LMFDB - Embedded newform 435.2.bm.a.43.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [435,2,Mod(37,435)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(435, base_ring=CyclotomicField(28))

chi = DirichletCharacter(H, H._module([0, 7, 3]))

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

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

chi := DirichletCharacter("435.37");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 435 = 3 \cdot 5 \cdot 29 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	435.bm (of order $28$, 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:	$3.47349248793$
Analytic rank:	$0$
Dimension:	$180$
Relative dimension:	$15$ over $\Q(\zeta_{28})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{28}]$

Embedding invariants

Embedding label			43.4
Character	$\chi$	$=$	435.43
Dual form			435.2.bm.a.172.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.25592 - 1.00156i) q^{2} +(-0.222521 + 0.974928i) q^{3} +(0.129161 + 0.565891i) q^{4} +(-2.00721 + 0.985438i) q^{5} +(1.25592 - 1.00156i) q^{6} +(0.245610 + 0.390886i) q^{7} +(-0.989403 + 2.05452i) q^{8} +(-0.900969 - 0.433884i) q^{9} +O(q^{10})$	\(q+(-1.25592 - 1.00156i) q^{2} +(-0.222521 + 0.974928i) q^{3} +(0.129161 + 0.565891i) q^{4} +(-2.00721 + 0.985438i) q^{5} +(1.25592 - 1.00156i) q^{6} +(0.245610 + 0.390886i) q^{7} +(-0.989403 + 2.05452i) q^{8} +(-0.900969 - 0.433884i) q^{9} +(3.50787 + 0.772717i) q^{10} +(0.550844 - 1.57422i) q^{11} -0.580444 q^{12} +(0.718304 - 2.05280i) q^{13} +(0.0830300 - 0.736912i) q^{14} +(-0.514084 - 2.17617i) q^{15} +(4.34625 - 2.09304i) q^{16} -1.28336i q^{17} +(0.696980 + 1.44729i) q^{18} +(1.78848 - 2.84635i) q^{19} +(-0.816905 - 1.00859i) q^{20} +(-0.435739 + 0.152472i) q^{21} +(-2.26849 + 1.42539i) q^{22} +(-0.0824751 + 0.731987i) q^{23} +(-1.78284 - 1.42177i) q^{24} +(3.05782 - 3.95597i) q^{25} +(-2.95813 + 1.85871i) q^{26} +(0.623490 - 0.781831i) q^{27} +(-0.189476 + 0.189476i) q^{28} +(1.46172 - 5.18299i) q^{29} +(-1.53392 + 3.24797i) q^{30} +(-0.536373 - 4.76044i) q^{31} +(-3.10849 - 0.709493i) q^{32} +(1.41218 + 0.887331i) q^{33} +(-1.28536 + 1.61179i) q^{34} +(-0.878185 - 0.542558i) q^{35} +(0.129161 - 0.565891i) q^{36} +(2.55045 + 1.22823i) q^{37} +(-5.09697 + 1.78351i) q^{38} +(1.84149 + 1.15708i) q^{39} +(-0.0386545 - 5.09885i) q^{40} +(-3.14762 - 3.14762i) q^{41} +(0.699960 + 0.244927i) q^{42} +(-0.493306 - 0.618587i) q^{43} +(0.961986 + 0.108390i) q^{44} +(2.23600 - 0.0169512i) q^{45} +(0.836710 - 0.836710i) q^{46} +(6.10419 - 2.93962i) q^{47} +(1.07343 + 4.70303i) q^{48} +(2.94472 - 6.11477i) q^{49} +(-7.80251 + 1.90578i) q^{50} +(1.25118 + 0.285574i) q^{51} +(1.25444 + 0.141341i) q^{52} +(-8.27657 + 0.932546i) q^{53} +(-1.56610 + 0.357452i) q^{54} +(0.445636 + 3.70262i) q^{55} +(-1.04609 + 0.117866i) q^{56} +(2.37701 + 2.37701i) q^{57} +(-7.02687 + 5.04539i) q^{58} -1.15462i q^{59} +(1.16508 - 0.571992i) q^{60} +(-1.11984 - 1.78221i) q^{61} +(-4.09423 + 6.51592i) q^{62} +(-0.0516878 - 0.458742i) q^{63} +(-2.82199 - 3.53866i) q^{64} +(0.581112 + 4.82825i) q^{65} +(-0.884863 - 2.52879i) q^{66} +(0.587831 + 1.67992i) q^{67} +(0.726241 - 0.165760i) q^{68} +(-0.695282 - 0.243290i) q^{69} +(0.559522 + 1.56096i) q^{70} +(-2.57968 - 5.35676i) q^{71} +(1.78284 - 1.42177i) q^{72} +(-1.64402 + 1.31106i) q^{73} +(-1.97300 - 4.09698i) q^{74} +(3.17636 + 3.86144i) q^{75} +(1.84173 + 0.644448i) q^{76} +(0.750634 - 0.171327i) q^{77} +(-1.15387 - 3.29756i) q^{78} +(1.45049 + 4.14525i) q^{79} +(-6.66129 + 8.48415i) q^{80} +(0.623490 + 0.781831i) q^{81} +(0.800617 + 7.10567i) q^{82} +(-0.0199234 + 0.0317078i) q^{83} +(-0.142563 - 0.226887i) q^{84} +(1.26467 + 2.57597i) q^{85} +1.27097i q^{86} +(4.72778 + 2.57840i) q^{87} +(2.68926 + 2.68926i) q^{88} +(10.6349 - 1.19827i) q^{89} +(-2.82521 - 2.21820i) q^{90} +(0.978831 - 0.223412i) q^{91} +(-0.424877 + 0.0478722i) q^{92} +(4.76044 + 0.536373i) q^{93} +(-10.6106 - 2.42179i) q^{94} +(-0.784962 + 7.47567i) q^{95} +(1.38341 - 2.87268i) q^{96} +(3.17217 + 13.8982i) q^{97} +(-9.82262 + 4.73033i) q^{98} +(-1.17932 + 1.17932i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 180 q - 30 q^{3} + 30 q^{4} + 10 q^{5} - 30 q^{9}+O(q^{10}) $ 180 * q - 30 * q^3 + 30 * q^4 + 10 * q^5 - 30 * q^9	$ 180 q - 30 q^{3} + 30 q^{4} + 10 q^{5} - 30 q^{9} - 4 q^{10} - 30 q^{11} - 180 q^{12} - 20 q^{13} - 10 q^{14} - 4 q^{15} - 14 q^{16} + 8 q^{19} + 2 q^{20} + 36 q^{22} + 64 q^{25} - 36 q^{26} - 30 q^{27} + 72 q^{28} + 12 q^{29} - 4 q^{30} - 20 q^{31} + 12 q^{33} + 40 q^{34} - 6 q^{35} + 30 q^{36} + 42 q^{37} + 16 q^{38} + 22 q^{39} + 18 q^{40} - 10 q^{41} + 4 q^{42} + 26 q^{43} + 4 q^{44} - 4 q^{45} + 12 q^{46} - 20 q^{47} - 70 q^{48} + 8 q^{50} + 12 q^{52} - 82 q^{53} + 48 q^{55} + 6 q^{56} + 8 q^{57} - 70 q^{58} - 40 q^{60} + 14 q^{61} + 110 q^{62} - 14 q^{63} - 74 q^{64} + 42 q^{65} + 22 q^{66} - 20 q^{67} - 98 q^{68} + 28 q^{69} + 8 q^{70} + 140 q^{71} + 98 q^{73} + 22 q^{75} - 4 q^{76} - 42 q^{77} + 34 q^{78} - 24 q^{79} - 62 q^{80} - 30 q^{81} + 6 q^{82} - 60 q^{83} - 68 q^{84} - 178 q^{85} - 44 q^{87} - 156 q^{88} - 12 q^{89} - 4 q^{90} - 56 q^{91} - 8 q^{92} + 8 q^{93} + 4 q^{95} - 42 q^{97} + 194 q^{98} + 12 q^{99}+O(q^{100}) $ 180 * q - 30 * q^3 + 30 * q^4 + 10 * q^5 - 30 * q^9 - 4 * q^10 - 30 * q^11 - 180 * q^12 - 20 * q^13 - 10 * q^14 - 4 * q^15 - 14 * q^16 + 8 * q^19 + 2 * q^20 + 36 * q^22 + 64 * q^25 - 36 * q^26 - 30 * q^27 + 72 * q^28 + 12 * q^29 - 4 * q^30 - 20 * q^31 + 12 * q^33 + 40 * q^34 - 6 * q^35 + 30 * q^36 + 42 * q^37 + 16 * q^38 + 22 * q^39 + 18 * q^40 - 10 * q^41 + 4 * q^42 + 26 * q^43 + 4 * q^44 - 4 * q^45 + 12 * q^46 - 20 * q^47 - 70 * q^48 + 8 * q^50 + 12 * q^52 - 82 * q^53 + 48 * q^55 + 6 * q^56 + 8 * q^57 - 70 * q^58 - 40 * q^60 + 14 * q^61 + 110 * q^62 - 14 * q^63 - 74 * q^64 + 42 * q^65 + 22 * q^66 - 20 * q^67 - 98 * q^68 + 28 * q^69 + 8 * q^70 + 140 * q^71 + 98 * q^73 + 22 * q^75 - 4 * q^76 - 42 * q^77 + 34 * q^78 - 24 * q^79 - 62 * q^80 - 30 * q^81 + 6 * q^82 - 60 * q^83 - 68 * q^84 - 178 * q^85 - 44 * q^87 - 156 * q^88 - 12 * q^89 - 4 * q^90 - 56 * q^91 - 8 * q^92 + 8 * q^93 + 4 * q^95 - 42 * q^97 + 194 * q^98 + 12 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/435\mathbb{Z}\right)^\times$.

$n$	$31$	$146$	$262$
$\chi(n)$	$e\left(\frac{13}{28}\right)$	$1$	$e\left(\frac{3}{4}\right)$

