LMFDB - Embedded newform 755.2.h.d.366.2

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [755,2,Mod(321,755)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(755, base_ring=CyclotomicField(10)) chi = DirichletCharacter(H, H._module([0, 6])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("755.321"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 755 = 5 \cdot 151 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	755.h (of order $5$, degree $4$, minimal)

Newform invariants

comment:select newform

sage:traces = [16,-4,-4] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(3)] == traces)

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

Self dual:	no
Analytic conductor:	$6.02870535261$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$4$ over $\Q(\zeta_{5})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 5 x^{15} + 14 x^{14} - 22 x^{13} + 54 x^{12} - 181 x^{11} + 697 x^{10} - 1743 x^{9} + 3507 x^{8} + \cdots + 16 $ x^16 - 5x^15 + 14x^14 - 22x^13 + 54x^12 - 181x^11 + 697x^10 - 1743x^9 + 3507x^8 - 5479x^7 + 7616x^6 - 7799x^5 + 6803x^4 - 3330x^3 + 948x^2 - 136*x + 16
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			366.2
Root			$0.334204 + 0.242813i$ of defining polynomial
Character	$\chi$	$=$	755.366
Dual form			755.2.h.d.361.2

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q-2.24302 q^{2} +(2.63865 - 1.91709i) q^{3} +3.03113 q^{4} +(-0.309017 + 0.951057i) q^{5} +(-5.91855 + 4.30007i) q^{6} +(0.681363 - 2.09702i) q^{7} -2.31285 q^{8} +(2.36019 - 7.26391i) q^{9} +(0.693131 - 2.13324i) q^{10} +(3.05442 + 2.21917i) q^{11} +(7.99810 - 5.81096i) q^{12} +(-0.127369 + 0.0925392i) q^{13} +(-1.52831 + 4.70365i) q^{14} +(1.00788 + 3.10192i) q^{15} -0.874500 q^{16} +(-1.14888 - 3.53589i) q^{17} +(-5.29394 + 16.2931i) q^{18} -2.51707 q^{19} +(-0.936671 + 2.88278i) q^{20} +(-2.22230 - 6.83954i) q^{21} +(-6.85112 - 4.97763i) q^{22} +5.87564 q^{23} +(-6.10280 + 4.43395i) q^{24} +(-0.809017 - 0.587785i) q^{25} +(0.285692 - 0.207567i) q^{26} +(-4.67425 - 14.3859i) q^{27} +(2.06530 - 6.35634i) q^{28} +(4.23104 + 3.07403i) q^{29} +(-2.26068 - 6.95767i) q^{30} +(-0.568350 - 1.74920i) q^{31} +6.58722 q^{32} +12.3139 q^{33} +(2.57696 + 7.93107i) q^{34} +(1.78383 + 1.29603i) q^{35} +(7.15404 - 22.0179i) q^{36} +(-2.95915 + 2.14995i) q^{37} +5.64584 q^{38} +(-0.158677 + 0.488357i) q^{39} +(0.714710 - 2.19965i) q^{40} +(-4.01859 + 2.91968i) q^{41} +(4.98466 + 15.3412i) q^{42} +(-3.14506 - 9.67948i) q^{43} +(9.25835 + 6.72659i) q^{44} +(6.17905 + 4.48934i) q^{45} -13.1792 q^{46} +(3.65121 - 2.65276i) q^{47} +(-2.30750 + 1.67650i) q^{48} +(1.72989 + 1.25684i) q^{49} +(1.81464 + 1.31841i) q^{50} +(-9.81012 - 7.12747i) q^{51} +(-0.386073 + 0.280499i) q^{52} +(7.49967 + 5.44883i) q^{53} +(10.4844 + 32.2678i) q^{54} +(-3.05442 + 2.21917i) q^{55} +(-1.57589 + 4.85009i) q^{56} +(-6.64167 + 4.82546i) q^{57} +(-9.49030 - 6.89510i) q^{58} -12.9924 q^{59} +(3.05500 + 9.40233i) q^{60} +(-0.639026 - 0.464279i) q^{61} +(1.27482 + 3.92349i) q^{62} +(-13.6244 - 9.89871i) q^{63} -13.0263 q^{64} +(-0.0486507 - 0.149732i) q^{65} -27.6203 q^{66} +(2.11841 + 6.51978i) q^{67} +(-3.48241 - 10.7177i) q^{68} +(15.5038 - 11.2642i) q^{69} +(-4.00116 - 2.90702i) q^{70} +(1.57823 - 4.85729i) q^{71} +(-5.45876 + 16.8003i) q^{72} +(-3.31475 + 10.2017i) q^{73} +(6.63743 - 4.82238i) q^{74} -3.26155 q^{75} -7.62957 q^{76} +(6.73480 - 4.89312i) q^{77} +(0.355915 - 1.09539i) q^{78} +(1.70550 - 5.24899i) q^{79} +(0.270235 - 0.831699i) q^{80} +(-21.3756 - 15.5303i) q^{81} +(9.01378 - 6.54889i) q^{82} +(-1.50326 - 4.62655i) q^{83} +(-6.73609 - 20.7315i) q^{84} +3.71785 q^{85} +(7.05442 + 21.7113i) q^{86} +17.0574 q^{87} +(-7.06441 - 5.13260i) q^{88} +(4.92187 + 15.1479i) q^{89} +(-13.8597 - 10.0697i) q^{90} +(0.107272 + 0.330148i) q^{91} +17.8099 q^{92} +(-4.85306 - 3.52595i) q^{93} +(-8.18972 + 5.95018i) q^{94} +(0.777818 - 2.39388i) q^{95} +(17.3814 - 12.6283i) q^{96} +(-2.38913 - 7.35298i) q^{97} +(-3.88017 - 2.81911i) q^{98} +(23.3288 - 16.9494i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 4 q^{2} - 4 q^{3} + 24 q^{4} + 4 q^{5} - 18 q^{6} - q^{7} - 18 q^{8} - q^{10} + 13 q^{11} - 19 q^{12} + 7 q^{13} - q^{14} - q^{15} + 16 q^{16} + 9 q^{17} - 3 q^{18} - 34 q^{19} - 9 q^{20} + 2 q^{21}+ \cdots + 75 q^{99}+O(q^{100}) $ 16 * q - 4 * q^2 - 4 * q^3 + 24 * q^4 + 4 * q^5 - 18 * q^6 - q^7 - 18 * q^8 - q^10 + 13 * q^11 - 19 * q^12 + 7 * q^13 - q^14 - q^15 + 16 * q^16 + 9 * q^17 - 3 * q^18 - 34 * q^19 - 9 * q^20 + 2 * q^21 + 14 * q^22 + 58 * q^23 + 8 * q^24 - 4 * q^25 - 19 * q^26 - 34 * q^27 + 19 * q^28 - 16 * q^29 - 12 * q^30 - 3 * q^31 + 14 * q^34 + 11 * q^35 + 57 * q^36 + 20 * q^37 - 16 * q^38 + 5 * q^39 + 3 * q^40 + 24 * q^41 + 34 * q^42 - 28 * q^43 + 73 * q^44 + 15 * q^45 - 22 * q^46 + 18 * q^47 - 74 * q^48 - 19 * q^49 + q^50 - 8 * q^51 + 2 * q^52 + 23 * q^53 + 48 * q^54 - 13 * q^55 - 7 * q^56 - 22 * q^57 + 8 * q^58 - 44 * q^59 - 6 * q^60 - 25 * q^61 + 56 * q^62 - 7 * q^63 + 42 * q^64 + 3 * q^65 - 102 * q^66 + 12 * q^67 - 8 * q^68 - 2 * q^69 + 6 * q^70 - 22 * q^71 - 39 * q^72 - 26 * q^73 - 2 * q^74 + 6 * q^75 + 16 * q^76 + 11 * q^77 + 12 * q^78 - 32 * q^79 - 21 * q^80 + 11 * q^81 + 46 * q^82 + 4 * q^83 - 19 * q^84 + 36 * q^85 + 39 * q^86 + 88 * q^87 + 24 * q^88 + 38 * q^89 - 22 * q^90 - 6 * q^91 + 114 * q^92 - 31 * q^93 - 31 * q^94 - 21 * q^95 + 59 * q^96 + 75 * q^97 - 56 * q^98 + 75 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/755\mathbb{Z}\right)^\times$.

$n$	$6$	$152$
$\chi(n)$	$e\left(\frac{4}{5}\right)$	$1$

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 $

$2$	−2.24302			−1.58605			−0.793027	−	0.609187i	$-0.791496\pi$
$2$	−2.24302			−1.58605			−0.793027	+	0.609187i	$0.791496\pi$
$3$	2.63865	−	1.91709i	1.52343	−	1.10683i	0.563670	−	0.826000i	$-0.309389\pi$
$3$	2.63865	−	1.91709i	1.52343	−	1.10683i	0.959756	−	0.280834i	$-0.0906110\pi$
$4$	3.03113			1.51557
$5$	−0.309017	+	0.951057i	−0.138197	+	0.425325i
$5$	−0.309017	+	0.951057i	−0.138197	+	0.425325i
$6$	−5.91855	+	4.30007i	−2.41624	+	1.75550i
$7$	0.681363	−	2.09702i	0.257531	−	0.792598i	−0.735790	−	0.677210i	$-0.763189\pi$
$7$	0.681363	−	2.09702i	0.257531	−	0.792598i	0.993320	−	0.115388i	$-0.0368112\pi$
$8$	−2.31285			−0.817716
$9$	2.36019	−	7.26391i	0.786729	−	2.42130i
$10$	0.693131	−	2.13324i	0.219187	−	0.674589i
$11$	3.05442	+	2.21917i	0.920942	+	0.669104i	0.943758	−	0.330636i	$-0.107263\pi$
$11$	3.05442	+	2.21917i	0.920942	+	0.669104i	−0.0228160	+	0.999740i	$0.507263\pi$
$12$	7.99810	−	5.81096i	2.30885	−	1.67748i
$13$	−0.127369	+	0.0925392i	−0.0353259	+	0.0256657i	−0.605308	−	0.795991i	$-0.706950\pi$
$13$	−0.127369	+	0.0925392i	−0.0353259	+	0.0256657i	0.569982	+	0.821657i	$0.306950\pi$
$14$	−1.52831	+	4.70365i	−0.408458	+	1.25710i
$15$	1.00788	+	3.10192i	0.260232	+	0.800913i
$16$	−0.874500			−0.218625
$17$	−1.14888	−	3.53589i	−0.278644	−	0.857579i	−0.988232	−	0.152962i	$-0.951119\pi$
$17$	−1.14888	−	3.53589i	−0.278644	−	0.857579i	0.709588	−	0.704617i	$-0.248881\pi$
$18$	−5.29394	+	16.2931i	−1.24779	+	3.84032i
$19$	−2.51707			−0.577456			−0.288728	−	0.957411i	$-0.593232\pi$
$19$	−2.51707			−0.577456			−0.288728	+	0.957411i	$0.593232\pi$
$20$	−0.936671	+	2.88278i	−0.209446	+	0.644609i
$21$	−2.22230	−	6.83954i	−0.484946	−	1.49251i
$22$	−6.85112	−	4.97763i	−1.46066	−	1.06123i
$23$	5.87564			1.22516			0.612578	−	0.790410i	$-0.290132\pi$
$23$	5.87564			1.22516			0.612578	+	0.790410i	$0.290132\pi$
$24$	−6.10280	+	4.43395i	−1.24573	+	0.905076i
$25$	−0.809017	−	0.587785i	−0.161803	−	0.117557i
$26$	0.285692	−	0.207567i	0.0560287	−	0.0407073i
$27$	−4.67425	−	14.3859i	−0.899560	−	2.76856i
$28$	2.06530	−	6.35634i	0.390305	−	1.20124i
$29$	4.23104	+	3.07403i	0.785684	+	0.570833i	0.906679	−	0.421820i	$-0.138609\pi$
$29$	4.23104	+	3.07403i	0.785684	+	0.570833i	−0.120996	+	0.992653i	$0.538609\pi$
$30$	−2.26068	−	6.95767i	−0.412742	−	1.27029i
$31$	−0.568350	−	1.74920i	−0.102079	−	0.314166i	0.886955	−	0.461856i	$-0.152816\pi$
$31$	−0.568350	−	1.74920i	−0.102079	−	0.314166i	−0.989034	+	0.147690i	$0.952816\pi$
$32$	6.58722			1.16447
$33$	12.3139			2.14357
$34$	2.57696	+	7.93107i	0.441945	+	1.36017i
$35$	1.78383	+	1.29603i	0.301522	+	0.219069i
$36$	7.15404	−	22.0179i	1.19234	−	3.66965i
$37$	−2.95915	+	2.14995i	−0.486482	+	0.353450i	−0.803830	−	0.594860i	$-0.797208\pi$
$37$	−2.95915	+	2.14995i	−0.486482	+	0.353450i	0.317348	+	0.948309i	$0.397208\pi$
$38$	5.64584			0.915876
$39$	−0.158677	+	0.488357i	−0.0254086	+	0.0781998i
$40$	0.714710	−	2.19965i	0.113006	−	0.347795i
$41$	−4.01859	+	2.91968i	−0.627599	+	0.455977i	−0.855567	−	0.517691i	$-0.826792\pi$
$41$	−4.01859	+	2.91968i	−0.627599	+	0.455977i	0.227969	+	0.973668i	$0.426792\pi$
$42$	4.98466	+	15.3412i	0.769150	+	2.36720i
$43$	−3.14506	−	9.67948i	−0.479616	−	1.47611i	−0.839629	−	0.543160i	$-0.817228\pi$
$43$	−3.14506	−	9.67948i	−0.479616	−	1.47611i	0.360013	−	0.932947i	$-0.382772\pi$
$44$	9.25835	+	6.72659i	1.39575	+	1.01407i
$45$	6.17905	+	4.48934i	0.921119	+	0.669232i
$46$	−13.1792			−1.94316
