LMFDB - Embedded newform 507.2.p.a.142.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [507,2,Mod(25,507)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(507, base_ring=CyclotomicField(26))

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

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

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

chi := DirichletCharacter("507.25");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 507 = 3 \cdot 13^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	507.p (of order $26$, degree $12$, 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:	$4.04841538248$
Analytic rank:	$0$
Dimension:	$168$
Relative dimension:	$14$ over $\Q(\zeta_{26})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{26}]$

Embedding invariants

Embedding label			142.8
Character	$\chi$	$=$	507.142
Dual form			507.2.p.a.25.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.00155211 - 0.000588639i) q^{2} +(0.568065 - 0.822984i) q^{3} +(-1.49702 + 1.32624i) q^{4} +(-0.897149 + 0.108934i) q^{5} +(0.000397260 - 0.00161175i) q^{6} +(-0.178306 + 0.339734i) q^{7} +(-0.00308573 + 0.00587937i) q^{8} +(-0.354605 - 0.935016i) q^{9} +(-0.00132835 + 0.000697174i) q^{10} +(-2.55908 - 0.970532i) q^{11} +(0.241073 + 1.98542i) q^{12} +(-3.58442 + 0.389780i) q^{13} +(-7.67707e-5 + 0.000632264i) q^{14} +(-0.419988 + 0.800220i) q^{15} +(0.482145 - 3.97082i) q^{16} +(-2.71636 - 1.42566i) q^{17} +(-0.00110077 - 0.00124252i) q^{18} +3.07285i q^{19} +(1.19858 - 1.35291i) q^{20} +(0.178306 + 0.339734i) q^{21} -0.00454328 q^{22} -2.75837 q^{23} +(0.00308573 + 0.00587937i) q^{24} +(-4.06170 + 1.00112i) q^{25} +(-0.00533399 + 0.00271491i) q^{26} +(-0.970942 - 0.239316i) q^{27} +(-0.183642 - 0.745066i) q^{28} +(-1.05871 - 2.79159i) q^{29} +(-0.000180828 + 0.00148925i) q^{30} +(-0.339201 + 1.37619i) q^{31} +(-0.00476712 - 0.0193409i) q^{32} +(-2.25246 + 1.55476i) q^{33} +(-0.00505529 - 0.000613824i) q^{34} +(0.122959 - 0.324216i) q^{35} +(1.77091 + 0.929445i) q^{36} +(0.0955204 - 0.387541i) q^{37} +(0.00180880 + 0.00476940i) q^{38} +(-1.71540 + 3.17134i) q^{39} +(0.00212790 - 0.00561081i) q^{40} +(-3.16600 - 2.18533i) q^{41} +(0.000476732 + 0.000422348i) q^{42} +(-8.01523 + 1.97558i) q^{43} +(5.11816 - 1.94106i) q^{44} +(0.419988 + 0.800220i) q^{45} +(-0.00428131 + 0.00162369i) q^{46} +(0.816367 - 0.921488i) q^{47} +(-2.99403 - 2.65248i) q^{48} +(3.89283 + 5.63973i) q^{49} +(-0.00571492 + 0.00394472i) q^{50} +(-2.71636 + 1.42566i) q^{51} +(4.84900 - 5.33732i) q^{52} +(6.40169 + 3.35987i) q^{53} +(-0.00164788 + 0.000200089i) q^{54} +(2.40160 + 0.591941i) q^{55} +(-0.00144722 - 0.00209666i) q^{56} +(2.52890 + 1.74558i) q^{57} +(-0.00328647 - 0.00370966i) q^{58} +(10.5595 - 1.28215i) q^{59} +(-0.432557 - 1.75495i) q^{60} +(-5.01265 + 2.63084i) q^{61} +(0.000283602 + 0.00233567i) q^{62} +(0.380885 + 0.0462478i) q^{63} +(4.54448 + 6.58382i) q^{64} +(3.17330 - 0.740154i) q^{65} +(-0.00258087 + 0.00373904i) q^{66} +(-1.83946 + 2.07632i) q^{67} +(5.95721 - 1.46832i) q^{68} +(-1.56693 + 2.27010i) q^{69} -0.000575597i q^{70} +(-5.39926 - 3.72684i) q^{71} +(0.00659152 + 0.000800356i) q^{72} +(8.45785 + 3.20764i) q^{73} +(-7.98635e-5 - 0.000657735i) q^{74} +(-1.48340 + 3.91141i) q^{75} +(-4.07534 - 4.60011i) q^{76} +(0.786023 - 0.696356i) q^{77} +(-0.000795721 + 0.00593203i) q^{78} +(-6.75856 - 5.98756i) q^{79} +3.61494i q^{80} +(-0.748511 + 0.663123i) q^{81} +(-0.00620036 - 0.00152825i) q^{82} +(9.78106 - 6.75138i) q^{83} +(-0.717498 - 0.272111i) q^{84} +(2.59228 + 0.983122i) q^{85} +(-0.0112776 + 0.00778439i) q^{86} +(-2.89885 - 0.714501i) q^{87} +(0.0136028 - 0.0120510i) q^{88} -9.44142i q^{89} +(0.00112291 + 0.000994811i) q^{90} +(0.506703 - 1.28725i) q^{91} +(4.12934 - 3.65827i) q^{92} +(0.939896 + 1.06092i) q^{93} +(0.000724670 - 0.00191080i) q^{94} +(-0.334736 - 2.75680i) q^{95} +(-0.0186253 - 0.00706365i) q^{96} +(-3.72809 - 0.452672i) q^{97} +(0.00936187 + 0.00646203i) q^{98} +2.73694i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 168 q - 14 q^{3} + 12 q^{4} - 14 q^{9} - 4 q^{10} + 12 q^{12} + 13 q^{13} + 2 q^{14} - 8 q^{16} - 4 q^{17} - 72 q^{22} + 48 q^{23} - 44 q^{25} - 39 q^{26} - 14 q^{27} + 45 q^{29} - 4 q^{30} - 26 q^{31}+ \cdots - 104 q^{98}+O(q^{100}) $ 168 * q - 14 * q^3 + 12 * q^4 - 14 * q^9 - 4 * q^10 + 12 * q^12 + 13 * q^13 + 2 * q^14 - 8 * q^16 - 4 * q^17 - 72 * q^22 + 48 * q^23 - 44 * q^25 - 39 * q^26 - 14 * q^27 + 45 * q^29 - 4 * q^30 - 26 * q^31 + 130 * q^32 + 13 * q^33 - 65 * q^34 - 35 * q^35 + 12 * q^36 + 61 * q^38 + 12 * q^40 - 63 * q^42 + 72 * q^43 - 39 * q^44 - 8 * q^48 - 68 * q^49 - 52 * q^50 - 4 * q^51 + 65 * q^52 - q^53 + 53 * q^55 - 14 * q^56 - 13 * q^57 - 26 * q^58 - 104 * q^59 + 117 * q^60 + 12 * q^61 + 49 * q^62 - 32 * q^64 - 52 * q^65 - 46 * q^66 + 26 * q^67 - 84 * q^68 - 4 * q^69 - 39 * q^71 - 52 * q^73 + 29 * q^74 + 8 * q^75 - 130 * q^76 + 60 * q^77 + 65 * q^78 + 14 * q^79 - 14 * q^81 + 45 * q^82 + 78 * q^83 - 13 * q^85 - 13 * q^86 - 46 * q^87 - 26 * q^88 - 4 * q^90 - 208 * q^91 + 82 * q^92 - 39 * q^93 + 25 * q^94 - 66 * q^95 + 65 * q^96 + 26 * q^97 - 104 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/507\mathbb{Z}\right)^\times$.

$n$	$170$	$340$
$\chi(n)$	$1$	$e\left(\frac{23}{26}\right)$

Coefficient data

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

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

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

$2$	0.00155211		0.000588639i	0.00109751		0.000416230i	−0.354056	−	0.935224i	$-0.615198\pi$
$2$	0.00155211		0.000588639i	0.00109751		0.000416230i	0.355154	+	0.934808i	$0.384429\pi$
$3$	0.568065	−	0.822984i	0.327972	−	0.475150i
$3$	0.568065	−	0.822984i	0.327972	−	0.475150i
$4$	−1.49702	+	1.32624i	−0.748510	+	0.663122i
$5$	−0.897149	+	0.108934i	−0.401217	+	0.0487166i	−0.318658	−	0.947870i	$-0.603232\pi$
$5$	−0.897149	+	0.108934i	−0.401217	+	0.0487166i	−0.0825587	+	0.996586i	$0.526309\pi$
$6$	0.000397260	−	0.00161175i	0.000162181	−	0.000657994i
$7$	−0.178306	+	0.339734i	−0.0673934	+	0.128407i	−0.916822	−	0.399296i	$-0.869255\pi$
$7$	−0.178306	+	0.339734i	−0.0673934	+	0.128407i	0.849429	+	0.527704i	$0.176947\pi$
$8$	−0.00308573	+	0.00587937i	−0.00109097	+	0.00207867i
$9$	−0.354605	−	0.935016i	−0.118202	−	0.311672i
$10$	−0.00132835		0.000697174i	−0.000420062		0.000220466i
$11$	−2.55908	−	0.970532i	−0.771592	−	0.292626i	−0.0627835	−	0.998027i	$-0.519998\pi$
$11$	−2.55908	−	0.970532i	−0.771592	−	0.292626i	−0.708809	+	0.705401i	$0.750767\pi$
$12$	0.241073	+	1.98542i	0.0695918	+	0.573140i
$13$	−3.58442	+	0.389780i	−0.994139	+	0.108106i
$13$	−3.58442	+	0.389780i	−0.994139	+	0.108106i
$14$	−7.67707e−5	0	0.000632264i	−2.05178e−5	0	0.000168980i
$15$	−0.419988	+	0.800220i	−0.108440	+	0.206616i
$16$	0.482145	−	3.97082i	0.120536	−	0.992705i
$17$	−2.71636	−	1.42566i	−0.658814	−	0.345772i	0.101961	−	0.994788i	$-0.467488\pi$
$17$	−2.71636	−	1.42566i	−0.658814	−	0.345772i	−0.760775	+	0.649016i	$0.775181\pi$
$18$	−0.00110077	−	0.00124252i	−0.000259455	−	0.000292864i
$19$			3.07285i			0.704959i	0.935820	+	0.352480i	$0.114661\pi$
$19$			3.07285i			0.704959i	−0.935820	+	0.352480i	$0.885339\pi$
$20$	1.19858	−	1.35291i	0.268010	−	0.302521i
$21$	0.178306	+	0.339734i	0.0389096	+	0.0741361i
$22$	−0.00454328			−0.000968630
$23$	−2.75837			−0.575161			−0.287580	−	0.957757i	$-0.592851\pi$
$23$	−2.75837			−0.575161			−0.287580	+	0.957757i	$0.592851\pi$
$24$	0.00308573	+	0.00587937i	0.000629872	+	0.00120012i
$25$	−4.06170	+	1.00112i	−0.812340	+	0.200224i
$26$	−0.00533399	+	0.00271491i	−0.00104608	+	0.000532438i
$27$	−0.970942	−	0.239316i	−0.186858	−	0.0460563i
$28$	−0.183642	−	0.745066i	−0.0347051	−	0.140804i
$29$	−1.05871	−	2.79159i	−0.196597	−	0.518384i	0.800075	−	0.599900i	$-0.204793\pi$
$29$	−1.05871	−	2.79159i	−0.196597	−	0.518384i	−0.996672	+	0.0815159i	$0.974024\pi$
$30$	−0.000180828		0.00148925i	−3.30145e−5		0.000271899i
$31$	−0.339201	+	1.37619i	−0.0609223	+	0.247171i	−0.993506	−	0.113783i	$-0.963703\pi$
$31$	−0.339201	+	1.37619i	−0.0609223	+	0.247171i	0.932583	+	0.360955i	$0.117549\pi$
$32$	−0.00476712	−	0.0193409i	−0.000842715	−	0.00341903i
$33$	−2.25246	+	1.55476i	−0.392102	+	0.270649i
$34$	−0.00505529		0.000613824i	−0.000866976		0.000105270i
$35$	0.122959	−	0.324216i	0.0207838	−	0.0548024i
$36$	1.77091	+	0.929445i	0.295152	+	0.154908i
$37$	0.0955204	−	0.387541i	0.0157035	−	0.0637114i	−0.962567	−	0.271043i	$-0.912632\pi$
$37$	0.0955204	−	0.387541i	0.0157035	−	0.0637114i	0.978271	+	0.207331i	$0.0664777\pi$
$38$	0.00180880	+	0.00476940i	0.000293425	+	0.000773699i
$39$	−1.71540	+	3.17134i	−0.274684	+	0.507821i
$40$	0.00212790	−	0.00561081i	0.000336450	−	0.000887147i
$41$	−3.16600	−	2.18533i	−0.494446	−	0.341291i	0.294605	−	0.955619i	$-0.404812\pi$
$41$	−3.16600	−	2.18533i	−0.494446	−	0.341291i	−0.789051	+	0.614328i	$0.789427\pi$
$42$	0.000476732	0	0.000422348i	7.35614e−5	0	6.51697e-5i
$43$	−8.01523	+	1.97558i	−1.22231	+	0.301273i	−0.797114	−	0.603829i	$-0.793641\pi$
$43$	−8.01523	+	1.97558i	−1.22231	+	0.301273i	−0.425196	+	0.905101i	$0.639795\pi$
$44$	5.11816	−	1.94106i	0.771591	−	0.292626i
$45$	0.419988	+	0.800220i	0.0626081	+	0.119290i
$46$	−0.00428131	+	0.00162369i	−0.000631244	+	0.000239399i
$47$	0.816367	−	0.921488i	0.119079	−	0.134413i	−0.685948	−	0.727651i	$-0.740612\pi$
$47$	0.816367	−	0.921488i	0.119079	−	0.134413i	0.805027	+	0.593238i	$0.202151\pi$
$48$	−2.99403	−	2.65248i	−0.432151	−	0.382852i
$49$	3.89283	+	5.63973i	0.556118	+	0.805676i
$50$	−0.00571492	+	0.00394472i	−0.000808212	+	0.000557868i
$51$	−2.71636	+	1.42566i	−0.380366	+	0.199632i
$52$	4.84900	−	5.33732i	0.672436	−	0.740154i
$53$	6.40169	+	3.35987i	0.879340	+	0.461513i	0.843054	−	0.537828i	$-0.180755\pi$
$53$	6.40169	+	3.35987i	0.879340	+	0.461513i	0.0362856	+	0.999341i	$0.488447\pi$
$54$	−0.00164788		0.000200089i	−0.000224248		2.72287e-5i
$55$	2.40160	+	0.591941i	0.323832	+	0.0798173i
$56$	−0.00144722	−	0.00209666i	−0.000193393	−	0.000280178i
$57$	2.52890	+	1.74558i	0.334961	+	0.231207i
