LMFDB - Embedded newform 72.2.n.b.13.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [72,2,Mod(13,72)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(72, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 3, 2]))

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

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

chi := DirichletCharacter("72.13");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 72 = 2^{3} \cdot 3^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	72.n (of order $6$, degree $2$, 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:	$0.574922894553$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(\zeta_{6})$
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} - x^{15} + x^{14} + 2 x^{12} - 4 x^{11} - 8 x^{9} + 4 x^{8} - 16 x^{7} - 32 x^{5} + 32 x^{4} + \cdots + 256 $ x^16 - x^15 + x^14 + 2x^12 - 4x^11 - 8x^9 + 4x^8 - 16x^7 - 32x^5 + 32x^4 + 64x^2 - 128*x + 256
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{2}\cdot 3^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			13.5
Root			$0.820200 + 1.15207i$ of defining polynomial
Character	$\chi$	$=$	72.13
Dual form			72.2.n.b.61.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.587625 + 1.28635i) q^{2} +(1.69028 - 0.378078i) q^{3} +(-1.30939 + 1.51178i) q^{4} +(-1.97542 - 1.14051i) q^{5} +(1.47959 + 1.95213i) q^{6} +(-0.907824 - 1.57240i) q^{7} +(-2.71411 - 0.795980i) q^{8} +(2.71411 - 1.27812i) q^{9} +(0.306290 - 3.21128i) q^{10} +(-4.24153 + 2.44885i) q^{11} +(-1.64168 + 3.05039i) q^{12} +(4.00895 + 2.31457i) q^{13} +(1.48919 - 2.09176i) q^{14} +(-3.77023 - 1.18092i) q^{15} +(-0.570971 - 3.95904i) q^{16} +1.92788 q^{17} +(3.23899 + 2.74025i) q^{18} -2.12907i q^{19} +(4.31082 - 1.49303i) q^{20} +(-2.12897 - 2.31457i) q^{21} +(-5.64250 - 4.01709i) q^{22} +(-1.15765 + 2.00511i) q^{23} +(-4.88856 - 0.319285i) q^{24} +(0.101535 + 0.175863i) q^{25} +(-0.621589 + 6.51702i) q^{26} +(4.10439 - 3.18653i) q^{27} +(3.56582 + 0.686457i) q^{28} +(3.16440 - 1.82697i) q^{29} +(-0.696398 - 5.54378i) q^{30} +(-2.65800 + 4.60379i) q^{31} +(4.75719 - 3.06090i) q^{32} +(-6.24353 + 5.74287i) q^{33} +(1.13287 + 2.47993i) q^{34} +4.14154i q^{35} +(-1.62161 + 5.77671i) q^{36} +7.98438i q^{37} +(2.73873 - 1.25109i) q^{38} +(7.65135 + 2.39658i) q^{39} +(4.45370 + 4.66788i) q^{40} +(-2.36240 + 4.09180i) q^{41} +(1.72631 - 4.09870i) q^{42} +(-2.20800 + 1.27479i) q^{43} +(1.85171 - 9.61877i) q^{44} +(-6.81924 - 0.570655i) q^{45} +(-3.25953 - 0.310892i) q^{46} +(-2.02005 - 3.49884i) q^{47} +(-2.46193 - 6.47603i) q^{48} +(1.85171 - 3.20726i) q^{49} +(-0.166557 + 0.233951i) q^{50} +(3.25866 - 0.728888i) q^{51} +(-8.74843 + 3.02998i) q^{52} -8.95958i q^{53} +(6.51083 + 3.40721i) q^{54} +11.1718 q^{55} +(1.21234 + 4.99028i) q^{56} +(-0.804954 - 3.59873i) q^{57} +(4.20960 + 2.99696i) q^{58} +(3.05255 + 1.76239i) q^{59} +(6.72202 - 4.15347i) q^{60} +(1.71675 - 0.991165i) q^{61} +(-7.48399 - 0.713818i) q^{62} +(-4.47365 - 3.10736i) q^{63} +(6.73283 + 4.32076i) q^{64} +(-5.27959 - 9.14451i) q^{65} +(-11.0562 - 4.65671i) q^{66} +(-7.72723 - 4.46132i) q^{67} +(-2.52435 + 2.91453i) q^{68} +(-1.19867 + 3.82688i) q^{69} +(-5.32747 + 2.43367i) q^{70} +13.3561 q^{71} +(-8.38377 + 1.30858i) q^{72} -11.5592 q^{73} +(-10.2707 + 4.69182i) q^{74} +(0.238112 + 0.258870i) q^{75} +(3.21869 + 2.78779i) q^{76} +(7.70112 + 4.44625i) q^{77} +(1.41328 + 11.2506i) q^{78} +(-4.97330 - 8.61401i) q^{79} +(-3.38742 + 8.47198i) q^{80} +(5.73283 - 6.93791i) q^{81} +(-6.65170 - 0.634435i) q^{82} +(3.12153 - 1.80221i) q^{83} +(6.28679 - 0.187853i) q^{84} +(-3.80838 - 2.19877i) q^{85} +(-2.93730 - 2.09116i) q^{86} +(4.65800 - 4.28448i) q^{87} +(13.4612 - 3.27028i) q^{88} +2.49965 q^{89} +(-3.27309 - 9.10726i) q^{90} -8.40489i q^{91} +(-1.51547 - 4.37559i) q^{92} +(-2.75218 + 8.78664i) q^{93} +(3.31370 - 4.65450i) q^{94} +(-2.42823 + 4.20582i) q^{95} +(6.88375 - 6.97237i) q^{96} +(6.99370 + 12.1134i) q^{97} +(5.21376 + 0.497285i) q^{98} +(-8.38208 + 12.0676i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + q^{2} - q^{4} - 7 q^{6} + 6 q^{7} - 2 q^{8} + 2 q^{9} - 16 q^{10} - 16 q^{12} + 16 q^{14} - 10 q^{15} - 9 q^{16} - 28 q^{17} + 4 q^{18} - 8 q^{20} + q^{22} - 10 q^{23} + 7 q^{24} + 2 q^{25} + 28 q^{26}+ \cdots + 66 q^{98}+O(q^{100}) $ 16 * q + q^2 - q^4 - 7 * q^6 + 6 * q^7 - 2 * q^8 + 2 * q^9 - 16 * q^10 - 16 * q^12 + 16 * q^14 - 10 * q^15 - 9 * q^16 - 28 * q^17 + 4 * q^18 - 8 * q^20 + q^22 - 10 * q^23 + 7 * q^24 + 2 * q^25 + 28 * q^26 + 4 * q^28 + 22 * q^30 - 10 * q^31 + 11 * q^32 + q^34 + 27 * q^36 + 23 * q^38 + 2 * q^39 + 6 * q^40 - 8 * q^41 + 8 * q^42 + 18 * q^44 - 20 * q^46 + 6 * q^47 + 39 * q^48 + 18 * q^49 - 23 * q^50 - 8 * q^52 - 29 * q^54 - 4 * q^55 + 10 * q^56 + 10 * q^57 - 14 * q^58 + 6 * q^60 - 52 * q^62 + 2 * q^63 + 26 * q^64 - 14 * q^65 - 72 * q^66 - 39 * q^68 + 72 * q^71 - 77 * q^72 - 44 * q^73 - 38 * q^74 + 5 * q^76 + 10 * q^78 - 30 * q^79 - 96 * q^80 + 10 * q^81 + 38 * q^82 - 28 * q^84 + 7 * q^86 + 42 * q^87 + 31 * q^88 + 64 * q^89 + 64 * q^90 - 30 * q^92 - 12 * q^94 + 44 * q^95 - 26 * q^96 + 66 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/72\mathbb{Z}\right)^\times$.

$n$	$37$	$55$	$65$
$\chi(n)$	$-1$	$1$	$e\left(\frac{1}{3}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	0.587625	+	1.28635i	0.415513	+	0.909587i
$2$	0.587625	+	1.28635i	0.415513	+	0.909587i
$3$	1.69028	−	0.378078i	0.975885	−	0.218283i
$3$	1.69028	−	0.378078i	0.975885	−	0.218283i
$4$	−1.30939	+	1.51178i	−0.654697	+	0.755891i
$5$	−1.97542	−	1.14051i	−0.883437	−	0.510052i	−0.0116467	−	0.999932i	$-0.503707\pi$
$5$	−1.97542	−	1.14051i	−0.883437	−	0.510052i	−0.871790	+	0.489880i	$0.837041\pi$
$6$	1.47959	+	1.95213i	0.604041	+	0.796953i
$7$	−0.907824	−	1.57240i	−0.343125	−	0.594311i	0.641886	−	0.766800i	$-0.278152\pi$
$7$	−0.907824	−	1.57240i	−0.343125	−	0.594311i	−0.985011	+	0.172490i	$0.944819\pi$
$8$	−2.71411	−	0.795980i	−0.959584	−	0.281421i
$9$	2.71411	−	1.27812i	0.904705	−	0.426039i
$10$	0.306290	−	3.21128i	0.0968573	−	1.01550i
$11$	−4.24153	+	2.44885i	−1.27887	+	0.738355i	−0.976640	−	0.214880i	$-0.931064\pi$
$11$	−4.24153	+	2.44885i	−1.27887	+	0.738355i	−0.302228	+	0.953236i	$0.597730\pi$
$12$	−1.64168	+	3.05039i	−0.473911	+	0.880573i
$13$	4.00895	+	2.31457i	1.11188	+	0.641946i	0.939317	−	0.343052i	$-0.111461\pi$
$13$	4.00895	+	2.31457i	1.11188	+	0.641946i	0.172567	+	0.984998i	$0.444794\pi$
$14$	1.48919	−	2.09176i	0.398004	−	0.559046i
$15$	−3.77023	−	1.18092i	−0.973469	−	0.304913i
$16$	−0.570971	−	3.95904i	−0.142743	−	0.989760i
$17$	1.92788			0.467579			0.233790	−	0.972287i	$-0.424887\pi$
$17$	1.92788			0.467579			0.233790	+	0.972287i	$0.424887\pi$
$18$	3.23899	+	2.74025i	0.763437	+	0.645883i
$19$		−	2.12907i		−	0.488442i	−0.969720	−	0.244221i	$-0.921468\pi$
$19$		−	2.12907i		−	0.488442i	0.969720	−	0.244221i	$-0.0785322\pi$
$20$	4.31082	−	1.49303i	0.963928	−	0.333852i
$21$	−2.12897	−	2.31457i	−0.464579	−	0.505080i
$22$	−5.64250	−	4.01709i	−1.20299	−	0.856446i
$23$	−1.15765	+	2.00511i	−0.241387	+	0.418094i	−0.961109	−	0.276168i	$-0.910936\pi$
$23$	−1.15765	+	2.00511i	−0.241387	+	0.418094i	0.719723	+	0.694261i	$0.244269\pi$
$24$	−4.88856	−	0.319285i	−0.997874	−	0.0651737i
$25$	0.101535	+	0.175863i	0.0203069	+	0.0351726i
$26$	−0.621589	+	6.51702i	−0.121904	+	1.27809i
$27$	4.10439	−	3.18653i	0.789891	−	0.613247i
$28$	3.56582	+	0.686457i	0.673877	+	0.129728i
$29$	3.16440	−	1.82697i	0.587615	−	0.339260i	−0.176539	−	0.984294i	$-0.556490\pi$
$29$	3.16440	−	1.82697i	0.587615	−	0.339260i	0.764154	+	0.645034i	$0.223157\pi$
$30$	−0.696398	−	5.54378i	−0.127144	−	1.01215i
$31$	−2.65800	+	4.60379i	−0.477391	+	0.826865i	−0.999664	−	0.0259130i	$-0.991751\pi$
$31$	−2.65800	+	4.60379i	−0.477391	+	0.826865i	0.522273	+	0.852778i	$0.325084\pi$
$32$	4.75719	−	3.06090i	0.840961	−	0.541095i
$33$	−6.24353	+	5.74287i	−1.08686	+	0.999706i
$34$	1.13287	+	2.47993i	0.194285	+	0.425304i
$35$			4.14154i			0.700048i
$36$	−1.62161	+	5.77671i	−0.270269	+	0.962785i
$37$			7.98438i			1.31262i	0.754489	+	0.656312i	$0.227885\pi$
$37$			7.98438i			1.31262i	−0.754489	+	0.656312i	$0.772115\pi$
$38$	2.73873	−	1.25109i	0.444280	−	0.202954i
$39$	7.65135	+	2.39658i	1.22520	+	0.383760i
$40$	4.45370	+	4.66788i	0.704192	+	0.738056i
$41$	−2.36240	+	4.09180i	−0.368946	+	0.639033i	−0.989401	−	0.145209i	$-0.953614\pi$
$41$	−2.36240	+	4.09180i	−0.368946	+	0.639033i	0.620455	+	0.784242i	$0.286948\pi$
$42$	1.72631	−	4.09870i	0.266376	−	0.632443i
$43$	−2.20800	+	1.27479i	−0.336717	+	0.194404i	−0.658819	−	0.752301i	$-0.728944\pi$
$43$	−2.20800	+	1.27479i	−0.336717	+	0.194404i	0.322102	+	0.946705i	$0.395610\pi$
$44$	1.85171	−	9.61877i	0.279156	−	1.45008i
$45$	−6.81924	−	0.570655i	−1.01655	−	0.0850683i
$46$	−3.25953	−	0.310892i	−0.480592	−	0.0458386i
$47$	−2.02005	−	3.49884i	−0.294655	−	0.510358i	0.680249	−	0.732981i	$-0.261871\pi$
$47$	−2.02005	−	3.49884i	−0.294655	−	0.510358i	−0.974905	+	0.222623i	$0.928538\pi$
$48$	−2.46193	−	6.47603i	−0.355349	−	0.934734i
$49$	1.85171	−	3.20726i	0.264530	−	0.458179i
$50$	−0.166557	+	0.233951i	−0.0235548	+	0.0330856i
$51$	3.25866	−	0.728888i	0.456304	−	0.102065i
$52$	−8.74843	+	3.02998i	−1.21319	+	0.420182i
$53$		−	8.95958i		−	1.23069i	−0.788257	−	0.615347i	$-0.789016\pi$
$53$		−	8.95958i		−	1.23069i	0.788257	−	0.615347i	$-0.210984\pi$
$54$	6.51083	+	3.40721i	0.886012	+	0.463662i
$55$	11.1718			1.50640
$56$	1.21234	+	4.99028i	0.162006	+	0.666854i
