LMFDB - Embedded newform 968.2.o.g.245.6

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [968,2,Mod(245,968)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("968.245"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(968, base_ring=CyclotomicField(10)) chi = DirichletCharacter(H, H._module([0, 5, 8])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 968 = 2^{3} \cdot 11^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	968.o (of order $10$, degree $4$, not minimal)

Newform invariants

comment:select newform

sage:traces = [40,0,0,4,0,-2] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(6)] == traces)

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

Self dual:	no
Analytic conductor:	$7.72951891566$
Analytic rank:	$0$
Dimension:	$40$
Relative dimension:	$10$ over $\Q(\zeta_{10})$
Twist minimal:	no (minimal twist has level 88)
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			245.6
Character	$\chi$	$=$	968.245
Dual form			968.2.o.g.565.6

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.110755 + 1.40987i) q^{2} +(2.23784 - 0.727117i) q^{3} +(-1.97547 + 0.312301i) q^{4} +(2.44985 - 3.37193i) q^{5} +(1.27299 + 3.07453i) q^{6} +(0.288382 - 0.887547i) q^{7} +(-0.659097 - 2.75056i) q^{8} +(2.05216 - 1.49098i) q^{9} +(5.02532 + 3.08051i) q^{10} +(-4.19369 + 2.13527i) q^{12} +(1.72410 + 2.37303i) q^{13} +(1.28327 + 0.308280i) q^{14} +(3.03058 - 9.32717i) q^{15} +(3.80494 - 1.23388i) q^{16} +(-1.97907 - 1.43788i) q^{17} +(2.32938 + 2.72815i) q^{18} +(-2.55153 + 0.829041i) q^{19} +(-3.78654 + 7.42623i) q^{20} -2.19587i q^{21} -3.47129 q^{23} +(-3.47493 - 5.67607i) q^{24} +(-3.82307 - 11.7662i) q^{25} +(-3.15471 + 2.69359i) q^{26} +(-0.640892 + 0.882112i) q^{27} +(-0.292506 + 1.84338i) q^{28} +(4.34866 + 1.41296i) q^{29} +(13.4857 + 3.23969i) q^{30} +(2.95923 - 2.15001i) q^{31} +(2.16103 + 5.22781i) q^{32} +(1.80803 - 2.94948i) q^{34} +(-2.28626 - 3.14676i) q^{35} +(-3.58834 + 3.58628i) q^{36} +(4.31595 + 1.40234i) q^{37} +(-1.45143 - 3.50550i) q^{38} +(5.58373 + 4.05682i) q^{39} +(-10.8894 - 4.51604i) q^{40} +(1.27506 + 3.92423i) q^{41} +(3.09590 - 0.243205i) q^{42} -11.4650i q^{43} -10.5724i q^{45} +(-0.384463 - 4.89406i) q^{46} +(1.00821 + 3.10297i) q^{47} +(7.61765 - 5.52786i) q^{48} +(4.95854 + 3.60259i) q^{49} +(16.1654 - 6.69320i) q^{50} +(-5.47434 - 1.77872i) q^{51} +(-4.14701 - 4.14940i) q^{52} +(0.382138 + 0.525968i) q^{53} +(-1.31464 - 0.805875i) q^{54} +(-2.63133 - 0.208231i) q^{56} +(-5.10709 + 3.71052i) q^{57} +(-1.51046 + 6.28753i) q^{58} +(-2.76724 - 0.899131i) q^{59} +(-3.07392 + 19.3720i) q^{60} +(-6.29283 + 8.66134i) q^{61} +(3.35898 + 3.93401i) q^{62} +(-0.731513 - 2.25136i) q^{63} +(-7.13118 + 3.62578i) q^{64} +12.2255 q^{65} +5.42623i q^{67} +(4.35863 + 2.22241i) q^{68} +(-7.76817 + 2.52403i) q^{69} +(4.18331 - 3.57185i) q^{70} +(6.27093 + 4.55610i) q^{71} +(-5.45362 - 4.66190i) q^{72} +(4.03732 - 12.4256i) q^{73} +(-1.49910 + 6.24025i) q^{74} +(-17.1108 - 23.5510i) q^{75} +(4.78154 - 2.43459i) q^{76} +(-5.10116 + 8.32165i) q^{78} +(-3.91294 + 2.84292i) q^{79} +(5.16097 - 15.8528i) q^{80} +(-3.14438 + 9.67741i) q^{81} +(-5.39144 + 2.23230i) q^{82} +(-0.387741 + 0.533679i) q^{83} +(0.685774 + 4.33787i) q^{84} +(-9.69685 + 3.15070i) q^{85} +(16.1641 - 1.26981i) q^{86} +10.7590 q^{87} -2.74629 q^{89} +(14.9058 - 1.17095i) q^{90} +(2.60337 - 0.845887i) q^{91} +(6.85741 - 1.08409i) q^{92} +(5.05897 - 6.96307i) q^{93} +(-4.26311 + 1.76512i) q^{94} +(-3.45539 + 10.6346i) q^{95} +(8.63726 + 10.1277i) q^{96} +(-1.47973 + 1.07509i) q^{97} +(-4.53000 + 7.38991i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q + 4 q^{4} - 2 q^{6} + 10 q^{9} + 40 q^{10} - 16 q^{12} + 12 q^{14} - 8 q^{15} + 4 q^{17} + 10 q^{18} - 12 q^{20} - 48 q^{23} + 6 q^{25} + 20 q^{26} + 12 q^{28} - 18 q^{30} + 4 q^{31} - 80 q^{32} - 32 q^{36}+ \cdots + 96 q^{98}+O(q^{100}) $ 40 * q + 4 * q^4 - 2 * q^6 + 10 * q^9 + 40 * q^10 - 16 * q^12 + 12 * q^14 - 8 * q^15 + 4 * q^17 + 10 * q^18 - 12 * q^20 - 48 * q^23 + 6 * q^25 + 20 * q^26 + 12 * q^28 - 18 * q^30 + 4 * q^31 - 80 * q^32 - 32 * q^36 - 8 * q^38 - 24 * q^39 - 20 * q^40 - 4 * q^41 - 20 * q^42 - 2 * q^46 + 4 * q^47 - 32 * q^48 + 6 * q^49 + 6 * q^50 + 20 * q^52 - 152 * q^54 - 32 * q^56 - 16 * q^57 - 36 * q^58 + 4 * q^60 - 22 * q^62 + 40 * q^63 + 16 * q^64 + 64 * q^65 + 28 * q^68 - 28 * q^70 + 12 * q^71 + 4 * q^72 + 4 * q^73 + 14 * q^74 + 176 * q^76 - 32 * q^78 - 16 * q^79 + 56 * q^80 + 6 * q^81 + 4 * q^82 + 52 * q^84 + 20 * q^86 + 128 * q^87 - 16 * q^89 + 36 * q^90 + 36 * q^92 - 24 * q^95 - 60 * q^96 + 20 * q^97 + 96 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/968\mathbb{Z}\right)^\times$.

$n$	$485$	$727$	$849$
$\chi(n)$	$-1$	$1$	$e\left(\frac{4}{5}\right)$

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 $

$2$	0.110755	+	1.40987i	0.0783158	+	0.996929i
$2$	0.110755	+	1.40987i	0.0783158	+	0.996929i
$3$	2.23784	−	0.727117i	1.29202	−	0.419801i	0.419219	−	0.907885i	$-0.362304\pi$
$3$	2.23784	−	0.727117i	1.29202	−	0.419801i	0.872797	+	0.488084i	$0.162304\pi$
$4$	−1.97547	+	0.312301i	−0.987733	+	0.156151i
$5$	2.44985	−	3.37193i	1.09561	−	1.50797i	0.254526	−	0.967066i	$-0.418081\pi$
$5$	2.44985	−	3.37193i	1.09561	−	1.50797i	0.841082	−	0.540908i	$-0.181919\pi$
$6$	1.27299	+	3.07453i	0.519697	+	1.25517i
$7$	0.288382	−	0.887547i	0.108998	−	0.335461i	−0.881650	−	0.471904i	$-0.843567\pi$
$7$	0.288382	−	0.887547i	0.108998	−	0.335461i	0.990648	+	0.136443i	$0.0435669\pi$
$8$	−0.659097	−	2.75056i	−0.233026	−	0.972470i
$9$	2.05216	−	1.49098i	0.684054	−	0.496995i
$10$	5.02532	+	3.08051i	1.58915	+	0.974144i
$11$		0			0
$11$		0			0
$12$	−4.19369	+	2.13527i	−1.21061	+	0.616401i
$13$	1.72410	+	2.37303i	0.478181	+	0.658159i	0.978154	−	0.207882i	$-0.0666569\pi$
$13$	1.72410	+	2.37303i	0.478181	+	0.658159i	−0.499973	+	0.866041i	$0.666657\pi$
$14$	1.28327	+	0.308280i	0.342967	+	0.0823913i
$15$	3.03058	−	9.32717i	0.782492	−	2.40826i
$16$	3.80494	−	1.23388i	0.951234	−	0.308470i
$17$	−1.97907	−	1.43788i	−0.479995	−	0.348736i	0.321329	−	0.946968i	$-0.395870\pi$
$17$	−1.97907	−	1.43788i	−0.479995	−	0.348736i	−0.801324	+	0.598231i	$0.795870\pi$
$18$	2.32938	+	2.72815i	0.549040	+	0.643031i
$19$	−2.55153	+	0.829041i	−0.585360	+	0.190195i	−0.586700	−	0.809804i	$-0.699573\pi$
$19$	−2.55153	+	0.829041i	−0.585360	+	0.190195i	0.00134028	+	0.999999i	$0.499573\pi$
$20$	−3.78654	+	7.42623i	−0.846697	+	1.66056i
$21$		−	2.19587i		−	0.479179i
$22$		0			0
$23$	−3.47129			−0.723813			−0.361907	−	0.932214i	$-0.617874\pi$
$23$	−3.47129			−0.723813			−0.361907	+	0.932214i	$0.617874\pi$
$24$	−3.47493	−	5.67607i	−0.709318	−	1.15862i
$25$	−3.82307	−	11.7662i	−0.764614	−	2.35324i
$26$	−3.15471	+	2.69359i	−0.618689	+	0.528256i
$27$	−0.640892	+	0.882112i	−0.123340	+	0.169762i
$28$	−0.292506	+	1.84338i	−0.0552785	+	0.348366i
$29$	4.34866	+	1.41296i	0.807525	+	0.262381i	0.683549	−	0.729904i	$-0.260435\pi$
$29$	4.34866	+	1.41296i	0.807525	+	0.262381i	0.123976	+	0.992285i	$0.460435\pi$
$30$	13.4857	+	3.23969i	2.46215	+	0.591484i
$31$	2.95923	−	2.15001i	0.531493	−	0.386153i	−0.289423	−	0.957201i	$-0.593463\pi$
$31$	2.95923	−	2.15001i	0.531493	−	0.386153i	0.820916	+	0.571049i	$0.193463\pi$
$32$	2.16103	+	5.22781i	0.382019	+	0.924154i
$33$		0			0
$34$	1.80803	−	2.94948i	0.310074	−	0.505832i
$35$	−2.28626	−	3.14676i	−0.386448	−	0.531900i
$36$	−3.58834	+	3.58628i	−0.598057	+	0.597714i
$37$	4.31595	+	1.40234i	0.709539	+	0.230543i	0.641482	−	0.767138i	$-0.278320\pi$
$37$	4.31595	+	1.40234i	0.709539	+	0.230543i	0.0680569	+	0.997681i	$0.478320\pi$
$38$	−1.45143	−	3.50550i	−0.235454	−	0.568667i
$39$	5.58373	+	4.05682i	0.894113	+	0.649611i
$40$	−10.8894	−	4.51604i	−1.72177	−	0.714048i
$41$	1.27506	+	3.92423i	0.199131	+	0.612862i	0.999903	+	0.0138937i	$0.00442263\pi$
$41$	1.27506	+	3.92423i	0.199131	+	0.612862i	−0.800772	+	0.598969i	$0.795577\pi$
$42$	3.09590	−	0.243205i	0.477707	−	0.0375273i
$43$		−	11.4650i		−	1.74839i	−0.485573	−	0.874196i	$-0.661389\pi$
$43$		−	11.4650i		−	1.74839i	0.485573	−	0.874196i	$-0.338611\pi$
$44$		0			0
$45$		−	10.5724i		−	1.57605i
$46$	−0.384463	−	4.89406i	−0.0566860	−	0.721590i
$47$	1.00821	+	3.10297i	0.147063	+	0.452614i	0.997271	−	0.0738340i	$-0.0235235\pi$
$47$	1.00821	+	3.10297i	0.147063	+	0.452614i	−0.850207	+	0.526448i	$0.823523\pi$
$48$	7.61765	−	5.52786i	1.09951	−	0.797878i
$49$	4.95854	+	3.60259i	0.708363	+	0.514656i
$50$	16.1654	−	6.69320i	2.28613	−	0.946561i
$51$	−5.47434	−	1.77872i	−0.766561	−	0.249071i
$52$	−4.14701	−	4.14940i	−0.575087	−	0.575418i
$53$	0.382138	+	0.525968i	0.0524907	+	0.0722472i	0.834455	−	0.551075i	$-0.185782\pi$
$53$	0.382138	+	0.525968i	0.0524907	+	0.0722472i	−0.781965	+	0.623323i	$0.785782\pi$
$54$	−1.31464	−	0.805875i	−0.178901	−	0.109666i
$55$		0			0
$56$	−2.63133	−	0.208231i	−0.351626	−	0.0278261i
$57$	−5.10709	+	3.71052i	−0.676450	+	0.491470i
$58$	−1.51046	+	6.28753i	−0.198333	+	0.825593i
$59$	−2.76724	−	0.899131i	−0.360264	−	0.117057i	0.123292	−	0.992370i	$-0.460655\pi$
$59$	−2.76724	−	0.899131i	−0.360264	−	0.117057i	−0.483556	+	0.875314i	$0.660655\pi$
$60$	−3.07392	+	19.3720i	−0.396842	+	2.50091i
