LMFDB - Embedded newform 429.2.s.a.199.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [429,2,Mod(166,429)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(429, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 0, 5]))

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

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

chi := DirichletCharacter("429.166");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 429 = 3 \cdot 11 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	429.s (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:	$3.42558224671$
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			199.4
Character	$\chi$	$=$	429.199
Dual form			429.2.s.a.166.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.00815 - 0.582055i) q^{2} +(0.500000 - 0.866025i) q^{3} +(-0.322425 - 0.558456i) q^{4} +1.30774i q^{5} +(-1.00815 + 0.582055i) q^{6} +(-2.07195 + 1.19624i) q^{7} +3.07889i q^{8} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})$	\(q+(-1.00815 - 0.582055i) q^{2} +(0.500000 - 0.866025i) q^{3} +(-0.322425 - 0.558456i) q^{4} +1.30774i q^{5} +(-1.00815 + 0.582055i) q^{6} +(-2.07195 + 1.19624i) q^{7} +3.07889i q^{8} +(-0.500000 - 0.866025i) q^{9} +(0.761176 - 1.31840i) q^{10} +(0.866025 + 0.500000i) q^{11} -0.644850 q^{12} +(-1.68191 + 3.18923i) q^{13} +2.78511 q^{14} +(1.13254 + 0.653870i) q^{15} +(1.14723 - 1.98707i) q^{16} +(1.71091 + 2.96339i) q^{17} +1.16411i q^{18} +(-7.44473 + 4.29822i) q^{19} +(0.730315 - 0.421648i) q^{20} +2.39248i q^{21} +(-0.582055 - 1.00815i) q^{22} +(-0.0396833 + 0.0687334i) q^{23} +(2.66640 + 1.53945i) q^{24} +3.28982 q^{25} +(3.55192 - 2.23625i) q^{26} -1.00000 q^{27} +(1.33610 + 0.771396i) q^{28} +(2.98104 - 5.16331i) q^{29} +(-0.761176 - 1.31840i) q^{30} +2.82525i q^{31} +(3.01964 - 1.74339i) q^{32} +(0.866025 - 0.500000i) q^{33} -3.98338i q^{34} +(-1.56437 - 2.70957i) q^{35} +(-0.322425 + 0.558456i) q^{36} +(-4.65493 - 2.68752i) q^{37} +10.0072 q^{38} +(1.92100 + 3.05119i) q^{39} -4.02639 q^{40} +(1.35400 + 0.781731i) q^{41} +(1.39256 - 2.41198i) q^{42} +(3.24684 + 5.62369i) q^{43} -0.644850i q^{44} +(1.13254 - 0.653870i) q^{45} +(0.0800132 - 0.0461957i) q^{46} +12.9309i q^{47} +(-1.14723 - 1.98707i) q^{48} +(-0.638014 + 1.10507i) q^{49} +(-3.31662 - 1.91485i) q^{50} +3.42183 q^{51} +(2.32333 - 0.0890113i) q^{52} -1.32448 q^{53} +(1.00815 + 0.582055i) q^{54} +(-0.653870 + 1.13254i) q^{55} +(-3.68310 - 6.37932i) q^{56} +8.59644i q^{57} +(-6.01065 + 3.47025i) q^{58} +(4.25746 - 2.45804i) q^{59} -0.843295i q^{60} +(0.0339076 + 0.0587297i) q^{61} +(1.64445 - 2.84828i) q^{62} +(2.07195 + 1.19624i) q^{63} -8.64793 q^{64} +(-4.17068 - 2.19950i) q^{65} -1.16411 q^{66} +(-13.0529 - 7.53610i) q^{67} +(1.10328 - 1.91094i) q^{68} +(0.0396833 + 0.0687334i) q^{69} +3.64220i q^{70} +(3.10656 - 1.79357i) q^{71} +(2.66640 - 1.53945i) q^{72} -2.67403i q^{73} +(3.12857 + 5.41885i) q^{74} +(1.64491 - 2.84907i) q^{75} +(4.80073 + 2.77170i) q^{76} -2.39248 q^{77} +(-0.160687 - 4.19418i) q^{78} -8.50791 q^{79} +(2.59857 + 1.50028i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(-0.910020 - 1.57620i) q^{82} +15.6075i q^{83} +(1.33610 - 0.771396i) q^{84} +(-3.87534 + 2.23743i) q^{85} -7.55935i q^{86} +(-2.98104 - 5.16331i) q^{87} +(-1.53945 + 2.66640i) q^{88} +(-6.46233 - 3.73103i) q^{89} -1.52235 q^{90} +(-0.330244 - 8.61989i) q^{91} +0.0511795 q^{92} +(2.44674 + 1.41263i) q^{93} +(7.52646 - 13.0362i) q^{94} +(-5.62095 - 9.73577i) q^{95} -3.48677i q^{96} +(8.29615 - 4.78979i) q^{97} +(1.28643 - 0.742718i) q^{98} -1.00000i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 12 q^{3} + 14 q^{4} + 6 q^{7} - 12 q^{9}+O(q^{10}) $ 24 * q + 12 * q^3 + 14 * q^4 + 6 * q^7 - 12 * q^9	$ 24 q + 12 q^{3} + 14 q^{4} + 6 q^{7} - 12 q^{9} + 28 q^{12} - 4 q^{13} + 20 q^{14} - 6 q^{15} - 14 q^{16} + 10 q^{17} - 18 q^{20} + 2 q^{22} - 14 q^{23} + 4 q^{25} - 34 q^{26} - 24 q^{27} - 30 q^{28} + 4 q^{29} + 30 q^{32} + 6 q^{35} + 14 q^{36} + 12 q^{38} - 2 q^{39} + 20 q^{40} - 30 q^{41} + 10 q^{42} - 4 q^{43} - 6 q^{45} - 24 q^{46} + 14 q^{48} + 18 q^{49} - 84 q^{50} + 20 q^{51} + 40 q^{52} - 56 q^{53} - 4 q^{55} + 26 q^{56} + 48 q^{58} + 60 q^{59} - 2 q^{61} + 18 q^{62} - 6 q^{63} - 48 q^{64} - 10 q^{65} + 4 q^{66} - 42 q^{67} - 18 q^{68} + 14 q^{69} + 6 q^{71} + 2 q^{75} - 48 q^{76} + 24 q^{77} - 26 q^{78} - 20 q^{79} + 30 q^{80} - 12 q^{81} - 10 q^{82} - 30 q^{84} + 6 q^{85} - 4 q^{87} - 12 q^{88} + 12 q^{89} + 18 q^{91} + 8 q^{92} + 12 q^{93} - 22 q^{94} + 4 q^{95} + 6 q^{97} - 114 q^{98}+O(q^{100}) $ 24 * q + 12 * q^3 + 14 * q^4 + 6 * q^7 - 12 * q^9 + 28 * q^12 - 4 * q^13 + 20 * q^14 - 6 * q^15 - 14 * q^16 + 10 * q^17 - 18 * q^20 + 2 * q^22 - 14 * q^23 + 4 * q^25 - 34 * q^26 - 24 * q^27 - 30 * q^28 + 4 * q^29 + 30 * q^32 + 6 * q^35 + 14 * q^36 + 12 * q^38 - 2 * q^39 + 20 * q^40 - 30 * q^41 + 10 * q^42 - 4 * q^43 - 6 * q^45 - 24 * q^46 + 14 * q^48 + 18 * q^49 - 84 * q^50 + 20 * q^51 + 40 * q^52 - 56 * q^53 - 4 * q^55 + 26 * q^56 + 48 * q^58 + 60 * q^59 - 2 * q^61 + 18 * q^62 - 6 * q^63 - 48 * q^64 - 10 * q^65 + 4 * q^66 - 42 * q^67 - 18 * q^68 + 14 * q^69 + 6 * q^71 + 2 * q^75 - 48 * q^76 + 24 * q^77 - 26 * q^78 - 20 * q^79 + 30 * q^80 - 12 * q^81 - 10 * q^82 - 30 * q^84 + 6 * q^85 - 4 * q^87 - 12 * q^88 + 12 * q^89 + 18 * q^91 + 8 * q^92 + 12 * q^93 - 22 * q^94 + 4 * q^95 + 6 * q^97 - 114 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/429\mathbb{Z}\right)^\times$.

$n$	$67$	$79$	$287$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$1$	$1$

Coefficient data

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

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

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

$2$	−1.00815	−	0.582055i	−0.712868	−	0.411575i	0.0992538	−	0.995062i	$-0.468354\pi$
$2$	−1.00815	−	0.582055i	−0.712868	−	0.411575i	−0.812122	+	0.583487i	$0.801688\pi$
$3$	0.500000	−	0.866025i	0.288675	−	0.500000i
$3$	0.500000	−	0.866025i	0.288675	−	0.500000i
$4$	−0.322425	−	0.558456i	−0.161212	−	0.279228i
$5$			1.30774i			0.584839i	0.956290	+	0.292419i	$0.0944603\pi$
$5$			1.30774i			0.584839i	−0.956290	+	0.292419i	$0.905540\pi$
$6$	−1.00815	+	0.582055i	−0.411575	+	0.237623i
$7$	−2.07195	+	1.19624i	−0.783124	+	0.452137i	−0.837536	−	0.546382i	$-0.816005\pi$
$7$	−2.07195	+	1.19624i	−0.783124	+	0.452137i	0.0544125	+	0.998519i	$0.482671\pi$
$8$			3.07889i			1.08855i
$9$	−0.500000	−	0.866025i	−0.166667	−	0.288675i
$10$	0.761176	−	1.31840i	0.240705	−	0.416913i
$11$	0.866025	+	0.500000i	0.261116	+	0.150756i
$11$	0.866025	+	0.500000i	0.261116	+	0.150756i
$12$	−0.644850			−0.186152
$13$	−1.68191	+	3.18923i	−0.466479	+	0.884532i
$13$	−1.68191	+	3.18923i	−0.466479	+	0.884532i
$14$	2.78511			0.744352
$15$	1.13254	+	0.653870i	0.292419	+	0.168828i
$16$	1.14723	−	1.98707i	0.286809	−	0.496767i
$17$	1.71091	+	2.96339i	0.414958	+	0.718728i	0.995424	−	0.0955564i	$-0.0304630\pi$
$17$	1.71091	+	2.96339i	0.414958	+	0.718728i	−0.580466	+	0.814284i	$0.697130\pi$
$18$			1.16411i			0.274383i
$19$	−7.44473	+	4.29822i	−1.70794	+	0.986079i	−0.770830	+	0.637041i	$0.780158\pi$
$19$	−7.44473	+	4.29822i	−1.70794	+	0.986079i	−0.937109	+	0.349038i	$0.886509\pi$
$20$	0.730315	−	0.421648i	0.163303	−	0.0942833i
$21$			2.39248i			0.522082i
$22$	−0.582055	−	1.00815i	−0.124094	−	0.214938i
$23$	−0.0396833	+	0.0687334i	−0.00827453	+	0.0143319i	−0.870133	−	0.492817i	$-0.835967\pi$
$23$	−0.0396833	+	0.0687334i	−0.00827453	+	0.0143319i	0.861858	+	0.507149i	$0.169301\pi$
$24$	2.66640	+	1.53945i	0.544277	+	0.314238i
$25$	3.28982			0.657963
$26$	3.55192	−	2.23625i	0.696589	−	0.438564i
$27$	−1.00000			−0.192450
$28$	1.33610	+	0.771396i	0.252498	+	0.145780i
$29$	2.98104	−	5.16331i	0.553564	−	0.958802i	−0.444449	−	0.895804i	$-0.646601\pi$
$29$	2.98104	−	5.16331i	0.553564	−	0.958802i	0.998014	−	0.0629977i	$-0.0200661\pi$
$30$	−0.761176	−	1.31840i	−0.138971	−	0.240705i
$31$			2.82525i			0.507431i	0.967279	+	0.253715i	$0.0816527\pi$
$31$			2.82525i			0.507431i	−0.967279	+	0.253715i	$0.918347\pi$
$32$	3.01964	−	1.74339i	0.533801	−	0.308190i
$33$	0.866025	−	0.500000i	0.150756	−	0.0870388i
$34$		−	3.98338i		−	0.683145i
$35$	−1.56437	−	2.70957i	−0.264427	−	0.458001i
$36$	−0.322425	+	0.558456i	−0.0537375	+	0.0930760i
$37$	−4.65493	−	2.68752i	−0.765266	−	0.441826i	0.0659176	−	0.997825i	$-0.479003\pi$
$37$	−4.65493	−	2.68752i	−0.765266	−	0.441826i	−0.831183	+	0.555999i	$0.812336\pi$
$38$	10.0072			1.62338
$39$	1.92100	+	3.05119i	0.307605	+	0.488582i
$40$	−4.02639			−0.636628
$41$	1.35400	+	0.781731i	0.211459	+	0.122086i	0.601989	−	0.798504i	$-0.294375\pi$
$41$	1.35400	+	0.781731i	0.211459	+	0.122086i	−0.390530	+	0.920590i	$0.627708\pi$
$42$	1.39256	−	2.41198i	0.214876	−	0.372176i
$43$	3.24684	+	5.62369i	0.495138	+	0.857605i	0.999984	−	0.00560451i	$-0.00178398\pi$
$43$	3.24684	+	5.62369i	0.495138	+	0.857605i	−0.504846	+	0.863210i	$0.668451\pi$
$44$		−	0.644850i		−	0.0972147i
$45$	1.13254	−	0.653870i	0.168828	−	0.0974731i
$46$	0.0800132	−	0.0461957i	0.0117973	−	0.00681118i
