85551	−	3.58711i	0.425693	−	0.154940i
$537$	−1.46277	+	4.01892i	−0.0631230	+	0.173429i
$538$	6.23991	−	7.43644i	0.269022	−	0.320608i
$539$	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	$-0.00279680\pi$
$542$	15.5020	+	2.73342i	0.665869	+	0.117411i
$543$	1.35960	−	0.784963i	0.0583458	−	0.0336860i
$544$	−1.07041	+	1.85400i	−0.0458933	+	0.0794895i
$545$		0			0
$546$	12.9122	+	4.69967i	0.552592	+	0.201127i
$547$	8.38627	+	23.0411i	0.358571	+	0.985166i	0.979526	+	0.201320i	$0.0645229\pi$
$547$	8.38627	+	23.0411i	0.358571	+	0.985166i	−0.620954	+	0.783847i	$0.713255\pi$
$548$	2.45579	+	2.92670i	0.104906	+	0.125022i
$549$	4.38318	+	24.8582i	0.187070	+	1.06092i
$550$		0			0
$551$	−28.6648	+	18.0411i	−1.22116	+	0.768576i
$552$			2.38573i			0.101543i
$553$	−21.3368	+	3.76225i	−0.907333	+	0.159987i
$554$	−22.6277	+	18.9869i	−0.961357	+	0.806674i
$555$		0			0
$556$	−13.6757	−	4.97754i	−0.579978	−	0.211095i
$557$	−10.9051	+	12.9962i	−0.462063	+	0.550666i	−0.945885	−	0.324501i	$-0.894804\pi$
$557$	−10.9051	+	12.9962i	−0.462063	+	0.550666i	0.483822	+	0.875166i	$0.339248\pi$
$558$	−11.4332	−	6.60097i	−0.484006	−	0.279441i
$559$	24.7845	+	42.9280i	1.04827	+	1.81566i
$560$		0			0
$561$	−1.67287	+	9.48733i	−0.0706287	+	0.400555i
$562$	−1.84766	+	1.06675i	−0.0779390	+	0.0449981i
$563$	2.37372	+	1.37047i	0.100040	+	0.0577582i	0.549185	−	0.835701i	$-0.314938\pi$
$563$	2.37372	+	1.37047i	0.100040	+	0.0577582i	−0.449145	+	0.893459i	$0.648271\pi$
$564$	2.80264	+	2.35169i	0.118012	+	0.0990241i
$565$		0			0
$566$	17.9832	−	6.54537i	0.755892	−	0.275122i
$567$	8.63251	+	10.2878i	0.362531	+	0.432048i
$568$	13.2758	−	2.34088i	0.557039	−	0.0982210i
$569$	19.0648			0.799238			0.399619	−	0.916681i	$-0.369143\pi$
$569$	19.0648			0.799238			0.399619	+	0.916681i	$0.369143\pi$
$570$		0			0
$571$	−8.52486			−0.356754			−0.178377	−	0.983962i	$-0.557085\pi$
$571$	−8.52486			−0.356754			−0.178377	+	0.983962i	$0.557085\pi$
$572$	20.8581	−	3.67784i	0.872121	−	0.153778i
$573$	−8.70813	−	10.3779i	−0.363787	−	0.433545i
$574$	23.9903	−	8.73174i	1.00133	−	0.364456i
$575$		0			0
$576$	−1.76379	−	1.47999i	−0.0734912	−	0.0616664i
$577$	−22.3658	−	12.9129i	−0.931099	−	0.537571i	−0.0439404	−	0.999034i	$-0.513991\pi$
$577$	−22.3658	−	12.9129i	−0.931099	−	0.537571i	−0.887159	+	0.461464i	$0.847324\pi$
$578$	10.7534	−	6.20846i	0.447281	−	0.258238i
$579$	0.774962	−	4.39503i	0.0322063	−	0.182651i
$580$		0			0
$581$	−18.2762	−	31.6554i	−0.758226	−	1.31329i
$582$	0.625574	+	0.361175i	0.0259309	+	0.0149712i
$583$	44.9653	−	53.5876i	1.86227	−	2.21937i
$584$	−3.16500	−	1.15197i	−0.130969	−	0.0476687i
$585$		0			0
$586$	−14.3314	+	12.0254i	−0.592023	+	0.496766i
$587$	18.9471	−	3.34088i	0.782030	−	0.137893i	0.231641	−	0.972801i	$-0.425591\pi$
$587$	18.9471	−	3.34088i	0.782030	−	0.137893i	0.550389	+	0.834908i	$0.314479\pi$
$588$		−	8.78424i		−	0.362256i
$589$	−24.4301	+	5.27552i	−1.00662	+	0.217374i
$590$		0			0
$591$	2.02722	+	11.4969i	0.0833888	+	0.472921i
$592$	−1.18763	−	1.41537i	−0.0488114	−	0.0581711i
$593$	4.74367	+	13.0331i	0.194799	+	0.535206i	0.998183	−	0.0602552i	$-0.0191914\pi$
$593$	4.74367	+	13.0331i	0.194799	+	0.535206i	−0.803384	+	0.595462i	$0.796969\pi$
$594$	−22.4222	−	8.16100i	−0.919993	−	0.334850i
$595$		0			0
$596$	−5.95266	+	10.3103i	−0.243831	+	0.422327i
$597$	−8.05984	+	4.65335i	−0.329867	+	0.190449i
$598$	11.0581	+	1.94985i	0.452201	+	0.0797352i
$599$	2.41256	−	13.6823i	0.0985745	−	0.559044i	−0.895019	−	0.446029i	$-0.852838\pi$