$57$	−0.804954	−	3.59873i	−0.106619	−	0.476663i
$58$	4.20960	+	2.99696i	0.552748	+	0.393520i
$59$	3.05255	+	1.76239i	0.397408	+	0.229444i	0.685365	−	0.728200i	$-0.259643\pi$
$59$	3.05255	+	1.76239i	0.397408	+	0.229444i	−0.287957	+	0.957643i	$0.592976\pi$
$60$	6.72202	−	4.15347i	0.867809	−	0.536211i
$61$	1.71675	−	0.991165i	0.219807	−	0.126906i	−0.386054	−	0.922476i	$-0.626162\pi$
$61$	1.71675	−	0.991165i	0.219807	−	0.126906i	0.605861	+	0.795571i	$0.292829\pi$
$62$	−7.48399	−	0.713818i	−0.950468	−	0.0906550i
$63$	−4.47365	−	3.10736i	−0.563627	−	0.391491i
$64$	6.73283	+	4.32076i	0.841604	+	0.540095i
$65$	−5.27959	−	9.14451i	−0.654852	−	1.13424i
$66$	−11.0562	−	4.65671i	−1.36092	−	0.573201i
$67$	−7.72723	−	4.46132i	−0.944031	−	0.545036i	−0.0528093	−	0.998605i	$-0.516818\pi$
$67$	−7.72723	−	4.46132i	−0.944031	−	0.545036i	−0.891222	+	0.453568i	$0.850151\pi$
$68$	−2.52435	+	2.91453i	−0.306123	+	0.353439i
$69$	−1.19867	+	3.82688i	−0.144303	+	0.460702i
$70$	−5.32747	+	2.43367i	−0.636754	+	0.290879i
$71$	13.3561			1.58508			0.792539	−	0.609821i	$-0.208759\pi$
$71$	13.3561			1.58508			0.792539	+	0.609821i	$0.208759\pi$
$72$	−8.38377	+	1.30858i	−0.988037	+	0.154217i
$73$	−11.5592			−1.35290			−0.676450	−	0.736489i	$-0.736482\pi$
$73$	−11.5592			−1.35290			−0.676450	+	0.736489i	$0.736482\pi$
$74$	−10.2707	+	4.69182i	−1.19395	+	0.545413i
$75$	0.238112	+	0.258870i	0.0274948	+	0.0298918i
$76$	3.21869	+	2.78779i	0.369209	+	0.319782i
$77$	7.70112	+	4.44625i	0.877625	+	0.506697i
$78$	1.41328	+	11.2506i	0.160022	+	1.27388i
$79$	−4.97330	−	8.61401i	−0.559540	−	0.969151i	−0.997535	−	0.0701739i	$-0.977645\pi$
$79$	−4.97330	−	8.61401i	−0.559540	−	0.969151i	0.437995	−	0.898977i	$-0.355689\pi$
$80$	−3.38742	+	8.47198i	−0.378725	+	0.947196i
$81$	5.73283	−	6.93791i	0.636981	−	0.770879i
$82$	−6.65170	−	0.634435i	−0.734558	−	0.0700616i
$83$	3.12153	−	1.80221i	0.342632	−	0.197819i	−0.318803	−	0.947821i	$-0.603281\pi$
$83$	3.12153	−	1.80221i	0.342632	−	0.197819i	0.661435	+	0.750002i	$0.269948\pi$
$84$	6.28679	−	0.187853i	0.685945	−	0.0204964i
$85$	−3.80838	−	2.19877i	−0.413077	−	0.238490i
$86$	−2.93730	−	2.09116i	−0.316737	−	0.225496i
$87$	4.65800	−	4.28448i	0.499390	−	0.459345i
$88$	13.4612	−	3.27028i	1.43497	−	0.348613i
$89$	2.49965			0.264962			0.132481	−	0.991186i	$-0.457706\pi$
$89$	2.49965			0.264962			0.132481	+	0.991186i	$0.457706\pi$
$90$	−3.27309	−	9.10726i	−0.345014	−	0.959989i
$91$		−	8.40489i		−	0.881072i
$92$	−1.51547	−	4.37559i	−0.157998	−	0.456187i
$93$	−2.75218	+	8.78664i	−0.285388	+	0.911132i
$94$	3.31370	−	4.65450i	0.341782	−	0.480075i
$95$	−2.42823	+	4.20582i	−0.249131	+	0.431508i
$96$	6.88375	−	6.97237i	0.702570	−	0.711615i
$97$	6.99370	+	12.1134i	0.710103	+	1.22993i	0.964818	+	0.262918i	$0.0846849\pi$
$97$	6.99370	+	12.1134i	0.710103	+	1.22993i	−0.254715	+	0.967016i	$0.581982\pi$
$98$	5.21376	+	0.497285i	0.526670	+	0.0502334i
$99$	−8.38208	+	12.0676i	−0.842430	+	1.21284i
$100$	−0.398816	−	0.0767760i	−0.0398816	−	0.00767760i
$101$	−1.13087	+	0.652911i	−0.112526	+	0.0649671i	−0.555207	−	0.831712i	$-0.687361\pi$
$101$	−1.13087	+	0.652911i	−0.112526	+	0.0649671i	0.442681	+	0.896679i	$0.354028\pi$
$102$	2.85247	+	3.76347i	0.282437	+	0.372639i
$103$	−3.22312	+	5.58261i	−0.317584	+	0.550071i	−0.979983	−	0.199080i	$-0.936205\pi$
$103$	−3.22312	+	5.58261i	−0.317584	+	0.550071i	0.662400	+	0.749151i	$0.269538\pi$
$104$	−9.03840	−	9.47305i	−0.886288	−	0.928909i
$105$	1.56582	+	7.00037i	0.152809	+	0.683166i
$106$	11.5252	−	5.26487i	1.11942	−	0.511370i
$107$		−	3.10427i		−	0.300101i	−0.988678	−	0.150051i	$-0.952056\pi$
$107$		−	3.10427i		−	0.300101i	0.988678	−	0.150051i	$-0.0479437\pi$
$108$	−0.556936	+	10.3774i	−0.0535912	+	0.998563i
$109$		−	18.0837i		−	1.73210i	−0.499955	−	0.866051i	$-0.666650\pi$
$109$		−	18.0837i		−	1.73210i	0.499955	−	0.866051i	$-0.333350\pi$
$110$	6.56480	+	14.3708i	0.625929	+	1.37020i
$111$	3.01872	+	13.4959i	0.286524	+	1.28097i
$112$	−5.70684	+	4.49191i	−0.539246	+	0.424445i
$113$	−1.41718	+	2.45463i	−0.133317	+	0.230913i	−0.924953	−	0.380080i	$-0.875896\pi$
$113$	−1.41718	+	2.45463i	−0.133317	+	0.230913i	0.791636	+	0.610993i	$0.209230\pi$
$114$	4.15622	−	3.15015i	0.389265	−	0.295039i
$115$	4.57370	−	2.64063i	0.426500	−	0.246240i
$116$	−1.38147	+	7.17611i	−0.128267	+	0.666285i
$117$	13.8390	+	1.15810i	1.27942	+	0.107066i
$118$	−0.473298	+	4.96227i	−0.0435706	+	0.456814i
$119$	−1.75018	−	3.03139i	−0.160438	−	0.277887i
$120$	9.29284	+	6.20619i	0.848316	+	0.566545i
$121$	6.49370	−	11.2474i	0.590337	−	1.02249i
$122$	2.28379	+	1.62591i	0.206764	+	0.147203i
$123$	−2.44611	+	7.80948i	−0.220558	+	0.704157i
$124$	−3.47956	−	10.0465i	−0.312474	−	0.902202i
$125$			10.9419i			0.978674i
$126$	1.36833	−	7.58064i	0.121901	−	0.675337i
$127$	−7.44962			−0.661047			−0.330523	−	0.943798i	$-0.607225\pi$
$127$	−7.44962			−0.661047			−0.330523	+	0.943798i	$0.607225\pi$
$128$	−1.60163	+	11.1998i	−0.141566	+	0.989929i
$129$	−3.25018	+	2.98955i	−0.286162	+	0.263215i
$130$	8.66063	−	12.1649i	0.759588	−	1.06694i
$131$	−3.12153	−	1.80221i	−0.272729	−	0.157460i	0.357398	−	0.933952i	$-0.383664\pi$
$131$	−3.12153	−	1.80221i	−0.272729	−	0.157460i	−0.630127	+	0.776492i	$0.716997\pi$
$132$	−0.506732	−	16.9585i	−0.0441053	−	1.47605i
$133$	−3.34774	+	1.93282i	−0.290286	+	0.167597i
$134$	1.19811	−	12.5615i	0.103501	−	1.08515i
$135$	−11.7422	+	1.61363i	−1.01061	+	0.138879i
$136$	−5.23248	−	1.53455i	−0.448682	−	0.131587i
$137$	5.88147	+	10.1870i	0.502488	+	0.870335i	0.999996	+	0.00287543i	$0.000915278\pi$
$137$	5.88147	+	10.1870i	0.502488	+	0.870335i	−0.497508	+	0.867460i	$0.665751\pi$
$138$	−5.62708	+	0.706862i	−0.479009	+	0.0601721i
$139$	11.0400	+	6.37395i	0.936400	+	0.540631i	0.888830	−	0.458237i	$-0.151519\pi$
$139$	11.0400	+	6.37395i	0.936400	+	0.540631i	0.0475703	+	0.998868i	$0.484852\pi$
$140$	−6.26110	−	5.42291i	−0.529160	−	0.458319i
$141$	−4.73730	−	5.15029i	−0.398952	−	0.433732i
$142$	7.84838	+	17.1806i	0.658621	+	1.44177i
$143$	−22.6721			−1.89594
$144$	−6.60980	−	10.0155i	−0.550817	−	0.834626i
$145$	−8.33472			−0.692161
$146$	−6.79246	−	14.8692i	−0.562148	−	1.23058i
$147$	1.91732	−	6.12126i	0.158138	−	0.504873i
$148$	−12.0706	−	10.4547i	−0.992201	−	0.859372i
$149$	−6.59790	−	3.80930i	−0.540521	−	0.312070i	0.204769	−	0.978810i	$-0.434356\pi$
$149$	−6.59790	−	3.80930i	−0.540521	−	0.312070i	−0.745290	+	0.666740i	$0.767689\pi$
$150$	−0.193077	+	0.458414i	−0.0157647	+	0.0374294i
$151$	2.26988	+	3.93155i	0.184720	+	0.319945i	0.943482	−	0.331423i	$-0.107529\pi$
$151$	2.26988	+	3.93155i	0.184720	+	0.319945i	−0.758762	+	0.651368i	$0.774195\pi$
$152$	−1.69470	+	5.77854i	−0.137458	+	0.468701i
$153$	5.23248	−	2.46405i	0.423021	−	0.199207i
$154$	−1.19406	+	12.5191i	−0.0962201	+	1.00882i
$155$	10.5014	−	6.06296i	0.843489	−	0.486989i
$156$	−13.6417	+	8.42911i	−1.09221	+	0.674869i
$157$	−11.4105	−	6.58787i	−0.910659	−	0.525769i	−0.0300161	−	0.999549i	$-0.509556\pi$
$157$	−11.4105	−	6.58787i	−0.910659	−	0.525769i	−0.880643	+	0.473780i	$0.842889\pi$
$158$	8.15820	−	11.4592i	0.649031	−	0.911645i
$159$	−3.38742	−	15.1442i	−0.268640	−	1.20102i
$160$	−12.8885	+	0.620936i	−1.01892	+	0.0490893i
$161$	4.20377			0.331303
$162$	12.2933	+	3.29754i	0.965856	+	0.259079i
$163$			20.5911i			1.61282i	0.591358	+	0.806409i	$0.298592\pi$
$163$			20.5911i			1.61282i	−0.591358	+	0.806409i	$0.701408\pi$
$164$	−3.09260	−	8.92923i	−0.241491	−	0.697256i
$165$	18.8834	−	4.22379i	1.47007	−	0.328822i
$166$	4.15257	+	2.95635i	0.322302	+	0.229457i
$167$	2.53912	−	4.39789i	0.196483	−	0.340319i	−0.750903	−	0.660413i	$-0.770381\pi$
$167$	2.53912	−	4.39789i	0.196483	−	0.340319i	0.947386	+	0.320094i	$0.103715\pi$
$168$	3.93592	+	7.97662i	0.303662	+	0.615410i
$169$	4.21446	+	7.29967i	0.324190	+	0.561513i
$170$	0.590490	−	6.19096i	0.0452885	−	0.474825i
$171$	−2.72120	−	5.77854i	−0.208095	−	0.441896i
$172$	0.963939	−	5.00722i	0.0734997	−	0.381797i
$173$	−11.0398	+	6.37385i	−0.839343	+	0.484595i	−0.857041	−	0.515248i	$-0.827700\pi$
$173$	−11.0398	+	6.37385i	−0.839343	+	0.484595i	0.0176977	+	0.999843i	$0.494366\pi$
$174$	8.24850	+	3.47415i	0.625317	+	0.263375i
$175$	0.184351	−	0.319306i	0.0139356	−	0.0241372i
$176$	12.1169	+	15.3942i	0.913344	+	1.16038i
$177$	5.82599	+	1.82484i	0.437908	+	0.137163i
$178$	1.46886	+	3.21543i	0.110095	+	0.241006i
$179$		−	8.82019i		−	0.659252i	−0.944112	−	0.329626i	$-0.893077\pi$
$179$		−	8.82019i		−	0.659252i	0.944112	−	0.329626i	$-0.106923\pi$
$180$	9.79178	−	9.56199i	0.729836	−	0.712708i
$181$			15.4369i			1.14741i	0.819061	+	0.573707i	$0.194495\pi$
$181$			15.4369i			1.14741i	−0.819061	+	0.573707i	$0.805505\pi$
$182$	10.8116	−	4.93892i	0.801412	−	0.366097i
$183$	2.52705	−	2.32441i	0.186805	−	0.171826i
$184$	4.73802	−	4.52063i	0.349291	−	0.333265i
$185$	9.10628	−	15.7725i	0.669507	−	1.15962i
$186$	−12.9199	+	1.62298i	−0.947336	+	0.119002i
$187$	−8.17715	+	4.72108i	−0.597972	+	0.345239i
$188$	7.93453	+	1.52748i	0.578685	+	0.111403i
$189$	−8.73656	−	3.56093i	−0.635491	−	0.259020i
$190$	−6.83704	−	0.652112i	−0.496011	−	0.0473092i
$191$	4.81698	+	8.34326i	0.348545	+	0.603697i	0.985991	−	0.166797i	$-0.0533426\pi$
$191$	4.81698	+	8.34326i	0.348545	+	0.603697i	−0.637446	+	0.770495i	$0.720009\pi$
$192$	13.0140	+	4.75777i	0.939203	+	0.343363i
$193$	3.49335	−	6.05066i	0.251457	−	0.435536i	−0.712470	−	0.701702i	$-0.752424\pi$
$193$	3.49335	−	6.05066i	0.251457	−	0.435536i	0.963927	+	0.266166i	$0.0857570\pi$
$194$	−11.4725	+	16.1145i	−0.823675	+	1.15695i
