LMFDB - Embedded newform 165.2.s.a.49.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [165,2,Mod(4,165)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(165, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 5, 2]))

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

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

chi := DirichletCharacter("165.4");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 165 = 3 \cdot 5 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	165.s (of order $10$, 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:	$1.31753163335$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$12$ over $\Q(\zeta_{10})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			49.4
Character	$\chi$	$=$	165.49
Dual form			165.2.s.a.64.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.20873 + 0.392740i) q^{2} +(-0.587785 + 0.809017i) q^{3} +(-0.311255 + 0.226140i) q^{4} +(-1.58253 - 1.57975i) q^{5} +(0.392740 - 1.20873i) q^{6} +(-0.284071 - 0.390991i) q^{7} +(1.78148 - 2.45199i) q^{8} +(-0.309017 - 0.951057i) q^{9} +O(q^{10})$	\(q+(-1.20873 + 0.392740i) q^{2} +(-0.587785 + 0.809017i) q^{3} +(-0.311255 + 0.226140i) q^{4} +(-1.58253 - 1.57975i) q^{5} +(0.392740 - 1.20873i) q^{6} +(-0.284071 - 0.390991i) q^{7} +(1.78148 - 2.45199i) q^{8} +(-0.309017 - 0.951057i) q^{9} +(2.53328 + 1.28796i) q^{10} +(-0.982188 - 3.16786i) q^{11} -0.384732i q^{12} +(2.99024 - 0.971588i) q^{13} +(0.496923 + 0.361035i) q^{14} +(2.20823 - 0.351741i) q^{15} +(-0.952550 + 2.93165i) q^{16} +(-2.38727 - 0.775672i) q^{17} +(0.747035 + 1.02821i) q^{18} +(-3.00966 - 2.18665i) q^{19} +(0.849814 + 0.133831i) q^{20} +0.483291 q^{21} +(2.43134 + 3.44333i) q^{22} -8.53218i q^{23} +(0.936579 + 2.88249i) q^{24} +(0.00879819 + 4.99999i) q^{25} +(-3.23281 + 2.34877i) q^{26} +(0.951057 + 0.309017i) q^{27} +(0.176837 + 0.0574579i) q^{28} +(-8.07636 + 5.86782i) q^{29} +(-2.53101 + 1.29242i) q^{30} +(-1.78916 - 5.50647i) q^{31} +2.14399i q^{32} +(3.14016 + 1.06741i) q^{33} +3.19020 q^{34} +(-0.168115 + 1.06752i) q^{35} +(0.311255 + 0.226140i) q^{36} +(-1.88541 - 2.59504i) q^{37} +(4.49665 + 1.46105i) q^{38} +(-0.971588 + 2.99024i) q^{39} +(-6.69277 + 1.06607i) q^{40} +(6.36344 + 4.62331i) q^{41} +(-0.584168 + 0.189808i) q^{42} +5.97016i q^{43} +(1.02209 + 0.763898i) q^{44} +(-1.01340 + 1.99324i) q^{45} +(3.35092 + 10.3131i) q^{46} +(-3.60369 + 4.96006i) q^{47} +(-1.81186 - 2.49381i) q^{48} +(2.09094 - 6.43526i) q^{49} +(-1.97433 - 6.04018i) q^{50} +(2.03074 - 1.47542i) q^{51} +(-0.711012 + 0.978624i) q^{52} +(1.50476 - 0.488926i) q^{53} -1.27093 q^{54} +(-3.45007 + 6.56483i) q^{55} -1.46477 q^{56} +(3.53807 - 1.14959i) q^{57} +(7.45759 - 10.2645i) q^{58} +(-0.305754 + 0.222143i) q^{59} +(-0.607779 + 0.608850i) q^{60} +(0.929682 - 2.86127i) q^{61} +(4.32522 + 5.95315i) q^{62} +(-0.284071 + 0.390991i) q^{63} +(-2.74713 - 8.45480i) q^{64} +(-6.26701 - 3.18626i) q^{65} +(-4.21482 - 0.0569445i) q^{66} -5.98082i q^{67} +(0.918461 - 0.298426i) q^{68} +(6.90268 + 5.01509i) q^{69} +(-0.216050 - 1.35636i) q^{70} +(2.57849 - 7.93579i) q^{71} +(-2.88249 - 0.936579i) q^{72} +(-0.0889998 - 0.122498i) q^{73} +(3.29812 + 2.39622i) q^{74} +(-4.05025 - 2.93180i) q^{75} +1.43126 q^{76} +(-0.959591 + 1.28392i) q^{77} -3.99597i q^{78} +(-2.31312 - 7.11905i) q^{79} +(6.13870 - 3.13463i) q^{80} +(-0.809017 + 0.587785i) q^{81} +(-9.50743 - 3.08915i) q^{82} +(-3.85865 - 1.25375i) q^{83} +(-0.150427 + 0.109291i) q^{84} +(2.55257 + 4.99881i) q^{85} +(-2.34472 - 7.21630i) q^{86} -9.98293i q^{87} +(-9.51731 - 3.23515i) q^{88} +17.0317 q^{89} +(0.442100 - 2.80729i) q^{90} +(-1.22932 - 0.893156i) q^{91} +(1.92947 + 2.65568i) q^{92} +(5.50647 + 1.78916i) q^{93} +(2.40787 - 7.41067i) q^{94} +(1.30853 + 8.21494i) q^{95} +(-1.73453 - 1.26021i) q^{96} +(3.43310 - 1.11548i) q^{97} +8.59967i q^{98} +(-2.70930 + 1.91304i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q + 12 q^{4} - 4 q^{5} + 4 q^{6} + 12 q^{9}+O(q^{10}) $ 48 * q + 12 * q^4 - 4 * q^5 + 4 * q^6 + 12 * q^9	$ 48 q + 12 q^{4} - 4 q^{5} + 4 q^{6} + 12 q^{9} - 12 q^{10} - 4 q^{14} + 10 q^{15} - 44 q^{16} - 16 q^{19} + 46 q^{20} - 32 q^{21} - 12 q^{24} + 14 q^{25} - 76 q^{26} + 4 q^{30} - 20 q^{31} - 24 q^{34} - 40 q^{35} - 12 q^{36} - 8 q^{39} - 72 q^{40} + 60 q^{41} - 48 q^{44} + 4 q^{45} + 108 q^{46} - 28 q^{49} - 38 q^{50} + 28 q^{51} + 16 q^{54} - 20 q^{55} + 24 q^{56} + 60 q^{59} + 48 q^{60} + 40 q^{61} + 64 q^{64} + 20 q^{65} + 12 q^{66} + 20 q^{69} + 86 q^{70} - 32 q^{71} - 32 q^{74} - 40 q^{75} - 136 q^{76} - 52 q^{79} + 42 q^{80} - 12 q^{81} - 70 q^{85} - 104 q^{86} + 40 q^{89} - 8 q^{90} - 40 q^{91} + 72 q^{94} - 2 q^{95} + 28 q^{96}+O(q^{100}) $ 48 * q + 12 * q^4 - 4 * q^5 + 4 * q^6 + 12 * q^9 - 12 * q^10 - 4 * q^14 + 10 * q^15 - 44 * q^16 - 16 * q^19 + 46 * q^20 - 32 * q^21 - 12 * q^24 + 14 * q^25 - 76 * q^26 + 4 * q^30 - 20 * q^31 - 24 * q^34 - 40 * q^35 - 12 * q^36 - 8 * q^39 - 72 * q^40 + 60 * q^41 - 48 * q^44 + 4 * q^45 + 108 * q^46 - 28 * q^49 - 38 * q^50 + 28 * q^51 + 16 * q^54 - 20 * q^55 + 24 * q^56 + 60 * q^59 + 48 * q^60 + 40 * q^61 + 64 * q^64 + 20 * q^65 + 12 * q^66 + 20 * q^69 + 86 * q^70 - 32 * q^71 - 32 * q^74 - 40 * q^75 - 136 * q^76 - 52 * q^79 + 42 * q^80 - 12 * q^81 - 70 * q^85 - 104 * q^86 + 40 * q^89 - 8 * q^90 - 40 * q^91 + 72 * q^94 - 2 * q^95 + 28 * q^96

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/165\mathbb{Z}\right)^\times$.

$n$	$46$	$56$	$67$
$\chi(n)$	$e\left(\frac{2}{5}\right)$	$1$	$-1$

Coefficient data

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

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

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

$2$	−1.20873	+	0.392740i	−0.854700	+	0.277709i	−0.703413	−	0.710781i	$-0.748342\pi$
$2$	−1.20873	+	0.392740i	−0.854700	+	0.277709i	−0.151287	+	0.988490i	$0.548342\pi$
$3$	−0.587785	+	0.809017i	−0.339358	+	0.467086i
$3$	−0.587785	+	0.809017i	−0.339358	+	0.467086i
$4$	−0.311255	+	0.226140i	−0.155627	+	0.113070i
$5$	−1.58253	−	1.57975i	−0.707729	−	0.706484i
$5$	−1.58253	−	1.57975i	−0.707729	−	0.706484i
$6$	0.392740	−	1.20873i	0.160335	−	0.493461i
$7$	−0.284071	−	0.390991i	−0.107369	−	0.147781i	0.751951	−	0.659219i	$-0.229113\pi$
$7$	−0.284071	−	0.390991i	−0.107369	−	0.147781i	−0.859320	+	0.511438i	$0.829113\pi$
$8$	1.78148	−	2.45199i	0.629848	−	0.866911i
$9$	−0.309017	−	0.951057i	−0.103006	−	0.317019i
$10$	2.53328	+	1.28796i	0.801092	+	0.407290i
$11$	−0.982188	−	3.16786i	−0.296141	−	0.955144i
$11$	−0.982188	−	3.16786i	−0.296141	−	0.955144i
$12$		−	0.384732i		−	0.111063i
$13$	2.99024	−	0.971588i	0.829343	−	0.269470i	0.136575	−	0.990630i	$-0.456391\pi$
$13$	2.99024	−	0.971588i	0.829343	−	0.269470i	0.692769	+	0.721160i	$0.256391\pi$
$14$	0.496923	+	0.361035i	0.132808	+	0.0964908i
$15$	2.20823	−	0.351741i	0.570162	−	0.0908192i
$16$	−0.952550	+	2.93165i	−0.238138	+	0.732912i
$17$	−2.38727	−	0.775672i	−0.578999	−	0.188128i	0.00485305	−	0.999988i	$-0.498455\pi$
$17$	−2.38727	−	0.775672i	−0.578999	−	0.188128i	−0.583852	+	0.811860i	$0.698455\pi$
$18$	0.747035	+	1.02821i	0.176078	+	0.242350i
$19$	−3.00966	−	2.18665i	−0.690464	−	0.501651i	0.186349	−	0.982484i	$-0.440335\pi$
$19$	−3.00966	−	2.18665i	−0.690464	−	0.501651i	−0.876813	+	0.480832i	$0.840335\pi$
$20$	0.849814	+	0.133831i	0.190024	+	0.0299255i
$21$	0.483291			0.105463
$22$	2.43134	+	3.44333i	0.518363	+	0.734121i
$23$		−	8.53218i		−	1.77908i	−0.456855	−	0.889541i	$-0.651024\pi$
$23$		−	8.53218i		−	1.77908i	0.456855	−	0.889541i	$-0.348976\pi$
$24$	0.936579	+	2.88249i	0.191178	+	0.588386i
$25$	0.00879819	+	4.99999i	0.00175964	+	0.999998i
$26$	−3.23281	+	2.34877i	−0.634005	+	0.460632i
$27$	0.951057	+	0.309017i	0.183031	+	0.0594703i
$28$	0.176837	+	0.0574579i	0.0334191	+	0.0108585i
$29$	−8.07636	+	5.86782i	−1.49974	+	1.08963i	−0.529258	+	0.848461i	$0.677529\pi$
$29$	−8.07636	+	5.86782i	−1.49974	+	1.08963i	−0.970484	+	0.241165i	$0.922471\pi$
$30$	−2.53101	+	1.29242i	−0.462096	+	0.235962i
$31$	−1.78916	−	5.50647i	−0.321343	−	0.988991i	−0.973065	−	0.230533i	$-0.925953\pi$
$31$	−1.78916	−	5.50647i	−0.321343	−	0.988991i	0.651722	−	0.758458i	$-0.274047\pi$
$32$			2.14399i			0.379008i
$33$	3.14016	+	1.06741i	0.546632	+	0.185813i
$34$	3.19020			0.547115
$35$	−0.168115	+	1.06752i	−0.0284166	+	0.180443i
$36$	0.311255	+	0.226140i	0.0518758	+	0.0376900i
$37$	−1.88541	−	2.59504i	−0.309959	−	0.426622i	0.625410	−	0.780297i	$-0.284932\pi$
$37$	−1.88541	−	2.59504i	−0.309959	−	0.426622i	−0.935368	+	0.353675i	$0.884932\pi$
$38$	4.49665	+	1.46105i	0.729452	+	0.237013i
$39$	−0.971588	+	2.99024i	−0.155579	+	0.478822i
$40$	−6.69277	+	1.06607i	−1.05822	+	0.168560i
$41$	6.36344	+	4.62331i	0.993802	+	0.722040i	0.960751	−	0.277414i	$-0.0894773\pi$
$41$	6.36344	+	4.62331i	0.993802	+	0.722040i	0.0330520	+	0.999454i	$0.489477\pi$
$42$	−0.584168	+	0.189808i	−0.0901390	+	0.0292879i
$43$			5.97016i			0.910441i	0.890379	+	0.455221i	$0.150440\pi$
$43$			5.97016i			0.910441i	−0.890379	+	0.455221i	$0.849560\pi$
$44$	1.02209	+	0.763898i	0.154086	+	0.115162i
$45$	−1.01340	+	1.99324i	−0.151069	+	0.297135i
$46$	3.35092	+	10.3131i	0.494067	+	1.52058i
$47$	−3.60369	+	4.96006i	−0.525653	+	0.723499i	−0.986460	−	0.164001i	$-0.947560\pi$
$47$	−3.60369	+	4.96006i	−0.525653	+	0.723499i	0.460808	+	0.887500i	$0.347560\pi$
$48$	−1.81186	−	2.49381i	−0.261519	−	0.359950i
$49$	2.09094	−	6.43526i	0.298706	−	0.919322i
$50$	−1.97433	−	6.04018i	−0.279212	−	0.854210i
$51$	2.03074	−	1.47542i	0.284360	−	0.206600i
$52$	−0.711012	+	0.978624i	−0.0985996	+	0.135711i