$47$	3.65121	−	2.65276i	0.532583	−	0.386944i	−0.288740	−	0.957408i	$-0.593236\pi$
$47$	3.65121	−	2.65276i	0.532583	−	0.386944i	0.821323	+	0.570463i	$0.193236\pi$
$48$	−2.30750	+	1.67650i	−0.333059	+	0.241982i
$49$	1.72989	+	1.25684i	0.247127	+	0.179548i
$50$	1.81464	+	1.31841i	0.256629	+	0.186452i
$51$	−9.81012	−	7.12747i	−1.37369	−	0.998046i
$52$	−0.386073	+	0.280499i	−0.0535387	+	0.0388981i
$53$	7.49967	+	5.44883i	1.03016	+	0.748454i	0.968340	−	0.249633i	$-0.0803101\pi$
$53$	7.49967	+	5.44883i	1.03016	+	0.748454i	0.0618182	+	0.998087i	$0.480310\pi$
$54$	10.4844	+	32.2678i	1.42675	+	4.39109i
$55$	−3.05442	+	2.21917i	−0.411858	+	0.299232i
$56$	−1.57589	+	4.85009i	−0.210587	+	0.648120i
$57$	−6.64167	+	4.82546i	−0.879711	+	0.639147i
$58$	−9.49030	−	6.89510i	−1.24614	−	0.905371i
$59$	−12.9924			−1.69147			−0.845735	−	0.533603i	$-0.820838\pi$
$59$	−12.9924			−1.69147			−0.845735	+	0.533603i	$0.820838\pi$
$60$	3.05500	+	9.40233i	0.394399	+	1.21384i
$61$	−0.639026	−	0.464279i	−0.0818188	−	0.0594449i	0.546124	−	0.837704i	$-0.316103\pi$
$61$	−0.639026	−	0.464279i	−0.0818188	−	0.0594449i	−0.627943	+	0.778260i	$0.716103\pi$
$62$	1.27482	+	3.92349i	0.161902	+	0.498284i
$63$	−13.6244	−	9.89871i	−1.71651	−	1.24712i
$64$	−13.0263			−1.62828
$65$	−0.0486507	−	0.149732i	−0.00603438	−	0.0185719i
$66$	−27.6203			−3.39982
$67$	2.11841	+	6.51978i	0.258804	+	0.796518i	0.993056	+	0.117641i	$0.0375332\pi$
$67$	2.11841	+	6.51978i	0.258804	+	0.796518i	−0.734252	+	0.678877i	$0.762467\pi$
$68$	−3.48241	−	10.7177i	−0.422304	−	1.29972i
$69$	15.5038	−	11.2642i	1.86644	−	1.35604i
$70$	−4.00116	−	2.90702i	−0.478231	−	0.347455i
$71$	1.57823	−	4.85729i	0.187301	−	0.576454i	−0.812679	−	0.582711i	$-0.801992\pi$
$71$	1.57823	−	4.85729i	0.187301	−	0.576454i	0.999980	+	0.00625730i	$0.00199177\pi$
$72$	−5.45876	+	16.8003i	−0.643321	+	1.97994i
$73$	−3.31475	+	10.2017i	−0.387962	+	1.19402i	0.546347	+	0.837559i	$0.316018\pi$
$73$	−3.31475	+	10.2017i	−0.387962	+	1.19402i	−0.934309	+	0.356465i	$0.883982\pi$
$74$	6.63743	−	4.82238i	0.771586	−	0.560590i
$75$	−3.26155			−0.376612
$76$	−7.62957			−0.875172
$77$	6.73480	−	4.89312i	0.767502	−	0.557623i
$78$	0.355915	−	1.09539i	0.0402995	−	0.124029i
$79$	1.70550	−	5.24899i	0.191884	−	0.590557i	−0.808115	−	0.589024i	$-0.799512\pi$
$79$	1.70550	−	5.24899i	0.191884	−	0.590557i	0.999999	−	0.00153257i	$-0.000487833\pi$
$80$	0.270235	−	0.831699i	0.0302132	−	0.0929868i
$81$	−21.3756	−	15.5303i	−2.37507	−	1.72559i
$82$	9.01378	−	6.54889i	0.995405	−	0.723204i
$83$	−1.50326	−	4.62655i	−0.165004	−	0.507830i	0.834033	−	0.551715i	$-0.186026\pi$
$83$	−1.50326	−	4.62655i	−0.165004	−	0.507830i	−0.999037	+	0.0438852i	$0.986026\pi$
$84$	−6.73609	−	20.7315i	−0.734967	−	2.26200i
$85$	3.71785			0.403258
$86$	7.05442	+	21.7113i	0.760697	+	2.34119i
$87$	17.0574			1.82875
$88$	−7.06441	−	5.13260i	−0.753069	−	0.547137i
$89$	4.92187	+	15.1479i	0.521717	+	1.60568i	0.770718	+	0.637176i	$0.219898\pi$
$89$	4.92187	+	15.1479i	0.521717	+	1.60568i	−0.249002	+	0.968503i	$0.580102\pi$
$90$	−13.8597	−	10.0697i	−1.46094	−	1.06144i
$91$	0.107272	+	0.330148i	0.0112451	+	0.0346090i
$92$	17.8099			1.85681
$93$	−4.85306	−	3.52595i	−0.503238	−	0.365624i
$94$	−8.18972	+	5.95018i	−0.844706	+	0.613714i
$95$	0.777818	−	2.39388i	0.0798024	−	0.245607i
$96$	17.3814	−	12.6283i	1.77398	−	1.28887i
$97$	−2.38913	−	7.35298i	−0.242579	−	0.746582i	−0.996025	−	0.0890720i	$-0.971610\pi$
$97$	−2.38913	−	7.35298i	−0.242579	−	0.746582i	0.753446	−	0.657510i	$-0.228390\pi$
$98$	−3.88017	−	2.81911i	−0.391957	−	0.284773i
$99$	23.3288	−	16.9494i	2.34464	−	1.70348i
$100$	−2.45224	−	1.78166i	−0.245224	−	0.178166i
$101$	−14.4702	−	10.5132i	−1.43984	−	1.04610i	−0.988076	−	0.153964i	$-0.950796\pi$
$101$	−14.4702	−	10.5132i	−1.43984	−	1.04610i	−0.451761	−	0.892139i	$-0.649204\pi$
$102$	22.0043	+	15.9871i	2.17875	+	1.58295i
$103$	13.1124	−	9.52674i	1.29201	−	0.938698i	0.292163	−	0.956369i	$-0.405625\pi$
$103$	13.1124	−	9.52674i	1.29201	−	0.938698i	0.999844	+	0.0176706i	$0.00562501\pi$
$104$	0.294586	−	0.214029i	0.0288865	−	0.0209873i
$105$	7.19151			0.701820
$106$	−16.8219	−	12.2218i	−1.63389	−	1.18709i
$107$	−0.162103	−	0.117775i	−0.0156711	−	0.0113857i	0.579922	−	0.814672i	$-0.303083\pi$
$107$	−0.162103	−	0.117775i	−0.0156711	−	0.0113857i	−0.595593	+	0.803286i	$0.703083\pi$
$108$	−14.1683	−	43.6055i	−1.36334	−	4.19594i
$109$	−4.64000	−	14.2805i	−0.444431	−	1.36782i	−0.883106	−	0.469173i	$-0.844552\pi$
$109$	−4.64000	−	14.2805i	−0.444431	−	1.36782i	0.438675	−	0.898646i	$-0.355448\pi$
$110$	6.85112	−	4.97763i	0.653229	−	0.474599i
$111$	−3.68652	+	11.3459i	−0.349909	+	1.07691i
$112$	−0.595852	+	1.83384i	−0.0563027	+	0.173282i
$113$	6.46101			0.607800			0.303900	−	0.952704i	$-0.401711\pi$
$113$	6.46101			0.607800			0.303900	+	0.952704i	$0.401711\pi$
$114$	14.8974	−	10.8236i	1.39527	−	1.01372i
$115$	−1.81567	+	5.58807i	−0.169312	+	0.521090i
$116$	12.8248	+	9.31779i	1.19076	+	0.865135i
$117$	0.371581	+	1.14361i	0.0343527	+	0.105727i
$118$	29.1423			2.68276
$119$	−8.19763			−0.751475
$120$	−2.33106	−	7.17428i	−0.212796	−	0.654919i
$121$	1.00560	+	3.09491i	0.0914179	+	0.281356i
$122$	1.43335	+	1.04139i	0.129769	+	0.0942828i
$123$	−5.00637	+	15.4080i	−0.451409	+	1.38930i
$124$	−1.72274	−	5.30206i	−0.154707	−	0.476139i
$125$	0.809017	−	0.587785i	0.0723607	−	0.0525731i
$126$	30.5598	+	22.2030i	2.72248	+	1.97800i
$127$	−17.0261	+	12.3702i	−1.51082	+	1.09768i	−0.545010	+	0.838430i	$0.683474\pi$
$127$	−17.0261	+	12.3702i	−1.51082	+	1.09768i	−0.965811	+	0.259246i	$0.916526\pi$
$128$	16.0437			1.41808
$129$	−26.8552	−	19.5114i	−2.36447	−	1.71789i
$130$	0.109124	+	0.335851i	0.00957085	+	0.0294560i
$131$	1.99318	−	6.13437i	0.174145	−	0.535962i	−0.825449	−	0.564477i	$-0.809078\pi$
$131$	1.99318	−	6.13437i	0.174145	−	0.535962i	0.999593	+	0.0285149i	$0.00907780\pi$
$132$	37.3251			3.24873
$133$	−1.71504	+	5.27834i	−0.148713	+	0.457690i
$134$	−4.75162	−	14.6240i	−0.410478	−	1.26332i
$135$	15.1262			1.30186
$136$	2.65719	+	8.17798i	0.227852	+	0.701256i
$137$	−6.02017	+	18.5282i	−0.514338	+	1.58297i	0.270145	+	0.962820i	$0.412928\pi$
$137$	−6.02017	+	18.5282i	−0.514338	+	1.58297i	−0.784483	+	0.620150i	$0.787072\pi$
$138$	−34.7753	+	25.2657i	−2.96027	+	2.15076i
$139$	−5.90389	+	4.28943i	−0.500761	+	0.363824i	−0.809308	−	0.587385i	$-0.800157\pi$
$139$	−5.90389	+	4.28943i	−0.500761	+	0.363824i	0.308546	+	0.951209i	$0.400157\pi$
$140$	5.40703	+	3.92843i	0.456977	+	0.332013i
$141$	4.54868	−	13.9994i	0.383068	−	1.17896i
$142$	−3.54000	+	10.8950i	−0.297070	+	0.914287i
$143$	−0.594399			−0.0497061
$144$	−2.06398	+	6.35229i	−0.171999	+	0.529358i
$145$	−4.23104	+	3.07403i	−0.351369	+	0.255284i
$146$	7.43504	−	22.8827i	0.615329	−	1.89379i
$147$	6.97405			0.575210
$148$	−8.96958	+	6.51678i	−0.737295	+	0.535676i
$149$	8.66586			0.709935			0.354968	−	0.934879i	$-0.384492\pi$
$149$	8.66586			0.709935			0.354968	+	0.934879i	$0.384492\pi$
$150$	7.31572			0.597326
$151$	−5.09428	+	11.1825i	−0.414567	+	0.910019i
$151$	−5.09428	+	11.1825i	−0.414567	+	0.910019i
$152$	5.82161			0.472195
$153$	−28.3960			−2.29568
$154$	−15.1063	+	10.9754i	−1.21730	+	0.884419i
$155$	1.83922			0.147730
$156$	−0.480971	+	1.48028i	−0.0385085	+	0.118517i
$157$	−3.08356	+	2.24034i	−0.246095	+	0.178799i	−0.703994	−	0.710205i	$-0.748602\pi$
$157$	−3.08356	+	2.24034i	−0.246095	+	0.178799i	0.457899	+	0.889004i	$0.348602\pi$
$158$	−3.82547	+	11.7736i	−0.304338	+	0.936655i
$159$	30.2349			2.39779
$160$	−2.03556	+	6.26482i	−0.160925	+	0.495277i
$161$	4.00344	−	12.3213i	0.315516	−	0.971057i
$162$	47.9459	+	34.8347i	3.76698	+	2.73687i
$163$	19.5710	−	14.2191i	1.53292	−	1.11373i	0.578325	−	0.815806i	$-0.303706\pi$
$163$	19.5710	−	14.2191i	1.53292	−	1.11373i	0.954590	−	0.297922i	$-0.0962936\pi$
$164$	−12.1809	+	8.84993i	−0.951167	+	0.691064i
$165$	−3.80520	+	11.7112i	−0.296235	+	0.911717i
$166$	3.37183	+	10.3774i	0.261705	+	0.805446i
$167$	3.32052			0.256950			0.128475	−	0.991713i	$-0.458992\pi$
$167$	3.32052			0.256950			0.128475	+	0.991713i	$0.458992\pi$
$168$	5.13985	+	15.8188i	0.396548	+	1.22045i
$169$	−4.00956	+	12.3402i	−0.308428	+	0.949243i
$170$	−8.33922			−0.639589
$171$	−5.94076	+	18.2838i	−0.454301	+	1.39820i
$172$	−9.53308	−	29.3398i	−0.726890	−	2.23714i
$173$	5.15432	+	3.74483i	0.391875	+	0.284714i	0.766224	−	0.642574i	$-0.222133\pi$
$173$	5.15432	+	3.74483i	0.391875	+	0.284714i	−0.374348	+	0.927288i	$0.622133\pi$
$174$	−38.2601			−2.90049
$175$	−1.78383	+	1.29603i	−0.134845	+	0.0979705i
$176$	−2.67109	−	1.94066i	−0.201341	−	0.146283i
$177$	−34.2825	+	24.9077i	−2.57683	+	1.87218i
$178$	−11.0398	−	33.9771i	−0.827471	−	2.54669i
$179$	−6.12176	+	18.8408i	−0.457562	+	1.40823i	0.410539	+	0.911843i	$0.365340\pi$
$179$	−6.12176	+	18.8408i	−0.457562	+	1.40823i	−0.868101	+	0.496387i	$0.834660\pi$
$180$	18.7295	+	13.6078i	1.39602	+	1.01427i
$181$	−0.790717	−	2.43358i	−0.0587735	−	0.180886i	0.917360	−	0.398060i	$-0.130316\pi$
$181$	−0.790717	−	2.43358i	−0.0587735	−	0.180886i	−0.976133	+	0.217173i	$0.930316\pi$
$182$	−0.240612	−	0.740529i	−0.0178354	−	0.0548917i
$183$	−2.57623			−0.190441
$184$	−13.5895			−1.00183
