LMFDB - Embedded newform 462.2.j.f.421.2

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [462,2,Mod(169,462)] 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("462.169"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(462, base_ring=CyclotomicField(10)) chi = DirichletCharacter(H, H._module([0, 0, 2])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 462 = 2 \cdot 3 \cdot 7 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	462.j (of order $5$, degree $4$, minimal)

Newform invariants

comment:select newform

sage:traces = [8,-2,2] 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:	$3.68908857338$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$2$ over $\Q(\zeta_{5})$
Coefficient field:	8.0.64000000.1
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 2x^{6} + 4x^{4} - 8x^{2} + 16 $ x^8 - 2x^6 + 4x^4 - 8*x^2 + 16
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			421.2
Root			$0.831254 + 1.14412i$ of defining polynomial
Character	$\chi$	$=$	462.421
Dual form			462.2.j.f.169.2

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.809017 + 0.587785i) q^{2} +(-0.309017 - 0.951057i) q^{3} +(0.309017 - 0.951057i) q^{4} +(0.0359800 + 0.0261410i) q^{5} +(0.809017 + 0.587785i) q^{6} +(-0.309017 + 0.951057i) q^{7} +(0.309017 + 0.951057i) q^{8} +(-0.809017 + 0.587785i) q^{9} -0.0444738 q^{10} +(-0.154014 + 3.31305i) q^{11} -1.00000 q^{12} +(4.52125 - 3.28488i) q^{13} +(-0.309017 - 0.951057i) q^{14} +(0.0137431 - 0.0422971i) q^{15} +(-0.809017 - 0.587785i) q^{16} +(2.18999 + 1.59112i) q^{17} +(0.309017 - 0.951057i) q^{18} +(1.10954 + 3.41481i) q^{19} +(0.0359800 - 0.0261410i) q^{20} +1.00000 q^{21} +(-1.82276 - 2.77084i) q^{22} +3.09945 q^{23} +(0.809017 - 0.587785i) q^{24} +(-1.54447 - 4.75340i) q^{25} +(-1.72696 + 5.31505i) q^{26} +(0.809017 + 0.587785i) q^{27} +(0.809017 + 0.587785i) q^{28} +(1.87573 - 5.77290i) q^{29} +(0.0137431 + 0.0422971i) q^{30} +(7.18277 - 5.21859i) q^{31} +1.00000 q^{32} +(3.19849 - 0.877312i) q^{33} -2.70698 q^{34} +(-0.0359800 + 0.0261410i) q^{35} +(0.309017 + 0.951057i) q^{36} +(-0.777675 + 2.39344i) q^{37} +(-2.90481 - 2.11047i) q^{38} +(-4.52125 - 3.28488i) q^{39} +(-0.0137431 + 0.0422971i) q^{40} +(2.13502 + 6.57092i) q^{41} +(-0.809017 + 0.587785i) q^{42} +12.7697 q^{43} +(3.10330 + 1.17026i) q^{44} -0.0444738 q^{45} +(-2.50750 + 1.82181i) q^{46} +(3.52125 + 10.8373i) q^{47} +(-0.309017 + 0.951057i) q^{48} +(-0.809017 - 0.587785i) q^{49} +(4.04348 + 2.93776i) q^{50} +(0.836503 - 2.57449i) q^{51} +(-1.72696 - 5.31505i) q^{52} +(-6.65303 + 4.83371i) q^{53} -1.00000 q^{54} +(-0.0921479 + 0.115177i) q^{55} -1.00000 q^{56} +(2.90481 - 2.11047i) q^{57} +(1.87573 + 5.77290i) q^{58} +(-1.02285 + 3.14800i) q^{59} +(-0.0359800 - 0.0261410i) q^{60} +(-9.81713 - 7.13256i) q^{61} +(-2.74357 + 8.44385i) q^{62} +(-0.309017 - 0.951057i) q^{63} +(-0.809017 + 0.587785i) q^{64} +0.248545 q^{65} +(-2.07196 + 2.58978i) q^{66} -1.01248 q^{67} +(2.18999 - 1.59112i) q^{68} +(-0.957782 - 2.94775i) q^{69} +(0.0137431 - 0.0422971i) q^{70} +(-2.85410 - 2.07363i) q^{71} +(-0.809017 - 0.587785i) q^{72} +(-0.196232 + 0.603941i) q^{73} +(-0.777675 - 2.39344i) q^{74} +(-4.04348 + 2.93776i) q^{75} +3.59055 q^{76} +(-3.10330 - 1.17026i) q^{77} +5.58857 q^{78} +(5.05982 - 3.67617i) q^{79} +(-0.0137431 - 0.0422971i) q^{80} +(0.309017 - 0.951057i) q^{81} +(-5.58956 - 4.06105i) q^{82} +(-4.43714 - 3.22377i) q^{83} +(0.309017 - 0.951057i) q^{84} +(0.0372024 + 0.114497i) q^{85} +(-10.3309 + 7.50582i) q^{86} -6.06998 q^{87} +(-3.19849 + 0.877312i) q^{88} -2.76195 q^{89} +(0.0359800 - 0.0261410i) q^{90} +(1.72696 + 5.31505i) q^{91} +(0.957782 - 2.94775i) q^{92} +(-7.18277 - 5.21859i) q^{93} +(-9.21875 - 6.69781i) q^{94} +(-0.0493454 + 0.151870i) q^{95} +(-0.309017 - 0.951057i) q^{96} +(-9.05000 + 6.57521i) q^{97} +1.00000 q^{98} +(-1.82276 - 2.77084i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 2 q^{2} + 2 q^{3} - 2 q^{4} - 6 q^{5} + 2 q^{6} + 2 q^{7} - 2 q^{8} - 2 q^{9} + 4 q^{10} + 14 q^{11} - 8 q^{12} + 8 q^{13} + 2 q^{14} - 4 q^{15} - 2 q^{16} - 4 q^{17} - 2 q^{18} - 2 q^{19} - 6 q^{20}+ \cdots - 6 q^{99}+O(q^{100}) $ 8 * q - 2 * q^2 + 2 * q^3 - 2 * q^4 - 6 * q^5 + 2 * q^6 + 2 * q^7 - 2 * q^8 - 2 * q^9 + 4 * q^10 + 14 * q^11 - 8 * q^12 + 8 * q^13 + 2 * q^14 - 4 * q^15 - 2 * q^16 - 4 * q^17 - 2 * q^18 - 2 * q^19 - 6 * q^20 + 8 * q^21 - 6 * q^22 + 4 * q^23 + 2 * q^24 - 8 * q^25 - 12 * q^26 + 2 * q^27 + 2 * q^28 + 4 * q^29 - 4 * q^30 - 10 * q^31 + 8 * q^32 + 6 * q^33 - 4 * q^34 + 6 * q^35 - 2 * q^36 - 20 * q^37 - 12 * q^38 - 8 * q^39 + 4 * q^40 + 12 * q^41 - 2 * q^42 + 48 * q^43 - 6 * q^44 + 4 * q^45 + 4 * q^46 + 2 * q^48 - 2 * q^49 + 2 * q^50 - 6 * q^51 - 12 * q^52 - 12 * q^53 - 8 * q^54 - 8 * q^55 - 8 * q^56 + 12 * q^57 + 4 * q^58 + 12 * q^59 + 6 * q^60 - 32 * q^61 + 20 * q^62 + 2 * q^63 - 2 * q^64 + 24 * q^65 - 4 * q^66 - 48 * q^67 - 4 * q^68 + 6 * q^69 - 4 * q^70 + 4 * q^71 - 2 * q^72 - 20 * q^74 - 2 * q^75 + 28 * q^76 + 6 * q^77 - 8 * q^78 + 40 * q^79 + 4 * q^80 - 2 * q^81 - 18 * q^82 - 32 * q^83 - 2 * q^84 - 42 * q^85 - 32 * q^86 + 16 * q^87 - 6 * q^88 + 12 * q^89 - 6 * q^90 + 12 * q^91 - 6 * q^92 + 10 * q^93 + 54 * q^95 + 2 * q^96 + 8 * q^97 + 8 * q^98 - 6 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/462\mathbb{Z}\right)^\times$.

$n$	$155$	$199$	$211$
$\chi(n)$	$1$	$1$	$e\left(\frac{4}{5}\right)$

Coefficient data

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

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

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

$2$	−0.809017	+	0.587785i	−0.572061	+	0.415627i
$2$	−0.809017	+	0.587785i	−0.572061	+	0.415627i
$3$	−0.309017	−	0.951057i	−0.178411	−	0.549093i
$3$	−0.309017	−	0.951057i	−0.178411	−	0.549093i
$4$	0.309017	−	0.951057i	0.154508	−	0.475528i
$5$	0.0359800	+	0.0261410i	0.0160908	+	0.0116906i	0.595802	−	0.803132i	$-0.296834\pi$
$5$	0.0359800	+	0.0261410i	0.0160908	+	0.0116906i	−0.579711	+	0.814822i	$0.696834\pi$
$6$	0.809017	+	0.587785i	0.330280	+	0.239962i
$7$	−0.309017	+	0.951057i	−0.116797	+	0.359466i
$7$	−0.309017	+	0.951057i	−0.116797	+	0.359466i
$8$	0.309017	+	0.951057i	0.109254	+	0.336249i
$9$	−0.809017	+	0.587785i	−0.269672	+	0.195928i
$10$	−0.0444738			−0.0140638
$11$	−0.154014	+	3.31305i	−0.0464370	+	0.998921i
$11$	−0.154014	+	3.31305i	−0.0464370	+	0.998921i
$12$	−1.00000			−0.288675
$13$	4.52125	−	3.28488i	1.25397	−	0.911061i	0.255523	−	0.966803i	$-0.417752\pi$
$13$	4.52125	−	3.28488i	1.25397	−	0.911061i	0.998445	+	0.0557414i	$0.0177522\pi$
$14$	−0.309017	−	0.951057i	−0.0825883	−	0.254181i
$15$	0.0137431	−	0.0422971i	0.00354847	−	0.0109211i
$16$	−0.809017	−	0.587785i	−0.202254	−	0.146946i
$17$	2.18999	+	1.59112i	0.531152	+	0.385904i	0.820788	−	0.571232i	$-0.193535\pi$
$17$	2.18999	+	1.59112i	0.531152	+	0.385904i	−0.289637	+	0.957137i	$0.593535\pi$
$18$	0.309017	−	0.951057i	0.0728360	−	0.224166i
$19$	1.10954	+	3.41481i	0.254546	+	0.783412i	0.993919	+	0.110116i	$0.0351221\pi$
$19$	1.10954	+	3.41481i	0.254546	+	0.783412i	−0.739373	+	0.673296i	$0.764878\pi$
$20$	0.0359800	−	0.0261410i	0.00804538	−	0.00584531i
$21$	1.00000			0.218218
$22$	−1.82276	−	2.77084i	−0.388614	−	0.590745i
$23$	3.09945			0.646279			0.323140	−	0.946351i	$-0.395262\pi$
$23$	3.09945			0.646279			0.323140	+	0.946351i	$0.395262\pi$
$24$	0.809017	−	0.587785i	0.165140	−	0.119981i
$25$	−1.54447	−	4.75340i	−0.308895	−	0.950680i
$26$	−1.72696	+	5.31505i	−0.338685	+	1.04237i
$27$	0.809017	+	0.587785i	0.155695	+	0.113119i
$28$	0.809017	+	0.587785i	0.152890	+	0.111081i
$29$	1.87573	−	5.77290i	0.348314	−	1.07200i	−0.611472	−	0.791266i	$-0.709422\pi$
$29$	1.87573	−	5.77290i	0.348314	−	1.07200i	0.959786	−	0.280734i	$-0.0905778\pi$
$30$	0.0137431	+	0.0422971i	0.00250914	+	0.00772235i
$31$	7.18277	−	5.21859i	1.29006	−	0.937286i	0.290256	−	0.956949i	$-0.406259\pi$
$31$	7.18277	−	5.21859i	1.29006	−	0.937286i	0.999807	+	0.0196633i	$0.00625943\pi$
$32$	1.00000			0.176777
$33$	3.19849	−	0.877312i	0.556785	−	0.152720i
$34$	−2.70698			−0.464243
$35$	−0.0359800	+	0.0261410i	−0.00608174	+	0.00441864i
$36$	0.309017	+	0.951057i	0.0515028	+	0.158509i
$37$	−0.777675	+	2.39344i	−0.127849	+	0.393479i	−0.994409	−	0.105593i	$-0.966326\pi$
$37$	−0.777675	+	2.39344i	−0.127849	+	0.393479i	0.866560	+	0.499072i	$0.166326\pi$
$38$	−2.90481	−	2.11047i	−0.471223	−	0.342364i
$39$	−4.52125	−	3.28488i	−0.723979	−	0.526002i
$40$	−0.0137431	+	0.0422971i	−0.00217298	+	0.00668775i
$41$	2.13502	+	6.57092i	0.333434	+	1.02621i	0.967488	+	0.252916i	$0.0813898\pi$
$41$	2.13502	+	6.57092i	0.333434	+	1.02621i	−0.634054	+	0.773289i	$0.718610\pi$
$42$	−0.809017	+	0.587785i	−0.124834	+	0.0906972i
$43$	12.7697			1.94736			0.973678	−	0.227929i	$-0.0731953\pi$
$43$	12.7697			1.94736			0.973678	+	0.227929i	$0.0731953\pi$
$44$	3.10330	+	1.17026i	0.467840	+	0.176424i
$45$	−0.0444738			−0.00662976
$46$	−2.50750	+	1.82181i	−0.369711	+	0.268611i
$47$	3.52125	+	10.8373i	0.513627	+	1.58078i	0.785767	+	0.618523i	$0.212269\pi$
$47$	3.52125	+	10.8373i	0.513627	+	1.58078i	−0.272140	+	0.962258i	$0.587731\pi$
$48$	−0.309017	+	0.951057i	−0.0446028	+	0.137273i
$49$	−0.809017	−	0.587785i	−0.115574	−	0.0839693i
$50$	4.04348	+	2.93776i	0.571835	+	0.415463i
$51$	0.836503	−	2.57449i	0.117134	−	0.360501i
$52$	−1.72696	−	5.31505i	−0.239487	−	0.737064i
