LMFDB - Embedded newform 430.2.q.c.81.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [430,2,Mod(31,430)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(430, base_ring=CyclotomicField(42))

chi = DirichletCharacter(H, H._module([0, 34]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("430.31");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 430 = 2 \cdot 5 \cdot 43 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	430.q (of order $21$, degree $12$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$3.43356728692$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$4$ over $\Q(\zeta_{21})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{21}]$

Embedding invariants

Embedding label			81.4
Character	$\chi$	$=$	430.81
Dual form			430.2.q.c.361.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.222521 - 0.974928i) q^{2} +(1.95105 + 0.601821i) q^{3} +(-0.900969 - 0.433884i) q^{4} +(0.365341 + 0.930874i) q^{5} +(1.02088 - 1.76822i) q^{6} +(2.34372 + 4.05945i) q^{7} +(-0.623490 + 0.781831i) q^{8} +(0.965710 + 0.658410i) q^{9} +O(q^{10})$	\(q+(0.222521 - 0.974928i) q^{2} +(1.95105 + 0.601821i) q^{3} +(-0.900969 - 0.433884i) q^{4} +(0.365341 + 0.930874i) q^{5} +(1.02088 - 1.76822i) q^{6} +(2.34372 + 4.05945i) q^{7} +(-0.623490 + 0.781831i) q^{8} +(0.965710 + 0.658410i) q^{9} +(0.988831 - 0.149042i) q^{10} +(1.10078 - 0.530106i) q^{11} +(-1.49672 - 1.38875i) q^{12} +(-3.31674 - 0.499919i) q^{13} +(4.47920 - 1.38165i) q^{14} +(0.152581 + 2.03606i) q^{15} +(0.623490 + 0.781831i) q^{16} +(-2.11526 + 5.38959i) q^{17} +(0.856793 - 0.794987i) q^{18} +(2.58731 - 1.76400i) q^{19} +(0.0747301 - 0.997204i) q^{20} +(2.12967 + 9.33070i) q^{21} +(-0.271869 - 1.19114i) q^{22} +(0.558189 - 7.44852i) q^{23} +(-1.68698 + 1.15017i) q^{24} +(-0.733052 + 0.680173i) q^{25} +(-1.22543 + 3.12234i) q^{26} +(-2.33115 - 2.92317i) q^{27} +(-0.350293 - 4.67434i) q^{28} +(8.01079 - 2.47100i) q^{29} +(2.01896 + 0.304309i) q^{30} +(-3.78601 - 3.51291i) q^{31} +(0.900969 - 0.433884i) q^{32} +(2.46670 - 0.371796i) q^{33} +(4.78377 + 3.26152i) q^{34} +(-2.92257 + 3.66479i) q^{35} +(-0.584401 - 1.01221i) q^{36} +(-0.0399786 + 0.0692449i) q^{37} +(-1.14404 - 2.91496i) q^{38} +(-6.17029 - 2.97145i) q^{39} +(-0.955573 - 0.294755i) q^{40} +(2.47658 - 10.8506i) q^{41} +9.57066 q^{42} +(-5.66557 - 3.30172i) q^{43} -1.22177 q^{44} +(-0.260083 + 1.13950i) q^{45} +(-7.13756 - 2.20165i) q^{46} +(9.95368 + 4.79344i) q^{47} +(0.745940 + 1.90062i) q^{48} +(-7.48607 + 12.9663i) q^{49} +(0.500000 + 0.866025i) q^{50} +(-7.37055 + 9.24238i) q^{51} +(2.77138 + 1.88949i) q^{52} +(-7.37185 + 1.11113i) q^{53} +(-3.36861 + 1.62224i) q^{54} +(0.895621 + 0.831015i) q^{55} +(-4.63509 - 0.698628i) q^{56} +(6.10958 - 1.88456i) q^{57} +(-0.626480 - 8.35979i) q^{58} +(-4.79469 - 6.01235i) q^{59} +(0.745940 - 1.90062i) q^{60} +(4.47270 - 4.15005i) q^{61} +(-4.26730 + 2.90940i) q^{62} +(-0.409423 + 5.46338i) q^{63} +(-0.222521 - 0.974928i) q^{64} +(-0.746381 - 3.27011i) q^{65} +(0.186419 - 2.48759i) q^{66} +(-0.293583 + 0.200161i) q^{67} +(4.24424 - 3.93808i) q^{68} +(5.57173 - 14.1965i) q^{69} +(2.92257 + 3.66479i) q^{70} +(0.716862 + 9.56586i) q^{71} +(-1.11688 + 0.344510i) q^{72} +(1.28619 + 0.193861i) q^{73} +(0.0586127 + 0.0543847i) q^{74} +(-1.83957 + 0.885888i) q^{75} +(-3.09645 + 0.466715i) q^{76} +(4.73185 + 3.22612i) q^{77} +(-4.26997 + 5.35437i) q^{78} +(2.04386 + 3.54008i) q^{79} +(-0.500000 + 0.866025i) q^{80} +(-4.07001 - 10.3702i) q^{81} +(-10.0275 - 4.82897i) q^{82} +(4.34227 + 1.33941i) q^{83} +(2.12967 - 9.33070i) q^{84} -5.78982 q^{85} +(-4.47964 + 4.78882i) q^{86} +17.1166 q^{87} +(-0.271869 + 1.19114i) q^{88} +(-5.37136 - 1.65684i) q^{89} +(1.05305 + 0.507124i) q^{90} +(-5.74413 - 14.6358i) q^{91} +(-3.73470 + 6.46869i) q^{92} +(-5.27258 - 9.13238i) q^{93} +(6.88816 - 8.63748i) q^{94} +(2.58731 + 1.76400i) q^{95} +(2.01896 - 0.304309i) q^{96} +(-10.4411 + 5.02818i) q^{97} +(10.9754 + 10.1836i) q^{98} +(1.41206 + 0.212833i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q + 8 q^{2} - 7 q^{3} - 8 q^{4} + 4 q^{5} + 7 q^{6} - 3 q^{7} + 8 q^{8} + 13 q^{9}+O(q^{10}) $ 48 * q + 8 * q^2 - 7 * q^3 - 8 * q^4 + 4 * q^5 + 7 * q^6 - 3 * q^7 + 8 * q^8 + 13 * q^9	\( 48 q + 8 q^{2} - 7 q^{3} - 8 q^{4} + 4 q^{5} + 7 q^{6} - 3 q^{7} + 8 q^{8} + 13 q^{9} - 4 q^{10} + q^{11} + 14 q^{12} - 23 q^{13} + 24 q^{14} - 8 q^{16} + 8 q^{17} - 20 q^{18} - 3 q^{19} + 4 q^{20} - 8 q^{21} - q^{22} + 7 q^{23} + 4 q^{25} - 19 q^{26} + 32 q^{27} + 4 q^{28} + 30 q^{29} + 9 q^{31} + 8 q^{32} + 39 q^{33} - 8 q^{34} - 22 q^{35} - 29 q^{36} - 37 q^{37} - 11 q^{38} - 52 q^{39} - 4 q^{40} - 28 q^{41} - 6 q^{42} + 41 q^{43} + 8 q^{44} + 2 q^{45} - 28 q^{46} + 3 q^{47} - 41 q^{49} + 24 q^{50} - 30 q^{51} - 9 q^{52} - 69 q^{53} + 3 q^{54} + 10 q^{55} - 11 q^{56} + 116 q^{57} + 5 q^{58} + 10 q^{59} - 19 q^{61} - 93 q^{62} + 34 q^{63} - 8 q^{64} - 3 q^{65} - 18 q^{66} + 3 q^{67} + 8 q^{68} + 42 q^{69} + 22 q^{70} - 36 q^{71} + 22 q^{72} - 56 q^{73} + 9 q^{74} - 10 q^{76} + 3 q^{77} + 45 q^{78} + 16 q^{79} - 24 q^{80} - 19 q^{81} + 14 q^{82} + 64 q^{83} - 8 q^{84} - 30 q^{85} + 36 q^{86} + 78 q^{87} - q^{88} - 75 q^{89} + 5 q^{90} + 5 q^{91} + 14 q^{92} - 10 q^{93} - 45 q^{94} - 3 q^{95} + 33 q^{97} - q^{98} - 11 q^{99}+O(q^{100}) \) 48 * q + 8 * q^2 - 7 * q^3 - 8 * q^4 + 4 * q^5 + 7 * q^6 - 3 * q^7 + 8 * q^8 + 13 * q^9 - 4 * q^10 + q^11 + 14 * q^12 - 23 * q^13 + 24 * q^14 - 8 * q^16 + 8 * q^17 - 20 * q^18 - 3 * q^19 + 4 * q^20 - 8 * q^21 - q^22 + 7 * q^23 + 4 * q^25 - 19 * q^26 + 32 * q^27 + 4 * q^28 + 30 * q^29 + 9 * q^31 + 8 * q^32 + 39 * q^33 - 8 * q^34 - 22 * q^35 - 29 * q^36 - 37 * q^37 - 11 * q^38 - 52 * q^39 - 4 * q^40 - 28 * q^41 - 6 * q^42 + 41 * q^43 + 8 * q^44 + 2 * q^45 - 28 * q^46 + 3 * q^47 - 41 * q^49 + 24 * q^50 - 30 * q^51 - 9 * q^52 - 69 * q^53 + 3 * q^54 + 10 * q^55 - 11 * q^56 + 116 * q^57 + 5 * q^58 + 10 * q^59 - 19 * q^61 - 93 * q^62 + 34 * q^63 - 8 * q^64 - 3 * q^65 - 18 * q^66 + 3 * q^67 + 8 * q^68 + 42 * q^69 + 22 * q^70 - 36 * q^71 + 22 * q^72 - 56 * q^73 + 9 * q^74 - 10 * q^76 + 3 * q^77 + 45 * q^78 + 16 * q^79 - 24 * q^80 - 19 * q^81 + 14 * q^82 + 64 * q^83 - 8 * q^84 - 30 * q^85 + 36 * q^86 + 78 * q^87 - q^88 - 75 * q^89 + 5 * q^90 + 5 * q^91 + 14 * q^92 - 10 * q^93 - 45 * q^94 - 3 * q^95 + 33 * q^97 - q^98 - 11 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/430\mathbb{Z}\right)^\times$.

$n$	$87$	$261$
$\chi(n)$	$1$	$e\left(\frac{2}{21}\right)$

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 $

$2$	0.222521	−	0.974928i	0.157346	−	0.689378i
$2$	0.222521	−	0.974928i	0.157346	−	0.689378i
$3$	1.95105	+	0.601821i	1.12644	+	0.347461i	0.801335	−	0.598216i	$-0.204124\pi$
$3$	1.95105	+	0.601821i	1.12644	+	0.347461i	0.325107	+	0.945677i	$0.394600\pi$
$4$	−0.900969	−	0.433884i	−0.450484	−	0.216942i
$5$	0.365341	+	0.930874i	0.163385	+	0.416299i
$5$	0.365341	+	0.930874i	0.163385	+	0.416299i
$6$	1.02088	−	1.76822i	0.416773	−	0.721873i
$7$	2.34372	+	4.05945i	0.885844	+	1.53433i	0.844743	+	0.535172i	$0.179753\pi$
$7$	2.34372	+	4.05945i	0.885844	+	1.53433i	0.0411006	+	0.999155i	$0.486914\pi$
$8$	−0.623490	+	0.781831i	−0.220437	+	0.276419i
$9$	0.965710	+	0.658410i	0.321903	+	0.219470i
$10$	0.988831	−	0.149042i	0.312696	−	0.0471313i
$11$	1.10078	−	0.530106i	0.331897	−	0.159833i	−0.260512	−	0.965471i	$-0.583891\pi$
$11$	1.10078	−	0.530106i	0.331897	−	0.159833i	0.592409	+	0.805638i	$0.298177\pi$
$12$	−1.49672	−	1.38875i	−0.432066	−	0.400898i
$13$	−3.31674	−	0.499919i	−0.919899	−	0.138652i	−0.328012	−	0.944674i	$-0.606379\pi$
$13$	−3.31674	−	0.499919i	−0.919899	−	0.138652i	−0.591887	+	0.806021i	$0.701617\pi$
$14$	4.47920	−	1.38165i	1.19712	−	0.369261i
$15$	0.152581	+	2.03606i	0.0393963	+	0.525707i
$16$	0.623490	+	0.781831i	0.155872	+	0.195458i
$17$	−2.11526	+	5.38959i	−0.513025	+	1.30717i	0.406326	+	0.913728i	$0.366810\pi$
$17$	−2.11526	+	5.38959i	−0.513025	+	1.30717i	−0.919351	+	0.393439i	$0.871285\pi$
$18$	0.856793	−	0.794987i	0.201948	−	0.187380i
$19$	2.58731	−	1.76400i	0.593569	−	0.404688i	−0.228940	−	0.973440i	$-0.573526\pi$
$19$	2.58731	−	1.76400i	0.593569	−	0.404688i	0.822509	+	0.568752i	$0.192574\pi$
$20$	0.0747301	−	0.997204i	0.0167102	−	0.222982i
$21$	2.12967	+	9.33070i	0.464733	+	2.03613i
$22$	−0.271869	−	1.19114i	−0.0579627	−	0.253951i
$23$	0.558189	−	7.44852i	0.116391	−	1.55312i	−0.567398	−	0.823444i	$-0.692050\pi$
$23$	0.558189	−	7.44852i	0.116391	−	1.55312i	0.683789	−	0.729680i	$-0.260331\pi$
$24$	−1.68698	+	1.15017i	−0.344354	+	0.234777i
$25$	−0.733052	+	0.680173i	−0.146610	+	0.136035i
$26$	−1.22543	+	3.12234i	−0.240326	+	0.612342i
$27$	−2.33115	−	2.92317i	−0.448630	−	0.562564i
$28$	−0.350293	−	4.67434i	−0.0661992	−	0.883367i
$29$	8.01079	−	2.47100i	1.48757	−	0.458854i	0.558732	−	0.829348i	$-0.311288\pi$
$29$	8.01079	−	2.47100i	1.48757	−	0.458854i	0.928835	+	0.370495i	$0.120812\pi$
$30$	2.01896	+	0.304309i	0.368610	+	0.0555590i
$31$	−3.78601	−	3.51291i	−0.679988	−	0.630937i	0.262596	−	0.964906i	$-0.415421\pi$
$31$	−3.78601	−	3.51291i	−0.679988	−	0.630937i	−0.942584	+	0.333969i	$0.891612\pi$
$32$	0.900969	−	0.433884i	0.159270	−	0.0767005i
$33$	2.46670	−	0.371796i	0.429398	−	0.0647213i
$34$	4.78377	+	3.26152i	0.820410	+	0.559346i
$35$	−2.92257	+	3.66479i	−0.494005	+	0.619463i
$36$	−0.584401	−	1.01221i	−0.0974002	−	0.168702i
$37$	−0.0399786	+	0.0692449i	−0.00657244	+	0.0113838i	−0.869293	−	0.494297i	$-0.835425\pi$
$37$	−0.0399786	+	0.0692449i	−0.00657244	+	0.0113838i	0.862720	+	0.505681i	$0.168759\pi$
$38$	−1.14404	−	2.91496i	−0.185588	−	0.472869i
$39$	−6.17029	−	2.97145i	−0.988036	−	0.475813i
$40$	−0.955573	−	0.294755i	−0.151089	−	0.0466049i
$41$	2.47658	−	10.8506i	0.386776	−	1.69458i	−0.288883	−	0.957364i	$-0.593284\pi$
$41$	2.47658	−	10.8506i	0.386776	−	1.69458i	0.675660	−	0.737214i	$-0.263859\pi$
$42$	9.57066			1.47678
$43$	−5.66557	−	3.30172i	−0.863991	−	0.503507i
$43$	−5.66557	−	3.30172i	−0.863991	−	0.503507i
