LMFDB - Embedded newform 525.2.z.a.64.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [525,2,Mod(64,525)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(525, base_ring=CyclotomicField(10))

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

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

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

chi := DirichletCharacter("525.64");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 525 = 3 \cdot 5^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	525.z (of order $10$, 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:	$4.19214610612$
Analytic rank:	$0$
Dimension:	$56$
Relative dimension:	$14$ over $\Q(\zeta_{10})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			64.9
Character	$\chi$	$=$	525.64
Dual form			525.2.z.a.484.9

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.342442 + 0.471330i) q^{2} +(-0.951057 - 0.309017i) q^{3} +(0.513148 - 1.57931i) q^{4} +(2.09675 + 0.776951i) q^{5} +(-0.180032 - 0.554082i) q^{6} -1.00000i q^{7} +(2.02826 - 0.659022i) q^{8} +(0.809017 + 0.587785i) q^{9} +O(q^{10})$	\(q+(0.342442 + 0.471330i) q^{2} +(-0.951057 - 0.309017i) q^{3} +(0.513148 - 1.57931i) q^{4} +(2.09675 + 0.776951i) q^{5} +(-0.180032 - 0.554082i) q^{6} -1.00000i q^{7} +(2.02826 - 0.659022i) q^{8} +(0.809017 + 0.587785i) q^{9} +(0.351813 + 1.25432i) q^{10} +(-1.58456 + 1.15125i) q^{11} +(-0.976065 + 1.34344i) q^{12} +(2.73259 - 3.76108i) q^{13} +(0.471330 - 0.342442i) q^{14} +(-1.75403 - 1.38685i) q^{15} +(-1.68170 - 1.22183i) q^{16} +(-0.819237 + 0.266186i) q^{17} +0.582596i q^{18} +(-0.216466 - 0.666214i) q^{19} +(2.30298 - 2.91272i) q^{20} +(-0.309017 + 0.951057i) q^{21} +(-1.08524 - 0.352616i) q^{22} +(2.42477 + 3.33741i) q^{23} -2.13264 q^{24} +(3.79270 + 3.25814i) q^{25} +2.70846 q^{26} +(-0.587785 - 0.809017i) q^{27} +(-1.57931 - 0.513148i) q^{28} +(0.689749 - 2.12283i) q^{29} +(0.0530126 - 1.30165i) q^{30} +(-2.50259 - 7.70218i) q^{31} -5.47632i q^{32} +(1.86276 - 0.605249i) q^{33} +(-0.406003 - 0.294978i) q^{34} +(0.776951 - 2.09675i) q^{35} +(1.34344 - 0.976065i) q^{36} +(4.43699 - 6.10699i) q^{37} +(0.239880 - 0.330166i) q^{38} +(-3.76108 + 2.73259i) q^{39} +(4.76478 + 0.194057i) q^{40} +(-2.75883 - 2.00441i) q^{41} +(-0.554082 + 0.180032i) q^{42} +11.0987i q^{43} +(1.00506 + 3.09327i) q^{44} +(1.23962 + 1.86100i) q^{45} +(-0.742682 + 2.28574i) q^{46} +(10.7427 + 3.49050i) q^{47} +(1.22183 + 1.68170i) q^{48} -1.00000 q^{49} +(-0.236883 + 2.90333i) q^{50} +0.861397 q^{51} +(-4.53768 - 6.24558i) q^{52} +(12.9495 + 4.20755i) q^{53} +(0.180032 - 0.554082i) q^{54} +(-4.21689 + 1.18276i) q^{55} +(-0.659022 - 2.02826i) q^{56} +0.700499i q^{57} +(1.23675 - 0.401845i) q^{58} +(-8.20741 - 5.96303i) q^{59} +(-3.09035 + 2.05850i) q^{60} +(-5.49865 + 3.99500i) q^{61} +(2.77328 - 3.81709i) q^{62} +(0.587785 - 0.809017i) q^{63} +(-0.782240 + 0.568331i) q^{64} +(8.65172 - 5.76295i) q^{65} +(0.923160 + 0.670715i) q^{66} +(-14.8422 + 4.82251i) q^{67} +1.43042i q^{68} +(-1.27478 - 3.92337i) q^{69} +(1.25432 - 0.351813i) q^{70} +(-1.39684 + 4.29902i) q^{71} +(2.02826 + 0.659022i) q^{72} +(5.78574 + 7.96339i) q^{73} +4.39782 q^{74} +(-2.60025 - 4.27068i) q^{75} -1.16324 q^{76} +(1.15125 + 1.58456i) q^{77} +(-2.57590 - 0.836961i) q^{78} +(-1.55060 + 4.77225i) q^{79} +(-2.57680 - 3.86846i) q^{80} +(0.309017 + 0.951057i) q^{81} -1.98671i q^{82} +(-6.27596 + 2.03918i) q^{83} +(1.34344 + 0.976065i) q^{84} +(-1.92455 - 0.0783816i) q^{85} +(-5.23116 + 3.80066i) q^{86} +(-1.31198 + 1.80579i) q^{87} +(-2.45521 + 3.37930i) q^{88} +(-7.26466 + 5.27809i) q^{89} +(-0.452649 + 1.22156i) q^{90} +(-3.76108 - 2.73259i) q^{91} +(6.51507 - 2.11687i) q^{92} +8.09855i q^{93} +(2.03355 + 6.25863i) q^{94} +(0.0637409 - 1.56507i) q^{95} +(-1.69228 + 5.20829i) q^{96} +(-12.4565 - 4.04735i) q^{97} +(-0.342442 - 0.471330i) q^{98} -1.95863 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 56 q + 12 q^{4} - 2 q^{5} + 14 q^{9}+O(q^{10}) $ 56 * q + 12 * q^4 - 2 * q^5 + 14 * q^9	$ 56 q + 12 q^{4} - 2 q^{5} + 14 q^{9} + 36 q^{10} + 12 q^{11} + 20 q^{13} - 4 q^{15} + 4 q^{16} - 22 q^{19} - 22 q^{20} + 14 q^{21} + 30 q^{22} - 10 q^{23} + 16 q^{25} - 60 q^{26} - 20 q^{28} - 18 q^{29} - 18 q^{30} + 16 q^{31} - 10 q^{33} + 6 q^{35} - 12 q^{36} + 10 q^{37} + 100 q^{38} - 22 q^{40} + 8 q^{41} - 66 q^{44} + 2 q^{45} + 40 q^{46} - 100 q^{47} - 56 q^{49} + 62 q^{50} + 32 q^{51} + 80 q^{52} - 30 q^{53} - 58 q^{55} - 40 q^{58} - 20 q^{59} + 66 q^{60} + 28 q^{61} - 50 q^{62} - 12 q^{64} + 78 q^{65} - 20 q^{67} + 4 q^{69} - 18 q^{70} + 40 q^{71} - 20 q^{73} + 100 q^{74} - 8 q^{75} - 164 q^{76} + 20 q^{77} - 90 q^{78} - 4 q^{79} - 158 q^{80} - 14 q^{81} + 30 q^{83} - 12 q^{84} + 46 q^{85} + 80 q^{86} - 40 q^{87} + 130 q^{88} - 38 q^{89} + 4 q^{90} - 100 q^{92} - 10 q^{94} + 8 q^{95} + 10 q^{96} - 130 q^{97} + 48 q^{99}+O(q^{100}) $ 56 * q + 12 * q^4 - 2 * q^5 + 14 * q^9 + 36 * q^10 + 12 * q^11 + 20 * q^13 - 4 * q^15 + 4 * q^16 - 22 * q^19 - 22 * q^20 + 14 * q^21 + 30 * q^22 - 10 * q^23 + 16 * q^25 - 60 * q^26 - 20 * q^28 - 18 * q^29 - 18 * q^30 + 16 * q^31 - 10 * q^33 + 6 * q^35 - 12 * q^36 + 10 * q^37 + 100 * q^38 - 22 * q^40 + 8 * q^41 - 66 * q^44 + 2 * q^45 + 40 * q^46 - 100 * q^47 - 56 * q^49 + 62 * q^50 + 32 * q^51 + 80 * q^52 - 30 * q^53 - 58 * q^55 - 40 * q^58 - 20 * q^59 + 66 * q^60 + 28 * q^61 - 50 * q^62 - 12 * q^64 + 78 * q^65 - 20 * q^67 + 4 * q^69 - 18 * q^70 + 40 * q^71 - 20 * q^73 + 100 * q^74 - 8 * q^75 - 164 * q^76 + 20 * q^77 - 90 * q^78 - 4 * q^79 - 158 * q^80 - 14 * q^81 + 30 * q^83 - 12 * q^84 + 46 * q^85 + 80 * q^86 - 40 * q^87 + 130 * q^88 - 38 * q^89 + 4 * q^90 - 100 * q^92 - 10 * q^94 + 8 * q^95 + 10 * q^96 - 130 * q^97 + 48 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/525\mathbb{Z}\right)^\times$.

$n$	$127$	$176$	$451$
$\chi(n)$	$e\left(\frac{3}{10}\right)$	$1$	$1$

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 $

$2$	0.342442	+	0.471330i	0.242143	+	0.333281i	0.912740	−	0.408541i	$-0.133962\pi$
$2$	0.342442	+	0.471330i	0.242143	+	0.333281i	−0.670597	+	0.741821i	$0.733962\pi$
$3$	−0.951057	−	0.309017i	−0.549093	−	0.178411i
$3$	−0.951057	−	0.309017i	−0.549093	−	0.178411i
$4$	0.513148	−	1.57931i	0.256574	−	0.789653i
$5$	2.09675	+	0.776951i	0.937694	+	0.347463i
$5$	2.09675	+	0.776951i	0.937694	+	0.347463i
$6$	−0.180032	−	0.554082i	−0.0734978	−	0.226203i
$7$		−	1.00000i		−	0.377964i
$7$		−	1.00000i		−	0.377964i
$8$	2.02826	−	0.659022i	0.717099	−	0.233000i
$9$	0.809017	+	0.587785i	0.269672	+	0.195928i
$10$	0.351813	+	1.25432i	0.111253	+	0.396651i
$11$	−1.58456	+	1.15125i	−0.477763	+	0.347115i	−0.800459	−	0.599387i	$-0.795411\pi$
$11$	−1.58456	+	1.15125i	−0.477763	+	0.347115i	0.322696	+	0.946503i	$0.395411\pi$
$12$	−0.976065	+	1.34344i	−0.281766	+	0.387817i
$13$	2.73259	−	3.76108i	0.757883	−	1.04314i	−0.239504	−	0.970895i	$-0.576985\pi$
$13$	2.73259	−	3.76108i	0.757883	−	1.04314i	0.997387	−	0.0722412i	$-0.0230151\pi$
$14$	0.471330	−	0.342442i	0.125968	−	0.0915214i
$15$	−1.75403	−	1.38685i	−0.452890	−	0.358084i
$16$	−1.68170	−	1.22183i	−0.420425	−	0.305456i
$17$	−0.819237	+	0.266186i	−0.198694	+	0.0645597i	−0.406673	−	0.913574i	$-0.633311\pi$
$17$	−0.819237	+	0.266186i	−0.198694	+	0.0645597i	0.207979	+	0.978133i	$0.433311\pi$
$18$			0.582596i			0.137319i
$19$	−0.216466	−	0.666214i	−0.0496607	−	0.152840i	0.923151	−	0.384438i	$-0.125605\pi$
$19$	−0.216466	−	0.666214i	−0.0496607	−	0.152840i	−0.972812	+	0.231598i	$0.925605\pi$
$20$	2.30298	−	2.91272i	0.514963	−	0.651303i
$21$	−0.309017	+	0.951057i	−0.0674330	+	0.207538i
$22$	−1.08524	−	0.352616i	−0.231374	−	0.0751779i
$23$	2.42477	+	3.33741i	0.505600	+	0.695899i	0.983170	−	0.182695i	$-0.0584821\pi$
$23$	2.42477	+	3.33741i	0.505600	+	0.695899i	−0.477569	+	0.878594i	$0.658482\pi$
$24$	−2.13264			−0.435324
$25$	3.79270	+	3.25814i	0.758539	+	0.651628i
$26$	2.70846			0.531173
$27$	−0.587785	−	0.809017i	−0.113119	−	0.155695i
$28$	−1.57931	−	0.513148i	−0.298461	−	0.0969758i
$29$	0.689749	−	2.12283i	0.128083	−	0.394199i	−0.866367	−	0.499408i	$-0.833551\pi$
$29$	0.689749	−	2.12283i	0.128083	−	0.394199i	0.994450	+	0.105208i	$0.0335510\pi$
$30$	0.0530126	−	1.30165i	0.00967873	−	0.237647i
$31$	−2.50259	−	7.70218i	−0.449479	−	1.38335i	−0.877497	−	0.479583i	$-0.840788\pi$
$31$	−2.50259	−	7.70218i	−0.449479	−	1.38335i	0.428018	−	0.903770i	$-0.359212\pi$
$32$		−	5.47632i		−	0.968086i
$33$	1.86276	−	0.605249i	0.324265	−	0.105360i
$34$	−0.406003	−	0.294978i	−0.0696289	−	0.0505883i
$35$	0.776951	−	2.09675i	0.131329	−	0.354415i
$36$	1.34344	−	0.976065i	0.223906	−	0.162678i
$37$	4.43699	−	6.10699i	0.729437	−	1.00398i	−0.269721	−	0.962939i	$-0.586931\pi$
$37$	4.43699	−	6.10699i	0.729437	−	1.00398i	0.999157	−	0.0410448i	$-0.0130686\pi$
$38$	0.239880	−	0.330166i	0.0389136	−	0.0535600i
$39$	−3.76108	+	2.73259i	−0.602255	+	0.437564i
$40$	4.76478	+	0.194057i	0.753378	+	0.0306831i
$41$	−2.75883	−	2.00441i	−0.430856	−	0.313035i	0.351135	−	0.936325i	$-0.385796\pi$
$41$	−2.75883	−	2.00441i	−0.430856	−	0.313035i	−0.781991	+	0.623289i	$0.785796\pi$
$42$	−0.554082	+	0.180032i	−0.0854967	+	0.0277796i
$43$			11.0987i			1.69254i	0.532757	+	0.846269i	$0.321156\pi$
$43$			11.0987i			1.69254i	−0.532757	+	0.846269i	$0.678844\pi$
$44$	1.00506	+	3.09327i	0.151519	+	0.466328i
$45$	1.23962	+	1.86100i	0.184792	+	0.277422i
$46$	−0.742682	+	2.28574i	−0.109502	+	0.337014i
$47$	10.7427	+	3.49050i	1.56698	+	0.509142i	0.958661	−	0.284552i	$-0.0918449\pi$