$53$	1.50476	−	0.488926i	0.206695	−	0.0671592i	−0.203840	−	0.979004i	$-0.565342\pi$
$53$	1.50476	−	0.488926i	0.206695	−	0.0671592i	0.410535	+	0.911845i	$0.365342\pi$
$54$	−1.27093			−0.172952
$55$	−3.45007	+	6.56483i	−0.465207	+	0.885202i
$56$	−1.46477			−0.195739
$57$	3.53807	−	1.14959i	0.468629	−	0.152267i
$58$	7.45759	−	10.2645i	0.979230	−	1.34779i
$59$	−0.305754	+	0.222143i	−0.0398058	+	0.0289206i	−0.607510	−	0.794312i	$-0.707832\pi$
$59$	−0.305754	+	0.222143i	−0.0398058	+	0.0289206i	0.567704	+	0.823232i	$0.307832\pi$
$60$	−0.607779	+	0.608850i	−0.0784640	+	0.0786022i
$61$	0.929682	−	2.86127i	0.119034	−	0.366348i	−0.873733	−	0.486405i	$-0.838308\pi$
$61$	0.929682	−	2.86127i	0.119034	−	0.366348i	0.992767	+	0.120057i	$0.0383079\pi$
$62$	4.32522	+	5.95315i	0.549303	+	0.756051i
$63$	−0.284071	+	0.390991i	−0.0357896	+	0.0492602i
$64$	−2.74713	−	8.45480i	−0.343391	−	1.05685i
$65$	−6.26701	−	3.18626i	−0.777326	−	0.395207i
$66$	−4.21482	−	0.0569445i	−0.518808	−	0.00700938i
$67$		−	5.98082i		−	0.730674i	−0.930875	−	0.365337i	$-0.880954\pi$
$67$		−	5.98082i		−	0.730674i	0.930875	−	0.365337i	$-0.119046\pi$
$68$	0.918461	−	0.298426i	0.111380	−	0.0361895i
$69$	6.90268	+	5.01509i	0.830985	+	0.603746i
$70$	−0.216050	−	1.35636i	−0.0258229	−	0.162116i
$71$	2.57849	−	7.93579i	0.306011	−	0.941805i	−0.673287	−	0.739381i	$-0.735118\pi$
$71$	2.57849	−	7.93579i	0.306011	−	0.941805i	0.979298	−	0.202424i	$-0.0648819\pi$
$72$	−2.88249	−	0.936579i	−0.339705	−	0.110377i
$73$	−0.0889998	−	0.122498i	−0.0104166	−	0.0143373i	0.803777	−	0.594931i	$-0.202821\pi$
$73$	−0.0889998	−	0.122498i	−0.0104166	−	0.0143373i	−0.814194	+	0.580594i	$0.802821\pi$
$74$	3.29812	+	2.39622i	0.383398	+	0.278555i
$75$	−4.05025	−	2.93180i	−0.467683	−	0.338536i
$76$	1.43126			0.164177
$77$	−0.959591	+	1.28392i	−0.109356	+	0.146317i
$78$		−	3.99597i		−	0.452454i
$79$	−2.31312	−	7.11905i	−0.260246	−	0.800956i	−0.992751	−	0.120193i	$-0.961649\pi$
$79$	−2.31312	−	7.11905i	−0.260246	−	0.800956i	0.732504	−	0.680763i	$-0.238351\pi$
$80$	6.13870	−	3.13463i	0.686328	−	0.350462i
$81$	−0.809017	+	0.587785i	−0.0898908	+	0.0653095i
$82$	−9.50743	−	3.08915i	−1.04992	−	0.341140i
$83$	−3.85865	−	1.25375i	−0.423542	−	0.137617i	0.0894877	−	0.995988i	$-0.471477\pi$
$83$	−3.85865	−	1.25375i	−0.423542	−	0.137617i	−0.513030	+	0.858371i	$0.671477\pi$
$84$	−0.150427	+	0.109291i	−0.0164129	+	0.0119247i
$85$	2.55257	+	4.99881i	0.276865	+	0.542198i
$86$	−2.34472	−	7.21630i	−0.252838	−	0.778154i
$87$		−	9.98293i		−	1.07028i
$88$	−9.51731	−	3.23515i	−1.01455	−	0.344868i
$89$	17.0317			1.80535			0.902677	−	0.430318i	$-0.141599\pi$
$89$	17.0317			1.80535			0.902677	+	0.430318i	$0.141599\pi$
$90$	0.442100	−	2.80729i	0.0466014	−	0.295915i
$91$	−1.22932	−	0.893156i	−0.128868	−	0.0936282i
$92$	1.92947	+	2.65568i	0.201161	+	0.276874i
$93$	5.50647	+	1.78916i	0.570994	+	0.185527i
$94$	2.40787	−	7.41067i	0.248353	−	0.764353i
$95$	1.30853	+	8.21494i	0.134252	+	0.842835i
$96$	−1.73453	−	1.26021i	−0.177030	−	0.128619i
$97$	3.43310	−	1.11548i	0.348578	−	0.113260i	−0.129494	−	0.991580i	$-0.541335\pi$
$97$	3.43310	−	1.11548i	0.348578	−	0.113260i	0.478073	+	0.878320i	$0.341335\pi$
$98$			8.59967i			0.868698i
$99$	−2.70930	+	1.91304i	−0.272295	+	0.192267i
$100$	−1.13344	−	1.55428i	−0.113344	−	0.155428i
$101$	2.34721	+	7.22397i	0.233556	+	0.718811i	0.997310	+	0.0733036i	$0.0233542\pi$
$101$	2.34721	+	7.22397i	0.233556	+	0.718811i	−0.763754	+	0.645508i	$0.776646\pi$
$102$	−1.87515	+	2.58093i	−0.185668	+	0.255550i
$103$	2.23804	+	3.08040i	0.220521	+	0.303521i	0.904916	−	0.425591i	$-0.139934\pi$
$103$	2.23804	+	3.08040i	0.220521	+	0.303521i	−0.684395	+	0.729111i	$0.739934\pi$
$104$	2.94472	−	9.06292i	0.288754	−	0.888692i
$105$	−0.764822	−	0.763478i	−0.0746390	−	0.0745078i
$106$	−1.62683	+	1.18196i	−0.158011	+	0.114802i
$107$	0.280647	−	0.386277i	0.0271312	−	0.0373428i	−0.795236	−	0.606300i	$-0.792653\pi$
$107$	0.280647	−	0.386277i	0.0271312	−	0.0373428i	0.822367	+	0.568957i	$0.192653\pi$
$108$	−0.365902	+	0.118889i	−0.0352089	+	0.0114401i
$109$	6.92083			0.662895			0.331447	−	0.943474i	$-0.392463\pi$
$109$	6.92083			0.662895			0.331447	+	0.943474i	$0.392463\pi$
$110$	1.59193	−	9.29008i	0.151784	−	0.885774i
$111$	3.20765			0.304456
$112$	1.41684	−	0.460359i	0.133879	−	0.0434998i
$113$	−6.38576	+	8.78924i	−0.600722	+	0.826822i	−0.995774	−	0.0918363i	$-0.970726\pi$
$113$	−6.38576	+	8.78924i	−0.600722	+	0.826822i	0.395053	+	0.918659i	$0.370726\pi$
$114$	−3.82508	+	2.77908i	−0.358251	+	0.260285i
$115$	−13.4787	+	13.5024i	−1.25689	+	1.25911i
$116$	1.18686	−	3.65277i	0.110197	−	0.339151i
$117$	−1.84807	−	2.54365i	−0.170854	−	0.235161i
$118$	0.282329	−	0.388592i	0.0259905	−	0.0357728i
$119$	0.374876	+	1.15375i	0.0343648	+	0.105764i
$120$	3.07145	−	6.04119i	0.280383	−	0.551482i
$121$	−9.07062	+	6.22286i	−0.824601	+	0.565714i
$122$			3.82362i			0.346174i
$123$	−7.48067	+	2.43062i	−0.674510	+	0.219161i
$124$	1.80212	+	1.30931i	0.161835	+	0.117580i
$125$	7.88480	−	7.92653i	0.705238	−	0.708971i
$126$	0.189808	−	0.584168i	0.0169094	−	0.0520418i
$127$	5.69890	+	1.85169i	0.505696	+	0.164311i	0.550744	−	0.834674i	$-0.314344\pi$
$127$	5.69890	+	1.85169i	0.505696	+	0.164311i	−0.0450480	+	0.998985i	$0.514344\pi$
$128$	4.12065	+	5.67159i	0.364218	+	0.501303i
$129$	−4.82996	−	3.50917i	−0.425255	−	0.308966i
$130$	8.82647	+	1.39002i	0.774133	+	0.121913i
$131$	−10.9819			−0.959491			−0.479746	−	0.877408i	$-0.659271\pi$
$131$	−10.9819			−0.959491			−0.479746	+	0.877408i	$0.659271\pi$
$132$	−1.21878	+	0.377879i	−0.106081	+	0.0328901i
$133$			1.79791i			0.155899i
$134$	2.34891	+	7.22919i	0.202915	+	0.624507i
$135$	−1.01691	−	1.99146i	−0.0875213	−	0.171397i
$136$	−6.15482	+	4.47174i	−0.527772	+	0.383449i
$137$	1.03865	+	0.337477i	0.0887377	+	0.0288326i	0.353049	−	0.935605i	$-0.385145\pi$
$137$	1.03865	+	0.337477i	0.0887377	+	0.0288326i	−0.264312	+	0.964437i	$0.585145\pi$
$138$	−10.3131	−	3.35092i	−0.877908	−	0.285250i
$139$	−6.81610	+	4.95218i	−0.578134	+	0.420039i	−0.838051	−	0.545592i	$-0.816305\pi$
$139$	−6.81610	+	4.95218i	−0.578134	+	0.420039i	0.259917	+	0.965631i	$0.416305\pi$
$140$	−0.189081	−	0.370287i	−0.0159803	−	0.0312949i
$141$	−1.89457	−	5.83090i	−0.159552	−	0.491050i
$142$			10.6049i			0.889943i
$143$	−6.01483	−	8.51837i	−0.502985	−	0.712342i
$144$	3.08252			0.256876
$145$	22.0507	+	3.47261i	1.83121	+	0.288384i
$146$	0.155686	+	0.113113i	0.0128847	+	0.00936128i
$147$	3.97721	+	5.47416i	0.328035	+	0.451501i
$148$	1.17368	+	0.381353i	0.0964762	+	0.0313470i
$149$	−5.32425	+	16.3864i	−0.436180	+	1.34242i	0.455693	+	0.890137i	$0.349391\pi$
$149$	−5.32425	+	16.3864i	−0.436180	+	1.34242i	−0.891873	+	0.452286i	$0.850609\pi$
$150$	6.04709	+	1.95306i	0.493743	+	0.159467i
$151$	10.5850	+	7.69049i	0.861399	+	0.625843i	0.928265	−	0.371919i	$-0.121300\pi$
$151$	10.5850	+	7.69049i	0.861399	+	0.625843i	−0.0668662	+	0.997762i	$0.521300\pi$
$152$	−10.7233	+	3.48421i	−0.869774	+	0.282607i
$153$			2.51013i			0.202932i
$154$	0.655637	−	1.92878i	0.0528327	−	0.155426i
$155$	−5.86743	+	11.5406i	−0.471283	+	0.926961i
$156$	−0.373801	−	1.15044i	−0.0299280	−	0.0921090i
$157$	13.8180	−	19.0188i	1.10280	−	1.51787i	0.271172	−	0.962531i	$-0.412589\pi$
$157$	13.8180	−	19.0188i	1.10280	−	1.51787i	0.831625	−	0.555338i	$-0.187411\pi$
$158$	5.59187	+	7.69654i	0.444865	+	0.612304i
$159$	−0.488926	+	1.50476i	−0.0387744	+	0.119335i
$160$	3.38697	−	3.39293i	0.267763	−	0.268235i
$161$	−3.33600	+	2.42375i	−0.262914	+	0.191018i
$162$	0.747035	−	1.02821i	0.0586926	−	0.0807835i
$163$	−18.9637	+	6.16167i	−1.48535	+	0.482619i	−0.935706	−	0.352780i	$-0.885236\pi$
$163$	−18.9637	+	6.16167i	−1.48535	+	0.482619i	−0.549643	+	0.835399i	$0.685236\pi$
$164$	−3.02617			−0.236304
$165$	−3.28316	−	6.64988i	−0.255594	−	0.517692i
$166$	5.15646			0.400219
$167$	18.3328	−	5.95668i	1.41863	−	0.460941i	0.503465	−	0.864016i	$-0.332058\pi$
$167$	18.3328	−	5.95668i	1.41863	−	0.460941i	0.915167	+	0.403074i	$0.132058\pi$
$168$	0.860973	−	1.18503i	0.0664255	−	0.0914268i
$169$	−2.51967	+	1.83065i	−0.193821	+	0.140819i
$170$	−5.04859	−	5.03971i	−0.387209	−	0.386528i
$171$	−1.14959	+	3.53807i	−0.0879113	+	0.270563i
$172$	−1.35009	−	1.85824i	−0.102944	−	0.141690i
$173$	2.27407	−	3.12998i	0.172894	−	0.237968i	−0.713772	−	0.700378i	$-0.753015\pi$
$173$	2.27407	−	3.12998i	0.172894	−	0.237968i	0.886667	+	0.462409i	$0.153015\pi$
$174$	3.92069	+	12.0666i	0.297227	+	0.914770i
$175$	1.95245	−	1.42379i	0.147591	−	0.107629i
$176$	10.2226	+	0.138113i	0.770559	+	0.0104107i
$177$		−	0.377932i		−	0.0284071i
$178$	−20.5867	+	6.68901i	−1.54304	+	0.501363i
$179$	−13.9040	−	10.1018i	−1.03923	−	0.755048i	−0.0690980	−	0.997610i	$-0.522012\pi$
$179$	−13.9040	−	10.1018i	−1.03923	−	0.755048i	−0.970136	+	0.242562i	$0.922012\pi$
$180$	−0.135326	−	0.849577i	−0.0100866	−	0.0633237i
$181$	−2.15994	+	6.64762i	−0.160547	+	0.494114i	−0.998681	−	0.0513516i	$-0.983647\pi$
$181$	−2.15994	+	6.64762i	−0.160547	+	0.494114i	0.838133	+	0.545465i	$0.183647\pi$
$182$	1.83670	+	0.596779i	0.136145	+	0.0442362i
$183$	1.76836	+	2.43394i	0.130721	+	0.179922i
$184$	−20.9209	−	15.1999i	−1.54231	−	1.12055i
$185$	−1.11579	+	7.08519i	−0.0820349	+	0.520914i
$186$	−7.35850			−0.539551
$187$	−0.112467	+	8.32440i	−0.00822441	+	0.608740i
$188$		−	2.35878i		−	0.172032i
$189$	−0.149345	−	0.459637i	−0.0108633	−	0.0334337i
$190$	−4.80799	−	9.41572i	−0.348808	−	0.683088i
$191$	8.08883	−	5.87688i	0.585287	−	0.425236i	−0.255339	−	0.966852i	$-0.582187\pi$
$191$	8.08883	−	5.87688i	0.585287	−	0.425236i	0.840626	+	0.541615i	$0.182187\pi$
$192$	8.45480	+	2.74713i	0.610173	+	0.198257i
