LMFDB - Embedded newform 240.2.bl.a.109.15

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			109.15
Character	$\chi$	$=$	240.109
Dual form			240.2.bl.a.229.15

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.456856 - 1.33839i) q^{2} +(-0.707107 + 0.707107i) q^{3} +(-1.58257 - 1.22290i) q^{4} +(1.65754 + 1.50085i) q^{5} +(0.623338 + 1.26943i) q^{6} +2.58977 q^{7} +(-2.35972 + 1.55940i) q^{8} -1.00000i q^{9} +O(q^{10})$	\(q+(0.456856 - 1.33839i) q^{2} +(-0.707107 + 0.707107i) q^{3} +(-1.58257 - 1.22290i) q^{4} +(1.65754 + 1.50085i) q^{5} +(0.623338 + 1.26943i) q^{6} +2.58977 q^{7} +(-2.35972 + 1.55940i) q^{8} -1.00000i q^{9} +(2.76598 - 1.53277i) 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} +(-0.787783 - 4.40220i) 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} +(-0.872013 + 3.03967i) q^{30} -3.05233 q^{31} +(5.64140 + 0.417848i) q^{32} +6.21722i q^{33} +(5.89449 + 2.01207i) q^{34} +(4.29266 + 3.88686i) q^{35} +(-1.22290 + 1.58257i) q^{36} +(-5.26234 - 5.26234i) q^{37} +(-8.14471 + 3.99936i) q^{38} +0.590389i q^{39} +(-6.25176 - 0.956812i) q^{40} +5.16508i q^{41} +(1.61430 + 3.28754i) q^{42} +(-2.66933 - 2.66933i) q^{43} +(-12.3335 + 1.58118i) q^{44} +(1.50085 - 1.65754i) q^{45} +(0.128405 - 0.376171i) q^{46} +7.45202i q^{47} +(-3.45045 - 2.02346i) q^{48} -0.293066 q^{49} +(6.88518 + 1.61069i) 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} +(3.66987 + 2.55578i) 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} +(7.16326 - 3.96952i) q^{70} -15.9477i q^{71} +(1.55940 + 2.35972i) q^{72} -10.5662 q^{73} +(-9.44719 + 4.63893i) q^{74} +(-3.86812 - 3.16822i) q^{75} +(1.63174 + 12.7279i) q^{76} +(11.3853 - 11.3853i) q^{77} +(0.790170 + 0.269723i) q^{78} +4.53907 q^{79} +(-4.13674 + 7.93016i) q^{80} -1.00000 q^{81} +(6.91288 + 2.35969i) q^{82} +(-4.56660 + 4.56660i) q^{83} +(5.13750 - 0.658637i) q^{84} +(-6.61000 + 7.30010i) q^{85} +(-4.79209 + 2.35310i) q^{86} -5.28505 q^{87} +(-3.51840 + 17.2294i) q^{88} +10.2745i q^{89} +(-1.53277 - 2.76598i) 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
$5$	1.65754	+	1.50085i	0.741276	+	0.671200i
$5$	1.65754	+	1.50085i	0.741276	+	0.671200i
$6$	0.623338	+	1.26943i	0.254477	+	0.518242i
$7$	2.58977			0.978843			0.489421	−	0.872047i	$-0.337208\pi$
$7$	2.58977			0.978843			0.489421	+	0.872047i	$0.337208\pi$
$8$	−2.35972	+	1.55940i	−0.834287	+	0.551331i
$9$		−	1.00000i		−	0.333333i
$10$	2.76598	−	1.53277i	0.874679	−	0.484703i
$11$	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	−0.646840	−	0.762625i	$-0.723910\pi$
$13$	0.417468	−	0.417468i	0.115785	−	0.115785i	0.762625	+	0.646840i	$0.223910\pi$
$14$	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	$0.179343\pi$
$17$			4.40417i			1.06817i	−0.845431	+	0.534084i	$0.820657\pi$
$18$	−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	$-0.513274\pi$
$20$	−0.787783	−	4.40220i	−0.176154	−	0.984363i
$21$	−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	$-0.490671\pi$
$23$	0.281063			0.0586056			0.0293028	+	0.999571i	$0.490671\pi$
$24$	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	$0.586739\pi$
$30$	−0.872013	+	3.03967i	−0.159207	+	0.554965i
$31$	−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
$35$	4.29266	+	3.88686i	0.725593	+	0.657000i
$36$	−1.22290	+	1.58257i	−0.203817	+	0.263761i
$37$	−5.26234	−	5.26234i	−0.865124	−	0.865124i	0.126804	−	0.991928i	$-0.459528\pi$
$37$	−5.26234	−	5.26234i	−0.865124	−	0.865124i	−0.991928	+	0.126804i	$0.959528\pi$
$38$	−8.14471	+	3.99936i	−1.32125	+	0.648782i
$39$			0.590389i			0.0945380i
$40$	−6.25176	−	0.956812i	−0.988490	−	0.151285i
$41$			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	0.473647	−	0.880715i	$-0.342937\pi$
$43$	−2.66933	−	2.66933i	−0.407069	−	0.407069i	−0.880715	+	0.473647i	$0.842937\pi$
$44$	−12.3335	+	1.58118i	−1.85934	+	0.238371i
$45$	1.50085	−	1.65754i	0.223733	−	0.247092i
$46$	0.128405	−	0.376171i	0.0189323	−	0.0554634i
$47$			7.45202i			1.08699i	0.839413	+	0.543495i	$0.182899\pi$
$47$			7.45202i			1.08699i	−0.839413	+	0.543495i	$0.817101\pi$
$48$	−3.45045	−	2.02346i	−0.498029	−	0.292062i
$49$	−0.293066			−0.0418665
$50$	6.88518	+	1.61069i	0.973711	+	0.227786i
$51$	−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	0.479782	−	0.877388i	$-0.340716\pi$
$53$	−2.89462	−	2.89462i	−0.397606	−	0.397606i	−0.877388	+	0.479782i	$0.840716\pi$
$54$	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	$0.389420\pi$
$60$	3.66987	+	2.55578i	0.473779	+	0.329950i
$61$	−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	−0.993131	−	0.117005i	$-0.962671\pi$
$67$	−7.17140	+	7.17140i	−0.876126	+	0.876126i	0.117005	+	0.993131i	$0.462671\pi$
$68$	5.38586	−	6.96989i	0.653132	−	0.845223i