$58$	−0.00328647	−	0.00370966i	−0.000431535	−	0.000487102i
$59$	10.5595	−	1.28215i	1.37473	−	0.166922i	0.600397	−	0.799702i	$-0.295009\pi$
$59$	10.5595	−	1.28215i	1.37473	−	0.166922i	0.774332	+	0.632780i	$0.218086\pi$
$60$	−0.432557	−	1.75495i	−0.0558428	−	0.226563i
$61$	−5.01265	+	2.63084i	−0.641803	+	0.336844i	−0.754032	−	0.656838i	$-0.771894\pi$
$61$	−5.01265	+	2.63084i	−0.641803	+	0.336844i	0.112228	+	0.993682i	$0.464201\pi$
$62$	0.000283602		0.00233567i	3.60175e−5		0.000296631i
$63$	0.380885	+	0.0462478i	0.0479870	+	0.00582668i
$64$	4.54448	+	6.58382i	0.568060	+	0.822977i
$65$	3.17330	−	0.740154i	0.393599	−	0.0918048i
$66$	−0.00258087	+	0.00373904i	−0.000317684	+	0.000460244i
$67$	−1.83946	+	2.07632i	−0.224726	+	0.253663i	−0.850050	−	0.526702i	$-0.823428\pi$
$67$	−1.83946	+	2.07632i	−0.224726	+	0.253663i	0.625324	+	0.780365i	$0.284967\pi$
$68$	5.95721	−	1.46832i	0.722418	−	0.178060i
$69$	−1.56693	+	2.27010i	−0.188637	+	0.273288i
$70$		0	0.000575597i		0	6.87970e-5i
$71$	−5.39926	−	3.72684i	−0.640774	−	0.442294i	0.202864	−	0.979207i	$-0.434975\pi$
$71$	−5.39926	−	3.72684i	−0.640774	−	0.442294i	−0.843638	+	0.536913i	$0.819590\pi$
$72$	0.00659152		0.000800356i	0.000776818		9.43228e-5i
$73$	8.45785	+	3.20764i	0.989916	+	0.375426i	0.795804	−	0.605554i	$-0.207048\pi$
$73$	8.45785	+	3.20764i	0.989916	+	0.375426i	0.194112	+	0.980979i	$0.437818\pi$
$74$	−7.98635e−5	0	0.000657735i	−9.28394e−6	0	7.64601e-5i
$75$	−1.48340	+	3.91141i	−0.171289	+	0.451651i
$76$	−4.07534	−	4.60011i	−0.467474	−	0.527669i
$77$	0.786023	−	0.696356i	0.0895756	−	0.0793571i
$78$	−0.000795721		0.00593203i	−9.00976e−5		0.000671670i
$79$	−6.75856	−	5.98756i	−0.760397	−	0.673653i	0.191010	−	0.981588i	$-0.438824\pi$
$79$	−6.75856	−	5.98756i	−0.760397	−	0.673653i	−0.951407	+	0.307935i	$0.900362\pi$
$80$			3.61494i			0.404162i
$81$	−0.748511	+	0.663123i	−0.0831679	+	0.0736803i
$82$	−0.00620036	−	0.00152825i	−0.000684715	−	0.000168767i
$83$	9.78106	−	6.75138i	1.07361	−	0.741060i	0.106218	−	0.994343i	$-0.466126\pi$
$83$	9.78106	−	6.75138i	1.07361	−	0.741060i	0.967392	+	0.253283i	$0.0815104\pi$
$84$	−0.717498	−	0.272111i	−0.0782855	−	0.0296898i
$85$	2.59228	+	0.983122i	0.281172	+	0.106635i
$86$	−0.0112776	+	0.00778439i	−0.00121610	+	0.000839412i
$87$	−2.89885	−	0.714501i	−0.310789	−	0.0766026i
$88$	0.0136028	−	0.0120510i	0.00145006	−	0.00128464i
$89$		−	9.44142i		−	1.00079i	−0.865798	−	0.500394i	$-0.833188\pi$
$89$		−	9.44142i		−	1.00079i	0.865798	−	0.500394i	$-0.166812\pi$
$90$	0.00112291		0.000994811i	0.000118365		0.000104862i
$91$	0.506703	−	1.28725i	0.0531169	−	0.134941i
$92$	4.12934	−	3.65827i	0.430513	−	0.381401i
$93$	0.939896	+	1.06092i	0.0974626	+	0.110013i
$94$	0.000724670	−	0.00191080i	7.47440e−5	−	0.000197084i
$95$	−0.334736	−	2.75680i	−0.0343432	−	0.282842i
$96$	−0.0186253	−	0.00706365i	−0.00190094	−	0.000720931i
$97$	−3.72809	−	0.452672i	−0.378530	−	0.0459619i	−0.0709396	−	0.997481i	$-0.522600\pi$
$97$	−3.72809	−	0.452672i	−0.378530	−	0.0459619i	−0.307591	+	0.951519i	$0.599523\pi$
$98$	0.00936187	+	0.00646203i	0.000945692	+	0.000652764i
$99$			2.73694i			0.275073i
$100$	4.75272	−	6.88550i	0.475272	−	0.688550i
$101$	−0.620037	+	0.152825i	−0.0616960	+	0.0152067i	−0.270043	−	0.962848i	$-0.587038\pi$
$101$	−0.620037	+	0.152825i	−0.0616960	+	0.0152067i	0.208347	+	0.978055i	$0.433192\pi$
$102$	−0.00337690	+	0.00381173i	−0.000334363	+	0.000377418i
$103$	−3.36753	+	4.87871i	−0.331813	+	0.480714i	−0.953009	−	0.302941i	$-0.902031\pi$
$103$	−3.36753	+	4.87871i	−0.331813	+	0.480714i	0.621196	+	0.783655i	$0.286647\pi$
$104$	0.00876890	−	0.0222769i	0.000859861	−	0.00218443i
$105$	−0.196976	−	0.285369i	−0.0192229	−	0.0278491i
$106$	0.0119139	+	0.00144661i	0.00115718	+	0.000140507i
$107$	−0.539110	−	4.43997i	−0.0521177	−	0.429228i	−0.995291	−	0.0969280i	$-0.969098\pi$
$107$	−0.539110	−	4.43997i	−0.0521177	−	0.429228i	0.943174	−	0.332300i	$-0.107825\pi$
$108$	1.77091	−	0.929445i	0.170406	−	0.0894359i
$109$	2.40222	+	9.74620i	0.230091	+	0.933516i	0.966435	+	0.256909i	$0.0827042\pi$
$109$	2.40222	+	9.74620i	0.230091	+	0.933516i	−0.736344	+	0.676607i	$0.763450\pi$
$110$	0.00407599		0.000494915i	0.000388631		4.71883e-5i
$111$	−0.264679	−	0.298760i	−0.0251222	−	0.0283571i
$112$	1.26305	+	0.871823i	0.119347	+	0.0823795i
$113$	−1.05144	−	1.52328i	−0.0989115	−	0.143298i	0.770403	−	0.637557i	$-0.220055\pi$
$113$	−1.05144	−	1.52328i	−0.0989115	−	0.143298i	−0.869315	+	0.494259i	$0.835440\pi$
$114$	0.00495265	+	0.00122072i	0.000463859	+	0.000114331i
$115$	2.47467	−	0.300479i	0.230764	−	0.0280198i
$116$	5.28723	+	2.77495i	0.490907	+	0.257648i
$117$	1.63550	+	3.21327i	0.151202	+	0.297067i
$118$	0.0156348	−	0.00820577i	0.00143930	−	0.000755403i
$119$	0.968688	−	0.668637i	0.0887995	−	0.0612939i
$120$	−0.00340882	−	0.00493853i	−0.000311181	−	0.000450824i
$121$	−2.62665	−	2.32701i	−0.238786	−	0.211546i
$122$	−0.00623158	+	0.00703400i	−0.000564180	+	0.000636828i
$123$	−3.59699	+	1.36416i	−0.324329	+	0.123002i
$124$	−1.31738	−	2.51005i	−0.118304	−	0.225409i
$125$	7.75994	−	2.94296i	0.694070	−	0.263226i
$126$	0.000618400	0	0.000152422i	5.50915e−5	0	1.35788e-5i
$127$	7.78455	+	6.89651i	0.690767	+	0.611967i	0.933691	−	0.358079i	$-0.116568\pi$
$127$	7.78455	+	6.89651i	0.690767	+	0.611967i	−0.242924	+	0.970045i	$0.578107\pi$
$128$	0.0437164	+	0.0301752i	0.00386402	+	0.00266714i
$129$	−2.92730	+	7.71866i	−0.257734	+	0.679590i
$130$	0.00448963	−	0.00301673i	0.000393767	−	0.000264585i
$131$	−2.06676	−	5.44959i	−0.180574	−	0.476133i	0.813914	−	0.580985i	$-0.197332\pi$
$131$	−2.06676	−	5.44959i	−0.180574	−	0.476133i	−0.994488	+	0.104852i	$0.966563\pi$
$132$	1.30998	−	5.31481i	0.114019	−	0.462595i
$133$	−1.04395	−	0.547908i	−0.0905220	−	0.0475096i
$134$	−0.00163285	+	0.00430546i	−0.000141057	+	0.000371935i
$135$	0.897149	+	0.108934i	0.0772143	+	0.00937551i
$136$	0.0167639	−	0.0115713i	0.00143749	−	0.000992230i
$137$	2.56439	+	10.4041i	0.219090	+	0.888885i	0.972794	+	0.231671i	$0.0744191\pi$
$137$	2.56439	+	10.4041i	0.219090	+	0.888885i	−0.753704	+	0.657214i	$0.771735\pi$
$138$	−0.00109579	+	0.00444580i	−9.32800e−5	+	0.000378452i
$139$	1.16364	−	9.58343i	0.0986985	−	0.812856i	−0.856348	−	0.516399i	$-0.827272\pi$
$139$	1.16364	−	9.58343i	0.0986985	−	0.812856i	0.955046	−	0.296456i	$-0.0958049\pi$
$140$	0.245917	+	0.648430i	0.0207838	+	0.0548024i
$141$	−0.294620	−	1.19532i	−0.0248115	−	0.100664i
$142$	−0.0105740	−	0.00260626i	−0.000887352	−	0.000218713i
$143$	9.55112	+	2.48131i	0.798705	+	0.207498i
$144$	−3.88375	+	0.957259i	−0.323646	+	0.0797716i
$145$	1.25392	+	2.38914i	0.104132	+	0.198407i
$146$	0.0150157			0.00124271
$147$	6.85279			0.565208
$148$	0.370978	+	0.706840i	0.0304942	+	0.0581019i
$149$	6.21607	−	7.01650i	0.509241	−	0.574814i	−0.436513	−	0.899698i	$-0.643787\pi$
$149$	6.21607	−	7.01650i	0.509241	−	0.574814i	0.945754	+	0.324884i	$0.105325\pi$
$150$			0.00694414i			0.000566987i
$151$	−1.31068	−	1.47945i	−0.106662	−	0.120396i	0.692755	−	0.721173i	$-0.256397\pi$
$151$	−1.31068	−	1.47945i	−0.106662	−	0.120396i	−0.799417	+	0.600777i	$0.794858\pi$
$152$	−0.0180664	−	0.00948198i	−0.00146538	−	0.000769090i
$153$	−0.369777	+	3.04539i	−0.0298947	+	0.246205i
$154$	0.000810094	−	0.00154351i	6.52793e−5	−	0.000124379i
$155$	0.154400	−	1.27160i	0.0124017	−	0.102137i
$156$	−1.63798	−	7.02260i	−0.131144	−	0.562258i
$157$	−0.0997026	−	0.821125i	−0.00795713	−	0.0655329i	0.988189	−	0.153237i	$-0.0489699\pi$
$157$	−0.0997026	−	0.821125i	−0.00795713	−	0.0655329i	−0.996147	+	0.0877046i	$0.972047\pi$
$158$	−0.0140145	−	0.00531502i	−0.00111494	−	0.000422840i
$159$	6.40169	−	3.35987i	0.507687	−	0.266455i
$160$	0.00638369	+	0.0168324i	0.000504675	+	0.00133072i
$161$	0.491835	−	0.937114i	0.0387620	−	0.0738549i
$162$	−0.000771433		0.00146984i	−6.06095e−5		0.000115482i
$163$	−3.04138	+	12.3394i	−0.238219	+	0.966493i	0.723031	+	0.690815i	$0.242748\pi$
$163$	−3.04138	+	12.3394i	−0.238219	+	0.966493i	−0.961250	+	0.275677i	$0.911098\pi$
$164$	7.63784	−	0.927402i	0.596415	−	0.0724179i
$165$	1.85142	−	1.64022i	0.144133	−	0.127691i
$166$	0.0112072	−	0.0162364i	0.000869846	−	0.00126019i
$167$	−14.7961	+	5.61142i	−1.14496	+	0.434225i	−0.852847	−	0.522160i	$-0.825126\pi$
$167$	−14.7961	+	5.61142i	−1.14496	+	0.434225i	−0.292109	+	0.956385i	$0.594357\pi$
$168$	−0.00254763			−0.000196554
$169$	12.6961	−	2.79427i	0.976626	−	0.214944i
$170$	0.00460221			0.000352974
$171$	2.87316	−	1.08965i	0.219716	−	0.0833273i
$172$	9.37886	−	13.5876i	0.715131	−	1.03605i
$173$	−15.9236	+	14.1071i	−1.21065	+	1.07254i	−0.215267	+	0.976555i	$0.569062\pi$
$173$	−15.9236	+	14.1071i	−1.21065	+	1.07254i	−0.995383	+	0.0959870i	$0.969399\pi$
$174$	−0.00491992		0.000597386i	−0.000372978		4.52877e-5i
$175$	0.384112	−	1.55840i	0.0290361	−	0.117804i
$176$	−5.08765	+	9.69371i	−0.383496	+	0.730691i
$177$	4.94328	−	9.41864i	0.371560	−	0.707948i
$178$	−0.00555758	−	0.0146541i	−0.000416559	−	0.00109837i
$179$	−0.614905	+	0.322727i	−0.0459601	+	0.0241217i	−0.487547	−	0.873097i	$-0.662108\pi$
$179$	−0.614905	+	0.322727i	−0.0459601	+	0.0241217i	0.441587	+	0.897219i	$0.354416\pi$
$180$	−1.69002	−	0.640939i	−0.125966	−	0.0477728i
$181$	1.72042	+	14.1689i	0.127878	+	1.05317i	0.905473	+	0.424403i	$0.139516\pi$
$181$	1.72042	+	14.1689i	0.127878	+	1.05317i	−0.777595	+	0.628765i	$0.783561\pi$
$182$	2.87347e−5	−	0.00229622i	2.12996e−6	−	0.000170207i
$183$	−0.682369	+	5.61981i	−0.0504422	+	0.415429i
$184$	0.00851160	−	0.0162175i	0.000627483	−	0.00119557i
$185$	−0.0434797	+	0.358088i	−0.00319669	+	0.0263271i
$186$	0.00208332	+	0.00109341i	0.000152757	+	8.01729e-5i
$187$	5.56774	+	6.28468i	0.407154	+	0.459581i
$188$			2.46219i			0.179573i
$189$	0.254429	−	0.287191i	0.0185070	−	0.0208900i
$190$	−0.00214231	−	0.00408182i	−0.000155419	−	0.000296127i
$191$	−18.8586			−1.36456			−0.682279	−	0.731092i	$-0.739011\pi$
$191$	−18.8586			−1.36456			−0.682279	+	0.731092i	$0.739011\pi$
$192$	7.99993			0.577345
$193$	−5.74104	−	10.9386i	−0.413249	−	0.787380i	0.586496	−	0.809952i	$-0.300507\pi$