$193$	22.6321	+	7.35361i	1.62909	+	0.529325i	0.974063	−	0.226277i	$-0.0726556\pi$
$193$	22.6321	+	7.35361i	1.62909	+	0.529325i	0.655031	+	0.755602i	$0.272656\pi$
$194$	−3.71159	+	2.69663i	−0.266477	+	0.193607i
$195$	6.26139	−	3.19728i	0.448387	−	0.228962i
$196$	0.804452	+	2.47585i	0.0574609	+	0.176846i
$197$		−	24.6381i		−	1.75539i	−0.479221	−	0.877694i	$-0.659081\pi$
$197$		−	24.6381i		−	1.75539i	0.479221	−	0.877694i	$-0.340919\pi$
$198$	2.52348	−	3.37639i	0.179336	−	0.239950i
$199$	15.3559			1.08855			0.544277	−	0.838906i	$-0.316804\pi$
$199$	15.3559			1.08855			0.544277	+	0.838906i	$0.316804\pi$
$200$	12.2756	+	8.88581i	0.868018	+	0.628321i
$201$	4.83859	+	3.51544i	0.341288	+	0.247960i
$202$	−5.67427	−	7.80997i	−0.399241	−	0.549507i
$203$	4.58852	+	1.49090i	0.322051	+	0.104641i
$204$	−0.298426	+	0.918461i	−0.0208940	+	0.0643051i
$205$	−2.76667	−	17.3692i	−0.193233	−	1.21311i
$206$	−3.91498	−	2.84440i	−0.272769	−	0.198178i
$207$	−8.11458	+	2.63659i	−0.564002	+	0.183256i
$208$			9.69182i			0.672007i
$209$	−3.97093	+	11.6819i	−0.274675	+	0.808052i
$210$	1.22431	+	0.622461i	0.0844854	+	0.0429539i
$211$	−7.99142	−	24.5951i	−0.550152	−	1.69319i	−0.708415	−	0.705797i	$-0.750589\pi$
$211$	−7.99142	−	24.5951i	−0.550152	−	1.69319i	0.158263	−	0.987397i	$-0.449411\pi$
$212$	−0.357798	+	0.492467i	−0.0245737	+	0.0338228i
$213$	4.90459	+	6.75059i	0.336057	+	0.462543i
$214$	−0.187519	+	0.577125i	−0.0128186	+	0.0394515i
$215$	9.43135	−	9.44796i	0.643213	−	0.644345i
$216$	2.45199	−	1.78148i	0.166837	−	0.121214i
$217$	−1.64473	+	2.26378i	−0.111651	+	0.153675i
$218$	−8.36540	+	2.71808i	−0.566576	+	0.184092i
$219$	0.151416			0.0102317
$220$	−0.410719	−	2.82353i	−0.0276907	−	0.190363i
$221$	−7.89216			−0.530884
$222$	−3.87717	+	1.25977i	−0.260219	+	0.0845502i
$223$	3.15527	−	4.34286i	0.211293	−	0.290819i	−0.690196	−	0.723623i	$-0.742476\pi$
$223$	3.15527	−	4.34286i	0.211293	−	0.290819i	0.901488	+	0.432803i	$0.142476\pi$
$224$	0.838282	−	0.609048i	0.0560101	−	0.0406937i
$225$	4.75256	−	1.55345i	0.316837	−	0.103563i
$226$	4.26676	−	13.1317i	0.283821	−	0.873510i
$227$	−4.54031	−	6.24920i	−0.301351	−	0.414774i	0.631309	−	0.775532i	$-0.282518\pi$
$227$	−4.54031	−	6.24920i	−0.301351	−	0.414774i	−0.932660	+	0.360758i	$0.882518\pi$
$228$	−0.841274	+	1.15791i	−0.0557147	+	0.0766847i
$229$	−2.49735	−	7.68605i	−0.165029	−	0.507908i	0.834009	−	0.551751i	$-0.186040\pi$
$229$	−2.49735	−	7.68605i	−0.165029	−	0.507908i	−0.999038	+	0.0438424i	$0.986040\pi$
$230$	10.9891	−	21.6144i	0.724602	−	1.42521i
$231$	−0.474682	−	1.53100i	−0.0312318	−	0.100732i
$232$			30.2566i			1.98644i
$233$	−24.2432	+	7.87710i	−1.58823	+	0.516046i	−0.964159	−	0.265325i	$-0.914521\pi$
$233$	−24.2432	+	7.87710i	−1.58823	+	0.516046i	−0.624067	+	0.781371i	$0.714521\pi$
$234$	3.23281	+	2.34877i	0.211335	+	0.153544i
$235$	13.5386	−	2.15651i	0.883160	−	0.140675i
$236$	0.0449319	−	0.138286i	0.00292482	−	0.00900167i
$237$	7.11905	+	2.31312i	0.462432	+	0.150253i
$238$	−0.906245	−	1.24734i	−0.0587432	−	0.0808530i
$239$	0.751468	+	0.545973i	0.0486084	+	0.0353161i	0.611824	−	0.790994i	$-0.290436\pi$
$239$	0.751468	+	0.545973i	0.0486084	+	0.0353161i	−0.563216	+	0.826310i	$0.690436\pi$
$240$	−1.07227	+	6.80880i	−0.0692146	+	0.439506i
$241$	10.3759			0.668369			0.334184	−	0.942508i	$-0.391539\pi$
$241$	10.3759			0.668369			0.334184	+	0.942508i	$0.391539\pi$
$242$	8.51995	−	11.0841i	0.547683	−	0.712515i
$243$		−	1.00000i		−	0.0641500i
$244$	0.357679	+	1.10082i	0.0228980	+	0.0704729i
$245$	−13.4751	+	6.88082i	−0.860890	+	0.439600i
$246$	8.08750	−	5.87591i	0.515640	−	0.374635i
$247$	−11.1241	−	3.61445i	−0.707812	−	0.229982i
$248$	−16.6892	−	5.42264i	−1.05976	−	0.344338i
$249$	3.28237	−	2.38478i	0.208012	−	0.151129i
$250$	−6.41752	+	12.6777i	−0.405879	+	0.801808i
$251$	7.27614	+	22.3936i	0.459266	+	1.41347i	0.866053	+	0.499951i	$0.166649\pi$
$251$	7.27614	+	22.3936i	0.459266	+	1.41347i	−0.406788	+	0.913523i	$0.633351\pi$
$252$		−	0.185938i		−	0.0117130i
$253$	−27.0287	+	8.38020i	−1.69928	+	0.526859i
$254$	−7.61566			−0.477849
$255$	−5.54449	−	0.873160i	−0.347209	−	0.0546794i
$256$	7.17596	+	5.21364i	0.448498	+	0.325853i
$257$	−9.46311	−	13.0249i	−0.590292	−	0.812468i	0.404484	−	0.914545i	$-0.367451\pi$
$257$	−9.46311	−	13.0249i	−0.590292	−	0.812468i	−0.994776	+	0.102077i	$0.967451\pi$
$258$	7.21630	+	2.34472i	0.449267	+	0.145976i
$259$	−0.479046	+	1.47435i	−0.0297665	+	0.0916118i
$260$	2.67118	−	0.425482i	0.165659	−	0.0263873i
$261$	8.07636	+	5.86782i	0.499914	+	0.363209i
$262$	13.2741	−	4.31302i	0.820077	−	0.266459i
$263$			2.19036i			0.135063i	0.997717	+	0.0675316i	$0.0215124\pi$
$263$			2.19036i			0.135063i	−0.997717	+	0.0675316i	$0.978488\pi$
$264$	8.21142	−	5.79809i	0.505378	−	0.356848i
$265$	−3.15371	−	1.60340i	−0.193731	−	0.0984962i
$266$	−0.706112	−	2.17319i	−0.0432945	−	0.133247i
$267$	−10.0110	+	13.7789i	−0.612661	+	0.843256i
$268$	1.35250	+	1.86156i	0.0826172	+	0.113713i
$269$	3.22461	−	9.92434i	0.196608	−	0.605098i	−0.803346	−	0.595513i	$-0.796949\pi$
$269$	3.22461	−	9.92434i	0.196608	−	0.605098i	0.999954	−	0.00958498i	$-0.00305104\pi$
$270$	2.01129	+	2.00775i	0.122403	+	0.122188i
$271$	1.39914	−	1.01653i	0.0849915	−	0.0617500i	−0.544478	−	0.838775i	$-0.683272\pi$
$271$	1.39914	−	1.01653i	0.0849915	−	0.0617500i	0.629470	+	0.777025i	$0.283272\pi$
$272$	4.54800	−	6.25978i	0.275763	−	0.379555i
$273$	1.44516	−	0.469560i	0.0874648	−	0.0284191i
$274$	−1.38798			−0.0838511
$275$	15.8306	−	4.93880i	0.954622	−	0.297821i
$276$	−3.28260			−0.197589
$277$	−11.0694	+	3.59666i	−0.665094	+	0.216102i	−0.622058	−	0.782971i	$-0.713703\pi$
$277$	−11.0694	+	3.59666i	−0.665094	+	0.216102i	−0.0430364	+	0.999074i	$0.513703\pi$
$278$	6.29389	−	8.66279i	0.377482	−	0.519560i
$279$	−4.68408	+	3.40319i	−0.280429	+	0.203743i
$280$	2.31805	+	2.31397i	0.138530	+	0.138286i
$281$	3.71316	−	11.4279i	0.221509	−	0.681733i	−0.777119	−	0.629354i	$-0.783320\pi$
$281$	3.71316	−	11.4279i	0.221509	−	0.681733i	0.998627	−	0.0523793i	$-0.0166805\pi$
$282$	4.58005	+	6.30390i	0.272738	+	0.375392i
$283$	16.2167	−	22.3203i	0.963981	−	1.32681i	0.0189517	−	0.999820i	$-0.493967\pi$
$283$	16.2167	−	22.3203i	0.963981	−	1.32681i	0.945029	−	0.326986i	$-0.106033\pi$
$284$	0.992030	+	3.05315i	0.0588661	+	0.181171i
$285$	−7.41516	−	3.77000i	−0.439236	−	0.223315i
$286$	10.6158	+	7.93413i	0.627725	+	0.469155i
$287$		−	3.80140i		−	0.224389i
$288$	2.03906	−	0.662531i	0.120153	−	0.0390400i
$289$	−8.65588	−	6.28886i	−0.509169	−	0.369933i
$290$	−28.0172	+	4.46276i	−1.64523	+	0.262062i
$291$	−1.11548	+	3.43310i	−0.0653907	+	0.201252i
$292$	0.0554033	+	0.0180016i	0.00324223	+	0.00105346i
$293$	2.01529	+	2.77380i	0.117734	+	0.162047i	0.863817	−	0.503806i	$-0.168067\pi$
$293$	2.01529	+	2.77380i	0.117734	+	0.162047i	−0.746082	+	0.665854i	$0.768067\pi$
$294$	−6.95728	−	5.05476i	−0.405757	−	0.294800i
$295$	0.834794	+	0.131466i	0.0486036	+	0.00765423i
$296$	−9.72183			−0.565070
$297$	0.0448053	−	3.31632i	0.00259987	−	0.192433i
$298$		−	21.8977i		−	1.26850i
$299$	−8.28976	−	25.5133i	−0.479409	−	1.47547i
$300$	1.92366	−	0.00338495i	0.111062	−	0.000195430i
$301$	2.33428	−	1.69595i	0.134546	−	0.0977531i
$302$	−15.8148	−	5.13854i	−0.910040	−	0.295690i
$303$	−7.22397	−	2.34721i	−0.415006	−	0.134844i
$304$	9.27734	−	6.74038i	0.532092	−	0.386587i
$305$	−5.99133	+	3.05938i	−0.343063	+	0.175179i
$306$	−0.985827	−	3.03406i	−0.0563560	−	0.173446i
$307$			15.3337i			0.875140i	0.899184	+	0.437570i	$0.144161\pi$
$307$			15.3337i			0.875140i	−0.899184	+	0.437570i	$0.855839\pi$
$308$	0.00833099	−	0.616629i	0.000474702	−	0.0351357i
$309$	−3.80758			−0.216606
$310$	2.55969	−	16.2538i	0.145381	−	0.923153i
$311$	3.51281	+	2.55220i	0.199193	+	0.144722i	0.682911	−	0.730502i	$-0.260714\pi$
$311$	3.51281	+	2.55220i	0.199193	+	0.144722i	−0.483718	+	0.875224i	$0.660714\pi$
$312$	5.60119	+	7.70938i	0.317105	+	0.436457i
$313$	9.93252	+	3.22727i	0.561419	+	0.182416i	0.575960	−	0.817478i	$-0.304629\pi$
$313$	9.93252	+	3.22727i	0.561419	+	0.182416i	−0.0145406	+	0.999894i	$0.504629\pi$
$314$	−9.23275	+	28.4155i	−0.521034	+	1.60358i
$315$	1.06722	−	0.169993i	0.0601309	−	0.00957804i
$316$	2.32987	+	1.69275i	0.131065	+	0.0952246i
$317$	15.8266	−	5.14239i	0.888912	−	0.288825i	0.171259	−	0.985226i	$-0.445216\pi$
$317$	15.8266	−	5.14239i	0.888912	−	0.288825i	0.717653	+	0.696401i	$0.245216\pi$
$318$		−	2.01087i		−	0.112764i
$319$	26.5209	+	19.8214i	1.48488	+	1.10979i
$320$	−9.00903	+	17.7197i	−0.503620	+	0.990564i
$321$	0.147545	+	0.454096i	0.00823515	+	0.0253452i
$322$	3.08042	−	4.23983i	0.171665	−	0.236277i
$323$	5.48877	+	7.55464i	0.305403	+	0.420351i
$324$	0.118889	−	0.365902i	0.00660493	−	0.0203279i
$325$	4.88424	+	14.9426i	0.270929	+	0.828868i
$326$	20.5020	−	14.8956i	1.13550	−	0.824989i
$327$	−4.06796	+	5.59907i	−0.224959	+	0.309629i
$328$	22.6727	−	7.36680i	1.25189	−	0.406763i
$329$	2.96304			0.163358
$330$	6.58012	+	6.74847i	0.362224	+	0.371491i
$331$	−32.0054			−1.75917			−0.879587	−	0.475738i	$-0.842181\pi$
$331$	−32.0054			−1.75917			−0.879587	+	0.475738i	$0.842181\pi$
$332$	1.48455	−	0.482359i	0.0814751	−	0.0264729i
$333$	−1.88541	+	2.59504i	−0.103320	+	0.142207i
$334$	−19.8199	+	14.4000i	−1.08450	+	0.787933i
$335$	−9.44819	+	9.46483i	−0.516210	+	0.517119i
$336$	−0.460359	+	1.41684i	−0.0251146	+	0.0772949i
$337$	8.42031	+	11.5896i	0.458683	+	0.631324i	0.974235	−	0.225535i	$-0.0724130\pi$
$337$	8.42031	+	11.5896i	0.458683	+	0.631324i	−0.515552	+	0.856858i	$0.672413\pi$
$338$	2.32663	−	3.20233i	0.126552	−	0.174184i
$339$	−3.35719	−	10.3324i	−0.182338	−	0.561177i
$340$	−1.92493	−	0.978668i	−0.104394	−	0.0530757i