$61$	−6.29283	+	8.66134i	−0.805714	+	1.10897i	0.186256	+	0.982501i	$0.440365\pi$
$61$	−6.29283	+	8.66134i	−0.805714	+	1.10897i	−0.991971	+	0.126469i	$0.959635\pi$
$62$	3.35898	+	3.93401i	0.426591	+	0.499619i
$63$	−0.731513	−	2.25136i	−0.0921619	−	0.283645i
$64$	−7.13118	+	3.62578i	−0.891398	+	0.453222i
$65$	12.2255			1.51639
$66$		0			0
$67$			5.42623i			0.662919i	0.943469	+	0.331460i	$0.107541\pi$
$67$			5.42623i			0.662919i	−0.943469	+	0.331460i	$0.892459\pi$
$68$	4.35863	+	2.22241i	0.528562	+	0.269507i
$69$	−7.76817	+	2.52403i	−0.935178	+	0.303858i
$70$	4.18331	−	3.57185i	0.500001	−	0.426917i
$71$	6.27093	+	4.55610i	0.744222	+	0.540709i	0.894031	−	0.448006i	$-0.147866\pi$
$71$	6.27093	+	4.55610i	0.744222	+	0.540709i	−0.149808	+	0.988715i	$0.547866\pi$
$72$	−5.45362	−	4.66190i	−0.642715	−	0.549410i
$73$	4.03732	−	12.4256i	0.472533	−	1.45431i	−0.376724	−	0.926326i	$-0.622949\pi$
$73$	4.03732	−	12.4256i	0.472533	−	1.45431i	0.849256	−	0.527981i	$-0.177051\pi$
$74$	−1.49910	+	6.24025i	−0.174267	+	0.725414i
$75$	−17.1108	−	23.5510i	−1.97579	−	2.71944i
$76$	4.78154	−	2.43459i	0.548481	−	0.279266i
$77$		0			0
$78$	−5.10116	+	8.32165i	−0.577593	+	0.942242i
$79$	−3.91294	+	2.84292i	−0.440240	+	0.319853i	−0.785730	−	0.618569i	$-0.787713\pi$
$79$	−3.91294	+	2.84292i	−0.440240	+	0.319853i	0.345490	+	0.938422i	$0.387713\pi$
$80$	5.16097	−	15.8528i	0.577014	−	1.77240i
$81$	−3.14438	+	9.67741i	−0.349376	+	1.07527i
$82$	−5.39144	+	2.23230i	−0.595385	+	0.246516i
$83$	−0.387741	+	0.533679i	−0.0425601	+	0.0585789i	−0.829767	−	0.558110i	$-0.811527\pi$
$83$	−0.387741	+	0.533679i	−0.0425601	+	0.0585789i	0.787207	+	0.616689i	$0.211527\pi$
$84$	0.685774	+	4.33787i	0.0748241	+	0.473301i
$85$	−9.69685	+	3.15070i	−1.05177	+	0.341741i
$86$	16.1641	−	1.26981i	1.74302	−	0.136927i
$87$	10.7590			1.15348
$88$		0			0
$89$	−2.74629			−0.291107			−0.145553	−	0.989350i	$-0.546496\pi$
$89$	−2.74629			−0.291107			−0.145553	+	0.989350i	$0.546496\pi$
$90$	14.9058	−	1.17095i	1.57121	−	0.123429i
$91$	2.60337	−	0.845887i	0.272908	−	0.0886731i
$92$	6.85741	−	1.08409i	0.714934	−	0.113024i
$93$	5.05897	−	6.96307i	0.524591	−	0.722037i
$94$	−4.26311	+	1.76512i	−0.439706	+	0.182058i
$95$	−3.45539	+	10.6346i	−0.354516	+	1.09109i
$96$	8.63726	+	10.1277i	0.881536	+	1.03365i
$97$	−1.47973	+	1.07509i	−0.150244	+	0.109159i	−0.660368	−	0.750942i	$-0.729600\pi$
$97$	−1.47973	+	1.07509i	−0.150244	+	0.109159i	0.510124	+	0.860101i	$0.329600\pi$
$98$	−4.53000	+	7.38991i	−0.457599	+	0.746493i
$99$		0			0
$100$	11.2269	+	22.0498i	1.12269	+	2.20498i
$101$	7.45377	+	10.2592i	0.741677	+	1.02083i	0.998520	+	0.0543782i	$0.0173177\pi$
$101$	7.45377	+	10.2592i	0.741677	+	1.02083i	−0.256843	+	0.966453i	$0.582682\pi$
$102$	1.90145	−	7.91511i	0.188272	−	0.783712i
$103$	−1.19480	+	3.67721i	−0.117727	+	0.362326i	−0.992506	−	0.122196i	$-0.961006\pi$
$103$	−1.19480	+	3.67721i	−0.117727	+	0.362326i	0.874779	+	0.484522i	$0.161006\pi$
$104$	5.39080	−	6.30631i	0.528612	−	0.618385i
$105$	−7.40434	−	5.37957i	−0.722589	−	0.524992i
$106$	−0.699222	+	0.597019i	−0.0679145	+	0.0579876i
$107$	−12.1565	+	3.94990i	−1.17522	+	0.381851i	−0.830588	−	0.556888i	$-0.811995\pi$
$107$	−12.1565	+	3.94990i	−1.17522	+	0.381851i	−0.344629	+	0.938739i	$0.611995\pi$
$108$	0.990576	−	1.94273i	0.0953182	−	0.186940i
$109$		−	1.85065i		−	0.177260i	−0.996065	−	0.0886299i	$-0.971751\pi$
$109$		−	1.85065i		−	0.177260i	0.996065	−	0.0886299i	$-0.0282489\pi$
$110$		0			0
$111$	10.6781			1.01352
$112$	0.00214582	−	3.73289i	0.000202761	−	0.352725i
$113$	5.15487	+	15.8651i	0.484929	+	1.49246i	0.832083	+	0.554651i	$0.187148\pi$
$113$	5.15487	+	15.8651i	0.484929	+	1.49246i	−0.347154	+	0.937808i	$0.612852\pi$
$114$	−5.79698	−	6.78937i	−0.542937	−	0.635883i
$115$	−8.50414	+	11.7049i	−0.793015	+	1.09149i
$116$	−9.03189	−	1.43317i	−0.838590	−	0.133067i
$117$	7.07629	+	2.29923i	0.654203	+	0.212563i
$118$	0.961171	−	4.00103i	0.0884830	−	0.368325i
$119$	−1.84691	+	1.34186i	−0.169306	+	0.123008i
$120$	−27.6524	−	2.18829i	−2.52431	−	0.199762i
$121$		0			0
$122$	−12.9083	−	7.91278i	−1.16866	−	0.716390i
$123$	5.70676	+	7.85468i	0.514561	+	0.708232i
$124$	−5.17441	+	5.17144i	−0.464676	+	0.464409i
$125$	−29.2211	−	9.49450i	−2.61361	−	0.849214i
$126$	3.09311	−	1.28069i	0.275556	−	0.114093i
$127$	5.26680	+	3.82656i	0.467353	+	0.339552i	0.796409	−	0.604758i	$-0.206730\pi$
$127$	5.26680	+	3.82656i	0.467353	+	0.339552i	−0.329056	+	0.944311i	$0.606730\pi$
$128$	−5.90169	−	9.65246i	−0.521641	−	0.853165i
$129$	−8.33638	−	25.6567i	−0.733977	−	2.25895i
$130$	1.35404	+	17.2364i	0.118757	+	1.51173i
$131$			6.91569i			0.604227i	0.953272	+	0.302114i	$0.0976922\pi$
$131$			6.91569i			0.604227i	−0.953272	+	0.302114i	$0.902308\pi$
$132$		0			0
$133$			2.50368i			0.217097i
$134$	−7.65027	+	0.600983i	−0.660883	+	0.0519171i
$135$	1.40433	+	4.32209i	0.120866	+	0.371986i
$136$	−2.65057	+	6.39125i	−0.227285	+	0.548045i
$137$	−4.70809	−	3.42063i	−0.402239	−	0.292244i	0.368213	−	0.929741i	$-0.379970\pi$
$137$	−4.70809	−	3.42063i	−0.402239	−	0.292244i	−0.770453	+	0.637497i	$0.779970\pi$
$138$	−4.41892	−	10.6726i	−0.376164	−	0.908509i
$139$	−9.06860	−	2.94657i	−0.769188	−	0.249924i	−0.101971	−	0.994787i	$-0.532515\pi$
$139$	−9.06860	−	2.94657i	−0.769188	−	0.249924i	−0.667217	+	0.744863i	$0.732515\pi$
$140$	5.49916	+	5.50233i	0.464764	+	0.465031i
$141$	4.51244	+	6.21084i	0.380016	+	0.523047i
$142$	−5.72896	+	9.34580i	−0.480764	+	0.784282i
$143$		0			0
$144$	5.96865	−	8.20522i	0.497388	−	0.683769i
$145$	15.4180	−	11.2018i	1.28039	−	0.930261i
$146$	17.9656	+	4.31590i	1.48685	+	0.357186i
$147$	13.7159	+	4.45657i	1.13127	+	0.367572i
$148$	−8.96398	−	1.42240i	−0.736834	−	0.116920i
$149$	8.18322	−	11.2632i	0.670396	−	0.922721i	−0.329373	−	0.944200i	$-0.606838\pi$
$149$	8.18322	−	11.2632i	0.670396	−	0.922721i	0.999769	+	0.0214790i	$0.00683752\pi$
$150$	31.3087	−	26.7324i	2.55635	−	2.18269i
$151$	4.70404	+	14.4775i	0.382809	+	1.17816i	0.938057	+	0.346480i	$0.112623\pi$
$151$	4.70404	+	14.4775i	0.382809	+	1.17816i	−0.555248	+	0.831685i	$0.687377\pi$
$152$	3.96203	+	6.47171i	0.321363	+	0.524925i
$153$	−6.20522			−0.501662
$154$		0			0
$155$		−	15.2455i		−	1.22455i
$156$	−12.2974	−	6.27031i	−0.984582	−	0.502026i
$157$	−0.831166	+	0.270062i	−0.0663343	+	0.0215533i	−0.341996	−	0.939701i	$-0.611103\pi$
$157$	−0.831166	+	0.270062i	−0.0663343	+	0.0215533i	0.275662	+	0.961255i	$0.411103\pi$
$158$	−4.44152	−	5.20186i	−0.353348	−	0.413838i
$159$	1.23760	+	0.899171i	0.0981483	+	0.0713089i
$160$	22.9220	+	5.52051i	1.81214	+	0.436435i
$161$	−1.00105	+	3.08093i	−0.0788942	+	0.242811i
$162$	−13.9921	−	3.36134i	−1.09933	−	0.264092i
$163$	4.42418	+	6.08936i	0.346528	+	0.476955i	0.946334	−	0.323190i	$-0.104755\pi$
$163$	4.42418	+	6.08936i	0.346528	+	0.476955i	−0.599806	+	0.800146i	$0.704755\pi$
$164$	−3.74438	−	7.35399i	−0.292387	−	0.574250i
$165$		0			0
$166$	−0.795363	−	0.487556i	−0.0617321	−	0.0378417i
$167$	−0.115612	+	0.0839969i	−0.00894631	+	0.00649988i	−0.592249	−	0.805755i	$-0.701760\pi$
$167$	−0.115612	+	0.0839969i	−0.00894631	+	0.00649988i	0.583303	+	0.812255i	$0.301760\pi$
$168$	−6.03989	+	1.44729i	−0.465987	+	0.111661i
$169$	1.35850	−	4.18104i	0.104500	−	0.321618i
$170$	−5.51605	−	13.3223i	−0.423062	−	1.02178i
$171$	−4.00006	+	5.50561i	−0.305892	+	0.421025i
$172$	3.58052	+	22.6487i	0.273012	+	1.72694i
$173$	−1.07383	+	0.348910i	−0.0816421	+	0.0265271i	−0.349553	−	0.936916i	$-0.613667\pi$
$173$	−1.07383	+	0.348910i	−0.0816421	+	0.0265271i	0.267911	+	0.963444i	$0.413667\pi$
$174$	1.19161	+	15.1687i	0.0903360	+	1.14994i
$175$	−11.5456			−0.872762
$176$		0			0
$177$	−6.84641			−0.514608
$178$	−0.304167	−	3.87192i	−0.0227983	−	0.290213i
$179$	−14.4199	+	4.68532i	−1.07780	+	0.350197i	−0.793519	−	0.608545i	$-0.791754\pi$
$179$	−14.4199	+	4.68532i	−1.07780	+	0.350197i	−0.284277	+	0.958742i	$0.591754\pi$
$180$	3.30179	+	20.8855i	0.246101	+	1.55671i
$181$	9.94596	−	13.6894i	0.739278	−	1.01753i	−0.259382	−	0.965775i	$-0.583519\pi$
$181$	9.94596	−	13.6894i	0.739278	−	1.01753i	0.998660	−	0.0517537i	$-0.0164811\pi$
$182$	1.48093	+	3.57673i	0.109774	+	0.265125i
$183$	−7.78452	+	23.9583i	−0.575448	+	1.77105i
$184$	2.28792	+	9.54799i	0.168667	+	0.703887i
$185$	15.3020	−	11.1176i	1.12503	−	0.817381i
$186$	10.3773	+	6.36129i	0.760903	+	0.466432i
$187$		0			0
$188$	−2.96075	−	5.81494i	−0.215935	−	0.424098i
$189$	0.598095	+	0.823206i	0.0435050	+	0.0598795i
$190$	−15.3761	−	3.69381i	−1.11550	−	0.267977i
$191$	−5.15195	+	15.8561i	−0.372782	+	1.14730i	0.572181	+	0.820127i	$0.306097\pi$
$191$	−5.15195	+	15.8561i	−0.372782	+	1.14730i	−0.944963	+	0.327177i	$0.893903\pi$
$192$	−13.3221	+	13.2991i	−0.961437	+	0.959780i
$193$	−0.146189	−	0.106213i	−0.0105229	−	0.00764537i	0.582511	−	0.812823i	$-0.302070\pi$
$193$	−0.146189	−	0.106213i	−0.0105229	−	0.00764537i	−0.593034	+	0.805177i	$0.702070\pi$
$194$	−1.67963	−	1.96716i	−0.120590	−	0.141234i
$195$	27.3587	−	8.88937i	1.95919	−	0.636581i
$196$	−10.9205	−	5.56824i	−0.780038	−	0.397732i
$197$			8.38885i			0.597681i	0.954303	+	0.298840i	$0.0965998\pi$
$197$			8.38885i			0.597681i	−0.954303	+	0.298840i	$0.903400\pi$