$53$	−6.65303	+	4.83371i	−0.913863	+	0.663961i	−0.941989	−	0.335644i	$-0.891046\pi$
$53$	−6.65303	+	4.83371i	−0.913863	+	0.663961i	0.0281257	+	0.999604i	$0.491046\pi$
$54$	−1.00000			−0.136083
$55$	−0.0921479	+	0.115177i	−0.0124252	+	0.0155305i
$56$	−1.00000			−0.133631
$57$	2.90481	−	2.11047i	0.384752	−	0.279539i
$58$	1.87573	+	5.77290i	0.246295	+	0.758018i
$59$	−1.02285	+	3.14800i	−0.133163	+	0.409835i	−0.995300	−	0.0968413i	$-0.969126\pi$
$59$	−1.02285	+	3.14800i	−0.133163	+	0.409835i	0.862136	+	0.506676i	$0.169126\pi$
$60$	−0.0359800	−	0.0261410i	−0.00464500	−	0.00337479i
$61$	−9.81713	−	7.13256i	−1.25696	−	0.913231i	−0.258351	−	0.966051i	$-0.583179\pi$
$61$	−9.81713	−	7.13256i	−1.25696	−	0.913231i	−0.998604	+	0.0528198i	$0.983179\pi$
$62$	−2.74357	+	8.44385i	−0.348434	+	1.07237i
$63$	−0.309017	−	0.951057i	−0.0389325	−	0.119822i
$64$	−0.809017	+	0.587785i	−0.101127	+	0.0734732i
$65$	0.248545			0.0308282
$66$	−2.07196	+	2.58978i	−0.255041	+	0.318780i
$67$	−1.01248			−0.123694			−0.0618469	−	0.998086i	$-0.519699\pi$
$67$	−1.01248			−0.123694			−0.0618469	+	0.998086i	$0.519699\pi$
$68$	2.18999	−	1.59112i	0.265576	−	0.192952i
$69$	−0.957782	−	2.94775i	−0.115303	−	0.354867i
$70$	0.0137431	−	0.0422971i	0.00164262	−	0.00505547i
$71$	−2.85410	−	2.07363i	−0.338720	−	0.246094i	0.405402	−	0.914139i	$-0.367132\pi$
$71$	−2.85410	−	2.07363i	−0.338720	−	0.246094i	−0.744121	+	0.668044i	$0.767132\pi$
$72$	−0.809017	−	0.587785i	−0.0953436	−	0.0692712i
$73$	−0.196232	+	0.603941i	−0.0229673	+	0.0706860i	−0.961883	−	0.273461i	$-0.911832\pi$
$73$	−0.196232	+	0.603941i	−0.0229673	+	0.0706860i	0.938916	+	0.344147i	$0.111832\pi$
$74$	−0.777675	−	2.39344i	−0.0904029	−	0.278232i
$75$	−4.04348	+	2.93776i	−0.466901	+	0.339224i
$76$	3.59055			0.411864
$77$	−3.10330	−	1.17026i	−0.353654	−	0.133364i
$78$	5.58857			0.632781
$79$	5.05982	−	3.67617i	0.569274	−	0.413602i	−0.265567	−	0.964092i	$-0.585559\pi$
$79$	5.05982	−	3.67617i	0.569274	−	0.413602i	0.834841	+	0.550491i	$0.185559\pi$
$80$	−0.0137431	−	0.0422971i	−0.00153653	−	0.00472896i
$81$	0.309017	−	0.951057i	0.0343352	−	0.105673i
$82$	−5.58956	−	4.06105i	−0.617264	−	0.448468i
$83$	−4.43714	−	3.22377i	−0.487040	−	0.353855i	0.317005	−	0.948424i	$-0.397323\pi$
$83$	−4.43714	−	3.22377i	−0.487040	−	0.353855i	−0.804045	+	0.594569i	$0.797323\pi$
$84$	0.309017	−	0.951057i	0.0337165	−	0.103769i
$85$	0.0372024	+	0.114497i	0.00403517	+	0.0124190i
$86$	−10.3309	+	7.50582i	−1.11401	+	0.809373i
$87$	−6.06998			−0.650770
$88$	−3.19849	+	0.877312i	−0.340960	+	0.0935217i
$89$	−2.76195			−0.292767			−0.146383	−	0.989228i	$-0.546763\pi$
$89$	−2.76195			−0.292767			−0.146383	+	0.989228i	$0.546763\pi$
$90$	0.0359800	−	0.0261410i	0.00379263	−	0.00275551i
$91$	1.72696	+	5.31505i	0.181035	+	0.557168i
$92$	0.957782	−	2.94775i	0.0998556	−	0.307324i
$93$	−7.18277	−	5.21859i	−0.744818	−	0.541142i
$94$	−9.21875	−	6.69781i	−0.950841	−	0.690827i
$95$	−0.0493454	+	0.151870i	−0.00506273	+	0.0155815i
$96$	−0.309017	−	0.951057i	−0.0315389	−	0.0970668i
$97$	−9.05000	+	6.57521i	−0.918888	+	0.667611i	−0.943247	−	0.332092i	$-0.892246\pi$
$97$	−9.05000	+	6.57521i	−0.918888	+	0.667611i	0.0243587	+	0.999703i	$0.492246\pi$
$98$	1.00000			0.101015
$99$	−1.82276	−	2.77084i	−0.183194	−	0.278480i
$100$	−4.99802			−0.499802
$101$	15.9771	−	11.6080i	1.58978	−	1.15504i	0.685516	−	0.728057i	$-0.259577\pi$
$101$	15.9771	−	11.6080i	1.58978	−	1.15504i	0.904260	−	0.426983i	$-0.140423\pi$
$102$	0.836503	+	2.57449i	0.0828262	+	0.254913i
$103$	−5.23832	+	16.1219i	−0.516147	+	1.58854i	0.265037	+	0.964238i	$0.414616\pi$
$103$	−5.23832	+	16.1219i	−0.516147	+	1.58854i	−0.781185	+	0.624300i	$0.785384\pi$
$104$	4.52125	+	3.28488i	0.443345	+	0.322109i
$105$	0.0359800	+	0.0261410i	0.00351129	+	0.00255110i
$106$	2.54123	−	7.82110i	0.246826	−	0.759652i
$107$	−0.126528	−	0.389412i	−0.0122319	−	0.0376459i	0.944754	−	0.327779i	$-0.106300\pi$
$107$	−0.126528	−	0.389412i	−0.0122319	−	0.0376459i	−0.956986	+	0.290134i	$0.906300\pi$
$108$	0.809017	−	0.587785i	0.0778477	−	0.0565597i
$109$	6.48263			0.620924			0.310462	−	0.950586i	$-0.399516\pi$
$109$	6.48263			0.620924			0.310462	+	0.950586i	$0.399516\pi$
$110$	0.00684958	−	0.147344i	0.000653082	−	0.0140487i
$111$	2.51661			0.238866
$112$	0.809017	−	0.587785i	0.0764449	−	0.0555405i
$113$	−3.75909	−	11.5693i	−0.353625	−	1.08835i	−0.956802	−	0.290739i	$-0.906099\pi$
$113$	−3.75909	−	11.5693i	−0.353625	−	1.08835i	0.603177	−	0.797607i	$-0.293901\pi$
$114$	−1.10954	+	3.41481i	−0.103918	+	0.319827i
$115$	0.111518	+	0.0810227i	0.0103991	+	0.00755541i
$116$	−4.91072	−	3.56785i	−0.455949	−	0.331266i
$117$	−1.72696	+	5.31505i	−0.159658	+	0.491376i
$118$	−1.02285	−	3.14800i	−0.0941608	−	0.289797i
$119$	−2.18999	+	1.59112i	−0.200756	+	0.145858i
$120$	0.0444738			0.00405988
$121$	−10.9526	−	1.02051i	−0.995687	−	0.0927738i
$122$	12.1346			1.09862
$123$	5.58956	−	4.06105i	0.503994	−	0.366173i
$124$	−2.74357	−	8.44385i	−0.246380	−	0.758280i
$125$	0.137404	−	0.422887i	0.0122898	−	0.0378242i
$126$	0.809017	+	0.587785i	0.0720730	+	0.0523641i
$127$	−15.2295	−	11.0648i	−1.35140	−	0.981846i	−0.998941	−	0.0460173i	$-0.985347\pi$
$127$	−15.2295	−	11.0648i	−1.35140	−	0.981846i	−0.352455	−	0.935829i	$-0.614653\pi$
$128$	0.309017	−	0.951057i	0.0273135	−	0.0840623i
$129$	−3.94604	−	12.1447i	−0.347430	−	1.06928i
$130$	−0.201077	+	0.146091i	−0.0176356	+	0.0128130i
$131$	−5.73889			−0.501409			−0.250705	−	0.968064i	$-0.580662\pi$
$131$	−5.73889			−0.501409			−0.250705	+	0.968064i	$0.580662\pi$
$132$	0.154014	−	3.31305i	0.0134052	−	0.288364i
$133$	−3.59055			−0.311340
$134$	0.819111	−	0.595119i	0.0707604	−	0.0514104i
$135$	0.0137431	+	0.0422971i	0.00118282	+	0.00364035i
$136$	−0.836503	+	2.57449i	−0.0717296	+	0.220761i
$137$	−14.9119	−	10.8342i	−1.27401	−	0.925625i	−0.274658	−	0.961542i	$-0.588565\pi$
$137$	−14.9119	−	10.8342i	−1.27401	−	0.925625i	−0.999355	+	0.0359172i	$0.988565\pi$
$138$	2.50750	+	1.82181i	0.213453	+	0.155083i
$139$	1.98063	−	6.09575i	0.167995	−	0.517035i	−0.831250	−	0.555899i	$-0.812374\pi$
$139$	1.98063	−	6.09575i	0.167995	−	0.517035i	0.999244	+	0.0388644i	$0.0123740\pi$
$140$	0.0137431	+	0.0422971i	0.00116151	+	0.00357475i
$141$	9.21875	−	6.69781i	0.776359	−	0.564057i
$142$	3.52786			0.296052
$143$	10.1866	+	15.4850i	0.851848	+	1.29492i
$144$	1.00000			0.0833333
$145$	0.218398	−	0.158676i	0.0181370	−	0.0131773i
$146$	−0.196232	−	0.603941i	−0.0162403	−	0.0499825i
$147$	−0.309017	+	0.951057i	−0.0254873	+	0.0784418i
$148$	2.03598	+	1.47923i	0.167357	+	0.121592i
$149$	−9.37999	−	6.81496i	−0.768439	−	0.558303i	0.133048	−	0.991110i	$-0.457523\pi$
$149$	−9.37999	−	6.81496i	−0.768439	−	0.558303i	−0.901487	+	0.432806i	$0.857523\pi$
$150$	1.54447	−	4.75340i	0.126106	−	0.388114i
$151$	6.49663	+	19.9946i	0.528688	+	1.62713i	0.756905	+	0.653524i	$0.226710\pi$
$151$	6.49663	+	19.9946i	0.528688	+	1.62713i	−0.228217	+	0.973610i	$0.573290\pi$
$152$	−2.90481	+	2.11047i	−0.235612	+	0.171182i
$153$	−2.70698			−0.218846
$154$	3.19849	−	0.877312i	0.257741	−	0.0706958i
$155$	0.394855			0.0317155
$156$	−4.52125	+	3.28488i	−0.361990	+	0.263001i
$157$	4.29104	+	13.2065i	0.342462	+	1.05399i	0.962928	+	0.269757i	$0.0869435\pi$
$157$	4.29104	+	13.2065i	0.342462	+	1.05399i	−0.620466	+	0.784233i	$0.713057\pi$
$158$	−1.93268	+	5.94817i	−0.153756	+	0.473211i
$159$	6.65303	+	4.83371i	0.527619	+	0.383338i
$160$	0.0359800	+	0.0261410i	0.00284447	+	0.00206663i
$161$	−0.957782	+	2.94775i	−0.0754838	+	0.232315i
$162$	0.309017	+	0.951057i	0.0242787	+	0.0747221i
$163$	−10.8541	+	7.88597i	−0.850159	+	0.617677i	−0.925190	−	0.379505i	$-0.876094\pi$
$163$	−10.8541	+	7.88597i	−0.850159	+	0.617677i	0.0750310	+	0.997181i	$0.476094\pi$
$164$	6.90907			0.539508
$165$	0.138016	+	0.0520460i	0.0107445	+	0.00405178i
$166$	5.48461			0.425689
$167$	−16.6909	+	12.1266i	−1.29158	+	0.938387i	−0.999836	−	0.0181094i	$-0.994235\pi$
$167$	−16.6909	+	12.1266i	−1.29158	+	0.938387i	−0.291743	+	0.956497i	$0.594235\pi$
$168$	0.309017	+	0.951057i	0.0238412	+	0.0733756i
$169$	5.63403	−	17.3398i	0.433387	−	1.33383i
$170$	−0.0973973	−	0.0707633i	−0.00747003	−	0.00542729i
$171$	−2.90481	−	2.11047i	−0.222137	−	0.161392i
$172$	3.94604	−	12.1447i	0.300883	−	0.926023i
$173$	2.84236	+	8.74790i	0.216101	+	0.665090i	0.999074	+	0.0430342i	$0.0137024\pi$
$173$	2.84236	+	8.74790i	0.216101	+	0.665090i	−0.782973	+	0.622056i	$0.786298\pi$
$174$	4.91072	−	3.56785i	0.372281	−	0.270478i
$175$	4.99802			0.377815
$176$	2.07196	−	2.58978i	0.156180	−	0.195212i
$177$	3.31001			0.248795
$178$	2.23447	−	1.62344i	0.167480	−	0.121682i
$179$	−3.34251	−	10.2872i	−0.249831	−	0.768900i	−0.994804	−	0.101806i	$-0.967538\pi$
$179$	−3.34251	−	10.2872i	−0.249831	−	0.768900i	0.744973	−	0.667094i	$-0.232462\pi$
$180$	−0.0137431	+	0.0422971i	−0.00102435	+	0.00315264i
$181$	4.78678	+	3.47780i	0.355799	+	0.258503i	0.751298	−	0.659964i	$-0.229428\pi$
$181$	4.78678	+	3.47780i	0.355799	+	0.258503i	−0.395499	+	0.918466i	$0.629428\pi$
$182$	−4.52125	−	3.28488i	−0.335137	−	0.243491i
$183$	−3.74981	+	11.5407i	−0.277194	+	0.853115i
$184$	0.957782	+	2.94775i	0.0706086	+	0.217311i
$185$	−0.0905477	+	0.0657867i	−0.00665720	+	0.00483674i
$186$	8.87839			0.650995
$187$	−5.60876	+	7.01050i	−0.410153	+	0.512658i
$188$	11.3950			0.831066
$189$	−0.809017	+	0.587785i	−0.0588473	+	0.0427551i
$190$	−0.0493454	−	0.151870i	−0.00357989	−	0.0110178i