$44$	−1.22177			−0.184189
$45$	−0.260083	+	1.13950i	−0.0387709	+	0.169866i
$46$	−7.13756	−	2.20165i	−1.05238	−	0.324615i
$47$	9.95368	+	4.79344i	1.45189	+	0.699195i	0.982923	−	0.184019i	$-0.0589108\pi$
$47$	9.95368	+	4.79344i	1.45189	+	0.699195i	0.468970	+	0.883214i	$0.344625\pi$
$48$	0.745940	+	1.90062i	0.107667	+	0.274332i
$49$	−7.48607	+	12.9663i	−1.06944	+	1.85232i
$50$	0.500000	+	0.866025i	0.0707107	+	0.122474i
$51$	−7.37055	+	9.24238i	−1.03208	+	1.29419i
$52$	2.77138	+	1.88949i	0.384321	+	0.262025i
$53$	−7.37185	+	1.11113i	−1.01260	+	0.152625i	−0.634324	−	0.773067i	$-0.718722\pi$
$53$	−7.37185	+	1.11113i	−1.01260	+	0.152625i	−0.378277	+	0.925692i	$0.623483\pi$
$54$	−3.36861	+	1.62224i	−0.458410	+	0.220758i
$55$	0.895621	+	0.831015i	0.120765	+	0.112054i
$56$	−4.63509	−	0.698628i	−0.619390	−	0.0933580i
$57$	6.10958	−	1.88456i	0.809234	−	0.249616i
$58$	−0.626480	−	8.35979i	−0.0822609	−	1.09769i
$59$	−4.79469	−	6.01235i	−0.624216	−	0.782742i	0.364715	−	0.931119i	$-0.381166\pi$
$59$	−4.79469	−	6.01235i	−0.624216	−	0.782742i	−0.988931	+	0.148377i	$0.952595\pi$
$60$	0.745940	−	1.90062i	0.0963005	−	0.245370i
$61$	4.47270	−	4.15005i	0.572670	−	0.531360i	−0.339803	−	0.940497i	$-0.610360\pi$
$61$	4.47270	−	4.15005i	0.572670	−	0.531360i	0.912473	+	0.409136i	$0.134170\pi$
$62$	−4.26730	+	2.90940i	−0.541948	+	0.369494i
$63$	−0.409423	+	5.46338i	−0.0515825	+	0.688321i
$64$	−0.222521	−	0.974928i	−0.0278151	−	0.121866i
$65$	−0.746381	−	3.27011i	−0.0925772	−	0.405607i
$66$	0.186419	−	2.48759i	0.0229466	−	0.306201i
$67$	−0.293583	+	0.200161i	−0.0358668	+	0.0244536i	−0.581121	−	0.813817i	$-0.697386\pi$
$67$	−0.293583	+	0.200161i	−0.0358668	+	0.0244536i	0.545254	+	0.838271i	$0.316433\pi$
$68$	4.24424	−	3.93808i	0.514689	−	0.477562i
$69$	5.57173	−	14.1965i	0.670758	−	1.70906i
$70$	2.92257	+	3.66479i	0.349314	+	0.438026i
$71$	0.716862	+	9.56586i	0.0850759	+	1.13526i	0.862424	+	0.506187i	$0.168946\pi$
$71$	0.716862	+	9.56586i	0.0850759	+	1.13526i	−0.777348	+	0.629071i	$0.783435\pi$
$72$	−1.11688	+	0.344510i	−0.131625	+	0.0406009i
$73$	1.28619	+	0.193861i	0.150537	+	0.0226898i	0.223878	−	0.974617i	$-0.428128\pi$
$73$	1.28619	+	0.193861i	0.150537	+	0.0226898i	−0.0733415	+	0.997307i	$0.523366\pi$
$74$	0.0586127	+	0.0543847i	0.00681359	+	0.00632209i
$75$	−1.83957	+	0.885888i	−0.212415	+	0.102294i
$76$	−3.09645	+	0.466715i	−0.355187	+	0.0535359i
$77$	4.73185	+	3.22612i	0.539245	+	0.367651i
$78$	−4.26997	+	5.35437i	−0.483479	+	0.606263i
$79$	2.04386	+	3.54008i	0.229953	+	0.398290i	0.957794	−	0.287456i	$-0.0928095\pi$
$79$	2.04386	+	3.54008i	0.229953	+	0.398290i	−0.727841	+	0.685746i	$0.759476\pi$
$80$	−0.500000	+	0.866025i	−0.0559017	+	0.0968246i
$81$	−4.07001	−	10.3702i	−0.452224	−	1.15225i
$82$	−10.0275	−	4.82897i	−1.10735	−	0.533270i
$83$	4.34227	+	1.33941i	0.476626	+	0.147020i	0.523754	−	0.851869i	$-0.324531\pi$
$83$	4.34227	+	1.33941i	0.476626	+	0.147020i	−0.0471289	+	0.998889i	$0.515007\pi$
$84$	2.12967	−	9.33070i	0.232366	−	1.01806i
$85$	−5.78982			−0.627994
$86$	−4.47964	+	4.78882i	−0.483052	+	0.516392i
$87$	17.1166			1.83509
$88$	−0.271869	+	1.19114i	−0.0289814	+	0.126976i
$89$	−5.37136	−	1.65684i	−0.569363	−	0.175625i	−0.00331050	−	0.999995i	$-0.501054\pi$
$89$	−5.37136	−	1.65684i	−0.569363	−	0.175625i	−0.566052	+	0.824369i	$0.691530\pi$
$90$	1.05305	+	0.507124i	0.111002	+	0.0534556i
$91$	−5.74413	−	14.6358i	−0.602149	−	1.53425i
$92$	−3.73470	+	6.46869i	−0.389370	+	0.674408i
$93$	−5.27258	−	9.13238i	−0.546741	−	0.946984i
$94$	6.88816	−	8.63748i	0.710459	−	0.890888i
$95$	2.58731	+	1.76400i	0.265452	+	0.180982i
$96$	2.01896	−	0.304309i	0.206059	−	0.0310584i
$97$	−10.4411	+	5.02818i	−1.06013	+	0.510534i	−0.880915	−	0.473275i	$-0.843072\pi$
$97$	−10.4411	+	5.02818i	−1.06013	+	0.510534i	−0.179220	+	0.983809i	$0.557357\pi$
$98$	10.9754	+	10.1836i	1.10868	+	1.02870i
$99$	1.41206	+	0.212833i	0.141917	+	0.0213906i
$100$	0.955573	−	0.294755i	0.0955573	−	0.0294755i
$101$	−0.232209	−	3.09862i	−0.0231057	−	0.308324i	−0.996768	−	0.0803304i	$-0.974402\pi$
$101$	−0.232209	−	3.09862i	−0.0231057	−	0.308324i	0.973663	−	0.227994i	$-0.0732166\pi$
$102$	7.37055	+	9.24238i	0.729793	+	0.915132i
$103$	−6.06627	+	15.4566i	−0.597728	+	1.52299i	0.236538	+	0.971622i	$0.423987\pi$
$103$	−6.06627	+	15.4566i	−0.597728	+	1.52299i	−0.834266	+	0.551363i	$0.814108\pi$
$104$	2.45881	−	2.28144i	0.241106	−	0.223714i
$105$	−7.90765	+	5.39134i	−0.771708	+	0.526141i
$106$	−0.557122	+	7.43427i	−0.0541124	+	0.722080i
$107$	0.657724	+	2.88168i	0.0635846	+	0.278582i	0.996718	−	0.0809470i	$-0.0257944\pi$
$107$	0.657724	+	2.88168i	0.0635846	+	0.278582i	−0.933134	+	0.359529i	$0.882937\pi$
$108$	0.831978	+	3.64513i	0.0800571	+	0.350753i
$109$	−0.291822	+	3.89409i	−0.0279515	+	0.372987i	0.965634	+	0.259905i	$0.0836912\pi$
$109$	−0.291822	+	3.89409i	−0.0279515	+	0.372987i	−0.993586	+	0.113082i	$0.963928\pi$
$110$	1.00947	−	0.688248i	0.0962495	−	0.0656218i
$111$	−0.119673	+	0.111041i	−0.0113589	+	0.0105395i
$112$	−1.71252	+	4.36342i	−0.161818	+	0.412304i
$113$	5.22207	+	6.54827i	0.491251	+	0.616009i	0.964231	−	0.265064i	$-0.0853931\pi$
$113$	5.22207	+	6.54827i	0.491251	+	0.616009i	−0.472980	+	0.881073i	$0.656822\pi$
$114$	−0.477797	−	6.37576i	−0.0447498	−	0.597144i
$115$	7.13756	−	2.20165i	0.665581	−	0.205305i
$116$	−8.28960	−	1.24946i	−0.769670	−	0.116009i
$117$	−2.87386	−	2.66655i	−0.265688	−	0.246523i
$118$	−6.92853	+	3.33661i	−0.637823	+	0.307159i
$119$	−26.8363	+	4.04493i	−2.46008	+	0.370798i
$120$	−1.68698	−	1.15017i	−0.154000	−	0.104995i
$121$	−5.92769	+	7.43309i	−0.538881	+	0.675735i
$122$	−3.05074	−	5.28403i	−0.276201	−	0.478394i
$123$	11.3620	−	19.6796i	1.02448	−	1.77445i
$124$	1.88689	+	4.80771i	0.169448	+	0.431745i
$125$	−0.900969	−	0.433884i	−0.0805851	−	0.0388077i
$126$	5.23529	+	1.61487i	0.466397	+	0.143864i
$127$	0.934023	−	4.09222i	0.0828811	−	0.363126i	−0.916432	−	0.400191i	$-0.868944\pi$
$127$	0.934023	−	4.09222i	0.0828811	−	0.363126i	0.999313	+	0.0370651i	$0.0118009\pi$
$128$	−1.00000			−0.0883883
$129$	−9.06679	−	9.85149i	−0.798286	−	0.867375i
$130$	−3.35421			−0.294183
$131$	−4.91194	+	21.5206i	−0.429159	+	1.88027i	0.0435567	+	0.999051i	$0.486131\pi$
$131$	−4.91194	+	21.5206i	−0.429159	+	1.88027i	−0.472715	+	0.881215i	$0.656726\pi$
$132$	−2.38374	−	0.735286i	−0.207478	−	0.0639985i
$133$	13.2248	+	6.36871i	1.14673	+	0.552238i
$134$	0.129815	+	0.330762i	0.0112143	+	0.0285735i
$135$	1.86944	−	3.23796i	0.160896	−	0.278679i
$136$	−2.89491	−	5.01413i	−0.248236	−	0.429958i
$137$	0.640022	−	0.802563i	0.0546808	−	0.0685676i	−0.753739	−	0.657174i	$-0.771752\pi$
$137$	0.640022	−	0.802563i	0.0546808	−	0.0685676i	0.808420	+	0.588606i	$0.200323\pi$
$138$	−12.6008	−	8.59106i	−1.07265	−	0.731320i
$139$	−11.7324	+	1.76837i	−0.995128	+	0.149991i	−0.626363	−	0.779531i	$-0.715457\pi$
$139$	−11.7324	+	1.76837i	−0.995128	+	0.149991i	−0.368765	+	0.929523i	$0.620219\pi$
$140$	4.22324	−	2.03381i	0.356929	−	0.171888i
$141$	16.5354	+	15.3426i	1.39253	+	1.29208i
$142$	9.48554	+	1.42971i	0.796009	+	0.119979i
$143$	−3.91600	+	1.20793i	−0.327473	+	0.101012i
$144$	0.0873447	+	1.16553i	0.00727872	+	0.0971278i
$145$	5.22686	+	6.55428i	0.434067	+	0.544303i
$146$	0.475204	−	1.21080i	0.0393282	−	0.100207i
$147$	−22.4091	+	20.7926i	−1.84827	+	1.71495i
$148$	0.0660637	−	0.0450415i	0.00543040	−	0.00370239i
$149$	1.71249	−	22.8516i	0.140292	−	1.87207i	−0.273732	−	0.961806i	$-0.588258\pi$
$149$	1.71249	−	22.8516i	0.140292	−	1.87207i	0.414024	−	0.910266i	$-0.364123\pi$
$150$	0.454335	+	1.99057i	0.0370963	+	0.162530i
$151$	−2.77342	−	12.1511i	−0.225698	−	0.988846i	−0.953105	−	0.302640i	$-0.902132\pi$
$151$	−2.77342	−	12.1511i	−0.225698	−	0.988846i	0.727407	−	0.686206i	$-0.240725\pi$
$152$	−0.234012	+	3.12267i	−0.0189809	+	0.253282i
$153$	−5.59128	+	3.81207i	−0.452028	+	0.308188i
$154$	4.19817	−	3.89534i	0.338298	−	0.313895i
$155$	1.88689	−	4.80771i	0.151558	−	0.386165i
$156$	4.26997	+	5.35437i	0.341871	+	0.428693i
$157$	−0.523677	−	6.98799i	−0.0417940	−	0.557702i	−0.978319	−	0.207102i	$-0.933597\pi$
$157$	−0.523677	−	6.98799i	−0.0417940	−	0.557702i	0.936525	−	0.350600i	$-0.114022\pi$
$158$	3.90612	−	1.20488i	0.310754	−	0.0958551i
$159$	−15.0516	−	2.26866i	−1.19367	−	0.179916i
$160$	0.733052	+	0.680173i	0.0579528	+	0.0537724i
$161$	31.5451	−	15.1913i	2.48610	−	1.19724i
$162$	−11.0159	+	1.66038i	−0.865489	+	0.130452i
$163$	−11.4339	−	7.79551i	−0.895574	−	0.610592i	0.0256304	−	0.999671i	$-0.491841\pi$
$163$	−11.4339	−	7.79551i	−0.895574	−	0.610592i	−0.921204	+	0.389080i	$0.872793\pi$
$164$	−6.93921	+	8.70150i	−0.541862	+	0.679473i
$165$	1.24728	+	2.16036i	0.0971009	+	0.168184i
$166$	2.27207	−	3.93535i	0.176347	−	0.305442i
$167$	5.93943	+	15.1334i	0.459607	+	1.17106i	0.953462	+	0.301515i	$0.0974922\pi$
$167$	5.93943	+	15.1334i	0.459607	+	1.17106i	−0.493855	+	0.869544i	$0.664413\pi$
$168$	−8.62287	−	4.15255i	−0.665269	−	0.320376i
$169$	−1.67158	−	0.515614i	−0.128583	−	0.0396626i
$170$	−1.28836	+	5.64465i	−0.0988123	+	0.432925i
$171$	3.66002			0.279889
$172$	3.67194	+	5.43294i	0.279983	+	0.414258i
$173$	12.7958			0.972846			0.486423	−	0.873723i	$-0.338301\pi$
$173$	12.7958			0.972846			0.486423	+	0.873723i	$0.338301\pi$
$174$	3.80880	−	16.6874i	0.288744	−	1.26507i
$175$	−4.47920	−	1.38165i	−0.338595	−	0.104443i
$176$	1.10078	+	0.530106i	0.0829742	+	0.0399583i
$177$	−5.73635	−	14.6160i	−0.431170	−	1.09860i
$178$	−2.81054	+	4.86800i	−0.210659	+	0.364872i
$179$	−0.0316691	−	0.0548524i	−0.00236706	−	0.00409986i	0.864839	−	0.502049i	$-0.167420\pi$
$179$	−0.0316691	−	0.0548524i	−0.00236706	−	0.00409986i	−0.867207	+	0.497949i	$0.834087\pi$
$180$	0.728736	−	0.913806i	0.0543168	−	0.0681111i
$181$	4.44170	+	3.02830i	0.330149	+	0.225092i	0.717037	−	0.697035i	$-0.245498\pi$
$181$	4.44170	+	3.02830i	0.330149	+	0.225092i	−0.386888	+	0.922127i	$0.626450\pi$
$182$	−15.5471	+	2.34334i	−1.15242	+	0.173700i
$183$	11.2241	−	5.40522i	0.829706	−	0.399566i