$198$		0			0
$199$	22.0996			1.56660			0.783298	−	0.621646i	$-0.213536\pi$
$199$	22.0996			1.56660			0.783298	+	0.621646i	$0.213536\pi$
$200$	−29.8439	+	18.2707i	−2.11028	+	1.29193i
$201$	3.94550	+	12.1430i	0.278294	+	0.856502i
$202$	−13.6386	+	11.6451i	−0.959611	+	0.819347i
$203$	2.50814	−	3.45216i	0.176037	−	0.242294i
$204$	11.3699	+	1.80416i	0.796050	+	0.126316i
$205$	16.3560	+	5.31438i	1.14235	+	0.371172i
$206$	−5.31671	−	1.27724i	−0.370433	−	0.0889894i
$207$	−7.12364	+	5.17563i	−0.495128	+	0.359731i
$208$	9.48814	+	6.90187i	0.657884	+	0.478559i
$209$		0			0
$210$	6.76442	−	11.0350i	0.466789	−	0.761485i
$211$	−8.83969	−	12.1668i	−0.608549	−	0.837596i	0.387908	−	0.921698i	$-0.373198\pi$
$211$	−8.83969	−	12.1668i	−0.608549	−	0.837596i	−0.996457	+	0.0841019i	$0.973198\pi$
$212$	−0.919161	−	0.919690i	−0.0631282	−	0.0631645i
$213$	17.3461	+	5.63610i	1.18854	+	0.386179i
$214$	−6.91524	−	16.7017i	−0.472716	−	1.14170i
$215$	−38.6591	−	28.0875i	−2.63653	−	1.91555i
$216$	2.84871	+	1.18141i	0.193830	+	0.0803851i
$217$	−1.05485	−	3.24648i	−0.0716076	−	0.220385i
$218$	2.60917	−	0.204969i	0.176715	−	0.0138823i
$219$		−	30.7421i		−	2.07736i
$220$		0			0
$221$		−	7.17543i		−	0.482672i
$222$	1.18265	+	15.0547i	0.0793744	+	1.01040i
$223$	−3.17564	−	9.77362i	−0.212657	−	0.654490i	−0.999312	−	0.0370972i	$-0.988189\pi$
$223$	−3.17564	−	9.77362i	−0.212657	−	0.654490i	0.786655	−	0.617393i	$-0.211811\pi$
$224$	5.26313	−	0.410412i	0.351657	−	0.0274218i
$225$	−25.3888	−	18.4460i	−1.69258	−	1.22973i
$226$	−21.7967	+	9.02483i	−1.44990	+	0.600323i
$227$	−14.9020	−	4.84194i	−0.989077	−	0.321371i	−0.230585	−	0.973052i	$-0.574064\pi$
$227$	−14.9020	−	4.84194i	−0.989077	−	0.321371i	−0.758493	+	0.651682i	$0.774064\pi$
$228$	8.93008	−	8.92495i	0.591409	−	0.591069i
$229$	8.27290	+	11.3867i	0.546689	+	0.752453i	0.989558	−	0.144134i	$-0.0460395\pi$
$229$	8.27290	+	11.3867i	0.546689	+	0.752453i	−0.442869	+	0.896586i	$0.646039\pi$
$230$	−17.4443	−	10.6933i	−1.15024	−	0.705098i
$231$		0			0
$232$	1.02026	−	12.8925i	0.0669831	−	0.846436i
$233$	9.78854	−	7.11179i	0.641269	−	0.465909i	−0.219017	−	0.975721i	$-0.570285\pi$
$233$	9.78854	−	7.11179i	0.641269	−	0.465909i	0.860286	+	0.509812i	$0.170285\pi$
$234$	−2.45787	+	10.2313i	−0.160676	+	0.668841i
$235$	12.9330	+	4.20218i	0.843654	+	0.274120i
$236$	5.74739	+	0.911991i	0.374123	+	0.0593656i
$237$	−6.68938	+	9.20714i	−0.434522	+	0.598068i
$238$	−2.09640	−	2.45529i	−0.135890	−	0.159153i
$239$	−6.72046	−	20.6835i	−0.434711	−	1.33790i	−0.893383	−	0.449296i	$-0.851675\pi$
$239$	−6.72046	−	20.6835i	−0.434711	−	1.33790i	0.458672	−	0.888606i	$-0.348325\pi$
$240$	0.0225503	−	39.2286i	0.00145561	−	2.53220i
$241$	−6.93967			−0.447024			−0.223512	−	0.974701i	$-0.571752\pi$
$241$	−6.93967			−0.447024			−0.223512	+	0.974701i	$0.571752\pi$
$242$		0			0
$243$			20.6718i			1.32609i
$244$	9.72633	−	19.0754i	0.622664	−	1.22118i
$245$	24.2954	−	7.89405i	1.55218	−	0.504333i
$246$	−10.4420	+	8.91573i	−0.665759	+	0.568446i
$247$	−6.36643	−	4.62549i	−0.405087	−	0.294313i
$248$	−7.86415	−	6.72248i	−0.499374	−	0.426878i
$249$	−0.479653	+	1.47622i	−0.0303968	+	0.0935517i
$250$	10.1496	−	42.2495i	0.641918	−	2.67209i
$251$	−10.4202	−	14.3421i	−0.657715	−	0.905268i	0.341688	−	0.939814i	$-0.389001\pi$
$251$	−10.4202	−	14.3421i	−0.657715	−	0.905268i	−0.999403	+	0.0345459i	$0.989001\pi$
$252$	2.14818	+	4.21904i	0.135323	+	0.265775i
$253$		0			0
$254$	−4.81162	+	7.84932i	−0.301908	+	0.492510i
$255$	−19.4090	+	14.1015i	−1.21544	+	0.883070i
$256$	12.9551	−	9.38968i	0.809692	−	0.586855i
$257$	5.48645	−	16.8855i	0.342235	−	1.05329i	−0.620812	−	0.783959i	$-0.713197\pi$
$257$	5.48645	−	16.8855i	0.342235	−	1.05329i	0.963047	−	0.269332i	$-0.0868029\pi$
$258$	35.2494	−	14.5948i	2.19453	−	0.908634i
$259$	2.48928	−	3.42621i	0.154677	−	0.212894i
$260$	−24.1510	+	3.81803i	−1.49778	+	0.236784i
$261$	11.0309	−	3.58414i	0.682793	−	0.221853i
$262$	−9.75023	+	0.765950i	−0.602371	+	0.0473205i
$263$	−27.6424			−1.70450			−0.852252	−	0.523132i	$-0.824763\pi$
$263$	−27.6424			−1.70450			−0.852252	+	0.523132i	$0.824763\pi$
$264$		0			0
$265$	2.70971			0.166456
$266$	−3.52986	+	0.277296i	−0.216430	+	0.0170021i
$267$	−6.14576	+	1.99688i	−0.376114	+	0.122207i
$268$	−1.69462	−	10.7193i	−0.103515	−	0.654787i
$269$	−6.24717	+	8.59849i	−0.380897	+	0.524259i	−0.955822	−	0.293947i	$-0.905031\pi$
$269$	−6.24717	+	8.59849i	−0.380897	+	0.524259i	0.574925	+	0.818206i	$0.305031\pi$
$270$	−5.93804	+	2.45862i	−0.361378	+	0.149627i
$271$	6.10249	−	18.7815i	0.370700	−	1.14090i	−0.575635	−	0.817707i	$-0.695245\pi$
$271$	6.10249	−	18.7815i	0.370700	−	1.14090i	0.946334	−	0.323189i	$-0.104755\pi$
$272$	−9.30440	−	3.02910i	−0.564162	−	0.183666i
$273$	5.21087	−	3.78592i	0.315376	−	0.229134i
$274$	4.30120	−	7.01665i	0.259845	−	0.423891i
$275$		0			0
$276$	14.5575	−	7.41215i	0.876259	−	0.446159i
$277$	7.36805	+	10.1413i	0.442703	+	0.609329i	0.970810	−	0.239849i	$-0.0770980\pi$
$277$	7.36805	+	10.1413i	0.442703	+	0.609329i	−0.528107	+	0.849178i	$0.677098\pi$
$278$	3.14988	−	13.1119i	0.188917	−	0.786399i
$279$	2.86720	−	8.82433i	0.171655	−	0.528299i
$280$	−7.14850	+	8.36252i	−0.427205	+	0.499756i
$281$	19.2576	+	13.9915i	1.14881	+	0.834663i	0.988323	−	0.152375i	$-0.0486921\pi$
$281$	19.2576	+	13.9915i	1.14881	+	0.834663i	0.160492	+	0.987037i	$0.448692\pi$
$282$	−8.25670	+	7.04984i	−0.491679	+	0.419812i
$283$	−26.3723	+	8.56886i	−1.56767	+	0.509366i	−0.958843	−	0.283938i	$-0.908359\pi$
$283$	−26.3723	+	8.56886i	−1.56767	+	0.509366i	−0.608825	+	0.793304i	$0.708359\pi$
$284$	−13.8109	−	7.04200i	−0.819525	−	0.417866i
$285$			26.3110i			1.55853i
$286$		0			0
$287$	3.85065			0.227297
$288$	12.2294	+	7.50625i	0.720622	+	0.442310i
$289$	−3.40407	−	10.4766i	−0.200239	−	0.616273i
$290$	17.5007	+	20.4967i	1.02768	+	1.20361i
$291$	−2.52969	+	3.48182i	−0.148293	+	0.204108i
$292$	−4.09507	+	25.8072i	−0.239646	+	1.51025i
$293$	−5.33913	−	1.73479i	−0.311915	−	0.101347i	0.148876	−	0.988856i	$-0.452434\pi$
$293$	−5.33913	−	1.73479i	−0.311915	−	0.101347i	−0.460792	+	0.887508i	$0.652434\pi$
$294$	−4.76408	+	19.8312i	−0.277847	+	1.15658i
$295$	−9.81114	+	7.12821i	−0.571227	+	0.415021i
$296$	1.01258	−	12.7956i	0.0588553	−	0.743728i
$297$		0			0
$298$	16.7860	+	10.2898i	0.972389	+	0.596073i
$299$	−5.98486	−	8.23745i	−0.346113	−	0.476384i
$300$	41.1568	+	41.1805i	2.37619	+	2.37756i
$301$	−10.1757	−	3.30629i	−0.586518	−	0.190571i
$302$	−19.8904	+	8.23554i	−1.14457	+	0.473902i
$303$	24.1400	+	17.5387i	1.38681	+	1.00757i
$304$	−8.68545	+	6.30273i	−0.498145	+	0.361486i
$305$	13.7889	+	42.4380i	0.789553	+	2.42999i
$306$	−0.687261	−	8.74856i	−0.0392881	−	0.500122i
$307$			27.8554i			1.58979i	0.606747	+	0.794895i	$0.292474\pi$
$307$			27.8554i			1.58979i	−0.606747	+	0.794895i	$0.707526\pi$
$308$		0			0
$309$			9.09775i			0.517553i
$310$	21.4942	−	1.68852i	1.22079	−	0.0959017i
$311$	−7.54235	−	23.2130i	−0.427687	−	1.31629i	−0.900398	−	0.435068i	$-0.856724\pi$
$311$	−7.54235	−	23.2130i	−0.427687	−	1.31629i	0.472710	−	0.881218i	$-0.343276\pi$
$312$	7.47831	−	18.0322i	0.423376	−	1.02087i
$313$	−7.39048	−	5.36950i	−0.417735	−	0.303502i	0.358991	−	0.933341i	$-0.383121\pi$
$313$	−7.39048	−	5.36950i	−0.417735	−	0.303502i	−0.776726	+	0.629839i	$0.783121\pi$
$314$	−0.472809	−	1.14193i	−0.0266821	−	0.0644426i
$315$	−9.38355	−	3.04890i	−0.528703	−	0.171786i
$316$	6.84203	−	6.83810i	0.384894	−	0.384673i
$317$	−10.5508	−	14.5219i	−0.592591	−	0.815632i	0.402414	−	0.915458i	$-0.368171\pi$
$317$	−10.5508	−	14.5219i	−0.592591	−	0.815632i	−0.995005	+	0.0998262i	$0.968171\pi$
$318$	−1.13064	+	1.84445i	−0.0634033	+	0.103431i
$319$		0			0
$320$	−5.24447	+	32.9285i	−0.293175	+	1.84076i
$321$	−24.3323	+	17.6785i	−1.35810	+	0.986715i
$322$	−4.45458	−	1.07013i	−0.248244	−	0.0596359i
$323$	6.24170	+	2.02805i	0.347298	+	0.112844i
$324$	3.18935	−	20.0994i	0.177186	−	1.11663i
$325$	21.3301	−	29.3584i	1.18318	−	1.62851i
$326$	−8.09520	+	6.91194i	−0.448352	+	0.382817i
$327$	−1.34564	−	4.14145i	−0.0744139	−	0.229023i
$328$	9.95346	−	6.09359i	0.549588	−	0.336462i
$329$	3.04478			0.167864
$330$		0			0
$331$			13.1934i			0.725173i	0.931950	+	0.362586i	$0.118106\pi$
$331$			13.1934i			0.725173i	−0.931950	+	0.362586i	$0.881894\pi$
$332$	0.599300	−	1.17536i	0.0328909	−	0.0645061i
$333$	10.9479	−	3.55719i	0.599942	−	0.194933i
$334$	−0.131229	−	0.153695i	−0.00718055	−	0.00840979i
$335$	18.2969	+	13.2935i	0.999665	+	0.726299i
$336$	−2.70945	−	8.35516i	−0.147812	−	0.455811i
$337$	7.37660	−	22.7028i	0.401829	−	1.23670i	−0.521686	−	0.853138i	$-0.674697\pi$
$337$	7.37660	−	22.7028i	0.401829	−	1.23670i	0.923514	−	0.383564i	$-0.125303\pi$
$338$	6.04518	+	1.45224i	0.328815	+	0.0789914i
$339$	23.0715	+	31.7552i	1.25307	+	1.72471i
$340$	18.1718	−	9.25244i	0.985506	−	0.501784i
$341$		0			0
$342$	−8.20522	−	5.02979i	−0.443688	−	0.271980i
$343$	9.91237	−	7.20176i	0.535218	−	0.388859i
$344$	−31.5351	+	7.55653i	−1.70026	+	0.407421i
$345$	−10.5200	+	32.3773i	−0.566378	+	1.74313i
$346$	−0.610850	−	1.47532i	−0.0328395	−	0.0793138i
$347$	−21.8780	+	30.1124i	−1.17447	+	1.61652i	−0.552256	+	0.833675i	$0.686233\pi$