$69$	−0.198741	+	0.198741i	−0.0239257	+	0.0239257i
$70$	7.16326	−	3.96952i	0.856173	−	0.474448i
$71$		−	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	$-0.712194\pi$
$73$	−10.5662			−1.23668			−0.618339	+	0.785912i	$0.712194\pi$
$74$	−9.44719	+	4.63893i	−1.09821	+	0.539264i
$75$	−3.86812	−	3.16822i	−0.446652	−	0.365835i
$76$	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	$0.417812\pi$
$80$	−4.13674	+	7.93016i	−0.462501	+	0.886619i
$81$	−1.00000			−0.111111
$82$	6.91288	+	2.35969i	0.763400	+	0.260585i
$83$	−4.56660	+	4.56660i	−0.501249	+	0.501249i	−0.911826	−	0.410577i	$-0.865327\pi$
$83$	−4.56660	+	4.56660i	−0.501249	+	0.501249i	0.410577	+	0.911826i	$0.365327\pi$
$84$	5.13750	−	0.658637i	0.560548	−	0.0718632i
$85$	−6.61000	+	7.30010i	−0.716955	+	0.791807i
$86$	−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	$0.816701\pi$
$90$	−1.53277	−	2.76598i	−0.161568	−	0.291560i
$91$	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	$-0.888140\pi$
$97$		−	6.78053i		−	0.688459i	0.938886	−	0.344229i	$-0.111860\pi$
$98$	−0.133889	+	0.392236i	−0.0135248	+	0.0396218i
$99$	−4.39624	−	4.39624i	−0.441838	−	0.441838i
$100$	5.30126	−	8.47919i	0.530126	−	0.847919i
$101$	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	$-0.425382\pi$
$103$	4.71475			0.464558			0.232279	+	0.972649i	$0.425382\pi$
$104$	−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	$-0.903115\pi$
$107$	−12.9687	−	12.9687i	−1.25373	−	1.25373i	−0.299696	−	0.954035i	$-0.596885\pi$
$108$	−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	$0.758256\pi$
$110$	5.42149	−	18.8983i	0.516919	−	1.80188i
$111$	7.44208			0.706371
$112$	2.61316	+	10.0241i	0.246921	+	0.947187i
$113$			12.1861i			1.14637i	0.819424	+	0.573187i	$0.194293\pi$
$113$			12.1861i			1.14637i	−0.819424	+	0.573187i	$0.805707\pi$
$114$	2.93120	−	8.58715i	0.274532	−	0.804260i
$115$	0.465874	+	0.421833i	0.0434430	+	0.0393361i
$116$	−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
$120$	5.09723	−	3.74409i	0.465311	−	0.341787i
$121$		−	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
$125$	−6.64708	+	8.98979i	−0.594533	+	0.804071i
$126$	−3.46612	−	1.18315i	−0.308787	−	0.105404i
$127$			6.75303i			0.599234i	0.954060	+	0.299617i	$0.0968589\pi$
$127$			6.75303i			0.599234i	−0.954060	+	0.299617i	$0.903141\pi$
$128$	−8.41690	−	7.56014i	−0.743956	−	0.668228i
$129$	3.77500			0.332370
$130$	0.514827	−	1.79459i	0.0451533	−	0.157396i
$131$	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	$-0.428765\pi$
$137$	5.19519			0.443855			0.221927	+	0.975063i	$0.428765\pi$
$138$	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	$0.231337\pi$
$140$	−2.04018	−	11.4007i	−0.172427	−	0.963536i
$141$	−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	$0.0227163\pi$
$150$	−6.00749	+	3.72963i	−0.490509	+	0.304523i
$151$			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
$155$	−5.05937	−	4.58109i	−0.406378	−	0.367962i
$156$	0.721987	−	0.934330i	0.0578052	−	0.0748063i
$157$	5.73516	−	5.73516i	0.457716	−	0.457716i	−0.440189	−	0.897905i	$-0.645089\pi$
$157$	5.73516	−	5.73516i	0.457716	−	0.457716i	0.897905	+	0.440189i	$0.145089\pi$
$158$	2.07370	−	6.07503i	0.164975	−	0.483304i
$159$	4.09361			0.324644
$160$	8.72374	+	9.15950i	0.689672	+	0.724122i
$161$	0.727889			0.0573657
$162$	−0.456856	+	1.33839i	−0.0358940	+	0.105154i
$163$	11.9561	−	11.9561i	0.936474	−	0.936474i	−0.0616255	−	0.998099i	$-0.519628\pi$
$163$	11.9561	−	11.9561i	0.936474	−	0.936474i	0.998099	+	0.0616255i	$0.0196285\pi$
$164$	6.31637	−	8.17407i	0.493226	−	0.638288i
$165$	−9.33111	+	10.3053i	−0.726426	+	0.802267i
$166$	4.02560	+	8.19815i	0.312447	+	0.636300i
$167$	9.23665			0.714754			0.357377	−	0.933960i	$-0.383671\pi$
$167$	9.23665			0.714754			0.357377	+	0.933960i	$0.383671\pi$
$168$	1.46558	−	7.17688i	0.113072	−	0.553708i
$169$			12.6514i			0.973188i
$170$	6.75056	+	12.1818i	0.517744	+	0.934304i
$171$	−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	−0.611598	−	0.791168i	$-0.709473\pi$
$173$	2.36187	−	2.36187i	0.179570	−	0.179570i	0.791168	+	0.611598i	$0.209473\pi$
$174$	−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	$0.586982\pi$
$180$	−4.40220	+	0.787783i	−0.328121	+	0.0587179i
$181$	−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
$190$	−19.5026	−	5.59487i	−1.41487	−	0.405894i
$191$	−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	$0.0661659\pi$
$193$			5.73404i			0.412745i	−0.978473	+	0.206373i	$0.933834\pi$
$194$	−9.07499	−	3.09772i	−0.651546	−	0.222404i
$195$	−0.886086	+	0.978596i	−0.0634539	+	0.0700787i
$196$	0.463796	+	0.358390i	0.0331283	+	0.0255993i
$197$	−3.23239	−	3.23239i	−0.230298	−	0.230298i	0.582519	−	0.812817i	$-0.302067\pi$
