LMFDB - Embedded newform 74.2.f.b.53.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [74,2,Mod(7,74)] 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("74.7"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(74, base_ring=CyclotomicField(18)) chi = DirichletCharacter(H, H._module([16])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 74 = 2 \cdot 37 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	74.f (of order $9$, degree $6$, minimal)

Newform invariants

comment:select newform

sage:traces = [12] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(1)] == traces)

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

Self dual:	no
Analytic conductor:	$0.590892974957$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$2$ over $\Q(\zeta_{9})$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 24x^{10} + 264x^{8} - 1687x^{6} + 6600x^{4} - 15000x^{2} + 15625 $ x^12 - 24x^10 + 264x^8 - 1687x^6 + 6600x^4 - 15000*x^2 + 15625
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			53.1
Root			$2.00752 - 0.984808i$ of defining polynomial
Character	$\chi$	$=$	74.53
Dual form			74.2.f.b.7.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.939693 - 0.342020i) q^{2} +(-2.04963 + 0.746005i) q^{3} +(0.766044 + 0.642788i) q^{4} +(-0.326352 + 1.85083i) q^{5} +2.18117 q^{6} +(-0.711830 + 4.03699i) q^{7} +(-0.500000 - 0.866025i) q^{8} +(1.34633 - 1.12971i) q^{9} +(0.939693 - 1.62760i) q^{10} +(-1.67088 - 2.89404i) q^{11} +(-2.04963 - 0.746005i) q^{12} +(1.48512 + 1.24616i) q^{13} +(2.04963 - 3.55007i) q^{14} +(-0.711830 - 4.03699i) q^{15} +(0.173648 + 0.984808i) q^{16} +(3.40626 - 2.85819i) q^{17} +(-1.65152 + 0.601105i) q^{18} +(0.0932770 - 0.0339500i) q^{19} +(-1.43969 + 1.20805i) q^{20} +(-1.55262 - 8.80536i) q^{21} +(0.580289 + 3.29098i) q^{22} +(-4.76146 + 8.24709i) q^{23} +(1.67088 + 1.40203i) q^{24} +(1.37939 + 0.502055i) q^{25} +(-0.969343 - 1.67895i) q^{26} +(1.35504 - 2.34700i) q^{27} +(-3.14022 + 2.63496i) q^{28} +(-0.387288 - 0.670802i) q^{29} +(-0.711830 + 4.03699i) q^{30} +10.3914 q^{31} +(0.173648 - 0.984808i) q^{32} +(5.58365 + 4.68524i) q^{33} +(-4.17840 + 1.52081i) q^{34} +(-7.23948 - 2.63496i) q^{35} +1.75751 q^{36} +(-3.50302 + 4.97281i) q^{37} -0.0992633 q^{38} +(-3.97359 - 1.44627i) q^{39} +(1.76604 - 0.642788i) q^{40} +(4.36218 + 3.66031i) q^{41} +(-1.55262 + 8.80536i) q^{42} -1.11986 q^{43} +(0.580289 - 3.29098i) q^{44} +(1.65152 + 2.86052i) q^{45} +(7.29498 - 6.12122i) q^{46} +(3.55724 - 6.16132i) q^{47} +(-1.09059 - 1.88895i) q^{48} +(-9.21271 - 3.35315i) q^{49} +(-1.12449 - 0.943555i) q^{50} +(-4.84936 + 8.39933i) q^{51} +(0.336649 + 1.90923i) q^{52} +(0.142188 + 0.806388i) q^{53} +(-2.07604 + 1.74200i) q^{54} +(5.90168 - 2.14804i) q^{55} +(3.85205 - 1.40203i) q^{56} +(-0.165857 + 0.139170i) q^{57} +(0.134504 + 0.762808i) q^{58} +(1.40642 + 7.97622i) q^{59} +(2.04963 - 3.55007i) q^{60} +(-8.19737 - 6.87841i) q^{61} +(-9.76476 - 3.55408i) q^{62} +(3.60225 + 6.23929i) q^{63} +(-0.500000 + 0.866025i) q^{64} +(-2.79111 + 2.34202i) q^{65} +(-3.64447 - 6.31240i) q^{66} +(2.28630 - 12.9663i) q^{67} +4.44656 q^{68} +(3.60687 - 20.4556i) q^{69} +(5.90168 + 4.95210i) q^{70} +(2.79386 - 1.01688i) q^{71} +(-1.65152 - 0.601105i) q^{72} -2.55740 q^{73} +(4.99257 - 3.47481i) q^{74} -3.20177 q^{75} +(0.0932770 + 0.0339500i) q^{76} +(12.8726 - 4.68524i) q^{77} +(3.23930 + 2.71810i) q^{78} +(-0.943888 + 5.35305i) q^{79} -1.87939 q^{80} +(-1.94203 + 11.0138i) q^{81} +(-2.84721 - 4.93152i) q^{82} +(0.504249 - 0.423115i) q^{83} +(4.47060 - 7.74331i) q^{84} +(4.17840 + 7.23720i) q^{85} +(1.05232 + 0.383014i) q^{86} +(1.29422 + 1.08598i) q^{87} +(-1.67088 + 2.89404i) q^{88} +(0.612149 + 3.47167i) q^{89} +(-0.573568 - 3.25286i) q^{90} +(-6.08790 + 5.10835i) q^{91} +(-8.94862 + 3.25703i) q^{92} +(-21.2986 + 7.75206i) q^{93} +(-5.45001 + 4.57310i) q^{94} +(0.0323948 + 0.183720i) q^{95} +(0.378757 + 2.14804i) q^{96} +(-1.81012 + 3.13522i) q^{97} +(7.51027 + 6.30186i) q^{98} +(-5.51897 - 2.00874i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 3 q^{3} - 6 q^{5} + 6 q^{7} - 6 q^{8} - 3 q^{9} + 3 q^{11} - 3 q^{12} - 6 q^{13} + 3 q^{14} + 6 q^{15} - 3 q^{17} + 6 q^{18} - 3 q^{19} - 6 q^{20} - 33 q^{21} - 3 q^{22} - 21 q^{23} - 3 q^{24} - 6 q^{25}+ \cdots - 33 q^{99}+O(q^{100}) $ 12 * q - 3 * q^3 - 6 * q^5 + 6 * q^7 - 6 * q^8 - 3 * q^9 + 3 * q^11 - 3 * q^12 - 6 * q^13 + 3 * q^14 + 6 * q^15 - 3 * q^17 + 6 * q^18 - 3 * q^19 - 6 * q^20 - 33 * q^21 - 3 * q^22 - 21 * q^23 - 3 * q^24 - 6 * q^25 + 3 * q^27 - 3 * q^28 + 6 * q^29 + 6 * q^30 + 42 * q^31 + 57 * q^33 - 3 * q^34 - 9 * q^35 + 24 * q^36 - 3 * q^37 + 42 * q^38 - 24 * q^39 + 12 * q^40 - 21 * q^41 - 33 * q^42 + 36 * q^43 - 3 * q^44 - 6 * q^45 + 3 * q^46 + 9 * q^47 - 12 * q^49 + 12 * q^50 + 3 * q^52 - 6 * q^53 - 27 * q^54 - 3 * q^56 - 36 * q^57 - 3 * q^58 - 6 * q^59 + 3 * q^60 - 18 * q^61 - 33 * q^62 + 36 * q^63 - 6 * q^64 + 3 * q^65 + 3 * q^66 - 27 * q^67 + 6 * q^68 - 12 * q^69 - 18 * q^71 + 6 * q^72 + 54 * q^73 + 3 * q^74 - 6 * q^75 - 3 * q^76 + 51 * q^77 - 33 * q^78 - 12 * q^79 - 36 * q^81 - 18 * q^82 - 6 * q^83 - 6 * q^84 + 3 * q^85 + 39 * q^87 + 3 * q^88 - 15 * q^89 - 15 * q^90 - 51 * q^91 - 6 * q^92 + 45 * q^93 - 12 * q^94 - 15 * q^95 + 6 * q^96 - 42 * q^97 + 51 * q^98 - 33 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/74\mathbb{Z}\right)^\times$.

$n$	$39$
$\chi(n)$	$e\left(\frac{1}{9}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−0.939693	−	0.342020i	−0.664463	−	0.241845i
$2$	−0.939693	−	0.342020i	−0.664463	−	0.241845i
$3$	−2.04963	+	0.746005i	−1.18336	+	0.430706i	−0.857386	−	0.514674i	$-0.827913\pi$
$3$	−2.04963	+	0.746005i	−1.18336	+	0.430706i	−0.325970	+	0.945380i	$0.605691\pi$
$4$	0.766044	+	0.642788i	0.383022	+	0.321394i
$5$	−0.326352	+	1.85083i	−0.145949	+	0.827718i	0.820651	+	0.571429i	$0.193611\pi$
$5$	−0.326352	+	1.85083i	−0.145949	+	0.827718i	−0.966600	+	0.256289i	$0.917500\pi$
$6$	2.18117			0.890460
$7$	−0.711830	+	4.03699i	−0.269046	+	1.52584i	0.488214	+	0.872724i	$0.337649\pi$
$7$	−0.711830	+	4.03699i	−0.269046	+	1.52584i	−0.757260	+	0.653113i	$0.773463\pi$
$8$	−0.500000	−	0.866025i	−0.176777	−	0.306186i
$9$	1.34633	−	1.12971i	0.448778	−	0.376569i
$10$	0.939693	−	1.62760i	0.297157	−	0.514691i
$11$	−1.67088	−	2.89404i	−0.503788	−	0.872586i	−0.999990	−	0.00437929i	$-0.998606\pi$
$11$	−1.67088	−	2.89404i	−0.503788	−	0.872586i	0.496203	−	0.868207i	$-0.334727\pi$
$12$	−2.04963	−	0.746005i	−0.591678	−	0.215353i
$13$	1.48512	+	1.24616i	0.411898	+	0.345623i	0.825071	−	0.565029i	$-0.191135\pi$
$13$	1.48512	+	1.24616i	0.411898	+	0.345623i	−0.413173	+	0.910653i	$0.635580\pi$
$14$	2.04963	−	3.55007i	0.547787	−	0.948795i
$15$	−0.711830	−	4.03699i	−0.183794	−	1.04235i
$16$	0.173648	+	0.984808i	0.0434120	+	0.246202i
$17$	3.40626	−	2.85819i	0.826140	−	0.693214i	−0.128261	−	0.991740i	$-0.540940\pi$
$17$	3.40626	−	2.85819i	0.826140	−	0.693214i	0.954401	+	0.298527i	$0.0964952\pi$
$18$	−1.65152	+	0.601105i	−0.389268	+	0.141682i
$19$	0.0932770	−	0.0339500i	0.0213992	−	0.00778868i	−0.331298	−	0.943526i	$-0.607487\pi$
$19$	0.0932770	−	0.0339500i	0.0213992	−	0.00778868i	0.352698	+	0.935737i	$0.385264\pi$
$20$	−1.43969	+	1.20805i	−0.321925	+	0.270127i
$21$	−1.55262	−	8.80536i	−0.338810	−	1.92149i
$22$	0.580289	+	3.29098i	0.123718	+	0.701640i
$23$	−4.76146	+	8.24709i	−0.992833	+	1.71964i	−0.392920	+	0.919573i	$0.628535\pi$
$23$	−4.76146	+	8.24709i	−0.992833	+	1.71964i	−0.599913	+	0.800065i	$0.704798\pi$
$24$	1.67088	+	1.40203i	0.341066	+	0.286188i
$25$	1.37939	+	0.502055i	0.275877	+	0.100411i
$26$	−0.969343	−	1.67895i	−0.190104	−	0.329269i
$27$	1.35504	−	2.34700i	0.260777	−	0.451680i
$28$	−3.14022	+	2.63496i	−0.593445	+	0.497960i
$29$	−0.387288	−	0.670802i	−0.0719175	−	0.124565i	0.827824	−	0.560988i	$-0.189579\pi$
$29$	−0.387288	−	0.670802i	−0.0719175	−	0.124565i	−0.899742	+	0.436423i	$0.856245\pi$
$30$	−0.711830	+	4.03699i	−0.129962	+	0.737049i
$31$	10.3914			1.86636			0.933179	−	0.359413i	$-0.117023\pi$
$31$	10.3914			1.86636			0.933179	+	0.359413i	$0.117023\pi$
$32$	0.173648	−	0.984808i	0.0306970	−	0.174091i
$33$	5.58365	+	4.68524i	0.971988	+	0.815595i
$34$	−4.17840	+	1.52081i	−0.716590	+	0.260817i
$35$	−7.23948	−	2.63496i	−1.22370	−	0.445389i
$36$	1.75751			0.292919
$37$	−3.50302	+	4.97281i	−0.575894	+	0.817525i
$37$	−3.50302	+	4.97281i	−0.575894	+	0.817525i
$38$	−0.0992633			−0.0161026
$39$	−3.97359	−	1.44627i	−0.636284	−	0.231588i
$40$	1.76604	−	0.642788i	0.279236	−	0.101634i
$41$	4.36218	+	3.66031i	0.681259	+	0.571644i	0.916374	−	0.400324i	$-0.131102\pi$
$41$	4.36218	+	3.66031i	0.681259	+	0.571644i	−0.235115	+	0.971968i	$0.575547\pi$
$42$	−1.55262	+	8.80536i	−0.239575	+	1.35870i
$43$	−1.11986			−0.170777			−0.0853884	−	0.996348i	$-0.527213\pi$
$43$	−1.11986			−0.170777			−0.0853884	+	0.996348i	$0.527213\pi$
$44$	0.580289	−	3.29098i	0.0874818	−	0.496134i
$45$	1.65152	+	2.86052i	0.246194	+	0.426421i
$46$	7.29498	−	6.12122i	1.07559	−	0.902524i
$47$	3.55724	−	6.16132i	0.518877	−	0.898721i	−0.480883	−	0.876785i	$-0.659684\pi$
$47$	3.55724	−	6.16132i	0.518877	−	0.898721i	0.999759	−	0.0219357i	$-0.00698290\pi$
$48$	−1.09059	−	1.88895i	−0.157413	−	0.272647i
$49$	−9.21271	−	3.35315i	−1.31610	−	0.479022i
$50$	−1.12449	−	0.943555i	−0.159026	−	0.133439i
$51$	−4.84936	+	8.39933i	−0.679046	+	1.17614i
$52$	0.336649	+	1.90923i	0.0466848	+	0.264763i
$53$	0.142188	+	0.806388i	0.0195310	+	0.110766i	0.993015	−	0.117990i	$-0.0376452\pi$
$53$	0.142188	+	0.806388i	0.0195310	+	0.110766i	−0.973484	+	0.228756i	$0.926534\pi$
