LMFDB - Embedded newform 560.2.cp.a.221.61

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [560,2,Mod(221,560)]

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

lf = mfeigenbasis(mf)

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")

//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);

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

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

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

Embedding invariants

Embedding label			221.61
Character	$\chi$	$=$	560.221
Dual form			560.2.cp.a.261.61

$q$-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 $\left(\mathbb{Z}/560\mathbb{Z}\right)^\times$.

$n$	$241$	$337$	$351$	$421$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$1$	$1$	$e\left(\frac{3}{4}\right)$

Coefficient data

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

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

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

$2$	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	−0.859170	−	0.511690i	$-0.829020\pi$
$3$	−2.33375	+	0.625325i	−1.34739	+	0.361032i	−0.488219	+	0.872721i	$0.662353\pi$
$4$	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	0.987044	−	0.160448i	$-0.0512940\pi$
$11$	0.172513	+	0.643828i	0.0520147	+	0.194121i	−0.935030	+	0.354570i	$0.884627\pi$
$12$	−3.54901	+	3.27935i	−1.02451	+	0.946666i
$13$	4.46689	+	4.46689i	1.23889	+	1.23889i	0.960455	+	0.278436i	$0.0898162\pi$
$13$	4.46689	+	4.46689i	1.23889	+	1.23889i	0.278436	+	0.960455i	$0.410184\pi$
$14$	−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	0.203754	+	0.979022i	$0.434686\pi$
$17$	−3.07576	+	5.32737i	−0.745981	+	1.29208i	−0.949735	+	0.313055i	$0.898648\pi$
$18$	2.89285	−	2.78086i	0.681850	−	0.655454i
$19$	−1.30140	+	4.85689i	−0.298561	+	1.11425i	0.639786	+	0.768553i	$0.279023\pi$
$19$	−1.30140	+	4.85689i	−0.298561	+	1.11425i	−0.938348	+	0.345693i	$0.887644\pi$
$20$	−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	−0.974083	−	0.226192i	$-0.927372\pi$
$23$	−6.06786	+	3.50328i	−1.26524	+	0.730485i	−0.291154	+	0.956676i	$0.594039\pi$
$24$	−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	0.682364	−	0.731012i	$-0.260952\pi$
$29$	−0.261977	−	0.261977i	−0.0486479	−	0.0486479i	−0.731012	+	0.682364i	$0.760952\pi$
$30$	3.31723	−	0.819039i	0.605640	−	0.149535i
$31$	−1.21140	+	2.09821i	−0.217574	+	0.376850i	−0.954066	−	0.299597i	$-0.903148\pi$
$31$	−1.21140	+	2.09821i	−0.217574	+	0.376850i	0.736492	+	0.676447i	$0.236481\pi$
$32$	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	0.474096	−	0.880473i	$-0.342775\pi$
$37$	2.70341	+	0.724376i	0.444438	+	0.119087i	−0.0296579	+	0.999560i	$0.509442\pi$
$38$	−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	$-0.868144\pi$
$41$		−	5.15441i		−	0.804984i	0.915424	−	0.402492i	$-0.131856\pi$
$42$	4.65086	−	7.75198i	0.717643	−	1.19616i
$43$	−1.41116	+	1.41116i	−0.215200	+	0.215200i	−0.806472	−	0.591272i	$-0.798626\pi$
$43$	−1.41116	+	1.41116i	−0.215200	+	0.215200i	0.591272	+	0.806472i	$0.298626\pi$
$44$	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	0.550337	−	0.834942i	$-0.314499\pi$
$47$	−3.07074	−	5.31867i	−0.447913	−	0.775808i	−0.998250	+	0.0591348i	$0.981166\pi$
$48$	−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	0.508969	+	0.860785i	$0.330027\pi$
$53$	3.62973	+	13.5463i	0.498581	+	1.86073i	−0.0103879	+	0.999946i	$0.503307\pi$
$54$	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	0.991083	−	0.133247i	$-0.0425403\pi$
$59$	0.508158	+	1.89647i	0.0661565	+	0.246899i	−0.924926	+	0.380146i	$0.875874\pi$
$60$	4.27684	−	2.24905i	0.552138	−	0.290352i
$61$	2.65920	−	9.92428i	0.340476	−	1.27067i	−0.557333	−	0.830289i	$-0.688175\pi$