$184$	5.47546	+	5.08049i	0.403656	+	0.374538i
$185$	−0.0790641	−	0.0119170i	−0.00581291	−	0.000876155i
$186$	−10.0767	+	3.10824i	−0.738857	+	0.227907i
$187$	0.528628	+	7.05404i	0.0386571	+	0.515843i
$188$	−6.88816	−	8.63748i	−0.502371	−	0.629953i
$189$	6.40288	−	16.3143i	0.465741	−	1.18669i
$190$	2.29550	−	2.12991i	0.166533	−	0.154520i
$191$	20.1368	−	13.7291i	1.45705	−	0.993400i	0.462783	−	0.886472i	$-0.346851\pi$
$191$	20.1368	−	13.7291i	1.45705	−	0.993400i	0.994267	−	0.106928i	$-0.0341014\pi$
$192$	0.152581	−	2.03606i	0.0110116	−	0.146940i
$193$	0.862289	+	3.77794i	0.0620689	+	0.271942i	0.996434	−	0.0843752i	$-0.0268894\pi$
$193$	0.862289	+	3.77794i	0.0620689	+	0.271942i	−0.934365	+	0.356317i	$0.884032\pi$
$194$	2.57874	+	11.2982i	0.185143	+	0.811164i
$195$	0.511789	−	6.82935i	0.0366500	−	0.489060i
$196$	12.3706	−	8.43411i	0.883612	−	0.602436i
$197$	−3.55703	+	3.30044i	−0.253428	+	0.235147i	−0.796648	−	0.604444i	$-0.793395\pi$
$197$	−3.55703	+	3.30044i	−0.253428	+	0.235147i	0.543220	+	0.839590i	$0.317205\pi$
$198$	0.521710	−	1.32929i	0.0370763	−	0.0944688i
$199$	4.72504	+	5.92501i	0.334949	+	0.420013i	0.920573	−	0.390570i	$-0.127722\pi$
$199$	4.72504	+	5.92501i	0.334949	+	0.420013i	−0.585624	+	0.810583i	$0.699151\pi$
$200$	−0.0747301	−	0.997204i	−0.00528422	−	0.0705130i
$201$	−0.693257	+	0.213841i	−0.0488986	+	0.0150832i
$202$	−3.07260	−	0.463120i	−0.216188	−	0.0325850i
$203$	28.8060	+	26.7280i	2.02178	+	1.87594i
$204$	10.6508	−	5.12913i	0.745702	−	0.359111i
$205$	11.0053	−	1.65879i	0.768645	−	0.115855i
$206$	13.7192	+	9.35360i	0.955863	+	0.651696i
$207$	5.44323	−	6.82559i	0.378330	−	0.474411i
$208$	−1.67710	−	2.90483i	−0.116286	−	0.201414i
$209$	1.91294	−	3.31331i	0.132321	−	0.229187i
$210$	3.49655	+	8.90908i	0.241285	+	0.614785i
$211$	−15.2437	−	7.34098i	−1.04942	−	0.505374i	−0.172000	−	0.985097i	$-0.555023\pi$
$211$	−15.2437	−	7.34098i	−1.04942	−	0.505374i	−0.877420	+	0.479723i	$0.840737\pi$
$212$	7.12391	+	2.19743i	0.489272	+	0.150920i
$213$	−4.35829	+	19.0949i	−0.298625	+	1.30836i
$214$	2.95578			0.202053
$215$	1.00362	−	6.48018i	0.0684462	−	0.441945i
$216$	3.73887			0.254398
$217$	5.38710	−	23.6024i	0.365700	−	1.60224i
$218$	3.73153	+	1.15102i	0.252731	+	0.0779571i
$219$	2.39275	+	1.15229i	0.161687	+	0.0778644i
$220$	−0.446363	−	1.13731i	−0.0300938	−	0.0766777i
$221$	9.71012	−	16.8184i	0.653173	−	1.13133i
$222$	0.0816268	+	0.141382i	0.00547843	+	0.00948893i
$223$	7.65067	−	9.59364i	0.512327	−	0.642438i	−0.456633	−	0.889655i	$-0.650945\pi$
$223$	7.65067	−	9.59364i	0.512327	−	0.642438i	0.968960	+	0.247217i	$0.0795162\pi$
$224$	3.87295	+	2.64053i	0.258772	+	0.176428i
$225$	−1.15575	+	0.174201i	−0.0770498	+	0.0116134i
$226$	7.54611	−	3.63401i	0.501960	−	0.241731i
$227$	5.03563	+	4.67238i	0.334226	+	0.310117i	0.829376	−	0.558691i	$-0.188696\pi$
$227$	5.03563	+	4.67238i	0.334226	+	0.310117i	−0.495149	+	0.868808i	$0.664887\pi$
$228$	−6.32222	−	0.952922i	−0.418699	−	0.0631088i
$229$	14.1194	−	4.35527i	0.933038	−	0.287804i	0.209278	−	0.977856i	$-0.432889\pi$
$229$	14.1194	−	4.35527i	0.933038	−	0.287804i	0.723760	+	0.690052i	$0.242412\pi$
$230$	−0.558189	−	7.44852i	−0.0368059	−	0.491141i
$231$	7.29056	+	9.14207i	0.479683	+	0.601504i
$232$	−3.06274	+	7.80373i	−0.201079	+	0.512340i
$233$	16.5493	−	15.3555i	1.08418	−	1.00597i	0.0842284	−	0.996446i	$-0.473157\pi$
$233$	16.5493	−	15.3555i	1.08418	−	1.00597i	0.999955	−	0.00952834i	$-0.00303301\pi$
$234$	−3.23919	+	2.20844i	−0.211752	+	0.144370i
$235$	−0.825599	+	11.0169i	−0.0538562	+	0.718660i
$236$	1.71121	+	7.49728i	0.111390	+	0.488032i
$237$	1.85720	+	8.13692i	0.120638	+	0.528550i
$238$	−2.02813	+	27.0636i	−0.131464	+	1.75427i
$239$	−4.62146	+	3.15086i	−0.298938	+	0.203812i	−0.703495	−	0.710701i	$-0.748378\pi$
$239$	−4.62146	+	3.15086i	−0.298938	+	0.203812i	0.404557	+	0.914513i	$0.367426\pi$
$240$	−1.49672	+	1.38875i	−0.0966128	+	0.0896436i
$241$	−3.10839	+	7.92004i	−0.200229	+	0.510175i	−0.995355	−	0.0962689i	$-0.969309\pi$
$241$	−3.10839	+	7.92004i	−0.200229	+	0.510175i	0.795127	+	0.606443i	$0.207404\pi$
$242$	5.92769	+	7.43309i	0.381046	+	0.477817i
$243$	−0.861583	−	11.4970i	−0.0552706	−	0.737534i
$244$	−5.83040	+	1.79844i	−0.373253	+	0.115133i
$245$	−14.8049	−	2.23148i	−0.945852	−	0.142564i
$246$	−16.6579	−	15.4563i	−1.06207	−	0.985458i
$247$	−9.46328	+	4.55728i	−0.602134	+	0.289973i
$248$	5.10704	−	0.769763i	0.324298	−	0.0488800i
$249$	7.66591	+	5.22653i	0.485807	+	0.331218i
$250$	−0.623490	+	0.781831i	−0.0394330	+	0.0494474i
$251$	7.15394	+	12.3910i	0.451552	+	0.782112i	0.998483	−	0.0550663i	$-0.0175370\pi$
$251$	7.15394	+	12.3910i	0.451552	+	0.782112i	−0.546930	+	0.837178i	$0.684204\pi$
$252$	2.73935	−	4.74469i	0.172563	−	0.298887i
$253$	−3.33406	−	8.49506i	−0.209611	−	0.534080i
$254$	−3.78178	−	1.82121i	−0.237290	−	0.114273i
$255$	−11.2962	−	3.48443i	−0.707398	−	0.218204i
$256$	−0.222521	+	0.974928i	−0.0139076	+	0.0609330i
$257$	3.19124			0.199064			0.0995321	−	0.995034i	$-0.468265\pi$
$257$	3.19124			0.199064			0.0995321	+	0.995034i	$0.468265\pi$
$258$	−11.6220	+	6.64730i	−0.723557	+	0.413843i
$259$	−0.374795			−0.0232886
$260$	−0.746381	+	3.27011i	−0.0462886	+	0.202804i
$261$	9.36303	+	2.88811i	0.579557	+	0.178770i
$262$	19.8881	+	9.57758i	1.22869	+	0.591705i
$263$	−1.96481	−	5.00625i	−0.121155	−	0.308698i	0.857411	−	0.514633i	$-0.172072\pi$
$263$	−1.96481	−	5.00625i	−0.121155	−	0.308698i	−0.978566	+	0.205935i	$0.933977\pi$
$264$	−1.24728	+	2.16036i	−0.0767650	+	0.132961i
$265$	−3.72756	−	6.45632i	−0.228982	−	0.396609i
$266$	9.15183	−	11.4760i	0.561134	−	0.703640i
$267$	−9.48269	−	6.46519i	−0.580331	−	0.395663i
$268$	0.351356	−	0.0529583i	0.0214625	−	0.00323494i
$269$	1.80282	−	0.868192i	0.109920	−	0.0529346i	−0.378116	−	0.925758i	$-0.623428\pi$
$269$	1.80282	−	0.868192i	0.109920	−	0.0529346i	0.488036	+	0.872824i	$0.337714\pi$
$270$	−2.74079	−	2.54308i	−0.166799	−	0.154767i
$271$	−28.0712	−	4.23106i	−1.70521	−	0.257019i	−0.777112	−	0.629363i	$-0.783316\pi$
$271$	−28.0712	−	4.23106i	−1.70521	−	0.257019i	−0.928095	+	0.372344i	$0.878554\pi$
$272$	−5.53259	+	1.70658i	−0.335463	+	0.103477i
$273$	−2.39898	−	32.0122i	−0.145193	−	1.93747i
$274$	−0.640022	−	0.802563i	−0.0386652	−	0.0484846i
$275$	−0.446363	+	1.13731i	−0.0269167	+	0.0685826i
$276$	−11.1796	+	10.3732i	−0.672933	+	0.624391i
$277$	−11.2815	+	7.69159i	−0.677840	+	0.462143i	−0.852666	−	0.522456i	$-0.825016\pi$
$277$	−11.2815	+	7.69159i	−0.677840	+	0.462143i	0.174827	+	0.984599i	$0.444063\pi$
$278$	−0.886665	+	11.8317i	−0.0531786	+	0.709620i
$279$	−1.34326	−	5.88520i	−0.0804188	−	0.352338i
$280$	−1.04305	−	4.56992i	−0.0623344	−	0.273105i
$281$	−0.862208	+	11.5054i	−0.0514350	+	0.686352i	0.910576	+	0.413342i	$0.135638\pi$
$281$	−0.862208	+	11.5054i	−0.0514350	+	0.686352i	−0.962011	+	0.273011i	$0.911981\pi$
$282$	18.6374	−	12.7068i	1.10984	−	0.756676i
$283$	−1.79883	+	1.66907i	−0.106930	+	0.0992162i	−0.731826	−	0.681491i	$-0.761332\pi$
$283$	−1.79883	+	1.66907i	−0.106930	+	0.0992162i	0.624896	+	0.780708i	$0.285141\pi$
$284$	3.50460	−	8.92958i	0.207960	−	0.529873i
$285$	3.98637	+	4.99874i	0.236132	+	0.296100i
$286$	0.306249	+	4.08661i	0.0181089	+	0.241646i
$287$	49.8518	−	15.3772i	2.94266	−	0.907690i
$288$	1.15575	+	0.174201i	0.0681031	+	0.0102649i
$289$	−12.1115	−	11.2378i	−0.712439	−	0.661047i
$290$	7.55303	−	3.63735i	0.443529	−	0.213593i
$291$	−23.3972	+	3.52657i	−1.37157	+	0.206731i
$292$	−1.07470	−	0.732719i	−0.0628921	−	0.0428791i
$293$	10.6991	−	13.4162i	0.625046	−	0.783783i	−0.363999	−	0.931399i	$-0.618589\pi$
$293$	10.6991	−	13.4162i	0.625046	−	0.783783i	0.989045	+	0.147617i	$0.0471602\pi$
$294$	15.2848	+	26.4740i	0.891427	+	1.54400i
$295$	3.84505	−	6.65981i	0.223867	−	0.387749i
$296$	−0.0292116	−	0.0744300i	−0.00169789	−	0.00432616i
$297$	−4.11567	−	1.98200i	−0.238815	−	0.115007i
$298$	−21.8976	−	6.75450i	−1.26849	−	0.391278i
$299$	−5.57502	+	24.4258i	−0.322412	+	1.41258i
$300$	2.04176			0.117881
$301$	0.124629	−	30.7374i	0.00718352	−	1.77167i
$302$	−12.4636			−0.717202
$303$	1.41176	−	6.18532i	0.0811035	−	0.355338i
$304$	2.99231	+	0.923004i	0.171620	+	0.0529379i
$305$	5.49724	+	2.64733i	0.314771	+	0.151586i
$306$	2.47232	+	6.29936i	0.141333	+	0.360111i
$307$	−4.58482	+	7.94114i	−0.261670	+	0.453225i	−0.966686	−	0.255966i	$-0.917606\pi$
$307$	−4.58482	+	7.94114i	−0.261670	+	0.453225i	0.705016	+	0.709191i	$0.250940\pi$
$308$	−2.86349	−	4.95971i	−0.163162	−	0.282606i
$309$	−21.1377	+	26.5059i	−1.20248	+	1.50787i
$310$	−4.26730	−	2.90940i	−0.242366	−	0.165243i
$311$	−10.6577	+	1.60638i	−0.604341	+	0.0910897i	−0.444083	−	0.895986i	$-0.646471\pi$
$311$	−10.6577	+	1.60638i	−0.604341	+	0.0910897i	−0.160258	+	0.987075i	$0.551232\pi$
$312$	6.17029	−	2.97145i	0.349324	−	0.168225i
$313$	−1.36279	−	1.26448i	−0.0770292	−	0.0714726i	0.640719	−	0.767776i	$-0.278636\pi$
$313$	−1.36279	−	1.26448i	−0.0770292	−	0.0714726i	−0.717748	+	0.696303i	$0.754827\pi$
$314$	−6.92932	−	1.04443i	−0.391044	−	0.0589404i
$315$	−5.23529	+	1.61487i	−0.294975	+	0.0909878i
$316$	−0.305476	−	4.07630i	−0.0171844	−	0.229310i
$317$	19.9558	+	25.0238i	1.12083	+	1.40548i	0.903081	+	0.429471i	$0.141300\pi$
$317$	19.9558	+	25.0238i	1.12083	+	1.40548i	0.217749	+	0.976005i	$0.430129\pi$
$318$	−5.56107	+	14.1694i	−0.311849	+	0.794579i
$319$	7.50820	−	6.96659i	0.420378	−	0.390054i
$320$	0.826239	−	0.563320i	0.0461882	−	0.0314905i
$321$	−0.450997	+	6.01814i	−0.0251722	+	0.335900i
$322$	−7.79100	−	34.1346i	−0.434175	−	1.90225i
$323$	4.03439	+	17.6758i	0.224479	+	0.983509i
$324$	−0.832516	+	11.1092i	−0.0462509	+	0.617175i
$325$	2.77138	−	1.88949i	0.153728	−	0.104810i
$326$	−10.1444	+	9.41258i	−0.561844	+	0.521315i
$327$	−2.91291	+	7.42197i	−0.161084	+	0.410436i
$328$	6.93921	+	8.70150i	0.383154	+	0.480460i
$329$	3.86995	+	51.6409i	0.213357	+	2.84706i
$330$	2.38374	−	0.735286i	0.131221	−	0.0404762i
$331$	6.25689	+	0.943075i	0.343910	+	0.0518361i	0.318726	−	0.947847i	$-0.396745\pi$
