LMFDB - Embedded newform 140.2.g.c.111.1

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			111.1
Root			$1.17915 + 0.780776i$ of defining polynomial
Character	$\chi$	$=$	140.111
Dual form			140.2.g.c.111.3

$q$-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} +(-3.47692 - 1.38241i) 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} +(1.08464 + 5.17915i) 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} +(10.5018 + 4.17548i) 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} +(5.26012 - 5.32270i) 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} +(1.38241 - 3.47692i) 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} +(-3.27608 - 15.6433i) 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} +(-9.64092 + 2.24782i) 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	$-0.837130\pi$
$3$	−3.02045			−1.74386			−0.871928	+	0.489634i	$0.837130\pi$
$4$	−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	$0.251781\pi$
$11$			4.71659i			1.42211i	−0.703139	+	0.711053i	$0.748219\pi$
$12$	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	$0.910544\pi$
$14$	−3.47692	−	1.38241i	−0.929245	−	0.369463i
$15$		−	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	$-0.318035\pi$
$19$	4.71659			1.08206			0.541030	+	0.841003i	$0.318035\pi$
$20$	−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	$0.233095\pi$
$23$			6.41273i			1.33715i	−0.743646	+	0.668573i	$0.766905\pi$
$24$	−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
$28$	1.08464	+	5.17915i	0.204977	+	0.978767i
$29$	−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	$-0.401465\pi$
$31$	3.39228			0.609272			0.304636	+	0.952469i	$0.401465\pi$
$32$	−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	$-0.0279516\pi$
$42$	10.5018	+	4.17548i	1.62047	+	0.644291i
$43$		−	0.371834i		−	0.0567042i	−0.999598	−	0.0283521i	$-0.990974\pi$
$43$		−	0.371834i		−	0.0567042i	0.999598	−	0.0283521i	$-0.00902596\pi$
$44$	−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	$-0.621023\pi$
$47$	−5.08842			−0.742223			−0.371111	+	0.928588i	$0.621023\pi$
$48$	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
$56$	5.26012	−	5.32270i	0.702913	−	0.711276i
$57$	−14.2462			−1.88696
$58$	1.56155	+	2.35829i	0.205042	+	0.309659i
$59$	2.06798			0.269227			0.134614	−	0.990898i	$-0.457021\pi$
$59$	2.06798			0.269227			0.134614	+	0.990898i	$0.457021\pi$
$60$	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	$-0.926150\pi$
$67$		−	3.76412i		−	0.459860i	0.973207	−	0.229930i	$-0.0738497\pi$
$68$	−2.06798	−	0.876894i	−0.250779	−	0.106339i
$69$		−	19.3693i		−	2.33179i
$70$	1.38241	−	3.47692i	0.165229	−	0.415571i
$71$		−	7.36520i		−	0.874089i	−0.899440	−	0.437044i	$-0.856025\pi$
$71$		−	7.36520i		−	0.874089i	0.899440	−	0.437044i	$-0.143975\pi$
$72$	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	$0.0237355\pi$
$79$			1.32431i			0.148996i	−0.997221	+	0.0744981i	$0.976265\pi$
$80$	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	$-0.553010\pi$
$83$	−3.02045			−0.331537			−0.165769	+	0.986165i	$0.553010\pi$
$84$	−3.27608	−	15.6433i	−0.357450	−	1.70683i
$85$	−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	$-0.0181589\pi$
$98$	−9.64092	+	2.24782i	−0.973880	+	0.227064i
$99$			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	$-0.375519\pi$
