LMFDB - Embedded newform 275.2.k.d.181.19

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [275,2,Mod(36,275)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("275.36"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(275, base_ring=CyclotomicField(10)) chi = DirichletCharacter(H, H._module([8, 8])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 275 = 5^{2} \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	275.k (of order $5$, degree $4$, minimal)

Newform invariants

comment:select newform

sage:traces = [100,2,8,-24,0,0,5,20,80,-22] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(10)] == traces)

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

Self dual:	no
Analytic conductor:	$2.19588605559$
Analytic rank:	$0$
Dimension:	$100$
Relative dimension:	$25$ over $\Q(\zeta_{5})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			181.19
Character	$\chi$	$=$	275.181
Dual form			275.2.k.d.196.19

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.20663 - 0.876668i) q^{2} +0.309228 q^{3} +(0.0693751 - 0.213515i) q^{4} +(0.504920 + 2.17831i) q^{5} +(0.373124 - 0.271091i) q^{6} +(2.02744 - 1.47302i) q^{7} +(0.818312 + 2.51851i) q^{8} -2.90438 q^{9} +(2.51891 + 2.18577i) q^{10} +(1.07375 - 3.13800i) q^{11} +(0.0214527 - 0.0660247i) q^{12} +6.00626 q^{13} +(1.15502 - 3.55477i) q^{14} +(0.156136 + 0.673597i) q^{15} +(3.55855 + 2.58543i) q^{16} +(-6.05478 + 4.39906i) q^{17} +(-3.50451 + 2.54618i) q^{18} +(-0.989834 - 3.04640i) q^{19} +(0.500131 + 0.0433131i) q^{20} +(0.626940 - 0.455499i) q^{21} +(-1.45537 - 4.72773i) q^{22} +(-2.19113 - 6.74361i) q^{23} +(0.253045 + 0.778793i) q^{24} +(-4.49011 + 2.19975i) q^{25} +(7.24733 - 5.26549i) q^{26} -1.82580 q^{27} +(-0.173857 - 0.535078i) q^{28} +(-0.111762 + 0.343967i) q^{29} +(0.778918 + 0.675903i) q^{30} +(-0.338108 + 1.04059i) q^{31} +1.26419 q^{32} +(0.332034 - 0.970359i) q^{33} +(-3.44937 + 10.6161i) q^{34} +(4.23239 + 3.67264i) q^{35} +(-0.201491 + 0.620127i) q^{36} +(-2.41879 - 7.44427i) q^{37} +(-3.86504 - 2.80812i) q^{38} +1.85730 q^{39} +(-5.07292 + 3.05418i) q^{40} +(-2.06329 + 1.49906i) q^{41} +(0.357164 - 1.09924i) q^{42} -6.81097 q^{43} +(-0.595518 - 0.446960i) q^{44} +(-1.46648 - 6.32665i) q^{45} +(-8.55579 - 6.21614i) q^{46} -0.0743774 q^{47} +(1.10040 + 0.799489i) q^{48} +(-0.222407 + 0.684499i) q^{49} +(-3.48945 + 6.59062i) q^{50} +(-1.87231 + 1.36031i) q^{51} +(0.416685 - 1.28242i) q^{52} +(1.99480 + 1.44931i) q^{53} +(-2.20307 + 1.60062i) q^{54} +(7.37772 + 0.754526i) q^{55} +(5.36888 + 3.90072i) q^{56} +(-0.306085 - 0.942032i) q^{57} +(0.166690 + 0.513019i) q^{58} +(-1.11297 - 3.42538i) q^{59} +(0.154655 + 0.0133936i) q^{60} +11.2908 q^{61} +(0.504280 + 1.55201i) q^{62} +(-5.88844 + 4.27820i) q^{63} +(-5.59168 + 4.06260i) q^{64} +(3.03268 + 13.0835i) q^{65} +(-0.450041 - 1.46195i) q^{66} +(12.9188 + 9.38603i) q^{67} +(0.519212 + 1.59797i) q^{68} +(-0.677560 - 2.08531i) q^{69} +(8.32661 + 0.721113i) q^{70} +(0.136508 + 0.420129i) q^{71} +(-2.37669 - 7.31469i) q^{72} +(-8.01056 - 5.82002i) q^{73} +(-9.44473 - 6.86200i) q^{74} +(-1.38847 + 0.680225i) q^{75} -0.719120 q^{76} +(-2.44538 - 7.94375i) q^{77} +(2.24108 - 1.62824i) q^{78} +(-2.61359 - 1.89888i) q^{79} +(-3.83511 + 9.05707i) q^{80} +8.14854 q^{81} +(-1.17544 + 3.61763i) q^{82} +(-1.02312 + 0.743342i) q^{83} +(-0.0537616 - 0.165461i) q^{84} +(-12.6397 - 10.9680i) q^{85} +(-8.21833 + 5.97096i) q^{86} +(-0.0345599 + 0.106364i) q^{87} +(8.78174 + 0.136380i) q^{88} +(-0.357172 - 1.09926i) q^{89} +(-7.31587 - 6.34831i) q^{90} +(12.1773 - 8.84732i) q^{91} -1.59187 q^{92} +(-0.104552 + 0.321779i) q^{93} +(-0.0897459 + 0.0652042i) q^{94} +(6.13622 - 3.69436i) q^{95} +0.390923 q^{96} +(-1.44853 - 1.05242i) q^{97} +(0.331715 + 1.02091i) q^{98} +(-3.11858 + 9.11395i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 100 q + 2 q^{2} + 8 q^{3} - 24 q^{4} + 5 q^{7} + 20 q^{8} + 80 q^{9} - 22 q^{10} - 53 q^{12} + 12 q^{13} + 15 q^{14} - 24 q^{15} - 8 q^{16} + 6 q^{17} - 21 q^{18} - 14 q^{19} + q^{20} - 22 q^{21} - 29 q^{22}+ \cdots - 84 q^{99}+O(q^{100}) $ 100 * q + 2 * q^2 + 8 * q^3 - 24 * q^4 + 5 * q^7 + 20 * q^8 + 80 * q^9 - 22 * q^10 - 53 * q^12 + 12 * q^13 + 15 * q^14 - 24 * q^15 - 8 * q^16 + 6 * q^17 - 21 * q^18 - 14 * q^19 + q^20 - 22 * q^21 - 29 * q^22 + 20 * q^23 - 18 * q^24 + 6 * q^25 - 37 * q^26 - 10 * q^27 + 26 * q^28 + 32 * q^29 + 20 * q^30 - 16 * q^31 - 98 * q^32 - 2 * q^33 - 14 * q^34 + 13 * q^35 - 10 * q^36 + 9 * q^37 - 67 * q^38 - 126 * q^39 + 49 * q^40 + 8 * q^41 - 24 * q^42 + 82 * q^43 + 46 * q^44 - 25 * q^45 + 29 * q^46 + 30 * q^47 + 83 * q^48 - 26 * q^49 + 4 * q^50 - 14 * q^51 + 17 * q^52 - 30 * q^53 - 22 * q^54 - 88 * q^55 + q^56 - 85 * q^57 + 50 * q^58 + 32 * q^59 - 39 * q^60 - 20 * q^61 + 38 * q^62 + 18 * q^63 - 44 * q^64 - 64 * q^65 + 22 * q^66 - 20 * q^67 + 5 * q^68 - 74 * q^69 + 47 * q^70 + 3 * q^71 + 107 * q^72 - 2 * q^73 - 3 * q^74 - 64 * q^75 - 156 * q^76 + 50 * q^77 + 30 * q^78 + 49 * q^79 + 96 * q^80 + 108 * q^81 - 59 * q^82 + 63 * q^83 + 24 * q^84 - 21 * q^85 + 9 * q^86 + 38 * q^87 - 37 * q^88 + 39 * q^89 - 166 * q^90 + 9 * q^91 + 30 * q^92 - 19 * q^93 + 66 * q^94 - 11 * q^95 - 116 * q^96 + 10 * q^97 + 122 * q^98 - 84 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/275\mathbb{Z}\right)^\times$.

$n$	$101$	$177$
$\chi(n)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{2}{5}\right)$

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 $

$2$	1.20663	−	0.876668i	0.853216	−	0.619898i	−0.0728147	−	0.997345i	$-0.523198\pi$
$2$	1.20663	−	0.876668i	0.853216	−	0.619898i	0.926031	+	0.377448i	$0.123198\pi$
$3$	0.309228			0.178533			0.0892665	−	0.996008i	$-0.471548\pi$
$3$	0.309228			0.178533			0.0892665	+	0.996008i	$0.471548\pi$
$4$	0.0693751	−	0.213515i	0.0346875	−	0.106757i
$5$	0.504920	+	2.17831i	0.225807	+	0.974172i
$5$	0.504920	+	2.17831i	0.225807	+	0.974172i
$6$	0.373124	−	0.271091i	0.152327	−	0.110672i
$7$	2.02744	−	1.47302i	0.766298	−	0.556748i	−0.134537	−	0.990909i	$-0.542955\pi$
$7$	2.02744	−	1.47302i	0.766298	−	0.556748i	0.900836	+	0.434160i	$0.142955\pi$
$8$	0.818312	+	2.51851i	0.289317	+	0.890426i
$9$	−2.90438			−0.968126
$10$	2.51891	+	2.18577i	0.796549	+	0.691202i
$11$	1.07375	−	3.13800i	0.323748	−	0.946143i
$11$	1.07375	−	3.13800i	0.323748	−	0.946143i
$12$	0.0214527	−	0.0660247i	0.00619287	−	0.0190597i
$13$	6.00626			1.66584			0.832918	−	0.553396i	$-0.186669\pi$
$13$	6.00626			1.66584			0.832918	+	0.553396i	$0.186669\pi$
$14$	1.15502	−	3.55477i	0.308691	−	0.950054i
$15$	0.156136	+	0.673597i	0.0403140	+	0.173922i
$16$	3.55855	+	2.58543i	0.889636	+	0.646359i
$17$	−6.05478	+	4.39906i	−1.46850	+	1.06693i	−0.487455	+	0.873148i	$0.662075\pi$
$17$	−6.05478	+	4.39906i	−1.46850	+	1.06693i	−0.981045	+	0.193780i	$0.937925\pi$
$18$	−3.50451	+	2.54618i	−0.826021	+	0.600139i
$19$	−0.989834	−	3.04640i	−0.227084	−	0.698891i	−0.998073	−	0.0620439i	$-0.980238\pi$
$19$	−0.989834	−	3.04640i	−0.227084	−	0.698891i	0.770990	−	0.636847i	$-0.219762\pi$
$20$	0.500131	+	0.0433131i	0.111833	+	0.00968509i
$21$	0.626940	−	0.455499i	0.136810	−	0.0993980i
$22$	−1.45537	−	4.72773i	−0.310285	−	1.00796i
$23$	−2.19113	−	6.74361i	−0.456882	−	1.40614i	−0.868911	−	0.494968i	$-0.835180\pi$
$23$	−2.19113	−	6.74361i	−0.456882	−	1.40614i	0.412029	−	0.911171i	$-0.364820\pi$
$24$	0.253045	+	0.778793i	0.0516526	+	0.158970i
$25$	−4.49011	+	2.19975i	−0.898022	+	0.439950i
$26$	7.24733	−	5.26549i	1.42132	−	1.03265i
$27$	−1.82580			−0.351376
$28$	−0.173857	−	0.535078i	−0.0328559	−	0.101120i
$29$	−0.111762	+	0.343967i	−0.0207536	+	0.0638731i	−0.960897	−	0.276906i	$-0.910691\pi$
$29$	−0.111762	+	0.343967i	−0.0207536	+	0.0638731i	0.940143	+	0.340779i	$0.110691\pi$
$30$	0.778918	+	0.675903i	0.142210	+	0.123402i
$31$	−0.338108	+	1.04059i	−0.0607259	+	0.186895i	−0.976817	−	0.214074i	$-0.931327\pi$
$31$	−0.338108	+	1.04059i	−0.0607259	+	0.186895i	0.916091	+	0.400969i	$0.131327\pi$
$32$	1.26419			0.223479
$33$	0.332034	−	0.970359i	0.0577997	−	0.168918i
$34$	−3.44937	+	10.6161i	−0.591562	+	1.82064i
$35$	4.23239	+	3.67264i	0.715404	+	0.620789i
$36$	−0.201491	+	0.620127i	−0.0335819	+	0.103354i
$37$	−2.41879	−	7.44427i	−0.397646	−	1.22383i	−0.926881	−	0.375354i	$-0.877521\pi$
$37$	−2.41879	−	7.44427i	−0.397646	−	1.22383i	0.529235	−	0.848475i	$-0.322479\pi$
$38$	−3.86504	−	2.80812i	−0.626993	−	0.455537i
$39$	1.85730			0.297407
$40$	−5.07292	+	3.05418i	−0.802098	+	0.482909i
$41$	−2.06329	+	1.49906i	−0.322231	+	0.234115i	−0.737127	−	0.675754i	$-0.763818\pi$
$41$	−2.06329	+	1.49906i	−0.322231	+	0.234115i	0.414896	+	0.909869i	$0.363818\pi$
$42$	0.357164	−	1.09924i	0.0551116	−	0.169616i
$43$	−6.81097			−1.03866			−0.519332	−	0.854573i	$-0.673819\pi$
$43$	−6.81097			−1.03866			−0.519332	+	0.854573i	$0.673819\pi$
$44$	−0.595518	−	0.446960i	−0.0897777	−	0.0673818i
$45$	−1.46648	−	6.32665i	−0.218610	−	0.943121i
$46$	−8.55579	−	6.21614i	−1.26148	−	0.916520i
$47$	−0.0743774			−0.0108491			−0.00542453	−	0.999985i	$-0.501727\pi$
$47$	−0.0743774			−0.0108491			−0.00542453	+	0.999985i	$0.501727\pi$
$48$	1.10040	+	0.799489i	0.158829	+	0.115396i
$49$	−0.222407	+	0.684499i	−0.0317725	+	0.0977856i
$50$	−3.48945	+	6.59062i	−0.493483	+	0.932054i
$51$	−1.87231	+	1.36031i	−0.262176	+	0.190482i
$52$	0.416685	−	1.28242i	0.0577838	−	0.177840i
$53$	1.99480	+	1.44931i	0.274007	+	0.199078i	0.716299	−	0.697793i	$-0.245835\pi$
