LMFDB - Embedded newform 160.2.u.a.43.18

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [160,2,Mod(43,160)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(160, base_ring=CyclotomicField(8))

chi = DirichletCharacter(H, H._module([4, 5, 6]))

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

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

chi := DirichletCharacter("160.43");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 160 = 2^{5} \cdot 5 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	160.u (of order $8$, degree $4$, 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:	$1.27760643234$
Analytic rank:	$0$
Dimension:	$88$
Relative dimension:	$22$ over $\Q(\zeta_{8})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{8}]$

Embedding invariants

Embedding label			43.18
Character	$\chi$	$=$	160.43
Dual form			160.2.u.a.67.18

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.02775 + 0.971453i) q^{2} +(-1.05354 + 2.54348i) q^{3} +(0.112559 + 1.99683i) q^{4} +(2.23055 + 0.156938i) q^{5} +(-3.55365 + 1.59060i) q^{6} -4.43630i q^{7} +(-1.82414 + 2.16160i) q^{8} +(-3.23800 - 3.23800i) q^{9} +O(q^{10})$	\(q+(1.02775 + 0.971453i) q^{2} +(-1.05354 + 2.54348i) q^{3} +(0.112559 + 1.99683i) q^{4} +(2.23055 + 0.156938i) q^{5} +(-3.55365 + 1.59060i) q^{6} -4.43630i q^{7} +(-1.82414 + 2.16160i) q^{8} +(-3.23800 - 3.23800i) q^{9} +(2.14000 + 2.32817i) q^{10} +(-1.11885 + 2.70115i) q^{11} +(-5.19748 - 1.81745i) q^{12} +(1.67896 - 4.05336i) q^{13} +(4.30965 - 4.55943i) q^{14} +(-2.74915 + 5.50802i) q^{15} +(-3.97466 + 0.449523i) q^{16} +(0.470736 + 0.470736i) q^{17} +(-0.182306 - 6.47343i) q^{18} +(0.824662 + 1.99091i) q^{19} +(-0.0623096 + 4.47170i) q^{20} +(11.2836 + 4.67383i) q^{21} +(-3.77395 + 1.68921i) q^{22} -3.01006i q^{23} +(-3.57616 - 6.91700i) q^{24} +(4.95074 + 0.700118i) q^{25} +(5.66321 - 2.53483i) q^{26} +(4.01672 - 1.66378i) q^{27} +(8.85854 - 0.499346i) q^{28} +(1.08758 + 2.62566i) q^{29} +(-8.17623 + 2.99022i) q^{30} +0.802456i q^{31} +(-4.52167 - 3.39920i) q^{32} +(-5.69155 - 5.69155i) q^{33} +(0.0265033 + 0.941098i) q^{34} +(0.696225 - 9.89540i) q^{35} +(6.10127 - 6.83020i) q^{36} +(-2.30469 - 5.56402i) q^{37} +(-1.08652 + 2.84729i) q^{38} +(8.54078 + 8.54078i) q^{39} +(-4.40809 + 4.53528i) q^{40} +(-1.94797 + 1.94797i) q^{41} +(7.05639 + 15.7651i) q^{42} +(3.47703 - 1.44023i) q^{43} +(-5.51968 - 1.93012i) q^{44} +(-6.71437 - 7.73070i) q^{45} +(2.92413 - 3.09360i) q^{46} +(-4.93072 + 4.93072i) q^{47} +(3.04412 - 10.5830i) q^{48} -12.6807 q^{49} +(4.40802 + 5.52896i) q^{50} +(-1.69325 + 0.701365i) q^{51} +(8.28286 + 2.89635i) q^{52} +(0.292968 + 0.707286i) q^{53} +(5.74448 + 2.19209i) q^{54} +(-2.91958 + 5.84947i) q^{55} +(9.58949 + 8.09244i) q^{56} -5.93265 q^{57} +(-1.43293 + 3.75507i) q^{58} +(3.32398 - 8.02481i) q^{59} +(-11.3080 - 4.86961i) q^{60} +(-11.7209 + 4.85497i) q^{61} +(-0.779548 + 0.824728i) q^{62} +(-14.3647 + 14.3647i) q^{63} +(-1.34501 - 7.88612i) q^{64} +(4.38113 - 8.77775i) q^{65} +(-0.320445 - 11.3786i) q^{66} +(-3.81672 - 1.58094i) q^{67} +(-0.886994 + 0.992965i) q^{68} +(7.65601 + 3.17122i) q^{69} +(10.3285 - 9.49370i) q^{70} +(8.00826 - 8.00826i) q^{71} +(12.9058 - 1.09268i) q^{72} +2.88538 q^{73} +(3.03653 - 7.95735i) q^{74} +(-6.99655 + 11.8545i) q^{75} +(-3.88269 + 1.87081i) q^{76} +(11.9831 + 4.96357i) q^{77} +(0.480862 + 17.0748i) q^{78} -9.01288i q^{79} +(-8.93624 + 0.378910i) q^{80} -1.76839i q^{81} +(-3.89440 + 0.109675i) q^{82} +(10.4111 + 4.31243i) q^{83} +(-8.06277 + 23.0576i) q^{84} +(0.976125 + 1.12388i) q^{85} +(4.97265 + 1.89757i) q^{86} -7.82411 q^{87} +(-3.79785 - 7.34579i) q^{88} +(0.306754 - 0.306754i) q^{89} +(0.609286 - 14.4680i) q^{90} +(-17.9819 - 7.44836i) q^{91} +(6.01057 - 0.338810i) q^{92} +(-2.04103 - 0.845421i) q^{93} +(-9.85753 + 0.277609i) q^{94} +(1.52700 + 4.57025i) q^{95} +(13.4095 - 7.91956i) q^{96} +(-4.14919 + 4.14919i) q^{97} +(-13.0327 - 12.3187i) q^{98} +(12.3692 - 5.12348i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 88 q - 4 q^{2} - 4 q^{3} - 4 q^{5} - 8 q^{6} - 16 q^{8}+O(q^{10}) $ 88 * q - 4 * q^2 - 4 * q^3 - 4 * q^5 - 8 * q^6 - 16 * q^8	$ 88 q - 4 q^{2} - 4 q^{3} - 4 q^{5} - 8 q^{6} - 16 q^{8} - 16 q^{10} - 8 q^{11} - 20 q^{12} - 4 q^{13} + 16 q^{14} - 8 q^{15} - 8 q^{16} + 4 q^{18} + 16 q^{19} + 24 q^{20} - 8 q^{21} - 20 q^{22} - 32 q^{24} - 4 q^{25} - 8 q^{26} - 16 q^{27} + 12 q^{28} + 8 q^{30} - 24 q^{32} - 8 q^{33} + 8 q^{34} - 8 q^{35} - 8 q^{36} - 4 q^{37} - 60 q^{38} + 16 q^{40} - 8 q^{41} + 60 q^{42} - 36 q^{43} + 16 q^{44} - 4 q^{45} - 8 q^{46} - 8 q^{47} - 24 q^{48} - 40 q^{49} - 12 q^{50} + 8 q^{51} - 56 q^{52} - 4 q^{53} - 56 q^{54} - 36 q^{55} + 40 q^{56} - 8 q^{57} - 36 q^{58} + 12 q^{60} - 40 q^{61} + 40 q^{62} + 56 q^{63} + 48 q^{64} - 8 q^{65} + 72 q^{66} + 20 q^{67} + 8 q^{68} + 24 q^{69} + 60 q^{70} + 24 q^{71} + 24 q^{72} - 8 q^{73} + 8 q^{75} + 56 q^{76} + 24 q^{77} + 32 q^{78} - 8 q^{80} + 84 q^{82} - 44 q^{83} + 56 q^{84} - 4 q^{85} + 24 q^{86} - 120 q^{87} + 104 q^{88} + 148 q^{90} - 8 q^{91} + 124 q^{92} + 8 q^{93} - 32 q^{94} + 24 q^{96} - 8 q^{97} - 16 q^{98}+O(q^{100}) $ 88 * q - 4 * q^2 - 4 * q^3 - 4 * q^5 - 8 * q^6 - 16 * q^8 - 16 * q^10 - 8 * q^11 - 20 * q^12 - 4 * q^13 + 16 * q^14 - 8 * q^15 - 8 * q^16 + 4 * q^18 + 16 * q^19 + 24 * q^20 - 8 * q^21 - 20 * q^22 - 32 * q^24 - 4 * q^25 - 8 * q^26 - 16 * q^27 + 12 * q^28 + 8 * q^30 - 24 * q^32 - 8 * q^33 + 8 * q^34 - 8 * q^35 - 8 * q^36 - 4 * q^37 - 60 * q^38 + 16 * q^40 - 8 * q^41 + 60 * q^42 - 36 * q^43 + 16 * q^44 - 4 * q^45 - 8 * q^46 - 8 * q^47 - 24 * q^48 - 40 * q^49 - 12 * q^50 + 8 * q^51 - 56 * q^52 - 4 * q^53 - 56 * q^54 - 36 * q^55 + 40 * q^56 - 8 * q^57 - 36 * q^58 + 12 * q^60 - 40 * q^61 + 40 * q^62 + 56 * q^63 + 48 * q^64 - 8 * q^65 + 72 * q^66 + 20 * q^67 + 8 * q^68 + 24 * q^69 + 60 * q^70 + 24 * q^71 + 24 * q^72 - 8 * q^73 + 8 * q^75 + 56 * q^76 + 24 * q^77 + 32 * q^78 - 8 * q^80 + 84 * q^82 - 44 * q^83 + 56 * q^84 - 4 * q^85 + 24 * q^86 - 120 * q^87 + 104 * q^88 + 148 * q^90 - 8 * q^91 + 124 * q^92 + 8 * q^93 - 32 * q^94 + 24 * q^96 - 8 * q^97 - 16 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/160\mathbb{Z}\right)^\times$.

$n$	$31$	$97$	$101$
$\chi(n)$	$-1$	$e\left(\frac{3}{4}\right)$	$e\left(\frac{5}{8}\right)$

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 $

$2$	1.02775	+	0.971453i	0.726732	+	0.686921i
$2$	1.02775	+	0.971453i	0.726732	+	0.686921i
$3$	−1.05354	+	2.54348i	−0.608263	+	1.46848i	0.256625	+	0.966511i	$0.417390\pi$
$3$	−1.05354	+	2.54348i	−0.608263	+	1.46848i	−0.864888	+	0.501966i	$0.832610\pi$
$4$	0.112559	+	1.99683i	0.0562796	+	0.998415i
$5$	2.23055	+	0.156938i	0.997534	+	0.0701849i
$5$	2.23055	+	0.156938i	0.997534	+	0.0701849i
$6$	−3.55365	+	1.59060i	−1.45077	+	0.649361i
$7$		−	4.43630i		−	1.67676i	−0.545084	−	0.838382i	$-0.683502\pi$
$7$		−	4.43630i		−	1.67676i	0.545084	−	0.838382i	$-0.316498\pi$
$8$	−1.82414	+	2.16160i	−0.644932	+	0.764240i
$9$	−3.23800	−	3.23800i	−1.07933	−	1.07933i
$10$	2.14000	+	2.32817i	0.676729	+	0.736232i
$11$	−1.11885	+	2.70115i	−0.337347	+	0.814427i	0.660622	+	0.750719i	$0.270293\pi$
$11$	−1.11885	+	2.70115i	−0.337347	+	0.814427i	−0.997969	+	0.0637085i	$0.979707\pi$
$12$	−5.19748	−	1.81745i	−1.50038	−	0.524654i
$13$	1.67896	−	4.05336i	0.465659	−	1.12420i	−0.500380	−	0.865806i	$-0.666806\pi$
$13$	1.67896	−	4.05336i	0.465659	−	1.12420i	0.966039	−	0.258395i	$-0.0831935\pi$
$14$	4.30965	−	4.55943i	1.15180	−	1.21856i
$15$	−2.74915	+	5.50802i	−0.709828	+	1.42216i
$16$	−3.97466	+	0.449523i	−0.993665	+	0.112381i
$17$	0.470736	+	0.470736i	0.114170	+	0.114170i	0.761884	−	0.647714i	$-0.224275\pi$
$17$	0.470736	+	0.470736i	0.114170	+	0.114170i	−0.647714	+	0.761884i	$0.724275\pi$
$18$	−0.182306	−	6.47343i	−0.0429698	−	1.52580i
$19$	0.824662	+	1.99091i	0.189190	+	0.456746i	0.989804	−	0.142435i	$-0.0454931\pi$
$19$	0.824662	+	1.99091i	0.189190	+	0.456746i	−0.800614	+	0.599181i	$0.795493\pi$
$20$	−0.0623096	+	4.47170i	−0.0139328	+	0.999903i
$21$	11.2836	+	4.67383i	2.46229	+	1.01991i
$22$	−3.77395	+	1.68921i	−0.804608	+	0.360140i
$23$		−	3.01006i		−	0.627641i	−0.949482	−	0.313820i	$-0.898391\pi$
$23$		−	3.01006i		−	0.627641i	0.949482	−	0.313820i	$-0.101609\pi$
$24$	−3.57616	−	6.91700i	−0.729981	−	1.41193i
$25$	4.95074	+	0.700118i	0.990148	+	0.140024i
$26$	5.66321	−	2.53483i	1.11065	−	0.497122i
$27$	4.01672	−	1.66378i	0.773017	−	0.320194i
$28$	8.85854	−	0.499346i	1.67411	−	0.0943676i
$29$	1.08758	+	2.62566i	0.201959	+	0.487572i	0.992115	−	0.125334i	$-0.0400003\pi$
$29$	1.08758	+	2.62566i	0.201959	+	0.487572i	−0.790156	+	0.612906i	$0.790000\pi$
$30$	−8.17623	+	2.99022i	−1.49277	+	0.545937i
$31$			0.802456i			0.144125i	0.997400	+	0.0720627i	$0.0229582\pi$
$31$			0.802456i			0.144125i	−0.997400	+	0.0720627i	$0.977042\pi$
$32$	−4.52167	−	3.39920i	−0.799325	−	0.600899i
$33$	−5.69155	−	5.69155i	−0.990772	−	0.990772i
$34$	0.0265033	+	0.941098i	0.00454528	+	0.161397i
$35$	0.696225	−	9.89540i	0.117683	−	1.67263i
$36$	6.10127	−	6.83020i	1.01688	−	1.13837i
$37$	−2.30469	−	5.56402i	−0.378889	−	0.914720i	−0.992175	−	0.124858i	$-0.960152\pi$
$37$	−2.30469	−	5.56402i	−0.378889	−	0.914720i	0.613285	−	0.789862i	$-0.289848\pi$
$38$	−1.08652	+	2.84729i	−0.176258	+	0.461891i
$39$	8.54078	+	8.54078i	1.36762	+	1.36762i
$40$	−4.40809	+	4.53528i	−0.696980	+	0.717091i
$41$	−1.94797	+	1.94797i	−0.304222	+	0.304222i	−0.842663	−	0.538441i	$-0.819013\pi$
$41$	−1.94797	+	1.94797i	−0.304222	+	0.304222i	0.538441	+	0.842663i	$0.319013\pi$
$42$	7.05639	+	15.7651i	1.08882	+	2.43260i
$43$	3.47703	−	1.44023i	0.530242	−	0.219634i	−0.101467	−	0.994839i	$-0.532354\pi$