$61$	2.65920	−	9.92428i	0.340476	−	1.27067i	0.897809	−	0.440385i	$-0.145158\pi$
$62$	−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	0.220292	−	0.975434i	$-0.429299\pi$
$67$	7.35689	−	1.97127i	0.898787	−	0.240829i	0.678495	+	0.734605i	$0.262632\pi$
$68$	−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	$-0.951564\pi$
$71$		−	2.55447i		−	0.303160i	0.988445	−	0.151580i	$-0.0484360\pi$
$72$	2.53219	−	7.61544i	0.298421	−	0.897488i
$73$	−7.60559	−	4.39109i	−0.890167	−	0.513938i	−0.0161698	−	0.999869i	$-0.505147\pi$
$73$	−7.60559	−	4.39109i	−0.890167	−	0.513938i	−0.873997	+	0.485931i	$0.838481\pi$
$74$	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	0.978877	+	0.204449i	$0.0655404\pi$
$79$	5.92395	+	10.2606i	0.666497	+	1.15441i	−0.312380	+	0.949957i	$0.601126\pi$
$80$	−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	0.902888	−	0.429876i	$-0.141443\pi$
$83$	4.30934	+	4.30934i	0.473012	+	0.473012i	−0.429876	+	0.902888i	$0.641443\pi$
$84$	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	−0.731866	−	0.681448i	$-0.761350\pi$
$89$	−4.78914	+	2.76501i	−0.507648	+	0.293090i	0.224219	+	0.974539i	$0.428017\pi$
$90$	−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	−0.976288	−	0.216476i	$-0.930544\pi$
$101$	−2.40228	−	8.96544i	−0.239036	−	0.892094i	0.737252	−	0.675618i	$-0.236123\pi$
$102$	0.414796	−	21.0147i	0.0410710	−	2.08076i
$103$	−8.79848	+	5.07980i	−0.866940	+	0.500528i	−0.866330	−	0.499472i	$-0.833527\pi$
$103$	−8.79848	+	5.07980i	−0.866940	+	0.500528i	−0.000609787		1.00000i	$0.500194\pi$
$104$	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	0.121057	−	0.992646i	$-0.461372\pi$
$107$	−2.79732	−	0.749539i	−0.270427	−	0.0724606i	−0.391484	+	0.920185i	$0.628038\pi$
$108$	0.233140	−	0.750299i	0.0224339	−	0.0721975i
$109$	−1.79453	+	0.480842i	−0.171885	+	0.0460563i	−0.343735	−	0.939067i	$-0.611692\pi$
$109$	−1.79453	+	0.480842i	−0.171885	+	0.0460563i	0.171850	+	0.985123i	$0.445025\pi$
$110$	−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	−0.143495	−	0.989651i	$-0.545834\pi$
$131$	5.44350	−	20.3154i	0.475601	−	1.77497i	0.619096	−	0.785316i	$-0.287499\pi$
$132$	−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	−0.0639549	−	0.997953i	$-0.520371\pi$
$137$	−11.2387	−	6.48865i	−0.960185	−	0.554363i	−0.896230	+	0.443590i	$0.853705\pi$
$138$	12.3770	−	20.4927i	1.05360	−	1.74445i
$139$	−9.77660	+	9.77660i	−0.829240	+	0.829240i	−0.987412	−	0.158171i	$-0.949440\pi$
$139$	−9.77660	+	9.77660i	−0.829240	+	0.829240i	0.158171	+	0.987412i	$0.449440\pi$
$140$	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	0.666095	−	0.745867i	$-0.267965\pi$
$149$	10.6199	+	2.84559i	0.870016	+	0.233120i	0.203921	+	0.978987i	$0.434631\pi$
$150$	−3.41618	−	0.0674299i	−0.278930	−	0.00550563i
$151$	5.75498	+	3.32264i	0.468334	+	0.270392i	0.715542	−	0.698570i	$-0.246180\pi$
$151$	5.75498	+	3.32264i	0.468334	+	0.270392i	−0.247208	+	0.968962i	$0.579513\pi$
$152$	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	0.309180	−	0.951003i	$-0.399945\pi$
$157$	13.1870	−	3.53346i	1.05244	−	0.282000i	0.743260	+	0.669003i	$0.233279\pi$
$158$	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	−0.775792	−	0.630989i	$-0.782649\pi$
$163$	2.70099	−	10.0802i	0.211558	−	0.789545i	0.987350	−	0.158556i	$-0.0506839\pi$
$164$	−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	$-0.962629\pi$
$167$		−	3.02745i		−	0.234271i	0.993116	−	0.117136i	$-0.0373712\pi$
$168$	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	0.379427	+	0.925222i	$0.376121\pi$
$173$	−5.41608	+	20.2131i	−0.411777	+	1.53677i	−0.791204	+	0.611552i	$0.790546\pi$
$174$	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	−0.731839	−	0.681477i	$-0.761338\pi$