$347$	−21.8780	+	30.1124i	−1.17447	+	1.61652i	−0.622215	+	0.782846i	$0.713767\pi$
$348$	−21.2540	+	3.36004i	−1.13933	+	0.180117i
$349$	27.0233	−	8.78041i	1.44652	−	0.470004i	0.522600	−	0.852578i	$-0.324962\pi$
$349$	27.0233	−	8.78041i	1.44652	−	0.470004i	0.923925	+	0.382574i	$0.124962\pi$
$350$	−1.27873	−	16.2777i	−0.0683511	−	0.870082i
$351$	−3.19824			−0.170709
$352$		0			0
$353$	−6.72158			−0.357754			−0.178877	−	0.983871i	$-0.557246\pi$
$353$	−6.72158			−0.357754			−0.178877	+	0.983871i	$0.557246\pi$
$354$	−0.758276	−	9.65255i	−0.0403019	−	0.513027i
$355$	30.7257	−	9.98338i	1.63075	−	0.529863i
$356$	5.42521	−	0.857671i	0.287536	−	0.0454565i
$357$	−3.15740	+	4.34578i	−0.167107	+	0.230003i
$358$	−8.20278	−	19.8113i	−0.433530	−	1.04706i
$359$	6.12657	−	18.8556i	0.323348	−	0.995163i	−0.648833	−	0.760931i	$-0.724743\pi$
$359$	6.12657	−	18.8556i	0.323348	−	0.995163i	0.972181	−	0.234232i	$-0.0752575\pi$
$360$	−29.0802	+	6.96827i	−1.53266	+	0.367260i
$361$	−9.54835	+	6.93728i	−0.502545	+	0.365120i
$362$	20.4019	+	12.5063i	1.07230	+	0.657319i
$363$		0			0
$364$	−4.87871	+	2.48406i	−0.255714	+	0.130200i
$365$	−32.0074	−	44.0545i	−1.67535	−	2.30592i
$366$	−34.6402	−	8.32165i	−1.81067	−	0.434980i
$367$	1.40548	−	4.32561i	0.0733653	−	0.225795i	−0.907649	−	0.419730i	$-0.862125\pi$
$367$	1.40548	−	4.32561i	0.0733653	−	0.225795i	0.981014	+	0.193934i	$0.0621249\pi$
$368$	−13.2080	+	4.28315i	−0.688516	+	0.223275i
$369$	8.46760	+	6.15207i	0.440806	+	0.320264i
$370$	17.3691	+	20.3426i	0.902978	+	1.05756i
$371$	0.577023	−	0.187486i	0.0299575	−	0.00973379i
$372$	−7.81925	+	15.3352i	−0.405409	+	0.795095i
$373$		−	33.3992i		−	1.72934i	−0.502336	−	0.864672i	$-0.667526\pi$
$373$		−	33.3992i		−	1.72934i	0.502336	−	0.864672i	$-0.332474\pi$
$374$		0			0
$375$	−72.2956			−3.73333
$376$	7.87039	−	4.81831i	0.405884	−	0.248486i
$377$	4.14454	+	12.7556i	0.213455	+	0.656945i
$378$	−1.09437	+	0.934410i	−0.0562884	+	0.0480609i
$379$	−5.43609	+	7.48213i	−0.279233	+	0.384331i	−0.925480	−	0.378797i	$-0.876338\pi$
$379$	−5.43609	+	7.48213i	−0.279233	+	0.384331i	0.646247	+	0.763129i	$0.276338\pi$
$380$	3.50481	−	22.0874i	0.179793	−	1.13306i
$381$	14.5686	+	4.73363i	0.746372	+	0.242511i
$382$	−22.9256	−	5.50743i	−1.17298	−	0.281785i
$383$	−25.5714	+	18.5787i	−1.30664	+	0.949328i	−0.999997	−	0.00249665i	$-0.999205\pi$
$383$	−25.5714	+	18.5787i	−1.30664	+	0.949328i	−0.306642	+	0.951825i	$0.599205\pi$
$384$	−20.2255	−	17.3094i	−1.03213	−	0.883318i
$385$		0			0
$386$	0.133555	−	0.217872i	0.00679777	−	0.0110894i
$387$	−17.0941	−	23.5280i	−0.868941	−	1.19600i
$388$	2.58741	−	2.58593i	0.131356	−	0.131281i
$389$	−4.75093	−	1.54367i	−0.240882	−	0.0782673i	0.186088	−	0.982533i	$-0.440419\pi$
$389$	−4.75093	−	1.54367i	−0.240882	−	0.0782673i	−0.426970	+	0.904266i	$0.640419\pi$
$390$	15.5630	+	37.5876i	0.788061	+	1.90332i
$391$	6.86991	+	4.99128i	0.347426	+	0.252420i
$392$	6.64099	−	16.0132i	0.335421	−	0.808791i
$393$	5.02852	+	15.4762i	0.253655	+	0.780671i
$394$	−11.8272	+	0.929109i	−0.595845	+	0.0468078i
$395$			20.1589i			1.01430i
$396$		0			0
$397$		−	17.7950i		−	0.893107i	−0.894757	−	0.446553i	$-0.852651\pi$
$397$		−	17.7950i		−	0.893107i	0.894757	−	0.446553i	$-0.147349\pi$
$398$	2.44764	+	31.1575i	0.122689	+	1.56178i
$399$	1.82047	+	5.60283i	0.0911374	+	0.280492i
$400$	−29.0646	−	40.0524i	−1.45323	−	2.00262i
$401$	9.84887	+	7.15562i	0.491829	+	0.357335i	0.805887	−	0.592069i	$-0.201689\pi$
$401$	9.84887	+	7.15562i	0.491829	+	0.357335i	−0.314058	+	0.949404i	$0.601689\pi$
$402$	−16.6831	+	6.90755i	−0.832076	+	0.344517i
$403$	10.2040	+	3.31550i	0.508300	+	0.165157i
$404$	−17.9286	−	17.9389i	−0.891983	−	0.892496i
$405$	24.9283	+	34.3109i	1.23870	+	1.70492i
$406$	5.14489	+	3.15381i	0.255337	+	0.156521i
$407$		0			0
$408$	−1.28436	+	16.2299i	−0.0635852	+	0.803497i
$409$	−0.475699	+	0.345616i	−0.0235218	+	0.0170896i	−0.599484	−	0.800387i	$-0.704628\pi$
$409$	−0.475699	+	0.345616i	−0.0235218	+	0.0170896i	0.575962	+	0.817476i	$0.304628\pi$
$410$	−5.68107	+	23.6484i	−0.280568	+	1.16791i
$411$	−13.0231	−	4.23147i	−0.642384	−	0.208723i
$412$	1.21189	−	7.63734i	0.0597053	−	0.376265i
$413$	−1.59604	+	2.19676i	−0.0785361	+	0.108096i
$414$	−8.08595	−	9.47018i	−0.397403	−	0.465434i
$415$	0.849623	+	2.61487i	0.0417064	+	0.128359i
$416$	−8.67988	+	14.1415i	−0.425566	+	0.693342i
$417$	−22.4365			−1.09872
$418$		0			0
$419$			11.1507i			0.544748i	0.962191	+	0.272374i	$0.0878088\pi$
$419$			11.1507i			0.544748i	−0.962191	+	0.272374i	$0.912191\pi$
$420$	16.3071	+	8.31477i	0.795703	+	0.405719i
$421$	−33.1346	+	10.7661i	−1.61488	+	0.524708i	−0.970727	−	0.240186i	$-0.922792\pi$
$421$	−33.1346	+	10.7661i	−1.61488	+	0.524708i	−0.644157	+	0.764893i	$0.722792\pi$
$422$	16.1745	−	13.8103i	0.787365	−	0.672277i
$423$	6.69549	+	4.86456i	0.325546	+	0.236523i
$424$	1.19484	−	1.39776i	0.0580266	−	0.0678811i
$425$	−9.35223	+	28.7832i	−0.453650	+	1.39619i
$426$	−6.02499	+	25.0800i	−0.291912	+	1.21513i
$427$	5.87261	+	8.08295i	0.284196	+	0.391162i
$428$	22.7813	−	11.5994i	1.10117	−	0.560678i
$429$		0			0
$430$	35.3180	−	57.6152i	1.70319	−	2.77845i
$431$	20.1160	−	14.6151i	0.968953	−	0.703986i	0.0137403	−	0.999906i	$-0.495626\pi$
$431$	20.1160	−	14.6151i	0.968953	−	0.703986i	0.955213	+	0.295920i	$0.0956262\pi$
$432$	−1.35013	+	4.14716i	−0.0649582	+	0.199530i
$433$	−0.169250	+	0.520897i	−0.00813362	+	0.0250327i	−0.955041	−	0.296474i	$-0.904189\pi$
$433$	−0.169250	+	0.520897i	−0.00813362	+	0.0250327i	0.946907	+	0.321507i	$0.104189\pi$
$434$	4.46028	−	1.84676i	0.214100	−	0.0886473i
$435$	26.3579	−	36.2785i	1.26376	−	1.73942i
$436$	0.577959	+	3.65589i	0.0276792	+	0.175085i
$437$	8.85707	−	2.87784i	0.423691	−	0.137666i
$438$	43.3423	−	3.40485i	2.07098	−	0.162690i
$439$	27.5308			1.31397			0.656987	−	0.753902i	$-0.271831\pi$
$439$	27.5308			1.31397			0.656987	+	0.753902i	$0.271831\pi$
$440$		0			0
$441$	15.5471			0.740340
$442$	10.1164	−	0.794717i	0.481189	−	0.0378008i
$443$	−7.66033	+	2.48899i	−0.363953	+	0.118256i	−0.485284	−	0.874357i	$-0.661284\pi$
$443$	−7.66033	+	2.48899i	−0.363953	+	0.118256i	0.121331	+	0.992612i	$0.461284\pi$
$444$	−21.0942	+	3.33477i	−1.00108	+	0.158261i
$445$	−6.72802	+	9.26032i	−0.318939	+	0.438981i
$446$	13.4278	−	5.55972i	0.635826	−	0.263261i
$447$	10.1230	−	31.1555i	0.478803	−	1.47360i
$448$	1.16155	+	7.37487i	0.0548779	+	0.348430i
$449$	27.3209	−	19.8498i	1.28935	−	0.936771i	0.289562	−	0.957159i	$-0.406490\pi$
$449$	27.3209	−	19.8498i	1.28935	−	0.936771i	0.999792	+	0.0203882i	$0.00649023\pi$
$450$	23.1945	−	37.8379i	1.09340	−	1.78369i
$451$		0			0
$452$	−15.1379	−	29.7310i	−0.712029	−	1.39843i
$453$	21.0537	+	28.9780i	0.989190	+	1.36150i
$454$	5.17603	−	21.5461i	0.242923	−	1.01121i
$455$	3.52561	−	10.8507i	0.165283	−	0.508689i
$456$	13.5721	+	11.6018i	0.635571	+	0.543303i
$457$	3.10031	+	2.25251i	0.145026	+	0.105368i	0.657933	−	0.753077i	$-0.271431\pi$
$457$	3.10031	+	2.25251i	0.145026	+	0.105368i	−0.512906	+	0.858445i	$0.671431\pi$
$458$	−15.1375	+	12.9249i	−0.707327	+	0.603939i
$459$	2.53674	−	0.824236i	0.118405	−	0.0384720i
$460$	13.1442	−	25.7786i	0.612850	−	1.20193i
$461$			15.8380i			0.737649i	0.929499	+	0.368825i	$0.120240\pi$
$461$			15.8380i			0.737649i	−0.929499	+	0.368825i	$0.879760\pi$
$462$		0			0
$463$	30.4131			1.41341			0.706707	−	0.707506i	$-0.250180\pi$
$463$	30.4131			1.41341			0.706707	+	0.707506i	$0.250180\pi$
$464$	18.2898	+	0.0105137i	0.849082	+	0.000488088i
$465$	−11.0853	−	34.1170i	−0.514068	−	1.58214i
$466$	11.1108	+	13.0129i	0.514700	+	0.602811i
$467$	−11.8624	+	16.3271i	−0.548925	+	0.755530i	−0.989866	−	0.142006i	$-0.954645\pi$
$467$	−11.8624	+	16.3271i	−0.548925	+	0.755530i	0.440941	+	0.897536i	$0.354645\pi$
$468$	−14.6970	−	2.33211i	−0.679370	−	0.107802i
$469$	4.81603	+	1.56482i	0.222384	+	0.0722569i
$470$	−4.49213	+	18.6992i	−0.207206	+	0.862531i
$471$	−1.66365	+	1.20871i	−0.0766568	+	0.0556945i
$472$	−0.649234	+	8.20408i	−0.0298834	+	0.377624i
$473$		0			0
$474$	−13.7218	−	8.41142i	−0.630261	−	0.386349i
$475$	19.5093	+	26.8523i	0.895149	+	1.23207i
$476$	3.22945	−	3.22759i	0.148021	−	0.147936i
$477$	1.56842	+	0.509610i	0.0718130	+	0.0233334i
$478$	28.4167	−	11.7658i	1.29975	−	0.538154i
$479$	−10.1616	−	7.38284i	−0.464296	−	0.337331i	0.330918	−	0.943659i	$-0.392642\pi$
$479$	−10.1616	−	7.38284i	−0.464296	−	0.337331i	−0.795214	+	0.606329i	$0.792642\pi$
$480$	55.3098	−	4.31299i	2.52453	−	0.196860i
$481$	4.11337	+	12.6597i	0.187554	+	0.577231i
$482$	−0.768605	−	9.78403i	−0.0350090	−	0.445651i
$483$			7.62250i			0.346836i
$484$		0			0
$485$			7.62338i			0.346160i
$486$	−29.1445	+	2.28951i	−1.32202	+	0.103854i
$487$	4.40407	+	13.5543i	0.199568	+	0.614206i	0.999893	+	0.0146398i	$0.00466015\pi$
$487$	4.40407	+	13.5543i	0.199568	+	0.614206i	−0.800325	+	0.599566i	$0.795340\pi$
$488$	27.9711	+	11.6002i	1.26619	+	0.525114i
$489$	14.3283	+	10.4101i	0.647947	+	0.470761i
$490$	13.8204	+	33.3790i	0.624344	+	1.50791i
$491$	19.4060	+	6.30538i	0.875779	+	0.284558i	0.712204	−	0.701973i	$-0.247697\pi$
$491$	19.4060	+	6.30538i	0.875779	+	0.284558i	0.163576	+	0.986531i	$0.447697\pi$
$492$	−13.7265	−	13.7344i	−0.618840	−	0.619196i
