LMFDB - Embedded newform 880.2.bk.b.243.15

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [880,2,Mod(243,880)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(880, base_ring=CyclotomicField(4)) chi = DirichletCharacter(H, H._module([2, 3, 3, 0])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("880.243"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 880 = 2^{4} \cdot 5 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	880.bk (of order $4$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [236] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(1)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$7.02683537787$
Analytic rank:	$0$
Dimension:	$236$
Relative dimension:	$118$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			243.15
Character	$\chi$	$=$	880.243
Dual form			880.2.bk.b.507.15

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.28261 + 0.595739i) q^{2} -0.00646194 q^{3} +(1.29019 - 1.52820i) q^{4} +(1.81833 - 1.30141i) q^{5} +(0.00828816 - 0.00384963i) q^{6} +(-1.60179 + 1.60179i) q^{7} +(-0.744402 + 2.72871i) q^{8} -2.99996 q^{9} +(-1.55692 + 2.75245i) q^{10} +(0.707107 + 0.707107i) q^{11} +(-0.00833712 + 0.00987516i) q^{12} +3.94151i q^{13} +(1.10023 - 3.00873i) q^{14} +(-0.0117500 + 0.00840960i) q^{15} +(-0.670821 - 3.94335i) q^{16} +(-1.82150 + 1.82150i) q^{17} +(3.84778 - 1.78719i) q^{18} +(-5.41058 - 5.41058i) q^{19} +(0.357182 - 4.45785i) q^{20} +(0.0103507 - 0.0103507i) q^{21} +(-1.32820 - 0.485693i) q^{22} +(-2.47940 - 2.47940i) q^{23} +(0.00481028 - 0.0176328i) q^{24} +(1.61268 - 4.73278i) q^{25} +(-2.34811 - 5.05542i) q^{26} +0.0387713 q^{27} +(0.381251 + 4.51449i) q^{28} +(-5.56147 + 5.56147i) q^{29} +(0.0100607 - 0.0177862i) q^{30} +0.407599i q^{31} +(3.20961 + 4.65815i) q^{32} +(-0.00456928 - 0.00456928i) q^{33} +(1.25114 - 3.42142i) q^{34} +(-0.828013 + 4.99718i) q^{35} +(-3.87052 + 4.58455i) q^{36} +6.88771i q^{37} +(10.1630 + 3.71638i) q^{38} -0.0254698i q^{39} +(2.19759 + 5.93048i) q^{40} +2.33536i q^{41} +(-0.00710961 + 0.0194422i) q^{42} -0.446436i q^{43} +(1.99291 - 0.168302i) q^{44} +(-5.45493 + 3.90416i) q^{45} +(4.65718 + 1.70303i) q^{46} +(-8.15854 - 8.15854i) q^{47} +(0.00433480 + 0.0254817i) q^{48} +1.86852i q^{49} +(0.751057 + 7.03107i) q^{50} +(0.0117704 - 0.0117704i) q^{51} +(6.02343 + 5.08529i) q^{52} +9.72138 q^{53} +(-0.0497286 + 0.0230976i) q^{54} +(2.20599 + 0.365524i) q^{55} +(-3.17845 - 5.56321i) q^{56} +(0.0349628 + 0.0349628i) q^{57} +(3.82003 - 10.4464i) q^{58} +(-3.21310 + 3.21310i) q^{59} +(-0.00230809 + 0.0288063i) q^{60} +(-3.02332 - 3.02332i) q^{61} +(-0.242823 - 0.522792i) q^{62} +(4.80531 - 4.80531i) q^{63} +(-6.89173 - 4.06252i) q^{64} +(5.12950 + 7.16698i) q^{65} +(0.00858271 + 0.00313852i) q^{66} +9.45206i q^{67} +(0.433545 + 5.13371i) q^{68} +(0.0160217 + 0.0160217i) q^{69} +(-1.91500 - 6.90273i) q^{70} -10.5193 q^{71} +(2.23318 - 8.18602i) q^{72} +(-5.87965 + 5.87965i) q^{73} +(-4.10328 - 8.83426i) q^{74} +(-0.0104211 + 0.0305830i) q^{75} +(-15.2491 + 1.28780i) q^{76} -2.26528 q^{77} +(0.0151733 + 0.0326678i) q^{78} -1.69281 q^{79} +(-6.35168 - 6.29732i) q^{80} +8.99962 q^{81} +(-1.39126 - 2.99536i) q^{82} -3.04457 q^{83} +(-0.00246362 - 0.0291723i) q^{84} +(-0.941586 + 5.68261i) q^{85} +(0.265959 + 0.572604i) q^{86} +(0.0359379 - 0.0359379i) q^{87} +(-2.45586 + 1.40312i) q^{88} -5.00722 q^{89} +(4.67070 - 8.25724i) q^{90} +(-6.31348 - 6.31348i) q^{91} +(-6.98792 + 0.590134i) q^{92} -0.00263388i q^{93} +(15.3246 + 5.60389i) q^{94} +(-16.8796 - 2.79688i) q^{95} +(-0.0207403 - 0.0301007i) q^{96} +(1.72845 - 1.72845i) q^{97} +(-1.11315 - 2.39658i) q^{98} +(-2.12129 - 2.12129i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 236 q + 4 q^{3} + 4 q^{5} - 4 q^{7} + 12 q^{8} + 240 q^{9} - 8 q^{12} + 12 q^{14} - 4 q^{15} - 8 q^{16} + 8 q^{17} + 28 q^{18} + 28 q^{19} + 4 q^{20} + 16 q^{21} + 4 q^{22} - 8 q^{23} + 12 q^{25} + 8 q^{26}+ \cdots + 8 q^{99}+O(q^{100}) $ 236 * q + 4 * q^3 + 4 * q^5 - 4 * q^7 + 12 * q^8 + 240 * q^9 - 8 * q^12 + 12 * q^14 - 4 * q^15 - 8 * q^16 + 8 * q^17 + 28 * q^18 + 28 * q^19 + 4 * q^20 + 16 * q^21 + 4 * q^22 - 8 * q^23 + 12 * q^25 + 8 * q^26 + 4 * q^27 - 36 * q^28 + 8 * q^29 - 56 * q^30 - 40 * q^32 - 4 * q^33 - 44 * q^34 - 28 * q^35 - 32 * q^36 - 12 * q^38 - 40 * q^40 - 20 * q^42 - 40 * q^46 - 48 * q^47 - 40 * q^48 - 28 * q^51 - 4 * q^52 + 28 * q^53 - 24 * q^56 - 16 * q^57 - 76 * q^58 + 8 * q^59 - 4 * q^60 - 24 * q^61 + 12 * q^62 - 24 * q^63 - 32 * q^65 - 4 * q^66 + 36 * q^68 + 48 * q^69 + 28 * q^70 - 4 * q^71 + 20 * q^72 + 8 * q^73 - 68 * q^75 - 24 * q^76 + 12 * q^77 + 8 * q^78 + 40 * q^79 + 112 * q^80 + 244 * q^81 - 64 * q^82 + 24 * q^83 - 104 * q^84 + 8 * q^85 + 72 * q^86 - 140 * q^87 - 32 * q^88 + 36 * q^89 - 136 * q^90 + 12 * q^91 + 72 * q^92 - 16 * q^94 - 36 * q^95 + 72 * q^96 + 20 * q^97 + 136 * q^98 + 8 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/880\mathbb{Z}\right)^\times$.

$n$	$111$	$177$	$321$	$661$
$\chi(n)$	$-1$	$e\left(\frac{3}{4}\right)$	$1$	$e\left(\frac{3}{4}\right)$

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 $

$2$	−1.28261	+	0.595739i	−0.906944	+	0.421251i
$2$	−1.28261	+	0.595739i	−0.906944	+	0.421251i
$3$	−0.00646194			−0.00373080			−0.00186540	−	0.999998i	$-0.500594\pi$
$3$	−0.00646194			−0.00373080			−0.00186540	+	0.999998i	$0.500594\pi$
$4$	1.29019	−	1.52820i	0.645095	−	0.764102i
$5$	1.81833	−	1.30141i	0.813184	−	0.582007i
$5$	1.81833	−	1.30141i	0.813184	−	0.582007i
$6$	0.00828816	−	0.00384963i	0.00338363	−	0.00157160i
$7$	−1.60179	+	1.60179i	−0.605421	+	0.605421i	−0.941746	−	0.336325i	$-0.890816\pi$
$7$	−1.60179	+	1.60179i	−0.605421	+	0.605421i	0.336325	+	0.941746i	$0.390816\pi$
$8$	−0.744402	+	2.72871i	−0.263186	+	0.964745i
$9$	−2.99996			−0.999986
$10$	−1.55692	+	2.75245i	−0.492341	+	0.870402i
$11$	0.707107	+	0.707107i	0.213201	+	0.213201i
$11$	0.707107	+	0.707107i	0.213201	+	0.213201i
$12$	−0.00833712	+	0.00987516i	−0.00240672	+	0.00285071i
$13$			3.94151i			1.09318i	0.837401	+	0.546588i	$0.184074\pi$
$13$			3.94151i			1.09318i	−0.837401	+	0.546588i	$0.815926\pi$
$14$	1.10023	−	3.00873i	0.294049	−	0.804117i
$15$	−0.0117500	+	0.00840960i	−0.00303383	+	0.00217135i
$16$	−0.670821	−	3.94335i	−0.167705	−	0.985837i
$17$	−1.82150	+	1.82150i	−0.441779	+	0.441779i	−0.892609	−	0.450831i	$-0.851128\pi$
$17$	−1.82150	+	1.82150i	−0.441779	+	0.441779i	0.450831	+	0.892609i	$0.351128\pi$
$18$	3.84778	−	1.78719i	0.906931	−	0.421245i
$19$	−5.41058	−	5.41058i	−1.24127	−	1.24127i	−0.959474	−	0.281797i	$-0.909069\pi$
$19$	−5.41058	−	5.41058i	−1.24127	−	1.24127i	−0.281797	−	0.959474i	$-0.590931\pi$
$20$	0.357182	−	4.45785i	0.0798683	−	0.996805i
$21$	0.0103507	−	0.0103507i	0.00225870	−	0.00225870i
$22$	−1.32820	−	0.485693i	−0.283172	−	0.103550i
$23$	−2.47940	−	2.47940i	−0.516990	−	0.516990i	0.399669	−	0.916659i	$-0.369125\pi$
$23$	−2.47940	−	2.47940i	−0.516990	−	0.516990i	−0.916659	+	0.399669i	$0.869125\pi$
$24$	0.00481028	−	0.0176328i	0.000981894	−	0.00359927i
$25$	1.61268	−	4.73278i	0.322537	−	0.946557i
$26$	−2.34811	−	5.05542i	−0.460502	−	0.991450i
$27$	0.0387713			0.00746155
$28$	0.381251	+	4.51449i	0.0720497	+	0.853158i
$29$	−5.56147	+	5.56147i	−1.03274	+	1.03274i	−0.0332934	+	0.999446i	$0.510600\pi$
$29$	−5.56147	+	5.56147i	−1.03274	+	1.03274i	−0.999446	+	0.0332934i	$0.989400\pi$
$30$	0.0100607	−	0.0177862i	0.00183683	−	0.00324730i
$31$			0.407599i			0.0732070i	0.999330	+	0.0366035i	$0.0116539\pi$
$31$			0.407599i			0.0732070i	−0.999330	+	0.0366035i	$0.988346\pi$
$32$	3.20961	+	4.65815i	0.567384	+	0.823453i
$33$	−0.00456928	−	0.00456928i	−0.000795409	−	0.000795409i
$34$	1.25114	−	3.42142i	0.214569	−	0.586768i
$35$	−0.828013	+	4.99718i	−0.139960	+	0.844678i
$36$	−3.87052	+	4.58455i	−0.645086	+	0.764092i
$37$			6.88771i			1.13233i	0.824291	+	0.566166i	$0.191574\pi$
$37$			6.88771i			1.13233i	−0.824291	+	0.566166i	$0.808426\pi$
$38$	10.1630	+	3.71638i	1.64865	+	0.602877i
$39$		−	0.0254698i		−	0.00407842i
$40$	2.19759	+	5.93048i	0.347469	+	0.937691i
$41$			2.33536i			0.364722i	0.983232	+	0.182361i	$0.0583739\pi$
$41$			2.33536i			0.364722i	−0.983232	+	0.182361i	$0.941626\pi$
$42$	−0.00710961	+	0.0194422i	−0.00109704	+	0.00300000i
$43$		−	0.446436i		−	0.0680808i	−0.999420	−	0.0340404i	$-0.989163\pi$
$43$		−	0.446436i		−	0.0680808i	0.999420	−	0.0340404i	$-0.0108375\pi$
$44$	1.99291	−	0.168302i	0.300442	−	0.0253725i
$45$	−5.45493	+	3.90416i	−0.813173	+	0.581998i
$46$	4.65718	+	1.70303i	0.686664	+	0.251098i
$47$	−8.15854	−	8.15854i	−1.19005	−	1.19005i	−0.977054	−	0.212992i	$-0.931679\pi$
$47$	−8.15854	−	8.15854i	−1.19005	−	1.19005i	−0.212992	−	0.977054i	$-0.568321\pi$
$48$	0.00433480	+	0.0254817i	0.000625675	+	0.00367796i
$49$			1.86852i			0.266931i
$50$	0.751057	+	7.03107i	0.106215	+	0.994343i
$51$	0.0117704	−	0.0117704i	0.00164819	−	0.00164819i
$52$	6.02343	+	5.08529i	0.835299	+	0.705203i
$53$	9.72138			1.33533			0.667667	−	0.744460i	$-0.267293\pi$
$53$	9.72138			1.33533			0.667667	+	0.744460i	$0.267293\pi$
$54$	−0.0497286	+	0.0230976i	−0.00676721	+	0.00314319i
$55$	2.20599	+	0.365524i	0.297456	+	0.0492872i
$56$	−3.17845	−	5.56321i	−0.424739	−	0.743415i
$57$	0.0349628	+	0.0349628i	0.00463094	+	0.00463094i