$47$	10.7427	+	3.49050i	1.56698	+	0.509142i	0.608317	+	0.793694i	$0.291845\pi$
$48$	1.22183	+	1.68170i	0.176355	+	0.242732i
$49$	−1.00000			−0.142857
$50$	−0.236883	+	2.90333i	−0.0335003	+	0.410593i
$51$	0.861397			0.120620
$52$	−4.53768	−	6.24558i	−0.629263	−	0.866107i
$53$	12.9495	+	4.20755i	1.77875	+	0.577952i	0.998850	−	0.0479488i	$-0.0152684\pi$
$53$	12.9495	+	4.20755i	1.77875	+	0.577952i	0.779903	+	0.625901i	$0.215268\pi$
$54$	0.180032	−	0.554082i	0.0244993	−	0.0754010i
$55$	−4.21689	+	1.18276i	−0.568605	+	0.159483i
$56$	−0.659022	−	2.02826i	−0.0880656	−	0.271038i
$57$			0.700499i			0.0927833i
$58$	1.23675	−	0.401845i	0.162394	−	0.0527649i
$59$	−8.20741	−	5.96303i	−1.06851	−	0.776321i	−0.0928691	−	0.995678i	$-0.529604\pi$
$59$	−8.20741	−	5.96303i	−1.06851	−	0.776321i	−0.975644	+	0.219358i	$0.929604\pi$
$60$	−3.09035	+	2.05850i	−0.398962	+	0.265751i
$61$	−5.49865	+	3.99500i	−0.704030	+	0.511508i	−0.881242	−	0.472665i	$-0.843292\pi$
$61$	−5.49865	+	3.99500i	−0.704030	+	0.511508i	0.177212	+	0.984173i	$0.443292\pi$
$62$	2.77328	−	3.81709i	0.352207	−	0.484772i
$63$	0.587785	−	0.809017i	0.0740540	−	0.101927i
$64$	−0.782240	+	0.568331i	−0.0977800	+	0.0710413i
$65$	8.65172	−	5.76295i	1.07311	−	0.714806i
$66$	0.923160	+	0.670715i	0.113633	+	0.0825593i
$67$	−14.8422	+	4.82251i	−1.81326	+	0.589164i	−0.813286	+	0.581865i	$0.802323\pi$
$67$	−14.8422	+	4.82251i	−1.81326	+	0.589164i	−0.999973	+	0.00729879i	$0.997677\pi$
$68$			1.43042i			0.173464i
$69$	−1.27478	−	3.92337i	−0.153465	−	0.472318i
$70$	1.25432	−	0.351813i	0.149920	−	0.0420497i
$71$	−1.39684	+	4.29902i	−0.165774	+	0.510200i	−0.999092	−	0.0425932i	$-0.986438\pi$
$71$	−1.39684	+	4.29902i	−0.165774	+	0.510200i	0.833318	+	0.552793i	$0.186438\pi$
$72$	2.02826	+	0.659022i	0.239033	+	0.0776665i
$73$	5.78574	+	7.96339i	0.677170	+	0.932044i	0.999896	−	0.0144483i	$-0.00459920\pi$
$73$	5.78574	+	7.96339i	0.677170	+	0.932044i	−0.322726	+	0.946492i	$0.604599\pi$
$74$	4.39782			0.511236
$75$	−2.60025	−	4.27068i	−0.300251	−	0.493136i
$76$	−1.16324			−0.133432
$77$	1.15125	+	1.58456i	0.131197	+	0.180578i
$78$	−2.57590	−	0.836961i	−0.291663	−	0.0947672i
$79$	−1.55060	+	4.77225i	−0.174456	+	0.536920i	−0.999608	−	0.0279903i	$-0.991089\pi$
$79$	−1.55060	+	4.77225i	−0.174456	+	0.536920i	0.825152	+	0.564910i	$0.191089\pi$
$80$	−2.57680	−	3.86846i	−0.288095	−	0.432507i
$81$	0.309017	+	0.951057i	0.0343352	+	0.105673i
$82$		−	1.98671i		−	0.219395i
$83$	−6.27596	+	2.03918i	−0.688876	+	0.223829i	−0.632477	−	0.774579i	$-0.717962\pi$
$83$	−6.27596	+	2.03918i	−0.688876	+	0.223829i	−0.0563986	+	0.998408i	$0.517962\pi$
$84$	1.34344	+	0.976065i	0.146581	+	0.106497i
$85$	−1.92455	−	0.0783816i	−0.208746	−	0.00850168i
$86$	−5.23116	+	3.80066i	−0.564090	+	0.409836i
$87$	−1.31198	+	1.80579i	−0.140659	+	0.193601i
$88$	−2.45521	+	3.37930i	−0.261726	+	0.360235i
$89$	−7.26466	+	5.27809i	−0.770053	+	0.559476i	−0.901977	−	0.431784i	$-0.857884\pi$
$89$	−7.26466	+	5.27809i	−0.770053	+	0.559476i	0.131924	+	0.991260i	$0.457884\pi$
$90$	−0.452649	+	1.22156i	−0.0477134	+	0.128763i
$91$	−3.76108	−	2.73259i	−0.394269	−	0.286453i
$92$	6.51507	−	2.11687i	0.679243	−	0.220699i
$93$			8.09855i			0.839781i
$94$	2.03355	+	6.25863i	0.209745	+	0.645529i
$95$	0.0637409	−	1.56507i	0.00653968	−	0.160572i
$96$	−1.69228	+	5.20829i	−0.172717	+	0.531569i
$97$	−12.4565	−	4.04735i	−1.26476	−	0.410947i	−0.401574	−	0.915827i	$-0.631537\pi$
$97$	−12.4565	−	4.04735i	−1.26476	−	0.410947i	−0.863190	+	0.504880i	$0.831537\pi$
$98$	−0.342442	−	0.471330i	−0.0345918	−	0.0476116i
$99$	−1.95863			−0.196849
$100$	7.09181	−	4.31792i	0.709181	−	0.431792i
$101$	−8.34387			−0.830246			−0.415123	−	0.909765i	$-0.636261\pi$
$101$	−8.34387			−0.830246			−0.415123	+	0.909765i	$0.636261\pi$
$102$	0.294978	+	0.406003i	0.0292072	+	0.0402002i
$103$	−0.639676	−	0.207843i	−0.0630292	−	0.0204794i	0.277333	−	0.960774i	$-0.410550\pi$
$103$	−0.639676	−	0.207843i	−0.0630292	−	0.0204794i	−0.340362	+	0.940295i	$0.610550\pi$
$104$	3.06376	−	9.42930i	0.300427	−	0.924619i
$105$	−1.38685	+	1.75403i	−0.135343	+	0.171176i
$106$	2.45130	+	7.54434i	0.238092	+	0.732771i
$107$		−	0.217806i		−	0.0210561i	−0.999945	−	0.0105280i	$-0.996649\pi$
$107$		−	0.217806i		−	0.0210561i	0.999945	−	0.0105280i	$-0.00335124\pi$
$108$	−1.57931	+	0.513148i	−0.151969	+	0.0493777i
$109$	8.15046	+	5.92166i	0.780673	+	0.567192i	0.905181	−	0.425027i	$-0.139735\pi$
$109$	8.15046	+	5.92166i	0.780673	+	0.567192i	−0.124508	+	0.992219i	$0.539735\pi$
$110$	−2.00151	−	1.58252i	−0.190836	−	0.150888i
$111$	−6.10699	+	4.43699i	−0.579650	+	0.421140i
$112$	−1.22183	+	1.68170i	−0.115452	+	0.158906i
$113$	2.80698	−	3.86348i	0.264059	−	0.363446i	−0.656314	−	0.754488i	$-0.727885\pi$
$113$	2.80698	−	3.86348i	0.264059	−	0.363446i	0.920373	+	0.391042i	$0.127885\pi$
$114$	−0.330166	+	0.239880i	−0.0309229	+	0.0224668i
$115$	2.49113	+	8.88164i	0.232299	+	0.828217i
$116$	−2.99865	−	2.17865i	−0.278418	−	0.202283i
$117$	4.42142	−	1.43661i	0.408760	−	0.132814i
$118$		−	5.91039i		−	0.544096i
$119$	0.266186	+	0.819237i	0.0244013	+	0.0750993i
$120$	−4.47161	−	1.65696i	−0.408200	−	0.151259i
$121$	−2.21373	+	6.81317i	−0.201248	+	0.619379i
$122$	−3.76593	−	1.22363i	−0.340952	−	0.110782i
$123$	2.00441	+	2.75883i	0.180731	+	0.248755i
$124$	−13.4483			−1.20769
$125$	5.42091	+	9.77823i	0.484861	+	0.874591i
$126$	0.582596			0.0519018
$127$	−3.77799	−	5.19995i	−0.335242	−	0.461421i	0.607802	−	0.794088i	$-0.292051\pi$
$127$	−3.77799	−	5.19995i	−0.335242	−	0.461421i	−0.943044	+	0.332667i	$0.892051\pi$
$128$	−10.9523	−	3.55863i	−0.968058	−	0.314541i
$129$	3.42969	−	10.5555i	0.301967	−	0.929360i
$130$	5.67896	+	2.10434i	0.498078	+	0.184563i
$131$	4.11249	+	12.6569i	0.359310	+	1.10584i	0.953468	+	0.301494i	$0.0974854\pi$
$131$	4.11249	+	12.6569i	0.359310	+	1.10584i	−0.594158	+	0.804348i	$0.702515\pi$
$132$		−	3.25246i		−	0.283090i
$133$	−0.666214	+	0.216466i	−0.0577681	+	0.0187700i
$134$	−7.35557	−	5.34413i	−0.635424	−	0.461663i
$135$	−0.603871	−	2.15298i	−0.0519729	−	0.185299i
$136$	−1.48621	+	1.07979i	−0.127441	+	0.0925913i
$137$	−0.343621	+	0.472954i	−0.0293575	+	0.0404072i	−0.823443	−	0.567398i	$-0.807950\pi$
$137$	−0.343621	+	0.472954i	−0.0293575	+	0.0404072i	0.794086	+	0.607806i	$0.207950\pi$
$138$	1.41266	−	1.94437i	0.120254	−	0.165515i
$139$	0.0865699	−	0.0628967i	0.00734276	−	0.00533483i	−0.584108	−	0.811676i	$-0.698555\pi$
$139$	0.0865699	−	0.0628967i	0.00734276	−	0.00533483i	0.591451	+	0.806341i	$0.298555\pi$
$140$	−2.91272	−	2.30298i	−0.246169	−	0.194638i
$141$	−9.13825	−	6.63933i	−0.769580	−	0.559132i
$142$	−2.50459	+	0.813792i	−0.210181	+	0.0682919i
$143$			9.10556i			0.761445i
$144$	−0.642352	−	1.97696i	−0.0535293	−	0.164746i
$145$	3.09556	−	3.91513i	0.257072	−	0.325134i
$146$	−1.77211	+	5.45399i	−0.146661	+	0.451375i
$147$	0.951057	+	0.309017i	0.0784418	+	0.0254873i
$148$	−7.36798	−	10.1412i	−0.605645	−	0.833598i
$149$	7.31378			0.599168			0.299584	−	0.954070i	$-0.403152\pi$
$149$	7.31378			0.599168			0.299584	+	0.954070i	$0.403152\pi$
$150$	1.12247	−	2.68803i	0.0916492	−	0.219477i
$151$	7.98773			0.650033			0.325016	−	0.945708i	$-0.394630\pi$
$151$	7.98773			0.650033			0.325016	+	0.945708i	$0.394630\pi$
$152$	−0.878100	−	1.20860i	−0.0712233	−	0.0980305i
$153$	−0.819237	−	0.266186i	−0.0662314	−	0.0215199i
$154$	−0.352616	+	1.08524i	−0.0284146	+	0.0874511i
$155$	0.736917	−	18.0939i	0.0591906	−	1.45334i
$156$	2.38560	+	7.34212i	0.191001	+	0.587840i
$157$		−	22.4087i		−	1.78841i	−0.447657	−	0.894206i	$-0.647741\pi$
$157$		−	22.4087i		−	1.78841i	0.447657	−	0.894206i	$-0.352259\pi$
$158$	−2.78030	+	0.903373i	−0.221188	+	0.0718685i
$159$	−11.0155	−	8.00324i	−0.873587	−	0.634698i
$160$	4.25483	−	11.4825i	0.336374	−	0.907768i
$161$	3.33741	−	2.42477i	0.263025	−	0.191099i
$162$	−0.342442	+	0.471330i	−0.0269047	+	0.0370312i
$163$	−7.53932	+	10.3770i	−0.590525	+	0.812788i	−0.994800	−	0.101849i	$-0.967524\pi$
$163$	−7.53932	+	10.3770i	−0.590525	+	0.812788i	0.404275	+	0.914638i	$0.367524\pi$
$164$	−4.58126	+	3.32848i	−0.357736	+	0.259910i
$165$	4.37599	+	0.178222i	0.340670	+	0.0138746i
$166$	−3.11028	−	2.25975i	−0.241404	−	0.175390i
$167$	−7.53911	+	2.44960i	−0.583394	+	0.189556i	−0.585820	−	0.810441i	$-0.699228\pi$
$167$	−7.53911	+	2.44960i	−0.583394	+	0.189556i	0.00242670	+	0.999997i	$0.499228\pi$
$168$			2.13264i			0.164537i
$169$	−2.66149	−	8.19123i	−0.204730	−	0.630094i
$170$	−0.622101	−	0.933938i	−0.0477130	−	0.0716298i
$171$	0.216466	−	0.666214i	0.0165536	−	0.0509466i
$172$	17.5283	+	5.69528i	1.33652	+	0.434261i
$173$	6.53717	+	8.99764i	0.497012	+	0.684078i	0.981662	−	0.190630i	$-0.0610532\pi$
$173$	6.53717	+	8.99764i	0.497012	+	0.684078i	−0.484650	+	0.874708i	$0.661053\pi$
$174$	−1.30040			−0.0985829
$175$	3.25814	−	3.79270i	0.246292	−	0.286701i
$176$	4.07138			0.306892
$177$	5.96303	+	8.20741i	0.448209	+	0.616907i
$178$	−4.97545	−	1.61662i	−0.372925	−	0.121171i
$179$	−3.63739	+	11.1947i	−0.271871	+	0.836733i	0.718159	+	0.695879i	$0.244985\pi$
$179$	−3.63739	+	11.1947i	−0.271871	+	0.836733i	−0.990030	+	0.140855i	$0.955015\pi$
$180$	3.57521	−	1.00278i	0.266480	−	0.0747425i
$181$	1.99554	+	6.14164i	0.148327	+	0.456504i	0.997424	−	0.0717333i	$-0.0228531\pi$
$181$	1.99554	+	6.14164i	0.148327	+	0.456504i	−0.849097	+	0.528238i	$0.822853\pi$
$182$		−	2.70846i		−	0.200765i
$183$	6.46405	−	2.10030i	0.477837	−	0.155259i
$184$	7.11751	+	5.17117i	0.524710	+	0.381224i
$185$	14.0481	−	9.35750i	1.03284	−	0.687977i
$186$	−3.81709	+	2.77328i	−0.279883	+	0.203347i