$54$	−2.07604	+	1.74200i	−0.282513	+	0.237057i
$55$	5.90168	−	2.14804i	0.795782	−	0.289641i
$56$	3.85205	−	1.40203i	0.514751	−	0.187354i
$57$	−0.165857	+	0.139170i	−0.0219682	+	0.0184335i
$58$	0.134504	+	0.762808i	0.0176612	+	0.100162i
$59$	1.40642	+	7.97622i	0.183101	+	1.03842i	0.928372	+	0.371653i	$0.121209\pi$
$59$	1.40642	+	7.97622i	0.183101	+	1.03842i	−0.745271	+	0.666762i	$0.767680\pi$
$60$	2.04963	−	3.55007i	0.264606	−	0.458312i
$61$	−8.19737	−	6.87841i	−1.04957	−	0.880691i	−0.0565183	−	0.998402i	$-0.518000\pi$
$61$	−8.19737	−	6.87841i	−1.04957	−	0.880691i	−0.993048	+	0.117711i	$0.962444\pi$
$62$	−9.76476	−	3.55408i	−1.24013	−	0.451369i
$63$	3.60225	+	6.23929i	0.453841	+	0.786076i
$64$	−0.500000	+	0.866025i	−0.0625000	+	0.108253i
$65$	−2.79111	+	2.34202i	−0.346195	+	0.290492i
$66$	−3.64447	−	6.31240i	−0.448603	−	0.777003i
$67$	2.28630	−	12.9663i	0.279317	−	1.58408i	−0.445591	−	0.895237i	$-0.647006\pi$
$67$	2.28630	−	12.9663i	0.279317	−	1.58408i	0.724907	−	0.688846i	$-0.241883\pi$
$68$	4.44656			0.539225
$69$	3.60687	−	20.4556i	0.434216	−	2.46256i
$70$	5.90168	+	4.95210i	0.705386	+	0.591889i
$71$	2.79386	−	1.01688i	0.331570	−	0.120682i	−0.170870	−	0.985294i	$-0.554658\pi$
$71$	2.79386	−	1.01688i	0.331570	−	0.120682i	0.502440	+	0.864612i	$0.332436\pi$
$72$	−1.65152	−	0.601105i	−0.194634	−	0.0708409i
$73$	−2.55740			−0.299321			−0.149660	−	0.988737i	$-0.547818\pi$
$73$	−2.55740			−0.299321			−0.149660	+	0.988737i	$0.547818\pi$
$74$	4.99257	−	3.47481i	0.580374	−	0.403938i
$75$	−3.20177			−0.369708
$76$	0.0932770	+	0.0339500i	0.0106996	+	0.00389434i
$77$	12.8726	−	4.68524i	1.46697	−	0.533932i
$78$	3.23930	+	2.71810i	0.366779	+	0.307764i
$79$	−0.943888	+	5.35305i	−0.106196	+	0.602265i	0.884540	+	0.466464i	$0.154472\pi$
$79$	−0.943888	+	5.35305i	−0.106196	+	0.602265i	−0.990736	+	0.135802i	$0.956639\pi$
$80$	−1.87939			−0.210122
$81$	−1.94203	+	11.0138i	−0.215781	+	1.22375i
$82$	−2.84721	−	4.93152i	−0.314422	−	0.544595i
$83$	0.504249	−	0.423115i	0.0553485	−	0.0464429i	−0.614694	−	0.788766i	$-0.710720\pi$
$83$	0.504249	−	0.423115i	0.0553485	−	0.0464429i	0.670042	+	0.742323i	$0.266276\pi$
$84$	4.47060	−	7.74331i	0.487782	−	0.844864i
$85$	4.17840	+	7.23720i	0.453211	+	0.784985i
$86$	1.05232	+	0.383014i	0.113475	+	0.0413015i
$87$	1.29422	+	1.08598i	0.138755	+	0.116429i
$88$	−1.67088	+	2.89404i	−0.178116	+	0.308506i
$89$	0.612149	+	3.47167i	0.0648877	+	0.367996i	0.999910	+	0.0134078i	$0.00426798\pi$
$89$	0.612149	+	3.47167i	0.0648877	+	0.367996i	−0.935022	+	0.354589i	$0.884621\pi$
$90$	−0.573568	−	3.25286i	−0.0604593	−	0.342882i
$91$	−6.08790	+	5.10835i	−0.638185	+	0.535501i
$92$	−8.94862	+	3.25703i	−0.932958	+	0.339569i
$93$	−21.2986	+	7.75206i	−2.20856	+	0.803852i
$94$	−5.45001	+	4.57310i	−0.562125	+	0.471679i
$95$	0.0323948	+	0.183720i	0.00332363	+	0.0188493i
$96$	0.378757	+	2.14804i	0.0386567	+	0.219233i
$97$	−1.81012	+	3.13522i	−0.183790	+	0.318334i	−0.943168	−	0.332316i	$-0.892170\pi$
$97$	−1.81012	+	3.13522i	−0.183790	+	0.318334i	0.759378	+	0.650650i	$0.225503\pi$
$98$	7.51027	+	6.30186i	0.758652	+	0.636584i
$99$	−5.51897	−	2.00874i	−0.554678	−	0.201886i
$100$	0.733956	+	1.27125i	0.0733956	+	0.127125i
$101$	−1.97406	+	3.41917i	−0.196426	+	0.340220i	−0.947367	−	0.320149i	$-0.896267\pi$
$101$	−1.97406	+	3.41917i	−0.196426	+	0.340220i	0.750941	+	0.660369i	$0.229600\pi$
$102$	7.42965	−	6.23421i	0.735645	−	0.617279i
$103$	0.989402	+	1.71369i	0.0974887	+	0.168855i	0.910645	−	0.413191i	$-0.135586\pi$
$103$	0.989402	+	1.71369i	0.0974887	+	0.168855i	−0.813156	+	0.582046i	$0.802252\pi$
$104$	0.336649	−	1.90923i	0.0330112	−	0.187216i
$105$	16.8040			1.63990
$106$	0.142188	−	0.806388i	0.0138105	−	0.0783233i
$107$	6.31896	+	5.30224i	0.610877	+	0.512587i	0.894921	−	0.446225i	$-0.147232\pi$
$107$	6.31896	+	5.30224i	0.610877	+	0.512587i	−0.284044	+	0.958811i	$0.591676\pi$
$108$	2.54664	−	0.926901i	0.245051	−	0.0891911i
$109$	8.25476	+	3.00449i	0.790663	+	0.287778i	0.705612	−	0.708599i	$-0.250672\pi$
$109$	8.25476	+	3.00449i	0.790663	+	0.287778i	0.0850513	+	0.996377i	$0.472895\pi$
$110$	−6.28044			−0.598816
$111$	3.47017	−	12.8057i	0.329374	−	1.21546i
$112$	−4.09926			−0.387344
$113$	−9.37522	−	3.41230i	−0.881946	−	0.321002i	−0.138951	−	0.990299i	$-0.544373\pi$
$113$	−9.37522	−	3.41230i	−0.881946	−	0.321002i	−0.742995	+	0.669297i	$0.766595\pi$
$114$	0.203453	−	0.0740509i	0.0190551	−	0.00693550i
$115$	−13.7101	−	11.5041i	−1.27847	−	1.07277i
$116$	0.134504	−	0.762808i	0.0124884	−	0.0708250i
$117$	3.40727			0.315002
$118$	1.40642	−	7.97622i	0.129472	−	0.734270i
$119$	9.11381	+	15.7856i	0.835462	+	1.44706i
$120$	−3.14022	+	2.63496i	−0.286661	+	0.240537i
$121$	−0.0836467	+	0.144880i	−0.00760425	+	0.0131709i
$122$	5.35046	+	9.26726i	0.484408	+	0.839018i
$123$	−11.6715	−	4.24807i	−1.05238	−	0.383036i
$124$	7.96030	+	6.67949i	0.714856	+	0.599836i
$125$	−6.07785	+	10.5271i	−0.543619	+	0.941576i
$126$	−1.25105	−	7.09506i	−0.111452	−	0.632078i
$127$	−2.91336	−	16.5225i	−0.258519	−	1.46613i	−0.786876	−	0.617112i	$-0.788303\pi$
$127$	−2.91336	−	16.5225i	−0.258519	−	1.46613i	0.528356	−	0.849023i	$-0.322808\pi$
$128$	0.766044	−	0.642788i	0.0677094	−	0.0568149i
$129$	2.29530	−	0.835420i	0.202090	−	0.0735546i
$130$	3.42381	−	1.24616i	0.300288	−	0.109296i
$131$	1.07527	−	0.902259i	0.0939468	−	0.0788307i	−0.594605	−	0.804018i	$-0.702691\pi$
$131$	1.07527	−	0.902259i	0.0939468	−	0.0788307i	0.688551	+	0.725188i	$0.258247\pi$
$132$	1.26571	+	7.17820i	0.110166	+	0.624782i
$133$	0.0706586	+	0.400725i	0.00612687	+	0.0347472i
$134$	−6.58315	+	11.4024i	−0.568698	+	0.985013i
$135$	3.90168	+	3.27390i	0.335803	+	0.281772i
$136$	−4.17840	−	1.52081i	−0.358295	−	0.130409i
$137$	−6.20963	−	10.7554i	−0.530525	−	0.918896i	−0.999366	−	0.0356133i	$-0.988662\pi$
$137$	−6.20963	−	10.7554i	−0.530525	−	0.918896i	0.468841	−	0.883283i	$-0.344672\pi$
$138$	−10.3856	+	17.9883i	−0.884078	+	1.53127i
$139$	14.0949	−	11.8270i	1.19551	−	1.00315i	0.195766	−	0.980651i	$-0.437281\pi$
$139$	14.0949	−	11.8270i	1.19551	−	1.00315i	0.999747	−	0.0225036i	$-0.00716372\pi$
$140$	−3.85205	−	6.67194i	−0.325557	−	0.563882i
$141$	−2.69466	+	15.2821i	−0.226931	+	1.28699i
$142$	−2.97316			−0.249502
$143$	1.12500	−	6.38018i	0.0940770	−	0.533537i
$144$	1.34633	+	1.12971i	0.112194	+	0.0941423i
$145$	1.36794	−	0.497888i	0.113601	−	0.0413473i
$146$	2.40317	+	0.874681i	0.198887	+	0.0723891i
$147$	21.3841			1.76373
$148$	−5.87993	+	1.55769i	−0.483327	+	0.128042i
$149$	12.4068			1.01640			0.508201	−	0.861238i	$-0.330311\pi$
$149$	12.4068			1.01640			0.508201	+	0.861238i	$0.330311\pi$
$150$	3.00868	+	1.09507i	0.245657	+	0.0894120i
$151$	11.7921	−	4.29198i	0.959628	−	0.349276i	0.185740	−	0.982599i	$-0.440532\pi$
$151$	11.7921	−	4.29198i	0.959628	−	0.349276i	0.773888	+	0.633323i	$0.218309\pi$
$152$	−0.0760401	−	0.0638052i	−0.00616767	−	0.00517529i
$153$	1.35704	−	7.69616i	0.109710	−	0.622198i
$154$	−13.6987			−1.10387
$155$	−3.39126	+	19.2328i	−0.272393	+	1.54482i
$156$	−2.11430	−	3.66208i	−0.169280	−	0.293201i
$157$	2.69131	−	2.25828i	0.214790	−	0.180230i	−0.529045	−	0.848594i	$-0.677450\pi$
$157$	2.69131	−	2.25828i	0.214790	−	0.180230i	0.743834	+	0.668364i	$0.233005\pi$
$158$	2.71782	−	4.70740i	0.216218	−	0.374500i
$159$	−0.893002	−	1.54672i	−0.0708197	−	0.122663i
$160$	1.76604	+	0.642788i	0.139618	+	0.0508168i
$161$	−29.9041	−	25.0925i	−2.35677	−	1.97756i
$162$	5.59184	−	9.68536i	0.439337	−	0.760954i
$163$	−0.415269	−	2.35511i	−0.0325264	−	0.184466i	0.964216	−	0.265118i	$-0.0854109\pi$
$163$	−0.415269	−	2.35511i	−0.0325264	−	0.184466i	−0.996742	+	0.0806519i	$0.974300\pi$
$164$	0.988827	+	5.60792i	0.0772144	+	0.437905i
$165$	−10.4938	+	8.80536i	−0.816943	+	0.685497i
$166$	−0.618553	+	0.225135i	−0.0480090	+	0.0174738i
$167$	14.6442	−	5.33004i	1.13320	−	0.412451i	0.293746	−	0.955884i	$-0.405098\pi$
$167$	14.6442	−	5.33004i	1.13320	−	0.412451i	0.839453	+	0.543433i	$0.182876\pi$
$168$	−6.84936	+	5.74729i	−0.528439	+	0.443413i
$169$	−1.60477	−	9.10110i	−0.123444	−	0.700085i
$170$	−1.45114	−	8.22984i	−0.111298	−	0.631200i
$171$	0.0872283	−	0.151084i	0.00667051	−	0.0115537i
$172$	−0.857861	−	0.719831i	−0.0654113	−	0.0548866i
$173$	16.7991	+	6.11436i	1.27721	+	0.464866i	0.889508	−	0.456919i	$-0.151047\pi$
$173$	16.7991	+	6.11436i	1.27721	+	0.464866i	0.387701	+	0.921785i	$0.373269\pi$
$174$	−0.844742	−	1.46314i	−0.0640397	−	0.110920i
$175$	−3.00868	+	5.21118i	−0.227435	+	0.393928i
$176$	2.55993	−	2.14804i	0.192962	−	0.161914i
$177$	−8.83294	−	15.2991i	−0.663925	−	1.14995i
$178$	0.612149	−	3.47167i	0.0458825	−	0.260213i
$179$	−20.4063			−1.52524			−0.762619	−	0.646848i	$-0.776087\pi$
$179$	−20.4063			−1.52524			−0.762619	+	0.646848i	$0.776087\pi$
$180$	−0.573568	+	3.25286i	−0.0427512	+	0.242454i
$181$	−14.0006	−	11.7479i	−1.04065	−	0.873212i	−0.0485737	−	0.998820i	$-0.515468\pi$
$181$	−14.0006	−	11.7479i	−1.04065	−	0.873212i	−0.992080	+	0.125607i	$0.959912\pi$
$182$	7.46791	−	2.71810i	0.553558	−	0.201479i
$183$	21.9329	+	7.98293i	1.62133	+	0.590115i
$184$	9.52292			0.702039
$185$	−8.06062	−	8.10640i	−0.592629	−	0.595994i
$186$	22.6655			1.66192
$187$	−13.9632	−	5.08218i	−1.02109	−	0.371646i
$188$	6.68542	−	2.43329i	0.487584	−	0.177466i
$189$	8.51024	+	7.14094i	0.619029	+	0.519427i
$190$	0.0323948	−	0.183720i	0.00235016	−	0.0133284i
$191$	5.76567			0.417189			0.208595	−	0.978002i	$-0.433111\pi$
$191$	5.76567			0.417189			0.208595	+	0.978002i	$0.433111\pi$
$192$	0.378757	−	2.14804i	0.0273344	−	0.155021i