$193$	−5.74104	−	10.9386i	−0.413249	−	0.787380i	−0.999745	+	0.0225721i	$0.992814\pi$
$194$	−0.00605288	+	0.00149190i	−0.000434571	+	0.000107112i
$195$	1.19350	−	3.03203i	0.0854686	−	0.217128i
$196$	−13.3073	−	3.27995i	−0.950521	−	0.234282i
$197$	6.00068	+	24.3457i	0.427531	+	1.73456i	0.650289	+	0.759687i	$0.274648\pi$
$197$	6.00068	+	24.3457i	0.427531	+	1.73456i	−0.222758	+	0.974874i	$0.571506\pi$
$198$	0.00161107	+	0.00424804i	0.000114494	+	0.000301895i
$199$	−0.354115	+	2.91640i	−0.0251025	+	0.206738i	−0.999864	−	0.0165124i	$-0.994744\pi$
$199$	−0.354115	+	2.91640i	−0.0251025	+	0.206738i	0.974761	+	0.223250i	$0.0716668\pi$
$200$	0.00664737	−	0.0269694i	0.000470040	−	0.00190703i
$201$	0.663847	+	2.69333i	0.0468241	+	0.189973i
$202$	−0.000872409	0	0.000602180i	−6.13825e−5	0	4.23692e-5i
$203$	1.13717	+	0.138078i	0.0798138	+	0.00969115i
$204$	2.17568	−	5.73679i	0.152328	−	0.401656i
$205$	3.07843	+	1.61568i	0.215007	+	0.112844i
$206$	−0.00235499	+	0.00955457i	−0.000164080	+	0.000665699i
$207$	0.978133	+	2.57912i	0.0679849	+	0.179261i
$208$	−0.180463	+	14.4210i	−0.0125129	+	0.999918i
$209$	2.98229	−	7.86366i	0.206290	−	0.543941i
$210$	−0.000473707	0	0.000326977i	−3.26889e−5	0	2.25635e-5i
$211$	−4.35845	−	3.86125i	−0.300048	−	0.265819i	0.499643	−	0.866232i	$-0.333465\pi$
$211$	−4.35845	−	3.86125i	−0.300048	−	0.265819i	−0.799691	+	0.600412i	$0.795003\pi$
$212$	−14.0395	+	3.46042i	−0.964234	+	0.237662i
$213$	−6.13426	+	2.32642i	−0.420312	+	0.159403i
$214$	−0.00345030	−	0.00657399i	−0.000235858	−	0.000449389i
$215$	6.97564	−	2.64551i	0.475735	−	0.180422i
$216$	0.00440309	−	0.00497006i	0.000299592	−	0.000338170i
$217$	−0.407058	−	0.360622i	−0.0276329	−	0.0244806i
$218$	0.00946551	+	0.0137132i	0.000641085	+	0.000928772i
$219$	7.44444	−	5.13853i	0.503049	−	0.347229i
$220$	−4.38030	+	2.29896i	−0.295320	+	0.154996i
$221$	10.2923	+	4.05137i	0.692333	+	0.272524i
$222$	−0.000586673	0	0.000307910i	−3.93749e−5	0	2.06655e-5i
$223$	11.2593	−	1.36713i	0.753980	−	0.0915497i	0.265483	−	0.964116i	$-0.414469\pi$
$223$	11.2593	−	1.36713i	0.753980	−	0.0915497i	0.488497	+	0.872566i	$0.337545\pi$
$224$	0.00742079	+	0.00182906i	0.000495822	+	0.000122209i
$225$	2.37636	+	3.44275i	0.158424	+	0.229517i
$226$	−0.00252862	−	0.00174538i	−0.000168201	−	0.000116101i
$227$	−17.7091	−	19.9894i	−1.17539	−	1.32674i	−0.934403	−	0.356217i	$-0.884066\pi$
$227$	−17.7091	−	19.9894i	−1.17539	−	1.32674i	−0.240990	−	0.970528i	$-0.577472\pi$
$228$	−6.10087	+	0.740780i	−0.404040	+	0.0490594i
$229$	−1.03793	−	4.21106i	−0.0685885	−	0.278274i	0.926627	−	0.375983i	$-0.122695\pi$
$229$	−1.03793	−	4.21106i	−0.0685885	−	0.278274i	−0.995215	+	0.0977085i	$0.968849\pi$
$230$	0.00366409	−	0.00192306i	0.000241603	−	0.000126803i
$231$	−0.126577	−	1.04246i	−0.00832819	−	0.0685888i
$232$	0.0196797	+	0.00238954i	0.00129203	+	0.000156881i
$233$	−12.2809	−	17.7920i	−0.804549	−	1.16559i	−0.983353	−	0.181706i	$-0.941838\pi$
$233$	−12.2809	−	17.7920i	−0.804549	−	1.16559i	0.178804	−	0.983885i	$-0.442777\pi$
$234$	0.00442994	+	0.00402464i	0.000289594	+	0.000263099i
$235$	−0.632021	+	0.915641i	−0.0412285	+	0.0597298i
$236$	−14.1073	+	15.9239i	−0.918308	+	1.03656i
$237$	−8.76696	+	2.16086i	−0.569475	+	0.140363i
$238$	0.00110993	−	0.00160801i	7.19459e−5	−	0.000104232i
$239$		−	4.06300i		−	0.262814i	−0.991329	−	0.131407i	$-0.958051\pi$
$239$		−	4.06300i		−	0.262814i	0.991329	−	0.131407i	$-0.0419494\pi$
$240$	2.97503	+	2.05352i	0.192038	+	0.132554i
$241$	−20.5959	−	2.50080i	−1.32670	−	0.161091i	−0.573675	−	0.819083i	$-0.694483\pi$
$241$	−20.5959	−	2.50080i	−1.32670	−	0.161091i	−0.753025	+	0.657992i	$0.771406\pi$
$242$	−0.00544663	−	0.00206563i	−0.000350122	−	0.000132784i
$243$	0.120537	+	0.992709i	0.00773243	+	0.0636823i
$244$	4.01489	−	10.5864i	0.257027	−	0.677725i
$245$	−4.10680	−	4.63562i	−0.262374	−	0.296159i
$246$	−0.00477993	+	0.00423465i	−0.000304757	+	0.000269991i
$247$	−1.19773	−	11.0144i	−0.0762100	−	0.700828i
$248$	−0.00704446	−	0.00624084i	−0.000447323	−	0.000396294i
$249$		−	11.8849i		−	0.753173i
$250$	0.0103120	−	0.00913560i	0.000652186	−	0.000577786i
$251$	−29.9865	−	7.39100i	−1.89273	−	0.466516i	−0.999869	−	0.0161789i	$-0.994850\pi$
$251$	−29.9865	−	7.39100i	−1.89273	−	0.466516i	−0.892859	−	0.450337i	$-0.851304\pi$
$252$	−0.631529	+	0.435913i	−0.0397826	+	0.0274599i
$253$	7.05890	+	2.67709i	0.443789	+	0.168307i
$254$	0.0161421	+	0.00612188i	0.00101284	+	0.000384121i
$255$	2.28168	−	1.57493i	0.142884	−	0.0986258i
$256$	−15.5349	−	3.82900i	−0.970928	−	0.239312i
$257$	−4.00183	+	3.54531i	−0.249627	+	0.221150i	−0.778652	−	0.627456i	$-0.784096\pi$
$257$	−4.00183	+	3.54531i	−0.249627	+	0.221150i	0.529025	+	0.848606i	$0.322558\pi$
$258$			0.0137033i			0.000853133i
$259$	0.114629	+	0.101553i	0.00712271	+	0.00631017i
$260$	−3.76886	+	5.31659i	−0.233735	+	0.329721i
$261$	−2.23475	+	1.97982i	−0.138328	+	0.122548i
$262$	−0.00641568	−	0.00724181i	−0.000396362	−	0.000447401i
$263$	−0.0802045	+	0.211482i	−0.00494562	+	0.0130405i	−0.937466	−	0.348076i	$-0.886835\pi$
$263$	−0.0802045	+	0.211482i	−0.00494562	+	0.0130405i	0.932521	+	0.361117i	$0.117604\pi$
$264$	−0.00219052	−	0.0180406i	−0.000134817	−	0.00111032i
$265$	−6.10927	−	2.31694i	−0.375290	−	0.142329i
$266$	−0.00194285		0.000235905i	−0.000119124		1.44642e-5i
$267$	−7.77014	−	5.36334i	−0.475525	−	0.328231i
$268$		−	5.54787i		−	0.338890i
$269$	−14.7604	+	21.3841i	−0.899957	+	1.30381i	0.0523363	+	0.998630i	$0.483333\pi$
$269$	−14.7604	+	21.3841i	−0.899957	+	1.30381i	−0.952294	+	0.305184i	$0.901282\pi$
$270$	0.00145660		0.000359019i	8.86457e−5		2.18492e-5i
$271$	5.53291	−	6.24537i	0.336101	−	0.379379i	−0.556026	−	0.831165i	$-0.687674\pi$
$271$	5.53291	−	6.24537i	0.336101	−	0.379379i	0.892126	+	0.451786i	$0.149213\pi$
$272$	−6.97070	+	10.0988i	−0.422661	+	0.612330i
$273$	−0.771546	−	1.14825i	−0.0466961	−	0.0694953i
$274$	0.0101045	+	0.0146389i	0.000610435	+	0.000884367i
$275$	11.3658	+	1.38006i	0.685386	+	0.0832209i
$276$	−0.664969	−	5.47652i	−0.0400265	−	0.329648i
$277$	4.02702	−	2.11355i	0.241960	−	0.126991i	−0.339385	−	0.940648i	$-0.610219\pi$
$277$	4.02702	−	2.11355i	0.241960	−	0.126991i	0.581345	+	0.813657i	$0.302527\pi$
$278$	−0.00383508	−	0.0155595i	−0.000230013	−	0.000933198i
$279$	1.40704	−	0.170846i	0.0842375	−	0.0102283i
$280$	0.00152677	+	0.00172336i	9.12417e−5	+	0.000102991i
$281$	2.20402	+	1.52132i	0.131481	+	0.0907545i	0.631990	−	0.774977i	$-0.282238\pi$
$281$	2.20402	+	1.52132i	0.131481	+	0.0907545i	−0.500509	+	0.865731i	$0.666854\pi$
$282$	−0.00116090	−	0.00168185i	−6.91304e−5	−	0.000100153i
$283$	−8.01560	−	1.97567i	−0.476478	−	0.117441i	−0.00623910	−	0.999981i	$-0.501986\pi$
$283$	−8.01560	−	1.97567i	−0.476478	−	0.117441i	−0.470239	+	0.882539i	$0.655832\pi$
$284$	13.0255	−	1.58158i	0.772921	−	0.0938496i
$285$	−2.45895	−	1.29056i	−0.145656	−	0.0764461i
$286$	0.0162850	−	0.00177088i	0.000962953	−	0.000104714i
$287$	1.30695	−	0.685940i	0.0771468	−	0.0404898i
$288$	−0.0163937	+	0.0113157i	−0.000966006	+	0.000666785i
$289$	−4.31098	−	6.24554i	−0.253587	−	0.367385i
$290$	0.00335256	+	0.00297011i	0.000196869	+	0.000174411i
$291$	−2.49034	+	2.81101i	−0.145986	+	0.164784i
$292$	−16.9157	+	6.41527i	−0.989915	+	0.375425i
$293$	9.21946	+	17.5662i	0.538607	+	1.02623i	0.990930	+	0.134376i	$0.0429029\pi$
$293$	9.21946	+	17.5662i	0.538607	+	1.02623i	−0.452324	+	0.891854i	$0.649405\pi$
$294$	0.0106363	−	0.00403382i	0.000620322	−	0.000235257i
$295$	−9.33376	+	2.30057i	−0.543433	+	0.133944i
$296$	0.00198375	+	0.00175745i	0.000115303	+	0.000102150i
$297$	2.25246	+	1.55476i	0.130701	+	0.0902162i
$298$	0.00551787	−	0.0145494i	0.000319641	−	0.000842825i
$299$	9.88717	−	1.07516i	0.571790	−	0.0621780i
$300$	−2.96680	−	7.82282i	−0.171288	−	0.451651i
$301$	0.757994	−	3.07530i	0.0436901	−	0.177258i
$302$	−0.00290518	−	0.00152476i	−0.000167174	−	8.77399e-5i
$303$	−0.226448	+	0.597095i	−0.0130091	+	0.0343022i
$304$	12.2017	+	1.48156i	0.699816	+	0.0849731i
$305$	4.21050	−	2.90630i	0.241093	−	0.166414i
$306$	0.00121870	+	0.00494445i	6.96682e−5	+	0.000282655i
$307$	4.92590	−	19.9852i	0.281136	−	1.14061i	−0.645229	−	0.763989i	$-0.723238\pi$
$307$	4.92590	−	19.9852i	0.281136	−	1.14061i	0.926366	−	0.376625i	$-0.122916\pi$
$308$	−0.253155	+	2.08492i	−0.0144248	+	0.118799i
$309$	2.10213	+	5.54285i	0.119586	+	0.315322i
$310$	−0.000508866	−	0.00206455i	−2.89016e−5	−	0.000117259i
$311$	−28.9059	−	7.12466i	−1.63910	−	0.404002i	−0.691225	−	0.722639i	$-0.742929\pi$
$311$	−28.9059	−	7.12466i	−1.63910	−	0.404002i	−0.947877	+	0.318637i	$0.896775\pi$
$312$	−0.0133522	−	0.0198714i	−0.000755921	−	0.00112500i
$313$	−27.3432	+	6.73950i	−1.54553	+	0.380939i	−0.917656	−	0.397376i	$-0.869921\pi$
$313$	−27.3432	+	6.73950i	−1.54553	+	0.380939i	−0.627874	+	0.778315i	$0.716075\pi$
$314$	−0.000638096	−	0.00121579i	−3.60098e−5	−	6.86110e-5i
$315$	−0.346749			−0.0195371
$316$	18.0586			1.01588
$317$	4.64424	+	8.84885i	0.260846	+	0.497001i	0.980294	−	0.197546i	$-0.0632972\pi$
$317$	4.64424	+	8.84885i	0.260846	+	0.497001i	−0.719447	+	0.694547i	$0.755605\pi$
$318$	0.00795840	−	0.00898318i	0.000446285	−	0.000503752i
$319$			8.17141i			0.457511i
$320$	−4.79427	−	5.41162i	−0.268008	−	0.302518i
$321$	−3.96027	−	2.07851i	−0.221041	−	0.116011i
$322$	0.000211762	−	0.00174402i	1.18011e−5	−	9.71904e-5i
$323$	4.38082	−	8.34695i	0.243755	−	0.464437i
$324$	0.241073	−	1.98542i	0.0133929	−	0.110301i
$325$	14.1686	−	5.17160i	0.785934	−	0.286869i
$326$	0.00254286	+	0.0209423i	0.000140836	+	0.00115989i
$327$	9.38558	+	3.55948i	0.519024	+	0.196840i
$328$	0.0226178	−	0.0118707i	0.00124886	−	0.000655452i
$329$	0.167498	+	0.441655i	0.00923444	+	0.0243492i
$330$	0.00190812	−	0.00363562i	0.000105039	−	0.000200134i
$331$	15.0961	−	28.7632i	0.829757	−	1.58097i	0.0159213	−	0.999873i	$-0.494932\pi$
$331$	15.0961	−	28.7632i	0.829757	−	1.58097i	0.813835	−	0.581096i	$-0.197376\pi$
$332$	−5.68846	+	23.0790i	−0.312195	+	1.26662i
$333$	−0.396230	+	0.0481110i	−0.0217132	+	0.00263647i
$334$	−0.0196621	+	0.0174191i	−0.00107586	+	0.000953132i
