LMFDB - Embedded newform 84.2.n.a.11.12

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [84,2,Mod(11,84)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(84, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 3, 4]))

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

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

chi := DirichletCharacter("84.11");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 84 = 2^{2} \cdot 3 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	84.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:	$0.670743376979$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$12$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			11.12
Character	$\chi$	$=$	84.11
Dual form			84.2.n.a.23.12

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.32175 - 0.502962i) q^{2} +(-1.03264 - 1.39056i) q^{3} +(1.49406 - 1.32958i) q^{4} +(-1.79791 + 1.03802i) q^{5} +(-2.06429 - 1.31860i) q^{6} +(2.61347 + 0.412056i) q^{7} +(1.30604 - 2.50883i) q^{8} +(-0.867316 + 2.87189i) q^{9} +O(q^{10})$	\(q+(1.32175 - 0.502962i) q^{2} +(-1.03264 - 1.39056i) q^{3} +(1.49406 - 1.32958i) q^{4} +(-1.79791 + 1.03802i) q^{5} +(-2.06429 - 1.31860i) q^{6} +(2.61347 + 0.412056i) q^{7} +(1.30604 - 2.50883i) q^{8} +(-0.867316 + 2.87189i) q^{9} +(-1.85431 + 2.27629i) q^{10} +(-1.99399 + 3.45368i) q^{11} +(-3.39169 - 0.704599i) q^{12} -1.30998 q^{13} +(3.66160 - 0.769840i) q^{14} +(3.30003 + 1.42820i) q^{15} +(0.464417 - 3.97295i) q^{16} +(2.54752 + 1.47081i) q^{17} +(0.298077 + 4.23216i) q^{18} +(-0.949883 + 0.548415i) q^{19} +(-1.30604 + 3.94134i) q^{20} +(-2.12578 - 4.05969i) q^{21} +(-0.898482 + 5.56781i) q^{22} +(-3.75063 - 6.49627i) q^{23} +(-4.83736 + 0.774586i) q^{24} +(-0.345008 + 0.597572i) q^{25} +(-1.73147 + 0.658872i) q^{26} +(4.88916 - 1.75957i) q^{27} +(4.45253 - 2.85919i) q^{28} -0.865568i q^{29} +(5.08015 + 0.227937i) q^{30} +(-3.18742 - 1.84026i) q^{31} +(-1.38440 - 5.48484i) q^{32} +(6.86162 - 0.793650i) q^{33} +(4.10695 + 0.662741i) q^{34} +(-5.12651 + 1.97200i) q^{35} +(2.52260 + 5.44394i) q^{36} +(-2.08850 - 3.61738i) q^{37} +(-0.979678 + 1.20262i) q^{38} +(1.35274 + 1.82161i) q^{39} +(0.256080 + 5.86637i) q^{40} -7.01712i q^{41} +(-4.85162 - 4.29672i) q^{42} +4.27597i q^{43} +(1.61283 + 7.81117i) q^{44} +(-1.42174 - 6.06370i) q^{45} +(-8.22478 - 6.70004i) q^{46} +(3.75063 + 6.49627i) q^{47} +(-6.00420 + 3.45682i) q^{48} +(6.66042 + 2.15379i) q^{49} +(-0.155459 + 0.963368i) q^{50} +(-0.585414 - 5.06129i) q^{51} +(-1.95719 + 1.74173i) q^{52} +(4.27909 + 2.47053i) q^{53} +(5.57726 - 4.78478i) q^{54} -8.27923i q^{55} +(4.44708 - 6.01859i) q^{56} +(1.74349 + 0.754555i) q^{57} +(-0.435348 - 1.14407i) q^{58} +(2.44458 - 4.23414i) q^{59} +(6.82935 - 2.25385i) q^{60} +(-2.05347 - 3.55672i) q^{61} +(-5.13856 - 0.829212i) q^{62} +(-3.45008 + 7.14821i) q^{63} +(-4.58850 - 6.55330i) q^{64} +(2.35524 - 1.35980i) q^{65} +(8.67019 - 4.50015i) q^{66} +(2.09778 + 1.21116i) q^{67} +(5.76170 - 1.18966i) q^{68} +(-5.16042 + 11.9238i) q^{69} +(-5.78413 + 5.18494i) q^{70} +0.901192 q^{71} +(6.07235 + 5.92677i) q^{72} +(-6.50543 + 11.2677i) q^{73} +(-4.57989 - 3.73085i) q^{74} +(1.18723 - 0.137321i) q^{75} +(-0.690016 + 2.08231i) q^{76} +(-6.63432 + 8.20446i) q^{77} +(2.70419 + 1.72734i) q^{78} +(-8.97336 + 5.18077i) q^{79} +(3.28904 + 7.62509i) q^{80} +(-7.49553 - 4.98167i) q^{81} +(-3.52935 - 9.27489i) q^{82} +12.4386 q^{83} +(-8.57373 - 3.23901i) q^{84} -6.10695 q^{85} +(2.15065 + 5.65178i) q^{86} +(-1.20363 + 0.893819i) q^{87} +(6.06049 + 9.51324i) q^{88} +(-7.38393 + 4.26311i) q^{89} +(-4.92900 - 7.29963i) q^{90} +(-3.42360 - 0.539786i) q^{91} +(-14.2410 - 4.71904i) q^{92} +(0.732462 + 6.33262i) q^{93} +(8.22478 + 6.70004i) q^{94} +(1.13854 - 1.97200i) q^{95} +(-6.19741 + 7.58894i) q^{96} +15.3909 q^{97} +(9.88670 - 0.503167i) q^{98} +(-8.18919 - 8.72195i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q - 2 q^{4} - 2 q^{9}+O(q^{10}) $ 24 * q - 2 * q^4 - 2 * q^9	$ 24 q - 2 q^{4} - 2 q^{9} - 10 q^{10} - 12 q^{12} - 24 q^{13} - 10 q^{16} - 10 q^{18} - 6 q^{21} + 28 q^{22} - 14 q^{24} - 12 q^{25} + 10 q^{28} - 14 q^{30} + 10 q^{33} - 8 q^{34} + 44 q^{36} - 8 q^{37} + 34 q^{40} + 38 q^{42} - 18 q^{45} + 24 q^{46} + 8 q^{48} + 16 q^{52} + 38 q^{54} - 4 q^{57} + 14 q^{58} + 14 q^{60} + 4 q^{61} - 68 q^{64} + 30 q^{66} + 36 q^{69} - 90 q^{70} + 20 q^{72} - 24 q^{76} - 104 q^{78} + 26 q^{81} - 68 q^{82} - 76 q^{84} - 40 q^{85} - 34 q^{88} - 40 q^{90} - 6 q^{93} - 24 q^{94} - 62 q^{96} + 72 q^{97}+O(q^{100}) $ 24 * q - 2 * q^4 - 2 * q^9 - 10 * q^10 - 12 * q^12 - 24 * q^13 - 10 * q^16 - 10 * q^18 - 6 * q^21 + 28 * q^22 - 14 * q^24 - 12 * q^25 + 10 * q^28 - 14 * q^30 + 10 * q^33 - 8 * q^34 + 44 * q^36 - 8 * q^37 + 34 * q^40 + 38 * q^42 - 18 * q^45 + 24 * q^46 + 8 * q^48 + 16 * q^52 + 38 * q^54 - 4 * q^57 + 14 * q^58 + 14 * q^60 + 4 * q^61 - 68 * q^64 + 30 * q^66 + 36 * q^69 - 90 * q^70 + 20 * q^72 - 24 * q^76 - 104 * q^78 + 26 * q^81 - 68 * q^82 - 76 * q^84 - 40 * q^85 - 34 * q^88 - 40 * q^90 - 6 * q^93 - 24 * q^94 - 62 * q^96 + 72 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/84\mathbb{Z}\right)^\times$.

$n$	$29$	$43$	$73$
$\chi(n)$	$-1$	$-1$	$e\left(\frac{2}{3}\right)$

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 $

$2$	1.32175	−	0.502962i	0.934620	−	0.355648i
$2$	1.32175	−	0.502962i	0.934620	−	0.355648i
$3$	−1.03264	−	1.39056i	−0.596194	−	0.802840i
$3$	−1.03264	−	1.39056i	−0.596194	−	0.802840i
$4$	1.49406	−	1.32958i	0.747029	−	0.664792i
$5$	−1.79791	+	1.03802i	−0.804051	+	0.464219i	−0.844886	−	0.534947i	$-0.820332\pi$
$5$	−1.79791	+	1.03802i	−0.804051	+	0.464219i	0.0408349	+	0.999166i	$0.486998\pi$
$6$	−2.06429	−	1.31860i	−0.842743	−	0.538315i
$7$	2.61347	+	0.412056i	0.987798	+	0.155742i
$7$	2.61347	+	0.412056i	0.987798	+	0.155742i
$8$	1.30604	−	2.50883i	0.461756	−	0.887007i
$9$	−0.867316	+	2.87189i	−0.289105	+	0.957297i
$10$	−1.85431	+	2.27629i	−0.586383	+	0.719827i
$11$	−1.99399	+	3.45368i	−0.601209	+	1.04132i	0.391429	+	0.920208i	$0.371981\pi$
$11$	−1.99399	+	3.45368i	−0.601209	+	1.04132i	−0.992638	+	0.121117i	$0.961353\pi$
$12$	−3.39169	−	0.704599i	−0.979096	−	0.203400i
$13$	−1.30998			−0.363324			−0.181662	−	0.983361i	$-0.558148\pi$
$13$	−1.30998			−0.363324			−0.181662	+	0.983361i	$0.558148\pi$
$14$	3.66160	−	0.769840i	0.978605	−	0.205748i
$15$	3.30003	+	1.42820i	0.852064	+	0.368760i
$16$	0.464417	−	3.97295i	0.116104	−	0.993237i
$17$	2.54752	+	1.47081i	0.617863	+	0.356724i	0.776037	−	0.630688i	$-0.217227\pi$
$17$	2.54752	+	1.47081i	0.617863	+	0.356724i	−0.158173	+	0.987411i	$0.550560\pi$
$18$	0.298077	+	4.23216i	0.0702574	+	0.997529i
$19$	−0.949883	+	0.548415i	−0.217918	+	0.125815i	−0.604986	−	0.796236i	$-0.706821\pi$
$19$	−0.949883	+	0.548415i	−0.217918	+	0.125815i	0.387068	+	0.922051i	$0.373488\pi$
$20$	−1.30604	+	3.94134i	−0.292040	+	0.881311i
$21$	−2.12578	−	4.05969i	−0.463883	−	0.885897i
$22$	−0.898482	+	5.56781i	−0.191557	+	1.18706i
$23$	−3.75063	−	6.49627i	−0.782059	−	1.35457i	−0.930740	−	0.365681i	$-0.880836\pi$
$23$	−3.75063	−	6.49627i	−0.782059	−	1.35457i	0.148681	−	0.988885i	$-0.452497\pi$
$24$	−4.83736	+	0.774586i	−0.987421	+	0.158112i
$25$	−0.345008	+	0.597572i	−0.0690016	+	0.119514i
$26$	−1.73147	+	0.658872i	−0.339570	+	0.129216i
$27$	4.88916	−	1.75957i	0.940920	−	0.338630i
$28$	4.45253	−	2.85919i	0.841450	−	0.540336i
$29$		−	0.865568i		−	0.160732i	−0.996765	−	0.0803660i	$-0.974391\pi$
$29$		−	0.865568i		−	0.160732i	0.996765	−	0.0803660i	$-0.0256089\pi$
$30$	5.08015	+	0.227937i	0.927505	+	0.0416154i
$31$	−3.18742	−	1.84026i	−0.572477	−	0.330520i	0.185661	−	0.982614i	$-0.440557\pi$
$31$	−3.18742	−	1.84026i	−0.572477	−	0.330520i	−0.758138	+	0.652094i	$0.773891\pi$
$32$	−1.38440	−	5.48484i	−0.244729	−	0.969591i
$33$	6.86162	−	0.793650i	1.19445	−	0.138157i
$34$	4.10695	+	0.662741i	0.704336	+	0.113659i
$35$	−5.12651	+	1.97200i	−0.866538	+	0.333330i
$36$	2.52260	+	5.44394i	0.420433	+	0.907324i
$37$	−2.08850	−	3.61738i	−0.343347	−	0.594694i	0.641705	−	0.766952i	$-0.278227\pi$
$37$	−2.08850	−	3.61738i	−0.343347	−	0.594694i	−0.985052	+	0.172257i	$0.944894\pi$
$38$	−0.979678	+	1.20262i	−0.158925	+	0.195091i
$39$	1.35274	+	1.82161i	0.216612	+	0.291691i
$40$	0.256080	+	5.86637i	0.0404899	+	0.927554i
$41$		−	7.01712i		−	1.09589i	−0.836514	−	0.547945i	$-0.815410\pi$
$41$		−	7.01712i		−	1.09589i	0.836514	−	0.547945i	$-0.184590\pi$
$42$	−4.85162	−	4.29672i	−0.748622	−	0.662998i
$43$			4.27597i			0.652080i	0.945356	+	0.326040i	$0.105714\pi$
$43$			4.27597i			0.652080i	−0.945356	+	0.326040i	$0.894286\pi$
$44$	1.61283	+	7.81117i	0.243143	+	1.17758i
$45$	−1.42174	−	6.06370i	−0.211940	−	0.903924i
$46$	−8.22478	−	6.70004i	−1.21268	−	0.987867i
$47$	3.75063	+	6.49627i	0.547085	+	0.947579i	0.998473	+	0.0552509i	$0.0175959\pi$
$47$	3.75063	+	6.49627i	0.547085	+	0.947579i	−0.451388	+	0.892328i	$0.649071\pi$
$48$	−6.00420	+	3.45682i	−0.866632	+	0.498949i
$49$	6.66042	+	2.15379i	0.951489	+	0.307684i
$50$	−0.155459	+	0.963368i	−0.0219853	+	0.136241i
$51$	−0.585414	−	5.06129i	−0.0819744	−	0.708722i
$52$	−1.95719	+	1.74173i	−0.271414	+	0.241535i
$53$	4.27909	+	2.47053i	0.587778	+	0.339354i	0.764218	−	0.644957i	$-0.223125\pi$
$53$	4.27909	+	2.47053i	0.587778	+	0.339354i	−0.176440	+	0.984311i	$0.556458\pi$
$54$	5.57726	−	4.78478i	0.758969	−	0.651126i
$55$		−	8.27923i		−	1.11637i
$56$	4.44708	−	6.01859i	0.594266	−	0.804268i
$57$	1.74349	+	0.754555i	0.230931	+	0.0999432i
$58$	−0.435348	−	1.14407i	−0.0571640	−	0.150223i
$59$	2.44458	−	4.23414i	0.318257	−	0.551238i	−0.661867	−	0.749621i	$-0.730236\pi$