$193$	0.179712	+	0.311271i	0.0129360	+	0.0224057i	0.872421	−	0.488755i	$-0.162549\pi$
$193$	0.179712	+	0.311271i	0.0129360	+	0.0224057i	−0.859485	+	0.511161i	$0.829216\pi$
$194$	2.77327	−	2.32705i	0.199109	−	0.167072i
$195$	3.97359	−	6.88246i	0.284555	−	0.492863i
$196$	−4.90198	−	8.49048i	−0.350141	−	0.606463i
$197$	−6.54591	−	2.38251i	−0.466376	−	0.169747i	0.0981338	−	0.995173i	$-0.468713\pi$
$197$	−6.54591	−	2.38251i	−0.466376	−	0.169747i	−0.564510	+	0.825426i	$0.690935\pi$
$198$	4.49911	+	3.77520i	0.319738	+	0.268292i
$199$	−5.58897	+	9.68037i	−0.396191	+	0.686223i	−0.993252	−	0.115972i	$-0.963002\pi$
$199$	−5.58897	+	9.68037i	−0.396191	+	0.686223i	0.597061	+	0.802196i	$0.296335\pi$
$200$	−0.254900	−	1.44561i	−0.0180242	−	0.102220i
$201$	4.98683	+	28.2817i	0.351744	+	1.99484i
$202$	3.02443	−	2.53780i	0.212798	−	0.178559i
$203$	2.98370	−	1.08598i	0.209415	−	0.0762208i
$204$	−9.11381	+	3.31716i	−0.638094	+	0.232247i
$205$	−8.19823	+	6.87913i	−0.572589	+	0.480459i
$206$	−0.343616	−	1.94874i	−0.0239408	−	0.135775i
$207$	2.90629	+	16.4824i	0.202001	+	1.14561i
$208$	−0.969343	+	1.67895i	−0.0672118	+	0.116414i
$209$	−0.254107	−	0.213221i	−0.0175770	−	0.0147488i
$210$	−15.7906	−	5.74729i	−1.08965	−	0.396601i
$211$	6.10513	+	10.5744i	0.420295	+	0.727972i	0.995968	−	0.0897080i	$-0.0285934\pi$
$211$	6.10513	+	10.5744i	0.420295	+	0.727972i	−0.575673	+	0.817680i	$0.695260\pi$
$212$	−0.409414	+	0.709125i	−0.0281187	+	0.0487029i
$213$	−4.96778	+	4.16846i	−0.340387	+	0.285618i
$214$	−4.12441	−	7.14368i	−0.281939	−	0.488332i
$215$	0.365468	−	2.07267i	0.0249247	−	0.141355i
$216$	−2.71008			−0.184397
$217$	−7.39693	+	41.9501i	−0.502137	+	2.84776i
$218$	−6.72934	−	5.64659i	−0.455769	−	0.382435i
$219$	5.24172	−	1.90783i	0.354203	−	0.128919i
$220$	5.90168	+	2.14804i	0.397891	+	0.144821i
$221$	8.62048			0.579876
$222$	−7.64070	+	10.8466i	−0.512810	+	0.727973i
$223$	−10.7545			−0.720177			−0.360088	−	0.932918i	$-0.617253\pi$
$223$	−10.7545			−0.720177			−0.360088	+	0.932918i	$0.617253\pi$
$224$	3.85205	+	1.40203i	0.257376	+	0.0936771i
$225$	2.42429	−	0.882369i	0.161619	−	0.0588246i
$226$	7.64275	+	6.41303i	0.508388	+	0.426588i
$227$	−0.514913	+	2.92021i	−0.0341759	+	0.193821i	−0.997116	−	0.0758946i	$-0.975819\pi$
$227$	−0.514913	+	2.92021i	−0.0341759	+	0.193821i	0.962940	+	0.269716i	$0.0869298\pi$
$228$	−0.216510			−0.0143388
$229$	−0.526610	+	2.98655i	−0.0347994	+	0.197357i	−0.997251	−	0.0740958i	$-0.976393\pi$
$229$	−0.526610	+	2.98655i	−0.0347994	+	0.197357i	0.962452	+	0.271453i	$0.0875041\pi$
$230$	8.94862	+	15.4995i	0.590055	+	1.02200i
$231$	−22.8888	+	19.2060i	−1.50597	+	1.26366i
$232$	−0.387288	+	0.670802i	−0.0254267	+	0.0440403i
$233$	0.144403	+	0.250113i	0.00946016	+	0.0163855i	0.870717	−	0.491785i	$-0.163655\pi$
$233$	0.144403	+	0.250113i	0.00946016	+	0.0163855i	−0.861257	+	0.508170i	$0.830322\pi$
$234$	−3.20178	−	1.16535i	−0.209307	−	0.0761815i
$235$	10.2427	+	8.59461i	0.668157	+	0.560651i
$236$	−4.04963	+	7.01417i	−0.263609	+	0.456583i
$237$	−2.05878	−	11.6759i	−0.133732	−	0.758433i
$238$	−3.16519	−	17.9507i	−0.205169	−	1.16357i
$239$	−3.85711	+	3.23650i	−0.249496	+	0.209352i	−0.758955	−	0.651143i	$-0.774290\pi$
$239$	−3.85711	+	3.23650i	−0.249496	+	0.209352i	0.509460	+	0.860495i	$0.329845\pi$
$240$	3.85205	−	1.40203i	0.248649	−	0.0905007i
$241$	16.3281	−	5.94293i	1.05178	−	0.382818i	0.242448	−	0.970164i	$-0.422050\pi$
$241$	16.3281	−	5.94293i	1.05178	−	0.382818i	0.809336	+	0.587347i	$0.199827\pi$
$242$	0.128154	−	0.107534i	0.00823807	−	0.00691256i
$243$	−2.82410	−	16.0162i	−0.181166	−	1.02744i
$244$	−1.85819	−	10.5383i	−0.118959	−	0.674648i
$245$	9.21271	−	15.9569i	0.588578	−	1.01945i
$246$	9.51468	+	7.98376i	0.606634	+	0.509026i
$247$	0.180835	+	0.0658185i	0.0115062	+	0.00418793i
$248$	−5.19572	−	8.99925i	−0.329928	−	0.571453i
$249$	−0.717878	+	1.24340i	−0.0454937	+	0.0787974i
$250$	9.31180	−	7.81353i	0.588930	−	0.494171i
$251$	0.877844	+	1.52047i	0.0554090	+	0.0959713i	0.892399	−	0.451246i	$-0.149020\pi$
$251$	0.877844	+	1.52047i	0.0554090	+	0.0959713i	−0.836990	+	0.547218i	$0.815687\pi$
$252$	−1.25105	+	7.09506i	−0.0788087	+	0.446947i
$253$	31.8232			2.00071
$254$	−2.91336	+	16.5225i	−0.182801	+	1.03671i
$255$	−13.9632	−	11.7165i	−0.874407	−	0.733715i
$256$	−0.939693	+	0.342020i	−0.0587308	+	0.0213763i
$257$	11.9849	+	4.36215i	0.747598	+	0.272103i	0.687595	−	0.726095i	$-0.258667\pi$
$257$	11.9849	+	4.36215i	0.747598	+	0.272103i	0.0600034	+	0.998198i	$0.480889\pi$
$258$	−2.44260			−0.152070
$259$	−17.5816	−	17.6815i	−1.09247	−	1.09867i
$260$	−3.64354			−0.225963
$261$	−1.27923	−	0.465601i	−0.0791823	−	0.0288200i
$262$	−1.31901	+	0.480082i	−0.0814890	+	0.0296596i
$263$	−20.1968	−	16.9472i	−1.24539	−	1.04501i	−0.997083	−	0.0763250i	$-0.975681\pi$
$263$	−20.1968	−	16.9472i	−1.24539	−	1.04501i	−0.248307	−	0.968681i	$-0.579874\pi$
$264$	1.26571	−	7.17820i	0.0778991	−	0.441788i
$265$	−1.53889			−0.0945334
$266$	0.0706586	−	0.400725i	0.00433235	−	0.0245700i
$267$	−3.84457	−	6.65898i	−0.235284	−	0.407523i
$268$	10.0860	−	8.46314i	0.616099	−	0.516968i
$269$	−6.80289	+	11.7829i	−0.414779	+	0.718419i	−0.995405	−	0.0957514i	$-0.969475\pi$
$269$	−6.80289	+	11.7829i	−0.414779	+	0.718419i	0.580626	+	0.814171i	$0.302808\pi$
$270$	−2.54664	−	4.41091i	−0.154984	−	0.268439i
$271$	4.05562	+	1.47612i	0.246361	+	0.0896682i	0.462249	−	0.886750i	$-0.347042\pi$
$271$	4.05562	+	1.47612i	0.246361	+	0.0896682i	−0.215888	+	0.976418i	$0.569265\pi$
$272$	3.40626	+	2.85819i	0.206535	+	0.173303i
$273$	8.66709	−	15.0118i	0.524556	−	0.908558i
$274$	2.15658	+	12.2306i	0.130284	+	0.738877i
$275$	−0.851812	−	4.83087i	−0.0513662	−	0.291312i
$276$	15.9116	−	13.3514i	0.957767	−	0.803662i
$277$	3.28276	−	1.19483i	0.197242	−	0.0717902i	−0.241510	−	0.970398i	$-0.577643\pi$
$277$	3.28276	−	1.19483i	0.197242	−	0.0717902i	0.438752	+	0.898608i	$0.355421\pi$
$278$	−17.2899	+	6.29302i	−1.03698	+	0.377430i
$279$	13.9903	−	11.7393i	0.837580	−	0.702813i
$280$	1.33780	+	7.58705i	0.0799490	+	0.453413i
$281$	−1.27419	−	7.22628i	−0.0760116	−	0.431083i	−0.998937	−	0.0461037i	$-0.985320\pi$
$281$	−1.27419	−	7.22628i	−0.0760116	−	0.431083i	0.922925	−	0.384980i	$-0.125792\pi$
$282$	7.75895	−	13.4389i	0.462039	−	0.800275i
$283$	10.7268	+	9.00087i	0.637643	+	0.535046i	0.903294	−	0.429023i	$-0.141142\pi$
$283$	10.7268	+	9.00087i	0.637643	+	0.535046i	−0.265650	+	0.964070i	$0.585587\pi$
$284$	2.79386	+	1.01688i	0.165785	+	0.0603408i
$285$	−0.203453	−	0.352391i	−0.0120515	−	0.0208739i
$286$	−3.23930	+	5.61063i	−0.191544	+	0.331764i
$287$	−17.8817	+	15.0046i	−1.05553	+	0.885691i
$288$	−0.878757	−	1.52205i	−0.0517812	−	0.0896877i
$289$	0.481334	−	2.72978i	0.0283138	−	0.160575i
$290$	−1.45573			−0.0854832
$291$	1.37119	−	7.77641i	0.0803807	−	0.455861i
$292$	−1.95908	−	1.64386i	−0.114646	−	0.0961998i
$293$	23.7505	−	8.64447i	1.38752	−	0.505015i	0.463070	−	0.886322i	$-0.346748\pi$
$293$	23.7505	−	8.64447i	1.38752	−	0.505015i	0.924449	+	0.381306i	$0.124526\pi$
$294$	−20.0945	−	7.31380i	−1.17194	−	0.426550i
$295$	−15.2216			−0.886238
$296$	6.05809	+	0.547303i	0.352119	+	0.0318113i
$297$	−9.05640			−0.525506
$298$	−11.6586	−	4.24337i	−0.675362	−	0.245812i
$299$	−17.3486	+	6.31436i	−1.00329	+	0.365169i
$300$	−2.45270	−	2.05806i	−0.141606	−	0.118822i
$301$	0.797148	−	4.52085i	0.0459469	−	0.260578i
$302$	−12.5489			−0.722108
$303$	1.49537	−	8.48069i	0.0859070	−	0.487203i
$304$	0.0496317	+	0.0859645i	0.00284657	+	0.00493040i
$305$	15.4060	−	12.9272i	0.882146	−	0.740209i
$306$	−3.90744	+	6.76789i	−0.223374	+	0.386895i
$307$	12.2995	+	21.3034i	0.701972	+	1.21585i	0.967773	+	0.251823i	$0.0810301\pi$
$307$	12.2995	+	21.3034i	0.701972	+	1.21585i	−0.265801	+	0.964028i	$0.585637\pi$
$308$	12.8726	+	4.68524i	0.733483	+	0.266966i
$309$	−3.30633	−	2.77434i	−0.188091	−	0.157827i
$310$	9.76476	−	16.9131i	0.554601	−	0.960597i
$311$	0.904212	+	5.12804i	0.0512732	+	0.290785i	0.999653	−	0.0263531i	$-0.00838941\pi$
$311$	0.904212	+	5.12804i	0.0512732	+	0.290785i	−0.948380	+	0.317138i	$0.897278\pi$
$312$	0.734290	+	4.16437i	0.0415710	+	0.235761i
$313$	5.54340	−	4.65147i	0.313332	−	0.262916i	−0.472536	−	0.881311i	$-0.656661\pi$
$313$	5.54340	−	4.65147i	0.313332	−	0.262916i	0.785867	+	0.618395i	$0.212217\pi$
$314$	−3.30138	+	1.20160i	−0.186308	+	0.0678104i
$315$	−12.7235	+	4.63097i	−0.716887	+	0.260926i
$316$	−4.16394	+	3.49396i	−0.234240	+	0.196550i
$317$	−2.31803	−	13.1462i	−0.130194	−	0.738365i	−0.978087	−	0.208198i	$-0.933240\pi$
$317$	−2.31803	−	13.1462i	−0.130194	−	0.738365i	0.847893	−	0.530167i	$-0.177871\pi$
$318$	0.310136	+	1.75887i	0.0173916	+	0.0986326i
$319$	−1.29422	+	2.24165i	−0.0724624	+	0.125508i
$320$	−1.43969	−	1.20805i	−0.0804813	−	0.0675318i
$321$	−16.9070	−	6.15366i	−0.943659	−	0.343464i
$322$	19.5185	+	33.8070i	1.08772	+	1.88399i
$323$	0.220690	−	0.382246i	0.0122795	−	0.0212688i
$324$	−8.56720	+	7.18874i	−0.475956	+	0.399374i
$325$	1.42291	+	2.46455i	0.0789288	+	0.136709i
$326$	−0.415269	+	2.35511i	−0.0229996	+	0.130437i
$327$	−19.1606			−1.05958
$328$	0.988827	−	5.60792i	0.0545988	−	0.309645i
$329$	22.3410	+	18.7463i	1.23170	+	1.03352i
$330$	12.8726	−	4.68524i	0.708612	−	0.257914i
$331$	4.29733	+	1.56410i	0.236203	+	0.0859708i	0.457410	−	0.889256i	$-0.348777\pi$
$331$	4.29733	+	1.56410i	0.236203	+	0.0859708i	−0.221207	+	0.975227i	$0.571000\pi$
$332$	0.658250			0.0361262
$333$	0.901584	+	10.6525i	0.0494065	+	0.583751i
$334$	−15.5840			−0.852717
$335$	23.2523	+	8.46314i	1.27041	+	0.462391i
$336$	8.40198	−	3.05807i	0.458366	−	0.166831i