$187$	0.991684	−	1.36494i	0.0725191	−	0.0998140i
$188$	11.0251	−	15.1748i	0.804091	−	1.10674i
$189$	−0.809017	+	0.587785i	−0.0588473	+	0.0427551i
$190$	0.759490	−	0.505900i	0.0550992	−	0.0367019i
$191$	12.7872	+	9.29044i	0.925249	+	0.672233i	0.944825	−	0.327576i	$-0.106232\pi$
$191$	12.7872	+	9.29044i	0.925249	+	0.672233i	−0.0195760	+	0.999808i	$0.506232\pi$
$192$	0.919578	−	0.298789i	0.0663649	−	0.0215632i
$193$			18.6218i			1.34043i	0.742167	+	0.670215i	$0.233798\pi$
$193$			18.6218i			1.34043i	−0.742167	+	0.670215i	$0.766202\pi$
$194$	−2.35797	−	7.25710i	−0.169293	−	0.521029i
$195$	−10.0091	+	2.80737i	−0.716768	+	0.201040i
$196$	−0.513148	+	1.57931i	−0.0366534	+	0.112808i
$197$	14.9291	+	4.85075i	1.06365	+	0.345601i	0.788012	−	0.615660i	$-0.211110\pi$
$197$	14.9291	+	4.85075i	1.06365	+	0.345601i	0.275639	+	0.961261i	$0.411110\pi$
$198$	−0.670715	−	0.923160i	−0.0476656	−	0.0656061i
$199$	3.37225			0.239052			0.119526	−	0.992831i	$-0.461862\pi$
$199$	3.37225			0.239052			0.119526	+	0.992831i	$0.461862\pi$
$200$	9.83977	+	4.10889i	0.695777	+	0.290542i
$201$	15.6060			1.10076
$202$	−2.85729	−	3.93272i	−0.201038	−	0.276705i
$203$	−2.12283	−	0.689749i	−0.148993	−	0.0484109i
$204$	0.442024	−	1.36041i	0.0309479	−	0.0952477i
$205$	−4.22724	−	6.34620i	−0.295243	−	0.443238i
$206$	−0.121089	−	0.372673i	−0.00843666	−	0.0259654i
$207$			4.12527i			0.286726i
$208$	−9.19077	+	2.98626i	−0.637265	+	0.207060i
$209$	1.10998	+	0.806450i	0.0767791	+	0.0557833i
$210$	−1.30165	−	0.0530126i	−0.0898221	−	0.00365821i
$211$	10.9041	−	7.92229i	0.750669	−	0.545393i	−0.145365	−	0.989378i	$-0.546436\pi$
$211$	10.9041	−	7.92229i	0.750669	−	0.545393i	0.896034	+	0.443985i	$0.146436\pi$
$212$	13.2900	−	18.2922i	0.912763	−	1.25631i
$213$	2.65694	−	3.65697i	0.182051	−	0.250571i
$214$	0.102658	−	0.0745858i	0.00701759	−	0.00509858i
$215$	−8.62315	+	23.2712i	−0.588094	+	1.58708i
$216$	−1.72534	−	1.25354i	−0.117395	−	0.0852923i
$217$	−7.70218	+	2.50259i	−0.522858	+	0.169887i
$218$			5.86938i			0.397525i
$219$	−3.04174	−	9.36152i	−0.205542	−	0.632593i
$220$	−0.295953	+	7.26669i	−0.0199531	+	0.489920i
$221$	−1.23749	+	3.80860i	−0.0832424	+	0.256194i
$222$	−4.18258	−	1.35900i	−0.280716	−	0.0912102i
$223$	−2.69548	−	3.71000i	−0.180502	−	0.248440i	0.709172	−	0.705035i	$-0.249069\pi$
$223$	−2.69548	−	3.71000i	−0.180502	−	0.248440i	−0.889675	+	0.456595i	$0.849069\pi$
$224$	−5.47632			−0.365902
$225$	1.15327	+	4.86518i	0.0768846	+	0.324345i
$226$	2.78220			0.185069
$227$	0.518638	+	0.713845i	0.0344232	+	0.0473795i	0.825882	−	0.563843i	$-0.190678\pi$
$227$	0.518638	+	0.713845i	0.0344232	+	0.0473795i	−0.791458	+	0.611223i	$0.790678\pi$
$228$	1.10630	+	0.359459i	0.0732667	+	0.0238058i
$229$	3.04318	−	9.36595i	0.201099	−	0.618919i	−0.798752	−	0.601660i	$-0.794506\pi$
$229$	3.04318	−	9.36595i	0.201099	−	0.618919i	0.999851	−	0.0172588i	$-0.00549393\pi$
$230$	−3.33312	+	4.21559i	−0.219780	+	0.277968i
$231$	−0.605249	−	1.86276i	−0.0398224	−	0.122561i
$232$		−	4.76021i		−	0.312523i
$233$	−15.0371	+	4.88586i	−0.985115	+	0.320083i	−0.756902	−	0.653528i	$-0.773288\pi$
$233$	−15.0371	+	4.88586i	−0.985115	+	0.320083i	−0.228213	+	0.973611i	$0.573288\pi$
$234$	2.19119	+	1.59199i	0.143243	+	0.104072i
$235$	19.8127	+	15.6652i	1.29244	+	1.02189i
$236$	−13.6291	+	9.90210i	−0.887177	+	0.644572i
$237$	2.94941	−	4.05952i	0.191585	−	0.263694i
$238$	−0.294978	+	0.406003i	−0.0191206	+	0.0263172i
$239$	−17.0278	+	12.3714i	−1.10144	+	0.800242i	−0.981294	−	0.192515i	$-0.938336\pi$
$239$	−17.0278	+	12.3714i	−1.10144	+	0.800242i	−0.120144	+	0.992756i	$0.538336\pi$
$240$	1.25526	+	4.47539i	0.0810268	+	0.288885i
$241$	−5.93536	−	4.31229i	−0.382330	−	0.277779i	0.379975	−	0.924997i	$-0.375933\pi$
$241$	−5.93536	−	4.31229i	−0.382330	−	0.277779i	−0.762305	+	0.647218i	$0.775933\pi$
$242$	−3.96933	+	1.28971i	−0.255158	+	0.0829058i
$243$		−	1.00000i		−	0.0641500i
$244$	3.48772	+	10.7341i	0.223278	+	0.687180i
$245$	−2.09675	−	0.776951i	−0.133956	−	0.0496376i
$246$	−0.613927	+	1.88947i	−0.0391426	+	0.120468i
$247$	−3.09720	−	1.00634i	−0.197070	−	0.0640319i
$248$	−10.1518	−	13.9728i	−0.644641	−	0.887273i
$249$	6.59893			0.418190
$250$	−2.75243	+	5.90351i	−0.174079	+	0.373371i
$251$	−6.91355			−0.436379			−0.218190	−	0.975906i	$-0.570015\pi$
$251$	−6.91355			−0.436379			−0.218190	+	0.975906i	$0.570015\pi$
$252$	−0.976065	−	1.34344i	−0.0614863	−	0.0846287i
$253$	−7.68440	−	2.49681i	−0.483114	−	0.156973i
$254$	1.15716	−	3.56136i	0.0726064	−	0.223460i
$255$	1.80613	+	0.669263i	0.113104	+	0.0419109i
$256$	−1.47566	−	4.54163i	−0.0922291	−	0.283852i
$257$			28.0847i			1.75187i	0.482427	+	0.875936i	$0.339755\pi$
$257$			28.0847i			1.75187i	−0.482427	+	0.875936i	$0.660245\pi$
$258$	6.14960	−	1.99812i	0.382857	−	0.124398i
$259$	−6.10699	−	4.43699i	−0.379470	−	0.275701i
$260$	−4.66186	−	16.6210i	−0.289116	−	1.03079i
$261$	1.80579	−	1.31198i	0.111775	−	0.0812095i
$262$	−4.55732	+	6.27261i	−0.281552	+	0.387523i
$263$	18.0807	−	24.8860i	1.11490	−	1.53453i	0.300917	−	0.953650i	$-0.402707\pi$
$263$	18.0807	−	24.8860i	1.11490	−	1.53453i	0.813987	−	0.580883i	$-0.197293\pi$
$264$	3.37930	−	2.45521i	0.207982	−	0.151107i
$265$	23.8828	+	18.8833i	1.46711	+	1.15999i
$266$	−0.330166	−	0.239880i	−0.0202438	−	0.0147080i
$267$	8.54012	−	2.77485i	0.522647	−	0.169818i
$268$			25.9150i			1.58301i
$269$	−7.60453	−	23.4043i	−0.463656	−	1.42699i	−0.860665	−	0.509172i	$-0.829952\pi$
$269$	−7.60453	−	23.4043i	−0.463656	−	1.42699i	0.397008	−	0.917815i	$-0.370048\pi$
$270$	0.807976	−	1.02189i	0.0491719	−	0.0621905i
$271$	6.30730	−	19.4119i	0.383141	−	1.17919i	−0.554678	−	0.832065i	$-0.687159\pi$
$271$	6.30730	−	19.4119i	0.383141	−	1.17919i	0.937820	−	0.347123i	$-0.112841\pi$
$272$	1.70294	+	0.553320i	0.103256	+	0.0335499i
$273$	2.73259	+	3.76108i	0.165384	+	0.227631i
$274$	−0.340588			−0.0205757
$275$	−9.76069	−	0.796375i	−0.588592	−	0.0480232i
$276$	−6.85035			−0.412343
$277$	−2.01725	−	2.77651i	−0.121205	−	0.166824i	0.744103	−	0.668065i	$-0.232877\pi$
$277$	−2.01725	−	2.77651i	−0.121205	−	0.166824i	−0.865308	+	0.501241i	$0.832877\pi$
$278$	0.0592902	+	0.0192646i	0.00355599	+	0.00115541i
$279$	2.50259	−	7.70218i	0.149826	−	0.461118i
$280$	0.194057	−	4.76478i	0.0115971	−	0.284750i
$281$	−0.564302	−	1.73674i	−0.0336635	−	0.103605i	0.932813	−	0.360361i	$-0.117346\pi$
$281$	−0.564302	−	1.73674i	−0.0336635	−	0.103605i	−0.966476	+	0.256756i	$0.917346\pi$
$282$		−	6.58072i		−	0.391876i
$283$	20.6456	−	6.70817i	1.22725	−	0.398759i	0.377535	−	0.925995i	$-0.376772\pi$
$283$	20.6456	−	6.70817i	1.22725	−	0.398759i	0.849719	+	0.527236i	$0.176772\pi$
$284$	6.07269	+	4.41207i	0.360348	+	0.261808i
$285$	−0.544253	+	1.46877i	−0.0322388	+	0.0870023i
$286$	−4.29173	+	3.11812i	−0.253775	+	0.184378i
$287$	−2.00441	+	2.75883i	−0.118316	+	0.162848i
$288$	3.21890	−	4.43044i	0.189676	−	0.261066i
$289$	−13.1530	+	9.55621i	−0.773706	+	0.562130i
$290$	2.90537	+	0.118328i	0.170609	+	0.00694846i
$291$	10.5961	+	7.69852i	0.621155	+	0.451296i
$292$	15.5456	−	5.05106i	0.909736	−	0.295591i
$293$		−	0.991459i		−	0.0579217i	−0.999581	−	0.0289608i	$-0.990780\pi$
$293$		−	0.991459i		−	0.0579217i	0.999581	−	0.0289608i	$-0.00921981\pi$
$294$	0.180032	+	0.554082i	0.0104997	+	0.0323147i
$295$	−12.5759	−	18.8797i	−0.732196	−	1.09922i
$296$	4.97474	−	15.3107i	0.289151	−	0.889914i
$297$	1.86276	+	0.605249i	0.108088	+	0.0351201i
$298$	2.50454	+	3.44720i	0.145084	+	0.199691i
$299$	19.1782			1.10910
$300$	−8.07903	+	1.91510i	−0.466443	+	0.110568i
$301$	11.0987			0.639719
$302$	2.73533	+	3.76486i	0.157401	+	0.216643i
$303$	7.93549	+	2.57840i	0.455882	+	0.148125i
$304$	−0.449966	+	1.38485i	−0.0258073	+	0.0794268i
$305$	−14.6332	+	4.10433i	−0.837895	+	0.235013i
$306$	−0.155079	−	0.477285i	−0.00886529	−	0.0272845i
$307$		−	22.0100i		−	1.25618i	−0.778141	−	0.628089i	$-0.783837\pi$
$307$		−	22.0100i		−	1.25618i	0.778141	−	0.628089i	$-0.216163\pi$
$308$	3.09327	−	1.00506i	0.176255	−	0.0572689i
$309$	0.544141	+	0.395342i	0.0309551	+	0.0224902i
$310$	8.78056	−	5.84878i	0.498703	−	0.332188i
$311$	0.362534	−	0.263396i	0.0205574	−	0.0149358i	−0.577459	−	0.816420i	$-0.695956\pi$
$311$	0.362534	−	0.263396i	0.0205574	−	0.0149358i	0.598017	+	0.801484i	$0.295956\pi$
$312$	−5.82763	+	8.02104i	−0.329924	+	0.454102i
$313$	8.82991	−	12.1533i	0.499096	−	0.686947i	−0.482937	−	0.875655i	$-0.660430\pi$
$313$	8.82991	−	12.1533i	0.499096	−	0.686947i	0.982033	+	0.188708i	$0.0604300\pi$
$314$	10.5619	−	7.67368i	0.596043	−	0.433051i
$315$	1.86100	−	1.23962i	0.104856	−	0.0698449i
$316$	6.74116	+	4.89774i	0.379220	+	0.275519i
$317$	−8.67985	+	2.82025i	−0.487509	+	0.158401i	−0.542450	−	0.840088i	$-0.682503\pi$
$317$	−8.67985	+	2.82025i	−0.487509	+	0.158401i	0.0549406	+	0.998490i	$0.482503\pi$
$318$		−	7.93259i		−	0.444838i
$319$	1.35096	+	4.15783i	0.0756392	+	0.232794i
$320$	−2.08172	+	0.583884i	−0.116372	+	0.0326401i
$321$	−0.0673057	+	0.207146i	−0.00375664	+	0.0115617i
$322$	2.28574	+	0.742682i	0.127379	+	0.0413880i
$323$	0.354674	+	0.488167i	0.0197346	+	0.0271623i
$324$	1.66058			0.0922545
$325$	22.6180	−	5.36149i	1.25462	−	0.297402i
$326$	−7.47277			−0.413878
$327$	−5.92166	−	8.15046i	−0.327468	−	0.450721i
$328$	−6.91657	−	2.24733i	−0.381904	−	0.124088i
$329$	3.49050	−	10.7427i	0.192438	−	0.592262i
$330$	1.41452	+	2.12357i	0.0778667	+	0.116899i
$331$	−10.0496	−	30.9296i	−0.552379	−	1.70005i	−0.702767	−	0.711420i	$-0.748053\pi$
$331$	−10.0496	−	30.9296i	−0.552379	−	1.70005i	0.150389	−	0.988627i	$-0.451947\pi$