$43$	3.47703	−	1.44023i	0.530242	−	0.219634i	0.631709	+	0.775205i	$0.282354\pi$
$44$	−5.51968	−	1.93012i	−0.832122	−	0.290977i
$45$	−6.71437	−	7.73070i	−1.00092	−	1.15242i
$46$	2.92413	−	3.09360i	0.431139	−	0.456127i
$47$	−4.93072	+	4.93072i	−0.719219	+	0.719219i	−0.968445	−	0.249226i	$-0.919824\pi$
$47$	−4.93072	+	4.93072i	−0.719219	+	0.719219i	0.249226	+	0.968445i	$0.419824\pi$
$48$	3.04412	−	10.5830i	0.439381	−	1.52753i
$49$	−12.6807			−1.81154
$50$	4.40802	+	5.52896i	0.623387	+	0.781913i
$51$	−1.69325	+	0.701365i	−0.237102	+	0.0982108i
$52$	8.28286	+	2.89635i	1.14863	+	0.401651i
$53$	0.292968	+	0.707286i	0.0402422	+	0.0971532i	0.942723	−	0.333577i	$-0.108256\pi$
$53$	0.292968	+	0.707286i	0.0402422	+	0.0971532i	−0.902481	+	0.430731i	$0.858256\pi$
$54$	5.74448	+	2.19209i	0.781725	+	0.298306i
$55$	−2.91958	+	5.84947i	−0.393676	+	0.788742i
$56$	9.58949	+	8.09244i	1.28145	+	1.08140i
$57$	−5.93265			−0.785799
$58$	−1.43293	+	3.75507i	−0.188153	+	0.493064i
$59$	3.32398	−	8.02481i	0.432746	−	1.04474i	−0.545652	−	0.838012i	$-0.683718\pi$
$59$	3.32398	−	8.02481i	0.432746	−	1.04474i	0.978398	−	0.206729i	$-0.0662820\pi$
$60$	−11.3080	−	4.86961i	−1.45986	−	0.628664i
$61$	−11.7209	+	4.85497i	−1.50071	+	0.621615i	−0.973617	−	0.228190i	$-0.926719\pi$
$61$	−11.7209	+	4.85497i	−1.50071	+	0.621615i	−0.527096	+	0.849806i	$0.676719\pi$
$62$	−0.779548	+	0.824728i	−0.0990027	+	0.104741i
$63$	−14.3647	+	14.3647i	−1.80979	+	1.80979i
$64$	−1.34501	−	7.88612i	−0.168126	−	0.985766i
$65$	4.38113	−	8.77775i	0.543413	−	1.08875i
$66$	−0.320445	−	11.3786i	−0.0394441	−	1.40061i
$67$	−3.81672	−	1.58094i	−0.466287	−	0.193142i	0.137155	−	0.990550i	$-0.456204\pi$
$67$	−3.81672	−	1.58094i	−0.466287	−	0.193142i	−0.603441	+	0.797407i	$0.706204\pi$
$68$	−0.886994	+	0.992965i	−0.107564	+	0.120415i
$69$	7.65601	+	3.17122i	0.921675	+	0.381770i
$70$	10.3285	−	9.49370i	1.23449	−	1.13471i
$71$	8.00826	−	8.00826i	0.950406	−	0.950406i	−0.0484209	−	0.998827i	$-0.515419\pi$
$71$	8.00826	−	8.00826i	0.950406	−	0.950406i	0.998827	+	0.0484209i	$0.0154189\pi$
$72$	12.9058	−	1.09268i	1.52097	−	0.128773i
$73$	2.88538			0.337708			0.168854	−	0.985641i	$-0.445993\pi$
$73$	2.88538			0.337708			0.168854	+	0.985641i	$0.445993\pi$
$74$	3.03653	−	7.95735i	0.352989	−	0.925024i
$75$	−6.99655	+	11.8545i	−0.807892	+	1.36884i
$76$	−3.88269	+	1.87081i	−0.445375	+	0.214596i
$77$	11.9831	+	4.96357i	1.36560	+	0.565651i
$78$	0.480862	+	17.0748i	0.0544469	+	1.93334i
$79$		−	9.01288i		−	1.01403i	−0.861938	−	0.507014i	$-0.830749\pi$
$79$		−	9.01288i		−	1.01403i	0.861938	−	0.507014i	$-0.169251\pi$
$80$	−8.93624	+	0.378910i	−0.999102	+	0.0423634i
$81$		−	1.76839i		−	0.196487i
$82$	−3.89440	+	0.109675i	−0.430065	+	0.0121115i
$83$	10.4111	+	4.31243i	1.14277	+	0.473350i	0.872103	−	0.489323i	$-0.162756\pi$
$83$	10.4111	+	4.31243i	1.14277	+	0.473350i	0.270666	+	0.962673i	$0.412756\pi$
$84$	−8.06277	+	23.0576i	−0.879720	+	2.51579i
$85$	0.976125	+	1.12388i	0.105876	+	0.121902i
$86$	4.97265	+	1.89757i	0.536215	+	0.204620i
$87$	−7.82411			−0.838833
$88$	−3.79785	−	7.34579i	−0.404852	−	0.783064i
$89$	0.306754	−	0.306754i	0.0325159	−	0.0325159i	−0.690662	−	0.723178i	$-0.742681\pi$
$89$	0.306754	−	0.306754i	0.0325159	−	0.0325159i	0.723178	+	0.690662i	$0.242681\pi$
$90$	0.609286	−	14.4680i	0.0642244	−	1.52506i
$91$	−17.9819	−	7.44836i	−1.88502	−	0.780800i
$92$	6.01057	−	0.338810i	0.626646	−	0.0353234i
$93$	−2.04103	−	0.845421i	−0.211645	−	0.0876661i
$94$	−9.85753	+	0.277609i	−1.01673	+	0.0286332i
$95$	1.52700	+	4.57025i	0.156667	+	0.468898i
$96$	13.4095	−	7.91956i	1.36861	−	0.808286i
$97$	−4.14919	+	4.14919i	−0.421287	+	0.421287i	−0.885647	−	0.464360i	$-0.846284\pi$
$97$	−4.14919	+	4.14919i	−0.421287	+	0.421287i	0.464360	+	0.885647i	$0.346284\pi$
$98$	−13.0327	−	12.3187i	−1.31650	−	1.24438i
$99$	12.3692	−	5.12348i	1.24315	−	0.514929i
$100$	−0.840766	+	9.96459i	−0.0840766	+	0.996459i
$101$	−7.36053	+	17.7699i	−0.732400	+	1.76817i	−0.0979696	+	0.995189i	$0.531235\pi$
$101$	−7.36053	+	17.7699i	−0.732400	+	1.76817i	−0.634430	+	0.772980i	$0.718765\pi$
$102$	−2.42158	−	0.924076i	−0.239772	−	0.0914972i
$103$	−16.4186			−1.61777			−0.808885	−	0.587967i	$-0.799929\pi$
$103$	−16.4186			−1.61777			−0.808885	+	0.587967i	$0.799929\pi$
$104$	5.69908	+	11.0231i	0.558841	+	1.08091i
$105$	24.4352	+	12.1961i	2.38463	+	1.19021i
$106$	−0.385996	+	1.01152i	−0.0374913	+	0.0982476i
$107$	−2.34483	−	5.66092i	−0.226683	−	0.547262i	0.769086	−	0.639145i	$-0.220712\pi$
$107$	−2.34483	−	5.66092i	−0.226683	−	0.547262i	−0.995770	+	0.0918826i	$0.970712\pi$
$108$	3.77440	+	7.83343i	0.363192	+	0.753772i
$109$	3.17654	−	1.31577i	0.304258	−	0.126028i	−0.225331	−	0.974282i	$-0.572346\pi$
$109$	3.17654	−	1.31577i	0.304258	−	0.126028i	0.529589	+	0.848255i	$0.322346\pi$
$110$	−8.68309	+	3.17559i	−0.827900	+	0.302781i
$111$	16.5801			1.57371
$112$	1.99422	+	17.6328i	0.188436	+	1.66614i
$113$	−6.55196	+	6.55196i	−0.616357	+	0.616357i	−0.944595	−	0.328238i	$-0.893545\pi$
$113$	−6.55196	+	6.55196i	−0.616357	+	0.616357i	0.328238	+	0.944595i	$0.393545\pi$
$114$	−6.09731	−	5.76329i	−0.571065	−	0.539781i
$115$	0.472393	−	6.71410i	0.0440509	−	0.626093i
$116$	−5.12057	+	2.46726i	−0.475433	+	0.229079i
$117$	−18.5612	+	7.68832i	−1.71599	+	0.710786i
$118$	11.2120	−	5.01844i	1.03214	−	0.461985i
$119$	2.08832	−	2.08832i	0.191436	−	0.191436i
$120$	−6.89128	−	15.9900i	−0.629085	−	1.45968i
$121$	1.73379	+	1.73379i	0.157618	+	0.157618i
$122$	−16.7626	−	6.39662i	−1.51762	−	0.579123i
$123$	−2.90235	−	7.00689i	−0.261696	−	0.631790i
$124$	−1.60237	+	0.0903238i	−0.143897	+	0.00811131i
$125$	10.9330	+	2.33861i	0.977879	+	0.209172i
$126$	−28.7181	+	0.808762i	−2.55841	+	0.0720502i
$127$	2.65171	+	2.65171i	0.235301	+	0.235301i	0.814901	−	0.579600i	$-0.196791\pi$
$127$	2.65171	+	2.65171i	0.235301	+	0.235301i	−0.579600	+	0.814901i	$0.696791\pi$
$128$	6.27866	−	9.41161i	0.554960	−	0.831877i
$129$			10.3611i			0.912244i
$130$	13.0299	−	4.76531i	1.14280	−	0.417945i
$131$	2.46318	+	5.94664i	0.215209	+	0.519560i	0.994209	−	0.107463i	$-0.0342729\pi$
$131$	2.46318	+	5.94664i	0.215209	+	0.519560i	−0.779000	+	0.627024i	$0.784273\pi$
$132$	10.7244	−	12.0057i	0.933442	−	1.04496i
$133$	8.83227	−	3.65845i	0.765855	−	0.317228i
$134$	−2.38685	−	5.33258i	−0.206192	−	0.460665i
$135$	9.22061	−	3.08077i	0.793584	−	0.265151i
$136$	−1.87623	+	0.158852i	−0.160885	+	0.0136214i
$137$		−	18.6142i		−	1.59032i	−0.606402	−	0.795159i	$-0.707388\pi$
$137$		−	18.6142i		−	1.59032i	0.606402	−	0.795159i	$-0.292612\pi$
$138$	4.78781	+	10.6967i	0.407565	+	0.910563i
$139$	−4.36358	−	1.80746i	−0.370114	−	0.153306i	0.189871	−	0.981809i	$-0.439193\pi$
$139$	−4.36358	−	1.80746i	−0.370114	−	0.153306i	−0.559985	+	0.828503i	$0.689193\pi$
$140$	19.8378	+	0.276424i	1.67660	+	0.0233621i
$141$	−7.34644	−	17.7359i	−0.618682	−	1.49363i
$142$	16.0102	−	0.450881i	1.34354	−	0.0378371i
$143$	9.07023	+	9.07023i	0.758491	+	0.758491i
$144$	14.3255	+	11.4144i	1.19379	+	0.951200i
$145$	2.01385	+	6.02735i	0.167241	+	0.500544i
$146$	2.96546	+	2.80301i	0.245424	+	0.231979i
$147$	13.3597	−	32.2532i	1.10189	−	2.66020i
$148$	10.8510	−	5.22837i	0.891946	−	0.429769i
$149$	1.30827	−	3.15845i	0.107178	−	0.258750i	−0.861187	−	0.508288i	$-0.830279\pi$
$149$	1.30827	−	3.15845i	0.107178	−	0.258750i	0.968365	+	0.249538i	$0.0802787\pi$
$150$	−18.7068	+	5.38669i	−1.52740	+	0.439821i
$151$	0.725285	+	0.725285i	0.0590229	+	0.0590229i	0.736002	−	0.676979i	$-0.236711\pi$
$151$	0.725285	+	0.725285i	0.0590229	+	0.0590229i	−0.676979	+	0.736002i	$0.736711\pi$
$152$	−5.80785	−	1.84912i	−0.471079	−	0.149983i
$153$		−	3.04848i		−	0.246455i
$154$	7.49383	+	16.7424i	0.603870	+	1.34914i
$155$	−0.125936	+	1.78992i	−0.0101154	+	0.143770i
$156$	−16.0931	+	18.0158i	−1.28848	+	1.44242i
$157$	2.10185	−	5.07432i	0.167746	−	0.404975i	−0.817544	−	0.575866i	$-0.804665\pi$
$157$	2.10185	−	5.07432i	0.167746	−	0.404975i	0.985290	+	0.170892i	$0.0546649\pi$
$158$	8.75559	−	9.26303i	0.696557	−	0.736927i
$159$	−2.10762			−0.167145
$160$	−9.55236	−	8.29171i	−0.755180	−	0.655517i
$161$	−13.3535			−1.05240
$162$	1.71790	−	1.81747i	0.134971	−	0.142794i
$163$	−8.20982	+	19.8203i	−0.643043	+	1.55244i	0.179512	+	0.983756i	$0.442548\pi$
$163$	−8.20982	+	19.8203i	−0.643043	+	1.55244i	−0.822555	+	0.568686i	$0.807452\pi$
$164$	−4.10903	−	3.67051i	−0.320862	−	0.286619i
$165$	−11.8021	−	13.5885i	−0.918792	−	1.05787i
$166$	6.51076	+	14.5460i	0.505333	+	1.12899i
$167$		−	7.63343i		−	0.590692i	−0.955390	−	0.295346i	$-0.904565\pi$
$167$		−	7.63343i		−	0.590692i	0.955390	−	0.295346i	$-0.0954350\pi$
$168$	−30.6859	+	15.8649i	−2.36747	+	1.22400i
$169$	−4.41846	−	4.41846i	−0.339881	−	0.339881i
$170$	−0.0885772	+	2.10333i	−0.00679356	+	0.161318i
$171$	3.77631	−	9.11682i	0.288782	−	0.697181i
$172$	3.26727	+	6.78093i	0.249127	+	0.517041i
$173$	−2.69706	+	6.51129i	−0.205054	+	0.495044i	−0.992632	−	0.121171i	$-0.961335\pi$
$173$	−2.69706	+	6.51129i	−0.205054	+	0.495044i	0.787578	+	0.616215i	$0.211335\pi$
$174$	−8.04127	−	7.60075i	−0.609607	−	0.576212i
$175$	3.10593	−	21.9630i	0.234787	−	1.66024i
$176$	3.23283	−	11.2391i	0.243684	−	0.847180i
$177$	16.9090	+	16.9090i	1.27095	+	1.27095i
$178$	0.613266	−	0.0172709i	0.0459662	−	0.00129451i
$179$	9.26742	+	22.3735i	0.692679	+	1.67228i	0.739311	+	0.673364i	$0.235151\pi$
$179$	9.26742	+	22.3735i	0.692679	+	1.67228i	−0.0466316	+	0.998912i	$0.514849\pi$
$180$	14.6811	−	14.2776i	1.09427	−	1.06419i
$181$	5.86533	+	2.42950i	0.435967	+	0.180583i	0.589862	−	0.807504i	$-0.299182\pi$
$181$	5.86533	+	2.42950i	0.435967	+	0.180583i	−0.153896	+	0.988087i	$0.549182\pi$
$182$	−11.2453	−	25.1237i	−0.833556	−	1.86229i
$183$		−	34.9268i		−	2.58187i
$184$	6.50653	+	5.49078i	0.479668	+	0.404785i