$103$	7.73704			0.762353			0.381176	+	0.924502i	$0.375519\pi$
$104$	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	$-0.911645\pi$
$107$		−	5.66906i		−	0.548049i	0.961723	−	0.274024i	$-0.0883549\pi$
$108$	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
$112$	−10.3832	−	2.04662i	−0.981123	−	0.193387i
$113$	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
$126$	−21.2895	−	8.46462i	−1.89662	−	0.754088i
$127$		−	17.7509i		−	1.57513i	−0.616229	−	0.787567i	$-0.711341\pi$
$127$		−	17.7509i		−	1.57513i	0.616229	−	0.787567i	$-0.288659\pi$
$128$	−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	$-0.777918\pi$
$131$	−17.5420			−1.53266			−0.766328	+	0.642450i	$0.777918\pi$
$132$	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	$-0.752396\pi$
$139$	−16.7984			−1.42482			−0.712410	+	0.701763i	$0.752396\pi$
$140$	−5.17915	+	1.08464i	−0.437718	+	0.0916684i
$141$	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	$-0.866416\pi$
$151$		−	10.0138i		−	0.814913i	0.913225	−	0.407456i	$-0.133584\pi$
$152$	13.1158	−	2.43845i	1.06383	−	0.197784i
$153$			6.87689i			0.555964i
$154$	6.52024	−	16.3992i	0.525416	−	1.32148i
$155$			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	$0.0377412\pi$
$163$			3.02045i			0.236580i	−0.992979	+	0.118290i	$0.962259\pi$
$164$	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	$-0.221841\pi$
$167$	19.8188			1.53363			0.766813	+	0.641870i	$0.221841\pi$
$168$	−15.8879	+	16.0769i	−1.22578	+	1.24036i
$169$	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	$-0.868306\pi$
$179$		−	10.7575i		−	0.804052i	0.915628	−	0.402026i	$-0.131694\pi$
$180$	−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	$-0.189986\pi$
$182$	2.76481	−	6.95383i	0.204941	−	0.515453i
$183$		−	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	$0.207925\pi$
$191$			16.7984i			1.21549i	−0.794133	+	0.607744i	$0.792075\pi$
$192$	−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
$196$	10.1779	+	9.61302i	0.726994	+	0.686644i
$197$	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	$-0.100742\pi$
$199$	26.8122			1.90067			0.950333	+	0.311235i	$0.100742\pi$
$200$	−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
$210$	−4.17548	+	10.5018i	−0.288136	+	0.724696i
$211$			22.0956i			1.52112i	0.649265	+	0.760562i	$0.275077\pi$
$211$			22.0956i			1.52112i	−0.649265	+	0.760562i	$0.724923\pi$
$212$	−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	$-0.741723\pi$
$223$	−20.5625			−1.37697			−0.688483	+	0.725252i	$0.741723\pi$
$224$	5.69372	+	13.8413i	0.380427	+	0.924811i
$225$	−6.12311			−0.408207
$226$	−14.4384	−	21.8053i	−0.960431	−	1.45047i
$227$	3.76412			0.249833			0.124917	−	0.992167i	$-0.460134\pi$
$227$	3.76412			0.249833			0.124917	+	0.992167i	$0.460134\pi$
$228$	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
$238$	1.55259	−	3.90495i	0.100639	−	0.253120i
$239$			3.97292i			0.256987i	0.991710	+	0.128493i	$0.0410141\pi$
$239$			3.97292i			0.256987i	−0.991710	+	0.128493i	$0.958986\pi$
$240$	−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	$-0.330872\pi$
$251$	16.0547			1.01336			0.506682	+	0.862133i	$0.330872\pi$
$252$	6.64134	+	31.7125i	0.418365	+	1.99770i
$253$	−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	$-0.806862\pi$
$263$		−	18.4945i		−	1.14042i	0.821499	−	0.570211i	$-0.193138\pi$