$47$			12.9309i			1.88616i	0.332568	+	0.943079i	$0.392085\pi$
$47$			12.9309i			1.88616i	−0.332568	+	0.943079i	$0.607915\pi$
$48$	−1.14723	−	1.98707i	−0.165589	−	0.286809i
$49$	−0.638014	+	1.10507i	−0.0911449	+	0.157868i
$50$	−3.31662	−	1.91485i	−0.469041	−	0.270801i
$51$	3.42183			0.479152
$52$	2.32333	−	0.0890113i	0.322188	−	0.0123436i
$53$	−1.32448			−0.181931			−0.0909657	−	0.995854i	$-0.528995\pi$
$53$	−1.32448			−0.181931			−0.0909657	+	0.995854i	$0.528995\pi$
$54$	1.00815	+	0.582055i	0.137192	+	0.0792076i
$55$	−0.653870	+	1.13254i	−0.0881678	+	0.152711i
$56$	−3.68310	−	6.37932i	−0.492175	−	0.852472i
$57$			8.59644i			1.13863i
$58$	−6.01065	+	3.47025i	−0.789237	+	0.455666i
$59$	4.25746	−	2.45804i	0.554274	−	0.320010i	−0.196570	−	0.980490i	$-0.562980\pi$
$59$	4.25746	−	2.45804i	0.554274	−	0.320010i	0.750844	+	0.660480i	$0.229647\pi$
$60$		−	0.843295i		−	0.108869i
$61$	0.0339076	+	0.0587297i	0.00434142	+	0.00751957i	0.868188	−	0.496236i	$-0.165285\pi$
$61$	0.0339076	+	0.0587297i	0.00434142	+	0.00751957i	−0.863847	+	0.503755i	$0.831951\pi$
$62$	1.64445	−	2.84828i	0.208846	−	0.361731i
$63$	2.07195	+	1.19624i	0.261041	+	0.150712i
$64$	−8.64793			−1.08099
$65$	−4.17068	−	2.19950i	−0.517309	−	0.272815i
$66$	−1.16411			−0.143292
$67$	−13.0529	−	7.53610i	−1.59467	−	0.920681i	−0.992491	−	0.122318i	$-0.960967\pi$
$67$	−13.0529	−	7.53610i	−1.59467	−	0.920681i	−0.602176	−	0.798363i	$-0.705699\pi$
$68$	1.10328	−	1.91094i	0.133793	−	0.231736i
$69$	0.0396833	+	0.0687334i	0.00477730	+	0.00827453i
$70$			3.64220i			0.435326i
$71$	3.10656	−	1.79357i	0.368681	−	0.212858i	−0.304201	−	0.952608i	$-0.598389\pi$
$71$	3.10656	−	1.79357i	0.368681	−	0.212858i	0.672882	+	0.739750i	$0.265056\pi$
$72$	2.66640	−	1.53945i	0.314238	−	0.181426i
$73$		−	2.67403i		−	0.312972i	−0.987680	−	0.156486i	$-0.949983\pi$
$73$		−	2.67403i		−	0.312972i	0.987680	−	0.156486i	$-0.0500166\pi$
$74$	3.12857	+	5.41885i	0.363689	+	0.629928i
$75$	1.64491	−	2.84907i	0.189938	−	0.328982i
$76$	4.80073	+	2.77170i	0.550682	+	0.317936i
$77$	−2.39248			−0.272649
$78$	−0.160687	−	4.19418i	−0.0181942	−	0.474897i
$79$	−8.50791			−0.957215			−0.478608	−	0.878029i	$-0.658858\pi$
$79$	−8.50791			−0.957215			−0.478608	+	0.878029i	$0.658858\pi$
$80$	2.59857	+	1.50028i	0.290529	+	0.167737i
$81$	−0.500000	+	0.866025i	−0.0555556	+	0.0962250i
$82$	−0.910020	−	1.57620i	−0.100495	−	0.174062i
$83$			15.6075i			1.71315i	0.516026	+	0.856573i	$0.327411\pi$
$83$			15.6075i			1.71315i	−0.516026	+	0.856573i	$0.672589\pi$
$84$	1.33610	−	0.771396i	0.145780	−	0.0841662i
$85$	−3.87534	+	2.23743i	−0.420340	+	0.242683i
$86$		−	7.55935i		−	0.815146i
$87$	−2.98104	−	5.16331i	−0.319601	−	0.553564i
$88$	−1.53945	+	2.66640i	−0.164106	+	0.284239i
$89$	−6.46233	−	3.73103i	−0.685005	−	0.395488i	0.116733	−	0.993163i	$-0.462758\pi$
$89$	−6.46233	−	3.73103i	−0.685005	−	0.395488i	−0.801738	+	0.597675i	$0.796091\pi$
$90$	−1.52235			−0.160470
$91$	−0.330244	−	8.61989i	−0.0346190	−	0.903610i
$92$	0.0511795			0.00533583
$93$	2.44674	+	1.41263i	0.253715	+	0.146483i
$94$	7.52646	−	13.0362i	0.776295	−	1.34458i
$95$	−5.62095	−	9.73577i	−0.576697	−	0.998869i
$96$		−	3.48677i		−	0.355867i
$97$	8.29615	−	4.78979i	0.842347	−	0.486329i	−0.0157144	−	0.999877i	$-0.505002\pi$
$97$	8.29615	−	4.78979i	0.842347	−	0.486329i	0.858061	+	0.513547i	$0.171669\pi$
$98$	1.28643	−	0.742718i	0.129949	−	0.0750259i
$99$		−	1.00000i		−	0.100504i
$100$	−1.06072	−	1.83722i	−0.106072	−	0.183722i
$101$	−6.87965	+	11.9159i	−0.684551	+	1.18568i	0.289027	+	0.957321i	$0.406668\pi$
$101$	−6.87965	+	11.9159i	−0.684551	+	1.18568i	−0.973578	+	0.228356i	$0.926665\pi$
$102$	−3.44971	−	1.99169i	−0.341572	−	0.197207i
$103$	3.26967			0.322170			0.161085	−	0.986941i	$-0.448501\pi$
$103$	3.26967			0.322170			0.161085	+	0.986941i	$0.448501\pi$
$104$	−9.81929	−	5.17843i	−0.962861	−	0.507787i
$105$	−3.12874			−0.305334
$106$	1.33527	+	0.770920i	0.129693	+	0.0748784i
$107$	6.22837	−	10.7879i	0.602119	−	1.04290i	−0.390380	−	0.920654i	$-0.627656\pi$
$107$	6.22837	−	10.7879i	0.602119	−	1.04290i	0.992500	−	0.122248i	$-0.0390102\pi$
$108$	0.322425	+	0.558456i	0.0310253	+	0.0537375i
$109$		−	16.4956i		−	1.57999i	−0.613114	−	0.789994i	$-0.710083\pi$
$109$		−	16.4956i		−	1.57999i	0.613114	−	0.789994i	$-0.289917\pi$
$110$	1.31840	−	0.761176i	0.125704	−	0.0725753i
$111$	−4.65493	+	2.68752i	−0.441826	+	0.255089i
$112$			5.48948i			0.518707i
$113$	−4.14601	−	7.18110i	−0.390024	−	0.675541i	0.602429	−	0.798173i	$-0.294200\pi$
$113$	−4.14601	−	7.18110i	−0.390024	−	0.675541i	−0.992452	+	0.122632i	$0.960866\pi$
$114$	5.00360	−	8.66648i	0.468630	−	0.811690i
$115$	−0.0898854	−	0.0518954i	−0.00838186	−	0.00483927i
$116$	−3.84464			−0.356966
$117$	3.60291	−	0.138034i	0.333089	−	0.0127613i
$118$	−5.72287			−0.526832
$119$	−7.08986	−	4.09333i	−0.649926	−	0.375235i
$120$	−2.01320	+	3.48696i	−0.183779	+	0.318314i
$121$	0.500000	+	0.866025i	0.0454545	+	0.0787296i
$122$		−	0.0789443i		−	0.00714728i
$123$	1.35400	−	0.781731i	0.122086	−	0.0704863i
$124$	1.57778	−	0.910932i	0.141689	−	0.0818041i
$125$			10.8409i			0.969642i
$126$	−1.39256	−	2.41198i	−0.124059	−	0.214876i
$127$	−10.0468	+	17.4016i	−0.891510	+	1.54414i	−0.0534454	+	0.998571i	$0.517020\pi$
$127$	−10.0468	+	17.4016i	−0.891510	+	1.54414i	−0.838065	+	0.545570i	$0.816313\pi$
$128$	2.67912	+	1.54679i	0.236803	+	0.136718i
$129$	6.49368			0.571737
$130$	2.92443	+	4.64499i	0.256489	+	0.407392i
$131$	−8.35408			−0.729899			−0.364950	−	0.931027i	$-0.618914\pi$
$131$	−8.35408			−0.729899			−0.364950	+	0.931027i	$0.618914\pi$
$132$	−0.558456	−	0.322425i	−0.0486074	−	0.0280635i
$133$	10.2834	−	17.8114i	0.891685	−	1.54444i
$134$	8.77285	+	15.1950i	0.757858	+	1.31265i
$135$		−	1.30774i		−	0.112552i
$136$	−9.12397	+	5.26772i	−0.782374	+	0.451704i
$137$	1.21463	−	0.701265i	0.103773	−	0.0599131i	−0.447215	−	0.894426i	$-0.647584\pi$
$137$	1.21463	−	0.701265i	0.103773	−	0.0599131i	0.550988	+	0.834513i	$0.314251\pi$
$138$		−	0.0923913i		−	0.00786487i
$139$	−5.97506	−	10.3491i	−0.506798	−	0.877800i	−0.999969	−	0.00786767i	$-0.997496\pi$
$139$	−5.97506	−	10.3491i	−0.506798	−	0.877800i	0.493171	−	0.869932i	$-0.335838\pi$
$140$	−1.00878	+	1.74727i	−0.0852579	+	0.147671i
$141$	11.1984	+	6.46543i	0.943079	+	0.544487i
$142$	−4.17583			−0.350428
$143$	−3.05119	+	1.92100i	−0.255154	+	0.160642i
$144$	−2.29447			−0.191206
$145$	6.75226	+	3.89842i	0.560745	+	0.323746i
$146$	−1.55643	+	2.69582i	−0.128811	+	0.223108i
$147$	0.638014	+	1.10507i	0.0526225	+	0.0911449i
$148$			3.46610i			0.284911i
$149$	6.61733	−	3.82052i	0.542113	−	0.312989i	−0.203822	−	0.979008i	$-0.565336\pi$
$149$	6.61733	−	3.82052i	0.542113	−	0.312989i	0.745935	+	0.666019i	$0.232003\pi$
$150$	−3.31662	+	1.91485i	−0.270801	+	0.156347i
$151$			14.2562i			1.16016i	0.814561	+	0.580078i	$0.196978\pi$
$151$			14.2562i			1.16016i	−0.814561	+	0.580078i	$0.803022\pi$
$152$	−13.2338	−	22.9215i	−1.07340	−	1.85918i
$153$	1.71091	−	2.96339i	0.138319	−	0.239576i
$154$	2.41198	+	1.39256i	0.194363	+	0.112215i
$155$	−3.69470			−0.296765
$156$	1.08458	−	2.05657i	0.0868360	−	0.164658i
$157$	7.09224			0.566022			0.283011	−	0.959117i	$-0.408667\pi$
$157$	7.09224			0.566022			0.283011	+	0.959117i	$0.408667\pi$
$158$	8.57724	+	4.95207i	0.682368	+	0.393966i
$159$	−0.662240	+	1.14703i	−0.0525191	+	0.0909657i
$160$	2.27990	+	3.94890i	0.180242	+	0.312188i
$161$		−	0.189883i		−	0.0149649i
$162$	1.00815	−	0.582055i	0.0792076	−	0.0457305i
$163$	17.3245	−	10.0023i	1.35696	−	0.783443i	0.367750	−	0.929925i	$-0.380128\pi$
$163$	17.3245	−	10.0023i	1.35696	−	0.783443i	0.989213	+	0.146482i	$0.0467949\pi$
$164$		−	1.00820i		−	0.0787270i
$165$	0.653870	+	1.13254i	0.0509037	+	0.0881678i
$166$	9.08442	−	15.7347i	0.705087	−	1.22125i
$167$	−9.97133	−	5.75695i	−0.771605	−	0.445486i	0.0618422	−	0.998086i	$-0.480302\pi$
$167$	−9.97133	−	5.75695i	−0.771605	−	0.445486i	−0.833447	+	0.552600i	$0.813636\pi$
$168$	−7.36620			−0.568315
$169$	−7.34234	−	10.7280i	−0.564795	−	0.825231i
$170$	5.20923			0.399530
$171$	7.44473	+	4.29822i	0.569313	+	0.328693i
$172$	2.09372	−	3.62644i	0.159645	−	0.276513i
$173$	6.72985	+	11.6564i	0.511661	+	0.886223i	0.999909	+	0.0135177i	$0.00430294\pi$
$173$	6.72985	+	11.6564i	0.511661	+	0.886223i	−0.488248	+	0.872705i	$0.662364\pi$
$174$			6.94050i			0.526158i
$175$	−6.81634	+	3.93541i	−0.515267	+	0.297489i
$176$	1.98707	−	1.14723i	0.149781	−	0.0864761i
$177$		−	4.91609i		−	0.369516i
$178$	4.34332	+	7.52286i	0.325546	+	0.563862i
$179$	−3.07562	+	5.32713i	−0.229883	+	0.398168i	−0.957773	−	0.287525i	$-0.907168\pi$
$179$	−3.07562	+	5.32713i	−0.229883	+	0.398168i	0.727891	+	0.685693i	$0.240501\pi$
$180$	−0.730315	−	0.421648i	−0.0544345	−	0.0314278i
$181$	−3.28294			−0.244019			−0.122009	−	0.992529i	$-0.538934\pi$
$181$	−3.28294			−0.244019			−0.122009	+	0.992529i	$0.538934\pi$
$182$	−4.68431	+	8.88235i	−0.347224	+	0.658404i
$183$	0.0678152			0.00501305
$184$	−0.211623	−	0.122181i	−0.0156011	−	0.00900727i
$185$	3.51458	−	6.08743i	0.258397	−	0.447557i
