LMFDB - Embedded newform 570.2.q.b.349.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [570,2,Mod(49,570)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(570, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 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("570.49");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 570 = 2 \cdot 3 \cdot 5 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	570.q (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:	$4.55147291521$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$6$ over $\Q(\zeta_{6})$
Coefficient field:	12.0.89539436150784.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 2x^{11} + 2x^{10} - 8x^{9} + 4x^{8} + 16x^{7} - 8x^{6} + 20x^{5} + 20x^{4} - 24x^{3} + 8x^{2} - 8x + 4 $ x^12 - 2x^11 + 2x^10 - 8x^9 + 4x^8 + 16x^7 - 8x^6 + 20x^5 + 20x^4 - 24x^3 + 8x^2 - 8*x + 4
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			349.3
Root			$0.312819 - 1.16746i$ of defining polynomial
Character	$\chi$	$=$	570.349
Dual form			570.2.q.b.49.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.866025 + 0.500000i) q^{2} +(-0.866025 + 0.500000i) q^{3} +(0.500000 - 0.866025i) q^{4} +(2.14894 - 0.618092i) q^{5} +(0.500000 - 0.866025i) q^{6} +3.53919i q^{7} +1.00000i q^{8} +(0.500000 - 0.866025i) q^{9} +O(q^{10})$	\(q+(-0.866025 + 0.500000i) q^{2} +(-0.866025 + 0.500000i) q^{3} +(0.500000 - 0.866025i) q^{4} +(2.14894 - 0.618092i) q^{5} +(0.500000 - 0.866025i) q^{6} +3.53919i q^{7} +1.00000i q^{8} +(0.500000 - 0.866025i) q^{9} +(-1.55199 + 1.60976i) q^{10} +3.34017 q^{11} +1.00000i q^{12} +(-1.48028 - 0.854638i) q^{13} +(-1.76959 - 3.06503i) q^{14} +(-1.55199 + 1.60976i) q^{15} +(-0.500000 - 0.866025i) q^{16} +(-3.29175 + 1.90049i) q^{17} +1.00000i q^{18} +(1.30878 - 4.15777i) q^{19} +(0.539189 - 2.17009i) q^{20} +(-1.76959 - 3.06503i) q^{21} +(-2.89267 + 1.67009i) q^{22} +(7.33350 + 4.23400i) q^{23} +(-0.500000 - 0.866025i) q^{24} +(4.23592 - 2.65649i) q^{25} +1.70928 q^{26} +1.00000i q^{27} +(3.06503 + 1.76959i) q^{28} +(-3.97887 + 6.89160i) q^{29} +(0.539189 - 2.17009i) q^{30} +1.07838 q^{31} +(0.866025 + 0.500000i) q^{32} +(-2.89267 + 1.67009i) q^{33} +(1.90049 - 3.29175i) q^{34} +(2.18754 + 7.60552i) q^{35} +(-0.500000 - 0.866025i) q^{36} -4.70928i q^{37} +(0.945448 + 4.25513i) q^{38} +1.70928 q^{39} +(0.618092 + 2.14894i) q^{40} +(5.96441 + 10.3307i) q^{41} +(3.06503 + 1.76959i) q^{42} +(-4.39800 + 2.53919i) q^{43} +(1.67009 - 2.89267i) q^{44} +(0.539189 - 2.17009i) q^{45} -8.46800 q^{46} +(4.73543 + 2.73400i) q^{47} +(0.866025 + 0.500000i) q^{48} -5.52586 q^{49} +(-2.34017 + 4.41855i) q^{50} +(1.90049 - 3.29175i) q^{51} +(-1.48028 + 0.854638i) q^{52} +(-10.8342 - 6.25513i) q^{53} +(-0.500000 - 0.866025i) q^{54} +(7.17785 - 2.06453i) q^{55} -3.53919 q^{56} +(0.945448 + 4.25513i) q^{57} -7.95774i q^{58} +(2.93302 + 5.08013i) q^{59} +(0.618092 + 2.14894i) q^{60} +(-6.92522 + 11.9948i) q^{61} +(-0.933903 + 0.539189i) q^{62} +(3.06503 + 1.76959i) q^{63} -1.00000 q^{64} +(-3.70928 - 0.921622i) q^{65} +(1.67009 - 2.89267i) q^{66} +(7.82551 + 4.51806i) q^{67} +3.80098i q^{68} -8.46800 q^{69} +(-5.69723 - 5.49280i) q^{70} +(4.04585 + 7.00763i) q^{71} +(0.866025 + 0.500000i) q^{72} +(5.11673 - 2.95415i) q^{73} +(2.35464 + 4.07835i) q^{74} +(-2.34017 + 4.41855i) q^{75} +(-2.94635 - 3.21233i) q^{76} +11.8215i q^{77} +(-1.48028 + 0.854638i) q^{78} +(-3.53919 - 6.13005i) q^{79} +(-1.60976 - 1.55199i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(-10.3307 - 5.96441i) q^{82} -4.68035i q^{83} -3.53919 q^{84} +(-5.89911 + 6.11866i) q^{85} +(2.53919 - 4.39800i) q^{86} -7.95774i q^{87} +3.34017i q^{88} +(4.66229 - 8.07532i) q^{89} +(0.618092 + 2.14894i) q^{90} +(3.02472 - 5.23898i) q^{91} +(7.33350 - 4.23400i) q^{92} +(-0.933903 + 0.539189i) q^{93} -5.46800 q^{94} +(0.242616 - 9.74377i) q^{95} -1.00000 q^{96} +(5.06662 - 2.92522i) q^{97} +(4.78553 - 2.76293i) q^{98} +(1.67009 - 2.89267i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 6 q^{4} + 6 q^{6} + 6 q^{9}+O(q^{10}) $ 12 * q + 6 * q^4 + 6 * q^6 + 6 * q^9	$ 12 q + 6 q^{4} + 6 q^{6} + 6 q^{9} - 2 q^{10} - 4 q^{11} - 18 q^{14} - 2 q^{15} - 6 q^{16} + 6 q^{19} - 18 q^{21} - 6 q^{24} - 2 q^{25} - 8 q^{26} - 16 q^{29} + 4 q^{34} + 2 q^{35} - 6 q^{36} - 8 q^{39} + 2 q^{40} + 10 q^{41} - 2 q^{44} + 28 q^{46} - 56 q^{49} + 16 q^{50} + 4 q^{51} - 6 q^{54} - 8 q^{55} - 36 q^{56} + 8 q^{59} + 2 q^{60} - 28 q^{61} - 12 q^{64} - 16 q^{65} - 2 q^{66} + 28 q^{69} + 16 q^{70} + 44 q^{71} + 14 q^{74} + 16 q^{75} - 12 q^{76} - 36 q^{79} - 6 q^{81} - 36 q^{84} - 32 q^{85} + 24 q^{86} + 6 q^{89} + 2 q^{90} + 64 q^{94} - 12 q^{95} - 12 q^{96} - 2 q^{99}+O(q^{100}) $ 12 * q + 6 * q^4 + 6 * q^6 + 6 * q^9 - 2 * q^10 - 4 * q^11 - 18 * q^14 - 2 * q^15 - 6 * q^16 + 6 * q^19 - 18 * q^21 - 6 * q^24 - 2 * q^25 - 8 * q^26 - 16 * q^29 + 4 * q^34 + 2 * q^35 - 6 * q^36 - 8 * q^39 + 2 * q^40 + 10 * q^41 - 2 * q^44 + 28 * q^46 - 56 * q^49 + 16 * q^50 + 4 * q^51 - 6 * q^54 - 8 * q^55 - 36 * q^56 + 8 * q^59 + 2 * q^60 - 28 * q^61 - 12 * q^64 - 16 * q^65 - 2 * q^66 + 28 * q^69 + 16 * q^70 + 44 * q^71 + 14 * q^74 + 16 * q^75 - 12 * q^76 - 36 * q^79 - 6 * q^81 - 36 * q^84 - 32 * q^85 + 24 * q^86 + 6 * q^89 + 2 * q^90 + 64 * q^94 - 12 * q^95 - 12 * q^96 - 2 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/570\mathbb{Z}\right)^\times$.

$n$	$191$	$211$	$457$
$\chi(n)$	$1$	$e\left(\frac{1}{3}\right)$	$-1$

Coefficient data

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

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

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

$2$	−0.866025	+	0.500000i	−0.612372	+	0.353553i
$2$	−0.866025	+	0.500000i	−0.612372	+	0.353553i
$3$	−0.866025	+	0.500000i	−0.500000	+	0.288675i
$3$	−0.866025	+	0.500000i	−0.500000	+	0.288675i
$4$	0.500000	−	0.866025i	0.250000	−	0.433013i
$5$	2.14894	−	0.618092i	0.961037	−	0.276419i
$5$	2.14894	−	0.618092i	0.961037	−	0.276419i
$6$	0.500000	−	0.866025i	0.204124	−	0.353553i
$7$			3.53919i			1.33769i	0.743403	+	0.668844i	$0.233211\pi$
$7$			3.53919i			1.33769i	−0.743403	+	0.668844i	$0.766789\pi$
$8$			1.00000i			0.353553i
$9$	0.500000	−	0.866025i	0.166667	−	0.288675i
$10$	−1.55199	+	1.60976i	−0.490784	+	0.509049i
$11$	3.34017			1.00710			0.503550	−	0.863966i	$-0.332027\pi$
$11$	3.34017			1.00710			0.503550	+	0.863966i	$0.332027\pi$
$12$			1.00000i			0.288675i
$13$	−1.48028	−	0.854638i	−0.410555	−	0.237034i	0.280473	−	0.959862i	$-0.409509\pi$
$13$	−1.48028	−	0.854638i	−0.410555	−	0.237034i	−0.691028	+	0.722828i	$0.742842\pi$
$14$	−1.76959	−	3.06503i	−0.472944	−	0.819163i
$15$	−1.55199	+	1.60976i	−0.400723	+	0.415637i
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	−3.29175	+	1.90049i	−0.798366	+	0.460937i	−0.842900	−	0.538071i	$-0.819153\pi$
$17$	−3.29175	+	1.90049i	−0.798366	+	0.460937i	0.0445332	+	0.999008i	$0.485820\pi$
$18$			1.00000i			0.235702i
$19$	1.30878	−	4.15777i	0.300255	−	0.953859i
$19$	1.30878	−	4.15777i	0.300255	−	0.953859i
$20$	0.539189	−	2.17009i	0.120566	−	0.485246i
$21$	−1.76959	−	3.06503i	−0.386157	−	0.668844i
$22$	−2.89267	+	1.67009i	−0.616720	+	0.356064i
$23$	7.33350	+	4.23400i	1.52914	+	0.882850i	0.999398	+	0.0346916i	$0.0110449\pi$
$23$	7.33350	+	4.23400i	1.52914	+	0.882850i	0.529743	+	0.848158i	$0.322288\pi$
$24$	−0.500000	−	0.866025i	−0.102062	−	0.176777i
$25$	4.23592	−	2.65649i	0.847185	−	0.531298i
$26$	1.70928			0.335216
$27$			1.00000i			0.192450i
$28$	3.06503	+	1.76959i	0.579236	+	0.334422i
$29$	−3.97887	+	6.89160i	−0.738858	+	1.27974i	0.214152	+	0.976800i	$0.431301\pi$
$29$	−3.97887	+	6.89160i	−0.738858	+	1.27974i	−0.953010	+	0.302939i	$0.902032\pi$
$30$	0.539189	−	2.17009i	0.0984420	−	0.396202i
$31$	1.07838			0.193682			0.0968412	−	0.995300i	$-0.469126\pi$
$31$	1.07838			0.193682			0.0968412	+	0.995300i	$0.469126\pi$
$32$	0.866025	+	0.500000i	0.153093	+	0.0883883i
$33$	−2.89267	+	1.67009i	−0.503550	+	0.290725i
$34$	1.90049	−	3.29175i	0.325932	−	0.564530i
$35$	2.18754	+	7.60552i	0.369762	+	1.28557i
$36$	−0.500000	−	0.866025i	−0.0833333	−	0.144338i
$37$		−	4.70928i		−	0.774200i	−0.922038	−	0.387100i	$-0.873477\pi$
$37$		−	4.70928i		−	0.774200i	0.922038	−	0.387100i	$-0.126523\pi$
$38$	0.945448	+	4.25513i	0.153372	+	0.690273i
$39$	1.70928			0.273703
$40$	0.618092	+	2.14894i	0.0977289	+	0.339778i
$41$	5.96441	+	10.3307i	0.931484	+	1.61338i	0.780787	+	0.624797i	$0.214818\pi$
$41$	5.96441	+	10.3307i	0.931484	+	1.61338i	0.150696	+	0.988580i	$0.451848\pi$
$42$	3.06503	+	1.76959i	0.472944	+	0.273054i
$43$	−4.39800	+	2.53919i	−0.670689	+	0.387223i	−0.796338	−	0.604852i	$-0.793232\pi$
$43$	−4.39800	+	2.53919i	−0.670689	+	0.387223i	0.125648	+	0.992075i	$0.459899\pi$
$44$	1.67009	−	2.89267i	0.251775	−	0.436087i
$45$	0.539189	−	2.17009i	0.0803775	−	0.323497i
$46$	−8.46800			−1.24854
$47$	4.73543	+	2.73400i	0.690733	+	0.398795i	0.803887	−	0.594783i	$-0.202762\pi$
$47$	4.73543	+	2.73400i	0.690733	+	0.398795i	−0.113154	+	0.993578i	$0.536095\pi$
$48$	0.866025	+	0.500000i	0.125000	+	0.0721688i
$49$	−5.52586			−0.789408