$191$	0.726585	−	2.23620i	0.0525739	−	0.161806i	−0.921322	−	0.388800i	$-0.872890\pi$
$191$	0.726585	−	2.23620i	0.0525739	−	0.161806i	0.973896	+	0.226994i	$0.0728898\pi$
$192$	0.809017	+	0.587785i	0.0583858	+	0.0424197i
$193$	16.4830	+	11.9756i	1.18647	+	0.862020i	0.992887	−	0.119064i	$-0.0379893\pi$
$193$	16.4830	+	11.9756i	1.18647	+	0.862020i	0.193583	+	0.981084i	$0.437989\pi$
$194$	3.45679	−	10.6389i	0.248183	−	0.763829i
$195$	−0.0768045	−	0.236380i	−0.00550009	−	0.0169275i
$196$	−0.809017	+	0.587785i	−0.0577869	+	0.0419847i
$197$	18.0417			1.28542			0.642710	−	0.766109i	$-0.277810\pi$
$197$	18.0417			1.28542			0.642710	+	0.766109i	$0.277810\pi$
$198$	3.10330	+	1.17026i	0.220542	+	0.0831670i
$199$	2.51341			0.178171			0.0890854	−	0.996024i	$-0.471606\pi$
$199$	2.51341			0.178171			0.0890854	+	0.996024i	$0.471606\pi$
$200$	4.04348	−	2.93776i	0.285918	−	0.207731i
$201$	0.312873	+	0.962923i	0.0220683	+	0.0679193i
$202$	−6.10269	+	18.7822i	−0.429384	+	1.32151i
$203$	4.91072	+	3.56785i	0.344665	+	0.250414i
$204$	−2.18999	−	1.59112i	−0.153330	−	0.111401i
$205$	−0.0949524	+	0.292234i	−0.00663177	+	0.0204105i
$206$	−5.23832	−	16.1219i	−0.364971	−	1.12327i
$207$	−2.50750	+	1.82181i	−0.174284	+	0.126624i
$208$	−5.58857			−0.387498
$209$	−11.4843	+	3.15003i	−0.794387	+	0.217892i
$210$	−0.0444738			−0.00306898
$211$	8.38749	−	6.09387i	0.577419	−	0.419519i	−0.260374	−	0.965508i	$-0.583846\pi$
$211$	8.38749	−	6.09387i	0.577419	−	0.419519i	0.837793	+	0.545989i	$0.183846\pi$
$212$	2.54123	+	7.82110i	0.174532	+	0.537155i
$213$	−1.09017	+	3.35520i	−0.0746972	+	0.229894i
$214$	0.331254	+	0.240670i	0.0226440	+	0.0164519i
$215$	0.459453	+	0.333812i	0.0313344	+	0.0227658i
$216$	−0.309017	+	0.951057i	−0.0210259	+	0.0647112i
$217$	2.74357	+	8.44385i	0.186246	+	0.573206i
$218$	−5.24456	+	3.81040i	−0.355207	+	0.258073i
$219$	0.635021			0.0429108
$220$	0.0810650	+	0.123230i	0.00546540	+	0.00830814i
$221$	15.1282			1.01763
$222$	−2.03598	+	1.47923i	−0.136646	+	0.0992792i
$223$	−0.885066	−	2.72395i	−0.0592684	−	0.182409i	0.917039	−	0.398797i	$-0.130572\pi$
$223$	−0.885066	−	2.72395i	−0.0592684	−	0.182409i	−0.976307	+	0.216388i	$0.930572\pi$
$224$	−0.309017	+	0.951057i	−0.0206471	+	0.0635451i
$225$	4.04348	+	2.93776i	0.269566	+	0.195851i
$226$	9.84142	+	7.15021i	0.654641	+	0.475625i
$227$	−0.235052	+	0.723415i	−0.0156009	+	0.0480148i	−0.958554	−	0.284911i	$-0.908036\pi$
$227$	−0.235052	+	0.723415i	−0.0156009	+	0.0480148i	0.942953	+	0.332926i	$0.108036\pi$
$228$	−1.10954	−	3.41481i	−0.0734811	−	0.226152i
$229$	2.48892	−	1.80830i	0.164472	−	0.119496i	−0.502505	−	0.864575i	$-0.667588\pi$
$229$	2.48892	−	1.80830i	0.164472	−	0.119496i	0.666977	+	0.745078i	$0.267588\pi$
$230$	−0.137844			−0.00908917
$231$	−0.154014	+	3.31305i	−0.0101334	+	0.217982i
$232$	6.06998			0.398514
$233$	6.55822	−	4.76482i	0.429643	−	0.312154i	−0.351863	−	0.936051i	$-0.614452\pi$
$233$	6.55822	−	4.76482i	0.429643	−	0.312154i	0.781506	+	0.623898i	$0.214452\pi$
$234$	−1.72696	−	5.31505i	−0.112895	−	0.347455i
$235$	−0.156603	+	0.481975i	−0.0102157	+	0.0314406i
$236$	2.67785	+	1.94557i	0.174313	+	0.126646i
$237$	−5.05982	−	3.67617i	−0.328670	−	0.238793i
$238$	0.836503	−	2.57449i	0.0542225	−	0.166880i
$239$	−4.51313	−	13.8900i	−0.291930	−	0.898469i	−0.984235	−	0.176864i	$-0.943405\pi$
$239$	−4.51313	−	13.8900i	−0.291930	−	0.898469i	0.692305	−	0.721605i	$-0.256595\pi$
$240$	−0.0359800	+	0.0261410i	−0.00232250	+	0.00168740i
$241$	−8.59136			−0.553418			−0.276709	−	0.960954i	$-0.589244\pi$
$241$	−8.59136			−0.553418			−0.276709	+	0.960954i	$0.589244\pi$
$242$	9.46065	−	5.61214i	0.608153	−	0.360762i
$243$	−1.00000			−0.0641500
$244$	−9.81713	+	7.13256i	−0.628478	+	0.456616i
$245$	−0.0137431	−	0.0422971i	−0.000878018	−	0.00270226i
$246$	−2.13502	+	6.57092i	−0.136124	+	0.418947i
$247$	16.2338	+	11.7945i	1.03293	+	0.750467i
$248$	7.18277	+	5.21859i	0.456106	+	0.331381i
$249$	−1.69484	+	5.21618i	−0.107406	+	0.330562i
$250$	0.137404	+	0.422887i	0.00869021	+	0.0267457i
$251$	−1.55038	+	1.12642i	−0.0978590	+	0.0710987i	−0.635639	−	0.771987i	$-0.719263\pi$
$251$	−1.55038	+	1.12642i	−0.0978590	+	0.0710987i	0.537780	+	0.843085i	$0.319263\pi$
$252$	−1.00000			−0.0629941
$253$	−0.477358	+	10.2686i	−0.0300113	+	0.645582i
$254$	18.8246			1.18116
$255$	0.0973973	−	0.0707633i	0.00609925	−	0.00443137i
$256$	0.309017	+	0.951057i	0.0193136	+	0.0594410i
$257$	1.52848	−	4.70416i	0.0953437	−	0.293438i	−0.891999	−	0.452037i	$-0.850698\pi$
$257$	1.52848	−	4.70416i	0.0953437	−	0.293438i	0.987343	+	0.158599i	$0.0506977\pi$
$258$	10.3309	+	7.50582i	0.643172	+	0.467292i
$259$	−2.03598	−	1.47923i	−0.126510	−	0.0919146i
$260$	0.0768045	−	0.236380i	0.00476322	−	0.0146597i
$261$	1.87573	+	5.77290i	0.116105	+	0.357333i
$262$	4.64286	−	3.37324i	0.286837	−	0.208399i
$263$	−21.2209			−1.30853			−0.654267	−	0.756264i	$-0.727023\pi$
$263$	−21.2209			−1.30853			−0.654267	+	0.756264i	$0.727023\pi$
$264$	1.82276	+	2.77084i	0.112183	+	0.170533i
$265$	−0.365734			−0.0224669
$266$	2.90481	−	2.11047i	0.178106	−	0.129401i
$267$	0.853491	+	2.62677i	0.0522328	+	0.160756i
$268$	−0.312873	+	0.962923i	−0.0191117	+	0.0588199i
$269$	15.7507	+	11.4436i	0.960337	+	0.697726i	0.953229	−	0.302249i	$-0.0977374\pi$
$269$	15.7507	+	11.4436i	0.960337	+	0.697726i	0.00710810	+	0.999975i	$0.497737\pi$
$270$	−0.0359800	−	0.0261410i	−0.00218967	−	0.00159089i
$271$	1.40233	−	4.31591i	0.0851852	−	0.262173i	−0.899387	−	0.437154i	$-0.855986\pi$
$271$	1.40233	−	4.31591i	0.0851852	−	0.262173i	0.984572	+	0.174981i	$0.0559864\pi$
$272$	−0.836503	−	2.57449i	−0.0507205	−	0.156102i
$273$	4.52125	−	3.28488i	0.273638	−	0.198810i
$274$	18.4322			1.11353
$275$	15.9861	−	4.38482i	0.963999	−	0.264415i
$276$	−3.09945			−0.186565
$277$	−3.41392	+	2.48036i	−0.205123	+	0.149030i	−0.685604	−	0.727975i	$-0.740462\pi$
$277$	−3.41392	+	2.48036i	−0.205123	+	0.149030i	0.480482	+	0.877005i	$0.340462\pi$
$278$	1.98063	+	6.09575i	0.118790	+	0.365599i
$279$	−2.74357	+	8.44385i	−0.164253	+	0.505520i
$280$	−0.0359800	−	0.0261410i	−0.00215022	−	0.00156222i
$281$	−23.3286	−	16.9492i	−1.39167	−	1.01110i	−0.995680	−	0.0928472i	$-0.970403\pi$
$281$	−23.3286	−	16.9492i	−1.39167	−	1.01110i	−0.395985	−	0.918257i	$-0.629597\pi$
$282$	−3.52125	+	10.8373i	−0.209687	+	0.645351i
$283$	3.17288	+	9.76512i	0.188608	+	0.580476i	0.999992	−	0.00403781i	$-0.00128528\pi$
$283$	3.17288	+	9.76512i	0.188608	+	0.580476i	−0.811384	+	0.584514i	$0.801285\pi$
$284$	−2.85410	+	2.07363i	−0.169360	+	0.123047i
$285$	0.159685			0.00945893
$286$	−17.3430	−	6.54010i	−1.02551	−	0.386724i
$287$	−6.90907			−0.407830
$288$	−0.809017	+	0.587785i	−0.0476718	+	0.0346356i
$289$	−2.98889	−	9.19886i	−0.175817	−	0.541109i
$290$	−0.0834207	+	0.256742i	−0.00489863	+	0.0150764i
$291$	9.05000	+	6.57521i	0.530520	+	0.385446i
$292$	0.513743	+	0.373256i	0.0300645	+	0.0218432i
$293$	6.38445	−	19.6493i	0.372984	−	1.14793i	−0.571845	−	0.820362i	$-0.693772\pi$
$293$	6.38445	−	19.6493i	0.372984	−	1.14793i	0.944829	−	0.327565i	$-0.106228\pi$
$294$	−0.309017	−	0.951057i	−0.0180222	−	0.0554667i
$295$	−0.119094	+	0.0865269i	−0.00693393	+	0.00503779i
$296$	−2.51661			−0.146275
$297$	−2.07196	+	2.58978i	−0.120227	+	0.150275i
$298$	11.5943			0.671640
$299$	14.0134	−	10.1813i	0.810414	−	0.588800i
$300$	1.54447	+	4.75340i	0.0891702	+	0.274438i
$301$	−3.94604	+	12.1447i	−0.227446	+	0.700007i
$302$	−17.0084	−	12.3573i	−0.978723	−	0.711084i
$303$	−15.9771	−	11.6080i	−0.917858	−	0.666863i
$304$	1.10954	−	3.41481i	0.0636365	−	0.195853i
$305$	−0.166768	−	0.513260i	−0.00954912	−	0.0293892i
$306$	2.18999	−	1.59112i	0.125194	−	0.0909585i
$307$	28.2701			1.61346			0.806730	−	0.590920i	$-0.201235\pi$
$307$	28.2701			1.61346			0.806730	+	0.590920i	$0.201235\pi$
$308$	−2.07196	+	2.58978i	−0.118061	+	0.147567i
$309$	16.9516			0.964341
$310$	−0.319445	+	0.232090i	−0.0181432	+	0.0131818i
$311$	−6.05859	−	18.6464i	−0.343551	−	1.05734i	−0.962355	−	0.271797i	$-0.912382\pi$
$311$	−6.05859	−	18.6464i	−0.343551	−	1.05734i	0.618803	−	0.785546i	$-0.287618\pi$
$312$	1.72696	−	5.31505i	0.0977700	−	0.300905i
$313$	−24.3118	−	17.6635i	−1.37418	−	0.998403i	−0.997397	−	0.0721022i	$-0.977029\pi$
$313$	−24.3118	−	17.6635i	−1.37418	−	0.998403i	−0.376786	−	0.926300i	$-0.622971\pi$
$314$	−11.2341	−	8.16204i	−0.633976	−	0.460611i
$315$	0.0137431	−	0.0422971i	0.000774339	−	0.00238317i
$316$	−1.93268	−	5.94817i	−0.108722	−	0.334611i
$317$	3.31233	−	2.40655i	0.186039	−	0.135165i	−0.490867	−	0.871234i	$-0.663320\pi$
$317$	3.31233	−	2.40655i	0.186039	−	0.135165i	0.676907	+	0.736069i	$0.263320\pi$
$318$	−8.22359			−0.461156
$319$	18.8370	+	7.10348i	1.05467	+	0.397719i
$320$	−0.0444738			−0.00248616
$321$	−0.331254	+	0.240670i	−0.0184888	+	0.0134329i
$322$	−0.957782	−	2.94775i	−0.0533751	−	0.164272i
$323$	−3.00350	+	9.24384i	−0.167119	+	0.514341i
$324$	−0.809017	−	0.587785i	−0.0449454	−	0.0326547i
$325$	−22.5973	−	16.4179i	−1.25347	−	0.910701i
$326$	4.14590	−	12.7598i	0.229620	−	0.706698i
$327$	−2.00324	−	6.16535i	−0.110780	−	0.340945i
$328$	−5.58956	+	4.06105i	−0.308632	+	0.224234i
$329$	−11.3950			−0.628227
$330$	−0.142249	+	0.0390174i	−0.00783054	+	0.00214783i
$331$	−19.9868			−1.09857			−0.549286	−	0.835634i	$-0.685100\pi$
$331$	−19.9868			−1.09857			−0.549286	+	0.835634i	$0.685100\pi$
$332$	−4.43714	+	3.22377i	−0.243520	+	0.176928i