$599$	2.41256	−	13.6823i	0.0985745	−	0.559044i	0.993593	−	0.113015i	$-0.0360509\pi$
$600$		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	$0.0428198\pi$
$602$	33.9252	−	40.4305i	1.38269	−	1.64782i
$603$	−8.25919	+	22.6919i	−0.336340	+	0.924087i
$604$	−4.89875	+	1.78300i	−0.199327	+	0.0725491i
$605$		0			0
$606$	0.573297	+	3.25133i	0.0232886	+	0.132076i
$607$		−	19.4066i		−	0.787689i	−0.919177	−	0.393844i	$-0.871145\pi$
$607$		−	19.4066i		−	0.787689i	0.919177	−	0.393844i	$-0.128855\pi$
$608$	−4.35573	+	0.166229i	−0.176648	+	0.00674149i
$609$	−27.1616			−1.10065
$610$		0			0
$611$	13.1909	−	11.0685i	0.533648	−	0.447784i
$612$	−1.68586	−	4.63187i	−0.0681470	−	0.187232i
$613$	−3.50579	+	9.63208i	−0.141598	+	0.389036i	−0.990138	−	0.140094i	$-0.955259\pi$
$613$	−3.50579	+	9.63208i	−0.141598	+	0.389036i	0.848541	+	0.529130i	$0.177482\pi$
$614$	11.7379	+	9.84929i	0.473704	+	0.397485i
$615$		0			0
$616$	−11.2756	−	19.5299i	−0.454306	−	0.786880i
$617$	−25.1911	−	4.44187i	−1.01416	−	0.178823i	−0.358218	−	0.933638i	$-0.616615\pi$
$617$	−25.1911	−	4.44187i	−1.01416	−	0.178823i	−0.655937	+	0.754815i	$0.727727\pi$
$618$	−6.96453	−	1.22803i	−0.280154	−	0.0493988i
$619$	6.47023	+	11.2068i	0.260061	+	0.450438i	0.966258	−	0.257577i	$-0.0829241\pi$
$619$	6.47023	+	11.2068i	0.260061	+	0.450438i	−0.706197	+	0.708015i	$0.749591\pi$
$620$		0			0
$621$	−9.69065	−	8.13142i	−0.388872	−	0.326303i
$622$	6.56352	−	18.0331i	0.263173	−	0.723063i
$623$	−4.72743	−	12.9885i	−0.189401	−	0.520374i
$624$	2.51496	−	2.11030i	0.100679	−	0.0844797i
$625$		0			0
$626$	26.5439			1.06091
$627$	−18.1629	+	7.40681i	−0.725358	+	0.295799i
$628$		−	4.08613i		−	0.163054i
$629$	−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	$0.173498\pi$
$632$	−1.77048	+	4.86436i	−0.0704259	+	0.193494i
$633$	−8.91130	+	10.6201i	−0.354192	+	0.422110i
$634$	−4.49102	+	7.77867i	−0.178361	+	0.308931i
$635$		0			0
$636$	1.88293	−	10.6786i	0.0746631	−	0.423435i
$637$	−40.7160	−	7.17932i	−1.61322	−	0.284455i
$638$	−36.2572	+	20.9331i	−1.43544	+	0.828750i
$639$	−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	$0.609018\pi$
$642$	−0.812423	−	2.23211i	−0.0320638	−	0.0880945i
$643$	29.0808	+	34.6571i	1.14683	+	1.36674i	0.919578	+	0.392907i	$0.128531\pi$
$643$	29.0808	+	34.6571i	1.14683	+	1.36674i	0.227255	+	0.973835i	$0.427025\pi$
$644$	−2.07609	−	11.7741i	−0.0818094	−	0.463964i
$645$		0			0
$646$	−8.25344	−	4.35421i	−0.324727	−	0.171314i
$647$		−	31.3588i		−	1.23284i	−0.787417	−	0.616420i	$-0.788582\pi$
$647$		−	31.3588i		−	1.23284i	0.787417	−	0.616420i	$-0.211418\pi$
$648$	3.15997	−	0.557188i	0.124135	−	0.0218884i
$649$	32.5137	−	27.2822i	1.27627	−	1.07092i
$650$		0			0
$651$	−18.8345	−	6.85519i	−0.738181	−	0.268676i
$652$	−3.09978	+	3.69418i	−0.121397	+	0.144675i
$653$	6.74989	+	3.89705i	0.264143	+	0.152503i	0.626223	−	0.779644i	$-0.284600\pi$
$653$	6.74989	+	3.89705i	0.264143	+	0.152503i	−0.362080	+	0.932147i	$0.617933\pi$
$654$	−5.01576	−	8.68755i	−0.196132	−	0.339710i
$655$		0			0
$656$	1.05921	−	6.00706i	0.0413551	−	0.234536i
$657$	6.71601	−	3.87749i	0.262016	−	0.151275i
$658$	−15.8781	−	9.16721i	−0.618992	−	0.357375i
$659$	−5.73729	−	4.81416i	−0.223493	−	0.187533i	0.524165	−	0.851617i	$-0.324377\pi$
$659$	−5.73729	−	4.81416i	−0.223493	−	0.187533i	−0.747658	+	0.664084i	$0.768822\pi$
$660$		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	$0.152343\pi$
$662$	−15.8702	−	18.9133i	−0.616812	−	0.735088i
$663$	6.92161	−	1.22047i	0.268813	−	0.0473990i
$664$	−8.73330			−0.338918
$665$		0			0
$666$	4.25409			0.164843