$185$	−4.26754	−	12.7726i	−0.313756	−	0.939057i
$186$	−1.27639	−	2.85165i	−0.0935893	−	0.209093i
$187$	−1.79821	+	0.744844i	−0.131498	+	0.0544684i
$188$	−10.4008	−	9.29081i	−0.758556	−	0.677602i
$189$	−7.38102	−	17.8194i	−0.536890	−	1.29617i
$190$	−2.87040	+	6.18051i	−0.208241	+	0.448381i
$191$		−	16.2533i		−	1.17605i	−0.808844	−	0.588023i	$-0.799907\pi$
$191$		−	16.2533i		−	1.17605i	0.808844	−	0.588023i	$-0.200093\pi$
$192$	21.4752	+	4.88738i	1.54984	+	0.352716i
$193$	10.4804	+	10.4804i	0.754392	+	0.754392i	0.975296	−	0.220903i	$-0.0709006\pi$
$193$	10.4804	+	10.4804i	0.754392	+	0.754392i	−0.220903	+	0.975296i	$0.570901\pi$
$194$	−8.29510	+	0.233607i	−0.595553	+	0.0167720i
$195$	17.7103	+	20.3910i	1.26826	+	1.46023i
$196$	−1.42733	−	25.3213i	−0.101952	−	1.80866i
$197$	5.02932	+	12.1418i	0.358324	+	0.865071i	0.995536	+	0.0943821i	$0.0300875\pi$
$197$	5.02932	+	12.1418i	0.358324	+	0.865071i	−0.637212	+	0.770689i	$0.719912\pi$
$198$	17.6897	+	6.75039i	1.25715	+	0.479729i
$199$	8.85497	+	8.85497i	0.627712	+	0.627712i	0.947492	−	0.319780i	$-0.103609\pi$
$199$	8.85497	+	8.85497i	0.627712	+	0.627712i	−0.319780	+	0.947492i	$0.603609\pi$
$200$	−10.5442	+	9.42439i	−0.745590	+	0.666405i
$201$	8.04215	−	8.04215i	0.567250	−	0.567250i
$202$	−24.8274	+	11.1127i	−1.74685	+	0.781885i
$203$	11.6482	−	4.82484i	0.817543	−	0.338638i
$204$	−1.59110	−	3.30218i	−0.111399	−	0.231199i
$205$	−4.65077	+	4.03935i	−0.324824	+	0.282120i
$206$	−16.8743	−	15.9499i	−1.17569	−	1.11128i
$207$	−9.74657	+	9.74657i	−0.677433	+	0.677433i
$208$	−4.85121	+	16.8655i	−0.336371	+	1.16941i
$209$	−6.30042			−0.435809
$210$	13.2655	+	36.2722i	0.915408	+	2.50302i
$211$	−14.4302	+	5.97720i	−0.993419	+	0.411488i	−0.819380	−	0.573251i	$-0.805682\pi$
$211$	−14.4302	+	5.97720i	−0.993419	+	0.411488i	−0.174039	+	0.984739i	$0.555682\pi$
$212$	−1.37935	+	0.664618i	−0.0947344	+	0.0456462i
$213$	11.9318	+	28.8059i	0.817552	+	1.97375i
$214$	3.08941	−	8.09593i	0.211188	−	0.553427i
$215$	7.98173	−	2.66684i	0.544350	−	0.181877i
$216$	−3.73065	+	11.7175i	−0.253838	+	0.797274i
$217$	3.55993			0.241664
$218$	4.54291	+	1.73358i	0.307685	+	0.117413i
$219$	−3.03987	+	7.33890i	−0.205415	+	0.495917i
$220$	−12.0090	−	5.17149i	−0.809648	−	0.348661i
$221$	2.69841	−	1.11772i	0.181515	−	0.0751858i
$222$	17.0402	+	16.1067i	1.14367	+	1.08101i
$223$	8.01851	−	8.01851i	0.536959	−	0.536959i	−0.385675	−	0.922635i	$-0.626031\pi$
$223$	8.01851	−	8.01851i	0.536959	−	0.536959i	0.922635	+	0.385675i	$0.126031\pi$
$224$	−15.0798	+	20.0595i	−1.00756	+	1.34028i
$225$	−13.7635	−	18.2975i	−0.917568	−	1.21983i
$226$	−13.0987	+	0.368888i	−0.871314	+	0.0245381i
$227$	−10.5301	−	4.36173i	−0.698910	−	0.289498i	0.00479665	−	0.999988i	$-0.498473\pi$
$227$	−10.5301	−	4.36173i	−0.698910	−	0.289498i	−0.703707	+	0.710490i	$0.748473\pi$
$228$	−0.667774	−	11.8465i	−0.0442244	−	0.784553i
$229$	−12.1678	−	5.04008i	−0.804072	−	0.333058i	−0.0574861	−	0.998346i	$-0.518309\pi$
$229$	−12.1678	−	5.04008i	−0.804072	−	0.333058i	−0.746586	+	0.665289i	$0.768309\pi$
$230$	7.00793	−	6.44154i	0.462089	−	0.424742i
$231$	−25.2494	+	25.2494i	−1.66129	+	1.66129i
$232$	−7.65952	−	2.43866i	−0.502872	−	0.160106i
$233$	−8.27906			−0.542379			−0.271190	−	0.962526i	$-0.587417\pi$
$233$	−8.27906			−0.542379			−0.271190	+	0.962526i	$0.587417\pi$
$234$	−26.5453	−	10.1297i	−1.73532	−	0.662197i
$235$	−11.7720	+	10.2244i	−0.767924	+	0.666967i
$236$	16.3983	+	5.73417i	1.06744	+	0.373262i
$237$	22.9241	+	9.49545i	1.48908	+	0.616796i
$238$	4.17499	−	0.117577i	0.270625	−	0.00762136i
$239$			9.48805i			0.613731i	0.951753	+	0.306866i	$0.0992802\pi$
$239$			9.48805i			0.613731i	−0.951753	+	0.306866i	$0.900720\pi$
$240$	8.45096	−	23.1283i	0.545507	−	1.49293i
$241$			27.9481i			1.80029i	0.435585	+	0.900147i	$0.356541\pi$
$241$			27.9481i			1.80029i	−0.435585	+	0.900147i	$0.643459\pi$
$242$	0.0976159	+	3.46621i	0.00627499	+	0.222817i
$243$	16.5480	+	6.85440i	1.06155	+	0.439710i
$244$	−11.0139	−	22.8583i	−0.705090	−	1.46335i
$245$	−28.2851	−	1.99009i	−1.80707	−	0.127142i
$246$	3.82396	−	10.0209i	0.243807	−	0.638907i
$247$	9.45445			0.601572
$248$	−1.73459	−	1.46379i	−0.110146	−	0.0929510i
$249$	−21.9371	+	21.9371i	−1.39021	+	1.39021i
$250$	8.96461	+	13.0244i	0.566972	+	0.823737i
$251$	21.4640	+	8.89067i	1.35479	+	0.561174i	0.937623	−	0.347654i	$-0.113022\pi$
$251$	21.4640	+	8.89067i	1.35479	+	0.561174i	0.417171	+	0.908828i	$0.363022\pi$
$252$	−30.3008	−	27.0671i	−1.90877	−	1.70506i
$253$	8.13062	+	3.36781i	0.511168	+	0.211733i
$254$	0.149296	+	5.30132i	0.00936769	+	0.332634i
$255$	−3.88695	+	1.29870i	−0.243410	+	0.0813276i
$256$	15.5959	−	3.57340i	0.974741	−	0.223338i
$257$	−10.0380	+	10.0380i	−0.626153	+	0.626153i	−0.947098	−	0.320945i	$-0.895999\pi$
$257$	−10.0380	+	10.0380i	−0.626153	+	0.626153i	0.320945	+	0.947098i	$0.395999\pi$
$258$	−10.0653	+	10.6487i	−0.626639	+	0.662957i
$259$	−24.6837	+	10.2243i	−1.53377	+	0.635308i
$260$	18.0208	+	7.76036i	1.11760	+	0.481277i
$261$	4.98028	−	12.0235i	0.308272	−	0.744234i
$262$	−3.24534	+	8.50455i	−0.200498	+	0.525413i
$263$	−0.651445			−0.0401698			−0.0200849	−	0.999798i	$-0.506394\pi$
$263$	−0.651445			−0.0401698			−0.0200849	+	0.999798i	$0.506394\pi$
$264$	22.6850	−	1.92064i	1.39617	−	0.118207i
$265$	0.542480	+	1.62362i	0.0333243	+	0.0997381i
$266$	12.6314	+	4.82015i	0.774482	+	0.295542i
$267$	0.457044	+	1.10340i	0.0279706	+	0.0675271i
$268$	2.72726	−	7.79929i	0.166594	−	0.476418i
$269$	−2.95731	+	1.22496i	−0.180311	+	0.0746871i	−0.471012	−	0.882127i	$-0.656111\pi$
$269$	−2.95731	+	1.22496i	−0.180311	+	0.0746871i	0.290702	+	0.956814i	$0.406111\pi$
$270$	12.4693	+	5.79111i	0.758860	+	0.352436i
$271$	21.6781			1.31685			0.658425	−	0.752646i	$-0.271223\pi$
$271$	21.6781			1.31685			0.658425	+	0.752646i	$0.271223\pi$
$272$	−2.08262	−	1.65941i	−0.126277	−	0.100616i
$273$	37.8894	−	37.8894i	2.29317	−	2.29317i
$274$	18.0828	−	19.1308i	1.09242	−	1.15573i
$275$	−7.43028	+	12.5894i	−0.448063	+	0.759167i
$276$	−5.47064	+	15.6447i	−0.329294	+	0.941701i
$277$	17.4930	−	7.24583i	1.05105	−	0.435360i	0.210784	−	0.977533i	$-0.432398\pi$
$277$	17.4930	−	7.24583i	1.05105	−	0.435360i	0.840267	+	0.542173i	$0.182398\pi$
$278$	−2.72884	−	6.09664i	−0.163665	−	0.365652i
$279$	2.59835	−	2.59835i	0.155559	−	0.155559i
$280$	20.1199	+	19.5556i	1.20239	+	1.16867i
$281$	−3.86198	−	3.86198i	−0.230387	−	0.230387i	0.582467	−	0.812854i	$-0.302087\pi$
$281$	−3.86198	−	3.86198i	−0.230387	−	0.230387i	−0.812854	+	0.582467i	$0.802087\pi$
$282$	9.67923	−	25.3649i	0.576390	−	1.51046i
$283$	−4.15227	−	10.0245i	−0.246827	−	0.595892i	0.751105	−	0.660183i	$-0.229521\pi$
$283$	−4.15227	−	10.0245i	−0.246827	−	0.595892i	−0.997931	+	0.0642911i	$0.979521\pi$
$284$	16.8925	+	15.0897i	1.00239	+	0.895411i
$285$	−13.2331	−	0.931059i	−0.783861	−	0.0551512i
$286$	0.510672	+	18.1333i	0.0301966	+	1.07224i
$287$	8.64179	+	8.64179i	0.510109	+	0.510109i
$288$	3.63456	+	25.6477i	0.214169	+	1.51131i
$289$		−	16.5568i		−	0.973930i
$290$	−3.78555	+	8.15100i	−0.222295	+	0.478643i
$291$	−6.18202	−	14.9247i	−0.362397	−	0.874903i
$292$	0.324776	+	5.76162i	0.0190061	+	0.337173i
$293$	−22.5324	+	9.33321i	−1.31635	+	0.545252i	−0.926732	−	0.375723i	$-0.877395\pi$
$293$	−22.5324	+	9.33321i	−1.31635	+	0.545252i	−0.389623	+	0.920975i	$0.627395\pi$
$294$	45.0629	−	20.1700i	2.62812	−	1.17634i
$295$	8.67373	−	17.3781i	0.505004	−	1.01179i
$296$	16.2313	+	5.16775i	0.943424	+	0.300370i
$297$			12.7113i			0.737583i
$298$	4.41286	−	1.97518i	0.255630	−	0.114419i
$299$	−12.2009	−	5.05376i	−0.705594	−	0.292266i
$300$	−24.4589	−	12.6366i	−1.41214	−	0.729574i
$301$	−6.38931	−	15.4252i	−0.368274	−	0.889091i
$302$	0.0408349	+	1.45000i	0.00234979	+	0.0834379i
$303$	−37.4427	−	37.4427i	−2.15102	−	2.15102i
$304$	−4.17271	−	7.54249i	−0.239321	−	0.432591i
$305$	−26.9061	+	8.98981i	−1.54064	+	0.514755i
$306$	2.96146	−	3.13309i	0.169295	−	0.179107i
$307$	−12.7870	+	30.8706i	−0.729793	+	1.76188i	−0.0865065	+	0.996251i	$0.527570\pi$
$307$	−12.7870	+	30.8706i	−0.729793	+	1.76188i	−0.643287	+	0.765625i	$0.722430\pi$
$308$	−8.56259	+	24.4869i	−0.487899	+	1.39527i
$309$	17.2977	−	41.7603i	0.984030	−	2.37566i
$310$	−1.86825	+	1.71726i	−0.106110	+	0.0975337i
$311$	−8.56825	−	8.56825i	−0.485861	−	0.485861i	0.421137	−	0.906997i	$-0.361631\pi$
$311$	−8.56825	−	8.56825i	−0.485861	−	0.485861i	−0.906997	+	0.421137i	$0.861631\pi$
$312$	−34.0413	+	2.88212i	−1.92721	+	0.163168i
$313$		−	29.5819i		−	1.67207i	−0.548678	−	0.836034i	$-0.684869\pi$
$313$		−	29.5819i		−	1.67207i	0.548678	−	0.836034i	$-0.315131\pi$
$314$	7.08965	−	3.17330i	0.400092	−	0.179080i
$315$	−34.2957	+	29.7869i	−1.93234	+	1.67830i
$316$	17.9972	−	1.01448i	1.01242	−	0.0570691i
$317$	4.42661	−	10.6868i	0.248623	−	0.600229i	−0.749465	−	0.662044i	$-0.769689\pi$
$317$	4.42661	−	10.6868i	0.248623	−	0.600229i	0.998088	+	0.0618154i	$0.0196890\pi$
$318$	−2.16612	−	2.04745i	−0.121470	−	0.114815i
$319$	−8.30914			−0.465223
$320$	−1.76247	−	17.8015i	−0.0985253	−	0.995135i
$321$	16.8688			0.941525
$322$	−13.7241	−	12.9723i	−0.764816	−	0.722919i
$323$	−0.548995	+	1.32539i	−0.0305469	+	0.0737467i
$324$	3.53117	−	0.199048i	0.196176	−	0.0110582i
$325$	11.1499	−	18.8917i	0.618486	−	1.04792i
$326$	−27.6921	+	12.3949i	−1.53372	+	0.686490i
$327$			9.46568i			0.523453i
$328$	−0.657352	−	7.76411i	−0.0362962	−	0.428701i
$329$	21.8741	+	21.8741i	1.20596	+	1.20596i
$330$	1.07097	−	25.4309i	0.0589547	−	1.39992i
$331$	1.61458	−	3.89795i	0.0887455	−	0.214251i	−0.873275	−	0.487228i	$-0.838008\pi$
$331$	1.61458	−	3.89795i	0.0887455	−	0.214251i	0.962021	+	0.272977i	$0.0880082\pi$
$332$	−7.43932	+	21.2746i	−0.408285	+	1.16760i
$333$	−10.5537	+	25.4789i	−0.578340	+	1.39624i