$264$	−7.36520	−	39.6155i	−0.453297	−	2.43817i
$265$			2.00000i			0.122859i
$266$	−16.3992	−	6.52024i	−1.00550	−	0.399781i
$267$		−	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	$-0.518427\pi$
$271$	−1.90495			−0.115717			−0.0578586	+	0.998325i	$0.518427\pi$
$272$	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
$280$	5.32270	+	5.26012i	0.318092	+	0.314352i
$281$	−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	$-0.453234\pi$
$283$	4.92539			0.292784			0.146392	+	0.989227i	$0.453234\pi$
$284$	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	$-0.152213\pi$
$294$	29.1199	−	6.78942i	1.69831	−	0.395967i
$295$			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	$-0.513930\pi$
$307$	−1.53311			−0.0874993			−0.0437496	+	0.999043i	$0.513930\pi$
$308$	−24.4279	+	5.11578i	−1.39191	+	0.291499i
$309$	−23.3693			−1.32943
$310$	4.00000	−	2.64861i	0.227185	−	0.150431i
$311$	−30.2045			−1.71274			−0.856369	−	0.516364i	$-0.827285\pi$
$311$	−30.2045			−1.71274			−0.856369	+	0.516364i	$0.827285\pi$
$312$	−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
$322$	8.86499	−	22.2965i	0.494027	−	1.24254i
$323$			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	$0.167600\pi$
$331$			18.2857i			1.00507i	−0.864556	+	0.502537i	$0.832400\pi$
$332$	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
$336$	31.3620	+	6.18170i	1.71094	+	0.337239i
$337$	−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	$-0.951375\pi$
$347$		−	5.66906i		−	0.304331i	0.988355	−	0.152166i	$-0.0486247\pi$
$348$	−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	$0.705240\pi$
$350$	3.47692	+	1.38241i	0.185849	+	0.0738927i
$351$		−	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	$0.139258\pi$
$359$			16.0547i			0.847335i	−0.905818	+	0.423668i	$0.860742\pi$
$360$	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
$364$	−10.3583	+	2.16927i	−0.542922	+	0.113701i
$365$	−15.3693			−0.804467
$366$	−7.12311	+	4.71659i	−0.372331	+	0.246540i
$367$	10.3857			0.542127			0.271063	−	0.962562i	$-0.412625\pi$
$367$	10.3857			0.542127			0.271063	+	0.962562i	$0.412625\pi$
$368$	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
$378$	32.7984	+	13.0405i	1.68697	+	0.670730i
$379$			14.8934i			0.765024i	0.923950	+	0.382512i	$0.124941\pi$
$379$			14.8934i			0.765024i	−0.923950	+	0.382512i	$0.875059\pi$
$380$	−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	$-0.337964\pi$
$383$	19.0752			0.974695			0.487348	+	0.873208i	$0.337964\pi$
$384$	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
$392$	3.38849	−	19.5069i	0.171145	−	0.985246i
$393$	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
$406$	6.95383	+	2.76481i	0.345113	+	0.137215i
$407$			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	$-0.304593\pi$
$419$	23.5829			1.15210			0.576051	+	0.817414i	$0.304593\pi$
$420$	15.6433	−	3.27608i	0.763317	−	0.159857i
$421$	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	$0.0452129\pi$
$431$			5.87787i			0.283127i	−0.989929	+	0.141563i	$0.954787\pi$
$432$	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	$0.747964\pi$
$434$	−11.7947	−	4.68951i	−0.566163	−	0.225104i
$435$			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	$-0.626494\pi$
$439$	−16.2177			−0.774031			−0.387015	+	0.922073i	$0.626494\pi$
$440$	−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	$-0.815571\pi$
