LMFDB - Embedded newform 429.2.bd.a.76.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [429,2,Mod(76,429)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(429, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([0, 6, 7]))

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

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

chi := DirichletCharacter("429.76");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 429 = 3 \cdot 11 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	429.bd (of order $12$, degree $4$, 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:	$56$
Relative dimension:	$14$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			76.6
Character	$\chi$	$=$	429.76
Dual form			429.2.bd.a.175.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.567668 - 0.152106i) q^{2} +(-0.500000 - 0.866025i) q^{3} +(-1.43294 - 0.827308i) q^{4} +(0.319197 + 0.319197i) q^{5} +(0.152106 + 0.567668i) q^{6} +(2.56095 - 0.686204i) q^{7} +(1.51872 + 1.51872i) q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})$	\(q+(-0.567668 - 0.152106i) q^{2} +(-0.500000 - 0.866025i) q^{3} +(-1.43294 - 0.827308i) q^{4} +(0.319197 + 0.319197i) q^{5} +(0.152106 + 0.567668i) q^{6} +(2.56095 - 0.686204i) q^{7} +(1.51872 + 1.51872i) q^{8} +(-0.500000 + 0.866025i) q^{9} +(-0.132646 - 0.229750i) q^{10} +(-1.39286 - 3.00997i) q^{11} +1.65462i q^{12} +(-0.950579 - 3.47799i) q^{13} -1.55814 q^{14} +(0.116834 - 0.436031i) q^{15} +(1.02349 + 1.77274i) q^{16} +(1.26519 - 2.19138i) q^{17} +(0.415562 - 0.415562i) q^{18} +(0.0778584 + 0.290572i) q^{19} +(-0.193316 - 0.721464i) q^{20} +(-1.87474 - 1.87474i) q^{21} +(0.332849 + 1.92053i) q^{22} +(-6.44179 + 3.71917i) q^{23} +(0.555890 - 2.07461i) q^{24} -4.79623i q^{25} +(0.0105901 + 2.11893i) q^{26} +1.00000 q^{27} +(-4.23738 - 1.13540i) q^{28} +(-5.97590 + 3.45019i) q^{29} +(-0.132646 + 0.229750i) q^{30} +(-6.46859 - 6.46859i) q^{31} +(-1.42314 - 5.31123i) q^{32} +(-1.91028 + 2.71124i) q^{33} +(-1.05153 + 1.05153i) q^{34} +(1.03648 + 0.598412i) q^{35} +(1.43294 - 0.827308i) q^{36} +(-5.82120 - 1.55979i) q^{37} -0.176791i q^{38} +(-2.53674 + 2.56222i) q^{39} +0.969541i q^{40} +(4.20288 + 1.12616i) q^{41} +(0.779072 + 1.34939i) q^{42} +(5.36362 - 9.29006i) q^{43} +(-0.494284 + 5.46544i) q^{44} +(-0.436031 + 0.116834i) q^{45} +(4.22251 - 1.13142i) q^{46} +(0.970470 - 0.970470i) q^{47} +(1.02349 - 1.77274i) q^{48} +(0.0253945 - 0.0146615i) q^{49} +(-0.729536 + 2.72267i) q^{50} -2.53039 q^{51} +(-1.51524 + 5.77017i) q^{52} +10.2029 q^{53} +(-0.567668 - 0.152106i) q^{54} +(0.516176 - 1.40537i) q^{55} +(4.93151 + 2.84721i) q^{56} +(0.212713 - 0.212713i) q^{57} +(3.91712 - 1.04959i) q^{58} +(0.614895 + 2.29482i) q^{59} +(-0.528148 + 0.528148i) q^{60} +(7.04069 + 4.06494i) q^{61} +(2.68810 + 4.65593i) q^{62} +(-0.686204 + 2.56095i) q^{63} -0.862487i q^{64} +(0.806741 - 1.41358i) q^{65} +(1.49680 - 1.24852i) q^{66} +(2.70208 - 10.0843i) q^{67} +(-3.62589 + 2.09341i) q^{68} +(6.44179 + 3.71917i) q^{69} +(-0.497355 - 0.497355i) q^{70} +(-1.78190 + 0.477459i) q^{71} +(-2.07461 + 0.555890i) q^{72} +(6.04986 + 6.04986i) q^{73} +(3.06726 + 1.77088i) q^{74} +(-4.15365 + 2.39811i) q^{75} +(0.128826 - 0.480784i) q^{76} +(-5.63250 - 6.75259i) q^{77} +(1.82975 - 1.06864i) q^{78} -7.16302i q^{79} +(-0.239158 + 0.892550i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(-2.21455 - 1.27857i) q^{82} +(-10.5149 + 10.5149i) q^{83} +(1.13540 + 4.23738i) q^{84} +(1.10333 - 0.295636i) q^{85} +(-4.45783 + 4.45783i) q^{86} +(5.97590 + 3.45019i) q^{87} +(2.45593 - 6.68668i) q^{88} +(4.12860 + 1.10626i) q^{89} +0.265292 q^{90} +(-4.82099 - 8.25465i) q^{91} +12.3076 q^{92} +(-2.36767 + 8.83626i) q^{93} +(-0.698520 + 0.403291i) q^{94} +(-0.0678974 + 0.117602i) q^{95} +(-3.88809 + 3.88809i) q^{96} +(12.8834 - 3.45209i) q^{97} +(-0.0166458 + 0.00446022i) q^{98} +(3.30314 + 0.298730i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 56 q - 28 q^{3} + 4 q^{5} - 28 q^{9}+O(q^{10}) $ 56 * q - 28 * q^3 + 4 * q^5 - 28 * q^9	$ 56 q - 28 q^{3} + 4 q^{5} - 28 q^{9} - 12 q^{11} + 24 q^{14} - 8 q^{15} + 68 q^{16} - 8 q^{20} - 10 q^{22} - 12 q^{23} - 48 q^{26} + 56 q^{27} + 4 q^{31} + 12 q^{33} + 32 q^{34} + 36 q^{37} - 12 q^{42} + 24 q^{44} + 4 q^{45} - 8 q^{47} + 68 q^{48} - 24 q^{49} - 56 q^{53} - 2 q^{55} + 72 q^{56} - 88 q^{58} + 56 q^{59} - 44 q^{60} + 20 q^{66} + 92 q^{67} + 12 q^{69} - 216 q^{70} + 72 q^{71} - 12 q^{75} - 12 q^{78} + 44 q^{80} - 28 q^{81} - 156 q^{82} - 120 q^{86} - 6 q^{88} - 56 q^{89} + 92 q^{91} + 32 q^{92} - 20 q^{93} - 44 q^{97}+O(q^{100}) $ 56 * q - 28 * q^3 + 4 * q^5 - 28 * q^9 - 12 * q^11 + 24 * q^14 - 8 * q^15 + 68 * q^16 - 8 * q^20 - 10 * q^22 - 12 * q^23 - 48 * q^26 + 56 * q^27 + 4 * q^31 + 12 * q^33 + 32 * q^34 + 36 * q^37 - 12 * q^42 + 24 * q^44 + 4 * q^45 - 8 * q^47 + 68 * q^48 - 24 * q^49 - 56 * q^53 - 2 * q^55 + 72 * q^56 - 88 * q^58 + 56 * q^59 - 44 * q^60 + 20 * q^66 + 92 * q^67 + 12 * q^69 - 216 * q^70 + 72 * q^71 - 12 * q^75 - 12 * q^78 + 44 * q^80 - 28 * q^81 - 156 * q^82 - 120 * q^86 - 6 * q^88 - 56 * q^89 + 92 * q^91 + 32 * q^92 - 20 * q^93 - 44 * q^97

Display 100 coefficients 10 coefficients

Character values

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

$n$	$67$	$79$	$287$
$\chi(n)$	$e\left(\frac{7}{12}\right)$	$-1$	$1$

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 $

$2$	−0.567668	−	0.152106i	−0.401402	−	0.107555i	0.0524693	−	0.998623i	$-0.483291\pi$
$2$	−0.567668	−	0.152106i	−0.401402	−	0.107555i	−0.453872	+	0.891067i	$0.649957\pi$
$3$	−0.500000	−	0.866025i	−0.288675	−	0.500000i
$3$	−0.500000	−	0.866025i	−0.288675	−	0.500000i
$4$	−1.43294	−	0.827308i	−0.716470	−	0.413654i
$5$	0.319197	+	0.319197i	0.142749	+	0.142749i	0.774870	−	0.632121i	$-0.217815\pi$
$5$	0.319197	+	0.319197i	0.142749	+	0.142749i	−0.632121	+	0.774870i	$0.717815\pi$
$6$	0.152106	+	0.567668i	0.0620971	+	0.231750i
$7$	2.56095	−	0.686204i	0.967947	−	0.259361i	0.259986	−	0.965612i	$-0.416282\pi$
$7$	2.56095	−	0.686204i	0.967947	−	0.259361i	0.707961	+	0.706252i	$0.249615\pi$
$8$	1.51872	+	1.51872i	0.536949	+	0.536949i
$9$	−0.500000	+	0.866025i	−0.166667	+	0.288675i
$10$	−0.132646	−	0.229750i	−0.0419464	−	0.0726533i
$11$	−1.39286	−	3.00997i	−0.419964	−	0.907541i
$11$	−1.39286	−	3.00997i	−0.419964	−	0.907541i
$12$			1.65462i			0.477647i
$13$	−0.950579	−	3.47799i	−0.263643	−	0.964620i
$13$	−0.950579	−	3.47799i	−0.263643	−	0.964620i
$14$	−1.55814			−0.416432
$15$	0.116834	−	0.436031i	0.0301665	−	0.112583i
$16$	1.02349	+	1.77274i	0.255873	+	0.443186i
$17$	1.26519	−	2.19138i	0.306855	−	0.531488i	−0.670818	−	0.741622i	$-0.734057\pi$
$17$	1.26519	−	2.19138i	0.306855	−	0.531488i	0.977673	+	0.210134i	$0.0673901\pi$
$18$	0.415562	−	0.415562i	0.0979489	−	0.0979489i
$19$	0.0778584	+	0.290572i	0.0178619	+	0.0666617i	0.974282	−	0.225334i	$-0.0723474\pi$
$19$	0.0778584	+	0.290572i	0.0178619	+	0.0666617i	−0.956420	+	0.291996i	$0.905681\pi$
$20$	−0.193316	−	0.721464i	−0.0432267	−	0.161324i
$21$	−1.87474	−	1.87474i	−0.409102	−	0.409102i
$22$	0.332849	+	1.92053i	0.0709637	+	0.409458i
$23$	−6.44179	+	3.71917i	−1.34321	+	0.775501i	−0.987277	−	0.159012i	$-0.949169\pi$
$23$	−6.44179	+	3.71917i	−1.34321	+	0.775501i	−0.355930	+	0.934513i	$0.615836\pi$
$24$	0.555890	−	2.07461i	0.113471	−	0.423478i
$25$		−	4.79623i		−	0.959245i
$26$	0.0105901	+	2.11893i	0.00207689	+	0.415557i
$27$	1.00000			0.192450
$28$	−4.23738	−	1.13540i	−0.800790	−	0.214571i
$29$	−5.97590	+	3.45019i	−1.10970	+	0.640683i	−0.938751	−	0.344597i	$-0.888016\pi$
$29$	−5.97590	+	3.45019i	−1.10970	+	0.640683i	−0.170945	+	0.985280i	$0.554682\pi$
$30$	−0.132646	+	0.229750i	−0.0242178	+	0.0419464i
$31$	−6.46859	−	6.46859i	−1.16179	−	1.16179i	−0.984083	−	0.177711i	$-0.943131\pi$
$31$	−6.46859	−	6.46859i	−1.16179	−	1.16179i	−0.177711	−	0.984083i	$-0.556869\pi$
$32$	−1.42314	−	5.31123i	−0.251578	−	0.938902i
$33$	−1.91028	+	2.71124i	−0.332537	+	0.471967i
$34$	−1.05153	+	1.05153i	−0.180337	+	0.180337i
$35$	1.03648	+	0.598412i	0.175197	+	0.101150i
$36$	1.43294	−	0.827308i	0.238823	−	0.137885i
$37$	−5.82120	−	1.55979i	−0.957000	−	0.256427i	−0.253670	−	0.967291i	$-0.581638\pi$
$37$	−5.82120	−	1.55979i	−0.957000	−	0.256427i	−0.703330	+	0.710864i	$0.748304\pi$
$38$		−	0.176791i		−	0.0286793i
$39$	−2.53674	+	2.56222i	−0.406203	+	0.410284i
$40$			0.969541i			0.153298i
$41$	4.20288	+	1.12616i	0.656380	+	0.175876i	0.571612	−	0.820524i	$-0.306318\pi$
$41$	4.20288	+	1.12616i	0.656380	+	0.175876i	0.0847682	+	0.996401i	$0.472985\pi$
$42$	0.779072	+	1.34939i	0.120213	+	0.208216i
$43$	5.36362	−	9.29006i	0.817944	−	1.41672i	−0.0892509	−	0.996009i	$-0.528447\pi$
$43$	5.36362	−	9.29006i	0.817944	−	1.41672i	0.907195	−	0.420711i	$-0.138219\pi$
$44$	−0.494284	+	5.46544i	−0.0745161	+	0.823945i
$45$	−0.436031	+	0.116834i	−0.0649997	+	0.0174166i
$46$	4.22251	−	1.13142i	0.622575	−	0.166819i
$47$	0.970470	−	0.970470i	0.141558	−	0.141558i	−0.632777	−	0.774334i	$-0.718085\pi$
$47$	0.970470	−	0.970470i	0.141558	−	0.141558i	0.774334	+	0.632777i	$0.218085\pi$
$48$	1.02349	−	1.77274i	0.147729	−	0.255873i
$49$	0.0253945	−	0.0146615i	0.00362779	−	0.00209451i
$50$	−0.729536	+	2.72267i	−0.103172	+	0.385043i
$51$	−2.53039			−0.354325
$52$	−1.51524	+	5.77017i	−0.210127	+	0.800178i
$53$	10.2029			1.40147			0.700737	−	0.713419i	$-0.252855\pi$
$53$	10.2029			1.40147			0.700737	+	0.713419i	$0.252855\pi$
$54$	−0.567668	−	0.152106i	−0.0772499	−	0.0206990i