$185$	−1.13030	−	3.47869i	−0.0831010	−	0.255758i
$186$	10.8855	+	7.90878i	0.798163	+	0.579900i
$187$	4.33756	−	13.3496i	0.317194	−	0.976223i
$188$	11.0673	−	8.04086i	0.807165	−	0.586440i
$189$	−33.3523			−2.42602
$190$	−1.74466	+	5.36951i	−0.126571	+	0.389545i
$191$	−2.53251	+	7.79425i	−0.183246	+	0.563972i	−0.999914	−	0.0131354i	$-0.995819\pi$
$191$	−2.53251	+	7.79425i	−0.183246	+	0.563972i	0.816668	+	0.577108i	$0.195819\pi$
$192$	−34.3718	+	24.9725i	−2.48057	+	1.80224i
$193$	5.34342	+	16.4453i	0.384627	+	1.18376i	0.936750	+	0.349999i	$0.113818\pi$
$193$	5.34342	+	16.4453i	0.384627	+	1.18376i	−0.552123	+	0.833763i	$0.686182\pi$
$194$	5.35886	+	16.4929i	0.384744	+	1.18412i
$195$	−0.415422	−	0.301821i	−0.0297490	−	0.0216139i
$196$	5.24352	+	3.80964i	0.374537	+	0.272117i
$197$	25.0308			1.78337			0.891687	−	0.452653i	$-0.149522\pi$
$197$	25.0308			1.78337			0.891687	+	0.452653i	$0.149522\pi$
$198$	−52.3270	+	38.0178i	−3.71872	+	2.70181i
$199$	13.9862	−	10.1616i	0.991458	−	0.720336i	0.0312181	−	0.999513i	$-0.490061\pi$
$199$	13.9862	−	10.1616i	0.991458	−	0.720336i	0.960240	+	0.279176i	$0.0900613\pi$
$200$	1.87113	+	1.35946i	0.132309	+	0.0961283i
$201$	18.0888	+	13.1423i	1.27588	+	0.926983i
$202$	32.4569	+	23.5813i	2.28366	+	1.65918i
$203$	9.32916	−	6.77803i	0.654779	−	0.475725i
$204$	−29.7358	−	21.6043i	−2.08192	−	1.51260i
$205$	−1.53497	−	4.72414i	−0.107207	−	0.329948i
$206$	−29.4114	+	21.3687i	−2.04919	+	1.48883i
$207$	13.8676	−	42.6802i	0.963866	−	2.96648i
$208$	0.111384	−	0.0809255i	0.00772312	−	0.00561118i
$209$	−7.68819	−	5.58580i	−0.531803	−	0.386378i
$210$	−16.1307			−1.11312
$211$	5.95086	+	18.3149i	0.409674	+	1.26085i	0.916929	+	0.399051i	$0.130660\pi$
$211$	5.95086	+	18.3149i	0.409674	+	1.26085i	−0.507255	+	0.861796i	$0.669340\pi$
$212$	22.7325	+	16.5161i	1.56127	+	1.13433i
$213$	−5.14748	−	15.8423i	−0.352699	−	1.08550i
$214$	0.363600	+	0.264171i	0.0248552	+	0.0180584i
$215$	10.1776			0.694107
$216$	10.8108	+	33.2723i	0.735585	+	2.26390i
$217$	−4.05536			−0.275296
$218$	10.4076	+	32.0313i	0.704892	+	2.16943i
$219$	10.8112	+	33.2735i	0.730555	+	2.24842i
$220$	−9.25835	+	6.72659i	−0.624198	+	0.453506i
$221$	0.473540	+	0.344047i	0.0318538	+	0.0231431i
$222$	8.26893	−	25.4491i	0.554974	−	1.70804i
$223$	2.10451	−	6.47702i	0.140928	−	0.433733i	−0.855537	−	0.517742i	$-0.826773\pi$
$223$	2.10451	−	6.47702i	0.140928	−	0.433733i	0.996465	+	0.0840093i	$0.0267725\pi$
$224$	4.48828	−	13.8135i	0.299886	−	0.922955i
$225$	−6.17905	+	4.48934i	−0.411937	+	0.299290i
$226$	−14.4922			−0.964004
$227$	−13.4313			−0.891464			−0.445732	−	0.895167i	$-0.647057\pi$
$227$	−13.4313			−0.891464			−0.445732	+	0.895167i	$0.647057\pi$
$228$	−20.1318	+	14.6266i	−1.33326	+	0.968670i
$229$	−8.24096	+	25.3631i	−0.544578	+	1.67604i	0.177413	+	0.984137i	$0.443227\pi$
$229$	−8.24096	+	25.3631i	−0.544578	+	1.67604i	−0.721991	+	0.691903i	$0.756773\pi$
$230$	4.07259	−	12.5341i	0.268539	−	0.826477i
$231$	8.39023	−	25.8225i	0.552037	−	1.69899i
$232$	−9.78575	−	7.10977i	−0.642466	−	0.466779i
$233$	−5.43004	+	3.94515i	−0.355734	+	0.258456i	−0.751270	−	0.659995i	$-0.770559\pi$
$233$	−5.43004	+	3.94515i	−0.355734	+	0.258456i	0.395537	+	0.918450i	$0.370559\pi$
$234$	−0.833463	−	2.56514i	−0.0544852	−	0.167688i
$235$	1.39464	+	4.29225i	0.0909761	+	0.279996i
$236$	−39.3818			−2.56354
$237$	−5.56257	−	17.1198i	−0.361328	−	1.11205i
$238$	18.3874			1.19188
$239$	10.0540	+	7.30469i	0.650342	+	0.472501i	0.863388	−	0.504541i	$-0.168338\pi$
$239$	10.0540	+	7.30469i	0.650342	+	0.472501i	−0.213046	+	0.977042i	$0.568338\pi$
$240$	−0.881387	−	2.71263i	−0.0568933	−	0.175100i
$241$	8.87609	+	6.44886i	0.571759	+	0.415407i	0.835744	−	0.549119i	$-0.185037\pi$
$241$	8.87609	+	6.44886i	0.571759	+	0.415407i	−0.263985	+	0.964527i	$0.585037\pi$
$242$	−2.25557	−	6.94194i	−0.144994	−	0.446245i
$243$	−40.7972			−2.61714
$244$	−1.93697	−	1.40729i	−0.124002	−	0.0900926i
$245$	−1.72989	+	1.25684i	−0.110519	+	0.0802964i
$246$	11.2294	−	34.5605i	0.715959	−	2.20350i
$247$	0.320597	−	0.232928i	0.0203991	−	0.0148208i
$248$	1.31451	+	4.04564i	0.0834713	+	0.256898i
$249$	−12.8361	−	9.32597i	−0.813455	−	0.591010i
$250$	−1.81464	+	1.31841i	−0.114768	+	0.0833838i
$251$	10.6726	+	7.75412i	0.673651	+	0.489436i	0.871245	−	0.490848i	$-0.163313\pi$
$251$	10.6726	+	7.75412i	0.673651	+	0.489436i	−0.197595	+	0.980284i	$0.563313\pi$
$252$	−41.2974	−	30.0043i	−2.60149	−	1.89009i
$253$	17.9467	+	13.0390i	1.12830	+	0.819757i
$254$	38.1898	−	27.7465i	2.39624	−	1.74097i
$255$	9.81012	−	7.12747i	0.614334	−	0.446340i
$256$	−9.93380			−0.620862
$257$	−1.52518	−	1.10811i	−0.0951382	−	0.0691219i	0.539199	−	0.842178i	$-0.318727\pi$
$257$	−1.52518	−	1.10811i	−0.0951382	−	0.0691219i	−0.634337	+	0.773056i	$0.718727\pi$
$258$	60.2367	+	43.7645i	3.75017	+	2.72466i
$259$	2.49223	+	7.67029i	0.154860	+	0.476609i
$260$	−0.147467	−	0.453856i	−0.00914550	−	0.0281470i
$261$	32.3155	−	23.4786i	2.00028	−	1.45329i
$262$	−4.47073	+	13.7595i	−0.276203	+	0.850065i
$263$	−8.62808	+	26.5545i	−0.532030	+	1.63742i	0.217950	+	0.975960i	$0.430063\pi$
$263$	−8.62808	+	26.5545i	−0.532030	+	1.63742i	−0.749980	+	0.661461i	$0.769937\pi$
$264$	−28.4802			−1.75283
$265$	−7.49967	+	5.44883i	−0.460701	+	0.334719i
$266$	3.84686	−	11.8394i	0.235866	−	0.725921i
$267$	42.0271	+	30.5345i	2.57202	+	1.86868i
$268$	6.42117	+	19.7623i	0.392235	+	1.20718i
$269$	12.5818			0.767128			0.383564	−	0.923514i	$-0.374697\pi$
$269$	12.5818			0.767128			0.383564	+	0.923514i	$0.374697\pi$
$270$	−33.9283			−2.06481
$271$	−3.37232	−	10.3789i	−0.204854	−	0.630475i	−0.999719	−	0.0236897i	$-0.992459\pi$
$271$	−3.37232	−	10.3789i	−0.204854	−	0.630475i	0.794865	−	0.606786i	$-0.207541\pi$
$272$	1.00470	+	3.09214i	0.0609186	+	0.187488i
$273$	0.915978	+	0.665497i	0.0554375	+	0.0402777i
$274$	13.5034	−	41.5591i	0.815768	−	2.51068i
$275$	−1.16668	−	3.59069i	−0.0703537	−	0.216527i
$276$	46.9940	−	34.1431i	2.82871	−	2.05518i
$277$	−13.8271	−	10.0460i	−0.830790	−	0.603604i	0.0889930	−	0.996032i	$-0.471635\pi$
$277$	−13.8271	−	10.0460i	−0.830790	−	0.603604i	−0.919783	+	0.392428i	$0.871635\pi$
$278$	13.2425	−	9.62126i	0.794234	−	0.577045i
$279$	−14.0474			−0.840999
$280$	−4.12573	−	2.99752i	−0.246560	−	0.179136i
$281$	6.38361	+	19.6467i	0.380814	+	1.17203i	0.939471	+	0.342627i	$0.111317\pi$
$281$	6.38361	+	19.6467i	0.380814	+	1.17203i	−0.558657	+	0.829399i	$0.688683\pi$
$282$	−10.2028	+	31.4009i	−0.607567	+	1.86990i
$283$	30.6056			1.81931			0.909657	−	0.415361i	$-0.136345\pi$
$283$	30.6056			1.81931			0.909657	+	0.415361i	$0.136345\pi$
$284$	4.78382	−	14.7231i	0.283868	−	0.873655i
$285$	−2.53689	−	7.80775i	−0.150273	−	0.462491i
$286$	1.33325			0.0788366
$287$	3.38450	+	10.4164i	0.199781	+	0.614862i
$288$	15.5471	−	47.8490i	0.916120	−	2.81953i
$289$	2.57070	−	1.86772i	0.151218	−	0.109866i
$290$	9.49030	−	6.89510i	0.557289	−	0.404894i
$291$	−20.4004	−	14.8218i	−1.19589	−	0.868867i
$292$	−10.0474	+	30.9229i	−0.587982	+	1.80962i
$293$	−4.32340	+	13.3060i	−0.252576	+	0.777348i	0.741722	+	0.670707i	$0.234009\pi$
$293$	−4.32340	+	13.3060i	−0.252576	+	0.777348i	−0.994298	+	0.106640i	$0.965991\pi$
$294$	−15.6429			−0.912314
$295$	4.01488	−	12.3565i	0.233755	−	0.719425i
$296$	6.84407	−	4.97251i	0.397804	−	0.289021i
$297$	17.6475	−	54.3134i	1.02401	−	3.15158i
$298$	−19.4377			−1.12600
$299$	−0.748376	+	0.543727i	−0.0432797	+	0.0314446i
$300$	−9.88620			−0.570780
$301$	−22.4410			−1.29348
$302$	11.4266	−	25.0826i	0.657525	−	1.44334i
$303$	−58.3366			−3.35135
$304$	2.20118			0.126246
$305$	0.639026	−	0.464279i	0.0365905	−	0.0265846i
$306$	63.6927			3.64107
$307$	2.75026	−	8.46442i	0.156965	−	0.483090i	−0.841389	−	0.540430i	$-0.818262\pi$
$307$	2.75026	−	8.46442i	0.156965	−	0.483090i	0.998355	+	0.0573396i	$0.0182618\pi$
$308$	20.4141	−	14.8317i	1.16320	−	0.845114i
$309$	16.3355	−	50.2755i	0.929294	−	2.86007i
$310$	−4.12540			−0.234307
$311$	−6.71965	+	20.6810i	−0.381036	+	1.17271i	0.558279	+	0.829653i	$0.311462\pi$
$311$	−6.71965	+	20.6810i	−0.381036	+	1.17271i	−0.939315	+	0.343056i	$0.888538\pi$
$312$	0.366996	−	1.12950i	0.0207770	−	0.0639452i
$313$	−6.93191	−	5.03633i	−0.391815	−	0.284670i	0.374384	−	0.927274i	$-0.377854\pi$
$313$	−6.93191	−	5.03633i	−0.391815	−	0.284670i	−0.766199	+	0.642604i	$0.777854\pi$
$314$	6.91649	−	5.02513i	0.390320	−	0.283584i
$315$	13.6244	−	9.89871i	0.767649	−	0.557729i
$316$	5.16959	−	15.9104i	0.290812	−	0.895028i
$317$	2.30850	+	7.10484i	0.129658	+	0.399047i	0.994721	−	0.102617i	$-0.0327215\pi$
$317$	2.30850	+	7.10484i	0.129658	+	0.399047i	−0.865063	+	0.501664i	$0.832721\pi$
$318$	−67.8175			−3.80302
$319$	6.10159	+	18.7788i	0.341623	+	1.05141i
$320$	4.02533	−	12.3887i	0.225023	−	0.692550i
$321$	−0.653519			−0.0364759
$322$	−8.97980	+	27.6370i	−0.500425	+	1.54015i
$323$	2.89181	+	8.90008i	0.160905	+	0.495214i
$324$	−64.7923	−	47.0744i	−3.59957	−	2.61524i
$325$	0.157437			0.00873304
$326$	−43.8980	+	31.8938i	−2.43129	+	1.76643i
$327$	−39.6203	−	28.7858i	−2.19101	−	1.59186i
$328$	9.29440	−	6.75278i	0.513197	−	0.372860i
$329$	−3.07508	−	9.46413i	−0.169535	−	0.521775i
