LMFDB - Embedded newform 140.2.g.c.111.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [140,2,Mod(111,140)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(140, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([1, 0, 1]))

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

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

chi := DirichletCharacter("140.111");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 140 = 2^{2} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	140.g (of order $2$, degree $1$, 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:	$1.11790562830$
Analytic rank:	$0$
Dimension:	$8$
Coefficient field:	8.0.342102016.5
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} + x^{6} + 4x^{4} + 4x^{2} + 16 $ x^8 + x^6 + 4x^4 + 4x^2 + 16
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			111.4
Root			$-1.17915 + 0.780776i$ of defining polynomial
Character	$\chi$	$=$	140.111
Dual form			140.2.g.c.111.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.780776 + 1.17915i) q^{2} +3.02045 q^{3} +(-0.780776 - 1.84130i) q^{4} +1.00000i q^{5} +(-2.35829 + 3.56155i) q^{6} +(-2.17238 + 1.51022i) q^{7} +(2.78078 + 0.516994i) q^{8} +6.12311 q^{9} +O(q^{10})$	\(q+(-0.780776 + 1.17915i) q^{2} +3.02045 q^{3} +(-0.780776 - 1.84130i) q^{4} +1.00000i q^{5} +(-2.35829 + 3.56155i) q^{6} +(-2.17238 + 1.51022i) q^{7} +(2.78078 + 0.516994i) q^{8} +6.12311 q^{9} +(-1.17915 - 0.780776i) q^{10} -4.71659i q^{11} +(-2.35829 - 5.56155i) q^{12} +2.00000i q^{13} +(-0.0846354 - 3.74070i) q^{14} +3.02045i q^{15} +(-2.78078 + 2.87529i) q^{16} +1.12311i q^{17} +(-4.78078 + 7.22004i) q^{18} -4.71659 q^{19} +(1.84130 - 0.780776i) q^{20} +(-6.56155 + 4.56155i) q^{21} +(5.56155 + 3.68260i) q^{22} -6.41273i q^{23} +(8.39919 + 1.56155i) q^{24} -1.00000 q^{25} +(-2.35829 - 1.56155i) q^{26} +9.43318 q^{27} +(4.47692 + 2.82085i) q^{28} -2.00000 q^{29} +(-3.56155 - 2.35829i) q^{30} -3.39228 q^{31} +(-1.21922 - 5.52390i) q^{32} -14.2462i q^{33} +(-1.32431 - 0.876894i) q^{34} +(-1.51022 - 2.17238i) q^{35} +(-4.78078 - 11.2745i) q^{36} +2.00000 q^{37} +(3.68260 - 5.56155i) q^{38} +6.04090i q^{39} +(-0.516994 + 2.78078i) q^{40} -1.12311i q^{41} +(-0.255637 - 11.2986i) q^{42} +0.371834i q^{43} +(-8.68466 + 3.68260i) q^{44} +6.12311i q^{45} +(7.56155 + 5.00691i) q^{46} +5.08842 q^{47} +(-8.39919 + 8.68466i) q^{48} +(2.43845 - 6.56155i) q^{49} +(0.780776 - 1.17915i) q^{50} +3.39228i q^{51} +(3.68260 - 1.56155i) q^{52} +2.00000 q^{53} +(-7.36520 + 11.1231i) q^{54} +4.71659 q^{55} +(-6.82167 + 3.07649i) q^{56} -14.2462 q^{57} +(1.56155 - 2.35829i) q^{58} -2.06798 q^{59} +(5.56155 - 2.35829i) q^{60} +2.00000i q^{61} +(2.64861 - 4.00000i) q^{62} +(-13.3017 + 9.24726i) q^{63} +(7.46543 + 2.87529i) q^{64} -2.00000 q^{65} +(16.7984 + 11.1231i) q^{66} +3.76412i q^{67} +(2.06798 - 0.876894i) q^{68} -19.3693i q^{69} +(3.74070 - 0.0846354i) q^{70} +7.36520i q^{71} +(17.0270 + 3.16561i) q^{72} +15.3693i q^{73} +(-1.56155 + 2.35829i) q^{74} -3.02045 q^{75} +(3.68260 + 8.68466i) q^{76} +(7.12311 + 10.2462i) q^{77} +(-7.12311 - 4.71659i) q^{78} -1.32431i q^{79} +(-2.87529 - 2.78078i) q^{80} +10.1231 q^{81} +(1.32431 + 0.876894i) q^{82} +3.02045 q^{83} +(13.5223 + 8.52024i) q^{84} -1.12311 q^{85} +(-0.438447 - 0.290319i) q^{86} -6.04090 q^{87} +(2.43845 - 13.1158i) q^{88} +12.0000i q^{89} +(-7.22004 - 4.78078i) q^{90} +(-3.02045 - 4.34475i) q^{91} +(-11.8078 + 5.00691i) q^{92} -10.2462 q^{93} +(-3.97292 + 6.00000i) q^{94} -4.71659i q^{95} +(-3.68260 - 16.6847i) q^{96} -1.12311i q^{97} +(5.83315 + 7.99839i) q^{98} -28.8802i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 2 q^{2} + 2 q^{4} + 14 q^{8} + 16 q^{9}+O(q^{10}) $ 8 * q + 2 * q^2 + 2 * q^4 + 14 * q^8 + 16 * q^9	$ 8 q + 2 q^{2} + 2 q^{4} + 14 q^{8} + 16 q^{9} - 6 q^{14} - 14 q^{16} - 30 q^{18} - 36 q^{21} + 28 q^{22} - 8 q^{25} + 14 q^{28} - 16 q^{29} - 12 q^{30} - 18 q^{32} - 30 q^{36} + 16 q^{37} + 8 q^{42} - 20 q^{44} + 44 q^{46} + 36 q^{49} - 2 q^{50} + 16 q^{53} + 2 q^{56} - 48 q^{57} - 4 q^{58} + 28 q^{60} + 2 q^{64} - 16 q^{65} + 4 q^{70} + 62 q^{72} + 4 q^{74} + 24 q^{77} - 24 q^{78} + 48 q^{81} + 8 q^{84} + 24 q^{85} - 20 q^{86} + 36 q^{88} - 12 q^{92} - 16 q^{93} + 26 q^{98}+O(q^{100}) $ 8 * q + 2 * q^2 + 2 * q^4 + 14 * q^8 + 16 * q^9 - 6 * q^14 - 14 * q^16 - 30 * q^18 - 36 * q^21 + 28 * q^22 - 8 * q^25 + 14 * q^28 - 16 * q^29 - 12 * q^30 - 18 * q^32 - 30 * q^36 + 16 * q^37 + 8 * q^42 - 20 * q^44 + 44 * q^46 + 36 * q^49 - 2 * q^50 + 16 * q^53 + 2 * q^56 - 48 * q^57 - 4 * q^58 + 28 * q^60 + 2 * q^64 - 16 * q^65 + 4 * q^70 + 62 * q^72 + 4 * q^74 + 24 * q^77 - 24 * q^78 + 48 * q^81 + 8 * q^84 + 24 * q^85 - 20 * q^86 + 36 * q^88 - 12 * q^92 - 16 * q^93 + 26 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/140\mathbb{Z}\right)^\times$.

$n$	$57$	$71$	$101$
$\chi(n)$	$1$	$-1$	$-1$

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 $

$2$	−0.780776	+	1.17915i	−0.552092	+	0.833783i
$2$	−0.780776	+	1.17915i	−0.552092	+	0.833783i
$3$	3.02045			1.74386			0.871928	−	0.489634i	$-0.162870\pi$
$3$	3.02045			1.74386			0.871928	+	0.489634i	$0.162870\pi$
$4$	−0.780776	−	1.84130i	−0.390388	−	0.920650i
$5$			1.00000i			0.447214i
$5$			1.00000i			0.447214i
$6$	−2.35829	+	3.56155i	−0.962770	+	1.45400i
$7$	−2.17238	+	1.51022i	−0.821081	+	0.570811i
$7$	−2.17238	+	1.51022i	−0.821081	+	0.570811i
$8$	2.78078	+	0.516994i	0.983153	+	0.182785i
$9$	6.12311			2.04104
$10$	−1.17915	−	0.780776i	−0.372879	−	0.246903i
$11$		−	4.71659i		−	1.42211i	−0.703139	−	0.711053i	$-0.748219\pi$
$11$		−	4.71659i		−	1.42211i	0.703139	−	0.711053i	$-0.251781\pi$
$12$	−2.35829	−	5.56155i	−0.680781	−	1.60548i
$13$			2.00000i			0.554700i	0.960769	+	0.277350i	$0.0894562\pi$
$13$			2.00000i			0.554700i	−0.960769	+	0.277350i	$0.910544\pi$
$14$	−0.0846354	−	3.74070i	−0.0226198	−	0.999744i
$15$			3.02045i			0.779876i
$16$	−2.78078	+	2.87529i	−0.695194	+	0.718822i
$17$			1.12311i			0.272393i	0.990682	+	0.136197i	$0.0434879\pi$
$17$			1.12311i			0.272393i	−0.990682	+	0.136197i	$0.956512\pi$
$18$	−4.78078	+	7.22004i	−1.12684	+	1.70178i
$19$	−4.71659			−1.08206			−0.541030	−	0.841003i	$-0.681965\pi$
$19$	−4.71659			−1.08206			−0.541030	+	0.841003i	$0.681965\pi$
$20$	1.84130	−	0.780776i	0.411727	−	0.174587i
$21$	−6.56155	+	4.56155i	−1.43185	+	0.995412i
$22$	5.56155	+	3.68260i	1.18573	+	0.785133i
$23$		−	6.41273i		−	1.33715i	−0.743646	−	0.668573i	$-0.766905\pi$
$23$		−	6.41273i		−	1.33715i	0.743646	−	0.668573i	$-0.233095\pi$
$24$	8.39919	+	1.56155i	1.71448	+	0.318751i
$25$	−1.00000			−0.200000
$26$	−2.35829	−	1.56155i	−0.462500	−	0.306246i
$27$	9.43318			1.81542
$28$	4.47692	+	2.82085i	0.846058	+	0.533091i
$29$	−2.00000			−0.371391			−0.185695	−	0.982607i	$-0.559454\pi$
$29$	−2.00000			−0.371391			−0.185695	+	0.982607i	$0.559454\pi$
$30$	−3.56155	−	2.35829i	−0.650248	−	0.430564i
$31$	−3.39228			−0.609272			−0.304636	−	0.952469i	$-0.598535\pi$
$31$	−3.39228			−0.609272			−0.304636	+	0.952469i	$0.598535\pi$
$32$	−1.21922	−	5.52390i	−0.215530	−	0.976497i
$33$		−	14.2462i		−	2.47995i
$34$	−1.32431	−	0.876894i	−0.227117	−	0.150386i
$35$	−1.51022	−	2.17238i	−0.255274	−	0.367199i
$36$	−4.78078	−	11.2745i	−0.796796	−	1.87908i
$37$	2.00000			0.328798			0.164399	−	0.986394i	$-0.447432\pi$
$37$	2.00000			0.328798			0.164399	+	0.986394i	$0.447432\pi$
$38$	3.68260	−	5.56155i	0.597397	−	0.902203i
$39$			6.04090i			0.967317i
$40$	−0.516994	+	2.78078i	−0.0817439	+	0.439679i
$41$		−	1.12311i		−	0.175400i	−0.996147	−	0.0876998i	$-0.972048\pi$
$41$		−	1.12311i		−	0.175400i	0.996147	−	0.0876998i	$-0.0279516\pi$
$42$	−0.255637	−	11.2986i	−0.0394456	−	1.74341i
$43$			0.371834i			0.0567042i	0.999598	+	0.0283521i	$0.00902596\pi$
$43$			0.371834i			0.0567042i	−0.999598	+	0.0283521i	$0.990974\pi$
$44$	−8.68466	+	3.68260i	−1.30926	+	0.555173i
$45$			6.12311i			0.912779i
$46$	7.56155	+	5.00691i	1.11489	+	0.738228i
$47$	5.08842			0.742223			0.371111	−	0.928588i	$-0.378977\pi$
$47$	5.08842			0.742223			0.371111	+	0.928588i	$0.378977\pi$
$48$	−8.39919	+	8.68466i	−1.21232	+	1.25352i
$49$	2.43845	−	6.56155i	0.348350	−	0.937365i
$50$	0.780776	−	1.17915i	0.110418	−	0.166757i
$51$			3.39228i			0.475014i
$52$	3.68260	−	1.56155i	0.510685	−	0.216548i
$53$	2.00000			0.274721			0.137361	−	0.990521i	$-0.456138\pi$
$53$	2.00000			0.274721			0.137361	+	0.990521i	$0.456138\pi$
$54$	−7.36520	+	11.1231i	−1.00228	+	1.51366i