$59$	2.44458	−	4.23414i	0.318257	−	0.551238i	0.980125	+	0.198383i	$0.0635691\pi$
$60$	6.82935	−	2.25385i	0.881665	−	0.290971i
$61$	−2.05347	−	3.55672i	−0.262920	−	0.455391i	0.704096	−	0.710104i	$-0.251352\pi$
$61$	−2.05347	−	3.55672i	−0.262920	−	0.455391i	−0.967017	+	0.254713i	$0.918019\pi$
$62$	−5.13856	−	0.829212i	−0.652597	−	0.105310i
$63$	−3.45008	+	7.14821i	−0.434669	+	0.900590i
$64$	−4.58850	−	6.55330i	−0.573562	−	0.819162i
$65$	2.35524	−	1.35980i	0.292131	−	0.168662i
$66$	8.67019	−	4.50015i	1.06723	−	0.553930i
$67$	2.09778	+	1.21116i	0.256285	+	0.147966i	0.622639	−	0.782509i	$-0.286061\pi$
$67$	2.09778	+	1.21116i	0.256285	+	0.147966i	−0.366354	+	0.930476i	$0.619394\pi$
$68$	5.76170	−	1.18966i	0.698709	−	0.144268i
$69$	−5.16042	+	11.9238i	−0.621242	+	1.43545i
$70$	−5.78413	+	5.18494i	−0.691336	+	0.619719i
$71$	0.901192			0.106952			0.0534759	−	0.998569i	$-0.482970\pi$
$71$	0.901192			0.106952			0.0534759	+	0.998569i	$0.482970\pi$
$72$	6.07235	+	5.92677i	0.715633	+	0.698476i
$73$	−6.50543	+	11.2677i	−0.761403	+	1.31879i	0.180725	+	0.983534i	$0.442156\pi$
$73$	−6.50543	+	11.2677i	−0.761403	+	1.31879i	−0.942128	+	0.335255i	$0.891178\pi$
$74$	−4.57989	−	3.73085i	−0.532401	−	0.433703i
$75$	1.18723	−	0.137321i	0.137089	−	0.0158564i
$76$	−0.690016	+	2.08231i	−0.0791503	+	0.238858i
$77$	−6.63432	+	8.20446i	−0.756051	+	0.934985i
$78$	2.70419	+	1.72734i	0.306189	+	0.195583i
$79$	−8.97336	+	5.18077i	−1.00958	+	0.582882i	−0.911069	−	0.412254i	$-0.864742\pi$
$79$	−8.97336	+	5.18077i	−1.00958	+	0.582882i	−0.0985123	+	0.995136i	$0.531408\pi$
$80$	3.28904	+	7.62509i	0.367726	+	0.852511i
$81$	−7.49553	−	4.98167i	−0.832836	−	0.553519i
$82$	−3.52935	−	9.27489i	−0.389751	−	1.02424i
$83$	12.4386			1.36531			0.682657	−	0.730739i	$-0.260824\pi$
$83$	12.4386			1.36531			0.682657	+	0.730739i	$0.260824\pi$
$84$	−8.57373	−	3.23901i	−0.935470	−	0.353405i
$85$	−6.10695			−0.662391
$86$	2.15065	+	5.65178i	0.231911	+	0.609447i
$87$	−1.20363	+	0.893819i	−0.129042	+	0.0958275i
$88$	6.06049	+	9.51324i	0.646050	+	1.01411i
$89$	−7.38393	+	4.26311i	−0.782695	+	0.451889i	−0.837385	−	0.546614i	$-0.815916\pi$
$89$	−7.38393	+	4.26311i	−0.782695	+	0.451889i	0.0546896	+	0.998503i	$0.482583\pi$
$90$	−4.92900	−	7.29963i	−0.519562	−	0.769449i
$91$	−3.42360	−	0.539786i	−0.358891	−	0.0565850i
$92$	−14.2410	−	4.71904i	−1.48473	−	0.491994i
$93$	0.732462	+	6.33262i	0.0759528	+	0.656662i
$94$	8.22478	+	6.70004i	0.848321	+	0.691056i
$95$	1.13854	−	1.97200i	0.116811	−	0.202323i
$96$	−6.19741	+	7.58894i	−0.632521	+	0.774543i
$97$	15.3909			1.56271			0.781354	−	0.624088i	$-0.214529\pi$
$97$	15.3909			1.56271			0.781354	+	0.624088i	$0.214529\pi$
$98$	9.88670	−	0.503167i	0.998707	−	0.0508275i
$99$	−8.18919	−	8.72195i	−0.823045	−	0.876588i
$100$	0.279059	+	1.35152i	0.0279059	+	0.135152i
$101$	−5.28731	−	3.05263i	−0.526107	−	0.303748i	0.213322	−	0.976982i	$-0.431572\pi$
$101$	−5.28731	−	3.05263i	−0.526107	−	0.303748i	−0.739430	+	0.673234i	$0.764905\pi$
$102$	−3.31941	−	6.39533i	−0.328671	−	0.633232i
$103$	6.17682	−	3.56619i	0.608620	−	0.351387i	−0.163805	−	0.986493i	$-0.552377\pi$
$103$	6.17682	−	3.56619i	0.608620	−	0.351387i	0.772425	+	0.635106i	$0.219044\pi$
$104$	−1.71090	+	3.28653i	−0.167767	+	0.322271i
$105$	8.03602	+	5.09235i	0.784235	+	0.496963i
$106$	6.89848	+	1.11321i	0.670040	+	0.108125i
$107$	−1.20838	−	2.09297i	−0.116818	−	0.202335i	0.801687	−	0.597744i	$-0.203936\pi$
$107$	−1.20838	−	2.09297i	−0.116818	−	0.202335i	−0.918505	+	0.395409i	$0.870603\pi$
$108$	4.96520	−	9.12945i	0.477776	−	0.878482i
$109$	3.39848	−	5.88634i	0.325516	−	0.563809i	−0.656101	−	0.754673i	$-0.727796\pi$
$109$	3.39848	−	5.88634i	0.325516	−	0.563809i	0.981617	+	0.190864i	$0.0611288\pi$
$110$	−4.16414	−	10.9431i	−0.397035	−	1.04338i
$111$	−2.87353	+	6.63963i	−0.272743	+	0.630206i
$112$	2.85082	−	10.1918i	0.269377	−	0.963035i
$113$			3.16365i			0.297611i	0.988867	+	0.148805i	$0.0475428\pi$
$113$			3.16365i			0.297611i	−0.988867	+	0.148805i	$0.952457\pi$
$114$	2.68397	+	0.120425i	0.251377	+	0.0112788i
$115$	13.4866	+	7.78649i	1.25763	+	0.726094i
$116$	−1.15085	−	1.29321i	−0.106853	−	0.120071i
$117$	1.13617	−	3.76213i	0.105039	−	0.347809i
$118$	1.10152	−	6.82601i	0.101403	−	0.628386i
$119$	6.05179	+	4.89363i	0.554767	+	0.448598i
$120$	7.89310	−	6.41393i	0.720538	−	0.585509i
$121$	−2.45196	−	4.24691i	−0.222905	−	0.386083i
$122$	−4.50308	−	3.66828i	−0.407690	−	0.332111i
$123$	−9.75772	+	7.24614i	−0.879824	+	0.653363i
$124$	−7.20896	+	1.48849i	−0.647384	+	0.133670i
$125$		−	11.8128i		−	1.05657i
$126$	−0.964870	+	11.1834i	−0.0859575	+	0.996299i
$127$		−	15.0889i		−	1.33892i	−0.742848	−	0.669460i	$-0.766526\pi$
$127$		−	15.0889i		−	1.33892i	0.742848	−	0.669460i	$-0.233474\pi$
$128$	−9.36092	−	6.35399i	−0.827396	−	0.561619i
$129$	5.94600	−	4.41553i	0.523516	−	0.388766i
$130$	2.42911	−	2.98191i	0.213047	−	0.261531i
$131$	−3.70488	−	6.41704i	−0.323697	−	0.560660i	0.657551	−	0.753410i	$-0.271593\pi$
$131$	−3.70488	−	6.41704i	−0.323697	−	0.560660i	−0.981248	+	0.192751i	$0.938259\pi$
$132$	9.19644	−	10.3089i	0.800447	−	0.897271i
$133$	−2.70847	+	1.04186i	−0.234854	+	0.0903407i
$134$	3.38192	+	0.545742i	0.292153	+	0.0471449i
$135$	−6.96381	+	8.23863i	−0.599349	+	0.709068i
$136$	7.01718	−	4.47035i	0.601719	−	0.383330i
$137$	13.0764	+	7.54965i	1.11719	+	0.645010i	0.940682	−	0.339290i	$-0.110187\pi$
$137$	13.0764	+	7.54965i	1.11719	+	0.645010i	0.176508	+	0.984299i	$0.443520\pi$
$138$	−0.823589	+	18.3558i	−0.0701085	+	1.56255i
$139$			14.4761i			1.22785i	0.789364	+	0.613925i	$0.210410\pi$
$139$			14.4761i			1.22785i	−0.789364	+	0.613925i	$0.789590\pi$
$140$	−5.03736	+	9.76241i	−0.425734	+	0.825074i
$141$	5.16042	−	11.9238i	0.434586	−	1.00416i
$142$	1.19115	−	0.453266i	0.0999593	−	0.0380372i
$143$	2.61209	−	4.52427i	0.218434	−	0.378338i
$144$	11.0071	+	4.77956i	0.917257	+	0.398296i
$145$	0.898482	+	1.55622i	0.0746148	+	0.129237i
$146$	−2.93132	+	18.1651i	−0.242598	+	1.50336i
$147$	−3.88283	−	11.4858i	−0.320251	−	0.947333i
$148$	−7.92995	−	2.62775i	−0.651838	−	0.216000i
$149$	9.86511	−	5.69562i	0.808181	−	0.466604i	−0.0381428	−	0.999272i	$-0.512144\pi$
$149$	9.86511	−	5.69562i	0.808181	−	0.466604i	0.846324	+	0.532669i	$0.178811\pi$
$150$	1.50015	−	0.778635i	0.122487	−	0.0635753i
$151$	0.795186	+	0.459101i	0.0647113	+	0.0373611i	0.532007	−	0.846740i	$-0.321438\pi$
$151$	0.795186	+	0.459101i	0.0647113	+	0.0373611i	−0.467295	+	0.884101i	$0.654771\pi$
$152$	0.135294	+	3.09935i	0.0109738	+	0.251391i
$153$	−6.43351	+	6.04054i	−0.520118	+	0.488348i
$154$	−4.64240	+	14.1811i	−0.374095	+	1.14274i
$155$	7.64093			0.613734
$156$	4.44305	+	0.923013i	0.355729	+	0.0739002i
$157$	4.36346	−	7.55773i	0.348242	−	0.603172i	−0.637695	−	0.770289i	$-0.720112\pi$
$157$	4.36346	−	7.55773i	0.348242	−	0.603172i	0.985937	+	0.167116i	$0.0534455\pi$
$158$	−9.25482	+	11.3610i	−0.736274	+	0.903829i
$159$	−0.983326	−	8.50150i	−0.0779829	−	0.674213i
$160$	8.18242	+	8.42422i	0.646877	+	0.665993i
$161$	−7.12531	−	18.5233i	−0.561553	−	1.45984i
$162$	−12.4128	−	2.81457i	−0.975244	−	0.221134i
$163$	7.78729	−	4.49599i	0.609948	−	0.352153i	−0.162997	−	0.986627i	$-0.552116\pi$
$163$	7.78729	−	4.49599i	0.609948	−	0.352153i	0.772945	+	0.634473i	$0.218783\pi$
$164$	−9.32984	−	10.4840i	−0.728538	−	0.818661i
$165$	−11.5128	+	8.54945i	−0.896267	+	0.665574i
$166$	16.4408	−	6.25615i	1.27605	−	0.485571i
$167$	−16.1830			−1.25228			−0.626141	−	0.779710i	$-0.715367\pi$
$167$	−16.1830			−1.25228			−0.626141	+	0.779710i	$0.715367\pi$
$168$	−12.9614	+	0.0310940i	−0.999997	+	0.00239896i
$169$	−11.2839			−0.867996
$170$	−8.07187	+	3.07156i	−0.619084	+	0.235578i
$171$	−0.751141	−	3.20361i	−0.0574412	−	0.244986i
$172$	5.68526	+	6.38855i	0.433497	+	0.487122i
$173$	3.66216	−	2.11435i	0.278429	−	0.160751i	−0.354283	−	0.935138i	$-0.615275\pi$
$173$	3.66216	−	2.11435i	0.278429	−	0.160751i	0.632712	+	0.774387i	$0.281942\pi$
$174$	−1.14134	+	1.78679i	−0.0865245	+	0.135456i
$175$	−1.14790	+	1.41957i	−0.0867731	+	0.107310i
$176$	12.7953	+	9.52595i	0.964479	+	0.718046i
$177$	−8.41219	+	0.972997i	−0.632299	+	0.0731349i
$178$	−7.61554	+	9.34862i	−0.570809	+	0.700709i
$179$	3.27593	−	5.67408i	0.244855	−	0.424101i	−0.717236	−	0.696830i	$-0.754593\pi$
$179$	3.27593	−	5.67408i	0.244855	−	0.424101i	0.962091	+	0.272729i	$0.0879264\pi$
$180$	−10.1864	−	7.16921i	−0.759246	−	0.534361i
$181$	−12.2839			−0.913058			−0.456529	−	0.889708i	$-0.650908\pi$
$181$	−12.2839			−0.913058			−0.456529	+	0.889708i	$0.650908\pi$
$182$	−4.79664	+	1.00848i	−0.355551	+	0.0747533i
$183$	−2.82534	+	6.52828i	−0.208855	+	0.482585i
$184$	−21.1966	+	0.925278i	−1.56263	+	0.0682124i
$185$	7.50987	+	4.33583i	0.552137	+	0.318776i
$186$	4.15320	+	8.00175i	0.304527	+	0.586717i
$187$	−10.1594	+	5.86554i	−0.742930	+	0.428931i
$188$	14.2410	+	4.71904i	1.03863	+	0.344171i
$189$	13.5027	−	2.58397i	0.982177	−	0.187956i
$190$	0.513020	−	3.17914i	0.0372184	−	0.230639i
$191$	11.8662	+	20.5529i	0.858611	+	1.48716i	0.873254	+	0.487266i	$0.162006\pi$
$191$	11.8662	+	20.5529i	0.858611	+	1.48716i	−0.0146426	+	0.999893i	$0.504661\pi$
$192$	−4.37449	+	13.1478i	−0.315702	+	0.948858i
$193$	1.98698	−	3.44155i	0.143026	−	0.247728i	−0.785609	−	0.618724i	$-0.787650\pi$
$193$	1.98698	−	3.44155i	0.143026	−	0.247728i	0.928635	+	0.370995i	$0.120983\pi$
$194$	20.3429	−	7.74104i	1.46054	−	0.555774i
$195$	−4.32298	−	1.87092i	−0.309575	−	0.133979i
$196$	12.8147	−	5.63770i	0.915335	−	0.402693i
$197$			19.7720i			1.40870i	0.709853	+	0.704350i	$0.248761\pi$