$493$	−6.57462	−	9.04918i	−0.296106	−	0.407555i
$494$	5.81622	−	9.48814i	0.261684	−	0.426892i
$495$		0			0
$496$	8.60683	−	11.8320i	0.386458	−	0.531271i
$497$	5.85217	−	4.25185i	0.262506	−	0.190722i
$498$	−2.13440	−	0.512749i	−0.0956449	−	0.0229768i
$499$	−31.7416	−	10.3135i	−1.42095	−	0.461694i	−0.505046	−	0.863093i	$-0.668524\pi$
$499$	−31.7416	−	10.3135i	−1.42095	−	0.461694i	−0.915904	+	0.401398i	$0.868524\pi$
$500$	60.6904	+	9.63029i	2.71416	+	0.430680i
$501$	−0.197645	+	0.272035i	−0.00883012	+	0.0121536i
$502$	19.0665	−	16.2796i	0.850978	−	0.726592i
$503$	4.57804	+	14.0898i	0.204125	+	0.628231i	0.999748	+	0.0224396i	$0.00714336\pi$
$503$	4.57804	+	14.0898i	0.204125	+	0.628231i	−0.795624	+	0.605791i	$0.792857\pi$
$504$	−5.71038	+	3.49594i	−0.254360	+	0.155721i
$505$	52.8541			2.35197
$506$		0			0
$507$		−	10.3443i		−	0.459405i
$508$	−11.5994	−	5.91441i	−0.514642	−	0.262409i
$509$	−22.7743	+	7.39983i	−1.00945	+	0.327992i	−0.766637	−	0.642080i	$-0.778072\pi$
$509$	−22.7743	+	7.39983i	−1.00945	+	0.327992i	−0.242817	+	0.970072i	$0.578072\pi$
$510$	−22.0309	−	25.8024i	−0.975546	−	1.14255i
$511$	−9.86402	−	7.16663i	−0.436358	−	0.317033i
$512$	14.6731	+	17.2250i	0.648464	+	0.761245i
$513$	0.903945	−	2.78206i	0.0399101	−	0.122831i
$514$	24.4141	+	5.86501i	1.07686	+	0.258695i
$515$	9.47222	+	13.0374i	0.417396	+	0.574496i
$516$	24.4809	+	48.0806i	1.07771	+	2.11663i
$517$		0			0
$518$	5.10621	+	3.13010i	0.224354	+	0.137529i
$519$	−2.14937	+	1.56161i	−0.0943467	+	0.0685469i
$520$	−8.05779	−	33.6270i	−0.353357	−	1.47464i
$521$	6.37059	−	19.6067i	0.279101	−	0.858983i	−0.709005	−	0.705204i	$-0.750855\pi$
$521$	6.37059	−	19.6067i	0.279101	−	0.858983i	0.988105	−	0.153780i	$-0.0491445\pi$
$522$	6.27490	+	15.1551i	0.274645	+	0.663321i
$523$	13.2848	−	18.2849i	0.580903	−	0.799545i	−0.412891	−	0.910781i	$-0.635481\pi$
$523$	13.2848	−	18.2849i	0.580903	−	0.799545i	0.993794	+	0.111236i	$0.0354808\pi$
$524$	−2.15978	−	13.6617i	−0.0943504	−	0.596815i
$525$	−25.8371	+	8.39497i	−1.12762	+	0.366387i
$526$	−3.06154	−	38.9722i	−0.133490	−	1.69927i
$527$	−8.94797			−0.389779
$528$		0			0
$529$	−10.9502			−0.476095
$530$	0.300115	+	3.82034i	0.0130362	+	0.165945i
$531$	−7.01942	+	2.28075i	−0.304617	+	0.0989760i
$532$	−0.781902	−	4.94594i	−0.0338998	−	0.214434i
$533$	−7.11397	+	9.79154i	−0.308140	+	0.424119i
$534$	−3.49601	−	8.44356i	−0.151287	−	0.365388i
$535$	−16.4629	+	50.6677i	−0.711755	+	2.19056i
$536$	14.9252	−	3.57641i	0.644669	−	0.154477i
$537$	−28.8627	+	20.9700i	−1.24552	+	0.904921i
$538$	−12.8147	−	7.85537i	−0.552479	−	0.338669i
$539$		0			0
$540$	−4.12400	−	8.09956i	−0.177469	−	0.348550i
$541$	3.08829	+	4.25066i	0.132776	+	0.182750i	0.870228	−	0.492649i	$-0.163971\pi$
$541$	3.08829	+	4.25066i	0.132776	+	0.182750i	−0.737452	+	0.675399i	$0.763971\pi$
$542$	27.1554	+	6.52356i	1.16642	+	0.280211i
$543$	12.3036	−	37.8666i	0.527999	−	1.62501i
$544$	3.24012	−	13.4535i	0.138919	−	0.576813i
$545$	−6.24026	−	4.53381i	−0.267303	−	0.194207i
$546$	5.91478	+	6.92733i	0.253129	+	0.296463i
$547$	29.8979	−	9.71442i	1.27834	−	0.415359i	0.410346	−	0.911930i	$-0.365408\pi$
$547$	29.8979	−	9.71442i	1.27834	−	0.415359i	0.867996	+	0.496571i	$0.165408\pi$
$548$	10.3689	+	5.28699i	0.442939	+	0.225849i
$549$			27.1570i			1.15903i
$550$		0			0
$551$	−12.2671			−0.522596
$552$	12.0625	+	19.7033i	0.513414	+	0.838626i
$553$	1.39480	+	4.29276i	0.0593130	+	0.182547i
$554$	−13.4818	+	11.5112i	−0.572787	+	0.489064i
$555$	26.1597	−	36.0057i	1.11042	−	1.52836i
$556$	18.8349	+	2.98871i	0.798779	+	0.126749i
$557$	13.2107	+	4.29241i	0.559755	+	0.181875i	0.575211	−	0.818005i	$-0.304920\pi$
$557$	13.2107	+	4.29241i	0.559755	+	0.181875i	−0.0154561	+	0.999881i	$0.504920\pi$
$558$	12.7587	+	3.06504i	0.540119	+	0.129753i
$559$	27.2067	−	19.7668i	1.15072	−	0.836047i
$560$	−12.5818	−	9.15226i	−0.531678	−	0.386754i
$561$		0			0
$562$	−17.5933	+	28.7004i	−0.742129	+	1.21065i
$563$	12.0590	+	16.5978i	0.508227	+	0.699514i	0.983619	−	0.180260i	$-0.0576939\pi$
$563$	12.0590	+	16.5978i	0.508227	+	0.699514i	−0.475392	+	0.879774i	$0.657694\pi$
$564$	−10.8538	−	10.8601i	−0.457028	−	0.457291i
$565$	66.1246	+	21.4852i	2.78188	+	0.903888i
$566$	−15.0019	−	36.2324i	−0.630575	−	1.52296i
$567$	7.68238	+	5.58158i	0.322630	+	0.234404i
$568$	8.39867	−	20.2515i	0.352400	−	0.849733i
$569$	−6.46796	−	19.9063i	−0.271151	−	0.834517i	−0.990212	−	0.139570i	$-0.955428\pi$
$569$	−6.46796	−	19.9063i	−0.271151	−	0.834517i	0.719061	−	0.694947i	$-0.244572\pi$
$570$	−37.0951	+	2.91408i	−1.55374	+	0.122057i
$571$		−	6.00582i		−	0.251336i	−0.992072	−	0.125668i	$-0.959893\pi$
$571$		−	6.00582i		−	0.251336i	0.992072	−	0.125668i	$-0.0401074\pi$
$572$		0			0
$573$			39.2293i			1.63883i
$574$	0.426480	+	5.42891i	0.0178009	+	0.226598i
$575$	13.2710	+	40.8438i	0.553437	+	1.70331i
$576$	−9.22837	+	18.0732i	−0.384516	+	0.753048i
$577$	36.7465	+	26.6979i	1.52978	+	1.11145i	0.956362	+	0.292185i	$0.0943824\pi$
$577$	36.7465	+	26.6979i	1.52978	+	1.11145i	0.573417	+	0.819264i	$0.305618\pi$
$578$	14.3937	−	5.95964i	0.598699	−	0.247888i
$579$	−0.404377	−	0.131390i	−0.0168053	−	0.00546039i
$580$	−26.9594	+	26.9439i	−1.11943	+	1.11878i
$581$	0.361848	+	0.498042i	0.0150120	+	0.0206622i
$582$	−5.18909	−	3.18090i	−0.215095	−	0.131853i
$583$		0			0
$584$	−36.8384	−	2.91522i	−1.52438	−	0.120633i
$585$	25.0887	−	18.2280i	1.03729	−	0.753635i
$586$	1.85449	−	7.71962i	0.0766083	−	0.318894i
$587$	4.70991	+	1.53034i	0.194399	+	0.0631641i	0.404598	−	0.914494i	$-0.367411\pi$
$587$	4.70991	+	1.53034i	0.194399	+	0.0631641i	−0.210199	+	0.977659i	$0.567411\pi$
$588$	−28.4871	−	4.52031i	−1.17479	−	0.186414i
$589$	−5.76811	+	7.93912i	−0.237671	+	0.327126i
$590$	−11.1365	−	13.0430i	−0.458482	−	0.536970i
$591$	6.09967	+	18.7729i	0.250907	+	0.772213i
$592$	18.1523	+	0.0104347i	0.746053	+	0.000428862i
$593$	−17.6332			−0.724110			−0.362055	−	0.932157i	$-0.617925\pi$
$593$	−17.6332			−0.724110			−0.362055	+	0.932157i	$0.617925\pi$
$594$		0			0
$595$			9.51502i			0.390078i
$596$	−12.6482	+	24.8058i	−0.518089	+	1.01608i
$597$	49.4552	−	16.0690i	2.02407	−	0.657659i
$598$	10.9509	−	9.35022i	0.447815	−	0.382359i
$599$	−36.5298	−	26.5404i	−1.49257	−	1.08441i	−0.973228	−	0.229844i	$-0.926178\pi$
$599$	−36.5298	−	26.5404i	−1.49257	−	1.08441i	−0.519338	−	0.854569i	$-0.673822\pi$
$600$	−53.5008	+	62.5867i	−2.18416	+	2.55509i
$601$	−4.83225	+	14.8721i	−0.197112	+	0.606647i	0.802834	+	0.596203i	$0.203325\pi$
$601$	−4.83225	+	14.8721i	−0.197112	+	0.606647i	−0.999945	+	0.0104444i	$0.996675\pi$
$602$	3.53442	−	14.7126i	0.144052	−	0.599641i
$603$	8.09042	+	11.1355i	0.329467	+	0.453473i
$604$	−13.8140	−	27.1308i	−0.562084	−	1.10394i
$605$		0			0
$606$	−22.0537	+	35.9767i	−0.895869	+	1.46145i
$607$	33.9235	−	24.6469i	1.37691	−	1.00039i	0.379751	−	0.925089i	$-0.376010\pi$
$607$	33.9235	−	24.6469i	1.37691	−	1.00039i	0.997161	−	0.0752967i	$-0.0239904\pi$
$608$	−9.84798	−	11.5473i	−0.399389	−	0.468305i
$609$	3.10269	−	9.54910i	0.125727	−	0.386949i
$610$	−58.3049	+	24.1408i	−2.36069	+	0.977434i
$611$	−5.62515	+	7.74236i	−0.227569	+	0.313222i
$612$	12.2582	−	1.93790i	0.495509	−	0.0783349i
$613$	26.5263	−	8.61893i	1.07139	−	0.348115i	0.280360	−	0.959895i	$-0.409546\pi$
$613$	26.5263	−	8.61893i	1.07139	−	0.348115i	0.791028	+	0.611780i	$0.209546\pi$
$614$	−39.2724	+	3.08513i	−1.58491	+	0.124506i
$615$	40.4662			1.63175
$616$		0			0
$617$	−14.7471			−0.593697			−0.296849	−	0.954925i	$-0.595936\pi$
$617$	−14.7471			−0.593697			−0.296849	+	0.954925i	$0.595936\pi$
$618$	−12.8266	+	1.00762i	−0.515963	+	0.0405326i
$619$	−4.87084	+	1.58263i	−0.195776	+	0.0636113i	−0.405264	−	0.914200i	$-0.632820\pi$
$619$	−4.87084	+	1.58263i	−0.195776	+	0.0636113i	0.209488	+	0.977811i	$0.432820\pi$
$620$	4.76120	+	30.1170i	0.191214	+	1.20953i
$621$	2.22472	−	3.06206i	0.0892749	−	0.122876i
$622$	31.8919	−	13.2047i	1.27875	−	0.529460i
$623$	−0.791981	+	2.43747i	−0.0317300	+	0.0976550i
$624$	26.2514	+	8.54628i	1.05090	+	0.342125i
$625$	−53.5575	+	38.9118i	−2.14230	+	1.55647i
$626$	6.75176	−	11.0143i	0.269855	−	0.440221i
$627$		0			0
$628$	1.55760	−	0.793073i	0.0621550	−	0.0316471i
$629$	−6.52518	−	8.98114i	−0.260176	−	0.358101i
$630$	3.25927	−	13.5673i	0.129853	−	0.540533i
$631$	−14.9903	+	46.1355i	−0.596755	+	1.83662i	−0.0509681	+	0.998700i	$0.516231\pi$
$631$	−14.9903	+	46.1355i	−0.596755	+	1.83662i	−0.545787	+	0.837924i	$0.683769\pi$
$632$	10.3986	+	8.88902i	0.413635	+	0.353586i
$633$	−28.6285	−	20.7998i	−1.13788	−	0.826718i
$634$	19.3054	−	16.4836i	0.766717	−	0.654648i
$635$	25.8058	−	8.38481i	1.02407	−	0.332741i
$636$	−2.72565	−	1.38978i	−0.108079	−	0.0551083i
$637$			17.9780i			0.712314i
$638$		0			0
$639$	19.6620			0.777818
$640$	−47.0057	−	3.74701i	−1.85806	−	0.148114i
$641$	−2.23158	−	6.86810i	−0.0881422	−	0.271274i	0.897264	−	0.441495i	$-0.145552\pi$
$641$	−2.23158	−	6.86810i	−0.0881422	−	0.271274i	−0.985406	+	0.170221i	$0.945552\pi$
$642$	−27.6193	−	32.3474i	−1.09005	−	1.27665i
$643$	7.03032	−	9.67641i	0.277249	−	0.381600i	−0.647571	−	0.762005i	$-0.724215\pi$
$643$	7.03032	−	9.67641i	0.277249	−	0.381600i	0.924820	+	0.380405i	$0.124215\pi$
