LMFDB - Embedded newform 560.2.cp.a.261.61

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [560,2,Mod(221,560)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("560.221"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(560, base_ring=CyclotomicField(12)) chi = DirichletCharacter(H, H._module([0, 9, 0, 8])) N = Newforms(chi, 2, names="a")

Level:	$N$	$=$	$560 = 2^{4} \cdot 5 \cdot 7$
Weight:	$k$	$=$	$2$
Character orbit:	$[\chi]$	$=$	560.cp (of order $12$ , degree $4$ , minimal)

Newform invariants

comment:select newform

sage:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)

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

Self dual:	no
Analytic conductor:	$4.47162251319$
Analytic rank:	$0$
Dimension:	$256$
Relative dimension:	$64$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			261.61
Character	$\chi$	$=$	560.261
Dual form			560.2.cp.a.221.61

$q$ -expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.37298 + 0.338996i) q^{2} +(-2.33375 - 0.625325i) q^{3} +(1.77016 + 0.930872i) q^{4} +(-0.965926 + 0.258819i) q^{5} +(-2.99221 - 1.64969i) q^{6} +(-2.28738 - 1.32962i) q^{7} +(2.11484 + 1.87815i) q^{8} +(2.45726 + 1.41870i) q^{9} +(-1.41394 + 0.0279089i) q^{10} +(0.172513 - 0.643828i) q^{11} +(-3.54901 - 3.27935i) q^{12} +(4.46689 - 4.46689i) q^{13} +(-2.68980 - 2.60096i) q^{14} +2.41607 q^{15} +(2.26696 + 3.29559i) q^{16} +(-3.07576 - 5.32737i) q^{17} +(2.89285 + 2.78086i) q^{18} +(-1.30140 - 4.85689i) q^{19} +(-1.95077 - 0.441001i) q^{20} +(4.50672 + 4.53336i) q^{21} +(0.455113 - 0.825483i) q^{22} +(-6.06786 - 3.50328i) q^{23} +(-3.76105 - 5.70559i) q^{24} +(0.866025 - 0.500000i) q^{25} +(7.64721 - 4.61870i) q^{26} +(0.277782 + 0.277782i) q^{27} +(-2.81133 - 4.48290i) q^{28} +(-0.261977 + 0.261977i) q^{29} +(3.31723 + 0.819039i) q^{30} +(-1.21140 - 2.09821i) q^{31} +(1.99530 + 5.29328i) q^{32} +(-0.805204 + 1.39465i) q^{33} +(-2.41701 - 8.35706i) q^{34} +(2.55357 + 0.692298i) q^{35} +(3.02913 + 4.79873i) q^{36} +(2.70341 - 0.724376i) q^{37} +(-0.140332 - 7.10959i) q^{38} +(-13.2178 + 7.63132i) q^{39} +(-2.52888 - 1.26679i) q^{40} +5.15441i q^{41} +(4.65086 + 7.75198i) q^{42} +(-1.41116 - 1.41116i) q^{43} +(0.904698 - 0.979093i) q^{44} +(-2.74072 - 0.734374i) q^{45} +(-7.14347 - 6.86693i) q^{46} +(-3.07074 + 5.31867i) q^{47} +(-3.22968 - 9.10866i) q^{48} +(3.46422 + 6.08270i) q^{49} +(1.35854 - 0.392912i) q^{50} +(3.84670 + 14.3561i) q^{51} +(12.0652 - 3.74902i) q^{52} +(3.62973 - 13.5463i) q^{53} +(0.287223 + 0.475557i) q^{54} +0.666540i q^{55} +(-2.34022 - 7.10798i) q^{56} +12.1485i q^{57} +(-0.448499 + 0.270881i) q^{58} +(0.508158 - 1.89647i) q^{59} +(4.27684 + 2.24905i) q^{60} +(2.65920 + 9.92428i) q^{61} +(-0.951949 - 3.29147i) q^{62} +(-3.73436 - 6.51234i) q^{63} +(0.945109 + 7.94398i) q^{64} +(-3.15856 + 5.47079i) q^{65} +(-1.57831 + 1.64188i) q^{66} +(7.35689 + 1.97127i) q^{67} +(-0.485496 - 12.2935i) q^{68} +(11.9702 + 11.9702i) q^{69} +(3.27132 + 1.81616i) q^{70} +2.55447i q^{71} +(2.53219 + 7.61544i) q^{72} +(-7.60559 + 4.39109i) q^{73} +(3.95729 - 0.0781107i) q^{74} +(-2.33375 + 0.625325i) q^{75} +(2.21745 - 9.80891i) q^{76} +(-1.25065 + 1.24330i) q^{77} +(-20.7348 + 5.99688i) q^{78} +(5.92395 - 10.2606i) q^{79} +(-3.04267 - 2.59656i) q^{80} +(-4.73067 - 8.19377i) q^{81} +(-1.74733 + 7.07692i) q^{82} +(4.30934 - 4.30934i) q^{83} +(3.75766 + 12.2200i) q^{84} +(4.34978 + 4.34978i) q^{85} +(-1.45912 - 2.41588i) q^{86} +(0.775209 - 0.447567i) q^{87} +(1.57404 - 1.03759i) q^{88} +(-4.78914 - 2.76501i) q^{89} +(-3.51401 - 1.93738i) q^{90} +(-16.1567 + 4.27820i) q^{91} +(-7.48000 - 11.8498i) q^{92} +(1.51504 + 5.65421i) q^{93} +(-6.01908 + 6.26147i) q^{94} +(2.51411 + 4.35456i) q^{95} +(-1.34650 - 13.6009i) q^{96} -1.44559 q^{97} +(2.69430 + 9.52579i) q^{98} +(1.33731 - 1.33731i) q^{99} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$256 q + 4 q^{4} + 8 q^{11} + 16 q^{14} - 20 q^{16} - 40 q^{18} - 16 q^{20} + 56 q^{22} - 40 q^{24} + 4 q^{28} - 32 q^{29} - 20 q^{32} + 16 q^{37} - 40 q^{38} - 60 q^{42} + 16 q^{43} + 32 q^{44} - 20 q^{46}+ \cdots - 80 q^{99}+O(q^{100})$ 256 * q + 4 * q^4 + 8 * q^11 + 16 * q^14 - 20 * q^16 - 40 * q^18 - 16 * q^20 + 56 * q^22 - 40 * q^24 + 4 * q^28 - 32 * q^29 - 20 * q^32 + 16 * q^37 - 40 * q^38 - 60 * q^42 + 16 * q^43 + 32 * q^44 - 20 * q^46 + 80 * q^47 - 160 * q^48 - 8 * q^50 - 40 * q^51 + 24 * q^52 - 16 * q^53 - 116 * q^54 - 96 * q^56 - 8 * q^58 + 16 * q^59 - 28 * q^60 + 88 * q^62 - 56 * q^64 - 16 * q^66 - 40 * q^67 - 20 * q^68 - 16 * q^70 + 76 * q^72 + 52 * q^74 - 48 * q^78 + 128 * q^81 - 80 * q^83 - 68 * q^84 + 52 * q^86 + 20 * q^88 - 72 * q^90 - 32 * q^91 - 112 * q^92 + 120 * q^94 + 140 * q^96 + 24 * q^98 - 80 * q^99

Character values

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

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

Coefficient data

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

Display

a_p

with

p

up to: 50 250 1000 (See

a_n

instead) (See

a_n

instead) (See

a_n

instead) Display

a_n

with

n

up to: 50 250 1000 (See only

a_p

) (See only

a_p

) (See only

a_p

)

