LMFDB - Embedded newform 468.2.bm.a.263.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [468,2,Mod(263,468)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(468, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 1, 2]))

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

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

chi := DirichletCharacter("468.263");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 468 = 2^{2} \cdot 3^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	468.bm (of order $6$, degree $2$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$3.73699881460$
Analytic rank:	$0$
Dimension:	$160$
Relative dimension:	$80$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			263.2
Character	$\chi$	$=$	468.263
Dual form			468.2.bm.a.347.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.40866 + 0.125217i) q^{2} +(1.69503 + 0.356177i) q^{3} +(1.96864 - 0.352777i) q^{4} +(-1.20784 + 0.697346i) q^{5} +(-2.43232 - 0.289485i) q^{6} +(0.468412 - 0.270438i) q^{7} +(-2.72897 + 0.743451i) q^{8} +(2.74628 + 1.20747i) q^{9} +O(q^{10})$	\(q+(-1.40866 + 0.125217i) q^{2} +(1.69503 + 0.356177i) q^{3} +(1.96864 - 0.352777i) q^{4} +(-1.20784 + 0.697346i) q^{5} +(-2.43232 - 0.289485i) q^{6} +(0.468412 - 0.270438i) q^{7} +(-2.72897 + 0.743451i) q^{8} +(2.74628 + 1.20747i) q^{9} +(1.61411 - 1.13356i) q^{10} -2.25302 q^{11} +(3.46256 + 0.103217i) q^{12} +(2.00261 + 2.99826i) q^{13} +(-0.625969 + 0.439608i) q^{14} +(-2.29571 + 0.751820i) q^{15} +(3.75110 - 1.38898i) q^{16} +(5.64286 + 3.25790i) q^{17} +(-4.01976 - 1.35703i) q^{18} +(1.04819 + 0.605174i) q^{19} +(-2.13179 + 1.79892i) q^{20} +(0.890298 - 0.291563i) q^{21} +(3.17374 - 0.282117i) q^{22} +(-1.37340 + 2.37879i) q^{23} +(-4.89050 + 0.288176i) q^{24} +(-1.52742 + 2.64556i) q^{25} +(-3.19643 - 3.97276i) q^{26} +(4.22496 + 3.02486i) q^{27} +(0.826731 - 0.697640i) q^{28} -4.52075i q^{29} +(3.13973 - 1.34652i) q^{30} +(5.80783 - 3.35315i) q^{31} +(-5.11009 + 2.42631i) q^{32} +(-3.81894 - 0.802475i) q^{33} +(-8.35681 - 3.88269i) q^{34} +(-0.377177 + 0.653290i) q^{35} +(5.83240 + 1.40824i) q^{36} +(-2.14426 - 3.71396i) q^{37} +(-1.55232 - 0.721232i) q^{38} +(2.32659 + 5.79543i) q^{39} +(2.77771 - 2.80100i) q^{40} +(3.04273 + 1.75672i) q^{41} +(-1.21762 + 0.522194i) q^{42} +(-2.83710 + 1.63800i) q^{43} +(-4.43539 + 0.794814i) q^{44} +(-4.15908 + 0.456681i) q^{45} +(1.63678 - 3.52288i) q^{46} +(-1.50905 + 2.61376i) q^{47} +(6.85296 - 1.01832i) q^{48} +(-3.35373 + 5.80883i) q^{49} +(1.82034 - 3.91796i) q^{50} +(8.40444 + 7.53211i) q^{51} +(5.00015 + 5.19601i) q^{52} -4.45322i q^{53} +(-6.33029 - 3.73195i) q^{54} +(2.72128 - 1.57113i) q^{55} +(-1.07723 + 1.08626i) q^{56} +(1.56117 + 1.39913i) q^{57} +(0.566076 + 6.36820i) q^{58} +7.57000 q^{59} +(-4.25420 + 2.28994i) q^{60} +(-3.85831 - 6.68279i) q^{61} +(-7.76138 + 5.45069i) q^{62} +(1.61293 - 0.177105i) q^{63} +(6.89456 - 4.05771i) q^{64} +(-4.50966 - 2.22489i) q^{65} +(5.48007 + 0.652216i) q^{66} +(4.52780 + 2.61412i) q^{67} +(12.2581 + 4.42297i) q^{68} +(-3.17523 + 3.54296i) q^{69} +(0.449511 - 0.967493i) q^{70} +(-4.75712 + 8.23957i) q^{71} +(-8.39220 - 1.25342i) q^{72} +8.09409 q^{73} +(3.48558 + 4.96321i) q^{74} +(-3.53131 + 3.94029i) q^{75} +(2.27701 + 0.821592i) q^{76} +(-1.05534 + 0.609302i) q^{77} +(-4.00306 - 7.87245i) q^{78} +(-3.22560 - 1.86230i) q^{79} +(-3.56212 + 4.29348i) q^{80} +(6.08406 + 6.63206i) q^{81} +(-4.50614 - 2.09362i) q^{82} +(2.76597 - 4.79079i) q^{83} +(1.64982 - 0.888060i) q^{84} -9.08754 q^{85} +(3.79140 - 2.66264i) q^{86} +(1.61019 - 7.66282i) q^{87} +(6.14843 - 1.67501i) q^{88} +(-7.91688 + 4.57081i) q^{89} +(5.80154 - 1.16410i) q^{90} +(1.74889 + 0.862836i) q^{91} +(-1.86454 + 5.16749i) q^{92} +(11.0388 - 3.61509i) q^{93} +(1.79845 - 3.87085i) q^{94} -1.68806 q^{95} +(-9.52597 + 2.29257i) q^{96} +(-6.34022 - 10.9816i) q^{97} +(3.99689 - 8.60260i) q^{98} +(-6.18741 - 2.72044i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 160 q - 2 q^{4} - 12 q^{5} - 6 q^{6} - 2 q^{9}+O(q^{10}) $ 160 * q - 2 * q^4 - 12 * q^5 - 6 * q^6 - 2 * q^9	$ 160 q - 2 q^{4} - 12 q^{5} - 6 q^{6} - 2 q^{9} - 4 q^{10} - 7 q^{12} - 2 q^{13} - 6 q^{14} - 2 q^{16} + 4 q^{18} - 3 q^{20} - 2 q^{21} - 18 q^{22} + 12 q^{24} + 60 q^{25} - 18 q^{26} + 6 q^{28} - 18 q^{30} - 26 q^{33} - 4 q^{34} - 2 q^{36} - 4 q^{37} - 42 q^{38} + 8 q^{40} - 6 q^{41} + 5 q^{42} + 8 q^{45} - 6 q^{46} + 33 q^{48} + 58 q^{49} - 96 q^{50} - 8 q^{52} + 7 q^{54} - 24 q^{56} - 12 q^{57} - 22 q^{58} - 39 q^{60} + 2 q^{61} + 3 q^{62} - 26 q^{64} - 6 q^{65} + 30 q^{66} - 66 q^{68} + 2 q^{69} - 27 q^{70} + 48 q^{72} - 16 q^{73} - 33 q^{74} + 9 q^{76} + 12 q^{77} - 26 q^{78} + 90 q^{80} - 10 q^{81} + 11 q^{82} - 13 q^{84} + 16 q^{85} - 60 q^{86} + 6 q^{88} - 57 q^{90} - 36 q^{92} - 102 q^{93} - 33 q^{94} + 93 q^{96} + 2 q^{97} - 9 q^{98}+O(q^{100}) $ 160 * q - 2 * q^4 - 12 * q^5 - 6 * q^6 - 2 * q^9 - 4 * q^10 - 7 * q^12 - 2 * q^13 - 6 * q^14 - 2 * q^16 + 4 * q^18 - 3 * q^20 - 2 * q^21 - 18 * q^22 + 12 * q^24 + 60 * q^25 - 18 * q^26 + 6 * q^28 - 18 * q^30 - 26 * q^33 - 4 * q^34 - 2 * q^36 - 4 * q^37 - 42 * q^38 + 8 * q^40 - 6 * q^41 + 5 * q^42 + 8 * q^45 - 6 * q^46 + 33 * q^48 + 58 * q^49 - 96 * q^50 - 8 * q^52 + 7 * q^54 - 24 * q^56 - 12 * q^57 - 22 * q^58 - 39 * q^60 + 2 * q^61 + 3 * q^62 - 26 * q^64 - 6 * q^65 + 30 * q^66 - 66 * q^68 + 2 * q^69 - 27 * q^70 + 48 * q^72 - 16 * q^73 - 33 * q^74 + 9 * q^76 + 12 * q^77 - 26 * q^78 + 90 * q^80 - 10 * q^81 + 11 * q^82 - 13 * q^84 + 16 * q^85 - 60 * q^86 + 6 * q^88 - 57 * q^90 - 36 * q^92 - 102 * q^93 - 33 * q^94 + 93 * q^96 + 2 * q^97 - 9 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/468\mathbb{Z}\right)^\times$.

$n$	$145$	$209$	$235$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{6}\right)$	$-1$

Coefficient data

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

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

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

$2$	−1.40866	+	0.125217i	−0.996072	+	0.0885420i
$2$	−1.40866	+	0.125217i	−0.996072	+	0.0885420i
$3$	1.69503	+	0.356177i	0.978628	+	0.205639i
$3$	1.69503	+	0.356177i	0.978628	+	0.205639i
$4$	1.96864	−	0.352777i	0.984321	−	0.176389i
$5$	−1.20784	+	0.697346i	−0.540162	+	0.311863i	−0.745145	−	0.666903i	$-0.767620\pi$
$5$	−1.20784	+	0.697346i	−0.540162	+	0.311863i	0.204983	+	0.978766i	$0.434286\pi$
$6$	−2.43232	−	0.289485i	−0.992992	−	0.118182i
$7$	0.468412	−	0.270438i	0.177043	−	0.102216i	−0.408860	−	0.912597i	$-0.634073\pi$
$7$	0.468412	−	0.270438i	0.177043	−	0.102216i	0.585903	+	0.810381i	$0.300740\pi$
$8$	−2.72897	+	0.743451i	−0.964837	+	0.262850i
$9$	2.74628	+	1.20747i	0.915425	+	0.402488i
$10$	1.61411	−	1.13356i	0.510427	−	0.358465i
$11$	−2.25302			−0.679311			−0.339656	−	0.940550i	$-0.610311\pi$
$11$	−2.25302			−0.679311			−0.339656	+	0.940550i	$0.610311\pi$
$12$	3.46256	+	0.103217i	0.999556	+	0.0297961i
$13$	2.00261	+	2.99826i	0.555425	+	0.831566i
$13$	2.00261	+	2.99826i	0.555425	+	0.831566i
$14$	−0.625969	+	0.439608i	−0.167297	+	0.117490i
$15$	−2.29571	+	0.751820i	−0.592749	+	0.194119i
$16$	3.75110	−	1.38898i	0.937774	−	0.347246i
$17$	5.64286	+	3.25790i	1.36859	+	0.790158i	0.990748	−	0.135711i	$-0.0433319\pi$
$17$	5.64286	+	3.25790i	1.36859	+	0.790158i	0.377845	+	0.925869i	$0.376665\pi$
$18$	−4.01976	−	1.35703i	−0.947467	−	0.319854i
$19$	1.04819	+	0.605174i	0.240472	+	0.138836i	0.615394	−	0.788220i	$-0.288997\pi$
$19$	1.04819	+	0.605174i	0.240472	+	0.138836i	−0.374922	+	0.927056i	$0.622330\pi$
$20$	−2.13179	+	1.79892i	−0.476683	+	0.402251i
$21$	0.890298	−	0.291563i	0.194279	−	0.0636243i
$22$	3.17374	−	0.282117i	0.676643	−	0.0601476i
$23$	−1.37340	+	2.37879i	−0.286373	+	0.496013i	−0.972941	−	0.231053i	$-0.925783\pi$
$23$	−1.37340	+	2.37879i	−0.286373	+	0.496013i	0.686568	+	0.727065i	$0.259116\pi$
$24$	−4.89050	+	0.288176i	−0.998268	+	0.0588236i
$25$	−1.52742	+	2.64556i	−0.305484	+	0.529113i
$26$	−3.19643	−	3.97276i	−0.626872	−	0.779122i
$27$	4.22496	+	3.02486i	0.813093	+	0.582134i
$28$	0.826731	−	0.697640i	0.156237	−	0.131842i
$29$		−	4.52075i		−	0.839482i	−0.907644	−	0.419741i	$-0.862121\pi$
$29$		−	4.52075i		−	0.839482i	0.907644	−	0.419741i	$-0.137879\pi$
$30$	3.13973	−	1.34652i	0.573233	−	0.245840i
$31$	5.80783	−	3.35315i	1.04312	−	0.602244i	0.122403	−	0.992481i	$-0.460940\pi$
$31$	5.80783	−	3.35315i	1.04312	−	0.602244i	0.920715	+	0.390236i	$0.127607\pi$
$32$	−5.11009	+	2.42631i	−0.903345	+	0.428914i
