LMFDB - Embedded newform 555.2.bb.a.454.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [555,2,Mod(454,555)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(555, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 3, 4]))

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

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

chi := DirichletCharacter("555.454");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 555 = 3 \cdot 5 \cdot 37 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	555.bb (of order $6$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$4.43169731218$
Analytic rank:	$0$
Dimension:	$72$
Relative dimension:	$36$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			454.10
Character	$\chi$	$=$	555.454
Dual form			555.2.bb.a.544.10

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.22378 - 0.706551i) q^{2} +(-0.866025 + 0.500000i) q^{3} +(-0.00157058 - 0.00272032i) q^{4} +(2.18051 + 0.495360i) q^{5} +1.41310 q^{6} +(-1.52412 + 0.879952i) q^{7} +2.83064i q^{8} +(0.500000 - 0.866025i) q^{9} +O(q^{10})$	\(q+(-1.22378 - 0.706551i) q^{2} +(-0.866025 + 0.500000i) q^{3} +(-0.00157058 - 0.00272032i) q^{4} +(2.18051 + 0.495360i) q^{5} +1.41310 q^{6} +(-1.52412 + 0.879952i) q^{7} +2.83064i q^{8} +(0.500000 - 0.866025i) q^{9} +(-2.31847 - 2.14685i) q^{10} +0.846645 q^{11} +(0.00272032 + 0.00157058i) q^{12} +(-2.41391 + 1.39367i) q^{13} +2.48692 q^{14} +(-2.13606 + 0.661260i) q^{15} +(1.99685 - 3.45865i) q^{16} +(-7.10393 - 4.10146i) q^{17} +(-1.22378 + 0.706551i) q^{18} +(2.47308 + 4.28350i) q^{19} +(-0.00207712 - 0.00670969i) q^{20} +(0.879952 - 1.52412i) q^{21} +(-1.03611 - 0.598198i) q^{22} -0.546337i q^{23} +(-1.41532 - 2.45141i) q^{24} +(4.50924 + 2.16027i) q^{25} +3.93881 q^{26} +1.00000i q^{27} +(0.00478751 + 0.00276407i) q^{28} -7.93980 q^{29} +(3.08128 + 0.699994i) q^{30} -8.23825 q^{31} +(0.0153885 - 0.00888453i) q^{32} +(-0.733216 + 0.423322i) q^{33} +(5.79578 + 10.0386i) q^{34} +(-3.75925 + 1.16375i) q^{35} -0.00314116 q^{36} +(5.01251 + 3.44597i) q^{37} -6.98944i q^{38} +(1.39367 - 2.41391i) q^{39} +(-1.40219 + 6.17224i) q^{40} +(0.878263 + 1.52120i) q^{41} +(-2.15374 + 1.24346i) q^{42} +12.0635i q^{43} +(-0.00132972 - 0.00230315i) q^{44} +(1.51925 - 1.64070i) q^{45} +(-0.386015 + 0.668597i) q^{46} +2.30221i q^{47} +3.99371i q^{48} +(-1.95137 + 3.37987i) q^{49} +(-3.99198 - 5.82971i) q^{50} +8.20292 q^{51} +(0.00758248 + 0.00437775i) q^{52} +(-6.20716 - 3.58371i) q^{53} +(0.706551 - 1.22378i) q^{54} +(1.84612 + 0.419394i) q^{55} +(-2.49083 - 4.31424i) q^{56} +(-4.28350 - 2.47308i) q^{57} +(9.71660 + 5.60988i) q^{58} +(-5.81448 + 10.0710i) q^{59} +(0.00515369 + 0.00477220i) q^{60} +(1.07162 + 1.85610i) q^{61} +(10.0818 + 5.82075i) q^{62} +1.75990i q^{63} -8.01253 q^{64} +(-5.95393 + 1.84316i) q^{65} +1.19640 q^{66} +(-0.693985 + 0.400673i) q^{67} +0.0257667i q^{68} +(0.273168 + 0.473141i) q^{69} +(5.42276 + 1.23192i) q^{70} +(-2.25563 - 3.90687i) q^{71} +(2.45141 + 1.41532i) q^{72} +9.25889i q^{73} +(-3.69947 - 7.75872i) q^{74} +(-4.98525 + 0.383768i) q^{75} +(0.00776834 - 0.0134552i) q^{76} +(-1.29039 + 0.745006i) q^{77} +(-3.41111 + 1.96940i) q^{78} +(-0.100682 - 0.174387i) q^{79} +(6.06743 - 6.55246i) q^{80} +(-0.500000 - 0.866025i) q^{81} -2.48215i q^{82} +(10.3362 + 5.96761i) q^{83} -0.00552814 q^{84} +(-13.4585 - 12.4623i) q^{85} +(8.52348 - 14.7631i) q^{86} +(6.87607 - 3.96990i) q^{87} +2.39655i q^{88} +(3.59590 - 6.22829i) q^{89} +(-3.01847 + 0.934429i) q^{90} +(2.45273 - 4.24825i) q^{91} +(-0.00148621 + 0.000858065i) q^{92} +(7.13454 - 4.11913i) q^{93} +(1.62663 - 2.81741i) q^{94} +(3.27070 + 10.5653i) q^{95} +(-0.00888453 + 0.0153885i) q^{96} -15.4988i q^{97} +(4.77611 - 2.75749i) q^{98} +(0.423322 - 0.733216i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 72 q + 32 q^{4} - 2 q^{5} + 36 q^{9}+O(q^{10}) $ 72 * q + 32 * q^4 - 2 * q^5 + 36 * q^9	$ 72 q + 32 q^{4} - 2 q^{5} + 36 q^{9} - 8 q^{11} - 16 q^{14} - 24 q^{16} + 4 q^{19} + 4 q^{20} + 12 q^{21} + 10 q^{25} + 24 q^{26} + 16 q^{29} + 12 q^{30} + 24 q^{31} - 44 q^{34} - 2 q^{35} + 64 q^{36} - 8 q^{39} + 46 q^{40} - 48 q^{41} - 8 q^{44} - 4 q^{45} - 64 q^{46} + 32 q^{49} - 46 q^{50} - 8 q^{51} - 12 q^{55} - 72 q^{56} + 32 q^{59} - 68 q^{60} - 8 q^{61} - 136 q^{64} - 42 q^{65} - 32 q^{66} - 4 q^{69} + 4 q^{70} + 12 q^{71} - 96 q^{74} - 8 q^{75} + 8 q^{76} - 8 q^{79} - 44 q^{80} - 36 q^{81} + 136 q^{84} + 4 q^{85} + 8 q^{86} + 8 q^{91} - 28 q^{94} + 18 q^{95} - 20 q^{96} - 4 q^{99}+O(q^{100}) $ 72 * q + 32 * q^4 - 2 * q^5 + 36 * q^9 - 8 * q^11 - 16 * q^14 - 24 * q^16 + 4 * q^19 + 4 * q^20 + 12 * q^21 + 10 * q^25 + 24 * q^26 + 16 * q^29 + 12 * q^30 + 24 * q^31 - 44 * q^34 - 2 * q^35 + 64 * q^36 - 8 * q^39 + 46 * q^40 - 48 * q^41 - 8 * q^44 - 4 * q^45 - 64 * q^46 + 32 * q^49 - 46 * q^50 - 8 * q^51 - 12 * q^55 - 72 * q^56 + 32 * q^59 - 68 * q^60 - 8 * q^61 - 136 * q^64 - 42 * q^65 - 32 * q^66 - 4 * q^69 + 4 * q^70 + 12 * q^71 - 96 * q^74 - 8 * q^75 + 8 * q^76 - 8 * q^79 - 44 * q^80 - 36 * q^81 + 136 * q^84 + 4 * q^85 + 8 * q^86 + 8 * q^91 - 28 * q^94 + 18 * q^95 - 20 * q^96 - 4 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/555\mathbb{Z}\right)^\times$.

$n$	$76$	$112$	$371$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$-1$	$1$

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 $

$2$	−1.22378	−	0.706551i	−0.865345	−	0.499607i	0.000453506	−	1.00000i	$-0.499856\pi$
$2$	−1.22378	−	0.706551i	−0.865345	−	0.499607i	−0.865799	+	0.500393i	$0.833189\pi$
$3$	−0.866025	+	0.500000i	−0.500000	+	0.288675i
$3$	−0.866025	+	0.500000i	−0.500000	+	0.288675i
$4$	−0.00157058	−	0.00272032i	−0.000785290	−	0.00136016i
$5$	2.18051	+	0.495360i	0.975153	+	0.221532i
$5$	2.18051	+	0.495360i	0.975153	+	0.221532i
$6$	1.41310			0.576897
$7$	−1.52412	+	0.879952i	−0.576064	+	0.332590i	−0.759567	−	0.650429i	$-0.774589\pi$
$7$	−1.52412	+	0.879952i	−0.576064	+	0.332590i	0.183504	+	0.983019i	$0.441256\pi$
$8$			2.83064i			1.00078i
$9$	0.500000	−	0.866025i	0.166667	−	0.288675i
$10$	−2.31847	−	2.14685i	−0.733165	−	0.678895i
$11$	0.846645			0.255273			0.127636	−	0.991821i	$-0.459261\pi$
$11$	0.846645			0.255273			0.127636	+	0.991821i	$0.459261\pi$
$12$	0.00272032	+	0.00157058i	0.000785290	+	0.000453387i
$13$	−2.41391	+	1.39367i	−0.669499	+	0.386535i	−0.795887	−	0.605446i	$-0.792995\pi$
$13$	−2.41391	+	1.39367i	−0.669499	+	0.386535i	0.126388	+	0.991981i	$0.459662\pi$
$14$	2.48692			0.664658
$15$	−2.13606	+	0.661260i	−0.551527	+	0.170737i
$16$	1.99685	−	3.45865i	0.499213	−	0.864663i
$17$	−7.10393	−	4.10146i	−1.72296	−	0.994750i	−0.912648	−	0.408747i	$-0.865966\pi$
$17$	−7.10393	−	4.10146i	−1.72296	−	0.994750i	−0.810309	−	0.586003i	$-0.800701\pi$
$18$	−1.22378	+	0.706551i	−0.288448	+	0.166536i
$19$	2.47308	+	4.28350i	0.567364	+	0.982703i	0.996825	+	0.0796178i	$0.0253700\pi$
$19$	2.47308	+	4.28350i	0.567364	+	0.982703i	−0.429462	+	0.903085i	$0.641297\pi$
$20$	−0.00207712	−	0.00670969i	−0.000464459	−	0.00150033i
$21$	0.879952	−	1.52412i	0.192021	−	0.332590i
$22$	−1.03611	−	0.598198i	−0.220899	−	0.127536i
$23$		−	0.546337i		−	0.113919i	−0.998376	−	0.0569595i	$-0.981859\pi$
$23$		−	0.546337i		−	0.113919i	0.998376	−	0.0569595i	$-0.0181406\pi$
$24$	−1.41532	−	2.45141i	−0.288901	−	0.500392i
$25$	4.50924	+	2.16027i	0.901848	+	0.432054i
$26$	3.93881			0.772463
$27$			1.00000i			0.192450i
$28$	0.00478751	+	0.00276407i	0.000904754	+	0.000522360i
$29$	−7.93980			−1.47438			−0.737192	−	0.675683i	$-0.763849\pi$
$29$	−7.93980			−1.47438			−0.737192	+	0.675683i	$0.763849\pi$
$30$	3.08128	+	0.699994i	0.562563	+	0.127801i
$31$	−8.23825			−1.47963			−0.739817	−	0.672808i	$-0.765088\pi$
$31$	−8.23825			−1.47963			−0.739817	+	0.672808i	$0.765088\pi$
$32$	0.0153885	−	0.00888453i	0.00272032	−	0.00157058i
$33$	−0.733216	+	0.423322i	−0.127636	+	0.0736909i
$34$	5.79578	+	10.0386i	0.993968	+	1.72160i
$35$	−3.75925	+	1.16375i	−0.635430	+	0.196710i
$36$	−0.00314116			−0.000523526
$37$	5.01251	+	3.44597i	0.824052	+	0.566514i
$37$	5.01251	+	3.44597i	0.824052	+	0.566514i
$38$		−	6.98944i		−	1.13384i
$39$	1.39367	−	2.41391i	0.223166	−	0.386535i
$40$	−1.40219	+	6.17224i	−0.221705	+	0.975917i
$41$	0.878263	+	1.52120i	0.137162	+	0.237571i	0.926421	−	0.376489i	$-0.122869\pi$
$41$	0.878263	+	1.52120i	0.137162	+	0.237571i	−0.789260	+	0.614060i	$0.789535\pi$
$42$	−2.15374	+	1.24346i	−0.332329	+	0.191870i
$43$			12.0635i			1.83967i	0.392309	+	0.919833i	$0.371676\pi$
$43$			12.0635i			1.83967i	−0.392309	+	0.919833i	$0.628324\pi$
$44$	−0.00132972	−	0.00230315i	−0.000200463	−	0.000347212i
$45$	1.51925	−	1.64070i	0.226476	−	0.244581i
$46$	−0.386015	+	0.668597i	−0.0569148	+	0.0985793i
$47$			2.30221i			0.335812i	0.985803	+	0.167906i	$0.0537005\pi$
$47$			2.30221i			0.335812i	−0.985803	+	0.167906i	$0.946300\pi$
$48$			3.99371i			0.576442i
$49$	−1.95137	+	3.37987i	−0.278767	+	0.482839i
$50$	−3.99198	−	5.82971i	−0.564552	−	0.824446i
$51$	8.20292			1.14864
$52$	0.00758248	+	0.00437775i	0.00105150	+	0.000607084i
$53$	−6.20716	−	3.58371i	−0.852619	−	0.492260i	0.00891470	−	0.999960i	$-0.497162\pi$
$53$	−6.20716	−	3.58371i	−0.852619	−	0.492260i	−0.861534	+	0.507700i	$0.830496\pi$