Coefficient data

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

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

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

$2$	−1.25592	−	1.00156i	−0.888066	−	0.708209i	0.0691427	−	0.997607i	$-0.477974\pi$
$2$	−1.25592	−	1.00156i	−0.888066	−	0.708209i	−0.957209	+	0.289398i	$0.906545\pi$
$3$	−0.222521	+	0.974928i	−0.128473	+	0.562875i
$3$	−0.222521	+	0.974928i	−0.128473	+	0.562875i
$4$	0.129161	+	0.565891i	0.0645805	+	0.282946i
$5$	−2.00721	+	0.985438i	−0.897654	+	0.440701i
$5$	−2.00721	+	0.985438i	−0.897654	+	0.440701i
$6$	1.25592	−	1.00156i	0.512725	−	0.408885i
$7$	0.245610	+	0.390886i	0.0928318	+	0.147741i	0.889912	−	0.456133i	$-0.150766\pi$
$7$	0.245610	+	0.390886i	0.0928318	+	0.147741i	−0.797080	+	0.603874i	$0.793623\pi$
$8$	−0.989403	+	2.05452i	−0.349807	+	0.726381i
$9$	−0.900969	−	0.433884i	−0.300323	−	0.144628i
$10$	3.50787	+	0.772717i	1.10928	+	0.244355i
$11$	0.550844	−	1.57422i	0.166086	−	0.474646i	−0.830518	−	0.556992i	$-0.811956\pi$
$11$	0.550844	−	1.57422i	0.166086	−	0.474646i	0.996604	+	0.0823459i	$0.0262412\pi$
$12$	−0.580444			−0.167560
$13$	0.718304	−	2.05280i	0.199222	−	0.569343i	−0.800321	−	0.599571i	$-0.795338\pi$
$13$	0.718304	−	2.05280i	0.199222	−	0.569343i	0.999543	+	0.0302284i	$0.00962346\pi$
$14$	0.0830300	−	0.736912i	0.0221907	−	0.196948i
$15$	−0.514084	−	2.17617i	−0.132736	−	0.561885i
$16$	4.34625	−	2.09304i	1.08656	−	0.523261i
$17$		−	1.28336i		−	0.311260i	−0.987815	−	0.155630i	$-0.950259\pi$
$17$		−	1.28336i		−	0.311260i	0.987815	−	0.155630i	$-0.0497407\pi$
$18$	0.696980	+	1.44729i	0.164280	+	0.341131i
$19$	1.78848	−	2.84635i	0.410306	−	0.652998i	−0.576090	−	0.817386i	$-0.695422\pi$
$19$	1.78848	−	2.84635i	0.410306	−	0.652998i	0.986396	+	0.164389i	$0.0525651\pi$
$20$	−0.816905	−	1.00859i	−0.182665	−	0.225527i
$21$	−0.435739	+	0.152472i	−0.0950860	+	0.0332720i
$22$	−2.26849	+	1.42539i	−0.483644	+	0.303894i
$23$	−0.0824751	+	0.731987i	−0.0171972	+	0.152630i	−0.999376	−	0.0353189i	$-0.988755\pi$
$23$	−0.0824751	+	0.731987i	−0.0171972	+	0.152630i	0.982179	+	0.187949i	$0.0601839\pi$
$24$	−1.78284	−	1.42177i	−0.363921	−	0.290217i
$25$	3.05782	−	3.95597i	0.611565	−	0.791194i
$26$	−2.95813	+	1.85871i	−0.580136	+	0.364524i
$27$	0.623490	−	0.781831i	0.119991	−	0.150464i
$28$	−0.189476	+	0.189476i	−0.0358075	+	0.0358075i
$29$	1.46172	−	5.18299i	0.271435	−	0.962457i
$29$	1.46172	−	5.18299i	0.271435	−	0.962457i
$30$	−1.53392	+	3.24797i	−0.280054	+	0.592996i
$31$	−0.536373	−	4.76044i	−0.0963355	−	0.855001i	−0.945223	−	0.326427i	$-0.894155\pi$
$31$	−0.536373	−	4.76044i	−0.0963355	−	0.855001i	0.848887	−	0.528574i	$-0.177273\pi$
$32$	−3.10849	−	0.709493i	−0.549509	−	0.125422i
$33$	1.41218	+	0.887331i	0.245829	+	0.154464i
$34$	−1.28536	+	1.61179i	−0.220437	+	0.276419i
$35$	−0.878185	−	0.542558i	−0.148440	−	0.0917091i
$36$	0.129161	−	0.565891i	0.0215268	−	0.0943152i
$37$	2.55045	+	1.22823i	0.419291	+	0.201920i	0.631620	−	0.775278i	$-0.282390\pi$
$37$	2.55045	+	1.22823i	0.419291	+	0.201920i	−0.212328	+	0.977198i	$0.568105\pi$
$38$	−5.09697	+	1.78351i	−0.826838	+	0.289323i
$39$	1.84149	+	1.15708i	0.294874	+	0.185282i
$40$	−0.0386545	−	5.09885i	−0.00611181	−	0.806199i
$41$	−3.14762	−	3.14762i	−0.491575	−	0.491575i	0.417227	−	0.908802i	$-0.363002\pi$
$41$	−3.14762	−	3.14762i	−0.491575	−	0.491575i	−0.908802	+	0.417227i	$0.863002\pi$
$42$	0.699960	+	0.244927i	0.108006	+	0.0377930i
$43$	−0.493306	−	0.618587i	−0.0752285	−	0.0943336i	0.742793	−	0.669521i	$-0.233501\pi$
$43$	−0.493306	−	0.618587i	−0.0752285	−	0.0943336i	−0.818022	+	0.575187i	$0.804929\pi$
$44$	0.961986	+	0.108390i	0.145025	+	0.0163404i
$45$	2.23600	−	0.0169512i	0.333324	−	0.00252693i
$46$	0.836710	−	0.836710i	0.123366	−	0.123366i
$47$	6.10419	−	2.93962i	0.890388	−	0.428788i	0.0679799	−	0.997687i	$-0.478345\pi$
$47$	6.10419	−	2.93962i	0.890388	−	0.428788i	0.822408	+	0.568899i	$0.192630\pi$
$48$	1.07343	+	4.70303i	0.154937	+	0.678823i
$49$	2.94472	−	6.11477i	0.420674	−	0.873539i
$50$	−7.80251	+	1.90578i	−1.10344	+	0.269517i
$51$	1.25118	+	0.285574i	0.175200	+	0.0399883i
$52$	1.25444	+	0.141341i	0.173959	+	0.0196005i
$53$	−8.27657	+	0.932546i	−1.13687	+	0.128095i	−0.660274	−	0.751025i	$-0.729560\pi$
$53$	−8.27657	+	0.932546i	−1.13687	+	0.128095i	−0.476601	+	0.879120i	$0.658131\pi$
$54$	−1.56610	+	0.357452i	−0.213119	+	0.0486431i
$55$	0.445636	+	3.70262i	0.0600895	+	0.499262i
$56$	−1.04609	+	0.117866i	−0.139789	+	0.0157505i
$57$	2.37701	+	2.37701i	0.314843	+	0.314843i
$58$	−7.02687	+	5.04539i	−0.922673	+	0.662492i
$59$		−	1.15462i		−	0.150319i	−0.997172	−	0.0751596i	$-0.976053\pi$
$59$		−	1.15462i		−	0.150319i	0.997172	−	0.0751596i	$-0.0239466\pi$
$60$	1.16508	−	0.571992i	0.150411	−	0.0738439i
$61$	−1.11984	−	1.78221i	−0.143380	−	0.228189i	0.767312	−	0.641274i	$-0.221594\pi$
$61$	−1.11984	−	1.78221i	−0.143380	−	0.228189i	−0.910692	+	0.413086i	$0.864451\pi$
$62$	−4.09423	+	6.51592i	−0.519967	+	0.827523i
$63$	−0.0516878	−	0.458742i	−0.00651205	−	0.0577960i
$64$	−2.82199	−	3.53866i	−0.352749	−	0.442333i
$65$	0.581112	+	4.82825i	0.0720781	+	0.598870i
$66$	−0.884863	−	2.52879i	−0.108919	−	0.311273i
$67$	0.587831	+	1.67992i	0.0718150	+	0.205235i	0.974196	−	0.225704i	$-0.0724681\pi$
$67$	0.587831	+	1.67992i	0.0718150	+	0.205235i	−0.902381	+	0.430939i	$0.858182\pi$
$68$	0.726241	−	0.165760i	0.0880696	−	0.0201013i
$69$	−0.695282	−	0.243290i	−0.0837021	−	0.0292886i
$70$	0.559522	+	1.56096i	0.0668757	+	0.186571i
$71$	−2.57968	−	5.35676i	−0.306152	−	0.635731i	0.689958	−	0.723849i	$-0.257629\pi$
$71$	−2.57968	−	5.35676i	−0.306152	−	0.635731i	−0.996110	+	0.0881183i	$0.971915\pi$
$72$	1.78284	−	1.42177i	0.210110	−	0.167557i
$73$	−1.64402	+	1.31106i	−0.192418	+	0.153448i	−0.714960	−	0.699165i	$-0.753555\pi$
$73$	−1.64402	+	1.31106i	−0.192418	+	0.153448i	0.522542	+	0.852614i	$0.324984\pi$
$74$	−1.97300	−	4.09698i	−0.229357	−	0.476265i
$75$	3.17636	+	3.86144i	0.366774	+	0.445881i
$76$	1.84173	+	0.644448i	0.211261	+	0.0739233i
$77$	0.750634	−	0.171327i	0.0855426	−	0.0195245i
$78$	−1.15387	−	3.29756i	−0.130650	−	0.373375i
$79$	1.45049	+	4.14525i	0.163192	+	0.466377i	0.996221	−	0.0868526i	$-0.0276809\pi$
$79$	1.45049	+	4.14525i	0.163192	+	0.466377i	−0.833029	+	0.553230i	$0.813395\pi$
$80$	−6.66129	+	8.48415i	−0.744755	+	0.948557i
$81$	0.623490	+	0.781831i	0.0692766	+	0.0868702i
$82$	0.800617	+	7.10567i	0.0884133	+	0.784690i
$83$	−0.0199234	+	0.0317078i	−0.00218687	+	0.00348039i	−0.847816	−	0.530291i	$-0.822083\pi$
$83$	−0.0199234	+	0.0317078i	−0.00218687	+	0.00348039i	0.845629	+	0.533771i	$0.179226\pi$
$84$	−0.142563	−	0.226887i	−0.0155549	−	0.0247554i
$85$	1.26467	+	2.57597i	0.137173	+	0.279403i
$86$			1.27097i			0.137052i
$87$	4.72778	+	2.57840i	0.506871	+	0.276433i
$88$	2.68926	+	2.68926i	0.286676	+	0.286676i
$89$	10.6349	−	1.19827i	1.12730	−	0.127016i	0.471440	−	0.881898i	$-0.343734\pi$
$89$	10.6349	−	1.19827i	1.12730	−	0.127016i	0.655861	+	0.754882i	$0.272306\pi$
$90$	−2.82521	−	2.21820i	−0.297803	−	0.233819i
$91$	0.978831	−	0.223412i	0.102609	−	0.0234199i
$92$	−0.424877	+	0.0478722i	−0.0442965	+	0.00499102i
$93$	4.76044	+	0.536373i	0.493635	+	0.0556193i
$94$	−10.6106	−	2.42179i	−1.09439	−	0.249788i
$95$	−0.784962	+	7.47567i	−0.0805354	+	0.766988i
$96$	1.38341	−	2.87268i	0.141194	−	0.293192i
$97$	3.17217	+	13.8982i	0.322085	+	1.41115i	0.833835	+	0.552014i	$0.186140\pi$
$97$	3.17217	+	13.8982i	0.322085	+	1.41115i	−0.511750	+	0.859135i	$0.671002\pi$
$98$	−9.82262	+	4.73033i	−0.992235	+	0.477835i
$99$	−1.17932	+	1.17932i	−0.118526	+	0.118526i
$100$	2.63360	+	1.21944i	0.263360	+	0.121944i
$101$	7.54575	+	0.850202i	0.750830	+	0.0845982i	0.479082	−	0.877770i	$-0.340970\pi$
$101$	7.54575	+	0.850202i	0.750830	+	0.0845982i	0.271748	+	0.962368i	$0.412398\pi$
$102$	−1.28536	−	1.61179i	−0.127269	−	0.159591i
$103$	3.38967	+	1.18610i	0.333994	+	0.116870i	0.492066	−	0.870558i	$-0.336242\pi$
$103$	3.38967	+	1.18610i	0.333994	+	0.116870i	−0.158071	+	0.987428i	$0.550528\pi$
$104$	3.50681	+	3.50681i	0.343871	+	0.343871i
$105$	0.724370	−	0.735437i	0.0706913	−	0.0717713i
$106$	11.3287	+	7.11828i	1.10034	+	0.691388i
$107$	15.1730	−	5.30927i	1.46683	−	0.513267i	0.525513	−	0.850785i	$-0.323873\pi$
$107$	15.1730	−	5.30927i	1.46683	−	0.513267i	0.941319	+	0.337519i	$0.109588\pi$
$108$	0.522962	+	0.251845i	0.0503221	+	0.0242338i
$109$	−2.44768	+	10.7240i	−0.234446	+	1.02717i	0.711459	+	0.702728i	$0.248035\pi$
$109$	−2.44768	+	10.7240i	−0.234446	+	1.02717i	−0.945904	+	0.324445i	$0.894822\pi$
$110$	3.14872	−	5.09651i	0.300218	−	0.485934i
$111$	−1.76497	+	2.21320i	−0.167523	+	0.210067i
$112$	1.88562	+	1.18481i	0.178175	+	0.111954i
$113$	−7.80108	−	1.78054i	−0.733864	−	0.167500i	−0.160773	−	0.986991i	$-0.551399\pi$
$113$	−7.80108	−	1.78054i	−0.733864	−	0.167500i	−0.573091	+	0.819492i	$0.694256\pi$
$114$	−0.604608	−	5.36604i	−0.0566267	−	0.502576i
$115$	−0.555782	−	1.55053i	−0.0518270	−	0.144588i
$116$	3.12181	+	0.157737i	0.289852	+	0.0146455i
$117$	−1.53784	+	1.53784i	−0.142174	+	0.142174i
$118$	−1.15642	+	1.45011i	−0.106457	+	0.133493i
$119$	0.501646	−	0.315205i	0.0459858	−	0.0288948i
$120$	4.97961	+	1.09692i	0.454574	+	0.100134i
$121$	6.42540	+	5.12409i	0.584127	+	0.465826i
$122$	−0.378569	+	3.35989i	−0.0342740	+	0.304190i
$123$	3.76911	−	2.36829i	0.339849	−	0.213542i
$124$	2.62462	−	0.918393i	0.235697	−	0.0824741i
$125$	−2.23934	+	10.9538i	−0.200293	+	0.979736i
$126$	−0.394542	+	0.627909i	−0.0351486	+	0.0559386i
$127$	−7.02577	−	14.5892i	−0.623436	−	1.29458i	−0.938425	−	0.345483i	$-0.887715\pi$
$127$	−7.02577	−	14.5892i	−0.623436	−	1.29458i	0.314989	−	0.949095i	$-0.397999\pi$
$128$			13.6475i			1.20628i
$129$	0.712848	−	0.343290i	0.0627628	−	0.0302250i
$130$	4.10595	−	6.64589i	0.360115	−	0.582883i
$131$	1.75953	−	15.6163i	0.153731	−	1.36440i	−0.645677	−	0.763610i	$-0.723425\pi$
$131$	1.75953	−	15.6163i	0.153731	−	1.36440i	0.799408	−	0.600788i	$-0.205147\pi$
$132$	−0.319734	+	0.913748i	−0.0278293	+	0.0795316i
$133$	1.55187			0.134564
$134$	0.944278	−	2.69859i	0.0815732	−	0.233123i
$135$	−0.481031	+	2.18371i	−0.0414006	+	0.187944i
$136$	2.63668	+	1.26976i	0.226093	+	0.108881i
$137$	5.63911	−	11.7097i	0.481782	−	1.00043i	−0.508462	−	0.861084i	$-0.669786\pi$
$137$	5.63911	−	11.7097i	0.481782	−	1.00043i	0.990244	−	0.139345i	$-0.0444999\pi$
$138$	0.629546	+	1.00192i	0.0535905	+	0.0852888i
$139$	−14.4165	+	11.4968i	−1.22280	+	0.975147i	−0.222795	+	0.974865i	$0.571518\pi$
$139$	−14.4165	+	11.4968i	−1.22280	+	0.975147i	−1.00000		0.000281327i	$0.999910\pi$
$140$	0.193602	−	0.567035i	0.0163623	−	0.0479232i
$141$	1.50761	+	6.60527i	0.126964	+	0.556264i
$142$	−2.12525	+	9.31135i	−0.178347	+	0.781391i
$143$	−2.83588	−	2.26154i	−0.237148	−	0.189120i
$144$	−4.82397			−0.401998
$145$	2.17352	+	11.8438i	0.180501	+	0.983575i
$146$	3.37786			0.279554
$147$	5.30620	+	4.23155i	0.437648	+	0.349013i
$148$	−0.365627	+	1.60192i	−0.0300544	+	0.131677i
$149$	0.968527	+	4.24339i	0.0793448	+	0.347632i	0.998981	−	0.0451396i	$-0.0143733\pi$
$149$	0.968527	+	4.24339i	0.0793448	+	0.347632i	−0.919636	+	0.392772i	$0.871516\pi$
$150$	−0.121773	−	8.03096i	−0.00994270	−	0.655725i
$151$	−4.03541	+	3.21813i	−0.328397	+	0.261888i	−0.773783	−	0.633451i	$-0.781638\pi$
