LMFDB - Embedded newform 560.2.bd.b.141.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [560,2,Mod(141,560)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(560, base_ring=CyclotomicField(4))

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

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

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

chi := DirichletCharacter("560.141");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 560 = 2^{4} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	560.bd (of order $4$, degree $2$, 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:	$4.47162251319$
Analytic rank:	$0$
Dimension:	$52$
Relative dimension:	$26$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			141.8
Character	$\chi$	$=$	560.141
Dual form			560.2.bd.b.421.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.807148 + 1.16125i) q^{2} +(2.00539 + 2.00539i) q^{3} +(-0.697026 - 1.87461i) q^{4} +(0.707107 - 0.707107i) q^{5} +(-3.94742 + 0.710123i) q^{6} +1.00000i q^{7} +(2.73950 + 0.703661i) q^{8} +5.04319i q^{9} +O(q^{10})$	\(q+(-0.807148 + 1.16125i) q^{2} +(2.00539 + 2.00539i) q^{3} +(-0.697026 - 1.87461i) q^{4} +(0.707107 - 0.707107i) q^{5} +(-3.94742 + 0.710123i) q^{6} +1.00000i q^{7} +(2.73950 + 0.703661i) q^{8} +5.04319i q^{9} +(0.250392 + 1.39187i) q^{10} +(4.24632 - 4.24632i) q^{11} +(2.36151 - 5.15713i) q^{12} +(3.19634 + 3.19634i) q^{13} +(-1.16125 - 0.807148i) q^{14} +2.83605 q^{15} +(-3.02831 + 2.61330i) q^{16} -1.88950 q^{17} +(-5.85642 - 4.07060i) q^{18} +(-1.39086 - 1.39086i) q^{19} +(-1.81842 - 0.832677i) q^{20} +(-2.00539 + 2.00539i) q^{21} +(1.50365 + 8.35847i) q^{22} +7.29574i q^{23} +(4.08265 + 6.90488i) q^{24} -1.00000i q^{25} +(-6.29169 + 1.13185i) q^{26} +(-4.09739 + 4.09739i) q^{27} +(1.87461 - 0.697026i) q^{28} +(0.0710013 + 0.0710013i) q^{29} +(-2.28911 + 3.29338i) q^{30} -9.55451 q^{31} +(-0.590413 - 5.62596i) q^{32} +17.0311 q^{33} +(1.52510 - 2.19419i) q^{34} +(0.707107 + 0.707107i) q^{35} +(9.45400 - 3.51523i) q^{36} +(8.01620 - 8.01620i) q^{37} +(2.73777 - 0.492514i) q^{38} +12.8198i q^{39} +(2.43468 - 1.43956i) q^{40} -1.80970i q^{41} +(-0.710123 - 3.94742i) q^{42} +(-2.23835 + 2.23835i) q^{43} +(-10.9200 - 5.00040i) q^{44} +(3.56607 + 3.56607i) q^{45} +(-8.47221 - 5.88874i) q^{46} -3.01597 q^{47} +(-11.3136 - 0.832260i) q^{48} -1.00000 q^{49} +(1.16125 + 0.807148i) q^{50} +(-3.78918 - 3.78918i) q^{51} +(3.76396 - 8.21982i) q^{52} +(-8.59501 + 8.59501i) q^{53} +(-1.45091 - 8.06531i) q^{54} -6.00521i q^{55} +(-0.703661 + 2.73950i) q^{56} -5.57844i q^{57} +(-0.139759 + 0.0251421i) q^{58} +(6.44071 - 6.44071i) q^{59} +(-1.97680 - 5.31648i) q^{60} +(-3.05212 - 3.05212i) q^{61} +(7.71190 - 11.0952i) q^{62} -5.04319 q^{63} +(7.00972 + 3.85536i) q^{64} +4.52031 q^{65} +(-13.7466 + 19.7774i) q^{66} +(-6.42396 - 6.42396i) q^{67} +(1.31703 + 3.54207i) q^{68} +(-14.6308 + 14.6308i) q^{69} +(-1.39187 + 0.250392i) q^{70} +10.2817i q^{71} +(-3.54869 + 13.8158i) q^{72} -14.0571i q^{73} +(2.83859 + 15.7791i) q^{74} +(2.00539 - 2.00539i) q^{75} +(-1.63785 + 3.57678i) q^{76} +(4.24632 + 4.24632i) q^{77} +(-14.8871 - 10.3475i) q^{78} -1.35079 q^{79} +(-0.293457 + 3.98922i) q^{80} -1.30417 q^{81} +(2.10152 + 1.46070i) q^{82} +(3.34300 + 3.34300i) q^{83} +(5.15713 + 2.36151i) q^{84} +(-1.33608 + 1.33608i) q^{85} +(-0.792617 - 4.40598i) q^{86} +0.284771i q^{87} +(14.6208 - 8.64483i) q^{88} -4.24285i q^{89} +(-7.01946 + 1.26277i) q^{90} +(-3.19634 + 3.19634i) q^{91} +(13.6767 - 5.08532i) q^{92} +(-19.1605 - 19.1605i) q^{93} +(2.43433 - 3.50231i) q^{94} -1.96697 q^{95} +(10.0982 - 12.4663i) q^{96} +2.54333 q^{97} +(0.807148 - 1.16125i) q^{98} +(21.4150 + 21.4150i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 52 q - 8 q^{4} + 12 q^{6}+O(q^{10}) $ 52 * q - 8 * q^4 + 12 * q^6	$ 52 q - 8 q^{4} + 12 q^{6} - 4 q^{10} - 4 q^{11} + 40 q^{12} + 8 q^{15} - 4 q^{16} + 8 q^{19} + 32 q^{22} + 12 q^{24} - 12 q^{26} - 24 q^{27} + 4 q^{28} + 4 q^{29} - 16 q^{34} + 4 q^{36} - 12 q^{37} + 16 q^{38} - 4 q^{42} + 36 q^{43} + 28 q^{44} - 16 q^{46} + 32 q^{48} - 52 q^{49} - 8 q^{51} - 80 q^{52} - 4 q^{53} + 48 q^{54} - 12 q^{56} - 56 q^{58} + 24 q^{59} - 16 q^{61} - 72 q^{62} - 68 q^{63} + 4 q^{64} + 40 q^{65} - 12 q^{66} - 12 q^{67} - 72 q^{69} - 8 q^{72} + 68 q^{74} - 4 q^{77} - 4 q^{78} - 16 q^{79} - 32 q^{80} - 116 q^{81} + 104 q^{82} + 16 q^{85} - 68 q^{86} - 48 q^{88} + 36 q^{90} + 64 q^{92} + 8 q^{93} - 72 q^{94} - 32 q^{95} - 52 q^{99}+O(q^{100}) $ 52 * q - 8 * q^4 + 12 * q^6 - 4 * q^10 - 4 * q^11 + 40 * q^12 + 8 * q^15 - 4 * q^16 + 8 * q^19 + 32 * q^22 + 12 * q^24 - 12 * q^26 - 24 * q^27 + 4 * q^28 + 4 * q^29 - 16 * q^34 + 4 * q^36 - 12 * q^37 + 16 * q^38 - 4 * q^42 + 36 * q^43 + 28 * q^44 - 16 * q^46 + 32 * q^48 - 52 * q^49 - 8 * q^51 - 80 * q^52 - 4 * q^53 + 48 * q^54 - 12 * q^56 - 56 * q^58 + 24 * q^59 - 16 * q^61 - 72 * q^62 - 68 * q^63 + 4 * q^64 + 40 * q^65 - 12 * q^66 - 12 * q^67 - 72 * q^69 - 8 * q^72 + 68 * q^74 - 4 * q^77 - 4 * q^78 - 16 * q^79 - 32 * q^80 - 116 * q^81 + 104 * q^82 + 16 * q^85 - 68 * q^86 - 48 * q^88 + 36 * q^90 + 64 * q^92 + 8 * q^93 - 72 * q^94 - 32 * q^95 - 52 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/560\mathbb{Z}\right)^\times$.

$n$	$241$	$337$	$351$	$421$
$\chi(n)$	$1$	$1$	$1$	$e\left(\frac{3}{4}\right)$

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 $

$2$	−0.807148	+	1.16125i	−0.570740	+	0.821131i
$2$	−0.807148	+	1.16125i	−0.570740	+	0.821131i
$3$	2.00539	+	2.00539i	1.15781	+	1.15781i	0.984945	+	0.172868i	$0.0553034\pi$
$3$	2.00539	+	2.00539i	1.15781	+	1.15781i	0.172868	+	0.984945i	$0.444697\pi$
$4$	−0.697026	−	1.87461i	−0.348513	−	0.937304i
$5$	0.707107	−	0.707107i	0.316228	−	0.316228i
$5$	0.707107	−	0.707107i	0.316228	−	0.316228i
$6$	−3.94742	+	0.710123i	−1.61153	+	0.289907i
$7$			1.00000i			0.377964i
$7$			1.00000i			0.377964i
$8$	2.73950	+	0.703661i	0.968560	+	0.248782i
$9$			5.04319i			1.68106i
$10$	0.250392	+	1.39187i	0.0791808	+	0.440148i
$11$	4.24632	−	4.24632i	1.28031	−	1.28031i	0.339826	−	0.940488i	$-0.389632\pi$
$11$	4.24632	−	4.24632i	1.28031	−	1.28031i	0.940488	−	0.339826i	$-0.110368\pi$
$12$	2.36151	−	5.15713i	0.681710	−	1.48874i
$13$	3.19634	+	3.19634i	0.886506	+	0.886506i	0.994186	−	0.107680i	$-0.0343421\pi$
$13$	3.19634	+	3.19634i	0.886506	+	0.886506i	−0.107680	+	0.994186i	$0.534342\pi$
$14$	−1.16125	−	0.807148i	−0.310358	−	0.215719i
$15$	2.83605			0.732265
$16$	−3.02831	+	2.61330i	−0.757078	+	0.653325i
$17$	−1.88950			−0.458271			−0.229135	−	0.973395i	$-0.573590\pi$
$17$	−1.88950			−0.458271			−0.229135	+	0.973395i	$0.573590\pi$
$18$	−5.85642	−	4.07060i	−1.38037	−	0.959449i
$19$	−1.39086	−	1.39086i	−0.319085	−	0.319085i	0.529331	−	0.848416i	$-0.322443\pi$
$19$	−1.39086	−	1.39086i	−0.319085	−	0.319085i	−0.848416	+	0.529331i	$0.822443\pi$
$20$	−1.81842	−	0.832677i	−0.406611	−	0.186192i
$21$	−2.00539	+	2.00539i	−0.437612	+	0.437612i
$22$	1.50365	+	8.35847i	0.320580	+	1.78203i
$23$			7.29574i			1.52127i	0.649182	+	0.760634i	$0.275112\pi$
$23$			7.29574i			1.52127i	−0.649182	+	0.760634i	$0.724888\pi$
$24$	4.08265	+	6.90488i	0.833368	+	1.40945i
$25$		−	1.00000i		−	0.200000i
$26$	−6.29169	+	1.13185i	−1.23390	+	0.221974i
$27$	−4.09739	+	4.09739i	−0.788543	+	0.788543i
$28$	1.87461	−	0.697026i	0.354268	−	0.131725i
$29$	0.0710013	+	0.0710013i	0.0131846	+	0.0131846i	0.713668	−	0.700484i	$-0.247032\pi$
$29$	0.0710013	+	0.0710013i	0.0131846	+	0.0131846i	−0.700484	+	0.713668i	$0.747032\pi$
$30$	−2.28911	+	3.29338i	−0.417933	+	0.601286i
$31$	−9.55451			−1.71604			−0.858020	−	0.513616i	$-0.828306\pi$
$31$	−9.55451			−1.71604			−0.858020	+	0.513616i	$0.828306\pi$
$32$	−0.590413	−	5.62596i	−0.104371	−	0.994538i
$33$	17.0311			2.96473
$34$	1.52510	−	2.19419i	0.261553	−	0.376300i
$35$	0.707107	+	0.707107i	0.119523	+	0.119523i
$36$	9.45400	−	3.51523i	1.57567	−	0.585872i
$37$	8.01620	−	8.01620i	1.31785	−	1.31785i	0.402384	−	0.915471i	$-0.368182\pi$
$37$	8.01620	−	8.01620i	1.31785	−	1.31785i	0.915471	−	0.402384i	$-0.131818\pi$
$38$	2.73777	−	0.492514i	0.444125	−	0.0798963i
$39$			12.8198i			2.05282i
$40$	2.43468	−	1.43956i	0.384957	−	0.227614i
$41$		−	1.80970i		−	0.282628i	−0.989965	−	0.141314i	$-0.954867\pi$
$41$		−	1.80970i		−	0.282628i	0.989965	−	0.141314i	$-0.0451327\pi$
$42$	−0.710123	−	3.94742i	−0.109574	−	0.609100i
$43$	−2.23835	+	2.23835i	−0.341346	+	0.341346i	−0.856873	−	0.515527i	$-0.827596\pi$
$43$	−2.23835	+	2.23835i	−0.341346	+	0.341346i	0.515527	+	0.856873i	$0.327596\pi$
$44$	−10.9200	−	5.00040i	−1.64625	−	0.753838i
$45$	3.56607	+	3.56607i	0.531599	+	0.531599i
$46$	−8.47221	−	5.88874i	−1.24916	−	0.868247i
$47$	−3.01597			−0.439925			−0.219962	−	0.975508i	$-0.570593\pi$
$47$	−3.01597			−0.439925			−0.219962	+	0.975508i	$0.570593\pi$
$48$	−11.3136	−	0.832260i	−1.63298	−	0.120126i
$49$	−1.00000			−0.142857
$50$	1.16125	+	0.807148i	0.164226	+	0.114148i
$51$	−3.78918	−	3.78918i	−0.530592	−	0.530592i