$54$	0.706551	−	1.22378i	0.0961495	−	0.166536i
$55$	1.84612	+	0.419394i	0.248930	+	0.0565510i
$56$	−2.49083	−	4.31424i	−0.332851	−	0.576515i
$57$	−4.28350	−	2.47308i	−0.567364	−	0.327568i
$58$	9.71660	+	5.60988i	1.27585	+	0.736613i
$59$	−5.81448	+	10.0710i	−0.756980	+	1.31113i	0.187404	+	0.982283i	$0.439993\pi$
$59$	−5.81448	+	10.0710i	−0.756980	+	1.31113i	−0.944384	+	0.328845i	$0.893341\pi$
$60$	0.00515369	+	0.00477220i	0.000665338	+	0.000616088i
$61$	1.07162	+	1.85610i	0.137207	+	0.237649i	0.926438	−	0.376447i	$-0.122854\pi$
$61$	1.07162	+	1.85610i	0.137207	+	0.237649i	−0.789231	+	0.614096i	$0.789521\pi$
$62$	10.0818	+	5.82075i	1.28039	+	0.739236i
$63$			1.75990i			0.221727i
$64$	−8.01253			−1.00157
$65$	−5.95393	+	1.84316i	−0.738494	+	0.228616i
$66$	1.19640			0.147266
$67$	−0.693985	+	0.400673i	−0.0847838	+	0.0489500i	−0.541793	−	0.840512i	$-0.682254\pi$
$67$	−0.693985	+	0.400673i	−0.0847838	+	0.0489500i	0.457009	+	0.889462i	$0.348921\pi$
$68$			0.0257667i			0.00312467i
$69$	0.273168	+	0.473141i	0.0328856	+	0.0569595i
$70$	5.42276	+	1.23192i	0.648144	+	0.147243i
$71$	−2.25563	−	3.90687i	−0.267694	−	0.463660i	0.700572	−	0.713582i	$-0.252928\pi$
$71$	−2.25563	−	3.90687i	−0.267694	−	0.463660i	−0.968266	+	0.249922i	$0.919595\pi$
$72$	2.45141	+	1.41532i	0.288901	+	0.166797i
$73$			9.25889i			1.08367i	0.840485	+	0.541835i	$0.182270\pi$
$73$			9.25889i			1.08367i	−0.840485	+	0.541835i	$0.817730\pi$
$74$	−3.69947	−	7.75872i	−0.430055	−	0.901932i
$75$	−4.98525	+	0.383768i	−0.575647	+	0.0443137i
$76$	0.00776834	−	0.0134552i	0.000891090	−	0.00154341i
$77$	−1.29039	+	0.745006i	−0.147053	+	0.0849013i
$78$	−3.41111	+	1.96940i	−0.386232	+	0.222991i
$79$	−0.100682	−	0.174387i	−0.0113277	−	0.0196201i	0.860306	−	0.509778i	$-0.170272\pi$
$79$	−0.100682	−	0.174387i	−0.0113277	−	0.0196201i	−0.871634	+	0.490158i	$0.836939\pi$
$80$	6.06743	−	6.55246i	0.678360	−	0.732587i
$81$	−0.500000	−	0.866025i	−0.0555556	−	0.0962250i
$82$		−	2.48215i		−	0.274108i
$83$	10.3362	+	5.96761i	1.13455	+	0.655031i	0.945074	−	0.326856i	$-0.105989\pi$
$83$	10.3362	+	5.96761i	1.13455	+	0.655031i	0.189472	+	0.981886i	$0.439322\pi$
$84$	−0.00552814			−0.000603169
$85$	−13.4585	−	12.4623i	−1.45978	−	1.35172i
$86$	8.52348	−	14.7631i	0.919111	−	1.59195i
$87$	6.87607	−	3.96990i	0.737192	−	0.425618i
$88$			2.39655i			0.255473i
$89$	3.59590	−	6.22829i	0.381165	−	0.660197i	−0.610064	−	0.792352i	$-0.708856\pi$
$89$	3.59590	−	6.22829i	0.381165	−	0.660197i	0.991229	+	0.132155i	$0.0421897\pi$
$90$	−3.01847	+	0.934429i	−0.318174	+	0.0984974i
$91$	2.45273	−	4.24825i	0.257116	−	0.445338i
$92$	−0.00148621		0.000858065i	−0.000154948		8.94595e-5i
$93$	7.13454	−	4.11913i	0.739817	−	0.427134i
$94$	1.62663	−	2.81741i	0.167774	−	0.290593i
$95$	3.27070	+	10.5653i	0.335567	+	1.08397i
$96$	−0.00888453	+	0.0153885i	−0.000906774	+	0.00157058i
$97$		−	15.4988i		−	1.57367i	−0.617166	−	0.786833i	$-0.711719\pi$
$97$		−	15.4988i		−	1.57367i	0.617166	−	0.786833i	$-0.288281\pi$
$98$	4.77611	−	2.75749i	0.482460	−	0.278548i
$99$	0.423322	−	0.733216i	0.0425455	−	0.0736909i
$100$	−0.00120548	−	0.0156595i	−0.000120548	−	0.00156595i
$101$	5.06595			0.504081			0.252041	−	0.967717i	$-0.418898\pi$
$101$	5.06595			0.504081			0.252041	+	0.967717i	$0.418898\pi$
$102$	−10.0386	−	5.79578i	−0.993968	−	0.573868i
$103$		−	8.66924i		−	0.854205i	−0.904203	−	0.427103i	$-0.859534\pi$
$103$		−	8.66924i		−	0.854205i	0.904203	−	0.427103i	$-0.140466\pi$
$104$	−3.94499	−	6.83293i	−0.386838	−	0.670024i
$105$	2.67373	−	2.88747i	0.260929	−	0.281788i
$106$	5.06414	+	8.77135i	0.491873	+	0.851949i
$107$	3.04776	−	1.75962i	0.294638	−	0.170109i	−0.345394	−	0.938458i	$-0.612255\pi$
$107$	3.04776	−	1.75962i	0.294638	−	0.170109i	0.640032	+	0.768349i	$0.278921\pi$
$108$	0.00272032	−	0.00157058i	0.000261763	−	0.000151129i
$109$	1.30862	−	2.26659i	0.125343	−	0.217100i	−0.796524	−	0.604607i	$-0.793330\pi$
$109$	1.30862	−	2.26659i	0.125343	−	0.217100i	0.921867	+	0.387507i	$0.126664\pi$
$110$	−1.96292	−	1.81762i	−0.187157	−	0.173303i
$111$	−6.06395	−	0.478041i	−0.575565	−	0.0453736i
$112$			7.02854i			0.664135i
$113$	−18.0697	−	10.4326i	−1.69986	−	0.981413i	−0.945883	−	0.324509i	$-0.894801\pi$
$113$	−18.0697	−	10.4326i	−1.69986	−	0.981413i	−0.753974	−	0.656904i	$-0.771866\pi$
$114$	3.49472	+	6.05303i	0.327310	+	0.566918i
$115$	0.270633	−	1.19129i	0.0252367	−	0.111089i
$116$	0.0124701	+	0.0215988i	0.00115782	+	0.00200540i
$117$			2.78735i			0.257690i
$118$	14.2313	−	8.21645i	1.31010	−	0.756386i
$119$	14.4363			1.32338
$120$	−1.87179	−	6.04641i	−0.170871	−	0.551960i
$121$	−10.2832			−0.934836
$122$		−	3.02862i		−	0.274198i
$123$	−1.52120	−	0.878263i	−0.137162	−	0.0791903i
$124$	0.0129388	+	0.0224107i	0.00116194	+	0.00201254i
$125$	8.76232	+	6.94419i	0.783726	+	0.621107i
$126$	1.24346	−	2.15374i	0.110776	−	0.191870i
$127$	14.4307	+	8.33159i	1.28052	+	0.739309i	0.976944	−	0.213497i	$-0.0684855\pi$
$127$	14.4307	+	8.33159i	1.28052	+	0.739309i	0.303578	+	0.952807i	$0.401819\pi$
$128$	9.77481	+	5.64349i	0.863980	+	0.498819i
$129$	−6.03175	−	10.4473i	−0.531066	−	0.919833i
$130$	8.58860	+	1.95113i	0.753270	+	0.171125i
$131$	0.227975	−	0.394864i	0.0199182	−	0.0344994i	−0.855894	−	0.517151i	$-0.826993\pi$
$131$	0.227975	−	0.394864i	0.0199182	−	0.0344994i	0.875813	+	0.482651i	$0.160326\pi$
$132$	0.00230315	+	0.00132972i	0.000200463	+	0.000115737i
$133$	−7.53855	−	4.35238i	−0.653675	−	0.377400i
$134$	1.13238			0.0978230
$135$	−0.495360	+	2.18051i	−0.0426338	+	0.187668i
$136$	11.6098	−	20.1087i	0.995529	−	1.72431i
$137$		−	15.2243i		−	1.30070i	−0.759636	−	0.650348i	$-0.774623\pi$
$137$		−	15.2243i		−	1.30070i	0.759636	−	0.650348i	$-0.225377\pi$
$138$		−	0.772030i		−	0.0657195i
$139$	−9.03715	+	15.6528i	−0.766521	+	1.32765i	0.172917	+	0.984936i	$0.444681\pi$
$139$	−9.03715	+	15.6528i	−0.766521	+	1.32765i	−0.939439	+	0.342717i	$0.888653\pi$
$140$	0.00906999	+	0.00839861i	0.000766554	+	0.000709812i
$141$	−1.15111	−	1.99377i	−0.0969406	−	0.167906i
$142$			6.37488i			0.534968i
$143$	−2.04373	+	1.17995i	−0.170905	+	0.0986720i
$144$	−1.99685	−	3.45865i	−0.166404	−	0.288221i
$145$	−17.3128	−	3.93306i	−1.43775	−	0.326623i
$146$	6.54188	−	11.3309i	0.541410	−	0.937749i
$147$		−	3.90274i		−	0.321893i
$148$	0.00150160	−	0.0190478i	0.000123431	−	0.00156572i
$149$	−9.74708			−0.798512			−0.399256	−	0.916840i	$-0.630732\pi$
$149$	−9.74708			−0.798512			−0.399256	+	0.916840i	$0.630732\pi$
$150$	6.37202	+	3.05269i	0.520273	+	0.249251i
$151$	−1.91208	−	3.31182i	−0.155603	−	0.269512i	0.777676	−	0.628666i	$-0.216399\pi$
$151$	−1.91208	−	3.31182i	−0.155603	−	0.269512i	−0.933278	+	0.359154i	$0.883065\pi$
$152$	−12.1251	+	7.00041i	−0.983473	+	0.567808i
$153$	−7.10393	+	4.10146i	−0.574319	+	0.331583i
$154$	2.10554			0.169669
$155$	−17.9636	−	4.08090i	−1.44287	−	0.327786i
$156$	−0.00875550			−0.000701001
$157$	1.25634	+	0.725350i	0.100267	+	0.0578893i	0.549295	−	0.835628i	$-0.314896\pi$
$157$	1.25634	+	0.725350i	0.100267	+	0.0578893i	−0.449028	+	0.893518i	$0.648230\pi$
$158$			0.284549i			0.0226375i
$159$	7.16741			0.568413
$160$	0.0379557	−	0.0117500i	0.00300066	−	0.000928917i
$161$	0.480750	+	0.832683i	0.0378884	+	0.0656246i
$162$			1.41310i			0.111024i
$163$	5.81708	+	3.35849i	0.455629	+	0.263058i	0.710205	−	0.703995i	$-0.248602\pi$
$163$	5.81708	+	3.35849i	0.455629	+	0.263058i	−0.254576	+	0.967053i	$0.581936\pi$
$164$	0.00275876	−	0.00477832i	0.000215423	−	0.000373124i
$165$	−1.80848	+	0.559853i	−0.140790	+	0.0435845i
$166$	−8.43285	−	14.6061i	−0.654516	−	1.13366i
$167$	−1.47984	+	0.854388i	−0.114514	+	0.0661145i	−0.556163	−	0.831073i	$-0.687727\pi$
$167$	−1.47984	+	0.854388i	−0.114514	+	0.0661145i	0.441649	+	0.897188i	$0.354394\pi$
$168$	4.31424	+	2.49083i	0.332851	+	0.192172i
$169$	−2.61535	+	4.52992i	−0.201181	+	0.348455i
$170$	7.66504	+	24.7602i	0.587882	+	1.89902i
$171$	4.94616			0.378243
$172$	0.0328166	−	0.0189467i	0.00250224	−	0.00144467i
$173$	−11.6300	−	6.71459i	−0.884213	−	0.510501i	−0.0121678	−	0.999926i	$-0.503873\pi$
$173$	−11.6300	−	6.71459i	−0.884213	−	0.510501i	−0.872045	+	0.489425i	$0.837207\pi$
$174$	−11.2198			−0.850568
$175$	−8.77356	+	0.675395i	−0.663219	+	0.0510551i
$176$	1.69063	−	2.92825i	0.127436	−	0.220725i
$177$		−	11.6290i		−	0.874085i
$178$	−8.80121	+	5.08138i	−0.659678	+	0.380865i
$179$	13.6782			1.02235			0.511177	−	0.859476i	$-0.329210\pi$
$179$	13.6782			1.02235			0.511177	+	0.859476i	$0.329210\pi$
$180$	−0.00684932	−	0.00155600i	−0.000510518	−	0.000115978i
$181$	−9.01144	−	15.6083i	−0.669815	−	1.16015i	−0.977956	−	0.208813i	$-0.933040\pi$
$181$	−9.01144	−	15.6083i	−0.669815	−	1.16015i	0.308141	−	0.951341i	$-0.400293\pi$
$182$	−6.00322	+	3.46596i	−0.444988	+	0.256914i
$183$	−1.85610	−	1.07162i	−0.137207	−	0.0792164i
$184$	1.54648			0.114008
$185$	9.22284	+	9.99697i	0.678076	+	0.734991i
$186$	−11.6415			−0.853596
$187$	−6.01451	−	3.47248i	−0.439824	−	0.253933i
$188$	0.00626276	−	0.00361580i	0.000456758	−	0.000263710i
$189$	−0.879952	−	1.52412i	−0.0640071	−	0.110863i
$190$	3.46228	−	15.2405i	0.251180	−	1.10566i
$191$	8.96643			0.648788			0.324394	−	0.945922i	$-0.394840\pi$