$33$	−3.81894	−	0.802475i	−0.664793	−	0.139693i
$34$	−8.35681	−	3.88269i	−1.43318	−	0.665876i
$35$	−0.377177	+	0.653290i	−0.0637546	+	0.110426i
$36$	5.83240	+	1.40824i	0.972066	+	0.234707i
$37$	−2.14426	−	3.71396i	−0.352514	−	0.610572i	0.634175	−	0.773189i	$-0.281340\pi$
$37$	−2.14426	−	3.71396i	−0.352514	−	0.610572i	−0.986689	+	0.162617i	$0.948006\pi$
$38$	−1.55232	−	0.721232i	−0.251820	−	0.116999i
$39$	2.32659	+	5.79543i	0.372552	+	0.928011i
$40$	2.77771	−	2.80100i	0.439195	−	0.442878i
$41$	3.04273	+	1.75672i	0.475194	+	0.274354i	0.718412	−	0.695618i	$-0.244869\pi$
$41$	3.04273	+	1.75672i	0.475194	+	0.274354i	−0.243217	+	0.969972i	$0.578203\pi$
$42$	−1.21762	+	0.522194i	−0.187882	+	0.0805763i
$43$	−2.83710	+	1.63800i	−0.432654	+	0.249793i	−0.700477	−	0.713675i	$-0.747029\pi$
$43$	−2.83710	+	1.63800i	−0.432654	+	0.249793i	0.267823	+	0.963468i	$0.413696\pi$
$44$	−4.43539	+	0.794814i	−0.668660	+	0.119823i
$45$	−4.15908	+	0.456681i	−0.619999	+	0.0680779i
$46$	1.63678	−	3.52288i	0.241330	−	0.519421i
$47$	−1.50905	+	2.61376i	−0.220118	+	0.381256i	−0.954844	−	0.297109i	$-0.903978\pi$
$47$	−1.50905	+	2.61376i	−0.220118	+	0.381256i	0.734726	+	0.678364i	$0.237311\pi$
$48$	6.85296	−	1.01832i	0.989139	−	0.146981i
$49$	−3.35373	+	5.80883i	−0.479104	+	0.829832i
$50$	1.82034	−	3.91796i	0.257435	−	0.554083i
$51$	8.40444	+	7.53211i	1.17686	+	1.05471i
$52$	5.00015	+	5.19601i	0.693395	+	0.720557i
$53$		−	4.45322i		−	0.611697i	−0.952080	−	0.305849i	$-0.901060\pi$
$53$		−	4.45322i		−	0.611697i	0.952080	−	0.305849i	$-0.0989401\pi$
$54$	−6.33029	−	3.73195i	−0.861443	−	0.507854i
$55$	2.72128	−	1.57113i	0.366938	−	0.211852i
$56$	−1.07723	+	1.08626i	−0.143950	+	0.145157i
$57$	1.56117	+	1.39913i	0.206782	+	0.185320i
$58$	0.566076	+	6.36820i	0.0743295	+	0.836185i
$59$	7.57000			0.985530			0.492765	−	0.870162i	$-0.335986\pi$
$59$	7.57000			0.985530			0.492765	+	0.870162i	$0.335986\pi$
$60$	−4.25420	+	2.28994i	−0.549214	+	0.295629i
$61$	−3.85831	−	6.68279i	−0.494006	−	0.855644i	0.505970	−	0.862551i	$-0.331135\pi$
$61$	−3.85831	−	6.68279i	−0.494006	−	0.855644i	−0.999976	+	0.00690709i	$0.997801\pi$
$62$	−7.76138	+	5.45069i	−0.985697	+	0.692238i
$63$	1.61293	−	0.177105i	0.203210	−	0.0223132i
$64$	6.89456	−	4.05771i	0.861820	−	0.507214i
$65$	−4.50966	−	2.22489i	−0.559354	−	0.275964i
$66$	5.48007	+	0.652216i	0.674551	+	0.0802822i
$67$	4.52780	+	2.61412i	0.553158	+	0.319366i	0.750395	−	0.660990i	$-0.229863\pi$
$67$	4.52780	+	2.61412i	0.553158	+	0.319366i	−0.197237	+	0.980356i	$0.563197\pi$
$68$	12.2581	+	4.42297i	1.48651	+	0.536364i
$69$	−3.17523	+	3.54296i	−0.382252	+	0.426522i
$70$	0.449511	−	0.967493i	0.0537269	−	0.115637i
$71$	−4.75712	+	8.23957i	−0.564566	+	0.977857i	0.432524	+	0.901622i	$0.357623\pi$
$71$	−4.75712	+	8.23957i	−0.564566	+	0.977857i	−0.997090	+	0.0762345i	$0.975710\pi$
$72$	−8.39220	−	1.25342i	−0.989030	−	0.147717i
$73$	8.09409			0.947341			0.473671	−	0.880702i	$-0.342929\pi$
$73$	8.09409			0.947341			0.473671	+	0.880702i	$0.342929\pi$
$74$	3.48558	+	4.96321i	0.405191	+	0.576962i
$75$	−3.53131	+	3.94029i	−0.407761	+	0.454985i
$76$	2.27701	+	0.821592i	0.261190	+	0.0942431i
$77$	−1.05534	+	0.609302i	−0.120267	+	0.0694364i
$78$	−4.00306	−	7.87245i	−0.453257	−	0.891380i
$79$	−3.22560	−	1.86230i	−0.362909	−	0.209525i	0.307447	−	0.951565i	$-0.400525\pi$
$79$	−3.22560	−	1.86230i	−0.362909	−	0.209525i	−0.670356	+	0.742040i	$0.733859\pi$
$80$	−3.56212	+	4.29348i	−0.398257	+	0.480026i
$81$	6.08406	+	6.63206i	0.676006	+	0.736896i
$82$	−4.50614	−	2.09362i	−0.497620	−	0.231201i
$83$	2.76597	−	4.79079i	0.303604	−	0.525858i	−0.673345	−	0.739328i	$-0.735143\pi$
$83$	2.76597	−	4.79079i	0.303604	−	0.525858i	0.976950	+	0.213470i	$0.0684766\pi$
$84$	1.64982	−	0.888060i	0.180010	−	0.0968953i
$85$	−9.08754			−0.985682
$86$	3.79140	−	2.66264i	0.408838	−	0.287120i
$87$	1.61019	−	7.66282i	0.172630	−	0.821541i
$88$	6.14843	−	1.67501i	0.655424	−	0.178557i
$89$	−7.91688	+	4.57081i	−0.839188	+	0.484505i	−0.856988	−	0.515336i	$-0.827667\pi$
$89$	−7.91688	+	4.57081i	−0.839188	+	0.484505i	0.0178003	+	0.999842i	$0.494334\pi$
$90$	5.80154	−	1.16410i	0.611536	−	0.122707i
$91$	1.74889	+	0.862836i	0.183334	+	0.0904498i
$92$	−1.86454	+	5.16749i	−0.194392	+	0.538748i
$93$	11.0388	−	3.61509i	1.14467	−	0.374867i
$94$	1.79845	−	3.87085i	0.185496	−	0.399248i
$95$	−1.68806			−0.173192
$96$	−9.52597	+	2.29257i	−0.972240	+	0.233984i
$97$	−6.34022	−	10.9816i	−0.643752	−	1.11501i	−0.984588	−	0.174889i	$-0.944043\pi$
$97$	−6.34022	−	10.9816i	−0.643752	−	1.11501i	0.340836	−	0.940123i	$-0.389290\pi$
$98$	3.99689	−	8.60260i	0.403747	−	0.868994i
$99$	−6.18741	−	2.72044i	−0.621858	−	0.273415i
$100$	−2.07364	+	5.74701i	−0.207364	+	0.574701i
$101$		−	15.8468i		−	1.57681i	−0.615155	−	0.788406i	$-0.710907\pi$
$101$		−	15.8468i		−	1.57681i	0.615155	−	0.788406i	$-0.289093\pi$
$102$	−12.7821	−	9.55780i	−1.26562	−	0.946363i
$103$	7.40828	−	4.27717i	0.729959	−	0.421442i	−0.0884481	−	0.996081i	$-0.528191\pi$
$103$	7.40828	−	4.27717i	0.729959	−	0.421442i	0.818407	+	0.574639i	$0.194857\pi$
$104$	−7.69413	−	6.69331i	−0.754472	−	0.656333i
$105$	−0.872016	+	0.973007i	−0.0851000	+	0.0949557i
$106$	0.557621	+	6.27307i	0.0541609	+	0.609295i
$107$	−7.86293	−	13.6190i	−0.760138	−	1.31660i	−0.942779	−	0.333419i	$-0.891798\pi$
$107$	−7.86293	−	13.6190i	−0.760138	−	1.31660i	0.182640	−	0.983180i	$-0.441536\pi$
$108$	9.38452	+	4.46439i	0.903026	+	0.429586i
$109$	−17.2010			−1.64755			−0.823777	−	0.566915i	$-0.808137\pi$
$109$	−17.2010			−1.64755			−0.823777	+	0.566915i	$0.808137\pi$
$110$	−3.63663	+	2.55394i	−0.346739	+	0.243509i
$111$	−2.31176	−	7.05903i	−0.219422	−	0.670014i
$112$	1.38143	−	1.66505i	0.130532	−	0.157333i
$113$		−	13.3664i		−	1.25741i	−0.777646	−	0.628703i	$-0.783586\pi$
$113$		−	13.3664i		−	1.25741i	0.777646	−	0.628703i	$-0.216414\pi$
$114$	−2.37435	−	1.77541i	−0.222379	−	0.166283i
$115$		−	3.83093i		−	0.357236i
$116$	−1.59482	−	8.89974i	−0.148075	−	0.826320i
$117$	1.87944	+	10.6521i	0.173754	+	0.984789i
$118$	−10.6636	+	0.947896i	−0.981660	+	0.0872609i
$119$	3.52424			0.323067
$120$	5.70597	−	3.75844i	0.520882	−	0.343097i
$121$	−5.92390			−0.538536
$122$	6.27185	+	8.93065i	0.567827	+	0.808543i
$123$	4.53182	+	4.06145i	0.408621	+	0.366209i
$124$	10.2506	−	8.65003i	0.920533	−	0.776795i
$125$		−	11.2340i		−	1.00480i
$126$	−2.24990	+	0.451448i	−0.200437	+	0.0402182i
$127$	−13.0496	+	7.53420i	−1.15797	+	0.668552i	−0.950816	−	0.309757i	$-0.899752\pi$
$127$	−13.0496	+	7.53420i	−1.15797	+	0.668552i	−0.207150	+	0.978309i	$0.566419\pi$
$128$	−9.20399	+	6.57925i	−0.813526	+	0.581529i
$129$	−5.39240	+	1.76596i	−0.474774	+	0.155484i
$130$	6.63116	+	2.56943i	0.581591	+	0.225354i
$131$	0.883324	+	1.52996i	0.0771764	+	0.133673i	0.902031	−	0.431672i	$-0.142076\pi$
$131$	0.883324	+	1.52996i	0.0771764	+	0.133673i	−0.824854	+	0.565345i	$0.808743\pi$
$132$	−7.80123	−	0.232549i	−0.679010	−	0.0202408i
$133$	0.654648			0.0567652
$134$	−6.70545	−	3.11545i	−0.579263	−	0.269134i
$135$	−7.21243	−	0.707281i	−0.620747	−	0.0608730i
$136$	−17.8213	−	4.69554i	−1.52816	−	0.402639i
$137$	19.2611	−	11.1204i	1.64559	−	0.950082i	0.666795	−	0.745241i	$-0.267666\pi$
$137$	19.2611	−	11.1204i	1.64559	−	0.950082i	0.978795	−	0.204841i	$-0.0656677\pi$
$138$	4.02917	−	5.38842i	0.342986	−	0.458693i
$139$		−	19.5345i		−	1.65690i	−0.560066	−	0.828448i	$-0.689224\pi$
$139$		−	19.5345i		−	1.65690i	0.560066	−	0.828448i	$-0.310776\pi$
$140$	−0.512061	+	1.41915i	−0.0432771	+	0.119940i
$141$	−3.48886	+	3.89291i	−0.293815	+	0.327842i
$142$	5.66942	−	12.2024i	0.475767	−	1.02400i
$143$	−4.51193	−	6.75513i	−0.377307	−	0.564892i
$144$	11.9787	+	0.714789i	0.998224	+	0.0595657i
$145$	3.15253	+	5.46034i	0.261803	+	0.453456i
$146$	−11.4018	+	1.01352i	−0.943620	+	0.0838795i
$147$	−7.75365	+	8.65163i	−0.639510	+	0.713574i
$148$	−5.53148	−	6.55502i	−0.454685	−	0.538819i
$149$			1.91871i			0.157187i	0.996907	+	0.0785934i	$0.0250429\pi$
$149$			1.91871i			0.157187i	−0.996907	+	0.0785934i	$0.974957\pi$
$150$	4.48103	−	5.99271i	0.365874	−	0.489302i
$151$	−17.1923	−	9.92597i	−1.39909	−	0.807764i	−0.404791	−	0.914409i	$-0.632656\pi$
$151$	−17.1923	−	9.92597i	−1.39909	−	0.807764i	−0.994297	+	0.106645i	$0.965989\pi$
$152$	−3.31040	−	0.872223i	−0.268509	−	0.0707466i
$153$	11.5630	+	15.7607i	0.934815	+	1.27417i
$154$	1.41032	−	0.990446i	0.113647	−	0.0798124i
$155$	−4.67661	+	8.10013i	−0.375635	+	0.650618i
$156$	6.62471	+	10.5884i	0.530401	+	0.847747i
$157$	4.51686	+	7.82344i	0.360485	+	0.624378i	0.988041	−	0.154193i	$-0.0492779\pi$
