LMFDB - Embedded newform 640.2.bm.a.341.39

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [640,2,Mod(21,640)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(640, base_ring=CyclotomicField(32))

chi = DirichletCharacter(H, H._module([0, 13, 0]))

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

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

chi := DirichletCharacter("640.21");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 640 = 2^{7} \cdot 5 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	640.bm (of order $32$, degree $16$, 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:	$5.11042572936$
Analytic rank:	$0$
Dimension:	$1024$
Relative dimension:	$64$ over $\Q(\zeta_{32})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{32}]$

Embedding invariants

Embedding label			341.39
Character	$\chi$	$=$	640.341
Dual form			640.2.bm.a.381.39

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.424169 - 1.34910i) q^{2} +(-0.733885 + 0.894242i) q^{3} +(-1.64016 - 1.14450i) q^{4} +(0.956940 - 0.290285i) q^{5} +(0.895134 + 1.36940i) q^{6} +(-2.73730 - 0.544483i) q^{7} +(-2.23975 + 1.72729i) q^{8} +(0.324190 + 1.62981i) q^{9} +O(q^{10})$	\(q+(0.424169 - 1.34910i) q^{2} +(-0.733885 + 0.894242i) q^{3} +(-1.64016 - 1.14450i) q^{4} +(0.956940 - 0.290285i) q^{5} +(0.895134 + 1.36940i) q^{6} +(-2.73730 - 0.544483i) q^{7} +(-2.23975 + 1.72729i) q^{8} +(0.324190 + 1.62981i) q^{9} +(0.0142803 - 1.41414i) q^{10} +(-0.192386 - 0.0189484i) q^{11} +(2.22715 - 0.626772i) q^{12} +(-0.880890 + 2.90390i) q^{13} +(-1.89564 + 3.46195i) q^{14} +(-0.442700 + 1.06877i) q^{15} +(1.38026 + 3.75432i) q^{16} +(0.271195 + 0.654723i) q^{17} +(2.33630 + 0.253950i) q^{18} +(-1.18022 + 0.630839i) q^{19} +(-1.90177 - 0.619100i) q^{20} +(2.49576 - 2.04822i) q^{21} +(-0.107168 + 0.251511i) q^{22} +(-2.13875 + 3.20086i) q^{23} +(0.0991055 - 3.27051i) q^{24} +(0.831470 - 0.555570i) q^{25} +(3.54402 + 2.42016i) q^{26} +(-4.75607 - 2.54217i) q^{27} +(3.86645 + 4.02587i) q^{28} +(0.817843 + 8.30370i) q^{29} +(1.25410 + 1.05059i) q^{30} +(3.08022 + 3.08022i) q^{31} +(5.65042 - 0.269648i) q^{32} +(0.158134 - 0.158134i) q^{33} +(0.998321 - 0.0881571i) q^{34} +(-2.77749 + 0.273559i) q^{35} +(1.33359 - 3.04419i) q^{36} +(-0.527757 + 0.987364i) q^{37} +(0.350456 + 1.85982i) q^{38} +(-1.95032 - 2.91886i) q^{39} +(-1.64190 + 2.30308i) q^{40} +(-0.526270 - 0.351642i) q^{41} +(-1.70464 - 4.23583i) q^{42} +(-2.72265 - 3.31756i) q^{43} +(0.293858 + 0.251263i) q^{44} +(0.783341 + 1.46553i) q^{45} +(3.41110 + 4.24310i) q^{46} +(-3.43532 + 1.42296i) q^{47} +(-4.37022 - 1.52095i) q^{48} +(0.729187 + 0.302039i) q^{49} +(-0.396838 - 1.35739i) q^{50} +(-0.784506 - 0.237977i) q^{51} +(4.76831 - 3.75470i) q^{52} +(-0.538466 + 5.46714i) q^{53} +(-5.44703 + 5.33812i) q^{54} +(-0.189602 + 0.0377143i) q^{55} +(7.07134 - 3.50860i) q^{56} +(0.302021 - 1.51836i) q^{57} +(11.5495 + 2.41882i) q^{58} +(0.0653058 + 0.215284i) q^{59} +(1.94930 - 1.24629i) q^{60} +(7.14281 + 5.86195i) q^{61} +(5.46207 - 2.84900i) q^{62} -4.63780i q^{63} +(2.03295 - 7.73738i) q^{64} +3.03457i q^{65} +(-0.146263 - 0.280414i) q^{66} +(-0.745737 - 0.612011i) q^{67} +(0.304524 - 1.38423i) q^{68} +(-1.29275 - 4.26162i) q^{69} +(-0.809065 + 3.86315i) q^{70} +(0.515284 - 2.59051i) q^{71} +(-3.54126 - 3.09040i) q^{72} +(-3.22229 + 0.640952i) q^{73} +(1.10820 + 1.13081i) q^{74} +(-0.113389 + 1.15126i) q^{75} +(2.65774 + 0.316075i) q^{76} +(0.516301 + 0.156618i) q^{77} +(-4.76511 + 1.39309i) q^{78} +(-5.46700 - 2.26450i) q^{79} +(2.41065 + 3.19199i) q^{80} +(1.15797 - 0.479646i) q^{81} +(-0.697629 + 0.560837i) q^{82} +(1.51223 + 2.82919i) q^{83} +(-6.43763 + 0.503021i) q^{84} +(0.449573 + 0.547807i) q^{85} +(-5.63060 + 2.26593i) q^{86} +(-8.02572 - 5.36262i) q^{87} +(0.463626 - 0.289867i) q^{88} +(-5.53182 - 8.27896i) q^{89} +(2.30942 - 0.435177i) q^{90} +(3.99238 - 7.46922i) q^{91} +(7.17126 - 2.80214i) q^{92} +(-5.01499 + 0.493934i) q^{93} +(0.462560 + 5.23818i) q^{94} +(-0.946274 + 0.946274i) q^{95} +(-3.90563 + 5.25074i) q^{96} +(-5.39606 - 5.39606i) q^{97} +(0.716780 - 0.855633i) q^{98} +(-0.0314874 - 0.319696i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 1024 q+O(q^{10}) $ 1024 * q	$ 1024 q - 192 q^{52} - 128 q^{54} - 32 q^{56} - 288 q^{58} - 192 q^{62} - 192 q^{64} - 192 q^{66} - 192 q^{68} - 288 q^{72} - 32 q^{74} - 128 q^{76} - 192 q^{78}+O(q^{100}) $ 1024 * q - 192 * q^52 - 128 * q^54 - 32 * q^56 - 288 * q^58 - 192 * q^62 - 192 * q^64 - 192 * q^66 - 192 * q^68 - 288 * q^72 - 32 * q^74 - 128 * q^76 - 192 * q^78

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/640\mathbb{Z}\right)^\times$.

