LMFDB - Embedded newform 234.2.y.a.119.3

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [234,2,Mod(11,234)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("234.11"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(234, base_ring=CyclotomicField(12)) chi = DirichletCharacter(H, H._module([2, 7])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 234 = 2 \cdot 3^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	234.y (of order $12$, degree $4$, minimal)

Newform invariants

comment:select newform

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

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

Self dual:	no
Analytic conductor:	$1.86849940730$
Analytic rank:	$0$
Dimension:	$56$
Relative dimension:	$14$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			119.3
Character	$\chi$	$=$	234.119
Dual form			234.2.y.a.59.3

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.707107 - 0.707107i) q^{2} +(-0.769968 - 1.55150i) q^{3} +1.00000i q^{4} +(0.891175 - 3.32591i) q^{5} +(-0.552626 + 1.64153i) q^{6} +(-0.00737496 + 0.0275237i) q^{7} +(0.707107 - 0.707107i) q^{8} +(-1.81430 + 2.38921i) q^{9} +(-2.98193 + 1.72162i) q^{10} +(3.07674 - 3.07674i) q^{11} +(1.55150 - 0.769968i) q^{12} +(-3.57728 - 0.450627i) q^{13} +(0.0246771 - 0.0142473i) q^{14} +(-5.84632 + 1.17819i) q^{15} -1.00000 q^{16} +(-3.35521 + 5.81139i) q^{17} +(2.97233 - 0.406522i) q^{18} +(-0.521462 - 1.94612i) q^{19} +(3.32591 + 0.891175i) q^{20} +(0.0483815 - 0.00975013i) q^{21} -4.35116 q^{22} +(0.264071 - 0.457384i) q^{23} +(-1.64153 - 0.552626i) q^{24} +(-5.93735 - 3.42793i) q^{25} +(2.21088 + 2.84816i) q^{26} +(5.10381 + 0.975270i) q^{27} +(-0.0275237 - 0.00737496i) q^{28} -8.30696i q^{29} +(4.96708 + 3.30087i) q^{30} +(1.39364 + 0.373424i) q^{31} +(0.707107 + 0.707107i) q^{32} +(-7.14254 - 2.40457i) q^{33} +(6.48176 - 1.73678i) q^{34} +(0.0849690 + 0.0490569i) q^{35} +(-2.38921 - 1.81430i) q^{36} +(-2.09857 + 7.83198i) q^{37} +(-1.00739 + 1.74484i) q^{38} +(2.05524 + 5.89712i) q^{39} +(-1.72162 - 2.98193i) q^{40} +(4.85352 - 1.30050i) q^{41} +(-0.0411053 - 0.0273165i) q^{42} +(7.58793 - 4.38090i) q^{43} +(3.07674 + 3.07674i) q^{44} +(6.32943 + 8.16340i) q^{45} +(-0.510146 + 0.136693i) q^{46} +(-0.207869 - 0.775777i) q^{47} +(0.769968 + 1.55150i) q^{48} +(6.06147 + 3.49959i) q^{49} +(1.77443 + 6.62226i) q^{50} +(11.5998 + 0.731018i) q^{51} +(0.450627 - 3.57728i) q^{52} -5.06566i q^{53} +(-2.91932 - 4.29856i) q^{54} +(-7.49104 - 12.9749i) q^{55} +(0.0142473 + 0.0246771i) q^{56} +(-2.61790 + 2.30750i) q^{57} +(-5.87391 + 5.87391i) q^{58} +(10.1180 - 10.1180i) q^{59} +(-1.17819 - 5.84632i) q^{60} +(0.0107467 + 0.0186139i) q^{61} +(-0.721399 - 1.24950i) q^{62} +(-0.0523795 - 0.0675565i) q^{63} -1.00000i q^{64} +(-4.68673 + 11.4961i) q^{65} +(3.35025 + 6.75082i) q^{66} +(-0.244574 - 0.912763i) q^{67} +(-5.81139 - 3.35521i) q^{68} +(-0.912957 - 0.0575347i) q^{69} +(-0.0253937 - 0.0947706i) q^{70} +(9.32969 - 2.49988i) q^{71} +(0.406522 + 2.97233i) q^{72} +(6.53713 + 6.53713i) q^{73} +(7.02196 - 4.05413i) q^{74} +(-0.746864 + 11.8512i) q^{75} +(1.94612 - 0.521462i) q^{76} +(0.0619924 + 0.107374i) q^{77} +(2.71661 - 5.62317i) q^{78} +(1.40950 - 2.44132i) q^{79} +(-0.891175 + 3.32591i) q^{80} +(-2.41664 - 8.66948i) q^{81} +(-4.35155 - 2.51237i) q^{82} +(-14.1896 + 3.80210i) q^{83} +(0.00975013 + 0.0483815i) q^{84} +(16.3381 + 16.3381i) q^{85} +(-8.46324 - 2.26772i) q^{86} +(-12.8882 + 6.39609i) q^{87} -4.35116i q^{88} +(-10.8696 - 2.91249i) q^{89} +(1.29681 - 10.2480i) q^{90} +(0.0387852 - 0.0951367i) q^{91} +(0.457384 + 0.264071i) q^{92} +(-0.493689 - 2.44975i) q^{93} +(-0.401572 + 0.695542i) q^{94} -6.93734 q^{95} +(0.552626 - 1.64153i) q^{96} +(-0.455998 - 0.122184i) q^{97} +(-1.81152 - 6.76070i) q^{98} +(1.76884 + 12.9331i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 56 q + 4 q^{7} + 24 q^{15} - 56 q^{16} - 8 q^{19} + 36 q^{27} - 4 q^{28} + 8 q^{31} - 36 q^{33} + 24 q^{35} - 24 q^{36} - 4 q^{37} - 36 q^{38} - 24 q^{39} - 48 q^{41} + 36 q^{42} + 12 q^{43} - 36 q^{45}+ \cdots - 24 q^{99}+O(q^{100}) $ 56 * q + 4 * q^7 + 24 * q^15 - 56 * q^16 - 8 * q^19 + 36 * q^27 - 4 * q^28 + 8 * q^31 - 36 * q^33 + 24 * q^35 - 24 * q^36 - 4 * q^37 - 36 * q^38 - 24 * q^39 - 48 * q^41 + 36 * q^42 + 12 * q^43 - 36 * q^45 + 60 * q^47 - 24 * q^50 - 4 * q^52 + 24 * q^57 - 60 * q^63 - 120 * q^65 - 56 * q^67 - 36 * q^69 + 24 * q^71 + 28 * q^73 + 48 * q^74 + 4 * q^76 - 24 * q^77 + 36 * q^78 - 24 * q^79 - 120 * q^81 - 60 * q^83 + 24 * q^84 + 48 * q^86 + 48 * q^87 + 4 * q^91 - 24 * q^92 + 20 * q^97 - 48 * q^98 - 24 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/234\mathbb{Z}\right)^\times$.

$n$	$145$	$209$
$\chi(n)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{1}{6}\right)$

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 $

$2$	−0.707107	−	0.707107i	−0.500000	−	0.500000i
$2$	−0.707107	−	0.707107i	−0.500000	−	0.500000i
$3$	−0.769968	−	1.55150i	−0.444541	−	0.895758i
$3$	−0.769968	−	1.55150i	−0.444541	−	0.895758i
$4$			1.00000i			0.500000i
$5$	0.891175	−	3.32591i	0.398545	−	1.48739i	−0.417111	−	0.908855i	$-0.636957\pi$
$5$	0.891175	−	3.32591i	0.398545	−	1.48739i	0.815657	−	0.578536i	$-0.196376\pi$
$6$	−0.552626	+	1.64153i	−0.225609	+	0.670150i
$7$	−0.00737496	+	0.0275237i	−0.00278747	+	0.0104030i	−0.967306	−	0.253614i	$-0.918381\pi$
$7$	−0.00737496	+	0.0275237i	−0.00278747	+	0.0104030i	0.964518	+	0.264017i	$0.0850474\pi$
$8$	0.707107	−	0.707107i	0.250000	−	0.250000i
$9$	−1.81430	+	2.38921i	−0.604766	+	0.796403i
$10$	−2.98193	+	1.72162i	−0.942969	+	0.544423i
$11$	3.07674	−	3.07674i	0.927671	−	0.927671i	−0.0698842	−	0.997555i	$-0.522263\pi$
$11$	3.07674	−	3.07674i	0.927671	−	0.927671i	0.997555	+	0.0698842i	$0.0222630\pi$
$12$	1.55150	−	0.769968i	0.447879	−	0.222271i
$13$	−3.57728	−	0.450627i	−0.992159	−	0.124981i
$13$	−3.57728	−	0.450627i	−0.992159	−	0.124981i
$14$	0.0246771	−	0.0142473i	0.00659523	−	0.00380776i
$15$	−5.84632	+	1.17819i	−1.50951	+	0.304206i
$16$	−1.00000			−0.250000
$17$	−3.35521	+	5.81139i	−0.813757	+	1.40947i	0.0964602	+	0.995337i	$0.469248\pi$
$17$	−3.35521	+	5.81139i	−0.813757	+	1.40947i	−0.910217	+	0.414131i	$0.864085\pi$
$18$	2.97233	−	0.406522i	0.700585	−	0.0958182i
$19$	−0.521462	−	1.94612i	−0.119632	−	0.446471i	0.879960	−	0.475048i	$-0.157569\pi$
$19$	−0.521462	−	1.94612i	−0.119632	−	0.446471i	−0.999592	+	0.0285767i	$0.990903\pi$
$20$	3.32591	+	0.891175i	0.743696	+	0.199273i
$21$	0.0483815	−	0.00975013i	0.0105577	−	0.00212765i
$22$	−4.35116			−0.927671
$23$	0.264071	−	0.457384i	0.0550626	−	0.0953712i	−0.837180	−	0.546927i	$-0.815798\pi$
$23$	0.264071	−	0.457384i	0.0550626	−	0.0953712i	0.892243	+	0.451556i	$0.149131\pi$
$24$	−1.64153	−	0.552626i	−0.335075	−	0.112804i
$25$	−5.93735	−	3.42793i	−1.18747	−	0.685587i
$26$	2.21088	+	2.84816i	0.433589	+	0.558570i
$27$	5.10381	+	0.975270i	0.982228	+	0.187691i
$28$	−0.0275237	−	0.00737496i	−0.00520149	−	0.00139374i
$29$		−	8.30696i		−	1.54256i	−0.636493	−	0.771282i	$-0.719616\pi$
$29$		−	8.30696i		−	1.54256i	0.636493	−	0.771282i	$-0.280384\pi$
$30$	4.96708	+	3.30087i	0.906860	+	0.602654i
$31$	1.39364	+	0.373424i	0.250305	+	0.0670689i	0.381790	−	0.924249i	$-0.375308\pi$
$31$	1.39364	+	0.373424i	0.250305	+	0.0670689i	−0.131485	+	0.991318i	$0.541975\pi$
$32$	0.707107	+	0.707107i	0.125000	+	0.125000i
$33$	−7.14254	−	2.40457i	−1.24336	−	0.418581i
$34$	6.48176	−	1.73678i	1.11161	−	0.297856i
$35$	0.0849690	+	0.0490569i	0.0143624	+	0.00829212i
$36$	−2.38921	−	1.81430i	−0.398201	−	0.302383i
$37$	−2.09857	+	7.83198i	−0.345003	+	1.28757i	0.547605	+	0.836737i	$0.315540\pi$
$37$	−2.09857	+	7.83198i	−0.345003	+	1.28757i	−0.892608	+	0.450833i	$0.851127\pi$
$38$	−1.00739	+	1.74484i	−0.163420	+	0.283051i
$39$	2.05524	+	5.89712i	0.329102	+	0.944294i
$40$	−1.72162	−	2.98193i	−0.272212	−	0.471484i
$41$	4.85352	−	1.30050i	0.757992	−	0.203103i	0.140932	−	0.990019i	$-0.454990\pi$
$41$	4.85352	−	1.30050i	0.757992	−	0.203103i	0.617060	+	0.786916i	$0.288323\pi$
$42$	−0.0411053	−	0.0273165i	−0.00634268	−	0.00421503i
$43$	7.58793	−	4.38090i	1.15715	−	0.668080i	0.206530	−	0.978440i	$-0.433783\pi$
$43$	7.58793	−	4.38090i	1.15715	−	0.668080i	0.950619	+	0.310360i	$0.100450\pi$
$44$	3.07674	+	3.07674i	0.463835	+	0.463835i
$45$	6.32943	+	8.16340i	0.943536	+	1.21693i
$46$	−0.510146	+	0.136693i	−0.0752169	+	0.0201543i
$47$	−0.207869	−	0.775777i	−0.0303208	−	0.113159i	0.949107	−	0.314954i	$-0.101989\pi$
$47$	−0.207869	−	0.775777i	−0.0303208	−	0.113159i	−0.979428	+	0.201795i	$0.935322\pi$
$48$	0.769968	+	1.55150i	0.111135	+	0.223940i
$49$	6.06147	+	3.49959i	0.865925	+	0.499942i
$50$	1.77443	+	6.62226i	0.250942	+	0.936529i
$51$	11.5998	+	0.731018i	1.62429	+	0.102363i
$52$	0.450627	−	3.57728i	0.0624907	−	0.496080i
$53$		−	5.06566i		−	0.695822i	−0.937527	−	0.347911i	$-0.886891\pi$
$53$		−	5.06566i		−	0.695822i	0.937527	−	0.347911i	$-0.113109\pi$
$54$	−2.91932	−	4.29856i	−0.397269	−	0.584959i
$55$	−7.49104	−	12.9749i	−1.01009	−	1.74953i
$56$	0.0142473	+	0.0246771i	0.00190388	+	0.00329761i
$57$	−2.61790	+	2.30750i	−0.346749	+	0.305636i
$58$	−5.87391	+	5.87391i	−0.771282	+	0.771282i
$59$	10.1180	−	10.1180i	1.31725	−	1.31725i	0.401298	−	0.915948i	$-0.368559\pi$
$59$	10.1180	−	10.1180i	1.31725	−	1.31725i	0.915948	−	0.401298i	$-0.131441\pi$
$60$	−1.17819	−	5.84632i	−0.152103	−	0.754757i
$61$	0.0107467	+	0.0186139i	0.00137598	+	0.00238327i	0.866713	−	0.498808i	$-0.166229\pi$