$332$			10.9581i			0.601402i
$333$	7.17920	−	2.33266i	0.393418	−	0.127829i
$334$	−3.73628	−	2.71456i	−0.204440	−	0.148534i
$335$	−34.8671	−	1.42004i	−1.90499	−	0.0775853i
$336$	1.68170	−	1.22183i	0.0917442	−	0.0666560i
$337$	−1.57225	+	2.16402i	−0.0856462	+	0.117882i	−0.849690	−	0.527282i	$-0.823211\pi$
$337$	−1.57225	+	2.16402i	−0.0856462	+	0.117882i	0.764044	+	0.645164i	$0.223211\pi$
$338$	2.94937	−	4.05946i	0.160425	−	0.220805i
$339$	−3.86348	+	2.80698i	−0.209836	+	0.152454i
$340$	−1.11137	+	2.99923i	−0.0602723	+	0.162656i
$341$	12.8327	+	9.32347i	0.694927	+	0.504894i
$342$	0.388134	−	0.126112i	0.0209879	−	0.00681937i
$343$			1.00000i			0.0539949i
$344$	7.31430	+	22.5111i	0.394361	+	1.21372i
$345$	0.375373	−	9.21675i	0.0202094	−	0.496213i
$346$	−2.00226	+	6.16233i	−0.107642	+	0.331289i
$347$	−19.6911	−	6.39804i	−1.05708	−	0.343465i	−0.271634	−	0.962401i	$-0.587564\pi$
$347$	−19.6911	−	6.39804i	−1.05708	−	0.343465i	−0.785442	+	0.618936i	$0.787564\pi$
$348$	2.17865	+	2.99865i	0.116788	+	0.160745i
$349$	8.87623			0.475133			0.237567	−	0.971371i	$-0.423650\pi$
$349$	8.87623			0.475133			0.237567	+	0.971371i	$0.423650\pi$
$350$	2.90333	+	0.236883i	0.155190	+	0.0126619i
$351$	−4.64895			−0.248143
$352$	6.30462	+	8.67757i	0.336037	+	0.462516i
$353$	1.49911	+	0.487089i	0.0797894	+	0.0259252i	0.348640	−	0.937257i	$-0.386644\pi$
$353$	1.49911	+	0.487089i	0.0797894	+	0.0259252i	−0.268850	+	0.963182i	$0.586644\pi$
$354$	−1.82641	+	5.62112i	−0.0970727	+	0.298759i
$355$	−6.26894	+	7.92869i	−0.332721	+	0.420811i
$356$	4.60787	+	14.1816i	0.244217	+	0.751622i
$357$		−	0.861397i		−	0.0455900i
$358$	−6.52201	+	2.11913i	−0.344699	+	0.111999i
$359$	−29.2704	−	21.2662i	−1.54483	−	1.12239i	−0.947211	−	0.320611i	$-0.896112\pi$
$359$	−29.2704	−	21.2662i	−1.54483	−	1.12239i	−0.597624	−	0.801777i	$-0.703888\pi$
$360$	3.74073	+	2.95766i	0.197154	+	0.155883i
$361$	14.9743	−	10.8795i	0.788123	−	0.572605i
$362$	−2.21138	+	3.04371i	−0.116228	+	0.159974i
$363$	4.21077	−	5.79563i	0.221008	−	0.304191i
$364$	−6.24558	+	4.53768i	−0.327358	+	0.237839i
$365$	5.94407	+	21.1924i	0.311127	+	1.10926i
$366$	3.20349	+	2.32748i	0.167449	+	0.121659i
$367$	4.40697	−	1.43191i	0.230042	−	0.0747452i	−0.191728	−	0.981448i	$-0.561409\pi$
$367$	4.40697	−	1.43191i	0.230042	−	0.0747452i	0.421770	+	0.906703i	$0.361409\pi$
$368$		−	8.57517i		−	0.447012i
$369$	−1.05378	−	3.24320i	−0.0548575	−	0.168834i
$370$	9.22112	+	3.41689i	0.479383	+	0.177636i
$371$	4.20755	−	12.9495i	0.218445	−	0.672305i
$372$	12.7901	+	4.15576i	0.663136	+	0.215466i
$373$	−5.43948	−	7.48680i	−0.281646	−	0.387652i	0.644632	−	0.764493i	$-0.277010\pi$
$373$	−5.43948	−	7.48680i	−0.281646	−	0.387652i	−0.926278	+	0.376841i	$0.877010\pi$
$374$	0.982930			0.0508261
$375$	−2.13395	−	10.9748i	−0.110197	−	0.566736i
$376$	24.0892			1.24231
$377$	−6.09933	−	8.39501i	−0.314132	−	0.432365i
$378$	−0.554082	−	0.180032i	−0.0284989	−	0.00925986i
$379$	0.199339	−	0.613502i	0.0102394	−	0.0315135i	−0.945806	−	0.324731i	$-0.894726\pi$
$379$	0.199339	−	0.613502i	0.0102394	−	0.0315135i	0.956046	+	0.293218i	$0.0947261\pi$
$380$	−2.43901	−	0.903776i	−0.125119	−	0.0463627i
$381$	1.98620	+	6.11291i	0.101756	+	0.313174i
$382$			9.20843i			0.471144i
$383$	34.7507	−	11.2912i	1.77568	−	0.576953i	0.777055	−	0.629432i	$-0.216712\pi$
$383$	34.7507	−	11.2912i	1.77568	−	0.576953i	0.998622	+	0.0524796i	$0.0167125\pi$
$384$	9.31661	+	6.76891i	0.475436	+	0.345425i
$385$	1.18276	+	4.21689i	0.0602788	+	0.214913i
$386$	−8.77704	+	6.37689i	−0.446739	+	0.324575i
$387$	−6.52366	+	8.97904i	−0.331616	+	0.456430i
$388$	−12.7840	+	17.5957i	−0.649011	+	0.893287i
$389$	3.90276	−	2.83552i	0.197878	−	0.143767i	−0.484434	−	0.874828i	$-0.660975\pi$
$389$	3.90276	−	2.83552i	0.197878	−	0.143767i	0.682312	+	0.731061i	$0.260975\pi$
$390$	−4.75074	−	3.75624i	−0.240563	−	0.190205i
$391$	−2.87484	−	2.08869i	−0.145387	−	0.105630i
$392$	−2.02826	+	0.659022i	−0.102443	+	0.0332857i
$393$		−	13.3083i		−	0.671315i
$394$	2.82603	+	8.69762i	0.142373	+	0.438180i
$395$	−6.95901	+	8.80146i	−0.350146	+	0.442850i
$396$	−1.00506	+	3.09327i	−0.0505064	+	0.155443i
$397$	4.63260	+	1.50522i	0.232504	+	0.0755450i	0.422952	−	0.906152i	$-0.360994\pi$
$397$	4.63260	+	1.50522i	0.232504	+	0.0755450i	−0.190448	+	0.981697i	$0.560994\pi$
$398$	1.15480	+	1.58944i	0.0578848	+	0.0796716i
$399$	0.700499			0.0350688
$400$	−2.39729	−	10.1132i	−0.119865	−	0.505661i
$401$	−22.7678			−1.13697			−0.568484	−	0.822694i	$-0.692470\pi$
$401$	−22.7678			−1.13697			−0.568484	+	0.822694i	$0.692470\pi$
$402$	5.34413	+	7.35557i	0.266541	+	0.366862i
$403$	−35.8071	−	11.6344i	−1.78368	−	0.579552i
$404$	−4.28164	+	13.1775i	−0.213019	+	0.655606i
$405$	−0.0909937	+	2.23422i	−0.00452151	+	0.111019i
$406$	−0.401845	−	1.23675i	−0.0199432	−	0.0613790i
$407$			14.7850i			0.732865i
$408$	1.74714	−	0.567680i	0.0864963	−	0.0281043i
$409$	0.125793	+	0.0913937i	0.00622004	+	0.00451913i	0.590891	−	0.806751i	$-0.298776\pi$
$409$	0.125793	+	0.0913937i	0.00622004	+	0.00451913i	−0.584671	+	0.811271i	$0.698776\pi$
$410$	1.54358	−	4.16563i	0.0762318	−	0.205726i
$411$	0.472954	−	0.343621i	0.0233291	−	0.0169496i
$412$	−0.656497	+	0.903591i	−0.0323433	+	0.0445167i
$413$	−5.96303	+	8.20741i	−0.293422	+	0.403860i
$414$	−1.94437	+	1.41266i	−0.0955603	+	0.0694287i
$415$	−14.7434	−	0.600461i	−0.723727	−	0.0294755i
$416$	−20.5969	−	14.9645i	−1.00985	−	0.733696i
$417$	−0.101769	+	0.0330667i	−0.00498365	+	0.00161929i
$418$			0.799331i			0.0390965i
$419$	7.70917	+	23.7264i	0.376618	+	1.15911i	0.942381	+	0.334542i	$0.108582\pi$
$419$	7.70917	+	23.7264i	0.376618	+	1.15911i	−0.565763	+	0.824568i	$0.691418\pi$
$420$	2.05850	+	3.09035i	0.100444	+	0.150794i
$421$	9.64487	−	29.6839i	0.470062	−	1.44670i	−0.382440	−	0.923980i	$-0.624916\pi$
$421$	9.64487	−	29.6839i	0.470062	−	1.44670i	0.852503	−	0.522723i	$-0.175084\pi$
$422$	7.46803	+	2.42651i	0.363538	+	0.118121i
$423$	6.63933	+	9.13825i	0.322815	+	0.444317i
$424$	29.0379			1.41020
$425$	−3.97439	−	1.65962i	−0.192786	−	0.0805036i
$426$	2.63349			0.127593
$427$	3.99500	+	5.49865i	0.193332	+	0.266098i
$428$	−0.343982	−	0.111767i	−0.0166270	−	0.00540244i
$429$	2.81377	−	8.65990i	0.135850	−	0.418104i
$430$	−13.9213	+	3.90467i	−0.671347	+	0.188300i
$431$	−4.62143	−	14.2233i	−0.222606	−	0.685112i	−0.998526	−	0.0542801i	$-0.982714\pi$
$431$	−4.62143	−	14.2233i	−0.222606	−	0.685112i	0.775919	−	0.630832i	$-0.217286\pi$
$432$			2.07869i			0.100011i
$433$	24.2389	−	7.87571i	1.16485	−	0.378483i	0.338131	−	0.941099i	$-0.390205\pi$
$433$	24.2389	−	7.87571i	1.16485	−	0.378483i	0.826718	+	0.562616i	$0.190205\pi$
$434$	−3.81709	−	2.77328i	−0.183226	−	0.133122i
$435$	−4.15390	+	2.76693i	−0.199164	+	0.132664i
$436$	13.5345	−	9.83339i	0.648185	−	0.470934i
$437$	1.69855	−	2.33785i	0.0812527	−	0.111835i
$438$	3.37075	−	4.63944i	0.161061	−	0.221681i
$439$	−22.4627	+	16.3201i	−1.07209	+	0.778916i	−0.976286	−	0.216484i	$-0.930541\pi$
$439$	−22.4627	+	16.3201i	−1.07209	+	0.778916i	−0.0958003	+	0.995401i	$0.530541\pi$
$440$	−7.77350	+	5.17796i	−0.370587	+	0.246850i
$441$	−0.809017	−	0.587785i	−0.0385246	−	0.0279898i
$442$	−2.21887	+	0.720956i	−0.105541	+	0.0342924i
$443$			18.0049i			0.855438i	0.903912	+	0.427719i	$0.140683\pi$
$443$			18.0049i			0.855438i	−0.903912	+	0.427719i	$0.859317\pi$
$444$	3.87358	+	11.9216i	0.183832	+	0.565776i
$445$	−19.3330	+	5.42253i	−0.916471	+	0.257052i
$446$	0.825595	−	2.54092i	0.0390930	−	0.120316i
$447$	−6.95581	−	2.26008i	−0.328999	−	0.106898i
$448$	0.568331	+	0.782240i	0.0268511	+	0.0369574i
$449$	−10.9775			−0.518062			−0.259031	−	0.965869i	$-0.583403\pi$
$449$	−10.9775			−0.518062			−0.259031	+	0.965869i	$0.583403\pi$
$450$	−1.89818	+	2.20961i	−0.0894810	+	0.104162i
$451$	6.67910			0.314507
$452$	−4.66123	−	6.41563i	−0.219246	−	0.301766i
$453$	−7.59679	−	2.46835i	−0.356928	−	0.115973i
$454$	−0.158853	+	0.488900i	−0.00745535	+	0.0229452i
$455$	−5.76295	−	8.65172i	−0.270171	−	0.405599i
$456$	0.461644	+	1.42080i	0.0216185	+	0.0665348i
$457$			18.1377i			0.848446i	0.905558	+	0.424223i	$0.139453\pi$
$457$			18.1377i			0.848446i	−0.905558	+	0.424223i	$0.860547\pi$
$458$	5.45657	−	1.77295i	0.254969	−	0.0828443i
$459$	0.696885	+	0.506316i	0.0325278	+	0.0236328i
$460$	15.3052	+	0.623338i	0.713607	+	0.0290633i
$461$	−11.8499	+	8.60948i	−0.551906	+	0.400983i	−0.828488	−	0.560007i	$-0.810798\pi$
$461$	−11.8499	+	8.60948i	−0.551906	+	0.400983i	0.276582	+	0.960990i	$0.410798\pi$
$462$	0.670715	−	0.923160i	0.0312045	−	0.0429493i
$463$	−6.82400	+	9.39243i	−0.317138	+	0.436503i	−0.937591	−	0.347741i	$-0.886949\pi$
$463$	−6.82400	+	9.39243i	−0.317138	+	0.436503i	0.620453	+	0.784244i	$0.286949\pi$
$464$	−3.75368	+	2.72720i	−0.174260	+	0.126607i
$465$	−6.29218	+	16.9806i	−0.291793	+	0.787457i
$466$	−7.45219	−	5.41434i	−0.345216	−	0.250814i
$467$	7.95546	−	2.58488i	0.368135	−	0.119614i	−0.119107	−	0.992881i	$-0.538003\pi$
$467$	7.95546	−	2.58488i	0.368135	−	0.119614i	0.487242	+	0.873267i	$0.338003\pi$
$468$		−	7.71997i		−	0.356856i
$469$	4.82251	+	14.8422i	0.222683	+	0.685347i
$470$	−0.598803	+	14.7027i	−0.0276207	+	0.678187i
$471$	−6.92468	+	21.3120i	−0.319072	+	0.982004i
$472$	−20.5766	−	6.68573i	−0.947113	−	0.307736i
$473$	−12.7774	−	17.5866i	−0.587505	−	0.808632i
$474$	2.92338			0.134275
$475$	1.34963	−	3.23202i	0.0619251	−	0.148295i
$476$	1.43042			0.0655632
$477$	8.00324	+	11.0155i	0.366443	+	0.504366i
$478$	−11.6621	−	3.78923i	−0.533410	−	0.173316i