$50$	−2.34017	+	4.41855i	−0.330950	+	0.624877i
$51$	1.90049	−	3.29175i	0.266122	−	0.460937i
$52$	−1.48028	+	0.854638i	−0.205277	+	0.118517i
$53$	−10.8342	−	6.25513i	−1.48819	−	0.859208i	−0.488283	−	0.872685i	$-0.662377\pi$
$53$	−10.8342	−	6.25513i	−1.48819	−	0.859208i	−0.999909	+	0.0134772i	$0.995710\pi$
$54$	−0.500000	−	0.866025i	−0.0680414	−	0.117851i
$55$	7.17785	−	2.06453i	0.967861	−	0.278382i
$56$	−3.53919			−0.472944
$57$	0.945448	+	4.25513i	0.125228	+	0.563606i
$58$		−	7.95774i		−	1.04490i
$59$	2.93302	+	5.08013i	0.381846	+	0.661377i	0.991326	−	0.131425i	$-0.0419551\pi$
$59$	2.93302	+	5.08013i	0.381846	+	0.661377i	−0.609480	+	0.792801i	$0.708622\pi$
$60$	0.618092	+	2.14894i	0.0797953	+	0.277428i
$61$	−6.92522	+	11.9948i	−0.886683	+	1.53578i	−0.0429107	+	0.999079i	$0.513663\pi$
$61$	−6.92522	+	11.9948i	−0.886683	+	1.53578i	−0.843772	+	0.536701i	$0.819670\pi$
$62$	−0.933903	+	0.539189i	−0.118606	+	0.0684771i
$63$	3.06503	+	1.76959i	0.386157	+	0.222948i
$64$	−1.00000			−0.125000
$65$	−3.70928	−	0.921622i	−0.460079	−	0.114313i
$66$	1.67009	−	2.89267i	0.205573	−	0.356064i
$67$	7.82551	+	4.51806i	0.956038	+	0.551969i	0.894951	−	0.446164i	$-0.147210\pi$
$67$	7.82551	+	4.51806i	0.956038	+	0.551969i	0.0610865	+	0.998132i	$0.480543\pi$
$68$			3.80098i			0.460937i
$69$	−8.46800			−1.01943
$70$	−5.69723	−	5.49280i	−0.680949	−	0.656515i
$71$	4.04585	+	7.00763i	0.480155	+	0.831652i	0.999741	−	0.0227659i	$-0.00724723\pi$
$71$	4.04585	+	7.00763i	0.480155	+	0.831652i	−0.519586	+	0.854418i	$0.673914\pi$
$72$	0.866025	+	0.500000i	0.102062	+	0.0589256i
$73$	5.11673	−	2.95415i	0.598868	−	0.345757i	−0.169728	−	0.985491i	$-0.554289\pi$
$73$	5.11673	−	2.95415i	0.598868	−	0.345757i	0.768596	+	0.639734i	$0.220956\pi$
$74$	2.35464	+	4.07835i	0.273721	+	0.474099i
$75$	−2.34017	+	4.41855i	−0.270220	+	0.510210i
$76$	−2.94635	−	3.21233i	−0.337969	−	0.368479i
$77$			11.8215i			1.34719i
$78$	−1.48028	+	0.854638i	−0.167608	+	0.0967687i
$79$	−3.53919	−	6.13005i	−0.398190	−	0.689685i	0.595313	−	0.803494i	$-0.297028\pi$
$79$	−3.53919	−	6.13005i	−0.398190	−	0.689685i	−0.993503	+	0.113809i	$0.963695\pi$
$80$	−1.60976	−	1.55199i	−0.179976	−	0.173518i
$81$	−0.500000	−	0.866025i	−0.0555556	−	0.0962250i
$82$	−10.3307	−	5.96441i	−1.14083	−	0.658658i
$83$		−	4.68035i		−	0.513735i	−0.966447	−	0.256867i	$-0.917310\pi$
$83$		−	4.68035i		−	0.513735i	0.966447	−	0.256867i	$-0.0826903\pi$
$84$	−3.53919			−0.386157
$85$	−5.89911	+	6.11866i	−0.639848	+	0.663661i
$86$	2.53919	−	4.39800i	0.273808	−	0.474249i
$87$		−	7.95774i		−	0.853159i
$88$			3.34017i			0.356064i
$89$	4.66229	−	8.07532i	0.494201	−	0.855982i	−0.505776	−	0.862665i	$-0.668794\pi$
$89$	4.66229	−	8.07532i	0.494201	−	0.855982i	0.999978	+	0.00668268i	$0.00212718\pi$
$90$	0.618092	+	2.14894i	0.0651526	+	0.226519i
$91$	3.02472	−	5.23898i	0.317077	−	0.549194i
$92$	7.33350	−	4.23400i	0.764570	−	0.441425i
$93$	−0.933903	+	0.539189i	−0.0968412	+	0.0559113i
$94$	−5.46800			−0.563981
$95$	0.242616	−	9.74377i	0.0248919	−	0.999690i
$96$	−1.00000			−0.102062
$97$	5.06662	−	2.92522i	0.514438	−	0.297011i	−0.220218	−	0.975451i	$-0.570677\pi$
$97$	5.06662	−	2.92522i	0.514438	−	0.297011i	0.734656	+	0.678440i	$0.237344\pi$
$98$	4.78553	−	2.76293i	0.483412	−	0.279098i
$99$	1.67009	−	2.89267i	0.167850	−	0.290725i
$100$	−0.182626	−	4.99666i	−0.0182626	−	0.499666i
$101$	4.32684	−	7.49431i	0.430537	−	0.745712i	−0.566383	−	0.824142i	$-0.691658\pi$
$101$	4.32684	−	7.49431i	0.430537	−	0.745712i	0.996920	+	0.0784306i	$0.0249909\pi$
$102$			3.80098i			0.376354i
$103$		−	0.751536i		−	0.0740510i	−0.999314	−	0.0370255i	$-0.988212\pi$
$103$		−	0.751536i		−	0.0740510i	0.999314	−	0.0370255i	$-0.0117883\pi$
$104$	0.854638	−	1.48028i	0.0838041	−	0.145153i
$105$	−5.69723	−	5.49280i	−0.555993	−	0.536043i
$106$	12.5103			1.21510
$107$		−	9.82377i		−	0.949700i	−0.880067	−	0.474850i	$-0.842502\pi$
$107$		−	9.82377i		−	0.949700i	0.880067	−	0.474850i	$-0.157498\pi$
$108$	0.866025	+	0.500000i	0.0833333	+	0.0481125i
$109$	−3.92522	−	6.79867i	−0.375968	−	0.651195i	0.614504	−	0.788914i	$-0.289356\pi$
$109$	−3.92522	−	6.79867i	−0.375968	−	0.651195i	−0.990471	+	0.137719i	$0.956023\pi$
$110$	−5.18393	+	5.37686i	−0.494268	+	0.512664i
$111$	2.35464	+	4.07835i	0.223492	+	0.387100i
$112$	3.06503	−	1.76959i	0.289618	−	0.167211i
$113$		−	7.98440i		−	0.751109i	−0.926800	−	0.375555i	$-0.877452\pi$
$113$		−	7.98440i		−	0.751109i	0.926800	−	0.375555i	$-0.122548\pi$
$114$	−2.94635	−	3.21233i	−0.275951	−	0.300862i
$115$	18.3763	+	4.56585i	1.71360	+	0.425768i
$116$	3.97887	+	6.89160i	0.369429	+	0.639869i
$117$	−1.48028	+	0.854638i	−0.136852	+	0.0790113i
$118$	−5.08013	−	2.93302i	−0.467664	−	0.270006i
$119$	−6.72620	−	11.6501i	−0.616590	−	1.06796i
$120$	−1.60976	−	1.55199i	−0.146950	−	0.141677i
$121$	0.156755			0.0142505
$122$		−	13.8504i		−	1.25396i
$123$	−10.3307	−	5.96441i	−0.931484	−	0.537792i
$124$	0.539189	−	0.933903i	0.0484206	−	0.0838669i
$125$	7.46081	−	8.32684i	0.667315	−	0.744775i
$126$	−3.53919			−0.315296
$127$	−16.1160	−	9.30458i	−1.43006	−	0.825648i	−0.432939	−	0.901423i	$-0.642523\pi$
$127$	−16.1160	−	9.30458i	−1.43006	−	0.825648i	−0.997125	+	0.0757754i	$0.975857\pi$
$128$	0.866025	−	0.500000i	0.0765466	−	0.0441942i
$129$	2.53919	−	4.39800i	0.223563	−	0.387223i
$130$	3.67314	−	1.05649i	0.322155	−	0.0926602i
$131$	3.79072	+	6.56573i	0.331197	+	0.573650i	0.982747	−	0.184956i	$-0.0592141\pi$
$131$	3.79072	+	6.56573i	0.331197	+	0.573650i	−0.651550	+	0.758606i	$0.725881\pi$
$132$			3.34017i			0.290725i
$133$	14.7151	+	4.63203i	1.27597	+	0.401648i
$134$	−9.03612			−0.780602
$135$	0.618092	+	2.14894i	0.0531969	+	0.184952i
$136$	−1.90049	−	3.29175i	−0.162966	−	0.282265i
$137$	9.88875	+	5.70928i	0.844853	+	0.487776i	0.858911	−	0.512125i	$-0.171142\pi$
$137$	9.88875	+	5.70928i	0.844853	+	0.487776i	−0.0140576	+	0.999901i	$0.504475\pi$
$138$	7.33350	−	4.23400i	0.624269	−	0.360422i
$139$	1.80098	−	3.11940i	0.152757	−	0.264584i	−0.779483	−	0.626424i	$-0.784518\pi$
$139$	1.80098	−	3.11940i	0.152757	−	0.264584i	0.932240	+	0.361840i	$0.117851\pi$
$140$	7.68035	+	1.90829i	0.649108	+	0.161280i
$141$	−5.46800			−0.460489
$142$	−7.00763	−	4.04585i	−0.588067	−	0.339521i
$143$	−4.94438	−	2.85464i	−0.413470	−	0.238717i
$144$	−1.00000			−0.0833333
$145$	−4.29072	+	17.2690i	−0.356325	+	1.43411i
$146$	−2.95415	+	5.11673i	−0.244487	+	0.423464i
$147$	4.78553	−	2.76293i	0.394704	−	0.227883i
$148$	−4.07835	−	2.35464i	−0.335238	−	0.193550i
$149$	−5.14896	−	8.91825i	−0.421819	−	0.730612i	0.574299	−	0.818646i	$-0.305275\pi$
$149$	−5.14896	−	8.91825i	−0.421819	−	0.730612i	−0.996117	+	0.0880341i	$0.971942\pi$
$150$	−0.182626	−	4.99666i	−0.0149114	−	0.407976i
$151$	−4.69594			−0.382151			−0.191075	−	0.981575i	$-0.561197\pi$
$151$	−4.69594			−0.382151			−0.191075	+	0.981575i	$0.561197\pi$
$152$	4.15777	+	1.30878i	0.337240	+	0.106156i
$153$			3.80098i			0.307291i
$154$	−5.91075	−	10.2377i	−0.476302	−	0.824979i
$155$	2.31737	−	0.666537i	0.186136	−	0.0535375i
$156$	0.854638	−	1.48028i	0.0684258	−	0.118517i
$157$	−9.10838	+	5.25872i	−0.726928	+	0.419692i	−0.817297	−	0.576216i	$-0.804529\pi$
$157$	−9.10838	+	5.25872i	−0.726928	+	0.419692i	0.0903695	+	0.995908i	$0.471195\pi$
$158$	6.13005	+	3.53919i	0.487681	+	0.281563i
$159$	12.5103			0.992128
$160$	2.17009	+	0.539189i	0.171560	+	0.0426266i
$161$	−14.9849	+	25.9546i	−1.18098	+	2.04551i
$162$	0.866025	+	0.500000i	0.0680414	+	0.0392837i
$163$		−	16.7792i		−	1.31425i	−0.753781	−	0.657126i	$-0.771772\pi$
$163$		−	16.7792i		−	1.31425i	0.753781	−	0.657126i	$-0.228228\pi$
$164$	11.9288			0.931484
$165$	−5.18393	+	5.37686i	−0.403568	+	0.418588i
$166$	2.34017	+	4.05330i	0.181633	+	0.314597i
$167$	10.0496	+	5.80212i	0.777659	+	0.448981i	0.835600	−	0.549339i	$-0.185120\pi$
$167$	10.0496	+	5.80212i	0.777659	+	0.448981i	−0.0579413	+	0.998320i	$0.518454\pi$
$168$	3.06503	−	1.76959i	0.236472	−	0.136527i
$169$	−5.03919	−	8.72813i	−0.387630	−	0.671395i
$170$	2.04945	−	8.24846i	0.157186	−	0.632628i
$171$	−2.94635	−	3.21233i	−0.225313	−	0.245653i
$172$			5.07838i			0.387223i
$173$	−7.70752	+	4.44994i	−0.585992	+	0.338323i	−0.763511	−	0.645795i	$-0.776526\pi$
$173$	−7.70752	+	4.44994i	−0.585992	+	0.338323i	0.177519	+	0.984117i	$0.443193\pi$
$174$	3.97887	+	6.89160i	0.301637	+	0.522451i
$175$	9.40182	+	14.9917i	0.710711	+	1.13327i
$176$	−1.67009	−	2.89267i	−0.125888	−	0.218044i
$177$	−5.08013	−	2.93302i	−0.381846	−	0.220459i
$178$			9.32457i			0.698906i
$179$	−21.8599			−1.63388			−0.816942	−	0.576719i	$-0.804333\pi$
$179$	−21.8599			−1.63388			−0.816942	+	0.576719i	$0.804333\pi$
$180$	−1.60976	−	1.55199i	−0.119984	−	0.115679i
$181$	2.66342	−	4.61318i	0.197971	−	0.342895i	−0.749900	−	0.661551i	$-0.769898\pi$
$181$	2.66342	−	4.61318i	0.197971	−	0.342895i	0.947870	+	0.318656i	$0.103232\pi$
$182$			6.04945i			0.448415i
$183$		−	13.8504i		−	1.02385i
$184$	−4.23400	+	7.33350i	−0.312135	+	0.540633i
$185$	−2.91077	−	10.1200i	−0.214004	−	0.744035i
$186$	0.539189	−	0.933903i	0.0395352	−	0.0684771i
$187$	−10.9950	+	6.34797i	−0.804035	+	0.464210i
$188$	4.73543	−	2.73400i	0.345366	−	0.199397i