$58$	3.82003	−	10.4464i	0.501594	−	1.37168i
$59$	−3.21310	+	3.21310i	−0.418310	+	0.418310i	−0.884621	−	0.466311i	$-0.845583\pi$
$59$	−3.21310	+	3.21310i	−0.418310	+	0.418310i	0.466311	+	0.884621i	$0.345583\pi$
$60$	−0.00230809	+	0.0288063i	−0.000297973	+	0.00371888i
$61$	−3.02332	−	3.02332i	−0.387097	−	0.387097i	0.486554	−	0.873651i	$-0.338254\pi$
$61$	−3.02332	−	3.02332i	−0.387097	−	0.387097i	−0.873651	+	0.486554i	$0.838254\pi$
$62$	−0.242823	−	0.522792i	−0.0308385	−	0.0663946i
$63$	4.80531	−	4.80531i	0.605412	−	0.605412i
$64$	−6.89173	−	4.06252i	−0.861466	−	0.507815i
$65$	5.12950	+	7.16698i	0.636236	+	0.888954i
$66$	0.00858271	+	0.00313852i	0.00105646	+	0.000386325i
$67$			9.45206i			1.15475i	0.816478	+	0.577377i	$0.195924\pi$
$67$			9.45206i			1.15475i	−0.816478	+	0.577377i	$0.804076\pi$
$68$	0.433545	+	5.13371i	0.0525750	+	0.622554i
$69$	0.0160217	+	0.0160217i	0.00192879	+	0.00192879i
$70$	−1.91500	−	6.90273i	−0.228886	−	0.825033i
$71$	−10.5193			−1.24841			−0.624205	−	0.781260i	$-0.714577\pi$
$71$	−10.5193			−1.24841			−0.624205	+	0.781260i	$0.714577\pi$
$72$	2.23318	−	8.18602i	0.263182	−	0.964732i
$73$	−5.87965	+	5.87965i	−0.688161	+	0.688161i	−0.961825	−	0.273664i	$-0.911764\pi$
$73$	−5.87965	+	5.87965i	−0.688161	+	0.688161i	0.273664	+	0.961825i	$0.411764\pi$
$74$	−4.10328	−	8.83426i	−0.476996	−	1.02696i
$75$	−0.0104211	+	0.0305830i	−0.00120332	+	0.00353142i
$76$	−15.2491	+	1.28780i	−1.74920	+	0.147721i
$77$	−2.26528			−0.258152
$78$	0.0151733	+	0.0326678i	0.00171804	+	0.00369890i
$79$	−1.69281			−0.190456			−0.0952281	−	0.995455i	$-0.530358\pi$
$79$	−1.69281			−0.190456			−0.0952281	+	0.995455i	$0.530358\pi$
$80$	−6.35168	−	6.29732i	−0.710139	−	0.704062i
$81$	8.99962			0.999958
$82$	−1.39126	−	2.99536i	−0.153639	−	0.330782i
$83$	−3.04457			−0.334185			−0.167092	−	0.985941i	$-0.553438\pi$
$83$	−3.04457			−0.334185			−0.167092	+	0.985941i	$0.553438\pi$
$84$	−0.00246362	−	0.0291723i	−0.000268803	−	0.00318296i
$85$	−0.941586	+	5.68261i	−0.102129	+	0.616366i
$86$	0.265959	+	0.572604i	0.0286791	+	0.0617455i
$87$	0.0359379	−	0.0359379i	0.00385294	−	0.00385294i
$88$	−2.45586	+	1.40312i	−0.261796	+	0.149573i
$89$	−5.00722			−0.530764			−0.265382	−	0.964143i	$-0.585498\pi$
$89$	−5.00722			−0.530764			−0.265382	+	0.964143i	$0.585498\pi$
$90$	4.67070	−	8.25724i	0.492335	−	0.870390i
$91$	−6.31348	−	6.31348i	−0.661832	−	0.661832i
$92$	−6.98792	+	0.590134i	−0.728541	+	0.0615257i
$93$		−	0.00263388i		−	0.000273121i
$94$	15.3246	+	5.60389i	1.58061	+	0.577997i
$95$	−16.8796	−	2.79688i	−1.73181	−	0.286954i
$96$	−0.0207403	−	0.0301007i	−0.00211680	−	0.00307214i
$97$	1.72845	−	1.72845i	0.175497	−	0.175497i	−0.613892	−	0.789390i	$-0.710397\pi$
$97$	1.72845	−	1.72845i	0.175497	−	0.175497i	0.789390	+	0.613892i	$0.210397\pi$
$98$	−1.11315	−	2.39658i	−0.112445	−	0.242092i
$99$	−2.12129	−	2.12129i	−0.213198	−	0.213198i
$100$	−5.15200	−	8.57070i	−0.515200	−	0.857070i
$101$	0.535082	−	0.535082i	0.0532427	−	0.0532427i	−0.679984	−	0.733227i	$-0.738013\pi$
$101$	0.535082	−	0.535082i	0.0532427	−	0.0532427i	0.733227	+	0.679984i	$0.238013\pi$
$102$	−0.00808479	+	0.0221090i	−0.000800513	+	0.00218912i
$103$	6.34984	+	6.34984i	0.625669	+	0.625669i	0.946975	−	0.321306i	$-0.104122\pi$
$103$	6.34984	+	6.34984i	0.625669	+	0.625669i	−0.321306	+	0.946975i	$0.604122\pi$
$104$	−10.7552	−	2.93406i	−1.05464	−	0.287709i
$105$	0.00535057	−	0.0322915i	0.000522162	−	0.00315132i
$106$	−12.4688	+	5.79141i	−1.21107	+	0.562511i
$107$	−16.7152			−1.61592			−0.807961	−	0.589236i	$-0.799429\pi$
$107$	−16.7152			−1.61592			−0.807961	+	0.589236i	$0.799429\pi$
$108$	0.0500224	−	0.0592506i	0.00481341	−	0.00570139i
$109$	12.5536	−	12.5536i	1.20241	−	1.20241i	0.228984	−	0.973430i	$-0.426460\pi$
$109$	12.5536	−	12.5536i	1.20241	−	1.20241i	0.973430	−	0.228984i	$-0.0735403\pi$
$110$	−3.04719	+	0.845369i	−0.290538	+	0.0806028i
$111$		−	0.0445079i		−	0.00422451i
$112$	7.39094	+	5.24191i	0.698379	+	0.495314i
$113$	−7.80420	−	7.80420i	−0.734158	−	0.734158i	0.237283	−	0.971441i	$-0.423743\pi$
$113$	−7.80420	−	7.80420i	−0.734158	−	0.734158i	−0.971441	+	0.237283i	$0.923743\pi$
$114$	−0.0656724	−	0.0240150i	−0.00615079	−	0.00224921i
$115$	−7.73508	−	1.28167i	−0.721300	−	0.119516i
$116$	1.32371	+	15.6744i	0.122904	+	1.45533i
$117$		−	11.8244i		−	1.09316i
$118$	2.20699	−	6.03534i	0.203170	−	0.555598i
$119$		−	5.83533i		−	0.534924i
$120$	−0.0142007	−	0.0383224i	−0.00129634	−	0.00349834i
$121$			1.00000i			0.0909091i
$122$	5.67886	+	2.07664i	0.514140	+	0.188010i
$123$		−	0.0150909i		−	0.00136070i
$124$	0.622895	+	0.525880i	0.0559376	+	0.0472255i
$125$	−3.22688	−	10.7045i	−0.288621	−	0.957444i
$126$	−3.30064	+	9.02607i	−0.294045	+	0.804106i
$127$	13.4711	+	13.4711i	1.19537	+	1.19537i	0.975538	+	0.219832i	$0.0705508\pi$
$127$	13.4711	+	13.4711i	1.19537	+	1.19537i	0.219832	+	0.975538i	$0.429449\pi$
$128$	11.2596	+	1.10496i	0.995219	+	0.0976657i
$129$			0.00288484i			0.000253996i
$130$	−10.8488	−	6.13661i	−0.951503	−	0.538216i
$131$	−9.53525	+	9.53525i	−0.833099	+	0.833099i	−0.987939	−	0.154841i	$-0.950514\pi$
$131$	−9.53525	+	9.53525i	−0.833099	+	0.833099i	0.154841	+	0.987939i	$0.450514\pi$
$132$	−0.0128780	+	0.00108756i	−0.00112089	+	9.46597e-5i
$133$	17.3332			1.50298
$134$	−5.63096	−	12.1233i	−0.486441	−	1.04730i
$135$	0.0704993	−	0.0504573i	0.00606761	−	0.00434267i
$136$	−3.61442	−	6.32628i	−0.309934	−	0.542474i
$137$	7.88170	+	7.88170i	0.673379	+	0.673379i	0.958493	−	0.285115i	$-0.0920316\pi$
$137$	7.88170	+	7.88170i	0.673379	+	0.673379i	−0.285115	+	0.958493i	$0.592032\pi$
$138$	−0.0300944	−	0.0110049i	−0.00256181	−	0.000936798i
$139$	9.87833	−	9.87833i	0.837869	−	0.837869i	−0.150709	−	0.988578i	$-0.548156\pi$
$139$	9.87833	−	9.87833i	0.837869	−	0.837869i	0.988578	+	0.150709i	$0.0481556\pi$
$140$	6.56842	+	7.71268i	0.555133	+	0.651841i
$141$	0.0527200	+	0.0527200i	0.00443982	+	0.00443982i
$142$	13.4922	−	6.26676i	1.13224	−	0.525895i
$143$	−2.78707	+	2.78707i	−0.233066	+	0.233066i
$144$	2.01243	+	11.8299i	0.167703	+	0.985823i
$145$	−2.87488	+	17.3503i	−0.238746	+	1.44087i
$146$	4.03858	−	11.0441i	0.334235	−	0.914012i
$147$		−	0.0120742i		−	0.000995867i
$148$	10.5258	+	8.88645i	0.865218	+	0.730462i
$149$	−12.7864	−	12.7864i	−1.04750	−	1.04750i	−0.998814	−	0.0486873i	$-0.984496\pi$
$149$	−12.7864	−	12.7864i	−1.04750	−	1.04750i	−0.0486873	−	0.998814i	$-0.515504\pi$
$150$	−0.00485328	−	0.0454343i	−0.000396269	−	0.00370970i
$151$	20.6204			1.67807			0.839033	−	0.544081i	$-0.183121\pi$
$151$	20.6204			1.67807			0.839033	+	0.544081i	$0.183121\pi$
$152$	18.7915	−	10.7363i	1.52420	−	0.870825i
$153$	5.46443	−	5.46443i	0.441773	−	0.441773i
$154$	2.90547	−	1.34951i	0.234130	−	0.108747i
$155$	0.530452	+	0.741152i	0.0426069	+	0.0595308i
$156$	−0.0389230	−	0.0328608i	−0.00311633	−	0.00263097i
$157$	−13.9058			−1.10981			−0.554903	−	0.831915i	$-0.687245\pi$
$157$	−13.9058			−1.10981			−0.554903	+	0.831915i	$0.687245\pi$
$158$	2.17122	−	1.00847i	0.172733	−	0.0802299i
$159$	−0.0628189			−0.00498187
$160$	11.8983	+	4.29308i	0.940643	+	0.339398i
$161$	7.94296			0.625993
$162$	−11.5430	+	5.36143i	−0.906906	+	0.421234i
$163$	−2.70639			−0.211981			−0.105990	−	0.994367i	$-0.533801\pi$
$163$	−2.70639			−0.211981			−0.105990	+	0.994367i	$0.533801\pi$
$164$	3.56891	+	3.01306i	0.278685	+	0.235280i
$165$	−0.0142550	−	0.00236199i	−0.00110975	−	0.000183881i
$166$	3.90500	−	1.81377i	0.303087	−	0.140776i
$167$	6.05382	−	6.05382i	0.468459	−	0.468459i	−0.432956	−	0.901415i	$-0.642530\pi$
$167$	6.05382	−	6.05382i	0.468459	−	0.468459i	0.901415	+	0.432956i	$0.142530\pi$
$168$	0.0205390	+	0.0359491i	0.00158462	+	0.00277353i
$169$	−2.53546			−0.195036
$170$	−2.17766	−	7.84953i	−0.167019	−	0.602031i
$171$	16.2315	+	16.2315i	1.24125	+	1.24125i
$172$	−0.682246	−	0.575987i	−0.0520207	−	0.0439186i
$173$			18.3525i			1.39531i	0.716432	+	0.697657i	$0.245774\pi$
$173$			18.3525i			1.39531i	−0.716432	+	0.697657i	$0.754226\pi$
$174$	−0.0246848	+	0.0675039i	−0.00187135	+	0.00511746i
$175$	4.99776	+	10.1641i	0.377795	+	0.768336i
$176$	2.31403	−	3.26271i	0.174426	−	0.245936i
$177$	0.0207629	−	0.0207629i	0.00156063	−	0.00156063i
$178$	6.42233	−	2.98300i	0.481374	−	0.223585i
$179$	−9.15675	−	9.15675i	−0.684407	−	0.684407i	0.276583	−	0.960990i	$-0.410798\pi$
$179$	−9.15675	−	9.15675i	−0.684407	−	0.684407i	−0.960990	+	0.276583i	$0.910798\pi$
$180$	−1.07153	+	13.3734i	−0.0798671	+	0.996792i
$181$	−1.12861	+	1.12861i	−0.0838892	+	0.0838892i	−0.747806	−	0.663917i	$-0.768893\pi$
$181$	−1.12861	+	1.12861i	−0.0838892	+	0.0838892i	0.663917	+	0.747806i	$0.268893\pi$
$182$	11.8589	+	4.33656i	0.879042	+	0.321447i
$183$	0.0195365	+	0.0195365i	0.00144418	+	0.00144418i
$184$	8.61123	−	4.91989i	0.634828	−	0.362699i
$185$	8.96371	+	12.5242i	0.659025	+	0.920795i
$186$	0.00156911	+	0.00337825i	0.000115052	+	0.000247705i
$187$	−2.57599			−0.188375
$188$	−22.9940	+	1.94186i	−1.67701	+	0.141624i
$189$	−0.0621037	+	0.0621037i	−0.00451738	+	0.00451738i
$190$	23.3162	−	6.46852i	1.69153	−	0.469276i
$191$			1.92751i			0.139470i	0.997566	+	0.0697348i	$0.0222153\pi$
$191$			1.92751i			0.139470i	−0.997566	+	0.0697348i	$0.977785\pi$
$192$	0.0445339	+	0.0262517i	0.00321396	+	0.00189456i
$193$	11.5345	+	11.5345i	0.830269	+	0.830269i	0.987553	−	0.157285i	$-0.0502740\pi$