$55$	0.516176	−	1.40537i	0.0696011	−	0.189500i
$56$	4.93151	+	2.84721i	0.659001	+	0.380474i
$57$	0.212713	−	0.212713i	0.0281745	−	0.0281745i
$58$	3.91712	−	1.04959i	0.514343	−	0.137818i
$59$	0.614895	+	2.29482i	0.0800525	+	0.298760i	0.994331	−	0.106325i	$-0.0339085\pi$
$59$	0.614895	+	2.29482i	0.0800525	+	0.298760i	−0.914279	+	0.405085i	$0.867242\pi$
$60$	−0.528148	+	0.528148i	−0.0681837	+	0.0681837i
$61$	7.04069	+	4.06494i	0.901468	+	0.520463i	0.877676	−	0.479254i	$-0.159093\pi$
$61$	7.04069	+	4.06494i	0.901468	+	0.520463i	0.0237918	+	0.999717i	$0.492426\pi$
$62$	2.68810	+	4.65593i	0.341389	+	0.591304i
$63$	−0.686204	+	2.56095i	−0.0864535	+	0.322649i
$64$		−	0.862487i		−	0.107811i
$65$	0.806741	−	1.41358i	0.100064	−	0.175334i
$66$	1.49680	−	1.24852i	0.184244	−	0.153682i
$67$	2.70208	−	10.0843i	0.330112	−	1.23199i	−0.578960	−	0.815356i	$-0.696541\pi$
$67$	2.70208	−	10.0843i	0.330112	−	1.23199i	0.909072	−	0.416639i	$-0.136792\pi$
$68$	−3.62589	+	2.09341i	−0.439704	+	0.253863i
$69$	6.44179	+	3.71917i	0.775501	+	0.447736i
$70$	−0.497355	−	0.497355i	−0.0594453	−	0.0594453i
$71$	−1.78190	+	0.477459i	−0.211473	+	0.0566640i	−0.363000	−	0.931789i	$-0.618248\pi$
$71$	−1.78190	+	0.477459i	−0.211473	+	0.0566640i	0.151527	+	0.988453i	$0.451581\pi$
$72$	−2.07461	+	0.555890i	−0.244495	+	0.0655123i
$73$	6.04986	+	6.04986i	0.708083	+	0.708083i	0.966132	−	0.258049i	$-0.0830796\pi$
$73$	6.04986	+	6.04986i	0.708083	+	0.708083i	−0.258049	+	0.966132i	$0.583080\pi$
$74$	3.06726	+	1.77088i	0.356562	+	0.205861i
$75$	−4.15365	+	2.39811i	−0.479623	+	0.276910i
$76$	0.128826	−	0.480784i	0.0147773	−	0.0551498i
$77$	−5.63250	−	6.75259i	−0.641883	−	0.769529i
$78$	1.82975	−	1.06864i	0.207179	−	0.120999i
$79$		−	7.16302i		−	0.805903i	−0.915221	−	0.402951i	$-0.867984\pi$
$79$		−	7.16302i		−	0.805903i	0.915221	−	0.402951i	$-0.132016\pi$
$80$	−0.239158	+	0.892550i	−0.0267387	+	0.0997901i
$81$	−0.500000	−	0.866025i	−0.0555556	−	0.0962250i
$82$	−2.21455	−	1.27857i	−0.244556	−	0.141194i
$83$	−10.5149	+	10.5149i	−1.15416	+	1.15416i	−0.168447	+	0.985711i	$0.553875\pi$
$83$	−10.5149	+	10.5149i	−1.15416	+	1.15416i	−0.985711	+	0.168447i	$0.946125\pi$
$84$	1.13540	+	4.23738i	0.123883	+	0.462336i
$85$	1.10333	−	0.295636i	0.119673	−	0.0320662i
$86$	−4.45783	+	4.45783i	−0.480700	+	0.480700i
$87$	5.97590	+	3.45019i	0.640683	+	0.369899i
$88$	2.45593	−	6.68668i	0.261803	−	0.712802i
$89$	4.12860	+	1.10626i	0.437631	+	0.117263i	0.470906	−	0.882183i	$-0.343927\pi$
$89$	4.12860	+	1.10626i	0.437631	+	0.117263i	−0.0332752	+	0.999446i	$0.510594\pi$
$90$	0.265292			0.0279643
$91$	−4.82099	−	8.25465i	−0.505377	−	0.865322i
$92$	12.3076			1.28316
$93$	−2.36767	+	8.83626i	−0.245516	+	0.916278i
$94$	−0.698520	+	0.403291i	−0.0720468	+	0.0415963i
$95$	−0.0678974	+	0.117602i	−0.00696612	+	0.0120657i
$96$	−3.88809	+	3.88809i	−0.396827	+	0.396827i
$97$	12.8834	−	3.45209i	1.30811	−	0.350507i	0.463599	−	0.886045i	$-0.346558\pi$
$97$	12.8834	−	3.45209i	1.30811	−	0.350507i	0.844511	+	0.535538i	$0.179891\pi$
$98$	−0.0166458	+	0.00446022i	−0.00168148	+	0.000450551i
$99$	3.30314	+	0.298730i	0.331978	+	0.0300235i
$100$	−3.96796	+	6.87270i	−0.396796	+	0.687270i
$101$	−3.31411	−	5.74020i	−0.329766	−	0.571171i	0.652699	−	0.757617i	$-0.273637\pi$
$101$	−3.31411	−	5.74020i	−0.329766	−	0.571171i	−0.982465	+	0.186446i	$0.940303\pi$
$102$	1.43642	+	0.384888i	0.142227	+	0.0381096i
$103$			8.57484i			0.844904i	0.906385	+	0.422452i	$0.138831\pi$
$103$			8.57484i			0.844904i	−0.906385	+	0.422452i	$0.861169\pi$
$104$	3.83843	−	6.72575i	0.376389	−	0.659514i
$105$		−	1.19682i		−	0.116798i
$106$	−5.79186	−	1.55192i	−0.562555	−	0.150736i
$107$	7.85252	−	4.53365i	0.759131	−	0.438285i	−0.0698524	−	0.997557i	$-0.522253\pi$
$107$	7.85252	−	4.53365i	0.759131	−	0.438285i	0.828984	+	0.559273i	$0.188920\pi$
$108$	−1.43294	−	0.827308i	−0.137885	−	0.0796078i
$109$	3.07353	−	3.07353i	0.294391	−	0.294391i	−0.544421	−	0.838812i	$-0.683251\pi$
$109$	3.07353	−	3.07353i	0.294391	−	0.294391i	0.838812	+	0.544421i	$0.183251\pi$
$110$	−0.506783	+	0.719271i	−0.0483198	+	0.0685798i
$111$	1.55979	+	5.82120i	0.148048	+	0.552524i
$112$	3.83757	+	3.83757i	0.362617	+	0.362617i
$113$	−7.18463	+	12.4441i	−0.675873	+	1.17065i	0.300340	+	0.953832i	$0.402900\pi$
$113$	−7.18463	+	12.4441i	−0.675873	+	1.17065i	−0.976213	+	0.216814i	$0.930433\pi$
$114$	−0.153106	+	0.0883955i	−0.0143397	+	0.00827900i
$115$	−3.24335	−	0.869052i	−0.302444	−	0.0810396i
$116$	11.4175			1.06008
$117$	3.48732	+	0.915768i	0.322402	+	0.0846628i
$118$		−	1.39623i		−	0.128533i
$119$	1.73636	−	6.48019i	0.159172	−	0.594038i
$120$	0.839648	−	0.484771i	0.0766490	−	0.0442533i
$121$	−7.11986	+	8.38496i	−0.647260	+	0.762269i
$122$	−3.37847	−	3.37847i	−0.305873	−	0.305873i
$123$	−1.12616	−	4.20288i	−0.101542	−	0.378961i
$124$	3.91759	+	14.6206i	0.351810	+	1.31297i
$125$	3.12692	−	3.12692i	0.279681	−	0.279681i
$126$	0.779072	−	1.34939i	0.0694053	−	0.120213i
$127$	−3.72334	−	6.44902i	−0.330393	−	0.572258i	0.652196	−	0.758051i	$-0.273848\pi$
$127$	−3.72334	−	6.44902i	−0.330393	−	0.572258i	−0.982589	+	0.185793i	$0.940515\pi$
$128$	−2.97747	+	11.1121i	−0.263174	+	0.982177i
$129$	−10.7272			−0.944480
$130$	−0.672976	+	0.679737i	−0.0590239	+	0.0596169i
$131$		−	16.5814i		−	1.44872i	−0.689420	−	0.724362i	$-0.742135\pi$
$131$		−	16.5814i		−	1.44872i	0.689420	−	0.724362i	$-0.257865\pi$
$132$	4.98035	−	2.30466i	0.433484	−	0.200595i
$133$	0.398783	+	0.690712i	0.0345788	+	0.0598923i
$134$	−3.06777	+	5.31354i	−0.265015	+	0.459020i
$135$	0.319197	+	0.319197i	0.0274721	+	0.0274721i
$136$	5.24957	−	1.40662i	0.450147	−	0.120616i
$137$	3.75050	+	13.9971i	0.320427	+	1.19585i	0.918830	+	0.394654i	$0.129136\pi$
$137$	3.75050	+	13.9971i	0.320427	+	1.19585i	−0.598403	+	0.801196i	$0.704198\pi$
$138$	−3.09109	−	3.09109i	−0.263131	−	0.263131i
$139$	10.2087	+	5.89399i	0.865890	+	0.499922i	0.865980	−	0.500078i	$-0.166695\pi$
$139$	10.2087	+	5.89399i	0.865890	+	0.499922i	−8.99754e−5		1.00000i	$0.500029\pi$
$140$	−0.990142	−	1.71498i	−0.0836823	−	0.144942i
$141$	−1.32569	−	0.355217i	−0.111643	−	0.0299146i
$142$	1.08415			0.0909802
$143$	−9.14462	+	7.70558i	−0.764711	+	0.644373i
$144$	−2.04699			−0.170582
$145$	−3.00878	−	0.806199i	−0.249865	−	0.0669512i
$146$	−2.51409	−	4.35454i	−0.208068	−	0.360384i
$147$	−0.0253945	−	0.0146615i	−0.00209451	−	0.00120926i
$148$	7.05101	+	7.05101i	0.579589	+	0.579589i
$149$	−1.37580	−	5.13456i	−0.112710	−	0.420639i	0.886395	−	0.462929i	$-0.153201\pi$
$149$	−1.37580	−	5.13456i	−0.112710	−	0.420639i	−0.999105	+	0.0422896i	$0.986535\pi$
$150$	2.72267	−	0.729536i	0.222305	−	0.0595664i
$151$	13.0380	+	13.0380i	1.06102	+	1.06102i	0.998013	+	0.0630018i	$0.0200674\pi$
$151$	13.0380	+	13.0380i	1.06102	+	1.06102i	0.0630018	+	0.998013i	$0.479933\pi$
$152$	−0.323052	+	0.559542i	−0.0262030	+	0.0453849i
$153$	1.26519	+	2.19138i	0.102285	+	0.177163i
$154$	2.17028	+	4.68997i	0.174886	+	0.377929i
$155$		−	4.12951i		−	0.331690i
$156$	5.75473	−	1.57284i	0.460748	−	0.125928i
$157$	−9.22126			−0.735937			−0.367968	−	0.929838i	$-0.619947\pi$
$157$	−9.22126			−0.735937			−0.367968	+	0.929838i	$0.619947\pi$
$158$	−1.08954	+	4.06622i	−0.0866792	+	0.323491i
$159$	−5.10144	−	8.83596i	−0.404571	−	0.700737i
$160$	1.24107	−	2.14959i	0.0981149	−	0.169940i
$161$	−13.9450	+	13.9450i	−1.09902	+	1.09902i
$162$	0.152106	+	0.567668i	0.0119506	+	0.0446002i
$163$	−1.12168	−	4.18618i	−0.0878570	−	0.327887i	0.907983	−	0.419007i	$-0.137622\pi$
$163$	−1.12168	−	4.18618i	−0.0878570	−	0.327887i	−0.995840	+	0.0911206i	$0.970955\pi$
$164$	−5.09080	−	5.09080i	−0.397524	−	0.397524i
$165$	−1.47518	+	0.255664i	−0.114842	+	0.0199034i
$166$	7.56834	−	4.36959i	0.587417	−	0.339146i
$167$	4.38763	−	16.3748i	0.339525	−	1.26712i	−0.559355	−	0.828928i	$-0.688951\pi$
$167$	4.38763	−	16.3748i	0.339525	−	1.26712i	0.898880	−	0.438195i	$-0.144382\pi$
$168$		−	5.69442i		−	0.439334i
$169$	−11.1928	+	6.61221i	−0.860984	+	0.508631i
$170$	−0.671292			−0.0514858
$171$	−0.290572	−	0.0778584i	−0.0222206	−	0.00595398i
$172$	−15.3715	+	8.87473i	−1.17206	+	0.676692i
$173$	10.4849	−	18.1604i	0.797155	−	1.38071i	−0.124307	−	0.992244i	$-0.539671\pi$
$173$	10.4849	−	18.1604i	0.797155	−	1.38071i	0.921462	−	0.388469i	$-0.126996\pi$
$174$	−2.86753	−	2.86753i	−0.217387	−	0.217387i
$175$	−3.29119	−	12.2829i	−0.248790	−	0.928499i
$176$	3.91032	−	5.54988i	0.294751	−	0.418338i
$177$	1.67992	−	1.67992i	0.126271	−	0.126271i
$178$	−2.17541	−	1.25597i	−0.163054	−	0.0941391i
$179$	14.3279	−	8.27219i	1.07091	−	0.618293i	0.142483	−	0.989797i	$-0.454491\pi$
$179$	14.3279	−	8.27219i	1.07091	−	0.618293i	0.928431	+	0.371505i	$0.121158\pi$
$180$	0.721464	+	0.193316i	0.0537747	+	0.0144089i
$181$		−	5.26862i		−	0.391613i	−0.980643	−	0.195807i	$-0.937267\pi$
$181$		−	5.26862i		−	0.391613i	0.980643	−	0.195807i	$-0.0627325\pi$
$182$	1.48114	+	5.41921i	0.109789	+	0.401698i
$183$		−	8.12989i		−	0.600979i
$184$	−15.4317	−	4.13490i	−1.13764	−	0.304829i
$185$	−1.36023	−	2.35599i	−0.100006	−	0.173216i
$186$	2.68810	−	4.65593i	0.197101	−	0.341389i
$187$	−8.35824	−	0.755903i	−0.611215	−	0.0552771i
$188$	−2.19350	+	0.587747i	−0.159978	+	0.0428659i
$189$	2.56095	−	0.686204i	0.186281	−	0.0499140i
$190$	0.0564312	−	0.0564312i	0.00409395	−	0.00409395i
$191$	7.84803	−	13.5932i	0.567864	−	0.983569i	−0.428913	−	0.903346i	$-0.641103\pi$
$191$	7.84803	−	13.5932i	0.567864	−	0.983569i	0.996777	−	0.0802229i	$-0.0255632\pi$