$333$	−0.777675	−	2.39344i	−0.0426163	−	0.131160i
$334$	6.37535	−	19.6213i	0.348844	−	1.07363i
$335$	−0.0364289	−	0.0264672i	−0.00199033	−	0.00144606i
$336$	−0.809017	−	0.587785i	−0.0441355	−	0.0320663i
$337$	−1.62891	+	5.01327i	−0.0887324	+	0.273090i	−0.985570	−	0.169270i	$-0.945859\pi$
$337$	−1.62891	+	5.01327i	−0.0887324	+	0.273090i	0.896837	+	0.442361i	$0.145859\pi$
$338$	5.63403	+	17.3398i	0.306451	+	0.943159i
$339$	−9.84142	+	7.15021i	−0.534513	+	0.388346i
$340$	0.120390			0.00652905
$341$	16.1832	+	24.6006i	0.876368	+	1.33220i
$342$	3.59055			0.194155
$343$	0.809017	−	0.587785i	0.0436828	−	0.0317374i
$344$	3.94604	+	12.1447i	0.212756	+	0.654797i
$345$	0.0425962	−	0.131097i	0.00229330	−	0.00705805i
$346$	−7.44141	−	5.40650i	−0.400052	−	0.290655i
$347$	6.20793	+	4.51032i	0.333259	+	0.242127i	0.741812	−	0.670608i	$-0.233967\pi$
$347$	6.20793	+	4.51032i	0.333259	+	0.242127i	−0.408553	+	0.912734i	$0.633967\pi$
$348$	−1.87573	+	5.77290i	−0.100550	+	0.309460i
$349$	−2.96468	−	9.12433i	−0.158695	−	0.488414i	0.839821	−	0.542863i	$-0.182660\pi$
$349$	−2.96468	−	9.12433i	−0.158695	−	0.488414i	−0.998517	+	0.0544489i	$0.982660\pi$
$350$	−4.04348	+	2.93776i	−0.216133	+	0.157030i
$351$	5.58857			0.298296
$352$	−0.154014	+	3.31305i	−0.00820897	+	0.176586i
$353$	18.9953			1.01102			0.505509	−	0.862822i	$-0.331305\pi$
$353$	18.9953			1.01102			0.505509	+	0.862822i	$0.331305\pi$
$354$	−2.67785	+	1.94557i	−0.142326	+	0.103406i
$355$	−0.0484840	−	0.149218i	−0.00257326	−	0.00791968i
$356$	−0.853491	+	2.62677i	−0.0452349	+	0.139219i
$357$	2.18999	+	1.59112i	0.115907	+	0.0842112i
$358$	8.75080	+	6.35783i	0.462494	+	0.336022i
$359$	1.87248	−	5.76291i	0.0988259	−	0.304155i	−0.889406	−	0.457118i	$-0.848882\pi$
$359$	1.87248	−	5.76291i	0.0988259	−	0.304155i	0.988232	+	0.152963i	$0.0488816\pi$
$360$	−0.0137431	−	0.0422971i	−0.000724328	−	0.00222925i
$361$	4.94145	−	3.59017i	0.260076	−	0.188956i
$362$	−5.91679			−0.310979
$363$	2.41396	+	10.7319i	0.126700	+	0.563276i
$364$	5.58857			0.292921
$365$	−0.0228481	+	0.0166001i	−0.00119592	+	0.000868889i
$366$	−3.74981	−	11.5407i	−0.196006	−	0.603244i
$367$	−2.73232	+	8.40921i	−0.142626	+	0.438957i	−0.996698	−	0.0811972i	$-0.974126\pi$
$367$	−2.73232	+	8.40921i	−0.142626	+	0.438957i	0.854072	+	0.520154i	$0.174126\pi$
$368$	−2.50750	−	1.82181i	−0.130713	−	0.0949684i
$369$	−5.58956	−	4.06105i	−0.290981	−	0.211410i
$370$	0.0345861	−	0.106445i	0.00179805	−	0.00553382i
$371$	−2.54123	−	7.82110i	−0.131934	−	0.406051i
$372$	−7.18277	+	5.21859i	−0.372409	+	0.270571i
$373$	22.8998			1.18571			0.592853	−	0.805310i	$-0.298001\pi$
$373$	22.8998			1.18571			0.592853	+	0.805310i	$0.298001\pi$
$374$	0.416913	−	8.96836i	0.0215581	−	0.463743i
$375$	−0.444650			−0.0229616
$376$	−9.21875	+	6.69781i	−0.475421	+	0.345413i
$377$	−10.4826	−	32.2622i	−0.539883	−	1.66159i
$378$	0.309017	−	0.951057i	0.0158941	−	0.0489171i
$379$	−17.6432	−	12.8185i	−0.906271	−	0.658444i	0.0337982	−	0.999429i	$-0.489240\pi$
$379$	−17.6432	−	12.8185i	−0.906271	−	0.658444i	−0.940069	+	0.340984i	$0.889240\pi$
$380$	0.129188	+	0.0938606i	0.00662721	+	0.00481495i
$381$	−5.81713	+	17.9033i	−0.298021	+	0.917214i
$382$	0.726585	+	2.23620i	0.0371753	+	0.114414i
$383$	−15.1177	+	10.9836i	−0.772476	+	0.561237i	−0.902712	−	0.430246i	$-0.858427\pi$
$383$	−15.1177	+	10.9836i	−0.772476	+	0.561237i	0.130235	+	0.991483i	$0.458427\pi$
$384$	−1.00000			−0.0510310
$385$	−0.0810650	−	0.123230i	−0.00413146	−	0.00628036i
$386$	−20.3741			−1.03701
$387$	−10.3309	+	7.50582i	−0.525148	+	0.381542i
$388$	3.45679	+	10.6389i	0.175492	+	0.540109i
$389$	6.90806	−	21.2608i	0.350252	−	1.07797i	−0.608459	−	0.793585i	$-0.708212\pi$
$389$	6.90806	−	21.2608i	0.350252	−	1.07797i	0.958711	−	0.284381i	$-0.0917880\pi$
$390$	0.201077	+	0.146091i	0.0101819	+	0.00739760i
$391$	6.78777	+	4.93160i	0.343272	+	0.249402i
$392$	0.309017	−	0.951057i	0.0156077	−	0.0480356i
$393$	1.77341	+	5.45801i	0.0894569	+	0.275320i
$394$	−14.5961	+	10.6047i	−0.735340	+	0.534256i
$395$	0.278151			0.0139953
$396$	−3.19849	+	0.877312i	−0.160730	+	0.0440866i
$397$	−9.97135			−0.500447			−0.250224	−	0.968188i	$-0.580504\pi$
$397$	−9.97135			−0.500447			−0.250224	+	0.968188i	$0.580504\pi$
$398$	−2.03339	+	1.47734i	−0.101925	+	0.0740526i
$399$	1.10954	+	3.41481i	0.0555465	+	0.170955i
$400$	−1.54447	+	4.75340i	−0.0772237	+	0.237670i
$401$	3.53659	+	2.56948i	0.176609	+	0.128314i	0.672578	−	0.740026i	$-0.265187\pi$
$401$	3.53659	+	2.56948i	0.176609	+	0.128314i	−0.495969	+	0.868340i	$0.665187\pi$
$402$	−0.819111	−	0.595119i	−0.0408535	−	0.0296818i
$403$	15.3326	−	47.1890i	0.763774	−	2.35065i
$404$	−6.10269	−	18.7822i	−0.303620	−	0.934447i
$405$	0.0359800	−	0.0261410i	0.00178786	−	0.00129896i
$406$	−6.06998			−0.301248
$407$	−7.80980	−	2.94510i	−0.387117	−	0.145983i
$408$	2.70698			0.134016
$409$	−14.5834	+	10.5955i	−0.721102	+	0.523911i	−0.886736	−	0.462276i	$-0.847033\pi$
$409$	−14.5834	+	10.5955i	−0.721102	+	0.523911i	0.165634	+	0.986187i	$0.447033\pi$
$410$	−0.0949524	−	0.292234i	−0.00468937	−	0.0144324i
$411$	−5.69585	+	17.5300i	−0.280956	+	0.864693i
$412$	13.7141	+	9.96388i	0.675646	+	0.490885i
$413$	−2.67785	−	1.94557i	−0.131768	−	0.0957354i
$414$	0.957782	−	2.94775i	0.0470724	−	0.144874i
$415$	−0.0753758	−	0.231983i	−0.00370005	−	0.0113876i
$416$	4.52125	−	3.28488i	0.221672	−	0.161054i
$417$	−6.40945			−0.313872
$418$	7.43947	−	9.29874i	0.363876	−	0.454816i
$419$	−20.9471			−1.02334			−0.511668	−	0.859184i	$-0.670972\pi$
$419$	−20.9471			−1.02334			−0.511668	+	0.859184i	$0.670972\pi$
$420$	0.0359800	−	0.0261410i	0.00175565	−	0.00127555i
$421$	8.38524	+	25.8071i	0.408671	+	1.25776i	0.917790	+	0.397065i	$0.129971\pi$
$421$	8.38524	+	25.8071i	0.408671	+	1.25776i	−0.509119	+	0.860696i	$0.670029\pi$
$422$	−3.20374	+	9.86009i	−0.155955	+	0.479982i
$423$	−9.21875	−	6.69781i	−0.448231	−	0.325659i
$424$	−6.65303	−	4.83371i	−0.323099	−	0.234745i
$425$	4.18086	−	12.8674i	0.202802	−	0.624159i
$426$	−1.09017	−	3.35520i	−0.0528189	−	0.162560i
$427$	9.81713	−	7.13256i	0.475084	−	0.345169i
$428$	−0.409452			−0.0197916
$429$	11.5793	−	14.4732i	0.559054	−	0.698772i
$430$	−0.567915			−0.0273873
$431$	−4.45150	+	3.23420i	−0.214421	+	0.155786i	−0.689812	−	0.723989i	$-0.742307\pi$
$431$	−4.45150	+	3.23420i	−0.214421	+	0.155786i	0.475391	+	0.879775i	$0.342307\pi$
$432$	−0.309017	−	0.951057i	−0.0148676	−	0.0457577i
$433$	2.09072	−	6.43457i	0.100474	−	0.309226i	−0.888168	−	0.459519i	$-0.848022\pi$
$433$	2.09072	−	6.43457i	0.100474	−	0.309226i	0.988641	+	0.150293i	$0.0480218\pi$
$434$	−7.18277	−	5.21859i	−0.344784	−	0.250500i
$435$	−0.218398	−	0.158676i	−0.0104714	−	0.00760791i
$436$	2.00324	−	6.16535i	0.0959380	−	0.295267i
$437$	3.43896	+	10.5840i	0.164508	+	0.506303i
$438$	−0.513743	+	0.373256i	−0.0245476	+	0.0178349i
$439$	9.02871			0.430917			0.215458	−	0.976513i	$-0.430875\pi$
$439$	9.02871			0.430917			0.215458	+	0.976513i	$0.430875\pi$
$440$	−0.138016	−	0.0520460i	−0.00657963	−	0.00248120i
$441$	1.00000			0.0476190
$442$	−12.2389	+	8.89211i	−0.582147	+	0.422954i
$443$	−11.3408	−	34.9035i	−0.538820	−	1.65832i	−0.735248	−	0.677798i	$-0.762934\pi$
$443$	−11.3408	−	34.9035i	−0.538820	−	1.65832i	0.196428	−	0.980518i	$-0.437066\pi$
$444$	0.777675	−	2.39344i	0.0369068	−	0.113588i
$445$	−0.0993752	−	0.0722003i	−0.00471084	−	0.00342262i
$446$	2.31713	+	1.68350i	0.109719	+	0.0797158i
$447$	−3.58284	+	11.0268i	−0.169462	+	0.521552i
$448$	−0.309017	−	0.951057i	−0.0145997	−	0.0449332i
$449$	−11.3605	+	8.25392i	−0.536137	+	0.389527i	−0.822648	−	0.568550i	$-0.807504\pi$
$449$	−11.3605	+	8.25392i	−0.536137	+	0.389527i	0.286511	+	0.958077i	$0.407504\pi$
$450$	−4.99802			−0.235609
$451$	−22.0986	+	6.06141i	−1.04058	+	0.285421i
$452$	−12.1647			−0.572178
$453$	17.0084	−	12.3573i	0.799124	−	0.580598i
$454$	−0.235052	−	0.723415i	−0.0110315	−	0.0339516i
$455$	−0.0768045	+	0.236380i	−0.00360065	+	0.0110817i
$456$	2.90481	+	2.11047i	0.136030	+	0.0988319i
$457$	−25.1457	−	18.2694i	−1.17627	−	0.854607i	−0.184521	−	0.982829i	$-0.559073\pi$
$457$	−25.1457	−	18.2694i	−1.17627	−	0.854607i	−0.991746	+	0.128221i	$0.959073\pi$
$458$	−0.950682	+	2.92590i	−0.0444224	+	0.136718i
$459$	0.836503	+	2.57449i	0.0390446	+	0.120167i
$460$	0.111518	−	0.0810227i	0.00519956	−	0.00377770i
$461$	−15.0728			−0.702009			−0.351004	−	0.936374i	$-0.614160\pi$
$461$	−15.0728			−0.702009			−0.351004	+	0.936374i	$0.614160\pi$
$462$	−1.82276	−	2.77084i	−0.0848025	−	0.128911i
$463$	−21.6250			−1.00500			−0.502499	−	0.864578i	$-0.667586\pi$
$463$	−21.6250			−1.00500			−0.502499	+	0.864578i	$0.667586\pi$
$464$	−4.91072	+	3.56785i	−0.227974	+	0.165633i
$465$	−0.122017	−	0.375530i	−0.00565840	−	0.0174148i
$466$	−2.50502	+	7.70965i	−0.116043	+	0.357142i
$467$	27.7614	+	20.1698i	1.28464	+	0.933349i	0.999683	−	0.0251899i	$-0.00801904\pi$
$467$	27.7614	+	20.1698i	1.28464	+	0.933349i	0.284962	+	0.958539i	$0.408019\pi$
$468$	4.52125	+	3.28488i	0.208995	+	0.151844i
$469$	0.312873	−	0.962923i	0.0144471	−	0.0444636i
$470$	−0.156603	−	0.481975i	−0.00722356	−	0.0222318i
$471$	11.2341	−	8.16204i	0.517640	−	0.376087i
$472$	−3.31001			−0.152355
$473$	−1.96671	+	42.3065i	−0.0904293	+	1.94525i
$474$	6.25428			0.287268
$475$	14.5183	−	10.5482i	0.666146	−	0.483984i
$476$	0.836503	+	2.57449i	0.0383411	+	0.118002i
$477$	2.54123	−	7.82110i	0.116355	−	0.358104i