$191$	8.96643			0.648788			0.324394	+	0.945922i	$0.394840\pi$
$192$	6.93905	−	4.00626i	0.500783	−	0.289127i
$193$		−	3.30812i		−	0.238124i	−0.992887	−	0.119062i	$-0.962011\pi$
$193$		−	3.30812i		−	0.238124i	0.992887	−	0.119062i	$-0.0379887\pi$
$194$	−10.9507	+	18.9672i	−0.786215	+	1.36176i
$195$	4.23467	−	4.57319i	0.303251	−	0.327493i
$196$	0.0122591			0.000875652
$197$	21.9617	+	12.6796i	1.56471	+	0.903385i	0.996770	+	0.0803136i	$0.0255922\pi$
$197$	21.9617	+	12.6796i	1.56471	+	0.903385i	0.567938	+	0.823071i	$0.307741\pi$
$198$	−1.03611	+	0.598198i	−0.0736331	+	0.0425121i
$199$	8.88400			0.629770			0.314885	−	0.949130i	$-0.398034\pi$
$199$	8.88400			0.629770			0.314885	+	0.949130i	$0.398034\pi$
$200$	−6.11496	+	12.7640i	−0.432393	+	0.902554i
$201$	0.400673	−	0.693985i	0.0282613	−	0.0489500i
$202$	−6.19963	−	3.57936i	−0.436204	−	0.251843i
$203$	12.1012	−	6.98664i	0.849339	−	0.490366i
$204$	−0.0128833	−	0.0223146i	−0.000902013	−	0.00156233i
$205$	1.16152	+	3.75204i	0.0811241	+	0.262054i
$206$	−6.12526	+	10.6093i	−0.426767	+	0.739182i
$207$	−0.473141	−	0.273168i	−0.0328856	−	0.0189865i
$208$			11.1318i			0.771855i
$209$	2.09382	+	3.62660i	0.144833	+	0.250857i
$210$	−5.31221	+	1.64450i	−0.366577	+	0.113482i
$211$	14.6726			1.01010			0.505051	−	0.863089i	$-0.331474\pi$
$211$	14.6726			1.01010			0.505051	+	0.863089i	$0.331474\pi$
$212$			0.0225140i			0.00154627i
$213$	3.90687	+	2.25563i	0.267694	+	0.154553i
$214$	−4.97306			−0.339951
$215$	−5.97577	+	26.3046i	−0.407544	+	1.79396i
$216$	−2.83064			−0.192601
$217$	12.5561	−	7.24927i	0.852363	−	0.492112i
$218$	−3.20293	+	1.84921i	−0.216930	+	0.125244i
$219$	−4.62944	−	8.01843i	−0.312829	−	0.541835i
$220$	−0.00175859	−	0.00568072i	−0.000118564	−	0.000382994i
$221$	22.8644			1.53802
$222$	7.08320	+	4.86951i	0.475393	+	0.326820i
$223$			4.98038i			0.333511i	0.985998	+	0.166755i	$0.0533290\pi$
$223$			4.98038i			0.333511i	−0.985998	+	0.166755i	$0.946671\pi$
$224$	−0.0156359	+	0.0270822i	−0.00104472	+	0.00180951i
$225$	4.12547	−	2.82498i	0.275031	−	0.188332i
$226$	14.7423	+	25.5344i	0.980642	+	1.69852i
$227$	−7.44896	+	4.30066i	−0.494405	+	0.285445i	−0.726400	−	0.687272i	$-0.758808\pi$
$227$	−7.44896	+	4.30066i	−0.494405	+	0.285445i	0.231995	+	0.972717i	$0.425475\pi$
$228$			0.0155367i			0.00102894i
$229$	6.40837	+	11.0996i	0.423477	+	0.733484i	0.996277	−	0.0862112i	$-0.0274760\pi$
$229$	6.40837	+	11.0996i	0.423477	+	0.733484i	−0.572800	+	0.819695i	$0.694143\pi$
$230$	−1.17291	+	1.26667i	−0.0773391	+	0.0835215i
$231$	0.745006	−	1.29039i	0.0490178	−	0.0849013i
$232$		−	22.4748i		−	1.47554i
$233$		−	9.83649i		−	0.644410i	−0.946670	−	0.322205i	$-0.895576\pi$
$233$		−	9.83649i		−	0.644410i	0.946670	−	0.322205i	$-0.104424\pi$
$234$	1.96940	−	3.41111i	0.128744	−	0.222991i
$235$	−1.14042	+	5.01999i	−0.0743929	+	0.327468i
$236$	0.0365284			0.00237780
$237$	0.174387	+	0.100682i	0.0113277	+	0.00654003i
$238$	−17.6669	−	10.2000i	−1.14518	−	0.661169i
$239$	8.13156	−	14.0843i	0.525987	−	0.911036i	−0.473555	−	0.880764i	$-0.657029\pi$
$239$	8.13156	−	14.0843i	0.525987	−	0.911036i	0.999542	−	0.0302715i	$-0.00963719\pi$
$240$	−1.97832	+	8.70832i	−0.127700	+	0.562119i
$241$	6.20127	+	10.7409i	0.399459	+	0.691884i	0.993659	−	0.112434i	$-0.0358646\pi$
$241$	6.20127	+	10.7409i	0.399459	+	0.691884i	−0.594200	+	0.804317i	$0.702531\pi$
$242$	12.5844	+	7.26560i	0.808955	+	0.467051i
$243$	0.866025	+	0.500000i	0.0555556	+	0.0320750i
$244$	0.00336613	−	0.00583031i	0.000215494	−	0.000373247i
$245$	−5.92923	+	6.40321i	−0.378805	+	0.409086i
$246$	1.24108	+	2.14961i	0.0791281	+	0.137054i
$247$	−11.9396	−	6.89333i	−0.759699	−	0.438612i
$248$		−	23.3196i		−	1.48079i
$249$	−11.9352			−0.756364
$250$	−5.81675	−	14.6892i	−0.367884	−	0.929027i
$251$	−27.9003			−1.76105			−0.880525	−	0.473999i	$-0.842810\pi$
$251$	−27.9003			−1.76105			−0.880525	+	0.473999i	$0.842810\pi$
$252$	0.00478751	−	0.00276407i	0.000301585	−	0.000174120i
$253$		−	0.462553i		−	0.0290805i
$254$	−11.7734	−	20.3921i	−0.738728	−	1.27952i
$255$	17.8865	+	4.06339i	1.12010	+	0.254460i
$256$	0.0376938	+	0.0652876i	0.00235586	+	0.00408047i
$257$	14.1942	+	8.19504i	0.885411	+	0.511192i	0.872439	−	0.488723i	$-0.162537\pi$
$257$	14.1942	+	8.19504i	0.885411	+	0.511192i	0.0129724	+	0.999916i	$0.495871\pi$
$258$			17.0470i			1.06130i
$259$	−10.6720	−	0.841306i	−0.663124	−	0.0522762i
$260$	0.0143651	+	0.0133018i	0.000890886	+	0.000824941i
$261$	−3.96990	+	6.87607i	−0.245731	+	0.425618i
$262$	−0.557983	+	0.322152i	−0.0344723	+	0.0199026i
$263$	−14.3868	+	8.30623i	−0.887129	+	0.512184i	−0.873002	−	0.487716i	$-0.837830\pi$
$263$	−14.3868	+	8.30623i	−0.887129	+	0.512184i	−0.0141267	+	0.999900i	$0.504497\pi$
$264$	−1.19827	−	2.07547i	−0.0737487	−	0.127737i
$265$	−11.7595	−	10.8891i	−0.722383	−	0.668911i
$266$	6.15037	+	10.6527i	0.377103	+	0.653162i
$267$			7.19181i			0.440131i
$268$	0.00217992	+	0.00125858i	0.000133160	+	7.68798e-5i
$269$	6.24336			0.380664			0.190332	−	0.981720i	$-0.439043\pi$
$269$	6.24336			0.380664			0.190332	+	0.981720i	$0.439043\pi$
$270$	2.14685	−	2.31847i	0.130653	−	0.141098i
$271$	13.8034	−	23.9081i	0.838495	−	1.45232i	−0.0526571	−	0.998613i	$-0.516769\pi$
$271$	13.8034	−	23.9081i	0.838495	−	1.45232i	0.891152	−	0.453704i	$-0.149898\pi$
$272$	−28.3710	+	16.3800i	−1.72025	+	0.993185i
$273$			4.90546i			0.296892i
$274$	−10.7567	+	18.6312i	−0.649837	+	1.12555i
$275$	3.81772	+	1.82898i	0.230217	+	0.110292i
$276$	0.000858065	−	0.00148621i	5.16495e−5	−	8.94595e-5i
$277$	−7.08960	+	4.09318i	−0.425972	+	0.245935i	−0.697629	−	0.716459i	$-0.745762\pi$
$277$	−7.08960	+	4.09318i	−0.425972	+	0.245935i	0.271657	+	0.962394i	$0.412428\pi$
$278$	22.1190	−	12.7704i	1.32661	−	0.765919i
$279$	−4.11913	+	7.13454i	−0.246606	+	0.427134i
$280$	−3.29417	−	10.6411i	−0.196865	−	0.635928i
$281$	0.992171	−	1.71849i	0.0591880	−	0.102517i	−0.834913	−	0.550382i	$-0.814482\pi$
$281$	0.992171	−	1.71849i	0.0591880	−	0.102517i	0.894101	+	0.447865i	$0.147816\pi$
$282$			3.25326i			0.193729i
$283$	−28.0497	+	16.1945i	−1.66738	+	0.962665i	−0.698344	+	0.715763i	$0.746079\pi$
$283$	−28.0497	+	16.1945i	−1.66738	+	0.962665i	−0.969040	+	0.246902i	$0.920587\pi$
$284$	−0.00708529	+	0.0122721i	−0.000420435	+	0.000728215i
$285$	−8.11515	−	7.51445i	−0.480700	−	0.445118i
$286$	3.33477			0.197189
$287$	−2.67716	−	1.54566i	−0.158028	−	0.0912373i
$288$		−	0.0177691i		−	0.00104705i
$289$	25.1439	+	43.5505i	1.47905	+	2.56180i
$290$	18.4082	+	17.0456i	1.08097	+	1.00095i
$291$	7.74940	+	13.4224i	0.454278	+	0.786833i
$292$	0.0251872	−	0.0145418i	0.00147397	−	0.000850995i
$293$	14.0041	−	8.08529i	0.818131	−	0.472348i	−0.0316408	−	0.999499i	$-0.510073\pi$
$293$	14.0041	−	8.08529i	0.818131	−	0.472348i	0.849771	+	0.527151i	$0.176740\pi$
$294$	−2.75749	+	4.77611i	−0.160820	+	0.278548i
$295$	−17.6673	+	19.0796i	−1.02863	+	1.11086i
$296$	−9.75431	+	14.1886i	−0.566958	+	0.824698i
$297$			0.846645i			0.0491273i
$298$	11.9283	+	6.88681i	0.690988	+	0.398942i
$299$	0.761415	+	1.31881i	0.0440338	+	0.0762687i
$300$	0.00887371	+	0.0129588i	0.000512324	+	0.000748174i
$301$	−10.6153	−	18.3862i	−0.611856	−	1.05977i
$302$			5.40393i			0.310961i
$303$	−4.38724	+	2.53298i	−0.252041	+	0.145516i
$304$	19.7535			1.13294
$305$	1.41724	+	4.57808i	0.0811509	+	0.262140i
$306$	11.5916			0.662645
$307$			16.6619i			0.950946i	0.879730	+	0.475473i	$0.157723\pi$
$307$			16.6619i			0.950946i	−0.879730	+	0.475473i	$0.842277\pi$
$308$	0.00405332	+	0.00234018i	0.000230959	+	0.000133344i
$309$	4.33462	+	7.50778i	0.246588	+	0.427103i
$310$	19.1002	+	17.6863i	1.08482	+	1.00452i
$311$	−10.8034	+	18.7120i	−0.612604	+	1.06106i	0.378196	+	0.925726i	$0.376545\pi$
$311$	−10.8034	+	18.7120i	−0.612604	+	1.06106i	−0.990800	+	0.135336i	$0.956789\pi$
$312$	6.83293	+	3.94499i	0.386838	+	0.223341i
$313$	−2.37995	−	1.37407i	−0.134523	−	0.0776669i	0.431228	−	0.902243i	$-0.358080\pi$
$313$	−2.37995	−	1.37407i	−0.134523	−	0.0776669i	−0.565751	+	0.824576i	$0.691414\pi$
$314$	−1.02499	−	1.77534i	−0.0578438	−	0.100188i
$315$	−0.871785	+	3.83748i	−0.0491195	+	0.216218i
$316$	−0.000316260	0	0.000547778i	−1.77910e−5	0	3.08149e-5i
$317$	−1.84913	−	1.06760i	−0.103857	−	0.0599621i	0.447172	−	0.894448i	$-0.352431\pi$
$317$	−1.84913	−	1.06760i	−0.103857	−	0.0599621i	−0.551029	+	0.834486i	$0.685765\pi$
$318$	−8.77135	−	5.06414i	−0.491873	−	0.283983i
$319$	−6.72219			−0.376371
$320$	−17.4714	−	3.96908i	−0.976680	−	0.221878i
$321$	−1.75962	+	3.04776i	−0.0982126	+	0.170109i
$322$		−	1.35870i		−	0.0757173i
$323$		−	40.5730i		−	2.25754i
$324$	−0.00157058	+	0.00272032i	−8.72544e−5	+	0.000151129i
$325$	−13.8956	+	1.06970i	−0.770790	+	0.0593360i
$326$	−4.74590	−	8.22013i	−0.262851	−	0.455271i
$327$			2.61724i			0.144734i
$328$	−4.30596	+	2.48605i	−0.237757	+	0.137269i
$329$	−2.02583	−	3.50885i	−0.111688	−	0.193449i
$330$	2.60875	+	0.592646i	0.143607	+	0.0326241i
$331$	8.94458	−	15.4925i	0.491639	−	0.851543i	−0.508315	−	0.861171i	$-0.669731\pi$
$331$	8.94458	−	15.4925i	0.491639	−	0.851543i	0.999954	+	0.00962810i	$0.00306477\pi$
$332$		−	0.0374904i		−	0.00205756i
$333$	5.49055	−	2.61798i	0.300881	−	0.143464i
$334$	2.41468			0.132125
$335$	−1.71172	+	0.529898i	−0.0935212	+	0.0289514i