$61$	0.0107467	+	0.0186139i	0.00137598	+	0.00238327i	−0.865337	+	0.501191i	$0.832895\pi$
$62$	−0.721399	−	1.24950i	−0.0916178	−	0.158687i
$63$	−0.0523795	−	0.0675565i	−0.00659920	−	0.00851133i
$64$		−	1.00000i		−	0.125000i
$65$	−4.68673	+	11.4961i	−0.581317	+	1.42592i
$66$	3.35025	+	6.75082i	0.412388	+	0.830969i
$67$	−0.244574	−	0.912763i	−0.0298795	−	0.111512i	0.949376	−	0.314143i	$-0.101717\pi$
$67$	−0.244574	−	0.912763i	−0.0298795	−	0.111512i	−0.979255	+	0.202632i	$0.935051\pi$
$68$	−5.81139	−	3.35521i	−0.704734	−	0.406878i
$69$	−0.912957	−	0.0575347i	−0.109907	−	0.00692636i
$70$	−0.0253937	−	0.0947706i	−0.00303513	−	0.0113273i
$71$	9.32969	−	2.49988i	1.10723	−	0.296682i	0.341525	−	0.939873i	$-0.389057\pi$
$71$	9.32969	−	2.49988i	1.10723	−	0.296682i	0.765706	+	0.643191i	$0.222390\pi$
$72$	0.406522	+	2.97233i	0.0479091	+	0.350292i
$73$	6.53713	+	6.53713i	0.765113	+	0.765113i	0.977242	−	0.212129i	$-0.0680396\pi$
$73$	6.53713	+	6.53713i	0.765113	+	0.765113i	−0.212129	+	0.977242i	$0.568040\pi$
$74$	7.02196	−	4.05413i	0.816286	−	0.471283i
$75$	−0.746864	+	11.8512i	−0.0862404	+	1.36846i
$76$	1.94612	−	0.521462i	0.223235	−	0.0598158i
$77$	0.0619924	+	0.107374i	0.00706469	+	0.0122364i
$78$	2.71661	−	5.62317i	0.307596	−	0.636698i
$79$	1.40950	−	2.44132i	0.158581	−	0.274670i	−0.775776	−	0.631008i	$-0.782641\pi$
$79$	1.40950	−	2.44132i	0.158581	−	0.274670i	0.934357	+	0.356338i	$0.115975\pi$
$80$	−0.891175	+	3.32591i	−0.0996364	+	0.371848i
$81$	−2.41664	−	8.66948i	−0.268515	−	0.963275i
$82$	−4.35155	−	2.51237i	−0.480548	−	0.277444i
$83$	−14.1896	+	3.80210i	−1.55752	+	0.417335i	−0.931876	−	0.362777i	$-0.881829\pi$
$83$	−14.1896	+	3.80210i	−1.55752	+	0.417335i	−0.625640	+	0.780112i	$0.715162\pi$
$84$	0.00975013	+	0.0483815i	0.00106383	+	0.00527885i
$85$	16.3381	+	16.3381i	1.77211	+	1.77211i
$86$	−8.46324	−	2.26772i	−0.912615	−	0.244534i
$87$	−12.8882	+	6.39609i	−1.38176	+	0.685733i
$88$		−	4.35116i		−	0.463835i
$89$	−10.8696	−	2.91249i	−1.15217	−	0.308724i	−0.368337	−	0.929692i	$-0.620073\pi$
$89$	−10.8696	−	2.91249i	−1.15217	−	0.308724i	−0.783835	+	0.620969i	$0.786739\pi$
$90$	1.29681	−	10.2480i	0.136696	−	1.08023i
$91$	0.0387852	−	0.0951367i	0.00406579	−	0.00997303i
$92$	0.457384	+	0.264071i	0.0476856	+	0.0275313i
$93$	−0.493689	−	2.44975i	−0.0511931	−	0.254027i
$94$	−0.401572	+	0.695542i	−0.0414189	+	0.0717397i
$95$	−6.93734			−0.711756
$96$	0.552626	−	1.64153i	0.0564022	−	0.167537i
$97$	−0.455998	−	0.122184i	−0.0462996	−	0.0124059i	0.235595	−	0.971851i	$-0.424296\pi$
$97$	−0.455998	−	0.122184i	−0.0462996	−	0.0124059i	−0.281895	+	0.959445i	$0.590963\pi$
$98$	−1.81152	−	6.76070i	−0.182991	−	0.682933i
$99$	1.76884	+	12.9331i	0.177776	+	1.29982i
$100$	3.42793	−	5.93735i	0.342793	−	0.593735i
$101$	−5.49087			−0.546362			−0.273181	−	0.961963i	$-0.588076\pi$
$101$	−5.49087			−0.546362			−0.273181	+	0.961963i	$0.588076\pi$
$102$	−7.68536	−	8.71918i	−0.760964	−	0.863327i
$103$	−3.62390	+	2.09226i	−0.357073	+	0.206156i	−0.667796	−	0.744344i	$-0.732762\pi$
$103$	−3.62390	+	2.09226i	−0.357073	+	0.206156i	0.310723	+	0.950501i	$0.399429\pi$
$104$	−2.84816	+	2.21088i	−0.279285	+	0.216794i
$105$	0.0106883	−	0.169602i	0.00104307	−	0.0165514i
$106$	−3.58197	+	3.58197i	−0.347911	+	0.347911i
$107$	2.85234	−	1.64680i	0.275746	−	0.159202i	−0.355750	−	0.934581i	$-0.615774\pi$
$107$	2.85234	−	1.64680i	0.275746	−	0.159202i	0.631496	+	0.775379i	$0.282441\pi$
$108$	−0.975270	+	5.10381i	−0.0938454	+	0.491114i
$109$	−5.40316	+	5.40316i	−0.517529	+	0.517529i	−0.916823	−	0.399294i	$-0.869255\pi$
$109$	−5.40316	+	5.40316i	−0.517529	+	0.517529i	0.399294	+	0.916823i	$0.369255\pi$
$110$	−3.87765	+	14.4716i	−0.369719	+	1.37981i
$111$	13.7671	−	2.77444i	1.30672	−	0.263338i
$112$	0.00737496	−	0.0275237i	0.000696868	−	0.00260075i
$113$		−	0.581902i		−	0.0547407i	−0.999625	−	0.0273704i	$-0.991287\pi$
$113$		−	0.581902i		−	0.0547407i	0.999625	−	0.0273704i	$-0.00871334\pi$
$114$	3.48278	+	0.219485i	0.326192	+	0.0205567i
$115$	−1.28588	−	1.28588i	−0.119909	−	0.119909i
$116$	8.30696			0.771282
$117$	7.56690	−	7.72930i	0.699560	−	0.714574i
$118$	−14.3089			−1.31725
$119$	−0.135206	−	0.135206i	−0.0123944	−	0.0123944i
$120$	−3.30087	+	4.96708i	−0.301327	+	0.453430i
$121$		−	7.93261i		−	0.721147i
$122$	0.00556292	−	0.0207611i	0.000503644	−	0.00187962i
$123$	−5.75477	−	6.52889i	−0.518890	−	0.588690i
$124$	−0.373424	+	1.39364i	−0.0335345	+	0.125152i
$125$	−4.51854	+	4.51854i	−0.404150	+	0.404150i
$126$	−0.0107318	+	0.0848076i	−0.000956064	+	0.00755526i
$127$	8.56275	−	4.94371i	0.759822	−	0.438683i	−0.0694101	−	0.997588i	$-0.522112\pi$
$127$	8.56275	−	4.94371i	0.759822	−	0.438683i	0.829232	+	0.558905i	$0.188778\pi$
$128$	−0.707107	+	0.707107i	−0.0625000	+	0.0625000i
$129$	−12.6394	−	8.39952i	−1.11284	−	0.739537i
$130$	11.4430	−	4.81497i	1.00362	−	0.422301i
$131$	−15.6965	+	9.06236i	−1.37141	+	0.791782i	−0.991105	−	0.133081i	$-0.957513\pi$
$131$	−15.6965	+	9.06236i	−1.37141	+	0.791782i	−0.380301	+	0.924863i	$0.624180\pi$
$132$	2.40457	−	7.14254i	0.209291	−	0.621678i
$133$	0.0574102			0.00497810
$134$	−0.472481	+	0.818361i	−0.0408161	+	0.0706956i
$135$	7.79204	−	16.1057i	0.670632	−	1.38615i
$136$	1.73678	+	6.48176i	0.148928	+	0.555806i
$137$	16.1465	+	4.32643i	1.37948	+	0.369632i	0.870934	−	0.491400i	$-0.163515\pi$
$137$	16.1465	+	4.32643i	1.37948	+	0.369632i	0.508551	+	0.861032i	$0.330181\pi$
$138$	0.604875	+	0.686241i	0.0514904	+	0.0584167i
$139$	5.08483			0.431289			0.215645	−	0.976472i	$-0.430815\pi$
$139$	5.08483			0.431289			0.215645	+	0.976472i	$0.430815\pi$
$140$	−0.0490569	+	0.0849690i	−0.00414606	+	0.00718119i
$141$	−1.04356	+	0.919831i	−0.0878840	+	0.0774638i
$142$	−8.36477	−	4.82940i	−0.701956	−	0.405275i
$143$	−12.3928	+	9.61989i	−1.03634	+	0.804456i
$144$	1.81430	−	2.38921i	0.151192	−	0.199101i
$145$	−27.6282	−	7.40295i	−2.29440	−	0.614782i
$146$		−	9.24490i		−	0.765113i
$147$	0.762477	−	12.0989i	0.0628881	−	0.997904i
$148$	−7.83198	−	2.09857i	−0.643785	−	0.172502i
$149$	3.73867	+	3.73867i	0.306284	+	0.306284i	0.843466	−	0.537182i	$-0.180511\pi$
$149$	3.73867	+	3.73867i	0.306284	+	0.306284i	−0.537182	+	0.843466i	$0.680511\pi$
$150$	8.90817	−	7.85195i	0.727349	−	0.641109i
$151$	9.40508	−	2.52008i	0.765375	−	0.205082i	0.145047	−	0.989425i	$-0.453667\pi$
$151$	9.40508	−	2.52008i	0.765375	−	0.205082i	0.620327	+	0.784343i	$0.287000\pi$
$152$	−1.74484	−	1.00739i	−0.141526	−	0.0817098i
$153$	−7.79727	−	18.5599i	−0.630372	−	1.50048i
$154$	0.0320896	−	0.119760i	0.00258586	−	0.00965055i
$155$	2.48395	−	4.30232i	0.199515	−	0.345571i
$156$	−5.89712	+	2.05524i	−0.472147	+	0.164551i
$157$	4.81339	+	8.33703i	0.384150	+	0.665368i	0.991651	−	0.128952i	$-0.0411612\pi$
$157$	4.81339	+	8.33703i	0.384150	+	0.665368i	−0.607501	+	0.794319i	$0.707828\pi$
$158$	−2.72294	+	0.729610i	−0.216626	+	0.0580446i
$159$	−7.85937	+	3.90040i	−0.623289	+	0.309322i
$160$	2.98193	−	1.72162i	0.235742	−	0.136106i
$161$	0.0106414	+	0.0106414i	0.000838659	+	0.000838659i
$162$	−4.42143	+	7.83907i	−0.347380	+	0.615895i
$163$	10.7066	−	2.86883i	0.838607	−	0.224704i	0.186142	−	0.982523i	$-0.440402\pi$
$163$	10.7066	−	2.86883i	0.838607	−	0.224704i	0.652465	+	0.757819i	$0.273735\pi$
$164$	1.30050	+	4.85352i	0.101552	+	0.378996i
$165$	−14.3626	+	21.6126i	−1.11813	+	1.68254i
$166$	12.7221	+	7.34510i	0.987425	+	0.570090i
$167$	3.86269	+	14.4157i	0.298904	+	1.11552i	0.938067	+	0.346453i	$0.112614\pi$
$167$	3.86269	+	14.4157i	0.298904	+	1.11552i	−0.639164	+	0.769071i	$0.720719\pi$
$168$	0.0273165	−	0.0411053i	0.00210751	−	0.00317134i
$169$	12.5939	+	3.22404i	0.968759	+	0.248003i
$170$		−	23.1055i		−	1.77211i
$171$	5.59578	+	2.28497i	0.427920	+	0.174736i
$172$	4.38090	+	7.58793i	0.334040	+	0.578574i
$173$	−9.53013	−	16.5067i	−0.724562	−	1.25498i	−0.959154	−	0.282884i	$-0.908709\pi$
$173$	−9.53013	−	16.5067i	−0.724562	−	1.25498i	0.234592	−	0.972094i	$-0.424625\pi$
$174$	13.6361	+	4.59064i	1.03375	+	0.348016i
$175$	0.138137	−	0.138137i	0.0104422	−	0.0104422i
$176$	−3.07674	+	3.07674i	−0.231918	+	0.231918i
$177$	−23.4885	−	7.90750i	−1.76550	−	0.594364i
$178$	5.62650	+	9.74539i	0.421724	+	0.730448i
$179$	12.0533	+	20.8769i	0.900906	+	1.56041i	0.826320	+	0.563200i	$0.190430\pi$
$179$	12.0533	+	20.8769i	0.900906	+	1.56041i	0.0745856	+	0.997215i	$0.476237\pi$
$180$	−8.16340	+	6.32943i	−0.608464	+	0.471768i
$181$		−	1.16505i		−	0.0865977i	−0.999062	−	0.0432988i	$-0.986213\pi$
$181$		−	1.16505i		−	0.0865977i	0.999062	−	0.0432988i	$-0.0137868\pi$
$182$	−0.0946971	+	0.0398465i	−0.00701941	+	0.00295362i
$183$	0.0206048	−	0.0310057i	0.00152315	−	0.00229201i
$184$	−0.136693	−	0.510146i	−0.0100771	−	0.0376084i
$185$	24.1783	+	13.9593i	1.77762	+	1.02631i
$186$	−1.38314	+	2.08133i	−0.101417	+	0.152610i
$187$	7.55702	+	28.2032i	0.552624	+	2.06242i
$188$	0.775777	−	0.207869i	0.0565793	−	0.0151604i
$189$	−0.0644834	+	0.133283i	−0.00469048	+	0.00969492i
$190$	4.90544	+	4.90544i	0.355878	+	0.355878i
$191$	−10.0152	+	5.78229i	−0.724676	+	0.418392i	−0.816471	−	0.577386i	$-0.804073\pi$
$191$	−10.0152	+	5.78229i	−0.724676	+	0.418392i	0.0917955	+	0.995778i	$0.470739\pi$
$192$	−1.55150	+	0.769968i	−0.111970	+	0.0555676i
$193$	1.39097	−	0.372710i	0.100124	−	0.0268283i	−0.208409	−	0.978042i	$-0.566829\pi$
$193$	1.39097	−	0.372710i	0.100124	−	0.0268283i	0.308533	+	0.951214i	$0.400162\pi$
$194$	0.236042	+	0.408837i	0.0169468	+	0.0293528i
$195$	21.4449	−	1.58019i	1.53570	−	0.113160i
$196$	−3.49959	+	6.06147i	−0.249971	+	0.432962i