$330$	8.53514	−	26.2685i	0.469844	−	1.44603i
$331$	17.0379	+	12.3788i	0.936487	+	0.680398i	0.947573	−	0.319541i	$-0.103529\pi$
$331$	17.0379	+	12.3788i	0.936487	+	0.680398i	−0.0110852	+	0.999939i	$0.503529\pi$
$332$	−4.55657	−	14.0237i	−0.250074	−	0.769650i
$333$	8.63289	+	26.5693i	0.473079	+	1.45599i
$334$	−7.44799			−0.407536
$335$	−6.85531			−0.374545
$336$	1.94340	+	5.98118i	0.106021	+	0.326300i
$337$	−26.0071	−	18.8953i	−1.41670	−	1.02929i	−0.992305	−	0.123814i	$-0.960487\pi$
$337$	−26.0071	−	18.8953i	−1.41670	−	1.02929i	−0.424393	−	0.905478i	$-0.639513\pi$
$338$	8.99352	−	27.6792i	0.489183	−	1.50555i
$339$	17.0483	−	12.3863i	0.925939	−	0.672734i
$340$	11.2693			0.611164
$341$	2.14579	−	6.60406i	0.116201	−	0.357630i
$342$	13.3252	−	41.0108i	0.720546	−	2.21761i
$343$	16.3011	−	11.8434i	0.880177	−	0.639486i
$344$	7.27404	+	22.3872i	0.392190	+	1.20704i
$345$	5.92192	+	18.2258i	0.318825	+	0.981243i
$346$	−11.5612	−	8.39972i	−0.621536	−	0.451572i
$347$	−14.1408	−	10.2739i	−0.759121	−	0.551533i	0.139520	−	0.990219i	$-0.455444\pi$
$347$	−14.1408	−	10.2739i	−0.759121	−	0.551533i	−0.898640	+	0.438686i	$0.855444\pi$
$348$	51.7033			2.77159
$349$	−5.20059	+	3.77845i	−0.278381	+	0.202256i	−0.718211	−	0.695825i	$-0.755039\pi$
$349$	−5.20059	+	3.77845i	−0.278381	+	0.202256i	0.439830	+	0.898081i	$0.355039\pi$
$350$	4.00116	−	2.90702i	0.213871	−	0.155387i
$351$	1.92661	+	1.39977i	0.102835	+	0.0747140i
$352$	20.1201	+	14.6181i	1.07241	+	0.779149i
$353$	9.01172	+	6.54740i	0.479645	+	0.348483i	0.801188	−	0.598412i	$-0.204201\pi$
$353$	9.01172	+	6.54740i	0.479645	+	0.348483i	−0.321543	+	0.946895i	$0.604201\pi$
$354$	76.8963	−	55.8684i	4.08699	−	2.96937i
$355$	4.13186	+	3.00197i	0.219296	+	0.159328i
$356$	14.9188	+	45.9154i	0.790696	+	2.43351i
$357$	−21.6307	+	15.7156i	−1.14482	+	0.831758i
$358$	13.7312	−	42.2603i	0.725717	−	2.23353i
$359$	−13.5976	+	9.87924i	−0.717654	+	0.521406i	−0.885634	−	0.464384i	$-0.846276\pi$
$359$	−13.5976	+	9.87924i	−0.717654	+	0.521406i	0.167980	+	0.985790i	$0.446276\pi$
$360$	−14.2912	−	10.3832i	−0.753213	−	0.547241i
$361$	−12.6644			−0.666545
$362$	1.77359	+	5.45856i	0.0932179	+	0.286895i
$363$	8.58665	+	6.23857i	0.450682	+	0.327440i
$364$	0.325155	+	1.00072i	0.0170427	+	0.0524522i
$365$	−8.67813	−	6.30503i	−0.454234	−	0.330020i
$366$	5.77854			0.302049
$367$	4.02577	+	12.3901i	0.210144	+	0.646756i	0.999463	+	0.0327727i	$0.0104337\pi$
$367$	4.02577	+	12.3901i	0.210144	+	0.646756i	−0.789319	+	0.613983i	$0.789566\pi$
$368$	−5.13825			−0.267850
$369$	11.7236	+	36.0817i	0.610309	+	1.87834i
$370$	2.53527	+	7.80277i	0.131803	+	0.405647i
$371$	16.5363	−	12.0143i	0.858521	−	0.623752i
$372$	−14.7103	−	10.6876i	−0.762691	−	0.554128i
$373$	−3.67841	+	11.3210i	−0.190461	+	0.586178i	−1.00000		0.000888547i	$-0.999717\pi$
$373$	−3.67841	+	11.3210i	−0.190461	+	0.586178i	0.809539	+	0.587066i	$0.199717\pi$
$374$	−9.72924	+	29.9435i	−0.503087	+	1.54834i
$375$	1.00788	−	3.10192i	0.0520465	−	0.160183i
$376$	−8.44469	+	6.13543i	−0.435502	+	0.316410i
$377$	−0.823372			−0.0424058
$378$	74.8098			3.84780
$379$	6.30985	−	4.58437i	0.324115	−	0.235483i	−0.413814	−	0.910361i	$-0.635804\pi$
$379$	6.30985	−	4.58437i	0.324115	−	0.235483i	0.737929	+	0.674878i	$0.235804\pi$
$380$	2.35767	−	7.25616i	0.120946	−	0.372233i
$381$	−21.2111	+	65.2812i	−1.08668	+	3.34446i
$382$	5.68046	−	17.4827i	0.290638	−	0.894490i
$383$	−18.9349	−	13.7570i	−0.967529	−	0.702951i	−0.0126418	−	0.999920i	$-0.504024\pi$
$383$	−18.9349	−	13.7570i	−0.967529	−	0.702951i	−0.954887	+	0.296969i	$0.904024\pi$
$384$	42.3337	−	30.7573i	2.16033	−	1.56957i
$385$	2.57246	+	7.91723i	0.131105	+	0.403499i
$386$	−11.9854	−	36.8872i	−0.610040	−	1.87751i
$387$	−77.7338			−3.95143
$388$	−7.24176	−	22.2878i	−0.367645	−	1.13149i
$389$	9.76106			0.494906			0.247453	−	0.968900i	$-0.420406\pi$
$389$	9.76106			0.494906			0.247453	+	0.968900i	$0.420406\pi$
$390$	0.931798	+	0.676991i	0.0471834	+	0.0342808i
$391$	−6.75041	−	20.7756i	−0.341383	−	1.05067i
$392$	−4.00097	−	2.90688i	−0.202080	−	0.146819i
$393$	−6.50085	−	20.0076i	−0.327925	−	1.00925i
$394$	−56.1446			−2.82853
$395$	4.46505	+	3.24405i	0.224661	+	0.163226i
$396$	70.7128	−	51.3758i	3.55345	−	2.58173i
$397$	10.8052	−	33.2549i	0.542295	−	1.66901i	−0.185040	−	0.982731i	$-0.559241\pi$
$397$	10.8052	−	33.2549i	0.542295	−	1.66901i	0.727335	−	0.686283i	$-0.240759\pi$
$398$	−31.3714	+	22.7926i	−1.57251	+	1.14249i
$399$	5.59369	+	17.2156i	0.280035	+	0.861858i
$400$	0.707486	+	0.514018i	0.0353743	+	0.0257009i
$401$	−20.9308	+	15.2071i	−1.04524	+	0.759409i	−0.971301	−	0.237854i	$-0.923556\pi$
$401$	−20.9308	+	15.2071i	−1.04524	+	0.759409i	−0.0739354	+	0.997263i	$0.523556\pi$
$402$	−40.5734	−	29.4783i	−2.02362	−	1.47025i
$403$	0.234260	+	0.170200i	0.0116693	+	0.00847825i
$404$	−43.8611	−	31.8669i	−2.18217	−	1.58544i
$405$	21.3756	−	15.5303i	1.06216	−	0.771706i
$406$	−20.9255	+	15.2033i	−1.03851	+	0.754525i
$407$	−13.8096			−0.684516
$408$	22.6893	+	16.4848i	1.12329	+	0.816118i
$409$	9.53475	+	6.92740i	0.471463	+	0.342538i	0.798011	−	0.602643i	$-0.205886\pi$
$409$	9.53475	+	6.92740i	0.471463	+	0.342538i	−0.326548	+	0.945181i	$0.605886\pi$
$410$	3.44296	+	10.5963i	0.170035	+	0.523315i
$411$	19.6351	+	60.4307i	0.968529	+	2.98082i
$412$	39.7455	−	28.8768i	1.95812	−	1.42266i
$413$	−8.85256	+	27.2454i	−0.435606	+	1.34066i
$414$	−31.1053	+	95.7324i	−1.52874	+	4.70499i
$415$	4.86464			0.238796
$416$	−0.839009	+	0.609576i	−0.0411358	+	0.0298869i
$417$	−7.35508	+	22.6366i	−0.360180	+	1.10852i
$418$	17.2448	+	12.5290i	0.843469	+	0.612816i
$419$	6.01662	+	18.5173i	0.293931	+	0.904628i	0.983578	+	0.180482i	$0.0577657\pi$
$419$	6.01662	+	18.5173i	0.293931	+	0.904628i	−0.689647	+	0.724146i	$0.742234\pi$
$420$	21.7984			1.06365
$421$	28.0429			1.36673			0.683364	−	0.730078i	$-0.260516\pi$
$421$	28.0429			1.36673			0.683364	+	0.730078i	$0.260516\pi$
$422$	−13.3479	−	41.0806i	−0.649765	−	1.99977i
$423$	−10.6519	−	32.7830i	−0.517911	−	1.59397i
$424$	−17.3456	−	12.6023i	−0.842377	−	0.612023i
$425$	−1.14888	+	3.53589i	−0.0557289	+	0.171516i
$426$	11.5459	+	35.5346i	0.559400	+	1.72166i
$427$	−1.40901	+	1.02371i	−0.0681868	+	0.0495406i
$428$	−0.491356	−	0.356991i	−0.0237506	−	0.0172558i
$429$	−1.56841	+	1.13952i	−0.0757236	+	0.0550164i
$430$	−22.8286			−1.10089
$431$	−6.98511	−	5.07498i	−0.336461	−	0.244453i	0.406706	−	0.913559i	$-0.366677\pi$
$431$	−6.98511	−	5.07498i	−0.336461	−	0.244453i	−0.743167	+	0.669106i	$0.766677\pi$
$432$	4.08763	+	12.5804i	0.196666	+	0.605277i
$433$	8.48588	−	26.1168i	0.407805	−	1.25510i	−0.510725	−	0.859744i	$-0.670623\pi$
$433$	8.48588	−	26.1168i	0.407805	−	1.25510i	0.918530	−	0.395351i	$-0.129377\pi$
$434$	9.09624			0.436634
$435$	−5.27104	+	16.2226i	−0.252727	+	0.777813i
$436$	−14.0645	−	43.2859i	−0.673565	−	2.07302i
$437$	−14.7894			−0.707473
$438$	−24.2498	−	74.6332i	−1.15870	−	3.56611i
$439$	1.15123	−	3.54311i	0.0549450	−	0.169103i	−0.919818	−	0.392345i	$-0.871664\pi$
$439$	1.15123	−	3.54311i	0.0549450	−	0.169103i	0.974763	+	0.223242i	$0.0716639\pi$
$440$	7.06441	−	5.13260i	0.336783	−	0.244687i
$441$	13.2124	−	9.59938i	0.629163	−	0.457114i
$442$	−1.06216	−	0.771704i	−0.0505218	−	0.0367062i
$443$	0.402178	−	1.23778i	0.0191081	−	0.0588085i	−0.941048	−	0.338274i	$-0.890157\pi$
$443$	0.402178	−	1.23778i	0.0191081	−	0.0588085i	0.960156	+	0.279465i	$0.0901571\pi$
$444$	−11.1743	+	34.3910i	−0.530310	+	1.63213i
$445$	−15.9275			−0.755036
$446$	−4.72046	+	14.5281i	−0.223520	+	0.687924i
$447$	22.8662	−	16.6133i	1.08153	−	0.785780i
$448$	−8.87560	+	27.3163i	−0.419333	+	1.29057i
$449$	−25.0356			−1.18150			−0.590752	−	0.806853i	$-0.701169\pi$
$449$	−25.0356			−1.18150			−0.590752	+	0.806853i	$0.701169\pi$
$450$	13.8597	−	10.0697i	0.653354	−	0.474689i
$451$	−18.7537			−0.883078
$452$	19.5842			0.921162
$453$	7.99586	+	39.2729i	0.375678	+	1.84520i
$454$	30.1266			1.41391
$455$	−0.347139			−0.0162741
$456$	15.3612	−	11.1606i	0.719354	−	0.522641i
$457$	−12.5712			−0.588054			−0.294027	−	0.955797i	$-0.594996\pi$
$457$	−12.5712			−0.588054			−0.294027	+	0.955797i	$0.594996\pi$
$458$	18.4846	−	56.8899i	0.863730	−	2.65829i
$459$	−45.4967	+	33.0553i	−2.12360	+	1.54289i
$460$	−5.50355	+	16.9382i	−0.256604	+	0.789747i
$461$	21.5696			1.00459			0.502297	−	0.864695i	$-0.332488\pi$
$461$	21.5696			1.00459			0.502297	+	0.864695i	$0.332488\pi$
$462$	−18.8194	+	57.9203i	−0.875560	+	2.69470i
$463$	3.76396	−	11.5843i	0.174926	−	0.538367i	−0.824704	−	0.565565i	$-0.808658\pi$
$463$	3.76396	−	11.5843i	0.174926	−	0.538367i	0.999630	+	0.0271975i	$0.00865830\pi$
$464$	−3.70004	−	2.68824i	−0.171770	−	0.124798i
$465$	4.85306	−	3.52595i	0.225055	−	0.163512i
$466$	12.1797	−	8.84905i	0.564213	−	0.409924i
$467$	10.8700	−	33.4543i	0.503002	−	1.54808i	−0.301101	−	0.953592i	$-0.597354\pi$
$467$	10.8700	−	33.4543i	0.503002	−	1.54808i	0.804103	−	0.594490i	$-0.202646\pi$
$468$	1.12631	+	3.46643i	0.0520638	+	0.160236i
$469$	15.1155			0.697969
$470$	−3.12820	−	9.62760i	−0.144293	−	0.444088i
$471$	−3.84151	+	11.8230i	−0.177008	+	0.544773i
$472$	30.0495			1.38314
$473$	11.8741	−	36.5446i	0.545970	−	1.68032i