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

$2$	1.37298	+	0.338996i	0.970845	+	0.239707i
$2$	1.37298	+	0.338996i	0.970845	+	0.239707i
$3$	−2.33375	−	0.625325i	−1.34739	−	0.361032i	−0.488219	−	0.872721i	$-0.662353\pi$
$3$	−2.33375	−	0.625325i	−1.34739	−	0.361032i	−0.859170	+	0.511690i	$0.829020\pi$
$4$	1.77016	+	0.930872i	0.885082	+	0.465436i
$5$	−0.965926	+	0.258819i	−0.431975	+	0.115747i
$5$	−0.965926	+	0.258819i	−0.431975	+	0.115747i
$6$	−2.99221	−	1.64969i	−1.22156	−	0.673484i
$7$	−2.28738	−	1.32962i	−0.864548	−	0.502550i
$7$	−2.28738	−	1.32962i	−0.864548	−	0.502550i
$8$	2.11484	+	1.87815i	0.747709	+	0.664026i
$9$	2.45726	+	1.41870i	0.819088	+	0.472901i
$10$	−1.41394	+	0.0279089i	−0.447127	+	0.00882557i
$11$	0.172513	−	0.643828i	0.0520147	−	0.194121i	−0.935030	−	0.354570i	$-0.884627\pi$
$11$	0.172513	−	0.643828i	0.0520147	−	0.194121i	0.987044	+	0.160448i	$0.0512940\pi$
$12$	−3.54901	−	3.27935i	−1.02451	−	0.946666i
$13$	4.46689	−	4.46689i	1.23889	−	1.23889i	0.278436	−	0.960455i	$-0.410184\pi$
$13$	4.46689	−	4.46689i	1.23889	−	1.23889i	0.960455	−	0.278436i	$-0.0898162\pi$
$14$	−2.68980	−	2.60096i	−0.718878	−	0.695136i
$15$	2.41607			0.623827
$16$	2.26696	+	3.29559i	0.566739	+	0.823898i
$17$	−3.07576	−	5.32737i	−0.745981	−	1.29208i	−0.949735	−	0.313055i	$-0.898648\pi$
$17$	−3.07576	−	5.32737i	−0.745981	−	1.29208i	0.203754	−	0.979022i	$-0.434686\pi$
$18$	2.89285	+	2.78086i	0.681850	+	0.655454i
$19$	−1.30140	−	4.85689i	−0.298561	−	1.11425i	−0.938348	−	0.345693i	$-0.887644\pi$
$19$	−1.30140	−	4.85689i	−0.298561	−	1.11425i	0.639786	−	0.768553i	$-0.279023\pi$
$20$	−1.95077	−	0.441001i	−0.436206	−	0.0986109i
$21$	4.50672	+	4.53336i	0.983447	+	0.989259i
$22$	0.455113	−	0.825483i	0.0970304	−	0.175994i
$23$	−6.06786	−	3.50328i	−1.26524	−	0.730485i	−0.291154	−	0.956676i	$-0.594039\pi$
$23$	−6.06786	−	3.50328i	−1.26524	−	0.730485i	−0.974083	+	0.226192i	$0.927372\pi$
$24$	−3.76105	−	5.70559i	−0.767721	−	1.16465i
$25$	0.866025	−	0.500000i	0.173205	−	0.100000i
$26$	7.64721	−	4.61870i	1.49974	−	0.905801i
$27$	0.277782	+	0.277782i	0.0534592	+	0.0534592i
$28$	−2.81133	−	4.48290i	−0.531291	−	0.847189i
$29$	−0.261977	+	0.261977i	−0.0486479	+	0.0486479i	−0.731012	−	0.682364i	$-0.760952\pi$
$29$	−0.261977	+	0.261977i	−0.0486479	+	0.0486479i	0.682364	+	0.731012i	$0.260952\pi$
$30$	3.31723	+	0.819039i	0.605640	+	0.149535i
$31$	−1.21140	−	2.09821i	−0.217574	−	0.376850i	0.736492	−	0.676447i	$-0.236481\pi$
$31$	−1.21140	−	2.09821i	−0.217574	−	0.376850i	−0.954066	+	0.299597i	$0.903148\pi$
$32$	1.99530	+	5.29328i	0.352722	+	0.935728i
$33$	−0.805204	+	1.39465i	−0.140168	+	0.242778i
$34$	−2.41701	−	8.35706i	−0.414513	−	1.43322i
$35$	2.55357	+	0.692298i	0.431632	+	0.117020i
$36$	3.02913	+	4.79873i	0.504855	+	0.799789i
$37$	2.70341	−	0.724376i	0.444438	−	0.119087i	−0.0296579	−	0.999560i	$-0.509442\pi$
$37$	2.70341	−	0.724376i	0.444438	−	0.119087i	0.474096	+	0.880473i	$0.342775\pi$
$38$	−0.140332	−	7.10959i	−0.0227649	−	1.15333i
$39$	−13.2178	+	7.63132i	−2.11655	+	1.22199i
$40$	−2.52888	−	1.26679i	−0.399851	−	0.200297i
$41$			5.15441i			0.804984i	0.915424	+	0.402492i	$0.131856\pi$
$41$			5.15441i			0.804984i	−0.915424	+	0.402492i	$0.868144\pi$
$42$	4.65086	+	7.75198i	0.717643	+	1.19616i
$43$	−1.41116	−	1.41116i	−0.215200	−	0.215200i	0.591272	−	0.806472i	$-0.298626\pi$
$43$	−1.41116	−	1.41116i	−0.215200	−	0.215200i	−0.806472	+	0.591272i	$0.798626\pi$
$44$	0.904698	−	0.979093i	0.136388	−	0.147604i
$45$	−2.74072	−	0.734374i	−0.408563	−	0.109474i
$46$	−7.14347	−	6.86693i	−1.05325	−	1.01247i
$47$	−3.07074	+	5.31867i	−0.447913	+	0.775808i	−0.998250	−	0.0591348i	$-0.981166\pi$
$47$	−3.07074	+	5.31867i	−0.447913	+	0.775808i	0.550337	+	0.834942i	$0.314499\pi$
$48$	−3.22968	−	9.10866i	−0.466164	−	1.31472i
$49$	3.46422	+	6.08270i	0.494888	+	0.868957i
$50$	1.35854	−	0.392912i	0.192126	−	0.0555662i
$51$	3.84670	+	14.3561i	0.538646	+	2.01025i
$52$	12.0652	−	3.74902i	1.67314	−	0.519895i
$53$	3.62973	−	13.5463i	0.498581	−	1.86073i	−0.0103879	−	0.999946i	$-0.503307\pi$
$53$	3.62973	−	13.5463i	0.498581	−	1.86073i	0.508969	−	0.860785i	$-0.330027\pi$
$54$	0.287223	+	0.475557i	0.0390861	+	0.0647151i
$55$			0.666540i			0.0898762i
$56$	−2.34022	−	7.10798i	−0.312725	−	0.949844i
$57$			12.1485i			1.60911i
$58$	−0.448499	+	0.270881i	−0.0588908	+	0.0355684i
$59$	0.508158	−	1.89647i	0.0661565	−	0.246899i	−0.924926	−	0.380146i	$-0.875874\pi$
$59$	0.508158	−	1.89647i	0.0661565	−	0.246899i	0.991083	+	0.133247i	$0.0425403\pi$
$60$	4.27684	+	2.24905i	0.552138	+	0.290352i
$61$	2.65920	+	9.92428i	0.340476	+	1.27067i	0.897809	+	0.440385i	$0.145158\pi$
$61$	2.65920	+	9.92428i	0.340476	+	1.27067i	−0.557333	+	0.830289i	$0.688175\pi$
$62$	−0.951949	−	3.29147i	−0.120898	−	0.418017i
$63$	−3.73436	−	6.51234i	−0.470485	−	0.820478i
$64$	0.945109	+	7.94398i	0.118139	+	0.992997i
$65$	−3.15856	+	5.47079i	−0.391772	+	0.678569i
$66$	−1.57831	+	1.64188i	−0.194277	+	0.202101i
$67$	7.35689	+	1.97127i	0.898787	+	0.240829i	0.678495	−	0.734605i	$-0.262632\pi$
$67$	7.35689	+	1.97127i	0.898787	+	0.240829i	0.220292	+	0.975434i	$0.429299\pi$
$68$	−0.485496	−	12.2935i	−0.0588750	−	1.49080i
$69$	11.9702	+	11.9702i	1.44104	+	1.44104i
$70$	3.27132	+	1.81616i	0.390998	+	0.217073i
$71$			2.55447i			0.303160i	0.988445	+	0.151580i	$0.0484360\pi$
$71$			2.55447i			0.303160i	−0.988445	+	0.151580i	$0.951564\pi$
$72$	2.53219	+	7.61544i	0.298421	+	0.897488i
$73$	−7.60559	+	4.39109i	−0.890167	+	0.513938i	−0.873997	−	0.485931i	$-0.838481\pi$
$73$	−7.60559	+	4.39109i	−0.890167	+	0.513938i	−0.0161698	+	0.999869i	$0.505147\pi$
$74$	3.95729	−	0.0781107i	0.460026	−	0.00908019i
$75$	−2.33375	+	0.625325i	−0.269478	+	0.0722064i
$76$	2.21745	−	9.80891i	0.254359	−	1.12516i
$77$	−1.25065	+	1.24330i	−0.142525	+	0.141687i
$78$	−20.7348	+	5.99688i	−2.34776	+	0.679012i
$79$	5.92395	−	10.2606i	0.666497	−	1.15441i	−0.312380	−	0.949957i	$-0.601126\pi$
$79$	5.92395	−	10.2606i	0.666497	−	1.15441i	0.978877	−	0.204449i	$-0.0655404\pi$
$80$	−3.04267	−	2.59656i	−0.340181	−	0.290305i
$81$	−4.73067	−	8.19377i	−0.525631	−	0.910419i
$82$	−1.74733	+	7.07692i	−0.192960	+	0.781515i
$83$	4.30934	−	4.30934i	0.473012	−	0.473012i	−0.429876	−	0.902888i	$-0.641443\pi$
$83$	4.30934	−	4.30934i	0.473012	−	0.473012i	0.902888	+	0.429876i	$0.141443\pi$
$84$	3.75766	+	12.2200i	0.409994	+	1.33331i
$85$	4.34978	+	4.34978i	0.471800	+	0.471800i
$86$	−1.45912	−	2.41588i	−0.157341	−	0.260511i
$87$	0.775209	−	0.447567i	0.0831111	−	0.0479842i
$88$	1.57404	−	1.03759i	0.167794	−	0.110607i
$89$	−4.78914	−	2.76501i	−0.507648	−	0.293090i	0.224219	−	0.974539i	$-0.428017\pi$
$89$	−4.78914	−	2.76501i	−0.507648	−	0.293090i	−0.731866	+	0.681448i	$0.761350\pi$
$90$	−3.51401	−	1.93738i	−0.370410	−	0.204218i
$91$	−16.1567	+	4.27820i	−1.69369	+	0.448477i
$92$	−7.48000	−	11.8498i	−0.779844	−	1.23543i
$93$	1.51504	+	5.65421i	0.157102	+	0.586314i
$94$	−6.01908	+	6.26147i	−0.620820	+	0.645822i
$95$	2.51411	+	4.35456i	0.257942	+	0.446769i
$96$	−1.34650	−	13.6009i	−0.137426	−	1.38813i
$97$	−1.44559			−0.146777			−0.0733886	−	0.997303i	$-0.523381\pi$
$97$	−1.44559			−0.146777			−0.0733886	+	0.997303i	$0.523381\pi$
$98$	2.69430	+	9.52579i	0.272165	+	0.962251i
$99$	1.33731	−	1.33731i	0.134405	−	0.134405i
$100$	1.99844	−	0.0789229i	0.199844	−	0.00789229i
$101$	−2.40228	+	8.96544i	−0.239036	+	0.892094i	0.737252	+	0.675618i	$0.236123\pi$
$101$	−2.40228	+	8.96544i	−0.239036	+	0.892094i	−0.976288	+	0.216476i	$0.930544\pi$
$102$	0.414796	+	21.0147i	0.0410710	+	2.08076i
$103$	−8.79848	−	5.07980i	−0.866940	−	0.500528i	−0.000609787	−	1.00000i	$-0.500194\pi$
$103$	−8.79848	−	5.07980i	−0.866940	−	0.500528i	−0.866330	+	0.499472i	$0.833527\pi$
$104$	17.8362	−	1.05728i	1.74899	−	0.103674i
$105$	−5.52648	−	3.21246i	−0.539329	−	0.313504i
$106$	9.57570	−	17.3684i	0.930075	−	1.68697i
$107$	−2.79732	+	0.749539i	−0.270427	+	0.0724606i	−0.391484	−	0.920185i	$-0.628038\pi$
$107$	−2.79732	+	0.749539i	−0.270427	+	0.0724606i	0.121057	+	0.992646i	$0.461372\pi$
$108$	0.233140	+	0.750299i	0.0224339	+	0.0721975i
$109$	−1.79453	−	0.480842i	−0.171885	−	0.0460563i	0.171850	−	0.985123i	$-0.445025\pi$
$109$	−1.79453	−	0.480842i	−0.171885	−	0.0460563i	−0.343735	+	0.939067i	$0.611692\pi$
$110$	−0.225954	+	0.915148i	−0.0215439	+	0.0872559i
$111$	−6.76204			−0.641825
$112$	−0.803503	−	10.5525i	−0.0759239	−	0.997114i
$113$	1.45609			0.136977			0.0684887	−	0.997652i	$-0.478182\pi$
$113$	1.45609			0.136977			0.0684887	+	0.997652i	$0.478182\pi$
$114$	−4.11831	+	16.6797i	−0.385715	+	1.56220i
$115$	6.76782	+	1.81343i	0.631102	+	0.169103i
$116$	−0.707609	+	0.219875i	−0.0656999	+	0.0204149i
$117$	17.3135	−	4.63914i	1.60063	−	0.428888i
$118$	1.34059	−	2.43156i	0.123411	−	0.223843i
$119$	−0.0479541	+	16.2753i	−0.00439594	+	1.49196i
$120$	5.10961	+	4.53774i	0.466441	+	0.414238i
$121$	9.14153	+	5.27786i	0.831048	+	0.479806i
$122$	0.286746	+	14.5273i	0.0259608	+	1.31524i
$123$	3.22319	−	12.0291i	0.290625	−	1.08463i
$124$	−0.191215	−	4.84183i	−0.0171716	−	0.434809i
$125$	−0.707107	+	0.707107i	−0.0632456	+	0.0632456i
$126$	−2.91955	−	10.2073i	−0.260095	−	0.909336i
$127$	5.10143			0.452679			0.226339	−	0.974048i	$-0.427324\pi$
$127$	5.10143			0.452679			0.226339	+	0.974048i	$0.427324\pi$
$128$	−1.39536	+	11.2273i	−0.123334	+	0.992365i
$129$	2.41086	+	4.17573i	0.212264	+	0.367652i
$130$	−6.19123	+	6.44057i	−0.543007	+	0.564875i
$131$	5.44350	+	20.3154i	0.475601	+	1.77497i	0.619096	+	0.785316i	$0.287499\pi$
$131$	5.44350	+	20.3154i	0.475601	+	1.77497i	−0.143495	+	0.989651i	$0.545834\pi$
$132$	−2.72359	+	1.71922i	−0.237058	+	0.149639i