$53$	1.99480	+	1.44931i	0.274007	+	0.199078i	−0.442292	+	0.896871i	$0.645835\pi$
$54$	−2.20307	+	1.60062i	−0.299799	+	0.217817i
$55$	7.37772	+	0.754526i	0.994811	+	0.101740i
$56$	5.36888	+	3.90072i	0.717446	+	0.521255i
$57$	−0.306085	−	0.942032i	−0.0405419	−	0.124775i
$58$	0.166690	+	0.513019i	0.0218875	+	0.0673627i
$59$	−1.11297	−	3.42538i	−0.144897	−	0.445946i	0.852101	−	0.523377i	$-0.175328\pi$
$59$	−1.11297	−	3.42538i	−0.144897	−	0.445946i	−0.996998	+	0.0774312i	$0.975328\pi$
$60$	0.154655	+	0.0133936i	0.0199658	+	0.00172911i
$61$	11.2908			1.44564			0.722822	−	0.691034i	$-0.242844\pi$
$61$	11.2908			1.44564			0.722822	+	0.691034i	$0.242844\pi$
$62$	0.504280	+	1.55201i	0.0640436	+	0.197106i
$63$	−5.88844	+	4.27820i	−0.741873	+	0.539003i
$64$	−5.59168	+	4.06260i	−0.698960	+	0.507824i
$65$	3.03268	+	13.0835i	0.376157	+	1.62281i
$66$	−0.450041	−	1.46195i	−0.0553962	−	0.179953i
$67$	12.9188	+	9.38603i	1.57828	+	1.14669i	0.918635	+	0.395108i	$0.129293\pi$
$67$	12.9188	+	9.38603i	1.57828	+	1.14669i	0.659644	+	0.751578i	$0.270707\pi$
$68$	0.519212	+	1.59797i	0.0629636	+	0.193782i
$69$	−0.677560	−	2.08531i	−0.0815686	−	0.251042i
$70$	8.32661	+	0.721113i	0.995220	+	0.0861895i
$71$	0.136508	+	0.420129i	0.0162006	+	0.0498602i	0.958830	−	0.283981i	$-0.0916552\pi$
$71$	0.136508	+	0.420129i	0.0162006	+	0.0498602i	−0.942629	+	0.333841i	$0.891655\pi$
$72$	−2.37669	−	7.31469i	−0.280095	−	0.862045i
$73$	−8.01056	−	5.82002i	−0.937566	−	0.681181i	0.0102678	−	0.999947i	$-0.496732\pi$
$73$	−8.01056	−	5.82002i	−0.937566	−	0.681181i	−0.947833	+	0.318766i	$0.896732\pi$
$74$	−9.44473	−	6.86200i	−1.09793	−	0.797691i
$75$	−1.38847	+	0.680225i	−0.160327	+	0.0785456i
$76$	−0.719120			−0.0824887
$77$	−2.44538	−	7.94375i	−0.278676	−	0.905274i
$78$	2.24108	−	1.62824i	0.253752	−	0.184362i
$79$	−2.61359	−	1.89888i	−0.294052	−	0.213641i	0.430971	−	0.902366i	$-0.358171\pi$
$79$	−2.61359	−	1.89888i	−0.294052	−	0.213641i	−0.725023	+	0.688724i	$0.758171\pi$
$80$	−3.83511	+	9.05707i	−0.428778	+	1.01261i
$81$	8.14854			0.905394
$82$	−1.17544	+	3.61763i	−0.129806	+	0.399501i
$83$	−1.02312	+	0.743342i	−0.112302	+	0.0815923i	−0.642519	−	0.766270i	$-0.722111\pi$
$83$	−1.02312	+	0.743342i	−0.112302	+	0.0815923i	0.530217	+	0.847862i	$0.322111\pi$
$84$	−0.0537616	−	0.165461i	−0.00586587	−	0.0180533i
$85$	−12.6397	−	10.9680i	−1.37097	−	1.18965i
$86$	−8.21833	+	5.97096i	−0.886205	+	0.643866i
$87$	−0.0345599	+	0.106364i	−0.00370521	+	0.0114035i
$88$	8.78174	+	0.136380i	0.936136	+	0.0145381i
$89$	−0.357172	−	1.09926i	−0.0378601	−	0.116521i	0.930340	−	0.366697i	$-0.119512\pi$
$89$	−0.357172	−	1.09926i	−0.0378601	−	0.116521i	−0.968200	+	0.250176i	$0.919512\pi$
$90$	−7.31587	−	6.34831i	−0.771160	−	0.669171i
$91$	12.1773	−	8.84732i	1.27653	−	0.927452i
$92$	−1.59187			−0.165964
$93$	−0.104552	+	0.321779i	−0.0108416	+	0.0333670i
$94$	−0.0897459	+	0.0652042i	−0.00925659	+	0.00672530i
$95$	6.13622	−	3.69436i	0.629563	−	0.379033i
$96$	0.390923			0.0398984
$97$	−1.44853	−	1.05242i	−0.147076	−	0.106857i	0.511814	−	0.859096i	$-0.328974\pi$
$97$	−1.44853	−	1.05242i	−0.147076	−	0.106857i	−0.658890	+	0.752239i	$0.728974\pi$
$98$	0.331715	+	1.02091i	0.0335083	+	0.103128i
$99$	−3.11858	+	9.11395i	−0.313429	+	0.915986i
$100$	0.158176	+	1.11131i	0.0158176	+	0.111131i
$101$	4.15124	+	12.7762i	0.413063	+	1.27128i	0.913972	+	0.405778i	$0.132999\pi$
$101$	4.15124	+	12.7762i	0.413063	+	1.27128i	−0.500908	+	0.865500i	$0.667001\pi$
$102$	−1.06664	+	3.28279i	−0.105613	+	0.325044i
$103$	2.22768	−	6.85609i	0.219500	−	0.675551i	−0.779304	−	0.626646i	$-0.784427\pi$
$103$	2.22768	−	6.85609i	0.219500	−	0.675551i	0.998803	−	0.0489044i	$-0.0155730\pi$
$104$	4.91499	+	15.1268i	0.481955	+	1.48330i
$105$	1.30877	+	1.13568i	0.127723	+	0.110831i
$106$	3.67755			0.357195
$107$	−10.9968	−	7.98966i	−1.06310	−	0.772390i	−0.0884436	−	0.996081i	$-0.528189\pi$
$107$	−10.9968	−	7.98966i	−1.06310	−	0.772390i	−0.974660	+	0.223691i	$0.928189\pi$
$108$	−0.126665	+	0.389835i	−0.0121884	+	0.0375119i
$109$	3.02626	−	9.31386i	0.289863	−	0.892106i	−0.695036	−	0.718975i	$-0.744611\pi$
$109$	3.02626	−	9.31386i	0.289863	−	0.892106i	0.984899	−	0.173131i	$-0.0553885\pi$
$110$	9.56364	−	5.55737i	0.911857	−	0.529875i
$111$	−0.747958	−	2.30198i	−0.0709930	−	0.218494i
$112$	11.0231			1.04159
$113$	−5.49466	+	3.99210i	−0.516894	+	0.375545i	−0.815432	−	0.578852i	$-0.803501\pi$
$113$	−5.49466	+	3.99210i	−0.516894	+	0.375545i	0.298539	+	0.954398i	$0.403501\pi$
$114$	−1.19518	−	0.868349i	−0.111939	−	0.0813284i
$115$	13.5834	−	8.17795i	1.26665	−	0.762598i
$116$	0.0656885	+	0.0477255i	0.00609902	+	0.00443120i
$117$	−17.4444			−1.61274
$118$	−4.34586	−	3.15746i	−0.400069	−	0.290667i
$119$	−5.79579	+	17.8376i	−0.531299	+	1.63517i
$120$	−1.56869	+	0.944440i	−0.143201	+	0.0862152i
$121$	−8.69412	−	6.73886i	−0.790375	−	0.612624i
$122$	13.6239	−	9.89832i	1.23345	−	0.896152i
$123$	−0.638026	+	0.463553i	−0.0575289	+	0.0417972i
$124$	0.198725	+	0.144382i	0.0178460	+	0.0129659i
$125$	−7.05889	−	8.67018i	−0.631367	−	0.775485i
$126$	−3.35460	+	10.3244i	−0.298852	+	0.919771i
$127$	10.3025			0.914196			0.457098	−	0.889416i	$-0.348889\pi$
$127$	10.3025			0.914196			0.457098	+	0.889416i	$0.348889\pi$
$128$	−3.96686	+	12.2087i	−0.350624	+	1.07911i
$129$	−2.10615			−0.185436
$130$	15.1292	+	13.1283i	1.32692	+	1.15143i
$131$	7.18936	+	5.22337i	0.628137	+	0.456368i	0.855754	−	0.517382i	$-0.173094\pi$
$131$	7.18936	+	5.22337i	0.628137	+	0.456368i	−0.227617	+	0.973751i	$0.573094\pi$
$132$	−0.184151	−	0.138213i	−0.0160283	−	0.0120299i
$133$	−6.49422	−	4.71833i	−0.563120	−	0.409131i
$134$	23.8166			2.05744
$135$	−0.921883	−	3.97717i	−0.0793431	−	0.342300i
$136$	−16.0337	−	11.6492i	−1.37488	−	0.998910i
$137$	5.29973	+	3.85048i	0.452787	+	0.328969i	0.790695	−	0.612210i	$-0.209719\pi$
$137$	5.29973	+	3.85048i	0.452787	+	0.328969i	−0.337908	+	0.941179i	$0.609719\pi$
$138$	−2.64569	−	1.92221i	−0.225216	−	0.163629i
$139$	12.8554	+	9.34002i	1.09038	+	0.792211i	0.979464	−	0.201619i	$-0.0646202\pi$
$139$	12.8554	+	9.34002i	1.09038	+	0.792211i	0.110920	+	0.993829i	$0.464620\pi$
$140$	1.07778	−	0.648887i	0.0910893	−	0.0548410i
$141$	−0.0229996			−0.00193691
$142$	0.533029	+	0.387268i	0.0447308	+	0.0324988i
$143$	6.44922	−	18.8477i	0.539311	−	1.57612i
$144$	−10.3354	−	7.50908i	−0.861280	−	0.625757i
$145$	−0.805699	−	0.0697763i	−0.0669097	−	0.00579461i
$146$	−14.7680			−1.22221
$147$	−0.0687746	+	0.211667i	−0.00567244	+	0.0174580i
$148$	−1.75726			−0.144446
$149$	−0.434883	+	1.33843i	−0.0356270	+	0.109649i	−0.967289	−	0.253679i	$-0.918359\pi$
$149$	−0.434883	+	1.33843i	−0.0356270	+	0.109649i	0.931661	+	0.363328i	$0.118359\pi$
$150$	−1.07904	+	2.03801i	−0.0881031	+	0.166403i
$151$	7.58986	+	5.51435i	0.617654	+	0.448752i	0.852101	−	0.523377i	$-0.175328\pi$
$151$	7.58986	+	5.51435i	0.617654	+	0.448752i	−0.234447	+	0.972129i	$0.575328\pi$
$152$	6.86237	−	4.98581i	0.556612	−	0.404402i
$153$	17.5854	−	12.7765i	1.42169	−	1.03292i
$154$	−9.91469	−	7.44138i	−0.798949	−	0.599644i
$155$	−2.43745	−	0.211091i	−0.195780	−	0.0169553i
$156$	0.128851	−	0.396562i	0.0103163	−	0.0317503i
$157$	4.69905	+	3.41406i	0.375025	+	0.272472i	0.759292	−	0.650750i	$-0.225546\pi$
$157$	4.69905	+	3.41406i	0.375025	+	0.272472i	−0.384266	+	0.923222i	$0.625546\pi$
$158$	−4.81833			−0.383326
$159$	0.616849	+	0.448167i	0.0489193	+	0.0355419i
$160$	0.638314	+	2.75380i	0.0504631	+	0.217707i
$161$	−14.3758	−	10.4447i	−1.13297	−	0.823154i
$162$	9.83228	−	7.14357i	0.772497	−	0.561252i
$163$	−21.7862			−1.70643			−0.853213	−	0.521563i	$-0.825349\pi$
$163$	−21.7862			−1.70643			−0.853213	+	0.521563i	$0.825349\pi$
$164$	0.176932	+	0.544539i	0.0138160	+	0.0425214i
$165$	2.28140	+	0.233321i	0.177607	+	0.0181640i
$166$	−0.582866	+	1.79388i	−0.0452392	+	0.139232i
$167$	−2.89179	+	8.90000i	−0.223773	+	0.688703i	0.774641	+	0.632402i	$0.217931\pi$
$167$	−2.89179	+	8.90000i	−0.223773	+	0.688703i	−0.998414	+	0.0563013i	$0.982069\pi$
$168$	1.66021	+	1.20621i	0.128088	+	0.0930613i
$169$	23.0751			1.77501
$170$	−24.8668	−	2.15355i	−1.90720	−	0.165170i
$171$	2.87485	+	8.84789i	0.219845	+	0.676615i
$172$	−0.472512	+	1.45424i	−0.0360287	+	0.110885i
$173$	3.98353	−	12.2600i	0.302862	−	0.932114i	−0.677604	−	0.735427i	$-0.736982\pi$
$173$	3.98353	−	12.2600i	0.302862	−	0.932114i	0.980466	−	0.196687i	$-0.0630182\pi$
$174$	0.0515452	+	0.158640i	0.00390763	+	0.0120265i
$175$	−5.86314	+	11.0739i	−0.443212	+	0.837105i
$176$	11.9341	−	8.39061i	0.899566	−	0.632466i
$177$	−0.344163	−	1.05922i	−0.0258688	−	0.0796161i
$178$	−1.39466	−	1.01328i	−0.104534	−	0.0759486i
$179$	6.88184			0.514373			0.257186	−	0.966362i	$-0.417205\pi$
$179$	6.88184			0.514373			0.257186	+	0.966362i	$0.417205\pi$
$180$	−1.45257	−	0.125797i	−0.108268	−	0.00937639i
$181$	2.14349	−	1.55733i	0.159324	−	0.115756i	−0.505267	−	0.862963i	$-0.668606\pi$
$181$	2.14349	−	1.55733i	0.159324	−	0.115756i	0.664591	+	0.747208i	$0.268606\pi$
$182$	6.93733	−	21.3509i	0.514229	−	1.58263i
$183$	3.49145			0.258095
$184$	15.1908	−	11.0367i	1.11988	−	0.813640i
$185$	14.9947	−	9.02764i	1.10243	−	0.663725i
$186$	0.155938	+	0.479927i	0.0114339	+	0.0351899i
$187$	7.30293	+	23.7234i	0.534043	+	1.73483i
$188$	−0.00515994	+	0.0158806i	−0.000376327	+	0.00115822i
$189$	−3.70169	+	2.68944i	−0.269259	+	0.195628i
$190$	4.16543	−	9.83715i	0.302192	−	0.713662i