$52$	3.76396	−	8.21982i	0.521967	−	1.13988i
$53$	−8.59501	+	8.59501i	−1.18062	+	1.18062i	−0.201031	+	0.979585i	$0.564429\pi$
$53$	−8.59501	+	8.59501i	−1.18062	+	1.18062i	−0.979585	+	0.201031i	$0.935571\pi$
$54$	−1.45091	−	8.06531i	−0.197444	−	1.09755i
$55$		−	6.00521i		−	0.809742i
$56$	−0.703661	+	2.73950i	−0.0940307	+	0.366081i
$57$		−	5.57844i		−	0.738882i
$58$	−0.139759	+	0.0251421i	−0.0183513	+	0.00330132i
$59$	6.44071	−	6.44071i	0.838510	−	0.838510i	−0.150153	−	0.988663i	$-0.547977\pi$
$59$	6.44071	−	6.44071i	0.838510	−	0.838510i	0.988663	+	0.150153i	$0.0479767\pi$
$60$	−1.97680	−	5.31648i	−0.255204	−	0.686355i
$61$	−3.05212	−	3.05212i	−0.390784	−	0.390784i	0.484183	−	0.874967i	$-0.339117\pi$
$61$	−3.05212	−	3.05212i	−0.390784	−	0.390784i	−0.874967	+	0.484183i	$0.839117\pi$
$62$	7.71190	−	11.0952i	0.979412	−	1.40909i
$63$	−5.04319			−0.635382
$64$	7.00972	+	3.85536i	0.876215	+	0.481920i
$65$	4.52031			0.560676
$66$	−13.7466	+	19.7774i	−1.69209	+	2.43443i
$67$	−6.42396	−	6.42396i	−0.784812	−	0.784812i	0.195826	−	0.980639i	$-0.437261\pi$
$67$	−6.42396	−	6.42396i	−0.784812	−	0.784812i	−0.980639	+	0.195826i	$0.937261\pi$
$68$	1.31703	+	3.54207i	0.159713	+	0.429539i
$69$	−14.6308	+	14.6308i	−1.76134	+	1.76134i
$70$	−1.39187	+	0.250392i	−0.166360	+	0.0299275i
$71$			10.2817i			1.22021i	0.792321	+	0.610104i	$0.208873\pi$
$71$			10.2817i			1.22021i	−0.792321	+	0.610104i	$0.791127\pi$
$72$	−3.54869	+	13.8158i	−0.418218	+	1.62821i
$73$		−	14.0571i		−	1.64526i	−0.568574	−	0.822632i	$-0.692505\pi$
$73$		−	14.0571i		−	1.64526i	0.568574	−	0.822632i	$-0.307495\pi$
$74$	2.83859	+	15.7791i	0.329980	+	1.83428i
$75$	2.00539	−	2.00539i	0.231563	−	0.231563i
$76$	−1.63785	+	3.57678i	−0.187875	+	0.410285i
$77$	4.24632	+	4.24632i	0.483913	+	0.483913i
$78$	−14.8871	−	10.3475i	−1.68563	−	1.17162i
$79$	−1.35079			−0.151976			−0.0759879	−	0.997109i	$-0.524211\pi$
$79$	−1.35079			−0.151976			−0.0759879	+	0.997109i	$0.524211\pi$
$80$	−0.293457	+	3.98922i	−0.0328095	+	0.446008i
$81$	−1.30417			−0.144908
$82$	2.10152	+	1.46070i	0.232074	+	0.161307i
$83$	3.34300	+	3.34300i	0.366941	+	0.366941i	0.866361	−	0.499419i	$-0.166453\pi$
$83$	3.34300	+	3.34300i	0.366941	+	0.366941i	−0.499419	+	0.866361i	$0.666453\pi$
$84$	5.15713	+	2.36151i	0.562689	+	0.257662i
$85$	−1.33608	+	1.33608i	−0.144918	+	0.144918i
$86$	−0.792617	−	4.40598i	−0.0854701	−	0.475109i
$87$			0.284771i			0.0305306i
$88$	14.6208	−	8.64483i	1.55858	−	0.921542i
$89$		−	4.24285i		−	0.449741i	−0.974389	−	0.224871i	$-0.927804\pi$
$89$		−	4.24285i		−	0.449741i	0.974389	−	0.224871i	$-0.0721959\pi$
$90$	−7.01946	+	1.26277i	−0.739916	+	0.133108i
$91$	−3.19634	+	3.19634i	−0.335068	+	0.335068i
$92$	13.6767	−	5.08532i	1.42589	−	0.530181i
$93$	−19.1605	−	19.1605i	−1.98685	−	1.98685i
$94$	2.43433	−	3.50231i	0.251082	−	0.361236i
$95$	−1.96697			−0.201807
$96$	10.0982	−	12.4663i	1.03065	−	1.27233i
$97$	2.54333			0.258236			0.129118	−	0.991629i	$-0.458785\pi$
$97$	2.54333			0.258236			0.129118	+	0.991629i	$0.458785\pi$
$98$	0.807148	−	1.16125i	0.0815342	−	0.117304i
$99$	21.4150	+	21.4150i	2.15229	+	2.15229i
$100$	−1.87461	+	0.697026i	−0.187461	+	0.0697026i
$101$	0.541054	−	0.541054i	0.0538369	−	0.0538369i	−0.679676	−	0.733513i	$-0.737880\pi$
$101$	0.541054	−	0.541054i	0.0538369	−	0.0538369i	0.733513	+	0.679676i	$0.237880\pi$
$102$	7.45864	−	1.34178i	0.738515	−	0.132856i
$103$		−	9.04153i		−	0.890889i	−0.895310	−	0.445444i	$-0.853046\pi$
$103$		−	9.04153i		−	0.890889i	0.895310	−	0.445444i	$-0.146954\pi$
$104$	6.50724	+	11.0055i	0.638087	+	1.07918i
$105$			2.83605i			0.276770i
$106$	−3.04356	−	16.9184i	−0.295616	−	1.64326i
$107$	−12.9086	+	12.9086i	−1.24792	+	1.24792i	−0.291290	+	0.956635i	$0.594084\pi$
$107$	−12.9086	+	12.9086i	−1.24792	+	1.24792i	−0.956635	+	0.291290i	$0.905916\pi$
$108$	10.5370	+	4.82501i	1.01392	+	0.464287i
$109$	0.268159	+	0.268159i	0.0256850	+	0.0256850i	0.719833	−	0.694148i	$-0.244219\pi$
$109$	0.268159	+	0.268159i	0.0256850	+	0.0256850i	−0.694148	+	0.719833i	$0.744219\pi$
$110$	6.97358	+	4.84709i	0.664904	+	0.462152i
$111$	32.1512			3.05166
$112$	−2.61330	−	3.02831i	−0.246934	−	0.286148i
$113$	11.4241			1.07469			0.537346	−	0.843362i	$-0.319427\pi$
$113$	11.4241			1.07469			0.537346	+	0.843362i	$0.319427\pi$
$114$	6.47799	+	4.50262i	0.606719	+	0.421709i
$115$	5.15887	+	5.15887i	0.481067	+	0.481067i
$116$	0.0836099	−	0.182589i	0.00776298	−	0.0169530i
$117$	−16.1198	+	16.1198i	−1.49027	+	1.49027i
$118$	2.28070	+	12.6779i	0.209956	+	1.16710i
$119$		−	1.88950i		−	0.173210i
$120$	7.76936	+	1.99562i	0.709243	+	0.182174i
$121$		−	25.0625i		−	2.27841i
$122$	6.00779	−	1.08078i	0.543920	−	0.0978489i
$123$	3.62916	−	3.62916i	0.327230	−	0.327230i
$124$	6.65974	+	17.9110i	0.598062	+	1.60845i
$125$	−0.707107	−	0.707107i	−0.0632456	−	0.0632456i
$126$	4.07060	−	5.85642i	0.362638	−	0.521732i
$127$	−3.58897			−0.318470			−0.159235	−	0.987241i	$-0.550903\pi$
$127$	−3.58897			−0.318470			−0.159235	+	0.987241i	$0.550903\pi$
$128$	−10.1349	+	5.02823i	−0.895810	+	0.444437i
$129$	−8.97754			−0.790429
$130$	−3.64856	+	5.24923i	−0.320000	+	0.460388i
$131$	−2.35913	−	2.35913i	−0.206118	−	0.206118i	0.596497	−	0.802615i	$-0.296559\pi$
$131$	−2.35913	−	2.35913i	−0.206118	−	0.206118i	−0.802615	+	0.596497i	$0.796559\pi$
$132$	−11.8711	−	31.9266i	−1.03325	−	2.77885i
$133$	1.39086	−	1.39086i	0.120603	−	0.120603i
$134$	12.6449	−	2.27477i	1.09236	−	0.196510i
$135$			5.79458i			0.498718i
$136$	−5.17628	−	1.32957i	−0.443863	−	0.114009i
$137$			7.69317i			0.657272i	0.944457	+	0.328636i	$0.106589\pi$
$137$			7.69317i			0.657272i	−0.944457	+	0.328636i	$0.893411\pi$
$138$	−5.18088	−	28.7993i	−0.441026	−	2.45156i
$139$	6.50335	−	6.50335i	0.551607	−	0.551607i	−0.375297	−	0.926904i	$-0.622459\pi$
$139$	6.50335	−	6.50335i	0.551607	−	0.551607i	0.926904	+	0.375297i	$0.122459\pi$
$140$	0.832677	−	1.81842i	0.0703740	−	0.153685i
$141$	−6.04820	−	6.04820i	−0.509351	−	0.509351i
$142$	−11.9396	−	8.29882i	−1.00195	−	0.696421i
$143$	27.1454			2.27001
$144$	−13.1794	−	15.2723i	−1.09828	−	1.27269i
$145$	0.100411			0.00833868
$146$	16.3239	+	11.3462i	1.35098	+	0.939018i
$147$	−2.00539	−	2.00539i	−0.165402	−	0.165402i
$148$	−20.6147	−	9.43974i	−1.69452	−	0.775941i
$149$	12.9401	−	12.9401i	1.06010	−	1.06010i	0.0620222	−	0.998075i	$-0.480245\pi$
$149$	12.9401	−	12.9401i	1.06010	−	1.06010i	0.998075	−	0.0620222i	$-0.0197550\pi$
$150$	0.710123	+	3.94742i	0.0579813	+	0.322305i
$151$		−	4.38451i		−	0.356807i	−0.983957	−	0.178403i	$-0.942907\pi$
$151$		−	4.38451i		−	0.356807i	0.983957	−	0.178403i	$-0.0570932\pi$
$152$	−2.83157	−	4.78896i	−0.229670	−	0.388436i
$153$		−	9.52910i		−	0.770382i
$154$	−8.35847	+	1.50365i	−0.673545	+	0.121168i
$155$	−6.75606	+	6.75606i	−0.542660	+	0.542660i
$156$	24.0322	−	8.93575i	1.92411	−	0.715433i
$157$	2.23654	+	2.23654i	0.178496	+	0.178496i	0.790700	−	0.612204i	$-0.209717\pi$
$157$	2.23654	+	2.23654i	0.178496	+	0.178496i	−0.612204	+	0.790700i	$0.709717\pi$
$158$	1.09029	−	1.56861i	0.0867385	−	0.124792i
$159$	−34.4727			−2.73387
$160$	−4.39564	−	3.56067i	−0.347506	−	0.281496i
$161$	−7.29574			−0.574985
$162$	1.05266	−	1.51448i	0.0827047	−	0.118988i
$163$	−1.39407	−	1.39407i	−0.109192	−	0.109192i	0.650400	−	0.759592i	$-0.274601\pi$
$163$	−1.39407	−	1.39407i	−0.109192	−	0.109192i	−0.759592	+	0.650400i	$0.774601\pi$
$164$	−3.39248	+	1.26141i	−0.264908	+	0.0984994i
$165$	12.0428	−	12.0428i	0.937530	−	0.937530i
$166$	−6.58036	+	1.18378i	−0.510735	+	0.0918790i
$167$		−	4.78833i		−	0.370532i	−0.982688	−	0.185266i	$-0.940685\pi$
$167$		−	4.78833i		−	0.370532i	0.982688	−	0.185266i	$-0.0593147\pi$
$168$	−6.90488	+	4.08265i	−0.532723	+	0.314984i
$169$			7.43321i			0.571786i
$170$	−0.473115	−	2.62994i	−0.0362862	−	0.201707i
$171$	7.01437	−	7.01437i	0.536402	−	0.536402i
$172$	5.75622	+	2.63584i	0.438908	+	0.200981i
$173$	−8.95425	−	8.95425i	−0.680779	−	0.680779i	0.279397	−	0.960176i	$-0.409865\pi$
$173$	−8.95425	−	8.95425i	−0.680779	−	0.680779i	−0.960176	+	0.279397i	$0.909865\pi$
$174$	−0.330691	−	0.229852i	−0.0250697	−	0.0174250i
$175$	1.00000			0.0755929
$176$	−1.76227	+	23.9561i	−0.132836	+	1.80576i
$177$	25.8323			1.94167
$178$	4.92703	+	3.42460i	0.369296	+	0.256685i
$179$	11.6109	+	11.6109i	0.867843	+	0.867843i	0.992233	−	0.124390i	$-0.0396975\pi$
$179$	11.6109	+	11.6109i	0.867843	+	0.867843i	−0.124390	+	0.992233i	$0.539697\pi$
$180$	4.19934	−	9.17063i	0.313001	−	0.683538i
$181$	0.371916	−	0.371916i	0.0276443	−	0.0276443i	−0.693150	−	0.720794i	$-0.743777\pi$
$181$	0.371916	−	0.371916i	0.0276443	−	0.0276443i	0.720794	+	0.693150i	$0.243777\pi$
$182$	−1.13185	−	6.29169i	−0.0838982	−	0.466371i
$183$		−	12.2414i		−	0.904908i
$184$	−5.13373	+	19.9867i	−0.378464	+	1.47344i
$185$		−	11.3366i		−	0.833485i
$186$	37.7156	−	6.78488i	2.76544	−	0.497492i
$187$	−8.02342	+	8.02342i	−0.586731	+	0.586731i
$188$	2.10221	+	5.65377i	0.153319	+	0.412343i
$189$	−4.09739	−	4.09739i	−0.298041	−	0.298041i
$190$	1.58764	−	2.28416i	0.115179	−	0.165710i