$197$	−3.23239	−	3.23239i	−0.230298	−	0.230298i	−0.812817	+	0.582519i	$0.802067\pi$
$198$	−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	$0.763901\pi$
$200$	−8.92654	−	10.9689i	−0.631201	−	0.775619i
$201$		−	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
$205$	−7.75200	+	8.56134i	−0.541423	+	0.597950i
$206$	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
$210$	−2.25832	+	7.87206i	−0.155839	+	0.543224i
$211$	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
$220$	−22.8164	−	15.8898i	−1.53828	−	1.07129i
$221$	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	$-0.945320\pi$
$223$		−	5.10536i		−	0.341880i	0.985281	−	0.170940i	$-0.0546805\pi$
$224$	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	−1.00000		0.000680242i	$-0.999783\pi$
$227$	−15.0563	+	15.0563i	−0.999320	+	0.999320i	0.000680242		1.00000i	$0.499783\pi$
$228$	−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	$-0.0554108\pi$
$230$	0.777413	−	0.430803i	0.0512611	−	0.0284063i
$231$			16.1012i			1.05938i
$232$	−14.6461	−	2.99087i	−0.961565	−	0.196360i
$233$	9.15254			0.599603			0.299802	−	0.954002i	$-0.403080\pi$
$233$	9.15254			0.599603			0.299802	+	0.954002i	$0.403080\pi$
$234$	−0.749457	+	0.368012i	−0.0489936	+	0.0240577i
$235$	−11.1844	+	12.3521i	−0.729588	+	0.805759i
$236$	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	$0.637219\pi$
$240$	−2.68235	−	8.53258i	−0.173145	−	0.550776i
$241$	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
$245$	−0.485769	−	0.439847i	−0.0310346	−	0.0281008i
$246$	−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
$250$	8.99508	+	13.0034i	0.568899	+	0.822408i
$251$	−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	$-0.822922\pi$
$257$		−	16.9307i		−	1.05610i	0.849212	−	0.528052i	$-0.177078\pi$
$258$	1.72463	−	5.05241i	0.107371	−	0.314550i
$259$	−13.6283	−	13.6283i	−0.846821	−	0.846821i
$260$	−2.16666	−	1.50891i	−0.134370	−	0.0935784i
$261$	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	$-0.520416\pi$
$263$	−2.07893			−0.128192			−0.0640962	+	0.997944i	$0.520416\pi$
$264$	−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	$0.993652\pi$
$270$	3.03967	+	0.872013i	0.184988	+	0.0530690i
$271$	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
$275$	24.0489	+	19.6975i	1.45021	+	1.18781i
$276$	0.557562	−	0.0714805i	0.0335613	−	0.00430262i
$277$	15.8235	+	15.8235i	0.950744	+	0.950744i	0.998843	−	0.0480985i	$-0.0153161\pi$
$277$	15.8235	+	15.8235i	0.950744	+	0.950744i	−0.0480985	+	0.998843i	$0.515316\pi$
$278$	−0.861278	−	1.75400i	−0.0516560	−	0.105198i
$279$			3.05233i			0.182738i
$280$	−16.1907	−	2.47793i	−0.967577	−	0.148084i
$281$			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	0.659578	−	0.751636i	$-0.270735\pi$
$283$	−1.54865	−	1.54865i	−0.0920579	−	0.0920579i	−0.751636	+	0.659578i	$0.770735\pi$
$284$	−19.5025	+	25.2383i	−1.15726	+	1.49762i
$285$	10.6349	+	9.62951i	0.629955	+	0.570403i
$286$	−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
$290$	16.0648	+	4.60863i	0.943359	+	0.270628i
$291$	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	$0.0920582\pi$
$293$	21.2881	+	21.2881i	1.24366	+	1.24366i	0.285194	+	0.958470i	$0.407942\pi$
$294$	−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
$300$	2.24713	+	9.74425i	0.129738	+	0.562584i
$301$	−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	−0.964034	−	0.265779i	$-0.914371\pi$
$307$	−12.2344	+	12.2344i	−0.698255	+	0.698255i	0.265779	+	0.964034i	$0.414371\pi$
$308$	−31.9410	+	4.09489i	−1.82001	+	0.233328i
$309$	−3.33383	+	3.33383i	−0.189655	+	0.189655i
$310$	−8.44267	+	4.67850i	−0.479512	+	0.265721i
$311$		−	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	$-0.411286\pi$
$313$	9.73432			0.550217			0.275108	+	0.961413i	$0.411286\pi$
$314$	−5.05573	−	10.2960i	−0.285311	−	0.581037i
$315$	3.88686	−	4.29266i	0.219000	−	0.241864i
$316$	−7.18337	−	5.55083i	−0.404096	−	0.312258i
$317$	−8.46658	+	8.46658i	−0.475530	+	0.475530i	−0.903699	−	0.428168i	$-0.859159\pi$
$317$	−8.46658	+	8.46658i	−0.475530	+	0.475530i	0.428168	+	0.903699i	$0.359159\pi$
$318$	1.87019	−	5.47883i	0.104875	−	0.307238i
$319$	32.8583			1.83971
$320$	16.2445	−	7.49118i	0.908092	−	0.418770i
$321$	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
$325$	2.28370	+	1.87049i	0.126677	+	0.103756i
$326$	−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
$330$	9.52954	+	17.1967i	0.524584	+	0.946646i
$331$	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	$-0.858053\pi$
$337$		−	15.8355i		−	0.862613i	0.902205	−	0.431307i	$-0.141947\pi$
$338$	16.9325	+	5.77988i	0.921009	+	0.314384i
$339$	−8.61689	−	8.61689i	−0.468005	−	0.468005i
$340$	19.3881	−	3.46953i	1.05146	−	0.188162i