$337$	2.49218	+	2.09118i	0.135757	+	0.113914i	0.708138	−	0.706074i	$-0.249536\pi$
$337$	2.49218	+	2.09118i	0.135757	+	0.113914i	−0.572380	+	0.819988i	$0.693980\pi$
$338$	−1.60477	+	9.10110i	−0.0872879	+	0.495035i
$339$	21.7613			1.18191
$340$	−1.45114	+	8.22984i	−0.0786993	+	0.446326i
$341$	−17.3628	−	30.0732i	−0.940248	−	1.62856i
$342$	−0.133641	+	0.112139i	−0.00722650	+	0.00606376i
$343$	5.74708	−	9.95424i	0.310313	−	0.537479i
$344$	0.559929	+	0.969826i	0.0301894	+	0.0522895i
$345$	36.6827	+	13.3514i	1.97493	+	0.718817i
$346$	−13.6947	−	11.4912i	−0.736233	−	0.617773i
$347$	−12.2387	+	21.1981i	−0.657008	+	1.13797i	0.324379	+	0.945927i	$0.394845\pi$
$347$	−12.2387	+	21.1981i	−0.657008	+	1.13797i	−0.981386	+	0.192044i	$0.938488\pi$
$348$	0.293376	+	1.66382i	0.0157266	+	0.0891899i
$349$	0.990209	+	5.61576i	0.0530047	+	0.300604i	0.999773	−	0.0213116i	$-0.00678421\pi$
$349$	0.990209	+	5.61576i	0.0530047	+	0.300604i	−0.946768	+	0.321916i	$0.895673\pi$
$350$	4.60956	−	3.86788i	0.246391	−	0.206747i
$351$	4.93713	−	1.79697i	0.263525	−	0.0959152i
$352$	−3.14022	+	1.14295i	−0.167374	+	0.0609192i
$353$	18.7175	−	15.7059i	0.996233	−	0.835939i	0.00977486	−	0.999952i	$-0.496889\pi$
$353$	18.7175	−	15.7059i	0.996233	−	0.835939i	0.986458	+	0.164014i	$0.0524441\pi$
$354$	3.06765	+	17.3975i	0.163044	+	0.924667i
$355$	0.970296	+	5.50282i	0.0514980	+	0.292059i
$356$	−1.76261	+	3.05294i	−0.0934184	+	0.161805i
$357$	−30.4561	−	25.5557i	−1.61191	−	1.35255i
$358$	19.1756	+	6.97936i	1.01346	+	0.368871i
$359$	−9.35461	−	16.2027i	−0.493717	−	0.855144i	0.506256	−	0.862383i	$-0.331029\pi$
$359$	−9.35461	−	16.2027i	−0.493717	−	0.855144i	−0.999974	+	0.00723934i	$0.997696\pi$
$360$	1.65152	−	2.86052i	0.0870429	−	0.150763i
$361$	−14.5473	+	12.2066i	−0.765647	+	0.642454i
$362$	9.13822	+	15.8279i	0.480294	+	0.831894i
$363$	0.0633635	−	0.359352i	0.00332572	−	0.0188611i
$364$	−7.94718			−0.416546
$365$	0.834611	−	4.73331i	0.0436855	−	0.247753i
$366$	−17.8799	−	15.0030i	−0.934597	−	0.784220i
$367$	−31.6892	+	11.5339i	−1.65416	+	0.602067i	−0.989430	−	0.145013i	$-0.953678\pi$
$367$	−31.6892	+	11.5339i	−1.65416	+	0.602067i	−0.664735	+	0.747080i	$0.731455\pi$
$368$	−8.94862	−	3.25703i	−0.466479	−	0.169784i
$369$	10.0080			0.520997
$370$	4.80196	+	10.3744i	0.249642	+	0.539340i
$371$	−3.35659			−0.174265
$372$	−21.2986	−	7.75206i	−1.10428	−	0.401926i
$373$	−29.5389	+	10.7513i	−1.52947	+	0.556681i	−0.963491	−	0.267740i	$-0.913723\pi$
$373$	−29.5389	+	10.7513i	−1.52947	+	0.556681i	−0.565977	+	0.824421i	$0.691501\pi$
$374$	11.3829	+	9.55137i	0.588595	+	0.493889i
$375$	4.60405	−	26.1109i	0.237752	−	1.34836i
$376$	−7.11448			−0.366901
$377$	0.260760	−	1.47885i	0.0134298	−	0.0761644i
$378$	−5.55466	−	9.62096i	−0.285701	−	0.494849i
$379$	5.33697	−	4.47825i	0.274142	−	0.230032i	−0.495343	−	0.868697i	$-0.664958\pi$
$379$	5.33697	−	4.47825i	0.274142	−	0.230032i	0.769485	+	0.638665i	$0.220513\pi$
$380$	−0.0932770	+	0.161560i	−0.00478501	+	0.00828788i
$381$	18.2972	+	31.6916i	0.937393	+	1.62361i
$382$	−5.41796	−	1.97198i	−0.277207	−	0.100895i
$383$	−2.20412	−	1.84948i	−0.112625	−	0.0945038i	0.584736	−	0.811224i	$-0.301198\pi$
$383$	−2.20412	−	1.84948i	−0.112625	−	0.0945038i	−0.697361	+	0.716720i	$0.745643\pi$
$384$	−1.09059	+	1.88895i	−0.0556537	+	0.0963951i
$385$	4.47060	+	25.3540i	0.227843	+	1.29216i
$386$	−0.0624134	−	0.353964i	−0.00317676	−	0.0180163i
$387$	−1.50770	+	1.26511i	−0.0766408	+	0.0643093i
$388$	−3.40192	+	1.23820i	−0.172706	+	0.0628599i
$389$	11.0993	−	4.03981i	0.562756	−	0.204827i	−0.0449488	−	0.998989i	$-0.514312\pi$
$389$	11.0993	−	4.03981i	0.562756	−	0.204827i	0.607705	+	0.794163i	$0.292090\pi$
$390$	−6.08790	+	5.10835i	−0.308273	+	0.258671i
$391$	7.35300	+	41.7009i	0.371857	+	2.10891i
$392$	1.70244	+	9.65502i	0.0859862	+	0.487652i
$393$	−1.53082	+	2.65146i	−0.0772196	+	0.133748i
$394$	5.33627	+	4.47766i	0.268837	+	0.225581i
$395$	−9.59957	−	3.49396i	−0.483007	−	0.175800i
$396$	−2.93658	−	5.08631i	−0.147569	−	0.255597i
$397$	15.6563	−	27.1174i	0.785765	−	1.36098i	−0.142776	−	0.989755i	$-0.545603\pi$
$397$	15.6563	−	27.1174i	0.785765	−	1.36098i	0.928541	−	0.371230i	$-0.121064\pi$
$398$	8.56279	−	7.18504i	0.429214	−	0.360153i
$399$	−0.443767	−	0.768626i	−0.0222161	−	0.0384794i
$400$	−0.254900	+	1.44561i	−0.0127450	+	0.0722805i
$401$	−14.0281			−0.700531			−0.350266	−	0.936650i	$-0.613909\pi$
$401$	−14.0281			−0.700531			−0.350266	+	0.936650i	$0.613909\pi$
$402$	4.98683	−	28.2817i	0.248720	−	1.41056i
$403$	15.4325	+	12.9494i	0.768749	+	0.645057i
$404$	−3.71001	+	1.35033i	−0.184580	+	0.0671817i
$405$	−19.7509	−	7.18874i	−0.981430	−	0.357211i
$406$	−3.17519			−0.157582
$407$	20.2446	+	1.82895i	1.00349	+	0.0906577i
$408$	9.69871			0.480158
$409$	0.0761808	+	0.0277275i	0.00376690	+	0.00137104i	0.343903	−	0.939005i	$-0.388251\pi$
$409$	0.0761808	+	0.0277275i	0.00376690	+	0.00137104i	−0.340136	+	0.940376i	$0.610473\pi$
$410$	10.0566	−	3.66031i	0.496661	−	0.180770i
$411$	20.7510	+	17.4122i	1.02357	+	0.858880i
$412$	−0.343616	+	1.94874i	−0.0169287	+	0.0960076i
$413$	−33.2010			−1.63372
$414$	2.90629	−	16.4824i	0.142836	−	0.810066i
$415$	0.618553	+	1.07136i	0.0303636	+	0.0525912i
$416$	1.48512	−	1.24616i	0.0728140	−	0.0610982i
$417$	−20.0663	+	34.7559i	−0.982652	+	1.70200i
$418$	0.165857	+	0.287272i	0.00811231	+	0.0140509i
$419$	−4.35652	−	1.58564i	−0.212830	−	0.0774637i	0.233405	−	0.972380i	$-0.425013\pi$
$419$	−4.35652	−	1.58564i	−0.212830	−	0.0774637i	−0.446235	+	0.894916i	$0.647235\pi$
$420$	12.8726	+	10.8014i	0.628118	+	0.527053i
$421$	9.66110	−	16.7335i	0.470853	−	0.815542i	−0.528591	−	0.848877i	$-0.677279\pi$
$421$	9.66110	−	16.7335i	0.470853	−	0.815542i	0.999444	+	0.0333350i	$0.0106128\pi$
$422$	−2.12029	−	12.0248i	−0.103214	−	0.585356i
$423$	−2.17126	−	12.3138i	−0.105570	−	0.598719i
$424$	0.627258	−	0.526332i	0.0304624	−	0.0255610i
$425$	6.13352	−	2.23242i	0.297519	−	0.108288i
$426$	6.09388	−	2.21799i	0.295250	−	0.107462i
$427$	33.6032	−	28.1964i	1.62617	−	1.36452i
$428$	1.43239	+	8.12350i	0.0692373	+	0.392664i
$429$	2.45381	+	13.9163i	0.118471	+	0.671884i
$430$	−1.05232	+	1.82268i	−0.0507475	+	0.0878972i
$431$	5.77729	+	4.84772i	0.278282	+	0.233507i	0.771237	−	0.636549i	$-0.219639\pi$
$431$	5.77729	+	4.84772i	0.278282	+	0.233507i	−0.492954	+	0.870055i	$0.664083\pi$
$432$	2.54664	+	0.926901i	0.122525	+	0.0445956i
$433$	−14.9169	−	25.8369i	−0.716863	−	1.24164i	−0.962237	−	0.272214i	$-0.912244\pi$
$433$	−14.9169	−	25.8369i	−0.716863	−	1.24164i	0.245374	−	0.969428i	$-0.421089\pi$
$434$	21.2986	−	36.8903i	1.02237	−	1.77079i
$435$	−2.43234	+	2.04097i	−0.116622	+	0.0978571i
$436$	4.39227	+	7.60763i	0.210351	+	0.364339i
$437$	−0.164146	+	0.930916i	−0.00785215	+	0.0445317i
$438$	−5.57812			−0.266533
$439$	3.81229	−	21.6206i	0.181951	−	1.03189i	−0.747860	−	0.663856i	$-0.768919\pi$
$439$	3.81229	−	21.6206i	0.181951	−	1.03189i	0.929811	−	0.368038i	$-0.119970\pi$
$440$	−4.81109	−	4.03699i	−0.229360	−	0.192456i
$441$	−16.1915	+	5.89321i	−0.771022	+	0.280629i
$442$	−8.10060	−	2.94838i	−0.385306	−	0.140240i
$443$	−34.6241			−1.64504			−0.822520	−	0.568736i	$-0.807433\pi$
$443$	−34.6241			−1.64504			−0.822520	+	0.568736i	$0.807433\pi$
$444$	10.8896	−	7.57915i	0.516800	−	0.359691i
$445$	−6.62526			−0.314068
$446$	10.1060	+	3.67827i	0.478531	+	0.174171i
$447$	−25.4293	+	9.25552i	−1.20277	+	0.437771i
$448$	−3.14022	−	2.63496i	−0.148361	−	0.124490i
$449$	−3.46279	+	19.6385i	−0.163419	+	0.926796i	0.787260	+	0.616621i	$0.211499\pi$
$449$	−3.46279	+	19.6385i	−0.163419	+	0.926796i	−0.950679	+	0.310175i	$0.899612\pi$
$450$	−2.57987			−0.121616
$451$	3.30441	−	18.7403i	0.155599	−	0.882444i
$452$	−4.98845	−	8.64025i	−0.234637	−	0.406403i
$453$	−20.9676	+	17.5939i	−0.985146	+	0.826635i
$454$	1.48263	−	2.56799i	0.0695834	−	0.120522i
$455$	−7.46791	−	12.9348i	−0.350101	−	0.606393i
$456$	0.203453	+	0.0740509i	0.00952757	+	0.00346775i
$457$	24.6964	+	20.7227i	1.15525	+	0.969368i	0.999829	−	0.0184812i	$-0.00588309\pi$
$457$	24.6964	+	20.7227i	1.15525	+	0.969368i	0.155418	+	0.987849i	$0.450328\pi$
$458$	1.51631	−	2.62633i	0.0708526	−	0.122720i
$459$	−2.09255	−	11.8674i	−0.0976719	−	0.553925i
$460$	−3.10782	−	17.6253i	−0.144903	−	0.821786i
$461$	5.61373	−	4.71048i	0.261458	−	0.219389i	−0.502630	−	0.864502i	$-0.667634\pi$
$461$	5.61373	−	4.71048i	0.261458	−	0.219389i	0.764087	+	0.645113i	$0.223190\pi$
$462$	28.0773	−	10.2193i	1.30627	−	0.475445i
$463$	−6.09514	+	2.21845i	−0.283265	+	0.103100i	−0.479745	−	0.877408i	$-0.659271\pi$
$463$	−6.09514	+	2.21845i	−0.283265	+	0.103100i	0.196480	+	0.980508i	$0.437049\pi$
$464$	0.593359	−	0.497888i	0.0275460	−	0.0231139i
$465$	−7.39693	−	41.9501i	−0.343025	−	1.94539i
$466$	−0.0501507	−	0.284419i	−0.00232318	−	0.0131754i
$467$	5.99288	−	10.3800i	0.277317	−	0.480328i	−0.693400	−	0.720553i	$-0.743888\pi$
$467$	5.99288	−	10.3800i	0.277317	−	0.480328i	0.970717	+	0.240225i	$0.0772214\pi$
$468$	2.61012	+	2.19015i	0.120653	+	0.101240i
$469$	50.7172	+	18.4596i	2.34190	+	0.852383i
$470$	−6.68542	−	11.5795i	−0.308375	−	0.534122i
$471$	−3.83151	+	6.63637i	−0.176547	+	0.305788i
$472$	6.20440	−	5.20611i	0.285580	−	0.239630i
$473$	1.87114	+	3.24091i	0.0860352	+	0.149017i
$474$	−2.05878	+	11.6759i	−0.0945630	+	0.536293i
$475$	0.145710			0.00668562
$476$	−3.16519	+	17.9507i	−0.145076	+	0.822769i
$477$	1.10241	+	0.925036i	0.0504761	+	0.0423545i
$478$	4.73144	−	1.72210i	0.216411	−	0.0787672i
$479$	−21.3237	−	7.76119i	−0.974305	−	0.354618i	−0.194681	−	0.980867i	$-0.562367\pi$
