LMFDB - Embedded newform 540.2.be.a.11.36

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [540,2,Mod(11,540)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(540, base_ring=CyclotomicField(18)) chi = DirichletCharacter(H, H._module([9, 13, 0])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("540.11"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 540 = 2^{2} \cdot 3^{3} \cdot 5 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	540.be (of order $18$, degree $6$, minimal)

Newform invariants

comment:select newform

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

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

Self dual:	no
Analytic conductor:	$4.31192170915$
Analytic rank:	$0$
Dimension:	$432$
Relative dimension:	$72$ over $\Q(\zeta_{18})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			11.36
Character	$\chi$	$=$	540.11
Dual form			540.2.be.a.491.36

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.0671210 - 1.41262i) q^{2} +(-1.51379 - 0.841696i) q^{3} +(-1.99099 - 0.189633i) q^{4} +(-0.342020 + 0.939693i) q^{5} +(-1.29060 + 2.08191i) q^{6} +(-0.394309 - 0.0695273i) q^{7} +(-0.401517 + 2.79978i) q^{8} +(1.58310 + 2.54830i) q^{9} +(1.30447 + 0.546218i) q^{10} +(0.956862 - 0.348269i) q^{11} +(2.85432 + 1.96287i) q^{12} +(-2.69861 + 2.26441i) q^{13} +(-0.124682 + 0.552342i) q^{14} +(1.30868 - 1.13462i) q^{15} +(3.92808 + 0.755115i) q^{16} +(1.24246 - 0.717336i) q^{17} +(3.70603 - 2.06527i) q^{18} +(3.48337 + 2.01113i) q^{19} +(0.859155 - 1.80606i) q^{20} +(0.538379 + 0.437138i) q^{21} +(-0.427747 - 1.37506i) q^{22} +(1.25612 + 7.12380i) q^{23} +(2.96438 - 3.90032i) q^{24} +(-0.766044 - 0.642788i) q^{25} +(3.01761 + 3.96411i) q^{26} +(-0.251577 - 5.19006i) q^{27} +(0.771881 + 0.213202i) q^{28} +(3.38853 - 4.03829i) q^{29} +(-1.51494 - 1.92483i) q^{30} +(2.98725 - 0.526732i) q^{31} +(1.33035 - 5.49820i) q^{32} +(-1.74162 - 0.278182i) q^{33} +(-0.929927 - 1.80327i) q^{34} +(0.200196 - 0.346750i) q^{35} +(-2.66869 - 5.37384i) q^{36} +(-1.28610 - 2.22759i) q^{37} +(3.07477 - 4.78570i) q^{38} +(5.99107 - 1.15641i) q^{39} +(-2.49361 - 1.33488i) q^{40} +(5.79728 + 6.90893i) q^{41} +(0.653646 - 0.731183i) q^{42} +(-1.71675 - 4.71674i) q^{43} +(-1.97115 + 0.511948i) q^{44} +(-2.93606 + 0.616055i) q^{45} +(10.1475 - 1.29626i) q^{46} +(-1.31085 + 7.43422i) q^{47} +(-5.31069 - 4.44933i) q^{48} +(-6.42720 - 2.33931i) q^{49} +(-0.959432 + 1.03898i) q^{50} +(-2.48460 + 0.0401173i) q^{51} +(5.80232 - 3.99666i) q^{52} +7.75107i q^{53} +(-7.34847 + 0.00702082i) q^{54} +1.01827i q^{55} +(0.352983 - 1.07606i) q^{56} +(-3.58033 - 5.97636i) q^{57} +(-5.47713 - 5.05776i) q^{58} +(8.12690 + 2.95795i) q^{59} +(-2.82073 + 2.01084i) q^{60} +(-1.09522 + 6.21129i) q^{61} +(-0.543565 - 4.25520i) q^{62} +(-0.447053 - 1.11488i) q^{63} +(-7.67757 - 2.24832i) q^{64} +(-1.20487 - 3.31034i) q^{65} +(-0.509865 + 2.44158i) q^{66} +(-1.41571 - 1.68718i) q^{67} +(-2.60976 + 1.19260i) q^{68} +(4.09458 - 11.8412i) q^{69} +(-0.476388 - 0.306075i) q^{70} +(6.20292 + 10.7438i) q^{71} +(-7.77031 + 3.40914i) q^{72} +(-3.96093 + 6.86053i) q^{73} +(-3.23306 + 1.66725i) q^{74} +(0.618595 + 1.61782i) q^{75} +(-6.55399 - 4.66470i) q^{76} +(-0.401514 + 0.0707977i) q^{77} +(-1.23145 - 8.54072i) q^{78} +(-1.49137 + 1.77734i) q^{79} +(-2.05306 + 3.43292i) q^{80} +(-3.98762 + 8.06839i) q^{81} +(10.1488 - 7.72562i) q^{82} +(6.77059 + 5.68120i) q^{83} +(-0.989010 - 0.972431i) q^{84} +(0.249128 + 1.41288i) q^{85} +(-6.77818 + 2.10852i) q^{86} +(-8.52852 + 3.26100i) q^{87} +(0.590882 + 2.81884i) q^{88} +(12.0640 + 6.96517i) q^{89} +(0.673179 + 4.18889i) q^{90} +(1.22153 - 0.705249i) q^{91} +(-1.15001 - 14.4216i) q^{92} +(-4.96540 - 1.71699i) q^{93} +(10.4137 + 2.35073i) q^{94} +(-3.08123 + 2.58546i) q^{95} +(-6.64167 + 7.20335i) q^{96} +(10.0881 - 3.67175i) q^{97} +(-3.73596 + 8.92218i) q^{98} +(2.40230 + 1.88702i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 432 q + 18 q^{12} + 30 q^{14} + 30 q^{24} + 12 q^{29} - 24 q^{30} + 60 q^{33} - 60 q^{36} - 60 q^{38} + 60 q^{41} - 60 q^{42} - 72 q^{44} + 12 q^{45} - 150 q^{48} + 54 q^{52} - 84 q^{54} - 84 q^{56} - 12 q^{57}+ \cdots + 36 q^{97}+O(q^{100}) $ 432 * q + 18 * q^12 + 30 * q^14 + 30 * q^24 + 12 * q^29 - 24 * q^30 + 60 * q^33 - 60 * q^36 - 60 * q^38 + 60 * q^41 - 60 * q^42 - 72 * q^44 + 12 * q^45 - 150 * q^48 + 54 * q^52 - 84 * q^54 - 84 * q^56 - 12 * q^57 + 54 * q^58 - 198 * q^62 - 48 * q^66 - 138 * q^68 - 48 * q^69 - 84 * q^72 - 84 * q^74 - 48 * q^77 - 78 * q^78 - 66 * q^84 + 54 * q^86 - 36 * q^89 + 120 * q^92 - 54 * q^94 + 210 * q^96 + 36 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/540\mathbb{Z}\right)^\times$.

$n$	$217$	$271$	$461$
$\chi(n)$	$1$	$-1$	$e\left(\frac{13}{18}\right)$

Coefficient data

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

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

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

$2$	0.0671210	−	1.41262i	0.0474617	−	0.998873i
$2$	0.0671210	−	1.41262i	0.0474617	−	0.998873i
$3$	−1.51379	−	0.841696i	−0.873985	−	0.485953i
$3$	−1.51379	−	0.841696i	−0.873985	−	0.485953i
$4$	−1.99099	−	0.189633i	−0.995495	−	0.0948165i
$5$	−0.342020	+	0.939693i	−0.152956	+	0.420243i
$5$	−0.342020	+	0.939693i	−0.152956	+	0.420243i
$6$	−1.29060	+	2.08191i	−0.526887	+	0.849936i
$7$	−0.394309	−	0.0695273i	−0.149035	−	0.0262789i	0.0986329	−	0.995124i	$-0.468553\pi$
$7$	−0.394309	−	0.0695273i	−0.149035	−	0.0262789i	−0.247668	+	0.968845i	$0.579664\pi$
$8$	−0.401517	+	2.79978i	−0.141958	+	0.989873i
$9$	1.58310	+	2.54830i	0.527698	+	0.849432i
$10$	1.30447	+	0.546218i	0.412510	+	0.172729i
$11$	0.956862	−	0.348269i	0.288505	−	0.105007i	−0.193714	−	0.981058i	$-0.562053\pi$
$11$	0.956862	−	0.348269i	0.288505	−	0.105007i	0.482219	+	0.876051i	$0.339831\pi$
$12$	2.85432	+	1.96287i	0.823971	+	0.566632i
$13$	−2.69861	+	2.26441i	−0.748461	+	0.628033i	−0.935095	−	0.354396i	$-0.884686\pi$
$13$	−2.69861	+	2.26441i	−0.748461	+	0.628033i	0.186634	+	0.982429i	$0.440242\pi$
$14$	−0.124682	+	0.552342i	−0.0333227	+	0.147620i
$15$	1.30868	−	1.13462i	0.337900	−	0.292957i
$16$	3.92808	+	0.755115i	0.982020	+	0.188779i
$17$	1.24246	−	0.717336i	0.301341	−	0.173979i	−0.341704	−	0.939808i	$-0.611004\pi$
$17$	1.24246	−	0.717336i	0.301341	−	0.173979i	0.643045	+	0.765828i	$0.277671\pi$
$18$	3.70603	−	2.06527i	0.873520	−	0.486788i
$19$	3.48337	+	2.01113i	0.799141	+	0.461384i	0.843171	−	0.537646i	$-0.180686\pi$
$19$	3.48337	+	2.01113i	0.799141	+	0.461384i	−0.0440297	+	0.999030i	$0.514020\pi$
$20$	0.859155	−	1.80606i	0.192113	−	0.403847i
$21$	0.538379	+	0.437138i	0.117484	+	0.0953913i
$22$	−0.427747	−	1.37506i	−0.0911959	−	0.293163i
$23$	1.25612	+	7.12380i	0.261919	+	1.48541i	0.777668	+	0.628675i	$0.216403\pi$
$23$	1.25612	+	7.12380i	0.261919	+	1.48541i	−0.515749	+	0.856740i	$0.672486\pi$
$24$	2.96438	−	3.90032i	0.605101	−	0.796149i
$25$	−0.766044	−	0.642788i	−0.153209	−	0.128558i
$26$	3.01761	+	3.96411i	0.591802	+	0.777425i
$27$	−0.251577	−	5.19006i	−0.0484161	−	0.998827i
$28$	0.771881	+	0.213202i	0.145872	+	0.0402914i
$29$	3.38853	−	4.03829i	0.629234	−	0.749892i	−0.353395	−	0.935474i	$-0.614973\pi$
$29$	3.38853	−	4.03829i	0.629234	−	0.749892i	0.982629	+	0.185582i	$0.0594172\pi$
$30$	−1.51494	−	1.92483i	−0.276589	−	0.351423i
$31$	2.98725	−	0.526732i	0.536525	−	0.0946038i	0.101181	−	0.994868i	$-0.467738\pi$
$31$	2.98725	−	0.526732i	0.536525	−	0.0946038i	0.435344	+	0.900264i	$0.356627\pi$
$32$	1.33035	−	5.49820i	0.235174	−	0.971953i
$33$	−1.74162	−	0.278182i	−0.303177	−	0.0484252i
$34$	−0.929927	−	1.80327i	−0.159481	−	0.309259i
$35$	0.200196	−	0.346750i	0.0338393	−	0.0586114i
$36$	−2.66869	−	5.37384i	−0.444781	−	0.895639i
$37$	−1.28610	−	2.22759i	−0.211433	−	0.366213i	0.740730	−	0.671803i	$-0.234480\pi$
$37$	−1.28610	−	2.22759i	−0.211433	−	0.366213i	−0.952163	+	0.305590i	$0.901146\pi$
$38$	3.07477	−	4.78570i	0.498793	−	0.776342i
$39$	5.99107	−	1.15641i	0.959339	−	0.185174i
$40$	−2.49361	−	1.33488i	−0.394274	−	0.211064i
$41$	5.79728	+	6.90893i	0.905383	+	1.07899i	0.996536	+	0.0831570i	$0.0265003\pi$
$41$	5.79728	+	6.90893i	0.905383	+	1.07899i	−0.0911531	+	0.995837i	$0.529055\pi$
$42$	0.653646	−	0.731183i	0.100860	−	0.112824i
$43$	−1.71675	−	4.71674i	−0.261802	−	0.719295i	−0.999046	−	0.0436687i	$-0.986095\pi$
$43$	−1.71675	−	4.71674i	−0.261802	−	0.719295i	0.737244	−	0.675627i	$-0.236127\pi$
$44$	−1.97115	+	0.511948i	−0.297161	+	0.0771790i
$45$	−2.93606	+	0.616055i	−0.437683	+	0.0918360i
$46$	10.1475	−	1.29626i	1.49617	−	0.191123i
$47$	−1.31085	+	7.43422i	−0.191208	+	1.08439i	0.726509	+	0.687157i	$0.241141\pi$
$47$	−1.31085	+	7.43422i	−0.191208	+	1.08439i	−0.917717	+	0.397235i	$0.869970\pi$
$48$	−5.31069	−	4.44933i	−0.766532	−	0.642206i
$49$	−6.42720	−	2.33931i	−0.918172	−	0.334187i
$50$	−0.959432	+	1.03898i	−0.135684	+	0.146935i
$51$	−2.48460	+	0.0401173i	−0.347914	+	0.00561755i
$52$	5.80232	−	3.99666i	0.804637	−	0.554238i
$53$			7.75107i			1.06469i	0.846527	+	0.532346i	$0.178689\pi$
$53$			7.75107i			1.06469i	−0.846527	+	0.532346i	$0.821311\pi$
$54$	−7.34847	+	0.00702082i	−1.00000	+	0.000955413i
$55$			1.01827i			0.137304i
$56$	0.352983	−	1.07606i	0.0471693	−	0.143795i
$57$	−3.58033	−	5.97636i	−0.474226	−	0.791588i
$58$	−5.47713	−	5.05776i	−0.719182	−	0.664116i
$59$	8.12690	+	2.95795i	1.05803	+	0.385092i	0.811689	−	0.584090i	$-0.198549\pi$
$59$	8.12690	+	2.95795i	1.05803	+	0.385092i	0.246344	+	0.969183i	$0.420771\pi$
$60$	−2.82073	+	2.01084i	−0.364155	+	0.259598i