$195$	−12.3813	−	13.4607i	−0.886646	−	0.963942i
$196$	2.42405	+	6.99894i	0.173147	+	0.499925i
$197$			4.31842i			0.307675i	0.988096	+	0.153837i	$0.0491632\pi$
$197$			4.31842i			0.307675i	−0.988096	+	0.153837i	$0.950837\pi$
$198$	−20.4487	−	3.69106i	−1.45323	−	0.262312i
$199$	5.90649			0.418700			0.209350	−	0.977841i	$-0.432865\pi$
$199$	5.90649			0.418700			0.209350	+	0.977841i	$0.432865\pi$
$200$	−0.135593	−	0.558132i	−0.00958787	−	0.0394659i
$201$	−14.7479	−	4.61939i	−1.04024	−	0.325827i
$202$	−1.50440	−	1.07103i	−0.105849	−	0.0753577i
$203$	−5.74544	−	3.31713i	−0.403251	−	0.232817i
$204$	−3.16495	+	5.88079i	−0.221591	+	0.411737i
$205$	9.33350	−	5.38870i	0.651880	−	0.376363i
$206$	−9.07518	−	0.865585i	−0.632298	−	0.0603082i
$207$	−0.579230	+	6.92170i	−0.0402593	+	0.481092i
$208$	6.87447	−	17.1932i	0.476659	−	1.19213i
$209$	5.21376	+	9.03050i	0.360644	+	0.624653i
$210$	−8.08481	+	6.12779i	−0.557905	+	0.422858i
$211$	15.8781	+	9.16723i	1.09309	+	0.631098i	0.934399	−	0.356229i	$-0.115938\pi$
$211$	15.8781	+	9.16723i	1.09309	+	0.631098i	0.158696	+	0.987328i	$0.449271\pi$
$212$	13.5449	+	11.7316i	0.930270	+	0.805732i
$213$	22.5756	−	5.04965i	1.54685	−	0.345996i
$214$	3.99318	−	1.82415i	0.272968	−	0.124696i
$215$	5.81565			0.396624
$216$	−13.6762	+	5.38158i	−0.930548	+	0.366170i
$217$	9.65199			0.655220
$218$	23.2619	−	10.6264i	1.57550	−	0.719712i
$219$	−19.5383	+	4.37027i	−1.32027	+	0.295315i
$220$	−14.6282	+	16.8893i	−0.986236	+	1.13867i
$221$	7.72877	+	4.46221i	0.519893	+	0.300161i
$222$	−15.5865	+	11.8136i	−1.04610	+	0.792879i
$223$	−2.63263	−	4.55986i	−0.176294	−	0.305350i	0.764314	−	0.644844i	$-0.223078\pi$
$223$	−2.63263	−	4.55986i	−0.176294	−	0.305350i	−0.940608	+	0.339494i	$0.889744\pi$
$224$	−9.13165	−	4.70145i	−0.610134	−	0.314129i
$225$	0.500350	+	0.347539i	0.0333567	+	0.0231693i
$226$	−3.99029	−	0.380591i	−0.265430	−	0.0253166i
$227$	−1.53638	+	0.887027i	−0.101973	+	0.0588741i	−0.550119	−	0.835086i	$-0.685418\pi$
$227$	−1.53638	+	0.887027i	−0.101973	+	0.0588741i	0.448146	+	0.893960i	$0.352084\pi$
$228$	6.49450	+	3.49524i	0.430109	+	0.231478i
$229$	3.30687	+	1.90922i	0.218524	+	0.126165i	0.605267	−	0.796023i	$-0.293066\pi$
$229$	3.30687	+	1.90922i	0.218524	+	0.126165i	−0.386742	+	0.922188i	$0.626400\pi$
$230$	6.08439	+	4.33168i	0.401193	+	0.285623i
$231$	14.6981	+	4.60379i	0.967064	+	0.302907i
$232$	−10.0428	+	2.43980i	−0.659341	+	0.160181i
$233$	−20.3207			−1.33125			−0.665627	−	0.746284i	$-0.731836\pi$
$233$	−20.3207			−1.33125			−0.665627	+	0.746284i	$0.731836\pi$
$234$	6.64245	+	18.4824i	0.434230	+	1.20823i
$235$			9.21558i			0.601158i
$236$	−6.66134	+	2.30713i	−0.433616	+	0.150181i
$237$	−11.6630	−	12.6798i	−0.757596	−	0.823642i
$238$	2.87099	−	4.03266i	0.186098	−	0.261398i
$239$	8.69811	−	15.0656i	0.562634	−	0.974510i	−0.434632	−	0.900608i	$-0.643121\pi$
$239$	8.69811	−	15.0656i	0.562634	−	0.974510i	0.997266	−	0.0739020i	$-0.0235452\pi$
$240$	−2.52263	+	15.6008i	−0.162835	+	1.00702i
$241$	−6.85611	−	11.8751i	−0.441641	−	0.764944i	0.556171	−	0.831068i	$-0.312270\pi$
$241$	−6.85611	−	11.8751i	−0.441641	−	0.764944i	−0.997811	+	0.0661240i	$0.978937\pi$
$242$	18.2840	+	1.74391i	1.17534	+	0.112103i
$243$	7.06704	−	13.8945i	0.453351	−	0.891332i
$244$	−0.749475	+	3.89317i	−0.0479802	+	0.249235i
$245$	−7.31583	+	4.22379i	−0.467391	+	0.269848i
$246$	−11.4831	+	1.44249i	−0.732137	+	0.0919696i
$247$	4.92788	−	8.53534i	0.313553	−	0.543090i
$248$	10.8786	−	10.3795i	0.690794	−	0.659099i
$249$	4.59489	−	4.22643i	0.291189	−	0.267839i
$250$	−14.0751	+	6.42974i	−0.890190	+	0.406652i
$251$		−	4.50751i		−	0.284512i	−0.989830	−	0.142256i	$-0.954564\pi$
$251$		−	4.50751i		−	0.284512i	0.989830	−	0.142256i	$-0.0454356\pi$
$252$	10.5554	−	2.69442i	0.664929	−	0.169732i
$253$		−	11.3396i		−	0.712916i
$254$	−4.37758	−	9.58282i	−0.274674	−	0.601280i
$255$	−7.26854	−	2.27668i	−0.455174	−	0.142571i
$256$	−15.3480	+	4.52100i	−0.959249	+	0.282562i
$257$	−4.11258	+	7.12320i	−0.256536	+	0.444333i	−0.965311	−	0.261101i	$-0.915914\pi$
$257$	−4.11258	+	7.12320i	−0.256536	+	0.444333i	0.708776	+	0.705434i	$0.249248\pi$
$258$	−5.75549	−	2.42413i	−0.358321	−	0.150920i
$259$	12.5546	−	7.24842i	0.780106	−	0.450395i
$260$	20.7376	+	3.99219i	1.28609	+	0.247585i
$261$	6.25347	−	9.00308i	0.387080	−	0.557277i
$262$	0.483993	−	5.07440i	0.0299012	−	0.313498i
$263$	2.51376	+	4.35395i	0.155005	+	0.268476i	0.933061	−	0.359719i	$-0.117127\pi$
$263$	2.51376	+	4.35395i	0.155005	+	0.268476i	−0.778056	+	0.628195i	$0.783794\pi$
$264$	21.5169	−	10.6171i	1.32427	−	0.653437i
$265$	−10.2185	+	17.6990i	−0.627718	+	1.08724i
$266$	−4.45350	−	3.17060i	−0.273062	−	0.194402i
$267$	4.22512	−	0.945062i	0.258573	−	0.0578369i
$268$	16.8625	−	5.84026i	1.03004	−	0.356751i
$269$			23.1577i			1.41195i	0.708236	+	0.705976i	$0.249491\pi$
$269$			23.1577i			1.41195i	−0.708236	+	0.705976i	$0.750509\pi$
$270$	−8.97570	−	14.1564i	−0.546244	−	0.861529i
$271$	20.9367			1.27181			0.635906	−	0.771766i	$-0.280627\pi$
$271$	20.9367			1.27181			0.635906	+	0.771766i	$0.280627\pi$
$272$	−1.10076	−	7.63255i	−0.0667436	−	0.462791i
$273$	−3.17770	−	14.2066i	−0.192323	−	0.859825i
$274$	−9.64797	+	13.5518i	−0.582855	+	0.818693i
$275$	−0.861323	−	0.497285i	−0.0519398	−	0.0299874i
$276$	−4.21588	−	6.82302i	−0.253766	−	0.410698i
$277$	−19.2687	+	11.1248i	−1.15775	+	0.668425i	−0.950763	−	0.309920i	$-0.899698\pi$
$277$	−19.2687	+	11.1248i	−1.15775	+	0.668425i	−0.206983	+	0.978345i	$0.566364\pi$
$278$	−1.71175	+	17.9468i	−0.102664	+	1.07638i
$279$	−1.32993	+	15.8924i	−0.0796208	+	0.951456i
$280$	3.29658	−	11.2406i	0.197008	−	0.671755i
$281$	−9.28029	−	16.0739i	−0.553616	−	0.958890i	−0.998010	−	0.0630590i	$-0.979914\pi$
$281$	−9.28029	−	16.0739i	−0.553616	−	0.958890i	0.444394	−	0.895831i	$-0.353419\pi$
$282$	3.84132	−	9.12026i	0.228747	−	0.543103i
$283$	−1.75962	−	1.01592i	−0.104599	−	0.0603901i	0.446788	−	0.894640i	$-0.352568\pi$
$283$	−1.75962	−	1.01592i	−0.104599	−	0.0603901i	−0.551387	+	0.834250i	$0.685901\pi$
$284$	−17.4884	+	20.1915i	−1.03775	+	1.19815i
$285$	−2.51427	+	8.02708i	−0.148932	+	0.475483i
$286$	−13.3227	−	29.1643i	−0.787787	−	1.72452i
$287$	8.57859			0.506378
$288$	8.99938	−	14.3879i	0.530294	−	0.847814i
$289$	−13.2833			−0.781370
$290$	−4.89768	−	10.7214i	−0.287602	−	0.629580i
$291$	16.4012	+	17.8310i	0.961453	+	1.04527i
$292$	15.1355	−	17.4750i	0.885739	−	1.02264i
$293$	−29.5484	−	17.0598i	−1.72623	−	0.996642i	−0.904057	−	0.427411i	$-0.859426\pi$
$293$	−29.5484	−	17.0598i	−1.72623	−	0.996642i	−0.822178	−	0.569231i	$-0.807241\pi$
$294$	9.00075	−	1.13066i	0.524934	−	0.0659412i
$295$	−4.02005	−	6.96294i	−0.234057	−	0.405398i
$296$	6.35541	−	21.6705i	0.369401	−	1.25957i
$297$	−9.60558	+	23.5668i	−0.557372	+	1.36748i
$298$	1.02300	−	10.7256i	0.0592611	−	0.621320i
$299$	−9.28192	+	5.35892i	−0.536787	+	0.309914i
$300$	−0.703138	+	0.0210102i	−0.0405957	+	0.00121302i
$301$	4.00895	+	2.31457i	0.231072	+	0.133410i
$302$	−3.72351	+	5.23013i	−0.214264	+	0.300960i
$303$	−1.66465	+	1.53116i	−0.0956315	+	0.0879630i
$304$	−8.42907	+	1.21564i	−0.483440	+	0.0697216i
$305$	−4.52174			−0.258914
$306$	6.24437	+	5.28287i	0.356967	+	0.302001i
$307$		−	4.77588i		−	0.272574i	−0.990669	−	0.136287i	$-0.956483\pi$
$307$		−	4.77588i		−	0.272574i	0.990669	−	0.136287i	$-0.0435169\pi$
$308$	−16.8056	+	5.82053i	−0.957586	+	0.331656i
$309$	−3.33733	+	10.6548i	−0.189854	+	0.606130i
$310$	13.9699	+	9.94568i	0.793440	+	0.564876i
$311$	−11.1771	+	19.3592i	−0.633793	+	1.09776i	0.352976	+	0.935632i	$0.385170\pi$
$311$	−11.1771	+	19.3592i	−0.633793	+	1.09776i	−0.986769	+	0.162130i	$0.948164\pi$
$312$	−18.8590	−	12.5949i	−1.06768	−	0.713047i
$313$	1.22411	+	2.12022i	0.0691907	+	0.119842i	0.898545	−	0.438881i	$-0.144625\pi$
$313$	1.22411	+	2.12022i	0.0691907	+	0.119842i	−0.829355	+	0.558723i	$0.811292\pi$
$314$	1.76920	−	18.5491i	0.0998420	−	1.04679i
$315$	5.29337	+	11.2406i	0.298248	+	0.633336i
$316$	19.5345	+	3.76059i	1.09890	+	0.211550i
$317$	14.2886	−	8.24953i	0.802528	−	0.463340i	−0.0418263	−	0.999125i	$-0.513318\pi$
$317$	14.2886	−	8.24953i	0.802528	−	0.463340i	0.844354	+	0.535785i	$0.179984\pi$
$318$	17.4903	−	13.2565i	0.980805	−	0.743389i
$319$	−8.94793	+	15.4983i	−0.500988	+	0.867737i
$320$	−8.37232	−	16.2142i	−0.468027	−	0.906402i
$321$	−1.17366	−	5.24710i	−0.0655071	−	0.292864i
$322$	2.47024	+	5.40752i	0.137661	+	0.301349i
$323$		−	4.10459i		−	0.228385i
$324$	2.98207	+	17.7513i	0.165671	+	0.986181i
$325$			0.940035i			0.0521438i
$326$	−26.4874	+	12.0998i	−1.46700	+	0.670148i
$327$	−6.83704	−	30.5665i	−0.378089	−	1.69033i
$328$	9.66883	−	9.22520i	0.533872	−	0.509376i
$329$	−3.66771	+	6.35266i	−0.202207	+	0.350233i
$330$	16.5296	+	21.8087i	0.909927	+	1.20053i
$331$	0.329200	−	0.190064i	0.0180945	−	0.0104469i	−0.490925	−	0.871202i	$-0.663341\pi$
$331$	0.329200	−	0.190064i	0.0180945	−	0.0104469i	0.509020	+	0.860755i	$0.330008\pi$
$332$	−1.36275	+	7.07888i	−0.0747909	+	0.388504i
$333$	10.2050	+	21.6705i	0.559229	+	1.18754i
$334$	7.14928	+	0.681893i	0.391191	+	0.0373115i
$335$	10.1764	+	17.6260i	0.555994	+	0.963010i
$336$	−7.94789	+	9.75023i	−0.433593	+	0.531918i
$337$	−2.51872	+	4.36255i	−0.137203	+	0.237643i	−0.926437	−	0.376450i	$-0.877145\pi$
$337$	−2.51872	+	4.36255i	−0.137203	+	0.237643i	0.789234	+	0.614093i	$0.210478\pi$
$338$	−6.91341	+	9.71074i	−0.376040	+	0.528195i
$339$	−1.46740	+	4.68483i	−0.0796982	+	0.254445i
$340$	8.31073	−	2.87838i	0.450713	−	0.156102i