$186$	−1.64445	−	2.84828i	−0.120577	−	0.208846i
$187$			3.42183i			0.250229i
$188$	7.22131	−	4.16923i	0.526668	−	0.304072i
$189$	2.07195	−	1.19624i	0.150712	−	0.0870137i
$190$			13.0868i			0.949416i
$191$	7.74162	+	13.4089i	0.560164	+	0.970232i	0.997482	+	0.0709252i	$0.0225952\pi$
$191$	7.74162	+	13.4089i	0.560164	+	0.970232i	−0.437318	+	0.899307i	$0.644071\pi$
$192$	−4.32396	+	7.48932i	−0.312055	+	0.540495i
$193$	15.6718	+	9.04812i	1.12808	+	0.651298i	0.943452	−	0.331511i	$-0.107558\pi$
$193$	15.6718	+	9.04812i	1.12808	+	0.651298i	0.184629	+	0.982808i	$0.440892\pi$
$194$	−11.1517			−0.800643
$195$	−3.99017	+	2.51216i	−0.285742	+	0.179900i
$196$	0.822847			0.0587748
$197$	12.1944	+	7.04045i	0.868817	+	0.501612i	0.866955	−	0.498387i	$-0.166074\pi$
$197$	12.1944	+	7.04045i	0.868817	+	0.501612i	0.00186193	+	0.999998i	$0.499407\pi$
$198$	−0.582055	+	1.00815i	−0.0413648	+	0.0716460i
$199$	0.259523	+	0.449508i	0.0183971	+	0.0318648i	0.875077	−	0.483983i	$-0.160810\pi$
$199$	0.259523	+	0.449508i	0.0183971	+	0.0318648i	−0.856680	+	0.515848i	$0.827477\pi$
$200$			10.1290i			0.716228i
$201$	−13.0529	+	7.53610i	−0.920681	+	0.531556i
$202$	13.8714	−	8.00866i	0.975989	−	0.563488i
$203$			14.2641i			1.00115i
$204$	−1.10328	−	1.91094i	−0.0772452	−	0.133793i
$205$	−1.02230	+	1.77068i	−0.0714006	+	0.123669i
$206$	−3.29631	−	1.90313i	−0.229665	−	0.132597i
$207$	0.0793666			0.00551636
$208$	4.40767	+	7.00087i	0.305617	+	0.485423i
$209$	−8.59644			−0.594628
$210$	3.15424	+	1.82110i	0.217663	+	0.125668i
$211$	−1.45368	+	2.51784i	−0.100075	+	0.173335i	−0.911715	−	0.410822i	$-0.865242\pi$
$211$	−1.45368	+	2.51784i	−0.100075	+	0.173335i	0.811640	+	0.584158i	$0.198575\pi$
$212$	0.427045	+	0.739664i	0.0293296	+	0.0508003i
$213$		−	3.58715i		−	0.245787i
$214$	−12.5582	+	7.25050i	−0.858464	+	0.495634i
$215$	−7.35432	+	4.24602i	−0.501561	+	0.289576i
$216$		−	3.07889i		−	0.209492i
$217$	−3.37969	−	5.85379i	−0.229428	−	0.397381i
$218$	−9.60132	+	16.6300i	−0.650283	+	1.12632i
$219$	−2.31578	−	1.33702i	−0.156486	−	0.0903472i
$220$	0.843295			0.0568550
$221$	−12.3285	+	0.472329i	−0.829307	+	0.0317723i
$222$	6.25714			0.419952
$223$	17.3941	+	10.0425i	1.16479	+	0.672493i	0.952448	−	0.304702i	$-0.0985568\pi$
$223$	17.3941	+	10.0425i	1.16479	+	0.672493i	0.212344	+	0.977195i	$0.431890\pi$
$224$	−4.17102	+	7.22442i	−0.278688	+	0.482702i
$225$	−1.64491	−	2.84907i	−0.109661	−	0.189938i
$226$			9.65281i			0.642095i
$227$	25.8006	−	14.8960i	1.71245	−	0.988681i	0.781208	−	0.624271i	$-0.214604\pi$
$227$	25.8006	−	14.8960i	1.71245	−	0.988681i	0.931239	−	0.364410i	$-0.118729\pi$
$228$	4.80073	−	2.77170i	0.317936	−	0.183561i
$229$			12.1812i			0.804957i	0.915429	+	0.402478i	$0.131851\pi$
$229$			12.1812i			0.804957i	−0.915429	+	0.402478i	$0.868149\pi$
$230$	0.0604119	+	0.104636i	0.00398344	+	0.00689953i
$231$	−1.19624	+	2.07195i	−0.0787069	+	0.136324i
$232$	15.8973	+	9.17829i	1.04371	+	0.602584i
$233$	18.3243			1.20046			0.600232	−	0.799826i	$-0.295075\pi$
$233$	18.3243			1.20046			0.600232	+	0.799826i	$0.295075\pi$
$234$	−3.71261	−	1.95793i	−0.242701	−	0.127994i
$235$	−16.9102			−1.10310
$236$	−2.74542	−	1.58507i	−0.178712	−	0.103179i
$237$	−4.25396	+	7.36807i	−0.276324	+	0.478608i
$238$	4.76509	+	8.25337i	0.308875	+	0.534987i
$239$			2.57563i			0.166604i	0.996524	+	0.0833019i	$0.0265466\pi$
$239$			2.57563i			0.166604i	−0.996524	+	0.0833019i	$0.973453\pi$
$240$	2.59857	−	1.50028i	0.167737	−	0.0968429i
$241$	16.3771	−	9.45532i	1.05494	−	0.609071i	0.130913	−	0.991394i	$-0.458209\pi$
$241$	16.3771	−	9.45532i	1.05494	−	0.609071i	0.924029	+	0.382323i	$0.124876\pi$
$242$		−	1.16411i		−	0.0748318i
$243$	0.500000	+	0.866025i	0.0320750	+	0.0555556i
$244$	0.0218653	−	0.0378718i	0.00139978	−	0.00242449i
$245$	−1.44515	−	0.834357i	−0.0923271	−	0.0533051i
$246$	−1.82004			−0.116042
$247$	−1.18660	−	30.9722i	−0.0755017	−	1.97071i
$248$	−8.69866			−0.552365
$249$	13.5165	+	7.80375i	0.856573	+	0.494543i
$250$	6.31001	−	10.9293i	0.399080	−	0.691227i
$251$	−1.24561	−	2.15746i	−0.0786223	−	0.136178i	0.824033	−	0.566541i	$-0.191719\pi$
$251$	−1.24561	−	2.15746i	−0.0786223	−	0.136178i	−0.902656	+	0.430363i	$0.858385\pi$
$252$		−	1.54279i		−	0.0971867i
$253$	−0.0687334	+	0.0396833i	−0.00432123	+	0.00249487i
$254$	20.2573	−	11.6956i	1.27106	−	0.733846i
$255$			4.47486i			0.280227i
$256$	6.84729	+	11.8599i	0.427956	+	0.741241i
$257$	2.59488	−	4.49447i	0.161864	−	0.280357i	−0.773673	−	0.633585i	$-0.781583\pi$
$257$	2.59488	−	4.49447i	0.161864	−	0.280357i	0.935537	+	0.353228i	$0.114916\pi$
$258$	−6.54659	−	3.77968i	−0.407573	−	0.235312i
$259$	12.8597			0.799063
$260$	0.116404	+	3.03832i	0.00721904	+	0.188428i
$261$	−5.96207			−0.369043
$262$	8.42215	+	4.86253i	0.520322	+	0.300408i
$263$	2.77204	−	4.80131i	0.170931	−	0.296061i	−0.767815	−	0.640672i	$-0.778656\pi$
$263$	2.77204	−	4.80131i	0.170931	−	0.296061i	0.938746	+	0.344611i	$0.111989\pi$
$264$	1.53945	+	2.66640i	0.0947464	+	0.164106i
$265$		−	1.73208i		−	0.106401i
$266$	−20.7344	+	11.9710i	−1.27131	+	0.733990i
$267$	−6.46233	+	3.73103i	−0.395488	+	0.228335i
$268$			9.71930i			0.593701i
$269$	5.20549	+	9.01617i	0.317384	+	0.549726i	0.979941	−	0.199286i	$-0.0638622\pi$
$269$	5.20549	+	9.01617i	0.317384	+	0.549726i	−0.662557	+	0.749011i	$0.730529\pi$
$270$	−0.761176	+	1.31840i	−0.0463237	+	0.0802350i
$271$	−20.6613	−	11.9288i	−1.25508	−	0.724623i	−0.282970	−	0.959129i	$-0.591320\pi$
$271$	−20.6613	−	11.9288i	−1.25508	−	0.724623i	−0.972115	+	0.234505i	$0.924653\pi$
$272$	7.85128			0.476054
$273$	−7.63017	−	4.02395i	−0.461799	−	0.243540i
$274$	−1.63270			−0.0986350
$275$	2.84907	+	1.64491i	0.171805	+	0.0991917i
$276$	0.0255897	−	0.0443227i	0.00154032	−	0.00266792i
$277$	14.1393	+	24.4900i	0.849548	+	1.47146i	0.881612	+	0.471975i	$0.156459\pi$
$277$	14.1393	+	24.4900i	0.849548	+	1.47146i	−0.0320640	+	0.999486i	$0.510208\pi$
$278$			13.9112i			0.834341i
$279$	2.44674	−	1.41263i	0.146483	−	0.0845718i
$280$	8.34248	−	4.81653i	0.498559	−	0.287843i
$281$		−	26.5953i		−	1.58654i	−0.608869	−	0.793271i	$-0.708377\pi$
$281$		−	26.5953i		−	1.58654i	0.608869	−	0.793271i	$-0.291623\pi$
$282$	−7.52646	−	13.0362i	−0.448194	−	0.776295i
$283$	0.526399	−	0.911750i	0.0312912	−	0.0541979i	−0.849956	−	0.526854i	$-0.823371\pi$
$283$	0.526399	−	0.911750i	0.0312912	−	0.0541979i	0.881247	+	0.472656i	$0.156705\pi$
$284$	−2.00326	−	1.15659i	−0.118872	−	0.0686307i
$285$	−11.2419			−0.665913
$286$	4.19418	−	0.160687i	0.248007	−	0.00950161i
$287$	−3.74056			−0.220798
$288$	−3.01964	−	1.74339i	−0.177934	−	0.102730i
$289$	2.64554	−	4.58221i	0.155620	−	0.269542i
$290$	−4.53818	−	7.86037i	−0.266491	−	0.461577i
$291$		−	9.57957i		−	0.561565i
$292$	−1.49333	+	0.862175i	−0.0873906	+	0.0504550i
$293$	−14.3312	+	8.27414i	−0.837239	+	0.483380i	−0.856325	−	0.516438i	$-0.827258\pi$
$293$	−14.3312	+	8.27414i	−0.837239	+	0.483380i	0.0190858	+	0.999818i	$0.493924\pi$
$294$		−	1.48544i		−	0.0866324i
$295$	3.21448	+	5.56765i	0.187154	+	0.324161i
$296$	8.27460	−	14.3320i	0.480951	−	0.833032i
$297$	−0.866025	−	0.500000i	−0.0502519	−	0.0290129i
$298$	−8.89500			−0.515273
$299$	−0.152463	−	0.242163i	−0.00881715	−	0.0140046i
$300$	−2.12144			−0.122481
$301$	−13.4546	−	7.76801i	−0.775509	−	0.447741i
$302$	8.29791	−	14.3724i	0.477491	−	0.827038i
$303$	6.87965	+	11.9159i	0.395225	+	0.684551i
$304$			19.7243i			1.13126i
$305$	−0.0768031	+	0.0443423i	−0.00439774	+	0.00253903i
$306$	−3.44971	+	1.99169i	−0.197207	+	0.113857i
$307$			1.16619i			0.0665578i	0.999446	+	0.0332789i	$0.0105950\pi$
$307$			1.16619i			0.0665578i	−0.999446	+	0.0332789i	$0.989405\pi$
$308$	0.771396	+	1.33610i	0.0439543	+	0.0761312i
$309$	1.63483	−	2.83162i	0.0930025	−	0.161085i
$310$	3.72480	+	2.15052i	0.211555	+	0.122141i
$311$	15.0478			0.853283			0.426641	−	0.904421i	$-0.359697\pi$
$311$	15.0478			0.853283			0.426641	+	0.904421i	$0.359697\pi$
$312$	−9.39430	+	5.91454i	−0.531847	+	0.334845i
$313$	6.14496			0.347334			0.173667	−	0.984804i	$-0.444438\pi$
$313$	6.14496			0.347334			0.173667	+	0.984804i	$0.444438\pi$
$314$	−7.15003	−	4.12807i	−0.403499	−	0.232961i
$315$	−1.56437	+	2.70957i	−0.0881424	+	0.152667i
$316$	2.74316	+	4.75130i	0.154315	+	0.267281i
$317$		−	14.7540i		−	0.828665i	−0.910126	−	0.414332i	$-0.864015\pi$
$317$		−	14.7540i		−	0.828665i	0.910126	−	0.414332i	$-0.135985\pi$
$318$	1.33527	−	0.770920i	0.0748784	−	0.0432310i
$319$	5.16331	−	2.98104i	0.289090	−	0.166906i
$320$		−	11.3092i		−	0.632205i
$321$	−6.22837	−	10.7879i	−0.347634	−	0.602119i
$322$	−0.110522	+	0.191430i	−0.00615917	+	0.0106680i
$323$	−25.4746	−	14.7078i	−1.41744	−	0.818362i
$324$	0.644850			0.0358250
$325$	−5.53319	+	10.4920i	−0.306926	+	0.581990i
$326$	−23.2876			−1.28978
$327$	−14.2856	−	8.24778i	−0.789994	−	0.456103i
$328$	−2.40687	+	4.16882i	−0.132897	+	0.230184i
$329$	−15.4684	−	26.7921i	−0.852802	−	1.47710i
$330$		−	1.52235i		−	0.0838027i
$331$	−8.35980	+	4.82653i	−0.459496	+	0.265290i	−0.711832	−	0.702349i	$-0.752134\pi$
$331$	−8.35980	+	4.82653i	−0.459496	+	0.265290i	0.252336	+	0.967640i	$0.418801\pi$