$191$	6.68042	+	20.5602i	0.483378	+	1.48769i	0.834316	+	0.551287i	$0.185863\pi$
$191$	6.68042	+	20.5602i	0.483378	+	1.48769i	−0.350938	+	0.936399i	$0.614137\pi$
$192$	−1.72911	+	1.25627i	−0.124788	+	0.0906634i
$193$	−6.34646	+	19.5324i	−0.456828	+	1.40597i	0.412148	+	0.911117i	$0.364779\pi$
$193$	−6.34646	+	19.5324i	−0.456828	+	1.40597i	−0.868976	+	0.494855i	$0.835221\pi$
$194$	−2.67046			−0.191728
$195$	0.937790	+	4.04579i	0.0671565	+	0.289725i
$196$	0.130721	+	0.0949744i	0.00933722	+	0.00678388i
$197$	−16.4307	+	11.9376i	−1.17064	+	0.850519i	−0.991085	−	0.133229i	$-0.957465\pi$
$197$	−16.4307	+	11.9376i	−1.17064	+	0.850519i	−0.179554	+	0.983748i	$0.557465\pi$
$198$	4.22694	+	13.7311i	0.300395	+	0.975828i
$199$	14.7091			1.04270			0.521349	−	0.853344i	$-0.325429\pi$
$199$	14.7091			1.04270			0.521349	+	0.853344i	$0.325429\pi$
$200$	−9.21439	−	9.50829i	−0.651556	−	0.672338i
$201$	3.99485	+	2.90243i	0.281775	+	0.204721i
$202$	16.2095	+	11.7769i	1.14050	+	0.828618i
$203$	0.280080	+	0.861998i	0.0196578	+	0.0605004i
$204$	0.160555	+	0.494137i	0.0112411	+	0.0345965i
$205$	−4.30723	−	3.73758i	−0.300830	−	0.261044i
$206$	−3.32253	−	10.2257i	−0.231492	−	0.712458i
$207$	6.36387	+	19.5860i	0.442320	+	1.36132i
$208$	21.3735	+	15.5288i	1.48199	+	1.07673i
$209$	−10.6224	−	0.164966i	−0.734769	−	0.0114109i
$210$	2.57482	+	0.222989i	0.177680	+	0.0153877i
$211$	−5.99841	+	4.35810i	−0.412948	+	0.300024i	−0.774794	−	0.632214i	$-0.782146\pi$
$211$	−5.99841	+	4.35810i	−0.412948	+	0.300024i	0.361846	+	0.932238i	$0.382146\pi$
$212$	0.447837	−	0.325373i	0.0307576	−	0.0223467i
$213$	0.0422122	+	0.129916i	0.00289233	+	0.00890169i
$214$	−20.2734			−1.38586
$215$	−3.43900	−	14.8364i	−0.234538	−	1.01184i
$216$	−1.49407	−	4.59829i	−0.101659	−	0.312874i
$217$	0.847314	+	2.60776i	0.0575194	+	0.177027i
$218$	−4.51359	−	13.8914i	−0.305699	−	0.940845i
$219$	−2.47709	−	1.79971i	−0.167386	−	0.121613i
$220$	0.672932	−	1.52290i	0.0453691	−	0.102674i
$221$	−36.3666	+	26.4219i	−2.44628	+	1.77733i
$222$	−2.92058	−	2.12192i	−0.196016	−	0.142414i
$223$	3.25177	−	10.0079i	0.217754	−	0.670179i	−0.781192	−	0.624291i	$-0.785388\pi$
$223$	3.25177	−	10.0079i	0.217754	−	0.670179i	0.998947	−	0.0458886i	$-0.0146119\pi$
$224$	2.56306	−	1.86217i	0.171252	−	0.124422i
$225$	13.0410	−	6.38890i	0.869399	−	0.425927i
$226$	−3.13027	+	9.63398i	−0.208222	+	0.640843i
$227$	−6.50463	−	4.72589i	−0.431727	−	0.313668i	0.350612	−	0.936521i	$-0.385974\pi$
$227$	−6.50463	−	4.72589i	−0.431727	−	0.313668i	−0.782339	+	0.622853i	$0.785974\pi$
$228$	−0.222372			−0.0147270
$229$	8.45917	+	6.14595i	0.558998	+	0.406136i	0.831092	−	0.556135i	$-0.187716\pi$
$229$	8.45917	+	6.14595i	0.558998	+	0.406136i	−0.272094	+	0.962271i	$0.587716\pi$
$230$	9.22073	−	21.7759i	0.607997	−	1.43586i
$231$	−0.756179	−	2.45643i	−0.0497530	−	0.161621i
$232$	−0.957739			−0.0628786
$233$	0.725476	−	2.23279i	0.0475275	−	0.146275i	−0.924476	−	0.381239i	$-0.875497\pi$
$233$	0.725476	−	2.23279i	0.0475275	−	0.146275i	0.972004	+	0.234965i	$0.0754974\pi$
$234$	−21.0490	+	15.2930i	−1.37602	+	0.999734i
$235$	−0.0375546	−	0.162017i	−0.00244979	−	0.0105688i
$236$	−0.808581			−0.0526341
$237$	−0.808196	−	0.587189i	−0.0524980	−	0.0381420i
$238$	8.64428	+	26.6044i	0.560326	+	1.72450i
$239$	−5.44116	+	16.7462i	−0.351959	+	1.08322i	0.605792	+	0.795623i	$0.292856\pi$
$239$	−5.44116	+	16.7462i	−0.351959	+	1.08322i	−0.957752	+	0.287597i	$0.907144\pi$
$240$	−1.18592	+	2.80070i	−0.0765511	+	0.180785i
$241$	7.42141	−	22.8407i	0.478055	−	1.47130i	−0.363738	−	0.931501i	$-0.618500\pi$
$241$	7.42141	−	22.8407i	0.478055	−	1.47130i	0.841793	−	0.539801i	$-0.181500\pi$
$242$	−16.3983	−	0.509452i	−1.05412	−	0.0327488i
$243$	7.99716			0.513018
$244$	0.783303	−	2.41076i	0.0501459	−	0.154333i
$245$	−1.60335	−	0.138856i	−0.102434	−	0.00887118i
$246$	−0.363479	+	1.11867i	−0.0231746	+	0.0713241i
$247$	−5.94520	−	18.2974i	−0.378284	−	1.16424i
$248$	−2.89741			−0.183985
$249$	−0.316378	+	0.229862i	−0.0200497	+	0.0145669i
$250$	−16.1183	−	4.27340i	−1.01941	−	0.270273i
$251$	−1.72690	−	5.31485i	−0.109001	−	0.335470i	0.881648	−	0.471908i	$-0.156435\pi$
$251$	−1.72690	−	5.31485i	−0.109001	−	0.335470i	−0.990649	+	0.136438i	$0.956435\pi$
$252$	0.504947	+	1.55407i	0.0318087	+	0.0978971i
$253$	−23.5142	−	0.365173i	−1.47832	−	0.0229583i
$254$	12.4313	−	9.03184i	0.780007	−	0.566708i
$255$	−3.90856	−	3.39163i	−0.244763	−	0.212392i
$256$	1.64481	+	5.06220i	0.102800	+	0.316387i
$257$	6.33627	−	4.60357i	0.395246	−	0.287163i	−0.372356	−	0.928090i	$-0.621450\pi$
$257$	6.33627	−	4.60357i	0.395246	−	0.287163i	0.767602	+	0.640927i	$0.221450\pi$
$258$	−2.54134	+	1.84639i	−0.158217	+	0.114951i
$259$	−15.8695	−	11.5298i	−0.986081	−	0.716430i
$260$	3.00391	+	0.260149i	0.186295	+	0.0161338i
$261$	0.324598	−	0.999010i	0.0200921	−	0.0618372i
$262$	13.2541			0.818838
$263$	−1.99985	+	6.15489i	−0.123316	+	0.379527i	−0.993590	−	0.113040i	$-0.963941\pi$
$263$	−1.99985	+	6.15489i	−0.123316	+	0.379527i	0.870275	+	0.492567i	$0.163941\pi$
$264$	2.71556	+	0.0421725i	0.167131	+	0.00259554i
$265$	−2.14983	+	5.07709i	−0.132063	+	0.311883i
$266$	−11.9725			−0.734083
$267$	−0.110448	−	0.339923i	−0.00675928	−	0.0208029i
$268$	2.90030	−	2.10719i	0.177164	−	0.128717i
$269$	4.09098	−	2.97227i	0.249432	−	0.181223i	−0.456043	−	0.889958i	$-0.650734\pi$
$269$	4.09098	−	2.97227i	0.249432	−	0.181223i	0.705475	+	0.708735i	$0.250734\pi$
$270$	−4.59903	−	3.99079i	−0.279888	−	0.242871i
$271$	0.886168	−	2.72735i	0.0538309	−	0.165674i	−0.920527	−	0.390680i	$-0.872240\pi$
$271$	0.886168	−	2.72735i	0.0538309	−	0.165674i	0.974358	+	0.225005i	$0.0722400\pi$
$272$	−32.9197			−1.99605
$273$	3.76557	−	2.73584i	0.227902	−	0.165581i
$274$	9.77041			0.590252
$275$	2.08156	+	16.4520i	0.125523	+	0.992091i
$276$	−0.492251			−0.0296300
$277$	−14.9690	+	10.8756i	−0.899401	+	0.653453i	−0.938312	−	0.345790i	$-0.887611\pi$
$277$	−14.9690	+	10.8756i	−0.899401	+	0.653453i	0.0389113	+	0.999243i	$0.487611\pi$
$278$	23.6999			1.42142
$279$	0.981993	−	3.02226i	0.0587904	−	0.180938i
$280$	−5.78614	+	13.6647i	−0.345788	+	0.816619i
$281$	−8.44466	+	6.13540i	−0.503766	+	0.366007i	−0.810454	−	0.585803i	$-0.800779\pi$
$281$	−8.44466	+	6.13540i	−0.503766	+	0.366007i	0.306688	+	0.951810i	$0.400779\pi$
$282$	−0.0277520	+	0.0201630i	−0.00165261	+	0.00120069i
$283$	4.08480	+	12.5717i	0.242816	+	0.747310i	0.995988	+	0.0894869i	$0.0285227\pi$
$283$	4.08480	+	12.5717i	0.242816	+	0.747310i	−0.753172	+	0.657824i	$0.771477\pi$
$284$	0.0991740			0.00588489
$285$	1.89749	−	1.14240i	0.112398	−	0.0676699i
$286$	−8.74131	−	28.3960i	−0.516885	−	1.67909i
$287$	−1.97503	+	6.07851i	−0.116582	+	0.358803i
$288$	−3.67168			−0.216356
$289$	12.0554	−	37.1027i	0.709141	−	2.18251i
$290$	−1.03335	+	0.622136i	−0.0606805	+	0.0365331i
$291$	−0.447926	−	0.325437i	−0.0262579	−	0.0190775i
$292$	−1.79839	+	1.30661i	−0.105243	+	0.0764634i
$293$	−8.31595	+	6.04189i	−0.485823	+	0.352971i	−0.803576	−	0.595202i	$-0.797072\pi$
$293$	−8.31595	+	6.04189i	−0.485823	+	0.352971i	0.317753	+	0.948174i	$0.397072\pi$
$294$	0.102576	+	0.315696i	0.00598234	+	0.0184117i
$295$	6.89959	−	4.15395i	0.401710	−	0.241852i
$296$	16.7691	−	12.1835i	0.974684	−	0.708149i
$297$	−1.96045	+	5.72937i	−0.113757	+	0.332452i
$298$	0.648619	+	1.99624i	0.0375735	+	0.115639i
$299$	−13.1605	−	40.5038i	−0.761091	−	2.34240i
$300$	0.0489126	+	0.343649i	0.00282397	+	0.0198406i
$301$	−13.8088	+	10.0327i	−0.795927	+	0.578274i
$302$	13.9924			0.805172
$303$	1.28368	+	3.95076i	0.0737455	+	0.226965i
$304$	4.35389	−	13.3999i	0.249713	−	0.768537i
$305$	5.70097	+	24.5950i	0.326437	+	1.40831i
$306$	10.0183	−	30.8331i	0.572706	−	1.76261i
$307$	−21.9100			−1.25047			−0.625234	−	0.780437i	$-0.714996\pi$
$307$	−21.9100			−1.25047			−0.625234	+	0.780437i	$0.714996\pi$
$308$	−1.86575	−	0.0289750i	−0.106311	−	0.00165100i
$309$	0.688861	−	2.12010i	0.0391880	−	0.120608i
$310$	−3.12615	+	1.88212i	−0.177554	+	0.106897i
$311$	−2.74016	+	8.43335i	−0.155380	+	0.478211i	−0.998199	−	0.0599858i	$-0.980894\pi$
$311$	−2.74016	+	8.43335i	−0.155380	+	0.478211i	0.842819	+	0.538197i	$0.180894\pi$
$312$	1.51985	+	4.67763i	0.0860448	+	0.264819i
$313$	2.92918	+	2.12818i	0.165567	+	0.120292i	0.667483	−	0.744625i	$-0.267371\pi$
$313$	2.92918	+	2.12818i	0.165567	+	0.120292i	−0.501916	+	0.864916i	$0.667371\pi$
$314$	8.66302			0.488882
$315$	−12.2925	−	10.6667i	−0.692601	−	0.601002i
$316$	−0.586758	+	0.426304i	−0.0330077	+	0.0239815i
$317$	−8.72398	+	26.8497i	−0.489988	+	1.50803i	0.334637	+	0.942347i	$0.391386\pi$
$317$	−8.72398	+	26.8497i	−0.489988	+	1.50803i	−0.824625	+	0.565680i	$0.808614\pi$
$318$	1.13720			0.0637711
$319$	0.959365	+	0.720043i	0.0537141	+	0.0403147i
$320$	−11.6730	−	10.1292i	−0.652538	−	0.566237i
$321$	−3.40053	−	2.47063i	−0.189799	−	0.137897i
$322$	−26.5028			−1.47694
$323$	19.3945	+	14.0909i	1.07914	+	0.784040i
$324$	0.565306	−	1.73983i	0.0314059	−	0.0966574i
$325$	−26.9688	+	13.2123i	−1.49596	+	0.732884i
$326$	−26.2879	+	19.0992i	−1.45595	+	1.05781i
$327$	0.935805	−	2.88011i	0.0517501	−	0.159270i
$328$	−5.46381	−	3.96969i	−0.301689	−	0.219190i
$329$	−0.150795	+	0.109559i	−0.00831361	+	0.00604019i
$330$	2.95735	−	1.71850i	0.162797	−	0.0946002i
$331$	10.3568	+	7.52467i	0.569262	+	0.413593i	0.834837	−	0.550497i	$-0.185562\pi$
$331$	10.3568	+	7.52467i	0.569262	+	0.413593i	−0.265575	+	0.964090i	$0.585562\pi$
$332$	0.0877351	+	0.270021i	0.00481509	+	0.0148193i