$133$	−3.48102	+	12.8399i	−0.301843	+	1.11336i
$134$	9.43263	+	5.20048i	0.814855	+	0.449253i
$135$	−0.340212	−	0.196422i	−0.0292808	−	0.0169053i
$136$	3.50086	−	17.0433i	0.300196	−	1.46145i
$137$	−11.2387	+	6.48865i	−0.960185	+	0.554363i	−0.896230	−	0.443590i	$-0.853705\pi$
$137$	−11.2387	+	6.48865i	−0.960185	+	0.554363i	−0.0639549	+	0.997953i	$0.520371\pi$
$138$	12.3770	+	20.4927i	1.05360	+	1.74445i
$139$	−9.77660	−	9.77660i	−0.829240	−	0.829240i	0.158171	−	0.987412i	$-0.449440\pi$
$139$	−9.77660	−	9.77660i	−0.829240	−	0.829240i	−0.987412	+	0.158171i	$0.949440\pi$
$140$	3.87580	+	3.60253i	0.327565	+	0.304469i
$141$	10.4922	−	10.4922i	0.883604	−	0.883604i
$142$	−0.865955	+	3.50724i	−0.0726693	+	0.294321i
$143$	−2.10531	−	3.64650i	−0.176055	−	0.304936i
$144$	0.895047	+	11.3143i	0.0745873	+	0.942856i
$145$	0.185246	−	0.320855i	0.0153838	−	0.0266456i
$146$	−11.9309	+	3.45062i	−0.987409	+	0.285576i
$147$	−4.28094	−	16.3617i	−0.353086	−	1.34949i
$148$	5.45978	+	1.23426i	0.448791	+	0.101456i
$149$	10.6199	−	2.84559i	0.870016	−	0.233120i	0.203921	−	0.978987i	$-0.434631\pi$
$149$	10.6199	−	2.84559i	0.870016	−	0.233120i	0.666095	+	0.745867i	$0.267965\pi$
$150$	−3.41618	+	0.0674299i	−0.278930	+	0.00550563i
$151$	5.75498	−	3.32264i	0.468334	−	0.270392i	−0.247208	−	0.968962i	$-0.579513\pi$
$151$	5.75498	−	3.32264i	0.468334	−	0.270392i	0.715542	+	0.698570i	$0.246180\pi$
$152$	6.36970	−	12.7158i	0.516651	−	1.03138i
$153$		−	17.4543i		−	1.41110i
$154$	−2.13860	+	1.28307i	−0.172333	+	0.103392i
$155$	1.71318	+	1.71318i	0.137606	+	0.137606i
$156$	−30.5015	+	1.20457i	−2.44207	+	0.0964430i
$157$	13.1870	+	3.53346i	1.05244	+	0.282000i	0.743260	−	0.669003i	$-0.233279\pi$
$157$	13.1870	+	3.53346i	1.05244	+	0.282000i	0.309180	+	0.951003i	$0.399945\pi$
$158$	11.6118	−	12.0794i	0.923784	−	0.960987i
$159$	−16.9417	+	29.3439i	−1.34357	+	2.32712i
$160$	−3.29731	−	4.59649i	−0.260675	−	0.363385i
$161$	9.22147	+	16.0813i	0.726754	+	1.26738i
$162$	−3.71748	−	12.8536i	−0.292073	−	1.00987i
$163$	2.70099	+	10.0802i	0.211558	+	0.789545i	0.987350	+	0.158556i	$0.0506839\pi$
$163$	2.70099	+	10.0802i	0.211558	+	0.789545i	−0.775792	+	0.630989i	$0.782649\pi$
$164$	−4.79810	+	9.12415i	−0.374668	+	0.712476i
$165$	0.416804	−	1.55553i	0.0324482	−	0.121098i
$166$	7.37750	−	4.45580i	0.572605	−	0.345837i
$167$			3.02745i			0.234271i	0.993116	+	0.117136i	$0.0373712\pi$
$167$			3.02745i			0.234271i	−0.993116	+	0.117136i	$0.962629\pi$
$168$	1.01668	+	18.0516i	0.0784384	+	1.39271i
$169$		−	26.9061i		−	2.06970i
$170$	4.49761	+	7.44673i	0.344951	+	0.571138i
$171$	3.69259	−	13.7809i	0.282380	−	1.05386i
$172$	−1.18438	−	3.81160i	−0.0903078	−	0.290632i
$173$	−5.41608	−	20.2131i	−0.411777	−	1.53677i	−0.791204	−	0.611552i	$-0.790546\pi$
$173$	−5.41608	−	20.2131i	−0.411777	−	1.53677i	0.379427	−	0.925222i	$-0.376121\pi$
$174$	1.21607	−	0.351709i	0.0921902	−	0.0266630i
$175$	−2.64574	−	0.00779548i	−0.199999	−	0.000589283i
$176$	2.51287	−	0.890996i	0.189415	−	0.0671614i
$177$	−2.37182	+	4.10812i	−0.178277	+	0.308785i
$178$	−5.63808	−	5.41981i	−0.422592	−	0.406232i
$179$	−13.7121	−	3.67415i	−1.02489	−	0.274619i	−0.293052	−	0.956096i	$-0.594671\pi$
$179$	−13.7121	−	3.67415i	−1.02489	−	0.274619i	−0.731839	+	0.681477i	$0.761338\pi$
$180$	−4.16792	−	3.85122i	−0.310658	−	0.287053i
$181$	−16.6444	−	16.6444i	−1.23717	−	1.23717i	−0.961153	−	0.276016i	$-0.910986\pi$
$181$	−16.6444	−	16.6444i	−1.23717	−	1.23717i	−0.276016	−	0.961153i	$-0.589014\pi$
$182$	−23.6332	+	0.396826i	−1.75181	+	0.0294147i
$183$		−	24.8236i		−	1.83501i
$184$	−6.25288	−	18.8052i	−0.460968	−	1.38634i
$185$	−2.42381	+	1.39939i	−0.178202	+	0.102885i
$186$	0.163369	+	8.27672i	0.0119788	+	0.606879i
$187$	−3.96052	+	1.06122i	−0.289622	+	0.0776039i
$188$	−10.3867	+	6.55645i	−0.757528	+	0.478178i
$189$	−0.266048	−	1.00474i	−0.0193522	−	0.0730839i
$190$	1.97565	+	6.83101i	0.143329	+	0.495574i
$191$	5.43366	−	9.41138i	0.393166	−	0.680984i	−0.599699	−	0.800226i	$-0.704713\pi$
$191$	5.43366	−	9.41138i	0.393166	−	0.680984i	0.992865	+	0.119242i	$0.0380464\pi$
$192$	2.76193	−	19.1302i	0.199325	−	1.38061i
$193$	0.392225	+	0.679354i	0.0282330	+	0.0489010i	0.879797	−	0.475350i	$-0.157679\pi$
$193$	0.392225	+	0.679354i	0.0282330	+	0.0489010i	−0.851564	+	0.524251i	$0.824345\pi$
$194$	−1.98477	−	0.490049i	−0.142498	−	0.0351835i
$195$	10.7923	−	10.7923i	0.772854	−	0.772854i
$196$	0.470016	+	13.9921i	0.0335726	+	0.999436i
$197$	−13.1751	−	13.1751i	−0.938690	−	0.938690i	0.0595365	−	0.998226i	$-0.481038\pi$
$197$	−13.1751	−	13.1751i	−0.938690	−	0.938690i	−0.998226	+	0.0595365i	$0.981038\pi$
$198$	2.28945	−	1.38276i	0.162704	−	0.0982685i
$199$	11.6395	−	6.72008i	0.825103	−	0.476374i	−0.0270699	−	0.999634i	$-0.508618\pi$
$199$	11.6395	−	6.72008i	0.825103	−	0.476374i	0.852173	+	0.523260i	$0.175284\pi$
$200$	2.77058	+	0.569104i	0.195910	+	0.0402418i
$201$	−15.9364	−	9.20090i	−1.12407	−	0.648982i
$202$	−6.33754	+	11.4950i	−0.445908	+	0.808787i
$203$	0.947572	−	0.250911i	0.0665065	−	0.0176105i
$204$	−6.55438	+	28.9934i	−0.458899	+	2.02994i
$205$	−1.33406	−	4.97878i	−0.0931748	−	0.347733i
$206$	−10.3581	−	9.95713i	−0.721685	−	0.693746i
$207$	−9.94023	−	17.2170i	−0.690893	−	1.19666i
$208$	24.8473	+	4.59479i	1.72285	+	0.318592i
$209$	−3.35151			−0.231829
$210$	−6.49874	−	6.28411i	−0.448456	−	0.433645i
$211$	7.15409	−	7.15409i	0.492508	−	0.492508i	−0.416587	−	0.909096i	$-0.636774\pi$
$211$	7.15409	−	7.15409i	0.492508	−	0.492508i	0.909096	+	0.416587i	$0.136774\pi$
$212$	19.0351	−	20.6004i	1.30734	−	1.41484i
$213$	1.59737	−	5.96148i	0.109450	−	0.408474i
$214$	−4.09476	+	0.0808241i	−0.279912	+	0.00552502i
$215$	1.72831	+	0.997842i	0.117870	+	0.0680522i
$216$	0.0657488	+	1.10918i	0.00447364	+	0.0754702i
$217$	−0.0188869	+	6.41011i	−0.00128213	+	0.435146i
$218$	−2.30085	−	1.26853i	−0.155833	−	0.0859154i
$219$	20.4954	−	5.49172i	1.38495	−	0.371096i
$220$	−0.620463	+	1.17988i	−0.0418316	+	0.0795478i
$221$	−37.5358	−	10.0577i	−2.52493	−	0.676553i
$222$	−9.28417	−	2.29231i	−0.623112	−	0.153850i
$223$	24.2146			1.62153			0.810765	−	0.585371i	$-0.199051\pi$
$223$	24.2146			1.62153			0.810765	+	0.585371i	$0.199051\pi$
$224$	2.47405	−	14.7607i	0.165304	−	0.986243i
$225$	2.83740			0.189160
$226$	1.99919	+	0.493609i	0.132984	+	0.0328344i
$227$	25.6587	+	6.87523i	1.70303	+	0.456325i	0.973699	−	0.227837i	$-0.0731655\pi$
$227$	25.6587	+	6.87523i	1.70303	+	0.456325i	0.729330	+	0.684163i	$0.239832\pi$
$228$	−11.3087	+	21.5049i	−0.748939	+	1.42420i
$229$	25.3595	−	6.79506i	1.67580	−	0.449030i	0.709137	−	0.705070i	$-0.249085\pi$
$229$	25.3595	−	6.79506i	1.67580	−	0.449030i	0.966666	+	0.256040i	$0.0824179\pi$
$230$	8.67735	+	4.78408i	0.572168	+	0.315453i
$231$	3.69617	−	2.11949i	0.243190	−	0.139452i
$232$	−1.04607	+	0.0620079i	−0.0686780	+	0.00407102i
$233$	20.6871	+	11.9437i	1.35526	+	0.782460i	0.988981	−	0.148046i	$-0.0472982\pi$
$233$	20.6871	+	11.9437i	1.35526	+	0.782460i	0.366279	+	0.930505i	$0.380632\pi$
$234$	25.3438	−	0.500246i	1.65677	−	0.0327021i
$235$	1.58953	−	5.93220i	0.103689	−	0.386974i
$236$	2.66489	−	2.88403i	0.173470	−	0.187735i
$237$	−20.2412	+	20.2412i	−1.31481	+	1.31481i
$238$	−5.58311	+	22.3295i	−0.361899	+	1.44740i
$239$	−7.76764			−0.502447			−0.251224	−	0.967929i	$-0.580833\pi$
$239$	−7.76764			−0.502447			−0.251224	+	0.967929i	$0.580833\pi$
$240$	5.47713	+	7.96238i	0.353547	+	0.513970i
$241$	−5.04575	−	8.73950i	−0.325026	−	0.562961i	0.656492	−	0.754333i	$-0.272040\pi$
$241$	−5.04575	−	8.73950i	−0.325026	−	0.562961i	−0.981518	+	0.191372i	$0.938706\pi$
$242$	10.7620	+	10.3454i	0.691806	+	0.665025i
$243$	5.61140	+	20.9420i	0.359971	+	1.34343i
$244$	−4.53101	+	20.0430i	−0.290068	+	1.28312i
$245$	−4.92049	−	4.97883i	−0.314359	−	0.318086i
$246$	8.50319	−	15.4231i	0.542144	−	0.983340i
$247$	−27.5083	−	15.8820i	−1.75031	−	1.01054i
$248$	1.37883	−	6.71257i	0.0875557	−	0.426249i
$249$	−12.7516	+	7.36217i	−0.808103	+	0.466558i
$250$	−1.21055	+	0.731139i	−0.0765620	+	0.0462413i
$251$	14.0786	+	14.0786i	0.888635	+	0.888635i	0.994392	−	0.105757i	$-0.0337265\pi$
$251$	14.0786	+	14.0786i	0.888635	+	0.888635i	−0.105757	+	0.994392i	$0.533727\pi$
$252$	−0.548274	−	15.0041i	−0.0345380	−	0.945171i
$253$	−3.30230	+	3.30230i	−0.207614	+	0.207614i
$254$	7.00418	+	1.72937i	0.439481	+	0.108510i
$255$	−7.43125	−	12.8713i	−0.465363	−	0.806033i
$256$	−5.72183	+	14.9419i	−0.357614	+	0.933869i
$257$	−4.20422	+	7.28192i	−0.262252	+	0.454234i	−0.966840	−	0.255383i	$-0.917798\pi$
$257$	−4.20422	+	7.28192i	−0.262252	+	0.454234i	0.704588	+	0.709617i	$0.251132\pi$
$258$	1.89451	+	6.55047i	0.117947	+	0.407815i
$259$	−7.14687	−	1.93759i	−0.444085	−	0.120396i
$260$	−10.6838	+	6.74398i	−0.662580	+	0.418244i
$261$	−1.01541	+	0.272079i	−0.0628526	+	0.0168413i
$262$	0.586982	+	29.7380i	0.0362639	+	1.83722i
$263$	−14.7377	+	8.50881i	−0.908765	+	0.524676i	−0.880033	−	0.474912i	$-0.842480\pi$
$263$	−14.7377	+	8.50881i	−0.908765	+	0.524676i	−0.0287312	+	0.999587i	$0.509147\pi$
$264$	−4.32225	+	1.43718i	−0.266016	+	0.0884523i
$265$			14.0242i			0.861499i
$266$	−9.13207	+	16.4489i	−0.559923	+	1.00855i
$267$	9.44760	+	9.44760i	0.578184	+	0.578184i
$268$	11.1879	+	10.3378i	0.683409	+	0.631482i
$269$	24.9658	+	6.68958i	1.52219	+	0.407871i	0.920464	−	0.390828i	$-0.127811\pi$
$269$	24.9658	+	6.68958i	1.52219	+	0.407871i	0.601731	+	0.798699i	$0.294478\pi$
$270$	−0.400519	−	0.385014i	−0.0243748	−	0.0234312i
$271$	0.00346800	−	0.00600675i	0.000210666	−	0.000364884i	−0.865920	−	0.500182i	$-0.833266\pi$
$271$	0.00346800	−	0.00600675i	0.000210666	−	0.000364884i	0.866131	+	0.499818i	$0.166600\pi$