$n$	$257$	$261$	$511$
$\chi(n)$	$1$	$e\left(\frac{29}{32}\right)$	$1$

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 $

$2$	0.424169	−	1.34910i	0.299933	−	0.953960i
$2$	0.424169	−	1.34910i	0.299933	−	0.953960i
$3$	−0.733885	+	0.894242i	−0.423709	+	0.516291i	−0.940487	−	0.339828i	$-0.889631\pi$
$3$	−0.733885	+	0.894242i	−0.423709	+	0.516291i	0.516779	+	0.856119i	$0.327131\pi$
$4$	−1.64016	−	1.14450i	−0.820081	−	0.572248i
$5$	0.956940	−	0.290285i	0.427957	−	0.129819i
$5$	0.956940	−	0.290285i	0.427957	−	0.129819i
$6$	0.895134	+	1.36940i	0.365437	+	0.559054i
$7$	−2.73730	−	0.544483i	−1.03460	−	0.205795i	−0.351553	−	0.936168i	$-0.614346\pi$
$7$	−2.73730	−	0.544483i	−1.03460	−	0.205795i	−0.683049	+	0.730373i	$0.739346\pi$
$8$	−2.23975	+	1.72729i	−0.791871	+	0.610689i
$9$	0.324190	+	1.62981i	0.108063	+	0.543271i
$10$	0.0142803	−	1.41414i	0.00451581	−	0.447191i
$11$	−0.192386	−	0.0189484i	−0.0580066	−	0.00571315i	0.0689722	−	0.997619i	$-0.478028\pi$
$11$	−0.192386	−	0.0189484i	−0.0580066	−	0.00571315i	−0.126979	+	0.991905i	$0.540528\pi$
$12$	2.22715	−	0.626772i	0.642922	−	0.180934i
$13$	−0.880890	+	2.90390i	−0.244315	+	0.805398i	0.745926	+	0.666029i	$0.232007\pi$
$13$	−0.880890	+	2.90390i	−0.244315	+	0.805398i	−0.990241	+	0.139369i	$0.955493\pi$
$14$	−1.89564	+	3.46195i	−0.506631	+	0.925244i
$15$	−0.442700	+	1.06877i	−0.114305	+	0.275956i
$16$	1.38026	+	3.75432i	0.345065	+	0.938579i
$17$	0.271195	+	0.654723i	0.0657744	+	0.158794i	0.953349	−	0.301871i	$-0.0976112\pi$
$17$	0.271195	+	0.654723i	0.0657744	+	0.158794i	−0.887574	+	0.460664i	$0.847611\pi$
$18$	2.33630	+	0.253950i	0.550671	+	0.0598567i
$19$	−1.18022	+	0.630839i	−0.270760	+	0.144724i	−0.601190	−	0.799106i	$-0.705306\pi$
$19$	−1.18022	+	0.630839i	−0.270760	+	0.144724i	0.330429	+	0.943831i	$0.392806\pi$
$20$	−1.90177	−	0.619100i	−0.425248	−	0.138435i
$21$	2.49576	−	2.04822i	0.544620	−	0.446958i
$22$	−0.107168	+	0.251511i	−0.0228482	+	0.0536224i
$23$	−2.13875	+	3.20086i	−0.445960	+	0.667426i	−0.984542	−	0.175147i	$-0.943960\pi$
$23$	−2.13875	+	3.20086i	−0.445960	+	0.667426i	0.538583	+	0.842573i	$0.318960\pi$
$24$	0.0991055	−	3.27051i	0.0202298	−	0.667590i
$25$	0.831470	−	0.555570i	0.166294	−	0.111114i
$26$	3.54402	+	2.42016i	0.695040	+	0.474632i
$27$	−4.75607	−	2.54217i	−0.915305	−	0.489241i
$28$	3.86645	+	4.02587i	0.730691	+	0.760817i
$29$	0.817843	+	8.30370i	0.151870	+	1.54196i	0.705207	+	0.709001i	$0.250854\pi$
$29$	0.817843	+	8.30370i	0.151870	+	1.54196i	−0.553337	+	0.832957i	$0.686646\pi$
$30$	1.25410	+	1.05059i	0.228967	+	0.191810i
$31$	3.08022	+	3.08022i	0.553224	+	0.553224i	0.927370	−	0.374146i	$-0.122064\pi$
$31$	3.08022	+	3.08022i	0.553224	+	0.553224i	−0.374146	+	0.927370i	$0.622064\pi$
$32$	5.65042	−	0.269648i	0.998863	−	0.0476675i
$33$	0.158134	−	0.158134i	0.0275276	−	0.0275276i
$34$	0.998321	−	0.0881571i	0.171211	−	0.0151188i
$35$	−2.77749	+	0.273559i	−0.469481	+	0.0462398i
$36$	1.33359	−	3.04419i	0.222265	−	0.507365i
$37$	−0.527757	+	0.987364i	−0.0867627	+	0.162322i	−0.921560	−	0.388236i	$-0.873085\pi$
$37$	−0.527757	+	0.987364i	−0.0867627	+	0.162322i	0.834797	+	0.550557i	$0.185585\pi$
$38$	0.350456	+	1.85982i	0.0568515	+	0.301702i
$39$	−1.95032	−	2.91886i	−0.312301	−	0.467392i
$40$	−1.64190	+	2.30308i	−0.259607	+	0.364148i
$41$	−0.526270	−	0.351642i	−0.0821896	−	0.0549173i	0.513796	−	0.857912i	$-0.328239\pi$
$41$	−0.526270	−	0.351642i	−0.0821896	−	0.0549173i	−0.595986	+	0.802995i	$0.703239\pi$
$42$	−1.70464	−	4.23583i	−0.263031	−	0.653603i
$43$	−2.72265	−	3.31756i	−0.415201	−	0.505924i	0.522848	−	0.852426i	$-0.324869\pi$
$43$	−2.72265	−	3.31756i	−0.415201	−	0.505924i	−0.938049	+	0.346502i	$0.887369\pi$
$44$	0.293858	+	0.251263i	0.0443007	+	0.0378794i
$45$	0.783341	+	1.46553i	0.116774	+	0.218468i
$46$	3.41110	+	4.24310i	0.502940	+	0.625611i
$47$	−3.43532	+	1.42296i	−0.501093	+	0.207560i	−0.618889	−	0.785478i	$-0.712417\pi$
$47$	−3.43532	+	1.42296i	−0.501093	+	0.207560i	0.117796	+	0.993038i	$0.462417\pi$
$48$	−4.37022	−	1.52095i	−0.630787	−	0.219530i
$49$	0.729187	+	0.302039i	0.104170	+	0.0431484i
$50$	−0.396838	−	1.35739i	−0.0561214	−	0.191965i
$51$	−0.784506	−	0.237977i	−0.109853	−	0.0333235i
$52$	4.76831	−	3.75470i	0.661245	−	0.520683i
$53$	−0.538466	+	5.46714i	−0.0739640	+	0.750969i	0.884649	+	0.466257i	$0.154398\pi$
$53$	−0.538466	+	5.46714i	−0.0739640	+	0.750969i	−0.958613	+	0.284712i	$0.908102\pi$
$54$	−5.44703	+	5.33812i	−0.741246	+	0.726426i
$55$	−0.189602	+	0.0377143i	−0.0255660	+	0.00508539i
$56$	7.07134	−	3.50860i	0.944948	−	0.468856i
$57$	0.302021	−	1.51836i	0.0400037	−	0.201112i
$58$	11.5495	+	2.41882i	1.51652	+	0.317606i
$59$	0.0653058	+	0.215284i	0.00850209	+	0.0280277i	0.961089	−	0.276240i	$-0.0890884\pi$
$59$	0.0653058	+	0.215284i	0.00850209	+	0.0280277i	−0.952587	+	0.304267i	$0.901588\pi$
$60$	1.94930	−	1.24629i	0.251654	−	0.160895i
$61$	7.14281	+	5.86195i	0.914543	+	0.750546i	0.968764	−	0.247983i	$-0.0797678\pi$
$61$	7.14281	+	5.86195i	0.914543	+	0.750546i	−0.0542218	+	0.998529i	$0.517268\pi$
$62$	5.46207	−	2.84900i	0.693684	−	0.361824i
$63$		−	4.63780i		−	0.584308i
$64$	2.03295	−	7.73738i	0.254119	−	0.967173i
$65$			3.03457i			0.376392i
$66$	−0.146263	−	0.280414i	−0.0180038	−	0.0345166i
$67$	−0.745737	−	0.612011i	−0.0911063	−	0.0747690i	0.587738	−	0.809052i	$-0.300019\pi$
$67$	−0.745737	−	0.612011i	−0.0911063	−	0.0747690i	−0.678844	+	0.734283i	$0.737519\pi$
$68$	0.304524	−	1.38423i	0.0369289	−	0.167863i
$69$	−1.29275	−	4.26162i	−0.155629	−	0.513039i
$70$	−0.809065	+	3.86315i	−0.0967017	+	0.461735i
$71$	0.515284	−	2.59051i	0.0611530	−	0.307437i	−0.938088	−	0.346398i	$-0.887405\pi$
$71$	0.515284	−	2.59051i	0.0611530	−	0.307437i	0.999241	+	0.0389610i	$0.0124048\pi$
$72$	−3.54126	−	3.09040i	−0.417342	−	0.364208i
$73$	−3.22229	+	0.640952i	−0.377140	+	0.0750178i	−0.380021	−	0.924978i	$-0.624083\pi$
$73$	−3.22229	+	0.640952i	−0.377140	+	0.0750178i	0.00288058	+	0.999996i	$0.499083\pi$
$74$	1.10820	+	1.13081i	0.128825	+	0.131454i
$75$	−0.113389	+	1.15126i	−0.0130931	+	0.132936i
$76$	2.65774	+	0.316075i	0.304864	+	0.0362563i
$77$	0.516301	+	0.156618i	0.0588380	+	0.0178483i
$78$	−4.76511	+	1.39309i	−0.539543	+	0.157737i
$79$	−5.46700	−	2.26450i	−0.615085	−	0.254777i	0.0533158	−	0.998578i	$-0.483021\pi$
$79$	−5.46700	−	2.26450i	−0.615085	−	0.254777i	−0.668401	+	0.743801i	$0.733021\pi$
$80$	2.41065	+	3.19199i	0.269518	+	0.356875i
$81$	1.15797	−	0.479646i	0.128663	−	0.0532940i
$82$	−0.697629	+	0.560837i	−0.0770403	+	0.0619341i
$83$	1.51223	+	2.82919i	0.165989	+	0.310544i	0.951140	−	0.308761i	$-0.0999144\pi$
$83$	1.51223	+	2.82919i	0.165989	+	0.310544i	−0.785150	+	0.619305i	$0.787414\pi$
$84$	−6.43763	+	0.503021i	−0.702403	+	0.0548841i
$85$	0.449573	+	0.547807i	0.0487631	+	0.0594180i
$86$	−5.63060	+	2.26593i	−0.607163	+	0.244342i
$87$	−8.02572	−	5.36262i	−0.860448	−	0.574933i
$88$	0.463626	−	0.289867i	0.0494227	−	0.0308999i
$89$	−5.53182	−	8.27896i	−0.586372	−	0.877568i	0.413079	−	0.910695i	$-0.364453\pi$
$89$	−5.53182	−	8.27896i	−0.586372	−	0.877568i	−0.999451	+	0.0331272i	$0.989453\pi$
$90$	2.30942	−	0.435177i	0.243434	−	0.0458716i
$91$	3.99238	−	7.46922i	0.418515	−	0.782987i
$92$	7.17126	−	2.80214i	0.747656	−	0.292143i
$93$	−5.01499	+	0.493934i	−0.520030	+	0.0512185i
$94$	0.462560	+	5.23818i	0.0477094	+	0.540277i
$95$	−0.946274	+	0.946274i	−0.0970857	+	0.0970857i
$96$	−3.90563	+	5.25074i	−0.398617	+	0.535901i
$97$	−5.39606	−	5.39606i	−0.547887	−	0.547887i	0.377942	−	0.925829i	$-0.376632\pi$
$97$	−5.39606	−	5.39606i	−0.547887	−	0.547887i	−0.925829	+	0.377942i	$0.876632\pi$
$98$	0.716780	−	0.855633i	0.0724057	−	0.0864320i
$99$	−0.0314874	−	0.319696i	−0.00316460	−	0.0321307i
$100$	−1.99959	−	0.0403886i	−0.199959	−	0.00403886i
$101$	−6.12475	−	3.27375i	−0.609436	−	0.325750i	0.137647	−	0.990481i	$-0.456046\pi$
$101$	−6.12475	−	3.27375i	−0.609436	−	0.325750i	−0.747083	+	0.664731i	$0.768546\pi$
$102$	−0.653819	+	0.957438i	−0.0647378	+	0.0948005i
$103$	1.89632	−	1.26708i	0.186850	−	0.124849i	−0.458627	−	0.888629i	$-0.651659\pi$
$103$	1.89632	−	1.26708i	0.186850	−	0.124849i	0.645477	+	0.763780i	$0.276659\pi$
$104$	−3.04291	−	8.02557i	−0.298382	−	0.786971i
$105$	1.79373	−	2.68451i	0.175050	−	0.261981i
$106$	7.14734	+	3.04544i	0.694211	+	0.295799i
$107$	−4.61130	+	3.78439i	−0.445791	+	0.365851i	−0.830343	−	0.557252i	$-0.811856\pi$
$107$	−4.61130	+	3.78439i	−0.445791	+	0.365851i	0.384553	+	0.923103i	$0.374356\pi$
$108$	4.89121	+	9.61287i	0.470657	+	0.924998i
$109$	17.5625	−	9.38735i	1.68218	−	0.899145i	0.699319	−	0.714810i	$-0.253487\pi$
$109$	17.5625	−	9.38735i	1.68218	−	0.899145i	0.982863	−	0.184336i	$-0.0590133\pi$
$110$	−0.0295430	+	0.271791i	−0.00281682	+	0.0259142i
$111$	−0.495629	−	1.19655i	−0.0470430	−	0.113572i
$112$	−1.73402	−	11.0282i	−0.163850	−	1.04207i
$113$	1.53512	−	3.70611i	0.144412	−	0.348642i	−0.835079	−	0.550130i	$-0.814578\pi$
$113$	1.53512	−	3.70611i	0.144412	−	0.348642i	0.979491	+	0.201489i	$0.0645780\pi$
$114$	−1.92032	−	1.05150i	−0.179855	−	0.0984820i
$115$	−1.11749	+	3.68388i	−0.104207	+	0.343523i
$116$	8.16216	−	14.5554i	0.757837	−	1.35144i
$117$	−5.01840	−	0.494269i	−0.463951	−	0.0456952i
$118$	0.318142	+	0.00321265i	0.0292873	+	0.000295749i
$119$	−0.385857	−	1.93983i	−0.0353714	−	0.177824i
$120$	−0.854540	−	3.15845i	−0.0780085	−	0.288326i
$121$	−10.7520	−	2.13870i	−0.977453	−	0.194428i
$122$	10.9381	−	7.14993i	0.990292	−	0.647324i
$123$	0.700675	−	0.212547i	0.0631777	−	0.0191648i
$124$	−1.52676	−	8.57736i	−0.137107	−	0.770270i
$125$	0.634393	−	0.773010i	0.0567419	−	0.0691402i
$126$	−6.25688	−	1.96721i	−0.557407	−	0.175253i
$127$	−7.12135			−0.631918			−0.315959	−	0.948773i	$-0.602326\pi$
$127$	−7.12135			−0.631918			−0.315959	+	0.948773i	$0.602326\pi$
$128$	−9.57622	−	6.02462i	−0.846426	−	0.532506i
$129$	4.96482			0.437128
$130$	4.09395	+	1.28717i	0.359063	+	0.112892i
$131$	1.27971	−	1.55933i	0.111809	−	0.136239i	−0.714099	−	0.700045i	$-0.753163\pi$
$131$	1.27971	−	1.55933i	0.111809	−	0.136239i	0.825908	+	0.563806i	$0.190663\pi$
$132$	−0.440348	+	0.0783815i	−0.0383274	+	0.00682223i
$133$	3.57409	−	1.08419i	0.309913	−	0.0940110i
$134$	−1.14198	+	0.746481i	−0.0986525	+	0.0644861i
$135$	−5.28922	−	1.05209i	−0.455224	−	0.0905497i
$136$	−1.73830	−	0.997982i	−0.149058	−	0.0855763i
$137$	−3.05481	−	15.3575i	−0.260990	−	1.31208i	−0.859569	−	0.511020i	$-0.829268\pi$
$137$	−3.05481	−	15.3575i	−0.260990	−	1.31208i	0.598579	−	0.801064i	$-0.295732\pi$
$138$	−6.29771	−	0.0635954i	−0.536097	−	0.00541360i
$139$	6.86581	+	0.676223i	0.582351	+	0.0573565i	0.384903	−	0.922957i	$-0.374235\pi$
$139$	6.86581	+	0.676223i	0.582351	+	0.0573565i	0.197447	+	0.980313i	$0.436735\pi$
$140$	4.86861	+	2.73014i	0.411473	+	0.230739i
$141$	1.24867	−	4.11630i	0.105157	−	0.346655i
$142$	−3.27630	−	1.79398i	−0.274941	−	0.150548i
$143$	0.224495	−	0.541979i	0.0187732	−	0.0453226i
$144$	−5.67137	+	3.46668i	−0.472614	+	0.288890i
$145$	3.19306	+	7.70874i	0.265170	+	0.640176i
$146$	−0.502082	+	4.61907i	−0.0415526	+	0.382277i
$147$	−0.805235	+	0.430407i	−0.0664147	+	0.0354994i
$148$	1.99564	−	1.01542i	0.164041	−	0.0834670i
$149$	5.86805	−	4.81579i	0.480730	−	0.394525i	−0.362580	−	0.931953i	$-0.618104\pi$
$149$	5.86805	−	4.81579i	0.480730	−	0.394525i	0.843310	+	0.537428i	$0.180604\pi$
$150$	1.50507	+	0.641302i	0.122889	+	0.0523621i
$151$	−8.80631	+	13.1796i	−0.716648	+	1.07254i	0.277095	+	0.960843i	$0.410628\pi$
