LMFDB - Embedded newform 140.2.c.b.139.16

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [140,2,Mod(139,140)]

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, 1, 1]))

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

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

chi := DirichletCharacter("140.139");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 140 = 2^{2} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	140.c (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:	$16$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 6x^{14} + 28x^{12} + 16x^{10} - 40x^{8} + 610x^{6} + 1625x^{4} - 524x^{2} + 1444 $ x^16 - 6x^14 + 28x^12 + 16x^10 - 40x^8 + 610x^6 + 1625x^4 - 524*x^2 + 1444
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{8} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			139.16
Root			$2.05580 - 0.953651i$ of defining polynomial
Character	$\chi$	$=$	140.139
Dual form			140.2.c.b.139.13

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.06789 + 0.927153i) q^{2} +0.662153i q^{3} +(0.280776 + 1.98019i) q^{4} +(-1.31119 + 1.81129i) q^{5} +(-0.613917 + 0.707107i) q^{6} +(-1.19935 - 2.35829i) q^{7} +(-1.53610 + 2.37495i) q^{8} +2.56155 q^{9} +O(q^{10})$	\(q+(1.06789 + 0.927153i) q^{2} +0.662153i q^{3} +(0.280776 + 1.98019i) q^{4} +(-1.31119 + 1.81129i) q^{5} +(-0.613917 + 0.707107i) q^{6} +(-1.19935 - 2.35829i) q^{7} +(-1.53610 + 2.37495i) q^{8} +2.56155 q^{9} +(-3.07955 + 0.718585i) q^{10} -3.09218i q^{11} +(-1.31119 + 0.185917i) q^{12} +4.66988 q^{13} +(0.905722 - 3.63038i) q^{14} +(-1.19935 - 0.868210i) q^{15} +(-3.84233 + 1.11198i) q^{16} -2.04750 q^{17} +(2.73546 + 2.37495i) q^{18} +5.60083 q^{19} +(-3.95486 - 2.08784i) q^{20} +(1.56155 - 0.794156i) q^{21} +(2.86692 - 3.30210i) q^{22} -1.87285 q^{23} +(-1.57258 - 1.01714i) q^{24} +(-1.56155 - 4.74990i) q^{25} +(4.98691 + 4.32969i) q^{26} +3.68260i q^{27} +(4.33313 - 3.03710i) q^{28} -3.56155 q^{29} +(-0.475813 - 2.03914i) q^{30} -8.74599 q^{31} +(-5.13416 - 2.37495i) q^{32} +2.04750 q^{33} +(-2.18650 - 1.89834i) q^{34} +(5.84414 + 0.919799i) q^{35} +(0.719224 + 5.07237i) q^{36} -3.70861i q^{37} +(5.98107 + 5.19283i) q^{38} +3.09218i q^{39} +(-2.28760 - 5.89634i) q^{40} -8.48528i q^{41} +(2.40387 + 0.599727i) q^{42} +4.27156 q^{43} +(6.12311 - 0.868210i) q^{44} +(-3.35869 + 4.63972i) q^{45} +(-2.00000 - 1.73642i) q^{46} -0.290319i q^{47} +(-0.736303 - 2.54421i) q^{48} +(-4.12311 + 5.65685i) q^{49} +(2.73632 - 6.52017i) q^{50} -1.35576i q^{51} +(1.31119 + 9.24726i) q^{52} +9.49980i q^{53} +(-3.41433 + 3.93261i) q^{54} +(5.60083 + 4.05444i) q^{55} +(7.44316 + 0.774180i) q^{56} +3.70861i q^{57} +(-3.80335 - 3.30210i) q^{58} -8.05650 q^{59} +(1.38247 - 2.61872i) q^{60} -6.45101i q^{61} +(-9.33976 - 8.10887i) q^{62} +(-3.07221 - 6.04090i) q^{63} +(-3.28078 - 7.29634i) q^{64} +(-6.12311 + 8.45851i) q^{65} +(2.18650 + 1.89834i) q^{66} +2.39871 q^{67} +(-0.574888 - 4.05444i) q^{68} -1.24012i q^{69} +(5.38810 + 6.40065i) q^{70} +9.65719i q^{71} +(-3.93481 + 6.08356i) q^{72} -4.09499 q^{73} +(3.43845 - 3.96039i) q^{74} +(3.14516 - 1.03399i) q^{75} +(1.57258 + 11.0907i) q^{76} +(-7.29226 + 3.70861i) q^{77} +(-2.86692 + 3.30210i) q^{78} +1.35576i q^{79} +(3.02390 - 8.41760i) q^{80} +5.24621 q^{81} +(7.86715 - 9.06134i) q^{82} +12.4536i q^{83} +(2.01103 + 2.86920i) q^{84} +(2.68466 - 3.70861i) q^{85} +(4.56155 + 3.96039i) q^{86} -2.35829i q^{87} +(7.34376 + 4.74990i) q^{88} +2.82843i q^{89} +(-7.88843 + 1.84069i) q^{90} +(-5.60083 - 11.0129i) q^{91} +(-0.525853 - 3.70861i) q^{92} -5.79119i q^{93} +(0.269170 - 0.310029i) q^{94} +(-7.34376 + 10.1447i) q^{95} +(1.57258 - 3.39960i) q^{96} +6.14249 q^{97} +(-9.64779 + 2.21815i) q^{98} -7.92077i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 12 q^{4} + 8 q^{9}+O(q^{10}) $ 16 * q - 12 * q^4 + 8 * q^9	$ 16 q - 12 q^{4} + 8 q^{9} - 4 q^{14} - 12 q^{16} - 8 q^{21} + 8 q^{25} - 24 q^{29} - 4 q^{30} + 28 q^{36} + 32 q^{44} - 32 q^{46} - 12 q^{50} - 20 q^{56} + 44 q^{60} - 36 q^{64} - 32 q^{65} + 40 q^{70} + 88 q^{74} - 48 q^{81} + 40 q^{84} - 56 q^{85} + 40 q^{86}+O(q^{100}) $ 16 * q - 12 * q^4 + 8 * q^9 - 4 * q^14 - 12 * q^16 - 8 * q^21 + 8 * q^25 - 24 * q^29 - 4 * q^30 + 28 * q^36 + 32 * q^44 - 32 * q^46 - 12 * q^50 - 20 * q^56 + 44 * q^60 - 36 * q^64 - 32 * q^65 + 40 * q^70 + 88 * q^74 - 48 * q^81 + 40 * q^84 - 56 * q^85 + 40 * q^86

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 $

$2$	1.06789	+	0.927153i	0.755112	+	0.655596i
$2$	1.06789	+	0.927153i	0.755112	+	0.655596i
$3$			0.662153i			0.382294i	0.981561	+	0.191147i	$0.0612208\pi$
$3$			0.662153i			0.382294i	−0.981561	+	0.191147i	$0.938779\pi$
$4$	0.280776	+	1.98019i	0.140388	+	0.990097i
$5$	−1.31119	+	1.81129i	−0.586383	+	0.810034i
$5$	−1.31119	+	1.81129i	−0.586383	+	0.810034i
$6$	−0.613917	+	0.707107i	−0.250631	+	0.288675i
$7$	−1.19935	−	2.35829i	−0.453313	−	0.891352i
$7$	−1.19935	−	2.35829i	−0.453313	−	0.891352i
$8$	−1.53610	+	2.37495i	−0.543094	+	0.839672i
$9$	2.56155			0.853851
$10$	−3.07955	+	0.718585i	−0.973840	+	0.227236i
$11$		−	3.09218i		−	0.932326i	−0.884699	−	0.466163i	$-0.845636\pi$
$11$		−	3.09218i		−	0.932326i	0.884699	−	0.466163i	$-0.154364\pi$
$12$	−1.31119	+	0.185917i	−0.378508	+	0.0536696i
$13$	4.66988			1.29519			0.647596	−	0.761984i	$-0.275775\pi$
$13$	4.66988			1.29519			0.647596	+	0.761984i	$0.275775\pi$
$14$	0.905722	−	3.63038i	0.242064	−	0.970260i
$15$	−1.19935	−	0.868210i	−0.309672	−	0.224171i
$16$	−3.84233	+	1.11198i	−0.960582	+	0.277996i
$17$	−2.04750			−0.496590			−0.248295	−	0.968684i	$-0.579870\pi$
$17$	−2.04750			−0.496590			−0.248295	+	0.968684i	$0.579870\pi$
$18$	2.73546	+	2.37495i	0.644753	+	0.559781i
$19$	5.60083			1.28492			0.642459	−	0.766320i	$-0.277914\pi$
$19$	5.60083			1.28492			0.642459	+	0.766320i	$0.277914\pi$
$20$	−3.95486	−	2.08784i	−0.884333	−	0.466856i
$21$	1.56155	−	0.794156i	0.340759	−	0.173299i
$22$	2.86692	−	3.30210i	0.611229	−	0.704011i
$23$	−1.87285			−0.390517			−0.195258	−	0.980752i	$-0.562555\pi$
$23$	−1.87285			−0.390517			−0.195258	+	0.980752i	$0.562555\pi$
$24$	−1.57258	−	1.01714i	−0.321002	−	0.207622i
$25$	−1.56155	−	4.74990i	−0.312311	−	0.949980i
$26$	4.98691	+	4.32969i	0.978014	+	0.849122i
$27$			3.68260i			0.708717i
$28$	4.33313	−	3.03710i	0.818884	−	0.573959i
$29$	−3.56155			−0.661364			−0.330682	−	0.943742i	$-0.607279\pi$
$29$	−3.56155			−0.661364			−0.330682	+	0.943742i	$0.607279\pi$
$30$	−0.475813	−	2.03914i	−0.0868712	−	0.372294i
$31$	−8.74599			−1.57083			−0.785414	−	0.618971i	$-0.787550\pi$
$31$	−8.74599			−1.57083			−0.785414	+	0.618971i	$0.787550\pi$
$32$	−5.13416	−	2.37495i	−0.907600	−	0.419836i
$33$	2.04750			0.356423
$34$	−2.18650	−	1.89834i	−0.374981	−	0.325563i
$35$	5.84414	+	0.919799i	0.987840	+	0.155474i
$36$	0.719224	+	5.07237i	0.119871	+	0.845395i
$37$		−	3.70861i		−	0.609692i	−0.952402	−	0.304846i	$-0.901395\pi$
$37$		−	3.70861i		−	0.609692i	0.952402	−	0.304846i	$-0.0986050\pi$
$38$	5.98107	+	5.19283i	0.970258	+	0.842388i
$39$			3.09218i			0.495144i
$40$	−2.28760	−	5.89634i	−0.361702	−	0.932294i
$41$		−	8.48528i		−	1.32518i	−0.748983	−	0.662589i	$-0.769458\pi$
$41$		−	8.48528i		−	1.32518i	0.748983	−	0.662589i	$-0.230542\pi$
$42$	2.40387	+	0.599727i	0.370925	+	0.0925399i
$43$	4.27156			0.651407			0.325703	−	0.945472i	$-0.394399\pi$
$43$	4.27156			0.651407			0.325703	+	0.945472i	$0.394399\pi$
$44$	6.12311	−	0.868210i	0.923093	−	0.130888i
$45$	−3.35869	+	4.63972i	−0.500683	+	0.691648i
$46$	−2.00000	−	1.73642i	−0.294884	−	0.256021i
$47$		−	0.290319i		−	0.0423474i	−0.999776	−	0.0211737i	$-0.993260\pi$
$47$		−	0.290319i		−	0.0423474i	0.999776	−	0.0211737i	$-0.00674031\pi$
$48$	−0.736303	−	2.54421i	−0.106276	−	0.367225i
$49$	−4.12311	+	5.65685i	−0.589015	+	0.808122i
$50$	2.73632	−	6.52017i	0.386974	−	0.922091i
$51$		−	1.35576i		−	0.189844i
$52$	1.31119	+	9.24726i	0.181830	+	1.28236i
$53$			9.49980i			1.30490i	0.757833	+	0.652449i	$0.226258\pi$
$53$			9.49980i			1.30490i	−0.757833	+	0.652449i	$0.773742\pi$
$54$	−3.41433	+	3.93261i	−0.464632	+	0.535161i
$55$	5.60083	+	4.05444i	0.755216	+	0.546700i
$56$	7.44316	+	0.774180i	0.994634	+	0.103454i
$57$			3.70861i			0.491217i
$58$	−3.80335	−	3.30210i	−0.499404	−	0.433587i
$59$	−8.05650			−1.04887			−0.524434	−	0.851451i	$-0.675723\pi$
$59$	−8.05650			−1.04887			−0.524434	+	0.851451i	$0.675723\pi$
$60$	1.38247	−	2.61872i	0.178477	−	0.338076i
$61$		−	6.45101i		−	0.825967i	−0.910738	−	0.412984i	$-0.864487\pi$
$61$		−	6.45101i		−	0.825967i	0.910738	−	0.412984i	$-0.135513\pi$
$62$	−9.33976	−	8.10887i	−1.18615	−	1.02983i
$63$	−3.07221	−	6.04090i	−0.387062	−	0.761081i