$193$	11.5345	+	11.5345i	0.830269	+	0.830269i	−0.157285	+	0.987553i	$0.550274\pi$
$194$	−1.18723	+	3.24663i	−0.0852378	+	0.233095i
$195$	−0.0331465	−	0.0463125i	−0.00237367	−	0.00331651i
$196$	2.85548	+	2.41074i	0.203963	+	0.172196i
$197$		−	17.8512i		−	1.27184i	−0.771753	−	0.635922i	$-0.780620\pi$
$197$		−	17.8512i		−	1.27184i	0.771753	−	0.635922i	$-0.219380\pi$
$198$	3.98453	+	1.45706i	0.283168	+	0.103549i
$199$		−	0.739848i		−	0.0524464i	−0.999656	−	0.0262232i	$-0.991652\pi$
$199$		−	0.739848i		−	0.0524464i	0.999656	−	0.0262232i	$-0.00834807\pi$
$200$	11.7139	+	7.92364i	0.828299	+	0.560286i
$201$		−	0.0610786i		−	0.00430816i
$202$	−0.367534	+	1.00507i	−0.0258596	+	0.0707167i
$203$		−	17.8166i		−	1.25048i
$204$	−0.00280154	−	0.0331737i	−0.000196147	−	0.00232262i
$205$	3.03925	+	4.24646i	0.212270	+	0.296586i
$206$	−11.9272	−	4.36154i	−0.831010	−	0.303883i
$207$	7.43809	+	7.43809i	0.516983	+	0.516983i
$208$	15.5427	−	2.64404i	1.07769	−	0.183331i
$209$		−	7.65171i		−	0.529280i
$210$	0.0123746	+	0.0446050i	0.000853927	+	0.00307804i
$211$	0.107395	−	0.107395i	0.00739338	−	0.00739338i	−0.703400	−	0.710794i	$-0.748336\pi$
$211$	0.107395	−	0.107395i	0.00739338	−	0.00739338i	0.710794	+	0.703400i	$0.248336\pi$
$212$	12.5424	−	14.8563i	0.861417	−	1.02033i
$213$	0.0679750			0.00465757
$214$	21.4392	−	9.95791i	1.46555	−	0.680709i
$215$	−0.580994	−	0.811770i	−0.0396235	−	0.0553623i
$216$	−0.0288615	+	0.105796i	−0.00196377	+	0.00719849i
$217$	−0.652890	−	0.652890i	−0.0443210	−	0.0443210i
$218$	−8.62271	+	23.5800i	−0.584004	+	1.59704i
$219$	0.0379939	−	0.0379939i	0.00256739	−	0.00256739i
$220$	3.40474	−	2.89961i	0.229548	−	0.195492i
$221$	−7.17945	−	7.17945i	−0.482942	−	0.482942i
$222$	0.0265151	+	0.0570864i	0.00177958	+	0.00383139i
$223$	−9.02041	+	9.02041i	−0.604051	+	0.604051i	−0.941385	−	0.337334i	$-0.890475\pi$
$223$	−9.02041	+	9.02041i	−0.604051	+	0.604051i	0.337334	+	0.941385i	$0.390475\pi$
$224$	−12.6025	−	2.32027i	−0.842042	−	0.155029i
$225$	−4.83798	+	14.1982i	−0.322532	+	0.946544i
$226$	14.6590	+	5.36050i	0.975105	+	0.356575i
$227$		−	0.679468i		−	0.0450979i	−0.999746	−	0.0225489i	$-0.992822\pi$
$227$		−	0.679468i		−	0.0450979i	0.999746	−	0.0225489i	$-0.00717816\pi$
$228$	0.0985390	−	0.00832167i	0.00652590	−	0.000551116i
$229$	19.2530	+	19.2530i	1.27227	+	1.27227i	0.944894	+	0.327378i	$0.106165\pi$
$229$	19.2530	+	19.2530i	1.27227	+	1.27227i	0.327378	+	0.944894i	$0.393835\pi$
$230$	10.6847	−	2.96420i	0.704525	−	0.195454i
$231$	0.0146381			0.000963115
$232$	−11.0357	−	19.3156i	−0.724528	−	1.26813i
$233$	−15.5974	+	15.5974i	−1.02182	+	1.02182i	−0.0220615	+	0.999757i	$0.507023\pi$
$233$	−15.5974	+	15.5974i	−1.02182	+	1.02182i	−0.999757	+	0.0220615i	$0.992977\pi$
$234$	7.04423	+	15.1661i	0.460496	+	0.991436i
$235$	−25.4525	−	4.21738i	−1.66034	−	0.275112i
$236$	0.764767	+	9.05579i	0.0497821	+	0.589482i
$237$	0.0109388			0.000710554
$238$	3.47634	+	7.48447i	0.225337	+	0.485146i
$239$	2.22342			0.143821			0.0719105	−	0.997411i	$-0.477090\pi$
$239$	2.22342			0.143821			0.0719105	+	0.997411i	$0.477090\pi$
$240$	0.0410441	+	0.0406929i	0.00264939	+	0.00262671i
$241$	0.947588			0.0610395			0.0305197	−	0.999534i	$-0.490284\pi$
$241$	0.947588			0.0610395			0.0305197	+	0.999534i	$0.490284\pi$
$242$	−0.595739	−	1.28261i	−0.0382956	−	0.0824495i
$243$	−0.174469			−0.0111922
$244$	−8.52092	+	0.719596i	−0.545496	+	0.0460674i
$245$	2.43170	+	3.39759i	0.155356	+	0.217064i
$246$	0.00899026	+	0.0193558i	0.000573198	+	0.00123408i
$247$	21.3258	−	21.3258i	1.35693	−	1.35693i
$248$	−1.11222	−	0.303418i	−0.0706261	−	0.0192670i
$249$	0.0196738			0.00124678
$250$	10.5159	+	11.8074i	0.665087	+	0.746766i
$251$	2.10397	+	2.10397i	0.132801	+	0.132801i	0.770383	−	0.637581i	$-0.220065\pi$
$251$	2.10397	+	2.10397i	0.132801	+	0.132801i	−0.637581	+	0.770383i	$0.720065\pi$
$252$	−1.14374	−	13.5433i	−0.0720487	−	0.853146i
$253$		−	3.50640i		−	0.220445i
$254$	−25.3035	−	9.25296i	−1.58768	−	0.580582i
$255$	0.00608447	−	0.0367207i	0.000381024	−	0.00229954i
$256$	−15.1000	+	5.29056i	−0.943750	+	0.330660i
$257$	13.7090	−	13.7090i	0.855143	−	0.855143i	−0.135618	−	0.990761i	$-0.543302\pi$
$257$	13.7090	−	13.7090i	0.855143	−	0.855143i	0.990761	+	0.135618i	$0.0433019\pi$
$258$	−0.00171861	−	0.00370013i	−0.000106996	−	0.000230360i
$259$	−11.0327	−	11.0327i	−0.685538	−	0.685538i
$260$	17.5706	+	1.40783i	1.08968	+	0.0873101i
$261$	16.6842	−	16.6842i	1.03272	−	1.03272i
$262$	6.54951	−	17.9106i	0.404630	−	1.10652i
$263$	−0.233915	−	0.233915i	−0.0144238	−	0.0144238i	0.699858	−	0.714282i	$-0.253247\pi$
$263$	−0.233915	−	0.233915i	−0.0144238	−	0.0144238i	−0.714282	+	0.699858i	$0.753247\pi$
$264$	0.0158696	−	0.00906686i	0.000976708	−	0.000558027i
$265$	17.6767	−	12.6515i	1.08587	−	0.777173i
$266$	−22.2318	+	10.3261i	−1.36312	+	0.633133i
$267$	0.0323563			0.00198018
$268$	14.4447	+	12.1950i	0.882350	+	0.744926i
$269$	12.8292	−	12.8292i	0.782208	−	0.782208i	−0.197995	−	0.980203i	$-0.563443\pi$
$269$	12.8292	−	12.8292i	0.782208	−	0.782208i	0.980203	+	0.197995i	$0.0634429\pi$
$270$	−0.0603639	+	0.106716i	−0.00367363	+	0.00649455i
$271$		−	14.5782i		−	0.885561i	−0.896630	−	0.442780i	$-0.853992\pi$
$271$		−	14.5782i		−	0.885561i	0.896630	−	0.442780i	$-0.146008\pi$
$272$	8.40471	+	5.96091i	0.509611	+	0.361433i
$273$	0.0407973	+	0.0407973i	0.00246916	+	0.00246916i
$274$	−14.8046	−	5.41373i	−0.894379	−	0.327055i
$275$	4.48692	−	2.20624i	0.270572	−	0.133042i
$276$	0.0451555	−	0.00381341i	0.00271804	−	0.000229540i
$277$		−	15.5404i		−	0.933730i	−0.884329	−	0.466865i	$-0.845383\pi$
$277$		−	15.5404i		−	0.933730i	0.884329	−	0.466865i	$-0.154617\pi$
$278$	−6.78516	+	18.5550i	−0.406947	+	1.11285i
$279$		−	1.22278i		−	0.0732060i
$280$	−13.0195	−	5.97932i	−0.778063	−	0.357333i
$281$			30.2654i			1.80549i	0.430181	+	0.902743i	$0.358450\pi$
$281$			30.2654i			1.80549i	−0.430181	+	0.902743i	$0.641550\pi$
$282$	−0.0990267	−	0.0362120i	−0.00589695	−	0.00215639i
$283$		−	28.0939i		−	1.67001i	−0.550242	−	0.835005i	$-0.685465\pi$
$283$		−	28.0939i		−	1.67001i	0.550242	−	0.835005i	$-0.314535\pi$
$284$	−13.5719	+	16.0756i	−0.805344	+	0.953914i
$285$	0.109075	+	0.0180733i	0.00646104	+	0.00107057i
$286$	1.91436	−	5.23509i	0.113199	−	0.309557i
$287$	−3.74076	−	3.74076i	−0.220810	−	0.220810i
$288$	−9.62870	−	13.9743i	−0.567376	−	0.823442i
$289$			10.3643i			0.609663i
$290$	−6.64892	−	23.9665i	−0.390438	−	1.40736i
$291$	−0.0111691	+	0.0111691i	−0.000654746	+	0.000654746i
$292$	1.39945	+	16.5712i	0.0818964	+	0.969755i
$293$	5.19918			0.303740			0.151870	−	0.988401i	$-0.451471\pi$
$293$	5.19918			0.303740			0.151870	+	0.988401i	$0.451471\pi$
$294$	0.00719310	+	0.0154866i	0.000419510	+	0.000903195i
$295$	−1.66094	+	10.0240i	−0.0967040	+	0.583623i
$296$	−18.7946	−	5.12723i	−1.09241	−	0.298014i
$297$	0.0274155	+	0.0274155i	0.00159081	+	0.00159081i
$298$	24.0173	+	8.78263i	1.39129	+	0.508764i
$299$	9.77256	−	9.77256i	0.565162	−	0.565162i
$300$	0.0332919	+	0.0553833i	0.00192211	+	0.00319756i
$301$	0.715098	+	0.715098i	0.0412176	+	0.0412176i
$302$	−26.4480	+	12.2844i	−1.52191	+	0.706887i
$303$	−0.00345767	+	0.00345767i	−0.000198638	+	0.000198638i
$304$	−17.7063	+	24.9653i	−1.01552	+	1.43186i
$305$	−9.43198	−	1.56284i	−0.540074	−	0.0894881i
$306$	−3.75337	+	10.2641i	−0.214566	+	0.586760i
$307$			14.9782i			0.854854i	0.904050	+	0.427427i	$0.140580\pi$
$307$			14.9782i			0.854854i	−0.904050	+	0.427427i	$0.859420\pi$
$308$	−2.92264	+	3.46181i	−0.166533	+	0.197255i
$309$	−0.0410323	−	0.0410323i	−0.00233425	−	0.00233425i
$310$	−1.12190	−	0.634600i	−0.0637195	−	0.0360428i
$311$	14.5788			0.826689			0.413345	−	0.910575i	$-0.364360\pi$
$311$	14.5788			0.826689			0.413345	+	0.910575i	$0.364360\pi$
$312$	0.0694996	+	0.0189597i	0.00393464	+	0.00107338i
$313$	−6.85967	+	6.85967i	−0.387732	+	0.387732i	−0.873878	−	0.486146i	$-0.838402\pi$
$313$	−6.85967	+	6.85967i	−0.387732	+	0.387732i	0.486146	+	0.873878i	$0.338402\pi$
$314$	17.8358	−	8.28425i	1.00653	−	0.467507i
$315$	2.48400	−	14.9913i	0.139958	−	0.844666i
$316$	−2.18405	+	2.58696i	−0.122862	+	0.145528i
$317$	2.24881			0.126306			0.0631528	−	0.998004i	$-0.479884\pi$
$317$	2.24881			0.126306			0.0631528	+	0.998004i	$0.479884\pi$
$318$	0.0805723	−	0.0374237i	0.00451827	−	0.00209862i
$319$	−7.86511			−0.440361
$320$	−17.8185	+	1.58193i	−0.996082	+	0.0884323i
$321$	0.108013			0.00602868
$322$	−10.1877	+	4.73193i	−0.567741	+	0.263700i
$323$	19.7107			1.09673
$324$	11.6112	−	13.7533i	0.645068	−	0.764071i
$325$	18.6543	+	6.35640i	1.03475	+	0.352590i
$326$	3.47125	−	1.61230i	0.192255	−	0.0892972i
$327$	−0.0811204	+	0.0811204i	−0.00448597	+	0.00448597i
$328$	−6.37252	−	1.73845i	−0.351863	−	0.0959896i
$329$	26.1366			1.44096
$330$	0.0196907	−	0.00546272i	0.00108394	−	0.000300713i
$331$	−15.0699	−	15.0699i	−0.828317	−	0.828317i	0.158967	−	0.987284i	$-0.449184\pi$
$331$	−15.0699	−	15.0699i	−0.828317	−	0.828317i	−0.987284	+	0.158967i	$0.949184\pi$
$332$	−3.92807	+	4.65272i	−0.215581	+	0.255351i
$333$		−	20.6628i		−	1.13232i
$334$	−4.15821	+	11.3712i	−0.227527	+	0.622204i
$335$	12.3010	+	17.1870i	0.672074	+	0.939027i
$336$	−0.0477598	−	0.0338729i	−0.00260551	−	0.00184792i
$337$	−6.38505	+	6.38505i	−0.347816	+	0.347816i	−0.859295	−	0.511480i	$-0.829098\pi$