$333$	7.02508	+	21.6210i	0.384972	+	1.18482i
$334$	4.31303	+	13.2741i	0.235999	+	0.726329i
$335$	−13.9228	+	32.8803i	−0.760684	+	1.79644i
$336$	3.40866			0.185958
$337$	2.94498	+	9.06373i	0.160423	+	0.493733i	0.998670	−	0.0515588i	$-0.0164190\pi$
$337$	2.94498	+	9.06373i	0.160423	+	0.493733i	−0.838246	+	0.545292i	$0.816419\pi$
$338$	27.8431	−	20.2292i	1.51447	−	1.10032i
$339$	−1.69910	+	1.23447i	−0.0922826	+	0.0670473i
$340$	−3.21872	+	1.93785i	−0.174560	+	0.105095i
$341$	2.90233	+	2.17831i	0.157170	+	0.117962i
$342$	11.2255	+	8.15583i	0.607008	+	0.441017i
$343$	5.97824	+	18.3991i	0.322795	+	0.993460i
$344$	−5.57350	−	17.1535i	−0.300503	−	0.924853i
$345$	4.20036	−	2.52885i	0.226140	−	0.136149i
$346$	−5.94134	−	18.2856i	−0.319408	−	0.983038i
$347$	−5.97730	−	18.3962i	−0.320878	−	0.987561i	−0.973267	−	0.229677i	$-0.926233\pi$
$347$	−5.97730	−	18.3962i	−0.320878	−	0.987561i	0.652389	−	0.757884i	$-0.273767\pi$
$348$	0.0203127	+	0.0147581i	0.00108888	+	0.000791116i
$349$	1.42217	+	1.03326i	0.0761268	+	0.0553093i	0.625198	−	0.780466i	$-0.285018\pi$
$349$	1.42217	+	1.03326i	0.0761268	+	0.0553093i	−0.549071	+	0.835776i	$0.685018\pi$
$350$	2.63346	+	18.5021i	0.140764	+	0.988978i
$351$	−10.9662			−0.585334
$352$	1.35742	−	3.96703i	0.0723508	−	0.211443i
$353$	−0.877645	+	0.637646i	−0.0467123	+	0.0339385i	−0.610896	−	0.791711i	$-0.709191\pi$
$353$	−0.877645	+	0.637646i	−0.0467123	+	0.0339385i	0.564184	+	0.825649i	$0.309191\pi$
$354$	−1.34386	−	0.976375i	−0.0714256	−	0.0518937i
$355$	−0.846248	+	0.509490i	−0.0449142	+	0.0270409i
$356$	−0.259487			−0.0137528
$357$	−1.79222	+	5.51589i	−0.0948544	+	0.291932i
$358$	8.30384	−	6.03309i	0.438871	−	0.318859i
$359$	0.761640	+	2.34409i	0.0401978	+	0.123716i	0.969142	−	0.246505i	$-0.0792820\pi$
$359$	0.761640	+	2.34409i	0.0401978	+	0.123716i	−0.928944	+	0.370221i	$0.879282\pi$
$360$	14.7337	−	8.87051i	0.776532	−	0.467517i
$361$	7.07056	−	5.13706i	0.372135	−	0.270372i
$362$	1.22113	−	3.75825i	0.0641811	−	0.197529i
$363$	−2.68847	−	2.08385i	−0.141108	−	0.109374i
$364$	−1.04423	−	3.21381i	−0.0547326	−	0.168450i
$365$	8.63313	−	20.3882i	0.451879	−	1.06717i
$366$	4.21289	−	3.06084i	0.220211	−	0.159993i
$367$	−13.7526			−0.717879			−0.358940	−	0.933361i	$-0.616862\pi$
$367$	−13.7526			−0.717879			−0.358940	+	0.933361i	$0.616862\pi$
$368$	9.63791	−	29.6625i	0.502411	−	1.54626i
$369$	5.99256	−	4.35385i	0.311960	−	0.226652i
$370$	10.1788	−	24.0384i	0.529169	−	1.24969i
$371$	6.17918			0.320807
$372$	0.0614513	+	0.0446470i	0.00318610	+	0.00231484i
$373$	1.96925	+	6.06074i	0.101964	+	0.313813i	0.989006	−	0.147876i	$-0.0472436\pi$
$373$	1.96925	+	6.06074i	0.101964	+	0.313813i	−0.887042	+	0.461689i	$0.847244\pi$
$374$	29.6095	+	22.2231i	1.53107	+	1.14913i
$375$	−2.18281	−	2.68107i	−0.112720	−	0.138450i
$376$	−0.0608639	−	0.187320i	−0.00313881	−	0.00966028i
$377$	−0.671269	+	2.06595i	−0.0345721	+	0.106402i
$378$	−2.10883	+	6.49031i	−0.108467	+	0.333826i
$379$	−9.50818	−	29.2632i	−0.488402	−	1.50315i	−0.826992	−	0.562214i	$-0.809950\pi$
$379$	−9.50818	−	29.2632i	−0.488402	−	1.50315i	0.338590	−	0.940934i	$-0.390050\pi$
$380$	−0.363098	−	1.56647i	−0.0186265	−	0.0803582i
$381$	3.18581			0.163214
$382$	26.0853	+	18.9521i	1.33464	+	0.969672i
$383$	9.88597	−	30.4259i	0.505150	−	1.55469i	−0.295370	−	0.955383i	$-0.595443\pi$
$383$	9.88597	−	30.4259i	0.505150	−	1.55469i	0.800519	−	0.599307i	$-0.204557\pi$
$384$	−1.22666	+	3.77528i	−0.0625979	+	0.192657i
$385$	16.0693	−	9.33776i	0.818966	−	0.475896i
$386$	9.46559	+	29.1321i	0.481786	+	1.48278i
$387$	19.7816			1.00556
$388$	−0.325198	+	0.236270i	−0.0165094	+	0.0119948i
$389$	−7.66856	−	5.57153i	−0.388811	−	0.282488i	0.376157	−	0.926556i	$-0.377245\pi$
$389$	−7.66856	−	5.57153i	−0.388811	−	0.282488i	−0.764968	+	0.644068i	$0.777245\pi$
$390$	4.67838	+	4.05965i	0.236899	+	0.205568i
$391$	42.9323	+	31.1922i	2.17118	+	1.57746i
$392$	−1.90591			−0.0962632
$393$	2.22315	+	1.61522i	0.112143	+	0.0814768i
$394$	−9.36046	+	28.8085i	−0.471573	+	1.45135i
$395$	2.81672	−	6.65201i	0.141724	−	0.334699i
$396$	1.72961	+	1.29814i	0.0869161	+	0.0652341i
$397$	23.5711	−	17.1254i	1.18300	−	0.859498i	0.190491	−	0.981689i	$-0.438992\pi$
$397$	23.5711	−	17.1254i	1.18300	−	0.859498i	0.992507	+	0.122191i	$0.0389920\pi$
$398$	17.7484	−	12.8950i	0.889647	−	0.646366i
$399$	−2.00820	−	1.45904i	−0.100536	−	0.0730434i
$400$	−21.6656	−	3.78098i	−1.08328	−	0.189049i
$401$	4.39110	−	13.5144i	0.219281	−	0.674877i	−0.779541	−	0.626351i	$-0.784548\pi$
$401$	4.39110	−	13.5144i	0.219281	−	0.674877i	0.998822	−	0.0485259i	$-0.0154524\pi$
$402$	7.36477			0.367321
$403$	−2.03076	+	6.25004i	−0.101159	+	0.311337i
$404$	3.01590			0.150046
$405$	4.11436	+	17.7501i	0.204444	+	0.882009i
$406$	1.09364	+	0.794575i	0.0542764	+	0.0394341i
$407$	−25.9573	−	0.403115i	−1.28666	−	0.0199817i
$408$	−4.95809	−	3.60226i	−0.245462	−	0.178339i
$409$	−16.8686			−0.834096			−0.417048	−	0.908884i	$-0.636935\pi$
$409$	−16.8686			−0.834096			−0.417048	+	0.908884i	$0.636935\pi$
$410$	−8.47385	−	0.733864i	−0.418493	−	0.0362430i
$411$	1.63883	+	1.19068i	0.0808374	+	0.0587318i
$412$	−1.30933	−	0.951284i	−0.0645061	−	0.0468664i
$413$	−7.30212	−	5.30530i	−0.359314	−	0.261057i
$414$	24.8492	+	18.0540i	1.22127	+	0.887307i
$415$	−2.13583	−	1.85335i	−0.104844	−	0.0909776i
$416$	7.59304			0.372279
$417$	3.97527	+	2.88820i	0.194670	+	0.141436i
$418$	−12.9620	+	9.11330i	−0.633991	+	0.445746i
$419$	11.2547	+	8.17698i	0.549826	+	0.399472i	0.827721	−	0.561140i	$-0.189637\pi$
$419$	11.2547	+	8.17698i	0.549826	+	0.399472i	−0.277896	+	0.960611i	$0.589637\pi$
$420$	0.333281	−	0.200654i	0.0162625	−	0.00979093i
$421$	3.37315			0.164398			0.0821988	−	0.996616i	$-0.473806\pi$
$421$	3.37315			0.164398			0.0821988	+	0.996616i	$0.473806\pi$
$422$	−3.41726	+	10.5172i	−0.166349	+	0.511971i
$423$	0.216020			0.0105032
$424$	−2.01772	+	6.20990i	−0.0979891	+	0.301579i
$425$	17.5098	−	33.0713i	0.849351	−	1.60419i
$426$	0.164828	+	0.119754i	0.00798592	+	0.00580211i
$427$	22.8915	−	16.6316i	1.10780	−	0.804860i
$428$	−2.46882	+	1.79370i	−0.119335	+	0.0867017i
$429$	1.99428	−	5.82823i	0.0962848	−	0.281389i
$430$	−17.1562	−	14.8872i	−0.827347	−	0.717927i
$431$	2.63563	−	8.11162i	0.126954	−	0.390723i	−0.867298	−	0.497789i	$-0.834145\pi$
$431$	2.63563	−	8.11162i	0.126954	−	0.390723i	0.994252	+	0.107066i	$0.0341455\pi$
$432$	−6.49719	−	4.72049i	−0.312596	−	0.227115i
$433$	−17.4426			−0.838238			−0.419119	−	0.907931i	$-0.637661\pi$
$433$	−17.4426			−0.838238			−0.419119	+	0.907931i	$0.637661\pi$
$434$	3.30854	+	2.40379i	0.158815	+	0.115386i
$435$	−0.249145	−	0.0215768i	−0.0119456	−	0.00103453i
$436$	−1.77870	−	1.29230i	−0.0851842	−	0.0618900i
$437$	−18.3748	+	13.3501i	−0.878988	+	0.638622i
$438$	−4.56669			−0.218205
$439$	−4.67547	−	14.3896i	−0.223148	−	0.686779i	−0.998474	−	0.0552179i	$-0.982415\pi$
$439$	−4.67547	−	14.3896i	−0.223148	−	0.686779i	0.775326	−	0.631561i	$-0.217585\pi$
$440$	4.13700	+	19.1983i	0.197224	+	0.915241i
$441$	0.645955	−	1.98804i	0.0307598	−	0.0946688i
$442$	−20.7178	+	63.7628i	−0.985445	+	3.03289i
$443$	16.9775	+	12.3348i	0.806624	+	0.586046i	0.912850	−	0.408296i	$-0.133877\pi$
$443$	16.9775	+	12.3348i	0.806624	+	0.586046i	−0.106226	+	0.994342i	$0.533877\pi$
$444$	−0.543395			−0.0257884
$445$	2.21419	−	1.33307i	0.104963	−	0.0631936i
$446$	−4.84994	−	14.9266i	−0.229651	−	0.706793i
$447$	−0.134478	+	0.413882i	−0.00636060	+	0.0195759i
$448$	−5.35250	+	16.4733i	−0.252882	+	0.778290i
$449$	5.29288	+	16.2898i	0.249786	+	0.768763i	0.994812	+	0.101728i	$0.0324370\pi$
$449$	5.29288	+	16.2898i	0.249786	+	0.768763i	−0.745026	+	0.667035i	$0.767563\pi$
$450$	10.1347	−	19.1417i	0.477754	−	0.902346i
$451$	2.48862	+	8.08422i	0.117184	+	0.380671i
$452$	0.471180	+	1.45014i	0.0221624	+	0.0682089i
$453$	2.34700	+	1.70519i	0.110272	+	0.0801170i
$454$	−11.9917			−0.562799
$455$	25.4208	+	22.0588i	1.19175	+	1.03413i
$456$	2.12204	−	1.54175i	0.0993736	−	0.0721992i
$457$	4.27935	−	13.1705i	0.200179	−	0.616089i	−0.799697	−	0.600403i	$-0.795007\pi$
$457$	4.27935	−	13.1705i	0.200179	−	0.616089i	0.999877	−	0.0156859i	$-0.00499319\pi$
$458$	15.5950			0.728708
$459$	11.0548	−	8.03180i	0.515995	−	0.374892i
$460$	−0.803766	−	3.46759i	−0.0374758	−	0.161677i
$461$	−3.68075	−	11.3282i	−0.171430	−	0.527606i	0.828023	−	0.560694i	$-0.189466\pi$
$461$	−3.68075	−	11.3282i	−0.171430	−	0.527606i	−0.999452	+	0.0330883i	$0.989466\pi$
$462$	−3.06590	−	2.30109i	−0.142639	−	0.107056i
$463$	12.7070	−	39.1081i	0.590544	−	1.81751i	0.0147830	−	0.999891i	$-0.495294\pi$
$463$	12.7070	−	39.1081i	0.590544	−	1.81751i	0.575761	−	0.817618i	$-0.304706\pi$
$464$	−1.28701	+	0.935070i	−0.0597481	+	0.0434095i
$465$	−0.753728	−	0.0652754i	−0.0349533	−	0.00302707i
$466$	−1.08203	−	3.33015i	−0.0501241	−	0.154266i
$467$	13.5329	−	9.83226i	0.626230	−	0.454983i	−0.228862	−	0.973459i	$-0.573500\pi$
$467$	13.5329	−	9.83226i	0.626230	−	0.454983i	0.855092	+	0.518476i	$0.173500\pi$
$468$	−1.21021	+	3.72464i	−0.0559420	+	0.172172i
$469$	40.0178			1.84785
$470$	−0.187350	−	0.162572i	−0.00864181	−	0.00749889i
$471$	1.45308	+	1.05572i	0.0669544	+	0.0486452i
$472$	7.71607	−	5.60605i	0.355161	−	0.258040i
$473$	−7.31328	+	21.3729i	−0.336265	+	0.982725i
$474$	−1.48996			−0.0684363
$475$	11.1458	+	11.5013i	0.511403	+	0.527715i
$476$	3.40650	+	2.47497i	0.156137	+	0.113440i
$477$	−5.79365	−	4.20933i	−0.265273	−	0.192732i