$334$	7.41551	−	7.84529i	0.405759	−	0.429275i
$335$	−8.26529	−	4.12536i	−0.451581	−	0.225392i
$336$	−46.9496	−	13.5046i	−2.56131	−	0.736738i
$337$	−10.5819	−	10.5819i	−0.576433	−	0.576433i	0.357485	−	0.933919i	$-0.383634\pi$
$337$	−10.5819	−	10.5819i	−0.576433	−	0.576433i	−0.933919	+	0.357485i	$0.883634\pi$
$338$	−0.248768	−	8.83341i	−0.0135312	−	0.480474i
$339$	−9.76199	−	23.5675i	−0.530198	−	1.28001i
$340$	−2.13432	+	2.07566i	−0.115750	+	0.112568i
$341$	−2.16755	−	0.897830i	−0.117380	−	0.0486202i
$342$	12.7377	−	5.70135i	0.688775	−	0.308294i
$343$			25.2015i			1.36075i
$344$	−3.22940	+	10.1431i	−0.174117	+	0.546881i
$345$	16.5795	+	8.27511i	0.892608	+	0.445517i
$346$	−9.09733	+	4.07194i	−0.489075	+	0.218909i
$347$	−6.77058	+	2.80447i	−0.363464	+	0.150552i	−0.556939	−	0.830554i	$-0.688024\pi$
$347$	−6.77058	+	2.80447i	−0.363464	+	0.150552i	0.193475	+	0.981105i	$0.438024\pi$
$348$	−0.880676	−	15.6234i	−0.0472092	−	0.837503i
$349$	8.58346	+	20.7223i	0.459462	+	1.10924i	0.968616	+	0.248564i	$0.0799585\pi$
$349$	8.58346	+	20.7223i	0.459462	+	1.10924i	−0.509154	+	0.860676i	$0.670041\pi$
$350$	24.5281	−	19.5553i	1.31108	−	1.04527i
$351$		−	19.0746i		−	1.01813i
$352$	14.2408	−	8.41050i	0.759038	−	0.448281i
$353$	14.3335	+	14.3335i	0.762896	+	0.762896i	0.976845	−	0.213949i	$-0.0686325\pi$
$353$	14.3335	+	14.3335i	0.762896	+	0.762896i	−0.213949	+	0.976845i	$0.568633\pi$
$354$	0.952006	+	33.8045i	0.0505986	+	1.79669i
$355$	19.1197	−	16.6061i	1.01477	−	0.881358i
$356$	0.647064	+	0.578008i	0.0342943	+	0.0306344i
$357$	3.11147	+	7.51174i	0.164676	+	0.397564i
$358$	−12.2102	+	31.9974i	−0.645329	+	1.69111i
$359$	6.59177	+	6.59177i	0.347900	+	0.347900i	0.859327	−	0.511427i	$-0.170883\pi$
$359$	6.59177	+	6.59177i	0.347900	+	0.347900i	−0.511427	+	0.859327i	$0.670883\pi$
$360$	28.9586	−	0.411859i	1.52625	−	0.0217069i
$361$	10.1514	−	10.1514i	0.534283	−	0.534283i
$362$	3.66798	+	8.19482i	0.192785	+	0.430710i
$363$	−6.23649	+	2.58324i	−0.327331	+	0.135585i
$364$	12.8491	−	36.7452i	0.673474	−	1.92597i
$365$	6.43600	+	0.452826i	0.336876	+	0.0237020i
$366$	33.9298	−	35.8962i	1.77354	−	1.87633i
$367$	−9.50155	+	9.50155i	−0.495977	+	0.495977i	−0.910183	−	0.414206i	$-0.864059\pi$
$367$	−9.50155	+	9.50155i	−0.495977	+	0.495977i	0.414206	+	0.910183i	$0.364059\pi$
$368$	1.35309	+	11.9640i	0.0705347	+	0.623665i
$369$	12.6151			0.656714
$370$	8.02195	−	17.2728i	0.417041	−	0.897968i
$371$	3.13773	−	1.29969i	0.162903	−	0.0674766i
$372$	1.45843	−	4.17074i	0.0756159	−	0.216243i
$373$	−9.86119	−	23.8070i	−0.510593	−	1.23268i	−0.943539	−	0.331261i	$-0.892526\pi$
$373$	−9.86119	−	23.8070i	−0.510593	−	1.23268i	0.432946	−	0.901420i	$-0.357474\pi$
$374$	−2.57170	−	0.981361i	−0.132980	−	0.0507450i
$375$	−17.4666	+	25.3440i	−0.901971	+	1.30876i
$376$	−1.66389	−	19.6526i	−0.0858087	−	1.01350i
$377$	12.4687			0.642173
$378$	9.72478	−	25.4842i	0.500189	−	1.31077i
$379$	3.32182	−	8.01958i	0.170630	−	0.411938i	−0.815312	−	0.579021i	$-0.803435\pi$
$379$	3.32182	−	8.01958i	0.170630	−	0.411938i	0.985943	+	0.167083i	$0.0534348\pi$
$380$	−8.95414	+	3.56359i	−0.459338	+	0.182808i
$381$	−9.53826	+	3.95088i	−0.488660	+	0.202409i
$382$	15.7893	−	16.7044i	0.807850	−	0.854670i
$383$	−7.43728	+	7.43728i	−0.380027	+	0.380027i	−0.871112	−	0.491085i	$-0.836601\pi$
$383$	−7.43728	+	7.43728i	−0.380027	+	0.380027i	0.491085	+	0.871112i	$0.336601\pi$
$384$	17.3234	+	25.8852i	0.884030	+	1.32095i
$385$	25.9500	+	12.9521i	1.32253	+	0.660101i
$386$	0.590064	+	20.9524i	0.0300335	+	1.06645i
$387$	−15.9221	−	6.59515i	−0.809366	−	0.335250i
$388$	−8.75226	−	7.81820i	−0.444329	−	0.396909i
$389$	−5.21013	−	2.15810i	−0.264164	−	0.109420i	0.246671	−	0.969099i	$-0.420663\pi$
$389$	−5.21013	−	2.15810i	−0.264164	−	0.109420i	−0.510834	+	0.859679i	$0.670663\pi$
$390$	−1.60710	+	38.1617i	−0.0813785	+	1.93239i
$391$	1.41694	−	1.41694i	0.0716578	−	0.0716578i
$392$	23.1315	−	27.4107i	1.16832	−	1.38445i
$393$	−17.7202			−0.893866
$394$	−6.62632	+	17.3646i	−0.333829	+	0.874815i
$395$	1.41447	−	20.1037i	0.0711695	−	1.01153i
$396$	11.6230	+	24.1224i	0.584077	+	1.21220i
$397$	−19.4832	−	8.07023i	−0.977836	−	0.405033i	−0.164213	−	0.986425i	$-0.552508\pi$
$397$	−19.4832	−	8.07023i	−0.977836	−	0.405033i	−0.813624	+	0.581392i	$0.802508\pi$
$398$	0.498552	+	17.7029i	0.0249901	+	0.887367i
$399$			26.3190i			1.31760i
$400$	−19.9922	−	0.557259i	−0.999612	−	0.0278630i
$401$		−	23.8052i		−	1.18877i	−0.804180	−	0.594386i	$-0.797395\pi$
$401$		−	23.8052i		−	1.18877i	0.804180	−	0.594386i	$-0.202605\pi$
$402$	16.0779	−	0.452789i	0.801895	−	0.0225830i
$403$	3.25264	+	1.34729i	0.162026	+	0.0671133i
$404$	−36.3119	−	12.6976i	−1.80659	−	0.631727i
$405$	0.277527	−	3.94448i	0.0137904	−	0.196003i
$406$	16.6586	+	6.35692i	0.826752	+	0.315489i
$407$	17.6079			0.872790
$408$	1.57265	−	4.93950i	0.0778579	−	0.244542i
$409$	16.8361	−	16.8361i	0.832494	−	0.832494i	−0.155364	−	0.987857i	$-0.549655\pi$
$409$	16.8361	−	16.8361i	0.832494	−	0.832494i	0.987857	+	0.155364i	$0.0496550\pi$
$410$	−8.70388	−	0.366545i	−0.429854	−	0.0181024i
$411$	47.3447	+	19.6108i	2.33534	+	0.967331i
$412$	−1.84806	−	32.7851i	−0.0910475	−	1.61521i
$413$	−35.6005	−	14.7462i	−1.75178	−	0.725613i
$414$	−19.4854	+	0.548750i	−0.957656	+	0.0269696i
$415$	22.5458	+	11.2530i	1.10673	+	0.552388i
$416$	−21.3699	+	12.6208i	−1.04774	+	0.618788i
$417$	9.19444	−	9.19444i	0.450254	−	0.450254i
$418$	−6.47529	−	6.12056i	−0.316717	−	0.299367i
$419$	20.8534	−	8.63775i	1.01875	−	0.421982i	0.190113	−	0.981762i	$-0.439115\pi$
$419$	20.8534	−	8.63775i	1.01875	−	0.421982i	0.828641	+	0.559781i	$0.189115\pi$
$420$	−21.6030	+	50.1658i	−1.05412	+	2.44784i
$421$	−6.63429	+	16.0166i	−0.323336	+	0.780601i	0.675720	+	0.737158i	$0.263833\pi$
$421$	−6.63429	+	16.0166i	−0.323336	+	0.780601i	−0.999056	+	0.0434432i	$0.986167\pi$
$422$	−20.6373	−	7.87520i	−1.00461	−	0.383359i
$423$	31.9313			1.55255
$424$	−2.06328	−	0.656913i	−0.100202	−	0.0319025i
$425$	2.00092	+	2.66006i	0.0970589	+	0.129032i
$426$	−15.7206	+	41.1965i	−0.761666	+	1.99598i
$427$	21.5381	+	51.9976i	1.04230	+	2.51634i
$428$	11.0400	−	5.31942i	0.533637	−	0.257124i
$429$	−32.6258	+	13.5140i	−1.57519	+	0.652464i
$430$	10.7940	+	5.01302i	0.520532	+	0.241749i
$431$	−18.0525			−0.869556			−0.434778	−	0.900538i	$-0.643173\pi$
$431$	−18.0525			−0.869556			−0.434778	+	0.900538i	$0.643173\pi$
$432$	−15.2172	+	8.41856i	−0.732137	+	0.405038i
$433$	19.0227	−	19.0227i	0.914175	−	0.914175i	−0.0824225	−	0.996597i	$-0.526266\pi$
$433$	19.0227	−	19.0227i	0.914175	−	0.914175i	0.996597	+	0.0824225i	$0.0262657\pi$
$434$	3.65874	+	3.45831i	0.175625	+	0.166004i
$435$	−17.4521	−	1.22790i	−0.836764	−	0.0588734i
$436$	2.98491	+	6.19492i	0.142951	+	0.296683i
$437$	5.99276	−	2.48228i	0.286672	−	0.118744i
$438$	−10.2536	+	4.58950i	−0.489938	+	0.219295i
$439$	−0.238822	+	0.238822i	−0.0113984	+	0.0113984i	−0.712783	−	0.701385i	$-0.752566\pi$
$439$	−0.238822	+	0.238822i	−0.0113984	+	0.0113984i	0.701385	+	0.712783i	$0.252566\pi$
$440$	−7.31848	−	16.9812i	−0.348895	−	0.809548i
$441$	41.0603	+	41.0603i	1.95525	+	1.95525i
$442$	3.85911	+	1.47264i	0.183559	+	0.0700462i
$443$	2.42320	+	5.85012i	0.115130	+	0.277948i	0.970932	−	0.239355i	$-0.0769361\pi$
$443$	2.42320	+	5.85012i	0.115130	+	0.277948i	−0.855802	+	0.517303i	$0.826936\pi$
$444$	1.86624	+	33.1076i	0.0885677	+	1.57122i
$445$	0.732374	−	0.636091i	0.0347178	−	0.0301536i
$446$	16.0307	−	0.451458i	0.759074	−	0.0213771i
$447$	6.65511	+	6.65511i	0.314776	+	0.314776i
$448$	−34.9852	+	5.96685i	−1.65290	+	0.281907i
$449$			7.03126i			0.331825i	0.986140	+	0.165913i	$0.0530570\pi$
$449$			7.03126i			0.331825i	−0.986140	+	0.165913i	$0.946943\pi$
$450$	3.62962	−	32.1759i	0.171102	−	1.51679i
$451$	−3.08227	−	7.44126i	−0.145139	−	0.350395i
$452$	−13.8206	−	12.3457i	−0.650068	−	0.580691i
$453$	−2.60886	+	1.08063i	−0.122575	+	0.0507723i
$454$	−6.58519	−	14.7123i	−0.309058	−	0.690484i
$455$	−38.9407	−	19.4360i	−1.82557	−	0.911174i
$456$	10.8220	−	12.8240i	0.506787	−	0.600539i
$457$			23.7619i			1.11153i	0.831339	+	0.555766i	$0.187575\pi$
$457$			23.7619i			1.11153i	−0.831339	+	0.555766i	$0.812425\pi$
$458$	−7.60934	−	17.0004i	−0.355561	−	0.794378i
$459$	2.67401	+	1.10761i	0.124812	+	0.0516989i
$460$	13.4601	+	0.187555i	0.627580	+	0.00874481i
$461$	−9.37725	−	22.6387i	−0.436742	−	1.05439i	−0.977067	−	0.212933i	$-0.931699\pi$
$461$	−9.37725	−	22.6387i	−0.436742	−	1.05439i	0.540325	−	0.841457i	$-0.318301\pi$
$462$	−50.4788	+	1.42159i	−2.34849	+	0.0661384i
$463$	17.8414	+	17.8414i	0.829158	+	0.829158i	0.987400	−	0.158242i	$-0.0505826\pi$
$463$	17.8414	+	17.8414i	0.829158	+	0.829158i	−0.158242	+	0.987400i	$0.550583\pi$
$464$	−5.50307	−	9.94720i	−0.255473	−	0.461787i
$465$	−4.41994	−	2.20607i	−0.204970	−	0.102304i
$466$	−8.50884	−	8.04272i	−0.394165	−	0.372572i
$467$	6.18853	−	14.9404i	0.286371	−	0.691361i	−0.713586	−	0.700567i	$-0.752930\pi$
$467$	6.18853	−	14.9404i	0.286371	−	0.691361i	0.999958	+	0.00920594i	$0.00293038\pi$
$468$	−17.4415	−	36.1983i	−0.806234	−	1.67327i
$469$	−7.01351	+	16.9321i	−0.323854	+	0.781852i
$470$	−22.0313	−	0.927801i	−1.01623	−	0.0427963i
$471$	10.6920	+	10.6920i	0.492662	+	0.492662i
$472$	11.2830	+	21.8235i	0.519341	+	1.00451i
$473$			11.0034i			0.505937i
$474$	14.3359	+	32.0286i	0.658471	+	1.47112i
$475$	2.68882	+	10.4338i	0.123371	+	0.478737i
$476$	4.40509	+	3.93497i	0.201907	+	0.180359i
$477$	1.34156	−	3.23882i	0.0614260	−	0.148295i
$478$	−9.21719	+	9.75139i	−0.421585	+	0.446018i
$479$	31.7717			1.45168			0.725842	−	0.687861i	$-0.241450\pi$
$479$	31.7717			1.45168			0.725842	+	0.687861i	$0.241450\pi$
$480$	31.1536	−	15.5605i	1.42196	−	0.710238i
$481$	−26.4225			−1.20476
$482$	−27.1502	+	28.7238i	−1.23666	+	1.30833i