$61$	−1.09522	+	6.21129i	−0.140228	+	0.795275i	0.830847	+	0.556501i	$0.187856\pi$
$61$	−1.09522	+	6.21129i	−0.140228	+	0.795275i	−0.971075	+	0.238774i	$0.923255\pi$
$62$	−0.543565	−	4.25520i	−0.0690328	−	0.540410i
$63$	−0.447053	−	1.11488i	−0.0563233	−	0.140462i
$64$	−7.67757	−	2.24832i	−0.959696	−	0.281040i
$65$	−1.20487	−	3.31034i	−0.149445	−	0.410597i
$66$	−0.509865	+	2.44158i	−0.0627600	+	0.300537i
$67$	−1.41571	−	1.68718i	−0.172957	−	0.206122i	0.672602	−	0.740005i	$-0.265177\pi$
$67$	−1.41571	−	1.68718i	−0.172957	−	0.206122i	−0.845558	+	0.533883i	$0.820732\pi$
$68$	−2.60976	+	1.19260i	−0.316480	+	0.144624i
$69$	4.09458	−	11.8412i	0.492930	−	1.42551i
$70$	−0.476388	−	0.306075i	−0.0569392	−	0.0365830i
$71$	6.20292	+	10.7438i	0.736151	+	1.27505i	0.954217	+	0.299117i	$0.0966920\pi$
$71$	6.20292	+	10.7438i	0.736151	+	1.27505i	−0.218066	+	0.975934i	$0.569975\pi$
$72$	−7.77031	+	3.40914i	−0.915740	+	0.401771i
$73$	−3.96093	+	6.86053i	−0.463591	+	0.802964i	−0.999137	−	0.0415426i	$-0.986773\pi$
$73$	−3.96093	+	6.86053i	−0.463591	+	0.802964i	0.535545	+	0.844506i	$0.320106\pi$
$74$	−3.23306	+	1.66725i	−0.375835	+	0.193814i
$75$	0.618595	+	1.61782i	0.0714292	+	0.186810i
$76$	−6.55399	−	4.66470i	−0.751794	−	0.535077i
$77$	−0.401514	+	0.0707977i	−0.0457567	+	0.00806814i
$78$	−1.23145	−	8.54072i	−0.139434	−	0.967046i
$79$	−1.49137	+	1.77734i	−0.167792	+	0.199967i	−0.843388	−	0.537306i	$-0.819442\pi$
$79$	−1.49137	+	1.77734i	−0.167792	+	0.199967i	0.675596	+	0.737272i	$0.263887\pi$
$80$	−2.05306	+	3.43292i	−0.229539	+	0.383812i
$81$	−3.98762	+	8.06839i	−0.443069	+	0.896488i
$82$	10.1488	−	7.72562i	1.12075	−	0.853152i
$83$	6.77059	+	5.68120i	0.743169	+	0.623593i	0.933687	−	0.358091i	$-0.116572\pi$
$83$	6.77059	+	5.68120i	0.743169	+	0.623593i	−0.190518	+	0.981684i	$0.561017\pi$
$84$	−0.989010	−	0.972431i	−0.107910	−	0.106101i
$85$	0.249128	+	1.41288i	0.0270217	+	0.153248i
$86$	−6.77818	+	2.10852i	−0.730910	+	0.227368i
$87$	−8.52852	+	3.26100i	−0.914353	+	0.349616i
$88$	0.590882	+	2.81884i	0.0629883	+	0.300490i
$89$	12.0640	+	6.96517i	1.27878	+	0.738306i	0.976625	−	0.214951i	$-0.0689592\pi$
$89$	12.0640	+	6.96517i	1.27878	+	0.738306i	0.302159	+	0.953257i	$0.402293\pi$
$90$	0.673179	+	4.18889i	0.0709593	+	0.441548i
$91$	1.22153	−	0.705249i	0.128051	−	0.0739301i
$92$	−1.15001	−	14.4216i	−0.119897	−	1.50356i
$93$	−4.96540	−	1.71699i	−0.514888	−	0.178044i
$94$	10.4137	+	2.35073i	1.07410	+	0.242459i
$95$	−3.08123	+	2.58546i	−0.316127	+	0.265262i
$96$	−6.64167	+	7.20335i	−0.677863	+	0.735188i
$97$	10.0881	−	3.67175i	1.02429	−	0.372810i	0.225384	−	0.974270i	$-0.427636\pi$
$97$	10.0881	−	3.67175i	1.02429	−	0.372810i	0.798903	+	0.601460i	$0.205414\pi$
$98$	−3.73596	+	8.92218i	−0.377389	+	0.901276i
$99$	2.40230	+	1.88702i	0.241440	+	0.189653i
$100$	1.40329	+	1.42505i	0.140329	+	0.142505i
$101$	−11.1297	−	1.96247i	−1.10745	−	0.195273i	−0.410124	−	0.912030i	$-0.634515\pi$
$101$	−11.1297	−	1.96247i	−1.10745	−	0.195273i	−0.697323	+	0.716757i	$0.745626\pi$
$102$	−0.110098	+	3.51249i	−0.0109014	+	0.347788i
$103$	2.56862	−	7.05722i	0.253093	−	0.695369i	−0.746458	−	0.665432i	$-0.768247\pi$
$103$	2.56862	−	7.05722i	0.253093	−	0.695369i	0.999552	−	0.0299364i	$-0.00953049\pi$
$104$	−5.25631	−	8.46473i	−0.515423	−	0.830035i
$105$	−0.594912	+	0.356400i	−0.0580574	+	0.0347811i
$106$	10.9493	+	0.520260i	1.06349	+	0.0505321i
$107$	−16.3411			−1.57975			−0.789875	−	0.613268i	$-0.789855\pi$
$107$	−16.3411			−1.57975			−0.789875	+	0.613268i	$0.789855\pi$
$108$	−0.483319	+	10.3811i	−0.0465074	+	0.998918i
$109$	−0.0210391			−0.00201518			−0.00100759	−	0.999999i	$-0.500321\pi$
$109$	−0.0210391			−0.00201518			−0.00100759	+	0.999999i	$0.500321\pi$
$110$	1.43843	+	0.0683474i	0.137149	+	0.00651667i
$111$	0.0719256	+	4.45459i	0.00682688	+	0.422811i
$112$	−1.49638	−	0.570857i	−0.141394	−	0.0539410i
$113$	−1.53534	+	4.21830i	−0.144432	+	0.396825i	−0.990723	−	0.135897i	$-0.956608\pi$
$113$	−1.53534	+	4.21830i	−0.144432	+	0.396825i	0.846291	+	0.532721i	$0.178831\pi$
$114$	−8.68264	+	4.65650i	−0.813204	+	0.436121i
$115$	−7.12380	−	1.25612i	−0.664298	−	0.117134i
$116$	−7.51232	+	7.39762i	−0.697501	+	0.686852i
$117$	−10.0425	−	3.29210i	−0.928433	−	0.304354i
$118$	4.72395	−	11.2817i	0.434874	−	1.03856i
$119$	−0.539788	+	0.196467i	−0.0494823	+	0.0180101i
$120$	2.65122	+	4.11959i	0.242022	+	0.376065i
$121$	−7.63220	+	6.40417i	−0.693836	+	0.582197i
$122$	8.70068	+	1.96404i	0.787723	+	0.177815i
$123$	−2.96062	−	15.3382i	−0.266950	−	1.38300i
$124$	−6.04746	+	0.482237i	−0.543078	+	0.0433062i
$125$	0.866025	−	0.500000i	0.0774597	−	0.0447214i
$126$	−1.60491	+	0.556683i	−0.142977	+	0.0495933i
$127$	8.80880	+	5.08576i	0.781655	+	0.451288i	0.837016	−	0.547178i	$-0.184298\pi$
$127$	8.80880	+	5.08576i	0.781655	+	0.451288i	−0.0553618	+	0.998466i	$0.517631\pi$
$128$	−3.69135	+	10.6946i	−0.326272	+	0.945276i
$129$	−1.37126	+	8.58511i	−0.120733	+	0.755877i
$130$	−4.75713	+	1.47982i	−0.417227	+	0.129789i
$131$	−0.561256	−	3.18304i	−0.0490371	−	0.278103i	0.950423	−	0.310960i	$-0.100651\pi$
$131$	−0.561256	−	3.18304i	−0.0490371	−	0.278103i	−0.999460	+	0.0328568i	$0.989539\pi$
$132$	3.41480	+	0.884126i	0.297220	+	0.0769533i
$133$	−1.23370	−	1.03520i	−0.106975	−	0.0897628i
$134$	−2.47837	+	1.88662i	−0.214098	+	0.162979i
$135$	4.96310	+	1.53870i	0.427156	+	0.132430i
$136$	1.50951	+	3.76665i	0.129440	+	0.322987i
$137$	13.2826	−	15.8296i	1.13481	−	1.35241i	0.207444	−	0.978247i	$-0.433485\pi$
$137$	13.2826	−	15.8296i	1.13481	−	1.35241i	0.927363	−	0.374164i	$-0.122070\pi$
$138$	−16.4522	−	6.57888i	−1.40051	−	0.560031i
$139$	−4.27621	+	0.754012i	−0.362704	+	0.0639544i	−0.352030	−	0.935989i	$-0.614509\pi$
$139$	−4.27621	+	0.754012i	−0.362704	+	0.0639544i	−0.0106733	+	0.999943i	$0.503397\pi$
$140$	−0.464343	+	0.652411i	−0.0392442	+	0.0551388i
$141$	8.24170	−	10.1505i	0.694077	−	0.854824i
$142$	15.5932	−	8.04123i	1.30855	−	0.674805i
$143$	−1.79358	+	3.10657i	−0.149987	+	0.259784i
$144$	4.29427	+	11.2053i	0.357856	+	0.933777i
$145$	2.63581	+	4.56535i	0.218892	+	0.379132i
$146$	9.42545	+	6.05577i	0.780056	+	0.501179i
$147$	7.76042	+	8.95097i	0.640069	+	0.738263i
$148$	2.13818	+	4.67899i	0.175758	+	0.384610i
$149$	1.75125	+	2.08706i	0.143468	+	0.170979i	0.832993	−	0.553283i	$-0.186625\pi$
$149$	1.75125	+	2.08706i	0.143468	+	0.170979i	−0.689525	+	0.724262i	$0.742181\pi$
$150$	2.32688	−	0.765250i	0.189989	−	0.0624824i
$151$	−1.26637	−	3.47932i	−0.103056	−	0.283143i	0.877439	−	0.479688i	$-0.159250\pi$
$151$	−1.26637	−	3.47932i	−0.103056	−	0.283143i	−0.980495	+	0.196545i	$0.937028\pi$
$152$	−7.02935	+	8.94519i	−0.570156	+	0.725551i
$153$	3.79492	+	2.03055i	0.306801	+	0.164160i
$154$	0.0730602	+	0.571938i	0.00588736	+	0.0460881i
$155$	−0.526732	+	2.98725i	−0.0423081	+	0.239941i
$156$	−12.1474	+	1.16630i	−0.972574	+	0.0933789i
$157$	−8.84405	−	3.21897i	−0.705832	−	0.256902i	−0.0359331	−	0.999354i	$-0.511440\pi$
$157$	−8.84405	−	3.21897i	−0.705832	−	0.256902i	−0.669899	+	0.742452i	$0.733663\pi$
$158$	2.41061	+	2.22603i	0.191778	+	0.177094i
$159$	6.52404	−	11.7335i	0.517390	−	0.930524i
$160$	4.71161	+	3.13061i	0.372486	+	0.247497i
$161$		−	2.89631i		−	0.228261i
$162$	11.1299	+	6.17455i	0.874449	+	0.485118i
$163$		−	11.8790i		−	0.930431i	−0.885197	−	0.465216i	$-0.845977\pi$
$163$		−	11.8790i		−	0.930431i	0.885197	−	0.465216i	$-0.154023\pi$
$164$	−10.2322	−	14.8550i	−0.798998	−	1.15998i
$165$	0.857075	−	1.54144i	0.0667232	−	0.120001i
$166$	8.47983	−	9.18294i	0.658162	−	0.712735i
$167$	−1.54604	−	0.562712i	−0.119636	−	0.0435440i	0.281508	−	0.959559i	$-0.409165\pi$
$167$	−1.54604	−	0.562712i	−0.119636	−	0.0435440i	−0.401145	+	0.916015i	$0.631387\pi$
$168$	−1.44006	+	1.33183i	−0.111103	+	0.102753i
$169$	−0.102442	+	0.580978i	−0.00788016	+	0.0446906i
$170$	2.01258	−	0.257090i	0.154358	−	0.0197179i
$171$	0.389568	+	12.0605i	0.0297910	+	0.922287i
$172$	2.52358	+	9.71652i	0.192422	+	0.740878i
$173$	−0.782085	−	2.14876i	−0.0594609	−	0.163367i	0.906405	−	0.422409i	$-0.138815\pi$
$173$	−0.782085	−	2.14876i	−0.0594609	−	0.163367i	−0.965866	+	0.259042i	$0.916593\pi$
$174$	4.03411	+	12.2664i	0.305825	+	0.929916i
$175$	0.257367	+	0.306718i	0.0194551	+	0.0231857i
$176$	4.02161	−	0.645488i	0.303140	−	0.0486555i
$177$	−9.81269	−	11.3181i	−0.737567	−	0.850719i
$178$	10.6489	−	16.5744i	0.798168	−	1.24230i
$179$	−4.68526	−	8.11511i	−0.350193	−	0.606552i	0.636090	−	0.771615i	$-0.280551\pi$
$179$	−4.68526	−	8.11511i	−0.350193	−	0.606552i	−0.986283	+	0.165063i	$0.947217\pi$
$180$	5.96250	−	0.669784i	0.444418	−	0.0499227i
$181$	−10.6009	+	18.3613i	−0.787958	+	1.36478i	0.139258	+	0.990256i	$0.455528\pi$
$181$	−10.6009	+	18.3613i	−0.787958	+	1.36478i	−0.927216	+	0.374527i	$0.877805\pi$
$182$	−0.914258	−	1.77289i	−0.0677693	−	0.131415i
$183$	6.88595	−	8.48073i	0.509024	−	0.626913i
$184$	−20.4494	+	0.656534i	−1.50755	+	0.0484003i
$185$	2.53312	−	0.446657i	0.186238	−	0.0328389i
$186$	−2.75874	+	6.89897i	−0.202281	+	0.505857i
$187$	0.939038	−	1.11910i	0.0686693	−	0.0818369i
$188$	4.01967	−	14.5529i	0.293164	−	1.06138i
$189$	−0.261652	+	2.06398i	−0.0190324	+	0.150132i
$190$	3.44545	+	4.52614i	0.249959	+	0.328361i
$191$	−14.9809	−	12.5705i	−1.08398	−	0.909566i	−0.0877339	−	0.996144i	$-0.527963\pi$
$191$	−14.9809	−	12.5705i	−1.08398	−	0.909566i	−0.996245	+	0.0865775i	$0.972407\pi$
$192$	9.72979	+	9.86565i	0.702187	+	0.711992i
$193$	0.919402	+	5.21419i	0.0661800	+	0.375326i	0.999852	+	0.0171966i	$0.00547411\pi$
$193$	0.919402	+	5.21419i	0.0661800	+	0.375326i	−0.933672	+	0.358129i	$0.883415\pi$
$194$	−4.50967	−	14.4970i	−0.323776	−	1.04083i