$197$			19.7720i			1.40870i	−0.709853	+	0.704350i	$0.751239\pi$
$198$	−15.2109	−	7.40940i	−1.08099	−	0.526563i
$199$	−6.63939	−	3.83325i	−0.470654	−	0.271732i	0.245859	−	0.969305i	$-0.420930\pi$
$199$	−6.63939	−	3.83325i	−0.470654	−	0.271732i	−0.716513	+	0.697573i	$0.754263\pi$
$200$	1.04861	+	1.64602i	0.0741481	+	0.116391i
$201$	−0.482067	−	4.16778i	−0.0340024	−	0.293973i
$202$	−8.52388	−	1.37550i	−0.599738	−	0.0967801i
$203$	0.356662	−	2.26213i	0.0250328	−	0.158771i
$204$	−7.60405	−	6.78350i	−0.532390	−	0.474940i
$205$	7.28394	+	12.6162i	0.508733	+	0.881151i
$206$	6.37056	−	7.82032i	0.443858	−	0.544868i
$207$	21.9096	−	5.13707i	1.52282	−	0.357051i
$208$	−0.608379	+	5.20450i	−0.0421835	+	0.360867i
$209$		−	4.37413i		−	0.302565i
$210$	13.1829	+	2.68901i	0.909706	+	0.185559i
$211$			11.7483i			0.808789i	0.914585	+	0.404395i	$0.132518\pi$
$211$			11.7483i			0.808789i	−0.914585	+	0.404395i	$0.867482\pi$
$212$	9.67799	−	1.99829i	0.664687	−	0.137243i
$213$	−0.930605	−	1.25316i	−0.0637640	−	0.0858652i
$214$	−2.64986	−	2.15862i	−0.181141	−	0.147560i
$215$	−4.43857	−	7.68782i	−0.302708	−	0.524305i
$216$	1.97099	−	14.5642i	0.134109	−	0.990967i
$217$	−7.57192	−	6.12284i	−0.514016	−	0.415646i
$218$	1.53134	−	9.48959i	0.103716	−	0.642716i
$219$	22.3862	−	2.58930i	1.51272	−	0.174969i
$220$	−11.0079	−	12.3696i	−0.742154	−	0.833961i
$221$	−3.33720	−	1.92674i	−0.224485	−	0.129606i
$222$	−0.458607	+	10.2212i	−0.0307797	+	0.686004i
$223$		−	14.5202i		−	0.972345i	−0.873863	−	0.486173i	$-0.838393\pi$
$223$		−	14.5202i		−	0.972345i	0.873863	−	0.486173i	$-0.161607\pi$
$224$	−1.35802	−	14.9049i	−0.0907366	−	0.995875i
$225$	−1.41693	−	1.50911i	−0.0944620	−	0.100607i
$226$	1.59119	+	4.18156i	0.105845	+	0.278153i
$227$	−10.7314	+	18.5874i	−0.712271	+	1.23369i	0.251732	+	0.967797i	$0.419000\pi$
$227$	−10.7314	+	18.5874i	−0.712271	+	1.23369i	−0.964003	+	0.265892i	$0.914333\pi$
$228$	3.60812	−	1.19077i	0.238953	−	0.0788604i
$229$	9.81541	+	17.0008i	0.648621	+	1.12344i	0.983453	+	0.181166i	$0.0579872\pi$
$229$	9.81541	+	17.0008i	0.648621	+	1.12344i	−0.334832	+	0.942278i	$0.608680\pi$
$230$	21.7422	+	3.50856i	1.43364	+	0.231348i
$231$	18.2596	+	0.753192i	1.20140	+	0.0495564i
$232$	−2.17157	−	1.13047i	−0.142570	−	0.0742190i
$233$	−12.3530	+	7.13202i	−0.809273	+	0.467234i	−0.846703	−	0.532065i	$-0.821416\pi$
$233$	−12.3530	+	7.13202i	−0.809273	+	0.467234i	0.0374302	+	0.999299i	$0.488083\pi$
$234$	−0.390476	−	5.54406i	−0.0255262	−	0.362426i
$235$	−13.4866	−	7.78649i	−0.879768	−	0.507934i
$236$	−1.97729	−	9.57632i	−0.128711	−	0.623365i
$237$	16.4704	+	7.12813i	1.06987	+	0.463022i
$238$	10.4603	+	3.42434i	0.678040	+	0.221967i
$239$	−15.2819			−0.988501			−0.494251	−	0.869320i	$-0.664557\pi$
$239$	−15.2819			−0.988501			−0.494251	+	0.869320i	$0.664557\pi$
$240$	7.20676	−	12.4476i	0.465194	−	0.803487i
$241$	2.95196	−	5.11294i	0.190152	−	0.329353i	−0.755148	−	0.655554i	$-0.772435\pi$
$241$	2.95196	−	5.11294i	0.190152	−	0.329353i	0.945301	+	0.326201i	$0.105769\pi$
$242$	−5.37691	−	4.38012i	−0.345641	−	0.281565i
$243$	0.812849	+	15.5673i	0.0521443	+	0.998640i
$244$	−7.79696	−	2.58368i	−0.499149	−	0.165403i
$245$	−14.2105	+	3.04136i	−0.907878	+	0.194305i
$246$	−9.25276	+	14.4854i	−0.589934	+	0.923554i
$247$	1.24433	−	0.718415i	0.0791749	−	0.0457116i
$248$	−8.77981	+	5.59325i	−0.557518	+	0.355171i
$249$	−12.8446	−	17.2966i	−0.813992	−	1.09613i
$250$	−5.94137	−	15.6135i	−0.375765	−	0.987487i
$251$	−23.7400			−1.49845			−0.749226	−	0.662314i	$-0.769575\pi$
$251$	−23.7400			−1.49845			−0.749226	+	0.662314i	$0.769575\pi$
$252$	4.34952	+	15.2670i	0.273994	+	0.961731i
$253$	29.9148			1.88073
$254$	−7.58913	−	19.9437i	−0.476184	−	1.25138i
$255$	6.30627	+	8.49208i	0.394914	+	0.531795i
$256$	−15.5686	−	3.69021i	−0.973040	−	0.230638i
$257$	−12.8177	+	7.40033i	−0.799549	+	0.461620i	−0.843314	−	0.537422i	$-0.819398\pi$
$257$	−12.8177	+	7.40033i	−0.799549	+	0.461620i	0.0437643	+	0.999042i	$0.486065\pi$
$258$	5.63829	−	8.82685i	0.351025	−	0.549536i
$259$	−3.96766	−	10.3145i	−0.246538	−	0.640911i
$260$	1.71090	−	5.16309i	0.106105	−	0.320202i
$261$	2.48582	+	0.750721i	0.153868	+	0.0464685i
$262$	−8.12447	−	6.61833i	−0.501931	−	0.408881i
$263$	6.95299	−	12.0429i	0.428740	−	0.742599i	−0.568022	−	0.823013i	$-0.692291\pi$
$263$	6.95299	−	12.0429i	0.428740	−	0.742599i	0.996761	+	0.0804148i	$0.0256245\pi$
$264$	6.97044	−	18.2512i	0.429001	−	1.12328i
$265$	−10.2579			−0.630138
$266$	−3.05590	+	2.73934i	−0.187369	+	0.167960i
$267$	13.5530	+	5.86554i	0.829433	+	0.358965i
$268$	4.74454	−	0.979641i	0.289819	−	0.0598411i
$269$	7.15156	+	4.12896i	0.436039	+	0.251747i	0.701916	−	0.712260i	$-0.252328\pi$
$269$	7.15156	+	4.12896i	0.436039	+	0.251747i	−0.265877	+	0.964007i	$0.585662\pi$
$270$	−5.06071	+	14.3920i	−0.307985	+	0.875866i
$271$	4.59472	−	2.65276i	0.279109	−	0.161144i	−0.353911	−	0.935279i	$-0.615148\pi$
$271$	4.59472	−	2.65276i	0.279109	−	0.161144i	0.633020	+	0.774135i	$0.281815\pi$
$272$	7.02656	−	9.43808i	0.426048	−	0.572268i
$273$	2.78473	+	5.31812i	0.168540	+	0.321868i
$274$	21.0809	+	3.40184i	1.27354	+	0.205513i
$275$	−1.37588	−	2.38310i	−0.0829688	−	0.143706i
$276$	8.14368	+	24.6760i	0.490192	+	1.48532i
$277$	−6.30239	+	10.9161i	−0.378674	+	0.655883i	−0.990870	−	0.134824i	$-0.956953\pi$
$277$	−6.30239	+	10.9161i	−0.378674	+	0.655883i	0.612196	+	0.790706i	$0.290287\pi$
$278$	7.28095	+	19.1339i	0.436683	+	1.14757i
$279$	8.04951	−	7.55783i	0.481912	−	0.452476i
$280$	−1.74801	+	15.4371i	−0.104464	+	0.922542i
$281$		−	2.02977i		−	0.121086i	−0.998166	−	0.0605428i	$-0.980717\pi$
$281$		−	2.02977i		−	0.121086i	0.998166	−	0.0605428i	$-0.0192832\pi$
$282$	0.823589	−	18.3558i	0.0490440	−	1.09307i
$283$	−6.64918	−	3.83891i	−0.395253	−	0.228199i	0.289181	−	0.957274i	$-0.406617\pi$
$283$	−6.64918	−	3.83891i	−0.395253	−	0.228199i	−0.684434	+	0.729075i	$0.739950\pi$
$284$	1.34643	−	1.19821i	0.0798961	−	0.0711006i
$285$	−3.91789	+	0.453163i	−0.232076	+	0.0268430i
$286$	1.17700	−	7.29374i	0.0695972	−	0.431288i
$287$	2.89144	−	18.3390i	0.170676	−	1.08252i
$288$	16.9526	+	0.781244i	0.998940	+	0.0460352i
$289$	−4.17344	−	7.22861i	−0.245497	−	0.425212i
$290$	1.97029	+	1.60503i	0.115699	+	0.0942506i
$291$	−15.8932	−	21.4020i	−0.931677	−	1.25461i
$292$	5.26190	+	25.4842i	0.307929	+	1.49135i
$293$		−	1.55539i		−	0.0908671i	−0.998967	−	0.0454336i	$-0.985533\pi$
$293$		−	1.55539i		−	0.0908671i	0.998967	−	0.0454336i	$-0.0144669\pi$
$294$	−10.9091	−	13.2285i	−0.636230	−	0.771500i
$295$			10.1501i			0.590964i
$296$	−11.8031	+	0.515232i	−0.686041	+	0.0299472i
$297$	−3.67192	+	20.3942i	−0.213066	+	1.18339i
$298$	10.1745	−	12.4900i	0.589395	−	0.723525i
$299$	4.91326	+	8.51001i	0.284141	+	0.492147i
$300$	1.59121	−	1.78368i	0.0918685	−	0.102981i
$301$	−1.76194	+	11.1751i	−0.101556	+	0.644123i
$302$	1.28195	+	0.206869i	0.0737679	+	0.0119040i
$303$	1.21501	+	10.5046i	0.0698008	+	0.603473i
$304$	1.73768	+	4.02853i	0.0996629	+	0.231052i
$305$	7.38393	+	4.26311i	0.422803	+	0.244105i
$306$	−5.46534	+	11.2199i	−0.312433	+	0.641399i
$307$			31.5800i			1.80237i	0.433437	+	0.901184i	$0.357301\pi$
$307$			31.5800i			1.80237i	−0.433437	+	0.901184i	$0.642699\pi$
$308$	0.996442	+	21.0788i	0.0567775	+	1.20108i
$309$	−11.3374	−	4.90665i	−0.644963	−	0.279130i
$310$	10.0994	−	3.84310i	0.573608	−	0.218273i
$311$	−9.13857	+	15.8285i	−0.518201	+	0.897550i	0.481575	+	0.876405i	$0.340065\pi$
$311$	−9.13857	+	15.8285i	−0.518201	+	0.897550i	−0.999776	+	0.0211458i	$0.993269\pi$
$312$	6.33686	−	1.01469i	0.358754	−	0.0574458i
$313$	−14.8909	−	25.7918i	−0.841683	−	1.45784i	−0.888471	−	0.458933i	$-0.848232\pi$
$313$	−14.8909	−	25.7918i	−0.841683	−	1.45784i	0.0467882	−	0.998905i	$-0.485101\pi$
$314$	1.96616	−	12.1841i	0.110957	−	0.687589i
$315$	−1.21708	−	16.4331i	−0.0685748	−	0.925902i
$316$	−6.51845	+	19.6712i	−0.366691	+	1.10659i
$317$	15.3252	−	8.84800i	0.860748	−	0.496953i	−0.00351474	−	0.999994i	$-0.501119\pi$
$317$	15.3252	−	8.84800i	0.860748	−	0.496953i	0.864263	+	0.503041i	$0.167785\pi$
$318$	−5.57565	−	10.7423i	−0.312667	−	0.602398i
$319$	2.98940	+	1.72593i	0.167374	+	0.0966336i
$320$	15.0522	+	7.01927i	0.841444	+	0.392389i
$321$	−1.66258	+	3.84160i	−0.0927964	+	0.214417i
$322$	−18.7344	−	20.8994i	−1.04403	−	1.16468i
$323$	−3.22646			−0.179525
$324$	−17.8223	+	2.52302i	−0.990128	+	0.140168i
$325$	0.451955	−	0.782809i	0.0250700	−	0.0434224i
$326$	8.03155	−	9.85930i	0.444827	−	0.546056i
$327$	−11.6947	+	1.35267i	−0.646719	+	0.0748028i
$328$	−17.6048	−	9.16466i	−0.972062	−	0.506034i
$329$	7.12531	+	18.5233i	0.392831	+	1.02122i
$330$	−10.9170	+	17.0907i	−0.600959	+	0.940814i
$331$	30.3818	−	17.5410i	1.66994	−	0.964138i	0.702268	−	0.711913i	$-0.252171\pi$
$331$	30.3818	−	17.5410i	1.66994	−	0.964138i	0.967668	−	0.252225i	$-0.0811625\pi$
$332$	18.5840	−	16.5382i	1.01993	−	0.907649i
$333$	12.2001	−	2.86053i	0.668563	−	0.156756i
$334$	−21.3900	+	8.13946i	−1.17041	+	0.445372i
$335$	−5.02884			−0.274755
$336$	−17.1162	+	6.56022i	−0.933764	+	0.357889i
$337$	−0.132987			−0.00724428			−0.00362214	−	0.999993i	$-0.501153\pi$
$337$	−0.132987			−0.00724428			−0.00362214	+	0.999993i	$0.501153\pi$
$338$	−14.9146	+	5.67540i	−0.811246	+	0.308701i
$339$	4.39924	−	3.26690i	0.238934	−	0.177434i
$340$	−9.12413	+	8.11969i	−0.494826	+	0.440352i
$341$	12.7113	−	7.33889i	0.688357	−	0.397423i
$342$	−2.60412	−	3.85658i	−0.140815	−	0.208540i
$343$	16.5193	+	8.37332i	0.891959	+	0.452117i
$344$	10.7277	+	5.58461i	0.578399	+	0.301102i
$345$	−3.09919	−	26.7945i	−0.166855	−	1.44257i
$346$	3.77703	−	4.63658i	0.203055	−	0.249264i