$443$		−	23.0481i		−	1.09505i	0.836790	−	0.547524i	$-0.184429\pi$
$444$	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
$448$	11.8754	−	17.5207i	0.561061	−	0.827775i
$449$	−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	$0.973168\pi$
$462$	−19.6940	+	49.5329i	−0.916250	+	2.30448i
$463$		−	28.6714i		−	1.33247i	−0.745741	−	0.666236i	$-0.767904\pi$
$463$		−	28.6714i		−	1.33247i	0.745741	−	0.666236i	$-0.232096\pi$
$464$	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	$-0.640751\pi$
$467$	−18.4945			−0.855824			−0.427912	+	0.903820i	$0.640751\pi$
$468$	−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
$476$	−5.81673	+	1.21816i	−0.266609	+	0.0558343i
$477$	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	$0.0966575\pi$
$487$			13.1973i			0.598026i	−0.954249	+	0.299013i	$0.903343\pi$
$488$	1.03399	+	5.56155i	0.0468064	+	0.251760i
$489$		−	9.12311i		−	0.412561i
$490$	−2.24782	−	9.64092i	−0.101546	−	0.435532i
$491$		−	31.5288i		−	1.42287i	−0.702750	−	0.711437i	$-0.748045\pi$
$491$		−	31.5288i		−	1.42287i	0.702750	−	0.711437i	$-0.251955\pi$
$492$	−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	$-0.816718\pi$
$499$		−	24.3266i		−	1.08901i	0.838758	−	0.544504i	$-0.183282\pi$
$500$	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	$-0.369229\pi$
$503$	17.9139			0.798741			0.399370	+	0.916790i	$0.369229\pi$
$504$	32.2083	−	32.5915i	1.43467	−	1.45174i
$505$	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
$518$	−6.95383	−	2.76481i	−0.305534	−	0.121479i
$519$			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	$-0.638185\pi$
$523$	−19.2382			−0.841227			−0.420614	+	0.907240i	$0.638185\pi$
$524$	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
$532$	5.11578	+	24.4279i	0.221797	+	1.05908i
$533$	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
$546$	−8.35097	+	21.0037i	−0.357388	+	0.898875i
$547$			30.5763i			1.30735i	0.756776	+	0.653674i	$0.226773\pi$
$547$			30.5763i			1.30735i	−0.756776	+	0.653674i	$0.773227\pi$
$548$	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
$560$	2.04662	−	10.3832i	0.0864853	−	0.438771i
$561$	16.0000			0.675521
$562$	22.9309	+	34.6307i	0.967280	+	1.46081i
$563$	38.1045			1.60592			0.802958	−	0.596036i	$-0.203259\pi$
$563$	38.1045			1.60592			0.802958	+	0.596036i	$0.203259\pi$
$564$	−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	$0.0215246\pi$
$571$			3.22925i			0.135140i	−0.997715	+	0.0675700i	$0.978475\pi$
$572$	7.36520	−	17.3693i	0.307955	−	0.726248i
$573$		−	50.7386i		−	2.11964i
$574$	−1.55259	+	3.90495i	−0.0648037	+	0.162989i
$575$		−	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	$-0.350824\pi$
$587$	21.8868			0.903365			0.451683	+	0.892179i	$0.350824\pi$
$588$	−30.7418	−	29.0356i	−1.26777	−	1.19741i
$589$	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	$-0.793094\pi$
$599$		−	29.6238i		−	1.21040i	0.796074	−	0.605199i	$-0.206906\pi$
$600$	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	$0.886442\pi$
$602$	−0.514026	+	1.29284i	−0.0209501	+	0.0526921i
$603$		−	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	$-0.220257\pi$
$607$	37.9415			1.54000			0.769999	+	0.638045i	$0.220257\pi$
$608$	−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
$616$	25.1050	+	24.8098i	1.01151	+	0.999616i