$151$	−8.80631	+	13.1796i	−0.716648	+	1.07254i	−0.993742	+	0.111696i	$0.964372\pi$
$152$	1.55375	−	3.45150i	0.126026	−	0.279953i
$153$	−0.979157	+	0.654252i	−0.0791602	+	0.0528931i
$154$	0.430293	−	0.630111i	0.0346740	−	0.0507758i
$155$	3.84173	+	2.05345i	0.308575	+	0.164937i
$156$	−0.141784	+	7.01954i	−0.0113518	+	0.562013i
$157$	2.15812	+	21.9117i	0.172236	+	1.74875i	0.561370	+	0.827565i	$0.310274\pi$
$157$	2.15812	+	21.9117i	0.172236	+	1.74875i	−0.389134	+	0.921181i	$0.627226\pi$
$158$	−5.37398	+	6.41501i	−0.427531	+	0.510351i
$159$	−4.49377	−	4.49377i	−0.356379	−	0.356379i
$160$	5.32884	−	1.89827i	0.421282	−	0.150071i
$161$	7.59720	−	7.59720i	0.598743	−	0.598743i
$162$	−0.155918	−	1.76567i	−0.0122501	−	0.138724i
$163$	−16.1629	+	1.59191i	−1.26598	+	0.124688i	−0.708624	−	0.705586i	$-0.750684\pi$
$163$	−16.1629	+	1.59191i	−1.26598	+	0.124688i	−0.557355	+	0.830274i	$0.688184\pi$
$164$	0.460715	+	1.17906i	0.0359758	+	0.0920694i
$165$	0.105421	−	0.197228i	0.00820700	−	0.0153542i
$166$	4.45831	−	0.840106i	0.346032	−	0.0652048i
$167$	−6.35767	−	9.51493i	−0.491971	−	0.736287i	0.499542	−	0.866290i	$-0.333502\pi$
$167$	−6.35767	−	9.51493i	−0.491971	−	0.736287i	−0.991514	+	0.130002i	$0.958502\pi$
$168$	−2.05202	+	8.89840i	−0.158316	+	0.686526i
$169$	3.15241	+	2.10638i	0.242493	+	0.162029i
$170$	0.929743	−	0.374158i	0.0713080	−	0.0286966i
$171$	−1.41077	−	1.71902i	−0.107884	−	0.131457i
$172$	0.668654	+	8.55740i	0.0509844	+	0.652496i
$173$	−0.239846	−	0.448721i	−0.0182352	−	0.0341156i	0.872639	−	0.488366i	$-0.162407\pi$
$173$	−0.239846	−	0.448721i	−0.0182352	−	0.0341156i	−0.890874	+	0.454251i	$0.849907\pi$
$174$	−10.6390	+	8.55287i	−0.806539	+	0.648392i
$175$	−2.57848	+	1.06804i	−0.194915	+	0.0807363i
$176$	−0.194404	−	0.748432i	−0.0146538	−	0.0564152i
$177$	−0.240443	−	0.0995949i	−0.0180728	−	0.00748601i
$178$	−13.5156	+	3.95133i	−1.01304	+	0.296164i
$179$	15.5198	+	4.70787i	1.16000	+	0.351883i	0.810890	−	0.585199i	$-0.198983\pi$
$179$	15.5198	+	4.70787i	1.16000	+	0.351883i	0.349111	+	0.937081i	$0.386483\pi$
$180$	0.392485	−	3.30023i	0.0292541	−	0.245985i
$181$	−2.04451	+	20.7582i	−0.151967	+	1.54295i	0.552684	+	0.833391i	$0.313604\pi$
$181$	−2.04451	+	20.7582i	−0.151967	+	1.54295i	−0.704651	+	0.709554i	$0.748896\pi$
$182$	−8.38331	−	8.55435i	−0.621412	−	0.634091i
$183$	−10.4840	+	2.08540i	−0.775000	+	0.154157i
$184$	−0.738553	−	10.8634i	−0.0544469	−	0.800857i
$185$	−0.218415	+	1.09805i	−0.0160582	+	0.0807301i
$186$	−1.46084	+	6.97525i	−0.107114	+	0.511450i
$187$	−0.0397682	−	0.131098i	−0.00290814	−	0.00958685i
$188$	7.26305	+	1.59783i	0.529713	+	0.116534i
$189$	11.6346	+	9.54827i	0.846293	+	0.694535i
$190$	0.875242	+	1.67800i	0.0634967	+	0.121735i
$191$			19.1518i			1.38578i	0.721045	+	0.692888i	$0.243662\pi$
$191$			19.1518i			1.38578i	−0.721045	+	0.692888i	$0.756338\pi$
$192$	5.42714	+	7.49630i	0.391670	+	0.540999i
$193$			4.16298i			0.299658i	0.988712	+	0.149829i	$0.0478723\pi$
$193$			4.16298i			0.299658i	−0.988712	+	0.149829i	$0.952128\pi$
$194$	−9.56868	+	4.99100i	−0.686991	+	0.358333i
$195$	−2.71364	−	2.22703i	−0.194328	−	0.159481i
$196$	−0.850301	−	1.32994i	−0.0607358	−	0.0949960i
$197$	−1.87620	−	6.18501i	−0.133674	−	0.440663i	0.864393	−	0.502817i	$-0.167703\pi$
$197$	−1.87620	−	6.18501i	−0.133674	−	0.440663i	−0.998067	+	0.0621537i	$0.980203\pi$
$198$	−0.444660	−	0.0931256i	−0.0316006	−	0.00661815i
$199$	−1.20624	+	6.06417i	−0.0855080	+	0.429878i	0.914190	+	0.405287i	$0.132828\pi$
$199$	−1.20624	+	6.06417i	−0.0855080	+	0.429878i	−0.999698	+	0.0245909i	$0.992172\pi$
$200$	−0.902653	+	2.68053i	−0.0638272	+	0.189542i
$201$	1.09457	−	0.217724i	0.0772051	−	0.0153571i
$202$	−7.01456	+	6.87430i	−0.493543	+	0.483674i
$203$	2.28254	−	23.1750i	0.160203	−	1.62657i
$204$	1.01435	+	1.28819i	0.0710189	+	0.0901910i
$205$	−0.605685	−	0.183733i	−0.0423029	−	0.0128324i
$206$	−0.905064	−	3.09579i	−0.0630588	−	0.215694i
$207$	−5.91017	−	2.44807i	−0.410785	−	0.170153i
$208$	−12.1180	+	0.701001i	−0.840234	+	0.0486057i
$209$	0.239011	−	0.0990015i	0.0165327	−	0.00684808i
$210$	−2.86083	−	3.55861i	−0.197416	−	0.245567i
$211$	10.1715	+	19.0295i	0.700232	+	1.31004i	0.940652	+	0.339373i	$0.110215\pi$
$211$	10.1715	+	19.0295i	0.700232	+	1.31004i	−0.240420	+	0.970669i	$0.577285\pi$
$212$	7.14029	−	8.35072i	0.490397	−	0.573530i
$213$	1.93838	+	2.36192i	0.132816	+	0.161836i
$214$	3.14957	+	7.82634i	0.215300	+	0.534998i
$215$	−3.56845	−	2.38436i	−0.243367	−	0.162612i
$216$	15.0435	−	2.52127i	1.02358	−	0.171551i
$217$	−6.75436	−	10.1086i	−0.458516	−	0.686217i
$218$	−5.21504	−	27.6755i	−0.353207	−	1.87442i
$219$	1.79162	−	3.35189i	0.121067	−	0.226500i
$220$	0.354142	+	0.155142i	0.0238763	+	0.0104597i
$221$	−2.14014	+	0.210786i	−0.143962	+	0.0141790i
$222$	−1.82451	+	0.161114i	−0.122453	+	0.0108132i
$223$	14.7196	−	14.7196i	0.985694	−	0.985694i	−0.0142049	−	0.999899i	$-0.504522\pi$
$223$	14.7196	−	14.7196i	0.985694	−	0.985694i	0.999899	+	0.0142049i	$0.00452171\pi$
$224$	−15.6137	−	2.33845i	−1.04324	−	0.156244i
$225$	1.17503	+	1.17503i	0.0783354	+	0.0783354i
$226$	−4.34878	−	3.64306i	−0.289276	−	0.242332i
$227$	2.66890	+	27.0978i	0.177141	+	1.79854i	0.514839	+	0.857287i	$0.327852\pi$
$227$	2.66890	+	27.0978i	0.177141	+	1.79854i	−0.337698	+	0.941255i	$0.609648\pi$
$228$	−2.23312	+	2.14470i	−0.147892	+	0.142036i
$229$	24.0441	+	12.8518i	1.58888	+	0.849272i	0.999131	+	0.0416837i	$0.0132722\pi$
$229$	24.0441	+	12.8518i	1.58888	+	0.849272i	0.589746	+	0.807589i	$0.299228\pi$
$230$	4.49593	+	3.07020i	0.296453	+	0.202443i
$231$	−0.518960	+	0.346758i	−0.0341451	+	0.0228150i
$232$	−16.1746	−	17.1856i	−1.06192	−	1.12829i
$233$	9.97474	−	14.9283i	0.653467	−	0.977982i	−0.345746	−	0.938328i	$-0.612374\pi$
$233$	9.97474	−	14.9283i	0.653467	−	0.977982i	0.999213	−	0.0396545i	$-0.0126257\pi$
$234$	−2.79547	+	6.56069i	−0.182746	+	0.428885i
$235$	−2.87434	+	2.35891i	−0.187501	+	0.153878i
$236$	0.139280	−	0.427844i	0.00906636	−	0.0278502i
$237$	6.03716	−	3.22693i	0.392156	−	0.209612i
$238$	−2.78070	−	0.302256i	−0.180246	−	0.0195923i
$239$	−5.33062	−	12.8693i	−0.344809	−	0.832443i	−0.997216	−	0.0745735i	$-0.976240\pi$
$239$	−5.33062	−	12.8693i	−0.344809	−	0.832443i	0.652406	−	0.757869i	$-0.273760\pi$
$240$	−4.62355	−	0.186853i	−0.298449	−	0.0120613i
$241$	2.04597	−	4.93941i	0.131793	−	0.318175i	−0.844183	−	0.536055i	$-0.819914\pi$
$241$	2.04597	−	4.93941i	0.131793	−	0.318175i	0.975976	+	0.217880i	$0.0699140\pi$
$242$	−7.44599	+	13.5984i	−0.478646	+	0.874136i
$243$	4.27549	−	14.0944i	0.274273	−	0.904155i
$244$	−5.00638	−	17.7895i	−0.320501	−	1.13885i
$245$	0.785465	+	0.0773616i	0.0501815	+	0.00494245i
$246$	0.0104561	−	1.03544i	0.000666654	−	0.0660172i
$247$	−0.792255	−	3.98294i	−0.0504100	−	0.253428i
$248$	−12.2194	−	1.57849i	−0.775930	−	0.100234i
$249$	−3.63979	−	0.723999i	−0.230662	−	0.0458815i
$250$	−0.773781	−	1.18375i	−0.0489382	−	0.0748669i
$251$	27.9146	−	8.46781i	1.76196	−	0.534484i	0.767634	−	0.640889i	$-0.221434\pi$
$251$	27.9146	−	8.46781i	1.76196	−	0.534484i	0.994323	+	0.106405i	$0.0339340\pi$
$252$	−5.30795	+	7.60675i	−0.334369	+	0.479180i
$253$	0.472116	−	0.575275i	0.0296817	−	0.0361673i
$254$	−3.02066	+	9.60744i	−0.189533	+	0.602824i
$255$	−0.819807			−0.0513383
$256$	−12.1898	+	10.3639i	−0.761861	+	0.647741i
$257$	5.74469			0.358344			0.179172	−	0.983818i	$-0.442658\pi$
$257$	5.74469			0.358344			0.179172	+	0.983818i	$0.442658\pi$
$258$	2.10592	−	6.69805i	0.131109	−	0.417003i
$259$	1.98223	−	2.41535i	0.123170	−	0.150083i
$260$	3.47305	−	4.97719i	0.215390	−	0.308672i
$261$	−13.2684	+	4.02491i	−0.821290	+	0.249136i
$262$	−1.56089	−	2.38788i	−0.0964319	−	0.147524i
$263$	3.95154	+	0.786011i	0.243663	+	0.0484675i	0.315411	−	0.948955i	$-0.397858\pi$
$263$	3.95154	+	0.786011i	0.243663	+	0.0484675i	−0.0717481	+	0.997423i	$0.522858\pi$
$264$	−0.0810373	+	0.627322i	−0.00498750	+	0.0386090i
$265$	1.07175	+	5.38804i	0.0658369	+	0.330984i
$266$	0.0533355	−	5.28169i	0.00327021	−	0.323841i
$267$	11.4631	+	1.12902i	0.701531	+	0.0690948i
$268$	0.522686	+	1.85729i	0.0319281	+	0.113452i
$269$	8.29886	−	27.3577i	0.505990	−	1.66803i	−0.216213	−	0.976346i	$-0.569371\pi$
$269$	8.29886	−	27.3577i	0.505990	−	1.66803i	0.722203	−	0.691681i	$-0.243129\pi$
$270$	−3.66291	+	6.68945i	−0.222917	+	0.407107i
$271$	−10.2613	+	24.7731i	−0.623332	+	1.50486i	0.224436	+	0.974489i	$0.427946\pi$
$271$	−10.2613	+	24.7731i	−0.623332	+	1.50486i	−0.847768	+	0.530367i	$0.822054\pi$
$272$	−2.08372	+	1.92184i	−0.126344	+	0.116529i
$273$	3.74934	+	9.05171i	0.226920	+	0.547834i
$274$	−22.0147	−	2.39294i	−1.32995	−	0.144563i
$275$	−0.170490	+	0.0911290i	−0.0102810	+	0.00549528i
$276$	−2.75709	+	8.46929i	−0.165957	+	0.509792i
$277$	−16.7281	+	13.7284i	−1.00509	+	0.824859i	−0.984581	−	0.174930i	$-0.944030\pi$
$277$	−16.7281	+	13.7284i	−1.00509	+	0.824859i	−0.0205131	+	0.999790i	$0.506530\pi$
$278$	3.82456	−	8.97586i	0.229382	−	0.538336i
$279$	−4.02161	+	6.01876i	−0.240767	+	0.360334i
$280$	5.74836	−	5.41022i	0.343530	−	0.323323i
$281$	14.4632	−	9.66403i	0.862805	−	0.576508i	−0.0435376	−	0.999052i	$-0.513863\pi$
$281$	14.4632	−	9.66403i	0.862805	−	0.576508i	0.906342	+	0.422544i	$0.138863\pi$
$282$	−5.02367	−	3.43058i	−0.299155	−	0.204288i
$283$	20.0837	+	10.7350i	1.19385	+	0.638127i	0.943932	−	0.330140i	$-0.107096\pi$
$283$	20.0837	+	10.7350i	1.19385	+	0.638127i	0.249919	+	0.968267i	$0.419596\pi$
$284$	−3.80997	+	3.65911i	−0.226080	+	0.217128i
$285$	−0.151741	−	1.54065i	−0.00898838	−	0.0912605i
$286$	−0.635962	−	0.532758i	−0.0376052	−	0.0315026i
$287$	1.24910	+	1.24910i	0.0737318	+	0.0737318i
$288$	2.27129	+	9.12172i	0.133837	+	0.537503i
$289$	11.6657	−	11.6657i	0.686218	−	0.686218i
$290$	11.7543	−	1.03797i	0.690236	−	0.0609515i
$291$	8.78547	−	0.865293i	0.515013	−	0.0507244i
$292$	6.01864	+	2.63663i	0.352214	+	0.154297i
$293$	0.194974	−	0.364771i	0.0113905	−	0.0213101i	−0.876162	−	0.482017i	$-0.839904\pi$
$293$	0.194974	−	0.364771i	0.0113905	−	0.0213101i	0.887552	+	0.460707i	$0.152404\pi$
$294$	0.239108	+	1.26891i	0.0139451	+	0.0740044i
$295$	0.124988	+	0.187057i	0.00727706	+	0.0108909i
$296$	−0.523419	−	3.12303i	−0.0304231	−	0.181523i
$297$	0.866831	+	0.579198i	0.0502986	+	0.0336085i
$298$	−4.00795	−	9.95932i	−0.232174	−	0.576928i
$299$	−7.41099	−	9.03032i	−0.428589	−	0.522237i
$300$	1.50359	−	1.75848i	0.0868097	−	0.101526i
$301$	5.64636	+	10.5636i	0.325451	+	0.608876i
$302$	14.0453	+	17.4710i	0.808213	+	1.00534i
$303$	7.42239	−	3.07445i	0.426405	−	0.176623i
$304$	−3.99737	−	3.56019i	−0.229265	−	0.204191i
$305$	8.53687	+	3.53609i	0.488820	+	0.202476i
$306$	0.467326	+	1.59850i	0.0267152	+	0.0913801i
$307$	4.82598	+	1.46394i	0.275433	+	0.0835517i	0.424979	−	0.905203i	$-0.360281\pi$
$307$	4.82598	+	1.46394i	0.275433	+	0.0835517i	−0.149546	+	0.988755i	$0.547781\pi$
$308$	−0.667568	−	0.847784i	−0.0380382	−	0.0483070i
$309$	−0.258605	+	2.62566i	−0.0147115	+	0.149369i
$310$	4.39985	−	4.31188i	0.249895	−	0.244898i
$311$	15.7720	−	3.13725i	0.894350	−	0.177897i	0.273542	−	0.961860i	$-0.411805\pi$
$311$	15.7720	−	3.13725i	0.894350	−	0.177897i	0.620808	+	0.783963i	$0.286805\pi$
$312$	9.40994	+	3.16875i	0.532733	+	0.179395i
$313$	0.803864	−	4.04130i	0.0454371	−	0.228428i	−0.951394	−	0.307977i	$-0.900348\pi$
$313$	0.803864	−	4.04130i	0.0454371	−	0.228428i	0.996831	+	0.0795492i	$0.0253481\pi$