$157$	4.51686	+	7.82344i	0.360485	+	0.624378i	−0.627556	+	0.778572i	$0.715945\pi$
$158$	4.77697	+	2.21945i	0.380035	+	0.176570i
$159$	1.58614	−	7.54836i	0.125789	−	0.598624i
$160$	4.48019	−	6.49409i	0.354190	−	0.513403i
$161$			1.48567i			0.117088i
$162$	−9.40081	−	8.58049i	−0.738597	−	0.674147i
$163$	20.7993	+	12.0085i	1.62912	+	0.940576i	0.984354	+	0.176199i	$0.0563804\pi$
$163$	20.7993	+	12.0085i	1.62912	+	0.940576i	0.644770	+	0.764376i	$0.276953\pi$
$164$	6.60977	+	2.38495i	0.516136	+	0.186233i
$165$	5.17227	−	1.69386i	0.402661	−	0.131867i
$166$	−3.29641	+	7.09494i	−0.255851	+	0.550674i
$167$	−2.49501	+	4.32148i	−0.193069	+	0.334406i	−0.946266	−	0.323389i	$-0.895178\pi$
$167$	−2.49501	+	4.32148i	−0.193069	+	0.334406i	0.753196	+	0.657796i	$0.228511\pi$
$168$	−2.21283	+	1.45756i	−0.170724	+	0.112453i
$169$	−4.97907	+	12.0087i	−0.383005	+	0.923746i
$170$	12.8013	−	1.13792i	0.981811	−	0.0872743i
$171$	2.14790	+	2.92763i	0.164254	+	0.223881i
$172$	−5.00739	+	4.22550i	−0.381810	+	0.322191i
$173$	13.9422	−	8.04953i	1.06001	−	0.611995i	0.134572	−	0.990904i	$-0.457034\pi$
$173$	13.9422	−	8.04953i	1.06001	−	0.611995i	0.925434	+	0.378909i	$0.123701\pi$
$174$	−1.30869	+	10.9959i	−0.0992115	+	0.833599i
$175$			1.65229i			0.124901i
$176$	−8.45130	+	3.12941i	−0.637040	+	0.235888i
$177$	12.8314	+	2.69626i	0.964468	+	0.202664i
$178$	10.5798	−	7.43005i	0.792993	−	0.556906i
$179$	8.25958	+	14.3060i	0.617350	+	1.06928i	0.989967	+	0.141297i	$0.0451272\pi$
$179$	8.25958	+	14.3060i	0.617350	+	1.06928i	−0.372617	+	0.927985i	$0.621540\pi$
$180$	−8.02663	+	2.36627i	−0.598269	+	0.176371i
$181$	−1.18401			−0.0880066			−0.0440033	−	0.999031i	$-0.514011\pi$
$181$	−1.18401			−0.0880066			−0.0440033	+	0.999031i	$0.514011\pi$
$182$	−2.57163	−	0.996451i	−0.190622	−	0.0738618i
$183$	−4.15971	−	12.7018i	−0.307494	−	0.938944i
$184$	1.97944	−	7.51271i	0.145927	−	0.553844i
$185$	5.17984	+	2.99058i	0.380829	+	0.219872i
$186$	−15.0972	+	6.47467i	−1.10698	+	0.474746i
$187$	−12.7135	−	7.34012i	−0.929701	−	0.536763i
$188$	−2.04871	+	5.67791i	−0.149418	+	0.414104i
$189$	2.79706	+	0.274291i	0.203456	+	0.0199517i
$190$	2.37790	−	0.211375i	0.172511	−	0.0153347i
$191$	−4.50907	−	7.80994i	−0.326265	−	0.565107i	0.655503	−	0.755193i	$-0.272457\pi$
$191$	−4.50907	−	7.80994i	−0.326265	−	0.565107i	−0.981768	+	0.190085i	$0.939123\pi$
$192$	13.1318	−	4.42227i	0.947704	−	0.319150i
$193$	1.48310	−	2.56880i	0.106756	−	0.184906i	−0.807699	−	0.589596i	$-0.799287\pi$
$193$	1.48310	−	2.56880i	0.106756	−	0.184906i	0.914454	+	0.404690i	$0.132620\pi$
$194$	10.3063	+	14.6754i	0.739949	+	1.05363i
$195$	−6.85156	−	5.37751i	−0.490650	−	0.385091i
$196$	−4.55306	+	12.6186i	−0.325219	+	0.901329i
$197$	−2.08513	+	1.20385i	−0.148559	+	0.0857707i	−0.572437	−	0.819949i	$-0.694002\pi$
$197$	−2.08513	+	1.20385i	−0.148559	+	0.0857707i	0.423878	+	0.905719i	$0.360669\pi$
$198$	9.05660	+	3.05741i	0.643625	+	0.217280i
$199$	5.67972	+	3.27919i	0.402625	+	0.232456i	0.687616	−	0.726075i	$-0.258657\pi$
$199$	5.67972	+	3.27919i	0.402625	+	0.232456i	−0.284991	+	0.958530i	$0.591991\pi$
$200$	2.20143	−	8.35523i	0.155665	−	0.590804i
$201$	6.74367	+	6.04373i	0.475662	+	0.426292i
$202$	1.98429	+	22.3227i	0.139614	+	1.57062i
$203$	−1.22258	−	2.11757i	−0.0858084	−	0.148625i
$204$	19.2025	+	11.8631i	1.34444	+	0.830586i
$205$	−4.90016			−0.342242
$206$	−9.90016	+	6.95272i	−0.689777	+	0.484419i
$207$	−6.64404	+	4.87449i	−0.461792	+	0.338801i
$208$	11.6765	+	8.46515i	0.809621	+	0.586952i
$209$	−2.36160	−	1.36347i	−0.163355	−	0.0943131i
$210$	1.10654	−	1.47983i	0.0763582	−	0.102118i
$211$	−4.88426	−	2.81993i	−0.336246	−	0.194132i	0.322365	−	0.946616i	$-0.395522\pi$
$211$	−4.88426	−	2.81993i	−0.336246	−	0.194132i	−0.658611	+	0.752484i	$0.728856\pi$
$212$	−1.57099	−	8.76680i	−0.107896	−	0.602106i
$213$	−10.9982	+	12.2720i	−0.753586	+	0.840861i
$214$	12.7815	+	18.2000i	0.873727	+	1.24412i
$215$	2.28451	−	3.95688i	0.155802	−	0.269857i
$216$	−13.7786	−	5.11369i	−0.937516	−	0.347943i
$217$	1.81364	−	3.14131i	0.123118	−	0.213246i
$218$	24.2303	−	2.15386i	1.64108	−	0.145878i
$219$	13.7197	+	2.88293i	0.927094	+	0.194810i
$220$	4.80297	−	4.05301i	0.323816	−	0.273254i
$221$	1.53244	+	23.4430i	0.103083	+	1.57695i
$222$	4.14039	+	9.65430i	0.277885	+	0.647954i
$223$			14.0363i			0.939942i	0.882682	+	0.469971i	$0.155736\pi$
$223$			14.0363i			0.939942i	−0.882682	+	0.469971i	$0.844264\pi$
$224$	−1.73746	+	2.51847i	−0.116089	+	0.168273i
$225$	−7.38914	+	5.42115i	−0.492609	+	0.361410i
$226$	1.67371	+	18.8287i	0.111333	+	1.25247i
$227$	2.63650	+	4.56655i	0.174991	+	0.303093i	0.940158	−	0.340739i	$-0.110677\pi$
$227$	2.63650	+	4.56655i	0.174991	+	0.303093i	−0.765167	+	0.643831i	$0.777344\pi$
$228$	3.56697	+	2.20364i	0.236228	+	0.145940i
$229$	−5.51546	−	9.55306i	−0.364472	−	0.631284i	0.624219	−	0.781249i	$-0.285417\pi$
$229$	−5.51546	−	9.55306i	−0.364472	−	0.631284i	−0.988691	+	0.149965i	$0.952084\pi$
$230$	0.479699	+	5.39648i	0.0316304	+	0.355833i
$231$	−2.00586	+	0.656898i	−0.131976	+	0.0432207i
$232$	3.36095	+	12.3370i	0.220657	+	0.809963i
$233$			10.2793i			0.673421i	0.941608	+	0.336711i	$0.109314\pi$
$233$			10.2793i			0.673421i	−0.941608	+	0.336711i	$0.890686\pi$
$234$	−3.98132	−	14.7699i	−0.260267	−	0.965537i
$235$		−	4.20933i		−	0.274586i
$236$	14.9026	−	2.67052i	0.970078	−	0.173836i
$237$	−4.80419	−	4.30555i	−0.312066	−	0.279676i
$238$	−4.96446	+	0.441296i	−0.321798	+	0.0286050i
$239$	−12.0834	−	20.9290i	−0.781608	−	1.35378i	−0.931005	−	0.365008i	$-0.881066\pi$
$239$	−12.0834	−	20.9290i	−0.781608	−	1.35378i	0.149396	−	0.988777i	$-0.452267\pi$
$240$	−7.56715	+	6.00884i	−0.488457	+	0.387869i
$241$	−4.27507	−	7.40464i	−0.275382	−	0.476975i	0.694850	−	0.719155i	$-0.255471\pi$
$241$	−4.27507	−	7.40464i	−0.275382	−	0.476975i	−0.970231	+	0.242180i	$0.922138\pi$
$242$	8.34476	−	0.741775i	0.536421	−	0.0476831i
$243$	7.95048	+	13.4086i	0.510024	+	0.860160i
$244$	−9.95317	−	11.7949i	−0.637186	−	0.755091i
$245$		−	9.35483i		−	0.597658i
$246$	−6.89235	−	5.15374i	−0.439440	−	0.328590i
$247$	0.284659	+	4.35468i	0.0181124	+	0.277081i
$248$	−13.3565	+	13.4685i	−0.848138	+	0.855250i
$249$	6.39477	−	7.13538i	0.405252	−	0.452186i
$250$	1.40669	+	15.8249i	0.0889671	+	1.00085i
$251$	3.22586	−	5.58735i	0.203614	−	0.352670i	−0.746076	−	0.665861i	$-0.768064\pi$
$251$	3.22586	−	5.58735i	0.203614	−	0.352670i	0.949690	+	0.313190i	$0.101398\pi$
$252$	3.11281	−	0.917663i	0.196088	−	0.0578073i
$253$	3.09429	−	5.35947i	0.194536	−	0.336947i
$254$	17.4390	−	12.2472i	1.09422	−	0.768455i
$255$	−15.4037	−	3.23678i	−0.964616	−	0.202695i
$256$	12.1415	−	10.4204i	0.758841	−	0.651276i
$257$	6.67978	+	3.85657i	0.416673	+	0.240566i	0.693653	−	0.720309i	$-0.256000\pi$
$257$	6.67978	+	3.85657i	0.416673	+	0.240566i	−0.276980	+	0.960876i	$0.589334\pi$
$258$	7.37493	−	3.16285i	0.459143	−	0.196911i
$259$	−2.00879	−	1.15978i	−0.124820	−	0.0720651i
$260$	−9.66279	−	2.78911i	−0.599261	−	0.172973i
$261$	5.45865	−	12.4152i	0.337882	−	0.768483i
$262$	−1.43588	−	2.04459i	−0.0887090	−	0.126315i
$263$	32.2029			1.98571			0.992857	−	0.119308i	$-0.0380676\pi$
$263$	32.2029			1.98571			0.992857	+	0.119308i	$0.0380676\pi$
$264$	11.0184	−	0.649266i	0.678135	−	0.0399596i
$265$	3.10544	+	5.37877i	0.190765	+	0.330415i
$266$	−0.922175	+	0.0819732i	−0.0565422	+	0.00502610i
$267$	−15.0474	+	4.92787i	−0.920886	+	0.301581i
$268$	9.83581	+	3.54897i	0.600818	+	0.216788i
$269$	−12.3389	−	7.12388i	−0.752317	−	0.434350i	0.0742134	−	0.997242i	$-0.476355\pi$
$269$	−12.3389	−	7.12388i	−0.752317	−	0.434350i	−0.826531	+	0.562892i	$0.809689\pi$
$270$	10.2484	+	0.0931957i	0.623699	+	0.00567171i
$271$	−0.193971	+	0.111989i	−0.0117829	+	0.00680285i	−0.505880	−	0.862604i	$-0.668832\pi$
$271$	−0.193971	+	0.111989i	−0.0117829	+	0.00680285i	0.494097	+	0.869407i	$0.335499\pi$
$272$	25.6921	+	4.38288i	1.55781	+	0.265751i
$273$	2.65710	+	2.08545i	0.160815	+	0.126217i
$274$	−25.7399	+	18.0767i	−1.55500	+	1.09205i
$275$	3.44130	−	5.96051i	0.207518	−	0.359432i
$276$	−5.00101	+	8.09496i	−0.301025	+	0.487260i
$277$	−7.94416	−	13.7597i	−0.477318	−	0.826740i	0.522344	−	0.852735i	$-0.325058\pi$
$277$	−7.94416	−	13.7597i	−0.477318	−	0.826740i	−0.999662	+	0.0259954i	$0.991724\pi$
$278$	2.44606	+	27.5175i	0.146705	+	1.65039i
$279$	19.9987	−	2.19593i	1.19729	−	0.131467i
$280$	0.543617	−	2.06322i	0.0324873	−	0.123301i
$281$	−4.34910	−	2.51096i	−0.259446	−	0.149791i	0.364636	−	0.931150i	$-0.381193\pi$
$281$	−4.34910	−	2.51096i	−0.259446	−	0.149791i	−0.624082	+	0.781359i	$0.714527\pi$