$644$	1.01537	−	6.39891i	0.0400113	−	0.252152i
$645$	−106.936	−	34.7455i	−4.21059	−	1.36810i
$646$	−2.16799	+	9.02461i	−0.0852983	+	0.355068i
$647$	21.1924	−	15.3972i	0.833158	−	0.605325i	−0.0872932	−	0.996183i	$-0.527822\pi$
$647$	21.1924	−	15.3972i	0.833158	−	0.605325i	0.920451	+	0.390858i	$0.127822\pi$
$648$	28.6908	+	2.27046i	1.12708	+	0.0891921i
$649$		0			0
$650$	43.7540	+	26.8211i	1.71617	+	1.05201i
$651$	−4.72114	−	6.49810i	−0.185036	−	0.254680i
$652$	−10.6415	−	10.6476i	−0.416754	−	0.416994i
$653$	−32.5433	−	10.5740i	−1.27352	−	0.413791i	−0.407225	−	0.913328i	$-0.633503\pi$
$653$	−32.5433	−	10.5740i	−1.27352	−	0.413791i	−0.866292	+	0.499537i	$0.833503\pi$
$654$	5.68986	−	2.35586i	0.222491	−	0.0921215i
$655$	23.3193	+	16.9424i	0.911159	+	0.661996i
$656$	9.69356	+	13.3582i	0.378470	+	0.521550i
$657$	−10.2411	−	31.5189i	−0.399544	−	1.22967i
$658$	0.337225	+	4.29274i	0.0131464	+	0.167349i
$659$			2.73052i			0.106366i	0.998585	+	0.0531831i	$0.0169367\pi$
$659$			2.73052i			0.106366i	−0.998585	+	0.0531831i	$0.983063\pi$
$660$		0			0
$661$			11.2478i			0.437488i	0.975782	+	0.218744i	$0.0701959\pi$
$661$			11.2478i			0.437488i	−0.975782	+	0.218744i	$0.929804\pi$
$662$	−18.6009	+	1.46124i	−0.722946	+	0.0567925i
$663$	−5.21738	−	16.0574i	−0.202626	−	0.623620i
$664$	1.72348	+	0.714758i	0.0668839	+	0.0277380i
$665$	8.44224	+	6.13365i	0.327376	+	0.237853i
$666$	6.22771	+	15.0411i	0.241319	+	0.582833i
$667$	−15.0954	−	4.90480i	−0.584497	−	0.189915i
$668$	0.202155	−	0.202039i	0.00782161	−	0.00781712i
$669$	−14.2131	−	19.5627i	−0.549512	−	0.756338i
$670$	−16.7156	+	27.2685i	−0.645779	+	1.05348i
$671$		0			0
$672$	11.4796	−	4.74534i	0.442835	−	0.183056i
$673$	16.2153	−	11.7811i	0.625054	−	0.454128i	−0.229629	−	0.973278i	$-0.573751\pi$
$673$	16.2153	−	11.7811i	0.625054	−	0.454128i	0.854683	+	0.519150i	$0.173751\pi$
$674$	32.8250	+	7.88558i	1.26437	+	0.303741i
$675$	12.8293	+	4.16848i	0.493799	+	0.160445i
$676$	−1.37793	+	8.68377i	−0.0529974	+	0.333991i
$677$	−15.9533	+	21.9578i	−0.613135	+	0.843908i	−0.996831	−	0.0795517i	$-0.974651\pi$
$677$	−15.9533	+	21.9578i	−0.613135	+	0.843908i	0.383696	+	0.923460i	$0.374651\pi$
$678$	−42.2154	+	36.0449i	−1.62127	+	1.38430i
$679$	0.527465	+	1.62337i	0.0202423	+	0.0622993i
$680$	15.0574	+	24.5952i	0.577423	+	0.943182i
$681$	−36.8688			−1.41282
$682$		0			0
$683$		−	41.8019i		−	1.59951i	−0.600330	−	0.799753i	$-0.704964\pi$
$683$		−	41.8019i		−	1.59951i	0.600330	−	0.799753i	$-0.295036\pi$
$684$	6.18258	−	12.1254i	0.236397	−	0.463625i
$685$	−23.0683	+	7.49533i	−0.881393	+	0.286382i
$686$	11.2514	+	13.1775i	0.429580	+	0.503120i
$687$	26.7929	+	19.4661i	1.02221	+	0.742680i
$688$	−14.1464	−	43.6235i	−0.539327	−	1.66313i
$689$	−0.589290	+	1.81365i	−0.0224501	+	0.0690945i
$690$	−46.8129	−	11.2459i	−1.78214	−	0.428124i
$691$	−16.9137	−	23.2797i	−0.643427	−	0.885601i	0.355366	−	0.934727i	$-0.384356\pi$
$691$	−16.9137	−	23.2797i	−0.643427	−	0.885601i	−0.998793	+	0.0491260i	$0.984356\pi$
$692$	2.01236	−	1.02462i	0.0764984	−	0.0389502i
$693$		0			0
$694$	−44.8777	−	27.5100i	−1.70354	−	1.04426i
$695$	−32.1523	+	23.3600i	−1.21961	+	0.886097i
$696$	−7.09121	−	29.5932i	−0.268792	−	1.12173i
$697$	3.11913	−	9.59971i	0.118146	−	0.363615i
$698$	15.3722	+	37.1269i	0.581847	+	1.40527i
$699$	16.7341	−	23.0325i	0.632940	−	0.871167i
$700$	22.8079	−	3.60569i	0.862056	−	0.136282i
$701$	−21.4773	+	6.97841i	−0.811188	+	0.263571i	−0.685101	−	0.728448i	$-0.740242\pi$
$701$	−21.4773	+	6.97841i	−0.811188	+	0.263571i	−0.126087	+	0.992019i	$0.540242\pi$
$702$	−0.354222	−	4.50910i	−0.0133692	−	0.170185i
$703$	−12.1749			−0.459184
$704$		0			0
$705$	31.9973			1.20509
$706$	−0.744450	−	9.47655i	−0.0280178	−	0.356655i
$707$	11.2551	−	3.65700i	0.423291	−	0.137536i
$708$	13.5249	−	2.13814i	0.508295	−	0.0803563i
$709$	−8.54760	+	11.7648i	−0.321012	+	0.441835i	−0.938776	−	0.344529i	$-0.888039\pi$
$709$	−8.54760	+	11.7648i	−0.321012	+	0.441835i	0.617764	+	0.786364i	$0.288039\pi$
$710$	17.4783	+	42.2135i	0.655949	+	1.58425i
$711$	−3.79124	+	11.6683i	−0.142183	+	0.437594i
$712$	1.81008	+	7.55385i	0.0678355	+	0.283093i
$713$	−10.2723	+	7.46329i	−0.384702	+	0.279502i
$714$	−6.47669	−	3.97020i	−0.242384	−	0.148581i
$715$		0			0
$716$	27.0229	−	13.7591i	1.00989	−	0.514200i
$717$	−30.0786	−	41.3996i	−1.12331	−	1.54610i
$718$	27.2626	+	6.54930i	1.01743	+	0.244418i
$719$	−1.84920	+	5.69125i	−0.0689635	+	0.212248i	−0.979599	−	0.200963i	$-0.935593\pi$
$719$	−1.84920	+	5.69125i	−0.0689635	+	0.212248i	0.910635	+	0.413211i	$0.135593\pi$
$720$	−13.0451	−	40.2275i	−0.486164	−	1.49919i
$721$	2.91914	+	2.12088i	0.108714	+	0.0789856i
$722$	−10.8382	−	12.6936i	−0.403356	−	0.472406i
$723$	−15.5299	+	5.04595i	−0.577561	+	0.187661i
$724$	−15.3727	+	30.1492i	−0.571322	+	1.12049i
$725$		−	56.5690i		−	2.10092i
$726$		0			0
$727$	−13.7234			−0.508973			−0.254486	−	0.967076i	$-0.581906\pi$
$727$	−13.7234			−0.508973			−0.254486	+	0.967076i	$0.581906\pi$
$728$	−4.04254	−	6.60322i	−0.149827	−	0.244732i
$729$	5.59764	+	17.2278i	0.207320	+	0.638066i
$730$	58.5661	−	50.0056i	2.16763	−	1.85079i
$731$	−16.4852	+	22.6900i	−0.609728	+	0.839219i
$732$	7.89586	−	49.7599i	0.291839	−	1.83918i
$733$	−44.1890	−	14.3579i	−1.63216	−	0.530320i	−0.657392	−	0.753549i	$-0.728340\pi$
$733$	−44.1890	−	14.3579i	−1.63216	−	0.530320i	−0.974766	+	0.223228i	$0.928340\pi$
$734$	6.25422	+	1.50246i	0.230847	+	0.0554566i
$735$	48.6292	−	35.3312i	1.79372	−	1.30321i
$736$	−7.50155	−	18.1472i	−0.276511	−	0.668915i
$737$		0			0
$738$	−7.73579	+	12.6196i	−0.284758	+	0.464534i
$739$	−7.39311	−	10.1757i	−0.271960	−	0.374321i	0.651090	−	0.759000i	$-0.274312\pi$
$739$	−7.39311	−	10.1757i	−0.271960	−	0.374321i	−0.923050	+	0.384680i	$0.874312\pi$
$740$	−26.7566	+	26.7413i	−0.983594	+	0.983029i
$741$	−17.6103	−	5.72194i	−0.646931	−	0.210201i
$742$	0.328239	+	0.792762i	0.0120500	+	0.0291032i
$743$	7.57418	+	5.50297i	0.277870	+	0.201884i	0.717988	−	0.696056i	$-0.245063\pi$
$743$	7.57418	+	5.50297i	0.277870	+	0.201884i	−0.440118	+	0.897940i	$0.645063\pi$
$744$	−22.4867	−	9.32566i	−0.824403	−	0.341895i
$745$	−17.9312	−	55.1866i	−0.656948	−	2.02188i
$746$	47.0885	−	3.69914i	1.72403	−	0.135435i
$747$			1.67331i			0.0612233i
$748$		0			0
$749$			11.9286i			0.435861i
$750$	−8.00712	−	101.927i	−0.292379	−	3.72186i
$751$	1.22435	+	3.76817i	0.0446773	+	0.137503i	0.970907	−	0.239457i	$-0.0769695\pi$
$751$	1.22435	+	3.76817i	0.0446773	+	0.137503i	−0.926230	+	0.376960i	$0.876969\pi$
$752$	7.66488	+	10.5626i	0.279509	+	0.385177i
$753$	−33.7471	−	24.5187i	−1.22981	−	0.893510i
$754$	−17.5247	+	7.25601i	−0.638211	+	0.264248i
$755$	60.3415	+	19.6061i	2.19605	+	0.713540i
$756$	−1.43860	−	1.43943i	−0.0523215	−	0.0523516i
$757$	−2.09768	−	2.88722i	−0.0762417	−	0.104938i	0.769193	−	0.639017i	$-0.220658\pi$
$757$	−2.09768	−	2.88722i	−0.0762417	−	0.104938i	−0.845435	+	0.534079i	$0.820658\pi$
$758$	−11.1509	−	6.83549i	−0.405019	−	0.248276i
$759$		0			0
$760$	31.5286	+	2.49503i	1.14366	+	0.0905042i
$761$	−40.2905	+	29.2728i	−1.46053	+	1.06114i	−0.477306	+	0.878737i	$0.658387\pi$
$761$	−40.2905	+	29.2728i	−1.46053	+	1.06114i	−0.983224	+	0.182401i	$0.941613\pi$
$762$	−5.06025	+	21.0641i	−0.183313	+	0.763072i
$763$	−1.64254	−	0.533693i	−0.0594638	−	0.0193210i
$764$	5.22563	−	32.9321i	0.189057	−	1.19144i
$765$	−15.2019	+	20.9236i	−0.549625	+	0.756494i
$766$	−29.0258	−	33.9947i	−1.04874	−	1.22828i
$767$	−2.63735	−	8.11694i	−0.0952293	−	0.293086i
$768$	22.1639	−	30.4324i	0.799773	−	1.09814i
$769$	30.5772			1.10264			0.551321	−	0.834293i	$-0.314124\pi$
$769$	30.5772			1.10264			0.551321	+	0.834293i	$0.314124\pi$
$770$		0			0
$771$		−	41.7764i		−	1.50454i
$772$	0.321963	+	0.164165i	0.0115877	+	0.00590842i
$773$	−22.7602	+	7.39524i	−0.818628	+	0.265988i	−0.688248	−	0.725476i	$-0.741620\pi$
$773$	−22.7602	+	7.39524i	−0.818628	+	0.265988i	−0.130380	+	0.991464i	$0.541620\pi$
$774$	31.2781	−	26.7063i	1.12427	−	0.959938i
$775$	−36.6107	−	26.5993i	−1.31510	−	0.955474i
$776$	3.93239	+	3.36151i	0.141165	+	0.120671i
$777$	3.07936	−	9.47729i	0.110471	−	0.339996i
$778$	1.65019	−	6.86917i	0.0591620	−	0.246272i
$779$	−6.50670	−	8.95571i	−0.233127	−	0.320871i
$780$	−51.2699	+	26.1048i	−1.83576	+	0.934701i
$781$		0			0
$782$	−6.27618	+	10.2385i	−0.224436	+	0.366128i
$783$	−4.03341	+	2.93044i	−0.144142	+	0.104725i
$784$	23.3121	+	7.58938i	0.832575	+	0.271049i
$785$	−1.12560	+	3.46425i	−0.0401745	+	0.123644i
$786$	−21.2625	+	8.80363i	−0.758408	+	0.314015i
$787$	−7.93466	+	10.9211i	−0.282840	+	0.389296i	−0.926672	−	0.375871i	$-0.877344\pi$
$787$	−7.93466	+	10.9211i	−0.282840	+	0.389296i	0.643832	+	0.765167i	$0.277344\pi$
$788$	−2.61985	−	16.5719i	−0.0933282	−	0.590349i
$789$	−61.8592	+	20.0993i	−2.20224	+	0.715553i
$790$	−28.4214	+	2.23270i	−1.01119	+	0.0794360i
$791$	15.5676			0.553519
$792$		0			0
$793$	−31.4031			−1.11516
$794$	25.0887	−	1.97089i	0.890364	−	0.0699444i
$795$	6.06389	−	1.97028i	0.215064	−	0.0698785i
$796$	−43.6569	+	6.90172i	−1.54738	+	0.244625i
$797$	14.0410	−	19.3257i	0.497357	−	0.684553i	−0.484367	−	0.874865i	$-0.660950\pi$
$797$	14.0410	−	19.3257i	0.497357	−	0.684553i	0.981724	+	0.190312i	$0.0609500\pi$