$617$	−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	$-0.635924\pi$
$619$	−20.6083			−0.828316			−0.414158	+	0.910205i	$0.635924\pi$
$620$	−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
$630$	8.46462	−	21.2895i	0.337238	−	0.848195i
$631$		−	14.1498i		−	0.563293i	−0.959518	−	0.281647i	$-0.909119\pi$
$631$		−	14.1498i		−	0.563293i	0.959518	−	0.281647i	$-0.0908806\pi$
$632$	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	$-0.733618\pi$
$643$	−33.9686			−1.33959			−0.669795	+	0.742546i	$0.733618\pi$
$644$	−33.2125	+	6.95547i	−1.30875	+	0.274084i
$645$	−1.12311			−0.0442222
$646$	6.24621	−	4.13595i	0.245754	−	0.162727i
$647$	−40.1725			−1.57934			−0.789672	−	0.613529i	$-0.789749\pi$
$647$	−40.1725			−1.57934			−0.789672	+	0.613529i	$0.789749\pi$
$648$	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
$658$	17.6920	+	7.03426i	0.689707	+	0.274224i
$659$			1.32431i			0.0515877i	0.999667	+	0.0257938i	$0.00821134\pi$
$659$			1.32431i			0.0515877i	−0.999667	+	0.0257938i	$0.991789\pi$
$660$	−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
$672$	−17.1976	−	41.8069i	−0.663411	−	1.61274i
$673$	−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	$-0.997736\pi$
$683$		−	0.371834i		−	0.0142278i	0.999975	−	0.00711392i	$-0.00226445\pi$
$684$	−22.5490	+	53.1771i	−0.862181	+	2.03328i
$685$		−	14.0000i		−	0.534913i
$686$	−17.5490	+	19.4431i	−0.670024	+	0.742339i
$687$			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	$-0.408575\pi$
$691$	14.8934			0.566573			0.283286	+	0.959035i	$0.408575\pi$
$692$	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
$700$	−1.08464	−	5.17915i	−0.0409954	−	0.195753i
$701$	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
$714$	−4.68951	+	11.7947i	−0.175500	+	0.441405i
$715$		−	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	$-0.638967\pi$
$719$	−22.6762			−0.845681			−0.422841	+	0.906204i	$0.638967\pi$
$720$	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	$-0.442778\pi$
$727$	9.64198			0.357601			0.178801	+	0.983885i	$0.442778\pi$
$728$	10.6454	+	10.5202i	0.394545	+	0.389906i
$729$	−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	$0.242835\pi$
$739$			37.5697i			1.38202i	−0.722844	+	0.691012i	$0.757165\pi$
$740$	−3.68260	−	1.56155i	−0.135375	−	0.0574038i
$741$		−	28.4924i		−	1.04670i
$742$	−6.95383	−	2.76481i	−0.255283	−	0.101499i
$743$			23.7917i			0.872835i	0.899744	+	0.436417i	$0.143753\pi$
$743$			23.7917i			0.872835i	−0.899744	+	0.436417i	$0.856247\pi$
$744$	−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	$-0.823344\pi$
$751$		−	28.8802i		−	1.05385i	0.849911	−	0.526926i	$-0.176656\pi$
$752$	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
$756$	−10.2316	−	48.8558i	−0.372118	−	1.77687i
$757$	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	$-0.163364\pi$
$770$	16.3992	+	6.52024i	0.590986	+	0.234973i
$771$			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
$784$	−25.6471	+	11.2350i	−0.915969	+	0.401249i
$785$	0.246211			0.00878766
$786$	−41.3693	−	62.4769i	−1.47559	−	2.22848i
$787$	−3.02045			−0.107667			−0.0538337	−	0.998550i	$-0.517144\pi$
$787$	−3.02045			−0.107667			−0.0538337	+	0.998550i	$0.517144\pi$
$788$	−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	$-0.0211778\pi$
$798$	49.5329	+	19.6940i	1.75345	+	0.697162i