$478$	8.11536	+	24.9765i	0.371188	+	1.14240i
$479$	3.88209	+	11.9478i	0.177377	+	0.545910i	0.999734	−	0.0230615i	$-0.00734134\pi$
$479$	3.88209	+	11.9478i	0.177377	+	0.545910i	−0.822357	+	0.568972i	$0.807341\pi$
$480$	0.197385	+	0.851553i	0.00900934	+	0.0388679i
$481$	−14.5279	−	44.7122i	−0.662414	−	2.03870i
$482$	−11.0689	−	34.0664i	−0.504173	−	1.55168i
$483$	−4.44541	−	3.22978i	−0.202273	−	0.146960i
$484$	−2.04200	+	1.38881i	−0.0928182	+	0.0631278i
$485$	1.56111	−	3.68674i	0.0708861	−	0.167406i
$486$	9.64962	−	7.01086i	0.437715	−	0.318019i
$487$	20.4838	−	14.8823i	0.928209	−	0.674383i	−0.0173445	−	0.999850i	$-0.505521\pi$
$487$	20.4838	−	14.8823i	0.928209	−	0.674383i	0.945554	+	0.325466i	$0.105521\pi$
$488$	9.23943	+	28.4361i	0.418250	+	1.28724i
$489$	−6.73690			−0.304653
$490$	−2.05638	+	1.23806i	−0.0928980	+	0.0559299i
$491$	0.265782	+	0.817994i	0.0119946	+	0.0369156i	0.956875	−	0.290501i	$-0.0938220\pi$
$491$	0.265782	+	0.817994i	0.0119946	+	0.0369156i	−0.944880	+	0.327417i	$0.893822\pi$
$492$	0.0547122	+	0.168387i	0.00246662	+	0.00759147i
$493$	−0.836438	−	2.57429i	−0.0376713	−	0.115940i
$494$	−23.2144	−	16.8663i	−1.04447	−	0.758850i
$495$	−21.4277	−	2.19143i	−0.963102	−	0.0984974i
$496$	−3.89354	+	2.82883i	−0.174825	+	0.127018i
$497$	0.895620	+	0.650706i	0.0401740	+	0.0291881i
$498$	−0.180239	+	0.554717i	−0.00807669	+	0.0248575i
$499$	−17.3125	+	12.5783i	−0.775014	+	0.563081i	−0.903478	−	0.428634i	$-0.858995\pi$
$499$	−17.3125	+	12.5783i	−0.775014	+	0.563081i	0.128465	+	0.991714i	$0.458995\pi$
$500$	−2.34092	+	0.905682i	−0.104689	+	0.0405033i
$501$	−0.894222	+	2.75213i	−0.0399509	+	0.122956i
$502$	−6.74309	−	4.89914i	−0.300959	−	0.218659i
$503$	14.2442			0.635119			0.317560	−	0.948238i	$-0.397137\pi$
$503$	14.2442			0.635119			0.317560	+	0.948238i	$0.397137\pi$
$504$	−15.5932	−	11.3292i	−0.694579	−	0.504641i
$505$	−25.7345	+	15.4937i	−1.14517	+	0.689458i
$506$	−28.6931	+	20.1735i	−1.27556	+	0.896821i
$507$	7.13548			0.316898
$508$	0.714734	−	2.19973i	0.0317112	−	0.0975970i
$509$	30.9281	−	22.4705i	1.37086	−	0.995990i	0.373193	−	0.927754i	$-0.378263\pi$
$509$	30.9281	−	22.4705i	1.37086	−	0.995990i	0.997669	−	0.0682357i	$-0.0217370\pi$
$510$	−7.68951	−	0.665938i	−0.340497	−	0.0294883i
$511$	−24.8139			−1.09770
$512$	−14.3482	−	10.4246i	−0.634106	−	0.460705i
$513$	1.80724	+	5.56211i	0.0797916	+	0.245573i
$514$	3.60973	−	11.1096i	0.159218	−	0.490024i
$515$	16.0595	+	1.39081i	0.707667	+	0.0612864i
$516$	−0.146114	+	0.449693i	−0.00643231	+	0.0197966i
$517$	−0.0798627	+	0.233396i	−0.00351236	+	0.0102648i
$518$	−29.2564			−1.28545
$519$	1.23182	−	3.79115i	0.0540709	−	0.166413i
$520$	−30.4692	+	18.3442i	−1.33616	+	0.804447i
$521$	8.14087	−	25.0550i	0.356658	−	1.09768i	−0.598384	−	0.801210i	$-0.704190\pi$
$521$	8.14087	−	25.0550i	0.356658	−	1.09768i	0.955042	−	0.296471i	$-0.0958098\pi$
$522$	−0.484130	−	1.49000i	−0.0211898	−	0.0652155i
$523$	−28.4055			−1.24209			−0.621043	−	0.783776i	$-0.713291\pi$
$523$	−28.4055			−1.24209			−0.621043	+	0.783776i	$0.713291\pi$
$524$	1.61403	−	1.17266i	0.0705092	−	0.0512279i
$525$	−1.81305	+	3.42435i	−0.0791280	+	0.149451i
$526$	2.98272	+	9.17988i	0.130053	+	0.400262i
$527$	−2.53044	−	7.78789i	−0.110228	−	0.339246i
$528$	3.69036	−	2.59462i	0.160602	−	0.112916i
$529$	−22.0678	+	16.0332i	−0.959469	+	0.697095i
$530$	1.85687	+	8.01085i	0.0806571	+	0.347969i
$531$	3.23249	+	9.94859i	0.140278	+	0.431732i
$532$	−1.45797	+	1.05928i	−0.0632110	+	0.0459255i
$533$	−12.3926	+	9.00377i	−0.536784	+	0.389997i
$534$	−0.431269	−	0.313335i	−0.0186628	−	0.0135593i
$535$	11.8515	−	27.9887i	0.512385	−	1.21006i
$536$	−13.0672	+	40.2167i	−0.564417	+	1.73710i
$537$	2.12806			0.0918326
$538$	2.33061	−	7.17287i	0.100480	−	0.309244i
$539$	1.90915	+	1.43290i	0.0822329	+	0.0617192i
$540$	−0.913139	−	0.0790810i	−0.0392953	−	0.00340310i
$541$	−43.2611			−1.85994			−0.929971	−	0.367633i	$-0.880168\pi$
$541$	−43.2611			−1.85994			−0.929971	+	0.367633i	$0.880168\pi$
$542$	−1.32170	−	4.06777i	−0.0567718	−	0.174726i
$543$	0.662826	−	0.481571i	0.0284446	−	0.0206662i
$544$	−7.65438	+	5.56124i	−0.328179	+	0.238436i
$545$	21.8165	+	1.88939i	0.934518	+	0.0809325i
$546$	2.14522	−	6.60230i	0.0918068	−	0.282552i
$547$	29.8150			1.27480			0.637400	−	0.770533i	$-0.280010\pi$
$547$	29.8150			1.27480			0.637400	+	0.770533i	$0.280010\pi$
$548$	1.18980	−	0.864442i	0.0508259	−	0.0369271i
$549$	−32.7929			−1.39957
$550$	16.9346	+	18.0266i	0.722093	+	0.768657i
$551$	1.15849			0.0493531
$552$	4.69742	−	3.41287i	0.199935	−	0.145262i
$553$	−8.09598			−0.344276
$554$	−8.52775	+	26.2457i	−0.362309	+	1.11507i
$555$	4.63677	−	2.79160i	0.196820	−	0.118497i
$556$	2.88608	−	2.09686i	0.122397	−	0.0889266i
$557$	−16.5976	+	12.0589i	−0.703264	+	0.510951i	−0.880994	−	0.473128i	$-0.843125\pi$
$557$	−16.5976	+	12.0589i	−0.703264	+	0.510951i	0.177729	+	0.984079i	$0.443125\pi$
$558$	−1.46462	−	4.50763i	−0.0620023	−	0.190823i
$559$	−40.9085			−1.73024
$560$	5.56579	+	24.0118i	0.235197	+	1.01468i
$561$	2.25827	+	7.33595i	0.0953443	+	0.309724i
$562$	−4.81087	+	14.8063i	−0.202934	+	0.624567i
$563$	8.54604			0.360173			0.180086	−	0.983651i	$-0.442362\pi$
$563$	8.54604			0.360173			0.180086	+	0.983651i	$0.442362\pi$
$564$	−0.00159560	+	0.00491075i	−6.71868e−5	+	0.000206780i
$565$	−11.4704	−	9.95340i	−0.482564	−	0.418743i
$566$	15.9501	+	11.5884i	0.670431	+	0.487096i
$567$	16.5206	−	12.0030i	0.693802	−	0.504077i
$568$	−0.946391	+	0.687594i	−0.0397097	+	0.0288508i
$569$	−2.44632	−	7.52901i	−0.102555	−	0.315633i	0.886594	−	0.462549i	$-0.153065\pi$
$569$	−2.44632	−	7.52901i	−0.102555	−	0.315633i	−0.989149	+	0.146917i	$0.953065\pi$
$570$	1.28807	−	3.04193i	0.0539512	−	0.127412i
$571$	−6.09902	+	4.43120i	−0.255236	+	0.185440i	−0.708044	−	0.706168i	$-0.750422\pi$
$571$	−6.09902	+	4.43120i	−0.255236	+	0.185440i	0.452808	+	0.891608i	$0.350422\pi$
$572$	−3.57683	−	2.68456i	−0.149555	−	0.112247i
$573$	2.06578	+	6.35780i	0.0862990	+	0.265601i
$574$	2.94571	+	9.06596i	0.122952	+	0.378406i
$575$	24.6727	+	25.4596i	1.02892	+	1.06174i
$576$	16.2404	−	11.7993i	0.676682	−	0.491638i
$577$	−8.74444			−0.364036			−0.182018	−	0.983295i	$-0.558263\pi$
$577$	−8.74444			−0.364036			−0.182018	+	0.983295i	$0.558263\pi$
$578$	−17.9803	−	55.3378i	−0.747883	−	2.30175i
$579$	−1.96250	+	6.03997i	−0.0815589	+	0.251012i
$580$	−0.0707937	+	0.167188i	−0.00293955	+	0.00694209i
$581$	−0.979358	+	3.01415i	−0.0406306	+	0.125048i
$582$	−0.825781			−0.0342297
$583$	6.68984	−	4.70349i	0.277065	−	0.194799i
$584$	8.10260	−	24.9372i	0.335288	−	1.03191i
$585$	−8.80804	−	37.9995i	−0.364168	−	1.57109i
$586$	−4.73754	+	14.5807i	−0.195706	+	0.602322i
$587$	−1.15322	−	3.54926i	−0.0475986	−	0.146493i	0.924432	−	0.381346i	$-0.124539\pi$
$587$	−1.15322	−	3.54926i	−0.0475986	−	0.146493i	−0.972031	+	0.234852i	$0.924539\pi$
$588$	0.0404226	+	0.0293688i	0.00166700	+	0.00121115i
$589$	3.50472			0.144409
$590$	4.68362	−	11.0609i	0.192822	−	0.455371i
$591$	−5.08084	+	3.69145i	−0.208998	+	0.151846i
$592$	10.6393	−	32.7444i	0.437272	−	1.34579i
$593$	3.53924			0.145339			0.0726697	−	0.997356i	$-0.476848\pi$
$593$	3.53924			0.145339			0.0726697	+	0.997356i	$0.476848\pi$
$594$	2.65721	+	8.63189i	0.109027	+	0.354171i
$595$	−41.7823	−	3.61849i	−1.71291	−	0.148344i
$596$	0.255605	+	0.185708i	0.0104700	+	0.00760689i
$597$	4.54846			0.186156
$598$	−51.3883	−	37.3358i	−2.10142	−	1.52677i
$599$	4.08694	−	12.5783i	0.166988	−	0.513936i	−0.832189	−	0.554492i	$-0.812913\pi$
$599$	4.08694	−	12.5783i	0.166988	−	0.513936i	0.999177	+	0.0405554i	$0.0129127\pi$
$600$	−2.84935	−	2.94023i	−0.116324	−	0.120034i
$601$	21.3749	−	15.5298i	0.871900	−	0.633473i	−0.0591960	−	0.998246i	$-0.518854\pi$
$601$	21.3749	−	15.5298i	0.871900	−	0.633473i	0.931096	+	0.364774i	$0.118854\pi$
$602$	−7.86679	+	24.2115i	−0.320626	+	0.986786i
$603$	−37.5210	−	27.2606i	−1.52797	−	1.11014i
$604$	1.70394	−	1.23799i	0.0693324	−	0.0503729i
$605$	10.2895	−	22.3411i	0.418329	−	0.908296i
$606$	5.01243	+	3.64174i	0.203616	+	0.147936i
$607$	−4.43491	−	13.6493i	−0.180007	−	0.554006i	0.819819	−	0.572622i	$-0.194074\pi$
$607$	−4.43491	−	13.6493i	−0.180007	−	0.554006i	−0.999827	+	0.0186164i	$0.994074\pi$
$608$	−1.25134	−	3.85122i	−0.0507484	−	0.156188i
$609$	0.0866087	+	0.266554i	0.00350956	+	0.0108013i
$610$	28.4406	+	24.6792i	1.15153	+	0.999233i
$611$	−0.446730			−0.0180727
$612$	−1.50799	−	4.64111i	−0.0609567	−	0.187606i
$613$	−16.8361	+	12.2321i	−0.680003	+	0.494051i	−0.873359	−	0.487078i	$-0.838063\pi$
$613$	−16.8361	+	12.2321i	−0.680003	+	0.494051i	0.193356	+	0.981129i	$0.438063\pi$
$614$	−26.4372	+	19.2078i	−1.06692	+	0.775162i
$615$	−1.33192	−	1.15577i	−0.0537081	−	0.0466049i
$616$	18.0053	−	12.6592i	0.725454	−	0.510052i
$617$	−20.2083	−	14.6822i	−0.813557	−	0.591084i	0.101302	−	0.994856i	$-0.467699\pi$
$617$	−20.2083	−	14.6822i	−0.813557	−	0.591084i	−0.914860	+	0.403772i	$0.867699\pi$
$618$	−1.02742	−	3.16208i	−0.0413289	−	0.127197i
$619$	4.76353	+	14.6607i	0.191463	+	0.589261i	1.00000		0.000816096i	$0.000259771\pi$
$619$	4.76353	+	14.6607i	0.191463	+	0.589261i	−0.808537	+	0.588445i	$0.799740\pi$
$620$	−0.214169	+	0.505786i	−0.00860124	+	0.0203129i
$621$	4.00057	+	12.3125i	0.160537	+	0.494083i
$622$	4.08689	+	12.5781i	0.163869	+	0.504338i
$623$	−2.34337	−	1.70256i	−0.0938853	−	0.0682116i
$624$	6.60930	+	4.80194i	0.264584	+	0.192231i
$625$	15.3222	−	19.7542i	0.612888	−	0.790169i
