LMFDB - Embedded newform 240.2.bl.a.109.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [240,2,Mod(109,240)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(240, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([0, 3, 0, 2]))

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

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

chi := DirichletCharacter("240.109");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 240 = 2^{4} \cdot 3 \cdot 5 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	240.bl (of order $4$, 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:	$1.91640964851$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$24$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			109.10
Character	$\chi$	$=$	240.109
Dual form			240.2.bl.a.229.10

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.456856 + 1.33839i) q^{2} +(0.707107 - 0.707107i) q^{3} +(-1.58257 - 1.22290i) q^{4} +(-1.50085 - 1.65754i) q^{5} +(0.623338 + 1.26943i) q^{6} -2.58977 q^{7} +(2.35972 - 1.55940i) q^{8} -1.00000i q^{9} +O(q^{10})$	\(q+(-0.456856 + 1.33839i) q^{2} +(0.707107 - 0.707107i) q^{3} +(-1.58257 - 1.22290i) q^{4} +(-1.50085 - 1.65754i) q^{5} +(0.623338 + 1.26943i) q^{6} -2.58977 q^{7} +(2.35972 - 1.55940i) q^{8} -1.00000i q^{9} +(2.90411 - 1.25146i) q^{10} +(4.39624 - 4.39624i) q^{11} +(-1.98376 + 0.254322i) q^{12} +(-0.417468 + 0.417468i) q^{13} +(1.18315 - 3.46612i) q^{14} +(-2.23332 - 0.110799i) q^{15} +(1.00903 + 3.87064i) q^{16} -4.40417i q^{17} +(1.33839 + 0.456856i) q^{18} +(-4.53682 - 4.53682i) q^{19} +(0.348184 + 4.45856i) q^{20} +(-1.83125 + 1.83125i) q^{21} +(3.87543 + 7.89232i) q^{22} -0.281063 q^{23} +(0.565912 - 2.77124i) q^{24} +(-0.494901 + 4.97545i) q^{25} +(-0.368012 - 0.749457i) q^{26} +(-0.707107 - 0.707107i) q^{27} +(4.09849 + 3.16704i) q^{28} +(3.73710 + 3.73710i) q^{29} +(1.16860 - 2.93843i) q^{30} -3.05233 q^{31} +(-5.64140 - 0.417848i) q^{32} -6.21722i q^{33} +(5.89449 + 2.01207i) q^{34} +(3.88686 + 4.29266i) q^{35} +(-1.22290 + 1.58257i) q^{36} +(5.26234 + 5.26234i) q^{37} +(8.14471 - 3.99936i) q^{38} +0.590389i q^{39} +(-6.12636 - 1.57091i) q^{40} +5.16508i q^{41} +(-1.61430 - 3.28754i) q^{42} +(2.66933 + 2.66933i) q^{43} +(-12.3335 + 1.58118i) q^{44} +(-1.65754 + 1.50085i) q^{45} +(0.128405 - 0.376171i) q^{46} -7.45202i q^{47} +(3.45045 + 2.02346i) q^{48} -0.293066 q^{49} +(-6.43298 - 2.93543i) q^{50} +(-3.11422 - 3.11422i) q^{51} +(1.17119 - 0.150149i) q^{52} +(2.89462 + 2.89462i) q^{53} +(1.26943 - 0.623338i) q^{54} +(-13.8850 - 0.688864i) q^{55} +(-6.11114 + 4.03849i) q^{56} -6.41604 q^{57} +(-6.70900 + 3.29437i) q^{58} +(-4.60721 + 4.60721i) q^{59} +(3.39888 + 2.90648i) q^{60} +(-0.211318 - 0.211318i) q^{61} +(1.39447 - 4.08520i) q^{62} +2.58977i q^{63} +(3.13655 - 7.35949i) q^{64} +(1.31853 + 0.0654147i) q^{65} +(8.32105 + 2.84037i) q^{66} +(7.17140 - 7.17140i) q^{67} +(-5.38586 + 6.96989i) q^{68} +(-0.198741 + 0.198741i) q^{69} +(-7.52099 + 3.24100i) q^{70} -15.9477i q^{71} +(-1.55940 - 2.35972i) q^{72} +10.5662 q^{73} +(-9.44719 + 4.63893i) q^{74} +(3.16822 + 3.86812i) q^{75} +(1.63174 + 12.7279i) q^{76} +(-11.3853 + 11.3853i) q^{77} +(-0.790170 - 0.269723i) q^{78} +4.53907 q^{79} +(4.90135 - 7.48176i) q^{80} -1.00000 q^{81} +(-6.91288 - 2.35969i) q^{82} +(4.56660 - 4.56660i) q^{83} +(5.13750 - 0.658637i) q^{84} +(-7.30010 + 6.61000i) q^{85} +(-4.79209 + 2.35310i) q^{86} +5.28505 q^{87} +(3.51840 - 17.2294i) q^{88} +10.2745i q^{89} +(-1.25146 - 2.90411i) q^{90} +(1.08115 - 1.08115i) q^{91} +(0.444800 + 0.343712i) q^{92} +(-2.15832 + 2.15832i) q^{93} +(9.97370 + 3.40450i) q^{94} +(-0.710893 + 14.3291i) q^{95} +(-4.28454 + 3.69361i) q^{96} +6.78053i q^{97} +(0.133889 - 0.392236i) q^{98} +(-4.39624 - 4.39624i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q+O(q^{10}) $ 48 * q	$ 48 q + 12 q^{10} - 16 q^{14} - 4 q^{16} + 8 q^{19} - 4 q^{24} - 40 q^{26} - 8 q^{30} - 48 q^{31} - 28 q^{34} + 24 q^{35} - 4 q^{36} - 16 q^{40} - 40 q^{44} - 4 q^{46} + 48 q^{49} - 32 q^{50} + 8 q^{51} - 4 q^{54} + 48 q^{56} - 32 q^{59} - 24 q^{60} + 16 q^{61} + 48 q^{64} + 16 q^{65} + 24 q^{66} - 16 q^{69} + 40 q^{74} - 16 q^{75} + 60 q^{76} - 96 q^{79} + 72 q^{80} - 48 q^{81} + 16 q^{86} + 8 q^{90} - 32 q^{91} + 44 q^{94} - 48 q^{95} - 40 q^{96}+O(q^{100}) $ 48 * q + 12 * q^10 - 16 * q^14 - 4 * q^16 + 8 * q^19 - 4 * q^24 - 40 * q^26 - 8 * q^30 - 48 * q^31 - 28 * q^34 + 24 * q^35 - 4 * q^36 - 16 * q^40 - 40 * q^44 - 4 * q^46 + 48 * q^49 - 32 * q^50 + 8 * q^51 - 4 * q^54 + 48 * q^56 - 32 * q^59 - 24 * q^60 + 16 * q^61 + 48 * q^64 + 16 * q^65 + 24 * q^66 - 16 * q^69 + 40 * q^74 - 16 * q^75 + 60 * q^76 - 96 * q^79 + 72 * q^80 - 48 * q^81 + 16 * q^86 + 8 * q^90 - 32 * q^91 + 44 * q^94 - 48 * q^95 - 40 * q^96

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/240\mathbb{Z}\right)^\times$.

$n$	$31$	$97$	$161$	$181$
$\chi(n)$	$1$	$-1$	$1$	$e\left(\frac{3}{4}\right)$

Coefficient data

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

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

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

$2$	−0.456856	+	1.33839i	−0.323046	+	0.946383i
$2$	−0.456856	+	1.33839i	−0.323046	+	0.946383i
$3$	0.707107	−	0.707107i	0.408248	−	0.408248i
$3$	0.707107	−	0.707107i	0.408248	−	0.408248i
$4$	−1.58257	−	1.22290i	−0.791283	−	0.611450i
$5$	−1.50085	−	1.65754i	−0.671200	−	0.741276i
$5$	−1.50085	−	1.65754i	−0.671200	−	0.741276i
$6$	0.623338	+	1.26943i	0.254477	+	0.518242i
$7$	−2.58977			−0.978843			−0.489421	−	0.872047i	$-0.662792\pi$
$7$	−2.58977			−0.978843			−0.489421	+	0.872047i	$0.662792\pi$
$8$	2.35972	−	1.55940i	0.834287	−	0.551331i
$9$		−	1.00000i		−	0.333333i
$10$	2.90411	−	1.25146i	0.918360	−	0.395747i
$11$	4.39624	−	4.39624i	1.32552	−	1.32552i	0.416278	−	0.909237i	$-0.363334\pi$
$11$	4.39624	−	4.39624i	1.32552	−	1.32552i	0.909237	−	0.416278i	$-0.136666\pi$
$12$	−1.98376	+	0.254322i	−0.572663	+	0.0734165i
$13$	−0.417468	+	0.417468i	−0.115785	+	0.115785i	−0.762625	−	0.646840i	$-0.776090\pi$
$13$	−0.417468	+	0.417468i	−0.115785	+	0.115785i	0.646840	+	0.762625i	$0.276090\pi$
$14$	1.18315	−	3.46612i	0.316211	−	0.926361i
$15$	−2.23332	−	0.110799i	−0.576641	−	0.0286083i
$16$	1.00903	+	3.87064i	0.252258	+	0.967660i
$17$		−	4.40417i		−	1.06817i	−0.845431	−	0.534084i	$-0.820657\pi$
$17$		−	4.40417i		−	1.06817i	0.845431	−	0.534084i	$-0.179343\pi$
$18$	1.33839	+	0.456856i	0.315461	+	0.107682i
$19$	−4.53682	−	4.53682i	−1.04082	−	1.04082i	−0.999131	−	0.0416882i	$-0.986726\pi$
$19$	−4.53682	−	4.53682i	−1.04082	−	1.04082i	−0.0416882	−	0.999131i	$-0.513274\pi$
$20$	0.348184	+	4.45856i	0.0778562	+	0.996965i
$21$	−1.83125	+	1.83125i	−0.399611	+	0.399611i
$22$	3.87543	+	7.89232i	0.826244	+	1.68265i
$23$	−0.281063			−0.0586056			−0.0293028	−	0.999571i	$-0.509329\pi$
$23$	−0.281063			−0.0586056			−0.0293028	+	0.999571i	$0.509329\pi$
$24$	0.565912	−	2.77124i	0.115516	−	0.565676i
$25$	−0.494901	+	4.97545i	−0.0989802	+	0.995089i
$26$	−0.368012	−	0.749457i	−0.0721731	−	0.146981i
$27$	−0.707107	−	0.707107i	−0.136083	−	0.136083i
$28$	4.09849	+	3.16704i	0.774542	+	0.598514i
$29$	3.73710	+	3.73710i	0.693962	+	0.693962i	0.963101	−	0.269140i	$-0.0867393\pi$
$29$	3.73710	+	3.73710i	0.693962	+	0.693962i	−0.269140	+	0.963101i	$0.586739\pi$
$30$	1.16860	−	2.93843i	0.213356	−	0.536482i
$31$	−3.05233			−0.548214			−0.274107	−	0.961699i	$-0.588382\pi$
$31$	−3.05233			−0.548214			−0.274107	+	0.961699i	$0.588382\pi$
$32$	−5.64140	−	0.417848i	−0.997268	−	0.0738659i
$33$		−	6.21722i		−	1.08228i
$34$	5.89449	+	2.01207i	1.01090	+	0.345067i
$35$	3.88686	+	4.29266i	0.657000	+	0.725593i
$36$	−1.22290	+	1.58257i	−0.203817	+	0.263761i
$37$	5.26234	+	5.26234i	0.865124	+	0.865124i	0.991928	−	0.126804i	$-0.0404719\pi$
$37$	5.26234	+	5.26234i	0.865124	+	0.865124i	−0.126804	+	0.991928i	$0.540472\pi$
$38$	8.14471	−	3.99936i	1.32125	−	0.648782i
$39$			0.590389i			0.0945380i
$40$	−6.12636	−	1.57091i	−0.968662	−	0.248383i
$41$			5.16508i			0.806649i	0.915057	+	0.403325i	$0.132145\pi$
$41$			5.16508i			0.806649i	−0.915057	+	0.403325i	$0.867855\pi$
$42$	−1.61430	−	3.28754i	−0.249093	−	0.507278i
$43$	2.66933	+	2.66933i	0.407069	+	0.407069i	0.880715	−	0.473647i	$-0.157063\pi$
$43$	2.66933	+	2.66933i	0.407069	+	0.407069i	−0.473647	+	0.880715i	$0.657063\pi$
$44$	−12.3335	+	1.58118i	−1.85934	+	0.238371i
$45$	−1.65754	+	1.50085i	−0.247092	+	0.223733i
$46$	0.128405	−	0.376171i	0.0189323	−	0.0554634i
$47$		−	7.45202i		−	1.08699i	−0.839413	−	0.543495i	$-0.817101\pi$
$47$		−	7.45202i		−	1.08699i	0.839413	−	0.543495i	$-0.182899\pi$
$48$	3.45045	+	2.02346i	0.498029	+	0.292062i
$49$	−0.293066			−0.0418665
$50$	−6.43298	−	2.93543i	−0.909761	−	0.415132i
$51$	−3.11422	−	3.11422i	−0.436078	−	0.436078i
$52$	1.17119	−	0.150149i	0.162415	−	0.0208219i
$53$	2.89462	+	2.89462i	0.397606	+	0.397606i	0.877388	−	0.479782i	$-0.159284\pi$
$53$	2.89462	+	2.89462i	0.397606	+	0.397606i	−0.479782	+	0.877388i	$0.659284\pi$
$54$	1.26943	−	0.623338i	0.172747	−	0.0848255i
$55$	−13.8850	−	0.688864i	−1.87226	−	0.0928863i
$56$	−6.11114	+	4.03849i	−0.816636	+	0.539666i
$57$	−6.41604			−0.849825
$58$	−6.70900	+	3.29437i	−0.880935	+	0.432573i