$341$	−15.6864	+	11.0762i	−0.849467	+	0.599809i
$342$		−	4.72805i		−	0.255664i
$343$	−6.32756	+	2.05595i	−0.341656	+	0.111011i
$344$	14.6388	+	10.6357i	0.789272	+	0.573439i
$345$	−3.00112	−	18.8410i	−0.161575	−	1.01437i
$346$	−1.51946	+	4.67642i	−0.0816866	+	0.251406i
$347$	15.2773	+	4.96389i	0.820128	+	0.266476i	0.688881	−	0.724874i	$-0.258102\pi$
$347$	15.2773	+	4.96389i	0.820128	+	0.266476i	0.131247	+	0.991350i	$0.458102\pi$
$348$	2.25754	+	3.10723i	0.121017	+	0.166565i
$349$	3.21732	+	2.33752i	0.172219	+	0.125125i	0.670556	−	0.741859i	$-0.266056\pi$
$349$	3.21732	+	2.33752i	0.172219	+	0.125125i	−0.498337	+	0.866984i	$0.666056\pi$
$350$	−1.80080	+	2.48779i	−0.0962569	+	0.132978i
$351$	3.14412			0.167821
$352$	6.79187	−	2.10580i	0.362008	−	0.112240i
$353$		−	9.37575i		−	0.499021i	−0.968372	−	0.249510i	$-0.919730\pi$
$353$		−	9.37575i		−	0.499021i	0.968372	−	0.249510i	$-0.0802696\pi$
$354$	0.148429	+	0.456818i	0.00788891	+	0.0242796i
$355$	−16.6171	+	8.48525i	−0.881943	+	0.450350i
$356$	−5.30119	+	3.85154i	−0.280963	+	0.204131i
$357$	−1.15375	−	0.374876i	−0.0610628	−	0.0198405i
$358$	20.7736	+	6.74974i	1.09792	+	0.356735i
$359$	17.5859	−	12.7769i	0.928148	−	0.674339i	−0.0173907	−	0.999849i	$-0.505536\pi$
$359$	17.5859	−	12.7769i	0.928148	−	0.674339i	0.945539	+	0.325510i	$0.105536\pi$
$360$	3.08207	+	6.03577i	0.162439	+	0.318113i
$361$	−1.59468	−	4.90793i	−0.0839306	−	0.258312i
$362$		−	8.88346i		−	0.466904i
$363$	0.297178	−	10.9960i	0.0155978	−	0.577140i
$364$	0.584611			0.0306419
$365$	−0.0526706	+	0.334454i	−0.00275691	+	0.0175061i
$366$	−3.09337	−	2.24747i	−0.161693	−	0.117477i
$367$	−18.4461	−	25.3888i	−0.962877	−	1.32529i	−0.945564	−	0.325437i	$-0.894489\pi$
$367$	−18.4461	−	25.3888i	−0.962877	−	1.32529i	−0.0173133	−	0.999850i	$-0.505511\pi$
$368$	25.0133	+	8.12733i	1.30391	+	0.423666i
$369$	2.43062	−	7.48067i	0.126533	−	0.389428i
$370$	−1.43394	−	9.00229i	−0.0745471	−	0.468007i
$371$	−0.618625	−	0.449458i	−0.0321174	−	0.0233347i
$372$	−2.11852	+	0.688347i	−0.109840	+	0.0356891i
$373$			23.2675i			1.20475i	0.798214	+	0.602374i	$0.205778\pi$
$373$			23.2675i			1.20475i	−0.798214	+	0.602374i	$0.794222\pi$
$374$	−3.13338	−	10.1061i	−0.162023	−	0.522574i
$375$	1.77813	+	11.0380i	0.0918223	+	0.570002i
$376$	5.74213	+	17.6725i	0.296128	+	0.911388i
$377$	−18.4491	+	25.3931i	−0.950179	+	1.30781i
$378$	0.361035	+	0.496923i	0.0185697	+	0.0255589i
$379$	−4.09427	+	12.6009i	−0.210309	+	0.647263i	0.789145	+	0.614207i	$0.210524\pi$
$379$	−4.09427	+	12.6009i	−0.210309	+	0.647263i	−0.999453	+	0.0330562i	$0.989476\pi$
$380$	−2.26501	−	2.26103i	−0.116193	−	0.115988i
$381$	−4.84778	+	3.52212i	−0.248359	+	0.180443i
$382$	−7.46912	+	10.2804i	−0.382153	+	0.525989i
$383$	19.6375	−	6.38061i	1.00343	−	0.326034i	0.239194	−	0.970972i	$-0.423117\pi$
$383$	19.6375	−	6.38061i	1.00343	−	0.326034i	0.764235	+	0.644938i	$0.223117\pi$
$384$	−7.01048			−0.357752
$385$	3.54685	−	0.515936i	0.180764	−	0.0262945i
$386$	−30.2441			−1.53938
$387$	5.67796	−	1.84488i	0.288627	−	0.0937806i
$388$	−0.816314	+	1.12356i	−0.0414421	+	0.0570401i
$389$	18.4848	−	13.4300i	0.937219	−	0.680929i	−0.0105307	−	0.999945i	$-0.503352\pi$
$389$	18.4848	−	13.4300i	0.937219	−	0.680929i	0.947750	+	0.319015i	$0.103352\pi$
$390$	−6.31262	+	6.32374i	−0.319652	+	0.320215i
$391$	−6.61817	+	20.3686i	−0.334695	+	1.03009i
$392$	−12.0542	−	16.5912i	−0.608831	−	0.837985i
$393$	6.45499	−	8.88453i	0.325611	−	0.448165i
$394$	9.67634	+	29.7807i	0.487487	+	1.50033i
$395$	−7.58572	+	14.9203i	−0.381679	+	0.750719i
$396$	0.410668	−	1.20812i	0.0206368	−	0.0607104i
$397$			7.71249i			0.387079i	0.981093	+	0.193539i	$0.0619967\pi$
$397$			7.71249i			0.387079i	−0.981093	+	0.193539i	$0.938003\pi$
$398$	−18.5612	+	6.03089i	−0.930387	+	0.302301i
$399$	−1.45454	−	1.05679i	−0.0728182	−	0.0529056i
$400$	−14.6666	−	4.73695i	−0.733330	−	0.236848i
$401$	−2.53112	+	7.78999i	−0.126398	+	0.389013i	−0.994153	−	0.107979i	$-0.965562\pi$
$401$	−2.53112	+	7.78999i	−0.126398	+	0.389013i	0.867755	+	0.496992i	$0.165562\pi$
$402$	−7.22919	−	2.34891i	−0.360559	−	0.117153i
$403$	−10.7000	−	14.7273i	−0.533007	−	0.733621i
$404$	−2.36421	−	1.71770i	−0.117624	−	0.0854586i
$405$	2.20885	+	0.347855i	0.109758	+	0.0172850i
$406$	−6.13181			−0.304317
$407$	−6.36889	+	8.52151i	−0.315694	+	0.422396i
$408$		−	7.60778i		−	0.376641i
$409$	1.05779	+	3.25553i	0.0523041	+	0.160975i	0.973797	−	0.227421i	$-0.0730292\pi$
$409$	1.05779	+	3.25553i	0.0523041	+	0.160975i	−0.921493	+	0.388396i	$0.873029\pi$
$410$	10.1657	+	19.9080i	0.502048	+	0.983186i
$411$	−0.883527	+	0.641920i	−0.0435812	+	0.0316636i
$412$	−1.39320	−	0.452678i	−0.0686381	−	0.0223019i
$413$	0.173712	+	0.0564424i	0.00854780	+	0.00277735i
$414$	8.77283	−	6.37383i	0.431161	−	0.313257i
$415$	4.12582	+	8.07980i	0.202529	+	0.396622i
$416$	2.08308	+	6.41106i	0.102131	+	0.314328i
$417$		−	8.42516i		−	0.412582i
$418$	0.211842	−	15.6798i	0.0103615	−	0.766922i
$419$	18.3593			0.896910			0.448455	−	0.893805i	$-0.351974\pi$
$419$	18.3593			0.896910			0.448455	+	0.893805i	$0.351974\pi$
$420$	0.410707	+	0.0646793i	0.0200405	+	0.00315603i
$421$	−28.7827	−	20.9119i	−1.40278	−	1.01918i	−0.994323	−	0.106407i	$-0.966065\pi$
$421$	−28.7827	−	20.9119i	−1.40278	−	1.01918i	−0.408462	−	0.912775i	$-0.633935\pi$
$422$	19.3189	+	26.5902i	0.940430	+	1.29439i
$423$	5.83090	+	1.89457i	0.283508	+	0.0921173i
$424$	1.48185	−	4.56068i	0.0719652	−	0.221486i
$425$	3.85735	−	11.9432i	0.187109	−	0.579329i
$426$	−8.57954	−	6.23340i	−0.415680	−	0.302009i
$427$	−1.38283	+	0.449307i	−0.0669196	+	0.0217435i
$428$			0.183696i			0.00887929i
$429$	10.4269	+	0.140873i	0.503417	+	0.00680143i
$430$	−7.68935	+	15.1241i	−0.370813	+	0.729348i
$431$	−3.33565	−	10.2661i	−0.160672	−	0.494499i	0.838019	−	0.545641i	$-0.183714\pi$
$431$	−3.33565	−	10.2661i	−0.160672	−	0.494499i	−0.998691	+	0.0511423i	$0.983714\pi$
$432$	−1.81186	+	2.49381i	−0.0871731	+	0.119983i
$433$	6.53523	+	8.99497i	0.314063	+	0.432271i	0.936643	−	0.350286i	$-0.113915\pi$
$433$	6.53523	+	8.99497i	0.314063	+	0.432271i	−0.622580	+	0.782556i	$0.713915\pi$
$434$	1.09896	−	3.38224i	0.0527516	−	0.162353i
$435$	−15.7705	+	15.7983i	−0.756137	+	0.757469i
$436$	−2.15414	+	1.56507i	−0.103165	+	0.0749535i
$437$	−18.6569	+	25.6790i	−0.892479	+	1.22839i
$438$	−0.183020	+	0.0594669i	−0.00874505	+	0.00284144i
$439$	12.5701			0.599937			0.299969	−	0.953949i	$-0.403024\pi$
$439$	12.5701			0.599937			0.299969	+	0.953949i	$0.403024\pi$
$440$	9.95071	+	20.1547i	0.474381	+	0.960836i
$441$	−6.76643			−0.322211
$442$	9.53947	−	3.09956i	0.453746	−	0.147431i
$443$	12.0838	−	16.6320i	0.574120	−	0.790209i	−0.418915	−	0.908025i	$-0.637590\pi$
$443$	12.0838	−	16.6320i	0.574120	−	0.790209i	0.993035	+	0.117817i	$0.0375896\pi$
$444$	−0.998395	+	0.725376i	−0.0473817	+	0.0344248i
$445$	−26.9531	−	26.9057i	−1.27770	−	1.27545i
$446$	−2.10825	+	6.48854i	−0.0998287	+	0.307241i
$447$	−10.1273	−	13.9391i	−0.479006	−	0.659296i
$448$	−2.52537	+	3.47587i	−0.119312	+	0.164219i
$449$	−4.44643	−	13.6847i	−0.209840	−	0.645821i	−0.999480	−	0.0322505i	$-0.989733\pi$
$449$	−4.44643	−	13.6847i	−0.209840	−	0.645821i	0.789640	−	0.613571i	$-0.210267\pi$
$450$	−5.13445	+	3.74422i	−0.242040	+	0.176504i
$451$	8.39589	−	24.6994i	0.395347	−	1.16305i
$452$		−	4.17977i		−	0.196600i
$453$	−12.4435	+	4.04313i	−0.584645	+	0.189963i
$454$	7.94231	+	5.77043i	0.372751	+	0.270820i
$455$	0.534480	+	3.35547i	0.0250568	+	0.157307i
$456$	3.48421	−	10.7233i	0.163163	−	0.502164i
$457$	−10.7419	−	3.49025i	−0.502485	−	0.163267i	0.0467970	−	0.998904i	$-0.485099\pi$
$457$	−10.7419	−	3.49025i	−0.502485	−	0.163267i	−0.549282	+	0.835637i	$0.685099\pi$
$458$	6.03723	+	8.30954i	0.282101	+	0.388279i
$459$	−2.03074	−	1.47542i	−0.0947867	−	0.0688666i
$460$	1.14187	−	7.25076i	0.0532399	−	0.338068i
$461$	35.8299			1.66876			0.834382	−	0.551186i	$-0.185825\pi$
$461$	35.8299			1.66876			0.834382	+	0.551186i	$0.185825\pi$
$462$	1.17504	+	1.66413i	0.0546680	+	0.0774224i
$463$		−	30.6184i		−	1.42296i	−0.702708	−	0.711479i	$-0.748026\pi$
$463$		−	30.6184i		−	1.42296i	0.702708	−	0.711479i	$-0.251974\pi$
$464$	−9.50924	−	29.2664i	−0.441455	−	1.35866i
$465$	−5.88773	−	11.5302i	−0.273037	−	0.534702i
$466$	26.2098	−	19.0425i	1.21415	−	0.882129i
$467$	38.1044	+	12.3809i	1.76326	+	0.572919i	0.997530	−	0.0702395i	$-0.0223763\pi$
$467$	38.1044	+	12.3809i	1.76326	+	0.572919i	0.765733	+	0.643158i	$0.222376\pi$
$468$	1.15044	+	0.373801i	0.0531792	+	0.0172790i
$469$	−2.33845	+	1.69898i	−0.107979	+	0.0784516i
$470$	−15.5175	+	7.92378i	−0.715770	+	0.365497i
$471$	7.26455	+	22.3580i	0.334733	+	1.03020i
$472$			1.14545i			0.0527236i
$473$	18.9126	−	5.86382i	0.869603	−	0.269619i
$474$	−9.51345			−0.436967
$475$	10.9067	−	15.0675i	0.500436	−	0.691346i
$476$	−0.377590	−	0.274335i	−0.0173068	−	0.0125741i
$477$	−0.929993	−	1.28003i	−0.0425815	−	0.0586084i
$478$	−1.12275	−	0.364802i	−0.0513532	−	0.0166857i
$479$	−6.09354	+	18.7540i	−0.278421	+	0.856892i	0.709873	+	0.704330i	$0.248752\pi$
$479$	−6.09354	+	18.7540i	−0.278421	+	0.856892i	−0.988294	+	0.152562i	$0.951248\pi$
$480$	0.754131	+	4.73443i	0.0344212	+	0.216096i
$481$	−8.15913	−	5.92795i	−0.372024	−	0.270291i
$482$	−12.5416	+	4.07502i	−0.571255	+	0.185612i
$483$		−	4.12353i		−	0.187627i
$484$	1.41604	−	3.98812i	0.0643653	−	0.181278i
$485$	−7.19516	−	3.65815i	−0.326715	−	0.166108i
$486$	0.392740	+	1.20873i	0.0178150	+	0.0548290i
$487$	10.6605	−	14.6729i	0.483072	−	0.664892i	−0.496020	−	0.868311i	$-0.665206\pi$
$487$	10.6605	−	14.6729i	0.483072	−	0.664892i	0.979092	+	0.203420i	$0.0652056\pi$