$331$	6.25689	+	0.943075i	0.343910	+	0.0518361i	0.0251835	+	0.999683i	$0.491983\pi$
$332$	−3.33110	−	3.09081i	−0.182818	−	0.169630i
$333$	−0.0841992	+	0.0405482i	−0.00461409	+	0.00222203i
$334$	16.0756	−	2.42301i	0.879620	−	0.132581i
$335$	−0.293583	−	0.200161i	−0.0160401	−	0.0109360i
$336$	−5.96721	+	7.48264i	−0.325538	+	0.408212i
$337$	−9.52340	−	16.4950i	−0.518773	−	0.898541i	−0.999762	−	0.0218145i	$-0.993056\pi$
$337$	−9.52340	−	16.4950i	−0.518773	−	0.898541i	0.480989	−	0.876727i	$-0.340278\pi$
$338$	−0.874648	+	1.51493i	−0.0475746	+	0.0824016i
$339$	6.24766	+	15.9188i	0.339326	+	0.864589i
$340$	5.21644	+	2.51211i	0.282901	+	0.136238i
$341$	−6.02977	−	1.85994i	−0.326530	−	0.100721i
$342$	0.814430	−	3.56825i	0.0440394	−	0.192949i
$343$	−37.3690			−2.01774
$344$	6.11381	−	2.37093i	0.329635	−	0.127832i
$345$	15.2508			0.821074
$346$	2.84733	−	12.4750i	0.153074	−	0.670659i
$347$	−9.99158	−	3.08199i	−0.536376	−	0.165450i	0.0147204	−	0.999892i	$-0.495314\pi$
$347$	−9.99158	−	3.08199i	−0.536376	−	0.165450i	−0.551096	+	0.834442i	$0.685790\pi$
$348$	−15.4215	−	7.42661i	−0.826680	−	0.398108i
$349$	5.36326	+	13.6654i	0.287089	+	0.731490i	0.999556	+	0.0297852i	$0.00948233\pi$
$349$	5.36326	+	13.6654i	0.287089	+	0.731490i	−0.712468	+	0.701705i	$0.752422\pi$
$350$	−2.34372	+	4.05945i	−0.125277	+	0.216987i
$351$	6.27048	+	10.8608i	0.334693	+	0.579706i
$352$	0.761761	−	0.955218i	0.0406020	−	0.0509133i
$353$	5.85103	+	3.98916i	0.311419	+	0.212322i	0.708936	−	0.705273i	$-0.249176\pi$
$353$	5.85103	+	3.98916i	0.311419	+	0.212322i	−0.397517	+	0.917595i	$0.630128\pi$
$354$	−15.5260	+	2.34017i	−0.825197	+	0.124378i
$355$	−8.64271	+	4.16211i	−0.458707	+	0.220902i
$356$	4.12055	+	3.82331i	0.218389	+	0.202635i
$357$	−54.7935	−	8.25878i	−2.89998	−	0.437101i
$358$	−0.0605242	+	0.0186692i	−0.00319880	+	0.000986700i
$359$	−2.04337	−	27.2669i	−0.107845	−	1.43909i	−0.744335	−	0.667807i	$-0.767233\pi$
$359$	−2.04337	−	27.2669i	−0.107845	−	1.43909i	0.636490	−	0.771285i	$-0.280386\pi$
$360$	−0.728736	−	0.913806i	−0.0384078	−	0.0481618i
$361$	−3.35901	+	8.55861i	−0.176790	+	0.450453i
$362$	3.94075	−	3.65648i	0.207121	−	0.192180i
$363$	−16.0386	+	10.9350i	−0.841810	+	0.573936i
$364$	−1.17496	+	15.6787i	−0.0615844	+	0.821787i
$365$	0.289436	+	1.26810i	0.0151498	+	0.0663755i
$366$	−2.77211	−	12.1454i	−0.144901	−	0.634852i
$367$	−0.896409	+	11.9617i	−0.0467922	+	0.624398i	0.923677	+	0.383172i	$0.125168\pi$
$367$	−0.896409	+	11.9617i	−0.0467922	+	0.624398i	−0.970469	+	0.241226i	$0.922451\pi$
$368$	6.17151	−	4.20767i	0.321712	−	0.219340i
$369$	9.53579	−	8.84792i	0.496413	−	0.460604i
$370$	−0.0292116	+	0.0744300i	−0.00151864	+	0.00386943i
$371$	−21.7881	−	27.3215i	−1.13118	−	1.41846i
$372$	0.788041	+	10.5157i	0.0408580	+	0.545212i
$373$	18.0436	−	5.56573i	0.934265	−	0.288182i	0.209997	−	0.977702i	$-0.432654\pi$
$373$	18.0436	−	5.56573i	0.934265	−	0.288182i	0.724267	+	0.689519i	$0.242178\pi$
$374$	6.99481	+	1.05430i	0.361693	+	0.0545165i
$375$	−1.49672	−	1.38875i	−0.0772902	−	0.0717149i
$376$	−9.95368	+	4.79344i	−0.513322	+	0.247203i
$377$	−27.8050	+	4.19094i	−1.43203	+	0.215844i
$378$	−14.4805	−	9.87262i	−0.744795	−	0.507793i
$379$	5.61477	−	7.04070i	0.288412	−	0.361657i	−0.616427	−	0.787412i	$-0.711420\pi$
$379$	5.61477	−	7.04070i	0.288412	−	0.361657i	0.904838	+	0.425756i	$0.139992\pi$
$380$	−1.56571	−	2.71189i	−0.0803194	−	0.139117i
$381$	4.28511	−	7.42203i	0.219533	−	0.380242i
$382$	−8.90397	−	22.6870i	−0.455567	−	1.16077i
$383$	−11.5519	−	5.56310i	−0.590275	−	0.284261i	0.114806	−	0.993388i	$-0.463375\pi$
$383$	−11.5519	−	5.56310i	−0.590275	−	0.284261i	−0.705081	+	0.709127i	$0.749089\pi$
$384$	−1.95105	−	0.601821i	−0.0995643	−	0.0307115i
$385$	−1.27437	+	5.58339i	−0.0649481	+	0.284556i
$386$	3.87509			0.197237
$387$	−3.29741	−	6.91877i	−0.167617	−	0.351701i
$388$	11.5888			0.588330
$389$	−4.85346	+	21.2644i	−0.246080	+	1.07815i	0.689293	+	0.724483i	$0.257921\pi$
$389$	−4.85346	+	21.2644i	−0.246080	+	1.07815i	−0.935373	+	0.353664i	$0.884936\pi$
$390$	−6.54424	−	2.01863i	−0.331381	−	0.102217i
$391$	38.9637	+	18.7639i	1.97048	+	0.948934i
$392$	−5.46994	−	13.9372i	−0.276274	−	0.703934i
$393$	−22.5350	+	39.0318i	−1.13674	+	1.96889i
$394$	2.42618	+	4.20227i	0.122229	+	0.211707i
$395$	−2.54866	+	3.19592i	−0.128237	+	0.160804i
$396$	−1.17987	−	0.804425i	−0.0592909	−	0.0404239i
$397$	27.0401	−	4.07564i	1.35710	−	0.204550i	0.570138	−	0.821549i	$-0.306890\pi$
$397$	27.0401	−	4.07564i	1.35710	−	0.204550i	0.786964	+	0.616998i	$0.211651\pi$
$398$	6.82788	−	3.28813i	0.342251	−	0.164819i
$399$	21.9694	+	20.3846i	1.09985	+	1.02051i
$400$	−0.988831	−	0.149042i	−0.0494415	−	0.00745211i
$401$	−16.6099	+	5.12348i	−0.829460	+	0.255855i	−0.680277	−	0.732955i	$-0.738141\pi$
$401$	−16.6099	+	5.12348i	−0.829460	+	0.255855i	−0.149183	+	0.988810i	$0.547664\pi$
$402$	0.0542158	+	0.723460i	0.00270404	+	0.0360829i
$403$	10.8011	+	13.5441i	0.538040	+	0.674680i
$404$	−1.13523	+	2.89251i	−0.0564797	+	0.143908i
$405$	8.16642	−	7.57733i	0.405793	−	0.376521i
$406$	32.4678	−	22.1362i	1.61135	−	1.09860i
$407$	−0.00730033	+	0.0974161i	−0.000361864	+	0.00482874i
$408$	−2.63052	−	11.5251i	−0.130230	−	0.570575i
$409$	1.07682	+	4.71786i	0.0532454	+	0.233283i	0.994548	−	0.104281i	$-0.0332541\pi$
$409$	1.07682	+	4.71786i	0.0532454	+	0.233283i	−0.941302	+	0.337564i	$0.890397\pi$
$410$	0.831719	−	11.0985i	0.0410757	−	0.548117i
$411$	1.73172	−	1.18066i	0.0854193	−	0.0582379i
$412$	12.1719	−	11.2939i	0.599666	−	0.556409i
$413$	13.1694	−	33.5551i	0.648024	−	1.65114i
$414$	−5.44323	−	6.82559i	−0.267520	−	0.335459i
$415$	0.339585	+	4.53144i	0.0166696	+	0.222440i
$416$	−3.20519	+	0.988670i	−0.157147	+	0.0484735i
$417$	−23.9548	−	3.61060i	−1.17307	−	0.176812i
$418$	−2.80457	−	2.60226i	−0.137176	−	0.127281i
$419$	−7.02649	+	3.38378i	−0.343267	+	0.165308i	−0.597572	−	0.801816i	$-0.703868\pi$
$419$	−7.02649	+	3.38378i	−0.343267	+	0.165308i	0.254305	+	0.967124i	$0.418153\pi$
$420$	9.46376	−	1.42643i	0.461784	−	0.0696028i
$421$	26.1867	+	17.8538i	1.27626	+	0.870139i	0.995962	−	0.0897741i	$-0.0286145\pi$
$421$	26.1867	+	17.8538i	1.27626	+	0.870139i	0.280297	+	0.959913i	$0.409567\pi$
$422$	−10.5490	+	13.2280i	−0.513516	+	0.643928i
$423$	6.45632	+	11.1827i	0.313917	+	0.543720i
$424$	3.72756	−	6.45632i	0.181026	−	0.313547i
$425$	−2.11526	−	5.38959i	−0.102605	−	0.261433i
$426$	17.6464	+	8.49805i	0.854970	+	0.411732i
$427$	27.3297	+	8.43009i	1.32258	+	0.407961i
$428$	0.657724	−	2.88168i	0.0317923	−	0.139291i
$429$	−8.36729			−0.403977
$430$	−6.09438	−	2.42043i	−0.293897	−	0.116724i
$431$	−33.3793			−1.60782			−0.803912	−	0.594748i	$-0.797252\pi$
$431$	−33.3793			−1.60782			−0.803912	+	0.594748i	$0.797252\pi$
$432$	0.831978	−	3.64513i	0.0400286	−	0.175377i
$433$	21.4623	+	6.62023i	1.03141	+	0.318148i	0.763851	−	0.645393i	$-0.223306\pi$
$433$	21.4623	+	6.62023i	1.03141	+	0.318148i	0.267560	+	0.963541i	$0.413783\pi$
$434$	−21.8119	−	10.5041i	−1.04701	−	0.504211i
$435$	6.25339	+	15.9334i	0.299827	+	0.763947i
$436$	1.95251	−	3.38184i	0.0935081	−	0.161961i
$437$	−11.6949	−	20.2562i	−0.559445	−	0.968987i
$438$	1.65583	−	2.07635i	0.0791188	−	0.0992119i
$439$	−2.79293	−	1.90419i	−0.133299	−	0.0908818i	0.494835	−	0.868987i	$-0.335229\pi$
$439$	−2.79293	−	1.90419i	−0.133299	−	0.0908818i	−0.628134	+	0.778105i	$0.716181\pi$
$440$	−1.20812	+	0.182095i	−0.0575950	+	0.00868106i
$441$	−15.7665	+	7.59274i	−0.750785	+	0.361559i
$442$	−14.2360	−	13.2091i	−0.677140	−	0.628294i
$443$	−15.0980	−	2.27566i	−0.717330	−	0.108120i	−0.219772	−	0.975551i	$-0.570531\pi$
$443$	−15.0980	−	2.27566i	−0.717330	−	0.108120i	−0.497557	+	0.867431i	$0.665770\pi$
$444$	0.156001	−	0.0481199i	0.00740347	−	0.00228367i
$445$	−0.420064	−	5.60537i	−0.0199130	−	0.265720i
$446$	−7.65067	−	9.59364i	−0.362270	−	0.454272i
$447$	17.0937	−	43.5540i	0.808504	−	2.06003i
$448$	3.43614	−	3.18827i	0.162342	−	0.150632i
$449$	1.58464	−	1.08039i	0.0747837	−	0.0509867i	−0.525351	−	0.850886i	$-0.676066\pi$
$449$	1.58464	−	1.08039i	0.0747837	−	0.0509867i	0.600135	+	0.799899i	$0.295114\pi$
$450$	−0.0873447	+	1.16553i	−0.00411747	+	0.0549438i
$451$	−3.02581	−	13.2569i	−0.142480	−	0.624244i
$452$	−1.86374	−	8.16556i	−0.0876627	−	0.384076i
$453$	1.90172	−	25.3767i	0.0893505	−	1.19230i
$454$	5.67577	−	3.86967i	0.266377	−	0.181613i
$455$	11.5255	−	10.6941i	0.540325	−	0.501348i
$456$	−2.33586	+	5.95167i	−0.109387	+	0.278712i
$457$	−18.8395	−	23.6239i	−0.881273	−	1.10508i	−0.993772	−	0.111430i	$-0.964457\pi$
$457$	−18.8395	−	23.6239i	−0.881273	−	1.10508i	0.112499	−	0.993652i	$-0.464114\pi$
$458$	−1.10420	−	14.7346i	−0.0515960	−	0.688501i
$459$	20.6857	−	6.38068i	0.965524	−	0.297825i
$460$	−7.38598	−	1.11326i	−0.344373	−	0.0519059i
$461$	−10.0863	−	9.35871i	−0.469765	−	0.435878i	0.409429	−	0.912342i	$-0.365728\pi$
$461$	−10.0863	−	9.35871i	−0.469765	−	0.435878i	−0.879194	+	0.476464i	$0.841918\pi$
$462$	10.5352	−	5.07347i	0.490140	−	0.236039i
$463$	−37.6809	+	5.67948i	−1.75118	+	0.263948i	−0.944846	−	0.327514i	$-0.893789\pi$
$463$	−37.6809	+	5.67948i	−1.75118	+	0.263948i	−0.806333	+	0.591462i	$0.798551\pi$
$464$	6.92655	+	4.72244i	0.321557	+	0.219234i
$465$	6.57480	−	8.24454i	0.304899	−	0.382331i
$466$	−11.2880	−	19.5513i	−0.522905	−	0.905698i
$467$	11.9898	−	20.7669i	0.554821	−	0.960977i	−0.443097	−	0.896474i	$-0.646120\pi$
$467$	11.9898	−	20.7669i	0.554821	−	0.960977i	0.997917	−	0.0645036i	$-0.0205464\pi$
$468$	1.43228	+	3.64940i	0.0662074	+	0.168694i
$469$	−1.50062	−	0.722661i	−0.0692922	−	0.0333694i
$470$	10.5569	+	3.25638i	0.486955	+	0.150206i
$471$	3.18379	−	13.9491i	0.146701	−	0.642741i
$472$	7.69009			0.353965
$473$	−7.98679	−	0.631102i	−0.367233	−	0.0290181i
$474$	8.34618			0.383353
$475$	−0.696808	+	3.05291i	−0.0319717	+	0.140077i
$476$	25.9337	+	7.99949i	1.18867	+	0.366656i
$477$	−7.85064	−	3.78067i	−0.359456	−	0.173105i
$478$	2.04349	+	5.20673i	0.0934670	+	0.238150i
$479$	−6.76923	+	11.7246i	−0.309294	+	0.535713i	−0.978208	−	0.207627i	$-0.933426\pi$