$59$	−4.60721	+	4.60721i	−0.599808	+	0.599808i	−0.940261	−	0.340453i	$-0.889420\pi$
$59$	−4.60721	+	4.60721i	−0.599808	+	0.599808i	0.340453	+	0.940261i	$0.389420\pi$
$60$	3.39888	+	2.90648i	0.438794	+	0.375224i
$61$	−0.211318	−	0.211318i	−0.0270564	−	0.0270564i	0.693449	−	0.720506i	$-0.256090\pi$
$61$	−0.211318	−	0.211318i	−0.0270564	−	0.0270564i	−0.720506	+	0.693449i	$0.756090\pi$
$62$	1.39447	−	4.08520i	0.177098	−	0.518821i
$63$			2.58977i			0.326281i
$64$	3.13655	−	7.35949i	0.392069	−	0.919936i
$65$	1.31853	+	0.0654147i	0.163543	+	0.00811370i
$66$	8.32105	+	2.84037i	1.02425	+	0.349625i
$67$	7.17140	−	7.17140i	0.876126	−	0.876126i	−0.117005	−	0.993131i	$-0.537329\pi$
$67$	7.17140	−	7.17140i	0.876126	−	0.876126i	0.993131	+	0.117005i	$0.0373294\pi$
$68$	−5.38586	+	6.96989i	−0.653132	+	0.845223i
$69$	−0.198741	+	0.198741i	−0.0239257	+	0.0239257i
$70$	−7.52099	+	3.24100i	−0.898930	+	0.387374i
$71$		−	15.9477i		−	1.89265i	−0.323222	−	0.946323i	$-0.604766\pi$
$71$		−	15.9477i		−	1.89265i	0.323222	−	0.946323i	$-0.395234\pi$
$72$	−1.55940	−	2.35972i	−0.183777	−	0.278096i
$73$	10.5662			1.23668			0.618339	−	0.785912i	$-0.287806\pi$
$73$	10.5662			1.23668			0.618339	+	0.785912i	$0.287806\pi$
$74$	−9.44719	+	4.63893i	−1.09821	+	0.539264i
$75$	3.16822	+	3.86812i	0.365835	+	0.446652i
$76$	1.63174	+	12.7279i	0.187174	+	1.45999i
$77$	−11.3853	+	11.3853i	−1.29747	+	1.29747i
$78$	−0.790170	−	0.269723i	−0.0894692	−	0.0305401i
$79$	4.53907			0.510685			0.255342	−	0.966851i	$-0.417812\pi$
$79$	4.53907			0.510685			0.255342	+	0.966851i	$0.417812\pi$
$80$	4.90135	−	7.48176i	0.547988	−	0.836486i
$81$	−1.00000			−0.111111
$82$	−6.91288	−	2.35969i	−0.763400	−	0.260585i
$83$	4.56660	−	4.56660i	0.501249	−	0.501249i	−0.410577	−	0.911826i	$-0.634673\pi$
$83$	4.56660	−	4.56660i	0.501249	−	0.501249i	0.911826	+	0.410577i	$0.134673\pi$
$84$	5.13750	−	0.658637i	0.560548	−	0.0718632i
$85$	−7.30010	+	6.61000i	−0.791807	+	0.716955i
$86$	−4.79209	+	2.35310i	−0.516745	+	0.253741i
$87$	5.28505			0.566617
$88$	3.51840	−	17.2294i	0.375062	−	1.83666i
$89$			10.2745i			1.08910i	0.838730	+	0.544548i	$0.183299\pi$
$89$			10.2745i			1.08910i	−0.838730	+	0.544548i	$0.816701\pi$
$90$	−1.25146	−	2.90411i	−0.131916	−	0.306120i
$91$	1.08115	−	1.08115i	0.113335	−	0.113335i
$92$	0.444800	+	0.343712i	0.0463737	+	0.0358344i
$93$	−2.15832	+	2.15832i	−0.223808	+	0.223808i
$94$	9.97370	+	3.40450i	1.02871	+	0.351147i
$95$	−0.710893	+	14.3291i	−0.0729361	+	1.47013i
$96$	−4.28454	+	3.69361i	−0.437289	+	0.376977i
$97$			6.78053i			0.688459i	0.938886	+	0.344229i	$0.111860\pi$
$97$			6.78053i			0.688459i	−0.938886	+	0.344229i	$0.888140\pi$
$98$	0.133889	−	0.392236i	0.0135248	−	0.0396218i
$99$	−4.39624	−	4.39624i	−0.441838	−	0.441838i
$100$	6.86769	−	7.26876i	0.686769	−	0.726876i
$101$	10.0764	−	10.0764i	1.00264	−	1.00264i	0.00264739	−	0.999996i	$-0.499157\pi$
$101$	10.0764	−	10.0764i	1.00264	−	1.00264i	0.999996	−	0.00264739i	$-0.000842692\pi$
$102$	5.59078	−	2.74529i	0.553570	−	0.271824i
$103$	−4.71475			−0.464558			−0.232279	−	0.972649i	$-0.574618\pi$
$103$	−4.71475			−0.464558			−0.232279	+	0.972649i	$0.574618\pi$
$104$	−0.334108	+	1.63611i	−0.0327620	+	0.160434i
$105$	5.78380	+	0.286945i	0.564441	+	0.0280030i
$106$	−5.19654	+	2.55170i	−0.504733	+	0.247843i
$107$	12.9687	+	12.9687i	1.25373	+	1.25373i	0.954035	+	0.299696i	$0.0968852\pi$
$107$	12.9687	+	12.9687i	1.25373	+	1.25373i	0.299696	+	0.954035i	$0.403115\pi$
$108$	0.254322	+	1.98376i	0.0244722	+	0.190888i
$109$	−0.382902	−	0.382902i	−0.0366754	−	0.0366754i	0.688531	−	0.725207i	$-0.258256\pi$
$109$	−0.382902	−	0.382902i	−0.0366754	−	0.0366754i	−0.725207	+	0.688531i	$0.758256\pi$
$110$	7.26543	−	18.2689i	0.692731	−	1.74187i
$111$	7.44208			0.706371
$112$	−2.61316	−	10.0241i	−0.246921	−	0.947187i
$113$		−	12.1861i		−	1.14637i	−0.819424	−	0.573187i	$-0.805707\pi$
$113$		−	12.1861i		−	1.14637i	0.819424	−	0.573187i	$-0.194293\pi$
$114$	2.93120	−	8.58715i	0.274532	−	0.804260i
$115$	0.421833	+	0.465874i	0.0393361	+	0.0434430i
$116$	−1.34411	−	10.4843i	−0.124797	−	0.973443i
$117$	0.417468	+	0.417468i	0.0385950	+	0.0385950i
$118$	−4.06141	−	8.27107i	−0.373883	−	0.761414i
$119$			11.4058i			1.04557i
$120$	−5.44279	+	3.22118i	−0.496857	+	0.294053i
$121$		−	27.6538i		−	2.51398i
$122$	0.379366	−	0.186283i	0.0343462	−	0.0168653i
$123$	3.65226	+	3.65226i	0.329313	+	0.329313i
$124$	4.83051	+	3.73269i	0.433793	+	0.335206i
$125$	8.98979	−	6.64708i	0.804071	−	0.594533i
$126$	−3.46612	−	1.18315i	−0.308787	−	0.105404i
$127$		−	6.75303i		−	0.599234i	−0.954060	−	0.299617i	$-0.903141\pi$
$127$		−	6.75303i		−	0.599234i	0.954060	−	0.299617i	$-0.0968589\pi$
$128$	8.41690	+	7.56014i	0.743956	+	0.668228i
$129$	3.77500			0.332370
$130$	−0.689928	+	1.73482i	−0.0605107	+	0.152154i
$131$	3.95303	+	3.95303i	0.345378	+	0.345378i	0.858385	−	0.513007i	$-0.171468\pi$
$131$	3.95303	+	3.95303i	0.345378	+	0.345378i	−0.513007	+	0.858385i	$0.671468\pi$
$132$	−7.60304	+	9.83916i	−0.661759	+	0.856389i
$133$	11.7494	+	11.7494i	1.01880	+	1.01880i
$134$	6.32183	+	12.8744i	0.546123	+	1.11218i
$135$	−0.110799	+	2.23332i	−0.00953609	+	0.192214i
$136$	−6.86786	−	10.3926i	−0.588914	−	0.891159i
$137$	−5.19519			−0.443855			−0.221927	−	0.975063i	$-0.571235\pi$
$137$	−5.19519			−0.443855			−0.221927	+	0.975063i	$0.571235\pi$
$138$	−0.175197	−	0.356789i	−0.0149138	−	0.0303719i
$139$	0.977024	−	0.977024i	0.0828701	−	0.0828701i	−0.664457	−	0.747327i	$-0.731337\pi$
$139$	0.977024	−	0.977024i	0.0828701	−	0.0828701i	0.747327	+	0.664457i	$0.231337\pi$
$140$	−0.901717	−	11.5467i	−0.0762090	−	0.975872i
$141$	−5.26938	−	5.26938i	−0.443761	−	0.443761i
$142$	21.3442	+	7.28580i	1.79117	+	0.611411i
$143$			3.67058i			0.306949i
$144$	3.87064	−	1.00903i	0.322553	−	0.0840859i
$145$	0.585580	−	11.8032i	0.0486298	−	0.980204i
$146$	−4.82722	+	14.1416i	−0.399503	+	1.17037i
$147$	−0.207229	+	0.207229i	−0.0170919	+	0.0170919i
$148$	−1.89269	−	14.7633i	−0.155578	−	1.21354i
$149$	11.3051	−	11.3051i	0.926150	−	0.926150i	−0.0713047	−	0.997455i	$-0.522716\pi$
$149$	11.3051	−	11.3051i	0.926150	−	0.926150i	0.997455	+	0.0713047i	$0.0227163\pi$
$150$	−6.62447	+	2.47314i	−0.540885	+	0.201931i
$151$			2.87287i			0.233791i	0.993144	+	0.116895i	$0.0372942\pi$
$151$			2.87287i			0.233791i	−0.993144	+	0.116895i	$0.962706\pi$
$152$	−17.7804	−	3.63091i	−1.44218	−	0.294506i
$153$	−4.40417			−0.356056
$154$	−10.0365	−	20.4393i	−0.808763	−	1.64705i
$155$	4.58109	+	5.05937i	0.367962	+	0.406378i
$156$	0.721987	−	0.934330i	0.0578052	−	0.0748063i
$157$	−5.73516	+	5.73516i	−0.457716	+	0.457716i	−0.897905	−	0.440189i	$-0.854911\pi$
$157$	−5.73516	+	5.73516i	−0.457716	+	0.457716i	0.440189	+	0.897905i	$0.354911\pi$
$158$	−2.07370	+	6.07503i	−0.164975	+	0.483304i
$159$	4.09361			0.324644
$160$	7.77429	+	9.97799i	0.614612	+	0.788830i
$161$	0.727889			0.0573657
$162$	0.456856	−	1.33839i	0.0358940	−	0.105154i
$163$	−11.9561	+	11.9561i	−0.936474	+	0.936474i	−0.998099	−	0.0616255i	$-0.980372\pi$
$163$	−11.9561	+	11.9561i	−0.936474	+	0.936474i	0.0616255	+	0.998099i	$0.480372\pi$
$164$	6.31637	−	8.17407i	0.493226	−	0.638288i
$165$	−10.3053	+	9.33111i	−0.802267	+	0.726426i
$166$	4.02560	+	8.19815i	0.312447	+	0.636300i
$167$	−9.23665			−0.714754			−0.357377	−	0.933960i	$-0.616329\pi$
$167$	−9.23665			−0.714754			−0.357377	+	0.933960i	$0.616329\pi$
$168$	−1.46558	+	7.17688i	−0.113072	+	0.553708i
$169$			12.6514i			0.973188i
$170$	−5.51165	−	12.7902i	−0.422724	−	0.980963i
$171$	−4.53682	+	4.53682i	−0.346940	+	0.346940i
$172$	−0.960066	−	7.48871i	−0.0732044	−	0.571008i
$173$	−2.36187	+	2.36187i	−0.179570	+	0.179570i	−0.791168	−	0.611598i	$-0.790527\pi$
$173$	−2.36187	+	2.36187i	−0.179570	+	0.179570i	0.611598	+	0.791168i	$0.290527\pi$
$174$	−2.41451	+	7.07345i	−0.183043	+	0.536237i
$175$	1.28168	−	12.8853i	0.0968861	−	0.974036i
$176$	21.4522	+	12.5803i	1.61702	+	0.948277i
$177$			6.51559i			0.489741i
$178$	−13.7513	−	4.69397i	−1.03070	−	0.351828i
$179$	9.27202	+	9.27202i	0.693023	+	0.693023i	0.962896	−	0.269873i	$-0.0869816\pi$
$179$	9.27202	+	9.27202i	0.693023	+	0.693023i	−0.269873	+	0.962896i	$0.586982\pi$
$180$	4.45856	−	0.348184i	0.332322	−	0.0259521i
$181$	−10.5707	+	10.5707i	−0.785715	+	0.785715i	−0.980789	−	0.195074i	$-0.937505\pi$
$181$	−10.5707	+	10.5707i	−0.785715	+	0.785715i	0.195074	+	0.980789i	$0.437505\pi$
$182$	0.953068	+	1.94093i	0.0706461	+	0.143871i
$183$	−0.298848			−0.0220915
$184$	−0.663229	+	0.438289i	−0.0488939	+	0.0323111i
$185$	0.824577	−	16.6206i	0.0606241	−	1.22197i
$186$	−1.90263	−	3.87472i	−0.139508	−	0.284108i
$187$	−19.3618	−	19.3618i	−1.41587	−	1.41587i
$188$	−9.11308	+	11.7933i	−0.664640	+	0.860116i
$189$	1.83125	+	1.83125i	0.133204	+	0.133204i
$190$	−18.8531	−	7.49777i	−1.36775	−	0.543945i
$191$	−8.32988			−0.602729			−0.301364	−	0.953509i	$-0.597442\pi$
$191$	−8.32988			−0.602729			−0.301364	+	0.953509i	$0.597442\pi$
$192$	−2.98607	−	7.42182i	−0.215501	−	0.535624i
$193$		−	5.73404i		−	0.412745i	−0.978473	−	0.206373i	$-0.933834\pi$
$193$		−	5.73404i		−	0.412745i	0.978473	−	0.206373i	$-0.0661659\pi$
$194$	−9.07499	−	3.09772i	−0.651546	−	0.222404i
$195$	0.978596	−	0.886086i	0.0700787	−	0.0634539i