$341$	−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	0.912541	−	0.408986i	$-0.134117\pi$
$347$	9.38020	+	9.38020i	0.503555	+	0.503555i	−0.408986	+	0.912541i	$0.634117\pi$
$348$	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	$0.744226\pi$
$350$	17.8311	+	4.17133i	0.953110	+	0.222967i
$351$	0.590389			0.0315127
$352$	26.6379	−	22.9640i	1.41980	−	1.22398i
$353$		−	8.95345i		−	0.476544i	−0.971198	−	0.238272i	$-0.923419\pi$
$353$		−	8.95345i		−	0.476544i	0.971198	−	0.238272i	$-0.0765810\pi$
$354$	−8.72038	−	2.97668i	−0.463483	−	0.158209i
$355$	23.9351	−	26.4340i	1.27034	−	1.40297i
$356$	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	$-0.0292478\pi$
$360$	−0.956812	+	6.25176i	−0.0504284	+	0.329497i
$361$			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
$365$	−17.5139	−	15.8582i	−0.916719	−	0.830058i
$366$	0.136530	−	0.399975i	0.00713656	−	0.0209070i
$367$		−	15.1190i		−	0.789206i	−0.918852	−	0.394603i	$-0.870882\pi$
$367$		−	15.1190i		−	0.789206i	0.918852	−	0.394603i	$-0.129118\pi$
$368$	0.283601	+	1.08789i	0.0147837	+	0.0567103i
$369$	5.16508			0.268883
$370$	−22.6215	−	6.48959i	−1.17603	−	0.337377i
$371$	−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	0.0135107	−	0.999909i	$-0.495699\pi$
$373$	−19.0505	−	19.0505i	−0.986398	−	0.986398i	−0.999909	+	0.0135107i	$0.995699\pi$
$374$	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	$0.209096\pi$
$380$	−16.3980	+	23.5461i	−0.841199	+	1.20789i
$381$	−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	$-0.973925\pi$
$383$		−	3.20268i		−	0.163649i	0.996647	−	0.0818246i	$-0.0260747\pi$
$384$	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	$0.0419605\pi$
$390$	0.904928	+	1.63300i	0.0458228	+	0.0826904i
$391$			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
$395$	7.52370	+	6.81246i	0.378558	+	0.342772i
$396$	1.58118	+	12.3335i	0.0794571	+	0.619781i
$397$	15.8392	−	15.8392i	0.794946	−	0.794946i	−0.187348	−	0.982294i	$-0.559989\pi$
$397$	15.8392	−	15.8392i	0.794946	−	0.794946i	0.982294	+	0.187348i	$0.0599891\pi$
$398$	25.5096	+	8.70764i	1.27868	+	0.436475i
$399$	16.6161			0.831845
$400$	−18.7588	+	6.93596i	−0.937940	+	0.346798i
$401$	−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
$405$	−1.65754	−	1.50085i	−0.0823640	−	0.0745778i
$406$	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	$-0.100309\pi$
$410$	7.91685	+	14.2865i	0.390985	+	0.705559i
$411$	−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	$-0.519337\pi$
$420$	9.50415	+	6.61890i	0.463755	+	0.322969i
$421$	−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
$430$	−11.4747	−	3.29185i	−0.553362	−	0.158747i
$431$	−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	$-0.731222\pi$
$433$		−	31.1117i		−	1.49513i	0.664187	−	0.747566i	$-0.268778\pi$
$434$	−3.61137	+	10.5798i	−0.173351	+	0.507844i
$435$	−8.76021	−	7.93207i	−0.420020	−	0.380314i
$436$	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	$0.996499\pi$
$440$	−31.6906	+	23.2779i	−1.51079	+	1.10973i
$441$			0.293066i			0.0139555i
$442$	3.30074	−	1.62079i	0.157000	−	0.0770930i
$443$	−2.88482	−	2.88482i	−0.137062	−	0.137062i	0.635247	−	0.772309i	$-0.280898\pi$
$443$	−2.88482	−	2.88482i	−0.137062	−	0.137062i	−0.772309	+	0.635247i	$0.780898\pi$
$444$	−11.7776	−	9.10092i	−0.558939	−	0.431910i
$445$	−15.4205	+	17.0304i	−0.731001	+	0.807321i
$446$	−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	$0.477283\pi$
$450$	1.61069	−	6.88518i	0.0759287	−	0.324570i
$451$	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	$-0.534988\pi$
$457$	−4.69013			−0.219395			−0.109698	+	0.993965i	$0.534988\pi$
$458$	−15.4489	−	31.4617i	−0.721879	−	1.47011i
$459$	−3.11422	+	3.11422i	−0.145359	+	0.145359i
$460$	−0.221416	−	1.23730i	−0.0103236	−	0.0576892i
$461$	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	$-0.797950\pi$
$463$		−	25.5190i		−	1.18597i	0.805215	−	0.592983i	$-0.202050\pi$
$464$	−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	−0.0456227	−	0.998959i	$-0.514527\pi$
$467$	20.6018	−	20.6018i	0.953336	−	0.953336i	0.998959	+	0.0456227i	$0.0145272\pi$
$468$	0.150149	+	1.17119i	0.00694065	+	0.0541384i
$469$	−18.5723	+	18.5723i	−0.857590	+	0.857590i
$470$	11.4222	+	20.6121i	0.526867	+	0.950766i
$471$			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
$475$	20.3275	−	24.8180i	0.932687	−	1.13873i
$476$	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	$0.252750\pi$
$480$	−12.6454	−	0.308126i	−0.577179	−	0.0140640i
$481$	−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
$485$	10.1766	−	11.2390i	0.462094	−	0.510338i
$486$	−0.623338	−	1.26943i	−0.0282752	−	0.0575825i
$487$	−4.53105			−0.205322			−0.102661	−	0.994716i	$-0.532736\pi$
$487$	−4.53105			−0.205322			−0.102661	+	0.994716i	$0.532736\pi$