$337$	−6.38505	+	6.38505i	−0.347816	+	0.347816i	0.511480	+	0.859295i	$0.329098\pi$
$338$	3.25202	−	1.51047i	0.176886	−	0.0821590i
$339$	0.0504303	+	0.0504303i	0.00273900	+	0.00273900i
$340$	7.46937	+	8.77058i	0.405083	+	0.475652i
$341$	−0.288216	+	0.288216i	−0.0156078	+	0.0156078i
$342$	−30.4885	−	11.1490i	−1.64863	−	0.602868i
$343$	−14.2055	−	14.2055i	−0.767027	−	0.767027i
$344$	1.21819	+	0.332328i	0.0656807	+	0.0179179i
$345$	0.0499836	+	0.00828208i	0.00269103	+	0.000445892i
$346$	−10.9333	−	23.5391i	−0.587778	−	1.26547i
$347$	−11.0863			−0.595144			−0.297572	−	0.954699i	$-0.596177\pi$
$347$	−11.0863			−0.595144			−0.297572	+	0.954699i	$0.596177\pi$
$348$	−0.00855376	−	0.101287i	−0.000458529	−	0.00542956i
$349$	19.8305	−	19.8305i	1.06150	−	1.06150i	0.0635198	−	0.997981i	$-0.479767\pi$
$349$	19.8305	−	19.8305i	1.06150	−	1.06150i	0.997981	−	0.0635198i	$-0.0202326\pi$
$350$	−12.4654	−	10.0593i	−0.666301	−	0.537691i
$351$			0.152817i			0.00815679i
$352$	−1.02428	+	5.56335i	−0.0545941	+	0.296528i
$353$	−4.72032	−	4.72032i	−0.251237	−	0.251237i	0.570241	−	0.821478i	$-0.306850\pi$
$353$	−4.72032	−	4.72032i	−0.251237	−	0.251237i	−0.821478	+	0.570241i	$0.806850\pi$
$354$	−0.0142615	+	0.0390000i	−0.000757988	+	0.00207282i
$355$	−19.1276	+	13.6899i	−1.01519	+	0.726583i
$356$	−6.46027	+	7.65206i	−0.342393	+	0.405558i
$357$			0.0377076i			0.00199570i
$358$	17.1996	+	6.28953i	0.909027	+	0.332412i
$359$		−	13.6874i		−	0.722393i	−0.932490	−	0.361196i	$-0.882368\pi$
$359$		−	13.6874i		−	0.722393i	0.932490	−	0.361196i	$-0.117632\pi$
$360$	−6.59268	−	17.7912i	−0.347465	−	0.937678i
$361$			39.5487i			2.08151i
$362$	0.775215	−	2.11993i	0.0407444	−	0.111421i
$363$		−	0.00646194i		−	0.000339164i
$364$	−17.7939	+	1.50270i	−0.932652	+	0.0787630i
$365$	−3.03936	+	18.3430i	−0.159087	+	0.960116i
$366$	−0.0366964	−	0.0134191i	−0.00191815	−	0.000701428i
$367$	16.2567	+	16.2567i	0.848594	+	0.848594i	0.989958	−	0.141363i	$-0.0451486\pi$
$367$	16.2567	+	16.2567i	0.848594	+	0.848594i	−0.141363	+	0.989958i	$0.545149\pi$
$368$	−8.11390	+	11.4404i	−0.422966	+	0.596370i
$369$		−	7.00598i		−	0.364717i
$370$	−18.9581	−	10.7236i	−0.985585	−	0.557494i
$371$	−15.5716	+	15.5716i	−0.808439	+	0.808439i
$372$	−0.00402511	−	0.00339821i	−0.000208692	−	0.000176189i
$373$	−13.7496			−0.711929			−0.355964	−	0.934500i	$-0.615848\pi$
$373$	−13.7496			−0.711929			−0.355964	+	0.934500i	$0.615848\pi$
$374$	3.30400	−	1.53462i	0.170846	−	0.0793532i
$375$	0.0208519	+	0.0691721i	0.00107679	+	0.00357203i
$376$	28.3355	−	16.1891i	1.46129	−	0.834888i
$377$	−21.9206	−	21.9206i	−1.12897	−	1.12897i
$378$	0.0426574	−	0.116653i	0.00219406	−	0.00599996i
$379$	16.9285	−	16.9285i	0.869559	−	0.869559i	−0.122865	−	0.992423i	$-0.539208\pi$
$379$	16.9285	−	16.9285i	0.869559	−	0.869559i	0.992423	+	0.122865i	$0.0392081\pi$
$380$	−26.0521	+	22.1870i	−1.33644	+	1.13817i
$381$	−0.0870496	−	0.0870496i	−0.00445969	−	0.00445969i
$382$	−1.14829	−	2.47225i	−0.0587518	−	0.126491i
$383$	−3.58262	+	3.58262i	−0.183063	+	0.183063i	−0.792689	−	0.609626i	$-0.791320\pi$
$383$	−3.58262	+	3.58262i	−0.183063	+	0.183063i	0.609626	+	0.792689i	$0.291320\pi$
$384$	−0.0727590	−	0.00714019i	−0.00371296	−	0.000364371i
$385$	−4.11903	+	2.94805i	−0.209925	+	0.150246i
$386$	−21.6658	−	7.92271i	−1.10276	−	0.403255i
$387$			1.33929i			0.0680799i
$388$	−0.411397	−	4.87145i	−0.0208855	−	0.247310i
$389$	9.59094	+	9.59094i	0.486280	+	0.486280i	0.907130	−	0.420850i	$-0.138268\pi$
$389$	9.59094	+	9.59094i	0.486280	+	0.486280i	−0.420850	+	0.907130i	$0.638268\pi$
$390$	0.0701043	+	0.0396544i	0.00354987	+	0.00200798i
$391$	9.03245			0.456791
$392$	−5.09864	−	1.39093i	−0.257520	−	0.0702525i
$393$	0.0616162	−	0.0616162i	0.00310813	−	0.00310813i
$394$	10.6347	+	22.8962i	0.535766	+	1.15349i
$395$	−3.07810	+	2.20304i	−0.154876	+	0.110847i
$396$	−5.97863	+	0.504899i	−0.300438	+	0.0253721i
$397$	−4.85580			−0.243706			−0.121853	−	0.992548i	$-0.538884\pi$
$397$	−4.85580			−0.243706			−0.121853	+	0.992548i	$0.538884\pi$
$398$	0.440756	+	0.948938i	0.0220931	+	0.0475660i
$399$	−0.112006			−0.00560733
$400$	−19.7448	−	3.18452i	−0.987242	−	0.159226i
$401$	3.37736			0.168657			0.0843286	−	0.996438i	$-0.473125\pi$
$401$	3.37736			0.168657			0.0843286	+	0.996438i	$0.473125\pi$
$402$	0.0363869	+	0.0783402i	0.00181482	+	0.00390726i
$403$	−1.60655			−0.0800282
$404$	−0.127358	−	1.50807i	−0.00633628	−	0.0750295i
$405$	16.3643	−	11.7122i	0.813150	−	0.581982i
$406$	10.6141	+	22.8519i	0.526768	+	1.13412i
$407$	−4.87035	+	4.87035i	−0.241414	+	0.241414i
$408$	0.0233562	+	0.0408800i	0.00115630	+	0.00202386i
$409$	−16.5185			−0.816789			−0.408394	−	0.912806i	$-0.633911\pi$
$409$	−16.5185			−0.816789			−0.408394	+	0.912806i	$0.633911\pi$
$410$	−6.42796	−	3.63597i	−0.317455	−	0.179568i
$411$	−0.0509310	−	0.0509310i	−0.00251224	−	0.00251224i
$412$	17.8964	−	1.51136i	0.881691	−	0.0744593i
$413$		−	10.2935i		−	0.506508i
$414$	−13.9713	−	5.10903i	−0.686654	−	0.251095i
$415$	−5.53604	+	3.96222i	−0.271754	+	0.194498i
$416$	−18.3601	+	12.6507i	−0.900180	+	0.620251i
$417$	−0.0638332	+	0.0638332i	−0.00312592	+	0.00312592i
$418$	4.55842	+	9.81418i	0.222960	+	0.480027i
$419$	3.48032	+	3.48032i	0.170025	+	0.170025i	0.786990	−	0.616966i	$-0.211638\pi$
$419$	3.48032	+	3.48032i	0.170025	+	0.170025i	−0.616966	+	0.786990i	$0.711638\pi$
$420$	−0.0424447	−	0.0498389i	−0.00207109	−	0.00243189i
$421$	15.9955	−	15.9955i	0.779575	−	0.779575i	−0.200184	−	0.979758i	$-0.564154\pi$
$421$	15.9955	−	15.9955i	0.779575	−	0.779575i	0.979758	+	0.200184i	$0.0641539\pi$
$422$	−0.0737668	+	0.201726i	−0.00359091	+	0.00981985i
$423$	24.4753	+	24.4753i	1.19003	+	1.19003i
$424$	−7.23661	+	26.5268i	−0.351441	+	1.28826i
$425$	5.68327	+	11.5583i	0.275679	+	0.560659i
$426$	−0.0871856	+	0.0404954i	−0.00422416	+	0.00196201i
$427$	9.68547			0.468713
$428$	−21.5658	+	25.5443i	−1.04242	+	1.23473i
$429$	0.0180098	−	0.0180098i	0.000869523	−	0.000869523i
$430$	1.22879	+	0.695065i	0.0592577	+	0.0335190i
$431$		−	38.0977i		−	1.83510i	−0.397619	−	0.917551i	$-0.630163\pi$
$431$		−	38.0977i		−	1.83510i	0.397619	−	0.917551i	$-0.369837\pi$
$432$	−0.0260086	−	0.152889i	−0.00125134	−	0.00735587i
$433$	−28.3845	−	28.3845i	−1.36407	−	1.36407i	−0.868657	−	0.495414i	$-0.835016\pi$
$433$	−28.3845	−	28.3845i	−1.36407	−	1.36407i	−0.495414	−	0.868657i	$-0.664984\pi$
$434$	1.22636	+	0.448453i	0.0588670	+	0.0215264i
$435$	0.0185773	−	0.112117i	0.000890714	−	0.00537559i
$436$	−2.98794	−	35.3809i	−0.143096	−	1.69444i
$437$			26.8299i			1.28345i
$438$	−0.0260970	+	0.0713660i	−0.00124696	+	0.00341000i
$439$		−	0.0216975i		−	0.00103556i	−1.00000		0.000517782i	$-0.999835\pi$
$439$		−	0.0216975i		−	0.00103556i	1.00000		0.000517782i	$-0.000164815\pi$
$440$	−2.63955	+	5.74741i	−0.125836	+	0.273997i
$441$		−	5.60547i		−	0.266927i
$442$	13.4855	+	4.93138i	0.641442	+	0.234562i
$443$		−	7.21854i		−	0.342963i	−0.985187	−	0.171482i	$-0.945145\pi$
$443$		−	7.21854i		−	0.342963i	0.985187	−	0.171482i	$-0.0548554\pi$
$444$	−0.0680173	−	0.0574237i	−0.00322796	−	0.00272521i
$445$	−9.10481	+	6.51643i	−0.431609	+	0.308908i
$446$	6.19588	−	16.9435i	0.293383	−	0.802298i
$447$	0.0826248	+	0.0826248i	0.00390802	+	0.00390802i
$448$	17.5464	−	4.53182i	0.828991	−	0.214108i
$449$			11.6755i			0.551003i	0.961301	+	0.275501i	$0.0888438\pi$
$449$			11.6755i			0.551003i	−0.961301	+	0.275501i	$0.911156\pi$
$450$	−2.25314	−	21.0929i	−0.106214	−	0.994329i
$451$	−1.65135	+	1.65135i	−0.0777589	+	0.0777589i
$452$	−21.9953	+	1.85752i	−1.03457	+	0.0873703i
$453$	−0.133248			−0.00626053
$454$	0.404786	+	0.871494i	0.0189975	+	0.0409013i
$455$	−19.6964	−	3.26362i	−0.923382	−	0.153001i
$456$	−0.121430	+	0.0693770i	−0.00568647	+	0.00324888i
$457$	17.2759	+	17.2759i	0.808130	+	0.808130i	0.984351	−	0.176220i	$-0.0563871\pi$
$457$	17.2759	+	17.2759i	0.808130	+	0.808130i	−0.176220	+	0.984351i	$0.556387\pi$
$458$	−36.1638	−	13.2243i	−1.68982	−	0.617933i
$459$	−0.0706220	+	0.0706220i	−0.00329635	+	0.00329635i
$460$	−11.9384	+	10.1672i	−0.556630	+	0.474047i
$461$	6.83582	+	6.83582i	0.318376	+	0.318376i	0.848143	−	0.529767i	$-0.177721\pi$
$461$	6.83582	+	6.83582i	0.318376	+	0.318376i	−0.529767	+	0.848143i	$0.677721\pi$
$462$	−0.0187750	+	0.00872048i	−0.000873491	+	0.000405713i
$463$	16.1902	−	16.1902i	0.752420	−	0.752420i	−0.222510	−	0.974930i	$-0.571425\pi$
$463$	16.1902	−	16.1902i	0.752420	−	0.752420i	0.974930	+	0.222510i	$0.0714250\pi$
$464$	25.6616	+	18.2001i	1.19131	+	0.844917i
$465$	−0.00342775	−	0.00478928i	−0.000158958	−	0.000222097i
$466$	10.7134	−	29.2974i	0.496290	−	1.35717i
$467$			22.0269i			1.01928i	0.860387	+	0.509642i	$0.170222\pi$
$467$			22.0269i			1.01928i	−0.860387	+	0.509642i	$0.829778\pi$
$468$	−18.0700	−	15.2557i	−0.835288	−	0.705193i
$469$	−15.1403	−	15.1403i	−0.699112	−	0.699112i
$470$	35.1582	−	9.75380i	1.62173	−	0.449909i
$471$	0.0898586			0.00414047
$472$	−6.37579	−	11.1595i	−0.293469	−	0.513656i
$473$	0.315678	−	0.315678i	0.0145149	−	0.0145149i
$474$	−0.0140303	+	0.00651670i	−0.000644433	+	0.000299322i
$475$	−34.3326	+	16.8815i	−1.57529	+	0.774578i
$476$	−8.91759	−	7.52869i	−0.408737	−	0.345077i
$477$	−29.1637			−1.33532
$478$	−2.85178	+	1.32458i	−0.130438	+	0.0605848i