$55$	4.71659			0.635985
$56$	−6.82167	+	3.07649i	−0.911584	+	0.411113i
$57$	−14.2462			−1.88696
$58$	1.56155	−	2.35829i	0.205042	−	0.309659i
$59$	−2.06798			−0.269227			−0.134614	−	0.990898i	$-0.542979\pi$
$59$	−2.06798			−0.269227			−0.134614	+	0.990898i	$0.542979\pi$
$60$	5.56155	−	2.35829i	0.717993	−	0.304455i
$61$			2.00000i			0.256074i	0.991769	+	0.128037i	$0.0408676\pi$
$61$			2.00000i			0.256074i	−0.991769	+	0.128037i	$0.959132\pi$
$62$	2.64861	−	4.00000i	0.336374	−	0.508001i
$63$	−13.3017	+	9.24726i	−1.67586	+	1.16505i
$64$	7.46543	+	2.87529i	0.933179	+	0.359411i
$65$	−2.00000			−0.248069
$66$	16.7984	+	11.1231i	2.06774	+	1.36916i
$67$			3.76412i			0.459860i	0.973207	+	0.229930i	$0.0738497\pi$
$67$			3.76412i			0.459860i	−0.973207	+	0.229930i	$0.926150\pi$
$68$	2.06798	−	0.876894i	0.250779	−	0.106339i
$69$		−	19.3693i		−	2.33179i
$70$	3.74070	−	0.0846354i	0.447099	−	0.0101159i
$71$			7.36520i			0.874089i	0.899440	+	0.437044i	$0.143975\pi$
$71$			7.36520i			0.874089i	−0.899440	+	0.437044i	$0.856025\pi$
$72$	17.0270	+	3.16561i	2.00665	+	0.373070i
$73$			15.3693i			1.79884i	0.437083	+	0.899421i	$0.356012\pi$
$73$			15.3693i			1.79884i	−0.437083	+	0.899421i	$0.643988\pi$
$74$	−1.56155	+	2.35829i	−0.181527	+	0.274146i
$75$	−3.02045			−0.348771
$76$	3.68260	+	8.68466i	0.422423	+	0.996199i
$77$	7.12311	+	10.2462i	0.811753	+	1.16766i
$78$	−7.12311	−	4.71659i	−0.806533	−	0.534049i
$79$		−	1.32431i		−	0.148996i	−0.997221	−	0.0744981i	$-0.976265\pi$
$79$		−	1.32431i		−	0.148996i	0.997221	−	0.0744981i	$-0.0237355\pi$
$80$	−2.87529	−	2.78078i	−0.321467	−	0.310900i
$81$	10.1231			1.12479
$82$	1.32431	+	0.876894i	0.146245	+	0.0968368i
$83$	3.02045			0.331537			0.165769	−	0.986165i	$-0.446990\pi$
$83$	3.02045			0.331537			0.165769	+	0.986165i	$0.446990\pi$
$84$	13.5223	+	8.52024i	1.47540	+	0.929634i
$85$	−1.12311			−0.121818
$86$	−0.438447	−	0.290319i	−0.0472790	−	0.0313059i
$87$	−6.04090			−0.647652
$88$	2.43845	−	13.1158i	0.259939	−	1.39815i
$89$			12.0000i			1.27200i	0.771690	+	0.635999i	$0.219412\pi$
$89$			12.0000i			1.27200i	−0.771690	+	0.635999i	$0.780588\pi$
$90$	−7.22004	−	4.78078i	−0.761059	−	0.503938i
$91$	−3.02045	−	4.34475i	−0.316629	−	0.455454i
$92$	−11.8078	+	5.00691i	−1.23104	+	0.522006i
$93$	−10.2462			−1.06248
$94$	−3.97292	+	6.00000i	−0.409775	+	0.618853i
$95$		−	4.71659i		−	0.483912i
$96$	−3.68260	−	16.6847i	−0.375854	−	1.70287i
$97$		−	1.12311i		−	0.114034i	−0.998373	−	0.0570170i	$-0.981841\pi$
$97$		−	1.12311i		−	0.114034i	0.998373	−	0.0570170i	$-0.0181589\pi$
$98$	5.83315	+	7.99839i	0.589238	+	0.807960i
$99$		−	28.8802i		−	2.90257i
$100$	0.780776	+	1.84130i	0.0780776	+	0.184130i
$101$		−	15.1231i		−	1.50481i	−0.658703	−	0.752403i	$-0.728895\pi$
$101$		−	15.1231i		−	1.50481i	0.658703	−	0.752403i	$-0.271105\pi$
$102$	−4.00000	−	2.64861i	−0.396059	−	0.262252i
$103$	−7.73704			−0.762353			−0.381176	−	0.924502i	$-0.624481\pi$
$103$	−7.73704			−0.762353			−0.381176	+	0.924502i	$0.624481\pi$
$104$	−1.03399	+	5.56155i	−0.101391	+	0.545355i
$105$	−4.56155	−	6.56155i	−0.445162	−	0.640342i
$106$	−1.56155	+	2.35829i	−0.151671	+	0.229058i
$107$			5.66906i			0.548049i	0.961723	+	0.274024i	$0.0883549\pi$
$107$			5.66906i			0.548049i	−0.961723	+	0.274024i	$0.911645\pi$
$108$	−7.36520	−	17.3693i	−0.708717	−	1.67136i
$109$	−7.12311			−0.682270			−0.341135	−	0.940014i	$-0.610811\pi$
$109$	−7.12311			−0.682270			−0.341135	+	0.940014i	$0.610811\pi$
$110$	−3.68260	+	5.56155i	−0.351122	+	0.530273i
$111$	6.04090			0.573376
$112$	1.69857	−	10.4458i	0.160499	−	0.987036i
$113$	18.4924			1.73962			0.869810	−	0.493386i	$-0.164241\pi$
$113$	18.4924			1.73962			0.869810	+	0.493386i	$0.164241\pi$
$114$	11.1231	−	16.7984i	1.04177	−	1.57331i
$115$	6.41273			0.597990
$116$	1.56155	+	3.68260i	0.144987	+	0.341921i
$117$			12.2462i			1.13216i
$118$	1.61463	−	2.43845i	0.148638	−	0.224477i
$119$	−1.69614	−	2.43981i	−0.155485	−	0.223657i
$120$	−1.56155	+	8.39919i	−0.142550	+	0.766738i
$121$	−11.2462			−1.02238
$122$	−2.35829	−	1.56155i	−0.213510	−	0.141376i
$123$		−	3.39228i		−	0.305872i
$124$	2.64861	+	6.24621i	0.237853	+	0.560926i
$125$		−	1.00000i		−	0.0894427i
$126$	−0.518231	−	22.9047i	−0.0461677	−	2.04051i
$127$			17.7509i			1.57513i	0.616229	+	0.787567i	$0.288659\pi$
$127$			17.7509i			1.57513i	−0.616229	+	0.787567i	$0.711341\pi$
$128$	−9.21922	+	6.55789i	−0.814872	+	0.579641i
$129$			1.12311i			0.0988839i
$130$	1.56155	−	2.35829i	0.136957	−	0.206836i
$131$	17.5420			1.53266			0.766328	−	0.642450i	$-0.222082\pi$
$131$	17.5420			1.53266			0.766328	+	0.642450i	$0.222082\pi$
$132$	−26.2316	+	11.1231i	−2.28316	+	0.968142i
$133$	10.2462	−	7.12311i	0.888459	−	0.617652i
$134$	−4.43845	−	2.93893i	−0.383423	−	0.253885i
$135$			9.43318i			0.811879i
$136$	−0.580639	+	3.12311i	−0.0497894	+	0.267804i
$137$	−14.0000			−1.19610			−0.598050	−	0.801459i	$-0.704058\pi$
$137$	−14.0000			−1.19610			−0.598050	+	0.801459i	$0.704058\pi$
$138$	22.8393	+	15.1231i	1.94421	+	1.28736i
$139$	16.7984			1.42482			0.712410	−	0.701763i	$-0.247604\pi$
$139$	16.7984			1.42482			0.712410	+	0.701763i	$0.247604\pi$
$140$	−2.82085	+	4.47692i	−0.238406	+	0.378369i
$141$	15.3693			1.29433
$142$	−8.68466	−	5.75058i	−0.728800	−	0.482578i
$143$	9.43318			0.788842
$144$	−17.0270	+	17.6057i	−1.41892	+	1.46714i
$145$		−	2.00000i		−	0.166091i
$146$	−18.1227	−	12.0000i	−1.49984	−	0.993127i
$147$	7.36520	−	19.8188i	0.607472	−	1.63463i
$148$	−1.56155	−	3.68260i	−0.128359	−	0.302708i
$149$	5.36932			0.439872			0.219936	−	0.975514i	$-0.429415\pi$
$149$	5.36932			0.439872			0.219936	+	0.975514i	$0.429415\pi$
$150$	2.35829	−	3.56155i	0.192554	−	0.290800i
$151$			10.0138i			0.814913i	0.913225	+	0.407456i	$0.133584\pi$
$151$			10.0138i			0.814913i	−0.913225	+	0.407456i	$0.866416\pi$
$152$	−13.1158	−	2.43845i	−1.06383	−	0.197784i
$153$			6.87689i			0.555964i
$154$	−17.6433	+	0.399190i	−1.42174	+	0.0321677i
$155$		−	3.39228i		−	0.272475i
$156$	11.1231	−	4.71659i	0.890561	−	0.377629i
$157$		−	0.246211i		−	0.0196498i	−0.999952	−	0.00982490i	$-0.996873\pi$
$157$		−	0.246211i		−	0.0196498i	0.999952	−	0.00982490i	$-0.00312741\pi$
$158$	1.56155	+	1.03399i	0.124230	+	0.0822596i
$159$	6.04090			0.479074
$160$	5.52390	−	1.21922i	0.436703	−	0.0963881i
$161$	9.68466	+	13.9309i	0.763258	+	1.09791i
$162$	−7.90388	+	11.9366i	−0.620988	+	0.937830i
$163$		−	3.02045i		−	0.236580i	−0.992979	−	0.118290i	$-0.962259\pi$
$163$		−	3.02045i		−	0.236580i	0.992979	−	0.118290i	$-0.0377412\pi$
$164$	−2.06798	+	0.876894i	−0.161482	+	0.0684739i
$165$	14.2462			1.10907
$166$	−2.35829	+	3.56155i	−0.183039	+	0.276430i
$167$	−19.8188			−1.53363			−0.766813	−	0.641870i	$-0.778159\pi$
$167$	−19.8188			−1.53363			−0.766813	+	0.641870i	$0.778159\pi$
$168$	−20.6045	+	9.29238i	−1.58967	+	0.716922i
$169$	9.00000			0.692308
$170$	0.876894	−	1.32431i	0.0672547	−	0.101570i
$171$	−28.8802			−2.20852
$172$	0.684658	−	0.290319i	0.0522047	−	0.0221366i
$173$		−	16.2462i		−	1.23518i	−0.786502	−	0.617588i	$-0.788110\pi$
$173$		−	16.2462i		−	1.23518i	0.786502	−	0.617588i	$-0.211890\pi$
$174$	4.71659	−	7.12311i	0.357564	−	0.540001i
$175$	2.17238	−	1.51022i	0.164216	−	0.114162i
$176$	13.5616	+	13.1158i	1.02224	+	0.988639i
$177$	−6.24621			−0.469494
$178$	−14.1498	−	9.36932i	−1.06057	−	0.702260i
$179$			10.7575i			0.804052i	0.915628	+	0.402026i	$0.131694\pi$
$179$			10.7575i			0.804052i	−0.915628	+	0.402026i	$0.868306\pi$
$180$	11.2745	−	4.78078i	0.840350	−	0.356338i
$181$		−	15.1231i		−	1.12409i	−0.827106	−	0.562046i	$-0.810014\pi$
$181$		−	15.1231i		−	1.12409i	0.827106	−	0.562046i	$-0.189986\pi$
$182$	7.48140	−	0.169271i	0.554558	−	0.0125472i
$183$			6.04090i			0.446556i
$184$	3.31534	−	17.8324i	0.244410	−	1.31462i
$185$			2.00000i			0.147043i
$186$	8.00000	−	12.0818i	0.586588	−	0.885880i
$187$	5.29723			0.387372
$188$	−3.97292	−	9.36932i	−0.289755	−	0.683328i
$189$	−20.4924	+	14.2462i	−1.49060	+	1.03626i
$190$	5.56155	+	3.68260i	0.403477	+	0.267164i
$191$		−	16.7984i		−	1.21549i	−0.794133	−	0.607744i	$-0.792075\pi$
$191$		−	16.7984i		−	1.21549i	0.794133	−	0.607744i	$-0.207925\pi$
$192$	22.5490	+	8.68466i	1.62733	+	0.626761i
$193$	−22.4924			−1.61904			−0.809520	−	0.587092i	$-0.800273\pi$
$193$	−22.4924			−1.61904			−0.809520	+	0.587092i	$0.800273\pi$
$194$	1.32431	+	0.876894i	0.0950797	+	0.0629573i
$195$	−6.04090			−0.432598
$196$	−13.9857	+	0.633191i	−0.998977	+	0.0452279i