$336$	−3.51427	−	6.08689i	−0.191719	−	0.332067i
$337$	6.23628	−	3.60052i	0.339712	−	0.196133i	−0.320433	−	0.947271i	$-0.603828\pi$
$337$	6.23628	−	3.60052i	0.339712	−	0.196133i	0.660145	+	0.751138i	$0.270495\pi$
$338$	6.40124	−	3.69576i	0.348182	−	0.201023i
$339$	20.8651			1.13324
$340$	−0.0127638	+	0.0561844i	−0.000692212	+	0.00304703i
$341$	−6.97487			−0.377711
$342$	−6.05303	−	3.49472i	−0.327310	−	0.188973i
$343$		−	19.1878i		−	1.03604i
$344$	−34.1475			−1.84111
$345$	0.361271	+	1.16701i	0.0194502	+	0.0628295i
$346$	9.48840	+	16.4344i	0.510100	+	0.883518i
$347$			12.1910i			0.654447i	0.944947	+	0.327223i	$0.106113\pi$
$347$			12.1910i			0.654447i	−0.944947	+	0.327223i	$0.893887\pi$
$348$	−0.0215988	−	0.0124701i	−0.00115782	−	0.000668467i
$349$	5.67757	−	9.83384i	0.303913	−	0.526393i	−0.673106	−	0.739546i	$-0.735040\pi$
$349$	5.67757	−	9.83384i	0.303913	−	0.526393i	0.977019	+	0.213153i	$0.0683734\pi$
$350$	11.2141	+	5.37243i	0.599420	+	0.287169i
$351$	−1.39367	−	2.41391i	−0.0743888	−	0.128845i
$352$	0.0130286	−	0.00752204i	0.000694424	−	0.000400926i
$353$	2.86518	+	1.65421i	0.152498	+	0.0880449i	0.574307	−	0.818640i	$-0.305271\pi$
$353$	2.86518	+	1.65421i	0.152498	+	0.0880449i	−0.421809	+	0.906685i	$0.638605\pi$
$354$	−8.21645	+	14.2313i	−0.436699	+	0.756386i
$355$	−2.98312	−	9.63631i	−0.158327	−	0.511442i
$356$	−0.0225906			−0.00119730
$357$	−12.5022	+	7.21817i	−0.661688	+	0.382026i
$358$	−16.7391	−	9.66432i	−0.884689	−	0.510775i
$359$	32.3030			1.70489			0.852443	−	0.522820i	$-0.175120\pi$
$359$	32.3030			1.70489			0.852443	+	0.522820i	$0.175120\pi$
$360$	4.64423	+	4.30045i	0.244772	+	0.226654i
$361$	−2.73226	+	4.73242i	−0.143803	+	0.249075i
$362$			25.4682i			1.33858i
$363$	8.90551	−	5.14160i	0.467418	−	0.269864i
$364$	−0.0154088			−0.000807642
$365$	−4.58648	+	20.1891i	−0.240067	+	1.05675i
$366$	1.51431	+	2.62286i	0.0791542	+	0.137099i
$367$	1.29772	−	0.749239i	0.0677404	−	0.0391099i	−0.465747	−	0.884918i	$-0.654214\pi$
$367$	1.29772	−	0.749239i	0.0677404	−	0.0391099i	0.533488	+	0.845808i	$0.320881\pi$
$368$	−1.88959	−	1.09095i	−0.0985016	−	0.0568699i
$369$	1.75653			0.0914410
$370$	−4.22338	−	18.7505i	−0.219563	−	0.974793i
$371$	12.6139			0.654884
$372$	−0.0224107	−	0.0129388i	−0.00116194	−	0.000670847i
$373$	16.2647	−	9.39044i	0.842155	−	0.486219i	−0.0158410	−	0.999875i	$-0.505043\pi$
$373$	16.2647	−	9.39044i	0.842155	−	0.486219i	0.857996	+	0.513656i	$0.171709\pi$
$374$	4.90697	+	8.49911i	0.253733	+	0.439479i
$375$	−11.0605	−	1.63268i	−0.571161	−	0.0843113i
$376$	−6.51674			−0.336075
$377$	19.1660	−	11.0655i	0.987099	−	0.569902i
$378$			2.48692i			0.127914i
$379$	13.6117	−	23.5761i	0.699185	−	1.21102i	−0.269564	−	0.962982i	$-0.586880\pi$
$379$	13.6117	−	23.5761i	0.699185	−	1.21102i	0.968749	−	0.248042i	$-0.0797871\pi$
$380$	0.0236041	−	0.0254910i	0.00121086	−	0.00130766i
$381$	−16.6632			−0.853681
$382$	−10.9730	−	6.33524i	−0.561426	−	0.324139i
$383$	−7.82792	+	4.51945i	−0.399988	+	0.230933i	−0.686479	−	0.727150i	$-0.740845\pi$
$383$	−7.82792	+	4.51945i	−0.399988	+	0.230933i	0.286491	+	0.958083i	$0.407511\pi$
$384$	−11.2870			−0.575986
$385$	−3.18275	+	0.985286i	−0.162208	+	0.0502148i
$386$	−2.33736	+	4.04843i	−0.118968	+	0.206059i
$387$	10.4473	+	6.03175i	0.531066	+	0.306611i
$388$	−0.0421618	+	0.0243421i	−0.00214044	+	0.00123578i
$389$	−5.95520	−	10.3147i	−0.301941	−	0.522977i	0.674635	−	0.738152i	$-0.264301\pi$
$389$	−5.95520	−	10.3147i	−0.301941	−	0.522977i	−0.976576	+	0.215175i	$0.930968\pi$
$390$	−8.41351	+	2.60458i	−0.426035	+	0.131888i
$391$	−2.24078	+	3.88114i	−0.113321	+	0.196278i
$392$	−9.56722	−	5.52363i	−0.483217	−	0.278986i
$393$			0.455949i			0.0229996i
$394$	−17.9176	−	31.0342i	−0.902675	−	1.56348i
$395$	−0.133155	−	0.430127i	−0.00669974	−	0.0216420i
$396$	−0.00265944			−0.000133642
$397$			33.3484i			1.67371i	0.547426	+	0.836854i	$0.315608\pi$
$397$			33.3484i			1.67371i	−0.547426	+	0.836854i	$0.684392\pi$
$398$	−10.8721	−	6.27700i	−0.544968	−	0.314638i
$399$	8.70477			0.435783
$400$	16.4759	−	11.2821i	0.823796	−	0.564107i
$401$	−28.1794			−1.40721			−0.703605	−	0.710591i	$-0.748428\pi$
$401$	−28.1794			−1.40721			−0.703605	+	0.710591i	$0.748428\pi$
$402$	−0.980673	+	0.566192i	−0.0489115	+	0.0282391i
$403$	19.8864	−	11.4814i	0.990613	−	0.571931i
$404$	−0.00795648	−	0.0137810i	−0.000395850	−	0.000685632i
$405$	−0.661260	−	2.13606i	−0.0328583	−	0.106141i
$406$	−19.7457			−0.979962
$407$	4.24382	+	2.91751i	0.210358	+	0.144616i
$408$			23.2195i			1.14954i
$409$	5.91121	−	10.2385i	0.292291	−	0.506262i	−0.682060	−	0.731296i	$-0.738916\pi$
$409$	5.91121	−	10.2385i	0.292291	−	0.506262i	0.974351	+	0.225034i	$0.0722492\pi$
$410$	1.22956	−	5.41235i	0.0607235	−	0.267297i
$411$	7.61213	+	13.1846i	0.375479	+	0.650348i
$412$	−0.0235831	+	0.0136157i	−0.00116186	+	0.000670799i
$413$		−	20.4658i		−	1.00706i
$414$	0.386015	+	0.668597i	0.0189716	+	0.0328598i
$415$	19.5821	+	18.1326i	0.961247	+	0.890093i
$416$	−0.0247643	+	0.0428930i	−0.00121417	+	0.00210300i
$417$		−	18.0743i		−	0.885103i
$418$		−	5.91757i		−	0.289438i
$419$	8.46660	−	14.6646i	0.413621	−	0.716412i	−0.581662	−	0.813431i	$-0.697597\pi$
$419$	8.46660	−	14.6646i	0.413621	−	0.716412i	0.995283	+	0.0970188i	$0.0309307\pi$
$420$	−0.0120541	−	0.00273842i	−0.000588182	−	0.000133621i
$421$	8.88257			0.432910			0.216455	−	0.976293i	$-0.430551\pi$
$421$	8.88257			0.432910			0.216455	+	0.976293i	$0.430551\pi$
$422$	−17.9561	−	10.3669i	−0.874087	−	0.504654i
$423$	1.99377	+	1.15111i	0.0969406	+	0.0559687i
$424$	10.1442	−	17.5703i	0.492646	−	0.853287i
$425$	−23.1731	−	33.8409i	−1.12406	−	1.64152i
$426$	−3.18744	−	5.52080i	−0.154432	−	0.267484i
$427$	−3.26656	−	1.88595i	−0.158080	−	0.0912674i
$428$	−0.00957349	−	0.00552726i	−0.000462752	−	0.000267170i
$429$	1.17995	−	2.04373i	0.0569683	−	0.0986720i
$430$	25.8986	−	27.9689i	1.24894	−	1.34878i
$431$	11.3464	+	19.6526i	0.546538	+	0.946632i	0.998508	+	0.0545990i	$0.0173880\pi$
$431$	11.3464	+	19.6526i	0.546538	+	0.946632i	−0.451970	+	0.892033i	$0.649279\pi$
$432$	3.45865	+	1.99685i	0.166404	+	0.0960737i
$433$		−	8.06466i		−	0.387563i	−0.981045	−	0.193781i	$-0.937925\pi$
$433$		−	8.06466i		−	0.387563i	0.981045	−	0.193781i	$-0.0620752\pi$
$434$	−20.4879			−0.983451
$435$	16.9599	−	5.25028i	0.813163	−	0.251732i
$436$	−0.00822116			−0.000393722
$437$	2.34023	−	1.35114i	0.111949	−	0.0646336i
$438$			13.0838i			0.625166i
$439$	−17.0968	−	29.6126i	−0.815988	−	1.41333i	−0.908617	−	0.417631i	$-0.862860\pi$
$439$	−17.0968	−	29.6126i	−0.815988	−	1.41333i	0.0926288	−	0.995701i	$-0.470473\pi$
$440$	−1.18715	+	5.22570i	−0.0565953	+	0.249125i
$441$	1.95137	+	3.37987i	0.0929224	+	0.160946i
$442$	−27.9810	−	16.1548i	−1.33092	−	0.768408i
$443$		−	7.25909i		−	0.344890i	−0.985019	−	0.172445i	$-0.944833\pi$
$443$		−	7.25909i		−	0.344890i	0.985019	−	0.172445i	$-0.0551667\pi$
$444$	0.00822349	+	0.0172467i	0.000390269	+	0.000818492i
$445$	10.9261	−	11.7996i	0.517949	−	0.559353i
$446$	3.51889	−	6.09490i	0.166624	−	0.288602i
$447$	8.44122	−	4.87354i	0.399256	−	0.230511i
$448$	12.2121	−	7.05063i	0.576965	−	0.333111i
$449$	−1.32570	−	2.29618i	−0.0625637	−	0.108363i	0.833047	−	0.553202i	$-0.186594\pi$
$449$	−1.32570	−	2.29618i	−0.0625637	−	0.108363i	−0.895611	+	0.444839i	$0.853261\pi$
$450$	−7.04467	+	0.542304i	−0.332089	+	0.0255645i
$451$	0.743576	+	1.28791i	0.0350136	+	0.0606454i
$452$			0.0655407i			0.00308277i
$453$	3.31182	+	1.91208i	0.155603	+	0.0898373i
$454$	12.1545			0.570441
$455$	7.45261	−	8.04837i	0.349384	−	0.377313i
$456$	7.00041	−	12.1251i	0.327824	−	0.567808i
$457$	−11.4513	+	6.61140i	−0.535668	+	0.309268i	−0.743321	−	0.668934i	$-0.766751\pi$
$457$	−11.4513	+	6.61140i	−0.535668	+	0.309268i	0.207653	+	0.978202i	$0.433417\pi$
$458$		−	18.1114i		−	0.846289i
$459$	4.10146	−	7.10393i	0.191440	−	0.331583i
$460$	−0.00366575	+	0.00113481i	−0.000170916	+	5.29107e-5i
$461$	−4.12937	+	7.15228i	−0.192324	+	0.333115i	−0.946020	−	0.324108i	$-0.894936\pi$
$461$	−4.12937	+	7.15228i	−0.192324	+	0.333115i	0.753696	+	0.657223i	$0.228269\pi$
$462$	−1.82345	+	1.05277i	−0.0848346	+	0.0489793i
$463$	−26.1590	+	15.1029i	−1.21571	+	0.701890i	−0.963997	−	0.265912i	$-0.914327\pi$
$463$	−26.1590	+	15.1029i	−1.21571	+	0.701890i	−0.251712	+	0.967802i	$0.580994\pi$
$464$	−15.8546	+	27.4610i	−0.736033	+	1.27485i
$465$	17.5974	−	5.44763i	0.816059	−	0.252628i
$466$	−6.94999	+	12.0377i	−0.321952	+	0.557637i
$467$		−	35.4147i		−	1.63880i	−0.573224	−	0.819399i	$-0.694308\pi$
$467$		−	35.4147i		−	1.63880i	0.573224	−	0.819399i	$-0.305692\pi$
$468$	0.00758248	−	0.00437775i	0.000350500	−	0.000202361i
$469$	0.705145	−	1.22135i	0.0325606	−	0.0563966i
$470$	4.94251	−	5.33761i	0.227981	−	0.246206i
$471$	−1.45070			−0.0668448
$472$	−28.5073	−	16.4587i	−1.31216	−	0.757574i
$473$			10.2135i			0.469617i
$474$	−0.142275	−	0.246427i	−0.00653489	−	0.0113188i
$475$	1.89818	+	24.6579i	0.0870945	+	1.13138i
$476$	−0.0226734	−	0.0392715i	−0.00103923	−	0.00180001i
$477$	−6.20716	+	3.58371i	−0.284206	+	0.164087i
$478$	−19.9025	+	11.4907i	−0.910320	+	0.525574i
$479$	−10.6426	+	18.4334i	−0.486271	+	0.842246i	−0.999875	−	0.0157812i	$-0.994976\pi$