$799$		−	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	$-0.545472\pi$
$811$	−8.10887			−0.284741			−0.142370	+	0.989813i	$0.545472\pi$
$812$	−2.16927	−	10.3583i	−0.0761265	−	0.363505i
$813$	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	$-0.830758\pi$
$823$		−	29.0890i		−	1.01398i	0.861953	−	0.506989i	$-0.169242\pi$
$824$	21.5150	−	4.00000i	0.749509	−	0.139347i
$825$			14.2462i			0.495989i
$826$	−7.19018	−	2.85878i	−0.250178	−	0.0994697i
$827$		−	24.5354i		−	0.853180i	−0.904445	−	0.426590i	$-0.859715\pi$
$827$		−	24.5354i		−	0.853180i	0.904445	−	0.426590i	$-0.140285\pi$
$828$	−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	$-0.560365\pi$
$839$	−10.9205			−0.377018			−0.188509	+	0.982071i	$0.560365\pi$
$840$	−16.0769	−	15.8879i	−0.554707	−	0.548185i
$841$	−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	$0.863751\pi$
$854$	2.76481	−	6.95383i	0.0946099	−	0.237955i
$855$			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	$-0.480682\pi$
$859$	3.55531			0.121306			0.0606528	+	0.998159i	$0.480682\pi$
$860$	−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	$-0.944334\pi$
$863$		−	10.2226i		−	0.347982i	0.984747	−	0.173991i	$-0.0556664\pi$
$864$	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
$868$	3.67939	+	17.5691i	0.124887	+	0.596335i
$869$	−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	$0.822781\pi$
$882$	−59.0324	+	13.7636i	−1.98772	+	0.463445i
$883$		−	31.3200i		−	1.05400i	−0.849865	−	0.527001i	$-0.823317\pi$
$883$		−	31.3200i		−	1.05400i	0.849865	−	0.527001i	$-0.176683\pi$
$884$	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	$-0.667983\pi$
$887$	−29.9957			−1.00716			−0.503578	+	0.863950i	$0.667983\pi$
$888$	−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
$896$	−29.9315	−	0.323119i	−0.999942	−	0.0107946i
$897$	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	$0.340577\pi$
$907$			52.8350i			1.75436i	−0.480166	+	0.877178i	$0.659423\pi$
$908$	−2.93893	+	6.93087i	−0.0975319	+	0.230009i
$909$		−	92.6004i		−	3.07136i
$910$	6.95383	+	2.76481i	0.230517	+	0.0916526i
$911$			2.06798i			0.0685151i	0.999413	+	0.0342575i	$0.0109066\pi$
$911$			2.06798i			0.0685151i	−0.999413	+	0.0342575i	$0.989093\pi$
$912$	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	$-0.951140\pi$
$919$		−	9.27015i		−	0.305794i	0.988242	−	0.152897i	$-0.0488603\pi$
$920$	−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
$924$	73.7832	−	15.4519i	2.42729	−	0.508332i
$925$	−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	$-0.213869\pi$
$938$	−5.20354	+	13.0875i	−0.169901	+	0.427323i
$939$		−	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	$0.198069\pi$
$947$			35.8735i			1.16573i	−0.812568	+	0.582867i	$0.801931\pi$
$948$	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
$952$	5.97796	+	5.90767i	0.193747	+	0.191469i
$953$	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
$966$	−26.7763	+	67.3455i	−0.861512	+	2.16681i
$967$			3.43806i			0.110560i	0.998471	+	0.0552802i	$0.0176052\pi$
$967$			3.43806i			0.110560i	−0.998471	+	0.0552802i	$0.982395\pi$
$968$	−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	$-0.444779\pi$
$971$	10.7575			0.345224			0.172612	+	0.984990i	$0.444779\pi$
$972$	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
$980$	−9.61302	+	10.1779i	−0.307077	+	0.325121i