$191$	7.10053			0.513777			0.256888	−	0.966441i	$-0.417303\pi$
$191$	7.10053			0.513777			0.256888	+	0.966441i	$0.417303\pi$
$192$	6.32573	+	21.7887i	0.456520	+	1.57247i
$193$	0.488355			0.0351526			0.0175763	−	0.999846i	$-0.494405\pi$
$193$	0.488355			0.0351526			0.0175763	+	0.999846i	$0.494405\pi$
$194$	−2.05284	+	2.95345i	−0.147385	+	0.212045i
$195$	9.06499	+	9.06499i	0.649158	+	0.649158i
$196$	0.697026	+	1.87461i	0.0497875	+	0.133901i
$197$	11.5915	−	11.5915i	0.825863	−	0.825863i	−0.161079	−	0.986942i	$-0.551497\pi$
$197$	11.5915	−	11.5915i	0.825863	−	0.825863i	0.986942	+	0.161079i	$0.0514973\pi$
$198$	−42.1533	+	7.58321i	−2.99571	+	0.538915i
$199$			4.86441i			0.344829i	0.985025	+	0.172414i	$0.0551568\pi$
$199$			4.86441i			0.344829i	−0.985025	+	0.172414i	$0.944843\pi$
$200$	0.703661	−	2.73950i	0.0497564	−	0.193712i
$201$		−	25.7651i		−	1.81733i
$202$	0.191591	+	1.06501i	0.0134803	+	0.0749340i
$203$	−0.0710013	+	0.0710013i	−0.00498331	+	0.00498331i
$204$	−4.46208	+	9.74439i	−0.312408	+	0.682244i
$205$	−1.27965	−	1.27965i	−0.0893747	−	0.0893747i
$206$	10.4995	+	7.29785i	0.731537	+	0.508465i
$207$	−36.7938			−2.55734
$208$	−18.0325	−	1.32652i	−1.25033	−	0.0919775i
$209$	−11.8121			−0.817059
$210$	−3.29338	−	2.28911i	−0.227265	−	0.157964i
$211$	14.9976	+	14.9976i	1.03248	+	1.03248i	0.999455	+	0.0330228i	$0.0105134\pi$
$211$	14.9976	+	14.9976i	1.03248	+	1.03248i	0.0330228	+	0.999455i	$0.489487\pi$
$212$	22.1032	+	10.1213i	1.51806	+	0.695136i
$213$	−20.6188	+	20.6188i	−1.41277	+	1.41277i
$214$	−4.57104	−	25.4094i	−0.312470	−	1.73695i
$215$			3.16551i			0.215886i
$216$	−14.1080	+	8.34162i	−0.959926	+	0.567576i
$217$		−	9.55451i		−	0.648602i
$218$	−0.527845	+	0.0949571i	−0.0357502	+	0.00643131i
$219$	28.1901	−	28.1901i	1.90491	−	1.90491i
$220$	−11.2574	+	4.18578i	−0.758975	+	0.282205i
$221$	−6.03949	−	6.03949i	−0.406260	−	0.406260i
$222$	−25.9508	+	37.3358i	−1.74170	+	2.50581i
$223$	−5.37178			−0.359721			−0.179861	−	0.983692i	$-0.557565\pi$
$223$	−5.37178			−0.359721			−0.179861	+	0.983692i	$0.557565\pi$
$224$	5.62596	−	0.590413i	0.375900	−	0.0394486i
$225$	5.04319			0.336212
$226$	−9.22097	+	13.2663i	−0.613370	+	0.882464i
$227$	−15.8055	−	15.8055i	−1.04905	−	1.04905i	−0.998734	−	0.0503127i	$-0.983978\pi$
$227$	−15.8055	−	15.8055i	−1.04905	−	1.04905i	−0.0503127	−	0.998734i	$-0.516022\pi$
$228$	−10.4574	+	3.88831i	−0.692557	+	0.257510i
$229$	0.0818183	−	0.0818183i	0.00540670	−	0.00540670i	−0.704398	−	0.709805i	$-0.748783\pi$
$229$	0.0818183	−	0.0818183i	0.00540670	−	0.00540670i	0.709805	+	0.704398i	$0.248783\pi$
$230$	−10.1547	+	1.82679i	−0.669583	+	0.120455i
$231$			17.0311i			1.12056i
$232$	0.144547	+	0.244469i	0.00948999	+	0.0160502i
$233$		−	17.1142i		−	1.12119i	−0.828091	−	0.560594i	$-0.810573\pi$
$233$		−	17.1142i		−	1.12119i	0.828091	−	0.560594i	$-0.189427\pi$
$234$	−5.70812	−	31.7302i	−0.373152	−	2.07427i
$235$	−2.13261	+	2.13261i	−0.139116	+	0.139116i
$236$	−16.5632	−	7.58447i	−1.07817	−	0.493707i
$237$	−2.70886	−	2.70886i	−0.175959	−	0.175959i
$238$	2.19419	+	1.52510i	0.142228	+	0.0988578i
$239$	−10.8283			−0.700424			−0.350212	−	0.936671i	$-0.613890\pi$
$239$	−10.8283			−0.700424			−0.350212	+	0.936671i	$0.613890\pi$
$240$	−8.58844	+	7.41145i	−0.554382	+	0.478407i
$241$	−7.13877			−0.459849			−0.229924	−	0.973208i	$-0.573848\pi$
$241$	−7.13877			−0.459849			−0.229924	+	0.973208i	$0.573848\pi$
$242$	29.1040	+	20.2292i	1.87087	+	1.30038i
$243$	9.67679	+	9.67679i	0.620766	+	0.620766i
$244$	−3.59412	+	7.84893i	−0.230090	+	0.502476i
$245$	−0.707107	+	0.707107i	−0.0451754	+	0.0451754i
$246$	1.28511	+	7.14364i	0.0819357	+	0.455462i
$247$		−	8.89133i		−	0.565742i
$248$	−26.1746	−	6.72314i	−1.66209	−	0.426920i
$249$			13.4080i			0.849699i
$250$	1.39187	−	0.250392i	0.0880296	−	0.0158362i
$251$	−18.0839	+	18.0839i	−1.14145	+	1.14145i	−0.153261	+	0.988186i	$0.548977\pi$
$251$	−18.0839	+	18.0839i	−1.14145	+	1.14145i	−0.988186	+	0.153261i	$0.951023\pi$
$252$	3.51523	+	9.45400i	0.221439	+	0.595546i
$253$	30.9801	+	30.9801i	1.94770	+	1.94770i
$254$	2.89683	−	4.16771i	0.181763	−	0.261506i
$255$	−5.35872			−0.335576
$256$	2.34133	−	15.8278i	0.146333	−	0.989235i
$257$	12.5522			0.782988			0.391494	−	0.920181i	$-0.371958\pi$
$257$	12.5522			0.782988			0.391494	+	0.920181i	$0.371958\pi$
$258$	7.24620	−	10.4252i	0.451129	−	0.649046i
$259$	8.01620	+	8.01620i	0.498102	+	0.498102i
$260$	−3.15077	−	8.47381i	−0.195403	−	0.525523i
$261$	−0.358073	+	0.358073i	−0.0221642	+	0.0221642i
$262$	4.64372	−	0.835385i	0.286890	−	0.0516102i
$263$			7.57379i			0.467020i	0.972354	+	0.233510i	$0.0750212\pi$
$263$			7.57379i			0.467020i	−0.972354	+	0.233510i	$0.924979\pi$
$264$	46.6566	+	11.9841i	2.87152	+	0.737571i
$265$			12.1552i			0.746687i
$266$	0.492514	+	2.73777i	0.0301979	+	0.167864i
$267$	8.50857	−	8.50857i	0.520716	−	0.520716i
$268$	−7.56475	+	16.5201i	−0.462091	+	1.00912i
$269$	0.543077	+	0.543077i	0.0331120	+	0.0331120i	0.723469	−	0.690357i	$-0.242547\pi$
$269$	0.543077	+	0.543077i	0.0331120	+	0.0331120i	−0.690357	+	0.723469i	$0.742547\pi$
$270$	−6.72899	−	4.67708i	−0.409513	−	0.284638i
$271$	−27.1988			−1.65221			−0.826104	−	0.563517i	$-0.809448\pi$
$271$	−27.1988			−1.65221			−0.826104	+	0.563517i	$0.809448\pi$
$272$	5.72199	−	4.93783i	0.346947	−	0.299400i
$273$	−12.8198			−0.775892
$274$	−8.93374	−	6.20953i	−0.539707	−	0.375131i
$275$	−4.24632	−	4.24632i	−0.256063	−	0.256063i
$276$	37.6251	+	17.2290i	2.26476	+	1.03706i
$277$	5.28670	−	5.28670i	0.317647	−	0.317647i	−0.530216	−	0.847863i	$-0.677889\pi$
$277$	5.28670	−	5.28670i	0.317647	−	0.317647i	0.847863	+	0.530216i	$0.177889\pi$
$278$	2.30288	+	12.8012i	0.138118	+	0.767766i
$279$		−	48.1852i		−	2.88477i
$280$	1.43956	+	2.43468i	0.0860299	+	0.145500i
$281$			10.4777i			0.625045i	0.949910	+	0.312523i	$0.101174\pi$
$281$			10.4777i			0.625045i	−0.949910	+	0.312523i	$0.898826\pi$
$282$	11.9053	−	2.14171i	0.708950	−	0.127537i
$283$	−2.56723	+	2.56723i	−0.152606	+	0.152606i	−0.779281	−	0.626675i	$-0.784415\pi$
$283$	−2.56723	+	2.56723i	−0.152606	+	0.152606i	0.626675	+	0.779281i	$0.284415\pi$
$284$	19.2741	−	7.16658i	1.14371	−	0.425258i
$285$	−3.94455	−	3.94455i	−0.233655	−	0.233655i
$286$	−21.9104	+	31.5227i	−1.29559	+	1.86398i
$287$	1.80970			0.106823
$288$	28.3728	−	2.97756i	1.67188	−	0.175454i
$289$	−13.4298			−0.789988
$290$	−0.0810465	+	0.116603i	−0.00475921	+	0.00684715i
$291$	5.10036	+	5.10036i	0.298988	+	0.298988i
$292$	−26.3516	+	9.79819i	−1.54211	+	0.573396i
$293$	−16.7521	+	16.7521i	−0.978666	+	0.978666i	−0.999777	−	0.0211107i	$-0.993280\pi$
$293$	−16.7521	+	16.7521i	−0.978666	+	0.978666i	0.0211107	+	0.999777i	$0.493280\pi$
$294$	3.94742	−	0.710123i	0.230218	−	0.0414152i
$295$		−	9.10855i		−	0.530320i
$296$	27.6011	−	16.3197i	1.60428	−	0.948563i
$297$			34.7977i			2.01917i
$298$	4.58219	+	25.4714i	0.265439	+	1.47552i
$299$	−23.3197	+	23.3197i	−1.34861	+	1.34861i
$300$	−5.15713	−	2.36151i	−0.297747	−	0.136342i
$301$	−2.23835	−	2.23835i	−0.129016	−	0.129016i
$302$	5.09154	+	3.53895i	0.292985	+	0.203644i
$303$	2.17005			0.124666
$304$	7.84669	+	0.577223i	0.450039	+	0.0331060i
$305$	−4.31634			−0.247153
$306$	11.0657	+	7.69139i	0.632584	+	0.439687i
$307$	−6.45124	−	6.45124i	−0.368192	−	0.368192i	0.498626	−	0.866817i	$-0.333838\pi$
$307$	−6.45124	−	6.45124i	−0.368192	−	0.368192i	−0.866817	+	0.498626i	$0.833838\pi$
$308$	5.00040	−	10.9200i	0.284924	−	0.622224i
$309$	18.1318	−	18.1318i	1.03148	−	1.03148i
$310$	−2.39237	−	13.2986i	−0.135877	−	0.755312i
$311$		−	5.52595i		−	0.313348i	−0.987650	−	0.156674i	$-0.949923\pi$
$311$		−	5.52595i		−	0.313348i	0.987650	−	0.156674i	$-0.0500772\pi$
$312$	−9.02082	+	35.1199i	−0.510703	+	1.98827i
$313$		−	8.81246i		−	0.498110i	−0.968489	−	0.249055i	$-0.919880\pi$
$313$		−	8.81246i		−	0.498110i	0.968489	−	0.249055i	$-0.0801200\pi$
$314$	−4.40242	+	0.791976i	−0.248443	+	0.0446938i
$315$	−3.56607	+	3.56607i	−0.200925	+	0.200925i
$316$	0.941535	+	2.53220i	0.0529655	+	0.142447i
$317$	18.1965	+	18.1965i	1.02202	+	1.02202i	0.999752	+	0.0222677i	$0.00708863\pi$
$317$	18.1965	+	18.1965i	1.02202	+	1.02202i	0.0222677	+	0.999752i	$0.492911\pi$
$318$	27.8246	−	40.0316i	1.56032	−	2.24486i
$319$	0.602989			0.0337609
$320$	7.68277	−	2.23047i	0.429480	−	0.124687i
$321$	−51.7737			−2.88973
$322$	5.88874	−	8.47221i	0.328167	−	0.472138i
$323$	2.62803	+	2.62803i	0.146227	+	0.146227i
$324$	0.909041	+	2.44481i	0.0505023	+	0.135823i
$325$	3.19634	−	3.19634i	0.177301	−	0.177301i
$326$	2.74409	−	0.493650i	0.151981	−	0.0273408i
$327$			1.07553i			0.0594768i
$328$	1.27342	−	4.95767i	0.0703126	−	0.273742i
$329$		−	3.01597i		−	0.166276i
$330$	4.26444	+	23.7051i	0.234750	+	1.30492i
$331$	4.71967	−	4.71967i	0.259416	−	0.259416i	−0.565400	−	0.824817i	$-0.691278\pi$
$331$	4.71967	−	4.71967i	0.259416	−	0.259416i	0.824817	+	0.565400i	$0.191278\pi$
$332$	3.93665	−	8.59696i	0.216052	−	0.471819i
$333$	40.4272	+	40.4272i	2.21540	+	2.21540i