$479$	−10.6426	+	18.4334i	−0.486271	+	0.842246i	0.513605	+	0.858027i	$0.328310\pi$
$480$	−0.0269956	+	0.0291536i	−0.00123218	+	0.00133068i
$481$	−16.9023	−	1.33247i	−0.770680	−	0.0607552i
$482$		−	17.5261i		−	0.798291i
$483$	−0.832683	−	0.480750i	−0.0378884	−	0.0218749i
$484$	0.0161506	+	0.0279736i	0.000734117	+	0.00127153i
$485$	7.67748	−	33.7953i	0.348617	−	1.53456i
$486$	−0.706551	−	1.22378i	−0.0320498	−	0.0555119i
$487$		−	16.9321i		−	0.767266i	−0.923486	−	0.383633i	$-0.874673\pi$
$487$		−	16.9321i		−	0.767266i	0.923486	−	0.383633i	$-0.125327\pi$
$488$	−5.25396	+	3.03337i	−0.237836	+	0.137314i
$489$	−6.71699			−0.303753
$490$	11.7803	−	3.64683i	0.532179	−	0.164747i
$491$	−32.6478			−1.47338			−0.736688	−	0.676233i	$-0.763611\pi$
$491$	−32.6478			−1.47338			−0.736688	+	0.676233i	$0.763611\pi$
$492$			0.00551752i			0.000248749i
$493$	56.4038	+	32.5648i	2.54030	+	1.46664i
$494$	9.74099	+	16.8719i	0.438268	+	0.759102i
$495$	1.28626	−	1.38909i	0.0578132	−	0.0624348i
$496$	−16.4506	+	28.4933i	−0.738653	+	1.27939i
$497$	6.87571	+	3.96969i	0.308418	+	0.178065i
$498$	14.6061	+	8.43285i	0.654516	+	0.377885i
$499$	14.8969	+	25.8023i	0.666879	+	1.15507i	0.978772	+	0.204951i	$0.0657036\pi$
$499$	14.8969	+	25.8023i	0.666879	+	1.15507i	−0.311893	+	0.950117i	$0.600963\pi$
$500$	0.00512851	−	0.0347427i	0.000229354	−	0.00155374i
$501$	0.854388	−	1.47984i	0.0381712	−	0.0661145i
$502$	34.1439	+	19.7130i	1.52392	+	0.879834i
$503$	15.8547	+	9.15371i	0.706925	+	0.408144i	0.809922	−	0.586538i	$-0.199510\pi$
$503$	15.8547	+	9.15371i	0.706925	+	0.408144i	−0.102996	+	0.994682i	$0.532843\pi$
$504$	−4.98166			−0.221901
$505$	11.0464	+	2.50947i	0.491556	+	0.111670i
$506$	−0.326817	+	0.566064i	−0.0145288	+	0.0251646i
$507$		−	5.23070i		−	0.232304i
$508$		−	0.0523417i		−	0.00232229i
$509$	8.33182	−	14.4311i	0.369302	−	0.639649i	−0.620155	−	0.784479i	$-0.712930\pi$
$509$	8.33182	−	14.4311i	0.369302	−	0.639649i	0.989457	+	0.144830i	$0.0462636\pi$
$510$	−19.0182	−	17.6105i	−0.842141	−	0.779804i
$511$	−8.14737	−	14.1117i	−0.360419	−	0.624263i
$512$		−	22.6805i		−	1.00235i
$513$	−4.28350	+	2.47308i	−0.189121	+	0.109189i
$514$	−11.5804	−	20.0579i	−0.510791	−	0.884716i
$515$	4.29439	−	18.9033i	0.189233	−	0.832981i
$516$	−0.0189467	+	0.0328166i	−0.000834081	+	0.00144467i
$517$			1.94915i			0.0857237i
$518$	12.4657	+	8.56987i	0.547713	+	0.376538i
$519$	13.4292			0.589475
$520$	−5.21733	−	16.8534i	−0.228795	−	0.739073i
$521$	13.6643	+	23.6673i	0.598646	+	1.03688i	0.993021	+	0.117935i	$0.0376275\pi$
$521$	13.6643	+	23.6673i	0.598646	+	1.03688i	−0.394376	+	0.918949i	$0.629039\pi$
$522$	9.71660	−	5.60988i	0.425284	−	0.245538i
$523$	−24.4102	+	14.0932i	−1.06738	+	0.616255i	−0.927466	−	0.373908i	$-0.878018\pi$
$523$	−24.4102	+	14.0932i	−1.06738	+	0.616255i	−0.139919	+	0.990163i	$0.544684\pi$
$524$	−0.00143221			−6.25664e−5
$525$	7.26043	−	4.97169i	0.316871	−	0.216982i
$526$	23.4751			1.02356
$527$	58.5240	+	33.7889i	2.54935	+	1.47187i
$528$			3.38125i			0.147150i
$529$	22.7015			0.987022
$530$	6.69743	+	21.6346i	0.290918	+	0.939746i
$531$	5.81448	+	10.0710i	0.252327	+	0.437043i
$532$			0.0273431i			0.00118547i
$533$	−4.24010	−	2.44802i	−0.183659	−	0.106036i
$534$	5.08138	−	8.80121i	0.219893	−	0.380865i
$535$	7.51731	−	2.32714i	0.325002	−	0.100611i
$536$	−1.13416	−	1.96443i	−0.0489883	−	0.0848503i
$537$	−11.8456	+	6.83908i	−0.511177	+	0.295128i
$538$	−7.64052	−	4.41125i	−0.329406	−	0.190183i
$539$	−1.65212	+	2.86155i	−0.0711617	+	0.123256i
$540$	0.00670969	−	0.00207712i	0.000288739	−	8.93852e-5i
$541$	−4.84046			−0.208107			−0.104054	−	0.994572i	$-0.533181\pi$
$541$	−4.84046			−0.208107			−0.104054	+	0.994572i	$0.533181\pi$
$542$	−33.7847	+	19.5056i	−1.45118	+	0.837837i
$543$	15.6083	+	9.01144i	0.669815	+	0.386718i
$544$	−0.145758			−0.00624933
$545$	3.97623	−	4.29409i	0.170323	−	0.183939i
$546$	3.46596	−	6.00322i	0.148329	−	0.256914i
$547$			1.38558i			0.0592430i	0.999561	+	0.0296215i	$0.00943020\pi$
$547$			1.38558i			0.0592430i	−0.999561	+	0.0296215i	$0.990570\pi$
$548$	−0.0414149	+	0.0239109i	−0.00176916	+	0.00102142i
$549$	2.14324			0.0914712
$550$	−3.37979	−	4.93569i	−0.144115	−	0.210459i
$551$	−19.6358	−	34.0102i	−0.836513	−	1.44888i
$552$	−1.33929	+	0.773242i	−0.0570042	+	0.0329114i
$553$	0.306904	+	0.177191i	0.0130509	+	0.00753494i
$554$	11.5682			0.491484
$555$	−12.9857	−	4.04621i	−0.551212	−	0.171752i
$556$	0.0567743			0.00240776
$557$	12.6204	+	7.28638i	0.534743	+	0.308734i	0.742946	−	0.669352i	$-0.233428\pi$
$557$	12.6204	+	7.28638i	0.534743	+	0.308734i	−0.208203	+	0.978086i	$0.566761\pi$
$558$	10.0818	−	5.82075i	0.426798	−	0.246412i
$559$	−16.8126	−	29.1202i	−0.711096	−	1.23165i
$560$	−3.48165	+	15.3258i	−0.147127	+	0.647633i
$561$	6.94495			0.293216
$562$	−2.42840	+	1.40204i	−0.102436	+	0.0591415i
$563$		−	1.01763i		−	0.0428878i	−0.999770	−	0.0214439i	$-0.993174\pi$
$563$		−	1.01763i		−	0.0428878i	0.999770	−	0.0214439i	$-0.00682633\pi$
$564$	−0.00361580	+	0.00626276i	−0.000152253	+	0.000263710i
$565$	−34.2333	−	31.6993i	−1.44021	−	1.33360i
$566$	45.7691			1.92382
$567$	1.52412	+	0.879952i	0.0640071	+	0.0369545i
$568$	11.0589	−	6.38489i	0.464023	−	0.267904i
$569$	22.3482			0.936886			0.468443	−	0.883494i	$-0.344815\pi$
$569$	22.3482			0.936886			0.468443	+	0.883494i	$0.344815\pi$
$570$	4.62184	+	14.9298i	0.193587	+	0.625342i
$571$	−4.68044	+	8.10676i	−0.195870	+	0.339257i	−0.947185	−	0.320686i	$-0.896086\pi$
$571$	−4.68044	+	8.10676i	−0.195870	+	0.339257i	0.751315	+	0.659944i	$0.229420\pi$
$572$	0.00641967	+	0.00370640i	0.000268420	+	0.000154972i
$573$	−7.76516	+	4.48322i	−0.324394	+	0.187289i
$574$	2.18417	+	3.78310i	0.0911656	+	0.157903i
$575$	1.18024	−	2.46356i	0.0492192	−	0.102738i
$576$	−4.00626	+	6.93905i	−0.166928	+	0.289127i
$577$	−0.291394	−	0.168236i	−0.0121309	−	0.00700377i	0.493922	−	0.869506i	$-0.335563\pi$
$577$	−0.291394	−	0.168236i	−0.0121309	−	0.00700377i	−0.506053	+	0.862502i	$0.668896\pi$
$578$		−	71.0618i		−	2.95578i
$579$	1.65406	+	2.86492i	0.0687405	+	0.119062i
$580$	0.0164920	+	0.0532736i	0.000684791	+	0.00221207i
$581$	−21.0048			−0.871428
$582$		−	21.9014i		−	0.907842i
$583$	−5.25526	−	3.03412i	−0.217651	−	0.125661i
$584$	−26.2086			−1.08452
$585$	−1.38074	+	6.07783i	−0.0570865	+	0.251287i
$586$	−22.8507			−0.943954
$587$	9.70454	−	5.60292i	0.400549	−	0.231257i	−0.286172	−	0.958178i	$-0.592383\pi$
$587$	9.70454	−	5.60292i	0.400549	−	0.231257i	0.686721	+	0.726921i	$0.259049\pi$
$588$	−0.0106167	+	0.00612956i	−0.000437826	+	0.000252779i
$589$	−20.3739	−	35.2886i	−0.839491	−	1.45404i
$590$	35.1016	−	10.8664i	1.44511	−	0.447364i
$591$	−25.3592			−1.04314
$592$	21.9277	−	10.4554i	0.901222	−	0.429716i
$593$			39.8830i			1.63780i	0.573936	+	0.818900i	$0.305416\pi$
$593$			39.8830i			1.63780i	−0.573936	+	0.818900i	$0.694584\pi$
$594$	0.598198	−	1.03611i	0.0245444	−	0.0425121i
$595$	31.4786	+	7.15118i	1.29050	+	0.293170i
$596$	0.0153086	+	0.0265152i	0.000627063	+	0.00108611i
$597$	−7.69377	+	4.44200i	−0.314885	+	0.181799i
$598$		−	2.15191i		−	0.0879983i
$599$	20.9686	+	36.3186i	0.856753	+	1.48394i	0.875009	+	0.484106i	$0.160855\pi$
$599$	20.9686	+	36.3186i	0.856753	+	1.48394i	−0.0182569	+	0.999833i	$0.505812\pi$
$600$	−1.08631	−	14.1115i	−0.0443485	−	0.576098i
$601$	−10.4238	+	18.0545i	−0.425195	+	0.736460i	−0.996439	−	0.0843208i	$-0.973128\pi$
$601$	−10.4238	+	18.0545i	−0.425195	+	0.736460i	0.571243	+	0.820781i	$0.306461\pi$
$602$			30.0010i			1.22275i
$603$			0.801345i			0.0326333i
$604$	−0.00600614	+	0.0104029i	−0.000244386	+	0.000423290i
$605$	−22.4226	−	5.09388i	−0.911608	−	0.207096i
$606$	7.15871			0.290803
$607$	−4.62975	−	2.67299i	−0.187916	−	0.108493i	0.403091	−	0.915160i	$-0.367936\pi$
$607$	−4.62975	−	2.67299i	−0.187916	−	0.108493i	−0.591006	+	0.806667i	$0.701269\pi$
$608$	0.0761138	+	0.0439443i	0.00308682	+	0.00178218i
$609$	−6.98664	+	12.1012i	−0.283113	+	0.490366i
$610$	1.50025	−	6.60393i	0.0607435	−	0.267385i
$611$	−3.20853	−	5.55734i	−0.129803	−	0.224826i
$612$	0.0223146	+	0.0128833i	0.000902013	+	0.000520778i
$613$	14.2619	+	8.23414i	0.576035	+	0.332574i	0.759556	−	0.650442i	$-0.225416\pi$
$613$	14.2619	+	8.23414i	0.576035	+	0.332574i	−0.183521	+	0.983016i	$0.558750\pi$
$614$	11.7725	−	20.3906i	0.475099	−	0.822896i
$615$	−2.88192	−	2.66860i	−0.116210	−	0.107608i
$616$	−2.10885	−	3.65263i	−0.0849679	−	0.147169i
$617$	−34.3244	−	19.8172i	−1.38185	−	0.797811i	−0.389470	−	0.921039i	$-0.627342\pi$
$617$	−34.3244	−	19.8172i	−1.38185	−	0.797811i	−0.992378	+	0.123229i	$0.960675\pi$
$618$		−	12.2505i		−	0.492788i
$619$	1.77245			0.0712409			0.0356204	−	0.999365i	$-0.488659\pi$
$619$	1.77245			0.0712409			0.0356204	+	0.999365i	$0.488659\pi$
$620$	0.0171119	+	0.0552761i	0.000687229	+	0.00221994i
$621$	0.546337			0.0219237
$622$	26.4420	−	15.2663i	1.06023	−	0.612123i
$623$			12.6569i			0.507087i
$624$	−5.56592	−	9.64046i	−0.222815	−	0.385927i
$625$	15.6664	+	19.4824i	0.626658	+	0.779294i
$626$	1.94170	+	3.36312i	0.0776059	+	0.134417i
$627$	−3.62660	−	2.09382i	−0.144833	−	0.0836192i
$628$		−	0.00455688i		−	0.000181839i
$629$	−21.4751	−	45.0386i	−0.856267	−	1.79580i
$630$	3.77826	−	4.08029i	0.150529	−	0.162563i