$488$	0.828178	+	0.169122i	0.0374899	+	0.00765578i
$489$			16.9085i			0.764628i
$490$	−0.810613	+	0.449201i	−0.0366198	+	0.0202928i
$491$	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	$-0.577444\pi$
$500$	21.5131	−	6.09823i	0.962093	−	0.272721i
$501$	−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	$-0.439880\pi$
$503$	8.42170			0.375505			0.187753	+	0.982216i	$0.439880\pi$
$504$	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	$0.499643\pi$
$510$	−13.3872	−	3.84049i	−0.592796	−	0.170060i
$511$	−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
$515$	7.81490	+	7.07612i	0.344365	+	0.311811i
$516$	−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
$520$	−3.00935	+	2.21047i	−0.131969	+	0.0969357i
$521$			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	$-0.945309\pi$
$523$	−26.4425	−	26.4425i	−1.15625	−	1.15625i	−0.170974	−	0.985276i	$-0.554691\pi$
$524$	−1.42177	−	11.0901i	−0.0621104	−	0.484473i
$525$	−10.0176	−	8.20499i	−0.437202	−	0.358095i
$526$	−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
$530$	−12.4432	−	3.56968i	−0.540498	−	0.155057i
$531$	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
$540$	2.55578	−	3.66987i	0.109983	−	0.157926i
$541$	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	−0.641884	−	0.766802i	$-0.721847\pi$
$547$	2.92159	−	2.92159i	0.124918	−	0.124918i	0.766802	+	0.641884i	$0.221847\pi$
$548$	−8.22173	−	6.35320i	−0.351215	−	0.271395i
$549$	−0.211318	+	0.211318i	−0.00901881	+	0.00901881i
$550$	37.3499	−	23.1879i	1.59260	−	0.988735i
$551$		−	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
$555$	12.3356	+	11.1694i	0.523616	+	0.474116i
$556$	−2.74101	+	0.351402i	−0.116245	+	0.0149028i
$557$	−25.5453	+	25.5453i	−1.08239	+	1.08239i	−0.0861022	+	0.996286i	$0.527441\pi$
$557$	−25.5453	+	25.5453i	−1.08239	+	1.08239i	−0.996286	+	0.0861022i	$0.972559\pi$
$558$	4.08520	+	1.39447i	0.172940	+	0.0590328i
$559$	−2.22872			−0.0942648
$560$	−10.7132	+	20.5373i	−0.452716	+	0.867860i
$561$	−27.3817			−1.15606
$562$	16.9368	+	5.78133i	0.714435	+	0.243871i
$563$	−11.6203	+	11.6203i	−0.489736	+	0.489736i	−0.908223	−	0.418487i	$-0.862561\pi$
$563$	−11.6203	+	11.6203i	−0.489736	+	0.489736i	0.418487	+	0.908223i	$0.362561\pi$
$564$	1.89522	+	14.7831i	0.0798030	+	0.622479i
$565$	−18.2895	+	20.1990i	−0.769447	+	0.849780i
$566$	−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	$-0.0902771\pi$
$570$	17.7466	−	9.83428i	0.743324	−	0.411913i
$571$	−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	$0.257023\pi$
$577$			34.7117i			1.44507i	−0.691335	+	0.722534i	$0.742977\pi$
$578$	−1.09495	+	3.20774i	−0.0455441	+	0.133424i
$579$	−4.05458	−	4.05458i	−0.168503	−	0.168503i
$580$	13.5074	−	19.3955i	0.560866	−	0.805354i
$581$	−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	$0.0373057\pi$
$587$	26.8949	+	26.8949i	1.11007	+	1.11007i	0.116931	+	0.993140i	$0.462694\pi$
$588$	−0.581373	+	0.0745331i	−0.0239754	+	0.00307369i
$589$	13.8479	+	13.8479i	0.570592	+	0.570592i
$590$	−5.68167	+	19.8052i	−0.233911	+	0.815368i
$591$	4.57128			0.188037
$592$	15.0588	−	25.6785i	0.618912	−	1.05538i
$593$			8.25028i			0.338798i	0.985548	+	0.169399i	$0.0541827\pi$
$593$			8.25028i			0.338798i	−0.985548	+	0.169399i	$0.945817\pi$
$594$	2.84037	−	8.32105i	0.116542	−	0.341417i
$595$	−17.1184	+	18.9056i	−0.701786	+	0.775055i
$596$	−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	$0.868344\pi$
$600$	14.0682	+	1.44418i	0.574332	+	0.0589583i
$601$		−	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
$605$	41.5042	−	45.8374i	1.68739	−	1.86355i
$606$	19.0724	+	6.51030i	0.774762	+	0.264463i
$607$		−	5.52944i		−	0.224433i	−0.993684	−	0.112217i	$-0.964205\pi$
$607$		−	5.52944i		−	0.224433i	0.993684	−	0.112217i	$-0.0357950\pi$
$608$	−23.6983	−	27.4897i	−0.961095	−	1.11486i
$609$	−13.6871			−0.554629
$610$	−0.908400	−	0.260599i	−0.0367800	−	0.0105514i
$611$	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	$0.0604122\pi$
$613$	28.9851	+	28.9851i	1.17070	+	1.17070i	0.188653	+	0.982044i	$0.439588\pi$
$614$	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	$-0.320467\pi$
$617$	26.5578			1.06918			0.534588	+	0.845113i	$0.320467\pi$
$618$	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	$0.196258\pi$
$620$	2.40457	+	13.4370i	0.0965700	+	0.539642i
$621$	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
$630$	−3.96952	−	7.16326i	−0.158149	−	0.285391i
$631$			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
$635$	−10.1353	+	11.1934i	−0.402206	+	0.444198i
$636$	−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
$640$	−2.60475	−	25.1638i	−0.102962	−	0.994685i
$641$	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	−0.905455	−	0.424441i	$-0.860471\pi$