$197$	18.0000			1.28245			0.641223	−	0.767354i	$-0.278427\pi$
$197$	18.0000			1.28245			0.641223	+	0.767354i	$0.278427\pi$
$198$	34.0540	+	22.5490i	2.42011	+	1.60248i
$199$	−26.8122			−1.90067			−0.950333	−	0.311235i	$-0.899258\pi$
$199$	−26.8122			−1.90067			−0.950333	+	0.311235i	$0.899258\pi$
$200$	−2.78078	−	0.516994i	−0.196631	−	0.0365570i
$201$			11.3693i			0.801930i
$202$	17.8324	+	11.8078i	1.25468	+	0.830791i
$203$	4.34475	−	3.02045i	0.304942	−	0.211994i
$204$	6.24621	−	2.64861i	0.437322	−	0.185440i
$205$	1.12311			0.0784411
$206$	6.04090	−	9.12311i	0.420889	−	0.635637i
$207$		−	39.2658i		−	2.72916i
$208$	−5.75058	−	5.56155i	−0.398731	−	0.385624i
$209$			22.2462i			1.53880i
$210$	11.2986	−	0.255637i	0.779677	−	0.0176406i
$211$		−	22.0956i		−	1.52112i	−0.649265	−	0.760562i	$-0.724923\pi$
$211$		−	22.0956i		−	1.52112i	0.649265	−	0.760562i	$-0.275077\pi$
$212$	−1.56155	−	3.68260i	−0.107248	−	0.252922i
$213$			22.2462i			1.52429i
$214$	−6.68466	−	4.42627i	−0.456954	−	0.302574i
$215$	−0.371834			−0.0253589
$216$	26.2316	+	4.87689i	1.78483	+	0.331831i
$217$	7.36932	−	5.12311i	0.500262	−	0.347779i
$218$	5.56155	−	8.39919i	0.376676	−	0.568865i
$219$			46.4222i			3.13692i
$220$	−3.68260	−	8.68466i	−0.248281	−	0.585520i
$221$	−2.24621			−0.151097
$222$	−4.71659	+	7.12311i	−0.316557	+	0.478072i
$223$	20.5625			1.37697			0.688483	−	0.725252i	$-0.258277\pi$
$223$	20.5625			1.37697			0.688483	+	0.725252i	$0.258277\pi$
$224$	10.9909	+	10.1587i	0.734363	+	0.678757i
$225$	−6.12311			−0.408207
$226$	−14.4384	+	21.8053i	−0.960431	+	1.45047i
$227$	−3.76412			−0.249833			−0.124917	−	0.992167i	$-0.539866\pi$
$227$	−3.76412			−0.249833			−0.124917	+	0.992167i	$0.539866\pi$
$228$	11.1231	+	26.2316i	0.736646	+	1.73723i
$229$		−	12.8769i		−	0.850929i	−0.904975	−	0.425465i	$-0.860111\pi$
$229$		−	12.8769i		−	0.850929i	0.904975	−	0.425465i	$-0.139889\pi$
$230$	−5.00691	+	7.56155i	−0.330146	+	0.498594i
$231$	21.5150	+	30.9481i	1.41558	+	2.03624i
$232$	−5.56155	−	1.03399i	−0.365134	−	0.0678846i
$233$	7.75379			0.507968			0.253984	−	0.967208i	$-0.418259\pi$
$233$	7.75379			0.507968			0.253984	+	0.967208i	$0.418259\pi$
$234$	−14.4401	−	9.56155i	−0.943978	−	0.625058i
$235$			5.08842i			0.331932i
$236$	1.61463	+	3.80776i	0.105103	+	0.247864i
$237$		−	4.00000i		−	0.259828i
$238$	4.20120	−	0.0950545i	0.272323	−	0.00616147i
$239$		−	3.97292i		−	0.256987i	−0.991710	−	0.128493i	$-0.958986\pi$
$239$		−	3.97292i		−	0.256987i	0.991710	−	0.128493i	$-0.0410141\pi$
$240$	−8.68466	−	8.39919i	−0.560592	−	0.542165i
$241$		−	25.6155i		−	1.65004i	−0.565103	−	0.825021i	$-0.691163\pi$
$241$		−	25.6155i		−	1.65004i	0.565103	−	0.825021i	$-0.308837\pi$
$242$	8.78078	−	13.2609i	0.564450	−	0.852445i
$243$	2.27678			0.146055
$244$	3.68260	−	1.56155i	0.235754	−	0.0999682i
$245$	6.56155	+	2.43845i	0.419202	+	0.155787i
$246$	4.00000	+	2.64861i	0.255031	+	0.168869i
$247$		−	9.43318i		−	0.600219i
$248$	−9.43318	−	1.75379i	−0.599007	−	0.111366i
$249$	9.12311			0.578153
$250$	1.17915	+	0.780776i	0.0745758	+	0.0493806i
$251$	−16.0547			−1.01336			−0.506682	−	0.862133i	$-0.669128\pi$
$251$	−16.0547			−1.01336			−0.506682	+	0.862133i	$0.669128\pi$
$252$	27.4126	+	17.2724i	1.72683	+	1.08806i
$253$	−30.2462			−1.90156
$254$	−20.9309	−	13.8594i	−1.31332	−	0.869619i
$255$	−3.39228			−0.212433
$256$	−0.534565	−	15.9911i	−0.0334103	−	0.999442i
$257$		−	11.3693i		−	0.709199i	−0.935018	−	0.354599i	$-0.884617\pi$
$257$		−	11.3693i		−	0.709199i	0.935018	−	0.354599i	$-0.115383\pi$
$258$	−1.32431	−	0.876894i	−0.0824477	−	0.0545931i
$259$	−4.34475	+	3.02045i	−0.269970	+	0.187682i
$260$	1.56155	+	3.68260i	0.0968434	+	0.228385i
$261$	−12.2462			−0.758021
$262$	−13.6964	+	20.6847i	−0.846168	+	1.27790i
$263$			18.4945i			1.14042i	0.821499	+	0.570211i	$0.193138\pi$
$263$			18.4945i			1.14042i	−0.821499	+	0.570211i	$0.806862\pi$
$264$	7.36520	−	39.6155i	0.453297	−	2.43817i
$265$			2.00000i			0.122859i
$266$	0.399190	+	17.6433i	0.0244759	+	1.08178i
$267$			36.2454i			2.21818i
$268$	6.93087	−	2.93893i	0.423370	−	0.179524i
$269$		−	0.246211i		−	0.0150118i	−0.999972	−	0.00750588i	$-0.997611\pi$
$269$		−	0.246211i		−	0.0150118i	0.999972	−	0.00750588i	$-0.00238922\pi$
$270$	−11.1231	−	7.36520i	−0.676931	−	0.448232i
$271$	1.90495			0.115717			0.0578586	−	0.998325i	$-0.481573\pi$
$271$	1.90495			0.115717			0.0578586	+	0.998325i	$0.481573\pi$
$272$	−3.22925	−	3.12311i	−0.195802	−	0.189366i
$273$	−9.12311	−	13.1231i	−0.552155	−	0.794246i
$274$	10.9309	−	16.5081i	0.660358	−	0.997288i
$275$			4.71659i			0.284421i
$276$	−35.6647	+	15.1231i	−2.14676	+	0.910304i
$277$	12.2462			0.735804			0.367902	−	0.929865i	$-0.380076\pi$
$277$	12.2462			0.735804			0.367902	+	0.929865i	$0.380076\pi$
$278$	−13.1158	+	19.8078i	−0.786632	+	1.18799i
$279$	−20.7713			−1.24355
$280$	−3.07649	−	6.82167i	−0.183855	−	0.407673i
$281$	−29.3693			−1.75203			−0.876013	−	0.482287i	$-0.839806\pi$
$281$	−29.3693			−1.75203			−0.876013	+	0.482287i	$0.839806\pi$
$282$	−12.0000	+	18.1227i	−0.714590	+	1.07919i
$283$	−4.92539			−0.292784			−0.146392	−	0.989227i	$-0.546766\pi$
$283$	−4.92539			−0.292784			−0.146392	+	0.989227i	$0.546766\pi$
$284$	13.5616	−	5.75058i	0.804730	−	0.341234i
$285$		−	14.2462i		−	0.843873i
$286$	−7.36520	+	11.1231i	−0.435514	+	0.657723i
$287$	1.69614	+	2.43981i	0.100120	+	0.144017i
$288$	−7.46543	−	33.8234i	−0.439905	−	1.99307i
$289$	15.7386			0.925802
$290$	2.35829	+	1.56155i	0.138484	+	0.0916975i
$291$		−	3.39228i		−	0.198859i
$292$	28.2995	−	12.0000i	1.65610	−	0.702247i
$293$		−	15.7538i		−	0.920346i	−0.887829	−	0.460173i	$-0.847787\pi$
$293$		−	15.7538i		−	0.920346i	0.887829	−	0.460173i	$-0.152213\pi$
$294$	17.6187	+	24.1587i	1.02755	+	1.40897i
$295$		−	2.06798i		−	0.120402i
$296$	5.56155	+	1.03399i	0.323259	+	0.0600993i
$297$		−	44.4924i		−	2.58171i
$298$	−4.19224	+	6.33122i	−0.242850	+	0.366757i
$299$	12.8255			0.741715
$300$	2.35829	+	5.56155i	0.136156	+	0.321096i
$301$	−0.561553	−	0.807764i	−0.0323674	−	0.0465587i
$302$	−11.8078	−	7.81855i	−0.679460	−	0.449907i
$303$		−	45.6786i		−	2.62416i
$304$	13.1158	−	13.5616i	0.752242	−	0.777808i
$305$	−2.00000			−0.114520
$306$	−8.10887	−	5.36932i	−0.463553	−	0.306943i
$307$	1.53311			0.0874993			0.0437496	−	0.999043i	$-0.486070\pi$
$307$	1.53311			0.0874993			0.0437496	+	0.999043i	$0.486070\pi$
$308$	13.3048	−	21.1158i	0.758112	−	1.20318i
$309$	−23.3693			−1.32943
$310$	4.00000	+	2.64861i	0.227185	+	0.150431i
$311$	30.2045			1.71274			0.856369	−	0.516364i	$-0.172715\pi$
$311$	30.2045			1.71274			0.856369	+	0.516364i	$0.172715\pi$
$312$	−3.12311	+	16.7984i	−0.176811	+	0.951021i
$313$			33.6155i			1.90006i	0.312156	+	0.950031i	$0.398949\pi$
$313$			33.6155i			1.90006i	−0.312156	+	0.950031i	$0.601051\pi$
$314$	0.290319	+	0.192236i	0.0163837	+	0.0108485i
$315$	−9.24726	−	13.3017i	−0.521024	−	0.749466i
$316$	−2.43845	+	1.03399i	−0.137173	+	0.0581663i
$317$	12.2462			0.687816			0.343908	−	0.939003i	$-0.388249\pi$
$317$	12.2462			0.687816			0.343908	+	0.939003i	$0.388249\pi$
$318$	−4.71659	+	7.12311i	−0.264493	+	0.399444i
$319$			9.43318i			0.528157i
$320$	−2.87529	+	7.46543i	−0.160734	+	0.417330i
$321$			17.1231i			0.955719i
$322$	−23.9881	+	0.542744i	−1.33680	+	0.0302459i
$323$		−	5.29723i		−	0.294746i
$324$	−7.90388	−	18.6397i	−0.439105	−	1.03554i
$325$		−	2.00000i		−	0.110940i
$326$	3.56155	+	2.35829i	0.197256	+	0.130614i
$327$	−21.5150			−1.18978
$328$	0.580639	−	3.12311i	0.0320604	−	0.172445i
$329$	−11.0540	+	7.68466i	−0.609425	+	0.423669i
$330$	−11.1231	+	16.7984i	−0.612307	+	0.924720i
$331$		−	18.2857i		−	1.00507i	−0.864556	−	0.502537i	$-0.832400\pi$
$331$		−	18.2857i		−	1.00507i	0.864556	−	0.502537i	$-0.167600\pi$
$332$	−2.35829	−	5.56155i	−0.129428	−	0.305230i
$333$	12.2462			0.671088
$334$	15.4741	−	23.3693i	0.846704	−	1.27871i
$335$	−3.76412			−0.205656
$336$	5.13043	−	31.5510i	0.279888	−	1.72125i
$337$	−12.2462			−0.667094			−0.333547	−	0.942734i	$-0.608246\pi$
$337$	−12.2462			−0.667094			−0.333547	+	0.942734i	$0.608246\pi$
$338$	−7.02699	+	10.6123i	−0.382218	+	0.577234i
$339$	55.8554			3.03365
$340$	0.876894	+	2.06798i	0.0475563	+	0.112152i
$341$			16.0000i			0.866449i
$342$	22.5490	−	34.0540i	1.21931	−	1.84143i
$343$	4.61219	+	17.9368i	0.249035	+	0.968495i
$344$	−0.192236	+	1.03399i	−0.0103647	+	0.0557489i
$345$	19.3693			1.04281
$346$	19.1567	+	12.6847i	1.02987	+	0.681931i