$334$	5.56048	+	3.86489i	0.304256	+	0.211477i
$335$	−9.08486			−0.496359
$336$	0.832260	−	11.3136i	0.0454035	−	0.617209i
$337$	−19.2480			−1.04851			−0.524253	−	0.851563i	$-0.675655\pi$
$337$	−19.2480			−1.04851			−0.524253	+	0.851563i	$0.675655\pi$
$338$	−8.63185	−	5.99970i	−0.469511	−	0.326341i
$339$	22.9099	+	22.9099i	1.24429	+	1.24429i
$340$	3.43590	+	1.57334i	0.186338	+	0.0853264i
$341$	−40.5715	+	40.5715i	−2.19707	+	2.19707i
$342$	2.48384	+	13.8071i	0.134311	+	0.746602i
$343$		−	1.00000i		−	0.0539949i
$344$	−7.70701	+	4.55693i	−0.415534	+	0.245693i
$345$			20.6911i			1.11397i
$346$	17.6256	−	3.17076i	0.947556	−	0.170461i
$347$	−1.95859	+	1.95859i	−0.105143	+	0.105143i	−0.757721	−	0.652578i	$-0.773687\pi$
$347$	−1.95859	+	1.95859i	−0.105143	+	0.105143i	0.652578	+	0.757721i	$0.273687\pi$
$348$	0.533834	−	0.198493i	0.0286165	−	0.0106403i
$349$	−16.8489	−	16.8489i	−0.901901	−	0.901901i	0.0936994	−	0.995601i	$-0.470131\pi$
$349$	−16.8489	−	16.8489i	−0.901901	−	0.901901i	−0.995601	+	0.0936994i	$0.970131\pi$
$350$	−0.807148	+	1.16125i	−0.0431439	+	0.0620717i
$351$	−26.1933			−1.39810
$352$	−26.3967	−	21.3826i	−1.40695	−	1.13969i
$353$	−20.0346			−1.06634			−0.533168	−	0.846009i	$-0.678999\pi$
$353$	−20.0346			−1.06634			−0.533168	+	0.846009i	$0.678999\pi$
$354$	−20.8505	+	29.9979i	−1.10819	+	1.59437i
$355$	7.27023	+	7.27023i	0.385864	+	0.385864i
$356$	−7.95368	+	2.95737i	−0.421544	+	0.156740i
$357$	3.78918	−	3.78918i	0.200545	−	0.200545i
$358$	−22.8550	+	4.11152i	−1.20793	+	0.217301i
$359$		−	11.1235i		−	0.587074i	−0.955948	−	0.293537i	$-0.905168\pi$
$359$		−	11.1235i		−	0.587074i	0.955948	−	0.293537i	$-0.0948325\pi$
$360$	7.25995	+	12.2786i	0.382633	+	0.647137i
$361$		−	15.1310i		−	0.796369i
$362$	0.131698	+	0.732081i	0.00692191	+	0.0384773i
$363$	50.2602	−	50.2602i	2.63797	−	2.63797i
$364$	8.21982	+	3.76396i	0.430836	+	0.197285i
$365$	−9.93991	−	9.93991i	−0.520278	−	0.520278i
$366$	14.2154	+	9.88060i	0.743049	+	0.516467i
$367$	−12.7001			−0.662942			−0.331471	−	0.943465i	$-0.607545\pi$
$367$	−12.7001			−0.662942			−0.331471	+	0.943465i	$0.607545\pi$
$368$	−19.0660	−	22.0938i	−0.993882	−	1.15172i
$369$	9.12666			0.475115
$370$	13.1647	+	9.15032i	0.684400	+	0.475703i
$371$	−8.59501	−	8.59501i	−0.446231	−	0.446231i
$372$	−22.5631	+	49.2739i	−1.16984	+	2.55473i
$373$	11.1021	−	11.1021i	0.574847	−	0.574847i	−0.358632	−	0.933479i	$-0.616757\pi$
$373$	11.1021	−	11.1021i	0.574847	−	0.574847i	0.933479	+	0.358632i	$0.116757\pi$
$374$	−2.84115	−	15.7933i	−0.146912	−	0.816653i
$375$		−	2.83605i		−	0.146453i
$376$	−8.26226	−	2.12222i	−0.426093	−	0.109445i
$377$			0.453889i			0.0233765i
$378$	8.06531	−	1.45091i	0.414835	−	0.0746270i
$379$	−18.2605	+	18.2605i	−0.937981	+	0.937981i	−0.998186	−	0.0602048i	$-0.980825\pi$
$379$	−18.2605	+	18.2605i	−0.937981	+	0.937981i	0.0602048	+	0.998186i	$0.480825\pi$
$380$	1.37103	+	3.68730i	0.0703324	+	0.189155i
$381$	−7.19729	−	7.19729i	−0.368729	−	0.368729i
$382$	−5.73118	+	8.24553i	−0.293233	+	0.421878i
$383$	10.5226			0.537679			0.268839	−	0.963185i	$-0.413360\pi$
$383$	10.5226			0.537679			0.268839	+	0.963185i	$0.413360\pi$
$384$	−30.4081	−	10.2409i	−1.55176	−	0.522606i
$385$	6.00521			0.306054
$386$	−0.394175	+	0.567105i	−0.0200630	+	0.0288649i
$387$	−11.2884	−	11.2884i	−0.573823	−	0.573823i
$388$	−1.77276	−	4.76774i	−0.0899984	−	0.242045i
$389$	0.113239	−	0.113239i	0.00574144	−	0.00574144i	−0.704230	−	0.709972i	$-0.748708\pi$
$389$	0.113239	−	0.113239i	0.00574144	−	0.00574144i	0.709972	+	0.704230i	$0.248708\pi$
$390$	−17.8436	+	3.20998i	−0.903543	+	0.162544i
$391$		−	13.7853i		−	0.697152i
$392$	−2.73950	−	0.703661i	−0.138366	−	0.0355403i
$393$		−	9.46195i		−	0.477292i
$394$	4.10465	+	22.8168i	0.206789	+	1.14949i
$395$	−0.955152	+	0.955152i	−0.0480589	+	0.0480589i
$396$	25.2179	−	55.0715i	1.26725	−	2.76745i
$397$	5.28638	+	5.28638i	0.265316	+	0.265316i	0.827210	−	0.561894i	$-0.189927\pi$
$397$	5.28638	+	5.28638i	0.265316	+	0.265316i	−0.561894	+	0.827210i	$0.689927\pi$
$398$	−5.64882	−	3.92629i	−0.283150	−	0.196807i
$399$	5.57844			0.279271
$400$	2.61330	+	3.02831i	0.130665	+	0.151416i
$401$	5.29274			0.264307			0.132153	−	0.991229i	$-0.457811\pi$
$401$	5.29274			0.264307			0.132153	+	0.991229i	$0.457811\pi$
$402$	29.9199	+	20.7963i	1.49227	+	1.03722i
$403$	−30.5395	−	30.5395i	−1.52128	−	1.52128i
$404$	−1.39139	−	0.637136i	−0.0692244	−	0.0316987i
$405$	−0.922188	+	0.922188i	−0.0458239	+	0.0458239i
$406$	−0.0251421	−	0.139759i	−0.00124778	−	0.00693613i
$407$		−	68.0787i		−	3.37454i
$408$	−7.71417	−	13.0468i	−0.381908	−	0.645912i
$409$		−	5.05352i		−	0.249881i	−0.992164	−	0.124940i	$-0.960126\pi$
$409$		−	5.05352i		−	0.249881i	0.992164	−	0.124940i	$-0.0398739\pi$
$410$	2.51887	−	0.453134i	0.124398	−	0.0223787i
$411$	−15.4278	+	15.4278i	−0.760998	+	0.760998i
$412$	−16.9493	+	6.30218i	−0.835034	+	0.310486i
$413$	6.44071	+	6.44071i	0.316927	+	0.316927i
$414$	29.6980	−	42.7270i	1.45958	−	2.09992i
$415$	4.72771			0.232074
$416$	16.0953	−	19.8697i	0.789139	−	0.974190i
$417$	26.0835			1.27732
$418$	9.53410	−	13.7168i	0.466328	−	0.670913i
$419$	−23.5218	−	23.5218i	−1.14912	−	1.14912i	−0.986727	−	0.162389i	$-0.948080\pi$
$419$	−23.5218	−	23.5218i	−1.14912	−	1.14912i	−0.162389	−	0.986727i	$-0.551920\pi$
$420$	5.31648	−	1.97680i	0.259418	−	0.0964580i
$421$	−16.3920	+	16.3920i	−0.798896	+	0.798896i	−0.982921	−	0.184026i	$-0.941087\pi$
$421$	−16.3920	+	16.3920i	−0.798896	+	0.798896i	0.184026	+	0.982921i	$0.441087\pi$
$422$	−29.5213	+	5.31076i	−1.43707	+	0.258524i
$423$		−	15.2101i		−	0.739541i
$424$	−29.5940	+	17.4981i	−1.43721	+	0.849781i
$425$			1.88950i			0.0916542i
$426$	−7.30125	−	40.5860i	−0.353747	−	1.96640i
$427$	3.05212	−	3.05212i	0.147702	−	0.147702i
$428$	33.1963	+	15.2010i	1.60460	+	0.734767i
$429$	54.4372	+	54.4372i	2.62825	+	2.62825i
$430$	−3.67596	−	2.55503i	−0.177271	−	0.123215i
$431$	−3.44838			−0.166103			−0.0830514	−	0.996545i	$-0.526467\pi$
$431$	−3.44838			−0.166103			−0.0830514	+	0.996545i	$0.526467\pi$
$432$	1.70046	−	23.1159i	0.0818136	−	1.11216i
$433$	27.5735			1.32510			0.662549	−	0.749018i	$-0.269474\pi$
$433$	27.5735			1.32510			0.662549	+	0.749018i	$0.269474\pi$
$434$	11.0952	+	7.71190i	0.532588	+	0.370183i
$435$	0.201363	+	0.201363i	0.00965463	+	0.00965463i
$436$	0.315780	−	0.689607i	0.0151231	−	0.0330262i
$437$	10.1474	−	10.1474i	0.485414	−	0.485414i
$438$	9.98231	+	55.4894i	0.476973	+	2.65139i
$439$		−	21.8348i		−	1.04212i	−0.853521	−	0.521059i	$-0.825537\pi$
$439$		−	21.8348i		−	1.04212i	0.853521	−	0.521059i	$-0.174463\pi$
$440$	4.22563	−	16.4513i	0.201449	−	0.784283i
$441$		−	5.04319i		−	0.240152i
$442$	11.8881	−	2.13863i	0.565461	−	0.101724i
$443$	−13.5426	+	13.5426i	−0.643429	+	0.643429i	−0.951397	−	0.307968i	$-0.900351\pi$
$443$	−13.5426	+	13.5426i	−0.643429	+	0.643429i	0.307968	+	0.951397i	$0.400351\pi$
$444$	−22.4102	−	60.2709i	−1.06354	−	2.86033i
$445$	−3.00015	−	3.00015i	−0.142221	−	0.142221i
$446$	4.33582	−	6.23801i	0.205307	−	0.295378i
$447$	51.9001			2.45479
$448$	−3.85536	+	7.00972i	−0.182149	+	0.331178i
$449$	34.4484			1.62572			0.812859	−	0.582460i	$-0.197910\pi$
$449$	34.4484			1.62572			0.812859	+	0.582460i	$0.197910\pi$
$450$	−4.07060	+	5.85642i	−0.191890	+	0.276075i
$451$	−7.68457	−	7.68457i	−0.361852	−	0.361852i
$452$	−7.96292	−	21.4158i	−0.374544	−	1.00731i
$453$	8.79266	−	8.79266i	0.413115	−	0.413115i
$454$	31.1115	−	5.59683i	1.46014	−	0.262672i
$455$			4.52031i			0.211915i
$456$	3.92533	−	15.2821i	0.183820	−	0.715651i
$457$			13.3038i			0.622324i	0.950357	+	0.311162i	$0.100718\pi$
$457$			13.3038i			0.622324i	−0.950357	+	0.311162i	$0.899282\pi$
$458$	0.0289724	+	0.161051i	0.00135379	+	0.00752543i
$459$	7.74201	−	7.74201i	0.361366	−	0.361366i
$460$	6.07499	−	13.2667i	0.283248	−	0.618564i
$461$	3.51980	+	3.51980i	0.163934	+	0.163934i	0.784307	−	0.620373i	$-0.213019\pi$
$461$	3.51980	+	3.51980i	0.163934	+	0.163934i	−0.620373	+	0.784307i	$0.713019\pi$
$462$	−19.7774	−	13.7466i	−0.920129	−	0.639549i
$463$	10.0668			0.467844			0.233922	−	0.972255i	$-0.424844\pi$
$463$	10.0668			0.467844			0.233922	+	0.972255i	$0.424844\pi$
$464$	−0.400562	−	0.0294664i	−0.0185956	−	0.00136794i
$465$	−27.0971			−1.25660
$466$	19.8739	+	13.8137i	0.920642	+	0.639906i
$467$	22.3554	+	22.3554i	1.03448	+	1.03448i	0.999384	+	0.0350992i	$0.0111747\pi$
$467$	22.3554	+	22.3554i	1.03448	+	1.03448i	0.0350992	+	0.999384i	$0.488825\pi$
$468$	41.4541	+	18.9823i	1.91622	+	0.877459i
$469$	6.42396	−	6.42396i	0.296631	−	0.296631i
$470$	−0.755174	−	4.19784i	−0.0348336	−	0.193632i
$471$			8.97029i			0.413329i
$472$	22.1764	−	13.1123i	1.02075	−	0.603541i
$473$			19.0095i			0.874059i
$474$	5.33213	−	0.959227i	0.244913	−	0.0440588i
$475$	−1.39086	+	1.39086i	−0.0638170	+	0.0638170i
$476$	−3.54207	+	1.31703i	−0.162351	+	0.0603659i
$477$	−43.3463	−	43.3463i	−1.98469	−	1.98469i
$478$	8.74002	−	12.5744i	0.399759	−	0.575140i
$479$	−34.6297			−1.58227			−0.791136	−	0.611640i	$-0.790510\pi$