$335$	1.42409	−	2.06315i	0.0778063	−	0.112722i
$336$	1.43499	−	0.544221i	0.0782853	−	0.0296897i
$337$	−8.40993			−0.458118			−0.229059	−	0.973413i	$-0.573565\pi$
$337$	−8.40993			−0.458118			−0.229059	+	0.973413i	$0.573565\pi$
$338$	0.0180610	−	0.0118105i	0.000982390	−	0.000642405i
$339$	−1.85092			−0.100528
$340$	−5.18455	+	1.96624i	−0.281172	+	0.106634i
$341$	2.20368	−	3.19258i	0.119336	−	0.172888i
$342$	0.00381806	−	0.00338251i	0.000206457	−	0.000182905i
$343$	−5.27632	+	0.640662i	−0.284895	+	0.0345925i
$344$	0.0131177	−	0.0532206i	0.000707259	−	0.00286946i
$345$	1.15848	−	2.20731i	0.0623706	−	0.118837i
$346$	−0.0164113	+	0.0312690i	−0.000882275	+	0.00168103i
$347$	12.0188	+	31.6908i	0.645200	+	1.70125i	0.710788	+	0.703407i	$0.248339\pi$
$347$	12.0188	+	31.6908i	0.645200	+	1.70125i	−0.0655874	+	0.997847i	$0.520892\pi$
$348$	5.28723	−	2.77495i	0.283425	−	0.148753i
$349$	6.39561	+	2.42554i	0.342349	+	0.129836i	0.519787	−	0.854296i	$-0.326011\pi$
$349$	6.39561	+	2.42554i	0.342349	+	0.129836i	−0.177437	+	0.984132i	$0.556781\pi$
$350$	−0.000321152	−	0.00264492i	−1.71663e−5	−	0.000141377i
$351$	3.57354	+	0.479354i	0.190742	+	0.0255860i
$352$	−0.00657156	+	0.0541217i	−0.000350266	+	0.00288470i
$353$	−12.2659	+	23.3708i	−0.652850	+	1.24390i	0.303821	+	0.952729i	$0.401738\pi$
$353$	−12.2659	+	23.3708i	−0.652850	+	1.24390i	−0.956671	+	0.291173i	$0.905955\pi$
$354$	0.00212836	−	0.0175286i	0.000113121	−	0.000931634i
$355$	5.24991	+	2.75537i	0.278637	+	0.146240i
$356$	12.5216	+	14.1340i	0.663645	+	0.749100i
$357$		−	1.17704i		−	0.0622958i
$358$	−0.000764432	0	0.000862865i	−4.04015e−5	0	4.56039e-5i
$359$	−9.85824	−	18.7833i	−0.520298	−	0.991345i	−0.993866	−	0.110588i	$-0.964727\pi$
$359$	−9.85824	−	18.7833i	−0.520298	−	0.991345i	0.473569	−	0.880757i	$-0.342966\pi$
$360$	−0.00600076			−0.000316268
$361$	9.55762			0.503033
$362$	0.0110107	+	0.0209791i	0.000578708	+	0.00110264i
$363$	−3.40720	+	0.839799i	−0.178832	+	0.0440780i
$364$	0.948663	+	2.59905i	0.0497235	+	0.136227i
$365$	−7.93737	−	1.95638i	−0.415461	−	0.102402i
$366$	0.00224893	+	0.00912425i	0.000117553	+	0.000476932i
$367$	2.82461	+	7.44790i	0.147444	+	0.388777i	0.988308	−	0.152468i	$-0.0487222\pi$
$367$	2.82461	+	7.44790i	0.147444	+	0.388777i	−0.840865	+	0.541245i	$0.817953\pi$
$368$	−1.32994	+	10.9530i	−0.0693277	+	0.570965i
$369$	−0.920642	+	3.73519i	−0.0479267	+	0.194446i
$370$	0.000143299	0	0.000581386i	7.44975e−6	0	3.02248e-5i
$371$	−2.28292	+	1.57579i	−0.118523	+	0.0818109i
$372$	−2.81408	−	0.341692i	−0.145903	−	0.0177159i
$373$	−3.51205	+	9.26051i	−0.181847	+	0.479491i	−0.994681	−	0.103005i	$-0.967154\pi$
$373$	−3.51205	+	9.26051i	−0.181847	+	0.479491i	0.812834	+	0.582495i	$0.197924\pi$
$374$	0.0123412	+	0.00647715i	0.000638147	+	0.000334925i
$375$	1.98614	−	8.05810i	0.102564	−	0.416118i
$376$	0.00289868	+	0.00764319i	0.000149488	+	0.000394167i
$377$	4.88296	+	9.59355i	0.251485	+	0.494093i
$378$	0.000225851	0	0.000595519i	1.16165e−5	0	3.06302e-5i
$379$	26.9916	+	18.6309i	1.38646	+	0.957007i	0.999389	+	0.0349595i	$0.0111302\pi$
$379$	26.9916	+	18.6309i	1.38646	+	0.957007i	0.387076	+	0.922048i	$0.373485\pi$
$380$	4.15729	+	3.68304i	0.213265	+	0.188936i
$381$	10.0978	−	2.48890i	0.517328	−	0.127510i
$382$	−0.0292706	+	0.0111009i	−0.00149761	+	0.000567970i
$383$	−15.5394	−	29.6078i	−0.794025	−	1.51289i	−0.857256	−	0.514890i	$-0.827833\pi$
$383$	−15.5394	−	29.6078i	−0.794025	−	1.51289i	0.0632307	−	0.997999i	$-0.479860\pi$
$384$	0.0496674	−	0.0188364i	0.00253458	−	0.000961240i
$385$	−0.629323	+	0.710359i	−0.0320733	+	0.0362032i
$386$	−0.0153496	−	0.0135986i	−0.000781276	−	0.000692150i
$387$	4.68943	+	6.79382i	0.238377	+	0.345349i
$388$	6.18138	−	4.26670i	0.313812	−	0.216609i
$389$	23.3996	−	12.2810i	1.18641	−	0.622674i	0.248185	−	0.968713i	$-0.420166\pi$
$389$	23.3996	−	12.2810i	1.18641	−	0.622674i	0.938220	+	0.346039i	$0.112474\pi$
$390$	6.76827e−5	−	0.00540859i	3.42725e−6	−	0.000273875i
$391$	7.49273	+	3.93249i	0.378924	+	0.198875i
$392$	−0.0451703	+	0.00548467i	−0.00228144	+	0.000277018i
$393$	−5.65898	−	1.39481i	−0.285458	−	0.0703590i
$394$	0.0236446	+	0.0342551i	0.00119120	+	0.00172575i
$395$	6.71567	+	4.63550i	0.337902	+	0.233237i
$396$	−3.62985	−	4.09725i	−0.182407	−	0.205895i
$397$	−2.23358	+	0.271205i	−0.112100	+	0.0136114i	−0.176394	−	0.984320i	$-0.556443\pi$
$397$	−2.23358	+	0.271205i	−0.112100	+	0.0136114i	0.0642944	+	0.997931i	$0.479520\pi$
$398$	0.00116708	+	0.00473503i	5.85004e−5	+	0.000237345i
$399$	−1.04395	+	0.547908i	−0.0522629	+	0.0274297i
$400$	2.01694	+	16.6110i	0.100847	+	0.830548i
$401$	18.8857	+	2.29314i	0.943105	+	0.114514i	0.577622	−	0.816304i	$-0.303981\pi$
$401$	18.8857	+	2.29314i	0.943105	+	0.114514i	0.365483	+	0.930818i	$0.380904\pi$
$402$	0.00261576	+	0.00378959i	0.000130462	+	0.000189008i
$403$	0.679426	−	5.06506i	0.0338446	−	0.252309i
$404$	0.725524	−	1.05110i	0.0360962	−	0.0522943i
$405$	0.599289	−	0.676457i	0.0297789	−	0.0336134i
$406$	0.00184630		0.000455071i	9.16301e−5		2.25848e-5i
$407$	−0.620566	+	0.899045i	−0.0307603	+	0.0445640i
$408$		−	0.0203697i		−	0.00100845i
$409$	0.0113671	+	0.00784615i	0.000562067	+	0.000387967i	0.568346	−	0.822790i	$-0.307584\pi$
$409$	0.0113671	+	0.00784615i	0.000562067	+	0.000387967i	−0.567784	+	0.823178i	$0.692199\pi$
$410$	0.00572912		0.000695641i	0.000282941		3.43553e-5i
$411$	10.0192	+	3.79977i	0.494209	+	0.187429i
$412$	−1.42910	−	11.7697i	−0.0704067	−	0.579851i
$413$	−1.44723	+	3.81604i	−0.0712136	+	0.187775i
$414$	0.00303634	+	0.00342732i	0.000149228	+	0.000168444i
$415$	−8.03961	+	7.12247i	−0.394649	+	0.349628i
$416$	0.0246261	+	0.0674680i	0.00120739	+	0.00330789i
$417$	−7.22598	−	6.40166i	−0.353858	−	0.313491i
$418$		−	0.0139608i		−	0.000682844i
$419$	10.4106	−	9.22301i	0.508592	−	0.450573i	−0.369385	−	0.929277i	$-0.620431\pi$
$419$	10.4106	−	9.22301i	0.508592	−	0.450573i	0.877977	+	0.478703i	$0.158893\pi$
$420$	0.673345	+	0.165965i	0.0328558	+	0.00809824i
$421$	0.521355	−	0.359866i	0.0254093	−	0.0175388i	−0.555292	−	0.831655i	$-0.687394\pi$
$421$	0.521355	−	0.359866i	0.0254093	−	0.0175388i	0.580702	+	0.814116i	$0.302778\pi$
$422$	−0.00903768	−	0.00342754i	−0.000439947	−	0.000166850i
$423$	−1.15109	−	0.436552i	−0.0559681	−	0.0212259i
$424$	−0.0395078	+	0.0272703i	−0.00191867	+	0.00132436i
$425$	12.4603	+	3.07119i	0.604413	+	0.148974i
$426$	−0.00815164	+	0.00722172i	−0.000394948	+	0.000349894i
$427$		−	2.17206i		−	0.105113i
$428$	6.69554	+	5.93173i	0.323641	+	0.286721i
$429$	7.46774	−	6.45087i	0.360546	−	0.311451i
$430$	0.00926973	−	0.00821227i	0.000447026	−	0.000396031i
$431$	0.746116	+	0.842190i	0.0359391	+	0.0405669i	0.766205	−	0.642596i	$-0.222142\pi$
$431$	0.746116	+	0.842190i	0.0359391	+	0.0405669i	−0.730266	+	0.683163i	$0.760604\pi$
$432$	−1.41841	+	3.74005i	−0.0682435	+	0.179943i
$433$	−0.186215	−	1.53362i	−0.00894893	−	0.0737011i	0.987550	−	0.157304i	$-0.0502803\pi$
$433$	−0.186215	−	1.53362i	−0.00894893	−	0.0737011i	−0.996499	+	0.0836030i	$0.973357\pi$
$434$	−0.000844075	0	0.000320116i	−4.05169e−5	0	1.53660e-5i
$435$	2.67853	+	0.325232i	0.128426	+	0.0155937i
$436$	−16.5220	−	11.4043i	−0.791260	−	0.546168i
$437$		−	8.47605i		−	0.405465i
$438$	0.00852987	−	0.0123577i	0.000407573	−	0.000590472i
$439$	15.1863	−	3.74309i	0.724803	−	0.178648i	0.140381	−	0.990098i	$-0.455167\pi$
$439$	15.1863	−	3.74309i	0.724803	−	0.178648i	0.584422	+	0.811450i	$0.301321\pi$
$440$	−0.0108909	+	0.0122933i	−0.000519205	+	0.000586061i
$441$	3.89283	−	5.63973i	0.185373	−	0.268559i
$442$	0.0183596		0.000229750i	0.000873275		1.09281e-5i
$443$	−18.6038	−	26.9522i	−0.883891	−	1.28054i	−0.959013	−	0.283363i	$-0.908550\pi$
$443$	−18.6038	−	26.9522i	−0.883891	−	1.28054i	0.0751212	−	0.997174i	$-0.476066\pi$
$444$	0.792458	+	0.0962218i	0.0376084	+	0.00456649i
$445$	1.02849	+	8.47036i	0.0487550	+	0.401533i
$446$	0.0166710	−	0.00874961i	0.000789394	−	0.000414306i
$447$	−2.24333	−	9.10155i	−0.106106	−	0.430489i
$448$	−3.04706	+	0.369980i	−0.143960	+	0.0174799i
$449$	12.3312	+	13.9191i	0.581948	+	0.656883i	0.963577	−	0.267433i	$-0.0861753\pi$
$449$	12.3312	+	13.9191i	0.581948	+	0.656883i	−0.381629	+	0.924316i	$0.624637\pi$
$450$	0.00571492	+	0.00394472i	0.000269404	+	0.000185956i
$451$	5.98112	+	8.66514i	0.281640	+	0.408026i
$452$	3.59427	+	0.885908i	0.169060	+	0.0416696i
$453$	−1.96211	+	0.238244i	−0.0921882	+	0.0111937i
$454$	−0.0392530	−	0.0206016i	−0.00184224	−	0.000966880i
$455$	−0.314363	+	1.21005i	−0.0147376	+	0.0567281i
$456$	−0.0180664	+	0.00948198i	−0.000846036	+	0.000444034i
$457$	−3.05532	+	2.10893i	−0.142922	+	0.0986518i	−0.637380	−	0.770550i	$-0.719982\pi$
$457$	−3.05532	+	2.10893i	−0.142922	+	0.0986518i	0.494458	+	0.869201i	$0.335366\pi$
$458$	−0.00408978	−	0.00592507i	−0.000191103	−	0.000276860i
$459$	2.29625	+	2.03430i	0.107180	+	0.0949528i
$460$	−3.30612	+	3.73184i	−0.154149	+	0.173998i
$461$	−10.3014	+	3.90680i	−0.479783	+	0.181958i	−0.582627	−	0.812740i	$-0.697975\pi$
$461$	−10.3014	+	3.90680i	−0.479783	+	0.181958i	0.102844	+	0.994698i	$0.467206\pi$
$462$	−0.000810094	−	0.00154351i	−3.76890e−5	−	7.18104e-5i
$463$	−10.3280	+	3.91690i	−0.479984	+	0.182034i	−0.582717	−	0.812675i	$-0.698010\pi$
$463$	−10.3280	+	3.91690i	−0.479984	+	0.182034i	0.102733	+	0.994709i	$0.467241\pi$
$464$	−11.5953	+	2.85799i	−0.538300	+	0.132679i
$465$	−0.958796	−	0.849419i	−0.0444631	−	0.0393909i
$466$	−0.0295344	−	0.0203861i	−0.00136815	−	0.000944369i
$467$	8.44254	−	22.2611i	0.390674	−	1.03012i	−0.585026	−	0.811014i	$-0.698916\pi$
$467$	8.44254	−	22.2611i	0.390674	−	1.03012i	0.975700	−	0.219109i	$-0.0703149\pi$
$468$	−6.70996	−	2.64126i	−0.310168	−	0.122092i
$469$	−0.377410	−	0.995149i	−0.0174272	−	0.0459517i
$470$	−0.000441987		0.00179321i	−2.03873e−5		8.27146e-5i
$471$	−0.732410	−	0.384398i	−0.0337477	−	0.0177121i
$472$	−0.0250455	+	0.0660395i	−0.00115281	+	0.00303972i
$473$	22.4290	+	2.72337i	1.03129	+	0.125221i
$474$	−0.0123353	+	0.00851447i	−0.000566581	+	0.000391083i
$475$	−3.07628	−	12.4810i	−0.141150	−	0.572666i