$179$	−13.7121	+	3.67415i	−1.02489	+	0.274619i	−0.293052	+	0.956096i	$0.594671\pi$
$180$	−4.16792	+	3.85122i	−0.310658	+	0.287053i
$181$	−16.6444	+	16.6444i	−1.23717	+	1.23717i	−0.276016	+	0.961153i	$0.589014\pi$
$181$	−16.6444	+	16.6444i	−1.23717	+	1.23717i	−0.961153	+	0.276016i	$0.910986\pi$
$182$	−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	0.992865	−	0.119242i	$-0.0380464\pi$
$191$	5.43366	+	9.41138i	0.393166	+	0.680984i	−0.599699	+	0.800226i	$0.704713\pi$
$192$	2.76193	+	19.1302i	0.199325	+	1.38061i
$193$	0.392225	−	0.679354i	0.0282330	−	0.0489010i	−0.851564	−	0.524251i	$-0.824345\pi$
$193$	0.392225	−	0.679354i	0.0282330	−	0.0489010i	0.879797	+	0.475350i	$0.157679\pi$
$194$	−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	−0.998226	−	0.0595365i	$-0.981038\pi$
$197$	−13.1751	+	13.1751i	−0.938690	+	0.938690i	0.0595365	+	0.998226i	$0.481038\pi$
$198$	2.28945	+	1.38276i	0.162704	+	0.0982685i
$199$	11.6395	+	6.72008i	0.825103	+	0.476374i	0.852173	−	0.523260i	$-0.175284\pi$
$199$	11.6395	+	6.72008i	0.825103	+	0.476374i	−0.0270699	+	0.999634i	$0.508618\pi$
$200$	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	0.909096	−	0.416587i	$-0.136774\pi$
$211$	7.15409	+	7.15409i	0.492508	+	0.492508i	−0.416587	+	0.909096i	$0.636774\pi$
$212$	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	0.729330	−	0.684163i	$-0.239832\pi$
$227$	25.6587	−	6.87523i	1.70303	−	0.456325i	0.973699	+	0.227837i	$0.0731655\pi$
$228$	−11.3087	−	21.5049i	−0.748939	−	1.42420i
$229$	25.3595	+	6.79506i	1.67580	+	0.449030i	0.966666	−	0.256040i	$-0.0824179\pi$
$229$	25.3595	+	6.79506i	1.67580	+	0.449030i	0.709137	+	0.705070i	$0.249085\pi$
$230$	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	0.366279	−	0.930505i	$-0.380632\pi$
$233$	20.6871	−	11.9437i	1.35526	−	0.782460i	0.988981	+	0.148046i	$0.0472982\pi$
$234$	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	−0.981518	−	0.191372i	$-0.938706\pi$
$241$	−5.04575	+	8.73950i	−0.325026	+	0.562961i	0.656492	+	0.754333i	$0.272040\pi$
$242$	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	−0.105757	−	0.994392i	$-0.533727\pi$
$251$	14.0786	−	14.0786i	0.888635	−	0.888635i	0.994392	+	0.105757i	$0.0337265\pi$
$252$	−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	0.704588	−	0.709617i	$-0.251132\pi$
$257$	−4.20422	−	7.28192i	−0.262252	−	0.454234i	−0.966840	+	0.255383i	$0.917798\pi$
$258$	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	−0.0287312	−	0.999587i	$-0.509147\pi$
$263$	−14.7377	−	8.50881i	−0.908765	−	0.524676i	−0.880033	+	0.474912i	$0.842480\pi$
$264$	−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	0.601731	−	0.798699i	$-0.294478\pi$
$269$	24.9658	−	6.68958i	1.52219	−	0.407871i	0.920464	+	0.390828i	$0.127811\pi$
$270$	−0.400519	+	0.385014i	−0.0243748	+	0.0234312i
$271$	0.00346800	+	0.00600675i	0.000210666	+	0.000364884i	0.866131	−	0.499818i	$-0.166600\pi$
$271$	0.00346800	+	0.00600675i	0.000210666	+	0.000364884i	−0.865920	+	0.500182i	$0.833266\pi$
$272$	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	0.622108	+	0.782931i	$0.286276\pi$
$277$	7.90245	+	29.4923i	0.474812	+	1.77202i	−0.147296	+	0.989092i	$0.547057\pi$
$278$	−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	$-0.935293\pi$
$281$		−	6.76844i		−	0.403771i	0.979409	−	0.201886i	$-0.0647069\pi$
$282$	17.9625	+	10.8488i	1.06965	+	0.646037i
$283$	−3.19075	−	11.9080i	−0.189670	−	0.707859i	−0.993582	−	0.113111i	$-0.963918\pi$
$283$	−3.19075	−	11.9080i	−0.189670	−	0.707859i	0.803912	−	0.594748i	$-0.202748\pi$
$284$	−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	−0.422331	+	0.906442i	$0.638788\pi$
$293$	−22.7449	+	22.7449i	−1.32877	+	1.32877i	−0.906442	+	0.422331i	$0.861212\pi$