$626$	5.40014			0.215833
$627$	−3.28476	−	0.0510120i	−0.131181	−	0.00203722i
$628$	1.05495	−	0.766465i	0.0420970	−	0.0305853i
$629$	47.3930	+	34.4330i	1.88968	+	1.37293i
$630$	−24.1836	−	2.09438i	−0.963499	−	0.0834423i
$631$	−40.2449			−1.60212			−0.801062	−	0.598582i	$-0.795731\pi$
$631$	−40.2449			−1.60212			−0.801062	+	0.598582i	$0.795731\pi$
$632$	2.64362	−	8.13622i	0.105157	−	0.323641i
$633$	−1.85488	+	1.34765i	−0.0737248	+	0.0535642i
$634$	13.0116	+	40.0456i	0.516757	+	1.59042i
$635$	5.20192	+	22.4420i	0.206432	+	0.890584i
$636$	0.138484	−	0.100615i	0.00549125	−	0.00398963i
$637$	−1.33584	+	4.11128i	−0.0529277	+	0.162895i
$638$	1.78884	+	0.0277805i	0.0708208	+	0.00109984i
$639$	−0.396472	−	1.22021i	−0.0156842	−	0.0482709i
$640$	−28.5974	−	2.47663i	−1.13041	−	0.0978975i
$641$	−4.77078	+	3.46618i	−0.188435	+	0.136906i	−0.678003	−	0.735059i	$-0.737154\pi$
$641$	−4.77078	+	3.46618i	−0.188435	+	0.136906i	0.489568	+	0.871965i	$0.337154\pi$
$642$	−6.26911			−0.247422
$643$	8.40696	−	25.8740i	0.331538	−	1.02037i	−0.636864	−	0.770976i	$-0.719769\pi$
$643$	8.40696	−	25.8740i	0.331538	−	1.02037i	0.968402	−	0.249393i	$-0.0802312\pi$
$644$	−3.22741	+	2.34485i	−0.127178	+	0.0924000i
$645$	−1.06343	−	4.58785i	−0.0418727	−	0.180646i
$646$	35.7551			1.40676
$647$	−22.3014	−	16.2029i	−0.876759	−	0.637003i	0.0556328	−	0.998451i	$-0.482282\pi$
$647$	−22.3014	−	16.2029i	−0.876759	−	0.637003i	−0.932392	+	0.361448i	$0.882282\pi$
$648$	6.66805	+	20.5222i	0.261946	+	0.806186i
$649$	−11.9439	−	0.185488i	−0.468839	−	0.00728103i
$650$	−20.9586	+	39.5850i	−0.822062	+	1.55265i
$651$	0.262013	+	0.806395i	0.0102691	+	0.0316051i
$652$	−1.51142	+	4.65167i	−0.0591917	+	0.182173i
$653$	1.62524	−	5.00196i	0.0636004	−	0.195742i	−0.914207	−	0.405247i	$-0.867185\pi$
$653$	1.62524	−	5.00196i	0.0636004	−	0.195742i	0.977807	+	0.209505i	$0.0671854\pi$
$654$	−1.39573	−	4.29562i	−0.0545774	−	0.167972i
$655$	−7.74810	+	18.2981i	−0.302743	+	0.714965i
$656$	−11.2180			−0.437990
$657$	23.2657	+	16.9035i	0.907682	+	0.659469i
$658$	−0.0859071	+	0.264395i	−0.00334901	+	0.0103072i
$659$	−2.59805	+	7.99599i	−0.101206	+	0.311479i	−0.988821	−	0.149106i	$-0.952360\pi$
$659$	−2.59805	+	7.99599i	−0.101206	+	0.311479i	0.887615	+	0.460585i	$0.152360\pi$
$660$	0.208090	−	0.470925i	0.00809988	−	0.0183307i
$661$	12.1895	+	37.5153i	0.474115	+	1.45918i	0.847147	+	0.531359i	$0.178318\pi$
$661$	12.1895	+	37.5153i	0.474115	+	1.45918i	−0.373031	+	0.927819i	$0.621682\pi$
$662$	19.0935			0.742090
$663$	−11.2456	+	8.17039i	−0.436742	+	0.317312i
$664$	−2.70934	−	1.96845i	−0.105143	−	0.0763908i
$665$	6.99894	−	16.5288i	0.271407	−	0.640961i
$666$	27.4311	+	19.9298i	1.06293	+	0.772266i
$667$	2.56446			0.0992964
$668$	1.69966	+	1.23488i	0.0657619	+	0.0477788i
$669$	1.00554	−	3.09473i	0.0388764	−	0.119649i
$670$	12.0255	+	51.8801i	0.464585	+	2.00430i
$671$	12.1235	−	35.4307i	0.468024	−	1.36779i
$672$	0.792571	−	0.575836i	0.0305741	−	0.0222134i
$673$	6.71553	−	4.87912i	0.258865	−	0.188076i	−0.450782	−	0.892634i	$-0.648855\pi$
$673$	6.71553	−	4.87912i	0.258865	−	0.188076i	0.709646	+	0.704558i	$0.248855\pi$
$674$	11.4994	+	8.35479i	0.442940	+	0.321815i
$675$	8.19805	−	4.01630i	0.315543	−	0.154588i
$676$	1.60084	−	4.92688i	0.0615707	−	0.189495i
$677$	33.9390			1.30438			0.652190	−	0.758055i	$-0.273850\pi$
$677$	33.9390			1.30438			0.652190	+	0.758055i	$0.273850\pi$
$678$	−0.967968	+	2.97910i	−0.0371746	+	0.114412i
$679$	−4.48703			−0.172196
$680$	17.2799	−	40.8085i	0.662653	−	1.56493i
$681$	−2.01142	−	1.46138i	−0.0770776	−	0.0560002i
$682$	5.41169	+	0.0840432i	0.207224	+	0.00321818i
$683$	−28.3208	−	20.5763i	−1.08367	−	0.787330i	−0.105348	−	0.994435i	$-0.533596\pi$
$683$	−28.3208	−	20.5763i	−1.08367	−	0.787330i	−0.978319	+	0.207106i	$0.933596\pi$
$684$	2.08860			0.0798595
$685$	−5.71162	+	13.4887i	−0.218230	+	0.515375i
$686$	23.3435	+	16.9600i	0.891257	+	0.647536i
$687$	2.61581	+	1.90050i	0.0997995	+	0.0725086i
$688$	−24.2372	−	17.6093i	−0.924033	−	0.671349i
$689$	11.9813	+	8.70491i	0.456450	+	0.331631i
$690$	2.85131	−	6.73371i	0.108548	−	0.256348i
$691$	−26.6486			−1.01376			−0.506880	−	0.862017i	$-0.669201\pi$
$691$	−26.6486			−1.01376			−0.506880	+	0.862017i	$0.669201\pi$
$692$	−2.34134	−	1.70108i	−0.0890044	−	0.0646655i
$693$	7.10229	+	23.0717i	0.269794	+	0.876420i
$694$	−23.3398	−	16.9573i	−0.885966	−	0.643692i
$695$	−13.8545	+	32.7192i	−0.525533	+	1.24111i
$696$	−0.296160			−0.0112259
$697$	5.89827	−	18.1530i	0.223413	−	0.687595i
$698$	2.62186			0.0992387
$699$	0.224338	−	0.690441i	0.00848523	−	0.0261149i
$700$	1.95768	+	2.02012i	0.0739932	+	0.0763532i
$701$	29.7061	+	21.5828i	1.12199	+	0.815170i	0.984509	−	0.175335i	$-0.0561008\pi$
$701$	29.7061	+	21.5828i	1.12199	+	0.815170i	0.137477	+	0.990505i	$0.456101\pi$
$702$	−13.2322	+	9.61374i	−0.499416	+	0.362847i
$703$	−20.2840	+	14.7372i	−0.765025	+	0.555823i
$704$	6.74437	+	21.9089i	0.254188	+	0.825724i
$705$	−0.0116129	−	0.0501003i	−0.000437369	−	0.00188689i
$706$	−0.499988	+	1.53881i	−0.0188173	+	0.0579137i
$707$	27.2359	+	19.7881i	1.02431	+	0.744206i
$708$	−0.250036			−0.00939693
$709$	17.3832	+	12.6296i	0.652840	+	0.474316i	0.864238	−	0.503084i	$-0.167801\pi$
$709$	17.3832	+	12.6296i	0.652840	+	0.474316i	−0.211397	+	0.977400i	$0.567801\pi$
$710$	−0.574455	+	1.35664i	−0.0215589	+	0.0509139i
$711$	7.59085	+	5.51508i	0.284679	+	0.206832i
$712$	2.47622	−	1.79908i	0.0928001	−	0.0674233i
$713$	7.75816			0.290545
$714$	2.67306	+	8.22682i	0.100037	+	0.307881i
$715$	44.3125	+	4.53188i	1.65719	+	0.169483i
$716$	0.477428	−	1.46937i	0.0178423	−	0.0549131i
$717$	−1.68256	+	5.17839i	−0.0628364	+	0.193391i
$718$	2.97401	+	2.16074i	0.110989	+	0.0806382i
$719$	−30.7611			−1.14719			−0.573597	−	0.819138i	$-0.694452\pi$
$719$	−30.7611			−1.14719			−0.573597	+	0.819138i	$0.694452\pi$
$720$	11.1386	−	26.3052i	0.415111	−	0.980335i
$721$	−5.58267	−	17.1817i	−0.207910	−	0.639880i
$722$	4.02805	−	12.3971i	0.149909	−	0.461371i
$723$	2.29491	−	7.06301i	0.0853486	−	0.262676i
$724$	−0.183809	−	0.565705i	−0.00683120	−	0.0210243i
$725$	−0.254819	−	1.79030i	−0.00946373	−	0.0664900i
$726$	−5.07083	−	0.157537i	−0.188196	−	0.00584675i
$727$	−2.94379	−	9.06005i	−0.109179	−	0.336019i	0.881509	−	0.472166i	$-0.156528\pi$
$727$	−2.94379	−	9.06005i	−0.109179	−	0.336019i	−0.990689	+	0.136148i	$0.956528\pi$
$728$	32.2469	+	23.4287i	1.19515	+	0.868326i
$729$	−21.9727			−0.813803
$730$	−7.45666	−	32.1694i	−0.275983	−	1.19064i
$731$	41.2390	−	29.9619i	1.52528	−	1.10818i
$732$	0.242220	−	0.745475i	0.00895269	−	0.0275536i
$733$	−9.49955			−0.350874			−0.175437	−	0.984491i	$-0.556134\pi$
$733$	−9.49955			−0.350874			−0.175437	+	0.984491i	$0.556134\pi$
$734$	−16.5943	+	12.0565i	−0.612506	+	0.445012i
$735$	−0.495802	−	0.0429382i	−0.0182879	−	0.00158380i
$736$	−2.77000	−	8.52519i	−0.102104	−	0.314243i
$737$	43.3249	−	30.4609i	1.59589	−	1.12204i
$738$	3.41392	−	10.5070i	0.125668	−	0.386767i
$739$	15.6393	−	11.3626i	0.575300	−	0.417980i	−0.261726	−	0.965142i	$-0.584292\pi$
$739$	15.6393	−	11.3626i	0.575300	−	0.417980i	0.837027	+	0.547162i	$0.184292\pi$
$740$	−0.887277	−	3.82787i	−0.0326169	−	0.140715i
$741$	−1.83842	−	5.65809i	−0.0675362	−	0.207855i
$742$	7.45599	−	5.41709i	0.273718	−	0.198868i
$743$	−7.03300	+	21.6454i	−0.258016	+	0.794091i	0.735205	+	0.677845i	$0.237086\pi$
$743$	−7.03300	+	21.6454i	−0.258016	+	0.794091i	−0.993220	+	0.116246i	$0.962914\pi$
$744$	−0.895960			−0.0328475
$745$	−3.13511	−	0.271511i	−0.114862	−	0.00994741i
$746$	7.68941	+	5.58669i	0.281529	+	0.204543i
$747$	2.97153	−	2.15895i	0.108723	−	0.0789917i
$748$	5.57193	+	0.0865317i	0.203730	+	0.00316391i
$749$	−34.0643			−1.24468
$750$	−4.98425	−	1.32145i	−0.181999	−	0.0482527i
$751$	−27.5785	−	20.0370i	−1.00636	−	0.731160i	−0.0429137	−	0.999079i	$-0.513664\pi$
$751$	−27.5785	−	20.0370i	−1.00636	−	0.731160i	−0.963441	+	0.267919i	$0.913664\pi$
$752$	−0.264675	−	0.192298i	−0.00965171	−	0.00701238i
$753$	−0.534006	−	1.64350i	−0.0194603	−	0.0598925i
$754$	1.00118	+	3.08132i	0.0364609	+	0.112215i
$755$	−8.17973	+	19.3174i	−0.297691	+	0.703032i
$756$	0.317429	+	0.976945i	0.0115448	+	0.0355312i
$757$	−3.80972	−	11.7251i	−0.138467	−	0.426156i	0.857647	−	0.514240i	$-0.171926\pi$
$757$	−3.80972	−	11.7251i	−0.138467	−	0.426156i	−0.996113	+	0.0880834i	$0.971926\pi$
$758$	−37.1269	−	26.9743i	−1.34851	−	0.979751i
$759$	−7.27125	−	0.112922i	−0.263930	−	0.00409881i
$760$	14.3256	+	12.4310i	0.519644	+	0.450919i
$761$	−40.3505	+	29.3163i	−1.46270	+	1.06272i	−0.480055	+	0.877238i	$0.659383\pi$
$761$	−40.3505	+	29.3163i	−1.46270	+	1.06272i	−0.982648	+	0.185478i	$0.940617\pi$
$762$	3.84410	−	2.79290i	0.139257	−	0.101176i
$763$	−7.58395	−	23.3410i	−0.274557	−	0.845001i
$764$	4.85336			0.175588
$765$	36.7105	+	31.8554i	1.32727	+	1.15173i
$766$	−14.7447	−	45.3795i	−0.532747	−	1.63963i
$767$	−6.68480	−	20.5737i	−0.241374	−	0.742873i
$768$	0.508621	+	1.56537i	0.0183533	+	0.0564856i
$769$	10.1343	+	7.36301i	0.365453	+	0.265517i	0.755323	−	0.655353i	$-0.227480\pi$
$769$	10.1343	+	7.36301i	0.365453	+	0.265517i	−0.389870	+	0.920870i	$0.627480\pi$
$770$	11.2036	−	25.3546i	0.403748	−	0.913717i
$771$	1.95935	−	1.42355i	0.0705644	−	0.0512680i
$772$	3.73016	+	2.71012i	0.134251	+	0.0975394i
$773$	10.8349	−	33.3463i	0.389703	−	1.19938i	−0.543307	−	0.839534i	$-0.682828\pi$
$773$	10.8349	−	33.3463i	0.389703	−	1.19938i	0.933010	−	0.359849i	$-0.117172\pi$