$479$	−5.68620			−0.259809			−0.129904	−	0.991527i	$-0.541467\pi$
$479$	−5.68620			−0.259809			−0.129904	+	0.991527i	$0.541467\pi$
$480$	−0.0768860	−	0.0277416i	−0.00350935	−	0.00126622i
$481$	−27.1479			−1.23784
$482$	−1.21539	+	0.564515i	−0.0553594	+	0.0257130i
$483$	−0.0513269			−0.00233546
$484$	1.52820	+	1.29019i	0.0694639	+	0.0586450i
$485$	0.893485	−	5.39231i	0.0405710	−	0.244852i
$486$	0.223776	−	0.103938i	0.0101507	−	0.00471473i
$487$	14.3704	−	14.3704i	0.651183	−	0.651183i	−0.302095	−	0.953278i	$-0.597686\pi$
$487$	14.3704	−	14.3704i	0.651183	−	0.651183i	0.953278	+	0.302095i	$0.0976859\pi$
$488$	10.5003	−	5.99921i	0.475328	−	0.271571i
$489$	0.0174885			0.000790859
$490$	−5.14301	−	2.90913i	−0.232337	−	0.131421i
$491$	−20.2871	−	20.2871i	−0.915545	−	0.915545i	0.0811566	−	0.996701i	$-0.474139\pi$
$491$	−20.2871	−	20.2871i	−0.915545	−	0.915545i	−0.996701	+	0.0811566i	$0.974139\pi$
$492$	−0.0230620	−	0.0194702i	−0.00103972	−	0.000877783i
$493$		−	20.2604i		−	0.912484i
$494$	−14.6481	+	40.0574i	−0.659051	+	1.80227i
$495$	−6.61788	−	1.09656i	−0.297452	−	0.0492865i
$496$	1.60731	−	0.273426i	0.0721702	−	0.0122772i
$497$	16.8497	−	16.8497i	0.755814	−	0.755814i
$498$	−0.0252339	+	0.0117204i	−0.00113076	+	0.000525206i
$499$	−8.21163	−	8.21163i	−0.367603	−	0.367603i	0.498999	−	0.866602i	$-0.333701\pi$
$499$	−8.21163	−	8.21163i	−0.367603	−	0.367603i	−0.866602	+	0.498999i	$0.833701\pi$
$500$	−20.5220	−	8.87957i	−0.917773	−	0.397106i
$501$	−0.0391194	+	0.0391194i	−0.00174773	+	0.00174773i
$502$	−3.95200	−	1.44516i	−0.176386	−	0.0645007i
$503$	4.97663	+	4.97663i	0.221897	+	0.221897i	0.809297	−	0.587400i	$-0.199848\pi$
$503$	4.97663	+	4.97663i	0.221897	+	0.221897i	−0.587400	+	0.809297i	$0.699848\pi$
$504$	9.53523	+	16.6894i	0.424733	+	0.743405i
$505$	0.276599	−	1.66932i	0.0123085	−	0.0742837i
$506$	2.08890	+	4.49735i	0.0928629	+	0.199932i
$507$	0.0163840			0.000727639
$508$	37.9670	−	3.20633i	1.68451	−	0.142258i
$509$	−22.8453	+	22.8453i	−1.01260	+	1.01260i	−0.0126826	+	0.999920i	$0.504037\pi$
$509$	−22.8453	+	22.8453i	−1.01260	+	1.01260i	−0.999920	+	0.0126826i	$0.995963\pi$
$510$	0.0140719	+	0.0507231i	0.000623115	+	0.00224606i
$511$		−	18.8360i		−	0.833254i
$512$	16.2157	−	15.7814i	0.716637	−	0.697446i
$513$	−0.209775	−	0.209775i	−0.00926181	−	0.00926181i
$514$	−9.41634	+	25.7503i	−0.415337	+	1.13580i
$515$	19.8099	+	3.28242i	0.872927	+	0.144641i
$516$	0.00440863	+	0.00372199i	0.000194079	+	0.000163852i
$517$		−	11.5379i		−	0.507437i
$518$	20.7233	+	7.57806i	0.910528	+	0.332961i
$519$		−	0.118593i		−	0.00520564i
$520$	−23.3750	+	8.66181i	−1.02506	+	0.379846i
$521$			3.18499i			0.139537i	0.997563	+	0.0697685i	$0.0222261\pi$
$521$			3.18499i			0.139537i	−0.997563	+	0.0697685i	$0.977774\pi$
$522$	−11.4599	+	31.3388i	−0.501587	+	1.37166i
$523$			27.0737i			1.18385i	0.805992	+	0.591926i	$0.201632\pi$
$523$			27.0737i			1.18385i	−0.805992	+	0.591926i	$0.798368\pi$
$524$	2.26953	+	26.8741i	0.0991451	+	1.17400i
$525$	−0.0322952	−	0.0656799i	−0.00140948	−	0.00286651i
$526$	0.439375	+	0.160670i	0.0191577	+	0.00700556i
$527$	−0.742442	−	0.742442i	−0.0323413	−	0.0323413i
$528$	−0.0149531	+	0.0210834i	−0.000650750	+	0.000917538i
$529$		−	10.7052i		−	0.465442i
$530$	−15.1354	+	26.7576i	−0.657440	+	1.16228i
$531$	9.63917	−	9.63917i	0.418305	−	0.418305i
$532$	22.3632	−	26.4888i	0.969567	−	1.14843i
$533$	−9.20483			−0.398705
$534$	−0.0415007	+	0.0192759i	−0.00179591	+	0.000834152i
$535$	−30.3939	+	21.7533i	−1.31404	+	0.940477i
$536$	−25.7920	−	7.03614i	−1.11404	−	0.303915i
$537$	0.0591703	+	0.0591703i	0.00255339	+	0.00255339i
$538$	−8.81202	+	24.0977i	−0.379913	+	1.03893i
$539$	−1.32124	+	1.32124i	−0.0569099	+	0.0569099i
$540$	0.0138484	−	0.172837i	0.000595941	−	0.00743771i
$541$	−6.59855	−	6.59855i	−0.283694	−	0.283694i	0.550886	−	0.834580i	$-0.314290\pi$
$541$	−6.59855	−	6.59855i	−0.283694	−	0.283694i	−0.834580	+	0.550886i	$0.814290\pi$
$542$	8.68479	+	18.6981i	0.373044	+	0.803154i
$543$	0.00729303	−	0.00729303i	0.000312974	−	0.000312974i
$544$	−14.3311	−	2.63852i	−0.614442	−	0.113126i
$545$	6.48930	−	39.1639i	0.277971	−	1.67760i
$546$	−0.0766316	−	0.0280226i	−0.00327953	−	0.00119926i
$547$			38.7650i			1.65747i	0.559641	+	0.828735i	$0.310939\pi$
$547$			38.7650i			1.65747i	−0.559641	+	0.828735i	$0.689061\pi$
$548$	22.2137	−	1.87596i	0.948924	−	0.0801372i
$549$	9.06984	+	9.06984i	0.387091	+	0.387091i
$550$	−4.44064	+	5.50279i	−0.189349	+	0.234640i
$551$	60.1815			2.56382
$552$	−0.0556452	+	0.0317920i	−0.00236842	+	0.00135316i
$553$	2.71153	−	2.71153i	0.115306	−	0.115306i
$554$	9.25800	+	19.9323i	0.393335	+	0.846841i
$555$	−0.0579229	−	0.0809303i	−0.00245869	−	0.00343530i
$556$	−2.35119	−	27.8410i	−0.0997128	−	1.18072i
$557$	−30.6493			−1.29865			−0.649326	−	0.760510i	$-0.724949\pi$
$557$	−30.6493			−1.29865			−0.649326	+	0.760510i	$0.724949\pi$
$558$	0.728458	+	1.56835i	0.0308381	+	0.0663937i
$559$	1.75963			0.0744244
$560$	20.2611	−	0.0870680i	0.856187	−	0.00367930i
$561$	0.0166459			0.000702790
$562$	−18.0303	−	38.8188i	−0.760563	−	1.63747i
$563$	−25.1261			−1.05894			−0.529469	−	0.848329i	$-0.677609\pi$
$563$	−25.1261			−1.05894			−0.529469	+	0.848329i	$0.677609\pi$
$564$	0.148586	−	0.0125482i	0.00625659	−	0.000528373i
$565$	−24.3471	−	4.03422i	−1.02429	−	0.169721i
$566$	16.7366	+	36.0336i	0.703494	+	1.51461i
$567$	−14.4155	+	14.4155i	−0.605396	+	0.605396i
$568$	7.83059	−	28.7041i	0.328564	−	1.20440i
$569$	14.7951			0.620243			0.310122	−	0.950697i	$-0.399630\pi$
$569$	14.7951			0.620243			0.310122	+	0.950697i	$0.399630\pi$
$570$	−0.150668	+	0.0417992i	−0.00631078	+	0.00175077i
$571$	23.0921	+	23.0921i	0.966375	+	0.966375i	0.999453	−	0.0330782i	$-0.0105310\pi$
$571$	23.0921	+	23.0921i	0.966375	+	0.966375i	−0.0330782	+	0.999453i	$0.510531\pi$
$572$	0.663364	+	7.85505i	0.0277366	+	0.328436i
$573$		−	0.0124554i		−	0.000520334i
$574$	7.02646	+	2.56943i	0.293279	+	0.107246i
$575$	−15.7329	+	7.73597i	−0.656109	+	0.322612i
$576$	20.6749	+	12.1874i	0.861454	+	0.507808i
$577$	0.793887	−	0.793887i	0.0330499	−	0.0330499i	−0.690389	−	0.723439i	$-0.742560\pi$
$577$	0.793887	−	0.793887i	0.0330499	−	0.0330499i	0.723439	+	0.690389i	$0.242560\pi$
$578$	−6.17440	−	13.2933i	−0.256821	−	0.552930i
$579$	−0.0745349	−	0.0745349i	−0.00309757	−	0.00309757i
$580$	22.8057	+	26.7787i	0.946957	+	1.11192i
$581$	4.87677	−	4.87677i	0.202322	−	0.202322i
$582$	0.00767177	−	0.0209795i	0.000318005	−	0.000869630i
$583$	6.87405	+	6.87405i	0.284694	+	0.284694i
$584$	−11.6670	−	20.4207i	−0.482786	−	0.845014i
$585$	−15.3883	−	21.5006i	−0.636227	−	0.888942i
$586$	−6.66854	+	3.09736i	−0.275475	+	0.127951i
$587$	0.895329			0.0369542			0.0184771	−	0.999829i	$-0.494118\pi$
$587$	0.895329			0.0369542			0.0184771	+	0.999829i	$0.494118\pi$
$588$	−0.0184519	−	0.0155781i	−0.000760944	−	0.000642428i
$589$	2.20535	−	2.20535i	0.0908697	−	0.0908697i
$590$	−3.84137	−	13.8465i	−0.158147	−	0.570050i
$591$			0.115353i			0.00474500i
$592$	27.1606	−	4.62042i	1.11630	−	0.189898i
$593$	−9.30198	−	9.30198i	−0.381987	−	0.381987i	0.489831	−	0.871817i	$-0.337059\pi$
$593$	−9.30198	−	9.30198i	−0.381987	−	0.381987i	−0.871817	+	0.489831i	$0.837059\pi$
$594$	−0.0514959	−	0.0188310i	−0.00211290	−	0.000772644i
$595$	−7.59414	−	10.6106i	−0.311329	−	0.434992i
$596$	−36.0371	+	3.04335i	−1.47614	+	0.124661i
$597$			0.00478085i			0.000195667i
$598$	−6.71251	+	18.3563i	−0.274495	+	0.750645i
$599$			25.2589i			1.03205i	0.856573	+	0.516025i	$0.172589\pi$
$599$			25.2589i			1.03205i	−0.856573	+	0.516025i	$0.827411\pi$
$600$	−0.0756946	−	0.0512021i	−0.00309022	−	0.00209032i
$601$			30.0197i			1.22453i	0.790654	+	0.612264i	$0.209741\pi$
$601$			30.0197i			1.22453i	−0.790654	+	0.612264i	$0.790259\pi$
$602$	−1.34321	−	0.491182i	−0.0547450	−	0.0200191i
$603$		−	28.3558i		−	1.15474i
$604$	26.6043	−	31.5122i	1.08251	−	1.28221i
$605$	1.30141	+	1.81833i	0.0529097	+	0.0739258i
$606$	0.00237498	−	0.00649472i	9.64770e−5	−	0.000263830i
$607$	−0.241710	−	0.241710i	−0.00981073	−	0.00981073i	0.702184	−	0.711995i	$-0.252208\pi$
$607$	−0.241710	−	0.241710i	−0.00981073	−	0.00981073i	−0.711995	+	0.702184i	$0.752208\pi$
$608$	7.83746	−	42.5691i	0.317851	−	1.72641i
$609$			0.115130i			0.00466531i
$610$	13.0286	−	3.61448i	0.527514	−	0.146346i
$611$	32.1569	−	32.1569i	1.30093	−	1.30093i
$612$	−1.30062	−	15.4009i	−0.0525743	−	0.622545i
$613$	−36.1840			−1.46146			−0.730730	−	0.682667i	$-0.760820\pi$
$613$	−36.1840			−1.46146			−0.730730	+	0.682667i	$0.760820\pi$
$614$	−8.92313	−	19.2113i	−0.360108	−	0.775305i
$615$	−0.0196394	−	0.0274404i	−0.000791939	−	0.00110650i
$616$	1.68628	−	6.18129i	0.0679421	−	0.249051i
$617$	−11.7413	−	11.7413i	−0.472686	−	0.472686i	0.430096	−	0.902783i	$-0.358480\pi$
$617$	−11.7413	−	11.7413i	−0.472686	−	0.472686i	−0.902783	+	0.430096i	$0.858480\pi$
$618$	0.0770731	+	0.0281840i	0.00310033	+	0.00113373i
$619$	−32.3783	+	32.3783i	−1.30139	+	1.30139i	−0.373941	+	0.927453i	$0.621994\pi$
$619$	−32.3783	+	32.3783i	−1.30139	+	1.30139i	−0.927453	+	0.373941i	$0.878006\pi$
$620$	1.81702	+	0.145587i	0.0729731	+	0.00584691i
$621$	−0.0961296	−	0.0961296i	−0.00385755	−	0.00385755i
$622$	−18.6990	+	8.68518i	−0.749761	+	0.348244i
$623$	8.02053	−	8.02053i	0.321336	−	0.321336i
$624$	−0.100436	+	0.0170856i	−0.00402066	+	0.000683973i