$483$	14.0685	−	33.9644i	0.640139	−	1.54543i
$484$	−3.26694	+	3.65725i	−0.148497	+	0.166238i
$485$	−9.90616	+	8.60383i	−0.449816	+	0.390680i
$486$	10.3485	+	23.1202i	0.469420	+	1.04876i
$487$		−	34.0481i		−	1.54287i	−0.636309	−	0.771434i	$-0.719540\pi$
$487$		−	34.0481i		−	1.54287i	0.636309	−	0.771434i	$-0.280460\pi$
$488$	10.8862	−	34.1921i	0.492794	−	1.54780i
$489$	−41.7630	−	41.7630i	−1.88859	−	1.88859i
$490$	−27.1369	−	29.5230i	−1.22592	−	1.33371i
$491$	4.72187	−	11.3996i	0.213095	−	0.514457i	−0.780801	−	0.624780i	$-0.785189\pi$
$491$	4.72187	−	11.3996i	0.213095	−	0.514457i	0.993896	+	0.110323i	$0.0351886\pi$
$492$	13.6649	−	6.58419i	0.616061	−	0.296838i
$493$	−0.724027	+	1.74795i	−0.0326085	+	0.0787239i
$494$	9.71686	+	9.18455i	0.437182	+	0.413233i
$495$	28.3942	−	9.48700i	1.27622	−	0.426409i
$496$	−0.360722	−	3.18949i	−0.0161969	−	0.143212i
$497$	−35.5271	−	35.5271i	−1.59361	−	1.59361i
$498$	−43.8568	+	1.23510i	−1.96527	+	0.0553462i
$499$	−15.2834	−	36.8975i	−0.684181	−	1.65176i	−0.756188	−	0.654354i	$-0.772940\pi$
$499$	−15.2834	−	36.8975i	−0.684181	−	1.65176i	0.0720071	−	0.997404i	$-0.477060\pi$
$500$	−3.43920	+	22.0946i	−0.153806	+	0.988101i
$501$	19.4154	+	8.04214i	0.867418	+	0.359296i
$502$	13.4228	+	29.9887i	0.599090	+	1.33846i
$503$			22.5806i			1.00682i	0.864048	+	0.503409i	$0.167921\pi$
$503$			22.5806i			1.00682i	−0.864048	+	0.503409i	$0.832079\pi$
$504$	−4.84744	−	57.2541i	−0.215922	−	2.55030i
$505$	−19.2068	+	38.4815i	−0.854693	+	1.71241i
$506$	5.08461	+	11.3598i	0.226039	+	0.505005i
$507$	15.8933	−	6.58321i	0.705845	−	0.292371i
$508$	−4.99654	+	5.59349i	−0.221686	+	0.248171i
$509$	1.29098	+	3.11671i	0.0572218	+	0.138146i	0.949905	−	0.312540i	$-0.101180\pi$
$509$	1.29098	+	3.11671i	0.0572218	+	0.138146i	−0.892683	+	0.450685i	$0.851180\pi$
$510$	−5.25645	−	2.44124i	−0.232759	−	0.108100i
$511$		−	12.8004i		−	0.566257i
$512$	19.5001	+	11.4781i	0.861791	+	0.507263i
$513$	6.62487	+	6.62487i	0.292495	+	0.292495i
$514$	−20.0680	+	0.565158i	−0.885163	+	0.0249281i
$515$	−36.6225	−	2.57670i	−1.61378	−	0.113543i
$516$	−20.6893	+	1.16624i	−0.910798	+	0.0513407i
$517$	−7.80186	−	18.8354i	−0.343125	−	0.828378i
$518$	−35.3012	−	13.4709i	−1.55105	−	0.591879i
$519$	−13.7198	−	13.7198i	−0.602234	−	0.602234i
$520$	10.9821	+	25.4821i	0.481599	+	1.11746i
$521$	−19.8491	+	19.8491i	−0.869606	+	0.869606i	−0.992429	−	0.122823i	$-0.960805\pi$
$521$	−19.8491	+	19.8491i	−0.869606	+	0.869606i	0.122823	+	0.992429i	$0.460805\pi$
$522$	16.7987	−	7.51907i	0.735261	−	0.329101i
$523$	15.2840	−	6.33082i	0.668321	−	0.276828i	−0.0226143	−	0.999744i	$-0.507199\pi$
$523$	15.2840	−	6.33082i	0.668321	−	0.276828i	0.690935	+	0.722917i	$0.257199\pi$
$524$	−11.5972	+	5.58790i	−0.506625	+	0.244108i
$525$	52.5901	+	31.0388i	2.29522	+	1.35464i
$526$	−0.669526	−	0.632848i	−0.0291927	−	0.0275935i
$527$	−0.377745	+	0.377745i	−0.0164548	+	0.0164548i
$528$	25.1805	+	20.0635i	1.09584	+	0.873152i
$529$	13.9395			0.606067
$530$	−1.01973	+	2.19567i	−0.0442943	+	0.0953740i
$531$	−36.7474	+	15.2213i	−1.59470	+	0.660547i
$532$	8.29945	+	17.2248i	0.359827	+	0.746788i
$533$	4.62528	+	11.1664i	0.200343	+	0.483671i
$534$	−0.602173	+	1.57802i	−0.0260586	+	0.0682877i
$535$	−4.34186	−	12.9950i	−0.187715	−	0.561822i
$536$	10.3796	−	5.36636i	0.448330	−	0.231791i
$537$	−66.6702			−2.87703
$538$	−4.22938	−	1.61393i	−0.182342	−	0.0695816i
$539$	14.1879	−	34.2526i	0.611116	−	1.47536i
$540$	7.18964	+	18.0652i	0.309393	+	0.777404i
$541$	33.7795	−	13.9919i	1.45229	−	0.601560i	0.489550	−	0.871975i	$-0.337161\pi$
$541$	33.7795	−	13.9919i	1.45229	−	0.601560i	0.962744	+	0.270416i	$0.0871612\pi$
$542$	22.2798	+	21.0592i	0.956998	+	0.904572i
$543$	−12.3588	+	12.3588i	−0.530365	+	0.530365i
$544$	−0.528387	−	3.72863i	−0.0226544	−	0.159864i
$545$	7.29195	−	2.43637i	0.312353	−	0.104363i
$546$	75.7489	−	2.13325i	3.24175	−	0.0912946i
$547$	3.88254	+	1.60820i	0.166005	+	0.0687617i	0.464139	−	0.885763i	$-0.346364\pi$
$547$	3.88254	+	1.60820i	0.166005	+	0.0687617i	−0.298133	+	0.954524i	$0.596364\pi$
$548$	37.1694	−	2.09520i	1.58780	−	0.0895024i
$549$	53.6728	+	22.2320i	2.29070	+	0.948839i
$550$	−19.8665	+	5.72062i	−0.847109	+	0.243928i
$551$	−4.33056	+	4.33056i	−0.184488	+	0.184488i
$552$	−20.8206	+	10.7644i	−0.886182	+	0.458165i
$553$	−39.9838			−1.70029
$554$	25.0175	+	9.54666i	1.06289	+	0.405599i
$555$	36.9827	+	2.60204i	1.56983	+	0.110451i
$556$	3.11802	−	8.91678i	0.132233	−	0.378156i
$557$	42.1879	+	17.4748i	1.78756	+	0.740431i	0.990667	+	0.136308i	$0.0435236\pi$
$557$	42.1879	+	17.4748i	1.78756	+	0.740431i	0.796891	+	0.604123i	$0.206476\pi$
$558$	5.19464	−	0.146292i	0.219907	−	0.00619304i
$559$		−	16.5118i		−	0.698373i
$560$	1.68096	+	39.6438i	0.0710334	+	1.67526i
$561$		−	5.35843i		−	0.226233i
$562$	−0.217437	−	7.72090i	−0.00917203	−	0.325687i
$563$	20.6149	+	8.53897i	0.868815	+	0.359875i	0.772149	−	0.635442i	$-0.219182\pi$
$563$	20.6149	+	8.53897i	0.868815	+	0.359875i	0.0966661	+	0.995317i	$0.469182\pi$
$564$	34.5886	−	16.6659i	1.45644	−	0.701762i
$565$	−15.6428	+	13.5862i	−0.658096	+	0.571578i
$566$	5.47078	−	14.3364i	0.229954	−	0.602604i
$567$	−7.84509			−0.329463
$568$	2.70243	+	31.9189i	0.113391	+	1.33929i
$569$	24.5443	−	24.5443i	1.02895	−	1.02895i	0.0293804	−	0.999568i	$-0.490647\pi$
$569$	24.5443	−	24.5443i	1.02895	−	1.02895i	0.999568	−	0.0293804i	$-0.00935341\pi$
$570$	−12.6959	−	13.8122i	−0.531772	−	0.578530i
$571$	−9.53471	−	3.94941i	−0.399015	−	0.165278i	0.174147	−	0.984720i	$-0.444283\pi$
$571$	−9.53471	−	3.94941i	−0.399015	−	0.165278i	−0.573162	+	0.819442i	$0.694283\pi$
$572$	−17.0908	+	19.1327i	−0.714601	+	0.799976i
$573$	41.3398	+	17.1235i	1.72700	+	0.715345i
$574$	0.486549	+	17.2767i	0.0203082	+	0.721117i
$575$	2.10740	−	14.9020i	0.0878845	−	0.621457i
$576$	−21.1801	+	29.8904i	−0.882506	+	1.24543i
$577$	16.7587	−	16.7587i	0.697672	−	0.697672i	−0.266236	−	0.963908i	$-0.585780\pi$
$577$	16.7587	−	16.7587i	0.697672	−	0.697672i	0.963908	+	0.266236i	$0.0857799\pi$
$578$	16.0842	−	17.0163i	0.669013	−	0.707787i
$579$	−37.6980	+	15.6150i	−1.56668	+	0.648939i
$580$	−11.8089	+	4.69974i	−0.490339	+	0.195146i
$581$	19.1312	−	46.1868i	0.793696	−	1.91615i
$582$	8.14506	−	21.3445i	0.337624	−	0.884758i
$583$	−2.23827			−0.0926998
$584$	−5.26335	+	6.23703i	−0.217799	+	0.258090i
$585$	−42.6085	+	14.2362i	−1.76164	+	0.588596i
$586$	−32.2245	−	12.2969i	−1.33118	−	0.507979i
$587$	−11.3133	−	27.3126i	−0.466948	−	1.12731i	−0.965488	−	0.260446i	$-0.916130\pi$
$587$	−11.3133	−	27.3126i	−0.466948	−	1.12731i	0.498540	−	0.866866i	$-0.333870\pi$
$588$	65.9079	+	23.0467i	2.71800	+	0.950429i
$589$	−1.59762	+	0.661755i	−0.0658287	+	0.0272671i
$590$	25.7965	−	9.43432i	1.06202	−	0.388405i
$591$	−36.1811			−1.48829
$592$	11.6615	+	21.0791i	0.479286	+	0.866346i
$593$	3.53725	−	3.53725i	0.145258	−	0.145258i	−0.630738	−	0.775996i	$-0.717248\pi$
$593$	3.53725	−	3.53725i	0.145258	−	0.145258i	0.775996	+	0.630738i	$0.217248\pi$
$594$	−12.3484	+	13.0641i	−0.506661	+	0.536025i
$595$	4.98586	−	4.33038i	0.204400	−	0.177528i
$596$	6.45414	+	2.25688i	0.264372	+	0.0924455i
$597$	−31.8515	+	13.1933i	−1.30360	+	0.539967i
$598$	−7.63000	−	17.0466i	−0.312014	−	0.697086i
$599$	6.77204	−	6.77204i	0.276698	−	0.276698i	−0.555091	−	0.831789i	$-0.687317\pi$
$599$	6.77204	−	6.77204i	0.276698	−	0.276698i	0.831789	+	0.555091i	$0.187317\pi$
$600$	−12.8619	−	36.7480i	−0.525086	−	1.50023i
$601$	−12.4844	−	12.4844i	−0.509251	−	0.509251i	0.405046	−	0.914296i	$-0.367256\pi$
$601$	−12.4844	−	12.4844i	−0.509251	−	0.509251i	−0.914296	+	0.405046i	$0.867256\pi$
$602$	8.41817	−	22.0602i	0.343099	−	0.899106i
$603$	7.23947	+	17.4776i	0.294814	+	0.711744i
$604$	−1.36663	+	1.52991i	−0.0556075	+	0.0622511i
$605$	3.59522	+	4.13942i	0.146167	+	0.168291i
$606$	−2.10809	−	74.8556i	−0.0856354	−	3.04080i
$607$	3.74382	+	3.74382i	0.151957	+	0.151957i	0.778991	−	0.627034i	$-0.215732\pi$
$607$	3.74382	+	3.74382i	0.151957	+	0.151957i	−0.627034	+	0.778991i	$0.715732\pi$
$608$	3.03865	−	11.8054i	0.123233	−	0.478773i
$609$			34.7101i			1.40652i
$610$	−36.3861	−	16.8987i	−1.47323	−	0.684208i
$611$	11.7075	+	28.2644i	0.473635	+	1.14346i
$612$	6.08730	−	0.343135i	0.246065	−	0.0138704i
$613$	29.2416	−	12.1122i	1.18106	−	0.489209i	0.296223	−	0.955119i	$-0.404273\pi$
$613$	29.2416	−	12.1122i	1.18106	−	0.489209i	0.884832	+	0.465910i	$0.154273\pi$
$614$	−43.1312	+	19.3054i	−1.74063	+	0.779103i
$615$	−5.37420	−	16.0847i	−0.216709	−	0.648600i
$616$	−32.5881	+	16.8484i	−1.31301	+	0.678842i
$617$			32.4983i			1.30833i	0.756351	+	0.654166i	$0.226980\pi$
$617$			32.4983i			1.30833i	−0.756351	+	0.654166i	$0.773020\pi$
$618$	58.3459	−	26.1154i	2.34702	−	1.05052i
$619$	−14.2532	−	5.90389i	−0.572886	−	0.237297i	0.0773824	−	0.997001i	$-0.475344\pi$
$619$	−14.2532	−	5.90389i	−0.572886	−	0.237297i	−0.650269	+	0.759704i	$0.725344\pi$
$620$	−3.58834	−	0.0500007i	−0.144111	−	0.00200807i
$621$	−5.00807	−	12.0905i	−0.200967	−	0.485177i
$622$	−0.482409	−	17.1297i	−0.0193428	−	0.686838i
$623$	−1.36085	−	1.36085i	−0.0545215	−	0.0545215i
$624$	−37.7860	−	30.1074i	−1.51265	−	1.20526i
$625$	24.0197	+	6.93221i	0.960787	+	0.277288i
$626$	28.7374	−	30.4029i	1.14858	−	1.21515i
$627$	6.63776	−	16.0250i	0.265087	−	0.639976i
$628$	10.3691	+	3.62588i	0.413773	+	0.144688i
$629$	1.53428	−	3.70409i	0.0611759	−	0.147692i
$630$	−64.1842	−	2.70298i	−2.55716	−	0.107689i
$631$	18.0320	+	18.0320i	0.717843	+	0.717843i	0.968163	−	0.250320i	$-0.0805359\pi$
$631$	18.0320	+	18.0320i	0.717843	+	0.717843i	−0.250320	+	0.968163i	$0.580536\pi$
$632$	19.4822	+	16.4408i	0.774961	+	0.653979i
$633$		−	43.0002i		−	1.70911i
$634$	14.9312	−	6.68314i	0.592992	−	0.265422i
$635$	5.49863	+	6.33094i	0.218207	+	0.251236i