$314$	30.4766	+	6.38275i	1.71989	+	0.360199i
$315$	−1.34628	−	4.43810i	−0.0758545	−	0.250059i
$316$	6.37504	+	9.97111i	0.358624	+	0.560919i
$317$	6.72741	+	5.52104i	0.377849	+	0.310093i	0.804079	−	0.594522i	$-0.202659\pi$
$317$	6.72741	+	5.52104i	0.377849	+	0.310093i	−0.426230	+	0.904615i	$0.640159\pi$
$318$	−7.96868	+	4.15645i	−0.446862	+	0.233082i
$319$		−	1.61301i		−	0.0903114i
$320$	−0.300631	−	7.99435i	−0.0168058	−	0.446898i
$321$		−	6.90092i		−	0.385172i
$322$	−7.02692	−	13.4719i	−0.391595	−	0.750760i
$323$	−0.733094	−	0.601634i	−0.0407904	−	0.0334758i
$324$	−2.44821	−	0.538592i	−0.136011	−	0.0299218i
$325$	0.880890	+	2.90390i	0.0488630	+	0.161080i
$326$	−4.70816	+	22.4807i	−0.260761	+	1.24509i
$327$	−4.49430	+	22.5944i	−0.248535	+	1.24947i
$328$	1.78610	−	0.121429i	0.0986209	−	0.00670481i
$329$	10.1783	−	2.02459i	0.561147	−	0.111619i
$330$	−0.221365	−	0.225882i	−0.0121858	−	0.0124344i
$331$	3.09894	−	31.4641i	0.170333	−	1.72942i	−0.407445	−	0.913230i	$-0.633580\pi$
$331$	3.09894	−	31.4641i	0.170333	−	1.72942i	0.577778	−	0.816194i	$-0.303920\pi$
$332$	0.757689	−	6.37107i	0.0415836	−	0.349658i
$333$	−1.78031	−	0.540052i	−0.0975605	−	0.0295947i
$334$	−15.5334	+	4.54122i	−0.849947	+	0.248485i
$335$	−0.891284	−	0.369182i	−0.0486960	−	0.0201706i
$336$	11.1345	+	6.54281i	0.607435	+	0.356939i
$337$	−30.5541	+	12.6559i	−1.66439	+	0.689412i	−0.998400	−	0.0565513i	$-0.981990\pi$
$337$	−30.5541	+	12.6559i	−1.66439	+	0.689412i	−0.665987	+	0.745963i	$0.731990\pi$
$338$	4.17888	−	3.35948i	0.227301	−	0.182731i
$339$	2.18756	+	4.09263i	0.118812	+	0.222281i
$340$	−0.110410	−	1.41303i	−0.00598784	−	0.0766321i
$341$	−0.534227	−	0.650957i	−0.0289300	−	0.0352513i
$342$	−2.91754	+	1.17411i	−0.157763	+	0.0634887i
$343$	14.4124	+	9.63009i	0.778199	+	0.519976i
$344$	11.8284	+	2.72770i	0.637747	+	0.147068i
$345$	−2.47417	−	3.70285i	−0.133205	−	0.199355i
$346$	−0.707106	+	0.133244i	−0.0380142	+	0.00716324i
$347$	7.59021	−	14.2003i	0.407464	−	0.762311i	−0.591570	−	0.806253i	$-0.701492\pi$
$347$	7.59021	−	14.2003i	0.407464	−	0.762311i	0.999034	+	0.0439425i	$0.0139918\pi$
$348$	7.02599	+	17.9810i	0.376632	+	0.963880i
$349$	20.9737	−	2.06573i	1.12270	−	0.110576i	0.480413	−	0.877042i	$-0.340487\pi$
$349$	20.9737	−	2.06573i	1.12270	−	0.110576i	0.642285	+	0.766466i	$0.277987\pi$
$350$	0.347187	+	3.93167i	0.0185579	+	0.210156i
$351$	11.5718	−	11.5718i	0.617656	−	0.617656i
$352$	−1.09217	−	0.0551898i	−0.0582130	−	0.00294163i
$353$	16.7326	+	16.7326i	0.890588	+	0.890588i	0.994578	−	0.103990i	$-0.0331610\pi$
$353$	16.7326	+	16.7326i	0.890588	+	0.890588i	−0.103990	+	0.994578i	$0.533161\pi$
$354$	−0.236352	+	0.282138i	−0.0125620	+	0.0149955i
$355$	−0.258889	−	2.62854i	−0.0137404	−	0.139508i
$356$	−0.402150	+	19.9100i	−0.0213139	+	1.05523i
$357$	2.01785	+	1.07857i	0.106796	+	0.0570837i
$358$	12.9344	−	18.9408i	0.683604	−	1.00105i
$359$	−14.4103	+	9.62862i	−0.760544	+	0.508179i	−0.874333	−	0.485326i	$-0.838701\pi$
$359$	−14.4103	+	9.62862i	−0.760544	+	0.508179i	0.113789	+	0.993505i	$0.463701\pi$
$360$	−4.28587	−	1.92936i	−0.225885	−	0.101686i
$361$	−9.56088	+	14.3089i	−0.503204	+	0.753098i
$362$	27.1378	+	11.5632i	1.42633	+	0.607750i
$363$	9.80324	−	8.04531i	0.514537	−	0.422269i
$364$	−15.0966	+	7.68147i	−0.791279	+	0.402618i
$365$	−2.89748	+	1.54873i	−0.151661	+	0.0810644i
$366$	−1.63357	+	15.0286i	−0.0853881	+	0.785556i
$367$	9.11820	+	22.0133i	0.475966	+	1.14908i	0.961485	+	0.274858i	$0.0886308\pi$
$367$	9.11820	+	22.0133i	0.475966	+	1.14908i	−0.485519	+	0.874226i	$0.661369\pi$
$368$	−14.9691	−	3.61151i	−0.780317	−	0.188263i
$369$	0.402500	−	0.971721i	0.0209533	−	0.0505858i
$370$	1.38874	+	0.760423i	0.0721969	+	0.0395325i
$371$	4.45071	−	14.6720i	0.231069	−	0.761733i
$372$	8.79070	+	4.92951i	0.455777	+	0.255583i
$373$	−13.1386	−	1.29404i	−0.680291	−	0.0670028i	−0.248031	−	0.968752i	$-0.579784\pi$
$373$	−13.1386	−	1.29404i	−0.680291	−	0.0670028i	−0.432259	+	0.901749i	$0.642284\pi$
$374$	−0.193734	−	0.00195636i	−0.0100177	−	0.000101161i
$375$	0.225686	+	1.13460i	0.0116544	+	0.0585906i
$376$	5.23640	−	9.12086i	0.270047	−	0.470373i
$377$	−24.8336	−	4.93971i	−1.27899	−	0.254408i
$378$	17.8166	−	11.6462i	0.916390	−	0.599016i
$379$	−0.968372	+	0.293752i	−0.0497419	+	0.0150890i	−0.315058	−	0.949073i	$-0.602024\pi$
$379$	−0.968372	+	0.293752i	−0.0497419	+	0.0150890i	0.265316	+	0.964162i	$0.414524\pi$
$380$	2.63505	−	0.469036i	0.135175	−	0.0240610i
$381$	5.22625	−	6.36821i	0.267749	−	0.326253i
$382$	25.8378	+	8.12360i	1.32198	+	0.415640i
$383$	31.0567			1.58692			0.793462	−	0.608620i	$-0.208276\pi$
$383$	31.0567			1.58692			0.793462	+	0.608620i	$0.208276\pi$
$384$	12.4153	−	4.14208i	0.633566	−	0.211374i
$385$	0.539533			0.0274972
$386$	5.61629	+	1.76581i	0.285862	+	0.0898772i
$387$	4.52435	−	5.51294i	0.229986	−	0.280238i
$388$	2.67464	+	15.0262i	0.135784	+	0.762838i
$389$	−31.5768	+	9.57873i	−1.60101	+	0.485661i	−0.959560	−	0.281505i	$-0.909167\pi$
$389$	−31.5768	+	9.57873i	−1.60101	+	0.485661i	−0.641449	+	0.767165i	$0.721667\pi$
$390$	−4.15553	+	2.71635i	−0.210424	+	0.137548i
$391$	−2.67569	−	0.532229i	−0.135316	−	0.0269160i
$392$	−2.15490	+	0.583024i	−0.108839	+	0.0294472i
$393$	0.455259	+	2.28874i	0.0229648	+	0.115452i
$394$	−9.14004	−	0.0922978i	−0.460469	−	0.00464990i
$395$	−5.88894	−	0.580010i	−0.296305	−	0.0291835i
$396$	−0.314247	+	0.560391i	−0.0157915	+	0.0281607i
$397$	0.824318	−	2.71741i	0.0413713	−	0.136383i	−0.933822	−	0.357738i	$-0.883548\pi$
$397$	0.824318	−	2.71741i	0.0413713	−	0.136383i	0.975193	+	0.221355i	$0.0710480\pi$
$398$	7.66955	+	4.19957i	0.384440	+	0.210506i
$399$	−1.65344	+	3.99177i	−0.0827758	+	0.199838i
$400$	3.23343	+	2.35477i	0.161671	+	0.117738i
$401$	−4.75003	−	11.4676i	−0.237205	−	0.572664i	0.759786	−	0.650173i	$-0.225304\pi$
$401$	−4.75003	−	11.4676i	−0.237205	−	0.572664i	−0.996992	+	0.0775085i	$0.975304\pi$
$402$	0.170551	−	1.56904i	0.00850632	−	0.0782567i
$403$	−11.6580	+	6.23133i	−0.580726	+	0.310405i
$404$	6.29879	+	12.3792i	0.313377	+	0.615890i
$405$	0.968872	−	0.795133i	0.0481436	−	0.0395105i
$406$	−30.2973	−	12.9095i	−1.50363	−	0.640688i
$407$	0.120242	−	0.179955i	0.00596018	−	0.00892003i
$408$	2.16815	−	0.822059i	0.107340	−	0.0406980i
$409$	11.1284	−	7.43577i	0.550265	−	0.367675i	−0.249140	−	0.968467i	$-0.580148\pi$
$409$	11.1284	−	7.43577i	0.550265	−	0.367675i	0.799405	+	0.600792i	$0.205148\pi$
$410$	−0.504787	+	0.739199i	−0.0249297	+	0.0365064i
$411$	15.9752	+	8.53894i	0.788000	+	0.421195i
$412$	−4.56045	−	0.0921138i	−0.224677	−	0.00453812i
$413$	−0.0615429	−	0.624856i	−0.00302833	−	0.0307471i
$414$	−5.80961	+	6.93503i	−0.285527	+	0.340838i
$415$	2.26839	+	2.26839i	0.111351	+	0.111351i
$416$	−4.19437	+	16.6458i	−0.205646	+	0.816128i
$417$	−5.64343	+	5.64343i	−0.276360	+	0.276360i
$418$	−0.0321823	−	0.364444i	−0.00157409	−	0.0178255i
$419$	−35.0315	+	3.45030i	−1.71140	+	0.168558i	−0.905744	−	0.423826i	$-0.860687\pi$
$419$	−35.0315	+	3.45030i	−1.71140	+	0.168558i	−0.805656	+	0.592384i	$0.798187\pi$
$420$	−6.01441	+	2.35011i	−0.293473	+	0.114673i
$421$	−18.4738	+	34.5621i	−0.900358	+	1.68445i	−0.188567	+	0.982060i	$0.560384\pi$
$421$	−18.4738	+	34.5621i	−0.900358	+	1.68445i	−0.711791	+	0.702391i	$0.752116\pi$
$422$	29.9871	−	5.65064i	1.45975	−	0.275069i
$423$	−3.43285	−	5.13763i	−0.166911	−	0.249800i
$424$	−8.23730	−	13.1751i	−0.400039	−	0.639840i
$425$	0.589235	+	0.393714i	0.0285821	+	0.0190979i
$426$	4.00868	−	1.61322i	0.194221	−	0.0781609i
$427$	−16.3603	−	19.9350i	−0.791729	−	0.964724i
$428$	11.8945	−	0.929406i	0.574942	−	0.0449246i
$429$	0.319907	+	0.598504i	0.0154452	+	0.0288960i
$430$	−4.73038	+	3.80284i	−0.228119	+	0.183389i
$431$	−34.8671	+	14.4424i	−1.67949	+	0.695668i	−0.999302	−	0.0373682i	$-0.988103\pi$
$431$	−34.8671	+	14.4424i	−1.67949	+	0.695668i	−0.680190	+	0.733036i	$0.738103\pi$
$432$	2.97951	−	21.3646i	0.143352	−	1.02791i
$433$	−6.60745	−	2.73690i	−0.317534	−	0.131527i	0.218223	−	0.975899i	$-0.429974\pi$
$433$	−6.60745	−	2.73690i	−0.317534	−	0.131527i	−0.535757	+	0.844372i	$0.679974\pi$
$434$	−16.5026	+	4.82457i	−0.792148	+	0.231587i
$435$	−9.23682	−	2.80196i	−0.442872	−	0.134344i
$436$	−39.5491	−	4.70343i	−1.89406	−	0.225254i
$437$	0.504957	−	5.12692i	0.0241554	−	0.245254i
$438$	−3.76209	−	3.83885i	−0.179760	−	0.183427i
$439$	−14.0294	+	2.79062i	−0.669586	+	0.133189i	−0.518166	−	0.855280i	$-0.673385\pi$
$439$	−14.0294	+	2.79062i	−0.669586	+	0.133189i	−0.151421	+	0.988469i	$0.548385\pi$
$440$	0.359518	−	0.411969i	0.0171394	−	0.0196398i
$441$	−0.255872	+	1.28636i	−0.0121844	+	0.0612551i
$442$	−0.623411	+	2.97669i	−0.0296526	+	0.141586i
$443$	9.52195	+	31.3896i	0.452401	+	1.49137i	0.825943	+	0.563754i	$0.190643\pi$
$443$	9.52195	+	31.3896i	0.452401	+	1.49137i	−0.373542	+	0.927613i	$0.621857\pi$
$444$	−0.556540	+	2.52979i	−0.0264122	+	0.120058i
$445$	−7.69688	−	6.31667i	−0.364867	−	0.299439i
$446$	−13.6146	−	26.1018i	−0.644671	−	1.23596i
$447$			8.78169i			0.415360i
$448$	−9.77767	+	20.0726i	−0.461951	+	0.948342i
$449$		−	3.15617i		−	0.148949i	−0.997223	−	0.0744743i	$-0.976272\pi$
$449$		−	3.15617i		−	0.148949i	0.997223	−	0.0744743i	$-0.0237279\pi$
$450$	2.08365	−	1.08683i	0.0982242	−	0.0512335i
$451$	0.0945840	+	0.0776231i	0.00445379	+	0.00365513i
$452$	−6.75948	+	4.32168i	−0.317939	+	0.203275i
$453$	−5.32291	−	17.5473i	−0.250092	−	0.824443i
$454$	37.6898	+	7.89341i	1.76887	+	0.370456i
$455$	1.65227	−	8.30653i	0.0774597	−	0.389416i
$456$	1.94620	+	3.92243i	0.0911391	+	0.183685i
$457$	−14.2706	+	2.83859i	−0.667549	+	0.132784i	−0.517220	−	0.855852i	$-0.673033\pi$
$457$	−14.2706	+	2.83859i	−0.667549	+	0.132784i	−0.150329	+	0.988636i	$0.548033\pi$
$458$	27.5372	−	26.9866i	1.28673	−	1.26100i
$459$	0.374595	−	3.80333i	0.0174846	−	0.177524i
$460$	6.04905	−	4.76319i	0.282038	−	0.222085i
$461$	−25.8690	−	7.84728i	−1.20484	−	0.365484i	−0.376875	−	0.926264i	$-0.623001\pi$
$461$	−25.8690	−	7.84728i	−1.20484	−	0.365484i	−0.827965	+	0.560780i	$0.810501\pi$
$462$	0.247686	+	0.847215i	0.0115234	+	0.0394160i
$463$	31.0112	+	12.8453i	1.44121	+	0.596970i	0.960092	−	0.279684i	$-0.0902297\pi$
$463$	31.0112	+	12.8453i	1.44121	+	0.596970i	0.481121	+	0.876654i	$0.340230\pi$
$464$	−30.0459	+	14.5317i	−1.39485	+	0.674617i
$465$	−4.65567	+	1.92844i	−0.215901	+	0.0894293i
$466$	−15.9088	−	19.7891i	−0.736960	−	0.916711i
$467$	4.55996	+	8.53108i	0.211010	+	0.394771i	0.965054	−	0.262053i	$-0.0843994\pi$
$467$	4.55996	+	8.53108i	0.211010	+	0.394771i	−0.754044	+	0.656824i	$0.771899\pi$
$468$	7.66529	+	6.55422i	0.354328	+	0.302969i
$469$	1.70808	+	2.08130i	0.0788717	+	0.0961054i
$470$	1.96321	+	4.87835i	0.0905559	+	0.225022i
$471$	−21.1782	−	14.1508i	−0.975839	−	0.652035i
$472$	−0.518127	−	0.369381i	−0.0238487	−	0.0170021i
$473$	0.460938	+	0.689843i	0.0211940	+	0.0317190i
$474$	−1.79269	−	9.51352i	−0.0823409	−	0.436971i
$475$	−0.630839	+	1.18022i	−0.0289449	+	0.0541521i
$476$	−1.58726	+	3.62325i	−0.0727521	+	0.166071i
$477$	−9.08499	+	0.894793i	−0.415973	+	0.0409698i
$478$	−19.6230	+	1.73282i	−0.897537	+	0.0792574i
$479$	−0.911436	+	0.911436i	−0.0416446	+	0.0416446i	−0.727622	−	0.685978i	$-0.759375\pi$
$479$	−0.911436	+	0.911436i	−0.0416446	+	0.0416446i	0.685978	+	0.727622i	$0.259375\pi$
$480$	−2.21325	+	6.15839i	−0.101021	+	0.281091i
$481$	−2.40231	−	2.40231i	−0.109536	−	0.109536i
$482$	−5.79594	−	4.85537i	−0.263998	−	0.221156i