$347$	0.0976681	−	0.169166i	0.00524310	−	0.00908131i	−0.863392	−	0.504534i	$-0.831664\pi$
$347$	0.0976681	−	0.169166i	0.00524310	−	0.00908131i	0.868635	+	0.495452i	$0.164998\pi$
$348$	−0.609879	+	2.93574i	−0.0326929	+	0.157372i
$349$	5.80782			0.310885			0.155443	−	0.987845i	$-0.450320\pi$
$349$	5.80782			0.310885			0.155443	+	0.987845i	$0.450320\pi$
$350$	−0.803249	+	2.45367i	−0.0429355	+	0.131154i
$351$	−6.40472	+	2.30501i	−0.341859	+	0.123032i
$352$	21.7034	+	6.15541i	1.15679	+	0.328085i
$353$	−17.3154	−	9.99704i	−0.921604	−	0.532089i	−0.0374578	−	0.999298i	$-0.511926\pi$
$353$	−17.3154	−	9.99704i	−0.921604	−	0.532089i	−0.884147	+	0.467210i	$0.845259\pi$
$354$	−10.6295	+	5.51708i	−0.564949	+	0.293229i
$355$	−1.62026	+	0.935460i	−0.0859947	+	0.0496490i
$356$	−5.36385	+	16.1869i	−0.284284	+	0.857903i
$357$	0.555572	−	13.4687i	0.0294040	−	0.712841i
$358$	1.47612	−	9.14741i	0.0780155	−	0.483455i
$359$	6.95299	+	12.0429i	0.366965	+	0.635601i	0.989089	−	0.147317i	$-0.0470637\pi$
$359$	6.95299	+	12.0429i	0.366965	+	0.635601i	−0.622125	+	0.782918i	$0.713730\pi$
$360$	−17.0697	−	4.35256i	−0.899651	−	0.229400i
$361$	−8.89848	+	15.4126i	−0.468341	+	0.811191i
$362$	−16.2363	+	6.17836i	−0.853363	+	0.324727i
$363$	−3.37360	+	7.79511i	−0.177068	+	0.409137i
$364$	−5.83275	+	3.74549i	−0.305719	+	0.196317i
$365$		−	27.0112i		−	1.41383i
$366$	−0.450916	+	10.0498i	−0.0235698	+	0.525312i
$367$	−16.2929	−	9.40672i	−0.850483	−	0.491027i	0.0103306	−	0.999947i	$-0.496712\pi$
$367$	−16.2929	−	9.40672i	−0.850483	−	0.491027i	−0.860814	+	0.508920i	$0.830045\pi$
$368$	−27.5512	+	11.8841i	−1.43621	+	0.619499i
$369$	20.1524	+	6.08606i	1.04909	+	0.316827i
$370$	12.1069	+	1.95371i	0.629410	+	0.101568i
$371$	10.1653	+	8.21988i	0.527754	+	0.426755i
$372$	9.51408	+	8.48742i	0.493282	+	0.440052i
$373$	−2.91150	−	5.04287i	−0.150752	−	0.261110i	0.780752	−	0.624841i	$-0.214836\pi$
$373$	−2.91150	−	5.04287i	−0.150752	−	0.261110i	−0.931504	+	0.363731i	$0.881503\pi$
$374$	−10.4781	+	12.8626i	−0.541809	+	0.665109i
$375$	−16.4264	+	12.1983i	−0.848253	+	0.629918i
$376$	21.1966	−	0.925278i	1.09313	−	0.0477176i
$377$			1.13388i			0.0583978i
$378$	16.5476	−	10.2067i	0.851116	−	0.524977i
$379$			12.0598i			0.619469i	0.950823	+	0.309735i	$0.100240\pi$
$379$			12.0598i			0.619469i	−0.950823	+	0.309735i	$0.899760\pi$
$380$	−0.920903	−	4.46007i	−0.0472413	−	0.228797i
$381$	−20.9820	+	15.5813i	−1.07494	+	0.798256i
$382$	26.0216	+	21.1976i	1.33138	+	1.08456i
$383$	−6.07589	−	10.5237i	−0.310463	−	0.537738i	0.667999	−	0.744162i	$-0.267151\pi$
$383$	−6.07589	−	10.5237i	−0.310463	−	0.537738i	−0.978463	+	0.206423i	$0.933818\pi$
$384$	0.830836	+	19.5783i	0.0423984	+	0.999101i
$385$	3.41150	−	21.6375i	0.173866	−	1.10275i
$386$	0.895325	−	5.54825i	0.0455708	−	0.282399i
$387$	−12.2801	−	3.70862i	−0.624234	−	0.188520i
$388$	22.9949	−	20.4635i	1.16739	−	1.03888i
$389$	1.04831	+	0.605241i	0.0531513	+	0.0306869i	0.526340	−	0.850274i	$-0.323564\pi$
$389$	1.04831	+	0.605241i	0.0531513	+	0.0306869i	−0.473189	+	0.880961i	$0.656897\pi$
$390$	−6.65492	−	0.298594i	−0.336985	−	0.0151199i
$391$		−	22.0658i		−	1.11592i
$392$	14.1023	−	13.8969i	0.712274	−	0.701902i
$393$	−5.09748	+	11.7783i	−0.257134	+	0.594139i
$394$	9.94459	+	26.1337i	0.501001	+	1.31660i
$395$	10.7555	−	18.6291i	0.541170	−	0.937334i
$396$	−23.8317	−	2.14288i	−1.19759	−	0.107684i
$397$	4.77851	+	8.27663i	0.239827	+	0.415392i	0.960664	−	0.277712i	$-0.0895760\pi$
$397$	4.77851	+	8.27663i	0.239827	+	0.415392i	−0.720838	+	0.693104i	$0.756243\pi$
$398$	−10.7036	−	1.72725i	−0.536524	−	0.0865792i
$399$	4.24563	+	2.69042i	0.212548	+	0.134689i
$400$	2.21389	+	1.64822i	0.110695	+	0.0824111i
$401$	9.73916	−	5.62291i	0.486351	−	0.280795i	−0.236709	−	0.971581i	$-0.576069\pi$
$401$	9.73916	−	5.62291i	0.486351	−	0.280795i	0.723059	+	0.690786i	$0.242735\pi$
$402$	−2.73341	−	5.26631i	−0.136330	−	0.262660i
$403$	4.17546	+	2.41071i	0.207995	+	0.120086i
$404$	−11.9583	+	2.46911i	−0.594947	+	0.122843i
$405$	18.6474	+	1.17607i	0.926597	+	0.0584393i
$406$	−0.666349	−	3.16937i	−0.0330704	−	0.157293i
$407$	16.6577			0.825693
$408$	−13.4625	−	5.14156i	−0.666494	−	0.254545i
$409$	7.78394	−	13.4822i	0.384891	−	0.666651i	−0.606863	−	0.794807i	$-0.707572\pi$
$409$	7.78394	−	13.4822i	0.384891	−	0.666651i	0.991754	+	0.128155i	$0.0409056\pi$
$410$	15.9730	+	13.0119i	0.788851	+	0.642611i
$411$	−3.00492	−	25.9795i	−0.148222	−	1.28148i
$412$	4.48698	−	13.5407i	0.221058	−	0.667101i
$413$	8.13353	−	10.0585i	0.400225	−	0.494945i
$414$	26.3753	−	17.8096i	1.29627	−	0.875295i
$415$	−22.3635	+	12.9116i	−1.09778	+	0.633805i
$416$	1.81354	+	7.18505i	0.0889161	+	0.352276i
$417$	20.1299	−	14.9486i	0.985768	−	0.732037i
$418$	−2.20002	−	5.78151i	−0.107607	−	0.282783i
$419$	18.0336			0.881000			0.440500	−	0.897753i	$-0.354801\pi$
$419$	18.0336			0.881000			0.440500	+	0.897753i	$0.354801\pi$
$420$	18.7770	−	3.07629i	0.916223	−	0.150108i
$421$	−12.4978			−0.609107			−0.304554	−	0.952495i	$-0.598507\pi$
$421$	−12.4978			−0.609107			−0.304554	+	0.952495i	$0.598507\pi$
$422$	5.90898	+	15.5284i	0.287644	+	0.755911i
$423$	−21.9096	+	5.13707i	−1.06528	+	0.249773i
$424$	11.7868	−	7.50890i	0.572419	−	0.364664i
$425$	−1.75783	+	1.01488i	−0.0852672	+	0.0492290i
$426$	−1.86032	−	1.18831i	−0.0901329	−	0.0575738i
$427$	−3.90112	−	10.1415i	−0.188788	−	0.490782i
$428$	−4.58816	−	1.52038i	−0.221777	−	0.0734903i
$429$	−8.98861	+	1.03967i	−0.433974	+	0.0501957i
$430$	−9.73337	−	7.92897i	−0.469385	−	0.382369i
$431$	−6.22304	+	10.7786i	−0.299753	+	0.519188i	−0.976079	−	0.217415i	$-0.930238\pi$
$431$	−6.22304	+	10.7786i	−0.299753	+	0.519188i	0.676326	+	0.736602i	$0.263571\pi$
$432$	−4.72007	−	20.2416i	−0.227095	−	0.973873i
$433$	−0.497837			−0.0239245			−0.0119623	−	0.999928i	$-0.503808\pi$
$433$	−0.497837			−0.0239245			−0.0119623	+	0.999928i	$0.503808\pi$
$434$	−13.0878	−	4.28449i	−0.628233	−	0.205662i
$435$	1.23621	−	2.85640i	0.0592715	−	0.136954i
$436$	−2.74885	−	13.3131i	−0.131646	−	0.637582i
$437$	7.12531	+	4.11380i	0.340850	+	0.196790i
$438$	28.2867	−	14.6818i	1.35159	−	0.701525i
$439$	−4.03571	+	2.33002i	−0.192614	+	0.111206i	−0.593206	−	0.805051i	$-0.702138\pi$
$439$	−4.03571	+	2.33002i	−0.192614	+	0.111206i	0.400592	+	0.916257i	$0.368805\pi$
$440$	−20.7712	−	10.8130i	−0.990228	−	0.515491i
$441$	−11.9621	+	17.2600i	−0.569625	+	0.821904i
$442$	−5.38003	−	0.868179i	−0.255902	−	0.0412951i
$443$	−11.0349	−	19.1130i	−0.524283	−	0.908086i	−0.999600	−	0.0282709i	$-0.991000\pi$
$443$	−11.0349	−	19.1130i	−0.524283	−	0.908086i	0.475317	−	0.879815i	$-0.342333\pi$
$444$	4.53473	+	13.7406i	0.215209	+	0.652100i
$445$	8.85044	−	15.3294i	0.419551	−	0.726684i
$446$	−7.30312	−	19.1921i	−0.345813	−	0.908773i
$447$	−18.1072	−	7.83651i	−0.856441	−	0.370654i
$448$	−9.29157	−	19.0175i	−0.438985	−	0.898494i
$449$			6.02866i			0.284510i	0.989830	+	0.142255i	$0.0454353\pi$
$449$			6.02866i			0.284510i	−0.989830	+	0.142255i	$0.954565\pi$
$450$	−2.63186	−	1.28201i	−0.124067	−	0.0604344i
$451$	24.2349	+	13.9920i	1.14118	+	0.658859i
$452$	4.20633	+	4.72667i	0.197849	+	0.222324i
$453$	−0.182732	−	1.57984i	−0.00858551	−	0.0742273i
$454$	−4.83554	+	29.9654i	−0.226943	+	1.40635i
$455$	6.71564	−	2.58329i	0.314834	−	0.121107i
$456$	4.17013	−	3.38865i	0.195284	−	0.158688i
$457$	19.1308	+	33.1356i	0.894902	+	1.55002i	0.833926	+	0.551877i	$0.186088\pi$
$457$	19.1308	+	33.1356i	0.894902	+	1.55002i	0.0609766	+	0.998139i	$0.480578\pi$
$458$	21.5243	+	17.5341i	1.00576	+	0.819312i
$459$	15.0432	+	2.70849i	0.702157	+	0.126421i
$460$	30.5025	−	6.29808i	1.42219	−	0.293650i
$461$			12.4563i			0.580148i	0.957004	+	0.290074i	$0.0936799\pi$
$461$			12.4563i			0.580148i	−0.957004	+	0.290074i	$0.906320\pi$
$462$	24.5136	−	8.18838i	1.14047	−	0.380958i
$463$		−	28.0609i		−	1.30410i	−0.758176	−	0.652050i	$-0.773909\pi$
$463$		−	28.0609i		−	1.30410i	0.758176	−	0.652050i	$-0.226091\pi$
$464$	−3.43886	−	0.401985i	−0.159645	−	0.0186617i
$465$	−7.89032	−	10.6252i	−0.365905	−	0.492731i
$466$	−12.7405	+	15.6399i	−0.590192	+	0.724503i
$467$	8.54830	+	14.8061i	0.395568	+	0.685144i	0.993174	−	0.116646i	$-0.0372144\pi$
$467$	8.54830	+	14.8061i	0.395568	+	0.685144i	−0.597605	+	0.801790i	$0.703881\pi$
$468$	−3.30456	−	7.13147i	−0.152753	−	0.329652i
$469$	4.98342	+	4.02972i	0.230113	+	0.186075i
$470$	−21.7422	−	3.50856i	−1.00289	−	0.161838i
$471$	−15.0154	+	1.73675i	−0.691871	+	0.0800253i
$472$	−7.43002	−	11.6630i	−0.341994	−	0.536834i
$473$	−14.7679	−	8.52623i	−0.679027	−	0.392036i
$474$	25.3550	+	1.13763i	1.16459	+	0.0522531i
$475$		−	0.756831i		−	0.0347258i
$476$	15.5482	−	0.734998i	0.712651	−	0.0336886i
$477$	−10.8064	+	10.1464i	−0.494792	+	0.464569i
$478$	−20.1988	+	7.68620i	−0.923873	+	0.351558i
$479$	8.21329	−	14.2258i	0.375275	−	0.649995i	−0.615093	−	0.788454i	$-0.710882\pi$
$479$	8.21329	−	14.2258i	0.375275	−	0.649995i	0.990368	+	0.138459i	$0.0442151\pi$
$480$	3.26489	−	20.0773i	0.149021	−	0.916400i
$481$	2.73590	+	4.73871i	0.124746	+	0.216067i
$482$	1.33014	−	8.24276i	0.0605862	−	0.375447i
$483$	−18.3998	+	29.0360i	−0.837222	+	1.32118i
$484$	−9.30998	−	3.08505i	−0.423181	−	0.140230i
$485$	−27.6715	+	15.9761i	−1.25650	+	0.725439i
$486$	8.90413	+	20.1672i	0.403899	+	0.914803i
$487$	27.7018	+	15.9937i	1.25529	+	0.724742i	0.972155	−	0.234339i	$-0.0752924\pi$
$487$	27.7018	+	15.9937i	1.25529	+	0.724742i	0.283134	+	0.959080i	$0.408626\pi$
$488$	−11.6051	+	0.506591i	−0.525340	+	0.0229323i
$489$	−14.2934	−	6.18596i	−0.646370	−	0.279739i
$490$	−17.2531	+	11.1673i	−0.779416	+	0.504487i
$491$	2.03844			0.0919935			0.0459968	−	0.998942i	$-0.485354\pi$