$798$	−7.69763	+	3.18717i	−0.272493	+	0.112824i
$799$	2.46636	−	7.59067i	0.0872535	−	0.268539i
$800$	53.2496	−	45.4133i	1.88266	−	1.60560i
$801$	−5.63584	+	4.09468i	−0.199133	+	0.144678i
$802$	−8.99768	+	14.6782i	−0.317719	+	0.518304i
$803$		0			0
$804$	−11.5865	−	22.7559i	−0.408624	−	0.802540i
$805$	7.93625	+	10.9233i	0.279716	+	0.384996i
$806$	−3.54427	+	14.7536i	−0.124841	+	0.519673i
$807$	−7.72803	+	23.7844i	−0.272040	+	0.837252i
$808$	23.3059	−	27.2639i	0.819898	−	0.959140i
$809$	−16.3306	−	11.8649i	−0.574155	−	0.417148i	0.262457	−	0.964944i	$-0.415467\pi$
$809$	−16.3306	−	11.8649i	−0.574155	−	0.417148i	−0.836612	+	0.547796i	$0.815467\pi$
$810$	−45.6129	+	38.9458i	−1.60268	+	1.36842i
$811$	−3.59503	+	1.16810i	−0.126238	+	0.0410174i	−0.371455	−	0.928451i	$-0.621141\pi$
$811$	−3.59503	+	1.16810i	−0.126238	+	0.0410174i	0.245216	+	0.969468i	$0.421141\pi$
$812$	−3.87664	+	7.60293i	−0.136043	+	0.266811i
$813$		−	46.4672i		−	1.62968i
$814$		0			0
$815$	31.3715			1.09890
$816$	−23.0242	−	0.0132353i	−0.806009	−	0.000463328i
$817$	9.50493	+	29.2532i	0.332535	+	1.02344i
$818$	−0.539959	−	0.632395i	−0.0188792	−	0.0221112i
$819$	4.08134	−	5.61749i	0.142614	−	0.196291i
$820$	−33.9703	−	5.39038i	−1.18630	−	0.188240i
$821$	30.9206	+	10.0467i	1.07914	+	0.350633i	0.794040	−	0.607866i	$-0.207974\pi$
$821$	30.9206	+	10.0467i	1.07914	+	0.350633i	0.285097	+	0.958499i	$0.407974\pi$
$822$	4.52345	−	18.8296i	0.157773	−	0.656757i
$823$	−16.7993	+	12.2054i	−0.585587	+	0.425454i	−0.840734	−	0.541448i	$-0.817876\pi$
$823$	−16.7993	+	12.2054i	−0.585587	+	0.425454i	0.255147	+	0.966902i	$0.417876\pi$
$824$	10.9019	+	0.862726i	0.379785	+	0.0300545i
$825$		0			0
$826$	−3.27392	−	2.00691i	−0.113914	−	0.0698293i
$827$	−6.59140	−	9.07228i	−0.229205	−	0.315474i	0.678888	−	0.734242i	$-0.262462\pi$
$827$	−6.59140	−	9.07228i	−0.229205	−	0.315474i	−0.908093	+	0.418768i	$0.862462\pi$
$828$	12.4562	−	12.4490i	0.432882	−	0.432633i
$829$	6.48815	+	2.10813i	0.225343	+	0.0732183i	0.419512	−	0.907750i	$-0.362201\pi$
$829$	6.48815	+	2.10813i	0.225343	+	0.0732183i	−0.194169	+	0.980968i	$0.562201\pi$
$830$	−3.59253	+	1.48747i	−0.124698	+	0.0516308i
$831$	23.8624	+	17.3370i	0.827776	+	0.601415i
$832$	−20.8990	−	10.6713i	−0.724541	−	0.369960i
$833$	−4.63321	−	14.2596i	−0.160531	−	0.494064i
$834$	−2.48497	−	31.6326i	−0.0860473	−	1.09535i
$835$			0.595616i			0.0206121i
$836$		0			0
$837$			3.98829i			0.137856i
$838$	−15.7211	+	1.23500i	−0.543075	+	0.0426624i
$839$	−5.98628	−	18.4239i	−0.206669	−	0.636063i	−0.999641	−	0.0268038i	$-0.991467\pi$
$839$	−5.98628	−	18.4239i	−0.206669	−	0.636063i	0.792971	−	0.609259i	$-0.208533\pi$
$840$	−9.91665	+	23.9117i	−0.342157	+	0.825034i
$841$	−6.54716	−	4.75679i	−0.225764	−	0.164027i
$842$	−18.8486	−	45.5231i	−0.649567	−	1.56883i
$843$	53.2689	+	17.3081i	1.83468	+	0.596123i
$844$	21.2622	+	21.2744i	0.731876	+	0.732296i
$845$	−10.7701	−	14.8237i	−0.370501	−	0.509951i
$846$	−6.11683	+	9.97855i	−0.210301	+	0.343070i
$847$		0			0
$848$	2.10299	+	1.52976i	0.0722170	+	0.0525322i
$849$	−52.7862	+	38.3514i	−1.81162	+	1.31622i
$850$	−41.6164	−	9.99754i	−1.42743	−	0.342913i
$851$	−14.9819	−	4.86792i	−0.513573	−	0.166870i
$852$	−36.0269	−	5.71671i	−1.23426	−	0.195851i
$853$	6.55434	−	9.02128i	0.224416	−	0.308883i	−0.681931	−	0.731417i	$-0.738859\pi$
$853$	6.55434	−	9.02128i	0.224416	−	0.308883i	0.906347	+	0.422534i	$0.138859\pi$
$854$	−10.7455	+	9.17485i	−0.367703	+	0.313957i
$855$	8.76499	+	26.9759i	0.299756	+	0.922555i
$856$	18.8768	+	30.8339i	0.645195	+	1.05388i
$857$	−30.4078			−1.03871			−0.519355	−	0.854558i	$-0.673828\pi$
$857$	−30.4078			−1.03871			−0.519355	+	0.854558i	$0.673828\pi$
$858$		0			0
$859$			27.7908i			0.948210i	0.880468	+	0.474105i	$0.157228\pi$
$859$			27.7908i			0.948210i	−0.880468	+	0.474105i	$0.842772\pi$
$860$	85.1416	+	43.4126i	2.90330	+	1.48036i
$861$	8.61712	−	2.79987i	0.293671	−	0.0954194i
$862$	22.8334	+	26.7422i	0.777708	+	0.910844i
$863$	−0.179462	−	0.130387i	−0.00610896	−	0.00443842i	0.584727	−	0.811230i	$-0.301202\pi$
$863$	−0.179462	−	0.130387i	−0.00610896	−	0.00443842i	−0.590836	+	0.806792i	$0.701202\pi$
$864$	−5.99649	−	1.44419i	−0.204005	−	0.0491323i
$865$	−1.45423	+	4.47567i	−0.0494455	+	0.152177i
$866$	−0.753143	−	0.180928i	−0.0255928	−	0.00614818i
$867$	−15.2355	−	20.9699i	−0.517425	−	0.712174i
$868$	3.09769	+	6.08388i	0.105142	+	0.206500i
$869$		0			0
$870$	54.0673	+	33.1432i	1.83305	+	1.12366i
$871$	−12.8766	+	9.35538i	−0.436306	+	0.316995i
$872$	−5.09032	+	1.21976i	−0.172380	+	0.0413062i
$873$	−1.43371	+	4.41252i	−0.0485239	+	0.149341i
$874$	5.03835	+	12.1686i	0.170425	+	0.411609i
$875$	−16.8536	+	23.1970i	−0.569757	+	0.784203i
$876$	9.60078	+	60.7299i	0.324380	+	2.05187i
$877$	14.7861	−	4.80428i	0.499290	−	0.162229i	−0.0485360	−	0.998821i	$-0.515456\pi$
$877$	14.7861	−	4.80428i	0.499290	−	0.162229i	0.547826	+	0.836592i	$0.315456\pi$
$878$	3.04918	+	38.8149i	0.102905	+	1.30994i
$879$	−13.2095			−0.445545
$880$		0			0
$881$	21.4338			0.722125			0.361062	−	0.932542i	$-0.382414\pi$
$881$	21.4338			0.722125			0.361062	+	0.932542i	$0.382414\pi$
$882$	1.72193	+	21.9195i	0.0579804	+	0.738066i
$883$	−13.5716	+	4.40968i	−0.456720	+	0.148397i	−0.528337	−	0.849035i	$-0.677184\pi$
$883$	−13.5716	+	4.40968i	−0.456720	+	0.148397i	0.0716166	+	0.997432i	$0.477184\pi$
$884$	2.24090	+	14.1748i	0.0753695	+	0.476751i
$885$	−16.7727	+	23.0856i	−0.563808	+	0.776015i
$886$	−4.35758	−	10.5244i	−0.146396	−	0.353574i
$887$	7.29616	−	22.4553i	0.244981	−	0.753974i	−0.750659	−	0.660690i	$-0.770264\pi$
$887$	7.29616	−	22.4553i	0.244981	−	0.753974i	0.995640	−	0.0932837i	$-0.0297364\pi$
$888$	−7.03789	−	29.3707i	−0.236176	−	0.985616i
$889$	4.91510	−	3.57103i	0.164847	−	0.119768i
$890$	−13.8010	−	8.46000i	−0.462611	−	0.283580i
$891$		0			0
$892$	9.32569	+	18.3157i	0.312247	+	0.613255i
$893$	−5.14497	−	7.08144i	−0.172170	−	0.236972i
$894$	45.0463	+	10.8215i	1.50657	+	0.361926i
$895$	−19.5281	+	60.1014i	−0.652753	+	2.00897i
$896$	−10.2690	+	2.45444i	−0.343062	+	0.0819969i
$897$	−19.3827	−	14.0824i	−0.647171	−	0.470197i
$898$	31.0116	+	36.3205i	1.03487	+	1.21203i
$899$	15.9066	−	5.16835i	0.530513	−	0.172374i
$900$	55.9154	+	28.5106i	1.86385	+	0.950352i
$901$		−	1.59039i		−	0.0529837i
$902$		0			0
$903$	−25.1756			−0.837792
$904$	40.2403	−	24.6354i	1.33837	−	0.819361i
$905$	−21.7937	−	67.0743i	−0.724449	−	2.22962i
$906$	−38.5234	+	32.8925i	−1.27985	+	1.09278i
$907$	26.6198	−	36.6389i	0.883894	−	1.21658i	−0.0914327	−	0.995811i	$-0.529145\pi$
$907$	26.6198	−	36.6389i	0.883894	−	1.21658i	0.975327	−	0.220765i	$-0.0708554\pi$
$908$	30.9505	+	4.91119i	1.02713	+	0.162984i
$909$	30.5927	+	9.94017i	1.01470	+	0.329694i
$910$	15.6886	+	3.76887i	0.520071	+	0.124937i
$911$	18.1656	−	13.1981i	0.601853	−	0.437272i	−0.244683	−	0.969603i	$-0.578684\pi$
$911$	18.1656	−	13.1981i	0.601853	−	0.437272i	0.846536	+	0.532331i	$0.178684\pi$
$912$	−14.8538	+	20.4198i	−0.491859	+	0.676168i
$913$		0			0
$914$	−2.83237	+	4.62051i	−0.0936864	+	0.152833i
$915$	61.7148	+	84.9431i	2.04023	+	2.80813i
$916$	−19.8989	−	19.9104i	−0.657479	−	0.657857i
$917$	6.13801	+	1.99436i	0.202695	+	0.0658595i
$918$	1.44302	+	3.48518i	0.0476268	+	0.115028i
$919$	−33.6008	−	24.4124i	−1.10839	−	0.805292i	−0.125980	−	0.992033i	$-0.540207\pi$
$919$	−33.6008	−	24.4124i	−1.10839	−	0.805292i	−0.982409	+	0.186741i	$0.940207\pi$
$920$	37.8002	+	15.6765i	1.24624	+	0.516838i
$921$	20.2541	+	62.3358i	0.667396	+	2.05403i
$922$	−22.3295	+	1.75414i	−0.735383	+	0.0577696i
$923$			22.7363i			0.748373i
$924$		0			0
$925$		−	56.1436i		−	1.84599i
$926$	3.36841	+	42.8784i	0.110693	+	1.40907i
$927$	3.03074	+	9.32765i	0.0995425	+	0.306360i
$928$	2.01087	+	25.7874i	0.0660100	+	0.846512i
$929$	30.1761	+	21.9242i	0.990046	+	0.719310i	0.959931	−	0.280236i	$-0.0904128\pi$
$929$	30.1761	+	21.9242i	0.990046	+	0.719310i	0.0301145	+	0.999546i	$0.490413\pi$
$930$	46.8728	−	19.4074i	1.53702	−	0.636395i
$931$	−15.6385	−	5.08127i	−0.512533	−	0.166532i
$932$	−17.1159	+	17.1061i	−0.560651	+	0.560328i
$933$	−33.7571	−	46.4626i	−1.10516	−	1.52112i
$934$	−24.3330	−	14.9161i	−0.796199	−	0.488069i
$935$		0			0
$936$	1.66020	−	20.9792i	0.0542653	−	0.685726i
$937$	−10.6707	+	7.75270i	−0.348596	+	0.253270i	−0.748280	−	0.663383i	$-0.769120\pi$
$937$	−10.6707	+	7.75270i	−0.348596	+	0.253270i	0.399684	+	0.916653i	$0.369120\pi$
$938$	−1.67280	+	6.96329i	−0.0546188	+	0.227360i
$939$	−20.4430	−	6.64232i	−0.667131	−	0.216764i
$940$	−26.8610	−	4.26228i	−0.876109	−	0.139020i
$941$	−14.5016	+	19.9597i	−0.472738	+	0.650668i	−0.977089	−	0.212831i	$-0.931732\pi$
$941$	−14.5016	+	19.9597i	−0.472738	+	0.650668i	0.504351	+	0.863499i	$0.331732\pi$
$942$	−1.88838	−	2.21166i	−0.0615268	−	0.0720596i
$943$	−4.42610	−	13.6221i	−0.144134	−	0.443598i
$944$	−11.6386	−	0.00669035i	−0.378804	−	0.000217752i
$945$	4.24104			0.137961
$946$		0			0
$947$		−	38.8667i		−	1.26300i	−0.775376	−	0.631500i	$-0.782440\pi$
$947$		−	38.8667i		−	1.26300i	0.775376	−	0.631500i	$-0.217560\pi$
$948$	10.3392	−	20.2775i	0.335803	−	0.658583i
$949$	36.4470	−	11.8424i	1.18312	−	0.384419i
$950$	−35.6974	+	30.4796i	−1.15818	+	0.988890i