$636$	−0.237232	−	4.20856i	−0.00940686	−	0.166880i
$637$	−21.2904	+	51.3997i	−0.843558	+	2.03653i
$638$	−8.53976	−	8.07194i	−0.338092	−	0.319571i
$639$	−51.8615			−2.05161
$640$	15.4819	−	20.0077i	0.611977	−	0.790875i
$641$	−21.2780			−0.840429			−0.420214	−	0.907425i	$-0.638045\pi$
$641$	−21.2780			−0.840429			−0.420214	+	0.907425i	$0.638045\pi$
$642$	17.3370	+	16.3872i	0.684236	+	0.646753i
$643$	−0.439310	+	1.06059i	−0.0173247	+	0.0418255i	−0.932305	−	0.361673i	$-0.882206\pi$
$643$	−0.439310	+	1.06059i	−0.0173247	+	0.0418255i	0.914980	+	0.403498i	$0.132206\pi$
$644$	−1.50306	−	26.6647i	−0.0592289	−	1.05074i
$645$	−1.62605	+	23.1110i	−0.0640257	+	0.909994i
$646$	−1.85179	+	0.828854i	−0.0728575	+	0.0326108i
$647$			50.3803i			1.98065i	0.138754	+	0.990327i	$0.455690\pi$
$647$			50.3803i			1.98065i	−0.138754	+	0.990327i	$0.544310\pi$
$648$	3.82254	+	3.22579i	0.150163	+	0.126721i
$649$	17.9572	+	17.9572i	0.704880	+	0.704880i
$650$	29.8117	−	8.58439i	1.16931	−	0.336708i
$651$	−3.75054	+	9.05461i	−0.146995	+	0.354878i
$652$	−40.5018	−	14.1627i	−1.58617	−	0.554653i
$653$	−6.42491	+	15.5111i	−0.251426	+	0.606996i	−0.998320	−	0.0579473i	$-0.981544\pi$
$653$	−6.42491	+	15.5111i	−0.251426	+	0.606996i	0.746894	+	0.664944i	$0.231544\pi$
$654$	−9.19546	+	9.72840i	−0.359571	+	0.380411i
$655$	4.56100	+	13.6509i	0.178213	+	0.533384i
$656$	6.86687	−	8.61819i	0.268106	−	0.336484i
$657$	−9.34286	−	9.34286i	−0.364500	−	0.364500i
$658$	1.23156	+	43.7309i	0.0480110	+	1.70481i
$659$	−4.76024	−	11.4922i	−0.185433	−	0.447674i	0.803638	−	0.595119i	$-0.202895\pi$
$659$	−4.76024	−	11.4922i	−0.185433	−	0.447674i	−0.989070	+	0.147445i	$0.952895\pi$
$660$	25.8056	−	25.0963i	1.00448	−	0.976872i
$661$	−30.4852	−	12.6274i	−1.18574	−	0.491148i	−0.299371	−	0.954137i	$-0.596777\pi$
$661$	−30.4852	−	12.6274i	−1.18574	−	0.491148i	−0.886364	+	0.462989i	$0.846777\pi$
$662$	5.44607	−	2.43764i	0.211668	−	0.0947417i
$663$			8.04090i			0.312283i
$664$	−28.3131	+	14.6382i	−1.09876	+	0.568071i
$665$	20.2750	−	6.77424i	0.786231	−	0.262694i
$666$	−35.5982	+	15.9336i	−1.37940	+	0.617416i
$667$	7.90338	−	3.27369i	0.306020	−	0.126758i
$668$	15.2427	−	0.859212i	0.589756	−	0.0332439i
$669$	11.9471	+	28.8427i	0.461900	+	1.11512i
$670$	−4.48710	−	12.2692i	−0.173352	−	0.474000i
$671$		−	37.0920i		−	1.43192i
$672$	−35.1335	−	59.4887i	−1.35530	−	2.29483i
$673$	−14.8060	−	14.8060i	−0.570728	−	0.570728i	0.361604	−	0.932332i	$-0.382229\pi$
$673$	−14.8060	−	14.8060i	−0.570728	−	0.570728i	−0.932332	+	0.361604i	$0.882229\pi$
$674$	−0.595782	−	21.1554i	−0.0229487	−	0.814877i
$675$	21.0506	−	5.42476i	0.810236	−	0.208799i
$676$	8.32557	−	9.32025i	0.320214	−	0.358471i
$677$	−0.953938	−	2.30301i	−0.0366628	−	0.0885119i	0.904488	−	0.426500i	$-0.140254\pi$
$677$	−0.953938	−	2.30301i	−0.0366628	−	0.0885119i	−0.941150	+	0.337988i	$0.890254\pi$
$678$	12.8618	−	33.7049i	0.493955	−	1.29443i
$679$	18.4071	+	18.4071i	0.706398	+	0.706398i
$680$	−4.20996	+	0.0598755i	−0.161445	+	0.00229612i
$681$	22.1879	−	22.1879i	0.850242	−	0.850242i
$682$	−1.35551	−	3.02842i	−0.0519053	−	0.115964i
$683$	−30.9242	+	12.8092i	−1.18328	+	0.490132i	−0.885562	−	0.464521i	$-0.846227\pi$
$683$	−30.9242	+	12.8092i	−1.18328	+	0.490132i	−0.297721	+	0.954653i	$0.596227\pi$
$684$	18.6298	+	6.51447i	0.712328	+	0.249087i
$685$	2.92128	−	41.5199i	0.111616	−	1.58640i
$686$	−24.4821	+	25.9010i	−0.934730	+	0.988903i
$687$	25.6386	−	25.6386i	0.978175	−	0.978175i
$688$	−13.1726	+	7.28745i	−0.502201	+	0.277831i
$689$	3.35877			0.127959
$690$	9.00074	+	24.6109i	0.342652	+	0.936922i
$691$	−7.29681	+	3.02244i	−0.277584	+	0.114979i	−0.517132	−	0.855905i	$-0.673001\pi$
$691$	−7.29681	+	3.02244i	−0.277584	+	0.114979i	0.239549	+	0.970884i	$0.423001\pi$
$692$	−13.3055	−	4.65267i	−0.505800	−	0.176868i
$693$	−22.7293	−	54.8733i	−0.863414	−	2.08447i
$694$	−9.68290	−	3.69500i	−0.367558	−	0.140260i
$695$	−9.44955	−	4.71644i	−0.358442	−	0.178905i
$696$	14.2723	−	16.9126i	0.540990	−	0.641070i
$697$	−1.83396			−0.0694662
$698$	−11.3090	+	29.6359i	−0.428054	+	1.12173i
$699$	8.72234	−	21.0576i	0.329909	−	0.796471i
$700$	44.2059	+	3.72989i	1.67083	+	0.140977i
$701$	4.91891	−	2.03748i	0.185785	−	0.0769546i	−0.287852	−	0.957675i	$-0.592941\pi$
$701$	4.91891	−	2.03748i	0.185785	−	0.0769546i	0.473637	+	0.880720i	$0.342941\pi$
$702$	18.5301	−	19.6040i	0.699373	−	0.739906i
$703$	9.17688	−	9.17688i	0.346113	−	0.346113i
$704$	22.8065	+	5.19035i	0.859551	+	0.195619i
$705$	−13.6032	−	40.7138i	−0.512326	−	1.53337i
$706$	0.807005	+	28.6557i	0.0303720	+	1.07847i
$707$	78.8325	+	32.6535i	2.96480	+	1.22806i
$708$	−31.8610	+	35.6676i	−1.19741	+	1.34047i
$709$	6.76840	+	2.80356i	0.254192	+	0.105290i	0.506141	−	0.862451i	$-0.331071\pi$
$709$	6.76840	+	2.80356i	0.254192	+	0.105290i	−0.251949	+	0.967741i	$0.581071\pi$
$710$	35.7823	+	1.50690i	1.34289	+	0.0565528i
$711$	−29.1837	+	29.1837i	−1.09447	+	1.09447i
$712$	0.103516	+	1.22264i	0.00387941	+	0.0458205i
$713$	2.41544			0.0904589
$714$	−4.09948	+	10.7429i	−0.153419	+	0.402042i
$715$	18.8082	+	21.6551i	0.703386	+	0.809855i
$716$	−43.6330	+	21.0238i	−1.63064	+	0.785697i
$717$	−24.1326	−	9.99606i	−0.901250	−	0.373310i
$718$	0.371129	+	13.1783i	0.0138504	+	0.491810i
$719$			16.7938i			0.626303i	0.949703	+	0.313152i	$0.101385\pi$
$719$			16.7938i			0.626303i	−0.949703	+	0.313152i	$0.898615\pi$
$720$	30.1625	+	27.7086i	1.12409	+	1.03264i
$721$			72.8377i			2.71262i
$722$	20.2947	−	0.571542i	0.755291	−	0.0212706i
$723$	−71.0853	−	29.4445i	−2.64369	−	1.09505i
$724$	−4.19110	+	11.9855i	−0.155761	+	0.445439i
$725$	3.54607	+	13.7604i	0.131698	+	0.511048i
$726$	−8.91907	−	3.40352i	−0.331018	−	0.126316i
$727$	−39.1185			−1.45082			−0.725412	−	0.688315i	$-0.758351\pi$
$727$	−39.1185			−1.45082			−0.725412	+	0.688315i	$0.758351\pi$
$728$	48.9020	−	25.2828i	1.81243	−	0.937044i
$729$	−31.1167	+	31.1167i	−1.15247	+	1.15247i
$730$	6.17473	+	6.71766i	0.228537	+	0.248632i
$731$	2.31473	+	0.958794i	0.0856135	+	0.0354623i
$732$	69.7430	−	3.93134i	2.57777	−	0.145306i
$733$	38.3647	+	15.8912i	1.41703	+	0.586954i	0.954113	−	0.299447i	$-0.0968020\pi$
$733$	38.3647	+	15.8912i	1.41703	+	0.586954i	0.462919	+	0.886400i	$0.346802\pi$
$734$	−18.9956	+	0.534956i	−0.701139	+	0.0197456i
$735$	34.8613	−	69.8458i	1.28588	−	2.57630i
$736$	−10.2318	+	13.6105i	−0.377148	+	0.501689i
$737$	8.54070	−	8.54070i	0.314601	−	0.314601i
$738$	12.9652	+	12.2549i	0.477256	+	0.451111i
$739$	10.0401	−	4.15876i	0.369333	−	0.152983i	−0.190295	−	0.981727i	$-0.560944\pi$
$739$	10.0401	−	4.15876i	0.369333	−	0.152983i	0.559627	+	0.828744i	$0.310944\pi$
$740$	25.0243	−	9.95921i	0.919910	−	0.366108i
$741$	−9.96067	+	24.0472i	−0.365914	+	0.883395i
$742$	4.48741	+	1.71240i	0.164738	+	0.0628640i
$743$	−10.0964			−0.370399			−0.185200	−	0.982701i	$-0.559293\pi$
$743$	−10.0964			−0.370399			−0.185200	+	0.982701i	$0.559293\pi$
$744$	5.55058	−	2.86971i	0.203494	−	0.105209i
$745$	3.41385	−	6.83976i	0.125074	−	0.250590i
$746$	12.9925	−	34.0475i	0.475690	−	1.24657i
$747$	−19.7476	−	47.6748i	−0.722525	−	1.74433i
$748$	−1.68973	−	3.50688i	−0.0617827	−	0.128224i
$749$	−25.1136	+	10.4024i	−0.917629	+	0.380094i
$750$	−42.5719	+	9.07948i	−1.55451	+	0.331536i
$751$	11.4681			0.418478			0.209239	−	0.977864i	$-0.432901\pi$
$751$	11.4681			0.418478			0.209239	+	0.977864i	$0.432901\pi$
$752$	17.3815	−	21.8144i	0.633836	−	0.795489i
$753$	−45.2264	+	45.2264i	−1.64814	+	1.64814i
$754$	12.8148	+	12.1128i	0.466688	+	0.441122i
$755$	1.50396	+	1.73161i	0.0547348	+	0.0630198i
$756$	34.7514	−	16.7444i	1.26390	−	0.608987i
$757$	11.9093	−	4.93300i	0.432851	−	0.179293i	−0.155609	−	0.987819i	$-0.549734\pi$
$757$	11.9093	−	4.93300i	0.432851	−	0.179293i	0.588461	+	0.808526i	$0.299734\pi$
$758$	11.2047	−	5.01517i	0.406972	−	0.182159i
$759$	−17.1319	+	17.1319i	−0.621849	+	0.621849i
$760$	−12.6645	−	5.03603i	−0.459390	−	0.182676i
$761$	3.64011	+	3.64011i	0.131954	+	0.131954i	0.769999	−	0.638045i	$-0.220257\pi$
$761$	3.64011	+	3.64011i	0.131954	+	0.131954i	−0.638045	+	0.769999i	$0.720257\pi$
$762$	−13.6411	−	5.20543i	−0.494164	−	0.188573i
$763$	−5.83714	−	14.0921i	−0.211319	−	0.510168i
$764$	32.4550	−	1.82945i	1.17418	−	0.0661874i
$765$	0.478424	−	6.79981i	0.0172974	−	0.245848i
$766$	−14.8687	+	0.418733i	−0.537227	+	0.0151294i
$767$	−26.9466	−	26.9466i	−0.972986	−	0.972986i
$768$	−7.34203	+	43.4324i	−0.264933	+	1.56723i
$769$			43.2137i			1.55833i	0.626821	+	0.779163i	$0.284356\pi$
$769$			43.2137i			1.55833i	−0.626821	+	0.779163i	$0.715644\pi$
$770$	14.0879	+	38.5208i	0.507692	+	1.38819i
$771$	−14.9559	−	36.1068i	−0.538625	−	1.30036i
$772$	−19.7478	+	22.1071i	−0.710740	+	0.795653i
$773$	−12.0592	+	4.99507i	−0.433738	+	0.179660i	−0.588860	−	0.808235i	$-0.700423\pi$
$773$	−12.0592	+	4.99507i	−0.433738	+	0.179660i	0.155122	+	0.987895i	$0.450423\pi$
$774$	−9.95714	−	22.2458i	−0.357902	−	0.799608i
$775$	−0.561814	+	3.97275i	−0.0201809	+	0.142705i
$776$	−1.40016	−	16.5376i	−0.0502629	−	0.593665i
$777$		−	73.5541i		−	2.63874i
$778$	−3.25823	−	7.27939i	−0.116813	−	0.260979i
$779$	−5.48466	−	2.27182i	−0.196508	−	0.0813964i
$780$	−38.7240	+	37.6596i	−1.38654	+	1.34843i
$781$	12.6715	+	30.5916i	0.453420	+	1.09465i
$782$	2.83276	−	0.0797765i	0.101299	−	0.00285280i
$783$	8.73702	+	8.73702i	0.312236	+	0.312236i
$784$	50.4017	−	5.70029i	1.80006	−	0.203582i
$785$	5.48465	−	10.9887i	0.195755	−	0.392203i
$786$	−18.2120	−	17.2143i	−0.649601	−	0.614015i
$787$	−3.10098	+	7.48644i	−0.110538	+	0.266863i	−0.969462	−	0.245240i	$-0.921133\pi$
$787$	−3.10098	+	7.48644i	−0.110538	+	0.266863i	0.858924	+	0.512103i	$0.171133\pi$
$788$	−23.6791	+	11.4094i	−0.843533	+	0.406442i
$789$	0.686325	−	1.65693i	0.0244338	−	0.0589884i