$196$	0.463796	+	0.358390i	0.0331283	+	0.0255993i
$197$	3.23239	+	3.23239i	0.230298	+	0.230298i	0.812817	−	0.582519i	$-0.197933\pi$
$197$	3.23239	+	3.23239i	0.230298	+	0.230298i	−0.582519	+	0.812817i	$0.697933\pi$
$198$	7.89232	−	3.87543i	0.560883	−	0.275415i
$199$			19.0599i			1.35112i	0.737303	+	0.675562i	$0.236099\pi$
$199$			19.0599i			1.35112i	−0.737303	+	0.675562i	$0.763901\pi$
$200$	6.59088	+	12.5124i	0.466046	+	0.884761i
$201$		−	10.1419i		−	0.715354i
$202$	8.88272	+	18.0897i	0.624986	+	1.27279i
$203$	−9.67824	−	9.67824i	−0.679279	−	0.679279i
$204$	1.12008	+	8.73684i	0.0784212	+	0.611701i
$205$	8.56134	−	7.75200i	0.597950	−	0.541423i
$206$	2.15396	−	6.31016i	0.150073	−	0.439650i
$207$			0.281063i			0.0195352i
$208$	−2.03711	−	1.19463i	−0.141248	−	0.0828328i
$209$	−39.8899			−2.75924
$210$	−3.02640	+	7.60988i	−0.208842	+	0.525131i
$211$	4.43719	+	4.43719i	0.305469	+	0.305469i	0.843149	−	0.537680i	$-0.180699\pi$
$211$	4.43719	+	4.43719i	0.305469	+	0.305469i	−0.537680	+	0.843149i	$0.680699\pi$
$212$	−1.04110	−	8.12075i	−0.0715027	−	0.557735i
$213$	−11.2767	−	11.2767i	−0.772670	−	0.772670i
$214$	−23.2820	+	11.4323i	−1.59152	+	0.781498i
$215$	0.418267	−	8.43078i	0.0285256	−	0.574975i
$216$	−2.77124	−	0.565912i	−0.188559	−	0.0385054i
$217$	7.90485			0.536616
$218$	0.687402	−	0.337541i	0.0465568	−	0.0228611i
$219$	7.47142	−	7.47142i	0.504871	−	0.504871i
$220$	21.1316	+	18.0702i	1.42469	+	1.21829i
$221$	1.83860	+	1.83860i	0.123678	+	0.123678i
$222$	−3.39995	+	9.96039i	−0.228190	+	0.668498i
$223$			5.10536i			0.341880i	0.985281	+	0.170940i	$0.0546805\pi$
$223$			5.10536i			0.341880i	−0.985281	+	0.170940i	$0.945320\pi$
$224$	14.6100	+	1.08213i	0.976169	+	0.0723031i
$225$	4.97545	+	0.494901i	0.331696	+	0.0329934i
$226$	16.3098	+	5.56730i	1.08491	+	0.370331i
$227$	15.0563	−	15.0563i	0.999320	−	0.999320i	−0.000680242	−	1.00000i	$-0.500217\pi$
$227$	15.0563	−	15.0563i	0.999320	−	0.999320i	1.00000		0.000680242i	$0.000216528\pi$
$228$	10.1538	+	7.84617i	0.672452	+	0.519626i
$229$	17.5250	−	17.5250i	1.15809	−	1.15809i	0.173200	−	0.984887i	$-0.444589\pi$
$229$	17.5250	−	17.5250i	1.15809	−	1.15809i	0.984887	−	0.173200i	$-0.0554108\pi$
$230$	−0.816237	+	0.351739i	−0.0538211	+	0.0231930i
$231$			16.1012i			1.05938i
$232$	14.6461	+	2.99087i	0.961565	+	0.196360i
$233$	−9.15254			−0.599603			−0.299802	−	0.954002i	$-0.596920\pi$
$233$	−9.15254			−0.599603			−0.299802	+	0.954002i	$0.596920\pi$
$234$	−0.749457	+	0.368012i	−0.0489936	+	0.0240577i
$235$	−12.3521	+	11.1844i	−0.805759	+	0.729588i
$236$	12.9254	−	1.65706i	0.841371	−	0.107865i
$237$	3.20960	−	3.20960i	0.208486	−	0.208486i
$238$	−15.2654	−	5.21081i	−0.989509	−	0.337766i
$239$	−12.9198			−0.835713			−0.417857	−	0.908513i	$-0.637219\pi$
$239$	−12.9198			−0.835713			−0.417857	+	0.908513i	$0.637219\pi$
$240$	−1.82463	−	8.75618i	−0.117779	−	0.565209i
$241$	10.7071			0.689703			0.344851	−	0.938657i	$-0.387929\pi$
$241$	10.7071			0.689703			0.344851	+	0.938657i	$0.387929\pi$
$242$	37.0115	+	12.6338i	2.37919	+	0.812131i
$243$	−0.707107	+	0.707107i	−0.0453609	+	0.0453609i
$244$	0.0760037	+	0.592844i	0.00486564	+	0.0379530i
$245$	0.439847	+	0.485769i	0.0281008	+	0.0310346i
$246$	−6.55670	+	3.21959i	−0.418040	+	0.205273i
$247$	3.78796			0.241022
$248$	−7.20264	+	4.75980i	−0.457368	+	0.302248i
$249$		−	6.45814i		−	0.409268i
$250$	4.78933	+	15.0686i	0.302904	+	0.953021i
$251$	−4.48257	+	4.48257i	−0.282937	+	0.282937i	−0.834279	−	0.551342i	$-0.814116\pi$
$251$	−4.48257	+	4.48257i	−0.282937	+	0.282937i	0.551342	+	0.834279i	$0.314116\pi$
$252$	3.16704	−	4.09849i	0.199505	−	0.258181i
$253$	−1.23562	+	1.23562i	−0.0776827	+	0.0776827i
$254$	9.03817	+	3.08516i	0.567105	+	0.193580i
$255$	−0.487979	+	9.83593i	−0.0305584	+	0.615950i
$256$	−13.9637	+	7.81119i	−0.872732	+	0.488199i
$257$			16.9307i			1.05610i	0.849212	+	0.528052i	$0.177078\pi$
$257$			16.9307i			1.05610i	−0.849212	+	0.528052i	$0.822922\pi$
$258$	−1.72463	+	5.05241i	−0.107371	+	0.314550i
$259$	−13.6283	−	13.6283i	−0.846821	−	0.846821i
$260$	−2.00666	−	1.71595i	−0.124448	−	0.106419i
$261$	3.73710	−	3.73710i	0.231321	−	0.231321i
$262$	−7.09666	+	3.48473i	−0.438433	+	0.215287i
$263$	2.07893			0.128192			0.0640962	−	0.997944i	$-0.479584\pi$
$263$	2.07893			0.128192			0.0640962	+	0.997944i	$0.479584\pi$
$264$	−9.69512	−	14.6709i	−0.596694	−	0.902931i
$265$	0.453569	−	9.14234i	0.0278625	−	0.561609i
$266$	−21.0930	+	10.3574i	−1.29329	+	0.635055i
$267$	7.26517	+	7.26517i	0.444621	+	0.444621i
$268$	−20.1191	+	2.57931i	−1.22897	+	0.157556i
$269$	−16.0709	−	16.0709i	−0.979860	−	0.979860i	0.0199408	−	0.999801i	$-0.493652\pi$
$269$	−16.0709	−	16.0709i	−0.979860	−	0.979860i	−0.999801	+	0.0199408i	$0.993652\pi$
$270$	−2.93843	−	1.16860i	−0.178827	−	0.0711186i
$271$	4.18571			0.254264			0.127132	−	0.991886i	$-0.459423\pi$
$271$	4.18571			0.254264			0.127132	+	0.991886i	$0.459423\pi$
$272$	17.0470	−	4.44394i	1.03362	−	0.269454i
$273$		−	1.52898i		−	0.0925378i
$274$	2.37345	−	6.95318i	0.143385	−	0.420057i
$275$	19.6975	+	24.0489i	1.18781	+	1.45021i
$276$	0.557562	−	0.0714805i	0.0335613	−	0.00430262i
$277$	−15.8235	−	15.8235i	−0.950744	−	0.950744i	0.0480985	−	0.998843i	$-0.484684\pi$
$277$	−15.8235	−	15.8235i	−0.950744	−	0.950744i	−0.998843	+	0.0480985i	$0.984684\pi$
$278$	0.861278	+	1.75400i	0.0516560	+	0.105198i
$279$			3.05233i			0.182738i
$280$	15.8659	+	4.06831i	0.948168	+	0.243128i
$281$			12.6546i			0.754911i	0.926028	+	0.377455i	$0.123201\pi$
$281$			12.6546i			0.754911i	−0.926028	+	0.377455i	$0.876799\pi$
$282$	9.45981	−	4.64513i	0.563324	−	0.276613i
$283$	1.54865	+	1.54865i	0.0920579	+	0.0920579i	0.751636	−	0.659578i	$-0.229265\pi$
$283$	1.54865	+	1.54865i	0.0920579	+	0.0920579i	−0.659578	+	0.751636i	$0.729265\pi$
$284$	−19.5025	+	25.2383i	−1.15726	+	1.49762i
$285$	9.62951	+	10.6349i	0.570403	+	0.629955i
$286$	−4.91266	−	1.67692i	−0.290492	−	0.0991586i
$287$		−	13.3764i		−	0.789583i
$288$	−0.417848	+	5.64140i	−0.0246220	+	0.332423i
$289$	−2.39672			−0.140983
$290$	15.5298	+	6.17610i	0.911940	+	0.362673i
$291$	4.79456	+	4.79456i	0.281062	+	0.281062i
$292$	−16.7217	−	12.9214i	−0.978562	−	0.756166i
$293$	−21.2881	−	21.2881i	−1.24366	−	1.24366i	−0.958470	−	0.285194i	$-0.907942\pi$
$293$	−21.2881	−	21.2881i	−1.24366	−	1.24366i	−0.285194	−	0.958470i	$-0.592058\pi$
$294$	−0.182679	−	0.372026i	−0.0106540	−	0.0216970i
$295$	14.5514	+	0.721922i	0.847215	+	0.0420319i
$296$	20.6237	+	4.21156i	1.19873	+	0.244792i
$297$	−6.21722			−0.360760
$298$	9.96582	+	20.2954i	0.577304	+	1.17568i
$299$	0.117335	−	0.117335i	0.00678565	−	0.00678565i
$300$	−0.283600	−	9.99598i	−0.0163737	−	0.577118i
$301$	−6.91296	−	6.91296i	−0.398456	−	0.398456i
$302$	−3.84501	−	1.31249i	−0.221256	−	0.0755251i
$303$		−	14.2502i		−	0.818655i
$304$	12.9826	−	22.1382i	0.744604	−	1.26971i
$305$	−0.0331122	+	0.667424i	−0.00189600	+	0.0382166i
$306$	2.01207	−	5.89449i	0.115022	−	0.336966i
$307$	12.2344	−	12.2344i	0.698255	−	0.698255i	−0.265779	−	0.964034i	$-0.585629\pi$
$307$	12.2344	−	12.2344i	0.698255	−	0.698255i	0.964034	+	0.265779i	$0.0856291\pi$
$308$	31.9410	−	4.09489i	1.82001	−	0.233328i
$309$	−3.33383	+	3.33383i	−0.189655	+	0.189655i
$310$	−8.86429	+	3.81987i	−0.503458	+	0.216954i
$311$		−	19.4874i		−	1.10503i	−0.833503	−	0.552515i	$-0.813668\pi$
$311$		−	19.4874i		−	1.10503i	0.833503	−	0.552515i	$-0.186332\pi$
$312$	0.920653	+	1.39315i	0.0521217	+	0.0788718i
$313$	−9.73432			−0.550217			−0.275108	−	0.961413i	$-0.588714\pi$
$313$	−9.73432			−0.550217			−0.275108	+	0.961413i	$0.588714\pi$
$314$	−5.05573	−	10.2960i	−0.285311	−	0.581037i
$315$	4.29266	−	3.88686i	0.241864	−	0.219000i
$316$	−7.18337	−	5.55083i	−0.404096	−	0.312258i
$317$	8.46658	−	8.46658i	0.475530	−	0.475530i	−0.428168	−	0.903699i	$-0.640841\pi$
$317$	8.46658	−	8.46658i	0.475530	−	0.475530i	0.903699	+	0.428168i	$0.140841\pi$
$318$	−1.87019	+	5.47883i	−0.104875	+	0.307238i
$319$	32.8583			1.83971
$320$	−16.9062	+	5.84652i	−0.945083	+	0.326830i
$321$	18.3405			1.02367
$322$	−0.332540	+	0.974199i	−0.0185317	+	0.0542900i
$323$	−19.9809	+	19.9809i	−1.11177	+	1.11177i
$324$	1.58257	+	1.22290i	0.0879203	+	0.0679389i
$325$	−1.87049	−	2.28370i	−0.103756	−	0.126677i
$326$	−10.5397	−	21.4641i	−0.583739	−	1.18879i
$327$	−0.541505			−0.0299453
$328$	8.05442	+	12.1881i	0.444731	+	0.672977i
$329$			19.2991i			1.06399i
$330$	−7.78061	−	18.0555i	−0.428308	−	0.993921i
$331$	7.11555	−	7.11555i	0.391106	−	0.391106i	−0.483975	−	0.875082i	$-0.660808\pi$
$331$	7.11555	−	7.11555i	0.391106	−	0.391106i	0.875082	+	0.483975i	$0.160808\pi$
$332$	−12.8114	+	1.64245i	−0.703119	+	0.0901411i
$333$	5.26234	−	5.26234i	0.288375	−	0.288375i
$334$	4.21982	−	12.3622i	0.230898	−	0.676431i
$335$	−22.6501	−	1.12371i	−1.23751	−	0.0613951i
$336$	−8.93589	−	5.24032i	−0.487493	−	0.285883i
$337$			15.8355i			0.862613i	0.902205	+	0.431307i	$0.141947\pi$
$337$			15.8355i			0.862613i	−0.902205	+	0.431307i	$0.858053\pi$
$338$	−16.9325	−	5.77988i	−0.921009	−	0.314384i
$339$	−8.61689	−	8.61689i	−0.468005	−	0.468005i
$340$	19.6363	−	1.53346i	1.06493	−	0.0831635i
$341$	−13.4188	+	13.4188i	−0.726667	+	0.726667i
$342$	−3.99936	−	8.14471i	−0.216261	−	0.440415i