$474$	12.4770	+	38.4001i	0.573086	+	1.76378i
$475$	2.03635	+	1.47950i	0.0934343	+	0.0678840i
$476$	−24.8481			−1.13891
$477$	57.2804	−	41.6167i	2.62269	−	1.90550i
$478$	−22.5514	−	16.3846i	−1.03148	−	0.749412i
$479$	16.9310	−	12.3011i	0.773595	−	0.562050i	−0.129455	−	0.991585i	$-0.541323\pi$
$479$	16.9310	−	12.3011i	0.773595	−	0.562050i	0.903050	+	0.429536i	$0.141323\pi$
$480$	6.63910	+	20.4330i	0.303032	+	0.932636i
$481$	0.177950	−	0.547675i	0.00811384	−	0.0249718i
$482$	−19.9092	−	14.4649i	−0.906841	−	0.658859i
$483$	−13.0574	−	40.1867i	−0.594134	−	1.82856i
$484$	3.04810	+	9.38108i	0.138550	+	0.426413i
$485$	7.73138			0.351064
$486$	91.5089			4.15093
$487$	5.24095	+	16.1300i	0.237490	+	0.730919i	0.996781	+	0.0801682i	$0.0255458\pi$
$487$	5.24095	+	16.1300i	0.237490	+	0.730919i	−0.759291	+	0.650751i	$0.774454\pi$
$488$	1.47797	+	1.07381i	0.0669046	+	0.0486090i
$489$	24.3815	−	75.0387i	1.10257	−	3.39337i
$490$	3.88017	−	2.81911i	0.175288	−	0.127354i
$491$	2.02042			0.0911801			0.0455900	−	0.998960i	$-0.485483\pi$
$491$	2.02042			0.0911801			0.0455900	+	0.998960i	$0.485483\pi$
$492$	−15.1750	+	46.7038i	−0.684141	+	2.10557i
$493$	6.00847	−	18.4922i	0.270608	−	0.832845i
$494$	−0.719106	+	0.522461i	−0.0323541	+	0.0235066i
$495$	8.91082	+	27.4247i	0.400512	+	1.23265i
$496$	0.497022	+	1.52968i	0.0223169	+	0.0686845i
$497$	−9.11048	−	6.61915i	−0.408661	−	0.296909i
$498$	28.7916	+	20.9183i	1.29018	+	0.937373i
$499$	3.85572			0.172606			0.0863028	−	0.996269i	$-0.472495\pi$
$499$	3.85572			0.172606			0.0863028	+	0.996269i	$0.472495\pi$
$500$	2.45224	−	1.78166i	0.109667	−	0.0796780i
$501$	8.76170	−	6.36574i	0.391444	−	0.284401i
$502$	−23.9389	−	17.3926i	−1.06845	−	0.776272i
$503$	−8.48961	−	6.16806i	−0.378533	−	0.275020i	0.382207	−	0.924077i	$-0.375164\pi$
$503$	−8.48961	−	6.16806i	−0.378533	−	0.275020i	−0.760740	+	0.649056i	$0.775164\pi$
$504$	31.5112	+	22.8942i	1.40362	+	1.01979i
$505$	14.4702	−	10.5132i	0.643915	−	0.467832i
$506$	−40.2547	−	29.2468i	−1.78954	−	1.30018i
$507$	13.0774	+	40.2481i	0.580788	+	1.78748i
$508$	−51.6083	+	37.4956i	−2.28975	+	1.66360i
$509$	3.05397	−	9.39916i	0.135365	−	0.416610i	−0.860282	−	0.509819i	$-0.829712\pi$
$509$	3.05397	−	9.39916i	0.135365	−	0.416610i	0.995647	+	0.0932086i	$0.0297123\pi$
$510$	−22.0043	+	15.9871i	−0.974366	+	0.707919i
$511$	19.1347	+	13.9022i	0.846470	+	0.614996i
$512$	−9.80570			−0.433355
$513$	11.7654	+	36.2102i	0.519456	+	1.59872i
$514$	3.42101	+	2.48551i	0.150894	+	0.109631i
$515$	5.00851	+	15.4146i	0.220701	+	0.679248i
$516$	−81.4016	−	59.1417i	−3.58351	−	2.60357i
$517$	17.0392			0.749384
$518$	−5.59011	−	17.2046i	−0.245616	−	0.755927i
$519$	20.7796			0.912125
$520$	0.112522	+	0.346307i	0.00493441	+	0.0151865i
$521$	5.74717	+	17.6880i	0.251788	+	0.774924i	0.994446	+	0.105253i	$0.0335652\pi$
$521$	5.74717	+	17.6880i	0.251788	+	0.774924i	−0.742657	+	0.669672i	$0.766435\pi$
$522$	−72.4843	+	52.6629i	−3.17255	+	2.30499i
$523$	−10.8378	−	7.87411i	−0.473903	−	0.344311i	0.325057	−	0.945694i	$-0.394616\pi$
$523$	−10.8378	−	7.87411i	−0.473903	−	0.344311i	−0.798961	+	0.601383i	$0.794616\pi$
$524$	6.04158	−	18.5941i	0.263928	−	0.812286i
$525$	−2.22230	+	6.83954i	−0.0969891	+	0.298502i
$526$	19.3529	−	59.5622i	0.843828	−	2.59704i
$527$	−5.53201	+	4.01924i	−0.240978	+	0.175081i
$528$	−10.7685			−0.468639
$529$	11.5232			0.501008
$530$	16.8219	−	12.2218i	0.730696	−	0.530882i
$531$	−30.6646	+	94.3759i	−1.33073	+	4.09556i
$532$	−5.19851	+	15.9994i	−0.225384	+	0.693660i
$533$	0.241660	−	0.743754i	0.0104675	−	0.0322156i
$534$	−94.2676	−	68.4894i	−4.07936	−	2.96383i
$535$	0.162103	−	0.117775i	0.00700833	−	0.00509185i
$536$	−4.89955	−	15.0793i	−0.211629	−	0.651326i
$537$	19.9664	+	61.4504i	0.861615	+	2.65178i
$538$	−28.2213			−1.21671
$539$	2.49468	+	7.67782i	0.107453	+	0.330707i
$540$	45.8495			1.97305
$541$	−6.58780	−	4.78632i	−0.283232	−	0.205780i	0.437094	−	0.899416i	$-0.356008\pi$
$541$	−6.58780	−	4.78632i	−0.283232	−	0.205780i	−0.720326	+	0.693636i	$0.756008\pi$
$542$	7.56418	+	23.2801i	0.324909	+	0.999968i
$543$	−6.75182	−	4.90548i	−0.289748	−	0.210514i
$544$	−7.56793	−	23.2917i	−0.324472	−	0.998623i
$545$	15.0154			0.643187
$546$	−2.05455	−	1.49272i	−0.0879268	−	0.0638826i
$547$	−11.7175	+	8.51328i	−0.501005	+	0.364002i	−0.809401	−	0.587257i	$-0.800208\pi$
$547$	−11.7175	+	8.51328i	−0.501005	+	0.364002i	0.308396	+	0.951258i	$0.400208\pi$
$548$	−18.2479	+	56.1614i	−0.779513	+	2.39910i
$549$	−4.88070	+	3.54604i	−0.208303	+	0.151341i
$550$	2.61690	+	8.05398i	0.111585	+	0.343423i
$551$	−10.6498	−	7.73755i	−0.453698	−	0.329631i
$552$	−35.8579	+	26.0523i	−1.52621	+	1.10886i
$553$	−9.84516	−	7.15292i	−0.418659	−	0.304173i
$554$	31.0144	+	22.5333i	1.31768	+	0.957348i
$555$	−9.65143	−	7.01217i	−0.409680	−	0.297650i
$556$	−17.8955	+	13.0018i	−0.758937	+	0.551400i
$557$	31.1383	−	22.6233i	1.31937	−	0.958579i	0.319431	−	0.947609i	$-0.396508\pi$
$557$	31.1383	−	22.6233i	1.31937	−	0.958579i	0.999940	−	0.0109700i	$-0.00349191\pi$
$558$	31.5087			1.33387
$559$	1.29631	+	0.941828i	0.0548283	+	0.0398351i
$560$	−1.55996	−	1.13338i	−0.0659203	−	0.0478939i
$561$	−14.1472	−	43.5406i	−0.597295	−	1.83828i
$562$	−14.3186	−	44.0680i	−0.603992	−	1.85890i
$563$	−20.4482	+	14.8565i	−0.861790	+	0.626127i	−0.928371	−	0.371654i	$-0.878791\pi$
$563$	−20.4482	+	14.8565i	−0.861790	+	0.626127i	0.0665812	+	0.997781i	$0.478791\pi$
$564$	13.7877	−	42.4340i	0.580565	−	1.78680i
$565$	−1.99656	+	6.14478i	−0.0839959	+	0.258513i
$566$	−68.6489			−2.88553
$567$	−47.1318	+	34.2433i	−1.97935	+	1.43808i
$568$	−3.65021	+	11.2342i	−0.153159	+	0.471376i
$569$	−17.0649	−	12.3984i	−0.715400	−	0.519768i	0.169512	−	0.985528i	$-0.445781\pi$
$569$	−17.0649	−	12.3984i	−0.715400	−	0.519768i	−0.884911	+	0.465760i	$0.845781\pi$
$570$	5.69030	+	17.5129i	0.238340	+	0.733536i
$571$	−25.7800			−1.07886			−0.539430	−	0.842030i	$-0.681360\pi$
$571$	−25.7800			−1.07886			−0.539430	+	0.842030i	$0.681360\pi$
$572$	−1.80170			−0.0753330
$573$	8.25990	+	25.4214i	0.345062	+	1.06199i
$574$	−7.59150	−	23.3642i	−0.316863	−	0.975204i
$575$	−4.75350	−	3.45362i	−0.198234	−	0.144026i
$576$	−30.7444	+	94.6216i	−1.28102	+	3.94257i
$577$	5.96650	+	18.3630i	0.248389	+	0.764462i	0.995061	+	0.0992693i	$0.0316505\pi$
$577$	5.96650	+	18.3630i	0.248389	+	0.764462i	−0.746672	+	0.665193i	$0.768349\pi$
$578$	−5.76613	+	4.18934i	−0.239839	+	0.174253i
$579$	45.6267	+	33.1497i	1.89618	+	1.37765i
$580$	−12.8248	+	9.31779i	−0.532522	+	0.386900i
$581$	−10.7262			−0.444999
$582$	45.7585	+	33.2455i	1.89675	+	1.37807i
$583$	10.8153	+	33.2860i	0.447923	+	1.37857i
$584$	7.66652	−	23.5951i	0.317243	−	0.976373i
$585$	−1.20246			−0.0497157
$586$	9.69746	−	29.8457i	0.400598	−	1.23292i
$587$	−8.26708	−	25.4435i	−0.341219	−	1.05016i	−0.963577	−	0.267431i	$-0.913825\pi$
$587$	−8.26708	−	25.4435i	−0.341219	−	1.05016i	0.622358	−	0.782733i	$-0.286175\pi$
$588$	21.1393			0.871769
$589$	1.43058	+	4.40286i	0.0589459	+	0.181417i
$590$	−9.00545	+	27.7159i	−0.370749	+	1.14105i
$591$	66.0477	−	47.9864i	2.71684	−	1.97390i
$592$	2.58778	−	1.88013i	0.106357	−	0.0772729i
$593$	−13.9400	−	10.1280i	−0.572449	−	0.415909i	0.263545	−	0.964647i	$-0.415108\pi$
$593$	−13.9400	−	10.1280i	−0.572449	−	0.415909i	−0.835994	+	0.548738i	$0.815108\pi$
$594$	−39.5837	+	121.826i	−1.62414	+	4.99858i
$595$	2.53321	−	7.79641i	0.103851	−	0.319622i
$596$	26.2674			1.07595
$597$	17.4241	−	53.6258i	0.713120	−	2.19476i
$598$	1.67862	−	1.21959i	0.0686440	−	0.0498728i
$599$	−5.11040	+	15.7282i	−0.208805	+	0.642637i	0.790730	+	0.612165i	$0.209701\pi$
$599$	−5.11040	+	15.7282i	−0.208805	+	0.642637i	−0.999536	+	0.0304722i	$0.990299\pi$
$600$	7.54348			0.307961
$601$	−33.1035	+	24.0511i	−1.35032	+	0.981064i	−0.351324	+	0.936254i	$0.614268\pi$
$601$	−33.1035	+	24.0511i	−1.35032	+	0.981064i	−0.998996	+	0.0448103i	$0.985732\pi$
$602$	50.3355			2.05152
$603$	52.3590			2.13222
$604$	−15.4414	+	33.8956i	−0.628303	+	1.37919i
$605$	−3.25418			−0.132301
$606$	130.850			5.31542
$607$	−9.22665	+	6.70356i	−0.374498	+	0.272089i	−0.759074	−	0.651005i	$-0.774348\pi$
$607$	−9.22665	+	6.70356i	−0.374498	+	0.272089i	0.384575	+	0.923094i	$0.374348\pi$
$608$	−16.5805			−0.672428
$609$	11.6223	−	35.7697i	0.470959	−	1.44946i
$610$	−1.43335	+	1.04139i	−0.0580345	+	0.0421645i
$611$	−0.219567	+	0.675759i	−0.00888275	+	0.0273383i
$612$	−86.0719			−3.47925
$613$	−11.7381	+	36.1262i	−0.474098	+	1.45912i	0.373072	+	0.927802i	$0.378304\pi$
$613$	−11.7381	+	36.1262i	−0.474098	+	1.45912i	−0.847170	+	0.531322i	$0.821696\pi$
$614$	−6.16888	+	18.9859i	−0.248956	+	0.766207i
$615$	−13.1069	−	9.52268i	−0.528519	−	0.383992i
$616$	−15.5766	+	11.3170i	−0.627598	+	0.455977i
$617$	−31.7388	+	23.0596i	−1.27776	+	0.928345i	−0.999483	−	0.0321572i	$-0.989762\pi$
$617$	−31.7388	+	23.0596i	−1.27776	+	0.928345i	−0.278274	+	0.960502i	$0.589762\pi$
$618$	−36.6408	+	112.769i	−1.47391	+	4.53623i
$619$	4.39003	+	13.5111i	0.176450	+	0.543058i	0.999697	−	0.0246261i	$-0.00783953\pi$
$619$	4.39003	+	13.5111i	0.176450	+	0.543058i	−0.823247	+	0.567684i	$0.807840\pi$
$620$	5.57491			0.223894
$621$	−27.4642	−	84.5262i	−1.10210	−	3.39192i