$332$	8.71610	−	5.03224i	0.478358	−	0.276180i
$333$			5.37505i			0.294551i
$334$	6.70172	+	11.6077i	0.366702	+	0.635146i
$335$	9.85526	−	17.0698i	0.538450	−	0.932623i
$336$	4.75403	+	2.74474i	0.259353	+	0.149738i
$337$	−7.58370			−0.413110			−0.206555	−	0.978435i	$-0.566225\pi$
$337$	−7.58370			−0.413110			−0.206555	+	0.978435i	$0.566225\pi$
$338$	1.15788	+	15.0891i	0.0629804	+	0.820737i
$339$	−8.29201			−0.450360
$340$	2.49901	+	1.44281i	0.135528	+	0.0782472i
$341$	−1.41263	+	2.44674i	−0.0764981	+	0.132499i
$342$	−5.00360	−	8.66648i	−0.270563	−	0.468630i
$343$		−	19.8003i		−	1.06911i
$344$	−17.3148	+	9.99668i	−0.933549	+	0.538985i
$345$	−0.0898854	+	0.0518954i	−0.00483927	+	0.00279395i
$346$		−	15.6686i		−	0.842347i
$347$	−14.7411	−	25.5323i	−0.791344	−	1.37065i	−0.925135	−	0.379638i	$-0.876049\pi$
$347$	−14.7411	−	25.5323i	−0.791344	−	1.37065i	0.133792	−	0.991009i	$-0.457285\pi$
$348$	−1.92232	+	3.32956i	−0.103047	+	0.178483i
$349$	−17.4515	−	10.0756i	−0.934156	−	0.539335i	−0.0460321	−	0.998940i	$-0.514658\pi$
$349$	−17.4515	−	10.0756i	−0.934156	−	0.539335i	−0.888123	+	0.459605i	$0.847991\pi$
$350$	9.16251			0.489757
$351$	1.68191	−	3.18923i	0.0897739	−	0.170228i
$352$	3.48677			0.185846
$353$	8.70839	+	5.02779i	0.463501	+	0.267602i	0.713515	−	0.700640i	$-0.247102\pi$
$353$	8.70839	+	5.02779i	0.463501	+	0.267602i	−0.250014	+	0.968242i	$0.580435\pi$
$354$	−2.86143	+	4.95615i	−0.152083	+	0.263416i
$355$	2.34553	+	4.06257i	0.124488	+	0.215619i
$356$			4.81190i			0.255030i
$357$	−7.08986	+	4.09333i	−0.375235	+	0.216642i
$358$	6.20136	−	3.58036i	0.327752	−	0.189228i
$359$			30.3660i			1.60266i	0.598224	+	0.801329i	$0.295873\pi$
$359$			30.3660i			1.60266i	−0.598224	+	0.801329i	$0.704127\pi$
$360$	2.01320	+	3.48696i	0.106105	+	0.183779i
$361$	27.4493	−	47.5437i	1.44470	−	2.50230i
$362$	3.30969	+	1.91085i	0.173953	+	0.100432i
$363$	1.00000			0.0524864
$364$	−4.70735	+	2.96369i	−0.246732	+	0.155340i
$365$	3.49694			0.183038
$366$	−0.0683678	−	0.0394722i	−0.00357364	−	0.00206324i
$367$	−4.46541	+	7.73432i	−0.233093	+	0.403728i	−0.958717	−	0.284363i	$-0.908218\pi$
$367$	−4.46541	+	7.73432i	−0.233093	+	0.403728i	0.725624	+	0.688091i	$0.241551\pi$
$368$	0.0910521	+	0.157707i	0.00474642	+	0.00822104i
$369$		−	1.56346i		−	0.0813906i
$370$	−7.08644	+	4.09136i	−0.368406	+	0.212700i
$371$	2.74426	−	1.58440i	0.142475	−	0.0822578i
$372$		−	1.82186i		−	0.0944593i
$373$	7.43720	+	12.8816i	0.385083	+	0.666984i	0.991781	−	0.127949i	$-0.0408394\pi$
$373$	7.43720	+	12.8816i	0.385083	+	0.666984i	−0.606697	+	0.794933i	$0.707506\pi$
$374$	1.99169	−	3.44971i	0.102988	−	0.178380i
$375$	9.38851	+	5.42046i	0.484821	+	0.279911i
$376$	−39.8127			−2.05318
$377$	11.4531	+	18.1914i	0.589865	+	0.936906i
$378$	−2.78511			−0.143251
$379$	−14.3589	−	8.29009i	−0.737565	−	0.425833i	0.0836185	−	0.996498i	$-0.473352\pi$
$379$	−14.3589	−	8.29009i	−0.737565	−	0.425833i	−0.821183	+	0.570665i	$0.806686\pi$
$380$	−3.62467	+	6.27811i	−0.185941	+	0.322060i
$381$	10.0468	+	17.4016i	0.514714	+	0.891510i
$382$		−	18.0242i		−	0.922197i
$383$	−9.42949	+	5.44412i	−0.481824	+	0.278181i	−0.721176	−	0.692751i	$-0.756398\pi$
$383$	−9.42949	+	5.44412i	−0.481824	+	0.278181i	0.239352	+	0.970933i	$0.423065\pi$
$384$	2.67912	−	1.54679i	0.136718	−	0.0789344i
$385$		−	3.12874i		−	0.159456i
$386$	−10.5330	−	18.2437i	−0.536115	−	0.928579i
$387$	3.24684	−	5.62369i	0.165046	−	0.285868i
$388$	−5.34977	−	3.08869i	−0.271594	−	0.156805i
$389$	24.9210			1.26354			0.631772	−	0.775155i	$-0.282328\pi$
$389$	24.9210			1.26354			0.631772	+	0.775155i	$0.282328\pi$
$390$	5.48489	−	0.210137i	0.277738	−	0.0106407i
$391$	−0.271579			−0.0137343
$392$	−3.40240	−	1.96438i	−0.171847	−	0.0992161i
$393$	−4.17704	+	7.23484i	−0.210704	+	0.364950i
$394$	−8.19586	−	14.1956i	−0.412901	−	0.715166i
$395$		−	11.1261i		−	0.559817i
$396$	−0.558456	+	0.322425i	−0.0280635	+	0.0162025i
$397$	5.54551	−	3.20170i	0.278321	−	0.160689i	−0.354342	−	0.935116i	$-0.615295\pi$
$397$	5.54551	−	3.20170i	0.278321	−	0.160689i	0.632663	+	0.774427i	$0.281962\pi$
$398$		−	0.604227i		−	0.0302872i
$399$	−10.2834	−	17.8114i	−0.514814	−	0.891685i
$400$	3.77419	−	6.53709i	0.188710	−	0.326855i
$401$	29.3274	+	16.9322i	1.46454	+	0.845552i	0.999216	−	0.0395886i	$-0.0126048\pi$
$401$	29.3274	+	16.9322i	1.46454	+	0.845552i	0.465323	+	0.885141i	$0.345938\pi$
$402$	17.5457			0.875100
$403$	−9.01038	−	4.75183i	−0.448839	−	0.236706i
$404$	8.87268			0.441432
$405$	−1.13254	−	0.653870i	−0.0562761	−	0.0324910i
$406$	8.30251	−	14.3804i	0.412047	−	0.713686i
$407$	−2.68752	−	4.65493i	−0.133216	−	0.230736i
$408$			10.5354i			0.521582i
$409$	−9.18530	+	5.30313i	−0.454184	+	0.262223i	−0.709595	−	0.704609i	$-0.751122\pi$
$409$	−9.18530	+	5.30313i	−0.454184	+	0.262223i	0.255412	+	0.966832i	$0.417789\pi$
$410$	2.06126	−	1.19007i	0.101798	−	0.0587733i
$411$		−	1.40253i		−	0.0691817i
$412$	−1.05422	−	1.82597i	−0.0519378	−	0.0899589i
$413$	−5.88083	+	10.1859i	−0.289377	+	0.501215i
$414$	−0.0800132	−	0.0461957i	−0.00393244	−	0.00227039i
$415$	−20.4105			−1.00191
$416$	0.481294	+	12.5625i	0.0235974	+	0.615929i
$417$	−11.9501			−0.585200
$418$	8.66648	+	5.00360i	0.423891	+	0.244734i
$419$	10.7688	−	18.6520i	0.526088	−	0.911211i	−0.473450	−	0.880821i	$-0.656992\pi$
$419$	10.7688	−	18.6520i	0.526088	−	0.911211i	0.999538	−	0.0303906i	$-0.00967511\pi$
$420$	1.00878	+	1.74727i	0.0492236	+	0.0852579i
$421$		−	2.43671i		−	0.118758i	−0.998236	−	0.0593790i	$-0.981088\pi$
$421$		−	2.43671i		−	0.118758i	0.998236	−	0.0593790i	$-0.0189120\pi$
$422$	2.93104	−	1.69224i	0.142681	−	0.0823768i
$423$	11.1984	−	6.46543i	0.544487	−	0.314360i
$424$		−	4.07794i		−	0.198042i
$425$	5.62860	+	9.74902i	0.273027	+	0.472897i
$426$	−2.08792	+	3.61638i	−0.101160	+	0.175214i
$427$	−0.140510	−	0.0811233i	−0.00679974	−	0.00392583i
$428$	−8.03272			−0.388276
$429$	0.138034	+	3.60291i	0.00666435	+	0.173950i
$430$	9.88567			0.476729
$431$	14.5070	+	8.37564i	0.698779	+	0.403440i	0.806893	−	0.590698i	$-0.201148\pi$
$431$	14.5070	+	8.37564i	0.698779	+	0.403440i	−0.108113	+	0.994139i	$0.534481\pi$
$432$	−1.14723	+	1.98707i	−0.0551964	+	0.0956029i
$433$	7.32805	+	12.6926i	0.352164	+	0.609966i	0.986628	−	0.162986i	$-0.0521127\pi$
$433$	7.32805	+	12.6926i	0.352164	+	0.609966i	−0.634465	+	0.772952i	$0.718779\pi$
$434$			7.86865i			0.377707i
$435$	6.75226	−	3.89842i	0.323746	−	0.186915i
$436$	−9.21205	+	5.31858i	−0.441177	+	0.254714i
$437$		−	0.682269i		−	0.0326374i
$438$	1.55643	+	2.69582i	0.0743693	+	0.128811i
$439$	6.70488	−	11.6132i	0.320007	−	0.554268i	−0.660482	−	0.750842i	$-0.729648\pi$
$439$	6.70488	−	11.6132i	0.320007	−	0.554268i	0.980489	+	0.196574i	$0.0629815\pi$
$440$	−3.48696	−	2.01320i	−0.166234	−	0.0959753i
$441$	1.27603			0.0607633
$442$	12.7039	+	6.69970i	0.604264	+	0.318672i
$443$	26.6599			1.26665			0.633324	−	0.773887i	$-0.281690\pi$
$443$	26.6599			1.26665			0.633324	+	0.773887i	$0.281690\pi$
$444$	3.00173	+	1.73305i	0.142456	+	0.0822469i
$445$	4.87921	−	8.45104i	0.231297	−	0.400618i
$446$	−11.6905	−	20.2486i	−0.553562	−	0.958798i
$447$		−	7.64103i		−	0.361409i
$448$	17.9181	−	10.3450i	0.846549	−	0.488756i
$449$	−31.0743	+	17.9407i	−1.46649	+	0.846676i	−0.999297	−	0.0374814i	$-0.988067\pi$
$449$	−31.0743	+	17.9407i	−1.46649	+	0.846676i	−0.467189	+	0.884158i	$0.654733\pi$
$450$			3.82971i			0.180534i
$451$	0.781731	+	1.35400i	0.0368103	+	0.0637573i
$452$	−2.67355	+	4.63073i	−0.125753	+	0.217811i
$453$	12.3463	+	7.12812i	0.580078	+	0.334908i
$454$	−34.6811			−1.62767
$455$	11.2726	−	0.431873i	0.528466	−	0.0202465i
$456$	−26.4675			−1.23945
$457$	15.3776	+	8.87825i	0.719333	+	0.415307i	0.814507	−	0.580153i	$-0.197007\pi$
$457$	15.3776	+	8.87825i	0.719333	+	0.415307i	−0.0951741	+	0.995461i	$0.530341\pi$
$458$	7.09013	−	12.2805i	0.331300	−	0.573828i
$459$	−1.71091	−	2.96339i	−0.0798587	−	0.138319i
$460$			0.0669294i			0.00312060i
$461$	4.85273	−	2.80172i	0.226014	−	0.130489i	−0.382718	−	0.923865i	$-0.625012\pi$
$461$	4.85273	−	2.80172i	0.226014	−	0.130489i	0.608732	+	0.793376i	$0.291679\pi$
$462$	2.41198	−	1.39256i	0.112215	−	0.0647875i
$463$			20.0140i			0.930128i	0.885277	+	0.465064i	$0.153969\pi$
$463$			20.0140i			0.930128i	−0.885277	+	0.465064i	$0.846031\pi$
$464$	−6.83990	−	11.8470i	−0.317534	−	0.549985i
$465$	−1.84735	+	3.19970i	−0.0856687	+	0.148383i
$466$	−18.4736	−	10.6657i	−0.855773	−	0.494081i
$467$	−38.3435			−1.77433			−0.887163	−	0.461456i	$-0.847327\pi$
$467$	−38.3435			−1.77433			−0.887163	+	0.461456i	$0.847327\pi$
$468$	−1.23875	−	1.96756i	−0.0572614	−	0.0909505i
$469$	36.0600			1.66510
$470$	17.0480	+	9.84265i	0.786364	+	0.454008i
$471$	3.54612	−	6.14206i	0.163397	−	0.283011i
$472$	7.56806	+	13.1083i	0.348348	+	0.603357i
$473$			6.49368i			0.298580i
$474$	8.57724	−	4.95207i	0.393966	−	0.227456i
$475$	−24.4918	+	14.1404i	−1.12376	+	0.648804i
$476$			5.27917i			0.241970i
$477$	0.662240	+	1.14703i	0.0303219	+	0.0525191i
$478$	1.49916	−	2.59662i	0.0685699	−	0.118767i
$479$	−36.2640	−	20.9370i	−1.65694	−	0.956636i	−0.974114	−	0.226057i	$-0.927416\pi$