$151$	−4.03541	+	3.21813i	−0.328397	+	0.261888i	0.445386	+	0.895339i	$0.353067\pi$
$152$	4.07834	+	6.49065i	0.330797	+	0.526461i
$153$	−0.556828	+	1.15626i	−0.0450168	+	0.0934784i
$154$	−1.11433	−	0.536631i	−0.0897950	−	0.0432430i
$155$	5.76774	+	9.02667i	0.463276	+	0.725040i
$156$	−0.416936	+	1.19153i	−0.0333816	+	0.0953990i
$157$	−16.5396			−1.32001			−0.660004	−	0.751262i	$-0.729445\pi$
$157$	−16.5396			−1.32001			−0.660004	+	0.751262i	$0.729445\pi$
$158$	2.33003	−	6.65883i	0.185367	−	0.529748i
$159$	0.932546	−	8.27657i	0.0739557	−	0.656375i
$160$	6.93858	−	1.63912i	0.548543	−	0.129584i
$161$	−0.306380	+	0.147545i	−0.0241461	+	0.0116282i
$162$		−	1.60638i		−	0.126209i
$163$	−10.0717	−	20.9142i	−0.788878	−	1.63812i	−0.769783	−	0.638305i	$-0.779636\pi$
$163$	−10.0717	−	20.9142i	−0.788878	−	1.63812i	−0.0190949	−	0.999818i	$-0.506078\pi$
$164$	1.37466	−	2.18776i	0.107343	−	0.170835i
$165$	−3.70896	−	0.389449i	−0.288742	−	0.0303185i
$166$	0.0567793	−	0.0198679i	0.00440693	−	0.00154205i
$167$	−15.3240	+	9.62873i	−1.18581	+	0.745093i	−0.972730	−	0.231941i	$-0.925492\pi$
$167$	−15.3240	+	9.62873i	−1.18581	+	0.745093i	−0.213080	+	0.977035i	$0.568349\pi$
$168$	0.117866	−	1.04609i	0.00909354	−	0.0807074i
$169$	6.46580	+	5.15630i	0.497369	+	0.396639i
$170$	0.991672	−	4.50184i	0.0760578	−	0.345276i
$171$	−2.84635	+	1.78848i	−0.217666	+	0.136769i
$172$	0.286337	−	0.359055i	0.0218330	−	0.0273777i
$173$	2.58681	−	2.58681i	0.196671	−	0.196671i	−0.601900	−	0.798571i	$-0.705589\pi$
$173$	2.58681	−	2.58681i	0.196671	−	0.196671i	0.798571	+	0.601900i	$0.205589\pi$
$174$	−3.35527	−	7.97340i	−0.254362	−	0.604462i
$175$	2.29736	+	0.223634i	0.173664	+	0.0169051i
$176$	−0.900809	−	7.99490i	−0.0679010	−	0.602638i
$177$	1.12567	+	0.256928i	0.0846109	+	0.0193119i
$178$	−14.5567	−	9.14659i	−1.09107	−	0.685566i
$179$	−5.20809	+	6.53074i	−0.389271	+	0.488130i	−0.937396	−	0.348266i	$-0.886770\pi$
$179$	−5.20809	+	6.53074i	−0.389271	+	0.488130i	0.548125	+	0.836397i	$0.315342\pi$
$180$	0.298397	+	1.26315i	0.0222412	+	0.0941493i
$181$	0.568624	−	2.49131i	0.0422655	−	0.185177i	−0.949389	−	0.314104i	$-0.898296\pi$
$181$	0.568624	−	2.49131i	0.0422655	−	0.185177i	0.991654	+	0.128927i	$0.0411531\pi$
$182$	−1.45309	−	0.699771i	−0.107710	−	0.0518705i
$183$	1.98671	−	0.695181i	0.146862	−	0.0513893i
$184$	−1.42228	−	0.893676i	−0.104852	−	0.0658827i
$185$	−6.32965	+	0.0479852i	−0.465365	+	0.00352794i
$186$	−5.44151	−	5.44151i	−0.398991	−	0.398991i
$187$	−2.02029	−	0.706929i	−0.147738	−	0.0516958i
$188$	2.45193	+	3.07462i	0.178825	+	0.224240i
$189$	0.458742	+	0.0516878i	0.0333686	+	0.00375973i
$190$	8.47318	−	8.60263i	0.614709	−	0.624100i
$191$	17.5022	−	17.5022i	1.26642	−	1.26642i	0.318490	−	0.947926i	$-0.396824\pi$
$191$	17.5022	−	17.5022i	1.26642	−	1.26642i	0.947926	−	0.318490i	$-0.103176\pi$
$192$	4.07789	−	1.96381i	0.294297	−	0.141726i
$193$	−3.34352	−	14.6489i	−0.240672	−	1.05445i	−0.940407	−	0.340050i	$-0.889556\pi$
$193$	−3.34352	−	14.6489i	−0.240672	−	1.05445i	0.699735	−	0.714402i	$-0.253301\pi$
$194$	9.93589	−	20.6321i	0.713355	−	1.48130i
$195$	−4.83650	−	0.507843i	−0.346349	−	0.0363674i
$196$	3.84064	+	0.876601i	0.274331	+	0.0626144i
$197$	−16.5211	−	1.86148i	−1.17708	−	0.132625i	−0.498323	−	0.866991i	$-0.666051\pi$
$197$	−16.5211	−	1.86148i	−1.17708	−	0.132625i	−0.678753	+	0.734367i	$0.737479\pi$
$198$	2.66229	−	0.299968i	0.189201	−	0.0213178i
$199$	−14.3046	+	3.26493i	−1.01403	+	0.231445i	−0.697076	−	0.716997i	$-0.745516\pi$
$199$	−14.3046	+	3.26493i	−1.01403	+	0.231445i	−0.316950	+	0.948442i	$0.602659\pi$
$200$	5.10219	+	10.1964i	0.360779	+	0.720994i
$201$	−1.76861	+	0.199274i	−0.124748	+	0.0140557i
$202$	−8.62530	−	8.62530i	−0.606874	−	0.606874i
$203$	2.38497	−	0.701625i	0.167392	−	0.0492444i
$204$			0.744917i			0.0521546i
$205$	9.41973	+	3.21616i	0.657903	+	0.224627i
$206$	−3.06920	−	4.88460i	−0.213841	−	0.340326i
$207$	0.391905	−	0.623713i	0.0272392	−	0.0433510i
$208$	−1.17466	−	10.4254i	−0.0814481	−	0.722872i
$209$	−3.49561	−	4.38336i	−0.241797	−	0.303203i
$210$	−1.64633	+	0.198147i	−0.113608	+	0.0136734i
$211$	−8.68105	−	24.8090i	−0.597628	−	1.70792i	−0.700891	−	0.713268i	$-0.747214\pi$
$211$	−8.68105	−	24.8090i	−0.597628	−	1.70792i	0.103264	−	0.994654i	$-0.467071\pi$
$212$	−1.59673	−	4.56319i	−0.109664	−	0.313401i
$213$	5.79649	−	1.32301i	0.397169	−	0.0906513i
$214$	−24.3736	−	8.52869i	−1.66614	−	0.583009i
$215$	1.59975	+	0.755513i	0.109102	+	0.0515256i
$216$	0.989403	+	2.05452i	0.0673203	+	0.139792i
$217$	1.72905	−	1.37887i	0.117376	−	0.0936039i
$218$	13.8148	−	11.0169i	0.935657	−	0.746161i
$219$	−0.912364	−	1.89454i	−0.0616518	−	0.128021i
$220$	−2.03772	+	0.730416i	−0.137383	+	0.0492447i
$221$	−2.63447	−	0.921840i	−0.177214	−	0.0620097i
$222$	4.43330	−	1.01187i	0.297543	−	0.0679123i
$223$	−6.13391	−	17.5297i	−0.410757	−	1.17388i	−0.944581	−	0.328280i	$-0.893531\pi$
$223$	−6.13391	−	17.5297i	−0.410757	−	1.17388i	0.533824	−	0.845596i	$-0.320755\pi$
$224$	−0.486146	−	1.38932i	−0.0324820	−	0.0928281i
$225$	−4.47144	+	2.23747i	−0.298096	+	0.149165i
$226$	8.01417	+	10.0495i	0.533095	+	0.668480i
$227$	−0.570621	−	5.06441i	−0.0378735	−	0.336136i	−0.998333	−	0.0577167i	$-0.981618\pi$
$227$	−0.570621	−	5.06441i	−0.0378735	−	0.336136i	0.960460	−	0.278420i	$-0.0898106\pi$
$228$	−1.03811	+	1.65215i	−0.0687507	+	0.109416i
$229$	7.35635	+	11.7076i	0.486121	+	0.773658i	0.996257	−	0.0864361i	$-0.0275479\pi$
$229$	7.35635	+	11.7076i	0.486121	+	0.773658i	−0.510136	+	0.860094i	$0.670405\pi$
$230$	−0.854930	+	2.50398i	−0.0563724	+	0.165108i
$231$			0.769937i			0.0506582i
$232$	9.20230	+	8.13120i	0.604160	+	0.533839i
$233$	−2.90279	−	2.90279i	−0.190168	−	0.190168i	0.605601	−	0.795769i	$-0.292933\pi$
$233$	−2.90279	−	2.90279i	−0.190168	−	0.190168i	−0.795769	+	0.605601i	$0.792933\pi$
$234$	3.47164	−	0.391160i	0.226948	−	0.0255710i
$235$	−9.35560	+	11.9158i	−0.610292	+	0.777298i
$236$	0.653391	−	0.149132i	0.0425322	−	0.00970769i
$237$	−4.36408	+	0.491714i	−0.283478	+	0.0319403i
$238$	−0.945721	−	0.106557i	−0.0613020	−	0.00690707i
$239$	10.7645	+	2.45692i	0.696297	+	0.158925i	0.555998	−	0.831184i	$-0.312336\pi$
$239$	10.7645	+	2.45692i	0.696297	+	0.158925i	0.140299	+	0.990109i	$0.455193\pi$
$240$	−6.78916	−	8.38218i	−0.438238	−	0.541067i
$241$	−1.39851	+	2.90403i	−0.0900857	+	0.187065i	−0.941144	−	0.338007i	$-0.890247\pi$
$241$	−1.39851	+	2.90403i	−0.0900857	+	0.187065i	0.851058	+	0.525072i	$0.175962\pi$
$242$	−2.93768	−	12.8708i	−0.188842	−	0.827369i
$243$	−0.900969	+	0.433884i	−0.0577972	+	0.0278337i
$244$	0.863898	−	0.863898i	0.0553054	−	0.0553054i
$245$	0.115046	+	15.1755i	0.00735000	+	0.969527i
$246$	−7.10567	−	0.800617i	−0.453041	−	0.0510455i
$247$	−4.55830	−	5.71593i	−0.290038	−	0.363696i
$248$	10.3111	+	3.60801i	0.654755	+	0.229109i
$249$	−0.0264795	−	0.0264795i	−0.00167807	−	0.00167807i
$250$	13.7833	−	11.5142i	0.871732	−	0.728221i
$251$	−12.8028	−	8.04453i	−0.808105	−	0.507766i	0.0634960	−	0.997982i	$-0.479775\pi$
$251$	−12.8028	−	8.04453i	−0.808105	−	0.507766i	−0.871601	+	0.490216i	$0.836918\pi$
$252$	0.252922	−	0.0885013i	0.0159326	−	0.00557505i
$253$	1.10688	+	0.533045i	0.0695889	+	0.0335122i
$254$	−5.78813	+	25.3595i	−0.363180	+	1.59119i
$255$	−2.79280	+	0.659753i	−0.174892	+	0.0413153i
$256$	8.02482	−	10.0628i	0.501551	−	0.628925i
$257$	8.16044	+	5.12755i	0.509034	+	0.319847i	0.761945	−	0.647642i	$-0.224245\pi$
$257$	8.16044	+	5.12755i	0.509034	+	0.319847i	−0.252910	+	0.967490i	$0.581388\pi$
$258$	−1.23910	−	0.282817i	−0.0771431	−	0.0176074i
$259$	0.146317	+	1.29860i	0.00909170	+	0.0806911i
$260$	−2.65721	+	0.952467i	−0.164793	+	0.0590695i
$261$	−3.56578	+	4.03549i	−0.220716	+	0.249791i
$262$	−17.8504	+	17.8504i	−1.10280	+	1.10280i
$263$	8.33537	−	10.4522i	0.513981	−	0.644512i	−0.455338	−	0.890319i	$-0.650482\pi$
$263$	8.33537	−	10.4522i	0.513981	−	0.644512i	0.969319	+	0.245807i	$0.0790530\pi$
$264$	−3.22025	+	2.02342i	−0.198193	+	0.124533i
$265$	15.6939	−	10.0279i	0.964068	−	0.616007i
$266$	−1.94901	−	1.55429i	−0.119502	−	0.0952994i
$267$	−1.19827	+	10.6349i	−0.0733329	+	0.650847i
$268$	−0.874730	+	0.549629i	−0.0534326	+	0.0335739i
$269$	−19.6998	+	6.89326i	−1.20112	+	0.420289i	−0.855360	−	0.518034i	$-0.826664\pi$
$269$	−19.6998	+	6.89326i	−1.20112	+	0.420289i	−0.345758	+	0.938324i	$0.612378\pi$
$270$	2.79125	−	2.26078i	0.169870	−	0.137587i
$271$	−12.3519	+	19.6579i	−0.750324	+	1.19413i	0.225215	+	0.974309i	$0.427691\pi$
$271$	−12.3519	+	19.6579i	−0.750324	+	1.19413i	−0.975539	+	0.219825i	$0.929451\pi$
$272$	−2.68612	−	5.57779i	−0.162870	−	0.338203i
$273$			1.00400i			0.0607650i
$274$	−18.8102	+	9.05853i	−1.13637	+	0.547246i
$275$	−4.54319	−	6.99282i	−0.273965	−	0.421683i
$276$	0.0478722	−	0.424877i	0.00288157	−	0.0255746i
$277$	−3.59837	+	10.2835i	−0.216205	+	0.617878i	−0.999995	−	0.00314781i	$-0.998998\pi$
$277$	−3.59837	+	10.2835i	−0.216205	+	0.617878i	0.783790	+	0.621026i	$0.213284\pi$
$278$	29.6207			1.77653
$279$	−1.58222	+	4.52174i	−0.0947253	+	0.270709i
$280$	1.98357	−	1.26744i	0.118541	−	0.0757438i
$281$	23.1097	+	11.1291i	1.37861	+	0.663904i	0.968703	−	0.248223i	$-0.0798465\pi$
$281$	23.1097	+	11.1291i	1.37861	+	0.663904i	0.409908	+	0.912127i	$0.365561\pi$
$282$	4.72214	−	9.80562i	0.281199	−	0.583916i
$283$	−0.734718	−	1.16930i	−0.0436745	−	0.0695075i	0.824173	−	0.566337i	$-0.191640\pi$
$283$	−0.734718	−	1.16930i	−0.0436745	−	0.0695075i	−0.867848	+	0.496830i	$0.834497\pi$
$284$	2.69815	−	2.15170i	0.160106	−	0.127680i
$285$	−7.11357	−	2.42878i	−0.421372	−	0.143868i
$286$	1.29656	+	5.68061i	0.0766673	+	0.335901i
$287$	0.457273	−	2.00344i	0.0269920	−	0.118260i
$288$	2.49282	+	1.98796i	0.146891	+	0.117141i
$289$	15.3530			0.903117
$290$	9.13252	−	17.0517i	0.536280	−	1.00131i
$291$	−14.2556			−0.835679
$292$	−0.954263	−	0.761000i	−0.0558440	−	0.0445341i
$293$	−6.52341	+	28.5809i	−0.381102	+	1.66972i	0.312933	+	0.949775i	$0.398689\pi$
$293$	−6.52341	+	28.5809i	−0.381102	+	1.66972i	−0.694035	+	0.719941i	$0.744169\pi$
$294$	−2.42599	−	10.6289i	−0.141486	−	0.619893i
$295$	1.13781	+	2.31758i	0.0662458	+	0.134935i
$296$	−5.04684	+	4.02472i	−0.293342	+	0.233932i
$297$	−0.887331	−	1.41218i	−0.0514881	−	0.0819429i
$298$	3.03362	−	6.29938i	0.175733	−	0.364913i
$299$	1.44338	+	0.695093i	0.0834726	+	0.0401983i
$300$	−1.77490	+	2.29622i	−0.102474	+	0.132572i
$301$	0.120636	−	0.344757i	0.00695333	−	0.0198715i
$302$	8.29129			0.477110
$303$	−2.50797	+	7.16737i	−0.144079	+	0.411755i
$304$	1.81565	−	16.1143i	0.104135	−	0.924219i
$305$	4.00401	+	2.47375i	0.229269	+	0.141646i
$306$	1.85740	−	0.894475i	0.106180	−	0.0511337i
$307$			1.49890i			0.0855466i	0.999085	+	0.0427733i	$0.0136193\pi$
$307$			1.49890i			0.0855466i	−0.999085	+	0.0427733i	$0.986381\pi$
$308$	0.193905	+	0.402648i	0.0110488	+	0.0229430i
$309$	−1.91063	+	3.04076i	−0.108692	+	0.172983i
$310$	1.79695	−	17.1135i	0.102060	−	0.971980i
$311$	25.3994	−	8.88763i	1.44027	−	0.503972i	0.506622	−	0.862168i	$-0.330894\pi$
$311$	25.3994	−	8.88763i	1.44027	−	0.503972i	0.933646	+	0.358197i	$0.116608\pi$
$312$	−4.19922	+	2.63855i	−0.237734	+	0.149378i
$313$	1.66320	−	14.7613i	0.0940096	−	0.834359i	−0.854896	−	0.518799i	$-0.826379\pi$
$313$	1.66320	−	14.7613i	0.0940096	−	0.834359i	0.948906	−	0.315560i	$-0.102192\pi$
$314$	20.7724	+	16.5654i	1.17225	+	0.934841i