$491$	2.03844			0.0919935			0.0459968	+	0.998942i	$0.485354\pi$
$492$	−4.94425	+	23.7999i	−0.222904	+	1.07298i
$493$	1.27309	−	2.20505i	0.0573369	−	0.0993104i
$494$	1.28336	−	1.57542i	0.0577412	−	0.0708814i
$495$	23.7770	+	7.18070i	1.06870	+	0.322749i
$496$	−8.79153	+	11.8088i	−0.394752	+	0.530231i
$497$	2.35524	+	0.371341i	0.105647	+	0.0166569i
$498$	−25.6769	−	16.4015i	−1.15061	−	0.734970i
$499$	−3.71805	+	2.14662i	−0.166443	+	0.0960957i	−0.580907	−	0.813970i	$-0.697302\pi$
$499$	−3.71805	+	2.14662i	−0.166443	+	0.0960957i	0.414465	+	0.910065i	$0.363969\pi$
$500$	−15.7060	−	17.6489i	−0.702396	−	0.789285i
$501$	16.7112	+	22.5035i	0.746603	+	1.00538i
$502$	−31.3783	+	11.9403i	−1.40048	+	0.532922i
$503$	26.3039			1.17283			0.586415	−	0.810010i	$-0.300539\pi$
$503$	26.3039			1.17283			0.586415	+	0.810010i	$0.300539\pi$
$504$	13.4277	+	17.9916i	0.598118	+	0.801408i
$505$	12.6748			0.564023
$506$	39.5399	−	15.0460i	1.75776	−	0.668876i
$507$	11.6522	+	15.6910i	0.517494	+	0.696862i
$508$	−20.0619	−	22.5436i	−0.890103	−	1.00021i
$509$	−35.3140	+	20.3886i	−1.56527	+	0.903707i	−0.568557	+	0.822644i	$0.692498\pi$
$509$	−35.3140	+	20.3886i	−1.56527	+	0.903707i	−0.996709	+	0.0810631i	$0.974168\pi$
$510$	12.6065	+	8.05261i	0.558226	+	0.356575i
$511$	−21.6447	+	26.7673i	−0.957503	+	1.18411i
$512$	−22.4339	+	2.95289i	−0.991448	+	0.130500i
$513$	−3.67916	+	4.35268i	−0.162439	+	0.192175i
$514$	−13.2198	+	16.2282i	−0.583100	+	0.715797i
$515$	−7.40358	+	12.8234i	−0.326241	+	0.565066i
$516$	3.01285	−	14.5028i	0.132633	−	0.638448i
$517$	−29.9148			−1.31565
$518$	−10.4321	−	11.6376i	−0.458358	−	0.511328i
$519$	−6.72182	−	2.90910i	−0.295055	−	0.127695i
$520$	−0.335461	−	7.68485i	−0.0147109	−	0.337003i
$521$	6.01740	+	3.47415i	0.263627	+	0.152205i	0.625988	−	0.779833i	$-0.284696\pi$
$521$	6.01740	+	3.47415i	0.263627	+	0.152205i	−0.362361	+	0.932038i	$0.618029\pi$
$522$	3.66322	−	0.258006i	0.160335	−	0.0112926i
$523$	−6.54296	+	3.77758i	−0.286104	+	0.165182i	−0.636183	−	0.771538i	$-0.719488\pi$
$523$	−6.54296	+	3.77758i	−0.286104	+	0.165182i	0.350080	+	0.936720i	$0.386154\pi$
$524$	−14.0673	−	4.66149i	−0.614533	−	0.203638i
$525$	3.15937	+	0.130321i	0.137886	+	0.00568766i
$526$	3.13299	−	19.4149i	0.136605	−	0.846528i
$527$	−5.41333	−	9.37617i	−0.235808	−	0.408432i
$528$	0.0335275	−	27.6295i	0.00145910	−	1.20242i
$529$	−16.6344	+	28.8116i	−0.723234	+	1.25268i
$530$	−13.5584	+	5.15934i	−0.588939	+	0.224107i
$531$	10.0398	+	10.6929i	0.435689	+	0.464033i
$532$	−2.66136	+	5.15773i	−0.115385	+	0.223616i
$533$			9.19231i			0.398163i
$534$	20.8639	+	0.936125i	0.902870	+	0.0405101i
$535$	4.34511	+	2.50865i	0.187855	+	0.108458i
$536$	5.77839	−	3.68117i	0.249588	−	0.159002i
$537$	−11.2730	+	1.30389i	−0.486466	+	0.0562672i
$538$	11.5293	+	1.86049i	0.497064	+	0.0802115i
$539$	−20.7193	+	18.7084i	−0.892443	+	0.805826i
$540$	0.549611	+	21.5679i	0.0236515	+	0.928136i
$541$	−5.57548	−	9.65701i	−0.239709	−	0.415187i	0.720922	−	0.693016i	$-0.243719\pi$
$541$	−5.57548	−	9.65701i	−0.239709	−	0.415187i	−0.960631	+	0.277829i	$0.910385\pi$
$542$	4.73884	−	5.81726i	0.203551	−	0.249873i
$543$	12.6849	+	17.0816i	0.544360	+	0.733040i
$544$	4.54037	−	16.0089i	0.194667	−	0.686376i
$545$			14.1108i			0.604442i
$546$	6.35555	+	5.62863i	0.271992	+	0.240883i
$547$		−	39.2870i		−	1.67979i	−0.542748	−	0.839896i	$-0.682616\pi$
$547$		−	39.2870i		−	1.67979i	0.542748	−	0.839896i	$-0.317384\pi$
$548$	29.5747	−	6.10651i	1.26337	−	0.260857i
$549$	11.9955	−	2.81255i	0.511957	−	0.120037i
$550$	−3.01718	−	2.45785i	−0.128653	−	0.104803i
$551$	0.474691	+	0.822189i	0.0202225	+	0.0350264i
$552$	23.1750	+	28.5196i	0.986395	+	1.21388i
$553$	−25.5863	+	9.84225i	−1.08804	+	0.418535i
$554$	−2.83983	+	17.5982i	−0.120653	+	0.747676i
$555$	−1.72575	−	14.9203i	−0.0732542	−	0.633330i
$556$	19.2472	+	21.6282i	0.816264	+	0.917240i
$557$	−25.5152	−	14.7312i	−1.08112	−	0.624182i	−0.149919	−	0.988698i	$-0.547901\pi$
$557$	−25.5152	−	14.7312i	−1.08112	−	0.624182i	−0.931197	+	0.364516i	$0.881234\pi$
$558$	6.83816	−	14.0382i	0.289482	−	0.594284i
$559$		−	5.60145i		−	0.236916i
$560$	5.45383	+	21.2832i	0.230466	+	0.899379i
$561$	18.6474	+	8.07030i	0.787294	+	0.340728i
$562$	−1.02090	−	2.68285i	−0.0430639	−	0.113169i
$563$	20.3385	−	35.2274i	0.857167	−	1.48466i	−0.0174537	−	0.999848i	$-0.505556\pi$
$563$	20.3385	−	35.2274i	0.857167	−	1.48466i	0.874620	−	0.484808i	$-0.161111\pi$
$564$	−8.14368	−	24.6760i	−0.342911	−	1.03905i
$565$	−3.28394	−	5.68796i	−0.138157	−	0.239294i
$566$	−10.7194	−	1.72980i	−0.450570	−	0.0727087i
$567$	−17.5366	−	16.1080i	−0.736467	−	0.676473i
$568$	1.17700	−	2.26094i	0.0493857	−	0.0948670i
$569$	4.30534	−	2.48569i	0.180489	−	0.104206i	−0.407033	−	0.913413i	$-0.633437\pi$
$569$	4.30534	−	2.48569i	0.180489	−	0.104206i	0.587523	+	0.809208i	$0.300103\pi$
$570$	−4.95055	+	2.56952i	−0.207356	+	0.107625i
$571$	−30.2952	−	17.4909i	−1.26781	−	0.731973i	−0.293240	−	0.956039i	$-0.594734\pi$
$571$	−30.2952	−	17.4909i	−1.26781	−	0.731973i	−0.974574	+	0.224066i	$0.928067\pi$
$572$	−2.11278	−	10.2325i	−0.0883398	−	0.427843i
$573$	16.3266	−	37.7245i	0.682052	−	1.57596i
$574$	−5.40206	−	25.6939i	−0.225478	−	1.07244i
$575$	5.17599			0.215854
$576$	22.8000	−	7.49389i	0.950001	−	0.312246i
$577$	7.33386	−	12.7026i	0.305313	−	0.528817i	−0.672018	−	0.740535i	$-0.734572\pi$
$577$	7.33386	−	12.7026i	0.305313	−	0.528817i	0.977331	+	0.211718i	$0.0679057\pi$
$578$	−9.15197	−	7.45535i	−0.380672	−	0.310102i
$579$	−6.83751	+	0.790861i	−0.284157	+	0.0328671i
$580$	3.41150	+	1.13047i	0.141655	+	0.0469402i
$581$	32.5079	+	5.12540i	1.34865	+	0.212637i
$582$	−31.7713	−	20.2944i	−1.31696	−	0.841230i
$583$	−17.0649	+	9.85242i	−0.706755	+	0.408045i
$584$	19.7725	+	31.0372i	0.818192	+	1.28433i
$585$	1.86245	+	7.94335i	0.0770030	+	0.328417i
$586$	−0.782305	−	2.05585i	−0.0323167	−	0.0849262i
$587$	18.7469			0.773769			0.386885	−	0.922128i	$-0.373551\pi$
$587$	18.7469			0.773769			0.386885	+	0.922128i	$0.373551\pi$
$588$	−21.0725	−	11.9979i	−0.869015	−	0.494785i
$589$	4.03690			0.166337
$590$	5.10514	+	13.4160i	0.210175	+	0.552327i
$591$	27.4942	−	20.4174i	1.13096	−	0.839859i
$592$	−15.3416	+	6.61752i	−0.630537	+	0.271978i
$593$	38.8836	−	22.4494i	1.59676	−	0.921888i	0.604651	−	0.796491i	$-0.293313\pi$
$593$	38.8836	−	22.4494i	1.59676	−	0.921888i	0.992107	−	0.125398i	$-0.0400207\pi$
$594$	5.40414	+	28.8029i	0.221735	+	1.18180i
$595$	−15.9603	−	2.51640i	−0.654309	−	0.103162i
$596$	7.16624	−	21.6261i	0.293541	−	0.885838i
$597$	1.52572	+	13.1908i	0.0624435	+	0.539865i
$598$	10.7743	+	8.77694i	0.440595	+	0.358916i
$599$	0.596454	−	1.03309i	0.0243704	−	0.0422108i	−0.853583	−	0.520957i	$-0.825575\pi$
$599$	0.596454	−	1.03309i	0.0243704	−	0.0422108i	0.877953	+	0.478746i	$0.158909\pi$
$600$	1.20606	−	3.15791i	0.0492371	−	0.128921i
$601$	37.4089			1.52594			0.762970	−	0.646434i	$-0.223741\pi$
$601$	37.4089			1.52594			0.762970	+	0.646434i	$0.223741\pi$
$602$	3.29181	+	15.6569i	0.134164	+	0.638128i
$603$	−5.29775	+	4.97415i	−0.215741	+	0.202563i
$604$	1.79847	−	0.371343i	0.0731786	−	0.0151097i
$605$	8.81680	+	5.09038i	0.358454	+	0.206953i
$606$	6.88936	+	13.2734i	0.279861	+	0.539194i
$607$	18.5588	−	10.7149i	0.753279	−	0.434906i	−0.0735982	−	0.997288i	$-0.523448\pi$
$607$	18.5588	−	10.7149i	0.753279	−	0.434906i	0.826878	+	0.562382i	$0.190115\pi$
$608$	4.32298	+	4.45073i	0.175320	+	0.180501i
$609$	−3.51394	+	1.84001i	−0.142392	+	0.0745608i
$610$	11.9039	+	1.92094i	0.481975	+	0.0777766i
$611$	−4.91326	−	8.51001i	−0.198769	−	0.344278i
$612$	−1.58064	+	17.5788i	−0.0638935	+	0.710580i
$613$	20.2674	−	35.1041i	0.818591	−	1.41784i	−0.0881290	−	0.996109i	$-0.528089\pi$
$613$	20.2674	−	35.1041i	0.818591	−	1.41784i	0.906720	−	0.421733i	$-0.138578\pi$
$614$	15.8836	+	41.7410i	0.641009	+	1.68453i
$615$	10.0219	−	23.1567i	0.404120	−	0.933768i
$616$	11.9189	+	27.3598i	0.480226	+	1.10236i
$617$		−	46.2548i		−	1.86215i	−0.364830	−	0.931074i	$-0.618873\pi$
$617$		−	46.2548i		−	1.86215i	0.364830	−	0.931074i	$-0.381127\pi$
$618$	−17.4531	−	0.783089i	−0.702067	−	0.0315004i
$619$	−22.3403	−	12.8982i	−0.897932	−	0.518421i	−0.0214035	−	0.999771i	$-0.506813\pi$
$619$	−22.3403	−	12.8982i	−0.897932	−	0.518421i	−0.876529	+	0.481349i	$0.840147\pi$
$620$	11.4160	−	10.1592i	0.458477	−	0.408005i
$621$	−29.7681	−	25.1618i	−1.19455	−	1.00971i
$622$	−4.11780	+	25.5177i	−0.165109	+	1.02317i
$623$	−21.0543	+	8.09892i	−0.843523	+	0.324476i
$624$	7.86540	−	4.52838i	0.314868	−	0.181280i
$625$	10.5369	+	18.2504i	0.421476	+	0.730018i
$626$	−32.6544	−	26.6008i	−1.30513	−	1.06318i
$627$	−6.08249	+	4.51689i	−0.242911	+	0.180387i
$628$	−3.52937	−	17.0933i	−0.140837	−	0.682095i
$629$		−	12.2871i		−	0.489920i
$630$	−9.87392	−	21.1084i	−0.393387	−	0.840978i
$631$			26.5913i			1.05858i	0.848440	+	0.529291i	$0.177542\pi$
$631$			26.5913i			1.05858i	−0.848440	+	0.529291i	$0.822458\pi$
$632$	1.27809	+	29.2790i	0.0508398	+	1.16466i
$633$	16.3368	−	12.1318i	0.649329	−	0.482195i
$634$	15.8059	−	19.4028i	0.627732	−	0.770586i
$635$	15.6626	+	27.1284i	0.621552	+	1.07656i
$636$	−12.7726	−	11.3943i	−0.506466	−	0.451814i
$637$	−8.72504	−	2.82143i	−0.345699	−	0.111789i
$638$	4.81932	+	0.777697i	0.190799	+	0.0307893i
$639$	−0.781618	+	2.58813i	−0.0309203	+	0.102385i
$640$	23.4257	+	1.70705i	0.925982	+	0.0674771i
$641$	−5.24154	−	3.02620i	−0.207028	−	0.119528i	0.392901	−	0.919581i	$-0.371471\pi$
$641$	−5.24154	−	3.02620i	−0.207028	−	0.119528i	−0.599930	+	0.800053i	$0.704805\pi$
$642$	−0.265344	+	5.91386i	−0.0104723	+	0.233401i
