LMFDB - Embedded newform 880.2.bk.b.507.15

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			507.15
Character	$\chi$	$=$	880.507
Dual form			880.2.bk.b.243.15

$q$-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 $\left(\mathbb{Z}/880\mathbb{Z}\right)^\times$.

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

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	0.336325	−	0.941746i	$-0.390816\pi$
$7$	−1.60179	−	1.60179i	−0.605421	−	0.605421i	−0.941746	+	0.336325i	$0.890816\pi$
$8$	−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	$-0.815926\pi$
$13$		−	3.94151i		−	1.09318i	0.837401	−	0.546588i	$-0.184074\pi$
$14$	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	0.450831	−	0.892609i	$-0.351128\pi$
$17$	−1.82150	−	1.82150i	−0.441779	−	0.441779i	−0.892609	+	0.450831i	$0.851128\pi$
$18$	3.84778	+	1.78719i	0.906931	+	0.421245i
$19$	−5.41058	+	5.41058i	−1.24127	+	1.24127i	−0.281797	+	0.959474i	$0.590931\pi$
$19$	−5.41058	+	5.41058i	−1.24127	+	1.24127i	−0.959474	+	0.281797i	$0.909069\pi$
$20$	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	−0.916659	−	0.399669i	$-0.869125\pi$
$23$	−2.47940	+	2.47940i	−0.516990	+	0.516990i	0.399669	+	0.916659i	$0.369125\pi$
$24$	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	−0.999446	−	0.0332934i	$-0.989400\pi$
$29$	−5.56147	−	5.56147i	−1.03274	−	1.03274i	−0.0332934	−	0.999446i	$-0.510600\pi$
$30$	0.0100607	+	0.0177862i	0.00183683	+	0.00324730i
$31$		−	0.407599i		−	0.0732070i	−0.999330	−	0.0366035i	$-0.988346\pi$
$31$		−	0.407599i		−	0.0732070i	0.999330	−	0.0366035i	$-0.0116539\pi$
$32$	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	$-0.808426\pi$
$37$		−	6.88771i		−	1.13233i	0.824291	−	0.566166i	$-0.191574\pi$
$38$	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	$-0.941626\pi$
$41$		−	2.33536i		−	0.364722i	0.983232	−	0.182361i	$-0.0583739\pi$
$42$	−0.00710961	−	0.0194422i	−0.00109704	−	0.00300000i
$43$			0.446436i			0.0680808i	0.999420	+	0.0340404i	$0.0108375\pi$
$43$			0.446436i			0.0680808i	−0.999420	+	0.0340404i	$0.989163\pi$
$44$	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	−0.212992	+	0.977054i	$0.568321\pi$
$47$	−8.15854	+	8.15854i	−1.19005	+	1.19005i	−0.977054	+	0.212992i	$0.931679\pi$
$48$	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	0.466311	−	0.884621i	$-0.345583\pi$
$59$	−3.21310	−	3.21310i	−0.418310	−	0.418310i	−0.884621	+	0.466311i	$0.845583\pi$
$60$	−0.00230809	−	0.0288063i	−0.000297973	−	0.00371888i
$61$	−3.02332	+	3.02332i	−0.387097	+	0.387097i	−0.873651	−	0.486554i	$-0.838254\pi$
$61$	−3.02332	+	3.02332i	−0.387097	+	0.387097i	0.486554	+	0.873651i	$0.338254\pi$
$62$	−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	$-0.804076\pi$
$67$		−	9.45206i		−	1.15475i	0.816478	−	0.577377i	$-0.195924\pi$
$68$	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	0.273664	−	0.961825i	$-0.411764\pi$
$73$	−5.87965	−	5.87965i	−0.688161	−	0.688161i	−0.961825	+	0.273664i	$0.911764\pi$
$74$	−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	0.789390	−	0.613892i	$-0.210397\pi$
$97$	1.72845	+	1.72845i	0.175497	+	0.175497i	−0.613892	+	0.789390i	$0.710397\pi$
$98$	−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	0.733227	−	0.679984i	$-0.238013\pi$