$294$	−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	0.519367	−	0.854551i	$-0.326168\pi$
$307$	−5.87291	−	5.87291i	−0.335184	−	0.335184i	−0.854551	+	0.519367i	$0.826168\pi$
$308$	−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	0.950922	+	0.309431i	$0.100138\pi$
$311$	29.8803	+	17.2514i	1.69436	+	0.978238i	0.743436	+	0.668807i	$0.233195\pi$
$312$	−42.2864	+	8.68604i	−2.39400	+	0.491750i
$313$	8.39607	−	4.84747i	0.474574	−	0.273995i	−0.243578	−	0.969881i	$-0.578321\pi$
$313$	8.39607	−	4.84747i	0.474574	−	0.273995i	0.718153	+	0.695886i	$0.244988\pi$
$314$	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	−0.873203	−	0.487357i	$-0.837961\pi$
$317$	2.25567	−	8.41829i	0.126691	−	0.472818i	0.999894	+	0.0145384i	$0.00462787\pi$
$318$	−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	0.855267	−	0.518188i	$-0.173393\pi$
$331$	24.3220	+	6.51705i	1.33686	+	0.358209i	0.481589	+	0.876397i	$0.340060\pi$
$332$	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	−0.955562	−	0.294790i	$-0.904750\pi$
$347$	−5.13043	−	19.1470i	−0.275416	−	1.02787i	0.680146	−	0.733076i	$-0.261916\pi$
$348$	1.78887	+	0.0706466i	0.0958937	+	0.00378706i
$349$	−4.39147	−	4.39147i	−0.235070	−	0.235070i	0.579735	−	0.814805i	$-0.303156\pi$
$349$	−4.39147	−	4.39147i	−0.235070	−	0.235070i	−0.814805	+	0.579735i	$0.803156\pi$
$350$	−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	−0.925588	−	0.378531i	$-0.876429\pi$
$353$	−2.53598	+	4.39244i	−0.134977	+	0.233786i	0.790612	+	0.612318i	$0.209763\pi$
$354$	−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	−0.353199	−	0.935548i	$-0.614906\pi$
$359$	5.31302	−	3.06747i	0.280410	−	0.161895i	0.633609	+	0.773653i	$0.281573\pi$
$360$	−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	−0.722698	−	0.691164i	$-0.757098\pi$
$367$	4.54442	−	7.87117i	0.237217	−	0.410872i	0.959915	+	0.280293i	$0.0904315\pi$
$368$	−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	−0.0650761	−	0.997880i	$-0.520729\pi$
$373$	−11.9814	−	3.21041i	−0.620374	−	0.166229i	−0.555298	+	0.831652i	$0.687396\pi$
$374$	−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	0.305083	−	0.952326i	$-0.401316\pi$
$379$	24.4791	−	24.4791i	1.25741	−	1.25741i	0.952326	−	0.305083i	$-0.0986841\pi$
$380$	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	0.855027	−	0.518584i	$-0.173540\pi$
$383$	−0.422585	−	0.731939i	−0.0215931	−	0.0374003i	−0.876620	+	0.481183i	$0.840207\pi$
$384$	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	0.923308	−	0.384061i	$-0.125475\pi$
$389$	−1.34770	−	5.02967i	−0.0683309	−	0.255014i	−0.991638	+	0.129047i	$0.958808\pi$
$390$	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	−0.888686	−	0.458517i	$-0.848381\pi$
$397$	2.19566	−	8.19433i	0.110197	−	0.411262i	0.998883	+	0.0472555i	$0.0150475\pi$
$398$	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	−0.995555	−	0.0941844i	$-0.969976\pi$
$401$	−11.6013	−	20.0941i	−0.579343	−	1.00345i	0.416211	−	0.909268i	$-0.363358\pi$
$402$	−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	0.905487	−	0.424373i	$-0.139506\pi$
$409$	20.0359	+	11.5677i	0.990713	+	0.571988i	0.0852255	+	0.996362i	$0.472839\pi$
$410$	−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	0.894644	−	0.446779i	$-0.147429\pi$
$419$	9.16757	+	9.16757i	0.447865	+	0.447865i	−0.446779	+	0.894644i	$0.647429\pi$
$420$	−6.79237	+	10.8310i	−0.331434	+	0.528500i
$421$	−4.48614	+	4.48614i	−0.218641	+	0.218641i	−0.807926	−	0.589284i	$-0.799410\pi$
$421$	−4.48614	+	4.48614i	−0.218641	+	0.218641i	0.589284	+	0.807926i	$0.299410\pi$
$422$	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	−0.975067	−	0.221912i	$-0.928770\pi$
$431$	−6.13166	+	10.6203i	−0.295352	+	0.511564i	0.679715	+	0.733476i	$0.262103\pi$