$347$			5.66906i			0.304331i	0.988355	+	0.152166i	$0.0486247\pi$
$347$			5.66906i			0.304331i	−0.988355	+	0.152166i	$0.951375\pi$
$348$	4.71659	+	11.1231i	0.252836	+	0.596261i
$349$			29.8617i			1.59846i	0.601024	+	0.799231i	$0.294760\pi$
$349$			29.8617i			1.59846i	−0.601024	+	0.799231i	$0.705240\pi$
$350$	0.0846354	+	3.74070i	0.00452395	+	0.199949i
$351$			18.8664i			1.00701i
$352$	−26.0540	+	5.75058i	−1.38868	+	0.306507i
$353$		−	19.3693i		−	1.03092i	−0.856912	−	0.515462i	$-0.827620\pi$
$353$		−	19.3693i		−	1.03092i	0.856912	−	0.515462i	$-0.172380\pi$
$354$	4.87689	−	7.36520i	0.259204	−	0.391456i
$355$	−7.36520			−0.390904
$356$	22.0956	−	9.36932i	1.17106	−	0.496573i
$357$	−5.12311	−	7.36932i	−0.271144	−	0.390026i
$358$	−12.6847	−	8.39919i	−0.670405	−	0.443911i
$359$		−	16.0547i		−	0.847335i	−0.905818	−	0.423668i	$-0.860742\pi$
$359$		−	16.0547i		−	0.847335i	0.905818	−	0.423668i	$-0.139258\pi$
$360$	−3.16561	+	17.0270i	−0.166842	+	0.897401i
$361$	3.24621			0.170853
$362$	17.8324	+	11.8078i	0.937248	+	0.620602i
$363$	−33.9686			−1.78289
$364$	−5.64171	+	8.95383i	−0.295706	+	0.469308i
$365$	−15.3693			−0.804467
$366$	−7.12311	−	4.71659i	−0.372331	−	0.246540i
$367$	−10.3857			−0.542127			−0.271063	−	0.962562i	$-0.587375\pi$
$367$	−10.3857			−0.542127			−0.271063	+	0.962562i	$0.587375\pi$
$368$	18.4384	+	17.8324i	0.961171	+	0.929576i
$369$		−	6.87689i		−	0.357997i
$370$	−2.35829	−	1.56155i	−0.122602	−	0.0811813i
$371$	−4.34475	+	3.02045i	−0.225568	+	0.156814i
$372$	8.00000	+	18.8664i	0.414781	+	0.978175i
$373$	−10.4924			−0.543277			−0.271639	−	0.962399i	$-0.587566\pi$
$373$	−10.4924			−0.543277			−0.271639	+	0.962399i	$0.587566\pi$
$374$	−4.13595	+	6.24621i	−0.213865	+	0.322984i
$375$		−	3.02045i		−	0.155975i
$376$	14.1498	+	2.63068i	0.729719	+	0.135667i
$377$		−	4.00000i		−	0.206010i
$378$	−0.798381	−	35.2867i	−0.0410643	−	1.81495i
$379$		−	14.8934i		−	0.765024i	−0.923950	−	0.382512i	$-0.875059\pi$
$379$		−	14.8934i		−	0.765024i	0.923950	−	0.382512i	$-0.124941\pi$
$380$	−8.68466	+	3.68260i	−0.445514	+	0.188913i
$381$			53.6155i			2.74681i
$382$	19.8078	+	13.1158i	1.01345	+	0.671062i
$383$	−19.0752			−0.974695			−0.487348	−	0.873208i	$-0.662036\pi$
$383$	−19.0752			−0.974695			−0.487348	+	0.873208i	$0.662036\pi$
$384$	−27.8462	+	19.8078i	−1.42102	+	1.01081i
$385$	−10.2462	+	7.12311i	−0.522195	+	0.363027i
$386$	17.5616	−	26.5219i	0.893860	−	1.34993i
$387$			2.27678i			0.115735i
$388$	−2.06798	+	0.876894i	−0.104986	+	0.0445176i
$389$	−7.12311			−0.361156			−0.180578	−	0.983561i	$-0.557797\pi$
$389$	−7.12311			−0.361156			−0.180578	+	0.983561i	$0.557797\pi$
$390$	4.71659	−	7.12311i	0.238834	−	0.360692i
$391$	7.20217			0.364230
$392$	10.1731	−	16.9855i	0.513817	−	0.857900i
$393$	52.9848			2.67273
$394$	−14.0540	+	21.2247i	−0.708029	+	1.06928i
$395$	1.32431			0.0666331
$396$	−53.1771	+	22.5490i	−2.67225	+	1.13313i
$397$		−	14.0000i		−	0.702640i	−0.936255	−	0.351320i	$-0.885733\pi$
$397$		−	14.0000i		−	0.702640i	0.936255	−	0.351320i	$-0.114267\pi$
$398$	20.9343	−	31.6155i	1.04934	−	1.58474i
$399$	30.9481	−	21.5150i	1.54935	−	1.07710i
$400$	2.78078	−	2.87529i	0.139039	−	0.143764i
$401$	6.00000			0.299626			0.149813	−	0.988714i	$-0.452133\pi$
$401$	6.00000			0.299626			0.149813	+	0.988714i	$0.452133\pi$
$402$	−13.4061	−	8.87689i	−0.668635	−	0.442739i
$403$		−	6.78456i		−	0.337963i
$404$	−27.8462	+	11.8078i	−1.38540	+	0.587458i
$405$			10.1231i			0.503021i
$406$	0.169271	+	7.48140i	0.00840077	+	0.371296i
$407$		−	9.43318i		−	0.467585i
$408$	−1.75379	+	9.43318i	−0.0868255	+	0.467012i
$409$		−	17.1231i		−	0.846683i	−0.905970	−	0.423342i	$-0.860857\pi$
$409$		−	17.1231i		−	0.846683i	0.905970	−	0.423342i	$-0.139143\pi$
$410$	−0.876894	+	1.32431i	−0.0433067	+	0.0654029i
$411$	−42.2863			−2.08583
$412$	6.04090	+	14.2462i	0.297614	+	0.701860i
$413$	4.49242	−	3.12311i	0.221058	−	0.153678i
$414$	46.3002	+	30.6578i	2.27553	+	1.50675i
$415$			3.02045i			0.148268i
$416$	11.0478	−	2.43845i	0.541663	−	0.119555i
$417$	50.7386			2.48468
$418$	−26.2316	−	17.3693i	−1.28303	−	0.849561i
$419$	−23.5829			−1.15210			−0.576051	−	0.817414i	$-0.695407\pi$
$419$	−23.5829			−1.15210			−0.576051	+	0.817414i	$0.695407\pi$
$420$	−8.52024	+	13.5223i	−0.415745	+	0.659820i
$421$	23.6155			1.15095			0.575475	−	0.817819i	$-0.304817\pi$
$421$	23.6155			1.15095			0.575475	+	0.817819i	$0.304817\pi$
$422$	26.0540	+	17.2517i	1.26829	+	0.839801i
$423$	31.1570			1.51490
$424$	5.56155	+	1.03399i	0.270093	+	0.0502149i
$425$		−	1.12311i		−	0.0544786i
$426$	−26.2316	−	17.3693i	−1.27092	−	0.841546i
$427$	−3.02045	−	4.34475i	−0.146170	−	0.210257i
$428$	10.4384	−	4.42627i	0.504561	−	0.213952i
$429$	28.4924			1.37563
$430$	0.290319	−	0.438447i	0.0140004	−	0.0211438i
$431$		−	5.87787i		−	0.283127i	−0.989929	−	0.141563i	$-0.954787\pi$
$431$		−	5.87787i		−	0.283127i	0.989929	−	0.141563i	$-0.0452129\pi$
$432$	−26.2316	+	27.1231i	−1.26207	+	1.30496i
$433$			29.6155i			1.42323i	0.702569	+	0.711616i	$0.252036\pi$
$433$			29.6155i			1.42323i	−0.702569	+	0.711616i	$0.747964\pi$
$434$	0.287107	+	12.6895i	0.0137816	+	0.609116i
$435$		−	6.04090i		−	0.289639i
$436$	5.56155	+	13.1158i	0.266350	+	0.628132i
$437$			30.2462i			1.44687i
$438$	−54.7386	−	36.2454i	−2.61551	−	1.73187i
$439$	16.2177			0.774031			0.387015	−	0.922073i	$-0.373506\pi$
$439$	16.2177			0.774031			0.387015	+	0.922073i	$0.373506\pi$
$440$	13.1158	+	2.43845i	0.625270	+	0.116248i
$441$	14.9309	−	40.1771i	0.710994	−	1.91319i
$442$	1.75379	−	2.64861i	0.0834192	−	0.125982i
$443$			23.0481i			1.09505i	0.836790	+	0.547524i	$0.184429\pi$
$443$			23.0481i			1.09505i	−0.836790	+	0.547524i	$0.815571\pi$
$444$	−4.71659	−	11.1231i	−0.223839	−	0.527879i
$445$	−12.0000			−0.568855
$446$	−16.0547	+	24.2462i	−0.760213	+	1.14809i
$447$	16.2177			0.767073
$448$	−20.5601	+	5.02827i	−0.971372	+	0.237563i
$449$	−15.6155			−0.736942			−0.368471	−	0.929639i	$-0.620119\pi$
$449$	−15.6155			−0.736942			−0.368471	+	0.929639i	$0.620119\pi$
$450$	4.78078	−	7.22004i	0.225368	−	0.340356i
$451$	−5.29723			−0.249437
$452$	−14.4384	−	34.0501i	−0.679127	−	1.60158i
$453$			30.2462i			1.42109i
$454$	2.93893	−	4.43845i	0.137931	−	0.208307i
$455$	4.34475	−	3.02045i	0.203685	−	0.141601i
$456$	−39.6155	−	7.36520i	−1.85517	−	0.344907i
$457$	6.00000			0.280668			0.140334	−	0.990104i	$-0.455182\pi$
$457$	6.00000			0.280668			0.140334	+	0.990104i	$0.455182\pi$
$458$	15.1838	+	10.0540i	0.709490	+	0.469791i
$459$			10.5945i			0.494507i
$460$	−5.00691	−	11.8078i	−0.233448	−	0.550540i
$461$			3.61553i			0.168392i	0.996449	+	0.0841960i	$0.0268322\pi$
$461$			3.61553i			0.168392i	−0.996449	+	0.0841960i	$0.973168\pi$
$462$	−53.2908	+	1.20573i	−2.47931	+	0.0560958i
$463$			28.6714i			1.33247i	0.745741	+	0.666236i	$0.232096\pi$
$463$			28.6714i			1.33247i	−0.745741	+	0.666236i	$0.767904\pi$
$464$	5.56155	−	5.75058i	0.258189	−	0.266964i
$465$		−	10.2462i		−	0.475157i
$466$	−6.05398	+	9.14286i	−0.280445	+	0.423535i
$467$	18.4945			0.855824			0.427912	−	0.903820i	$-0.359249\pi$
$467$	18.4945			0.855824			0.427912	+	0.903820i	$0.359249\pi$
$468$	22.5490	−	9.56155i	1.04233	−	0.441983i
$469$	−5.68466	−	8.17708i	−0.262493	−	0.377583i
$470$	−6.00000	−	3.97292i	−0.276759	−	0.183257i
$471$		−	0.743668i		−	0.0342664i
$472$	−5.75058	−	1.06913i	−0.264692	−	0.0492107i
$473$	1.75379			0.0806393
$474$	4.71659	+	3.12311i	0.216640	+	0.143449i
$475$	4.71659			0.216412
$476$	−3.16812	+	5.02805i	−0.145210	+	0.230460i
$477$	12.2462			0.560715
$478$	4.68466	+	3.10196i	0.214271	+	0.141880i
$479$		0			0			−	1.00000i	$-0.5\pi$
$479$		0			0				1.00000i	$0.5\pi$
$480$	16.6847	−	3.68260i	0.761547	−	0.168087i
$481$			4.00000i			0.182384i
$482$	30.2045	+	20.0000i	1.37578	+	0.910975i
$483$	29.2520	+	42.0775i	1.33101	+	1.91459i
$484$	8.78078	+	20.7077i	0.399126	+	0.941257i
$485$	1.12311			0.0509976
$486$	−1.77766	+	2.68466i	−0.0806361	+	0.121779i
$487$		−	13.1973i		−	0.598026i	−0.954249	−	0.299013i	$-0.903343\pi$
$487$		−	13.1973i		−	0.598026i	0.954249	−	0.299013i	$-0.0966575\pi$
$488$	−1.03399	+	5.56155i	−0.0468064	+	0.251760i
$489$		−	9.12311i		−	0.412561i
$490$	−7.99839	+	5.83315i	−0.361331	+	0.263515i
$491$			31.5288i			1.42287i	0.702750	+	0.711437i	$0.251955\pi$
$491$			31.5288i			1.42287i	−0.702750	+	0.711437i	$0.748045\pi$
$492$	−6.24621	+	2.64861i	−0.281601	+	0.119409i
$493$		−	2.24621i		−	0.101164i
$494$	11.1231	+	7.36520i	0.500452	+	0.331376i
$495$	28.8802			1.29807