$189$	−3.53919			−0.257438
$190$	4.66178	+	8.55966i	0.338201	+	0.620983i
$191$	8.99386			0.650773			0.325386	−	0.945581i	$-0.394506\pi$
$191$	8.99386			0.650773			0.325386	+	0.945581i	$0.394506\pi$
$192$	0.866025	−	0.500000i	0.0625000	−	0.0360844i
$193$	2.02042	−	1.16649i	0.145433	−	0.0839660i	−0.425518	−	0.904950i	$-0.639908\pi$
$193$	2.02042	−	1.16649i	0.145433	−	0.0839660i	0.570951	+	0.820984i	$0.306575\pi$
$194$	−2.92522	+	5.06662i	−0.210018	+	0.363762i
$195$	3.67314	−	1.05649i	0.263039	−	0.0756568i
$196$	−2.76293	+	4.78553i	−0.197352	+	0.341824i
$197$		−	24.0856i		−	1.71603i	−0.513628	−	0.858013i	$-0.671699\pi$
$197$		−	24.0856i		−	1.71603i	0.513628	−	0.858013i	$-0.328301\pi$
$198$			3.34017i			0.237376i
$199$	0.652028	−	1.12935i	0.0462210	−	0.0800572i	−0.841989	−	0.539494i	$-0.818615\pi$
$199$	0.652028	−	1.12935i	0.0462210	−	0.0800572i	0.888210	+	0.459437i	$0.151949\pi$
$200$	2.65649	+	4.23592i	0.187842	+	0.299525i
$201$	−9.03612			−0.637359
$202$			8.65368i			0.608871i
$203$	−24.3907	−	14.0820i	−1.71189	−	0.988361i
$204$	−1.90049	−	3.29175i	−0.133061	−	0.230469i
$205$	19.2025	+	18.5134i	1.34116	+	1.29304i
$206$	0.375768	+	0.650849i	0.0261810	+	0.0453468i
$207$	7.33350	−	4.23400i	0.509714	−	0.294283i
$208$			1.70928i			0.118517i
$209$	4.37156	−	13.8877i	0.302387	−	0.960631i
$210$	7.68035	+	1.90829i	0.529994	+	0.131685i
$211$	−3.49220	−	6.04867i	−0.240413	−	0.416408i	0.720419	−	0.693539i	$-0.243950\pi$
$211$	−3.49220	−	6.04867i	−0.240413	−	0.416408i	−0.960832	+	0.277132i	$0.910616\pi$
$212$	−10.8342	+	6.25513i	−0.744096	+	0.429604i
$213$	−7.00763	−	4.04585i	−0.480155	−	0.277217i
$214$	4.91189	+	8.50763i	0.335770	+	0.581570i
$215$	−7.88161	+	8.17495i	−0.537522	+	0.557527i
$216$	−1.00000			−0.0680414
$217$			3.81658i			0.259087i
$218$	6.79867	+	3.92522i	0.460464	+	0.265849i
$219$	−2.95415	+	5.11673i	−0.199623	+	0.345757i
$220$	1.80098	−	7.24846i	0.121422	−	0.488691i
$221$	6.49693			0.437031
$222$	−4.07835	−	2.35464i	−0.273721	−	0.158033i
$223$	−8.67180	+	5.00667i	−0.580707	+	0.335271i	−0.761414	−	0.648266i	$-0.775495\pi$
$223$	−8.67180	+	5.00667i	−0.580707	+	0.335271i	0.180708	+	0.983537i	$0.442161\pi$
$224$	−1.76959	+	3.06503i	−0.118236	+	0.204791i
$225$	−0.182626	−	4.99666i	−0.0121751	−	0.333111i
$226$	3.99220	+	6.91469i	0.265557	+	0.459959i
$227$			14.2485i			0.945704i	0.881142	+	0.472852i	$0.156775\pi$
$227$			14.2485i			0.945704i	−0.881142	+	0.472852i	$0.843225\pi$
$228$	4.15777	+	1.30878i	0.275355	+	0.0866763i
$229$	15.8576			1.04790			0.523951	−	0.851749i	$-0.324458\pi$
$229$	15.8576			1.04790			0.523951	+	0.851749i	$0.324458\pi$
$230$	−18.1973	+	5.23400i	−1.19989	+	0.345120i
$231$	−5.91075	−	10.2377i	−0.388899	−	0.673593i
$232$	−6.89160	−	3.97887i	−0.452456	−	0.261226i
$233$	−21.3006	+	12.2979i	−1.39545	+	0.805663i	−0.993912	−	0.110179i	$-0.964857\pi$
$233$	−21.3006	+	12.2979i	−1.39545	+	0.805663i	−0.401538	+	0.915843i	$0.631524\pi$
$234$	0.854638	−	1.48028i	0.0558694	−	0.0967687i
$235$	11.8660	+	2.94828i	0.774055	+	0.192325i
$236$	5.86603			0.381846
$237$	6.13005	+	3.53919i	0.398190	+	0.229895i
$238$	11.6501	+	6.72620i	0.755165	+	0.435995i
$239$	−0.156755			−0.0101397			−0.00506983	−	0.999987i	$-0.501614\pi$
$239$	−0.156755			−0.0101397			−0.00506983	+	0.999987i	$0.501614\pi$
$240$	2.17009	+	0.539189i	0.140078	+	0.0348045i
$241$	12.7968	−	22.1647i	0.824313	−	1.42775i	−0.0781302	−	0.996943i	$-0.524895\pi$
$241$	12.7968	−	22.1647i	0.824313	−	1.42775i	0.902443	−	0.430809i	$-0.141772\pi$
$242$	−0.135754	+	0.0783777i	−0.00872661	+	0.00503831i
$243$	0.866025	+	0.500000i	0.0555556	+	0.0320750i
$244$	6.92522	+	11.9948i	0.443342	+	0.767890i
$245$	−11.8748	+	3.41549i	−0.758651	+	0.218208i
$246$	11.9288			0.760553
$247$	−5.49075	+	5.03612i	−0.349368	+	0.320440i
$248$			1.07838i			0.0684771i
$249$	2.34017	+	4.05330i	0.148302	+	0.256867i
$250$	−2.29783	+	10.9417i	−0.145328	+	0.692011i
$251$	5.32684	−	9.22636i	0.336227	−	0.582363i	−0.647493	−	0.762072i	$-0.724182\pi$
$251$	5.32684	−	9.22636i	0.336227	−	0.582363i	0.983720	+	0.179709i	$0.0575156\pi$
$252$	3.06503	−	1.76959i	0.193079	−	0.111474i
$253$	24.4952	+	14.1423i	1.54000	+	0.889118i
$254$	18.6092			1.16764
$255$	2.04945	−	8.24846i	0.128341	−	0.516539i
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	16.7899	+	9.69368i	1.04733	+	0.604675i	0.921900	−	0.387428i	$-0.126636\pi$
$257$	16.7899	+	9.69368i	1.04733	+	0.604675i	0.125428	+	0.992103i	$0.459970\pi$
$258$			5.07838i			0.316166i
$259$	16.6670			1.03564
$260$	−2.65279	+	2.75152i	−0.164519	+	0.170642i
$261$	3.97887	+	6.89160i	0.246286	+	0.426580i
$262$	−6.56573	−	3.79072i	−0.405632	−	0.234192i
$263$	26.5877	−	15.3504i	1.63947	−	0.946548i	0.658454	−	0.752621i	$-0.271211\pi$
$263$	26.5877	−	15.3504i	1.63947	−	0.946548i	0.981016	−	0.193927i	$-0.0621225\pi$
$264$	−1.67009	−	2.89267i	−0.102787	−	0.178032i
$265$	−27.1483	−	6.74539i	−1.66771	−	0.414366i
$266$	−15.0597	+	3.34612i	−0.923370	+	0.205164i
$267$			9.32457i			0.570655i
$268$	7.82551	−	4.51806i	0.478019	−	0.275984i
$269$	−14.1334	−	24.4797i	−0.861726	−	1.49255i	−0.870262	−	0.492590i	$-0.836050\pi$
$269$	−14.1334	−	24.4797i	−0.861726	−	1.49255i	0.00853563	−	0.999964i	$-0.497283\pi$
$270$	−1.60976	−	1.55199i	−0.0979666	−	0.0944514i
$271$	5.80817	+	10.0600i	0.352821	+	0.611104i	0.986743	−	0.162293i	$-0.0518890\pi$
$271$	5.80817	+	10.0600i	0.352821	+	0.611104i	−0.633921	+	0.773398i	$0.718556\pi$
$272$	3.29175	+	1.90049i	0.199592	+	0.115234i
$273$			6.04945i			0.366129i
$274$	−11.4186			−0.689820
$275$	14.1487	−	8.87314i	0.853200	−	0.535070i
$276$	−4.23400	+	7.33350i	−0.254857	+	0.441425i
$277$		−	26.1750i		−	1.57270i	−0.617779	−	0.786352i	$-0.711967\pi$
$277$		−	26.1750i		−	1.57270i	0.617779	−	0.786352i	$-0.288033\pi$
$278$			3.60197i			0.216032i
$279$	0.539189	−	0.933903i	0.0322804	−	0.0559113i
$280$	−7.60552	+	2.18754i	−0.454517	+	0.130731i
$281$	−12.0139	+	20.8086i	−0.716686	+	1.24134i	0.245619	+	0.969366i	$0.421009\pi$
$281$	−12.0139	+	20.8086i	−0.716686	+	1.24134i	−0.962305	+	0.271971i	$0.912325\pi$
$282$	4.73543	−	2.73400i	0.281991	−	0.162807i
$283$	−17.5920	+	10.1568i	−1.04574	+	0.603756i	−0.921453	−	0.388490i	$-0.872997\pi$
$283$	−17.5920	+	10.1568i	−1.04574	+	0.603756i	−0.124284	+	0.992247i	$0.539663\pi$
$284$	8.09171			0.480155
$285$	4.66178	+	8.55966i	0.276140	+	0.507031i
$286$	5.70928			0.337597
$287$	−36.5621	+	21.1092i	−2.15819	+	1.24603i
$288$	0.866025	−	0.500000i	0.0510310	−	0.0294628i
$289$	−1.27626	+	2.21055i	−0.0750741	+	0.130032i
$290$	−4.91862	−	17.1007i	−0.288831	−	1.00419i
$291$	−2.92522	+	5.06662i	−0.171479	+	0.297011i
$292$		−	5.90829i		−	0.345757i
$293$		−	5.32457i		−	0.311065i	−0.987831	−	0.155532i	$-0.950291\pi$
$293$		−	5.32457i		−	0.311065i	0.987831	−	0.155532i	$-0.0497093\pi$
$294$	−2.76293	+	4.78553i	−0.161137	+	0.279098i
$295$	9.44288	+	9.10405i	0.549785	+	0.530058i
$296$	4.70928			0.273721
$297$			3.34017i			0.193816i
$298$	8.91825	+	5.14896i	0.516621	+	0.298271i
$299$	−7.23707	−	12.5350i	−0.418531	−	0.724916i
$300$	2.65649	+	4.23592i	0.153373	+	0.244561i
$301$	−8.98667	−	15.5654i	−0.517983	−	0.897173i
$302$	4.06681	−	2.34797i	0.234018	−	0.135111i
$303$			8.65368i			0.497141i
$304$	−4.25513	+	0.945448i	−0.244048	+	0.0542251i
$305$	−7.46800	+	30.0566i	−0.427616	+	1.72104i
$306$	−1.90049	−	3.29175i	−0.108644	−	0.188177i
$307$	−3.18301	+	1.83771i	−0.181664	+	0.104884i	−0.588074	−	0.808807i	$-0.700114\pi$
$307$	−3.18301	+	1.83771i	−0.181664	+	0.104884i	0.406410	+	0.913691i	$0.366780\pi$
$308$	10.2377	+	5.91075i	0.583348	+	0.336796i
$309$	0.375768	+	0.650849i	0.0213767	+	0.0370255i
$310$	−1.67364	+	1.73592i	−0.0950562	+	0.0985939i
$311$	−13.7321			−0.778674			−0.389337	−	0.921095i	$-0.627296\pi$
$311$	−13.7321			−0.778674			−0.389337	+	0.921095i	$0.627296\pi$
$312$			1.70928i			0.0967687i
$313$	−15.5384	−	8.97107i	−0.878279	−	0.507075i	−0.00818874	−	0.999966i	$-0.502607\pi$
$313$	−15.5384	−	8.97107i	−0.878279	−	0.507075i	−0.870091	+	0.492892i	$0.835940\pi$
$314$	5.25872	−	9.10838i	0.296767	−	0.514015i
$315$	7.68035	+	1.90829i	0.432738	+	0.107520i
$316$	−7.07838			−0.398190
$317$	6.35055	+	3.66649i	0.356682	+	0.205931i	0.667625	−	0.744498i	$-0.267311\pi$
$317$	6.35055	+	3.66649i	0.356682	+	0.205931i	−0.310942	+	0.950429i	$0.600645\pi$
$318$	−10.8342	+	6.25513i	−0.607552	+	0.350770i
$319$	−13.2901	+	23.0192i	−0.744103	+	1.28883i
$320$	−2.14894	+	0.618092i	−0.120130	+	0.0345524i
$321$	4.91189	+	8.50763i	0.274155	+	0.474850i
$322$		−	29.9698i		−	1.67015i
$323$	3.59363	+	16.1737i	0.199955	+	0.899928i
$324$	−1.00000			−0.0555556
$325$	−8.54067	+	0.312158i	−0.473751	+	0.0173154i
$326$	8.38962	+	14.5313i	0.464658	+	0.804812i
$327$	6.79867	+	3.92522i	0.375968	+	0.217065i
$328$	−10.3307	+	5.96441i	−0.570415	+	0.329329i
$329$	−9.67614	+	16.7596i	−0.533463	+	0.923985i
$330$	1.80098	−	7.24846i	0.0991409	−	0.399015i
$331$	21.4813			1.18072			0.590360	−	0.807140i	$-0.298986\pi$
$331$	21.4813			1.18072			0.590360	+	0.807140i	$0.298986\pi$
$332$	−4.05330	−	2.34017i	−0.222454	−	0.128434i
$333$	−4.07835	−	2.35464i	−0.223492	−	0.129033i