$195$	−0.962393	+	6.02528i	−0.0689184	+	0.431479i
$196$	12.3529	+	5.87635i	0.882349	+	0.419739i
$197$	−9.33277	−	5.38828i	−0.664933	−	0.383899i	0.129221	−	0.991616i	$-0.458752\pi$
$197$	−9.33277	−	5.38828i	−0.664933	−	0.383899i	−0.794154	+	0.607717i	$0.792086\pi$
$198$	2.82689	−	3.26687i	0.200898	−	0.232167i
$199$	3.34013	−	1.92843i	0.236776	−	0.136703i	−0.376918	−	0.926247i	$-0.623016\pi$
$199$	3.34013	−	1.92843i	0.236776	−	0.136703i	0.613694	+	0.789544i	$0.289683\pi$
$200$	2.10725	−	1.88667i	0.149005	−	0.133408i
$201$	0.722992	+	3.74563i	0.0509959	+	0.264196i
$202$	−3.51926	+	15.5903i	−0.247614	+	1.09693i
$203$	−1.61690	+	1.35674i	−0.113484	+	0.0952244i
$204$	4.95442	+	0.391289i	0.346879	+	0.0273957i
$205$	−8.47506	+	3.08467i	−0.591924	+	0.215443i
$206$	−9.79676	−	4.10217i	−0.682573	−	0.285812i
$207$	−16.1650	+	14.4786i	−1.12354	+	1.00633i
$208$	−12.3103	+	6.85700i	−0.853563	+	0.475448i
$209$	4.03352	+	0.711219i	0.279005	+	0.0491960i
$210$	0.463527	+	0.864306i	0.0319864	+	0.0596428i
$211$	9.59610	−	26.3651i	0.660623	−	1.81505i	0.0865415	−	0.996248i	$-0.472418\pi$
$211$	9.59610	−	26.3651i	0.660623	−	1.81505i	0.574081	−	0.818798i	$-0.305359\pi$
$212$	1.46986	−	15.4323i	0.100950	−	1.05989i
$213$	−0.346901	−	21.4847i	−0.0237693	−	1.47211i
$214$	−1.09683	+	23.0837i	−0.0749777	+	1.57797i
$215$	5.01944			0.342323
$216$	14.6321	+	1.37953i	0.995585	+	0.0938654i
$217$	−1.21452			−0.0824470
$218$	−0.00141216	+	0.0297202i	−9.56438e−5	+	0.00201291i
$219$	11.7705	−	7.05147i	0.795375	−	0.476494i
$220$	0.193098	−	2.02737i	0.0130187	−	0.136685i
$221$	−1.72859	+	4.74925i	−0.116277	+	0.319469i
$222$	6.29747	+	0.197393i	0.422659	+	0.0132482i
$223$	−24.2272	−	4.27191i	−1.62237	−	0.286068i	−0.712724	−	0.701445i	$-0.752539\pi$
$223$	−24.2272	−	4.27191i	−1.62237	−	0.286068i	−0.909650	+	0.415376i	$0.863650\pi$
$224$	−0.906843	+	2.07549i	−0.0605910	+	0.138675i
$225$	0.425291	−	2.96970i	0.0283527	−	0.197980i
$226$	5.85581	+	2.45198i	0.389523	+	0.163104i
$227$	−15.3358	+	5.58177i	−1.01787	+	0.370475i	−0.796451	−	0.604703i	$-0.793292\pi$
$227$	−15.3358	+	5.58177i	−1.01787	+	0.370475i	−0.221421	+	0.975178i	$0.571069\pi$
$228$	5.99508	+	12.5778i	0.397034	+	0.832986i
$229$	14.9946	−	12.5820i	0.990872	−	0.831440i	0.00517819	−	0.999987i	$-0.498352\pi$
$229$	14.9946	−	12.5820i	0.990872	−	0.831440i	0.985694	+	0.168546i	$0.0539073\pi$
$230$	−2.25257	+	9.97891i	−0.148530	+	0.657990i
$231$	0.667396	+	0.230780i	0.0439114	+	0.0151842i
$232$	9.94579	+	11.1086i	0.652973	+	0.729314i
$233$	21.1249	−	12.1965i	1.38394	−	0.799017i	0.391314	−	0.920257i	$-0.372021\pi$
$233$	21.1249	−	12.1965i	1.38394	−	0.799017i	0.992623	+	0.121240i	$0.0386872\pi$
$234$	−5.32455	+	13.9653i	−0.348076	+	0.912942i
$235$	−6.53754	−	3.77445i	−0.426462	−	0.246218i
$236$	−15.6197	−	7.43038i	−1.01675	−	0.483676i
$237$	3.75359	−	1.43524i	0.243822	−	0.0932287i
$238$	0.241302	+	0.775703i	0.0156413	+	0.0502813i
$239$	−1.90394	−	10.7978i	−0.123156	−	0.698452i	−0.982386	−	0.186863i	$-0.940168\pi$
$239$	−1.90394	−	10.7978i	−0.123156	−	0.698452i	0.859230	−	0.511589i	$-0.170943\pi$
$240$	5.99737	−	3.46866i	0.387128	−	0.223901i
$241$	0.0761557	+	0.0639022i	0.00490562	+	0.00411630i	0.645237	−	0.763982i	$-0.276759\pi$
$241$	0.0761557	+	0.0639022i	0.00490562	+	0.00411630i	−0.640332	+	0.768099i	$0.721203\pi$
$242$	8.53438	+	11.2112i	0.548611	+	0.720686i
$243$	12.8275	−	8.85745i	0.822887	−	0.568206i
$244$	3.35843	−	12.1589i	0.215002	−	0.778396i
$245$	4.39647	−	5.23950i	0.280880	−	0.334740i
$246$	−21.8658	+	3.15272i	−1.39411	+	0.201010i
$247$	−13.9543	+	2.46052i	−0.887891	+	0.156559i
$248$	0.275306	+	8.57513i	0.0174820	+	0.544521i
$249$	−5.46738	−	14.2989i	−0.346481	−	0.906156i
$250$	−0.648181	−	1.25693i	−0.0409946	−	0.0794949i
$251$	9.82371	−	17.0152i	0.620067	−	1.07399i	−0.369406	−	0.929268i	$-0.620439\pi$
$251$	9.82371	−	17.0152i	0.620067	−	1.07399i	0.989473	−	0.144719i	$-0.0462280\pi$
$252$	0.678658	+	2.30450i	0.0427515	+	0.145170i
$253$	3.68293	+	6.37903i	0.231544	+	0.401046i
$254$	7.77550	−	12.1021i	0.487879	−	0.759355i
$255$	0.812085	−	2.34848i	0.0508547	−	0.147068i
$256$	14.8596	+	5.93230i	0.928725	+	0.370769i
$257$	12.7986	+	15.2527i	0.798352	+	0.951439i	0.999605	−	0.0281002i	$-0.00894573\pi$
$257$	12.7986	+	15.2527i	0.798352	+	0.951439i	−0.201253	+	0.979539i	$0.564501\pi$
$258$	12.0355	+	2.51332i	0.749295	+	0.156472i
$259$	0.352242	+	0.967776i	0.0218872	+	0.0601347i
$260$	1.77112	+	6.81934i	0.109840	+	0.422917i
$261$	15.6551	+	2.24197i	0.969028	+	0.138775i
$262$	−4.53410	+	0.579192i	−0.280117	+	0.0357826i
$263$	−5.53840	+	31.4098i	−0.341512	+	1.93681i	0.00823146	+	0.999966i	$0.497380\pi$
$263$	−5.53840	+	31.4098i	−0.341512	+	1.93681i	−0.349744	+	0.936845i	$0.613731\pi$
$264$	1.47814	−	4.76447i	0.0909731	−	0.293233i
$265$	−7.28362	−	2.65102i	−0.447429	−	0.162851i
$266$	−1.54514	+	1.67326i	−0.0947389	+	0.102594i
$267$	−12.3998	−	20.6980i	−0.758855	−	1.26670i
$268$	2.49872	+	3.62762i	0.152634	+	0.221592i
$269$			16.8861i			1.02956i	0.857322	+	0.514780i	$0.172127\pi$
$269$			16.8861i			1.02956i	−0.857322	+	0.514780i	$0.827873\pi$
$270$	2.50673	−	6.90770i	0.152554	−	0.420389i
$271$			25.4896i			1.54838i	0.632952	+	0.774191i	$0.281843\pi$
$271$			25.4896i			1.54838i	−0.632952	+	0.774191i	$0.718157\pi$
$272$	5.42216	−	1.87955i	0.328767	−	0.113964i
$273$	−2.44273	+	0.0394414i	−0.147841	+	0.00238710i
$274$	−21.4696	−	19.8257i	−1.29703	−	1.19772i
$275$	−0.956862	−	0.348269i	−0.0577009	−	0.0210014i
$276$	−10.3977	+	22.7992i	−0.625871	+	1.37235i
$277$	5.15854	−	29.2556i	0.309947	−	1.75780i	−0.289307	−	0.957236i	$-0.593425\pi$
$277$	5.15854	−	29.2556i	0.309947	−	1.75780i	0.599253	−	0.800559i	$-0.295464\pi$
$278$	0.778108	+	6.09127i	0.0466678	+	0.365330i
$279$	6.07136	+	6.77852i	0.363483	+	0.405819i
$280$	0.890441	+	0.699731i	0.0532141	+	0.0418169i
$281$	−9.24459	−	25.3993i	−0.551486	−	1.51520i	−0.831682	−	0.555253i	$-0.812622\pi$
$281$	−9.24459	−	25.3993i	−0.551486	−	1.51520i	0.280196	−	0.959943i	$-0.409601\pi$
$282$	−13.7856	−	12.3237i	−0.820919	−	0.733866i
$283$	2.06296	+	2.45854i	0.122630	+	0.146145i	0.823866	−	0.566784i	$-0.191813\pi$
$283$	2.06296	+	2.45854i	0.122630	+	0.146145i	−0.701236	+	0.712929i	$0.747368\pi$
$284$	−10.3126	−	22.5670i	−0.611939	−	1.33911i
$285$	6.84048	−	1.32037i	0.405195	−	0.0782120i
$286$	4.26801	+	2.74216i	0.252373	+	0.162147i
$287$	−1.80556	−	3.12732i	−0.106579	−	0.184600i
$288$	16.1171	−	5.31405i	0.949709	−	0.313134i
$289$	−7.47086	+	12.9399i	−0.439462	+	0.761171i
$290$	6.62603	−	3.41696i	0.389094	−	0.200651i
$291$	−18.3617	−	2.93283i	−1.07638	−	0.171926i
$292$	9.18715	−	12.9081i	0.537637	−	0.755390i
$293$	26.3584	−	4.64770i	1.53988	−	0.271522i	0.661666	−	0.749799i	$-0.269850\pi$
$293$	26.3584	−	4.64770i	1.53988	−	0.271522i	0.878209	+	0.478277i	$0.158739\pi$
$294$	13.1652	−	10.3617i	0.767810	−	0.604308i
$295$	−5.55913	+	6.62511i	−0.323665	+	0.385729i
$296$	6.75315	−	2.70638i	0.392519	−	0.157305i
$297$	−2.04826	−	4.87855i	−0.118852	−	0.283082i
$298$	3.06577	−	2.33377i	0.177595	−	0.135192i
$299$	−19.5210	−	16.3800i	−1.12893	−	0.947282i
$300$	−0.924825	−	3.33837i	−0.0533948	−	0.192741i
$301$	0.348989	+	1.97921i	0.0201154	+	0.114080i
$302$	−4.99996	+	1.55536i	−0.287715	+	0.0895010i
$303$	15.1962	+	12.3386i	0.872998	+	0.708833i
$304$	12.1643	+	10.5302i	0.697673	+	0.603949i
$305$	−5.46212	−	3.15356i	−0.312760	−	0.180572i
$306$	3.12311	−	5.22448i	0.178536	−	0.298664i
$307$	−7.39968	+	4.27221i	−0.422322	+	0.243828i	−0.696070	−	0.717974i	$-0.745070\pi$
$307$	−7.39968	+	4.27221i	−0.422322	+	0.243828i	0.273748	+	0.961801i	$0.411737\pi$
$308$	0.812835	−	0.0648172i	0.0463156	−	0.00369330i
$309$	−9.82837	+	8.52112i	−0.559117	+	0.484750i
$310$	4.18449	+	0.944579i	0.237663	+	0.0536485i
$311$	23.5566	−	19.7663i	1.33577	−	1.12085i	0.353081	−	0.935593i	$-0.385134\pi$
$311$	23.5566	−	19.7663i	1.33577	−	1.12085i	0.982691	−	0.185253i	$-0.0593104\pi$
$312$	0.832193	+	17.2380i	0.0471136	+	0.975910i
$313$	23.2508	−	8.46260i	1.31421	−	0.478334i	0.412613	−	0.910906i	$-0.364616\pi$
$313$	23.2508	−	8.46260i	1.31421	−	0.478334i	0.901599	+	0.432572i	$0.142394\pi$
$314$	−5.14080	+	12.2772i	−0.290112	+	0.692843i
$315$	1.20055	−	0.0387792i	0.0676433	−	0.00218496i
$316$	3.30634	−	3.25586i	0.185996	−	0.183156i
$317$	−8.48024	−	1.49530i	−0.476298	−	0.0839841i	−0.0696545	−	0.997571i	$-0.522190\pi$
$317$	−8.48024	−	1.49530i	−0.476298	−	0.0839841i	−0.406643	+	0.913587i	$0.633301\pi$
$318$	−16.1370	−	10.0036i	−0.904919	−	0.560972i
$319$	1.83594	−	5.04421i	0.102793	−	0.282421i
$320$	4.73861	−	6.44558i	0.264896	−	0.360319i
$321$	24.7369	+	13.7542i	1.38068	+	0.767685i
$322$	−4.09139	−	0.194404i	−0.228004	−	0.0108337i
$323$	5.77061			0.321086
$324$	9.46934	−	15.3079i	0.526074	−	0.850439i
$325$	3.52279			0.195409
$326$	−16.7804	−	0.797328i	−0.929383	−	0.0441599i
$327$	0.0318486	+	0.0177085i	0.00176123	+	0.000979282i
$328$	−21.6712	+	13.4571i	−1.19659	+	0.743043i
$329$	1.03376	−	2.84024i	0.0569932	−	0.156587i
$330$	−2.11995	−	1.31418i	−0.116699	−	0.0723435i
$331$	−18.5033	−	3.26264i	−1.01704	−	0.179331i	−0.359811	−	0.933025i	$-0.617159\pi$
$331$	−18.5033	−	3.26264i	−1.01704	−	0.179331i	−0.657225	+	0.753695i	$0.728270\pi$
$332$	−12.4028	−	12.5951i	−0.680694	−	0.691248i
$333$	3.64053	−	6.80384i	0.199500	−	0.372848i
$334$	−0.898670	+	2.14620i	−0.0491730	+	0.117435i
$335$	2.06963	−	0.753284i	0.113076	−	0.0411563i
$336$	1.78470	+	2.12365i	0.0973636	+	0.115855i
$337$	7.94960	−	6.67051i	0.433042	−	0.363366i	−0.400056	−	0.916491i	$-0.631009\pi$