$643$	−12.1973	+	12.1973i	−0.481014	+	0.481014i	0.424441	+	0.905455i	$0.360471\pi$
$644$	−1.15193	−	0.890136i	−0.0453925	−	0.0350763i
$645$	6.25722	+	5.66570i	0.246378	+	0.223087i
$646$	−17.6139	−	35.8707i	−0.693008	−	1.41131i
$647$	16.5371			0.650142			0.325071	−	0.945690i	$-0.394612\pi$
$647$	16.5371			0.650142			0.325071	+	0.945690i	$0.394612\pi$
$648$	2.35972	−	1.55940i	0.0926985	−	0.0612590i
$649$			40.5088i			1.59011i
$650$	3.54676	−	2.20193i	0.139115	−	0.0863669i
$651$	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	−0.758544	−	0.651622i	$-0.774089\pi$
$653$	−2.73228	+	2.73228i	−0.106923	+	0.106923i	0.651622	+	0.758544i	$0.274089\pi$
$654$	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	$0.622612\pi$
$660$	27.3695	−	4.89782i	1.06535	−	0.190647i
$661$	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
$670$	−8.84386	+	30.8280i	−0.341668	+	1.19099i
$671$	−1.85800			−0.0717274
$672$	−11.0960	+	9.56562i	−0.428037	+	0.369002i
$673$		−	17.6236i		−	0.679341i	−0.940545	−	0.339670i	$-0.889684\pi$
$673$		−	17.6236i		−	0.679341i	0.940545	−	0.339670i	$-0.110316\pi$
$674$	−21.1940	−	7.23453i	−0.816363	−	0.278663i
$675$	−3.16822	+	3.86812i	−0.121945	+	0.148884i
$676$	15.4714	−	20.0217i	0.595056	−	0.770067i
$677$	−33.4900	−	33.4900i	−1.28713	−	1.28713i	−0.936525	−	0.350601i	$-0.885977\pi$
$677$	−33.4900	−	33.4900i	−1.28713	−	1.28713i	−0.350601	−	0.936525i	$-0.614023\pi$
$678$	−15.4694	+	7.59607i	−0.594100	+	0.291725i
$679$		−	17.5601i		−	0.673893i
$680$	4.21396	−	27.5338i	0.161598	−	1.05587i
$681$		−	21.2928i		−	0.815941i
$682$	11.8291	+	24.0899i	0.452959	+	0.922452i
$683$	−0.602993	−	0.602993i	−0.0230729	−	0.0230729i	0.695476	−	0.718549i	$-0.255193\pi$
$683$	−0.602993	−	0.602993i	−0.0230729	−	0.0230729i	−0.718549	+	0.695476i	$0.755193\pi$
$684$	12.7279	−	1.63174i	0.486664	−	0.0623912i
$685$	8.61125	+	7.79720i	0.329019	+	0.297916i
$686$	−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
$690$	−0.245090	+	0.854338i	−0.00933043	+	0.0325241i
$691$	−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
$700$	13.7291	−	21.9592i	0.518910	−	0.829979i
$701$	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	$-0.0446110\pi$
$710$	−24.4441	−	44.1110i	−0.917371	−	1.65546i
$711$		−	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
$715$	5.50899	−	6.08415i	0.206024	−	0.227534i
$716$	−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	$0.372104\pi$
$720$	7.93016	+	4.13674i	0.295540	+	0.154167i
$721$	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
$725$	−16.7442	+	20.4432i	−0.621865	+	0.759242i
$726$	35.1045	−	17.2377i	1.30285	−	0.639749i
$727$	19.5823			0.726269			0.363134	−	0.931737i	$-0.381707\pi$
$727$	19.5823			0.726269			0.363134	+	0.931737i	$0.381707\pi$
$728$	−0.865265	+	4.23715i	−0.0320689	+	0.157039i
$729$			1.00000i			0.0370370i
$730$	−29.2258	+	16.1955i	−1.08170	+	0.599421i
$731$	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	−0.776407	−	0.630232i	$-0.782960\pi$
$733$	−3.95752	+	3.95752i	−0.146174	+	0.146174i	0.630232	+	0.776407i	$0.282960\pi$
$734$	−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	$0.766126\pi$
$740$	−19.0203	+	27.3115i	−0.699201	+	1.00399i
$741$	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	$-0.437977\pi$
$743$	10.5553			0.387238			0.193619	+	0.981077i	$0.437977\pi$
$744$	−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
$750$	−15.5553	−	2.83432i	−0.567998	−	0.103495i
$751$	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
$755$	−4.31174	+	4.76191i	−0.156920	+	0.173304i
$756$	−0.658637	−	5.13750i	−0.0239544	−	0.186849i
$757$	4.11693	+	4.11693i	0.149632	+	0.149632i	0.777954	−	0.628321i	$-0.216258\pi$
$757$	4.11693	+	4.11693i	0.149632	+	0.149632i	−0.628321	+	0.777954i	$0.716258\pi$
$758$	−3.11025	−	6.33403i	−0.112969	−	0.230063i
$759$			1.74743i			0.0634276i
$760$	24.0223	+	32.7040i	0.871379	+	1.18630i
$761$			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
$765$	7.30010	+	6.61000i	0.263936	+	0.238985i
$766$	−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	$0.485966\pi$
$770$	14.0404	−	48.9423i	0.505983	−	1.76376i
$771$	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	0.451857	−	0.892091i	$-0.350762\pi$
$773$	−12.2398	−	12.2398i	−0.440234	−	0.440234i	−0.892091	+	0.451857i	$0.850762\pi$
$774$	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
$780$	2.59901	−	0.465099i	0.0930596	−	0.0166532i
$781$	−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	−0.952753	−	0.303745i	$-0.901763\pi$
$787$	−18.2070	+	18.2070i	−0.649009	+	0.649009i	0.303745	+	0.952753i	$0.401763\pi$
$788$	1.16258	+	9.06835i	0.0414152	+	0.323046i
$789$	1.47003	−	1.47003i	0.0523343	−	0.0523343i