$101$	0.535082	+	0.535082i	0.0532427	+	0.0532427i	−0.679984	+	0.733227i	$0.738013\pi$
$102$	−0.00808479	−	0.0221090i	−0.000800513	−	0.00218912i
$103$	6.34984	−	6.34984i	0.625669	−	0.625669i	−0.321306	−	0.946975i	$-0.604122\pi$
$103$	6.34984	−	6.34984i	0.625669	−	0.625669i	0.946975	+	0.321306i	$0.104122\pi$
$104$	−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	0.973430	+	0.228984i	$0.0735403\pi$
$109$	12.5536	+	12.5536i	1.20241	+	1.20241i	0.228984	+	0.973430i	$0.426460\pi$
$110$	−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	−0.971441	−	0.237283i	$-0.923743\pi$
$113$	−7.80420	+	7.80420i	−0.734158	+	0.734158i	0.237283	+	0.971441i	$0.423743\pi$
$114$	−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	0.219832	−	0.975538i	$-0.429449\pi$
$127$	13.4711	−	13.4711i	1.19537	−	1.19537i	0.975538	−	0.219832i	$-0.0705508\pi$
$128$	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	0.154841	−	0.987939i	$-0.450514\pi$
$131$	−9.53525	−	9.53525i	−0.833099	−	0.833099i	−0.987939	+	0.154841i	$0.950514\pi$
$132$	−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	−0.285115	−	0.958493i	$-0.592032\pi$
$137$	7.88170	−	7.88170i	0.673379	−	0.673379i	0.958493	+	0.285115i	$0.0920316\pi$
$138$	−0.0300944	+	0.0110049i	−0.00256181	+	0.000936798i
$139$	9.87833	+	9.87833i	0.837869	+	0.837869i	0.988578	−	0.150709i	$-0.0481556\pi$
$139$	9.87833	+	9.87833i	0.837869	+	0.837869i	−0.150709	+	0.988578i	$0.548156\pi$
$140$	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	−0.0486873	+	0.998814i	$0.515504\pi$
$149$	−12.7864	+	12.7864i	−1.04750	+	1.04750i	−0.998814	+	0.0486873i	$0.984496\pi$
$150$	−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	0.901415	−	0.432956i	$-0.142530\pi$
$167$	6.05382	+	6.05382i	0.468459	+	0.468459i	−0.432956	+	0.901415i	$0.642530\pi$
$168$	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	$-0.754226\pi$
$173$		−	18.3525i		−	1.39531i	0.716432	−	0.697657i	$-0.245774\pi$
$174$	−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	−0.960990	−	0.276583i	$-0.910798\pi$
$179$	−9.15675	+	9.15675i	−0.684407	+	0.684407i	0.276583	+	0.960990i	$0.410798\pi$
$180$	−1.07153	−	13.3734i	−0.0798671	−	0.996792i
$181$	−1.12861	−	1.12861i	−0.0838892	−	0.0838892i	0.663917	−	0.747806i	$-0.268893\pi$
$181$	−1.12861	−	1.12861i	−0.0838892	−	0.0838892i	−0.747806	+	0.663917i	$0.768893\pi$
$182$	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	$-0.977785\pi$
$191$		−	1.92751i		−	0.139470i	0.997566	−	0.0697348i	$-0.0222153\pi$
$192$	0.0445339	−	0.0262517i	0.00321396	−	0.00189456i
$193$	11.5345	−	11.5345i	0.830269	−	0.830269i	−0.157285	−	0.987553i	$-0.550274\pi$
$193$	11.5345	−	11.5345i	0.830269	−	0.830269i	0.987553	+	0.157285i	$0.0502740\pi$
$194$	−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	$0.219380\pi$
$197$			17.8512i			1.27184i	−0.771753	+	0.635922i	$0.780620\pi$
$198$	3.98453	−	1.45706i	0.283168	−	0.103549i
$199$			0.739848i			0.0524464i	0.999656	+	0.0262232i	$0.00834807\pi$
$199$			0.739848i			0.0524464i	−0.999656	+	0.0262232i	$0.991652\pi$
$200$	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	0.710794	−	0.703400i	$-0.248336\pi$
$211$	0.107395	+	0.107395i	0.00739338	+	0.00739338i	−0.703400	+	0.710794i	$0.748336\pi$
$212$	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	0.337334	−	0.941385i	$-0.390475\pi$