$774$	23.8691	−	17.3419i	0.857958	−	0.623343i
$775$	−0.770892	−	5.41611i	−0.0276913	−	0.194552i
$776$	1.46517	−	4.50933i	0.0525965	−	0.161876i
$777$	−4.90729	−	3.56536i	−0.176048	−	0.127906i
$778$	−14.1375			−0.506854
$779$	6.60906	+	4.80176i	0.236794	+	0.172041i
$780$	0.928895	+	0.0804455i	0.0332598	+	0.00288041i
$781$	1.46494	+	0.0227504i	0.0524198	+	0.000814075i
$782$	79.1486			2.83035
$783$	0.204055	−	0.628015i	0.00729231	−	0.0224434i
$784$	−2.56117	+	1.86080i	−0.0914705	+	0.0664572i
$785$	−5.06426	+	11.9598i	−0.180751	+	0.426865i
$786$	4.09853			0.146190
$787$	−0.860291	−	0.625038i	−0.0306661	−	0.0222802i	0.572347	−	0.820012i	$-0.306033\pi$
$787$	−0.860291	−	0.625038i	−0.0306661	−	0.0222802i	−0.603013	+	0.797732i	$0.706033\pi$
$788$	1.40897	+	4.33637i	0.0501925	+	0.154477i
$789$	−0.618409	+	1.90327i	−0.0220159	+	0.0677581i
$790$	−2.43287	−	10.4958i	−0.0865576	−	0.373425i
$791$	−5.25962	+	16.1875i	−0.187011	+	0.575560i
$792$	−25.5055	−	0.396098i	−0.906298	−	0.0140747i
$793$	67.8157			2.40821
$794$	13.4283	−	41.3280i	0.476552	−	1.46668i
$795$	−0.664789	+	1.56998i	−0.0235776	+	0.0556814i
$796$	1.02044	−	3.14060i	0.0361686	−	0.111316i
$797$	4.15878	+	12.7994i	0.147312	+	0.453379i	0.997301	−	0.0734212i	$-0.0233917\pi$
$797$	4.15878	+	12.7994i	0.147312	+	0.453379i	−0.849989	+	0.526800i	$0.823392\pi$
$798$	−3.70225			−0.131058
$799$	0.450339	−	0.327190i	0.0159318	−	0.0115752i
$800$	−5.67635	+	2.78090i	−0.200689	+	0.0983196i
$801$	1.03736	+	3.19267i	0.0366534	+	0.112807i
$802$	−6.54922	−	20.1564i	−0.231261	−	0.711748i
$803$	−26.8646	+	18.8879i	−0.948030	+	0.666541i
$804$	0.896853	−	0.651602i	0.0316296	−	0.0229802i
$805$	15.4931	−	36.5888i	0.546060	−	1.28959i
$806$	3.02883	+	9.32179i	0.106686	+	0.328346i
$807$	1.26505	−	0.919111i	0.0445318	−	0.0323542i
$808$	−28.7799	+	20.9098i	−1.01247	+	0.735605i
$809$	25.9566	+	18.8586i	0.912587	+	0.663033i	0.941668	−	0.336544i	$-0.109258\pi$
$809$	25.9566	+	18.8586i	0.912587	+	0.663033i	−0.0290807	+	0.999577i	$0.509258\pi$
$810$	20.5255	+	17.8109i	0.721191	+	0.625810i
$811$	−2.72318	+	8.38107i	−0.0956236	+	0.294299i	−0.987416	−	0.158146i	$-0.949448\pi$
$811$	−2.72318	+	8.38107i	−0.0956236	+	0.294299i	0.891792	+	0.452445i	$0.149448\pi$
$812$	0.203480			0.00714074
$813$	0.274028	−	0.843372i	0.00961059	−	0.0295784i
$814$	−31.6743	+	22.2695i	−1.11018	+	0.780546i
$815$	−11.0003	−	47.4572i	−0.385323	−	1.66235i
$816$	−10.1797			−0.356361
$817$	6.74174	+	20.7489i	0.235863	+	0.725913i
$818$	−20.3541	+	14.7881i	−0.711664	+	0.517054i
$819$	−35.3675	+	25.6960i	−1.23584	+	0.897890i
$820$	−1.09684	+	0.660361i	−0.0383034	+	0.0230608i
$821$	14.9531	−	46.0210i	0.521868	−	1.60614i	−0.248560	−	0.968617i	$-0.579957\pi$
$821$	14.9531	−	46.0210i	0.521868	−	1.60614i	0.770428	−	0.637528i	$-0.220043\pi$
$822$	3.02129			0.105379
$823$	−11.2602	+	8.18101i	−0.392506	+	0.285172i	−0.766482	−	0.642266i	$-0.777994\pi$
$823$	−11.2602	+	8.18101i	−0.392506	+	0.285172i	0.373976	+	0.927438i	$0.377994\pi$
$824$	19.0900			0.665033
$825$	0.643677	+	5.08741i	0.0224100	+	0.177121i
$826$	−13.4619			−0.468401
$827$	9.98538	−	7.25481i	0.347226	−	0.252274i	−0.400478	−	0.916306i	$-0.631156\pi$
$827$	9.98538	−	7.25481i	0.347226	−	0.252274i	0.747704	+	0.664032i	$0.231156\pi$
$828$	4.62339			0.160674
$829$	3.34623	−	10.2986i	0.116219	−	0.357686i	−0.875980	−	0.482347i	$-0.839784\pi$
$829$	3.34623	−	10.2986i	0.116219	−	0.357686i	0.992199	+	0.124661i	$0.0397843\pi$
$830$	−4.20193	−	0.363902i	−0.145851	−	0.0126312i
$831$	−4.62884	+	3.36305i	−0.160573	+	0.116663i
$832$	−33.5851	+	24.4010i	−1.16435	+	0.845952i
$833$	−1.66452	−	5.12287i	−0.0576723	−	0.177497i
$834$	7.32867			0.253771
$835$	−20.8471	−	1.80543i	−0.721445	−	0.0624796i
$836$	−0.772155	+	2.25660i	−0.0267055	+	0.0780461i
$837$	0.617317	−	1.89991i	0.0213376	−	0.0656704i
$838$	20.7487			0.716752
$839$	3.19727	−	9.84020i	0.110382	−	0.339721i	−0.880574	−	0.473909i	$-0.842843\pi$
$839$	3.19727	−	9.84020i	0.110382	−	0.339721i	0.990956	+	0.134188i	$0.0428425\pi$
$840$	−1.78924	+	4.22550i	−0.0617346	+	0.145794i
$841$	23.3557	+	16.9689i	0.805368	+	0.585134i
$842$	4.07015	−	2.95714i	0.140267	−	0.101910i
$843$	−2.61133	+	1.89724i	−0.0899389	+	0.0653444i
$844$	0.514378	+	1.58309i	0.0177056	+	0.0544923i
$845$	11.6511	+	50.2649i	0.400810	+	1.72917i
$846$	0.260656	−	0.189378i	0.00896154	−	0.00651094i
$847$	−27.5532	−	0.856005i	−0.946740	−	0.0294127i
$848$	3.35150	+	10.3148i	0.115091	+	0.354213i
$849$	1.26313	+	3.88753i	0.0433507	+	0.133420i
$850$	−7.86463	−	55.2551i	−0.269754	−	1.89523i
$851$	−44.9013	+	32.6227i	−1.53920	+	1.11829i
$852$	0.0306674			0.00105065
$853$	15.7803	+	48.5667i	0.540307	+	1.66289i	0.731895	+	0.681418i	$0.238636\pi$
$853$	15.7803	+	48.5667i	0.540307	+	1.66289i	−0.191588	+	0.981475i	$0.561364\pi$
$854$	13.0411	−	40.1364i	0.446258	−	1.37344i
$855$	−17.8219	+	10.7298i	−0.609497	+	0.366952i
$856$	11.1232	−	34.2336i	0.380182	−	1.17008i
$857$	−44.8864			−1.53329			−0.766644	−	0.642072i	$-0.778075\pi$
$857$	−44.8864			−1.53329			−0.766644	+	0.642072i	$0.778075\pi$
$858$	−2.70306	−	8.78084i	−0.0922810	−	0.299773i
$859$	−0.615385	+	1.89396i	−0.0209967	+	0.0646211i	−0.961006	−	0.276528i	$-0.910816\pi$
$859$	−0.615385	+	1.89396i	−0.0209967	+	0.0646211i	0.940009	+	0.341149i	$0.110816\pi$
$860$	−3.40638	−	0.295004i	−0.116157	−	0.0100596i
$861$	−0.610735	+	1.87965i	−0.0208138	+	0.0640583i
$862$	−3.93098	−	12.0983i	−0.133890	−	0.412070i
$863$	−43.2487	−	31.4220i	−1.47220	−	1.06962i	−0.979968	−	0.199156i	$-0.936180\pi$
$863$	−43.2487	−	31.4220i	−1.47220	−	1.06962i	−0.492235	−	0.870462i	$-0.663820\pi$
$864$	−2.30816			−0.0785251
$865$	28.7176	+	2.48704i	0.976427	+	0.0845620i
$866$	−21.0468	+	15.2914i	−0.715198	+	0.519622i
$867$	3.72787	−	11.4732i	0.126605	−	0.389650i
$868$	0.615578			0.0208941
$869$	−8.76505	+	6.16253i	−0.297334	+	0.209049i
$870$	−0.319541	+	0.192382i	−0.0108335	+	0.00652237i
$871$	77.5934	+	56.3749i	2.62915	+	1.91019i
$872$	25.9334			0.878217
$873$	4.20707	+	3.05662i	0.142388	+	0.103451i
$874$	−10.4680	+	32.2173i	−0.354086	+	1.08977i
$875$	−27.0828	−	7.18036i	−0.915565	−	0.242740i
$876$	−0.556114	+	0.404040i	−0.0187893	+	0.0136513i
$877$	−1.72250	+	5.30130i	−0.0581646	+	0.179012i	−0.975918	−	0.218139i	$-0.930001\pi$
$877$	−1.72250	+	5.30130i	−0.0581646	+	0.179012i	0.917753	+	0.397152i	$0.130001\pi$
$878$	−18.2565	−	13.2641i	−0.616126	−	0.447642i
$879$	−2.57153	+	1.86832i	−0.0867355	+	0.0630170i
$880$	24.3032	+	21.7596i	0.819259	+	0.733516i
$881$	34.9606	+	25.4004i	1.17785	+	0.855760i	0.991928	−	0.126803i	$-0.0404717\pi$
$881$	34.9606	+	25.4004i	1.17785	+	0.855760i	0.185925	+	0.982564i	$0.440472\pi$
$882$	−0.963426	−	2.96512i	−0.0324403	−	0.0998408i
$883$	−11.6132	−	35.7416i	−0.390814	−	1.20280i	−0.932174	−	0.362010i	$-0.882091\pi$
$883$	−11.6132	−	35.7416i	−0.390814	−	1.20280i	0.541361	−	0.840791i	$-0.317909\pi$
$884$	3.11852	+	9.59781i	0.104887	+	0.322809i
$885$	2.13355	−	1.28452i	0.0717184	−	0.0431786i
$886$	31.2991			1.05151
$887$	−7.41252	−	22.8134i	−0.248888	−	0.765999i	−0.994973	−	0.100148i	$-0.968069\pi$
$887$	−7.41252	−	22.8134i	−0.248888	−	0.765999i	0.746085	−	0.665851i	$-0.231931\pi$
$888$	5.18548	−	3.76747i	0.174013	−	0.126428i
$889$	20.8876	−	15.1757i	0.700547	−	0.508977i
$890$	1.50305	−	3.54964i	0.0503824	−	0.118984i
$891$	8.74950	−	25.5702i	0.293119	−	0.856632i
$892$	−1.91124	−	1.38860i	−0.0639932	−	0.0464938i
$893$	0.0736213	+	0.226583i	0.00246364	+	0.00758231i
$894$	0.200571	+	0.617295i	0.00670810	+	0.0206454i
$895$	3.47478	+	14.9908i	0.116149	+	0.501088i
$896$	9.94113	+	30.5957i	0.332110	+	1.02213i
$897$	−4.06960	−	12.5249i	−0.135880	−	0.418195i
$898$	20.6673	+	15.0157i	0.689676	+	0.501079i
$899$	−0.320141	−	0.232596i	−0.0106773	−	0.00775750i
$900$	−0.459404	−	3.22767i	−0.0153135	−	0.107589i
$901$	−18.4537			−0.614780
$902$	10.0900	+	7.57297i	0.335961	+	0.252152i
$903$	−4.27007	+	3.10239i	−0.142099	+	0.103241i
$904$	−14.5505	−	10.5715i	−0.483942	−	0.351604i
$905$	4.47465	+	3.88286i	0.148742	+	0.129071i
$906$	4.32685			0.143750
$907$	−0.415545	+	1.27892i	−0.0137980	+	0.0424657i	−0.957718	−	0.287707i	$-0.907107\pi$
$907$	−0.415545	+	1.27892i	−0.0137980	+	0.0424657i	0.943920	+	0.330173i	$0.107107\pi$
$908$	−1.46031	+	1.06097i	−0.0484619	+	0.0352097i
$909$	−12.0568	−	37.1069i	−0.399897	−	1.23076i
$910$	50.0118	+	4.33119i	1.65787	+	0.143578i
$911$	35.6553	−	25.9051i	1.18131	−	0.858275i	0.188994	−	0.981978i	$-0.439477\pi$
$911$	35.6553	−	25.9051i	1.18131	−	0.858275i	0.992319	+	0.123704i	$0.0394772\pi$
$912$	1.34635	−	4.14363i	0.0445820	−	0.137209i
$913$	1.23403	+	4.00872i	0.0408405	+	0.132669i
$914$	−6.38255	−	19.6435i	−0.211116	−	0.649748i
$915$	1.76290	+	7.60548i	0.0582797	+	0.251429i
$916$	1.89910	−	1.37978i	0.0627482	−	0.0455892i
$917$	22.2701			0.735423
$918$	6.29786	−	19.3828i	0.207860	−	0.639728i
$919$	−31.0485	+	22.5580i	−1.02419	+	0.744121i	−0.967138	−	0.254250i	$-0.918171\pi$
$919$	−31.0485	+	22.5580i	−1.02419	+	0.744121i	−0.0570560	+	0.998371i	$0.518171\pi$
$920$	31.7116	+	27.5176i	1.04550	+	0.907229i
$921$	−6.77518			−0.223250
$922$	−14.3724	−	10.4421i	−0.473328	−	0.343893i
$923$	0.819904	+	2.52340i	0.0269875	+	0.0830589i
$924$	−0.576944	−	0.00895990i	−0.0189801	−	0.000294759i
$925$	27.2361	+	28.1049i	0.895519	+	0.924082i
$926$	−18.9522	−	58.3288i	−0.622808	−	1.91680i
$927$	−6.47002	+	19.9127i	−0.212503	+	0.654018i
$928$	−0.141288	+	0.434839i	−0.00463800	+	0.0142743i