$488$	−5.35961	−	7.37686i	−0.242618	−	0.333935i
$489$	6.16167	−	18.9637i	0.278640	−	0.857567i
$490$	13.5853	−	13.6092i	0.613722	−	0.614802i
$491$	8.75115	−	6.35808i	0.394934	−	0.286936i	−0.372540	−	0.928016i	$-0.621513\pi$
$491$	8.75115	−	6.35808i	0.394934	−	0.286936i	0.767474	+	0.641080i	$0.221513\pi$
$492$	1.77874	−	2.44822i	0.0801916	−	0.110374i
$493$	23.8320	−	7.74348i	1.07334	−	0.348749i
$494$	14.8656			0.668835
$495$	7.30966	+	1.25257i	0.328545	+	0.0562987i
$496$	17.8473			0.801367
$497$	−3.83530	+	1.24616i	−0.172037	+	0.0558981i
$498$	−3.03089	+	4.17166i	−0.135817	+	0.186937i
$499$	−4.58883	+	3.33398i	−0.205424	+	0.149250i	−0.685741	−	0.727846i	$-0.740522\pi$
$499$	−4.58883	+	3.33398i	−0.205424	+	0.149250i	0.480317	+	0.877095i	$0.340522\pi$
$500$	−0.661677	+	4.25024i	−0.0295911	+	0.190076i
$501$	−5.95668	+	18.3328i	−0.266125	+	0.819047i
$502$	−17.5897	−	24.2102i	−0.785068	−	1.08055i
$503$	18.3933	−	25.3161i	0.820115	−	1.12879i	−0.169569	−	0.985518i	$-0.554237\pi$
$503$	18.3933	−	25.3161i	0.820115	−	1.12879i	0.989683	−	0.143273i	$-0.0457626\pi$
$504$	0.452640	+	1.39308i	0.0201622	+	0.0620528i
$505$	7.69751	−	15.1401i	0.342535	−	0.673727i
$506$	29.3791	−	20.7446i	1.30606	−	0.922211i
$507$		−	3.11448i		−	0.138319i
$508$	−2.19255	+	0.712403i	−0.0972787	+	0.0316078i
$509$	−23.4452	−	17.0339i	−1.03919	−	0.755015i	−0.0690620	−	0.997612i	$-0.522001\pi$
$509$	−23.4452	−	17.0339i	−1.03919	−	0.755015i	−0.970127	+	0.242597i	$0.922001\pi$
$510$	7.04470	−	1.12213i	0.311945	−	0.0496885i
$511$	−0.0226132	+	0.0695962i	−0.00100035	+	0.00307876i
$512$	−24.0561	−	7.81630i	−1.06314	−	0.345435i
$513$	−2.18665	−	3.00966i	−0.0965429	−	0.132880i
$514$	16.5537	+	12.0270i	0.730152	+	0.530487i
$515$	1.32449	−	8.41036i	0.0583638	−	0.370605i
$516$	2.29691			0.101116
$517$	19.2522	+	6.54427i	0.846713	+	0.287817i
$518$		−	1.97023i		−	0.0865670i
$519$	1.19555	+	3.67952i	0.0524787	+	0.161513i
$520$	−18.9772	+	9.69042i	−0.832206	+	0.424953i
$521$	−17.3374	+	12.5964i	−0.759565	+	0.551856i	−0.898777	−	0.438406i	$-0.855543\pi$
$521$	−17.3374	+	12.5964i	−0.759565	+	0.551856i	0.139212	+	0.990263i	$0.455543\pi$
$522$	−12.0666	−	3.92069i	−0.528143	−	0.171604i
$523$	−32.7761	−	10.6496i	−1.43320	−	0.465674i	−0.513428	−	0.858133i	$-0.671625\pi$
$523$	−32.7761	−	10.6496i	−1.43320	−	0.465674i	−0.919770	+	0.392458i	$0.871625\pi$
$524$	3.41816	−	2.48344i	0.149323	−	0.108490i
$525$	0.00425209	+	2.41645i	0.000185576	+	0.105463i
$526$	−0.860240	−	2.64755i	−0.0375083	−	0.115439i
$527$			14.5333i			0.633079i
$528$	−6.12044	+	8.18909i	−0.266358	+	0.356384i
$529$	−49.7980			−2.16513
$530$	4.44170	+	0.699490i	0.192935	+	0.0303839i
$531$	0.305754	+	0.222143i	0.0132686	+	0.00964019i
$532$	−0.406580	−	0.559609i	−0.0176275	−	0.0242621i
$533$	23.5202	+	7.64217i	1.01877	+	0.331019i
$534$	6.68901	−	20.5867i	0.289462	−	0.890872i
$535$	−1.05435	+	0.167944i	−0.0455836	+	0.00726086i
$536$	−14.6649	−	10.6547i	−0.633429	−	0.460213i
$537$	16.3451	−	5.31086i	0.705345	−	0.229180i
$538$			13.2623i			0.571777i
$539$	−22.4397	−	0.303172i	−0.966545	−	0.0130585i
$540$	0.766865	+	0.389888i	0.0330006	+	0.0167781i
$541$	−5.01668	−	15.4398i	−0.215684	−	0.663807i	−0.999104	−	0.0423147i	$-0.986527\pi$
$541$	−5.01668	−	15.4398i	−0.215684	−	0.663807i	0.783420	−	0.621492i	$-0.213473\pi$
$542$	−1.29194	+	1.77821i	−0.0554937	+	0.0763806i
$543$	−4.10846	−	5.65480i	−0.176311	−	0.242671i
$544$	1.66304	−	5.11830i	0.0713022	−	0.219445i
$545$	−10.9524	−	10.9332i	−0.469150	−	0.468325i
$546$	−1.56239	+	1.13514i	−0.0668640	+	0.0485795i
$547$	−0.0775502	+	0.106739i	−0.00331581	+	0.00456382i	−0.810672	−	0.585501i	$-0.800898\pi$
$547$	−0.0775502	+	0.106739i	−0.00331581	+	0.00456382i	0.807356	+	0.590065i	$0.200898\pi$
$548$	−0.399601	+	0.129838i	−0.0170701	+	0.00554642i
$549$	−3.00852			−0.128400
$550$	−17.1952	+	12.1870i	−0.733208	+	0.519654i
$551$	37.1380			1.58213
$552$	24.5939	−	7.99105i	1.04679	−	0.340122i
$553$	−2.12639	+	2.92673i	−0.0904234	+	0.124457i
$554$	11.9673	−	8.69476i	0.508442	−	0.369405i
$555$	−5.07619	−	5.06727i	−0.215472	−	0.215094i
$556$	1.00166	−	3.08278i	0.0424797	−	0.130739i
$557$	−3.32267	−	4.57327i	−0.140786	−	0.193776i	0.732801	−	0.680443i	$-0.238212\pi$
$557$	−3.32267	−	4.57327i	−0.140786	−	0.193776i	−0.873587	+	0.486667i	$0.838212\pi$
$558$	4.32522	−	5.95315i	0.183101	−	0.252017i
$559$	5.80054	+	17.8522i	0.245337	+	0.755068i
$560$	−2.96944	−	1.50972i	−0.125482	−	0.0637972i
$561$	−6.66847	−	4.98394i	−0.281543	−	0.210422i
$562$			15.2716i			0.644192i
$563$	−33.6716	+	10.9406i	−1.41909	+	0.461090i	−0.915313	−	0.402744i	$-0.868056\pi$
$563$	−33.6716	+	10.9406i	−1.41909	+	0.461090i	−0.503776	+	0.863834i	$0.668056\pi$
$564$	1.90829	+	1.38646i	0.0803536	+	0.0583803i
$565$	23.9904	−	3.82135i	1.00928	−	0.160765i
$566$	−10.8355	+	33.3481i	−0.455449	+	1.40173i
$567$	0.459637	+	0.149345i	0.0193029	+	0.00627191i
$568$	−14.8650	−	20.4599i	−0.623721	−	0.858478i
$569$	9.76497	+	7.09467i	0.409369	+	0.297424i	0.773346	−	0.633984i	$-0.218581\pi$
$569$	9.76497	+	7.09467i	0.409369	+	0.297424i	−0.363977	+	0.931408i	$0.618581\pi$
$570$	10.4435	+	1.64468i	0.437432	+	0.0688879i
$571$	−2.74339			−0.114807			−0.0574037	−	0.998351i	$-0.518282\pi$
$571$	−2.74339			−0.114807			−0.0574037	+	0.998351i	$0.518282\pi$
$572$	3.79849	+	1.29119i	0.158823	+	0.0539874i
$573$			9.99835i			0.417687i
$574$	1.49296	+	4.59485i	0.0623149	+	0.191786i
$575$	42.6608	−	0.0750677i	1.77908	−	0.00313054i
$576$	−7.19208	+	5.22536i	−0.299670	+	0.217723i
$577$	−20.8487	−	6.77416i	−0.867944	−	0.282012i	−0.159001	−	0.987278i	$-0.550827\pi$
$577$	−20.8487	−	6.77416i	−0.867944	−	0.282012i	−0.708943	+	0.705266i	$0.750827\pi$
$578$	12.9325	+	4.20202i	0.537921	+	0.174781i
$579$	−19.2520	+	13.9874i	−0.800086	+	0.581297i
$580$	−7.64869	+	3.90568i	−0.317595	+	0.162175i
$581$	0.605927	+	1.86485i	0.0251381	+	0.0773671i
$582$		−	4.58778i		−	0.190170i
$583$	−3.02681	−	4.28665i	−0.125357	−	0.177535i
$584$	−0.458915			−0.0189900
$585$	−1.09370	+	6.94488i	−0.0452189	+	0.287136i
$586$	−3.52531	−	2.56129i	−0.145629	−	0.105806i
$587$	9.08718	+	12.5074i	0.375068	+	0.516237i	0.954270	−	0.298947i	$-0.0966355\pi$
$587$	9.08718	+	12.5074i	0.375068	+	0.516237i	−0.579201	+	0.815184i	$0.696636\pi$
$588$	−2.47585	−	0.804452i	−0.102102	−	0.0331751i
$589$	−6.65594	+	20.4849i	−0.274253	+	0.844065i
$590$	−1.06067	+	0.168951i	−0.0436671	+	0.00695558i
$591$	19.9326	+	14.4819i	0.819918	+	0.595705i
$592$	9.40369	−	3.05544i	0.386489	−	0.125578i
$593$			44.6178i			1.83223i	0.400910	+	0.916117i	$0.368694\pi$
$593$			44.6178i			1.83223i	−0.400910	+	0.916117i	$0.631306\pi$
$594$	1.24829	+	4.02613i	0.0512181	+	0.165194i
$595$	1.22938	−	2.41805i	0.0503996	−	0.0991304i
$596$	−2.04841	−	6.30436i	−0.0839062	−	0.258237i
$597$	−9.02600	+	12.4232i	−0.369410	+	0.508449i
$598$	20.0401	+	27.5829i	0.819502	+	1.12795i
$599$	−12.1492	+	37.3913i	−0.496402	+	1.52777i	0.318359	+	0.947970i	$0.396868\pi$
$599$	−12.1492	+	37.3913i	−0.496402	+	1.52777i	−0.814761	+	0.579798i	$0.803132\pi$
$600$	−14.4042	+	4.70825i	−0.588049	+	0.192213i
$601$	9.20734	−	6.68952i	0.375575	−	0.272871i	−0.383944	−	0.923356i	$-0.625434\pi$
$601$	9.20734	−	6.68952i	0.375575	−	0.272871i	0.759519	+	0.650485i	$0.225434\pi$
$602$	−2.15544	+	2.96671i	−0.0878492	+	0.120914i
$603$	−5.68810	+	1.84818i	−0.231637	+	0.0752636i
$604$	−5.03377			−0.204821
$605$	24.1851	+	4.48143i	0.983262	+	0.182196i
$606$	9.65365			0.392153
$607$	−27.5789	+	8.96094i	−1.11939	+	0.363713i	−0.809536	−	0.587070i	$-0.800281\pi$
$607$	−27.5789	+	8.96094i	−1.11939	+	0.363713i	−0.309858	+	0.950783i	$0.600281\pi$
$608$	4.68816	−	6.45270i	0.190130	−	0.261692i
$609$	−3.90323	+	2.83586i	−0.158167	+	0.114915i
$610$	6.04035	−	6.05099i	0.244567	−	0.244997i
$611$	−5.95677	+	18.3331i	−0.240985	+	0.741676i
$612$	−0.567640	−	0.781290i	−0.0229455	−	0.0315818i
$613$	−8.01390	+	11.0302i	−0.323679	+	0.445505i	−0.939586	−	0.342313i	$-0.888790\pi$
$613$	−8.01390	+	11.0302i	−0.323679	+	0.445505i	0.615907	+	0.787819i	$0.288790\pi$
$614$	−6.02215	−	18.5343i	−0.243034	−	0.747982i
$615$	15.6781	+	7.97105i	0.632204	+	0.321424i
$616$	1.43868	+	4.64019i	0.0579662	+	0.186959i
$617$			16.8378i			0.677863i	0.940811	+	0.338932i	$0.110066\pi$
$617$			16.8378i			0.677863i	−0.940811	+	0.338932i	$0.889934\pi$
$618$	4.60233	−	1.49539i	0.185133	−	0.0601533i
$619$	18.0629	+	13.1235i	0.726009	+	0.527476i	0.888298	−	0.459267i	$-0.151888\pi$
$619$	18.0629	+	13.1235i	0.726009	+	0.527476i	−0.162290	+	0.986743i	$0.551888\pi$
$620$	−0.783517	−	4.91892i	−0.0314668	−	0.197548i
$621$	2.63659	−	8.11458i	0.105803	−	0.325627i
$622$	−5.24838	−	1.70530i	−0.210441	−	0.0683764i
$623$	−4.83821	−	6.65923i	−0.193839	−	0.266796i
$624$	−7.84085	−	5.69671i	−0.313885	−	0.228051i
$625$	−24.9998	+	0.0879818i	−0.999994	+	0.00351927i
$626$	−13.2732			−0.530503
$627$	−7.11678	−	10.0790i	−0.284217	−	0.402516i
$628$			9.04451i			0.360915i
$629$	2.48808	+	7.65753i	0.0992063	+	0.305326i
$630$	−1.22321	+	0.624614i	−0.0487340	+	0.0248852i
$631$	−10.2085	+	7.41689i	−0.406393	+	0.295262i	−0.772140	−	0.635453i	$-0.780814\pi$
$631$	−10.2085	+	7.41689i	−0.406393	+	0.295262i	0.365747	+	0.930714i	$0.380814\pi$
$632$	−21.5766	−	7.01068i	−0.858273	−	0.278870i
$633$	24.5951	+	7.99142i	0.977566	+	0.317630i
$634$	−17.1105	+	12.4315i	−0.679544	+	0.493718i
$635$	−6.09349	−	11.9332i	−0.241813	−	0.473554i
$636$	−0.188106	−	0.578930i	−0.00745888	−	0.0229561i
$637$		−	21.2745i		−	0.842926i
$638$	−39.8412	−	13.5429i	−1.57733	−	0.536169i
$639$	−8.34418			−0.330091
$640$	2.43863	−	15.4851i	0.0963952	−	0.612101i
$641$	19.6268	+	14.2597i	0.775212	+	0.563224i	0.903538	−	0.428508i	$-0.140960\pi$