$64$	−3.28078	−	7.29634i	−0.410097	−	0.912042i
$65$	−6.12311	+	8.45851i	−0.759478	+	1.04915i
$66$	2.18650	+	1.89834i	0.269139	+	0.233670i
$67$	2.39871			0.293049			0.146524	−	0.989207i	$-0.453191\pi$
$67$	2.39871			0.293049			0.146524	+	0.989207i	$0.453191\pi$
$68$	−0.574888	−	4.05444i	−0.0697154	−	0.491673i
$69$		−	1.24012i		−	0.149292i
$70$	5.38810	+	6.40065i	0.644001	+	0.765024i
$71$			9.65719i			1.14610i	0.819521	+	0.573049i	$0.194240\pi$
$71$			9.65719i			1.14610i	−0.819521	+	0.573049i	$0.805760\pi$
$72$	−3.93481	+	6.08356i	−0.463722	+	0.716954i
$73$	−4.09499			−0.479282			−0.239641	−	0.970862i	$-0.577030\pi$
$73$	−4.09499			−0.479282			−0.239641	+	0.970862i	$0.577030\pi$
$74$	3.43845	−	3.96039i	0.399711	−	0.460386i
$75$	3.14516	−	1.03399i	0.363172	−	0.119395i
$76$	1.57258	+	11.0907i	0.180387	+	1.27219i
$77$	−7.29226	+	3.70861i	−0.831030	+	0.422635i
$78$	−2.86692	+	3.30210i	−0.324615	+	0.373890i
$79$			1.35576i			0.152534i	0.997087	+	0.0762672i	$0.0243002\pi$
$79$			1.35576i			0.152534i	−0.997087	+	0.0762672i	$0.975700\pi$
$80$	3.02390	−	8.41760i	0.338083	−	0.941116i
$81$	5.24621			0.582912
$82$	7.86715	−	9.06134i	0.868781	−	1.00066i
$83$			12.4536i			1.36696i	0.729968	+	0.683482i	$0.239535\pi$
$83$			12.4536i			1.36696i	−0.729968	+	0.683482i	$0.760465\pi$
$84$	2.01103	+	2.86920i	0.219421	+	0.313055i
$85$	2.68466	−	3.70861i	0.291192	−	0.402255i
$86$	4.56155	+	3.96039i	0.491885	+	0.427059i
$87$		−	2.35829i		−	0.252836i
$88$	7.34376	+	4.74990i	0.782848	+	0.506341i
$89$			2.82843i			0.299813i	0.988700	+	0.149906i	$0.0478972\pi$
$89$			2.82843i			0.299813i	−0.988700	+	0.149906i	$0.952103\pi$
$90$	−7.88843	+	1.84069i	−0.831514	+	0.194026i
$91$	−5.60083	−	11.0129i	−0.587127	−	1.15447i
$92$	−0.525853	−	3.70861i	−0.0548240	−	0.386649i
$93$		−	5.79119i		−	0.600518i
$94$	0.269170	−	0.310029i	0.0277628	−	0.0319770i
$95$	−7.34376	+	10.1447i	−0.753454	+	1.04083i
$96$	1.57258	−	3.39960i	0.160501	−	0.346970i
$97$	6.14249			0.623675			0.311837	−	0.950135i	$-0.399056\pi$
$97$	6.14249			0.623675			0.311837	+	0.950135i	$0.399056\pi$
$98$	−9.64779	+	2.21815i	−0.974574	+	0.224067i
$99$		−	7.92077i		−	0.796068i
$100$	8.96727	−	4.42584i	0.896727	−	0.442584i
$101$		−	2.38247i		−	0.237064i	−0.992950	−	0.118532i	$-0.962181\pi$
$101$		−	2.38247i		−	0.237064i	0.992950	−	0.118532i	$-0.0378189\pi$
$102$	1.25699	−	1.44780i	0.124461	−	0.143353i
$103$		−	1.03399i		−	0.101882i	−0.998702	−	0.0509409i	$-0.983778\pi$
$103$		−	1.03399i		−	0.101882i	0.998702	−	0.0509409i	$-0.0162220\pi$
$104$	−7.17341	+	11.0907i	−0.703411	+	1.08754i
$105$	−0.609048	+	3.86972i	−0.0594370	+	0.377646i
$106$	−8.80776	+	10.1447i	−0.855486	+	0.985344i
$107$	14.6875			1.41990			0.709948	−	0.704254i	$-0.248718\pi$
$107$	14.6875			1.41990			0.709948	+	0.704254i	$0.248718\pi$
$108$	−7.29226	+	1.03399i	−0.701698	+	0.0994955i
$109$	0.438447			0.0419956			0.0209978	−	0.999780i	$-0.493316\pi$
$109$	0.438447			0.0419956			0.0209978	+	0.999780i	$0.493316\pi$
$110$	2.22199	+	9.52251i	0.211858	+	0.907936i
$111$	2.45567			0.233082
$112$	7.23069	+	7.72768i	0.683236	+	0.730197i
$113$		−	3.70861i		−	0.348877i	−0.984668	−	0.174438i	$-0.944189\pi$
$113$		−	3.70861i		−	0.348877i	0.984668	−	0.174438i	$-0.0558110\pi$
$114$	−3.43845	+	3.96039i	−0.322040	+	0.370924i
$115$	2.45567	−	3.39228i	0.228992	−	0.316332i
$116$	−1.00000	−	7.05256i	−0.0928477	−	0.654814i
$117$	11.9621			1.10590
$118$	−8.60345	−	7.46960i	−0.792012	−	0.687633i
$119$	2.45567	+	4.82860i	0.225111	+	0.442637i
$120$	3.90428	−	1.51474i	0.356411	−	0.138277i
$121$	1.43845			0.130768
$122$	5.98107	−	6.88897i	0.541501	−	0.623698i
$123$	5.61856			0.506608
$124$	−2.45567	−	17.3188i	−0.220526	−	1.55527i
$125$	10.6509	+	3.39960i	0.952650	+	0.304070i
$126$	2.32006	−	9.29941i	0.206687	−	0.828458i
$127$	−17.0862			−1.51616			−0.758079	−	0.652163i	$-0.773862\pi$
$127$	−17.0862			−1.51616			−0.758079	+	0.652163i	$0.773862\pi$
$128$	3.26131	−	10.8335i	0.288262	−	0.957552i
$129$			2.82843i			0.249029i
$130$	−14.3811	+	3.35570i	−1.26131	+	0.294315i
$131$	−5.60083			−0.489347			−0.244673	−	0.969606i	$-0.578681\pi$
$131$	−5.60083			−0.489347			−0.244673	+	0.969606i	$0.578681\pi$
$132$	0.574888	+	4.05444i	0.0500376	+	0.352893i
$133$	−6.71737	−	13.2084i	−0.582470	−	1.14531i
$134$	2.56155	+	2.22397i	0.221284	+	0.192121i
$135$	−6.67026	−	4.82860i	−0.574085	−	0.415579i
$136$	3.14516	−	4.86270i	0.269695	−	0.416973i
$137$		−	13.2084i		−	1.12847i	−0.825614	−	0.564235i	$-0.809171\pi$
$137$		−	13.2084i		−	1.12847i	0.825614	−	0.564235i	$-0.190829\pi$
$138$	1.14978	−	1.32431i	0.0978755	−	0.112732i
$139$	14.3468			1.21688			0.608441	−	0.793599i	$-0.291795\pi$
$139$	14.3468			1.21688			0.608441	+	0.793599i	$0.291795\pi$
$140$	−0.180482	+	11.8308i	−0.0152535	+	0.999884i
$141$	0.192236			0.0161892
$142$	−8.95369	+	10.3128i	−0.751377	+	0.865432i
$143$		−	14.4401i		−	1.20754i
$144$	−9.84233	+	2.84840i	−0.820194	+	0.237367i
$145$	4.66988	−	6.45101i	0.387812	−	0.535727i
$146$	−4.37300	−	3.79668i	−0.361912	−	0.314216i
$147$	−3.74571	−	2.73013i	−0.308941	−	0.225177i
$148$	7.34376	−	1.04129i	0.603654	−	0.0855935i
$149$	−2.00000			−0.163846			−0.0819232	−	0.996639i	$-0.526106\pi$
$149$	−2.00000			−0.163846			−0.0819232	+	0.996639i	$0.526106\pi$
$150$	4.31735	+	1.81186i	0.352510	+	0.147938i
$151$		−	18.9337i		−	1.54080i	−0.637558	−	0.770402i	$-0.720055\pi$
$151$		−	18.9337i		−	1.54080i	0.637558	−	0.770402i	$-0.279945\pi$
$152$	−8.60345	+	13.3017i	−0.697832	+	1.07891i
$153$	−5.24477			−0.424014
$154$	−11.2258	−	2.80065i	−0.904599	−	0.225683i
$155$	11.4677	−	15.8415i	0.921106	−	1.27242i
$156$	−6.12311	+	0.868210i	−0.490241	+	0.0695124i
$157$	−2.62238			−0.209289			−0.104644	−	0.994510i	$-0.533370\pi$
$157$	−2.62238			−0.209289			−0.104644	+	0.994510i	$0.533370\pi$
$158$	−1.25699	+	1.44780i	−0.100001	+	0.115181i
$159$	−6.29033			−0.498855
$160$	11.0336	−	6.18545i	0.872282	−	0.489003i
$161$	2.24621	+	4.41674i	0.177026	+	0.348088i
$162$	5.60237	+	4.86404i	0.440164	+	0.382155i
$163$	−15.7392			−1.23279			−0.616396	−	0.787436i	$-0.711408\pi$
$163$	−15.7392			−1.23279			−0.616396	+	0.787436i	$0.711408\pi$
$164$	16.8025	−	2.38247i	1.31205	−	0.186039i
$165$	−2.68466	+	3.70861i	−0.209000	+	0.288715i
$166$	−11.5464	+	13.2991i	−0.896175	+	1.03221i
$167$			8.39919i			0.649949i	0.945723	+	0.324974i	$0.105356\pi$
$167$			8.39919i			0.649949i	−0.945723	+	0.324974i	$0.894644\pi$
$168$	−0.512626	+	4.92851i	−0.0395499	+	0.380243i
$169$	8.80776			0.677520
$170$	6.30537	−	1.47130i	0.483599	−	0.112843i
$171$	14.3468			1.09713
$172$	1.19935	+	8.45851i	0.0914498	+	0.644955i
$173$	−8.76487			−0.666381			−0.333190	−	0.942860i	$-0.608125\pi$
$173$	−8.76487			−0.666381			−0.333190	+	0.942860i	$0.608125\pi$
$174$	2.18650	−	2.51840i	0.165758	−	0.190919i
$175$	−9.32881	+	9.37941i	−0.705192	+	0.709017i
$176$	3.43845	+	11.8812i	0.259183	+	0.895576i
$177$		−	5.33464i		−	0.400976i
$178$	−2.62238	+	3.02045i	−0.196556	+	0.226392i
$179$			1.73642i			0.129786i	0.997892	+	0.0648931i	$0.0206706\pi$
$179$			1.73642i			0.129786i	−0.997892	+	0.0648931i	$0.979329\pi$
$180$	−10.1306	−	5.34812i	−0.755089	−	0.398626i
$181$			9.27944i			0.689735i	0.938651	+	0.344868i	$0.112076\pi$
$181$			9.27944i			0.689735i	−0.938651	+	0.344868i	$0.887924\pi$
$182$	4.22961	−	16.9534i	0.313520	−	1.25667i
$183$	4.27156			0.315763
$184$	2.87689	−	4.44793i	0.212087	−	0.327906i
$185$	6.71737	+	4.86270i	0.493871	+	0.357513i
$186$	5.36932	−	6.18435i	0.393697	−	0.453459i
$187$			6.33122i			0.462984i
$188$	0.574888	−	0.0815148i	0.0419280	−	0.00594508i
$189$	8.68466	−	4.41674i	0.631716	−	0.321270i
$190$	−17.2480	+	4.02467i	−1.25130	+	0.291980i
$191$			13.7245i			0.993067i	0.868018	+	0.496534i	$0.165394\pi$
$191$			13.7245i			0.993067i	−0.868018	+	0.496534i	$0.834606\pi$
$192$	4.83129	−	2.17238i	0.348669	−	0.156778i
$193$			3.70861i			0.266952i	0.991052	+	0.133476i	$0.0426138\pi$
$193$			3.70861i			0.266952i	−0.991052	+	0.133476i	$0.957386\pi$
$194$	6.55950	+	5.69502i	0.470944	+	0.408879i
$195$	−5.60083	−	4.05444i	−0.401084	−	0.290344i
$196$	−12.3593	−	6.57623i	−0.882810	−	0.469731i
$197$			11.1258i			0.792683i	0.918103	+	0.396341i	$0.129720\pi$
$197$			11.1258i			0.792683i	−0.918103	+	0.396341i	$0.870280\pi$
$198$	7.34376	−	8.45851i	0.521899	−	0.601120i
$199$	6.29033			0.445909			0.222955	−	0.974829i	$-0.428430\pi$
$199$	6.29033			0.445909			0.222955	+	0.974829i	$0.428430\pi$
$200$	13.6795	+	3.58773i	0.967285	+	0.253690i
$201$			1.58831i			0.112031i
$202$	2.20891	−	2.54421i	0.155418	−	0.179010i
$203$	4.27156	+	8.39919i	0.299805	+	0.589508i
$204$	2.68466	−	0.380664i	0.187964	−	0.0266518i