$667$	−21.8586	+	3.85426i	−0.846369	+	0.149238i
$668$	3.31563	+	3.95141i	0.128285	+	0.152885i
$669$	15.2115	−	5.53653i	0.588111	−	0.214055i
$670$		0			0
$671$	45.2492	+	37.9686i	1.74683	+	1.46576i
$672$	−3.02728	−	1.74780i	−0.116780	−	0.0674230i
$673$	32.6126	−	18.8289i	1.25712	−	0.725801i	0.284610	−	0.958644i	$-0.408136\pi$
$673$	32.6126	−	18.8289i	1.25712	−	0.725801i	0.972514	+	0.232843i	$0.0748027\pi$
$674$	4.95422	−	28.0968i	0.190830	−	1.08225i
$675$		0			0
$676$	−1.22602	−	2.12353i	−0.0471547	−	0.0816743i
$677$	−8.77843	−	5.06823i	−0.337383	−	0.194788i	0.321731	−	0.946831i	$-0.395735\pi$
$677$	−8.77843	−	5.06823i	−0.337383	−	0.194788i	−0.659114	+	0.752043i	$0.729069\pi$
$678$	2.74222	−	3.26805i	0.105314	−	0.125509i
$679$	−3.40164	−	1.23810i	−0.130543	−	0.0475137i
$680$		0			0
$681$	1.72837	−	1.45028i	0.0662313	−	0.0555747i
$682$	−30.4247	+	5.36470i	−1.16502	+	0.205425i
$683$			16.0866i			0.615537i	0.951461	+	0.307769i	$0.0995822\pi$
$683$			16.0866i			0.615537i	−0.951461	+	0.307769i	$0.900418\pi$
$684$	6.15326	−	7.92860i	0.235276	−	0.303158i
$685$		0			0
$686$	2.55662	+	14.4993i	0.0976121	+	0.553586i
$687$	0.653447	+	0.778748i	0.0249306	+	0.0297111i
$688$	−4.31289	−	11.8496i	−0.164427	−	0.451761i
$689$	−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	$0.879715\pi$
$692$	−7.24533	+	4.18309i	−0.275426	+	0.159017i
$693$	51.1343	+	9.01636i	1.94243	+	0.342503i
$694$	0.740206	−	4.19791i	0.0280978	−	0.159351i
$695$		0			0
$696$	−3.24480	+	5.62016i	−0.122994	+	0.213031i
$697$	8.39376	−	10.0033i	0.317936	−	0.378902i
$698$	−3.92953	+	10.7963i	−0.148735	+	0.408646i
$699$	−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	$0.814519\pi$
$702$			17.4082i			0.657031i
$703$	5.96753	−	5.40828i	0.225070	−	0.203977i
$704$	−5.38803			−0.203069
$705$		0			0
$706$	19.7625	−	16.5827i	0.743773	−	0.624099i
$707$	−5.65869	−	15.5471i	−0.212817	−	0.584710i
$708$	2.25018	−	6.18232i	0.0845670	−	0.232346i
$709$	4.92868	+	4.13565i	0.185101	+	0.155318i	0.730629	−	0.682774i	$-0.239227\pi$
$709$	4.92868	+	4.13565i	0.185101	+	0.155318i	−0.545529	+	0.838092i	$0.683671\pi$
$710$		0			0
$711$	−5.95939	−	10.3220i	−0.223495	−	0.387104i
$712$	−3.25227	−	0.573463i	−0.121884	−	0.0214914i
$713$	−16.1300	−	2.84415i	−0.604073	−	0.106514i
$714$	−3.74172	−	6.48084i	−0.140030	−	0.242539i
$715$		0			0
$716$	−3.92277	−	3.29160i	−0.146601	−	0.123013i
$717$	−1.82975	+	5.02718i	−0.0683331	+	0.187744i
$718$	8.07404	+	22.1832i	0.301320	+	0.827871i
$719$	10.5258	−	8.83217i	0.392545	−	0.329384i	−0.425059	−	0.905166i	$-0.639747\pi$
$719$	10.5258	−	8.83217i	0.392545	−	0.329384i	0.817604	+	0.575782i	$0.195302\pi$
$720$		0			0
$721$	35.4401			1.31986
$722$	−1.44810	−	18.9447i	−0.0538927	−	0.705050i
$723$			21.5912i			0.802986i
$724$	0.326411	+	1.85117i	0.0121310	+	0.0687982i
$725$		0			0
$726$	−14.1510	+	5.15054i	−0.525193	+	0.191154i
$727$	16.0302	−	44.0426i	0.594527	−	1.63345i	−0.167477	−	0.985876i	$-0.553562\pi$
$727$	16.0302	−	44.0426i	0.594527	−	1.63345i	0.762003	−	0.647573i	$-0.224216\pi$
$728$	−10.5754	+	12.6033i	−0.391952	+	0.467110i
$729$	1.85403	−	3.21128i	0.0686679	−	0.118936i
$730$		0			0
$731$	4.68776	−	26.5856i	0.173383	−	0.983304i
$732$	9.01700	+	1.58994i	0.333278	+	0.0587659i
$733$	36.1943	−	20.8968i	1.33687	−	0.771840i	0.350525	−	0.936553i	$-0.386003\pi$
$733$	36.1943	−	20.8968i	1.33687	−	0.771840i	0.986341	+	0.164713i	$0.0526699\pi$
$734$	10.2193	−	17.7004i	0.377202	−	0.653333i
$735$		0			0
$736$	−2.68425	−	0.976988i	−0.0989428	−	0.0360122i
$737$	19.3275	+	53.1018i	0.711937	+	1.95603i