$631$	4.89549	−	8.47924i	0.194886	−	0.337553i	−0.751977	−	0.659189i	$-0.770900\pi$
$631$	4.89549	−	8.47924i	0.194886	−	0.337553i	0.946863	+	0.321636i	$0.104233\pi$
$632$	0.493628	−	0.284996i	0.0196355	−	0.0113365i
$633$	−12.7068	+	7.33629i	−0.505051	+	0.291591i
$634$	1.50862	+	2.61301i	0.0599150	+	0.103776i
$635$	27.3392	+	25.3155i	1.08492	+	1.00462i
$636$	−0.0112570	−	0.0194977i	−0.000446369	−	0.000773133i
$637$		−	10.8783i		−	0.431013i
$638$	8.22650	+	4.74957i	0.325690	+	0.188037i
$639$	−4.51126			−0.178463
$640$	18.5185	+	17.1477i	0.732008	+	0.677824i
$641$	−18.6913	+	32.3742i	−0.738260	+	1.27870i	0.215018	+	0.976610i	$0.431019\pi$
$641$	−18.6913	+	32.3742i	−0.738260	+	1.27870i	−0.953278	+	0.302094i	$0.902314\pi$
$642$	4.30680	−	2.48653i	0.169976	−	0.0981355i
$643$			28.2000i			1.11210i	0.831149	+	0.556049i	$0.187683\pi$
$643$			28.2000i			1.11210i	−0.831149	+	0.556049i	$0.812317\pi$
$644$	0.00151011	−	0.00261559i	5.95067e−5	−	0.000103069i
$645$	−7.97712	−	25.7683i	−0.314099	−	1.01463i
$646$	−28.6669	+	49.6525i	−1.12788	+	1.95355i
$647$	−5.94866	+	3.43446i	−0.233866	+	0.135023i	−0.612354	−	0.790584i	$-0.709777\pi$
$647$	−5.94866	+	3.43446i	−0.233866	+	0.135023i	0.378488	+	0.925606i	$0.376444\pi$
$648$	2.45141	−	1.41532i	0.0963005	−	0.0555991i
$649$	−4.92279	+	8.52653i	−0.193237	+	0.334696i
$650$	17.7610	+	8.50889i	0.696644	+	0.333746i
$651$	−7.24927	+	12.5561i	−0.284121	+	0.492112i
$652$		−	0.0210991i		−	0.000826306i
$653$	13.3580	−	7.71224i	0.522739	−	0.301803i	−0.215316	−	0.976544i	$-0.569078\pi$
$653$	13.3580	−	7.71224i	0.522739	−	0.301803i	0.738054	+	0.674741i	$0.235745\pi$
$654$	1.84921	−	3.20293i	0.0723099	−	0.125244i
$655$	0.692700	−	0.748074i	0.0270660	−	0.0292297i
$656$	7.01505			0.273892
$657$	8.01843	+	4.62944i	0.312829	+	0.180612i
$658$			5.72542i			0.223200i
$659$	−2.85607	−	4.94686i	−0.111257	−	0.192702i	0.805021	−	0.593247i	$-0.202154\pi$
$659$	−2.85607	−	4.94686i	−0.111257	−	0.192702i	−0.916277	+	0.400545i	$0.868821\pi$
$660$	0.00436334	+	0.00404036i	0.000169843	+	0.000157271i
$661$	4.85926	+	8.41648i	0.189003	+	0.327363i	0.944918	−	0.327307i	$-0.106141\pi$
$661$	4.85926	+	8.41648i	0.189003	+	0.327363i	−0.755915	+	0.654670i	$0.772808\pi$
$662$	−21.8924	+	12.6396i	−0.850874	+	0.491252i
$663$	−19.8011	+	11.4322i	−0.769012	+	0.443989i
$664$	−16.8922	+	29.2581i	−0.655544	+	1.13544i
$665$	−14.2819	−	13.2247i	−0.553828	−	0.512832i
$666$	−8.56898	−	0.675521i	−0.332041	−	0.0261759i
$667$			4.33781i			0.167961i
$668$	0.00464842	+	0.00268377i	0.000179853	+	0.000103838i
$669$	−2.49019	−	4.31314i	−0.0962763	−	0.166755i
$670$	2.46917	+	0.560937i	0.0953924	+	0.0216709i
$671$	0.907281	+	1.57146i	0.0350252	+	0.0606654i
$672$		−	0.0312718i		−	0.00120634i
$673$	−3.05525	+	1.76395i	−0.117771	+	0.0679954i	−0.557729	−	0.830023i	$-0.688327\pi$
$673$	−3.05525	+	1.76395i	−0.117771	+	0.0679954i	0.439957	+	0.898019i	$0.354994\pi$
$674$	−10.1758			−0.391957
$675$	−2.16027	+	4.50924i	−0.0831489	+	0.173561i
$676$	0.0164305			0.000631941
$677$		−	12.5543i		−	0.482500i	−0.970463	−	0.241250i	$-0.922443\pi$
$677$		−	12.5543i		−	0.482500i	0.970463	−	0.241250i	$-0.0775573\pi$
$678$	−25.5344	−	14.7423i	−0.980642	−	0.566174i
$679$	13.6382	+	23.6221i	0.523386	+	0.906531i
$680$	35.2762	−	38.0962i	1.35278	−	1.46092i
$681$	4.30066	−	7.44896i	0.164802	−	0.285445i
$682$	8.53573	+	4.92811i	0.326850	+	0.188707i
$683$	0.536332	+	0.309651i	0.0205222	+	0.0118485i	0.510226	−	0.860040i	$-0.329562\pi$
$683$	0.536332	+	0.309651i	0.0205222	+	0.0118485i	−0.489704	+	0.871889i	$0.662895\pi$
$684$	−0.00776834	−	0.0134552i	−0.000297030	−	0.000514471i
$685$	7.54149	−	33.1966i	0.288145	−	1.26838i
$686$	−13.5571	+	23.4817i	−0.517614	+	0.896534i
$687$	−11.0996	−	6.40837i	−0.423477	−	0.244495i
$688$	41.7235	+	24.0891i	1.59069	+	0.918387i
$689$	19.9781			0.761103
$690$	0.382432	−	1.68342i	0.0145590	−	0.0640866i
$691$	−7.74622	+	13.4169i	−0.294680	+	0.510401i	−0.974910	−	0.222597i	$-0.928546\pi$
$691$	−7.74622	+	13.4169i	−0.294680	+	0.510401i	0.680230	+	0.732999i	$0.261880\pi$
$692$			0.0421832i			0.00160356i
$693$			1.49001i			0.0566009i
$694$	8.61356	−	14.9191i	0.326966	−	0.566322i
$695$	−27.4594	+	29.6544i	−1.04159	+	1.12486i
$696$	11.2374	+	19.4637i	0.425952	+	0.737770i
$697$		−	14.4086i		−	0.545766i
$698$	−13.8962	+	8.02299i	−0.525980	+	0.303674i
$699$	4.91825	+	8.51865i	0.186025	+	0.322205i
$700$	0.0156169	+	0.0228062i	0.000590262	+	0.000861992i
$701$	2.40326	−	4.16258i	0.0907701	−	0.157218i	−0.817065	−	0.576545i	$-0.804401\pi$
$701$	2.40326	−	4.16258i	0.0907701	−	0.157218i	0.907835	+	0.419327i	$0.137734\pi$
$702$			3.93881i			0.148661i
$703$	−2.36447	+	29.9933i	−0.0891776	+	1.13122i
$704$	−6.78376			−0.255673
$705$	−1.52236	−	4.91765i	−0.0573354	−	0.185209i
$706$	−2.33757	−	4.04879i	−0.0879757	−	0.152378i
$707$	−7.72113	+	4.45779i	−0.290383	+	0.167653i
$708$	−0.0316345	+	0.0182642i	−0.00118890	+	0.000686410i
$709$	24.2314			0.910030			0.455015	−	0.890484i	$-0.349634\pi$
$709$	24.2314			0.910030			0.455015	+	0.890484i	$0.349634\pi$
$710$	−3.15786	+	13.9005i	−0.118512	+	0.521675i
$711$	−0.201365			−0.00755177
$712$	17.6301	+	10.1787i	0.660714	+	0.381464i
$713$			4.50086i			0.168559i
$714$	20.4000			0.763452
$715$	−5.04086	+	1.56050i	−0.188517	+	0.0583595i
$716$	−0.0214826	−	0.0372090i	−0.000802844	−	0.00139057i
$717$			16.2631i			0.607357i
$718$	−39.5318	−	22.8237i	−1.47532	−	0.851774i
$719$	−18.7187	+	32.4217i	−0.698089	+	1.20913i	0.271039	+	0.962568i	$0.412633\pi$
$719$	−18.7187	+	32.4217i	−0.698089	+	1.20913i	−0.969128	+	0.246558i	$0.920701\pi$
$720$	−2.64088	−	8.53078i	−0.0984198	−	0.317924i
$721$	7.62851	+	13.2130i	0.284100	+	0.492076i
$722$	6.68739	−	3.86097i	0.248879	−	0.143690i
$723$	−10.7409	−	6.20127i	−0.399459	−	0.230628i
$724$	−0.0283064	+	0.0490281i	−0.00105200	+	0.00182211i
$725$	−35.8025	−	17.1521i	−1.32967	−	0.637014i
$726$	−14.5312			−0.539304
$727$	−16.9502	+	9.78618i	−0.628647	+	0.362949i	−0.780228	−	0.625495i	$-0.784897\pi$
$727$	−16.9502	+	9.78618i	−0.628647	+	0.362949i	0.151581	+	0.988445i	$0.451564\pi$
$728$	12.0253	+	6.94280i	0.445687	+	0.257317i
$729$	−1.00000			−0.0370370
$730$	19.8775	−	21.4665i	0.735698	−	0.794510i
$731$	49.4779	−	85.6983i	1.83001	−	3.16967i
$732$			0.00673226i			0.000248831i
$733$	−1.68555	+	0.973151i	−0.0622571	+	0.0359442i	−0.530805	−	0.847494i	$-0.678111\pi$
$733$	−1.68555	+	0.973151i	−0.0622571	+	0.0359442i	0.468548	+	0.883438i	$0.344777\pi$
$734$	−2.11750			−0.0781584
$735$	1.93326	−	8.50996i	0.0713094	−	0.313895i
$736$	−0.00485394	−	0.00840728i	−0.000178919	−	0.000309896i
$737$	−0.587559	+	0.339227i	−0.0216430	+	0.0124956i
$738$	−2.14961	−	1.24108i	−0.0791281	−	0.0456846i
$739$	−18.5876			−0.683758			−0.341879	−	0.939744i	$-0.611063\pi$
$739$	−18.5876			−0.683758			−0.341879	+	0.939744i	$0.611063\pi$
$740$	0.0127098	−	0.0407901i	0.000467221	−	0.00149947i
$741$	13.7867			0.506466
$742$	−15.4367	−	8.91240i	−0.566700	−	0.327185i
$743$	−17.3113	+	9.99468i	−0.635090	+	0.366669i	−0.782721	−	0.622373i	$-0.786169\pi$
$743$	−17.3113	+	9.99468i	−0.635090	+	0.366669i	0.147631	+	0.989043i	$0.452835\pi$
$744$	11.6598	+	20.1953i	0.427468	+	0.740397i
$745$	−21.2536	−	4.82831i	−0.778671	−	0.176896i
$746$	−26.5393			−0.971673
$747$	10.3362	−	5.96761i	0.378182	−	0.218344i
$748$			0.0218152i			0.000797643i
$749$	−3.09677	+	5.36376i	−0.113153	+	0.195988i
$750$	12.3821	+	9.81285i	0.452129	+	0.358315i
$751$	−17.8662			−0.651945			−0.325973	−	0.945379i	$-0.605692\pi$
$751$	−17.8662			−0.651945			−0.325973	+	0.945379i	$0.605692\pi$
$752$	7.96255	+	4.59718i	0.290364	+	0.167642i
$753$	24.1624	−	13.9501i	0.880525	−	0.508372i
$754$	−31.2733			−1.13891
$755$	−2.52876	−	8.16861i	−0.0920311	−	0.297286i
$756$	−0.00276407	+	0.00478751i	−0.000100528	+	0.000174120i
$757$	34.3811	+	19.8499i	1.24960	+	0.721458i	0.971030	−	0.238957i	$-0.0768056\pi$
$757$	34.3811	+	19.8499i	1.24960	+	0.721458i	0.278572	+	0.960415i	$0.410139\pi$
$758$	−33.3155	+	19.2347i	−1.21007	+	0.698636i
$759$	0.231276	+	0.400583i	0.00839480	+	0.0145402i
$760$	−29.9065	+	9.25819i	−1.08482	+	0.335830i
$761$	−6.78141	+	11.7457i	−0.245826	+	0.425783i	−0.962364	−	0.271765i	$-0.912393\pi$
$761$	−6.78141	+	11.7457i	−0.245826	+	0.425783i	0.716538	+	0.697549i	$0.245726\pi$
$762$	20.3921	+	11.7734i	0.738728	+	0.426505i
$763$			4.60608i			0.166751i
$764$	−0.0140825	−	0.0243916i	−0.000509487	−	0.000882457i
$765$	−17.5219	+	5.42426i	−0.633505	+	0.196115i
$766$	12.7729			0.461503
$767$		−	32.4139i		−	1.17040i
$768$	−0.0652876	−	0.0376938i	−0.00235586	−	0.00136016i
$769$	−13.9572			−0.503309			−0.251655	−	0.967817i	$-0.580975\pi$
$769$	−13.9572			−0.503309			−0.251655	+	0.967817i	$0.580975\pi$
$770$	4.59115	+	1.04300i	0.165454	+	0.0375871i
$771$	−16.3901			−0.590274
$772$	−0.00899917	+	0.00519567i	−0.000323887	+	0.000186996i
$773$	−3.48485	+	2.01198i	−0.125341	+	0.0723659i	−0.561360	−	0.827572i	$-0.689722\pi$
$773$	−3.48485	+	2.01198i	−0.125341	+	0.0723659i	0.436018	+	0.899938i	$0.356388\pi$
$774$	−8.52348	−	14.7631i	−0.306370	−	0.530649i
$775$	−37.1482	−	17.7969i	−1.33440	−	0.639282i
$776$	43.8716			1.57490
$777$	9.66284	−	4.60739i	0.346653	−	0.165289i