$337$	7.94960	−	6.67051i	0.433042	−	0.363366i	0.833098	+	0.553125i	$0.186565\pi$
$338$	0.813825	+	0.183708i	0.0442662	+	0.00999238i
$339$	5.87470	−	5.09332i	0.319070	−	0.276631i
$340$	−0.228084	−	2.86026i	−0.0123696	−	0.155120i
$341$	2.67494	−	1.54438i	0.144856	−	0.0836326i
$342$	17.0630	+	0.259200i	0.922662	+	0.0140159i
$343$	4.79891	+	2.77065i	0.259117	+	0.149601i
$344$	13.8951	−	2.91268i	0.749176	−	0.157041i
$345$	9.72664	+	7.89757i	0.523665	+	0.425191i
$346$	−3.08788	+	0.960562i	−0.166005	+	0.0516401i
$347$	2.23328	+	12.6655i	0.119889	+	0.679922i	0.984213	+	0.176987i	$0.0566351\pi$
$347$	2.23328	+	12.6655i	0.119889	+	0.679922i	−0.864325	+	0.502934i	$0.832254\pi$
$348$	17.5986	−	4.87532i	0.943383	−	0.261345i
$349$	16.6161	+	13.9426i	0.889442	+	0.746330i	0.968098	−	0.250572i	$-0.0806185\pi$
$349$	16.6161	+	13.9426i	0.889442	+	0.746330i	−0.0786564	+	0.996902i	$0.525063\pi$
$350$	0.450551	−	0.342974i	0.0240829	−	0.0183328i
$351$	12.4313	+	13.4363i	0.663534	+	0.717176i
$352$	−0.641895	−	5.72434i	−0.0342131	−	0.305108i
$353$	−15.6741	+	18.6797i	−0.834250	+	0.994221i	0.165717	+	0.986173i	$0.447006\pi$
$353$	−15.6741	+	18.6797i	−0.834250	+	0.994221i	−0.999968	+	0.00804736i	$0.997438\pi$
$354$	−16.6468	+	13.1019i	−0.884767	+	0.696359i
$355$	−12.2174	+	2.15425i	−0.648430	+	0.114336i
$356$	−22.6985	−	16.1553i	−1.20302	−	0.856230i
$357$	0.982489	+	0.156929i	0.0519989	+	0.00830556i
$358$	−11.7780	+	6.07380i	−0.622489	+	0.321010i
$359$	6.42496	−	11.1284i	0.339097	−	0.587333i	−0.645166	−	0.764042i	$-0.723212\pi$
$359$	6.42496	−	11.1284i	0.339097	−	0.587333i	0.984263	+	0.176709i	$0.0565453\pi$
$360$	−0.545940	−	8.46770i	−0.0287736	−	0.446287i
$361$	−1.41073	−	2.44346i	−0.0742492	−	0.128603i
$362$	25.2260	+	16.2075i	1.32585	+	0.851845i
$363$	16.9439	−	3.27056i	0.889323	−	0.171660i
$364$	−2.56578	+	1.17250i	−0.134484	+	0.0614557i
$365$	−5.09207	−	6.06849i	−0.266531	−	0.317639i
$366$	−11.5179	−	10.2965i	−0.602048	−	0.538205i
$367$	2.36204	+	6.48966i	0.123298	+	0.338758i	0.985950	−	0.167039i	$-0.0534207\pi$
$367$	2.36204	+	6.48966i	0.123298	+	0.338758i	−0.862653	+	0.505797i	$0.831198\pi$
$368$	−0.445156	+	28.9314i	−0.0232053	+	1.50815i
$369$	−8.42835	+	25.7107i	−0.438762	+	1.33844i
$370$	−0.460931	−	3.60831i	−0.0239627	−	0.187587i
$371$	0.538911	−	3.05632i	0.0279789	−	0.158676i
$372$	9.56046	+	4.36012i	0.495687	+	0.226062i
$373$	24.1280	+	8.78188i	1.24930	+	0.454709i	0.880166	−	0.474667i	$-0.157431\pi$
$373$	24.1280	+	8.78188i	1.24930	+	0.454709i	0.369136	+	0.929375i	$0.379654\pi$
$374$	−1.51784	−	1.40162i	−0.0784855	−	0.0724760i
$375$	−1.73183	+	0.0279627i	−0.0894311	+	0.00144399i
$376$	−20.2879	−	6.65507i	−1.04627	−	0.343209i
$377$			18.5708i			0.956445i
$378$	2.89805	+	0.508151i	0.149060	+	0.0261365i
$379$		−	0.0723385i		−	0.00371578i	−0.999998	−	0.00185789i	$-0.999409\pi$
$379$		−	0.0723385i		−	0.00371578i	0.999998	−	0.00185789i	$-0.000591385\pi$
$380$	6.62498	−	4.56331i	0.339854	−	0.234093i
$381$	−9.05397	−	15.1131i	−0.463849	−	0.774267i
$382$	−18.7628	+	20.3186i	−0.959989	+	1.03959i
$383$	23.3268	+	8.49028i	1.19195	+	0.433833i	0.860407	−	0.509608i	$-0.170210\pi$
$383$	23.3268	+	8.49028i	1.19195	+	0.433833i	0.331540	+	0.943441i	$0.392432\pi$
$384$	14.5895	−	13.0823i	0.744517	−	0.667604i
$385$	0.0707977	−	0.401514i	0.00360818	−	0.0204630i
$386$	7.42738	−	0.948784i	0.378044	−	0.0482918i
$387$	9.30185	−	11.8418i	0.472840	−	0.601954i
$388$	−20.7815	+	5.39739i	−1.05502	+	0.274011i
$389$	3.32419	+	9.13314i	0.168543	+	0.463069i	0.994993	−	0.0999414i	$-0.0318655\pi$
$389$	3.32419	+	9.13314i	0.168543	+	0.463069i	−0.826450	+	0.563010i	$0.809643\pi$
$390$	8.44683	+	1.76392i	0.427722	+	0.0893195i
$391$	6.67083	+	7.94999i	0.337359	+	0.402048i
$392$	9.13019	−	17.0555i	0.461144	−	0.861433i
$393$	−1.82953	+	5.29085i	−0.0922876	+	0.266888i
$394$	−8.23802	+	12.8220i	−0.415025	+	0.645963i
$395$	−1.16008	−	2.00931i	−0.0583699	−	0.101100i
$396$	−4.42511	−	4.21260i	−0.222370	−	0.211691i
$397$	−7.17697	+	12.4309i	−0.360202	+	0.623888i	−0.987994	−	0.154493i	$-0.950626\pi$
$397$	−7.17697	+	12.4309i	−0.360202	+	0.623888i	0.627792	+	0.778381i	$0.283959\pi$
$398$	−2.49994	−	4.84778i	−0.125311	−	0.242997i
$399$	0.996234	+	2.60546i	0.0498741	+	0.130436i
$400$	−2.52370	−	3.10337i	−0.126185	−	0.155169i
$401$	−4.41984	+	0.779338i	−0.220717	+	0.0389183i	−0.282913	−	0.959146i	$-0.591301\pi$
$401$	−4.41984	+	0.779338i	−0.220717	+	0.0389183i	0.0621962	+	0.998064i	$0.480190\pi$
$402$	5.33967	−	0.769902i	0.266319	−	0.0383992i
$403$	−6.86869	+	8.18578i	−0.342154	+	0.407763i
$404$	21.7870	+	6.01781i	1.08394	+	0.299397i
$405$	−6.21796	−	6.50669i	−0.308973	−	0.323320i
$406$	1.80803	+	2.37513i	0.0897310	+	0.117876i
$407$	−2.00642	−	1.68358i	−0.0994544	−	0.0834522i
$408$	0.885288	−	6.97245i	0.0438283	−	0.345188i
$409$	−1.52704	−	8.66025i	−0.0755070	−	0.428222i	−0.999004	−	0.0446164i	$-0.985793\pi$
$409$	−1.52704	−	8.66025i	−0.0755070	−	0.428222i	0.923497	−	0.383605i	$-0.125318\pi$
$410$	3.78861	+	12.1791i	0.187106	+	0.601482i
$411$	−33.4307	+	12.7827i	−1.64901	+	0.630523i
$412$	−6.45237	+	13.5638i	−0.317886	+	0.668238i
$413$	−2.99885	−	1.73139i	−0.147564	−	0.0851960i
$414$	19.3678	+	23.8068i	0.951874	+	1.17004i
$415$	−7.65426	+	4.41919i	−0.375733	+	0.216930i
$416$	8.86006	+	17.8500i	0.434400	+	0.875166i
$417$	7.10792	+	2.45786i	0.348076	+	0.120362i
$418$	1.27542	−	5.65010i	0.0623826	−	0.276355i
$419$	4.68079	−	3.92765i	0.228672	−	0.191878i	−0.521252	−	0.853403i	$-0.674535\pi$
$419$	4.68079	−	3.92765i	0.228672	−	0.191878i	0.749923	+	0.661525i	$0.230090\pi$
$420$	1.25205	−	0.596775i	0.0610937	−	0.0291196i
$421$	17.4058	−	6.33519i	0.848306	−	0.308758i	0.118956	−	0.992899i	$-0.462045\pi$
$421$	17.4058	−	6.33519i	0.848306	−	0.308758i	0.729349	+	0.684141i	$0.239823\pi$
$422$	−36.5997	−	15.3253i	−1.78165	−	0.746024i
$423$	−21.0198	+	8.42864i	−1.02202	+	0.409814i
$424$	−21.7013	−	3.11218i	−1.05391	−	0.151141i
$425$	−1.41288	−	0.249128i	−0.0685345	−	0.0120845i
$426$	−30.3731	−	0.952039i	−1.47158	−	0.0461264i
$427$	0.863709	−	2.37302i	0.0417978	−	0.114839i
$428$	32.5349	+	3.09880i	1.57263	+	0.149786i
$429$	5.32988	−	3.19303i	0.257329	−	0.154161i
$430$	0.336910	−	7.09057i	0.0162473	−	0.341938i
$431$	−3.00589			−0.144789			−0.0723943	−	0.997376i	$-0.523064\pi$
$431$	−3.00589			−0.144789			−0.0723943	+	0.997376i	$0.523064\pi$
$432$	2.93087	−	20.5769i	0.141012	−	0.990008i
$433$	−33.4636			−1.60816			−0.804079	−	0.594522i	$-0.797341\pi$
$433$	−33.4636			−1.60816			−0.804079	+	0.594522i	$0.797341\pi$
$434$	−0.0815199	+	1.71566i	−0.00391308	+	0.0823541i
$435$	−0.147409	−	9.12951i	−0.00706771	−	0.437727i
$436$	0.0418885	+	0.00398970i	0.00200610	+	0.000191072i
$437$	−9.95134	+	27.3411i	−0.476037	+	1.30790i
$438$	−9.17100	−	17.1005i	−0.438207	−	0.817094i
$439$	−3.28787	−	0.579739i	−0.156921	−	0.0276694i	0.0946356	−	0.995512i	$-0.469831\pi$
$439$	−3.28787	−	0.579739i	−0.156921	−	0.0276694i	−0.251557	+	0.967843i	$0.580943\pi$
$440$	−2.85094	−	0.408853i	−0.135913	−	0.0194913i
$441$	−4.21362	−	20.0818i	−0.200649	−	0.956274i
$442$	6.59286	+	2.76061i	0.313590	+	0.131309i
$443$	0.549307	−	0.199931i	0.0260984	−	0.00949902i	−0.328938	−	0.944352i	$-0.606691\pi$
$443$	0.549307	−	0.199931i	0.0260984	−	0.00949902i	0.355036	+	0.934853i	$0.384468\pi$
$444$	0.701535	−	8.88268i	0.0332934	−	0.421554i
$445$	−10.6713	+	8.95425i	−0.505866	+	0.424472i
$446$	−7.66074	+	33.9371i	−0.362747	+	1.60697i
$447$	−0.894350	−	4.63339i	−0.0423013	−	0.219152i
$448$	2.87102	+	1.42033i	0.135643	+	0.0671044i
$449$	7.62442	−	4.40196i	0.359819	−	0.207741i	−0.309183	−	0.951003i	$-0.600055\pi$
$449$	7.62442	−	4.40196i	0.359819	−	0.207741i	0.669001	+	0.743261i	$0.266722\pi$
$450$	−4.16651	−	0.800104i	−0.196411	−	0.0377173i
$451$	7.95337	+	4.59188i	0.374509	+	0.216223i
$452$	3.85677	−	8.10745i	0.181407	−	0.381342i
$453$	−1.01152	+	6.33284i	−0.0475253	+	0.297543i
$454$	6.85556	+	22.0383i	0.321748	+	1.03431i
$455$	0.244930	+	1.38907i	0.0114825	+	0.0651205i
$456$	18.1701	−	7.62453i	0.850891	−	0.357051i
$457$	−29.6357	−	24.8673i	−1.38630	−	1.16324i	−0.966813	−	0.255484i	$-0.917765\pi$
$457$	−29.6357	−	24.8673i	−1.38630	−	1.16324i	−0.419488	−	0.907761i	$-0.637790\pi$
$458$	−16.7671	−	22.0262i	−0.783475	−	1.02922i
$459$	−4.03559	−	6.26798i	−0.188365	−	0.292564i
$460$	13.9452	+	3.85183i	0.650199	+	0.179592i
$461$	1.88230	−	2.24324i	0.0876675	−	0.104478i	−0.720427	−	0.693530i	$-0.756054\pi$
$461$	1.88230	−	2.24324i	0.0876675	−	0.104478i	0.808095	+	0.589052i	$0.200499\pi$
$462$	0.370801	−	0.927286i	0.0172512	−	0.0431413i
$463$	13.4293	−	2.36795i	0.624113	−	0.110048i	0.147356	−	0.989083i	$-0.452924\pi$
$463$	13.4293	−	2.36795i	0.624113	−	0.110048i	0.476756	+	0.879036i	$0.341812\pi$
$464$	16.3598	−	13.3040i	0.759484	−	0.617623i
$465$	3.31171	−	4.07870i	0.153577	−	0.189145i
$466$	−15.8110	−	30.6601i	−0.732432	−	1.42030i
$467$	11.3988	−	19.7433i	0.527475	−	0.913613i	−0.472012	−	0.881592i	$-0.656472\pi$
$467$	11.3988	−	19.7433i	0.527475	−	0.913613i	0.999487	−	0.0320213i	$-0.0101944\pi$
$468$	19.3703	+	8.45893i	0.895393	+	0.391014i
$469$	0.440923	+	0.763701i	0.0203599	+	0.0352644i
$470$	−5.77067	+	8.98172i	−0.266181	+	0.414296i
$471$	10.6786	+	12.3168i	0.492044	+	0.567530i
$472$	−11.5447	+	21.5659i	−0.531388	+	0.992651i
$473$	−3.28539	−	3.91537i	−0.151062	−	0.180029i
$474$	−1.77550	−	5.39874i	−0.0815514	−	0.247972i
$475$	−1.37569	−	3.77968i	−0.0631211	−	0.173424i
$476$	1.11197	−	0.288802i	0.0509670	−	0.0132372i
$477$	−19.7520	+	12.2707i	−0.904382	+	0.561836i
$478$	−15.3810	+	1.96479i	−0.703510	+	0.0898674i