$341$		−	26.0361i		−	1.40994i
$342$	5.83418	−	6.89603i	0.315476	−	0.372894i
$343$	−19.4337			−1.04932
$344$	7.00747	−	1.70240i	0.377817	−	0.0917873i
$345$	6.73248	−	6.19262i	0.362465	−	0.333399i
$346$	−14.6863	−	10.4557i	−0.789540	−	0.562100i
$347$	8.40337	+	4.85169i	0.451116	+	0.260452i	0.708302	−	0.705910i	$-0.249462\pi$
$347$	8.40337	+	4.85169i	0.451116	+	0.260452i	−0.257185	+	0.966362i	$0.582795\pi$
$348$	0.378048	+	12.6520i	0.0202655	+	0.678216i
$349$	26.1239	−	15.0827i	1.39838	−	0.807356i	0.404158	−	0.914689i	$-0.367564\pi$
$349$	26.1239	−	15.0827i	1.39838	−	0.807356i	0.994223	+	0.107333i	$0.0342312\pi$
$350$	0.519068	+	0.0495084i	0.0277454	+	0.00264633i
$351$	23.8298	−	3.27473i	1.27194	−	0.174792i
$352$	−12.6821	+	24.6325i	−0.675958	+	1.31292i
$353$	13.2376	+	22.9282i	0.704565	+	1.22034i	0.966848	+	0.255352i	$0.0821913\pi$
$353$	13.2376	+	22.9282i	0.704565	+	1.22034i	−0.262283	+	0.964991i	$0.584475\pi$
$354$	1.07612	+	8.56659i	0.0571950	+	0.455309i
$355$	−26.3840	−	15.2328i	−1.40032	−	0.808473i
$356$	−3.27303	+	3.77893i	−0.173470	+	0.200283i
$357$	−4.10439	−	4.46221i	−0.217228	−	0.236165i
$358$	11.3458	−	5.18296i	0.599647	−	0.273928i
$359$	−23.4619			−1.23827			−0.619135	−	0.785285i	$-0.712517\pi$
$359$	−23.4619			−1.23827			−0.619135	+	0.785285i	$0.712517\pi$
$360$	18.0540	+	6.97680i	0.951527	+	0.367710i
$361$	14.4671			0.761424
$362$	−19.8572	+	9.07108i	−1.04367	+	0.476766i
$363$	6.72379	−	21.4665i	0.352908	−	1.12670i
$364$	12.7064	+	11.0053i	0.665995	+	0.576835i
$365$	22.8343	+	13.1834i	1.19520	+	0.690050i
$366$	4.47497	+	1.88479i	0.233910	+	0.0985197i
$367$	9.62599	+	16.6727i	0.502472	+	0.870308i	0.999996	+	0.00285720i	$0.000909476\pi$
$367$	9.62599	+	16.6727i	0.502472	+	0.870308i	−0.497524	+	0.867450i	$0.665757\pi$
$368$	8.59928	+	3.43832i	0.448269	+	0.179235i
$369$	−1.18203	+	14.1251i	−0.0615340	+	0.735321i
$370$	25.6401	+	2.44553i	1.33296	+	0.127137i
$371$	−14.0880	+	8.13373i	−0.731414	+	0.422282i
$372$	−9.67980	−	15.6659i	−0.501874	−	0.812238i
$373$	9.09206	+	5.24930i	0.470769	+	0.271799i	0.716562	−	0.697524i	$-0.245715\pi$
$373$	9.09206	+	5.24930i	0.470769	+	0.271799i	−0.245793	+	0.969322i	$0.579048\pi$
$374$	−10.8781	−	7.74446i	−0.562491	−	0.400456i
$375$	4.13690	+	18.4949i	0.213628	+	0.955074i
$376$	2.69765	+	11.1042i	0.139121	+	0.572653i
$377$	16.9146			0.871145
$378$	−0.553207	−	13.3308i	−0.0284539	−	0.685661i
$379$		−	35.5203i		−	1.82455i	−0.409574	−	0.912277i	$-0.634323\pi$
$379$		−	35.5203i		−	1.82455i	0.409574	−	0.912277i	$-0.365677\pi$
$380$	−3.17877	−	9.17802i	−0.163067	−	0.470823i
$381$	−12.5920	+	2.81654i	−0.645106	+	0.144296i
$382$	−7.90178	+	11.0990i	−0.404290	+	0.567876i
$383$	18.0395	−	31.2453i	0.921774	−	1.59656i	0.125105	−	0.992144i	$-0.460073\pi$
$383$	18.0395	−	31.2453i	0.921774	−	1.59656i	0.796669	−	0.604416i	$-0.206593\pi$
$384$	1.52717	+	19.5363i	0.0779330	+	0.996959i
$385$	−10.1420	−	17.5664i	−0.516884	−	0.895269i
$386$	9.83605	+	0.938156i	0.500642	+	0.0477509i
$387$	−4.36343	+	6.28201i	−0.221806	+	0.319332i
$388$	−27.4704	−	5.28833i	−1.39460	−	0.268474i
$389$	17.5243	−	10.1177i	0.888519	−	0.512987i	0.0150612	−	0.999887i	$-0.495206\pi$
$389$	17.5243	−	10.1177i	0.888519	−	0.512987i	0.873458	+	0.486900i	$0.161872\pi$
$390$	10.0396	−	23.8366i	0.508376	−	1.20701i
$391$	−2.23181	+	3.86560i	−0.112867	+	0.195492i
$392$	−7.57866	+	7.23093i	−0.382780	+	0.365217i
$393$	−5.95764	−	1.86607i	−0.300523	−	0.0941309i
$394$	−5.55500	+	2.53761i	−0.279857	+	0.127843i
$395$			22.6884i			1.14158i
$396$	−7.26817	−	28.4732i	−0.365239	−	1.43083i
$397$		−	3.99499i		−	0.200503i	−0.994962	−	0.100251i	$-0.968035\pi$
$397$		−	3.99499i		−	0.200503i	0.994962	−	0.100251i	$-0.0319647\pi$
$398$	3.47080	+	7.59781i	0.173975	+	0.380844i
$399$	−4.92788	+	4.53272i	−0.246702	+	0.226920i
$400$	0.638275	−	0.502392i	0.0319138	−	0.0251196i
$401$	14.0124	−	24.2702i	0.699747	−	1.21200i	−0.268807	−	0.963194i	$-0.586629\pi$
$401$	14.0124	−	24.2702i	0.699747	−	1.21200i	0.968554	−	0.248803i	$-0.0800372\pi$
$402$	−2.72408	−	21.6855i	−0.135865	−	1.08157i
$403$	−21.3116	+	12.3042i	−1.06161	+	0.612918i
$404$	0.493702	−	2.56455i	0.0245626	−	0.127591i
$405$	−19.2375	+	7.16696i	−0.955921	+	0.356129i
$406$	0.890832	−	9.33988i	0.0442112	−	0.463531i
$407$	−19.5525	−	33.8660i	−0.969183	−	1.67867i
$408$	−9.42456	−	0.615542i	−0.466585	−	0.0304739i
$409$	8.22481	−	14.2458i	0.406691	−	0.704409i	−0.587826	−	0.808987i	$-0.700016\pi$
$409$	8.22481	−	14.2458i	0.406691	−	0.704409i	0.994517	+	0.104579i	$0.0333494\pi$
$410$	12.4164	+	8.83962i	0.613200	+	0.436558i
$411$	13.7928	+	14.9953i	0.680350	+	0.739662i
$412$	−4.21936	−	12.1825i	−0.207873	−	0.600189i
$413$		−	6.39976i		−	0.314912i
$414$	−9.24410	+	3.32227i	−0.454323	+	0.163281i
$415$	−8.22179			−0.403592
$416$	26.1560	−	1.26014i	1.28240	−	0.0617832i
$417$	21.0706	+	6.59979i	1.03183	+	0.323193i
$418$	−8.55266	+	12.0133i	−0.418324	+	0.587588i
$419$	20.5573	+	11.8688i	1.00429	+	0.579827i	0.909515	−	0.415672i	$-0.136453\pi$
$419$	20.5573	+	11.8688i	1.00429	+	0.579827i	0.0947752	+	0.995499i	$0.469787\pi$
$420$	−12.6333	−	6.79906i	−0.616443	−	0.331760i
$421$	−25.9420	+	14.9776i	−1.26433	+	0.729963i	−0.973910	−	0.226935i	$-0.927130\pi$
$421$	−25.9420	+	14.9776i	−1.26433	+	0.729963i	−0.290424	+	0.956898i	$0.593796\pi$
$422$	−2.46190	+	25.8117i	−0.119844	+	1.25649i
$423$	−9.95458	−	6.91437i	−0.484008	−	0.336188i
$424$	−7.13165	+	24.3173i	−0.346343	+	1.18095i
$425$	0.195746	+	0.339043i	0.00949509	+	0.0164460i
$426$	19.7616	+	26.0728i	0.957452	+	1.26323i
$427$	−3.11701	−	1.79961i	−0.150843	−	0.0870891i
$428$	4.69298	+	4.06472i	0.226844	+	0.196475i
$429$	−38.3223	+	8.57182i	−1.85022	+	0.413851i
$430$	3.41742	+	7.48096i	0.164803	+	0.360764i
$431$	−11.0367			−0.531621			−0.265810	−	0.964025i	$-0.585640\pi$
$431$	−11.0367			−0.531621			−0.265810	+	0.964025i	$0.585640\pi$
$432$	−14.9591	−	14.4300i	−0.719719	−	0.694266i
$433$	34.9394			1.67908			0.839541	−	0.543297i	$-0.182824\pi$
$433$	34.9394			1.67908			0.839541	+	0.543297i	$0.182824\pi$
$434$	5.67175	+	12.4158i	0.272252	+	0.595979i
$435$	−14.0880	+	3.15117i	−0.675469	+	0.151087i
$436$	27.3386	+	23.6787i	1.30928	+	1.13400i
$437$	4.26901	+	2.46472i	0.204215	+	0.117903i
$438$	−17.1029	−	22.5650i	−0.817207	−	1.07820i
$439$	−6.58518	−	11.4059i	−0.314293	−	0.544372i	0.664994	−	0.746849i	$-0.268434\pi$
$439$	−6.58518	−	11.4059i	−0.314293	−	0.544372i	−0.979287	+	0.202477i	$0.935101\pi$
$440$	−30.3214	−	8.89249i	−1.44552	−	0.423933i
$441$	0.926503	−	11.0716i	0.0441192	−	0.527217i
$442$	−1.19835	+	12.5640i	−0.0569996	+	0.597609i
$443$	23.6849	−	13.6745i	1.12530	−	0.649694i	0.182554	−	0.983196i	$-0.441564\pi$
$443$	23.6849	−	13.6745i	1.12530	−	0.649694i	0.942749	+	0.333502i	$0.108230\pi$
$444$	−24.3555	−	13.1078i	−1.15586	−	0.622067i
$445$	−4.93787	−	2.85088i	−0.234077	−	0.135145i
$446$	4.31857	−	6.06597i	0.204490	−	0.287232i
$447$	−12.5925	−	3.94427i	−0.595606	−	0.186558i
$448$	0.681725	−	14.5092i	0.0322085	−	0.685495i
$449$	−13.8225			−0.652323			−0.326161	−	0.945314i	$-0.605755\pi$
$449$	−13.8225			−0.652323			−0.326161	+	0.945314i	$0.605755\pi$
$450$	−0.153039	+	0.847848i	−0.00721434	+	0.0399679i
$451$		−	23.1407i		−	1.08965i
$452$	−1.85522	−	5.35656i	−0.0872622	−	0.251951i
$453$	5.32317	+	5.78723i	0.250104	+	0.271908i
$454$	−2.04384	−	1.45508i	−0.0959222	−	0.0682902i
$455$	−9.58588	+	16.6032i	−0.449393	+	0.778371i
$456$	−0.679779	+	10.4081i	−0.0318336	+	0.487403i
$457$	−2.86205	−	4.95722i	−0.133881	−	0.231889i	0.791288	−	0.611443i	$-0.209411\pi$
$457$	−2.86205	−	4.95722i	−0.133881	−	0.231889i	−0.925170	+	0.379554i	$0.876077\pi$
$458$	−0.512731	+	5.37570i	−0.0239584	+	0.251190i
$459$	7.91277	−	6.14324i	0.369337	−	0.286742i
$460$	−1.99672	+	10.3721i	−0.0930977	+	0.483600i
$461$	19.3717	−	11.1843i	0.902231	−	0.520903i	0.0243074	−	0.999705i	$-0.492262\pi$
$461$	19.3717	−	11.1843i	0.902231	−	0.520903i	0.877923	+	0.478801i	$0.158929\pi$
$462$	2.71488	+	21.6122i	0.126308	+	1.00549i
$463$	18.5733	−	32.1699i	0.863174	−	1.49506i	−0.00567564	−	0.999984i	$-0.501807\pi$
$463$	18.5733	−	32.1699i	0.863174	−	1.49506i	0.868849	−	0.495077i	$-0.164860\pi$
$464$	−9.03982	−	11.4848i	−0.419663	−	0.533171i
$465$	15.4580	−	14.2184i	0.716847	−	0.659365i
$466$	−11.9410	−	26.1396i	−0.553154	−	1.21089i
$467$			22.6850i			1.04974i	0.851184	+	0.524868i	$0.175885\pi$
$467$			22.6850i			1.04974i	−0.851184	+	0.524868i	$0.824115\pi$
$468$	−19.8716	+	19.4052i	−0.918563	+	0.897007i
$469$			16.2004i			0.748063i
$470$	−11.8545	+	5.41530i	−0.546806	+	0.249789i
$471$	−21.7778	−	6.82130i	−1.00347	−	0.314309i
$472$	−6.88214	−	7.21310i	−0.316776	−	0.332010i
$473$	6.24353	−	10.8141i	0.287078	−	0.497233i
$474$	9.45719	−	22.4537i	0.434383	−	1.03133i
$475$	0.374425	−	0.216174i	0.0171798	−	0.00991875i
$476$	6.87447	+	1.32340i	0.315091	+	0.0606582i
$477$	−11.4514	−	24.3173i	−0.524324	−	1.11341i
$478$	24.4908	+	2.33592i	1.12018	+	0.106842i
$479$	13.1576	+	22.7897i	0.601188	+	1.04129i	0.992641	+	0.121091i	$0.0386392\pi$
$479$	13.1576	+	22.7897i	0.601188	+	1.04129i	−0.391453	+	0.920198i	$0.628027\pi$
$480$	−21.5504	+	5.92240i	−0.983637	+	0.270319i
$481$	−18.4804	+	32.0090i	−0.842634	+	1.45948i
$482$	11.2468	−	15.7975i	0.512276	−	0.719555i
$483$	7.10556	−	1.58935i	0.323314	−	0.0723180i
$484$	8.50083	+	24.5444i	0.386402	+	1.11565i
$485$		−	31.9056i		−	1.44876i
$486$	22.0260	+	0.925941i	0.999118	+	0.0420015i
$487$	−24.0388			−1.08930			−0.544652	−	0.838662i	$-0.683338\pi$