$496$	9.43318	−	9.75379i	0.423562	−	0.437958i
$497$	−11.1231	−	16.0000i	−0.498939	−	0.717698i
$498$	−7.12311	+	10.7575i	−0.319194	+	0.482054i
$499$			24.3266i			1.08901i	0.838758	+	0.544504i	$0.183282\pi$
$499$			24.3266i			1.08901i	−0.838758	+	0.544504i	$0.816718\pi$
$500$	−1.84130	+	0.780776i	−0.0823455	+	0.0349174i
$501$	−59.8617			−2.67443
$502$	12.5351	−	18.9309i	0.559471	−	0.844926i
$503$	−17.9139			−0.798741			−0.399370	−	0.916790i	$-0.630771\pi$
$503$	−17.9139			−0.798741			−0.399370	+	0.916790i	$0.630771\pi$
$504$	−41.7698	+	18.8377i	−1.86058	+	0.839097i
$505$	15.1231			0.672969
$506$	23.6155	−	35.6647i	1.04984	−	1.58549i
$507$	27.1840			1.20729
$508$	32.6847	−	13.8594i	1.45015	−	0.614914i
$509$		−	23.6155i		−	1.04674i	−0.852106	−	0.523370i	$-0.824675\pi$
$509$		−	23.6155i		−	1.04674i	0.852106	−	0.523370i	$-0.175325\pi$
$510$	2.64861	−	4.00000i	0.117283	−	0.177123i
$511$	−23.2111	−	33.3880i	−1.02680	−	1.47700i
$512$	19.2732	+	11.8551i	0.851763	+	0.523927i
$513$	−44.4924			−1.96439
$514$	13.4061	+	8.87689i	0.591318	+	0.391543i
$515$		−	7.73704i		−	0.340935i
$516$	2.06798	−	0.876894i	0.0910375	−	0.0386031i
$517$		−	24.0000i		−	1.05552i
$518$	−0.169271	−	7.48140i	−0.00743733	−	0.328714i
$519$		−	49.0708i		−	2.15397i
$520$	−5.56155	−	1.03399i	−0.243890	−	0.0453434i
$521$		−	9.75379i		−	0.427321i	−0.976908	−	0.213661i	$-0.931461\pi$
$521$		−	9.75379i		−	0.427321i	0.976908	−	0.213661i	$-0.0685387\pi$
$522$	9.56155	−	14.4401i	0.418498	−	0.632025i
$523$	19.2382			0.841227			0.420614	−	0.907240i	$-0.361815\pi$
$523$	19.2382			0.841227			0.420614	+	0.907240i	$0.361815\pi$
$524$	−13.6964	−	32.3002i	−0.598331	−	1.41104i
$525$	6.56155	−	4.56155i	0.286370	−	0.199082i
$526$	−21.8078	−	14.4401i	−0.950864	−	0.629618i
$527$		−	3.80989i		−	0.165961i
$528$	40.9620	+	39.6155i	1.78264	+	1.72404i
$529$	−18.1231			−0.787961
$530$	−2.35829	−	1.56155i	−0.102438	−	0.0678295i
$531$	−12.6624			−0.549503
$532$	−21.1158	−	13.3048i	−0.915485	−	0.576836i
$533$	2.24621			0.0972942
$534$	−42.7386	−	28.2995i	−1.84948	−	1.22464i
$535$	−5.66906			−0.245095
$536$	−1.94602	+	10.4672i	−0.0840555	+	0.452113i
$537$			32.4924i			1.40215i
$538$	0.290319	+	0.192236i	0.0125166	+	0.00828788i
$539$	−30.9481	−	11.5012i	−1.33303	−	0.495390i
$540$	17.3693	−	7.36520i	0.747456	−	0.316948i
$541$	30.0000			1.28980			0.644900	−	0.764267i	$-0.276899\pi$
$541$	30.0000			1.28980			0.644900	+	0.764267i	$0.276899\pi$
$542$	−1.48734	+	2.24621i	−0.0638866	+	0.0964830i
$543$		−	45.6786i		−	1.96025i
$544$	6.20393	−	1.36932i	0.265991	−	0.0587090i
$545$		−	7.12311i		−	0.305120i
$546$	22.5972	−	0.511274i	0.967070	−	0.0218805i
$547$		−	30.5763i		−	1.30735i	−0.756776	−	0.653674i	$-0.773227\pi$
$547$		−	30.5763i		−	1.30735i	0.756776	−	0.653674i	$-0.226773\pi$
$548$	10.9309	+	25.7782i	0.466944	+	1.10119i
$549$			12.2462i			0.522656i
$550$	−5.56155	−	3.68260i	−0.237145	−	0.157027i
$551$	9.43318			0.401867
$552$	10.0138	−	53.8617i	0.426216	−	2.29251i
$553$	2.00000	+	2.87689i	0.0850487	+	0.122338i
$554$	−9.56155	+	14.4401i	−0.406231	+	0.613500i
$555$			6.04090i			0.256422i
$556$	−13.1158	−	30.9309i	−0.556233	−	1.31176i
$557$	−26.4924			−1.12252			−0.561260	−	0.827640i	$-0.689683\pi$
$557$	−26.4924			−1.12252			−0.561260	+	0.827640i	$0.689683\pi$
$558$	16.2177	−	24.4924i	0.686552	−	1.03685i
$559$	−0.743668			−0.0314538
$560$	10.4458	+	1.69857i	0.441416	+	0.0717775i
$561$	16.0000			0.675521
$562$	22.9309	−	34.6307i	0.967280	−	1.46081i
$563$	−38.1045			−1.60592			−0.802958	−	0.596036i	$-0.796741\pi$
$563$	−38.1045			−1.60592			−0.802958	+	0.596036i	$0.796741\pi$
$564$	−12.0000	−	28.2995i	−0.505291	−	1.19163i
$565$			18.4924i			0.777982i
$566$	3.84563	−	5.80776i	0.161644	−	0.244119i
$567$	−21.9912	+	15.2882i	−0.923544	+	0.642042i
$568$	−3.80776	+	20.4810i	−0.159770	+	0.859363i
$569$	−28.8769			−1.21058			−0.605291	−	0.796004i	$-0.706943\pi$
$569$	−28.8769			−1.21058			−0.605291	+	0.796004i	$0.706943\pi$
$570$	16.7984	+	11.1231i	0.703607	+	0.465896i
$571$		−	3.22925i		−	0.135140i	−0.997715	−	0.0675700i	$-0.978475\pi$
$571$		−	3.22925i		−	0.135140i	0.997715	−	0.0675700i	$-0.0215246\pi$
$572$	−7.36520	−	17.3693i	−0.307955	−	0.726248i
$573$		−	50.7386i		−	2.11964i
$574$	−4.20120	+	0.0950545i	−0.175355	+	0.00396750i
$575$			6.41273i			0.267429i
$576$	45.7116	+	17.6057i	1.90465	+	0.733571i
$577$			45.6155i			1.89900i	0.313768	+	0.949500i	$0.398409\pi$
$577$			45.6155i			1.89900i	−0.313768	+	0.949500i	$0.601591\pi$
$578$	−12.2884	+	18.5582i	−0.511128	+	0.771918i
$579$	−67.9372			−2.82337
$580$	−3.68260	+	1.56155i	−0.152912	+	0.0648400i
$581$	−6.56155	+	4.56155i	−0.272219	+	0.189245i
$582$	4.00000	+	2.64861i	0.165805	+	0.109789i
$583$		−	9.43318i		−	0.390682i
$584$	−7.94584	+	42.7386i	−0.328801	+	1.76854i
$585$	−12.2462			−0.506319
$586$	18.5760	+	12.3002i	0.767369	+	0.508116i
$587$	−21.8868			−0.903365			−0.451683	−	0.892179i	$-0.649176\pi$
$587$	−21.8868			−0.903365			−0.451683	+	0.892179i	$0.649176\pi$
$588$	−42.2430	+	1.91252i	−1.74207	+	0.0788710i
$589$	16.0000			0.659269
$590$	2.43845	+	1.61463i	0.100389	+	0.0664731i
$591$	54.3681			2.23640
$592$	−5.56155	+	5.75058i	−0.228578	+	0.236347i
$593$		−	11.3693i		−	0.466882i	−0.972371	−	0.233441i	$-0.925001\pi$
$593$		−	11.3693i		−	0.466882i	0.972371	−	0.233441i	$-0.0749986\pi$
$594$	52.4631	+	34.7386i	2.15259	+	1.42534i
$595$	2.43981	−	1.69614i	0.100022	−	0.0695350i
$596$	−4.19224	−	9.88653i	−0.171721	−	0.404968i
$597$	−80.9848			−3.31449
$598$	−10.0138	+	15.1231i	−0.409495	+	0.618430i
$599$			29.6238i			1.21040i	0.796074	+	0.605199i	$0.206906\pi$
$599$			29.6238i			1.21040i	−0.796074	+	0.605199i	$0.793094\pi$
$600$	−8.39919	−	1.56155i	−0.342896	−	0.0637501i
$601$			17.1231i			0.698466i	0.937036	+	0.349233i	$0.113558\pi$
$601$			17.1231i			0.698466i	−0.937036	+	0.349233i	$0.886442\pi$
$602$	1.39092	−	0.0314703i	0.0566897	−	0.00128263i
$603$			23.0481i			0.938590i
$604$	18.4384	−	7.81855i	0.750250	−	0.318132i
$605$		−	11.2462i		−	0.457224i
$606$	53.8617	+	35.6647i	2.18798	+	1.44878i
$607$	−37.9415			−1.54000			−0.769999	−	0.638045i	$-0.779743\pi$
$607$	−37.9415			−1.54000			−0.769999	+	0.638045i	$0.779743\pi$
$608$	5.75058	+	26.0540i	0.233217	+	1.05663i
$609$	13.1231	−	9.12311i	0.531775	−	0.369687i
$610$	1.56155	−	2.35829i	0.0632254	−	0.0954846i
$611$			10.1768i			0.411711i
$612$	12.6624	−	5.36932i	0.511848	−	0.217042i
$613$	28.2462			1.14085			0.570427	−	0.821348i	$-0.306778\pi$
$613$	28.2462			1.14085			0.570427	+	0.821348i	$0.306778\pi$
$614$	−1.19702	+	1.80776i	−0.0483077	+	0.0729554i
$615$	3.39228			0.136790
$616$	14.5105	+	32.1750i	0.584646	+	1.29637i
$617$	−26.0000			−1.04672			−0.523360	−	0.852111i	$-0.675322\pi$
$617$	−26.0000			−1.04672			−0.523360	+	0.852111i	$0.675322\pi$
$618$	18.2462	−	27.5559i	0.733970	−	1.10846i
$619$	20.6083			0.828316			0.414158	−	0.910205i	$-0.364076\pi$
$619$	20.6083			0.828316			0.414158	+	0.910205i	$0.364076\pi$
$620$	−6.24621	+	2.64861i	−0.250854	+	0.106371i
$621$		−	60.4924i		−	2.42748i
$622$	−23.5829	+	35.6155i	−0.945590	+	1.42805i
$623$	−18.1227	−	26.0685i	−0.726070	−	1.04441i
$624$	−17.3693	−	16.7984i	−0.695329	−	0.672473i
$625$	1.00000			0.0400000
$626$	−39.6377	−	26.2462i	−1.58424	−	1.04901i
$627$			67.1935i			2.68345i
$628$	−0.453349	+	0.192236i	−0.0180906	+	0.00767105i
$629$			2.24621i			0.0895623i
$630$	22.9047	−	0.518231i	0.912545	−	0.0206468i
$631$			14.1498i			0.563293i	0.959518	+	0.281647i	$0.0908806\pi$
$631$			14.1498i			0.563293i	−0.959518	+	0.281647i	$0.909119\pi$
$632$	0.684658	−	3.68260i	0.0272343	−	0.146486i
$633$		−	66.7386i		−	2.65262i
$634$	−9.56155	+	14.4401i	−0.379738	+	0.573489i
$635$	−17.7509			−0.704421
$636$	−4.71659	−	11.1231i	−0.187025	−	0.441060i
$637$	13.1231	+	4.87689i	0.519956	+	0.193230i
$638$	−11.1231	−	7.36520i	−0.440368	−	0.291591i
$639$			45.0979i			1.78405i
$640$	−6.55789	−	9.21922i	−0.259223	−	0.364422i
$641$	−7.12311			−0.281346			−0.140673	−	0.990056i	$-0.544927\pi$
$641$	−7.12311			−0.281346			−0.140673	+	0.990056i	$0.544927\pi$
$642$	−20.1907	−	13.3693i	−0.796862	−	0.527645i
$643$	33.9686			1.33959			0.669795	−	0.742546i	$-0.266382\pi$
$643$	33.9686			1.33959			0.669795	+	0.742546i	$0.266382\pi$
$644$	18.0894	−	28.7093i	0.712821	−	1.13130i
$645$	−1.12311			−0.0442222
$646$	6.24621	+	4.13595i	0.245754	+	0.162727i
$647$	40.1725			1.57934			0.789672	−	0.613529i	$-0.210251\pi$