$981$	−43.6155			−1.39254
$982$	−37.1771	+	24.6169i	−1.18637	+	0.785558i
$983$	−28.5083			−0.909275			−0.454637	−	0.890677i	$-0.650231\pi$
$983$	−28.5083			−0.909275			−0.454637	+	0.890677i	$0.650231\pi$
$984$	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	$-0.716840\pi$
$991$		−	48.9078i		−	1.55361i	0.629743	−	0.776804i	$-0.283160\pi$
$992$	−4.13595	+	18.7386i	−0.131317	+	0.594952i
$993$		−	55.2311i		−	1.75270i
$994$	−10.1817	+	25.6082i	−0.322944	+	0.812243i
$995$			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.111.1	✓	8
3.2	odd	2		1260.2.c.c.811.7		8
4.3	odd	2	inner	140.2.g.c.111.4	yes	8
5.2	odd	4		700.2.c.j.699.7		8
5.3	odd	4		700.2.c.i.699.2		8
5.4	even	2		700.2.g.j.251.8		8
7.2	even	3		980.2.o.e.31.4		16
7.3	odd	6		980.2.o.e.411.7		16
7.4	even	3		980.2.o.e.411.8		16
7.5	odd	6		980.2.o.e.31.3		16
7.6	odd	2	inner	140.2.g.c.111.2	yes	8
8.3	odd	2		2240.2.k.e.1791.1		8
8.5	even	2		2240.2.k.e.1791.7		8
12.11	even	2		1260.2.c.c.811.5		8
20.3	even	4		700.2.c.i.699.8		8
20.7	even	4		700.2.c.j.699.1		8
20.19	odd	2		700.2.g.j.251.5		8
21.20	even	2		1260.2.c.c.811.8		8
28.3	even	6		980.2.o.e.411.4		16
28.11	odd	6		980.2.o.e.411.3		16
28.19	even	6		980.2.o.e.31.8		16
28.23	odd	6		980.2.o.e.31.7		16
28.27	even	2	inner	140.2.g.c.111.3	yes	8
35.13	even	4		700.2.c.j.699.2		8
35.27	even	4		700.2.c.i.699.7		8
35.34	odd	2		700.2.g.j.251.7		8
56.13	odd	2		2240.2.k.e.1791.2		8
56.27	even	2		2240.2.k.e.1791.8		8
84.83	odd	2		1260.2.c.c.811.6		8
140.27	odd	4		700.2.c.i.699.1		8
140.83	odd	4		700.2.c.j.699.8		8
140.139	even	2		700.2.g.j.251.6		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
140.2.g.c.111.1	✓	8	1.1	even	1	trivial
140.2.g.c.111.2	yes	8	7.6	odd	2	inner
140.2.g.c.111.3	yes	8	28.27	even	2	inner
140.2.g.c.111.4	yes	8	4.3	odd	2	inner
700.2.c.i.699.1		8	140.27	odd	4
700.2.c.i.699.2		8	5.3	odd	4
700.2.c.i.699.7		8	35.27	even	4
700.2.c.i.699.8		8	20.3	even	4
700.2.c.j.699.1		8	20.7	even	4
700.2.c.j.699.2		8	35.13	even	4
700.2.c.j.699.7		8	5.2	odd	4
700.2.c.j.699.8		8	140.83	odd	4
700.2.g.j.251.5		8	20.19	odd	2
700.2.g.j.251.6		8	140.139	even	2
700.2.g.j.251.7		8	35.34	odd	2
700.2.g.j.251.8		8	5.4	even	2
980.2.o.e.31.3		16	7.5	odd	6
980.2.o.e.31.4		16	7.2	even	3
980.2.o.e.31.7		16	28.23	odd	6
980.2.o.e.31.8		16	28.19	even	6
980.2.o.e.411.3		16	28.11	odd	6
980.2.o.e.411.4		16	28.3	even	6
980.2.o.e.411.7		16	7.3	odd	6
980.2.o.e.411.8		16	7.4	even	3
1260.2.c.c.811.5		8	12.11	even	2
1260.2.c.c.811.6		8	84.83	odd	2
1260.2.c.c.811.7		8	3.2	odd	2
1260.2.c.c.811.8		8	21.20	even	2
2240.2.k.e.1791.1		8	8.3	odd	2
2240.2.k.e.1791.2		8	56.13	odd	2
2240.2.k.e.1791.7		8	8.5	even	2
2240.2.k.e.1791.8		8	56.27	even	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} +(-3.47692 - 1.38241i) 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} +(1.08464 + 5.17915i) 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} +(10.5018 + 4.17548i) 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} +(5.26012 - 5.32270i) 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} +(1.38241 - 3.47692i) 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} +(-3.27608 - 15.6433i) 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} +(-9.64092 + 2.24782i) 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

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more