$476$	−0.563369	+	2.28568i	−0.0258220	+	0.104764i
$477$	0.871459	−	7.17711i	0.0399014	−	0.328617i
$478$	−0.00239164	−	0.00630624i	−0.000109391	−	0.000288441i
$479$	3.66289	+	14.8609i	0.167362	+	0.679014i	0.993331	+	0.115298i	$0.0367824\pi$
$479$	3.66289	+	14.8609i	0.167362	+	0.679014i	−0.825969	+	0.563716i	$0.809371\pi$
$480$	0.0174791	+	0.00430822i	0.000797810	+	0.000196643i
$481$	−0.191329	+	1.42634i	−0.00872387	+	0.0650357i
$482$	−0.0334393	+	0.00824204i	−0.00152312	+	0.000375415i
$483$	−0.491835	−	0.937114i	−0.0223793	−	0.0426402i
$484$	7.01833			0.319015
$485$	3.39396			0.154112
$486$	0.000771433		0.00146984i	3.49929e−5		6.66735e-5i
$487$	22.3335	−	25.2093i	1.01203	−	1.14234i	0.0222469	−	0.999753i	$-0.492918\pi$
$487$	22.3335	−	25.2093i	1.01203	−	1.14234i	0.989782	−	0.142592i	$-0.0455435\pi$
$488$		−	0.0375893i		−	0.00170159i
$489$	8.42739	+	9.51256i	0.381100	+	0.430173i
$490$	−0.00910292	−	0.00477758i	−0.000411228	−	0.000215829i
$491$	1.47975	−	12.1868i	0.0667800	−	0.549983i	−0.920471	−	0.390811i	$-0.872195\pi$
$491$	1.47975	−	12.1868i	0.0667800	−	0.549983i	0.987251	−	0.159172i	$-0.0508824\pi$
$492$	3.57555	−	6.81265i	0.161198	−	0.307138i
$493$	−1.10401	+	9.09231i	−0.0497219	+	0.409497i
$494$	−0.00834250	−	0.0163905i	−0.000375347	−	0.000737444i
$495$	−0.298144	−	2.45544i	−0.0134006	−	0.110364i
$496$	5.30106	+	2.01043i	0.238025	+	0.0902709i
$497$	2.22886	−	1.16979i	0.0999779	−	0.0524724i
$498$	−0.00699590	−	0.0184467i	−0.000313494	−	0.000826615i
$499$	10.1053	−	19.2539i	0.452373	−	0.861925i	−0.547314	−	0.836927i	$-0.684350\pi$
$499$	10.1053	−	19.2539i	0.452373	−	0.861925i	0.999688	−	0.0249980i	$-0.00795793\pi$
$500$	−7.71370	+	14.6972i	−0.344967	+	0.657280i
$501$	−3.78703	+	15.3646i	−0.169192	+	0.686440i
$502$	−0.0508930	+	0.00617953i	−0.00227146	+	0.000275806i
$503$	6.29951	−	5.58087i	0.280881	−	0.248839i	−0.510905	−	0.859637i	$-0.670690\pi$
$503$	6.29951	−	5.58087i	0.280881	−	0.248839i	0.791786	+	0.610798i	$0.209151\pi$
$504$	−0.00144722	+	0.00209666i	−6.44642e−5	+	9.33925e-5i
$505$	0.539618	−	0.204650i	0.0240127	−	0.00910680i
$506$	0.0125320			0.000557118
$507$	4.91259	−	12.0360i	0.218176	−	0.534540i
$508$	−20.8001			−0.922854
$509$	−6.17568	+	2.34213i	−0.273732	+	0.103813i	−0.487651	−	0.873038i	$-0.662146\pi$
$509$	−6.17568	+	2.34213i	−0.273732	+	0.103813i	0.213919	+	0.976851i	$0.431377\pi$
$510$	0.00261436	−	0.00378755i	0.000115766	−	0.000167715i
$511$	−2.59783	+	2.30148i	−0.114921	+	0.101811i
$512$	−0.131830	+	0.0160070i	−0.00582611	+	0.000707418i
$513$	0.735380	−	2.98355i	0.0324678	−	0.131727i
$514$	−0.00412438	+	0.00785835i	−0.000181919	+	0.000346617i
$515$	2.48972	−	4.74377i	0.109710	−	0.209035i
$516$	−5.85459	−	15.4373i	−0.257734	−	0.679589i
$517$	−2.98348	+	1.56585i	−0.131213	+	0.0688661i
$518$	0.000237695	0	9.01459e-5i	1.04437e−5	0	3.96078e-6i
$519$	2.56426	+	21.1186i	0.112559	+	0.927004i
$520$	−0.00544030	+	0.0209409i	−0.000238573	+	0.000918320i
$521$	−0.750514	+	6.18104i	−0.0328806	+	0.270796i	0.966992	+	0.254808i	$0.0820124\pi$
$521$	−0.750514	+	6.18104i	−0.0328806	+	0.270796i	−0.999872	+	0.0159878i	$0.994911\pi$
$522$	−0.00230319	+	0.00438837i	−0.000100808	+	0.000192074i
$523$	2.54673	−	20.9742i	0.111361	−	0.917137i	−0.824766	−	0.565474i	$-0.808693\pi$
$523$	2.54673	−	20.9742i	0.111361	−	0.917137i	0.936127	−	0.351663i	$-0.114384\pi$
$524$	10.3215	+	5.41712i	0.450895	+	0.236648i
$525$	−1.06434	−	1.20139i	−0.0464516	−	0.0524331i
$526$		0	0.000375455i		0	1.63706e-5i
$527$	2.88337	−	3.25465i	0.125601	−	0.141775i
$528$	5.08765	+	9.69371i	0.221412	+	0.421865i
$529$	−15.3914			−0.669190
$530$	−0.0108461			−0.000471125
$531$	−4.94328	−	9.41864i	−0.214520	−	0.408734i
$532$	2.28947	−	0.564304i	0.0992613	−	0.0244657i
$533$	12.2001	+	6.59910i	0.528444	+	0.285839i
$534$	−0.0152172	−	0.00375070i	−0.000658512	−	0.000162309i
$535$	0.967324	+	3.92459i	0.0418210	+	0.169675i
$536$	−0.00653138	−	0.0172218i	−0.000282113	−	0.000743870i
$537$	−0.0837067	+	0.689387i	−0.00361221	+	0.0297492i
$538$	−0.0103223	+	0.0418791i	−0.000445025	+	0.00180554i
$539$	−4.48852	−	18.2107i	−0.193334	−	0.784388i
$540$	−1.48752	+	1.02676i	−0.0640127	+	0.0441848i
$541$	37.3380	+	4.53366i	1.60529	+	0.194917i	0.873573	−	0.486694i	$-0.161797\pi$
$541$	37.3380	+	4.53366i	1.60529	+	0.194917i	0.731715	+	0.681611i	$0.238720\pi$
$542$	0.00491144	−	0.0129504i	0.000210964	−	0.000556267i
$543$	12.6381	+	6.63299i	0.542353	+	0.284649i
$544$	−0.0146243	+	0.0593332i	−0.000627013	+	0.00254389i
$545$	−3.21684	−	8.48210i	−0.137794	−	0.363333i
$546$	−0.00187343	−	0.00132805i	−8.01755e−5	−	5.68354e-5i
$547$	2.05665	−	5.42294i	0.0879360	−	0.231868i	−0.883833	−	0.467803i	$-0.845046\pi$
$547$	2.05665	−	5.42294i	0.0879360	−	0.231868i	0.971769	+	0.235934i	$0.0758151\pi$
$548$	−17.6373	−	12.1742i	−0.753430	−	0.520055i
$549$	4.23739	+	3.75400i	0.180847	+	0.160217i
$550$	0.0184534	−	0.00454836i	0.000786857	−	0.000193943i
$551$	8.57811	−	3.25325i	0.365440	−	0.138593i
$552$	−0.00851160	−	0.0162175i	−0.000362278	−	0.000690262i
$553$	3.23927	−	1.22849i	0.137748	−	0.0522409i
$554$	0.00500628	−	0.00565092i	0.000212697	−	0.000240085i
$555$	0.270001	+	0.239200i	0.0114609	+	0.0101535i
$556$	10.9680	+	15.8898i	0.465145	+	0.673879i
$557$	−26.4795	+	18.2775i	−1.12197	+	0.774441i	−0.976627	−	0.214940i	$-0.931045\pi$
$557$	−26.4795	+	18.2775i	−1.12197	+	0.774441i	−0.145345	+	0.989381i	$0.546429\pi$
$558$	0.00208332	−	0.00109341i	8.81941e−5	−	4.62879e-5i
$559$	27.9599	−	10.2055i	1.18258	−	0.431645i
$560$	−1.22812	−	0.644566i	−0.0518974	−	0.0272379i
$561$	8.33503	−	1.01206i	0.351905	−	0.0427290i
$562$	0.00431639	+	0.00106390i	0.000182076	+	4.48777e-5i
$563$	−10.6799	−	15.4725i	−0.450104	−	0.652088i	0.530592	−	0.847628i	$-0.321970\pi$
$563$	−10.6799	−	15.4725i	−0.450104	−	0.652088i	−0.980696	+	0.195539i	$0.937354\pi$
$564$	2.02634	+	1.39868i	0.0853243	+	0.0588951i
$565$	1.10924	+	1.25207i	0.0466660	+	0.0526750i
$566$	−0.0136041	+	0.00165183i	−0.000571821	+	6.94317e-5i
$567$	−0.0918213	−	0.372534i	−0.00385613	−	0.0156449i
$568$	0.0385721	−	0.0202442i	0.00161845	−	0.000849428i
$569$	−3.07546	−	25.3287i	−0.128930	−	1.06183i	−0.903272	−	0.429068i	$-0.858842\pi$
$569$	−3.07546	−	25.3287i	−0.128930	−	1.06183i	0.774342	−	0.632767i	$-0.218081\pi$
$570$	−0.00457624		0.000555657i	−0.000191678		2.32739e-5i
$571$	−3.89351	−	5.64072i	−0.162938	−	0.236057i	0.733007	−	0.680221i	$-0.238116\pi$
$571$	−3.89351	−	5.64072i	−0.162938	−	0.236057i	−0.895945	+	0.444164i	$0.853501\pi$
$572$	−17.5890	+	8.95253i	−0.735435	+	0.374324i
$573$	−10.7129	+	15.5203i	−0.447537	+	0.648369i
$574$	0.00162476	−	0.00183398i	6.78162e−5	−	7.65487e-5i
$575$	11.2037	−	2.76146i	0.467226	−	0.115161i
$576$	4.54448	−	6.58382i	0.189353	−	0.274326i
$577$			1.09335i			0.0455169i	0.999741	+	0.0227585i	$0.00724487\pi$
$577$			1.09335i			0.0455169i	−0.999741	+	0.0227585i	$0.992755\pi$
$578$	−0.0103675	−	0.00715617i	−0.000431231	−	0.000297657i
$579$	−12.2636	−	1.48907i	−0.509658	−	0.0618836i
$580$	−5.04572	−	1.91359i	−0.209512	−	0.0794574i
$581$	0.549650	+	4.52677i	0.0228033	+	0.187802i
$582$	−0.00221062	+	0.00582892i	−9.16330e−5	+	0.000241616i
$583$	−13.1216	−	14.8112i	−0.543441	−	0.613418i
$584$	−0.0449575	+	0.0398289i	−0.00186036	+	0.00164813i
$585$	−1.81732	−	2.70462i	−0.0751371	−	0.111822i
$586$	0.0246498	+	0.0218378i	0.00101827	+	0.000902112i
$587$			25.1178i			1.03672i	0.855162	+	0.518360i	$0.173457\pi$
$587$			25.1178i			1.03672i	−0.855162	+	0.518360i	$0.826543\pi$
$588$	−10.2588	+	9.08846i	−0.423064	+	0.374802i
$589$	−4.22882	−	1.04231i	−0.174246	−	0.0429477i
$590$	−0.0131329	+	0.00906495i	−0.000540671	+	0.000373198i
$591$	23.4449	+	8.89148i	0.964395	+	0.365747i
$592$	−1.49280	−	0.566145i	−0.0613538	−	0.0232684i
$593$	−21.8824	+	15.1044i	−0.898604	+	0.620262i	−0.925240	−	0.379383i	$-0.876136\pi$
$593$	−21.8824	+	15.1044i	−0.898604	+	0.620262i	0.0266352	+	0.999645i	$0.491521\pi$
$594$	0.00441126	+	0.00108728i	0.000180996	+	4.46115e-5i
$595$	−0.796220	+	0.705389i	−0.0326418	+	0.0289181i
$596$			18.7479i			0.767942i
$597$	2.19899	+	1.94813i	0.0899986	+	0.0797318i
$598$	0.0147131	−	0.00748874i	0.000601664	−	0.000306237i
$599$	3.36240	−	2.97882i	0.137384	−	0.121711i	−0.591632	−	0.806208i	$-0.701516\pi$
$599$	3.36240	−	2.97882i	0.137384	−	0.121711i	0.729016	+	0.684496i	$0.239978\pi$
$600$	−0.0184193	−	0.0207911i	−0.000751963	−	0.000848791i
$601$	−7.72994	+	20.3822i	−0.315311	+	0.831407i	0.679868	+	0.733334i	$0.262037\pi$
$601$	−7.72994	+	20.3822i	−0.315311	+	0.831407i	−0.995179	+	0.0980726i	$0.968732\pi$
$602$	−0.000633750	−	0.00521940i	−2.58297e−5	−	0.000212727i
$603$	2.59368	+	0.983652i	0.105623	+	0.0400574i
$604$	3.92422	+	0.476487i	0.159674	+	0.0193880i
$605$	2.60999	+	1.80154i	0.106111	+	0.0732431i
$606$			0.00106006i			4.30618e-5i
$607$	1.99613	−	2.89190i	0.0810206	−	0.117379i	−0.780378	−	0.625308i	$-0.784973\pi$
$607$	1.99613	−	2.89190i	0.0810206	−	0.117379i	0.861399	+	0.507929i	$0.169589\pi$
$608$	0.0594317	−	0.0146486i	0.00241028	−	0.000594080i
$609$	0.759623	−	0.857437i	0.0307815	−	0.0347451i
$610$	0.00482441	−	0.00698937i	0.000195335	−	0.000282991i
$611$	−2.56702	+	3.62120i	−0.103851	+	0.146498i
$612$	−3.48536	−	5.04941i	−0.140887	−	0.204110i
$613$	27.2467	+	3.30835i	1.10048	+	0.133623i	0.650568	−	0.759448i	$-0.274531\pi$
$613$	27.2467	+	3.30835i	1.10048	+	0.133623i	0.449916	+	0.893071i	$0.351454\pi$
$614$	−0.00411849	−	0.0339188i	−0.000166209	−	0.00136885i
$615$	3.07843	−	1.61568i	0.124134	−	0.0651506i
$616$	0.00166868	+	0.00677009i	6.72329e−5	+	0.000272775i
$617$	−15.8113	+	1.91984i	−0.636541	+	0.0772900i	−0.432444	−	0.901661i	$-0.642349\pi$
$617$	−15.8113	+	1.91984i	−0.636541	+	0.0772900i	−0.204097	+	0.978951i	$0.565426\pi$
$618$	0.00652547	+	0.00736574i	0.000262493	+	0.000296293i
$619$	22.0454	+	15.2169i	0.886080	+	0.611617i	0.921766	−	0.387746i	$-0.126746\pi$
$619$	22.0454	+	15.2169i	0.886080	+	0.611617i	−0.0356860	+	0.999363i	$0.511362\pi$
$620$	1.45531	+	2.10838i	0.0584466	+	0.0846746i
$621$	2.67822	+	0.660122i	0.107473	+	0.0264898i