$282$	4.42715	−	5.92065i	0.263633	−	0.352570i
$283$	−22.0818	−	12.7490i	−1.31263	−	0.757847i	−0.330098	−	0.943947i	$-0.607082\pi$
$283$	−22.0818	−	12.7490i	−1.31263	−	0.757847i	−0.982531	+	0.186100i	$0.940415\pi$
$284$	−6.45833	+	17.8990i	−0.383231	+	1.06211i
$285$	−2.86132	−	0.601250i	−0.169490	−	0.0356150i
$286$	7.20163	+	8.95070i	0.425841	+	0.529266i
$287$	1.90033			0.112173
$288$	−16.9634	+	0.493046i	−0.999578	+	0.0290530i
$289$	12.7279	+	22.0453i	0.748699	+	1.29678i
$290$	−5.12456	−	7.29700i	−0.300925	−	0.428495i
$291$	−6.83550	−	20.8724i	−0.400704	−	1.22356i
$292$	15.9344	−	2.85541i	0.932487	−	0.167100i
$293$		−	1.32569i		−	0.0774474i	−0.999250	−	0.0387237i	$-0.987671\pi$
$293$		−	1.32569i		−	0.0774474i	0.999250	−	0.0387237i	$-0.0123292\pi$
$294$	9.83892	−	13.1581i	0.573817	−	0.767395i
$295$	−9.14334	+	5.27891i	−0.532346	+	0.307350i
$296$	8.61277	+	8.54115i	0.500607	+	0.496444i
$297$	−9.51891	−	6.81506i	−0.552343	−	0.395450i
$298$	−0.240256	−	2.70281i	−0.0139176	−	0.156569i
$299$	−9.88261	+	0.646012i	−0.571526	+	0.0373598i
$300$	−5.56185	+	9.00278i	−0.321113	+	0.519776i
$301$	−0.885955	+	1.53452i	−0.0510656	+	0.0884482i
$302$	25.4610	+	11.8295i	1.46511	+	0.680713i
$303$	5.64426	−	26.8608i	0.324254	−	1.54311i
$304$	4.77245	+	0.814145i	0.273719	+	0.0466944i
$305$	9.32044	+	5.38116i	0.533687	+	0.308124i
$306$	−18.2619	−	20.7535i	−1.04396	−	1.18640i
$307$			16.8552i			0.961976i	0.876727	+	0.480988i	$0.159722\pi$
$307$			16.8552i			0.961976i	−0.876727	+	0.480988i	$0.840278\pi$
$308$	−1.86264	+	1.57180i	−0.106134	+	0.0895615i
$309$	14.0807	−	4.61128i	0.801023	−	0.262327i
$310$	5.57348	−	11.9959i	0.316552	−	0.681323i
$311$	5.70766	+	9.88595i	0.323651	+	0.560581i	0.981239	−	0.192798i	$-0.0617561\pi$
$311$	5.70766	+	9.88595i	0.323651	+	0.560581i	−0.657587	+	0.753379i	$0.728423\pi$
$312$	−10.6578	−	14.0859i	−0.603379	−	0.797454i
$313$	−9.18406	+	15.9073i	−0.519114	+	0.899132i	0.480639	+	0.876918i	$0.340405\pi$
$313$	−9.18406	+	15.9073i	−0.519114	+	0.899132i	−0.999753	+	0.0222132i	$0.992929\pi$
$314$	−7.34235	−	10.4550i	−0.414353	−	0.590008i
$315$	−1.82466	+	1.33869i	−0.102808	+	0.0754265i
$316$	−7.00703	−	2.52829i	−0.394176	−	0.142227i
$317$	−2.31519	−	1.33668i	−0.130034	−	0.0750753i	0.433572	−	0.901119i	$-0.357253\pi$
$317$	−2.31519	−	1.33668i	−0.130034	−	0.0750753i	−0.563606	+	0.826044i	$0.690586\pi$
$318$	−1.28914	+	10.8317i	−0.0722915	+	0.607410i
$319$			10.1853i			0.570270i
$320$	−5.49789	+	9.70895i	−0.307341	+	0.542747i
$321$	−8.47715	−	25.8853i	−0.473148	−	1.44477i
$322$	−0.186032	−	2.09281i	−0.0103672	−	0.116628i
$323$	3.94320	+	6.82982i	0.219405	+	0.380021i
$324$	14.3170	+	10.9098i	0.795387	+	0.606102i
$325$	−10.9909	+	0.718459i	−0.609666	+	0.0398529i
$326$	−30.8028	−	14.3114i	−1.70601	−	0.792636i
$327$	−29.1562	−	6.12659i	−1.61234	−	0.338801i
$328$	−9.60955	−	2.53192i	−0.530599	−	0.139802i
$329$			1.63242i			0.0899982i
$330$	−7.07386	+	3.03374i	−0.389403	+	0.167002i
$331$	8.99558	−	5.19360i	0.494442	−	0.285466i	−0.231973	−	0.972722i	$-0.574518\pi$
$331$	8.99558	−	5.19360i	0.494442	−	0.285466i	0.726415	+	0.687256i	$0.241185\pi$
$332$	3.75511	−	10.4071i	0.206089	−	0.571165i
$333$	−1.40424	−	12.7887i	−0.0769519	−	0.700816i
$334$	2.97349	−	6.39991i	0.162702	−	0.350188i
$335$	−7.29179			−0.398393
$336$	2.93462	−	2.33029i	0.160096	−	0.127128i
$337$	1.72298	+	2.98429i	0.0938568	+	0.162565i	0.909131	−	0.416510i	$-0.136747\pi$
$337$	1.72298	+	2.98429i	0.0938568	+	0.162565i	−0.815274	+	0.579075i	$0.803414\pi$
$338$	5.51011	−	17.5396i	0.299711	−	0.954030i
$339$	4.76081	−	22.6565i	0.258572	−	1.23053i
$340$	−17.8901	+	3.20588i	−0.970228	+	0.173863i
$341$	−13.0852	+	7.55472i	−0.708601	+	0.409111i
$342$	−3.39224	−	3.85508i	−0.183432	−	0.208459i
$343$			7.41403i			0.400320i
$344$	6.52459	−	6.57930i	0.351783	−	0.354732i
$345$	1.36449	−	6.49355i	0.0734617	−	0.349601i
$346$	−18.6319	+	13.0849i	−1.00166	+	0.703446i
$347$	−24.9731			−1.34063			−0.670313	−	0.742079i	$-0.733840\pi$
$347$	−24.9731			−1.34063			−0.670313	+	0.742079i	$0.733840\pi$
$348$	0.466617	−	15.6534i	0.0250133	−	0.839109i
$349$	25.8253			1.38240			0.691198	−	0.722666i	$-0.257083\pi$
$349$	25.8253			1.38240			0.691198	+	0.722666i	$0.257083\pi$
$350$	−0.206895	−	2.32751i	−0.0110590	−	0.124411i
$351$	−0.608329	+	18.7251i	−0.0324702	+	0.999473i
$352$	11.5131	−	5.46652i	0.613652	−	0.291366i
$353$			24.8719i			1.32380i	0.749592	+	0.661900i	$0.230250\pi$
$353$			24.8719i			1.32380i	−0.749592	+	0.661900i	$0.769750\pi$
$354$	−18.4127	−	2.19140i	−0.978624	−	0.116472i
$355$		−	13.2694i		−	0.704268i
$356$	−13.9730	+	11.7912i	−0.740569	+	0.624932i
$357$	5.97371	+	1.25526i	0.316162	+	0.0664352i
$358$	−13.4263	−	19.1181i	−0.709602	−	1.01042i
$359$	35.8432			1.89173			0.945865	−	0.324561i	$-0.105217\pi$
$359$	35.8432			1.89173			0.945865	+	0.324561i	$0.105217\pi$
$360$	11.0105	−	4.33834i	0.580303	−	0.228650i
$361$	−8.76753	−	15.1858i	−0.461449	−	0.799253i
$362$	1.66786	−	0.148258i	0.0876610	−	0.00779229i
$363$	−10.0412	−	2.10996i	−0.527027	−	0.110744i
$364$	3.74733	+	1.08165i	0.196413	+	0.0566937i
$365$	−9.77635	+	5.64438i	−0.511717	+	0.295440i
$366$	7.45010	+	17.3716i	0.389423	+	0.908030i
$367$			29.0081i			1.51421i	0.653293	+	0.757105i	$0.273387\pi$
$367$			29.0081i			1.51421i	−0.653293	+	0.757105i	$0.726613\pi$
$368$	−1.84764	+	10.8307i	−0.0963149	+	0.564590i
$369$	6.23499	+	8.49842i	0.324581	+	0.442410i
$370$	−7.67110	−	3.56410i	−0.398801	−	0.185289i
$371$	−1.20432	−	2.08594i	−0.0625252	−	0.108297i
$372$	20.4561	−	11.0110i	1.06060	−	0.570896i
$373$	17.2400			0.892653			0.446327	−	0.894870i	$-0.352732\pi$
$373$	17.2400			0.892653			0.446327	+	0.894870i	$0.352732\pi$
$374$	18.8281	+	8.74779i	0.973575	+	0.452337i
$375$	4.00130	−	19.0420i	0.206626	−	0.983326i
$376$	2.17496	−	8.25477i	0.112165	−	0.425707i
$377$	13.5544	−	9.05332i	0.698085	−	0.466270i
$378$	−3.97444	−	0.0361422i	−0.204423	−	0.00185896i
$379$	−4.55170	+	2.62792i	−0.233805	+	0.134987i	−0.612326	−	0.790605i	$-0.709766\pi$
$379$	−4.55170	+	2.62792i	−0.233805	+	0.134987i	0.378521	+	0.925593i	$0.376433\pi$
$380$	−3.32319	+	0.595510i	−0.170476	+	0.0305490i
$381$	−24.8030	+	8.12274i	−1.27070	+	0.416140i
$382$	7.32968	+	10.4369i	0.375019	+	0.534000i
$383$	22.2580			1.13733			0.568664	−	0.822570i	$-0.307460\pi$
$383$	22.2580			1.13733			0.568664	+	0.822570i	$0.307460\pi$
$384$	−17.9445	+	7.87379i	−0.915724	+	0.401808i
$385$	0.849788	−	1.47188i	0.0433092	−	0.0750138i
$386$	−1.76752	+	3.80427i	−0.0899643	+	0.193632i
$387$	−9.76929	+	1.07270i	−0.496601	+	0.0545285i
$388$	−16.3557	−	19.3821i	−0.830334	−	0.983978i
$389$	5.46973	+	3.15795i	0.277326	+	0.160114i	0.632212	−	0.774795i	$-0.282147\pi$
$389$	5.46973	+	3.15795i	0.277326	+	0.160114i	−0.354886	+	0.934910i	$0.615480\pi$
$390$	10.3249	+	6.71714i	0.522820	+	0.340135i
$391$	−15.4998	+	8.94879i	−0.783857	+	0.452560i
$392$	4.83365	−	18.3454i	0.244136	−	0.926585i
$393$	0.952325	+	2.90796i	0.0480385	+	0.146687i
$394$	2.78649	−	1.95691i	0.140381	−	0.0985875i
$395$	5.19467			0.261372
$396$	−13.1405	−	3.17280i	−0.660335	−	0.159439i
$397$	0.0326983	−	0.0566351i	0.00164108	−	0.00284243i	−0.865204	−	0.501421i	$-0.832811\pi$
$397$	0.0326983	−	0.0566351i	0.00164108	−	0.00284243i	0.866845	+	0.498578i	$0.166144\pi$
$398$	−8.41141	−	3.90806i	−0.421626	−	0.195893i
$399$	1.10965	+	0.233171i	0.0555520	+	0.0116731i
$400$	−2.05485	+	12.0453i	−0.102742	+	0.602266i
$401$	4.97955	+	2.87495i	0.248667	+	0.143568i	0.619154	−	0.785270i	$-0.287476\pi$
$401$	4.97955	+	2.87495i	0.248667	+	0.143568i	−0.370487	+	0.928838i	$0.620809\pi$
$402$	−10.2563	−	7.66913i	−0.511539	−	0.382501i
$403$	21.6845	+	10.6983i	1.08018	+	0.532920i
$404$	−5.59038	−	31.1966i	−0.278132	−	1.55209i
$405$	−11.9734	−	3.76777i	−0.594963	−	0.187222i
$406$	1.98736	+	2.82985i	0.0986309	+	0.140443i
$407$	4.83106	+	8.36764i	0.239467	+	0.414768i
$408$	−28.5352	−	14.3066i	−1.41270	−	0.708284i
$409$	−6.58765			−0.325738			−0.162869	−	0.986648i	$-0.552075\pi$
$409$	−6.58765			−0.325738			−0.162869	+	0.986648i	$0.552075\pi$
$410$	6.90266	−	0.613586i	0.340898	−	0.0303028i
$411$	36.6091	−	11.9891i	1.80579	−	0.591379i
$412$	13.0753	−	11.0337i	0.644176	−	0.543591i
$413$	3.54588	−	2.04722i	0.174481	−	0.100737i
$414$	8.74881	−	7.69845i	0.429981	−	0.378358i
$415$			7.71534i			0.378731i
$416$	−17.5082	−	10.4624i	−0.858412	−	0.512962i
$417$	6.95775	−	33.1117i	0.340723	−	1.62148i
$418$	3.49742	+	1.62495i	0.171064	+	0.0794789i