$641$	19.6268	+	14.2597i	0.775212	+	0.563224i	−0.128326	+	0.991732i	$0.540960\pi$
$642$	−0.356683	−	0.490932i	−0.0140772	−	0.0193755i
$643$	17.7163	+	5.75639i	0.698665	+	0.227010i	0.636749	−	0.771072i	$-0.280279\pi$
$643$	17.7163	+	5.75639i	0.698665	+	0.227010i	0.0619159	+	0.998081i	$0.480279\pi$
$644$	0.490241	−	1.50881i	0.0193182	−	0.0594553i
$645$	2.09995	+	13.1835i	0.0826855	+	0.519099i
$646$	−9.60143	−	6.97585i	−0.377763	−	0.274461i
$647$	3.11855	−	1.01328i	0.122603	−	0.0398361i	−0.247073	−	0.968997i	$-0.579469\pi$
$647$	3.11855	−	1.01328i	0.122603	−	0.0398361i	0.369676	+	0.929161i	$0.379469\pi$
$648$			3.03083i			0.119062i
$649$	1.00402	+	0.750398i	0.0394114	+	0.0294557i
$650$	−11.7723	−	16.1433i	−0.461747	−	0.633194i
$651$	−0.864685	−	2.66123i	−0.0338897	−	0.104302i
$652$	4.50914	−	6.20629i	0.176591	−	0.243057i
$653$	−7.23624	−	9.95983i	−0.283176	−	0.389758i	0.643607	−	0.765356i	$-0.277437\pi$
$653$	−7.23624	−	9.95983i	−0.283176	−	0.389758i	−0.926783	+	0.375598i	$0.877437\pi$
$654$	2.71808	−	8.36540i	0.106285	−	0.327113i
$655$	17.3791	+	17.3486i	0.679059	+	0.677866i
$656$	−19.6154	+	14.2514i	−0.765853	+	0.556425i
$657$	−0.0889998	+	0.122498i	−0.00347221	+	0.00477909i
$658$	−3.58151	+	1.16370i	−0.139622	+	0.0453659i
$659$	−28.5993			−1.11407			−0.557035	−	0.830489i	$-0.688061\pi$
$659$	−28.5993			−1.11407			−0.557035	+	0.830489i	$0.688061\pi$
$660$	2.52570	+	1.32735i	0.0983128	+	0.0516671i
$661$	37.2512			1.44890			0.724452	−	0.689325i	$-0.242093\pi$
$661$	37.2512			1.44890			0.724452	+	0.689325i	$0.242093\pi$
$662$	38.6858	−	12.5698i	1.50357	−	0.488538i
$663$	4.63889	−	6.38489i	0.180160	−	0.247969i
$664$	−9.94830	+	7.22786i	−0.386069	+	0.280496i
$665$	2.84025	−	2.84525i	0.110140	−	0.110334i
$666$	1.25977	−	3.87717i	0.0488151	−	0.150237i
$667$	50.0652	+	68.9089i	1.93853	+	2.66816i
$668$	−4.35912	+	5.99981i	−0.168659	+	0.232140i
$669$	1.65882	+	5.10534i	0.0641339	+	0.197384i
$670$	7.70308	−	15.1511i	0.297596	−	0.585337i
$671$	−9.97721	−	0.134797i	−0.385166	−	0.00520380i
$672$			1.03617i			0.0399713i
$673$	22.6824	−	7.36996i	0.874343	−	0.284091i	0.162736	−	0.986670i	$-0.447968\pi$
$673$	22.6824	−	7.36996i	0.874343	−	0.284091i	0.711606	+	0.702578i	$0.247968\pi$
$674$	−14.7295	−	10.7016i	−0.567361	−	0.412212i
$675$	−1.53672	+	4.75799i	−0.0591482	+	0.183135i
$676$	0.370277	−	1.13959i	0.0142414	−	0.0438306i
$677$	−4.63459	−	1.50587i	−0.178122	−	0.0578753i	0.218598	−	0.975815i	$-0.429852\pi$
$677$	−4.63459	−	1.50587i	−0.178122	−	0.0578753i	−0.396720	+	0.917940i	$0.629852\pi$
$678$	8.11586	+	11.1705i	0.311688	+	0.429001i
$679$	−1.41139	−	1.02543i	−0.0541641	−	0.0393525i
$680$	16.8044	+	2.64640i	0.644420	+	0.101485i
$681$	7.72444			0.296001
$682$	14.6105	−	19.5488i	0.559467	−	0.748561i
$683$		−	23.6494i		−	0.904919i	−0.891785	−	0.452459i	$-0.850547\pi$
$683$		−	23.6494i		−	0.904919i	0.891785	−	0.452459i	$-0.149453\pi$
$684$	−0.442284	−	1.36121i	−0.0169111	−	0.0520471i
$685$	−1.11056	−	2.17487i	−0.0424324	−	0.0830975i
$686$	6.84085	−	4.97017i	0.261185	−	0.189762i
$687$	7.68605	+	2.49735i	0.293241	+	0.0952798i
$688$	−17.5024	−	5.68688i	−0.667273	−	0.216810i
$689$	4.02456	−	2.92402i	0.153324	−	0.111396i
$690$	11.0271	+	21.5950i	0.419796	+	0.822107i
$691$	4.30419	+	13.2469i	0.163739	+	0.503937i	0.998941	−	0.0460061i	$-0.0146494\pi$
$691$	4.30419	+	13.2469i	0.163739	+	0.503937i	−0.835202	+	0.549943i	$0.814649\pi$
$692$			1.48848i			0.0565835i
$693$	1.51761	+	0.515871i	0.0576494	+	0.0195963i
$694$	−20.4156			−0.774966
$695$	18.6099	+	2.93073i	0.705913	+	0.111169i
$696$	−24.4781	−	17.7844i	−0.927839	−	0.674115i
$697$	−11.6051	−	15.9731i	−0.439575	−	0.605023i
$698$	−4.80690	−	1.56186i	−0.181944	−	0.0591172i
$699$	7.87710	−	24.2432i	0.297939	−	0.916963i
$700$	−0.285733	+	0.884690i	−0.0107997	+	0.0334381i
$701$	−33.3958	−	24.2635i	−1.26134	−	0.916419i	−0.262520	−	0.964927i	$-0.584554\pi$
$701$	−33.3958	−	24.2635i	−1.26134	−	0.916419i	−0.998823	+	0.0485072i	$0.984554\pi$
$702$	−3.80039	+	1.23482i	−0.143437	+	0.0466054i
$703$			11.9329i			0.450058i
$704$	−24.0854	+	17.0067i	−0.907752	+	0.640965i
$705$	−6.21313	+	12.2205i	−0.234000	+	0.460251i
$706$	3.68223	+	11.3327i	0.138582	+	0.426513i
$707$	2.15773	−	2.96986i	0.0811497	−	0.111693i
$708$	0.0854656	+	0.117633i	0.00321199	+	0.00442093i
$709$	−6.87397	+	21.1559i	−0.258157	+	0.794526i	0.735034	+	0.678030i	$0.237166\pi$
$709$	−6.87397	+	21.1559i	−0.258157	+	0.794526i	−0.993191	+	0.116496i	$0.962834\pi$
$710$	16.7530	−	16.7825i	0.628731	−	0.629838i
$711$	−6.05583	+	4.39982i	−0.227111	+	0.165006i
$712$	30.3416	−	41.7616i	1.13710	−	1.56508i
$713$	−46.9822	+	15.2654i	−1.75950	+	0.571695i
$714$	1.54180			0.0577003
$715$	−3.93823	+	22.9825i	−0.147281	+	0.859496i
$716$	6.61212			0.247106
$717$	−0.883403	+	0.287035i	−0.0329913	+	0.0107195i
$718$	−16.2386	+	22.3505i	−0.606018	+	0.834112i
$719$	28.1014	−	20.4168i	1.04800	−	0.761420i	0.0761724	−	0.997095i	$-0.475730\pi$
$719$	28.1014	−	20.4168i	1.04800	−	0.761420i	0.971832	+	0.235675i	$0.0757301\pi$
$720$	−4.87817	−	4.86960i	−0.181799	−	0.181479i
$721$	0.568644	−	1.75011i	0.0211774	−	0.0651773i
$722$	3.85507	+	5.30605i	0.143471	+	0.197471i
$723$	−6.09879	+	8.39426i	−0.226816	+	0.312186i
$724$	−0.830999	−	2.55755i	−0.0308838	−	0.0950507i
$725$	−29.4101	−	40.3301i	−1.09226	−	1.49782i
$726$	3.95935	+	13.4079i	0.146945	+	0.497613i
$727$			7.34209i			0.272303i	0.990688	+	0.136152i	$0.0434734\pi$
$727$			7.34209i			0.272303i	−0.990688	+	0.136152i	$0.956527\pi$
$728$	−4.38003	+	1.42316i	−0.162335	+	0.0527457i
$729$	0.809017	+	0.587785i	0.0299636	+	0.0217698i
$730$	−0.0676887	−	0.424949i	−0.00250527	−	0.0157281i
$731$	4.63089	−	14.2524i	0.171280	−	0.527145i
$732$	−1.10082	−	0.357679i	−0.0406875	−	0.0132202i
$733$	18.9400	+	26.0687i	0.699566	+	0.962870i	0.999959	+	0.00905455i	$0.00288219\pi$
$733$	18.9400	+	26.0687i	0.699566	+	0.962870i	−0.300393	+	0.953816i	$0.597118\pi$
$734$	32.2675	+	23.4437i	1.19101	+	0.865323i
$735$	2.35374	−	14.9460i	0.0868188	−	0.551291i
$736$	18.2929			0.674287
$737$	−18.9464	+	5.87429i	−0.697899	+	0.216382i
$738$			9.99670i			0.367984i
$739$	12.9785	+	39.9438i	0.477423	+	1.46936i	0.842662	+	0.538443i	$0.180987\pi$
$739$	12.9785	+	39.9438i	0.477423	+	1.46936i	−0.365239	+	0.930914i	$0.619013\pi$
$740$	−1.25495	−	2.45763i	−0.0461328	−	0.0903441i
$741$	9.46275	−	6.87509i	0.347623	−	0.252563i
$742$	0.924269	+	0.300313i	0.0339310	+	0.0110248i
$743$	6.60590	+	2.14639i	0.242347	+	0.0787433i	0.427672	−	0.903934i	$-0.359334\pi$
$743$	6.60590	+	2.14639i	0.242347	+	0.0787433i	−0.185325	+	0.982677i	$0.559334\pi$
$744$	14.1967	−	10.3145i	0.520475	−	0.378147i
$745$	34.3121	−	17.5209i	1.25710	−	0.641917i
$746$	−9.13809	−	28.1241i	−0.334569	−	1.02970i
$747$			4.05723i			0.148446i
$748$	−1.84747	−	2.61644i	−0.0675503	−	0.0956666i
$749$	−0.230755			−0.00843159
$750$	−6.48435	−	12.6436i	−0.236775	−	0.461681i
$751$	−1.30384	−	0.947292i	−0.0475777	−	0.0345672i	0.563742	−	0.825951i	$-0.309361\pi$
$751$	−1.30384	−	0.947292i	−0.0475777	−	0.0345672i	−0.611320	+	0.791384i	$0.709361\pi$
$752$	−11.1084	−	15.2895i	−0.405083	−	0.557549i
$753$	−22.3936	−	7.27614i	−0.816070	−	0.265157i
$754$	12.3271	−	37.9390i	0.448928	−	1.38166i
$755$	−4.60212	−	28.8921i	−0.167488	−	1.05149i
$756$	0.150427	+	0.109291i	0.00547096	+	0.00397489i
$757$	−8.78193	+	2.85342i	−0.319185	+	0.103709i	−0.464228	−	0.885716i	$-0.653668\pi$
$757$	−8.78193	+	2.85342i	−0.319185	+	0.103709i	0.145043	+	0.989425i	$0.453668\pi$
$758$		−	16.8390i		−	0.611620i
$759$	9.10735	−	26.7924i	0.330576	−	0.972504i
$760$	22.4741	+	11.4262i	0.815222	+	0.414473i
$761$	8.35526	+	25.7148i	0.302878	+	0.932162i	0.980461	+	0.196716i	$0.0630276\pi$
$761$	8.35526	+	25.7148i	0.302878	+	0.932162i	−0.677583	+	0.735447i	$0.736972\pi$
$762$	4.47637	−	6.16119i	0.162162	−	0.223197i
$763$	−1.96601	−	2.70598i	−0.0711743	−	0.0979630i
$764$	−1.18869	+	3.65841i	−0.0430053	+	0.132357i
$765$	3.96537	−	3.97235i	0.143368	−	0.143621i
$766$	−21.2305	+	15.4248i	−0.767088	+	0.557322i
$767$	−0.698446	+	0.961328i	−0.0252194	+	0.0347115i
$768$	−8.43585	+	2.74097i	−0.304402	+	0.0989063i
$769$	−12.6433			−0.455927			−0.227964	−	0.973670i	$-0.573207\pi$
$769$	−12.6433			−0.455927			−0.227964	+	0.973670i	$0.573207\pi$
$770$	−4.08455	+	2.01662i	−0.147197	+	0.0726738i
$771$	16.0996			0.579813
$772$	−8.70729	+	2.82917i	−0.313382	+	0.101824i
$773$	6.84569	−	9.42229i	0.246222	−	0.338896i	−0.667961	−	0.744196i	$-0.732833\pi$
$773$	6.84569	−	9.42229i	0.246222	−	0.338896i	0.914184	+	0.405300i	$0.132833\pi$
$774$	−6.13855	+	4.45992i	−0.220646	+	0.160309i
$775$	27.5166	−	8.99423i	0.988424	−	0.323082i
$776$	3.38084	−	10.4051i	0.121365	−	0.373523i
$777$	−0.911200	−	1.25416i	−0.0326891	−	0.0449927i
$778$	−17.0687	+	23.4930i	−0.611941	+	0.842264i
$779$	−9.04226	−	27.8292i	−0.323973	−	0.997085i
$780$	−1.22586	+	2.41112i	−0.0438927	+	0.0863319i
$781$	−27.6720	−	0.373864i	−0.990182	−	0.0133779i
$782$		−	27.2194i		−	0.973363i
$783$	−9.49433	+	3.08489i	−0.339300	+	0.110245i
$784$	16.8742	+	12.2598i	0.602649	+	0.437850i
$785$	−51.9124	+	8.26893i	−1.85283	+	0.295131i
$786$	−4.31302	+	13.2741i	−0.153840	+	0.473472i
$787$	8.43964	+	2.74221i	0.300841	+	0.0977491i	0.455548	−	0.890211i	$-0.349443\pi$
$787$	8.43964	+	2.74221i	0.300841	+	0.0977491i	−0.154707	+	0.987960i	$0.549443\pi$
$788$	5.57165	+	7.66871i	0.198482	+	0.273187i
$789$	−1.77204	−	1.28746i	−0.0630862	−	0.0458348i
$790$	3.30930	−	21.0137i	0.117740	−	0.747635i
$791$	5.25052			0.186687
$792$	−0.135797	+	10.0512i	−0.00482535	+	0.357154i
$793$		−	9.45915i		−	0.335904i