$432$	−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	−0.842278	−	0.539043i	$-0.818786\pi$
$439$	−16.6905	+	9.63624i	−0.796592	+	0.459913i	0.0456860	+	0.998956i	$0.485453\pi$
$440$	−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	0.229012	−	0.973424i	$-0.426451\pi$
$443$	−1.24960	−	0.334828i	−0.0593701	−	0.0159082i	−0.288382	+	0.957515i	$0.593117\pi$
$444$	−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	−0.632022	−	0.774950i	$-0.717775\pi$
$457$	−5.91958	+	3.41767i	−0.276906	+	0.159872i	0.355116	+	0.934822i	$0.384441\pi$
$458$	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	0.0442358	−	0.999021i	$-0.485915\pi$
$461$	−20.5001	−	20.5001i	−0.954785	−	0.954785i	−0.999021	+	0.0442358i	$0.985915\pi$
$462$	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	−0.865073	−	0.501647i	$-0.832728\pi$
$467$	2.91577	−	10.8818i	0.134926	−	0.503549i	0.999998	−	0.00190252i	$-0.000605590\pi$
$468$	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	−0.540452	−	0.841375i	$-0.681747\pi$
$479$	10.0331	−	17.3779i	0.458426	−	0.794017i	0.998878	+	0.0473578i	$0.0150801\pi$
$480$	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	0.455394	−	0.890290i	$-0.349498\pi$
$487$	−1.94028	−	1.12022i	−0.0879224	−	0.0507620i	−0.543317	+	0.839528i	$0.682832\pi$
$488$	−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	−0.889206	−	0.457506i	$-0.848743\pi$
$491$	−9.56584	+	9.56584i	−0.431700	+	0.431700i	0.457506	+	0.889206i	$0.348743\pi$
$492$	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	−0.991127	−	0.132917i	$-0.957565\pi$
$499$	−1.48164	+	5.52954i	−0.0663272	+	0.247536i	0.924800	+	0.380454i	$0.124232\pi$
$500$	−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	$0.105616\pi$
$503$			14.6115i			0.651496i	−0.945457	+	0.325748i	$0.894384\pi$
$504$	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	−0.999936	−	0.0113333i	$-0.996392\pi$
$509$	−2.89456	+	10.8027i	−0.128299	+	0.478820i	0.871636	+	0.490153i	$0.163059\pi$
$510$	−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	−0.000927970	−	1.00000i	$-0.500295\pi$
$521$	−19.7992	−	11.4311i	−0.867417	−	0.500803i	−0.866489	+	0.499196i	$0.833629\pi$
$522$	−1.48638	−	0.0293388i	−0.0650571	−	0.00128412i
$523$	5.39339	+	1.44515i	0.235836	+	0.0631922i	0.374801	−	0.927105i	$-0.377711\pi$
$523$	5.39339	+	1.44515i	0.235836	+	0.0631922i	−0.138965	+	0.990297i	$0.544378\pi$
$524$	−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	0.641468	+	0.767150i	$0.278326\pi$
$541$	−6.92280	+	25.8362i	−0.297634	+	1.11079i	−0.939103	+	0.343637i	$0.888341\pi$
$542$	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	0.426506	−	0.904485i	$-0.359744\pi$
$547$	−11.1790	−	11.1790i	−0.477978	−	0.477978i	−0.904485	+	0.426506i	$0.859744\pi$
$548$	−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	−0.101904	−	0.994794i	$-0.532494\pi$
$557$	7.25114	−	1.94294i	0.307241	−	0.0823249i	0.409145	+	0.912469i	$0.365827\pi$
$558$	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	−0.265543	−	0.964099i	$-0.585551\pi$
$563$	−0.319386	+	0.0855792i	−0.0134605	+	0.00360673i	0.252083	+	0.967706i	$0.418885\pi$
$564$	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	0.0331871	−	0.999449i	$-0.489434\pi$
$569$	21.8340	−	12.6059i	0.915329	−	0.528465i	0.882142	+	0.470984i	$0.156101\pi$
$570$	−0.339052	+	17.1773i	−0.0142013	+	0.719477i
$571$	1.51125	+	5.64006i	0.0632438	+	0.236029i	0.990311	−	0.138865i	$-0.0443456\pi$
$571$	1.51125	+	5.64006i	0.0632438	+	0.236029i	−0.927067	+	0.374895i	$0.877679\pi$
$572$	−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	−0.929716	−	0.368277i	$-0.879948\pi$
$577$	−3.50514	+	6.07109i	−0.145921	+	0.252743i	0.783795	+	0.621019i	$0.213281\pi$