$205$	15.3693	+	11.1258i	1.07344	+	0.777062i
$206$	0.958664	−	1.10418i	0.0667933	−	0.0769322i
$207$	−4.79741			−0.333443
$208$	−17.9432	+	5.19283i	−1.24414	+	0.360058i
$209$		−	17.3188i		−	1.19796i
$210$	−4.23821	+	3.56775i	−0.292465	+	0.246198i
$211$			25.1181i			1.72920i	0.502461	+	0.864600i	$0.332428\pi$
$211$			25.1181i			1.72920i	−0.502461	+	0.864600i	$0.667572\pi$
$212$	−18.8114	+	2.66732i	−1.29197	+	0.183192i
$213$	−6.39454			−0.438147
$214$	15.6847	+	13.6176i	1.07218	+	0.930879i
$215$	−5.60083	+	7.73704i	−0.381974	+	0.527662i
$216$	−8.74599	−	5.65685i	−0.595090	−	0.384900i
$217$	10.4895	+	20.6256i	0.712076	+	1.40016i
$218$	0.468213	+	0.406507i	0.0317114	+	0.0275322i
$219$		−	2.71151i		−	0.183227i
$220$	−6.45598	+	12.2291i	−0.435262	+	0.824487i
$221$	−9.56155			−0.643180
$222$	2.62238	+	2.27678i	0.176003	+	0.152807i
$223$		−	19.1567i		−	1.28283i	−0.767196	−	0.641413i	$-0.778349\pi$
$223$		−	19.1567i		−	1.28283i	0.767196	−	0.641413i	$-0.221651\pi$
$224$	0.556839	+	14.9563i	0.0372054	+	0.999308i
$225$	−4.00000	−	12.1671i	−0.266667	−	0.811141i
$226$	3.43845	−	3.96039i	0.228722	−	0.263441i
$227$		−	14.0683i		−	0.933743i	−0.884325	−	0.466871i	$-0.845381\pi$
$227$		−	14.0683i		−	0.933743i	0.884325	−	0.466871i	$-0.154619\pi$
$228$	−7.34376	+	1.04129i	−0.486353	+	0.0689611i
$229$			8.03932i			0.531253i	0.964076	+	0.265627i	$0.0855788\pi$
$229$			8.03932i			0.531253i	−0.964076	+	0.265627i	$0.914421\pi$
$230$	5.76755	−	1.34580i	0.380301	−	0.0887396i
$231$	−2.45567	−	4.82860i	−0.161571	−	0.317698i
$232$	5.47091	−	8.45851i	0.359183	−	0.555328i
$233$			7.41722i			0.485918i	0.970037	+	0.242959i	$0.0781181\pi$
$233$			7.41722i			0.485918i	−0.970037	+	0.242959i	$0.921882\pi$
$234$	12.7742	+	11.0907i	0.835079	+	0.725024i
$235$	0.525853	+	0.380664i	0.0343029	+	0.0248318i
$236$	−2.26208	−	15.9534i	−0.147249	−	1.03848i
$237$	−0.897718			−0.0583131
$238$	−1.85446	+	7.43319i	−0.120207	+	0.481822i
$239$		−	3.09218i		−	0.200016i	−0.994987	−	0.100008i	$-0.968113\pi$
$239$		−	3.09218i		−	0.200016i	0.994987	−	0.100008i	$-0.0318869\pi$
$240$	5.57374	+	2.00229i	0.359784	+	0.129247i
$241$			18.9071i			1.21791i	0.793204	+	0.608956i	$0.208411\pi$
$241$			18.9071i			1.21791i	−0.793204	+	0.608956i	$0.791589\pi$
$242$	1.53610	+	1.33366i	0.0987444	+	0.0857309i
$243$			14.5216i			0.931561i
$244$	12.7742	−	1.81129i	0.817787	−	0.115956i
$245$	−4.84003	−	14.8854i	−0.309218	−	0.950991i
$246$	6.00000	+	5.20926i	0.382546	+	0.332130i
$247$	26.1552			1.66422
$248$	13.4347	−	20.7713i	0.853107	−	1.31898i
$249$	−8.24621			−0.522582
$250$	8.22209	+	13.5055i	0.520010	+	0.854160i
$251$	3.14516			0.198521			0.0992605	−	0.995061i	$-0.468352\pi$
$251$	3.14516			0.198521			0.0992605	+	0.995061i	$0.468352\pi$
$252$	11.0995	−	7.77970i	0.699205	−	0.490075i
$253$			5.79119i			0.364089i
$254$	−18.2462	−	15.8415i	−1.14487	−	0.993987i
$255$	2.45567	+	1.77766i	0.153780	+	0.111321i
$256$	13.5270	−	8.54521i	0.845437	−	0.534076i
$257$	−28.0193			−1.74779			−0.873897	−	0.486111i	$-0.838415\pi$
$257$	−28.0193			−1.74779			−0.873897	+	0.486111i	$0.838415\pi$
$258$	−2.62238	+	3.02045i	−0.163262	+	0.188045i
$259$	−8.74599	+	4.44793i	−0.543450	+	0.276381i
$260$	−18.4687	−	9.74998i	−1.14538	−	0.604668i
$261$	−9.12311			−0.564706
$262$	−5.98107	−	5.19283i	−0.369512	−	0.320814i
$263$	11.9935			0.739553			0.369776	−	0.929121i	$-0.379434\pi$
$263$	11.9935			0.739553			0.369776	+	0.929121i	$0.379434\pi$
$264$	−3.14516	+	4.86270i	−0.193571	+	0.299278i
$265$	−17.2069	−	12.4561i	−1.05701	−	0.765170i
$266$	5.07280	−	20.3332i	0.311033	−	1.24671i
$267$	−1.87285			−0.114617
$268$	0.673500	+	4.74990i	0.0411406	+	0.290146i
$269$		−	16.5246i		−	1.00752i	−0.863843	−	0.503761i	$-0.831949\pi$
$269$		−	16.5246i		−	1.00752i	0.863843	−	0.503761i	$-0.168051\pi$
$270$	−2.64626	−	11.3408i	−0.161046	−	0.690177i
$271$	8.74599			0.531281			0.265641	−	0.964072i	$-0.414417\pi$
$271$	8.74599			0.531281			0.265641	+	0.964072i	$0.414417\pi$
$272$	7.86715	−	2.27678i	0.477016	−	0.138050i
$273$	7.29226	−	3.70861i	0.441348	−	0.224455i
$274$	12.2462	−	14.1051i	0.739821	−	0.852122i
$275$	−14.6875	+	4.82860i	−0.885691	+	0.291175i
$276$	2.45567	−	0.348195i	0.147814	−	0.0209589i
$277$			2.08258i			0.125130i	0.998041	+	0.0625651i	$0.0199281\pi$
$277$			2.08258i			0.125130i	−0.998041	+	0.0625651i	$0.980072\pi$
$278$	15.3208	+	13.3017i	0.918882	+	0.797783i
$279$	−22.4033			−1.34125
$280$	−11.1617	+	12.4666i	−0.667038	+	0.745024i
$281$	−20.0540			−1.19632			−0.598160	−	0.801377i	$-0.704101\pi$
$281$	−20.0540			−1.19632			−0.598160	+	0.801377i	$0.704101\pi$
$282$	0.205287	+	0.178232i	0.0122246	+	0.0106136i
$283$			19.5285i			1.16085i	0.814314	+	0.580425i	$0.197113\pi$
$283$			19.5285i			1.16085i	−0.814314	+	0.580425i	$0.802887\pi$
$284$	−19.1231	+	2.71151i	−1.13475	+	0.160899i
$285$	−6.71737	−	4.86270i	−0.397903	−	0.288041i
$286$	13.3882	−	15.4204i	0.791659	−	0.911828i
$287$	−20.0108	+	10.1768i	−1.18120	+	0.600720i
$288$	−13.1514	−	6.08356i	−0.774955	−	0.358477i
$289$	−12.8078			−0.753398
$290$	10.9680	−	2.55928i	0.644062	−	0.150286i
$291$			4.06727i			0.238427i
$292$	−1.14978	−	8.10887i	−0.0672856	−	0.474536i
$293$	15.1594			0.885622			0.442811	−	0.896615i	$-0.353981\pi$
$293$	15.1594			0.885622			0.442811	+	0.896615i	$0.353981\pi$
$294$	−1.46875	−	6.38832i	−0.0856595	−	0.372574i
$295$	10.5636	−	14.5927i	0.615038	−	0.849618i
$296$	8.80776	+	5.69681i	0.511941	+	0.331120i
$297$	11.3873			0.660755
$298$	−2.13578	−	1.85431i	−0.123722	−	0.107417i
$299$	−8.74599			−0.505794
$300$	2.93058	+	5.93771i	0.169197	+	0.342814i
$301$	−5.12311	−	10.0736i	−0.295291	−	0.580632i
$302$	17.5544	−	20.2191i	1.01014	−	1.16348i
$303$	1.57756			0.0906284
$304$	−21.5202	+	6.22803i	−1.23427	+	0.357202i
$305$	11.6847	+	8.45851i	0.669062	+	0.484333i
$306$	−5.60083	−	4.86270i	−0.320178	−	0.277982i
$307$		−	26.1500i		−	1.49246i	−0.665687	−	0.746231i	$-0.731861\pi$
$307$		−	26.1500i		−	1.49246i	0.665687	−	0.746231i	$-0.268139\pi$
$308$	−9.39126	−	13.3988i	−0.535117	−	0.763467i
$309$	0.684658			0.0389489
$310$	26.9337	−	6.28474i	1.52973	−	0.356949i
$311$	19.9477			1.13113			0.565564	−	0.824704i	$-0.308659\pi$
$311$	19.9477			1.13113			0.565564	+	0.824704i	$0.308659\pi$
$312$	−7.34376	−	4.74990i	−0.415759	−	0.268910i
$313$	11.3873			0.643646			0.321823	−	0.946800i	$-0.395704\pi$
$313$	11.3873			0.643646			0.321823	+	0.946800i	$0.395704\pi$
$314$	−2.80042	−	2.43135i	−0.158037	−	0.137209i
$315$	14.9701	+	2.35611i	0.843468	+	0.132752i
$316$	−2.68466	+	0.380664i	−0.151024	+	0.0214140i
$317$		−	31.7515i		−	1.78334i	−0.452686	−	0.891670i	$-0.649534\pi$
$317$		−	31.7515i		−	1.78334i	0.452686	−	0.891670i	$-0.350466\pi$
$318$	−6.71737	−	5.83209i	−0.376692	−	0.327047i
$319$			11.0129i			0.616607i
$320$	17.5175	+	3.62445i	0.979259	+	0.202613i
$321$			9.72540i			0.542819i
$322$	−1.69628	+	6.79917i	−0.0945302	+	0.378903i
$323$	−11.4677			−0.638079
$324$	1.47301	+	10.3885i	0.0818340	+	0.577140i
$325$	−7.29226	−	22.1815i	−0.404502	−	1.23041i
$326$	−16.8078	−	14.5927i	−0.930896	−	0.808213i
$327$			0.290319i			0.0160547i
$328$	20.1521	+	13.0343i	1.11271	+	0.719697i
$329$	−0.684658	+	0.348195i	−0.0377464	+	0.0191966i
$330$	−6.30537	+	1.47130i	−0.347099	+	0.0809923i
$331$			1.73642i			0.0954423i	0.998861	+	0.0477211i	$0.0151959\pi$
$331$			1.73642i			0.0954423i	−0.998861	+	0.0477211i	$0.984804\pi$
$332$	−24.6606	+	3.49668i	−1.35343	+	0.191905i
$333$		−	9.49980i		−	0.520586i
$334$	−7.78733	+	8.96941i	−0.426104	+	0.490784i
$335$	−3.14516	+	4.34475i	−0.171839	+	0.237379i
$336$	−5.11691	+	4.78783i	−0.279150	+	0.261197i
$337$			5.33464i			0.290596i	0.989388	+	0.145298i	$0.0464141\pi$
$337$			5.33464i			0.290596i	−0.989388	+	0.145298i	$0.953586\pi$
$338$	9.40572	+	8.16614i	0.511604	+	0.444179i
$339$	2.45567			0.133374
$340$	8.09755	+	4.27485i	0.439151	+	0.231836i
$341$			27.0442i			1.46452i
$342$	15.3208	+	13.3017i	0.828455	+	0.719273i
$343$	18.2856	+	2.93893i	0.987329	+	0.158687i
$344$	−6.56155	+	10.1447i	−0.353775	+	0.546968i
$345$	2.24621	+	1.62603i	0.120932	+	0.0875425i
$346$	−9.35991	−	8.12637i	−0.503192	−	0.436876i
$347$	4.27156			0.229309			0.114655	−	0.993405i	$-0.463424\pi$
$347$	4.27156			0.229309			0.114655	+	0.993405i	$0.463424\pi$
$348$	4.66988	−	0.662153i	0.250332	−	0.0354952i
$349$			36.3236i			1.94436i	0.234241	+	0.972179i	$0.424740\pi$
$349$			36.3236i			1.94436i	−0.234241	+	0.972179i	$0.575260\pi$
$350$	−18.6583	+	1.36694i	−0.997327	+	0.0730661i
$351$			17.1973i			0.917924i
$352$	−7.34376	+	15.8757i	−0.391424	+	0.846179i
$353$	27.1216			1.44353			0.721767	−	0.692136i	$-0.243330\pi$