$192$	−0.746936	+	0.431244i	−0.0539054	+	0.0311223i
$193$	−6.76280	+	25.2391i	−0.486797	+	1.81675i	0.0850321	+	0.996378i	$0.472901\pi$
$193$	−6.76280	+	25.2391i	−0.486797	+	1.81675i	−0.571829	+	0.820373i	$0.693766\pi$
$194$	−7.83858			−0.562777
$195$	−1.62757	+	0.00813436i	−0.116553	+	0.000582514i
$196$	−0.0485184			−0.00346560
$197$	6.39356	+	1.71315i	0.455522	+	0.122057i	0.479282	−	0.877661i	$-0.340897\pi$
$197$	6.39356	+	1.71315i	0.455522	+	0.122057i	−0.0237598	+	0.999718i	$0.507564\pi$
$198$	−1.82965	−	0.672009i	−0.130028	−	0.0477576i
$199$	8.61992	+	4.97672i	0.611050	+	0.352790i	0.773376	−	0.633947i	$-0.218566\pi$
$199$	8.61992	+	4.97672i	0.611050	+	0.352790i	−0.162326	+	0.986737i	$0.551900\pi$
$200$	7.28413	−	7.28413i	0.515066	−	0.515066i
$201$	−10.0843	+	2.70208i	−0.711292	+	0.190590i
$202$	1.00819	+	3.76263i	0.0709362	+	0.264738i
$203$	−12.9364	+	12.9364i	−0.907959	+	0.907959i
$204$	3.62589	+	2.09341i	0.253863	+	0.146568i
$205$	0.982080	+	1.70101i	0.0685915	+	0.118804i
$206$	1.30429	−	4.86767i	0.0908740	−	0.339147i
$207$		−	7.43834i		−	0.517000i
$208$	5.19267	−	5.24483i	0.360047	−	0.363664i
$209$	0.766166	−	0.639078i	0.0529968	−	0.0442060i
$210$	−0.182045	+	0.679399i	−0.0125623	+	0.0468830i
$211$	16.4939	−	9.52275i	1.13549	−	0.655573i	0.190177	−	0.981750i	$-0.439094\pi$
$211$	16.4939	−	9.52275i	1.13549	−	0.655573i	0.945309	+	0.326176i	$0.105760\pi$
$212$	−14.6201	−	8.44093i	−1.00411	−	0.579726i
$213$	1.30444	+	1.30444i	0.0893789	+	0.0893789i
$214$	−5.14722	+	1.37919i	−0.351857	+	0.0942798i
$215$	4.67741	−	1.25331i	0.318996	−	0.0854748i
$216$	1.51872	+	1.51872i	0.103336	+	0.103336i
$217$	−21.0045	−	12.1270i	−1.42588	−	0.823231i
$218$	−2.21225	+	1.27724i	−0.149832	+	0.0865058i
$219$	2.21440	−	8.26427i	0.149636	−	0.558447i
$220$	−1.90232	+	1.58678i	−0.128255	+	0.106980i
$221$	−8.82426	−	2.31725i	−0.593584	−	0.155875i
$222$		−	3.54177i		−	0.237708i
$223$	−4.20702	+	15.7008i	−0.281723	+	1.05140i	0.669478	+	0.742832i	$0.266518\pi$
$223$	−4.20702	+	15.7008i	−0.281723	+	1.05140i	−0.951201	+	0.308573i	$0.900149\pi$
$224$	−7.28917	−	12.6252i	−0.487028	−	0.843558i
$225$	4.15365	+	2.39811i	0.276910	+	0.159874i
$226$	5.97132	−	5.97132i	0.397206	−	0.397206i
$227$	3.73659	+	13.9451i	0.248006	+	0.925572i	0.971849	+	0.235606i	$0.0757076\pi$
$227$	3.73659	+	13.9451i	0.248006	+	0.925572i	−0.723842	+	0.689965i	$0.757626\pi$
$228$	−0.480784	+	0.128826i	−0.0318407	+	0.00853170i
$229$	−7.48746	+	7.48746i	−0.494785	+	0.494785i	−0.909810	−	0.415025i	$-0.863773\pi$
$229$	−7.48746	+	7.48746i	−0.494785	+	0.494785i	0.415025	+	0.909810i	$0.363773\pi$
$230$	1.70896	+	0.986667i	0.112685	+	0.0650589i
$231$	−3.03166	+	8.25419i	−0.199469	+	0.543086i
$232$	−14.3156	−	3.83585i	−0.939864	−	0.251836i
$233$	−16.5273			−1.08274			−0.541371	−	0.840784i	$-0.682094\pi$
$233$	−16.5273			−1.08274			−0.541371	+	0.840784i	$0.682094\pi$
$234$	−1.84035	−	1.05030i	−0.120307	−	0.0686599i
$235$	0.619542			0.0404145
$236$	1.01741	−	3.79704i	0.0662281	−	0.247166i
$237$	−6.20336	+	3.58151i	−0.402951	+	0.232644i
$238$	−1.97136	+	3.41449i	−0.127784	+	0.221328i
$239$	16.3459	−	16.3459i	1.05733	−	1.05733i	0.0590754	−	0.998254i	$-0.481185\pi$
$239$	16.3459	−	16.3459i	1.05733	−	1.05733i	0.998254	−	0.0590754i	$-0.0188152\pi$
$240$	0.892550	−	0.239158i	0.0576138	−	0.0154376i
$241$	10.6537	−	2.85464i	0.686263	−	0.183884i	0.101194	−	0.994867i	$-0.467734\pi$
$241$	10.6537	−	2.85464i	0.686263	−	0.183884i	0.585070	+	0.810983i	$0.301067\pi$
$242$	5.31713	−	3.67690i	0.341798	−	0.236360i
$243$	−0.500000	+	0.866025i	−0.0320750	+	0.0555556i
$244$	−6.72592	−	11.6496i	−0.430583	−	0.745792i
$245$	0.0127858	+	0.00342594i	0.000816853	+	0.000218875i
$246$			2.55714i			0.163037i
$247$	0.936594	−	0.547002i	0.0595940	−	0.0348049i
$248$		−	19.6480i		−	1.24765i
$249$	14.3636	+	3.84871i	0.910255	+	0.243902i
$250$	−2.25068	+	1.29943i	−0.142346	+	0.0821833i
$251$	−6.27841	−	3.62484i	−0.396290	−	0.228798i	0.288592	−	0.957452i	$-0.406813\pi$
$251$	−6.27841	−	3.62484i	−0.396290	−	0.228798i	−0.684882	+	0.728654i	$0.740146\pi$
$252$	3.10198	−	3.10198i	0.195406	−	0.195406i
$253$	20.1671	+	14.2093i	1.26790	+	0.893332i
$254$	1.13269	+	4.22725i	0.0710711	+	0.265241i
$255$	−0.807692	−	0.807692i	−0.0505796	−	0.0505796i
$256$	2.51794	−	4.36121i	0.157372	−	0.272575i
$257$	−14.8364	+	8.56577i	−0.925466	+	0.534318i	−0.885375	−	0.464878i	$-0.846098\pi$
$257$	−14.8364	+	8.56577i	−0.925466	+	0.534318i	−0.0400913	+	0.999196i	$0.512765\pi$
$258$	6.08951	+	1.63168i	0.379116	+	0.101584i
$259$	−15.9781			−0.992832
$260$	−2.32548	+	1.35816i	−0.144220	+	0.0842294i
$261$		−	6.90037i		−	0.427122i
$262$	−2.52213	+	9.41274i	−0.155818	+	0.581521i
$263$	−22.3054	+	12.8780i	−1.37541	+	0.794093i	−0.991603	−	0.129321i	$-0.958720\pi$
$263$	−22.3054	+	12.8780i	−1.37541	+	0.794093i	−0.383806	+	0.923414i	$0.625387\pi$
$264$	−7.01880	+	1.21644i	−0.431977	+	0.0748665i
$265$	3.25673	+	3.25673i	0.200059	+	0.200059i
$266$	−0.121315	−	0.452753i	−0.00743828	−	0.0277600i
$267$	−1.10626	−	4.12860i	−0.0677017	−	0.252666i
$268$	−12.2148	+	12.2148i	−0.746135	+	0.746135i
$269$	−2.12583	+	3.68204i	−0.129614	+	0.224498i	−0.923527	−	0.383533i	$-0.874707\pi$
$269$	−2.12583	+	3.68204i	−0.129614	+	0.224498i	0.793913	+	0.608031i	$0.208041\pi$
$270$	−0.132646	−	0.229750i	−0.00807259	−	0.0139821i
$271$	0.710934	−	2.65324i	0.0431862	−	0.161173i	−0.940965	−	0.338503i	$-0.890079\pi$
$271$	0.710934	−	2.65324i	0.0431862	−	0.161173i	0.984151	+	0.177330i	$0.0567461\pi$
$272$	5.17967			0.314064
$273$	−4.73824	+	8.30243i	−0.286771	+	0.502486i
$274$		−	8.51617i		−	0.514480i
$275$	−14.4365	+	6.68049i	−0.870554	+	0.402849i
$276$	−6.15380	−	10.6587i	−0.370415	−	0.641578i
$277$	1.74984	−	3.03081i	0.105138	−	0.182104i	−0.808657	−	0.588281i	$-0.799805\pi$
$277$	1.74984	−	3.03081i	0.105138	−	0.182104i	0.913794	+	0.406177i	$0.133138\pi$
$278$	−4.89864	−	4.89864i	−0.293801	−	0.293801i
$279$	8.83626	−	2.36767i	0.529013	−	0.141749i
$280$	0.665303	+	2.48294i	0.0397594	+	0.148384i
$281$	13.1094	+	13.1094i	0.782039	+	0.782039i	0.980175	−	0.198136i	$-0.0634887\pi$
$281$	13.1094	+	13.1094i	0.782039	+	0.782039i	−0.198136	+	0.980175i	$0.563489\pi$
$282$	0.698520	+	0.403291i	0.0415963	+	0.0240156i
$283$	−14.0020	−	24.2522i	−0.832332	−	1.44164i	−0.896184	−	0.443683i	$-0.853672\pi$
$283$	−14.0020	−	24.2522i	−0.832332	−	1.44164i	0.0638517	−	0.997959i	$-0.479662\pi$
$284$	2.94836	+	0.790012i	0.174953	+	0.0468786i
$285$	0.135795			0.00804379
$286$	6.36318	−	2.98326i	0.376263	−	0.176404i
$287$	11.5361			0.680956
$288$	5.31123	+	1.42314i	0.312967	+	0.0838593i
$289$	5.29857	+	9.17739i	0.311681	+	0.539846i
$290$	1.58536	+	0.915308i	0.0930955	+	0.0537487i
$291$	−9.43130	−	9.43130i	−0.552873	−	0.552873i
$292$	−3.66399	−	13.6742i	−0.214419	−	0.800222i
$293$	−7.19069	+	1.92674i	−0.420085	+	0.112561i	−0.462668	−	0.886532i	$-0.653108\pi$
$293$	−7.19069	+	1.92674i	−0.420085	+	0.112561i	0.0425835	+	0.999093i	$0.486441\pi$
$294$	0.0121856	+	0.0121856i	0.000710676	+	0.000710676i
$295$	−0.536226	+	0.928771i	−0.0312203	+	0.0540751i
$296$	−6.47190	−	11.2097i	−0.376171	−	0.651548i
$297$	−1.39286	−	3.00997i	−0.0808222	−	0.174656i
$298$			3.12399i			0.180968i
$299$	19.0587	+	18.8691i	1.10219	+	1.09123i
$300$	7.93591			0.458180
$301$	7.36107	−	27.4719i	0.424285	−	1.58345i
$302$	−5.41809	−	9.38440i	−0.311776	−	0.540012i
$303$	−3.31411	+	5.74020i	−0.190390	+	0.329766i
$304$	−0.435421	+	0.435421i	−0.0249731	+	0.0249731i
$305$	0.949849	+	3.54488i	0.0543882	+	0.202979i
$306$	−0.384888	−	1.43642i	−0.0220026	−	0.0821147i
$307$	9.71336	+	9.71336i	0.554371	+	0.554371i	0.927699	−	0.373328i	$-0.121784\pi$
$307$	9.71336	+	9.71336i	0.554371	+	0.554371i	−0.373328	+	0.927699i	$0.621784\pi$
$308$	2.48457	+	14.3359i	0.141571	+	0.816862i
$309$	7.42603	−	4.28742i	0.422452	−	0.243903i
$310$	−0.628125	+	2.34419i	−0.0356751	+	0.133141i
$311$		−	18.1049i		−	1.02664i	−0.858199	−	0.513318i	$-0.828416\pi$
$311$		−	18.1049i		−	1.02664i	0.858199	−	0.513318i	$-0.171584\pi$
$312$	−7.74389	+	0.0387028i	−0.438411	+	0.00219112i
$313$	34.3284			1.94036			0.970178	−	0.242393i	$-0.0779324\pi$
$313$	34.3284			1.94036			0.970178	+	0.242393i	$0.0779324\pi$
$314$	5.23462	+	1.40261i	0.295407	+	0.0791540i
$315$	−1.03648	+	0.598412i	−0.0583990	+	0.0337167i
$316$	−5.92602	+	10.2642i	−0.333365	+	0.577405i
$317$	5.99141	+	5.99141i	0.336511	+	0.336511i	0.855053	−	0.518541i	$-0.173525\pi$
$317$	5.99141	+	5.99141i	0.336511	+	0.336511i	−0.518541	+	0.855053i	$0.673525\pi$
$318$	1.55192	+	5.79186i	0.0870276	+	0.324791i
$319$	18.7086	+	13.1816i	1.04748	+	0.738030i
$320$	0.275303	−	0.275303i	0.0153899	−	0.0153899i
$321$	−7.85252	−	4.53365i	−0.438285	−	0.253044i
$322$	10.0372	−	5.79501i	0.559354	−	0.322943i
$323$	0.735259	+	0.197012i	0.0409109	+	0.0109620i
$324$			1.65462i			0.0919231i
$325$	−16.6812	+	4.55919i	−0.925307	+	0.252899i
$326$			2.54698i			0.141064i
$327$	−4.19852	−	1.12499i	−0.232179	−	0.0622121i
$328$	4.67268	+	8.09332i	0.258006	+	0.446879i
$329$	1.81938	−	3.15126i	0.100306	−	0.173735i
$330$	0.876299	+	0.0792508i	0.0482387	+	0.00436261i
$331$	−17.9271	+	4.80355i	−0.985363	+	0.264027i	−0.715302	−	0.698816i	$-0.753711\pi$
$331$	−17.9271	+	4.80355i	−0.985363	+	0.264027i	−0.270061	+	0.962843i	$0.587044\pi$
$332$	23.7662	−	6.36814i	1.30434	−	0.349497i
$333$	4.26142	−	4.26142i	0.233524	−	0.233524i
$334$	−4.98144	+	8.62810i	−0.272572	+	0.472109i
$335$	4.08138	−	2.35638i	0.222989	−	0.128743i
$336$	1.40465	−	5.24222i	0.0766299	−	0.285987i