$738$	9.02756	+	10.7586i	0.332309	+	0.396031i
$739$	−2.10661	−	11.9472i	−0.0774930	−	0.439484i	−0.998725	−	0.0504720i	$-0.983927\pi$
$739$	−2.10661	−	11.9472i	−0.0774930	−	0.439484i	0.921233	−	0.389012i	$-0.127184\pi$
$740$		0			0
$741$	9.60996	+	10.6037i	0.353031	+	0.389536i
$742$			54.3398i			1.99488i
$743$	−42.9128	+	7.56669i	−1.57432	+	0.277595i	−0.891510	−	0.453001i	$-0.850353\pi$
$743$	−42.9128	+	7.56669i	−1.57432	+	0.277595i	−0.682810	+	0.730596i	$0.739242\pi$
$744$	−3.66845	+	3.07820i	−0.134492	+	0.112852i
$745$		0			0
$746$	4.78544	+	1.74176i	0.175207	+	0.0637703i
$747$	12.9252	−	15.4037i	0.472909	−	0.563591i
$748$	−9.98939	−	5.76738i	−0.365248	−	0.210876i
$749$	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	$0.976724\pi$
$752$	−3.79367	+	2.19028i	−0.138341	+	0.0798711i
$753$	−13.6376	−	7.87367i	−0.496982	−	0.286932i
$754$	23.3981	+	19.6333i	0.852109	+	0.715004i
$755$		0			0
$756$	17.4175	−	6.33945i	0.633468	−	0.230564i
$757$	−5.92151	−	7.05698i	−0.215221	−	0.256490i	0.647623	−	0.761961i	$-0.275763\pi$
$757$	−5.92151	−	7.05698i	−0.215221	−	0.256490i	−0.862844	+	0.505471i	$0.831319\pi$
$758$	8.11961	−	1.43171i	0.294918	−	0.0520019i
$759$	−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	$0.748834\pi$
$762$	9.06206	−	1.59789i	0.328284	−	0.0578853i
$763$	32.3138	+	38.5101i	1.16984	+	1.39416i
$764$	15.2426	−	5.54785i	0.551458	−	0.200714i
$765$		0			0
$766$	1.07800	+	0.904546i	0.0389496	+	0.0326826i
$767$	−26.8167	−	15.4826i	−0.968295	−	0.559045i
$768$	−0.723294	+	0.417594i	−0.0260996	+	0.0150686i
$769$	−1.08826	+	6.17181i	−0.0392435	+	0.222561i	−0.998122	−	0.0612554i	$-0.980490\pi$
$769$	−1.08826	+	6.17181i	−0.0392435	+	0.222561i	0.958879	+	0.283817i	$0.0916007\pi$
$770$		0			0
$771$	−6.40915	−	11.1010i	−0.230820	−	0.399792i
$772$	4.62761	+	2.67175i	0.166551	+	0.0961585i
$773$	7.96222	−	9.48900i	0.286381	−	0.341296i	−0.603605	−	0.797284i	$-0.706270\pi$
$773$	7.96222	−	9.48900i	0.286381	−	0.341296i	0.889986	+	0.455988i	$0.150714\pi$
$774$	27.2832	+	9.93027i	0.980674	+	0.356936i
$775$		0			0
$776$	−0.662549	+	0.555945i	−0.0237841	+	0.0199573i
$777$	6.36046	−	1.12152i	0.228180	−	0.0402343i
$778$		−	39.2500i		−	1.40718i
$779$	26.3412	+	3.61507i	0.943771	+	0.129523i
$780$		0			0
$781$	12.6127	+	71.5303i	0.451319	+	2.55956i
$782$	−3.93082	−	4.68457i	−0.140566	−	0.167520i
$783$	−11.7692	−	32.3356i	−0.420597	−	1.15558i
$784$	9.88339	+	3.59726i	0.352978	+	0.128474i
$785$		0			0
$786$	−8.77282	+	15.1950i	−0.312916	+	0.541987i
$787$	0.461905	−	0.266681i	0.0164652	−	0.00950616i	−0.491745	−	0.870739i	$-0.663641\pi$
$787$	0.461905	−	0.266681i	0.0164652	−	0.00950616i	0.508210	+	0.861233i	$0.330307\pi$
$788$	−13.7657	−	2.42727i	−0.490383	−	0.0864678i
$789$	−1.34847	+	7.64758i	−0.0480070	+	0.272261i
$790$		0			0
$791$	−10.6895	+	18.5148i	−0.380076	+	0.658311i
$792$	7.97425	−	9.50335i	0.283353	−	0.337687i
$793$	14.7391	−	40.4954i	0.523401	−	1.43803i
$794$	−5.48819	+	1.99754i	−0.194769	+	0.0708900i
$795$		0			0
$796$	−1.93501	−	10.9740i	−0.0685844	−	0.388962i
$797$			2.72969i			0.0966907i	0.998831	+	0.0483453i	$0.0153948\pi$
$797$			2.72969i			0.0966907i	−0.998831	+	0.0483453i	$0.984605\pi$
$798$	7.10973	−	13.4766i	0.251682	−	0.477065i
$799$	−9.37793			−0.331767
$800$		0			0
$801$	5.82481	−	4.88759i	0.205809	−	0.172695i
$802$	6.21531	+	17.0764i	0.219470	+	0.602989i
$803$	6.20683	−	17.0531i	0.219034	−	0.601792i
$804$	6.71014	+	5.63047i	0.236648	+	0.198571i
$805$		0			0
$806$	11.2696	+	19.5195i	0.396954	+	0.687545i