$353$	27.1216			1.44353			0.721767	+	0.692136i	$0.243330\pi$
$354$	4.94602	−	5.69681i	0.262878	−	0.302782i
$355$	−17.4920	−	12.6624i	−0.928378	−	0.672052i
$356$	−5.60083	+	0.794156i	−0.296843	+	0.0420902i
$357$	−3.19727	+	1.62603i	−0.169218	+	0.0860586i
$358$	−1.60993	+	1.85431i	−0.0850873	+	0.0980031i
$359$		−	26.4738i		−	1.39724i	−0.715495	−	0.698618i	$-0.753799\pi$
$359$		−	26.4738i		−	1.39724i	0.715495	−	0.698618i	$-0.246201\pi$
$360$	−5.85981	−	15.1038i	−0.308839	−	0.796040i
$361$	12.3693			0.651017
$362$	−8.60345	+	9.90941i	−0.452187	+	0.520827i
$363$			0.952473i			0.0499919i
$364$	20.2352	−	14.1829i	1.06061	−	0.743386i
$365$	5.36932	−	7.41722i	0.281043	−	0.388235i
$366$	4.56155	+	3.96039i	0.238436	+	0.207013i
$367$			31.8191i			1.66094i	0.557061	+	0.830472i	$0.311929\pi$
$367$			31.8191i			1.66094i	−0.557061	+	0.830472i	$0.688071\pi$
$368$	7.19612	−	2.08258i	0.375124	−	0.108562i
$369$		−	21.7355i		−	1.13150i
$370$	2.66495	+	11.4209i	0.138544	+	0.593742i
$371$	22.4033	−	11.3936i	1.16312	−	0.591527i
$372$	11.4677	−	1.62603i	0.594571	−	0.0843057i
$373$			22.7082i			1.17579i	0.808938	+	0.587893i	$0.200043\pi$
$373$			22.7082i			1.17579i	−0.808938	+	0.587893i	$0.799957\pi$
$374$	−5.87000	+	6.76104i	−0.303531	+	0.349605i
$375$	−2.25106	+	7.05256i	−0.116244	+	0.364193i
$376$	0.689494	+	0.445960i	0.0355579	+	0.0229986i
$377$	−16.6320			−0.856593
$378$	13.3692	+	3.33541i	0.687640	+	0.171555i
$379$		−	5.20926i		−	0.267582i	−0.991010	−	0.133791i	$-0.957285\pi$
$379$		−	5.20926i		−	0.267582i	0.991010	−	0.133791i	$-0.0427150\pi$
$380$	−22.1505	−	11.6937i	−1.13630	−	0.599872i
$381$		−	11.3137i		−	0.579619i
$382$	−12.7247	+	14.6562i	−0.651051	+	0.749877i
$383$		−	26.9752i		−	1.37837i	−0.724586	−	0.689185i	$-0.757969\pi$
$383$		−	26.9752i		−	1.37837i	0.724586	−	0.689185i	$-0.242031\pi$
$384$	7.17341	+	2.15949i	0.366067	+	0.110201i
$385$	2.84418	−	18.0711i	0.144953	−	0.920989i
$386$	−3.43845	+	3.96039i	−0.175012	+	0.201578i
$387$	10.9418			0.556204
$388$	1.72466	+	12.1633i	0.0875566	+	0.617498i
$389$	16.9309			0.858429			0.429215	−	0.903203i	$-0.358790\pi$
$389$	16.9309			0.858429			0.429215	+	0.903203i	$0.358790\pi$
$390$	−2.22199	−	9.52251i	−0.112515	−	0.482191i
$391$	3.83466			0.193927
$392$	−7.10123	−	18.4817i	−0.358666	−	0.933466i
$393$		−	3.70861i		−	0.187075i
$394$	−10.3153	+	11.8812i	−0.519679	+	0.598564i
$395$	−2.45567	−	1.77766i	−0.123558	−	0.0894436i
$396$	15.6847	−	2.22397i	0.788184	−	0.111758i
$397$	12.8599			0.645418			0.322709	−	0.946498i	$-0.395407\pi$
$397$	12.8599			0.645418			0.322709	+	0.946498i	$0.395407\pi$
$398$	6.71737	+	5.83209i	0.336712	+	0.292336i
$399$	8.74599	−	4.44793i	0.437847	−	0.222675i
$400$	11.2818	+	16.5143i	0.564090	+	0.825713i
$401$	17.5616			0.876982			0.438491	−	0.898736i	$-0.355513\pi$
$401$	17.5616			0.876982			0.438491	+	0.898736i	$0.355513\pi$
$402$	−1.47261	+	1.69614i	−0.0734469	+	0.0845958i
$403$	−40.8427			−2.03452
$404$	4.71774	−	0.668940i	0.234717	−	0.0332810i
$405$	−6.87879	+	9.50242i	−0.341810	+	0.472179i
$406$	−3.22578	+	12.9298i	−0.160093	+	0.641695i
$407$	−11.4677			−0.568432
$408$	3.21985	+	2.08258i	0.159406	+	0.103103i
$409$			4.76493i			0.235611i	0.993037	+	0.117805i	$0.0375859\pi$
$409$			4.76493i			0.235611i	−0.993037	+	0.117805i	$0.962414\pi$
$410$	6.09739	+	26.1309i	0.301129	+	1.29051i
$411$	8.74599			0.431408
$412$	2.04750	−	0.290319i	0.100873	−	0.0143030i
$413$	9.66259	+	18.9996i	0.475465	+	0.934909i
$414$	−5.12311	−	4.44793i	−0.251787	−	0.218604i
$415$	−22.5571	−	16.3291i	−1.10729	−	0.801564i
$416$	−23.9759	−	11.0907i	−1.17552	−	0.543768i
$417$			9.49980i			0.465207i
$418$	16.0571	−	18.4945i	0.785380	−	0.904597i
$419$	−20.6372			−1.00819			−0.504095	−	0.863648i	$-0.668174\pi$
$419$	−20.6372			−1.00819			−0.504095	+	0.863648i	$0.668174\pi$
$420$	−7.83379	−	0.119507i	−0.382250	−	0.00583135i
$421$	8.43845			0.411265			0.205632	−	0.978629i	$-0.434075\pi$
$421$	8.43845			0.411265			0.205632	+	0.978629i	$0.434075\pi$
$422$	−23.2883	+	26.8233i	−1.13366	+	1.30574i
$423$		−	0.743668i		−	0.0361584i
$424$	−22.5616	−	14.5927i	−1.09569	−	0.708683i
$425$	3.19727	+	9.72540i	0.155090	+	0.471751i
$426$	−6.82867	−	5.92872i	−0.330850	−	0.287247i
$427$	−15.2134	+	7.73704i	−0.736227	+	0.374421i
$428$	4.12391	+	29.0841i	0.199337	+	1.40584i
$429$	9.56155			0.461636
$430$	−13.1545	+	3.06948i	−0.634366	+	0.148023i
$431$		−	15.4609i		−	0.744724i	−0.928087	−	0.372362i	$-0.878548\pi$
$431$		−	15.4609i		−	0.744724i	0.928087	−	0.372362i	$-0.121452\pi$
$432$	−4.09499	−	14.1498i	−0.197020	−	0.680781i
$433$	−38.5088			−1.85062			−0.925308	−	0.379218i	$-0.876193\pi$
$433$	−38.5088			−1.85062			−0.925308	+	0.379218i	$0.876193\pi$
$434$	−7.92144	+	31.7513i	−0.380241	+	1.52411i
$435$	4.27156	+	3.09218i	0.204806	+	0.148258i
$436$	0.123106	+	0.868210i	0.00589569	+	0.0415797i
$437$	−10.4895			−0.501782
$438$	2.51398	−	2.89560i	0.120123	−	0.138357i
$439$	23.7823			1.13507			0.567534	−	0.823350i	$-0.307898\pi$
$439$	23.7823			1.13507			0.567534	+	0.823350i	$0.307898\pi$
$440$	−18.2325	+	7.07367i	−0.869202	+	0.337224i
$441$	−10.5616	+	14.4903i	−0.502931	+	0.690016i
$442$	−10.2107	−	8.86502i	−0.485673	−	0.421666i
$443$	−13.8664			−0.658812			−0.329406	−	0.944188i	$-0.606848\pi$
$443$	−13.8664			−0.658812			−0.329406	+	0.944188i	$0.606848\pi$
$444$	0.689494	+	4.86270i	0.0327219	+	0.230773i
$445$	−5.12311	−	3.70861i	−0.242858	−	0.175805i
$446$	17.7612	−	20.4572i	0.841015	−	0.968677i
$447$		−	1.32431i		−	0.0626376i
$448$	−13.2721	+	16.4879i	−0.627048	+	0.778981i
$449$	18.6847			0.881784			0.440892	−	0.897560i	$-0.354662\pi$
$449$	18.6847			0.881784			0.440892	+	0.897560i	$0.354662\pi$
$450$	7.00922	−	16.7018i	0.330418	−	0.787328i
$451$	−26.2380			−1.23550
$452$	7.34376	−	1.04129i	0.345422	−	0.0489782i
$453$	12.5370			0.589041
$454$	13.0434	−	15.0233i	0.612158	−	0.705080i
$455$	27.2914	+	4.29535i	1.27944	+	0.201369i
$456$	−8.80776	−	5.69681i	−0.412461	−	0.266777i
$457$		−	37.5427i		−	1.75617i	−0.478504	−	0.878086i	$-0.658821\pi$
$457$		−	37.5427i		−	1.75617i	0.478504	−	0.878086i	$-0.341179\pi$
$458$	−7.45368	+	8.58511i	−0.348287	+	0.401156i
$459$		−	7.54011i		−	0.351942i
$460$	7.40687	+	3.91023i	0.345347	+	0.182315i
$461$			19.7012i			0.917578i	0.888545	+	0.458789i	$0.151717\pi$
$461$			19.7012i			0.917578i	−0.888545	+	0.458789i	$0.848283\pi$
$462$	1.85446	−	7.43319i	0.0862774	−	0.345823i
$463$	27.2069			1.26441			0.632206	−	0.774800i	$-0.282150\pi$
$463$	27.2069			1.26441			0.632206	+	0.774800i	$0.282150\pi$
$464$	13.6847	−	3.96039i	0.635294	−	0.183856i
$465$	10.4895	+	7.59336i	0.486440	+	0.352134i
$466$	−6.87689	+	7.92077i	−0.318566	+	0.366923i
$467$		−	31.0297i		−	1.43588i	−0.696104	−	0.717941i	$-0.745085\pi$
$467$		−	31.0297i		−	1.43588i	0.696104	−	0.717941i	$-0.254915\pi$
$468$	3.35869	+	23.6873i	0.155255	+	1.09495i
$469$	−2.87689	−	5.65685i	−0.132843	−	0.261209i
$470$	0.208619	+	0.894053i	0.00962288	+	0.0412396i
$471$		−	1.73642i		−	0.0800100i
$472$	12.3756	−	19.1338i	0.569634	−	0.880704i
$473$		−	13.2084i		−	0.607323i
$474$	−0.958664	−	0.832322i	−0.0440329	−	0.0382298i
$475$	−8.74599	−	26.6034i	−0.401294	−	1.22065i
$476$	−8.87206	+	6.21845i	−0.406650	+	0.285022i
$477$			24.3342i			1.11419i
$478$	2.86692	−	3.30210i	0.131130	−	0.151035i
$479$	−3.83466			−0.175210			−0.0876050	−	0.996155i	$-0.527921\pi$
$479$	−3.83466			−0.175210			−0.0876050	+	0.996155i	$0.527921\pi$
$480$	4.09572	+	7.30593i	0.186943	+	0.333469i
$481$		−	17.3188i		−	0.789667i
$482$	−17.5297	+	20.1907i	−0.798458	+	0.919659i
$483$	−2.92456	+	1.48734i	−0.133072	+	0.0676762i
$484$	0.403882	+	2.84840i	0.0183583	+	0.129473i
$485$	−8.05398	+	11.1258i	−0.365712	+	0.505198i
$486$	−13.4637	+	15.5075i	−0.610728	+	0.703433i
$487$	38.9699			1.76589			0.882947	−	0.469473i	$-0.155556\pi$
$487$	38.9699			1.76589			0.882947	+	0.469473i	$0.155556\pi$
$488$	15.3208	+	9.90941i	0.693541	+	0.448578i
$489$		−	10.4218i		−	0.471290i
$490$	8.63239	−	20.3834i	0.389972	−	0.920827i
$491$		−	6.56502i		−	0.296275i	−0.988967	−	0.148138i	$-0.952672\pi$
$491$		−	6.56502i		−	0.296275i	0.988967	−	0.148138i	$-0.0473278\pi$
$492$	1.57756	+	11.1258i	0.0711218	+	0.501591i
$493$	7.29226			0.328427
$494$	27.9309	+	24.2499i	1.25667	+	1.09105i
$495$	14.3468	+	10.3857i	0.644842	+	0.466800i
$496$	33.6050	−	9.72540i	1.50891	−	0.436683i
$497$	22.7745	−	11.5824i	1.02158	−	0.519541i
$498$	−8.80604	−	7.64550i	−0.394608	−	0.342603i
$499$			34.0139i			1.52267i	0.648357	+	0.761336i	$0.275456\pi$
$499$			34.0139i			1.52267i	−0.648357	+	0.761336i	$0.724544\pi$
$500$	−3.74133	+	22.0455i	−0.167318	+	0.985903i
$501$	−5.56155			−0.248472