$343$	18.8874			1.01982
$344$	10.4614	+	2.13632i	0.564041	+	0.115182i
$345$	0.627703	+	0.0311416i	0.0337944	+	0.00167661i
$346$	−2.08207	−	4.24014i	−0.111933	−	0.227951i
$347$	−9.38020	−	9.38020i	−0.503555	−	0.503555i	0.408986	−	0.912541i	$-0.365883\pi$
$347$	−9.38020	−	9.38020i	−0.503555	−	0.503555i	−0.912541	+	0.408986i	$0.865883\pi$
$348$	−8.36395	−	6.46309i	−0.448355	−	0.346458i
$349$	0.479184	+	0.479184i	0.0256501	+	0.0256501i	0.719816	−	0.694165i	$-0.244226\pi$
$349$	0.479184	+	0.479184i	0.0256501	+	0.0256501i	−0.694165	+	0.719816i	$0.744226\pi$
$350$	16.6600	+	7.60210i	0.890513	+	0.406350i
$351$	0.590389			0.0315127
$352$	−26.6379	+	22.9640i	−1.41980	+	1.22398i
$353$			8.95345i			0.476544i	0.971198	+	0.238272i	$0.0765810\pi$
$353$			8.95345i			0.476544i	−0.971198	+	0.238272i	$0.923419\pi$
$354$	−8.72038	−	2.97668i	−0.463483	−	0.158209i
$355$	−26.4340	+	23.9351i	−1.40297	+	1.27034i
$356$	12.5647	−	16.2601i	0.665928	−	0.861783i
$357$	8.06513	+	8.06513i	0.426852	+	0.426852i
$358$	−16.6455	+	8.17359i	−0.879744	+	0.431988i
$359$		−	3.47704i		−	0.183511i	−0.995782	−	0.0917556i	$-0.970752\pi$
$359$		−	3.47704i		−	0.183511i	0.995782	−	0.0917556i	$-0.0292478\pi$
$360$	−1.57091	+	6.12636i	−0.0827944	+	0.322887i
$361$			22.1655i			1.16661i
$362$	−9.31843	−	18.9770i	−0.489766	−	0.997409i
$363$	−19.5542	−	19.5542i	−1.02633	−	1.02633i
$364$	−3.03313	+	0.388853i	−0.158979	+	0.0203814i
$365$	−15.8582	−	17.5139i	−0.830058	−	0.916719i
$366$	0.136530	−	0.399975i	0.00713656	−	0.0209070i
$367$			15.1190i			0.789206i	0.918852	+	0.394603i	$0.129118\pi$
$367$			15.1190i			0.789206i	−0.918852	+	0.394603i	$0.870882\pi$
$368$	−0.283601	−	1.08789i	−0.0147837	−	0.0567103i
$369$	5.16508			0.268883
$370$	21.8680	+	8.69679i	1.13687	+	0.452125i
$371$	−7.49640	−	7.49640i	−0.389194	−	0.389194i
$372$	6.05510	−	0.776275i	0.313942	−	0.0402480i
$373$	19.0505	+	19.0505i	0.986398	+	0.986398i	0.999909	−	0.0135107i	$-0.00430073\pi$
$373$	19.0505	+	19.0505i	0.986398	+	0.986398i	−0.0135107	+	0.999909i	$0.504301\pi$
$374$	34.7591	−	17.0680i	1.79735	−	0.882567i
$375$	1.65655	−	11.0569i	0.0855438	−	0.570978i
$376$	−11.6207	−	17.5847i	−0.599291	−	0.906861i
$377$	−3.12024			−0.160701
$378$	−3.28754	+	1.61430i	−0.169093	+	0.0830309i
$379$	3.52823	−	3.52823i	0.181233	−	0.181233i	−0.610660	−	0.791893i	$-0.709096\pi$
$379$	3.52823	−	3.52823i	0.181233	−	0.181233i	0.791893	+	0.610660i	$0.209096\pi$
$380$	18.6481	−	21.8074i	0.956625	−	1.11869i
$381$	−4.77511	−	4.77511i	−0.244636	−	0.244636i
$382$	3.80555	−	11.1486i	0.194709	−	0.570413i
$383$			3.20268i			0.163649i	0.996647	+	0.0818246i	$0.0260747\pi$
$383$			3.20268i			0.163649i	−0.996647	+	0.0818246i	$0.973925\pi$
$384$	11.2975	−	0.605821i	0.576522	−	0.0309157i
$385$	35.9591	+	1.78400i	1.83265	+	0.0909211i
$386$	7.67438	+	2.61963i	0.390615	+	0.133336i
$387$	2.66933	−	2.66933i	0.135690	−	0.135690i
$388$	8.29192	−	10.7306i	0.420958	−	0.544766i
$389$	16.9595	−	16.9595i	0.859882	−	0.859882i	−0.131441	−	0.991324i	$-0.541961\pi$
$389$	16.9595	−	16.9595i	0.859882	−	0.859882i	0.991324	+	0.131441i	$0.0419605\pi$
$390$	0.738850	+	1.71455i	0.0374131	+	0.0868199i
$391$			1.23785i			0.0626007i
$392$	−0.691553	+	0.457006i	−0.0349287	+	0.0230823i
$393$	5.59043			0.282000
$394$	−5.80292	+	2.84945i	−0.292347	+	0.143553i
$395$	−6.81246	−	7.52370i	−0.342772	−	0.378558i
$396$	1.58118	+	12.3335i	0.0794571	+	0.619781i
$397$	−15.8392	+	15.8392i	−0.794946	+	0.794946i	−0.982294	−	0.187348i	$-0.940011\pi$
$397$	−15.8392	+	15.8392i	−0.794946	+	0.794946i	0.187348	+	0.982294i	$0.440011\pi$
$398$	−25.5096	−	8.70764i	−1.27868	−	0.436475i
$399$	16.6161			0.831845
$400$	−19.7575	+	3.10480i	−0.987877	+	0.155240i
$401$	−10.8608			−0.542364			−0.271182	−	0.962528i	$-0.587414\pi$
$401$	−10.8608			−0.542364			−0.271182	+	0.962528i	$0.587414\pi$
$402$	13.5738	+	4.63338i	0.676999	+	0.231092i
$403$	1.27425	−	1.27425i	0.0634750	−	0.0634750i
$404$	−28.2691	+	3.62416i	−1.40644	+	0.180308i
$405$	1.50085	+	1.65754i	0.0745778	+	0.0823640i
$406$	17.3748	−	8.53169i	0.862297	−	0.423421i
$407$	46.2690			2.29347
$408$	−12.2050	−	2.49237i	−0.604237	−	0.123391i
$409$		−	12.5363i		−	0.619880i	−0.950756	−	0.309940i	$-0.899691\pi$
$409$		−	12.5363i		−	0.619880i	0.950756	−	0.309940i	$-0.100309\pi$
$410$	6.46389	+	14.9999i	0.319229	+	0.740794i
$411$	−3.67355	+	3.67355i	−0.181203	+	0.181203i
$412$	7.46140	+	5.76566i	0.367597	+	0.284054i
$413$	11.9316	−	11.9316i	0.587118	−	0.587118i
$414$	−0.376171	−	0.128405i	−0.0184878	−	0.00631077i
$415$	−14.4231	−	0.715558i	−0.708002	−	0.0351253i
$416$	2.52954	−	2.18067i	0.124021	−	0.106916i
$417$		−	1.38172i		−	0.0676631i
$418$	18.2239	−	53.3882i	0.891361	−	2.61130i
$419$	−21.6745	−	21.6745i	−1.05887	−	1.05887i	−0.998155	−	0.0607123i	$-0.980663\pi$
$419$	−21.6745	−	21.6745i	−1.05887	−	1.05887i	−0.0607123	−	0.998155i	$-0.519337\pi$
$420$	−8.80234	−	7.52712i	−0.429510	−	0.367286i
$421$	−9.02933	+	9.02933i	−0.440063	+	0.440063i	−0.892033	−	0.451970i	$-0.850721\pi$
$421$	−9.02933	+	9.02933i	−0.440063	+	0.440063i	0.451970	+	0.892033i	$0.350721\pi$
$422$	−7.96585	+	3.91153i	−0.387771	+	0.190410i
$423$	−7.45202			−0.362330
$424$	11.3443	+	2.31662i	0.550930	+	0.112505i
$425$	21.9127	+	2.17963i	1.06292	+	0.105727i
$426$	20.2445	−	9.94082i	0.980849	−	0.481634i
$427$	0.547265	+	0.547265i	0.0264840	+	0.0264840i
$428$	−4.66440	−	36.3832i	−0.225462	−	1.75865i
$429$	2.59549	+	2.59549i	0.125312	+	0.125312i
$430$	11.0926	+	4.41145i	0.534931	+	0.212739i
$431$	−22.1994			−1.06931			−0.534653	−	0.845072i	$-0.679558\pi$
$431$	−22.1994			−1.06931			−0.534653	+	0.845072i	$0.679558\pi$
$432$	2.02346	−	3.45045i	0.0973539	−	0.166010i
$433$			31.1117i			1.49513i	0.664187	+	0.747566i	$0.268778\pi$
$433$			31.1117i			1.49513i	−0.664187	+	0.747566i	$0.731222\pi$
$434$	−3.61137	+	10.5798i	−0.173351	+	0.507844i
$435$	−7.93207	−	8.76021i	−0.380314	−	0.420020i
$436$	0.137717	+	1.07422i	0.00659544	+	0.0514457i
$437$	1.27513	+	1.27513i	0.0609979	+	0.0609979i
$438$	6.58630	+	13.4130i	0.314705	+	0.640898i
$439$			0.460911i			0.0219981i	0.999940	+	0.0109990i	$0.00350117\pi$
$439$			0.460911i			0.0219981i	−0.999940	+	0.0109990i	$0.996499\pi$
$440$	−33.8390	+	20.0268i	−1.61321	+	0.954740i
$441$			0.293066i			0.0139555i
$442$	−3.30074	+	1.62079i	−0.157000	+	0.0770930i
$443$	2.88482	+	2.88482i	0.137062	+	0.137062i	0.772309	−	0.635247i	$-0.219102\pi$
$443$	2.88482	+	2.88482i	0.137062	+	0.137062i	−0.635247	+	0.772309i	$0.719102\pi$
$444$	−11.7776	−	9.10092i	−0.558939	−	0.431910i
$445$	17.0304	−	15.4205i	0.807321	−	0.731001i
$446$	−6.83295	−	2.33241i	−0.323550	−	0.110443i
$447$		−	15.9878i		−	0.756198i
$448$	−8.12295	+	19.0594i	−0.383774	+	0.900473i
$449$	3.02196			0.142615			0.0713075	−	0.997454i	$-0.477283\pi$
$449$	3.02196			0.142615			0.0713075	+	0.997454i	$0.477283\pi$
$450$	−2.93543	+	6.43298i	−0.138377	+	0.303254i
$451$	22.7069	+	22.7069i	1.06923	+	1.06923i
$452$	−14.9024	+	19.2854i	−0.700951	+	0.907107i
$453$	2.03143	+	2.03143i	0.0954447	+	0.0954447i
$454$	13.2726	+	27.0297i	0.622914	+	1.26857i
$455$	−3.41469	−	0.169409i	−0.160083	−	0.00794204i
$456$	−15.1400	+	10.0052i	−0.708998	+	0.468535i
$457$	4.69013			0.219395			0.109698	−	0.993965i	$-0.465012\pi$
$457$	4.69013			0.219395			0.109698	+	0.993965i	$0.465012\pi$
$458$	15.4489	+	31.4617i	0.721879	+	1.47011i
$459$	−3.11422	+	3.11422i	−0.145359	+	0.145359i
$460$	−0.0978615	−	1.25314i	−0.00456281	−	0.0584278i
$461$	20.9304	+	20.9304i	0.974824	+	0.974824i	0.999691	−	0.0248664i	$-0.00791605\pi$
$461$	20.9304	+	20.9304i	0.974824	+	0.974824i	−0.0248664	+	0.999691i	$0.507916\pi$
$462$	−21.5496	−	7.35592i	−1.00258	−	0.342228i
$463$			25.5190i			1.18597i	0.805215	+	0.592983i	$0.202050\pi$
$463$			25.5190i			1.18597i	−0.805215	+	0.592983i	$0.797950\pi$
$464$	−10.6941	+	18.2358i	−0.496462	+	0.846576i
$465$	6.81683	+	0.338196i	0.316123	+	0.0156835i
$466$	4.18139	−	12.2497i	0.193699	−	0.567454i
$467$	−20.6018	+	20.6018i	−0.953336	+	0.953336i	−0.998959	−	0.0456227i	$-0.985473\pi$
$467$	−20.6018	+	20.6018i	−0.953336	+	0.953336i	0.0456227	+	0.998959i	$0.485473\pi$
$468$	−0.150149	−	1.17119i	−0.00694065	−	0.0541384i
$469$	−18.5723	+	18.5723i	−0.857590	+	0.857590i
$470$	−9.32592	−	21.6415i	−0.430173	−	0.998247i
$471$			8.11074i			0.373723i
$472$	−3.68725	+	18.0562i	−0.169719	+	0.831105i
$473$	23.4700			1.07915
$474$	2.82937	+	5.76202i	0.129957	+	0.264658i
$475$	24.8180	−	20.3275i	1.13873	−	0.932687i
$476$	13.9482	−	18.0504i	0.639313	−	0.827341i
$477$	2.89462	−	2.89462i	0.132535	−	0.132535i
$478$	5.90249	−	17.2917i	0.269973	−	0.790905i
$479$	30.6830			1.40194			0.700972	−	0.713189i	$-0.252750\pi$
$479$	30.6830			1.40194			0.700972	+	0.713189i	$0.252750\pi$
$480$	12.5528	+	1.55825i	0.572953	+	0.0711242i
$481$	−4.39372			−0.200337
$482$	−4.89158	+	14.3302i	−0.222806	+	0.652723i
$483$	0.514696	−	0.514696i	0.0234195	−	0.0234195i
$484$	−33.8178	+	43.7640i	−1.53717	+	1.98927i
$485$	11.2390	−	10.1766i	0.510338	−	0.462094i
$486$	−0.623338	−	1.26943i	−0.0282752	−	0.0575825i
$487$	4.53105			0.205322			0.102661	−	0.994716i	$-0.467264\pi$
$487$	4.53105			0.205322			0.102661	+	0.994716i	$0.467264\pi$
$488$	−0.828178	−	0.169122i	−0.0374899	−	0.00765578i