$479$	−34.6297			−1.58227			−0.791136	+	0.611640i	$0.790510\pi$
$480$	−1.67444	−	15.9555i	−0.0764274	−	0.728266i
$481$	51.2450			2.33657
$482$	5.76204	−	8.28993i	0.262454	−	0.377596i
$483$	−14.6308	−	14.6308i	−0.665725	−	0.665725i
$484$	−46.9824	+	17.4692i	−2.13556	+	0.794055i
$485$	1.79840	−	1.79840i	0.0816612	−	0.0816612i
$486$	−19.0478	+	3.42662i	−0.864027	+	0.155435i
$487$			26.0570i			1.18076i	0.807127	+	0.590378i	$0.201021\pi$
$487$			26.0570i			1.18076i	−0.807127	+	0.590378i	$0.798979\pi$
$488$	−6.21362	−	10.5089i	−0.281277	−	0.475717i
$489$		−	5.59131i		−	0.252848i
$490$	−0.250392	−	1.39187i	−0.0113115	−	0.0628783i
$491$	0.607000	−	0.607000i	0.0273935	−	0.0273935i	−0.693277	−	0.720671i	$-0.743834\pi$
$491$	0.607000	−	0.607000i	0.0273935	−	0.0273935i	0.720671	+	0.693277i	$0.243834\pi$
$492$	−9.33286	−	4.27363i	−0.420758	−	0.192670i
$493$	−0.134157	−	0.134157i	−0.00604212	−	0.00604212i
$494$	10.3251	+	7.17662i	0.464548	+	0.322891i
$495$	30.2854			1.36123
$496$	28.9340	−	24.9688i	1.29918	−	1.12113i
$497$	−10.2817			−0.461196
$498$	−15.5701	−	10.8223i	−0.697714	−	0.484957i
$499$	−6.21783	−	6.21783i	−0.278348	−	0.278348i	0.554101	−	0.832449i	$-0.313062\pi$
$499$	−6.21783	−	6.21783i	−0.278348	−	0.278348i	−0.832449	+	0.554101i	$0.813062\pi$
$500$	−0.832677	+	1.81842i	−0.0372384	+	0.0813222i
$501$	9.60248	−	9.60248i	0.429007	−	0.429007i
$502$	−6.40364	−	35.5964i	−0.285809	−	1.58875i
$503$			30.9804i			1.38135i	0.723166	+	0.690674i	$0.242686\pi$
$503$			30.9804i			1.38135i	−0.723166	+	0.690674i	$0.757314\pi$
$504$	−13.8158	−	3.54869i	−0.615405	−	0.158071i
$505$		−	0.765166i		−	0.0340494i
$506$	−60.9812	+	10.9703i	−2.71095	+	0.487688i
$507$	−14.9065	+	14.9065i	−0.662021	+	0.662021i
$508$	2.50161	+	6.72792i	0.110991	+	0.298503i
$509$	11.9538	+	11.9538i	0.529842	+	0.529842i	0.920525	−	0.390683i	$-0.127761\pi$
$509$	11.9538	+	11.9538i	0.529842	+	0.529842i	−0.390683	+	0.920525i	$0.627761\pi$
$510$	4.32527	−	6.22283i	0.191526	−	0.275552i
$511$	14.0571			0.621852
$512$	16.4903	+	15.4942i	0.728774	+	0.684755i
$513$	11.3978			0.503225
$514$	−10.1315	+	14.5764i	−0.446882	+	0.642936i
$515$	−6.39333	−	6.39333i	−0.281724	−	0.281724i
$516$	6.25758	+	16.8294i	0.275474	+	0.740872i
$517$	−12.8068	+	12.8068i	−0.563242	+	0.563242i
$518$	−15.7791	+	2.83859i	−0.693294	+	0.124721i
$519$		−	35.9135i		−	1.57643i
$520$	12.3834	+	3.18077i	0.543048	+	0.139486i
$521$			42.1163i			1.84515i	0.385821	+	0.922574i	$0.373918\pi$
$521$			42.1163i			1.84515i	−0.385821	+	0.922574i	$0.626082\pi$
$522$	−0.126796	−	0.704831i	−0.00554972	−	0.0308496i
$523$	−20.3497	+	20.3497i	−0.889832	+	0.889832i	−0.994507	−	0.104674i	$-0.966620\pi$
$523$	−20.3497	+	20.3497i	−0.889832	+	0.889832i	0.104674	+	0.994507i	$0.466620\pi$
$524$	−2.77807	+	6.06682i	−0.121361	+	0.265030i
$525$	2.00539	+	2.00539i	0.0875224	+	0.0875224i
$526$	−8.79510	−	6.11317i	−0.383485	−	0.266547i
$527$	18.0532			0.786411
$528$	−51.5754	+	44.5073i	−2.24453	+	1.93693i
$529$	−30.2278			−1.31425
$530$	−14.1153	−	9.81103i	−0.613128	−	0.426164i
$531$	32.4817	+	32.4817i	1.40959	+	1.40959i
$532$	−3.57678	−	1.63785i	−0.155073	−	0.0710099i
$533$	5.78442	−	5.78442i	0.250551	−	0.250551i
$534$	3.01295	+	16.7483i	0.130383	+	0.724769i
$535$			18.2556i			0.789257i
$536$	−13.0782	−	22.1187i	−0.564890	−	0.955384i
$537$			46.5690i			2.00960i
$538$	−1.06899	+	0.192308i	−0.0460876	+	0.00829097i
$539$	−4.24632	+	4.24632i	−0.182902	+	0.182902i
$540$	10.8626	−	4.03897i	0.467451	−	0.173810i
$541$	4.30506	+	4.30506i	0.185089	+	0.185089i	0.793569	−	0.608480i	$-0.208221\pi$
$541$	4.30506	+	4.30506i	0.185089	+	0.185089i	−0.608480	+	0.793569i	$0.708221\pi$
$542$	21.9534	−	31.5847i	0.942981	−	1.35668i
$543$	1.49168			0.0640139
$544$	1.11558	+	10.6302i	0.0478303	+	0.455768i
$545$	0.379234			0.0162446
$546$	10.3475	−	14.8871i	0.442832	−	0.637109i
$547$	−12.5707	−	12.5707i	−0.537483	−	0.537483i	0.385306	−	0.922789i	$-0.374096\pi$
$547$	−12.5707	−	12.5707i	−0.537483	−	0.537483i	−0.922789	+	0.385306i	$0.874096\pi$
$548$	14.4217	−	5.36234i	0.616064	−	0.229068i
$549$	15.3924	−	15.3924i	0.656931	−	0.656931i
$550$	8.35847	−	1.50365i	0.356406	−	0.0641160i
$551$		−	0.197506i		−	0.00841403i
$552$	−50.3762	+	29.7860i	−2.14416	+	1.26778i
$553$		−	1.35079i		−	0.0574414i
$554$	1.87206	+	10.4064i	0.0795362	+	0.442124i
$555$	22.7343	−	22.7343i	0.965019	−	0.965019i
$556$	−16.7242	−	7.65823i	−0.709265	−	0.324781i
$557$	3.76491	+	3.76491i	0.159524	+	0.159524i	0.782356	−	0.622832i	$-0.214018\pi$
$557$	3.76491	+	3.76491i	0.159524	+	0.159524i	−0.622832	+	0.782356i	$0.714018\pi$
$558$	55.9553	+	38.8926i	2.36878	+	1.64645i
$559$	−14.3091			−0.605210
$560$	−3.98922	−	0.293457i	−0.168575	−	0.0124008i
$561$	−32.1802			−1.35865
$562$	−12.1672	−	8.45703i	−0.513244	−	0.356738i
$563$	19.3985	+	19.3985i	0.817551	+	0.817551i	0.985753	−	0.168202i	$-0.0537960\pi$
$563$	19.3985	+	19.3985i	0.817551	+	0.817551i	−0.168202	+	0.985753i	$0.553796\pi$
$564$	−7.12226	+	15.5538i	−0.299901	+	0.654932i
$565$	8.07809	−	8.07809i	0.339848	−	0.339848i
$566$	−0.909076	−	5.05335i	−0.0382113	−	0.212408i
$567$		−	1.30417i		−	0.0547701i
$568$	−7.23481	+	28.1666i	−0.303566	+	1.18185i
$569$		−	5.30203i		−	0.222273i	−0.993805	−	0.111136i	$-0.964551\pi$
$569$		−	5.30203i		−	0.222273i	0.993805	−	0.111136i	$-0.0354490\pi$
$570$	7.76446	−	1.39679i	0.325218	−	0.0585053i
$571$	−0.750198	+	0.750198i	−0.0313948	+	0.0313948i	−0.722630	−	0.691235i	$-0.757067\pi$
$571$	−0.750198	+	0.750198i	−0.0313948	+	0.0313948i	0.691235	+	0.722630i	$0.257067\pi$
$572$	−18.9210	−	50.8870i	−0.791129	−	2.12769i
$573$	14.2393	+	14.2393i	0.594857	+	0.594857i
$574$	−1.46070	+	2.10152i	−0.0609682	+	0.0877159i
$575$	7.29574			0.304253
$576$	−19.4433	+	35.3513i	−0.810137	+	1.47297i
$577$	23.5642			0.980993			0.490496	−	0.871443i	$-0.336816\pi$
$577$	23.5642			0.980993			0.490496	+	0.871443i	$0.336816\pi$
$578$	10.8398	−	15.5954i	0.450877	−	0.648684i
$579$	0.979343	+	0.979343i	0.0407001	+	0.0407001i
$580$	−0.0699890	−	0.188231i	−0.00290614	−	0.00781588i
$581$	−3.34300	+	3.34300i	−0.138691	+	0.138691i
$582$	−10.0396	+	1.80607i	−0.416153	+	0.0748642i
$583$			72.9944i			3.02312i
$584$	9.89147	−	38.5096i	0.409312	−	1.59354i
$585$			22.7968i			0.942531i
$586$	−5.93203	−	32.9748i	−0.245050	−	1.36218i
$587$	19.0407	−	19.0407i	0.785894	−	0.785894i	−0.194924	−	0.980818i	$-0.562446\pi$
$587$	19.0407	−	19.0407i	0.785894	−	0.785894i	0.980818	+	0.194924i	$0.0624462\pi$
$588$	−2.36151	+	5.15713i	−0.0973872	+	0.212676i
$589$	13.2890	+	13.2890i	0.547563	+	0.547563i
$590$	10.5773	+	7.35194i	0.435462	+	0.302675i
$591$	46.4911			1.91239
$592$	−3.32681	+	45.2243i	−0.136731	+	1.85871i
$593$	26.8156			1.10118			0.550591	−	0.834775i	$-0.314402\pi$
$593$	26.8156			1.10118			0.550591	+	0.834775i	$0.314402\pi$
$594$	−40.4090	−	28.0869i	−1.65800	−	1.15242i
$595$	−1.33608	−	1.33608i	−0.0547738	−	0.0547738i
$596$	−33.2773	−	15.2381i	−1.36309	−	0.624176i
$597$	−9.75504	+	9.75504i	−0.399247	+	0.399247i
$598$	−8.25767	−	45.9025i	−0.337681	−	1.87709i
$599$		−	31.7190i		−	1.29600i	−0.761638	−	0.648002i	$-0.775605\pi$
$599$		−	31.7190i		−	1.29600i	0.761638	−	0.648002i	$-0.224395\pi$
$600$	6.90488	−	4.08265i	0.281891	−	0.166674i
$601$			26.8408i			1.09486i	0.836852	+	0.547429i	$0.184393\pi$
$601$			26.8408i			1.09486i	−0.836852	+	0.547429i	$0.815607\pi$
$602$	4.40598	−	0.792617i	0.179574	−	0.0323047i
$603$	32.3972	−	32.3972i	1.31932	−	1.31932i
$604$	−8.21924	+	3.05612i	−0.334436	+	0.124352i
$605$	−17.7219	−	17.7219i	−0.720497	−	0.720497i
$606$	−1.75155	+	2.51998i	−0.0711519	+	0.102367i
$607$	14.7538			0.598839			0.299419	−	0.954122i	$-0.403207\pi$
$607$	14.7538			0.598839			0.299419	+	0.954122i	$0.403207\pi$
$608$	−7.00374	+	8.64610i	−0.284039	+	0.350646i
$609$	−0.284771			−0.0115395
$610$	3.48393	−	5.01238i	0.141060	−	0.202945i
$611$	−9.64008	−	9.64008i	−0.389996	−	0.389996i
$612$	−17.8633	+	6.64202i	−0.722082	+	0.268488i
$613$	32.8990	−	32.8990i	1.32878	−	1.32878i	0.422340	−	0.906438i	$-0.361209\pi$
$613$	32.8990	−	32.8990i	1.32878	−	1.32878i	0.906438	−	0.422340i	$-0.138791\pi$
$614$	12.6986	−	2.28443i	0.512475	−	0.0921921i
$615$		−	5.13240i		−	0.206958i
$616$	8.64483	+	14.6208i	0.348310	+	0.589088i
$617$		−	3.32852i		−	0.134001i	−0.997753	−	0.0670005i	$-0.978657\pi$
$617$		−	3.32852i		−	0.134001i	0.997753	−	0.0670005i	$-0.0213429\pi$
$618$	6.42061	+	35.6907i	0.258275	+	1.43569i
$619$	25.1347	−	25.1347i	1.01025	−	1.01025i	0.0103008	−	0.999947i	$-0.496721\pi$
$619$	25.1347	−	25.1347i	1.01025	−	1.01025i	0.999947	−	0.0103008i	$-0.00327891\pi$
$620$	17.3741	+	7.95582i	0.697761	+	0.319513i
$621$	−29.8935	−	29.8935i	−1.19958	−	1.19958i
$622$	6.41703	+	4.46025i	0.257300	+	0.178840i
$623$	4.24285			0.169986
$624$	−33.5021	−	38.8224i	−1.34116	−	1.55414i
$625$	−1.00000			−0.0400000
$626$	10.2335	+	7.11296i	0.409013	+	0.284291i
$627$	−23.6878	−	23.6878i	−0.946002	−	0.946002i
$628$	2.63371	−	5.75157i	0.105097	−	0.229513i
$629$	−15.1466	+	15.1466i	−0.603934	+	0.603934i