$478$	11.8155	+	8.58449i	0.540430	+	0.392645i
$479$	6.53680	+	4.74926i	0.298674	+	0.216999i	0.727021	−	0.686615i	$-0.240904\pi$
$479$	6.53680	+	4.74926i	0.298674	+	0.216999i	−0.428348	+	0.903614i	$0.640904\pi$
$480$	0.0137431	−	0.0422971i	0.000627286	−	0.00193059i
$481$	4.34609	+	13.3759i	0.198165	+	0.609888i
$482$	6.95055	−	5.04987i	0.316589	−	0.230015i
$483$	3.09945			0.141030
$484$	−4.35509	+	10.1011i	−0.197959	+	0.459143i
$485$	−0.497502			−0.0225904
$486$	0.809017	−	0.587785i	0.0366978	−	0.0266625i
$487$	4.20251	+	12.9340i	0.190434	+	0.586096i	1.00000		0.000933674i	$-0.000297198\pi$
$487$	4.20251	+	12.9340i	0.190434	+	0.586096i	−0.809565	+	0.587030i	$0.800297\pi$
$488$	3.74981	−	11.5407i	0.169746	−	0.522424i
$489$	10.8541	+	7.88597i	0.490839	+	0.356616i
$490$	0.0359800	+	0.0261410i	0.00162541	+	0.00118093i
$491$	−11.1056	+	34.1795i	−0.501188	+	1.54250i	0.305898	+	0.952064i	$0.401043\pi$
$491$	−11.1056	+	34.1795i	−0.501188	+	1.54250i	−0.807086	+	0.590434i	$0.798957\pi$
$492$	−2.13502	−	6.57092i	−0.0962542	−	0.296240i
$493$	13.2932	−	9.65809i	0.598697	−	0.434979i
$494$	−20.0660			−0.902813
$495$	0.00684958	−	0.147344i	0.000307866	−	0.00662261i
$496$	−8.87839			−0.398651
$497$	2.85410	−	2.07363i	0.128024	−	0.0930149i
$498$	−1.69484	−	5.21618i	−0.0759475	−	0.233742i
$499$	5.70323	−	17.5527i	0.255312	−	0.785769i	−0.738456	−	0.674301i	$-0.764445\pi$
$499$	5.70323	−	17.5527i	0.255312	−	0.785769i	0.993768	−	0.111467i	$-0.0355551\pi$
$500$	−0.359729	−	0.261359i	−0.0160876	−	0.0116883i
$501$	16.6909	+	12.1266i	0.745694	+	0.541778i
$502$	0.592192	−	1.82258i	0.0264308	−	0.0813457i
$503$	8.45030	+	26.0074i	0.376780	+	1.15961i	0.942270	+	0.334855i	$0.108687\pi$
$503$	8.45030	+	26.0074i	0.376780	+	1.15961i	−0.565489	+	0.824756i	$0.691313\pi$
$504$	0.809017	−	0.587785i	0.0360365	−	0.0261820i
$505$	0.878300			0.0390838
$506$	−5.64955	−	8.58806i	−0.251153	−	0.381786i
$507$	−18.2321			−0.809717
$508$	−15.2295	+	11.0648i	−0.675698	+	0.490923i
$509$	−7.06749	−	21.7515i	−0.313261	−	0.964119i	−0.976464	−	0.215679i	$-0.930803\pi$
$509$	−7.06749	−	21.7515i	−0.313261	−	0.964119i	0.663203	−	0.748439i	$-0.269197\pi$
$510$	−0.0372024	+	0.114497i	−0.00164735	+	0.00507003i
$511$	−0.513743	−	0.373256i	−0.0227267	−	0.0165119i
$512$	−0.809017	−	0.587785i	−0.0357538	−	0.0259767i
$513$	−1.10954	+	3.41481i	−0.0489874	+	0.150768i
$514$	1.52848	+	4.70416i	0.0674182	+	0.207492i
$515$	−0.609918	+	0.443131i	−0.0268762	+	0.0195267i
$516$	−12.7697			−0.562153
$517$	−36.4468	+	9.99697i	−1.60293	+	0.439666i
$518$	2.51661			0.110573
$519$	7.44141	−	5.40650i	0.326641	−	0.237319i
$520$	0.0768045	+	0.236380i	0.00336810	+	0.0103660i
$521$	−1.63587	+	5.03468i	−0.0716686	+	0.220573i	−0.980475	−	0.196646i	$-0.936995\pi$
$521$	−1.63587	+	5.03468i	−0.0716686	+	0.220573i	0.908806	+	0.417219i	$0.136995\pi$
$522$	−4.91072	−	3.56785i	−0.214936	−	0.156160i
$523$	4.83285	+	3.51127i	0.211326	+	0.153537i	0.688413	−	0.725319i	$-0.258308\pi$
$523$	4.83285	+	3.51127i	0.211326	+	0.153537i	−0.477087	+	0.878856i	$0.658308\pi$
$524$	−1.77341	+	5.45801i	−0.0774720	+	0.238434i
$525$	−1.54447	−	4.75340i	−0.0674064	−	0.207455i
$526$	17.1680	−	12.4733i	0.748562	−	0.543862i
$527$	24.0336			1.04692
$528$	−3.10330	−	1.17026i	−0.135054	−	0.0509292i
$529$	−13.3934			−0.582323
$530$	0.295885	−	0.214973i	0.0128524	−	0.00933783i
$531$	−1.02285	−	3.14800i	−0.0443878	−	0.136612i
$532$	−1.10954	+	3.41481i	−0.0481047	+	0.148051i
$533$	31.2376	+	22.6955i	1.35305	+	0.983050i
$534$	−2.23447	−	1.62344i	−0.0966949	−	0.0702529i
$535$	0.00562716	−	0.0173186i	0.000243284	−	0.000748750i
$536$	−0.312873	−	0.962923i	−0.0135140	−	0.0415919i
$537$	−8.75080	+	6.35783i	−0.377625	+	0.274361i
$538$	−19.4689			−0.839365
$539$	2.07196	−	2.58978i	0.0892456	−	0.111550i
$540$	0.0444738			0.00191385
$541$	−2.02350	+	1.47016i	−0.0869972	+	0.0632072i	−0.630434	−	0.776243i	$-0.717123\pi$
$541$	−2.02350	+	1.47016i	−0.0869972	+	0.0632072i	0.543436	+	0.839450i	$0.317123\pi$
$542$	1.40233	+	4.31591i	0.0602350	+	0.185384i
$543$	1.82839	−	5.62720i	0.0784636	−	0.241486i
$544$	2.18999	+	1.59112i	0.0938952	+	0.0682189i
$545$	0.233245	+	0.169463i	0.00999113	+	0.00725898i
$546$	−1.72696	+	5.31505i	−0.0739072	+	0.227463i
$547$	−5.70399	−	17.5551i	−0.243885	−	0.750601i	−0.995818	−	0.0913609i	$-0.970878\pi$
$547$	−5.70399	−	17.5551i	−0.243885	−	0.750601i	0.751933	−	0.659240i	$-0.229122\pi$
$548$	−14.9119	+	10.8342i	−0.637007	+	0.462812i
$549$	12.1346			0.517894
$550$	−10.3557	+	12.9438i	−0.441569	+	0.551925i
$551$	21.7946			0.928479
$552$	2.50750	−	1.82181i	0.106726	−	0.0775413i
$553$	1.93268	+	5.94817i	0.0821858	+	0.252942i
$554$	1.30400	−	4.01330i	0.0554017	−	0.170509i
$555$	0.0905477	+	0.0657867i	0.00384354	+	0.00279249i
$556$	−5.18536	−	3.76738i	−0.219908	−	0.159773i
$557$	1.31730	−	4.05425i	0.0558160	−	0.171784i	−0.919262	−	0.393646i	$-0.871214\pi$
$557$	1.31730	−	4.05425i	0.0558160	−	0.171784i	0.975078	+	0.221862i	$0.0712135\pi$
$558$	−2.74357	−	8.44385i	−0.116145	−	0.357457i
$559$	57.7348	−	41.9468i	2.44192	−	1.77416i
$560$	0.0444738			0.00187936
$561$	8.40058	+	3.16788i	0.354673	+	0.133748i
$562$	28.8357			1.21636
$563$	−21.6834	+	15.7539i	−0.913845	+	0.663948i	−0.941984	−	0.335656i	$-0.891042\pi$
$563$	−21.6834	+	15.7539i	−0.913845	+	0.663948i	0.0281390	+	0.999604i	$0.491042\pi$
$564$	−3.52125	−	10.8373i	−0.148271	−	0.456332i
$565$	0.167181	−	0.514529i	0.00703335	−	0.0216464i
$566$	−8.30671	−	6.03517i	−0.349157	−	0.253677i
$567$	0.809017	+	0.587785i	0.0339755	+	0.0246847i
$568$	1.09017	−	3.35520i	0.0457425	−	0.140781i
$569$	4.37897	+	13.4771i	0.183576	+	0.564989i	0.999921	−	0.0125758i	$-0.00400310\pi$
$569$	4.37897	+	13.4771i	0.183576	+	0.564989i	−0.816345	+	0.577565i	$0.804003\pi$
$570$	−0.129188	+	0.0938606i	−0.00541109	+	0.00393139i
$571$	−2.27324			−0.0951323			−0.0475661	−	0.998868i	$-0.515146\pi$
$571$	−2.27324			−0.0951323			−0.0475661	+	0.998868i	$0.515146\pi$
$572$	17.8750	−	4.90292i	0.747390	−	0.205001i
$573$	−2.35128			−0.0982261
$574$	5.58956	−	4.06105i	0.233304	−	0.169505i
$575$	−4.78701	−	14.7329i	−0.199632	−	0.614405i
$576$	0.309017	−	0.951057i	0.0128757	−	0.0396274i
$577$	2.77464	+	2.01589i	0.115510	+	0.0839227i	0.644040	−	0.764991i	$-0.277257\pi$
$577$	2.77464	+	2.01589i	0.115510	+	0.0839227i	−0.528531	+	0.848914i	$0.677257\pi$
$578$	7.82502	+	5.68521i	0.325478	+	0.236473i
$579$	6.29593	−	19.3769i	0.261650	−	0.805276i
$580$	−0.0834207	−	0.256742i	−0.00346385	−	0.0106606i
$581$	4.43714	−	3.22377i	0.184084	−	0.133745i
$582$	−11.1864			−0.463692
$583$	−14.9896	−	22.7862i	−0.620807	−	0.943710i
$584$	−0.635021			−0.0262774
$585$	−0.201077	+	0.146091i	−0.00831351	+	0.00604012i
$586$	6.38445	+	19.6493i	0.263739	+	0.811706i
$587$	−3.50733	+	10.7945i	−0.144763	+	0.445535i	−0.996980	−	0.0776528i	$-0.975257\pi$
$587$	−3.50733	+	10.7945i	−0.144763	+	0.445535i	0.852217	+	0.523188i	$0.175257\pi$
$588$	0.809017	+	0.587785i	0.0333633	+	0.0242399i
$589$	25.7901	+	18.7376i	1.06266	+	0.772069i
$590$	0.0454899	−	0.140004i	0.00187279	−	0.00576385i
$591$	−5.57520	−	17.1587i	−0.229333	−	0.705815i
$592$	2.03598	−	1.47923i	0.0836783	−	0.0607958i
$593$	−7.78935			−0.319870			−0.159935	−	0.987128i	$-0.551129\pi$
$593$	−7.78935			−0.319870			−0.159935	+	0.987128i	$0.551129\pi$
$594$	0.154014	−	3.31305i	0.00631927	−	0.135936i
$595$	−0.120390			−0.00493549
$596$	−9.37999	+	6.81496i	−0.384219	+	0.279152i
$597$	−0.776686	−	2.39039i	−0.0317877	−	0.0978323i
$598$	−5.35263	+	16.4737i	−0.218885	+	0.673660i
$599$	−37.4943	−	27.2412i	−1.53197	−	1.11304i	−0.955129	−	0.296192i	$-0.904283\pi$
$599$	−37.4943	−	27.2412i	−1.53197	−	1.11304i	−0.576846	−	0.816853i	$-0.695717\pi$
$600$	−4.04348	−	2.93776i	−0.165075	−	0.119934i
$601$	2.83589	−	8.72798i	0.115678	−	0.356022i	−0.876409	−	0.481567i	$-0.840068\pi$
$601$	2.83589	−	8.72798i	0.115678	−	0.356022i	0.992088	+	0.125545i	$0.0400679\pi$
$602$	−3.94604	−	12.1447i	−0.160829	−	0.494980i
$603$	0.819111	−	0.595119i	0.0333568	−	0.0242351i
$604$	21.0235			0.855435
$605$	−0.367396	−	0.323029i	−0.0149368	−	0.0131330i
$606$	19.7487			0.802237
$607$	11.2028	−	8.13932i	0.454708	−	0.330365i	−0.336744	−	0.941596i	$-0.609326\pi$
$607$	11.2028	−	8.13932i	0.454708	−	0.330365i	0.791452	+	0.611231i	$0.209326\pi$
$608$	1.10954	+	3.41481i	0.0449978	+	0.138489i
$609$	1.87573	−	5.77290i	0.0760083	−	0.233930i
$610$	0.436605	+	0.317212i	0.0176776	+	0.0128435i
$611$	51.5196	+	37.4312i	2.08426	+	1.51430i
$612$	−0.836503	+	2.57449i	−0.0338136	+	0.104068i
$613$	5.24781	+	16.1511i	0.211957	+	0.652336i	0.999356	+	0.0358923i	$0.0114273\pi$
$613$	5.24781	+	16.1511i	0.211957	+	0.652336i	−0.787399	+	0.616444i	$0.788573\pi$
$614$	−22.8710	+	16.6167i	−0.922998	+	0.670597i
$615$	0.307273			0.0123904
$616$	0.154014	−	3.31305i	0.00620540	−	0.133486i
$617$	20.2082			0.813550			0.406775	−	0.913528i	$-0.366653\pi$
$617$	20.2082			0.813550			0.406775	+	0.913528i	$0.366653\pi$
$618$	−13.7141	+	9.96388i	−0.551662	+	0.400806i
$619$	−8.24408	−	25.3727i	−0.331358	−	1.01981i	−0.968488	−	0.249058i	$-0.919879\pi$
$619$	−8.24408	−	25.3727i	−0.331358	−	1.01981i	0.637131	−	0.770756i	$-0.280121\pi$
$620$	0.122017	−	0.375530i	0.00490032	−	0.0150816i
$621$	2.50750	+	1.82181i	0.100623	+	0.0731067i
$622$	15.8616	+	11.5241i	0.635992	+	0.462076i
$623$	0.853491	−	2.62677i	0.0341944	−	0.105239i