$483$	1.21826	+	12.3692i	0.0554328	+	0.562819i
$484$	15.1873	+	15.8134i	0.690330	+	0.718792i
$485$	−6.73010	−	3.59731i	−0.305598	−	0.163346i
$486$	−17.2013	−	11.7465i	−0.780265	−	0.532831i
$487$	6.69550	−	4.47379i	0.303402	−	0.202727i	−0.394544	−	0.918877i	$-0.629097\pi$
$487$	6.69550	−	4.47379i	0.303402	−	0.202727i	0.697946	+	0.716150i	$0.254097\pi$
$488$	−26.1234	−	0.791611i	−1.18255	−	0.0358345i
$489$	10.4382	−	15.6218i	0.472031	−	0.706444i
$490$	0.437539	−	1.02686i	0.0197660	−	0.0463888i
$491$	11.7407	−	9.63533i	0.529850	−	0.434836i	−0.331049	−	0.943614i	$-0.607402\pi$
$491$	11.7407	−	9.63533i	0.529850	−	0.434836i	0.860898	+	0.508777i	$0.169902\pi$
$492$	−1.39248	−	0.453308i	−0.0627778	−	0.0204367i
$493$	−5.21483	+	2.78738i	−0.234864	+	0.125537i
$494$	−5.70944	−	0.620603i	−0.256880	−	0.0279223i
$495$	−0.122934	−	0.296790i	−0.00552549	−	0.0133397i
$496$	−7.31262	+	15.8156i	−0.328346	+	0.710142i
$497$	−2.82097	+	6.81043i	−0.126538	+	0.305490i
$498$	−2.52063	+	4.60335i	−0.112952	+	0.206281i
$499$	0.470975	−	1.55260i	0.0210837	−	0.0695038i	−0.945767	−	0.324845i	$-0.894688\pi$
$499$	0.470975	−	1.55260i	0.0210837	−	0.0695038i	0.966851	+	0.255341i	$0.0821878\pi$
$500$	−1.92521	+	0.541801i	−0.0860982	+	0.0242301i
$501$	13.1744	+	1.29757i	0.588591	+	0.0579711i
$502$	0.416565	−	41.2515i	0.0185922	−	1.84115i
$503$	−5.82737	−	29.2962i	−0.259830	−	1.30625i	−0.861602	−	0.507584i	$-0.830539\pi$
$503$	−5.82737	−	29.2962i	−0.259830	−	1.30625i	0.601773	−	0.798667i	$-0.294461\pi$
$504$	8.01082	+	10.3875i	0.356830	+	0.462697i
$505$	−6.81134	−	1.35486i	−0.303101	−	0.0602905i
$506$	−0.575849	−	0.880948i	−0.0255996	−	0.0391629i
$507$	−4.19712	+	1.27318i	−0.186401	+	0.0565440i
$508$	11.6802	+	8.15035i	0.518223	+	0.361613i
$509$	2.88976	−	3.52119i	0.128086	−	0.156074i	−0.705018	−	0.709189i	$-0.749061\pi$
$509$	2.88976	−	3.52119i	0.128086	−	0.156074i	0.833105	+	0.553115i	$0.186561\pi$
$510$	−0.347737	+	1.10600i	−0.0153980	+	0.0489747i
$511$	9.16934			0.405628
$512$	8.81139	+	20.8413i	0.389412	+	0.921064i
$513$	7.21689			0.318633
$514$	2.43672	−	7.75018i	0.107479	−	0.341846i
$515$	1.44685	−	1.76300i	0.0637560	−	0.0776869i
$516$	−8.14310	−	5.68221i	−0.358480	−	0.250145i
$517$	0.687871	−	0.208663i	0.0302525	−	0.00917701i
$518$	−2.41776	−	3.69875i	−0.106230	−	0.162514i
$519$	0.577284	+	0.114829i	0.0253400	+	0.00504043i
$520$	−5.24158	−	6.79668i	−0.229858	−	0.298054i
$521$	0.878277	+	4.41540i	0.0384780	+	0.193442i	0.995244	−	0.0974183i	$-0.0310585\pi$
$521$	0.878277	+	4.41540i	0.0384780	+	0.193442i	−0.956766	+	0.290860i	$0.906058\pi$
$522$	−0.198001	+	19.6076i	−0.00866628	+	0.858202i
$523$	12.3416	+	1.21554i	0.539659	+	0.0531517i	0.364175	−	0.931331i	$-0.381351\pi$
$523$	12.3416	+	1.21554i	0.539659	+	0.0531517i	0.175484	+	0.984482i	$0.443851\pi$
$524$	−3.88358	+	1.09293i	−0.169655	+	0.0477450i
$525$	0.937221	−	3.08960i	0.0409037	−	0.134841i
$526$	2.73653	−	4.99764i	0.119318	−	0.217907i
$527$	−1.18135	+	2.85203i	−0.0514604	+	0.124236i
$528$	0.811950	+	0.375419i	0.0353356	+	0.0163380i
$529$	3.13045	+	7.55756i	0.136106	+	0.328590i
$530$	7.72362	+	0.839540i	0.335493	+	0.0364673i
$531$	−0.329702	+	0.176229i	−0.0143079	+	0.00764771i
$532$	−7.10293	−	2.31229i	−0.307951	−	0.100250i
$533$	1.48472	−	1.21848i	0.0643104	−	0.0527782i
$534$	6.38546	−	14.9860i	0.276326	−	0.648509i
$535$	−3.31418	+	4.96003i	−0.143285	+	0.214441i
$536$	2.72738	+	0.0826473i	0.117805	+	0.00356982i
$537$	−15.5997	+	10.4234i	−0.673177	+	0.449802i
$538$	−33.3882	−	22.8003i	−1.43947	−	0.982991i
$539$	−0.134562	−	0.0719250i	−0.00579600	−	0.00309803i
$540$	7.47107	+	7.77910i	0.321503	+	0.334759i
$541$	−0.263131	−	2.67161i	−0.0113129	−	0.114862i	0.987870	−	0.155285i	$-0.0496294\pi$
$541$	−0.263131	−	2.67161i	−0.0113129	−	0.114862i	−0.999183	+	0.0404230i	$0.987129\pi$
$542$	29.0689	+	24.3516i	1.24862	+	1.04599i
$543$	−17.0624	−	17.0624i	−0.732219	−	0.732219i
$544$	1.70891	+	3.62633i	0.0732690	+	0.155478i
$545$	14.0813	−	14.0813i	0.603175	−	0.603175i
$546$	13.8020	−	1.21880i	0.590673	−	0.0521596i
$547$	9.91476	−	0.976518i	0.423924	−	0.0417529i	0.116194	−	0.993227i	$-0.462931\pi$
$547$	9.91476	−	0.976518i	0.423924	−	0.0417529i	0.307730	+	0.951474i	$0.400431\pi$
$548$	−12.5663	+	28.6851i	−0.536804	+	1.22537i
$549$	−7.23826	+	13.5418i	−0.308921	+	0.577951i
$550$	0.0506257	+	0.268663i	0.00215869	+	0.0114558i
$551$	−6.20353	−	9.28424i	−0.264279	−	0.395522i
$552$	10.2565	+	7.31201i	0.436545	+	0.311220i
$553$	13.7318	+	9.17531i	0.583937	+	0.390174i
$554$	11.4255	+	28.3911i	0.485422	+	1.20622i
$555$	−0.821628	−	1.00116i	−0.0348762	−	0.0424968i
$556$	−10.4871	−	8.96701i	−0.444752	−	0.380286i
$557$	5.97412	+	11.1768i	0.253132	+	0.473576i	0.976105	−	0.217300i	$-0.0697250\pi$
$557$	5.97412	+	11.1768i	0.253132	+	0.473576i	−0.722973	+	0.690876i	$0.757225\pi$
$558$	6.41410	+	7.97854i	0.271530	+	0.337759i
$559$	12.0322	−	4.98392i	0.508909	−	0.210797i
$560$	−4.86068	−	10.0500i	−0.205401	−	0.424689i
$561$	0.146419	+	0.0606487i	0.00618181	+	0.00256059i
$562$	−6.90292	−	23.6116i	−0.291182	−	0.995995i
$563$	21.7391	+	6.59448i	0.916194	+	0.277924i	0.712959	−	0.701206i	$-0.247355\pi$
$563$	21.7391	+	6.59448i	0.916194	+	0.277924i	0.203235	+	0.979130i	$0.434855\pi$
$564$	−6.75910	+	5.32230i	−0.284609	+	0.224109i
$565$	0.393192	−	3.99215i	0.0165417	−	0.167951i
$566$	23.0014	−	22.5415i	0.966823	−	0.947492i
$567$	−3.43086	+	0.682441i	−0.144083	+	0.0286598i
$568$	3.32045	+	6.69213i	0.139323	+	0.280796i
$569$	3.21888	−	16.1824i	0.134943	−	0.678402i	−0.852791	−	0.522253i	$-0.825092\pi$
$569$	3.21888	−	16.1824i	0.134943	−	0.678402i	0.987733	−	0.156149i	$-0.0499081\pi$
$570$	−2.14287	−	0.448783i	−0.0897548	−	0.0187975i
$571$	5.39111	+	17.7721i	0.225611	+	0.743739i	0.994535	+	0.104400i	$0.0332922\pi$
$571$	5.39111	+	17.7721i	0.225611	+	0.743739i	−0.768924	+	0.639340i	$0.779208\pi$
$572$	−0.988501	+	0.632000i	−0.0413313	+	0.0264252i
$573$	−17.1263	−	14.0552i	−0.715463	−	0.587166i
$574$	2.21499	−	1.15533i	0.0924517	−	0.0482226i
$575$			3.84964i			0.160541i
$576$	13.2696	+	0.804948i	0.552898	+	0.0335395i
$577$			32.9505i			1.37175i	0.727721	+	0.685874i	$0.240580\pi$
$577$			32.9505i			1.37175i	−0.727721	+	0.685874i	$0.759420\pi$
$578$	−10.7900	−	20.6865i	−0.448805	−	0.860444i
$579$	−3.72271	−	3.05515i	−0.154711	−	0.126968i
$580$	3.58548	−	16.2980i	0.148879	−	0.676739i
$581$	−2.59899	−	8.56773i	−0.107824	−	0.355449i
$582$	2.55915	−	12.2195i	0.106080	−	0.506516i
$583$	0.207187	−	1.04160i	0.00858080	−	0.0431386i
$584$	6.11000	−	7.00139i	0.252834	−	0.289719i
$585$	−4.94579	+	0.983778i	−0.204483	+	0.0406742i
$586$	−0.409411	−	0.417764i	−0.0169126	−	0.0172577i
$587$	−0.0470854	+	0.478066i	−0.00194342	+	0.0197319i	−0.996108	−	0.0881464i	$-0.971906\pi$
$587$	−0.0470854	+	0.478066i	−0.00194342	+	0.0197319i	0.994164	+	0.107878i	$0.0344057\pi$
$588$	1.81331	+	0.215651i	0.0747798	+	0.00889330i
$589$	−5.57845	−	1.69221i	−0.229856	−	0.0697261i
$590$	0.305375	−	0.0892774i	0.0125721	−	0.00367549i
$591$	6.90781	+	2.86131i	0.284149	+	0.117698i
$592$	−4.43532	−	0.618548i	−0.182290	−	0.0254222i
$593$	−33.2236	+	13.7617i	−1.36433	+	0.565124i	−0.940245	−	0.340499i	$-0.889404\pi$
$593$	−33.2236	+	13.7617i	−1.36433	+	0.565124i	−0.424085	+	0.905623i	$0.639404\pi$
$594$	1.14908	−	0.923767i	0.0471474	−	0.0379026i
$595$	−0.932345	−	1.74430i	−0.0382224	−	0.0715091i
$596$	−15.1362	+	1.18271i	−0.620003	+	0.0484455i
$597$	−4.53759	−	5.52908i	−0.185711	−	0.226290i
$598$	−15.3264	+	6.16782i	−0.626741	+	0.252221i
$599$	−19.9659	−	13.3408i	−0.815783	−	0.545089i	0.0762345	−	0.997090i	$-0.475710\pi$
$599$	−19.9659	−	13.3408i	−0.815783	−	0.545089i	−0.892017	+	0.452001i	$0.850710\pi$
$600$	−1.73459	−	2.77439i	−0.0708145	−	0.113264i
$601$	−5.84899	−	8.75363i	−0.238585	−	0.357068i	0.692783	−	0.721146i	$-0.256384\pi$
$601$	−5.84899	−	8.75363i	−0.238585	−	0.357068i	−0.931369	+	0.364078i	$0.881384\pi$
$602$	16.6464	−	3.13678i	0.678456	−	0.127845i
$603$	0.755703	−	1.41382i	0.0307746	−	0.0575753i
$604$	29.5277	−	11.5378i	1.20147	−	0.469468i
$605$	−10.9098	+	1.07453i	−0.443548	+	0.0436857i
$606$	−0.999411	−	11.3177i	−0.0405983	−	0.459749i
$607$	28.4679	−	28.4679i	1.15548	−	1.15548i	0.170040	−	0.985437i	$-0.445610\pi$
$607$	28.4679	−	28.4679i	1.15548	−	1.15548i	0.985437	−	0.170040i	$-0.0543897\pi$
$608$	−6.49862	+	3.88275i	−0.263554	+	0.157466i
$609$	19.0489	+	19.0489i	0.771902	+	0.771902i
$610$	8.39163	−	10.0172i	0.339767	−	0.405586i
$611$	−1.10599	−	11.2293i	−0.0447436	−	0.454290i
$612$	2.35476	+	0.0475625i	0.0951857	+	0.00192260i
$613$	−27.0828	−	14.4760i	−1.09386	−	0.584682i	−0.177132	−	0.984187i	$-0.556682\pi$
$613$	−27.0828	−	14.4760i	−1.09386	−	0.584682i	−0.916731	+	0.399505i	$0.869182\pi$
$614$	4.02204	−	5.88979i	0.162316	−	0.237692i
$615$	0.608805	−	0.406791i	0.0245494	−	0.0164034i
$616$	−1.42691	+	0.541015i	−0.0574918	+	0.0217981i
$617$	26.5452	−	39.7277i	1.06867	−	1.59938i	0.306650	−	0.951823i	$-0.400792\pi$
$617$	26.5452	−	39.7277i	1.06867	−	1.59938i	0.762020	−	0.647554i	$-0.224208\pi$
$618$	3.43260	+	1.46261i	0.138079	+	0.0588348i
$619$	−9.92483	+	8.14510i	−0.398913	+	0.327379i	−0.812368	−	0.583145i	$-0.801822\pi$
$619$	−9.92483	+	8.14510i	−0.398913	+	0.327379i	0.413455	+	0.910524i	$0.364322\pi$
$620$	−3.95089	−	7.76483i	−0.158672	−	0.311843i
$621$	18.3092	−	9.78645i	0.734721	−	0.392717i
$622$	2.45753	−	22.6088i	0.0985379	−	0.906532i
$623$	10.6345	+	25.6740i	0.426062	+	1.02861i
$624$	8.26638	−	11.3509i	0.330920	−	0.454400i
$625$	0.382683	−	0.923880i	0.0153073	−	0.0369552i
$626$	−5.11116	−	2.79869i	−0.204283	−	0.111858i
$627$	−0.0868752	+	0.286389i	−0.00346946	+	0.0114373i
$628$	21.5382	−	38.4087i	0.859468	−	1.53267i
$629$	−0.789574	−	0.0777663i	−0.0314824	−	0.00310074i
$630$	−6.55851	−	0.0662290i	−0.261297	−	0.00263863i
$631$	−4.11355	−	20.6802i	−0.163758	−	0.823267i	−0.972102	−	0.234557i	$-0.924636\pi$
$631$	−4.11355	−	20.6802i	−0.163758	−	0.823267i	0.808345	−	0.588710i	$-0.200364\pi$
$632$	16.1562	−	4.37116i	0.642657	−	0.173875i
$633$	−24.4816	−	4.86970i	−0.973057	−	0.193553i
$634$	10.3020	−	6.73412i	0.409146	−	0.267446i
$635$	−6.81471	+	2.06722i	−0.270433	+	0.0820351i
$636$	2.22741	+	12.5136i	0.0883225	+	0.496197i
$637$	−1.51942	+	1.85142i	−0.0602018	+	0.0733561i
$638$	−2.17612	−	0.684190i	−0.0861535	−	0.0270874i
$639$	4.38910			0.173630
$640$	−10.9127	−	2.98537i	−0.431363	−	0.118007i
$641$	−11.9000			−0.470021			−0.235010	−	0.971993i	$-0.575512\pi$
$641$	−11.9000			−0.470021			−0.235010	+	0.971993i	$0.575512\pi$
$642$	−9.31006	−	2.92716i	−0.367439	−	0.115526i
$643$	−5.86407	+	7.14539i	−0.231256	+	0.281787i	−0.875690	−	0.482873i	$-0.839593\pi$
$643$	−5.86407	+	7.14539i	−0.231256	+	0.281787i	0.644434	+	0.764660i	$0.277093\pi$
$644$	−21.1556	+	3.76567i	−0.833648	+	0.148388i
$645$	4.75103	−	1.44121i	0.187072	−	0.0567476i
$646$	−1.12262	+	0.733825i	−0.0441690	+	0.0288719i
$647$	27.9029	+	5.55023i	1.09698	+	0.218202i	0.710219	−	0.703980i	$-0.248596\pi$
$647$	27.9029	+	5.55023i	1.09698	+	0.218202i	0.386756	+	0.922182i	$0.373596\pi$
$648$	−1.76507	+	3.07443i	−0.0693385	+	0.120775i
$649$	−0.00848464	−	0.0426552i	−0.000333051	−	0.00167436i
$650$	4.29131	+	0.0433345i	0.168319	+	0.00169972i
$651$	13.9965	+	1.37853i	0.548565	+	0.0540289i
$652$	28.3318	+	15.8874i	1.10956	+	0.622199i
$653$	6.76202	−	22.2914i	0.264618	−	0.872330i	−0.719451	−	0.694543i	$-0.755606\pi$