$334$	−11.6042			−0.634956
$335$	19.6092	+	4.87217i	1.07136	+	0.266195i
$336$	−1.76959	+	3.06503i	−0.0965393	+	0.167211i
$337$	17.6151	−	10.1701i	0.959556	−	0.554000i	0.0635196	−	0.997981i	$-0.479767\pi$
$337$	17.6151	−	10.1701i	0.959556	−	0.554000i	0.896036	+	0.443981i	$0.146434\pi$
$338$	8.72813	+	5.03919i	0.474748	+	0.274096i
$339$	3.99220	+	6.91469i	0.216827	+	0.375555i
$340$	2.34936	+	8.16810i	0.127412	+	0.442978i
$341$	3.60197			0.195058
$342$	4.15777	+	1.30878i	0.224827	+	0.0707709i
$343$			5.21727i			0.281706i
$344$	−2.53919	−	4.39800i	−0.136904	−	0.237124i
$345$	−18.1973	+	5.23400i	−0.979708	+	0.281789i
$346$	4.44994	−	7.70752i	0.239230	−	0.414359i
$347$	7.97084	−	4.60197i	0.427897	−	0.247047i	−0.270553	−	0.962705i	$-0.587207\pi$
$347$	7.97084	−	4.60197i	0.427897	−	0.247047i	0.698450	+	0.715658i	$0.253873\pi$
$348$	−6.89160	−	3.97887i	−0.369429	−	0.213290i
$349$	−8.24846			−0.441530			−0.220765	−	0.975327i	$-0.570855\pi$
$349$	−8.24846			−0.441530			−0.220765	+	0.975327i	$0.570855\pi$
$350$	−15.6381	−	8.28231i	−0.835891	−	0.442708i
$351$	0.854638	−	1.48028i	0.0456172	−	0.0790113i
$352$	2.89267	+	1.67009i	0.154180	+	0.0890159i
$353$		−	6.24005i		−	0.332125i	−0.986115	−	0.166062i	$-0.946895\pi$
$353$		−	6.24005i		−	0.332125i	0.986115	−	0.166062i	$-0.0531053\pi$
$354$	5.86603			0.311776
$355$	13.0257	+	12.5583i	0.691331	+	0.666525i
$356$	−4.66229	−	8.07532i	−0.247101	−	0.427991i
$357$	11.6501	+	6.72620i	0.616590	+	0.355988i
$358$	18.9312	−	10.9299i	1.00055	−	0.577665i
$359$	0.401626	+	0.695636i	0.0211970	+	0.0367143i	0.876429	−	0.481531i	$-0.159919\pi$
$359$	0.401626	+	0.695636i	0.0211970	+	0.0367143i	−0.855232	+	0.518245i	$0.826586\pi$
$360$	2.17009	+	0.539189i	0.114374	+	0.0284177i
$361$	−15.5742	−	10.8833i	−0.819693	−	0.572803i
$362$			5.32684i			0.279973i
$363$	−0.135754	+	0.0783777i	−0.00712525	+	0.00411376i
$364$	−3.02472	−	5.23898i	−0.158539	−	0.274597i
$365$	9.16964	−	9.51090i	0.479961	−	0.497824i
$366$	6.92522	+	11.9948i	0.361987	+	0.626980i
$367$	2.54265	+	1.46800i	0.132725	+	0.0766289i	0.564892	−	0.825165i	$-0.308918\pi$
$367$	2.54265	+	1.46800i	0.132725	+	0.0766289i	−0.432167	+	0.901793i	$0.642251\pi$
$368$		−	8.46800i		−	0.441425i
$369$	11.9288			0.620989
$370$	7.58078	+	7.30877i	0.394106	+	0.379965i
$371$	22.1381	−	38.3443i	1.14935	−	1.99074i
$372$			1.07838i			0.0559113i
$373$			25.5152i			1.32113i	0.750771	+	0.660563i	$0.229682\pi$
$373$			25.5152i			1.32113i	−0.750771	+	0.660563i	$0.770318\pi$
$374$	6.34797	−	10.9950i	0.328246	−	0.568538i
$375$	−2.29783	+	10.9417i	−0.118659	+	0.565025i
$376$	−2.73400	+	4.73543i	−0.140995	+	0.244211i
$377$	11.7797	−	6.80098i	0.606683	−	0.350269i
$378$	3.06503	−	1.76959i	0.157648	−	0.0910181i
$379$	26.6537			1.36911			0.684554	−	0.728962i	$-0.259997\pi$
$379$	26.6537			1.36911			0.684554	+	0.728962i	$0.259997\pi$
$380$	−8.31705	−	5.08200i	−0.426656	−	0.260701i
$381$	18.6092			0.953376
$382$	−7.78891	+	4.49693i	−0.398515	+	0.230083i
$383$	−8.35837	+	4.82571i	−0.427093	+	0.246582i	−0.698107	−	0.715993i	$-0.745974\pi$
$383$	−8.35837	+	4.82571i	−0.427093	+	0.246582i	0.271015	+	0.962575i	$0.412641\pi$
$384$	−0.500000	+	0.866025i	−0.0255155	+	0.0441942i
$385$	7.30678	+	25.4038i	0.372388	+	1.29470i
$386$	−1.16649	+	2.02042i	−0.0593729	+	0.102837i
$387$			5.07838i			0.258148i
$388$		−	5.85043i		−	0.297011i
$389$	−10.2407	+	17.7374i	−0.519222	+	0.899319i	0.480528	+	0.876979i	$0.340445\pi$
$389$	−10.2407	+	17.7374i	−0.519222	+	0.899319i	−0.999750	+	0.0223401i	$0.992888\pi$
$390$	−2.65279	+	2.75152i	−0.134329	+	0.139328i
$391$	−32.1867			−1.62775
$392$		−	5.52586i		−	0.279098i
$393$	−6.56573	−	3.79072i	−0.331197	−	0.191217i
$394$	12.0428	+	20.8587i	0.606707	+	1.05085i
$395$	−11.3945	−	10.9856i	−0.573317	−	0.552746i
$396$	−1.67009	−	2.89267i	−0.0839250	−	0.145362i
$397$	−0.296562	+	0.171220i	−0.0148840	+	0.00859330i	−0.507424	−	0.861697i	$-0.669402\pi$
$397$	−0.296562	+	0.171220i	−0.0148840	+	0.00859330i	0.492540	+	0.870290i	$0.336069\pi$
$398$			1.30406i			0.0653664i
$399$	−15.0597	+	3.34612i	−0.753928	+	0.167515i
$400$	−4.41855	−	2.34017i	−0.220928	−	0.117009i
$401$	−4.06278	−	7.03694i	−0.202886	−	0.351408i	0.746571	−	0.665305i	$-0.231699\pi$
$401$	−4.06278	−	7.03694i	−0.202886	−	0.351408i	−0.949457	+	0.313897i	$0.898365\pi$
$402$	7.82551	−	4.51806i	0.390301	−	0.225340i
$403$	−1.59630	−	0.921622i	−0.0795172	−	0.0459093i
$404$	−4.32684	−	7.49431i	−0.215268	−	0.372856i
$405$	−1.60976	−	1.55199i	−0.0799894	−	0.0771192i
$406$	28.1639			1.39775
$407$		−	15.7298i		−	0.779697i
$408$	3.29175	+	1.90049i	0.162966	+	0.0940884i
$409$	6.03725	−	10.4568i	0.298523	−	0.517057i	−0.677275	−	0.735730i	$-0.736839\pi$
$409$	6.03725	−	10.4568i	0.298523	−	0.517057i	0.975798	+	0.218673i	$0.0701728\pi$
$410$	−25.8865	−	6.43188i	−1.27845	−	0.317648i
$411$	−11.4186			−0.563236
$412$	−0.650849	−	0.375768i	−0.0320650	−	0.0185128i
$413$	−17.9795	+	10.3805i	−0.884716	+	0.510791i
$414$	−4.23400	+	7.33350i	−0.208090	+	0.360422i
$415$	−2.89288	−	10.0578i	−0.142006	−	0.493718i
$416$	−0.854638	−	1.48028i	−0.0419021	−	0.0725765i
$417$			3.60197i			0.176389i
$418$	3.15796	+	14.2129i	0.154461	+	0.695174i
$419$	15.2290			0.743985			0.371992	−	0.928236i	$-0.378675\pi$
$419$	15.2290			0.743985			0.371992	+	0.928236i	$0.378675\pi$
$420$	−7.60552	+	2.18754i	−0.371111	+	0.106741i
$421$	−4.80458	−	8.32177i	−0.234161	−	0.405578i	0.724868	−	0.688888i	$-0.241901\pi$
$421$	−4.80458	−	8.32177i	−0.234161	−	0.405578i	−0.959028	+	0.283310i	$0.908568\pi$
$422$	6.04867	+	3.49220i	0.294445	+	0.169998i
$423$	4.73543	−	2.73400i	0.230244	−	0.132932i
$424$	6.25513	−	10.8342i	0.303776	−	0.526155i
$425$	−8.89496	+	16.7948i	−0.431469	+	0.814669i
$426$	8.09171			0.392045
$427$	−42.4520	−	24.5096i	−2.05439	−	1.18611i
$428$	−8.50763	−	4.91189i	−0.411232	−	0.237425i
$429$	5.70928			0.275646
$430$	2.73820	−	11.0205i	0.132048	−	0.531457i
$431$	6.62730	−	11.4788i	0.319226	−	0.552916i	−0.661101	−	0.750297i	$-0.729910\pi$
$431$	6.62730	−	11.4788i	0.319226	−	0.552916i	0.980327	+	0.197381i	$0.0632438\pi$
$432$	0.866025	−	0.500000i	0.0416667	−	0.0240563i
$433$	−13.2965	−	7.67675i	−0.638990	−	0.368921i	0.145235	−	0.989397i	$-0.453606\pi$
$433$	−13.2965	−	7.67675i	−0.638990	−	0.368921i	−0.784225	+	0.620476i	$0.786939\pi$
$434$	−1.90829	−	3.30526i	−0.0916009	−	0.158657i
$435$	−4.91862	−	17.1007i	−0.235830	−	0.819918i
$436$	−7.85043			−0.375968
$437$	27.2020	−	24.9497i	1.30125	−	1.19350i
$438$		−	5.90829i		−	0.282309i
$439$	10.4263	+	18.0590i	0.497623	+	0.861908i	0.999996	−	0.00274309i	$-0.000873154\pi$
$439$	10.4263	+	18.0590i	0.497623	+	0.861908i	−0.502374	+	0.864651i	$0.667540\pi$
$440$	2.06453	+	7.17785i	0.0984228	+	0.342190i
$441$	−2.76293	+	4.78553i	−0.131568	+	0.227883i
$442$	−5.62651	+	3.24846i	−0.267626	+	0.154514i
$443$	22.0694	+	12.7418i	1.04855	+	0.605381i	0.922243	−	0.386610i	$-0.126354\pi$
$443$	22.0694	+	12.7418i	1.04855	+	0.605381i	0.126308	+	0.991991i	$0.459687\pi$
$444$	4.70928			0.223492
$445$	5.02771	−	20.2351i	0.238336	−	0.959237i
$446$	5.00667	−	8.67180i	0.237072	−	0.410622i
$447$	8.91825	+	5.14896i	0.421819	+	0.243537i
$448$		−	3.53919i		−	0.167211i
$449$	19.1412			0.903327			0.451664	−	0.892188i	$-0.350831\pi$
$449$	19.1412			0.903327			0.451664	+	0.892188i	$0.350831\pi$
$450$	2.65649	+	4.23592i	0.125228	+	0.199683i
$451$	19.9221	+	34.5062i	0.938097	+	1.62483i
$452$	−6.91469	−	3.99220i	−0.325240	−	0.187777i
$453$	4.06681	−	2.34797i	0.191075	−	0.110317i
$454$	−7.12423	−	12.3395i	−0.334357	−	0.579123i
$455$	3.26180	−	13.1278i	0.152915	−	0.615442i
$456$	−4.25513	+	0.945448i	−0.199265	+	0.0442746i
$457$		−	32.0216i		−	1.49791i	−0.662623	−	0.748953i	$-0.730557\pi$
$457$		−	32.0216i		−	1.49791i	0.662623	−	0.748953i	$-0.269443\pi$
$458$	−13.7331	+	7.92881i	−0.641706	+	0.370489i
$459$	−1.90049	−	3.29175i	−0.0887074	−	0.153646i
$460$	13.1423	−	13.6314i	0.612762	−	0.635568i
$461$	−20.6381	−	35.7462i	−0.961211	−	1.66487i	−0.719466	−	0.694527i	$-0.755614\pi$
$461$	−20.6381	−	35.7462i	−0.961211	−	1.66487i	−0.241745	−	0.970340i	$-0.577720\pi$
$462$	10.2377	+	5.91075i	0.476302	+	0.274993i
$463$			8.16168i			0.379305i	0.981851	+	0.189653i	$0.0607362\pi$
$463$			8.16168i			0.379305i	−0.981851	+	0.189653i	$0.939264\pi$
$464$	7.95774			0.369429
$465$	−1.67364	+	1.73592i	−0.0776130	+	0.0805016i
$466$	12.2979	−	21.3006i	0.569690	−	0.986732i
$467$		−	17.8238i		−	0.824786i	−0.911006	−	0.412393i	$-0.864693\pi$
$467$		−	17.8238i		−	0.824786i	0.911006	−	0.412393i	$-0.135307\pi$
$468$			1.70928i			0.0790113i
$469$	−15.9903	+	27.6959i	−0.738362	+	1.27888i
$470$	−11.7504	+	3.37973i	−0.542007	+	0.155895i
$471$	5.25872	−	9.10838i	0.242309	−	0.419692i
$472$	−5.08013	+	2.93302i	−0.233832	+	0.135003i
$473$	−14.6901	+	8.48133i	−0.675451	+	0.389972i
$474$	−7.07838			−0.325121
$475$	−5.50118	−	21.0888i	−0.252411	−	0.967620i
$476$	−13.4524			−0.616590
$477$	−10.8342	+	6.25513i	−0.496064	+	0.286403i
$478$	0.135754	−	0.0783777i	0.00620925	−	0.00358491i
$479$	−11.5694	+	20.0389i	−0.528621	+	0.915599i	0.470822	+	0.882228i	$0.343958\pi$