$419$	−7.25203	+	12.5609i	−0.354285	+	0.613639i	−0.986995	−	0.160749i	$-0.948609\pi$
$419$	−7.25203	+	12.5609i	−0.354285	+	0.613639i	0.632710	+	0.774388i	$0.281942\pi$
$420$	−1.37343	+	2.22313i	−0.0670166	+	0.108478i
$421$	−11.8435	+	20.5136i	−0.577218	+	0.999771i	0.418579	+	0.908180i	$0.362528\pi$
$421$	−11.8435	+	20.5136i	−0.577218	+	0.999771i	−0.995797	+	0.0915903i	$0.970805\pi$
$422$	7.23336	+	3.36072i	0.352114	+	0.163597i
$423$	−7.30029	+	5.35597i	−0.354952	+	0.260416i
$424$	3.31075	+	12.1527i	0.160784	+	0.590188i
$425$	−17.2380	+	9.95236i	−0.836165	+	0.482760i
$426$	13.9561	−	18.6642i	0.676174	−	0.904283i
$427$	−3.61456	−	2.08687i	−0.174921	−	0.100991i
$428$	−20.2838	−	24.0371i	−0.980453	−	1.16188i
$429$	−5.24185	−	13.0572i	−0.253079	−	0.630408i
$430$	−2.72262	+	5.85996i	−0.131296	+	0.282592i
$431$	−5.49901	−	9.52456i	−0.264878	−	0.458782i	0.702654	−	0.711532i	$-0.251998\pi$
$431$	−5.49901	−	9.52456i	−0.264878	−	0.458782i	−0.967532	+	0.252750i	$0.918665\pi$
$432$	20.0497	+	5.47813i	0.964641	+	0.263567i
$433$	15.4445	−	26.7506i	0.742214	−	1.28555i	−0.209271	−	0.977858i	$-0.567109\pi$
$433$	15.4445	−	26.7506i	0.742214	−	1.28555i	0.951485	−	0.307695i	$-0.0995576\pi$
$434$	−2.16145	+	4.65214i	−0.103753	+	0.223310i
$435$	3.39879	+	10.3783i	0.162959	+	0.497602i
$436$	−33.8625	+	6.06810i	−1.62172	+	0.290610i
$437$	−2.87917	+	1.66229i	−0.137729	+	0.0795180i
$438$	−19.6874	−	2.34312i	−0.940702	−	0.111958i
$439$			14.9648i			0.714229i	0.934061	+	0.357114i	$0.116239\pi$
$439$			14.9648i			0.714229i	−0.934061	+	0.357114i	$0.883761\pi$
$440$	−6.25824	+	6.31072i	−0.298350	+	0.300852i
$441$	−16.2242	+	11.9031i	−0.772581	+	0.566815i
$442$	−5.09416	−	32.8314i	−0.242304	−	1.56163i
$443$	11.8161	−	20.4662i	0.561402	−	0.972377i	−0.435973	−	0.899960i	$-0.643596\pi$
$443$	11.8161	−	20.4662i	0.561402	−	0.972377i	0.997374	−	0.0724166i	$-0.0230711\pi$
$444$	−7.04129	−	13.0812i	−0.334165	−	0.620805i
$445$	6.37488	−	11.0416i	0.302198	−	0.523422i
$446$	−1.75759	−	19.7724i	−0.0832244	−	0.936250i
$447$	−0.683401	+	3.25228i	−0.0323238	+	0.153827i
$448$	2.13214	−	3.76523i	0.100734	−	0.177890i
$449$	−23.8934	−	13.7949i	−1.12760	−	0.651019i	−0.184269	−	0.982876i	$-0.558992\pi$
$449$	−23.8934	−	13.7949i	−1.12760	−	0.651019i	−0.943330	+	0.331856i	$0.892325\pi$
$450$	9.72995	−	8.56179i	0.458674	−	0.403607i
$451$	−6.85533	−	3.95793i	−0.322805	−	0.186371i
$452$	−4.71536	−	26.3137i	−0.221792	−	1.23769i
$453$	−25.6061	−	22.9484i	−1.20308	−	1.07821i
$454$	−4.28574	−	6.10258i	−0.201140	−	0.286408i
$455$	−2.71407	+	0.177415i	−0.127238	+	0.00831734i
$456$	−5.30058	−	2.65754i	−0.248222	−	0.124451i
$457$	26.5429			1.24163			0.620813	−	0.783959i	$-0.286803\pi$
$457$	26.5429			1.24163			0.620813	+	0.783959i	$0.286803\pi$
$458$	8.96562	+	12.7664i	0.418936	+	0.596534i
$459$	13.9861	+	30.8333i	0.652817	+	1.43918i
$460$	−1.35146	−	7.54173i	−0.0630124	−	0.351635i
$461$	−28.4540	+	16.4279i	−1.32524	+	0.765126i	−0.984559	−	0.175055i	$-0.943990\pi$
$461$	−28.4540	+	16.4279i	−1.32524	+	0.765126i	−0.340678	+	0.940180i	$0.610656\pi$
$462$	2.74332	−	1.17651i	0.127631	−	0.0547364i
$463$	17.0550	−	9.84670i	0.792612	−	0.457615i	−0.0482691	−	0.998834i	$-0.515371\pi$
$463$	17.0550	−	9.84670i	0.792612	−	0.457615i	0.840881	+	0.541219i	$0.182037\pi$
$464$	−6.27925	−	16.9578i	−0.291507	−	0.787245i
$465$	−10.8121	+	12.0643i	−0.501399	+	0.559468i
$466$	−1.28715	−	14.4801i	−0.0596261	−	0.670776i
$467$	−5.92436			−0.274147			−0.137073	−	0.990561i	$-0.543770\pi$
$467$	−5.92436			−0.274147			−0.137073	+	0.990561i	$0.543770\pi$
$468$	7.45777	+	20.3072i	0.344736	+	0.938700i
$469$	2.82783			0.130577
$470$	0.527081	+	5.92951i	0.0243124	+	0.273508i
$471$	4.86970	+	14.8698i	0.224384	+	0.685164i
$472$	−20.6583	+	5.62792i	−0.950876	+	0.259046i
$473$	6.39205	−	3.69045i	0.293907	−	0.169687i
$474$	7.30660	+	5.46349i	0.335603	+	0.250946i
$475$	−3.20205	+	1.84871i	−0.146920	+	0.0848245i
$476$	6.93797	−	1.24327i	0.318001	−	0.0569853i
$477$	5.37711	−	12.2298i	0.246201	−	0.559963i
$478$	19.6420	+	27.9688i	0.898405	+	1.27926i
$479$	3.48174			0.159085			0.0795423	−	0.996831i	$-0.474654\pi$
$479$	3.48174			0.159085			0.0795423	+	0.996831i	$0.474654\pi$
$480$	9.90712	−	9.41195i	0.452196	−	0.429595i
$481$	6.84129	−	13.8667i	0.311936	−	0.632266i
$482$	6.94931	+	9.89531i	0.316532	+	0.450719i
$483$	−0.529164	+	2.51827i	−0.0240778	+	0.114585i
$484$	−11.6620	+	2.08982i	−0.530092	+	0.0949916i
$485$	15.3159	+	8.84266i	0.695461	+	0.401524i
$486$	−12.8785	−	17.8926i	−0.584181	−	0.811623i
$487$	34.8181	+	20.1022i	1.57776	+	0.910918i	0.995172	+	0.0981489i	$0.0312921\pi$
$487$	34.8181	+	20.1022i	1.57776	+	0.910918i	0.582585	+	0.812770i	$0.302041\pi$
$488$	15.4976	+	15.3687i	0.701541	+	0.695708i
$489$	30.9783	+	27.7630i	1.40089	+	1.25549i
$490$	1.17139	+	13.1778i	0.0529179	+	0.595311i
$491$	−19.2479	+	33.3383i	−0.868644	+	1.50454i	−0.00526188	+	0.999986i	$0.501675\pi$
$491$	−19.2479	+	33.3383i	−0.868644	+	1.50454i	−0.863382	+	0.504550i	$0.831658\pi$
$492$	10.3543	+	6.39681i	0.466809	+	0.288391i
$493$	14.7282	−	25.5099i	0.663323	−	1.14891i
$494$	−0.946268	−	6.09861i	−0.0425746	−	0.274390i
$495$	9.37049	−	1.02891i	0.421172	−	0.0462461i
$496$	17.1283	−	20.6450i	0.769082	−	0.926987i
$497$			5.14602i			0.230830i
$498$	−8.11459	+	10.8521i	−0.363623	+	0.486292i
$499$	29.6449	−	17.1155i	1.32709	−	0.766194i	0.342239	−	0.939613i	$-0.388815\pi$
$499$	29.6449	−	17.1155i	1.32709	−	0.766194i	0.984848	+	0.173419i	$0.0554816\pi$
$500$	−3.96310	−	22.1157i	−0.177235	−	0.989046i
$501$	−5.76833	+	6.43639i	−0.257710	+	0.287557i
$502$	−3.84450	+	8.27460i	−0.171588	+	0.369314i
$503$	−15.6790	+	27.1569i	−0.699094	+	1.21087i	0.269687	+	0.962948i	$0.413080\pi$
$503$	−15.6790	+	27.1569i	−0.699094	+	1.21087i	−0.968781	+	0.247918i	$0.920253\pi$
$504$	−4.26998	+	1.68245i	−0.190200	+	0.0749423i
$505$	11.0507	+	19.1403i	0.491749	+	0.851734i
$506$	−3.68770	+	7.93712i	−0.163938	+	0.352848i
$507$	−12.7169	+	18.5817i	−0.564778	+	0.825243i
$508$	−23.0321	+	19.4357i	−1.02188	+	0.862321i
$509$	−19.7746	−	11.4169i	−0.876495	−	0.506045i	−0.00699373	−	0.999976i	$-0.502226\pi$
$509$	−19.7746	−	11.4169i	−0.876495	−	0.506045i	−0.869501	+	0.493931i	$0.835560\pi$
$510$	22.1038	+	2.63071i	0.978775	+	0.116490i
$511$	3.79137	−	2.18895i	0.167720	−	0.0968333i
$512$	−15.7984	+	16.1991i	−0.698195	+	0.715908i
$513$	2.59800	+	5.72746i	0.114705	+	0.252874i
$514$	−9.89244	−	4.59617i	−0.436337	−	0.202728i
$515$	−5.96533	+	10.3323i	−0.262864	+	0.455294i
$516$	−9.99271	+	5.37885i	−0.439905	+	0.236791i
$517$	3.39993	−	5.88885i	0.149529	−	0.258991i
$518$	2.97493	+	1.38220i	0.130711	+	0.0607302i
$519$	26.4996	−	8.67833i	1.16320	−	0.380936i
$520$	13.9608	+	2.71896i	0.612222	+	0.119234i
$521$			28.1173i			1.23184i	0.787808	+	0.615920i	$0.211216\pi$
$521$			28.1173i			1.23184i	−0.787808	+	0.615920i	$0.788784\pi$
$522$	−6.13477	+	18.1723i	−0.268512	+	0.795382i
$523$	30.9191	−	17.8511i	1.35200	−	0.780575i	0.363467	−	0.931607i	$-0.381593\pi$
$523$	30.9191	−	17.8511i	1.35200	−	0.780575i	0.988529	+	0.151032i	$0.0482595\pi$
$524$	2.27868	+	2.70033i	0.0995447	+	0.117964i
$525$	−0.588507	+	2.80068i	−0.0256846	+	0.122232i
$526$	−45.3629	+	4.03236i	−1.97792	+	0.175819i
$527$	43.6970			1.90347
$528$	−15.4399	+	2.29429i	−0.671933	+	0.0998460i
$529$	7.72756	+	13.3845i	0.335981	+	0.581936i
$530$	−5.04802	−	7.18800i	−0.219272	−	0.312227i
$531$	20.7893	+	9.14052i	0.902179	+	0.396665i
$532$	1.28877	−	0.230945i	0.0558751	−	0.0100127i
$533$	0.826317	+	12.6409i	0.0357918	+	0.547538i
$534$	20.5796	−	8.82588i	0.890566	−	0.381933i
$535$	18.9943	+	10.9664i	0.821195	+	0.474117i
$536$	−14.2997	−	3.76768i	−0.617653	−	0.162739i
$537$	8.90479	+	27.1911i	0.384270	+	1.17338i
$538$	18.2734	+	8.49007i	0.787821	+	0.366033i
$539$	7.55601	−	13.0874i	0.325461	−	0.563714i
$540$	−14.4482	+	1.15200i	−0.621752	+	0.0495742i
$541$	−12.4829			−0.536683			−0.268341	−	0.963324i	$-0.586476\pi$
$541$	−12.4829			−0.536683			−0.268341	+	0.963324i	$0.586476\pi$
$542$	0.259216	−	0.182043i	0.0111343	−	0.00781942i
$543$	−2.00693	−	0.421717i	−0.0861257	−	0.0180976i
$544$	−36.7402	−	2.95689i	−1.57522	−	0.126776i
$545$	20.7760	−	11.9950i	0.889945	−	0.513810i
$546$	−4.00409	−	2.60497i	−0.171359	−	0.111483i
$547$	−34.7731	−	20.0763i	−1.48679	−	0.858399i	−0.486904	−	0.873456i	$-0.661874\pi$
$547$	−34.7731	−	20.0763i	−1.48679	−	0.858399i	−0.999887	+	0.0150570i	$0.995207\pi$
$548$	33.9952	−	28.6870i	1.45220	−	1.22545i
$549$	−2.52675	−	23.0116i	−0.107839	−	0.982110i
$550$	−4.10126	+	8.82724i	−0.174878	+	0.376395i