$479$	−5.21008	+	29.5478i	−0.238055	+	1.35008i	0.598029	+	0.801474i	$0.295951\pi$
$479$	−5.21008	+	29.5478i	−0.238055	+	1.35008i	−0.836084	+	0.548601i	$0.815161\pi$
$480$	−4.49735	−	8.70482i	−0.205275	−	0.397319i
$481$	8.51484	+	3.09915i	0.388243	+	0.141309i
$482$	0.0953812	−	0.103290i	0.00434449	−	0.00470472i
$483$	−2.43782	+	4.38440i	−0.110924	+	0.199497i
$484$	16.4101	−	11.3033i	0.745912	−	0.513787i
$485$			10.7355i			0.487474i
$486$	−11.6512	−	18.7149i	−0.528510	−	0.848927i
$487$			23.1967i			1.05114i	0.850749	+	0.525572i	$0.176149\pi$
$487$			23.1967i			1.05114i	−0.850749	+	0.525572i	$0.823851\pi$
$488$	−16.9505	−	5.56031i	−0.767314	−	0.251703i
$489$	−9.99847	+	17.9822i	−0.452146	+	0.813183i
$490$	−7.10633	−	6.56222i	−0.321031	−	0.296451i
$491$	6.72410	+	2.44737i	0.303455	+	0.110448i	0.489260	−	0.872138i	$-0.337267\pi$
$491$	6.72410	+	2.44737i	0.303455	+	0.110448i	−0.185805	+	0.982587i	$0.559489\pi$
$492$	2.98594	+	31.0996i	0.134617	+	1.40208i
$493$	1.31331	−	7.44814i	0.0591484	−	0.335447i
$494$	2.53915	+	19.8773i	0.114242	+	0.894321i
$495$	−2.59486	+	1.61202i	−0.116630	+	0.0724549i
$496$	12.1319	+	0.186669i	0.544737	+	0.00838166i
$497$	−1.69888	−	4.66764i	−0.0762052	−	0.209372i
$498$	−20.5659	+	6.76357i	−0.921580	+	0.303083i
$499$	16.5407	+	19.7125i	0.740465	+	0.882451i	0.996446	−	0.0842303i	$-0.0268431\pi$
$499$	16.5407	+	19.7125i	0.740465	+	0.882451i	−0.255982	+	0.966682i	$0.582399\pi$
$500$	−1.81906	+	0.831268i	−0.0813510	+	0.0371754i
$501$	1.86674	+	2.15312i	0.0833998	+	0.0961943i
$502$	−23.3766	−	15.0192i	−1.04335	−	0.670342i
$503$	−4.80582	−	8.32393i	−0.214281	−	0.371146i	0.738769	−	0.673959i	$-0.235408\pi$
$503$	−4.80582	−	8.32393i	−0.214281	−	0.371146i	−0.953050	+	0.302813i	$0.902074\pi$
$504$	3.30093	−	0.804006i	0.147035	−	0.0358133i
$505$	5.65070	−	9.78730i	0.251453	−	0.435529i
$506$	9.25834	−	4.77442i	0.411583	−	0.212249i
$507$	0.644082	−	0.793251i	0.0286047	−	0.0352295i
$508$	−16.5738	−	11.7961i	−0.735343	−	0.523369i
$509$	−32.5785	+	5.74447i	−1.44402	+	0.254619i	−0.840101	−	0.542429i	$-0.817505\pi$
$509$	−32.5785	+	5.74447i	−1.44402	+	0.254619i	−0.603915	+	0.797049i	$0.706393\pi$
$510$	−3.26300	−	1.30480i	−0.144488	−	0.0577775i
$511$	2.03882	−	2.42977i	0.0901922	−	0.107487i
$512$	9.37748	−	20.5928i	0.414430	−	0.910081i
$513$	9.56153	−	18.5849i	0.422152	−	0.820542i
$514$	22.4054	−	17.0557i	0.988258	−	0.752296i
$515$	5.75310	+	4.82742i	0.253512	+	0.212722i
$516$	4.35819	−	16.8328i	0.191859	−	0.741024i
$517$	1.33480	+	7.57005i	0.0587046	+	0.332930i
$518$	1.39074	−	0.432626i	0.0611057	−	0.0190085i
$519$	−0.624695	+	3.91104i	−0.0274211	+	0.171676i
$520$	9.75201	−	2.04421i	0.427654	−	0.0896443i
$521$	−34.0789	−	19.6754i	−1.49302	−	0.861996i	−0.493054	−	0.869999i	$-0.664119\pi$
$521$	−34.0789	−	19.6754i	−1.49302	−	0.861996i	−0.999968	+	0.00800243i	$0.997453\pi$
$522$	4.21784	−	21.9643i	0.184610	−	0.961349i
$523$	−24.6769	+	14.2472i	−1.07904	+	0.622986i	−0.930638	−	0.365940i	$-0.880747\pi$
$523$	−24.6769	+	14.2472i	−1.07904	+	0.622986i	−0.148405	+	0.988927i	$0.547414\pi$
$524$	0.513845	+	6.44383i	0.0224474	+	0.281500i
$525$	−0.131435	−	0.680930i	−0.00573630	−	0.0297182i
$526$	43.9984	+	9.93191i	1.91842	+	0.433052i
$527$	3.33369	−	2.79730i	0.145218	−	0.121852i
$528$	−6.63117	−	2.40784i	−0.288584	−	0.104788i
$529$	−27.5578	+	10.0302i	−1.19816	+	0.436096i
$530$	−4.23377	+	10.1110i	−0.183903	+	0.439196i
$531$	5.32793	+	25.3925i	0.231212	+	1.10194i
$532$	2.25997	+	2.29501i	0.0979822	+	0.0995014i
$533$	−31.2893	−	5.51714i	−1.35529	−	0.238974i
$534$	−30.0707	+	16.1269i	−1.30129	+	0.697880i
$535$	5.58897	−	15.3556i	0.241632	−	0.663879i
$536$	5.29217	−	3.28625i	0.228587	−	0.141945i
$537$	0.262025	+	16.2281i	0.0113072	+	0.700294i
$538$	23.8536	+	1.13341i	1.02840	+	0.0488648i
$539$	−6.96466			−0.299989
$540$	−9.58970	−	4.00470i	−0.412675	−	0.172335i
$541$	−33.4157			−1.43665			−0.718327	−	0.695705i	$-0.755092\pi$
$541$	−33.4157			−1.43665			−0.718327	+	0.695705i	$0.755092\pi$
$542$	36.0071	+	1.71089i	1.54664	+	0.0734889i
$543$	31.5021	−	18.8723i	1.35188	−	0.809889i
$544$	−2.29115	−	7.78561i	−0.0982322	−	0.333805i
$545$	0.00719578	−	0.0197702i	0.000308233	−	0.000846864i
$546$	−0.108243	+	3.45330i	−0.00463238	+	0.147788i
$547$	31.3889	+	5.53471i	1.34209	+	0.236647i	0.798141	−	0.602470i	$-0.205817\pi$
$547$	31.3889	+	5.53471i	1.34209	+	0.236647i	0.543951	+	0.839117i	$0.316928\pi$
$548$	−29.4473	+	28.9977i	−1.25793	+	1.23872i
$549$	−17.5620	+	7.04213i	−0.749530	+	0.300551i
$550$	−0.556198	+	1.32831i	−0.0237163	+	0.0566392i
$551$	19.9250	−	7.25212i	0.848835	−	0.308951i
$552$	31.5087	+	16.2184i	1.34110	+	0.690300i
$553$	0.711634	−	0.597132i	0.0302617	−	0.0253926i
$554$	−40.9807	−	9.25072i	−1.74110	−	0.393026i
$555$	−4.21055	−	1.45597i	−0.178728	−	0.0618026i
$556$	8.65688	−	0.690318i	0.367133	−	0.0292760i
$557$	−20.9613	+	12.1020i	−0.888158	+	0.512778i	−0.873340	−	0.487112i	$-0.838050\pi$
$557$	−20.9613	+	12.1020i	−0.888158	+	0.512778i	−0.0148187	+	0.999890i	$0.504717\pi$
$558$	9.98298	−	8.12155i	0.422613	−	0.343812i
$559$	15.3135	+	8.84123i	0.647690	+	0.373944i
$560$	1.04822	−	1.21089i	0.0442954	−	0.0511694i
$561$	−2.36345	+	0.903697i	−0.0997848	+	0.0381541i
$562$	−36.5001	+	11.3543i	−1.53966	+	0.478951i
$563$	−1.06749	−	6.05405i	−0.0449895	−	0.255148i	0.954015	−	0.299759i	$-0.0969063\pi$
$563$	−1.06749	−	6.05405i	−0.0449895	−	0.255148i	−0.999004	+	0.0446111i	$0.985795\pi$
$564$	−18.3340	+	18.6466i	−0.772001	+	0.785163i
$565$	−3.43879	−	2.88549i	−0.144671	−	0.121393i
$566$	3.61145	−	2.74915i	0.151800	−	0.115556i
$567$	2.13333	−	2.90419i	0.0895913	−	0.121965i
$568$	−32.5708	+	13.0530i	−1.36664	+	0.547693i
$569$	2.21629	−	2.64128i	0.0929119	−	0.110728i	−0.717585	−	0.696471i	$-0.754753\pi$
$569$	2.21629	−	2.64128i	0.0929119	−	0.110728i	0.810497	+	0.585743i	$0.199197\pi$
$570$	−1.40604	−	9.75163i	−0.0588926	−	0.408451i
$571$	−37.6493	+	6.63859i	−1.57557	+	0.277816i	−0.891990	−	0.452055i	$-0.850691\pi$
$571$	−37.6493	+	6.63859i	−1.57557	+	0.277816i	−0.683585	+	0.729871i	$0.739580\pi$
$572$	4.16010	−	5.84503i	0.173943	−	0.244393i
$573$	12.0974	+	31.6383i	0.505374	+	1.32171i
$574$	−4.53891	+	2.34066i	−0.189450	+	0.0976974i
$575$	3.61685	−	6.26456i	0.150833	−	0.261250i
$576$	−6.42494	−	23.1240i	−0.267706	−	0.963501i
$577$	2.36765	+	4.10089i	0.0985666	+	0.170722i	0.911092	−	0.412204i	$-0.135241\pi$
$577$	2.36765	+	4.10089i	0.0985666	+	0.170722i	−0.812525	+	0.582926i	$0.801908\pi$
$578$	17.7777	+	11.4220i	0.739456	+	0.475094i
$579$	2.99699	−	8.66703i	0.124550	−	0.360189i
$580$	−4.38212	−	9.58940i	−0.181958	−	0.398178i
$581$	−2.27471	−	2.71089i	−0.0943708	−	0.112467i
$582$	−5.37543	+	25.7412i	−0.222819	+	1.06701i
$583$	2.69946	+	7.41670i	0.111800	+	0.307168i
$584$	−17.6176	−	13.8444i	−0.729022	−	0.572883i
$585$	6.52831	−	8.31094i	0.269912	−	0.343615i
$586$	−4.79623	−	37.5464i	−0.198130	−	1.55103i
$587$	0.988515	−	5.60615i	0.0408004	−	0.231391i	−0.957588	−	0.288141i	$-0.906963\pi$
$587$	0.988515	−	5.60615i	0.0408004	−	0.231391i	0.998388	+	0.0567504i	$0.0180739\pi$
$588$	−13.7535	−	19.2929i	−0.567185	−	0.795626i
$589$	11.4650	+	4.17293i	0.472408	+	0.171942i
$590$	8.98563	+	8.29762i	0.369932	+	0.341608i
$591$	9.59253	+	16.0121i	0.394584	+	0.658648i
$592$	−3.36981	−	9.72128i	−0.138498	−	0.399542i
$593$		−	11.3524i		−	0.466187i	−0.972454	−	0.233094i	$-0.925115\pi$
$593$		−	11.3524i		−	0.466187i	0.972454	−	0.233094i	$-0.0748848\pi$
$594$	−7.02902	+	2.56596i	−0.288404	+	0.105283i
$595$		−	0.574431i		−	0.0235494i
$596$	−3.09095	−	4.48741i	−0.126610	−	0.183812i
$597$	−6.67940	+	0.107848i	−0.273369	+	0.00441393i
$598$	−24.4490	+	26.4762i	−0.999795	+	1.08269i
$599$	3.20971	+	1.16824i	0.131145	+	0.0477329i	0.406759	−	0.913536i	$-0.366659\pi$
$599$	3.20971	+	1.16824i	0.131145	+	0.0477329i	−0.275614	+	0.961268i	$0.588881\pi$
$600$	−4.77792	+	1.08235i	−0.195058	+	0.0441868i
$601$	−0.0744401	+	0.422171i	−0.00303647	+	0.0172207i	−0.986288	−	0.165031i	$-0.947228\pi$
$601$	−0.0744401	+	0.422171i	−0.00303647	+	0.0172207i	0.983252	+	0.182252i	$0.0583386\pi$
$602$	2.81930	−	0.360141i	0.114906	−	0.0146783i
$603$	2.05822	−	6.27862i	0.0838174	−	0.255685i
$604$	1.86153	+	7.16744i	0.0757447	+	0.291639i
$605$	−3.40759	−	9.36227i	−0.138538	−	0.380631i
$606$	18.4497	−	20.6383i	0.749469	−	0.838372i
$607$	12.1293	+	14.4551i	0.492312	+	0.586714i	0.953804	−	0.300430i	$-0.0971301\pi$
$607$	12.1293	+	14.4551i	0.492312	+	0.586714i	−0.461492	+	0.887144i	$0.652686\pi$
$608$	15.6917	−	16.4768i	0.636381	−	0.668222i
$609$	3.58960	−	0.692875i	0.145458	−	0.0280767i
$610$	−4.82140	+	7.50423i	−0.195213	+	0.303837i
$611$	−13.2966	−	23.0304i	−0.537923	−	0.931710i
$612$	−7.17058	−	4.76244i	−0.289854	−	0.192510i
$613$	7.44387	−	12.8932i	0.300655	−	0.520750i	−0.675629	−	0.737241i	$-0.736128\pi$
$613$	7.44387	−	12.8932i	0.300655	−	0.520750i	0.976285	+	0.216491i	$0.0694614\pi$
$614$	5.53833	+	10.7397i	0.223509	+	0.433419i
$615$	15.4258	+	2.46390i	0.622027	+	0.0993539i
$616$	−0.0370037	−	1.15258i	−0.00149092	−	0.0464387i
$617$	23.5196	−	4.14713i	0.946862	−	0.166957i	0.321165	−	0.947023i	$-0.395926\pi$
$617$	23.5196	−	4.14713i	0.946862	−	0.166957i	0.625697	+	0.780066i	$0.284815\pi$
$618$	11.3774	+	14.4557i	0.457667	+	0.581494i
$619$	5.95362	−	7.09525i	0.239296	−	0.285182i	−0.633008	−	0.774145i	$-0.718180\pi$
$619$	5.95362	−	7.09525i	0.239296	−	0.285182i	0.872305	+	0.488963i	$0.162625\pi$
$620$	1.61520	−	5.84769i	0.0648679	−	0.234849i
$621$	36.6569	−	8.31151i	1.47099	−	0.333529i
$622$	−26.3412	−	34.6032i	−1.05618	−	1.38746i
$623$	−4.27268	−	3.58521i	−0.171181	−	0.143638i