$624$	1.72696	+	5.31505i	0.0691339	+	0.212772i
$625$	−20.2014	+	14.6772i	−0.808057	+	0.587088i
$626$	30.0510			1.20108
$627$	6.54471	+	9.94883i	0.261370	+	0.397318i
$628$	13.8861			0.554116
$629$	−5.51136	+	4.00424i	−0.219752	+	0.159659i
$630$	0.0137431	+	0.0422971i	0.000547540	+	0.00168516i
$631$	−12.2697	+	37.7623i	−0.488449	+	1.50329i	0.338473	+	0.940976i	$0.390090\pi$
$631$	−12.2697	+	37.7623i	−0.488449	+	1.50329i	−0.826922	+	0.562316i	$0.809910\pi$
$632$	5.05982	+	3.67617i	0.201269	+	0.146230i
$633$	−8.38749	−	6.09387i	−0.333373	−	0.242210i
$634$	−1.26520	+	3.89388i	−0.0502474	+	0.154646i
$635$	−0.258710	−	0.796227i	−0.0102666	−	0.0315973i
$636$	6.65303	−	4.83371i	0.263810	−	0.191669i
$637$	−5.58857			−0.221427
$638$	−19.4148	+	5.32527i	−0.768638	+	0.210829i
$639$	3.52786			0.139560
$640$	0.0359800	−	0.0261410i	0.00142224	−	0.00103331i
$641$	−3.47951	−	10.7088i	−0.137432	−	0.422973i	0.858528	−	0.512766i	$-0.171379\pi$
$641$	−3.47951	−	10.7088i	−0.137432	−	0.422973i	−0.995960	+	0.0897934i	$0.971379\pi$
$642$	0.126528	−	0.389412i	0.00499365	−	0.0153689i
$643$	21.1721	+	15.3824i	0.834947	+	0.606625i	0.920955	−	0.389670i	$-0.127411\pi$
$643$	21.1721	+	15.3824i	0.834947	+	0.606625i	−0.0860075	+	0.996294i	$0.527411\pi$
$644$	2.50750	+	1.82181i	0.0988095	+	0.0717893i
$645$	0.175495	−	0.540119i	0.00691012	−	0.0212672i
$646$	−3.00350	−	9.24384i	−0.118171	−	0.363694i
$647$	37.4234	−	27.1897i	1.47126	−	1.06894i	0.491020	−	0.871148i	$-0.336624\pi$
$647$	37.4234	−	27.1897i	1.47126	−	1.06894i	0.980245	−	0.197788i	$-0.0633757\pi$
$648$	1.00000			0.0392837
$649$	−10.2719	−	3.87358i	−0.403209	−	0.152051i
$650$	27.9318			1.09558
$651$	7.18277	−	5.21859i	0.281515	−	0.204532i
$652$	4.14590	+	12.7598i	0.162366	+	0.499711i
$653$	8.91856	−	27.4485i	0.349010	−	1.07414i	−0.610392	−	0.792100i	$-0.708988\pi$
$653$	8.91856	−	27.4485i	0.349010	−	1.07414i	0.959402	−	0.282043i	$-0.0910121\pi$
$654$	5.24456	+	3.81040i	0.205079	+	0.148998i
$655$	−0.206485	−	0.150020i	−0.00806805	−	0.00586178i
$656$	2.13502	−	6.57092i	0.0833586	−	0.256551i
$657$	−0.196232	−	0.603941i	−0.00765576	−	0.0235620i
$658$	9.21875	−	6.69781i	0.359384	−	0.261108i
$659$	−48.7813			−1.90025			−0.950124	−	0.311871i	$-0.899044\pi$
$659$	−48.7813			−1.90025			−0.950124	+	0.311871i	$0.899044\pi$
$660$	0.0921479	−	0.115177i	0.00358685	−	0.00448328i
$661$	−9.92428			−0.386010			−0.193005	−	0.981198i	$-0.561823\pi$
$661$	−9.92428			−0.386010			−0.193005	+	0.981198i	$0.561823\pi$
$662$	16.1696	−	11.7479i	0.628451	−	0.456596i
$663$	−4.67486	−	14.3877i	−0.181556	−	0.558773i
$664$	1.69484	−	5.21618i	0.0657725	−	0.202427i
$665$	−0.129188	−	0.0938606i	−0.00500970	−	0.00363976i
$666$	2.03598	+	1.47923i	0.0788926	+	0.0573188i
$667$	5.81372	−	17.8928i	0.225108	−	0.692811i
$668$	6.37535	+	19.6213i	0.246670	+	0.759171i
$669$	−2.31713	+	1.68350i	−0.0895855	+	0.0650877i
$670$	0.0450287			0.00173961
$671$	25.1425	−	31.4261i	0.970615	−	1.21319i
$672$	1.00000			0.0385758
$673$	−27.7912	+	20.1915i	−1.07127	+	0.778325i	−0.976141	−	0.217139i	$-0.930327\pi$
$673$	−27.7912	+	20.1915i	−1.07127	+	0.778325i	−0.0951321	+	0.995465i	$0.530327\pi$
$674$	−1.62891	−	5.01327i	−0.0627433	−	0.193104i
$675$	1.54447	−	4.75340i	0.0594468	−	0.182959i
$676$	−14.7501	−	10.7166i	−0.567311	−	0.412176i
$677$	19.3432	+	14.0537i	0.743421	+	0.540127i	0.893780	−	0.448505i	$-0.148043\pi$
$677$	19.3432	+	14.0537i	0.743421	+	0.540127i	−0.150360	+	0.988631i	$0.548043\pi$
$678$	3.75909	−	11.5693i	0.144367	−	0.444316i
$679$	−3.45679	−	10.6389i	−0.132660	−	0.408284i
$680$	−0.0973973	+	0.0707633i	−0.00373501	+	0.00271365i
$681$	0.760644			0.0291479
$682$	−27.5523	−	10.3901i	−1.05503	−	0.397856i
$683$	−10.8197			−0.414005			−0.207002	−	0.978340i	$-0.566371\pi$
$683$	−10.8197			−0.414005			−0.207002	+	0.978340i	$0.566371\pi$
$684$	−2.90481	+	2.11047i	−0.111068	+	0.0806959i
$685$	−0.253316	−	0.779627i	−0.00967871	−	0.0297880i
$686$	−0.309017	+	0.951057i	−0.0117983	+	0.0363115i
$687$	−2.48892	−	1.80830i	−0.0949581	−	0.0689911i
$688$	−10.3309	−	7.50582i	−0.393861	−	0.286157i
$689$	−14.2018	+	43.7088i	−0.541047	+	1.66517i
$690$	0.0425962	+	0.131097i	0.00162161	+	0.00499080i
$691$	19.7368	−	14.3396i	0.750821	−	0.545504i	−0.145260	−	0.989394i	$-0.546402\pi$
$691$	19.7368	−	14.3396i	0.750821	−	0.545504i	0.896081	+	0.443890i	$0.146402\pi$
$692$	9.19808			0.349659
$693$	3.19849	−	0.877312i	0.121501	−	0.0333263i
$694$	−7.67342			−0.291279
$695$	0.230612	−	0.167550i	0.00874762	−	0.00635552i
$696$	−1.87573	−	5.77290i	−0.0710993	−	0.218821i
$697$	−5.77946	+	17.7874i	−0.218913	+	0.673744i
$698$	7.76162	+	5.63915i	0.293782	+	0.213445i
$699$	−6.55822	−	4.76482i	−0.248055	−	0.180222i
$700$	1.54447	−	4.75340i	0.0583756	−	0.179662i
$701$	2.35891	+	7.25998i	0.0890949	+	0.274206i	0.985670	−	0.168686i	$-0.0539525\pi$
$701$	2.35891	+	7.25998i	0.0890949	+	0.274206i	−0.896575	+	0.442892i	$0.853952\pi$
$702$	−4.52125	+	3.28488i	−0.170644	+	0.123980i
$703$	−9.03601			−0.340799
$704$	−1.82276	−	2.77084i	−0.0686979	−	0.104430i
$705$	0.506778			0.0190864
$706$	−15.3675	+	11.1652i	−0.578364	+	0.420206i
$707$	6.10269	+	18.7822i	0.229515	+	0.706375i
$708$	1.02285	−	3.14800i	0.0384410	−	0.118309i
$709$	−23.4440	−	17.0331i	−0.880458	−	0.639690i	0.0529144	−	0.998599i	$-0.483149\pi$
$709$	−23.4440	−	17.0331i	−0.880458	−	0.639690i	−0.933373	+	0.358909i	$0.883149\pi$
$710$	0.126933	+	0.0922220i	0.00476370	+	0.00346103i
$711$	−1.93268	+	5.94817i	−0.0724811	+	0.223074i
$712$	−0.853491	−	2.62677i	−0.0319859	−	0.0984425i
$713$	22.2626	−	16.1747i	0.833741	−	0.605748i
$714$	−2.70698			−0.101306
$715$	−0.0382794	+	0.823440i	−0.00143157	+	0.0307949i
$716$	−10.8166			−0.404235
$717$	−11.8155	+	8.58449i	−0.441259	+	0.320594i
$718$	1.87248	+	5.76291i	0.0698805	+	0.215070i
$719$	−0.784542	+	2.41457i	−0.0292585	+	0.0900483i	−0.964619	−	0.263646i	$-0.915075\pi$
$719$	−0.784542	+	2.41457i	−0.0292585	+	0.0900483i	0.935361	+	0.353695i	$0.115075\pi$
$720$	0.0359800	+	0.0261410i	0.00134090	+	0.000974218i
$721$	−13.7141	−	9.96388i	−0.510740	−	0.371074i
$722$	−1.88747	+	5.80902i	−0.0702442	+	0.216189i
$723$	2.65488	+	8.17087i	0.0987359	+	0.303878i
$724$	4.78678	−	3.47780i	0.177899	−	0.129251i
$725$	−30.3379			−1.12672
$726$	−8.26097	−	7.26336i	−0.306593	−	0.269569i
$727$	−18.6427			−0.691421			−0.345710	−	0.938341i	$-0.612362\pi$
$727$	−18.6427			−0.691421			−0.345710	+	0.938341i	$0.612362\pi$
$728$	−4.52125	+	3.28488i	−0.167569	+	0.121746i
$729$	0.309017	+	0.951057i	0.0114451	+	0.0352243i
$730$	0.00872719	−	0.0268595i	0.000323008	−	0.000994116i
$731$	27.9655	+	20.3181i	1.03434	+	0.751493i
$732$	9.81713	+	7.13256i	0.362852	+	0.263627i
$733$	8.74108	−	26.9023i	0.322859	−	0.993659i	−0.649538	−	0.760329i	$-0.725038\pi$
$733$	8.74108	−	26.9023i	0.322859	−	0.993659i	0.972398	−	0.233330i	$-0.0749622\pi$
$734$	−2.73232	−	8.40921i	−0.100852	−	0.310390i
$735$	−0.0359800	+	0.0261410i	−0.00132714	+	0.000964226i
$736$	3.09945			0.114247
$737$	0.155936	−	3.35438i	0.00574396	−	0.123560i
$738$	6.90907			0.254327
$739$	37.0567	−	26.9233i	1.36315	−	0.990390i	0.364917	−	0.931040i	$-0.381097\pi$
$739$	37.0567	−	26.9233i	1.36315	−	0.990390i	0.998237	−	0.0593499i	$-0.0189028\pi$
$740$	0.0345861	+	0.106445i	0.00127141	+	0.00391300i
$741$	6.20074	−	19.0839i	0.227790	−	0.701066i
$742$	6.65303	+	4.83371i	0.244240	+	0.177451i
$743$	−1.16046	−	0.843123i	−0.0425731	−	0.0309312i	0.566295	−	0.824202i	$-0.308376\pi$
$743$	−1.16046	−	0.843123i	−0.0425731	−	0.0309312i	−0.608868	+	0.793271i	$0.708376\pi$
$744$	2.74357	−	8.44385i	0.100584	−	0.309567i
$745$	−0.159342	−	0.490405i	−0.00583785	−	0.0179670i
$746$	−18.5263	+	13.4602i	−0.678297	+	0.492812i
$747$	5.48461			0.200671
$748$	4.93418	+	7.50061i	0.180411	+	0.274249i
$749$	0.409452			0.0149611
$750$	0.359729	−	0.261359i	0.0131355	−	0.00954346i
$751$	3.27181	+	10.0696i	0.119390	+	0.367445i	0.992837	−	0.119474i	$-0.0381207\pi$
$751$	3.27181	+	10.0696i	0.119390	+	0.367445i	−0.873447	+	0.486919i	$0.838121\pi$
$752$	3.52125	−	10.8373i	0.128407	−	0.395195i
$753$	1.55038	+	1.12642i	0.0564989	+	0.0410489i
$754$	27.4439	+	19.9392i	0.999448	+	0.726141i
$755$	−0.288929	+	0.889234i	−0.0105152	+	0.0323625i
$756$	0.309017	+	0.951057i	0.0112388	+	0.0345896i
$757$	19.6330	−	14.2642i	0.713574	−	0.518441i	−0.170751	−	0.985314i	$-0.554619\pi$
$757$	19.6330	−	14.2642i	0.713574	−	0.518441i	0.884325	+	0.466873i	$0.154619\pi$
$758$	21.8082			0.792110
$759$	9.91354	−	2.71918i	0.359839	−	0.0987000i
$760$	−0.159685			−0.00579239
$761$	1.25823	−	0.914160i	0.0456109	−	0.0331383i	−0.564746	−	0.825265i	$-0.691026\pi$
$761$	1.25823	−	0.914160i	0.0456109	−	0.0331383i	0.610357	+	0.792126i	$0.291026\pi$
$762$	−5.81713	−	17.9033i	−0.210732	−	0.648568i
$763$	−2.00324	+	6.16535i	−0.0725223	+	0.223201i
$764$	−1.90222	−	1.38205i	−0.0688201	−	0.0500007i
$765$	−0.0973973	−	0.0707633i	−0.00352141	−	0.00255845i
$766$	5.77443	−	17.7719i	0.208639	−	0.642124i
$767$	5.71626	+	17.5928i	0.206402	+	0.635240i
$768$	0.809017	−	0.587785i	0.0291929	−	0.0212099i
$769$	26.3090			0.948727			0.474363	−	0.880329i	$-0.342678\pi$
$769$	26.3090			0.948727			0.474363	+	0.880329i	$0.342678\pi$
$770$	0.138016	+	0.0520460i	0.00497373	+	0.00187561i
$771$	−4.94625			−0.178135
$772$	16.4830	−	11.9756i	0.593235	−	0.431010i
$773$	16.7195	+	51.4574i	0.601359	+	1.85079i	0.520110	+	0.854099i	$0.325891\pi$