$479$	−21.3237	−	7.76119i	−0.974305	−	0.354618i	−0.779623	+	0.626249i	$0.784590\pi$
$480$	−4.09926			−0.187105
$481$	−11.3993	+	3.01988i	−0.519765	+	0.137694i
$482$	−17.3760			−0.791454
$483$	80.0114	+	29.1218i	3.64064	+	1.32509i
$484$	−0.157204	+	0.0572177i	−0.00714566	+	0.00260081i
$485$	−5.21204	−	4.37342i	−0.236666	−	0.198587i
$486$	−2.82410	+	16.0162i	−0.128104	+	0.726511i
$487$	12.3108			0.557856			0.278928	−	0.960312i	$-0.410021\pi$
$487$	12.3108			0.557856			0.278928	+	0.960312i	$0.410021\pi$
$488$	−1.85819	+	10.5383i	−0.0841165	+	0.477048i
$489$	2.60807	+	4.51731i	0.117941	+	0.204280i
$490$	−14.1147	+	11.8436i	−0.637637	+	0.535041i
$491$	−0.575398	+	0.996619i	−0.0259674	+	0.0449768i	−0.878717	−	0.477343i	$-0.841600\pi$
$491$	−0.575398	+	0.996619i	−0.0259674	+	0.0449768i	0.852750	+	0.522320i	$0.174933\pi$
$492$	−6.21026	−	10.7565i	−0.279980	−	0.484940i
$493$	−3.23649	−	1.17798i	−0.145764	−	0.0530538i
$494$	−0.147418	−	0.123698i	−0.00663264	−	0.00556545i
$495$	5.51897	−	9.55914i	0.248059	−	0.429652i
$496$	1.80445	+	10.2336i	0.0810224	+	0.459501i
$497$	2.11638	+	12.0026i	0.0949327	+	0.538390i
$498$	1.09985	−	0.922887i	0.0492856	−	0.0413555i
$499$	−26.2321	+	9.54769i	−1.17431	+	0.427413i	−0.854189	−	0.519963i	$-0.825946\pi$
$499$	−26.2321	+	9.54769i	−1.17431	+	0.427413i	−0.320120	+	0.947377i	$0.603723\pi$
$500$	−11.4226	+	4.15749i	−0.510835	+	0.185929i
$501$	−26.0389	+	21.8492i	−1.16333	+	0.976151i
$502$	−0.304872	−	1.72902i	−0.0136071	−	0.0771697i
$503$	−2.84222	−	16.1191i	−0.126728	−	0.718713i	−0.980266	−	0.197682i	$-0.936659\pi$
$503$	−2.84222	−	16.1191i	−0.126728	−	0.718713i	0.853538	−	0.521031i	$-0.174452\pi$
$504$	3.60225	−	6.23929i	0.160457	−	0.277920i
$505$	−5.68407	−	4.76950i	−0.252938	−	0.212240i
$506$	−29.9041	−	10.8842i	−1.32940	−	0.483861i
$507$	10.0787	+	17.4567i	0.447609	+	0.775281i
$508$	8.38869	−	14.5296i	0.372188	−	0.644648i
$509$	3.32007	−	2.78587i	0.147159	−	0.123481i	−0.566236	−	0.824243i	$-0.691601\pi$
$509$	3.32007	−	2.78587i	0.147159	−	0.123481i	0.713395	+	0.700762i	$0.247156\pi$
$510$	9.11381	+	15.7856i	0.403566	+	0.698997i
$511$	1.82043	−	10.3242i	0.0805311	−	0.456715i
$512$	1.00000			0.0441942
$513$	0.0467133	−	0.264924i	0.00206244	−	0.0116967i
$514$	−9.77019	−	8.19816i	−0.430944	−	0.361605i
$515$	−3.49466	+	1.27195i	−0.153993	+	0.0560488i
$516$	2.29530	+	0.835420i	0.101045	+	0.0367773i
$517$	−23.7748			−1.04561
$518$	10.4739	+	22.6284i	0.460196	+	0.994234i
$519$	−38.9932			−1.71161
$520$	3.42381	+	1.24616i	0.150144	+	0.0546479i
$521$	−1.75997	+	0.640577i	−0.0771057	+	0.0280642i	−0.380285	−	0.924869i	$-0.624174\pi$
$521$	−1.75997	+	0.640577i	−0.0771057	+	0.0280642i	0.303179	+	0.952934i	$0.401952\pi$
$522$	1.04284	+	0.875044i	0.0456437	+	0.0382996i
$523$	6.43474	−	36.4932i	0.281371	−	1.59574i	−0.436595	−	0.899658i	$-0.643816\pi$
$523$	6.43474	−	36.4932i	0.281371	−	1.59574i	0.717966	−	0.696078i	$-0.245073\pi$
$524$	1.40367			0.0613194
$525$	2.27911	−	12.9255i	0.0994686	−	0.564115i
$526$	13.1825	+	22.8328i	0.574786	+	0.995559i
$527$	35.3960	−	29.7007i	1.54187	−	1.29378i
$528$	−3.64447	+	6.31240i	−0.158605	+	0.274712i
$529$	−33.8430	−	58.6178i	−1.47144	−	2.54860i
$530$	1.44609	+	0.526332i	0.0628140	+	0.0228624i
$531$	10.9043	+	9.14980i	0.473207	+	0.397068i
$532$	−0.203453	+	0.352391i	−0.00882082	+	0.0152781i
$533$	1.91702	+	10.8720i	0.0830356	+	0.470918i
$534$	1.33520	+	7.57232i	0.0577799	+	0.327686i
$535$	−11.8758	+	9.96494i	−0.513434	+	0.430822i
$536$	−12.3723	+	4.50314i	−0.534401	+	0.194506i
$537$	41.8254	−	15.2232i	1.80490	−	0.656929i
$538$	10.4226	−	8.74563i	0.449352	−	0.377051i
$539$	5.68913	+	32.2646i	0.245048	+	1.38974i
$540$	0.884439	+	5.01590i	0.0380602	+	0.215850i
$541$	−7.75312	+	13.4288i	−0.333332	+	0.577349i	−0.983163	−	0.182730i	$-0.941506\pi$
$541$	−7.75312	+	13.4288i	−0.333332	+	0.577349i	0.649831	+	0.760079i	$0.274840\pi$
$542$	−3.30617	−	2.77421i	−0.142012	−	0.119162i
$543$	37.4600	+	13.6343i	1.60756	+	0.585104i
$544$	−2.22328	−	3.85083i	−0.0953223	−	0.165103i
$545$	−8.25476	+	14.2977i	−0.353595	+	0.612445i
$546$	−13.2787	+	11.1422i	−0.568278	+	0.476842i
$547$	20.5925	+	35.6673i	0.880472	+	1.52502i	0.850817	+	0.525462i	$0.176107\pi$
$547$	20.5925	+	35.6673i	0.880472	+	1.52502i	0.0296544	+	0.999560i	$0.490559\pi$
$548$	2.15658	−	12.2306i	0.0921247	−	0.522465i
$549$	−18.8070			−0.802663
$550$	−0.851812	+	4.83087i	−0.0363214	+	0.205989i
$551$	−0.0588988	−	0.0494220i	−0.00250917	−	0.00210545i
$552$	−19.5185	+	7.10415i	−0.830762	+	0.302373i
$553$	−20.9383	−	7.62092i	−0.890388	−	0.324075i
$554$	−3.49344			−0.148422
$555$	22.5687	+	10.6019i	0.957989	+	0.450024i
$556$	18.3996			0.780315
$557$	11.4686	+	4.17423i	0.485940	+	0.176868i	0.573359	−	0.819304i	$-0.305640\pi$
$557$	11.4686	+	4.17423i	0.485940	+	0.176868i	−0.0874196	+	0.996172i	$0.527862\pi$
$558$	−17.1617	+	6.24634i	−0.726512	+	0.264429i
$559$	−1.66312	−	1.39553i	−0.0703426	−	0.0590245i
$560$	1.33780	−	7.58705i	0.0565325	−	0.320611i
$561$	32.4107			1.36838
$562$	−1.27419	+	7.22628i	−0.0537484	+	0.304822i
$563$	5.70965	+	9.88940i	0.240633	+	0.416788i	0.960895	−	0.276914i	$-0.0893117\pi$
$563$	5.70965	+	9.88940i	0.240633	+	0.416788i	−0.720262	+	0.693702i	$0.755978\pi$
$564$	−11.8874	+	9.97471i	−0.500550	+	0.420011i
$565$	9.37522	−	16.2384i	0.394418	−	0.683153i
$566$	−7.00144	−	12.1268i	−0.294292	−	0.509729i
$567$	−43.0801	−	15.6799i	−1.80919	−	0.658493i
$568$	−2.27757	−	1.91111i	−0.0955648	−	0.0801884i
$569$	11.1732	−	19.3526i	0.468406	−	0.811303i	−0.530942	−	0.847408i	$-0.678162\pi$
$569$	11.1732	−	19.3526i	0.468406	−	0.811303i	0.999348	+	0.0361049i	$0.0114951\pi$
$570$	0.0706586	+	0.400725i	0.00295956	+	0.0167845i
$571$	−2.29253	−	13.0016i	−0.0959395	−	0.544100i	−0.994455	−	0.105159i	$-0.966465\pi$
$571$	−2.29253	−	13.0016i	−0.0959395	−	0.544100i	0.898516	−	0.438941i	$-0.144646\pi$
$572$	4.96290	−	4.16437i	0.207509	−	0.174121i
$573$	−11.8175	+	4.30122i	−0.493683	+	0.179686i
$574$	21.9352	−	7.98376i	0.915558	−	0.333236i
$575$	−10.7084	+	8.98540i	−0.446571	+	0.374717i
$576$	0.305189	+	1.73081i	0.0127162	+	0.0721172i
$577$	5.09708	+	28.9070i	0.212194	+	1.20341i	0.885709	+	0.464241i	$0.153673\pi$
$577$	5.09708	+	28.9070i	0.212194	+	1.20341i	−0.673515	+	0.739174i	$0.735216\pi$
$578$	−1.38595	+	2.40053i	−0.0576478	+	0.0998489i
$579$	−0.600553	−	0.503924i	−0.0249581	−	0.0209424i
$580$	1.36794	+	0.497888i	0.0568004	+	0.0206737i
$581$	1.34917	+	2.33683i	0.0559730	+	0.0969481i
$582$	−3.94819	+	6.83846i	−0.163658	+	0.283463i
$583$	2.09614	−	1.75887i	0.0868133	−	0.0728450i
$584$	1.27870	+	2.21477i	0.0529129	+	0.0916478i
$585$	−1.11197	+	6.30628i	−0.0459742	+	0.260733i
$586$	−25.2747			−1.04409
$587$	−3.68838	+	20.9178i	−0.152236	+	0.863371i	0.809034	+	0.587762i	$0.199991\pi$
$587$	−3.68838	+	20.9178i	−0.152236	+	0.863371i	−0.961270	+	0.275609i	$0.911120\pi$
$588$	16.3812	+	13.7455i	0.675549	+	0.566853i
$589$	0.969282	−	0.352790i	0.0399386	−	0.0145365i
$590$	14.3037	+	5.20611i	0.588872	+	0.214332i
$591$	15.1941			0.625000
$592$	−5.50555	−	2.58629i	−0.226277	−	0.106296i
$593$	31.4119			1.28993			0.644965	−	0.764212i	$-0.276872\pi$
$593$	31.4119			1.28993			0.644965	+	0.764212i	$0.276872\pi$
$594$	8.51024	+	3.09747i	0.349179	+	0.127091i
$595$	−32.1908	+	11.7165i	−1.31969	+	0.480329i
$596$	9.50414	+	7.97492i	0.389305	+	0.326666i
$597$	4.23372	−	24.0106i	0.173274	−	0.982688i
$598$	18.4620			0.754965
$599$	−3.52563	+	19.9949i	−0.144053	+	0.816967i	0.824069	+	0.566490i	$0.191699\pi$
$599$	−3.52563	+	19.9949i	−0.144053	+	0.816967i	−0.968122	+	0.250478i	$0.919412\pi$
$600$	1.60088	+	2.77281i	0.0653558	+	0.113200i
$601$	−34.1524	+	28.6573i	−1.39311	+	1.16896i	−0.429044	+	0.903284i	$0.641149\pi$
$601$	−34.1524	+	28.6573i	−1.39311	+	1.16896i	−0.964063	+	0.265672i	$0.914406\pi$
$602$	−2.29530	+	3.97557i	−0.0935493	+	0.162032i
$603$	−11.5700	−	20.0398i	−0.471166	−	0.816083i
$604$	11.7921	+	4.29198i	0.479814	+	0.174638i
$605$	−0.240851	−	0.202098i	−0.00979199	−	0.00821646i
$606$	−4.30576	+	7.45779i	−0.174910	+	0.302952i
$607$	−3.49184	−	19.8032i	−0.141730	−	0.803788i	−0.969935	−	0.243364i	$-0.921749\pi$
$607$	−3.49184	−	19.8032i	−0.141730	−	0.803788i	0.828205	−	0.560425i	$-0.189362\pi$
$608$	−0.0172369	−	0.0977553i	−0.000699048	−	0.00396450i
$609$	−5.30534	+	4.45171i	−0.214983	+	0.180393i
$610$	−18.8983	+	6.87841i	−0.765169	+	0.278499i
$611$	12.9609	−	4.71739i	0.524343	−	0.190845i
$612$	5.98655	−	5.02331i	0.241992	−	0.203055i
$613$	5.59486	+	31.7300i	0.225974	+	1.28156i	0.860814	+	0.508920i	$0.169955\pi$
$613$	5.59486	+	31.7300i	0.225974	+	1.28156i	−0.634839	+	0.772644i	$0.718934\pi$
$614$	−4.27159	−	24.2254i	−0.172387	−	0.977656i
$615$	11.6715	−	20.2156i	0.470639	−	0.815172i
$616$	−10.4938	−	8.80536i	−0.422808	−	0.354778i
$617$	−36.5834	−	13.3153i	−1.47279	−	0.536052i	−0.523934	−	0.851759i	$-0.675536\pi$
$617$	−36.5834	−	13.3153i	−1.47279	−	0.536052i	−0.948857	+	0.315707i	$0.897758\pi$
$618$	2.15806	+	3.73786i	0.0868097	+	0.150359i
$619$	13.1812	−	22.8305i	0.529796	−	0.917634i	−0.469600	−	0.882879i	$-0.655602\pi$
$619$	13.1812	−	22.8305i	0.529796	−	0.917634i	0.999396	−	0.0347545i	$-0.0110649\pi$
$620$	−14.9605	+	12.5533i	−0.600827	+	0.504154i
$621$	12.9039	+	22.3503i	0.517817	+	0.896885i
$622$	0.904212	−	5.12804i	0.0362556	−	0.205616i
$623$	−14.4508			−0.578961
$624$	0.734290	−	4.16437i	0.0293951	−	0.166708i
$625$	−11.8780	−	9.96686i	−0.475122	−	0.398674i
$626$	−6.79999	+	2.47499i	−0.271782	+	0.0989206i
$627$	0.679890	+	0.247460i	0.0271522	+	0.00988259i
$628$	3.51326			0.140194