$487$	−24.0388			−1.08930			−0.544652	+	0.838662i	$0.683338\pi$
$488$	−5.44840	+	1.32364i	−0.246637	+	0.0599183i
$489$	7.78504	+	34.8048i	0.352051	+	1.57393i
$490$	−9.73224	−	6.92871i	−0.439658	−	0.313007i
$491$	−27.2256	−	15.7187i	−1.22867	−	0.709374i	−0.261920	−	0.965090i	$-0.584356\pi$
$491$	−27.2256	−	15.7187i	−1.22867	−	0.709374i	−0.966752	+	0.255715i	$0.917689\pi$
$492$	−8.60331	−	13.9237i	−0.387867	−	0.627728i
$493$	6.10058	−	3.52217i	0.274756	−	0.158631i
$494$	13.8752	+	1.32340i	0.624274	+	0.0595428i
$495$	30.3214	−	14.2788i	1.36285	−	0.641785i
$496$	19.7442	+	7.89449i	0.886542	+	0.354473i
$497$	−12.1250	−	21.0011i	−0.543881	−	0.942029i
$498$	8.13674	+	3.42708i	0.364616	+	0.153571i
$499$	−5.08156	−	2.93384i	−0.227482	−	0.131337i	0.381928	−	0.924192i	$-0.375260\pi$
$499$	−5.08156	−	2.93384i	−0.227482	−	0.131337i	−0.609410	+	0.792855i	$0.708594\pi$
$500$	−16.5418	−	14.3273i	−0.739771	−	0.640736i
$501$	2.62909	−	8.39366i	0.117459	−	0.375001i
$502$	5.79824	−	2.64873i	0.258788	−	0.118218i
$503$	32.4317			1.44606			0.723029	−	0.690818i	$-0.242749\pi$
$503$	32.4317			1.44606			0.723029	+	0.690818i	$0.242749\pi$
$504$	9.66860	+	11.9947i	0.430673	+	0.534285i
$505$	2.97861			0.132546
$506$	14.5867	−	6.66344i	0.648459	−	0.296226i
$507$	9.88348	+	10.7451i	0.438941	+	0.477207i
$508$	9.75449	−	11.2622i	0.432786	−	0.499679i
$509$	13.6855	+	7.90133i	0.606599	+	0.350220i	0.771633	−	0.636068i	$-0.219440\pi$
$509$	13.6855	+	7.90133i	0.606599	+	0.350220i	−0.165034	+	0.986288i	$0.552773\pi$
$510$	−1.34257	−	10.6877i	−0.0594500	−	0.473260i
$511$	10.4937	+	18.1756i	0.464214	+	0.804042i
$512$	−14.8344	−	17.0862i	−0.655596	−	0.755112i
$513$	−6.78434	−	8.73854i	−0.299536	−	0.385816i
$514$	−11.5796	−	1.10445i	−0.510753	−	0.0487153i
$515$	12.7341	−	7.35202i	0.561130	−	0.323969i
$516$	−0.263788	−	8.82806i	−0.0116126	−	0.388634i
$517$	17.1362	+	9.89361i	0.753650	+	0.435120i
$518$	16.7014	+	11.8903i	0.733818	+	0.522430i
$519$	−16.2506	+	14.9475i	−0.713324	+	0.656124i
$520$	7.05056	+	29.0217i	0.309187	+	1.27269i
$521$	5.50310			0.241095			0.120548	−	0.992708i	$-0.461535\pi$
$521$	5.50310			0.241095			0.120548	+	0.992708i	$0.461535\pi$
$522$	15.2558	+	2.75372i	0.667728	+	0.120527i
$523$			38.5894i			1.68740i	0.536818	+	0.843698i	$0.319626\pi$
$523$			38.5894i			1.68740i	−0.536818	+	0.843698i	$0.680374\pi$
$524$	6.81187	−	2.35926i	0.297578	−	0.103065i
$525$	0.190883	−	0.609416i	0.00833083	−	0.0265971i
$526$	−4.12356	+	5.79206i	−0.179796	+	0.252546i
$527$	−5.12430	+	8.87555i	−0.223218	+	0.386625i
$528$	26.3011	+	21.4394i	1.14461	+	0.933028i
$529$	8.81970	+	15.2762i	0.383465	+	0.664181i
$530$	−28.7717	−	2.74423i	−1.24976	−	0.119202i
$531$	10.5375	+	0.881812i	0.457289	+	0.0382674i
$532$	1.46151	−	7.59189i	0.0633647	−	0.329150i
$533$	−18.9415	+	10.9359i	−0.820449	+	0.473686i
$534$	3.69846	+	4.87964i	0.160048	+	0.211163i
$535$	−3.54046	+	6.13225i	−0.153067	+	0.265120i
$536$	17.4215	+	18.2592i	0.752492	+	0.788679i
$537$	−3.33472	−	14.9086i	−0.143904	−	0.643354i
$538$	−29.7889	+	13.6080i	−1.28429	+	0.586685i
$539$			18.1382i			0.781268i
$540$	12.9357	−	19.8645i	0.556664	−	0.854833i
$541$			22.5666i			0.970214i	0.874455	+	0.485107i	$0.161219\pi$
$541$			22.5666i			0.970214i	−0.874455	+	0.485107i	$0.838781\pi$
$542$	12.3029	+	26.9319i	0.528455	+	1.15682i
$543$	5.83634	+	26.0927i	0.250461	+	1.11974i
$544$	9.17129	−	5.90104i	0.393216	−	0.253005i
$545$	−20.6246	+	35.7229i	−0.883463	+	1.53020i
$546$	16.4074	−	12.4358i	0.702173	−	0.532204i
$547$	11.2679	−	6.50552i	0.481780	−	0.278156i	−0.239378	−	0.970927i	$-0.576943\pi$
$547$	11.2679	−	6.50552i	0.481780	−	0.278156i	0.721158	+	0.692770i	$0.243610\pi$
$548$	−23.1017	−	4.44731i	−0.986856	−	0.189980i
$549$	3.39262	−	4.88434i	0.144794	−	0.208458i
$550$	0.133548	−	1.40018i	0.00569452	−	0.0597039i
$551$	−3.88974	−	6.73723i	−0.165709	−	0.287016i
$552$	6.29944	−	9.43248i	0.268122	−	0.401473i
$553$	−9.02976	+	15.6400i	−0.383985	+	0.665081i
$554$	−25.6332	−	18.2491i	−1.08905	−	0.775331i
$555$	9.42895	−	30.1029i	0.400236	−	1.27780i
$556$	−24.0917	+	8.34406i	−1.02172	+	0.353867i
$557$		−	5.73693i		−	0.243081i	−0.992586	−	0.121541i	$-0.961217\pi$
$557$		−	5.73693i		−	0.243081i	0.992586	−	0.121541i	$-0.0387835\pi$
$558$	−21.2248	+	7.62804i	−0.898516	+	0.322921i
$559$	−11.8024			−0.499186
$560$	16.3965	−	2.36470i	0.692879	−	0.0999268i
$561$	−12.0368	+	11.0716i	−0.508192	+	0.467442i
$562$	15.2234	−	21.3831i	0.642160	−	0.901993i
$563$	−13.2510	−	7.65045i	−0.558462	−	0.322428i	0.194066	−	0.980988i	$-0.437832\pi$
$563$	−13.2510	−	7.65045i	−0.558462	−	0.322428i	−0.752528	+	0.658560i	$0.771166\pi$
$564$	13.9891	−	0.418003i	0.589047	−	0.0176011i
$565$	5.59908	−	3.23263i	0.235555	−	0.135998i
$566$	0.272830	−	2.86047i	0.0114679	−	0.120235i
$567$	−16.1136	−	2.71589i	−0.676706	−	0.114057i
$568$	−36.2500	−	10.6312i	−1.52102	−	0.446075i
$569$	6.63095	+	11.4851i	0.277984	+	0.481482i	0.970884	−	0.239552i	$-0.0770005\pi$
$569$	6.63095	+	11.4851i	0.277984	+	0.481482i	−0.692900	+	0.721034i	$0.743667\pi$
$570$	−11.8031	+	1.48268i	−0.494377	+	0.0621026i
$571$	−23.4262	−	13.5251i	−0.980357	−	0.566009i	−0.0779788	−	0.996955i	$-0.524847\pi$
$571$	−23.4262	−	13.5251i	−0.980357	−	0.566009i	−0.902378	+	0.430946i	$0.858180\pi$
$572$	29.6867	−	34.2753i	1.24126	−	1.43312i
$573$	11.2965	+	12.2813i	0.471917	+	0.513058i
$574$	5.04099	+	11.0351i	0.210407	+	0.460595i
$575$	−0.470166			−0.0196073
$576$	23.7961	+	3.12169i	0.991505	+	0.130070i
$577$	−4.78434			−0.199174			−0.0995872	−	0.995029i	$-0.531752\pi$
$577$	−4.78434			−0.199174			−0.0995872	+	0.995029i	$0.531752\pi$
$578$	−7.80559	−	17.0870i	−0.324670	−	0.710724i
$579$	3.61713	−	11.5481i	0.150323	−	0.479922i
$580$	10.9134	−	12.6003i	0.453156	−	0.523198i
$581$	−5.66760	−	3.27219i	−0.235132	−	0.135753i
$582$	−13.2992	+	31.5756i	−0.551269	+	1.30885i
$583$	21.9406	+	38.0023i	0.908689	+	1.57390i
$584$	31.3729	+	9.20087i	1.29822	+	0.380735i
$585$	−26.0172	−	18.0713i	−1.07568	−	0.747157i
$586$	4.58148	−	48.0343i	0.189259	−	1.98428i
$587$	−37.0796	+	21.4079i	−1.53044	+	0.883598i	−0.531095	+	0.847312i	$0.678219\pi$
$587$	−37.0796	+	21.4079i	−1.53044	+	0.883598i	−0.999341	+	0.0362861i	$0.988447\pi$
$588$	6.74348	+	10.9137i	0.278097	+	0.450074i
$589$	9.80179	+	5.65906i	0.403876	+	0.233178i
$590$	6.59449	−	9.26279i	0.271491	−	0.381343i
$591$	1.63270	+	7.29935i	0.0671602	+	0.300255i
$592$	31.6105	−	4.55885i	1.29918	−	0.187368i
$593$	−0.825572			−0.0339022			−0.0169511	−	0.999856i	$-0.505396\pi$
$593$	−0.825572			−0.0339022			−0.0169511	+	0.999856i	$0.505396\pi$
$594$	−35.9596	+	1.49227i	−1.47544	+	0.0612286i
$595$			7.98438i			0.327328i
$596$	14.3981	−	4.98671i	0.589768	−	0.204264i
$597$	9.98364	−	2.23311i	0.408603	−	0.0913952i
$598$	−12.3477	−	8.79077i	−0.504936	−	0.359481i
$599$	−0.961228	+	1.66490i	−0.0392747	+	0.0680258i	−0.884995	−	0.465601i	$-0.845838\pi$
$599$	−0.961228	+	1.66490i	−0.0392747	+	0.0680258i	0.845720	+	0.533627i	$0.179171\pi$
$600$	−0.440208	−	0.892136i	−0.0179714	−	0.0364213i
$601$	−21.5937	−	37.4014i	−0.880825	−	1.52563i	−0.850425	−	0.526096i	$-0.823655\pi$
$601$	−21.5937	−	37.4014i	−0.880825	−	1.52563i	−0.0303994	−	0.999538i	$-0.509678\pi$
$602$	−0.621589	+	6.51702i	−0.0253341	+	0.265614i
$603$	−26.6747	−	2.23222i	−1.08628	−	0.0909030i
$604$	−8.91581	−	1.71638i	−0.362779	−	0.0698386i
$605$	−25.6556	+	14.8123i	−1.04305	+	0.602205i
$606$	−2.94780	−	1.24157i	−0.119746	−	0.0504354i
$607$	20.5078	−	35.5206i	0.832386	−	1.44174i	−0.0637546	−	0.997966i	$-0.520307\pi$
$607$	20.5078	−	35.5206i	0.832386	−	1.44174i	0.896141	−	0.443770i	$-0.146359\pi$
$608$	−6.51686	−	10.1284i	−0.264294	−	0.410761i
$609$	−10.9656	−	3.43467i	−0.444347	−	0.139180i
$610$	−2.65709	−	5.81654i	−0.107582	−	0.235505i
$611$		−	18.7022i		−	0.756611i
$612$	−3.12627	+	11.1368i	−0.126372	+	0.450178i
$613$		−	5.05878i		−	0.204322i	−0.994768	−	0.102161i	$-0.967424\pi$
$613$		−	5.05878i		−	0.204322i	0.994768	−	0.102161i	$-0.0325757\pi$
$614$	6.14345	−	2.80642i	0.247930	−	0.113258i
$615$	13.7389	−	12.6372i	0.554007	−	0.509582i
$616$	−17.3626	−	18.1976i	−0.699559	−	0.733201i
$617$	−16.0739	+	27.8408i	−0.647112	+	1.12083i	0.336698	+	0.941613i	$0.390690\pi$
$617$	−16.0739	+	27.8408i	−0.647112	+	1.12083i	−0.983809	+	0.179217i	$0.942643\pi$
$618$	−15.6669	+	1.96804i	−0.630215	+	0.0791663i
$619$	27.3562	−	15.7941i	1.09954	−	0.634820i	0.163440	−	0.986553i	$-0.447741\pi$
$619$	27.3562	−	15.7941i	1.09954	−	0.634820i	0.936100	+	0.351734i	$0.114408\pi$
$620$	−4.58454	+	23.8146i	−0.184120	+	0.956416i
$621$	1.63788	+	11.9186i	0.0657259	+	0.478278i
$622$	−31.4707	−	3.00165i	−1.26186	−	0.120355i
$623$	−2.26924	−	3.93044i	−0.0909153	−	0.157470i
$624$	5.11946	−	31.6604i	0.204942	−	1.26743i
$625$	12.9871	−	22.4942i	0.519482	−	0.899770i
$626$	−2.00803	+	2.82053i	−0.0802569	+	0.112731i
$627$	12.2270	+	13.2929i	0.488298	+	0.530867i
$628$	24.9003	−	8.62411i	0.993631	−	0.344139i
$629$			15.3929i			0.613756i
$630$	−11.3488	+	13.4144i	−0.452149	+	0.534442i
$631$	−15.4885			−0.616586			−0.308293	−	0.951292i	$-0.599758\pi$
$631$	−15.4885			−0.616586			−0.308293	+	0.951292i	$0.599758\pi$
$632$	6.64153	+	27.3380i	0.264186	+	1.08745i
$633$	30.3044	+	9.49205i	1.20449	+	0.377275i
$634$	19.0081	+	13.5325i	0.754909	+	0.537445i
$635$	14.7162	+	8.49638i	0.583993	+	0.337168i
$636$	27.3303	+	14.7087i	1.08372	+	0.583239i
$637$	14.8468	−	8.57182i	0.588253	−	0.339628i
$638$	−25.1942	−	2.40301i	−0.997449	−	0.0951361i