$624$	24.4066	−	0.0185392i	0.977046	−	0.000742160i
$625$	0.173648	+	0.984808i	0.00694593	+	0.0393923i
$626$	−10.3938	−	33.4126i	−0.415420	−	1.33543i
$627$	−5.50726	−	4.47163i	−0.219939	−	0.178580i
$628$	16.9980	+	8.08606i	0.678293	+	0.322669i
$629$	−3.19585	−	1.84513i	−0.127427	−	0.0735700i
$630$	0.0258018	−	1.69852i	0.00102797	−	0.0676708i
$631$	39.7645	−	22.9581i	1.58300	−	0.913946i	0.588583	−	0.808437i	$-0.299686\pi$
$631$	39.7645	−	22.9581i	1.58300	−	0.913946i	0.994418	−	0.105510i	$-0.0336474\pi$
$632$	−4.37736	−	4.88914i	−0.174122	−	0.194479i
$633$	−36.7178	+	31.8341i	−1.45940	+	1.26529i
$634$	−2.68149	+	11.8790i	−0.106495	+	0.471775i
$635$	−7.79184	+	6.53813i	−0.309210	+	0.259458i
$636$	−15.2144	+	22.1240i	−0.603288	+	0.877274i
$637$	22.6417	−	8.24090i	0.897097	−	0.326516i
$638$	−7.00232	−	2.93206i	−0.277224	−	0.116081i
$639$	−17.5585	+	32.8153i	−0.694603	+	1.29815i
$640$	−8.78710	−	7.12649i	−0.347341	−	0.281699i
$641$	−9.78074	−	1.72461i	−0.386316	−	0.0681179i	−0.0228827	−	0.999738i	$-0.507284\pi$
$641$	−9.78074	−	1.72461i	−0.386316	−	0.0681179i	−0.363433	+	0.931620i	$0.618396\pi$
$642$	21.0898	−	34.0206i	0.832349	−	1.34269i
$643$	6.83655	−	18.7833i	0.269607	−	0.740739i	−0.728822	−	0.684704i	$-0.759932\pi$
$643$	6.83655	−	18.7833i	0.269607	−	0.740739i	0.998429	−	0.0560358i	$-0.0178461\pi$
$644$	−0.549237	+	5.76653i	−0.0216430	+	0.227233i
$645$	−7.59836	−	4.22485i	−0.299185	−	0.166353i
$646$	0.387330	−	8.15168i	0.0152393	−	0.320724i
$647$	−23.6410			−0.929424			−0.464712	−	0.885462i	$-0.653842\pi$
$647$	−23.6410			−0.929424			−0.464712	+	0.885462i	$0.653842\pi$
$648$	−20.9886	−	14.4041i	−0.824512	−	0.565845i
$649$	8.80649			0.345685
$650$	0.236453	−	4.97637i	0.00927447	−	0.195189i
$651$	1.83852	+	1.02226i	0.0720574	+	0.0400654i
$652$	−2.25264	+	23.6509i	−0.0882203	+	0.926240i
$653$	−1.23643	+	3.39707i	−0.0483853	+	0.132938i	−0.961532	−	0.274695i	$-0.911423\pi$
$653$	−1.23643	+	3.39707i	−0.0483853	+	0.132938i	0.913146	+	0.407632i	$0.133645\pi$
$654$	0.0271531	−	0.0438014i	0.00106177	−	0.00171277i
$655$	3.18304	+	0.561256i	0.124372	+	0.0219301i
$656$	17.5551	+	31.5164i	0.685413	+	1.23051i
$657$	−23.7532	+	0.767257i	−0.926699	+	0.0299335i
$658$	−3.94279	−	1.65095i	−0.153706	−	0.0643609i
$659$	11.3160	−	4.11868i	0.440808	−	0.160441i	−0.112075	−	0.993700i	$-0.535750\pi$
$659$	11.3160	−	4.11868i	0.440808	−	0.160441i	0.552883	+	0.833259i	$0.313528\pi$
$660$	−1.99874	+	2.90647i	−0.0778007	+	0.113134i
$661$	18.6845	−	15.6782i	0.726744	−	0.609811i	−0.202498	−	0.979283i	$-0.564906\pi$
$661$	18.6845	−	15.6782i	0.726744	−	0.609811i	0.929242	+	0.369472i	$0.120461\pi$
$662$	−5.85083	+	25.9192i	−0.227399	+	1.00738i
$663$	6.61414	−	5.73441i	0.256872	−	0.222706i
$664$	−18.6246	+	16.6751i	−0.722776	+	0.647119i
$665$	1.39471	−	0.805239i	0.0540847	−	0.0312258i
$666$	−9.36688	−	5.59937i	−0.362959	−	0.216971i
$667$	33.0244	+	19.0666i	1.27871	+	0.738263i
$668$	2.97144	+	1.41353i	0.114968	+	0.0546913i
$669$	33.0792	+	26.8587i	1.27891	+	1.03842i
$670$	−0.925188	−	2.97416i	−0.0357431	−	0.114902i
$671$	1.11523	+	6.32478i	0.0430530	+	0.244165i
$672$	3.11970	−	2.37857i	0.120345	−	0.0917552i
$673$	−32.0273	−	26.8741i	−1.23456	−	1.03592i	−0.997929	−	0.0643204i	$-0.979512\pi$
$673$	−32.0273	−	26.8741i	−1.23456	−	1.03592i	−0.236632	−	0.971599i	$-0.576044\pi$
$674$	−8.88930	−	11.6775i	−0.342403	−	0.449800i
$675$	−3.14339	+	4.13753i	−0.120989	+	0.159253i
$676$	0.314134	−	1.13729i	0.0120821	−	0.0437421i
$677$	−15.0903	+	17.9839i	−0.579966	+	0.691177i	−0.973644	−	0.228072i	$-0.926758\pi$
$677$	−15.0903	+	17.9839i	−0.579966	+	0.691177i	0.393678	+	0.919248i	$0.371202\pi$
$678$	−6.80061	−	8.64059i	−0.261176	−	0.331840i
$679$	−4.23310	+	0.746410i	−0.162452	+	0.0286446i
$680$	−4.05577	+	0.130211i	−0.155532	+	0.00499338i
$681$	27.9132	+	4.45847i	1.06964	+	0.170849i
$682$	−2.00207	−	3.88233i	−0.0766633	−	0.148662i
$683$	12.4716	−	21.6014i	0.477212	−	0.826555i	−0.522447	−	0.852672i	$-0.674981\pi$
$683$	12.4716	−	21.6014i	0.477212	−	0.826555i	0.999659	+	0.0261166i	$0.00831411\pi$
$684$	1.51144	−	24.0862i	0.0577913	−	0.920957i
$685$	10.3320	+	17.8956i	0.394766	+	0.683754i
$686$	4.23598	−	6.59306i	0.161731	−	0.251724i
$687$	−33.2888	+	6.42551i	−1.27005	+	0.245148i
$688$	−3.18186	−	19.8241i	−0.121307	−	0.755785i
$689$	−17.5516	−	20.9171i	−0.668662	−	0.796880i
$690$	11.8091	−	13.2099i	0.449566	−	0.502894i
$691$	−7.75613	−	21.3098i	−0.295057	−	0.810663i	−0.995307	−	0.0967654i	$-0.969150\pi$
$691$	−7.75613	−	21.3098i	−0.295057	−	0.810663i	0.700250	−	0.713898i	$-0.253072\pi$
$692$	1.14965	+	4.42647i	0.0437030	+	0.168269i
$693$	−0.816048	−	0.911096i	−0.0309991	−	0.0346097i
$694$	18.0415	−	2.30465i	0.684845	−	0.0874831i
$695$	0.754012	−	4.27621i	0.0286013	−	0.162206i
$696$	−5.70574	−	25.1874i	−0.216276	−	0.954724i
$697$	12.1589	+	4.42549i	0.460552	+	0.167627i
$698$	20.8109	−	22.5364i	0.787704	−	0.853017i
$699$	−42.2443	+	0.682093i	−1.59783	+	0.0257991i
$700$	−0.454251	−	0.659478i	−0.0171691	−	0.0249259i
$701$		−	32.3722i		−	1.22268i	−0.791368	−	0.611340i	$-0.790631\pi$
$701$		−	32.3722i		−	1.22268i	0.791368	−	0.611340i	$-0.209369\pi$
$702$	19.8148	−	16.6589i	0.747861	−	0.628748i
$703$		−	10.3460i		−	0.390208i
$704$	−8.12939	+	0.522530i	−0.306388	+	0.0196936i
$705$	6.71950	+	11.2163i	0.253071	+	0.422432i
$706$	25.3353	+	23.3954i	0.953505	+	0.880497i
$707$	4.25210	+	1.54764i	0.159917	+	0.0582049i
$708$	17.3907	+	24.3950i	0.653582	+	0.916820i
$709$	−0.482494	+	2.73636i	−0.0181204	+	0.102766i	−0.992527	−	0.122029i	$-0.961060\pi$
$709$	−0.482494	+	2.73636i	−0.0181204	+	0.102766i	0.974406	+	0.224795i	$0.0721712\pi$
$710$	2.22310	+	17.4031i	0.0834313	+	0.653126i
$711$	−6.89017	−	0.986742i	−0.258402	−	0.0370057i
$712$	−24.3449	+	30.9800i	−0.912362	+	1.16103i
$713$	7.50466	+	20.6189i	0.281052	+	0.772184i
$714$	0.287627	−	1.37735i	0.0107642	−	0.0515461i
$715$	−2.30578	−	2.74792i	−0.0862313	−	0.102766i
$716$	7.78941	+	17.0456i	0.291104	+	0.637023i
$717$	−6.20631	+	17.9481i	−0.231779	+	0.670285i
$718$	−15.2889	−	9.82298i	−0.570577	−	0.366590i
$719$	21.1292	+	36.5969i	0.787988	+	1.36484i	0.927198	+	0.374572i	$0.122210\pi$
$719$	21.1292	+	36.5969i	0.787988	+	1.36484i	−0.139210	+	0.990263i	$0.544456\pi$
$720$	−11.9983	+	0.202845i	−0.447150	+	0.00755960i
$721$	−1.50350	+	2.60414i	−0.0559932	+	0.0969831i
$722$	−3.54637	+	1.82882i	−0.131982	+	0.0680618i
$723$	−0.0614972	−	0.160834i	−0.00228710	−	0.00598149i
$724$	24.5882	−	34.5468i	0.913812	−	1.28392i
$725$	−5.19153	+	0.915406i	−0.192808	+	0.0339973i
$726$	−3.48276	−	24.1548i	−0.129257	−	0.896468i
$727$	5.40360	−	6.43976i	0.200408	−	0.238838i	−0.656475	−	0.754348i	$-0.727953\pi$
$727$	5.40360	−	6.43976i	0.200408	−	0.238838i	0.856883	+	0.515510i	$0.172398\pi$
$728$	1.48408	+	3.70318i	0.0550037	+	0.137249i
$729$	−26.8734	+	2.61140i	−0.995312	+	0.0967186i
$730$	−8.91426	+	6.78583i	−0.329931	+	0.251155i
$731$	−5.51648	−	4.62888i	−0.204034	−	0.171205i
$732$	−15.3181	+	15.5792i	−0.566172	+	0.575825i
$733$	8.33761	+	47.2849i	0.307957	+	1.74651i	0.609251	+	0.792977i	$0.291470\pi$
$733$	8.33761	+	47.2849i	0.307957	+	1.74651i	−0.301295	+	0.953531i	$0.597419\pi$
$734$	9.32597	−	2.90108i	0.344228	−	0.107081i
$735$	−11.0654	+	4.23100i	−0.408153	+	0.156063i
$736$	40.8391	+	2.57074i	1.50535	+	0.0947587i
$737$	−1.94223	−	1.12135i	−0.0715431	−	0.0413054i
$738$	35.7537	+	13.6318i	1.31611	+	0.501793i
$739$	17.7147	−	10.2276i	0.651646	−	0.376228i	−0.137441	−	0.990510i	$-0.543888\pi$
$739$	17.7147	−	10.2276i	0.651646	−	0.376228i	0.789087	+	0.614282i	$0.210554\pi$
$740$	−5.12811	+	0.408927i	−0.188513	+	0.0150324i
$741$	23.1948	+	8.02058i	0.852083	+	0.294643i
$742$	−4.28124	−	0.966419i	−0.157169	−	0.0354784i
$743$	−13.9490	+	11.7046i	−0.511739	+	0.429400i	−0.861740	−	0.507349i	$-0.830625\pi$
$743$	−13.9490	+	11.7046i	−0.511739	+	0.429400i	0.350002	+	0.936749i	$0.386181\pi$
$744$	6.80090	−	13.2126i	0.249333	−	0.484399i
$745$	−2.56016	+	0.931822i	−0.0937970	+	0.0341393i
$746$	14.0250	−	33.4943i	0.513490	−	1.22631i
$747$	−3.75889	+	26.2474i	−0.137530	+	0.960340i
$748$	−2.08183	+	2.05005i	−0.0761194	+	0.0749572i
$749$	6.44343	+	1.13615i	0.235438	+	0.0415140i
$750$	−0.0767412	+	2.44829i	−0.00280219	+	0.0893988i
$751$	−1.05323	+	2.89372i	−0.0384328	+	0.105593i	−0.957425	−	0.288683i	$-0.906783\pi$
$751$	−1.05323	+	2.89372i	−0.0384328	+	0.105593i	0.918992	+	0.394277i	$0.129005\pi$
$752$	−10.7628	+	28.2124i	−0.392480	+	1.02880i
$753$	−29.1926	+	17.4887i	−1.06384	+	0.637325i
$754$	26.2335	+	1.24649i	0.955367	+	0.0453945i
$755$	3.70262			0.134752
$756$	0.912344	−	4.05974i	0.0331816	−	0.147651i
$757$	42.2657			1.53617			0.768087	−	0.640346i	$-0.221209\pi$
$757$	42.2657			1.53617			0.768087	+	0.640346i	$0.221209\pi$
$758$	−0.102187	−	0.00485544i	−0.00371159	−	0.000176357i
$759$	−0.205970	−	12.7564i	−0.00747623	−	0.463028i
$760$	−6.00155	−	9.66487i	−0.217699	−	0.350582i
$761$	11.5394	−	31.7043i	0.418303	−	1.14928i	−0.534362	−	0.845256i	$-0.679448\pi$
$761$	11.5394	−	31.7043i	0.418303	−	1.14928i	0.952665	−	0.304023i	$-0.0983298\pi$
$762$	−21.9568	+	11.7754i	−0.795409	+	0.426578i
$763$	0.00829589	+	0.00146279i	0.000300331	+	5.29565e-5i
$764$	27.4430	+	27.8685i	0.992854	+	1.00825i
$765$	−3.20603	+	2.87157i	−0.115914	+	0.103822i
$766$	13.5593	−	32.3821i	0.489916	−	1.17001i
$767$	−28.6294	+	10.4202i	−1.03375	+	0.376253i
$768$	−17.5011	−	21.4875i	−0.631515	−	0.775363i
$769$	40.8222	−	34.2539i	1.47209	−	1.23523i	0.557919	−	0.829896i	$-0.311600\pi$
$769$	40.8222	−	34.2539i	1.47209	−	1.23523i	0.914169	−	0.405333i	$-0.132844\pi$