$629$	2.28103	+	26.9510i	0.0909507	+	1.07461i
$630$	13.5400			0.539448
$631$	−38.8218	−	14.1300i	−1.54547	−	0.562506i	−0.578122	−	0.815950i	$-0.696214\pi$
$631$	−38.8218	−	14.1300i	−1.54547	−	0.562506i	−0.967350	+	0.253445i	$0.918436\pi$
$632$	5.10782	−	1.85910i	0.203178	−	0.0739509i
$633$	−20.4018	−	17.1192i	−0.810900	−	0.680426i
$634$	−2.31803	+	13.1462i	−0.0920608	+	0.522103i
$635$	31.5312			1.25128
$636$	0.310136	−	1.75887i	0.0122977	−	0.0697438i
$637$	−9.50340	−	16.4604i	−0.376538	−	0.652184i
$638$	1.98286	−	1.66382i	0.0785021	−	0.0658711i
$639$	2.61268	−	4.52530i	0.103356	−	0.179018i
$640$	0.939693	+	1.62760i	0.0371446	+	0.0643364i
$641$	41.1013	+	14.9596i	1.62340	+	0.590871i	0.984026	−	0.178023i	$-0.0569701\pi$
$641$	41.1013	+	14.9596i	1.62340	+	0.590871i	0.639377	+	0.768893i	$0.279192\pi$
$642$	13.7827	+	11.5651i	0.543961	+	0.456438i
$643$	1.65777	−	2.87133i	0.0653759	−	0.113234i	−0.831485	−	0.555548i	$-0.812509\pi$
$643$	1.65777	−	2.87133i	0.0653759	−	0.113234i	0.896861	+	0.442313i	$0.145842\pi$
$644$	−6.77870	−	38.4439i	−0.267118	−	1.51490i
$645$	0.797148	+	4.52085i	0.0313877	+	0.178008i
$646$	−0.338117	+	0.283714i	−0.0133030	+	0.0111626i
$647$	21.4630	−	7.81189i	0.843797	−	0.307117i	0.116288	−	0.993216i	$-0.462900\pi$
$647$	21.4630	−	7.81189i	0.843797	−	0.307117i	0.727509	+	0.686099i	$0.240678\pi$
$648$	10.5092	−	3.82505i	0.412841	−	0.150262i
$649$	20.7335	−	17.3975i	0.813863	−	0.682912i
$650$	−0.494171	−	2.80258i	−0.0193830	−	0.109926i
$651$	−16.1340	−	91.5004i	−0.632341	−	3.58618i
$652$	1.19572	−	2.07105i	0.0468280	−	0.0811084i
$653$	1.62966	+	1.36745i	0.0637735	+	0.0535124i	0.674117	−	0.738624i	$-0.264524\pi$
$653$	1.62966	+	1.36745i	0.0637735	+	0.0535124i	−0.610344	+	0.792137i	$0.708969\pi$
$654$	18.0051	+	6.55331i	0.704054	+	0.256255i
$655$	1.31901	+	2.28460i	0.0515382	+	0.0892667i
$656$	−2.84721	+	4.93152i	−0.111165	+	0.192543i
$657$	−3.44311	+	2.88911i	−0.134328	+	0.112715i
$658$	−14.5821	−	25.2569i	−0.568468	−	0.984615i
$659$	−1.48751	+	8.43610i	−0.0579452	+	0.328624i	−0.999976	−	0.00690225i	$-0.997803\pi$
$659$	−1.48751	+	8.43610i	−0.0579452	+	0.328624i	0.942031	+	0.335526i	$0.108914\pi$
$660$	−13.6987			−0.533222
$661$	0.139199	−	0.789436i	0.00541421	−	0.0307055i	−0.981981	−	0.188980i	$-0.939482\pi$
$661$	0.139199	−	0.789436i	0.00541421	−	0.0307055i	0.987395	+	0.158274i	$0.0505930\pi$
$662$	−3.50322	−	2.93955i	−0.136156	−	0.114249i
$663$	−17.6688	+	6.43092i	−0.686200	+	0.249756i
$664$	−0.618553	−	0.225135i	−0.0240045	−	0.00873692i
$665$	−0.764734			−0.0296551
$666$	2.79614	−	10.3184i	0.108348	−	0.399829i
$667$	7.37622			0.285609
$668$	14.6442	+	5.33004i	0.566599	+	0.206225i
$669$	22.0428	−	8.02294i	0.852225	−	0.310185i
$670$	−18.9554	−	15.9055i	−0.732312	−	0.614483i
$671$	−6.20962	+	35.2165i	−0.239720	+	1.35952i
$672$	−8.94120			−0.344914
$673$	7.47353	−	42.3845i	0.288083	−	1.63380i	−0.405976	−	0.913884i	$-0.633068\pi$
$673$	7.47353	−	42.3845i	0.288083	−	1.63380i	0.694059	−	0.719918i	$-0.255821\pi$
$674$	−1.62665	−	2.81744i	−0.0626563	−	0.108524i
$675$	3.04744	−	2.55711i	0.117296	−	0.0984231i
$676$	4.62075	−	8.00337i	0.177721	−	0.307822i
$677$	−9.99716	−	17.3156i	−0.384222	−	0.665492i	0.607439	−	0.794367i	$-0.292197\pi$
$677$	−9.99716	−	17.3156i	−0.384222	−	0.665492i	−0.991661	+	0.128874i	$0.958864\pi$
$678$	−20.4490	−	7.44281i	−0.785338	−	0.285840i
$679$	−11.3684	−	9.53918i	−0.436277	−	0.366080i
$680$	4.17840	−	7.23720i	0.160234	−	0.277534i
$681$	−1.12311	−	6.36949i	−0.0430378	−	0.244079i
$682$	6.03003	+	34.1980i	0.230902	+	1.30951i
$683$	28.2126	−	23.6732i	1.07953	−	0.905830i	0.0836451	−	0.996496i	$-0.473344\pi$
$683$	28.2126	−	23.6732i	1.07953	−	0.905830i	0.995881	+	0.0906653i	$0.0288993\pi$
$684$	0.163936	−	0.0596677i	0.00626823	−	0.00228145i
$685$	21.9330	−	7.98295i	0.838016	−	0.305013i
$686$	−8.80504	+	7.38831i	−0.336178	+	0.282087i
$687$	−1.14863	−	6.51419i	−0.0438228	−	0.248532i
$688$	−0.194461	−	1.10284i	−0.00741377	−	0.0420456i
$689$	−0.793725	+	1.37477i	−0.0302385	+	0.0523746i
$690$	−29.9041	−	25.0925i	−1.13843	−	0.955254i
$691$	−0.825837	−	0.300580i	−0.0314163	−	0.0114346i	0.326264	−	0.945279i	$-0.394210\pi$
$691$	−0.825837	−	0.300580i	−0.0314163	−	0.0114346i	−0.357681	+	0.933844i	$0.616432\pi$
$692$	8.93860	+	15.4821i	0.339794	+	0.588541i
$693$	12.0378	−	20.8501i	0.457280	−	0.792031i
$694$	18.7508	−	15.7338i	0.711770	−	0.597246i
$695$	17.2899	+	29.9471i	0.655845	+	1.13596i
$696$	0.293376	−	1.66382i	0.0111204	−	0.0630668i
$697$	25.3206			0.959087
$698$	0.990209	−	5.61576i	0.0374800	−	0.212559i
$699$	−0.482559	−	0.404915i	−0.0182521	−	0.0153153i
$700$	−5.65446	+	2.05806i	−0.213719	+	0.0777872i
$701$	19.5851	+	7.12840i	0.739719	+	0.269236i	0.684273	−	0.729226i	$-0.260120\pi$
$701$	19.5851	+	7.12840i	0.739719	+	0.269236i	0.0554462	+	0.998462i	$0.482342\pi$
$702$	−5.25399			−0.198299
$703$	−0.157924	+	0.582776i	−0.00595623	+	0.0219798i
$704$	3.34175			0.125947
$705$	−27.4053	−	9.97471i	−1.03214	−	0.375669i
$706$	−22.9604	+	8.35691i	−0.864127	+	0.314517i
$707$	−12.3979	−	10.4031i	−0.466273	−	0.391249i
$708$	3.06765	−	17.3975i	0.115289	−	0.653838i
$709$	−21.6348			−0.812512			−0.406256	−	0.913759i	$-0.633166\pi$
$709$	−21.6348			−0.812512			−0.406256	+	0.913759i	$0.633166\pi$
$710$	0.970296	−	5.50282i	0.0364146	−	0.206517i
$711$	4.77660	+	8.27331i	0.179136	+	0.310273i
$712$	2.70048	−	2.26597i	0.101205	−	0.0849209i
$713$	−49.4784	+	85.6991i	−1.85298	+	3.20946i
$714$	19.8788	+	34.4311i	0.743945	+	1.28855i
$715$	11.4415	+	4.16437i	0.427888	+	0.155738i
$716$	−15.6321	−	13.1169i	−0.584200	−	0.490202i
$717$	5.49121	−	9.51105i	0.205073	−	0.355197i
$718$	3.24882	+	18.4250i	0.121245	+	0.687614i
$719$	4.46063	+	25.2975i	0.166353	+	0.943437i	0.947658	+	0.319287i	$0.103443\pi$
$719$	4.46063	+	25.2975i	0.166353	+	0.943437i	−0.781305	+	0.624150i	$0.785445\pi$
$720$	−2.53028	+	2.12316i	−0.0942979	+	0.0791254i
$721$	−7.62245	+	2.77434i	−0.283875	+	0.103322i
$722$	17.8449	−	6.49501i	0.664118	−	0.241719i
$723$	−29.0331	+	24.3616i	−1.07975	+	0.906019i
$724$	−3.17367	−	17.9988i	−0.117949	−	0.668919i
$725$	−0.197439	−	1.11973i	−0.00733272	−	0.0415859i
$726$	−0.182448	+	0.316009i	−0.00677128	+	0.0117282i
$727$	20.4343	+	17.1464i	0.757868	+	0.635927i	0.937571	−	0.347794i	$-0.113069\pi$
$727$	20.4343	+	17.1464i	0.757868	+	0.635927i	−0.179703	+	0.983721i	$0.557514\pi$
$728$	7.46791	+	2.71810i	0.276779	+	0.100739i
$729$	0.961018	+	1.66453i	0.0355933	+	0.0616493i
$730$	−2.40317	+	4.16241i	−0.0889452	+	0.154058i
$731$	−3.81453	+	3.20077i	−0.141086	+	0.118385i
$732$	11.6703	+	20.2135i	0.431345	+	0.747112i
$733$	−1.97614	+	11.2073i	−0.0729906	+	0.413950i	0.926317	+	0.376745i	$0.122957\pi$
$733$	−1.97614	+	11.2073i	−0.0729906	+	0.413950i	−0.999308	+	0.0372052i	$0.988154\pi$
$734$	33.7230			1.24474
$735$	−6.97875	+	39.5785i	−0.257415	+	1.45987i
$736$	7.29498	+	6.12122i	0.268897	+	0.225631i
$737$	−41.3451	+	15.0484i	−1.52297	+	0.554314i
$738$	−9.40447	−	3.42295i	−0.346183	−	0.126000i
$739$	3.18059			0.117000			0.0584999	−	0.998287i	$-0.481368\pi$
$739$	3.18059			0.117000			0.0584999	+	0.998287i	$0.481368\pi$
$740$	−0.964102	−	11.3911i	−0.0354411	−	0.418746i
$741$	−0.419746			−0.0154197
$742$	3.15416	+	1.14802i	0.115793	+	0.0421452i
$743$	49.7669	−	18.1137i	1.82577	−	0.664527i	0.831776	−	0.555112i	$-0.187325\pi$
$743$	49.7669	−	18.1137i	1.82577	−	0.664527i	0.993996	−	0.109415i	$-0.0348976\pi$
$744$	17.3628	+	14.5691i	0.636551	+	0.534130i
$745$	−4.04897	+	22.9629i	−0.148343	+	0.841295i
$746$	31.4347			1.15091
$747$	0.200891	−	1.13931i	0.00735020	−	0.0416851i
$748$	−7.42965	−	12.8685i	−0.271655	−	0.470520i
$749$	−25.9031	+	21.7353i	−0.946478	+	0.794189i
$750$	−13.2568	+	22.9615i	−0.484071	+	0.838436i
$751$	3.21483	+	5.56825i	0.117311	+	0.203188i	0.918701	−	0.394954i	$-0.129239\pi$
$751$	3.21483	+	5.56825i	0.117311	+	0.203188i	−0.801390	+	0.598142i	$0.795906\pi$
$752$	6.68542	+	2.43329i	0.243792	+	0.0887331i
$753$	−2.93354	−	2.46153i	−0.106904	−	0.0897031i
$754$	−0.750829	+	1.30047i	−0.0273436	+	0.0473605i
$755$	4.09536	+	23.2259i	0.149045	+	0.845278i
$756$	1.92911	+	10.9405i	0.0701612	+	0.397904i
$757$	−24.3176	+	20.4049i	−0.883837	+	0.741627i	−0.966964	−	0.254912i	$-0.917954\pi$
$757$	−24.3176	+	20.4049i	−0.883837	+	0.741627i	0.0831276	+	0.996539i	$0.473509\pi$
$758$	−6.54676	+	2.38282i	−0.237789	+	0.0865481i
$759$	−65.2259	+	23.7403i	−2.36755	+	0.861718i
$760$	0.142909	−	0.119915i	0.00518384	−	0.00434976i
$761$	−4.00842	−	22.7329i	−0.145305	−	0.824065i	−0.967122	−	0.254314i	$-0.918150\pi$
$761$	−4.00842	−	22.7329i	−0.145305	−	0.824065i	0.821817	−	0.569752i	$-0.192961\pi$
$762$	−6.35454	−	36.0384i	−0.230201	−	1.30553i
$763$	−18.0051	+	31.1857i	−0.651827	+	1.12900i
$764$	4.41676	+	3.70610i	0.159793	+	0.134082i
$765$	13.8014	+	5.02331i	0.498992	+	0.181618i
$766$	1.43864	+	2.49179i	0.0519801	+	0.0900321i
$767$	−7.85096	+	13.5983i	−0.283482	+	0.491005i
$768$	1.67088	−	1.40203i	0.0602925	−	0.0505914i
$769$	−23.5799	−	40.8416i	−0.850312	−	1.47278i	−0.880926	−	0.473253i	$-0.843080\pi$
$769$	−23.5799	−	40.8416i	−0.850312	−	1.47278i	0.0306140	−	0.999531i	$-0.490254\pi$
$770$	4.47060	−	25.3540i	0.161109	−	0.913696i
$771$	−27.8188			−1.00187
$772$	−0.0624134	+	0.353964i	−0.00224631	+	0.0127394i
$773$	−3.06540	−	2.57218i	−0.110255	−	0.0925148i	0.585994	−	0.810316i	$-0.300704\pi$
$773$	−3.06540	−	2.57218i	−0.110255	−	0.0925148i	−0.696248	+	0.717801i	$0.745149\pi$
$774$	1.84947	−	0.673152i	0.0664778	−	0.0241960i
$775$	14.3338	+	5.21707i	0.514885	+	0.187403i