$223$	−9.02041	−	9.02041i	−0.604051	−	0.604051i	−0.941385	+	0.337334i	$0.890475\pi$
$224$	−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	$0.00717816\pi$
$227$			0.679468i			0.0450979i	−0.999746	+	0.0225489i	$0.992822\pi$
$228$	0.0985390	+	0.00832167i	0.00652590	+	0.000551116i
$229$	19.2530	−	19.2530i	1.27227	−	1.27227i	0.327378	−	0.944894i	$-0.393835\pi$
$229$	19.2530	−	19.2530i	1.27227	−	1.27227i	0.944894	−	0.327378i	$-0.106165\pi$
$230$	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	−0.999757	−	0.0220615i	$-0.992977\pi$
$233$	−15.5974	−	15.5974i	−1.02182	−	1.02182i	−0.0220615	−	0.999757i	$-0.507023\pi$
$234$	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	−0.637581	−	0.770383i	$-0.720065\pi$
$251$	2.10397	−	2.10397i	0.132801	−	0.132801i	0.770383	+	0.637581i	$0.220065\pi$
$252$	−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	0.990761	−	0.135618i	$-0.0433019\pi$
$257$	13.7090	+	13.7090i	0.855143	+	0.855143i	−0.135618	+	0.990761i	$0.543302\pi$
$258$	−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	−0.714282	−	0.699858i	$-0.753247\pi$
$263$	−0.233915	+	0.233915i	−0.0144238	+	0.0144238i	0.699858	+	0.714282i	$0.253247\pi$
$264$	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	0.980203	−	0.197995i	$-0.0634429\pi$
$269$	12.8292	+	12.8292i	0.782208	+	0.782208i	−0.197995	+	0.980203i	$0.563443\pi$
$270$	−0.0603639	−	0.106716i	−0.00367363	−	0.00649455i
$271$			14.5782i			0.885561i	0.896630	+	0.442780i	$0.146008\pi$
$271$			14.5782i			0.885561i	−0.896630	+	0.442780i	$0.853992\pi$
$272$	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	$0.154617\pi$
$277$			15.5404i			0.933730i	−0.884329	+	0.466865i	$0.845383\pi$
$278$	−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	$-0.641550\pi$
$281$		−	30.2654i		−	1.80549i	0.430181	−	0.902743i	$-0.358450\pi$
$282$	−0.0990267	+	0.0362120i	−0.00589695	+	0.00215639i
$283$			28.0939i			1.67001i	0.550242	+	0.835005i	$0.314535\pi$
$283$			28.0939i			1.67001i	−0.550242	+	0.835005i	$0.685465\pi$
$284$	−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	$-0.859420\pi$
$307$		−	14.9782i		−	0.854854i	0.904050	−	0.427427i	$-0.140580\pi$
$308$	−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	0.486146	−	0.873878i	$-0.338402\pi$
$313$	−6.85967	−	6.85967i	−0.387732	−	0.387732i	−0.873878	+	0.486146i	$0.838402\pi$
$314$	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	−0.987284	−	0.158967i	$-0.949184\pi$
$331$	−15.0699	+	15.0699i	−0.828317	+	0.828317i	0.158967	+	0.987284i	$0.449184\pi$
$332$	−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	0.511480	−	0.859295i	$-0.329098\pi$
$337$	−6.38505	−	6.38505i	−0.347816	−	0.347816i	−0.859295	+	0.511480i	$0.829098\pi$
$338$	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	0.997981	+	0.0635198i	$0.0202326\pi$
$349$	19.8305	+	19.8305i	1.06150	+	1.06150i	0.0635198	+	0.997981i	$0.479767\pi$
$350$	−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	−0.821478	−	0.570241i	$-0.806850\pi$
$353$	−4.72032	+	4.72032i	−0.251237	+	0.251237i	0.570241	+	0.821478i	$0.306850\pi$
$354$	−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	$0.117632\pi$
$359$			13.6874i			0.722393i	−0.932490	+	0.361196i	$0.882368\pi$