$272$	10.5842	−	22.2133i	0.641763	−	1.34688i
$273$	40.3810	+	0.118980i	2.44397	+	0.00720098i
$274$	−17.6301	+	5.09894i	−1.06508	+	0.308038i
$275$	−0.172513	−	0.643828i	−0.0104029	−	0.0388243i
$276$	10.0465	+	32.3318i	0.604725	+	1.94615i
$277$	7.90245	−	29.4923i	0.474812	−	1.77202i	−0.147296	−	0.989092i	$-0.547057\pi$
$277$	7.90245	−	29.4923i	0.474812	−	1.77202i	0.622108	−	0.782931i	$-0.286276\pi$
$278$	−10.1089	−	16.7373i	−0.606290	−	1.00384i
$279$		−	6.87447i		−	0.411564i
$280$	4.10016	+	6.26009i	0.245031	+	0.374112i
$281$			6.76844i			0.403771i	0.979409	+	0.201886i	$0.0647069\pi$
$281$			6.76844i			0.403771i	−0.979409	+	0.201886i	$0.935293\pi$
$282$	17.9625	−	10.8488i	1.06965	−	0.646037i
$283$	−3.19075	+	11.9080i	−0.189670	+	0.707859i	0.803912	+	0.594748i	$0.202748\pi$
$283$	−3.19075	+	11.9080i	−0.189670	+	0.707859i	−0.993582	+	0.113111i	$0.963918\pi$
$284$	−2.37788	+	4.52182i	−0.141101	+	0.268321i
$285$	−3.14427	−	11.7346i	−0.186251	−	0.695097i
$286$	−1.65440	−	5.72028i	−0.0978269	−	0.338247i
$287$	6.85342	−	11.7901i	0.404544	−	0.695948i
$288$	−2.60661	+	15.8377i	−0.153596	+	0.933246i
$289$	−10.4206	+	18.0490i	−0.612975	+	1.06170i
$290$	0.363108	−	0.377731i	0.0213224	−	0.0221811i
$291$	3.37364	+	0.903963i	0.197766	+	0.0529913i
$292$	−17.5507	+	0.693115i	−1.02708	+	0.0405615i
$293$	−22.7449	−	22.7449i	−1.32877	−	1.32877i	−0.906442	−	0.422331i	$-0.861212\pi$
$293$	−22.7449	−	22.7449i	−1.32877	−	1.32877i	−0.422331	−	0.906442i	$-0.638788\pi$
$294$	−0.331085	−	23.9156i	−0.0193093	−	1.39479i
$295$			1.96337i			0.114312i
$296$	7.07777	+	3.54546i	0.411387	+	0.206076i
$297$	0.226765	−	0.130923i	0.0131582	−	0.00759691i
$298$	15.5456	−	0.306845i	0.900531	−	0.0177751i
$299$	−42.7532	+	11.4557i	−2.47248	+	0.662499i
$300$	−4.71321	−	1.06549i	−0.272117	−	0.0615161i
$301$	1.35155	+	5.10417i	0.0779022	+	0.294200i
$302$	9.02785	−	2.61101i	0.519494	−	0.150247i
$303$	11.2126	−	19.4208i	0.644149	−	1.11570i
$304$	13.0561	−	15.2992i	0.748818	−	0.877470i
$305$	−5.13718	−	8.89786i	−0.294154	−	0.509490i
$306$	5.91696	−	23.9645i	0.338250	−	1.36996i
$307$	−5.87291	+	5.87291i	−0.335184	+	0.335184i	−0.854551	−	0.519367i	$-0.826168\pi$
$307$	−5.87291	+	5.87291i	−0.335184	+	0.335184i	0.519367	+	0.854551i	$0.326168\pi$
$308$	−3.37121	+	1.03665i	−0.192093	+	0.0590688i
$309$	17.3569	+	17.3569i	0.987399	+	0.987399i
$310$	1.77141	+	2.93293i	0.100609	+	0.166579i
$311$	29.8803	−	17.2514i	1.69436	−	0.978238i	0.743436	−	0.668807i	$-0.233195\pi$
$311$	29.8803	−	17.2514i	1.69436	−	0.978238i	0.950922	−	0.309431i	$-0.100138\pi$
$312$	−42.2864	−	8.68604i	−2.39400	−	0.491750i
$313$	8.39607	+	4.84747i	0.474574	+	0.273995i	0.718153	−	0.695886i	$-0.244988\pi$
$313$	8.39607	+	4.84747i	0.474574	+	0.273995i	−0.243578	+	0.969881i	$0.578321\pi$
$314$	16.9077	+	9.32173i	0.954159	+	0.526056i
$315$	5.29263	+	5.32391i	0.298206	+	0.299969i
$316$	20.0377	−	12.6485i	1.12721	−	0.711532i
$317$	2.25567	+	8.41829i	0.126691	+	0.472818i	0.999894	−	0.0145384i	$-0.00462787\pi$
$317$	2.25567	+	8.41829i	0.126691	+	0.472818i	−0.873203	+	0.487357i	$0.837961\pi$
$318$	−33.2082	+	34.5455i	−1.86222	+	1.93722i
$319$	0.123474	+	0.213863i	0.00691320	+	0.0119740i
$320$	−2.96896	−	7.42868i	−0.165970	−	0.415276i
$321$	6.99693			0.390531
$322$	7.20942	+	25.2054i	0.401765	+	1.40464i
$323$	−21.8716	+	21.8716i	−1.21697	+	1.21697i
$324$	−0.746717	−	18.9080i	−0.0414843	−	1.05044i
$325$	1.63499	−	6.10188i	0.0906931	−	0.338471i
$326$	0.291252	+	14.7556i	0.0161310	+	0.817238i
$327$	3.88729	+	2.24433i	0.214968	+	0.124112i
$328$	−9.68076	+	10.9008i	−0.534530	+	0.601894i
$329$	14.0958	−	8.08290i	0.777124	−	0.445625i
$330$	1.09959	−	1.99443i	0.0605302	−	0.109790i
$331$	24.3220	−	6.51705i	1.33686	−	0.358209i	0.481589	−	0.876397i	$-0.340060\pi$
$331$	24.3220	−	6.51705i	1.33686	−	0.358209i	0.855267	+	0.518188i	$0.173393\pi$
$332$	11.6397	−	3.61679i	0.638810	−	0.198497i
$333$	7.67066	+	2.05535i	0.420350	+	0.112632i
$334$	−1.02629	+	4.15664i	−0.0561563	+	0.227441i
$335$	−7.61641			−0.416129
$336$	−4.72355	+	25.1292i	−0.257691	+	1.37091i
$337$	−0.485881			−0.0264676			−0.0132338	−	0.999912i	$-0.504213\pi$
$337$	−0.485881			−0.0264676			−0.0132338	+	0.999912i	$0.504213\pi$
$338$	9.12108	−	36.9417i	0.496121	−	2.00936i
$339$	−3.39814	−	0.910530i	−0.184562	−	0.0494532i
$340$	3.65073	+	11.7489i	0.197989	+	0.637174i
$341$	−1.55987	+	0.417965i	−0.0844716	+	0.0226341i
$342$	9.74156	−	17.6692i	0.526763	−	0.955442i
$343$	0.163703	−	18.5195i	0.00883915	−	0.999961i
$344$	−0.334011	−	5.63475i	−0.0180086	−	0.303806i
$345$	−14.6604	−	8.46418i	−0.789289	−	0.455696i
$346$	−0.584026	−	29.5883i	−0.0313974	−	1.59068i
$347$	−5.13043	+	19.1470i	−0.275416	+	1.02787i	0.680146	+	0.733076i	$0.261916\pi$
$347$	−5.13043	+	19.1470i	−0.275416	+	1.02787i	−0.955562	+	0.294790i	$0.904750\pi$
$348$	1.78887	−	0.0706466i	0.0958937	−	0.00378706i
$349$	−4.39147	+	4.39147i	−0.235070	+	0.235070i	−0.814805	−	0.579735i	$-0.803156\pi$
$349$	−4.39147	+	4.39147i	−0.235070	+	0.235070i	0.579735	+	0.814805i	$0.303156\pi$
$350$	−3.62991	−	0.907599i	−0.194027	−	0.0485132i
$351$	2.48164			0.132460
$352$	3.75217	−	0.371468i	0.199992	−	0.0197993i
$353$	−2.53598	−	4.39244i	−0.134977	−	0.233786i	0.790612	−	0.612318i	$-0.209763\pi$
$353$	−2.53598	−	4.39244i	−0.134977	−	0.233786i	−0.925588	+	0.378531i	$0.876429\pi$
$354$	−4.64911	+	4.83634i	−0.247097	+	0.257048i
$355$	−0.661145	−	2.46743i	−0.0350899	−	0.130957i
$356$	−5.90369	−	9.35259i	−0.312895	−	0.495686i
$357$	10.2893	−	37.9525i	0.544566	−	2.00866i
$358$	−17.5810	−	9.69290i	−0.929183	−	0.512286i
$359$	5.31302	+	3.06747i	0.280410	+	0.161895i	0.633609	−	0.773653i	$-0.281573\pi$
$359$	5.31302	+	3.06747i	0.280410	+	0.161895i	−0.353199	+	0.935548i	$0.614906\pi$
$360$	−4.41693	−	6.70057i	−0.232793	−	0.353151i
$361$	−5.44121	+	3.14148i	−0.286380	+	0.165341i
$362$	−17.2101	−	28.4949i	−0.904542	−	1.49766i
$363$	−18.0336	−	18.0336i	−0.946520	−	0.946520i
$364$	−32.5825	−	7.46673i	−1.70779	−	0.391363i
$365$	6.20994	−	6.20994i	0.325043	−	0.325043i
$366$	8.41511	−	34.0824i	0.439865	−	1.78152i
$367$	4.54442	+	7.87117i	0.237217	+	0.410872i	0.959915	−	0.280293i	$-0.0904315\pi$
$367$	4.54442	+	7.87117i	0.237217	+	0.410872i	−0.722698	+	0.691164i	$0.757098\pi$
$368$	−2.21019	−	27.9390i	−0.115214	−	1.45642i
$369$	−7.31258	+	12.6658i	−0.380677	+	0.659353i
$370$	−3.80224	+	1.09967i	−0.197669	+	0.0571692i
$371$	−26.3140	+	26.1594i	−1.36616	+	1.35813i
$372$	−2.58147	+	11.4192i	−0.133843	+	0.592057i
$373$	−11.9814	+	3.21041i	−0.620374	+	0.166229i	−0.555298	−	0.831652i	$-0.687396\pi$
$373$	−11.9814	+	3.21041i	−0.620374	+	0.166229i	−0.0650761	+	0.997880i	$0.520729\pi$
$374$	−5.79747	+	0.114433i	−0.299780	+	0.00591719i
$375$	2.09238	−	1.20804i	0.108050	−	0.0623827i
$376$	−16.4834	+	5.48084i	−0.850065	+	0.282653i
$377$			2.34044i			0.120539i
$378$	−0.0246774	−	1.46968i	−0.00126927	−	0.0755920i
$379$	24.4791	+	24.4791i	1.25741	+	1.25741i	0.952326	+	0.305083i	$0.0986841\pi$
$379$	24.4791	+	24.4791i	1.25741	+	1.25741i	0.305083	+	0.952326i	$0.401316\pi$
$380$	0.396842	+	10.0486i	0.0203575	+	0.515482i
$381$	−11.9055	−	3.19006i	−0.609935	−	0.163432i
$382$	10.6507	−	11.0797i	0.544940	−	0.566885i
$383$	−0.422585	+	0.731939i	−0.0215931	+	0.0374003i	−0.876620	−	0.481183i	$-0.840207\pi$
$383$	−0.422585	+	0.731939i	−0.0215931	+	0.0374003i	0.855027	+	0.518584i	$0.173540\pi$
$384$	10.2772	−	25.3292i	0.524454	−	1.29257i
$385$	0.886245	−	1.52463i	0.0451672	−	0.0777023i
$386$	0.308220	+	1.06570i	0.0156880	+	0.0542429i
$387$	−1.46558	−	5.46961i	−0.0744996	−	0.278036i
$388$	−2.55893	−	1.34566i	−0.129910	−	0.0683154i
$389$	−1.34770	+	5.02967i	−0.0683309	+	0.255014i	−0.991638	−	0.129047i	$-0.958808\pi$
$389$	−1.34770	+	5.02967i	−0.0683309	+	0.255014i	0.923308	+	0.384061i	$0.125475\pi$
$390$	18.4762	−	11.1591i	0.935580	−	0.565064i
$391$			43.1010i			2.17971i
$392$	−4.09795	+	19.3703i	−0.206978	+	0.978346i
$393$		−	50.8150i		−	2.56328i
$394$	−13.6229	−	22.5556i	−0.686313	−	1.13633i
$395$	−3.06646	+	11.4442i	−0.154291	+	0.575820i
$396$	3.61212	−	1.12239i	0.181516	−	0.0564024i
$397$	2.19566	+	8.19433i	0.110197	+	0.411262i	0.998883	−	0.0472555i	$-0.0150475\pi$
$397$	2.19566	+	8.19433i	0.110197	+	0.411262i	−0.888686	+	0.458517i	$0.848381\pi$
$398$	18.2589	−	5.28080i	0.915237	−	0.264702i
$399$	16.1529	−	27.7883i	0.808659	−	1.39116i
$400$	3.61104	+	1.72059i	0.180552	+	0.0860294i
$401$	−11.6013	+	20.0941i	−0.579343	+	1.00345i	0.416211	+	0.909268i	$0.363358\pi$
$401$	−11.6013	+	20.0941i	−0.579343	+	1.00345i	−0.995555	+	0.0941844i	$0.969976\pi$
$402$	−18.7614	−	18.0351i	−0.935732	−	0.899508i
$403$	−14.7837	−	3.96127i	−0.736426	−	0.197325i
$404$	−12.5981	+	13.6341i	−0.626779	+	0.678320i
$405$	6.69018	+	6.69018i	0.332438	+	0.332438i
$406$	1.38606	−	0.0232733i	0.0687889	−	0.00115503i
$407$		−	1.86549i		−	0.0924691i
$408$	−18.8277	+	37.5855i	−0.932110	+	1.86076i
$409$	20.0359	−	11.5677i	0.990713	−	0.571988i	0.0852255	−	0.996362i	$-0.472839\pi$
$409$	20.0359	−	11.5677i	0.990713	−	0.571988i	0.905487	+	0.424373i	$0.139506\pi$
$410$	−0.143854	−	7.28802i	−0.00710444	−	0.359930i
$411$	30.2857	−	8.11504i	1.49389	−	0.400285i
$412$	−10.8461	−	17.1823i	−0.534349	−	0.846513i
$413$	−3.68394	+	3.66229i	−0.181275	+	0.180210i
$414$	−7.81127	−	27.0083i	−0.383903	−	1.32739i
$415$	−3.04716	+	5.27784i	−0.149579	+	0.259079i
$416$	32.5572	+	14.7317i	1.59625	+	0.722281i
$417$	16.7025	+	28.9297i	0.817927	+	1.41669i
$418$	−4.60156	−	1.13615i	−0.225070	−	0.0555708i
$419$	9.16757	−	9.16757i	0.447865	−	0.447865i	−0.446779	−	0.894644i	$-0.647429\pi$
$419$	9.16757	−	9.16757i	0.447865	−	0.447865i	0.894644	+	0.446779i	$0.147429\pi$