$776$	3.62024			0.129959
$777$	49.2263	+	23.1245i	1.76598	+	0.829587i
$778$	−11.8116			−0.423467
$779$	0.531159	+	0.193326i	0.0190308	+	0.00692663i
$780$	7.46791	−	2.71810i	0.267394	−	0.0973235i
$781$	−7.61108	−	6.38645i	−0.272346	−	0.228525i
$782$	7.35300	−	41.7009i	0.262943	−	1.49122i
$783$	−2.09916			−0.0750179
$784$	1.70244	−	9.65502i	0.0608014	−	0.344822i
$785$	3.30138	+	5.71816i	0.117831	+	0.204090i
$786$	2.34535	−	1.96798i	0.0836559	−	0.0701956i
$787$	−5.78344	+	10.0172i	−0.206157	+	0.357075i	−0.950501	−	0.310722i	$-0.899429\pi$
$787$	−5.78344	+	10.0172i	−0.206157	+	0.357075i	0.744344	+	0.667797i	$0.232763\pi$
$788$	−3.48300	−	6.03274i	−0.124077	−	0.214907i
$789$	54.0387	+	19.6685i	1.92383	+	0.700217i
$790$	7.82564	+	6.56649i	0.278424	+	0.233625i
$791$	20.4490	−	35.4186i	0.727081	−	1.25934i
$792$	1.01987	+	5.78394i	0.0362393	+	0.205523i
$793$	−3.60245	−	20.4305i	−0.127927	−	0.725509i
$794$	−23.9868	+	20.1273i	−0.851259	+	0.714291i
$795$	3.15416	−	1.14802i	0.111867	−	0.0407161i
$796$	−10.5038	+	3.82308i	−0.372298	+	0.135505i
$797$	−28.0792	+	23.5612i	−0.994615	+	0.834581i	−0.986229	−	0.165384i	$-0.947114\pi$
$797$	−28.0792	+	23.5612i	−0.994615	+	0.834581i	−0.00838538	+	0.999965i	$0.502669\pi$
$798$	0.154119	+	0.874049i	0.00545574	+	0.0309410i
$799$	−5.49335	−	31.1543i	−0.194341	−	1.10216i
$800$	0.733956	−	1.27125i	0.0259492	−	0.0449454i
$801$	4.74613	+	3.98248i	0.167696	+	0.140714i
$802$	13.1821	+	4.79790i	0.465477	+	0.169420i
$803$	4.27309	+	7.40121i	0.150794	+	0.261183i
$804$	−14.3590	+	24.8705i	−0.506403	+	0.877115i
$805$	56.2012	−	47.1584i	1.98083	−	1.66212i
$806$	−10.0729	−	17.4467i	−0.354802	−	0.614534i
$807$	5.15328	−	29.2257i	0.181404	−	1.02879i
$808$	3.94811			0.138894
$809$	−1.35385	+	7.67809i	−0.0475990	+	0.269947i	−0.999314	−	0.0370359i	$-0.988208\pi$
$809$	−1.35385	+	7.67809i	−0.0475990	+	0.269947i	0.951715	+	0.306983i	$0.0993195\pi$
$810$	16.1011	+	13.5104i	0.565734	+	0.474707i
$811$	27.9730	−	10.1813i	0.982265	−	0.357515i	0.199545	−	0.979889i	$-0.436054\pi$
$811$	27.9730	−	10.1813i	0.982265	−	0.357515i	0.782720	+	0.622374i	$0.213832\pi$
$812$	2.98370	+	1.08598i	0.104707	+	0.0381104i
$813$	−9.41372			−0.330154
$814$	−18.3982	−	8.64272i	−0.644856	−	0.302927i
$815$	4.49443			0.157433
$816$	−9.11381	−	3.31716i	−0.319047	−	0.116124i
$817$	−0.104457	+	0.0380192i	−0.00365449	+	0.00133012i
$818$	−0.0621032	−	0.0521107i	−0.00217139	−	0.00182201i
$819$	−2.42539	+	13.7551i	−0.0847501	+	0.480642i
$820$	−10.7020			−0.373731
$821$	6.80968	−	38.6196i	0.237659	−	1.34783i	−0.599281	−	0.800539i	$-0.704547\pi$
$821$	6.80968	−	38.6196i	0.237659	−	1.34783i	0.836940	−	0.547294i	$-0.184342\pi$
$822$	−13.5443	−	23.4594i	−0.472411	−	0.818240i
$823$	−9.28031	+	7.78710i	−0.323491	+	0.271441i	−0.790042	−	0.613053i	$-0.789941\pi$
$823$	−9.28031	+	7.78710i	−0.323491	+	0.271441i	0.466550	+	0.884495i	$0.345497\pi$
$824$	0.989402	−	1.71369i	0.0344674	−	0.0596994i
$825$	5.34975	+	9.26604i	0.186254	+	0.322602i
$826$	31.1987	+	11.3554i	1.08554	+	0.395105i
$827$	−10.7589	−	9.02779i	−0.374124	−	0.313927i	0.436267	−	0.899817i	$-0.356300\pi$
$827$	−10.7589	−	9.02779i	−0.374124	−	0.313927i	−0.810390	+	0.585890i	$0.800745\pi$
$828$	−8.36833	+	14.4944i	−0.290820	+	0.503714i
$829$	5.56767	+	31.5758i	0.193373	+	1.09667i	0.914716	+	0.404096i	$0.132414\pi$
$829$	5.56767	+	31.5758i	0.193373	+	1.09667i	−0.721343	+	0.692578i	$0.756475\pi$
$830$	−0.214821	−	1.21831i	−0.00745655	−	0.0422882i
$831$	−5.83710	+	4.89791i	−0.202487	+	0.169907i
$832$	−1.82177	+	0.663070i	−0.0631585	+	0.0229878i
$833$	−40.9649	+	14.9100i	−1.41935	+	0.516601i
$834$	30.7434	−	25.7968i	1.06456	−	0.893269i
$835$	5.08586	+	28.8433i	0.176003	+	0.998165i
$836$	−0.0576014	−	0.326674i	−0.00199219	−	0.0112982i
$837$	14.0808	−	24.3887i	0.486704	−	0.842996i
$838$	3.55146	+	2.98003i	0.122683	+	0.102944i
$839$	10.3875	+	3.78073i	0.358616	+	0.130525i	0.515044	−	0.857164i	$-0.327776\pi$
$839$	10.3875	+	3.78073i	0.358616	+	0.130525i	−0.156428	+	0.987689i	$0.549998\pi$
$840$	−8.40198	−	14.5527i	−0.289896	−	0.502114i
$841$	14.2000	−	24.5951i	0.489656	−	0.848109i
$842$	−14.8017	+	12.4201i	−0.510099	+	0.428024i
$843$	8.00245	+	13.8607i	0.275619	+	0.477386i
$844$	−2.12029	+	12.0248i	−0.0729834	+	0.413909i
$845$	17.3683			0.597489
$846$	−2.17126	+	12.3138i	−0.0746494	+	0.423358i
$847$	−0.525338	−	0.440811i	−0.0180508	−	0.0151464i
$848$	−0.769446	+	0.280056i	−0.0264229	+	0.00961715i
$849$	−28.7007	−	10.4462i	−0.985007	−	0.358513i
$850$	−6.52715			−0.223880
$851$	−24.3317	−	52.5676i	−0.834080	−	1.80199i
$852$	−6.48497			−0.222172
$853$	−48.0604	−	17.4925i	−1.64556	−	0.598933i	−0.657558	−	0.753404i	$-0.728411\pi$
$853$	−48.0604	−	17.4925i	−1.64556	−	0.598933i	−0.987997	+	0.154471i	$0.950633\pi$
$854$	−41.2204	+	15.0030i	−1.41053	+	0.513392i
$855$	0.251164	+	0.210751i	0.00858962	+	0.00720755i
$856$	1.43239	−	8.12350i	0.0489581	−	0.277655i
$857$	−11.4315			−0.390493			−0.195246	−	0.980754i	$-0.562551\pi$
$857$	−11.4315			−0.390493			−0.195246	+	0.980754i	$0.562551\pi$
$858$	2.45381	−	13.9163i	0.0837718	−	0.475094i
$859$	5.49634	+	9.51995i	0.187533	+	0.324816i	0.944427	−	0.328721i	$-0.106618\pi$
$859$	5.49634	+	9.51995i	0.187533	+	0.324816i	−0.756894	+	0.653537i	$0.773284\pi$
$860$	1.61225	−	1.35284i	0.0549773	−	0.0461314i
$861$	25.4575	−	44.0937i	0.867590	−	1.50271i
$862$	−3.77086	−	6.53132i	−0.128436	−	0.222458i
$863$	14.1266	+	5.14167i	0.480876	+	0.175024i	0.571073	−	0.820899i	$-0.306527\pi$
$863$	14.1266	+	5.14167i	0.480876	+	0.175024i	−0.0901969	+	0.995924i	$0.528750\pi$
$864$	−2.07604	−	1.74200i	−0.0706283	−	0.0592642i
$865$	−16.7991	+	29.0968i	−0.571185	+	0.989322i
$866$	5.18060	+	29.3806i	0.176044	+	0.998395i
$867$	1.04987	+	5.95412i	0.0356555	+	0.202213i
$868$	−32.6314	+	27.3810i	−1.10758	+	0.929371i
$869$	17.0691	−	6.21263i	0.579028	−	0.210749i
$870$	2.98370	−	1.08598i	0.101157	−	0.0368181i
$871$	19.5535	−	16.4074i	0.662546	−	0.555942i
$872$	−1.52542	−	8.65108i	−0.0516572	−	0.292962i
$873$	1.10486	+	6.26596i	0.0373938	+	0.212071i
$874$	0.472638	−	0.818634i	0.0159872	−	0.0276907i
$875$	−38.1715	−	32.0297i	−1.29043	−	1.08280i
$876$	5.24172	+	1.90783i	0.177101	+	0.0644596i
$877$	14.7236	+	25.5020i	0.497180	+	0.861141i	0.999995	−	0.00325344i	$-0.00103560\pi$
$877$	14.7236	+	25.5020i	0.497180	+	0.861141i	−0.502815	+	0.864394i	$0.667702\pi$
$878$	−10.9771	+	19.0128i	−0.370458	+	0.641652i
$879$	−42.2309	+	35.4360i	−1.42441	+	1.19523i
$880$	3.14022	+	5.43902i	0.105857	+	0.183349i
$881$	3.19146	−	18.0997i	0.107523	−	0.609793i	−0.882660	−	0.470013i	$-0.844249\pi$
$881$	3.19146	−	18.0997i	0.107523	−	0.609793i	0.990183	−	0.139780i	$-0.0446396\pi$
$882$	17.2306			0.580184
$883$	5.06999	−	28.7534i	0.170619	−	0.967628i	−0.772461	−	0.635062i	$-0.780975\pi$
$883$	5.06999	−	28.7534i	0.170619	−	0.967628i	0.943080	−	0.332566i	$-0.107914\pi$
$884$	6.60367	+	5.54114i	0.222106	+	0.186369i
$885$	31.1987	−	11.3554i	1.04873	−	0.381708i
$886$	32.5360	+	11.8421i	1.09307	+	0.397844i
$887$	−36.5446			−1.22705			−0.613524	−	0.789676i	$-0.710249\pi$
$887$	−36.5446			−1.22705			−0.613524	+	0.789676i	$0.710249\pi$
$888$	−12.8251	+	3.39760i	−0.430384	+	0.114016i
$889$	68.7749			2.30664
$890$	6.22571	+	2.26597i	0.208686	+	0.0759556i
$891$	35.1192	−	12.7823i	1.17654	−	0.428225i
$892$	−8.23845	−	6.91288i	−0.275844	−	0.231460i
$893$	0.122631	−	0.695478i	0.00410371	−	0.0232733i
$894$	27.0613			0.905066
$895$	6.65963	−	37.7686i	0.222607	−	1.26247i
$896$	2.04963	+	3.55007i	0.0684734	+	0.118599i
$897$	30.8476	−	25.8842i	1.02997	−	0.864249i
$898$	9.97070	−	17.2698i	0.332727	−	0.576299i
$899$	−4.02448	−	6.97060i	−0.134224	−	0.232482i
$900$	2.42429	+	0.882369i	0.0808096	+	0.0294123i
$901$	2.78914	+	2.34037i	0.0929198	+	0.0779689i
$902$	−9.51468	+	16.4799i	−0.316804	+	0.548721i
$903$	1.73872	+	9.86076i	0.0578609	+	0.328145i
$904$	1.73247	+	9.82533i	0.0576211	+	0.326785i
$905$	26.3125	−	22.0788i	0.874656	−	0.733923i
$906$	25.7206	−	9.36154i	0.854510	−	0.311016i
$907$	−17.1239	+	6.23258i	−0.568589	+	0.206949i	−0.610286	−	0.792181i	$-0.708946\pi$
$907$	−17.1239	+	6.23258i	−0.568589	+	0.206949i	0.0416975	+	0.999130i	$0.486723\pi$
$908$	−2.27152	+	1.90603i	−0.0753832	+	0.0632540i
$909$	1.20492	+	6.83345i	0.0399647	+	0.226651i
$910$	2.59358	+	14.7089i	0.0859763	+	0.487596i
$911$	26.2373	−	45.4443i	0.869280	−	1.50564i	0.00654696	−	0.999979i	$-0.497916\pi$
$911$	26.2373	−	45.4443i	0.869280	−	1.50564i	0.862733	−	0.505659i	$-0.168751\pi$
$912$	−0.165857	−	0.139170i	−0.00549206	−	0.00460839i
$913$	−2.06705	−	0.752344i	−0.0684093	−	0.0248990i
$914$	−16.1194	−	27.9196i	−0.533183	−	0.923499i
$915$	−21.9329	+	37.9889i	−0.725080	+	1.25588i
$916$	−2.32313	+	1.94933i	−0.0767582	+	0.0644078i
$917$	2.87700	+	4.98311i	0.0950068	+	0.164557i
$918$	−2.09255	+	11.8674i	−0.0690645	+	0.391684i
$919$	−44.3955			−1.46447			−0.732236	−	0.681051i	$-0.761523\pi$
$919$	−44.3955			−1.46447			−0.732236	+	0.681051i	$0.761523\pi$
$920$	−3.10782	+	17.6253i	−0.102462	+	0.581090i
$921$	−41.1020	−	34.4887i	−1.35436	−	1.13644i
$922$	−6.88626	+	2.50640i	−0.226787	+	0.0825437i
$923$	5.41641	+	1.97141i	0.178283	+	0.0648898i
$924$	−29.8793			−0.982955
$925$	−7.32864	+	5.10071i	−0.240964	+	0.167710i
$926$	6.48631			0.213153
$927$	3.26804	+	1.18947i	0.107336	+	0.0390673i
$928$	−0.727863	+	0.264920i	−0.0238933	+	0.00869644i
$929$	22.9234	+	19.2350i	0.752092	+	0.631080i	0.936055	−	0.351853i	$-0.114448\pi$
$929$	22.9234	+	19.2350i	0.752092	+	0.631080i	−0.183963	+	0.982933i	$0.558893\pi$
$930$	−7.39693	+	41.9501i	−0.242555	+	1.37560i