$630$	−1.26277	−	7.01946i	−0.0503100	−	0.279662i
$631$			33.5859i			1.33703i	0.743698	+	0.668516i	$0.233070\pi$
$631$			33.5859i			1.33703i	−0.743698	+	0.668516i	$0.766930\pi$
$632$	−3.70049	−	0.950498i	−0.147198	−	0.0378088i
$633$			60.1521i			2.39083i
$634$	−35.8181	+	6.44353i	−1.42252	+	0.255905i
$635$	−2.53779	+	2.53779i	−0.100709	+	0.100709i
$636$	24.0284	+	64.6229i	0.952787	+	2.56246i
$637$	−3.19634	−	3.19634i	−0.126644	−	0.126644i
$638$	−0.486701	+	0.700224i	−0.0192687	+	0.0277221i
$639$	−51.8523			−2.05125
$640$	−3.61099	+	10.7220i	−0.142737	+	0.423823i
$641$	5.72496			0.226122			0.113061	−	0.993588i	$-0.463934\pi$
$641$	5.72496			0.226122			0.113061	+	0.993588i	$0.463934\pi$
$642$	41.7890	−	60.1225i	1.64928	−	2.37284i
$643$	20.2653	+	20.2653i	0.799186	+	0.799186i	0.982967	−	0.183781i	$-0.0588338\pi$
$643$	20.2653	+	20.2653i	0.799186	+	0.799186i	−0.183781	+	0.982967i	$0.558834\pi$
$644$	5.08532	+	13.6767i	0.200390	+	0.538936i
$645$	−6.34808	+	6.34808i	−0.249956	+	0.249956i
$646$	−5.17302	+	0.930604i	−0.203530	+	0.0366141i
$647$			19.6615i			0.772972i	0.922295	+	0.386486i	$0.126311\pi$
$647$			19.6615i			0.772972i	−0.922295	+	0.386486i	$0.873689\pi$
$648$	−3.57278	−	0.917695i	−0.140352	−	0.0360505i
$649$		−	54.6987i		−	2.14711i
$650$	1.13185	+	6.29169i	0.0443947	+	0.246780i
$651$	19.1605	−	19.1605i	0.750960	−	0.750960i
$652$	−1.64163	+	3.58504i	−0.0642913	+	0.140401i
$653$	−3.24961	−	3.24961i	−0.127167	−	0.127167i	0.640659	−	0.767826i	$-0.278661\pi$
$653$	−3.24961	−	3.24961i	−0.127167	−	0.127167i	−0.767826	+	0.640659i	$0.778661\pi$
$654$	−1.24896	−	0.868110i	−0.0488383	−	0.0339458i
$655$	−3.33631			−0.130361
$656$	4.72929	+	5.48034i	0.184648	+	0.213971i
$657$	70.8928			2.76579
$658$	3.50231	+	2.43433i	0.136534	+	0.0949002i
$659$	30.5441	+	30.5441i	1.18983	+	1.18983i	0.977114	+	0.212717i	$0.0682311\pi$
$659$	30.5441	+	30.5441i	1.18983	+	1.18983i	0.212717	+	0.977114i	$0.431769\pi$
$660$	−30.9696	−	14.1814i	−1.20549	−	0.552009i
$661$	−6.92446	+	6.92446i	−0.269330	+	0.269330i	−0.828830	−	0.559500i	$-0.810993\pi$
$661$	−6.92446	+	6.92446i	−0.269330	+	0.269330i	0.559500	+	0.828830i	$0.310993\pi$
$662$	1.67127	+	9.29021i	0.0649557	+	0.361074i
$663$		−	24.2231i		−	0.940746i
$664$	6.80580	+	11.5105i	0.264116	+	0.446693i
$665$		−	1.96697i		−	0.0762760i
$666$	−79.5770	+	14.3156i	−3.08354	+	0.554717i
$667$	−0.518007	+	0.518007i	−0.0200573	+	0.0200573i
$668$	−8.97625	+	3.33759i	−0.347302	+	0.129135i
$669$	−10.7725	−	10.7725i	−0.416490	−	0.416490i
$670$	7.33282	−	10.5498i	0.283292	−	0.407576i
$671$	−25.9205			−1.00065
$672$	12.4663	+	10.0982i	0.480896	+	0.389548i
$673$	8.16111			0.314588			0.157294	−	0.987552i	$-0.449723\pi$
$673$	8.16111			0.314588			0.157294	+	0.987552i	$0.449723\pi$
$674$	15.5360	−	22.3518i	0.598424	−	0.860961i
$675$	4.09739	+	4.09739i	0.157709	+	0.157709i
$676$	13.9344	−	5.18114i	0.535937	−	0.199275i
$677$	−17.4422	+	17.4422i	−0.670360	+	0.670360i	−0.957799	−	0.287439i	$-0.907196\pi$
$677$	−17.4422	+	17.4422i	−0.670360	+	0.670360i	0.287439	+	0.957799i	$0.407196\pi$
$678$	−45.0958	+	8.11255i	−1.73190	+	0.311561i
$679$			2.54333i			0.0976039i
$680$	−4.60033	+	2.72004i	−0.176415	+	0.104309i
$681$		−	63.3923i		−	2.42920i
$682$	−14.3667	−	79.8611i	−0.550128	−	3.05804i
$683$	−30.5930	+	30.5930i	−1.17061	+	1.17061i	−0.188542	+	0.982065i	$0.560376\pi$
$683$	−30.5930	+	30.5930i	−1.17061	+	1.17061i	−0.982065	+	0.188542i	$0.939624\pi$
$684$	−18.0384	−	8.26000i	−0.689715	−	0.315829i
$685$	5.43990	+	5.43990i	0.207848	+	0.207848i
$686$	1.16125	+	0.807148i	0.0443369	+	0.0308170i
$687$	0.328155			0.0125199
$688$	0.928942	−	12.6279i	0.0354156	−	0.481435i
$689$	−54.9452			−2.09325
$690$	−24.0276	−	16.7008i	−0.914716	−	0.635787i
$691$	−19.1138	−	19.1138i	−0.727124	−	0.727124i	0.242922	−	0.970046i	$-0.421894\pi$
$691$	−19.1138	−	19.1138i	−0.727124	−	0.727124i	−0.970046	+	0.242922i	$0.921894\pi$
$692$	−10.5444	+	23.0270i	−0.400837	+	0.875357i
$693$	−21.4150	+	21.4150i	−0.813489	+	0.813489i
$694$	−0.693552	−	3.85530i	−0.0263269	−	0.146345i
$695$		−	9.19713i		−	0.348867i
$696$	−0.200382	+	0.780130i	−0.00759547	+	0.0295707i
$697$			3.41943i			0.129520i
$698$	33.1654	−	5.96632i	1.25533	−	0.225828i
$699$	34.3206	−	34.3206i	1.29813	−	1.29813i
$700$	−0.697026	−	1.87461i	−0.0263451	−	0.0708535i
$701$	−15.1156	−	15.1156i	−0.570907	−	0.570907i	0.361475	−	0.932382i	$-0.382273\pi$
$701$	−15.1156	−	15.1156i	−0.570907	−	0.570907i	−0.932382	+	0.361475i	$0.882273\pi$
$702$	21.1419	−	30.4171i	0.797948	−	1.14802i
$703$	−22.2988			−0.841016
$704$	46.1366	−	13.3944i	1.73884	−	0.504822i
$705$	−8.55345			−0.322142
$706$	16.1709	−	23.2653i	0.608600	−	0.875602i
$707$	0.541054	+	0.541054i	0.0203484	+	0.0203484i
$708$	−18.0058	−	48.4254i	−0.676698	−	1.81994i
$709$	−29.3194	+	29.3194i	−1.10111	+	1.10111i	−0.106836	+	0.994277i	$0.534072\pi$
$709$	−29.3194	+	29.3194i	−1.10111	+	1.10111i	−0.994277	+	0.106836i	$0.965928\pi$
$710$	−14.3107	+	2.57444i	−0.537073	+	0.0966171i
$711$		−	6.81228i		−	0.255481i
$712$	2.98553	−	11.6233i	0.111887	−	0.435601i
$713$		−	69.7072i		−	2.61056i
$714$	1.34178	+	7.45864i	0.0502148	+	0.279133i
$715$	19.1947	−	19.1947i	0.717841	−	0.717841i
$716$	13.6729	−	29.8591i	0.510978	−	1.11589i
$717$	−21.7149	−	21.7149i	−0.810960	−	0.810960i
$718$	12.9172	+	8.97828i	0.482065	+	0.335067i
$719$	23.3687			0.871505			0.435752	−	0.900067i	$-0.356482\pi$
$719$	23.3687			0.871505			0.435752	+	0.900067i	$0.356482\pi$
$720$	−20.1184	−	1.47996i	−0.749768	−	0.0551549i
$721$	9.04153			0.336724
$722$	17.5710	+	12.2130i	0.653924	+	0.454519i
$723$	−14.3160	−	14.3160i	−0.532419	−	0.532419i
$724$	−0.956432	−	0.437962i	−0.0355455	−	0.0162767i
$725$	0.0710013	−	0.0710013i	0.00263692	−	0.00263692i
$726$	17.7975	+	98.9322i	0.660527	+	3.67172i
$727$			45.4372i			1.68517i	0.538561	+	0.842587i	$0.318968\pi$
$727$			45.4372i			1.68517i	−0.538561	+	0.842587i	$0.681032\pi$
$728$	−11.0055	+	6.50724i	−0.407892	+	0.241174i
$729$			42.7240i			1.58237i
$730$	19.5657	−	3.51979i	0.724160	−	0.130273i
$731$	4.22936	−	4.22936i	0.156429	−	0.156429i
$732$	−22.9478	+	8.53255i	−0.848174	+	0.315372i
$733$	25.6921	+	25.6921i	0.948959	+	0.948959i	0.998759	−	0.0497999i	$-0.0158584\pi$
$733$	25.6921	+	25.6921i	0.948959	+	0.948959i	−0.0497999	+	0.998759i	$0.515858\pi$
$734$	10.2509	−	14.7481i	0.378367	−	0.544362i
$735$	−2.83605			−0.104609
$736$	41.0455	−	4.30750i	1.51296	−	0.158776i
$737$	−54.5565			−2.00961
$738$	−7.36656	+	10.5984i	−0.271167	+	0.390132i
$739$	−32.1797	−	32.1797i	−1.18375	−	1.18375i	−0.978765	−	0.204983i	$-0.934286\pi$
$739$	−32.1797	−	32.1797i	−1.18375	−	1.18375i	−0.204983	−	0.978765i	$-0.565714\pi$
$740$	−21.2517	+	7.90191i	−0.781228	+	0.290480i
$741$	17.8306	−	17.8306i	0.655023	−	0.655023i
$742$	16.9184	−	3.04356i	0.621096	−	0.111732i
$743$			30.3884i			1.11484i	0.830230	+	0.557421i	$0.188209\pi$
$743$			30.3884i			1.11484i	−0.830230	+	0.557421i	$0.811791\pi$
$744$	−39.0078	−	65.9728i	−1.43009	−	2.41868i
$745$		−	18.3001i		−	0.670464i
$746$	3.93135	+	21.8535i	0.143937	+	0.800113i
$747$	−16.8593	+	16.8593i	−0.616851	+	0.616851i
$748$	20.6333	+	9.44824i	0.754428	+	0.345462i
$749$	−12.9086	−	12.9086i	−0.471671	−	0.471671i
$750$	3.29338	+	2.28911i	0.120257	+	0.0835865i
$751$	25.2391			0.920987			0.460493	−	0.887663i	$-0.347673\pi$
$751$	25.2391			0.920987			0.460493	+	0.887663i	$0.347673\pi$
$752$	9.13330	−	7.88164i	0.333057	−	0.287414i
$753$	−72.5306			−2.64316
$754$	−0.527081	−	0.366355i	−0.0191952	−	0.0133419i
$755$	−3.10032	−	3.10032i	−0.112832	−	0.112832i
$756$	−4.82501	+	10.5370i	−0.175484	+	0.383226i
$757$	5.04085	−	5.04085i	0.183213	−	0.183213i	−0.609541	−	0.792754i	$-0.708646\pi$
$757$	5.04085	−	5.04085i	0.183213	−	0.183213i	0.792754	+	0.609541i	$0.208646\pi$
$758$	−6.46619	−	35.9441i	−0.234863	−	1.30555i
$759$			124.254i			4.51015i
$760$	−5.38852	−	1.38408i	−0.195462	−	0.0502060i
$761$			24.7274i			0.896366i	0.893942	+	0.448183i	$0.147929\pi$
$761$			24.7274i			0.896366i	−0.893942	+	0.448183i	$0.852071\pi$
$762$	14.1672	−	2.54861i	0.513222	−	0.0923265i
$763$	−0.268159	+	0.268159i	−0.00970801	+	0.00970801i
$764$	−4.94925	−	13.3107i	−0.179058	−	0.481565i
$765$	−6.73809	−	6.73809i	−0.243616	−	0.243616i
$766$	−8.49328	+	12.2194i	−0.306875	+	0.441505i
$767$	41.1735			1.48669
$768$	36.4361	−	27.0456i	1.31478	−	0.975923i
$769$	33.4831			1.20743			0.603715	−	0.797200i	$-0.293686\pi$
$769$	33.4831			1.20743			0.603715	+	0.797200i	$0.293686\pi$
$770$	−4.84709	+	6.97358i	−0.174677	+	0.251310i
$771$	25.1722	+	25.1722i	0.906553	+	0.906553i
$772$	−0.340396	−	0.915475i	−0.0122511	−	0.0329487i
$773$	−27.1079	+	27.1079i	−0.975005	+	0.975005i	−0.999695	−	0.0246905i	$-0.992140\pi$
$773$	−27.1079	+	27.1079i	−0.975005	+	0.975005i	0.0246905	+	0.999695i	$0.492140\pi$
$774$	22.2202	−	3.99731i	0.798688	−	0.143681i
$775$			9.55451i			0.343208i
$776$	6.96744	+	1.78964i	0.250117	+	0.0642443i
$777$			32.1512i			1.15342i