$653$	6.76202	−	22.2914i	0.264618	−	0.872330i	0.984069	−	0.177786i	$-0.0568936\pi$
$654$	28.5758	+	15.6471i	1.11740	+	0.611850i
$655$	0.771957	−	1.86367i	0.0301628	−	0.0728195i
$656$	0.593788	−	2.46114i	0.0231835	−	0.0960914i
$657$	−2.08927	−	5.04394i	−0.0815100	−	0.196783i
$658$	1.58593	−	14.5903i	0.0618262	−	0.568790i
$659$	−16.3731	+	8.75163i	−0.637807	+	0.340915i	−0.758402	−	0.651787i	$-0.774020\pi$
$659$	−16.3731	+	8.75163i	−0.637807	+	0.340915i	0.120595	+	0.992702i	$0.461520\pi$
$660$	−0.398634	+	0.202833i	−0.0155168	+	0.00789525i
$661$	5.94647	−	4.88014i	0.231291	−	0.189815i	−0.511608	−	0.859219i	$-0.670950\pi$
$661$	5.94647	−	4.88014i	0.231291	−	0.189815i	0.742899	+	0.669403i	$0.233450\pi$
$662$	−41.1339	−	17.5269i	−1.59871	−	0.681202i
$663$	1.38213	−	2.06850i	0.0536774	−	0.0803338i
$664$	−8.27385	−	3.72461i	−0.321088	−	0.144543i
$665$	3.10547	−	2.07501i	0.120425	−	0.0804653i
$666$	−1.48374	+	2.17275i	−0.0574937	+	0.0841925i
$667$	−28.3282	−	15.1417i	−1.09687	−	0.586290i
$668$	−0.462187	+	22.8823i	−0.0178826	+	0.885345i
$669$	2.36038	+	23.9653i	0.0912574	+	0.926552i
$670$	−0.876119	+	1.04584i	−0.0338474	+	0.0404043i
$671$	−1.26310	−	1.26310i	−0.0487615	−	0.0487615i
$672$	13.5498	−	12.2463i	0.522696	−	0.472411i
$673$	−10.6704	+	10.6704i	−0.411315	+	0.411315i	−0.882197	−	0.470881i	$-0.843936\pi$
$673$	−10.6704	+	10.6704i	−0.411315	+	0.411315i	0.470881	+	0.882197i	$0.343936\pi$
$674$	4.11405	+	46.5889i	0.158467	+	1.79454i
$675$	−5.36688	+	0.528591i	−0.206571	+	0.0203455i
$676$	−2.75973	−	7.06272i	−0.106143	−	0.271643i
$677$	−3.68160	+	6.88779i	−0.141495	+	0.264719i	−0.942680	−	0.333698i	$-0.891703\pi$
$677$	−3.68160	+	6.88779i	−0.141495	+	0.264719i	0.801185	+	0.598417i	$0.204203\pi$
$678$	6.44928	−	1.21527i	0.247683	−	0.0466723i
$679$	11.8326	+	17.7087i	0.454092	+	0.679597i
$680$	−1.95315	−	0.450407i	−0.0748999	−	0.0172723i
$681$	−26.1906	−	17.5000i	−1.00363	−	0.670602i
$682$	−1.10481	+	0.444611i	−0.0423054	+	0.0170250i
$683$	5.89543	+	7.18360i	0.225582	+	0.274873i	0.873486	−	0.486850i	$-0.161854\pi$
$683$	5.89543	+	7.18360i	0.225582	+	0.274873i	−0.647903	+	0.761722i	$0.724354\pi$
$684$	0.346469	+	4.43409i	0.0132476	+	0.169542i
$685$	−7.38133	−	13.8095i	−0.282026	−	0.527633i
$686$	19.1053	−	15.3591i	0.729444	−	0.586413i
$687$	−29.1382	+	12.0694i	−1.11169	+	0.460478i
$688$	8.69721	−	14.8008i	0.331578	−	0.564275i
$689$	−15.4017	−	6.37960i	−0.586759	−	0.243043i
$690$	−6.04500	+	1.76727i	−0.230129	+	0.0672789i
$691$	−10.6596	−	3.23356i	−0.405511	−	0.123011i	0.0809383	−	0.996719i	$-0.474208\pi$
$691$	−10.6596	−	3.23356i	−0.405511	−	0.123011i	−0.486450	+	0.873709i	$0.661708\pi$
$692$	−0.120172	+	1.01048i	−0.00456827	+	0.0384126i
$693$	−0.0878789	+	0.892249i	−0.00333824	+	0.0338937i
$694$	−15.9381	−	16.2633i	−0.605003	−	0.617346i
$695$	6.76647	−	1.34593i	0.256667	−	0.0510542i
$696$	27.2384	−	1.85182i	1.03247	−	0.0701931i
$697$	0.0875064	−	0.439925i	0.00331454	−	0.0166633i
$698$	6.10952	−	29.1720i	0.231249	−	1.10417i
$699$	6.02915	+	19.8755i	0.228044	+	0.751759i
$700$	5.45149	+	1.19930i	0.206047	+	0.0453292i
$701$	−22.8811	−	18.7780i	−0.864206	−	0.709236i	0.0939205	−	0.995580i	$-0.470060\pi$
$701$	−22.8811	−	18.7780i	−0.864206	−	0.709236i	−0.958127	+	0.286344i	$0.907560\pi$
$702$	−10.7031	−	20.5199i	−0.403964	−	0.774475i
$703$		−	1.49823i		−	0.0565069i
$704$	−0.537722	+	1.45004i	−0.0202662	+	0.0546506i
$705$		−	4.30152i		−	0.162005i
$706$	29.6715	−	15.4766i	1.11670	−	0.582469i
$707$	14.9828	+	12.2961i	0.563485	+	0.462441i
$708$	0.280380	+	0.438538i	0.0105373	+	0.0164813i
$709$	−5.66065	−	18.6607i	−0.212590	−	0.700816i	−0.996772	−	0.0802848i	$-0.974417\pi$
$709$	−5.66065	−	18.6607i	−0.212590	−	0.700816i	0.784182	−	0.620531i	$-0.213083\pi$
$710$	−3.65599	−	0.765678i	−0.137207	−	0.0287354i
$711$	1.91837	−	9.64432i	0.0719447	−	0.361690i
$712$	26.6900	+	8.98774i	1.00025	+	0.336830i
$713$	−16.4472	+	3.27155i	−0.615951	+	0.122520i
$714$	2.31101	−	2.26480i	0.0864873	−	0.0847580i
$715$	0.0575002	−	0.583809i	0.00215039	−	0.0218332i
$716$	−20.0668	−	25.4840i	−0.749931	−	0.952381i
$717$	15.4203	+	4.67769i	0.575881	+	0.174692i
$718$	6.87763	+	23.5251i	0.256671	+	0.877948i
$719$	18.5489	+	7.68320i	0.691756	+	0.286535i	0.700732	−	0.713425i	$-0.252857\pi$
$719$	18.5489	+	7.68320i	0.691756	+	0.286535i	−0.00897542	+	0.999960i	$0.502857\pi$
$720$	−4.42084	+	4.96372i	−0.164755	+	0.184987i
$721$	−5.88071	+	2.43587i	−0.219009	+	0.0907165i
$722$	15.2487	+	18.9680i	0.567499	+	0.705916i
$723$	2.91552	+	5.45455i	0.108429	+	0.202857i
$724$	27.1110	−	31.7069i	1.00757	−	1.17838i
$725$	5.29330	+	6.44991i	0.196588	+	0.239544i
$726$	−6.69573	−	16.6382i	−0.248502	−	0.617500i
$727$	−39.7225	−	26.5418i	−1.47323	−	0.984379i	−0.994311	−	0.106519i	$-0.966030\pi$
$727$	−39.7225	−	26.5418i	−1.47323	−	0.984379i	−0.478917	−	0.877860i	$-0.658970\pi$
$728$	3.95957	+	23.6252i	0.146751	+	0.875607i
$729$	11.5551	+	17.2934i	0.427966	+	0.640497i
$730$	0.860382	+	4.56592i	0.0318442	+	0.168992i
$731$	1.43371	−	2.68229i	0.0530278	−	0.0992080i
$732$	19.5822	+	8.57851i	0.723778	+	0.317071i
$733$	6.07105	−	0.597946i	0.224239	−	0.0220856i	0.0147265	−	0.999892i	$-0.495312\pi$
$733$	6.07105	−	0.597946i	0.224239	−	0.0220856i	0.209513	+	0.977806i	$0.432812\pi$
$734$	33.5659	−	2.96405i	1.23894	−	0.109405i
$735$	−0.645621	+	0.645621i	−0.0238141	+	0.0238141i
$736$	−11.2217	+	18.6629i	−0.413638	+	0.687925i
$737$	0.131873	+	0.131873i	0.00485760	+	0.00485760i
$738$	−1.14022	−	0.955188i	−0.0419722	−	0.0351610i
$739$	−2.02480	−	20.5581i	−0.0744834	−	0.756243i	−0.957794	−	0.287455i	$-0.907191\pi$
$739$	−2.02480	−	20.5581i	−0.0744834	−	0.756243i	0.883311	−	0.468788i	$-0.155309\pi$
$740$	1.61495	−	1.55100i	0.0593666	−	0.0570159i
$741$	4.14313	+	2.21455i	0.152202	+	0.0813535i
$742$	−17.9062	−	12.2279i	−0.657358	−	0.448899i
$743$	11.5907	−	7.74463i	0.425220	−	0.284123i	−0.324490	−	0.945889i	$-0.605193\pi$
$743$	11.5907	−	7.74463i	0.425220	−	0.284123i	0.749710	+	0.661766i	$0.230193\pi$
$744$	10.3792	−	9.76862i	0.380518	−	0.358135i
$745$	4.21743	−	6.31183i	0.154515	−	0.231247i
$746$	−7.31878	+	17.1764i	−0.267959	+	0.628874i
$747$	−4.12080	+	3.38186i	−0.150772	+	0.123736i
$748$	−0.0848151	+	0.260537i	−0.00310115	+	0.00952617i
$749$	14.6830	−	7.84824i	0.536506	−	0.286769i
$750$	1.62642	+	0.176789i	0.0593886	+	0.00645541i
$751$	19.1639	+	46.2658i	0.699302	+	1.68826i	0.725144	+	0.688598i	$0.241773\pi$
$751$	19.1639	+	46.2658i	0.699302	+	1.68826i	−0.0258420	+	0.999666i	$0.508227\pi$
$752$	−10.0839	−	10.9332i	−0.367721	−	0.398694i
$753$	−12.9139	+	31.1768i	−0.470608	+	1.13615i
$754$	−17.1978	+	31.4078i	−0.626307	+	1.14380i
$755$	−4.60129	+	15.1684i	−0.167458	+	0.552035i
$756$	−8.15467	−	28.9765i	−0.296583	−	1.05386i
$757$	25.7866	+	2.53976i	0.937231	+	0.0923092i	0.555086	−	0.831793i	$-0.312685\pi$
$757$	25.7866	+	2.53976i	0.937231	+	0.0923092i	0.382145	+	0.924102i	$0.375185\pi$
$758$	−0.0144508	+	1.43103i	−0.000524878	+	0.0519775i
$759$	0.167956	+	0.844372i	0.00609642	+	0.0306488i
$760$	0.484929	−	3.75391i	0.0175902	−	0.136168i
$761$	−23.8774	−	4.74951i	−0.865554	−	0.172169i	−0.257707	−	0.966223i	$-0.582967\pi$
$761$	−23.8774	−	4.74951i	−0.865554	−	0.172169i	−0.607848	+	0.794054i	$0.707967\pi$
$762$	−6.37456	−	9.75195i	−0.230926	−	0.353276i
$763$	−53.1851	+	16.1335i	−1.92543	+	0.584072i
$764$	21.9192	−	31.4121i	0.793008	−	1.13645i
$765$	−0.747076	+	0.910315i	−0.0270106	+	0.0329125i
$766$	13.1733	−	41.8987i	0.475971	−	1.51386i
$767$	−0.682693			−0.0246506
$768$	−0.321899	−	18.5065i	−0.0116155	−	0.667795i
$769$	−18.9671			−0.683971			−0.341986	−	0.939705i	$-0.611099\pi$
$769$	−18.9671			−0.683971			−0.341986	+	0.939705i	$0.611099\pi$
$770$	0.228853	−	0.727886i	0.00824730	−	0.0262312i
$771$	−4.21594	+	5.13714i	−0.151833	+	0.185009i
$772$	4.76451	−	6.82796i	0.171478	−	0.245744i
$773$	−39.4641	+	11.9713i	−1.41943	+	0.430578i	−0.904433	−	0.426616i	$-0.859705\pi$
$773$	−39.4641	+	11.9713i	−1.41943	+	0.430578i	−0.514993	+	0.857194i	$0.672205\pi$
$774$	−5.51844	−	8.44224i	−0.198356	−	0.303450i
$775$	4.27239	+	0.849831i	0.153469	+	0.0305268i
$776$	21.4064	+	2.76527i	0.768444	+	0.0992673i
$777$	0.705181	+	3.54519i	0.0252982	+	0.127183i
$778$	−0.471216	+	46.6634i	−0.0168939	+	1.67296i
$779$	0.842943	+	0.0830226i	0.0302016	+	0.00297459i
$780$	1.90199	+	6.75843i	0.0681020	+	0.241991i
$781$	−0.148219	+	0.488614i	−0.00530371	+	0.0174840i
$782$	−1.85298	+	3.38403i	−0.0662623	+	0.121013i
$783$	17.2197	−	41.5720i	0.615382	−	1.48566i
$784$	−0.127483	+	3.15449i	−0.00455298	+	0.112660i
$785$	8.42583	+	20.3417i	0.300731	+	0.726028i
$786$	3.28086	+	0.356622i	0.117024	+	0.0127203i
$787$	36.0745	−	19.2822i	1.28592	−	0.687338i	0.320304	−	0.947315i	$-0.396215\pi$
$787$	36.0745	−	19.2822i	1.28592	−	0.687338i	0.965615	+	0.259977i	$0.0837149\pi$
$788$	−4.00144	+	12.2917i	−0.142545	+	0.437874i
$789$	−3.60286	+	2.95679i	−0.128265	+	0.105265i
$790$	−3.28040	+	7.69877i	−0.116711	+	0.273910i
$791$	−6.22000	+	9.30889i	−0.221158	+	0.330986i
$792$	0.622732	+	0.661652i	0.0221278	+	0.0235108i
$793$	−23.3146	+	15.5783i	−0.827924	+	0.553201i
$794$	−3.31642	−	2.26473i	−0.117695	−	0.0803724i
$795$	−5.60475	−	2.99580i	−0.198780	−	0.106250i
$796$	8.91884	−	8.56569i	0.316120	−	0.303603i
$797$	2.08438	+	21.1630i	0.0738324	+	0.749633i	0.958819	+	0.284017i	$0.0916672\pi$
$797$	2.08438	+	21.1630i	0.0738324	+	0.749633i	−0.884987	+	0.465616i	$0.845833\pi$
$798$	4.68397	+	3.92385i	0.165811	+	0.138903i
$799$	−1.86329	−	1.86329i	−0.0659183	−	0.0659183i
$800$	4.54835	−	3.36341i	0.160808	−	0.118915i
$801$	11.6998	−	11.6998i	0.413392	−	0.413392i
$802$	−17.4858	+	1.54409i	−0.617445	+	0.0545237i
$803$	0.632068	−	0.0622533i	0.0223052	−	0.00219687i
$804$	−2.04446	−	0.895630i	−0.0721025	−	0.0315864i
$805$	5.06472	−	9.47542i	0.178508	−	0.333965i
$806$	3.46175	+	18.3710i	0.121935	+	0.647090i
$807$	18.3740	+	27.4986i	0.646794	+	0.967996i
$808$	19.3726	−	3.24684i	0.681526	−	0.114223i
$809$	3.60031	+	2.40565i	0.126580	+	0.0845781i	0.617248	−	0.786768i	$-0.288247\pi$
$809$	3.60031	+	2.40565i	0.126580	+	0.0845781i	−0.490668	+	0.871346i	$0.663247\pi$
$810$	−0.661751	−	1.64438i	−0.0232516	−	0.0577776i
$811$	−25.2998	−	30.8279i	−0.888396	−	1.08251i	−0.996091	−	0.0883298i	$-0.971847\pi$
$811$	−25.2998	−	30.8279i	−0.888396	−	1.08251i	0.107695	−	0.994184i	$-0.465653\pi$
$812$	−30.2674	+	35.3984i	−1.06218	+	1.24224i
$813$	−14.6225	−	27.3567i	−0.512832	−	0.959441i
$814$	−0.191775	−	0.238550i	−0.00672171	−	0.00836118i
$815$	−15.0049	+	6.21521i	−0.525597	+	0.217709i
$816$	−0.189380	−	3.27375i	−0.00662961	−	0.114604i
$817$	5.30617	+	2.19789i	0.185639	+	0.0768943i
$818$	−5.31130	−	18.1674i	−0.185705	−	0.635209i
$819$	13.4677	+	4.08539i	0.470601	+	0.142755i
$820$	0.783141	+	0.994556i	0.0273485	+	0.0347314i
$821$	−0.0212771	+	0.216030i	−0.000742574	+	0.00753949i	−0.995549	−	0.0942467i	$-0.969956\pi$
$821$	−0.0212771	+	0.216030i	−0.000742574	+	0.00753949i	0.994806	+	0.101786i	$0.0324558\pi$
$822$	18.2961	−	17.9303i	0.638150	−	0.625391i
$823$	16.4619	−	3.27448i	0.573826	−	0.114141i	0.100357	−	0.994951i	$-0.468002\pi$
$823$	16.4619	−	3.27448i	0.573826	−	0.114141i	0.473469	+	0.880810i	$0.343002\pi$
$824$	−2.05867	+	6.11344i	−0.0717172	+	0.212972i
$825$	0.0436290	−	0.219338i	0.00151897	−	0.00763636i
$826$	−0.869100	−	0.182017i	−0.0302399	−	0.00633317i
$827$	8.10939	+	26.7331i	0.281991	+	0.929600i	0.977474	+	0.211057i	$0.0676906\pi$