$489$			16.9085i			0.764628i
$490$	−0.851094	+	0.366760i	−0.0384485	+	0.0165685i
$491$	2.06787	−	2.06787i	0.0933215	−	0.0933215i	−0.658905	−	0.752226i	$-0.728980\pi$
$491$	2.06787	−	2.06787i	0.0933215	−	0.0933215i	0.752226	+	0.658905i	$0.228980\pi$
$492$	−1.31359	−	10.2463i	−0.0592214	−	0.461939i
$493$	16.4588	−	16.4588i	0.741268	−	0.741268i
$494$	−1.73055	+	5.06976i	−0.0778612	+	0.228099i
$495$	−0.688864	+	13.8850i	−0.0309621	+	0.624086i
$496$	−3.07989	−	11.8145i	−0.138291	−	0.530485i
$497$			41.3010i			1.85260i
$498$	8.64350	+	2.95044i	0.387325	+	0.132212i
$499$	−27.0618	−	27.0618i	−1.21145	−	1.21145i	−0.970549	−	0.240906i	$-0.922556\pi$
$499$	−27.0618	−	27.0618i	−1.21145	−	1.21145i	−0.240906	−	0.970549i	$-0.577444\pi$
$500$	−22.3557	−	0.474177i	−0.999775	−	0.0212058i
$501$	−6.53130	+	6.53130i	−0.291797	+	0.291797i
$502$	−3.95153	−	8.04730i	−0.176365	−	0.359169i
$503$	−8.42170			−0.375505			−0.187753	−	0.982216i	$-0.560120\pi$
$503$	−8.42170			−0.375505			−0.187753	+	0.982216i	$0.560120\pi$
$504$	4.03849	+	6.11114i	0.179889	+	0.272212i
$505$	−31.8254	−	1.57892i	−1.41621	−	0.0702609i
$506$	−1.08924	−	2.21824i	−0.0484225	−	0.0986126i
$507$	8.94592	+	8.94592i	0.397302	+	0.397302i
$508$	−8.25828	+	10.6871i	−0.366402	+	0.474164i
$509$	22.5863	+	22.5863i	1.00112	+	1.00112i	0.999999	+	0.00112047i	$0.000356656\pi$
$509$	22.5863	+	22.5863i	1.00112	+	1.00112i	0.00112047	+	0.999999i	$0.499643\pi$
$510$	−12.9414	−	5.14670i	−0.573053	−	0.227900i
$511$	−27.3640			−1.21051
$512$	−4.07501	−	22.2575i	−0.180092	−	0.983650i
$513$			6.41604i			0.283275i
$514$	−22.6598	−	7.73486i	−0.999480	−	0.341170i
$515$	7.07612	+	7.81490i	0.311811	+	0.344365i
$516$	−5.97418	−	4.61645i	−0.262999	−	0.203228i
$517$	−32.7609	−	32.7609i	−1.44082	−	1.44082i
$518$	24.4661	−	12.0138i	1.07498	−	0.527855i
$519$			3.34020i			0.146618i
$520$	3.21337	−	1.90175i	0.140915	−	0.0833974i
$521$			30.9260i			1.35489i	0.735572	+	0.677447i	$0.236914\pi$
$521$			30.9260i			1.35489i	−0.735572	+	0.677447i	$0.763086\pi$
$522$	3.29437	+	6.70900i	0.144191	+	0.293645i
$523$	26.4425	+	26.4425i	1.15625	+	1.15625i	0.985276	+	0.170974i	$0.0546913\pi$
$523$	26.4425	+	26.4425i	1.15625	+	1.15625i	0.170974	+	0.985276i	$0.445309\pi$
$524$	−1.42177	−	11.0901i	−0.0621104	−	0.484473i
$525$	−8.20499	−	10.0176i	−0.358095	−	0.437202i
$526$	−0.949771	+	2.78242i	−0.0414120	+	0.121319i
$527$			13.4430i			0.585585i
$528$	24.0646	−	6.27336i	1.04728	−	0.273013i
$529$	−22.9210			−0.996565
$530$	12.0288	+	4.78378i	0.522497	+	0.207794i
$531$	4.60721	+	4.60721i	0.199936	+	0.199936i
$532$	−4.22584	−	32.9624i	−0.183214	−	1.42910i
$533$	−2.15626	−	2.15626i	−0.0933978	−	0.0933978i
$534$	−13.0428	+	6.40449i	−0.564415	+	0.277149i
$535$	2.03211	−	40.9602i	0.0878560	−	1.77086i
$536$	5.73942	−	28.1056i	0.247905	−	1.21398i
$537$	13.1126			0.565851
$538$	28.8512	−	14.1670i	1.24386	−	0.610784i
$539$	−1.28839	+	1.28839i	−0.0554947	+	0.0554947i
$540$	2.90648	−	3.39888i	0.125075	−	0.146265i
$541$	21.6730	+	21.6730i	0.931794	+	0.931794i	0.997818	−	0.0660242i	$-0.0210315\pi$
$541$	21.6730	+	21.6730i	0.931794	+	0.931794i	−0.0660242	+	0.997818i	$0.521031\pi$
$542$	−1.91227	+	5.60211i	−0.0821389	+	0.240631i
$543$			14.9492i			0.641533i
$544$	−1.84028	+	24.8457i	−0.0789012	+	1.06525i
$545$	−0.0599984	+	1.20935i	−0.00257005	+	0.0518031i
$546$	2.04636	+	0.698521i	0.0875763	+	0.0298939i
$547$	−2.92159	+	2.92159i	−0.124918	+	0.124918i	−0.766802	−	0.641884i	$-0.778153\pi$
$547$	−2.92159	+	2.92159i	−0.124918	+	0.124918i	0.641884	+	0.766802i	$0.278153\pi$
$548$	8.22173	+	6.35320i	0.351215	+	0.271395i
$549$	−0.211318	+	0.211318i	−0.00901881	+	0.00901881i
$550$	−41.1858	+	15.3761i	−1.75617	+	0.655638i
$551$		−	33.9091i		−	1.44458i
$552$	−0.159057	+	0.778891i	−0.00676990	+	0.0331518i
$553$	−11.7552			−0.499880
$554$	28.4071	−	13.9490i	1.20690	−	0.592635i
$555$	−11.1694	−	12.3356i	−0.474116	−	0.523616i
$556$	−2.74101	+	0.351402i	−0.116245	+	0.0149028i
$557$	25.5453	−	25.5453i	1.08239	−	1.08239i	0.0861022	−	0.996286i	$-0.472559\pi$
$557$	25.5453	−	25.5453i	1.08239	−	1.08239i	0.996286	−	0.0861022i	$-0.0274412\pi$
$558$	−4.08520	−	1.39447i	−0.172940	−	0.0590328i
$559$	−2.22872			−0.0942648
$560$	−12.6934	+	19.3761i	−0.536394	+	0.818789i
$561$	−27.3817			−1.15606
$562$	−16.9368	−	5.78133i	−0.714435	−	0.243871i
$563$	11.6203	−	11.6203i	0.489736	−	0.489736i	−0.418487	−	0.908223i	$-0.637439\pi$
$563$	11.6203	−	11.6203i	0.489736	−	0.489736i	0.908223	+	0.418487i	$0.137439\pi$
$564$	1.89522	+	14.7831i	0.0798030	+	0.622479i
$565$	−20.1990	+	18.2895i	−0.849780	+	0.769447i
$566$	−2.78021	+	1.36519i	−0.116861	+	0.0573832i
$567$	2.58977			0.108760
$568$	−24.8689	−	37.6321i	−1.04347	−	1.57901i
$569$		−	13.3498i		−	0.559654i	−0.960050	−	0.279827i	$-0.909723\pi$
$569$		−	13.3498i		−	0.559654i	0.960050	−	0.279827i	$-0.0902771\pi$
$570$	−18.6329	+	8.02943i	−0.780445	+	0.336316i
$571$	−23.5430	+	23.5430i	−0.985244	+	0.985244i	−0.999893	−	0.0146492i	$-0.995337\pi$
$571$	−23.5430	+	23.5430i	−0.985244	+	0.985244i	0.0146492	+	0.999893i	$0.495337\pi$
$572$	4.48875	−	5.80893i	0.187684	−	0.242884i
$573$	−5.89011	+	5.89011i	−0.246063	+	0.246063i
$574$	17.9028	+	6.11108i	0.747248	+	0.255071i
$575$	0.139098	−	1.39841i	0.00580080	−	0.0583179i
$576$	−7.35949	−	3.13655i	−0.306645	−	0.130690i
$577$		−	34.7117i		−	1.44507i	−0.691335	−	0.722534i	$-0.742977\pi$
$577$		−	34.7117i		−	1.44507i	0.691335	−	0.722534i	$-0.257023\pi$
$578$	1.09495	−	3.20774i	0.0455441	−	0.133424i
$579$	−4.05458	−	4.05458i	−0.168503	−	0.168503i
$580$	−15.3609	+	17.9633i	−0.637826	+	0.745884i
$581$	−11.8265	+	11.8265i	−0.490644	+	0.490644i
$582$	−8.60741	+	4.22656i	−0.356789	+	0.175197i
$583$	25.4508			1.05407
$584$	24.9332	−	16.4769i	1.03174	−	0.681818i
$585$	0.0654147	−	1.31853i	0.00270457	−	0.0545145i
$586$	38.2173	−	18.7662i	1.57874	−	0.775223i
$587$	−26.8949	−	26.8949i	−1.11007	−	1.11007i	−0.993140	−	0.116931i	$-0.962694\pi$
$587$	−26.8949	−	26.8949i	−1.11007	−	1.11007i	−0.116931	−	0.993140i	$-0.537306\pi$
$588$	0.581373	−	0.0745331i	0.0239754	−	0.00307369i
$589$	13.8479	+	13.8479i	0.570592	+	0.570592i
$590$	−7.61410	+	19.1456i	−0.313467	+	0.788212i
$591$	4.57128			0.188037
$592$	−15.0588	+	25.6785i	−0.618912	+	1.05538i
$593$		−	8.25028i		−	0.338798i	−0.985548	−	0.169399i	$-0.945817\pi$
$593$		−	8.25028i		−	0.338798i	0.985548	−	0.169399i	$-0.0541827\pi$
$594$	2.84037	−	8.32105i	0.116542	−	0.341417i
$595$	18.9056	−	17.1184i	0.775055	−	0.701786i
$596$	−31.7161	+	4.06606i	−1.29914	+	0.166552i
$597$	13.4774	+	13.4774i	0.551594	+	0.551594i
$598$	0.103434	+	0.210645i	0.00422975	+	0.00861390i
$599$			19.6734i			0.803832i	0.915677	+	0.401916i	$0.131656\pi$
$599$			19.6734i			0.803832i	−0.915677	+	0.401916i	$0.868344\pi$
$600$	13.5081	+	4.18715i	0.551464	+	0.170940i
$601$		−	30.0313i		−	1.22500i	−0.790470	−	0.612501i	$-0.790164\pi$
$601$		−	30.0313i		−	1.22500i	0.790470	−	0.612501i	$-0.209836\pi$
$602$	12.4104	−	6.09400i	0.505812	−	0.248373i
$603$	−7.17140	−	7.17140i	−0.292042	−	0.292042i
$604$	3.51323	−	4.54651i	0.142951	−	0.184995i
$605$	−45.8374	+	41.5042i	−1.86355	+	1.68739i
$606$	19.0724	+	6.51030i	0.774762	+	0.264463i
$607$			5.52944i			0.224433i	0.993684	+	0.112217i	$0.0357950\pi$
$607$			5.52944i			0.224433i	−0.993684	+	0.112217i	$0.964205\pi$
$608$	23.6983	+	27.4897i	0.961095	+	1.11486i
$609$	−13.6871			−0.554629
$610$	−0.878145	−	0.349233i	−0.0355550	−	0.0141400i
$611$	3.11098	+	3.11098i	0.125857	+	0.125857i
$612$	6.96989	+	5.38586i	0.281741	+	0.217711i
$613$	−28.9851	−	28.9851i	−1.17070	−	1.17070i	−0.982044	−	0.188653i	$-0.939588\pi$
$613$	−28.9851	−	28.9851i	−1.17070	−	1.17070i	−0.188653	−	0.982044i	$-0.560412\pi$
$614$	10.7850	+	21.9638i	0.435249	+	0.886385i
$615$	0.572287	−	11.5353i	0.0230768	−	0.465147i
$616$	−9.11185	+	44.6202i	−0.367127	+	1.79780i
$617$	−26.5578			−1.06918			−0.534588	−	0.845113i	$-0.679533\pi$
$617$	−26.5578			−1.06918			−0.534588	+	0.845113i	$0.679533\pi$
$618$	−2.93888	−	5.98504i	−0.118219	−	0.240753i
$619$	5.91235	−	5.91235i	0.237638	−	0.237638i	−0.578234	−	0.815871i	$-0.696258\pi$
$619$	5.91235	−	5.91235i	0.237638	−	0.237638i	0.815871	+	0.578234i	$0.196258\pi$
$620$	−1.06277	−	13.6090i	−0.0426819	−	0.546550i
$621$	0.198741	+	0.198741i	0.00797522	+	0.00797522i
$622$	26.0817	+	8.90293i	1.04578	+	0.356975i
$623$		−	26.6087i		−	1.06605i
$624$	−2.28519	+	0.595721i	−0.0914806	+	0.0238479i
$625$	−24.5101	−	4.92471i	−0.980406	−	0.196988i
$626$	4.44718	−	13.0283i	0.177745	−	0.520716i
$627$	−28.2064	+	28.2064i	−1.12646	+	1.12646i
$628$	16.0898	−	2.06274i	0.642053	−	0.0823124i
$629$	23.1763	−	23.1763i	0.924098	−	0.924098i
$630$	3.24100	+	7.52099i	0.129125	+	0.299643i
$631$			37.6881i			1.50034i	0.661246	+	0.750169i	$0.270028\pi$
$631$			37.6881i			1.50034i	−0.661246	+	0.750169i	$0.729972\pi$
$632$	10.7109	−	7.07822i	0.426058	−	0.281556i
$633$	6.27514			0.249414
$634$	7.46357	+	15.1996i	0.296416	+	0.603652i
$635$	−11.1934	+	10.1353i	−0.444198	+	0.402206i
$636$	−6.47840	−	5.00607i	−0.256885	−	0.198504i
$637$	0.122346	−	0.122346i	0.00484751	−	0.00484751i
$638$	−15.0115	+	43.9772i	−0.594311	+	1.74107i
$639$	−15.9477			−0.630882