$622$	15.0723	−	46.3878i	0.604344	−	1.85998i
$623$	35.1191			1.40702
$624$	0.138763	−	0.427069i	0.00555497	−	0.0170964i
$625$	0.309017	+	0.951057i	0.0123607	+	0.0380423i
$626$	15.5484	+	11.2966i	0.621439	+	0.451502i
$627$	−30.9949			−1.23782
$628$	−9.34669	+	6.79077i	−0.372974	+	0.270981i
$629$	11.0017	+	7.99320i	0.438666	+	0.318710i
$630$	−30.5598	+	22.2030i	−1.21753	+	0.884589i
$631$	−1.18588	−	3.64977i	−0.0472092	−	0.145295i	0.924673	−	0.380762i	$-0.124338\pi$
$631$	−1.18588	−	3.64977i	−0.0472092	−	0.145295i	−0.971882	+	0.235467i	$0.924338\pi$
$632$	−3.94456	+	12.1401i	−0.156906	+	0.482908i
$633$	50.8135	+	36.9182i	2.01966	+	1.46737i
$634$	−5.17801	−	15.9363i	−0.205645	−	0.632910i
$635$	−6.50339	−	20.0154i	−0.258079	−	0.794286i
$636$	91.6461			3.63400
$637$	−0.336641			−0.0133382
$638$	−13.6860	−	42.1211i	−0.541833	−	1.66759i
$639$	−31.5580	−	22.9282i	−1.24842	−	0.907027i
$640$	−4.95777	+	15.2585i	−0.195973	+	0.603144i
$641$	7.04031	−	5.11509i	0.278076	−	0.202034i	−0.440002	−	0.897997i	$-0.645022\pi$
$641$	7.04031	−	5.11509i	0.278076	−	0.202034i	0.718078	+	0.695963i	$0.245022\pi$
$642$	1.46586			0.0578527
$643$	8.63100	−	26.5635i	0.340374	−	1.04756i	−0.623641	−	0.781711i	$-0.714347\pi$
$643$	8.63100	−	26.5635i	0.340374	−	1.04756i	0.964014	−	0.265851i	$-0.0856529\pi$
$644$	12.1350	−	37.3476i	0.478185	−	1.47170i
$645$	26.8552	−	19.5114i	1.05742	−	0.768262i
$646$	−6.48639	−	19.9631i	−0.255204	−	0.785436i
$647$	5.56980	+	17.1421i	0.218971	+	0.673925i	0.998848	+	0.0479912i	$0.0152819\pi$
$647$	5.56980	+	17.1421i	0.218971	+	0.673925i	−0.779876	+	0.625934i	$0.784718\pi$
$648$	49.4386	+	35.9192i	1.94213	+	1.41104i
$649$	−39.6843	−	28.8324i	−1.55775	−	1.13177i
$650$	−0.353134			−0.0138511
$651$	−10.7007	+	7.77450i	−0.419393	+	0.304707i
$652$	59.3222	−	43.1001i	2.32324	−	1.68793i
$653$	−22.3649	−	16.2491i	−0.875206	−	0.635875i	0.0567727	−	0.998387i	$-0.481919\pi$
$653$	−22.3649	−	16.2491i	−0.875206	−	0.635875i	−0.931979	+	0.362513i	$0.881919\pi$
$654$	88.8691	+	64.5671i	3.47506	+	2.52478i
$655$	5.21821	+	3.79125i	0.203892	+	0.148136i
$656$	3.51426	−	2.55326i	0.137209	−	0.0996880i
$657$	66.2812	+	48.1561i	2.58587	+	1.87875i
$658$	6.89747	+	21.2282i	0.268891	+	0.827563i
$659$	−0.763969	+	0.555056i	−0.0297600	+	0.0216219i	−0.602566	−	0.798069i	$-0.705855\pi$
$659$	−0.763969	+	0.555056i	−0.0297600	+	0.0216219i	0.572806	+	0.819691i	$0.305855\pi$
$660$	−11.5341	+	35.4982i	−0.448963	+	1.38177i
$661$	15.5434	−	11.2930i	0.604569	−	0.439245i	−0.242929	−	0.970044i	$-0.578108\pi$
$661$	15.5434	−	11.2930i	0.604569	−	0.439245i	0.847498	+	0.530799i	$0.178108\pi$
$662$	−38.2163	−	27.7658i	−1.48532	−	1.07915i
$663$	1.90908			0.0741425
$664$	3.47681	+	10.7005i	0.134926	+	0.415261i
$665$	−4.49003	−	3.26219i	−0.174116	−	0.126502i
$666$	−19.3637	−	59.5954i	−0.750329	−	2.30928i
$667$	24.8601	+	18.0619i	0.962586	+	0.699359i
$668$	10.0649			0.389424
$669$	−6.86397	−	21.1251i	−0.265377	−	0.816745i
$670$	15.3766			0.594049
$671$	−0.921540	−	2.83621i	−0.0355757	−	0.109491i
$672$	−14.6388	−	45.0535i	−0.564703	−	1.73798i
$673$	12.4770	−	9.06505i	0.480952	−	0.349432i	−0.320742	−	0.947167i	$-0.603932\pi$
$673$	12.4770	−	9.06505i	0.480952	−	0.349432i	0.801694	+	0.597735i	$0.203932\pi$
$674$	58.3345	+	42.3825i	2.24696	+	1.63251i
$675$	−4.67425	+	14.3859i	−0.179912	+	0.553712i
$676$	−12.1535	+	37.4047i	−0.467443	+	1.43864i
$677$	15.8963	−	48.9239i	0.610946	−	1.88030i	0.161844	−	0.986816i	$-0.448256\pi$
$677$	15.8963	−	48.9239i	0.610946	−	1.88030i	0.449102	−	0.893481i	$-0.351744\pi$
$678$	−38.2398	+	27.7828i	−1.46859	+	1.06699i
$679$	−17.0472			−0.654211
$680$	−8.59884			−0.329750
$681$	−35.4404	+	25.7490i	−1.35808	+	0.986702i
$682$	−4.81304	+	14.8130i	−0.184301	+	0.567220i
$683$	6.89372	−	21.2167i	0.263781	−	0.811833i	−0.728191	−	0.685374i	$-0.759639\pi$
$683$	6.89372	−	21.2167i	0.263781	−	0.811833i	0.991972	−	0.126459i	$-0.0403613\pi$
$684$	−18.0072	+	55.4205i	−0.688524	+	2.11906i
$685$	−15.7610	−	11.4510i	−0.602198	−	0.437522i
$686$	−36.5637	+	26.5651i	−1.39601	+	1.01426i
$687$	26.8783	+	82.7230i	1.02547	+	3.15608i
$688$	2.75035	+	8.46471i	0.104856	+	0.322714i
$689$	−1.45946			−0.0556009
$690$	−13.2830	−	40.8808i	−0.505674	−	1.55630i
$691$	−14.9324			−0.568054			−0.284027	−	0.958816i	$-0.591671\pi$
$691$	−14.9324			−0.568054			−0.284027	+	0.958816i	$0.591671\pi$
$692$	15.6234	+	11.3511i	0.593913	+	0.431503i
$693$	−19.6478	−	60.4697i	−0.746358	−	2.29705i
$694$	31.7182	+	23.0446i	1.20401	+	0.874761i
$695$	−2.25508	−	6.94044i	−0.0855402	−	0.263266i
$696$	−39.4513			−1.49540
$697$	14.9405	+	10.8549i	0.565913	+	0.411160i
$698$	11.6650	−	8.47514i	0.441528	−	0.320789i
$699$	−6.76475	+	20.8198i	−0.255866	+	0.787476i
$700$	−5.40703	+	3.92843i	−0.204366	+	0.148481i
$701$	−4.56594	−	14.0525i	−0.172453	−	0.530757i	0.827055	−	0.562122i	$-0.190015\pi$
$701$	−4.56594	−	14.0525i	−0.172453	−	0.530757i	−0.999508	+	0.0313647i	$0.990015\pi$
$702$	−4.32143	−	3.13970i	−0.163102	−	0.118500i
$703$	7.44839	−	5.41157i	0.280921	−	0.204101i
$704$	−39.7877	−	28.9074i	−1.49955	−	1.08949i
$705$	11.9086	+	8.65211i	0.448504	+	0.325857i
$706$	−20.2135	−	14.6859i	−0.760743	−	0.552712i
$707$	−31.9058	+	23.1809i	−1.19994	+	0.871809i
$708$	−103.915	+	75.4985i	−3.90536	+	2.83741i
$709$	−39.7234			−1.49184			−0.745922	−	0.666034i	$-0.767991\pi$
$709$	−39.7234			−1.49184			−0.745922	+	0.666034i	$0.767991\pi$
$710$	−9.26783	−	6.73347i	−0.347816	−	0.252703i
$711$	−34.1029	−	24.7772i	−1.27896	−	0.929217i
$712$	−11.3835	−	35.0349i	−0.426616	−	1.31299i
$713$	−3.33942	−	10.2777i	−0.125062	−	0.384902i
$714$	48.5180	−	35.2504i	1.81574	−	1.31921i
$715$	0.183679	−	0.565307i	0.00686922	−	0.0211413i
$716$	−18.5559	+	57.1091i	−0.693465	+	2.13427i
$717$	40.5329			1.51373
$718$	30.4997	−	22.1593i	1.13824	−	0.826978i
$719$	13.5609	−	41.7363i	0.505738	−	1.55650i	−0.293789	−	0.955870i	$-0.594916\pi$
$719$	13.5609	−	41.7363i	0.505738	−	1.55650i	0.799527	−	0.600630i	$-0.205084\pi$
$720$	−5.40358	−	3.92593i	−0.201380	−	0.146311i
$721$	−11.0434	−	33.9882i	−0.411279	−	1.26579i
$722$	28.4064			1.05718
$723$	35.7840			1.33082
$724$	−2.39677	−	7.37649i	−0.0890751	−	0.274145i
$725$	−1.61611	−	4.97388i	−0.0600209	−	0.184725i
$726$	−19.2600	−	13.9932i	−0.714806	−	0.519337i
$727$	−9.23877	+	28.4340i	−0.342647	+	1.05456i	0.620184	+	0.784456i	$0.287058\pi$
$727$	−9.23877	+	28.4340i	−0.342647	+	1.05456i	−0.962831	+	0.270103i	$0.912942\pi$
$728$	−0.248103	−	0.763583i	−0.00919532	−	0.0283003i
$729$	−43.5228	+	31.6211i	−1.61195	+	1.17115i
$730$	19.4652	+	14.1423i	0.720439	+	0.523430i
$731$	−30.6123	+	22.2411i	−1.13224	+	0.822618i
$732$	−7.80890			−0.288625
$733$	−11.1921	−	8.13154i	−0.413390	−	0.300345i	0.361583	−	0.932340i	$-0.382236\pi$
$733$	−11.1921	−	8.13154i	−0.413390	−	0.300345i	−0.774973	+	0.631995i	$0.782236\pi$
$734$	−9.02989	−	27.7911i	−0.333299	−	1.02579i
$735$	−2.15510	+	6.63271i	−0.0794920	+	0.244651i
$736$	38.7042			1.42665
$737$	−7.99798	+	24.6153i	−0.294609	+	0.906715i
$738$	−26.2964	−	80.9319i	−0.967983	−	2.97914i
$739$	−23.2323			−0.854614			−0.427307	−	0.904107i	$-0.640538\pi$
$739$	−23.2323			−0.854614			−0.427307	+	0.904107i	$0.640538\pi$
$740$	−3.42608	−	10.5444i	−0.125945	−	0.387619i
$741$	0.399401	−	1.22923i	0.0146724	−	0.0451569i
$742$	−37.0912	+	26.9483i	−1.36166	+	0.989304i
$743$	−4.86031	+	3.53122i	−0.178307	+	0.129548i	−0.673359	−	0.739316i	$-0.735149\pi$
$743$	−4.86031	+	3.53122i	−0.178307	+	0.129548i	0.495052	+	0.868864i	$0.335149\pi$
$744$	11.2244	+	8.15500i	0.411506	+	0.298977i
$745$	−2.67790	+	8.24173i	−0.0981106	+	0.301953i
$746$	8.25073	−	25.3931i	0.302081	−	0.929709i
$747$	−37.1548			−1.35942
$748$	13.1477	−	40.4646i	0.480729	−	1.47953i
$749$	−0.357427	+	0.259686i	−0.0130601	+	0.00948872i
$750$	−2.26068	+	6.95767i	−0.0825485	+	0.254058i
$751$	30.5466			1.11466			0.557330	−	0.830291i	$-0.311826\pi$
$751$	30.5466			1.11466			0.557330	+	0.830291i	$0.311826\pi$
$752$	−3.19298	+	2.31984i	−0.116436	+	0.0845957i
$753$	43.0267			1.56798
$754$	1.84684			0.0672579
$755$	−9.06097	−	8.30053i	−0.329763	−	0.302087i
$756$	−101.095			−3.67680
$757$	−41.2490			−1.49922			−0.749611	−	0.661879i	$-0.769759\pi$
$757$	−41.2490			−1.49922			−0.749611	+	0.661879i	$0.769759\pi$
$758$	−14.1531	+	10.2828i	−0.514064	+	0.373489i
$759$	72.3521			2.62621
$760$	−1.79897	+	5.53668i	−0.0652557	+	0.200836i
$761$	−23.5151	+	17.0847i	−0.852421	+	0.619320i	−0.925813	−	0.377983i	$-0.876618\pi$
$761$	−23.5151	+	17.0847i	−0.852421	+	0.619320i	0.0733913	+	0.997303i	$0.476618\pi$
$762$	47.5770	−	146.427i	1.72353	−	5.30449i
$763$	−33.1079			−1.19859
$764$	−7.67636	+	23.6254i	−0.277721	+	0.854738i
$765$	8.77483	−	27.0062i	0.317255	−	0.976410i
$766$	42.4714	+	30.8572i	1.53455	+	1.11492i
$767$	1.65484	−	1.20231i	0.0597527	−	0.0434129i
$768$	−26.2118	+	19.0440i	−0.945838	+	0.687191i
$769$	0.261405	−	0.804523i	0.00942652	−	0.0290118i	−0.946233	−	0.323487i	$-0.895145\pi$
$769$	0.261405	−	0.804523i	0.00942652	−	0.0290118i	0.955659	+	0.294475i	$0.0951448\pi$
$770$	−5.77009	−	17.7585i	−0.207939	−	0.639972i
$771$	−6.14877			−0.221442