$479$	2.07185	−	6.37650i	0.0946652	−	0.291350i	−0.892501	−	0.451045i	$-0.851051\pi$
$479$	2.07185	−	6.37650i	0.0946652	−	0.291350i	0.987166	+	0.159696i	$0.0510513\pi$
$480$	−7.59486	+	9.60565i	−0.346656	+	0.438436i
$481$	−10.8444	−	33.3758i	−0.494464	−	1.52180i
$482$		−	4.27422i		−	0.194686i
$483$	−3.92337	+	1.27478i	−0.178519	+	0.0580044i
$484$	9.62411	+	6.99232i	0.437459	+	0.317833i
$485$	−22.9735	−	18.1643i	−1.04317	−	0.824800i
$486$	0.471330	−	0.342442i	0.0213800	−	0.0155335i
$487$	5.98428	−	8.23665i	0.271173	−	0.373238i	−0.651612	−	0.758552i	$-0.725907\pi$
$487$	5.98428	−	8.23665i	0.271173	−	0.373238i	0.922785	+	0.385314i	$0.125907\pi$
$488$	−8.51991	+	11.7267i	−0.385678	+	0.530841i
$489$	10.3770	−	7.53932i	0.469264	−	0.340940i
$490$	−0.351813	−	1.25432i	−0.0158933	−	0.0566644i
$491$	14.9561	+	10.8662i	0.674959	+	0.490386i	0.871681	−	0.490073i	$-0.163030\pi$
$491$	14.9561	+	10.8662i	0.674959	+	0.490386i	−0.196723	+	0.980459i	$0.563030\pi$
$492$	5.38559	−	1.74988i	0.242801	−	0.0788909i
$493$			1.92270i			0.0865941i
$494$	−0.586290	−	1.80442i	−0.0263784	−	0.0811845i
$495$	−4.10674	−	1.52176i	−0.184584	−	0.0683978i
$496$	−5.20212	+	16.0105i	−0.233582	+	0.718892i
$497$	4.29902	+	1.39684i	0.192838	+	0.0626567i
$498$	2.25975	+	3.11028i	0.101262	+	0.139375i
$499$	8.68503			0.388795			0.194398	−	0.980923i	$-0.437725\pi$
$499$	8.68503			0.388795			0.194398	+	0.980923i	$0.437725\pi$
$500$	18.2246	−	3.54360i	0.815027	−	0.158475i
$501$	7.92709			0.354156
$502$	−2.36749	−	3.25856i	−0.105666	−	0.145437i
$503$	−39.3793	−	12.7951i	−1.75584	−	0.570506i	−0.759083	−	0.650994i	$-0.774352\pi$
$503$	−39.3793	−	12.7951i	−1.75584	−	0.570506i	−0.996756	+	0.0804878i	$0.974352\pi$
$504$	0.659022	−	2.02826i	0.0293552	−	0.0903460i
$505$	−17.4950	−	6.48277i	−0.778516	−	0.288480i
$506$	−1.45463	−	4.47691i	−0.0646664	−	0.199023i
$507$			8.61277i			0.382506i
$508$	−10.1510	+	3.29826i	−0.450377	+	0.146336i
$509$	−23.0834	−	16.7711i	−1.02315	−	0.743365i	−0.0562273	−	0.998418i	$-0.517907\pi$
$509$	−23.0834	−	16.7711i	−1.02315	−	0.743365i	−0.966927	+	0.255053i	$0.917907\pi$
$510$	0.303050	+	1.08047i	0.0134193	+	0.0478439i
$511$	7.96339	−	5.78574i	0.352280	−	0.255946i
$512$	−11.9025	+	16.3824i	−0.526023	+	0.724009i
$513$	−0.411743	+	0.566715i	−0.0181789	+	0.0250211i
$514$	−13.2371	+	9.61735i	−0.583866	+	0.424203i
$515$	−1.17976	−	0.932792i	−0.0519862	−	0.0411037i
$516$	−14.9104	−	10.8331i	−0.656395	−	0.476899i
$517$	−21.0408	+	6.83658i	−0.925375	+	0.300673i
$518$		−	4.39782i		−	0.193229i
$519$	−3.43679	−	10.5774i	−0.150858	−	0.464294i
$520$	13.7500	−	17.3905i	0.602979	−	0.762622i
$521$	−6.96232	+	21.4278i	−0.305025	+	0.938770i	0.674643	+	0.738144i	$0.264297\pi$
$521$	−6.96232	+	21.4278i	−0.305025	+	0.938770i	−0.979668	+	0.200626i	$0.935703\pi$
$522$	1.23675	+	0.401845i	0.0541312	+	0.0175883i
$523$	2.44983	+	3.37190i	0.107124	+	0.147443i	0.859213	−	0.511618i	$-0.170954\pi$
$523$	2.44983	+	3.37190i	0.107124	+	0.147443i	−0.752089	+	0.659061i	$0.770954\pi$
$524$	22.0995			0.965422
$525$	−4.27068	+	2.60025i	−0.186388	+	0.113484i
$526$	17.9211			0.781397
$527$	4.10043	+	5.64376i	0.178618	+	0.245846i
$528$	−3.87211	−	1.25813i	−0.168512	−	0.0547529i
$529$	1.84858	−	5.68935i	0.0803732	−	0.247363i
$530$	−0.721815	+	17.7231i	−0.0313537	+	0.769843i
$531$	−3.13495	−	9.64839i	−0.136045	−	0.418704i
$532$			1.16324i			0.0504326i
$533$	−15.0775	+	4.89897i	−0.653077	+	0.212198i
$534$	4.23237	+	3.07499i	0.183152	+	0.133068i
$535$	0.169224	−	0.456684i	0.00731621	−	0.0197442i
$536$	−26.9257	+	19.5626i	−1.16301	+	0.844977i
$537$	6.91872	−	9.52281i	0.298565	−	0.410939i
$538$	8.42707	−	11.5989i	0.363317	−	0.500062i
$539$	1.58456	−	1.15125i	0.0682519	−	0.0495879i
$540$	−3.71010	−	0.151102i	−0.159657	−	0.00650241i
$541$	29.9699	+	21.7744i	1.28851	+	0.936156i	0.999774	−	0.0212538i	$-0.00676579\pi$
$541$	29.9699	+	21.7744i	1.28851	+	0.936156i	0.288734	+	0.957409i	$0.406766\pi$
$542$	11.3093	−	3.67461i	0.485776	−	0.157838i
$543$		−	6.45770i		−	0.277126i
$544$	1.45772	+	4.48641i	0.0624993	+	0.192353i
$545$	12.4886	+	18.7487i	0.534954	+	0.803107i
$546$	−0.836961	+	2.57590i	−0.0358186	+	0.110238i
$547$	−36.5479	−	11.8751i	−1.56268	−	0.507744i	−0.605155	−	0.796108i	$-0.706889\pi$
$547$	−36.5479	−	11.8751i	−1.56268	−	0.507744i	−0.957521	+	0.288364i	$0.906889\pi$
$548$	0.570611	+	0.785379i	0.0243753	+	0.0335497i
$549$	−6.79671			−0.290076
$550$	−2.96711	−	4.87322i	−0.126518	−	0.207795i
$551$	−1.56356			−0.0666101
$552$	−5.17117	−	7.11751i	−0.220100	−	0.302941i
$553$	4.77225	+	1.55060i	0.202937	+	0.0659381i
$554$	0.617862	−	1.90158i	0.0262504	−	0.0807906i
$555$	−16.2521	+	4.55841i	−0.689865	+	0.193494i
$556$	−0.0549100	−	0.168996i	−0.00232870	−	0.00716701i
$557$		−	3.09829i		−	0.131279i	−0.997843	−	0.0656393i	$-0.979091\pi$
$557$		−	3.09829i		−	0.131279i	0.997843	−	0.0656393i	$-0.0209087\pi$
$558$	4.48726	−	1.45800i	0.189961	−	0.0617221i
$559$	41.7432	+	30.3282i	1.76555	+	1.28275i
$560$	−3.86846	+	2.57680i	−0.163472	+	0.108890i
$561$	−1.36494	+	0.991684i	−0.0576276	+	0.0418689i
$562$	0.625340	−	0.860706i	0.0263784	−	0.0363067i
$563$	16.9013	−	23.2627i	0.712306	−	0.980406i	−0.287438	−	0.957799i	$-0.592804\pi$
$563$	16.9013	−	23.2627i	0.712306	−	0.980406i	0.999744	−	0.0226065i	$-0.00719647\pi$
$564$	−15.1748	+	11.0251i	−0.638975	+	0.464242i
$565$	8.88727	−	5.91986i	0.373890	−	0.249050i
$566$	10.2317	+	7.43375i	0.430070	+	0.312464i
$567$	0.951057	−	0.309017i	0.0399406	−	0.0129775i
$568$			9.64009i			0.404489i
$569$	3.35973	+	10.3402i	0.140847	+	0.433483i	0.996454	−	0.0841440i	$-0.0268156\pi$
$569$	3.35973	+	10.3402i	0.140847	+	0.433483i	−0.855607	+	0.517627i	$0.826816\pi$
$570$	−0.878650	+	0.246444i	−0.0368026	+	0.0103224i
$571$	2.71865	−	8.36714i	0.113772	−	0.350154i	−0.877917	−	0.478813i	$-0.841067\pi$
$571$	2.71865	−	8.36714i	0.113772	−	0.350154i	0.991689	+	0.128659i	$0.0410673\pi$
$572$	14.3805	+	4.67250i	0.601278	+	0.195367i
$573$	−9.29044	−	12.7872i	−0.388114	−	0.534193i
$574$	−1.98671			−0.0829237
$575$	−1.67733	+	20.5580i	−0.0699495	+	0.857330i
$576$	−0.966902			−0.0402876
$577$	−2.60336	−	3.58321i	−0.108379	−	0.149171i	0.751382	−	0.659868i	$-0.229388\pi$
$577$	−2.60336	−	3.58321i	−0.108379	−	0.149171i	−0.859761	+	0.510696i	$0.829388\pi$
$578$	−9.00826	−	2.92696i	−0.374694	−	0.121746i
$579$	5.75446	−	17.7104i	0.239147	−	0.736020i
$580$	−4.59472	−	6.89788i	−0.190785	−	0.286419i
$581$	2.03918	+	6.27596i	0.0845995	+	0.260371i
$582$			7.63056i			0.316297i
$583$	−25.3632	+	8.24102i	−1.05044	+	0.341308i
$584$	16.9831	+	12.3389i	0.702764	+	0.510588i
$585$	10.3868	+	0.423025i	0.429440	+	0.0174899i
$586$	0.467305	−	0.339517i	0.0193042	−	0.0140253i
$587$	−5.44240	+	7.49082i	−0.224632	+	0.309179i	−0.906426	−	0.422365i	$-0.861200\pi$
$587$	−5.44240	+	7.49082i	−0.224632	+	0.309179i	0.681794	+	0.731544i	$0.261200\pi$
$588$	0.976065	−	1.34344i	0.0402523	−	0.0554025i
$589$	−4.58957	+	3.33452i	−0.189110	+	0.137397i
$590$	4.59208	−	12.3926i	0.189053	−	0.510195i
$591$	−12.6994	−	9.22667i	−0.522384	−	0.379534i
$592$	−14.9234	+	4.84889i	−0.613346	+	0.199288i
$593$			29.3272i			1.20432i	0.798374	+	0.602162i	$0.205694\pi$
$593$			29.3272i			1.20432i	−0.798374	+	0.602162i	$0.794306\pi$
$594$	0.352616	+	1.08524i	0.0144680	+	0.0445279i
$595$	−0.0783816	+	1.92455i	−0.00321333	+	0.0788987i
$596$	3.75305	−	11.5507i	0.153731	−	0.473135i
$597$	−3.20720	−	1.04208i	−0.131262	−	0.0426496i
$598$	6.56741	+	9.03926i	0.268561	+	0.369643i
$599$	32.3360			1.32122			0.660608	−	0.750731i	$-0.270299\pi$
$599$	32.3360			1.32122			0.660608	+	0.750731i	$0.270299\pi$
$600$	−8.08846	−	6.94844i	−0.330210	−	0.283669i
$601$	−39.7187			−1.62016			−0.810080	−	0.586319i	$-0.800577\pi$
$601$	−39.7187			−1.62016			−0.810080	+	0.586319i	$0.800577\pi$
$602$	3.80066	+	5.23116i	0.154903	+	0.213206i
$603$	−14.8422	−	4.82251i	−0.604420	−	0.196388i
$604$	4.09889	−	12.6151i	0.166781	−	0.513300i
$605$	−9.93513	+	12.5655i	−0.403920	+	0.510861i
$606$	1.50216	+	4.62319i	0.0610213	+	0.187804i
$607$			32.4413i			1.31675i	0.752688	+	0.658377i	$0.228757\pi$
$607$			32.4413i			1.31675i	−0.752688	+	0.658377i	$0.771243\pi$
$608$	−3.64840	+	1.18544i	−0.147962	+	0.0480758i
$609$	1.80579	+	1.31198i	0.0731741	+	0.0531641i
$610$	−6.94551	−	5.49158i	−0.281216	−	0.222348i
$611$	42.4833	−	30.8659i	1.71869	−	1.24870i
$612$	−0.840780	+	1.15723i	−0.0339865	+	0.0467784i
$613$	4.03289	−	5.55080i	0.162887	−	0.224195i	−0.719770	−	0.694213i	$-0.755753\pi$
$613$	4.03289	−	5.55080i	0.162887	−	0.224195i	0.882657	+	0.470018i	$0.155753\pi$
$614$	10.3740	−	7.53715i	0.418660	−	0.304175i
$615$	2.05926	+	7.34189i	0.0830373	+	0.296053i
$616$	3.37930	+	2.45521i	0.136156	+	0.0989231i
$617$	−8.31947	+	2.70316i	−0.334929	+	0.108825i	−0.471653	−	0.881784i	$-0.656343\pi$
$617$	−8.31947	+	2.70316i	−0.334929	+	0.108825i	0.136724	+	0.990609i	$0.456343\pi$
$618$			0.391852i			0.0157626i
$619$	5.27267	+	16.2276i	0.211927	+	0.652243i	0.999358	+	0.0358401i	$0.0114107\pi$
$619$	5.27267	+	16.2276i	0.211927	+	0.652243i	−0.787431	+	0.616403i	$0.788589\pi$
$620$	−28.1977	−	10.4487i	−1.13245	−	0.419629i
$621$	1.27478	−	3.92337i	0.0511551	−	0.157439i
$622$	0.248293	+	0.0806753i	0.00995565	+	0.00323479i
$623$	5.27809	+	7.26466i	0.211462	+	0.291053i
$624$	9.66375			0.386860
$625$	3.76907	+	24.7142i	0.150763	+	0.988570i
$626$	8.75196			0.349799
$627$	−0.806450	−	1.10998i	−0.0322065	−	0.0443284i
$628$	−35.3903	−	11.4990i	−1.41222	−	0.458860i
$629$	−2.00935	+	6.18414i	−0.0801180	+	0.246578i
$630$	1.22156	+	0.452649i	0.0486680	+	0.0180340i