$625$	−19.7985	−	15.2650i	−0.791940	−	0.610599i
$626$	4.71173	−	12.8849i	0.188318	−	0.514983i
$627$			0.0494449i			0.00197464i
$628$	−17.9412	+	21.2510i	−0.715931	+	0.848006i
$629$	−12.5460	−	12.5460i	−0.500240	−	0.500240i
$630$	5.74491	+	20.7079i	0.228883	+	0.825022i
$631$	40.4467			1.61016			0.805079	−	0.593168i	$-0.202123\pi$
$631$	40.4467			1.61016			0.805079	+	0.593168i	$0.202123\pi$
$632$	1.26013	−	4.61919i	0.0501254	−	0.183742i
$633$	−0.000693980	0	0.000693980i	−2.75832e−5	0	2.75832e-5i
$634$	−2.88435	+	1.33970i	−0.114552	+	0.0532064i
$635$	42.0264	+	6.96361i	1.66777	+	0.276343i
$636$	−0.0810483	+	0.0960002i	−0.00321378	+	0.00380666i
$637$	−7.36477			−0.291803
$638$	10.0879	−	4.68555i	0.399383	−	0.185503i
$639$	31.5575			1.24839
$640$	21.9118	−	12.6442i	0.866139	−	0.499804i
$641$	32.7230			1.29248			0.646239	−	0.763135i	$-0.276341\pi$
$641$	32.7230			1.29248			0.646239	+	0.763135i	$0.276341\pi$
$642$	−0.138538	+	0.0643474i	−0.00546768	+	0.00253959i
$643$	16.4946			0.650482			0.325241	−	0.945631i	$-0.394555\pi$
$643$	16.4946			0.650482			0.325241	+	0.945631i	$0.394555\pi$
$644$	10.2479	−	12.1385i	0.403825	−	0.478323i
$645$	0.00375435	+	0.00524561i	0.000147827	+	0.000206546i
$646$	−25.2812	+	11.7425i	−0.994677	+	0.462001i
$647$	0.609080	−	0.609080i	0.0239454	−	0.0239454i	−0.695033	−	0.718978i	$-0.744610\pi$
$647$	0.609080	−	0.609080i	0.0239454	−	0.0239454i	0.718978	+	0.695033i	$0.244610\pi$
$648$	−6.69934	+	24.5574i	−0.263175	+	0.964705i
$649$	−4.54401			−0.178368
$650$	−27.7130	+	2.96029i	−1.08699	+	0.116112i
$651$	0.00421893	+	0.00421893i	0.000165353	+	0.000165353i
$652$	−3.49176	+	4.13592i	−0.136748	+	0.161975i
$653$		−	28.2986i		−	1.10741i	−0.832712	−	0.553706i	$-0.813213\pi$
$653$		−	28.2986i		−	1.10741i	0.832712	−	0.553706i	$-0.186787\pi$
$654$	0.0557194	−	0.152373i	0.00217880	−	0.00595824i
$655$	−4.92904	+	29.7475i	−0.192594	+	1.16233i
$656$	9.20913	−	1.56661i	0.359556	−	0.0611657i
$657$	17.6387	−	17.6387i	0.688151	−	0.688151i
$658$	−33.5231	+	15.5706i	−1.30687	+	0.607005i
$659$	−0.286312	−	0.286312i	−0.0111531	−	0.0111531i	0.701508	−	0.712661i	$-0.252510\pi$
$659$	−0.286312	−	0.286312i	−0.0111531	−	0.0111531i	−0.712661	+	0.701508i	$0.752510\pi$
$660$	−0.0220012	+	0.0187371i	−0.000856396	+	0.000729340i
$661$	−34.7849	+	34.7849i	−1.35297	+	1.35297i	−0.470660	+	0.882315i	$0.655984\pi$
$661$	−34.7849	+	34.7849i	−1.35297	+	1.35297i	−0.882315	+	0.470660i	$0.844016\pi$
$662$	28.3066	+	10.3511i	1.10017	+	0.402308i
$663$	0.0463932	+	0.0463932i	0.00180176	+	0.00180176i
$664$	2.26638	−	8.30774i	0.0879527	−	0.322403i
$665$	31.5176	−	22.5576i	1.22220	−	0.874746i
$666$	12.3097	+	26.5024i	0.476990	+	1.02695i
$667$	27.5782			1.06783
$668$	−1.44090	−	17.0621i	−0.0557501	−	0.660151i
$669$	0.0582893	−	0.0582893i	0.00225359	−	0.00225359i
$670$	−26.0164	−	14.7161i	−1.00510	−	0.568533i
$671$		−	4.27562i		−	0.165059i
$672$	0.0814368	+	0.0149934i	0.00314149	+	0.000578384i
$673$	7.65788	+	7.65788i	0.295190	+	0.295190i	0.839126	−	0.543937i	$-0.183067\pi$
$673$	7.65788	+	7.65788i	0.295190	+	0.295190i	−0.543937	+	0.839126i	$0.683067\pi$
$674$	4.38572	−	11.9934i	0.168932	−	0.461967i
$675$	0.0625259	−	0.183496i	0.00240662	−	0.00706278i
$676$	−3.27123	+	3.87471i	−0.125816	+	0.149027i
$677$		−	6.42929i		−	0.247098i	−0.992338	−	0.123549i	$-0.960572\pi$
$677$		−	6.42929i		−	0.247098i	0.992338	−	0.123549i	$-0.0394276\pi$
$678$	−0.0947258	−	0.0346392i	−0.00363792	−	0.00133031i
$679$			5.53723i			0.212500i
$680$	−14.8053	−	6.79946i	−0.567757	−	0.260748i
$681$			0.00439068i			0.000168251i
$682$	0.197968	−	0.541371i	0.00758059	−	0.0207302i
$683$			50.2180i			1.92154i	0.277349	+	0.960769i	$0.410544\pi$
$683$			50.2180i			1.92154i	−0.277349	+	0.960769i	$0.589456\pi$
$684$	45.7468	−	3.86334i	1.74917	−	0.147719i
$685$	24.5889	+	4.07428i	0.939492	+	0.155670i
$686$	26.6830	+	9.75740i	1.01876	+	0.372539i
$687$	−0.124411	−	0.124411i	−0.00474659	−	0.00474659i
$688$	−1.76045	+	0.299478i	−0.0671166	+	0.0114175i
$689$			38.3169i			1.45976i
$690$	−0.0690435	+	0.0191545i	−0.00262844	+	0.000729198i
$691$	5.16638	−	5.16638i	0.196538	−	0.196538i	−0.601976	−	0.798514i	$-0.705620\pi$
$691$	5.16638	−	5.16638i	0.196538	−	0.196538i	0.798514	+	0.601976i	$0.205620\pi$
$692$	28.0464	+	23.6782i	1.06616	+	0.900110i
$693$	6.79574			0.258149
$694$	14.2194	−	6.60454i	0.539762	−	0.250705i
$695$	5.10639	−	30.8178i	0.193697	−	1.16899i
$696$	0.0713118	+	0.124816i	0.00270307	+	0.00473115i
$697$	−4.25386	−	4.25386i	−0.161126	−	0.161126i
$698$	−13.6210	+	37.2486i	−0.515563	+	1.40988i
$699$	0.100789	−	0.100789i	0.00381220	−	0.00381220i
$700$	21.9809	+	5.47606i	0.830801	+	0.206976i
$701$	34.1560	+	34.1560i	1.29005	+	1.29005i	0.934752	+	0.355302i	$0.115622\pi$
$701$	34.1560	+	34.1560i	1.29005	+	1.29005i	0.355302	+	0.934752i	$0.384378\pi$
$702$	−0.0910393	−	0.196006i	−0.00343606	−	0.00739775i
$703$	37.2665	−	37.2665i	1.40553	−	1.40553i
$704$	−2.00056	−	7.74582i	−0.0753988	−	0.291932i
$705$	0.164473	+	0.0272525i	0.00619440	+	0.00102639i
$706$	8.86641	+	3.24226i	0.333692	+	0.122024i
$707$			1.71418i			0.0644685i
$708$	−0.00494188	−	0.0585179i	−0.000185727	−	0.00219924i
$709$	17.1228	+	17.1228i	0.643059	+	0.643059i	0.951306	−	0.308247i	$-0.0997423\pi$
$709$	17.1228	+	17.1228i	0.643059	+	0.643059i	−0.308247	+	0.951306i	$0.599742\pi$
$710$	16.3777	−	28.9539i	0.614645	−	1.08662i
$711$	5.07836			0.190454
$712$	3.72739	−	13.6633i	0.139690	−	0.512052i
$713$	1.01060	−	1.01060i	0.0378473	−	0.0378473i
$714$	−0.0224639	−	0.0483642i	−0.000840689	−	0.00180998i
$715$	−1.44071	+	8.69492i	−0.0538796	+	0.325172i
$716$	−25.8073	+	2.17944i	−0.964465	+	0.0814497i
$717$	−0.0143676			−0.000536567
$718$	8.15412	+	17.5556i	0.304309	+	0.655170i
$719$	−9.86550			−0.367921			−0.183960	−	0.982934i	$-0.558892\pi$
$719$	−9.86550			−0.367921			−0.183960	+	0.982934i	$0.558892\pi$
$720$	19.0548	+	18.8917i	0.710129	+	0.704052i
$721$	−20.3423			−0.757586
$722$	−23.5607	−	50.7256i	−0.876838	−	1.88781i
$723$	−0.00612325			−0.000227726
$724$	0.268627	+	3.18088i	0.00998345	+	0.118216i
$725$	17.3523	+	35.2901i	0.644450	+	1.31064i
$726$	0.00384963	+	0.00828816i	0.000142873	+	0.000307602i
$727$	−26.9835	+	26.9835i	−1.00076	+	1.00076i	−0.000763290		1.00000i	$0.500243\pi$
$727$	−26.9835	+	26.9835i	−1.00076	+	1.00076i	−1.00000		0.000763290i	$0.999757\pi$
$728$	21.9274	−	12.5279i	0.812684	−	0.464314i
$729$	−26.9977			−0.999916
$730$	−7.02931	−	25.3376i	−0.260167	−	0.937787i
$731$	0.813183	+	0.813183i	0.0300767	+	0.0300767i
$732$	0.0550616	−	0.00464999i	0.00203514	−	0.000171868i
$733$		−	24.8719i		−	0.918665i	−0.888264	−	0.459333i	$-0.848089\pi$
$733$		−	24.8719i		−	0.918665i	0.888264	−	0.459333i	$-0.151911\pi$
$734$	−30.5359	−	11.1663i	−1.12710	−	0.412156i
$735$	−0.0157135	−	0.0219550i	−0.000579601	−	0.000809823i
$736$	3.59152	−	19.5073i	0.132385	−	0.719049i
$737$	−6.68362	+	6.68362i	−0.246194	+	0.246194i
$738$	4.17374	+	8.98595i	0.153637	+	0.330778i
$739$	−36.6314	−	36.6314i	−1.34751	−	1.34751i	−0.888361	−	0.459146i	$-0.848155\pi$
$739$	−36.6314	−	36.6314i	−1.34751	−	1.34751i	−0.459146	−	0.888361i	$-0.651845\pi$
$740$	30.7044	+	2.46016i	1.12872	+	0.0904374i
$741$	−0.137806	+	0.137806i	−0.00506243	+	0.00506243i
$742$	10.6957	−	29.2490i	0.392653	−	1.07376i
$743$	−17.3017	−	17.3017i	−0.634740	−	0.634740i	0.314513	−	0.949253i	$-0.398159\pi$
$743$	−17.3017	−	17.3017i	−0.634740	−	0.634740i	−0.949253	+	0.314513i	$0.898159\pi$
$744$	0.00718710	+	0.00196067i	0.000263492	+	7.18815e-5i
$745$	−39.8902	−	6.60965i	−1.46146	−	0.242159i
$746$	17.6354	−	8.19119i	0.645679	−	0.299901i
$747$	9.13357			0.334180
$748$	−3.32352	+	3.93664i	−0.121520	+	0.143938i
$749$	26.7743	−	26.7743i	0.978313	−	0.978313i
$750$	−0.0679534	−	0.0762987i	−0.00248131	−	0.00278603i
$751$			36.1384i			1.31871i	0.751832	+	0.659355i	$0.229170\pi$
$751$			36.1384i			1.31871i	−0.751832	+	0.659355i	$0.770830\pi$
$752$	−26.6991	+	37.6449i	−0.973615	+	1.37277i
$753$	−0.0135957	−	0.0135957i	−0.000495456	−	0.000495456i
$754$	41.1745	+	15.0567i	1.49949	+	0.548331i
$755$	37.4948	−	26.8355i	1.36458	−	0.976645i
$756$	0.0147816	+	0.175033i	0.000537602	+	0.00636588i
$757$		−	11.6389i		−	0.423022i	−0.977376	−	0.211511i	$-0.932162\pi$
$757$		−	11.6389i		−	0.423022i	0.977376	−	0.211511i	$-0.0678384\pi$
$758$	−11.6277	+	31.7977i	−0.422339	+	1.15494i
$759$			0.0226581i			0.000822438i
$760$	20.1971	−	43.9775i	0.732625	−	1.59523i
$761$			16.2624i			0.589512i	0.955573	+	0.294756i	$0.0952384\pi$
$761$			16.2624i			0.589512i	−0.955573	+	0.294756i	$0.904762\pi$
$762$	0.163510	+	0.0597920i	0.00592333	+	0.00216604i
$763$			40.2164i			1.45593i
$764$	2.94563	+	2.48685i	0.106569	+	0.0899712i
$765$	2.82472	−	17.0476i	0.102128	−	0.616357i
$766$	2.46080	−	6.72941i	0.0889125	−	0.243144i
$767$	−12.6645	−	12.6645i	−0.457287	−	0.457287i
$768$	0.0975752	−	0.0341873i	0.00352094	−	0.00123363i
$769$			37.4541i			1.35063i	0.737530	+	0.675314i	$0.235992\pi$
$769$			37.4541i			1.35063i	−0.737530	+	0.675314i	$0.764008\pi$
$770$	3.52686	−	6.23507i	0.127099	−	0.224696i
$771$	−0.0885866	+	0.0885866i	−0.00319037	+	0.00319037i
$772$	32.5087	−	2.74538i	1.17001	−	0.0988082i
$773$	−53.2470			−1.91516			−0.957580	−	0.288168i	$-0.906954\pi$