$479$	−6.76923	+	11.7246i	−0.309294	+	0.535713i	0.668914	+	0.743340i	$0.266759\pi$
$480$	1.02088	+	1.76822i	0.0465967	+	0.0807078i
$481$	0.167215	−	0.209682i	0.00762437	−	0.00956066i
$482$	7.02979	+	4.79283i	0.320198	+	0.218307i
$483$	70.6887	−	10.6546i	3.21645	−	0.484801i
$484$	8.56576	−	4.12505i	0.389353	−	0.187502i
$485$	−8.49516	−	7.88236i	−0.385746	−	0.357920i
$486$	−11.4005	−	1.71835i	−0.517137	−	0.0779458i
$487$	−23.9589	+	7.39035i	−1.08568	+	0.334889i	−0.785417	−	0.618967i	$-0.787551\pi$
$487$	−23.9589	+	7.39035i	−1.08568	+	0.334889i	−0.300265	+	0.953856i	$0.597075\pi$
$488$	0.455964	+	6.08441i	0.0206405	+	0.275428i
$489$	−17.6167	−	22.0906i	−0.796655	−	0.998973i
$490$	−5.46994	+	13.9372i	−0.247107	+	0.629617i
$491$	−19.5814	+	18.1689i	−0.883695	+	0.819949i	−0.984577	−	0.174949i	$-0.944024\pi$
$491$	−19.5814	+	18.1689i	−0.883695	+	0.819949i	0.100882	+	0.994898i	$0.467833\pi$
$492$	−18.7755	+	12.8009i	−0.846466	+	0.577111i
$493$	−3.62720	+	48.4017i	−0.163361	+	2.17990i
$494$	2.33724	+	10.2401i	0.105157	+	0.460724i
$495$	0.317762	+	1.39220i	0.0142823	+	0.0625749i
$496$	0.385961	−	5.15029i	0.0173301	−	0.231255i
$497$	−37.1520	+	25.3298i	−1.66649	+	1.13620i
$498$	6.80132	−	6.31070i	0.304774	−	0.282789i
$499$	−7.61167	+	19.3942i	−0.340745	+	0.868204i	0.653084	+	0.757285i	$0.273475\pi$
$499$	−7.61167	+	19.3942i	−0.340745	+	0.868204i	−0.993829	+	0.110919i	$0.964621\pi$
$500$	0.623490	+	0.781831i	0.0278833	+	0.0349646i
$501$	2.48055	+	33.1006i	0.110823	+	1.47883i
$502$	13.6722	−	4.21732i	0.610221	−	0.188228i
$503$	−10.6854	−	1.61056i	−0.476437	−	0.0718113i	−0.0935657	−	0.995613i	$-0.529827\pi$
$503$	−10.6854	−	1.61056i	−0.476437	−	0.0718113i	−0.382871	+	0.923802i	$0.625065\pi$
$504$	−4.01617	−	3.72646i	−0.178894	−	0.165990i
$505$	2.79959	−	1.34821i	0.124580	−	0.0599946i
$506$	−9.02397	+	1.36014i	−0.401164	+	0.0604658i
$507$	−2.95104	−	2.01198i	−0.131060	−	0.0893553i
$508$	−2.61707	+	3.28171i	−0.116114	+	0.145602i
$509$	−9.83777	−	17.0395i	−0.436051	−	0.755263i	0.561329	−	0.827592i	$-0.310290\pi$
$509$	−9.83777	−	17.0395i	−0.436051	−	0.755263i	−0.997381	+	0.0723294i	$0.976957\pi$
$510$	−5.91072	+	10.2377i	−0.261731	+	0.453332i
$511$	2.22749	+	5.67556i	0.0985386	+	0.251072i
$512$	0.900969	+	0.433884i	0.0398176	+	0.0191751i
$513$	−11.1879	−	3.45100i	−0.493956	−	0.152365i
$514$	0.710118	−	3.11123i	0.0313220	−	0.137230i
$515$	−16.6044			−0.731678
$516$	3.89449	+	12.8098i	0.171446	+	0.563921i
$517$	13.4978			0.593633
$518$	−0.0833997	+	0.365398i	−0.00366437	+	0.0160547i
$519$	24.9653	+	7.70077i	1.09586	+	0.338027i
$520$	3.02204	+	1.45534i	0.132525	+	0.0638207i
$521$	13.0263	+	33.1905i	0.570694	+	1.45410i	0.866657	+	0.498905i	$0.166264\pi$
$521$	13.0263	+	33.1905i	0.570694	+	1.45410i	−0.295963	+	0.955199i	$0.595640\pi$
$522$	4.89917	−	8.48561i	0.214431	−	0.371405i
$523$	16.6354	+	28.8133i	0.727414	+	1.25992i	0.957973	+	0.286859i	$0.0926112\pi$
$523$	16.6354	+	28.8133i	0.727414	+	1.25992i	−0.230559	+	0.973058i	$0.574055\pi$
$524$	13.7630	−	17.2582i	0.601238	−	0.753928i
$525$	−7.90765	−	5.39134i	−0.345118	−	0.235298i
$526$	−5.31794	+	0.801551i	−0.231873	+	0.0349493i
$527$	26.9415	−	12.9744i	1.17359	−	0.565172i
$528$	1.82865	+	1.69674i	0.0795816	+	0.0738410i
$529$	−32.4258	−	4.88740i	−1.40982	−	0.212495i
$530$	−7.12391	+	2.19743i	−0.309443	+	0.0954504i
$531$	−0.671689	−	8.96306i	−0.0291488	−	0.388964i
$532$	−9.15183	−	11.4760i	−0.396782	−	0.497549i
$533$	−13.6386	+	34.7505i	−0.590753	+	1.50521i
$534$	−8.41319	+	7.80630i	−0.364074	+	0.337812i
$535$	−2.44218	+	1.66505i	−0.105585	+	0.0719865i
$536$	0.0265534	−	0.354331i	0.00114693	−	0.0153048i
$537$	−0.0287768	−	0.126079i	−0.00124181	−	0.00544072i
$538$	−0.445260	−	1.95081i	−0.0191965	−	0.0841054i
$539$	−1.36700	+	18.2414i	−0.0588809	+	0.785711i
$540$	−3.08920	+	2.10618i	−0.132938	+	0.0906357i
$541$	7.80451	−	7.24153i	0.335542	−	0.311338i	−0.494348	−	0.869264i	$-0.664593\pi$
$541$	7.80451	−	7.24153i	0.335542	−	0.311338i	0.829890	+	0.557926i	$0.188403\pi$
$542$	−10.3714	+	26.4259i	−0.445490	+	1.13509i
$543$	6.84351	+	8.58149i	0.293683	+	0.368267i
$544$	0.432674	+	5.77363i	0.0185507	+	0.247542i
$545$	−3.73153	+	1.15102i	−0.159841	+	0.0493044i
$546$	−31.7434	−	4.78455i	−1.35849	−	0.204760i
$547$	−5.38580	−	4.99730i	−0.230280	−	0.213669i	0.556590	−	0.830787i	$-0.312109\pi$
$547$	−5.38580	−	4.99730i	−0.230280	−	0.213669i	−0.786870	+	0.617118i	$0.788300\pi$
$548$	−0.924859	+	0.445389i	−0.0395080	+	0.0190261i
$549$	7.05176	−	1.06288i	0.300962	−	0.0453627i
$550$	1.00947	+	0.688248i	0.0430441	+	0.0293470i
$551$	16.3675	−	20.5242i	0.697280	−	0.874362i
$552$	7.62538	+	13.2076i	0.324558	+	0.562151i
$553$	−9.58050	+	16.5939i	−0.407404	+	0.705645i
$554$	4.98838	+	12.7102i	0.211936	+	0.540004i
$555$	−0.147086	−	0.0708331i	−0.00624347	−	0.00300670i
$556$	11.3378	+	3.49724i	0.480829	+	0.148316i
$557$	9.20901	−	40.3473i	0.390198	−	1.70957i	−0.273758	−	0.961799i	$-0.588267\pi$
$557$	9.20901	−	40.3473i	0.390198	−	1.70957i	0.663956	−	0.747771i	$-0.268876\pi$
$558$	−6.03655			−0.255547
$559$	17.1406	+	13.7833i	0.724972	+	0.582970i
$560$	−4.68745			−0.198081
$561$	−3.21389	+	14.0810i	−0.135690	+	0.594499i
$562$	11.0250	+	3.40077i	0.465063	+	0.143453i
$563$	−35.6434	−	17.1650i	−1.50219	−	0.723417i	−0.511466	−	0.859304i	$-0.670897\pi$
$563$	−35.6434	−	17.1650i	−1.50219	−	0.723417i	−0.990724	+	0.135887i	$0.956612\pi$
$564$	−8.24096	−	20.9976i	−0.347007	−	0.884160i
$565$	−4.18777	+	7.25344i	−0.176181	+	0.305154i
$566$	1.22695	+	2.12514i	0.0515725	+	0.0893262i
$567$	32.5584	−	40.8269i	1.36732	−	1.71457i
$568$	−7.92585	−	5.40375i	−0.332561	−	0.226736i
$569$	12.7356	−	1.91959i	0.533905	−	0.0804733i	0.123444	−	0.992351i	$-0.460606\pi$
$569$	12.7356	−	1.91959i	0.533905	−	0.0804733i	0.410461	+	0.911878i	$0.365368\pi$
$570$	5.76047	−	2.77409i	0.241279	−	0.116194i
$571$	−20.5432	−	19.0613i	−0.859708	−	0.797692i	0.121106	−	0.992640i	$-0.461356\pi$
$571$	−20.5432	−	19.0613i	−0.859708	−	0.797692i	−0.980814	+	0.194947i	$0.937546\pi$
$572$	4.05230	+	0.610786i	0.169435	+	0.0255382i
$573$	47.5505	−	14.6674i	1.98645	−	0.612739i
$574$	−3.89864	−	52.0237i	−0.162726	−	2.17143i
$575$	4.65710	+	5.83982i	0.194214	+	0.243537i
$576$	0.427011	−	1.08801i	0.0177921	−	0.0453336i
$577$	−30.3479	+	28.1587i	−1.26340	+	1.17226i	−0.286613	+	0.958047i	$0.592529\pi$
$577$	−30.3479	+	28.1587i	−1.26340	+	1.17226i	−0.976786	+	0.214216i	$0.931280\pi$
$578$	−13.6511	+	9.30716i	−0.567811	+	0.387127i
$579$	−0.591267	+	7.88990i	−0.0245722	+	0.327893i
$580$	−1.86545	−	8.17305i	−0.0774584	−	0.339367i
$581$	4.73980	+	20.7664i	0.196640	+	0.861536i
$582$	−1.76823	+	23.5954i	−0.0732954	+	0.978059i
$583$	−7.52574	+	5.13097i	−0.311684	+	0.212503i
$584$	−0.953491	+	0.884711i	−0.0394557	+	0.0366096i
$585$	1.43228	−	3.64940i	0.0592177	−	0.150884i
$586$	−10.6991	−	13.4162i	−0.441974	−	0.554218i
$587$	2.55073	+	34.0371i	0.105280	+	1.40486i	0.760458	+	0.649387i	$0.224975\pi$
$587$	2.55073	+	34.0371i	0.105280	+	1.40486i	−0.655178	+	0.755475i	$0.727406\pi$
$588$	29.2115	−	9.01055i	1.20466	−	0.371589i
$589$	−15.9923	−	2.41046i	−0.658952	−	0.0993211i
$590$	−5.63723	−	5.23059i	−0.232081	−	0.215340i
$591$	−8.92624	+	4.29865i	−0.367176	+	0.176823i
$592$	−0.0790641	+	0.0119170i	−0.00324951	+	0.000489785i
$593$	−11.6433	−	7.93829i	−0.478134	−	0.325987i	0.300157	−	0.953890i	$-0.402961\pi$
$593$	−11.6433	−	7.93829i	−0.478134	−	0.325987i	−0.778291	+	0.627903i	$0.783913\pi$
$594$	−2.84813	+	3.57144i	−0.116860	+	0.146538i
$595$	−13.5697	−	23.5035i	−0.556304	−	0.963548i
$596$	−11.4578	+	19.8455i	−0.469330	+	0.812904i
$597$	5.65302	+	14.4037i	0.231363	+	0.589502i
$598$	22.5728	+	10.8705i	0.923071	+	0.444528i
$599$	16.2276	+	5.00555i	0.663042	+	0.204521i	0.607969	−	0.793961i	$-0.291985\pi$
$599$	16.2276	+	5.00555i	0.663042	+	0.204521i	0.0550731	+	0.998482i	$0.482461\pi$
$600$	0.454335	−	1.99057i	0.0185482	−	0.0812648i
$601$	27.6549			1.12807			0.564033	−	0.825752i	$-0.309249\pi$
$601$	27.6549			1.12807			0.564033	+	0.825752i	$0.309249\pi$
$602$	−29.9390	−	6.96122i	−1.22022	−	0.283718i
$603$	−0.415304			−0.0169125
$604$	−2.77342	+	12.1511i	−0.112849	+	0.494423i
$605$	−9.08490	−	2.80232i	−0.369354	−	0.113930i
$606$	−5.71610	−	2.75273i	−0.232201	−	0.111822i
$607$	9.43921	+	24.0507i	0.383126	+	0.976189i	0.984210	+	0.177003i	$0.0566403\pi$
$607$	9.43921	+	24.0507i	0.383126	+	0.976189i	−0.601084	+	0.799186i	$0.705264\pi$
$608$	1.56571	−	2.71189i	0.0634980	−	0.109982i
$609$	40.1165	+	69.4839i	1.62560	+	2.81563i
$610$	3.80421	−	4.77032i	0.154028	−	0.193145i
$611$	−30.6175	−	20.8746i	−1.23865	−	0.844497i
$612$	6.69157	−	1.00859i	0.270491	−	0.0407699i
$613$	29.4670	−	14.1906i	1.19016	−	0.573152i	0.269306	−	0.963055i	$-0.413206\pi$
$613$	29.4670	−	14.1906i	1.19016	−	0.573152i	0.920856	+	0.389903i	$0.127491\pi$
$614$	6.72182	+	6.23694i	0.271271	+	0.251703i
$615$	22.4703	+	3.38685i	0.906089	+	0.136571i
$616$	−5.47255	+	1.68806i	−0.220495	+	0.0680138i
$617$	0.809464	+	10.8015i	0.0325878	+	0.434854i	0.989506	+	0.144495i	$0.0461557\pi$
$617$	0.809464	+	10.8015i	0.0325878	+	0.434854i	−0.956918	+	0.290359i	$0.906225\pi$
$618$	21.1377	+	26.5059i	0.850284	+	1.06622i
$619$	10.4114	−	26.5278i	0.418469	−	1.06624i	−0.553857	−	0.832612i	$-0.686845\pi$
$619$	10.4114	−	26.5278i	0.418469	−	1.06624i	0.972326	−	0.233629i	$-0.0750603\pi$
$620$	−3.78601	+	3.51291i	−0.152050	+	0.141082i
$621$	−23.0745	+	15.7319i	−0.925948	+	0.631301i
$622$	−0.805445	+	10.7479i	−0.0322954	+	0.430952i
$623$	−5.86310	−	25.6879i	−0.234900	−	1.02916i
$624$	−1.52393	−	6.67679i	−0.0610062	−	0.267286i
$625$	0.0747301	−	0.997204i	0.00298920	−	0.0398882i
$626$	−1.53602	+	1.04724i	−0.0613919	+	0.0418563i
$627$	5.72627	−	5.31320i	0.228685	−	0.212189i
$628$	−2.56016	+	6.52318i	−0.102161	+	0.260303i
$629$	−0.288637	−	0.361939i	−0.0115087	−	0.0144314i
$630$	0.409423	+	5.46338i	0.0163118	+	0.217666i
$631$	4.67607	−	1.44238i	0.186152	−	0.0574202i	−0.200278	−	0.979739i	$-0.564184\pi$