$360$	−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	−0.141363	−	0.989958i	$-0.545149\pi$
$367$	16.2567	−	16.2567i	0.848594	−	0.848594i	0.989958	+	0.141363i	$0.0451486\pi$
$368$	−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	0.992423	−	0.122865i	$-0.0392081\pi$
$379$	16.9285	+	16.9285i	0.869559	+	0.869559i	−0.122865	+	0.992423i	$0.539208\pi$
$380$	−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	0.609626	−	0.792689i	$-0.291320\pi$
$383$	−3.58262	−	3.58262i	−0.183063	−	0.183063i	−0.792689	+	0.609626i	$0.791320\pi$
$384$	−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	−0.420850	−	0.907130i	$-0.638268\pi$
$389$	9.59094	−	9.59094i	0.486280	−	0.486280i	0.907130	+	0.420850i	$0.138268\pi$
$390$	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	−0.616966	−	0.786990i	$-0.711638\pi$
$419$	3.48032	−	3.48032i	0.170025	−	0.170025i	0.786990	+	0.616966i	$0.211638\pi$
$420$	−0.0424447	+	0.0498389i	−0.00207109	+	0.00243189i
$421$	15.9955	+	15.9955i	0.779575	+	0.779575i	0.979758	−	0.200184i	$-0.0641539\pi$
$421$	15.9955	+	15.9955i	0.779575	+	0.779575i	−0.200184	+	0.979758i	$0.564154\pi$
$422$	−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	$0.369837\pi$
$431$			38.0977i			1.83510i	−0.397619	+	0.917551i	$0.630163\pi$
$432$	−0.0260086	+	0.152889i	−0.00125134	+	0.00735587i
$433$	−28.3845	+	28.3845i	−1.36407	+	1.36407i	−0.495414	+	0.868657i	$0.664984\pi$
$433$	−28.3845	+	28.3845i	−1.36407	+	1.36407i	−0.868657	+	0.495414i	$0.835016\pi$
$434$	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	$0.000164815\pi$
$439$			0.0216975i			0.00103556i	−1.00000		0.000517782i	$0.999835\pi$
$440$	−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	$0.0548554\pi$
$443$			7.21854i			0.342963i	−0.985187	+	0.171482i	$0.945145\pi$
$444$	−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	$-0.911156\pi$
$449$		−	11.6755i		−	0.551003i	0.961301	−	0.275501i	$-0.0888438\pi$
$450$	−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	−0.176220	−	0.984351i	$-0.556387\pi$
$457$	17.2759	−	17.2759i	0.808130	−	0.808130i	0.984351	+	0.176220i	$0.0563871\pi$
$458$	−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	−0.529767	−	0.848143i	$-0.677721\pi$
$461$	6.83582	−	6.83582i	0.318376	−	0.318376i	0.848143	+	0.529767i	$0.177721\pi$
$462$	−0.0187750	−	0.00872048i	−0.000873491	−	0.000405713i
$463$	16.1902	+	16.1902i	0.752420	+	0.752420i	0.974930	−	0.222510i	$-0.0714250\pi$
$463$	16.1902	+	16.1902i	0.752420	+	0.752420i	−0.222510	+	0.974930i	$0.571425\pi$
$464$	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	$-0.829778\pi$
$467$		−	22.0269i		−	1.01928i	0.860387	−	0.509642i	$-0.170222\pi$
$468$	−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	0.953278	−	0.302095i	$-0.0976859\pi$
$487$	14.3704	+	14.3704i	0.651183	+	0.651183i	−0.302095	+	0.953278i	$0.597686\pi$
$488$	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	−0.996701	−	0.0811566i	$-0.974139\pi$
$491$	−20.2871	+	20.2871i	−0.915545	+	0.915545i	0.0811566	+	0.996701i	$0.474139\pi$
$492$	−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	−0.866602	−	0.498999i	$-0.833701\pi$
$499$	−8.21163	+	8.21163i	−0.367603	+	0.367603i	0.498999	+	0.866602i	$0.333701\pi$
$500$	−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	−0.587400	−	0.809297i	$-0.699848\pi$