$807$	7.98448	+	1.40788i	0.281067	+	0.0495597i
$808$	−3.89294	−	0.686429i	−0.136953	−	0.0241485i
$809$	−14.7742	−	25.5896i	−0.519433	−	0.899684i	−0.999745	−	0.0225862i	$-0.992810\pi$
$809$	−14.7742	−	25.5896i	−0.519433	−	0.899684i	0.480312	−	0.877098i	$-0.340523\pi$
$810$		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	$0.900717\pi$
$812$	11.1230	−	30.5603i	0.390342	−	1.07246i
$813$	4.49648	+	12.3540i	0.157698	+	0.433273i
$814$	7.62603	−	6.39900i	0.267292	−	0.224285i
$815$		0			0
$816$	−1.78798			−0.0625918
$817$	50.8966	−	20.7555i	1.78065	−	0.726144i
$818$		−	12.0035i		−	0.419693i
$819$	−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	$0.555784\pi$
$822$	−1.09134	+	2.99843i	−0.0380648	+	0.104582i
$823$	−19.2303	+	22.9178i	−0.670327	+	0.798864i	−0.988828	−	0.149058i	$-0.952376\pi$
$823$	−19.2303	+	22.9178i	−0.670327	+	0.798864i	0.318502	+	0.947922i	$0.396820\pi$
$824$	4.23376	−	7.33309i	0.147490	−	0.255460i
$825$		0			0
$826$	−5.72520	+	32.4692i	−0.199205	+	1.12975i
$827$	15.6755	+	2.76402i	0.545092	+	0.0961144i	0.439412	−	0.898286i	$-0.355187\pi$
$827$	15.6755	+	2.76402i	0.545092	+	0.0961144i	0.105680	+	0.994400i	$0.466298\pi$
$828$	5.69588	−	3.28852i	0.197945	−	0.114284i
$829$	16.9348	−	29.3319i	0.588169	−	1.01874i	−0.406304	−	0.913738i	$-0.633182\pi$
$829$	16.9348	−	29.3319i	0.588169	−	1.01874i	0.994472	−	0.105000i	$-0.0334842\pi$
$830$		0			0
$831$	−23.1822	−	8.43765i	−0.804183	−	0.292699i
$832$	1.34445	+	3.69385i	0.0466104	+	0.128061i
$833$	14.4732	+	17.2485i	0.501468	+	0.597627i
$834$	−2.11066	−	11.9701i	−0.0730860	−	0.414491i
$835$		0			0
$836$	−0.895650	−	23.4688i	−0.0309767	−	0.811685i
$837$		−	25.3926i		−	0.877696i
$838$	−21.9945	+	3.87822i	−0.759788	+	0.133971i
$839$	−23.5861	+	19.7911i	−0.814284	+	0.683265i	−0.951626	−	0.307259i	$-0.900588\pi$
$839$	−23.5861	+	19.7911i	−0.814284	+	0.683265i	0.137343	+	0.990524i	$0.456144\pi$
$840$		0			0
$841$	−29.4842	−	10.7314i	−1.01670	−	0.370047i
$842$	−8.41142	+	10.0243i	−0.289877	+	0.345462i
$843$	−1.54315	−	0.890936i	−0.0531488	−	0.0306855i
$844$	−8.29965	−	14.3754i	−0.285686	−	0.494822i
$845$		0			0
$846$	1.75142	−	9.93282i	0.0602152	−	0.341497i
$847$	65.3561	−	37.7334i	2.24566	−	1.29653i
$848$	11.2437	+	6.49157i	0.386112	+	0.222922i
$849$	12.2439	+	10.2739i	0.420210	+	0.352598i
$850$		0			0
$851$	4.95950	−	1.80511i	0.170009	−	0.0618784i
$852$	7.23702	+	8.62475i	0.247936	+	0.295479i
$853$	−6.49532	+	1.14530i	−0.222396	+	0.0392143i	−0.283735	−	0.958903i	$-0.591574\pi$
$853$	−6.49532	+	1.14530i	−0.222396	+	0.0392143i	0.0613399	+	0.998117i	$0.480463\pi$
$854$	−45.8844			−1.57013
$855$		0			0
$856$	2.84411			0.0972097
$857$	−34.8066	+	6.13734i	−1.18897	+	0.209647i	−0.732925	−	0.680309i	$-0.761845\pi$
$857$	−34.8066	+	6.13734i	−1.18897	+	0.209647i	−0.456045	+	0.889957i	$0.650734\pi$
$858$	11.3704	+	13.5507i	0.388178	+	0.462613i
$859$	−47.8371	+	17.4113i	−1.63218	+	0.594065i	−0.985647	−	0.168820i	$-0.946004\pi$
$859$	−47.8371	+	17.4113i	−1.63218	+	0.594065i	−0.646534	+	0.762885i	$0.723782\pi$
$860$		0			0
$861$	16.3338	+	13.7057i	0.556654	+	0.467088i
$862$	7.38082	+	4.26132i	0.251392	+	0.145141i
$863$	−32.5126	+	18.7712i	−1.10674	+	0.638978i	−0.937984	−	0.346679i	$-0.887309\pi$
$863$	−32.5126	+	18.7712i	−1.10674	+	0.638978i	−0.168759	+	0.985657i	$0.553976\pi$
$864$	0.769010	−	4.36127i	0.0261622	−	0.148373i
$865$		0			0
$866$	−8.44842	−	14.6331i	−0.287089	−	0.497252i
$867$	8.98108	+	5.18523i	0.305014	+	0.176100i
$868$	15.4259	−	18.3839i	0.523590	−	0.623990i
$869$	−26.2093	−	9.53941i	−0.889090	−	0.323602i