$479$	−36.2640	−	20.9370i	−1.65694	−	0.956636i	−0.682828	−	0.730579i	$-0.739250\pi$
$480$	4.55979			0.208125
$481$	16.4003	−	10.3254i	0.747790	−	0.470800i
$482$	−22.0141			−1.00271
$483$	−0.164444	−	0.0949415i	−0.00748244	−	0.00431999i
$484$	0.322425	−	0.558456i	0.0146557	−	0.0253844i
$485$	6.26379	+	10.8492i	0.284424	+	0.492637i
$486$		−	1.16411i		−	0.0528051i
$487$	−17.1498	+	9.90143i	−0.777131	+	0.448677i	−0.835412	−	0.549624i	$-0.814771\pi$
$487$	−17.1498	+	9.90143i	−0.777131	+	0.448677i	0.0582817	+	0.998300i	$0.481438\pi$
$488$	−0.180823	+	0.104398i	−0.00818545	+	0.00472587i
$489$		−	20.0047i		−	0.904642i
$490$	0.971282	+	1.68231i	0.0438781	+	0.0759990i
$491$	17.6163	−	30.5124i	0.795013	−	1.37700i	−0.127817	−	0.991798i	$-0.540797\pi$
$491$	17.6163	−	30.5124i	0.795013	−	1.37700i	0.922831	−	0.385206i	$-0.125870\pi$
$492$	−0.873125	−	0.504099i	−0.0393635	−	0.0227265i
$493$	20.4012			0.918823
$494$	−16.8312	+	31.9152i	−0.757272	+	1.43593i
$495$	1.30774			0.0587785
$496$	5.61398	+	3.24123i	0.252075	+	0.145536i
$497$	−4.29109	+	7.43239i	−0.192482	+	0.333388i
$498$	−9.08442	−	15.7347i	−0.407082	−	0.705087i
$499$		−	3.13018i		−	0.140126i	−0.997543	−	0.0700630i	$-0.977680\pi$
$499$		−	3.13018i		−	0.140126i	0.997543	−	0.0700630i	$-0.0223200\pi$
$500$	6.05418	−	3.49538i	0.270751	−	0.156318i
$501$	−9.97133	+	5.75695i	−0.445486	+	0.257202i
$502$			2.90006i			0.129436i
$503$	4.56301	+	7.90337i	0.203455	+	0.352394i	0.949639	−	0.313345i	$-0.101450\pi$
$503$	4.56301	+	7.90337i	0.203455	+	0.352394i	−0.746185	+	0.665739i	$0.768116\pi$
$504$	−3.68310	+	6.37932i	−0.164058	+	0.284157i
$505$	−15.5829	−	8.99679i	−0.693430	−	0.400352i
$506$	0.0923913			0.00410730
$507$	−12.9619	+	0.994649i	−0.575658	+	0.0441739i
$508$	12.9574			0.574890
$509$	1.64980	+	0.952511i	0.0731260	+	0.0422193i	0.536117	−	0.844144i	$-0.319891\pi$
$509$	1.64980	+	0.952511i	0.0731260	+	0.0422193i	−0.462991	+	0.886363i	$0.653224\pi$
$510$	2.60461	−	4.51132i	0.115334	−	0.199765i
$511$	3.19879	+	5.54047i	0.141506	+	0.245096i
$512$		−	22.1292i		−	0.977980i
$513$	7.44473	−	4.29822i	0.328693	−	0.189771i
$514$	−5.23205	+	3.02072i	−0.230776	+	0.133238i
$515$			4.27587i			0.188418i
$516$	−2.09372	−	3.62644i	−0.0921710	−	0.159645i
$517$	−6.46543	+	11.1984i	−0.284349	+	0.492507i
$518$	−12.9645	−	7.48505i	−0.569627	−	0.328874i
$519$	13.4597			0.590815
$520$	6.77204	−	12.8411i	0.296974	−	0.563118i
$521$	3.53937			0.155063			0.0775314	−	0.996990i	$-0.475296\pi$
$521$	3.53937			0.155063			0.0775314	+	0.996990i	$0.475296\pi$
$522$	6.01065	+	3.47025i	0.263079	+	0.151889i
$523$	−8.71764	+	15.0994i	−0.381196	+	0.660251i	−0.991233	−	0.132122i	$-0.957821\pi$
$523$	−8.71764	+	15.0994i	−0.381196	+	0.660251i	0.610038	+	0.792372i	$0.291154\pi$
$524$	2.69356	+	4.66539i	0.117669	+	0.203808i
$525$			7.87083i			0.343511i
$526$	−5.58925	+	3.22695i	−0.243703	+	0.140702i
$527$	−8.37234	+	4.83377i	−0.364705	+	0.210562i
$528$		−	2.29447i		−	0.0998540i
$529$	11.4969	+	19.9131i	0.499863	+	0.865788i
$530$	−1.00816	+	1.74619i	−0.0437918	+	0.0758496i
$531$	−4.25746	−	2.45804i	−0.184758	−	0.106670i
$532$	−13.2625			−0.575002
$533$	−4.77042	+	3.00340i	−0.206630	+	0.130092i
$534$	8.68665			0.375908
$535$	14.1077	+	8.14509i	0.609929	+	0.352143i
$536$	23.2029	−	40.1885i	1.00221	−	1.73588i
$537$	3.07562	+	5.32713i	0.132723	+	0.229883i
$538$		−	12.1195i		−	0.522509i
$539$	−1.10507	+	0.638014i	−0.0475989	+	0.0274812i
$540$	−0.730315	+	0.421648i	−0.0314278	+	0.0181448i
$541$		−	31.6232i		−	1.35959i	−0.733402	−	0.679795i	$-0.762069\pi$
$541$		−	31.6232i		−	1.35959i	0.733402	−	0.679795i	$-0.237931\pi$
$542$	13.8864	+	24.0520i	0.596474	+	1.03312i
$543$	−1.64147	+	2.84311i	−0.0704422	+	0.122009i
$544$	10.3327	+	5.96557i	0.443010	+	0.255772i
$545$	21.5719			0.924039
$546$	5.35018	+	8.49791i	0.228967	+	0.363677i
$547$	−5.82768			−0.249174			−0.124587	−	0.992209i	$-0.539761\pi$
$547$	−5.82768			−0.249174			−0.124587	+	0.992209i	$0.539761\pi$
$548$	−0.783252	−	0.452211i	−0.0334589	−	0.0193175i
$549$	0.0339076	−	0.0587297i	0.00144714	−	0.00250652i
$550$	−1.91485	−	3.31662i	−0.0816496	−	0.141421i
$551$			51.2526i			2.18343i
$552$	−0.211623	+	0.122181i	−0.00900727	+	0.00520035i
$553$	17.6280	−	10.1775i	0.749618	−	0.432792i
$554$		−	32.9194i		−	1.39861i
$555$	−3.51458	−	6.08743i	−0.149186	−	0.258397i
$556$	−3.85302	+	6.67362i	−0.163404	+	0.283025i
$557$	17.5634	+	10.1402i	0.744184	+	0.429655i	0.823589	−	0.567187i	$-0.191968\pi$
$557$	17.5634	+	10.1402i	0.744184	+	0.429655i	−0.0794043	+	0.996842i	$0.525302\pi$
$558$	−3.28891			−0.139230
$559$	−23.3961	+	0.896350i	−0.989551	+	0.0379116i
$560$	−7.17881			−0.303360
$561$	2.96339	+	1.71091i	0.125114	+	0.0722349i
$562$	−15.4799	+	26.8120i	−0.652980	+	1.13100i
$563$	5.72321	+	9.91289i	0.241204	+	0.417778i	0.961058	−	0.276348i	$-0.0891242\pi$
$563$	5.72321	+	9.91289i	0.241204	+	0.417778i	−0.719853	+	0.694126i	$0.755791\pi$
$564$		−	8.33846i		−	0.351112i
$565$	9.39100	−	5.42190i	0.395082	−	0.228101i
$566$	−1.06138	+	0.612786i	−0.0446130	+	0.0257573i
$567$		−	2.39248i		−	0.100475i
$568$	5.52222	+	9.56477i	0.231707	+	0.401329i
$569$	−6.49986	+	11.2581i	−0.272488	+	0.471964i	−0.969498	−	0.245098i	$-0.921180\pi$
$569$	−6.49986	+	11.2581i	−0.272488	+	0.471964i	0.697010	+	0.717061i	$0.254513\pi$
$570$	11.3335	+	6.54340i	0.474708	+	0.274073i
$571$	−18.4373			−0.771575			−0.385787	−	0.922588i	$-0.626070\pi$
$571$	−18.4373			−0.771575			−0.385787	+	0.922588i	$0.626070\pi$
$572$	2.05657	+	1.08458i	0.0859896	+	0.0453486i
$573$	15.4832			0.646822
$574$	3.77103	+	2.17721i	0.157400	+	0.0908749i
$575$	−0.130551	+	0.226120i	−0.00544434	+	0.00942988i
$576$	4.32396	+	7.48932i	0.180165	+	0.312055i
$577$			25.8420i			1.07582i	0.843003	+	0.537908i	$0.180785\pi$
$577$			25.8420i			1.07582i	−0.843003	+	0.537908i	$0.819215\pi$
$578$	−5.33420	+	3.07970i	−0.221873	+	0.128099i
$579$	15.6718	−	9.04812i	0.651298	−	0.376027i
$580$		−	5.02779i		−	0.208767i
$581$	−18.6703	−	32.3380i	−0.774576	−	1.34160i
$582$	−5.57584	+	9.65763i	−0.231126	+	0.400322i
$583$	−1.14703	−	0.662240i	−0.0475053	−	0.0274272i
$584$	8.23307			0.340687
$585$	0.180513	+	4.71167i	0.00746328	+	0.194803i
$586$	19.2640			0.795788
$587$	22.3197	+	12.8863i	0.921231	+	0.531873i	0.884028	−	0.467435i	$-0.154822\pi$
$587$	22.3197	+	12.8863i	0.921231	+	0.531873i	0.0372036	+	0.999308i	$0.488155\pi$
$588$	0.411423	−	0.712606i	0.0169668	−	0.0293874i
$589$	−12.1436	−	21.0333i	−0.500367	−	0.866661i
$590$		−	7.48402i		−	0.308112i
$591$	12.1944	−	7.04045i	0.501612	−	0.289606i
$592$	−10.6806	+	6.16644i	−0.438970	+	0.253439i
$593$			21.4278i			0.879934i	0.898014	+	0.439967i	$0.145010\pi$
$593$			21.4278i			0.879934i	−0.898014	+	0.439967i	$0.854990\pi$
$594$	0.582055	+	1.00815i	0.0238820	+	0.0413648i
$595$	5.35301	−	9.27169i	0.219452	−	0.380102i
$596$	−4.26718	−	2.46366i	−0.174791	−	0.100915i
$597$	0.519047			0.0212432
$598$	0.0127532	+	0.332878i	0.000521516	+	0.0136124i
$599$	7.36504			0.300927			0.150464	−	0.988616i	$-0.451923\pi$
$599$	7.36504			0.300927			0.150464	+	0.988616i	$0.451923\pi$
$600$	8.77197	+	5.06450i	0.358114	+	0.206757i
$601$	4.38084	−	7.58784i	0.178698	−	0.309514i	−0.762737	−	0.646709i	$-0.776145\pi$
$601$	4.38084	−	7.58784i	0.178698	−	0.309514i	0.941435	+	0.337195i	$0.109478\pi$
$602$	9.04281	+	15.6626i	0.368557	+	0.638360i
$603$			15.0722i			0.613788i
$604$	7.96148	−	4.59656i	0.323948	−	0.187031i
$605$	−1.13254	+	0.653870i	−0.0460441	+	0.0265836i
$606$		−	16.0173i		−	0.650659i
$607$	−8.56949	−	14.8428i	−0.347825	−	0.602450i	0.638038	−	0.770005i	$-0.279746\pi$
$607$	−8.56949	−	14.8428i	−0.347825	−	0.602450i	−0.985863	+	0.167555i	$0.946413\pi$
$608$	−14.9869	+	25.9581i	−0.607800	+	1.05274i
$609$	12.3531	+	7.13207i	0.500574	+	0.289006i
$610$	0.103239			0.00418001
$611$	−41.2394	−	21.7486i	−1.66837	−	0.879853i
$612$	−2.20657			−0.0891951
$613$	−38.6392	−	22.3083i	−1.56062	−	0.901025i	−0.997194	−	0.0748588i	$-0.976149\pi$
$613$	−38.6392	−	22.3083i	−1.56062	−	0.901025i	−0.563427	−	0.826166i	$-0.690517\pi$
$614$	0.678785	−	1.17569i	0.0273935	−	0.0474470i
$615$	1.02230	+	1.77068i	0.0412231	+	0.0714006i
$616$		−	7.36620i		−	0.296793i
$617$	1.99801	−	1.15355i	0.0804368	−	0.0464402i	−0.459242	−	0.888311i	$-0.651879\pi$
$617$	1.99801	−	1.15355i	0.0804368	−	0.0464402i	0.539679	+	0.841871i	$0.318546\pi$
$618$	−3.29631	+	1.90313i	−0.132597	+	0.0765549i
$619$		−	18.3271i		−	0.736626i	−0.929702	−	0.368313i	$-0.879935\pi$
$619$		−	18.3271i		−	0.736626i	0.929702	−	0.368313i	$-0.120065\pi$
$620$	1.19126	+	2.06333i	0.0478422	+	0.0828652i
$621$	0.0396833	−	0.0687334i	0.00159243	−	0.00275818i
$622$	−15.1704	−	8.75865i	−0.608278	−	0.351190i
$623$	17.8528			0.715259
$624$	8.26676	−	0.316715i	0.330935	−	0.0126788i
$625$	2.27199			0.0908794
$626$	−6.19503	−	3.57670i	−0.247603	−	0.142954i
$627$	−4.29822	+	7.44473i	−0.171654	+	0.297314i
$628$	−2.28671	−	3.96070i	−0.0912498	−	0.158049i
$629$		−	18.3925i		−	0.733357i
$630$	3.15424	−	1.82110i	0.125668	−	0.0725543i
$631$	25.3170	−	14.6168i	1.00785	−	0.581884i	0.0972908	−	0.995256i	$-0.468982\pi$