$315$	0.555810	+	0.869858i	0.0313164	+	0.0490110i
$316$	−2.15842	+	1.35622i	−0.121420	+	0.0762935i
$317$	18.7521	−	23.5144i	1.05322	−	1.32070i	0.108046	−	0.994146i	$-0.465541\pi$
$317$	18.7521	−	23.5144i	1.05322	−	1.32070i	0.945178	−	0.326556i	$-0.105888\pi$
$318$	−9.46068	+	9.46068i	−0.530528	+	0.530528i
$319$	−7.35399	−	5.15610i	−0.411744	−	0.288686i
$320$	9.15147	+	4.32196i	0.511583	+	0.241605i
$321$	1.79984	+	15.9740i	0.100457	+	0.891584i
$322$	0.532562	+	0.121554i	0.0296785	+	0.00677393i
$323$	−3.65288	−	2.29526i	−0.203252	−	0.127712i
$324$	−0.361901	+	0.453810i	−0.0201056	+	0.0252116i
$325$	−5.92435	−	9.11868i	−0.328624	−	0.505813i
$326$	−8.29753	+	36.3538i	−0.459557	+	2.01345i
$327$	−9.91047	−	4.77263i	−0.548050	−	0.263927i
$328$	9.58109	−	3.35257i	0.529027	−	0.185115i
$329$	2.64830	+	1.66404i	0.146006	+	0.0917415i
$330$	4.26808	+	4.20385i	0.234950	+	0.231414i
$331$	−2.74085	−	2.74085i	−0.150651	−	0.150651i	0.627758	−	0.778409i	$-0.283973\pi$
$331$	−2.74085	−	2.74085i	−0.150651	−	0.150651i	−0.778409	+	0.627758i	$0.783973\pi$
$332$	−0.0205165	−	0.00717904i	−0.00112599	−	0.000394001i
$333$	−1.76497	−	2.21320i	−0.0967196	−	0.121282i
$334$	28.8894	+	3.25506i	1.58076	+	0.178109i
$335$	−2.83536	−	2.79270i	−0.154912	−	0.152581i
$336$	−1.57470	+	1.57470i	−0.0859069	+	0.0859069i
$337$	17.7490	−	8.54748i	0.966851	−	0.465611i	0.117288	−	0.993098i	$-0.462580\pi$
$337$	17.7490	−	8.54748i	0.966851	−	0.465611i	0.849563	+	0.527487i	$0.176866\pi$
$338$	−2.95616	−	12.9518i	−0.160794	−	0.704483i
$339$	3.47181	−	7.20928i	0.188563	−	0.391554i
$340$	−1.29437	+	1.04838i	−0.0701973	+	0.0568564i
$341$	−7.78945	−	1.77789i	−0.421823	−	0.0962783i
$342$	5.36604	+	0.604608i	0.290162	+	0.0326935i
$343$	6.32462	−	0.712614i	0.341497	−	0.0384775i
$344$	1.75897	−	0.401474i	0.0948375	−	0.0216461i
$345$	1.63533	−	0.196823i	0.0880430	−	0.0105966i
$346$	−5.83965	+	0.657970i	−0.313941	+	0.0353727i
$347$	−20.7891	−	20.7891i	−1.11602	−	1.11602i	−0.992320	−	0.123699i	$-0.960524\pi$
$347$	−20.7891	−	20.7891i	−1.11602	−	1.11602i	−0.123699	−	0.992320i	$-0.539476\pi$
$348$	−0.848450	+	3.00844i	−0.0454817	+	0.161269i
$349$			13.6232i			0.729234i	0.931157	+	0.364617i	$0.118800\pi$
$349$			13.6232i			0.729234i	−0.931157	+	0.364617i	$0.881200\pi$
$350$	−2.66131	−	2.58181i	−0.142253	−	0.138004i
$351$	−1.15708	−	1.84149i	−0.0617606	−	0.0982914i
$352$	−2.82920	+	4.50264i	−0.150797	+	0.239991i
$353$	3.83320	+	34.0206i	0.204021	+	1.81073i	0.511614	+	0.859216i	$0.329048\pi$
$353$	3.83320	+	34.0206i	0.204021	+	1.81073i	−0.307593	+	0.951518i	$0.599524\pi$
$354$	−1.15642	−	1.45011i	−0.0614632	−	0.0770724i
$355$	10.4567	+	8.21006i	0.554986	+	0.435745i
$356$	2.05171	+	5.86345i	0.108740	+	0.310762i
$357$	0.195675	+	0.559208i	0.0103562	+	0.0295964i
$358$	13.0818	−	2.98584i	0.691397	−	0.157807i
$359$	−5.38162	−	1.88311i	−0.284031	−	0.0993868i	0.184504	−	0.982832i	$-0.440932\pi$
$359$	−5.38162	−	1.88311i	−0.284031	−	0.0993868i	−0.468535	+	0.883445i	$0.655218\pi$
$360$	−2.17748	+	4.61068i	−0.114763	+	0.243004i
$361$	3.34074	+	6.93712i	0.175829	+	0.365112i
$362$	−3.20933	+	2.55936i	−0.168679	+	0.134517i
$363$	−6.42540	+	5.12409i	−0.337246	+	0.268945i
$364$	0.252854	+	0.525056i	0.0132531	+	0.0275204i
$365$	2.00793	−	4.25167i	0.105100	−	0.222543i
$366$	−3.19141	−	1.11672i	−0.166818	−	0.0583720i
$367$	26.6592	−	6.08478i	1.39160	−	0.317623i	0.539931	−	0.841709i	$-0.318450\pi$
$367$	26.6592	−	6.08478i	1.39160	−	0.317623i	0.851665	+	0.524086i	$0.175593\pi$
$368$	1.17362	+	3.35402i	0.0611793	+	0.174840i
$369$	1.47021	+	4.20161i	0.0765359	+	0.218727i
$370$	7.99756	+	6.27925i	0.415774	+	0.326443i
$371$	−2.39733	−	3.00615i	−0.124463	−	0.156072i
$372$	0.311335	+	2.76317i	0.0161420	+	0.143264i
$373$	−5.70593	+	9.08093i	−0.295442	+	0.470193i	−0.961153	−	0.276017i	$-0.910985\pi$
$373$	−5.70593	+	9.08093i	−0.295442	+	0.470193i	0.665711	+	0.746210i	$0.268128\pi$
$374$	1.82928	+	2.91128i	0.0945898	+	0.150539i
$375$	−10.1808	−	4.62064i	−0.525737	−	0.238609i
$376$			15.4496i			0.796753i
$377$	−9.58965	−	6.72358i	−0.493892	−	0.346282i
$378$	−0.524373	−	0.524373i	−0.0269708	−	0.0269708i
$379$	29.3123	−	3.30270i	1.50567	−	0.169648i	0.679753	−	0.733441i	$-0.262087\pi$
$379$	29.3123	−	3.30270i	1.50567	−	0.169648i	0.825916	+	0.563793i	$0.190658\pi$
$380$	−4.33181	+	0.521362i	−0.222217	+	0.0267453i
$381$	15.7868	−	3.60322i	0.808780	−	0.184599i
$382$	−39.5108	+	4.45180i	−2.02155	+	0.227774i
$383$	2.50101	+	0.281796i	0.127795	+	0.0143991i	0.175630	−	0.984456i	$-0.443804\pi$
$383$	2.50101	+	0.281796i	0.127795	+	0.0143991i	−0.0478351	+	0.998855i	$0.515232\pi$
$384$	−13.3053	−	3.03686i	−0.678986	−	0.154974i
$385$	−1.33785	+	1.08359i	−0.0681832	+	0.0552250i
$386$	−10.4726	+	21.7465i	−0.533040	+	1.10687i
$387$	0.176059	+	0.771365i	0.00894958	+	0.0392107i
$388$	−7.45515	+	3.59021i	−0.378478	+	0.182265i
$389$	2.20569	−	2.20569i	0.111833	−	0.111833i	−0.648976	−	0.760809i	$-0.724802\pi$
$389$	2.20569	−	2.20569i	0.111833	−	0.111833i	0.760809	+	0.648976i	$0.224802\pi$
$390$	5.56560	+	5.48185i	0.281825	+	0.277584i
$391$	0.939400	+	0.105845i	0.0475075	+	0.00535281i
$392$	9.64938	+	12.0999i	0.487367	+	0.611139i
$393$	14.8332	+	5.19036i	0.748236	+	0.261819i
$394$	18.8847	+	18.8847i	0.951396	+	0.951396i
$395$	−6.99632	−	6.89104i	−0.352023	−	0.346726i
$396$	−0.819691	−	0.515046i	−0.0411910	−	0.0258820i
$397$	2.98809	−	1.04558i	0.149968	−	0.0524761i	−0.254251	−	0.967138i	$-0.581829\pi$
$397$	2.98809	−	1.04558i	0.149968	−	0.0524761i	0.404219	+	0.914662i	$0.367543\pi$
$398$	21.2354	+	10.2264i	1.06443	+	0.512604i
$399$	−0.345323	+	1.51296i	−0.0172878	+	0.0757426i
$400$	5.01004	−	23.5938i	0.250502	−	1.17969i
$401$	−13.7660	+	17.2621i	−0.687443	+	0.862026i	−0.996016	−	0.0891743i	$-0.971577\pi$
$401$	−13.7660	+	17.2621i	−0.687443	+	0.862026i	0.308573	+	0.951201i	$0.400149\pi$
$402$	2.42081	+	1.52110i	0.120739	+	0.0758653i
$403$	−10.1575	−	2.31838i	−0.505981	−	0.115487i
$404$	0.493495	+	4.37989i	0.0245523	+	0.217908i
$405$	−2.02192	−	0.954893i	−0.100470	−	0.0474490i
$406$	−3.69804	−	1.50751i	−0.183531	−	0.0748163i
$407$	3.33841	−	3.33841i	0.165479	−	0.165479i
$408$	−1.82464	+	2.28802i	−0.0903330	+	0.113274i
$409$	−12.1203	+	7.61567i	−0.599309	+	0.376571i	−0.797255	−	0.603642i	$-0.793716\pi$
$409$	−12.1203	+	7.61567i	−0.599309	+	0.376571i	0.197947	+	0.980213i	$0.436573\pi$
$410$	−8.60921	−	13.4736i	−0.425178	−	0.665416i
$411$	10.1613	+	8.10338i	0.501221	+	0.399710i
$412$	−0.233389	+	2.07138i	−0.0114982	+	0.102050i
$413$	0.451326	−	0.283587i	0.0222083	−	0.0139544i
$414$	−1.11688	+	0.390815i	−0.0548919	+	0.0192075i
$415$	0.00874434	−	0.0832777i	0.000429243	−	0.00408794i
$416$	−3.68929	+	5.87147i	−0.180882	+	0.287872i
$417$	−8.00058	−	16.6134i	−0.391790	−	0.813560i
$418$			9.00619i			0.440507i
$419$	−15.8299	+	7.62329i	−0.773342	+	0.372422i	−0.778565	−	0.627564i	$-0.784052\pi$
$419$	−15.8299	+	7.62329i	−0.773342	+	0.372422i	0.00522248	+	0.999986i	$0.498338\pi$
$420$	0.509738	+	0.314925i	0.0248726	+	0.0153668i
$421$	−2.53478	+	22.4968i	−0.123538	+	1.09643i	0.767041	+	0.641598i	$0.221728\pi$
$421$	−2.53478	+	22.4968i	−0.123538	+	1.09643i	−0.890579	+	0.454829i	$0.849701\pi$
$422$	−13.9450	+	39.8526i	−0.678833	+	1.93999i
$423$	−6.77514			−0.329419
$424$	6.27293	−	17.9270i	0.304641	−	0.870613i
$425$	−5.07692	−	3.92428i	−0.246267	−	0.190355i
$426$	−8.60498	−	4.14394i	−0.416913	−	0.200775i
$427$	0.421598	−	0.875457i	0.0204025	−	0.0423663i
$428$	4.96424	+	7.90054i	0.239955	+	0.381887i
$429$	2.83588	−	2.26154i	0.136918	−	0.109188i
$430$	−1.25246	−	2.55111i	−0.0603990	−	0.123025i
$431$	−6.27398	−	27.4881i	−0.302207	−	1.32406i	−0.866787	−	0.498678i	$-0.833819\pi$
$431$	−6.27398	−	27.4881i	−0.302207	−	1.32406i	0.564580	−	0.825378i	$-0.309038\pi$
$432$	1.07343	−	4.70303i	0.0516457	−	0.226274i
$433$	−6.62344	−	5.28202i	−0.318302	−	0.253838i	0.451284	−	0.892380i	$-0.350966\pi$
$433$	−6.62344	−	5.28202i	−0.318302	−	0.253838i	−0.769586	+	0.638543i	$0.779538\pi$
$434$	−3.55256			−0.170529
$435$	−12.0305	−	0.516471i	−0.576819	−	0.0247629i
$436$	−6.38476			−0.305775
$437$	1.93599	+	1.54390i	0.0926107	+	0.0738546i
$438$	−0.751645	+	3.29317i	−0.0359150	+	0.157354i
$439$	6.37272	+	27.9207i	0.304153	+	1.33258i	0.863793	+	0.503847i	$0.168082\pi$
$439$	6.37272	+	27.9207i	0.304153	+	1.33258i	−0.559640	+	0.828736i	$0.689061\pi$
$440$	−8.04801	−	2.74782i	−0.383674	−	0.130997i
$441$	−5.30620	+	4.23155i	−0.252676	+	0.201503i
$442$	2.38539	+	3.79633i	0.113462	+	0.180573i
$443$	−6.69772	+	13.9080i	−0.318218	+	0.660787i	−0.997313	−	0.0732639i	$-0.976658\pi$
$443$	−6.69772	+	13.9080i	−0.318218	+	0.660787i	0.679094	+	0.734051i	$0.262373\pi$
$444$	−1.48039	−	0.712920i	−0.0702564	−	0.0338337i
$445$	−20.1658	+	12.8853i	−0.955949	+	0.610820i
$446$	−9.85336	+	28.1593i	−0.466570	+	1.33338i
$447$	−4.35252			−0.205867
$448$	0.690105	−	1.97221i	0.0326044	−	0.0931780i
$449$	3.87123	−	34.3581i	0.182695	−	1.62146i	−0.483267	−	0.875473i	$-0.660550\pi$
$449$	3.87123	−	34.3581i	0.182695	−	1.62146i	0.665962	−	0.745986i	$-0.268021\pi$
$450$	7.85670	+	1.66834i	0.370368	+	0.0786461i
$451$	−6.68890	+	3.22120i	−0.314968	+	0.151681i
$452$		−	4.64454i		−	0.218461i
$453$	−2.23949	−	4.65034i	−0.105220	−	0.218492i
$454$	−4.35565	+	6.93198i	−0.204421	+	0.325334i
$455$	−1.74457	+	1.41301i	−0.0817865	+	0.0662430i
$456$	−7.23543	+	2.53179i	−0.338830	+	0.118562i
$457$	25.0063	−	15.7125i	1.16975	−	0.735000i	0.200162	−	0.979763i	$-0.435853\pi$
$457$	25.0063	−	15.7125i	1.16975	−	0.735000i	0.969583	+	0.244763i	$0.0787102\pi$
$458$	2.48686	−	22.0715i	0.116204	−	1.03133i
$459$	−1.00337	−	0.800160i	−0.0468332	−	0.0373483i
$460$	0.805645	−	0.514780i	0.0375634	−	0.0240018i
$461$	−27.1551	+	17.0627i	−1.26474	+	0.794687i	−0.986171	−	0.165730i	$-0.947002\pi$
$461$	−27.1551	+	17.0627i	−1.26474	+	0.794687i	−0.278566	+	0.960417i	$0.589859\pi$
$462$	0.771138	−	0.966976i	0.0358766	−	0.0449878i
$463$	−20.8350	+	20.8350i	−0.968285	+	0.968285i	−0.999512	−	0.0312271i	$-0.990059\pi$
$463$	−20.8350	+	20.8350i	−0.968285	+	0.968285i	0.0312271	+	0.999512i	$0.490059\pi$
$464$	−4.49520	−	25.5860i	−0.208684	−	1.18780i
$465$	−10.0838	+	3.61451i	−0.467625	+	0.167619i
$466$	0.738342	+	6.55296i	0.0342030	+	0.303560i
$467$	7.66787	+	1.75014i	0.354827	+	0.0809868i	0.396219	−	0.918156i	$-0.370322\pi$
$467$	7.66787	+	1.75014i	0.354827	+	0.0809868i	−0.0413922	+	0.999143i	$0.513179\pi$
$468$	−1.06888	−	0.671623i	−0.0494091	−	0.0310458i
$469$	−0.512281	+	0.642380i	−0.0236550	+	0.0296624i
$470$	23.6842	−	5.59499i	1.09247	−	0.258078i
$471$	3.68042	−	16.1250i	0.169585	−	0.742999i
$472$	2.37219	+	1.14239i	0.109189	+	0.0525826i
$473$	−1.24553	+	0.435829i	−0.0572694	+	0.0200394i
$474$	5.97340	+	3.75334i	0.274367	+	0.172396i
$475$	−5.79123	−	15.7788i	−0.265720	−	0.723982i
$476$	0.243165	+	0.243165i	0.0111454	+	0.0111454i
$477$	7.86155	+	2.75088i	0.359956	+	0.125954i
$478$	−11.0585	−	13.8670i	−0.505806	−	0.634260i
$479$	21.4021	+	2.41143i	0.977886	+	0.110181i	0.586416	−	0.810010i	$-0.300538\pi$
$479$	21.4021	+	2.41143i	0.977886	+	0.110181i	0.391469	+	0.920191i	$0.371967\pi$
$480$	0.0540477	+	7.12935i	0.00246693	+	0.325409i
$481$	4.35331	−	4.35331i	0.198494	−	0.198494i
$482$	4.66496	−	2.24653i	0.212483	−	0.102327i
$483$	−0.0756695	−	0.331530i	−0.00344308	−	0.0150851i