$420$	−6.79237	−	10.8310i	−0.331434	−	0.528500i
$421$	−4.48614	−	4.48614i	−0.218641	−	0.218641i	0.589284	−	0.807926i	$-0.299410\pi$
$421$	−4.48614	−	4.48614i	−0.218641	−	0.218641i	−0.807926	+	0.589284i	$0.799410\pi$
$422$	12.2477	−	7.39724i	0.596207	−	0.360092i
$423$	−15.0912	+	8.71292i	−0.733760	+	0.423637i
$424$	33.1183	−	21.8312i	1.60837	−	1.06021i
$425$	−5.32737	−	3.07576i	−0.258415	−	0.149196i
$426$	4.21409	−	7.64351i	0.204173	−	0.370329i
$427$	7.11292	−	26.2363i	0.344218	−	1.26966i
$428$	−5.64943	−	1.27714i	−0.273076	−	0.0617328i
$429$	2.63301	+	9.82651i	0.127123	+	0.474429i
$430$	2.03468	+	1.95591i	0.0981209	+	0.0943224i
$431$	−6.13166	−	10.6203i	−0.295352	−	0.511564i	0.679715	−	0.733476i	$-0.262103\pi$
$431$	−6.13166	−	10.6203i	−0.295352	−	0.511564i	−0.975067	+	0.221912i	$0.928770\pi$
$432$	−0.285736	+	1.54517i	−0.0137475	+	0.0743423i
$433$	10.4637			0.502855			0.251427	−	0.967876i	$-0.419100\pi$
$433$	10.4637			0.502855			0.251427	+	0.967876i	$0.419100\pi$
$434$	−2.19893	+	8.79456i	−0.105552	+	0.422153i
$435$	−0.632956	+	0.632956i	−0.0303479	+	0.0303479i
$436$	−2.72900	−	2.52164i	−0.130696	−	0.120765i
$437$	−9.11833	+	34.0301i	−0.436189	+	1.62788i
$438$	30.0015	−	0.592182i	1.43353	−	0.0282955i
$439$	−16.6905	−	9.63624i	−0.796592	−	0.459913i	0.0456860	−	0.998956i	$-0.485453\pi$
$439$	−16.6905	−	9.63624i	−0.796592	−	0.459913i	−0.842278	+	0.539043i	$0.818786\pi$
$440$	−1.25186	+	1.40963i	−0.0596801	+	0.0672013i
$441$	−0.117042	+	19.8615i	−0.00557342	+	0.945785i
$442$	−48.1265	−	26.5335i	−2.28914	−	1.26207i
$443$	−1.24960	+	0.334828i	−0.0593701	+	0.0159082i	−0.288382	−	0.957515i	$-0.593117\pi$
$443$	−1.24960	+	0.334828i	−0.0593701	+	0.0159082i	0.229012	+	0.973424i	$0.426451\pi$
$444$	−11.9699	−	6.29459i	−0.568067	−	0.298728i
$445$	5.34159	+	1.43127i	0.253216	+	0.0678489i
$446$	33.2463	+	8.20866i	1.57426	+	0.388692i
$447$	−26.5636			−1.25641
$448$	8.40066	−	19.4275i	0.396894	−	0.917865i
$449$	−31.2656			−1.47551			−0.737757	−	0.675066i	$-0.764115\pi$
$449$	−31.2656			−1.47551			−0.737757	+	0.675066i	$0.764115\pi$
$450$	3.89571	+	0.961869i	0.183645	+	0.0453430i
$451$	3.31855	+	0.889204i	0.156265	+	0.0418710i
$452$	2.57752	+	1.35543i	0.121236	+	0.0637542i
$453$	−15.5084	+	4.15546i	−0.728648	+	0.195241i
$454$	32.8983	+	18.1378i	1.54399	+	0.851248i
$455$	14.4989	−	8.31409i	0.679720	−	0.389771i
$456$	−22.8168	+	25.6922i	−1.06849	+	1.20315i
$457$	−5.91958	−	3.41767i	−0.276906	−	0.159872i	0.355116	−	0.934822i	$-0.384441\pi$
$457$	−5.91958	−	3.41767i	−0.276906	−	0.159872i	−0.632022	+	0.774950i	$0.717775\pi$
$458$	37.1217	−	0.732723i	1.73458	−	0.0342379i
$459$	0.625457	−	2.33424i	0.0291938	−	0.108953i
$460$	10.2921	+	9.51004i	0.479870	+	0.443408i
$461$	−20.5001	+	20.5001i	−0.954785	+	0.954785i	−0.999021	−	0.0442358i	$-0.985915\pi$
$461$	−20.5001	+	20.5001i	−0.954785	+	0.954785i	0.0442358	+	0.999021i	$0.485915\pi$
$462$	5.79327	−	1.65703i	0.269528	−	0.0770922i
$463$	3.86257			0.179509			0.0897544	−	0.995964i	$-0.471392\pi$
$463$	3.86257			0.179509			0.0897544	+	0.995964i	$0.471392\pi$
$464$	−1.45726	−	0.269479i	−0.0676516	−	0.0125102i
$465$	−2.92683	−	5.06942i	−0.135729	−	0.235089i
$466$	24.3542	+	23.4114i	1.12819	+	1.08451i
$467$	2.91577	+	10.8818i	0.134926	+	0.503549i	0.999998	+	0.00190252i	$0.000605590\pi$
$467$	2.91577	+	10.8818i	0.134926	+	0.503549i	−0.865073	+	0.501647i	$0.832728\pi$
$468$	34.9662	+	7.90462i	1.61631	+	0.365391i
$469$	−14.2070	−	14.2909i	−0.656017	−	0.659894i
$470$	4.19339	−	7.60597i	0.193427	−	0.350837i
$471$	−28.5656	−	16.4924i	−1.31623	−	0.759929i
$472$	4.63653	−	3.05634i	0.213414	−	0.140679i
$473$	−1.15199	+	0.665101i	−0.0529685	+	0.0305814i
$474$	−34.6525	+	20.9291i	−1.59164	+	0.961307i
$475$	−3.55549	−	3.55549i	−0.163137	−	0.163137i
$476$	−15.2351	+	28.7653i	−0.698300	+	1.31846i
$477$	28.1374	−	28.1374i	1.28832	−	1.28832i
$478$	−10.6648	−	2.63320i	−0.487798	−	0.120440i
$479$	10.0331	+	17.3779i	0.458426	+	0.794017i	0.998878	−	0.0473578i	$-0.0150801\pi$
$479$	10.0331	+	17.3779i	0.458426	+	0.794017i	−0.540452	+	0.841375i	$0.681747\pi$
$480$	4.82078	+	12.7889i	0.220038	+	0.583733i
$481$	8.84011	−	15.3115i	0.403074	−	0.698145i
$482$	−3.96507	−	13.7097i	−0.180604	−	0.624459i
$483$	−11.4645	−	43.2961i	−0.521654	−	1.97004i
$484$	11.2690	+	17.8523i	0.512226	+	0.811467i
$485$	1.39633	−	0.374146i	0.0634041	−	0.0169891i
$486$	0.605087	+	30.6553i	0.0274473	+	1.39055i
$487$	−1.94028	+	1.12022i	−0.0879224	+	0.0507620i	−0.543317	−	0.839528i	$-0.682832\pi$
$487$	−1.94028	+	1.12022i	−0.0879224	+	0.0507620i	0.455394	+	0.890290i	$0.349498\pi$
$488$	−13.0155	+	25.9827i	−0.589183	+	1.17618i
$489$		−	25.2137i		−	1.14020i
$490$	−5.06795	−	8.50388i	−0.228947	−	0.384166i
$491$	−9.56584	−	9.56584i	−0.431700	−	0.431700i	0.457506	−	0.889206i	$-0.348743\pi$
$491$	−9.56584	−	9.56584i	−0.431700	−	0.431700i	−0.889206	+	0.457506i	$0.848743\pi$
$492$	16.9031	−	18.2931i	0.762051	−	0.824716i
$493$	2.20143	+	0.589871i	0.0991473	+	0.0265664i
$494$	−32.3846	−	31.1309i	−1.45705	−	1.40064i
$495$	−0.945621	+	1.63786i	−0.0425025	+	0.0736165i
$496$	4.16864	−	8.74883i	0.187178	−	0.392834i
$497$	3.39647	−	5.84304i	0.152353	−	0.262096i
$498$	−20.0035	+	5.78537i	−0.896380	+	0.259249i
$499$	−1.48164	−	5.52954i	−0.0663272	−	0.247536i	0.924800	−	0.380454i	$-0.124232\pi$
$499$	−1.48164	−	5.52954i	−0.0663272	−	0.247536i	−0.991127	+	0.132917i	$0.957565\pi$
$500$	−1.90992	+	0.593469i	−0.0854142	+	0.0265407i
$501$	1.89314	−	7.06530i	0.0845794	−	0.315655i
$502$	14.5571	+	24.1023i	0.649716	+	1.07574i
$503$		−	14.6115i		−	0.651496i	−0.945457	−	0.325748i	$-0.894384\pi$
$503$		−	14.6115i		−	0.651496i	0.945457	−	0.325748i	$-0.105616\pi$
$504$	4.33357	−	20.7863i	0.193032	−	0.925894i
$505$		−	9.28170i		−	0.413030i
$506$	−5.65346	+	3.41453i	−0.251327	+	0.151794i
$507$	−16.8251	+	62.7921i	−0.747228	+	2.78869i
$508$	9.03037	+	4.74878i	0.400658	+	0.210693i
$509$	−2.89456	−	10.8027i	−0.128299	−	0.478820i	0.871636	−	0.490153i	$-0.163059\pi$
$509$	−2.89456	−	10.8027i	−0.128299	−	0.478820i	−0.999936	+	0.0113333i	$0.996392\pi$
$510$	−5.83966	−	20.1913i	−0.258584	−	0.894084i
$511$	23.2354	+	0.0684613i	1.02787	+	0.00302855i
$512$	−12.9212	+	18.5753i	−0.571043	+	0.820920i
$513$	0.987650	−	1.71066i	0.0436058	−	0.0755275i
$514$	−8.24086	+	8.57274i	−0.363489	+	0.378127i
$515$	9.81343	+	2.62950i	0.432431	+	0.115870i
$516$	0.380544	+	9.63592i	0.0167525	+	0.424198i
$517$	2.89457	+	2.89457i	0.127303	+	0.127303i
$518$	−9.15569	−	5.08303i	−0.402278	−	0.223336i
$519$			50.5591i			2.21930i
$520$	−16.9548	+	5.63761i	−0.743519	+	0.247225i
$521$	−19.7992	+	11.4311i	−0.867417	+	0.500803i	−0.866489	−	0.499196i	$-0.833629\pi$
$521$	−19.7992	+	11.4311i	−0.867417	+	0.500803i	−0.000927970		1.00000i	$0.500295\pi$
$522$	−1.48638	+	0.0293388i	−0.0650571	+	0.00128412i
$523$	5.39339	−	1.44515i	0.235836	−	0.0631922i	−0.138965	−	0.990297i	$-0.544378\pi$
$523$	5.39339	−	1.44515i	0.235836	−	0.0631922i	0.374801	+	0.927105i	$0.377711\pi$
$524$	−9.27517	+	41.0288i	−0.405188	+	1.79235i
$525$	6.16961	+	1.67264i	0.269264	+	0.0730000i
$526$	−23.1190	+	6.68643i	−1.00804	+	0.291542i
$527$	−7.45196	+	12.9072i	−0.324612	+	0.562245i
$528$	−6.42157	+	0.507996i	−0.279463	+	0.0221077i
$529$	13.0460	+	22.5963i	0.567216	+	0.982446i
$530$	−4.75415	+	19.2550i	−0.206507	+	0.836382i
$531$	3.93921	−	3.93921i	0.170947	−	0.170947i
$532$	−18.1143	+	19.4883i	−0.785354	+	0.844927i
$533$	23.0242	+	23.0242i	0.997287	+	0.997287i
$534$	9.76869	+	16.1741i	0.422733	+	0.699922i
$535$	2.50801	−	1.44800i	0.108431	−	0.0626024i
$536$	11.8563	+	17.9863i	0.512115	+	0.776889i
$537$	29.7031	+	17.1491i	1.28178	+	0.740037i
$538$	32.0099	+	17.6480i	1.38005	+	0.760859i
$539$	4.51383	−	1.18101i	0.194425	−	0.0508699i
$540$	−0.419388	−	0.664392i	−0.0180476	−	0.0285909i
$541$	−6.92280	−	25.8362i	−0.297634	−	1.11079i	−0.939103	−	0.343637i	$-0.888341\pi$
$541$	−6.92280	−	25.8362i	−0.297634	−	1.11079i	0.641468	−	0.767150i	$-0.278326\pi$
$542$	0.00679776	−	0.00707152i	0.000291989	−	0.000303748i
$543$	28.4357	+	49.2520i	1.22029	+	2.11361i
$544$	22.0622	−	26.9105i	0.945909	−	1.15378i
$545$	1.85783			0.0795808
$546$	55.4021	+	13.8524i	2.37099	+	0.592826i
$547$	−11.1790	+	11.1790i	−0.477978	+	0.477978i	−0.904485	−	0.426506i	$-0.859744\pi$
$547$	−11.1790	+	11.1790i	−0.477978	+	0.477978i	0.426506	+	0.904485i	$0.359744\pi$
$548$	−25.9344	+	1.02421i	−1.10786	+	0.0437519i
$549$	−7.54523	+	28.1592i	−0.322023	+	1.20180i
$550$	−0.0186024	−	0.942446i	−0.000793209	−	0.0401860i
$551$	1.61333	+	0.931456i	0.0687301	+	0.0396814i
$552$	2.83324	+	47.7967i	0.120591	+	2.03436i
$553$	−27.1930	+	15.5933i	−1.15637	+	0.663093i
$554$	20.8477	−	37.8136i	0.885735	−	1.60655i
$555$	6.53163	−	1.75015i	0.277252	−	0.0742895i
$556$	−8.20542	−	26.4069i	−0.347987	−	1.11990i
$557$	7.25114	+	1.94294i	0.307241	+	0.0823249i	0.409145	−	0.912469i	$-0.365827\pi$
$557$	7.25114	+	1.94294i	0.307241	+	0.0823249i	−0.101904	+	0.994794i	$0.532494\pi$
$558$	2.33042	−	9.43853i	0.0986545	−	0.399565i
$559$	−12.6070			−0.533219
$560$	3.50730	+	9.98493i	0.148211	+	0.421940i
$561$	9.90645			0.418251
$562$	−2.29448	+	9.29295i	−0.0967866	+	0.392000i
$563$	−0.319386	−	0.0855792i	−0.0134605	−	0.00360673i	0.252083	−	0.967706i	$-0.418885\pi$
$563$	−0.319386	−	0.0855792i	−0.0134605	−	0.00360673i	−0.265543	+	0.964099i	$0.585551\pi$
$564$	28.3398	−	8.80603i	1.19332	−	0.370801i
$565$	−1.40647	+	0.376864i	−0.0591708	+	0.0158548i
$566$	−8.41762	+	15.2679i	−0.353819	+	0.641757i
$567$	−0.0737558	+	25.0323i	−0.00309745	+	1.05126i
$568$	−4.79767	+	5.40229i	−0.201306	+	0.226675i