$773$	−53.2470			−1.91516			−0.957580	+	0.288168i	$0.906954\pi$
$774$	−0.797867	−	1.71779i	−0.0286787	−	0.0617446i
$775$	1.92908	+	0.657329i	0.0692946	+	0.0236119i
$776$	3.42978	+	6.00310i	0.123122	+	0.215499i
$777$	0.0712925	+	0.0712925i	0.00255760	+	0.00255760i
$778$	−18.0152	−	6.58776i	−0.645875	−	0.236183i
$779$	12.6356	−	12.6356i	0.452719	−	0.452719i
$780$	−0.113540	−	0.00909733i	−0.00406540	−	0.000325737i
$781$	−7.43827	−	7.43827i	−0.266162	−	0.266162i
$782$	−11.5851	+	5.38098i	−0.414283	+	0.192424i
$783$	−0.215626	+	0.215626i	−0.00770583	+	0.00770583i
$784$	7.36822	−	1.25344i	0.263151	−	0.0447657i
$785$	−25.2855	+	18.0971i	−0.902477	+	0.645915i
$786$	−0.0423225	+	0.115737i	−0.00150959	+	0.00412820i
$787$			46.0951i			1.64311i	0.570126	+	0.821557i	$0.306894\pi$
$787$			46.0951i			1.64311i	−0.570126	+	0.821557i	$0.693106\pi$
$788$	−27.2803	−	23.0314i	−0.971820	−	0.820460i
$789$	0.00151155	+	0.00151155i	5.38125e−5	+	5.38125e-5i
$790$	2.63557	−	4.65938i	0.0937695	−	0.165773i
$791$	25.0014			0.888949
$792$	7.36748	−	4.20930i	0.261792	−	0.149571i
$793$	11.9164	−	11.9164i	0.423165	−	0.423165i
$794$	6.22811	−	2.89279i	0.221027	−	0.102661i
$795$	−0.114226	+	0.0817529i	−0.00405117	+	0.00289948i
$796$	−1.13064	−	0.954544i	−0.0400745	−	0.0338329i
$797$	24.9734			0.884605			0.442302	−	0.896866i	$-0.354162\pi$
$797$	24.9734			0.884605			0.442302	+	0.896866i	$0.354162\pi$
$798$	0.143661	−	0.0667266i	0.00508553	−	0.00236209i
$799$	29.7216			1.05147
$800$	27.2221	−	7.67826i	0.962448	−	0.271468i
$801$	15.0215			0.530757
$802$	−4.33184	+	2.01202i	−0.152963	+	0.0710470i
$803$	−8.31508			−0.293433
$804$	−0.0933407	−	0.0788030i	−0.00329187	−	0.00277917i
$805$	14.4430	−	10.3370i	0.509048	−	0.364332i
$806$	2.06059	−	0.957087i	0.0725811	−	0.0337120i
$807$	−0.0829013	+	0.0829013i	−0.00291826	+	0.00291826i
$808$	1.06177	+	1.85840i	0.0373529	+	0.0653784i
$809$	15.8180			0.556130			0.278065	−	0.960562i	$-0.410307\pi$
$809$	15.8180			0.556130			0.278065	+	0.960562i	$0.410307\pi$
$810$	−14.0117	+	24.7710i	−0.492321	+	0.870366i
$811$	−16.3543	−	16.3543i	−0.574276	−	0.574276i	0.359044	−	0.933320i	$-0.383103\pi$
$811$	−16.3543	−	16.3543i	−0.574276	−	0.574276i	−0.933320	+	0.359044i	$0.883103\pi$
$812$	−27.2275	−	22.9869i	−0.955498	−	0.806681i
$813$			0.0942032i			0.00330385i
$814$	3.34531	−	9.14822i	0.117253	−	0.320645i
$815$	−4.92113	+	3.52212i	−0.172380	+	0.123374i
$816$	−0.0543107	−	0.0385190i	−0.00190126	−	0.00134844i
$817$	−2.41548	+	2.41548i	−0.0845068	+	0.0845068i
$818$	21.1869	−	9.84073i	0.740782	−	0.344073i
$819$	18.9402	+	18.9402i	0.661823	+	0.661823i
$820$	10.4107	+	0.834147i	0.363557	+	0.0291297i
$821$	13.6783	−	13.6783i	0.477376	−	0.477376i	−0.426915	−	0.904292i	$-0.640400\pi$
$821$	13.6783	−	13.6783i	0.477376	−	0.477376i	0.904292	+	0.426915i	$0.140400\pi$
$822$	0.0956664	+	0.0349832i	0.00333675	+	0.00122018i
$823$	−32.5637	−	32.5637i	−1.13510	−	1.13510i	−0.989317	−	0.145782i	$-0.953430\pi$
$823$	−32.5637	−	32.5637i	−1.13510	−	1.13510i	−0.145782	−	0.989317i	$-0.546570\pi$
$824$	−22.0537	+	12.6001i	−0.768278	+	0.438944i
$825$	−0.0289942	+	0.0142566i	−0.00100945	+	0.000496352i
$826$	6.13221	+	13.2025i	0.213367	+	0.459374i
$827$	−17.1664			−0.596933			−0.298467	−	0.954420i	$-0.596475\pi$
$827$	−17.1664			−0.596933			−0.298467	+	0.954420i	$0.596475\pi$
$828$	20.9635	−	1.77038i	0.728531	−	0.0615249i
$829$	33.1556	−	33.1556i	1.15154	−	1.15154i	0.165297	−	0.986244i	$-0.447142\pi$
$829$	33.1556	−	33.1556i	1.15154	−	1.15154i	0.986244	−	0.165297i	$-0.0528581\pi$
$830$	4.74015	−	8.38003i	0.164533	−	0.290875i
$831$			0.100421i			0.00348356i
$832$	16.0124	−	27.1638i	0.555131	−	0.941735i
$833$	−3.40351	−	3.40351i	−0.117924	−	0.117924i
$834$	0.0438453	−	0.119901i	0.00151824	−	0.00415184i
$835$	3.12939	−	18.8863i	0.108297	−	0.653589i
$836$	−11.6934	−	9.87216i	−0.404424	−	0.341436i
$837$			0.0158032i			0.000546238i
$838$	−6.53726	−	2.39054i	−0.225826	−	0.0825797i
$839$			38.8334i			1.34068i	0.742055	+	0.670339i	$0.233851\pi$
$839$			38.8334i			1.34068i	−0.742055	+	0.670339i	$0.766149\pi$
$840$	0.0841311	+	0.0386380i	0.00290280	+	0.00133314i
$841$		−	32.8599i		−	1.13310i
$842$	−10.9869	+	30.0452i	−0.378634	+	1.03543i
$843$		−	0.195573i		−	0.00673591i
$844$	−0.0255617	−	0.302682i	−0.000879868	−	0.0104187i
$845$	−4.61032	+	3.29967i	−0.158600	+	0.113512i
$846$	−45.9732	−	16.8114i	−1.58059	−	0.577989i
$847$	−1.60179	−	1.60179i	−0.0550383	−	0.0550383i
$848$	−6.52130	−	38.3348i	−0.223942	−	1.31642i
$849$			0.181541i			0.00623048i
$850$	−14.1751	−	11.4390i	−0.486203	−	0.392356i
$851$	17.0774	−	17.0774i	0.585405	−	0.585405i
$852$	0.0877007	−	0.103880i	0.00300458	−	0.00355886i
$853$	−33.2632			−1.13891			−0.569456	−	0.822022i	$-0.692846\pi$
$853$	−33.2632			−1.13891			−0.569456	+	0.822022i	$0.692846\pi$
$854$	−12.4227	+	5.77002i	−0.425096	+	0.197446i
$855$	50.6381	+	8.39053i	1.73179	+	0.286950i
$856$	12.4428	−	45.6110i	0.425288	−	1.55895i
$857$	27.5982	+	27.5982i	0.942738	+	0.942738i	0.998447	−	0.0557092i	$-0.0177420\pi$
$857$	27.5982	+	27.5982i	0.942738	+	0.942738i	−0.0557092	+	0.998447i	$0.517742\pi$
$858$	−0.0123705	+	0.0338288i	−0.000422321	+	0.00115490i
$859$	−20.0662	+	20.0662i	−0.684651	+	0.684651i	−0.961044	−	0.276394i	$-0.910861\pi$
$859$	−20.0662	+	20.0662i	−0.684651	+	0.684651i	0.276394	+	0.961044i	$0.410861\pi$
$860$	−1.99014	−	0.159459i	−0.0678633	−	0.00543750i
$861$	0.0241726	+	0.0241726i	0.000823799	+	0.000823799i
$862$	22.6963	+	48.8646i	0.773039	+	1.66433i
$863$	−36.7937	+	36.7937i	−1.25247	+	1.25247i	−0.297865	+	0.954608i	$0.596274\pi$
$863$	−36.7937	+	36.7937i	−1.25247	+	1.25247i	−0.954608	+	0.297865i	$0.903726\pi$
$864$	0.124441	+	0.180603i	0.00423357	+	0.00614424i
$865$	23.8841	+	33.3710i	0.812082	+	1.13465i
$866$	53.3160	+	19.4965i	1.81175	+	0.662520i
$867$		−	0.0669733i		−	0.00227453i
$868$	−1.84010	+	0.155398i	−0.0624571	+	0.00527454i
$869$	−1.19700	−	1.19700i	−0.0406054	−	0.0406054i
$870$	0.0429649	+	0.154870i	0.00145665	+	0.00525057i
$871$	−37.2554			−1.26235
$872$	24.9102	+	43.6000i	0.843565	+	1.47648i
$873$	−5.18527	+	5.18527i	−0.175495	+	0.175495i
$874$	−15.9836	−	34.4124i	−0.540655	−	1.16402i
$875$	22.3153	+	11.9777i	0.754393	+	0.404919i
$876$	−0.00904313	−	0.107082i	−0.000305539	−	0.00361796i
$877$	−20.4004			−0.688872			−0.344436	−	0.938810i	$-0.611930\pi$
$877$	−20.4004			−0.688872			−0.344436	+	0.938810i	$0.611930\pi$
$878$	0.0129260	+	0.0278295i	0.000436233	+	0.000939199i
$879$	−0.0335968			−0.00113319
$880$	−0.0384359	−	8.94419i	−0.00129567	−	0.301509i
$881$	−28.4195			−0.957478			−0.478739	−	0.877957i	$-0.658906\pi$
$881$	−28.4195			−0.957478			−0.478739	+	0.877957i	$0.658906\pi$
$882$	3.33940	+	7.18965i	0.112443	+	0.242088i
$883$	−1.92290			−0.0647107			−0.0323554	−	0.999476i	$-0.510301\pi$
$883$	−1.92290			−0.0647107			−0.0323554	+	0.999476i	$0.510301\pi$
$884$	−20.2345	+	1.70882i	−0.680561	+	0.0574738i
$885$	0.0107329	−	0.0647748i	0.000360783	−	0.00217738i
$886$	4.30037	+	9.25859i	0.144474	+	0.311048i
$887$	−14.3157	+	14.3157i	−0.480676	+	0.480676i	−0.905347	−	0.424672i	$-0.860390\pi$
$887$	−14.3157	+	14.3157i	−0.480676	+	0.480676i	0.424672	+	0.905347i	$0.360390\pi$
$888$	0.121449	+	0.0331318i	0.00407557	+	0.00111183i
$889$	−43.1559			−1.44740
$890$	7.79585	−	13.7821i	0.261317	−	0.461978i
$891$	6.36370	+	6.36370i	0.213192	+	0.213192i
$892$	2.14699	+	25.4231i	0.0718867	+	0.851227i
$893$			88.2848i			2.95434i
$894$	−0.155198	−	0.0567528i	−0.00519061	−	0.00189810i
$895$	−28.5667	−	4.73338i	−0.954879	−	0.158220i
$896$	−19.8055	+	16.2657i	−0.661655	+	0.543398i
$897$	−0.0631496	+	0.0631496i	−0.00210851	+	0.00210851i
$898$	−6.95557	−	14.9752i	−0.232110	−	0.499729i
$899$	−2.26685	−	2.26685i	−0.0756037	−	0.0756037i
$900$	15.4558	+	25.7117i	0.515193	+	0.857058i
$901$	−17.7075	+	17.7075i	−0.589922	+	0.589922i
$902$	1.13427	−	3.10181i	0.0377670	−	0.103279i
$903$	−0.00462092	−	0.00462092i	−0.000153775	−	0.000153775i
$904$	27.1049	−	15.4859i	0.901495	−	0.515055i
$905$	−0.583413	+	3.52098i	−0.0193933	+	0.117041i
$906$	0.170905	−	0.0793809i	0.00567795	−	0.00263726i
$907$	1.49090			0.0495046			0.0247523	−	0.999694i	$-0.492120\pi$
$907$	1.49090			0.0495046			0.0247523	+	0.999694i	$0.492120\pi$
$908$	−1.03837	−	0.876643i	−0.0344594	−	0.0290924i
$909$	−1.60523	+	1.60523i	−0.0532420	+	0.0532420i
$910$	27.2071	−	7.54797i	0.901907	−	0.250213i
$911$		−	1.00771i		−	0.0333870i	−0.999861	−	0.0166935i	$-0.994686\pi$
$911$		−	1.00771i		−	0.0333870i	0.999861	−	0.0166935i	$-0.00531395\pi$
$912$	0.114417	−	0.161324i	0.00378872	−	0.00534198i
$913$	−2.15283	−	2.15283i	−0.0712484	−	0.0712484i
$914$	−32.4501	−	11.8663i	−1.07335	−	0.392503i
$915$	0.0609489	+	0.0100990i	0.00201491	+	0.000333862i
$916$	54.2624	−	4.58250i	1.79288	−	0.151410i
$917$		−	30.5470i		−	1.00875i
$918$	0.0485084	−	0.132653i	0.00160102	−	0.00437820i
$919$			38.8562i			1.28175i	0.767647	+	0.640873i	$0.221428\pi$
$919$			38.8562i			1.28175i	−0.767647	+	0.640873i	$0.778572\pi$
$920$	9.25532	−	20.1527i	0.305139	−	0.664415i
$921$		−	0.0967885i		−	0.00318929i
$922$	−12.8401	−	4.69534i	−0.422865	−	0.154633i
$923$		−	41.4619i		−	1.36473i
$924$	0.0188859	−	0.0223700i	0.000621301	−	0.000735918i
$925$	32.5980	+	11.1077i	1.07182	+	0.365219i
$926$	−11.1206	+	30.4108i	−0.365445	+	0.999361i