$778$	0.0400987	+	0.222900i	0.00143761	+	0.00799135i
$779$	−2.51704	+	2.51704i	−0.0901823	+	0.0901823i
$780$	10.6748	−	23.3118i	0.382218	−	0.834698i
$781$	43.6593	+	43.6593i	1.56225	+	1.56225i
$782$	16.0082	+	11.1268i	0.572453	+	0.397892i
$783$	−0.581840			−0.0207933
$784$	3.02831	−	2.61330i	0.108154	−	0.0933321i
$785$	3.16295			0.112891
$786$	10.9877	+	7.63719i	0.391920	+	0.272410i
$787$	−30.7982	−	30.7982i	−1.09784	−	1.09784i	−0.994663	−	0.103174i	$-0.967100\pi$
$787$	−30.7982	−	30.7982i	−1.09784	−	1.09784i	−0.103174	−	0.994663i	$-0.532900\pi$
$788$	−29.8092	−	13.6500i	−1.06191	−	0.486261i
$789$	−15.1884	+	15.1884i	−0.540722	+	0.540722i
$790$	−0.338226	−	1.88012i	−0.0120336	−	0.0668918i
$791$			11.4241i			0.406196i
$792$	43.5975	+	73.7353i	1.54917	+	2.62007i
$793$		−	19.5112i		−	0.692864i
$794$	−10.4057	+	1.87195i	−0.369285	+	0.0664329i
$795$	−24.3759	+	24.3759i	−0.864524	+	0.864524i
$796$	9.11886	−	3.39062i	0.323209	−	0.120177i
$797$	−37.5197	−	37.5197i	−1.32902	−	1.32902i	−0.906229	−	0.422786i	$-0.861052\pi$
$797$	−37.5197	−	37.5197i	−1.32902	−	1.32902i	−0.422786	−	0.906229i	$-0.638948\pi$
$798$	−4.50262	+	6.47799i	−0.159391	+	0.229318i
$799$	5.69868			0.201605
$800$	−5.62596	+	0.590413i	−0.198908	+	0.0208742i
$801$	21.3975			0.756043
$802$	−4.27202	+	6.14622i	−0.150850	+	0.217031i
$803$	−59.6912	−	59.6912i	−2.10646	−	2.10646i
$804$	−48.2995	+	17.9589i	−1.70339	+	0.633363i
$805$	−5.15887	+	5.15887i	−0.181826	+	0.181826i
$806$	60.1140	−	10.8143i	2.11743	−	0.380916i
$807$			2.17816i			0.0766750i
$808$	1.86294	−	1.10150i	0.0655379	−	0.0387506i
$809$		−	3.57657i		−	0.125746i	−0.998022	−	0.0628728i	$-0.979974\pi$
$809$		−	3.57657i		−	0.125746i	0.998022	−	0.0628728i	$-0.0200263\pi$
$810$	−0.326554	−	1.81524i	−0.0114739	−	0.0637810i
$811$	−1.41315	+	1.41315i	−0.0496224	+	0.0496224i	−0.731483	−	0.681860i	$-0.761171\pi$
$811$	−1.41315	+	1.41315i	−0.0496224	+	0.0496224i	0.681860	+	0.731483i	$0.261171\pi$
$812$	0.182589	+	0.0836099i	0.00640763	+	0.00293413i
$813$	−54.5442	−	54.5442i	−1.91295	−	1.91295i
$814$	79.0568	+	54.9496i	2.77094	+	1.92598i
$815$	−1.97151			−0.0690591
$816$	21.3771	+	1.57256i	0.748348	+	0.0550504i
$817$	6.22647			0.217837
$818$	5.86843	+	4.07894i	0.205185	+	0.142617i
$819$	−16.1198	−	16.1198i	−0.563270	−	0.563270i
$820$	−1.50690	+	3.29079i	−0.0526231	+	0.114920i
$821$	20.6442	−	20.6442i	0.720488	−	0.720488i	−0.248217	−	0.968705i	$-0.579844\pi$
$821$	20.6442	−	20.6442i	0.720488	−	0.720488i	0.968705	+	0.248217i	$0.0798444\pi$
$822$	−5.46310	−	30.3682i	−0.190548	−	1.05921i
$823$			30.4917i			1.06287i	0.847098	+	0.531436i	$0.178348\pi$
$823$			30.4917i			1.06287i	−0.847098	+	0.531436i	$0.821652\pi$
$824$	6.36218	−	24.7693i	0.221637	−	0.862879i
$825$		−	17.0311i		−	0.592946i
$826$	−12.6779	+	2.28070i	−0.441121	+	0.0793558i
$827$	−12.9323	+	12.9323i	−0.449700	+	0.449700i	−0.895255	−	0.445554i	$-0.853007\pi$
$827$	−12.9323	+	12.9323i	−0.449700	+	0.449700i	0.445554	+	0.895255i	$0.353007\pi$
$828$	25.6462	+	68.9739i	0.891267	+	2.39701i
$829$	24.8019	+	24.8019i	0.861407	+	0.861407i	0.991502	−	0.130095i	$-0.0415282\pi$
$829$	24.8019	+	24.8019i	0.861407	+	0.861407i	−0.130095	+	0.991502i	$0.541528\pi$
$830$	−3.81596	+	5.49007i	−0.132454	+	0.190563i
$831$	21.2038			0.735552
$832$	10.0824	+	34.7285i	0.349545	+	1.20399i
$833$	1.88950			0.0654673
$834$	−21.0532	+	30.2896i	−0.729014	+	1.04884i
$835$	−3.38586	−	3.38586i	−0.117173	−	0.117173i
$836$	8.23332	+	22.1430i	0.284755	+	0.765833i
$837$	39.1485	−	39.1485i	1.35317	−	1.35317i
$838$	46.3004	−	8.32924i	1.59942	−	0.287729i
$839$			7.59932i			0.262358i	0.991359	+	0.131179i	$0.0418762\pi$
$839$			7.59932i			0.262358i	−0.991359	+	0.131179i	$0.958124\pi$
$840$	−1.99562	+	7.76936i	−0.0688554	+	0.268068i
$841$		−	28.9899i		−	0.999652i
$842$	−5.80451	−	32.2660i	−0.200037	−	1.11196i
$843$	−21.0118	+	21.0118i	−0.723686	+	0.723686i
$844$	17.6609	−	38.5683i	0.607914	−	1.32758i
$845$	5.25607	+	5.25607i	0.180814	+	0.180814i
$846$	17.6628	+	12.2768i	0.607260	+	0.422085i
$847$	25.0625			0.861158
$848$	3.56703	−	48.4897i	0.122492	−	1.66514i
$849$	−10.2966			−0.353379
$850$	−2.19419	−	1.52510i	−0.0752601	−	0.0523107i
$851$	58.4841	+	58.4841i	2.00481	+	2.00481i
$852$	53.0239	+	24.2803i	1.81657	+	0.831829i
$853$	−13.6647	+	13.6647i	−0.467870	+	0.467870i	−0.901224	−	0.433354i	$-0.857330\pi$
$853$	−13.6647	+	13.6647i	−0.467870	+	0.467870i	0.433354	+	0.901224i	$0.357330\pi$
$854$	1.08078	+	6.00779i	0.0369834	+	0.205582i
$855$		−	9.91981i		−	0.339250i
$856$	−44.4465	+	26.2799i	−1.51915	+	0.898228i
$857$			7.08036i			0.241860i	0.992661	+	0.120930i	$0.0385877\pi$
$857$			7.08036i			0.241860i	−0.992661	+	0.120930i	$0.961412\pi$
$858$	−107.154	+	19.2766i	−3.65819	+	0.658092i
$859$	0.0841770	−	0.0841770i	0.00287208	−	0.00287208i	−0.705669	−	0.708541i	$-0.749354\pi$
$859$	0.0841770	−	0.0841770i	0.00287208	−	0.00287208i	0.708541	+	0.705669i	$0.249354\pi$
$860$	5.93409	−	2.20644i	0.202351	−	0.0752390i
$861$	3.62916	+	3.62916i	0.123681	+	0.123681i
$862$	2.78335	−	4.00445i	0.0948014	−	0.136392i
$863$	27.4876			0.935688			0.467844	−	0.883811i	$-0.345031\pi$
$863$	27.4876			0.935688			0.467844	+	0.883811i	$0.345031\pi$
$864$	25.4709	+	20.6326i	0.866537	+	0.701935i
$865$	−12.6632			−0.430562
$866$	−22.2559	+	32.0199i	−0.756286	+	1.08808i
$867$	−26.9320	−	26.9320i	−0.914658	−	0.914658i
$868$	−17.9110	+	6.65974i	−0.607938	+	0.226046i
$869$	−5.73589	+	5.73589i	−0.194577	+	0.194577i
$870$	−0.396364	+	0.0713042i	−0.0134380	+	0.00241744i
$871$		−	41.0664i		−	1.39148i
$872$	0.545929	+	0.923315i	0.0184875	+	0.0312674i
$873$			12.8265i			0.434110i
$874$	3.59325	+	19.9741i	0.121544	+	0.675633i
$875$	0.707107	−	0.707107i	0.0239046	−	0.0239046i
$876$	−72.4946	−	33.1961i	−2.44936	−	1.12159i
$877$	33.1562	+	33.1562i	1.11961	+	1.11961i	0.991799	+	0.127806i	$0.0407936\pi$
$877$	33.1562	+	33.1562i	1.11961	+	1.11961i	0.127806	+	0.991799i	$0.459206\pi$
$878$	25.3558	+	17.6239i	0.855715	+	0.594778i
$879$	−67.1889			−2.26623
$880$	15.6934	+	18.1856i	0.529025	+	0.613038i
$881$	−16.0170			−0.539625			−0.269812	−	0.962913i	$-0.586962\pi$
$881$	−16.0170			−0.539625			−0.269812	+	0.962913i	$0.586962\pi$
$882$	5.85642	+	4.07060i	0.197196	+	0.137064i
$883$	32.3591	+	32.3591i	1.08897	+	1.08897i	0.995635	+	0.0933341i	$0.0297525\pi$
$883$	32.3591	+	32.3591i	1.08897	+	1.08897i	0.0933341	+	0.995635i	$0.470248\pi$
$884$	−7.11199	+	15.5313i	−0.239202	+	0.522376i
$885$	18.2662	−	18.2662i	0.614011	−	0.614011i
$886$	−4.79553	−	26.6573i	−0.161109	−	0.895569i
$887$		−	35.2386i		−	1.18320i	−0.806233	−	0.591598i	$-0.798497\pi$
$887$		−	35.2386i		−	1.18320i	0.806233	−	0.591598i	$-0.201503\pi$
$888$	88.0783	+	22.6236i	2.95571	+	0.759197i
$889$		−	3.58897i		−	0.120370i
$890$	5.90550	−	1.06237i	0.197953	−	0.0356108i
$891$	−5.53793	+	5.53793i	−0.185528	+	0.185528i
$892$	3.74427	+	10.0700i	0.125367	+	0.337168i
$893$	4.19480	+	4.19480i	0.140373	+	0.140373i
$894$	−41.8910	+	60.2692i	−1.40104	+	2.01570i
$895$	16.4204			0.548872
$896$	−5.02823	−	10.1349i	−0.167981	−	0.338584i
$897$	−93.5302			−3.12288
$898$	−27.8049	+	40.0033i	−0.927862	+	1.33493i
$899$	−0.678383	−	0.678383i	−0.0226253	−	0.0226253i
$900$	−3.51523	−	9.45400i	−0.117174	−	0.315133i
$901$	16.2403	−	16.2403i	0.541042	−	0.541042i
$902$	15.1263	−	2.72116i	0.503652	−	0.0906048i
$903$		−	8.97754i		−	0.298754i
$904$	31.2964	+	8.03872i	1.04090	+	0.267364i
$905$		−	0.525969i		−	0.0174838i
$906$	3.11354	+	17.3075i	0.103441	+	0.575003i
$907$	−10.2565	+	10.2565i	−0.340560	+	0.340560i	−0.856578	−	0.516018i	$-0.827414\pi$
$907$	−10.2565	+	10.2565i	−0.340560	+	0.340560i	0.516018	+	0.856578i	$0.327414\pi$
$908$	−18.6123	+	40.6459i	−0.617669	+	1.34888i
$909$	2.72864	+	2.72864i	0.0905032	+	0.0905032i
$910$	−5.24923	−	3.64856i	−0.174010	−	0.120949i
$911$	54.6781			1.81157			0.905783	−	0.423742i	$-0.139284\pi$
$911$	54.6781			1.81157			0.905783	+	0.423742i	$0.139284\pi$
$912$	14.5781	+	16.8932i	0.482730	+	0.559391i
$913$	28.3909			0.939601
$914$	−15.4491	−	10.7381i	−0.511010	−	0.355185i
$915$	−8.65596	−	8.65596i	−0.286157	−	0.286157i
$916$	−0.210407	−	0.0963478i	−0.00695203	−	0.00318342i
$917$	2.35913	−	2.35913i	0.0779053	−	0.0779053i
$918$	2.74150	+	15.2394i	0.0904830	+	0.502975i
$919$		−	17.6469i		−	0.582119i	−0.956705	−	0.291060i	$-0.905992\pi$
$919$		−	17.6469i		−	0.582119i	0.956705	−	0.291060i	$-0.0940078\pi$
$920$	10.5026	+	17.7628i	0.346261	+	0.585623i
$921$		−	25.8745i		−	0.852594i
$922$	−6.92839	+	1.24639i	−0.228174	+	0.0410476i
$923$	−32.8637	+	32.8637i	−1.08172	+	1.08172i
$924$	31.9266	−	11.8711i	1.05031	−	0.390530i
$925$	−8.01620	−	8.01620i	−0.263571	−	0.263571i
$926$	−8.12539	+	11.6901i	−0.267017	+	0.384161i
$927$	45.5981			1.49764
$928$	0.357530	−	0.441371i	0.0117365	−	0.0144887i
$929$	28.7903			0.944580			0.472290	−	0.881443i	$-0.343427\pi$
$929$	28.7903			0.944580			0.472290	+	0.881443i	$0.343427\pi$
$930$	21.8713	−	31.4666i	0.717190	−	1.03183i
$931$	1.39086	+	1.39086i	0.0455836	+	0.0455836i