$502$	3.35869	+	2.91605i	0.149906	+	0.130149i
$503$		−	7.81855i		−	0.348612i	−0.984692	−	0.174306i	$-0.944232\pi$
$503$		−	7.81855i		−	0.348612i	0.984692	−	0.174306i	$-0.0557682\pi$
$504$	19.0661	+	1.98310i	0.849269	+	0.0883344i
$505$	4.31534	+	3.12387i	0.192030	+	0.139010i
$506$	−5.36932	+	6.18435i	−0.238695	+	0.274928i
$507$			5.83209i			0.259012i
$508$	−4.79741	−	33.8340i	−0.212851	−	1.50114i
$509$		−	1.14235i		−	0.0506338i	−0.999679	−	0.0253169i	$-0.991941\pi$
$509$		−	1.14235i		−	0.0506338i	0.999679	−	0.0253169i	$-0.00805948\pi$
$510$	0.974225	+	4.17512i	0.0431394	+	0.184877i
$511$	4.91134	+	9.65719i	0.217265	+	0.427209i
$512$	22.3680	+	3.41624i	0.988537	+	0.150978i
$513$			20.6256i			0.910644i
$514$	−29.9215	−	25.9781i	−1.31978	−	1.14585i
$515$	1.87285	+	1.35576i	0.0825278	+	0.0597417i
$516$	−5.60083	+	0.794156i	−0.246563	+	0.0349608i
$517$	−0.897718			−0.0394816
$518$	−13.4637	−	3.35897i	−0.591560	−	0.147585i
$519$		−	5.80369i		−	0.254754i
$520$	−10.6828	−	27.5352i	−0.468473	−	1.20750i
$521$		−	2.82843i		−	0.123916i	−0.998079	−	0.0619578i	$-0.980266\pi$
$521$		−	2.82843i		−	0.123916i	0.998079	−	0.0619578i	$-0.0197344\pi$
$522$	−9.74247	−	8.45851i	−0.426416	−	0.370219i
$523$			7.15640i			0.312927i	0.987684	+	0.156464i	$0.0500094\pi$
$523$			7.15640i			0.312927i	−0.987684	+	0.156464i	$0.949991\pi$
$524$	−1.57258	−	11.0907i	−0.0686985	−	0.484501i
$525$	−6.21061	−	6.17710i	−0.271053	−	0.269591i
$526$	12.8078	+	11.1198i	0.558445	+	0.484848i
$527$	17.9074			0.780058
$528$	−7.86715	+	2.27678i	−0.342374	+	0.0990841i
$529$	−19.4924			−0.847497
$530$	−6.82641	−	29.2551i	−0.296520	−	1.27076i
$531$	−20.6372			−0.895576
$532$	24.2691	−	17.0103i	1.05220	−	0.737490i
$533$		−	39.6252i		−	1.71636i
$534$	−2.00000	−	1.73642i	−0.0865485	−	0.0751422i
$535$	−19.2582	+	26.6034i	−0.832603	+	1.15016i
$536$	−3.68466	+	5.69681i	−0.159153	+	0.246065i
$537$	−1.14978			−0.0496165
$538$	15.3208	−	17.6465i	0.660528	−	0.760793i
$539$	17.4920	+	12.7494i	0.753433	+	0.549154i
$540$	7.68870	−	14.5642i	0.330869	−	0.626742i
$541$	−23.5616			−1.01299			−0.506495	−	0.862243i	$-0.669059\pi$
$541$	−23.5616			−1.01299			−0.506495	+	0.862243i	$0.669059\pi$
$542$	9.33976	+	8.10887i	0.401177	+	0.348306i
$543$	−6.14441			−0.263682
$544$	10.5122	+	4.86270i	0.450706	+	0.208486i
$545$	−0.574888	+	0.794156i	−0.0246255	+	0.0340179i
$546$	11.2258	+	2.80065i	0.480419	+	0.119857i
$547$	−37.3923			−1.59878			−0.799390	−	0.600812i	$-0.794844\pi$
$547$	−37.3923			−1.59878			−0.799390	+	0.600812i	$0.794844\pi$
$548$	26.1552	−	3.70861i	1.11729	−	0.158424i
$549$		−	16.5246i		−	0.705253i
$550$	−20.1615	−	8.46117i	−0.859689	−	0.360786i
$551$	−19.9477			−0.849799
$552$	2.94521	+	1.90495i	0.125357	+	0.0810799i
$553$	3.19727	−	1.62603i	0.135962	−	0.0691458i
$554$	−1.93087	+	2.22397i	−0.0820348	+	0.0944873i
$555$	−3.21985	+	4.44793i	−0.136675	+	0.188804i
$556$	4.02825	+	28.4095i	0.170836	+	1.20483i
$557$		−	9.49980i		−	0.402519i	−0.979538	−	0.201260i	$-0.935496\pi$
$557$		−	9.49980i		−	0.402519i	0.979538	−	0.201260i	$-0.0645035\pi$
$558$	−23.9243	−	20.7713i	−1.01280	−	0.879319i
$559$	19.9477			0.843696
$560$	−23.4779	+	2.96441i	−0.992123	+	0.125269i
$561$	−4.19224			−0.176996
$562$	−21.4154	−	18.5931i	−0.903355	−	0.784302i
$563$			27.9277i			1.17701i	0.808493	+	0.588506i	$0.200284\pi$
$563$			27.9277i			1.17701i	−0.808493	+	0.588506i	$0.799716\pi$
$564$	0.0539753	+	0.380664i	0.00227277	+	0.0160289i
$565$	6.71737	+	4.86270i	0.282602	+	0.204575i
$566$	−18.1059	+	20.8543i	−0.761048	+	0.876571i
$567$	−6.29206	−	12.3721i	−0.264242	−	0.519580i
$568$	−22.9354	−	14.8344i	−0.962346	−	0.622439i
$569$	13.8617			0.581114			0.290557	−	0.956858i	$-0.406159\pi$
$569$	13.8617			0.581114			0.290557	+	0.956858i	$0.406159\pi$
$570$	−2.66495	−	11.4209i	−0.111622	−	0.478367i
$571$			17.5780i			0.735615i	0.929902	+	0.367807i	$0.119891\pi$
$571$			17.5780i			0.735615i	−0.929902	+	0.367807i	$0.880109\pi$
$572$	28.5942	−	4.05444i	1.19558	−	0.169524i
$573$	−9.08770			−0.379644
$574$	−30.8048	−	7.68531i	−1.28577	−	0.320779i
$575$	2.92456	+	8.89586i	0.121963	+	0.370983i
$576$	−8.40388	−	18.6899i	−0.350162	−	0.778748i
$577$	18.9316			0.788132			0.394066	−	0.919082i	$-0.371068\pi$
$577$	18.9316			0.788132			0.394066	+	0.919082i	$0.371068\pi$
$578$	−13.6773	−	11.8748i	−0.568900	−	0.493925i
$579$	−2.45567			−0.102054
$580$	14.0854	+	7.43597i	0.584866	+	0.308762i
$581$	29.3693	−	14.9363i	1.21844	−	0.619662i
$582$	−3.77098	+	4.34339i	−0.156312	+	0.180039i
$583$	29.3751			1.21659
$584$	6.29033	−	9.72540i	0.260296	−	0.402440i
$585$	−15.6847	+	21.6669i	−0.648481	+	0.895817i
$586$	16.1886	+	14.0551i	0.668744	+	0.580610i
$587$			9.06134i			0.374002i	0.982360	+	0.187001i	$0.0598767\pi$
$587$			9.06134i			0.374002i	−0.982360	+	0.187001i	$0.940123\pi$
$588$	4.35448	−	8.18378i	0.179576	−	0.337493i
$589$	−48.9848			−2.01839
$590$	24.8104	−	5.78928i	1.02143	−	0.238341i
$591$	−7.36701			−0.303038
$592$	4.12391	+	14.2497i	0.169492	+	0.585659i
$593$	−31.2165			−1.28191			−0.640955	−	0.767579i	$-0.721461\pi$
$593$	−31.2165			−1.28191			−0.640955	+	0.767579i	$0.721461\pi$
$594$	12.1603	+	10.5577i	0.498944	+	0.433188i
$595$	−11.9658	−	1.88328i	−0.490552	−	0.0772071i
$596$	−0.561553	−	3.96039i	−0.0230021	−	0.162224i
$597$			4.16516i			0.170469i
$598$	−9.33976	−	8.10887i	−0.381931	−	0.331596i
$599$		−	14.4858i		−	0.591873i	−0.955208	−	0.295937i	$-0.904368\pi$
$599$		−	14.4858i		−	0.591873i	0.955208	−	0.295937i	$-0.0956317\pi$
$600$	−2.37562	+	9.05792i	−0.0969845	+	0.369788i
$601$		−	39.4024i		−	1.60726i	−0.595130	−	0.803630i	$-0.702899\pi$
$601$		−	39.4024i		−	1.60726i	0.595130	−	0.803630i	$-0.297101\pi$
$602$	3.86885	−	15.5074i	0.157682	−	0.632034i
$603$	6.14441			0.250220
$604$	37.4924	−	5.31614i	1.52555	−	0.216311i
$605$	−1.88608	+	2.60545i	−0.0766801	+	0.105926i
$606$	1.68466	+	1.46264i	0.0684346	+	0.0594156i
$607$			10.6302i			0.431466i	0.976452	+	0.215733i	$0.0692141\pi$
$607$			10.6302i			0.431466i	−0.976452	+	0.215733i	$0.930786\pi$
$608$	−28.7556	−	13.3017i	−1.16619	−	0.539455i
$609$	−5.56155	+	2.82843i	−0.225365	+	0.114614i
$610$	4.63560	+	19.8662i	0.187690	+	0.804360i
$611$		−	1.35576i		−	0.0548480i
$612$	−1.47261	−	10.3857i	−0.0595266	−	0.419815i
$613$		−	13.6650i		−	0.551923i	−0.961169	−	0.275961i	$-0.911004\pi$
$613$		−	13.6650i		−	0.551923i	0.961169	−	0.275961i	$-0.0889962\pi$
$614$	24.2451	−	27.9254i	0.978452	−	1.12698i
$615$	−7.36701	+	10.1768i	−0.297066	+	0.410370i
$616$	2.39390	−	23.0156i	0.0964530	−	0.927324i
$617$			35.9166i			1.44595i	0.690875	+	0.722974i	$0.257226\pi$
$617$			35.9166i			1.44595i	−0.690875	+	0.722974i	$0.742774\pi$
$618$	0.731140	+	0.634783i	0.0294107	+	0.0255347i
$619$	10.5122			0.422520			0.211260	−	0.977430i	$-0.432243\pi$
$619$	10.5122			0.422520			0.211260	+	0.977430i	$0.432243\pi$
$620$	34.5892	+	18.2603i	1.38913	+	0.733350i
$621$		−	6.89697i		−	0.276766i
$622$	21.3019	+	18.4945i	0.854128	+	0.741563i
$623$	6.67026	−	3.39228i	0.267238	−	0.135909i
$624$	−3.43845	−	11.8812i	−0.137648	−	0.475627i
$625$	−20.1231	+	14.8344i	−0.804924	+	0.593378i
$626$	12.1603	+	10.5577i	0.486024	+	0.421971i
$627$	11.4677			0.457975
$628$	−0.736303	−	5.19283i	−0.0293817	−	0.207216i
$629$			7.59336i			0.302767i
$630$	13.8019	+	16.3956i	0.549881	+	0.653217i
$631$		−	32.2775i		−	1.28495i	−0.766308	−	0.642474i	$-0.777908\pi$
$631$		−	32.2775i		−	1.28495i	0.766308	−	0.642474i	$-0.222092\pi$
$632$	−3.21985	−	2.08258i	−0.128079	−	0.0828406i
$633$	−16.6320			−0.661063
$634$	29.4384	−	33.9071i	1.16915	−	1.34662i
$635$	22.4033	−	30.9481i	0.889049	−	1.22814i
$636$	−1.76618	−	12.4561i	−0.0700334	−	0.493915i
$637$	−19.2544	+	26.4168i	−0.762887	+	1.04667i
$638$	−10.2107	+	11.7606i	−0.404245	+	0.465607i
$639$			24.7374i			0.978597i
$640$	15.3464	+	20.1119i	0.606618	+	0.794994i
$641$	−17.8617			−0.705496			−0.352748	−	0.935718i	$-0.614753\pi$
$641$	−17.8617			−0.705496			−0.352748	+	0.935718i	$0.614753\pi$
$642$	−9.01693	+	10.3857i	−0.355870	+	0.409889i
$643$		−	0.499124i		−	0.0196835i	−0.999952	−	0.00984176i	$-0.996867\pi$
$643$		−	0.499124i		−	0.0196835i	0.999952	−	0.00984176i	$-0.00313278\pi$
$644$	−8.11531	+	5.68805i	−0.319788	+	0.224140i
$645$	−5.12311	−	3.70861i	−0.201722	−	0.146026i
$646$	−12.2462	−	10.6323i	−0.481821	−	0.418322i
$647$			5.87787i			0.231083i	0.993303	+	0.115541i	$0.0368603\pi$
$647$			5.87787i			0.231083i	−0.993303	+	0.115541i	$0.963140\pi$
$648$	−8.05872	+	12.4595i	−0.316576	+	0.489455i
$649$			24.9121i			0.977886i
$650$	12.7783	−	30.4484i	0.501205	−	1.19428i
$651$	−13.6573	+	6.94568i	−0.535273	+	0.272223i
$652$	−4.41921	−	31.1667i	−0.173069	−	1.22058i