$643$			9.95426i			0.392558i	0.980548	+	0.196279i	$0.0628858\pi$
$643$			9.95426i			0.392558i	−0.980548	+	0.196279i	$0.937114\pi$
$644$	−35.2738	−	18.2011i	−1.38998	−	0.717225i
$645$	−6.10695	+	14.1108i	−0.240461	+	0.555614i
$646$	−4.26458	+	1.62279i	−0.167787	+	0.0638477i
$647$	−15.4951	+	26.8383i	−0.609175	+	1.05512i	0.382201	+	0.924079i	$0.375166\pi$
$647$	−15.4951	+	26.8383i	−0.609175	+	1.05512i	−0.991377	+	0.131044i	$0.958167\pi$
$648$	−22.2877	+	12.2987i	−0.875543	+	0.483140i
$649$	9.74892	+	16.8856i	0.382679	+	0.662819i
$650$	0.203649	−	1.26200i	0.00798778	−	0.0494996i
$651$	−0.695124	+	16.8519i	−0.0272440	+	0.660478i
$652$	5.65686	−	17.0711i	0.221540	−	0.668557i
$653$	−7.01889	+	4.05236i	−0.274670	+	0.158581i	−0.631008	−	0.775776i	$-0.717359\pi$
$653$	−7.01889	+	4.05236i	−0.274670	+	0.158581i	0.356338	+	0.934357i	$0.384025\pi$
$654$	−14.7772	+	7.66990i	−0.577833	+	0.299917i
$655$	13.3221	+	7.69152i	0.520538	+	0.300533i
$656$	−27.8786	−	3.25887i	−1.08848	−	0.127238i
$657$	−26.7174	−	28.4556i	−1.04235	−	1.11016i
$658$	18.7344	+	20.8994i	0.730343	+	0.814744i
$659$	−38.3085			−1.49229			−0.746143	−	0.665785i	$-0.768097\pi$
$659$	−38.3085			−1.49229			−0.746143	+	0.665785i	$0.768097\pi$
$660$	−5.83353	+	28.0805i	−0.227070	+	1.09303i
$661$	−3.32843	+	5.76501i	−0.129461	+	0.224233i	−0.923468	−	0.383676i	$-0.874658\pi$
$661$	−3.32843	+	5.76501i	−0.129461	+	0.224233i	0.794007	+	0.607909i	$0.207991\pi$
$662$	31.3348	−	38.4657i	1.21786	−	1.49501i
$663$	0.766883	+	6.63021i	0.0297833	+	0.257496i
$664$	16.2454	−	31.2064i	0.630442	−	1.21104i
$665$	3.78811	−	4.68463i	0.146896	−	0.181662i
$666$	14.6868	−	9.91711i	0.569102	−	0.384280i
$667$	−5.62297	+	3.24642i	−0.217722	+	0.125702i
$668$	−24.1784	+	21.5167i	−0.935491	+	0.832506i
$669$	−20.1912	+	14.9941i	−0.780638	+	0.579706i
$670$	−6.64688	+	2.52932i	−0.256791	+	0.0977160i
$671$	16.3784			0.632280
$672$	−19.3238	+	17.2798i	−0.745432	+	0.666582i
$673$	−22.0809			−0.851156			−0.425578	−	0.904922i	$-0.639929\pi$
$673$	−22.0809			−0.851156			−0.425578	+	0.904922i	$0.639929\pi$
$674$	−0.175776	+	0.0668876i	−0.00677065	+	0.00257642i
$675$	−0.635331	+	3.52869i	−0.0244539	+	0.135819i
$676$	−16.8589	+	15.0029i	−0.648418	+	0.577036i
$677$	39.0358	−	22.5373i	1.50027	−	0.866180i	0.500267	−	0.865871i	$-0.333235\pi$
$677$	39.0358	−	22.5373i	1.50027	−	0.866180i	1.00000		0.000308342i	$-9.81484e-5\pi$
$678$	4.17158	−	6.53069i	0.160208	−	0.250810i
$679$	40.2236	+	6.34190i	1.54364	+	0.243380i
$680$	−7.97594	+	15.3213i	−0.305863	+	0.587546i
$681$	36.9286	−	4.27135i	1.41511	−	0.163678i
$682$	13.1100	−	16.0935i	0.502009	−	0.616252i
$683$	−7.80843	+	13.5246i	−0.298781	+	0.517505i	−0.975857	−	0.218408i	$-0.929913\pi$
$683$	−7.80843	+	13.5246i	−0.298781	+	0.517505i	0.677076	+	0.735913i	$0.263247\pi$
$684$	−5.38171	−	3.78768i	−0.205775	−	0.144825i
$685$	−31.3469			−1.19770
$686$	26.0459	+	2.75886i	0.994437	+	0.105334i
$687$	13.5049	−	31.2046i	0.515242	−	1.19053i
$688$	16.9882	+	1.98584i	0.647670	+	0.0757093i
$689$	−5.60554	−	3.23636i	−0.213554	−	0.123295i
$690$	−17.5730	−	33.8570i	−0.668993	−	1.28891i
$691$	33.1799	−	19.1564i	1.26222	−	0.728744i	0.288718	−	0.957414i	$-0.406771\pi$
$691$	33.1799	−	19.1564i	1.26222	−	0.728744i	0.973504	+	0.228670i	$0.0734376\pi$
$692$	2.66028	−	8.02811i	0.101129	−	0.305183i
$693$	−17.8083	−	26.1689i	−0.676480	−	0.994075i
$694$	0.0440088	−	0.272719i	0.00167055	−	0.0103523i
$695$	−15.0266	−	26.0268i	−0.569991	−	0.987254i
$696$	0.670457	+	4.18706i	0.0254136	+	0.158710i
$697$	10.3208	−	17.8762i	0.390930	−	0.677110i
$698$	7.67650	−	2.92111i	0.290560	−	0.110566i
$699$	22.6737	+	9.81282i	0.857598	+	0.371155i
$700$	0.172409	+	3.64715i	0.00651644	+	0.137849i
$701$			36.6488i			1.38420i	0.721799	+	0.692102i	$0.243315\pi$
$701$			36.6488i			1.38420i	−0.721799	+	0.692102i	$0.756685\pi$
$702$	−7.30612	+	6.26798i	−0.275752	+	0.236570i
$703$	3.96766	+	2.29073i	0.149643	+	0.0863964i
$704$	31.7824	−	2.78005i	1.19784	−	0.104777i
$705$	3.09919	+	26.7945i	0.116722	+	1.00914i
$706$	−27.9148	−	4.50462i	−1.05059	−	0.169534i
$707$	−12.5604	−	10.1566i	−0.472381	−	0.381979i
$708$	−11.2746	+	12.6384i	−0.423726	+	0.474981i
$709$	−18.2674	−	31.6400i	−0.686045	−	1.18827i	−0.973107	−	0.230353i	$-0.926012\pi$
$709$	−18.2674	−	31.6400i	−0.686045	−	1.18827i	0.287062	−	0.957912i	$-0.407322\pi$
$710$	−1.67109	+	2.05138i	−0.0627147	+	0.0769868i
$711$	−7.09588	−	30.2639i	−0.266116	−	1.13498i
$712$	1.05171	+	24.0929i	0.0394144	+	0.902918i
$713$			27.6084i			1.03394i
$714$	−6.03994	−	18.0818i	−0.226039	−	0.676693i
$715$			10.8457i			0.405604i
$716$	−2.64973	−	12.8330i	−0.0990251	−	0.479593i
$717$	15.7806	+	21.2503i	0.589338	+	0.793609i
$718$	15.2473	+	12.4207i	0.569023	+	0.463535i
$719$	−12.2687	−	21.2499i	−0.457543	−	0.792488i	0.541287	−	0.840838i	$-0.317937\pi$
$719$	−12.2687	−	21.2499i	−0.457543	−	0.792488i	−0.998830	+	0.0483494i	$0.984604\pi$
$720$	−24.7511	+	2.83240i	−0.922418	+	0.105557i
$721$	17.6124	−	6.77492i	0.655919	−	0.252311i
$722$	−4.00962	+	24.8473i	−0.149223	+	0.924720i
$723$	−10.1581	+	1.17494i	−0.377786	+	0.0436966i
$724$	−18.3529	+	16.3325i	−0.682081	+	0.606993i
$725$	0.517239	+	0.298628i	0.0192098	+	0.0110908i
$726$	−0.538418	+	12.0000i	−0.0199826	+	0.445362i
$727$			7.89691i			0.292880i	0.989220	+	0.146440i	$0.0467816\pi$
$727$			7.89691i			0.292880i	−0.989220	+	0.146440i	$0.953218\pi$
$728$	−5.82560	+	7.88426i	−0.215911	+	0.292210i
$729$	20.8078	−	17.2057i	0.770660	−	0.637247i
$730$	−13.5856	−	35.7021i	−0.502826	−	1.32139i
$731$	−6.28914	+	10.8931i	−0.232612	+	0.402896i
$732$	4.45868	+	13.5102i	0.164797	+	0.499350i
$733$	−2.92236	−	5.06167i	−0.107940	−	0.186957i	0.806996	−	0.590557i	$-0.201092\pi$
$733$	−2.92236	−	5.06167i	−0.107940	−	0.186957i	−0.914935	+	0.403600i	$0.867759\pi$
$734$	−26.2664	−	4.23863i	−0.969511	−	0.156451i
$735$	18.9035	+	16.6200i	0.697268	+	0.613037i
$736$	−30.4386	+	29.5650i	−1.12198	+	1.08978i
$737$	−8.36590	+	4.83005i	−0.308162	+	0.177917i
$738$	29.6975	−	2.09164i	1.09318	−	0.0769943i
$739$	−1.22939	−	0.709786i	−0.0452237	−	0.0261099i	0.477218	−	0.878785i	$-0.341645\pi$
$739$	−1.22939	−	0.709786i	−0.0452237	−	0.0261099i	−0.522441	+	0.852675i	$0.674979\pi$
$740$	16.9850	−	3.50702i	0.624382	−	0.128921i
$741$	−2.28394	−	0.988455i	−0.0839027	−	0.0363118i
$742$	17.5702	+	5.75190i	0.645024	+	0.211159i
$743$	−1.70600			−0.0625872			−0.0312936	−	0.999510i	$-0.509963\pi$
$743$	−1.70600			−0.0625872			−0.0312936	+	0.999510i	$0.509963\pi$
$744$	16.8441	+	6.43305i	0.617535	+	0.235847i
$745$	−11.8244	+	20.4805i	−0.433212	+	0.750346i
$746$	−6.38466	−	5.20105i	−0.233759	−	0.190424i
$747$	−10.7882	+	35.7223i	−0.394720	+	1.30701i
$748$	−7.38003	+	22.2713i	−0.269841	+	0.814318i
$749$	−2.29563	−	5.96782i	−0.0838805	−	0.218059i
$750$	−15.5763	+	24.3850i	−0.568765	+	0.890413i
$751$	−23.1969	+	13.3927i	−0.846466	+	0.488707i	−0.859457	−	0.511208i	$-0.829198\pi$
$751$	−23.1969	+	13.3927i	−0.846466	+	0.488707i	0.0129912	+	0.999916i	$0.495865\pi$
$752$	27.5512	−	11.8841i	1.00469	−	0.433367i
$753$	24.5148	+	33.0118i	0.893369	+	1.20302i
$754$	0.570299	+	1.49871i	0.0207691	+	0.0545798i
$755$	−1.90623			−0.0693749
$756$	16.7382	−	21.8136i	0.608763	−	0.793352i
$757$	−23.8816			−0.867992			−0.433996	−	0.900915i	$-0.642897\pi$
$757$	−23.8816			−0.867992			−0.433996	+	0.900915i	$0.642897\pi$
$758$	6.06562	+	15.9400i	0.220313	+	0.578969i
$759$	−30.8911	−	41.5983i	−1.12128	−	1.50992i
$760$	−3.46045	−	5.43193i	−0.125524	−	0.197037i
$761$	−13.0696	+	7.54576i	−0.473774	+	0.273533i	−0.717818	−	0.696231i	$-0.754859\pi$
$761$	−13.0696	+	7.54576i	−0.473774	+	0.273533i	0.244044	+	0.969764i	$0.421526\pi$
$762$	−19.8961	+	31.1478i	−0.720761	+	1.12837i
$763$	11.3073	−	13.9834i	0.409352	−	0.506233i
$764$	45.0557	+	14.9301i	1.63006	+	0.540153i
$765$	5.29665	−	17.5385i	0.191501	−	0.634105i
$766$	−13.3239	−	10.8538i	−0.481411	−	0.392165i
$767$	−3.20236	+	5.54665i	−0.115631	+	0.200278i
$768$	10.9453	+	25.4598i	0.394955	+	0.918701i
$769$	12.6792			0.457222			0.228611	−	0.973518i	$-0.426582\pi$
$769$	12.6792			0.457222			0.228611	+	0.973518i	$0.426582\pi$
$770$	−6.37368	−	30.3153i	−0.229691	−	1.09249i
$771$	23.5267	+	10.1820i	0.847294	+	0.366695i
$772$	−1.60716	−	7.78373i	−0.0578431	−	0.280143i
$773$	−33.5367	−	19.3624i	−1.20623	−	0.696417i	−0.244296	−	0.969701i	$-0.578557\pi$
$773$	−33.5367	−	19.3624i	−1.20623	−	0.696417i	−0.961934	+	0.273283i	$0.911890\pi$
$774$	−18.0966	+	1.27457i	−0.650468	+	0.0458134i
$775$	2.19937	−	1.26981i	0.0790037	−	0.0456128i
$776$	20.1012	−	38.6132i	0.721590	−	1.38613i
$777$	−10.2458	+	16.1684i	−0.367565	+	0.580038i
$778$	1.69002	+	0.272719i	0.0605900	+	0.00977745i
$779$	3.84829	+	6.66544i	0.137879	+	0.238814i
$780$	−8.94633	+	2.95251i	−0.320330	+	0.105717i
$781$	−1.79696	+	3.11243i	−0.0643004	+	0.111372i
$782$	−11.0983	−	29.1655i	−0.396873	−	1.04296i
$783$	−1.52303	−	4.23190i	−0.0544286	−	0.151236i
$784$	11.6501	−	25.4612i	0.416075	−	0.909330i
$785$			18.1175i			0.646642i
$786$	−0.813544	+	18.1319i	−0.0290182	+	0.646743i
$787$	17.6523	+	10.1915i	0.629235	+	0.363289i	0.780456	−	0.625211i	$-0.214987\pi$
$787$	17.6523	+	10.1915i	0.629235	+	0.363289i	−0.151221	+	0.988500i	$0.548320\pi$
$788$	26.2886	+	29.5406i	0.936492	+	1.05234i
$789$	−23.9263	+	2.76744i	−0.851800	+	0.0985235i
$790$	4.84640	−	30.0327i	0.172427	−	1.06852i
$791$	−1.30360	+	8.26808i	−0.0463506	+	0.293979i
$792$	−32.5774	+	9.15408i	−1.15759	+	0.325276i
$793$	2.69002	+	4.65925i	0.0955253	+	0.165455i
$794$	10.4788	+	8.53624i	0.371880	+	0.302940i
$795$	10.5927	+	14.2642i	0.375685	+	0.505900i