$790$	20.9835	−	19.2876i	0.746561	−	0.686222i
$791$	29.0665	+	29.0665i	1.03348	+	1.03348i
$792$	−11.4882	+	36.0831i	−0.408217	+	1.28216i
$793$			55.6605i			1.97656i
$794$	−12.1842	−	27.2213i	−0.432400	−	0.966047i
$795$	−4.70116	−	0.330766i	−0.166733	−	0.0117311i
$796$	−16.6852	+	18.6786i	−0.591390	+	0.662045i
$797$	16.9901	−	41.0178i	0.601821	−	1.45292i	−0.269884	−	0.962893i	$-0.586985\pi$
$797$	16.9901	−	41.0178i	0.601821	−	1.45292i	0.871705	−	0.490031i	$-0.163015\pi$
$798$	−25.5677	+	27.0495i	−0.905086	+	0.957541i
$799$	−4.64213			−0.164227
$800$	−20.0058	−	19.9942i	−0.707310	−	0.706903i
$801$	−1.98654			−0.0701910
$802$	23.1256	−	24.4659i	0.816593	−	0.863919i
$803$	−3.22832	+	7.79385i	−0.113925	+	0.275039i
$804$	16.9640	+	15.1536i	0.598275	+	0.534426i
$805$	−29.7857	−	2.09568i	−1.04981	−	0.0738629i
$806$	2.03409	+	4.54447i	0.0716478	+	0.160072i
$807$		−	8.81241i		−	0.310211i
$808$	−24.9847	−	48.3253i	−0.878958	−	1.70008i
$809$	−29.7719	−	29.7719i	−1.04673	−	1.04673i	−0.998853	−	0.0478717i	$-0.984756\pi$
$809$	−29.7719	−	29.7719i	−1.04673	−	1.04673i	−0.0478717	−	0.998853i	$-0.515244\pi$
$810$	4.11711	−	3.78435i	0.144660	−	0.132969i
$811$	2.01347	−	4.86096i	0.0707026	−	0.170691i	−0.884578	−	0.466393i	$-0.845553\pi$
$811$	2.01347	−	4.86096i	0.0707026	−	0.170691i	0.955280	+	0.295701i	$0.0955534\pi$
$812$	10.9455	+	22.7164i	0.384112	+	0.797189i
$813$	−22.8388	+	55.1377i	−0.800992	+	1.93376i
$814$	18.0966	+	17.1052i	0.634285	+	0.599538i
$815$	−21.4230	+	42.9217i	−0.750415	+	1.50348i
$816$	6.41480	−	3.54884i	0.224563	−	0.124234i
$817$	5.73475	+	5.73475i	0.200634	+	0.200634i
$818$	33.6589	−	0.947907i	1.17686	−	0.0331428i
$819$	34.1077	+	82.3433i	1.19182	+	2.87731i
$820$	−8.58938	−	8.83213i	−0.299954	−	0.308431i
$821$	−9.77236	−	4.04785i	−0.341058	−	0.141271i	0.205579	−	0.978640i	$-0.434092\pi$
$821$	−9.77236	−	4.04785i	−0.341058	−	0.141271i	−0.546637	+	0.837370i	$0.684092\pi$
$822$	29.6078	+	66.1483i	1.03269	+	2.30719i
$823$		−	6.06110i		−	0.211277i	−0.994405	−	0.105638i	$-0.966311\pi$
$823$		−	6.06110i		−	0.211277i	0.994405	−	0.105638i	$-0.0336886\pi$
$824$	29.9498	−	35.4904i	1.04335	−	1.23636i
$825$	−24.1926	−	32.1622i	−0.842280	−	1.11974i
$826$	−22.2633	−	49.7396i	−0.774639	−	1.73066i
$827$	−40.2852	+	16.6867i	−1.40085	+	0.580252i	−0.949973	−	0.312332i	$-0.898890\pi$
$827$	−40.2852	+	16.6867i	−1.40085	+	0.580252i	−0.450880	+	0.892585i	$0.648890\pi$
$828$	−20.5593	−	18.3652i	−0.714485	−	0.638234i
$829$	−10.9231	−	26.3708i	−0.379376	−	0.915895i	−0.992083	−	0.125585i	$-0.959919\pi$
$829$	−10.9231	−	26.3708i	−0.379376	−	0.915895i	0.612707	−	0.790310i	$-0.290081\pi$
$830$	12.2398	+	33.4675i	0.424848	+	1.16167i
$831$			52.1267i			1.80826i
$832$	−34.2235	−	7.78867i	−1.18649	−	0.270024i
$833$	−5.96928	−	5.96928i	−0.206823	−	0.206823i
$834$	18.3816	−	0.517665i	0.636502	−	0.0179253i
$835$	1.19798	−	17.0268i	0.0414577	−	0.589236i
$836$	−0.709171	−	12.5809i	−0.0245272	−	0.435119i
$837$	1.33511	+	3.22324i	0.0461481	+	0.111411i
$838$	29.8233	+	11.3806i	1.03023	+	0.393135i
$839$	2.66951	+	2.66951i	0.0921617	+	0.0921617i	0.751685	−	0.659523i	$-0.229242\pi$
$839$	2.66951	+	2.66951i	0.0921617	+	0.0921617i	−0.659523	+	0.751685i	$0.729242\pi$
$840$	−70.9363	+	30.5718i	−2.44753	+	1.05483i
$841$	14.7949	−	14.7949i	0.510167	−	0.510167i
$842$	−22.3778	+	10.0162i	−0.771190	+	0.345182i
$843$	13.8916	−	5.75410i	0.478453	−	0.198182i
$844$	−13.5597	−	28.1420i	−0.466745	−	0.968686i
$845$	−9.16218	−	10.5490i	−0.315189	−	0.362898i
$846$	32.8176	+	31.0198i	1.12829	+	1.06648i
$847$	7.69163	−	7.69163i	0.264287	−	0.264287i
$848$	−1.48239	−	2.67953i	−0.0509054	−	0.0920153i
$849$	29.8716			1.02519
$850$	−0.527669	+	4.67769i	−0.0180989	+	0.160443i
$851$	−16.7480	+	6.93726i	−0.574115	+	0.237806i
$852$	−56.1774	+	27.0681i	−1.92461	+	0.927338i
$853$	−18.1396	−	43.7929i	−0.621088	−	1.49944i	−0.850427	−	0.526093i	$-0.823656\pi$
$853$	−18.1396	−	43.7929i	−0.621088	−	1.49944i	0.229339	−	0.973347i	$-0.426344\pi$
$854$	−28.3773	+	74.3640i	−0.971052	+	2.54468i
$855$	9.85404	−	19.7429i	0.337001	−	0.675193i
$856$	16.5139	+	5.25775i	0.564435	+	0.179706i
$857$	48.6153			1.66067			0.830334	−	0.557267i	$-0.188150\pi$
$857$	48.6153			1.66067			0.830334	+	0.557267i	$0.188150\pi$
$858$	−46.6596	−	17.8053i	−1.59293	−	0.607863i
$859$	−19.3315	+	46.6704i	−0.659582	+	1.59237i	0.138868	+	0.990311i	$0.455654\pi$
$859$	−19.3315	+	46.6704i	−0.659582	+	1.59237i	−0.798450	+	0.602061i	$0.794346\pi$
$860$	6.22364	+	15.6380i	0.212224	+	0.533251i
$861$	−31.0847	+	12.8757i	−1.05936	+	0.438803i
$862$	−18.5535	−	17.5371i	−0.631935	−	0.597316i
$863$	−0.462262	+	0.462262i	−0.0157356	+	0.0157356i	−0.714931	−	0.699195i	$-0.753542\pi$
$863$	−0.462262	+	0.462262i	−0.0157356	+	0.0157356i	0.699195	+	0.714931i	$0.253542\pi$
$864$	−23.8178	−	6.13055i	−0.810297	−	0.208566i
$865$	−7.03782	+	14.1005i	−0.239293	+	0.479432i
$866$	38.0304	−	1.07102i	1.29233	−	0.0363946i
$867$	42.1119	+	17.4433i	1.43019	+	0.592406i
$868$	0.400703	+	7.10858i	0.0136008	+	0.241281i
$869$	24.3452	+	10.0841i	0.825853	+	0.342079i
$870$	−16.7436	−	18.2159i	−0.567662	−	0.617576i
$871$	−12.8162	+	12.8162i	−0.434261	+	0.434261i
$872$	−2.95031	+	9.26656i	−0.0999101	+	0.313805i
$873$	26.8702			0.909417
$874$	8.57050	+	3.27050i	0.289901	+	0.110626i
$875$	10.3748	−	48.5021i	0.350732	−	1.63967i
$876$	−14.9967	−	5.24405i	−0.506691	−	0.177180i
$877$	−32.4583	−	13.4447i	−1.09604	−	0.453995i	−0.239931	−	0.970790i	$-0.577125\pi$
$877$	−32.4583	−	13.4447i	−1.09604	−	0.453995i	−0.856109	+	0.516795i	$0.827125\pi$
$878$	−0.477455	+	0.0134461i	−0.0161133	+	0.000453785i
$879$		−	67.1435i		−	2.26469i
$880$	8.97485	−	24.5621i	0.302542	−	0.827987i
$881$		−	18.5543i		−	0.625110i	−0.949900	−	0.312555i	$-0.898815\pi$
$881$		−	18.5543i		−	0.625110i	0.949900	−	0.312555i	$-0.101185\pi$
$882$	2.31177	+	82.0880i	0.0778414	+	2.76405i
$883$	48.3840	+	20.0413i	1.62825	+	0.674444i	0.995035	−	0.0995295i	$-0.0317338\pi$
$883$	48.3840	+	20.0413i	1.62825	+	0.674444i	0.633218	+	0.773974i	$0.281734\pi$
$884$	2.53562	+	5.26245i	0.0852822	+	0.176995i
$885$	35.0627	+	40.3700i	1.17862	+	1.35702i
$886$	−3.19266	+	8.36651i	−0.107260	+	0.281078i
$887$	17.4110			0.584605			0.292303	−	0.956326i	$-0.405579\pi$
$887$	17.4110			0.584605			0.292303	+	0.956326i	$0.405579\pi$
$888$	−30.2444	+	35.8394i	−1.01494	+	1.20269i
$889$	11.7638	−	11.7638i	0.394545	−	0.394545i
$890$	1.37063	+	0.0577212i	0.0459437	+	0.00193482i
$891$	4.77668	+	1.97856i	0.160025	+	0.0662844i
$892$	16.9142	+	15.1090i	0.566328	+	0.505888i
$893$	−13.8828	−	5.75044i	−0.464570	−	0.192431i
$894$	0.374696	+	13.3049i	0.0125317	+	0.444984i
$895$	17.1602	+	51.3598i	0.573603	+	1.71677i
$896$	−41.7527	−	27.8540i	−1.39486	−	0.930537i
$897$	25.7082	−	25.7082i	0.858373	−	0.858373i
$898$	−6.83053	+	7.22641i	−0.227938	+	0.241148i
$899$	−2.10697	+	0.872737i	−0.0702715	+	0.0291074i
$900$	34.9877	−	29.5429i	1.16626	−	0.984765i
$901$	−0.195035	+	0.470855i	−0.00649754	+	0.0156865i
$902$	4.06102	−	10.6421i	0.135217	−	0.354342i
$903$	45.9649			1.52962
$904$	−2.21099	−	26.1144i	−0.0735364	−	0.868552i
$905$	12.7017	+	6.33963i	0.422217	+	0.210736i
$906$	−3.73105	−	1.42377i	−0.123956	−	0.0473015i
$907$	−9.67594	−	23.3598i	−0.321284	−	0.775649i	−0.999180	−	0.0404906i	$-0.987108\pi$
$907$	−9.67594	−	23.3598i	−0.321284	−	0.775649i	0.677896	−	0.735158i	$-0.262892\pi$
$908$	7.52437	−	21.5179i	0.249705	−	0.714095i
$909$	81.3723	−	33.7055i	2.69895	−	1.11794i
$910$	−21.1403	−	57.8045i	−0.700795	−	1.91620i
$911$	10.5628			0.349962			0.174981	−	0.984572i	$-0.444014\pi$
$911$	10.5628			0.349962			0.174981	+	0.984572i	$0.444014\pi$
$912$	23.5803	−	2.66686i	0.780821	−	0.0883087i
$913$	−23.2970	+	23.2970i	−0.771019	+	0.771019i
$914$	−23.0835	+	24.4214i	−0.763535	+	0.807787i
$915$	5.48136	−	77.9062i	0.181208	−	2.57550i
$916$	8.69458	−	24.8644i	0.287277	−	0.821542i
$917$	26.3811	−	10.9274i	0.871180	−	0.360854i
$918$	1.67224	+	3.73603i	0.0551920	+	0.123307i
$919$	−34.4600	+	34.4600i	−1.13673	+	1.13673i	−0.147699	+	0.989032i	$0.547187\pi$
$919$	−34.4600	+	34.4600i	−1.13673	+	1.13673i	−0.989032	+	0.147699i	$0.952813\pi$
$920$	13.6515	+	13.2686i	0.450075	+	0.437453i
$921$	−65.0469	−	65.0469i	−2.14337	−	2.14337i
$922$	12.3549	−	32.3766i	0.406887	−	1.06627i
$923$	−19.0149	−	45.9059i	−0.625882	−	1.51101i
$924$	−53.2609	−	47.5768i	−1.75215	−	1.56516i
$925$	−7.51447	−	29.1596i	−0.247074	−	0.958762i
$926$	1.00450	+	35.6686i	0.0330100	+	1.17214i
$927$	53.1633	+	53.1633i	1.74611	+	1.74611i
$928$	4.00744	−	15.5693i	0.131551	−	0.511086i
$929$		−	3.84043i		−	0.126000i	−0.998014	−	0.0630002i	$-0.979933\pi$
$929$		−	3.84043i		−	0.126000i	0.998014	−	0.0630002i	$-0.0200669\pi$
$930$	−2.39952	−	6.56107i	−0.0786834	−	0.215146i
$931$	−10.4573	−	25.2462i	−0.342725	−	0.827412i
$932$	−0.931884	−	16.5319i	−0.0305249	−	0.541520i
$933$	30.8201	−	12.7661i	1.00901	−	0.417944i
$934$	20.8742	−	9.34324i	0.683026	−	0.305720i
$935$	−4.12790	+	1.37921i	−0.134997	+	0.0451049i
$936$	17.2393	−	54.1465i	0.563485	−	1.76984i
$937$			11.2848i			0.368660i	0.982864	+	0.184330i	$0.0590115\pi$
$937$			11.2848i			0.368660i	−0.982864	+	0.184330i	$0.940989\pi$
$938$	−23.6569	+	10.5888i	−0.772426	+	0.345735i
$939$	75.2408	+	31.1658i	2.45539	+	1.01706i
$940$	−21.7415	−	22.3559i	−0.709128	−	0.729170i
$941$	14.7952	+	35.7188i	0.482310	+	1.16440i	0.958509	+	0.285062i	$0.0920141\pi$
$941$	14.7952	+	35.7188i	0.482310	+	1.16440i	−0.476199	+	0.879337i	$0.657986\pi$
$942$	0.601981	+	21.3756i	0.0196136	+	0.696453i
$943$	5.86351	+	5.86351i	0.190942	+	0.190942i
$944$	−9.60437	+	33.3901i	−0.312596	+	1.08676i
$945$	−13.6672	−	40.9054i	−0.444595	−	1.33065i
$946$	−10.6893	+	11.3088i	−0.347538	+	0.367681i