$772$	16.1966	+	49.8480i	0.582928	+	1.79407i
$773$	10.0816	−	31.0280i	0.362610	−	1.11600i	−0.588853	−	0.808240i	$-0.700420\pi$
$773$	10.0816	−	31.0280i	0.362610	−	1.11600i	0.951464	−	0.307760i	$-0.0995795\pi$
$774$	174.358			6.26718
$775$	−0.568350	+	1.74920i	−0.0204157	+	0.0628331i
$776$	5.52569	+	17.0063i	0.198361	+	0.610492i
$777$	21.2808	+	15.4614i	0.763444	+	0.554674i
$778$	−21.8942			−0.784947
$779$	10.1151	−	7.34904i	0.362410	−	0.263307i
$780$	−1.25920	−	0.914861i	−0.0450865	−	0.0327573i
$781$	15.5997	−	11.3339i	0.558201	−	0.405557i
$782$	15.1413	+	46.6001i	0.541452	+	1.66642i
$783$	24.4456	−	75.2359i	0.873616	−	2.68871i
$784$	−1.51279	−	1.09911i	−0.0540282	−	0.0392538i
$785$	−1.17782	−	3.62495i	−0.0420381	−	0.129380i
$786$	14.5815	+	44.8774i	0.520106	+	1.60072i
$787$	−17.9645			−0.640366			−0.320183	−	0.947356i	$-0.603744\pi$
$787$	−17.9645			−0.640366			−0.320183	+	0.947356i	$0.603744\pi$
$788$	75.8718			2.70282
$789$	28.1409	+	86.6089i	1.00184	+	3.08336i
$790$	−10.0152	−	7.27647i	−0.356325	−	0.258885i
$791$	4.40229	−	13.5488i	0.156527	−	0.481742i
$792$	−53.9561	+	39.2014i	−1.91725	+	1.39296i
$793$	0.124356			0.00441602
$794$	−24.2362	+	74.5913i	−0.860110	+	2.64715i
$795$	−9.34310	+	28.7551i	−0.331366	+	1.01984i
$796$	42.3941	−	30.8011i	1.50262	−	1.09172i
$797$	−3.09253	−	9.51782i	−0.109543	−	0.337138i	0.881227	−	0.472693i	$-0.156718\pi$
$797$	−3.09253	−	9.51782i	−0.109543	−	0.337138i	−0.990770	+	0.135555i	$0.956718\pi$
$798$	−12.5467	−	38.6149i	−0.444150	−	1.36695i
$799$	−13.5747	−	9.86256i	−0.480237	−	0.348912i
$800$	−5.32917	−	3.87187i	−0.188415	−	0.136891i
$801$	121.650			4.29829
$802$	46.9483	−	34.1099i	1.65780	−	1.20446i
$803$	−32.7640	+	23.8045i	−1.15622	+	0.840041i
$804$	54.8294	+	39.8359i	1.93369	+	1.40490i
$805$	10.4812	+	7.61500i	0.369412	+	0.268394i
$806$	−0.525449	−	0.381761i	−0.0185082	−	0.0134470i
$807$	33.1991	−	24.1205i	1.16866	−	0.849083i
$808$	33.4674	+	24.3155i	1.17738	+	0.855415i
$809$	−9.90046	−	30.4705i	−0.348082	−	1.07129i	−0.959913	−	0.280297i	$-0.909567\pi$
$809$	−9.90046	−	30.4705i	−0.348082	−	1.07129i	0.611832	−	0.790988i	$-0.290433\pi$
$810$	−47.9459	+	34.8347i	−1.68465	+	1.22397i
$811$	10.5387	−	32.4348i	0.370064	−	1.13894i	−0.576684	−	0.816967i	$-0.695654\pi$
$811$	10.5387	−	32.4348i	0.370064	−	1.13894i	0.946749	−	0.321974i	$-0.104346\pi$
$812$	28.2779	−	20.5451i	0.992361	−	0.720992i
$813$	−28.7958	−	20.9213i	−1.00991	−	0.733744i
$814$	30.9752			1.08568
$815$	7.47544	+	23.0070i	0.261853	+	0.805901i
$816$	8.57896	+	6.23298i	0.300324	+	0.218198i
$817$	7.91633	+	24.3639i	0.276957	+	0.852386i
$818$	−21.3866	−	15.5383i	−0.747765	−	0.543283i
$819$	2.65135			0.0926456
$820$	−4.65268	−	14.3195i	−0.162479	−	0.500058i
$821$	38.0630			1.32841			0.664203	−	0.747552i	$-0.268771\pi$
$821$	38.0630			1.32841			0.664203	+	0.747552i	$0.268771\pi$
$822$	−44.0419	−	135.547i	−1.53614	−	4.72775i
$823$	3.93143	+	12.0997i	0.137041	+	0.421769i	0.995902	−	0.0904399i	$-0.0288273\pi$
$823$	3.93143	+	12.0997i	0.137041	+	0.421769i	−0.858861	+	0.512209i	$0.828827\pi$
$824$	−30.3271	+	22.0339i	−1.05649	+	0.767588i
$825$	−9.96215	−	7.23793i	−0.346838	−	0.251992i
$826$	19.8564	−	61.1119i	0.690894	−	2.12635i
$827$	−5.61628	+	17.2851i	−0.195297	+	0.601063i	0.804676	+	0.593715i	$0.202339\pi$
$827$	−5.61628	+	17.2851i	−0.195297	+	0.601063i	−0.999973	+	0.00734862i	$0.997661\pi$
$828$	42.0346	−	129.369i	1.46080	−	4.49589i
$829$	43.0762	−	31.2967i	1.49610	−	1.08698i	0.524195	−	0.851598i	$-0.324366\pi$
$829$	43.0762	−	31.2967i	1.49610	−	1.08698i	0.971903	−	0.235381i	$-0.0756336\pi$
$830$	−10.9115			−0.378743
$831$	−55.7440			−1.93374
$832$	1.65914	−	1.20544i	0.0575205	−	0.0417911i
$833$	2.45660	−	7.56065i	0.0851163	−	0.261961i
$834$	16.4976	−	50.7743i	0.571264	−	1.75817i
$835$	−1.02610	+	3.15800i	−0.0355096	+	0.109287i
$836$	−23.3039	−	16.9313i	−0.805983	−	0.585581i
$837$	−22.5072	+	16.3524i	−0.777961	+	0.565222i
$838$	−13.4954	−	41.5346i	−0.466191	−	1.43479i
$839$	2.67097	+	8.22040i	0.0922122	+	0.283800i	0.986517	−	0.163658i	$-0.0523294\pi$
$839$	2.67097	+	8.22040i	0.0922122	+	0.283800i	−0.894305	+	0.447458i	$0.852329\pi$
$840$	−16.6329			−0.573889
$841$	−0.509467	−	1.56798i	−0.0175678	−	0.0540682i
$842$	−62.9008			−2.16770
$843$	54.5087	+	39.6029i	1.87738	+	1.36400i
$844$	18.0378	+	55.5148i	0.620888	+	1.91090i
$845$	−10.4972	−	7.62664i	−0.361114	−	0.262364i
$846$	23.8923	+	73.5330i	0.821435	+	2.52812i
$847$	7.17526			0.246545
$848$	−6.55846	−	4.76500i	−0.225219	−	0.163631i
$849$	80.7575	−	58.6738i	2.77159	−	2.01368i
$850$	2.57696	−	7.93107i	0.0883890	−	0.272033i
$851$	−17.3869	+	12.6323i	−0.596016	+	0.433031i
$852$	−15.6027	−	48.0201i	−0.534539	−	1.64514i
$853$	−38.4322	−	27.9226i	−1.31589	−	0.956051i	−0.999974	−	0.00726499i	$-0.997687\pi$
$853$	−38.4322	−	27.9226i	−1.31589	−	0.956051i	−0.315918	−	0.948786i	$-0.602313\pi$
$854$	3.16044	−	2.29619i	0.108148	−	0.0785740i
$855$	−15.5531	−	11.3000i	−0.531905	−	0.386452i
$856$	0.374920	+	0.272396i	0.0128145	+	0.00931029i
$857$	−10.6400	−	7.73041i	−0.363455	−	0.264066i	0.391036	−	0.920375i	$-0.372117\pi$
$857$	−10.6400	−	7.73041i	−0.363455	−	0.264066i	−0.754492	+	0.656309i	$0.772117\pi$
$858$	3.51798	−	2.55596i	0.120102	−	0.0872590i
$859$	3.73774	−	2.71562i	0.127530	−	0.0926559i	−0.522192	−	0.852828i	$-0.674885\pi$
$859$	3.73774	−	2.71562i	0.127530	−	0.0926559i	0.649722	+	0.760172i	$0.274885\pi$
$860$	30.8497			1.05197
$861$	28.8998	+	20.9969i	0.984901	+	0.715573i
$862$	15.6677	+	11.3833i	0.533645	+	0.387716i
$863$	0.770156	+	2.37030i	0.0262164	+	0.0806858i	0.963309	−	0.268396i	$-0.0864935\pi$
$863$	0.770156	+	2.37030i	0.0262164	+	0.0806858i	−0.937092	+	0.349082i	$0.886494\pi$
$864$	−30.7903	−	94.7629i	−1.04751	−	3.22390i
$865$	−5.15432	+	3.74483i	−0.175252	+	0.127328i
$866$	−19.0340	+	58.5806i	−0.646801	+	1.99065i
$867$	3.20258	−	9.85654i	0.108765	−	0.334746i
$868$	−12.2923			−0.417229
$869$	16.8577	−	12.2478i	0.571858	−	0.415479i
$870$	11.8230	−	36.3876i	0.400838	−	1.23365i
$871$	−0.873155	−	0.634384i	−0.0295857	−	0.0214953i
$872$	10.7316	+	33.0285i	0.363419	+	1.11849i
$873$	−59.0502			−1.99855
$874$	33.1729			1.12209
$875$	−0.681363	−	2.09702i	−0.0230343	−	0.0708922i
$876$	32.7703	+	100.857i	1.10720	+	3.40763i
$877$	−7.59796	−	5.52024i	−0.256565	−	0.186405i	0.452066	−	0.891984i	$-0.350687\pi$
$877$	−7.59796	−	5.52024i	−0.256565	−	0.186405i	−0.708631	+	0.705579i	$0.750687\pi$
$878$	−2.58222	+	7.94726i	−0.0871458	+	0.268207i
$879$	14.1010	+	43.3984i	0.475615	+	1.46379i
$880$	2.67109	−	1.94066i	0.0900425	−	0.0654197i
$881$	−14.2566	−	10.3580i	−0.480316	−	0.348970i	0.321132	−	0.947034i	$-0.395937\pi$
$881$	−14.2566	−	10.3580i	−0.480316	−	0.348970i	−0.801448	+	0.598065i	$0.795937\pi$
$882$	−29.6357	+	21.5316i	−0.997886	+	0.725007i
$883$	9.50378			0.319828			0.159914	−	0.987131i	$-0.448878\pi$
$883$	9.50378			0.319828			0.159914	+	0.987131i	$0.448878\pi$
$884$	1.43536	+	1.04285i	0.0482765	+	0.0350749i
$885$	−13.0947	−	40.3015i	−0.440175	−	1.35472i
$886$	−0.902093	+	2.77636i	−0.0303064	+	0.0932735i
$887$	37.9394			1.27388			0.636940	−	0.770913i	$-0.280200\pi$
$887$	37.9394			1.27388			0.636940	+	0.770913i	$0.280200\pi$
$888$	8.52636	−	26.2414i	0.286126	−	0.880605i
$889$	14.3395	+	44.1326i	0.480933	+	1.48016i
$890$	35.7257			1.19753
$891$	−30.8258	−	94.8720i	−1.03270	−	3.17833i
$892$	6.37905	−	19.6327i	0.213586	−	0.657351i
$893$	−9.19034	+	6.67718i	−0.307543	+	0.223443i
$894$	−51.2893	+	37.2639i	−1.71537	+	1.24629i
$895$	−16.0270	−	11.6443i	−0.535723	−	0.389225i
$896$	10.9316	−	33.6439i	0.365198	−	1.12396i
$897$	−0.932329	+	2.86941i	−0.0311296	+	0.0958069i
$898$	56.1554			1.87393
$899$	2.97238	−	9.14806i	0.0991345	−	0.305105i
$900$	−18.7295	+	13.6078i	−0.624317	+	0.453593i
$901$	10.6502	−	32.7780i	0.354811	−	1.09200i
$902$	42.0649			1.40061
$903$	−59.2139	+	43.0214i	−1.97052	+	1.43166i
$904$	−14.9433			−0.497008
$905$	2.55881			0.0850578
$906$	−17.9349	−	88.0899i	−0.595846	−	2.92659i
$907$	−48.6362			−1.61494			−0.807469	−	0.589911i	$-0.799163\pi$
$907$	−48.6362			−1.61494			−0.807469	+	0.589911i	$0.799163\pi$
$908$	−40.7119			−1.35107
$909$	−110.519	+	80.2970i	−3.66570	+	2.66328i
$910$	0.778638			0.0258116
$911$	−11.0790	+	34.0977i	−0.367064	+	1.12971i	0.581614	+	0.813465i	$0.302421\pi$
$911$	−11.0790	+	34.0977i	−0.367064	+	1.12971i	−0.948678	+	0.316243i	$0.897579\pi$
$912$	5.80814	−	4.21986i	0.192327	−	0.139734i
$913$	5.67551	−	17.4674i	0.187832	−	0.578087i
$914$	28.1973			0.932685
$915$	0.796100	−	2.45014i	0.0263182	−	0.0809992i
$916$	−24.9795	+	76.8788i	−0.825344	+	2.54015i
$917$	−11.5058	−	8.35946i	−0.379955	−	0.276054i
$918$	102.050	−	74.1436i	3.36815	−	2.44710i
$919$	−1.47540	+	1.07194i	−0.0486690	+	0.0353601i	−0.611854	−	0.790971i	$-0.709576\pi$
$919$	−1.47540	+	1.07194i	−0.0486690	+	0.0353601i	0.563185	+	0.826331i	$0.309576\pi$
$920$	4.19938	−	12.9244i	0.138449	−	0.426104i
$921$	−8.97011	−	27.6072i	−0.295575	−	0.909687i
$922$	−48.3809			−1.59334
$923$	0.248472	+	0.764717i	0.00817855	+	0.0251710i
$924$	25.4319	−	78.2713i	0.836648	−	2.57494i
$925$	3.65771			0.120265