$631$	25.3170	−	14.6168i	1.00785	−	0.581884i	0.910562	+	0.413372i	$0.135649\pi$
$632$		−	26.1950i		−	1.04198i
$633$	1.45368	+	2.51784i	0.0577784	+	0.100075i
$634$	−8.58761	+	14.8742i	−0.341058	+	0.590729i
$635$	−22.7567	−	13.1386i	−0.903074	−	0.521390i
$636$	0.854091			0.0338669
$637$	−2.45124	−	3.89341i	−0.0971219	−	0.154263i
$638$	−6.94050			−0.274777
$639$	−3.10656	−	1.79357i	−0.122894	−	0.0709527i
$640$	−2.02280	+	3.50359i	−0.0799582	+	0.138492i
$641$	5.73961	+	9.94129i	0.226701	+	0.392657i	0.956828	−	0.290653i	$-0.0938727\pi$
$641$	5.73961	+	9.94129i	0.226701	+	0.392657i	−0.730128	+	0.683311i	$0.760539\pi$
$642$			14.5010i			0.572309i
$643$	−30.3392	+	17.5164i	−1.19646	+	0.690778i	−0.959765	−	0.280805i	$-0.909399\pi$
$643$	−30.3392	+	17.5164i	−1.19646	+	0.690778i	−0.236698	+	0.971583i	$0.576065\pi$
$644$	−0.106041	+	0.0612230i	−0.00417861	+	0.00241252i
$645$			8.49204i			0.334374i
$646$	17.1214	+	29.6552i	0.673634	+	1.16677i
$647$	8.61547	−	14.9224i	0.338709	−	0.586662i	−0.645481	−	0.763776i	$-0.723343\pi$
$647$	8.61547	−	14.9224i	0.338709	−	0.586662i	0.984190	+	0.177115i	$0.0566764\pi$
$648$	−2.66640	−	1.53945i	−0.104746	−	0.0604752i
$649$	4.91609			0.192973
$650$	11.6852	−	7.35685i	0.458330	−	0.288559i
$651$	−6.75937			−0.264921
$652$	−11.1717	−	6.45000i	−0.437519	−	0.252601i
$653$	−10.9748	+	19.0090i	−0.429478	+	0.743878i	−0.996827	−	0.0795995i	$-0.974636\pi$
$653$	−10.9748	+	19.0090i	−0.429478	+	0.743878i	0.567349	+	0.823478i	$0.307969\pi$
$654$	9.60132	+	16.6300i	0.375441	+	0.650283i
$655$		−	10.9250i		−	0.426873i
$656$	3.10671	−	1.79366i	0.121297	−	0.0700306i
$657$	−2.31578	+	1.33702i	−0.0903472	+	0.0521620i
$658$			36.0139i			1.40397i
$659$	19.8212	+	34.3313i	0.772123	+	1.33736i	0.936397	+	0.350942i	$0.114138\pi$
$659$	19.8212	+	34.3313i	0.772123	+	1.33736i	−0.164274	+	0.986415i	$0.552528\pi$
$660$	0.421648	−	0.730315i	0.0164126	−	0.0284275i
$661$	−6.66909	−	3.85040i	−0.259398	−	0.149763i	0.364662	−	0.931140i	$-0.381184\pi$
$661$	−6.66909	−	3.85040i	−0.259398	−	0.149763i	−0.624060	+	0.781377i	$0.714518\pi$
$662$	11.2372			0.436747
$663$	−5.75522	+	10.9130i	−0.223514	+	0.423825i
$664$	−48.0538			−1.86485
$665$	23.2927	+	13.4480i	0.903250	+	0.521492i
$666$	3.12857	−	5.41885i	0.121230	−	0.209976i
$667$	0.236595	+	0.409794i	0.00916098	+	0.0158673i
$668$			7.42473i			0.287272i
$669$	17.3941	−	10.0425i	0.672493	−	0.388264i
$670$	−19.8711	+	11.4726i	−0.767688	+	0.443225i
$671$			0.0678152i			0.00261798i
$672$	4.17102	+	7.22442i	0.160901	+	0.278688i
$673$	−7.85407	+	13.6036i	−0.302752	+	0.524382i	−0.976758	−	0.214344i	$-0.931239\pi$
$673$	−7.85407	+	13.6036i	−0.302752	+	0.524382i	0.674006	+	0.738726i	$0.264572\pi$
$674$	7.64549	+	4.41413i	0.294493	+	0.170026i
$675$	−3.28982			−0.126625
$676$	−3.62377	+	7.55935i	−0.139376	+	0.290744i
$677$	18.9933			0.729971			0.364986	−	0.931013i	$-0.381074\pi$
$677$	18.9933			0.729971			0.364986	+	0.931013i	$0.381074\pi$
$678$	8.35958	+	4.82641i	0.321048	+	0.185357i
$679$	−11.4595	+	19.8484i	−0.439774	+	0.761712i
$680$	−6.88881	−	11.9318i	−0.264174	−	0.457563i
$681$		−	29.7920i		−	1.14163i
$682$	2.84828	−	1.64445i	0.109066	−	0.0629693i
$683$	−22.3338	+	12.8944i	−0.854579	+	0.493391i	−0.862193	−	0.506580i	$-0.830910\pi$
$683$	−22.3338	+	12.8944i	−0.854579	+	0.493391i	0.00761442	+	0.999971i	$0.497576\pi$
$684$		−	5.54341i		−	0.211957i
$685$	0.917072	+	1.58842i	0.0350395	+	0.0606903i
$686$	−11.5248	+	19.9616i	−0.440020	+	0.762137i
$687$	10.5492	+	6.09060i	0.402478	+	0.232371i
$688$	14.8996			0.568040
$689$	2.22766	−	4.22407i	0.0848671	−	0.160924i
$690$	0.120824			0.00459968
$691$	26.2227	+	15.1397i	0.997560	+	0.575942i	0.907525	−	0.419997i	$-0.137969\pi$
$691$	26.2227	+	15.1397i	0.997560	+	0.575942i	0.0900347	+	0.995939i	$0.471302\pi$
$692$	4.33974	−	7.51665i	0.164972	−	0.285740i
$693$	1.19624	+	2.07195i	0.0454414	+	0.0787069i
$694$			34.3205i			1.30279i
$695$	13.5339	−	7.81382i	0.513372	−	0.296395i
$696$	15.8973	−	9.17829i	0.602584	−	0.347902i
$697$			5.34990i			0.202642i
$698$	11.7291	+	20.3154i	0.443953	+	0.768950i
$699$	9.16215	−	15.8693i	0.346544	−	0.600232i
$700$	4.39551	+	2.53775i	0.166135	+	0.0959180i
$701$	−14.2798			−0.539341			−0.269671	−	0.962953i	$-0.586915\pi$
$701$	−14.2798			−0.539341			−0.269671	+	0.962953i	$0.586915\pi$
$702$	−3.55192	+	2.23625i	−0.134059	+	0.0844018i
$703$	46.2063			1.74270
$704$	−7.48932	−	4.32396i	−0.282265	−	0.162965i
$705$	−8.45509	+	14.6447i	−0.318437	+	0.551550i
$706$	−5.85290	−	10.1375i	−0.220277	−	0.381531i
$707$		−	32.9189i		−	1.23804i
$708$	−2.74542	+	1.58507i	−0.103179	+	0.0595705i
$709$	−20.6277	+	11.9094i	−0.774690	+	0.447267i	−0.834545	−	0.550940i	$-0.814269\pi$
$709$	−20.6277	+	11.9094i	−0.774690	+	0.447267i	0.0598553	+	0.998207i	$0.480936\pi$
$710$		−	5.46090i		−	0.204944i
$711$	4.25396	+	7.36807i	0.159536	+	0.276324i
$712$	11.4874	−	19.8968i	0.430510	−	0.745665i
$713$	−0.194190	−	0.112115i	−0.00727245	−	0.00419875i
$714$	9.53017			0.356658
$715$	−2.51216	−	3.99017i	−0.0939495	−	0.149224i
$716$	3.96662			0.148240
$717$	2.23056	+	1.28782i	0.0833019	+	0.0480944i
$718$	17.6747	−	30.6135i	0.659614	−	1.14248i
$719$	6.97678	+	12.0841i	0.260190	+	0.450663i	0.966292	−	0.257447i	$-0.0828814\pi$
$719$	6.97678	+	12.0841i	0.260190	+	0.450663i	−0.706102	+	0.708110i	$0.749548\pi$
$720$		−	3.00057i		−	0.111825i
$721$	−6.77459	+	3.91131i	−0.252299	+	0.145665i
$722$	−55.3460	+	31.9540i	−2.05977	+	1.18921i
$723$		−	18.9106i		−	0.703294i
$724$	1.05850	+	1.83338i	0.0393389	+	0.0681369i
$725$	9.80706	−	16.9863i	0.364225	−	0.630856i
$726$	−1.00815	−	0.582055i	−0.0374159	−	0.0216021i
$727$	−41.2948			−1.53154			−0.765770	−	0.643115i	$-0.777642\pi$
$727$	−41.2948			−1.53154			−0.765770	+	0.643115i	$0.777642\pi$
$728$	26.5397	−	1.01679i	0.983628	−	0.0376846i
$729$	1.00000			0.0370370
$730$	−3.52543	−	2.03541i	−0.130482	−	0.0753339i
$731$	−11.1101	+	19.2433i	−0.410923	+	0.711740i
$732$	−0.0218653	−	0.0378718i	−0.000808165	−	0.00139978i
$733$		−	21.9541i		−	0.810894i	−0.914119	−	0.405447i	$-0.867116\pi$
$733$		−	21.9541i		−	0.810894i	0.914119	−	0.405447i	$-0.132884\pi$
$734$	9.00360	−	5.19823i	0.332329	−	0.191870i
$735$	−1.44515	+	0.834357i	−0.0533051	+	0.0307757i
$736$			0.276733i			0.0102005i
$737$	−7.53610	−	13.0529i	−0.277596	−	0.480810i
$738$	−0.910020	+	1.57620i	−0.0334983	+	0.0580208i
$739$	−3.40505	−	1.96591i	−0.125257	−	0.0723171i	0.436062	−	0.899916i	$-0.356373\pi$
$739$	−3.40505	−	1.96591i	−0.125257	−	0.0723171i	−0.561319	+	0.827599i	$0.689706\pi$
$740$	−4.53275			−0.166627
$741$	−27.4160	−	14.4585i	−1.00715	−	0.531145i
$742$	−3.68882			−0.135421
$743$	−11.4143	−	6.59004i	−0.418750	−	0.241765i	0.275793	−	0.961217i	$-0.411060\pi$
$743$	−11.4143	−	6.59004i	−0.418750	−	0.241765i	−0.694542	+	0.719452i	$0.744393\pi$
$744$	−4.34933	+	7.53326i	−0.159454	+	0.276183i
$745$	4.99624	+	8.65374i	0.183048	+	0.317049i
$746$		−	17.3154i		−	0.633962i
$747$	13.5165	−	7.80375i	0.494543	−	0.285524i
$748$	1.91094	−	1.10328i	0.0698709	−	0.0403400i
$749$			29.8025i			1.08896i
$750$	−6.31001	−	10.9293i	−0.230409	−	0.399080i
$751$	−21.1153	+	36.5728i	−0.770509	+	1.33456i	0.166776	+	0.985995i	$0.446664\pi$
$751$	−21.1153	+	36.5728i	−0.770509	+	1.33456i	−0.937284	+	0.348565i	$0.886669\pi$
$752$	25.6945	+	14.8347i	0.936982	+	0.540967i
$753$	−2.49122			−0.0907852
$754$	−0.958026	−	25.0060i	−0.0348893	−	0.910665i
$755$	−18.6434			−0.678504
$756$	−1.33610	−	0.771396i	−0.0485934	−	0.0280554i
$757$	−15.5019	+	26.8500i	−0.563425	+	0.975881i	0.433769	+	0.901024i	$0.357183\pi$
$757$	−15.5019	+	26.8500i	−0.563425	+	0.975881i	−0.997194	+	0.0748571i	$0.976150\pi$
$758$	9.65057	+	16.7153i	0.350524	+	0.607126i
$759$			0.0793666i			0.00288082i
$760$	29.9754	−	17.3063i	1.08732	−	0.627766i
$761$	−24.2531	+	14.0025i	−0.879173	+	0.507591i	−0.870386	−	0.492370i	$-0.836131\pi$
$761$	−24.2531	+	14.0025i	−0.879173	+	0.507591i	−0.00878765	+	0.999961i	$0.502797\pi$
$762$		−	23.3912i		−	0.847373i
$763$	19.7327	+	34.1780i	0.714371	+	1.23733i
$764$	4.99218	−	8.64671i	0.180611	−	0.312827i
$765$	3.87534	+	2.23743i	0.140113	+	0.0808945i
$766$	12.6751			0.457970
$767$	0.678588	+	17.7122i	0.0245024	+	0.639551i
$768$	13.6946			0.494161
$769$	−17.4897	−	10.0977i	−0.630694	−	0.364132i	0.150327	−	0.988636i	$-0.451968\pi$
$769$	−17.4897	−	10.0977i	−0.630694	−	0.364132i	−0.781021	+	0.624505i	$0.785301\pi$
$770$	−1.82110	+	3.15424i	−0.0656279	+	0.113671i
$771$	−2.59488	−	4.49447i	−0.0934523	−	0.161864i
$772$		−	11.6693i		−	0.419989i
$773$	44.4279	−	25.6505i	1.59796	−	0.922584i	0.606083	−	0.795402i	$-0.292740\pi$
$773$	44.4279	−	25.6505i	1.59796	−	0.922584i	0.991879	−	0.127182i	$-0.0405933\pi$
$774$	−6.54659	+	3.77968i	−0.235312	+	0.135858i
$775$			9.29457i			0.333871i
$776$	14.7472	+	25.5430i	0.529395	+	0.916940i
$777$	6.42985	−	11.1368i	0.230670	−	0.399532i
$778$	−25.1240	−	14.5054i	−0.900740	−	0.520042i
$779$	−13.4402			−0.481545
$780$	2.68946	+	1.41835i	0.0962981	+	0.0507850i
$781$	3.58715			0.128358