$551$	2.73584	−	4.73861i	0.116551	−	0.201872i
$552$	6.03108	−	12.0293i	0.256700	−	0.511999i
$553$	−2.01455			−0.0856673
$554$	12.9136	+	18.3880i	0.548645	+	0.781230i
$555$	7.71482	+	6.91407i	0.327476	+	0.293486i
$556$	−6.89133	−	38.4565i	−0.292257	−	1.63092i
$557$	−26.3901	+	15.2363i	−1.11818	+	0.645583i	−0.940936	−	0.338584i	$-0.890052\pi$
$557$	−26.3901	+	15.2363i	−1.11818	+	0.645583i	−0.177246	+	0.984167i	$0.556719\pi$
$558$	−27.8964	+	5.59750i	−1.18095	+	0.236961i
$559$	−10.5928	−	5.22607i	−0.448026	−	0.221039i
$560$	−0.507420	+	2.97445i	−0.0214424	+	0.125693i
$561$	−18.9354	−	16.9700i	−0.799452	−	0.716474i
$562$	6.44082	+	2.99250i	0.271690	+	0.126231i
$563$	−18.1616			−0.765419			−0.382709	−	0.923869i	$-0.625009\pi$
$563$	−18.1616			−0.765419			−0.382709	+	0.923869i	$0.625009\pi$
$564$	−5.49497	+	8.89454i	−0.231380	+	0.374528i
$565$	9.32101	+	16.1445i	0.392138	+	0.679202i
$566$	32.7022	+	15.1939i	1.37457	+	0.638647i
$567$	4.64341	+	1.46118i	0.195005	+	0.0613638i
$568$	6.85632	−	26.0222i	0.287685	−	1.09187i
$569$			9.99863i			0.419164i	0.977791	+	0.209582i	$0.0672104\pi$
$569$			9.99863i			0.419164i	−0.977791	+	0.209582i	$0.932790\pi$
$570$	4.10591	+	0.488669i	0.171978	+	0.0204681i
$571$	−19.4973	+	11.2568i	−0.815935	+	0.471080i	−0.849013	−	0.528372i	$-0.822803\pi$
$571$	−19.4973	+	11.2568i	−0.815935	+	0.471080i	0.0330775	+	0.999453i	$0.489469\pi$
$572$	−11.2654	−	11.7067i	−0.471031	−	0.489483i
$573$	−4.86130	−	14.8441i	−0.203084	−	0.620123i
$574$	−2.67692	+	0.237955i	−0.111733	+	0.00993204i
$575$	−4.19550	−	7.26682i	−0.174964	−	0.303047i
$576$	23.8339	−	2.81865i	0.993080	−	0.117444i
$577$	−11.5190			−0.479540			−0.239770	−	0.970830i	$-0.577072\pi$
$577$	−11.5190			−0.479540			−0.239770	+	0.970830i	$0.577072\pi$
$578$	−20.6897	−	29.4606i	−0.860578	−	1.22540i
$579$	3.42884	−	3.82595i	0.142498	−	0.159001i
$580$	8.13247	+	9.63730i	0.337683	+	0.400167i
$581$		−	2.99209i		−	0.124133i
$582$	12.2425	+	28.5462i	0.507467	+	1.18328i
$583$			10.0332i			0.415533i
$584$	−22.0885	+	6.01755i	−0.914030	+	0.249008i
$585$	−9.69828	−	11.5554i	−0.400974	−	0.477758i
$586$	0.165999	+	1.86744i	0.00685735	+	0.0771433i
$587$	−33.4390			−1.38017			−0.690087	−	0.723726i	$-0.742428\pi$
$587$	−33.4390			−1.38017			−0.690087	+	0.723726i	$0.742428\pi$
$588$	−12.2121	+	19.7673i	−0.503617	+	0.815188i
$589$	8.11696			0.334454
$590$	12.2188	−	8.58109i	0.503042	−	0.353278i
$591$	−3.96314	+	1.29789i	−0.163022	+	0.0533880i
$592$	−13.2020	−	10.9531i	−0.542597	−	0.450170i
$593$			5.34897i			0.219656i	0.993951	+	0.109828i	$0.0350300\pi$
$593$			5.34897i			0.219656i	−0.993951	+	0.109828i	$0.964970\pi$
$594$	14.2623	+	8.40816i	0.585188	+	0.344991i
$595$	−4.25671	+	2.45762i	−0.174508	+	0.100752i
$596$	0.676877	+	3.77725i	0.0277260	+	0.154722i
$597$	8.45935	+	7.58133i	0.346218	+	0.310283i
$598$	13.8403	−	2.14748i	0.565974	−	0.0878172i
$599$	−1.84175	−	3.19000i	−0.0752518	−	0.130340i	0.825944	−	0.563752i	$-0.190643\pi$
$599$	−1.84175	−	3.19000i	−0.0752518	−	0.130340i	−0.901196	+	0.433412i	$0.857309\pi$
$600$	6.70744	−	13.3783i	0.273830	−	0.546166i
$601$	45.0381			1.83714			0.918570	−	0.395257i	$-0.129345\pi$
$601$	45.0381			1.83714			0.918570	+	0.395257i	$0.129345\pi$
$602$	1.05586	−	2.27255i	0.0430337	−	0.0926223i
$603$	9.27811	+	12.6463i	0.377834	+	0.514996i
$604$	−37.3471	−	13.4756i	−1.51963	−	0.548316i
$605$	7.15511	−	4.13101i	0.290897	−	0.167949i
$606$	−4.58740	+	38.5445i	−0.186350	+	1.56576i
$607$		−	36.9827i		−	1.50108i	−0.660825	−	0.750540i	$-0.729793\pi$
$607$		−	36.9827i		−	1.50108i	0.660825	−	0.750540i	$-0.270207\pi$
$608$	−6.82469	−	0.549260i	−0.276778	−	0.0222754i
$609$	−1.31808	−	4.02481i	−0.0534115	−	0.163094i
$610$	−13.8031	−	6.41314i	−0.558873	−	0.259660i
$611$	−10.8588	+	0.709821i	−0.439298	+	0.0287163i
$612$	28.3235	+	26.9479i	1.14491	+	1.08930i
$613$	8.97994	+	15.5537i	0.362696	+	0.628208i	0.988404	−	0.151850i	$-0.0485229\pi$
$613$	8.97994	+	15.5537i	0.362696	+	0.628208i	−0.625707	+	0.780058i	$0.715190\pi$
$614$	−2.11056	−	23.7432i	−0.0851753	−	0.958198i
$615$	−8.30594	−	1.74533i	−0.334928	−	0.0703784i
$616$	2.42701	−	2.44736i	0.0977871	−	0.0986070i
$617$		−	20.0638i		−	0.807738i	−0.914817	−	0.403869i	$-0.867665\pi$
$617$		−	20.0638i		−	0.807738i	0.914817	−	0.403869i	$-0.132335\pi$
$618$	−19.2575	+	8.25888i	−0.774650	+	0.332221i
$619$	−6.89088	−	3.97845i	−0.276968	−	0.159907i	0.355082	−	0.934835i	$-0.384453\pi$
$619$	−6.89088	−	3.97845i	−0.276968	−	0.159907i	−0.632050	+	0.774928i	$0.717786\pi$
$620$	−6.34903	+	17.5961i	−0.254983	+	0.706675i
$621$	−12.9980	+	5.89597i	−0.521594	+	0.236597i
$622$	−9.27803	−	13.2112i	−0.372015	−	0.529722i
$623$	−2.47224	+	4.28205i	−0.0990483	+	0.171557i
$624$	16.7770	+	18.5076i	0.671618	+	0.740898i
$625$	0.196904	+	0.341047i	0.00787615	+	0.0136419i
$626$	10.9453	−	23.5579i	0.437464	−	0.941564i
$627$	−3.51735	−	3.15227i	−0.140469	−	0.125890i
$628$	11.6520	+	13.8081i	0.464966	+	0.551003i
$629$		−	27.9432i		−	1.11417i
$630$	2.40270	−	2.11423i	0.0957257	−	0.0842330i
$631$	−29.6175	−	17.0997i	−1.17905	−	0.680727i	−0.223258	−	0.974759i	$-0.571669\pi$
$631$	−29.6175	−	17.0997i	−1.17905	−	0.680727i	−0.955796	+	0.294032i	$0.905003\pi$
$632$	10.1871	+	2.68409i	0.405221	+	0.106767i
$633$	−7.27458	−	6.51953i	−0.289139	−	0.259128i
$634$	3.42870	+	1.59302i	0.136171	+	0.0632670i
$635$	10.5079	−	18.2002i	0.416993	−	0.722252i
$636$	0.459647	−	15.4196i	0.0182262	−	0.611425i
$637$	−24.1326	+	1.57751i	−0.956167	+	0.0625032i
$638$	−1.27538	−	14.3477i	−0.0504928	−	0.568030i
$639$	−23.0133	+	16.8841i	−0.910394	+	0.667923i
$640$	6.52892	−	14.3650i	0.258078	−	0.567828i
$641$	−7.49751	+	4.32869i	−0.296134	+	0.170973i	−0.640705	−	0.767787i	$-0.721358\pi$
$641$	−7.49751	+	4.32869i	−0.296134	+	0.170973i	0.344571	+	0.938760i	$0.388024\pi$
$642$	15.1827	+	35.4020i	0.599213	+	1.39721i
$643$		−	18.2630i		−	0.720222i	−0.932909	−	0.360111i	$-0.882739\pi$
$643$		−	18.2630i		−	0.720222i	0.932909	−	0.360111i	$-0.117261\pi$
$644$	0.524112	+	2.92476i	0.0206529	+	0.115252i
$645$	5.28167	−	5.89336i	0.207965	−	0.232051i
$646$	−6.40983	−	9.12713i	−0.252191	−	0.359102i
$647$	−10.5904	−	18.3432i	−0.416353	−	0.721144i	0.579217	−	0.815174i	$-0.303359\pi$
$647$	−10.5904	−	18.3432i	−0.416353	−	0.721144i	−0.995569	+	0.0940295i	$0.970025\pi$
$648$	−21.5338	−	13.5755i	−0.845928	−	0.533296i
$649$	−17.0554			−0.669482
$650$	15.3925	−	2.38832i	0.603743	−	0.0936775i
$651$	4.19304	−	4.67866i	0.164338	−	0.183371i
$652$	45.1826	+	16.3029i	1.76949	+	0.638469i
$653$	−5.82038	−	3.36040i	−0.227769	−	0.131502i	0.381773	−	0.924256i	$-0.375313\pi$
$653$	−5.82038	−	3.36040i	−0.227769	−	0.131502i	−0.609542	+	0.792753i	$0.708647\pi$
$654$	41.8383	+	4.97942i	1.63601	+	0.194711i
$655$	−2.13383	−	1.23196i	−0.0833754	−	0.0481368i
$656$	13.8536	+	2.36333i	0.540893	+	0.0922725i
$657$	22.2286	+	9.77333i	0.867220	+	0.381294i
$658$	−0.204407	−	2.29952i	−0.00796863	−	0.0896448i
$659$	−13.4691	−	23.3292i	−0.524684	−	0.908779i	−0.999587	−	0.0287406i	$-0.990850\pi$
$659$	−13.4691	−	23.3292i	−0.524684	−	0.908779i	0.474903	−	0.880038i	$-0.342483\pi$
$660$	9.58479	−	5.15927i	0.373087	−	0.200824i
$661$	14.5816	−	25.2560i	0.567158	−	0.982346i	−0.429688	−	0.902978i	$-0.641376\pi$
$661$	14.5816	−	25.2560i	0.567158	−	0.982346i	0.996845	−	0.0793684i	$-0.0252903\pi$
$662$	−12.0214	+	8.44242i	−0.467224	+	0.328124i
$663$	−5.75235	+	40.2826i	−0.223403	+	1.56445i
$664$	−3.98652	+	15.1303i	−0.154707	+	0.587169i
$665$	−0.790709	+	0.456516i	−0.0306624	+	0.0177029i
$666$	3.57946	+	17.8391i	0.138701	+	0.691250i
$667$	10.7539	+	6.20878i	0.416394	+	0.240405i
$668$	−3.38726	+	9.38763i	−0.131057	+	0.363218i
$669$	−4.99942	+	23.7920i	−0.193289	+	0.919853i
$670$	10.2717	−	0.913059i	0.396829	−	0.0352746i
$671$	8.69286	+	15.0565i	0.335584	+	0.581249i
$672$	−3.84208	+	3.65005i	−0.148212	+	0.140804i
$673$	−13.8499			−0.533875			−0.266937	−	0.963714i	$-0.586012\pi$
$673$	−13.8499			−0.533875			−0.266937	+	0.963714i	$0.586012\pi$
$674$	−2.80078	−	3.98811i	−0.107882	−	0.153616i
$675$	−14.4557	+	6.55718i	−0.556401	+	0.252386i
$676$	−5.56561	+	25.3973i	−0.214062	+	0.976820i
$677$	10.5808	+	6.10883i	0.406654	+	0.234782i	0.689351	−	0.724428i	$-0.257896\pi$
$677$	10.5808	+	6.10883i	0.406654	+	0.234782i	−0.282697	+	0.959209i	$0.591229\pi$
$678$	−3.86937	+	32.5114i	−0.148602	+	1.24859i
$679$	−5.93968	−	3.42927i	−0.227944	−	0.131603i
$680$	24.7996	−	6.75614i	0.951023	−	0.259086i
$681$	2.84245	+	8.67952i	0.108923	+	0.332600i
$682$	17.4866	−	12.2805i	0.669595	−	0.470245i