$337$	9.43355			0.513878			0.256939	−	0.966428i	$-0.417286\pi$
$337$	9.43355			0.513878			0.256939	+	0.966428i	$0.417286\pi$
$338$	7.35956	−	2.05105i	0.400307	−	0.111562i
$339$	14.3693			0.780431
$340$	−1.82558	−	0.489164i	−0.0990062	−	0.0265286i
$341$	−10.4604	+	28.4802i	−0.566463	+	1.54229i
$342$	0.153106	+	0.0883955i	0.00827900	+	0.00477988i
$343$	−13.0682	+	13.0682i	−0.705618	+	0.705618i
$344$	22.2548	−	5.96316i	1.19990	−	0.321512i
$345$	0.869052	+	3.24335i	0.0467882	+	0.174616i
$346$	−8.71428	+	8.71428i	−0.468483	+	0.468483i
$347$	20.4403	+	11.8012i	1.09729	+	0.633523i	0.935509	−	0.353303i	$-0.114942\pi$
$347$	20.4403	+	11.8012i	1.09729	+	0.633523i	0.161785	+	0.986826i	$0.448275\pi$
$348$	−5.70873	−	9.88781i	−0.306020	−	0.530042i
$349$	0.0184802	−	0.0689692i	0.000989224	−	0.00369183i	−0.965429	−	0.260664i	$-0.916058\pi$
$349$	0.0184802	−	0.0689692i	0.000989224	−	0.00369183i	0.966419	+	0.256973i	$0.0827250\pi$
$350$			7.47321i			0.399460i
$351$	−0.950579	−	3.47799i	−0.0507382	−	0.185641i
$352$	−14.0044	+	11.6814i	−0.746438	+	0.622623i
$353$	−4.90286	+	18.2977i	−0.260953	+	0.973889i	0.703728	+	0.710469i	$0.251517\pi$
$353$	−4.90286	+	18.2977i	−0.260953	+	0.973889i	−0.964681	+	0.263420i	$0.915149\pi$
$354$	−1.20917	+	0.698113i	−0.0642665	+	0.0371043i
$355$	−0.721181	−	0.416374i	−0.0382763	−	0.0220988i
$356$	−5.00082	−	5.00082i	−0.265043	−	0.265043i
$357$	−6.48019	+	1.73636i	−0.342968	+	0.0918980i
$358$	−9.39172	+	2.51650i	−0.496368	+	0.133001i
$359$	−16.0222	−	16.0222i	−0.845622	−	0.845622i	0.143962	−	0.989583i	$-0.454016\pi$
$359$	−16.0222	−	16.0222i	−0.845622	−	0.845622i	−0.989583	+	0.143962i	$0.954016\pi$
$360$	−0.839648	−	0.484771i	−0.0442533	−	0.0255497i
$361$	16.3761	−	9.45475i	0.861901	−	0.497619i
$362$	−0.801390	+	2.99083i	−0.0421201	+	0.157194i
$363$	10.8215	+	1.97350i	0.567983	+	0.103582i
$364$	0.0790504	+	15.8169i	0.00414337	+	0.829029i
$365$			3.86220i			0.202157i
$366$	−1.23661	+	4.61508i	−0.0646385	+	0.241234i
$367$	1.50595	+	2.60838i	0.0786098	+	0.136156i	0.902650	−	0.430375i	$-0.141619\pi$
$367$	1.50595	+	2.60838i	0.0786098	+	0.136156i	−0.824041	+	0.566531i	$0.808285\pi$
$368$	−13.1863	−	7.61309i	−0.687382	−	0.396860i
$369$	−3.07672	+	3.07672i	−0.160168	+	0.160168i
$370$	0.413799	+	1.54432i	0.0215124	+	0.0802854i
$371$	26.1291	−	7.00126i	1.35655	−	0.363487i
$372$	10.7030	−	10.7030i	0.554927	−	0.554927i
$373$	7.66457	+	4.42514i	0.396857	+	0.229125i	0.685127	−	0.728424i	$-0.259747\pi$
$373$	7.66457	+	4.42514i	0.396857	+	0.229125i	−0.288270	+	0.957549i	$0.593080\pi$
$374$	4.62973	+	1.70044i	0.239398	+	0.0879278i
$375$	−4.27146	−	1.14453i	−0.220577	−	0.0591035i
$376$	2.94775			0.152018
$377$	17.6803	+	17.5044i	0.910580	+	0.901523i
$378$	−1.55814			−0.0801423
$379$	8.68163	−	32.4003i	0.445945	−	1.66429i	−0.267483	−	0.963562i	$-0.586192\pi$
$379$	8.68163	−	32.4003i	0.445945	−	1.66429i	0.713429	−	0.700728i	$-0.247141\pi$
$380$	0.194586	−	0.112344i	0.00998203	−	0.00576313i
$381$	−3.72334	+	6.44902i	−0.190753	+	0.330393i
$382$	−6.52269	+	6.52269i	−0.333730	+	0.333730i
$383$	−5.33790	+	1.43029i	−0.272754	+	0.0730842i	−0.392603	−	0.919708i	$-0.628426\pi$
$383$	−5.33790	+	1.43029i	−0.272754	+	0.0730842i	0.119849	+	0.992792i	$0.461759\pi$
$384$	11.1121	−	2.97747i	0.567060	−	0.151943i
$385$	0.357528	−	3.95328i	0.0182213	−	0.201478i
$386$	7.67806	−	13.2988i	0.390803	−	0.676890i
$387$	5.36362	+	9.29006i	0.272648	+	0.472240i
$388$	−21.3171	−	5.71189i	−1.08221	−	0.289977i
$389$			2.13638i			0.108319i	0.998532	+	0.0541595i	$0.0172479\pi$
$389$			2.13638i			0.108319i	−0.998532	+	0.0541595i	$0.982752\pi$
$390$	0.925158	+	0.242946i	0.0468472	+	0.0123021i
$391$			18.8219i			0.951864i
$392$	0.0608340	+	0.0163004i	0.00307258	+	0.000823295i
$393$	−14.3599	+	8.29070i	−0.724362	+	0.418210i
$394$	−3.36884	−	1.94500i	−0.169720	−	0.0979878i
$395$	2.28641	−	2.28641i	0.115042	−	0.115042i
$396$	−4.48606	−	3.16078i	−0.225433	−	0.158835i
$397$	5.17712	+	19.3213i	0.259832	+	0.969708i	0.965338	+	0.261003i	$0.0840534\pi$
$397$	5.17712	+	19.3213i	0.259832	+	0.969708i	−0.705505	+	0.708704i	$0.749280\pi$
$398$	−4.13627	−	4.13627i	−0.207332	−	0.207332i
$399$	0.398783	−	0.690712i	0.0199641	−	0.0345788i
$400$	8.50248	−	4.90891i	0.425124	−	0.245445i
$401$	8.34335	+	2.23559i	0.416647	+	0.111640i	0.461051	−	0.887373i	$-0.347472\pi$
$401$	8.34335	+	2.23559i	0.416647	+	0.111640i	−0.0444045	+	0.999014i	$0.514139\pi$
$402$	6.13555			0.306013
$403$	−16.3488	+	28.6466i	−0.814391	+	1.42699i
$404$			10.9672i			0.545636i
$405$	0.116834	−	0.436031i	0.00580554	−	0.0216666i
$406$	9.31131	−	5.37589i	0.462113	−	0.266801i
$407$	3.41323	+	19.6942i	0.169188	+	0.976206i
$408$	−3.84295	−	3.84295i	−0.190254	−	0.190254i
$409$	−5.18277	−	19.3424i	−0.256271	−	0.956418i	−0.967379	−	0.253334i	$-0.918473\pi$
$409$	−5.18277	−	19.3424i	−0.256271	−	0.956418i	0.711107	−	0.703083i	$-0.248194\pi$
$410$	−0.298761	−	1.11499i	−0.0147548	−	0.0550655i
$411$	10.2466	−	10.2466i	0.505426	−	0.505426i
$412$	7.09404	−	12.2872i	0.349498	−	0.605349i
$413$	3.14942	+	5.45496i	0.154973	+	0.268421i
$414$	−1.13142	+	4.22251i	−0.0556062	+	0.207525i
$415$	−6.71263			−0.329510
$416$	−17.1196	+	9.99841i	−0.839357	+	0.490212i
$417$		−	11.7880i		−	0.577260i
$418$	−0.532136	+	0.246246i	−0.0260276	+	0.0120443i
$419$	−14.9043	−	25.8150i	−0.728123	−	1.26115i	−0.957675	−	0.287850i	$-0.907059\pi$
$419$	−14.9043	−	25.8150i	−0.728123	−	1.26115i	0.229552	−	0.973296i	$-0.426274\pi$
$420$	−0.990142	+	1.71498i	−0.0483140	+	0.0836823i
$421$	3.80891	+	3.80891i	0.185635	+	0.185635i	0.793806	−	0.608171i	$-0.208096\pi$
$421$	3.80891	+	3.80891i	0.185635	+	0.185635i	−0.608171	+	0.793806i	$0.708096\pi$
$422$	−10.8115	+	2.89694i	−0.526297	+	0.141021i
$423$	0.355217	+	1.32569i	0.0172712	+	0.0644571i
$424$	15.4953	+	15.4953i	0.752520	+	0.752520i
$425$	−10.5104	−	6.06816i	−0.509827	−	0.294349i
$426$	−0.542077	−	0.938905i	−0.0262637	−	0.0454901i
$427$	20.8202	+	5.57876i	1.00756	+	0.269975i
$428$	−15.0029			−0.725193
$429$	11.2455	+	4.06668i	0.542940	+	0.196341i
$430$	−2.84585			−0.137239
$431$	−1.27033	−	0.340384i	−0.0611897	−	0.0163957i	0.228094	−	0.973639i	$-0.426751\pi$
$431$	−1.27033	−	0.340384i	−0.0611897	−	0.0163957i	−0.289284	+	0.957243i	$0.593417\pi$
$432$	1.02349	+	1.77274i	0.0492429	+	0.0852911i
$433$	9.49586	+	5.48244i	0.456342	+	0.263469i	0.710505	−	0.703692i	$-0.248467\pi$
$433$	9.49586	+	5.48244i	0.456342	+	0.263469i	−0.254163	+	0.967161i	$0.581800\pi$
$434$	10.0790	+	10.0790i	0.483808	+	0.483808i
$435$	0.806199	+	3.00878i	0.0386543	+	0.144260i
$436$	−6.94694	+	1.86143i	−0.332698	+	0.0891462i
$437$	−1.58223	−	1.58223i	−0.0756885	−	0.0756885i
$438$	−2.51409	+	4.35454i	−0.120128	+	0.208068i
$439$	0.571965	+	0.990673i	0.0272984	+	0.0472822i	0.879352	−	0.476173i	$-0.157976\pi$
$439$	0.571965	+	0.990673i	0.0272984	+	0.0472822i	−0.852053	+	0.523455i	$0.824643\pi$
$440$	2.91829	−	1.35044i	0.139124	−	0.0643797i
$441$			0.0293231i			0.00139634i
$442$	4.65679	+	2.65765i	0.221501	+	0.126412i
$443$	22.3559			1.06216			0.531081	−	0.847321i	$-0.321786\pi$
$443$	22.3559			1.06216			0.531081	+	0.847321i	$0.321786\pi$
$444$	2.58085	−	9.63185i	0.122482	−	0.457108i
$445$	0.964723	+	1.67095i	0.0457323	+	0.0792106i
$446$	4.77639	−	8.27295i	0.226169	−	0.391735i
$447$	−3.75876	+	3.75876i	−0.177783	+	0.177783i
$448$	−0.591842	−	2.20878i	−0.0279619	−	0.104355i
$449$	−6.96042	−	25.9766i	−0.328482	−	1.22591i	−0.910765	−	0.412926i	$-0.864507\pi$
$449$	−6.96042	−	25.9766i	−0.328482	−	1.22591i	0.582282	−	0.812987i	$-0.302160\pi$
$450$	−1.99313	−	1.99313i	−0.0939571	−	0.0939571i
$451$	−2.46434	−	14.2191i	−0.116041	−	0.669553i
$452$	20.5903	−	11.8878i	0.968486	−	0.559155i
$453$	4.77223	−	17.8102i	0.224219	−	0.836796i
$454$		−	8.48458i		−	0.398201i
$455$	1.09601	−	4.17370i	0.0513819	−	0.195666i
$456$	0.646104			0.0302566
$457$	4.19398	+	1.12377i	0.196186	+	0.0525679i	0.355574	−	0.934648i	$-0.384285\pi$
$457$	4.19398	+	1.12377i	0.196186	+	0.0525679i	−0.159388	+	0.987216i	$0.550952\pi$
$458$	5.38928	−	3.11150i	0.251825	−	0.145391i
$459$	1.26519	−	2.19138i	0.0590542	−	0.102285i
$460$	3.92855	+	3.92855i	0.183169	+	0.183169i
$461$	−0.337183	−	1.25838i	−0.0157042	−	0.0586087i	0.957629	−	0.288004i	$-0.0929917\pi$
$461$	−0.337183	−	1.25838i	−0.0157042	−	0.0586087i	−0.973333	+	0.229396i	$0.926325\pi$
$462$	2.97649	−	4.22451i	0.138479	−	0.196542i
$463$	−8.79193	+	8.79193i	−0.408595	+	0.408595i	−0.881249	−	0.472653i	$-0.843296\pi$
$463$	−8.79193	+	8.79193i	−0.408595	+	0.408595i	0.472653	+	0.881249i	$0.343296\pi$
$464$	−12.2326	−	7.06248i	−0.567883	−	0.327868i
$465$	−3.57626	+	2.06476i	−0.165845	+	0.0957507i
$466$	9.38204	+	2.51391i	0.434615	+	0.116455i
$467$		−	25.2519i		−	1.16852i	−0.811567	−	0.584260i	$-0.801385\pi$
$467$		−	25.2519i		−	1.16852i	0.811567	−	0.584260i	$-0.198615\pi$
$468$	−4.23949	−	4.19732i	−0.195971	−	0.194021i
$469$		−	27.6796i		−	1.27812i
$470$	−0.351695	−	0.0942363i	−0.0162225	−	0.00434679i
$471$	4.61063	+	7.98585i	0.212447	+	0.367968i
$472$	−2.55133	+	4.41904i	−0.117435	+	0.203403i
$473$	−35.4336	−	3.20455i	−1.62924	−	0.147345i
$474$	4.06622	−	1.08954i	0.186768	−	0.0500442i
$475$	1.39365	−	0.373427i	0.0639449	−	0.0171340i
$476$	−7.84921	+	7.84921i	−0.359768	+	0.359768i
$477$	−5.10144	+	8.83596i	−0.233579	+	0.404571i
$478$	−11.7654	+	6.79274i	−0.538136	+	0.310693i
$479$	−3.33568	+	12.4489i	−0.152411	+	0.568806i	0.846902	+	0.531749i	$0.178465\pi$