$484$	−2.06976	+	4.29791i	−0.0940802	+	0.195360i
$485$	−20.0630	−	24.7707i	−0.911016	−	1.12478i
$486$	1.56610	+	0.357452i	0.0710398	+	0.0162144i
$487$	1.52323	+	0.171627i	0.0690241	+	0.00777715i	0.146409	−	0.989224i	$-0.453228\pi$
$487$	1.52323	+	0.171627i	0.0690241	+	0.00777715i	−0.0773849	+	0.997001i	$0.524657\pi$
$488$	4.76955	−	0.537399i	0.215907	−	0.0243269i
$489$	22.6310	−	5.16537i	1.02341	−	0.233586i
$490$	15.0547	−	19.1744i	0.680101	−	0.866210i
$491$	13.8123	−	1.55627i	0.623339	−	0.0702334i	0.205355	−	0.978688i	$-0.434165\pi$
$491$	13.8123	−	1.55627i	0.623339	−	0.0702334i	0.417984	+	0.908454i	$0.362737\pi$
$492$	1.82702	+	1.82702i	0.0823683	+	0.0823683i
$493$	−6.65162	−	1.87591i	−0.299574	−	0.0844869i
$494$			11.7441i			0.528394i
$495$	1.20500	−	3.52930i	0.0541609	−	0.158630i
$496$	−12.2950	−	19.5674i	−0.552063	−	0.878603i
$497$	1.46029	−	2.32403i	0.0655028	−	0.104247i
$498$	0.00673523	+	0.0597768i	0.000301813	+	0.00267866i
$499$	−0.565417	−	0.709010i	−0.0253115	−	0.0317397i	0.769015	−	0.639231i	$-0.220747\pi$
$499$	−0.565417	−	0.709010i	−0.0253115	−	0.0317397i	−0.794326	+	0.607492i	$0.792176\pi$
$500$	−6.48789	+	0.147577i	−0.290147	+	0.00659984i
$501$	−5.97740	−	17.0824i	−0.267050	−	0.763186i
$502$	8.02215	+	22.9260i	0.358046	+	1.02324i
$503$	10.5163	−	2.40028i	0.468899	−	0.107023i	0.0184588	−	0.999830i	$-0.494124\pi$
$503$	10.5163	−	2.40028i	0.468899	−	0.107023i	0.450441	+	0.892806i	$0.351267\pi$
$504$	0.993632	+	0.347687i	0.0442599	+	0.0154872i
$505$	−15.9838	+	5.72933i	−0.711268	+	0.254952i
$506$	−0.856270	−	1.77806i	−0.0380659	−	0.0790446i
$507$	−6.46580	+	5.15630i	−0.287156	+	0.229000i
$508$	7.34842	−	5.86017i	0.326034	−	0.260003i
$509$	8.55453	+	17.7637i	0.379173	+	0.787360i	0.999994	+	0.00340821i	$0.00108487\pi$
$509$	8.55453	+	17.7637i	0.379173	+	0.787360i	−0.620822	+	0.783952i	$0.713201\pi$
$510$	4.16831	+	1.96856i	0.184576	+	0.0871695i
$511$	−0.916264	−	0.320615i	−0.0405331	−	0.0141832i
$512$	6.45371	−	1.47302i	0.285216	−	0.0650988i
$513$	−1.11027	−	3.17296i	−0.0490195	−	0.140090i
$514$	−5.11328	−	14.6129i	−0.225537	−	0.644549i
$515$	−7.97263	+	0.959560i	−0.351316	+	0.0422833i
$516$	0.286337	+	0.359055i	0.0126053	+	0.0158065i
$517$	−1.26516	−	11.2286i	−0.0556418	−	0.493834i
$518$	1.11686	−	1.77748i	0.0490721	−	0.0780979i
$519$	1.94633	+	3.09757i	0.0854344	+	0.135968i
$520$	−10.4947	−	3.58317i	−0.460221	−	0.157133i
$521$		−	1.27797i		−	0.0559891i	−0.999608	−	0.0279945i	$-0.991088\pi$
$521$		−	1.27797i		−	0.0559891i	0.999608	−	0.0279945i	$-0.00891211\pi$
$522$	8.52011	−	1.49690i	0.372915	−	0.0655173i
$523$	−5.60756	−	5.60756i	−0.245201	−	0.245201i	0.573797	−	0.818998i	$-0.305470\pi$
$523$	−5.60756	−	5.60756i	−0.245201	−	0.245201i	−0.818998	+	0.573797i	$0.805470\pi$
$524$	9.06437	−	1.02131i	0.395979	−	0.0446161i
$525$	−0.729239	+	2.19000i	−0.0318266	+	0.0955795i
$526$	−20.9370	+	4.77874i	−0.912898	+	0.208363i
$527$	−6.10935	+	0.688358i	−0.266127	+	0.0299854i
$528$	7.99490	+	0.900809i	0.347933	+	0.0392027i
$529$	21.8943	+	4.99724i	0.951928	+	0.217271i
$530$	−29.7537	−	3.12421i	−1.29242	−	0.135707i
$531$	−0.500972	+	1.04028i	−0.0217403	+	0.0451443i
$532$	0.200441	+	0.878188i	0.00869020	+	0.0380743i
$533$	−8.72236	+	4.20047i	−0.377808	+	0.181943i
$534$	12.1564	−	12.1564i	0.526061	−	0.526061i
$535$	−25.2236	+	25.6089i	−1.09051	+	1.10717i
$536$	−4.03303	−	0.454414i	−0.174200	−	0.0196277i
$537$	−5.20809	−	6.53074i	−0.224746	−	0.281822i
$538$	31.6453	+	11.0732i	1.36432	+	0.477398i
$539$	−8.00393	−	8.00393i	−0.344754	−	0.344754i
$540$	−1.29788	+	0.00983922i	−0.0558517	+	0.000423413i
$541$	27.9867	+	17.5852i	1.20324	+	0.756047i	0.975995	−	0.217791i	$-0.0698850\pi$
$541$	27.9867	+	17.5852i	1.20324	+	0.756047i	0.227246	+	0.973837i	$0.427028\pi$
$542$	35.2015	−	12.3175i	1.51203	−	0.529084i
$543$	2.30231	+	1.10874i	0.0988017	+	0.0475804i
$544$	−0.910533	+	3.98931i	−0.0390388	+	0.171040i
$545$	−5.65481	−	23.9374i	−0.242226	−	1.02537i
$546$	1.00557	−	1.26094i	0.0430344	−	0.0539634i
$547$	−19.8694	−	12.4848i	−0.849555	−	0.533811i	0.0354613	−	0.999371i	$-0.488710\pi$
$547$	−19.8694	−	12.4848i	−0.849555	−	0.533811i	−0.885016	+	0.465560i	$0.845853\pi$
$548$	7.35479	+	1.67868i	0.314181	+	0.0717098i
$549$	0.235666	+	2.09160i	0.0100580	+	0.0892671i
$550$	−1.29785	+	13.3327i	−0.0553406	+	0.568507i
$551$	−12.1383	−	13.4303i	−0.517110	−	0.572148i
$552$	1.18776	−	1.18776i	0.0505542	−	0.0505542i
$553$	−1.26407	+	1.58509i	−0.0537535	+	0.0674048i
$554$	14.8188	−	9.31128i	0.629591	−	0.395598i
$555$	1.36170	−	6.18163i	0.0578008	−	0.262396i
$556$	−8.36800	−	6.67326i	−0.354882	−	0.283009i
$557$	−2.57215	+	22.8285i	−0.108986	+	0.967274i	0.813585	+	0.581446i	$0.197513\pi$
$557$	−2.57215	+	22.8285i	−0.108986	+	0.967274i	−0.922571	+	0.385828i	$0.873916\pi$
$558$	6.51592	−	4.09423i	0.275841	−	0.173322i
$559$	−1.62418	+	0.568324i	−0.0686953	+	0.0240375i
$560$	−4.95241	−	0.520014i	−0.209278	−	0.0219746i
$561$	1.13876	−	1.81233i	0.0480786	−	0.0765166i
$562$	−17.8775	−	37.1229i	−0.754115	−	1.56594i
$563$			7.75167i			0.326694i	0.986569	+	0.163347i	$0.0522290\pi$
$563$			7.75167i			0.326694i	−0.986569	+	0.163347i	$0.947771\pi$
$564$	−3.54314	+	1.70629i	−0.149193	+	0.0718477i
$565$	17.4131	−	4.11354i	0.732573	−	0.173058i
$566$	−0.248377	+	2.20440i	−0.0104400	+	0.0926580i
$567$	−0.152472	+	0.435739i	−0.00640320	+	0.0182993i
$568$	13.5579			0.568877
$569$	8.67905	−	24.8033i	0.363845	−	1.03981i	−0.605869	−	0.795564i	$-0.707175\pi$
$569$	8.67905	−	24.8033i	0.363845	−	1.03981i	0.969714	−	0.244244i	$-0.0785398\pi$
$570$	6.50148	+	10.1750i	0.272317	+	0.426184i
$571$	−27.5818	−	13.2827i	−1.15426	−	0.555863i	−0.243951	−	0.969788i	$-0.578444\pi$
$571$	−27.5818	−	13.2827i	−1.15426	−	0.555863i	−0.910311	+	0.413924i	$0.864158\pi$
$572$	0.913501	−	1.89690i	0.0381954	−	0.0793135i
$573$	13.1688	+	20.9580i	0.550134	+	0.875534i
$574$	−2.58087	+	2.05817i	−0.107723	+	0.0859064i
$575$	2.64352	+	2.56455i	0.110243	+	0.106949i
$576$	1.00716	+	4.41264i	0.0419649	+	0.183860i
$577$	−0.569014	+	2.49301i	−0.0236884	+	0.103785i	−0.985390	−	0.170313i	$-0.945522\pi$
$577$	−0.569014	+	2.49301i	−0.0236884	+	0.103785i	0.961702	+	0.274098i	$0.0883793\pi$
$578$	−19.2821	−	15.3769i	−0.802028	−	0.639596i
$579$	15.0256			0.624444
$580$	−6.42158	+	2.75973i	−0.266641	+	0.114592i
$581$	−0.0172875			−0.000717207
$582$	17.9038	+	14.2778i	0.742138	+	0.591836i
$583$	−3.09107	+	13.5429i	−0.128019	+	0.560888i
$584$	−1.06700	−	4.67484i	−0.0441528	−	0.193446i
$585$	1.57133	−	4.60223i	0.0649666	−	0.190279i
$586$	36.8184	−	29.3617i	1.52095	−	1.21292i
$587$	−3.29819	−	5.24903i	−0.136131	−	0.216651i	0.771701	−	0.635986i	$-0.219406\pi$
$587$	−3.29819	−	5.24903i	−0.136131	−	0.216651i	−0.907832	+	0.419335i	$0.862263\pi$
$588$	−1.70925	+	3.54928i	−0.0704881	+	0.146370i
$589$	−14.5092	−	6.98726i	−0.597841	−	0.287905i
$590$	0.892198	−	4.05026i	0.0367312	−	0.166747i
$591$	5.49108	−	15.6926i	0.225873	−	0.645508i
$592$	13.6556			0.561243
$593$	7.44539	−	21.2777i	0.305746	−	0.873771i	−0.683815	−	0.729655i	$-0.739681\pi$
$593$	7.44539	−	21.2777i	0.305746	−	0.873771i	0.989561	−	0.144116i	$-0.0460337\pi$
$594$	−0.299968	+	2.66229i	−0.0123078	+	0.109235i
$595$	−0.696296	+	1.12702i	−0.0285453	+	0.0462035i
$596$	−2.27620	+	1.09616i	−0.0932370	+	0.0449006i
$597$		−	14.6725i		−	0.600504i
$598$	−1.11658	−	2.31861i	−0.0456604	−	0.0948148i
$599$	−12.3815	+	19.7050i	−0.505894	+	0.805126i	−0.997853	−	0.0654922i	$-0.979138\pi$
$599$	−12.3815	+	19.7050i	−0.505894	+	0.805126i	0.491959	+	0.870619i	$0.336281\pi$
$600$	−11.0761	+	2.70535i	−0.452180	+	0.110446i
$601$	−3.62932	+	1.26996i	−0.148043	+	0.0518026i	−0.403283	−	0.915075i	$-0.632131\pi$
$601$	−3.62932	+	1.26996i	−0.148043	+	0.0518026i	0.255240	+	0.966878i	$0.417845\pi$
$602$	−0.496803	+	0.312162i	−0.0202482	+	0.0127228i
$603$	0.199274	−	1.76861i	0.00811508	−	0.0720234i
$604$	−2.34233	−	1.86795i	−0.0953082	−	0.0760057i
$605$	−17.9466	−	3.95331i	−0.729634	−	0.160725i
$606$	10.3284	−	6.48973i	0.419561	−	0.263627i
$607$	7.33257	−	9.19475i	0.297620	−	0.373204i	−0.610427	−	0.792073i	$-0.709002\pi$
$607$	7.33257	−	9.19475i	0.297620	−	0.373204i	0.908047	+	0.418869i	$0.137573\pi$
$608$	−7.57895	+	7.57895i	−0.307367	+	0.307367i
$609$	0.153328	+	2.48130i	0.00621318	+	0.100547i
$610$	−2.55109	−	7.11708i	−0.103291	−	0.288162i
$611$	−1.64978	−	14.6422i	−0.0667429	−	0.592360i
$612$	−0.726241	−	0.165760i	−0.0293565	−	0.00670044i
$613$	9.52083	+	5.98234i	0.384543	+	0.241624i	0.710405	−	0.703793i	$-0.248512\pi$
$613$	9.52083	+	5.98234i	0.384543	+	0.241624i	−0.325862	+	0.945417i	$0.605655\pi$
$614$	1.50123	−	1.88249i	0.0605849	−	0.0759710i
$615$	−5.23162	+	8.46789i	−0.210959	+	0.341458i
$616$	−0.390684	+	1.71170i	−0.0157411	+	0.0689664i
$617$	38.5976	+	18.5876i	1.55388	+	0.748310i	0.996630	−	0.0820327i	$-0.0261412\pi$
$617$	38.5976	+	18.5876i	1.55388	+	0.748310i	0.557253	+	0.830343i	$0.311855\pi$
$618$	5.44509	−	1.90532i	0.219034	−	0.0766432i
$619$	11.1644	+	7.01508i	0.448737	+	0.281960i	0.737382	−	0.675476i	$-0.236062\pi$
$619$	11.1644	+	7.01508i	0.448737	+	0.281960i	−0.288645	+	0.957436i	$0.593205\pi$
$620$	−4.36315	+	4.42981i	−0.175228	+	0.177905i
$621$	0.520868	+	0.520868i	0.0209017	+	0.0209017i
$622$	−40.8010	−	14.2769i	−1.63597	−	0.572451i
$623$	3.08043	+	3.86274i	0.123415	+	0.154757i
$624$	10.4254	+	1.17466i	0.417350	+	0.0470241i
$625$	−6.29943	−	24.1933i	−0.251977	−	0.967733i
$626$	−16.8732	+	16.8732i	−0.674387	+	0.674387i
$627$	5.05131	−	2.43258i	0.201730	−	0.0971480i
$628$	−2.13628	−	9.35964i	−0.0852467	−	0.373490i
$629$	1.57626	−	3.27314i	0.0628496	−	0.130509i
$630$	0.173164	−	1.64915i	0.00689902	−	0.0657035i
$631$	35.8100	+	8.17341i	1.42557	+	0.325378i	0.864603	−	0.502456i	$-0.167570\pi$
$631$	35.8100	+	8.17341i	1.42557	+	0.325378i	0.560972	+	0.827835i	$0.310427\pi$
$632$	−9.95160	−	1.12128i	−0.395853	−	0.0446020i
$633$	26.1187	−	2.94287i	1.03813	−	0.116969i
$634$	−47.1022	+	10.7508i	−1.87067	+	0.426967i
$635$	28.4789	+	22.3601i	1.13015	+	0.887334i
$636$	4.80409	−	0.541291i	0.190495	−	0.0214636i
$637$	−10.4372	−	10.4372i	−0.413536	−	0.413536i
$638$	4.07186	+	13.8411i	0.161206	+	0.547974i
$639$			5.94556i			0.235203i
$640$	−13.4488	−	27.3935i	−0.531610	−	1.08282i
$641$	1.89036	+	3.00849i	0.0746648	+	0.118828i	0.881970	−	0.471306i	$-0.156217\pi$
$641$	1.89036	+	3.00849i	0.0746648	+	0.118828i	−0.807305	+	0.590135i	$0.799075\pi$
$642$	13.7385	−	21.8647i	0.542215	−	0.862930i
$643$	4.77401	+	42.3705i	0.188269	+	1.67093i	0.632151	+	0.774845i	$0.282172\pi$
$643$	4.77401	+	42.3705i	0.188269	+	1.67093i	−0.443882	+	0.896085i	$0.646399\pi$
$644$	−0.123067	−	0.154321i	−0.00484950	−	0.00608109i
$645$	−1.09255	+	1.39152i	−0.0430191	+	0.0547912i
$646$	2.28887	+	6.54123i	0.0900546	+	0.257361i
$647$	7.60075	+	21.7217i	0.298816	+	0.853968i	0.991192	+	0.132431i	$0.0422783\pi$
$647$	7.60075	+	21.7217i	0.298816	+	0.853968i	−0.692376	+	0.721537i	$0.743436\pi$
$648$	−2.22317	+	0.507423i	−0.0873343	+	0.0199335i
$649$	−1.81763	−	0.636017i	−0.0713484	−	0.0249659i
$650$	−1.69241	+	17.3859i	−0.0663816	+	0.681930i
$651$	0.959551	+	1.99253i	0.0376078	+	0.0780933i
$652$	10.5343	−	8.40080i	0.412554	−	0.329001i
$653$	−17.5868	+	14.0250i	−0.688223	+	0.548839i	−0.903963	−	0.427612i	$-0.859355\pi$
$653$	−17.5868	+	14.0250i	−0.688223	+	0.548839i	0.215740	+	0.976451i	$0.430784\pi$