$569$	21.8340	+	12.6059i	0.915329	+	0.528465i	0.882142	−	0.470984i	$-0.156101\pi$
$569$	21.8340	+	12.6059i	0.915329	+	0.528465i	0.0331871	+	0.999449i	$0.489434\pi$
$570$	−0.339052	−	17.1773i	−0.0142013	−	0.719477i
$571$	1.51125	−	5.64006i	0.0632438	−	0.236029i	−0.927067	−	0.374895i	$-0.877679\pi$
$571$	1.51125	−	5.64006i	0.0632438	−	0.236029i	0.990311	+	0.138865i	$0.0443456\pi$
$572$	−0.332314	−	8.41468i	−0.0138948	−	0.351835i
$573$	−18.5660	+	18.5660i	−0.775604	+	0.775604i
$574$	13.4064	−	13.8643i	0.559573	−	0.578686i
$575$	−7.00656			−0.292194
$576$	−8.94775	+	20.8613i	−0.372823	+	0.869220i
$577$	−3.50514	−	6.07109i	−0.145921	−	0.252743i	0.783795	−	0.621019i	$-0.213281\pi$
$577$	−3.50514	−	6.07109i	−0.145921	−	0.252743i	−0.929716	+	0.368277i	$0.879948\pi$
$578$	−20.4258	+	21.2484i	−0.849602	+	0.883817i
$579$	−0.490537	−	1.83071i	−0.0203860	−	0.0760817i
$580$	0.626590	−	0.395526i	0.0260177	−	0.0164233i
$581$	−15.5869	+	4.12731i	−0.646653	+	0.171230i
$582$	4.32550	+	2.38478i	0.179298	+	0.0988521i
$583$	−8.09533	−	4.67384i	−0.335274	−	0.193571i
$584$	−24.3317	−	4.99798i	−1.00685	−	0.206818i
$585$	−15.5229	+	8.96213i	−0.641791	+	0.370538i
$586$	−23.5179	−	38.9388i	−0.971517	−	1.60855i
$587$	21.2114	+	21.2114i	0.875487	+	0.875487i	0.993064	−	0.117577i	$-0.0375127\pi$
$587$	21.2114	+	21.2114i	0.875487	+	0.875487i	−0.117577	+	0.993064i	$0.537513\pi$
$588$	7.65272	−	32.9479i	0.315593	−	1.35875i
$589$	−8.61424	+	8.61424i	−0.354944	+	0.354944i
$590$	−0.665575	+	2.69567i	−0.0274013	+	0.110979i
$591$	22.5087	+	38.9862i	0.925883	+	1.60368i
$592$	8.51575	+	7.26720i	0.349995	+	0.298680i
$593$	−9.10588	+	15.7718i	−0.373934	+	0.647672i	−0.990167	−	0.139892i	$-0.955325\pi$
$593$	−9.10588	+	15.7718i	−0.373934	+	0.647672i	0.616233	+	0.787564i	$0.288658\pi$
$594$	0.355726	−	0.102882i	0.0145956	−	0.00422131i
$595$	−4.16604	−	15.7332i	−0.170791	−	0.644997i
$596$	21.4478	+	4.84860i	0.878538	+	0.198606i
$597$	−31.3659	+	8.40447i	−1.28372	+	0.343972i
$598$	−62.5828	+	1.23529i	−2.55920	+	0.0505146i
$599$	26.0855	−	15.0605i	1.06582	−	0.615354i	0.138786	−	0.990322i	$-0.455680\pi$
$599$	26.0855	−	15.0605i	1.06582	−	0.615354i	0.927038	+	0.374969i	$0.122347\pi$
$600$	−6.10996	−	3.06066i	−0.249438	−	0.124951i
$601$		−	31.9836i		−	1.30464i	−0.757945	−	0.652319i	$-0.773796\pi$
$601$		−	31.9836i		−	1.30464i	0.757945	−	0.652319i	$-0.226204\pi$
$602$	0.125364	+	7.46611i	0.00510944	+	0.304296i
$603$	15.2812	+	15.2812i	0.622298	+	0.622298i
$604$	13.2802	−	0.524465i	0.540364	−	0.0213402i
$605$	−10.1960	−	2.73202i	−0.414528	−	0.111073i
$606$	21.9783	−	22.8634i	0.892809	−	0.928764i
$607$	23.3254	−	40.4007i	0.946748	−	1.63981i	0.194534	−	0.980896i	$-0.437681\pi$
$607$	23.3254	−	40.4007i	0.946748	−	1.63981i	0.752214	−	0.658919i	$-0.228986\pi$
$608$	23.1122	−	16.5796i	0.937322	−	0.672391i
$609$	−2.36829	−	0.00697801i	−0.0959681	−	0.000282763i
$610$	−4.03692	−	13.9581i	−0.163450	−	0.565147i
$611$	10.0413	+	37.4745i	0.406226	+	1.51606i
$612$	16.2478	−	30.8970i	0.656777	−	1.24894i
$613$	−2.75281	+	10.2736i	−0.111185	+	0.414948i	−0.998973	−	0.0453040i	$-0.985574\pi$
$613$	−2.75281	+	10.2736i	−0.111185	+	0.414948i	0.887788	+	0.460252i	$0.152241\pi$
$614$	−10.0543	+	6.07250i	−0.405758	+	0.245066i
$615$			12.4534i			0.502171i
$616$	−4.98003	+	0.280478i	−0.200651	+	0.0113008i
$617$			35.6050i			1.43340i	0.697380	+	0.716702i	$0.254349\pi$
$617$			35.6050i			1.43340i	−0.697380	+	0.716702i	$0.745651\pi$
$618$	17.9468	+	29.7146i	0.721926	+	1.19530i
$619$	7.38406	−	27.5577i	0.296790	−	1.10764i	−0.642995	−	0.765871i	$-0.722308\pi$
$619$	7.38406	−	27.5577i	0.296790	−	1.10764i	0.939785	−	0.341766i	$-0.111025\pi$
$620$	1.43786	+	4.62736i	0.0577458	+	0.185839i
$621$	−0.712394	−	2.65869i	−0.0285874	−	0.106690i
$622$	46.8733	−	13.5566i	1.87945	−	0.543569i
$623$	7.27816	+	12.6924i	0.291593	+	0.508509i
$624$	−55.1139	−	26.2607i	−2.20632	−	1.05127i
$625$	0.500000	−	0.866025i	0.0200000	−	0.0346410i
$626$	9.88439	+	9.50173i	0.395060	+	0.379766i
$627$	7.82157	+	2.09578i	0.312363	+	0.0836975i
$628$	20.0540	+	18.5302i	0.800242	+	0.739437i
$629$	−12.1741	−	12.1741i	−0.485411	−	0.485411i
$630$	5.46191	+	9.10383i	0.217608	+	0.362705i
$631$			32.3871i			1.28931i	0.764473	+	0.644656i	$0.222999\pi$
$631$			32.3871i			1.28931i	−0.764473	+	0.644656i	$0.777001\pi$
$632$	31.7991	−	10.5734i	1.26490	−	0.420589i
$633$	−21.1695	+	12.2222i	−0.841411	+	0.485789i
$634$	0.243233	+	12.3228i	0.00966002	+	0.489402i
$635$	−4.92761	+	1.32035i	−0.195546	+	0.0523964i
$636$	−57.3050	+	36.1730i	−2.27229	+	1.43435i
$637$	42.6450	+	11.6965i	1.68966	+	0.463430i
$638$	0.0970286	+	0.335487i	0.00384140	+	0.0132821i
$639$	−3.62403	+	6.27700i	−0.143364	+	0.248314i
$640$	−1.55803	−	11.2059i	−0.0615867	−	0.442953i
$641$	−13.1783	−	22.8254i	−0.520510	−	0.901549i	−0.999716	−	0.0238469i	$-0.992409\pi$
$641$	−13.1783	−	22.8254i	−0.520510	−	0.901549i	0.479206	−	0.877703i	$-0.340925\pi$
$642$	9.60667	+	2.37193i	0.379145	+	0.0936128i
$643$	17.1546	−	17.1546i	0.676510	−	0.676510i	−0.282699	−	0.959209i	$-0.591230\pi$
$643$	17.1546	−	17.1546i	0.676510	−	0.676510i	0.959209	+	0.282699i	$0.0912297\pi$
$644$	1.35388	+	37.0505i	0.0533505	+	1.45999i
$645$	−3.40947	−	3.40947i	−0.134248	−	0.134248i
$646$	−37.4438	+	22.6150i	−1.47321	+	0.889774i
$647$	−19.9982	+	11.5460i	−0.786210	+	0.453919i	−0.838627	−	0.544707i	$-0.816641\pi$
$647$	−19.9982	+	11.5460i	−0.786210	+	0.453919i	0.0524166	+	0.998625i	$0.483308\pi$
$648$	5.38450	−	26.2134i	0.211523	−	1.02976i
$649$	−1.13334	−	0.654332i	−0.0444874	−	0.0256848i
$650$	4.31333	−	7.82352i	0.169183	−	0.306864i
$651$	4.05248	−	14.9478i	0.158829	−	0.585849i
$652$	−4.60221	+	20.3579i	−0.180237	+	0.797278i
$653$	1.13330	+	4.22953i	0.0443494	+	0.165514i	0.984549	−	0.175110i	$-0.0560282\pi$
$653$	1.13330	+	4.22953i	0.0443494	+	0.165514i	−0.940199	+	0.340624i	$0.889362\pi$
$654$	4.57636	+	4.39920i	0.178950	+	0.172022i
$655$	−10.5160	−	18.2143i	−0.410896	−	0.711692i
$656$	−16.9868	+	11.6848i	−0.663224	+	0.456216i
$657$	−24.9186			−0.972167
$658$	22.0933	−	6.31928i	0.861287	−	0.246351i
$659$	19.9517	−	19.9517i	0.777207	−	0.777207i	−0.202148	−	0.979355i	$-0.564792\pi$
$659$	19.9517	−	19.9517i	0.777207	−	0.777207i	0.979355	+	0.202148i	$0.0647922\pi$
$660$	2.18581	−	2.36556i	0.0850827	−	0.0920793i
$661$	−3.30191	+	12.3229i	−0.128429	+	0.479305i	−0.999939	−	0.0110739i	$-0.996475\pi$
$661$	−3.30191	+	12.3229i	−0.128429	+	0.479305i	0.871509	+	0.490379i	$0.163142\pi$
$662$	35.6029	−	0.702745i	1.38375	−	0.0273130i
$663$	81.3097	+	46.9442i	3.15781	+	1.82316i
$664$	17.2072	−	1.01999i	0.667767	−	0.0395831i
$665$	0.0391974	−	13.3034i	0.00152001	−	0.515882i
$666$	9.83493	+	5.42228i	0.381096	+	0.210109i
$667$	2.50742	−	0.671861i	0.0970877	−	0.0260146i
$668$	−2.81817	+	5.35908i	−0.109038	+	0.207349i
$669$	−56.5108	−	15.1420i	−2.18483	−	0.585424i
$670$	−10.4572	−	2.58194i	−0.403997	−	0.0997489i
$671$	6.84828			0.264375
$672$	−15.0041	+	32.9007i	−0.578794	+	1.26917i
$673$	−6.23529			−0.240353			−0.120176	−	0.992753i	$-0.538346\pi$
$673$	−6.23529			−0.240353			−0.120176	+	0.992753i	$0.538346\pi$
$674$	−0.667106	−	0.164712i	−0.0256960	−	0.00634446i
$675$	0.379457	+	0.101675i	0.0146053	+	0.00391348i
$676$	25.0462	−	47.6282i	0.963314	−	1.83186i
$677$	−17.0748	+	4.57518i	−0.656238	+	0.175838i	−0.571547	−	0.820569i	$-0.693657\pi$
$677$	−17.0748	+	4.57518i	−0.656238	+	0.175838i	−0.0846901	+	0.996407i	$0.526990\pi$
$678$	−4.35693	−	2.40210i	−0.167327	−	0.0922521i
$679$	3.30661	+	1.92208i	0.126896	+	0.0737628i
$680$	1.02956	+	17.3686i	0.0394817	+	0.666057i
$681$	−55.5817	−	32.0901i	−2.12989	−	1.22970i
$682$	−2.28336	+	0.0450699i	−0.0874344	+	0.00172582i
$683$	−6.96566	+	25.9962i	−0.266533	+	0.994716i	0.694772	+	0.719230i	$0.255505\pi$
$683$	−6.96566	+	25.9962i	−0.266533	+	0.994716i	−0.961305	+	0.275486i	$0.911161\pi$
$684$	19.3648	−	20.9572i	0.740431	−	0.801318i
$685$	9.17634	−	9.17634i	0.350610	−	0.350610i
$686$	6.50281	−	25.3715i	0.248279	−	0.968689i
$687$	−63.4318			−2.42007
$688$	1.45157	−	7.84965i	0.0553406	−	0.299265i
$689$	−44.2963	−	76.7235i	−1.68755	−	2.92293i
$690$	−17.2591	−	16.5910i	−0.657044	−	0.631608i
$691$	−1.61434	−	6.02480i	−0.0614124	−	0.229194i	0.928398	−	0.371588i	$-0.121187\pi$
$691$	−1.61434	−	6.02480i	−0.0614124	−	0.229194i	−0.989810	+	0.142394i	$0.954520\pi$
$692$	9.22845	−	40.8222i	0.350813	−	1.55183i
$693$	−4.83705	+	1.28082i	−0.183744	+	0.0486544i
$694$	−13.5348	+	24.5493i	−0.513772	+	0.931880i
$695$	11.9738	+	6.91310i	0.454194	+	0.262229i
$696$	2.48004	+	0.509425i	0.0940058	+	0.0193097i
$697$	27.4595	−	15.8537i	1.04010	−	0.600503i
$698$	−7.51810	+	4.54072i	−0.284564	+	0.171869i
$699$	−40.8098	−	40.8098i	−1.54357	−	1.54357i
$700$	−4.67613	−	2.47664i	−0.176741	−	0.0936083i
$701$	33.9928	−	33.9928i	1.28389	−	1.28389i	0.345455	−	0.938435i	$-0.387724\pi$
$701$	33.9928	−	33.9928i	1.28389	−	1.28389i	0.938435	−	0.345455i	$-0.112276\pi$
$702$	3.40725	+	0.841267i	0.128598	+	0.0317516i
$703$	−7.03642	−	12.1874i	−0.265384	−	0.459658i
$704$	5.27760	+	0.761953i	0.198907	+	0.0287172i
$705$	−7.41912	+	12.8503i	−0.279420	+	0.483970i
$706$	−1.99283	−	6.89044i	−0.0750013	−	0.259325i
$707$	17.4156	−	17.3132i	0.654980	−	0.651131i
$708$	−8.02265	+	5.06418i	−0.301509	+	0.190323i
$709$	−10.7696	+	2.88570i	−0.404460	+	0.108375i	−0.455313	−	0.890331i	$-0.650473\pi$
$709$	−10.7696	+	2.88570i	−0.404460	+	0.108375i	0.0508529	+	0.998706i	$0.483806\pi$
$710$	−0.0712924	−	3.61186i	−0.00267556	−	0.135551i
$711$	29.1134	−	16.8087i	1.09184	−	0.630374i
$712$	−4.93517	−	14.8423i	−0.184953	−	0.556238i
$713$			16.9755i			0.635738i
$714$	26.9927	−	48.6201i	1.01018	−	1.81956i