$197$	1.07594	−	4.01546i	0.0766575	−	0.286090i	−0.916947	−	0.399010i	$-0.869354\pi$
$197$	1.07594	−	4.01546i	0.0766575	−	0.286090i	0.993604	+	0.112920i	$0.0360205\pi$
$198$	7.89431	−	10.3958i	0.561024	−	0.738800i
$199$	1.78437	+	1.03021i	0.126491	+	0.0730295i	0.561910	−	0.827198i	$-0.310067\pi$
$199$	1.78437	+	1.03021i	0.126491	+	0.0730295i	−0.435419	+	0.900228i	$0.643400\pi$
$200$	−6.62226	+	1.77443i	−0.468264	+	0.125471i
$201$	−1.22784	+	1.08225i	−0.0866049	+	0.0763363i
$202$	3.88263	+	3.88263i	0.273181	+	0.273181i
$203$	0.228638	+	0.0612635i	0.0160473	+	0.00429985i
$204$	−0.731018	+	11.5998i	−0.0511815	+	0.812146i
$205$		−	17.3013i		−	1.20838i
$206$	4.04193	+	1.08303i	0.281615	+	0.0754585i
$207$	0.613682	+	1.46075i	0.0426539	+	0.101529i
$208$	3.57728	+	0.450627i	0.248040	+	0.0312453i
$209$	−7.59210	−	4.38330i	−0.525157	−	0.303199i
$210$	−0.127484	+	0.112369i	−0.00879724	+	0.00775417i
$211$	−9.57481	+	16.5841i	−0.659157	+	1.14169i	0.321677	+	0.946849i	$0.395753\pi$
$211$	−9.57481	+	16.5841i	−0.659157	+	1.14169i	−0.980834	+	0.194844i	$0.937580\pi$
$212$	5.06566			0.347911
$213$	−11.0621	−	12.5502i	−0.757965	−	0.859924i
$214$	−3.18137	−	0.852446i	−0.217474	−	0.0582720i
$215$	−7.80829	−	29.1409i	−0.532521	−	1.98739i
$216$	4.29856	−	2.91932i	0.292480	−	0.198634i
$217$	−0.0205560	+	0.0356041i	−0.00139543	+	0.00241696i
$218$	7.64122			0.517529
$219$	5.10897	−	15.1757i	0.345232	−	1.02548i
$220$	12.9749	−	7.49104i	0.874765	−	0.505046i
$221$	14.6213	−	19.2770i	0.983534	−	1.29671i
$222$	−11.6967	−	7.77302i	−0.785029	−	0.521691i
$223$	18.6817	−	18.6817i	1.25102	−	1.25102i	0.295754	−	0.955264i	$-0.404429\pi$
$223$	18.6817	−	18.6817i	1.25102	−	1.25102i	0.955264	−	0.295754i	$-0.0955710\pi$
$224$	−0.0246771	+	0.0142473i	−0.00164881	+	0.000951939i
$225$	18.9622	−	7.96628i	1.26415	−	0.531085i
$226$	−0.411467	+	0.411467i	−0.0273704	+	0.0273704i
$227$	1.32881	−	4.95918i	0.0881962	−	0.329153i	−0.907704	−	0.419611i	$-0.862167\pi$
$227$	1.32881	−	4.95918i	0.0881962	−	0.329153i	0.995900	+	0.0904584i	$0.0288332\pi$
$228$	−2.30750	−	2.61790i	−0.152818	−	0.173374i
$229$	2.05522	−	7.67020i	0.135813	−	0.506861i	−0.864180	−	0.503182i	$-0.832162\pi$
$229$	2.05522	−	7.67020i	0.135813	−	0.506861i	0.999993	−	0.00367870i	$-0.00117097\pi$
$230$			1.81852i			0.119909i
$231$	0.118858	−	0.178856i	0.00782031	−	0.0117678i
$232$	−5.87391	−	5.87391i	−0.385641	−	0.385641i
$233$	0.240333			0.0157448			0.00787238	−	0.999969i	$-0.497494\pi$
$233$	0.240333			0.0157448			0.00787238	+	0.999969i	$0.497494\pi$
$234$	−10.8160	+	0.114834i	−0.707067	+	0.00750692i
$235$	−2.76541			−0.180395
$236$	10.1180	+	10.1180i	0.658623	+	0.658623i
$237$	−4.87298	−	0.307096i	−0.316534	−	0.0199480i
$238$			0.191211i			0.0123944i
$239$	−1.74060	+	6.49603i	−0.112590	+	0.420193i	−0.999095	−	0.0425261i	$-0.986459\pi$
$239$	−1.74060	+	6.49603i	−0.112590	+	0.420193i	0.886505	+	0.462719i	$0.153126\pi$
$240$	5.84632	−	1.17819i	0.377378	−	0.0760516i
$241$	−6.71652	+	25.0664i	−0.432649	+	1.61467i	0.313980	+	0.949430i	$0.398337\pi$
$241$	−6.71652	+	25.0664i	−0.432649	+	1.61467i	−0.746630	+	0.665240i	$0.768329\pi$
$242$	−5.60920	+	5.60920i	−0.360573	+	0.360573i
$243$	−11.5900	+	10.4246i	−0.743496	+	0.668740i
$244$	−0.0186139	+	0.0107467i	−0.00119163	+	0.000687990i
$245$	17.0412	−	17.0412i	1.08872	−	1.08872i
$246$	−0.547384	+	8.68586i	−0.0348999	+	0.553790i
$247$	0.988441	+	7.19681i	0.0628930	+	0.457922i
$248$	1.24950	−	0.721399i	0.0793434	−	0.0458089i
$249$	16.8245	+	19.0877i	1.06621	+	1.20964i
$250$	6.39018			0.404150
$251$	−10.2804	+	17.8061i	−0.648892	+	1.12391i	0.334496	+	0.942397i	$0.391434\pi$
$251$	−10.2804	+	17.8061i	−0.648892	+	1.12391i	−0.983388	+	0.181517i	$0.941899\pi$
$252$	0.0675565	−	0.0523795i	0.00425566	−	0.00329960i
$253$	−0.594774	−	2.21973i	−0.0373931	−	0.139553i
$254$	−9.55051	−	2.55905i	−0.599252	−	0.160569i
$255$	12.7687	−	37.9283i	0.799608	−	2.37516i
$256$	1.00000			0.0625000
$257$	7.71905	−	13.3698i	0.481501	−	0.833984i	−0.518274	−	0.855215i	$-0.673425\pi$
$257$	7.71905	−	13.3698i	0.481501	−	0.833984i	0.999775	+	0.0212306i	$0.00675841\pi$
$258$	2.99806	+	14.8768i	0.186651	+	0.926188i
$259$	−0.200088	−	0.115521i	−0.0124329	−	0.00717813i
$260$	−11.4961	−	4.68673i	−0.712959	−	0.290658i
$261$	19.8471	+	15.0713i	1.22850	+	0.932891i
$262$	17.5071	+	4.69102i	1.08159	+	0.289812i
$263$		−	12.6233i		−	0.778388i	−0.921156	−	0.389194i	$-0.872754\pi$
$263$		−	12.6233i		−	0.778388i	0.921156	−	0.389194i	$-0.127246\pi$
$264$	−6.75082	+	3.35025i	−0.415485	+	0.206194i
$265$	−16.8479	−	4.51439i	−1.03496	−	0.277317i
$266$	−0.0405952	−	0.0405952i	−0.00248905	−	0.00248905i
$267$	3.85049	+	19.1067i	0.235646	+	1.16931i
$268$	0.912763	−	0.244574i	0.0557559	−	0.0149397i
$269$	13.5676	+	7.83325i	0.827230	+	0.477602i	0.852903	−	0.522069i	$-0.174840\pi$
$269$	13.5676	+	7.83325i	0.827230	+	0.477602i	−0.0256732	+	0.999670i	$0.508173\pi$
$270$	−16.8982	+	5.87862i	−1.02839	+	0.357761i
$271$	−4.43051	+	16.5349i	−0.269134	+	1.00442i	0.690537	+	0.723297i	$0.257374\pi$
$271$	−4.43051	+	16.5349i	−0.269134	+	1.00442i	−0.959671	+	0.281126i	$0.909292\pi$
$272$	3.35521	−	5.81139i	0.203439	−	0.352367i
$273$	−0.177468	+	0.0130770i	−0.0107408	+	0.000791454i
$274$	−8.35802	−	14.4765i	−0.504926	−	0.874558i
$275$	−28.8145	+	7.72083i	−1.73758	+	0.465583i
$276$	0.0575347	−	0.912957i	0.00346318	−	0.0549536i
$277$	−16.9335	+	9.77658i	−1.01744	+	0.587418i	−0.913361	−	0.407151i	$-0.866522\pi$
$277$	−16.9335	+	9.77658i	−1.01744	+	0.587418i	−0.104077	+	0.994569i	$0.533189\pi$
$278$	−3.59552	−	3.59552i	−0.215645	−	0.215645i
$279$	−3.42066	+	2.65219i	−0.204790	+	0.158782i
$280$	0.0947706	−	0.0253937i	0.00566363	−	0.00151756i
$281$	7.92083	+	29.5609i	0.472517	+	1.76346i	0.630679	+	0.776044i	$0.282777\pi$
$281$	7.92083	+	29.5609i	0.472517	+	1.76346i	−0.158162	+	0.987413i	$0.550557\pi$
$282$	1.38833	+	0.0874927i	0.0826739	+	0.00521012i
$283$	−20.4545	−	11.8094i	−1.21589	−	0.701995i	−0.251855	−	0.967765i	$-0.581041\pi$
$283$	−20.4545	−	11.8094i	−1.21589	−	0.701995i	−0.964036	+	0.265770i	$0.914374\pi$
$284$	2.49988	+	9.32969i	0.148341	+	0.553615i
$285$	5.34153	+	10.7633i	0.316405	+	0.637561i
$286$	15.5653	+	1.96075i	0.920397	+	0.115942i
$287$			0.143178i			0.00845153i
$288$	−2.97233	+	0.406522i	−0.175146	+	0.0239546i
$289$	−14.0148	−	24.2744i	−0.824401	−	1.42790i
$290$	14.3014	+	24.7708i	0.839808	+	1.45459i
$291$	0.161535	+	0.801559i	0.00946935	+	0.0469882i
$292$	−6.53713	+	6.53713i	−0.382557	+	0.382557i
$293$	−15.6173	+	15.6173i	−0.912375	+	0.912375i	−0.996459	−	0.0840837i	$-0.973204\pi$
$293$	−15.6173	+	15.6173i	−0.912375	+	0.912375i	0.0840837	+	0.996459i	$0.473204\pi$
$294$	−9.09440	+	8.01610i	−0.530396	+	0.467508i
$295$	−24.6345	−	42.6683i	−1.43428	−	2.48424i
$296$	4.05413	+	7.02196i	0.235642	+	0.408143i
$297$	18.7037	−	12.7024i	1.08530	−	0.737069i
$298$		−	5.28728i		−	0.306284i
$299$	−1.15076	+	1.51719i	−0.0665504	+	0.0877416i
$300$	−11.8512	−	0.746864i	−0.684229	−	0.0431202i
$301$	0.0646178	+	0.241157i	0.00372451	+	0.0139001i
$302$	−8.43236	−	4.86843i	−0.485228	−	0.280147i
$303$	4.22779	+	8.51908i	0.242880	+	0.489408i
$304$	0.521462	+	1.94612i	0.0299079	+	0.111618i
$305$	0.0714854	−	0.0191545i	0.00409324	−	0.00109678i
$306$	−7.61032	+	18.6373i	−0.435053	+	1.06542i
$307$	2.99786	+	2.99786i	0.171097	+	0.171097i	0.787461	−	0.616364i	$-0.211395\pi$
$307$	2.99786	+	2.99786i	0.171097	+	0.171097i	−0.616364	+	0.787461i	$0.711395\pi$
$308$	−0.107374	+	0.0619924i	−0.00611820	+	0.00353234i
$309$	6.03642	+	4.01151i	0.343400	+	0.228207i
$310$	−4.79862	+	1.28579i	−0.272543	+	0.0730277i
$311$	−15.1300	−	26.2059i	−0.857943	−	1.48600i	−0.873888	−	0.486128i	$-0.838409\pi$
$311$	−15.1300	−	26.2059i	−0.857943	−	1.48600i	0.0159450	−	0.999873i	$-0.494924\pi$
$312$	5.62317	+	2.71661i	0.318349	+	0.153798i
$313$	−16.7332	+	28.9828i	−0.945817	+	1.63820i	−0.191710	+	0.981452i	$0.561403\pi$
$313$	−16.7332	+	28.9828i	−0.945817	+	1.63820i	−0.754107	+	0.656751i	$0.771930\pi$
$314$	2.49159	−	9.29875i	0.140609	−	0.524759i
$315$	−0.271366	+	0.114005i	−0.0152898	+	0.00642344i
$316$	2.44132	+	1.40950i	0.137335	+	0.0792905i
$317$	10.7787	−	2.88814i	0.605392	−	0.162214i	0.0569135	−	0.998379i	$-0.481874\pi$
$317$	10.7787	−	2.88814i	0.605392	−	0.162214i	0.548478	+	0.836165i	$0.315207\pi$
$318$	8.31541	+	2.79942i	0.466305	+	0.156984i
$319$	−25.5583	−	25.5583i	−1.43099	−	1.43099i
$320$	−3.32591	−	0.891175i	−0.185924	−	0.0498182i
$321$	−4.75122	−	3.15742i	−0.265187	−	0.176230i
$322$		−	0.0150492i		−	0.000838659i
$323$	13.0593	+	3.49922i	0.726638	+	0.194702i
$324$	8.66948	−	2.41664i	0.481638	−	0.134258i
$325$	19.6949	+	14.9382i	1.09247	+	0.828623i
$326$	−9.59929	−	5.54215i	−0.531655	−	0.306951i
$327$	12.5433	+	4.22274i	0.693643	+	0.233518i
$328$	2.51237	−	4.35155i	0.138722	−	0.240274i
$329$	0.0228853			0.00126171
$330$	25.4383	−	5.12648i	1.40033	−	0.282203i
$331$	−3.99853	−	1.07140i	−0.219779	−	0.0588897i	0.147249	−	0.989099i	$-0.452958\pi$
$331$	−3.99853	−	1.07140i	−0.219779	−	0.0588897i	−0.367028	+	0.930210i	$0.619625\pi$
$332$	−3.80210	−	14.1896i	−0.208668	−	0.778758i
$333$	−14.9048	−	19.2235i	−0.816778	−	1.05344i
$334$	7.46214	−	12.9248i	0.408310	−	0.707213i
$335$	−3.25372			−0.177770
$336$	−0.0483815	+	0.00975013i	−0.00263943	+	0.000531913i
$337$	14.3966	−	8.31187i	0.784232	−	0.452777i	−0.0536959	−	0.998557i	$-0.517100\pi$
$337$	14.3966	−	8.31187i	0.784232	−	0.452777i	0.837928	+	0.545781i	$0.183767\pi$
$338$	−6.62547	−	11.1849i	−0.360378	−	0.608381i