$647$	40.1725			1.57934			0.789672	+	0.613529i	$0.210251\pi$
$648$	28.1501	+	5.23358i	1.10584	+	0.205595i
$649$			9.75379i			0.382870i
$650$	2.35829	+	1.56155i	0.0924999	+	0.0612491i
$651$	22.2586	−	15.4741i	0.872385	−	0.606477i
$652$	−5.56155	+	2.35829i	−0.217807	+	0.0923579i
$653$	−22.9848			−0.899466			−0.449733	−	0.893163i	$-0.648481\pi$
$653$	−22.9848			−0.899466			−0.449733	+	0.893163i	$0.648481\pi$
$654$	16.7984	−	25.3693i	0.656869	−	0.992019i
$655$			17.5420i			0.685425i
$656$	3.22925	+	3.12311i	0.126081	+	0.121937i
$657$			94.1080i			3.67150i
$658$	−0.430661	−	19.0343i	−0.0167889	−	0.742033i
$659$		−	1.32431i		−	0.0515877i	−0.999667	−	0.0257938i	$-0.991789\pi$
$659$		−	1.32431i		−	0.0515877i	0.999667	−	0.0257938i	$-0.00821134\pi$
$660$	−11.1231	−	26.2316i	−0.432966	−	1.02106i
$661$		−	12.2462i		−	0.476322i	−0.971226	−	0.238161i	$-0.923455\pi$
$661$		−	12.2462i		−	0.476322i	0.971226	−	0.238161i	$-0.0765447\pi$
$662$	21.5616	+	14.2771i	0.838014	+	0.554894i
$663$	−6.78456			−0.263491
$664$	8.39919	+	1.56155i	0.325952	+	0.0606000i
$665$	7.12311	+	10.2462i	0.276222	+	0.397331i
$666$	−9.56155	+	14.4401i	−0.370503	+	0.559542i
$667$			12.8255i			0.496604i
$668$	15.4741	+	36.4924i	0.598710	+	1.41193i
$669$	62.1080			2.40123
$670$	2.93893	−	4.43845i	0.113541	−	0.171472i
$671$	9.43318			0.364164
$672$	33.1976	+	30.6838i	1.28062	+	1.18365i
$673$	−14.0000			−0.539660			−0.269830	−	0.962908i	$-0.586968\pi$
$673$	−14.0000			−0.539660			−0.269830	+	0.962908i	$0.586968\pi$
$674$	9.56155	−	14.4401i	0.368297	−	0.556211i
$675$	−9.43318			−0.363083
$676$	−7.02699	−	16.5717i	−0.270269	−	0.637373i
$677$		−	32.7386i		−	1.25825i	−0.777305	−	0.629124i	$-0.783414\pi$
$677$		−	32.7386i		−	1.25825i	0.777305	−	0.629124i	$-0.216586\pi$
$678$	−43.6106	+	65.8617i	−1.67485	+	2.52940i
$679$	1.69614	+	2.43981i	0.0650919	+	0.0936313i
$680$	−3.12311	−	0.580639i	−0.119766	−	0.0222665i
$681$	−11.3693			−0.435673
$682$	−18.8664	−	12.4924i	−0.722430	−	0.478360i
$683$			0.371834i			0.0142278i	0.999975	+	0.00711392i	$0.00226445\pi$
$683$			0.371834i			0.0142278i	−0.999975	+	0.00711392i	$0.997736\pi$
$684$	22.5490	+	53.1771i	0.862181	+	2.03328i
$685$		−	14.0000i		−	0.534913i
$686$	−24.7512	−	8.56616i	−0.945004	−	0.327058i
$687$		−	38.8940i		−	1.48390i
$688$	−1.06913	−	1.03399i	−0.0407602	−	0.0394204i
$689$			4.00000i			0.152388i
$690$	−15.1231	+	22.8393i	−0.575727	+	0.869476i
$691$	−14.8934			−0.566573			−0.283286	−	0.959035i	$-0.591425\pi$
$691$	−14.8934			−0.566573			−0.283286	+	0.959035i	$0.591425\pi$
$692$	−29.9142	+	12.6847i	−1.13717	+	0.482198i
$693$	43.6155	+	62.7386i	1.65682	+	2.38324i
$694$	−6.68466	−	4.42627i	−0.253746	−	0.168019i
$695$			16.7984i			0.637199i
$696$	−16.7984	−	3.12311i	−0.636741	−	0.118381i
$697$	1.26137			0.0477777
$698$	−35.2114	−	23.3153i	−1.33277	−	0.882499i
$699$	23.4199			0.885823
$700$	−4.47692	−	2.82085i	−0.169212	−	0.106618i
$701$	11.1231			0.420114			0.210057	−	0.977689i	$-0.432635\pi$
$701$	11.1231			0.420114			0.210057	+	0.977689i	$0.432635\pi$
$702$	−22.2462	−	14.7304i	−0.839629	−	0.555963i
$703$	−9.43318			−0.355779
$704$	13.5616	−	35.2114i	0.511120	−	1.32708i
$705$			15.3693i			0.578842i
$706$	22.8393	+	15.1231i	0.859568	+	0.569166i
$707$	22.8393	+	32.8531i	0.858959	+	1.23557i
$708$	4.87689	+	11.5012i	0.183285	+	0.432240i
$709$	44.7386			1.68019			0.840097	−	0.542436i	$-0.182498\pi$
$709$	44.7386			1.68019			0.840097	+	0.542436i	$0.182498\pi$
$710$	5.75058	−	8.68466i	0.215815	−	0.325929i
$711$		−	8.10887i		−	0.304106i
$712$	−6.20393	+	33.3693i	−0.232502	+	1.25057i
$713$			21.7538i			0.814686i
$714$	12.6895	−	0.287107i	0.474893	−	0.0107447i
$715$			9.43318i			0.352781i
$716$	19.8078	−	8.39919i	0.740251	−	0.313892i
$717$		−	12.0000i		−	0.448148i
$718$	18.9309	+	12.5351i	0.706494	+	0.467807i
$719$	22.6762			0.845681			0.422841	−	0.906204i	$-0.361033\pi$
$719$	22.6762			0.845681			0.422841	+	0.906204i	$0.361033\pi$
$720$	−17.6057	−	17.0270i	−0.656125	−	0.634558i
$721$	16.8078	−	11.6847i	0.625954	−	0.435159i
$722$	−2.53457	+	3.82776i	−0.0943267	+	0.142455i
$723$		−	77.3704i		−	2.87743i
$724$	−27.8462	+	11.8078i	−1.03490	+	0.438832i
$725$	2.00000			0.0742781
$726$	26.5219	−	40.0540i	0.984319	−	1.48654i
$727$	−9.64198			−0.357601			−0.178801	−	0.983885i	$-0.557222\pi$
$727$	−9.64198			−0.357601			−0.178801	+	0.983885i	$0.557222\pi$
$728$	−6.15298	−	13.6433i	−0.228045	−	0.505656i
$729$	−23.4924			−0.870090
$730$	12.0000	−	18.1227i	0.444140	−	0.670751i
$731$	−0.417609			−0.0154458
$732$	11.1231	−	4.71659i	0.411122	−	0.174330i
$733$			0.738634i			0.0272821i	0.999907	+	0.0136410i	$0.00434221\pi$
$733$			0.738634i			0.0272821i	−0.999907	+	0.0136410i	$0.995658\pi$
$734$	8.10887	−	12.2462i	0.299304	−	0.452016i
$735$	19.8188	+	7.36520i	0.731029	+	0.271670i
$736$	−35.4233	+	7.81855i	−1.30572	+	0.288196i
$737$	17.7538			0.653969
$738$	8.10887	+	5.36932i	0.298492	+	0.197647i
$739$		−	37.5697i		−	1.38202i	−0.722844	−	0.691012i	$-0.757165\pi$
$739$		−	37.5697i		−	1.38202i	0.722844	−	0.691012i	$-0.242835\pi$
$740$	3.68260	−	1.56155i	0.135375	−	0.0574038i
$741$		−	28.4924i		−	1.04670i
$742$	−0.169271	−	7.48140i	−0.00621413	−	0.274651i
$743$		−	23.7917i		−	0.872835i	−0.899744	−	0.436417i	$-0.856247\pi$
$743$		−	23.7917i		−	0.872835i	0.899744	−	0.436417i	$-0.143753\pi$
$744$	−28.4924	−	5.29723i	−1.04458	−	0.194206i
$745$			5.36932i			0.196717i
$746$	8.19224	−	12.3721i	0.299939	−	0.452975i
$747$	18.4945			0.676679
$748$	−4.13595	−	9.75379i	−0.151225	−	0.356634i
$749$	−8.56155	−	12.3153i	−0.312832	−	0.449993i
$750$	3.56155	+	2.35829i	0.130050	+	0.0861127i
$751$			28.8802i			1.05385i	0.849911	+	0.526926i	$0.176656\pi$
$751$			28.8802i			1.05385i	−0.849911	+	0.526926i	$0.823344\pi$
$752$	−14.1498	+	14.6307i	−0.515989	+	0.533526i
$753$	−48.4924			−1.76716
$754$	4.71659	+	3.12311i	0.171768	+	0.113737i
$755$	−10.0138			−0.364440
$756$	42.2316	+	26.6096i	1.53595	+	0.967782i
$757$	4.24621			0.154331			0.0771656	−	0.997018i	$-0.475413\pi$
$757$	4.24621			0.154331			0.0771656	+	0.997018i	$0.475413\pi$
$758$	17.5616	+	11.6284i	0.637864	+	0.422364i
$759$	−91.3571			−3.31605
$760$	2.43845	−	13.1158i	0.0884518	−	0.475759i
$761$		−	47.2311i		−	1.71212i	−0.516873	−	0.856062i	$-0.672904\pi$
$761$		−	47.2311i		−	1.71212i	0.516873	−	0.856062i	$-0.327096\pi$
$762$	−63.2206	−	41.8617i	−2.29024	−	1.51649i
$763$	15.4741	−	10.7575i	0.560199	−	0.389447i
$764$	−30.9309	+	13.1158i	−1.11904	+	0.474512i
$765$	−6.87689			−0.248635
$766$	14.8934	−	22.4924i	0.538122	−	0.812684i
$767$		−	4.13595i		−	0.149341i
$768$	−1.61463	−	48.3002i	−0.0582628	−	1.74288i
$769$		−	27.2311i		−	0.981977i	−0.871166	−	0.490989i	$-0.836636\pi$
$769$		−	27.2311i		−	0.981977i	0.871166	−	0.490989i	$-0.163364\pi$
$770$	−0.399190	−	17.6433i	−0.0143858	−	0.635822i
$771$		−	34.3404i		−	1.23674i
$772$	17.5616	+	41.4153i	0.632054	+	1.49057i
$773$		−	32.7386i		−	1.17753i	−0.808305	−	0.588763i	$-0.799615\pi$
$773$		−	32.7386i		−	1.17753i	0.808305	−	0.588763i	$-0.200385\pi$
$774$	−2.68466	−	1.77766i	−0.0964981	−	0.0638965i
$775$	3.39228			0.121854
$776$	0.580639	−	3.12311i	0.0208437	−	0.112113i
$777$	−13.1231	+	9.12311i	−0.470789	+	0.327290i
$778$	5.56155	−	8.39919i	0.199391	−	0.301126i
$779$			5.29723i			0.189793i
$780$	4.71659	+	11.1231i	0.168881	+	0.398271i
$781$	34.7386			1.24305
$782$	−5.62329	+	8.49242i	−0.201088	+	0.303688i
$783$	−18.8664			−0.674229
$784$	12.0856	+	25.2574i	0.431628	+	0.902052i
$785$	0.246211			0.00878766
$786$	−41.3693	+	62.4769i	−1.47559	+	2.22848i
$787$	3.02045			0.107667			0.0538337	−	0.998550i	$-0.482856\pi$
$787$	3.02045			0.107667			0.0538337	+	0.998550i	$0.482856\pi$
$788$	−14.0540	−	33.1434i	−0.500652	−	1.18069i
$789$			55.8617i			1.98873i
$790$	−1.03399	+	1.56155i	−0.0367876	+	0.0555576i
$791$	−40.1725	+	27.9277i	−1.42837	+	0.992995i
$792$	14.9309	−	80.3093i	0.530545	−	2.85367i
$793$	−4.00000			−0.142044
$794$	16.5081	+	10.9309i	0.585849	+	0.387922i
$795$			6.04090i			0.214248i
$796$	20.9343	+	49.3693i	0.741998	+	1.74985i
$797$		−	3.75379i		−	0.132966i	−0.997788	−	0.0664830i	$-0.978822\pi$
$797$		−	3.75379i		−	0.132966i	0.997788	−	0.0664830i	$-0.0211778\pi$
$798$	1.20573	+	53.2908i	0.0426825	+	1.88647i
$799$			5.71484i			0.202176i
$800$	1.21922	+	5.52390i	0.0431061	+	0.195299i
$801$			73.4773i			2.59619i
$802$	−4.68466	+	7.07488i	−0.165421	+	0.249823i
$803$	72.4908			2.55814
$804$	20.9343	−	8.87689i	0.738297	−	0.313064i