$639$	36.2500	−	17.0707i	1.43403	−	0.675305i
$640$	15.9374	−	20.2976i	0.629980	−	0.802334i
$641$	−15.2248	−	26.3701i	−0.601344	−	1.04156i	−0.992618	−	0.121284i	$-0.961299\pi$
$641$	−15.2248	−	26.3701i	−0.601344	−	1.04156i	0.391274	−	0.920274i	$-0.372034\pi$
$642$	6.05994	−	4.59306i	0.239167	−	0.181273i
$643$	14.5911	+	8.42419i	0.575418	+	0.332218i	0.759310	−	0.650729i	$-0.225537\pi$
$643$	14.5911	+	8.42419i	0.575418	+	0.332218i	−0.183893	+	0.982946i	$0.558870\pi$
$644$	−5.50439	+	6.35518i	−0.216903	+	0.250429i
$645$	9.83009	−	2.19877i	0.387060	−	0.0865764i
$646$	5.27994	−	2.41196i	0.207736	−	0.0948971i
$647$	18.6734			0.734126			0.367063	−	0.930196i	$-0.380363\pi$
$647$	18.6734			0.734126			0.367063	+	0.930196i	$0.380363\pi$
$648$	−21.0820	+	14.2671i	−0.828179	+	0.560463i
$649$	−17.2633			−0.677644
$650$	−1.20922	+	0.552388i	−0.0474293	+	0.0216664i
$651$	16.3146	−	3.64920i	0.639419	−	0.143024i
$652$	−31.1292	−	26.9619i	−1.21912	−	1.05591i
$653$	−31.4276	−	18.1448i	−1.22986	−	0.710059i	−0.262858	−	0.964834i	$-0.584665\pi$
$653$	−31.4276	−	18.1448i	−1.22986	−	0.710059i	−0.967000	+	0.254775i	$0.917999\pi$
$654$	35.3017	−	26.7565i	1.38040	−	1.04626i
$655$	4.11089	+	7.12028i	0.160626	+	0.278212i
$656$	17.5485	+	7.01655i	0.685153	+	0.273950i
$657$	−31.3729	+	14.7740i	−1.22397	+	0.576388i
$658$	−10.3270	−	0.984980i	−0.402588	−	0.0383985i
$659$	−19.3088	+	11.1480i	−0.752166	+	0.434263i	−0.826476	−	0.562972i	$-0.809658\pi$
$659$	−19.3088	+	11.1480i	−0.752166	+	0.434263i	0.0743103	+	0.997235i	$0.476324\pi$
$660$	−18.3404	+	34.0782i	−0.713899	+	1.32649i
$661$	−5.19793	−	3.00103i	−0.202176	−	0.116726i	0.395494	−	0.918469i	$-0.370573\pi$
$661$	−5.19793	−	3.00103i	−0.202176	−	0.116726i	−0.597670	+	0.801742i	$0.703907\pi$
$662$	0.437935	+	0.311781i	0.0170208	+	0.0121177i
$663$	14.7509	+	4.62032i	0.572877	+	0.179438i
$664$	−9.90671	+	2.40674i	−0.384455	+	0.0933998i
$665$	8.81762			0.341933
$666$	−21.8792	+	25.8613i	−0.847801	+	1.00211i
$667$			8.45996i			0.327571i
$668$	3.32394	+	9.59717i	0.128607	+	0.371326i
$669$	−6.17388	−	6.71211i	−0.238696	−	0.259505i
$670$	−16.6933	+	23.4478i	−0.644919	+	0.905869i
$671$	−4.85442	+	8.40810i	−0.187403	+	0.324591i
$672$	−17.2126	−	4.49430i	−0.663990	−	0.173371i
$673$	−3.70444	−	6.41629i	−0.142796	−	0.247330i	0.785753	−	0.618541i	$-0.212276\pi$
$673$	−3.70444	−	6.41629i	−0.142796	−	0.247330i	−0.928548	+	0.371211i	$0.878943\pi$
$674$	−7.09183	−	0.676414i	−0.273167	−	0.0260545i
$675$	0.977130	+	0.398269i	0.0376098	+	0.0153294i
$676$	−16.5539	−	3.18679i	−0.636689	−	0.122569i
$677$	−8.57613	+	4.95143i	−0.329607	+	0.190299i	−0.655667	−	0.755050i	$-0.727612\pi$
$677$	−8.57613	+	4.95143i	−0.329607	+	0.190299i	0.326059	+	0.945349i	$0.394279\pi$
$678$	−6.88861	+	0.865334i	−0.264556	+	0.0332329i
$679$	12.6981	−	21.9938i	0.487309	−	0.844043i
$680$	8.58620	+	8.99910i	0.329266	+	0.345100i
$681$	−2.26154	+	2.08020i	−0.0866626	+	0.0797133i
$682$	33.4916	−	15.2995i	1.28246	−	0.585847i
$683$		−	39.0736i		−	1.49511i	−0.664200	−	0.747555i	$-0.731228\pi$
$683$		−	39.0736i		−	1.49511i	0.664200	−	0.747555i	$-0.268772\pi$
$684$	12.2990	+	3.45252i	0.470265	+	0.132011i
$685$		−	26.8316i		−	1.02518i
$686$	−11.4197	−	24.9985i	−0.436006	−	0.954447i
$687$	6.31139	+	1.97687i	0.240794	+	0.0754224i
$688$	6.30765	+	8.01369i	0.240477	+	0.305519i
$689$	20.7376	−	35.9185i	0.790039	−	1.36839i
$690$	11.9220	+	5.02140i	0.453865	+	0.191161i
$691$	−2.07502	+	1.19801i	−0.0789375	+	0.0455746i	−0.538949	−	0.842338i	$-0.681179\pi$
$691$	−2.07502	+	1.19801i	−0.0789375	+	0.0455746i	0.460012	+	0.887913i	$0.347845\pi$
$692$	4.81962	−	25.0357i	0.183215	−	0.951715i
$693$	26.5846	+	2.22468i	1.00986	+	0.0845086i
$694$	−1.30294	+	13.6606i	−0.0494590	+	0.518551i
$695$	−14.5391	−	25.1825i	−0.551500	−	0.955227i
$696$	−16.0527	+	7.92091i	−0.608476	+	0.300241i
$697$	−4.55443	+	7.88850i	−0.172511	+	0.298798i
$698$	34.7526	+	24.7416i	1.31541	+	0.936483i
$699$	−34.3478	+	7.68281i	−1.29915	+	0.290591i
$700$	0.241332	+	0.696796i	0.00912150	+	0.0263364i
$701$			30.9184i			1.16777i	0.811836	+	0.583885i	$0.198468\pi$
$701$			30.9184i			1.16777i	−0.811836	+	0.583885i	$0.801532\pi$
$702$	18.2154	+	28.7291i	0.687496	+	1.08431i
$703$	16.9993			0.641141
$704$	−39.1384	−	1.83895i	−1.47508	−	0.0693079i
$705$	3.48421	+	15.5769i	0.131223	+	0.586662i
$706$	−21.7149	+	30.5013i	−0.817252	+	1.14793i
$707$	2.05327	+	1.18546i	0.0772212	+	0.0445837i
$708$	−10.3873	+	6.41820i	−0.390378	+	0.241211i
$709$	4.46959	−	2.58052i	0.167859	−	0.0969133i	−0.413717	−	0.910406i	$-0.635770\pi$
$709$	4.46959	−	2.58052i	0.167859	−	0.0969133i	0.581576	+	0.813492i	$0.302436\pi$
$710$	4.09084	−	42.8902i	0.153526	−	1.60964i
$711$	−24.5078	−	17.0229i	−0.919115	−	0.638410i
$712$	−6.78434	−	1.98967i	−0.254254	−	0.0745661i
$713$	−6.15406	−	10.6591i	−0.230471	−	0.399188i
$714$	3.32812	−	7.90179i	0.124552	−	0.295717i
$715$	44.7870	+	25.8578i	1.67494	+	0.967027i
$716$	13.3342	+	11.5491i	0.498322	+	0.431610i
$717$	9.00631	−	28.7536i	0.336347	−	1.07382i
$718$	−13.7868	−	30.1802i	−0.514518	−	1.12631i
$719$	14.7871			0.551465			0.275733	−	0.961234i	$-0.411080\pi$
$719$	14.7871			0.551465			0.275733	+	0.961234i	$0.411080\pi$
$720$	1.63434	+	27.3234i	0.0609083	+	1.01828i
$721$	11.7041			0.435884
$722$	8.50120	+	18.6097i	0.316382	+	0.692582i
$723$	−16.0785	−	17.4802i	−0.597965	−	0.650095i
$724$	−23.3372	−	20.2130i	−0.867320	−	0.751208i
$725$	0.642593	+	0.371001i	0.0238653	+	0.0137786i
$726$	31.5644	−	3.96506i	1.17147	−	0.147157i
$727$	−1.06681	−	1.84777i	−0.0395658	−	0.0685299i	0.845564	−	0.533873i	$-0.179264\pi$
$727$	−1.06681	−	1.84777i	−0.0395658	−	0.0685299i	−0.885130	+	0.465344i	$0.845931\pi$
$728$	−6.69012	+	22.8118i	−0.247952	+	0.845463i
$729$	6.69210	−	26.1575i	0.247855	−	0.968797i
$730$	−3.54046	+	37.1198i	−0.131038	+	1.37386i
$731$	−4.25675	+	2.45764i	−0.157442	+	0.0908990i
$732$	0.205098	+	6.86393i	0.00758065	+	0.253698i
$733$	−22.2298	−	12.8344i	−0.821076	−	0.474048i	0.0297113	−	0.999559i	$-0.490541\pi$
$733$	−22.2298	−	12.8344i	−0.821076	−	0.474048i	−0.850787	+	0.525510i	$0.823875\pi$
$734$	−15.7905	+	22.1797i	−0.582837	+	0.818667i
$735$	−10.7689	+	9.90536i	−0.397217	+	0.365365i
$736$	0.630266	+	13.0821i	0.0232319	+	0.482214i
$737$	43.7003			1.60972
$738$	−18.8644	+	6.77973i	−0.694407	+	0.249565i
$739$		−	5.46282i		−	0.200953i	−0.994939	−	0.100476i	$-0.967963\pi$
$739$		−	5.46282i		−	0.200953i	0.994939	−	0.100476i	$-0.0320367\pi$
$740$	11.9209	+	34.4192i	0.438222	+	1.26527i
$741$	5.10249	−	16.2903i	0.187445	−	0.598438i
$742$	−18.7413	−	13.3426i	−0.688015	−	0.489821i
$743$	−16.8170	+	29.1279i	−0.616955	+	1.06860i	0.373083	+	0.927798i	$0.378301\pi$
$743$	−16.8170	+	29.1279i	−0.616955	+	1.06860i	−0.990038	+	0.140800i	$0.955033\pi$
$744$	14.4637	−	21.6573i	0.530266	−	0.793994i
$745$	8.68910	+	15.0500i	0.318344	+	0.551388i
$746$	−1.40972	+	14.7802i	−0.0516137	+	0.541141i
$747$	6.16874	−	8.88109i	0.225702	−	0.324942i
$748$	3.56987	−	18.5438i	0.130527	−	0.678029i
$749$	−4.88115	+	2.81813i	−0.178353	+	0.102972i
$750$	−21.3600	+	16.1896i	−0.779958	+	0.591160i
$751$	−12.6727	+	21.9498i	−0.462435	+	0.800961i	−0.999082	−	0.0428462i	$-0.986357\pi$
$751$	−12.6727	+	21.9498i	−0.462435	+	0.800961i	0.536647	+	0.843807i	$0.319691\pi$
$752$	−12.6986	+	9.99521i	−0.463072	+	0.364488i
$753$	−1.70419	−	7.61897i	−0.0621042	−	0.277651i
$754$	9.93943	+	21.7581i	0.361973	+	0.792383i
$755$		−	10.3553i		−	0.376868i
$756$	16.8230	−	8.54510i	0.611845	−	0.310782i
$757$			3.95103i			0.143603i	0.997419	+	0.0718014i	$0.0228748\pi$
$757$			3.95103i			0.143603i	−0.997419	+	0.0718014i	$0.977125\pi$
$758$	45.6915	−	20.8726i	1.65959	−	0.758126i
$759$	−4.28726	−	19.1672i	−0.155618	−	0.695724i
$760$	9.93823	−	9.48224i	0.360498	−	0.343957i
$761$	−23.3979	+	40.5264i	−0.848175	+	1.46908i	0.0346607	+	0.999399i	$0.488965\pi$
$761$	−23.3979	+	40.5264i	−0.848175	+	1.46908i	−0.882835	+	0.469682i	$0.844368\pi$
$762$	−11.0224	−	14.5426i	−0.399299	−	0.526823i
$763$	−28.4347	+	16.4168i	−1.02941	+	0.594328i
$764$	−18.9205	−	3.64239i	−0.684521	−	0.131777i
$765$	−13.1467	−	1.10015i	−0.475318	−	0.0397761i
$766$	50.7928	+	4.84459i	1.83522	+	0.175042i
$767$	8.15835	+	14.1307i	0.294581	+	0.510229i
$768$	−24.2331	+	13.4445i	−0.874438	+	0.485136i
$769$	2.60083	−	4.50478i	0.0937885	−	0.162446i	−0.815314	−	0.579019i	$-0.803436\pi$
$769$	2.60083	−	4.50478i	0.0937885	−	0.162446i	0.909102	+	0.416573i	$0.136769\pi$
$770$	16.6369	−	23.3686i	0.599553	−	0.842147i
$771$	−4.25830	+	13.5951i	−0.153359	+	0.489615i
$772$	4.57311	+	13.2039i	0.164590	+	0.475219i
$773$			38.8477i			1.39725i	0.715486	+	0.698627i	$0.246205\pi$
$773$			38.8477i			1.39725i	−0.715486	+	0.698627i	$0.753795\pi$
$774$	−10.6449	−	1.92144i	−0.382624	−	0.0690648i
$775$	−1.07952			−0.0387773
$776$	−9.33965	−	38.4441i	−0.335274	−	1.38006i
$777$	18.4804	−	16.9985i	0.662981	−	0.609818i
$778$	23.3126	+	16.5970i	0.835798	+	0.595033i
$779$	8.71173	+	5.02972i	0.312130	+	0.180209i
$780$	36.5617	−	1.09249i	1.30912	−	0.0391173i
$781$	−56.6503	+	32.7071i	−2.02711	+	1.17035i
$782$	−6.28399	−	0.599362i	−0.224715	−	0.0214332i
$783$	7.16627	−	17.5821i	0.256102	−	0.628331i
$784$	−13.7549	−	5.49974i	−0.491247	−	0.196419i
$785$	15.0271	+	26.0277i	0.536340	+	0.928968i
$786$	−1.10043	−	8.76016i	−0.0392512	−	0.312465i
$787$	40.8579	+	23.5893i	1.45643	+	0.840869i	0.998833	−	0.0482918i	$-0.0153777\pi$
$787$	40.8579	+	23.5893i	1.45643	+	0.840869i	0.457595	+	0.889161i	$0.348711\pi$