$339$	−0.902820	+	0.448046i	−0.0490345	+	0.0243345i
$340$	−16.3381	+	16.3381i	−0.886056	+	0.886056i
$341$	5.43678	−	3.13893i	0.294418	−	0.169982i
$342$	−2.34110	−	5.57253i	−0.126592	−	0.301328i
$343$	−0.282066	+	0.282066i	−0.0152301	+	0.0152301i
$344$	2.26772	−	8.46324i	0.122267	−	0.456307i
$345$	−1.00496	+	2.98514i	−0.0541052	+	0.160714i
$346$	−4.93316	+	18.4108i	−0.265208	+	0.989770i
$347$			20.3538i			1.09265i	0.837574	+	0.546324i	$0.183973\pi$
$347$			20.3538i			1.09265i	−0.837574	+	0.546324i	$0.816027\pi$
$348$	−6.39609	−	12.8882i	−0.342867	−	0.690882i
$349$	−13.8299	−	13.8299i	−0.740298	−	0.740298i	0.232337	−	0.972635i	$-0.425363\pi$
$349$	−13.8299	−	13.8299i	−0.740298	−	0.740298i	−0.972635	+	0.232337i	$0.925363\pi$
$350$	−0.195355			−0.0104422
$351$	−17.8183	−	5.78873i	−0.951069	−	0.308979i
$352$	4.35116			0.231918
$353$	−7.15642	−	7.15642i	−0.380898	−	0.380898i	0.490528	−	0.871426i	$-0.336804\pi$
$353$	−7.15642	−	7.15642i	−0.380898	−	0.380898i	−0.871426	+	0.490528i	$0.836804\pi$
$354$	11.0174	+	22.2003i	0.585570	+	1.17993i
$355$		−	33.2575i		−	1.76513i
$356$	2.91249	−	10.8696i	0.154362	−	0.576086i
$357$	−0.105668	+	0.313877i	−0.00559255	+	0.0166121i
$358$	6.23925	−	23.2852i	0.329754	−	1.23066i
$359$	1.10596	−	1.10596i	0.0583705	−	0.0583705i	−0.677319	−	0.735689i	$-0.736858\pi$
$359$	1.10596	−	1.10596i	0.0583705	−	0.0583705i	0.735689	+	0.677319i	$0.236858\pi$
$360$	10.2480	+	1.29681i	0.540116	+	0.0683478i
$361$	12.9390	−	7.47034i	0.681001	−	0.393176i
$362$	−0.823817	+	0.823817i	−0.0432988	+	0.0432988i
$363$	−12.3074	+	6.10786i	−0.645973	+	0.320579i
$364$	0.0951367	+	0.0387852i	0.00498652	+	0.00203290i
$365$	27.5676	−	15.9162i	1.44296	−	0.833091i
$366$	−0.0364941	+	0.00735452i	−0.00190758	+	0.000384427i
$367$	−6.23361			−0.325392			−0.162696	−	0.986676i	$-0.552019\pi$
$367$	−6.23361			−0.325392			−0.162696	+	0.986676i	$0.552019\pi$
$368$	−0.264071	+	0.457384i	−0.0137656	+	0.0238428i
$369$	−5.69858	+	13.9556i	−0.296656	+	0.726498i
$370$	−7.22588	−	26.9673i	−0.375656	−	1.40197i
$371$	0.139426	+	0.0373590i	0.00723863	+	0.00193958i
$372$	2.44975	−	0.493689i	0.127014	−	0.0255966i
$373$	−21.1091			−1.09299			−0.546493	−	0.837463i	$-0.684038\pi$
$373$	−21.1091			−1.09299			−0.546493	+	0.837463i	$0.684038\pi$
$374$	14.5990	−	25.2863i	0.754899	−	1.30752i
$375$	10.4896	+	3.53138i	0.541683	+	0.182360i
$376$	−0.695542	−	0.401572i	−0.0358699	−	0.0207095i
$377$	−3.74334	+	29.7163i	−0.192792	+	1.53047i
$378$	0.139842	−	0.0486488i	0.00719270	−	0.00250222i
$379$	1.28885	+	0.345346i	0.0662038	+	0.0177393i	0.291769	−	0.956489i	$-0.405756\pi$
$379$	1.28885	+	0.345346i	0.0662038	+	0.0177393i	−0.225565	+	0.974228i	$0.572423\pi$
$380$		−	6.93734i		−	0.355878i
$381$	−14.2632	−	9.47861i	−0.730726	−	0.485604i
$382$	11.1705	+	2.99313i	0.571534	+	0.153142i
$383$	−18.2839	−	18.2839i	−0.934261	−	0.934261i	0.0637072	−	0.997969i	$-0.479708\pi$
$383$	−18.2839	−	18.2839i	−0.934261	−	0.934261i	−0.997969	+	0.0637072i	$0.979708\pi$
$384$	1.64153	+	0.552626i	0.0837687	+	0.0282011i
$385$	0.412362	−	0.110492i	0.0210159	−	0.00563120i
$386$	−1.24711	−	0.720021i	−0.0634764	−	0.0366481i
$387$	−3.29991	+	26.0774i	−0.167744	+	1.32559i
$388$	0.122184	−	0.455998i	0.00620297	−	0.0231498i
$389$	−7.30331	+	12.6497i	−0.370292	+	0.641365i	−0.989610	−	0.143775i	$-0.954076\pi$
$389$	−7.30331	+	12.6497i	−0.370292	+	0.641365i	0.619318	+	0.785140i	$0.287409\pi$
$390$	−16.2812	−	14.0464i	−0.824429	−	0.711269i
$391$	1.77202	+	3.06924i	0.0896151	+	0.155218i
$392$	6.76070	−	1.81152i	0.341467	−	0.0914957i
$393$	26.1460	+	17.3753i	1.31889	+	0.876469i
$394$	−3.60016	+	2.07856i	−0.181374	+	0.104716i
$395$	−6.86351	−	6.86351i	−0.345341	−	0.345341i
$396$	−12.9331	+	1.76884i	−0.649912	+	0.0888878i
$397$	2.88194	−	0.772213i	0.144640	−	0.0387563i	−0.185772	−	0.982593i	$-0.559479\pi$
$397$	2.88194	−	0.772213i	0.144640	−	0.0387563i	0.330413	+	0.943837i	$0.392812\pi$
$398$	−0.533275	−	1.99021i	−0.0267307	−	0.0997601i
$399$	−0.0442040	−	0.0890719i	−0.00221297	−	0.00445917i
$400$	5.93735	+	3.42793i	0.296868	+	0.171397i
$401$	2.86637	+	10.6974i	0.143140	+	0.534205i	0.999831	+	0.0183755i	$0.00584944\pi$
$401$	2.86637	+	10.6974i	0.143140	+	0.534205i	−0.856691	+	0.515829i	$0.827484\pi$
$402$	1.63348	+	0.102942i	0.0814706	+	0.00513429i
$403$	−4.81715	−	1.96385i	−0.239960	−	0.0978264i
$404$		−	5.49087i		−	0.273181i
$405$	−30.9875	+	0.311492i	−1.53978	+	0.0154782i
$406$	−0.118352	−	0.204992i	−0.00587371	−	0.0101736i
$407$	17.6402	+	30.5537i	0.874391	+	1.51449i
$408$	8.71918	−	7.68536i	0.431664	−	0.380482i
$409$	10.3795	−	10.3795i	0.513233	−	0.513233i	−0.402283	−	0.915515i	$-0.631783\pi$
$409$	10.3795	−	10.3795i	0.513233	−	0.513233i	0.915515	+	0.402283i	$0.131783\pi$
$410$	−12.2339	+	12.2339i	−0.604189	+	0.604189i
$411$	−5.71980	−	28.3824i	−0.282137	−	1.40000i
$412$	−2.09226	−	3.62390i	−0.103078	−	0.178537i
$413$	0.203864	+	0.353103i	0.0100315	+	0.0173751i
$414$	0.598968	−	1.46685i	0.0294377	−	0.0720916i
$415$			50.5818i			2.48296i
$416$	−2.21088	−	2.84816i	−0.108397	−	0.139643i
$417$	−3.91515	−	7.88911i	−0.191726	−	0.386331i
$418$	2.26896	+	8.46789i	0.110979	+	0.414178i
$419$	24.3908	+	14.0820i	1.19157	+	0.687953i	0.958662	−	0.284546i	$-0.0918428\pi$
$419$	24.3908	+	14.0820i	1.19157	+	0.687953i	0.232907	+	0.972499i	$0.425176\pi$
$420$	0.169602	+	0.0106883i	0.00827571	+	0.000521536i
$421$	−1.88397	−	7.03106i	−0.0918189	−	0.342673i	0.904699	−	0.426051i	$-0.140096\pi$
$421$	−1.88397	−	7.03106i	−0.0918189	−	0.342673i	−0.996518	+	0.0833784i	$0.973429\pi$
$422$	18.4971	−	4.95629i	0.900425	−	0.241268i
$423$	2.23063	+	0.910849i	0.108457	+	0.0442870i
$424$	−3.58197	−	3.58197i	−0.173956	−	0.173956i
$425$	39.8421	−	23.0028i	1.93262	−	1.11580i
$426$	−1.05221	+	16.6964i	−0.0509798	+	0.808944i
$427$	−0.000591581	0	0.000158514i	−2.86286e−5	0	7.67101e-6i
$428$	1.64680	+	2.85234i	0.0796011	+	0.137873i
$429$	24.4673	+	11.8204i	1.18129	+	0.570696i
$430$	−15.0845	+	26.1270i	−0.727437	+	1.25996i
$431$	4.90556	−	18.3078i	0.236292	−	0.881855i	−0.741270	−	0.671207i	$-0.765776\pi$
$431$	4.90556	−	18.3078i	0.236292	−	0.881855i	0.977562	−	0.210648i	$-0.0675573\pi$
$432$	−5.10381	−	0.975270i	−0.245557	−	0.0469227i
$433$	27.2951	+	15.7588i	1.31172	+	0.757322i	0.982381	−	0.186890i	$-0.0598407\pi$
$433$	27.2951	+	15.7588i	1.31172	+	0.757322i	0.329339	+	0.944212i	$0.393174\pi$
$434$	0.0397112	−	0.0106406i	0.00190620	−	0.000510764i
$435$	9.78715	+	48.5652i	0.469258	+	2.32852i
$436$	−5.40316	−	5.40316i	−0.258764	−	0.258764i
$437$	−1.02783	−	0.275406i	−0.0491677	−	0.0131744i
$438$	−14.3434	+	7.11827i	−0.685356	+	0.340124i
$439$		−	12.8872i		−	0.615072i	−0.951536	−	0.307536i	$-0.900495\pi$
$439$		−	12.8872i		−	0.615072i	0.951536	−	0.307536i	$-0.0995045\pi$
$440$	−14.4716	−	3.87765i	−0.689905	−	0.184860i
$441$	−19.3586	+	8.13282i	−0.921838	+	0.387277i
$442$	−23.9697	+	3.29210i	−1.14012	+	0.156589i
$443$	−10.9018	−	6.29415i	−0.517959	−	0.299044i	0.218140	−	0.975917i	$-0.430001\pi$
$443$	−10.9018	−	6.29415i	−0.517959	−	0.299044i	−0.736099	+	0.676874i	$0.763334\pi$
$444$	2.77444	+	13.7671i	0.131669	+	0.653360i
$445$	−19.3734	+	33.5557i	−0.918386	+	1.59069i
$446$	−26.4199			−1.25102
$447$	2.92189	−	8.67920i	0.138201	−	0.410512i
$448$	0.0275237	+	0.00737496i	0.00130037	+	0.000348434i
$449$	1.16977	+	4.36565i	0.0552050	+	0.206028i	0.988020	−	0.154329i	$-0.0493216\pi$
$449$	1.16977	+	4.36565i	0.0552050	+	0.206028i	−0.932814	+	0.360357i	$0.882655\pi$
$450$	−19.0413	−	7.77528i	−0.897615	−	0.366530i
$451$	10.9317	−	18.9343i	0.514754	−	0.891581i
$452$	0.581902			0.0273704
$453$	−11.1515	−	12.6516i	−0.523944	−	0.594424i
$454$	−4.44628	+	2.56706i	−0.208674	+	0.120478i
$455$	−0.281852	−	0.213779i	−0.0132134	−	0.0100221i
$456$	−0.219485	+	3.48278i	−0.0102783	+	0.163096i
$457$	7.19189	−	7.19189i	0.336422	−	0.336422i	−0.518597	−	0.855019i	$-0.673545\pi$
$457$	7.19189	−	7.19189i	0.336422	−	0.336422i	0.855019	+	0.518597i	$0.173545\pi$
$458$	−6.87691	+	3.97039i	−0.321337	+	0.185524i
$459$	−22.7920	+	26.3880i	−1.06384	+	1.23168i
$460$	1.28588	−	1.28588i	0.0599547	−	0.0599547i
$461$	7.04174	−	26.2801i	0.327966	−	1.22399i	−0.583330	−	0.812236i	$-0.698250\pi$
$461$	7.04174	−	26.2801i	0.327966	−	1.22399i	0.911296	−	0.411752i	$-0.135083\pi$
$462$	−0.210516	+	0.0424244i	−0.00979408	+	0.00197376i
$463$	−3.06727	+	11.4472i	−0.142548	+	0.531996i	0.857304	+	0.514810i	$0.172138\pi$
$463$	−3.06727	+	11.4472i	−0.142548	+	0.531996i	−0.999852	+	0.0171864i	$0.994529\pi$
$464$			8.30696i			0.385641i
$465$	−8.58761	−	0.541192i	−0.398241	−	0.0250972i
$466$	−0.169941	−	0.169941i	−0.00787238	−	0.00787238i
$467$	0.615879			0.0284995			0.0142497	−	0.999898i	$-0.495464\pi$
$467$	0.615879			0.0284995			0.0142497	+	0.999898i	$0.495464\pi$
$468$	7.72930	+	7.56690i	0.357287	+	0.349780i
$469$	0.0269263			0.00124334
$470$	1.95544	+	1.95544i	0.0901977	+	0.0901977i
$471$	9.22874	−	13.8872i	0.425238	−	0.639889i
$472$		−	14.3089i		−	0.658623i
$473$	9.86721	−	36.8249i	0.453695	−	1.69321i
$474$	3.22857	+	3.66286i	0.148293	+	0.168241i
$475$	−3.57507	+	13.3423i	−0.164036	+	0.612189i
$476$	0.135206	−	0.135206i	0.00619718	−	0.00619718i
$477$	12.1029	+	9.19063i	0.554155	+	0.420810i
$478$	5.82418	−	3.36259i	0.266392	−	0.153801i
$479$	−14.1707	+	14.1707i	−0.647474	+	0.647474i	−0.952382	−	0.304908i	$-0.901374\pi$
$479$	−14.1707	+	14.1707i	−0.647474	+	0.647474i	0.304908	+	0.952382i	$0.401374\pi$
$480$	−4.96708	−	3.30087i	−0.226715	−	0.150663i
$481$	11.0365	−	27.0715i	0.503220	−	1.23436i