$870$		0			0
$871$	31.5820	−	26.5005i	1.07012	−	0.897935i
$872$	11.8286	−	2.08571i	0.400568	−	0.0706309i
$873$		−	1.99139i		−	0.0673984i
$874$	3.80929	−	11.8543i	0.128851	−	0.400977i
$875$		0			0
$876$	−0.488475	−	2.77028i	−0.0165040	−	0.0935990i
$877$	−11.8349	−	14.1043i	−0.399637	−	0.476269i	0.528272	−	0.849075i	$-0.322840\pi$
$877$	−11.8349	−	14.1043i	−0.399637	−	0.476269i	−0.927909	+	0.372806i	$0.878396\pi$
$878$	6.83824	+	18.7879i	0.230779	+	0.634061i
$879$	−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	$-0.216969\pi$
$882$	−20.9722	+	12.1083i	−0.706169	+	0.407707i
$883$	−19.6991	−	3.47349i	−0.662929	−	0.116892i	−0.167948	−	0.985796i	$-0.553714\pi$
$883$	−19.6991	−	3.47349i	−0.662929	−	0.116892i	−0.494981	+	0.868904i	$0.664825\pi$
$884$	−1.46131	+	8.28749i	−0.0491491	+	0.278738i
$885$		0			0
$886$	10.1114	−	17.5134i	0.339698	−	0.588375i
$887$	−15.8521	+	18.8918i	−0.532262	+	0.634325i	−0.963434	−	0.267944i	$-0.913656\pi$
$887$	−15.8521	+	18.8918i	−0.532262	+	0.634325i	0.431172	+	0.902270i	$0.358100\pi$
$888$	0.527777	−	1.45005i	0.0177110	−	0.0486606i
$889$	−43.3327	+	15.7718i	−1.45333	+	0.528970i
$890$		0			0
$891$	3.00214	+	17.0260i	0.100576	+	0.570393i
$892$			19.3822i			0.648963i
$893$	−10.1709	−	16.1601i	−0.340355	−	0.540777i
$894$	−9.94318			−0.332550
$895$		0			0
$896$	3.20621	−	2.69033i	0.107112	−	0.0898777i
$897$	3.20750	+	8.81252i	0.107095	+	0.294242i
$898$	6.19615	−	17.0238i	0.206768	−	0.568091i
$899$	−34.1297	−	28.6382i	−1.13829	−	0.955139i
$900$		0			0
$901$	13.8972	+	24.0707i	0.462984	+	0.801912i
$902$	32.3662	+	5.70704i	1.07768	+	0.190024i
$903$	43.4101	+	7.65437i	1.44460	+	0.254721i
$904$	2.55400	+	4.42365i	0.0849446	+	0.147128i
$905$		0			0
$906$	−3.33532	−	2.79866i	−0.110808	−	0.0929794i
$907$	−8.99422	+	24.7114i	−0.298648	+	0.820529i	0.696078	+	0.717966i	$0.254927\pi$
$907$	−8.99422	+	24.7114i	−0.298648	+	0.820529i	−0.994727	+	0.102563i	$0.967296\pi$
$908$	0.923955	+	2.53854i	0.0306625	+	0.0842446i
$909$	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	$0.326099\pi$
$912$	−1.93916	−	3.08105i	−0.0642119	−	0.102024i
$913$		−	47.0553i		−	1.55730i
$914$	2.53077	+	14.3527i	0.0837106	+	0.474746i
$915$		0			0
$916$	−1.14379	+	0.416304i	−0.0377918	+	0.0137551i
$917$	30.0729	−	82.6246i	0.993095	−	2.72851i
$918$	6.09407	−	7.26263i	0.201134	−	0.239703i
$919$	−7.75554	+	13.4330i	−0.255832	+	0.443113i	−0.965121	−	0.261804i	$-0.915683\pi$
$919$	−7.75554	+	13.4330i	−0.255832	+	0.443113i	0.709289	+	0.704917i	$0.249016\pi$
$920$		0			0
$921$	−2.22224	+	12.6030i	−0.0732254	+	0.415282i
$922$	16.1514	+	2.84793i	0.531918	+	0.0937914i
$923$	45.8915	−	26.4955i	1.51054	−	0.872109i
$924$	9.41722	−	16.3111i	0.309804	−	0.536596i
$925$		0			0
$926$	30.7556	+	11.1941i	1.01069	+	0.367862i
$927$	6.66807	+	18.3204i	0.219008	+	0.601720i
$928$	−4.99461	−	5.95234i	−0.163956	−	0.195395i
$929$	−5.96023	−	33.8021i	−0.195549	−	1.10901i	−0.911635	−	0.411000i	$-0.865180\pi$
$929$	−5.96023	−	33.8021i	−0.195549	−	1.10901i	0.716087	−	0.698011i	$-0.245932\pi$
$930$		0			0
$931$	−14.0258	+	43.6473i	−0.459676	+	1.43048i
$932$		−	8.08440i		−	0.264813i
$933$	15.7841	−	2.78317i	0.516749	−	0.0911169i
$934$	10.6299	−	8.91954i	0.347821	−	0.291856i
$935$		0			0
$936$	−8.50494	−	3.09554i	−0.277993	−	0.101181i
$937$	9.29262	−	11.0745i	0.303577	−	0.361789i	−0.592592	−	0.805503i	$-0.701895\pi$
$937$	9.29262	−	11.0745i	0.303577	−	0.361789i	0.896168	+	0.443715i	$0.146340\pi$
$938$	−38.0156	−	21.9483i	−1.24125	−	0.716639i