$926$	−8.44263	+	25.9838i	−0.277442	+	0.853879i
$927$	−38.2536	−	117.732i	−1.25641	−	3.86684i
$928$	27.8708	+	20.2493i	0.914903	+	0.664716i
$929$	−33.8008			−1.10897			−0.554484	−	0.832194i	$-0.687084\pi$
$929$	−33.8008			−1.10897			−0.554484	+	0.832194i	$0.687084\pi$
$930$	−10.8855	+	7.90878i	−0.356949	+	0.259339i
$931$	−4.35425	−	3.16355i	−0.142705	−	0.103681i
$932$	−16.4592	+	11.9583i	−0.539138	+	0.391707i
$933$	21.9165	+	67.4520i	0.717514	+	2.20828i
$934$	−24.3816	+	75.0387i	−0.797789	+	2.45534i
$935$	11.3559	+	8.25054i	0.371377	+	0.269821i
$936$	−0.859411	−	2.64499i	−0.0280907	−	0.0864544i
$937$	0.952255	+	2.93074i	0.0311088	+	0.0957431i	0.965405	−	0.260754i	$-0.0839711\pi$
$937$	0.952255	+	2.93074i	0.0311088	+	0.0957431i	−0.934297	+	0.356497i	$0.883971\pi$
$938$	−33.9044			−1.10702
$939$	−27.9460			−0.911983
$940$	4.22733	+	13.0104i	0.137880	+	0.424352i
$941$	10.4376	+	7.58334i	0.340255	+	0.247210i	0.744770	−	0.667322i	$-0.232559\pi$
$941$	10.4376	+	7.58334i	0.340255	+	0.247210i	−0.404514	+	0.914532i	$0.632559\pi$
$942$	8.61658	−	26.5191i	0.280743	−	0.864040i
$943$	−23.6118	+	17.1550i	−0.768907	+	0.558643i
$944$	11.3619			0.369798
$945$	10.3064	−	31.7199i	0.335268	−	1.03185i
$946$	−26.6337	+	81.9702i	−0.865938	+	2.66508i
$947$	1.46853	−	1.06695i	0.0477209	−	0.0346713i	−0.563669	−	0.826001i	$-0.690611\pi$
$947$	1.46853	−	1.06695i	0.0477209	−	0.0346713i	0.611390	+	0.791329i	$0.290611\pi$
$948$	−16.8609	−	51.8925i	−0.547617	−	1.68539i
$949$	−0.521864	−	1.60613i	−0.0169404	−	0.0521373i
$950$	−4.56758	−	3.31854i	−0.148192	−	0.107668i
$951$	19.7120	+	14.3216i	0.639204	+	0.464409i
$952$	18.9599			0.614493
$953$	24.9624	−	18.1363i	0.808612	−	0.587491i	−0.104816	−	0.994492i	$-0.533425\pi$
$953$	24.9624	−	18.1363i	0.808612	−	0.587491i	0.913428	+	0.407000i	$0.133425\pi$
$954$	−128.481	+	93.3470i	−4.15973	+	3.02222i
$955$	−6.63019	−	4.81711i	−0.214548	−	0.155878i
$956$	30.4751	+	22.1415i	0.985636	+	0.716107i
$957$	52.1006	+	37.8533i	1.68417	+	1.22362i
$958$	−37.9764	+	27.5915i	−1.22696	+	0.891441i
$959$	34.7520	+	25.2488i	1.12220	+	0.815327i
$960$	−13.1288	−	40.4064i	−0.423732	−	1.30411i
$961$	22.3428	−	16.2330i	0.720737	−	0.523646i
$962$	−0.399146	+	1.22845i	−0.0128690	+	0.0396067i
$963$	−1.23810	+	0.899532i	−0.0398972	+	0.0289870i
$964$	26.9046	+	19.5473i	0.866539	+	0.629578i
$965$	−17.2917			−0.556638
$966$	29.2881	+	90.1395i	0.942329	+	2.90019i
$967$	6.46970	+	4.70051i	0.208051	+	0.151158i	0.686932	−	0.726722i	$-0.258957\pi$
$967$	6.46970	+	4.70051i	0.208051	+	0.151158i	−0.478880	+	0.877880i	$0.658957\pi$
$968$	−2.32580	−	7.15806i	−0.0747539	−	0.230069i
$969$	24.6928	+	17.9403i	0.793246	+	0.576327i
$970$	−17.3416			−0.556806
$971$	−4.20326	−	12.9363i	−0.134889	−	0.415146i	0.860684	−	0.509140i	$-0.170037\pi$
$971$	−4.20326	−	12.9363i	−0.134889	−	0.415146i	−0.995573	+	0.0939941i	$0.970037\pi$
$972$	−123.662			−3.96645
$973$	4.97232	+	15.3032i	0.159405	+	0.490598i
$974$	−11.7555	−	36.1798i	−0.376672	−	1.15928i
$975$	0.415422	−	0.301821i	0.0133041	−	0.00966602i
$976$	0.558828	+	0.406012i	0.0178877	+	0.0129961i
$977$	−1.68998	+	5.20124i	−0.0540674	+	0.166402i	−0.974444	−	0.224631i	$-0.927882\pi$
$977$	−1.68998	+	5.20124i	−0.0540674	+	0.166402i	0.920377	+	0.391033i	$0.127882\pi$
$978$	−54.6883	+	168.313i	−1.74874	+	5.38206i
$979$	−18.5824	+	57.1906i	−0.593895	+	1.82782i
$980$	−5.24352	+	3.80964i	−0.167498	+	0.121695i
$981$	−114.683			−3.66155
$982$	−4.53183			−0.144617
$983$	−37.6716	+	27.3700i	−1.20154	+	0.872967i	−0.994435	−	0.105353i	$-0.966403\pi$
$983$	−37.6716	+	27.3700i	−1.20154	+	0.872967i	−0.207101	+	0.978320i	$0.566403\pi$
$984$	11.5790	−	35.6365i	0.369125	−	1.13605i
$985$	−7.73496	+	23.8057i	−0.246456	+	0.758514i
$986$	−13.4771	+	41.4783i	−0.429199	+	1.32094i
$987$	−26.2577	−	19.0773i	−0.835792	−	0.607238i
$988$	0.971773	−	0.706034i	0.0309162	−	0.0224619i
$989$	−18.4792	−	56.8732i	−0.587605	−	1.80846i
$990$	−19.9871	−	61.5141i	−0.635233	−	1.95505i
$991$	31.4945			1.00046			0.500229	−	0.865893i	$-0.333249\pi$
$991$	31.4945			1.00046			0.500229	+	0.865893i	$0.333249\pi$
$992$	−3.74384	−	11.5224i	−0.118867	−	0.365836i
$993$	68.6883			2.17976
$994$	20.4350	+	14.8469i	0.648158	+	0.470914i
$995$	5.34227	+	16.4418i	0.169361	+	0.521240i
$996$	−38.9079	−	28.2683i	−1.23284	−	0.895714i
$997$	10.0570	+	30.9522i	0.318508	+	0.980266i	0.974287	+	0.225313i	$0.0723404\pi$
$997$	10.0570	+	30.9522i	0.318508	+	0.980266i	−0.655779	+	0.754953i	$0.727660\pi$
$998$	−8.64844			−0.273762
$999$	44.7607	+	32.5206i	1.41617	+	1.02890i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	755.2.h.d.366.2	yes	16
151.59	even	5	inner	755.2.h.d.361.2	✓	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
755.2.h.d.361.2	✓	16	151.59	even	5	inner
755.2.h.d.366.2	yes	16	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:	\( N \)	\(=\)	\( 755 = 5 \cdot 151 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	755.h (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q-2.24302 q^{2} +(2.63865 - 1.91709i) q^{3} +3.03113 q^{4} +(-0.309017 + 0.951057i) q^{5} +(-5.91855 + 4.30007i) q^{6} +(0.681363 - 2.09702i) q^{7} -2.31285 q^{8} +(2.36019 - 7.26391i) q^{9} +(0.693131 - 2.13324i) q^{10} +(3.05442 + 2.21917i) q^{11} +(7.99810 - 5.81096i) q^{12} +(-0.127369 + 0.0925392i) q^{13} +(-1.52831 + 4.70365i) q^{14} +(1.00788 + 3.10192i) q^{15} -0.874500 q^{16} +(-1.14888 - 3.53589i) q^{17} +(-5.29394 + 16.2931i) q^{18} -2.51707 q^{19} +(-0.936671 + 2.88278i) q^{20} +(-2.22230 - 6.83954i) q^{21} +(-6.85112 - 4.97763i) q^{22} +5.87564 q^{23} +(-6.10280 + 4.43395i) q^{24} +(-0.809017 - 0.587785i) q^{25} +(0.285692 - 0.207567i) q^{26} +(-4.67425 - 14.3859i) q^{27} +(2.06530 - 6.35634i) q^{28} +(4.23104 + 3.07403i) q^{29} +(-2.26068 - 6.95767i) q^{30} +(-0.568350 - 1.74920i) q^{31} +6.58722 q^{32} +12.3139 q^{33} +(2.57696 + 7.93107i) q^{34} +(1.78383 + 1.29603i) q^{35} +(7.15404 - 22.0179i) q^{36} +(-2.95915 + 2.14995i) q^{37} +5.64584 q^{38} +(-0.158677 + 0.488357i) q^{39} +(0.714710 - 2.19965i) q^{40} +(-4.01859 + 2.91968i) q^{41} +(4.98466 + 15.3412i) q^{42} +(-3.14506 - 9.67948i) q^{43} +(9.25835 + 6.72659i) q^{44} +(6.17905 + 4.48934i) q^{45} -13.1792 q^{46} +(3.65121 - 2.65276i) q^{47} +(-2.30750 + 1.67650i) q^{48} +(1.72989 + 1.25684i) q^{49} +(1.81464 + 1.31841i) q^{50} +(-9.81012 - 7.12747i) q^{51} +(-0.386073 + 0.280499i) q^{52} +(7.49967 + 5.44883i) q^{53} +(10.4844 + 32.2678i) q^{54} +(-3.05442 + 2.21917i) q^{55} +(-1.57589 + 4.85009i) q^{56} +(-6.64167 + 4.82546i) q^{57} +(-9.49030 - 6.89510i) q^{58} -12.9924 q^{59} +(3.05500 + 9.40233i) q^{60} +(-0.639026 - 0.464279i) q^{61} +(1.27482 + 3.92349i) q^{62} +(-13.6244 - 9.89871i) q^{63} -13.0263 q^{64} +(-0.0486507 - 0.149732i) q^{65} -27.6203 q^{66} +(2.11841 + 6.51978i) q^{67} +(-3.48241 - 10.7177i) q^{68} +(15.5038 - 11.2642i) q^{69} +(-4.00116 - 2.90702i) q^{70} +(1.57823 - 4.85729i) q^{71} +(-5.45876 + 16.8003i) q^{72} +(-3.31475 + 10.2017i) q^{73} +(6.63743 - 4.82238i) q^{74} -3.26155 q^{75} -7.62957 q^{76} +(6.73480 - 4.89312i) q^{77} +(0.355915 - 1.09539i) q^{78} +(1.70550 - 5.24899i) q^{79} +(0.270235 - 0.831699i) q^{80} +(-21.3756 - 15.5303i) q^{81} +(9.01378 - 6.54889i) q^{82} +(-1.50326 - 4.62655i) q^{83} +(-6.73609 - 20.7315i) q^{84} +3.71785 q^{85} +(7.05442 + 21.7113i) q^{86} +17.0574 q^{87} +(-7.06441 - 5.13260i) q^{88} +(4.92187 + 15.1479i) q^{89} +(-13.8597 - 10.0697i) q^{90} +(0.107272 + 0.330148i) q^{91} +17.8099 q^{92} +(-4.85306 - 3.52595i) q^{93} +(-8.18972 + 5.95018i) q^{94} +(0.777818 - 2.39388i) q^{95} +(17.3814 - 12.6283i) q^{96} +(-2.38913 - 7.35298i) q^{97} +(-3.88017 - 2.81911i) q^{98} +(23.3288 - 16.9494i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 4 q^{2} - 4 q^{3} + 24 q^{4} + 4 q^{5} - 18 q^{6} - q^{7} - 18 q^{8} - q^{10} + 13 q^{11} - 19 q^{12} + 7 q^{13} - q^{14} - q^{15} + 16 q^{16} + 9 q^{17} - 3 q^{18} - 34 q^{19} - 9 q^{20} + 2 q^{21}+ \cdots + 75 q^{99}+O(q^{100}) \) 16 * q - 4 * q^2 - 4 * q^3 + 24 * q^4 + 4 * q^5 - 18 * q^6 - q^7 - 18 * q^8 - q^10 + 13 * q^11 - 19 * q^12 + 7 * q^13 - q^14 - q^15 + 16 * q^16 + 9 * q^17 - 3 * q^18 - 34 * q^19 - 9 * q^20 + 2 * q^21 + 14 * q^22 + 58 * q^23 + 8 * q^24 - 4 * q^25 - 19 * q^26 - 34 * q^27 + 19 * q^28 - 16 * q^29 - 12 * q^30 - 3 * q^31 + 14 * q^34 + 11 * q^35 + 57 * q^36 + 20 * q^37 - 16 * q^38 + 5 * q^39 + 3 * q^40 + 24 * q^41 + 34 * q^42 - 28 * q^43 + 73 * q^44 + 15 * q^45 - 22 * q^46 + 18 * q^47 - 74 * q^48 - 19 * q^49 + q^50 - 8 * q^51 + 2 * q^52 + 23 * q^53 + 48 * q^54 - 13 * q^55 - 7 * q^56 - 22 * q^57 + 8 * q^58 - 44 * q^59 - 6 * q^60 - 25 * q^61 + 56 * q^62 - 7 * q^63 + 42 * q^64 + 3 * q^65 - 102 * q^66 + 12 * q^67 - 8 * q^68 - 2 * q^69 + 6 * q^70 - 22 * q^71 - 39 * q^72 - 26 * q^73 - 2 * q^74 + 6 * q^75 + 16 * q^76 + 11 * q^77 + 12 * q^78 - 32 * q^79 - 21 * q^80 + 11 * q^81 + 46 * q^82 + 4 * q^83 - 19 * q^84 + 36 * q^85 + 39 * q^86 + 88 * q^87 + 24 * q^88 + 38 * q^89 - 22 * q^90 - 6 * q^91 + 114 * q^92 - 31 * q^93 - 31 * q^94 - 21 * q^95 + 59 * q^96 + 75 * q^97 - 56 * q^98 + 75 * q^99

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