$932$	−32.0824	+	11.9290i	−1.05089	+	0.390748i
$933$	11.0817	−	11.0817i	0.362798	−	0.362798i
$934$	−44.0044	+	7.91620i	−1.43987	+	0.259026i
$935$			11.3468i			0.371081i
$936$	−55.5029	+	32.8172i	−1.81417	+	1.07266i
$937$		−	21.3212i		−	0.696534i	−0.937395	−	0.348267i	$-0.886770\pi$
$937$		−	21.3212i		−	0.696534i	0.937395	−	0.348267i	$-0.113230\pi$
$938$	2.27477	+	12.6449i	0.0742739	+	0.412872i
$939$	17.6724	−	17.6724i	0.576718	−	0.576718i
$940$	5.48430	+	2.51133i	0.178878	+	0.0819105i
$941$	−24.5808	−	24.5808i	−0.801312	−	0.801312i	0.181989	−	0.983301i	$-0.441747\pi$
$941$	−24.5808	−	24.5808i	−0.801312	−	0.801312i	−0.983301	+	0.181989i	$0.941747\pi$
$942$	−10.4168	−	7.24035i	−0.339397	−	0.235903i
$943$	13.2031			0.429952
$944$	−2.67297	+	36.3360i	−0.0869978	+	1.18264i
$945$	−5.79458			−0.188498
$946$	−22.0749	−	15.3435i	−0.717717	−	0.498860i
$947$	32.4717	+	32.4717i	1.05519	+	1.05519i	0.998385	+	0.0568019i	$0.0180904\pi$
$947$	32.4717	+	32.4717i	1.05519	+	1.05519i	0.0568019	+	0.998385i	$0.481910\pi$
$948$	−3.18991	+	6.96620i	−0.103603	+	0.226252i
$949$	44.9315	−	44.9315i	1.45854	−	1.45854i
$950$	−0.492514	−	2.73777i	−0.0159793	−	0.0888251i
$951$			72.9824i			2.36662i
$952$	1.32957	−	5.17628i	0.0430915	−	0.167764i
$953$			11.7786i			0.381547i	0.981634	+	0.190774i	$0.0610997\pi$
$953$			11.7786i			0.381547i	−0.981634	+	0.190774i	$0.938900\pi$
$954$	85.3229	−	15.3492i	2.76243	−	0.496949i
$955$	5.02084	−	5.02084i	0.162470	−	0.162470i
$956$	7.54759	+	20.2988i	0.244107	+	0.656510i
$957$	1.20923	+	1.20923i	0.0390888	+	0.0390888i
$958$	27.9513	−	40.2139i	0.903065	−	1.29925i
$959$	−7.69317			−0.248426
$960$	19.8799	+	10.9340i	0.641622	+	0.352893i
$961$	60.2887			1.94480
$962$	−41.3623	+	59.5085i	−1.33357	+	1.91863i
$963$	−65.1006	−	65.1006i	−2.09784	−	2.09784i
$964$	4.97591	+	13.3824i	0.160263	+	0.431018i
$965$	0.345319	−	0.345319i	0.0111162	−	0.0111162i
$966$	28.7993	−	5.18088i	0.926603	−	0.166692i
$967$		−	37.3484i		−	1.20104i	−0.799609	−	0.600522i	$-0.794960\pi$
$967$		−	37.3484i		−	1.20104i	0.799609	−	0.600522i	$-0.205040\pi$
$968$	17.6355	−	68.6588i	0.566827	−	2.20678i
$969$			10.5405i			0.338608i
$970$	0.636827	+	3.53998i	0.0204473	+	0.113662i
$971$	19.4658	−	19.4658i	0.624686	−	0.624686i	−0.322040	−	0.946726i	$-0.604369\pi$
$971$	19.4658	−	19.4658i	0.624686	−	0.624686i	0.946726	+	0.322040i	$0.104369\pi$
$972$	11.3952	−	24.8852i	0.365502	−	0.798192i
$973$	6.50335	+	6.50335i	0.208488	+	0.208488i
$974$	−30.2588	−	21.0318i	−0.969555	−	0.673904i
$975$	12.8198			0.410563
$976$	17.2189	+	1.26666i	0.551162	+	0.0405449i
$977$	42.2447			1.35153			0.675763	−	0.737119i	$-0.263814\pi$
$977$	42.2447			1.35153			0.675763	+	0.737119i	$0.263814\pi$
$978$	6.49294	+	4.51301i	0.207621	+	0.144310i
$979$	−18.0165	−	18.0165i	−0.575810	−	0.575810i
$980$	1.81842	+	0.832677i	0.0580873	+	0.0265989i
$981$	−1.35238	+	1.35238i	−0.0431781	+	0.0431781i
$982$	0.214943	+	1.19482i	0.00685911	+	0.0381282i
$983$		−	48.9667i		−	1.56180i	−0.624659	−	0.780898i	$-0.714762\pi$
$983$		−	48.9667i		−	1.56180i	0.624659	−	0.780898i	$-0.285238\pi$
$984$	12.4958	−	7.38838i	0.398351	−	0.235533i
$985$		−	16.3929i		−	0.522321i
$986$	0.264075	−	0.0475059i	0.00840985	−	0.00151290i
$987$	6.04820	−	6.04820i	0.192516	−	0.192516i
$988$	−16.6678	+	6.19748i	−0.530272	+	0.197168i
$989$	−16.3304	−	16.3304i	−0.519278	−	0.519278i
$990$	−24.4448	+	35.1690i	−0.776906	+	1.11775i
$991$	−53.7618			−1.70780			−0.853901	−	0.520436i	$-0.825769\pi$
$991$	−53.7618			−1.70780			−0.853901	+	0.520436i	$0.825769\pi$
$992$	5.64110	+	53.7533i	0.179105	+	1.70667i
$993$	18.9296			0.600711
$994$	8.29882	−	11.9396i	0.263223	−	0.378702i
$995$	3.43966	+	3.43966i	0.109044	+	0.109044i
$996$	25.1348	−	9.34574i	0.796426	−	0.296131i
$997$	−25.5795	+	25.5795i	−0.810112	+	0.810112i	−0.984650	−	0.174538i	$-0.944157\pi$
$997$	−25.5795	+	25.5795i	−0.810112	+	0.810112i	0.174538	+	0.984650i	$0.444157\pi$
$998$	12.2392	−	2.20178i	0.387425	−	0.0696961i
$999$			65.6910i			2.07837i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	560.2.bd.b.141.8	✓	52
4.3	odd	2		2240.2.bd.b.1681.4		52
16.5	even	4	inner	560.2.bd.b.421.8	yes	52
16.11	odd	4		2240.2.bd.b.561.4		52

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
560.2.bd.b.141.8	✓	52	1.1	even	1	trivial
560.2.bd.b.421.8	yes	52	16.5	even	4	inner
2240.2.bd.b.561.4		52	16.11	odd	4
2240.2.bd.b.1681.4		52	4.3	odd	2

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:	\( N \)	\(=\)	\( 560 = 2^{4} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	560.bd (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.807148 + 1.16125i) q^{2} +(2.00539 + 2.00539i) q^{3} +(-0.697026 - 1.87461i) q^{4} +(0.707107 - 0.707107i) q^{5} +(-3.94742 + 0.710123i) q^{6} +1.00000i q^{7} +(2.73950 + 0.703661i) q^{8} +5.04319i q^{9} +O(q^{10})\)	\(q+(-0.807148 + 1.16125i) q^{2} +(2.00539 + 2.00539i) q^{3} +(-0.697026 - 1.87461i) q^{4} +(0.707107 - 0.707107i) q^{5} +(-3.94742 + 0.710123i) q^{6} +1.00000i q^{7} +(2.73950 + 0.703661i) q^{8} +5.04319i q^{9} +(0.250392 + 1.39187i) q^{10} +(4.24632 - 4.24632i) q^{11} +(2.36151 - 5.15713i) q^{12} +(3.19634 + 3.19634i) q^{13} +(-1.16125 - 0.807148i) q^{14} +2.83605 q^{15} +(-3.02831 + 2.61330i) q^{16} -1.88950 q^{17} +(-5.85642 - 4.07060i) q^{18} +(-1.39086 - 1.39086i) q^{19} +(-1.81842 - 0.832677i) q^{20} +(-2.00539 + 2.00539i) q^{21} +(1.50365 + 8.35847i) q^{22} +7.29574i q^{23} +(4.08265 + 6.90488i) q^{24} -1.00000i q^{25} +(-6.29169 + 1.13185i) q^{26} +(-4.09739 + 4.09739i) q^{27} +(1.87461 - 0.697026i) q^{28} +(0.0710013 + 0.0710013i) q^{29} +(-2.28911 + 3.29338i) q^{30} -9.55451 q^{31} +(-0.590413 - 5.62596i) q^{32} +17.0311 q^{33} +(1.52510 - 2.19419i) q^{34} +(0.707107 + 0.707107i) q^{35} +(9.45400 - 3.51523i) q^{36} +(8.01620 - 8.01620i) q^{37} +(2.73777 - 0.492514i) q^{38} +12.8198i q^{39} +(2.43468 - 1.43956i) q^{40} -1.80970i q^{41} +(-0.710123 - 3.94742i) q^{42} +(-2.23835 + 2.23835i) q^{43} +(-10.9200 - 5.00040i) q^{44} +(3.56607 + 3.56607i) q^{45} +(-8.47221 - 5.88874i) q^{46} -3.01597 q^{47} +(-11.3136 - 0.832260i) q^{48} -1.00000 q^{49} +(1.16125 + 0.807148i) q^{50} +(-3.78918 - 3.78918i) q^{51} +(3.76396 - 8.21982i) q^{52} +(-8.59501 + 8.59501i) q^{53} +(-1.45091 - 8.06531i) q^{54} -6.00521i q^{55} +(-0.703661 + 2.73950i) q^{56} -5.57844i q^{57} +(-0.139759 + 0.0251421i) q^{58} +(6.44071 - 6.44071i) q^{59} +(-1.97680 - 5.31648i) q^{60} +(-3.05212 - 3.05212i) q^{61} +(7.71190 - 11.0952i) q^{62} -5.04319 q^{63} +(7.00972 + 3.85536i) q^{64} +4.52031 q^{65} +(-13.7466 + 19.7774i) q^{66} +(-6.42396 - 6.42396i) q^{67} +(1.31703 + 3.54207i) q^{68} +(-14.6308 + 14.6308i) q^{69} +(-1.39187 + 0.250392i) q^{70} +10.2817i q^{71} +(-3.54869 + 13.8158i) q^{72} -14.0571i q^{73} +(2.83859 + 15.7791i) q^{74} +(2.00539 - 2.00539i) q^{75} +(-1.63785 + 3.57678i) q^{76} +(4.24632 + 4.24632i) q^{77} +(-14.8871 - 10.3475i) q^{78} -1.35079 q^{79} +(-0.293457 + 3.98922i) q^{80} -1.30417 q^{81} +(2.10152 + 1.46070i) q^{82} +(3.34300 + 3.34300i) q^{83} +(5.15713 + 2.36151i) q^{84} +(-1.33608 + 1.33608i) q^{85} +(-0.792617 - 4.40598i) q^{86} +0.284771i q^{87} +(14.6208 - 8.64483i) q^{88} -4.24285i q^{89} +(-7.01946 + 1.26277i) q^{90} +(-3.19634 + 3.19634i) q^{91} +(13.6767 - 5.08532i) q^{92} +(-19.1605 - 19.1605i) q^{93} +(2.43433 - 3.50231i) q^{94} -1.96697 q^{95} +(10.0982 - 12.4663i) q^{96} +2.54333 q^{97} +(0.807148 - 1.16125i) q^{98} +(21.4150 + 21.4150i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 52 q - 8 q^{4} + 12 q^{6}+O(q^{10}) \) 52 * q - 8 * q^4 + 12 * q^6	\( 52 q - 8 q^{4} + 12 q^{6} - 4 q^{10} - 4 q^{11} + 40 q^{12} + 8 q^{15} - 4 q^{16} + 8 q^{19} + 32 q^{22} + 12 q^{24} - 12 q^{26} - 24 q^{27} + 4 q^{28} + 4 q^{29} - 16 q^{34} + 4 q^{36} - 12 q^{37} + 16 q^{38} - 4 q^{42} + 36 q^{43} + 28 q^{44} - 16 q^{46} + 32 q^{48} - 52 q^{49} - 8 q^{51} - 80 q^{52} - 4 q^{53} + 48 q^{54} - 12 q^{56} - 56 q^{58} + 24 q^{59} - 16 q^{61} - 72 q^{62} - 68 q^{63} + 4 q^{64} + 40 q^{65} - 12 q^{66} - 12 q^{67} - 72 q^{69} - 8 q^{72} + 68 q^{74} - 4 q^{77} - 4 q^{78} - 16 q^{79} - 32 q^{80} - 116 q^{81} + 104 q^{82} + 16 q^{85} - 68 q^{86} - 48 q^{88} + 36 q^{90} + 64 q^{92} + 8 q^{93} - 72 q^{94} - 32 q^{95} - 52 q^{99}+O(q^{100}) \) 52 * q - 8 * q^4 + 12 * q^6 - 4 * q^10 - 4 * q^11 + 40 * q^12 + 8 * q^15 - 4 * q^16 + 8 * q^19 + 32 * q^22 + 12 * q^24 - 12 * q^26 - 24 * q^27 + 4 * q^28 + 4 * q^29 - 16 * q^34 + 4 * q^36 - 12 * q^37 + 16 * q^38 - 4 * q^42 + 36 * q^43 + 28 * q^44 - 16 * q^46 + 32 * q^48 - 52 * q^49 - 8 * q^51 - 80 * q^52 - 4 * q^53 + 48 * q^54 - 12 * q^56 - 56 * q^58 + 24 * q^59 - 16 * q^61 - 72 * q^62 - 68 * q^63 + 4 * q^64 + 40 * q^65 - 12 * q^66 - 12 * q^67 - 72 * q^69 - 8 * q^72 + 68 * q^74 - 4 * q^77 - 4 * q^78 - 16 * q^79 - 32 * q^80 - 116 * q^81 + 104 * q^82 + 16 * q^85 - 68 * q^86 - 48 * q^88 + 36 * q^90 + 64 * q^92 + 8 * q^93 - 72 * q^94 - 32 * q^95 - 52 * q^99

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