$631$	4.88048	+	15.0206i	0.194289	+	0.597959i	0.999984	+	0.00562924i	$0.00179185\pi$
$631$	4.88048	+	15.0206i	0.194289	+	0.597959i	−0.805695	+	0.592330i	$0.798208\pi$
$632$			10.7013i			0.425673i
$633$	−12.8185	+	4.16499i	−0.509491	+	0.165544i
$634$	−4.30161	−	3.12531i	−0.170839	−	0.124122i
$635$	−3.88137	−	13.8383i	−0.154028	−	0.549156i
$636$	−18.2922	+	13.2900i	−0.725331	+	0.526984i
$637$	−2.73259	+	3.76108i	−0.108269	+	0.149020i
$638$	−1.49708	+	2.06056i	−0.0592702	+	0.0815784i
$639$	−3.65697	+	2.65694i	−0.144667	+	0.105107i
$640$	−20.1994	−	15.9710i	−0.798451	−	0.631308i
$641$	−6.88585	−	5.00286i	−0.271975	−	0.197601i	0.443435	−	0.896307i	$-0.353760\pi$
$641$	−6.88585	−	5.00286i	−0.271975	−	0.197601i	−0.715409	+	0.698705i	$0.753760\pi$
$642$	−0.120682	+	0.0392121i	−0.00476295	+	0.00154758i
$643$		−	32.8760i		−	1.29650i	−0.761426	−	0.648252i	$-0.775500\pi$
$643$		−	32.8760i		−	1.29650i	0.761426	−	0.648252i	$-0.224500\pi$
$644$	−2.11687	−	6.51507i	−0.0834165	−	0.256730i
$645$	15.3923	−	19.4675i	0.606071	−	0.766532i
$646$	−0.108633	+	0.334337i	−0.00427410	+	0.0131543i
$647$	18.1443	+	5.89543i	0.713324	+	0.231773i	0.643126	−	0.765760i	$-0.277637\pi$
$647$	18.1443	+	5.89543i	0.713324	+	0.231773i	0.0701978	+	0.997533i	$0.477637\pi$
$648$	1.25354	+	1.72534i	0.0492435	+	0.0677779i
$649$	19.8701			0.779969
$650$	10.2724	+	8.82455i	0.402916	+	0.346127i
$651$	8.09855			0.317407
$652$	12.5197	+	17.2318i	0.490308	+	0.674851i
$653$	0.516042	+	0.167672i	0.0201943	+	0.00656152i	0.319097	−	0.947722i	$-0.396621\pi$
$653$	0.516042	+	0.167672i	0.0201943	+	0.00656152i	−0.298902	+	0.954284i	$0.596621\pi$
$654$	1.81374	−	5.58211i	0.0709228	−	0.218278i
$655$	−1.21097	+	29.7336i	−0.0473166	+	1.16179i
$656$	2.19048	+	6.74161i	0.0855239	+	0.263216i
$657$			9.84329i			0.384023i
$658$	6.25863	−	2.03355i	0.243987	−	0.0792762i
$659$	−0.0203216	−	0.0147645i	−0.000791616	−	0.000575143i	0.587389	−	0.809304i	$-0.300156\pi$
$659$	−0.0203216	−	0.0147645i	−0.000791616	−	0.000575143i	−0.588181	+	0.808729i	$0.700156\pi$
$660$	2.52700	−	6.81958i	0.0983633	−	0.265452i
$661$	26.1899	−	19.0281i	1.01867	−	0.740105i	0.0526584	−	0.998613i	$-0.483231\pi$
$661$	26.1899	−	19.0281i	1.01867	−	0.740105i	0.966009	+	0.258507i	$0.0832306\pi$
$662$	11.1367	−	15.3283i	0.432839	−	0.595751i
$663$	2.35384	−	3.23978i	0.0914156	−	0.125823i
$664$	−11.3854	+	8.27199i	−0.441840	+	0.321016i
$665$	−1.56507	−	0.0637409i	−0.0606906	−	0.00247177i
$666$	3.55791	+	2.58497i	0.137866	+	0.100166i
$667$	8.75724	−	2.84540i	0.339082	−	0.110174i
$668$			13.1636i			0.509314i
$669$	1.41710	+	4.36137i	0.0547881	+	0.168620i
$670$	−11.2706	−	16.9202i	−0.435423	−	0.653685i
$671$	4.11370	−	12.6607i	0.158808	−	0.488759i
$672$	5.20829	+	1.69228i	0.200914	+	0.0652810i
$673$	19.6773	+	27.0835i	0.758504	+	1.04399i	0.997337	+	0.0729307i	$0.0232352\pi$
$673$	19.6773	+	27.0835i	0.758504	+	1.04399i	−0.238833	+	0.971061i	$0.576765\pi$
$674$	−1.55837			−0.0600264
$675$	0.406599	−	4.98344i	0.0156500	−	0.191813i
$676$	−14.3022			−0.550085
$677$	−11.4560	−	15.7679i	−0.440291	−	0.606008i	0.529986	−	0.848006i	$-0.322197\pi$
$677$	−11.4560	−	15.7679i	−0.440291	−	0.606008i	−0.970277	+	0.241998i	$0.922197\pi$
$678$	−2.64603	−	0.859748i	−0.101620	−	0.0330184i
$679$	−4.04735	+	12.4565i	−0.155323	+	0.478036i
$680$	−3.95514	+	1.10934i	−0.151673	+	0.0425413i
$681$	−0.272664	−	0.839175i	−0.0104485	−	0.0321572i
$682$			9.24116i			0.353862i
$683$	31.1602	−	10.1246i	1.19231	−	0.387405i	0.355384	−	0.934720i	$-0.384350\pi$
$683$	31.1602	−	10.1246i	1.19231	−	0.387405i	0.836927	+	0.547315i	$0.184350\pi$
$684$	−0.941077	−	0.683732i	−0.0359830	−	0.0261432i
$685$	−1.08795	+	0.724688i	−0.0415684	+	0.0276889i
$686$	−0.471330	+	0.342442i	−0.0179955	+	0.0130745i
$687$	−5.78847	+	7.96715i	−0.220844	+	0.303966i
$688$	13.5607	−	18.6647i	0.516996	−	0.711584i
$689$	51.2106	−	37.2067i	1.95097	−	1.41746i
$690$	4.47268	−	2.97927i	0.170272	−	0.113419i
$691$	−24.7186	−	17.9591i	−0.940341	−	0.683198i	0.00816190	−	0.999967i	$-0.497402\pi$
$691$	−24.7186	−	17.9591i	−0.940341	−	0.683198i	−0.948503	+	0.316769i	$0.897402\pi$
$692$	17.5646	−	5.70707i	0.667705	−	0.216950i
$693$			1.95863i			0.0744020i
$694$	−3.72747	−	11.4720i	−0.141493	−	0.435471i
$695$	0.230383	−	0.0646179i	0.00873892	−	0.00245110i
$696$	−1.47099	+	4.52723i	−0.0557576	+	0.171604i
$697$	2.79368	+	0.907721i	0.105818	+	0.0343824i
$698$	3.03959	+	4.18363i	0.115050	+	0.158353i
$699$	15.8110			0.598026
$700$	−4.31792	−	7.09181i	−0.163202	−	0.268045i
$701$	28.8105			1.08816			0.544078	−	0.839034i	$-0.316879\pi$
$701$	28.8105			1.08816			0.544078	+	0.839034i	$0.316879\pi$
$702$	−1.59199	−	2.19119i	−0.0600860	−	0.0827012i
$703$	−5.02902	−	1.63403i	−0.189673	−	0.0616285i
$704$	0.585216	−	1.80111i	0.0220562	−	0.0678819i
$705$	−14.0022	−	21.0210i	−0.527352	−	0.791695i
$706$	0.283776	+	0.873374i	0.0106801	+	0.0328699i
$707$			8.34387i			0.313803i
$708$	16.0219	−	5.20584i	0.602141	−	0.195648i
$709$	−28.9966	−	21.0672i	−1.08899	−	0.791197i	−0.109761	−	0.993958i	$-0.535009\pi$
$709$	−28.9966	−	21.0672i	−1.08899	−	0.791197i	−0.979228	+	0.202761i	$0.935009\pi$
$710$	−5.88378	−	0.239631i	−0.220814	−	0.00899318i
$711$	−4.05952	+	2.94941i	−0.152244	+	0.110612i
$712$	−11.2563	+	15.4929i	−0.421846	+	0.580622i
$713$	19.6372	−	27.0282i	0.735417	−	1.01222i
$714$	0.406003	−	0.294978i	0.0151943	−	0.0110393i
$715$	−7.07457	+	19.0920i	−0.264574	+	0.714002i
$716$	15.8134	+	11.4891i	0.590974	+	0.429368i
$717$	20.0174	−	6.50405i	0.747563	−	0.242898i
$718$		−	21.0785i		−	0.786642i
$719$	11.4549	+	35.2546i	0.427196	+	1.31477i	0.900876	+	0.434077i	$0.142925\pi$
$719$	11.4549	+	35.2546i	0.427196	+	1.31477i	−0.473680	+	0.880697i	$0.657075\pi$
$720$	0.189148	−	4.64425i	0.00704913	−	0.173081i
$721$	−0.207843	+	0.639676i	−0.00774049	+	0.0238228i
$722$	10.2557	+	3.33227i	0.381677	+	0.124014i
$723$	4.31229	+	5.93536i	0.160376	+	0.220738i
$724$	10.7235			0.398537
$725$	9.53248	−	5.80394i	0.354027	−	0.215553i
$726$	4.17360			0.154897
$727$	−3.43295	−	4.72505i	−0.127321	−	0.175242i	0.740597	−	0.671949i	$-0.234543\pi$
$727$	−3.43295	−	4.72505i	−0.127321	−	0.175242i	−0.867919	+	0.496706i	$0.834543\pi$
$728$	−9.42930	−	3.06376i	−0.349473	−	0.113551i
$729$	−0.309017	+	0.951057i	−0.0114451	+	0.0352243i
$730$	−7.95315	+	10.0588i	−0.294359	+	0.372293i
$731$	−2.95432	−	9.09247i	−0.109270	−	0.336297i
$732$		−	11.2865i		−	0.417161i
$733$	−31.4910	+	10.2320i	−1.16315	+	0.377929i	−0.826080	−	0.563552i	$-0.809434\pi$
$733$	−31.4910	+	10.2320i	−1.16315	+	0.377929i	−0.337065	+	0.941481i	$0.609434\pi$
$734$	2.18403	+	1.58679i	0.0806141	+	0.0585696i
$735$	1.75403	+	1.38685i	0.0646985	+	0.0511549i
$736$	18.2768	−	13.2788i	0.673690	−	0.489465i
$737$	17.9664	−	24.7286i	0.661801	−	0.910890i
$738$	1.16776	−	1.60728i	0.0429858	−	0.0591649i
$739$	10.5302	−	7.65066i	0.387361	−	0.281434i	−0.377012	−	0.926208i	$-0.623049\pi$
$739$	10.5302	−	7.65066i	0.387361	−	0.281434i	0.764373	+	0.644774i	$0.223049\pi$
$740$	−7.56962	−	26.9880i	−0.278265	−	0.992099i
$741$	2.63463	+	1.91417i	0.0967857	+	0.0703189i
$742$	7.54434	−	2.45130i	0.276961	−	0.0899902i
$743$			29.3143i			1.07544i	0.843124	+	0.537718i	$0.180714\pi$
$743$			29.3143i			1.07544i	−0.843124	+	0.537718i	$0.819286\pi$
$744$	5.33713	+	16.4260i	0.195669	+	0.602206i
$745$	15.3351	+	5.68244i	0.561836	+	0.208189i
$746$	1.66605	−	5.12759i	0.0609986	−	0.187734i
$747$	−6.27596	−	2.03918i	−0.229625	−	0.0746098i
$748$	−1.64677	−	2.26659i	−0.0602120	−	0.0828746i
$749$	−0.217806			−0.00795845
$750$	4.44200	−	4.76402i	0.162199	−	0.173958i
$751$	−31.4682			−1.14829			−0.574146	−	0.818753i	$-0.694666\pi$
$751$	−31.4682			−1.14829			−0.574146	+	0.818753i	$0.694666\pi$
$752$	−13.8011	−	18.9956i	−0.503275	−	0.692699i
$753$	6.57517	+	2.13640i	0.239613	+	0.0778549i
$754$	1.86816	−	5.74960i	0.0680343	−	0.209388i
$755$	16.7483	+	6.20608i	0.609531	+	0.225862i
$756$	0.513148	+	1.57931i	0.0186630	+	0.0574388i
$757$		−	29.2266i		−	1.06226i	−0.847291	−	0.531129i	$-0.821768\pi$
$757$		−	29.2266i		−	1.06226i	0.847291	−	0.531129i	$-0.178232\pi$
$758$	0.357424	−	0.116134i	0.0129822	−	0.00421818i
$759$	6.53674	+	4.74922i	0.237269	+	0.172386i
$760$	−0.902130	−	3.21637i	−0.0327237	−	0.116670i
$761$	32.2345	−	23.4197i	1.16850	−	0.848964i	0.177670	−	0.984090i	$-0.443144\pi$
$761$	32.2345	−	23.4197i	1.16850	−	0.848964i	0.990828	+	0.135127i	$0.0431441\pi$
$762$	−2.20104	+	3.02947i	−0.0797353	+	0.109746i
$763$	5.92166	−	8.15046i	0.214378	−	0.295066i
$764$	21.2342	−	15.4275i	0.768226	−	0.558149i
$765$	−1.51092	−	1.19463i	−0.0546274	−	0.0431920i
$766$	17.2220	+	12.5125i	0.622255	+	0.452094i
$767$	−44.8549	+	14.5742i	−1.61962	+	0.526245i
$768$			4.77535i			0.172316i
$769$	13.3024	+	40.9407i	0.479698	+	1.47636i	0.839515	+	0.543337i	$0.182839\pi$
$769$	13.3024	+	40.9407i	0.479698	+	1.47636i	−0.359816	+	0.933023i	$0.617161\pi$
$770$	−1.58252	+	2.00151i	−0.0570302	+	0.0721293i
$771$	8.67864	−	26.7101i	0.312553	−	0.961940i
$772$	29.4096	+	9.55576i	1.05847	+	0.343919i
$773$	3.58325	+	4.93192i	0.128881	+	0.177389i	0.868581	−	0.495548i	$-0.165033\pi$
$773$	3.58325	+	4.93192i	0.128881	+	0.177389i	−0.739700	+	0.672937i	$0.765033\pi$
$774$	−6.46607			−0.232418
$775$	15.6032	−	37.3658i	0.560484	−	1.34222i
$776$	−27.9323			−1.00271
$777$	4.43699	+	6.10699i	0.159176	+	0.219087i
$778$	2.67293	+	0.868489i	0.0958293	+	0.0311368i
$779$	−0.738170	+	2.27185i	−0.0264477	+	0.0813976i
$780$	−0.702468	+	17.2481i	−0.0251524	+	0.617580i
$781$	−2.73588	−	8.42017i	−0.0978975	−	0.301298i