$947$	−10.5343	+	25.4321i	−0.342320	+	0.826433i	0.655161	+	0.755490i	$0.272601\pi$
$947$	−10.5343	+	25.4321i	−0.342320	+	0.826433i	−0.997480	+	0.0709433i	$0.977399\pi$
$948$	−16.3805	+	46.8442i	−0.532014	+	1.52143i
$949$	4.84443	−	11.6955i	0.157257	−	0.379652i
$950$	−7.37254	+	13.3355i	−0.239197	+	0.432660i
$951$	22.5179	+	22.5179i	0.730194	+	0.730194i
$952$	0.704715	+	8.32352i	0.0228399	+	0.269767i
$953$			27.9623i			0.905788i	0.891564	+	0.452894i	$0.149608\pi$
$953$			27.9623i			0.905788i	−0.891564	+	0.452894i	$0.850392\pi$
$954$	4.52516	−	2.02545i	0.146507	−	0.0655763i
$955$	2.55076	−	36.2538i	0.0825406	−	1.17315i
$956$	−18.9460	+	1.06797i	−0.612758	+	0.0345405i
$957$	8.75403	−	21.1341i	0.282978	−	0.683169i
$958$	32.6535	+	30.8647i	1.05499	+	0.997192i
$959$	−82.5781			−2.66659
$960$	47.1346	+	14.2718i	1.52126	+	0.460621i
$961$	30.3561			0.979228
$962$	−27.1558	−	25.6682i	−0.875539	−	0.827576i
$963$	−10.7375	+	25.9226i	−0.346011	+	0.835345i
$964$	−55.8076	+	3.14581i	−1.79744	+	0.101320i
$965$	21.7322	+	25.0218i	0.699585	+	0.805479i
$966$	47.4537	−	21.2401i	1.52680	−	0.683390i
$967$			3.64966i			0.117365i	0.998277	+	0.0586827i	$0.0186900\pi$
$967$			3.64966i			0.117365i	−0.998277	+	0.0586827i	$0.981310\pi$
$968$	−6.91045	+	0.585077i	−0.222110	+	0.0188051i
$969$	−2.79271	−	2.79271i	−0.0897148	−	0.0897148i
$970$	−18.5393	−	0.780743i	−0.595262	−	0.0250682i
$971$	−20.3814	+	49.2050i	−0.654070	+	1.57906i	0.152749	+	0.988265i	$0.451187\pi$
$971$	−20.3814	+	49.2050i	−0.654070	+	1.57906i	−0.806819	+	0.590799i	$0.798813\pi$
$972$	−11.8245	+	33.8151i	−0.379269	+	1.08462i
$973$	−8.01841	+	19.3582i	−0.257058	+	0.620594i
$974$	33.0762	−	34.9931i	1.05983	−	1.12125i
$975$	36.3036	+	48.2627i	1.16265	+	1.54564i
$976$	44.4043	−	24.5657i	1.42135	−	0.786329i
$977$	−4.19452	−	4.19452i	−0.134194	−	0.134194i	0.636819	−	0.771013i	$-0.280250\pi$
$977$	−4.19452	−	4.19452i	−0.134194	−	0.134194i	−0.771013	+	0.636819i	$0.780250\pi$
$978$	−2.35133	−	83.4928i	−0.0751874	−	2.66981i
$979$	0.485377	+	1.17180i	0.0155127	+	0.0374510i
$980$	0.790132	−	56.7045i	0.0252398	−	1.81136i
$981$	−14.5461	−	6.02519i	−0.464421	−	0.192370i
$982$	15.9271	−	7.12892i	0.508254	−	0.227493i
$983$		−	44.6077i		−	1.42277i	−0.702805	−	0.711383i	$-0.748069\pi$
$983$		−	44.6077i		−	1.42277i	0.702805	−	0.711383i	$-0.251931\pi$
$984$	20.4404	+	6.50786i	0.651616	+	0.207463i
$985$	9.31264	+	27.8723i	0.296725	+	0.888086i
$986$	−2.44218	+	1.09311i	−0.0777748	+	0.0348117i
$987$	−78.6817	+	32.5910i	−2.50447	+	1.03738i
$988$	1.06419	+	18.8789i	0.0338563	+	0.600619i
$989$	−4.33519	−	10.4661i	−0.137851	−	0.332802i
$990$	38.3984	+	17.8333i	1.22038	+	0.566779i
$991$		−	25.4745i		−	0.809223i	−0.914489	−	0.404612i	$-0.867407\pi$
$991$		−	25.4745i		−	0.809223i	0.914489	−	0.404612i	$-0.132593\pi$
$992$	2.72770	−	3.62844i	0.0866047	−	0.115203i
$993$	8.21331	+	8.21331i	0.260642	+	0.260642i
$994$	−2.00024	−	71.0260i	−0.0634438	−	2.25281i
$995$	18.3618	+	21.1412i	0.582108	+	0.670220i
$996$	−46.2739	−	41.3355i	−1.46624	−	1.30976i
$997$	−20.4196	−	49.2973i	−0.646695	−	1.56126i	−0.817483	−	0.575953i	$-0.804631\pi$
$997$	−20.4196	−	49.2973i	−0.646695	−	1.56126i	0.170787	−	0.985308i	$-0.445369\pi$
$998$	20.1365	−	52.7687i	0.637411	−	1.67036i
$999$	−18.5146	−	18.5146i	−0.585776	−	0.585776i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	160.2.u.a.43.18	✓	88
4.3	odd	2		640.2.u.a.463.20		88
5.2	odd	4		160.2.ba.a.107.6	yes	88
5.3	odd	4		800.2.bb.b.107.17		88
5.4	even	2		800.2.v.b.43.5		88
20.7	even	4		640.2.ba.a.207.3		88
32.3	odd	8		160.2.ba.a.3.6	yes	88
32.29	even	8		640.2.ba.a.303.3		88
160.3	even	8		800.2.v.b.707.5		88
160.67	even	8	inner	160.2.u.a.67.18	yes	88
160.99	odd	8		800.2.bb.b.643.17		88
160.157	odd	8		640.2.u.a.47.20		88

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
160.2.u.a.43.18	✓	88	1.1	even	1	trivial
160.2.u.a.67.18	yes	88	160.67	even	8	inner
160.2.ba.a.3.6	yes	88	32.3	odd	8
160.2.ba.a.107.6	yes	88	5.2	odd	4
640.2.u.a.47.20		88	160.157	odd	8
640.2.u.a.463.20		88	4.3	odd	2
640.2.ba.a.207.3		88	20.7	even	4
640.2.ba.a.303.3		88	32.29	even	8
800.2.v.b.43.5		88	5.4	even	2
800.2.v.b.707.5		88	160.3	even	8
800.2.bb.b.107.17		88	5.3	odd	4
800.2.bb.b.643.17		88	160.99	odd	8

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:	\( N \)	\(=\)	\( 160 = 2^{5} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	160.u (of order \(8\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(1.02775 + 0.971453i) q^{2} +(-1.05354 + 2.54348i) q^{3} +(0.112559 + 1.99683i) q^{4} +(2.23055 + 0.156938i) q^{5} +(-3.55365 + 1.59060i) q^{6} -4.43630i q^{7} +(-1.82414 + 2.16160i) q^{8} +(-3.23800 - 3.23800i) q^{9} +O(q^{10})\)	\(q+(1.02775 + 0.971453i) q^{2} +(-1.05354 + 2.54348i) q^{3} +(0.112559 + 1.99683i) q^{4} +(2.23055 + 0.156938i) q^{5} +(-3.55365 + 1.59060i) q^{6} -4.43630i q^{7} +(-1.82414 + 2.16160i) q^{8} +(-3.23800 - 3.23800i) q^{9} +(2.14000 + 2.32817i) q^{10} +(-1.11885 + 2.70115i) q^{11} +(-5.19748 - 1.81745i) q^{12} +(1.67896 - 4.05336i) q^{13} +(4.30965 - 4.55943i) q^{14} +(-2.74915 + 5.50802i) q^{15} +(-3.97466 + 0.449523i) q^{16} +(0.470736 + 0.470736i) q^{17} +(-0.182306 - 6.47343i) q^{18} +(0.824662 + 1.99091i) q^{19} +(-0.0623096 + 4.47170i) q^{20} +(11.2836 + 4.67383i) q^{21} +(-3.77395 + 1.68921i) q^{22} -3.01006i q^{23} +(-3.57616 - 6.91700i) q^{24} +(4.95074 + 0.700118i) q^{25} +(5.66321 - 2.53483i) q^{26} +(4.01672 - 1.66378i) q^{27} +(8.85854 - 0.499346i) q^{28} +(1.08758 + 2.62566i) q^{29} +(-8.17623 + 2.99022i) q^{30} +0.802456i q^{31} +(-4.52167 - 3.39920i) q^{32} +(-5.69155 - 5.69155i) q^{33} +(0.0265033 + 0.941098i) q^{34} +(0.696225 - 9.89540i) q^{35} +(6.10127 - 6.83020i) q^{36} +(-2.30469 - 5.56402i) q^{37} +(-1.08652 + 2.84729i) q^{38} +(8.54078 + 8.54078i) q^{39} +(-4.40809 + 4.53528i) q^{40} +(-1.94797 + 1.94797i) q^{41} +(7.05639 + 15.7651i) q^{42} +(3.47703 - 1.44023i) q^{43} +(-5.51968 - 1.93012i) q^{44} +(-6.71437 - 7.73070i) q^{45} +(2.92413 - 3.09360i) q^{46} +(-4.93072 + 4.93072i) q^{47} +(3.04412 - 10.5830i) q^{48} -12.6807 q^{49} +(4.40802 + 5.52896i) q^{50} +(-1.69325 + 0.701365i) q^{51} +(8.28286 + 2.89635i) q^{52} +(0.292968 + 0.707286i) q^{53} +(5.74448 + 2.19209i) q^{54} +(-2.91958 + 5.84947i) q^{55} +(9.58949 + 8.09244i) q^{56} -5.93265 q^{57} +(-1.43293 + 3.75507i) q^{58} +(3.32398 - 8.02481i) q^{59} +(-11.3080 - 4.86961i) q^{60} +(-11.7209 + 4.85497i) q^{61} +(-0.779548 + 0.824728i) q^{62} +(-14.3647 + 14.3647i) q^{63} +(-1.34501 - 7.88612i) q^{64} +(4.38113 - 8.77775i) q^{65} +(-0.320445 - 11.3786i) q^{66} +(-3.81672 - 1.58094i) q^{67} +(-0.886994 + 0.992965i) q^{68} +(7.65601 + 3.17122i) q^{69} +(10.3285 - 9.49370i) q^{70} +(8.00826 - 8.00826i) q^{71} +(12.9058 - 1.09268i) q^{72} +2.88538 q^{73} +(3.03653 - 7.95735i) q^{74} +(-6.99655 + 11.8545i) q^{75} +(-3.88269 + 1.87081i) q^{76} +(11.9831 + 4.96357i) q^{77} +(0.480862 + 17.0748i) q^{78} -9.01288i q^{79} +(-8.93624 + 0.378910i) q^{80} -1.76839i q^{81} +(-3.89440 + 0.109675i) q^{82} +(10.4111 + 4.31243i) q^{83} +(-8.06277 + 23.0576i) q^{84} +(0.976125 + 1.12388i) q^{85} +(4.97265 + 1.89757i) q^{86} -7.82411 q^{87} +(-3.79785 - 7.34579i) q^{88} +(0.306754 - 0.306754i) q^{89} +(0.609286 - 14.4680i) q^{90} +(-17.9819 - 7.44836i) q^{91} +(6.01057 - 0.338810i) q^{92} +(-2.04103 - 0.845421i) q^{93} +(-9.85753 + 0.277609i) q^{94} +(1.52700 + 4.57025i) q^{95} +(13.4095 - 7.91956i) q^{96} +(-4.14919 + 4.14919i) q^{97} +(-13.0327 - 12.3187i) q^{98} +(12.3692 - 5.12348i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 88 q - 4 q^{2} - 4 q^{3} - 4 q^{5} - 8 q^{6} - 16 q^{8}+O(q^{10}) \) 88 * q - 4 * q^2 - 4 * q^3 - 4 * q^5 - 8 * q^6 - 16 * q^8	\( 88 q - 4 q^{2} - 4 q^{3} - 4 q^{5} - 8 q^{6} - 16 q^{8} - 16 q^{10} - 8 q^{11} - 20 q^{12} - 4 q^{13} + 16 q^{14} - 8 q^{15} - 8 q^{16} + 4 q^{18} + 16 q^{19} + 24 q^{20} - 8 q^{21} - 20 q^{22} - 32 q^{24} - 4 q^{25} - 8 q^{26} - 16 q^{27} + 12 q^{28} + 8 q^{30} - 24 q^{32} - 8 q^{33} + 8 q^{34} - 8 q^{35} - 8 q^{36} - 4 q^{37} - 60 q^{38} + 16 q^{40} - 8 q^{41} + 60 q^{42} - 36 q^{43} + 16 q^{44} - 4 q^{45} - 8 q^{46} - 8 q^{47} - 24 q^{48} - 40 q^{49} - 12 q^{50} + 8 q^{51} - 56 q^{52} - 4 q^{53} - 56 q^{54} - 36 q^{55} + 40 q^{56} - 8 q^{57} - 36 q^{58} + 12 q^{60} - 40 q^{61} + 40 q^{62} + 56 q^{63} + 48 q^{64} - 8 q^{65} + 72 q^{66} + 20 q^{67} + 8 q^{68} + 24 q^{69} + 60 q^{70} + 24 q^{71} + 24 q^{72} - 8 q^{73} + 8 q^{75} + 56 q^{76} + 24 q^{77} + 32 q^{78} - 8 q^{80} + 84 q^{82} - 44 q^{83} + 56 q^{84} - 4 q^{85} + 24 q^{86} - 120 q^{87} + 104 q^{88} + 148 q^{90} - 8 q^{91} + 124 q^{92} + 8 q^{93} - 32 q^{94} + 24 q^{96} - 8 q^{97} - 16 q^{98}+O(q^{100}) \) 88 * q - 4 * q^2 - 4 * q^3 - 4 * q^5 - 8 * q^6 - 16 * q^8 - 16 * q^10 - 8 * q^11 - 20 * q^12 - 4 * q^13 + 16 * q^14 - 8 * q^15 - 8 * q^16 + 4 * q^18 + 16 * q^19 + 24 * q^20 - 8 * q^21 - 20 * q^22 - 32 * q^24 - 4 * q^25 - 8 * q^26 - 16 * q^27 + 12 * q^28 + 8 * q^30 - 24 * q^32 - 8 * q^33 + 8 * q^34 - 8 * q^35 - 8 * q^36 - 4 * q^37 - 60 * q^38 + 16 * q^40 - 8 * q^41 + 60 * q^42 - 36 * q^43 + 16 * q^44 - 4 * q^45 - 8 * q^46 - 8 * q^47 - 24 * q^48 - 40 * q^49 - 12 * q^50 + 8 * q^51 - 56 * q^52 - 4 * q^53 - 56 * q^54 - 36 * q^55 + 40 * q^56 - 8 * q^57 - 36 * q^58 + 12 * q^60 - 40 * q^61 + 40 * q^62 + 56 * q^63 + 48 * q^64 - 8 * q^65 + 72 * q^66 + 20 * q^67 + 8 * q^68 + 24 * q^69 + 60 * q^70 + 24 * q^71 + 24 * q^72 - 8 * q^73 + 8 * q^75 + 56 * q^76 + 24 * q^77 + 32 * q^78 - 8 * q^80 + 84 * q^82 - 44 * q^83 + 56 * q^84 - 4 * q^85 + 24 * q^86 - 120 * q^87 + 104 * q^88 + 148 * q^90 - 8 * q^91 + 124 * q^92 + 8 * q^93 - 32 * q^94 + 24 * q^96 - 8 * q^97 - 16 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more