$939$	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	$0.106290\pi$
$942$	2.95547	−	1.70634i	0.0962945	−	0.0555957i
$943$	15.0896	+	8.71200i	0.491386	+	0.283702i
$944$	6.03442	+	5.06348i	0.196404	+	0.164802i
$945$		0			0
$946$	63.8459	−	23.2380i	2.07581	−	0.755532i
$947$	28.5068	+	33.9731i	0.926348	+	1.10398i	0.994335	+	0.106292i	$0.0338978\pi$
$947$	28.5068	+	33.9731i	0.926348	+	1.10398i	−0.0679874	+	0.997686i	$0.521658\pi$
$948$	−4.25770	+	0.750747i	−0.138284	+	0.0243831i
$949$	−13.2398			−0.429782
$950$		0			0
$951$	−7.50169			−0.243259
$952$	8.82405	−	1.55592i	0.285989	−	0.0504276i
$953$	−2.76012	−	3.28938i	−0.0894089	−	0.106553i	0.719485	−	0.694508i	$-0.244378\pi$
$953$	−2.76012	−	3.28938i	−0.0894089	−	0.106553i	−0.808894	+	0.587954i	$0.799933\pi$
$954$	−28.0904	+	10.2241i	−0.909461	+	0.331017i
$955$		0			0
$956$	−4.90692	−	4.11739i	−0.158701	−	0.133166i
$957$	−30.2816	−	17.4831i	−0.978864	−	0.565148i
$958$	−8.23546	+	4.75475i	−0.266076	+	0.153619i
$959$	2.77672	−	15.7476i	0.0896650	−	0.508516i
$960$		0			0
$961$	−0.938425	−	1.62540i	−0.0302718	−	0.0524323i
$962$	−6.28982	−	3.63143i	−0.202792	−	0.117082i
$963$	−4.20927	+	5.01641i	−0.135642	+	0.161652i
$964$	−24.2929	−	8.84188i	−0.782421	−	0.284778i
$965$		0			0
$966$	7.64916	−	6.41841i	0.246108	−	0.206509i
$967$	−32.3599	+	5.70593i	−1.04063	+	0.183490i	−0.667746	−	0.744390i	$-0.732741\pi$
$967$	−32.3599	+	5.70593i	−1.04063	+	0.183490i	−0.372879	+	0.927880i	$0.621629\pi$
$968$		−	18.0309i		−	0.579535i
$969$	−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	$0.998149\pi$
$972$	10.2624	+	12.2303i	0.329168	+	0.392287i
$973$	20.8331	+	57.2384i	0.667877	+	1.83498i
$974$	35.5063	+	12.9232i	1.13770	+	0.414087i
$975$		0			0
$976$	−5.48146	+	9.49417i	−0.175457	+	0.303901i
$977$	15.5518	−	8.97886i	0.497548	−	0.287259i	−0.230153	−	0.973155i	$-0.573923\pi$
$977$	15.5518	−	8.97886i	0.497548	−	0.287259i	0.727700	+	0.685895i	$0.240589\pi$
$978$	−3.96642	−	0.699387i	−0.126832	−	0.0223639i
$979$	3.08984	−	17.5233i	0.0987516	−	0.560048i
$980$		0			0
$981$	−13.8275	+	23.9500i	−0.441480	+	0.764665i
$982$	10.1984	−	12.1540i	0.325445	−	0.387851i
$983$	5.96541	−	16.3898i	0.190267	−	0.522755i	−0.807476	−	0.589900i	$-0.799167\pi$
$983$	5.96541	−	16.3898i	0.190267	−	0.522755i	0.997743	+	0.0671457i	$0.0213892\pi$
$984$	4.78719	−	1.74239i	0.152610	−	0.0555455i
$985$		0			0
$986$	−2.88857	−	16.3819i	−0.0919907	−	0.521705i
$987$		−	15.3127i		−	0.487408i
$988$	−15.8659	+	6.47008i	−0.504762	+	0.205841i
$989$	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	$0.381115\pi$
$992$	−1.96109	−	5.38804i	−0.0622646	−	0.171070i
$993$	7.05262	−	19.3769i	0.223808	−	0.614907i
$994$	−43.2216	−	36.2672i	−1.37091	−	1.15033i
$995$		0			0
$996$	−3.64697	−	6.31674i	−0.115559	−	0.200154i
$997$	37.9346	+	6.68890i	1.20140	+	0.211840i	0.738305	−	0.674467i	$-0.235627\pi$
$997$	37.9346	+	6.68890i	1.20140	+	0.211840i	0.463098	+	0.886307i	$0.346738\pi$
$998$	−34.8572	−	6.14627i	−1.10339	−	0.194557i
$999$	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.u.h.199.2		48
5.2	odd	4		950.2.l.j.351.2	✓	24
5.3	odd	4		950.2.l.k.351.3	yes	24
5.4	even	2	inner	950.2.u.h.199.7		48
19.17	even	9	inner	950.2.u.h.549.7		48
95.17	odd	36		950.2.l.j.701.2	yes	24
95.74	even	18	inner	950.2.u.h.549.2		48
95.93	odd	36		950.2.l.k.701.3	yes	24

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