$790$	12.5550	−	6.95732i	0.446685	−	0.247530i
$791$			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
$795$	6.78533	+	6.14389i	0.240651	+	0.217901i
$796$	23.3084	−	30.1636i	0.826145	−	1.06912i
$797$	−5.02164	+	5.02164i	−0.177876	+	0.177876i	−0.790429	−	0.612553i	$-0.790142\pi$
$797$	−5.02164	+	5.02164i	−0.177876	+	0.177876i	0.612553	+	0.790429i	$0.290142\pi$
$798$	7.59115	−	22.2388i	0.268724	−	0.787245i
$799$	−32.8200			−1.16109
$800$	0.712952	+	28.2753i	0.0252067	+	0.999682i
$801$	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
$805$	1.20651	+	1.09245i	0.0425238	+	0.0385039i
$806$	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	$-0.136464\pi$
$810$	−2.76598	+	1.53277i	−0.0971865	+	0.0538559i
$811$	−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
$820$	22.7377	−	4.06896i	0.794036	−	0.142094i
$821$	−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	$-0.264511\pi$
$823$	38.6799			1.34830			0.674148	+	0.738596i	$0.264511\pi$
$824$	−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	0.103658	−	0.994613i	$-0.466945\pi$
$827$	−25.6217	−	25.6217i	−0.890955	−	0.890955i	−0.994613	+	0.103658i	$0.966945\pi$
$828$	−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	$0.869216\pi$
$830$	−5.63158	+	19.6306i	−0.195475	+	0.681389i
$831$	−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
$835$	15.3102	+	13.8628i	0.529830	+	0.479743i
$836$	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	$0.919069\pi$
$840$	13.2007	−	9.69636i	0.455467	−	0.334556i
$841$		−	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
$845$	−18.9879	+	20.9703i	−0.653204	+	0.721401i
$846$	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
$850$	−7.09376	+	30.3235i	−0.243314	+	1.04009i
$851$	−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	0.881414	−	0.472344i	$-0.156592\pi$
$853$	11.9474	+	11.9474i	0.409070	+	0.409070i	−0.472344	+	0.881414i	$0.656592\pi$
$854$	−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	$-0.398583\pi$
$857$	18.3405			0.626498			0.313249	+	0.949671i	$0.398583\pi$
$858$	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	$0.388090\pi$
$860$	−9.64807	+	13.8538i	−0.328996	+	0.472410i
$861$	−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	$-0.757578\pi$
$863$		−	40.5444i		−	1.38015i	0.723740	−	0.690073i	$-0.242422\pi$
$864$	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
$870$	−14.6183	+	8.10075i	−0.495608	+	0.274641i
$871$			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
$875$	−17.2144	+	23.2815i	−0.581954	+	0.787060i
$876$	−20.9608	+	2.68721i	−0.708200	+	0.0907926i
$877$	31.0594	−	31.0594i	1.04880	−	1.04880i	0.0500546	−	0.998746i	$-0.484060\pi$
$877$	31.0594	−	31.0594i	1.04880	−	1.04880i	0.998746	−	0.0500546i	$-0.0159395\pi$
$878$	0.616878	+	0.210570i	0.0208186	+	0.00710638i
$879$	−30.1059			−1.01545
$880$	16.6768	+	53.0489i	0.562174	+	1.78828i
$881$	−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	−0.335812	−	0.941929i	$-0.609011\pi$
$883$	18.0110	−	18.0110i	0.606117	−	0.606117i	0.941929	+	0.335812i	$0.109011\pi$
$884$	−0.661283	−	5.15814i	−0.0222413	−	0.173487i
$885$	9.77891	−	10.7999i	0.328715	−	0.363034i
$886$	−5.17896	+	2.54307i	−0.173991	+	0.0854359i
$887$	37.8699			1.27155			0.635774	−	0.771876i	$-0.280681\pi$
$887$	37.8699			1.27155			0.635774	+	0.771876i	$0.280681\pi$
$888$	−17.5612	+	11.6052i	−0.589316	+	0.389444i
$889$			17.4888i			0.586556i
$890$	15.7484	+	28.4191i	0.527888	+	0.952609i
$891$	−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
$900$	−8.47919	−	5.30126i	−0.282640	−	0.176709i
$901$	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	0.453989	−	0.891007i	$-0.350001\pi$
$907$	−13.1614	−	13.1614i	−0.437018	−	0.437018i	−0.891007	+	0.453989i	$0.850001\pi$
$908$	42.2398	−	5.41523i	1.40178	−	0.179711i
$909$	−10.0764	−	10.0764i	−0.334215	−	0.334215i
$910$	1.33329	−	4.64758i	0.0441980	−	0.154066i
$911$	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
$915$	0.495354	+	0.448526i	0.0163759	+	0.0148278i
$916$	−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	$0.786856\pi$
$920$	−1.75714	−	0.268924i	−0.0579311	−	0.00886617i
$921$		−	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
$925$	23.5782	−	28.7869i	0.775246	−	0.946506i
$926$	−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	$0.287950\pi$
$930$	2.66167	−	9.27807i	0.0872796	−	0.304240i
$931$	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	$-0.617778\pi$
$937$	−22.1390			−0.723251			−0.361625	+	0.932323i	$0.617778\pi$
$938$	16.3721	+	33.3418i	0.534568	+	1.08865i
$939$	−6.88321	+	6.88321i	−0.224625	+	0.224625i
$940$	32.8053	−	5.87058i	1.06999	−	0.191477i
$941$	−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	−0.772503	−	0.635011i	$-0.780995\pi$