$805$	−13.9309	+	9.68466i	−0.490999	+	0.341339i
$806$	8.00000	+	5.29723i	0.281788	+	0.186587i
$807$		−	0.743668i		−	0.0261784i
$808$	7.81855	−	42.0540i	0.275056	−	1.47945i
$809$	46.9848			1.65190			0.825950	−	0.563744i	$-0.190640\pi$
$809$	46.9848			1.65190			0.825950	+	0.563744i	$0.190640\pi$
$810$	−11.9366	−	7.90388i	−0.419410	−	0.277714i
$811$	8.10887			0.284741			0.142370	−	0.989813i	$-0.454528\pi$
$811$	8.10887			0.284741			0.142370	+	0.989813i	$0.454528\pi$
$812$	−8.95383	−	5.64171i	−0.314218	−	0.197985i
$813$	5.75379			0.201794
$814$	11.1231	+	7.36520i	0.389865	+	0.258150i
$815$	3.02045			0.105802
$816$	−9.75379	−	9.43318i	−0.341451	−	0.330227i
$817$		−	1.75379i		−	0.0613573i
$818$	20.1907	+	13.3693i	0.705950	+	0.467447i
$819$	−18.4945	−	26.6034i	−0.646251	−	0.929598i
$820$	−0.876894	−	2.06798i	−0.0306225	−	0.0722168i
$821$	15.6155			0.544986			0.272493	−	0.962158i	$-0.412152\pi$
$821$	15.6155			0.544986			0.272493	+	0.962158i	$0.412152\pi$
$822$	33.0161	−	49.8617i	1.15157	−	1.73913i
$823$			29.0890i			1.01398i	0.861953	+	0.506989i	$0.169242\pi$
$823$			29.0890i			1.01398i	−0.861953	+	0.506989i	$0.830758\pi$
$824$	−21.5150	−	4.00000i	−0.749509	−	0.139347i
$825$			14.2462i			0.495989i
$826$	0.175024	+	7.73567i	0.00608986	+	0.269159i
$827$			24.5354i			0.853180i	0.904445	+	0.426590i	$0.140285\pi$
$827$			24.5354i			0.853180i	−0.904445	+	0.426590i	$0.859715\pi$
$828$	−72.3002	+	30.6578i	−2.51261	+	1.06543i
$829$			15.7538i			0.547152i	0.961850	+	0.273576i	$0.0882065\pi$
$829$			15.7538i			0.547152i	−0.961850	+	0.273576i	$0.911794\pi$
$830$	−3.56155	−	2.35829i	−0.123623	−	0.0818576i
$831$	36.9890			1.28314
$832$	−5.75058	+	14.9309i	−0.199365	+	0.517635i
$833$	7.36932	+	2.73863i	0.255332	+	0.0948880i
$834$	−39.6155	+	59.8283i	−1.37177	+	2.07169i
$835$		−	19.8188i		−	0.685859i
$836$	40.9620	−	17.3693i	1.41670	−	0.600730i
$837$	−32.0000			−1.10608
$838$	18.4130	−	27.8078i	0.636067	−	0.960603i
$839$	10.9205			0.377018			0.188509	−	0.982071i	$-0.439635\pi$
$839$	10.9205			0.377018			0.188509	+	0.982071i	$0.439635\pi$
$840$	−9.29238	−	20.6045i	−0.320617	−	0.710923i
$841$	−25.0000			−0.862069
$842$	−18.4384	+	27.8462i	−0.635431	+	0.959643i
$843$	−88.7085			−3.05528
$844$	−40.6847	+	17.2517i	−1.40042	+	0.593829i
$845$			9.00000i			0.309609i
$846$	−24.3266	+	36.7386i	−0.836366	+	1.26310i
$847$	24.4310	−	16.9843i	0.839460	−	0.583587i
$848$	−5.56155	+	5.75058i	−0.190985	+	0.197476i
$849$	−14.8769			−0.510574
$850$	1.32431	+	0.876894i	0.0454234	+	0.0300772i
$851$		−	12.8255i		−	0.439651i
$852$	40.9620	−	17.3693i	1.40333	−	0.595063i
$853$			24.2462i			0.830174i	0.909782	+	0.415087i	$0.136249\pi$
$853$			24.2462i			0.830174i	−0.909782	+	0.415087i	$0.863751\pi$
$854$	7.48140	−	0.169271i	0.256008	−	0.00579233i
$855$		−	28.8802i		−	0.987681i
$856$	−2.93087	+	15.7644i	−0.100175	+	0.538816i
$857$			25.6155i			0.875010i	0.899216	+	0.437505i	$0.144138\pi$
$857$			25.6155i			0.875010i	−0.899216	+	0.437505i	$0.855862\pi$
$858$	−22.2462	+	33.5968i	−0.759473	+	1.14697i
$859$	−3.55531			−0.121306			−0.0606528	−	0.998159i	$-0.519318\pi$
$859$	−3.55531			−0.121306			−0.0606528	+	0.998159i	$0.519318\pi$
$860$	0.290319	+	0.684658i	0.00989981	+	0.0233467i
$861$	5.12311	+	7.36932i	0.174595	+	0.251146i
$862$	6.93087	+	4.58930i	0.236066	+	0.156312i
$863$			10.2226i			0.347982i	0.984747	+	0.173991i	$0.0556664\pi$
$863$			10.2226i			0.347982i	−0.984747	+	0.173991i	$0.944334\pi$
$864$	−11.5012	−	52.1080i	−0.391277	−	1.77275i
$865$	16.2462			0.552388
$866$	−34.9211	−	23.1231i	−1.18667	−	0.785755i
$867$	47.5377			1.61447
$868$	−15.1870	−	9.56913i	−0.515479	−	0.324797i
$869$	−6.24621			−0.211888
$870$	7.12311	+	4.71659i	0.241496	+	0.159907i
$871$	−7.52823			−0.255084
$872$	−19.8078	−	3.68260i	−0.670776	−	0.124709i
$873$		−	6.87689i		−	0.232748i
$874$	−35.6647	−	23.6155i	−1.20638	−	0.798807i
$875$	1.51022	+	2.17238i	0.0510549	+	0.0734398i
$876$	85.4773	−	36.2454i	2.88801	−	1.22462i
$877$	0.738634			0.0249419			0.0124709	−	0.999922i	$-0.496030\pi$
$877$	0.738634			0.0249419			0.0124709	+	0.999922i	$0.496030\pi$
$878$	−12.6624	+	19.1231i	−0.427336	+	0.645374i
$879$		−	47.5835i		−	1.60495i
$880$	−13.1158	+	13.5616i	−0.442133	+	0.457160i
$881$			31.3693i			1.05686i	0.848977	+	0.528430i	$0.177219\pi$
$881$			31.3693i			1.05686i	−0.848977	+	0.528430i	$0.822781\pi$
$882$	35.7170	+	48.9750i	1.20265	+	1.64907i
$883$			31.3200i			1.05400i	0.849865	+	0.527001i	$0.176683\pi$
$883$			31.3200i			1.05400i	−0.849865	+	0.527001i	$0.823317\pi$
$884$	1.75379	+	4.13595i	0.0589863	+	0.139107i
$885$		−	6.24621i		−	0.209964i
$886$	−27.1771	−	17.9954i	−0.913032	−	0.604567i
$887$	29.9957			1.00716			0.503578	−	0.863950i	$-0.332017\pi$
$887$	29.9957			1.00716			0.503578	+	0.863950i	$0.332017\pi$
$888$	16.7984	+	3.12311i	0.563717	+	0.104805i
$889$	−26.8078	−	38.5616i	−0.899104	−	1.29331i
$890$	9.36932	−	14.1498i	0.314060	−	0.474301i
$891$		−	47.7465i		−	1.59957i
$892$	−16.0547	−	37.8617i	−0.537552	−	1.26770i
$893$	−24.0000			−0.803129
$894$	−12.6624	+	19.1231i	−0.423495	+	0.639572i
$895$	−10.7575			−0.359583
$896$	10.1238	−	28.1693i	0.338211	−	0.941070i
$897$	38.7386			1.29345
$898$	12.1922	−	18.4130i	0.406860	−	0.614450i
$899$	6.78456			0.226278
$900$	4.78078	+	11.2745i	0.159359	+	0.375816i
$901$			2.24621i			0.0748321i
$902$	4.13595	−	6.24621i	0.137712	−	0.207976i
$903$	−1.69614	−	2.43981i	−0.0564440	−	0.0811918i
$904$	51.4233	+	9.56047i	1.71031	+	0.317976i
$905$	15.1231			0.502709
$906$	−35.6647	−	23.6155i	−1.18488	−	0.784573i
$907$		−	52.8350i		−	1.75436i	−0.480166	−	0.877178i	$-0.659423\pi$
$907$		−	52.8350i		−	1.75436i	0.480166	−	0.877178i	$-0.340577\pi$
$908$	2.93893	+	6.93087i	0.0975319	+	0.230009i
$909$		−	92.6004i		−	3.07136i
$910$	0.169271	+	7.48140i	0.00561127	+	0.248006i
$911$		−	2.06798i		−	0.0685151i	−0.999413	−	0.0342575i	$-0.989093\pi$
$911$		−	2.06798i		−	0.0685151i	0.999413	−	0.0342575i	$-0.0109066\pi$
$912$	39.6155	−	40.9620i	1.31180	−	1.35639i
$913$		−	14.2462i		−	0.471481i
$914$	−4.68466	+	7.07488i	−0.154955	+	0.234016i
$915$	−6.04090			−0.199706
$916$	−23.7102	+	10.0540i	−0.783408	+	0.332193i
$917$	−38.1080	+	26.4924i	−1.25844	+	0.874857i
$918$	−12.4924	−	8.27190i	−0.412311	−	0.273013i
$919$			9.27015i			0.305794i	0.988242	+	0.152897i	$0.0488603\pi$
$919$			9.27015i			0.305794i	−0.988242	+	0.152897i	$0.951140\pi$
$920$	17.8324	+	3.31534i	0.587916	+	0.109304i
$921$	4.63068			0.152586
$922$	−4.26324	−	2.82292i	−0.140402	−	0.0929679i
$923$	−14.7304			−0.484857
$924$	40.1865	−	63.7791i	1.32204	−	2.09818i
$925$	−2.00000			−0.0657596
$926$	−33.8078	−	22.3859i	−1.11099	−	0.735647i
$927$	−47.3747			−1.55599
$928$	2.43845	+	11.0478i	0.0800460	+	0.362662i
$929$		−	21.1231i		−	0.693027i	−0.938045	−	0.346513i	$-0.887366\pi$
$929$		−	21.1231i		−	0.693027i	0.938045	−	0.346513i	$-0.112634\pi$
$930$	12.0818	+	8.00000i	0.396178	+	0.262330i
$931$	−11.5012	+	30.9481i	−0.376935	+	1.01428i
$932$	−6.05398	−	14.2771i	−0.198305	−	0.467661i
$933$	91.2311			2.98677
$934$	−14.4401	+	21.8078i	−0.472494	+	0.713572i
$935$			5.29723i			0.173238i
$936$	−6.33122	+	34.0540i	−0.206942	+	1.11309i
$937$		−	38.1080i		−	1.24493i	−0.782647	−	0.622466i	$-0.786131\pi$
$937$		−	38.1080i		−	1.24493i	0.782647	−	0.622466i	$-0.213869\pi$
$938$	14.0804	−	0.318577i	0.459742	−	0.0104019i
$939$			101.534i			3.31344i
$940$	9.36932	−	3.97292i	0.305593	−	0.129582i
$941$			26.6307i			0.868135i	0.900880	+	0.434068i	$0.142922\pi$
$941$			26.6307i			0.868135i	−0.900880	+	0.434068i	$0.857078\pi$
$942$	0.876894	+	0.580639i	0.0285708	+	0.0189182i
$943$	−7.20217			−0.234535
$944$	5.75058	−	5.94602i	0.187165	−	0.193527i
$945$	−14.2462	−	20.4924i	−0.463429	−	0.666619i
$946$	−1.36932	+	2.06798i	−0.0445203	+	0.0672357i
$947$		−	35.8735i		−	1.16573i	−0.812568	−	0.582867i	$-0.801931\pi$
$947$		−	35.8735i		−	1.16573i	0.812568	−	0.582867i	$-0.198069\pi$
$948$	−7.36520	+	3.12311i	−0.239211	+	0.101434i
$949$	−30.7386			−0.997818
$950$	−3.68260	+	5.56155i	−0.119479	+	0.180441i
$951$	36.9890			1.19945
$952$	−3.45522	−	7.66146i	−0.111984	−	0.248309i
$953$	28.2462			0.914985			0.457492	−	0.889214i	$-0.348748\pi$
$953$	28.2462			0.914985			0.457492	+	0.889214i	$0.348748\pi$
$954$	−9.56155	+	14.4401i	−0.309567	+	0.467515i
$955$	16.7984			0.543583
$956$	−7.31534	+	3.10196i	−0.236595	+	0.100325i
$957$			28.4924i			0.921029i
$958$		0			0
$959$	30.4133	−	21.1431i	0.982096	−	0.682747i