$479$	−3.33568	+	12.4489i	−0.152411	+	0.568806i	−0.999313	+	0.0370570i	$0.988202\pi$
$480$	−2.48213			−0.113293
$481$	0.108597	+	21.7288i	0.00495161	+	0.990747i
$482$	−6.48196			−0.295245
$483$	19.0492	+	5.10422i	0.866768	+	0.232250i
$484$	17.1393	−	6.12483i	0.779058	−	0.278401i
$485$	5.21424	+	3.01044i	0.236766	+	0.136697i
$486$	0.415562	−	0.415562i	0.0188503	−	0.0188503i
$487$	−19.7994	+	5.30522i	−0.897195	+	0.240403i	−0.677811	−	0.735236i	$-0.737071\pi$
$487$	−19.7994	+	5.30522i	−0.897195	+	0.240403i	−0.219383	+	0.975639i	$0.570405\pi$
$488$	4.51933	+	16.8664i	0.204580	+	0.763504i
$489$	−3.06449	+	3.06449i	−0.138581	+	0.138581i
$490$	−0.00673697	−	0.00388959i	−0.000304345	−	0.000175714i
$491$	3.06530	+	5.30925i	0.138335	+	0.239603i	0.926866	−	0.375391i	$-0.122492\pi$
$491$	3.06530	+	5.30925i	0.138335	+	0.239603i	−0.788532	+	0.614994i	$0.789158\pi$
$492$	−1.86336	+	6.95416i	−0.0840068	+	0.313518i
$493$			17.4606i			0.786387i
$494$	−0.614877	+	0.168054i	−0.0276646	+	0.00756111i
$495$	0.958999	+	1.14971i	0.0431038	+	0.0516755i
$496$	4.84659	−	18.0877i	0.217618	−	0.812163i
$497$	−4.23572	+	2.44549i	−0.189998	+	0.109695i
$498$	−7.56834	−	4.36959i	−0.339146	−	0.195806i
$499$	3.80669	+	3.80669i	0.170411	+	0.170411i	0.787160	−	0.616749i	$-0.211551\pi$
$499$	3.80669	+	3.80669i	0.170411	+	0.170411i	−0.616749	+	0.787160i	$0.711551\pi$
$500$	−7.06762	+	1.89376i	−0.316074	+	0.0846917i
$501$	−16.3748	+	4.38763i	−0.731574	+	0.196025i
$502$	3.01270	+	3.01270i	0.134463	+	0.134463i
$503$	−1.41052	−	0.814365i	−0.0628920	−	0.0363107i	0.468224	−	0.883610i	$-0.344894\pi$
$503$	−1.41052	−	0.814365i	−0.0628920	−	0.0363107i	−0.531116	+	0.847299i	$0.678227\pi$
$504$	−4.93151	+	2.84721i	−0.219667	+	0.126825i
$505$	0.774402	−	2.89011i	0.0344604	−	0.128608i
$506$	−9.28692	−	11.1337i	−0.412854	−	0.494955i
$507$	11.3227	+	6.38714i	0.502860	+	0.283663i
$508$			12.3214i			0.546674i
$509$	−6.48554	+	24.2044i	−0.287467	+	1.07284i	0.659551	+	0.751659i	$0.270746\pi$
$509$	−6.48554	+	24.2044i	−0.287467	+	1.07284i	−0.947018	+	0.321180i	$0.895920\pi$
$510$	0.335646	+	0.581356i	0.0148627	+	0.0257429i
$511$	19.6448	+	11.3419i	0.869036	+	0.501738i
$512$	14.1765	−	14.1765i	0.626517	−	0.626517i
$513$	0.0778584	+	0.290572i	0.00343753	+	0.0128290i
$514$	9.72504	−	2.60582i	0.428953	−	0.114938i
$515$	−2.73706	+	2.73706i	−0.120609	+	0.120609i
$516$	15.3715	+	8.87473i	0.676692	+	0.390688i
$517$	−4.27282	−	1.56935i	−0.187918	−	0.0690201i
$518$	9.07027	+	2.43037i	0.398525	+	0.106784i
$519$	−20.9699			−0.920475
$520$	3.37205	−	0.921626i	0.147874	−	0.0404160i
$521$	6.70913			0.293933			0.146966	−	0.989142i	$-0.453049\pi$
$521$	6.70913			0.293933			0.146966	+	0.989142i	$0.453049\pi$
$522$	−1.04959	+	3.91712i	−0.0459393	+	0.171448i
$523$	5.87643	−	3.39276i	0.256958	−	0.148355i	−0.365988	−	0.930620i	$-0.619269\pi$
$523$	5.87643	−	3.39276i	0.256958	−	0.148355i	0.622946	+	0.782265i	$0.285936\pi$
$524$	−13.7179	+	23.7601i	−0.599270	+	1.03797i
$525$	−8.99169	+	8.99169i	−0.392430	+	0.392430i
$526$	14.6209	−	3.91766i	0.637501	−	0.170818i
$527$	−22.3592	+	5.99112i	−0.973981	+	0.260977i
$528$	−6.76149	−	0.611497i	−0.294256	−	0.0266120i
$529$	16.1645	−	27.9977i	0.702803	−	1.21729i
$530$	−1.35337	−	2.34411i	−0.0587868	−	0.101822i
$531$	−2.29482	−	0.614895i	−0.0995866	−	0.0266842i
$532$		−	1.31966i		−	0.0572147i
$533$	−0.0784067	−	15.6881i	−0.00339617	−	0.679526i
$534$			2.51195i			0.108702i
$535$	3.95363	+	1.05937i	0.170930	+	0.0458006i
$536$	19.4190	−	11.2115i	0.838771	−	0.484265i
$537$	−14.3279	−	8.27219i	−0.618293	−	0.356971i
$538$	1.76683	−	1.76683i	0.0761734	−	0.0761734i
$539$	−0.0795019	−	0.0560153i	−0.00342439	−	0.00241275i
$540$	−0.193316	−	0.721464i	−0.00831898	−	0.0310469i
$541$	13.4157	+	13.4157i	0.576786	+	0.576786i	0.934016	−	0.357231i	$-0.116279\pi$
$541$	13.4157	+	13.4157i	0.576786	+	0.576786i	−0.357231	+	0.934016i	$0.616279\pi$
$542$	−0.807150	+	1.39803i	−0.0346701	+	0.0600503i
$543$	−4.56276	+	2.63431i	−0.195807	+	0.113049i
$544$	−13.4395	−	3.60110i	−0.576213	−	0.154396i
$545$	1.96212			0.0840481
$546$	3.95260	−	3.99231i	0.169156	−	0.170855i
$547$			6.26813i			0.268006i	0.990981	+	0.134003i	$0.0427832\pi$
$547$			6.26813i			0.268006i	−0.990981	+	0.134003i	$0.957217\pi$
$548$	6.20564	−	23.1598i	0.265092	−	0.989336i
$549$	−7.04069	+	4.06494i	−0.300489	+	0.173488i
$550$	9.21129	−	1.59642i	0.392771	−	0.0680716i
$551$	−1.46780	−	1.46780i	−0.0625304	−	0.0625304i
$552$	4.13490	+	15.4317i	0.175993	+	0.656815i
$553$	−4.91529	−	18.3441i	−0.209019	−	0.780071i
$554$	−1.45433	+	1.45433i	−0.0617887	+	0.0617887i
$555$	−1.36023	+	2.35599i	−0.0577386	+	0.100006i
$556$	−9.75230	−	16.8915i	−0.413590	−	0.716358i
$557$	7.56493	−	28.2327i	0.320536	−	1.19626i	−0.598187	−	0.801356i	$-0.704112\pi$
$557$	7.56493	−	28.2327i	0.320536	−	1.19626i	0.918723	−	0.394901i	$-0.129221\pi$
$558$	−5.37621			−0.227593
$559$	−37.4092	−	9.82366i	−1.58224	−	0.415496i
$560$			2.44988i			0.103526i
$561$	3.52449	+	7.61640i	0.148804	+	0.321564i
$562$	−5.44775	−	9.43579i	−0.229800	−	0.398025i
$563$	12.4428	−	21.5516i	0.524403	−	0.908292i	−0.475194	−	0.879881i	$-0.657622\pi$
$563$	12.4428	−	21.5516i	0.524403	−	0.908292i	0.999596	−	0.0284107i	$-0.00904461\pi$
$564$	1.60576	+	1.60576i	0.0676145	+	0.0676145i
$565$	−6.26544	+	1.67882i	−0.263589	+	0.0706285i
$566$	4.25958	+	15.8970i	0.179044	+	0.668200i
$567$	−1.87474	−	1.87474i	−0.0787318	−	0.0787318i
$568$	−3.43134	−	1.98108i	−0.143976	−	0.0831244i
$569$	14.2751	+	24.7252i	0.598443	+	1.03653i	0.993051	+	0.117684i	$0.0375471\pi$
$569$	14.2751	+	24.7252i	0.598443	+	1.03653i	−0.394608	+	0.918850i	$0.629120\pi$
$570$	−0.0770864	−	0.0206552i	−0.00322879	−	0.000865153i
$571$	−7.15113			−0.299266			−0.149633	−	0.988742i	$-0.547809\pi$
$571$	−7.15113			−0.299266			−0.149633	+	0.988742i	$0.547809\pi$
$572$	19.4786	−	3.47622i	0.814440	−	0.145348i
$573$	−15.6961			−0.655712
$574$	−6.54870	−	1.75472i	−0.273337	−	0.0732405i
$575$	17.8380	+	30.8963i	0.743895	+	1.28846i
$576$	0.746936	+	0.431244i	0.0311223	+	0.0179685i
$577$	−4.29972	−	4.29972i	−0.179000	−	0.179000i	0.611920	−	0.790920i	$-0.290397\pi$
$577$	−4.29972	−	4.29972i	−0.179000	−	0.179000i	−0.790920	+	0.611920i	$0.790397\pi$
$578$	−1.61189	−	6.01566i	−0.0670458	−	0.250218i
$579$	25.2391	−	6.76280i	1.04890	−	0.281052i
$580$	3.64442	+	3.64442i	0.151326	+	0.151326i
$581$	−19.7127	+	34.1434i	−0.817820	+	1.41651i
$582$	3.91929	+	6.78841i	0.162460	+	0.281389i
$583$	−14.2112	−	30.7104i	−0.588569	−	1.27190i
$584$			18.3761i			0.760408i
$585$	0.820830	+	1.40545i	0.0339371	+	0.0581082i
$586$	4.37500			0.180729
$587$	−3.32312	+	12.4021i	−0.137160	+	0.511888i	0.862820	+	0.505512i	$0.168696\pi$
$587$	−3.32312	+	12.4021i	−0.137160	+	0.511888i	−0.999980	+	0.00637610i	$0.997970\pi$
$588$	0.0242592	+	0.0420182i	0.00100043	+	0.00173280i
$589$	1.37596	−	2.38322i	0.0566953	−	0.0981991i
$590$	0.445671	−	0.445671i	0.0183480	−	0.0183480i
$591$	−1.71315	−	6.39356i	−0.0704696	−	0.262996i
$592$	−3.19286	−	11.9159i	−0.131226	−	0.489741i
$593$	−23.5066	−	23.5066i	−0.965301	−	0.965301i	0.0341170	−	0.999418i	$-0.489138\pi$
$593$	−23.5066	−	23.5066i	−0.965301	−	0.965301i	−0.999418	+	0.0341170i	$0.989138\pi$
$594$	0.332849	+	1.92053i	0.0136570	+	0.0788003i
$595$	2.62270	−	1.51421i	0.107520	−	0.0620768i
$596$	−2.27642	+	8.49572i	−0.0932459	+	0.347998i
$597$		−	9.95343i		−	0.407367i
$598$	−7.94889	−	13.6103i	−0.325054	−	0.556568i
$599$	−12.1101			−0.494805			−0.247403	−	0.968913i	$-0.579577\pi$
$599$	−12.1101			−0.494805			−0.247403	+	0.968913i	$0.579577\pi$
$600$	−9.95030	−	2.66618i	−0.406219	−	0.108846i
$601$	37.5970	−	21.7066i	1.53361	−	0.885432i	0.534421	−	0.845218i	$-0.320530\pi$
$601$	37.5970	−	21.7066i	1.53361	−	0.885432i	0.999191	−	0.0402133i	$-0.0128038\pi$
$602$	−8.35729	+	14.4753i	−0.340618	+	0.589967i
$603$	7.38223	+	7.38223i	0.300628	+	0.300628i
$604$	−7.89621	−	29.4690i	−0.321292	−	1.19908i
$605$	−4.94909	+	0.403817i	−0.201209	+	0.0164175i
$606$	2.75444	−	2.75444i	0.111891	−	0.111891i
$607$	−18.6075	−	10.7430i	−0.755254	−	0.436046i	0.0723349	−	0.997380i	$-0.476955\pi$
$607$	−18.6075	−	10.7430i	−0.755254	−	0.436046i	−0.827589	+	0.561334i	$0.810288\pi$
$608$	1.43249	−	0.827048i	0.0580951	−	0.0335412i
$609$	17.6715	+	4.73506i	0.716085	+	0.191874i
$610$		−	2.15680i		−	0.0873261i
$611$	−4.29779	−	2.45277i	−0.173870	−	0.0992286i
$612$		−	4.18682i		−	0.169242i
$613$	−4.57896	−	1.22693i	−0.184943	−	0.0495552i	0.165159	−	0.986267i	$-0.447186\pi$
$613$	−4.57896	−	1.22693i	−0.184943	−	0.0495552i	−0.350102	+	0.936712i	$0.613853\pi$
$614$	−4.03651	−	6.99143i	−0.162900	−	0.282151i
$615$	0.982080	−	1.70101i	0.0396013	−	0.0685915i
$616$	1.70110	−	18.8095i	0.0685391	−	0.757856i
$617$	−2.86479	+	0.767618i	−0.115332	+	0.0309031i	−0.316023	−	0.948751i	$-0.602348\pi$
$617$	−2.86479	+	0.767618i	−0.115332	+	0.0309031i	0.200691	+	0.979655i	$0.435681\pi$
$618$	−4.86767	+	1.30429i	−0.195806	+	0.0524661i
$619$	−21.8233	+	21.8233i	−0.877151	+	0.877151i	−0.993239	−	0.116088i	$-0.962965\pi$
$619$	−21.8233	+	21.8233i	−0.877151	+	0.877151i	0.116088	+	0.993239i	$0.462965\pi$
$620$	−3.41638	+	5.91734i	−0.137205	+	0.237646i
$621$	−6.44179	+	3.71917i	−0.258500	+	0.149245i
$622$	−2.75387	+	10.2776i	−0.110420	+	0.412094i
$623$	11.3322			0.454017
$624$	−7.13849	−	1.87456i	−0.285768	−	0.0750427i
$625$	−21.9849			−0.879397
$626$	−19.4872	−	5.22157i	−0.778863	−	0.208696i
$627$	−0.936541	−	0.343980i	−0.0374019	−	0.0137372i
$628$	13.2135	+	7.62883i	0.527277	+	0.304423i