$788$	−6.52851	−	5.65451i	−0.232568	−	0.201434i
$789$	5.89509	+	6.40902i	0.209871	+	0.228167i
$790$	−29.1853	+	13.3323i	−1.03836	+	0.474341i
$791$	5.14621			0.182978
$792$	32.3555	−	26.0809i	1.14970	−	0.926746i
$793$	9.17648			0.325866
$794$	5.13895	−	2.34755i	0.182375	−	0.0833115i
$795$	−10.5806	+	33.7797i	−0.375255	+	1.19804i
$796$	−7.73392	+	8.92932i	−0.274122	+	0.316492i
$797$	−6.35645	−	3.66990i	−0.225157	−	0.129995i	0.383179	−	0.923674i	$-0.374829\pi$
$797$	−6.35645	−	3.66990i	−0.225157	−	0.129995i	−0.608336	+	0.793680i	$0.708163\pi$
$798$	−8.72641	−	3.67544i	−0.308912	−	0.130109i
$799$	−3.89442	−	6.74533i	−0.137775	−	0.238633i
$800$	1.02132	+	0.525828i	0.0361091	+	0.0185908i
$801$	6.78434	−	3.19485i	0.239713	−	0.112884i
$802$	39.4541	+	3.76310i	1.39317	+	0.132880i
$803$	49.0286	−	28.3067i	1.73018	−	0.998920i
$804$	26.2944	−	16.2470i	0.927331	−	0.572989i
$805$	−8.30423	−	4.79445i	−0.292686	−	0.168982i
$806$	−28.3508	−	20.1839i	−0.998614	−	0.710947i
$807$	8.75542	+	39.1431i	0.308205	+	1.37790i
$808$	3.58903	−	0.871921i	0.126262	−	0.0306741i
$809$	2.25520			0.0792887			0.0396443	−	0.999214i	$-0.487378\pi$
$809$	2.25520			0.0792887			0.0396443	+	0.999214i	$0.487378\pi$
$810$	−20.5237	−	20.5347i	−0.721129	−	0.721517i
$811$			15.9986i			0.561785i	0.959739	+	0.280893i	$0.0906305\pi$
$811$			15.9986i			0.561785i	−0.959739	+	0.280893i	$0.909369\pi$
$812$	12.5378	−	4.34242i	0.439992	−	0.152389i
$813$	35.3889	−	7.91569i	1.24114	−	0.277615i
$814$	32.0740	−	45.0519i	1.12419	−	1.57907i
$815$	23.4844	−	40.6761i	0.822622	−	1.42482i
$816$	−4.74630	−	12.4850i	−0.166154	−	0.437062i
$817$	2.71411	+	4.70098i	0.0949548	+	0.164467i
$818$	23.1582	+	2.20881i	0.809707	+	0.0772293i
$819$	−10.7424	−	22.8118i	−0.375371	−	0.797110i
$820$	−4.07470	+	21.1662i	−0.142295	+	0.739154i
$821$	25.2413	−	14.5731i	0.880928	−	0.508604i	0.00996351	−	0.999950i	$-0.496828\pi$
$821$	25.2413	−	14.5731i	0.880928	−	0.508604i	0.870964	+	0.491347i	$0.163495\pi$
$822$	−11.1842	+	26.5540i	−0.390093	+	0.926178i
$823$	−4.15695	+	7.20005i	−0.144902	+	0.250978i	−0.929336	−	0.369234i	$-0.879620\pi$
$823$	−4.15695	+	7.20005i	−0.144902	+	0.250978i	0.784434	+	0.620212i	$0.212953\pi$
$824$	13.1916	−	12.5863i	0.459550	−	0.438465i
$825$	−1.64389	−	0.514906i	−0.0572330	−	0.0179267i
$826$	8.23234	−	3.76066i	0.286440	−	0.130850i
$827$		−	43.5035i		−	1.51277i	−0.654129	−	0.756383i	$-0.726965\pi$
$827$		−	43.5035i		−	1.51277i	0.654129	−	0.756383i	$-0.273035\pi$
$828$	−9.70567	−	9.93891i	−0.337295	−	0.345401i
$829$		−	15.9248i		−	0.553092i	−0.961001	−	0.276546i	$-0.910810\pi$
$829$		−	15.9248i		−	0.553092i	0.961001	−	0.276546i	$-0.0891897\pi$
$830$	−4.83132	−	10.5761i	−0.167698	−	0.367102i
$831$	−28.3636	+	26.0892i	−0.983921	+	0.905023i
$832$	16.9909	+	32.9053i	0.589054	+	1.14079i
$833$	3.56987	−	6.18320i	0.123689	−	0.214235i
$834$	3.89194	+	30.9823i	0.134767	+	1.07283i
$835$	−10.0317	+	5.79180i	−0.347161	+	0.200433i
$836$	−20.4790	−	3.94242i	−0.708282	−	0.136351i
$837$	3.76062	+	27.3656i	0.129986	+	0.945892i
$838$	−3.18741	+	33.4183i	−0.110107	+	1.15442i
$839$	−21.0582	−	36.4739i	−0.727009	−	1.25922i	−0.958142	−	0.286295i	$-0.907576\pi$
$839$	−21.0582	−	36.4739i	−0.727009	−	1.25922i	0.231132	−	0.972922i	$-0.425757\pi$
$840$	1.32233	−	20.2462i	0.0456247	−	0.698559i
$841$	−7.82437	+	13.5522i	−0.269806	+	0.467318i
$842$	−34.5106	−	24.5692i	−1.18931	−	0.846712i
$843$	−21.7635	−	23.6608i	−0.749575	−	0.814922i
$844$	−34.6496	+	12.0007i	−1.19269	+	0.413082i
$845$		−	19.2266i		−	0.661415i
$846$	3.04475	−	16.8681i	0.104681	−	0.579938i
$847$	−23.5806			−0.810238
$848$	−35.4713	+	5.11567i	−1.21809	+	0.175673i
$849$	−3.35836	−	1.05192i	−0.115259	−	0.0361017i
$850$	−0.321102	+	0.451028i	−0.0110137	+	0.0154701i
$851$	−16.0095	−	9.24311i	−0.548800	−	0.316850i
$852$	−21.9264	+	40.7414i	−0.751186	+	1.39578i
$853$	34.2013	−	19.7461i	1.17103	−	0.676095i	0.217108	−	0.976148i	$-0.430338\pi$
$853$	34.2013	−	19.7461i	1.17103	−	0.676095i	0.953923	+	0.300053i	$0.0970043\pi$
$854$	0.483293	−	5.06706i	0.0165379	−	0.173391i
$855$	−1.21496	+	14.5186i	−0.0415509	+	0.496526i
$856$	−2.47094	+	8.42535i	−0.0844549	+	0.287972i
$857$	−12.6170	−	21.8532i	−0.430988	−	0.746493i	0.565971	−	0.824425i	$-0.308501\pi$
$857$	−12.6170	−	21.8532i	−0.430988	−	0.746493i	−0.996959	+	0.0779326i	$0.975168\pi$
$858$	−33.5455	−	44.2589i	−1.14522	−	1.51097i
$859$	−47.5539	−	27.4552i	−1.62252	−	0.936761i	−0.986244	−	0.165297i	$-0.947142\pi$
$859$	−47.5539	−	27.4552i	−1.62252	−	0.936761i	−0.636274	−	0.771463i	$-0.719525\pi$
$860$	−7.61498	+	8.79199i	−0.259669	+	0.299805i
$861$	14.5003	−	3.24338i	0.494167	−	0.110534i
$862$	−6.48546	−	14.1971i	−0.220896	−	0.483555i
$863$	−54.3877			−1.85138			−0.925689	−	0.378285i	$-0.876514\pi$
$863$	−54.3877			−1.85138			−0.925689	+	0.378285i	$0.876514\pi$
$864$	9.77177	−	27.7221i	0.332442	−	0.943124i
$865$	29.0778			0.988675
$866$	20.5313	+	44.9443i	0.697681	+	1.52727i
$867$	−22.4525	+	5.02212i	−0.762527	+	0.170560i
$868$	−12.6383	+	14.5917i	−0.428971	+	0.495275i
$869$	42.1888	+	24.3577i	1.43116	+	0.826278i
$870$	−12.3320	−	16.2704i	−0.418093	−	0.551620i
$871$	−20.6521	−	35.7704i	−0.699768	−	1.21203i
$872$	−14.3942	+	49.0812i	−0.487451	+	1.66210i
$873$	34.4641	+	23.9385i	1.16643	+	0.810196i
$874$	−0.661911	+	6.93977i	−0.0223895	+	0.234741i
$875$	17.2050	−	9.93334i	0.581637	−	0.335808i
$876$	18.9764	−	35.2600i	0.641154	−	1.19133i
$877$	−5.90001	−	3.40637i	−0.199229	−	0.115025i	0.397067	−	0.917790i	$-0.370028\pi$
$877$	−5.90001	−	3.40637i	−0.199229	−	0.115025i	−0.596296	+	0.802765i	$0.703361\pi$
$878$	10.8023	−	15.1732i	0.364561	−	0.512071i
$879$	−56.3951	−	17.6642i	−1.90216	−	0.595800i
$880$	−6.37875	−	44.2294i	−0.215028	−	1.49097i
$881$	−43.2881			−1.45841			−0.729207	−	0.684293i	$-0.760111\pi$
$881$	−43.2881			−1.45841			−0.729207	+	0.684293i	$0.760111\pi$
$882$	14.7863	−	5.31411i	0.497882	−	0.178935i
$883$			31.1510i			1.04832i	0.851621	+	0.524158i	$0.175620\pi$
$883$			31.1510i			1.04832i	−0.851621	+	0.524158i	$0.824380\pi$
$884$	−16.8659	+	5.84143i	−0.567262	+	0.196469i
$885$	−9.42756	−	10.2494i	−0.316904	−	0.344531i
$886$	31.5080	+	22.4316i	1.05853	+	0.753605i
$887$	−24.8886	+	43.1083i	−0.835677	+	1.44743i	0.0578015	+	0.998328i	$0.481591\pi$
$887$	−24.8886	+	43.1083i	−0.835677	+	1.44743i	−0.893478	+	0.449107i	$0.851742\pi$
$888$	2.54929	−	39.0322i	0.0855486	−	1.30983i
$889$	6.76295	+	11.7138i	0.226822	+	0.392867i
$890$	0.765617	−	8.02708i	0.0256636	−	0.269068i
$891$	−7.32608	+	43.4662i	−0.245433	+	1.45617i
$892$	10.3407	+	1.99068i	0.346231	+	0.0666529i
$893$	−7.44926	+	4.30083i	−0.249280	+	0.143922i
$894$	−2.32596	−	18.5162i	−0.0777918	−	0.619273i
$895$	−10.0595	+	17.4236i	−0.336253	+	0.582407i
$896$	19.0645	−	7.64902i	0.636900	−	0.255536i
$897$	−13.6630	+	12.5674i	−0.456194	+	0.419613i
$898$	−8.12242	−	17.7805i	−0.271049	−	0.593344i
$899$			19.4243i			0.647838i
$900$	−1.18056	+	0.301354i	−0.0393520	+	0.0100451i
$901$		−	17.2730i		−	0.575447i
$902$	29.7670	−	13.5980i	0.991133	−	0.452765i
$903$	7.65135	+	2.39658i	0.254621	+	0.0797532i
$904$	5.80024	−	5.53411i	0.192913	−	0.184062i
$905$	17.6059	−	30.4944i	0.585241	−	1.01367i
$906$	−4.31639	+	10.2482i	−0.143402	+	0.340473i
$907$	16.6712	−	9.62515i	0.553559	−	0.319598i	−0.196997	−	0.980404i	$-0.563119\pi$
$907$	16.6712	−	9.62515i	0.553559	−	0.319598i	0.750556	+	0.660806i	$0.229786\pi$
$908$	0.670731	−	3.48413i	0.0222590	−	0.115625i
$909$	−2.23483	+	3.21747i	−0.0741245	+	0.106717i
$910$	−26.9905	−	2.57433i	−0.894725	−	0.0853383i
$911$	11.1396	+	19.2944i	0.369072	+	0.639252i	0.989421	−	0.145074i	$-0.0463421\pi$
$911$	11.1396	+	19.2944i	0.369072	+	0.639252i	−0.620348	+	0.784326i	$0.713009\pi$
$912$	−13.7879	+	5.24162i	−0.456563	+	0.173567i
$913$	−8.82669	+	15.2883i	−0.292121	+	0.505968i
$914$	4.69491	−	6.59459i	0.155294	−	0.218130i
$915$	−7.64302	+	1.70957i	−0.252670	+	0.0565166i
$916$	−7.21633	+	2.49934i	−0.238434	+	0.0825807i
$917$			6.54438i			0.216114i
$918$	12.5521	+	6.56868i	0.414281	+	0.216799i
$919$	28.0122			0.924039			0.462019	−	0.886870i	$-0.347125\pi$
$919$	28.0122			0.924039			0.462019	+	0.886870i	$0.347125\pi$
$920$	−14.5154	+	3.52639i	−0.478559	+	0.116262i
$921$	−1.80565	−	8.07259i	−0.0594983	−	0.266001i
$922$	25.7702	+	18.3467i	0.848696	+	0.604215i
$923$	53.5440	+	30.9136i	1.76242	+	1.01753i
$924$	−26.2056	+	16.1922i	−0.862099	+	0.532683i
$925$	−1.40416	+	0.810691i	−0.0461684	+	0.0266554i
$926$	52.2958	+	4.98794i	1.71855	+	0.163914i
$927$	−1.61269	+	19.2714i	−0.0529677	+	0.632955i
$928$	9.46151	−	18.3772i	0.310589	−	0.603260i
$929$	−3.94220	−	6.82809i	−0.129339	−	0.224022i	0.794081	−	0.607811i	$-0.207952\pi$
$929$	−3.94220	−	6.82809i	−0.129339	−	0.224022i	−0.923421	+	0.383789i	$0.874619\pi$
$930$	27.3734	+	11.5293i	0.897609	+	0.378060i
$931$	−6.82847	−	3.94242i	−0.223794	−	0.129208i
$932$	26.6078	−	30.7205i	0.871569	−	1.00628i
$933$	−11.5731	+	36.9484i	−0.378886	+	1.20964i
$934$	−29.1808	+	13.3303i	−0.954827	+	0.436179i
$935$	21.5378			0.704361
$936$	−36.6389	−	14.1588i	−1.19758	−	0.462795i
$937$	−8.98600			−0.293560			−0.146780	−	0.989169i	$-0.546891\pi$
$937$	−8.98600			−0.293560			−0.146780	+	0.989169i	$0.546891\pi$
$938$	−20.8393	+	9.51973i	−0.680429	+	0.310830i
$939$	2.87070	+	3.12096i	0.0936817	+	0.101849i
$940$	−13.9320	−	12.0668i	−0.454410	−	0.393577i
$941$	21.0227	+	12.1375i	0.685322	+	0.395671i	0.801857	−	0.597516i	$-0.203845\pi$
$941$	21.0227	+	12.1375i	0.685322	+	0.395671i	−0.116535	+	0.993187i	$0.537179\pi$