$683$	3.22662	−	5.58867i	0.123463	−	0.213845i	−0.797668	−	0.603097i	$-0.793933\pi$
$683$	3.22662	−	5.58867i	0.123463	−	0.213845i	0.921131	+	0.389252i	$0.127267\pi$
$684$	5.26124	+	5.00572i	0.201169	+	0.191399i
$685$	−15.5096	+	26.8634i	−0.592590	+	1.02640i
$686$	−0.928365	−	10.4438i	−0.0354451	−	0.398748i
$687$	−5.94631	−	18.1572i	−0.226866	−	0.692742i
$688$	−8.36709	+	10.0850i	−0.318992	+	0.384487i
$689$	13.3519	−	8.91809i	0.508667	−	0.339752i
$690$	−1.10900	+	9.31806i	−0.0422188	+	0.354733i
$691$			0.0811900i			0.00308861i	0.999999	+	0.00154431i	$0.000491568\pi$
$691$			0.0811900i			0.00308861i	−0.999999	+	0.00154431i	$0.999508\pi$
$692$	24.6075	−	20.7651i	0.935437	−	0.789372i
$693$	−3.63397	+	0.399022i	−0.138043	+	0.0151576i
$694$	35.1786	−	3.12706i	1.33536	−	0.118702i
$695$	13.6223	+	23.5945i	0.516724	+	0.894992i
$696$	1.30277	+	22.1087i	0.0493814	+	0.838029i
$697$	11.4464	+	19.8258i	0.433565	+	0.750957i
$698$	−36.3790	+	3.23377i	−1.37697	+	0.122400i
$699$	−3.66126	+	17.4238i	−0.138482	+	0.659029i
$700$	0.582889	+	3.25276i	0.0220311	+	0.122943i
$701$		−	26.1503i		−	0.987684i	−0.869552	−	0.493842i	$-0.835592\pi$
$701$		−	26.1503i		−	0.987684i	0.869552	−	0.493842i	$-0.164408\pi$
$702$	−1.48778	−	26.4535i	−0.0561527	−	0.998422i
$703$		−	5.19060i		−	0.195767i
$704$	−15.5336	+	9.14210i	−0.585444	+	0.344556i
$705$	1.49927	−	7.13495i	0.0564657	−	0.268718i
$706$	−3.11440	−	35.0361i	−0.117212	−	1.31860i
$707$	−4.28556	−	7.42282i	−0.161175	−	0.279164i
$708$	26.2116	+	0.781351i	0.985093	+	0.0293650i
$709$	1.55624	+	2.69548i	0.0584458	+	0.101231i	0.893768	−	0.448530i	$-0.148052\pi$
$709$	1.55624	+	2.69548i	0.0584458	+	0.101231i	−0.835322	+	0.549761i	$0.814719\pi$
$710$	1.66156	+	18.6921i	0.0623573	+	0.701502i
$711$	−6.60973	−	9.00920i	−0.247884	−	0.337871i
$712$	18.2068	−	18.3594i	0.682327	−	0.688049i
$713$			18.4208i			0.689866i
$714$	−8.57210	−	1.02022i	−0.320803	−	0.0381806i
$715$	10.1603	+	5.01273i	0.379975	+	0.187465i
$716$	21.3070	+	25.2496i	0.796280	+	0.943623i
$717$	−13.0273	−	39.7792i	−0.486512	−	1.48558i
$718$	−50.4908	+	4.48818i	−1.88430	+	0.167498i
$719$	−19.9811	+	34.6084i	−0.745171	+	1.29067i	0.204944	+	0.978774i	$0.434299\pi$
$719$	−19.9811	+	34.6084i	−0.745171	+	1.29067i	−0.950115	+	0.311900i	$0.899035\pi$
$720$	−14.9668	+	7.48994i	−0.557779	+	0.279134i
$721$	2.31342	−	4.00696i	0.0861562	−	0.149227i
$722$	14.2520	+	20.2938i	0.530404	+	0.755256i
$723$	−4.60902	−	14.0738i	−0.171411	−	0.523410i
$724$	−2.33089	+	0.417691i	−0.0866267	+	0.0155234i
$725$	11.9599	+	6.90507i	0.444181	+	0.256448i
$726$	14.4088	+	1.71488i	0.534762	+	0.0636452i
$727$	−4.66907	−	2.69569i	−0.173166	−	0.0999775i	0.410912	−	0.911675i	$-0.365210\pi$
$727$	−4.66907	−	2.69569i	−0.173166	−	0.0999775i	−0.584078	+	0.811698i	$0.698544\pi$
$728$	−5.41415	−	1.05444i	−0.200662	−	0.0390802i
$729$	8.70050	+	25.5598i	0.322241	+	0.946658i
$730$	13.0648	−	9.17517i	0.483549	−	0.339588i
$731$	−21.3458			−0.789503
$732$	−12.6699	−	23.5378i	−0.468292	−	0.869984i
$733$	−11.5118	−	19.9391i	−0.425199	−	0.736466i	0.571240	−	0.820783i	$-0.306462\pi$
$733$	−11.5118	−	19.9391i	−0.425199	−	0.736466i	−0.996439	+	0.0843171i	$0.973129\pi$
$734$	−3.63232	−	40.8625i	−0.134071	−	1.50826i
$735$	3.33198	−	15.8567i	0.122902	−	0.584885i
$736$	1.24650	−	15.4881i	0.0459467	−	0.570900i
$737$	−10.2012	−	5.88967i	−0.375767	−	0.216949i
$738$	−9.84713	−	11.1907i	−0.362478	−	0.411934i
$739$	28.4597	−	16.4312i	1.04691	−	0.604432i	0.125125	−	0.992141i	$-0.460067\pi$
$739$	28.4597	−	16.4312i	1.04691	−	0.604432i	0.921782	+	0.387709i	$0.126734\pi$
$740$	11.2522	+	4.06005i	0.413641	+	0.149250i
$741$	−1.06853	+	7.48271i	−0.0392535	+	0.274884i
$742$	1.95767	+	2.78758i	0.0718684	+	0.102335i
$743$	23.4305	−	40.5828i	0.859581	−	1.48884i	−0.0127486	−	0.999919i	$-0.504058\pi$
$743$	23.4305	−	40.5828i	0.859581	−	1.48884i	0.872329	−	0.488919i	$-0.162609\pi$
$744$	−27.4369	+	18.0723i	−1.00588	+	0.662561i
$745$	−1.33800	−	2.31749i	−0.0490207	−	0.0849063i
$746$	−24.2853	+	2.15875i	−0.889147	+	0.0790373i
$747$	13.3808	−	9.81703i	0.489578	−	0.359186i
$748$	−27.6177	−	9.96505i	−1.00980	−	0.364358i
$749$	−7.36619	−	4.25287i	−0.269155	−	0.155396i
$750$	−3.25208	+	27.3248i	−0.118749	+	0.997759i
$751$	18.9213	+	10.9242i	0.690448	+	0.398630i	0.803780	−	0.594927i	$-0.202819\pi$
$751$	18.9213	+	10.9242i	0.690448	+	0.398630i	−0.113332	+	0.993557i	$0.536152\pi$
$752$	−2.03014	+	11.9005i	−0.0740316	+	0.433967i
$753$	7.45802	−	8.32176i	0.271785	−	0.303262i
$754$	−17.9598	+	14.4503i	−0.654059	+	0.526248i
$755$	27.6873			1.00765
$756$	5.60316	−	0.446757i	0.203785	−	0.0162484i
$757$	13.1301	+	22.7420i	0.477221	+	0.826570i	0.999659	−	0.0261065i	$-0.00831091\pi$
$757$	13.1301	+	22.7420i	0.477221	+	0.826570i	−0.522438	+	0.852677i	$0.674978\pi$
$758$	6.08273	−	4.27180i	0.220935	−	0.155159i
$759$	7.15385	−	7.98236i	0.259668	−	0.289741i
$760$	4.60667	−	1.25499i	0.167102	−	0.0455233i
$761$			13.8928i			0.503613i	0.967778	+	0.251807i	$0.0810247\pi$
$761$			13.8928i			0.503613i	−0.967778	+	0.251807i	$0.918975\pi$
$762$	33.9219	−	14.5479i	1.22886	−	0.527016i
$763$	−8.05714	+	4.65179i	−0.291688	+	0.168406i
$764$	−11.6319	−	13.7843i	−0.420828	−	0.498697i
$765$	−24.9569	−	10.9729i	−0.902318	−	0.396726i
$766$	−31.3539	+	2.78708i	−1.13286	+	0.100701i
$767$	15.1598	+	22.6968i	0.547389	+	0.819534i
$768$	24.2917	−	13.3384i	0.876551	−	0.481310i
$769$	−0.178980	+	0.310002i	−0.00645418	+	0.0111790i	−0.869234	−	0.494400i	$-0.835388\pi$
$769$	−0.178980	+	0.310002i	−0.00645418	+	0.0111790i	0.862780	+	0.505579i	$0.168721\pi$
$770$	−1.01276	+	2.17978i	−0.0364973	+	0.0785538i
$771$	9.94882	+	8.91620i	0.358298	+	0.321109i
$772$	2.01347	−	5.58024i	0.0724664	−	0.200837i
$773$	40.9099	+	23.6194i	1.47143	+	0.849530i	0.999485	−	0.0320991i	$-0.0102192\pi$
$773$	40.9099	+	23.6194i	1.47143	+	0.849530i	0.471944	+	0.881629i	$0.343553\pi$
$774$	13.6273	−	2.73436i	0.489823	−	0.0982844i
$775$			20.4867i			0.735903i
$776$	25.4666	+	25.2548i	0.914196	+	0.906594i
$777$	−2.99188	−	2.68135i	−0.107333	−	0.0961928i
$778$	−8.10041	−	3.76357i	−0.290414	−	0.134930i
$779$	2.12624	+	3.68276i	0.0761805	+	0.131949i
$780$	−15.3853	−	8.16931i	−0.550883	−	0.292508i
$781$	10.7179	−	18.5639i	0.383516	−	0.664269i
$782$	20.7133	−	14.5466i	0.740707	−	0.520187i
$783$	13.6746	−	19.1000i	0.488691	−	0.682577i
$784$	−4.51179	+	26.4477i	−0.161135	+	0.944562i
$785$	−10.9113	−	6.29963i	−0.389440	−	0.224843i
$786$	−1.70563	−	3.97707i	−0.0608378	−	0.141857i
$787$			38.9260i			1.38756i	0.720186	+	0.693781i	$0.244056\pi$
$787$			38.9260i			1.38756i	−0.720186	+	0.693781i	$0.755944\pi$
$788$	−3.68018	+	3.10553i	−0.131101	+	0.110630i
$789$	54.5849	+	11.4699i	1.94328	+	0.408341i
$790$	−7.31753	+	0.650463i	−0.260346	+	0.0231424i
$791$	−3.61478	−	6.26099i	−0.128527	−	0.222615i
$792$	18.9078	+	2.82397i	0.671859	+	0.100346i
$793$	12.3100	−	24.9513i	0.437141	−	0.886046i
$794$	−0.0389691	+	0.0838740i	−0.00138296	+	0.00297658i
$795$	3.34802	+	10.2233i	0.118742	+	0.362583i
$796$	12.3382	+	4.45187i	0.437315	+	0.157792i
$797$			14.8471i			0.525911i	0.964808	+	0.262956i	$0.0846973\pi$
$797$			14.8471i			0.525911i	−0.964808	+	0.262956i	$0.915303\pi$
$798$	−1.59232	−	0.189511i	−0.0563673	−	0.00670861i
$799$	−17.0307	+	9.83270i	−0.602504	+	0.347856i
$800$	1.38629	−	17.2251i	0.0490129	−	0.608998i
$801$	−27.2610	+	2.99335i	−0.963221	+	0.105765i
$802$	−7.37449	−	3.42629i	−0.260402	−	0.120987i
$803$	−18.2361			−0.643539
$804$	15.4080	+	9.51892i	0.543397	+	0.335706i
$805$	−1.03603	−	1.79445i	−0.0365152	−	0.0632462i
$806$	−31.8856	−	12.3550i	−1.12312	−	0.435185i
$807$	−18.3775	−	16.4701i	−0.646919	−	0.579773i
$808$	11.7813	+	43.2454i	0.414464	+	1.52137i
$809$	−17.3493	+	10.0166i	−0.609970	+	0.352166i	−0.772954	−	0.634462i	$-0.781222\pi$
$809$	−17.3493	+	10.0166i	−0.609970	+	0.352166i	0.162984	+	0.986629i	$0.447888\pi$
$810$	17.3382	+	3.80823i	0.609203	+	0.133807i
$811$		−	51.1717i		−	1.79688i	−0.439095	−	0.898441i	$-0.644701\pi$
$811$		−	51.1717i		−	1.79688i	0.439095	−	0.898441i	$-0.355299\pi$
$812$	−3.15386	−	3.73744i	−0.110679	−	0.131159i
$813$	−0.368675	+	0.120737i	−0.0129300	+	0.00423444i
$814$	−7.85309	−	11.1822i	−0.275251	−	0.391937i
$815$	−33.4962			−1.17332
$816$	41.9878	+	16.5801i	1.46987	+	0.580418i
$817$	−3.96510			−0.138721
$818$	9.27975	−	0.824888i	0.324459	−	0.0288415i
$819$	3.76109	+	4.48131i	0.131423	+	0.156590i
$820$	−9.64667	+	1.72867i	−0.336876	+	0.0603676i
$821$			49.4994i			1.72754i	0.503887	+	0.863770i	$0.331903\pi$