$654$	7.66664	+	15.9199i	0.299789	+	0.622519i
$655$	11.8571	+	33.0791i	0.463295	+	1.29251i
$656$	−20.2684	−	7.09223i	−0.791350	−	0.276905i
$657$	2.05006	−	0.467913i	0.0799805	−	0.0182550i
$658$	−1.65941	−	4.74233i	−0.0646906	−	0.184875i
$659$	−11.8626	−	33.9013i	−0.462100	−	1.32061i	−0.905525	−	0.424294i	$-0.860522\pi$
$659$	−11.8626	−	33.9013i	−0.462100	−	1.32061i	0.443425	−	0.896312i	$-0.353763\pi$
$660$	−0.258667	−	2.14917i	−0.0100686	−	0.0836562i
$661$	−5.75815	−	7.22049i	−0.223966	−	0.280845i	0.657135	−	0.753773i	$-0.271768\pi$
$661$	−5.75815	−	7.22049i	−0.223966	−	0.280845i	−0.881101	+	0.472929i	$0.843197\pi$
$662$	0.697152	+	6.18740i	0.0270956	+	0.240480i
$663$	1.48495	−	2.36329i	0.0576708	−	0.0917825i
$664$	−0.0454320	−	0.0723047i	−0.00176310	−	0.00280597i
$665$	−3.11493	+	1.52927i	−0.120792	+	0.0593025i
$666$			4.54731i			0.176205i
$667$	3.67332	+	1.49743i	0.142232	+	0.0579807i
$668$	−7.42808	−	7.42808i	−0.287401	−	0.287401i
$669$	18.4551	−	2.07939i	0.713516	−	0.0803940i
$670$	0.763926	+	6.34718i	0.0295130	+	0.245213i
$671$	−3.42245	+	0.781152i	−0.132122	+	0.0301560i
$672$	1.46267	−	0.164803i	0.0564237	−	0.00635742i
$673$	30.1879	+	3.40136i	1.16366	+	0.131113i	0.672595	−	0.740011i	$-0.265180\pi$
$673$	30.1879	+	3.40136i	1.16366	+	0.131113i	0.491063	+	0.871124i	$0.336608\pi$
$674$	−30.8521	−	7.04179i	−1.18838	−	0.271240i
$675$	−1.18638	−	4.85721i	−0.0456639	−	0.186954i
$676$	−2.08278	+	4.32494i	−0.0801069	+	0.166344i
$677$	−1.89641	−	8.30873i	−0.0728851	−	0.319330i	0.925322	−	0.379182i	$-0.123794\pi$
$677$	−1.89641	−	8.30873i	−0.0728851	−	0.319330i	−0.998207	+	0.0598513i	$0.980937\pi$
$678$	−11.5808	+	5.57703i	−0.444758	+	0.214184i
$679$	−4.65349	+	4.65349i	−0.178585	+	0.178585i
$680$	−6.54364	+	0.0496075i	−0.250937	+	0.00190236i
$681$	5.06441	+	0.570621i	0.194068	+	0.0218663i
$682$	8.00223	+	10.0345i	0.306421	+	0.384240i
$683$	19.8741	+	6.95424i	0.760461	+	0.266097i	0.682525	−	0.730862i	$-0.260882\pi$
$683$	19.8741	+	6.95424i	0.760461	+	0.266097i	0.0779351	+	0.996958i	$0.475167\pi$
$684$	−1.37972	−	1.37972i	−0.0527550	−	0.0527550i
$685$	0.220311	+	29.0609i	0.00841767	+	1.11036i
$686$	−8.65691	−	5.43950i	−0.330523	−	0.207681i
$687$	−13.0510	+	4.56673i	−0.497926	+	0.174232i
$688$	−3.43876	−	1.65602i	−0.131102	−	0.0631352i
$689$	−4.03077	+	17.6600i	−0.153560	+	0.672791i
$690$	−2.25096	−	1.39068i	−0.0856926	−	0.0529424i
$691$	6.40182	−	8.02763i	0.243537	−	0.305385i	−0.645008	−	0.764176i	$-0.723146\pi$
$691$	6.40182	−	8.02763i	0.243537	−	0.305385i	0.888544	+	0.458791i	$0.151717\pi$
$692$	1.79797	+	1.12974i	0.0683484	+	0.0429461i
$693$	−0.750634	−	0.171327i	−0.0285142	−	0.00650818i
$694$	5.28785	+	46.9309i	0.200724	+	1.78147i
$695$	17.6077	−	37.2832i	0.667898	−	1.41423i
$696$	−9.97503	+	7.16221i	−0.378103	+	0.271483i
$697$	−4.03952	+	4.03952i	−0.153008	+	0.153008i
$698$	13.6445	−	17.1096i	0.516451	−	0.647609i
$699$	3.47594	−	2.18408i	0.131472	−	0.0826093i
$700$	0.170177	+	1.32894i	0.00643210	+	0.0502293i
$701$	3.01629	+	2.40541i	0.113924	+	0.0908511i	0.678795	−	0.734328i	$-0.262503\pi$
$701$	3.01629	+	2.40541i	0.113924	+	0.0908511i	−0.564871	+	0.825179i	$0.691074\pi$
$702$	−0.391160	+	3.47164i	−0.0147634	+	0.131029i
$703$	8.05741	−	5.06281i	0.303891	−	0.190947i
$704$	−7.12512	+	2.49319i	−0.268538	+	0.0939655i
$705$	−9.53518	−	11.7725i	−0.359116	−	0.443380i
$706$	29.2595	−	46.5662i	1.10119	−	1.75254i
$707$	1.52098	+	3.15834i	0.0572023	+	0.118782i
$708$			0.670195i			0.0251875i
$709$	24.3970	−	11.7490i	0.916250	−	0.441243i	0.0845193	−	0.996422i	$-0.473065\pi$
$709$	24.3970	−	11.7490i	0.916250	−	0.441243i	0.831731	+	0.555179i	$0.187350\pi$
$710$	−4.90991	−	20.7842i	−0.184266	−	0.780016i
$711$	0.491714	−	4.36408i	0.0184407	−	0.163666i
$712$	−8.06037	+	23.0352i	−0.302075	+	0.863281i
$713$	3.52882			0.132155
$714$	0.314328	−	0.898299i	0.0117634	−	0.0336180i
$715$	7.92083	+	1.74481i	0.296222	+	0.0652522i
$716$	−4.36837	−	2.10370i	−0.163254	−	0.0786188i
$717$	−4.79065	+	9.94789i	−0.178910	+	0.371511i
$718$	4.87282	+	7.75504i	0.181852	+	0.289416i
$719$	0.425593	−	0.339399i	0.0158719	−	0.0126575i	−0.615522	−	0.788120i	$-0.711055\pi$
$719$	0.425593	−	0.339399i	0.0158719	−	0.0126575i	0.631394	+	0.775462i	$0.282483\pi$
$720$	9.68275	−	4.75373i	0.360855	−	0.177161i
$721$	0.368908	+	1.61629i	0.0137389	+	0.0601938i
$722$	2.75225	−	12.0584i	0.102428	−	0.448767i
$723$	−2.52002	−	2.00965i	−0.0937206	−	0.0747397i
$724$	1.48325			0.0551246
$725$	−16.0341	−	21.6312i	−0.595490	−	0.803363i
$726$	13.2018			0.489966
$727$	2.35799	+	1.88044i	0.0874532	+	0.0697416i	0.666240	−	0.745737i	$-0.267902\pi$
$727$	2.35799	+	1.88044i	0.0874532	+	0.0697416i	−0.578787	+	0.815479i	$0.696474\pi$
$728$	−0.509455	+	2.23207i	−0.0188817	+	0.0827259i
$729$	−0.222521	−	0.974928i	−0.00824152	−	0.0361084i
$730$	−6.78009	+	3.32867i	−0.250943	+	0.123200i
$731$	−0.793867	+	0.633088i	−0.0293622	+	0.0234156i
$732$	0.650003	+	1.03447i	0.0240248	+	0.0382353i
$733$	−2.69671	+	5.59978i	−0.0996053	+	0.206833i	−0.944817	−	0.327600i	$-0.893760\pi$
$733$	−2.69671	+	5.59978i	−0.0996053	+	0.206833i	0.845211	+	0.534432i	$0.179475\pi$
$734$	−39.5759	−	19.0588i	−1.46077	−	0.703471i
$735$	−14.8206	−	3.26470i	−0.546667	−	0.120420i
$736$	0.775713	−	2.21686i	0.0285932	−	0.0817146i
$737$	2.96838			0.109342
$738$	2.36170	−	6.74936i	0.0869355	−	0.248447i
$739$	2.56627	−	22.7763i	0.0944019	−	0.837840i	−0.853893	−	0.520449i	$-0.825765\pi$
$739$	2.56627	−	22.7763i	0.0944019	−	0.837840i	0.948295	−	0.317391i	$-0.102807\pi$
$740$	−0.844698	−	3.57570i	−0.0310517	−	0.131445i
$741$	6.58694	−	3.17210i	0.241977	−	0.116530i
$742$			6.17654i			0.226748i
$743$	−7.09238	−	14.7275i	−0.260194	−	0.540299i	0.729417	−	0.684070i	$-0.239792\pi$
$743$	−7.09238	−	14.7275i	−0.260194	−	0.540299i	−0.989611	+	0.143771i	$0.954077\pi$
$744$	−5.81198	+	9.24972i	−0.213078	+	0.339111i
$745$	−6.12564	−	7.56298i	−0.224426	−	0.277086i
$746$	16.2613	−	5.69006i	0.595367	−	0.208328i
$747$	0.0317078	−	0.0199234i	0.00116013	−	0.000728958i
$748$	0.139103	−	1.23457i	0.00508610	−	0.0451404i
$749$	5.80196	+	4.62691i	0.211999	+	0.169064i
$750$	8.15844	+	15.9999i	0.297904	+	0.584232i
$751$	−19.2066	+	12.0683i	−0.700861	+	0.440380i	−0.834759	−	0.550615i	$-0.814393\pi$
$751$	−19.2066	+	12.0683i	−0.700861	+	0.440380i	0.133899	+	0.990995i	$0.457250\pi$
$752$	20.3776	−	25.5527i	0.743094	−	0.931810i
$753$	10.6917	−	10.6917i	0.389628	−	0.389628i
$754$	5.30972	+	18.0489i	0.193369	+	0.657300i
$755$	4.92867	−	10.4361i	0.179373	−	0.379810i
$756$	0.0300019	+	0.266274i	0.00109116	+	0.00968430i
$757$	−17.7165	−	4.04369i	−0.643919	−	0.146970i	−0.111922	−	0.993717i	$-0.535701\pi$
$757$	−17.7165	−	4.04369i	−0.643919	−	0.146970i	−0.531996	+	0.846747i	$0.678558\pi$
$758$	−40.1216	−	25.2100i	−1.45728	−	0.915670i
$759$	−0.765984	+	0.960513i	−0.0278034	+	0.0348644i
$760$	−14.5822	−	9.00917i	−0.528954	−	0.326797i
$761$	3.81598	−	16.7189i	0.138329	−	0.606060i	−0.857473	−	0.514529i	$-0.827967\pi$
$761$	3.81598	−	16.7189i	0.138329	−	0.606060i	0.995802	−	0.0915308i	$-0.0291760\pi$
$762$	−23.4357	−	11.2860i	−0.848985	−	0.408850i
$763$	−4.79303	+	1.67715i	−0.173519	+	0.0607171i
$764$	12.1650	+	7.64375i	0.440113	+	0.276541i
$765$	−0.0217544	−	2.86959i	−0.000786532	−	0.103750i
$766$	−2.85882	−	2.85882i	−0.103293	−	0.103293i
$767$	−2.37021	−	0.829371i	−0.0855831	−	0.0299468i
$768$	8.02482	+	10.0628i	0.289571	+	0.363110i
$769$	34.2837	+	3.86284i	1.23630	+	0.139298i	0.705815	−	0.708396i	$-0.250581\pi$
$769$	34.2837	+	3.86284i	1.23630	+	0.139298i	0.530486	+	0.847694i	$0.322009\pi$
$770$	2.76551	−	0.0209654i	0.0996621	−	0.000755540i
$771$	−6.81486	+	6.81486i	−0.245431	+	0.245431i
$772$	7.85784	−	3.78414i	0.282810	−	0.136194i
$773$	1.17946	+	5.16754i	0.0424221	+	0.185863i	0.991700	−	0.128576i	$-0.0410406\pi$
$773$	1.17946	+	5.16754i	0.0424221	+	0.185863i	−0.949278	+	0.314439i	$0.898183\pi$
$774$	0.551452	−	1.14510i	0.0198215	−	0.0411599i
$775$	−20.4723	−	12.4347i	−0.735387	−	0.446668i
$776$	−31.6926	−	7.23363i	−1.13770	−	0.259672i
$777$	−1.29860	−	0.146317i	−0.0465870	−	0.00524910i
$778$	−4.97928	+	0.561030i	−0.178516	+	0.0201139i
$779$	−14.5887	+	3.32977i	−0.522694	+	0.119301i
$780$	−0.337303	−	2.80253i	−0.0120774	−	0.100347i
$781$	−9.85374	+	1.11025i	−0.352595	+	0.0397279i
$782$	−1.07380	−	1.07380i	−0.0383989	−	0.0383989i
$783$	−3.14085	−	4.37436i	−0.112245	−	0.156327i
$784$		−	32.7397i		−	1.16928i
$785$	33.1986	−	16.2988i	1.18491	−	0.581729i
$786$	−13.4308	−	21.3750i	−0.479060	−	0.762420i
$787$	−2.11475	+	3.36561i	−0.0753827	+	0.119971i	−0.882288	−	0.470710i	$-0.843998\pi$
$787$	−2.11475	+	3.36561i	−0.0753827	+	0.119971i	0.806905	+	0.590681i	$0.201141\pi$
$788$	−1.08048	−	9.58955i	−0.0384906	−	0.341614i
$789$	8.33537	+	10.4522i	0.296747	+	0.372109i
$790$	1.88500	+	15.6618i	0.0670654	+	0.557222i
$791$	−1.22003	−	3.48665i	−0.0433793	−	0.123971i
$792$	−1.25611	−	3.58976i	−0.0446340	−	0.127557i
$793$	−4.46290	+	1.01863i	−0.158482	+	0.0361725i
$794$	−4.80000	−	1.67959i	−0.170346	−	0.0596065i
$795$	6.28423	+	17.5318i	0.222879	+	0.621790i
$796$	−3.69519	−	7.67315i	−0.130973	−	0.271967i
$797$	−41.9284	+	33.4368i	−1.48518	+	1.18439i	−0.547544	+	0.836777i	$0.684437\pi$
$797$	−41.9284	+	33.4368i	−1.48518	+	1.18439i	−0.937637	+	0.347616i	$0.886991\pi$
$798$	1.94901	−	1.55429i	0.0689943	−	0.0550211i
$799$	−3.77258	−	7.83385i	−0.133464	−	0.277142i
$800$	−12.3120	+	10.1276i	−0.435294	+	0.358065i
$801$	−10.1017	−	3.53472i	−0.356924	−	0.124893i
$802$	34.5780	−	7.89219i	1.22099	−	0.278683i
$803$	1.15831	+	3.31025i	0.0408757	+	0.116816i
$804$	−0.341203	−	0.975103i	−0.0120333	−	0.0343892i
$805$	0.469574	−	0.598072i	0.0165503	−	0.0210793i
$806$	10.4350	+	13.0850i	0.367556	+	0.460900i
$807$	−2.33681	−	20.7398i	−0.0822597	−	0.730075i
$808$	−9.21254	+	14.6617i	−0.324096	+	0.515796i
$809$	−28.9709	−	46.1069i	−1.01856	−	1.62103i	−0.754243	−	0.656596i	$-0.771996\pi$
$809$	−28.9709	−	46.1069i	−1.01856	−	1.62103i	−0.264318	−	0.964435i	$-0.585147\pi$
$810$	1.58298	+	3.22434i	0.0556204	+	0.113292i
$811$		−	0.191938i		−	0.00673987i	−0.999994	−	0.00336993i	$-0.998927\pi$
$811$		−	0.191938i		−	0.00673987i	0.999994	−	0.00336993i	$-0.00107269\pi$
$812$	0.705089	+	1.25901i	0.0247438	+	0.0441826i
$813$	−16.4165	−	16.4165i	−0.575752	−	0.575752i
$814$	−7.53638	+	0.849146i	−0.264150	+	0.0297625i
$815$	40.8257	+	32.0541i	1.43006	+	1.12281i
$816$	6.03566	−	1.37760i	0.211290	−	0.0482256i
$817$	−2.64298	+	0.297793i	−0.0924663	+	0.0104184i
$818$	22.8496	+	2.57453i	0.798917	+	0.0900163i
$819$	−0.978831	−	0.223412i	−0.0342031	−	0.00780664i
$820$	−0.603337	+	5.74595i	−0.0210695	+	0.200657i
$821$	−19.1941	+	39.8569i	−0.669878	+	1.39102i	0.237785	+	0.971318i	$0.423579\pi$
$821$	−19.1941	+	39.8569i	−0.669878	+	1.39102i	−0.907663	+	0.419699i	$0.862136\pi$
$822$	−4.64574	−	20.3543i	−0.162039	−	0.709939i
$823$	8.37070	−	4.03112i	0.291784	−	0.140516i	−0.282265	−	0.959336i	$-0.591086\pi$
$823$	8.37070	−	4.03112i	0.291784	−	0.140516i	0.574050	+	0.818820i	$0.305372\pi$
$824$	−5.79061	+	5.79061i	−0.201725	+	0.201725i
$825$	7.82845	−	2.87324i	0.272552	−	0.100033i
$826$	−0.850856	−	0.0958684i	−0.0296051	−	0.00333569i
$827$	16.8200	+	21.0917i	0.584890	+	0.733429i	0.982938	−	0.183935i	$-0.0588837\pi$