$782$		−	2.07025i		−	0.0740321i
$783$	−2.12283	+	0.689749i	−0.0758637	+	0.0246496i
$784$	1.68170	+	1.22183i	0.0600607	+	0.0436366i
$785$	17.4105	−	46.9854i	0.621407	−	1.67698i
$786$	6.27261	−	4.55732i	0.223737	−	0.162554i
$787$	−1.90046	+	2.61576i	−0.0677442	+	0.0932419i	−0.841545	−	0.540188i	$-0.818353\pi$
$787$	−1.90046	+	2.61576i	−0.0677442	+	0.0932419i	0.773800	+	0.633429i	$0.218353\pi$
$788$	15.3216	−	21.0884i	0.545811	−	0.751244i
$789$	−24.8860	+	18.0807i	−0.885963	+	0.643690i
$790$	−6.53145	−	0.266009i	−0.232379	−	0.00946416i
$791$	−3.86348	−	2.80698i	−0.137370	−	0.0998049i
$792$	−3.97261	+	1.29078i	−0.141160	+	0.0458658i
$793$			31.5976i			1.12206i
$794$	0.876938	+	2.69894i	0.0311214	+	0.0957817i
$795$	−16.8786	−	25.3393i	−0.598623	−	0.898692i
$796$	1.73046	−	5.32582i	0.0613346	−	0.188769i
$797$	−37.1469	−	12.0698i	−1.31581	−	0.427533i	−0.434756	−	0.900548i	$-0.643165\pi$
$797$	−37.1469	−	12.0698i	−1.31581	−	0.427533i	−0.881054	+	0.473016i	$0.843165\pi$
$798$	0.239880	+	0.330166i	0.00849165	+	0.0116878i
$799$	−9.72991			−0.344219
$800$	17.8426	−	20.7700i	0.630832	−	0.734331i
$801$	−8.97962			−0.317279
$802$	−7.79663	−	10.7311i	−0.275309	−	0.378930i
$803$	−18.3357	−	5.95764i	−0.647053	−	0.210240i
$804$	8.00817	−	24.6466i	0.282426	−	0.869219i
$805$	8.88164	−	2.49113i	0.313037	−	0.0878008i
$806$	−6.77818	−	20.8611i	−0.238751	−	0.734800i
$807$			24.6088i			0.866270i
$808$	−16.9236	+	5.49880i	−0.595368	+	0.193447i
$809$	−40.0594	−	29.1049i	−1.40841	−	1.02327i	−0.993551	−	0.113390i	$-0.963829\pi$
$809$	−40.0594	−	29.1049i	−1.40841	−	1.02327i	−0.414864	−	0.909883i	$-0.636171\pi$
$810$	−1.08421	+	0.722200i	−0.0380954	+	0.0253755i
$811$	4.80904	−	3.49397i	0.168868	−	0.122690i	−0.500141	−	0.865944i	$-0.666719\pi$
$811$	4.80904	−	3.49397i	0.168868	−	0.122690i	0.669009	+	0.743254i	$0.266719\pi$
$812$	−2.17865	+	2.99865i	−0.0764556	+	0.105232i
$813$	−11.9972	+	16.5127i	−0.420760	+	0.579127i
$814$	−6.96862	+	5.06300i	−0.244250	+	0.177458i
$815$	−23.8705	+	15.9002i	−0.836146	+	0.556961i
$816$	−1.44861	−	1.05248i	−0.0507115	−	0.0368441i
$817$	7.39411	−	2.40249i	0.258687	−	0.0840526i
$818$			0.0905869i			0.00316730i
$819$	−1.43661	−	4.42142i	−0.0501991	−	0.154497i
$820$	−12.1918	+	3.41956i	−0.425756	+	0.119416i
$821$	16.8496	−	51.8578i	0.588056	−	1.80985i	0.00141950	−	0.999999i	$-0.499548\pi$
$821$	16.8496	−	51.8578i	0.588056	−	1.80985i	0.586636	−	0.809851i	$-0.300452\pi$
$822$	0.323918	+	0.105247i	0.0112979	+	0.00367093i
$823$	−13.5716	−	18.6798i	−0.473078	−	0.651136i	0.504079	−	0.863658i	$-0.331832\pi$
$823$	−13.5716	−	18.6798i	−0.473078	−	0.651136i	−0.977156	+	0.212522i	$0.931832\pi$
$824$	−1.43440			−0.0499699
$825$	9.03688	+	3.77362i	0.314624	+	0.131380i
$826$	−5.91039			−0.205649
$827$	27.5361	+	37.9002i	0.957525	+	1.31792i	0.948102	+	0.317965i	$0.103000\pi$
$827$	27.5361	+	37.9002i	0.957525	+	1.31792i	0.00942310	+	0.999956i	$0.497000\pi$
$828$	6.51507	+	2.11687i	0.226414	+	0.0735665i
$829$	9.61933	−	29.6052i	0.334093	−	1.02823i	−0.633074	−	0.774091i	$-0.718207\pi$
$829$	9.61933	−	29.6052i	0.334093	−	1.02823i	0.967167	−	0.254141i	$-0.0817928\pi$
$830$	−4.76575	−	7.15465i	−0.165422	−	0.248342i
$831$	1.06053	+	3.26398i	0.0367895	+	0.113226i
$832$			4.49508i			0.155839i
$833$	0.819237	−	0.266186i	0.0283849	−	0.00922281i
$834$	−0.0504353	−	0.0366434i	−0.00174643	−	0.00126886i
$835$	−17.7108	−	0.721314i	−0.612908	−	0.0249621i
$836$	1.84322	−	1.33918i	0.0637490	−	0.0463164i
$837$	−4.76021	+	6.55187i	−0.164537	+	0.226466i
$838$	−8.54303	+	11.7585i	−0.295114	+	0.406190i
$839$	29.8038	−	21.6537i	1.02894	−	0.747570i	0.0608450	−	0.998147i	$-0.480620\pi$
$839$	29.8038	−	21.6537i	1.02894	−	0.747570i	0.968097	+	0.250577i	$0.0806205\pi$
$840$	−1.65696	+	4.47161i	−0.0571705	+	0.154285i
$841$	19.4308	+	14.1173i	0.670029	+	0.486805i
$842$	17.2937	−	5.61907i	0.595981	−	0.193646i
$843$			1.82612i			0.0628950i
$844$	−6.91631	−	21.2862i	−0.238069	−	0.732702i
$845$	0.783707	−	19.2428i	0.0269603	−	0.661972i
$846$	−2.03355	+	6.25863i	−0.0699150	+	0.215176i
$847$	6.81317	+	2.21373i	0.234103	+	0.0760647i
$848$	−16.6363	−	22.8979i	−0.571292	−	0.786317i
$849$	−21.7081			−0.745019
$850$	−0.578764	−	2.44157i	−0.0198515	−	0.0837453i
$851$	31.1403			1.06747
$852$	−4.41207	−	6.07269i	−0.151155	−	0.208047i
$853$	17.5519	+	5.70294i	0.600964	+	0.195265i	0.593670	−	0.804708i	$-0.297678\pi$
$853$	17.5519	+	5.70294i	0.600964	+	0.195265i	0.00729369	+	0.999973i	$0.497678\pi$
$854$	−1.22363	+	3.76593i	−0.0418716	+	0.128868i
$855$	0.971490	−	1.22870i	0.0332242	−	0.0420206i
$856$	−0.143539	−	0.441767i	−0.00490606	−	0.0150993i
$857$			34.6813i			1.18469i	0.805684	+	0.592345i	$0.201798\pi$
$857$			34.6813i			1.18469i	−0.805684	+	0.592345i	$0.798202\pi$
$858$	5.04523	−	1.63929i	0.172241	−	0.0559646i
$859$	3.03825	+	2.20741i	0.103664	+	0.0753160i	0.638409	−	0.769697i	$-0.279593\pi$
$859$	3.03825	+	2.20741i	0.103664	+	0.0753160i	−0.534746	+	0.845013i	$0.679593\pi$
$860$	32.3274	+	25.5602i	1.10235	+	0.871594i
$861$	2.75883	−	2.00441i	0.0940206	−	0.0683099i
$862$	5.12130	−	7.04887i	0.174432	−	0.240085i
$863$	13.5589	−	18.6622i	0.461550	−	0.635269i	−0.513279	−	0.858222i	$-0.671570\pi$
$863$	13.5589	−	18.6622i	0.461550	−	0.635269i	0.974829	+	0.222953i	$0.0715696\pi$
$864$	−4.43044	+	3.21890i	−0.150727	+	0.109509i
$865$	6.71606	+	23.9448i	0.228353	+	0.814148i
$866$	12.0125	+	8.72758i	0.408201	+	0.296575i
$867$	15.4623	−	5.02400i	0.525126	−	0.170624i
$868$			13.4483i			0.456465i
$869$	−3.03704	−	9.34705i	−0.103025	−	0.317077i
$870$	−2.72661	−	1.01035i	−0.0924406	−	0.0342539i
$871$	−22.4196	+	69.0005i	−0.759660	+	2.33799i
$872$	20.4338	+	6.63934i	0.691975	+	0.224836i
$873$	−7.69852	−	10.5961i	−0.260556	−	0.358624i
$874$	1.68356			0.0569471
$875$	9.77823	−	5.42091i	0.330564	−	0.183260i
$876$	−16.3456			−0.552266
$877$	29.4786	+	40.5738i	0.995421	+	1.37008i	0.928093	+	0.372349i	$0.121447\pi$
$877$	29.4786	+	40.5738i	0.995421	+	1.37008i	0.0673283	+	0.997731i	$0.478553\pi$
$878$	−15.3843	−	4.99867i	−0.519196	−	0.168697i
$879$	−0.306378	+	0.942934i	−0.0103339	+	0.0318044i
$880$	8.53666	+	3.16326i	0.287771	+	0.106634i
$881$	2.88710	+	8.88557i	0.0972687	+	0.299362i	0.987838	−	0.155485i	$-0.0496939\pi$
$881$	2.88710	+	8.88557i	0.0972687	+	0.299362i	−0.890570	+	0.454847i	$0.849694\pi$
$882$		−	0.582596i		−	0.0196170i
$883$	20.0266	−	6.50705i	0.673950	−	0.218980i	0.0480055	−	0.998847i	$-0.484714\pi$
$883$	20.0266	−	6.50705i	0.673950	−	0.218980i	0.625945	+	0.779867i	$0.284714\pi$
$884$	5.37993	+	3.90875i	0.180946	+	0.131465i
$885$	6.12622	+	21.8418i	0.205930	+	0.734205i
$886$	−8.48625	+	6.16562i	−0.285101	+	0.207138i
$887$	−14.0679	+	19.3628i	−0.472353	+	0.650138i	−0.977013	−	0.213180i	$-0.931618\pi$
$887$	−14.0679	+	19.3628i	−0.472353	+	0.650138i	0.504660	+	0.863318i	$0.331618\pi$
$888$	−9.46251	+	13.0240i	−0.317541	+	0.437058i
$889$	−5.19995	+	3.77799i	−0.174401	+	0.126710i
$890$	−9.17622	−	7.25532i	−0.307587	−	0.243199i
$891$	−1.58456	−	1.15125i	−0.0530848	−	0.0385684i
$892$	−7.24241	+	2.35320i	−0.242494	+	0.0787911i
$893$		−	7.91248i		−	0.264781i
$894$	−1.31671	−	4.05243i	−0.0440375	−	0.135534i
$895$	−16.3244	+	20.6464i	−0.545666	+	0.690135i
$896$	−3.55863	+	10.9523i	−0.118885	+	0.365892i
$897$	−18.2395	−	5.92639i	−0.609001	−	0.197876i
$898$	−3.75917	−	5.17405i	−0.125445	−	0.172660i
$899$	−18.0766			−0.602887
$900$	8.27541	+	0.675191i	0.275847	+	0.0225064i
$901$	−11.7287			−0.390740
$902$	2.28720	+	3.14806i	0.0761555	+	0.104819i
$903$	−10.5555	−	3.42969i	−0.351265	−	0.114133i
$904$	3.14718	−	9.68602i	0.104674	−	0.322152i
$905$	−0.587610	+	14.4279i	−0.0195328	+	0.479599i
$906$	−1.43805	−	4.42586i	−0.0477760	−	0.147039i
$907$		−	50.2597i		−	1.66884i	−0.551126	−	0.834422i	$-0.685801\pi$
$907$		−	50.2597i		−	1.66884i	0.551126	−	0.834422i	$-0.314199\pi$
$908$	1.39352	−	0.452781i	0.0462455	−	0.0150261i
$909$	−6.75033	−	4.90440i	−0.223894	−	0.162669i
$910$	2.10434	−	5.67896i	0.0697583	−	0.188256i
$911$	26.1369	−	18.9896i	0.865955	−	0.629153i	−0.0635436	−	0.997979i	$-0.520240\pi$
$911$	26.1369	−	18.9896i	0.865955	−	0.629153i	0.929498	+	0.368826i	$0.120240\pi$
$912$	0.855887	−	1.17803i	0.0283413	−	0.0390084i
$913$	7.59703	−	10.4564i	0.251425	−	0.346057i
$914$	−8.54885	+	6.21110i	−0.282771	+	0.205445i
$915$	15.1853	+	0.618457i	0.502011	+	0.0204456i
$916$	−13.2301	−	9.61223i	−0.437135	−	0.317597i
$917$	12.6569	−	4.11249i	0.417969	−	0.135806i
$918$			0.501847i			0.0165634i
$919$	−7.59848	−	23.3857i	−0.250651	−	0.771424i	−0.994656	−	0.103249i	$-0.967076\pi$
$919$	−7.59848	−	23.3857i	−0.250651	−	0.771424i	0.744005	−	0.668174i	$-0.232924\pi$
$920$	10.9059	+	16.3726i	0.359556	+	0.539788i
$921$	−6.80147	+	20.9328i	−0.224116	+	0.689759i
$922$	−8.11582	−	2.63699i	−0.267280	−	0.0868446i
$923$	12.3520	+	17.0011i	0.406571	+	0.559597i
$924$	−3.25246			−0.106998
$925$	36.7256	−	8.70564i	1.20753	−	0.286240i
$926$	−6.76376			−0.222271
$927$	−0.395342	−	0.544141i	−0.0129847	−	0.0178719i
$928$	−11.6253	−	3.77729i	−0.381619	−	0.123996i
$929$	−2.89926	+	8.92299i	−0.0951215	+	0.292754i	−0.987285	−	0.158958i	$-0.949187\pi$
$929$	−2.89926	+	8.92299i	−0.0951215	+	0.292754i	0.892164	+	0.451712i	$0.149187\pi$
$930$	−10.1582	+	2.84918i	−0.333100	+	0.0934281i
$931$	0.216466	+	0.666214i	0.00709439	+	0.0218343i
$932$			26.2554i			0.860025i
$933$	−0.426184	+	0.138476i	−0.0139526	+	0.00453349i
$934$	3.94261	+	2.86448i	0.129006	+	0.0937285i
$935$	3.13980	−	2.09144i	0.102682	−	0.0683973i