$782$	0.273792	+	0.158074i	0.00979077	+	0.00565270i
$783$	−2.98104	+	5.16331i	−0.106534	+	0.184521i
$784$	1.46390	+	2.53556i	0.0522823	+	0.0905556i
$785$			9.27480i			0.331032i
$786$	8.42215	−	4.86253i	0.300408	−	0.173441i
$787$	37.2290	−	21.4942i	1.32707	−	0.766186i	0.342226	−	0.939618i	$-0.388819\pi$
$787$	37.2290	−	21.4942i	1.32707	−	0.766186i	0.984846	+	0.173432i	$0.0554857\pi$
$788$		−	9.08007i		−	0.323464i
$789$	−2.77204	−	4.80131i	−0.0986871	−	0.170931i
$790$	−6.47602	+	11.2168i	−0.230406	+	0.399076i
$791$	17.1806	+	9.91925i	0.610873	+	0.352688i
$792$	3.07889			0.109404
$793$	−0.244332	+	0.00936082i	−0.00867648	+	0.000332412i
$794$	−7.45427			−0.264542
$795$	−1.50002	−	0.866038i	−0.0532003	−	0.0307152i
$796$	0.167354	−	0.289865i	0.00593169	−	0.0102740i
$797$	1.56222	+	2.70584i	0.0553366	+	0.0958459i	0.892367	−	0.451311i	$-0.149043\pi$
$797$	1.56222	+	2.70584i	0.0553366	+	0.0958459i	−0.837030	+	0.547157i	$0.815710\pi$
$798$			23.9420i			0.847538i
$799$	−38.3192	+	22.1236i	−1.35563	+	0.782676i
$800$	9.93405	−	5.73543i	0.351222	−	0.202778i
$801$			7.46205i			0.263659i
$802$	−19.7109	−	34.1403i	−0.696016	−	1.20553i
$803$	1.33702	−	2.31578i	0.0471823	−	0.0817222i
$804$	8.41716	+	4.85965i	0.296851	+	0.171387i
$805$	0.248318			0.00875204
$806$	6.31797	+	10.0351i	0.222541	+	0.353471i
$807$	10.4110			0.366484
$808$	−36.6878	−	21.1817i	−1.29067	−	0.745170i
$809$	−6.62139	+	11.4686i	−0.232796	+	0.403214i	−0.958630	−	0.284656i	$-0.908121\pi$
$809$	−6.62139	+	11.4686i	−0.232796	+	0.403214i	0.725834	+	0.687870i	$0.241454\pi$
$810$	0.761176	+	1.31840i	0.0267450	+	0.0463237i
$811$			15.6878i			0.550873i	0.961319	+	0.275437i	$0.0888224\pi$
$811$			15.6878i			0.550873i	−0.961319	+	0.275437i	$0.911178\pi$
$812$	7.96590	−	4.59912i	0.279548	−	0.161397i
$813$	−20.6613	+	11.9288i	−0.724623	+	0.418362i
$814$			6.25714i			0.219313i
$815$	13.0804	+	22.6560i	0.458188	+	0.793605i
$816$	3.92564	−	6.79941i	0.137425	−	0.238027i
$817$	−48.3437	−	27.9113i	−1.69133	−	0.976491i
$818$	12.3469			0.431698
$819$	−7.29992	+	4.59595i	−0.255080	+	0.160595i
$820$	1.31846			0.0460426
$821$	−25.7338	−	14.8574i	−0.898115	−	0.518527i	−0.0215267	−	0.999768i	$-0.506853\pi$
$821$	−25.7338	−	14.8574i	−0.898115	−	0.518527i	−0.876588	+	0.481241i	$0.840186\pi$
$822$	−0.816350	+	1.41396i	−0.0284735	+	0.0493175i
$823$	7.83604	+	13.5724i	0.273147	+	0.473105i	0.969666	−	0.244434i	$-0.0786020\pi$
$823$	7.83604	+	13.5724i	0.273147	+	0.473105i	−0.696519	+	0.717539i	$0.745269\pi$
$824$			10.0670i			0.350699i
$825$	2.84907	−	1.64491i	0.0991917	−	0.0572684i
$826$	11.8575	−	6.84593i	0.412575	−	0.238200i
$827$		−	28.2982i		−	0.984024i	−0.870589	−	0.492012i	$-0.836262\pi$
$827$		−	28.2982i		−	0.984024i	0.870589	−	0.492012i	$-0.163738\pi$
$828$	−0.0255897	−	0.0443227i	−0.000889305	−	0.00154032i
$829$	15.9670	−	27.6557i	0.554558	−	0.960523i	−0.443379	−	0.896334i	$-0.646221\pi$
$829$	15.9670	−	27.6557i	0.554558	−	0.960523i	0.997938	−	0.0641892i	$-0.0204461\pi$
$830$	20.5769	+	11.8801i	0.714233	+	0.412363i
$831$	28.2786			0.980974
$832$	14.5451	−	27.5802i	0.504259	−	0.956171i
$833$	−4.36635			−0.151285
$834$	12.0475	+	6.95562i	0.417171	+	0.240854i
$835$	7.52859	−	13.0399i	0.260538	−	0.451264i
$836$	2.77170	+	4.80073i	0.0958614	+	0.166037i
$837$		−	2.82525i		−	0.0976551i
$838$	−21.7130	+	12.5360i	−0.750063	+	0.433049i
$839$	29.2109	−	16.8649i	1.00847	−	0.582242i	0.0977291	−	0.995213i	$-0.468842\pi$
$839$	29.2109	−	16.8649i	1.00847	−	0.582242i	0.910744	+	0.412971i	$0.135509\pi$
$840$		−	9.63307i		−	0.332372i
$841$	−3.27315	−	5.66926i	−0.112867	−	0.195492i
$842$	−1.41830	+	2.45656i	−0.0488778	+	0.0846588i
$843$	−23.0322	−	13.2976i	−0.793271	−	0.457995i
$844$	1.87480			0.0645334
$845$	14.0294	−	9.60187i	0.482627	−	0.330314i
$846$	−15.0529			−0.517530
$847$	−2.07195	−	1.19624i	−0.0711931	−	0.0411033i
$848$	−1.51949	+	2.63183i	−0.0521795	+	0.0903776i
$849$	−0.526399	−	0.911750i	−0.0180660	−	0.0312912i
$850$		−	13.1046i		−	0.449484i
$851$	0.369446	−	0.213300i	0.0126644	−	0.00731181i
$852$	−2.00326	+	1.15659i	−0.0686307	+	0.0396240i
$853$			39.6846i			1.35877i	0.733780	+	0.679387i	$0.237754\pi$
$853$			39.6846i			1.35877i	−0.733780	+	0.679387i	$0.762246\pi$
$854$	0.0944364	+	0.163569i	0.00323155	+	0.00559721i
$855$	−5.62095	+	9.73577i	−0.192232	+	0.332956i
$856$	33.2147	+	19.1765i	1.13525	+	0.655439i
$857$	−14.6094			−0.499046			−0.249523	−	0.968369i	$-0.580274\pi$
$857$	−14.6094			−0.499046			−0.249523	+	0.968369i	$0.580274\pi$
$858$	1.95793	−	3.71261i	0.0668426	−	0.126746i
$859$	−14.0269			−0.478592			−0.239296	−	0.970947i	$-0.576917\pi$
$859$	−14.0269			−0.478592			−0.239296	+	0.970947i	$0.576917\pi$
$860$	4.74243	+	2.73805i	0.161716	+	0.0933666i
$861$	−1.87028	+	3.23942i	−0.0637389	+	0.110399i
$862$	−9.75016	−	16.8878i	−0.332092	−	0.575200i
$863$		−	16.4026i		−	0.558350i	−0.960240	−	0.279175i	$-0.909939\pi$
$863$		−	16.4026i		−	0.558350i	0.960240	−	0.279175i	$-0.0900610\pi$
$864$	−3.01964	+	1.74339i	−0.102730	+	0.0593112i
$865$	−15.2436	+	8.80089i	−0.518298	+	0.299239i
$866$		−	17.0613i		−	0.579767i
$867$	−2.64554	−	4.58221i	−0.0898473	−	0.155620i
$868$	−2.17939	+	3.77481i	−0.0739733	+	0.128125i
$869$	−7.36807	−	4.25396i	−0.249945	−	0.144306i
$870$	−9.07637			−0.307718
$871$	45.9882	−	28.9536i	1.55825	−	0.981056i
$872$	50.7881			1.71990
$873$	−8.29615	−	4.78979i	−0.280782	−	0.162110i
$874$	−0.397118	+	0.687829i	−0.0134327	+	0.0232662i
$875$	−12.9684	−	22.4619i	−0.438410	−	0.759349i
$876$			1.72435i			0.0582604i
$877$	−25.9851	+	15.0025i	−0.877456	+	0.506599i	−0.869819	−	0.493372i	$-0.835764\pi$
$877$	−25.9851	+	15.0025i	−0.877456	+	0.506599i	−0.00763701	+	0.999971i	$0.502431\pi$
$878$	−13.5190	+	7.80522i	−0.456245	+	0.263413i
$879$			16.5483i			0.558159i
$880$	1.50028	+	2.59857i	0.0505746	+	0.0875977i
$881$	−13.0740	+	22.6449i	−0.440476	+	0.762926i	−0.997725	−	0.0674191i	$-0.978524\pi$
$881$	−13.0740	+	22.6449i	−0.440476	+	0.762926i	0.557249	+	0.830345i	$0.311857\pi$
$882$	−1.28643	−	0.742718i	−0.0433162	−	0.0250086i
$883$	40.7268			1.37057			0.685283	−	0.728277i	$-0.259678\pi$
$883$	40.7268			1.37057			0.685283	+	0.728277i	$0.259678\pi$
$884$	4.23880	+	6.73266i	0.142566	+	0.226444i
$885$	6.42896			0.216107
$886$	−26.8771	−	15.5175i	−0.902954	−	0.521320i
$887$	−16.3263	+	28.2780i	−0.548184	+	0.949482i	0.450215	+	0.892920i	$0.351347\pi$
$887$	−16.3263	+	28.2780i	−0.548184	+	0.949482i	−0.998399	+	0.0565621i	$0.981986\pi$
$888$	−8.27460	−	14.3320i	−0.277677	−	0.480951i
$889$		−	48.0736i		−	1.61234i
$890$	−9.83794	+	5.67994i	−0.329768	+	0.190392i
$891$	−0.866025	+	0.500000i	−0.0290129	+	0.0167506i
$892$		−	12.9518i		−	0.433657i
$893$	−55.5796	−	96.2667i	−1.85990	−	3.22144i
$894$	−4.44750	+	7.70330i	−0.148747	+	0.257637i
$895$	−6.96650	−	4.02211i	−0.232864	−	0.134444i
$896$	−7.40134			−0.247261
$897$	−0.285950	+	0.0109553i	−0.00954761	+	0.000365787i
$898$	41.7700			1.39388
$899$	14.5877	+	8.42219i	0.486525	+	0.280896i
$900$	−1.06072	+	1.83722i	−0.0353573	+	0.0612406i
$901$	−2.26607	−	3.92495i	−0.0754938	−	0.130759i
$902$		−	1.82004i		−	0.0606007i
$903$	−13.4546	+	7.76801i	−0.447741	+	0.258503i
$904$	22.1098	−	12.7651i	0.735362	−	0.424561i
$905$		−	4.29323i		−	0.142712i
$906$	−8.29791	−	14.3724i	−0.275679	−	0.477491i
$907$	−2.11005	+	3.65471i	−0.0700629	+	0.121353i	−0.898929	−	0.438095i	$-0.855653\pi$
$907$	−2.11005	+	3.65471i	−0.0700629	+	0.121353i	0.828866	+	0.559448i	$0.188987\pi$
$908$	−16.6375	−	9.60567i	−0.552135	−	0.318775i
$909$	13.7593			0.456367
$910$	−11.6158	−	6.12586i	−0.385060	−	0.203070i
$911$	56.5470			1.87348			0.936742	−	0.350020i	$-0.113825\pi$
$911$	56.5470			1.87348			0.936742	+	0.350020i	$0.113825\pi$
$912$	17.0817	+	9.86213i	0.565632	+	0.326568i
$913$	−7.80375	+	13.5165i	−0.258266	+	0.447331i
$914$	−10.3353	−	17.9012i	−0.341860	−	0.592119i
$915$			0.0886846i			0.00293182i
$916$	6.80267	−	3.92752i	0.224767	−	0.129769i
$917$	17.3092	−	9.99349i	0.571601	−	0.330014i
$918$			3.98338i			0.131471i
$919$	20.1217	+	34.8518i	0.663754	+	1.14966i	0.979622	+	0.200852i	$0.0643710\pi$
$919$	20.1217	+	34.8518i	0.663754	+	1.14966i	−0.315868	+	0.948803i	$0.602296\pi$
$920$	0.159780	−	0.276748i	0.00526780	−	0.00912410i
$921$	1.00995	+	0.583094i	0.0332789	+	0.0192136i
$922$	−6.52302			−0.214824
$923$	0.495149	+	12.9242i	0.0162980	+	0.425404i
$924$	1.54279			0.0507541
$925$	−15.3139	−	8.84146i	−0.503517	−	0.290706i
$926$	11.6492	−	20.1771i	0.382817	−	0.663059i
$927$	−1.63483	−	2.83162i	−0.0536950	−	0.0930025i
$928$		−	20.7884i		−	0.682413i
$929$	18.9100	−	10.9177i	0.620418	−	0.358198i	−0.156614	−	0.987660i	$-0.550058\pi$
$929$	18.9100	−	10.9177i	0.620418	−	0.358198i	0.777032	+	0.629462i	$0.216725\pi$
$930$	3.72480	−	2.15052i	0.122141	−	0.0705182i
$931$		−	10.9693i		−	0.359504i
$932$	−5.90821	−	10.2333i	−0.193530	−	0.335203i
$933$	7.52390	−	13.0318i	0.246322	−	0.426641i
$934$	38.6560	+	22.3180i	1.26486	+	0.730268i
$935$	−4.47486			−0.146344
$936$	0.424993	+	11.0930i	0.0138913	+	0.362585i
$937$	13.2598			0.433180			0.216590	−	0.976263i	$-0.430507\pi$