$653$			11.1258i			0.435387i	0.976017	+	0.217694i	$0.0698534\pi$
$653$			11.1258i			0.435387i	−0.976017	+	0.217694i	$0.930147\pi$
$654$	−0.269170	+	0.310029i	−0.0105254	+	0.0121231i
$655$	7.34376	−	10.1447i	0.286945	−	0.396388i
$656$	9.43549	+	32.6032i	0.368394	+	1.27294i
$657$	−10.4895			−0.409236
$658$	−1.05397	−	0.262949i	−0.0410880	−	0.0102508i
$659$			19.6950i			0.767210i	0.923497	+	0.383605i	$0.125318\pi$
$659$			19.6950i			0.767210i	−0.923497	+	0.383605i	$0.874682\pi$
$660$	−8.09755	−	4.27485i	−0.315197	−	0.166398i
$661$		−	42.3286i		−	1.64639i	−0.567756	−	0.823197i	$-0.692188\pi$
$661$		−	42.3286i		−	1.64639i	0.567756	−	0.823197i	$-0.307812\pi$
$662$	−1.60993	+	1.85431i	−0.0625716	+	0.0720696i
$663$		−	6.33122i		−	0.245884i
$664$	−29.5767	−	19.1300i	−1.14780	−	0.742390i
$665$	32.7320	+	5.15164i	1.26929	+	0.199772i
$666$	8.80776	−	10.1447i	0.341294	−	0.393101i
$667$	6.67026			0.258274
$668$	−16.6320	+	2.35829i	−0.643512	+	0.0912452i
$669$	12.6847			0.490417
$670$	−7.38694	+	1.72367i	−0.285382	+	0.0665913i
$671$	−19.9477			−0.770071
$672$	−9.90334	+	0.368713i	−0.382030	+	0.0142234i
$673$		−	5.79119i		−	0.223234i	−0.993751	−	0.111617i	$-0.964397\pi$
$673$		−	5.79119i		−	0.223234i	0.993751	−	0.111617i	$-0.0356030\pi$
$674$	−4.94602	+	5.69681i	−0.190514	+	0.219433i
$675$	17.4920	−	5.75058i	0.673267	−	0.221340i
$676$	2.47301	+	17.4411i	0.0951159	+	0.670811i
$677$	−6.46532			−0.248482			−0.124241	−	0.992252i	$-0.539650\pi$
$677$	−6.46532			−0.248482			−0.124241	+	0.992252i	$0.539650\pi$
$678$	2.62238	+	2.27678i	0.100712	+	0.0874392i
$679$	−7.36701	−	14.4858i	−0.282720	−	0.555914i
$680$	4.68385	+	12.0727i	0.179618	+	0.462968i
$681$	9.31534			0.356965
$682$	−25.0741	+	28.8802i	−0.960135	+	1.10588i
$683$	−5.32326			−0.203689			−0.101845	−	0.994800i	$-0.532474\pi$
$683$	−5.32326			−0.203689			−0.101845	+	0.994800i	$0.532474\pi$
$684$	4.02825	+	28.4095i	0.154024	+	1.08626i
$685$	23.9243	+	17.3188i	0.914100	+	0.661716i
$686$	16.8021	+	20.0920i	0.641509	+	0.767116i
$687$	−5.32326			−0.203095
$688$	−16.4127	+	4.74990i	−0.625730	+	0.181088i
$689$			44.3629i			1.69009i
$690$	0.891128	+	3.81900i	0.0339247	+	0.145387i
$691$	12.9678			0.493320			0.246660	−	0.969102i	$-0.420667\pi$
$691$	12.9678			0.493320			0.246660	+	0.969102i	$0.420667\pi$
$692$	−2.46097	−	17.3561i	−0.0935520	−	0.659781i
$693$	−18.6795	+	9.49980i	−0.709576	+	0.360868i
$694$	4.56155	+	3.96039i	0.173154	+	0.150334i
$695$	−18.8114	+	25.9863i	−0.713559	+	0.985716i
$696$	5.60083	+	3.62258i	0.212299	+	0.137314i
$697$			17.3736i			0.658071i
$698$	−33.6775	+	38.7896i	−1.27471	+	1.46821i
$699$	−4.91134			−0.185764
$700$	−21.1923	−	15.8393i	−0.800995	−	0.598670i
$701$	47.6695			1.80045			0.900226	−	0.435423i	$-0.143401\pi$
$701$	47.6695			1.80045			0.900226	+	0.435423i	$0.143401\pi$
$702$	−15.9445	+	18.3648i	−0.601787	+	0.693135i
$703$		−	20.7713i		−	0.783404i
$704$	−22.5616	+	10.1447i	−0.850321	+	0.382344i
$705$	−0.252058	+	0.348195i	−0.00949306	+	0.0131138i
$706$	28.9628	+	25.1458i	1.09003	+	0.946375i
$707$	−5.61856	+	2.85742i	−0.211308	+	0.107464i
$708$	10.5636	−	1.49784i	0.397005	−	0.0562923i
$709$	10.1922			0.382777			0.191389	−	0.981514i	$-0.438701\pi$
$709$	10.1922			0.382777			0.191389	+	0.981514i	$0.438701\pi$
$710$	−6.93951	−	29.7398i	−0.260435	−	1.11612i
$711$			3.47284i			0.130242i
$712$	−6.71737	−	4.34475i	−0.251744	−	0.162827i
$713$	16.3800			0.613434
$714$	−4.92191	−	1.22794i	−0.184198	−	0.0459544i
$715$	26.1552	+	18.9337i	0.978149	+	0.708081i
$716$	−3.43845	+	0.487546i	−0.128501	+	0.0182204i
$717$	2.04750			0.0764651
$718$	24.5453	−	28.2711i	0.916022	−	1.05507i
$719$	−36.0607			−1.34484			−0.672418	−	0.740172i	$-0.734744\pi$
$719$	−36.0607			−1.34484			−0.672418	+	0.740172i	$0.734744\pi$
$720$	7.74589	−	21.5621i	0.288672	−	0.803573i
$721$	−2.43845	+	1.24012i	−0.0908125	+	0.0461843i
$722$	13.2091	+	11.4682i	0.491590	+	0.426804i
$723$	−12.5194			−0.465601
$724$	−18.3751	+	2.60545i	−0.682904	+	0.0968307i
$725$	5.56155	+	16.9170i	0.206551	+	0.628282i
$726$	−0.883088	+	1.01714i	−0.0327745	+	0.0377494i
$727$		−	6.20393i		−	0.230091i	−0.993360	−	0.115045i	$-0.963299\pi$
$727$		−	6.20393i		−	0.230091i	0.993360	−	0.115045i	$-0.0367014\pi$
$728$	34.7587	+	3.61532i	1.28824	+	0.133993i
$729$	6.12311			0.226782
$730$	12.6107	−	2.94260i	0.466744	−	0.108910i
$731$	−8.74599			−0.323482
$732$	1.19935	+	8.45851i	0.0443294	+	0.312636i
$733$	−11.0644			−0.408674			−0.204337	−	0.978901i	$-0.565504\pi$
$733$	−11.0644			−0.408674			−0.204337	+	0.978901i	$0.565504\pi$
$734$	−29.5012	+	33.9793i	−1.08891	+	1.25420i
$735$	9.85640	−	3.20484i	0.363559	−	0.118212i
$736$	9.61553	+	4.44793i	0.354433	+	0.163953i
$737$		−	7.41722i		−	0.273217i
$738$	20.1521	−	23.2111i	0.741810	−	0.854413i
$739$			14.6996i			0.540732i	0.962758	+	0.270366i	$0.0871447\pi$
$739$			14.6996i			0.540732i	−0.962758	+	0.270366i	$0.912855\pi$
$740$	−7.74300	+	14.6670i	−0.284638	+	0.539171i
$741$			17.3188i			0.636220i
$742$	34.4879	+	8.60418i	1.26609	+	0.315869i
$743$	4.79741			0.176000			0.0880000	−	0.996120i	$-0.471952\pi$
$743$	4.79741			0.176000			0.0880000	+	0.996120i	$0.471952\pi$
$744$	13.7538	+	8.89586i	0.504238	+	0.326138i
$745$	2.62238	−	3.62258i	0.0960767	−	0.132721i
$746$	−21.0540	+	24.2499i	−0.770841	+	0.887851i
$747$			31.9006i			1.16718i
$748$	−12.5370	+	1.77766i	−0.458399	+	0.0649975i
$749$	−17.6155	−	34.6375i	−0.643657	−	1.26563i
$750$	−8.94268	+	5.44428i	−0.326541	+	0.198797i
$751$		−	24.3567i		−	0.888790i	−0.895831	−	0.444395i	$-0.853419\pi$
$751$		−	24.3567i		−	0.888790i	0.895831	−	0.444395i	$-0.146581\pi$
$752$	0.322830	+	1.11550i	0.0117724	+	0.0406782i
$753$			2.08258i			0.0758934i
$754$	−17.7612	−	15.4204i	−0.646823	−	0.561578i
$755$	34.2945	+	24.8257i	1.24810	+	0.903501i
$756$	11.1844	+	15.9572i	0.406774	+	0.580357i
$757$		−	28.4994i		−	1.03583i	−0.855433	−	0.517914i	$-0.826709\pi$
$757$		−	28.4994i		−	1.03583i	0.855433	−	0.517914i	$-0.173291\pi$
$758$	4.82978	−	5.56292i	0.175425	−	0.202054i
$759$	−3.83466			−0.139189
$760$	−12.8125	−	33.0244i	−0.464757	−	1.19792i
$761$		−	3.52482i		−	0.127775i	−0.997957	−	0.0638873i	$-0.979650\pi$
$761$		−	3.52482i		−	0.127775i	0.997957	−	0.0638873i	$-0.0203498\pi$
$762$	10.4895	−	12.0818i	0.379996	−	0.437677i
$763$	−0.525853	−	1.03399i	−0.0190372	−	0.0374329i
$764$	−27.1771	+	3.85350i	−0.983232	+	0.139415i
$765$	6.87689	−	9.49980i	0.248635	−	0.343466i
$766$	25.0101	−	28.8066i	0.903653	−	1.04082i
$767$	−37.6229			−1.35848
$768$	5.65824	+	8.95694i	0.204174	+	0.323206i
$769$		−	8.83348i		−	0.318543i	−0.987235	−	0.159272i	$-0.949085\pi$
$769$		−	8.83348i		−	0.318543i	0.987235	−	0.159272i	$-0.0509146\pi$
$770$	19.7919	−	16.6610i	0.713252	−	0.600419i
$771$		−	18.5531i		−	0.668172i
$772$	−7.34376	+	1.04129i	−0.264308	+	0.0374769i
$773$	−48.4234			−1.74167			−0.870835	−	0.491575i	$-0.836421\pi$
$773$	−48.4234			−1.74167			−0.870835	+	0.491575i	$0.836421\pi$
$774$	11.6847	+	10.1447i	0.419996	+	0.364645i
$775$	13.6573	+	41.5426i	0.490586	+	1.49225i
$776$	−9.43549	+	14.5881i	−0.338714	+	0.523682i
$777$	−2.94521	−	5.79119i	−0.105659	−	0.207758i
$778$	18.0803	+	15.6975i	0.648210	+	0.562783i
$779$		−	47.5246i		−	1.70275i
$780$	6.45598	−	12.2291i	0.231161	−	0.437873i
$781$	29.8617			1.06854
$782$	4.09499	+	3.55531i	0.146437	+	0.127138i
$783$		−	13.1158i		−	0.468720i
$784$	9.55200	−	26.3203i	0.341143	−	0.940011i
$785$	3.43845	−	4.74990i	0.122723	−	0.169531i
$786$	3.43845	−	3.96039i	0.122645	−	0.141262i
$787$		−	37.4882i		−	1.33631i	−0.744023	−	0.668154i	$-0.767085\pi$
$787$		−	37.4882i		−	1.33631i	0.744023	−	0.668154i	$-0.232915\pi$
$788$	−22.0313	+	3.12387i	−0.784832	+	0.111283i
$789$			7.94156i			0.282727i
$790$	−0.974225	−	4.17512i	−0.0346614	−	0.148544i
$791$	−8.74599	+	4.44793i	−0.310972	+	0.158150i
$792$	18.8114	+	12.1671i	0.668435	+	0.432340i
$793$		−	30.1254i		−	1.06979i
$794$	13.7329	+	11.9231i	0.487363	+	0.423133i
$795$	8.24782	−	11.3936i	0.292520	−	0.404090i
$796$	1.76618	+	12.4561i	0.0626004	+	0.441493i
$797$	47.2737			1.67452			0.837260	−	0.546805i	$-0.184156\pi$
$797$	47.2737			1.67452			0.837260	+	0.546805i	$0.184156\pi$
$798$	13.4637	+	3.35897i	0.476609	+	0.118906i
$799$			0.594427i			0.0210293i
$800$	−3.26351	+	28.0954i	−0.115383	+	0.993321i
$801$			7.24517i			0.255995i
$802$	18.7538	+	16.2822i	0.662220	+	0.574946i
$803$			12.6624i			0.446847i
$804$	−3.14516	+	0.445960i	−0.110921	+	0.0157278i
$805$	−10.9452	−	1.72265i	−0.385768	−	0.0607153i
$806$	−43.6155	−	37.8674i	−1.53629	−	1.33382i
$807$	10.9418			0.385170
$808$	5.65824	+	3.65971i	0.199056	+	0.128748i
$809$	10.0540			0.353479			0.176739	−	0.984258i	$-0.443445\pi$