$629$	−10.7830	+	10.7830i	−0.429948	+	0.429948i
$630$	0.679399	−	0.182045i	0.0270679	−	0.00725283i
$631$	−3.93608	−	14.6897i	−0.156693	−	0.584786i	−0.998954	−	0.0457168i	$-0.985443\pi$
$631$	−3.93608	−	14.6897i	−0.156693	−	0.584786i	0.842262	−	0.539069i	$-0.181224\pi$
$632$	10.8786	−	10.8786i	0.432728	−	0.432728i
$633$	−16.4939	−	9.52275i	−0.655573	−	0.378495i
$634$	−2.48980	−	4.31247i	−0.0988827	−	0.171270i
$635$	0.870027	−	3.24698i	0.0345260	−	0.128853i
$636$			16.8819i			0.669409i
$637$	−0.0751322	−	0.0743849i	−0.00297684	−	0.00294724i
$638$	−8.61526	−	10.3285i	−0.341081	−	0.408909i
$639$	0.477459	−	1.78190i	0.0188880	−	0.0704909i
$640$	−4.49734	+	2.59654i	−0.177773	+	0.102637i
$641$	−18.0484	−	10.4202i	−0.712867	−	0.411574i	0.0992545	−	0.995062i	$-0.468354\pi$
$641$	−18.0484	−	10.4202i	−0.712867	−	0.411574i	−0.812122	+	0.583488i	$0.801688\pi$
$642$	3.76803	+	3.76803i	0.148712	+	0.148712i
$643$	−27.5928	+	7.39348i	−1.08816	+	0.291570i	−0.757933	−	0.652333i	$-0.773791\pi$
$643$	−27.5928	+	7.39348i	−1.08816	+	0.291570i	−0.330223	+	0.943903i	$0.607124\pi$
$644$	31.5191	−	8.44552i	1.24203	−	0.332800i
$645$	−3.42410	−	3.42410i	−0.134824	−	0.134824i
$646$	−0.387417	−	0.223675i	−0.0152427	−	0.00880038i
$647$	−18.2662	+	10.5460i	−0.718117	+	0.414605i	−0.814059	−	0.580782i	$-0.802747\pi$
$647$	−18.2662	+	10.5460i	−0.718117	+	0.414605i	0.0959421	+	0.995387i	$0.469414\pi$
$648$	0.555890	−	2.07461i	0.0218374	−	0.0814984i
$649$	6.05087	−	5.04719i	0.237518	−	0.198119i
$650$	10.1629	−	0.0507926i	0.398621	−	0.00199225i
$651$			24.2539i			0.950586i
$652$	−1.85595	+	6.92652i	−0.0726848	+	0.271263i
$653$	−1.33488	−	2.31209i	−0.0522381	−	0.0904790i	0.838724	−	0.544557i	$-0.183302\pi$
$653$	−1.33488	−	2.31209i	−0.0522381	−	0.0904790i	−0.890962	+	0.454078i	$0.849969\pi$
$654$	2.21225	+	1.27724i	0.0865058	+	0.0499441i
$655$	5.29273	−	5.29273i	0.206804	−	0.206804i
$656$	2.30523	+	8.60325i	0.0900042	+	0.335900i
$657$	−8.26427	+	2.21440i	−0.322420	+	0.0863921i
$658$	−1.51213	+	1.51213i	−0.0589491	+	0.0589491i
$659$	3.09262	+	1.78553i	0.120471	+	0.0695542i	0.559025	−	0.829151i	$-0.311176\pi$
$659$	3.09262	+	1.78553i	0.120471	+	0.0695542i	−0.438553	+	0.898705i	$0.644509\pi$
$660$	2.32535	+	0.854073i	0.0905141	+	0.0332447i
$661$	−32.7508	−	8.77556i	−1.27386	−	0.341330i	−0.442351	−	0.896842i	$-0.645856\pi$
$661$	−32.7508	−	8.77556i	−1.27386	−	0.341330i	−0.831508	+	0.555512i	$0.812522\pi$
$662$	10.9073			0.423924
$663$	2.40533	+	8.80066i	0.0934155	+	0.341789i
$664$	−31.9383			−1.23945
$665$	−0.0931828	+	0.347763i	−0.00361348	+	0.0134857i
$666$	−3.06726	+	1.77088i	−0.118854	+	0.0686203i
$667$	25.6637	−	44.4508i	0.993701	−	1.72114i
$668$	−19.8342	+	19.8342i	−0.767410	+	0.767410i
$669$	15.7008	−	4.20702i	0.607029	−	0.162653i
$670$	−2.67529	+	0.716842i	−0.103355	+	0.0276940i
$671$	2.42864	−	26.8542i	0.0937567	−	1.03669i
$672$	−7.28917	+	12.6252i	−0.281186	+	0.487028i
$673$	6.41841	+	11.1170i	0.247411	+	0.428529i	0.962807	−	0.270191i	$-0.0870868\pi$
$673$	6.41841	+	11.1170i	0.247411	+	0.428529i	−0.715395	+	0.698720i	$0.753753\pi$
$674$	−5.35513	−	1.43490i	−0.206272	−	0.0552704i
$675$		−	4.79623i		−	0.184607i
$676$	21.5089	−	0.215002i	0.827267	−	0.00826933i
$677$		−	30.0573i		−	1.15519i	−0.816322	−	0.577597i	$-0.803991\pi$
$677$		−	30.0573i		−	1.15519i	0.816322	−	0.577597i	$-0.196009\pi$
$678$	−8.15698	−	2.18566i	−0.313267	−	0.0839396i
$679$	30.6248	−	17.6813i	1.17527	−	0.678545i
$680$	2.12463	+	1.22666i	0.0814760	+	0.0470402i
$681$	10.2086	−	10.2086i	0.391193	−	0.391193i
$682$	10.2701	−	14.5762i	0.393261	−	0.558151i
$683$	3.01901	+	11.2671i	0.115519	+	0.431123i	0.999325	−	0.0367300i	$-0.0116942\pi$
$683$	3.01901	+	11.2671i	0.115519	+	0.431123i	−0.883806	+	0.467853i	$0.845027\pi$
$684$	0.351959	+	0.351959i	0.0134575	+	0.0134575i
$685$	−3.27067	+	5.66497i	−0.124966	+	0.216447i
$686$	9.40618	−	5.43066i	0.359130	−	0.207344i
$687$	10.2281	+	2.74060i	0.390225	+	0.104560i
$688$	21.9585			0.837160
$689$	−9.69866	−	35.4855i	−0.369489	−	1.35189i
$690$		−	1.97333i		−	0.0751236i
$691$	4.04131	−	15.0824i	0.153739	−	0.573761i	−0.845471	−	0.534021i	$-0.820680\pi$
$691$	4.04131	−	15.0824i	0.153739	−	0.573761i	0.999210	−	0.0397400i	$-0.0126530\pi$
$692$	−30.0485	+	17.3485i	−1.14227	+	0.659492i
$693$	8.66417	−	1.50160i	0.329124	−	0.0570410i
$694$	−9.80829	−	9.80829i	−0.372317	−	0.372317i
$695$	1.37724	+	5.13993i	0.0522417	+	0.194969i
$696$	3.83585	+	14.3156i	0.145397	+	0.542631i
$697$	7.78530	−	7.78530i	0.294889	−	0.294889i
$698$	−0.0209813	+	0.0363407i	−0.000794154	+	0.00137551i
$699$	8.26366	+	14.3131i	0.312560	+	0.541371i
$700$	−5.44565	+	20.3235i	−0.205826	+	0.768154i
$701$	29.7524			1.12373			0.561867	−	0.827228i	$-0.310083\pi$
$701$	29.7524			1.12373			0.561867	+	0.827228i	$0.310083\pi$
$702$	0.0105901	+	2.11893i	0.000399698	+	0.0799740i
$703$		−	1.81292i		−	0.0683755i
$704$	−2.59606	+	1.20133i	−0.0978428	+	0.0452767i
$705$	−0.309771	−	0.536539i	−0.0116667	−	0.0202072i
$706$	5.56640	−	9.64128i	0.209494	−	0.362854i
$707$	−12.4262	−	12.4262i	−0.467335	−	0.467335i
$708$	−3.79704	+	1.01741i	−0.142702	+	0.0382368i
$709$	−7.72957	−	28.8472i	−0.290290	−	1.08338i	−0.944886	−	0.327399i	$-0.893828\pi$
$709$	−7.72957	−	28.8472i	−0.290290	−	1.08338i	0.654596	−	0.755979i	$-0.272839\pi$
$710$	0.346059	+	0.346059i	0.0129873	+	0.0129873i
$711$	6.20336	+	3.58151i	0.232644	+	0.134317i
$712$	4.59010	+	7.95028i	0.172021	+	0.297949i
$713$	65.7272	+	17.6115i	2.46150	+	0.659557i
$714$	3.94271			0.147552
$715$	−5.37853	−	0.459336i	−0.201146	−	0.0171782i
$716$	−27.3746			−1.02304
$717$	−22.3289	−	5.98302i	−0.833889	−	0.223440i
$718$	6.65824	+	11.5324i	0.248483	+	0.430386i
$719$	−3.10261	−	1.79129i	−0.115708	−	0.0668039i	0.441029	−	0.897493i	$-0.354614\pi$
$719$	−3.10261	−	1.79129i	−0.115708	−	0.0668039i	−0.556737	+	0.830689i	$0.687947\pi$
$720$	−0.653392	−	0.653392i	−0.0243505	−	0.0243505i
$721$	5.88409	+	21.9597i	0.219135	+	0.817823i
$722$	−10.7343	+	2.87626i	−0.399490	+	0.107043i
$723$	−7.79903	−	7.79903i	−0.290049	−	0.290049i
$724$	−4.35877	+	7.54961i	−0.161992	+	0.280579i
$725$	16.5479	+	28.6618i	0.614573	+	1.06447i
$726$	−5.84285	−	2.76631i	−0.216849	−	0.102668i
$727$		−	10.4217i		−	0.386518i	−0.981148	−	0.193259i	$-0.938094\pi$
$727$		−	10.4217i		−	0.386518i	0.981148	−	0.193259i	$-0.0619058\pi$
$728$	5.21477	−	19.8582i	0.193272	−	0.735995i
$729$	1.00000			0.0370370
$730$	0.587464	−	2.19245i	0.0217430	−	0.0811461i
$731$	−13.5720	−	23.5074i	−0.501980	−	0.869454i
$732$	−6.72592	+	11.6496i	−0.248597	+	0.430583i
$733$	1.88409	−	1.88409i	0.0695905	−	0.0695905i	−0.671455	−	0.741045i	$-0.734330\pi$
$733$	1.88409	−	1.88409i	0.0695905	−	0.0695905i	0.741045	+	0.671455i	$0.234330\pi$
$734$	−0.458128	−	1.70976i	−0.0169098	−	0.0631083i
$735$	−0.00342594	−	0.0127858i	−0.000126368	−	0.000471610i
$736$	28.9209	+	28.9209i	1.06604	+	1.06604i
$737$	−34.1171	+	5.91288i	−1.25672	+	0.217804i
$738$	2.21455	−	1.27857i	0.0815186	−	0.0470648i
$739$	−10.0721	+	37.5895i	−0.370507	+	1.38275i	0.489292	+	0.872120i	$0.337255\pi$
$739$	−10.0721	+	37.5895i	−0.370507	+	1.38275i	−0.859799	+	0.510632i	$0.829411\pi$
$740$			4.50132i			0.165472i
$741$	−0.942015	−	0.537613i	−0.0346058	−	0.0197497i
$742$	−15.8976			−0.583618
$743$	−13.0618	−	3.49990i	−0.479192	−	0.128399i	0.0111346	−	0.999938i	$-0.496456\pi$
$743$	−13.0618	−	3.49990i	−0.479192	−	0.128399i	−0.490326	+	0.871539i	$0.663122\pi$
$744$	−17.0156	+	9.82399i	−0.623824	+	0.360165i
$745$	1.19978	−	2.07809i	0.0439567	−	0.0761352i
$746$	−3.67784	−	3.67784i	−0.134655	−	0.134655i
$747$	−3.84871	−	14.3636i	−0.140817	−	0.525536i
$748$	11.3515	+	7.99800i	0.415051	+	0.292436i
$749$	16.9989	−	16.9989i	0.621125	−	0.621125i
$750$	2.25068	+	1.29943i	0.0821833	+	0.0474485i
$751$	15.4607	−	8.92623i	0.564168	−	0.325723i	−0.190648	−	0.981658i	$-0.561059\pi$
$751$	15.4607	−	8.92623i	0.564168	−	0.325723i	0.754817	+	0.655936i	$0.227726\pi$
$752$	2.71366	+	0.727124i	0.0989571	+	0.0265155i
$753$			7.24969i			0.264193i
$754$	−7.37400	−	12.6260i	−0.268545	−	0.459811i
$755$			8.32336i			0.302918i
$756$	−4.23738	−	1.13540i	−0.154112	−	0.0412942i
$757$	0.533739	+	0.924462i	0.0193991	+	0.0336002i	0.875562	−	0.483106i	$-0.160491\pi$
$757$	0.533739	+	0.924462i	0.0193991	+	0.0336002i	−0.856163	+	0.516706i	$0.827158\pi$
$758$	−9.85657	+	17.0721i	−0.358007	+	0.620086i
$759$	2.22206	−	24.5699i	0.0806556	−	0.891831i
$760$	−0.281721	+	0.0754870i	−0.0102191	+	0.00273820i
$761$	14.2274	−	3.81222i	0.515743	−	0.138193i	0.00844603	−	0.999964i	$-0.497312\pi$
$761$	14.2274	−	3.81222i	0.515743	−	0.138193i	0.507297	+	0.861771i	$0.330645\pi$
$762$	3.09456	−	3.09456i	0.112104	−	0.112104i
$763$	5.76208	−	9.98021i	0.208601	−	0.361308i
$764$	−22.4915	+	12.9855i	−0.813714	+	0.469798i
$765$	−0.295636	+	1.10333i	−0.0106887	+	0.0398909i
$766$	3.24771			0.117345
$767$	7.39684	−	4.32000i	0.267085	−	0.155986i
$768$	−5.03589			−0.181717
$769$	16.8688	+	4.51997i	0.608303	+	0.162994i	0.549805	−	0.835293i	$-0.314702\pi$
$769$	16.8688	+	4.51997i	0.608303	+	0.162994i	0.0584985	+	0.998287i	$0.481369\pi$
$770$	−0.804276	+	2.18977i	−0.0289841	+	0.0789139i
$771$	14.8364	+	8.56577i	0.534318	+	0.308489i
$772$	30.5712	−	30.5712i	1.10028	−	1.10028i
$773$	−30.7221	+	8.23197i	−1.10500	+	0.296083i	−0.764798	−	0.644270i	$-0.777161\pi$
$773$	−30.7221	+	8.23197i	−1.10500	+	0.296083i	−0.340200	+	0.940353i	$0.610495\pi$
$774$	−1.63168	−	6.08951i	−0.0586495	−	0.218883i