$794$	−3.02900	−	9.32230i	−0.107495	−	0.330836i
$795$	3.15088	−	1.60895i	0.111750	−	0.0570635i
$796$	−4.77961	+	3.47259i	−0.169409	+	0.123083i
$797$	−6.58549	−	2.13975i	−0.233270	−	0.0757940i	0.190049	−	0.981775i	$-0.439135\pi$
$797$	−6.58549	−	2.13975i	−0.233270	−	0.0757940i	−0.423319	+	0.905981i	$0.639135\pi$
$798$	2.17319	+	0.706112i	0.0769301	+	0.0249961i
$799$	12.4504	−	9.04573i	0.440463	−	0.320015i
$800$	−10.7200	+	0.0188633i	−0.379008	+	0.000666918i
$801$	−5.26308	−	16.1981i	−0.185962	−	0.572331i
$802$		−	10.4100i		−	0.367591i
$803$	−0.300641	+	0.402254i	−0.0106094	+	0.0141952i
$804$	−2.30101			−0.0811505
$805$	9.10823	+	1.43439i	0.321023	+	0.0505555i
$806$	18.7174	+	13.5990i	0.659294	+	0.479005i
$807$	6.13358	+	8.44215i	0.215912	+	0.297178i
$808$	21.8946	+	7.11399i	0.770250	+	0.250269i
$809$	9.55702	−	29.4135i	0.336007	−	1.03412i	−0.630217	−	0.776419i	$-0.717034\pi$
$809$	9.55702	−	29.4135i	0.336007	−	1.03412i	0.966224	−	0.257704i	$-0.0829659\pi$
$810$	−2.80651	+	0.447039i	−0.0986107	+	0.0157073i
$811$	2.15039	+	1.56235i	0.0755103	+	0.0548615i	0.624900	−	0.780705i	$-0.285140\pi$
$811$	2.15039	+	1.56235i	0.0755103	+	0.0548615i	−0.549390	+	0.835566i	$0.685140\pi$
$812$	−1.76535	+	0.573598i	−0.0619517	+	0.0201293i
$813$			1.72943i			0.0606537i
$814$	4.35152	−	12.8015i	0.152521	−	0.448692i
$815$	39.7445	+	20.2068i	1.39219	+	0.707813i
$816$	2.39102	+	7.35881i	0.0837026	+	0.257610i
$817$	13.0546	−	17.9682i	0.456724	−	0.628627i
$818$	−2.55715	−	3.51961i	−0.0894086	−	0.123060i
$819$	−0.469560	+	1.44516i	−0.0164077	+	0.0504979i
$820$	4.78900	+	4.78058i	0.167239	+	0.166945i
$821$	6.93437	−	5.03812i	0.242011	−	0.175832i	−0.460168	−	0.887832i	$-0.652211\pi$
$821$	6.93437	−	5.03812i	0.242011	−	0.175832i	0.702179	+	0.712001i	$0.252211\pi$
$822$	0.815836	−	1.12290i	0.0284556	−	0.0391657i
$823$	−41.9313	+	13.6243i	−1.46163	+	0.474913i	−0.928568	−	0.371161i	$-0.878960\pi$
$823$	−41.9313	+	13.6243i	−1.46163	+	0.474913i	−0.533065	+	0.846075i	$0.678960\pi$
$824$	11.5401			0.402020
$825$	−5.30943	+	15.7102i	−0.184850	+	0.546959i
$826$	−0.232137			−0.00807710
$827$	−32.2923	+	10.4924i	−1.12291	+	0.364857i	−0.810879	−	0.585214i	$-0.801011\pi$
$827$	−32.2923	+	10.4924i	−1.12291	+	0.364857i	−0.312035	+	0.950071i	$0.601011\pi$
$828$	1.92947	−	2.65568i	0.0670535	−	0.0922913i
$829$	14.7717	−	10.7323i	0.513042	−	0.372747i	−0.300934	−	0.953645i	$-0.597298\pi$
$829$	14.7717	−	10.7323i	0.513042	−	0.372747i	0.813977	+	0.580898i	$0.197298\pi$
$830$	−8.16025	−	8.14590i	−0.283246	−	0.282748i
$831$	3.59666	−	11.0694i	0.124767	−	0.383992i
$832$	−16.4292	−	22.6128i	−0.569579	−	0.783958i
$833$	−9.98330	+	13.7408i	−0.345901	+	0.476092i
$834$	3.30889	+	10.1837i	0.114578	+	0.352634i
$835$	−38.4222	−	19.5345i	−1.32965	−	0.676020i
$836$	−1.40577	−	4.53403i	−0.0486194	−	0.156813i
$837$		−	5.78984i		−	0.200126i
$838$	−22.1914	+	7.21042i	−0.766589	+	0.249080i
$839$	−21.6302	−	15.7153i	−0.746758	−	0.542551i	0.148063	−	0.988978i	$-0.452696\pi$
$839$	−21.6302	−	15.7153i	−0.746758	−	0.542551i	−0.894820	+	0.446427i	$0.852696\pi$
$840$	−3.23456	+	0.515221i	−0.111603	+	0.0177768i
$841$	21.8348	−	67.2005i	0.752923	−	2.31726i
$842$	43.0034	+	13.9727i	1.48200	+	0.481530i
$843$	7.06285	+	9.72118i	0.243258	+	0.334815i
$844$	8.04929	+	5.84815i	0.277068	+	0.201302i
$845$	6.87941	+	1.08339i	0.236659	+	0.0372697i
$846$	−7.79204			−0.267896
$847$	5.00978	+	1.77879i	0.172138	+	0.0611200i
$848$			4.87716i			0.167482i
$849$	8.52561	+	26.2391i	0.292598	+	0.900524i
$850$	0.0280680	+	15.9510i	0.000962725	+	0.547114i
$851$	−22.1413	+	16.0866i	−0.758995	+	0.551442i
$852$	−3.05315	−	0.992030i	−0.104599	−	0.0339864i
$853$	−41.5629	−	13.5046i	−1.42309	−	0.462389i	−0.506506	−	0.862237i	$-0.669063\pi$
$853$	−41.5629	−	13.5046i	−1.42309	−	0.462389i	−0.916582	+	0.399848i	$0.869063\pi$
$854$	1.49500	−	1.08618i	0.0511578	−	0.0371683i
$855$	7.40852	−	3.78304i	0.253366	−	0.129377i
$856$	−0.447184	−	1.37629i	−0.0152844	−	0.0470406i
$857$		−	26.0587i		−	0.890148i	−0.895494	−	0.445074i	$-0.853177\pi$
$857$		−	26.0587i		−	0.890148i	0.895494	−	0.445074i	$-0.146823\pi$
$858$	−12.6586	+	3.92479i	−0.432159	+	0.133990i
$859$	44.2849			1.51098			0.755491	−	0.655159i	$-0.227398\pi$
$859$	44.2849			1.51098			0.755491	+	0.655159i	$0.227398\pi$
$860$	−0.798992	+	5.07353i	−0.0272454	+	0.173006i
$861$	3.07539	+	2.23440i	0.104809	+	0.0761483i
$862$	8.06378	+	11.0988i	0.274653	+	0.378028i
$863$	−21.1529	−	6.87301i	−0.720054	−	0.233960i	−0.0740076	−	0.997258i	$-0.523579\pi$
$863$	−21.1529	−	6.87301i	−0.720054	−	0.233960i	−0.646047	+	0.763298i	$0.723579\pi$
$864$	−0.662531	+	2.03906i	−0.0225398	+	0.0693702i
$865$	−8.54336	+	1.36084i	−0.290483	+	0.0462700i
$866$	−11.4320	−	8.30583i	−0.388475	−	0.282244i
$867$	10.1756	−	3.30625i	0.345581	−	0.112286i
$868$		−	1.07655i		−	0.0365405i
$869$	−20.2802	+	14.3199i	−0.687959	+	0.485768i
$870$	12.8576	−	25.2895i	0.435915	−	0.857395i
$871$	−5.81090	−	17.8841i	−0.196895	−	0.605980i
$872$	12.3293	−	16.9698i	0.417523	−	0.574671i
$873$	−2.12177	−	2.92037i	−0.0718111	−	0.0988395i
$874$	12.4659	−	38.3662i	0.421666	−	1.29776i
$875$	−5.33905	−	0.831182i	−0.180493	−	0.0280991i
$876$	−0.0471288	+	0.0342411i	−0.00159234	+	0.00115690i
$877$	−29.5153	+	40.6243i	−0.996660	+	1.37178i	−0.0693072	+	0.997595i	$0.522079\pi$
$877$	−29.5153	+	40.6243i	−0.996660	+	1.37178i	−0.927352	+	0.374189i	$0.877921\pi$
$878$	−15.1938	+	4.93677i	−0.512766	+	0.166608i
$879$	−3.42861			−0.115644
$880$	−15.9594	−	16.3677i	−0.537992	−	0.551756i
$881$	−31.5451			−1.06278			−0.531391	−	0.847126i	$-0.678331\pi$
$881$	−31.5451			−1.06278			−0.531391	+	0.847126i	$0.678331\pi$
$882$	8.17877	−	2.65744i	0.275394	−	0.0894808i
$883$	−10.0189	+	13.7898i	−0.337163	+	0.464065i	−0.943610	−	0.331059i	$-0.892594\pi$
$883$	−10.0189	+	13.7898i	−0.337163	+	0.464065i	0.606447	+	0.795124i	$0.292594\pi$
$884$	2.45647	−	1.78473i	0.0826201	−	0.0600270i
$885$	−0.597038	+	0.598089i	−0.0200692	+	0.0201045i
$886$	−8.07403	+	24.8493i	−0.271252	+	0.834829i
$887$	−8.59633	−	11.8318i	−0.288636	−	0.397274i	0.639934	−	0.768430i	$-0.278962\pi$
$887$	−8.59633	−	11.8318i	−0.288636	−	0.397274i	−0.928571	+	0.371156i	$0.878962\pi$
$888$	5.71435	−	7.86513i	0.191761	−	0.263936i
$889$	−0.894903	−	2.75423i	−0.0300141	−	0.0923739i
$890$	43.1460	+	21.9362i	1.44626	+	0.735302i
$891$	2.65663	+	1.98553i	0.0890003	+	0.0665179i
$892$			2.06527i			0.0691503i
$893$	21.6918	−	7.04809i	0.725888	−	0.235855i
$894$	17.7156	+	12.8711i	0.592499	+	0.430476i
$895$	6.04512	+	37.9513i	0.202066	+	1.26857i
$896$	1.04698	−	3.22227i	0.0349772	−	0.107649i
$897$	25.5133	+	8.28976i	0.851863	+	0.276787i
$898$	10.7491	+	14.7948i	0.358700	+	0.493709i
$899$	46.7608	+	33.9737i	1.55956	+	1.13309i
$900$	−1.12796	+	1.55826i	−0.0375986	+	0.0519420i
$901$	−3.97152			−0.132311
$902$	−0.447905	+	33.1523i	−0.0149136	+	1.10385i
$903$			2.88533i			0.0960177i
$904$	10.1751	+	31.3157i	0.338418	+	1.04154i
$905$	13.9197	−	7.10789i	0.462708	−	0.236274i
$906$	13.4529	−	9.77409i	0.446942	−	0.324722i
$907$	7.72315	+	2.50940i	0.256443	+	0.0833234i	0.434417	−	0.900712i	$-0.356954\pi$
$907$	7.72315	+	2.50940i	0.256443	+	0.0833234i	−0.177974	+	0.984035i	$0.556954\pi$
$908$	2.82639	+	0.918349i	0.0937970	+	0.0304765i
$909$	6.14507	−	4.46466i	0.203819	−	0.148083i
$910$	−1.96387	−	3.84593i	−0.0651015	−	0.127491i
$911$	2.24743	+	6.91687i	0.0744605	+	0.229166i	0.981359	−	0.192183i	$-0.0615567\pi$
$911$	2.24743	+	6.91687i	0.0744605	+	0.229166i	−0.906899	+	0.421349i	$0.861557\pi$
$912$			11.4674i			0.379724i
$913$	−0.181785	+	13.4551i	−0.00601622	+	0.445298i
$914$	14.3548			0.474814
$915$	1.04653	−	6.64534i	0.0345971	−	0.219688i
$916$	2.51543	+	1.82757i	0.0831123	+	0.0603846i
$917$	3.11964	+	4.29381i	0.103020	+	0.141794i
$918$	3.03406	+	0.985827i	0.100139	+	0.0325371i
$919$	15.2273	−	46.8648i	0.502303	−	1.54593i	−0.302956	−	0.953005i	$-0.597973\pi$
$919$	15.2273	−	46.8648i	0.502303	−	1.54593i	0.805258	−	0.592924i	$-0.202027\pi$
$920$	9.09588	+	57.1039i	0.299882	+	1.88266i
$921$	−12.4052	−	9.01292i	−0.408766	−	0.296986i
$922$	−43.3086	+	14.0718i	−1.42629	+	0.463431i
$923$		−	26.2352i		−	0.863541i
$924$	0.493966	+	0.369185i	0.0162503	+	0.0121453i
$925$	12.9586	−	9.44985i	0.426076	−	0.310709i
$926$	12.0251	+	37.0093i	0.395168	+	1.21620i
$927$	2.23804	−	3.08040i	0.0735069	−	0.101174i
$928$	−12.5806	−	17.3157i	−0.412977	−	0.568415i
$929$	−5.39879	+	16.6158i	−0.177128	+	0.545145i	−0.999724	−	0.0234811i	$-0.992525\pi$
$929$	−5.39879	+	16.6158i	−0.177128	+	0.545145i	0.822596	+	0.568627i	$0.192525\pi$
$930$	11.6450	+	11.6246i	0.381856	+	0.381185i
$931$	−20.3647	+	14.7958i	−0.667425	+	0.484913i
$932$	5.76449	−	7.93414i	0.188822	−	0.259892i
$933$	−4.12955	+	1.34177i	−0.135195	+	0.0439277i
$934$	−50.9204			−1.66617
$935$	13.3284	−	12.9959i	0.435886	−	0.425012i
$936$	−9.52931			−0.311475
$937$	28.8059	−	9.35962i	0.941049	−	0.305765i	0.201976	−	0.979390i	$-0.435264\pi$
$937$	28.8059	−	9.35962i	0.941049	−	0.305765i	0.739073	+	0.673625i	$0.235264\pi$
$938$	2.15929	−	2.97201i	0.0705033	−	0.0970394i
$939$	−8.44910	+	6.13863i	−0.275726	+	0.200327i
$940$	−3.72628	+	3.73284i	−0.121538	+	0.121752i
$941$	13.7734	−	42.3902i	0.449001	−	1.38188i	−0.429036	−	0.903288i	$-0.641147\pi$
$941$	13.7734	−	42.3902i	0.449001	−	1.38188i	0.878036	−	0.478594i	$-0.158853\pi$
$942$	−17.5617	−	24.1717i	−0.572192	−	0.787555i
$943$	39.4469	−	54.2940i	1.28457	−	1.76806i
$944$	−0.360000	−	1.10796i	−0.0117170	−	0.0360612i
$945$	−0.489767	+	0.963317i	−0.0159321	+	0.0313367i
$946$	−20.5573	+	14.5155i	−0.668374	+	0.471939i
$947$			6.29059i			0.204417i	0.994763	+	0.102208i	$0.0325908\pi$