$770$	−0.562434	−	0.126960i	−0.0202687	−	0.00457533i
$771$	−6.53612	−	33.8619i	−0.235392	−	1.21951i
$772$	−0.841738	−	10.5557i	−0.0302948	−	0.379910i
$773$	31.1821	−	18.0030i	1.12154	−	0.647523i	0.179748	−	0.983713i	$-0.442472\pi$
$773$	31.1821	−	18.0030i	1.12154	−	0.647523i	0.941794	+	0.336190i	$0.109138\pi$
$774$	−16.1037	−	13.9348i	−0.578834	−	0.500877i
$775$	−2.62694	−	1.51666i	−0.0943624	−	0.0544802i
$776$	6.22959	+	29.7187i	0.223629	+	1.06684i
$777$	0.281355	−	1.76149i	0.0100936	−	0.0631930i
$778$	13.1248	−	4.08279i	0.470546	−	0.146375i
$779$	6.29936	+	35.7255i	0.225698	+	1.28000i
$780$	3.05871	−	11.8138i	0.109519	−	0.423001i
$781$	9.67706	+	8.12002i	0.346272	+	0.290557i
$782$	11.6781	−	8.88974i	0.417607	−	0.317896i
$783$	−21.8114	−	16.5707i	−0.779477	−	0.592189i
$784$	−23.4801	−	14.0423i	−0.838575	−	0.501510i
$785$	6.04969	−	7.20973i	0.215923	−	0.257326i
$786$	7.35115	+	2.93956i	0.262207	+	0.104851i
$787$	37.9079	−	6.68418i	1.35127	−	0.238265i	0.549297	−	0.835627i	$-0.314895\pi$
$787$	37.9079	−	6.68418i	1.35127	−	0.238265i	0.801972	+	0.597362i	$0.203784\pi$
$788$	17.5597	+	12.4978i	0.625537	+	0.445216i
$789$	34.8215	−	42.8861i	1.23968	−	1.52678i
$790$	−2.91626	+	1.50388i	−0.103756	+	0.0535057i
$791$	0.898685	−	1.55657i	0.0319536	−	0.0553452i
$792$	−6.24782	+	5.96824i	−0.222007	+	0.212072i
$793$	−11.1093	−	19.2419i	−0.394504	−	0.683300i
$794$	17.0784	+	10.9727i	0.606089	+	0.389407i
$795$	8.79449	+	10.1437i	0.311908	+	0.359759i
$796$	−7.01586	+	3.20608i	−0.248671	+	0.113636i
$797$	27.5779	+	32.8660i	0.976858	+	1.16417i	0.986424	+	0.164220i	$0.0525108\pi$
$797$	27.5779	+	32.8660i	0.976858	+	1.16417i	−0.00956536	+	0.999954i	$0.503045\pi$
$798$	3.74740	−	1.23242i	0.132656	−	0.0436272i
$799$	3.70414	+	10.1771i	0.131043	+	0.360038i
$800$	−4.55328	+	3.35673i	−0.160983	+	0.118678i
$801$	1.34920	+	41.7692i	0.0476715	+	1.47584i
$802$	0.804243	+	6.29587i	0.0283988	+	0.222315i
$803$	−1.40075	+	7.94405i	−0.0494314	+	0.280339i
$804$	−0.729175	−	7.59461i	−0.0257160	−	0.267841i
$805$	2.72164	+	0.990597i	0.0959254	+	0.0349140i
$806$	11.1024	+	10.2523i	0.391064	+	0.361121i
$807$	14.2129	−	25.5619i	0.500319	−	0.899820i
$808$	9.96325	−	30.3728i	0.350506	−	1.06851i
$809$			46.8705i			1.64788i	0.566679	+	0.823939i	$0.308228\pi$
$809$			46.8705i			1.64788i	−0.566679	+	0.823939i	$0.691772\pi$
$810$	−9.60883	+	8.34688i	−0.337620	+	0.293279i
$811$			53.5082i			1.87893i	0.342649	+	0.939464i	$0.388676\pi$
$811$			53.5082i			1.87893i	−0.342649	+	0.939464i	$0.611324\pi$
$812$	3.47651	−	2.39464i	0.122002	−	0.0840353i
$813$	21.4545	−	38.5858i	0.752441	−	1.35326i
$814$	−2.51294	+	2.72130i	−0.0880784	+	0.0953816i
$815$	11.1626	+	4.06284i	0.391008	+	0.142315i
$816$	−9.79000	−	1.71857i	−0.342718	−	0.0601621i
$817$	3.50587	−	19.8828i	0.122655	−	0.695610i
$818$	−12.3361	+	1.57584i	−0.431323	+	0.0550978i
$819$	3.73097	+	1.99633i	0.130371	+	0.0697576i
$820$	17.4587	−	4.53439i	0.609685	−	0.158348i
$821$	1.33346	+	3.66365i	0.0465381	+	0.127862i	0.960784	−	0.277297i	$-0.0894384\pi$
$821$	1.33346	+	3.66365i	0.0465381	+	0.127862i	−0.914246	+	0.405159i	$0.867216\pi$
$822$	15.8132	+	48.0828i	0.551547	+	1.67708i
$823$	12.3044	+	14.6639i	0.428906	+	0.511150i	0.936606	−	0.350384i	$-0.113949\pi$
$823$	12.3044	+	14.6639i	0.428906	+	0.511150i	−0.507700	+	0.861534i	$0.669504\pi$
$824$	18.7273	+	10.0252i	0.652398	+	0.349243i
$825$	1.15535	+	1.33259i	0.0402240	+	0.0463949i
$826$	−2.64708	+	4.12003i	−0.0921037	+	0.143354i
$827$	−2.42589	−	4.20177i	−0.0843565	−	0.146110i	0.820760	−	0.571273i	$-0.193550\pi$
$827$	−2.42589	−	4.20177i	−0.0843565	−	0.146110i	−0.905117	+	0.425163i	$0.860217\pi$
$828$	34.9299	−	25.7614i	1.21390	−	0.895269i
$829$	18.5977	−	32.2121i	0.645924	−	1.11877i	−0.338163	−	0.941088i	$-0.609806\pi$
$829$	18.5977	−	32.2121i	0.645924	−	1.11877i	0.984087	−	0.177686i	$-0.0568612\pi$
$830$	5.72887	+	11.1092i	0.198852	+	0.385605i
$831$	−32.4332	+	39.9447i	−1.12510	+	1.38567i
$832$	25.8099	−	11.3178i	0.894798	−	0.392374i
$833$	−9.66362	+	1.70396i	−0.334825	+	0.0590386i
$834$	3.94911	−	9.87581i	0.136747	−	0.341971i
$835$	1.05755	−	1.26034i	0.0365981	−	0.0436159i
$836$	−7.89583	−	2.18092i	−0.273083	−	0.0754286i
$837$	−3.48529	−	15.3715i	−0.120469	−	0.531315i
$838$	−5.23409	−	6.87580i	−0.180809	−	0.237521i
$839$	−24.4761	−	20.5379i	−0.845008	−	0.709046i	0.113676	−	0.993518i	$-0.463737\pi$
$839$	−24.4761	−	20.5379i	−0.845008	−	0.709046i	−0.958684	+	0.284472i	$0.908182\pi$
$840$	−0.758977	−	1.80872i	−0.0261872	−	0.0624069i
$841$	0.210128	+	1.19169i	0.00724578	+	0.0410929i
$842$	−7.78091	−	25.0130i	−0.268148	−	0.862004i
$843$	−7.38416	+	46.2302i	−0.254324	+	1.59225i
$844$	−24.1054	+	50.6728i	−0.829743	+	1.74423i
$845$	−0.510903	−	0.294970i	−0.0175756	−	0.0101473i
$846$	10.4956	+	30.2587i	0.360846	+	1.04032i
$847$	3.45471	−	1.99458i	0.118705	−	0.0685345i
$848$	−5.85295	+	30.4468i	−0.200991	+	1.04555i
$849$	−1.05353	−	5.45808i	−0.0361572	−	0.187321i
$850$	−0.446757	+	1.97913i	−0.0153236	+	0.0678837i
$851$	14.2534	−	11.9600i	0.488600	−	0.409984i
$852$	−3.38354	+	42.8417i	−0.115918	+	1.46773i
$853$	−13.9591	+	5.08070i	−0.477951	+	0.173960i	−0.569751	−	0.821818i	$-0.692960\pi$
$853$	−13.9591	+	5.08070i	−0.477951	+	0.173960i	0.0917997	+	0.995777i	$0.470738\pi$
$854$	−3.29420	−	1.37937i	−0.112725	−	0.0472011i
$855$	−11.4664	−	3.75885i	−0.392142	−	0.128550i
$856$	6.56121	−	45.7514i	0.224257	−	1.56375i
$857$	27.0455	+	4.76885i	0.923856	+	0.162901i	0.615289	−	0.788302i	$-0.289039\pi$
$857$	27.0455	+	4.76885i	0.923856	+	0.162901i	0.308567	+	0.951202i	$0.400150\pi$
$858$	−4.15279	−	7.74342i	−0.141774	−	0.264356i
$859$	16.6882	−	45.8503i	0.569392	−	1.56439i	−0.236064	−	0.971738i	$-0.575857\pi$
$859$	16.6882	−	45.8503i	0.569392	−	1.56439i	0.805456	−	0.592655i	$-0.201920\pi$
$860$	−9.99366	−	0.951853i	−0.340781	−	0.0324579i
$861$	0.100977	+	6.25383i	0.00344128	+	0.213130i
$862$	−0.201758	+	4.24618i	−0.00687192	+	0.144625i
$863$	−21.3680			−0.727375			−0.363687	−	0.931521i	$-0.618482\pi$
$863$	−21.3680			−0.727375			−0.363687	+	0.931521i	$0.618482\pi$
$864$	−28.8707	−	5.52136i	−0.982200	−	0.187840i
$865$	2.28666			0.0777489
$866$	−2.24611	+	47.2714i	−0.0763260	+	1.60635i
$867$	22.2008	−	13.3001i	0.753977	−	0.451694i
$868$	2.41810	+	0.230313i	0.0820755	+	0.00781734i
$869$	−0.808039	+	2.22007i	−0.0274108	+	0.0753107i
$870$	−12.9064	−	0.404550i	−0.437569	−	0.0137155i
$871$	7.64092	+	1.34730i	0.258903	+	0.0456515i
$872$	0.00844753	−	0.0589048i	0.000286070	−	0.00199477i
$873$	25.3271	+	19.8946i	0.857192	+	0.673331i
$874$	37.9546	+	15.8926i	1.28383	+	0.537576i
$875$	−0.376245	+	0.136942i	−0.0127194	+	0.00462949i
$876$	−24.7721	+	11.8073i	−0.836971	+	0.398933i
$877$	−3.35252	+	2.81310i	−0.113206	+	0.0949915i	−0.697634	−	0.716455i	$-0.745764\pi$
$877$	−3.35252	+	2.81310i	−0.113206	+	0.0949915i	0.584427	+	0.811446i	$0.301319\pi$
$878$	−1.03964	+	4.60559i	−0.0350860	+	0.155431i
$879$	−43.8130	−	15.1502i	−1.47777	−	0.511002i
$880$	−0.768912	+	3.99985i	−0.0259200	+	0.134835i
$881$	40.4299	−	23.3422i	1.36212	−	0.786419i	0.372212	−	0.928148i	$-0.378599\pi$
$881$	40.4299	−	23.3422i	1.36212	−	0.786419i	0.989906	+	0.141729i	$0.0452661\pi$
$882$	−28.6507	+	4.60434i	−0.964720	+	0.155036i
$883$	−18.9479	−	10.9396i	−0.637647	−	0.368146i	0.146060	−	0.989276i	$-0.453341\pi$
$883$	−18.9479	−	10.9396i	−0.637647	−	0.368146i	−0.783708	+	0.621130i	$0.786674\pi$
$884$	4.34221	−	9.12791i	0.146044	−	0.307005i
$885$	13.9917	−	5.34990i	0.470324	−	0.179835i
$886$	−0.245557	−	0.789381i	−0.00824964	−	0.0265198i
$887$	−0.0384613	−	0.218125i	−0.00129140	−	0.00732391i	0.984155	−	0.177309i	$-0.0567392\pi$
$887$	−0.0384613	−	0.218125i	−0.00129140	−	0.00732391i	−0.985447	+	0.169985i	$0.945628\pi$
$888$	−12.5008	−	1.58722i	−0.419498	−	0.0532635i
$889$	−3.11979	−	2.61781i	−0.104634	−	0.0877987i
$890$	11.9327	+	15.6754i	0.399984	+	0.525442i
$891$	−1.00563	+	9.10910i	−0.0336898	+	0.305166i
$892$	47.4260	+	13.0996i	1.58794	+	0.438607i
$893$	−19.5174	+	23.2599i	−0.653123	+	0.778362i
$894$	−6.60524	+	0.952379i	−0.220912	+	0.0318523i
$895$	9.22816	−	1.62717i	0.308463	−	0.0543904i
$896$	2.19910	−	3.96032i	0.0734667	−	0.132305i
$897$	15.7635	+	41.2266i	0.526329	+	1.37652i
$898$	−5.70654	−	11.0659i	−0.190430	−	0.369273i
$899$	7.99527	−	13.8482i	0.266657	−	0.461864i
$900$	−1.40990	+	5.83200i	−0.0469968	+	0.194400i
$901$	5.56012	+	9.63041i	0.185234	+	0.320835i
$902$	7.02042	−	10.9269i	0.233754	−	0.363825i
$903$	1.13760	−	3.28985i	0.0378570	−	0.109479i
$904$	−11.1939	−	5.99233i	−0.372303	−	0.199302i
$905$	−13.6282	−	16.2415i	−0.453018	−	0.539886i
$906$	8.87801	+	1.85396i	0.294952	+	0.0615936i
$907$	−1.64070	−	4.50778i	−0.0544784	−	0.149678i	0.909468	−	0.415773i	$-0.136489\pi$
$907$	−1.64070	−	4.50778i	−0.0544784	−	0.149678i	−0.963947	+	0.266095i	$0.914267\pi$
$908$	31.5919	−	8.20507i	1.04841	−	0.272295i
$909$	−12.6184	−	31.4686i	−0.418527	−	1.04375i
$910$	1.97867	−	0.252758i	0.0655921	−	0.00837883i
$911$	7.44219	−	42.2068i	0.246571	−	1.39837i	−0.570245	−	0.821474i	$-0.693152\pi$
$911$	7.44219	−	42.2068i	0.246571	−	1.39837i	0.816816	−	0.576898i	$-0.195737\pi$
$912$	−9.55096	−	26.1792i	−0.316264	−	0.866879i
$913$	8.45711	+	3.07814i	0.279889	+	0.101871i
$914$	−37.1173	+	40.1949i	−1.22773	+	1.32953i
$915$	5.61414	+	9.37125i	0.185598	+	0.309804i
$916$	−32.2401	+	22.2071i	−1.06524	+	0.733743i
$917$			1.29412i			0.0427357i
$918$	−9.12515	+	5.28004i	−0.301175	+	0.174267i
$919$		−	26.7720i		−	0.883126i	−0.897230	−	0.441563i	$-0.854424\pi$
$919$		−	26.7720i		−	0.883126i	0.897230	−	0.441563i	$-0.145576\pi$