$479$	−11.5694	+	20.0389i	−0.528621	+	0.915599i	−0.999443	+	0.0333707i	$0.989376\pi$
$480$	−2.14894	+	0.618092i	−0.0980854	+	0.0282119i
$481$	−4.02472	+	6.97103i	−0.183512	+	0.317851i
$482$			25.5936i			1.16575i
$483$		−	29.9698i		−	1.36368i
$484$	0.0783777	−	0.135754i	0.00356262	−	0.00617065i
$485$	9.07984	−	9.41777i	0.412294	−	0.427639i
$486$	−1.00000			−0.0453609
$487$		−	10.8855i		−	0.493269i	−0.969109	−	0.246635i	$-0.920675\pi$
$487$		−	10.8855i		−	0.493269i	0.969109	−	0.246635i	$-0.0793248\pi$
$488$	−11.9948	−	6.92522i	−0.542980	−	0.313490i
$489$	8.38962	+	14.5313i	0.379392	+	0.657126i
$490$	8.57610	−	8.89528i	0.387429	−	0.401848i
$491$	−15.3732	−	26.6272i	−0.693784	−	1.20167i	−0.970589	−	0.240743i	$-0.922609\pi$
$491$	−15.3732	−	26.6272i	−0.693784	−	1.20167i	0.276805	−	0.960926i	$-0.410724\pi$
$492$	−10.3307	+	5.96441i	−0.465742	+	0.268896i
$493$		−	30.2472i		−	1.36227i
$494$	2.23707	−	7.10678i	0.100651	−	0.319749i
$495$	1.80098	−	7.24846i	0.0809482	−	0.325794i
$496$	−0.539189	−	0.933903i	−0.0242103	−	0.0419335i
$497$	−24.8013	+	14.3190i	−1.11249	+	0.642297i
$498$	−4.05330	−	2.34017i	−0.181633	−	0.104866i
$499$	−3.29545	−	5.70789i	−0.147525	−	0.255520i	0.782787	−	0.622289i	$-0.213797\pi$
$499$	−3.29545	−	5.70789i	−0.147525	−	0.255520i	−0.930312	+	0.366769i	$0.880464\pi$
$500$	−3.48085	−	10.6247i	−0.155668	−	0.475150i
$501$	−11.6042			−0.518439
$502$			10.6537i			0.475497i
$503$	11.1192	+	6.41968i	0.495781	+	0.286240i	0.726970	−	0.686669i	$-0.240928\pi$
$503$	11.1192	+	6.41968i	0.495781	+	0.286240i	−0.231188	+	0.972909i	$0.574261\pi$
$504$	−1.76959	+	3.06503i	−0.0788240	+	0.136527i
$505$	4.66597	−	18.7792i	0.207633	−	0.835665i
$506$	−28.2846			−1.25740
$507$	8.72813	+	5.03919i	0.387630	+	0.223798i
$508$	−16.1160	+	9.30458i	−0.715032	+	0.412824i
$509$	−11.4319	+	19.8006i	−0.506709	+	0.877646i	0.493261	+	0.869882i	$0.335805\pi$
$509$	−11.4319	+	19.8006i	−0.506709	+	0.877646i	−0.999970	+	0.00776458i	$0.997528\pi$
$510$	2.34936	+	8.16810i	0.104031	+	0.361690i
$511$	10.4553	+	18.1091i	0.462514	+	0.801098i
$512$		−	1.00000i		−	0.0441942i
$513$	4.15777	+	1.30878i	0.183570	+	0.0577842i
$514$	−19.3874			−0.855140
$515$	−0.464518	−	1.61501i	−0.0204691	−	0.0711658i
$516$	−2.53919	−	4.39800i	−0.111782	−	0.193611i
$517$	15.8171	+	9.13203i	0.695637	+	0.401626i
$518$	−14.4341	+	8.33351i	−0.634196	+	0.366153i
$519$	4.44994	−	7.70752i	0.195331	−	0.338323i
$520$	0.921622	−	3.70928i	0.0404158	−	0.162662i
$521$	3.34632			0.146605			0.0733024	−	0.997310i	$-0.476646\pi$
$521$	3.34632			0.146605			0.0733024	+	0.997310i	$0.476646\pi$
$522$	−6.89160	−	3.97887i	−0.301637	−	0.174150i
$523$	38.8290	+	22.4179i	1.69787	+	0.980268i	0.947773	+	0.318944i	$0.103328\pi$
$523$	38.8290	+	22.4179i	1.69787	+	0.980268i	0.750101	+	0.661324i	$0.230005\pi$
$524$	7.58145			0.331197
$525$	−15.6381	−	8.28231i	−0.682502	−	0.361470i
$526$	−15.3504	+	26.5877i	−0.669311	+	1.15928i
$527$	−3.54975	+	2.04945i	−0.154629	+	0.0892754i
$528$	2.89267	+	1.67009i	0.125888	+	0.0726812i
$529$	24.3535	+	42.1815i	1.05885	+	1.83398i
$530$	26.8839	−	7.73249i	1.16776	−	0.335878i
$531$	5.86603			0.254564
$532$	11.3690	−	10.4277i	0.492910	−	0.452097i
$533$		−	20.3896i		−	0.883173i
$534$	−4.66229	−	8.07532i	−0.201757	−	0.349453i
$535$	−6.07199	−	21.1107i	−0.262515	−	0.912697i
$536$	−4.51806	+	7.82551i	−0.195150	+	0.338010i
$537$	18.9312	−	10.9299i	0.816942	−	0.471662i
$538$	24.4797	+	14.1334i	1.05539	+	0.609332i
$539$	−18.4573			−0.795013
$540$	2.17009	+	0.539189i	0.0933857	+	0.0232030i
$541$	3.98440	−	6.90119i	0.171303	−	0.296705i	−0.767573	−	0.640962i	$-0.778536\pi$
$541$	3.98440	−	6.90119i	0.171303	−	0.296705i	0.938876	+	0.344257i	$0.111869\pi$
$542$	−10.0600	−	5.80817i	−0.432116	−	0.249482i
$543$			5.32684i			0.228597i
$544$	−3.80098			−0.162966
$545$	−12.6373	−	12.1838i	−0.541321	−	0.521898i
$546$	−3.02472	−	5.23898i	−0.129446	−	0.224207i
$547$	−17.2203	−	9.94214i	−0.736287	−	0.425095i	0.0844310	−	0.996429i	$-0.473093\pi$
$547$	−17.2203	−	9.94214i	−0.736287	−	0.425095i	−0.820718	+	0.571334i	$0.806426\pi$
$548$	9.88875	−	5.70928i	0.422427	−	0.243888i
$549$	6.92522	+	11.9948i	0.295561	+	0.511927i
$550$	−7.81658	+	14.7587i	−0.333300	+	0.629314i
$551$	23.4463	+	25.5629i	0.998844	+	1.08901i
$552$		−	8.46800i		−	0.360422i
$553$	21.6954	−	12.5259i	0.922583	−	0.532654i
$554$	13.0875	+	22.6682i	0.556035	+	0.963080i
$555$	7.58078	+	7.30877i	0.321786	+	0.310240i
$556$	−1.80098	−	3.11940i	−0.0763787	−	0.132292i
$557$	17.1356	+	9.89322i	0.726057	+	0.419189i	0.816978	−	0.576669i	$-0.195648\pi$
$557$	17.1356	+	9.89322i	0.726057	+	0.419189i	−0.0909212	+	0.995858i	$0.528981\pi$
$558$			1.07838i			0.0456514i
$559$	8.68035			0.367140
$560$	5.49280	−	5.69723i	0.232113	−	0.240752i
$561$	6.34797	−	10.9950i	0.268012	−	0.464210i
$562$		−	24.0277i		−	1.01355i
$563$		−	32.6681i		−	1.37679i	−0.725334	−	0.688397i	$-0.758315\pi$
$563$		−	32.6681i		−	1.37679i	0.725334	−	0.688397i	$-0.241685\pi$
$564$	−2.73400	+	4.73543i	−0.115122	+	0.199397i
$565$	−4.93509	−	17.1580i	−0.207621	−	0.721844i
$566$	10.1568	−	17.5920i	0.426920	−	0.739448i
$567$	3.06503	−	1.76959i	0.128719	−	0.0743160i
$568$	−7.00763	+	4.04585i	−0.294033	+	0.169760i
$569$	−11.0650			−0.463871			−0.231935	−	0.972731i	$-0.574506\pi$
$569$	−11.0650			−0.463871			−0.231935	+	0.972731i	$0.574506\pi$
$570$	−8.31705	−	5.08200i	−0.348363	−	0.212861i
$571$	−30.4040			−1.27237			−0.636184	−	0.771538i	$-0.719488\pi$
$571$	−30.4040			−1.27237			−0.636184	+	0.771538i	$0.719488\pi$
$572$	−4.94438	+	2.85464i	−0.206735	+	0.119358i
$573$	−7.78891	+	4.49693i	−0.325386	+	0.187862i
$574$	21.1092	−	36.5621i	0.881079	−	1.52607i
$575$	42.3117	−	1.54648i	1.76452	−	0.0644926i
$576$	−0.500000	+	0.866025i	−0.0208333	+	0.0360844i
$577$			15.0010i			0.624502i	0.950000	+	0.312251i	$0.101083\pi$
$577$			15.0010i			0.624502i	−0.950000	+	0.312251i	$0.898917\pi$
$578$		−	2.55252i		−	0.106171i
$579$	−1.16649	+	2.02042i	−0.0484778	+	0.0839660i
$580$	12.8100	+	12.3504i	0.531907	+	0.512821i
$581$	16.5646			0.687217
$582$		−	5.85043i		−	0.242508i
$583$	−36.1881	−	20.8932i	−1.49876	−	0.865309i
$584$	2.95415	+	5.11673i	0.122243	+	0.211732i
$585$	−2.65279	+	2.75152i	−0.109679	+	0.113761i
$586$	2.66229	+	4.61122i	0.109978	+	0.190488i
$587$	0.566107	−	0.326842i	0.0233657	−	0.0134902i	−0.488272	−	0.872692i	$-0.662372\pi$
$587$	0.566107	−	0.326842i	0.0233657	−	0.0134902i	0.511637	+	0.859201i	$0.329039\pi$
$588$		−	5.52586i		−	0.227883i
$589$	1.41136	−	4.48365i	0.0581542	−	0.184746i
$590$	−12.7298	−	3.16290i	−0.524077	−	0.130214i
$591$	12.0428	+	20.8587i	0.495374	+	0.858013i
$592$	−4.07835	+	2.35464i	−0.167619	+	0.0967750i
$593$	−36.3095	−	20.9633i	−1.49105	−	0.860858i	−0.491103	−	0.871102i	$-0.663406\pi$
$593$	−36.3095	−	20.9633i	−1.49105	−	0.860858i	−0.999948	+	0.0102432i	$0.996739\pi$
$594$	−1.67009	−	2.89267i	−0.0685245	−	0.118688i
$595$	−21.6551	−	20.8781i	−0.887772	−	0.855917i
$596$	−10.2979			−0.421819
$597$			1.30406i			0.0533714i
$598$	12.5350	+	7.23707i	0.512593	+	0.295946i
$599$	−8.45722	+	14.6483i	−0.345553	+	0.598515i	−0.985454	−	0.169942i	$-0.945642\pi$
$599$	−8.45722	+	14.6483i	−0.345553	+	0.598515i	0.639901	+	0.768457i	$0.278975\pi$
$600$	−4.41855	−	2.34017i	−0.180387	−	0.0955372i
$601$	−4.42243			−0.180395			−0.0901973	−	0.995924i	$-0.528750\pi$
$601$	−4.42243			−0.180395			−0.0901973	+	0.995924i	$0.528750\pi$
$602$	15.5654	+	8.98667i	0.634397	+	0.366269i
$603$	7.82551	−	4.51806i	0.318679	−	0.183990i
$604$	−2.34797	+	4.06681i	−0.0955376	+	0.165476i
$605$	0.336859	−	0.0968893i	0.0136953	−	0.00393911i
$606$	−4.32684	−	7.49431i	−0.175766	−	0.304436i
$607$			15.6030i			0.633307i	0.948541	+	0.316653i	$0.102559\pi$
$607$			15.6030i			0.633307i	−0.948541	+	0.316653i	$0.897441\pi$
$608$	3.21233	−	2.94635i	0.130277	−	0.119490i
$609$	28.1639			1.14126
$610$	−8.56084	−	29.7638i	−0.346618	−	1.20510i
$611$	−4.67316	−	8.09415i	−0.189056	−	0.327454i
$612$	3.29175	+	1.90049i	0.133061	+	0.0768228i
$613$	−3.51225	+	2.02780i	−0.141858	+	0.0819019i	−0.569249	−	0.822165i	$-0.692766\pi$
$613$	−3.51225	+	2.02780i	−0.141858	+	0.0819019i	0.427391	+	0.904067i	$0.359433\pi$
$614$	1.83771	−	3.18301i	0.0741640	−	0.128456i
$615$	−25.8865	−	6.43188i	−1.04385	−	0.259359i
$616$	−11.8215			−0.476302
$617$	−17.4062	−	10.0494i	−0.700745	−	0.404576i	0.106880	−	0.994272i	$-0.465914\pi$
$617$	−17.4062	−	10.0494i	−0.700745	−	0.404576i	−0.807625	+	0.589696i	$0.799247\pi$
$618$	−0.650849	−	0.375768i	−0.0261810	−	0.0151156i
$619$	17.0917			0.686974			0.343487	−	0.939157i	$-0.388392\pi$
$619$	17.0917			0.686974			0.343487	+	0.939157i	$0.388392\pi$
$620$	0.581449	−	2.34017i	0.0233516	−	0.0939836i
$621$	−4.23400	+	7.33350i	−0.169905	+	0.294283i
$622$	11.8923	−	6.86603i	0.476838	−	0.275303i
$623$	28.5801	+	16.5007i	1.14504	+	0.661087i
$624$	−0.854638	−	1.48028i	−0.0342129	−	0.0592585i
$625$	10.8861	−	22.5054i	0.435445	−	0.900216i
$626$	17.9421			0.717112
$627$	3.15796	+	14.2129i	0.126117	+	0.567607i
$628$			10.5174i			0.419692i
$629$	8.94994	+	15.5018i	0.356857	+	0.618095i
$630$	−7.60552	+	2.18754i	−0.303011	+	0.0871538i