$775$	−31.0248	+	31.0248i	−1.11445	+	1.11445i
$776$	24.8090	+	14.3235i	0.890593	+	0.514184i
$777$	7.98906	+	13.8375i	0.286606	+	0.496416i
$778$	0.324958	−	1.21276i	0.0116503	−	0.0434795i
$779$			1.30892i			0.0468969i
$780$	2.33894	+	1.33485i	0.0837475	+	0.0477952i
$781$	3.91909	+	4.69844i	0.140236	+	0.168123i
$782$	2.86293	−	10.6846i	0.102378	−	0.382080i
$783$	−5.97590	+	3.45019i	−0.213561	+	0.123300i
$784$	0.0519823	+	0.0300120i	0.00185651	+	0.00107186i
$785$	−2.94340	−	2.94340i	−0.105054	−	0.105054i
$786$	9.41274	−	2.52213i	0.335741	−	0.0899616i
$787$	−31.1334	+	8.34216i	−1.10979	+	0.297366i	−0.766743	−	0.641954i	$-0.778124\pi$
$787$	−31.1334	+	8.34216i	−1.10979	+	0.297366i	−0.343042	+	0.939320i	$0.611457\pi$
$788$	−7.74429	−	7.74429i	−0.275879	−	0.275879i
$789$	22.3054	+	12.8780i	0.794093	+	0.458470i
$790$	−1.64570	+	0.950147i	−0.0585515	+	0.0338047i
$791$	−9.86024	+	36.7989i	−0.350590	+	1.30842i
$792$	4.56286	+	5.47024i	0.162134	+	0.194376i
$793$	7.44509	−	28.3515i	0.264383	−	1.00679i
$794$		−	11.7556i		−	0.417189i
$795$	1.19205	−	4.44878i	0.0422775	−	0.157782i
$796$	−8.23455	−	14.2627i	−0.291866	−	0.505527i
$797$	5.68776	+	3.28383i	0.201471	+	0.116319i	0.597341	−	0.801987i	$-0.296224\pi$
$797$	5.68776	+	3.28383i	0.201471	+	0.116319i	−0.395871	+	0.918306i	$0.629557\pi$
$798$	−0.331438	+	0.331438i	−0.0117328	+	0.0117328i
$799$	−0.898836	−	3.35450i	−0.0317985	−	0.118674i
$800$	−25.4739	+	6.82570i	−0.900637	+	0.241325i
$801$	−3.02235	+	3.02235i	−0.106789	+	0.106789i
$802$	−4.39621	−	2.53815i	−0.155236	−	0.0896253i
$803$	9.78328	−	26.6366i	0.345244	−	0.939984i
$804$	16.6857	+	4.47091i	0.588458	+	0.157677i
$805$	−8.90239			−0.313768
$806$	13.6380	−	13.7750i	0.480379	−	0.485204i
$807$	4.25166			0.149665
$808$	3.68456	−	13.7510i	0.129622	−	0.483757i
$809$	−9.04322	+	5.22111i	−0.317943	+	0.183564i	−0.650475	−	0.759527i	$-0.725430\pi$
$809$	−9.04322	+	5.22111i	−0.317943	+	0.183564i	0.332532	+	0.943092i	$0.392097\pi$
$810$	−0.132646	+	0.229750i	−0.00466071	+	0.00807259i
$811$	4.01098	−	4.01098i	0.140845	−	0.140845i	−0.633169	−	0.774014i	$-0.718246\pi$
$811$	4.01098	−	4.01098i	0.140845	−	0.140845i	0.774014	+	0.633169i	$0.218246\pi$
$812$	29.2395	−	7.83471i	1.02611	−	0.274944i
$813$	−2.65324	+	0.710934i	−0.0930533	+	0.0249336i
$814$	1.05803	−	11.6990i	0.0370840	−	0.410048i
$815$	0.978177	−	1.69425i	0.0342640	−	0.0593471i
$816$	−2.58984	−	4.48573i	−0.0906624	−	0.157032i
$817$	3.11703	+	0.835205i	0.109051	+	0.0292201i
$818$			11.7684i			0.411472i
$819$	9.55923	−	0.0477757i	0.334027	−	0.00166942i
$820$		−	3.24993i		−	0.113493i
$821$	12.2333	+	3.27791i	0.426946	+	0.114400i	0.465892	−	0.884841i	$-0.345733\pi$
$821$	12.2333	+	3.27791i	0.426946	+	0.114400i	−0.0389462	+	0.999241i	$0.512400\pi$
$822$	−7.37522	+	4.25808i	−0.257240	+	0.148518i
$823$	27.7292	+	16.0095i	0.966579	+	0.558055i	0.898192	−	0.439604i	$-0.144881\pi$
$823$	27.7292	+	16.0095i	0.966579	+	0.558055i	0.0683877	+	0.997659i	$0.478215\pi$
$824$	−13.0228	+	13.0228i	−0.453670	+	0.453670i
$825$	13.0037	+	9.16214i	0.452732	+	0.318985i
$826$	−0.958095	−	3.57566i	−0.0333364	−	0.124413i
$827$	26.1390	+	26.1390i	0.908944	+	0.908944i	0.996187	−	0.0872432i	$-0.0278057\pi$
$827$	26.1390	+	26.1390i	0.908944	+	0.908944i	−0.0872432	+	0.996187i	$0.527806\pi$
$828$	−6.15380	+	10.6587i	−0.213859	+	0.370415i
$829$	−17.9311	+	10.3525i	−0.622774	+	0.359559i	−0.777948	−	0.628328i	$-0.783739\pi$
$829$	−17.9311	+	10.3525i	−0.622774	+	0.359559i	0.155174	+	0.987887i	$0.450406\pi$
$830$	3.81055	+	1.02103i	0.132266	+	0.0354406i
$831$	−3.49968			−0.121402
$832$	−2.99972	+	0.819862i	−0.103997	+	0.0284236i
$833$		−	0.0741988i		−	0.00257083i
$834$	−1.79303	+	6.69167i	−0.0620875	+	0.231714i
$835$	6.62732	−	3.82628i	0.229348	−	0.132414i
$836$	−1.62658	+	0.281905i	−0.0562566	+	0.00974990i
$837$	−6.46859	−	6.46859i	−0.223587	−	0.223587i
$838$	4.53408	+	16.9214i	0.156627	+	0.584541i
$839$	−6.97334	−	26.0249i	−0.240746	−	0.898478i	−0.975474	−	0.220116i	$-0.929357\pi$
$839$	−6.97334	−	26.0249i	−0.240746	−	0.898478i	0.734727	−	0.678363i	$-0.237310\pi$
$840$	1.81764	−	1.81764i	0.0627146	−	0.0627146i
$841$	9.30756	−	16.1212i	0.320950	−	0.555902i
$842$	−1.58284	−	2.74156i	−0.0545483	−	0.0944804i
$843$	4.79836	−	17.9077i	0.165264	−	0.616775i
$844$	−31.5130			−1.08472
$845$	−5.68330	−	1.46211i	−0.195512	−	0.0502981i
$846$		−	0.806581i		−	0.0277308i
$847$	−12.4798	+	26.3591i	−0.428811	+	0.905710i
$848$	10.4426	+	18.0871i	0.358600	+	0.621113i
$849$	−14.0020	+	24.2522i	−0.480547	+	0.832332i
$850$	5.04339	+	5.04339i	0.172987	+	0.172987i
$851$	43.3001	−	11.6022i	1.48431	−	0.397719i
$852$	−0.790012	−	2.94836i	−0.0270653	−	0.101009i
$853$	−30.9810	−	30.9810i	−1.06077	−	1.06077i	−0.998030	−	0.0627392i	$-0.980016\pi$
$853$	−30.9810	−	30.9810i	−1.06077	−	1.06077i	−0.0627392	−	0.998030i	$-0.519984\pi$
$854$	−10.9704	−	6.33377i	−0.375400	−	0.216737i
$855$	−0.0678974	−	0.117602i	−0.00232204	−	0.00402189i
$856$	18.8111	+	5.04043i	0.642951	+	0.172278i
$857$	−30.0589			−1.02679			−0.513397	−	0.858151i	$-0.671613\pi$
$857$	−30.0589			−1.02679			−0.513397	+	0.858151i	$0.671613\pi$
$858$	−5.76517	−	4.01904i	−0.196820	−	0.137208i
$859$	5.08554			0.173516			0.0867582	−	0.996229i	$-0.472349\pi$
$859$	5.08554			0.173516			0.0867582	+	0.996229i	$0.472349\pi$
$860$	−7.73931	−	2.07374i	−0.263908	−	0.0707140i
$861$	−5.76807	−	9.99058i	−0.196575	−	0.340478i
$862$	0.669352	+	0.386451i	0.0227982	+	0.0131626i
$863$	41.0263	+	41.0263i	1.39655	+	1.39655i	0.809678	+	0.586874i	$0.199642\pi$
$863$	41.0263	+	41.0263i	1.39655	+	1.39655i	0.586874	+	0.809678i	$0.300358\pi$
$864$	−1.42314	−	5.31123i	−0.0484162	−	0.180692i
$865$	9.14351	−	2.45000i	0.310889	−	0.0833024i
$866$	−4.55659	−	4.55659i	−0.154839	−	0.154839i
$867$	5.29857	−	9.17739i	0.179949	−	0.311681i
$868$	20.0655	+	34.7544i	0.681066	+	1.17964i
$869$	−21.5605	+	9.97711i	−0.731389	+	0.338450i
$870$		−	1.83062i		−	0.0620637i
$871$	−37.6416	+	0.188128i	−1.27544	+	0.00637446i
$872$	9.33566			0.316145
$873$	−3.45209	+	12.8834i	−0.116836	+	0.436037i
$874$	0.657516	+	1.13885i	0.0222408	+	0.0385222i
$875$	5.86218	−	10.1536i	0.198178	−	0.343254i
$876$	−10.0102	+	10.0102i	−0.338213	+	0.338213i
$877$	3.54861	+	13.2436i	0.119828	+	0.447204i	0.999603	−	0.0281868i	$-0.00897331\pi$
$877$	3.54861	+	13.2436i	0.119828	+	0.447204i	−0.879775	+	0.475391i	$0.842307\pi$
$878$	−0.173999	−	0.649373i	−0.00587218	−	0.0219153i
$879$	5.26395	+	5.26395i	0.177549	+	0.177549i
$880$	3.01966	−	0.523342i	0.101793	−	0.0176418i
$881$	−39.0551	+	22.5485i	−1.31580	+	0.759677i	−0.983050	−	0.183338i	$-0.941310\pi$
$881$	−39.0551	+	22.5485i	−1.31580	+	0.759677i	−0.332750	+	0.943015i	$0.607976\pi$
$882$	0.00446022	−	0.0166458i	0.000150184	−	0.000560493i
$883$		−	37.4180i		−	1.25922i	−0.776912	−	0.629609i	$-0.783215\pi$
$883$		−	37.4180i		−	1.25922i	0.776912	−	0.629609i	$-0.216785\pi$
$884$	10.7276	+	10.6209i	0.360807	+	0.357218i
$885$	1.07245			0.0360501
$886$	−12.6908	−	3.40048i	−0.426355	−	0.114241i
$887$	24.5726	−	14.1870i	0.825067	−	0.476353i	−0.0270937	−	0.999633i	$-0.508625\pi$
$887$	24.5726	−	14.1870i	0.825067	−	0.476353i	0.852161	+	0.523280i	$0.175292\pi$
$888$	−6.47190	+	11.2097i	−0.217183	+	0.376171i
$889$	−13.9606	−	13.9606i	−0.468224	−	0.468224i
$890$	−0.293481	−	1.09529i	−0.00983751	−	0.0367141i
$891$	−1.91028	+	2.71124i	−0.0639968	+	0.0908300i
$892$	19.0178	−	19.0178i	0.636764	−	0.636764i
$893$	0.357550	+	0.206432i	0.0119650	+	0.00690798i
$894$	2.70546	−	1.56200i	0.0904841	−	0.0522410i
$895$	7.21386	+	1.93295i	0.241133	+	0.0646114i
$896$			30.5006i			1.01895i
$897$	6.81179	−	25.9398i	0.227439	−	0.866106i
$898$			15.8048i			0.527414i
$899$	60.9735	+	16.3378i	2.03358	+	0.544896i
$900$	−3.96796	−	6.87270i	−0.132265	−	0.229090i
$901$	12.9086	−	22.3584i	0.430049	−	0.744867i
$902$	−0.763895	+	8.44660i	−0.0254349	+	0.281241i
$903$	−27.4719	+	7.36107i	−0.914207	+	0.244961i
$904$	−29.8106	+	7.98773i	−0.991487	+	0.265668i
$905$	1.68173	−	1.68173i	0.0559025	−	0.0559025i
$906$	−5.41809	+	9.38440i	−0.180004	+	0.311776i
$907$	18.4029	−	10.6249i	0.611058	−	0.352795i	−0.162321	−	0.986738i	$-0.551898\pi$
$907$	18.4029	−	10.6249i	0.611058	−	0.352795i	0.773379	+	0.633943i	$0.218565\pi$
$908$	6.18262	−	23.0739i	0.205178	−	0.765733i
$909$	6.62821			0.219844
$910$	−1.25702	+	2.20257i	−0.0416698	+	0.0730145i
$911$	4.40823			0.146051			0.0730257	−	0.997330i	$-0.476735\pi$
$911$	4.40823			0.146051			0.0730257	+	0.997330i	$0.476735\pi$
$912$	0.594796	+	0.159375i	0.0196957	+	0.00527744i
$913$	46.2953	+	17.0037i	1.53215	+	0.562740i
$914$	−2.20986	−	1.27586i	−0.0730955	−	0.0422017i
$915$	2.59504	−	2.59504i	0.0857892	−	0.0857892i
$916$	16.9235	−	4.53464i	0.559169	−	0.149829i
$917$	−11.3782	−	42.4641i	−0.375742	−	1.40229i
$918$	−1.05153	+	1.05153i	−0.0347058	+	0.0347058i
$919$	−39.3266	−	22.7052i	−1.29727	−	0.748976i	−0.317334	−	0.948314i	$-0.602788\pi$
$919$	−39.3266	−	22.7052i	−1.29727	−	0.748976i	−0.979931	+	0.199337i	$0.936121\pi$
$920$	−3.60589	−	6.24559i	−0.118883	−	0.205911i
$921$	3.55534	−	13.2687i	0.117152	−	0.437218i
$922$			0.765632i			0.0252147i
$923$	3.35444	+	5.74357i	0.110413	+	0.189052i
$924$	11.1729	−	9.31963i	0.367563	−	0.306593i
$925$	−7.48109	+	27.9198i	−0.245977	+	0.917998i
$926$	6.32821	−	3.65359i	0.207958	−	0.120064i
$927$	−7.42603	−	4.28742i	−0.243903	−	0.140817i
$928$	26.8293	+	26.8293i	0.880714	+	0.880714i
$929$	−18.0522	+	4.83708i	−0.592275	+	0.158700i	−0.542493	−	0.840061i	$-0.682519\pi$