$920$	6.37718	−	19.4407i	0.210249	−	0.640942i
$921$	14.7974	−	0.238925i	0.487592	−	0.00787286i
$922$	−3.04250	−	2.80954i	−0.100199	−	0.0925274i
$923$	−41.0676	−	14.9474i	−1.35175	−	0.491999i
$924$	−1.28501	−	0.586041i	−0.0422739	−	0.0192793i
$925$	−0.446657	+	2.53312i	−0.0146860	+	0.0832884i
$926$	−2.44362	−	19.1294i	−0.0803024	−	0.628632i
$927$	22.0502	−	4.62666i	0.724225	−	0.151959i
$928$	−17.6954	−	24.0031i	−0.580880	−	0.787941i
$929$	−2.12205	−	5.83027i	−0.0696221	−	0.191285i	0.900002	−	0.435887i	$-0.143565\pi$
$929$	−2.12205	−	5.83027i	−0.0696221	−	0.191285i	−0.969624	+	0.244601i	$0.921343\pi$
$930$	−5.53937	−	4.95196i	−0.181643	−	0.162381i
$931$	−17.6837	−	21.0746i	−0.579560	−	0.690693i
$932$	−44.3723	+	20.2770i	−1.45346	+	0.664197i
$933$	−52.2969	+	10.0945i	−1.71212	+	0.330479i
$934$	−27.1247	−	17.4274i	−0.887549	−	0.570242i
$935$	0.730442	+	1.26516i	0.0238880	+	0.0413753i
$936$	13.2494	−	26.7951i	0.433070	−	0.875825i
$937$	17.5876	−	30.4626i	0.574562	−	0.995170i	−0.421528	−	0.906816i	$-0.638506\pi$
$937$	17.5876	−	30.4626i	0.574562	−	0.995170i	0.996089	−	0.0883543i	$-0.0281608\pi$
$938$	1.10841	−	0.571596i	0.0361910	−	0.0186633i
$939$	−42.3197	−	6.75954i	−1.38105	−	0.220589i
$940$	12.3004	+	8.75463i	0.401195	+	0.285544i
$941$	−55.1840	+	9.73043i	−1.79895	+	0.317203i	−0.970179	−	0.242390i	$-0.922069\pi$
$941$	−55.1840	+	9.73043i	−1.79895	+	0.317203i	−0.828768	+	0.559593i	$0.810958\pi$
$942$	18.1158	−	14.2581i	0.590243	−	0.464554i
$943$	−41.9358	+	49.9771i	−1.36562	+	1.62748i
$944$	29.6895	+	17.7558i	0.966311	+	0.577902i
$945$	−1.85002	−	0.951794i	−0.0601810	−	0.0309619i
$946$	−5.75145	+	4.37820i	−0.186996	+	0.142348i
$947$	26.7983	+	22.4865i	0.870829	+	0.730712i	0.964272	−	0.264913i	$-0.0853431\pi$
$947$	26.7983	+	22.4865i	0.870829	+	0.730712i	−0.0934437	+	0.995625i	$0.529788\pi$
$948$	−7.74553	+	2.14574i	−0.251563	+	0.0696903i
$949$	−4.84601	−	27.4831i	−0.157308	−	0.892138i
$950$	−5.43159	+	1.68963i	−0.176224	+	0.0548190i
$951$	11.5787	+	9.40134i	0.375465	+	0.304859i
$952$	−0.333331	−	1.59017i	−0.0108033	−	0.0515379i
$953$	11.8818	+	6.85995i	0.384888	+	0.222215i	0.679943	−	0.733265i	$-0.262004\pi$
$953$	11.8818	+	6.85995i	0.384888	+	0.222215i	−0.295055	+	0.955480i	$0.595338\pi$
$954$	16.0080	+	28.7257i	0.518279	+	0.930029i
$955$	16.9361	−	9.77808i	0.548040	−	0.316411i
$956$	1.74311	+	21.8594i	0.0563763	+	0.706983i
$957$	−7.02491	+	6.09055i	−0.227083	+	0.196879i
$958$	41.3902	+	9.34315i	1.33726	+	0.301863i
$959$	−6.33803	+	5.31824i	−0.204666	+	0.171735i
$960$	−12.5985	+	5.76876i	−0.406614	+	0.186186i
$961$	−20.4843	+	7.45567i	−0.660783	+	0.240505i
$962$	4.94944	−	11.8202i	0.159576	−	0.381099i
$963$	−25.8695	−	41.6418i	−0.833632	−	1.34189i
$964$	−0.139507	−	0.141670i	−0.00449322	−	0.00456289i
$965$	−5.21419	−	0.919402i	−0.167851	−	0.0295966i
$966$	6.02986	+	3.73799i	0.194008	+	0.120268i
$967$	12.7927	−	35.1476i	0.411385	−	1.13027i	−0.545070	−	0.838391i	$-0.683497\pi$
$967$	12.7927	−	35.1476i	0.411385	−	1.13027i	0.956455	−	0.291881i	$-0.0942810\pi$
$968$	−14.8658	−	23.9399i	−0.477806	−	0.769457i
$969$	−8.73547	−	4.85710i	−0.280624	−	0.156033i
$970$	15.1652	+	0.720577i	0.486924	+	0.0231363i
$971$	−33.0455			−1.06048			−0.530241	−	0.847847i	$-0.677898\pi$
$971$	−33.0455			−1.06048			−0.530241	+	0.847847i	$0.677898\pi$
$972$	−27.2191	+	15.2026i	−0.873055	+	0.487623i
$973$	1.73857			0.0557361
$974$	32.7682	+	1.55699i	1.04996	+	0.0498891i
$975$	−5.33275	−	2.96512i	−0.170785	−	0.0949598i
$976$	−8.99234	+	23.5714i	−0.287838	+	0.754503i
$977$	−1.91115	+	5.25083i	−0.0611430	+	0.167989i	−0.966503	−	0.256657i	$-0.917379\pi$
$977$	−1.91115	+	5.25083i	−0.0611430	+	0.167989i	0.905360	+	0.424646i	$0.139601\pi$
$978$	24.7309	+	15.3310i	0.790807	+	0.490232i
$979$	13.9694	+	2.46318i	0.446463	+	0.0787234i
$980$	−9.74690	+	9.59808i	−0.311353	+	0.306599i
$981$	−0.0333068	−	0.0536137i	−0.00106341	−	0.00171175i
$982$	3.90854	−	9.33433i	0.124726	−	0.297870i
$983$	0.509382	−	0.185400i	0.0162468	−	0.00591334i	−0.333884	−	0.942614i	$-0.608359\pi$
$983$	0.509382	−	0.185400i	0.0162468	−	0.00591334i	0.350131	+	0.936701i	$0.386137\pi$
$984$	44.1324	−	2.13056i	1.40689	−	0.0679198i
$985$	8.25532	−	6.92704i	0.263036	−	0.220714i
$986$	−10.4332	−	2.35513i	−0.332262	−	0.0750026i
$987$	−3.95551	+	3.42940i	−0.125905	+	0.109159i
$988$	28.2495	−	2.25267i	0.898735	−	0.0716670i
$989$	31.4446	−	18.1546i	0.999881	−	0.577282i
$990$	2.10300	+	3.77375i	0.0668378	+	0.119937i
$991$	−48.8608	−	28.2098i	−1.55211	−	0.896113i	−0.997970	−	0.0636927i	$-0.979712\pi$
$991$	−48.8608	−	28.2098i	−1.55211	−	0.896113i	−0.554144	−	0.832421i	$-0.686954\pi$
$992$	1.07800	−	17.1252i	0.0342264	−	0.543726i
$993$	25.2639	+	20.5131i	0.801727	+	0.650964i
$994$	−6.70763	+	2.08658i	−0.212753	+	0.0661822i
$995$	0.669736	+	3.79826i	0.0212320	+	0.120413i
$996$	8.17396	+	29.5058i	0.259002	+	0.934926i
$997$	25.1499	+	21.1033i	0.796507	+	0.668348i	0.947347	−	0.320210i	$-0.103753\pi$
$997$	25.1499	+	21.1033i	0.796507	+	0.668348i	−0.150840	+	0.988558i	$0.548198\pi$
$998$	28.9565	−	22.0426i	0.916601	−	0.697747i
$999$	−11.2377	+	7.23533i	−0.355547	+	0.228916i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	540.2.be.a.11.36	✓	432
4.3	odd	2	inner	540.2.be.a.11.69	yes	432
27.5	odd	18	inner	540.2.be.a.491.69	yes	432
108.59	even	18	inner	540.2.be.a.491.36	yes	432

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
540.2.be.a.11.36	✓	432	1.1	even	1	trivial
540.2.be.a.11.69	yes	432	4.3	odd	2	inner
540.2.be.a.491.36	yes	432	108.59	even	18	inner
540.2.be.a.491.69	yes	432	27.5	odd	18	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 540 = 2^{2} \cdot 3^{3} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	540.be (of order \(18\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(0.0671210 - 1.41262i) q^{2} +(-1.51379 - 0.841696i) q^{3} +(-1.99099 - 0.189633i) q^{4} +(-0.342020 + 0.939693i) q^{5} +(-1.29060 + 2.08191i) q^{6} +(-0.394309 - 0.0695273i) q^{7} +(-0.401517 + 2.79978i) q^{8} +(1.58310 + 2.54830i) q^{9} +(1.30447 + 0.546218i) q^{10} +(0.956862 - 0.348269i) q^{11} +(2.85432 + 1.96287i) q^{12} +(-2.69861 + 2.26441i) q^{13} +(-0.124682 + 0.552342i) q^{14} +(1.30868 - 1.13462i) q^{15} +(3.92808 + 0.755115i) q^{16} +(1.24246 - 0.717336i) q^{17} +(3.70603 - 2.06527i) q^{18} +(3.48337 + 2.01113i) q^{19} +(0.859155 - 1.80606i) q^{20} +(0.538379 + 0.437138i) q^{21} +(-0.427747 - 1.37506i) q^{22} +(1.25612 + 7.12380i) q^{23} +(2.96438 - 3.90032i) q^{24} +(-0.766044 - 0.642788i) q^{25} +(3.01761 + 3.96411i) q^{26} +(-0.251577 - 5.19006i) q^{27} +(0.771881 + 0.213202i) q^{28} +(3.38853 - 4.03829i) q^{29} +(-1.51494 - 1.92483i) q^{30} +(2.98725 - 0.526732i) q^{31} +(1.33035 - 5.49820i) q^{32} +(-1.74162 - 0.278182i) q^{33} +(-0.929927 - 1.80327i) q^{34} +(0.200196 - 0.346750i) q^{35} +(-2.66869 - 5.37384i) q^{36} +(-1.28610 - 2.22759i) q^{37} +(3.07477 - 4.78570i) q^{38} +(5.99107 - 1.15641i) q^{39} +(-2.49361 - 1.33488i) q^{40} +(5.79728 + 6.90893i) q^{41} +(0.653646 - 0.731183i) q^{42} +(-1.71675 - 4.71674i) q^{43} +(-1.97115 + 0.511948i) q^{44} +(-2.93606 + 0.616055i) q^{45} +(10.1475 - 1.29626i) q^{46} +(-1.31085 + 7.43422i) q^{47} +(-5.31069 - 4.44933i) q^{48} +(-6.42720 - 2.33931i) q^{49} +(-0.959432 + 1.03898i) q^{50} +(-2.48460 + 0.0401173i) q^{51} +(5.80232 - 3.99666i) q^{52} +7.75107i q^{53} +(-7.34847 + 0.00702082i) q^{54} +1.01827i q^{55} +(0.352983 - 1.07606i) q^{56} +(-3.58033 - 5.97636i) q^{57} +(-5.47713 - 5.05776i) q^{58} +(8.12690 + 2.95795i) q^{59} +(-2.82073 + 2.01084i) q^{60} +(-1.09522 + 6.21129i) q^{61} +(-0.543565 - 4.25520i) q^{62} +(-0.447053 - 1.11488i) q^{63} +(-7.67757 - 2.24832i) q^{64} +(-1.20487 - 3.31034i) q^{65} +(-0.509865 + 2.44158i) q^{66} +(-1.41571 - 1.68718i) q^{67} +(-2.60976 + 1.19260i) q^{68} +(4.09458 - 11.8412i) q^{69} +(-0.476388 - 0.306075i) q^{70} +(6.20292 + 10.7438i) q^{71} +(-7.77031 + 3.40914i) q^{72} +(-3.96093 + 6.86053i) q^{73} +(-3.23306 + 1.66725i) q^{74} +(0.618595 + 1.61782i) q^{75} +(-6.55399 - 4.66470i) q^{76} +(-0.401514 + 0.0707977i) q^{77} +(-1.23145 - 8.54072i) q^{78} +(-1.49137 + 1.77734i) q^{79} +(-2.05306 + 3.43292i) q^{80} +(-3.98762 + 8.06839i) q^{81} +(10.1488 - 7.72562i) q^{82} +(6.77059 + 5.68120i) q^{83} +(-0.989010 - 0.972431i) q^{84} +(0.249128 + 1.41288i) q^{85} +(-6.77818 + 2.10852i) q^{86} +(-8.52852 + 3.26100i) q^{87} +(0.590882 + 2.81884i) q^{88} +(12.0640 + 6.96517i) q^{89} +(0.673179 + 4.18889i) q^{90} +(1.22153 - 0.705249i) q^{91} +(-1.15001 - 14.4216i) q^{92} +(-4.96540 - 1.71699i) q^{93} +(10.4137 + 2.35073i) q^{94} +(-3.08123 + 2.58546i) q^{95} +(-6.64167 + 7.20335i) q^{96} +(10.0881 - 3.67175i) q^{97} +(-3.73596 + 8.92218i) q^{98} +(2.40230 + 1.88702i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 432 q + 18 q^{12} + 30 q^{14} + 30 q^{24} + 12 q^{29} - 24 q^{30} + 60 q^{33} - 60 q^{36} - 60 q^{38} + 60 q^{41} - 60 q^{42} - 72 q^{44} + 12 q^{45} - 150 q^{48} + 54 q^{52} - 84 q^{54} - 84 q^{56} - 12 q^{57}+ \cdots + 36 q^{97}+O(q^{100}) \) 432 * q + 18 * q^12 + 30 * q^14 + 30 * q^24 + 12 * q^29 - 24 * q^30 + 60 * q^33 - 60 * q^36 - 60 * q^38 + 60 * q^41 - 60 * q^42 - 72 * q^44 + 12 * q^45 - 150 * q^48 + 54 * q^52 - 84 * q^54 - 84 * q^56 - 12 * q^57 + 54 * q^58 - 198 * q^62 - 48 * q^66 - 138 * q^68 - 48 * q^69 - 84 * q^72 - 84 * q^74 - 48 * q^77 - 78 * q^78 - 66 * q^84 + 54 * q^86 - 36 * q^89 + 120 * q^92 - 54 * q^94 + 210 * q^96 + 36 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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