$715$	2.97736	+	2.97736i	0.111347	+	0.111347i
$716$	−20.8525	−	19.2681i	−0.779295	−	0.720081i
$717$	18.1277	+	4.85731i	0.676992	+	0.181399i
$718$	6.25482	+	6.01268i	0.233428	+	0.224391i
$719$	0.404807	−	0.701146i	0.0150967	−	0.0261483i	−0.858378	−	0.513017i	$-0.828528\pi$
$719$	0.404807	−	0.701146i	0.0150967	−	0.0261483i	0.873475	+	0.486869i	$0.161861\pi$
$720$	−3.79290	−	10.6971i	−0.141353	−	0.398657i
$721$	13.3713	+	23.3181i	0.497971	+	0.868411i
$722$	−8.53564	+	2.46865i	−0.317664	+	0.0918738i
$723$	6.31048	+	23.5510i	0.234689	+	0.875872i
$724$	−13.9695	−	44.9571i	−0.519173	−	1.67082i
$725$	−0.0958903	+	0.357867i	−0.00356128	+	0.0132909i
$726$	−18.6465	−	30.8732i	−0.692037	−	1.14581i
$727$			35.4672i			1.31541i	0.753277	+	0.657704i	$0.228472\pi$
$727$			35.4672i			1.31541i	−0.753277	+	0.657704i	$0.771528\pi$
$728$	−42.2040	−	21.2970i	−1.56419	−	0.789321i
$729$		−	23.9983i		−	0.888825i
$730$	10.6313	−	6.42099i	0.393481	−	0.237652i
$731$	−3.17739	+	11.8582i	−0.117520	+	0.438590i
$732$	23.1076	−	43.9419i	0.854082	−	1.62414i
$733$	−6.69573	−	24.9888i	−0.247312	−	0.922982i	−0.972207	−	0.234122i	$-0.924778\pi$
$733$	−6.69573	−	24.9888i	−0.247312	−	0.922982i	0.724895	−	0.688860i	$-0.241888\pi$
$734$	3.57112	+	12.3475i	0.131812	+	0.455755i
$735$	8.36980	+	14.6962i	0.308725	+	0.542079i
$736$	6.43665	−	39.1090i	0.237258	−	1.44158i
$737$	2.53832	−	4.39650i	0.0935003	−	0.161947i
$738$	−14.3337	+	14.9109i	−0.527630	+	0.548879i
$739$	−6.48108	−	1.73660i	−0.238411	−	0.0638819i	0.137635	−	0.990483i	$-0.456050\pi$
$739$	−6.48108	−	1.73660i	−0.238411	−	0.0638819i	−0.376046	+	0.926601i	$0.622716\pi$
$740$	−5.59319	+	0.220887i	−0.205610	+	0.00811999i
$741$	54.2661	+	54.2661i	1.99352	+	1.99352i
$742$	−44.9967	+	26.9961i	−1.65188	+	0.991058i
$743$		−	13.4802i		−	0.494541i	−0.968946	−	0.247271i	$-0.920466\pi$
$743$		−	13.4802i		−	0.494541i	0.968946	−	0.247271i	$-0.0795337\pi$
$744$	−7.41538	+	14.8032i	−0.271861	+	0.542713i
$745$	−9.52154	+	5.49726i	−0.348842	+	0.201404i
$746$	−17.5386	+	0.346184i	−0.642133	+	0.0126747i
$747$	16.7029	−	4.47552i	0.611126	−	0.163751i
$748$	−7.99862	−	1.80821i	−0.292459	−	0.0661146i
$749$	7.39513	+	2.00489i	0.270212	+	0.0732571i
$750$	3.28232	−	0.949304i	0.119853	−	0.0346637i
$751$	13.1435	−	22.7652i	0.479614	−	0.830715i	−0.520113	−	0.854097i	$-0.674110\pi$
$751$	13.1435	−	22.7652i	0.479614	−	0.830715i	0.999727	+	0.0233823i	$0.00744348\pi$
$752$	−24.4894	+	1.93730i	−0.893036	+	0.0706461i
$753$	−24.0522	−	41.6597i	−0.876512	−	1.51816i
$754$	−0.793401	+	3.21339i	−0.0288940	+	0.117025i
$755$	−4.69892	+	4.69892i	−0.171011	+	0.171011i
$756$	0.464333	−	2.02621i	0.0168876	−	0.0736924i
$757$	3.97788	+	3.97788i	0.144579	+	0.144579i	0.775691	−	0.631113i	$-0.217401\pi$
$757$	3.97788	+	3.97788i	0.144579	+	0.144579i	−0.631113	+	0.775691i	$0.717401\pi$
$758$	25.3111	+	41.9078i	0.919340	+	1.52216i
$759$	9.77173	−	5.64171i	0.354691	−	0.204781i
$760$	−2.86158	+	13.9311i	−0.103800	+	0.505334i
$761$	−14.9331	−	8.62165i	−0.541325	−	0.312534i	0.204290	−	0.978910i	$-0.434511\pi$
$761$	−14.9331	−	8.62165i	−0.541325	−	0.312534i	−0.745616	+	0.666376i	$0.767845\pi$
$762$	−15.2646	−	8.41579i	−0.552977	−	0.304872i
$763$	3.46543	+	3.48591i	0.125457	+	0.126198i
$764$	18.3793	−	11.6016i	0.664938	−	0.419732i
$765$	4.51752	+	16.8596i	0.163331	+	0.609560i
$766$	−0.828327	+	0.861685i	−0.0299287	+	0.0311339i
$767$	−6.20144	−	10.7412i	−0.223921	−	0.387842i
$768$	22.6969	−	31.2926i	0.819002	−	1.12918i
$769$	−33.9360			−1.22376			−0.611881	−	0.790950i	$-0.709587\pi$
$769$	−33.9360			−1.22376			−0.611881	+	0.790950i	$0.709587\pi$
$770$	1.73364	−	1.79286i	0.0624762	−	0.0646101i
$771$	14.3651	−	14.3651i	0.517348	−	0.517348i
$772$	0.0619112	+	1.56768i	0.00222823	+	0.0564220i
$773$	−4.00589	+	14.9502i	−0.144082	+	0.537721i	0.855713	+	0.517451i	$0.173119\pi$
$773$	−4.00589	+	14.9502i	−0.144082	+	0.537721i	−0.999795	+	0.0202695i	$0.993548\pi$
$774$	−0.158036	−	8.00651i	−0.00568048	−	0.287788i
$775$	−2.09821	−	1.21140i	−0.0753699	−	0.0435148i
$776$	−3.05719	−	2.71503i	−0.109747	−	0.0974639i
$777$	15.4674	+	8.99095i	0.554888	+	0.322549i
$778$	−3.55540	+	6.44878i	−0.127467	+	0.231200i
$779$	25.0344	−	6.70794i	0.896950	−	0.240337i
$780$	29.1504	−	9.05790i	1.04375	−	0.324325i
$781$	1.64464	+	0.440679i	0.0588498	+	0.0157687i
$782$	−14.6111	+	59.1769i	−0.522491	+	2.11616i
$783$	−0.145545			−0.00520136
$784$	−12.1929	+	25.2058i	−0.435459	+	0.900209i
$785$	−13.6522			−0.487269
$786$	17.2261	−	69.7681i	0.614434	−	2.48855i
$787$	−29.3304	−	7.85905i	−1.04552	−	0.280145i	−0.305118	−	0.952315i	$-0.598696\pi$
$787$	−29.3304	−	7.85905i	−1.04552	−	0.280145i	−0.740397	+	0.672170i	$0.765363\pi$
$788$	−11.0578	−	35.5865i	−0.393917	−	1.26772i
$789$	39.7148	−	10.6415i	1.41388	−	0.378849i
$790$	−8.08974	+	14.6732i	−0.287820	+	0.522048i
$791$	−3.33063	−	1.93605i	−0.118424	−	0.0688379i
$792$	5.33987	−	0.316531i	0.189744	−	0.0112474i
$793$	56.2090	+	32.4523i	1.99604	+	1.15241i
$794$	0.236762	+	11.9950i	0.00840238	+	0.425686i
$795$	8.76968	−	32.7289i	0.311029	−	1.16077i
$796$	26.8594	−	1.06074i	0.952005	−	0.0375968i
$797$	28.5639	−	28.5639i	1.01179	−	1.01179i	0.0118570	−	0.999930i	$-0.496226\pi$
$797$	28.5639	−	28.5639i	1.01179	−	1.01179i	0.999930	−	0.0118570i	$-0.00377428\pi$
$798$	31.5979	−	32.6771i	1.11855	−	1.15676i
$799$	37.7794			1.33654
$800$	4.37462	+	3.58646i	0.154666	+	0.126801i
$801$	−7.84545	−	13.5887i	−0.277205	−	0.480134i
$802$	−22.7403	+	23.6561i	−0.802987	+	0.835325i
$803$	1.51504	+	5.65421i	0.0534646	+	0.199533i
$804$	−19.6452	−	31.1219i	−0.692834	−	1.09758i
$805$	−13.0694	−	13.1466i	−0.460636	−	0.463358i
$806$	−18.9548	−	10.4504i	−0.667656	−	0.368098i
$807$	−54.0808	−	31.2236i	−1.90373	−	1.09912i
$808$	−21.9189	+	14.4486i	−0.771103	+	0.508301i
$809$	−2.13057	+	1.23008i	−0.0749067	+	0.0432474i	−0.536986	−	0.843591i	$-0.680437\pi$
$809$	−2.13057	+	1.23008i	−0.0749067	+	0.0432474i	0.462079	+	0.886839i	$0.347104\pi$
$810$	6.91756	+	11.4535i	0.243058	+	0.402433i
$811$	−4.70638	−	4.70638i	−0.165263	−	0.165263i	0.619630	−	0.784894i	$-0.287283\pi$
$811$	−4.70638	−	4.70638i	−0.165263	−	0.165263i	−0.784894	+	0.619630i	$0.787283\pi$
$812$	1.91092	+	0.437914i	0.0670602	+	0.0153678i
$813$	−0.0118496	+	0.0118496i	−0.000415583	+	0.000415583i
$814$	0.632395	−	2.56129i	0.0221655	−	0.0897732i
$815$	−5.21791	−	9.03769i	−0.182776	−	0.316576i
$816$	−38.5915	+	45.2217i	−1.35097	+	1.58308i
$817$	−5.01737	+	8.69033i	−0.175535	+	0.304036i
$818$	31.4304	−	9.09021i	1.09894	−	0.317832i
$819$	−45.7708	−	12.4089i	−1.59936	−	0.433603i
$820$	2.27310	−	10.0551i	0.0793802	−	0.351139i
$821$	6.70013	−	1.79530i	0.233836	−	0.0626562i	−0.139998	−	0.990152i	$-0.544710\pi$
$821$	6.70013	−	1.79530i	0.233836	−	0.0626562i	0.373834	+	0.927496i	$0.378043\pi$
$822$	44.3328	−	0.875059i	1.54628	−	0.0305212i
$823$	−42.4229	+	24.4929i	−1.47877	+	0.853769i	−0.999712	−	0.0240139i	$-0.992355\pi$
$823$	−42.4229	+	24.4929i	−1.47877	+	0.853769i	−0.479059	+	0.877783i	$0.659022\pi$
$824$	−9.06676	−	27.2678i	−0.315855	−	0.949920i
$825$			1.61041i			0.0560672i
$826$	−6.29949	+	3.77942i	−0.219187	+	0.131503i
$827$	−30.1155	−	30.1155i	−1.04722	−	1.04722i	−0.998829	−	0.0483886i	$-0.984591\pi$
$827$	−30.1155	−	30.1155i	−1.04722	−	1.04722i	−0.0483886	−	0.998829i	$-0.515409\pi$
$828$	−1.56902	−	39.7299i	−0.0545273	−	1.38071i
$829$	−47.9217	−	12.8406i	−1.66439	−	0.445972i	−0.700800	−	0.713357i	$-0.747174\pi$
$829$	−47.9217	−	12.8406i	−1.66439	−	0.445972i	−0.963590	+	0.267386i	$0.913840\pi$
$830$	−5.97287	+	6.21341i	−0.207321	+	0.215671i
$831$	−36.8846	+	63.8861i	−1.27951	+	2.21618i
$832$	39.7065	+	31.2631i	1.37658	+	1.08385i
$833$	21.7497	−	37.1641i	0.753582	−	1.28766i
$834$	13.1253	+	45.3820i	0.454491	+	1.57145i
$835$	−0.783562	−	2.92429i	−0.0271163	−	0.101199i
$836$	−5.93271	−	3.11982i	−0.205187	−	0.107901i
$837$	0.246339	−	0.919350i	0.00851473	−	0.0317774i
$838$	15.6947	−	9.47915i	0.542164	−	0.327452i
$839$		−	2.31443i		−	0.0799031i	−0.999202	−	0.0399516i	$-0.987280\pi$
$839$		−	2.31443i		−	0.0799031i	0.999202	−	0.0399516i	$-0.0127204\pi$
$840$	−5.65414	−	17.1734i	−0.195086	−	0.592538i
$841$			28.8627i			0.995267i
$842$	−4.63861	−	7.68018i	−0.159857	−	0.264676i
$843$	4.23248	−	15.7958i	0.145774	−	0.544037i
$844$	19.3235	−	6.00437i	0.665141	−	0.206679i
$845$	6.96382	+	25.9893i	0.239563	+	0.894060i
$846$	−23.6736	+	6.84682i	−0.813916	+	0.235399i
$847$	−13.8926	−	24.2272i	−0.477355	−	0.832458i
$848$	52.8716	−	18.7468i	1.81562	−	0.643768i
$849$	14.8928	−	25.7951i	0.511119	−	0.885285i
$850$	−6.27172	−	6.02892i	−0.215118	−	0.206790i
$851$	−18.9416	−	5.07539i	−0.649310	−	0.173982i
$852$	8.37699	−	9.06584i	0.286991	−	0.310591i
$853$	23.3587	+	23.3587i	0.799787	+	0.799787i	0.983062	−	0.183275i	$-0.0586699\pi$
$853$	23.3587	+	23.3587i	0.799787	+	0.799787i	−0.183275	+	0.983062i	$0.558670\pi$
$854$	18.6599	−	33.6108i	0.638530	−	1.15014i
$855$			14.2671i			0.487924i
$856$	−7.32363	−	3.66862i	−0.250316	−	0.125391i
$857$	−5.89990	+	3.40631i	−0.201537	+	0.116357i	−0.597372	−	0.801964i	$-0.703788\pi$
$857$	−5.89990	+	3.40631i	−0.201537	+	0.116357i	0.395835	+	0.918322i	$0.370455\pi$
$858$	0.283922	+	14.3842i	0.00969293	+	0.491069i
$859$	−1.65293	+	0.442902i	−0.0563973	+	0.0151116i	−0.286907	−	0.957958i	$-0.592627\pi$
$859$	−1.65293	+	0.442902i	−0.0563973	+	0.0151116i	0.230510	+	0.973070i	$0.425961\pi$
$860$	2.13053	+	3.37518i	0.0726506	+	0.115093i
$861$	−23.3668	+	23.2295i	−0.796338	+	0.791659i
$862$	−4.81840	−	16.6602i	−0.164115	−	0.567447i
$863$	−1.58824	+	2.75092i	−0.0540645	+	0.0936424i	−0.891791	−	0.452448i	$-0.850551\pi$