$951$	−34.1701	−	24.8260i	−1.10804	−	0.805038i
$952$	4.90816	+	4.19563i	0.159074	+	0.135981i
$953$	16.2483	−	50.0072i	0.526335	−	1.61989i	−0.235326	−	0.971916i	$-0.575616\pi$
$953$	16.2483	−	50.0072i	0.526335	−	1.61989i	0.761661	−	0.647976i	$-0.224384\pi$
$954$	−0.544773	+	2.26771i	−0.0176377	+	0.0734198i
$955$	40.8441	+	56.2170i	1.32168	+	1.81914i
$956$	19.7355	+	38.7607i	0.638292	+	1.25361i
$957$		0			0
$958$	9.28340	−	15.1442i	0.299933	−	0.489288i
$959$	−4.39370	+	3.19221i	−0.141880	+	0.103082i
$960$	12.2066	+	77.5019i	0.393966	+	2.50136i
$961$	−5.44501	+	16.7580i	−0.175646	+	0.540581i
$962$	−17.3929	+	7.20144i	−0.560769	+	0.232184i
$963$	−19.0580	+	26.2310i	−0.614134	+	0.845283i
$964$	13.7091	−	2.16727i	0.441540	−	0.0698030i
$965$	−0.716285	+	0.232735i	−0.0230580	+	0.00749201i
$966$	−10.7467	+	0.844233i	−0.345771	+	0.0271627i
$967$	−2.98370			−0.0959493			−0.0479746	−	0.998849i	$-0.515277\pi$
$967$	−2.98370			−0.0959493			−0.0479746	+	0.998849i	$0.515277\pi$
$968$		0			0
$969$	15.4425			0.496086
$970$	−10.7480	+	0.844330i	−0.345097	+	0.0271098i
$971$	14.3079	−	4.64893i	0.459164	−	0.149191i	−0.0702964	−	0.997526i	$-0.522395\pi$
$971$	14.3079	−	4.64893i	0.459164	−	0.149191i	0.529460	+	0.848335i	$0.322395\pi$
$972$	−6.45581	−	40.8364i	−0.207070	−	1.30983i
$973$	−5.23043	+	7.19907i	−0.167680	+	0.230792i
$974$	−18.6221	+	7.71038i	−0.596690	+	0.247057i
$975$	26.3863	−	81.2088i	0.845039	−	2.60076i
$976$	−13.2568	+	40.7204i	−0.424338	+	1.30343i
$977$	9.24812	−	6.71916i	0.295874	−	0.214965i	−0.429938	−	0.902859i	$-0.641464\pi$
$977$	9.24812	−	6.71916i	0.295874	−	0.214965i	0.725811	+	0.687894i	$0.241464\pi$
$978$	−13.0899	+	21.3540i	−0.418570	+	0.682824i
$979$		0			0
$980$	−45.5294	+	23.1819i	−1.45438	+	0.740519i
$981$	−2.75929	−	3.79783i	−0.0880972	−	0.121255i
$982$	−6.74045	+	28.0582i	−0.215097	+	0.895375i
$983$	17.9549	−	55.2595i	0.572672	−	1.76250i	−0.0713009	−	0.997455i	$-0.522715\pi$
$983$	17.9549	−	55.2595i	0.572672	−	1.76250i	0.643973	−	0.765048i	$-0.277285\pi$
$984$	17.8435	−	20.8738i	0.568829	−	0.665432i
$985$	28.2866	+	20.5514i	0.901287	+	0.654823i
$986$	12.0300	−	10.2716i	0.383113	−	0.327114i
$987$	6.81372	−	2.21391i	0.216883	−	0.0704696i
$988$	14.0212	+	7.14925i	0.446075	+	0.227448i
$989$			39.7982i			1.26551i
$990$		0			0
$991$	30.2307			0.960311			0.480156	−	0.877183i	$-0.340580\pi$
$991$	30.2307			0.960311			0.480156	+	0.877183i	$0.340580\pi$
$992$	17.6348	+	10.8241i	0.559905	+	0.343664i
$993$	9.59312	+	29.5246i	0.304429	+	0.936935i
$994$	6.64272	+	7.77988i	0.210694	+	0.246763i
$995$	54.1407	−	74.5182i	1.71637	−	2.36239i
$996$	0.486513	−	3.06602i	0.0154158	−	0.0971506i
$997$	−12.7437	−	4.14069i	−0.403598	−	0.131137i	0.100181	−	0.994969i	$-0.468058\pi$
$997$	−12.7437	−	4.14069i	−0.403598	−	0.131137i	−0.503780	+	0.863832i	$0.668058\pi$
$998$	11.0251	−	45.8938i	0.348994	−	1.45274i
$999$	−4.00308	+	2.90841i	−0.126652	+	0.0920179i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	968.2.o.g.245.6		40
8.5	even	2	inner	968.2.o.g.245.2		40
11.2	odd	10		968.2.c.d.485.4		10
11.3	even	5	inner	968.2.o.g.269.10		40
11.4	even	5	inner	968.2.o.g.565.2		40
11.5	even	5	inner	968.2.o.g.493.4		40
11.6	odd	10		968.2.o.h.493.7		40
11.7	odd	10		968.2.o.h.565.9		40
11.8	odd	10		968.2.o.h.269.1		40
11.9	even	5		88.2.c.a.45.7	✓	10
11.10	odd	2		968.2.o.h.245.5		40
33.20	odd	10		792.2.f.g.397.4		10
44.31	odd	10		352.2.c.a.177.9		10
44.35	even	10		3872.2.c.f.1937.9		10
88.5	even	10	inner	968.2.o.g.493.10		40
88.13	odd	10		968.2.c.d.485.3		10
88.21	odd	2		968.2.o.h.245.9		40
88.29	odd	10		968.2.o.h.565.5		40
88.35	even	10		3872.2.c.f.1937.2		10
88.37	even	10	inner	968.2.o.g.565.6		40
88.53	even	10		88.2.c.a.45.8	yes	10
88.61	odd	10		968.2.o.h.493.1		40
88.69	even	10	inner	968.2.o.g.269.4		40
88.75	odd	10		352.2.c.a.177.2		10
88.85	odd	10		968.2.o.h.269.7		40
132.119	even	10		3168.2.f.g.1585.1		10
176.53	even	20		2816.2.a.o.1.1		5
176.75	odd	20		2816.2.a.p.1.5		5
176.141	even	20		2816.2.a.r.1.5		5
176.163	odd	20		2816.2.a.q.1.1		5
264.53	odd	10		792.2.f.g.397.3		10
264.251	even	10		3168.2.f.g.1585.10		10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
88.2.c.a.45.7	✓	10	11.9	even	5
88.2.c.a.45.8	yes	10	88.53	even	10
352.2.c.a.177.2		10	88.75	odd	10
352.2.c.a.177.9		10	44.31	odd	10
792.2.f.g.397.3		10	264.53	odd	10
792.2.f.g.397.4		10	33.20	odd	10
968.2.c.d.485.3		10	88.13	odd	10
968.2.c.d.485.4		10	11.2	odd	10
968.2.o.g.245.2		40	8.5	even	2	inner
968.2.o.g.245.6		40	1.1	even	1	trivial
968.2.o.g.269.4		40	88.69	even	10	inner
968.2.o.g.269.10		40	11.3	even	5	inner
968.2.o.g.493.4		40	11.5	even	5	inner
968.2.o.g.493.10		40	88.5	even	10	inner
968.2.o.g.565.2		40	11.4	even	5	inner
968.2.o.g.565.6		40	88.37	even	10	inner
968.2.o.h.245.5		40	11.10	odd	2
968.2.o.h.245.9		40	88.21	odd	2
968.2.o.h.269.1		40	11.8	odd	10
968.2.o.h.269.7		40	88.85	odd	10
968.2.o.h.493.1		40	88.61	odd	10
968.2.o.h.493.7		40	11.6	odd	10
968.2.o.h.565.5		40	88.29	odd	10
968.2.o.h.565.9		40	11.7	odd	10
2816.2.a.o.1.1		5	176.53	even	20
2816.2.a.p.1.5		5	176.75	odd	20
2816.2.a.q.1.1		5	176.163	odd	20
2816.2.a.r.1.5		5	176.141	even	20
3168.2.f.g.1585.1		10	132.119	even	10
3168.2.f.g.1585.10		10	264.251	even	10
3872.2.c.f.1937.2		10	88.35	even	10
3872.2.c.f.1937.9		10	44.35	even	10

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 968 = 2^{3} \cdot 11^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	968.o (of order \(10\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.110755 + 1.40987i) q^{2} +(2.23784 - 0.727117i) q^{3} +(-1.97547 + 0.312301i) q^{4} +(2.44985 - 3.37193i) q^{5} +(1.27299 + 3.07453i) q^{6} +(0.288382 - 0.887547i) q^{7} +(-0.659097 - 2.75056i) q^{8} +(2.05216 - 1.49098i) q^{9} +(5.02532 + 3.08051i) q^{10} +(-4.19369 + 2.13527i) q^{12} +(1.72410 + 2.37303i) q^{13} +(1.28327 + 0.308280i) q^{14} +(3.03058 - 9.32717i) q^{15} +(3.80494 - 1.23388i) q^{16} +(-1.97907 - 1.43788i) q^{17} +(2.32938 + 2.72815i) q^{18} +(-2.55153 + 0.829041i) q^{19} +(-3.78654 + 7.42623i) q^{20} -2.19587i q^{21} -3.47129 q^{23} +(-3.47493 - 5.67607i) q^{24} +(-3.82307 - 11.7662i) q^{25} +(-3.15471 + 2.69359i) q^{26} +(-0.640892 + 0.882112i) q^{27} +(-0.292506 + 1.84338i) q^{28} +(4.34866 + 1.41296i) q^{29} +(13.4857 + 3.23969i) q^{30} +(2.95923 - 2.15001i) q^{31} +(2.16103 + 5.22781i) q^{32} +(1.80803 - 2.94948i) q^{34} +(-2.28626 - 3.14676i) q^{35} +(-3.58834 + 3.58628i) q^{36} +(4.31595 + 1.40234i) q^{37} +(-1.45143 - 3.50550i) q^{38} +(5.58373 + 4.05682i) q^{39} +(-10.8894 - 4.51604i) q^{40} +(1.27506 + 3.92423i) q^{41} +(3.09590 - 0.243205i) q^{42} -11.4650i q^{43} -10.5724i q^{45} +(-0.384463 - 4.89406i) q^{46} +(1.00821 + 3.10297i) q^{47} +(7.61765 - 5.52786i) q^{48} +(4.95854 + 3.60259i) q^{49} +(16.1654 - 6.69320i) q^{50} +(-5.47434 - 1.77872i) q^{51} +(-4.14701 - 4.14940i) q^{52} +(0.382138 + 0.525968i) q^{53} +(-1.31464 - 0.805875i) q^{54} +(-2.63133 - 0.208231i) q^{56} +(-5.10709 + 3.71052i) q^{57} +(-1.51046 + 6.28753i) q^{58} +(-2.76724 - 0.899131i) q^{59} +(-3.07392 + 19.3720i) q^{60} +(-6.29283 + 8.66134i) q^{61} +(3.35898 + 3.93401i) q^{62} +(-0.731513 - 2.25136i) q^{63} +(-7.13118 + 3.62578i) q^{64} +12.2255 q^{65} +5.42623i q^{67} +(4.35863 + 2.22241i) q^{68} +(-7.76817 + 2.52403i) q^{69} +(4.18331 - 3.57185i) q^{70} +(6.27093 + 4.55610i) q^{71} +(-5.45362 - 4.66190i) q^{72} +(4.03732 - 12.4256i) q^{73} +(-1.49910 + 6.24025i) q^{74} +(-17.1108 - 23.5510i) q^{75} +(4.78154 - 2.43459i) q^{76} +(-5.10116 + 8.32165i) q^{78} +(-3.91294 + 2.84292i) q^{79} +(5.16097 - 15.8528i) q^{80} +(-3.14438 + 9.67741i) q^{81} +(-5.39144 + 2.23230i) q^{82} +(-0.387741 + 0.533679i) q^{83} +(0.685774 + 4.33787i) q^{84} +(-9.69685 + 3.15070i) q^{85} +(16.1641 - 1.26981i) q^{86} +10.7590 q^{87} -2.74629 q^{89} +(14.9058 - 1.17095i) q^{90} +(2.60337 - 0.845887i) q^{91} +(6.85741 - 1.08409i) q^{92} +(5.05897 - 6.96307i) q^{93} +(-4.26311 + 1.76512i) q^{94} +(-3.45539 + 10.6346i) q^{95} +(8.63726 + 10.1277i) q^{96} +(-1.47973 + 1.07509i) q^{97} +(-4.53000 + 7.38991i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q + 4 q^{4} - 2 q^{6} + 10 q^{9} + 40 q^{10} - 16 q^{12} + 12 q^{14} - 8 q^{15} + 4 q^{17} + 10 q^{18} - 12 q^{20} - 48 q^{23} + 6 q^{25} + 20 q^{26} + 12 q^{28} - 18 q^{30} + 4 q^{31} - 80 q^{32} - 32 q^{36}+ \cdots + 96 q^{98}+O(q^{100}) \) 40 * q + 4 * q^4 - 2 * q^6 + 10 * q^9 + 40 * q^10 - 16 * q^12 + 12 * q^14 - 8 * q^15 + 4 * q^17 + 10 * q^18 - 12 * q^20 - 48 * q^23 + 6 * q^25 + 20 * q^26 + 12 * q^28 - 18 * q^30 + 4 * q^31 - 80 * q^32 - 32 * q^36 - 8 * q^38 - 24 * q^39 - 20 * q^40 - 4 * q^41 - 20 * q^42 - 2 * q^46 + 4 * q^47 - 32 * q^48 + 6 * q^49 + 6 * q^50 + 20 * q^52 - 152 * q^54 - 32 * q^56 - 16 * q^57 - 36 * q^58 + 4 * q^60 - 22 * q^62 + 40 * q^63 + 16 * q^64 + 64 * q^65 + 28 * q^68 - 28 * q^70 + 12 * q^71 + 4 * q^72 + 4 * q^73 + 14 * q^74 + 176 * q^76 - 32 * q^78 - 16 * q^79 + 56 * q^80 + 6 * q^81 + 4 * q^82 + 52 * q^84 + 20 * q^86 + 128 * q^87 - 16 * q^89 + 36 * q^90 + 36 * q^92 - 24 * q^95 - 60 * q^96 + 20 * q^97 + 96 * q^98

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