$622$	−0.0490590	+	0.00595685i	−0.00196709	+	0.000238848i
$623$	3.20757	+	1.68346i	0.128509	+	0.0674466i
$624$	11.7657	+	8.34059i	0.471007	+	0.333891i
$625$	11.8792	−	6.23470i	0.475169	−	0.249388i
$626$	−0.0384726	+	0.0265557i	−0.00153767	+	0.00106138i
$627$	−4.77753	−	6.92145i	−0.190796	−	0.276416i
$628$	1.23827	+	1.09701i	0.0494123	+	0.0437755i
$629$	−0.811968	+	0.916523i	−0.0323753	+	0.0365442i
$630$	−0.000538193	0	0.000204110i	−2.14421e−5	0	8.13192e-6i
$631$	18.6677	+	35.5683i	0.743148	+	1.41595i	0.903367	+	0.428868i	$0.141088\pi$
$631$	18.6677	+	35.5683i	0.743148	+	1.41595i	−0.160219	+	0.987081i	$0.551220\pi$
$632$	0.0560582	−	0.0212601i	0.00222987	−	0.000845679i
$633$	−5.65362	+	1.39349i	−0.224711	+	0.0553864i
$634$	0.0124172	+	0.0110006i	0.000493148	+	0.000436891i
$635$	−7.73516	−	5.33920i	−0.306961	−	0.211880i
$636$	−5.12746	+	13.5200i	−0.203317	+	0.536102i
$637$	−16.1518	−	18.6978i	−0.639957	−	0.740835i
$638$	0.00481001	+	0.0126829i	0.000190430	+	0.000502123i
$639$	−1.57005	+	6.36995i	−0.0621103	+	0.251991i
$640$	−0.0425072	−	0.0223095i	−0.00168024	−	0.000881859i
$641$	5.51734	−	14.5480i	0.217922	−	0.574613i	−0.780820	−	0.624756i	$-0.785198\pi$
$641$	5.51734	−	14.5480i	0.217922	−	0.574613i	0.998742	+	0.0501431i	$0.0159677\pi$
$642$	−0.00737028		0.000894914i	−0.000290882		3.53195e-5i
$643$	−24.4605	+	16.8839i	−0.964630	+	0.665836i	−0.942601	−	0.333921i	$-0.891628\pi$
$643$	−24.4605	+	16.8839i	−0.964630	+	0.665836i	−0.0220290	+	0.999757i	$0.507013\pi$
$644$	0.506554	+	2.05517i	0.0199610	+	0.0809851i
$645$	1.78540	−	7.24366i	0.0703002	−	0.285219i
$646$	0.00188619	−	0.0155341i	7.42110e−5	−	0.000611182i
$647$	−1.24978	−	3.29540i	−0.0491339	−	0.129555i	0.908203	−	0.418531i	$-0.137455\pi$
$647$	−1.24978	−	3.29540i	−0.0491339	−	0.129555i	−0.957337	+	0.288975i	$0.906685\pi$
$648$	−0.00158904	−	0.00644699i	−6.24234e−5	−	0.000253262i
$649$	−28.2670	−	6.96718i	−1.10958	−	0.273486i
$650$	0.0189471	−	0.0163671i	0.000743166	−	0.000641971i
$651$	−0.528021	+	0.130145i	−0.0206948	+	0.00510080i
$652$	−11.8120	−	22.5059i	−0.462593	−	0.881397i
$653$	−7.19423			−0.281532			−0.140766	−	0.990043i	$-0.544956\pi$
$653$	−7.19423			−0.281532			−0.140766	+	0.990043i	$0.544956\pi$
$654$	0.0166627			0.000651564
$655$	2.44783	+	4.66396i	0.0956447	+	0.182236i
$656$	−10.2040	+	11.5180i	−0.398400	+	0.449701i
$657$		−	9.04567i		−	0.352905i
$658$	0.000519950	0	0.000586902i	2.02698e−5	0	2.28798e-5i
$659$	21.2610	+	11.1587i	0.828212	+	0.434679i	0.824875	−	0.565315i	$-0.191245\pi$
$659$	21.2610	+	11.1587i	0.828212	+	0.434679i	0.00333728	+	0.999994i	$0.498938\pi$
$660$	−0.596288	+	4.91087i	−0.0232105	+	0.191155i
$661$	7.40321	−	14.1056i	0.287952	−	0.548646i	−0.697915	−	0.716181i	$-0.745888\pi$
$661$	7.40321	−	14.1056i	0.287952	−	0.548646i	0.985866	+	0.167535i	$0.0535808\pi$
$662$	0.00649971	−	0.0535299i	0.000252618	−	0.00208050i
$663$	9.18088	−	6.16893i	0.356556	−	0.239581i
$664$	0.00951212	+	0.0783394i	0.000369142	+	0.00304016i
$665$	0.996264	+	0.377833i	0.0386335	+	0.0146517i
$666$	−0.000586673	0	0.000307910i	−2.27331e−5	0	1.19313e-5i
$667$	2.92031	+	7.70024i	0.113075	+	0.298154i
$668$	14.7079	−	28.0236i	0.569067	−	1.08427i
$669$	5.27090	−	10.0429i	0.203785	−	0.388279i
$670$	0.000995897	−	0.00404051i	3.84749e−5	−	0.000156099i
$671$	15.3811	−	1.86760i	0.593780	−	0.0720980i
$672$	0.00572077	−	0.00506816i	0.000220684	−	0.000195509i
$673$	−21.8495	+	31.6544i	−0.842235	+	1.22019i	0.131230	+	0.991352i	$0.458108\pi$
$673$	−21.8495	+	31.6544i	−0.842235	+	1.22019i	−0.973465	+	0.228837i	$0.926508\pi$
$674$	−0.0130532	+	0.00495041i	−0.000502789	+	0.000190683i
$675$	4.18326			0.161014
$676$	−15.3005	+	21.0213i	−0.588480	+	0.808510i
$677$	37.1971			1.42960			0.714801	−	0.699328i	$-0.246517\pi$
$677$	37.1971			1.42960			0.714801	+	0.699328i	$0.246517\pi$
$678$	−0.00287284	+	0.00108952i	−0.000110331	+	4.18429e-5i
$679$	0.818531	−	1.18585i	0.0314123	−	0.0455086i
$680$	−0.0137792	+	0.0122073i	−0.000528409	+	0.000468129i
$681$	−26.5109	+	3.21900i	−1.01590	+	0.123352i
$682$	0.00154108	−	0.00625242i	5.90111e−5	−	0.000239417i
$683$	19.2078	−	36.5974i	0.734966	−	1.40036i	−0.174532	−	0.984652i	$-0.555841\pi$
$683$	19.2078	−	36.5974i	0.734966	−	1.40036i	0.909498	−	0.415709i	$-0.136467\pi$
$684$	−2.85604	+	5.44173i	−0.109203	+	0.208070i
$685$	−3.43400	−	9.05470i	−0.131206	−	0.345962i
$686$	−0.00781233	+	0.00410023i	−0.000298276	+	0.000156547i
$687$	−4.05524	−	1.53795i	−0.154717	−	0.0586765i
$688$	3.98016	+	32.7795i	0.151742	+	1.24971i
$689$	−24.2560	−	9.54793i	−0.924079	−	0.363747i
$690$	0.000498791	−	0.00410792i	1.89887e−5	−	0.000156386i
$691$	−12.4724	+	23.7641i	−0.474471	+	0.904028i	0.524155	+	0.851623i	$0.324381\pi$
$691$	−12.4724	+	23.7641i	−0.474471	+	0.904028i	−0.998626	+	0.0524056i	$0.983311\pi$
$692$	5.12852	−	42.2372i	0.194957	−	1.60562i
$693$	−0.929831	−	0.488013i	−0.0353214	−	0.0185381i
$694$	0.0373089	+	0.0421131i	0.00141623	+	0.00159859i
$695$			8.72452i			0.330940i
$696$	0.0131459	−	0.0148386i	0.000498293	−	0.000562457i
$697$	5.48446	+	10.4498i	0.207739	+	0.395813i
$698$	0.0113545			0.000429773
$699$	−21.6189			−0.817700
$700$	1.49180	+	2.84239i	0.0563847	+	0.107432i
$701$	17.9025	−	4.41256i	0.676166	−	0.166660i	0.113744	−	0.993510i	$-0.463716\pi$
$701$	17.9025	−	4.41256i	0.676166	−	0.166660i	0.562422	+	0.826850i	$0.309870\pi$
$702$	0.00582871	−	0.00135951i	0.000219990	−	5.13116e-5i
$703$	1.19085	+	0.293519i	0.0449139	+	0.0110703i
$704$	−5.23989	−	21.2591i	−0.197486	−	0.801232i
$705$	0.394529	+	1.04029i	0.0148588	+	0.0391795i
$706$	−0.00528117	+	0.0434943i	−0.000198759	+	0.00163693i
$707$	0.0586365	−	0.237898i	0.00220525	−	0.00894706i
$708$	5.09122	+	20.6559i	0.191340	+	0.776296i
$709$	−4.32175	+	2.98309i	−0.162307	+	0.112032i	−0.646450	−	0.762957i	$-0.723747\pi$
$709$	−4.32175	+	2.98309i	−0.162307	+	0.112032i	0.484143	+	0.874989i	$0.339132\pi$
$710$	0.00977037	+	0.00118634i	0.000366676	+	4.45225e-5i
$711$	−3.20185	+	8.44258i	−0.120079	+	0.316621i
$712$	0.0555096	+	0.0291337i	0.00208031	+	0.00109183i
$713$	0.935642	−	3.79605i	0.0350401	−	0.142163i
$714$	−0.000692853	−	0.00182690i	−2.59294e−5	−	6.83702e-5i
$715$	−8.83907	−	1.18567i	−0.330563	−	0.0443416i
$716$	0.492510	−	1.29864i	0.0184060	−	0.0485325i
$717$	−3.34379	−	2.30805i	−0.124876	−	0.0861957i
$718$	−0.0263577	−	0.0233509i	−0.000983659	−	0.000871446i
$719$	−40.0901	+	9.88132i	−1.49511	+	0.368511i	−0.900269	−	0.435334i	$-0.856630\pi$
$719$	−40.0901	+	9.88132i	−1.49511	+	0.368511i	−0.594839	+	0.803845i	$0.702784\pi$
$720$	3.38002	−	1.28187i	0.125966	−	0.0477726i
$721$	−1.05701	−	2.01397i	−0.0393652	−	0.0750042i
$722$	0.0148345	−	0.00562599i	0.000552083	−	0.000209378i
$723$	−13.7579	+	15.5295i	−0.511663	+	0.577548i
$724$	−21.3670	−	18.9295i	−0.794097	−	0.703508i
$725$	7.09487	+	10.2787i	0.263497	+	0.381741i
$726$	−0.00479402	+	0.00330907i	−0.000177923	+	0.000122811i
$727$	4.21508	−	2.21225i	0.156329	−	0.0820476i	−0.384745	−	0.923023i	$-0.625710\pi$
$727$	4.21508	−	2.21225i	0.156329	−	0.0820476i	0.541073	+	0.840975i	$0.318018\pi$
$728$	0.00600467	+	0.00695120i	0.000222548	+	0.000257629i
$729$	0.885456	+	0.464723i	0.0327947	+	0.0172120i
$730$	−0.0134713	+	0.00163571i	−0.000498595	+	6.05404e-5i
$731$	24.5887	+	6.06058i	0.909447	+	0.224159i
$732$	−6.43172	−	9.31796i	−0.237723	−	0.344402i
$733$	−29.3991	−	20.2927i	−1.08588	−	0.749529i	−0.116033	−	0.993245i	$-0.537018\pi$
$733$	−29.3991	−	20.2927i	−1.08588	−	0.749529i	−0.969847	+	0.243717i	$0.921633\pi$
$734$	0.00876824	+	0.00989730i	0.000323642	+	0.000365316i
$735$	−6.14797	+	0.746499i	−0.226771	+	0.0275350i
$736$	0.0131495	+	0.0533496i	0.000484696	+	0.00196649i
$737$	6.72247	−	3.52822i	0.247625	−	0.129964i
$738$	0.000769738		0.00633936i	2.83344e−5		0.000233355i
$739$	−2.82415	−	0.342914i	−0.103888	−	0.0126143i	0.0684275	−	0.997656i	$-0.478202\pi$
$739$	−2.82415	−	0.342914i	−0.103888	−	0.0126143i	−0.172316	+	0.985042i	$0.555125\pi$
$740$	−0.409821	−	0.593729i	−0.0150653	−	0.0218259i
$741$	−9.74504	−	5.27116i	−0.357993	−	0.193641i
$742$	−0.00261578	+	0.00378962i	−9.60285e−5	+	0.000139121i
$743$	−8.73638	+	9.86134i	−0.320507	+	0.361777i	−0.886578	−	0.462579i	$-0.846924\pi$
$743$	−8.73638	+	9.86134i	−0.320507	+	0.361777i	0.566071	+	0.824356i	$0.308463\pi$
$744$	−0.00913782	+	0.00225227i	−0.000335009	+	8.25723e-5i
$745$	−4.81241	+	6.97198i	−0.176313	+	0.255434i
$746$			0.0164407i			0.000601936i
$747$	−9.78106	−	6.75138i	−0.357870	−	0.247020i
$748$	−16.6700	−	2.02411i	−0.609517	−	0.0740088i
$749$	1.60454	+	0.608520i	0.0586285	+	0.0222349i
$750$	−0.00166059	−	0.0136762i	−6.06362e−5	−	0.000499384i
$751$	−5.79626	+	15.2835i	−0.211509	+	0.557702i	−0.998221	−	0.0596169i	$-0.981012\pi$
$751$	−5.79626	+	15.2835i	−0.211509	+	0.557702i	0.786713	+	0.617319i	$0.211781\pi$
$752$	−3.26545	−	3.68593i	−0.119079	−	0.134412i
$753$	−23.1169	+	20.4798i	−0.842427	+	0.746325i
$754$	0.0132260	+	0.0120160i	0.000481664	+	0.000437596i
$755$	1.33704	+	1.18451i	0.0486597	+	0.0431087i
$756$			0.767364i			0.0279088i
$757$	−39.1795	+	34.7100i	−1.42400	+	1.26156i	−0.507429	+	0.861693i	$0.669404\pi$
$757$	−39.1795	+	34.7100i	−1.42400	+	1.26156i	−0.916575	+	0.399864i	$0.869057\pi$
$758$	0.0528609	+	0.0130290i	0.00191999	+	0.000473236i
$759$	6.21311	−	4.28860i	0.225522	−	0.155666i
$760$	0.0172411	+	0.00653870i	0.000625402	+	0.000237184i
$761$	2.64851	+	1.00445i	0.0960083	+	0.0364111i	0.402141	−	0.915578i	$-0.368266\pi$
$761$	2.64851	+	1.00445i	0.0960083	+	0.0364111i	−0.306133	+	0.951989i	$0.599035\pi$
$762$	0.0142079	−	0.00980703i	0.000514699	−	0.000355271i
$763$	−3.73945	−	0.921691i	−0.135377	−	0.0333675i
$764$	28.2316	−	25.0110i	1.02138	−	0.904867i
$765$		−	2.77244i		−	0.100238i
$766$	−0.0415472	−	0.0368076i	−0.00150116	−	0.00132991i
$767$	−37.3499	+	8.71166i	−1.34863	+	0.314560i
$768$	−11.9760	+	10.6098i	−0.432147	+	0.382849i
$769$	−34.8860	−	39.3782i	−1.25802	−	1.42001i	−0.865990	−	0.500061i	$-0.833311\pi$
$769$	−34.8860	−	39.3782i	−1.25802	−	1.42001i	−0.392032	−	0.919952i	$-0.628228\pi$
$770$	−0.000558635		0.00147300i	−2.01318e−5		5.30833e-5i