$937$	13.2598			0.433180			0.216590	+	0.976263i	$0.430507\pi$
$938$	−36.3538	−	20.9889i	−1.18699	−	0.685311i
$939$	3.07248	−	5.32169i	0.100267	−	0.173667i
$940$	5.45226	+	9.44360i	0.177833	+	0.308016i
$941$		−	6.50152i		−	0.211944i	−0.994369	−	0.105972i	$-0.966205\pi$
$941$		−	6.50152i		−	0.211944i	0.994369	−	0.105972i	$-0.0337953\pi$
$942$	−7.15003	+	4.12807i	−0.232961	+	0.134500i
$943$	−0.107462	+	0.0620433i	−0.00349945	+	0.00202041i
$944$		−	11.2798i		−	0.367127i
$945$	1.56437	+	2.70957i	0.0508890	+	0.0881424i
$946$	3.77968	−	6.54659i	0.122888	−	0.212848i
$947$	30.8882	+	17.8333i	1.00373	+	0.579505i	0.909350	−	0.416032i	$-0.136579\pi$
$947$	30.8882	+	17.8333i	1.00373	+	0.579505i	0.0943811	+	0.995536i	$0.469913\pi$
$948$	5.48632			0.178188
$949$	8.52810	+	4.49749i	0.276834	+	0.145995i
$950$	32.9218			1.06813
$951$	−12.7773	−	7.37698i	−0.414332	−	0.239215i
$952$	12.6029	−	21.8289i	0.408464	−	0.707480i
$953$	−14.8156	−	25.6614i	−0.479926	−	0.831256i	0.519809	−	0.854282i	$-0.326003\pi$
$953$	−14.8156	−	25.6614i	−0.479926	−	0.831256i	−0.999735	+	0.0230267i	$0.992670\pi$
$954$		−	1.54184i		−	0.0499189i
$955$	−17.5353	+	10.1240i	−0.567430	+	0.327606i
$956$	1.43838	−	0.830448i	0.0465204	−	0.0268586i
$957$		−	5.96207i		−	0.192726i
$958$	24.3730	+	42.2152i	0.787455	+	1.36391i
$959$	−1.67776	+	2.90597i	−0.0541779	+	0.0938388i
$960$	−9.79408	−	5.65462i	−0.316103	−	0.182502i
$961$	23.0179			0.742514
$962$	−22.5439	+	0.863700i	−0.726845	+	0.0278468i
$963$	−12.4567			−0.401413
$964$	−10.5608	−	6.09726i	−0.340139	−	0.196380i
$965$	−11.8326	+	20.4946i	−0.380904	+	0.659745i
$966$	0.110522	+	0.191430i	0.00355600	+	0.00615917i
$967$			49.6180i			1.59561i	0.602918	+	0.797803i	$0.294005\pi$
$967$			49.6180i			1.59561i	−0.602918	+	0.797803i	$0.705995\pi$
$968$	−2.66640	+	1.53945i	−0.0857014	+	0.0494797i
$969$	−25.4746	+	14.7078i	−0.818362	+	0.472482i
$970$		−	14.5835i		−	0.468247i
$971$	−22.7273	−	39.3648i	−0.729352	−	1.26328i	−0.957157	−	0.289568i	$-0.906488\pi$
$971$	−22.7273	−	39.3648i	−0.729352	−	1.26328i	0.227805	−	0.973707i	$-0.426845\pi$
$972$	0.322425	−	0.558456i	0.0103418	−	0.0179125i
$973$	24.7601	+	14.2952i	0.793771	+	0.458284i
$974$	23.0527			0.738656
$975$	6.31972	+	10.0379i	0.202393	+	0.321469i
$976$	0.155600			0.00498063
$977$	−11.1629	−	6.44491i	−0.357133	−	0.206191i	0.310689	−	0.950512i	$-0.399440\pi$
$977$	−11.1629	−	6.44491i	−0.357133	−	0.206191i	−0.667823	+	0.744320i	$0.732774\pi$
$978$	−11.6438	+	20.1677i	−0.372328	+	0.644891i
$979$	−3.73103	−	6.46233i	−0.119244	−	0.206537i
$980$			1.07607i			0.0343738i
$981$	−14.2856	+	8.24778i	−0.456103	+	0.263331i
$982$	−35.5197	+	20.5073i	−1.13348	+	0.654415i
$983$		−	52.3528i		−	1.66979i	−0.550406	−	0.834897i	$-0.685527\pi$
$983$		−	52.3528i		−	1.66979i	0.550406	−	0.834897i	$-0.314473\pi$
$984$	2.40687	+	4.16882i	0.0767281	+	0.132897i
$985$	−9.20708	+	15.9471i	−0.293362	+	0.508118i
$986$	−20.5674	−	11.8746i	−0.655000	−	0.378165i
$987$	−30.9368			−0.984730
$988$	−16.9140	+	10.6489i	−0.538106	+	0.338785i
$989$	−0.515381			−0.0163882
$990$	−1.31840	−	0.761176i	−0.0419014	−	0.0241918i
$991$	−13.1534	+	22.7823i	−0.417830	+	0.723703i	−0.995721	−	0.0924109i	$-0.970543\pi$
$991$	−13.1534	+	22.7823i	−0.417830	+	0.723703i	0.577891	+	0.816114i	$0.303876\pi$
$992$	4.92551	+	8.53124i	0.156385	+	0.270867i
$993$			9.65306i			0.306331i
$994$	8.65212	−	4.99530i	0.274429	−	0.158441i
$995$	−0.587839	+	0.339389i	−0.0186357	+	0.0107594i
$996$		−	10.0645i		−	0.318906i
$997$	−13.3465	−	23.1168i	−0.422688	−	0.732117i	0.573513	−	0.819196i	$-0.305580\pi$
$997$	−13.3465	−	23.1168i	−0.422688	−	0.732117i	−0.996201	+	0.0870789i	$0.972247\pi$
$998$	−1.82193	+	3.15568i	−0.0576723	+	0.0998913i
$999$	4.65493	+	2.68752i	0.147275	+	0.0850295i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	429.2.s.a.199.4	yes	24
13.6	odd	12		5577.2.a.z.1.9		12
13.7	odd	12		5577.2.a.be.1.4		12
13.10	even	6	inner	429.2.s.a.166.4	✓	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
429.2.s.a.166.4	✓	24	13.10	even	6	inner
429.2.s.a.199.4	yes	24	1.1	even	1	trivial
5577.2.a.z.1.9		12	13.6	odd	12
5577.2.a.be.1.4		12	13.7	odd	12

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:	\( N \)	\(=\)	\( 429 = 3 \cdot 11 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	429.s (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.00815 - 0.582055i) q^{2} +(0.500000 - 0.866025i) q^{3} +(-0.322425 - 0.558456i) q^{4} +1.30774i q^{5} +(-1.00815 + 0.582055i) q^{6} +(-2.07195 + 1.19624i) q^{7} +3.07889i q^{8} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})\)	\(q+(-1.00815 - 0.582055i) q^{2} +(0.500000 - 0.866025i) q^{3} +(-0.322425 - 0.558456i) q^{4} +1.30774i q^{5} +(-1.00815 + 0.582055i) q^{6} +(-2.07195 + 1.19624i) q^{7} +3.07889i q^{8} +(-0.500000 - 0.866025i) q^{9} +(0.761176 - 1.31840i) q^{10} +(0.866025 + 0.500000i) q^{11} -0.644850 q^{12} +(-1.68191 + 3.18923i) q^{13} +2.78511 q^{14} +(1.13254 + 0.653870i) q^{15} +(1.14723 - 1.98707i) q^{16} +(1.71091 + 2.96339i) q^{17} +1.16411i q^{18} +(-7.44473 + 4.29822i) q^{19} +(0.730315 - 0.421648i) q^{20} +2.39248i q^{21} +(-0.582055 - 1.00815i) q^{22} +(-0.0396833 + 0.0687334i) q^{23} +(2.66640 + 1.53945i) q^{24} +3.28982 q^{25} +(3.55192 - 2.23625i) q^{26} -1.00000 q^{27} +(1.33610 + 0.771396i) q^{28} +(2.98104 - 5.16331i) q^{29} +(-0.761176 - 1.31840i) q^{30} +2.82525i q^{31} +(3.01964 - 1.74339i) q^{32} +(0.866025 - 0.500000i) q^{33} -3.98338i q^{34} +(-1.56437 - 2.70957i) q^{35} +(-0.322425 + 0.558456i) q^{36} +(-4.65493 - 2.68752i) q^{37} +10.0072 q^{38} +(1.92100 + 3.05119i) q^{39} -4.02639 q^{40} +(1.35400 + 0.781731i) q^{41} +(1.39256 - 2.41198i) q^{42} +(3.24684 + 5.62369i) q^{43} -0.644850i q^{44} +(1.13254 - 0.653870i) q^{45} +(0.0800132 - 0.0461957i) q^{46} +12.9309i q^{47} +(-1.14723 - 1.98707i) q^{48} +(-0.638014 + 1.10507i) q^{49} +(-3.31662 - 1.91485i) q^{50} +3.42183 q^{51} +(2.32333 - 0.0890113i) q^{52} -1.32448 q^{53} +(1.00815 + 0.582055i) q^{54} +(-0.653870 + 1.13254i) q^{55} +(-3.68310 - 6.37932i) q^{56} +8.59644i q^{57} +(-6.01065 + 3.47025i) q^{58} +(4.25746 - 2.45804i) q^{59} -0.843295i q^{60} +(0.0339076 + 0.0587297i) q^{61} +(1.64445 - 2.84828i) q^{62} +(2.07195 + 1.19624i) q^{63} -8.64793 q^{64} +(-4.17068 - 2.19950i) q^{65} -1.16411 q^{66} +(-13.0529 - 7.53610i) q^{67} +(1.10328 - 1.91094i) q^{68} +(0.0396833 + 0.0687334i) q^{69} +3.64220i q^{70} +(3.10656 - 1.79357i) q^{71} +(2.66640 - 1.53945i) q^{72} -2.67403i q^{73} +(3.12857 + 5.41885i) q^{74} +(1.64491 - 2.84907i) q^{75} +(4.80073 + 2.77170i) q^{76} -2.39248 q^{77} +(-0.160687 - 4.19418i) q^{78} -8.50791 q^{79} +(2.59857 + 1.50028i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(-0.910020 - 1.57620i) q^{82} +15.6075i q^{83} +(1.33610 - 0.771396i) q^{84} +(-3.87534 + 2.23743i) q^{85} -7.55935i q^{86} +(-2.98104 - 5.16331i) q^{87} +(-1.53945 + 2.66640i) q^{88} +(-6.46233 - 3.73103i) q^{89} -1.52235 q^{90} +(-0.330244 - 8.61989i) q^{91} +0.0511795 q^{92} +(2.44674 + 1.41263i) q^{93} +(7.52646 - 13.0362i) q^{94} +(-5.62095 - 9.73577i) q^{95} -3.48677i q^{96} +(8.29615 - 4.78979i) q^{97} +(1.28643 - 0.742718i) q^{98} -1.00000i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 12 q^{3} + 14 q^{4} + 6 q^{7} - 12 q^{9}+O(q^{10}) \) 24 * q + 12 * q^3 + 14 * q^4 + 6 * q^7 - 12 * q^9	\( 24 q + 12 q^{3} + 14 q^{4} + 6 q^{7} - 12 q^{9} + 28 q^{12} - 4 q^{13} + 20 q^{14} - 6 q^{15} - 14 q^{16} + 10 q^{17} - 18 q^{20} + 2 q^{22} - 14 q^{23} + 4 q^{25} - 34 q^{26} - 24 q^{27} - 30 q^{28} + 4 q^{29} + 30 q^{32} + 6 q^{35} + 14 q^{36} + 12 q^{38} - 2 q^{39} + 20 q^{40} - 30 q^{41} + 10 q^{42} - 4 q^{43} - 6 q^{45} - 24 q^{46} + 14 q^{48} + 18 q^{49} - 84 q^{50} + 20 q^{51} + 40 q^{52} - 56 q^{53} - 4 q^{55} + 26 q^{56} + 48 q^{58} + 60 q^{59} - 2 q^{61} + 18 q^{62} - 6 q^{63} - 48 q^{64} - 10 q^{65} + 4 q^{66} - 42 q^{67} - 18 q^{68} + 14 q^{69} + 6 q^{71} + 2 q^{75} - 48 q^{76} + 24 q^{77} - 26 q^{78} - 20 q^{79} + 30 q^{80} - 12 q^{81} - 10 q^{82} - 30 q^{84} + 6 q^{85} - 4 q^{87} - 12 q^{88} + 12 q^{89} + 18 q^{91} + 8 q^{92} + 12 q^{93} - 22 q^{94} + 4 q^{95} + 6 q^{97} - 114 q^{98}+O(q^{100}) \) 24 * q + 12 * q^3 + 14 * q^4 + 6 * q^7 - 12 * q^9 + 28 * q^12 - 4 * q^13 + 20 * q^14 - 6 * q^15 - 14 * q^16 + 10 * q^17 - 18 * q^20 + 2 * q^22 - 14 * q^23 + 4 * q^25 - 34 * q^26 - 24 * q^27 - 30 * q^28 + 4 * q^29 + 30 * q^32 + 6 * q^35 + 14 * q^36 + 12 * q^38 - 2 * q^39 + 20 * q^40 - 30 * q^41 + 10 * q^42 - 4 * q^43 - 6 * q^45 - 24 * q^46 + 14 * q^48 + 18 * q^49 - 84 * q^50 + 20 * q^51 + 40 * q^52 - 56 * q^53 - 4 * q^55 + 26 * q^56 + 48 * q^58 + 60 * q^59 - 2 * q^61 + 18 * q^62 - 6 * q^63 - 48 * q^64 - 10 * q^65 + 4 * q^66 - 42 * q^67 - 18 * q^68 + 14 * q^69 + 6 * q^71 + 2 * q^75 - 48 * q^76 + 24 * q^77 - 26 * q^78 - 20 * q^79 + 30 * q^80 - 12 * q^81 - 10 * q^82 - 30 * q^84 + 6 * q^85 - 4 * q^87 - 12 * q^88 + 12 * q^89 + 18 * q^91 + 8 * q^92 + 12 * q^93 - 22 * q^94 + 4 * q^95 + 6 * q^97 - 114 * q^98

Introduction

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