$482$	22.4739	−	12.9753i	1.02366	−	0.591010i
$483$	0.00831658	−	0.0247036i	0.000378418	−	0.00112405i
$484$	7.93261			0.360573
$485$	−0.812748	+	1.40772i	−0.0369050	+	0.0639213i
$486$	15.5667	+	0.824012i	0.706118	+	0.0373779i
$487$	−5.47316	−	20.4261i	−0.248012	−	0.925595i	−0.971845	−	0.235620i	$-0.924288\pi$
$487$	−5.47316	−	20.4261i	−0.248012	−	0.925595i	0.723833	−	0.689975i	$-0.242379\pi$
$488$	0.0207611	+	0.00556292i	0.000939812	+	0.000251822i
$489$	−12.6947	−	14.4024i	−0.574076	−	0.651299i
$490$	−24.0998			−1.08872
$491$	−9.87564	+	17.1051i	−0.445681	+	0.771943i	−0.998099	−	0.0616246i	$-0.980372\pi$
$491$	−9.87564	+	17.1051i	−0.445681	+	0.771943i	0.552418	+	0.833567i	$0.313705\pi$
$492$	6.52889	−	5.75477i	0.294345	−	0.259445i
$493$	48.2750	+	27.8716i	2.17420	+	1.25527i
$494$	4.38998	−	5.78784i	0.197514	−	0.260407i
$495$	44.5906	+	5.64262i	2.00420	+	0.253617i
$496$	−1.39364	−	0.373424i	−0.0625761	−	0.0167672i
$497$			0.275224i			0.0123455i
$498$	1.60032	−	25.3938i	0.0717121	−	1.13792i
$499$	5.12859	+	1.37420i	0.229587	+	0.0615177i	0.371778	−	0.928321i	$-0.378748\pi$
$499$	5.12859	+	1.37420i	0.229587	+	0.0615177i	−0.142191	+	0.989839i	$0.545415\pi$
$500$	−4.51854	−	4.51854i	−0.202075	−	0.202075i
$501$	19.3919	−	17.0926i	0.866365	−	0.763641i
$502$	19.8602	−	5.32152i	0.886403	−	0.237511i
$503$	16.2322	+	9.37164i	0.723756	+	0.417861i	0.816134	−	0.577863i	$-0.196113\pi$
$503$	16.2322	+	9.37164i	0.723756	+	0.417861i	−0.0923776	+	0.995724i	$0.529447\pi$
$504$	−0.0848076	−	0.0107318i	−0.00377763	−	0.000478032i
$505$	−4.89333	+	18.2621i	−0.217750	+	0.812654i
$506$	−1.14901	+	1.99015i	−0.0510799	+	0.0884731i
$507$	−4.69479	−	22.0218i	−0.208503	−	0.978022i
$508$	4.94371	+	8.56275i	0.219342	+	0.379911i
$509$	−16.5036	+	4.42212i	−0.731509	+	0.196007i	−0.605301	−	0.795997i	$-0.706947\pi$
$509$	−16.5036	+	4.42212i	−0.731509	+	0.196007i	−0.126208	+	0.992004i	$0.540281\pi$
$510$	−35.8482	+	17.7905i	−1.58738	+	0.787777i
$511$	−0.228137	+	0.131715i	−0.0100922	+	0.00582673i
$512$	−0.707107	−	0.707107i	−0.0312500	−	0.0312500i
$513$	−0.763446	−	10.4412i	−0.0337070	−	0.460990i
$514$	−14.9121	+	3.99567i	−0.657743	+	0.176242i
$515$	3.72914	+	13.9173i	0.164325	+	0.613271i
$516$	8.39952	−	12.6394i	0.369768	−	0.556419i
$517$	−3.02642	−	1.74730i	−0.133102	−	0.0768463i
$518$	0.0597981	+	0.223169i	0.00262738	+	0.00980550i
$519$	−18.2722	+	27.4956i	−0.802060	+	1.20692i
$520$	4.81497	+	11.4430i	0.211150	+	0.501809i
$521$			6.18564i			0.270998i	0.990777	+	0.135499i	$0.0432637\pi$
$521$			6.18564i			0.270998i	−0.990777	+	0.135499i	$0.956736\pi$
$522$	−3.37697	−	24.6910i	−0.147806	−	1.08070i
$523$	3.32093	+	5.75201i	0.145214	+	0.251518i	0.929453	−	0.368941i	$-0.120280\pi$
$523$	3.32093	+	5.75201i	0.145214	+	0.251518i	−0.784239	+	0.620459i	$0.786946\pi$
$524$	−9.06236	−	15.6965i	−0.395891	−	0.685703i
$525$	−0.320681	−	0.107959i	−0.0139957	−	0.00471170i
$526$	−8.92605	+	8.92605i	−0.389194	+	0.389194i
$527$	−6.84605	+	6.84605i	−0.298219	+	0.298219i
$528$	7.14254	+	2.40457i	0.310839	+	0.104645i
$529$	11.3605	+	19.6770i	0.493936	+	0.855523i
$530$	8.72113	+	15.1054i	0.378822	+	0.656139i
$531$	5.81691	+	42.5309i	0.252432	+	1.84568i
$532$			0.0574102i			0.00248905i
$533$	−17.9484	+	2.46512i	−0.777433	+	0.106776i
$534$	10.7877	−	16.2332i	0.466831	−	0.702477i
$535$	−2.93517	−	10.9542i	−0.126899	−	0.473592i
$536$	−0.818361	−	0.472481i	−0.0353478	−	0.0204081i
$537$	23.1099	−	34.7752i	0.997265	−	1.50066i
$538$	−4.05479	−	15.1327i	−0.174814	−	0.652416i
$539$	29.4169	−	7.88223i	1.26708	−	0.339512i
$540$	16.1057	+	7.79204i	0.693077	+	0.335316i
$541$	4.34283	+	4.34283i	0.186713	+	0.186713i	0.794273	−	0.607561i	$-0.207852\pi$
$541$	4.34283	+	4.34283i	0.186713	+	0.186713i	−0.607561	+	0.794273i	$0.707852\pi$
$542$	14.8248	−	8.55909i	0.636779	−	0.367644i
$543$	−1.80758	+	0.897053i	−0.0775706	+	0.0384962i
$544$	−6.48176	+	1.73678i	−0.277903	+	0.0744639i
$545$	13.1553	+	22.7856i	0.563509	+	0.976027i
$546$	0.134736	+	0.116242i	0.00576615	+	0.00497469i
$547$	−16.4189	+	28.4384i	−0.702022	+	1.21594i	0.265733	+	0.964047i	$0.414386\pi$
$547$	−16.4189	+	28.4384i	−0.702022	+	1.21594i	−0.967755	+	0.251892i	$0.918947\pi$
$548$	−4.32643	+	16.1465i	−0.184816	+	0.689742i
$549$	−0.0639703	−	0.00809498i	−0.00273019	−	0.000345486i
$550$	25.8344	+	14.9155i	1.10158	+	0.635999i
$551$	−16.1664	+	4.33176i	−0.688710	+	0.184539i
$552$	−0.686241	+	0.604875i	−0.0292084	+	0.0257452i
$553$	0.0567993	+	0.0567993i	0.00241535	+	0.00241535i
$554$	18.8869	+	5.06073i	0.802428	+	0.215010i
$555$	3.04140	−	48.2608i	0.129100	−	2.04856i
$556$			5.08483i			0.215645i
$557$	7.73861	+	2.07355i	0.327895	+	0.0878593i	0.419011	−	0.907981i	$-0.362377\pi$
$557$	7.73861	+	2.07355i	0.327895	+	0.0878593i	−0.0911160	+	0.995840i	$0.529043\pi$
$558$	4.29415	+	0.543394i	0.181786	+	0.0230037i
$559$	−29.1183	+	12.2524i	−1.23157	+	0.518220i
$560$	−0.0849690	−	0.0490569i	−0.00359059	−	0.00207303i
$561$	37.9386	−	33.4403i	1.60177	−	1.41185i
$562$	15.3019	−	26.5036i	0.645470	−	1.11799i
$563$	14.8846			0.627313			0.313656	−	0.949537i	$-0.398446\pi$
$563$	14.8846			0.627313			0.313656	+	0.949537i	$0.398446\pi$
$564$	−0.919831	−	1.04356i	−0.0387319	−	0.0439420i
$565$	−1.93535	−	0.518576i	−0.0814209	−	0.0218167i
$566$	6.11299	+	22.8140i	0.256948	+	0.958943i
$567$	0.256439	−	0.00257777i	0.0107694	−	0.000108256i
$568$	4.82940	−	8.36477i	0.202637	−	0.350978i
$569$	−8.90454			−0.373298			−0.186649	−	0.982427i	$-0.559763\pi$
$569$	−8.90454			−0.373298			−0.186649	+	0.982427i	$0.559763\pi$
$570$	3.83375	−	11.3878i	0.160578	−	0.476983i
$571$	−0.862884	+	0.498186i	−0.0361106	+	0.0208484i	−0.517947	−	0.855413i	$-0.673303\pi$
$571$	−0.862884	+	0.498186i	−0.0361106	+	0.0208484i	0.481836	+	0.876261i	$0.339970\pi$
$572$	−9.61989	−	12.3928i	−0.402228	−	0.518169i
$573$	16.6826	+	11.0864i	0.696926	+	0.463142i
$574$	0.101242	−	0.101242i	0.00422576	−	0.00422576i
$575$	−3.13576	+	1.81043i	−0.130770	+	0.0755003i
$576$	2.38921	+	1.81430i	0.0995504	+	0.0755958i
$577$	−15.1503	+	15.1503i	−0.630713	+	0.630713i	−0.948247	−	0.317534i	$-0.897145\pi$
$577$	−15.1503	+	15.1503i	−0.630713	+	0.630713i	0.317534	+	0.948247i	$0.397145\pi$
$578$	−7.25460	+	27.0745i	−0.301752	+	1.12615i
$579$	−1.64926	−	1.87112i	−0.0685411	−	0.0777611i
$580$	7.40295	−	27.6282i	0.307391	−	1.14720i
$581$		−	0.418592i		−	0.0173661i
$582$	0.452565	−	0.681010i	0.0187594	−	0.0282288i
$583$	−15.5857	−	15.5857i	−0.645494	−	0.645494i
$584$	9.24490			0.382557
$585$	−18.9635	−	32.0550i	−0.784045	−	1.32531i
$586$	22.0863			0.912375
$587$	−4.52599	−	4.52599i	−0.186808	−	0.186808i	0.607507	−	0.794314i	$-0.292170\pi$
$587$	−4.52599	−	4.52599i	−0.186808	−	0.186808i	−0.794314	+	0.607507i	$0.792170\pi$
$588$	12.0989	+	0.762477i	0.498952	+	0.0314440i
$589$		−	2.90691i		−	0.119777i
$590$	−12.7518	+	47.5903i	−0.524982	+	1.95926i
$591$	−7.05842	+	1.42246i	−0.290345	+	0.0585120i
$592$	2.09857	−	7.83198i	0.0862508	−	0.321892i
$593$	−24.4287	+	24.4287i	−1.00317	+	1.00317i	−0.00317304	+	0.999995i	$0.501010\pi$
$593$	−24.4287	+	24.4287i	−1.00317	+	1.00317i	−0.999995	+	0.00317304i	$0.998990\pi$
$594$	−22.2075	−	4.24356i	−0.911184	−	0.174115i
$595$	−0.570177	+	0.329192i	−0.0233750	+	0.0134955i
$596$	−3.73867	+	3.73867i	−0.153142	+	0.153142i
$597$	0.224457	−	3.56168i	0.00918643	−	0.145770i
$598$	1.88653	−	0.259104i	0.0771460	−	0.0105956i
$599$	36.9806	−	21.3507i	1.51099	−	0.872368i	0.511068	−	0.859540i	$-0.329250\pi$
$599$	36.9806	−	21.3507i	1.51099	−	0.872368i	0.999918	−	0.0128274i	$-0.00408321\pi$
$600$	7.85195	+	8.90817i	0.320554	+	0.363675i
$601$	−27.0330			−1.10270			−0.551349	−	0.834275i	$-0.685887\pi$
$601$	−27.0330			−1.10270			−0.551349	+	0.834275i	$0.685887\pi$
$602$	0.124832	−	0.216215i	0.00508777	−	0.00881228i
$603$	2.62451	+	1.07169i	0.106878	+	0.0436424i
$604$	2.52008	+	9.40508i	0.102541	+	0.382687i
$605$	−26.3831	−	7.06934i	−1.07263	−	0.287410i
$606$	3.03440	−	9.01340i	0.123264	−	0.366144i
$607$	47.0756			1.91074			0.955370	−	0.295412i	$-0.0954569\pi$
$607$	47.0756			1.91074			0.955370	+	0.295412i	$0.0954569\pi$
$608$	1.00739	−	1.74484i	0.0408549	−	0.0707628i
$609$	−0.0809940	−	0.401903i	−0.00328204	−	0.0162859i
$610$	−0.0640921	−	0.0370036i	−0.00259501	−	0.00149823i
$611$	0.394019	+	2.86884i	0.0159403	+	0.116061i
$612$	18.5599	−	7.79727i	0.750239	−	0.315186i
$613$	22.7568	+	6.09767i	0.919139	+	0.246283i	0.687217	−	0.726452i	$-0.258832\pi$
$613$	22.7568	+	6.09767i	0.919139	+	0.246283i	0.231922	+	0.972734i	$0.425499\pi$
$614$		−	4.23961i		−	0.171097i
$615$	−26.8430	+	13.3215i	−1.08241	+	0.537174i
$616$	0.119760	+	0.0320896i	0.00482527	+	0.00129293i
$617$	−3.43163	−	3.43163i	−0.138152	−	0.138152i	0.634649	−	0.772801i	$-0.281145\pi$
$617$	−3.43163	−	3.43163i	−0.138152	−	0.138152i	−0.772801	+	0.634649i	$0.781145\pi$
$618$	−1.43183	−	7.10496i	−0.0575968	−	0.285803i
$619$	24.6854	−	6.61442i	0.992188	−	0.265856i	0.274019	−	0.961724i	$-0.411647\pi$
$619$	24.6854	−	6.61442i	0.992188	−	0.265856i	0.718170	+	0.695868i	$0.244980\pi$
$620$	4.30232	+	2.48395i	0.172785	+	0.0997577i
$621$	1.79384	−	2.07686i	0.0719843	−	0.0833415i
$622$	−7.83186	+	29.2289i	−0.314029	+	1.17197i
$623$	0.160325	−	0.277691i	0.00642329	−	0.0111255i
$624$	−2.05524	−	5.89712i	−0.0822756	−	0.236074i
$625$	−6.13822	−	10.6317i	−0.245529	−	0.425268i
$626$	32.3261	−	8.66175i	1.29201	−	0.346193i
$627$	−0.955016	+	15.1541i	−0.0381397	+	0.605198i
$628$	−8.33703	+	4.81339i	−0.332684	+	0.192075i
$629$	−38.4735	−	38.4735i	−1.53404	−	1.53404i