$863$	−1.58824	+	2.75092i	−0.0540645	+	0.0936424i	0.837727	+	0.546090i	$0.183884\pi$
$864$	−0.916119	+	2.02463i	−0.0311670	+	0.0688795i
$865$	10.4631	+	18.1226i	0.355755	+	0.616186i
$866$	14.3665	+	3.54717i	0.488194	+	0.120538i
$867$	35.6055	−	35.6055i	1.20923	−	1.20923i
$868$	−6.00042	+	11.3294i	−0.203668	+	0.384543i
$869$	−5.58409	−	5.58409i	−0.189427	−	0.189427i
$870$	−1.08361	+	0.654468i	−0.0367377	+	0.0221885i
$871$	41.6678	−	24.0569i	1.41186	−	0.815138i
$872$	−2.89205	−	4.38730i	−0.0979371	−	0.148573i
$873$	−3.55219	−	2.05086i	−0.120223	−	0.0694111i
$874$	−24.0554	+	43.6316i	−0.813685	+	1.47586i
$875$	2.55761	−	0.677238i	0.0864629	−	0.0228948i
$876$	41.3922	+	9.35733i	1.39851	+	0.316155i
$877$	0.412005	+	1.53762i	0.0139124	+	0.0519218i	0.972533	−	0.232765i	$-0.0747772\pi$
$877$	0.412005	+	1.53762i	0.0139124	+	0.0519218i	−0.958621	+	0.284686i	$0.908111\pi$
$878$	−19.6491	−	18.8884i	−0.663124	−	0.637452i
$879$	38.8579	+	67.3039i	1.31064	+	2.27010i
$880$	−2.19664	+	1.51102i	−0.0740488	+	0.0509363i
$881$	−21.2032			−0.714355			−0.357177	−	0.934037i	$-0.616261\pi$
$881$	−21.2032			−0.714355			−0.357177	+	0.934037i	$0.616261\pi$
$882$	−6.89366	+	27.2298i	−0.232122	+	0.916875i
$883$	−26.5925	+	26.5925i	−0.894909	+	0.894909i	−0.994980	−	0.100071i	$-0.968093\pi$
$883$	−26.5925	+	26.5925i	−0.894909	+	0.894909i	0.100071	+	0.994980i	$0.468093\pi$
$884$	−57.0821	−	52.7448i	−1.91988	−	1.77400i
$885$	1.22775	−	4.58201i	0.0412702	−	0.154023i
$886$	−1.82918	+	0.0361051i	−0.0614525	+	0.00121297i
$887$	19.7490	+	11.4021i	0.663107	+	0.382845i	0.793460	−	0.608623i	$-0.208278\pi$
$887$	19.7490	+	11.4021i	0.663107	+	0.382845i	−0.130353	+	0.991468i	$0.541611\pi$
$888$	−14.3006	−	12.7001i	−0.479898	−	0.426188i
$889$	−11.6689	−	6.78297i	−0.391363	−	0.227494i
$890$	6.84871	+	3.77589i	0.229569	+	0.126568i
$891$	−6.09148	+	1.63221i	−0.204072	+	0.0546810i
$892$	42.8638	+	22.5407i	1.43519	+	0.754719i
$893$	29.8284	+	7.99250i	0.998170	+	0.267459i
$894$	−36.4713	−	9.00495i	−1.21978	−	0.301171i
$895$	14.1958			0.474514
$896$	18.1198	−	23.8259i	0.605340	−	0.795967i
$897$	106.939			3.57058
$898$	−42.9271	−	10.5989i	−1.43250	−	0.353690i
$899$	0.867042	+	0.232323i	0.0289175	+	0.00774842i
$900$	5.02267	+	2.64126i	0.167422	+	0.0880420i
$901$	−83.3304	+	22.3283i	−2.77614	+	0.743864i
$902$	4.25488	+	2.34584i	0.141672	+	0.0781079i
$903$	0.0375876	−	12.7570i	0.00125084	−	0.424527i
$904$	3.07940	+	2.73475i	0.102419	+	0.0909565i
$905$	20.3852	+	11.7694i	0.677625	+	0.391227i
$906$	−22.7014	+	0.448091i	−0.754205	+	0.0148868i
$907$	−2.20271	+	8.22062i	−0.0731398	+	0.272961i	−0.992805	−	0.119742i	$-0.961793\pi$
$907$	−2.20271	+	8.22062i	−0.0731398	+	0.272961i	0.919665	+	0.392703i	$0.128460\pi$
$908$	39.0202	+	36.0553i	1.29493	+	1.19654i
$909$	−18.6223	+	18.6223i	−0.617663	+	0.617663i
$910$	22.7252	−	6.50003i	0.753334	−	0.215474i
$911$	−27.4401			−0.909131			−0.454566	−	0.890713i	$-0.650206\pi$
$911$	−27.4401			−0.909131			−0.454566	+	0.890713i	$0.650206\pi$
$912$	−40.0366	+	27.5402i	−1.32574	+	0.911947i
$913$	−2.03106	−	3.51789i	−0.0672181	−	0.116425i
$914$	−6.96891	−	6.69912i	−0.230511	−	0.221587i
$915$	6.42482	+	23.9778i	0.212398	+	0.792681i
$916$	51.2158	+	11.5781i	1.69222	+	0.382551i
$917$	14.5605	−	53.7069i	0.480829	−	1.77356i
$918$	1.65004	−	2.99284i	0.0544594	−	0.0987784i
$919$	−44.9992	−	25.9803i	−1.48439	−	0.857010i	−0.484543	−	0.874767i	$-0.661014\pi$
$919$	−44.9992	−	25.9803i	−1.48439	−	0.857010i	−0.999842	+	0.0177572i	$0.994347\pi$
$920$	10.9070	+	16.5461i	0.359592	+	0.545509i
$921$	17.3783	−	10.0334i	0.572636	−	0.330612i
$922$	−35.0958	+	21.1968i	−1.15582	+	0.698081i
$923$	11.4105	+	11.4105i	0.375582	+	0.375582i
$924$	8.51579	−	0.311180i	0.280149	−	0.0102371i
$925$	1.97903	−	1.97903i	0.0650702	−	0.0650702i
$926$	5.30324	+	1.30940i	0.174275	+	0.0430294i
$927$	−14.4135	−	24.9648i	−0.473400	−	0.819953i
$928$	−1.90944	−	0.863995i	−0.0626804	−	0.0283620i
$929$	20.5182	−	35.5386i	0.673181	−	1.16598i	−0.303816	−	0.952731i	$-0.598261\pi$
$929$	20.5182	−	35.5386i	0.673181	−	1.16598i	0.976997	−	0.213253i	$-0.0684058\pi$
$930$	−2.29998	−	7.95242i	−0.0754192	−	0.260770i
$931$	25.0346	−	24.7413i	0.820477	−	0.810864i
$932$	25.5015	+	40.3994i	0.835331	+	1.32333i
$933$	−80.5209	+	21.5755i	−2.63613	+	0.706350i
$934$	0.314412	+	15.9289i	0.0102879	+	0.521211i
$935$	3.55090	−	2.05012i	0.116127	−	0.0670459i
$936$	45.3283	+	22.7063i	1.48160	+	0.742178i
$937$			24.5964i			0.803530i	0.915743	+	0.401765i	$0.131603\pi$
$937$			24.5964i			0.803530i	−0.915743	+	0.401765i	$0.868397\pi$
$938$	−14.6613	−	24.4373i	−0.478710	−	0.797906i
$939$	−16.5631	−	16.5631i	−0.540515	−	0.540515i
$940$	8.33585	−	9.02132i	0.271885	−	0.294243i
$941$	49.0638	+	13.1466i	1.59943	+	0.428567i	0.944871	−	0.327442i	$-0.106187\pi$
$941$	49.0638	+	13.1466i	1.59943	+	0.428567i	0.654562	+	0.756009i	$0.272853\pi$
$942$	−33.6293	−	32.3274i	−1.09570	−	1.05328i
$943$	18.0574	−	31.2763i	0.588028	−	1.01850i
$944$	7.40196	−	2.62453i	0.240913	−	0.0854213i
$945$	0.517028	+	0.901644i	0.0168189	+	0.0293305i
$946$	−1.80713	+	0.522653i	−0.0587548	+	0.0169929i
$947$	0.0482778	+	0.180175i	0.00156882	+	0.00585491i	0.966706	−	0.255890i	$-0.0823686\pi$
$947$	0.0482778	+	0.180175i	0.00156882	+	0.00585491i	−0.965137	+	0.261745i	$0.915702\pi$
$948$	−54.6722	+	16.9883i	−1.77567	+	0.551754i
$949$	−14.3588	+	53.5878i	−0.466106	+	1.73953i
$950$	−3.67633	−	6.08692i	−0.119276	−	0.197486i
$951$		−	21.0567i		−	0.682810i
$952$	−30.6689	+	34.3296i	−0.993984	+	1.11263i
$953$			20.4226i			0.661553i	0.943709	+	0.330776i	$0.107311\pi$
$953$			20.4226i			0.661553i	−0.943709	+	0.330776i	$0.892689\pi$
$954$	48.1706	−	29.0937i	1.55958	−	0.941943i
$955$	−2.81267	+	10.4970i	−0.0910159	+	0.339676i
$956$	−13.7500	−	7.23068i	−0.444707	−	0.233857i
$957$	−0.154422	−	0.576313i	−0.00499177	−	0.0186295i
$958$	7.88428	+	27.2608i	0.254730	+	0.880755i
$959$	34.3346	+	0.101164i	1.10872	+	0.00326677i
$960$	2.28345	+	19.1932i	0.0736981	+	0.619459i
$961$	12.5650	−	21.7632i	0.405323	−	0.702040i
$962$	17.3279	−	18.0257i	0.558673	−	0.581172i
$963$	−7.93712	−	2.12674i	−0.255770	−	0.0685334i
$964$	−0.796451	−	20.1673i	−0.0256520	−	0.649545i
$965$	−0.554691	−	0.554691i	−0.0178561	−	0.0178561i
$966$	−1.06340	−	63.3312i	−0.0342142	−	2.03765i
$967$			8.04389i			0.258674i	0.991601	+	0.129337i	$0.0412849\pi$
$967$			8.04389i			0.258674i	−0.991601	+	0.129337i	$0.958715\pi$
$968$	9.42026	+	28.3310i	0.302779	+	0.910593i
$969$	64.7197	−	37.3660i	2.07910	−	1.20037i
$970$	2.04397	−	0.0403448i	0.0656280	−	0.00129539i
$971$	−5.39764	+	1.44629i	−0.173219	+	0.0464138i	−0.344386	−	0.938828i	$-0.611913\pi$
$971$	−5.39764	+	1.44629i	−0.173219	+	0.0464138i	0.171167	+	0.985242i	$0.445246\pi$
$972$	−9.56125	+	42.2943i	−0.306677	+	1.35659i
$973$	9.36363	+	35.3620i	0.300184	+	1.13365i
$974$	−3.04372	+	0.880296i	−0.0975270	+	0.0282065i
$975$	−7.63132	+	13.2178i	−0.244398	+	0.423310i
$976$	−26.6781	+	31.2615i	−0.853944	+	1.00066i
$977$	2.23096	+	3.86414i	0.0713747	+	0.123625i	0.899504	−	0.436912i	$-0.143928\pi$
$977$	2.23096	+	3.86414i	0.0713747	+	0.123625i	−0.828129	+	0.560537i	$0.810595\pi$
$978$	8.54735	−	34.6180i	0.273314	−	1.10696i
$979$	−2.60638	+	2.60638i	−0.0833003	+	0.0833003i
$980$	−4.07542	−	13.3937i	−0.130185	−	0.427846i
$981$	−3.72746	−	3.72746i	−0.119009	−	0.119009i
$982$	−9.89095	−	16.3765i	−0.315633	−	0.522596i
$983$	38.5161	−	22.2373i	1.22847	−	0.709258i	0.261761	−	0.965133i	$-0.415697\pi$
$983$	38.5161	−	22.2373i	1.22847	−	0.709258i	0.966710	+	0.255874i	$0.0823634\pi$
$984$	29.4090	−	19.3860i	0.937523	−	0.618003i
$985$	16.1362	+	9.31623i	0.514142	+	0.296840i
$986$	2.82256	+	1.55616i	0.0898886	+	0.0495582i
$987$	−37.9504	+	10.0490i	−1.20797	+	0.319864i
$988$	−33.9102	−	53.7204i	−1.07883	−	1.70907i
$989$	3.61904	+	13.5064i	0.115079	+	0.429479i
$990$	−1.85355	+	1.92820i	−0.0589097	+	0.0612821i
$991$	−0.898084	−	1.55553i	−0.0285286	−	0.0494130i	0.851409	−	0.524503i	$-0.175749\pi$
$991$	−0.898084	−	1.55553i	−0.0285286	−	0.0494130i	−0.879937	+	0.475090i	$0.842415\pi$
$992$	8.68930	−	10.5988i	0.275885	−	0.336513i
$993$	−60.8366			−1.93059
$994$	6.64407	−	6.87100i	0.210737	−	0.217935i
$995$	−9.50362	+	9.50362i	−0.301285	+	0.301285i
$996$	−29.4257	+	1.16209i	−0.932390	+	0.0368222i
$997$	7.25316	−	27.0692i	0.229710	−	0.857289i	−0.750753	−	0.660583i	$-0.770309\pi$
$997$	7.25316	−	27.0692i	0.229710	−	0.857289i	0.980463	−	0.196706i	$-0.0630244\pi$
$998$	−0.159767	−	8.09423i	−0.00505735	−	0.256219i
$999$	0.952177	+	0.549740i	0.0301255	+	0.0173930i

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

)

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	560.2.cp.a.261.61	yes	256
7.4	even	3	inner	560.2.cp.a.501.17	yes	256
16.13	even	4	inner	560.2.cp.a.541.17	yes	256
112.109	even	12	inner	560.2.cp.a.221.61	✓	256

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
560.2.cp.a.221.61	✓	256	112.109	even	12	inner
560.2.cp.a.261.61	yes	256	1.1	even	1	trivial
560.2.cp.a.501.17	yes	256	7.4	even	3	inner
560.2.cp.a.541.17	yes	256	16.13	even	4	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 $\F_{q}$
Belyi maps

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more

Newspace parameters

Newform invariants

Embedding invariants

$q$ -expansion

Character values

Coefficient data

Twists

This project is supported by grants from the US National Science Foundation, the UK Engineering and Physical Sciences Research Council, and the Simons Foundation.

Label	560.2.cp.a.261.61

Level	$560$
Weight	$2$
Character	560.261
Analytic conductor	$4.472$
Analytic rank	$0$
Dimension	$256$
Inner twists	$4$