$796$	−15.0163	+	3.10052i	−0.532237	+	0.109895i
$797$			27.9005i			0.988287i	0.869380	+	0.494143i	$0.164518\pi$
$797$			27.9005i			0.988287i	−0.869380	+	0.494143i	$0.835482\pi$
$798$	6.96486	+	1.42067i	0.246553	+	0.0502913i
$799$			22.0658i			0.780632i
$800$	3.75521	+	1.06504i	0.132767	+	0.0376547i
$801$	−5.83900	−	24.9033i	−0.206311	−	0.879915i
$802$	10.0447	−	12.3305i	0.354689	−	0.435406i
$803$	−25.9435	−	44.9354i	−0.915525	−	1.58574i
$804$	−6.26165	−	5.58596i	−0.220831	−	0.197002i
$805$	32.0383	+	25.9069i	1.12920	+	0.913100i
$806$	6.73142	+	1.08625i	0.237104	+	0.0382617i
$807$	−1.64342	−	14.2084i	−0.0578510	−	0.500159i
$808$	−14.5640	+	9.27812i	−0.512360	+	0.326403i
$809$	12.3530	+	7.13202i	0.434309	+	0.250748i	0.701181	−	0.712984i	$-0.252657\pi$
$809$	12.3530	+	7.13202i	0.434309	+	0.250748i	−0.266872	+	0.963732i	$0.585990\pi$
$810$	25.2388	−	7.82447i	0.886800	−	0.274924i
$811$		−	38.4069i		−	1.34865i	−0.738435	−	0.674325i	$-0.764435\pi$
$811$		−	38.4069i		−	1.34865i	0.738435	−	0.674325i	$-0.235565\pi$
$812$	−2.47482	−	3.85397i	−0.0868492	−	0.135248i
$813$	−8.43351	−	3.64989i	−0.295776	−	0.128007i
$814$	22.0174	−	8.37821i	0.771710	−	0.293656i
$815$	−9.33391	+	16.1668i	−0.326953	+	0.566299i
$816$	−20.3801	−	0.0247307i	−0.713447	−	0.000865746i
$817$	−2.34501	−	4.06167i	−0.0820415	−	0.142100i
$818$	3.50741	−	21.7351i	0.122634	−	0.759951i
$819$	4.51955	−	9.36404i	0.157926	−	0.327206i
$820$	27.6569	+	9.16466i	0.965820	+	0.320044i
$821$	−45.7169	+	26.3947i	−1.59553	+	0.921181i	−0.603198	+	0.797591i	$0.706107\pi$
$821$	−45.7169	+	26.3947i	−1.59553	+	0.921181i	−0.992333	+	0.123589i	$0.960559\pi$
$822$	−17.0385	−	32.8271i	−0.594286	−	1.14498i
$823$	4.96238	+	2.86503i	0.172978	+	0.0998687i	0.583989	−	0.811761i	$-0.301491\pi$
$823$	4.96238	+	2.86503i	0.172978	+	0.0998687i	−0.411012	+	0.911630i	$0.634824\pi$
$824$	−0.879777	−	20.1542i	−0.0306485	−	0.702105i
$825$	−1.89305	+	4.37413i	−0.0659077	+	0.152288i
$826$	5.69148	−	17.3857i	0.198032	−	0.604925i
$827$	44.5253			1.54830			0.774149	−	0.633003i	$-0.218178\pi$
$827$	44.5253			1.54830			0.774149	+	0.633003i	$0.218178\pi$
$828$	25.9040	−	36.8057i	0.900226	−	1.27909i
$829$	−13.0293	+	22.5674i	−0.452526	+	0.783799i	−0.998542	−	0.0539760i	$-0.982811\pi$
$829$	−13.0293	+	22.5674i	−0.452526	+	0.783799i	0.546016	+	0.837775i	$0.316144\pi$
$830$	−23.0650	+	28.3139i	−0.800597	+	0.982790i
$831$	21.6875	−	2.50849i	0.752332	−	0.0870186i
$832$	6.01086	+	8.58471i	0.208389	+	0.297621i
$833$	13.7997	+	15.2830i	0.478132	+	0.529525i
$834$	19.0882	−	29.8830i	0.660971	−	1.03476i
$835$	29.0957	−	16.7984i	1.00690	−	0.581333i
$836$	−5.81577	−	6.53520i	−0.201142	−	0.226025i
$837$	−18.8219	−	3.38883i	−0.650579	−	0.117135i
$838$	23.8360	−	9.07023i	0.823400	−	0.313326i
$839$	−46.0533			−1.58994			−0.794968	−	0.606652i	$-0.792512\pi$
$839$	−46.0533			−1.58994			−0.794968	+	0.606652i	$0.792512\pi$
$840$	23.2713	−	13.5102i	0.802935	−	0.466146i
$841$	28.2508			0.974165
$842$	−16.5190	+	6.28594i	−0.569284	+	0.216628i
$843$	−2.82251	+	2.09601i	−0.0972124	+	0.0721905i
$844$	15.6204	+	17.5527i	0.537676	+	0.604189i
$845$	20.2875	−	11.7130i	0.697912	−	0.402940i
$846$	−26.3753	+	17.8096i	−0.906801	+	0.612307i
$847$	−4.65814	−	12.1095i	−0.160056	−	0.416087i
$848$	11.8026	−	15.8532i	0.405302	−	0.544403i
$849$	1.52797	+	13.2103i	0.0524397	+	0.453376i
$850$	−1.81297	+	2.22554i	−0.0621842	+	0.0763355i
$851$	−15.6663	+	27.1349i	−0.537035	+	0.930173i
$852$	−3.05656	−	0.634979i	−0.104716	−	0.0217540i
$853$	46.3274			1.58622			0.793109	−	0.609079i	$-0.208461\pi$
$853$	46.3274			1.58622			0.793109	+	0.609079i	$0.208461\pi$
$854$	−10.2571	−	11.4425i	−0.350991	−	0.391553i
$855$	4.67591	+	4.98011i	0.159913	+	0.170316i
$856$	−6.82910	+	0.298106i	−0.233414	+	0.0101890i
$857$	−35.6333	−	20.5729i	−1.21721	−	0.702756i	−0.252890	−	0.967495i	$-0.581381\pi$
$857$	−35.6333	−	20.5729i	−1.21721	−	0.702756i	−0.964320	+	0.264739i	$0.914714\pi$
$858$	−11.3578	+	5.89512i	−0.387749	+	0.201256i
$859$	−49.7193	+	28.7054i	−1.69640	+	0.979417i	−0.747277	+	0.664512i	$0.768639\pi$
$859$	−49.7193	+	28.7054i	−1.69640	+	0.979417i	−0.949123	+	0.314905i	$0.898027\pi$
$860$	−16.8531	−	5.58461i	−0.574685	−	0.190434i
$861$	−28.4873	+	14.9168i	−0.970845	+	0.508364i
$862$	−2.80407	+	17.3766i	−0.0955072	+	0.591850i
$863$	12.7433	+	22.0721i	0.433788	+	0.751343i	0.997196	−	0.0748356i	$-0.0238432\pi$
$863$	12.7433	+	22.0721i	0.433788	+	0.751343i	−0.563408	+	0.826179i	$0.690510\pi$
$864$	−16.4195	−	24.3803i	−0.558603	−	0.829435i
$865$	−4.38950	+	7.60283i	−0.149247	+	0.258504i
$866$	−0.658017	+	0.250393i	−0.0223603	+	0.00850871i
$867$	−5.74216	+	13.2680i	−0.195014	+	0.450604i
$868$	−19.4537	+	0.919620i	−0.660302	+	0.0312139i
$869$		−	41.3215i		−	1.40174i
$870$	0.197295	−	4.39722i	0.00668893	−	0.149080i
$871$	−2.74806	−	1.58659i	−0.0931145	−	0.0537597i
$872$	−10.3293	−	16.2140i	−0.349794	−	0.549077i
$873$	−13.3488	+	44.2010i	−0.451787	+	1.49598i
$874$	11.4870	+	1.85366i	0.388553	+	0.0627010i
$875$	4.86751	−	30.8723i	0.164552	−	1.04367i
$876$	30.0036	−	33.6329i	1.01373	−	1.13635i
$877$	−20.9313	−	36.2541i	−0.706801	−	1.22422i	−0.966038	−	0.258402i	$-0.916804\pi$
$877$	−20.9313	−	36.2541i	−0.706801	−	1.22422i	0.259236	−	0.965814i	$-0.416529\pi$
$878$	−4.16230	+	5.10952i	−0.140471	+	0.172438i
$879$	−2.16287	+	1.60616i	−0.0729518	+	0.0541744i
$880$	−32.8929	−	3.84502i	−1.10882	−	0.129616i
$881$			38.5556i			1.29897i	0.760373	+	0.649486i	$0.225016\pi$
$881$			38.5556i			1.29897i	−0.760373	+	0.649486i	$0.774984\pi$
$882$	−7.12985	+	28.8299i	−0.240075	+	0.970754i
$883$		−	4.56420i		−	0.153597i	−0.997047	−	0.0767987i	$-0.975530\pi$
$883$		−	4.56420i		−	0.153597i	0.997047	−	0.0767987i	$-0.0244699\pi$
$884$	−7.54773	+	1.55844i	−0.253858	+	0.0524159i
$885$	14.1144	−	10.4814i	0.474450	−	0.352329i
$886$	−24.1985	−	19.7125i	−0.812965	−	0.662255i
$887$	20.2446	+	35.0647i	0.679747	+	1.17736i	0.975057	+	0.221955i	$0.0712437\pi$
$887$	20.2446	+	35.0647i	0.679747	+	1.17736i	−0.295310	+	0.955401i	$0.595423\pi$
$888$	12.9048	+	15.8809i	0.433056	+	0.532927i
$889$	6.21745	−	39.4342i	0.208527	−	1.32258i
$890$	3.98797	−	24.7131i	0.133677	−	0.828385i
$891$	32.1511	−	15.9538i	1.07710	−	0.534472i
$892$	−19.3058	−	21.6940i	−0.646407	−	0.726370i
$893$	−7.12531	−	4.11380i	−0.238439	−	0.137663i
$894$	−27.8747	−	1.25069i	−0.932269	−	0.0418292i
$895$			13.6020i			0.454665i
$896$	−21.8463	−	20.4632i	−0.729832	−	0.683626i
$897$	6.76007	−	15.6199i	0.225712	−	0.521535i
$898$	3.03219	+	7.96840i	0.101185	+	0.265909i
$899$	−1.59287	+	2.75893i	−0.0531251	+	0.0920154i
$900$	−4.12346	−	0.370770i	−0.137449	−	0.0123590i
$901$	7.26737	+	12.5874i	0.242111	+	0.419349i
$902$	39.0700	+	6.30475i	1.30089	+	0.209925i
$903$	17.3591	−	9.08977i	0.577675	−	0.302489i
$904$	7.93706	+	4.13186i	0.263983	+	0.137424i
$905$	22.0854	−	12.7510i	0.734145	−	0.423859i
$906$	−1.03613	−	1.99625i	−0.0344230	−	0.0663209i
$907$	2.36697	+	1.36657i	0.0785940	+	0.0453763i	0.538782	−	0.842445i	$-0.318885\pi$
$907$	2.36697	+	1.36657i	0.0785940	+	0.0453763i	−0.460188	+	0.887822i	$0.652218\pi$
$908$	8.68010	+	42.0390i	0.288059	+	1.39511i
$909$	13.3526	−	12.5370i	0.442878	−	0.415826i
$910$	7.57711	−	6.79219i	0.251179	−	0.225159i
$911$	−5.16105			−0.170993			−0.0854966	−	0.996338i	$-0.527248\pi$
$911$	−5.16105			−0.170993			−0.0854966	+	0.996338i	$0.527248\pi$
$912$	3.80751	−	6.57637i	0.126079	−	0.217765i
$913$	−24.8024	+	42.9590i	−0.820839	+	1.42174i
$914$	41.9521	+	34.1749i	1.38765	+	1.13041i
$915$	−1.69681	−	14.6701i	−0.0560949	−	0.484977i
$916$	37.2688	+	12.3498i	1.23139	+	0.408048i
$917$	−7.03841	−	18.2973i	−0.232429	−	0.604232i
$918$	21.2457	−	3.98622i	0.701212	−	0.131565i
$919$	34.5011	−	19.9192i	1.13809	−	0.657074i	0.192130	−	0.981370i	$-0.438461\pi$
$919$	34.5011	−	19.9192i	1.13809	−	0.657074i	0.945956	+	0.324296i	$0.105127\pi$
$920$	37.1491	−	23.6661i	1.22477	−	0.780249i
$921$	43.9139	−	32.6108i	1.44701	−	1.07456i
$922$	6.26505	+	16.4641i	0.206328	+	0.542218i
$923$	−1.18055			−0.0388582
$924$	28.2824	−	23.1524i	0.930423	−	0.761658i
$925$	2.88220			0.0947660
$926$	−14.1136	−	37.0895i	−0.463801	−	1.21884i
$927$	4.88445	+	20.8322i	0.160426	+	0.684218i
$928$	−4.74750	+	1.19829i	−0.155844	+	0.0393358i
$929$	22.2777	−	12.8621i	0.730909	−	0.421990i	−0.0878459	−	0.996134i	$-0.527998\pi$
$929$	22.2777	−	12.8621i	0.730909	−	0.421990i	0.818754	+	0.574144i	$0.194665\pi$
$930$	−15.7731	−	10.0753i	−0.517220	−	0.330382i
$931$	−7.50779	+	1.60683i	−0.246058	+	0.0526617i
$932$	−8.97351	+	27.0800i	−0.293937	+	0.887035i
$933$	31.4473	−	3.63735i	1.02954	−	0.119082i
$934$	18.7456	+	15.2705i	0.613376	+	0.499666i
$935$	12.1772	−	21.0915i	0.398236	−	0.689765i
$936$	−7.95468	−	7.76397i	−0.260007	−	0.253773i
$937$	20.2068			0.660127			0.330063	−	0.943959i	$-0.392930\pi$
$937$	20.2068			0.660127			0.330063	+	0.943959i	$0.392930\pi$
$938$	8.61365	+	2.81982i	0.281246	+	0.0920702i
$939$	−20.4881	+	47.3403i	−0.668604	+	1.54489i
$940$	−30.5025	+	6.29808i	−0.994883	+	0.205421i
$941$	41.4712	+	23.9434i	1.35192	+	0.780533i	0.988519	−	0.151099i	$-0.0482813\pi$
$941$	41.4712	+	23.9434i	1.35192	+	0.780533i	0.363403	+	0.931632i	$0.381615\pi$
$942$	−18.9731	+	9.84771i	−0.618175	+	0.320856i
$943$	−45.5851	+	26.3186i	−1.48446	+	0.857051i
$944$	−15.6867	−	11.6786i	−0.510559	−	0.380106i
$945$	−21.5944	+	18.6619i	−0.702467	+	0.607072i
$946$	−23.8078	−	3.84188i	−0.774059	−	0.124910i
$947$	−3.16035	−	5.47389i	−0.102698	−	0.177878i	0.810098	−	0.586295i	$-0.199414\pi$
$947$	−3.16035	−	5.47389i	−0.102698	−	0.177878i	−0.912795	+	0.408418i	$0.866081\pi$