$947$	−4.23108	+	4.23108i	−0.137492	+	0.137492i	0.635011	+	0.772503i	$0.280995\pi$
$948$	9.00444	−	1.15439i	0.292451	−	0.0374927i
$949$	−4.41104	+	4.41104i	−0.143189	+	0.143189i
$950$	−23.9294	−	38.5443i	−0.776373	−	1.25054i
$951$		−	11.9736i		−	0.388269i
$952$	−17.7862	−	26.9145i	−0.576454	−	0.872304i
$953$	−0.585699			−0.0189726			−0.00948632	−	0.999955i	$-0.503020\pi$
$953$	−0.585699			−0.0189726			−0.00948632	+	0.999955i	$0.503020\pi$
$954$	2.55170	+	5.19654i	0.0826143	+	0.168244i
$955$	−13.8071	−	12.5019i	−0.446789	−	0.404552i
$956$	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
$960$	−6.18949	+	16.7836i	−0.199765	+	0.541689i
$961$	−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
$965$	−8.60594	+	9.50443i	−0.277035	+	0.305958i
$966$	0.453721	+	0.924004i	0.0145982	+	0.0297293i
$967$	−41.5832			−1.33722			−0.668612	−	0.743611i	$-0.733111\pi$
$967$	−41.5832			−1.33722			−0.668612	+	0.743611i	$0.733111\pi$
$968$	43.1233	+	65.2552i	1.38604	+	2.09738i
$969$			28.2573i			0.907756i
$970$	−10.3930	−	18.7548i	−0.333698	−	0.602180i
$971$	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	$0.0897457\pi$
$977$			17.3929i			0.556448i	−0.960516	+	0.278224i	$0.910254\pi$
$978$	22.6301	+	7.72473i	0.723631	+	0.247010i
$979$	45.1692	+	45.1692i	1.44361	+	1.44361i
$980$	0.230872	+	1.29013i	0.00737494	+	0.0412118i
$981$	−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	$-0.348717\pi$
$983$	28.6927			0.915154			0.457577	+	0.889170i	$0.348717\pi$
$984$	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
$990$	−18.8983	−	5.42149i	−0.600627	−	0.172306i
$991$	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
$995$	−28.6061	+	31.5927i	−0.906875	+	1.00156i
$996$	−7.89766	+	10.2204i	−0.250247	+	0.323847i
$997$	−25.4723	−	25.4723i	−0.806717	−	0.806717i	0.177419	−	0.984135i	$-0.443225\pi$
$997$	−25.4723	−	25.4723i	−0.806717	−	0.806717i	−0.984135	+	0.177419i	$0.943225\pi$
$998$	−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.109.15	yes	48
3.2	odd	2		720.2.bm.h.109.10		48
4.3	odd	2		960.2.bl.a.529.22		48
5.4	even	2	inner	240.2.bl.a.109.10	✓	48
8.3	odd	2		1920.2.bl.b.289.3		48
8.5	even	2		1920.2.bl.a.289.22		48
15.14	odd	2		720.2.bm.h.109.15		48
16.3	odd	4		1920.2.bl.b.1249.22		48
16.5	even	4	inner	240.2.bl.a.229.10	yes	48
16.11	odd	4		960.2.bl.a.49.4		48
16.13	even	4		1920.2.bl.a.1249.3		48
20.19	odd	2		960.2.bl.a.529.4		48
40.19	odd	2		1920.2.bl.b.289.22		48
40.29	even	2		1920.2.bl.a.289.3		48
48.5	odd	4		720.2.bm.h.469.15		48
80.19	odd	4		1920.2.bl.b.1249.3		48
80.29	even	4		1920.2.bl.a.1249.22		48
80.59	odd	4		960.2.bl.a.49.22		48
80.69	even	4	inner	240.2.bl.a.229.15	yes	48
240.149	odd	4		720.2.bm.h.469.10		48

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

\(f(q)\)	\(=\)	\(q+(0.456856 - 1.33839i) q^{2} +(-0.707107 + 0.707107i) q^{3} +(-1.58257 - 1.22290i) q^{4} +(1.65754 + 1.50085i) q^{5} +(0.623338 + 1.26943i) q^{6} +2.58977 q^{7} +(-2.35972 + 1.55940i) q^{8} -1.00000i q^{9} +O(q^{10})\)	\(q+(0.456856 - 1.33839i) q^{2} +(-0.707107 + 0.707107i) q^{3} +(-1.58257 - 1.22290i) q^{4} +(1.65754 + 1.50085i) q^{5} +(0.623338 + 1.26943i) q^{6} +2.58977 q^{7} +(-2.35972 + 1.55940i) q^{8} -1.00000i q^{9} +(2.76598 - 1.53277i) 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} +(-0.787783 - 4.40220i) 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} +(-0.872013 + 3.03967i) q^{30} -3.05233 q^{31} +(5.64140 + 0.417848i) q^{32} +6.21722i q^{33} +(5.89449 + 2.01207i) q^{34} +(4.29266 + 3.88686i) q^{35} +(-1.22290 + 1.58257i) q^{36} +(-5.26234 - 5.26234i) q^{37} +(-8.14471 + 3.99936i) q^{38} +0.590389i q^{39} +(-6.25176 - 0.956812i) q^{40} +5.16508i q^{41} +(1.61430 + 3.28754i) q^{42} +(-2.66933 - 2.66933i) q^{43} +(-12.3335 + 1.58118i) q^{44} +(1.50085 - 1.65754i) q^{45} +(0.128405 - 0.376171i) q^{46} +7.45202i q^{47} +(-3.45045 - 2.02346i) q^{48} -0.293066 q^{49} +(6.88518 + 1.61069i) 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} +(3.66987 + 2.55578i) 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} +(7.16326 - 3.96952i) q^{70} -15.9477i q^{71} +(1.55940 + 2.35972i) q^{72} -10.5662 q^{73} +(-9.44719 + 4.63893i) q^{74} +(-3.86812 - 3.16822i) q^{75} +(1.63174 + 12.7279i) q^{76} +(11.3853 - 11.3853i) q^{77} +(0.790170 + 0.269723i) q^{78} +4.53907 q^{79} +(-4.13674 + 7.93016i) q^{80} -1.00000 q^{81} +(6.91288 + 2.35969i) q^{82} +(-4.56660 + 4.56660i) q^{83} +(5.13750 - 0.658637i) q^{84} +(-6.61000 + 7.30010i) q^{85} +(-4.79209 + 2.35310i) q^{86} -5.28505 q^{87} +(-3.51840 + 17.2294i) q^{88} +10.2745i q^{89} +(-1.53277 - 2.76598i) 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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