$578$	−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	−0.117577	−	0.993064i	$-0.537513\pi$
$587$	21.2114	−	21.2114i	0.875487	−	0.875487i	0.993064	+	0.117577i	$0.0375127\pi$
$588$	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	0.616233	−	0.787564i	$-0.288658\pi$
$593$	−9.10588	−	15.7718i	−0.373934	−	0.647672i	−0.990167	+	0.139892i	$0.955325\pi$
$594$	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	0.927038	−	0.374969i	$-0.122347\pi$
$599$	26.0855	+	15.0605i	1.06582	+	0.615354i	0.138786	+	0.990322i	$0.455680\pi$
$600$	−6.10996	+	3.06066i	−0.249438	+	0.124951i
$601$			31.9836i			1.30464i	0.757945	+	0.652319i	$0.226204\pi$
$601$			31.9836i			1.30464i	−0.757945	+	0.652319i	$0.773796\pi$
$602$	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	0.752214	+	0.658919i	$0.228986\pi$
$607$	23.3254	+	40.4007i	0.946748	+	1.63981i	0.194534	+	0.980896i	$0.437681\pi$
$608$	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	0.887788	−	0.460252i	$-0.152241\pi$
$613$	−2.75281	−	10.2736i	−0.111185	−	0.414948i	−0.998973	+	0.0453040i	$0.985574\pi$
$614$	−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	$-0.745651\pi$
$617$		−	35.6050i		−	1.43340i	0.697380	−	0.716702i	$-0.254349\pi$
$618$	17.9468	−	29.7146i	0.721926	−	1.19530i
$619$	7.38406	+	27.5577i	0.296790	+	1.10764i	0.939785	+	0.341766i	$0.111025\pi$
$619$	7.38406	+	27.5577i	0.296790	+	1.10764i	−0.642995	+	0.765871i	$0.722308\pi$
$620$	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	$-0.777001\pi$
$631$		−	32.3871i		−	1.28931i	0.764473	−	0.644656i	$-0.222999\pi$
$632$	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	0.479206	+	0.877703i	$0.340925\pi$
$641$	−13.1783	+	22.8254i	−0.520510	+	0.901549i	−0.999716	+	0.0238469i	$0.992409\pi$
$642$	9.60667	−	2.37193i	0.379145	−	0.0936128i
$643$	17.1546	+	17.1546i	0.676510	+	0.676510i	0.959209	−	0.282699i	$-0.0912297\pi$
$643$	17.1546	+	17.1546i	0.676510	+	0.676510i	−0.282699	+	0.959209i	$0.591230\pi$
$644$	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	0.0524166	−	0.998625i	$-0.483308\pi$
$647$	−19.9982	−	11.5460i	−0.786210	−	0.453919i	−0.838627	+	0.544707i	$0.816641\pi$
$648$	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	−0.940199	−	0.340624i	$-0.889362\pi$
$653$	1.13330	−	4.22953i	0.0443494	−	0.165514i	0.984549	+	0.175110i	$0.0560282\pi$
$654$	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	0.979355	−	0.202148i	$-0.0647922\pi$
$659$	19.9517	+	19.9517i	0.777207	+	0.777207i	−0.202148	+	0.979355i	$0.564792\pi$
$660$	2.18581	+	2.36556i	0.0850827	+	0.0920793i
$661$	−3.30191	−	12.3229i	−0.128429	−	0.479305i	0.871509	−	0.490379i	$-0.163142\pi$
$661$	−3.30191	−	12.3229i	−0.128429	−	0.479305i	−0.999939	+	0.0110739i	$0.996475\pi$
$662$	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	−0.0846901	−	0.996407i	$-0.526990\pi$
$677$	−17.0748	−	4.57518i	−0.656238	−	0.175838i	−0.571547	+	0.820569i	$0.693657\pi$
$678$	−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	−0.961305	−	0.275486i	$-0.911161\pi$
$683$	−6.96566	−	25.9962i	−0.266533	−	0.994716i	0.694772	−	0.719230i	$-0.255505\pi$
$684$	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	−0.989810	−	0.142394i	$-0.954520\pi$
$691$	−1.61434	+	6.02480i	−0.0614124	+	0.229194i	0.928398	+	0.371588i	$0.121187\pi$
$692$	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	0.938435	+	0.345455i	$0.112276\pi$
$701$	33.9928	+	33.9928i	1.28389	+	1.28389i	0.345455	+	0.938435i	$0.387724\pi$
$702$	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	0.0508529	−	0.998706i	$-0.483806\pi$
$709$	−10.7696	−	2.88570i	−0.404460	−	0.108375i	−0.455313	+	0.890331i	$0.650473\pi$
$710$	−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	0.873475	−	0.486869i	$-0.161861\pi$