$948$	34.0852	−	11.2489i	1.10704	−	0.365348i
$949$	8.52200	−	14.7605i	0.276636	−	0.479148i
$950$	−0.380657	−	1.00034i	−0.0123502	−	0.0324554i
$951$	−28.1290	−	12.1738i	−0.912147	−	0.394763i
$952$	20.1812	−	8.79165i	0.654077	−	0.284939i
$953$			3.70027i			0.119863i	0.998202	+	0.0599317i	$0.0190883\pi$
$953$			3.70027i			0.119863i	−0.998202	+	0.0599317i	$0.980912\pi$
$954$	−9.18019	+	18.8462i	−0.297220	+	0.610168i
$955$	−42.6689	−	24.6349i	−1.38073	−	0.797167i
$956$	−22.8320	+	20.3185i	−0.738439	+	0.657147i
$957$	−0.686958	−	5.93920i	−0.0222062	−	0.191987i
$958$	3.70087	−	22.9340i	0.119570	−	0.740964i
$959$	31.0638	+	25.1189i	1.00310	+	0.811133i
$960$	−5.78276	−	28.1794i	−0.186638	−	0.909485i
$961$	−8.72691	−	15.1155i	−0.281513	−	0.487595i
$962$	5.99957	+	4.88735i	0.193434	+	0.157575i
$963$	7.05882	−	1.65506i	0.227467	−	0.0533336i
$964$	−2.38768	−	11.5639i	−0.0769021	−	0.372448i
$965$			8.25014i			0.265581i
$966$	−9.71602	+	47.6328i	−0.312608	+	1.53256i
$967$			14.5970i			0.469409i	0.972067	+	0.234705i	$0.0754123\pi$
$967$			14.5970i			0.469409i	−0.972067	+	0.234705i	$0.924588\pi$
$968$	−13.8572	+	0.604896i	−0.445386	+	0.0194421i
$969$	3.33176	+	4.48658i	0.107032	+	0.144130i
$970$	−28.5394	+	35.0342i	−0.916346	+	1.12488i
$971$	−4.10729	−	7.11403i	−0.131809	−	0.228300i	0.792565	−	0.609788i	$-0.208745\pi$
$971$	−4.10729	−	7.11403i	−0.131809	−	0.228300i	−0.924374	+	0.381488i	$0.875412\pi$
$972$	21.9124	+	22.1776i	0.702840	+	0.711348i
$973$	−5.96498	+	37.8329i	−0.191228	+	1.21287i
$974$	44.6592	+	7.20668i	1.43097	+	0.230917i
$975$	−1.55525	+	0.179888i	−0.0498078	+	0.00576103i
$976$	−15.0843	+	6.50654i	−0.482838	+	0.208269i
$977$	−30.8426	−	17.8070i	−0.986744	−	0.569697i	−0.0824443	−	0.996596i	$-0.526273\pi$
$977$	−30.8426	−	17.8070i	−0.986744	−	0.569697i	−0.904299	+	0.426899i	$0.859606\pi$
$978$	−22.0036	−	0.987262i	−0.703599	−	0.0315692i
$979$		−	34.0023i		−	1.08672i
$980$	−17.1876	+	23.4381i	−0.549038	+	0.748701i
$981$	13.9574	+	14.8654i	0.445625	+	0.474615i
$982$	2.69431	−	1.02526i	0.0859790	−	0.0327173i
$983$	15.5749	−	26.9764i	0.496761	−	0.860415i	−0.503232	−	0.864151i	$-0.667856\pi$
$983$	15.5749	−	26.9764i	0.496761	−	0.860415i	0.999993	+	0.00373618i	$0.00118926\pi$
$984$	5.43536	+	33.9443i	0.173273	+	1.08210i
$985$	−20.5239	−	35.5484i	−0.653945	−	1.13267i
$986$	0.573647	−	3.55484i	0.0182687	−	0.113209i
$987$	18.3998	−	29.0360i	0.585674	−	0.924226i
$988$	0.903910	−	2.72779i	0.0287572	−	0.0867827i
$989$	27.7779	−	16.0376i	0.883285	−	0.509965i
$990$	35.0390	−	2.46785i	1.11361	−	0.0784333i
$991$	−30.1606	−	17.4132i	−0.958083	−	0.553149i	−0.0625004	−	0.998045i	$-0.519907\pi$
$991$	−30.1606	−	17.4132i	−0.958083	−	0.553149i	−0.895582	+	0.444896i	$0.853241\pi$
$992$	−5.68085	+	20.0301i	−0.180367	+	0.635957i
$993$	−55.7652	−	24.1343i	−1.76966	−	0.765879i
$994$	3.29981	−	0.693774i	0.104664	−	0.0220052i
$995$	15.9161			0.504573
$996$	−42.1878	−	8.76423i	−1.33677	−	0.277705i
$997$	−4.22860	+	7.32414i	−0.133921	+	0.231958i	−0.925185	−	0.379517i	$-0.876090\pi$
$997$	−4.22860	+	7.32414i	−0.133921	+	0.231958i	0.791264	+	0.611475i	$0.209424\pi$
$998$	−3.83467	+	4.70733i	−0.121384	+	0.149008i
$999$	−16.5761	−	14.0111i	−0.524443	−	0.443292i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	84.2.n.a.11.12	yes	24
3.2	odd	2	inner	84.2.n.a.11.1	✓	24
4.3	odd	2	inner	84.2.n.a.11.10	yes	24
7.2	even	3	inner	84.2.n.a.23.3	yes	24
7.3	odd	6		588.2.e.d.491.6		12
7.4	even	3		588.2.e.e.491.6		12
7.5	odd	6		588.2.n.e.275.3		24
7.6	odd	2		588.2.n.e.263.12		24
12.11	even	2	inner	84.2.n.a.11.3	yes	24
21.2	odd	6	inner	84.2.n.a.23.10	yes	24
21.5	even	6		588.2.n.e.275.10		24
21.11	odd	6		588.2.e.e.491.7		12
21.17	even	6		588.2.e.d.491.7		12
21.20	even	2		588.2.n.e.263.1		24
28.3	even	6		588.2.e.d.491.8		12
28.11	odd	6		588.2.e.e.491.8		12
28.19	even	6		588.2.n.e.275.1		24
28.23	odd	6	inner	84.2.n.a.23.1	yes	24
28.27	even	2		588.2.n.e.263.10		24
84.11	even	6		588.2.e.e.491.5		12
84.23	even	6	inner	84.2.n.a.23.12	yes	24
84.47	odd	6		588.2.n.e.275.12		24
84.59	odd	6		588.2.e.d.491.5		12
84.83	odd	2		588.2.n.e.263.3		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
84.2.n.a.11.1	✓	24	3.2	odd	2	inner
84.2.n.a.11.3	yes	24	12.11	even	2	inner
84.2.n.a.11.10	yes	24	4.3	odd	2	inner
84.2.n.a.11.12	yes	24	1.1	even	1	trivial
84.2.n.a.23.1	yes	24	28.23	odd	6	inner
84.2.n.a.23.3	yes	24	7.2	even	3	inner
84.2.n.a.23.10	yes	24	21.2	odd	6	inner
84.2.n.a.23.12	yes	24	84.23	even	6	inner
588.2.e.d.491.5		12	84.59	odd	6
588.2.e.d.491.6		12	7.3	odd	6
588.2.e.d.491.7		12	21.17	even	6
588.2.e.d.491.8		12	28.3	even	6
588.2.e.e.491.5		12	84.11	even	6
588.2.e.e.491.6		12	7.4	even	3
588.2.e.e.491.7		12	21.11	odd	6
588.2.e.e.491.8		12	28.11	odd	6
588.2.n.e.263.1		24	21.20	even	2
588.2.n.e.263.3		24	84.83	odd	2
588.2.n.e.263.10		24	28.27	even	2
588.2.n.e.263.12		24	7.6	odd	2
588.2.n.e.275.1		24	28.19	even	6
588.2.n.e.275.3		24	7.5	odd	6
588.2.n.e.275.10		24	21.5	even	6
588.2.n.e.275.12		24	84.47	odd	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 $\F_{q}$

Level:	\( N \)	\(=\)	\( 84 = 2^{2} \cdot 3 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	84.n (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.32175 - 0.502962i) q^{2} +(-1.03264 - 1.39056i) q^{3} +(1.49406 - 1.32958i) q^{4} +(-1.79791 + 1.03802i) q^{5} +(-2.06429 - 1.31860i) q^{6} +(2.61347 + 0.412056i) q^{7} +(1.30604 - 2.50883i) q^{8} +(-0.867316 + 2.87189i) q^{9} +O(q^{10})\)	\(q+(1.32175 - 0.502962i) q^{2} +(-1.03264 - 1.39056i) q^{3} +(1.49406 - 1.32958i) q^{4} +(-1.79791 + 1.03802i) q^{5} +(-2.06429 - 1.31860i) q^{6} +(2.61347 + 0.412056i) q^{7} +(1.30604 - 2.50883i) q^{8} +(-0.867316 + 2.87189i) q^{9} +(-1.85431 + 2.27629i) q^{10} +(-1.99399 + 3.45368i) q^{11} +(-3.39169 - 0.704599i) q^{12} -1.30998 q^{13} +(3.66160 - 0.769840i) q^{14} +(3.30003 + 1.42820i) q^{15} +(0.464417 - 3.97295i) q^{16} +(2.54752 + 1.47081i) q^{17} +(0.298077 + 4.23216i) q^{18} +(-0.949883 + 0.548415i) q^{19} +(-1.30604 + 3.94134i) q^{20} +(-2.12578 - 4.05969i) q^{21} +(-0.898482 + 5.56781i) q^{22} +(-3.75063 - 6.49627i) q^{23} +(-4.83736 + 0.774586i) q^{24} +(-0.345008 + 0.597572i) q^{25} +(-1.73147 + 0.658872i) q^{26} +(4.88916 - 1.75957i) q^{27} +(4.45253 - 2.85919i) q^{28} -0.865568i q^{29} +(5.08015 + 0.227937i) q^{30} +(-3.18742 - 1.84026i) q^{31} +(-1.38440 - 5.48484i) q^{32} +(6.86162 - 0.793650i) q^{33} +(4.10695 + 0.662741i) q^{34} +(-5.12651 + 1.97200i) q^{35} +(2.52260 + 5.44394i) q^{36} +(-2.08850 - 3.61738i) q^{37} +(-0.979678 + 1.20262i) q^{38} +(1.35274 + 1.82161i) q^{39} +(0.256080 + 5.86637i) q^{40} -7.01712i q^{41} +(-4.85162 - 4.29672i) q^{42} +4.27597i q^{43} +(1.61283 + 7.81117i) q^{44} +(-1.42174 - 6.06370i) q^{45} +(-8.22478 - 6.70004i) q^{46} +(3.75063 + 6.49627i) q^{47} +(-6.00420 + 3.45682i) q^{48} +(6.66042 + 2.15379i) q^{49} +(-0.155459 + 0.963368i) q^{50} +(-0.585414 - 5.06129i) q^{51} +(-1.95719 + 1.74173i) q^{52} +(4.27909 + 2.47053i) q^{53} +(5.57726 - 4.78478i) q^{54} -8.27923i q^{55} +(4.44708 - 6.01859i) q^{56} +(1.74349 + 0.754555i) q^{57} +(-0.435348 - 1.14407i) q^{58} +(2.44458 - 4.23414i) q^{59} +(6.82935 - 2.25385i) q^{60} +(-2.05347 - 3.55672i) q^{61} +(-5.13856 - 0.829212i) q^{62} +(-3.45008 + 7.14821i) q^{63} +(-4.58850 - 6.55330i) q^{64} +(2.35524 - 1.35980i) q^{65} +(8.67019 - 4.50015i) q^{66} +(2.09778 + 1.21116i) q^{67} +(5.76170 - 1.18966i) q^{68} +(-5.16042 + 11.9238i) q^{69} +(-5.78413 + 5.18494i) q^{70} +0.901192 q^{71} +(6.07235 + 5.92677i) q^{72} +(-6.50543 + 11.2677i) q^{73} +(-4.57989 - 3.73085i) q^{74} +(1.18723 - 0.137321i) q^{75} +(-0.690016 + 2.08231i) q^{76} +(-6.63432 + 8.20446i) q^{77} +(2.70419 + 1.72734i) q^{78} +(-8.97336 + 5.18077i) q^{79} +(3.28904 + 7.62509i) q^{80} +(-7.49553 - 4.98167i) q^{81} +(-3.52935 - 9.27489i) q^{82} +12.4386 q^{83} +(-8.57373 - 3.23901i) q^{84} -6.10695 q^{85} +(2.15065 + 5.65178i) q^{86} +(-1.20363 + 0.893819i) q^{87} +(6.06049 + 9.51324i) q^{88} +(-7.38393 + 4.26311i) q^{89} +(-4.92900 - 7.29963i) q^{90} +(-3.42360 - 0.539786i) q^{91} +(-14.2410 - 4.71904i) q^{92} +(0.732462 + 6.33262i) q^{93} +(8.22478 + 6.70004i) q^{94} +(1.13854 - 1.97200i) q^{95} +(-6.19741 + 7.58894i) q^{96} +15.3909 q^{97} +(9.88670 - 0.503167i) q^{98} +(-8.18919 - 8.72195i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - 2 q^{4} - 2 q^{9}+O(q^{10}) \) 24 * q - 2 * q^4 - 2 * q^9	\( 24 q - 2 q^{4} - 2 q^{9} - 10 q^{10} - 12 q^{12} - 24 q^{13} - 10 q^{16} - 10 q^{18} - 6 q^{21} + 28 q^{22} - 14 q^{24} - 12 q^{25} + 10 q^{28} - 14 q^{30} + 10 q^{33} - 8 q^{34} + 44 q^{36} - 8 q^{37} + 34 q^{40} + 38 q^{42} - 18 q^{45} + 24 q^{46} + 8 q^{48} + 16 q^{52} + 38 q^{54} - 4 q^{57} + 14 q^{58} + 14 q^{60} + 4 q^{61} - 68 q^{64} + 30 q^{66} + 36 q^{69} - 90 q^{70} + 20 q^{72} - 24 q^{76} - 104 q^{78} + 26 q^{81} - 68 q^{82} - 76 q^{84} - 40 q^{85} - 34 q^{88} - 40 q^{90} - 6 q^{93} - 24 q^{94} - 62 q^{96} + 72 q^{97}+O(q^{100}) \) 24 * q - 2 * q^4 - 2 * q^9 - 10 * q^10 - 12 * q^12 - 24 * q^13 - 10 * q^16 - 10 * q^18 - 6 * q^21 + 28 * q^22 - 14 * q^24 - 12 * q^25 + 10 * q^28 - 14 * q^30 + 10 * q^33 - 8 * q^34 + 44 * q^36 - 8 * q^37 + 34 * q^40 + 38 * q^42 - 18 * q^45 + 24 * q^46 + 8 * q^48 + 16 * q^52 + 38 * q^54 - 4 * q^57 + 14 * q^58 + 14 * q^60 + 4 * q^61 - 68 * q^64 + 30 * q^66 + 36 * q^69 - 90 * q^70 + 20 * q^72 - 24 * q^76 - 104 * q^78 + 26 * q^81 - 68 * q^82 - 76 * q^84 - 40 * q^85 - 34 * q^88 - 40 * q^90 - 6 * q^93 - 24 * q^94 - 62 * q^96 + 72 * q^97

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