$827$	16.8200	+	21.0917i	0.584890	+	0.733429i	−0.398048	+	0.917365i	$0.630312\pi$
$828$	0.403572	+	0.141216i	0.0140251	+	0.00490760i
$829$	26.0093	+	26.0093i	0.903341	+	0.903341i	0.995724	−	0.0923826i	$-0.0294483\pi$
$829$	26.0093	+	26.0093i	0.903341	+	0.903341i	−0.0923826	+	0.995724i	$0.529448\pi$
$830$	−0.0943897	+	0.0958318i	−0.00327631	+	0.00332637i
$831$	−9.22500	−	5.79645i	−0.320012	−	0.201077i
$832$	−9.29120	+	3.25113i	−0.322114	+	0.112713i
$833$	−7.84743	−	3.77912i	−0.271897	−	0.130939i
$834$	−6.59122	+	28.8780i	−0.228235	+	0.999965i
$835$	21.2701	−	34.4278i	0.736083	−	1.19142i
$836$	2.02901	−	2.54430i	0.0701748	−	0.0879964i
$837$	−4.05629	−	2.54873i	−0.140206	−	0.0880972i
$838$	27.5162	+	6.28040i	0.950532	+	0.216953i
$839$	1.73771	+	15.4226i	0.0599924	+	0.532447i	0.987383	+	0.158352i	$0.0506180\pi$
$839$	1.73771	+	15.4226i	0.0599924	+	0.532447i	−0.927390	+	0.374095i	$0.877953\pi$
$840$	0.794273	+	2.21587i	0.0274050	+	0.0764548i
$841$	−24.7267	−	15.1522i	−0.852646	−	0.522490i
$842$	25.7153	−	25.7153i	0.886209	−	0.886209i
$843$	−15.9924	+	20.0539i	−0.550809	+	0.690692i
$844$	12.9179	−	8.11688i	0.444654	−	0.279395i
$845$	−18.0595	−	3.97816i	−0.621265	−	0.136853i
$846$	8.50900	+	6.78570i	0.292546	+	0.233297i
$847$	−0.424791	+	3.77012i	−0.0145960	+	0.129543i
$848$	−34.0202	+	21.3763i	−1.16826	+	0.734065i
$849$	1.30347	−	0.456104i	0.0447350	−	0.0156535i
$850$	2.44579	+	10.0134i	0.0838899	+	0.343457i
$851$	−1.10940	+	1.76560i	−0.0380297	+	0.0605239i
$852$	1.49736	+	3.10930i	0.0512988	+	0.106523i
$853$		−	23.2993i		−	0.797753i	−0.917005	−	0.398877i	$-0.869400\pi$
$853$		−	23.2993i		−	0.797753i	0.917005	−	0.398877i	$-0.130600\pi$
$854$	−1.40631	+	0.677244i	−0.0481230	+	0.0231748i
$855$	3.95080	−	6.39477i	0.135115	−	0.218696i
$856$	−4.10425	+	36.4262i	−0.140280	+	1.24502i
$857$	−10.5693	+	30.2053i	−0.361040	+	1.03179i	0.609902	+	0.792477i	$0.291209\pi$
$857$	−10.5693	+	30.2053i	−0.361040	+	1.03179i	−0.970942	+	0.239316i	$0.923077\pi$
$858$	−5.82669			−0.198920
$859$	4.29957	−	12.2875i	0.146699	−	0.419243i	−0.846962	−	0.531653i	$-0.821571\pi$
$859$	4.29957	−	12.2875i	0.146699	−	0.419243i	0.993662	+	0.112410i	$0.0358569\pi$
$860$	−0.220913	+	1.00287i	−0.00753307	+	0.0341975i
$861$	1.85146	+	0.891617i	0.0630976	+	0.0303862i
$862$	−19.6514	+	40.8065i	−0.669329	+	1.38988i
$863$	−7.40418	−	11.7837i	−0.252041	−	0.401121i	0.696608	−	0.717452i	$-0.254692\pi$
$863$	−7.40418	−	11.7837i	−0.252041	−	0.401121i	−0.948649	+	0.316331i	$0.897549\pi$
$864$	−2.49282	+	1.98796i	−0.0848074	+	0.0676317i
$865$	−2.64314	+	7.74141i	−0.0898694	+	0.263216i
$866$	3.02823	+	13.2675i	0.102903	+	0.450849i
$867$	−3.41636	+	14.9681i	−0.116026	+	0.508342i
$868$	1.00362	+	0.800358i	0.0340650	+	0.0271659i
$869$	7.32454			0.248468
$870$	14.5920	+	12.6979i	0.494716	+	0.430500i
$871$	3.87078			0.131156
$872$	−19.6109	−	15.6392i	−0.664108	−	0.529609i
$873$	3.17217	−	13.8982i	0.107362	−	0.470383i
$874$	−0.885130	−	3.87801i	−0.0299400	−	0.131176i
$875$	−4.83168	+	1.81503i	−0.163341	+	0.0613592i
$876$	0.954263	−	0.761000i	0.0322416	−	0.0257118i
$877$	−17.7234	−	28.2066i	−0.598475	−	0.952468i	−0.999340	−	0.0363305i	$-0.988433\pi$
$877$	−17.7234	−	28.2066i	−0.598475	−	0.952468i	0.400865	−	0.916137i	$-0.368710\pi$
$878$	19.9606	−	41.4487i	0.673639	−	1.39883i
$879$	−26.4128	−	12.7197i	−0.890880	−	0.429025i
$880$	9.68660	+	15.1598i	0.326535	+	0.511037i
$881$	−16.7971	+	48.0033i	−0.565908	+	1.61727i	0.203897	+	0.978992i	$0.434639\pi$
$881$	−16.7971	+	48.0033i	−0.565908	+	1.61727i	−0.769805	+	0.638279i	$0.779647\pi$
$882$	10.9023			0.367099
$883$	3.67956	−	10.5156i	0.123827	−	0.353877i	−0.865237	−	0.501363i	$-0.832832\pi$
$883$	3.67956	−	10.5156i	0.123827	−	0.353877i	0.989064	+	0.147485i	$0.0471179\pi$
$884$	0.181391	−	1.60989i	0.00610084	−	0.0541464i
$885$	−2.51266	+	0.593573i	−0.0844620	+	0.0199527i
$886$	22.3414	−	10.7591i	0.750575	−	0.361458i
$887$			38.6464i			1.29762i	0.760951	+	0.648809i	$0.224733\pi$
$887$			38.6464i			1.29762i	−0.760951	+	0.648809i	$0.775267\pi$
$888$	−2.80079	−	5.81589i	−0.0939883	−	0.195169i
$889$	3.97710	−	6.32951i	0.133387	−	0.212285i
$890$	38.2319	+	4.01443i	1.28153	+	0.134564i
$891$	1.57422	−	0.550844i	0.0527384	−	0.0184540i
$892$	9.12765	−	5.73528i	0.305616	−	0.192031i
$893$	2.55003	−	22.6321i	0.0853334	−	0.757355i
$894$	5.46640	+	4.35931i	0.182824	+	0.145797i
$895$	4.01812	−	18.2408i	0.134311	−	0.609724i
$896$	−5.33462	+	3.35196i	−0.178217	+	0.111981i
$897$	−0.998847	+	1.25252i	−0.0333505	+	0.0418203i
$898$	−39.2736	+	39.2736i	−1.31058	+	1.31058i
$899$	−25.4574	−	4.17844i	−0.849050	−	0.139359i
$900$	−1.84370	−	2.24135i	−0.0614566	−	0.0747118i
$901$	1.19679	+	10.6218i	0.0398708	+	0.353863i
$902$	11.6269	+	2.65377i	0.387134	+	0.0883608i
$903$	0.309270	+	0.194327i	0.0102918	+	0.00646679i
$904$	11.3766	−	14.2658i	0.378379	−	0.474472i
$905$	1.31368	+	5.56093i	0.0436681	+	0.184852i
$906$	−1.84499	+	8.08341i	−0.0612955	+	0.268553i
$907$	52.4529	+	25.2600i	1.74167	+	0.838743i	0.982111	+	0.188303i	$0.0602988\pi$
$907$	52.4529	+	25.2600i	1.74167	+	0.838743i	0.759558	+	0.650440i	$0.225416\pi$
$908$	2.79220	−	0.977034i	0.0926625	−	0.0324240i
$909$	−6.42960	−	4.03998i	−0.213256	−	0.133998i
$910$	3.60624	−	0.0273390i	0.119546	−	0.000906278i
$911$	1.34936	+	1.34936i	0.0447062	+	0.0447062i	0.729106	−	0.684400i	$-0.239936\pi$
$911$	1.34936	+	1.34936i	0.0447062	+	0.0447062i	−0.684400	+	0.729106i	$0.739936\pi$
$912$	15.3063	+	5.35590i	0.506842	+	0.177352i
$913$	0.0389405	+	0.0488299i	0.00128874	+	0.00161603i
$914$	−47.1428	−	5.31172i	−1.55934	−	0.175696i
$915$	−3.30270	+	3.35316i	−0.109184	+	0.110852i
$916$	−5.67506	+	5.67506i	−0.187509	+	0.187509i
$917$	6.53633	−	3.14773i	0.215849	−	0.103947i
$918$	0.458739	+	2.00987i	0.0151406	+	0.0663355i
$919$	9.91489	−	20.5885i	0.327062	−	0.679151i	−0.670995	−	0.741462i	$-0.734133\pi$
$919$	9.91489	−	20.5885i	0.327062	−	0.679151i	0.998057	+	0.0623109i	$0.0198470\pi$
$920$	3.73548	+	0.392233i	0.123155	+	0.0129316i
$921$	−1.46132	−	0.333536i	−0.0481520	−	0.0109904i
$922$	51.1937	+	5.76815i	1.68598	+	0.189964i
$923$	−12.8493	+	1.44777i	−0.422941	+	0.0476540i
$924$	−0.435701	+	0.0994459i	−0.0143335	+	0.00327153i
$925$	12.6577	−	6.33379i	0.416182	−	0.208254i
$926$	47.0345	−	5.29952i	1.54565	−	0.174153i
$927$	−2.53936	−	2.53936i	−0.0834036	−	0.0834036i
$928$	−8.22106	+	15.0742i	−0.269869	+	0.494835i
$929$			41.6045i			1.36500i	0.730885	+	0.682501i	$0.239108\pi$
$929$			41.6045i			1.36500i	−0.730885	+	0.682501i	$0.760892\pi$
$930$	16.2845	+	5.56000i	0.533991	+	0.182320i
$931$	−12.1382	−	19.3179i	−0.397814	−	0.633117i
$932$	1.26773	−	2.01759i	0.0415260	−	0.0660883i
$933$	3.01290	+	26.7403i	0.0986381	+	0.875437i
$934$	−7.87732	−	9.87785i	−0.257754	−	0.323213i
$935$	4.75179	−	0.571910i	0.155400	−	0.0187035i
$936$	−1.63798	−	4.68107i	−0.0535390	−	0.153006i
$937$	−9.24431	−	26.4187i	−0.301998	−	0.863062i	−0.990461	−	0.137790i	$-0.956000\pi$
$937$	−9.24431	−	26.4187i	−0.301998	−	0.863062i	0.688463	−	0.725271i	$-0.258286\pi$
$938$	1.28676	−	0.293695i	0.0420143	−	0.00958950i
$939$	14.0211	+	4.90620i	0.457562	+	0.160108i
$940$	−7.95140	−	3.75520i	−0.259346	−	0.122481i
$941$	−6.85125	−	14.2268i	−0.223344	−	0.463779i	0.758944	−	0.651156i	$-0.225716\pi$
$941$	−6.85125	−	14.2268i	−0.223344	−	0.463779i	−0.982288	+	0.187377i	$0.940001\pi$
$942$	−20.7724	+	16.5654i	−0.676801	+	0.539731i
$943$	2.56361	−	2.04441i	0.0834828	−	0.0665753i
$944$	−2.41668	−	5.01828i	−0.0786561	−	0.163331i
$945$	−0.971729	+	0.348313i	−0.0316103	+	0.0113306i
$946$	2.00079	+	0.700105i	0.0650512	+	0.0227624i
$947$	−54.9361	+	12.5388i	−1.78518	+	0.407456i	−0.982092	−	0.188401i	$-0.939669\pi$
$947$	−54.9361	+	12.5388i	−1.78518	+	0.407456i	−0.803090	+	0.595857i	$0.796812\pi$
$948$	−0.841926	−	2.40609i	−0.0273445	−	0.0781461i
$949$	1.51044	+	4.31658i	0.0490309	+	0.140122i
$950$	−8.53013	+	25.6171i	−0.276754	+	0.831129i
$951$	18.7521	+	23.5144i	0.608079	+	0.762507i
$952$	0.151264	+	1.34250i	0.00490249	+	0.0435108i
$953$	2.62914	−	4.18425i	0.0851662	−	0.135541i	−0.801425	−	0.598096i	$-0.795924\pi$
$953$	2.62914	−	4.18425i	0.0851662	−	0.135541i	0.886591	+	0.462555i	$0.153067\pi$
$954$	−7.11828	−	11.3287i	−0.230463	−	0.366779i
$955$	−17.8834	+	52.3781i	−0.578692	+	1.69491i
$956$			6.40887i			0.207278i
$957$	6.66324	−	6.02227i	0.215392	−	0.194672i
$958$	−24.4640	−	24.4640i	−0.790396	−	0.790396i
$959$	5.96219	−	0.671777i	0.192529	−	0.0216928i
$960$	−6.25000	+	7.96030i	−0.201718	+	0.256918i
$961$	7.84863	−	1.79140i	0.253182	−	0.0577871i
$962$	−9.82748	+	1.10729i	−0.316851	+	0.0357005i
$963$	−15.9740	−	1.79984i	−0.514756	−	0.0579991i
$964$	−1.82400	−	0.416315i	−0.0587470	−	0.0134086i
$965$	21.1468	+	26.1087i	0.680738	+	0.840469i
$966$	−0.237012	+	0.492161i	−0.00762575	+	0.0158350i
$967$	5.39165	+	23.6223i	0.173384	+	0.759643i	0.984589	+	0.174882i	$0.0559545\pi$
$967$	5.39165	+	23.6223i	0.173384	+	0.759643i	−0.811206	+	0.584761i	$0.801188\pi$
$968$	−16.8848	+	8.13130i	−0.542699	+	0.261350i
$969$	3.05055	−	3.05055i	0.0979979	−	0.0979979i
$970$	0.388180	+	51.2042i	0.0124637	+	1.64407i
$971$	56.5611	+	6.37291i	1.81513	+	0.204516i	0.953166	−	0.302448i	$-0.0978040\pi$
$971$	56.5611	+	6.37291i	1.81513	+	0.204516i	0.861967	+	0.506965i	$0.169233\pi$
$972$	−0.361901	−	0.453810i	−0.0116080	−	0.0145560i
$973$	−8.03478	−	2.81149i	−0.257583	−	0.0901323i
$974$	−1.74115	−	1.74115i	−0.0557901	−	0.0557901i
$975$	10.2083	−	3.74672i	0.326929	−	0.119991i
$976$	−8.59734	−	5.40206i	−0.275194	−	0.172916i
$977$	−33.9542	+	11.8811i	−1.08629	+	0.380110i	−0.813263	−	0.581896i	$-0.802311\pi$
$977$	−33.9542	+	11.8811i	−1.08629	+	0.380110i	−0.273028	+	0.962006i	$0.588025\pi$
$978$	−33.5960	−	16.1790i	−1.07428	−	0.517347i
$979$	3.97185	−	17.4018i	0.126941	−	0.556164i
$980$	−8.57282	+	2.02519i	−0.273849	+	0.0646922i
$981$	6.85826	−	8.59998i	0.218967	−	0.274576i
$982$	−18.9057	−	11.8793i	−0.603306	−	0.379082i
$983$	−30.7382	−	7.01578i	−0.980395	−	0.223769i	−0.297850	−	0.954613i	$-0.596270\pi$
$983$	−30.7382	−	7.01578i	−0.980395	−	0.223769i	−0.682545	+	0.730844i	$0.739127\pi$
$984$	1.13652	+	10.0869i	0.0362309	+	0.321558i
$985$	34.9957	−	12.5441i	1.11505	−	0.399688i
$986$	6.47504	+	9.01798i	0.206207	+	0.287191i
$987$	−2.21162	+	2.21162i	−0.0703967	+	0.0703967i
$988$	2.64584	−	3.31778i	0.0841754	−	0.105553i
$989$	0.493483	−	0.310076i	0.0156918	−	0.00985983i
$990$	−5.04819	+	3.22562i	−0.160442	+	0.102517i
$991$	43.7531	+	34.8919i	1.38986	+	1.10838i	0.980613	+	0.195955i	$0.0627807\pi$
$991$	43.7531	+	34.8919i	1.38986	+	1.10838i	0.409249	+	0.912423i	$0.365791\pi$
$992$	−1.71019	+	15.1784i	−0.0542986	+	0.481914i
$993$	3.28203	−	2.06223i	0.104152	−	0.0654430i
$994$	−4.16166	+	1.45623i	−0.132000	+	0.0461887i
$995$	25.4950	−	20.6497i	0.808246	−	0.654640i
$996$	0.0115644	−	0.0184046i	0.000366432	−	0.000583173i
$997$	−23.9467	−	49.7258i	−0.758399	−	1.57483i	−0.817059	−	0.576554i	$-0.804397\pi$
$997$	−23.9467	−	49.7258i	−0.758399	−	1.57483i	0.0586600	−	0.998278i	$-0.481317\pi$
$998$			1.45676i			0.0461128i
$999$	2.55045	−	1.22823i	0.0806927	−	0.0388595i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	435.2.bm.a.43.4	yes	180
5.2	odd	4		435.2.bd.b.217.12	✓	180
29.27	odd	28		435.2.bd.b.433.12	yes	180
145.27	even	28	inner	435.2.bm.a.172.4	yes	180