$631$	−5.80652	+	10.0572i	−0.231154	+	0.400370i	−0.958148	−	0.286274i	$-0.907583\pi$
$631$	−5.80652	+	10.0572i	−0.231154	+	0.400370i	0.726994	+	0.686644i	$0.240917\pi$
$632$	6.13005	−	3.53919i	0.243840	−	0.140781i
$633$	6.04867	+	3.49220i	0.240413	+	0.138803i
$634$	−7.33299			−0.291230
$635$	−40.3835	−	10.0338i	−1.60257	−	0.398181i
$636$	6.25513	−	10.8342i	0.248032	−	0.429604i
$637$	8.17979	+	4.72261i	0.324095	+	0.187116i
$638$		−	26.5802i		−	1.05232i
$639$	8.09171			0.320103
$640$	1.55199	−	1.60976i	0.0613480	−	0.0636312i
$641$	−3.14116	−	5.44064i	−0.124068	−	0.214893i	0.797300	−	0.603583i	$-0.206261\pi$
$641$	−3.14116	−	5.44064i	−0.124068	−	0.214893i	−0.921368	+	0.388691i	$0.872928\pi$
$642$	−8.50763	−	4.91189i	−0.335770	−	0.193857i
$643$	11.3358	−	6.54472i	0.447040	−	0.258099i	−0.259539	−	0.965733i	$-0.583571\pi$
$643$	11.3358	−	6.54472i	0.447040	−	0.258099i	0.706579	+	0.707634i	$0.250237\pi$
$644$	14.9849	+	25.9546i	0.590489	+	1.02276i
$645$	2.73820	−	11.0205i	0.107817	−	0.433933i
$646$	−11.1990	−	12.2100i	−0.440619	−	0.480396i
$647$			7.89496i			0.310383i	0.987884	+	0.155191i	$0.0495994\pi$
$647$			7.89496i			0.310383i	−0.987884	+	0.155191i	$0.950401\pi$
$648$	0.866025	−	0.500000i	0.0340207	−	0.0196419i
$649$	9.79678	+	16.9685i	0.384557	+	0.666073i
$650$	7.24036	−	4.54067i	0.283990	−	0.178100i
$651$	−1.90829	−	3.30526i	−0.0747918	−	0.129543i
$652$	−14.5313	−	8.38962i	−0.569088	−	0.328563i
$653$			36.7620i			1.43861i	0.694695	+	0.719305i	$0.255540\pi$
$653$			36.7620i			1.43861i	−0.694695	+	0.719305i	$0.744460\pi$
$654$	−7.85043			−0.306976
$655$	12.2043	+	11.7664i	0.476861	+	0.459750i
$656$	5.96441	−	10.3307i	0.232871	−	0.403344i
$657$		−	5.90829i		−	0.230504i
$658$		−	19.3523i		−	0.754430i
$659$	−14.8805	+	25.7738i	−0.579662	+	1.00400i	0.415856	+	0.909430i	$0.363482\pi$
$659$	−14.8805	+	25.7738i	−0.579662	+	1.00400i	−0.995518	+	0.0945733i	$0.969851\pi$
$660$	2.06453	+	7.17785i	0.0803619	+	0.279397i
$661$	−2.94441	+	5.09987i	−0.114524	+	0.198362i	−0.917589	−	0.397529i	$-0.869868\pi$
$661$	−2.94441	+	5.09987i	−0.114524	+	0.198362i	0.803065	+	0.595891i	$0.203201\pi$
$662$	−18.6034	+	10.7407i	−0.723041	+	0.417448i
$663$	−5.62651	+	3.24846i	−0.218515	+	0.126160i
$664$	4.68035			0.181633
$665$	34.4851	+	0.858663i	1.33727	+	0.0332975i
$666$	4.70928			0.182481
$667$	−58.3581	+	33.6931i	−2.25963	+	1.30460i
$668$	10.0496	−	5.80212i	0.388829	−	0.224491i
$669$	5.00667	−	8.67180i	0.193569	−	0.335271i
$670$	−19.4181	+	5.58515i	−0.750187	+	0.215773i
$671$	−23.1314	+	40.0648i	−0.892979	+	1.54668i
$672$		−	3.53919i		−	0.136527i
$673$		−	8.96719i		−	0.345660i	−0.984952	−	0.172830i	$-0.944709\pi$
$673$		−	8.96719i		−	0.345660i	0.984952	−	0.172830i	$-0.0552911\pi$
$674$	−10.1701	+	17.6151i	−0.391737	+	0.678509i
$675$	2.65649	+	4.23592i	0.102248	+	0.163041i
$676$	−10.0784			−0.387630
$677$			20.9721i			0.806024i	0.915195	+	0.403012i	$0.132037\pi$
$677$			20.9721i			0.806024i	−0.915195	+	0.403012i	$0.867963\pi$
$678$	−6.91469	−	3.99220i	−0.265557	−	0.153320i
$679$	10.3529	+	17.9317i	0.397308	+	0.688157i
$680$	−6.11866	−	5.89911i	−0.234640	−	0.226220i
$681$	−7.12423	−	12.3395i	−0.273001	−	0.472852i
$682$	−3.11940	+	1.80098i	−0.119448	+	0.0689632i
$683$		−	7.46922i		−	0.285802i	−0.989737	−	0.142901i	$-0.954357\pi$
$683$		−	7.46922i		−	0.285802i	0.989737	−	0.142901i	$-0.0456430\pi$
$684$	−4.25513	+	0.945448i	−0.162699	+	0.0361501i
$685$	24.7792	+	6.15676i	0.946766	+	0.235238i
$686$	−2.60863	−	4.51829i	−0.0995981	−	0.172509i
$687$	−13.7331	+	7.92881i	−0.523951	+	0.302503i
$688$	4.39800	+	2.53919i	0.167672	+	0.0968057i
$689$	10.6917	+	18.5186i	0.407323	+	0.705504i
$690$	13.1423	−	13.6314i	0.500318	−	0.518939i
$691$	4.35804			0.165788			0.0828938	−	0.996558i	$-0.473584\pi$
$691$	4.35804			0.165788			0.0828938	+	0.996558i	$0.473584\pi$
$692$			8.89988i			0.338323i
$693$	10.2377	+	5.91075i	0.388899	+	0.224531i
$694$	−4.60197	+	7.97084i	−0.174688	+	0.302569i
$695$	1.94214	−	7.81658i	0.0736696	−	0.296500i
$696$	7.95774			0.301637
$697$	−39.2666	−	22.6706i	−1.48733	−	0.858711i
$698$	7.14338	−	4.12423i	0.270381	−	0.156104i
$699$	12.2979	−	21.3006i	0.465150	−	0.805663i
$700$	17.6841	−	0.646348i	0.668398	−	0.0244297i
$701$	10.1990	+	17.6652i	0.385212	+	0.667206i	0.991799	−	0.127811i	$-0.0407952\pi$
$701$	10.1990	+	17.6652i	0.385212	+	0.667206i	−0.606587	+	0.795017i	$0.707462\pi$
$702$			1.70928i			0.0645124i
$703$	−19.5801	−	6.16342i	−0.738478	−	0.232458i
$704$	−3.34017			−0.125888
$705$	−11.7504	+	3.37973i	−0.442547	+	0.127288i
$706$	3.12003	+	5.40405i	0.117424	+	0.203384i
$707$	26.5238	+	15.3135i	0.997529	+	0.575924i
$708$	−5.08013	+	2.93302i	−0.190923	+	0.110229i
$709$	14.4377	−	25.0069i	0.542221	−	0.939154i	−0.456555	−	0.889695i	$-0.650917\pi$
$709$	14.4377	−	25.0069i	0.542221	−	0.939154i	0.998776	−	0.0494590i	$-0.0157497\pi$
$710$	−17.5597	−	4.36296i	−0.659004	−	0.163739i
$711$	−7.07838			−0.265460
$712$	8.07532	+	4.66229i	0.302635	+	0.174727i
$713$	7.90829	+	4.56585i	0.296168	+	0.170992i
$714$	−13.4524			−0.503443
$715$	−12.3896	−	3.07838i	−0.463346	−	0.115125i
$716$	−10.9299	+	18.9312i	−0.408471	+	0.707493i
$717$	0.135754	−	0.0783777i	0.00506983	−	0.00292707i
$718$	−0.695636	−	0.401626i	−0.0259609	−	0.0149885i
$719$	−18.1701	−	31.4715i	−0.677630	−	1.17369i	−0.975693	−	0.219143i	$-0.929674\pi$
$719$	−18.1701	−	31.4715i	−0.677630	−	1.17369i	0.298063	−	0.954546i	$-0.403660\pi$
$720$	−2.14894	+	0.618092i	−0.0800864	+	0.0230349i
$721$	2.65983			0.0990571
$722$	18.9293	+	1.63809i	0.704474	+	0.0609632i
$723$			25.5936i			0.951835i
$724$	−2.66342	−	4.61318i	−0.0989853	−	0.171448i
$725$	1.45329	+	39.7621i	0.0539739	+	1.47673i
$726$	0.0783777	−	0.135754i	0.00290887	−	0.00503831i
$727$	−25.7020	+	14.8390i	−0.953233	+	0.550350i	−0.894084	−	0.447900i	$-0.852172\pi$
$727$	−25.7020	+	14.8390i	−0.953233	+	0.550350i	−0.0591495	+	0.998249i	$0.518839\pi$
$728$	5.23898	+	3.02472i	0.194169	+	0.112104i
$729$	−1.00000			−0.0370370
$730$	−3.18568	+	12.8215i	−0.117907	+	0.474545i
$731$	9.65142	−	16.7167i	0.356971	−	0.618291i
$732$	−11.9948	−	6.92522i	−0.443342	−	0.255963i
$733$			29.8248i			1.10160i	0.834636	+	0.550802i	$0.185678\pi$
$733$			29.8248i			1.10160i	−0.834636	+	0.550802i	$0.814322\pi$
$734$	−2.93600			−0.108370
$735$	8.57610	−	8.89528i	0.316334	−	0.328107i
$736$	4.23400	+	7.33350i	0.156067	+	0.270316i
$737$	26.1385	+	15.0911i	0.962826	+	0.555888i
$738$	−10.3307	+	5.96441i	−0.380277	+	0.219553i
$739$	−26.6737	−	46.2002i	−0.981207	−	1.69950i	−0.657709	−	0.753272i	$-0.728474\pi$
$739$	−26.6737	−	46.2002i	−0.981207	−	1.69950i	−0.323498	−	0.946229i	$-0.604859\pi$
$740$	−10.2195	−	2.53919i	−0.375678	−	0.0933424i
$741$	2.23707	−	7.10678i	0.0821809	−	0.261074i
$742$			44.2762i			1.62543i
$743$	7.56947	−	4.37024i	0.277697	−	0.160328i	−0.354683	−	0.934986i	$-0.615411\pi$
$743$	7.56947	−	4.37024i	0.277697	−	0.160328i	0.632380	+	0.774658i	$0.282078\pi$
$744$	−0.539189	−	0.933903i	−0.0197676	−	0.0342385i
$745$	−16.5771	−	15.9823i	−0.607339	−	0.585546i
$746$	−12.7576	−	22.0968i	−0.467089	−	0.809021i
$747$	−4.05330	−	2.34017i	−0.148302	−	0.0856225i
$748$			12.6959i			0.464210i
$749$	34.7682			1.27040
$750$	−3.48085	−	10.6247i	−0.127103	−	0.387958i
$751$	−19.4101	+	33.6193i	−0.708286	+	1.22679i	0.257206	+	0.966356i	$0.417198\pi$
$751$	−19.4101	+	33.6193i	−0.708286	+	1.22679i	−0.965492	+	0.260431i	$0.916135\pi$
$752$		−	5.46800i		−	0.199397i
$753$			10.6537i			0.388242i
$754$	−6.80098	+	11.7797i	−0.247677	+	0.428990i
$755$	−10.0913	+	2.90253i	−0.367261	+	0.105634i
$756$	−1.76959	+	3.06503i	−0.0643595	+	0.111474i
$757$	44.1922	−	25.5144i	1.60619	−	0.927336i	0.615981	−	0.787761i	$-0.288760\pi$
$757$	44.1922	−	25.5144i	1.60619	−	0.927336i	0.990212	−	0.139575i	$-0.0445736\pi$
$758$	−23.0828	+	13.3268i	−0.838404	+	0.484053i
$759$	−28.2846			−1.02667
$760$	9.74377	+	0.242616i	0.353444	+	0.00880060i
$761$	−24.2546			−0.879229			−0.439614	−	0.898187i	$-0.644885\pi$
$761$	−24.2546			−0.879229			−0.439614	+	0.898187i	$0.644885\pi$
$762$	−16.1160	+	9.30458i	−0.583821	+	0.337069i
$763$	24.0618	−	13.8921i	0.871095	−	0.502927i
$764$	4.49693	−	7.78891i	0.162693	−	0.281793i
$765$	2.34936	+	8.16810i	0.0849412	+	0.295318i
$766$	4.82571	−	8.35837i	0.174360	−	0.302000i
$767$		−	10.0267i		−	0.362042i
$768$		−	1.00000i		−	0.0360844i
$769$	8.02472	−	13.8992i	0.289379	−	0.501219i	−0.684283	−	0.729217i	$-0.739885\pi$
$769$	8.02472	−	13.8992i	0.289379	−	0.501219i	0.973662	+	0.227998i	$0.0732179\pi$
$770$	−19.0297	−	18.3469i	−0.685784	−	0.661177i
$771$	−19.3874			−0.698218
$772$		−	2.33299i		−	0.0839660i
$773$	−6.20751	−	3.58391i	−0.223269	−	0.128904i	0.384194	−	0.923252i	$-0.374479\pi$
$773$	−6.20751	−	3.58391i	−0.223269	−	0.128904i	−0.607463	+	0.794348i	$0.707813\pi$
$774$	−2.53919	−	4.39800i	−0.0912693	−	0.158083i
$775$	4.56793	−	2.86470i	0.164085	−	0.102903i
$776$	2.92522	+	5.06662i	0.105009	+	0.181881i
$777$	−14.4341	+	8.33351i	−0.517819	+	0.298963i
$778$		−	20.4813i		−	0.734291i
$779$	50.7586	−	11.2781i	1.81862	−	0.404079i
$780$	0.921622	−	3.70928i	0.0329994	−	0.132813i