$503$	4.97663	−	4.97663i	0.221897	−	0.221897i	0.809297	+	0.587400i	$0.199848\pi$
$504$	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	−0.999920	−	0.0126826i	$-0.995963\pi$
$509$	−22.8453	−	22.8453i	−1.01260	−	1.01260i	−0.0126826	−	0.999920i	$-0.504037\pi$
$510$	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	$-0.977774\pi$
$521$		−	3.18499i		−	0.139537i	0.997563	−	0.0697685i	$-0.0222261\pi$
$522$	−11.4599	−	31.3388i	−0.501587	−	1.37166i
$523$		−	27.0737i		−	1.18385i	−0.805992	−	0.591926i	$-0.798368\pi$
$523$		−	27.0737i		−	1.18385i	0.805992	−	0.591926i	$-0.201632\pi$
$524$	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	−0.834580	−	0.550886i	$-0.814290\pi$
$541$	−6.59855	+	6.59855i	−0.283694	+	0.283694i	0.550886	+	0.834580i	$0.314290\pi$
$542$	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	$-0.689061\pi$
$547$		−	38.7650i		−	1.65747i	0.559641	−	0.828735i	$-0.310939\pi$
$548$	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	−0.0330782	−	0.999453i	$-0.510531\pi$
$571$	23.0921	−	23.0921i	0.966375	−	0.966375i	0.999453	+	0.0330782i	$0.0105310\pi$
$572$	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	0.723439	−	0.690389i	$-0.242560\pi$
$577$	0.793887	+	0.793887i	0.0330499	+	0.0330499i	−0.690389	+	0.723439i	$0.742560\pi$
$578$	−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	−0.871817	−	0.489831i	$-0.837059\pi$
$593$	−9.30198	+	9.30198i	−0.381987	+	0.381987i	0.489831	+	0.871817i	$0.337059\pi$
$594$	−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	$-0.827411\pi$
$599$		−	25.2589i		−	1.03205i	0.856573	−	0.516025i	$-0.172589\pi$
$600$	−0.0756946	+	0.0512021i	−0.00309022	+	0.00209032i
$601$		−	30.0197i		−	1.22453i	−0.790654	−	0.612264i	$-0.790259\pi$
$601$		−	30.0197i		−	1.22453i	0.790654	−	0.612264i	$-0.209741\pi$
$602$	−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	−0.711995	−	0.702184i	$-0.752208\pi$
$607$	−0.241710	+	0.241710i	−0.00981073	+	0.00981073i	0.702184	+	0.711995i	$0.252208\pi$
$608$	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	−0.902783	−	0.430096i	$-0.858480\pi$
$617$	−11.7413	+	11.7413i	−0.472686	+	0.472686i	0.430096	+	0.902783i	$0.358480\pi$
$618$	0.0770731	−	0.0281840i	0.00310033	−	0.00113373i
$619$	−32.3783	−	32.3783i	−1.30139	−	1.30139i	−0.927453	−	0.373941i	$-0.878006\pi$
$619$	−32.3783	−	32.3783i	−1.30139	−	1.30139i	−0.373941	−	0.927453i	$-0.621994\pi$
$620$	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	0.718978	−	0.695033i	$-0.244610\pi$
$647$	0.609080	+	0.609080i	0.0239454	+	0.0239454i	−0.695033	+	0.718978i	$0.744610\pi$
$648$	−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	$0.186787\pi$
$653$			28.2986i			1.10741i	−0.832712	+	0.553706i	$0.813213\pi$
$654$	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	−0.712661	−	0.701508i	$-0.752510\pi$
$659$	−0.286312	+	0.286312i	−0.0111531	+	0.0111531i	0.701508	+	0.712661i	$0.252510\pi$
$660$	−0.0220012	−	0.0187371i	−0.000856396	−	0.000729340i
$661$	−34.7849	−	34.7849i	−1.35297	−	1.35297i	−0.882315	−	0.470660i	$-0.844016\pi$
$661$	−34.7849	−	34.7849i	−1.35297	−	1.35297i	−0.470660	−	0.882315i	$-0.655984\pi$
$662$	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	−0.543937	−	0.839126i	$-0.683067\pi$
$673$	7.65788	−	7.65788i	0.295190	−	0.295190i	0.839126	+	0.543937i	$0.183067\pi$