$927$	−19.0493	−	19.0493i	−0.625660	−	0.625660i
$928$	−43.7563	−	8.05604i	−1.43637	−	0.264452i
$929$		−	52.0096i		−	1.70638i	−0.521602	−	0.853189i	$-0.674665\pi$
$929$		−	52.0096i		−	1.70638i	0.521602	−	0.853189i	$-0.325335\pi$
$930$	0.00724963	+	0.00410074i	0.000237725	+	0.000134469i
$931$	10.1098	−	10.1098i	0.331334	−	0.331334i
$932$	3.71241	+	43.9596i	0.121604	+	1.43994i
$933$	−0.0942074			−0.00308421
$934$	−13.1223	−	28.2520i	−0.429374	−	0.924433i
$935$	−4.68401	+	3.35241i	−0.153184	+	0.109636i
$936$	32.2652	+	8.80207i	1.05462	+	0.287705i
$937$	−20.2617	−	20.2617i	−0.661919	−	0.661919i	0.293913	−	0.955832i	$-0.405042\pi$
$937$	−20.2617	−	20.2617i	−0.661919	−	0.661919i	−0.955832	+	0.293913i	$0.905042\pi$
$938$	28.4387	+	10.3994i	0.928557	+	0.339554i
$939$	0.0443268	−	0.0443268i	0.00144655	−	0.00144655i
$940$	−39.2836	+	33.4555i	−1.28129	+	1.09120i
$941$	−38.4343	−	38.4343i	−1.25292	−	1.25292i	−0.954404	−	0.298517i	$-0.903508\pi$
$941$	−38.4343	−	38.4343i	−1.25292	−	1.25292i	−0.298517	−	0.954404i	$-0.596492\pi$
$942$	−0.115254	+	0.0535323i	−0.00375517	+	0.00174418i
$943$	5.79028	−	5.79028i	0.188558	−	0.188558i
$944$	14.8258	+	10.5150i	0.482539	+	0.342233i
$945$	−0.0321032	+	0.193747i	−0.00104432	+	0.00630260i
$946$	−0.216831	+	0.592954i	−0.00704977	+	0.0192786i
$947$			22.1551i			0.719943i	0.932963	+	0.359972i	$0.117214\pi$
$947$			22.1551i			0.719943i	−0.932963	+	0.359972i	$0.882786\pi$
$948$	0.0141132	−	0.0167168i	0.000458375	−	0.000542936i
$949$	−23.1747	−	23.1747i	−0.752282	−	0.752282i
$950$	33.9785	−	42.1058i	1.10241	−	1.36609i
$951$	−0.0145317			−0.000471221
$952$	15.9229	+	4.34384i	0.516066	+	0.140785i
$953$	−4.48082	+	4.48082i	−0.145148	+	0.145148i	−0.775947	−	0.630799i	$-0.782727\pi$
$953$	−4.48082	+	4.48082i	−0.145148	+	0.145148i	0.630799	+	0.775947i	$0.282727\pi$
$954$	37.4058	−	17.3740i	1.21106	−	0.562503i
$955$	2.50847	+	3.50486i	0.0811723	+	0.113415i
$956$	2.86863	−	3.39784i	0.0927782	−	0.109894i
$957$	0.0508238			0.00164290
$958$	7.29319	−	3.38749i	0.235632	−	0.109445i
$959$	−25.2497			−0.815355
$960$	0.115142	−	0.0102223i	0.00371618	−	0.000329923i
$961$	30.8339			0.994641
$962$	34.8203	−	16.1731i	1.12265	−	0.521441i
$963$	50.1450			1.61590
$964$	1.22257	−	1.44811i	0.0393763	−	0.0466404i
$965$	35.9845	+	5.96249i	1.15838	+	0.191939i
$966$	0.0658326	−	0.0305775i	0.00211813	−	0.000983814i
$967$	−13.9849	+	13.9849i	−0.449723	+	0.449723i	−0.895262	−	0.445539i	$-0.853012\pi$
$967$	−13.9849	+	13.9849i	−0.449723	+	0.449723i	0.445539	+	0.895262i	$0.353012\pi$
$968$	−2.72871	−	0.744402i	−0.0877041	−	0.0239260i
$969$	−0.127370			−0.00409170
$970$	2.06642	+	7.44853i	0.0663486	+	0.239158i
$971$	−24.5226	−	24.5226i	−0.786968	−	0.786968i	0.194028	−	0.980996i	$-0.437845\pi$
$971$	−24.5226	−	24.5226i	−0.786968	−	0.786968i	−0.980996	+	0.194028i	$0.937845\pi$
$972$	−0.225098	+	0.266624i	−0.00722003	+	0.00855198i
$973$			31.6461i			1.01453i
$974$	−9.87062	+	26.9926i	−0.316275	+	0.864898i
$975$	−0.120543	−	0.0410747i	−0.00386046	−	0.00131544i
$976$	−9.89391	+	13.9501i	−0.316696	+	0.446532i
$977$	19.7120	−	19.7120i	0.630642	−	0.630642i	−0.317587	−	0.948229i	$-0.602873\pi$
$977$	19.7120	−	19.7120i	0.630642	−	0.630642i	0.948229	+	0.317587i	$0.102873\pi$
$978$	−0.0224310	+	0.0104186i	−0.000717265	+	0.000333150i
$979$	−3.54064	−	3.54064i	−0.113159	−	0.113159i
$980$	8.32957	+	0.667400i	0.266078	+	0.0213193i
$981$	−37.6602	+	37.6602i	−1.20240	+	1.20240i
$982$	38.1063	+	13.9347i	1.21602	+	0.444674i
$983$	19.6743	+	19.6743i	0.627514	+	0.627514i	0.947442	−	0.319928i	$-0.103659\pi$
$983$	19.6743	+	19.6743i	0.627514	+	0.627514i	−0.319928	+	0.947442i	$0.603659\pi$
$984$	0.0411788	+	0.0112337i	0.00131273	+	0.000358118i
$985$	−23.2316	−	32.4594i	−0.740222	−	1.03424i
$986$	12.0699	+	25.9863i	0.384385	+	0.827572i
$987$	−0.168893			−0.00537592
$988$	−5.07587	−	60.1046i	−0.161485	−	1.91218i
$989$	−1.10689	+	1.10689i	−0.0351971	+	0.0351971i
$990$	9.14143	−	2.53607i	0.290534	−	0.0806017i
$991$		−	33.7960i		−	1.07357i	−0.843721	−	0.536783i	$-0.819640\pi$
$991$		−	33.7960i		−	1.07357i	0.843721	−	0.536783i	$-0.180360\pi$
$992$	−1.89866	+	1.30823i	−0.0602825	+	0.0415365i
$993$	0.0973808	+	0.0973808i	0.00309029	+	0.00309029i
$994$	−11.5736	+	31.6497i	−0.367093	+	1.00387i
$995$	−0.962843	−	1.34529i	−0.0305242	−	0.0426486i
$996$	0.0253829	−	0.0300656i	0.000804289	−	0.000952665i
$997$		−	4.89110i		−	0.154903i	−0.996996	−	0.0774513i	$-0.975322\pi$
$997$		−	4.89110i		−	0.154903i	0.996996	−	0.0774513i	$-0.0246782\pi$
$998$	15.4243	+	5.64035i	0.488249	+	0.178542i
$999$			0.267046i			0.00844895i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	880.2.bk.b.243.15	yes	236
5.2	odd	4		880.2.s.b.67.44	✓	236
16.11	odd	4		880.2.s.b.683.44	yes	236
80.27	even	4	inner	880.2.bk.b.507.15	yes	236

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
880.2.s.b.67.44	✓	236	5.2	odd	4
880.2.s.b.683.44	yes	236	16.11	odd	4
880.2.bk.b.243.15	yes	236	1.1	even	1	trivial
880.2.bk.b.507.15	yes	236	80.27	even	4	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 880 = 2^{4} \cdot 5 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	880.bk (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.28261 + 0.595739i) q^{2} -0.00646194 q^{3} +(1.29019 - 1.52820i) q^{4} +(1.81833 - 1.30141i) q^{5} +(0.00828816 - 0.00384963i) q^{6} +(-1.60179 + 1.60179i) q^{7} +(-0.744402 + 2.72871i) q^{8} -2.99996 q^{9} +(-1.55692 + 2.75245i) q^{10} +(0.707107 + 0.707107i) q^{11} +(-0.00833712 + 0.00987516i) q^{12} +3.94151i q^{13} +(1.10023 - 3.00873i) q^{14} +(-0.0117500 + 0.00840960i) q^{15} +(-0.670821 - 3.94335i) q^{16} +(-1.82150 + 1.82150i) q^{17} +(3.84778 - 1.78719i) q^{18} +(-5.41058 - 5.41058i) q^{19} +(0.357182 - 4.45785i) q^{20} +(0.0103507 - 0.0103507i) q^{21} +(-1.32820 - 0.485693i) q^{22} +(-2.47940 - 2.47940i) q^{23} +(0.00481028 - 0.0176328i) q^{24} +(1.61268 - 4.73278i) q^{25} +(-2.34811 - 5.05542i) q^{26} +0.0387713 q^{27} +(0.381251 + 4.51449i) q^{28} +(-5.56147 + 5.56147i) q^{29} +(0.0100607 - 0.0177862i) q^{30} +0.407599i q^{31} +(3.20961 + 4.65815i) q^{32} +(-0.00456928 - 0.00456928i) q^{33} +(1.25114 - 3.42142i) q^{34} +(-0.828013 + 4.99718i) q^{35} +(-3.87052 + 4.58455i) q^{36} +6.88771i q^{37} +(10.1630 + 3.71638i) q^{38} -0.0254698i q^{39} +(2.19759 + 5.93048i) q^{40} +2.33536i q^{41} +(-0.00710961 + 0.0194422i) q^{42} -0.446436i q^{43} +(1.99291 - 0.168302i) q^{44} +(-5.45493 + 3.90416i) q^{45} +(4.65718 + 1.70303i) q^{46} +(-8.15854 - 8.15854i) q^{47} +(0.00433480 + 0.0254817i) q^{48} +1.86852i q^{49} +(0.751057 + 7.03107i) q^{50} +(0.0117704 - 0.0117704i) q^{51} +(6.02343 + 5.08529i) q^{52} +9.72138 q^{53} +(-0.0497286 + 0.0230976i) q^{54} +(2.20599 + 0.365524i) q^{55} +(-3.17845 - 5.56321i) q^{56} +(0.0349628 + 0.0349628i) q^{57} +(3.82003 - 10.4464i) q^{58} +(-3.21310 + 3.21310i) q^{59} +(-0.00230809 + 0.0288063i) q^{60} +(-3.02332 - 3.02332i) q^{61} +(-0.242823 - 0.522792i) q^{62} +(4.80531 - 4.80531i) q^{63} +(-6.89173 - 4.06252i) q^{64} +(5.12950 + 7.16698i) q^{65} +(0.00858271 + 0.00313852i) q^{66} +9.45206i q^{67} +(0.433545 + 5.13371i) q^{68} +(0.0160217 + 0.0160217i) q^{69} +(-1.91500 - 6.90273i) q^{70} -10.5193 q^{71} +(2.23318 - 8.18602i) q^{72} +(-5.87965 + 5.87965i) q^{73} +(-4.10328 - 8.83426i) q^{74} +(-0.0104211 + 0.0305830i) q^{75} +(-15.2491 + 1.28780i) q^{76} -2.26528 q^{77} +(0.0151733 + 0.0326678i) q^{78} -1.69281 q^{79} +(-6.35168 - 6.29732i) q^{80} +8.99962 q^{81} +(-1.39126 - 2.99536i) q^{82} -3.04457 q^{83} +(-0.00246362 - 0.0291723i) q^{84} +(-0.941586 + 5.68261i) q^{85} +(0.265959 + 0.572604i) q^{86} +(0.0359379 - 0.0359379i) q^{87} +(-2.45586 + 1.40312i) q^{88} -5.00722 q^{89} +(4.67070 - 8.25724i) q^{90} +(-6.31348 - 6.31348i) q^{91} +(-6.98792 + 0.590134i) q^{92} -0.00263388i q^{93} +(15.3246 + 5.60389i) q^{94} +(-16.8796 - 2.79688i) q^{95} +(-0.0207403 - 0.0301007i) q^{96} +(1.72845 - 1.72845i) q^{97} +(-1.11315 - 2.39658i) q^{98} +(-2.12129 - 2.12129i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 236 q + 4 q^{3} + 4 q^{5} - 4 q^{7} + 12 q^{8} + 240 q^{9} - 8 q^{12} + 12 q^{14} - 4 q^{15} - 8 q^{16} + 8 q^{17} + 28 q^{18} + 28 q^{19} + 4 q^{20} + 16 q^{21} + 4 q^{22} - 8 q^{23} + 12 q^{25} + 8 q^{26}+ \cdots + 8 q^{99}+O(q^{100}) \) 236 * q + 4 * q^3 + 4 * q^5 - 4 * q^7 + 12 * q^8 + 240 * q^9 - 8 * q^12 + 12 * q^14 - 4 * q^15 - 8 * q^16 + 8 * q^17 + 28 * q^18 + 28 * q^19 + 4 * q^20 + 16 * q^21 + 4 * q^22 - 8 * q^23 + 12 * q^25 + 8 * q^26 + 4 * q^27 - 36 * q^28 + 8 * q^29 - 56 * q^30 - 40 * q^32 - 4 * q^33 - 44 * q^34 - 28 * q^35 - 32 * q^36 - 12 * q^38 - 40 * q^40 - 20 * q^42 - 40 * q^46 - 48 * q^47 - 40 * q^48 - 28 * q^51 - 4 * q^52 + 28 * q^53 - 24 * q^56 - 16 * q^57 - 76 * q^58 + 8 * q^59 - 4 * q^60 - 24 * q^61 + 12 * q^62 - 24 * q^63 - 32 * q^65 - 4 * q^66 + 36 * q^68 + 48 * q^69 + 28 * q^70 - 4 * q^71 + 20 * q^72 + 8 * q^73 - 68 * q^75 - 24 * q^76 + 12 * q^77 + 8 * q^78 + 40 * q^79 + 112 * q^80 + 244 * q^81 - 64 * q^82 + 24 * q^83 - 104 * q^84 + 8 * q^85 + 72 * q^86 - 140 * q^87 - 32 * q^88 + 36 * q^89 - 136 * q^90 + 12 * q^91 + 72 * q^92 - 16 * q^94 - 36 * q^95 + 72 * q^96 + 20 * q^97 + 136 * q^98 + 8 * q^99

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