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.u (of order \(18\), degree \(6\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.984808 + 0.173648i) q^{2} +(-0.536848 - 0.639791i) q^{3} +(0.939693 - 0.342020i) q^{4} +(0.639791 + 0.536848i) q^{6} +(-3.62467 - 2.09271i) q^{7} +(-0.866025 + 0.500000i) q^{8} +(0.399818 - 2.26748i) q^{9} +O(q^{10})\)	\(q+(-0.984808 + 0.173648i) q^{2} +(-0.536848 - 0.639791i) q^{3} +(0.939693 - 0.342020i) q^{4} +(0.639791 + 0.536848i) q^{6} +(-3.62467 - 2.09271i) q^{7} +(-0.866025 + 0.500000i) q^{8} +(0.399818 - 2.26748i) q^{9} +(-2.69402 - 4.66617i) q^{11} +(-0.723294 - 0.417594i) q^{12} +(-2.52674 + 3.01125i) q^{13} +(3.93300 + 1.43150i) q^{14} +(0.766044 - 0.642788i) q^{16} +(2.10829 - 0.371748i) q^{17} +2.30246i q^{18} +(2.92715 + 3.22983i) q^{19} +(0.607005 + 3.44250i) q^{21} +(3.46336 + 4.12747i) q^{22} +(0.976988 + 2.68425i) q^{23} +(0.784820 + 0.285651i) q^{24} +(1.96545 - 3.40427i) q^{26} +(-3.83524 + 2.21428i) q^{27} +(-4.12183 - 0.726789i) q^{28} +(-1.34929 + 7.65218i) q^{29} +(-2.86692 + 4.96565i) q^{31} +(-0.642788 + 0.766044i) q^{32} +(-1.53910 + 4.22863i) q^{33} +(-2.01170 + 0.732201i) q^{34} +(-0.399818 - 2.26748i) q^{36} -1.84763i q^{37} +(-3.44353 - 2.67247i) q^{38} +3.28305 q^{39} +(4.67266 - 3.92083i) q^{41} +(-1.19557 - 3.28479i) q^{42} +(4.31289 - 11.8496i) q^{43} +(-4.12747 - 3.46336i) q^{44} +(-1.42826 - 2.47382i) q^{46} +(-4.31400 - 0.760675i) q^{47} +(-0.822499 - 0.145029i) q^{48} +(5.25884 + 9.10858i) q^{49} +(-1.36967 - 1.14929i) q^{51} +(-1.34445 + 3.69385i) q^{52} +(4.44050 + 12.2002i) q^{53} +(3.39247 - 2.84662i) q^{54} +4.18541 q^{56} +(0.494982 - 3.60669i) q^{57} -7.77023i q^{58} +(1.36789 + 7.75770i) q^{59} +(-10.3018 + 3.74954i) q^{61} +(1.96109 - 5.38804i) q^{62} +(-6.19439 + 7.38218i) q^{63} +(0.500000 - 0.866025i) q^{64} +(0.781420 - 4.43165i) q^{66} +(-10.3287 - 1.82123i) q^{67} +(1.85400 - 1.07041i) q^{68} +(1.19287 - 2.06610i) q^{69} +(-12.6676 - 4.61063i) q^{71} +(0.787488 + 2.16361i) q^{72} +(2.16499 + 2.58013i) q^{73} +(0.320837 + 1.81956i) q^{74} +(3.85529 + 2.03391i) q^{76} +22.5511i q^{77} +(-3.23317 + 0.570095i) q^{78} +(3.96546 - 3.32742i) q^{79} +(-3.01521 - 1.09745i) q^{81} +(-3.92083 + 4.67266i) q^{82} +(7.56326 + 4.36665i) q^{83} +(1.74780 + 3.02728i) q^{84} +(-2.18971 + 12.4185i) q^{86} +(5.62016 - 3.24480i) q^{87} +(4.66617 + 2.69402i) q^{88} +(2.52982 + 2.12277i) q^{89} +(15.4603 - 5.62708i) q^{91} +(1.83614 + 2.18822i) q^{92} +(4.71607 - 0.831571i) q^{93} +4.38055 q^{94} +0.835188 q^{96} +(0.851757 - 0.150188i) q^{97} +(-6.76064 - 8.05701i) q^{98} +(-11.6576 + 4.24301i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q+O(q^{10}) \) 48 * q	\( 48 q - 12 q^{11} + 30 q^{14} + 30 q^{19} - 36 q^{21} - 18 q^{26} + 24 q^{29} + 18 q^{31} + 18 q^{34} - 132 q^{39} + 36 q^{41} - 6 q^{46} + 54 q^{49} - 6 q^{51} - 54 q^{54} - 12 q^{56} - 72 q^{59} + 24 q^{61} + 24 q^{64} + 96 q^{66} - 42 q^{69} - 78 q^{71} - 36 q^{74} + 12 q^{76} + 84 q^{79} - 72 q^{81} - 18 q^{84} - 78 q^{86} + 72 q^{89} + 24 q^{91} - 24 q^{94} + 12 q^{96} - 102 q^{99}+O(q^{100}) \) 48 * q - 12 * q^11 + 30 * q^14 + 30 * q^19 - 36 * q^21 - 18 * q^26 + 24 * q^29 + 18 * q^31 + 18 * q^34 - 132 * q^39 + 36 * q^41 - 6 * q^46 + 54 * q^49 - 6 * q^51 - 54 * q^54 - 12 * q^56 - 72 * q^59 + 24 * q^61 + 24 * q^64 + 96 * q^66 - 42 * q^69 - 78 * q^71 - 36 * q^74 + 12 * q^76 + 84 * q^79 - 72 * q^81 - 18 * q^84 - 78 * q^86 + 72 * q^89 + 24 * q^91 - 24 * q^94 + 12 * q^96 - 102 * q^99

Introduction

L-functions

Modular forms

Varieties

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Groups

Database

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