$929$	1.39575	+	4.29568i	0.0457931	+	0.140937i	0.971339	−	0.237699i	$-0.0763933\pi$
$929$	1.39575	+	4.29568i	0.0457931	+	0.140937i	−0.925546	+	0.378636i	$0.876393\pi$
$930$	−0.966695	+	0.582006i	−0.0316992	+	0.0190847i
$931$	2.30540			0.0755565
$932$	−0.426402	−	0.309799i	−0.0139673	−	0.0101478i
$933$	−0.847335	+	2.60783i	−0.0277405	+	0.0853765i
$934$	7.70963	−	23.7278i	0.252267	−	0.776397i
$935$	−47.9897	+	27.8865i	−1.56943	+	0.911986i
$936$	−14.2750	−	43.9339i	−0.466593	−	1.43602i
$937$	−22.8959			−0.747976			−0.373988	−	0.927433i	$-0.622010\pi$
$937$	−22.8959			−0.747976			−0.373988	+	0.927433i	$0.622010\pi$
$938$	48.2866	−	35.0823i	1.57661	−	1.14548i
$939$	0.905786	+	0.658092i	0.0295592	+	0.0214760i
$940$	−0.0371984	−	0.00322151i	−0.00121328	−	0.000105074i
$941$	−36.9133	−	26.8191i	−1.20334	−	0.874277i	−0.208730	−	0.977973i	$-0.566933\pi$
$941$	−36.9133	−	26.8191i	−1.20334	−	0.874277i	−0.994609	+	0.103696i	$0.966933\pi$
$942$	2.67885			0.0872816
$943$	14.6300	+	10.6293i	0.476419	+	0.346139i
$944$	4.89553	−	15.0669i	0.159336	−	0.490385i
$945$	−7.72750	−	6.70550i	−0.251376	−	0.218130i
$946$	9.91247	+	32.2004i	0.322282	+	1.04693i
$947$	−11.6400	+	8.45699i	−0.378251	+	0.274815i	−0.760624	−	0.649193i	$-0.775107\pi$
$947$	−11.6400	+	8.45699i	−0.378251	+	0.274815i	0.382373	+	0.924008i	$0.375107\pi$
$948$	−0.181442	+	0.131825i	−0.00589296	+	0.00428149i
$949$	−48.1135	−	34.9565i	−1.56183	−	1.13474i
$950$	23.5316	+	4.10664i	0.763467	+	0.133237i
$951$	−2.69770	+	8.30267i	−0.0874790	+	0.269233i
$952$	−49.6669			−1.60971
$953$	2.63528	−	8.11056i	0.0853651	−	0.262727i	−0.899258	−	0.437418i	$-0.855893\pi$
$953$	2.63528	−	8.11056i	0.0853651	−	0.262727i	0.984623	+	0.174692i	$0.0558929\pi$
$954$	−10.6810			−0.345810
$955$	−41.4136	+	24.9333i	−1.34011	+	0.806823i
$956$	3.19807	+	2.32353i	0.103433	+	0.0751485i
$957$	0.296663	+	0.222658i	0.00958975	+	0.00719750i
$958$	15.1585	+	11.0133i	0.489750	+	0.355824i
$959$	16.4167			0.530122
$960$	−3.60961	−	3.13222i	−0.116500	−	0.101092i
$961$	24.1110	+	17.5177i	0.777775	+	0.565086i
$962$	−56.7275	−	41.2149i	−1.82897	−	1.32882i
$963$	31.9389	+	23.2050i	1.02922	+	0.747771i
$964$	−4.36197	−	3.16916i	−0.140490	−	0.102072i
$965$	−45.7521	−	3.96229i	−1.47281	−	0.127551i
$966$	−8.19541			−0.263683
$967$	38.8419	+	28.2203i	1.24907	+	0.907503i	0.998168	−	0.0605088i	$-0.0192723\pi$
$967$	38.8419	+	28.2203i	1.24907	+	0.907503i	0.250904	+	0.968012i	$0.419272\pi$
$968$	9.85735	−	27.4107i	0.316827	−	0.881013i
$969$	5.99733	+	4.35731i	0.192662	+	0.139977i
$970$	−1.34837	−	5.81710i	−0.0432934	−	0.186776i
$971$	8.68490			0.278712			0.139356	−	0.990242i	$-0.455497\pi$
$971$	8.68490			0.278712			0.139356	+	0.990242i	$0.455497\pi$
$972$	0.554804	−	1.70751i	0.0177953	−	0.0547684i
$973$	39.8216			1.27662
$974$	11.6695	−	35.9150i	0.373914	−	1.15079i
$975$	−8.33951	+	4.08560i	−0.267078	+	0.130844i
$976$	40.1790	+	29.1917i	1.28610	+	0.934405i
$977$	−6.65024	+	4.83168i	−0.212760	+	0.154579i	−0.689062	−	0.724703i	$-0.741977\pi$
$977$	−6.65024	+	4.83168i	−0.212760	+	0.154579i	0.476302	+	0.879282i	$0.341977\pi$
$978$	−8.12895	+	5.90603i	−0.259935	+	0.188854i
$979$	−3.83300	−	0.0595261i	−0.122503	−	0.00190246i
$980$	−0.140880	+	0.332706i	−0.00450026	+	0.0106279i
$981$	−8.78940	+	27.0510i	−0.280624	+	0.863671i
$982$	1.03781	+	0.754013i	0.0331179	+	0.0240615i
$983$	39.7123			1.26662			0.633312	−	0.773896i	$-0.281695\pi$
$983$	39.7123			1.26662			0.633312	+	0.773896i	$0.281695\pi$
$984$	−1.68957	−	1.22754i	−0.0538614	−	0.0391326i
$985$	−34.3001	−	29.7637i	−1.09289	−	0.948351i
$986$	−3.26607	−	2.37294i	−0.104013	−	0.0755697i
$987$	−0.0466302	+	0.0338788i	−0.00148425	+	0.00107837i
$988$	−4.31922			−0.137413
$989$	14.9237	+	45.9305i	0.474547	+	1.46051i
$990$	−27.7764	+	16.1407i	−0.882793	+	0.512986i
$991$	6.86301	−	21.1222i	0.218011	−	0.670968i	−0.780916	−	0.624637i	$-0.785247\pi$
$991$	6.86301	−	21.1222i	0.218011	−	0.670968i	0.998926	−	0.0463310i	$-0.0147529\pi$
$992$	−0.427432	+	1.31550i	−0.0135710	+	0.0417672i
$993$	3.20262	+	2.32684i	0.101632	+	0.0738401i
$994$	1.65113			0.0523708
$995$	7.42690	+	32.0410i	0.235448	+	1.01577i
$996$	0.0271302	+	0.0834981i	0.000859652	+	0.00264574i
$997$	−6.57385	+	20.2322i	−0.208196	+	0.640762i	0.791371	+	0.611336i	$0.209368\pi$
$997$	−6.57385	+	20.2322i	−0.208196	+	0.640762i	−0.999567	+	0.0294253i	$0.990632\pi$
$998$	−9.86282	+	30.3546i	−0.312202	+	0.960859i
$999$	4.41623	+	13.5917i	0.139723	+	0.430024i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	275.2.k.d.181.19	✓	100
11.9	even	5		275.2.l.d.31.7	yes	100
25.21	even	5		275.2.l.d.71.7	yes	100
275.196	even	5	inner	275.2.k.d.196.19	yes	100

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
275.2.k.d.181.19	✓	100	1.1	even	1	trivial
275.2.k.d.196.19	yes	100	275.196	even	5	inner
275.2.l.d.31.7	yes	100	11.9	even	5
275.2.l.d.71.7	yes	100	25.21	even	5

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:	\( N \)	\(=\)	\( 275 = 5^{2} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	275.k (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(1.20663 - 0.876668i) q^{2} +0.309228 q^{3} +(0.0693751 - 0.213515i) q^{4} +(0.504920 + 2.17831i) q^{5} +(0.373124 - 0.271091i) q^{6} +(2.02744 - 1.47302i) q^{7} +(0.818312 + 2.51851i) q^{8} -2.90438 q^{9} +(2.51891 + 2.18577i) q^{10} +(1.07375 - 3.13800i) q^{11} +(0.0214527 - 0.0660247i) q^{12} +6.00626 q^{13} +(1.15502 - 3.55477i) q^{14} +(0.156136 + 0.673597i) q^{15} +(3.55855 + 2.58543i) q^{16} +(-6.05478 + 4.39906i) q^{17} +(-3.50451 + 2.54618i) q^{18} +(-0.989834 - 3.04640i) q^{19} +(0.500131 + 0.0433131i) q^{20} +(0.626940 - 0.455499i) q^{21} +(-1.45537 - 4.72773i) q^{22} +(-2.19113 - 6.74361i) q^{23} +(0.253045 + 0.778793i) q^{24} +(-4.49011 + 2.19975i) q^{25} +(7.24733 - 5.26549i) q^{26} -1.82580 q^{27} +(-0.173857 - 0.535078i) q^{28} +(-0.111762 + 0.343967i) q^{29} +(0.778918 + 0.675903i) q^{30} +(-0.338108 + 1.04059i) q^{31} +1.26419 q^{32} +(0.332034 - 0.970359i) q^{33} +(-3.44937 + 10.6161i) q^{34} +(4.23239 + 3.67264i) q^{35} +(-0.201491 + 0.620127i) q^{36} +(-2.41879 - 7.44427i) q^{37} +(-3.86504 - 2.80812i) q^{38} +1.85730 q^{39} +(-5.07292 + 3.05418i) q^{40} +(-2.06329 + 1.49906i) q^{41} +(0.357164 - 1.09924i) q^{42} -6.81097 q^{43} +(-0.595518 - 0.446960i) q^{44} +(-1.46648 - 6.32665i) q^{45} +(-8.55579 - 6.21614i) q^{46} -0.0743774 q^{47} +(1.10040 + 0.799489i) q^{48} +(-0.222407 + 0.684499i) q^{49} +(-3.48945 + 6.59062i) q^{50} +(-1.87231 + 1.36031i) q^{51} +(0.416685 - 1.28242i) q^{52} +(1.99480 + 1.44931i) q^{53} +(-2.20307 + 1.60062i) q^{54} +(7.37772 + 0.754526i) q^{55} +(5.36888 + 3.90072i) q^{56} +(-0.306085 - 0.942032i) q^{57} +(0.166690 + 0.513019i) q^{58} +(-1.11297 - 3.42538i) q^{59} +(0.154655 + 0.0133936i) q^{60} +11.2908 q^{61} +(0.504280 + 1.55201i) q^{62} +(-5.88844 + 4.27820i) q^{63} +(-5.59168 + 4.06260i) q^{64} +(3.03268 + 13.0835i) q^{65} +(-0.450041 - 1.46195i) q^{66} +(12.9188 + 9.38603i) q^{67} +(0.519212 + 1.59797i) q^{68} +(-0.677560 - 2.08531i) q^{69} +(8.32661 + 0.721113i) q^{70} +(0.136508 + 0.420129i) q^{71} +(-2.37669 - 7.31469i) q^{72} +(-8.01056 - 5.82002i) q^{73} +(-9.44473 - 6.86200i) q^{74} +(-1.38847 + 0.680225i) q^{75} -0.719120 q^{76} +(-2.44538 - 7.94375i) q^{77} +(2.24108 - 1.62824i) q^{78} +(-2.61359 - 1.89888i) q^{79} +(-3.83511 + 9.05707i) q^{80} +8.14854 q^{81} +(-1.17544 + 3.61763i) q^{82} +(-1.02312 + 0.743342i) q^{83} +(-0.0537616 - 0.165461i) q^{84} +(-12.6397 - 10.9680i) q^{85} +(-8.21833 + 5.97096i) q^{86} +(-0.0345599 + 0.106364i) q^{87} +(8.78174 + 0.136380i) q^{88} +(-0.357172 - 1.09926i) q^{89} +(-7.31587 - 6.34831i) q^{90} +(12.1773 - 8.84732i) q^{91} -1.59187 q^{92} +(-0.104552 + 0.321779i) q^{93} +(-0.0897459 + 0.0652042i) q^{94} +(6.13622 - 3.69436i) q^{95} +0.390923 q^{96} +(-1.44853 - 1.05242i) q^{97} +(0.331715 + 1.02091i) q^{98} +(-3.11858 + 9.11395i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 100 q + 2 q^{2} + 8 q^{3} - 24 q^{4} + 5 q^{7} + 20 q^{8} + 80 q^{9} - 22 q^{10} - 53 q^{12} + 12 q^{13} + 15 q^{14} - 24 q^{15} - 8 q^{16} + 6 q^{17} - 21 q^{18} - 14 q^{19} + q^{20} - 22 q^{21} - 29 q^{22}+ \cdots - 84 q^{99}+O(q^{100}) \) 100 * q + 2 * q^2 + 8 * q^3 - 24 * q^4 + 5 * q^7 + 20 * q^8 + 80 * q^9 - 22 * q^10 - 53 * q^12 + 12 * q^13 + 15 * q^14 - 24 * q^15 - 8 * q^16 + 6 * q^17 - 21 * q^18 - 14 * q^19 + q^20 - 22 * q^21 - 29 * q^22 + 20 * q^23 - 18 * q^24 + 6 * q^25 - 37 * q^26 - 10 * q^27 + 26 * q^28 + 32 * q^29 + 20 * q^30 - 16 * q^31 - 98 * q^32 - 2 * q^33 - 14 * q^34 + 13 * q^35 - 10 * q^36 + 9 * q^37 - 67 * q^38 - 126 * q^39 + 49 * q^40 + 8 * q^41 - 24 * q^42 + 82 * q^43 + 46 * q^44 - 25 * q^45 + 29 * q^46 + 30 * q^47 + 83 * q^48 - 26 * q^49 + 4 * q^50 - 14 * q^51 + 17 * q^52 - 30 * q^53 - 22 * q^54 - 88 * q^55 + q^56 - 85 * q^57 + 50 * q^58 + 32 * q^59 - 39 * q^60 - 20 * q^61 + 38 * q^62 + 18 * q^63 - 44 * q^64 - 64 * q^65 + 22 * q^66 - 20 * q^67 + 5 * q^68 - 74 * q^69 + 47 * q^70 + 3 * q^71 + 107 * q^72 - 2 * q^73 - 3 * q^74 - 64 * q^75 - 156 * q^76 + 50 * q^77 + 30 * q^78 + 49 * q^79 + 96 * q^80 + 108 * q^81 - 59 * q^82 + 63 * q^83 + 24 * q^84 - 21 * q^85 + 9 * q^86 + 38 * q^87 - 37 * q^88 + 39 * q^89 - 166 * q^90 + 9 * q^91 + 30 * q^92 - 19 * q^93 + 66 * q^94 - 11 * q^95 - 116 * q^96 + 10 * q^97 + 122 * q^98 - 84 * q^99

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