$931$	−0.973173			−0.0318945
$932$	−0.0501507	+	0.284419i	−0.00164274	+	0.00931644i
$933$	−5.67884	−	9.83605i	−0.185917	−	0.322018i
$934$	−9.18162	+	7.70429i	−0.300432	+	0.252092i
$935$	13.9632	−	24.1849i	0.456644	−	0.790931i
$936$	−1.70363	−	2.95078i	−0.0556850	−	0.0964492i
$937$	−9.34478	−	3.40122i	−0.305281	−	0.111113i	0.184837	−	0.982769i	$-0.440824\pi$
$937$	−9.34478	−	3.40122i	−0.305281	−	0.111113i	−0.490118	+	0.871656i	$0.663046\pi$
$938$	−41.3451	−	34.6926i	−1.34996	−	1.13275i
$939$	−7.89191	+	13.6692i	−0.257543	+	0.446077i
$940$	2.32182	+	13.1677i	0.0757295	+	0.429483i
$941$	2.14576	+	12.1692i	0.0699497	+	0.396704i	0.999601	+	0.0282626i	$0.00899747\pi$
$941$	2.14576	+	12.1692i	0.0699497	+	0.396704i	−0.929651	+	0.368442i	$0.879891\pi$
$942$	5.87021	−	4.92569i	0.191262	−	0.160488i
$943$	−50.9573	+	18.5469i	−1.65940	+	0.603971i
$944$	−7.61082	+	2.77011i	−0.247711	+	0.0901594i
$945$	−15.9940	+	13.4206i	−0.520285	+	0.436571i
$946$	−0.649841	−	3.68543i	−0.0211282	−	0.119824i
$947$	−4.86165	−	27.5718i	−0.157982	−	0.895962i	−0.956008	−	0.293339i	$-0.905233\pi$
$947$	−4.86165	−	27.5718i	−0.157982	−	0.895962i	0.798026	−	0.602623i	$-0.205878\pi$
$948$	5.92803	−	10.2676i	0.192533	−	0.333477i
$949$	−3.79804	−	3.18693i	−0.123290	−	0.103452i
$950$	−0.136922	−	0.0498357i	−0.00444235	−	0.00161688i
$951$	14.5583	+	25.2156i	0.472084	+	0.817673i
$952$	9.11381	−	15.7856i	0.295380	−	0.511614i
$953$	33.5552	−	28.1562i	1.08696	−	0.912068i	0.0904798	−	0.995898i	$-0.471160\pi$
$953$	33.5552	−	28.1562i	1.08696	−	0.912068i	0.996480	+	0.0838307i	$0.0267155\pi$
$954$	−0.719550	−	1.24630i	−0.0232963	−	0.0403504i
$955$	−1.88164	+	10.6713i	−0.0608884	+	0.345315i
$956$	−5.03510			−0.162847
$957$	0.980388	−	5.56006i	0.0316914	−	0.179731i
$958$	17.3832	+	14.5863i	0.561627	+	0.471261i
$959$	47.8396	−	17.4122i	1.54482	−	0.562269i
$960$	3.85205	+	1.40203i	0.124324	+	0.0452503i
$961$	76.9820			2.48329
$962$	11.7447	+	1.06105i	0.378665	+	0.0342096i
$963$	14.4974			0.467172
$964$	16.3281	+	5.94293i	0.525892	+	0.191409i
$965$	−0.634759	+	0.231033i	−0.0204336	+	0.00743723i
$966$	−65.2259	−	54.7310i	−2.09861	−	1.76094i
$967$	−9.60416	+	54.4679i	−0.308849	+	1.75157i	0.295961	+	0.955200i	$0.404360\pi$
$967$	−9.60416	+	54.4679i	−0.308849	+	1.75157i	−0.604810	+	0.796370i	$0.706751\pi$
$968$	0.167293			0.00537702
$969$	−0.167176	+	0.948100i	−0.00537046	+	0.0304574i
$970$	3.40192	+	5.89229i	0.109229	+	0.189190i
$971$	−42.2703	+	35.4690i	−1.35652	+	1.13825i	−0.379477	+	0.925201i	$0.623896\pi$
$971$	−42.2703	+	35.4690i	−1.35652	+	1.13825i	−0.977041	+	0.213053i	$0.931659\pi$
$972$	8.13166	−	14.0844i	0.260823	−	0.451759i
$973$	37.7123	+	65.3197i	1.20900	+	2.09405i
$974$	−11.5684	−	4.21055i	−0.370675	−	0.134915i
$975$	−4.75501	−	3.98992i	−0.152282	−	0.127780i
$976$	5.35046	−	9.26726i	0.171264	−	0.296638i
$977$	−4.43401	−	25.1465i	−0.141857	−	0.804509i	−0.969837	−	0.243753i	$-0.921621\pi$
$977$	−4.43401	−	25.1465i	−0.141857	−	0.804509i	0.827981	−	0.560757i	$-0.189490\pi$
$978$	−0.905773	−	5.13689i	−0.0289634	−	0.164260i
$979$	9.02433	−	7.57232i	0.288419	−	0.242012i
$980$	17.3142	−	6.30186i	0.553083	−	0.201306i
$981$	14.5079	−	5.28043i	0.463200	−	0.168591i
$982$	0.881561	−	0.739718i	0.0281318	−	0.0236053i
$983$	−5.43056	−	30.7982i	−0.173208	−	0.982311i	−0.940192	−	0.340645i	$-0.889355\pi$
$983$	−5.43056	−	30.7982i	−0.173208	−	0.982311i	0.766984	−	0.641666i	$-0.221757\pi$
$984$	2.15680	+	12.2318i	0.0687563	+	0.389937i
$985$	6.54591	−	11.3378i	0.208570	−	0.361254i
$986$	2.63841	+	2.21389i	0.0840240	+	0.0705045i
$987$	−59.7757	−	21.7566i	−1.90268	−	0.692519i
$988$	0.0962202	+	0.166658i	0.00306117	+	0.00530210i
$989$	5.33216	−	9.23557i	0.169553	−	0.293674i
$990$	−8.45556	+	7.09506i	−0.268735	+	0.225496i
$991$	3.80674	+	6.59347i	0.120925	+	0.209448i	0.920133	−	0.391607i	$-0.128081\pi$
$991$	3.80674	+	6.59347i	0.120925	+	0.209448i	−0.799208	+	0.601055i	$0.794747\pi$
$992$	1.80445	−	10.2336i	0.0572915	−	0.324916i
$993$	−9.97478			−0.316540
$994$	2.11638	−	12.0026i	0.0671276	−	0.380699i
$995$	−16.0928	−	13.5035i	−0.510176	−	0.428088i
$996$	−1.34917	+	0.491058i	−0.0427501	+	0.0155598i
$997$	−14.6618	−	5.33644i	−0.464342	−	0.169007i	0.0992454	−	0.995063i	$-0.468357\pi$
$997$	−14.6618	−	5.33644i	−0.464342	−	0.169007i	−0.563588	+	0.826056i	$0.690579\pi$
$998$	27.9156			0.883653
$999$	6.92443	+	14.9599i	0.219079	+	0.473311i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	74.2.f.b.53.1	yes	12
3.2	odd	2		666.2.x.g.127.1		12
4.3	odd	2		592.2.bc.d.497.2		12
37.7	even	9	inner	74.2.f.b.7.1	✓	12
37.9	even	9		2738.2.a.t.1.5		6
37.28	even	18		2738.2.a.q.1.5		6
111.44	odd	18		666.2.x.g.451.1		12
148.7	odd	18		592.2.bc.d.81.2		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
74.2.f.b.7.1	✓	12	37.7	even	9	inner
74.2.f.b.53.1	yes	12	1.1	even	1	trivial
592.2.bc.d.81.2		12	148.7	odd	18
592.2.bc.d.497.2		12	4.3	odd	2
666.2.x.g.127.1		12	3.2	odd	2
666.2.x.g.451.1		12	111.44	odd	18
2738.2.a.q.1.5		6	37.28	even	18
2738.2.a.t.1.5		6	37.9	even	9

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:	\( N \)	\(=\)	\( 74 = 2 \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	74.f (of order \(9\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.939693 - 0.342020i) q^{2} +(-2.04963 + 0.746005i) q^{3} +(0.766044 + 0.642788i) q^{4} +(-0.326352 + 1.85083i) q^{5} +2.18117 q^{6} +(-0.711830 + 4.03699i) q^{7} +(-0.500000 - 0.866025i) q^{8} +(1.34633 - 1.12971i) q^{9} +(0.939693 - 1.62760i) q^{10} +(-1.67088 - 2.89404i) q^{11} +(-2.04963 - 0.746005i) q^{12} +(1.48512 + 1.24616i) q^{13} +(2.04963 - 3.55007i) q^{14} +(-0.711830 - 4.03699i) q^{15} +(0.173648 + 0.984808i) q^{16} +(3.40626 - 2.85819i) q^{17} +(-1.65152 + 0.601105i) q^{18} +(0.0932770 - 0.0339500i) q^{19} +(-1.43969 + 1.20805i) q^{20} +(-1.55262 - 8.80536i) q^{21} +(0.580289 + 3.29098i) q^{22} +(-4.76146 + 8.24709i) q^{23} +(1.67088 + 1.40203i) q^{24} +(1.37939 + 0.502055i) q^{25} +(-0.969343 - 1.67895i) q^{26} +(1.35504 - 2.34700i) q^{27} +(-3.14022 + 2.63496i) q^{28} +(-0.387288 - 0.670802i) q^{29} +(-0.711830 + 4.03699i) q^{30} +10.3914 q^{31} +(0.173648 - 0.984808i) q^{32} +(5.58365 + 4.68524i) q^{33} +(-4.17840 + 1.52081i) q^{34} +(-7.23948 - 2.63496i) q^{35} +1.75751 q^{36} +(-3.50302 + 4.97281i) q^{37} -0.0992633 q^{38} +(-3.97359 - 1.44627i) q^{39} +(1.76604 - 0.642788i) q^{40} +(4.36218 + 3.66031i) q^{41} +(-1.55262 + 8.80536i) q^{42} -1.11986 q^{43} +(0.580289 - 3.29098i) q^{44} +(1.65152 + 2.86052i) q^{45} +(7.29498 - 6.12122i) q^{46} +(3.55724 - 6.16132i) q^{47} +(-1.09059 - 1.88895i) q^{48} +(-9.21271 - 3.35315i) q^{49} +(-1.12449 - 0.943555i) q^{50} +(-4.84936 + 8.39933i) q^{51} +(0.336649 + 1.90923i) q^{52} +(0.142188 + 0.806388i) q^{53} +(-2.07604 + 1.74200i) q^{54} +(5.90168 - 2.14804i) q^{55} +(3.85205 - 1.40203i) q^{56} +(-0.165857 + 0.139170i) q^{57} +(0.134504 + 0.762808i) q^{58} +(1.40642 + 7.97622i) q^{59} +(2.04963 - 3.55007i) q^{60} +(-8.19737 - 6.87841i) q^{61} +(-9.76476 - 3.55408i) q^{62} +(3.60225 + 6.23929i) q^{63} +(-0.500000 + 0.866025i) q^{64} +(-2.79111 + 2.34202i) q^{65} +(-3.64447 - 6.31240i) q^{66} +(2.28630 - 12.9663i) q^{67} +4.44656 q^{68} +(3.60687 - 20.4556i) q^{69} +(5.90168 + 4.95210i) q^{70} +(2.79386 - 1.01688i) q^{71} +(-1.65152 - 0.601105i) q^{72} -2.55740 q^{73} +(4.99257 - 3.47481i) q^{74} -3.20177 q^{75} +(0.0932770 + 0.0339500i) q^{76} +(12.8726 - 4.68524i) q^{77} +(3.23930 + 2.71810i) q^{78} +(-0.943888 + 5.35305i) q^{79} -1.87939 q^{80} +(-1.94203 + 11.0138i) q^{81} +(-2.84721 - 4.93152i) q^{82} +(0.504249 - 0.423115i) q^{83} +(4.47060 - 7.74331i) q^{84} +(4.17840 + 7.23720i) q^{85} +(1.05232 + 0.383014i) q^{86} +(1.29422 + 1.08598i) q^{87} +(-1.67088 + 2.89404i) q^{88} +(0.612149 + 3.47167i) q^{89} +(-0.573568 - 3.25286i) q^{90} +(-6.08790 + 5.10835i) q^{91} +(-8.94862 + 3.25703i) q^{92} +(-21.2986 + 7.75206i) q^{93} +(-5.45001 + 4.57310i) q^{94} +(0.0323948 + 0.183720i) q^{95} +(0.378757 + 2.14804i) q^{96} +(-1.81012 + 3.13522i) q^{97} +(7.51027 + 6.30186i) q^{98} +(-5.51897 - 2.00874i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 3 q^{3} - 6 q^{5} + 6 q^{7} - 6 q^{8} - 3 q^{9} + 3 q^{11} - 3 q^{12} - 6 q^{13} + 3 q^{14} + 6 q^{15} - 3 q^{17} + 6 q^{18} - 3 q^{19} - 6 q^{20} - 33 q^{21} - 3 q^{22} - 21 q^{23} - 3 q^{24} - 6 q^{25}+ \cdots - 33 q^{99}+O(q^{100}) \) 12 * q - 3 * q^3 - 6 * q^5 + 6 * q^7 - 6 * q^8 - 3 * q^9 + 3 * q^11 - 3 * q^12 - 6 * q^13 + 3 * q^14 + 6 * q^15 - 3 * q^17 + 6 * q^18 - 3 * q^19 - 6 * q^20 - 33 * q^21 - 3 * q^22 - 21 * q^23 - 3 * q^24 - 6 * q^25 + 3 * q^27 - 3 * q^28 + 6 * q^29 + 6 * q^30 + 42 * q^31 + 57 * q^33 - 3 * q^34 - 9 * q^35 + 24 * q^36 - 3 * q^37 + 42 * q^38 - 24 * q^39 + 12 * q^40 - 21 * q^41 - 33 * q^42 + 36 * q^43 - 3 * q^44 - 6 * q^45 + 3 * q^46 + 9 * q^47 - 12 * q^49 + 12 * q^50 + 3 * q^52 - 6 * q^53 - 27 * q^54 - 3 * q^56 - 36 * q^57 - 3 * q^58 - 6 * q^59 + 3 * q^60 - 18 * q^61 - 33 * q^62 + 36 * q^63 - 6 * q^64 + 3 * q^65 + 3 * q^66 - 27 * q^67 + 6 * q^68 - 12 * q^69 - 18 * q^71 + 6 * q^72 + 54 * q^73 + 3 * q^74 - 6 * q^75 - 3 * q^76 + 51 * q^77 - 33 * q^78 - 12 * q^79 - 36 * q^81 - 18 * q^82 - 6 * q^83 - 6 * q^84 + 3 * q^85 + 39 * q^87 + 3 * q^88 - 15 * q^89 - 15 * q^90 - 51 * q^91 - 6 * q^92 + 45 * q^93 - 12 * q^94 - 15 * q^95 + 6 * q^96 - 42 * q^97 + 51 * q^98 - 33 * q^99

Introduction

L-functions

Modular forms

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Database

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