$674$	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	$0.0394276\pi$
$677$			6.42929i			0.247098i	−0.992338	+	0.123549i	$0.960572\pi$
$678$	−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	$-0.589456\pi$
$683$		−	50.2180i		−	1.92154i	0.277349	−	0.960769i	$-0.410544\pi$
$684$	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	0.798514	−	0.601976i	$-0.205620\pi$
$691$	5.16638	+	5.16638i	0.196538	+	0.196538i	−0.601976	+	0.798514i	$0.705620\pi$
$692$	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	0.355302	−	0.934752i	$-0.384378\pi$
$701$	34.1560	−	34.1560i	1.29005	−	1.29005i	0.934752	−	0.355302i	$-0.115622\pi$
$702$	−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	−0.308247	−	0.951306i	$-0.599742\pi$
$709$	17.1228	−	17.1228i	0.643059	−	0.643059i	0.951306	+	0.308247i	$0.0997423\pi$
$710$	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	−1.00000		0.000763290i	$-0.999757\pi$
$727$	−26.9835	−	26.9835i	−1.00076	−	1.00076i	−0.000763290	−	1.00000i	$-0.500243\pi$
$728$	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	$0.151911\pi$
$733$			24.8719i			0.918665i	−0.888264	+	0.459333i	$0.848089\pi$
$734$	−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	−0.459146	+	0.888361i	$0.651845\pi$
$739$	−36.6314	+	36.6314i	−1.34751	+	1.34751i	−0.888361	+	0.459146i	$0.848155\pi$
$740$	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	−0.949253	−	0.314513i	$-0.898159\pi$
$743$	−17.3017	+	17.3017i	−0.634740	+	0.634740i	0.314513	+	0.949253i	$0.398159\pi$
$744$	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	$-0.770830\pi$
$751$		−	36.1384i		−	1.31871i	0.751832	−	0.659355i	$-0.229170\pi$
$752$	−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	$0.0678384\pi$
$757$			11.6389i			0.423022i	−0.977376	+	0.211511i	$0.932162\pi$
$758$	−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	$-0.904762\pi$
$761$		−	16.2624i		−	0.589512i	0.955573	−	0.294756i	$-0.0952384\pi$
$762$	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	$-0.764008\pi$
$769$		−	37.4541i		−	1.35063i	0.737530	−	0.675314i	$-0.235992\pi$
$770$	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	$-0.693106\pi$
$787$		−	46.0951i		−	1.64311i	0.570126	−	0.821557i	$-0.306894\pi$
$788$	−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	−0.933320	−	0.359044i	$-0.883103\pi$
$811$	−16.3543	+	16.3543i	−0.574276	+	0.574276i	0.359044	+	0.933320i	$0.383103\pi$
$812$	−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	0.904292	−	0.426915i	$-0.140400\pi$
$821$	13.6783	+	13.6783i	0.477376	+	0.477376i	−0.426915	+	0.904292i	$0.640400\pi$
$822$	0.0956664	−	0.0349832i	0.00333675	−	0.00122018i
$823$	−32.5637	+	32.5637i	−1.13510	+	1.13510i	−0.145782	+	0.989317i	$0.546570\pi$
$823$	−32.5637	+	32.5637i	−1.13510	+	1.13510i	−0.989317	+	0.145782i	$0.953430\pi$
$824$	−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	0.986244	+	0.165297i	$0.0528581\pi$
$829$	33.1556	+	33.1556i	1.15154	+	1.15154i	0.165297	+	0.986244i	$0.447142\pi$
$830$	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	$-0.766149\pi$
$839$		−	38.8334i		−	1.34068i	0.742055	−	0.670339i	$-0.233851\pi$
$840$	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	−0.0557092	−	0.998447i	$-0.517742\pi$