$771$	0.644436	+	5.30741i	0.0232088	+	0.191142i
$772$	23.1017	+	8.76133i	0.831449	+	0.315327i
$773$	18.0544	+	2.19220i	0.649372	+	0.0788480i	0.438593	−	0.898686i	$-0.355477\pi$
$773$	18.0544	+	2.19220i	0.649372	+	0.0788480i	0.210779	+	0.977534i	$0.432400\pi$
$774$	0.0112776	+	0.00778439i	0.000405366	+	0.000279804i
$775$		−	5.92926i		−	0.212985i
$776$	0.0141653	−	0.0205220i	0.000508505	−	0.000736697i
$777$	0.148693	−	0.0366495i	0.00533433	−	0.00131479i
$778$	0.0290897	−	0.0328355i	0.00104292	−	0.00117721i
$779$	6.71519	−	9.72863i	0.240596	−	0.348564i
$780$	2.23451	+	6.12188i	0.0800083	+	0.219199i
$781$	10.2001	+	14.7774i	0.364989	+	0.528778i
$782$	0.0139444	+	0.00169315i	0.000498650	+	6.05471e-5i
$783$	0.359874	+	2.96383i	0.0128609	+	0.105919i
$784$	24.2713	−	12.7385i	0.866831	−	0.454948i
$785$	0.178896	+	0.725810i	0.00638508	+	0.0259053i
$786$	−0.00960442	+	0.00116619i	−0.000342578	+	4.15965e-5i
$787$	−8.69855	−	9.81863i	−0.310070	−	0.349997i	0.572731	−	0.819743i	$-0.305884\pi$
$787$	−8.69855	−	9.81863i	−0.310070	−	0.349997i	−0.882801	+	0.469747i	$0.844345\pi$
$788$	−41.2715	−	28.4877i	−1.47024	−	1.01483i
$789$	0.128485	+	0.186142i	0.00457418	+	0.00662685i
$790$	0.0131521	+	0.00324171i	0.000467931	+	0.000115335i
$791$	0.704989	−	0.0856012i	0.0250665	−	0.00304363i
$792$	−0.0160915	−	0.00844546i	−0.000571786	−	0.000300096i
$793$	16.9420	−	11.3839i	0.601627	−	0.404253i
$794$	−0.00330712	+	0.00173571i	−0.000117365	+	6.15981e-5i
$795$	−5.37727	+	3.71166i	−0.190712	+	0.131639i
$796$	−3.33774	−	4.83555i	−0.118303	−	0.171391i
$797$	9.50981	+	8.42495i	0.336855	+	0.298427i	0.814544	−	0.580102i	$-0.196987\pi$
$797$	9.50981	+	8.42495i	0.336855	+	0.298427i	−0.477690	+	0.878529i	$0.658526\pi$
$798$	−0.00129781	+	0.00146492i	−4.59420e−5	+	5.18577e-5i
$799$	−3.53127	+	1.33923i	−0.124927	+	0.0473787i
$800$	0.0387252	+	0.0737847i	0.00136914	+	0.00260868i
$801$	−8.82788	+	3.34797i	−0.311918	+	0.118295i
$802$	0.0306625	−	0.00755763i	0.00108273	−	0.000266869i
$803$	−18.5312	−	16.4172i	−0.653952	−	0.579351i
$804$	−4.56581	−	3.15155i	−0.161024	−	0.111147i
$805$	−0.339166	+	0.894308i	−0.0119540	+	0.0315202i
$806$	−0.00192695	−	0.00826149i	−6.78738e−5	−	0.000290998i
$807$	9.21393	+	24.2951i	0.324346	+	0.855229i
$808$	0.00101475	−	0.00411701i	3.56988e−5	−	0.000144836i
$809$	36.7773	+	19.3022i	1.29302	+	0.678631i	0.964053	−	0.265710i	$-0.0856064\pi$
$809$	36.7773	+	19.3022i	1.29302	+	0.678631i	0.328969	+	0.944341i	$0.393299\pi$
$810$	0.000531975	−	0.00140270i	1.86917e−5	−	4.92860e-5i
$811$	−34.4151	−	4.17875i	−1.20848	−	0.146736i	−0.508603	−	0.861001i	$-0.669838\pi$
$811$	−34.4151	−	4.17875i	−1.20848	−	0.146736i	−0.699875	+	0.714265i	$0.746761\pi$
$812$	−1.88549	+	1.30146i	−0.0661678	+	0.0456723i
$813$	−1.99678	−	8.10127i	−0.0700303	−	0.284124i
$814$	−0.000433975		0.00176071i	−1.52108e−5		6.17128e-5i
$815$	1.38440	−	11.4015i	0.0484933	−	0.399379i
$816$	4.35134	+	11.4735i	0.152327	+	0.401654i
$817$	−6.07064	−	24.6296i	−0.212385	−	0.861679i
$818$	2.22616e−5	0	5.48699e-6i	7.78358e−7	0	1.91848e-7i
$819$	−1.38328	−	0.0173102i	−0.0483357	−	0.000604869i
$820$	−6.75126	+	1.66404i	−0.235764	+	0.0581106i
$821$	−22.6514	−	43.1586i	−0.790539	−	1.50625i	−0.860929	−	0.508726i	$-0.830117\pi$
$821$	−22.6514	−	43.1586i	−0.790539	−	1.50625i	0.0703901	−	0.997520i	$-0.477576\pi$
$822$	0.0177876			0.000620413
$823$	−9.11738			−0.317812			−0.158906	−	0.987294i	$-0.550797\pi$
$823$	−9.11738			−0.317812			−0.158906	+	0.987294i	$0.550797\pi$
$824$	−0.0182925	−	0.0348534i	−0.000637248	−	0.00121417i
$825$	7.59230	−	8.56994i	0.264330	−	0.298367i
$826$			0.00677482i			0.000235726i
$827$	−20.2787	−	22.8899i	−0.705159	−	0.795960i	0.281361	−	0.959602i	$-0.409214\pi$
$827$	−20.2787	−	22.8899i	−0.705159	−	0.795960i	−0.986520	+	0.163642i	$0.947676\pi$
$828$	−4.88483	−	2.56376i	−0.169760	−	0.0890967i
$829$	−0.585981	+	4.82598i	−0.0203519	+	0.167613i	−0.999341	−	0.0362997i	$-0.988443\pi$
$829$	−0.585981	+	4.82598i	−0.0203519	+	0.167613i	0.978989	+	0.203913i	$0.0653660\pi$
$830$	−0.00828582	+	0.0157873i	−0.000287605	+	0.000547985i
$831$	0.548197	−	4.51481i	0.0190167	−	0.156617i
$832$	−18.8556	−	21.8278i	−0.653699	−	0.756744i
$833$	−2.53400	−	20.8694i	−0.0877979	−	0.723081i
$834$	−0.0149838	−	0.00568261i	−0.000518847	−	0.000196773i
$835$	12.6630	−	6.64607i	0.438222	−	0.229997i
$836$	5.96458	+	15.7273i	0.206289	+	0.543940i
$837$	0.658688	−	1.25503i	0.0227676	−	0.0433800i
$838$	0.0107294	−	0.0204432i	0.000370642	−	0.000706200i
$839$	3.31451	−	13.4475i	0.114430	−	0.464260i	−0.885570	−	0.464506i	$-0.846232\pi$
$839$	3.31451	−	13.4475i	0.114430	−	0.464260i	1.00000		0.000245778i	$7.82334e-5\pi$
$840$	0.00228560		0.000277522i	7.88607e−5		9.57543e-6i
$841$	15.0347	−	13.3196i	0.518439	−	0.459297i
$842$	0.000597371	0	0.000865442i	2.05868e−5	0	2.98251e-5i
$843$	2.50405	−	0.949660i	0.0862440	−	0.0327080i
$844$	11.6456			0.400859
$845$	−11.0859	+	3.88991i	−0.381368	+	0.133817i
$846$	−0.00204360			−7.02604e−5
$847$	1.25891	−	0.477443i	0.0432568	−	0.0164051i
$848$	16.4280	−	23.8000i	0.564139	−	0.817296i
$849$	−6.17932	+	5.47440i	−0.212074	+	0.187881i
$850$	0.0211476	−	0.00256778i	0.000725356	−	8.80742e-5i
$851$	−0.263481	+	1.06898i	−0.00903201	+	0.0366443i
$852$	6.09771	−	11.6182i	0.208904	−	0.398033i
$853$	−21.3386	+	40.6573i	−0.730619	+	1.39208i	0.182013	+	0.983296i	$0.441739\pi$
$853$	−21.3386	+	40.6573i	−0.730619	+	1.39208i	−0.912632	+	0.408782i	$0.865954\pi$
$854$	−0.00127856	−	0.00337129i	−4.37514e−5	−	0.000115363i
$855$	−2.45895	+	1.29056i	−0.0840944	+	0.0441361i
$856$	0.0277678	+	0.0105309i	0.000949083	+	0.000359940i
$857$	1.10745	+	9.12066i	0.0378297	+	0.311556i	0.999325	+	0.0367346i	$0.0116956\pi$
$857$	1.10745	+	9.12066i	0.0378297	+	0.311556i	−0.961495	+	0.274821i	$0.911381\pi$
$858$	0.00779354	−	0.0144083i	0.000266067	−	0.000491890i
$859$	−2.54394	+	20.9512i	−0.0867981	+	0.714847i	0.882732	+	0.469876i	$0.155701\pi$
$859$	−2.54394	+	20.9512i	−0.0867981	+	0.714847i	−0.969530	+	0.244971i	$0.921222\pi$
$860$	−6.93408	+	13.2118i	−0.236450	+	0.450518i
$861$	0.177914	−	1.46526i	0.00606330	−	0.0499358i
$862$	0.00165380		0.000867982i	5.63287e−5		2.95636e-5i
$863$	0.929130	+	1.04877i	0.0316280	+	0.0357006i	0.764112	−	0.645084i	$-0.223178\pi$
$863$	0.929130	+	1.04877i	0.0316280	+	0.0357006i	−0.732484	+	0.680784i	$0.761639\pi$
$864$			0.0199198i			0.000677685i
$865$	12.7491	−	14.3908i	0.433483	−	0.489301i
$866$	−0.00119178	−	0.00227074i	−4.04982e−5	−	7.71628e-5i
$867$	−7.58889			−0.257732
$868$	1.08765			0.0369171
$869$	11.4846	+	21.8820i	0.389588	+	0.742297i
$870$	0.00434882	−	0.00107189i	0.000147439	−	3.63404e-5i
$871$	5.78409	−	8.15940i	0.195987	−	0.276471i
$872$	−0.0647141	−	0.0159506i	−0.00219150	−	0.000540155i
$873$	0.898744	+	3.64635i	0.0304179	+	0.123410i
$874$	−0.00498933	−	0.0131558i	−0.000168767	−	0.000445001i
$875$	−0.383823	+	3.16106i	−0.0129756	+	0.106863i
$876$	−4.32953	+	17.5656i	−0.146281	+	0.593487i
$877$	6.84424	+	27.7682i	0.231114	+	0.937665i	0.965806	+	0.259265i	$0.0834803\pi$
$877$	6.84424	+	27.7682i	0.231114	+	0.937665i	−0.734693	+	0.678400i	$0.762674\pi$
$878$	0.0213675	−	0.0147489i	0.000721120	−	0.000497753i
$879$	19.6940	+	2.39128i	0.664261	+	0.0806559i
$880$	3.50841	−	9.25092i	0.118268	−	0.311848i
$881$	−5.01971	−	2.63455i	−0.169118	−	0.0887602i	0.378040	−	0.925789i	$-0.376598\pi$
$881$	−5.01971	−	2.63455i	−0.169118	−	0.0887602i	−0.547158	+	0.837029i	$0.684290\pi$
$882$	0.00272234	−	0.0110450i	9.16660e−5	−	0.000371904i
$883$	−8.85746	−	23.3552i	−0.298077	−	0.785965i	−0.997461	−	0.0712183i	$-0.977311\pi$
$883$	−8.85746	−	23.3552i	−0.298077	−	0.785965i	0.699384	−	0.714746i	$-0.253458\pi$
$884$	−20.7808	+	7.58508i	−0.698935	+	0.255114i
$885$	−3.40885	+	8.98841i	−0.114587	+	0.302142i
$886$	−0.0447402	−	0.0308820i	−0.00150308	−	0.00103750i
$887$	−12.3355	−	10.9283i	−0.414185	−	0.366936i	0.430144	−	0.902760i	$-0.358463\pi$
$887$	−12.3355	−	10.9283i	−0.414185	−	0.366936i	−0.844330	+	0.535824i	$0.820001\pi$
$888$	0.00257325		0.000634249i	8.63526e−5		2.12840e-5i
$889$	−3.73102	+	1.41499i	−0.125134	+	0.0474572i
$890$	0.00658231	+	0.0125415i	0.000220639	+	0.000420393i
$891$	2.55908	−	0.970532i	0.0857325	−	0.0325140i
$892$	−15.0423	+	16.9792i	−0.503653	+	0.568506i
$893$	2.83159	+	2.50857i	0.0947555	+	0.0839460i
$894$	−0.00883943	−	0.0128061i	−0.000295635	−	0.000428301i
$895$	0.516505	−	0.356518i	0.0172649	−	0.0119171i
$896$	−0.0180465	+	0.00947151i	−0.000602890	+	0.000316421i
$897$	4.73171	−	8.74774i	0.157987	−	0.292079i
$898$	0.0273328	+	0.0143454i	0.000912108	+	0.000478711i
$899$	4.20087	−	0.510078i	0.140107	−	0.0170121i
$900$	−8.12339	−	2.00224i	−0.270780	−	0.0667412i
$901$	−12.5993	−	18.2532i	−0.419743	−	0.608103i
$902$	0.0143840	+	0.00992856i	0.000478935	+	0.000330585i
$903$	−2.10034	−	2.37079i	−0.0698948	−	0.0788949i
$904$	0.0122004	−	0.00148140i	0.000405779	−	4.92705e-5i
$905$	−3.08694	−	12.5242i	−0.102613	−	0.416319i
$906$	−0.00290518	+	0.00152476i	−9.65182e−5	+	5.06567e-5i
$907$	5.52903	+	45.5357i	0.183589	+	1.51199i	0.735179	+	0.677873i	$0.237098\pi$
$907$	5.52903	+	45.5357i	0.183589	+	1.51199i	−0.551591	+	0.834115i	$0.685979\pi$
$908$	53.0217	+	6.43800i	1.75959	+	0.213652i
$909$	0.362762	+	0.525552i	0.0120321	+	0.0174315i
$910$	0.000224356		0.00206318i	7.43734e−6		6.83939e-5i
$911$	13.1842	−	19.1006i	0.436811	−	0.632830i	−0.541321	−	0.840816i	$-0.682075\pi$
$911$	13.1842	−	19.1006i	0.436811	−	0.632830i	0.978132	+	0.207986i	$0.0666909\pi$
$912$	8.15066	−	9.20019i	0.269895	−	0.304649i
$913$	−31.5829	+	7.78450i	−1.04524	+	0.257629i
$914$	−0.00350080	+	0.00507178i	−0.000115796	+	0.000167760i
$915$		−	5.11614i		−	0.169134i
$916$	7.13869	+	4.92748i	0.235869	+	0.162809i
$917$	2.21993	+	0.269548i	0.0733085	+	0.00890127i
$918$	0.00476150	+	0.00180580i	0.000157153	+	5.96002e-5i
$919$	5.42933	+	44.7145i	0.179097	+	1.47500i	0.754054	+	0.656813i	$0.228096\pi$
$919$	5.42933	+	44.7145i	0.179097	+	1.47500i	−0.574957	+	0.818184i	$0.694981\pi$
$920$	−0.00586954	+	0.0154767i	−0.000193513	+	0.000510252i