$630$	0.272498	+	0.111271i	0.0108566	+	0.00443316i
$631$	18.8379	−	5.04759i	0.749924	−	0.200942i	0.136440	−	0.990648i	$-0.456434\pi$
$631$	18.8379	−	5.04759i	0.749924	−	0.200942i	0.613484	+	0.789707i	$0.289767\pi$
$632$	−0.729610	−	2.72294i	−0.0290223	−	0.108313i
$633$	33.1024	+	2.08612i	1.31570	+	0.0829158i
$634$	−9.66391	−	5.57946i	−0.383803	−	0.221589i
$635$	−8.81142	−	32.8847i	−0.349670	−	1.30499i
$636$	−3.90040	−	7.85937i	−0.154661	−	0.311644i
$637$	−20.1066	−	15.2505i	−0.796652	−	0.604246i
$638$			36.1449i			1.43099i
$639$	−10.9541	+	26.8261i	−0.433338	+	1.06122i
$640$	1.72162	+	2.98193i	0.0680529	+	0.117871i
$641$	−11.4390	−	19.8130i	−0.451814	−	0.782566i	0.546684	−	0.837339i	$-0.315890\pi$
$641$	−11.4390	−	19.8130i	−0.451814	−	0.782566i	−0.998499	+	0.0547731i	$0.982556\pi$
$642$	1.12699	+	5.59225i	0.0444786	+	0.220709i
$643$	9.35496	−	9.35496i	0.368924	−	0.368924i	−0.498161	−	0.867085i	$-0.665991\pi$
$643$	9.35496	−	9.35496i	0.368924	−	0.368924i	0.867085	+	0.498161i	$0.165991\pi$
$644$	−0.0106414	+	0.0106414i	−0.000419330	+	0.000419330i
$645$	−39.2000	+	34.5521i	−1.54350	+	1.36049i
$646$	−6.75998	−	11.7086i	−0.265968	−	0.460670i
$647$	−5.87399	−	10.1741i	−0.230930	−	0.399983i	0.727152	−	0.686477i	$-0.240844\pi$
$647$	−5.87399	−	10.1741i	−0.230930	−	0.399983i	−0.958082	+	0.286493i	$0.907510\pi$
$648$	−7.83907	−	4.42143i	−0.307948	−	0.173690i
$649$		−	62.2606i		−	2.44394i
$650$	−3.36346	−	24.4893i	−0.131926	−	0.960548i
$651$	0.0710671	+	0.00447866i	0.00278534	+	0.000175533i
$652$	2.86883	+	10.7066i	0.112352	+	0.419303i
$653$	−7.98654	−	4.61103i	−0.312537	−	0.180444i	0.335524	−	0.942032i	$-0.391087\pi$
$653$	−7.98654	−	4.61103i	−0.312537	−	0.180444i	−0.648061	+	0.761588i	$0.724420\pi$
$654$	−5.88349	−	11.8553i	−0.230063	−	0.463581i
$655$	16.1523	+	60.2811i	0.631122	+	2.35538i
$656$	−4.85352	+	1.30050i	−0.189498	+	0.0507759i
$657$	−27.4789	+	3.75826i	−1.07205	+	0.146624i
$658$	−0.0161823	−	0.0161823i	−0.000630853	−	0.000630853i
$659$	3.69702	−	2.13448i	0.144015	−	0.0831474i	−0.426261	−	0.904600i	$-0.640169\pi$
$659$	3.69702	−	2.13448i	0.144015	−	0.0831474i	0.570276	+	0.821453i	$0.306836\pi$
$660$	−21.6126	−	14.3626i	−0.841268	−	0.559064i
$661$	43.1340	−	11.5577i	1.67772	−	0.449543i	0.710543	−	0.703654i	$-0.248449\pi$
$661$	43.1340	−	11.5577i	1.67772	−	0.449543i	0.967175	+	0.254110i	$0.0817827\pi$
$662$	2.06979	+	3.58499i	0.0804448	+	0.139335i
$663$	−41.1662	−	7.84222i	−1.59876	−	0.304567i
$664$	−7.34510	+	12.7221i	−0.285045	+	0.493713i
$665$	0.0511626	−	0.190941i	0.00198400	−	0.00740438i
$666$	−3.05377	+	24.1323i	−0.118331	+	0.935109i
$667$	−3.79947	−	2.19363i	−0.147116	−	0.0849375i
$668$	−14.4157	+	3.86269i	−0.557762	+	0.149452i
$669$	−43.3689	−	14.6003i	−1.67674	−	0.564481i
$670$	2.30073	+	2.30073i	0.0888850	+	0.0888850i
$671$	0.0903350	+	0.0242052i	0.00348734	+	0.000934431i
$672$	0.0411053	+	0.0273165i	0.00158567	+	0.00105376i
$673$			5.63994i			0.217404i	0.994074	+	0.108702i	$0.0346694\pi$
$673$			5.63994i			0.217404i	−0.994074	+	0.108702i	$0.965331\pi$
$674$	−16.0573	−	4.30254i	−0.618504	−	0.165728i
$675$	−26.9599	−	23.2860i	−1.03769	−	0.896280i
$676$	−3.22404	+	12.5939i	−0.124001	+	0.484380i
$677$	−21.2676	−	12.2789i	−0.817381	−	0.471915i	0.0321318	−	0.999484i	$-0.489770\pi$
$677$	−21.2676	−	12.2789i	−0.817381	−	0.471915i	−0.849512	+	0.527569i	$0.823104\pi$
$678$	0.955206	+	0.321574i	0.0366845	+	0.0123500i
$679$	0.00672593	−	0.0116497i	0.000258118	−	0.000447073i
$680$	23.1055			0.886056
$681$	−8.71731	+	1.75676i	−0.334048	+	0.0673194i
$682$	−6.06394	−	1.62483i	−0.232200	−	0.0622179i
$683$	−7.16139	−	26.7267i	−0.274023	−	1.02267i	−0.956493	−	0.291755i	$-0.905761\pi$
$683$	−7.16139	−	26.7267i	−0.274023	−	1.02267i	0.682470	−	0.730913i	$-0.260906\pi$
$684$	−2.28497	+	5.59578i	−0.0873679	+	0.213960i
$685$	28.7786	−	49.8460i	1.09957	−	1.90452i
$686$	0.398902			0.0152301
$687$	−13.4828	+	2.71713i	−0.514400	+	0.103665i
$688$	−7.58793	+	4.38090i	−0.289287	+	0.167020i
$689$	−2.28272	+	18.1213i	−0.0869648	+	0.690367i
$690$	2.82143	−	1.40020i	0.107410	−	0.0533046i
$691$	−5.58645	+	5.58645i	−0.212518	+	0.212518i	−0.805336	−	0.592818i	$-0.798015\pi$
$691$	−5.58645	+	5.58645i	−0.212518	+	0.212518i	0.592818	+	0.805336i	$0.298015\pi$
$692$	16.5067	−	9.53013i	0.627489	−	0.362281i
$693$	−0.369012	−	0.0466958i	−0.0140176	−	0.00177383i
$694$	14.3923	−	14.3923i	0.546324	−	0.546324i
$695$	4.53147	−	16.9117i	0.171888	−	0.641496i
$696$	−4.59064	+	13.6361i	−0.174008	+	0.516875i
$697$	−8.72687	+	32.5691i	−0.330554	+	1.23364i
$698$			19.5584i			0.740298i
$699$	−0.185049	−	0.372877i	−0.00699920	−	0.0141035i
$700$	0.138137	+	0.138137i	0.00522109	+	0.00522109i
$701$	−39.9569			−1.50915			−0.754575	−	0.656214i	$-0.772157\pi$
$701$	−39.9569			−1.50915			−0.754575	+	0.656214i	$0.772157\pi$
$702$	8.50617	+	16.6927i	0.321045	+	0.630024i
$703$	16.3363			0.616136
$704$	−3.07674	−	3.07674i	−0.115959	−	0.115959i
$705$	2.12928	+	4.29053i	0.0801932	+	0.161591i
$706$			10.1207i			0.380898i
$707$	0.0404949	−	0.151129i	0.00152297	−	0.00568380i
$708$	7.90750	−	23.4885i	0.297182	−	0.882752i
$709$	−13.1727	+	49.1613i	−0.494712	+	1.84629i	0.0369258	+	0.999318i	$0.488243\pi$
$709$	−13.1727	+	49.1613i	−0.494712	+	1.84629i	−0.531638	+	0.846972i	$0.678423\pi$
$710$	−23.5166	+	23.5166i	−0.882564	+	0.882564i
$711$	3.27558	+	7.79687i	0.122844	+	0.292406i
$712$	−9.74539	+	5.62650i	−0.365224	+	0.210862i
$713$	0.538817	−	0.538817i	0.0201789	−	0.0201789i
$714$	0.296663	−	0.147226i	0.0111023	−	0.00550980i
$715$	20.9507	+	49.7904i	0.783513	+	1.86205i
$716$	−20.8769	+	12.0533i	−0.780207	+	0.450453i
$717$	11.4188	−	2.30118i	0.426442	−	0.0859393i
$718$	−1.56407			−0.0583705
$719$	0.750575	−	1.30003i	0.0279917	−	0.0484831i	−0.851690	−	0.524046i	$-0.824422\pi$
$719$	0.750575	−	1.30003i	0.0279917	−	0.0484831i	0.879682	+	0.475563i	$0.157755\pi$
$720$	−6.32943	−	8.16340i	−0.235884	−	0.304232i
$721$	−0.0308606	−	0.115173i	−0.00114931	−	0.00428928i
$722$	−14.4316	−	3.86693i	−0.537088	−	0.143912i
$723$	44.0620	−	8.87965i	1.63868	−	0.330238i
$724$	1.16505			0.0432988
$725$	−28.4757	+	49.3214i	−1.05756	+	1.83175i
$726$	13.0216	+	4.38377i	0.483276	+	0.162697i
$727$	−41.9032	−	24.1928i	−1.55410	−	0.897261i	−0.997801	−	0.0662809i	$-0.978887\pi$
$727$	−41.9032	−	24.1928i	−1.55410	−	0.897261i	−0.556301	−	0.830981i	$-0.687780\pi$
$728$	−0.0398465	−	0.0946971i	−0.00147681	−	0.00350971i
$729$	25.0977	+	9.95518i	0.929544	+	0.368710i
$730$	−30.7477	−	8.23882i	−1.13802	−	0.304932i
$731$			58.7952i			2.17462i
$732$	0.0310057	+	0.0206048i	0.00114600	+	0.000761576i
$733$	22.9793	+	6.15729i	0.848761	+	0.227425i	0.656882	−	0.753994i	$-0.271875\pi$
$733$	22.9793	+	6.15729i	0.848761	+	0.227425i	0.191879	+	0.981419i	$0.438542\pi$
$734$	4.40783	+	4.40783i	0.162696	+	0.162696i
$735$	−39.5605	−	13.3182i	−1.45921	−	0.491249i
$736$	0.510146	−	0.136693i	0.0188042	−	0.00503857i
$737$	−3.56082	−	2.05584i	−0.131164	−	0.0757279i
$738$	13.8976	−	5.83857i	0.511577	−	0.214921i
$739$	12.0076	−	44.8128i	0.441705	−	1.64847i	−0.282786	−	0.959183i	$-0.591259\pi$
$739$	12.0076	−	44.8128i	0.441705	−	1.64847i	0.724491	−	0.689284i	$-0.242075\pi$
$740$	−13.9593	+	24.1783i	−0.513155	+	0.888811i
$741$	10.4048	−	7.07487i	0.382229	−	0.259902i
$742$	−0.0721721	−	0.125006i	−0.00264952	−	0.00458911i
$743$	−34.8450	+	9.33669i	−1.27834	+	0.342530i	−0.833220	−	0.552941i	$-0.813505\pi$
$743$	−34.8450	+	9.33669i	−1.27834	+	0.342530i	−0.445119	+	0.895471i	$0.646839\pi$
$744$	−2.08133	−	1.38314i	−0.0763051	−	0.0507085i
$745$	15.7663	−	9.10267i	0.577632	−	0.333496i
$746$	14.9264	+	14.9264i	0.546493	+	0.546493i
$747$	16.6602	−	40.8002i	0.609566	−	1.49280i
$748$	−28.2032	+	7.55702i	−1.03121	+	0.276312i
$749$	0.0242902	+	0.0906521i	0.000887543	+	0.00331236i
$750$	−4.92023	−	9.91436i	−0.179661	−	0.362021i
$751$	−15.1601	−	8.75269i	−0.553200	−	0.319390i	0.197212	−	0.980361i	$-0.436811\pi$
$751$	−15.1601	−	8.75269i	−0.553200	−	0.319390i	−0.750412	+	0.660971i	$0.770145\pi$
$752$	0.207869	+	0.775777i	0.00758019	+	0.0282897i
$753$	35.5418	+	2.23985i	1.29521	+	0.0816246i
$754$	23.6596	−	18.3657i	0.861630	−	0.668839i
$755$		−	33.5263i		−	1.22015i
$756$	−0.133283	−	0.0644834i	−0.00484746	−	0.00234524i
$757$	0.816598	+	1.41439i	0.0296798	+	0.0514068i	0.880484	−	0.474076i	$-0.157218\pi$
$757$	0.816598	+	1.41439i	0.0296798	+	0.0514068i	−0.850804	+	0.525483i	$0.823885\pi$
$758$	−0.667158	−	1.15555i	−0.0242323	−	0.0419715i
$759$	−2.98595	+	2.63191i	−0.108383	+	0.0955322i
$760$	−4.90544	+	4.90544i	−0.177939	+	0.177939i
$761$	12.5216	−	12.5216i	0.453909	−	0.453909i	−0.442741	−	0.896650i	$-0.645994\pi$
$761$	12.5216	−	12.5216i	0.453909	−	0.453909i	0.896650	+	0.442741i	$0.145994\pi$
$762$	3.38322	+	16.7880i	0.122561	+	0.608165i
$763$	−0.108867	−	0.188563i	−0.00394125	−	0.00682644i
$764$	−5.78229	−	10.0152i	−0.209196	−	0.362338i
$765$	−68.6772	+	9.39291i	−2.48303	+	0.339601i
$766$			25.8573i			0.934261i
$767$	−40.7542	+	31.6353i	−1.47155	+	1.14229i
$768$	−0.769968	−	1.55150i	−0.0277838	−	0.0559849i
$769$	5.30157	+	19.7857i	0.191179	+	0.713492i	0.993223	+	0.116226i	$0.0370796\pi$
$769$	5.30157	+	19.7857i	0.191179	+	0.713492i	−0.802043	+	0.597266i	$0.796254\pi$
$770$	−0.369714	−	0.213454i	−0.0133236	−	0.00769236i
$771$	−26.6866	−	1.68179i	−0.961096	−	0.0605684i
$772$	0.372710	+	1.39097i	0.0134141	+	0.0500622i
$773$	−8.74973	+	2.34448i	−0.314706	+	0.0843252i	−0.412715	−	0.910860i	$-0.635419\pi$