$809$	10.0540			0.353479			0.176739	+	0.984258i	$0.443445\pi$
$810$	−16.1560	+	3.76985i	−0.567663	+	0.132459i
$811$	−3.14516			−0.110442			−0.0552208	−	0.998474i	$-0.517586\pi$
$811$	−3.14516			−0.110442			−0.0552208	+	0.998474i	$0.517586\pi$
$812$	−15.4327	+	10.8168i	−0.541580	+	0.379595i
$813$			5.79119i			0.203106i
$814$	−12.2462	−	10.6323i	−0.429229	−	0.372661i
$815$	20.6372	−	28.5083i	0.722888	−	0.998604i
$816$	1.50758	+	5.20926i	0.0527758	+	0.182361i
$817$	23.9243			0.837005
$818$	−4.41782	+	5.08842i	−0.154465	+	0.177913i
$819$	−14.3468	−	28.2102i	−0.501319	−	0.985746i
$820$	−17.7160	+	33.5581i	−0.618668	+	1.17190i
$821$	−7.06913			−0.246714			−0.123357	−	0.992362i	$-0.539366\pi$
$821$	−7.06913			−0.246714			−0.123357	+	0.992362i	$0.539366\pi$
$822$	9.33976	+	8.10887i	0.325761	+	0.282829i
$823$	−3.21985			−0.112237			−0.0561185	−	0.998424i	$-0.517872\pi$
$823$	−3.21985			−0.112237			−0.0561185	+	0.998424i	$0.517872\pi$
$824$	2.45567	+	1.58831i	0.0855473	+	0.0553314i
$825$	−3.19727	−	9.72540i	−0.111315	−	0.338595i
$826$	−7.29695	+	29.2482i	−0.253893	+	1.01767i
$827$	2.39871			0.0834112			0.0417056	−	0.999130i	$-0.486721\pi$
$827$	2.39871			0.0834112			0.0417056	+	0.999130i	$0.486721\pi$
$828$	−1.34700	−	9.49980i	−0.0468115	−	0.330141i
$829$			25.9018i			0.899607i	0.893128	+	0.449803i	$0.148506\pi$
$829$			25.9018i			0.899607i	−0.893128	+	0.449803i	$0.851494\pi$
$830$	−8.94898	−	38.3516i	−0.310624	−	1.33120i
$831$	−1.37899			−0.0478366
$832$	−15.3208	−	34.0730i	−0.531154	−	1.18127i
$833$	8.44204	−	11.5824i	0.292499	−	0.401306i
$834$	−8.80776	+	10.1447i	−0.304988	+	0.351284i
$835$	−15.2134	−	11.0129i	−0.526481	−	0.381119i
$836$	34.2945	−	4.86270i	1.18610	−	0.168180i
$837$		−	32.2080i		−	1.11327i
$838$	−22.0382	−	19.1338i	−0.761297	−	0.660966i
$839$	47.2623			1.63168			0.815838	−	0.578280i	$-0.196276\pi$
$839$	47.2623			1.63168			0.815838	+	0.578280i	$0.196276\pi$
$840$	−8.25483	−	7.39074i	−0.284819	−	0.255005i
$841$	−16.3153			−0.562598
$842$	9.01133	+	7.82373i	0.310551	+	0.269623i
$843$		−	13.2788i		−	0.457346i
$844$	−49.7386	+	7.05256i	−1.71207	+	0.242759i
$845$	−11.5487	+	15.9534i	−0.397286	+	0.548815i
$846$	0.689494	−	0.794156i	0.0237053	−	0.0273036i
$847$	−1.72521	−	3.39228i	−0.0592788	−	0.116560i
$848$	−10.5636	−	36.5014i	−0.362756	−	1.25346i
$849$	−12.9309			−0.443786
$850$	−5.60259	+	13.3500i	−0.192167	+	0.457902i
$851$			6.94568i			0.238095i
$852$	−1.79544	−	12.6624i	−0.0615107	−	0.433808i
$853$	45.2262			1.54851			0.774257	−	0.632871i	$-0.218124\pi$
$853$	45.2262			1.54851			0.774257	+	0.632871i	$0.218124\pi$
$854$	−23.4196	−	5.84282i	−0.801403	−	0.199937i
$855$	−18.8114	+	25.9863i	−0.643338	+	0.888712i
$856$	−22.5616	+	34.8821i	−0.771138	+	1.19225i
$857$	−14.5845			−0.498198			−0.249099	−	0.968478i	$-0.580134\pi$
$857$	−14.5845			−0.498198			−0.249099	+	0.968478i	$0.580134\pi$
$858$	10.2107	+	8.86502i	0.348587	+	0.302647i
$859$	3.14516			0.107312			0.0536558	−	0.998559i	$-0.482913\pi$
$859$	3.14516			0.107312			0.0536558	+	0.998559i	$0.482913\pi$
$860$	−16.8934	−	8.91835i	−0.576060	−	0.304113i
$861$	−6.73863	−	13.2502i	−0.229652	−	0.451566i
$862$	14.3346	−	16.5105i	0.488238	−	0.562350i
$863$	−28.8492			−0.982038			−0.491019	−	0.871149i	$-0.663375\pi$
$863$	−28.8492			−0.982038			−0.491019	+	0.871149i	$0.663375\pi$
$864$	8.74599	−	18.9071i	0.297545	−	0.643232i
$865$	11.4924	−	15.8757i	0.390754	−	0.539791i
$866$	−41.1232	−	35.7035i	−1.39742	−	1.21326i
$867$		−	8.48071i		−	0.288020i
$868$	−37.8975	+	26.5625i	−1.28633	+	0.901590i
$869$	4.19224			0.142212
$870$	1.69463	+	7.26249i	0.0574535	+	0.246221i
$871$	11.2017			0.379554
$872$	−0.673500	+	1.04129i	−0.0228076	+	0.0352625i
$873$	15.7343			0.532525
$874$	−11.2017	−	9.72540i	−0.378902	−	0.328966i
$875$	−4.75698	−	29.1954i	−0.160815	−	0.986985i
$876$	5.36932	−	0.761329i	0.181412	−	0.0257229i
$877$			3.70861i			0.125231i	0.998038	+	0.0626154i	$0.0199442\pi$
$877$			3.70861i			0.125231i	−0.998038	+	0.0626154i	$0.980056\pi$
$878$	25.3969	+	22.0498i	0.857103	+	0.744146i
$879$			10.0379i			0.338569i
$880$	−26.0287	−	9.35045i	−0.877427	−	0.315203i
$881$		−	54.0883i		−	1.82228i	−0.412095	−	0.911141i	$-0.635203\pi$
$881$		−	54.0883i		−	1.82228i	0.412095	−	0.911141i	$-0.364797\pi$
$882$	−24.7133	+	5.68190i	−0.832141	+	0.191320i
$883$	−19.7155			−0.663479			−0.331740	−	0.943371i	$-0.607636\pi$
$883$	−19.7155			−0.663479			−0.331740	+	0.943371i	$0.607636\pi$
$884$	−2.68466	−	18.9337i	−0.0902948	−	0.636810i
$885$	9.66259	+	6.99474i	0.324804	+	0.235125i
$886$	−14.8078	−	12.8563i	−0.497477	−	0.431914i
$887$		−	15.3110i		−	0.514095i	−0.966399	−	0.257047i	$-0.917250\pi$
$887$		−	15.3110i		−	0.514095i	0.966399	−	0.257047i	$-0.0827496\pi$
$888$	−3.77216	+	5.83209i	−0.126585	+	0.195712i
$889$	20.4924	+	40.2944i	0.687294	+	1.35143i
$890$	−2.03246	−	8.71029i	−0.0681283	−	0.291969i
$891$		−	16.2222i		−	0.543464i
$892$	37.9339	−	5.37874i	1.27012	−	0.180094i
$893$		−	1.62603i		−	0.0544130i
$894$	1.22783	−	1.41421i	0.0410649	−	0.0472984i
$895$	−3.14516	−	2.27678i	−0.105131	−	0.0761044i
$896$	−29.4599	+	5.30202i	−0.984188	+	0.177128i
$897$		−	5.79119i		−	0.193362i
$898$	19.9532	+	17.3235i	0.665845	+	0.578094i
$899$	31.1493			1.03889
$900$	22.9701	−	11.3370i	0.765671	−	0.377900i
$901$		−	19.4508i		−	0.648000i
$902$	−28.0193	−	24.3266i	−0.932940	−	0.809988i
$903$	6.67026	−	3.39228i	0.221972	−	0.112888i
$904$	8.80776	+	5.69681i	0.292942	+	0.189473i
$905$	−16.8078	−	12.1671i	−0.558709	−	0.404449i
$906$	13.3882	+	11.6237i	0.444792	+	0.386173i
$907$	−2.62926			−0.0873033			−0.0436516	−	0.999047i	$-0.513899\pi$
$907$	−2.62926			−0.0873033			−0.0436516	+	0.999047i	$0.513899\pi$
$908$	27.8579	−	3.95003i	0.924495	−	0.131086i
$909$		−	6.10281i		−	0.202418i
$910$	25.1618	+	29.8903i	0.834105	+	0.990853i
$911$		−	40.3652i		−	1.33736i	−0.743551	−	0.668679i	$-0.766860\pi$
$911$		−	40.3652i		−	1.33736i	0.743551	−	0.668679i	$-0.233140\pi$
$912$	−4.12391	−	14.2497i	−0.136556	−	0.471855i
$913$	38.5088			1.27446
$914$	34.8078	−	40.0914i	1.15134	−	1.32611i
$915$	−5.60083	+	7.73704i	−0.185158	+	0.255779i
$916$	−15.9194	+	2.25725i	−0.525992	+	0.0745817i
$917$	6.71737	+	13.2084i	0.221827	+	0.436180i
$918$	6.99083	−	8.05200i	0.230732	−	0.265756i
$919$			11.7743i			0.388398i	0.980962	+	0.194199i	$0.0622107\pi$
$919$			11.7743i			0.388398i	−0.980962	+	0.194199i	$0.937789\pi$
$920$	4.28434	+	11.0430i	0.141251	+	0.364076i
$921$	17.3153			0.570560
$922$	−18.2660	+	21.0387i	−0.601560	+	0.692874i
$923$			45.0979i			1.48442i
$924$	8.87206	−	6.21845i	0.291869	−	0.204572i
$925$	−17.6155	+	5.79119i	−0.579195	+	0.190413i
$926$	29.0540	+	25.2250i	0.954773	+	0.828943i
$927$		−	2.64861i		−	0.0869919i
$928$	18.2856	+	8.45851i	0.600254	+	0.277664i
$929$		−	17.6670i		−	0.579634i	−0.957082	−	0.289817i	$-0.906406\pi$
$929$		−	17.6670i		−	0.579634i	0.957082	−	0.289817i	$-0.0935944\pi$
$930$	4.16146	+	17.8343i	0.136460	+	0.584809i
$931$	−23.0928	+	31.6831i	−0.756837	+	1.03837i
$932$	−14.6875	+	2.08258i	−0.481106	+	0.0682172i
$933$			13.2084i			0.432424i
$934$	28.7692	−	33.1363i	0.941358	−	1.08425i
$935$	−11.4677	−	8.30144i	−0.375033	−	0.271486i
$936$	−18.3751	+	28.4095i	−0.600608	+	0.928593i
$937$	−38.7609			−1.26626			−0.633131	−	0.774045i	$-0.718231\pi$
$937$	−38.7609			−1.26626			−0.633131	+	0.774045i	$0.718231\pi$
$938$	2.17256	−	8.70822i	0.0709366	−	0.284333i
$939$			7.54011i			0.246062i
$940$	−0.606142	+	1.14817i	−0.0197702	+	0.0374492i
$941$			37.9119i			1.23589i	0.786220	+	0.617946i	$0.212035\pi$
$941$			37.9119i			1.23589i	−0.786220	+	0.617946i	$0.787965\pi$
$942$	1.60993	−	1.85431i	0.0524542	−	0.0604165i
$943$			15.8917i			0.517504i
$944$	30.9557	−	8.95869i	1.00752	−	0.291581i
$945$	−3.38725	+	21.5216i	−0.110187	+	0.700099i
$946$	12.2462	−	14.1051i	0.398159	−	0.458597i
$947$	41.5991			1.35179			0.675895	−	0.736998i	$-0.263757\pi$
$947$	41.5991			1.35179			0.675895	+	0.736998i	$0.263757\pi$
$948$	−0.252058	−	1.77766i	−0.00818647	−	0.0577356i
$949$	−19.1231			−0.620762
$950$	15.3256	−	36.5184i	0.497230	−	1.18481i
$951$	21.0243			0.681761
$952$	−15.2398	−	1.58513i	−0.493926	−	0.0513743i
$953$			24.7908i			0.803053i	0.915848	+	0.401526i	$0.131520\pi$
$953$			24.7908i			0.803053i	−0.915848	+	0.401526i	$0.868480\pi$
$954$	−22.5616	+	25.9863i	−0.730457	+	0.841337i
$955$	−24.8590	−	17.9954i	−0.804418	−	0.582317i
$956$	6.12311	−	0.868210i	0.198035	−	0.0280799i
$957$	−7.29226			−0.235725
$958$	−4.09499	−	3.55531i	−0.132303	−	0.114867i
$959$	−31.1493	+	15.8415i	−1.00586	+	0.511550i
$960$	−2.39994	+	11.5993i	−0.0774578	+	0.374365i
$961$	45.4924			1.46750