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
435.2.bd.b.217.12	✓	180	5.2	odd	4
435.2.bd.b.433.12	yes	180	29.27	odd	28
435.2.bm.a.43.4	yes	180	1.1	even	1	trivial
435.2.bm.a.172.4	yes	180	145.27	even	28	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:	\( N \)	\(=\)	\( 435 = 3 \cdot 5 \cdot 29 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	435.bm (of order \(28\), degree \(12\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.25592 - 1.00156i) q^{2} +(-0.222521 + 0.974928i) q^{3} +(0.129161 + 0.565891i) q^{4} +(-2.00721 + 0.985438i) q^{5} +(1.25592 - 1.00156i) q^{6} +(0.245610 + 0.390886i) q^{7} +(-0.989403 + 2.05452i) q^{8} +(-0.900969 - 0.433884i) q^{9} +O(q^{10})\)	\(q+(-1.25592 - 1.00156i) q^{2} +(-0.222521 + 0.974928i) q^{3} +(0.129161 + 0.565891i) q^{4} +(-2.00721 + 0.985438i) q^{5} +(1.25592 - 1.00156i) q^{6} +(0.245610 + 0.390886i) q^{7} +(-0.989403 + 2.05452i) q^{8} +(-0.900969 - 0.433884i) q^{9} +(3.50787 + 0.772717i) q^{10} +(0.550844 - 1.57422i) q^{11} -0.580444 q^{12} +(0.718304 - 2.05280i) q^{13} +(0.0830300 - 0.736912i) q^{14} +(-0.514084 - 2.17617i) q^{15} +(4.34625 - 2.09304i) q^{16} -1.28336i q^{17} +(0.696980 + 1.44729i) q^{18} +(1.78848 - 2.84635i) q^{19} +(-0.816905 - 1.00859i) q^{20} +(-0.435739 + 0.152472i) q^{21} +(-2.26849 + 1.42539i) q^{22} +(-0.0824751 + 0.731987i) q^{23} +(-1.78284 - 1.42177i) q^{24} +(3.05782 - 3.95597i) q^{25} +(-2.95813 + 1.85871i) q^{26} +(0.623490 - 0.781831i) q^{27} +(-0.189476 + 0.189476i) q^{28} +(1.46172 - 5.18299i) q^{29} +(-1.53392 + 3.24797i) q^{30} +(-0.536373 - 4.76044i) q^{31} +(-3.10849 - 0.709493i) q^{32} +(1.41218 + 0.887331i) q^{33} +(-1.28536 + 1.61179i) q^{34} +(-0.878185 - 0.542558i) q^{35} +(0.129161 - 0.565891i) q^{36} +(2.55045 + 1.22823i) q^{37} +(-5.09697 + 1.78351i) q^{38} +(1.84149 + 1.15708i) q^{39} +(-0.0386545 - 5.09885i) q^{40} +(-3.14762 - 3.14762i) q^{41} +(0.699960 + 0.244927i) q^{42} +(-0.493306 - 0.618587i) q^{43} +(0.961986 + 0.108390i) q^{44} +(2.23600 - 0.0169512i) q^{45} +(0.836710 - 0.836710i) q^{46} +(6.10419 - 2.93962i) q^{47} +(1.07343 + 4.70303i) q^{48} +(2.94472 - 6.11477i) q^{49} +(-7.80251 + 1.90578i) q^{50} +(1.25118 + 0.285574i) q^{51} +(1.25444 + 0.141341i) q^{52} +(-8.27657 + 0.932546i) q^{53} +(-1.56610 + 0.357452i) q^{54} +(0.445636 + 3.70262i) q^{55} +(-1.04609 + 0.117866i) q^{56} +(2.37701 + 2.37701i) q^{57} +(-7.02687 + 5.04539i) q^{58} -1.15462i q^{59} +(1.16508 - 0.571992i) q^{60} +(-1.11984 - 1.78221i) q^{61} +(-4.09423 + 6.51592i) q^{62} +(-0.0516878 - 0.458742i) q^{63} +(-2.82199 - 3.53866i) q^{64} +(0.581112 + 4.82825i) q^{65} +(-0.884863 - 2.52879i) q^{66} +(0.587831 + 1.67992i) q^{67} +(0.726241 - 0.165760i) q^{68} +(-0.695282 - 0.243290i) q^{69} +(0.559522 + 1.56096i) q^{70} +(-2.57968 - 5.35676i) q^{71} +(1.78284 - 1.42177i) q^{72} +(-1.64402 + 1.31106i) q^{73} +(-1.97300 - 4.09698i) q^{74} +(3.17636 + 3.86144i) q^{75} +(1.84173 + 0.644448i) q^{76} +(0.750634 - 0.171327i) q^{77} +(-1.15387 - 3.29756i) q^{78} +(1.45049 + 4.14525i) q^{79} +(-6.66129 + 8.48415i) q^{80} +(0.623490 + 0.781831i) q^{81} +(0.800617 + 7.10567i) q^{82} +(-0.0199234 + 0.0317078i) q^{83} +(-0.142563 - 0.226887i) q^{84} +(1.26467 + 2.57597i) q^{85} +1.27097i q^{86} +(4.72778 + 2.57840i) q^{87} +(2.68926 + 2.68926i) q^{88} +(10.6349 - 1.19827i) q^{89} +(-2.82521 - 2.21820i) q^{90} +(0.978831 - 0.223412i) q^{91} +(-0.424877 + 0.0478722i) q^{92} +(4.76044 + 0.536373i) q^{93} +(-10.6106 - 2.42179i) q^{94} +(-0.784962 + 7.47567i) q^{95} +(1.38341 - 2.87268i) q^{96} +(3.17217 + 13.8982i) q^{97} +(-9.82262 + 4.73033i) q^{98} +(-1.17932 + 1.17932i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 180 q - 30 q^{3} + 30 q^{4} + 10 q^{5} - 30 q^{9}+O(q^{10}) \) 180 * q - 30 * q^3 + 30 * q^4 + 10 * q^5 - 30 * q^9	\( 180 q - 30 q^{3} + 30 q^{4} + 10 q^{5} - 30 q^{9} - 4 q^{10} - 30 q^{11} - 180 q^{12} - 20 q^{13} - 10 q^{14} - 4 q^{15} - 14 q^{16} + 8 q^{19} + 2 q^{20} + 36 q^{22} + 64 q^{25} - 36 q^{26} - 30 q^{27} + 72 q^{28} + 12 q^{29} - 4 q^{30} - 20 q^{31} + 12 q^{33} + 40 q^{34} - 6 q^{35} + 30 q^{36} + 42 q^{37} + 16 q^{38} + 22 q^{39} + 18 q^{40} - 10 q^{41} + 4 q^{42} + 26 q^{43} + 4 q^{44} - 4 q^{45} + 12 q^{46} - 20 q^{47} - 70 q^{48} + 8 q^{50} + 12 q^{52} - 82 q^{53} + 48 q^{55} + 6 q^{56} + 8 q^{57} - 70 q^{58} - 40 q^{60} + 14 q^{61} + 110 q^{62} - 14 q^{63} - 74 q^{64} + 42 q^{65} + 22 q^{66} - 20 q^{67} - 98 q^{68} + 28 q^{69} + 8 q^{70} + 140 q^{71} + 98 q^{73} + 22 q^{75} - 4 q^{76} - 42 q^{77} + 34 q^{78} - 24 q^{79} - 62 q^{80} - 30 q^{81} + 6 q^{82} - 60 q^{83} - 68 q^{84} - 178 q^{85} - 44 q^{87} - 156 q^{88} - 12 q^{89} - 4 q^{90} - 56 q^{91} - 8 q^{92} + 8 q^{93} + 4 q^{95} - 42 q^{97} + 194 q^{98} + 12 q^{99}+O(q^{100}) \) 180 * q - 30 * q^3 + 30 * q^4 + 10 * q^5 - 30 * q^9 - 4 * q^10 - 30 * q^11 - 180 * q^12 - 20 * q^13 - 10 * q^14 - 4 * q^15 - 14 * q^16 + 8 * q^19 + 2 * q^20 + 36 * q^22 + 64 * q^25 - 36 * q^26 - 30 * q^27 + 72 * q^28 + 12 * q^29 - 4 * q^30 - 20 * q^31 + 12 * q^33 + 40 * q^34 - 6 * q^35 + 30 * q^36 + 42 * q^37 + 16 * q^38 + 22 * q^39 + 18 * q^40 - 10 * q^41 + 4 * q^42 + 26 * q^43 + 4 * q^44 - 4 * q^45 + 12 * q^46 - 20 * q^47 - 70 * q^48 + 8 * q^50 + 12 * q^52 - 82 * q^53 + 48 * q^55 + 6 * q^56 + 8 * q^57 - 70 * q^58 - 40 * q^60 + 14 * q^61 + 110 * q^62 - 14 * q^63 - 74 * q^64 + 42 * q^65 + 22 * q^66 - 20 * q^67 - 98 * q^68 + 28 * q^69 + 8 * q^70 + 140 * q^71 + 98 * q^73 + 22 * q^75 - 4 * q^76 - 42 * q^77 + 34 * q^78 - 24 * q^79 - 62 * q^80 - 30 * q^81 + 6 * q^82 - 60 * q^83 - 68 * q^84 - 178 * q^85 - 44 * q^87 - 156 * q^88 - 12 * q^89 - 4 * q^90 - 56 * q^91 - 8 * q^92 + 8 * q^93 + 4 * q^95 - 42 * q^97 + 194 * q^98 + 12 * q^99

Introduction

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