$719$	0.404807	+	0.701146i	0.0150967	+	0.0261483i	−0.858378	+	0.513017i	$0.828528\pi$
$720$	−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	$-0.771528\pi$
$727$		−	35.4672i		−	1.31541i	0.753277	−	0.657704i	$-0.228472\pi$
$728$	−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	0.724895	+	0.688860i	$0.241888\pi$
$733$	−6.69573	+	24.9888i	−0.247312	+	0.922982i	−0.972207	+	0.234122i	$0.924778\pi$
$734$	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	−0.376046	−	0.926601i	$-0.622716\pi$
$739$	−6.48108	+	1.73660i	−0.238411	+	0.0638819i	0.137635	+	0.990483i	$0.456050\pi$
$740$	−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	$0.0795337\pi$
$743$			13.4802i			0.494541i	−0.968946	+	0.247271i	$0.920466\pi$
$744$	−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	0.999727	−	0.0233823i	$-0.00744348\pi$
$751$	13.1435	+	22.7652i	0.479614	+	0.830715i	−0.520113	+	0.854097i	$0.674110\pi$
$752$	−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	−0.631113	−	0.775691i	$-0.717401\pi$
$757$	3.97788	−	3.97788i	0.144579	−	0.144579i	0.775691	+	0.631113i	$0.217401\pi$
$758$	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	−0.745616	−	0.666376i	$-0.767845\pi$
$761$	−14.9331	+	8.62165i	−0.541325	+	0.312534i	0.204290	+	0.978910i	$0.434511\pi$
$762$	−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	−0.999795	−	0.0202695i	$-0.993548\pi$
$773$	−4.00589	−	14.9502i	−0.144082	−	0.537721i	0.855713	−	0.517451i	$-0.173119\pi$
$774$	−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	−0.740397	−	0.672170i	$-0.765363\pi$
$787$	−29.3304	+	7.85905i	−1.04552	+	0.280145i	−0.305118	+	0.952315i	$0.598696\pi$
$788$	−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	0.999930	+	0.0118570i	$0.00377428\pi$
$797$	28.5639	+	28.5639i	1.01179	+	1.01179i	0.0118570	+	0.999930i	$0.496226\pi$
$798$	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	0.462079	−	0.886839i	$-0.347104\pi$
$809$	−2.13057	−	1.23008i	−0.0749067	−	0.0432474i	−0.536986	+	0.843591i	$0.680437\pi$
$810$	6.91756	−	11.4535i	0.243058	−	0.402433i
$811$	−4.70638	+	4.70638i	−0.165263	+	0.165263i	−0.784894	−	0.619630i	$-0.787283\pi$
$811$	−4.70638	+	4.70638i	−0.165263	+	0.165263i	0.619630	+	0.784894i	$0.287283\pi$
$812$	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	0.373834	−	0.927496i	$-0.378043\pi$
$821$	6.70013	+	1.79530i	0.233836	+	0.0626562i	−0.139998	+	0.990152i	$0.544710\pi$
$822$	44.3328	+	0.875059i	1.54628	+	0.0305212i
$823$	−42.4229	−	24.4929i	−1.47877	−	0.853769i	−0.479059	−	0.877783i	$-0.659022\pi$
$823$	−42.4229	−	24.4929i	−1.47877	−	0.853769i	−0.999712	+	0.0240139i	$0.992355\pi$
$824$	−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	−0.0483886	+	0.998829i	$0.515409\pi$
$827$	−30.1155	+	30.1155i	−1.04722	+	1.04722i	−0.998829	+	0.0483886i	$0.984591\pi$
$828$	−1.56902	+	39.7299i	−0.0545273	+	1.38071i
$829$	−47.9217	+	12.8406i	−1.66439	+	0.445972i	−0.963590	−	0.267386i	$-0.913840\pi$
$829$	−47.9217	+	12.8406i	−1.66439	+	0.445972i	−0.700800	+	0.713357i	$0.747174\pi$
$830$	−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	$0.0127204\pi$
$839$			2.31443i			0.0799031i	−0.999202	+	0.0399516i	$0.987280\pi$
$840$	−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	−0.183275	−	0.983062i	$-0.558670\pi$
$853$	23.3587	−	23.3587i	0.799787	−	0.799787i	0.983062	+	0.183275i	$0.0586699\pi$
$854$	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	0.395835	−	0.918322i	$-0.370455\pi$
$857$	−5.89990	−	3.40631i	−0.201537	−	0.116357i	−0.597372	+	0.801964i	$0.703788\pi$
$858$	0.283922	−	14.3842i	0.00969293	−	0.491069i
$859$	−1.65293	−	0.442902i	−0.0563973	−	0.0151116i	0.230510	−	0.973070i	$-0.425961\pi$