$947$			6.29059i			0.204417i	−0.994763	+	0.102208i	$0.967409\pi$
$948$	−2.73893	+	0.889931i	−0.0889562	+	0.0289036i
$949$	−0.385148	−	0.279827i	−0.0125024	−	0.00908355i
$950$	−7.26567	+	22.4961i	−0.235730	+	0.729868i
$951$	−5.14239	+	15.8266i	−0.166753	+	0.513214i
$952$	3.49682	+	1.13618i	0.113333	+	0.0368240i
$953$	6.64875	+	9.15123i	0.215374	+	0.296437i	0.903011	−	0.429618i	$-0.141352\pi$
$953$	6.64875	+	9.15123i	0.215374	+	0.296437i	−0.687637	+	0.726055i	$0.741352\pi$
$954$	1.62683	+	1.18196i	0.0526704	+	0.0382673i
$955$	−22.0848	−	3.47797i	−0.714647	−	0.112545i
$956$	−0.357364			−0.0115580
$957$	−31.6245	+	9.80510i	−1.02227	+	0.316954i
$958$		−	25.0617i		−	0.809705i
$959$	−0.163100	−	0.501969i	−0.00526676	−	0.0162094i
$960$	−9.04020	−	17.7039i	−0.291771	−	0.571390i
$961$	−2.04058	+	1.48257i	−0.0658253	+	0.0478248i
$962$	12.1903	+	3.96087i	0.393031	+	0.127704i
$963$	−0.454096	−	0.147545i	−0.0146330	−	0.00475457i
$964$	−3.22954	+	2.34640i	−0.104017	+	0.0755724i
$965$	−24.1991	−	47.3903i	−0.778997	−	1.52555i
$966$	1.61947	+	4.98422i	0.0521056	+	0.160365i
$967$		−	22.1756i		−	0.713120i	−0.934272	−	0.356560i	$-0.883950\pi$
$967$		−	22.1756i		−	0.713120i	0.934272	−	0.356560i	$-0.116050\pi$
$968$	−0.900695	+	33.3270i	−0.0289494	+	1.07117i
$969$	−9.33805			−0.299981
$970$	10.1337	+	1.59588i	0.325373	+	0.0512406i
$971$	−4.35085	−	3.16108i	−0.139626	−	0.101444i	0.515780	−	0.856721i	$-0.327502\pi$
$971$	−4.35085	−	3.16108i	−0.139626	−	0.101444i	−0.655405	+	0.755277i	$0.727502\pi$
$972$	0.226140	+	0.311255i	0.00725344	+	0.00998350i
$973$	3.87252	+	1.25826i	0.124147	+	0.0403379i
$974$	−7.12299	+	21.9223i	−0.228235	+	0.702436i
$975$	−14.9597	−	4.83162i	−0.479095	−	0.154736i
$976$	7.50266	+	5.45100i	0.240154	+	0.174482i
$977$	3.18365	−	1.03443i	0.101854	−	0.0330944i	−0.257647	−	0.966239i	$-0.582947\pi$
$977$	3.18365	−	1.03443i	0.101854	−	0.0330944i	0.359501	+	0.933145i	$0.382947\pi$
$978$			25.3419i			0.810343i
$979$	−16.7283	−	53.9539i	−0.534639	−	1.72437i
$980$	2.63815	−	5.18894i	0.0842725	−	0.165754i
$981$	−2.13865	−	6.58210i	−0.0682819	−	0.210150i
$982$	−8.08069	+	11.1221i	−0.257865	+	0.354921i
$983$	12.6433	+	17.4021i	0.403260	+	0.555040i	0.961558	−	0.274600i	$-0.0885455\pi$
$983$	12.6433	+	17.4021i	0.403260	+	0.555040i	−0.558298	+	0.829640i	$0.688546\pi$
$984$	−7.36680	+	22.6727i	−0.234845	+	0.722778i
$985$	−38.9219	+	38.9904i	−1.24015	+	1.24234i
$986$	−25.7652	+	18.7195i	−0.820532	+	0.596151i
$987$	−1.74163	+	2.39715i	−0.0554368	+	0.0763022i
$988$	4.27981	−	1.39060i	0.136159	−	0.0442407i
$989$	50.9385			1.61975
$990$	−9.32732	+	1.35678i	−0.296442	+	0.0431213i
$991$	−3.42838			−0.108906			−0.0544530	−	0.998516i	$-0.517341\pi$
$991$	−3.42838			−0.108906			−0.0544530	+	0.998516i	$0.517341\pi$
$992$	11.8058	−	3.83595i	0.374836	−	0.121792i
$993$	18.8123	−	25.8929i	0.596990	−	0.821686i
$994$	4.14641	−	3.01255i	0.131516	−	0.0955522i
$995$	−24.3012	−	24.2585i	−0.770401	−	0.769046i
$996$	−0.482359	+	1.48455i	−0.0152841	+	0.0470397i
$997$	30.1834	+	41.5439i	0.955919	+	1.31571i	0.948847	+	0.315735i	$0.102251\pi$
$997$	30.1834	+	41.5439i	0.955919	+	1.31571i	0.00707192	+	0.999975i	$0.497749\pi$
$998$	4.23727	−	5.83210i	0.134128	−	0.184612i
$999$	−0.991217	−	3.05065i	−0.0313607	−	0.0965184i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	165.2.s.a.49.4	✓	48
3.2	odd	2		495.2.ba.c.379.9		48
5.2	odd	4		825.2.n.o.676.2		24
5.3	odd	4		825.2.n.p.676.5		24
5.4	even	2	inner	165.2.s.a.49.9	yes	48
11.3	even	5		1815.2.c.j.364.18		24
11.8	odd	10		1815.2.c.k.364.7		24
11.9	even	5	inner	165.2.s.a.64.9	yes	48
15.14	odd	2		495.2.ba.c.379.4		48
33.20	odd	10		495.2.ba.c.64.4		48
55.3	odd	20		9075.2.a.dy.1.10		12
55.8	even	20		9075.2.a.ea.1.3		12
55.9	even	10	inner	165.2.s.a.64.4	yes	48
55.14	even	10		1815.2.c.j.364.7		24
55.19	odd	10		1815.2.c.k.364.18		24
55.42	odd	20		825.2.n.o.526.2		24
55.47	odd	20		9075.2.a.dz.1.3		12
55.52	even	20		9075.2.a.dx.1.10		12
55.53	odd	20		825.2.n.p.526.5		24
165.119	odd	10		495.2.ba.c.64.9		48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
165.2.s.a.49.4	✓	48	1.1	even	1	trivial
165.2.s.a.49.9	yes	48	5.4	even	2	inner
165.2.s.a.64.4	yes	48	55.9	even	10	inner
165.2.s.a.64.9	yes	48	11.9	even	5	inner
495.2.ba.c.64.4		48	33.20	odd	10
495.2.ba.c.64.9		48	165.119	odd	10
495.2.ba.c.379.4		48	15.14	odd	2
495.2.ba.c.379.9		48	3.2	odd	2
825.2.n.o.526.2		24	55.42	odd	20
825.2.n.o.676.2		24	5.2	odd	4
825.2.n.p.526.5		24	55.53	odd	20
825.2.n.p.676.5		24	5.3	odd	4
1815.2.c.j.364.7		24	55.14	even	10
1815.2.c.j.364.18		24	11.3	even	5
1815.2.c.k.364.7		24	11.8	odd	10
1815.2.c.k.364.18		24	55.19	odd	10
9075.2.a.dx.1.10		12	55.52	even	20
9075.2.a.dy.1.10		12	55.3	odd	20
9075.2.a.dz.1.3		12	55.47	odd	20
9075.2.a.ea.1.3		12	55.8	even	20

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:	\( N \)	\(=\)	\( 165 = 3 \cdot 5 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	165.s (of order \(10\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.20873 + 0.392740i) q^{2} +(-0.587785 + 0.809017i) q^{3} +(-0.311255 + 0.226140i) q^{4} +(-1.58253 - 1.57975i) q^{5} +(0.392740 - 1.20873i) q^{6} +(-0.284071 - 0.390991i) q^{7} +(1.78148 - 2.45199i) q^{8} +(-0.309017 - 0.951057i) q^{9} +O(q^{10})\)	\(q+(-1.20873 + 0.392740i) q^{2} +(-0.587785 + 0.809017i) q^{3} +(-0.311255 + 0.226140i) q^{4} +(-1.58253 - 1.57975i) q^{5} +(0.392740 - 1.20873i) q^{6} +(-0.284071 - 0.390991i) q^{7} +(1.78148 - 2.45199i) q^{8} +(-0.309017 - 0.951057i) q^{9} +(2.53328 + 1.28796i) q^{10} +(-0.982188 - 3.16786i) q^{11} -0.384732i q^{12} +(2.99024 - 0.971588i) q^{13} +(0.496923 + 0.361035i) q^{14} +(2.20823 - 0.351741i) q^{15} +(-0.952550 + 2.93165i) q^{16} +(-2.38727 - 0.775672i) q^{17} +(0.747035 + 1.02821i) q^{18} +(-3.00966 - 2.18665i) q^{19} +(0.849814 + 0.133831i) q^{20} +0.483291 q^{21} +(2.43134 + 3.44333i) q^{22} -8.53218i q^{23} +(0.936579 + 2.88249i) q^{24} +(0.00879819 + 4.99999i) q^{25} +(-3.23281 + 2.34877i) q^{26} +(0.951057 + 0.309017i) q^{27} +(0.176837 + 0.0574579i) q^{28} +(-8.07636 + 5.86782i) q^{29} +(-2.53101 + 1.29242i) q^{30} +(-1.78916 - 5.50647i) q^{31} +2.14399i q^{32} +(3.14016 + 1.06741i) q^{33} +3.19020 q^{34} +(-0.168115 + 1.06752i) q^{35} +(0.311255 + 0.226140i) q^{36} +(-1.88541 - 2.59504i) q^{37} +(4.49665 + 1.46105i) q^{38} +(-0.971588 + 2.99024i) q^{39} +(-6.69277 + 1.06607i) q^{40} +(6.36344 + 4.62331i) q^{41} +(-0.584168 + 0.189808i) q^{42} +5.97016i q^{43} +(1.02209 + 0.763898i) q^{44} +(-1.01340 + 1.99324i) q^{45} +(3.35092 + 10.3131i) q^{46} +(-3.60369 + 4.96006i) q^{47} +(-1.81186 - 2.49381i) q^{48} +(2.09094 - 6.43526i) q^{49} +(-1.97433 - 6.04018i) q^{50} +(2.03074 - 1.47542i) q^{51} +(-0.711012 + 0.978624i) q^{52} +(1.50476 - 0.488926i) q^{53} -1.27093 q^{54} +(-3.45007 + 6.56483i) q^{55} -1.46477 q^{56} +(3.53807 - 1.14959i) q^{57} +(7.45759 - 10.2645i) q^{58} +(-0.305754 + 0.222143i) q^{59} +(-0.607779 + 0.608850i) q^{60} +(0.929682 - 2.86127i) q^{61} +(4.32522 + 5.95315i) q^{62} +(-0.284071 + 0.390991i) q^{63} +(-2.74713 - 8.45480i) q^{64} +(-6.26701 - 3.18626i) q^{65} +(-4.21482 - 0.0569445i) q^{66} -5.98082i q^{67} +(0.918461 - 0.298426i) q^{68} +(6.90268 + 5.01509i) q^{69} +(-0.216050 - 1.35636i) q^{70} +(2.57849 - 7.93579i) q^{71} +(-2.88249 - 0.936579i) q^{72} +(-0.0889998 - 0.122498i) q^{73} +(3.29812 + 2.39622i) q^{74} +(-4.05025 - 2.93180i) q^{75} +1.43126 q^{76} +(-0.959591 + 1.28392i) q^{77} -3.99597i q^{78} +(-2.31312 - 7.11905i) q^{79} +(6.13870 - 3.13463i) q^{80} +(-0.809017 + 0.587785i) q^{81} +(-9.50743 - 3.08915i) q^{82} +(-3.85865 - 1.25375i) q^{83} +(-0.150427 + 0.109291i) q^{84} +(2.55257 + 4.99881i) q^{85} +(-2.34472 - 7.21630i) q^{86} -9.98293i q^{87} +(-9.51731 - 3.23515i) q^{88} +17.0317 q^{89} +(0.442100 - 2.80729i) q^{90} +(-1.22932 - 0.893156i) q^{91} +(1.92947 + 2.65568i) q^{92} +(5.50647 + 1.78916i) q^{93} +(2.40787 - 7.41067i) q^{94} +(1.30853 + 8.21494i) q^{95} +(-1.73453 - 1.26021i) q^{96} +(3.43310 - 1.11548i) q^{97} +8.59967i q^{98} +(-2.70930 + 1.91304i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q + 12 q^{4} - 4 q^{5} + 4 q^{6} + 12 q^{9}+O(q^{10}) \) 48 * q + 12 * q^4 - 4 * q^5 + 4 * q^6 + 12 * q^9	\( 48 q + 12 q^{4} - 4 q^{5} + 4 q^{6} + 12 q^{9} - 12 q^{10} - 4 q^{14} + 10 q^{15} - 44 q^{16} - 16 q^{19} + 46 q^{20} - 32 q^{21} - 12 q^{24} + 14 q^{25} - 76 q^{26} + 4 q^{30} - 20 q^{31} - 24 q^{34} - 40 q^{35} - 12 q^{36} - 8 q^{39} - 72 q^{40} + 60 q^{41} - 48 q^{44} + 4 q^{45} + 108 q^{46} - 28 q^{49} - 38 q^{50} + 28 q^{51} + 16 q^{54} - 20 q^{55} + 24 q^{56} + 60 q^{59} + 48 q^{60} + 40 q^{61} + 64 q^{64} + 20 q^{65} + 12 q^{66} + 20 q^{69} + 86 q^{70} - 32 q^{71} - 32 q^{74} - 40 q^{75} - 136 q^{76} - 52 q^{79} + 42 q^{80} - 12 q^{81} - 70 q^{85} - 104 q^{86} + 40 q^{89} - 8 q^{90} - 40 q^{91} + 72 q^{94} - 2 q^{95} + 28 q^{96}+O(q^{100}) \) 48 * q + 12 * q^4 - 4 * q^5 + 4 * q^6 + 12 * q^9 - 12 * q^10 - 4 * q^14 + 10 * q^15 - 44 * q^16 - 16 * q^19 + 46 * q^20 - 32 * q^21 - 12 * q^24 + 14 * q^25 - 76 * q^26 + 4 * q^30 - 20 * q^31 - 24 * q^34 - 40 * q^35 - 12 * q^36 - 8 * q^39 - 72 * q^40 + 60 * q^41 - 48 * q^44 + 4 * q^45 + 108 * q^46 - 28 * q^49 - 38 * q^50 + 28 * q^51 + 16 * q^54 - 20 * q^55 + 24 * q^56 + 60 * q^59 + 48 * q^60 + 40 * q^61 + 64 * q^64 + 20 * q^65 + 12 * q^66 + 20 * q^69 + 86 * q^70 - 32 * q^71 - 32 * q^74 - 40 * q^75 - 136 * q^76 - 52 * q^79 + 42 * q^80 - 12 * q^81 - 70 * q^85 - 104 * q^86 + 40 * q^89 - 8 * q^90 - 40 * q^91 + 72 * q^94 - 2 * q^95 + 28 * q^96

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