$942$	−4.02256	−	32.0222i	−0.131062	−	1.04334i
$943$	−5.46967	−	9.47375i	−0.178117	−	0.308508i
$944$	5.23445	−	13.0914i	0.170367	−	0.426090i
$945$	13.1971	+	16.9985i	0.429302	+	0.552961i
$946$	17.5796	+	1.67673i	0.571561	+	0.0545151i
$947$	1.71382	−	0.989473i	0.0556916	−	0.0321536i	−0.471896	−	0.881654i	$-0.656430\pi$
$947$	1.71382	−	0.989473i	0.0556916	−	0.0321536i	0.527587	+	0.849501i	$0.323097\pi$
$948$	34.4406	−	1.02911i	1.11858	−	0.0334239i
$949$	−46.3402	−	26.7545i	−1.50427	−	0.868488i
$950$	0.498097	+	0.354612i	0.0161604	+	0.0115051i
$951$	21.0328	−	19.3462i	0.682036	−	0.627345i
$952$	2.33725	+	9.62065i	0.0757506	+	0.311807i
$953$	28.9674			0.938347			0.469173	−	0.883106i	$-0.344552\pi$
$953$	28.9674			0.938347			0.469173	+	0.883106i	$0.344552\pi$
$954$	24.5515	−	29.0200i	0.794884	−	0.939556i
$955$		−	21.9753i		−	0.711104i
$956$	11.3866	+	32.8764i	0.368269	+	1.06330i
$957$	−9.26498	+	29.5795i	−0.299494	+	0.956169i
$958$	−21.5838	+	30.3171i	−0.697341	+	0.979503i
$959$	10.6787	−	18.4960i	0.344833	−	0.597268i
$960$	−20.2818	−	24.2412i	−0.654593	−	0.782382i
$961$	1.37008	+	2.37304i	0.0441961	+	0.0765498i
$962$	−52.0343	−	4.96300i	−1.67765	−	0.160014i
$963$	−3.96762	−	8.42535i	−0.127855	−	0.271503i
$964$	26.9300	+	5.18428i	0.867355	+	0.166975i
$965$	−13.8017	+	7.96842i	−0.444293	+	0.256512i
$966$	6.21987	+	8.20630i	0.200121	+	0.264033i
$967$	0.00531192	−	0.00920052i	0.000170820	−	0.000295869i	−0.865940	−	0.500148i	$-0.833279\pi$
$967$	0.00531192	−	0.00920052i	0.000170820	−	0.000295869i	0.866111	+	0.499852i	$0.166612\pi$
$968$	−26.5774	+	25.3579i	−0.854229	+	0.815035i
$969$	−1.55185	−	6.93791i	−0.0498527	−	0.222878i
$970$	41.0418	−	18.7485i	1.31777	−	0.601979i
$971$			17.0984i			0.548715i	0.961628	+	0.274357i	$0.0884651\pi$
$971$			17.0984i			0.548715i	−0.961628	+	0.274357i	$0.911535\pi$
$972$	11.7519	+	28.8772i	0.376943	+	0.926237i
$973$		−	23.1457i		−	0.742017i
$974$	−14.1258	−	30.9224i	−0.452620	−	0.990817i
$975$	0.355407	+	1.58893i	0.0113821	+	0.0508864i
$976$	−4.90427	−	6.23074i	−0.156982	−	0.199441i
$977$	−5.50612	+	9.53688i	−0.176156	+	0.305112i	−0.940561	−	0.339625i	$-0.889700\pi$
$977$	−5.50612	+	9.53688i	−0.176156	+	0.305112i	0.764404	+	0.644737i	$0.223033\pi$
$978$	−40.1965	+	30.4664i	−1.28534	+	0.974209i
$979$	−10.6023	+	6.12126i	−0.338852	+	0.195636i
$980$	3.19385	−	16.5905i	0.102024	−	0.529966i
$981$	−23.1131	−	49.0812i	−0.737943	−	1.56704i
$982$	4.22133	−	44.2583i	0.134708	−	1.41234i
$983$	22.7443	+	39.3943i	0.725432	+	1.25648i	0.958796	+	0.284095i	$0.0916932\pi$
$983$	22.7443	+	39.3943i	0.725432	+	1.25648i	−0.233364	+	0.972389i	$0.574973\pi$
$984$	12.8552	−	19.2488i	0.409809	−	0.613628i
$985$	4.92521	−	8.53071i	0.156930	−	0.271811i
$986$	8.11560	+	5.77777i	0.258453	+	0.184002i
$987$	−3.79767	+	12.1245i	−0.120881	+	0.385926i
$988$	6.45103	+	18.6260i	0.205235	+	0.592572i
$989$		−	5.90304i		−	0.187706i
$990$	36.1852	+	30.6134i	1.15004	+	0.972957i
$991$	3.93737			0.125075			0.0625374	−	0.998043i	$-0.480081\pi$
$991$	3.93737			0.125075			0.0625374	+	0.998043i	$0.480081\pi$
$992$	1.44711	+	30.0370i	0.0459458	+	0.953675i
$993$	0.484583	−	0.445725i	0.0153778	−	0.0141447i
$994$	19.8898	−	27.9378i	0.630868	−	0.886132i
$995$	−11.6678	−	6.73642i	−0.369895	−	0.213559i
$996$	0.372926	+	12.4805i	0.0118166	+	0.395461i
$997$	−2.16558	+	1.25030i	−0.0685847	+	0.0395974i	−0.533900	−	0.845547i	$-0.679274\pi$
$997$	−2.16558	+	1.25030i	−0.0685847	+	0.0395974i	0.465316	+	0.885145i	$0.345941\pi$
$998$	0.787897	−	8.26066i	0.0249404	−	0.261487i
$999$	25.4424	+	32.7710i	0.804963	+	1.03683i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	72.2.n.b.13.5	✓	16
3.2	odd	2		216.2.n.b.37.4		16
4.3	odd	2		288.2.r.b.49.1		16
8.3	odd	2		288.2.r.b.49.8		16
8.5	even	2	inner	72.2.n.b.13.6	yes	16
9.2	odd	6		216.2.n.b.181.3		16
9.4	even	3		648.2.d.j.325.1		8
9.5	odd	6		648.2.d.k.325.8		8
9.7	even	3	inner	72.2.n.b.61.6	yes	16
12.11	even	2		864.2.r.b.145.7		16
24.5	odd	2		216.2.n.b.37.3		16
24.11	even	2		864.2.r.b.145.2		16
36.7	odd	6		288.2.r.b.241.8		16
36.11	even	6		864.2.r.b.721.2		16
36.23	even	6		2592.2.d.k.1297.2		8
36.31	odd	6		2592.2.d.j.1297.7		8
72.5	odd	6		648.2.d.k.325.7		8
72.11	even	6		864.2.r.b.721.7		16
72.13	even	6		648.2.d.j.325.2		8
72.29	odd	6		216.2.n.b.181.4		16
72.43	odd	6		288.2.r.b.241.1		16
72.59	even	6		2592.2.d.k.1297.7		8
72.61	even	6	inner	72.2.n.b.61.5	yes	16
72.67	odd	6		2592.2.d.j.1297.2		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
72.2.n.b.13.5	✓	16	1.1	even	1	trivial
72.2.n.b.13.6	yes	16	8.5	even	2	inner
72.2.n.b.61.5	yes	16	72.61	even	6	inner
72.2.n.b.61.6	yes	16	9.7	even	3	inner
216.2.n.b.37.3		16	24.5	odd	2
216.2.n.b.37.4		16	3.2	odd	2
216.2.n.b.181.3		16	9.2	odd	6
216.2.n.b.181.4		16	72.29	odd	6
288.2.r.b.49.1		16	4.3	odd	2
288.2.r.b.49.8		16	8.3	odd	2
288.2.r.b.241.1		16	72.43	odd	6
288.2.r.b.241.8		16	36.7	odd	6
648.2.d.j.325.1		8	9.4	even	3
648.2.d.j.325.2		8	72.13	even	6
648.2.d.k.325.7		8	72.5	odd	6
648.2.d.k.325.8		8	9.5	odd	6
864.2.r.b.145.2		16	24.11	even	2
864.2.r.b.145.7		16	12.11	even	2
864.2.r.b.721.2		16	36.11	even	6
864.2.r.b.721.7		16	72.11	even	6
2592.2.d.j.1297.2		8	72.67	odd	6
2592.2.d.j.1297.7		8	36.31	odd	6
2592.2.d.k.1297.2		8	36.23	even	6
2592.2.d.k.1297.7		8	72.59	even	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 72 = 2^{3} \cdot 3^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	72.n (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.587625 + 1.28635i) q^{2} +(1.69028 - 0.378078i) q^{3} +(-1.30939 + 1.51178i) q^{4} +(-1.97542 - 1.14051i) q^{5} +(1.47959 + 1.95213i) q^{6} +(-0.907824 - 1.57240i) q^{7} +(-2.71411 - 0.795980i) q^{8} +(2.71411 - 1.27812i) q^{9} +(0.306290 - 3.21128i) q^{10} +(-4.24153 + 2.44885i) q^{11} +(-1.64168 + 3.05039i) q^{12} +(4.00895 + 2.31457i) q^{13} +(1.48919 - 2.09176i) q^{14} +(-3.77023 - 1.18092i) q^{15} +(-0.570971 - 3.95904i) q^{16} +1.92788 q^{17} +(3.23899 + 2.74025i) q^{18} -2.12907i q^{19} +(4.31082 - 1.49303i) q^{20} +(-2.12897 - 2.31457i) q^{21} +(-5.64250 - 4.01709i) q^{22} +(-1.15765 + 2.00511i) q^{23} +(-4.88856 - 0.319285i) q^{24} +(0.101535 + 0.175863i) q^{25} +(-0.621589 + 6.51702i) q^{26} +(4.10439 - 3.18653i) q^{27} +(3.56582 + 0.686457i) q^{28} +(3.16440 - 1.82697i) q^{29} +(-0.696398 - 5.54378i) q^{30} +(-2.65800 + 4.60379i) q^{31} +(4.75719 - 3.06090i) q^{32} +(-6.24353 + 5.74287i) q^{33} +(1.13287 + 2.47993i) q^{34} +4.14154i q^{35} +(-1.62161 + 5.77671i) q^{36} +7.98438i q^{37} +(2.73873 - 1.25109i) q^{38} +(7.65135 + 2.39658i) q^{39} +(4.45370 + 4.66788i) q^{40} +(-2.36240 + 4.09180i) q^{41} +(1.72631 - 4.09870i) q^{42} +(-2.20800 + 1.27479i) q^{43} +(1.85171 - 9.61877i) q^{44} +(-6.81924 - 0.570655i) q^{45} +(-3.25953 - 0.310892i) q^{46} +(-2.02005 - 3.49884i) q^{47} +(-2.46193 - 6.47603i) q^{48} +(1.85171 - 3.20726i) q^{49} +(-0.166557 + 0.233951i) q^{50} +(3.25866 - 0.728888i) q^{51} +(-8.74843 + 3.02998i) q^{52} -8.95958i q^{53} +(6.51083 + 3.40721i) q^{54} +11.1718 q^{55} +(1.21234 + 4.99028i) q^{56} +(-0.804954 - 3.59873i) q^{57} +(4.20960 + 2.99696i) q^{58} +(3.05255 + 1.76239i) q^{59} +(6.72202 - 4.15347i) q^{60} +(1.71675 - 0.991165i) q^{61} +(-7.48399 - 0.713818i) q^{62} +(-4.47365 - 3.10736i) q^{63} +(6.73283 + 4.32076i) q^{64} +(-5.27959 - 9.14451i) q^{65} +(-11.0562 - 4.65671i) q^{66} +(-7.72723 - 4.46132i) q^{67} +(-2.52435 + 2.91453i) q^{68} +(-1.19867 + 3.82688i) q^{69} +(-5.32747 + 2.43367i) q^{70} +13.3561 q^{71} +(-8.38377 + 1.30858i) q^{72} -11.5592 q^{73} +(-10.2707 + 4.69182i) q^{74} +(0.238112 + 0.258870i) q^{75} +(3.21869 + 2.78779i) q^{76} +(7.70112 + 4.44625i) q^{77} +(1.41328 + 11.2506i) q^{78} +(-4.97330 - 8.61401i) q^{79} +(-3.38742 + 8.47198i) q^{80} +(5.73283 - 6.93791i) q^{81} +(-6.65170 - 0.634435i) q^{82} +(3.12153 - 1.80221i) q^{83} +(6.28679 - 0.187853i) q^{84} +(-3.80838 - 2.19877i) q^{85} +(-2.93730 - 2.09116i) q^{86} +(4.65800 - 4.28448i) q^{87} +(13.4612 - 3.27028i) q^{88} +2.49965 q^{89} +(-3.27309 - 9.10726i) q^{90} -8.40489i q^{91} +(-1.51547 - 4.37559i) q^{92} +(-2.75218 + 8.78664i) q^{93} +(3.31370 - 4.65450i) q^{94} +(-2.42823 + 4.20582i) q^{95} +(6.88375 - 6.97237i) q^{96} +(6.99370 + 12.1134i) q^{97} +(5.21376 + 0.497285i) q^{98} +(-8.38208 + 12.0676i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + q^{2} - q^{4} - 7 q^{6} + 6 q^{7} - 2 q^{8} + 2 q^{9} - 16 q^{10} - 16 q^{12} + 16 q^{14} - 10 q^{15} - 9 q^{16} - 28 q^{17} + 4 q^{18} - 8 q^{20} + q^{22} - 10 q^{23} + 7 q^{24} + 2 q^{25} + 28 q^{26}+ \cdots + 66 q^{98}+O(q^{100}) \) 16 * q + q^2 - q^4 - 7 * q^6 + 6 * q^7 - 2 * q^8 + 2 * q^9 - 16 * q^10 - 16 * q^12 + 16 * q^14 - 10 * q^15 - 9 * q^16 - 28 * q^17 + 4 * q^18 - 8 * q^20 + q^22 - 10 * q^23 + 7 * q^24 + 2 * q^25 + 28 * q^26 + 4 * q^28 + 22 * q^30 - 10 * q^31 + 11 * q^32 + q^34 + 27 * q^36 + 23 * q^38 + 2 * q^39 + 6 * q^40 - 8 * q^41 + 8 * q^42 + 18 * q^44 - 20 * q^46 + 6 * q^47 + 39 * q^48 + 18 * q^49 - 23 * q^50 - 8 * q^52 - 29 * q^54 - 4 * q^55 + 10 * q^56 + 10 * q^57 - 14 * q^58 + 6 * q^60 - 52 * q^62 + 2 * q^63 + 26 * q^64 - 14 * q^65 - 72 * q^66 - 39 * q^68 + 72 * q^71 - 77 * q^72 - 44 * q^73 - 38 * q^74 + 5 * q^76 + 10 * q^78 - 30 * q^79 - 96 * q^80 + 10 * q^81 + 38 * q^82 - 28 * q^84 + 7 * q^86 + 42 * q^87 + 31 * q^88 + 64 * q^89 + 64 * q^90 - 30 * q^92 - 12 * q^94 + 44 * q^95 - 26 * q^96 + 66 * q^98

Introduction

L-functions

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