$640$	−0.101240	−	25.2980i	−0.00400188	−	0.999992i
$641$	36.5113			1.44211			0.721055	−	0.692878i	$-0.243657\pi$
$641$	36.5113			1.44211			0.721055	+	0.692878i	$0.243657\pi$
$642$	−8.37896	+	24.5467i	−0.330691	+	0.968781i
$643$	12.1973	−	12.1973i	0.481014	−	0.481014i	−0.424441	−	0.905455i	$-0.639529\pi$
$643$	12.1973	−	12.1973i	0.481014	−	0.481014i	0.905455	+	0.424441i	$0.139529\pi$
$644$	−1.15193	−	0.890136i	−0.0453925	−	0.0350763i
$645$	−5.66570	−	6.25722i	−0.223087	−	0.246378i
$646$	−17.6139	−	35.8707i	−0.693008	−	1.41131i
$647$	−16.5371			−0.650142			−0.325071	−	0.945690i	$-0.605388\pi$
$647$	−16.5371			−0.650142			−0.325071	+	0.945690i	$0.605388\pi$
$648$	−2.35972	+	1.55940i	−0.0926985	+	0.0612590i
$649$			40.5088i			1.59011i
$650$	3.91102	−	1.46012i	0.153403	−	0.0572705i
$651$	5.58957	−	5.58957i	0.219073	−	0.219073i
$652$	33.5424	−	4.30020i	1.31362	−	0.168409i
$653$	2.73228	−	2.73228i	0.106923	−	0.106923i	−0.651622	−	0.758544i	$-0.725911\pi$
$653$	2.73228	−	2.73228i	0.106923	−	0.106923i	0.758544	+	0.651622i	$0.225911\pi$
$654$	0.247390	−	0.724744i	0.00967370	−	0.0283397i
$655$	0.619416	−	12.4852i	0.0242026	−	0.487838i
$656$	−19.9922	+	5.21172i	−0.780562	+	0.203484i
$657$		−	10.5662i		−	0.412226i
$658$	−25.8296	−	8.81688i	−1.00694	−	0.343718i
$659$	14.1442	+	14.1442i	0.550982	+	0.550982i	0.926724	−	0.375743i	$-0.122612\pi$
$659$	14.1442	+	14.1442i	0.550982	+	0.550982i	−0.375743	+	0.926724i	$0.622612\pi$
$660$	27.7198	−	2.16473i	1.07899	−	0.0842621i
$661$	14.2173	−	14.2173i	0.552991	−	0.552991i	−0.374312	−	0.927303i	$-0.622121\pi$
$661$	14.2173	−	14.2173i	0.552991	−	0.552991i	0.927303	+	0.374312i	$0.122121\pi$
$662$	6.27259	+	12.7742i	0.243791	+	0.496481i
$663$	2.60018			0.100982
$664$	3.65474	−	17.8970i	0.141831	−	0.694539i
$665$	1.84105	−	37.1091i	0.0713929	−	1.43903i
$666$	4.63893	+	9.44719i	0.179755	+	0.366071i
$667$	−1.05036	−	1.05036i	−0.0406701	−	0.0406701i
$668$	14.6176	+	11.2955i	0.565572	+	0.437036i
$669$	3.61003	+	3.61003i	0.139572	+	0.139572i
$670$	11.8518	−	29.8013i	0.457875	−	1.15132i
$671$	−1.85800			−0.0717274
$672$	11.0960	−	9.56562i	0.428037	−	0.369002i
$673$			17.6236i			0.679341i	0.940545	+	0.339670i	$0.110316\pi$
$673$			17.6236i			0.679341i	−0.940545	+	0.339670i	$0.889684\pi$
$674$	−21.1940	−	7.23453i	−0.816363	−	0.278663i
$675$	3.86812	−	3.16822i	0.148884	−	0.121945i
$676$	15.4714	−	20.0217i	0.595056	−	0.770067i
$677$	33.4900	+	33.4900i	1.28713	+	1.28713i	0.936525	+	0.350601i	$0.114023\pi$
$677$	33.4900	+	33.4900i	1.28713	+	1.28713i	0.350601	+	0.936525i	$0.385977\pi$
$678$	15.4694	−	7.59607i	0.594100	−	0.291725i
$679$		−	17.5601i		−	0.673893i
$680$	−6.91857	+	26.9815i	−0.265315	+	1.03469i
$681$		−	21.2928i		−	0.815941i
$682$	−11.8291	−	24.0899i	−0.452959	−	0.922452i
$683$	0.602993	+	0.602993i	0.0230729	+	0.0230729i	0.718549	−	0.695476i	$-0.244807\pi$
$683$	0.602993	+	0.602993i	0.0230729	+	0.0230729i	−0.695476	+	0.718549i	$0.744807\pi$
$684$	12.7279	−	1.63174i	0.486664	−	0.0623912i
$685$	7.79720	+	8.61125i	0.297916	+	0.329019i
$686$	−8.62881	+	25.2787i	−0.329450	+	0.965144i
$687$		−	24.7841i		−	0.945574i
$688$	−7.63857	+	13.0254i	−0.291218	+	0.496590i
$689$	−2.41682			−0.0920736
$690$	−0.328449	+	0.825884i	−0.0125039	+	0.0314409i
$691$	−14.0957	−	14.0957i	−0.536226	−	0.536226i	0.386192	−	0.922418i	$-0.373790\pi$
$691$	−14.0957	−	14.0957i	−0.536226	−	0.536226i	−0.922418	+	0.386192i	$0.873790\pi$
$692$	6.62616	−	0.849486i	0.251889	−	0.0322926i
$693$	11.3853	+	11.3853i	0.432490	+	0.432490i
$694$	16.8397	−	8.26895i	0.639228	−	0.313885i
$695$	−3.08582	−	0.153094i	−0.117052	−	0.00580717i
$696$	12.4712	−	8.24151i	0.472721	−	0.312394i
$697$	22.7479			0.861637
$698$	−0.860252	+	0.422416i	−0.0325610	+	0.0159887i
$699$	−6.47183	+	6.47183i	−0.244787	+	0.244787i
$700$	−17.7858	+	18.8245i	−0.672239	+	0.711497i
$701$	23.9043	+	23.9043i	0.902854	+	0.902854i	0.995682	−	0.0928282i	$-0.0295907\pi$
$701$	23.9043	+	23.9043i	0.902854	+	0.902854i	−0.0928282	+	0.995682i	$0.529591\pi$
$702$	−0.269723	+	0.790170i	−0.0101800	+	0.0298231i
$703$		−	47.7487i		−	1.80087i
$704$	−18.5650	−	46.1431i	−0.699696	−	1.73908i
$705$	−0.825679	+	16.6428i	−0.0310969	+	0.626803i
$706$	−11.9832	−	4.09043i	−0.450993	−	0.153945i
$707$	−26.0957	+	26.0957i	−0.981431	+	0.981431i
$708$	7.96791	−	10.3113i	0.299452	−	0.387524i
$709$	30.0855	−	30.0855i	1.12989	−	1.12989i	0.139691	−	0.990195i	$-0.455389\pi$
$709$	30.0855	−	30.0855i	1.12989	−	1.12989i	0.990195	−	0.139691i	$-0.0446110\pi$
$710$	−19.9580	−	46.3139i	−0.749009	−	1.73813i
$711$		−	4.53907i		−	0.170228i
$712$	16.0221	+	24.2450i	0.600452	+	0.908618i
$713$	0.857896			0.0321285
$714$	−14.4789	+	7.10967i	−0.541858	+	0.266073i
$715$	6.08415	−	5.50899i	0.227534	−	0.206024i
$716$	−3.33483	−	26.0123i	−0.124628	−	0.972127i
$717$	−9.13569	+	9.13569i	−0.341178	+	0.341178i
$718$	4.65363	+	1.58850i	0.173672	+	0.0592825i
$719$	20.9727			0.782148			0.391074	−	0.920359i	$-0.372104\pi$
$719$	20.9727			0.782148			0.391074	+	0.920359i	$0.372104\pi$
$720$	−7.48176	−	4.90135i	−0.278829	−	0.182663i
$721$	12.2101			0.454729
$722$	−29.6661	−	10.1265i	−1.10406	−	0.376868i
$723$	7.57104	−	7.57104i	0.281570	−	0.281570i
$724$	29.6558	−	3.80193i	1.10215	−	0.141297i
$725$	−20.4432	+	16.7442i	−0.759242	+	0.621865i
$726$	35.1045	−	17.2377i	1.30285	−	0.639749i
$727$	−19.5823			−0.726269			−0.363134	−	0.931737i	$-0.618293\pi$
$727$	−19.5823			−0.726269			−0.363134	+	0.931737i	$0.618293\pi$
$728$	0.865265	−	4.23715i	0.0320689	−	0.157039i
$729$			1.00000i			0.0370370i
$730$	30.6853	−	13.2232i	1.13571	−	0.489411i
$731$	11.7562	−	11.7562i	0.434818	−	0.434818i
$732$	0.472947	+	0.365461i	0.0174806	+	0.0135078i
$733$	3.95752	−	3.95752i	0.146174	−	0.146174i	−0.630232	−	0.776407i	$-0.717040\pi$
$733$	3.95752	−	3.95752i	0.146174	−	0.146174i	0.776407	+	0.630232i	$0.217040\pi$
$734$	−20.2351	−	6.90721i	−0.746892	−	0.254950i
$735$	0.654510	+	0.0324715i	0.0241420	+	0.00119773i
$736$	1.58559	+	0.117442i	0.0584455	+	0.00432896i
$737$		−	63.0544i		−	2.32264i
$738$	−2.35969	+	6.91288i	−0.0868615	+	0.254467i
$739$	−1.94684	−	1.94684i	−0.0716155	−	0.0716155i	0.670392	−	0.742007i	$-0.266126\pi$
$739$	−1.94684	−	1.94684i	−0.0716155	−	0.0716155i	−0.742007	+	0.670392i	$0.766126\pi$
$740$	−21.6302	+	25.2947i	−0.795143	+	0.929853i
$741$	2.67849	−	2.67849i	0.0983969	−	0.0983969i
$742$	13.4579	−	6.60833i	0.494054	−	0.242599i
$743$	−10.5553			−0.387238			−0.193619	−	0.981077i	$-0.562023\pi$
$743$	−10.5553			−0.387238			−0.193619	+	0.981077i	$0.562023\pi$
$744$	−1.72735	+	8.45872i	−0.0633277	+	0.310112i
$745$	−35.7060	−	1.77144i	−1.30816	−	0.0649006i
$746$	−34.2003	+	16.7936i	−1.25216	+	0.614859i
$747$	−4.56660	−	4.56660i	−0.167083	−	0.167083i
$748$	6.96377	+	54.3188i	0.254621	+	1.98609i
$749$	−33.5860	−	33.5860i	−1.22721	−	1.22721i
$750$	14.0417	+	7.26853i	0.512729	+	0.265409i
$751$	49.4390			1.80405			0.902027	−	0.431680i	$-0.142079\pi$
$751$	49.4390			1.80405			0.902027	+	0.431680i	$0.142079\pi$
$752$	28.8441	−	7.51932i	1.05184	−	0.274201i
$753$			6.33931i			0.231017i
$754$	1.42550	−	4.17609i	0.0519136	−	0.152084i
$755$	4.76191	−	4.31174i	0.173304	−	0.156920i
$756$	−0.658637	−	5.13750i	−0.0239544	−	0.186849i
$757$	−4.11693	−	4.11693i	−0.149632	−	0.149632i	0.628321	−	0.777954i	$-0.283742\pi$
$757$	−4.11693	−	4.11693i	−0.149632	−	0.149632i	−0.777954	+	0.628321i	$0.783742\pi$
$758$	3.11025	+	6.33403i	0.112969	+	0.230063i
$759$			1.74743i			0.0634276i
$760$	20.6672	+	34.9212i	0.749680	+	1.26672i
$761$			14.6496i			0.531049i	0.964104	+	0.265525i	$0.0855452\pi$
$761$			14.6496i			0.531049i	−0.964104	+	0.265525i	$0.914455\pi$
$762$	8.57249	−	4.20942i	0.310548	−	0.152491i
$763$	0.991630	+	0.991630i	0.0358994	+	0.0358994i
$764$	13.1826	+	10.1866i	0.476929	+	0.368539i
$765$	6.61000	+	7.30010i	0.238985	+	0.263936i
$766$	−4.28643	−	1.46316i	−0.154875	−	0.0528662i
$767$		−	3.84673i		−	0.138897i
$768$	−4.35049	+	15.3972i	−0.156985	+	0.555598i
$769$	2.44453			0.0881520			0.0440760	−	0.999028i	$-0.485966\pi$
$769$	2.44453			0.0881520			0.0440760	+	0.999028i	$0.485966\pi$
$770$	−18.8158	+	47.3123i	−0.678075	+	1.70502i
$771$	11.9718	+	11.9718i	0.431153	+	0.431153i
$772$	−7.01216	+	9.07450i	−0.252373	+	0.326598i
$773$	12.2398	+	12.2398i	0.440234	+	0.440234i	0.892091	−	0.451857i	$-0.149238\pi$
$773$	12.2398	+	12.2398i	0.440234	+	0.440234i	−0.451857	+	0.892091i	$0.649238\pi$
$774$	2.35310	+	4.79209i	0.0845804	+	0.172248i
$775$	1.51060	−	15.1867i	0.0542624	−	0.545522i
$776$	10.5736	+	16.0002i	0.379569	+	0.574372i
$777$	−19.2733			−0.691426
$778$	14.9504	+	30.4465i	0.535997	+	1.09156i
$779$	23.4330	−	23.4330i	0.839576	−	0.839576i
$780$	−2.63229	+	0.205564i	−0.0942510	+	0.00736037i
$781$	−70.1100	−	70.1100i	−2.50873	−	2.50873i
$782$	−1.65672	−	0.565518i	−0.0592442	−	0.0202229i
$783$		−	5.28505i		−	0.188872i
$784$	−0.295712	−	1.13435i	−0.0105612	−	0.0405126i
$785$	18.1139	+	0.898665i	0.646512	+	0.0320747i
$786$	−2.55402	+	7.48217i	−0.0910989	+	0.266880i
$787$	18.2070	−	18.2070i	0.649009	−	0.649009i	−0.303745	−	0.952753i	$-0.598237\pi$
$787$	18.2070	−	18.2070i	0.649009	−	0.649009i	0.952753	+	0.303745i	$0.0982370\pi$
$788$	−1.16258	−	9.06835i	−0.0414152	−	0.323046i