$936$	8.02104	−	5.82763i	0.262176	−	0.190482i
$937$	−8.46003	+	11.6442i	−0.276377	+	0.380400i	−0.924530	−	0.381110i	$-0.875542\pi$
$937$	−8.46003	+	11.6442i	−0.276377	+	0.380400i	0.648153	+	0.761510i	$0.275542\pi$
$938$	−5.34413	+	7.35557i	−0.174492	+	0.240168i
$939$	−12.1533	+	8.82991i	−0.396609	+	0.288153i
$940$	34.9070	−	23.2517i	1.13854	−	0.758388i
$941$	−3.60007	−	2.61560i	−0.117359	−	0.0852662i	0.527558	−	0.849519i	$-0.323108\pi$
$941$	−3.60007	−	2.61560i	−0.117359	−	0.0852662i	−0.644917	+	0.764253i	$0.723108\pi$
$942$	−12.4163	+	4.03429i	−0.404544	+	0.131444i
$943$		−	14.0676i		−	0.458103i
$944$	6.51660	+	20.0560i	0.212097	+	0.652769i
$945$	−2.15298	+	0.603871i	−0.0700366	+	0.0196439i
$946$	3.91358	−	12.0448i	0.127241	−	0.391609i
$947$	−37.1496	−	12.0706i	−1.20720	−	0.392243i	−0.364795	−	0.931088i	$-0.618861\pi$
$947$	−37.1496	−	12.0706i	−1.20720	−	0.392243i	−0.842405	+	0.538845i	$0.818861\pi$
$948$	−4.89774	−	6.74116i	−0.159071	−	0.218943i
$949$	45.7610			1.48546
$950$	1.98552	−	0.470658i	0.0644187	−	0.0152702i
$951$	9.12654			0.295948
$952$	1.07979	+	1.48621i	0.0349962	+	0.0481682i
$953$	11.7004	+	3.80169i	0.379013	+	0.123149i	0.492327	−	0.870410i	$-0.336147\pi$
$953$	11.7004	+	3.80169i	0.379013	+	0.123149i	−0.113314	+	0.993559i	$0.536147\pi$
$954$	−2.45130	+	7.54434i	−0.0793639	+	0.244257i
$955$	19.5933	+	29.4147i	0.634024	+	0.951838i
$956$	10.8005	+	33.2405i	0.349313	+	1.07508i
$957$		−	4.37180i		−	0.141320i
$958$	3.71492	−	1.20705i	0.120024	−	0.0389981i
$959$	0.472954	+	0.343621i	0.0152725	+	0.0110961i
$960$	2.16027	+	0.0879819i	0.0697223	+	0.00283960i
$961$	−27.9811	+	20.3295i	−0.902617	+	0.655790i
$962$	12.0174	−	16.5406i	0.387457	−	0.533289i
$963$	0.128023	−	0.176209i	0.00412548	−	0.00567824i
$964$	−9.85615	+	7.16091i	−0.317445	+	0.230637i
$965$	−14.4682	+	39.0453i	−0.465749	+	1.25691i
$966$	−1.94437	−	1.41266i	−0.0625589	−	0.0454517i
$967$	−9.55802	+	3.10559i	−0.307365	+	0.0998690i	−0.458638	−	0.888623i	$-0.651663\pi$
$967$	−9.55802	+	3.10559i	−0.307365	+	0.0998690i	0.151273	+	0.988492i	$0.451663\pi$
$968$			15.2778i			0.491047i
$969$	−0.186463	−	0.573874i	−0.00599006	−	0.0184355i
$970$	0.694333	−	17.0483i	0.0222937	−	0.547389i
$971$	−4.23882	+	13.0458i	−0.136030	+	0.418658i	−0.995749	−	0.0921099i	$-0.970639\pi$
$971$	−4.23882	+	13.0458i	−0.136030	+	0.418658i	0.859719	+	0.510768i	$0.170639\pi$
$972$	−1.57931	−	0.513148i	−0.0506563	−	0.0164592i
$973$	−0.0628967	−	0.0865699i	−0.00201638	−	0.00277530i
$974$	5.93145			0.190056
$975$	−23.1678	−	1.89026i	−0.741963	−	0.0605367i
$976$	14.1283			0.452235
$977$	−32.8495	−	45.2135i	−1.05095	−	1.44651i	−0.887983	−	0.459877i	$-0.847894\pi$
$977$	−32.8495	−	45.2135i	−1.05095	−	1.44651i	−0.162967	−	0.986632i	$-0.552106\pi$
$978$	7.10702	+	2.30921i	0.227258	+	0.0738405i
$979$	5.43490	−	16.7269i	0.173700	−	0.534594i
$980$	−2.30298	+	2.91272i	−0.0735662	+	0.0930433i
$981$	3.11320	+	9.58144i	0.0993968	+	0.305912i
$982$			10.7703i			0.343694i
$983$	29.1251	−	9.46332i	0.928946	−	0.301833i	0.194815	−	0.980840i	$-0.437589\pi$
$983$	29.1251	−	9.46332i	0.928946	−	0.301833i	0.734132	+	0.679007i	$0.237589\pi$
$984$	5.88359	+	4.27468i	0.187562	+	0.136272i
$985$	27.5337	+	21.7699i	0.877296	+	0.693648i
$986$	−0.906228	+	0.658413i	−0.0288602	+	0.0209681i
$987$	−6.63933	+	9.13825i	−0.211332	+	0.290874i
$988$	−3.17864	+	4.37502i	−0.101126	+	0.139188i
$989$	−37.0410	+	26.9119i	−1.17783	+	0.855747i
$990$	−0.689069	−	2.45674i	−0.0219001	−	0.0780805i
$991$	−39.7467	−	28.8777i	−1.26260	−	0.917329i	−0.263713	−	0.964601i	$-0.584947\pi$
$991$	−39.7467	−	28.8777i	−1.26260	−	0.917329i	−0.998882	+	0.0472719i	$0.984947\pi$
$992$	−42.1796	+	13.7050i	−1.33920	+	0.435134i
$993$			32.5213i			1.03203i
$994$	0.813792	+	2.50459i	0.0258119	+	0.0794409i
$995$	7.07075	+	2.62007i	0.224158	+	0.0830619i
$996$	3.38623	−	10.4217i	0.107297	−	0.330225i
$997$	−54.8732	−	17.8294i	−1.73785	−	0.564662i	−0.743304	−	0.668954i	$-0.766742\pi$
$997$	−54.8732	−	17.8294i	−1.73785	−	0.564662i	−0.994547	+	0.104292i	$0.966742\pi$
$998$	2.97412	+	4.09352i	0.0941440	+	0.129578i
$999$	−7.54866			−0.238829

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	525.2.z.a.64.9	✓	56
25.9	even	10	inner	525.2.z.a.484.9	yes	56

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
525.2.z.a.64.9	✓	56	1.1	even	1	trivial
525.2.z.a.484.9	yes	56	25.9	even	10	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:	\( N \)	\(=\)	\( 525 = 3 \cdot 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	525.z (of order \(10\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.342442 + 0.471330i) q^{2} +(-0.951057 - 0.309017i) q^{3} +(0.513148 - 1.57931i) q^{4} +(2.09675 + 0.776951i) q^{5} +(-0.180032 - 0.554082i) q^{6} -1.00000i q^{7} +(2.02826 - 0.659022i) q^{8} +(0.809017 + 0.587785i) q^{9} +O(q^{10})\)	\(q+(0.342442 + 0.471330i) q^{2} +(-0.951057 - 0.309017i) q^{3} +(0.513148 - 1.57931i) q^{4} +(2.09675 + 0.776951i) q^{5} +(-0.180032 - 0.554082i) q^{6} -1.00000i q^{7} +(2.02826 - 0.659022i) q^{8} +(0.809017 + 0.587785i) q^{9} +(0.351813 + 1.25432i) q^{10} +(-1.58456 + 1.15125i) q^{11} +(-0.976065 + 1.34344i) q^{12} +(2.73259 - 3.76108i) q^{13} +(0.471330 - 0.342442i) q^{14} +(-1.75403 - 1.38685i) q^{15} +(-1.68170 - 1.22183i) q^{16} +(-0.819237 + 0.266186i) q^{17} +0.582596i q^{18} +(-0.216466 - 0.666214i) q^{19} +(2.30298 - 2.91272i) q^{20} +(-0.309017 + 0.951057i) q^{21} +(-1.08524 - 0.352616i) q^{22} +(2.42477 + 3.33741i) q^{23} -2.13264 q^{24} +(3.79270 + 3.25814i) q^{25} +2.70846 q^{26} +(-0.587785 - 0.809017i) q^{27} +(-1.57931 - 0.513148i) q^{28} +(0.689749 - 2.12283i) q^{29} +(0.0530126 - 1.30165i) q^{30} +(-2.50259 - 7.70218i) q^{31} -5.47632i q^{32} +(1.86276 - 0.605249i) q^{33} +(-0.406003 - 0.294978i) q^{34} +(0.776951 - 2.09675i) q^{35} +(1.34344 - 0.976065i) q^{36} +(4.43699 - 6.10699i) q^{37} +(0.239880 - 0.330166i) q^{38} +(-3.76108 + 2.73259i) q^{39} +(4.76478 + 0.194057i) q^{40} +(-2.75883 - 2.00441i) q^{41} +(-0.554082 + 0.180032i) q^{42} +11.0987i q^{43} +(1.00506 + 3.09327i) q^{44} +(1.23962 + 1.86100i) q^{45} +(-0.742682 + 2.28574i) q^{46} +(10.7427 + 3.49050i) q^{47} +(1.22183 + 1.68170i) q^{48} -1.00000 q^{49} +(-0.236883 + 2.90333i) q^{50} +0.861397 q^{51} +(-4.53768 - 6.24558i) q^{52} +(12.9495 + 4.20755i) q^{53} +(0.180032 - 0.554082i) q^{54} +(-4.21689 + 1.18276i) q^{55} +(-0.659022 - 2.02826i) q^{56} +0.700499i q^{57} +(1.23675 - 0.401845i) q^{58} +(-8.20741 - 5.96303i) q^{59} +(-3.09035 + 2.05850i) q^{60} +(-5.49865 + 3.99500i) q^{61} +(2.77328 - 3.81709i) q^{62} +(0.587785 - 0.809017i) q^{63} +(-0.782240 + 0.568331i) q^{64} +(8.65172 - 5.76295i) q^{65} +(0.923160 + 0.670715i) q^{66} +(-14.8422 + 4.82251i) q^{67} +1.43042i q^{68} +(-1.27478 - 3.92337i) q^{69} +(1.25432 - 0.351813i) q^{70} +(-1.39684 + 4.29902i) q^{71} +(2.02826 + 0.659022i) q^{72} +(5.78574 + 7.96339i) q^{73} +4.39782 q^{74} +(-2.60025 - 4.27068i) q^{75} -1.16324 q^{76} +(1.15125 + 1.58456i) q^{77} +(-2.57590 - 0.836961i) q^{78} +(-1.55060 + 4.77225i) q^{79} +(-2.57680 - 3.86846i) q^{80} +(0.309017 + 0.951057i) q^{81} -1.98671i q^{82} +(-6.27596 + 2.03918i) q^{83} +(1.34344 + 0.976065i) q^{84} +(-1.92455 - 0.0783816i) q^{85} +(-5.23116 + 3.80066i) q^{86} +(-1.31198 + 1.80579i) q^{87} +(-2.45521 + 3.37930i) q^{88} +(-7.26466 + 5.27809i) q^{89} +(-0.452649 + 1.22156i) q^{90} +(-3.76108 - 2.73259i) q^{91} +(6.51507 - 2.11687i) q^{92} +8.09855i q^{93} +(2.03355 + 6.25863i) q^{94} +(0.0637409 - 1.56507i) q^{95} +(-1.69228 + 5.20829i) q^{96} +(-12.4565 - 4.04735i) q^{97} +(-0.342442 - 0.471330i) q^{98} -1.95863 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 56 q + 12 q^{4} - 2 q^{5} + 14 q^{9}+O(q^{10}) \) 56 * q + 12 * q^4 - 2 * q^5 + 14 * q^9	\( 56 q + 12 q^{4} - 2 q^{5} + 14 q^{9} + 36 q^{10} + 12 q^{11} + 20 q^{13} - 4 q^{15} + 4 q^{16} - 22 q^{19} - 22 q^{20} + 14 q^{21} + 30 q^{22} - 10 q^{23} + 16 q^{25} - 60 q^{26} - 20 q^{28} - 18 q^{29} - 18 q^{30} + 16 q^{31} - 10 q^{33} + 6 q^{35} - 12 q^{36} + 10 q^{37} + 100 q^{38} - 22 q^{40} + 8 q^{41} - 66 q^{44} + 2 q^{45} + 40 q^{46} - 100 q^{47} - 56 q^{49} + 62 q^{50} + 32 q^{51} + 80 q^{52} - 30 q^{53} - 58 q^{55} - 40 q^{58} - 20 q^{59} + 66 q^{60} + 28 q^{61} - 50 q^{62} - 12 q^{64} + 78 q^{65} - 20 q^{67} + 4 q^{69} - 18 q^{70} + 40 q^{71} - 20 q^{73} + 100 q^{74} - 8 q^{75} - 164 q^{76} + 20 q^{77} - 90 q^{78} - 4 q^{79} - 158 q^{80} - 14 q^{81} + 30 q^{83} - 12 q^{84} + 46 q^{85} + 80 q^{86} - 40 q^{87} + 130 q^{88} - 38 q^{89} + 4 q^{90} - 100 q^{92} - 10 q^{94} + 8 q^{95} + 10 q^{96} - 130 q^{97} + 48 q^{99}+O(q^{100}) \) 56 * q + 12 * q^4 - 2 * q^5 + 14 * q^9 + 36 * q^10 + 12 * q^11 + 20 * q^13 - 4 * q^15 + 4 * q^16 - 22 * q^19 - 22 * q^20 + 14 * q^21 + 30 * q^22 - 10 * q^23 + 16 * q^25 - 60 * q^26 - 20 * q^28 - 18 * q^29 - 18 * q^30 + 16 * q^31 - 10 * q^33 + 6 * q^35 - 12 * q^36 + 10 * q^37 + 100 * q^38 - 22 * q^40 + 8 * q^41 - 66 * q^44 + 2 * q^45 + 40 * q^46 - 100 * q^47 - 56 * q^49 + 62 * q^50 + 32 * q^51 + 80 * q^52 - 30 * q^53 - 58 * q^55 - 40 * q^58 - 20 * q^59 + 66 * q^60 + 28 * q^61 - 50 * q^62 - 12 * q^64 + 78 * q^65 - 20 * q^67 + 4 * q^69 - 18 * q^70 + 40 * q^71 - 20 * q^73 + 100 * q^74 - 8 * q^75 - 164 * q^76 + 20 * q^77 - 90 * q^78 - 4 * q^79 - 158 * q^80 - 14 * q^81 + 30 * q^83 - 12 * q^84 + 46 * q^85 + 80 * q^86 - 40 * q^87 + 130 * q^88 - 38 * q^89 + 4 * q^90 - 100 * q^92 - 10 * q^94 + 8 * q^95 + 10 * q^96 - 130 * q^97 + 48 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more