$960$	−8.68466	+	22.5490i	−0.280296	+	0.727764i
$961$	−19.4924			−0.628788
$962$	−4.71659	−	3.12311i	−0.152069	−	0.100693i
$963$			34.7123i			1.11859i
$964$	−47.1659	+	20.0000i	−1.51911	+	0.644157i
$965$		−	22.4924i		−	0.724057i
$966$	−72.4548	+	1.63933i	−2.33120	+	0.0527446i
$967$		−	3.43806i		−	0.110560i	−0.998471	−	0.0552802i	$-0.982395\pi$
$967$		−	3.43806i		−	0.110560i	0.998471	−	0.0552802i	$-0.0176052\pi$
$968$	−31.2732	−	5.81422i	−1.00516	−	0.186876i
$969$		−	16.0000i		−	0.513994i
$970$	−0.876894	+	1.32431i	−0.0281554	+	0.0425209i
$971$	−10.7575			−0.345224			−0.172612	−	0.984990i	$-0.555221\pi$
$971$	−10.7575			−0.345224			−0.172612	+	0.984990i	$0.555221\pi$
$972$	−1.77766	−	4.19224i	−0.0570183	−	0.134466i
$973$	−36.4924	+	25.3693i	−1.16989	+	0.813303i
$974$	15.5616	+	10.3041i	0.498624	+	0.330166i
$975$		−	6.04090i		−	0.193463i
$976$	−5.75058	−	5.56155i	−0.184071	−	0.178021i
$977$	22.4924			0.719596			0.359798	−	0.933030i	$-0.382846\pi$
$977$	22.4924			0.719596			0.359798	+	0.933030i	$0.382846\pi$
$978$	10.7575	+	7.12311i	0.343986	+	0.227772i
$979$	56.5991			1.80891
$980$	−0.633191	−	13.9857i	−0.0202265	−	0.446756i
$981$	−43.6155			−1.39254
$982$	−37.1771	−	24.6169i	−1.18637	−	0.785558i
$983$	28.5083			0.909275			0.454637	−	0.890677i	$-0.349769\pi$
$983$	28.5083			0.909275			0.454637	+	0.890677i	$0.349769\pi$
$984$	1.75379	−	9.43318i	0.0559087	−	0.300719i
$985$			18.0000i			0.573528i
$986$	2.64861	+	1.75379i	0.0843490	+	0.0558520i
$987$	−33.3880	+	23.2111i	−1.06275	+	0.738818i
$988$	−17.3693	+	7.36520i	−0.552592	+	0.234318i
$989$	2.38447			0.0758218
$990$	−22.5490	+	34.0540i	−0.716653	+	1.08231i
$991$			48.9078i			1.55361i	0.629743	+	0.776804i	$0.283160\pi$
$991$			48.9078i			1.55361i	−0.629743	+	0.776804i	$0.716840\pi$
$992$	4.13595	+	18.7386i	0.131317	+	0.594952i
$993$		−	55.2311i		−	1.75270i
$994$	27.5510	−	0.623357i	0.873865	−	0.0197717i
$995$		−	26.8122i		−	0.850004i
$996$	−7.12311	−	16.7984i	−0.225704	−	0.532277i
$997$		−	5.50758i		−	0.174427i	−0.996190	−	0.0872134i	$-0.972204\pi$
$997$		−	5.50758i		−	0.174427i	0.996190	−	0.0872134i	$-0.0277962\pi$
$998$	−28.6847	−	18.9936i	−0.907997	−	0.601233i
$999$	18.8664			0.596905

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	140.2.g.c.111.4	yes	8
3.2	odd	2		1260.2.c.c.811.5		8
4.3	odd	2	inner	140.2.g.c.111.1	✓	8
5.2	odd	4		700.2.c.j.699.1		8
5.3	odd	4		700.2.c.i.699.8		8
5.4	even	2		700.2.g.j.251.5		8
7.2	even	3		980.2.o.e.31.7		16
7.3	odd	6		980.2.o.e.411.4		16
7.4	even	3		980.2.o.e.411.3		16
7.5	odd	6		980.2.o.e.31.8		16
7.6	odd	2	inner	140.2.g.c.111.3	yes	8
8.3	odd	2		2240.2.k.e.1791.7		8
8.5	even	2		2240.2.k.e.1791.1		8
12.11	even	2		1260.2.c.c.811.7		8
20.3	even	4		700.2.c.i.699.2		8
20.7	even	4		700.2.c.j.699.7		8
20.19	odd	2		700.2.g.j.251.8		8
21.20	even	2		1260.2.c.c.811.6		8
28.3	even	6		980.2.o.e.411.7		16
28.11	odd	6		980.2.o.e.411.8		16
28.19	even	6		980.2.o.e.31.3		16
28.23	odd	6		980.2.o.e.31.4		16
28.27	even	2	inner	140.2.g.c.111.2	yes	8
35.13	even	4		700.2.c.j.699.8		8
35.27	even	4		700.2.c.i.699.1		8
35.34	odd	2		700.2.g.j.251.6		8
56.13	odd	2		2240.2.k.e.1791.8		8
56.27	even	2		2240.2.k.e.1791.2		8
84.83	odd	2		1260.2.c.c.811.8		8
140.27	odd	4		700.2.c.i.699.7		8
140.83	odd	4		700.2.c.j.699.2		8
140.139	even	2		700.2.g.j.251.7		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
140.2.g.c.111.1	✓	8	4.3	odd	2	inner
140.2.g.c.111.2	yes	8	28.27	even	2	inner
140.2.g.c.111.3	yes	8	7.6	odd	2	inner
140.2.g.c.111.4	yes	8	1.1	even	1	trivial
700.2.c.i.699.1		8	35.27	even	4
700.2.c.i.699.2		8	20.3	even	4
700.2.c.i.699.7		8	140.27	odd	4
700.2.c.i.699.8		8	5.3	odd	4
700.2.c.j.699.1		8	5.2	odd	4
700.2.c.j.699.2		8	140.83	odd	4
700.2.c.j.699.7		8	20.7	even	4
700.2.c.j.699.8		8	35.13	even	4
700.2.g.j.251.5		8	5.4	even	2
700.2.g.j.251.6		8	35.34	odd	2
700.2.g.j.251.7		8	140.139	even	2
700.2.g.j.251.8		8	20.19	odd	2
980.2.o.e.31.3		16	28.19	even	6
980.2.o.e.31.4		16	28.23	odd	6
980.2.o.e.31.7		16	7.2	even	3
980.2.o.e.31.8		16	7.5	odd	6
980.2.o.e.411.3		16	7.4	even	3
980.2.o.e.411.4		16	7.3	odd	6
980.2.o.e.411.7		16	28.3	even	6
980.2.o.e.411.8		16	28.11	odd	6
1260.2.c.c.811.5		8	3.2	odd	2
1260.2.c.c.811.6		8	21.20	even	2
1260.2.c.c.811.7		8	12.11	even	2
1260.2.c.c.811.8		8	84.83	odd	2
2240.2.k.e.1791.1		8	8.5	even	2
2240.2.k.e.1791.2		8	56.27	even	2
2240.2.k.e.1791.7		8	8.3	odd	2
2240.2.k.e.1791.8		8	56.13	odd	2

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:	\( N \)	\(=\)	\( 140 = 2^{2} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	140.g (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.780776 + 1.17915i) q^{2} +3.02045 q^{3} +(-0.780776 - 1.84130i) q^{4} +1.00000i q^{5} +(-2.35829 + 3.56155i) q^{6} +(-2.17238 + 1.51022i) q^{7} +(2.78078 + 0.516994i) q^{8} +6.12311 q^{9} +O(q^{10})\)	\(q+(-0.780776 + 1.17915i) q^{2} +3.02045 q^{3} +(-0.780776 - 1.84130i) q^{4} +1.00000i q^{5} +(-2.35829 + 3.56155i) q^{6} +(-2.17238 + 1.51022i) q^{7} +(2.78078 + 0.516994i) q^{8} +6.12311 q^{9} +(-1.17915 - 0.780776i) q^{10} -4.71659i q^{11} +(-2.35829 - 5.56155i) q^{12} +2.00000i q^{13} +(-0.0846354 - 3.74070i) q^{14} +3.02045i q^{15} +(-2.78078 + 2.87529i) q^{16} +1.12311i q^{17} +(-4.78078 + 7.22004i) q^{18} -4.71659 q^{19} +(1.84130 - 0.780776i) q^{20} +(-6.56155 + 4.56155i) q^{21} +(5.56155 + 3.68260i) q^{22} -6.41273i q^{23} +(8.39919 + 1.56155i) q^{24} -1.00000 q^{25} +(-2.35829 - 1.56155i) q^{26} +9.43318 q^{27} +(4.47692 + 2.82085i) q^{28} -2.00000 q^{29} +(-3.56155 - 2.35829i) q^{30} -3.39228 q^{31} +(-1.21922 - 5.52390i) q^{32} -14.2462i q^{33} +(-1.32431 - 0.876894i) q^{34} +(-1.51022 - 2.17238i) q^{35} +(-4.78078 - 11.2745i) q^{36} +2.00000 q^{37} +(3.68260 - 5.56155i) q^{38} +6.04090i q^{39} +(-0.516994 + 2.78078i) q^{40} -1.12311i q^{41} +(-0.255637 - 11.2986i) q^{42} +0.371834i q^{43} +(-8.68466 + 3.68260i) q^{44} +6.12311i q^{45} +(7.56155 + 5.00691i) q^{46} +5.08842 q^{47} +(-8.39919 + 8.68466i) q^{48} +(2.43845 - 6.56155i) q^{49} +(0.780776 - 1.17915i) q^{50} +3.39228i q^{51} +(3.68260 - 1.56155i) q^{52} +2.00000 q^{53} +(-7.36520 + 11.1231i) q^{54} +4.71659 q^{55} +(-6.82167 + 3.07649i) q^{56} -14.2462 q^{57} +(1.56155 - 2.35829i) q^{58} -2.06798 q^{59} +(5.56155 - 2.35829i) q^{60} +2.00000i q^{61} +(2.64861 - 4.00000i) q^{62} +(-13.3017 + 9.24726i) q^{63} +(7.46543 + 2.87529i) q^{64} -2.00000 q^{65} +(16.7984 + 11.1231i) q^{66} +3.76412i q^{67} +(2.06798 - 0.876894i) q^{68} -19.3693i q^{69} +(3.74070 - 0.0846354i) q^{70} +7.36520i q^{71} +(17.0270 + 3.16561i) q^{72} +15.3693i q^{73} +(-1.56155 + 2.35829i) q^{74} -3.02045 q^{75} +(3.68260 + 8.68466i) q^{76} +(7.12311 + 10.2462i) q^{77} +(-7.12311 - 4.71659i) q^{78} -1.32431i q^{79} +(-2.87529 - 2.78078i) q^{80} +10.1231 q^{81} +(1.32431 + 0.876894i) q^{82} +3.02045 q^{83} +(13.5223 + 8.52024i) q^{84} -1.12311 q^{85} +(-0.438447 - 0.290319i) q^{86} -6.04090 q^{87} +(2.43845 - 13.1158i) q^{88} +12.0000i q^{89} +(-7.22004 - 4.78078i) q^{90} +(-3.02045 - 4.34475i) q^{91} +(-11.8078 + 5.00691i) q^{92} -10.2462 q^{93} +(-3.97292 + 6.00000i) q^{94} -4.71659i q^{95} +(-3.68260 - 16.6847i) q^{96} -1.12311i q^{97} +(5.83315 + 7.99839i) q^{98} -28.8802i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 2 q^{2} + 2 q^{4} + 14 q^{8} + 16 q^{9}+O(q^{10}) \) 8 * q + 2 * q^2 + 2 * q^4 + 14 * q^8 + 16 * q^9	\( 8 q + 2 q^{2} + 2 q^{4} + 14 q^{8} + 16 q^{9} - 6 q^{14} - 14 q^{16} - 30 q^{18} - 36 q^{21} + 28 q^{22} - 8 q^{25} + 14 q^{28} - 16 q^{29} - 12 q^{30} - 18 q^{32} - 30 q^{36} + 16 q^{37} + 8 q^{42} - 20 q^{44} + 44 q^{46} + 36 q^{49} - 2 q^{50} + 16 q^{53} + 2 q^{56} - 48 q^{57} - 4 q^{58} + 28 q^{60} + 2 q^{64} - 16 q^{65} + 4 q^{70} + 62 q^{72} + 4 q^{74} + 24 q^{77} - 24 q^{78} + 48 q^{81} + 8 q^{84} + 24 q^{85} - 20 q^{86} + 36 q^{88} - 12 q^{92} - 16 q^{93} + 26 q^{98}+O(q^{100}) \) 8 * q + 2 * q^2 + 2 * q^4 + 14 * q^8 + 16 * q^9 - 6 * q^14 - 14 * q^16 - 30 * q^18 - 36 * q^21 + 28 * q^22 - 8 * q^25 + 14 * q^28 - 16 * q^29 - 12 * q^30 - 18 * q^32 - 30 * q^36 + 16 * q^37 + 8 * q^42 - 20 * q^44 + 44 * q^46 + 36 * q^49 - 2 * q^50 + 16 * q^53 + 2 * q^56 - 48 * q^57 - 4 * q^58 + 28 * q^60 + 2 * q^64 - 16 * q^65 + 4 * q^70 + 62 * q^72 + 4 * q^74 + 24 * q^77 - 24 * q^78 + 48 * q^81 + 8 * q^84 + 24 * q^85 - 20 * q^86 + 36 * q^88 - 12 * q^92 - 16 * q^93 + 26 * q^98

Introduction

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