$773$	−8.74973	+	2.34448i	−0.314706	+	0.0843252i	0.0980088	+	0.995186i	$0.468753\pi$
$774$	20.7729	−	16.1061i	0.746667	−	0.578923i
$775$	−6.99444	−	6.99444i	−0.251248	−	0.251248i
$776$	−0.408837	+	0.236042i	−0.0146764	+	0.00847342i
$777$	−0.0251692	+	0.399384i	−0.000902942	+	0.0143278i
$778$	14.1089	−	3.78047i	0.505829	−	0.135536i
$779$	−5.06185	−	8.76738i	−0.181360	−	0.314124i
$780$	1.58019	+	21.4449i	0.0565800	+	0.767849i
$781$	21.0135	−	36.3965i	0.751923	−	1.30237i
$782$	0.917267	−	3.42329i	0.0328014	−	0.122416i
$783$	8.10153	−	42.3971i	0.289525	−	1.51515i
$784$	−6.06147	−	3.49959i	−0.216481	−	0.124986i
$785$	32.0178	−	8.57914i	1.14276	−	0.306203i
$786$	−6.20181	−	30.7742i	−0.221211	−	1.09768i
$787$	−13.3787	−	13.3787i	−0.476900	−	0.476900i	0.427239	−	0.904139i	$-0.359486\pi$
$787$	−13.3787	−	13.3787i	−0.476900	−	0.476900i	−0.904139	+	0.427239i	$0.859486\pi$
$788$	4.01546	+	1.07594i	0.143045	+	0.0383288i
$789$	−19.5851	+	9.71956i	−0.697248	+	0.346026i
$790$			9.70646i			0.345341i
$791$	0.0160161	+	0.00429150i	0.000569467	+	0.000152588i
$792$	10.3958	+	7.89431i	0.369400	+	0.280512i
$793$	−0.0300562	−	0.0714299i	−0.00106733	−	0.00253655i
$794$	−2.58388	−	1.49180i	−0.0916983	−	0.0529421i
$795$	5.96830	+	29.6155i	0.211674	+	1.05035i
$796$	−1.03021	+	1.78437i	−0.0365147	+	0.0632454i
$797$	33.7072			1.19397			0.596986	−	0.802252i	$-0.296365\pi$
$797$	33.7072			1.19397			0.596986	+	0.802252i	$0.296365\pi$
$798$	−0.0317264	+	0.0942403i	−0.00112310	+	0.00333607i
$799$	5.20578	+	1.39488i	0.184167	+	0.0493475i
$800$	−1.77443	−	6.62226i	−0.0627355	−	0.234132i
$801$	26.6792	−	20.6855i	0.942663	−	0.730888i
$802$	5.53740	−	9.59106i	0.195533	−	0.338672i
$803$	40.2260			1.41955
$804$	−1.08225	−	1.22784i	−0.0381682	−	0.0433025i
$805$	0.0448757	−	0.0259090i	0.00158166	−	0.000913171i
$806$	2.01759	+	4.79490i	0.0710666	+	0.168893i
$807$	1.70668	−	27.0814i	0.0600778	−	0.953312i
$808$	−3.88263	+	3.88263i	−0.136591	+	0.136591i
$809$	9.20764	−	5.31603i	0.323723	−	0.186902i	−0.329328	−	0.944216i	$-0.606822\pi$
$809$	9.20764	−	5.31603i	0.323723	−	0.186902i	0.653051	+	0.757314i	$0.273489\pi$
$810$	22.1318	+	21.6912i	0.777631	+	0.762153i
$811$	7.65216	−	7.65216i	0.268704	−	0.268704i	−0.559874	−	0.828578i	$-0.689151\pi$
$811$	7.65216	−	7.65216i	0.268704	−	0.268704i	0.828578	+	0.559874i	$0.189151\pi$
$812$	−0.0612635	+	0.228638i	−0.00214993	+	0.00802363i
$813$	29.0652	−	5.85740i	1.01936	−	0.205428i
$814$	9.13123	−	34.0782i	0.320049	−	1.19444i
$815$		−	38.1659i		−	1.33689i
$816$	−11.5998	−	0.731018i	−0.406073	−	0.0255908i
$817$	−12.4826	−	12.4826i	−0.436710	−	0.436710i
$818$	−14.6788			−0.513233
$819$	0.156933	+	0.265272i	0.00548370	+	0.00926937i
$820$	17.3013			0.604189
$821$	10.8656	+	10.8656i	0.379212	+	0.379212i	0.870818	−	0.491606i	$-0.163590\pi$
$821$	10.8656	+	10.8656i	0.379212	+	0.379212i	−0.491606	+	0.870818i	$0.663590\pi$
$822$	−16.0249	+	24.1139i	−0.558932	+	0.841069i
$823$			15.2209i			0.530567i	0.964170	+	0.265284i	$0.0854656\pi$
$823$			15.2209i			0.530567i	−0.964170	+	0.265284i	$0.914534\pi$
$824$	−1.08303	+	4.04193i	−0.0377292	+	0.140807i
$825$	34.1651	+	38.7609i	1.18948	+	1.34948i
$826$	0.105528	−	0.393835i	0.00367178	−	0.0137033i
$827$	−16.9790	+	16.9790i	−0.590418	+	0.590418i	−0.937744	−	0.347326i	$-0.887090\pi$
$827$	−16.9790	+	16.9790i	−0.590418	+	0.590418i	0.347326	+	0.937744i	$0.387090\pi$
$828$	−1.46075	+	0.613682i	−0.0507646	+	0.0213269i
$829$	−14.6492	+	8.45773i	−0.508788	+	0.293749i	−0.732335	−	0.680944i	$-0.761570\pi$
$829$	−14.6492	+	8.45773i	−0.508788	+	0.293749i	0.223547	+	0.974693i	$0.428236\pi$
$830$	35.7667	−	35.7667i	1.24148	−	1.24148i
$831$	28.2066	+	18.7447i	0.978477	+	0.650247i
$832$	−0.450627	+	3.57728i	−0.0156227	+	0.124020i
$833$	−40.6750	+	23.4837i	−1.40930	+	0.813662i
$834$	−2.81001	+	8.34687i	−0.0973026	+	0.289029i
$835$	51.3878			1.77835
$836$	4.38330	−	7.59210i	0.151600	−	0.262578i
$837$	6.74866	+	3.26506i	0.233268	+	0.112857i
$838$	−7.28940	−	27.2044i	−0.251808	−	0.939761i
$839$	22.8417	+	6.12041i	0.788583	+	0.211300i	0.630565	−	0.776136i	$-0.282823\pi$
$839$	22.8417	+	6.12041i	0.788583	+	0.211300i	0.158017	+	0.987436i	$0.449490\pi$
$840$	−0.112369	−	0.127484i	−0.00387709	−	0.00439862i
$841$	−40.0056			−1.37950
$842$	−3.63954	+	6.30387i	−0.125427	+	0.217246i
$843$	39.7650	−	35.0501i	1.36958	−	1.20719i
$844$	−16.5841	−	9.57481i	−0.570847	−	0.329579i
$845$	21.9462	−	39.0129i	0.754972	−	1.34208i
$846$	−0.933225	−	2.22136i	−0.0320849	−	0.0763719i
$847$	0.218335	+	0.0585027i	0.00750208	+	0.00201018i
$848$			5.06566i			0.173956i
$849$	−2.57298	+	40.8279i	−0.0883045	+	1.40121i
$850$	−44.4381	−	11.9071i	−1.52421	−	0.408412i
$851$	3.02805	+	3.02805i	0.103800	+	0.103800i
$852$	12.5502	−	11.0621i	0.429962	−	0.378982i
$853$	55.3955	−	14.8432i	1.89671	−	0.508221i	0.899208	−	0.437522i	$-0.144144\pi$
$853$	55.3955	−	14.8432i	1.89671	−	0.508221i	0.997498	−	0.0706986i	$-0.0225229\pi$
$854$	0.000530397	0	0.000306225i	1.81498e−5	0	1.04788e-5i
$855$	12.5864	−	16.5747i	0.430446	−	0.566844i
$856$	0.852446	−	3.18137i	0.0291360	−	0.108737i
$857$	−9.63613	+	16.6903i	−0.329164	+	0.570129i	−0.982346	−	0.187072i	$-0.940100\pi$
$857$	−9.63613	+	16.6903i	−0.329164	+	0.570129i	0.653182	+	0.757201i	$0.273434\pi$
$858$	−8.94270	−	25.6593i	−0.305299	−	0.875994i
$859$	−21.1198	−	36.5805i	−0.720597	−	1.24811i	−0.960761	−	0.277378i	$-0.910534\pi$
$859$	−21.1198	−	36.5805i	−0.720597	−	1.24811i	0.240164	−	0.970732i	$-0.422799\pi$
$860$	29.1409	−	7.80829i	0.993697	−	0.266260i
$861$	0.222140	−	0.110242i	0.00757053	−	0.00375705i
$862$	−16.4143	+	9.47681i	−0.559074	+	0.322781i
$863$	−4.51248	−	4.51248i	−0.153607	−	0.153607i	0.626120	−	0.779727i	$-0.284642\pi$
$863$	−4.51248	−	4.51248i	−0.153607	−	0.153607i	−0.779727	+	0.626120i	$0.784642\pi$
$864$	2.91932	+	4.29856i	0.0993172	+	0.146240i
$865$	−63.3927	+	16.9860i	−2.15542	+	0.577542i
$866$	−8.15738	−	30.4438i	−0.277199	−	1.03452i
$867$	−26.8707	+	40.4344i	−0.912577	+	1.37323i
$868$	−0.0356041	−	0.0205560i	−0.00120848	−	0.000697717i
$869$	−3.17465	−	11.8480i	−0.107693	−	0.401914i
$870$	27.4202	−	41.2613i	0.929632	−	1.39889i
$871$	0.463595	+	3.37542i	0.0157083	+	0.114372i
$872$			7.64122i			0.258764i
$873$	1.11924	−	0.867796i	0.0378806	−	0.0293705i
$874$	0.532043	+	0.921525i	0.0179966	+	0.0311711i
$875$	−0.0910429	−	0.157691i	−0.00307781	−	0.00533093i
$876$	15.1757	+	5.10897i	0.512740	+	0.172616i
$877$	−8.53740	+	8.53740i	−0.288288	+	0.288288i	−0.836403	−	0.548115i	$-0.815346\pi$
$877$	−8.53740	+	8.53740i	−0.288288	+	0.288288i	0.548115	+	0.836403i	$0.315346\pi$
$878$	−9.11262	+	9.11262i	−0.307536	+	0.307536i
$879$	36.2551	+	12.2054i	1.22286	+	0.411679i
$880$	7.49104	+	12.9749i	0.252523	+	0.437382i
$881$	23.1313	+	40.0646i	0.779314	+	1.34981i	0.932337	+	0.361589i	$0.117766\pi$
$881$	23.1313	+	40.0646i	0.779314	+	1.34981i	−0.153023	+	0.988223i	$0.548901\pi$
$882$	19.4394	+	7.93782i	0.654557	+	0.267280i
$883$			5.00836i			0.168545i	0.996443	+	0.0842723i	$0.0268566\pi$
$883$			5.00836i			0.168545i	−0.996443	+	0.0842723i	$0.973143\pi$
$884$	19.2770	+	14.6213i	0.648356	+	0.491767i
$885$	−47.2320	+	71.0736i	−1.58769	+	2.38911i
$886$	3.25809	+	12.1594i	0.109458	+	0.408502i
$887$	−18.7915	−	10.8493i	−0.630958	−	0.364284i	0.150165	−	0.988661i	$-0.452019\pi$
$887$	−18.7915	−	10.8493i	−0.630958	−	0.364284i	−0.781123	+	0.624377i	$0.785353\pi$
$888$	7.77302	−	11.6967i	0.260845	−	0.392514i
$889$	0.0729193	+	0.272138i	0.00244563	+	0.00912723i
$890$	37.4265	−	10.0284i	1.25454	−	0.336153i
$891$	−34.1091	−	19.2383i	−1.14270	−	0.644509i
$892$	18.6817	+	18.6817i	0.625509	+	0.625509i
$893$	−1.40136	+	0.809076i	−0.0468947	+	0.0270747i
$894$	−8.20321	+	4.07104i	−0.274356	+	0.136156i
$895$	80.1764	−	21.4832i	2.68000	−	0.718104i
$896$	−0.0142473	−	0.0246771i	−0.000475970	−	0.000824403i
$897$	3.23998	+	0.617220i	0.108180	+	0.0206084i
$898$	2.25983	−	3.91414i	0.0754115	−	0.130616i
$899$	3.10202	−	11.5769i	0.103458	−	0.386111i
$900$	7.96628	+	18.9622i	0.265543	+	0.632073i
$901$	29.4385	+	16.9963i	0.980740	+	0.566230i
$902$	−21.1185	+	5.65867i	−0.703167	+	0.188413i
$903$	0.324401	−	0.285938i	0.0107954	−	0.00951541i
$904$	−0.411467	−	0.411467i	−0.0136852	−	0.0136852i
$905$	−3.87486	−	1.03827i	−0.128805	−	0.0345131i
$906$	−1.06071	+	16.8313i	−0.0352398	+	0.559184i
$907$		−	30.7861i		−	1.02224i	−0.859511	−	0.511118i	$-0.829232\pi$
$907$		−	30.7861i		−	1.02224i	0.859511	−	0.511118i	$-0.170768\pi$
$908$	4.95918	+	1.32881i	0.164576	+	0.0440981i
$909$	9.96208	−	13.1188i	0.330421	−	0.435124i
$910$	0.0481342	+	0.350464i	0.00159563	+	0.0116178i
$911$	13.1044	+	7.56582i	0.434168	+	0.250667i	0.701120	−	0.713043i	$-0.252684\pi$
$911$	13.1044	+	7.56582i	0.434168	+	0.250667i	−0.266953	+	0.963710i	$0.586017\pi$
$912$	2.61790	−	2.30750i	0.0866872	−	0.0764089i
$913$	−31.9597	+	55.3559i	−1.05771	+	1.83201i
$914$	−10.1709			−0.336422
$915$	−0.0847596	−	0.0961612i	−0.00280207	−	0.00317899i
$916$	7.67020	+	2.05522i	0.253431	+	0.0679065i
$917$	−0.133669	−	0.498859i	−0.00441414	−	0.0164738i
$918$	34.7755	−	2.54274i	1.14776	−	0.0839228i
$919$	−26.7304	+	46.2985i	−0.881755	+	1.52724i	−0.0323673	+	0.999476i	$0.510305\pi$
$919$	−26.7304	+	46.2985i	−0.881755	+	1.52724i	−0.849388	+	0.527769i	$0.823029\pi$
$920$	−1.81852			−0.0599547
$921$	2.34292	−	6.95943i	0.0772018	−	0.229321i
$922$	−23.5621	+	13.6036i	−0.775977	+	0.448011i
$923$	−34.5014	+	4.73858i	−1.13563	+	0.155972i
$924$	0.178856	+	0.118858i	0.00588392	+	0.00391016i
$925$	39.3075	−	39.3075i	1.29242	−	1.29242i