$789$	1.47003	−	1.47003i	0.0523343	−	0.0523343i
$790$	13.1819	−	5.68047i	0.468992	−	0.202102i
$791$			31.5593i			1.12212i
$792$	−17.2294	−	3.51840i	−0.612219	−	0.125021i
$793$	0.176437			0.00626545
$794$	−13.9628	−	28.4352i	−0.495520	−	1.00913i
$795$	−6.14389	−	6.78533i	−0.217901	−	0.240651i
$796$	23.3084	−	30.1636i	0.826145	−	1.06912i
$797$	5.02164	−	5.02164i	0.177876	−	0.177876i	−0.612553	−	0.790429i	$-0.709858\pi$
$797$	5.02164	−	5.02164i	0.177876	−	0.177876i	0.790429	+	0.612553i	$0.209858\pi$
$798$	−7.59115	+	22.2388i	−0.268724	+	0.787245i
$799$	−32.8200			−1.16109
$800$	4.87092	−	27.8617i	0.172213	−	0.985060i
$801$	10.2745			0.363032
$802$	4.96183	−	14.5360i	0.175208	−	0.513284i
$803$	46.4514	−	46.4514i	1.63923	−	1.63923i
$804$	−12.4025	+	16.0502i	−0.437403	+	0.566047i
$805$	−1.09245	−	1.20651i	−0.0385039	−	0.0425238i
$806$	1.12329	+	2.28759i	0.0395663	+	0.0805769i
$807$	−22.7277			−0.800053
$808$	8.06438	−	39.4908i	0.283704	−	1.38928i
$809$		−	23.6476i		−	0.831404i	−0.909501	−	0.415702i	$-0.863536\pi$
$809$		−	23.6476i		−	0.831404i	0.909501	−	0.415702i	$-0.136464\pi$
$810$	−2.90411	+	1.25146i	−0.102040	+	0.0439719i
$811$	−24.2614	+	24.2614i	−0.851934	+	0.851934i	−0.990371	−	0.138438i	$-0.955792\pi$
$811$	−24.2614	+	24.2614i	−0.851934	+	0.851934i	0.138438	+	0.990371i	$0.455792\pi$
$812$	3.48093	+	27.1520i	0.122157	+	0.952848i
$813$	2.95975	−	2.95975i	0.103803	−	0.103803i
$814$	−21.1383	+	61.9259i	−0.740896	+	2.17050i
$815$	37.7621	+	1.87345i	1.32275	+	0.0656240i
$816$	8.91168	−	15.1964i	0.311971	−	0.531979i
$817$		−	24.2205i		−	0.847369i
$818$	16.7784	+	5.72728i	0.586644	+	0.200250i
$819$	−1.08115	−	1.08115i	−0.0377784	−	0.0377784i
$820$	−23.0288	+	1.79839i	−0.804201	+	0.0628027i
$821$	−38.9257	+	38.9257i	−1.35852	+	1.35852i	−0.482771	+	0.875746i	$0.660370\pi$
$821$	−38.9257	+	38.9257i	−1.35852	+	1.35852i	−0.875746	+	0.482771i	$0.839630\pi$
$822$	−3.23836	−	6.59492i	−0.112951	−	0.230024i
$823$	−38.6799			−1.34830			−0.674148	−	0.738596i	$-0.735489\pi$
$823$	−38.6799			−1.34830			−0.674148	+	0.738596i	$0.735489\pi$
$824$	−11.1255	+	7.35217i	−0.387574	+	0.256125i
$825$	30.9334	+	3.07691i	1.07696	+	0.107124i
$826$	10.5181	+	21.4202i	0.365973	+	0.745305i
$827$	25.6217	+	25.6217i	0.890955	+	0.890955i	0.994613	−	0.103658i	$-0.0330548\pi$
$827$	25.6217	+	25.6217i	0.890955	+	0.890955i	−0.103658	+	0.994613i	$0.533055\pi$
$828$	0.343712	−	0.444800i	0.0119448	−	0.0154579i
$829$	−14.8962	−	14.8962i	−0.517367	−	0.517367i	0.399407	−	0.916774i	$-0.369216\pi$
$829$	−14.8962	−	14.8962i	−0.517367	−	0.517367i	−0.916774	+	0.399407i	$0.869216\pi$
$830$	7.54697	−	18.9768i	0.261959	−	0.658695i
$831$	−22.3779			−0.776279
$832$	1.76294	+	4.38176i	0.0611191	+	0.151910i
$833$			1.29071i			0.0447205i
$834$	1.84928	+	0.631246i	0.0640353	+	0.0218583i
$835$	13.8628	+	15.3102i	0.479743	+	0.529830i
$836$	63.1284	+	48.7814i	2.18334	+	1.68714i
$837$	2.15832	+	2.15832i	0.0746025	+	0.0746025i
$838$	38.9110	−	19.1068i	1.34416	−	0.660032i
$839$			14.5709i			0.503045i	0.967851	+	0.251522i	$0.0809312\pi$
$839$			14.5709i			0.503045i	−0.967851	+	0.251522i	$0.919069\pi$
$840$	14.0956	−	8.34214i	0.486345	−	0.287831i
$841$		−	1.06820i		−	0.0368344i
$842$	−7.95965	−	16.2098i	−0.274308	−	0.558628i
$843$	8.94816	+	8.94816i	0.308191	+	0.308191i
$844$	−1.59591	−	12.4484i	−0.0549334	−	0.428492i
$845$	20.9703	−	18.9879i	0.721401	−	0.653204i
$846$	3.40450	−	9.97370i	0.117049	−	0.342903i
$847$			71.6171i			2.46079i
$848$	−8.28326	+	14.1248i	−0.284448	+	0.485047i
$849$	2.19013			0.0751650
$850$	−12.9281	+	28.3319i	−0.443431	+	0.971778i
$851$	−1.47905	−	1.47905i	−0.0507011	−	0.0507011i
$852$	4.05586	+	31.6365i	0.138951	+	1.08385i
$853$	−11.9474	−	11.9474i	−0.409070	−	0.409070i	0.472344	−	0.881414i	$-0.343408\pi$
$853$	−11.9474	−	11.9474i	−0.409070	−	0.409070i	−0.881414	+	0.472344i	$0.843408\pi$
$854$	−0.982474	+	0.482432i	−0.0336196	+	0.0165085i
$855$	14.3291	+	0.710893i	0.490044	+	0.0243120i
$856$	50.8258	+	10.3791i	1.73719	+	0.354750i
$857$	−18.3405			−0.626498			−0.313249	−	0.949671i	$-0.601417\pi$
$857$	−18.3405			−0.626498			−0.313249	+	0.949671i	$0.601417\pi$
$858$	−4.65954	+	2.28801i	−0.159074	+	0.0781114i
$859$	−17.4227	+	17.4227i	−0.594455	+	0.594455i	−0.938832	−	0.344377i	$-0.888090\pi$
$859$	−17.4227	+	17.4227i	−0.594455	+	0.594455i	0.344377	+	0.938832i	$0.388090\pi$
$860$	−10.9719	+	12.8308i	−0.374140	+	0.437526i
$861$	−9.45853	−	9.45853i	−0.322346	−	0.322346i
$862$	10.1419	−	29.7114i	0.345435	−	1.01197i
$863$			40.5444i			1.38015i	0.723740	+	0.690073i	$0.242422\pi$
$863$			40.5444i			1.38015i	−0.723740	+	0.690073i	$0.757578\pi$
$864$	3.69361	+	4.28454i	0.125659	+	0.145763i
$865$	7.45973	+	0.370091i	0.253638	+	0.0125835i
$866$	−41.6395	−	14.2135i	−1.41497	−	0.482996i
$867$	−1.69474	+	1.69474i	−0.0575562	+	0.0575562i
$868$	−12.5099	−	9.66684i	−0.424615	−	0.328114i
$869$	19.9548	−	19.9548i	0.676921	−	0.676921i
$870$	15.3484	−	6.61404i	0.520358	−	0.224237i
$871$			5.98767i			0.202884i
$872$	−1.50064	−	0.306444i	−0.0508180	−	0.0103775i
$873$	6.78053			0.229486
$874$	−2.28917	+	1.12407i	−0.0774325	+	0.0380223i
$875$	−23.2815	+	17.2144i	−0.787060	+	0.581954i
$876$	−20.9608	+	2.68721i	−0.708200	+	0.0907926i
$877$	−31.0594	+	31.0594i	−1.04880	+	1.04880i	−0.0500546	+	0.998746i	$0.515940\pi$
$877$	−31.0594	+	31.0594i	−1.04880	+	1.04880i	−0.998746	+	0.0500546i	$0.984060\pi$
$878$	−0.616878	−	0.210570i	−0.0208186	−	0.00710638i
$879$	−30.1059			−1.01545
$880$	−11.3441	−	54.4391i	−0.382409	−	1.83514i
$881$	−18.0615			−0.608506			−0.304253	−	0.952591i	$-0.598407\pi$
$881$	−18.0615			−0.608506			−0.304253	+	0.952591i	$0.598407\pi$
$882$	−0.392236	−	0.133889i	−0.0132073	−	0.00450827i
$883$	−18.0110	+	18.0110i	−0.606117	+	0.606117i	−0.941929	−	0.335812i	$-0.890989\pi$
$883$	−18.0110	+	18.0110i	−0.606117	+	0.606117i	0.335812	+	0.941929i	$0.390989\pi$
$884$	−0.661283	−	5.15814i	−0.0222413	−	0.173487i
$885$	10.7999	−	9.77891i	0.363034	−	0.328715i
$886$	−5.17896	+	2.54307i	−0.173991	+	0.0854359i
$887$	−37.8699			−1.27155			−0.635774	−	0.771876i	$-0.719319\pi$
$887$	−37.8699			−1.27155			−0.635774	+	0.771876i	$0.719319\pi$
$888$	17.5612	−	11.6052i	0.589316	−	0.389444i
$889$			17.4888i			0.586556i
$890$	12.8582	+	29.8383i	0.431006	+	1.00018i
$891$	−4.39624	+	4.39624i	−0.147279	+	0.147279i
$892$	6.24334	−	8.07957i	0.209043	−	0.270524i
$893$	−33.8085	+	33.8085i	−1.13136	+	1.13136i
$894$	21.3979	+	7.30413i	0.715653	+	0.244287i
$895$	1.45287	−	29.2847i	0.0485641	−	0.978879i
$896$	−21.7979	−	19.5791i	−0.728216	−	0.654091i
$897$		−	0.165936i		−	0.00554046i
$898$	−1.38060	+	4.04455i	−0.0460712	+	0.134968i
$899$	−11.4069	−	11.4069i	−0.380440	−	0.380440i
$900$	−7.26876	−	6.86769i	−0.242292	−	0.228923i
$901$	12.7484	−	12.7484i	0.424710	−	0.424710i
$902$	−40.7644	+	20.0169i	−1.35731	+	0.666489i
$903$	−9.77640			−0.325338
$904$	−19.0030	−	28.7558i	−0.632032	−	0.956405i
$905$	33.3865	+	1.65637i	1.10980	+	0.0550595i
$906$	−3.64690	+	1.79077i	−0.121160	+	0.0594943i
$907$	13.1614	+	13.1614i	0.437018	+	0.437018i	0.891007	−	0.453989i	$-0.149999\pi$
$907$	13.1614	+	13.1614i	0.437018	+	0.437018i	−0.453989	+	0.891007i	$0.649999\pi$
$908$	−42.2398	+	5.41523i	−1.40178	+	0.179711i
$909$	−10.0764	−	10.0764i	−0.334215	−	0.334215i
$910$	1.78676	−	4.49279i	0.0592304	−	0.148935i
$911$	4.85931			0.160996			0.0804981	−	0.996755i	$-0.474349\pi$
$911$	4.85931			0.160996			0.0804981	+	0.996755i	$0.474349\pi$
$912$	−6.47398	−	24.8342i	−0.214375	−	0.822342i
$913$		−	40.1517i		−	1.32883i
$914$	−2.14271	+	6.27722i	−0.0708746	+	0.207632i
$915$	0.448526	+	0.495354i	0.0148278	+	0.0163759i
$916$	−49.1659	+	6.30316i	−1.62449	+	0.208262i
$917$	−10.2375	−	10.2375i	−0.338071	−	0.338071i
$918$	−2.74529	−	5.59078i	−0.0906079	−	0.184523i
$919$			37.6319i			1.24136i	0.784063	+	0.620681i	$0.213144\pi$
$919$			37.6319i			1.24136i	−0.784063	+	0.620681i	$0.786856\pi$
$920$	1.72189	+	0.441525i	0.0567691	+	0.0145567i
$921$		−	17.3021i		−	0.570123i
$922$	−37.5751	+	18.4508i	−1.23747	+	0.607645i
$923$	6.65767	+	6.65767i	0.219140	+	0.219140i
$924$	19.6902	−	25.4812i	0.647758	−	0.838270i
$925$	−28.7869	+	23.5782i	−0.946506	+	0.775246i
$926$	−34.1543	−	11.6585i	−1.12238	−	0.383121i
$927$			4.71475i			0.154853i
$928$	−19.5209	−	22.6440i	−0.640806	−	0.743326i
$929$	37.6717			1.23597			0.617984	−	0.786191i	$-0.287950\pi$
$929$	37.6717			1.23597			0.617984	+	0.786191i	$0.287950\pi$
$930$	−3.56694	+	8.96906i	−0.116965	+	0.294107i
$931$	1.32959	+	1.32959i	0.0435755	+	0.0435755i
$932$	14.4845	+	11.1926i	0.474456	+	0.366627i
$933$	−13.7797	−	13.7797i	−0.451126	−	0.451126i
$934$	−18.1611	−	36.9852i	−0.594250	−	1.21019i
$935$	−3.03387	+	61.1521i	−0.0992182	+	1.99989i
$936$	1.63611	+	0.334108i	0.0534779	+	0.0109207i
$937$	22.1390			0.723251			0.361625	−	0.932323i	$-0.382222\pi$
$937$	22.1390			0.723251			0.361625	+	0.932323i	$0.382222\pi$
$938$	−16.3721	−	33.3418i	−0.534568	−	1.08865i
$939$	−6.88321	+	6.88321i	−0.224625	+	0.224625i
$940$	33.2253	−	2.59467i	1.08369	−	0.0846289i
$941$	−6.24976	−	6.24976i	−0.203736	−	0.203736i	0.597862	−	0.801599i	$-0.296017\pi$
$941$	−6.24976	−	6.24976i	−0.203736	−	0.203736i	−0.801599	+	0.597862i	$0.796017\pi$