$631$	4.67607	−	1.44238i	0.186152	−	0.0574202i	0.386429	+	0.922319i	$0.373708\pi$
$632$	−4.04207	−	0.609244i	−0.160785	−	0.0242344i
$633$	−25.3233	−	23.4966i	−1.00651	−	0.933907i
$634$	28.8370	−	13.8872i	1.14526	−	0.551529i
$635$	4.15058	−	0.625599i	0.164711	−	0.0248261i
$636$	12.5767	+	8.57463i	0.498697	+	0.340006i
$637$	31.3115	−	39.2633i	1.24061	−	1.55567i
$638$	−5.12119	−	8.87017i	−0.202750	−	0.351173i
$639$	−5.60597	+	9.70983i	−0.221769	+	0.384115i
$640$	−0.365341	−	0.930874i	−0.0144414	−	0.0367960i
$641$	4.03023	+	1.94086i	0.159185	+	0.0766593i	0.511780	−	0.859117i	$-0.328986\pi$
$641$	4.03023	+	1.94086i	0.159185	+	0.0766593i	−0.352595	+	0.935776i	$0.614701\pi$
$642$	5.76690	+	1.77885i	0.227601	+	0.0702057i
$643$	−6.02436	+	26.3944i	−0.237578	+	1.04090i	0.705601	+	0.708609i	$0.250677\pi$
$643$	−6.02436	+	26.3944i	−0.237578	+	1.04090i	−0.943179	+	0.332286i	$0.892180\pi$
$644$	−35.0124			−1.37968
$645$	5.85802	−	12.0392i	0.230659	−	0.474043i
$646$	18.1304			0.713330
$647$	2.95954	−	12.9666i	0.116352	−	0.509770i	−0.882844	−	0.469667i	$-0.844374\pi$
$647$	2.95954	−	12.9666i	0.116352	−	0.509770i	0.999196	−	0.0401034i	$-0.0127687\pi$
$648$	10.6454	+	3.28366i	0.418190	+	0.128994i
$649$	−8.46507	−	4.07656i	−0.332283	−	0.160019i
$650$	−1.22543	−	3.12234i	−0.0480653	−	0.122468i
$651$	24.7149	−	42.8075i	0.968655	−	1.67776i
$652$	6.91926	+	11.9845i	0.270979	+	0.469350i
$653$	16.0434	−	20.1178i	0.627826	−	0.787269i	−0.361596	−	0.932335i	$-0.617768\pi$
$653$	16.0434	−	20.1178i	0.627826	−	0.787269i	0.989422	+	0.145066i	$0.0463394\pi$
$654$	6.58770	+	4.49142i	0.257599	+	0.175628i
$655$	−21.8275	+	3.28997i	−0.852872	+	0.128550i
$656$	10.0275	−	4.82897i	0.391506	−	0.188540i
$657$	1.11444	+	1.03405i	0.0434785	+	0.0403422i
$658$	51.2073	+	7.71826i	1.99627	+	0.300889i
$659$	38.7847	−	11.9635i	1.51084	−	0.466032i	0.574908	−	0.818218i	$-0.305038\pi$
$659$	38.7847	−	11.9635i	1.51084	−	0.466032i	0.935930	+	0.352186i	$0.114562\pi$
$660$	−0.186419	−	2.48759i	−0.00725636	−	0.0968294i
$661$	11.8019	+	14.7991i	0.459041	+	0.575619i	0.956450	−	0.291897i	$-0.0942866\pi$
$661$	11.8019	+	14.7991i	0.459041	+	0.575619i	−0.497409	+	0.867516i	$0.665715\pi$
$662$	2.31172	−	5.89017i	0.0898475	−	0.228928i
$663$	29.0667	−	26.9699i	1.12886	−	1.04742i
$664$	−3.75455	+	2.55981i	−0.145705	+	0.0993399i
$665$	−1.09692	+	14.6373i	−0.0425366	+	0.567612i
$666$	0.0207955	+	0.0911110i	0.000805809	+	0.00353048i
$667$	−13.9338	−	61.0478i	−0.539518	−	2.36378i
$668$	1.21490	−	16.2118i	0.0470060	−	0.627252i
$669$	20.7005	−	14.1134i	0.800329	−	0.545655i
$670$	−0.260471	+	0.241682i	−0.0100629	+	0.00933698i
$671$	2.72347	−	6.93929i	0.105138	−	0.267888i
$672$	5.96721	+	7.48264i	0.230190	+	0.288649i
$673$	0.256567	+	3.42364i	0.00988992	+	0.131972i	0.999963	−	0.00858042i	$-0.00273127\pi$
$673$	0.256567	+	3.42364i	0.00988992	+	0.131972i	−0.990073	+	0.140552i	$0.955112\pi$
$674$	−18.2006	+	5.61415i	−0.701061	+	0.216249i
$675$	3.69711	+	0.557250i	0.142302	+	0.0214486i
$676$	1.28232	+	1.18982i	0.0493202	+	0.0457624i
$677$	13.6636	−	6.58004i	0.525134	−	0.252891i	−0.152483	−	0.988306i	$-0.548727\pi$
$677$	13.6636	−	6.58004i	0.525134	−	0.252891i	0.677617	+	0.735415i	$0.263013\pi$
$678$	16.9099	−	2.54876i	0.649421	−	0.0978844i
$679$	−44.8827	−	30.6005i	−1.72244	−	1.17434i
$680$	3.60989	−	4.52666i	0.138433	−	0.173590i
$681$	7.01285	+	12.1466i	0.268733	+	0.465459i
$682$	−3.15506	+	5.46472i	−0.120813	+	0.209255i
$683$	9.27813	+	23.6403i	0.355018	+	0.904571i	0.991121	+	0.132966i	$0.0424503\pi$
$683$	9.27813	+	23.6403i	0.355018	+	0.904571i	−0.636103	+	0.771604i	$0.719454\pi$
$684$	−3.29756	−	1.58802i	−0.126085	−	0.0607195i
$685$	0.980911	+	0.302571i	0.0374787	+	0.0115606i
$686$	−8.31538	+	36.4321i	−0.317483	+	1.39098i
$687$	30.1689			1.15101
$688$	−0.951037	−	6.48811i	−0.0362579	−	0.247357i
$689$	25.0060			0.952653
$690$	3.39361	−	14.8684i	0.129193	−	0.566030i
$691$	28.8096	+	8.88659i	1.09597	+	0.338062i	0.789458	−	0.613805i	$-0.210362\pi$
$691$	28.8096	+	8.88659i	1.09597	+	0.338062i	0.306512	+	0.951867i	$0.400838\pi$
$692$	−11.5286	−	5.55189i	−0.438252	−	0.211051i
$693$	2.44549	+	6.23100i	0.0928963	+	0.236696i
$694$	−5.22806	+	9.05526i	−0.198454	+	0.343733i
$695$	−5.93245	−	10.2753i	−0.225031	−	0.389765i
$696$	−10.6720	+	13.3823i	−0.404522	+	0.507254i
$697$	53.2416	+	36.2995i	2.01667	+	1.37494i
$698$	14.5162	−	2.18796i	0.549446	−	0.0828156i
$699$	41.5299	−	19.9998i	1.57081	−	0.756461i
$700$	3.43614	+	3.18827i	0.129874	+	0.120505i
$701$	0.0821206	+	0.0123777i	0.00310165	+	0.000467499i	0.150593	−	0.988596i	$-0.451882\pi$
$701$	0.0821206	+	0.0123777i	0.00310165	+	0.000467499i	−0.147491	+	0.989063i	$0.547120\pi$
$702$	11.9838	−	3.69651i	0.452299	−	0.139516i
$703$	0.0187109	+	0.249680i	0.000705695	+	0.00941685i
$704$	−0.761761	−	0.955218i	−0.0287100	−	0.0360011i
$705$	−8.24096	+	20.9976i	−0.310373	+	0.790816i
$706$	5.19112	−	4.81666i	0.195371	−	0.181277i
$707$	12.0344	−	8.20495i	0.452602	−	0.308579i
$708$	−1.17336	+	15.6574i	−0.0440977	+	0.588443i
$709$	2.28765	+	10.0229i	0.0859147	+	0.376417i	0.999546	−	0.0301267i	$-0.00959109\pi$
$709$	2.28765	+	10.0229i	0.0859147	+	0.376417i	−0.913631	+	0.406544i	$0.866734\pi$
$710$	2.13457	+	9.35217i	0.0801091	+	0.350981i
$711$	−0.357041	+	4.76439i	−0.0133901	+	0.178678i
$712$	4.64436	−	3.16647i	0.174055	−	0.118669i
$713$	−28.2793	+	26.2393i	−1.05907	+	0.982671i
$714$	−20.2444	+	51.5819i	−0.757628	+	1.93040i
$715$	−2.55510	−	3.20400i	−0.0955555	−	0.119823i
$716$	0.00473327	+	0.0631610i	0.000176890	+	0.00236044i
$717$	−10.9130	+	3.36621i	−0.407553	+	0.125713i
$718$	−27.0380	−	4.07532i	−1.00905	−	0.152089i
$719$	−22.4759	−	20.8546i	−0.838208	−	0.777744i	0.138940	−	0.990301i	$-0.455630\pi$
$719$	−22.4759	−	20.8546i	−0.838208	−	0.777744i	−0.977149	+	0.212557i	$0.931821\pi$
$720$	−1.05305	+	0.507124i	−0.0392450	+	0.0188994i
$721$	−76.9630	+	11.6003i	−2.86625	+	0.432018i
$722$	7.59658	+	5.17926i	0.282715	+	0.192752i
$723$	−10.8311	+	13.5817i	−0.402812	+	0.505110i
$724$	−2.68791	−	4.65559i	−0.0998952	−	0.173024i
$725$	−4.19162	+	7.26010i	−0.155673	+	0.269633i
$726$	7.09186	+	18.0698i	0.263204	+	0.670632i
$727$	3.05473	+	1.47108i	0.113294	+	0.0545593i	0.489672	−	0.871907i	$-0.337116\pi$
$727$	3.05473	+	1.47108i	0.113294	+	0.0545593i	−0.376379	+	0.926466i	$0.622831\pi$
$728$	15.0241	+	4.63434i	0.556832	+	0.171760i
$729$	−2.19870	+	9.63316i	−0.0814335	+	0.356784i
$730$	1.30071			0.0481416
$731$	29.7790	−	23.5511i	1.10142	−	0.871069i
$732$	−12.4578			−0.460452
$733$	−11.0468	+	48.3993i	−0.408023	+	1.78767i	0.185277	+	0.982686i	$0.440682\pi$
$733$	−11.0468	+	48.3993i	−0.408023	+	1.78767i	−0.593300	+	0.804981i	$0.702175\pi$
$734$	11.4624	+	3.53567i	0.423084	+	0.130504i
$735$	−27.5423	−	13.2636i	−1.01591	−	0.489237i
$736$	−2.72888	−	6.95307i	−0.100588	−	0.256294i
$737$	−0.217062	+	0.375963i	−0.00799559	+	0.0138488i
$738$	−6.50417	−	11.2656i	−0.239422	−	0.414691i
$739$	20.0750	−	25.1732i	0.738470	−	0.926012i	−0.260754	−	0.965405i	$-0.583971\pi$
$739$	20.0750	−	25.1732i	0.738470	−	0.926012i	0.999224	+	0.0393931i	$0.0125424\pi$
$740$	0.0660637	+	0.0450415i	0.00242855	+	0.00165576i
$741$	−21.2060	+	3.19630i	−0.779023	+	0.117419i
$742$	−31.4848	+	15.1623i	−1.15584	+	0.556624i
$743$	17.3504	+	16.0988i	0.636525	+	0.590609i	0.930986	−	0.365054i	$-0.118950\pi$
$743$	17.3504	+	16.0988i	0.636525	+	0.590609i	−0.294461	+	0.955664i	$0.595140\pi$
$744$	10.4274	+	1.57167i	0.382286	+	0.0576204i
$745$	21.8976	−	6.75450i	0.802264	−	0.247466i
$746$	−1.41109	−	18.8297i	−0.0516638	−	0.689406i
$747$	3.31149	+	4.15247i	0.121161	+	0.151931i
$748$	2.58436	−	6.58484i	0.0944935	−	0.240765i
$749$	−10.1565	+	9.42385i	−0.371110	+	0.344340i
$750$	−1.68698	+	1.15017i	−0.0616000	+	0.0419982i
$751$	2.29220	−	30.5873i	0.0836435	−	1.11614i	−0.784599	−	0.620004i	$-0.787131\pi$
$751$	2.29220	−	30.5873i	0.0836435	−	1.11614i	0.868242	−	0.496141i	$-0.165250\pi$
$752$	2.45836	+	10.7708i	0.0896470	+	0.392769i
$753$	6.50057	+	28.4809i	0.236894	+	1.03790i
$754$	−2.10134	+	28.0405i	−0.0765264	+	1.02117i
$755$	10.2979	−	7.02102i	0.374780	−	0.255521i
$756$	−12.8473	+	11.9206i	−0.467252	+	0.433546i
$757$	2.80614	−	7.14992i	0.101991	−	0.259868i	−0.870765	−	0.491699i	$-0.836376\pi$
$757$	2.80614	−	7.14992i	0.101991	−	0.259868i	0.972756	+	0.231830i	$0.0744714\pi$
$758$	−5.61477	−	7.04070i	−0.203938	−	0.255730i
$759$	−1.39244	−	18.5808i	−0.0505424	−	0.674441i
$760$	−2.99231	+	0.923004i	−0.108542	+	0.0334809i
$761$	18.7814	+	2.83083i	0.680824	+	0.102618i	0.480344	−	0.877080i	$-0.340512\pi$
$761$	18.7814	+	2.83083i	0.680824	+	0.102618i	0.200480	+	0.979698i	$0.435750\pi$
$762$	−6.28242	−	5.82924i	−0.227588	−	0.211171i
$763$	−16.4918	+	7.94204i	−0.597044	+	0.287521i
$764$	−24.0995	+	3.63241i	−0.871888	+	0.131416i
$765$	−5.59128	−	3.81207i	−0.202153	−	0.137826i
$766$	−7.99417	+	10.0244i	−0.288841	+	0.362195i
$767$	12.8971	+	22.3384i	0.465686	+	0.806593i
$768$	−1.02088	+	1.76822i	−0.0368379	+	0.0638051i
$769$	−17.6208	−	44.8971i	−0.635423	−	1.61903i	−0.777288	−	0.629145i	$-0.783405\pi$
$769$	−17.6208	−	44.8971i	−0.635423	−	1.61903i	0.141865	−	0.989886i	$-0.454690\pi$
$770$	5.15983	+	2.48484i	0.185947	+	0.0895475i
$771$	6.22628	+	1.92055i	0.224234	+	0.0691671i
$772$	0.862289	−	3.77794i	0.0310345	−	0.135971i
$773$	4.67748			0.168237			0.0841187	−	0.996456i	$-0.473193\pi$
$773$	4.67748			0.168237			0.0841187	+	0.996456i	$0.473193\pi$
$774$	−7.47904	+	1.67517i	−0.268829	+	0.0602126i
$775$	5.16473			0.185523
$776$	2.57874	−	11.2982i	0.0925715	−	0.405582i
$777$	−0.731245	−	0.225559i	−0.0262333	−	0.00809189i
$778$	19.6512	+	9.46354i	0.704531	+	0.339284i
$779$	−12.7327	−	32.4425i	−0.456197	−	1.16237i
$780$	−3.42425	+	5.93098i	−0.122608	+	0.212363i
$781$	5.86002	+	10.1499i	0.209688	+	0.363191i
$782$	26.9637	−	33.8115i	0.964221	−	1.20910i
$783$	−25.8975	−	17.6566i	−0.925502	−	0.630996i
$784$	−14.8049	+	2.23148i	−0.528747	+	0.0796958i
$785$	6.31362	−	3.04048i	0.225343	−	0.108519i