$929$	−18.0522	+	4.83708i	−0.592275	+	0.158700i	−0.0497822	+	0.998760i	$0.515853\pi$
$930$	2.34419	−	0.628125i	0.0768691	−	0.0205970i
$931$	0.00623740	+	0.00623740i	0.000204423	+	0.000204423i
$932$	23.6827	+	13.6732i	0.775751	+	0.447880i
$933$	−15.6793	+	9.05245i	−0.513318	+	0.296364i
$934$	−3.84098	+	14.3347i	−0.125681	+	0.469046i
$935$	−2.42664	−	2.90920i	−0.0793596	−	0.0951412i
$936$	3.90546	+	6.68705i	0.127654	+	0.218573i
$937$			28.7183i			0.938187i	0.883148	+	0.469094i	$0.155419\pi$
$937$			28.7183i			0.938187i	−0.883148	+	0.469094i	$0.844581\pi$
$938$	−4.21024	+	15.7128i	−0.137469	+	0.513041i
$939$	−17.1642	−	29.7293i	−0.560133	−	0.970178i
$940$	−0.887766	−	0.512552i	−0.0289557	−	0.0167176i
$941$	−1.04550	+	1.04550i	−0.0340822	+	0.0340822i	−0.723942	−	0.689860i	$-0.757672\pi$
$941$	−1.04550	+	1.04550i	−0.0340822	+	0.0340822i	0.689860	+	0.723942i	$0.257672\pi$
$942$	−1.40261	−	5.23462i	−0.0456996	−	0.170553i
$943$	−31.2625	+	8.37676i	−1.01805	+	0.272785i
$944$	−3.43878	+	3.43878i	−0.111923	+	0.111923i
$945$	1.03648	+	0.598412i	0.0337167	+	0.0194663i
$946$	19.6271	+	7.20879i	0.638132	+	0.234378i
$947$	−44.0900	−	11.8139i	−1.43273	−	0.383899i	−0.542750	−	0.839895i	$-0.682617\pi$
$947$	−44.0900	−	11.8139i	−1.43273	−	0.383899i	−0.889982	+	0.455995i	$0.849283\pi$
$948$	11.8520			0.384937
$949$	15.2905	−	26.7922i	0.496350	−	0.869713i
$950$	−0.847930			−0.0275105
$951$	2.19301	−	8.18442i	0.0711132	−	0.265398i
$952$	12.4786	−	7.20455i	0.404435	−	0.233501i
$953$	6.80960	−	11.7946i	0.220585	−	0.382064i	−0.734401	−	0.678716i	$-0.762537\pi$
$953$	6.80960	−	11.7946i	0.220585	−	0.382064i	0.954986	+	0.296652i	$0.0958701\pi$
$954$	4.23993	−	4.23993i	0.137273	−	0.137273i
$955$	6.84397	−	1.83384i	0.221466	−	0.0593415i
$956$	−36.9458	+	9.89960i	−1.19491	+	0.320176i
$957$	2.06135	−	22.7929i	0.0666339	−	0.736790i
$958$	3.78712	−	6.55948i	0.122356	−	0.211927i
$959$	19.2097	+	33.2721i	0.620313	+	1.07441i
$960$	−0.376071	−	0.100768i	−0.0121376	−	0.00325227i
$961$			52.6854i			1.69953i
$962$	3.24344	−	12.3513i	0.104573	−	0.398220i
$963$			9.06730i			0.292190i
$964$	−17.6277	−	4.72334i	−0.567751	−	0.152128i
$965$	−10.2149	+	5.89758i	−0.328830	+	0.189850i
$966$	−10.0372	−	5.79501i	−0.322943	−	0.186451i
$967$	−17.9358	+	17.9358i	−0.576777	+	0.576777i	−0.934014	−	0.357237i	$-0.883719\pi$
$967$	−17.9358	+	17.9358i	−0.576777	+	0.576777i	0.357237	+	0.934014i	$0.383719\pi$
$968$	−23.5475	+	1.92134i	−0.756845	+	0.0617542i
$969$	−0.197012	−	0.735259i	−0.00632894	−	0.0236199i
$970$	−2.50205	−	2.50205i	−0.0803360	−	0.0803360i
$971$	2.40484	−	4.16531i	0.0771751	−	0.133671i	−0.824855	−	0.565344i	$-0.808743\pi$
$971$	2.40484	−	4.16531i	0.0771751	−	0.133671i	0.902030	+	0.431673i	$0.142077\pi$
$972$	1.43294	−	0.827308i	0.0459616	−	0.0265359i
$973$	30.1884	+	8.08896i	0.967796	+	0.259320i
$974$	12.0464			0.385992
$975$	12.2890	+	12.1668i	0.393563	+	0.389648i
$976$			16.6418i			0.532690i
$977$	−1.76984	+	6.60514i	−0.0566223	+	0.211317i	−0.988441	−	0.151607i	$-0.951555\pi$
$977$	−1.76984	+	6.60514i	−0.0566223	+	0.211317i	0.931819	+	0.362925i	$0.118222\pi$
$978$	2.20575	−	1.27349i	0.0705320	−	0.0407216i
$979$	−2.42078	−	13.9678i	−0.0773686	−	0.446414i
$980$	−0.0154869	−	0.0154869i	−0.000494712	−	0.000494712i
$981$	1.12499	+	4.19852i	0.0359182	+	0.134048i
$982$	−0.932503	−	3.48015i	−0.0297574	−	0.111056i
$983$	−26.0985	+	26.0985i	−0.832413	+	0.832413i	−0.987846	−	0.155433i	$-0.950323\pi$
$983$	−26.0985	+	26.0985i	−0.832413	+	0.832413i	0.155433	+	0.987846i	$0.450323\pi$
$984$	4.67268	−	8.09332i	0.148960	−	0.258006i
$985$	1.49397	+	2.58764i	0.0476019	+	0.0824490i
$986$	2.65587	−	9.91184i	0.0845801	−	0.315657i
$987$	−3.63876			−0.115823
$988$	−1.79462	+	0.00896926i	−0.0570945	+	0.000285350i
$989$			79.7928i			2.53726i
$990$	−0.369516	−	0.798522i	−0.0117440	−	0.0253787i
$991$	27.6003	+	47.8052i	0.876753	+	1.51858i	0.854883	+	0.518821i	$0.173629\pi$
$991$	27.6003	+	47.8052i	0.876753	+	1.51858i	0.0218702	+	0.999761i	$0.493038\pi$
$992$	−25.1505	+	43.5619i	−0.798529	+	1.38309i
$993$	13.1236	+	13.1236i	0.416463	+	0.416463i
$994$	2.77646	−	0.743950i	0.0880640	−	0.0235967i
$995$	1.16290	+	4.34000i	0.0368664	+	0.137587i
$996$	−17.3981	−	17.3981i	−0.551279	−	0.551279i
$997$	38.6476	+	22.3132i	1.22398	+	0.706666i	0.965764	−	0.259421i	$-0.0835318\pi$
$997$	38.6476	+	22.3132i	1.22398	+	0.706666i	0.258217	+	0.966087i	$0.416865\pi$
$998$	−1.58192	−	2.73996i	−0.0500747	−	0.0867320i
$999$	−5.82120	−	1.55979i	−0.184175	−	0.0493495i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	429.2.bd.a.76.6	✓	56
11.10	odd	2	inner	429.2.bd.a.76.9	yes	56
13.6	odd	12	inner	429.2.bd.a.175.9	yes	56
143.32	even	12	inner	429.2.bd.a.175.6	yes	56

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
429.2.bd.a.76.6	✓	56	1.1	even	1	trivial
429.2.bd.a.76.9	yes	56	11.10	odd	2	inner
429.2.bd.a.175.6	yes	56	143.32	even	12	inner
429.2.bd.a.175.9	yes	56	13.6	odd	12	inner

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.bd (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.567668 - 0.152106i) q^{2} +(-0.500000 - 0.866025i) q^{3} +(-1.43294 - 0.827308i) q^{4} +(0.319197 + 0.319197i) q^{5} +(0.152106 + 0.567668i) q^{6} +(2.56095 - 0.686204i) q^{7} +(1.51872 + 1.51872i) q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})\)	\(q+(-0.567668 - 0.152106i) q^{2} +(-0.500000 - 0.866025i) q^{3} +(-1.43294 - 0.827308i) q^{4} +(0.319197 + 0.319197i) q^{5} +(0.152106 + 0.567668i) q^{6} +(2.56095 - 0.686204i) q^{7} +(1.51872 + 1.51872i) q^{8} +(-0.500000 + 0.866025i) q^{9} +(-0.132646 - 0.229750i) q^{10} +(-1.39286 - 3.00997i) q^{11} +1.65462i q^{12} +(-0.950579 - 3.47799i) q^{13} -1.55814 q^{14} +(0.116834 - 0.436031i) q^{15} +(1.02349 + 1.77274i) q^{16} +(1.26519 - 2.19138i) q^{17} +(0.415562 - 0.415562i) q^{18} +(0.0778584 + 0.290572i) q^{19} +(-0.193316 - 0.721464i) q^{20} +(-1.87474 - 1.87474i) q^{21} +(0.332849 + 1.92053i) q^{22} +(-6.44179 + 3.71917i) q^{23} +(0.555890 - 2.07461i) q^{24} -4.79623i q^{25} +(0.0105901 + 2.11893i) q^{26} +1.00000 q^{27} +(-4.23738 - 1.13540i) q^{28} +(-5.97590 + 3.45019i) q^{29} +(-0.132646 + 0.229750i) q^{30} +(-6.46859 - 6.46859i) q^{31} +(-1.42314 - 5.31123i) q^{32} +(-1.91028 + 2.71124i) q^{33} +(-1.05153 + 1.05153i) q^{34} +(1.03648 + 0.598412i) q^{35} +(1.43294 - 0.827308i) q^{36} +(-5.82120 - 1.55979i) q^{37} -0.176791i q^{38} +(-2.53674 + 2.56222i) q^{39} +0.969541i q^{40} +(4.20288 + 1.12616i) q^{41} +(0.779072 + 1.34939i) q^{42} +(5.36362 - 9.29006i) q^{43} +(-0.494284 + 5.46544i) q^{44} +(-0.436031 + 0.116834i) q^{45} +(4.22251 - 1.13142i) q^{46} +(0.970470 - 0.970470i) q^{47} +(1.02349 - 1.77274i) q^{48} +(0.0253945 - 0.0146615i) q^{49} +(-0.729536 + 2.72267i) q^{50} -2.53039 q^{51} +(-1.51524 + 5.77017i) q^{52} +10.2029 q^{53} +(-0.567668 - 0.152106i) q^{54} +(0.516176 - 1.40537i) q^{55} +(4.93151 + 2.84721i) q^{56} +(0.212713 - 0.212713i) q^{57} +(3.91712 - 1.04959i) q^{58} +(0.614895 + 2.29482i) q^{59} +(-0.528148 + 0.528148i) q^{60} +(7.04069 + 4.06494i) q^{61} +(2.68810 + 4.65593i) q^{62} +(-0.686204 + 2.56095i) q^{63} -0.862487i q^{64} +(0.806741 - 1.41358i) q^{65} +(1.49680 - 1.24852i) q^{66} +(2.70208 - 10.0843i) q^{67} +(-3.62589 + 2.09341i) q^{68} +(6.44179 + 3.71917i) q^{69} +(-0.497355 - 0.497355i) q^{70} +(-1.78190 + 0.477459i) q^{71} +(-2.07461 + 0.555890i) q^{72} +(6.04986 + 6.04986i) q^{73} +(3.06726 + 1.77088i) q^{74} +(-4.15365 + 2.39811i) q^{75} +(0.128826 - 0.480784i) q^{76} +(-5.63250 - 6.75259i) q^{77} +(1.82975 - 1.06864i) q^{78} -7.16302i q^{79} +(-0.239158 + 0.892550i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(-2.21455 - 1.27857i) q^{82} +(-10.5149 + 10.5149i) q^{83} +(1.13540 + 4.23738i) q^{84} +(1.10333 - 0.295636i) q^{85} +(-4.45783 + 4.45783i) q^{86} +(5.97590 + 3.45019i) q^{87} +(2.45593 - 6.68668i) q^{88} +(4.12860 + 1.10626i) q^{89} +0.265292 q^{90} +(-4.82099 - 8.25465i) q^{91} +12.3076 q^{92} +(-2.36767 + 8.83626i) q^{93} +(-0.698520 + 0.403291i) q^{94} +(-0.0678974 + 0.117602i) q^{95} +(-3.88809 + 3.88809i) q^{96} +(12.8834 - 3.45209i) q^{97} +(-0.0166458 + 0.00446022i) q^{98} +(3.30314 + 0.298730i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 56 q - 28 q^{3} + 4 q^{5} - 28 q^{9}+O(q^{10}) \) 56 * q - 28 * q^3 + 4 * q^5 - 28 * q^9	\( 56 q - 28 q^{3} + 4 q^{5} - 28 q^{9} - 12 q^{11} + 24 q^{14} - 8 q^{15} + 68 q^{16} - 8 q^{20} - 10 q^{22} - 12 q^{23} - 48 q^{26} + 56 q^{27} + 4 q^{31} + 12 q^{33} + 32 q^{34} + 36 q^{37} - 12 q^{42} + 24 q^{44} + 4 q^{45} - 8 q^{47} + 68 q^{48} - 24 q^{49} - 56 q^{53} - 2 q^{55} + 72 q^{56} - 88 q^{58} + 56 q^{59} - 44 q^{60} + 20 q^{66} + 92 q^{67} + 12 q^{69} - 216 q^{70} + 72 q^{71} - 12 q^{75} - 12 q^{78} + 44 q^{80} - 28 q^{81} - 156 q^{82} - 120 q^{86} - 6 q^{88} - 56 q^{89} + 92 q^{91} + 32 q^{92} - 20 q^{93} - 44 q^{97}+O(q^{100}) \) 56 * q - 28 * q^3 + 4 * q^5 - 28 * q^9 - 12 * q^11 + 24 * q^14 - 8 * q^15 + 68 * q^16 - 8 * q^20 - 10 * q^22 - 12 * q^23 - 48 * q^26 + 56 * q^27 + 4 * q^31 + 12 * q^33 + 32 * q^34 + 36 * q^37 - 12 * q^42 + 24 * q^44 + 4 * q^45 - 8 * q^47 + 68 * q^48 - 24 * q^49 - 56 * q^53 - 2 * q^55 + 72 * q^56 - 88 * q^58 + 56 * q^59 - 44 * q^60 + 20 * q^66 + 92 * q^67 + 12 * q^69 - 216 * q^70 + 72 * q^71 - 12 * q^75 - 12 * q^78 + 44 * q^80 - 28 * q^81 - 156 * q^82 - 120 * q^86 - 6 * q^88 - 56 * q^89 + 92 * q^91 + 32 * q^92 - 20 * q^93 - 44 * q^97

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