$921$	−13.6492	−	15.4068i	−0.449758	−	0.507672i
$922$	−0.0136892	+	0.0121276i	−0.000450830	+	0.000399400i
$923$	20.8059	+	11.2540i	0.684833	+	0.370431i
$924$	1.57204	+	1.39271i	0.0517164	+	0.0458168i
$925$			1.66970i			0.0548995i
$926$	−0.0137246	+	0.0121589i	−0.000451019	+	0.000399568i
$927$	5.75582	+	1.41868i	0.189046	+	0.0465956i
$928$	−0.0489449	+	0.0337842i	−0.00160670	+	0.00110902i
$929$	−6.86207	−	2.60244i	−0.225137	−	0.0853832i	0.239457	−	0.970907i	$-0.423031\pi$
$929$	−6.86207	−	2.60244i	−0.225137	−	0.0853832i	−0.464594	+	0.885524i	$0.653800\pi$
$930$	−0.00198816		0.000754010i	−6.51943e−5		2.47250e-5i
$931$	−17.3300	+	11.9621i	−0.567969	+	0.392041i
$932$	41.9813	+	10.3474i	1.37514	+	0.338942i
$933$	−22.2839	+	19.7418i	−0.729542	+	0.646318i
$934$		−	0.0395214i		−	0.00129318i
$935$	−5.67971	−	5.03178i	−0.185746	−	0.164557i
$936$	−0.0239387		0.000299568i	−0.000782463		9.79167e-6i
$937$	4.52124	−	4.00547i	0.147703	−	0.130853i	−0.586036	−	0.810285i	$-0.699312\pi$
$937$	4.52124	−	4.00547i	0.147703	−	0.130853i	0.733738	+	0.679432i	$0.237774\pi$
$938$	−0.00117157	−	0.00132243i	−3.82530e−5	−	4.31787e-5i
$939$	−9.98622	+	26.3315i	−0.325888	+	0.859296i
$940$	−0.268215	−	2.20895i	−0.00874820	−	0.0720479i
$941$	31.6026	+	11.9853i	1.03022	+	0.390709i	0.811049	−	0.584978i	$-0.198897\pi$
$941$	31.6026	+	11.9853i	1.03022	+	0.390709i	0.219167	+	0.975687i	$0.429666\pi$
$942$	−0.00136305		0.000165505i	−4.44107e−5		5.39244e-6i
$943$	8.73301	+	6.02796i	0.284386	+	0.196297i
$944$		−	42.5480i		−	1.38482i
$945$	−0.196976	+	0.285369i	−0.00640762	+	0.00928304i
$946$	0.0364154	−	0.00897559i	0.00118397	−	0.000291821i
$947$	−25.8304	+	29.1565i	−0.839375	+	0.947458i	−0.999212	−	0.0396853i	$-0.987364\pi$
$947$	−25.8304	+	29.1565i	−0.839375	+	0.947458i	0.159838	+	0.987143i	$0.448903\pi$
$948$	10.2585	−	14.8620i	0.333180	−	0.482695i
$949$	−31.5668	−	8.20083i	−1.02470	−	0.266210i
$950$	−0.0121215	−	0.0175611i	−0.000393274	−	0.000569756i
$951$	9.92069	+	1.20459i	0.321700	+	0.0390615i
$952$	0.000942054		0.00775851i	3.05321e−5		0.000251455i
$953$	1.14362	−	0.600219i	0.0370456	−	0.0194430i	−0.446099	−	0.894984i	$-0.647187\pi$
$953$	1.14362	−	0.600219i	0.0370456	−	0.0194430i	0.483144	+	0.875541i	$0.339495\pi$
$954$	−0.00287212	−	0.0116527i	−9.29884e−5	−	0.000377269i
$955$	16.9189	−	2.05433i	0.547484	−	0.0664765i
$956$	5.38853	+	6.08239i	0.174278	+	0.196719i
$957$	6.72494	+	4.64189i	0.217386	+	0.150051i
$958$	0.0144330	+	0.0209097i	0.000466308	+	0.000675563i
$959$	−3.99188	−	0.983911i	−0.128905	−	0.0317721i
$960$	−7.17713	+	0.871461i	−0.231641	+	0.0281263i
$961$	25.6703	+	13.4728i	0.828074	+	0.434607i
$962$	0.000542636		0.00232647i	1.74953e−5		7.50084e-5i
$963$	−3.96027	+	2.07851i	−0.127618	+	0.0669791i
$964$	34.1492	−	23.5715i	1.09987	−	0.759186i
$965$	6.34214	+	9.18818i	0.204161	+	0.295778i
$966$	−0.00131501	−	0.00116499i	−4.23096e−5	−	3.74830e-5i
$967$	−4.42865	+	4.99891i	−0.142416	+	0.160754i	−0.815391	−	0.578911i	$-0.803478\pi$
$967$	−4.42865	+	4.99891i	−0.142416	+	0.160754i	0.672975	+	0.739665i	$0.265016\pi$
$968$	0.0217865	−	0.00826253i	0.000700244	−	0.000265568i
$969$	−4.38082	−	8.34695i	−0.140732	−	0.268143i
$970$	0.00526781	−	0.00199782i	0.000169139	−	6.41461e-5i
$971$	−13.7116	+	3.37961i	−0.440027	+	0.108457i	−0.453104	−	0.891458i	$-0.649683\pi$
$971$	−13.7116	+	3.37961i	−0.440027	+	0.108457i	0.0130773	+	0.999914i	$0.495837\pi$
$972$	−1.49702	−	1.32624i	−0.0480169	−	0.0425393i
$973$	3.04833	+	2.10411i	0.0977251	+	0.0674548i
$974$	0.0198250	−	0.0522741i	0.000635233	−	0.00167497i
$975$	3.79255	−	14.5984i	0.121459	−	0.467522i
$976$	8.02977	+	21.1728i	0.257027	+	0.677723i
$977$	0.0233469	−	0.0947221i	0.000746934	−	0.00303043i	−0.970567	−	0.240831i	$-0.922580\pi$
$977$	0.0233469	−	0.0947221i	0.000746934	−	0.00303043i	0.971314	+	0.237800i	$0.0764263\pi$
$978$	0.0186797	+	0.00980387i	0.000597311	+	0.000313493i
$979$	−9.16320	+	24.1614i	−0.292857	+	0.772201i
$980$	12.2959	+	1.49299i	0.392779	+	0.0476920i
$981$	8.26101	−	5.70217i	0.263754	−	0.182056i
$982$	−0.00487689	−	0.0197863i	−0.000155628	−	0.000631407i
$983$	−5.02679	+	20.3945i	−0.160330	+	0.650483i	0.834683	+	0.550731i	$0.185651\pi$
$983$	−5.02679	+	20.3945i	−0.160330	+	0.650483i	−0.995012	+	0.0997520i	$0.968195\pi$
$984$	0.00307895	−	0.0253574i	9.81533e−5	−	0.000808365i
$985$	−8.03557	−	21.1881i	−0.256034	−	0.675107i
$986$	0.00363854	+	0.0147621i	0.000115875	+	0.000470122i
$987$	0.458624	+	0.113041i	0.0145982	+	0.00359813i
$988$	16.4008	+	14.9002i	0.521778	+	0.474040i
$989$	22.1090	−	5.44938i	0.703025	−	0.173280i
$990$	−0.00190812	−	0.00363562i	−6.06441e−5	−	0.000115548i
$991$	−18.3962			−0.584374			−0.292187	−	0.956361i	$-0.594383\pi$
$991$	−18.3962			−0.584374			−0.292187	+	0.956361i	$0.594383\pi$
$992$	0.0282339			0.000896426
$993$	−15.0961	−	28.7632i	−0.479060	−	0.912773i
$994$	0.00277085	−	0.00312764i	8.78860e−5	−	9.92028e-5i
$995$		−	2.65502i		−	0.0841697i
$996$	15.7622	+	17.7919i	0.499445	+	0.563757i
$997$	10.3281	+	5.42062i	0.327095	+	0.171673i	0.620275	−	0.784385i	$-0.287021\pi$
$997$	10.3281	+	5.42062i	0.327095	+	0.171673i	−0.293180	+	0.956057i	$0.594713\pi$
$998$	0.00435087	−	0.0358326i	0.000137724	−	0.00113426i
$999$	−0.185489	+	0.353421i	−0.00586863	+	0.0111817i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	507.2.p.a.142.8	yes	168
169.25	even	26	inner	507.2.p.a.25.8	✓	168

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
507.2.p.a.25.8	✓	168	169.25	even	26	inner
507.2.p.a.142.8	yes	168	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 507 = 3 \cdot 13^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	507.p (of order \(26\), degree \(12\), minimal)

\(f(q)\)	\(=\)	\(q+(0.00155211 - 0.000588639i) q^{2} +(0.568065 - 0.822984i) q^{3} +(-1.49702 + 1.32624i) q^{4} +(-0.897149 + 0.108934i) q^{5} +(0.000397260 - 0.00161175i) q^{6} +(-0.178306 + 0.339734i) q^{7} +(-0.00308573 + 0.00587937i) q^{8} +(-0.354605 - 0.935016i) q^{9} +(-0.00132835 + 0.000697174i) q^{10} +(-2.55908 - 0.970532i) q^{11} +(0.241073 + 1.98542i) q^{12} +(-3.58442 + 0.389780i) q^{13} +(-7.67707e-5 + 0.000632264i) q^{14} +(-0.419988 + 0.800220i) q^{15} +(0.482145 - 3.97082i) q^{16} +(-2.71636 - 1.42566i) q^{17} +(-0.00110077 - 0.00124252i) q^{18} +3.07285i q^{19} +(1.19858 - 1.35291i) q^{20} +(0.178306 + 0.339734i) q^{21} -0.00454328 q^{22} -2.75837 q^{23} +(0.00308573 + 0.00587937i) q^{24} +(-4.06170 + 1.00112i) q^{25} +(-0.00533399 + 0.00271491i) q^{26} +(-0.970942 - 0.239316i) q^{27} +(-0.183642 - 0.745066i) q^{28} +(-1.05871 - 2.79159i) q^{29} +(-0.000180828 + 0.00148925i) q^{30} +(-0.339201 + 1.37619i) q^{31} +(-0.00476712 - 0.0193409i) q^{32} +(-2.25246 + 1.55476i) q^{33} +(-0.00505529 - 0.000613824i) q^{34} +(0.122959 - 0.324216i) q^{35} +(1.77091 + 0.929445i) q^{36} +(0.0955204 - 0.387541i) q^{37} +(0.00180880 + 0.00476940i) q^{38} +(-1.71540 + 3.17134i) q^{39} +(0.00212790 - 0.00561081i) q^{40} +(-3.16600 - 2.18533i) q^{41} +(0.000476732 + 0.000422348i) q^{42} +(-8.01523 + 1.97558i) q^{43} +(5.11816 - 1.94106i) q^{44} +(0.419988 + 0.800220i) q^{45} +(-0.00428131 + 0.00162369i) q^{46} +(0.816367 - 0.921488i) q^{47} +(-2.99403 - 2.65248i) q^{48} +(3.89283 + 5.63973i) q^{49} +(-0.00571492 + 0.00394472i) q^{50} +(-2.71636 + 1.42566i) q^{51} +(4.84900 - 5.33732i) q^{52} +(6.40169 + 3.35987i) q^{53} +(-0.00164788 + 0.000200089i) q^{54} +(2.40160 + 0.591941i) q^{55} +(-0.00144722 - 0.00209666i) q^{56} +(2.52890 + 1.74558i) q^{57} +(-0.00328647 - 0.00370966i) q^{58} +(10.5595 - 1.28215i) q^{59} +(-0.432557 - 1.75495i) q^{60} +(-5.01265 + 2.63084i) q^{61} +(0.000283602 + 0.00233567i) q^{62} +(0.380885 + 0.0462478i) q^{63} +(4.54448 + 6.58382i) q^{64} +(3.17330 - 0.740154i) q^{65} +(-0.00258087 + 0.00373904i) q^{66} +(-1.83946 + 2.07632i) q^{67} +(5.95721 - 1.46832i) q^{68} +(-1.56693 + 2.27010i) q^{69} -0.000575597i q^{70} +(-5.39926 - 3.72684i) q^{71} +(0.00659152 + 0.000800356i) q^{72} +(8.45785 + 3.20764i) q^{73} +(-7.98635e-5 - 0.000657735i) q^{74} +(-1.48340 + 3.91141i) q^{75} +(-4.07534 - 4.60011i) q^{76} +(0.786023 - 0.696356i) q^{77} +(-0.000795721 + 0.00593203i) q^{78} +(-6.75856 - 5.98756i) q^{79} +3.61494i q^{80} +(-0.748511 + 0.663123i) q^{81} +(-0.00620036 - 0.00152825i) q^{82} +(9.78106 - 6.75138i) q^{83} +(-0.717498 - 0.272111i) q^{84} +(2.59228 + 0.983122i) q^{85} +(-0.0112776 + 0.00778439i) q^{86} +(-2.89885 - 0.714501i) q^{87} +(0.0136028 - 0.0120510i) q^{88} -9.44142i q^{89} +(0.00112291 + 0.000994811i) q^{90} +(0.506703 - 1.28725i) q^{91} +(4.12934 - 3.65827i) q^{92} +(0.939896 + 1.06092i) q^{93} +(0.000724670 - 0.00191080i) q^{94} +(-0.334736 - 2.75680i) q^{95} +(-0.0186253 - 0.00706365i) q^{96} +(-3.72809 - 0.452672i) q^{97} +(0.00936187 + 0.00646203i) q^{98} +2.73694i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 168 q - 14 q^{3} + 12 q^{4} - 14 q^{9} - 4 q^{10} + 12 q^{12} + 13 q^{13} + 2 q^{14} - 8 q^{16} - 4 q^{17} - 72 q^{22} + 48 q^{23} - 44 q^{25} - 39 q^{26} - 14 q^{27} + 45 q^{29} - 4 q^{30} - 26 q^{31}+ \cdots - 104 q^{98}+O(q^{100}) \) 168 * q - 14 * q^3 + 12 * q^4 - 14 * q^9 - 4 * q^10 + 12 * q^12 + 13 * q^13 + 2 * q^14 - 8 * q^16 - 4 * q^17 - 72 * q^22 + 48 * q^23 - 44 * q^25 - 39 * q^26 - 14 * q^27 + 45 * q^29 - 4 * q^30 - 26 * q^31 + 130 * q^32 + 13 * q^33 - 65 * q^34 - 35 * q^35 + 12 * q^36 + 61 * q^38 + 12 * q^40 - 63 * q^42 + 72 * q^43 - 39 * q^44 - 8 * q^48 - 68 * q^49 - 52 * q^50 - 4 * q^51 + 65 * q^52 - q^53 + 53 * q^55 - 14 * q^56 - 13 * q^57 - 26 * q^58 - 104 * q^59 + 117 * q^60 + 12 * q^61 + 49 * q^62 - 32 * q^64 - 52 * q^65 - 46 * q^66 + 26 * q^67 - 84 * q^68 - 4 * q^69 - 39 * q^71 - 52 * q^73 + 29 * q^74 + 8 * q^75 - 130 * q^76 + 60 * q^77 + 65 * q^78 + 14 * q^79 - 14 * q^81 + 45 * q^82 + 78 * q^83 - 13 * q^85 - 13 * q^86 - 46 * q^87 - 26 * q^88 - 4 * q^90 - 208 * q^91 + 82 * q^92 - 39 * q^93 + 25 * q^94 - 66 * q^95 + 65 * q^96 + 26 * q^97 - 104 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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