$786$	33.0387	+	30.6554i	1.17845	+	1.09344i
$787$	27.9253	+	4.20906i	0.995430	+	0.150037i	0.626501	−	0.779421i	$-0.284486\pi$
$787$	27.9253	+	4.20906i	0.995430	+	0.150037i	0.368929	+	0.929458i	$0.379725\pi$
$788$	4.63678	−	1.43026i	0.165179	−	0.0509508i
$789$	−0.820583	−	10.9499i	−0.0292135	−	0.389828i
$790$	2.54866	+	3.19592i	0.0906772	+	0.113706i
$791$	−14.3433	+	36.5460i	−0.509988	+	1.29943i
$792$	−1.04680	+	0.971292i	−0.0371965	+	0.0345133i
$793$	−16.9095	+	11.5287i	−0.600473	+	0.409396i
$794$	2.04353	−	27.2690i	0.0725223	−	0.967742i
$795$	−3.38712	−	14.8400i	−0.120129	−	0.526319i
$796$	−1.68635	−	7.38837i	−0.0597710	−	0.261874i
$797$	0.684909	−	9.13948i	0.0242607	−	0.323737i	−0.971848	−	0.235607i	$-0.924292\pi$
$797$	0.684909	−	9.13948i	0.0242607	−	0.323737i	0.996109	−	0.0881294i	$-0.0280889\pi$
$798$	24.7622	−	16.8826i	0.876573	−	0.597637i
$799$	−46.8892	+	43.5069i	−1.65882	+	1.53916i
$800$	−0.365341	+	0.930874i	−0.0129168	+	0.0329114i
$801$	−4.09629	−	5.13658i	−0.144735	−	0.181492i
$802$	1.29897	+	17.3336i	0.0458683	+	0.612069i
$803$	1.51857	−	0.468417i	0.0535892	−	0.0165301i
$804$	0.717385	+	0.108128i	0.0253002	+	0.00381340i
$805$	25.6659	+	23.8145i	0.904605	+	0.839351i
$806$	15.6080	−	7.51642i	0.549768	−	0.264754i
$807$	4.03989	−	0.608916i	0.142211	−	0.0214349i
$808$	2.56738	+	1.75041i	0.0903201	+	0.0615792i
$809$	0.928694	−	1.16455i	0.0326512	−	0.0409433i	−0.765238	−	0.643748i	$-0.777379\pi$
$809$	0.928694	−	1.16455i	0.0326512	−	0.0409433i	0.797889	+	0.602804i	$0.205950\pi$
$810$	−5.57015	−	9.64779i	−0.195715	−	0.338989i
$811$	4.76289	−	8.24957i	0.167248	−	0.289682i	−0.770203	−	0.637798i	$-0.779845\pi$
$811$	4.76289	−	8.24957i	0.167248	−	0.289682i	0.937451	+	0.348117i	$0.113179\pi$
$812$	−14.3564	−	36.5796i	−0.503812	−	1.28369i
$813$	−52.2222	−	25.1489i	−1.83151	−	0.882010i
$814$	0.0933492	+	0.0287944i	0.00327189	+	0.00100924i
$815$	3.07936	−	13.4916i	0.107865	−	0.472589i
$816$	−11.8214			−0.413833
$817$	−20.4828	+	1.45148i	−0.716601	+	0.0507808i
$818$	4.83919			0.169198
$819$	4.08920	−	17.9159i	0.142888	−	0.626034i
$820$	−10.6352	−	3.28052i	−0.371397	−	0.114561i
$821$	−40.4845	−	19.4963i	−1.41292	−	0.680426i	−0.437183	−	0.899373i	$-0.644024\pi$
$821$	−40.4845	−	19.4963i	−1.41292	−	0.680426i	−0.975737	+	0.218947i	$0.929738\pi$
$822$	−0.765720	−	1.95102i	−0.0267075	−	0.0680497i
$823$	−14.0461	+	24.3286i	−0.489617	+	0.848041i	−0.999929	−	0.0119485i	$-0.996197\pi$
$823$	−14.0461	+	24.3286i	−0.489617	+	0.848041i	0.510312	+	0.859989i	$0.329530\pi$
$824$	−8.30221	−	14.3798i	−0.289221	−	0.500946i
$825$	−1.55534	+	1.95033i	−0.0541499	+	0.0679018i
$826$	−29.7833	−	20.3059i	−1.03629	−	0.706534i
$827$	22.1071	−	3.33211i	0.768740	−	0.115869i	0.247049	−	0.969003i	$-0.420539\pi$
$827$	22.1071	−	3.33211i	0.768740	−	0.115869i	0.521692	+	0.853134i	$0.325301\pi$
$828$	−7.86569	+	3.78792i	−0.273352	+	0.131639i
$829$	−12.3287	−	11.4394i	−0.428195	−	0.397307i	0.436419	−	0.899744i	$-0.356247\pi$
$829$	−12.3287	−	11.4394i	−0.428195	−	0.397307i	−0.864614	+	0.502437i	$0.832437\pi$
$830$	4.49339	+	0.677270i	0.155968	+	0.0235084i
$831$	−26.6398	+	8.21728i	−0.924124	+	0.285054i
$832$	0.250660	+	3.34483i	0.00869008	+	0.115961i
$833$	−54.0478	−	67.7738i	−1.87265	−	2.34822i
$834$	−8.85051	+	22.5507i	−0.306468	+	0.780868i
$835$	−11.9174	+	11.0577i	−0.412418	+	0.382668i
$836$	−3.16109	+	2.15520i	−0.109329	+	0.0745390i
$837$	−1.44306	+	19.2563i	−0.0498794	+	0.665595i
$838$	1.73540	+	7.60328i	0.0599484	+	0.262651i
$839$	1.73934	+	7.62056i	0.0600488	+	0.263091i	0.996037	−	0.0889406i	$-0.0283481\pi$
$839$	1.73934	+	7.62056i	0.0600488	+	0.263091i	−0.935988	+	0.352032i	$0.885491\pi$
$840$	0.715216	−	9.54390i	0.0246773	−	0.329296i
$841$	34.1060	−	23.2531i	1.17607	−	0.801831i
$842$	23.2332	−	21.5573i	0.800669	−	0.742913i
$843$	−8.60638	+	21.9287i	−0.296419	+	0.755264i
$844$	10.5490	+	13.2280i	0.363111	+	0.455326i
$845$	−0.130725	−	1.74440i	−0.00449708	−	0.0600093i
$846$	12.3390	−	3.80606i	0.424222	−	0.130855i
$847$	−44.0671	−	6.64205i	−1.51416	−	0.228223i
$848$	−5.46499	−	5.07077i	−0.187668	−	0.174131i
$849$	−4.51411	+	2.17388i	−0.154924	+	0.0746074i
$850$	−5.72515	+	0.862927i	−0.196371	+	0.0295982i
$851$	0.493456	+	0.336433i	0.0169155	+	0.0115328i
$852$	12.2117	−	15.3129i	0.418365	−	0.524613i
$853$	18.0171	+	31.2066i	0.616895	+	1.06849i	0.990049	+	0.140724i	$0.0449431\pi$
$853$	18.0171	+	31.2066i	0.616895	+	1.06849i	−0.373154	+	0.927770i	$0.621724\pi$
$854$	14.3002	−	24.7686i	0.489341	−	0.847564i
$855$	1.33715	+	3.40701i	0.0457297	+	0.116517i
$856$	−2.66307	−	1.28247i	−0.0910219	−	0.0438338i
$857$	−36.2033	−	11.1672i	−1.23668	−	0.381465i	−0.393614	−	0.919276i	$-0.628775\pi$
$857$	−36.2033	−	11.1672i	−1.23668	−	0.381465i	−0.843066	+	0.537811i	$0.819252\pi$
$858$	−1.86190	+	8.15751i	−0.0635641	+	0.278493i
$859$	30.7307			1.04852			0.524259	−	0.851559i	$-0.324342\pi$
$859$	30.7307			1.04852			0.524259	+	0.851559i	$0.324342\pi$
$860$	−3.71587	+	5.40299i	−0.126710	+	0.184240i
$861$	106.518			3.63012
$862$	−7.42759	+	32.5424i	−0.252985	+	1.10840i
$863$	−0.785751	−	0.242372i	−0.0267473	−	0.00825044i	0.281353	−	0.959604i	$-0.409217\pi$
$863$	−0.785751	−	0.242372i	−0.0267473	−	0.00825044i	−0.308100	+	0.951354i	$0.599693\pi$
$864$	−3.36861	−	1.62224i	−0.114602	−	0.0551896i
$865$	4.67483	+	11.9113i	0.158949	+	0.404995i
$866$	11.2301	−	19.4510i	0.381613	−	0.660973i
$867$	−16.8670	−	29.2145i	−0.572833	−	0.992176i
$868$	−15.0943	+	18.9277i	−0.512334	+	0.642447i
$869$	4.12646	+	2.81337i	0.139980	+	0.0954370i
$870$	16.9254	−	2.55110i	0.573825	−	0.0864902i
$871$	1.07380	−	0.517116i	0.0363844	−	0.0175218i
$872$	−2.86258	−	2.65608i	−0.0969391	−	0.0899464i
$873$	−13.3937	−	2.01877i	−0.453308	−	0.0683251i
$874$	−22.3507	+	6.89429i	−0.756025	+	0.233203i
$875$	−0.350293	−	4.67434i	−0.0118421	−	0.158021i
$876$	−1.65583	−	2.07635i	−0.0559455	−	0.0701534i
$877$	−8.93227	+	22.7590i	−0.301621	+	0.768518i	0.697052	+	0.717021i	$0.254495\pi$
$877$	−8.93227	+	22.7590i	−0.301621	+	0.768518i	−0.998673	+	0.0514977i	$0.983601\pi$
$878$	−2.47793	+	2.29918i	−0.0836260	+	0.0775936i
$879$	28.9486	−	19.7368i	0.976412	−	0.665707i
$880$	−0.0913030	+	1.21835i	−0.00307782	+	0.0410707i
$881$	−4.53418	−	19.8655i	−0.152760	−	0.669286i	−0.992076	−	0.125642i	$-0.959901\pi$
$881$	−4.53418	−	19.8655i	−0.152760	−	0.669286i	0.839315	−	0.543645i	$-0.182956\pi$
$882$	3.89400	+	17.0607i	0.131118	+	0.574465i
$883$	2.38173	−	31.7819i	0.0801514	−	1.06955i	−0.801609	−	0.597849i	$-0.796022\pi$
$883$	2.38173	−	31.7819i	0.0801514	−	1.06955i	0.881760	−	0.471698i	$-0.156359\pi$
$884$	−16.0458	+	10.9398i	−0.539677	+	0.367946i
$885$	11.5099	−	10.6796i	0.386901	−	0.358992i
$886$	−5.57824	+	14.2131i	−0.187405	+	0.477499i
$887$	14.5923	+	18.2982i	0.489961	+	0.614392i	0.963932	−	0.266149i	$-0.0857512\pi$
$887$	14.5923	+	18.2982i	0.489961	+	0.614392i	−0.473971	+	0.880541i	$0.657180\pi$
$888$	−0.0122000	−	0.162797i	−0.000409404	−	0.00546312i
$889$	18.8013	−	5.79942i	0.630574	−	0.194506i
$890$	−5.55830	−	0.837779i	−0.186315	−	0.0280824i
$891$	−9.97749	−	9.25776i	−0.334259	−	0.310147i
$892$	−11.0555	+	5.32407i	−0.370167	+	0.178263i
$893$	34.2088	−	5.15615i	1.14475	−	0.172544i
$894$	−38.6583	−	26.3568i	−1.29293	−	0.881503i
$895$	0.0394907	−	0.0495198i	0.00132003	−	0.00165526i
$896$	−2.34372	−	4.05945i	−0.0782983	−	0.135617i
$897$	−25.5771	+	44.3009i	−0.853995	+	1.47916i
$898$	−0.700685	−	1.78532i	−0.0233822	−	0.0595768i
$899$	−39.0094	−	18.7859i	−1.30104	−	0.626546i
$900$	1.11688	+	0.344510i	0.0372292	+	0.0114837i
$901$	9.60484	−	42.0816i	0.319984	−	1.40194i
$902$	−13.5979			−0.452759
$903$	18.7416	−	59.8953i	0.623680	−	1.99319i
$904$	−8.37555			−0.278567
$905$	−1.19623	+	5.24103i	−0.0397640	+	0.174218i
$906$	−24.3172	−	7.50087i	−0.807886	−	0.249200i
$907$	4.21167	+	2.02824i	0.139846	+	0.0673465i	0.502498	−	0.864578i	$-0.332414\pi$
$907$	4.21167	+	2.02824i	0.139846	+	0.0673465i	−0.362652	+	0.931925i	$0.618129\pi$
$908$	−2.50968	−	6.39455i	−0.0832865	−	0.212211i
$909$	1.81591	−	3.14526i	0.0602301	−	0.104322i
$910$	−7.86133	−	13.6162i	−0.260601	−	0.451373i
$911$	1.93725	−	2.42923i	0.0641839	−	0.0804840i	−0.748703	−	0.662905i	$-0.769323\pi$
$911$	1.93725	−	2.42923i	0.0641839	−	0.0804840i	0.812887	+	0.582421i	$0.197895\pi$
$912$	5.28267	+	3.60166i	0.174927	+	0.119263i
$913$	5.48989	−	0.827468i	0.181689	−	0.0273852i
$914$	−27.2238	+	13.1103i	−0.900484	+	0.433650i
$915$	9.13219	+	8.47343i	0.301901	+	0.280123i
$916$	−14.6108	−	2.20223i	−0.482756	−	0.0727637i
$917$	−98.8741	+	30.4986i	−3.26511	+	1.00715i
$918$	−1.61771	−	21.5869i	−0.0533925	−	0.712473i
$919$	35.4560	+	44.4604i	1.16959	+	1.46661i	0.855941	+	0.517073i	$0.172978\pi$
$919$	35.4560	+	44.4604i	1.16959	+	1.46661i	0.313644	+	0.949541i	$0.398450\pi$
$920$	−2.72888	+	6.95307i	−0.0899685	+	0.229236i
$921$	−13.7244	+	12.7344i	−0.452234	+	0.419612i
$922$	−11.3685	+	7.75090i	−0.374401	+	0.255262i
$923$	2.40450	−	32.0859i	0.0791452	−	1.05612i
$924$	−2.60197	−	11.4000i	−0.0855985	−	0.375032i
$925$	−0.0177921	−	0.0779525i	−0.000585002	−	0.00256306i
$926$	−2.84770	+	37.9999i	−0.0935813	+	1.24876i
$927$	−16.0350	+	10.9325i	−0.526660	+	0.359071i
$928$	6.14535	−	5.70205i	0.201731	−	0.187179i
$929$	19.9500	−	50.8317i	0.654537	−	1.66773i	−0.0864847	−	0.996253i	$-0.527563\pi$
$929$	19.9500	−	50.8317i	0.654537	−	1.66773i	0.741022	−	0.671481i	$-0.234341\pi$
$930$	−6.57480	−	8.24454i	−0.215596	−	0.270349i
$931$	3.50366	+	46.7531i	0.114828	+	1.53227i
$932$	−21.5730	+	6.65438i	−0.706646	+	0.217971i
$933$	−21.7604	−	3.27986i	−0.712405	−	0.107378i
$934$	−17.5783	−	16.3102i	−0.575178	−	0.533687i
$935$	−6.37329	+	3.06922i	−0.208429	+	0.100374i
$936$	3.87662	−	0.584306i	0.126711	−	0.0190986i
$937$	−9.91091	−	6.75714i	−0.323775	−	0.220746i	0.390514	−	0.920597i	$-0.372297\pi$
$937$	−9.91091	−	6.75714i	−0.323775	−	0.220746i	−0.714289	+	0.699851i	$0.753250\pi$
$938$	−1.03846	+	1.30219i	−0.0339070	+	0.0425180i
$939$	−1.89788	−	3.28722i	−0.0619349	−	0.107274i