$827$	8.10939	+	26.7331i	0.281991	+	0.929600i	−0.695483	+	0.718543i	$0.744809\pi$
$828$	6.89182	+	10.7794i	0.239507	+	0.374610i
$829$	26.0537	+	21.3817i	0.904882	+	0.742617i	0.966819	−	0.255463i	$-0.0822278\pi$
$829$	26.0537	+	21.3817i	0.904882	+	0.742617i	−0.0619370	+	0.998080i	$0.519728\pi$
$830$	4.02247	−	2.09811i	0.139622	−	0.0728265i
$831$		−	25.0340i		−	0.868421i
$832$	20.6778	+	12.7193i	0.716874	+	0.440962i
$833$			0.559326i			0.0193795i
$834$	5.21980	+	10.0073i	0.180747	+	0.346526i
$835$	−8.84595	−	7.25968i	−0.306127	−	0.251232i
$836$	−0.505323	−	0.111168i	−0.0174770	−	0.00384484i
$837$	−6.81929	−	22.4802i	−0.235709	−	0.777029i
$838$	−10.2045	+	48.7246i	−0.352507	+	1.68316i
$839$	6.01897	−	30.2594i	0.207798	−	1.04467i	−0.726225	−	0.687457i	$-0.758727\pi$
$839$	6.01897	−	30.2594i	0.207798	−	1.04467i	0.934023	−	0.357213i	$-0.116273\pi$
$840$	0.619411	+	9.11090i	0.0213717	+	0.314356i
$841$	−39.8398	+	7.92463i	−1.37379	+	0.273263i
$842$	38.7918	+	39.5832i	1.33685	+	1.36413i
$843$	−1.97238	+	20.0259i	−0.0679324	+	0.689730i
$844$	5.09630	−	42.8526i	0.175422	−	1.47505i
$845$	3.62812	+	1.10058i	0.124811	+	0.0378611i
$846$	−8.38731	+	2.45205i	−0.288362	+	0.0843033i
$847$	28.2669	+	11.7085i	0.971262	+	0.402310i
$848$	−21.2686	+	5.52450i	−0.730366	+	0.189712i
$849$	−24.3388	+	10.0814i	−0.835304	+	0.345994i
$850$	0.781096	−	0.627938i	0.0267914	−	0.0215381i
$851$	−2.03168	−	3.80100i	−0.0696449	−	0.130297i
$852$	−0.476046	−	6.09240i	−0.0163091	−	0.208722i
$853$	−19.3472	−	23.5746i	−0.662436	−	0.807180i	0.328070	−	0.944653i	$-0.393602\pi$
$853$	−19.3472	−	23.5746i	−0.662436	−	0.807180i	−0.990505	+	0.137473i	$0.956102\pi$
$854$	−33.8340	+	13.6159i	−1.15777	+	0.465925i
$855$	−1.84902	−	1.23548i	−0.0632353	−	0.0422525i
$856$	3.79141	−	16.4411i	0.129588	−	0.561946i
$857$	−17.3069	−	25.9017i	−0.591194	−	0.884784i	0.408414	−	0.912797i	$-0.366082\pi$
$857$	−17.3069	−	25.9017i	−0.591194	−	0.884784i	−0.999608	+	0.0280126i	$0.991082\pi$
$858$	0.943138	−	0.177721i	0.0321982	−	0.00606729i
$859$	9.34031	−	17.4745i	0.318687	−	0.596222i	−0.670665	−	0.741760i	$-0.733991\pi$
$859$	9.34031	−	17.4745i	0.318687	−	0.596222i	0.989353	+	0.145538i	$0.0464913\pi$
$860$	3.12395	+	7.99482i	0.106526	+	0.272621i
$861$	−2.03369	+	0.200301i	−0.0693078	+	0.00682622i
$862$	4.69479	+	53.1654i	0.159905	+	1.81082i
$863$	11.2333	−	11.2333i	0.382386	−	0.382386i	−0.489575	−	0.871961i	$-0.662848\pi$
$863$	11.2333	−	11.2333i	0.382386	−	0.382386i	0.871961	+	0.489575i	$0.162848\pi$
$864$	−27.5593	−	13.0819i	−0.937586	−	0.445054i
$865$	−0.359775	−	0.359775i	−0.0122327	−	0.0122327i
$866$	−6.49503	+	7.75323i	−0.220710	+	0.263466i
$867$	1.87067	+	18.9932i	0.0635313	+	0.645044i
$868$	−0.491025	+	24.3101i	−0.0166665	+	0.825138i
$869$	1.00887	+	0.539250i	0.0342234	+	0.0182928i
$870$	−7.69811	+	11.2729i	−0.260990	+	0.382188i
$871$	2.43413	−	1.62644i	0.0824774	−	0.0551097i
$872$	−23.1209	+	51.3608i	−0.782973	+	1.73930i
$873$	7.04522	−	10.5439i	0.238445	−	0.356858i
$874$	−6.70255	−	2.85592i	−0.226717	−	0.0966029i
$875$	−2.15741	+	1.77054i	−0.0729339	+	0.0598553i
$876$	−6.77477	+	3.44713i	−0.228898	+	0.116468i
$877$	19.0836	−	10.2004i	0.644406	−	0.344442i	−0.116608	−	0.993178i	$-0.537202\pi$
$877$	19.0836	−	10.2004i	0.644406	−	0.344442i	0.761014	+	0.648736i	$0.224702\pi$
$878$	−2.18600	+	20.1108i	−0.0737739	+	0.678707i
$879$	0.183105	+	0.442054i	0.00617596	+	0.0149101i
$880$	−0.403292	−	0.659772i	−0.0135950	−	0.0222409i
$881$	8.09528	−	19.5437i	0.272737	−	0.658445i	−0.726861	−	0.686784i	$-0.759022\pi$
$881$	8.09528	−	19.5437i	0.272737	−	0.658445i	0.999598	+	0.0283388i	$0.00902172\pi$
$882$	1.62690	+	0.890831i	0.0547804	+	0.0299958i
$883$	−4.22464	+	13.9268i	−0.142171	+	0.468674i	−0.998890	−	0.0471095i	$-0.984999\pi$
$883$	−4.22464	+	13.9268i	−0.142171	+	0.468674i	0.856719	+	0.515783i	$0.172499\pi$
$884$	3.75143	+	2.10366i	0.126174	+	0.0707539i
$885$	−0.259001	−	0.0255094i	−0.00870622	−	0.000857488i
$886$	46.3868	+	0.468422i	1.55840	+	0.0157370i
$887$	−6.88117	−	34.5940i	−0.231047	−	1.16155i	−0.905865	−	0.423567i	$-0.860778\pi$
$887$	−6.88117	−	34.5940i	−0.231047	−	1.16155i	0.674818	−	0.737984i	$-0.264222\pi$
$888$	3.17688	+	1.82389i	0.106609	+	0.0612056i
$889$	19.4933	+	3.87745i	0.653783	+	0.130046i
$890$	−11.7866	+	7.70456i	−0.395088	+	0.258257i
$891$	−0.231865	+	0.0703356i	−0.00776778	+	0.00235633i
$892$	−40.9889	+	7.29598i	−1.37241	+	0.244287i
$893$	3.15677	−	3.84654i	0.105637	−	0.128719i
$894$	11.8474	+	3.72492i	0.396237	+	0.124580i
$895$	16.2181			0.542112
$896$	22.9327	+	21.7053i	0.766127	+	0.725122i
$897$	13.5141			0.451223
$898$	−4.25799	−	1.33875i	−0.142091	−	0.0446746i
$899$	−23.0581	+	28.0964i	−0.769031	+	0.937067i
$900$	−0.582422	−	3.27206i	−0.0194141	−	0.109069i
$901$	−3.72549	+	1.13011i	−0.124114	+	0.0376496i
$902$	0.144841	−	0.0946783i	0.00482268	−	0.00315244i
$903$	−13.5902	−	2.70326i	−0.452253	−	0.0899588i
$904$	2.96324	+	10.9524i	0.0985558	+	0.364270i
$905$	4.06932	+	20.4579i	0.135269	+	0.680042i
$906$	−25.9309	−	0.261855i	−0.861496	−	0.00869955i
$907$	−30.2141	−	2.97583i	−1.00324	−	0.0988109i	−0.416967	−	0.908922i	$-0.636907\pi$
$907$	−30.2141	−	2.97583i	−1.00324	−	0.0988109i	−0.586277	+	0.810111i	$0.699407\pi$
$908$	26.6359	−	47.4992i	0.883942	−	1.57632i
$909$	3.35002	−	11.0435i	0.111113	−	0.366291i
$910$	−10.5055	−	5.75246i	−0.348255	−	0.190692i
$911$	−11.4213	+	27.5735i	−0.378405	+	0.913552i	0.613860	+	0.789415i	$0.289616\pi$
$911$	−11.4213	+	27.5735i	−0.378405	+	0.913552i	−0.992265	+	0.124136i	$0.960384\pi$
$912$	6.11728	−	0.961851i	0.202563	−	0.0318501i
$913$	−0.237324	−	0.572951i	−0.00785429	−	0.0189619i
$914$	−2.22358	+	20.4565i	−0.0735494	+	0.676642i
$915$	−9.42720	+	5.03895i	−0.311654	+	0.166582i
$916$	−24.7273	−	48.5974i	−0.817013	−	1.60570i
$917$	−4.35198	+	3.57158i	−0.143715	+	0.117944i
$918$	−4.97219	−	2.11862i	−0.164107	−	0.0699249i
$919$	−16.5177	+	24.7205i	−0.544869	+	0.815454i	−0.997073	−	0.0764605i	$-0.975638\pi$
$919$	−16.5177	+	24.7205i	−0.544869	+	0.815454i	0.452203	+	0.891915i	$0.350638\pi$
$920$	−3.86022	−	10.1812i	−0.127268	−	0.335664i
$921$	−4.85083	+	3.24122i	−0.159840	+	0.106802i
$922$	−21.5596	+	31.5714i	−0.710028	+	1.03975i
$923$	7.06868	+	3.77829i	0.232668	+	0.124364i
$924$	1.24804	+	0.0252085i	0.0410576	+	0.000829298i
$925$	0.109736	+	1.11417i	0.00360810	+	0.0366336i
$926$	30.4836	−	36.3888i	1.00175	−	1.19581i
$927$	2.67988	+	2.67988i	0.0880187	+	0.0880187i
$928$	6.86024	+	46.6989i	0.225198	+	1.53297i
$929$	11.5645	−	11.5645i	0.379418	−	0.379418i	−0.491474	−	0.870892i	$-0.663542\pi$
$929$	11.5645	−	11.5645i	0.379418	−	0.379418i	0.870892	+	0.491474i	$0.163542\pi$
$930$	0.626877	+	7.09896i	0.0205561	+	0.232784i
$931$	−1.05114	+	0.103528i	−0.0344496	+	0.00339299i
$932$	−33.4455	+	13.0687i	−1.09554	+	0.428079i
$933$	−8.76940	+	16.4064i	−0.287097	+	0.537121i
$934$	13.4435	−	2.53324i	0.439885	−	0.0828900i
$935$	−0.0761116	−	0.113909i	−0.00248912	−	0.00372523i
$936$	12.0937	−	7.56118i	0.395295	−	0.247145i
$937$	33.6076	+	22.4559i	1.09791	+	0.733602i	0.966228	−	0.257690i	$-0.0829614\pi$
$937$	33.6076	+	22.4559i	1.09791	+	0.733602i	0.131685	+	0.991292i	$0.457961\pi$
$938$	3.53240	−	1.42155i	0.115337	−	0.0464153i
$939$	3.02395	+	3.68470i	0.0986830	+	0.120246i
$940$	7.41414	−	0.579322i	0.241822	−	0.0188954i
$941$	6.21071	+	11.6194i	0.202463	+	0.378782i	0.962577	−	0.271008i	$-0.0873569\pi$
$941$	6.21071	+	11.6194i	0.202463	+	0.378782i	−0.760114	+	0.649790i	$0.774857\pi$
$942$	−28.0740	+	22.5692i	−0.914702	+	0.735345i
$943$	2.25112	−	0.932443i	0.0733065	−	0.0303645i
$944$	−0.718107	+	0.542327i	−0.0233724	+	0.0176512i
$945$	13.9053	+	5.75978i	0.452341	+	0.187366i
$946$	1.12619	−	0.329244i	0.0366154	−	0.0107046i
$947$	20.3282	+	6.16649i	0.660578	+	0.200384i	0.602735	−	0.797942i	$-0.294078\pi$
$947$	20.3282	+	6.16649i	0.660578	+	0.200384i	0.0578431	+	0.998326i	$0.481578\pi$
$948$	−13.5951	−	1.61682i	−0.441549	−	0.0525119i
$949$	0.977213	−	9.92181i	0.0317217	−	0.322076i
$950$	1.32465	+	1.35168i	0.0429774	+	0.0438543i
$951$	−9.87430	+	1.96412i	−0.320196	+	0.0636910i
$952$	4.21487	+	3.67825i	0.136605	+	0.119213i
$953$	2.20993	−	11.1101i	0.0715868	−	0.359891i	−0.928343	−	0.371724i	$-0.878767\pi$
$953$	2.20993	−	11.1101i	0.0715868	−	0.359891i	0.999930	+	0.0118331i	$0.00376668\pi$
$954$	−2.64640	+	12.6361i	−0.0856804	+	0.409110i
$955$	5.55948	+	18.3271i	0.179900	+	0.593052i
$956$	−5.98573	+	27.2085i	−0.193592	+	0.879987i
$957$	1.44242	+	1.18377i	0.0466270	+	0.0382658i
$958$	0.843019	+	1.61622i	0.0272367	+	0.0522178i
$959$			43.7015i			1.41119i
$960$	7.36951	+	5.59810i	0.237850	+	0.180678i
$961$		−	12.0245i		−	0.387886i
$962$	−4.25996	+	2.22198i	−0.137347	+	0.0716396i
$963$	−7.66279	−	6.28869i	−0.246930	−	0.202650i
$964$	−9.00885	+	5.75982i	−0.290156	+	0.185511i
$965$	1.20845	+	3.98372i	0.0389013	+	0.128241i
$966$	17.2041	+	3.60308i	0.553533	+	0.115927i
$967$	−5.12699	+	25.7751i	−0.164873	+	0.828872i	0.806486	+	0.591253i	$0.201367\pi$
$967$	−5.12699	+	25.7751i	−0.164873	+	0.828872i	−0.971359	+	0.237618i	$0.923633\pi$
$968$	27.7759	−	13.7816i	0.892751	−	0.442958i
$969$	1.07601	−	0.214032i	0.0345665	−	0.00687571i
$970$	−7.70785	+	7.55373i	−0.247484	+	0.242536i
$971$	−1.16328	+	11.8110i	−0.0373314	+	0.379032i	0.958307	+	0.285739i	$0.0922392\pi$
$971$	−1.16328	+	11.8110i	−0.0373314	+	0.379032i	−0.995639	+	0.0932925i	$0.970261\pi$
$972$	−23.1435	+	18.2238i	−0.742327	+	0.584529i
$973$	−18.4256	−	5.58934i	−0.590697	−	0.179186i
$974$	−3.19558	−	10.9306i	−0.102393	−	0.350238i
$975$	−3.24326	−	1.34340i	−0.103868	−	0.0430234i
$976$	−12.1487	+	34.9074i	−0.388870	+	1.11736i
$977$	−22.4984	+	9.31916i	−0.719789	+	0.298146i	−0.712348	−	0.701826i	$-0.752368\pi$
$977$	−22.4984	+	9.31916i	−0.719789	+	0.298146i	−0.00744053	+	0.999972i	$0.502368\pi$
$978$	−16.6479	−	20.7085i	−0.532342	−	0.662185i
$979$	0.907373	+	1.69758i	0.0289998	+	0.0542548i
$980$	−1.19975	−	1.02585i	−0.0383246	−	0.0327695i
$981$	20.9932	+	25.5803i	0.670262	+	0.816717i
$982$	−8.01902	−	19.9264i	−0.255897	−	0.635877i
$983$	44.2261	+	29.5509i	1.41059	+	0.942528i	0.999522	+	0.0309248i	$0.00984524\pi$
$983$	44.2261	+	29.5509i	1.41059	+	0.942528i	0.411071	+	0.911603i	$0.365155\pi$
$984$	−1.20221	+	1.68632i	−0.0383249	+	0.0537579i
$985$	−3.59083	−	5.37405i	−0.114413	−	0.171231i
$986$	1.54850	+	8.21766i	0.0493143	+	0.261704i
$987$	−5.65922	+	10.5877i	−0.180135	+	0.337009i
$988$	−3.25903	+	7.43939i	−0.103683	+	0.236679i
$989$	16.4421	−	1.61941i	0.522829	−	0.0514942i
$990$	−0.452546	+	0.0399622i	−0.0143828	+	0.00127008i
$991$	18.8221	−	18.8221i	0.597902	−	0.597902i	−0.341852	−	0.939754i	$-0.611054\pi$
$991$	18.8221	−	18.8221i	0.597902	−	0.597902i	0.939754	+	0.341852i	$0.111054\pi$
$992$	18.2351	+	16.5740i	0.578966	+	0.526224i
$993$	25.8622	+	25.8622i	0.820714	+	0.820714i
$994$	7.99141	+	6.69456i	0.253472	+	0.212338i
$995$	0.606038	+	6.15320i	0.0192127	+	0.195070i
$996$	5.14122	+	5.35320i	0.162906	+	0.169622i
$997$	14.8518	+	7.93847i	0.470362	+	0.251414i	0.689508	−	0.724278i	$-0.257827\pi$
$997$	14.8518	+	7.93847i	0.470362	+	0.251414i	−0.219146	+	0.975692i	$0.570327\pi$
$998$	−1.89484	−	1.29396i	−0.0599801	−	0.0409595i
$999$	5.02009	−	3.35432i	0.158829	−	0.106126i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	640.2.bm.a.341.39	✓	1024
128.125	even	32	inner	640.2.bm.a.381.39	yes	1024