$857$	27.5982	−	27.5982i	0.942738	−	0.942738i	0.998447	+	0.0557092i	$0.0177420\pi$
$858$	−0.0123705	−	0.0338288i	−0.000422321	−	0.00115490i
$859$	−20.0662	−	20.0662i	−0.684651	−	0.684651i	0.276394	−	0.961044i	$-0.410861\pi$
$859$	−20.0662	−	20.0662i	−0.684651	−	0.684651i	−0.961044	+	0.276394i	$0.910861\pi$
$860$	−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	−0.954608	−	0.297865i	$-0.903726\pi$
$863$	−36.7937	−	36.7937i	−1.25247	−	1.25247i	−0.297865	−	0.954608i	$-0.596274\pi$
$864$	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	0.424672	−	0.905347i	$-0.360390\pi$
$887$	−14.3157	−	14.3157i	−0.480676	−	0.480676i	−0.905347	+	0.424672i	$0.860390\pi$
$888$	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	$0.00531395\pi$
$911$			1.00771i			0.0333870i	−0.999861	+	0.0166935i	$0.994686\pi$
$912$	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	$-0.778572\pi$
$919$		−	38.8562i		−	1.28175i	0.767647	−	0.640873i	$-0.221428\pi$
$920$	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	$0.325335\pi$
$929$			52.0096i			1.70638i	−0.521602	+	0.853189i	$0.674665\pi$
$930$	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	−0.955832	−	0.293913i	$-0.905042\pi$
$937$	−20.2617	+	20.2617i	−0.661919	+	0.661919i	0.293913	+	0.955832i	$0.405042\pi$
$938$	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	−0.298517	+	0.954404i	$0.596492\pi$
$941$	−38.4343	+	38.4343i	−1.25292	+	1.25292i	−0.954404	+	0.298517i	$0.903508\pi$
$942$	−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	$-0.882786\pi$
$947$		−	22.1551i		−	0.719943i	0.932963	−	0.359972i	$-0.117214\pi$
$948$	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	0.630799	−	0.775947i	$-0.282727\pi$
$953$	−4.48082	−	4.48082i	−0.145148	−	0.145148i	−0.775947	+	0.630799i	$0.782727\pi$
$954$	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	0.445539	−	0.895262i	$-0.353012\pi$
$967$	−13.9849	−	13.9849i	−0.449723	−	0.449723i	−0.895262	+	0.445539i	$0.853012\pi$
$968$	−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	−0.980996	−	0.194028i	$-0.937845\pi$
$971$	−24.5226	+	24.5226i	−0.786968	+	0.786968i	0.194028	+	0.980996i	$0.437845\pi$
$972$	−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	0.948229	−	0.317587i	$-0.102873\pi$
$977$	19.7120	+	19.7120i	0.630642	+	0.630642i	−0.317587	+	0.948229i	$0.602873\pi$
$978$	−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	−0.319928	−	0.947442i	$-0.603659\pi$
$983$	19.6743	−	19.6743i	0.627514	−	0.627514i	0.947442	+	0.319928i	$0.103659\pi$
$984$	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	$0.180360\pi$
$991$			33.7960i			1.07357i	−0.843721	+	0.536783i	$0.819640\pi$
$992$	−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	$0.0246782\pi$
$997$			4.89110i			0.154903i	−0.996996	+	0.0774513i	$0.975322\pi$
$998$	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.507.15	yes	236
5.3	odd	4		880.2.s.b.683.44	yes	236
16.3	odd	4		880.2.s.b.67.44	✓	236
80.3	even	4	inner	880.2.bk.b.243.15	yes	236

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
880.2.s.b.67.44	✓	236	16.3	odd	4
880.2.s.b.683.44	yes	236	5.3	odd	4
880.2.bk.b.243.15	yes	236	80.3	even	4	inner
880.2.bk.b.507.15	yes	236	1.1	even	1	trivial

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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