$942$	−10.8553	−	3.70544i	−0.353685	−	0.120730i
$943$		−	1.45171i		−	0.0472742i
$944$	−22.4817	−	13.1840i	−0.731717	−	0.429104i
$945$	0.286945	−	5.78380i	0.00933433	−	0.188147i
$946$	−10.7224	+	31.4120i	−0.348615	+	1.02129i
$947$	4.23108	−	4.23108i	0.137492	−	0.137492i	−0.635011	−	0.772503i	$-0.719005\pi$
$947$	4.23108	−	4.23108i	0.137492	−	0.137492i	0.772503	+	0.635011i	$0.219005\pi$
$948$	−9.00444	+	1.15439i	−0.292451	+	0.0374927i
$949$	−4.41104	+	4.41104i	−0.143189	+	0.143189i
$950$	15.8678	+	42.5028i	0.514819	+	1.37897i
$951$		−	11.9736i		−	0.388269i
$952$	17.7862	+	26.9145i	0.576454	+	0.872304i
$953$	0.585699			0.0189726			0.00948632	−	0.999955i	$-0.496980\pi$
$953$	0.585699			0.0189726			0.00948632	+	0.999955i	$0.496980\pi$
$954$	2.55170	+	5.19654i	0.0826143	+	0.168244i
$955$	12.5019	+	13.8071i	0.404552	+	0.446789i
$956$	20.4465	+	15.7996i	0.661286	+	0.510997i
$957$	23.2344	−	23.2344i	0.751060	−	0.751060i
$958$	−14.0177	+	41.0658i	−0.452892	+	1.32678i
$959$	13.4544			0.434464
$960$	−7.82035	+	16.0886i	−0.252401	+	0.519256i
$961$	−21.6833			−0.699461
$962$	2.00730	−	5.88051i	0.0647179	−	0.189595i
$963$	12.9687	−	12.9687i	0.417910	−	0.417910i
$964$	−16.9446	−	13.0937i	−0.545750	−	0.421719i
$965$	−9.50443	+	8.60594i	−0.305958	+	0.277035i
$966$	0.453721	+	0.924004i	0.0145982	+	0.0297293i
$967$	41.5832			1.33722			0.668612	−	0.743611i	$-0.266889\pi$
$967$	41.5832			1.33722			0.668612	+	0.743611i	$0.266889\pi$
$968$	−43.1233	−	65.2552i	−1.38604	−	2.09738i
$969$			28.2573i			0.907756i
$970$	8.48558	+	19.6914i	0.272455	+	0.632253i
$971$	18.8728	−	18.8728i	0.605656	−	0.605656i	−0.336152	−	0.941808i	$-0.609126\pi$
$971$	18.8728	−	18.8728i	0.605656	−	0.605656i	0.941808	+	0.336152i	$0.109126\pi$
$972$	1.98376	−	0.254322i	0.0636293	−	0.00815739i
$973$	−2.53027	+	2.53027i	−0.0811168	+	0.0811168i
$974$	−2.07004	+	6.06431i	−0.0663283	+	0.194313i
$975$	−2.93745	−	0.292184i	−0.0940737	−	0.00935739i
$976$	0.604708	−	1.03116i	0.0193562	−	0.0330066i
$977$		−	17.3929i		−	0.556448i	−0.960516	−	0.278224i	$-0.910254\pi$
$977$		−	17.3929i		−	0.556448i	0.960516	−	0.278224i	$-0.0897457\pi$
$978$	−22.6301	−	7.72473i	−0.723631	−	0.247010i
$979$	45.1692	+	45.1692i	1.44361	+	1.44361i
$980$	−0.102041	−	1.30665i	−0.00325957	−	0.0417394i
$981$	−0.382902	+	0.382902i	−0.0122251	+	0.0122251i
$982$	1.82289	+	3.71232i	0.0581708	+	0.118465i
$983$	−28.6927			−0.915154			−0.457577	−	0.889170i	$-0.651283\pi$
$983$	−28.6927			−0.915154			−0.457577	+	0.889170i	$0.651283\pi$
$984$	14.3136	+	2.92298i	0.456302	+	0.0931811i
$985$	0.506495	−	10.2091i	0.0161383	−	0.325290i
$986$	14.5090	+	29.5476i	0.462060	+	0.940987i
$987$	13.6465	+	13.6465i	0.434373	+	0.434373i
$988$	−5.99470	−	4.63230i	−0.190717	−	0.147373i
$989$	−0.750248	−	0.750248i	−0.0238565	−	0.0238565i
$990$	−18.2689	−	7.26543i	−0.580623	−	0.230910i
$991$	5.67944			0.180413			0.0902066	−	0.995923i	$-0.471247\pi$
$991$	5.67944			0.180413			0.0902066	+	0.995923i	$0.471247\pi$
$992$	17.2194	+	1.27541i	0.546717	+	0.0404943i
$993$		−	10.0629i		−	0.319337i
$994$	−55.2768	−	18.8686i	−1.75327	−	0.598475i
$995$	31.5927	−	28.6061i	1.00156	−	0.906875i
$996$	−7.89766	+	10.2204i	−0.250247	+	0.323847i
$997$	25.4723	+	25.4723i	0.806717	+	0.806717i	0.984135	−	0.177419i	$-0.0567747\pi$
$997$	25.4723	+	25.4723i	0.806717	+	0.806717i	−0.177419	+	0.984135i	$0.556775\pi$
$998$	48.5826	−	23.8559i	1.53786	−	0.755145i
$999$		−	7.44208i		−	0.235457i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	240.2.bl.a.109.10	✓	48
3.2	odd	2		720.2.bm.h.109.15		48
4.3	odd	2		960.2.bl.a.529.4		48
5.4	even	2	inner	240.2.bl.a.109.15	yes	48
8.3	odd	2		1920.2.bl.b.289.22		48
8.5	even	2		1920.2.bl.a.289.3		48
15.14	odd	2		720.2.bm.h.109.10		48
16.3	odd	4		1920.2.bl.b.1249.3		48
16.5	even	4	inner	240.2.bl.a.229.15	yes	48
16.11	odd	4		960.2.bl.a.49.22		48
16.13	even	4		1920.2.bl.a.1249.22		48
20.19	odd	2		960.2.bl.a.529.22		48
40.19	odd	2		1920.2.bl.b.289.3		48
40.29	even	2		1920.2.bl.a.289.22		48
48.5	odd	4		720.2.bm.h.469.10		48
80.19	odd	4		1920.2.bl.b.1249.22		48
80.29	even	4		1920.2.bl.a.1249.3		48
80.59	odd	4		960.2.bl.a.49.4		48
80.69	even	4	inner	240.2.bl.a.229.10	yes	48
240.149	odd	4		720.2.bm.h.469.15		48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
240.2.bl.a.109.10	✓	48	1.1	even	1	trivial
240.2.bl.a.109.15	yes	48	5.4	even	2	inner
240.2.bl.a.229.10	yes	48	80.69	even	4	inner
240.2.bl.a.229.15	yes	48	16.5	even	4	inner
720.2.bm.h.109.10		48	15.14	odd	2
720.2.bm.h.109.15		48	3.2	odd	2
720.2.bm.h.469.10		48	48.5	odd	4
720.2.bm.h.469.15		48	240.149	odd	4
960.2.bl.a.49.4		48	80.59	odd	4
960.2.bl.a.49.22		48	16.11	odd	4
960.2.bl.a.529.4		48	4.3	odd	2
960.2.bl.a.529.22		48	20.19	odd	2
1920.2.bl.a.289.3		48	8.5	even	2
1920.2.bl.a.289.22		48	40.29	even	2
1920.2.bl.a.1249.3		48	80.29	even	4
1920.2.bl.a.1249.22		48	16.13	even	4
1920.2.bl.b.289.3		48	40.19	odd	2
1920.2.bl.b.289.22		48	8.3	odd	2
1920.2.bl.b.1249.3		48	16.3	odd	4
1920.2.bl.b.1249.22		48	80.19	odd	4

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:	\( N \)	\(=\)	\( 240 = 2^{4} \cdot 3 \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	240.bl (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.456856 + 1.33839i) q^{2} +(0.707107 - 0.707107i) q^{3} +(-1.58257 - 1.22290i) q^{4} +(-1.50085 - 1.65754i) q^{5} +(0.623338 + 1.26943i) q^{6} -2.58977 q^{7} +(2.35972 - 1.55940i) q^{8} -1.00000i q^{9} +O(q^{10})\)	\(q+(-0.456856 + 1.33839i) q^{2} +(0.707107 - 0.707107i) q^{3} +(-1.58257 - 1.22290i) q^{4} +(-1.50085 - 1.65754i) q^{5} +(0.623338 + 1.26943i) q^{6} -2.58977 q^{7} +(2.35972 - 1.55940i) q^{8} -1.00000i q^{9} +(2.90411 - 1.25146i) q^{10} +(4.39624 - 4.39624i) q^{11} +(-1.98376 + 0.254322i) q^{12} +(-0.417468 + 0.417468i) q^{13} +(1.18315 - 3.46612i) q^{14} +(-2.23332 - 0.110799i) q^{15} +(1.00903 + 3.87064i) q^{16} -4.40417i q^{17} +(1.33839 + 0.456856i) q^{18} +(-4.53682 - 4.53682i) q^{19} +(0.348184 + 4.45856i) q^{20} +(-1.83125 + 1.83125i) q^{21} +(3.87543 + 7.89232i) q^{22} -0.281063 q^{23} +(0.565912 - 2.77124i) q^{24} +(-0.494901 + 4.97545i) q^{25} +(-0.368012 - 0.749457i) q^{26} +(-0.707107 - 0.707107i) q^{27} +(4.09849 + 3.16704i) q^{28} +(3.73710 + 3.73710i) q^{29} +(1.16860 - 2.93843i) q^{30} -3.05233 q^{31} +(-5.64140 - 0.417848i) q^{32} -6.21722i q^{33} +(5.89449 + 2.01207i) q^{34} +(3.88686 + 4.29266i) q^{35} +(-1.22290 + 1.58257i) q^{36} +(5.26234 + 5.26234i) q^{37} +(8.14471 - 3.99936i) q^{38} +0.590389i q^{39} +(-6.12636 - 1.57091i) q^{40} +5.16508i q^{41} +(-1.61430 - 3.28754i) q^{42} +(2.66933 + 2.66933i) q^{43} +(-12.3335 + 1.58118i) q^{44} +(-1.65754 + 1.50085i) q^{45} +(0.128405 - 0.376171i) q^{46} -7.45202i q^{47} +(3.45045 + 2.02346i) q^{48} -0.293066 q^{49} +(-6.43298 - 2.93543i) q^{50} +(-3.11422 - 3.11422i) q^{51} +(1.17119 - 0.150149i) q^{52} +(2.89462 + 2.89462i) q^{53} +(1.26943 - 0.623338i) q^{54} +(-13.8850 - 0.688864i) q^{55} +(-6.11114 + 4.03849i) q^{56} -6.41604 q^{57} +(-6.70900 + 3.29437i) q^{58} +(-4.60721 + 4.60721i) q^{59} +(3.39888 + 2.90648i) q^{60} +(-0.211318 - 0.211318i) q^{61} +(1.39447 - 4.08520i) q^{62} +2.58977i q^{63} +(3.13655 - 7.35949i) q^{64} +(1.31853 + 0.0654147i) q^{65} +(8.32105 + 2.84037i) q^{66} +(7.17140 - 7.17140i) q^{67} +(-5.38586 + 6.96989i) q^{68} +(-0.198741 + 0.198741i) q^{69} +(-7.52099 + 3.24100i) q^{70} -15.9477i q^{71} +(-1.55940 - 2.35972i) q^{72} +10.5662 q^{73} +(-9.44719 + 4.63893i) q^{74} +(3.16822 + 3.86812i) q^{75} +(1.63174 + 12.7279i) q^{76} +(-11.3853 + 11.3853i) q^{77} +(-0.790170 - 0.269723i) q^{78} +4.53907 q^{79} +(4.90135 - 7.48176i) q^{80} -1.00000 q^{81} +(-6.91288 - 2.35969i) q^{82} +(4.56660 - 4.56660i) q^{83} +(5.13750 - 0.658637i) q^{84} +(-7.30010 + 6.61000i) q^{85} +(-4.79209 + 2.35310i) q^{86} +5.28505 q^{87} +(3.51840 - 17.2294i) q^{88} +10.2745i q^{89} +(-1.25146 - 2.90411i) q^{90} +(1.08115 - 1.08115i) q^{91} +(0.444800 + 0.343712i) q^{92} +(-2.15832 + 2.15832i) q^{93} +(9.97370 + 3.40450i) q^{94} +(-0.710893 + 14.3291i) q^{95} +(-4.28454 + 3.69361i) q^{96} +6.78053i q^{97} +(0.133889 - 0.392236i) q^{98} +(-4.39624 - 4.39624i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q+O(q^{10}) \) 48 * q	\( 48 q + 12 q^{10} - 16 q^{14} - 4 q^{16} + 8 q^{19} - 4 q^{24} - 40 q^{26} - 8 q^{30} - 48 q^{31} - 28 q^{34} + 24 q^{35} - 4 q^{36} - 16 q^{40} - 40 q^{44} - 4 q^{46} + 48 q^{49} - 32 q^{50} + 8 q^{51} - 4 q^{54} + 48 q^{56} - 32 q^{59} - 24 q^{60} + 16 q^{61} + 48 q^{64} + 16 q^{65} + 24 q^{66} - 16 q^{69} + 40 q^{74} - 16 q^{75} + 60 q^{76} - 96 q^{79} + 72 q^{80} - 48 q^{81} + 16 q^{86} + 8 q^{90} - 32 q^{91} + 44 q^{94} - 48 q^{95} - 40 q^{96}+O(q^{100}) \) 48 * q + 12 * q^10 - 16 * q^14 - 4 * q^16 + 8 * q^19 - 4 * q^24 - 40 * q^26 - 8 * q^30 - 48 * q^31 - 28 * q^34 + 24 * q^35 - 4 * q^36 - 16 * q^40 - 40 * q^44 - 4 * q^46 + 48 * q^49 - 32 * q^50 + 8 * q^51 - 4 * q^54 + 48 * q^56 - 32 * q^59 - 24 * q^60 + 16 * q^61 + 48 * q^64 + 16 * q^65 + 24 * q^66 - 16 * q^69 + 40 * q^74 - 16 * q^75 + 60 * q^76 - 96 * q^79 + 72 * q^80 - 48 * q^81 + 16 * q^86 + 8 * q^90 - 32 * q^91 + 44 * q^94 - 48 * q^95 - 40 * q^96

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