$859$	−1.65293	−	0.442902i	−0.0563973	−	0.0151116i	−0.286907	+	0.957958i	$0.592627\pi$
$860$	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	0.837727	−	0.546090i	$-0.183884\pi$
$863$	−1.58824	−	2.75092i	−0.0540645	−	0.0936424i	−0.891791	+	0.452448i	$0.850551\pi$
$864$	−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	−0.958621	−	0.284686i	$-0.908111\pi$
$877$	0.412005	−	1.53762i	0.0139124	−	0.0519218i	0.972533	+	0.232765i	$0.0747772\pi$
$878$	−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	0.100071	−	0.994980i	$-0.468093\pi$
$883$	−26.5925	−	26.5925i	−0.894909	−	0.894909i	−0.994980	+	0.100071i	$0.968093\pi$
$884$	−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	−0.130353	−	0.991468i	$-0.541611\pi$
$887$	19.7490	−	11.4021i	0.663107	−	0.382845i	0.793460	+	0.608623i	$0.208278\pi$
$888$	−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	0.919665	−	0.392703i	$-0.128460\pi$
$907$	−2.20271	−	8.22062i	−0.0731398	−	0.272961i	−0.992805	+	0.119742i	$0.961793\pi$
$908$	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	−0.999842	−	0.0177572i	$-0.994347\pi$
$919$	−44.9992	+	25.9803i	−1.48439	+	0.857010i	−0.484543	+	0.874767i	$0.661014\pi$
$920$	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	0.976997	+	0.213253i	$0.0684058\pi$
$929$	20.5182	+	35.5386i	0.673181	+	1.16598i	−0.303816	+	0.952731i	$0.598261\pi$
$930$	−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	$-0.868397\pi$
$937$		−	24.5964i		−	0.803530i	0.915743	−	0.401765i	$-0.131603\pi$
$938$	−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	0.654562	−	0.756009i	$-0.272853\pi$
$941$	49.0638	−	13.1466i	1.59943	−	0.428567i	0.944871	+	0.327442i	$0.106187\pi$
$942$	−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	−0.965137	−	0.261745i	$-0.915702\pi$
$947$	0.0482778	−	0.180175i	0.00156882	−	0.00585491i	0.966706	+	0.255890i	$0.0823686\pi$
$948$	−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	$-0.892689\pi$
$953$		−	20.4226i		−	0.661553i	0.943709	−	0.330776i	$-0.107311\pi$
$954$	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	$-0.958715\pi$
$967$		−	8.04389i		−	0.258674i	0.991601	−	0.129337i	$-0.0412849\pi$
$968$	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	0.171167	−	0.985242i	$-0.445246\pi$
$971$	−5.39764	−	1.44629i	−0.173219	−	0.0464138i	−0.344386	+	0.938828i	$0.611913\pi$
$972$	−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	−0.828129	−	0.560537i	$-0.810595\pi$
$977$	2.23096	−	3.86414i	0.0713747	−	0.123625i	0.899504	+	0.436912i	$0.143928\pi$
$978$	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	0.966710	−	0.255874i	$-0.0823634\pi$
$983$	38.5161	+	22.2373i	1.22847	+	0.709258i	0.261761	+	0.965133i	$0.415697\pi$
$984$	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	−0.879937	−	0.475090i	$-0.842415\pi$
$991$	−0.898084	+	1.55553i	−0.0285286	+	0.0494130i	0.851409	+	0.524503i	$0.175749\pi$
$992$	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	0.980463	+	0.196706i	$0.0630244\pi$
$997$	7.25316	+	27.0692i	0.229710	+	0.857289i	−0.750753	+	0.660583i	$0.770309\pi$
$998$	−0.159767	+	8.09423i	−0.00505735	+	0.256219i
$999$	0.952177	−	0.549740i	0.0301255	−	0.0173930i

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
560.2.cp.a.221.61	✓	256	1.1	even	1	trivial
560.2.cp.a.261.61	yes	256	112.37	even	12	inner
560.2.cp.a.501.17	yes	256	16.5	even	4	inner
560.2.cp.a.541.17	yes	256	7.2	even	3	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:	\( N \)	\(=\)	\( 560 = 2^{4} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	560.cp (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(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

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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