$926$	10.2633	−	5.92551i	0.337272	−	0.194724i
$927$	1.57599	−	12.4542i	0.0517624	−	0.409051i
$928$	5.87391	−	5.87391i	0.192821	−	0.192821i
$929$	−13.9078	+	51.9045i	−0.456299	+	1.70293i	0.227940	+	0.973675i	$0.426801\pi$
$929$	−13.9078	+	51.9045i	−0.456299	+	1.70293i	−0.684239	+	0.729257i	$0.739866\pi$
$930$	5.68968	+	6.45504i	0.186572	+	0.211669i
$931$	3.64981	−	13.6213i	0.119618	−	0.446419i
$932$			0.240333i			0.00787238i
$933$	−29.0088	+	43.6519i	−0.949707	+	1.42910i
$934$	−0.435492	−	0.435492i	−0.0142497	−	0.0142497i
$935$	100.536			3.28787
$936$	−0.114834	−	10.8160i	−0.00375346	−	0.353533i
$937$	−2.41921			−0.0790323			−0.0395162	−	0.999219i	$-0.512582\pi$
$937$	−2.41921			−0.0790323			−0.0395162	+	0.999219i	$0.512582\pi$
$938$	−0.0190398	−	0.0190398i	−0.000621671	−	0.000621671i
$939$	57.8508	+	3.64576i	1.88789	+	0.118975i
$940$		−	2.76541i		−	0.0901977i
$941$	−0.0115889	+	0.0432503i	−0.000377786	+	0.00140992i	−0.966114	−	0.258114i	$-0.916899\pi$
$941$	−0.0115889	+	0.0432503i	−0.000377786	+	0.00140992i	0.965737	+	0.259524i	$0.0835656\pi$
$942$	−16.3454	+	3.29403i	−0.532563	+	0.107325i
$943$	0.686846	−	2.56335i	0.0223668	−	0.0834740i
$944$	−10.1180	+	10.1180i	−0.329311	+	0.329311i
$945$	0.385822	+	0.333244i	0.0125508	+	0.0108404i
$946$	−33.0163	+	19.0620i	−1.07345	+	0.619759i
$947$	16.6276	−	16.6276i	0.540323	−	0.540323i	−0.383301	−	0.923624i	$-0.625213\pi$
$947$	16.6276	−	16.6276i	0.540323	−	0.540323i	0.923624	+	0.383301i	$0.125213\pi$
$948$	0.307096	−	4.87298i	0.00997400	−	0.158267i
$949$	−20.4393	−	26.3309i	−0.663489	−	0.854739i
$950$	11.9624	−	6.90651i	0.388112	−	0.224077i
$951$	−12.7802	−	14.4994i	−0.414426	−	0.470174i
$952$	−0.191211			−0.00619718
$953$	13.8021	−	23.9060i	0.447095	−	0.774392i	−0.551100	−	0.834439i	$-0.685792\pi$
$953$	13.8021	−	23.9060i	0.447095	−	0.774392i	0.998196	+	0.0600474i	$0.0191252\pi$
$954$	−2.05931	−	15.0568i	−0.0666725	−	0.487483i
$955$	10.3061	+	38.4627i	0.333496	+	1.24462i
$956$	−6.49603	−	1.74060i	−0.210096	−	0.0562952i
$957$	−19.9746	+	59.3328i	−0.645688	+	1.91796i
$958$	20.0403			0.647474
$959$	−0.238159	+	0.412503i	−0.00769055	+	0.0133204i
$960$	1.17819	+	5.84632i	0.0380258	+	0.188689i
$961$	−25.0440	−	14.4592i	−0.807871	−	0.466425i
$962$	−26.9464	+	11.3385i	−0.868788	+	0.365567i
$963$	−1.24045	+	9.80263i	−0.0399730	+	0.315885i
$964$	−25.0664	−	6.71652i	−0.807335	−	0.216325i
$965$		−	4.95840i		−	0.159617i
$966$	−0.0233488	+	0.0115874i	−0.000751236	+	0.000372819i
$967$	31.0146	+	8.31034i	0.997363	+	0.267243i	0.720340	−	0.693621i	$-0.243986\pi$
$967$	31.0146	+	8.31034i	0.997363	+	0.267243i	0.277023	+	0.960863i	$0.410652\pi$
$968$	−5.60920	−	5.60920i	−0.180287	−	0.180287i
$969$	−4.62618	−	22.9557i	−0.148614	−	0.737445i
$970$	1.57011	−	0.420710i	0.0504132	−	0.0135082i
$971$	−16.6187	−	9.59478i	−0.533318	−	0.307911i	0.209049	−	0.977905i	$-0.432963\pi$
$971$	−16.6187	−	9.59478i	−0.533318	−	0.307911i	−0.742366	+	0.669994i	$0.766297\pi$
$972$	−10.4246	−	11.5900i	−0.334370	−	0.371748i
$973$	−0.0375004	+	0.139953i	−0.00120221	+	0.00448670i
$974$	−10.5733	+	18.3135i	−0.338791	+	0.586804i
$975$	8.01221	−	42.0585i	0.256596	−	1.34695i
$976$	−0.0107467	−	0.0186139i	−0.000343995	−	0.000595817i
$977$	29.5657	−	7.92211i	0.945891	−	0.253451i	0.247273	−	0.968946i	$-0.420465\pi$
$977$	29.5657	−	7.92211i	0.945891	−	0.253451i	0.698618	+	0.715495i	$0.253799\pi$
$978$	−1.20750	+	19.1606i	−0.0386116	+	0.612687i
$979$	−42.4038	+	24.4818i	−1.35523	+	0.782443i
$980$	17.0412	+	17.0412i	0.544360	+	0.544360i
$981$	−3.10633	−	22.7122i	−0.0991774	−	0.725145i
$982$	19.0783	−	5.11201i	0.608812	−	0.163131i
$983$	−5.86347	−	21.8828i	−0.187016	−	0.697952i	−0.994190	−	0.107639i	$-0.965671\pi$
$983$	−5.86347	−	21.8828i	−0.187016	−	0.697952i	0.807175	−	0.590313i	$-0.200996\pi$
$984$	−8.68586	−	0.547384i	−0.276895	−	0.0174500i
$985$	−12.3962	−	7.15696i	−0.394976	−	0.228040i
$986$	−14.4274	−	53.8437i	−0.459462	−	1.71473i
$987$	−0.0176209	−	0.0355065i	−0.000560880	−	0.00113018i
$988$	−7.19681	+	0.988441i	−0.228961	+	0.0314465i
$989$		−	4.62747i		−	0.147145i
$990$	−27.5404	−	35.5203i	−0.875291	−	1.12891i
$991$	−18.1139	−	31.3742i	−0.575408	−	0.996636i	−0.995997	−	0.0893845i	$-0.971510\pi$
$991$	−18.1139	−	31.3742i	−0.575408	−	0.996636i	0.420589	−	0.907251i	$-0.361823\pi$
$992$	0.721399	+	1.24950i	0.0229045	+	0.0396717i
$993$	1.41646	+	7.02867i	0.0449500	+	0.223048i
$994$	0.194613	−	0.194613i	0.00617275	−	0.00617275i
$995$	5.01657	−	5.01657i	0.159036	−	0.159036i
$996$	−19.0877	+	16.8245i	−0.604818	+	0.533106i
$997$	8.88423	+	15.3879i	0.281366	+	0.487341i	0.971722	−	0.236130i	$-0.0758790\pi$
$997$	8.88423	+	15.3879i	0.281366	+	0.487341i	−0.690355	+	0.723471i	$0.742546\pi$
$998$	−2.65476	−	4.59817i	−0.0840348	−	0.145553i
$999$	−18.3490	+	37.9262i	−0.580537	+	1.19993i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	234.2.y.a.119.3	yes	56
3.2	odd	2		702.2.bb.a.197.8		56
9.4	even	3		702.2.bc.a.665.8		56
9.5	odd	6		234.2.z.a.41.2	yes	56
13.7	odd	12		234.2.z.a.137.2	yes	56
39.20	even	12		702.2.bc.a.683.8		56
117.59	even	12	inner	234.2.y.a.59.3	✓	56
117.85	odd	12		702.2.bb.a.449.8		56

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
234.2.y.a.59.3	✓	56	117.59	even	12	inner
234.2.y.a.119.3	yes	56	1.1	even	1	trivial
234.2.z.a.41.2	yes	56	9.5	odd	6
234.2.z.a.137.2	yes	56	13.7	odd	12
702.2.bb.a.197.8		56	3.2	odd	2
702.2.bb.a.449.8		56	117.85	odd	12
702.2.bc.a.665.8		56	9.4	even	3
702.2.bc.a.683.8		56	39.20	even	12

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:	\( N \)	\(=\)	\( 234 = 2 \cdot 3^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	234.y (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.707107 - 0.707107i) q^{2} +(-0.769968 - 1.55150i) q^{3} +1.00000i q^{4} +(0.891175 - 3.32591i) q^{5} +(-0.552626 + 1.64153i) q^{6} +(-0.00737496 + 0.0275237i) q^{7} +(0.707107 - 0.707107i) q^{8} +(-1.81430 + 2.38921i) q^{9} +(-2.98193 + 1.72162i) q^{10} +(3.07674 - 3.07674i) q^{11} +(1.55150 - 0.769968i) q^{12} +(-3.57728 - 0.450627i) q^{13} +(0.0246771 - 0.0142473i) q^{14} +(-5.84632 + 1.17819i) q^{15} -1.00000 q^{16} +(-3.35521 + 5.81139i) q^{17} +(2.97233 - 0.406522i) q^{18} +(-0.521462 - 1.94612i) q^{19} +(3.32591 + 0.891175i) q^{20} +(0.0483815 - 0.00975013i) q^{21} -4.35116 q^{22} +(0.264071 - 0.457384i) q^{23} +(-1.64153 - 0.552626i) q^{24} +(-5.93735 - 3.42793i) q^{25} +(2.21088 + 2.84816i) q^{26} +(5.10381 + 0.975270i) q^{27} +(-0.0275237 - 0.00737496i) q^{28} -8.30696i q^{29} +(4.96708 + 3.30087i) q^{30} +(1.39364 + 0.373424i) q^{31} +(0.707107 + 0.707107i) q^{32} +(-7.14254 - 2.40457i) q^{33} +(6.48176 - 1.73678i) q^{34} +(0.0849690 + 0.0490569i) q^{35} +(-2.38921 - 1.81430i) q^{36} +(-2.09857 + 7.83198i) q^{37} +(-1.00739 + 1.74484i) q^{38} +(2.05524 + 5.89712i) q^{39} +(-1.72162 - 2.98193i) q^{40} +(4.85352 - 1.30050i) q^{41} +(-0.0411053 - 0.0273165i) q^{42} +(7.58793 - 4.38090i) q^{43} +(3.07674 + 3.07674i) q^{44} +(6.32943 + 8.16340i) q^{45} +(-0.510146 + 0.136693i) q^{46} +(-0.207869 - 0.775777i) q^{47} +(0.769968 + 1.55150i) q^{48} +(6.06147 + 3.49959i) q^{49} +(1.77443 + 6.62226i) q^{50} +(11.5998 + 0.731018i) q^{51} +(0.450627 - 3.57728i) q^{52} -5.06566i q^{53} +(-2.91932 - 4.29856i) q^{54} +(-7.49104 - 12.9749i) q^{55} +(0.0142473 + 0.0246771i) q^{56} +(-2.61790 + 2.30750i) q^{57} +(-5.87391 + 5.87391i) q^{58} +(10.1180 - 10.1180i) q^{59} +(-1.17819 - 5.84632i) q^{60} +(0.0107467 + 0.0186139i) q^{61} +(-0.721399 - 1.24950i) q^{62} +(-0.0523795 - 0.0675565i) q^{63} -1.00000i q^{64} +(-4.68673 + 11.4961i) q^{65} +(3.35025 + 6.75082i) q^{66} +(-0.244574 - 0.912763i) q^{67} +(-5.81139 - 3.35521i) q^{68} +(-0.912957 - 0.0575347i) q^{69} +(-0.0253937 - 0.0947706i) q^{70} +(9.32969 - 2.49988i) q^{71} +(0.406522 + 2.97233i) q^{72} +(6.53713 + 6.53713i) q^{73} +(7.02196 - 4.05413i) q^{74} +(-0.746864 + 11.8512i) q^{75} +(1.94612 - 0.521462i) q^{76} +(0.0619924 + 0.107374i) q^{77} +(2.71661 - 5.62317i) q^{78} +(1.40950 - 2.44132i) q^{79} +(-0.891175 + 3.32591i) q^{80} +(-2.41664 - 8.66948i) q^{81} +(-4.35155 - 2.51237i) q^{82} +(-14.1896 + 3.80210i) q^{83} +(0.00975013 + 0.0483815i) q^{84} +(16.3381 + 16.3381i) q^{85} +(-8.46324 - 2.26772i) q^{86} +(-12.8882 + 6.39609i) q^{87} -4.35116i q^{88} +(-10.8696 - 2.91249i) q^{89} +(1.29681 - 10.2480i) q^{90} +(0.0387852 - 0.0951367i) q^{91} +(0.457384 + 0.264071i) q^{92} +(-0.493689 - 2.44975i) q^{93} +(-0.401572 + 0.695542i) q^{94} -6.93734 q^{95} +(0.552626 - 1.64153i) q^{96} +(-0.455998 - 0.122184i) q^{97} +(-1.81152 - 6.76070i) q^{98} +(1.76884 + 12.9331i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 56 q + 4 q^{7} + 24 q^{15} - 56 q^{16} - 8 q^{19} + 36 q^{27} - 4 q^{28} + 8 q^{31} - 36 q^{33} + 24 q^{35} - 24 q^{36} - 4 q^{37} - 36 q^{38} - 24 q^{39} - 48 q^{41} + 36 q^{42} + 12 q^{43} - 36 q^{45}+ \cdots - 24 q^{99}+O(q^{100}) \) 56 * q + 4 * q^7 + 24 * q^15 - 56 * q^16 - 8 * q^19 + 36 * q^27 - 4 * q^28 + 8 * q^31 - 36 * q^33 + 24 * q^35 - 24 * q^36 - 4 * q^37 - 36 * q^38 - 24 * q^39 - 48 * q^41 + 36 * q^42 + 12 * q^43 - 36 * q^45 + 60 * q^47 - 24 * q^50 - 4 * q^52 + 24 * q^57 - 60 * q^63 - 120 * q^65 - 56 * q^67 - 36 * q^69 + 24 * q^71 + 28 * q^73 + 48 * q^74 + 4 * q^76 - 24 * q^77 + 36 * q^78 - 24 * q^79 - 120 * q^81 - 60 * q^83 + 24 * q^84 + 48 * q^86 + 48 * q^87 + 4 * q^91 - 24 * q^92 + 20 * q^97 - 48 * q^98 - 24 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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