$781$	13.5139	+	23.4067i	0.483564	+	0.837557i
$782$	27.8745	−	16.0934i	0.996791	−	0.575498i
$783$	−6.89160	−	3.97887i	−0.246286	−	0.142193i
$784$	2.76293	+	4.78553i	0.0986760	+	0.170912i
$785$	−16.3230	+	16.9305i	−0.582594	+	0.604276i
$786$	7.58145			0.270421
$787$			14.1001i			0.502615i	0.967907	+	0.251307i	$0.0808605\pi$
$787$			14.1001i			0.502615i	−0.967907	+	0.251307i	$0.919139\pi$
$788$	−20.8587	−	12.0428i	−0.743061	−	0.429006i
$789$	−15.3504	+	26.5877i	−0.546490	+	0.946548i
$790$	15.3607	+	3.81658i	0.546509	+	0.135788i
$791$	28.2583			1.00475
$792$	2.89267	+	1.67009i	0.102787	+	0.0593439i
$793$	20.5025	−	11.8371i	0.728064	−	0.420348i
$794$	0.171220	−	0.296562i	0.00607638	−	0.0105246i
$795$	26.8839	−	7.73249i	0.953472	−	0.274243i
$796$	−0.652028	−	1.12935i	−0.0231105	−	0.0400286i
$797$			11.3102i			0.400628i	0.979732	+	0.200314i	$0.0641962\pi$
$797$			11.3102i			0.400628i	−0.979732	+	0.200314i	$0.935804\pi$
$798$	11.3690	−	10.4277i	0.402459	−	0.369136i
$799$	−20.7838			−0.735277
$800$	4.99666	−	0.182626i	0.176659	−	0.00645681i
$801$	−4.66229	−	8.07532i	−0.164734	−	0.285327i
$802$	7.03694	+	4.06278i	0.248483	+	0.143462i
$803$	17.0908	−	9.86736i	0.603120	−	0.348211i
$804$	−4.51806	+	7.82551i	−0.159340	+	0.275984i
$805$	−16.1594	+	65.0372i	−0.569544	+	2.29226i
$806$	1.84324			0.0649255
$807$	24.4797	+	14.1334i	0.861726	+	0.497518i
$808$	7.49431	+	4.32684i	0.263649	+	0.152218i
$809$	22.9132			0.805586			0.402793	−	0.915291i	$-0.368040\pi$
$809$	22.9132			0.805586			0.402793	+	0.915291i	$0.368040\pi$
$810$	2.17009	+	0.539189i	0.0762491	+	0.0189452i
$811$	14.1140	−	24.4461i	0.495609	−	0.858419i	−0.504379	−	0.863483i	$-0.668278\pi$
$811$	14.1140	−	24.4461i	0.495609	−	0.858419i	0.999987	+	0.00506334i	$0.00161172\pi$
$812$	−24.3907	+	14.0820i	−0.855945	+	0.494180i
$813$	−10.0600	−	5.80817i	−0.352821	−	0.203701i
$814$	7.86490	+	13.6224i	0.275665	+	0.477465i
$815$	−10.3711	−	36.0577i	−0.363284	−	1.26304i
$816$	−3.80098			−0.133061
$817$	4.80134	+	21.6092i	0.167978	+	0.756009i
$818$			12.0745i			0.422175i
$819$	−3.02472	−	5.23898i	−0.105692	−	0.183065i
$820$	25.6344	−	7.37310i	0.895190	−	0.257480i
$821$	−23.0856	+	39.9854i	−0.805692	+	1.39550i	0.110131	+	0.993917i	$0.464873\pi$
$821$	−23.0856	+	39.9854i	−0.805692	+	1.39550i	−0.915823	+	0.401582i	$0.868460\pi$
$822$	9.88875	−	5.70928i	0.344910	−	0.199134i
$823$	−4.05420	−	2.34070i	−0.141321	−	0.0815915i	0.427673	−	0.903934i	$-0.359334\pi$
$823$	−4.05420	−	2.34070i	−0.141321	−	0.0815915i	−0.568993	+	0.822342i	$0.692667\pi$
$824$	0.751536			0.0261810
$825$	−7.81658	+	14.7587i	−0.272138	+	0.513833i
$826$	10.3805	−	17.9795i	0.361184	−	0.625588i
$827$	19.7336	+	11.3932i	0.686205	+	0.396181i	0.802189	−	0.597070i	$-0.203669\pi$
$827$	19.7336	+	11.3932i	0.686205	+	0.396181i	−0.115983	+	0.993251i	$0.537002\pi$
$828$		−	8.46800i		−	0.294283i
$829$	5.39189			0.187268			0.0936340	−	0.995607i	$-0.470152\pi$
$829$	5.39189			0.187268			0.0936340	+	0.995607i	$0.470152\pi$
$830$	7.53421	+	7.26387i	0.261516	+	0.252133i
$831$	13.0875	+	22.6682i	0.454000	+	0.786352i
$832$	1.48028	+	0.854638i	0.0513193	+	0.0296292i
$833$	18.1897	−	10.5018i	0.630237	−	0.363868i
$834$	−1.80098	−	3.11940i	−0.0623630	−	0.108016i
$835$	25.1822	+	6.25687i	0.871466	+	0.216528i
$836$	−9.84131	−	10.7297i	−0.340369	−	0.371095i
$837$			1.07838i			0.0372742i
$838$	−13.1887	+	7.61450i	−0.455596	+	0.263038i
$839$	20.8732	+	36.1535i	0.720624	+	1.24816i	0.960750	+	0.277415i	$0.0894777\pi$
$839$	20.8732	+	36.1535i	0.720624	+	1.24816i	−0.240127	+	0.970742i	$0.577189\pi$
$840$	5.49280	−	5.69723i	0.189520	−	0.196573i
$841$	−17.1628	−	29.7269i	−0.591821	−	1.02506i
$842$	8.32177	+	4.80458i	0.286787	+	0.165577i
$843$		−	24.0277i		−	0.827558i
$844$	−6.98440			−0.240413
$845$	−16.2237	−	15.6416i	−0.558113	−	0.538087i
$846$	−2.73400	+	4.73543i	−0.0939968	+	0.162807i
$847$			0.554787i			0.0190627i
$848$			12.5103i			0.429604i
$849$	10.1568	−	17.5920i	0.348579	−	0.603756i
$850$	−0.694159	−	18.9922i	−0.0238095	−	0.651428i
$851$	19.9391	−	34.5355i	0.683503	−	1.18386i
$852$	−7.00763	+	4.04585i	−0.240077	+	0.138609i
$853$	−26.5700	+	15.3402i	−0.909738	+	0.525238i	−0.880347	−	0.474330i	$-0.842690\pi$
$853$	−26.5700	+	15.3402i	−0.909738	+	0.525238i	−0.0293912	+	0.999568i	$0.509357\pi$
$854$	49.0193			1.67741
$855$	−8.31705	−	5.08200i	−0.284437	−	0.173801i
$856$	9.82377			0.335770
$857$	36.7427	−	21.2134i	1.25511	−	0.724636i	0.282987	−	0.959124i	$-0.408675\pi$
$857$	36.7427	−	21.2134i	1.25511	−	0.724636i	0.972119	+	0.234488i	$0.0753414\pi$
$858$	−4.94438	+	2.85464i	−0.168798	+	0.0974557i
$859$	−19.5983	+	33.9452i	−0.668685	+	1.15820i	0.309587	+	0.950871i	$0.399809\pi$
$859$	−19.5983	+	33.9452i	−0.668685	+	1.15820i	−0.978272	+	0.207325i	$0.933524\pi$
$860$	3.13890	+	10.9132i	0.107036	+	0.372135i
$861$	21.1092	−	36.5621i	0.719398	−	1.24603i
$862$			13.2546i			0.451454i
$863$			30.9565i			1.05377i	0.849936	+	0.526886i	$0.176641\pi$
$863$			30.9565i			1.05377i	−0.849936	+	0.526886i	$0.823359\pi$
$864$	−0.500000	+	0.866025i	−0.0170103	+	0.0294628i
$865$	−13.8126	+	14.3266i	−0.469641	+	0.487120i
$866$	15.3535			0.521733
$867$		−	2.55252i		−	0.0866881i
$868$	3.30526	+	1.90829i	0.112188	+	0.0647716i
$869$	−11.8215	−	20.4754i	−0.401017	−	0.694582i
$870$	12.8100	+	12.3504i	0.434300	+	0.418717i
$871$	−7.72261	−	13.3759i	−0.261671	−	0.453227i
$872$	6.79867	−	3.92522i	0.230232	−	0.132925i
$873$		−	5.85043i		−	0.198007i
$874$	−11.0828	+	35.2080i	−0.374880	+	1.19093i
$875$	29.4703	+	26.4052i	0.996277	+	0.892659i
$876$	2.95415	+	5.11673i	0.0998113	+	0.172878i
$877$	10.3903	−	5.99887i	0.350857	−	0.202567i	−0.314206	−	0.949355i	$-0.601738\pi$
$877$	10.3903	−	5.99887i	0.350857	−	0.202567i	0.665063	+	0.746788i	$0.268405\pi$
$878$	−18.0590	−	10.4263i	−0.609461	−	0.351872i
$879$	2.66229	+	4.61122i	0.0897967	+	0.155532i
$880$	−5.37686	−	5.18393i	−0.181254	−	0.174750i
$881$	−5.79872			−0.195364			−0.0976819	−	0.995218i	$-0.531143\pi$
$881$	−5.79872			−0.195364			−0.0976819	+	0.995218i	$0.531143\pi$
$882$		−	5.52586i		−	0.186065i
$883$	−24.0657	−	13.8943i	−0.809876	−	0.467582i	0.0370369	−	0.999314i	$-0.488208\pi$
$883$	−24.0657	−	13.8943i	−0.809876	−	0.467582i	−0.846913	+	0.531732i	$0.821541\pi$
$884$	3.24846	−	5.62651i	0.109258	−	0.189240i
$885$	−12.7298	−	3.16290i	−0.427907	−	0.106320i
$886$	−25.4836			−0.856138
$887$	9.90849	+	5.72067i	0.332694	+	0.192081i	0.657037	−	0.753859i	$-0.271810\pi$
$887$	9.90849	+	5.72067i	0.332694	+	0.192081i	−0.324342	+	0.945940i	$0.605143\pi$
$888$	−4.07835	+	2.35464i	−0.136861	+	0.0790165i
$889$	32.9307	−	57.0376i	1.10446	−	1.91298i
$890$	5.76344	+	20.0380i	0.193191	+	0.671675i
$891$	−1.67009	−	2.89267i	−0.0559500	−	0.0969082i
$892$			10.0133i			0.335271i
$893$	17.5650	−	16.1106i	0.587790	−	0.539121i
$894$	−10.2979			−0.344414
$895$	−46.9757	+	13.5114i	−1.57022	+	0.451637i
$896$	1.76959	+	3.06503i	0.0591180	+	0.102395i
$897$	12.5350	+	7.23707i	0.418531	+	0.241639i
$898$	−16.5767	+	9.57058i	−0.553173	+	0.319374i
$899$	−4.29072	+	7.43175i	−0.143104	+	0.247863i
$900$	−4.41855	−	2.34017i	−0.147285	−	0.0780058i
$901$	47.5513			1.58416
$902$	−34.5062	−	19.9221i	−1.14893	−	0.663335i
$903$	15.5654	+	8.98667i	0.517983	+	0.299058i
$904$	7.98440			0.265557
$905$	2.87217	−	11.5597i	0.0954743	−	0.384258i
$906$	−2.34797	+	4.06681i	−0.0780062	+	0.135111i
$907$	−12.3187	+	7.11223i	−0.409037	+	0.236158i	−0.690376	−	0.723451i	$-0.742555\pi$
$907$	−12.3187	+	7.11223i	−0.409037	+	0.236158i	0.281339	+	0.959608i	$0.409222\pi$
$908$	12.3395	+	7.12423i	0.409502	+	0.236426i
$909$	−4.32684	−	7.49431i	−0.143512	−	0.248571i
$910$	3.73912	+	12.9999i	0.123950	+	0.430943i
$911$	−14.4391			−0.478388			−0.239194	−	0.970972i	$-0.576883\pi$
$911$	−14.4391			−0.478388			−0.239194	+	0.970972i	$0.576883\pi$
$912$	3.21233	−	2.94635i	0.106371	−	0.0975633i
$913$		−	15.6332i		−	0.517382i
$914$	16.0108	+	27.7315i	0.529590	+	0.917276i
$915$	−8.56084	−	29.7638i	−0.283013	−	0.983961i
$916$	7.92881	−	13.7331i	0.261975	−	0.453754i
$917$	−23.2374	+	13.4161i	−0.767365	+	0.443038i
$918$	3.29175	+	1.90049i	0.108644	+	0.0627256i
$919$	−31.4030			−1.03589			−0.517944	−	0.855415i	$-0.673302\pi$
$919$	−31.4030			−1.03589			−0.517944	+	0.855415i	$0.673302\pi$
$920$	−4.56585	+	18.3763i	−0.150532	+	0.605848i
$921$	1.83771	−	3.18301i	0.0605547	−	0.104884i
$922$	35.7462	+	20.6381i	1.17724	+	0.679679i
$923$		−	13.8310i		−	0.455252i
$924$	−11.8215			−0.388899
$925$	−12.5101	−	19.9481i	−0.411331	−	0.655891i
$926$	−4.08084	−	7.06822i	−0.134105	−	0.232276i
$927$	−0.650849	−	0.375768i	−0.0213767	−	0.0123418i
$928$	−6.89160	+	3.97887i	−0.226228	+	0.130613i
$929$	−4.50780	−	7.80774i	−0.147896	−	0.256164i	0.782554	−	0.622583i	$-0.213917\pi$
$929$	−4.50780	−	7.80774i	−0.147896	−	0.256164i	−0.930450	+	0.366420i	$0.880583\pi$
$930$	0.581449	−	2.34017i	0.0190665	−	0.0767373i
$931$	−7.23215	+	22.9753i	−0.237024	+	0.752984i
$932$			24.5958i			0.805663i
$933$	11.8923	−	6.86603i	0.389337	−	0.224784i
$934$	8.91189	+	15.4358i	0.291606	+	0.505076i
$935$	−19.7040	+	20.4374i	−0.644391	+	0.668373i