$773$	16.7195	+	51.4574i	0.601359	+	1.85079i	0.0812487	+	0.996694i	$0.474109\pi$
$774$	3.94604	−	12.1447i	0.141838	−	0.436531i
$775$	−35.8996	−	26.0826i	−1.28955	−	0.936915i
$776$	−9.05000	−	6.57521i	−0.324876	−	0.236036i
$777$	−0.777675	+	2.39344i	−0.0278989	+	0.0858641i
$778$	6.90806	+	21.2608i	0.247666	+	0.762237i
$779$	−20.0696	+	14.5814i	−0.719067	+	0.522433i
$780$	−0.248545			−0.00889933
$781$	7.30959	−	9.13641i	0.261558	−	0.326926i
$782$	−8.39014			−0.300031
$783$	4.91072	−	3.56785i	0.175495	−	0.127504i
$784$	0.309017	+	0.951057i	0.0110363	+	0.0339663i
$785$	−0.190839	+	0.587341i	−0.00681133	+	0.0209631i
$786$	−4.64286	−	3.37324i	−0.165605	−	0.120319i
$787$	21.9999	+	15.9839i	0.784212	+	0.569763i	0.906240	−	0.422763i	$-0.138940\pi$
$787$	21.9999	+	15.9839i	0.784212	+	0.569763i	−0.122028	+	0.992527i	$0.538940\pi$
$788$	5.57520	−	17.1587i	0.198608	−	0.611254i
$789$	6.55761	+	20.1822i	0.233457	+	0.718507i
$790$	−0.225029	+	0.163493i	−0.00800618	+	0.00581683i
$791$	12.1647			0.432526
$792$	2.07196	−	2.58978i	0.0736239	−	0.0920240i
$793$	−67.8153			−2.40819
$794$	8.06699	−	5.86101i	0.286287	−	0.207999i
$795$	0.113018	+	0.347834i	0.00400834	+	0.0123364i
$796$	0.776686	−	2.39039i	0.0275289	−	0.0847253i
$797$	13.5029	+	9.81046i	0.478299	+	0.347504i	0.800667	−	0.599110i	$-0.204479\pi$
$797$	13.5029	+	9.81046i	0.478299	+	0.347504i	−0.322368	+	0.946614i	$0.604479\pi$
$798$	−2.90481	−	2.11047i	−0.102829	−	0.0747099i
$799$	−9.53195	+	29.3363i	−0.337216	+	1.03784i
$800$	−1.54447	−	4.75340i	−0.0546054	−	0.168058i
$801$	2.23447	−	1.62344i	0.0789510	−	0.0573613i
$802$	−4.37147			−0.154362
$803$	−1.97066	−	0.743143i	−0.0695432	−	0.0262249i
$804$	1.01248			0.0357073
$805$	−0.111518	+	0.0810227i	−0.00393050	+	0.00285567i
$806$	15.3326	+	47.1890i	0.540069	+	1.66216i
$807$	6.01623	−	18.5161i	0.211781	−	0.651796i
$808$	15.9771	+	11.6080i	0.562071	+	0.408368i
$809$	28.5589	+	20.7492i	1.00408	+	0.729505i	0.962959	−	0.269650i	$-0.0869079\pi$
$809$	28.5589	+	20.7492i	1.00408	+	0.729505i	0.0411186	+	0.999154i	$0.486908\pi$
$810$	−0.0137431	+	0.0422971i	−0.000482885	+	0.00148617i
$811$	−4.16091	−	12.8060i	−0.146109	−	0.449678i	0.851043	−	0.525096i	$-0.175971\pi$
$811$	−4.16091	−	12.8060i	−0.146109	−	0.449678i	−0.997152	+	0.0754185i	$0.975971\pi$
$812$	4.91072	−	3.56785i	0.172332	−	0.125207i
$813$	−4.53802			−0.159155
$814$	8.04935	−	2.20785i	0.282129	−	0.0773851i
$815$	−0.596678			−0.0209007
$816$	−2.18999	+	1.59112i	−0.0766651	+	0.0557005i
$817$	14.1685	+	43.6060i	0.495692	+	1.52558i
$818$	5.57036	−	17.1438i	0.194763	−	0.599419i
$819$	−4.52125	−	3.28488i	−0.157985	−	0.114783i
$820$	0.248589	+	0.180610i	0.00868109	+	0.00630718i
$821$	−15.8932	+	48.9142i	−0.554676	+	1.70712i	0.142122	+	0.989849i	$0.454608\pi$
$821$	−15.8932	+	48.9142i	−0.554676	+	1.70712i	−0.696798	+	0.717268i	$0.745392\pi$
$822$	−5.69585	−	17.5300i	−0.198666	−	0.611430i
$823$	−44.2005	+	32.1136i	−1.54073	+	1.11941i	−0.590861	+	0.806774i	$0.701212\pi$
$823$	−44.2005	+	32.1136i	−1.54073	+	1.11941i	−0.949873	+	0.312635i	$0.898788\pi$
$824$	−16.9516			−0.590536
$825$	−9.11020	−	13.8487i	−0.317176	−	0.482150i
$826$	3.31001			0.115170
$827$	−12.2730	+	8.91685i	−0.426774	+	0.310069i	−0.780358	−	0.625334i	$-0.784963\pi$
$827$	−12.2730	+	8.91685i	−0.426774	+	0.310069i	0.353584	+	0.935403i	$0.384963\pi$
$828$	0.957782	+	2.94775i	0.0332852	+	0.102441i
$829$	9.25973	−	28.4985i	0.321604	−	0.989794i	−0.651347	−	0.758780i	$-0.725796\pi$
$829$	9.25973	−	28.4985i	0.321604	−	0.989794i	0.972950	−	0.231014i	$-0.0742043\pi$
$830$	0.197337	+	0.143373i	0.00684965	+	0.00497656i
$831$	3.41392	+	2.48036i	0.118428	+	0.0860426i
$832$	−1.72696	+	5.31505i	−0.0598717	+	0.184266i
$833$	−0.836503	−	2.57449i	−0.0289831	−	0.0892009i
$834$	5.18536	−	3.76738i	0.179554	−	0.130454i
$835$	−0.917541			−0.0317528
$836$	−0.552995	+	11.8957i	−0.0191257	+	0.411420i
$837$	8.87839			0.306882
$838$	16.9466	−	12.3124i	0.585411	−	0.425326i
$839$	−5.31949	−	16.3717i	−0.183649	−	0.565214i	0.816273	−	0.577666i	$-0.196036\pi$
$839$	−5.31949	−	16.3717i	−0.183649	−	0.565214i	−0.999922	+	0.0124519i	$0.996036\pi$
$840$	−0.0137431	+	0.0422971i	−0.000474184	+	0.00145939i
$841$	−6.34648	−	4.61099i	−0.218844	−	0.159000i
$842$	−21.9528	−	15.9497i	−0.756545	−	0.549662i
$843$	−8.91072	+	27.4244i	−0.306901	+	0.944546i
$844$	−3.20374	−	9.86009i	−0.110277	−	0.339398i
$845$	0.655992	−	0.476606i	0.0225668	−	0.0163957i
$846$	11.3950			0.391768
$847$	4.35509	−	10.1011i	0.149643	−	0.347080i
$848$	8.22359			0.282399
$849$	8.30671	−	6.03517i	0.285085	−	0.207127i
$850$	4.18086	+	12.8674i	0.143402	+	0.441347i
$851$	−2.41036	+	7.41833i	−0.0826262	+	0.254297i
$852$	2.85410	+	2.07363i	0.0977799	+	0.0710413i
$853$	1.32248	+	0.960840i	0.0452809	+	0.0328985i	0.610196	−	0.792251i	$-0.291091\pi$
$853$	1.32248	+	0.960840i	0.0452809	+	0.0328985i	−0.564915	+	0.825149i	$0.691091\pi$
$854$	−3.74981	+	11.5407i	−0.128316	+	0.394916i
$855$	−0.0493454	−	0.151870i	−0.00168758	−	0.00519383i
$856$	0.331254	−	0.240670i	0.0113220	−	0.00822593i
$857$	−1.49784			−0.0511654			−0.0255827	−	0.999673i	$-0.508144\pi$
$857$	−1.49784			−0.0511654			−0.0255827	+	0.999673i	$0.508144\pi$
$858$	−0.860718	+	18.5152i	−0.0293844	+	0.632098i
$859$	−17.5329			−0.598216			−0.299108	−	0.954219i	$-0.596689\pi$
$859$	−17.5329			−0.598216			−0.299108	+	0.954219i	$0.596689\pi$
$860$	0.459453	−	0.333812i	0.0156672	−	0.0113829i
$861$	2.13502	+	6.57092i	0.0727613	+	0.223936i
$862$	1.70032	−	5.23305i	0.0579132	−	0.178238i
$863$	−23.3672	−	16.9773i	−0.795429	−	0.577913i	0.114141	−	0.993465i	$-0.463589\pi$
$863$	−23.3672	−	16.9773i	−0.795429	−	0.577913i	−0.909570	+	0.415552i	$0.863589\pi$
$864$	0.809017	+	0.587785i	0.0275233	+	0.0199969i
$865$	−0.126411	+	0.389052i	−0.00429809	+	0.0132282i
$866$	2.09072	+	6.43457i	0.0710455	+	0.218656i
$867$	−7.82502	+	5.68521i	−0.265751	+	0.193080i
$868$	8.87839			0.301352
$869$	11.4000	+	17.3296i	0.386720	+	0.587866i
$870$	0.269955			0.00915233
$871$	−4.57766	+	3.32586i	−0.155108	+	0.112693i
$872$	2.00324	+	6.16535i	0.0678384	+	0.208785i
$873$	3.45679	−	10.6389i	0.116995	−	0.360073i
$874$	−9.00332	−	6.54129i	−0.304542	−	0.221262i
$875$	0.359729	+	0.261359i	0.0121611	+	0.00883553i
$876$	0.196232	−	0.603941i	0.00663008	−	0.0204053i
$877$	14.8332	+	45.6518i	0.500880	+	1.54155i	0.807588	+	0.589747i	$0.200773\pi$
$877$	14.8332	+	45.6518i	0.500880	+	1.54155i	−0.306708	+	0.951804i	$0.599227\pi$
$878$	−7.30438	+	5.30694i	−0.246511	+	0.179101i
$879$	−20.6605			−0.696862
$880$	0.142249	−	0.0390174i	0.00479521	−	0.00131527i
$881$	−1.08115			−0.0364248			−0.0182124	−	0.999834i	$-0.505798\pi$
$881$	−1.08115			−0.0364248			−0.0182124	+	0.999834i	$0.505798\pi$
$882$	−0.809017	+	0.587785i	−0.0272410	+	0.0197918i
$883$	−7.61441	−	23.4348i	−0.256245	−	0.788642i	−0.993582	−	0.113116i	$-0.963917\pi$
$883$	−7.61441	−	23.4348i	−0.256245	−	0.788642i	0.737336	−	0.675526i	$-0.236083\pi$
$884$	4.67486	−	14.3877i	0.157232	−	0.483912i
$885$	0.119094	+	0.0865269i	0.00400330	+	0.00290857i
$886$	29.6907	+	21.5716i	0.997479	+	0.724711i
$887$	10.3676	−	31.9083i	0.348111	−	1.07138i	−0.611786	−	0.791023i	$-0.709549\pi$
$887$	10.3676	−	31.9083i	0.348111	−	1.07138i	0.959897	−	0.280353i	$-0.0904514\pi$
$888$	0.777675	+	2.39344i	0.0260971	+	0.0803185i
$889$	15.2295	−	11.0648i	0.510779	−	0.371103i
$890$	0.122834			0.00411742
$891$	3.10330	+	1.17026i	0.103965	+	0.0392053i
$892$	−2.86413			−0.0958983
$893$	−33.1003	+	24.0488i	−1.10766	+	0.804763i
$894$	−3.58284	−	11.0268i	−0.119828	−	0.368793i
$895$	0.148654	−	0.457510i	0.00496895	−	0.0152929i
$896$	0.809017	+	0.587785i	0.0270274	+	0.0196365i
$897$	−14.0134	−	10.1813i	−0.467893	−	0.339944i
$898$	4.33934	−	13.3551i	0.144806	−	0.445666i
$899$	−16.6534	−	51.2540i	−0.555423	−	1.70942i
$900$	4.04348	−	2.93776i	0.134783	−	0.0979255i
$901$	−22.2611			−0.741625
$902$	14.3153	−	17.8930i	0.476648	−	0.595772i
$903$	12.7697			0.424948
$904$	9.84142	−	7.15021i	0.327321	−	0.237812i
$905$	0.0813153	+	0.250263i	0.00270301	+	0.00831901i
$906$	−6.49663	+	19.9946i	−0.215836	+	0.664275i
$907$	−16.3505	−	11.8794i	−0.542910	−	0.394447i	0.282254	−	0.959340i	$-0.408918\pi$
$907$	−16.3505	−	11.8794i	−0.542910	−	0.394447i	−0.825165	+	0.564892i	$0.808918\pi$
$908$	0.615374	+	0.447095i	0.0204219	+	0.0148374i
$909$	−6.10269	+	18.7822i	−0.202413	+	0.622965i
$910$	−0.0768045	−	0.236380i	−0.00254605	−	0.00783592i
$911$	−20.8882	+	15.1762i	−0.692058	+	0.502809i	−0.877336	−	0.479877i	$-0.840681\pi$
$911$	−20.8882	+	15.1762i	−0.692058	+	0.502809i	0.185278	+	0.982686i	$0.440681\pi$
$912$	−3.59055			−0.118895
$913$	11.3639	−	14.2040i	0.376090	−	0.470083i
$914$	31.0818			1.02809
$915$	−0.436605	+	0.317212i	−0.0144337	+	0.0104867i
$916$	−0.950682	−	2.92590i	−0.0314114	−	0.0966744i
$917$	1.77341	−	5.45801i	0.0585633	−	0.180239i
$918$	−2.18999	−	1.59112i	−0.0722806	−	0.0525149i
$919$	28.6686	+	20.8289i	0.945690	+	0.687084i	0.949783	−	0.312908i	$-0.101303\pi$
$919$	28.6686	+	20.8289i	0.945690	+	0.687084i	−0.00409394	+	0.999992i	$0.501303\pi$
$920$	−0.0425962	+	0.131097i	−0.00140435	+	0.00432216i
$921$	−8.73594	−	26.8865i	−0.287859	−	0.885939i
$922$	12.1941	−	8.85955i	0.401592	−	0.291774i
$923$	−19.7157			−0.648951
$924$	3.10330	+	1.17026i	0.102091	+	0.0384989i
$925$	12.5781			0.413564
$926$	17.4950	−	12.7108i	0.574921	−	0.417704i
$927$	−5.23832	−	16.1219i	−0.172049	−	0.529513i