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
640.2.bm.a.341.39	✓	1024	1.1	even	1	trivial
640.2.bm.a.381.39	yes	1024	128.125	even	32	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:	\( N \)	\(=\)	\( 640 = 2^{7} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	640.bm (of order \(32\), degree \(16\), minimal)

\(f(q)\)	\(=\)	\(q+(0.424169 - 1.34910i) q^{2} +(-0.733885 + 0.894242i) q^{3} +(-1.64016 - 1.14450i) q^{4} +(0.956940 - 0.290285i) q^{5} +(0.895134 + 1.36940i) q^{6} +(-2.73730 - 0.544483i) q^{7} +(-2.23975 + 1.72729i) q^{8} +(0.324190 + 1.62981i) q^{9} +O(q^{10})\)	\(q+(0.424169 - 1.34910i) q^{2} +(-0.733885 + 0.894242i) q^{3} +(-1.64016 - 1.14450i) q^{4} +(0.956940 - 0.290285i) q^{5} +(0.895134 + 1.36940i) q^{6} +(-2.73730 - 0.544483i) q^{7} +(-2.23975 + 1.72729i) q^{8} +(0.324190 + 1.62981i) q^{9} +(0.0142803 - 1.41414i) q^{10} +(-0.192386 - 0.0189484i) q^{11} +(2.22715 - 0.626772i) q^{12} +(-0.880890 + 2.90390i) q^{13} +(-1.89564 + 3.46195i) q^{14} +(-0.442700 + 1.06877i) q^{15} +(1.38026 + 3.75432i) q^{16} +(0.271195 + 0.654723i) q^{17} +(2.33630 + 0.253950i) q^{18} +(-1.18022 + 0.630839i) q^{19} +(-1.90177 - 0.619100i) q^{20} +(2.49576 - 2.04822i) q^{21} +(-0.107168 + 0.251511i) q^{22} +(-2.13875 + 3.20086i) q^{23} +(0.0991055 - 3.27051i) q^{24} +(0.831470 - 0.555570i) q^{25} +(3.54402 + 2.42016i) q^{26} +(-4.75607 - 2.54217i) q^{27} +(3.86645 + 4.02587i) q^{28} +(0.817843 + 8.30370i) q^{29} +(1.25410 + 1.05059i) q^{30} +(3.08022 + 3.08022i) q^{31} +(5.65042 - 0.269648i) q^{32} +(0.158134 - 0.158134i) q^{33} +(0.998321 - 0.0881571i) q^{34} +(-2.77749 + 0.273559i) q^{35} +(1.33359 - 3.04419i) q^{36} +(-0.527757 + 0.987364i) q^{37} +(0.350456 + 1.85982i) q^{38} +(-1.95032 - 2.91886i) q^{39} +(-1.64190 + 2.30308i) q^{40} +(-0.526270 - 0.351642i) q^{41} +(-1.70464 - 4.23583i) q^{42} +(-2.72265 - 3.31756i) q^{43} +(0.293858 + 0.251263i) q^{44} +(0.783341 + 1.46553i) q^{45} +(3.41110 + 4.24310i) q^{46} +(-3.43532 + 1.42296i) q^{47} +(-4.37022 - 1.52095i) q^{48} +(0.729187 + 0.302039i) q^{49} +(-0.396838 - 1.35739i) q^{50} +(-0.784506 - 0.237977i) q^{51} +(4.76831 - 3.75470i) q^{52} +(-0.538466 + 5.46714i) q^{53} +(-5.44703 + 5.33812i) q^{54} +(-0.189602 + 0.0377143i) q^{55} +(7.07134 - 3.50860i) q^{56} +(0.302021 - 1.51836i) q^{57} +(11.5495 + 2.41882i) q^{58} +(0.0653058 + 0.215284i) q^{59} +(1.94930 - 1.24629i) q^{60} +(7.14281 + 5.86195i) q^{61} +(5.46207 - 2.84900i) q^{62} -4.63780i q^{63} +(2.03295 - 7.73738i) q^{64} +3.03457i q^{65} +(-0.146263 - 0.280414i) q^{66} +(-0.745737 - 0.612011i) q^{67} +(0.304524 - 1.38423i) q^{68} +(-1.29275 - 4.26162i) q^{69} +(-0.809065 + 3.86315i) q^{70} +(0.515284 - 2.59051i) q^{71} +(-3.54126 - 3.09040i) q^{72} +(-3.22229 + 0.640952i) q^{73} +(1.10820 + 1.13081i) q^{74} +(-0.113389 + 1.15126i) q^{75} +(2.65774 + 0.316075i) q^{76} +(0.516301 + 0.156618i) q^{77} +(-4.76511 + 1.39309i) q^{78} +(-5.46700 - 2.26450i) q^{79} +(2.41065 + 3.19199i) q^{80} +(1.15797 - 0.479646i) q^{81} +(-0.697629 + 0.560837i) q^{82} +(1.51223 + 2.82919i) q^{83} +(-6.43763 + 0.503021i) q^{84} +(0.449573 + 0.547807i) q^{85} +(-5.63060 + 2.26593i) q^{86} +(-8.02572 - 5.36262i) q^{87} +(0.463626 - 0.289867i) q^{88} +(-5.53182 - 8.27896i) q^{89} +(2.30942 - 0.435177i) q^{90} +(3.99238 - 7.46922i) q^{91} +(7.17126 - 2.80214i) q^{92} +(-5.01499 + 0.493934i) q^{93} +(0.462560 + 5.23818i) q^{94} +(-0.946274 + 0.946274i) q^{95} +(-3.90563 + 5.25074i) q^{96} +(-5.39606 - 5.39606i) q^{97} +(0.716780 - 0.855633i) q^{98} +(-0.0314874 - 0.319696i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 1024 q+O(q^{10}) \) 1024 * q	\( 1024 q - 192 q^{52} - 128 q^{54} - 32 q^{56} - 288 q^{58} - 192 q^{62} - 192 q^{64} - 192 q^{66} - 192 q^{68} - 288 q^{72} - 32 q^{74} - 128 q^{76} - 192 q^{78}+O(q^{100}) \) 1024 * q - 192 * q^52 - 128 * q^54 - 32 * q^56 - 288 * q^58 - 192 * q^62 - 192 * q^64 - 192 * q^66 - 192 * q^68 - 288 * q^72 - 32 * q^74 - 128 * q^76 - 192 * q^78

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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