$962$	16.0571	−	18.4945i	0.517703	−	0.596287i
$963$	37.6229			1.21238
$964$	−37.4396	+	5.30866i	−1.20585	+	0.170980i
$965$	−6.71737	−	4.86270i	−0.216240	−	0.156536i
$966$	−4.50209	−	1.12320i	−0.144852	−	0.0361384i
$967$	18.1379			0.583277			0.291638	−	0.956529i	$-0.405800\pi$
$967$	18.1379			0.583277			0.291638	+	0.956529i	$0.405800\pi$
$968$	−2.20960	+	3.41624i	−0.0710193	+	0.109802i
$969$		−	7.59336i		−	0.243934i
$970$	−18.9161	+	4.41389i	−0.607359	+	0.141722i
$971$	−32.9155			−1.05631			−0.528154	−	0.849148i	$-0.677116\pi$
$971$	−32.9155			−1.05631			−0.528154	+	0.849148i	$0.677116\pi$
$972$	−28.7556	+	4.07732i	−0.922335	+	0.130780i
$973$	−17.2069	−	33.8340i	−0.551628	−	1.08467i
$974$	41.6155	+	36.1310i	1.33345	+	1.15771i
$975$	14.6875	−	4.82860i	0.470377	−	0.154639i
$976$	7.17341	+	24.7869i	0.229615	+	0.793409i
$977$		−	5.79119i		−	0.185277i	−0.995700	−	0.0926383i	$-0.970470\pi$
$977$		−	5.79119i		−	0.185277i	0.995700	−	0.0926383i	$-0.0295300\pi$
$978$	9.66259	−	11.1293i	0.308975	−	0.355876i
$979$	8.74599			0.279523
$980$	28.1169	−	13.7637i	0.898162	−	0.439664i
$981$	1.12311			0.0358580
$982$	6.08677	−	7.01071i	0.194237	−	0.223721i
$983$		−	38.4406i		−	1.22607i	−0.790057	−	0.613033i	$-0.789949\pi$
$983$		−	38.4406i		−	1.22607i	0.790057	−	0.613033i	$-0.210051\pi$
$984$	−8.63068	+	13.3438i	−0.275136	+	0.425385i
$985$	−20.1521	−	14.5881i	−0.642100	−	0.464815i
$986$	7.78733	+	6.76104i	0.247999	+	0.215315i
$987$	−0.230559	−	0.453349i	−0.00733876	−	0.0144303i
$988$	7.34376	+	51.7924i	0.233636	+	1.64773i
$989$	−8.00000			−0.254385
$990$	5.69174	+	24.3924i	0.180896	+	0.775242i
$991$			50.2361i			1.59580i	0.602787	+	0.797902i	$0.294057\pi$
$991$			50.2361i			1.59580i	−0.602787	+	0.797902i	$0.705943\pi$
$992$	44.9033	+	20.7713i	1.42568	+	0.659489i
$993$	−1.14978			−0.0364871
$994$	35.0593	+	8.74673i	1.11201	+	0.277430i
$995$	−8.24782	+	11.3936i	−0.261474	+	0.361202i
$996$	−2.31534	−	16.3291i	−0.0733644	−	0.517407i
$997$	−26.7987			−0.848724			−0.424362	−	0.905493i	$-0.639502\pi$
$997$	−26.7987			−0.848724			−0.424362	+	0.905493i	$0.639502\pi$
$998$	−31.5361	+	36.3231i	−0.998258	+	1.14979i
$999$	13.6573			0.432099

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	140.2.c.b.139.16	yes	16
4.3	odd	2	inner	140.2.c.b.139.3	yes	16
5.2	odd	4		700.2.g.l.251.8		16
5.3	odd	4		700.2.g.l.251.9		16
5.4	even	2	inner	140.2.c.b.139.1	✓	16
7.2	even	3		980.2.s.f.619.9		32
7.3	odd	6		980.2.s.f.19.3		32
7.4	even	3		980.2.s.f.19.4		32
7.5	odd	6		980.2.s.f.619.10		32
7.6	odd	2	inner	140.2.c.b.139.15	yes	16
8.3	odd	2		2240.2.e.f.2239.11		16
8.5	even	2		2240.2.e.f.2239.7		16
20.3	even	4		700.2.g.l.251.12		16
20.7	even	4		700.2.g.l.251.5		16
20.19	odd	2	inner	140.2.c.b.139.14	yes	16
28.3	even	6		980.2.s.f.19.8		32
28.11	odd	6		980.2.s.f.19.7		32
28.19	even	6		980.2.s.f.619.13		32
28.23	odd	6		980.2.s.f.619.14		32
28.27	even	2	inner	140.2.c.b.139.4	yes	16
35.4	even	6		980.2.s.f.19.13		32
35.9	even	6		980.2.s.f.619.8		32
35.13	even	4		700.2.g.l.251.10		16
35.19	odd	6		980.2.s.f.619.7		32
35.24	odd	6		980.2.s.f.19.14		32
35.27	even	4		700.2.g.l.251.7		16
35.34	odd	2	inner	140.2.c.b.139.2	yes	16
40.19	odd	2		2240.2.e.f.2239.5		16
40.29	even	2		2240.2.e.f.2239.9		16
56.13	odd	2		2240.2.e.f.2239.10		16
56.27	even	2		2240.2.e.f.2239.6		16
140.19	even	6		980.2.s.f.619.4		32
140.27	odd	4		700.2.g.l.251.6		16
140.39	odd	6		980.2.s.f.19.10		32
140.59	even	6		980.2.s.f.19.9		32
140.79	odd	6		980.2.s.f.619.3		32
140.83	odd	4		700.2.g.l.251.11		16
140.139	even	2	inner	140.2.c.b.139.13	yes	16
280.69	odd	2		2240.2.e.f.2239.8		16
280.139	even	2		2240.2.e.f.2239.12		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
140.2.c.b.139.1	✓	16	5.4	even	2	inner
140.2.c.b.139.2	yes	16	35.34	odd	2	inner
140.2.c.b.139.3	yes	16	4.3	odd	2	inner
140.2.c.b.139.4	yes	16	28.27	even	2	inner
140.2.c.b.139.13	yes	16	140.139	even	2	inner
140.2.c.b.139.14	yes	16	20.19	odd	2	inner
140.2.c.b.139.15	yes	16	7.6	odd	2	inner
140.2.c.b.139.16	yes	16	1.1	even	1	trivial
700.2.g.l.251.5		16	20.7	even	4
700.2.g.l.251.6		16	140.27	odd	4
700.2.g.l.251.7		16	35.27	even	4
700.2.g.l.251.8		16	5.2	odd	4
700.2.g.l.251.9		16	5.3	odd	4
700.2.g.l.251.10		16	35.13	even	4
700.2.g.l.251.11		16	140.83	odd	4
700.2.g.l.251.12		16	20.3	even	4
980.2.s.f.19.3		32	7.3	odd	6
980.2.s.f.19.4		32	7.4	even	3
980.2.s.f.19.7		32	28.11	odd	6
980.2.s.f.19.8		32	28.3	even	6
980.2.s.f.19.9		32	140.59	even	6
980.2.s.f.19.10		32	140.39	odd	6
980.2.s.f.19.13		32	35.4	even	6
980.2.s.f.19.14		32	35.24	odd	6
980.2.s.f.619.3		32	140.79	odd	6
980.2.s.f.619.4		32	140.19	even	6
980.2.s.f.619.7		32	35.19	odd	6
980.2.s.f.619.8		32	35.9	even	6
980.2.s.f.619.9		32	7.2	even	3
980.2.s.f.619.10		32	7.5	odd	6
980.2.s.f.619.13		32	28.19	even	6
980.2.s.f.619.14		32	28.23	odd	6
2240.2.e.f.2239.5		16	40.19	odd	2
2240.2.e.f.2239.6		16	56.27	even	2
2240.2.e.f.2239.7		16	8.5	even	2
2240.2.e.f.2239.8		16	280.69	odd	2
2240.2.e.f.2239.9		16	40.29	even	2
2240.2.e.f.2239.10		16	56.13	odd	2
2240.2.e.f.2239.11		16	8.3	odd	2
2240.2.e.f.2239.12		16	280.139	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.c (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(1.06789 + 0.927153i) q^{2} +0.662153i q^{3} +(0.280776 + 1.98019i) q^{4} +(-1.31119 + 1.81129i) q^{5} +(-0.613917 + 0.707107i) q^{6} +(-1.19935 - 2.35829i) q^{7} +(-1.53610 + 2.37495i) q^{8} +2.56155 q^{9} +O(q^{10})\)	\(q+(1.06789 + 0.927153i) q^{2} +0.662153i q^{3} +(0.280776 + 1.98019i) q^{4} +(-1.31119 + 1.81129i) q^{5} +(-0.613917 + 0.707107i) q^{6} +(-1.19935 - 2.35829i) q^{7} +(-1.53610 + 2.37495i) q^{8} +2.56155 q^{9} +(-3.07955 + 0.718585i) q^{10} -3.09218i q^{11} +(-1.31119 + 0.185917i) q^{12} +4.66988 q^{13} +(0.905722 - 3.63038i) q^{14} +(-1.19935 - 0.868210i) q^{15} +(-3.84233 + 1.11198i) q^{16} -2.04750 q^{17} +(2.73546 + 2.37495i) q^{18} +5.60083 q^{19} +(-3.95486 - 2.08784i) q^{20} +(1.56155 - 0.794156i) q^{21} +(2.86692 - 3.30210i) q^{22} -1.87285 q^{23} +(-1.57258 - 1.01714i) q^{24} +(-1.56155 - 4.74990i) q^{25} +(4.98691 + 4.32969i) q^{26} +3.68260i q^{27} +(4.33313 - 3.03710i) q^{28} -3.56155 q^{29} +(-0.475813 - 2.03914i) q^{30} -8.74599 q^{31} +(-5.13416 - 2.37495i) q^{32} +2.04750 q^{33} +(-2.18650 - 1.89834i) q^{34} +(5.84414 + 0.919799i) q^{35} +(0.719224 + 5.07237i) q^{36} -3.70861i q^{37} +(5.98107 + 5.19283i) q^{38} +3.09218i q^{39} +(-2.28760 - 5.89634i) q^{40} -8.48528i q^{41} +(2.40387 + 0.599727i) q^{42} +4.27156 q^{43} +(6.12311 - 0.868210i) q^{44} +(-3.35869 + 4.63972i) q^{45} +(-2.00000 - 1.73642i) q^{46} -0.290319i q^{47} +(-0.736303 - 2.54421i) q^{48} +(-4.12311 + 5.65685i) q^{49} +(2.73632 - 6.52017i) q^{50} -1.35576i q^{51} +(1.31119 + 9.24726i) q^{52} +9.49980i q^{53} +(-3.41433 + 3.93261i) q^{54} +(5.60083 + 4.05444i) q^{55} +(7.44316 + 0.774180i) q^{56} +3.70861i q^{57} +(-3.80335 - 3.30210i) q^{58} -8.05650 q^{59} +(1.38247 - 2.61872i) q^{60} -6.45101i q^{61} +(-9.33976 - 8.10887i) q^{62} +(-3.07221 - 6.04090i) q^{63} +(-3.28078 - 7.29634i) q^{64} +(-6.12311 + 8.45851i) q^{65} +(2.18650 + 1.89834i) q^{66} +2.39871 q^{67} +(-0.574888 - 4.05444i) q^{68} -1.24012i q^{69} +(5.38810 + 6.40065i) q^{70} +9.65719i q^{71} +(-3.93481 + 6.08356i) q^{72} -4.09499 q^{73} +(3.43845 - 3.96039i) q^{74} +(3.14516 - 1.03399i) q^{75} +(1.57258 + 11.0907i) q^{76} +(-7.29226 + 3.70861i) q^{77} +(-2.86692 + 3.30210i) q^{78} +1.35576i q^{79} +(3.02390 - 8.41760i) q^{80} +5.24621 q^{81} +(7.86715 - 9.06134i) q^{82} +12.4536i q^{83} +(2.01103 + 2.86920i) q^{84} +(2.68466 - 3.70861i) q^{85} +(4.56155 + 3.96039i) q^{86} -2.35829i q^{87} +(7.34376 + 4.74990i) q^{88} +2.82843i q^{89} +(-7.88843 + 1.84069i) q^{90} +(-5.60083 - 11.0129i) q^{91} +(-0.525853 - 3.70861i) q^{92} -5.79119i q^{93} +(0.269170 - 0.310029i) q^{94} +(-7.34376 + 10.1447i) q^{95} +(1.57258 - 3.39960i) q^{96} +6.14249 q^{97} +(-9.64779 + 2.21815i) q^{98} -7.92077i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 12 q^{4} + 8 q^{9}+O(q^{10}) \) 16 * q - 12 * q^4 + 8 * q^9	\( 16 q - 12 q^{4} + 8 q^{9} - 4 q^{14} - 12 q^{16} - 8 q^{21} + 8 q^{25} - 24 q^{29} - 4 q^{30} + 28 q^{36} + 32 q^{44} - 32 q^{46} - 12 q^{50} - 20 q^{56} + 44 q^{60} - 36 q^{64} - 32 q^{65} + 40 q^{70} + 88 q^{74} - 48 q^{81} + 40 q^{84} - 56 q^{85} + 40 q^{86}+O(q^{100}) \) 16 * q - 12 * q^4 + 8 * q^9 - 4 * q^14 - 12 * q^16 - 8 * q^21 + 8 * q^25 - 24 * q^29 - 4 * q^30 + 28 * q^36 + 32 * q^44 - 32 * q^46 - 12 * q^50 - 20 * q^56 + 44 * q^60 - 36 * q^64 - 32 * q^65 + 40 * q^70 + 88 * q^74 - 48 * q^81 + 40 * q^84 - 56 * q^85 + 40 * q^86

Introduction

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