$936$	−0.854638	−	1.48028i	−0.0279347	−	0.0483843i
$937$	−3.87759	−	2.23873i	−0.126675	−	0.0731360i	0.435323	−	0.900274i	$-0.356634\pi$
$937$	−3.87759	−	2.23873i	−0.126675	−	0.0731360i	−0.561999	+	0.827138i	$0.689967\pi$
$938$		−	31.9805i		−	1.04420i
$939$	17.9421			0.585520
$940$	8.48630	−	8.80214i	0.276793	−	0.287094i
$941$	25.5603	−	44.2718i	0.833243	−	1.44322i	−0.0622107	−	0.998063i	$-0.519815\pi$
$941$	25.5603	−	44.2718i	0.833243	−	1.44322i	0.895453	−	0.445155i	$-0.146852\pi$
$942$			10.5174i			0.342677i
$943$			101.013i			3.28944i
$944$	2.93302	−	5.08013i	0.0954615	−	0.165344i
$945$	−7.60552	+	2.18754i	−0.247408	+	0.0711608i
$946$	8.48133	−	14.6901i	0.275752	−	0.477616i
$947$	−38.2595	+	22.0892i	−1.24327	+	0.717801i	−0.969758	−	0.244068i	$-0.921518\pi$
$947$	−38.2595	+	22.0892i	−1.24327	+	0.717801i	−0.273510	+	0.961869i	$0.588185\pi$
$948$	6.13005	−	3.53919i	0.199095	−	0.114948i
$949$	−10.0989			−0.327824
$950$	15.3086	+	15.5128i	0.496675	+	0.503303i
$951$	−7.33299			−0.237788
$952$	11.6501	−	6.72620i	0.377583	−	0.217997i
$953$	−28.4107	+	16.4030i	−0.920314	+	0.531344i	−0.883735	−	0.467987i	$-0.844979\pi$
$953$	−28.4107	+	16.4030i	−0.920314	+	0.531344i	−0.0365790	+	0.999331i	$0.511646\pi$
$954$	6.25513	−	10.8342i	0.202517	−	0.350770i
$955$	19.3273	−	5.55903i	0.625417	−	0.179886i
$956$	−0.0783777	+	0.135754i	−0.00253492	+	0.00439061i
$957$		−	26.5802i		−	0.859217i
$958$		−	23.1389i		−	0.747584i
$959$	−20.2062	+	34.9982i	−0.652492	+	1.13015i
$960$	1.55199	−	1.60976i	0.0500904	−	0.0519546i
$961$	−29.8371			−0.962487
$962$		−	8.04945i		−	0.259525i
$963$	−8.50763	−	4.91189i	−0.274155	−	0.158283i
$964$	−12.7968	−	22.1647i	−0.412156	−	0.713876i
$965$	3.62078	−	3.75554i	0.116557	−	0.120895i
$966$	14.9849	+	25.9546i	0.482132	+	0.835077i
$967$	−0.442803	+	0.255652i	−0.0142396	+	0.00822122i	−0.507103	−	0.861886i	$-0.669284\pi$
$967$	−0.442803	+	0.255652i	−0.0142396	+	0.00822122i	0.492863	+	0.870107i	$0.335950\pi$
$968$			0.156755i			0.00503831i
$969$	−11.1990	−	12.2100i	−0.359764	−	0.392242i
$970$	−3.15449	+	12.6959i	−0.101285	+	0.407642i
$971$	27.4482	+	47.5417i	0.880855	+	1.52568i	0.850392	+	0.526149i	$0.176365\pi$
$971$	27.4482	+	47.5417i	0.880855	+	1.52568i	0.0304620	+	0.999536i	$0.490302\pi$
$972$	0.866025	−	0.500000i	0.0277778	−	0.0160375i
$973$	11.0401	+	6.37402i	0.353930	+	0.204342i
$974$	5.44275	+	9.42712i	0.174397	+	0.302065i
$975$	7.24036	−	4.54067i	0.231877	−	0.145418i
$976$	13.8504			0.443342
$977$		−	16.6114i		−	0.531447i	−0.964049	−	0.265723i	$-0.914389\pi$
$977$		−	16.6114i		−	0.531447i	0.964049	−	0.265723i	$-0.0856107\pi$
$978$	−14.5313	−	8.38962i	−0.464658	−	0.268271i
$979$	15.5728	−	26.9730i	0.497710	−	0.862060i
$980$	−2.97948	+	11.9916i	−0.0951760	+	0.383057i
$981$	−7.85043			−0.250645
$982$	26.6272	+	15.3732i	0.849708	+	0.490579i
$983$	−11.6583	+	6.73093i	−0.371842	+	0.214683i	−0.674263	−	0.738491i	$-0.735539\pi$
$983$	−11.6583	+	6.73093i	−0.371842	+	0.214683i	0.302421	+	0.953175i	$0.402205\pi$
$984$	5.96441	−	10.3307i	0.190138	−	0.329329i
$985$	−14.8871	−	51.7585i	−0.474342	−	1.64916i
$986$	15.1236	+	26.1949i	0.481634	+	0.834215i
$987$		−	19.3523i		−	0.615990i
$988$	1.61603	+	7.27319i	0.0514128	+	0.231391i
$989$	−43.0037			−1.36744
$990$	2.06453	+	7.17785i	0.0656152	+	0.228127i
$991$	−12.9077	−	22.3568i	−0.410026	−	0.710186i	0.584866	−	0.811130i	$-0.301147\pi$
$991$	−12.9077	−	22.3568i	−0.410026	−	0.710186i	−0.994892	+	0.100944i	$0.967814\pi$
$992$	0.933903	+	0.539189i	0.0296514	+	0.0171193i
$993$	−18.6034	+	10.7407i	−0.590360	+	0.340845i
$994$	14.3190	−	24.8013i	0.454172	−	0.786650i
$995$	0.703132	−	2.82991i	0.0222908	−	0.0897143i
$996$	4.68035			0.148302
$997$	18.8310	+	10.8721i	0.596384	+	0.344322i	0.767618	−	0.640908i	$-0.221442\pi$
$997$	18.8310	+	10.8721i	0.596384	+	0.344322i	−0.171234	+	0.985230i	$0.554775\pi$
$998$	5.70789	+	3.29545i	0.180680	+	0.104316i
$999$	4.70928			0.148995

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	570.2.q.b.349.3	yes	12
3.2	odd	2		1710.2.t.b.919.4		12
5.4	even	2	inner	570.2.q.b.349.4	yes	12
15.14	odd	2		1710.2.t.b.919.3		12
19.11	even	3	inner	570.2.q.b.49.4	yes	12
57.11	odd	6		1710.2.t.b.1189.3		12
95.49	even	6	inner	570.2.q.b.49.3	✓	12
285.239	odd	6		1710.2.t.b.1189.4		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
570.2.q.b.49.3	✓	12	95.49	even	6	inner
570.2.q.b.49.4	yes	12	19.11	even	3	inner
570.2.q.b.349.3	yes	12	1.1	even	1	trivial
570.2.q.b.349.4	yes	12	5.4	even	2	inner
1710.2.t.b.919.3		12	15.14	odd	2
1710.2.t.b.919.4		12	3.2	odd	2
1710.2.t.b.1189.3		12	57.11	odd	6
1710.2.t.b.1189.4		12	285.239	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:	\( N \)	\(=\)	\( 570 = 2 \cdot 3 \cdot 5 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	570.q (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.866025 + 0.500000i) q^{2} +(-0.866025 + 0.500000i) q^{3} +(0.500000 - 0.866025i) q^{4} +(2.14894 - 0.618092i) q^{5} +(0.500000 - 0.866025i) q^{6} +3.53919i q^{7} +1.00000i q^{8} +(0.500000 - 0.866025i) q^{9} +O(q^{10})\)	\(q+(-0.866025 + 0.500000i) q^{2} +(-0.866025 + 0.500000i) q^{3} +(0.500000 - 0.866025i) q^{4} +(2.14894 - 0.618092i) q^{5} +(0.500000 - 0.866025i) q^{6} +3.53919i q^{7} +1.00000i q^{8} +(0.500000 - 0.866025i) q^{9} +(-1.55199 + 1.60976i) q^{10} +3.34017 q^{11} +1.00000i q^{12} +(-1.48028 - 0.854638i) q^{13} +(-1.76959 - 3.06503i) q^{14} +(-1.55199 + 1.60976i) q^{15} +(-0.500000 - 0.866025i) q^{16} +(-3.29175 + 1.90049i) q^{17} +1.00000i q^{18} +(1.30878 - 4.15777i) q^{19} +(0.539189 - 2.17009i) q^{20} +(-1.76959 - 3.06503i) q^{21} +(-2.89267 + 1.67009i) q^{22} +(7.33350 + 4.23400i) q^{23} +(-0.500000 - 0.866025i) q^{24} +(4.23592 - 2.65649i) q^{25} +1.70928 q^{26} +1.00000i q^{27} +(3.06503 + 1.76959i) q^{28} +(-3.97887 + 6.89160i) q^{29} +(0.539189 - 2.17009i) q^{30} +1.07838 q^{31} +(0.866025 + 0.500000i) q^{32} +(-2.89267 + 1.67009i) q^{33} +(1.90049 - 3.29175i) q^{34} +(2.18754 + 7.60552i) q^{35} +(-0.500000 - 0.866025i) q^{36} -4.70928i q^{37} +(0.945448 + 4.25513i) q^{38} +1.70928 q^{39} +(0.618092 + 2.14894i) q^{40} +(5.96441 + 10.3307i) q^{41} +(3.06503 + 1.76959i) q^{42} +(-4.39800 + 2.53919i) q^{43} +(1.67009 - 2.89267i) q^{44} +(0.539189 - 2.17009i) q^{45} -8.46800 q^{46} +(4.73543 + 2.73400i) q^{47} +(0.866025 + 0.500000i) q^{48} -5.52586 q^{49} +(-2.34017 + 4.41855i) q^{50} +(1.90049 - 3.29175i) q^{51} +(-1.48028 + 0.854638i) q^{52} +(-10.8342 - 6.25513i) q^{53} +(-0.500000 - 0.866025i) q^{54} +(7.17785 - 2.06453i) q^{55} -3.53919 q^{56} +(0.945448 + 4.25513i) q^{57} -7.95774i q^{58} +(2.93302 + 5.08013i) q^{59} +(0.618092 + 2.14894i) q^{60} +(-6.92522 + 11.9948i) q^{61} +(-0.933903 + 0.539189i) q^{62} +(3.06503 + 1.76959i) q^{63} -1.00000 q^{64} +(-3.70928 - 0.921622i) q^{65} +(1.67009 - 2.89267i) q^{66} +(7.82551 + 4.51806i) q^{67} +3.80098i q^{68} -8.46800 q^{69} +(-5.69723 - 5.49280i) q^{70} +(4.04585 + 7.00763i) q^{71} +(0.866025 + 0.500000i) q^{72} +(5.11673 - 2.95415i) q^{73} +(2.35464 + 4.07835i) q^{74} +(-2.34017 + 4.41855i) q^{75} +(-2.94635 - 3.21233i) q^{76} +11.8215i q^{77} +(-1.48028 + 0.854638i) q^{78} +(-3.53919 - 6.13005i) q^{79} +(-1.60976 - 1.55199i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(-10.3307 - 5.96441i) q^{82} -4.68035i q^{83} -3.53919 q^{84} +(-5.89911 + 6.11866i) q^{85} +(2.53919 - 4.39800i) q^{86} -7.95774i q^{87} +3.34017i q^{88} +(4.66229 - 8.07532i) q^{89} +(0.618092 + 2.14894i) q^{90} +(3.02472 - 5.23898i) q^{91} +(7.33350 - 4.23400i) q^{92} +(-0.933903 + 0.539189i) q^{93} -5.46800 q^{94} +(0.242616 - 9.74377i) q^{95} -1.00000 q^{96} +(5.06662 - 2.92522i) q^{97} +(4.78553 - 2.76293i) q^{98} +(1.67009 - 2.89267i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 6 q^{4} + 6 q^{6} + 6 q^{9}+O(q^{10}) \) 12 * q + 6 * q^4 + 6 * q^6 + 6 * q^9	\( 12 q + 6 q^{4} + 6 q^{6} + 6 q^{9} - 2 q^{10} - 4 q^{11} - 18 q^{14} - 2 q^{15} - 6 q^{16} + 6 q^{19} - 18 q^{21} - 6 q^{24} - 2 q^{25} - 8 q^{26} - 16 q^{29} + 4 q^{34} + 2 q^{35} - 6 q^{36} - 8 q^{39} + 2 q^{40} + 10 q^{41} - 2 q^{44} + 28 q^{46} - 56 q^{49} + 16 q^{50} + 4 q^{51} - 6 q^{54} - 8 q^{55} - 36 q^{56} + 8 q^{59} + 2 q^{60} - 28 q^{61} - 12 q^{64} - 16 q^{65} - 2 q^{66} + 28 q^{69} + 16 q^{70} + 44 q^{71} + 14 q^{74} + 16 q^{75} - 12 q^{76} - 36 q^{79} - 6 q^{81} - 36 q^{84} - 32 q^{85} + 24 q^{86} + 6 q^{89} + 2 q^{90} + 64 q^{94} - 12 q^{95} - 12 q^{96} - 2 q^{99}+O(q^{100}) \) 12 * q + 6 * q^4 + 6 * q^6 + 6 * q^9 - 2 * q^10 - 4 * q^11 - 18 * q^14 - 2 * q^15 - 6 * q^16 + 6 * q^19 - 18 * q^21 - 6 * q^24 - 2 * q^25 - 8 * q^26 - 16 * q^29 + 4 * q^34 + 2 * q^35 - 6 * q^36 - 8 * q^39 + 2 * q^40 + 10 * q^41 - 2 * q^44 + 28 * q^46 - 56 * q^49 + 16 * q^50 + 4 * q^51 - 6 * q^54 - 8 * q^55 - 36 * q^56 + 8 * q^59 + 2 * q^60 - 28 * q^61 - 12 * q^64 - 16 * q^65 - 2 * q^66 + 28 * q^69 + 16 * q^70 + 44 * q^71 + 14 * q^74 + 16 * q^75 - 12 * q^76 - 36 * q^79 - 6 * q^81 - 36 * q^84 - 32 * q^85 + 24 * q^86 + 6 * q^89 + 2 * q^90 + 64 * q^94 - 12 * q^95 - 12 * q^96 - 2 * q^99

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