$940$	5.52387	−	9.56763i	0.180169	−	0.312062i
$941$	15.8899	+	40.4867i	0.517995	+	1.31983i	0.915533	+	0.402243i	$0.131769\pi$
$941$	15.8899	+	40.4867i	0.517995	+	1.31983i	−0.397538	+	0.917586i	$0.630135\pi$
$942$	−12.8909	−	6.20794i	−0.420009	−	0.202266i
$943$	−79.4385	−	24.5035i	−2.58687	−	0.797944i
$944$	1.71121	−	7.49728i	0.0556950	−	0.244016i
$945$	17.5258			0.570113
$946$	−2.39251	+	7.64611i	−0.0777871	+	0.248596i
$947$	−50.1234			−1.62879			−0.814395	−	0.580311i	$-0.802931\pi$
$947$	−50.1234			−1.62879			−0.814395	+	0.580311i	$0.802931\pi$
$948$	1.85720	−	8.13692i	0.0603190	−	0.264275i
$949$	−4.16904	−	1.28598i	−0.135333	−	0.0417446i
$950$	2.82132	+	1.35867i	0.0915356	+	0.0440812i
$951$	23.8750	+	60.8326i	0.774201	+	1.97263i
$952$	13.5697	−	23.5035i	0.439797	−	0.761751i
$953$	−13.8902	−	24.0586i	−0.449949	−	0.779334i	0.548433	−	0.836194i	$-0.315224\pi$
$953$	−13.8902	−	24.0586i	−0.449949	−	0.779334i	−0.998382	+	0.0568599i	$0.981891\pi$
$954$	−5.43281	+	6.81253i	−0.175894	+	0.220564i
$955$	20.1368	+	13.7291i	0.651612	+	0.444262i
$956$	5.53090	−	0.833649i	0.178882	−	0.0269621i
$957$	18.8415	−	9.07361i	0.609061	−	0.293308i
$958$	9.92439	+	9.20849i	0.320643	+	0.297513i
$959$	4.75800	+	0.717152i	0.153644	+	0.0231581i
$960$	1.95105	−	0.601821i	0.0629700	−	0.0194237i
$961$	−0.323250	−	4.31347i	−0.0104274	−	0.139144i
$962$	−0.167215	−	0.209682i	−0.00539124	−	0.00676041i
$963$	−1.26215	+	3.21592i	−0.0406723	+	0.103631i
$964$	6.23694	−	5.78703i	0.200878	−	0.186388i
$965$	−3.20175	+	2.18292i	−0.103068	+	0.0702706i
$966$	5.34224	−	71.2872i	0.171884	−	2.29363i
$967$	11.4130	+	50.0037i	0.367018	+	1.60801i	0.734926	+	0.678148i	$0.237217\pi$
$967$	11.4130	+	50.0037i	0.367018	+	1.60801i	−0.367908	+	0.929862i	$0.619926\pi$
$968$	−2.11557	−	9.26891i	−0.0679969	−	0.297914i
$969$	−2.76636	+	36.9145i	−0.0888682	+	1.18586i
$970$	−9.57508	+	6.52818i	−0.307437	+	0.209607i
$971$	38.8312	−	36.0301i	1.24615	−	1.15626i	0.264745	−	0.964318i	$-0.414712\pi$
$971$	38.8312	−	36.0301i	1.24615	−	1.15626i	0.981406	−	0.191942i	$-0.0614784\pi$
$972$	−4.21211	+	10.7323i	−0.135104	+	0.344238i
$973$	−34.6761	−	43.4824i	−1.11166	−	1.39398i
$974$	1.87370	+	25.0027i	0.0600371	+	0.801139i
$975$	6.54424	−	2.01863i	0.209583	−	0.0646479i
$976$	6.03332	+	0.909377i	0.193122	+	0.0291085i
$977$	0.373901	+	0.346930i	0.0119622	+	0.0110993i	0.686131	−	0.727478i	$-0.259308\pi$
$977$	0.373901	+	0.346930i	0.0119622	+	0.0110993i	−0.674169	+	0.738577i	$0.735498\pi$
$978$	−25.4569	+	12.2594i	−0.814021	+	0.392012i
$979$	−6.79097	+	1.02357i	−0.217040	+	0.0327136i
$980$	12.3706	+	8.43411i	0.395163	+	0.269418i
$981$	−2.84573	+	3.56843i	−0.0908570	+	0.113931i
$982$	13.3561	+	23.1334i	0.426209	+	0.738216i
$983$	4.77605	−	8.27235i	0.152332	−	0.263847i	−0.779752	−	0.626088i	$-0.784655\pi$
$983$	4.77605	−	8.27235i	0.152332	−	0.263847i	0.932084	+	0.362241i	$0.117988\pi$
$984$	8.30204	+	21.1533i	0.264660	+	0.674341i
$985$	−4.37183	−	2.10536i	−0.139298	−	0.0670824i
$986$	46.3810	+	14.3066i	1.47707	+	0.455617i
$987$	−23.5281	+	103.083i	−0.748907	+	3.28118i
$988$	10.5035			0.334159
$989$	−27.7554	+	40.3571i	−0.882569	+	1.28328i
$990$	1.42801			0.0453850
$991$	0.765654	−	3.35455i	0.0243218	−	0.106561i	−0.961310	−	0.275469i	$-0.911167\pi$
$991$	0.765654	−	3.35455i	0.0243218	−	0.106561i	0.985632	+	0.168908i	$0.0540241\pi$
$992$	−4.93528	−	1.52233i	−0.156695	−	0.0483341i
$993$	11.6400	+	5.60552i	0.369384	+	0.177886i
$994$	16.4276	+	41.8569i	0.521053	+	1.32762i
$995$	−3.78919	+	6.56307i	−0.120125	+	0.208063i
$996$	−4.63904	−	8.03506i	−0.146994	−	0.254600i
$997$	18.4316	−	23.1124i	0.583733	−	0.731979i	−0.399011	−	0.916946i	$-0.630647\pi$
$997$	18.4316	−	23.1124i	0.583733	−	0.731979i	0.982745	+	0.184967i	$0.0592180\pi$
$998$	17.2142	+	11.7364i	0.544906	+	0.371511i
$999$	0.295611	−	0.0445561i	0.00935271	−	0.00140969i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	430.2.q.c.81.4	✓	48
43.17	even	21	inner	430.2.q.c.361.4	yes	48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
430.2.q.c.81.4	✓	48	1.1	even	1	trivial
430.2.q.c.361.4	yes	48	43.17	even	21	inner

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 $\F_{q}$

Level:	\( N \)	\(=\)	\( 430 = 2 \cdot 5 \cdot 43 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	430.q (of order \(21\), degree \(12\), minimal)

\(f(q)\)	\(=\)	\(q+(0.222521 - 0.974928i) q^{2} +(1.95105 + 0.601821i) q^{3} +(-0.900969 - 0.433884i) q^{4} +(0.365341 + 0.930874i) q^{5} +(1.02088 - 1.76822i) q^{6} +(2.34372 + 4.05945i) q^{7} +(-0.623490 + 0.781831i) q^{8} +(0.965710 + 0.658410i) q^{9} +O(q^{10})\)	\(q+(0.222521 - 0.974928i) q^{2} +(1.95105 + 0.601821i) q^{3} +(-0.900969 - 0.433884i) q^{4} +(0.365341 + 0.930874i) q^{5} +(1.02088 - 1.76822i) q^{6} +(2.34372 + 4.05945i) q^{7} +(-0.623490 + 0.781831i) q^{8} +(0.965710 + 0.658410i) q^{9} +(0.988831 - 0.149042i) q^{10} +(1.10078 - 0.530106i) q^{11} +(-1.49672 - 1.38875i) q^{12} +(-3.31674 - 0.499919i) q^{13} +(4.47920 - 1.38165i) q^{14} +(0.152581 + 2.03606i) q^{15} +(0.623490 + 0.781831i) q^{16} +(-2.11526 + 5.38959i) q^{17} +(0.856793 - 0.794987i) q^{18} +(2.58731 - 1.76400i) q^{19} +(0.0747301 - 0.997204i) q^{20} +(2.12967 + 9.33070i) q^{21} +(-0.271869 - 1.19114i) q^{22} +(0.558189 - 7.44852i) q^{23} +(-1.68698 + 1.15017i) q^{24} +(-0.733052 + 0.680173i) q^{25} +(-1.22543 + 3.12234i) q^{26} +(-2.33115 - 2.92317i) q^{27} +(-0.350293 - 4.67434i) q^{28} +(8.01079 - 2.47100i) q^{29} +(2.01896 + 0.304309i) q^{30} +(-3.78601 - 3.51291i) q^{31} +(0.900969 - 0.433884i) q^{32} +(2.46670 - 0.371796i) q^{33} +(4.78377 + 3.26152i) q^{34} +(-2.92257 + 3.66479i) q^{35} +(-0.584401 - 1.01221i) q^{36} +(-0.0399786 + 0.0692449i) q^{37} +(-1.14404 - 2.91496i) q^{38} +(-6.17029 - 2.97145i) q^{39} +(-0.955573 - 0.294755i) q^{40} +(2.47658 - 10.8506i) q^{41} +9.57066 q^{42} +(-5.66557 - 3.30172i) q^{43} -1.22177 q^{44} +(-0.260083 + 1.13950i) q^{45} +(-7.13756 - 2.20165i) q^{46} +(9.95368 + 4.79344i) q^{47} +(0.745940 + 1.90062i) q^{48} +(-7.48607 + 12.9663i) q^{49} +(0.500000 + 0.866025i) q^{50} +(-7.37055 + 9.24238i) q^{51} +(2.77138 + 1.88949i) q^{52} +(-7.37185 + 1.11113i) q^{53} +(-3.36861 + 1.62224i) q^{54} +(0.895621 + 0.831015i) q^{55} +(-4.63509 - 0.698628i) q^{56} +(6.10958 - 1.88456i) q^{57} +(-0.626480 - 8.35979i) q^{58} +(-4.79469 - 6.01235i) q^{59} +(0.745940 - 1.90062i) q^{60} +(4.47270 - 4.15005i) q^{61} +(-4.26730 + 2.90940i) q^{62} +(-0.409423 + 5.46338i) q^{63} +(-0.222521 - 0.974928i) q^{64} +(-0.746381 - 3.27011i) q^{65} +(0.186419 - 2.48759i) q^{66} +(-0.293583 + 0.200161i) q^{67} +(4.24424 - 3.93808i) q^{68} +(5.57173 - 14.1965i) q^{69} +(2.92257 + 3.66479i) q^{70} +(0.716862 + 9.56586i) q^{71} +(-1.11688 + 0.344510i) q^{72} +(1.28619 + 0.193861i) q^{73} +(0.0586127 + 0.0543847i) q^{74} +(-1.83957 + 0.885888i) q^{75} +(-3.09645 + 0.466715i) q^{76} +(4.73185 + 3.22612i) q^{77} +(-4.26997 + 5.35437i) q^{78} +(2.04386 + 3.54008i) q^{79} +(-0.500000 + 0.866025i) q^{80} +(-4.07001 - 10.3702i) q^{81} +(-10.0275 - 4.82897i) q^{82} +(4.34227 + 1.33941i) q^{83} +(2.12967 - 9.33070i) q^{84} -5.78982 q^{85} +(-4.47964 + 4.78882i) q^{86} +17.1166 q^{87} +(-0.271869 + 1.19114i) q^{88} +(-5.37136 - 1.65684i) q^{89} +(1.05305 + 0.507124i) q^{90} +(-5.74413 - 14.6358i) q^{91} +(-3.73470 + 6.46869i) q^{92} +(-5.27258 - 9.13238i) q^{93} +(6.88816 - 8.63748i) q^{94} +(2.58731 + 1.76400i) q^{95} +(2.01896 - 0.304309i) q^{96} +(-10.4411 + 5.02818i) q^{97} +(10.9754 + 10.1836i) q^{98} +(1.41206 + 0.212833i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q + 8 q^{2} - 7 q^{3} - 8 q^{4} + 4 q^{5} + 7 q^{6} - 3 q^{7} + 8 q^{8} + 13 q^{9}+O(q^{10}) \) 48 * q + 8 * q^2 - 7 * q^3 - 8 * q^4 + 4 * q^5 + 7 * q^6 - 3 * q^7 + 8 * q^8 + 13 * q^9	\( 48 q + 8 q^{2} - 7 q^{3} - 8 q^{4} + 4 q^{5} + 7 q^{6} - 3 q^{7} + 8 q^{8} + 13 q^{9} - 4 q^{10} + q^{11} + 14 q^{12} - 23 q^{13} + 24 q^{14} - 8 q^{16} + 8 q^{17} - 20 q^{18} - 3 q^{19} + 4 q^{20} - 8 q^{21} - q^{22} + 7 q^{23} + 4 q^{25} - 19 q^{26} + 32 q^{27} + 4 q^{28} + 30 q^{29} + 9 q^{31} + 8 q^{32} + 39 q^{33} - 8 q^{34} - 22 q^{35} - 29 q^{36} - 37 q^{37} - 11 q^{38} - 52 q^{39} - 4 q^{40} - 28 q^{41} - 6 q^{42} + 41 q^{43} + 8 q^{44} + 2 q^{45} - 28 q^{46} + 3 q^{47} - 41 q^{49} + 24 q^{50} - 30 q^{51} - 9 q^{52} - 69 q^{53} + 3 q^{54} + 10 q^{55} - 11 q^{56} + 116 q^{57} + 5 q^{58} + 10 q^{59} - 19 q^{61} - 93 q^{62} + 34 q^{63} - 8 q^{64} - 3 q^{65} - 18 q^{66} + 3 q^{67} + 8 q^{68} + 42 q^{69} + 22 q^{70} - 36 q^{71} + 22 q^{72} - 56 q^{73} + 9 q^{74} - 10 q^{76} + 3 q^{77} + 45 q^{78} + 16 q^{79} - 24 q^{80} - 19 q^{81} + 14 q^{82} + 64 q^{83} - 8 q^{84} - 30 q^{85} + 36 q^{86} + 78 q^{87} - q^{88} - 75 q^{89} + 5 q^{90} + 5 q^{91} + 14 q^{92} - 10 q^{93} - 45 q^{94} - 3 q^{95} + 33 q^{97} - q^{98} - 11 q^{99}+O(q^{100}) \) 48 * q + 8 * q^2 - 7 * q^3 - 8 * q^4 + 4 * q^5 + 7 * q^6 - 3 * q^7 + 8 * q^8 + 13 * q^9 - 4 * q^10 + q^11 + 14 * q^12 - 23 * q^13 + 24 * q^14 - 8 * q^16 + 8 * q^17 - 20 * q^18 - 3 * q^19 + 4 * q^20 - 8 * q^21 - q^22 + 7 * q^23 + 4 * q^25 - 19 * q^26 + 32 * q^27 + 4 * q^28 + 30 * q^29 + 9 * q^31 + 8 * q^32 + 39 * q^33 - 8 * q^34 - 22 * q^35 - 29 * q^36 - 37 * q^37 - 11 * q^38 - 52 * q^39 - 4 * q^40 - 28 * q^41 - 6 * q^42 + 41 * q^43 + 8 * q^44 + 2 * q^45 - 28 * q^46 + 3 * q^47 - 41 * q^49 + 24 * q^50 - 30 * q^51 - 9 * q^52 - 69 * q^53 + 3 * q^54 + 10 * q^55 - 11 * q^56 + 116 * q^57 + 5 * q^58 + 10 * q^59 - 19 * q^61 - 93 * q^62 + 34 * q^63 - 8 * q^64 - 3 * q^65 - 18 * q^66 + 3 * q^67 + 8 * q^68 + 42 * q^69 + 22 * q^70 - 36 * q^71 + 22 * q^72 - 56 * q^73 + 9 * q^74 - 10 * q^76 + 3 * q^77 + 45 * q^78 + 16 * q^79 - 24 * q^80 - 19 * q^81 + 14 * q^82 + 64 * q^83 - 8 * q^84 - 30 * q^85 + 36 * q^86 + 78 * q^87 - q^88 - 75 * q^89 + 5 * q^90 + 5 * q^91 + 14 * q^92 - 10 * q^93 - 45 * q^94 - 3 * q^95 + 33 * q^97 - q^98 - 11 * q^99

Introduction

L-functions

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