$778$			16.8306i			0.603407i
$779$	−4.34403	+	7.52408i	−0.155641	+	0.269578i
$780$	−0.0190914	−	0.00433712i	−0.000683583	−	0.000155294i
$781$	−1.90972	−	3.30773i	−0.0683351	−	0.118360i
$782$	5.48445	−	3.16645i	0.196123	−	0.113232i
$783$		−	7.93980i		−	0.283745i
$784$	7.79320	+	13.4982i	0.278329	+	0.482079i
$785$	2.38016	+	2.20397i	0.0849515	+	0.0786632i
$786$	0.322152	−	0.557983i	0.0114908	−	0.0199026i
$787$			6.44339i			0.229682i	0.993384	+	0.114841i	$0.0366359\pi$
$787$			6.44339i			0.229682i	−0.993384	+	0.114841i	$0.963364\pi$
$788$		−	0.0796573i		−	0.00283767i
$789$	8.30623	−	14.3868i	0.295710	−	0.512184i
$790$	−0.140954	+	0.620462i	−0.00501493	+	0.0220751i
$791$	36.7206			1.30563
$792$	2.07547	+	1.19827i	0.0737487	+	0.0425788i
$793$	−5.17359	−	2.98698i	−0.183720	−	0.106071i
$794$	23.5624	−	40.8112i	0.836197	−	1.44834i
$795$	15.6286	+	3.55045i	0.554289	+	0.125921i
$796$	−0.0139530	−	0.0241673i	−0.000494552	−	0.000856589i
$797$	−10.4028	−	6.00608i	−0.368487	−	0.212746i	0.304310	−	0.952573i	$-0.401574\pi$
$797$	−10.4028	−	6.00608i	−0.368487	−	0.212746i	−0.672797	+	0.739827i	$0.734907\pi$
$798$	−10.6527	−	6.15037i	−0.377103	−	0.217721i
$799$	9.44242	−	16.3547i	0.334049	−	0.578589i
$800$	0.0885832	−	0.00681920i	0.00313189	−	0.000241095i
$801$	−3.59590	−	6.22829i	−0.127055	−	0.220066i
$802$	34.4854	+	19.9102i	1.21772	+	0.703053i
$803$			7.83899i			0.276632i
$804$	−0.00251715			−8.87731e−5
$805$	0.635802	+	2.05382i	0.0224091	+	0.0723875i
$806$	−32.4489			−1.14296
$807$	−5.40691	+	3.12168i	−0.190332	+	0.109888i
$808$			14.3399i			0.504476i
$809$	4.27239	+	7.40000i	0.150209	+	0.260170i	0.931304	−	0.364242i	$-0.118672\pi$
$809$	4.27239	+	7.40000i	0.150209	+	0.260170i	−0.781095	+	0.624412i	$0.785339\pi$
$810$	−0.699994	+	3.08128i	−0.0245953	+	0.108265i
$811$	−11.1266	−	19.2718i	−0.390708	−	0.676725i	0.601835	−	0.798620i	$-0.294436\pi$
$811$	−11.1266	−	19.2718i	−0.390708	−	0.676725i	−0.992543	+	0.121895i	$0.961103\pi$
$812$	−0.0380119	−	0.0219462i	−0.00133395	−	0.000770159i
$813$			27.6068i			0.968211i
$814$	−3.13214	−	6.56887i	−0.109781	−	0.230239i
$815$	11.0205	+	10.2048i	0.386033	+	0.357458i
$816$	16.3800	−	28.3710i	0.573416	−	0.993185i
$817$	−51.6740	+	29.8340i	−1.80785	+	1.04376i
$818$	−14.4681	+	8.35315i	−0.505864	+	0.292061i
$819$	−2.45273	−	4.24825i	−0.0857053	−	0.148446i
$820$	0.00838249	−	0.00905258i	0.000292729	−	0.000316130i
$821$	9.78724	+	16.9520i	0.341577	+	0.591629i	0.984726	−	0.174112i	$-0.0557056\pi$
$821$	9.78724	+	16.9520i	0.341577	+	0.591629i	−0.643149	+	0.765741i	$0.722372\pi$
$822$		−	21.5134i		−	0.750368i
$823$	−6.58486	−	3.80177i	−0.229534	−	0.132521i	0.380823	−	0.924648i	$-0.375641\pi$
$823$	−6.58486	−	3.80177i	−0.229534	−	0.132521i	−0.610357	+	0.792126i	$0.708974\pi$
$824$	24.5395			0.854875
$825$	−4.22074	+	0.324915i	−0.146947	+	0.0113121i
$826$	−14.4602	+	25.0457i	−0.503133	+	0.871452i
$827$	−31.6856	+	18.2937i	−1.10182	+	0.636133i	−0.936697	−	0.350141i	$-0.886134\pi$
$827$	−31.6856	+	18.2937i	−1.10182	+	0.636133i	−0.165118	+	0.986274i	$0.552800\pi$
$828$			0.00171613i			5.96396e-5i
$829$	−17.9259	+	31.0485i	−0.622591	+	1.07836i	0.366410	+	0.930453i	$0.380587\pi$
$829$	−17.9259	+	31.0485i	−0.622591	+	1.07836i	−0.989001	+	0.147906i	$0.952747\pi$
$830$	−11.1526	−	36.0261i	−0.387113	−	1.25048i
$831$	4.09318	−	7.08960i	0.141991	−	0.245935i
$832$	19.3415	−	11.1668i	0.670547	−	0.387141i
$833$	27.7248	−	16.0069i	0.960608	−	0.554607i
$834$	−12.7704	+	22.1190i	−0.442204	+	0.765919i
$835$	−3.65004	+	1.12995i	−0.126315	+	0.0391034i
$836$	0.00657702	−	0.0113917i	0.000227471	−	0.000393992i
$837$		−	8.23825i		−	0.284756i
$838$	−20.7226	+	11.9642i	−0.715849	+	0.413296i
$839$	3.21065	−	5.56101i	0.110844	−	0.191987i	−0.805267	−	0.592913i	$-0.797978\pi$
$839$	3.21065	−	5.56101i	0.110844	−	0.191987i	0.916111	+	0.400925i	$0.131311\pi$
$840$	8.17339	+	7.56838i	0.282009	+	0.261134i
$841$	34.0405			1.17381
$842$	−10.8703	−	6.27599i	−0.374617	−	0.216285i
$843$			1.98434i			0.0683444i
$844$	−0.0230445	−	0.0399142i	−0.000793223	−	0.00137390i
$845$	−7.94674	+	8.58199i	−0.273376	+	0.295230i
$846$	−1.62663	−	2.81741i	−0.0559247	−	0.0968644i
$847$	15.6728	−	9.04871i	0.538525	−	0.310917i
$848$	−24.7896	+	14.3123i	−0.851278	+	0.491485i
$849$	16.1945	−	28.0497i	0.555795	−	0.962665i
$850$	4.44847	+	57.7868i	0.152581	+	1.98207i
$851$	1.88266	−	2.73852i	0.0645368	−	0.0938753i
$852$		−	0.0141706i		−	0.000485476i
$853$	−8.61281	−	4.97261i	−0.294897	−	0.170259i	0.345251	−	0.938510i	$-0.387794\pi$
$853$	−8.61281	−	4.97261i	−0.294897	−	0.170259i	−0.640148	+	0.768251i	$0.721127\pi$
$854$	2.66504	+	4.61598i	0.0911957	+	0.157956i
$855$	10.7852	+	2.45013i	0.368844	+	0.0837927i
$856$	4.98087	+	8.62712i	0.170243	+	0.294869i
$857$			29.5733i			1.01021i	0.863059	+	0.505103i	$0.168545\pi$
$857$			29.5733i			1.01021i	−0.863059	+	0.505103i	$0.831455\pi$
$858$	−2.88799	+	1.66738i	−0.0985945	+	0.0569236i
$859$	32.7608			1.11778			0.558892	−	0.829240i	$-0.311227\pi$
$859$	32.7608			1.11778			0.558892	+	0.829240i	$0.311227\pi$
$860$	0.0809424	−	0.0250574i	0.00276011	−	0.000854450i
$861$	3.09131			0.105352
$862$		−	32.0673i		−	1.09222i
$863$	18.8036	+	10.8563i	0.640083	+	0.369552i	0.784647	−	0.619943i	$-0.212844\pi$
$863$	18.8036	+	10.8563i	0.640083	+	0.369552i	−0.144563	+	0.989496i	$0.546178\pi$
$864$	0.00888453	+	0.0153885i	0.000302258	+	0.000523526i
$865$	−22.0332	−	20.4023i	−0.749151	−	0.693697i
$866$	−5.69809	+	9.86939i	−0.193629	+	0.335375i
$867$	−43.5505	−	25.1439i	−1.47905	−	0.853932i
$868$	−0.0394407	−	0.0227711i	−0.00133870	−	0.000772901i
$869$	−0.0852423	−	0.147644i	−0.00289165	−	0.00500848i
$870$	−24.4648	−	5.55782i	−0.829434	−	0.188428i
$871$	1.11681	−	1.93438i	0.0378418	−	0.0655439i
$872$	6.41592	+	3.70423i	0.217270	+	0.125441i
$873$	−13.4224	−	7.74940i	−0.454278	−	0.262278i
$874$	−3.81859			−0.129166
$875$	−19.4654	−	2.87336i	−0.658050	−	0.0971374i
$876$	−0.0145418	+	0.0251872i	−0.000491322	+	0.000850995i
$877$		−	56.9241i		−	1.92219i	−0.276217	−	0.961095i	$-0.589081\pi$
$877$		−	56.9241i		−	1.92219i	0.276217	−	0.961095i	$-0.410919\pi$
$878$			48.3192i			1.63069i
$879$	−8.08529	+	14.0041i	−0.272710	+	0.472348i
$880$	5.13696	−	5.54761i	0.173167	−	0.187010i
$881$	27.9678	+	48.4417i	0.942261	+	1.63204i	0.761146	+	0.648581i	$0.224637\pi$
$881$	27.9678	+	48.4417i	0.942261	+	1.63204i	0.181115	+	0.983462i	$0.442029\pi$
$882$		−	5.51497i		−	0.185699i
$883$	−3.92800	+	2.26783i	−0.132188	+	0.0763187i	−0.564636	−	0.825340i	$-0.690983\pi$
$883$	−3.92800	+	2.26783i	−0.132188	+	0.0763187i	0.432448	+	0.901659i	$0.357650\pi$
$884$	−0.0359103	−	0.0621985i	−0.00120779	−	0.00209196i
$885$	5.76051	−	25.3570i	0.193638	−	0.852367i
$886$	−5.12892	+	8.88355i	−0.172309	+	0.298449i
$887$		−	23.2980i		−	0.782271i	−0.920333	−	0.391136i	$-0.872082\pi$
$887$		−	23.2980i		−	0.782271i	0.920333	−	0.391136i	$-0.127918\pi$
$888$	1.35316	−	17.1649i	0.0454092	−	0.576016i
$889$	−29.3256			−0.983549
$890$	−21.7082	+	6.72023i	−0.727661	+	0.225263i
$891$	−0.423322	−	0.733216i	−0.0141818	−	0.0245636i
$892$	0.0135482	−	0.00782208i	0.000453629	−	0.000261903i
$893$	−9.86153	+	5.69355i	−0.330003	+	0.190528i
$894$	−13.7736			−0.460659
$895$	29.8253	+	6.77561i	0.996951	+	0.226484i
$896$	−19.8640			−0.663610
$897$	−1.31881	−	0.761415i	−0.0440338	−	0.0254229i
$898$			3.74670i			0.125029i
$899$	65.4101			2.18155
$900$	−0.0141642	−	0.00678576i	−0.000472141	−	0.000226192i
$901$	29.3968	+	50.9168i	0.979350	+	1.69628i
$902$		−	2.10150i		−	0.0699723i
$903$	18.3862	+	10.6153i	0.611856	+	0.353255i
$904$	29.5309	−	51.1490i	0.982182	−	1.70119i
$905$	−11.9178	−	38.4979i	−0.396162	−	1.27971i
$906$	−2.70196	−	4.67994i	−0.0897667	−	0.155481i
$907$	2.16671	−	1.25095i	0.0719446	−	0.0415372i	−0.463596	−	0.886047i	$-0.653441\pi$
$907$	2.16671	−	1.25095i	0.0719446	−	0.0415372i	0.535541	+	0.844509i	$0.320108\pi$
$908$	0.0233984	+	0.0135090i	0.000776502	+	0.000448313i
$909$	2.53298	−	4.38724i	0.0840135	−	0.145516i
$910$	−14.8070	+	4.58380i	−0.490846	+	0.151952i
$911$	−49.2425			−1.63148			−0.815739	−	0.578420i	$-0.803669\pi$
$911$	−49.2425			−1.63148			−0.815739	+	0.578420i	$0.803669\pi$
$912$	−17.1071	+	9.87676i	−0.566471	+	0.327052i
$913$	8.75109	+	5.05245i	0.289619	+	0.167212i
$914$	18.6852			0.618050
$915$	−3.51641	−	3.25611i	−0.116249	−	0.107644i
$916$	0.0201297	−	0.0348657i	0.000665105	−	0.00115200i
$917$			0.802427i			0.0264985i
$918$	−10.0386	+	5.79578i	−0.331323	+	0.191289i
$919$	−1.29630			−0.0427611			−0.0213806	−	0.999771i	$-0.506806\pi$
$919$	−1.29630			−0.0427611			−0.0213806	+	0.999771i	$0.506806\pi$
$920$	3.37212	+	0.766066i	0.111176	+	0.0252565i
$921$	−8.33096	−	14.4296i	−0.274514	−	0.475473i
$922$	10.1069	−	5.83523i	0.332853	−	0.192173i
$923$	10.8898	+	6.28722i	0.358442	+	0.206946i
$924$	−0.00468037			−0.000153973
$925$	15.1584	+	26.3671i	0.498404	+	0.866945i
$926$	42.6838			1.40268
$927$	−7.50778	−	4.33462i	−0.246588	−	0.142368i
$928$	−0.122181	+	0.0705414i	−0.00401080	+	0.00231564i
$929$	−5.44585	−	9.43249i	−0.178672	−	0.309470i	0.762754	−	0.646689i	$-0.223847\pi$
$929$	−5.44585	−	9.43249i	−0.178672	−	0.309470i	−0.941426	+	0.337219i	$0.890514\pi$