$928$	1.87573	−	5.77290i	0.0615738	−	0.189505i
$929$	−32.9832	−	23.9637i	−1.08214	−	0.786223i	−0.104088	−	0.994568i	$-0.533192\pi$
$929$	−32.9832	−	23.9637i	−1.08214	−	0.786223i	−0.978055	+	0.208345i	$0.933192\pi$
$930$	0.319445	+	0.232090i	0.0104750	+	0.00761054i
$931$	1.10954	−	3.41481i	0.0363637	−	0.111916i
$932$	−2.50502	−	7.70965i	−0.0820545	−	0.252538i
$933$	−15.8616	+	11.5241i	−0.519286	+	0.377283i
$934$	−34.3150			−1.12282
$935$	−0.385065	+	0.105619i	−0.0125930	+	0.00345412i
$936$	−5.58857			−0.182668
$937$	−5.91802	+	4.29969i	−0.193333	+	0.140465i	−0.680241	−	0.732989i	$-0.738125\pi$
$937$	−5.91802	+	4.29969i	−0.193333	+	0.140465i	0.486908	+	0.873453i	$0.338125\pi$
$938$	0.312873	+	0.962923i	0.0102156	+	0.0314405i
$939$	−9.28627	+	28.5802i	−0.303046	+	0.932680i
$940$	0.409992	+	0.297877i	0.0133725	+	0.00971567i
$941$	5.96607	+	4.33460i	0.194488	+	0.141304i	0.680768	−	0.732499i	$-0.261646\pi$
$941$	5.96607	+	4.33460i	0.194488	+	0.141304i	−0.486279	+	0.873803i	$0.661646\pi$
$942$	−4.29104	+	13.2065i	−0.139810	+	0.430290i
$943$	6.61738	+	20.3662i	0.215492	+	0.663215i
$944$	2.67785	−	1.94557i	0.0871566	−	0.0633230i
$945$	−0.0444738			−0.00144673
$946$	−23.2760	−	35.3827i	−0.756769	−	1.15039i
$947$	5.35736			0.174091			0.0870453	−	0.996204i	$-0.472258\pi$
$947$	5.35736			0.174091			0.0870453	+	0.996204i	$0.472258\pi$
$948$	−5.05982	+	3.67617i	−0.164335	+	0.119397i
$949$	1.09666	+	3.37517i	0.0355990	+	0.109563i
$950$	−5.54551	+	17.0673i	−0.179920	+	0.553737i
$951$	−3.31233	−	2.40655i	−0.107410	−	0.0780377i
$952$	−2.18999	−	1.59112i	−0.0709781	−	0.0515686i
$953$	−5.55598	+	17.0995i	−0.179976	+	0.553909i	−0.999826	−	0.0186700i	$-0.994057\pi$
$953$	−5.55598	+	17.0995i	−0.179976	+	0.553909i	0.819850	+	0.572578i	$0.194057\pi$
$954$	2.54123	+	7.82110i	0.0822753	+	0.253217i
$955$	0.0845991	−	0.0614648i	0.00273756	−	0.00198896i
$956$	−14.6048			−0.472353
$957$	0.934862	−	20.1101i	0.0302198	−	0.650068i
$958$	−8.07993			−0.261051
$959$	14.9119	−	10.8342i	0.481532	−	0.349853i
$960$	0.0137431	+	0.0422971i	0.000443558	+	0.00136513i
$961$	14.7790	−	45.4850i	0.476741	−	1.46726i
$962$	−11.3782	−	8.26676i	−0.366848	−	0.266531i
$963$	0.331254	+	0.240670i	0.0106745	+	0.00775548i
$964$	−2.65488	+	8.17087i	−0.0855078	+	0.263166i
$965$	0.280004	+	0.861763i	0.00901364	+	0.0277411i
$966$	−2.50750	+	1.82181i	−0.0806776	+	0.0586157i
$967$	33.2965			1.07074			0.535372	−	0.844616i	$-0.320171\pi$
$967$	33.2965			1.07074			0.535372	+	0.844616i	$0.320171\pi$
$968$	−2.41396	−	10.7319i	−0.0775877	−	0.344935i
$969$	9.71955			0.312237
$970$	0.402488	−	0.292424i	0.0129231	−	0.00938918i
$971$	−3.68059	−	11.3277i	−0.118116	−	0.363523i	0.874468	−	0.485083i	$-0.161210\pi$
$971$	−3.68059	−	11.3277i	−0.118116	−	0.363523i	−0.992584	+	0.121560i	$0.961210\pi$
$972$	−0.309017	+	0.951057i	−0.00991172	+	0.0305052i
$973$	5.18536	+	3.76738i	0.166235	+	0.120777i
$974$	−11.0023	−	7.99366i	−0.352537	−	0.256133i
$975$	−8.63140	+	26.5647i	−0.276426	+	0.850752i
$976$	3.74981	+	11.5407i	0.120029	+	0.369410i
$977$	−2.98786	+	2.17081i	−0.0955900	+	0.0694502i	−0.634554	−	0.772879i	$-0.718816\pi$
$977$	−2.98786	+	2.17081i	−0.0955900	+	0.0694502i	0.538964	+	0.842329i	$0.318816\pi$
$978$	−13.4164			−0.429009
$979$	0.425380	−	9.15048i	0.0135952	−	0.292451i
$980$	−0.0444738			−0.00142066
$981$	−5.24456	+	3.81040i	−0.167446	+	0.121657i
$982$	−11.1056	−	34.1795i	−0.354393	−	1.09071i
$983$	−14.1609	+	43.5828i	−0.451663	+	1.39008i	0.423346	+	0.905968i	$0.360855\pi$
$983$	−14.1609	+	43.5828i	−0.451663	+	1.39008i	−0.875009	+	0.484107i	$0.839145\pi$
$984$	5.58956	+	4.06105i	0.178189	+	0.129462i
$985$	0.649142	+	0.471630i	0.0206834	+	0.0150274i
$986$	−5.07756	+	15.6271i	−0.161702	+	0.497669i
$987$	3.52125	+	10.8373i	0.112083	+	0.344955i
$988$	16.2338	−	11.7945i	0.516465	−	0.375233i
$989$	39.5789			1.25854
$990$	0.0810650	+	0.123230i	0.00257641	+	0.00391649i
$991$	−25.4738			−0.809203			−0.404601	−	0.914493i	$-0.632590\pi$
$991$	−25.4738			−0.809203			−0.404601	+	0.914493i	$0.632590\pi$
$992$	7.18277	−	5.21859i	0.228053	−	0.165690i
$993$	6.17625	+	19.0085i	0.195997	+	0.603218i
$994$	−1.09017	+	3.35520i	−0.0345781	+	0.106420i
$995$	0.0904325	+	0.0657031i	0.00286690	+	0.00208293i
$996$	4.43714	+	3.22377i	0.140596	+	0.102149i
$997$	−1.37235	+	4.22366i	−0.0434628	+	0.133765i	−0.970433	−	0.241370i	$-0.922403\pi$
$997$	−1.37235	+	4.22366i	−0.0434628	+	0.133765i	0.926970	+	0.375134i	$0.122403\pi$
$998$	5.70323	+	17.5527i	0.180533	+	0.555622i
$999$	−2.03598	+	1.47923i	−0.0644156	+	0.0468006i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	462.2.j.f.421.2	yes	8
11.2	odd	10		5082.2.a.bx.1.2		4
11.4	even	5	inner	462.2.j.f.169.2	✓	8
11.9	even	5		5082.2.a.cc.1.2		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
462.2.j.f.169.2	✓	8	11.4	even	5	inner
462.2.j.f.421.2	yes	8	1.1	even	1	trivial
5082.2.a.bx.1.2		4	11.2	odd	10
5082.2.a.cc.1.2		4	11.9	even	5

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 462 = 2 \cdot 3 \cdot 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	462.j (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.809017 + 0.587785i) q^{2} +(-0.309017 - 0.951057i) q^{3} +(0.309017 - 0.951057i) q^{4} +(0.0359800 + 0.0261410i) q^{5} +(0.809017 + 0.587785i) q^{6} +(-0.309017 + 0.951057i) q^{7} +(0.309017 + 0.951057i) q^{8} +(-0.809017 + 0.587785i) q^{9} -0.0444738 q^{10} +(-0.154014 + 3.31305i) q^{11} -1.00000 q^{12} +(4.52125 - 3.28488i) q^{13} +(-0.309017 - 0.951057i) q^{14} +(0.0137431 - 0.0422971i) q^{15} +(-0.809017 - 0.587785i) q^{16} +(2.18999 + 1.59112i) q^{17} +(0.309017 - 0.951057i) q^{18} +(1.10954 + 3.41481i) q^{19} +(0.0359800 - 0.0261410i) q^{20} +1.00000 q^{21} +(-1.82276 - 2.77084i) q^{22} +3.09945 q^{23} +(0.809017 - 0.587785i) q^{24} +(-1.54447 - 4.75340i) q^{25} +(-1.72696 + 5.31505i) q^{26} +(0.809017 + 0.587785i) q^{27} +(0.809017 + 0.587785i) q^{28} +(1.87573 - 5.77290i) q^{29} +(0.0137431 + 0.0422971i) q^{30} +(7.18277 - 5.21859i) q^{31} +1.00000 q^{32} +(3.19849 - 0.877312i) q^{33} -2.70698 q^{34} +(-0.0359800 + 0.0261410i) q^{35} +(0.309017 + 0.951057i) q^{36} +(-0.777675 + 2.39344i) q^{37} +(-2.90481 - 2.11047i) q^{38} +(-4.52125 - 3.28488i) q^{39} +(-0.0137431 + 0.0422971i) q^{40} +(2.13502 + 6.57092i) q^{41} +(-0.809017 + 0.587785i) q^{42} +12.7697 q^{43} +(3.10330 + 1.17026i) q^{44} -0.0444738 q^{45} +(-2.50750 + 1.82181i) q^{46} +(3.52125 + 10.8373i) q^{47} +(-0.309017 + 0.951057i) q^{48} +(-0.809017 - 0.587785i) q^{49} +(4.04348 + 2.93776i) q^{50} +(0.836503 - 2.57449i) q^{51} +(-1.72696 - 5.31505i) q^{52} +(-6.65303 + 4.83371i) q^{53} -1.00000 q^{54} +(-0.0921479 + 0.115177i) q^{55} -1.00000 q^{56} +(2.90481 - 2.11047i) q^{57} +(1.87573 + 5.77290i) q^{58} +(-1.02285 + 3.14800i) q^{59} +(-0.0359800 - 0.0261410i) q^{60} +(-9.81713 - 7.13256i) q^{61} +(-2.74357 + 8.44385i) q^{62} +(-0.309017 - 0.951057i) q^{63} +(-0.809017 + 0.587785i) q^{64} +0.248545 q^{65} +(-2.07196 + 2.58978i) q^{66} -1.01248 q^{67} +(2.18999 - 1.59112i) q^{68} +(-0.957782 - 2.94775i) q^{69} +(0.0137431 - 0.0422971i) q^{70} +(-2.85410 - 2.07363i) q^{71} +(-0.809017 - 0.587785i) q^{72} +(-0.196232 + 0.603941i) q^{73} +(-0.777675 - 2.39344i) q^{74} +(-4.04348 + 2.93776i) q^{75} +3.59055 q^{76} +(-3.10330 - 1.17026i) q^{77} +5.58857 q^{78} +(5.05982 - 3.67617i) q^{79} +(-0.0137431 - 0.0422971i) q^{80} +(0.309017 - 0.951057i) q^{81} +(-5.58956 - 4.06105i) q^{82} +(-4.43714 - 3.22377i) q^{83} +(0.309017 - 0.951057i) q^{84} +(0.0372024 + 0.114497i) q^{85} +(-10.3309 + 7.50582i) q^{86} -6.06998 q^{87} +(-3.19849 + 0.877312i) q^{88} -2.76195 q^{89} +(0.0359800 - 0.0261410i) q^{90} +(1.72696 + 5.31505i) q^{91} +(0.957782 - 2.94775i) q^{92} +(-7.18277 - 5.21859i) q^{93} +(-9.21875 - 6.69781i) q^{94} +(-0.0493454 + 0.151870i) q^{95} +(-0.309017 - 0.951057i) q^{96} +(-9.05000 + 6.57521i) q^{97} +1.00000 q^{98} +(-1.82276 - 2.77084i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 2 q^{2} + 2 q^{3} - 2 q^{4} - 6 q^{5} + 2 q^{6} + 2 q^{7} - 2 q^{8} - 2 q^{9} + 4 q^{10} + 14 q^{11} - 8 q^{12} + 8 q^{13} + 2 q^{14} - 4 q^{15} - 2 q^{16} - 4 q^{17} - 2 q^{18} - 2 q^{19} - 6 q^{20}+ \cdots - 6 q^{99}+O(q^{100}) \) 8 * q - 2 * q^2 + 2 * q^3 - 2 * q^4 - 6 * q^5 + 2 * q^6 + 2 * q^7 - 2 * q^8 - 2 * q^9 + 4 * q^10 + 14 * q^11 - 8 * q^12 + 8 * q^13 + 2 * q^14 - 4 * q^15 - 2 * q^16 - 4 * q^17 - 2 * q^18 - 2 * q^19 - 6 * q^20 + 8 * q^21 - 6 * q^22 + 4 * q^23 + 2 * q^24 - 8 * q^25 - 12 * q^26 + 2 * q^27 + 2 * q^28 + 4 * q^29 - 4 * q^30 - 10 * q^31 + 8 * q^32 + 6 * q^33 - 4 * q^34 + 6 * q^35 - 2 * q^36 - 20 * q^37 - 12 * q^38 - 8 * q^39 + 4 * q^40 + 12 * q^41 - 2 * q^42 + 48 * q^43 - 6 * q^44 + 4 * q^45 + 4 * q^46 + 2 * q^48 - 2 * q^49 + 2 * q^50 - 6 * q^51 - 12 * q^52 - 12 * q^53 - 8 * q^54 - 8 * q^55 - 8 * q^56 + 12 * q^57 + 4 * q^58 + 12 * q^59 + 6 * q^60 - 32 * q^61 + 20 * q^62 + 2 * q^63 - 2 * q^64 + 24 * q^65 - 4 * q^66 - 48 * q^67 - 4 * q^68 + 6 * q^69 - 4 * q^70 + 4 * q^71 - 2 * q^72 - 20 * q^74 - 2 * q^75 + 28 * q^76 + 6 * q^77 - 8 * q^78 + 40 * q^79 + 4 * q^80 - 2 * q^81 - 18 * q^82 - 32 * q^83 - 2 * q^84 - 42 * q^85 - 32 * q^86 + 16 * q^87 - 6 * q^88 + 12 * q^89 - 6 * q^90 + 12 * q^91 - 6 * q^92 + 10 * q^93 + 54 * q^95 + 2 * q^96 + 8 * q^97 + 8 * q^98 - 6 * q^99

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