$930$	−25.3844	−	5.76673i	−0.832387	−	0.189098i
$931$	−19.3036			−0.632650
$932$	−0.0267584	+	0.0154490i	−0.000876502	+	0.000506048i
$933$		−	21.6068i		−	0.707374i
$934$	−25.0223	+	43.3399i	−0.818755	+	1.41812i
$935$	−11.3946	−	10.5511i	−0.372642	−	0.345058i
$936$	−7.88998			−0.257892
$937$	−27.9911	−	16.1607i	−0.914430	−	0.527946i	−0.0325760	−	0.999469i	$-0.510371\pi$
$937$	−27.9911	−	16.1607i	−0.914430	−	0.527946i	−0.881854	+	0.471523i	$0.843704\pi$
$938$	−1.72589	+	0.996442i	−0.0563523	+	0.0325350i
$939$	2.74814			0.0896820
$940$	0.0154471	−	0.00478198i	0.000503830	−	0.000155971i
$941$	−23.7802	+	41.1885i	−0.775212	+	1.34271i	0.159463	+	0.987204i	$0.449024\pi$
$941$	−23.7802	+	41.1885i	−0.775212	+	1.34271i	−0.934675	+	0.355503i	$0.884310\pi$
$942$	1.77534	+	1.02499i	0.0578438	+	0.0333961i
$943$	0.831085	−	0.479827i	0.0270638	−	0.0156253i
$944$	23.2213	+	40.2205i	0.755789	+	1.30907i
$945$	−1.16375	−	3.75925i	−0.0378569	−	0.122288i
$946$	7.21636	−	12.4991i	0.234624	−	0.406381i
$947$	16.2034	+	9.35502i	0.526539	+	0.303997i	0.739606	−	0.673040i	$-0.235012\pi$
$947$	16.2034	+	9.35502i	0.526539	+	0.303997i	−0.213067	+	0.977038i	$0.568345\pi$
$948$		0	0.000632519i		0	2.05433e-5i
$949$	−12.9039	−	22.3501i	−0.418877	−	0.725516i
$950$	15.0991	−	31.5170i	0.489879	−	1.02255i
$951$	2.13519			0.0692383
$952$			40.8641i			1.32441i
$953$	−44.5269	−	25.7076i	−1.44237	−	0.832752i	−0.444361	−	0.895848i	$-0.646569\pi$
$953$	−44.5269	−	25.7076i	−1.44237	−	0.832752i	−0.998007	+	0.0630964i	$0.979902\pi$
$954$	10.1283			0.327915
$955$	19.5514	+	4.44161i	0.632668	+	0.143727i
$956$	−0.0510850			−0.00165221
$957$	5.82159	−	3.36110i	0.188185	−	0.108649i
$958$	26.0484	−	15.0390i	0.841584	−	0.485889i
$959$	13.3966	+	23.2036i	0.432599	+	0.749284i
$960$	17.1152	−	5.29837i	0.552391	−	0.171004i
$961$	36.8688			1.18932
$962$	19.7433	+	13.5730i	0.636550	+	0.437611i
$963$		−	3.51925i		−	0.113406i
$964$	0.0194792	−	0.0337389i	0.000627382	−	0.00108666i
$965$	1.63871	−	7.21339i	0.0527520	−	0.232207i
$966$	0.679349	+	1.17667i	0.0218577	+	0.0378586i
$967$	−36.3486	+	20.9859i	−1.16889	+	0.674860i	−0.953419	−	0.301649i	$-0.902463\pi$
$967$	−36.3486	+	20.9859i	−1.16889	+	0.674860i	−0.215473	+	0.976510i	$0.569129\pi$
$968$		−	29.1081i		−	0.935568i
$969$	20.2865	+	35.1372i	0.651696	+	1.12877i
$970$	−33.2737	+	35.9336i	−1.06835	+	1.15376i
$971$	−6.78475	+	11.7515i	−0.217733	+	0.377124i	−0.954115	−	0.299442i	$-0.903199\pi$
$971$	−6.78475	+	11.7515i	−0.217733	+	0.377124i	0.736382	+	0.676566i	$0.236533\pi$
$972$		−	0.00314116i		−	0.000100753i
$973$		−	31.8090i		−	1.01975i
$974$	−11.9634	+	20.7212i	−0.383331	+	0.663949i
$975$	11.4991	−	7.87419i	0.368266	−	0.252176i
$976$	8.55947			0.273982
$977$	44.9528	+	25.9535i	1.43817	+	0.830327i	0.997723	−	0.0674521i	$-0.0214870\pi$
$977$	44.9528	+	25.9535i	1.43817	+	0.830327i	0.440446	+	0.897779i	$0.354820\pi$
$978$	8.22013	+	4.74590i	0.262851	+	0.151757i
$979$	3.04445	−	5.27314i	0.0973011	−	0.168530i
$980$	0.0267311	+	0.00607268i	0.000853895	+	0.000193985i
$981$	−1.30862	−	2.26659i	−0.0417810	−	0.0723668i
$982$	39.9539	+	23.0674i	1.27498	+	0.736110i
$983$	7.12191	+	4.11183i	0.227154	+	0.131147i	0.609258	−	0.792972i	$-0.291467\pi$
$983$	7.12191	+	4.11183i	0.227154	+	0.131147i	−0.382105	+	0.924119i	$0.624801\pi$
$984$	2.48605	−	4.30596i	0.0792523	−	0.137269i
$985$	41.6068	+	38.5269i	1.32570	+	1.22757i
$986$	−46.0174	−	79.7044i	−1.46549	−	2.53831i
$987$	3.50885	+	2.02583i	0.111688	+	0.0644830i
$988$			0.0433061i			0.00137775i
$989$	6.59073			0.209573
$990$	−2.55557	+	0.791129i	−0.0812213	+	0.0251437i
$991$	12.4229			0.394627			0.197314	−	0.980340i	$-0.436778\pi$
$991$	12.4229			0.394627			0.197314	+	0.980340i	$0.436778\pi$
$992$	−0.126774	+	0.0731930i	−0.00402508	+	0.00232388i
$993$			17.8892i			0.567695i
$994$	−5.60958	−	9.71608i	−0.177925	−	0.308175i
$995$	19.3716	+	4.40077i	0.614122	+	0.139514i
$996$	0.0187452	+	0.0324677i	0.000593965	+	0.00102878i
$997$	−21.6641	−	12.5078i	−0.686110	−	0.396126i	0.116043	−	0.993244i	$-0.462979\pi$
$997$	−21.6641	−	12.5078i	−0.686110	−	0.396126i	−0.802153	+	0.597119i	$0.796312\pi$
$998$		−	42.1018i		−	1.33271i
$999$	−3.44597	+	5.01251i	−0.109026	+	0.158589i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	555.2.bb.a.454.10	✓	72
5.4	even	2	inner	555.2.bb.a.454.27	yes	72
37.26	even	3	inner	555.2.bb.a.544.27	yes	72
185.174	even	6	inner	555.2.bb.a.544.10	yes	72

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
555.2.bb.a.454.10	✓	72	1.1	even	1	trivial
555.2.bb.a.454.27	yes	72	5.4	even	2	inner
555.2.bb.a.544.10	yes	72	185.174	even	6	inner
555.2.bb.a.544.27	yes	72	37.26	even	3	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 555 = 3 \cdot 5 \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	555.bb (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.22378 - 0.706551i) q^{2} +(-0.866025 + 0.500000i) q^{3} +(-0.00157058 - 0.00272032i) q^{4} +(2.18051 + 0.495360i) q^{5} +1.41310 q^{6} +(-1.52412 + 0.879952i) q^{7} +2.83064i q^{8} +(0.500000 - 0.866025i) q^{9} +O(q^{10})\)	\(q+(-1.22378 - 0.706551i) q^{2} +(-0.866025 + 0.500000i) q^{3} +(-0.00157058 - 0.00272032i) q^{4} +(2.18051 + 0.495360i) q^{5} +1.41310 q^{6} +(-1.52412 + 0.879952i) q^{7} +2.83064i q^{8} +(0.500000 - 0.866025i) q^{9} +(-2.31847 - 2.14685i) q^{10} +0.846645 q^{11} +(0.00272032 + 0.00157058i) q^{12} +(-2.41391 + 1.39367i) q^{13} +2.48692 q^{14} +(-2.13606 + 0.661260i) q^{15} +(1.99685 - 3.45865i) q^{16} +(-7.10393 - 4.10146i) q^{17} +(-1.22378 + 0.706551i) q^{18} +(2.47308 + 4.28350i) q^{19} +(-0.00207712 - 0.00670969i) q^{20} +(0.879952 - 1.52412i) q^{21} +(-1.03611 - 0.598198i) q^{22} -0.546337i q^{23} +(-1.41532 - 2.45141i) q^{24} +(4.50924 + 2.16027i) q^{25} +3.93881 q^{26} +1.00000i q^{27} +(0.00478751 + 0.00276407i) q^{28} -7.93980 q^{29} +(3.08128 + 0.699994i) q^{30} -8.23825 q^{31} +(0.0153885 - 0.00888453i) q^{32} +(-0.733216 + 0.423322i) q^{33} +(5.79578 + 10.0386i) q^{34} +(-3.75925 + 1.16375i) q^{35} -0.00314116 q^{36} +(5.01251 + 3.44597i) q^{37} -6.98944i q^{38} +(1.39367 - 2.41391i) q^{39} +(-1.40219 + 6.17224i) q^{40} +(0.878263 + 1.52120i) q^{41} +(-2.15374 + 1.24346i) q^{42} +12.0635i q^{43} +(-0.00132972 - 0.00230315i) q^{44} +(1.51925 - 1.64070i) q^{45} +(-0.386015 + 0.668597i) q^{46} +2.30221i q^{47} +3.99371i q^{48} +(-1.95137 + 3.37987i) q^{49} +(-3.99198 - 5.82971i) q^{50} +8.20292 q^{51} +(0.00758248 + 0.00437775i) q^{52} +(-6.20716 - 3.58371i) q^{53} +(0.706551 - 1.22378i) q^{54} +(1.84612 + 0.419394i) q^{55} +(-2.49083 - 4.31424i) q^{56} +(-4.28350 - 2.47308i) q^{57} +(9.71660 + 5.60988i) q^{58} +(-5.81448 + 10.0710i) q^{59} +(0.00515369 + 0.00477220i) q^{60} +(1.07162 + 1.85610i) q^{61} +(10.0818 + 5.82075i) q^{62} +1.75990i q^{63} -8.01253 q^{64} +(-5.95393 + 1.84316i) q^{65} +1.19640 q^{66} +(-0.693985 + 0.400673i) q^{67} +0.0257667i q^{68} +(0.273168 + 0.473141i) q^{69} +(5.42276 + 1.23192i) q^{70} +(-2.25563 - 3.90687i) q^{71} +(2.45141 + 1.41532i) q^{72} +9.25889i q^{73} +(-3.69947 - 7.75872i) q^{74} +(-4.98525 + 0.383768i) q^{75} +(0.00776834 - 0.0134552i) q^{76} +(-1.29039 + 0.745006i) q^{77} +(-3.41111 + 1.96940i) q^{78} +(-0.100682 - 0.174387i) q^{79} +(6.06743 - 6.55246i) q^{80} +(-0.500000 - 0.866025i) q^{81} -2.48215i q^{82} +(10.3362 + 5.96761i) q^{83} -0.00552814 q^{84} +(-13.4585 - 12.4623i) q^{85} +(8.52348 - 14.7631i) q^{86} +(6.87607 - 3.96990i) q^{87} +2.39655i q^{88} +(3.59590 - 6.22829i) q^{89} +(-3.01847 + 0.934429i) q^{90} +(2.45273 - 4.24825i) q^{91} +(-0.00148621 + 0.000858065i) q^{92} +(7.13454 - 4.11913i) q^{93} +(1.62663 - 2.81741i) q^{94} +(3.27070 + 10.5653i) q^{95} +(-0.00888453 + 0.0153885i) q^{96} -15.4988i q^{97} +(4.77611 - 2.75749i) q^{98} +(0.423322 - 0.733216i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 72 q + 32 q^{4} - 2 q^{5} + 36 q^{9}+O(q^{10}) \) 72 * q + 32 * q^4 - 2 * q^5 + 36 * q^9	\( 72 q + 32 q^{4} - 2 q^{5} + 36 q^{9} - 8 q^{11} - 16 q^{14} - 24 q^{16} + 4 q^{19} + 4 q^{20} + 12 q^{21} + 10 q^{25} + 24 q^{26} + 16 q^{29} + 12 q^{30} + 24 q^{31} - 44 q^{34} - 2 q^{35} + 64 q^{36} - 8 q^{39} + 46 q^{40} - 48 q^{41} - 8 q^{44} - 4 q^{45} - 64 q^{46} + 32 q^{49} - 46 q^{50} - 8 q^{51} - 12 q^{55} - 72 q^{56} + 32 q^{59} - 68 q^{60} - 8 q^{61} - 136 q^{64} - 42 q^{65} - 32 q^{66} - 4 q^{69} + 4 q^{70} + 12 q^{71} - 96 q^{74} - 8 q^{75} + 8 q^{76} - 8 q^{79} - 44 q^{80} - 36 q^{81} + 136 q^{84} + 4 q^{85} + 8 q^{86} + 8 q^{91} - 28 q^{94} + 18 q^{95} - 20 q^{96} - 4 q^{99}+O(q^{100}) \) 72 * q + 32 * q^4 - 2 * q^5 + 36 * q^9 - 8 * q^11 - 16 * q^14 - 24 * q^16 + 4 * q^19 + 4 * q^20 + 12 * q^21 + 10 * q^25 + 24 * q^26 + 16 * q^29 + 12 * q^30 + 24 * q^31 - 44 * q^34 - 2 * q^35 + 64 * q^36 - 8 * q^39 + 46 * q^40 - 48 * q^41 - 8 * q^44 - 4 * q^45 - 64 * q^46 + 32 * q^49 - 46 * q^50 - 8 * q^51 - 12 * q^55 - 72 * q^56 + 32 * q^59 - 68 * q^60 - 8 * q^61 - 136 * q^64 - 42 * q^65 - 32 * q^66 - 4 * q^69 + 4 * q^70 + 12 * q^71 - 96 * q^74 - 8 * q^75 + 8 * q^76 - 8 * q^79 - 44 * q^80 - 36 * q^81 + 136 * q^84 + 4 * q^85 + 8 * q^86 + 8 * q^91 - 28 * q^94 + 18 * q^95 - 20 * q^96 - 4 * q^99

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