$821$			49.4994i			1.72754i	−0.503887	+	0.863770i	$0.668097\pi$
$822$	−50.0685	+	21.4727i	−1.74634	+	0.748945i
$823$		−	27.5361i		−	0.959850i	−0.877310	−	0.479925i	$-0.840664\pi$
$823$		−	27.5361i		−	0.959850i	0.877310	−	0.479925i	$-0.159336\pi$
$824$	−17.0371	+	17.1800i	−0.593516	+	0.598492i
$825$	7.95612	−	8.87755i	0.276997	−	0.309077i
$826$	−4.73859	+	3.32783i	−0.164877	+	0.115790i
$827$	−40.1789			−1.39716			−0.698578	−	0.715534i	$-0.746184\pi$
$827$	−40.1789			−1.39716			−0.698578	+	0.715534i	$0.746184\pi$
$828$	−11.3601	+	11.9400i	−0.394791	+	0.414943i
$829$	−2.15481	−	3.73225i	−0.0748398	−	0.129626i	0.826177	−	0.563411i	$-0.190511\pi$
$829$	−2.15481	−	3.73225i	−0.0748398	−	0.129626i	−0.901017	+	0.433785i	$0.857178\pi$
$830$	−0.966094	−	10.8683i	−0.0335336	−	0.377244i
$831$	−8.56472	−	26.1527i	−0.297107	−	0.907226i
$832$	25.9732	+	12.5456i	0.900459	+	0.434941i
$833$	−37.8492	+	21.8522i	−1.31140	+	0.757135i
$834$	−5.65495	+	47.5143i	−0.195815	+	1.64528i
$835$		−	6.95953i		−	0.240845i
$836$	−5.13014	−	1.85106i	−0.177430	−	0.0640204i
$837$	34.6806	+	3.40092i	1.19874	+	0.117553i
$838$	8.64280	−	18.6021i	0.298560	−	0.642598i
$839$	5.46990	+	9.47414i	0.188842	+	0.327084i	0.944864	−	0.327462i	$-0.106193\pi$
$839$	5.46990	+	9.47414i	0.188842	+	0.327084i	−0.756023	+	0.654546i	$0.772860\pi$
$840$	1.65632	−	3.30361i	0.0571485	−	0.113985i
$841$	8.56282			0.295270
$842$	14.1148	−	30.3797i	0.486429	−	1.04695i
$843$	−6.47753	−	5.80521i	−0.223098	−	0.199942i
$844$	−10.6102	−	3.82837i	−0.365217	−	0.131778i
$845$	−2.36031	−	17.9767i	−0.0811970	−	0.618417i
$846$	9.61297	−	8.45885i	0.330501	−	0.290821i
$847$	−2.77483	+	1.60205i	−0.0953442	+	0.0550470i
$848$	−6.18545	−	16.7045i	−0.212409	−	0.573634i
$849$	−32.8886	−	29.4749i	−1.12873	−	1.01158i
$850$	23.0362	−	16.1780i	0.790137	−	0.554900i
$851$	11.7797			0.403802
$852$	−17.3223	+	28.0390i	−0.593452	+	0.960601i
$853$	−5.29998	+	9.17983i	−0.181468	+	0.314311i	−0.942381	−	0.334543i	$-0.891418\pi$
$853$	−5.29998	+	9.17983i	−0.181468	+	0.314311i	0.760913	+	0.648854i	$0.224751\pi$
$854$	5.35300	+	2.48708i	0.183176	+	0.0851061i
$855$	−4.63588	−	2.03828i	−0.158544	−	0.0697076i
$856$	31.5828	+	31.3201i	1.07948	+	1.07050i
$857$	14.9361	+	8.62337i	0.510208	+	0.294569i	0.732919	−	0.680316i	$-0.238157\pi$
$857$	14.9361	+	8.62337i	0.510208	+	0.294569i	−0.222711	+	0.974884i	$0.571491\pi$
$858$	9.01897	+	17.7368i	0.307902	+	0.605524i
$859$	0.708253	−	0.408910i	0.0241653	−	0.0139518i	−0.487869	−	0.872917i	$-0.662226\pi$
$859$	0.708253	−	0.408910i	0.0241653	−	0.0139518i	0.512034	+	0.858965i	$0.328892\pi$
$860$	3.10148	−	8.59560i	0.105759	−	0.293108i
$861$	3.22113	+	0.676856i	0.109776	+	0.0230672i
$862$	8.93887	+	12.7283i	0.304459	+	0.433527i
$863$	−26.8092			−0.912597			−0.456299	−	0.889827i	$-0.650825\pi$
$863$	−26.8092			−0.912597			−0.456299	+	0.889827i	$0.650825\pi$
$864$	−28.9291	−	5.20625i	−0.984189	−	0.177120i
$865$	−11.2266	+	19.4451i	−0.381716	+	0.661152i
$866$	−18.4064	+	39.6164i	−0.625474	+	1.34622i
$867$	13.7221	+	41.9009i	0.466028	+	1.42303i
$868$	2.46222	−	6.82393i	0.0835732	−	0.231619i
$869$	7.26735	+	4.19580i	0.246528	+	0.142333i
$870$	−6.08728	−	14.1939i	−0.206378	−	0.481219i
$871$	1.22962	+	18.8106i	0.0416640	+	0.637372i
$872$	46.9409	−	12.7881i	1.58962	−	0.433059i
$873$	−4.15211	−	37.8141i	−0.140528	−	1.27981i
$874$	3.84762	−	2.70212i	0.130148	−	0.0914005i
$875$	−3.03810	−	5.26215i	−0.102707	−	0.177893i
$876$	28.0263	+	0.835445i	0.946920	+	0.0282271i
$877$	−3.77195			−0.127370			−0.0636848	−	0.997970i	$-0.520285\pi$
$877$	−3.77195			−0.127370			−0.0636848	+	0.997970i	$0.520285\pi$
$878$	−1.87385	−	21.0802i	−0.0632393	−	0.711424i
$879$	0.472180	−	2.24708i	0.0159262	−	0.0757922i
$880$	8.02552	−	9.67329i	0.270540	−	0.326087i
$881$	20.4608	−	11.8130i	0.689341	−	0.397991i	−0.114024	−	0.993478i	$-0.536374\pi$
$881$	20.4608	−	11.8130i	0.689341	−	0.397991i	0.803365	+	0.595487i	$0.203041\pi$
$882$	21.3639	−	18.7990i	0.719360	−	0.632995i
$883$			28.4071i			0.955975i	0.878367	+	0.477987i	$0.158634\pi$
$883$			28.4071i			0.955975i	−0.878367	+	0.477987i	$0.841366\pi$
$884$	11.2870	+	45.6103i	0.379622	+	1.53404i
$885$	−17.3785	+	5.69128i	−0.584172	+	0.191310i
$886$	−14.0822	+	30.3094i	−0.473101	+	1.01827i
$887$	15.8355	−	27.4278i	0.531703	−	0.920936i	−0.467612	−	0.883934i	$-0.654886\pi$
$887$	15.8355	−	27.4278i	0.531703	−	0.920936i	0.999315	−	0.0370027i	$-0.0117810\pi$
$888$	11.5568	+	17.5452i	0.387820	+	0.588779i
$889$	−4.07506	+	7.05822i	−0.136673	+	0.236725i
$890$	−7.59743	+	16.3521i	−0.254666	+	0.548124i
$891$	−13.7075	−	14.9422i	−0.459219	−	0.500582i
$892$	4.95169	+	27.6325i	0.165795	+	0.925204i
$893$	−3.16355	+	1.82648i	−0.105864	+	0.0611208i
$894$	0.555438	−	4.66692i	0.0185766	−	0.156085i
$895$	−19.9525	−	11.5196i	−0.666938	−	0.385057i
$896$	−2.53198	+	5.57091i	−0.0845876	+	0.186111i
$897$	−16.9815	−	2.42495i	−0.566994	−	0.0809668i
$898$	35.3850	+	16.4404i	1.18081	+	0.548623i
$899$	−15.1588	−	26.2558i	−0.505573	−	0.875678i
$900$	−12.6341	+	13.2790i	−0.421137	+	0.442634i
$901$	14.5082	−	25.1289i	0.483337	−	0.837165i
$902$	10.1524	+	4.71696i	0.338039	+	0.157058i
$903$	−2.04828	+	2.28550i	−0.0681626	+	0.0760568i
$904$	9.93726	+	36.4765i	0.330508	+	1.21319i
$905$	1.43009	−	0.825663i	0.0475378	−	0.0274460i
$906$	38.9438	+	29.1201i	1.29382	+	0.967450i
$907$		−	59.0261i		−	1.95993i	−0.199174	−	0.979964i	$-0.563826\pi$
$907$		−	59.0261i		−	1.95993i	0.199174	−	0.979964i	$-0.436174\pi$
$908$	6.80130	+	8.05981i	0.225709	+	0.267474i
$909$	19.1344	−	43.5196i	0.634649	−	1.44345i
$910$	3.80099	−	0.589766i	0.126002	−	0.0195506i
$911$	−14.1700	+	24.5432i	−0.469474	+	0.813153i	−0.999391	−	0.0348969i	$-0.988890\pi$
$911$	−14.1700	+	24.5432i	−0.469474	+	0.813153i	0.529917	+	0.848049i	$0.322223\pi$
$912$	7.79947	+	3.07984i	0.258266	+	0.101984i
$913$	−6.23178	+	10.7938i	−0.206242	+	0.357221i
$914$	−37.3899	+	3.32364i	−1.23675	+	0.109936i
$915$	13.8818	+	12.4410i	0.458918	+	0.411286i
$916$	−14.2281	−	16.8608i	−0.470109	−	0.557097i
$917$	0.827519	+	0.477768i	0.0273271	+	0.0157773i
$918$	−23.5626	−	41.6823i	−0.777680	−	1.37572i
$919$	−21.9878	−	12.6947i	−0.725312	−	0.418759i	0.0913926	−	0.995815i	$-0.470868\pi$
$919$	−21.9878	−	12.6947i	−0.725312	−	0.418759i	−0.816705	+	0.577056i	$0.804202\pi$
$920$	2.84811	+	10.4545i	0.0938993	+	0.344675i
$921$	−6.00344	+	28.5701i	−0.197820	+	0.941417i
$922$	38.0250	−	26.7043i	1.25229	−	0.879460i
$923$	−34.2310	+	2.23763i	−1.12673	+	0.0736525i
$924$	−3.71708	+	2.00082i	−0.122283	+	0.0658221i
$925$	13.1007			0.430749
$926$	−22.7917	+	16.0062i	−0.748981	+	0.525997i
$927$	25.5097	−	2.80105i	0.837848	−	0.0919986i
$928$	10.9687	+	23.1014i	0.360066	+	0.758342i
$929$	−16.3353	+	9.43118i	−0.535943	+	0.309427i	−0.743433	−	0.668810i	$-0.766804\pi$
$929$	−16.3353	+	9.43118i	−0.535943	+	0.309427i	0.207490	+	0.978237i	$0.433471\pi$
$930$	13.7199	−	18.3483i	0.449894	−	0.601666i
$931$	−7.03070	+	4.05918i	−0.230422	+	0.133034i
$932$	3.62631	+	20.2363i	0.118784	+	0.662862i
$933$	6.15351	+	18.7900i	0.201457	+	0.615155i
$934$	8.34541	−	0.741833i	0.273070	−	0.0242735i
$935$	20.4744			0.669585
$936$	−13.0483	−	27.6721i	−0.426496	−	0.904489i
$937$	47.9720			1.56718			0.783589	−	0.621280i	$-0.213387\pi$
$937$	47.9720			1.56718			0.783589	+	0.621280i	$0.213387\pi$
$938$	−3.98345	+	0.354094i	−0.130064	+	0.0115616i
$939$	−21.2331	+	23.6922i	−0.692916	+	0.773165i
$940$	−1.48495	−	8.28665i	−0.0484339	−	0.270281i
$941$	43.6089	−	25.1776i	1.42161	−	0.820767i	0.425174	−	0.905112i	$-0.360213\pi$
$941$	43.6089	−	25.1776i	1.42161	−	0.820767i	0.996437	+	0.0843445i	$0.0268796\pi$
$942$	−8.72171	−	20.3367i	−0.284169	−	0.662605i
$943$	−8.35775	+	4.82535i	−0.272166	+	0.157135i
$944$	28.3958	−	10.5146i	0.924205	−	0.342221i
$945$	−3.56967	+	1.61922i	−0.116121	+	0.0526731i
$946$	−8.54211	+	5.99898i	−0.277728	+	0.195044i
$947$	−22.3920			−0.727642			−0.363821	−	0.931469i	$-0.618528\pi$
$947$	−22.3920			−0.727642			−0.363821	+	0.931469i	$0.618528\pi$
$948$	−10.9766	−	6.78128i	−0.356504	−	0.220246i
$949$	16.2093	+	24.2681i	0.526177	+	0.787777i
$950$	4.27911	−	3.00515i	0.138833	−	0.0974999i
$951$	−3.44824	−	3.09033i	−0.111817	−	0.100211i
$952$	−9.61755	+	2.62010i	−0.311707	+	0.0849179i
$953$	41.7784	+	24.1208i	1.35334	+	0.781349i	0.988715	−	0.149807i	$-0.0478651\pi$
$953$	41.7784	+	24.1208i	1.35334	+	0.781349i	0.364621	+	0.931156i	$0.381198\pi$
$954$	−6.04314	+	17.9009i	−0.195654	+	0.579563i
$955$	10.8925	+	6.28876i	0.352472	+	0.203500i
$956$	−31.1711	−	36.9390i	−1.00815	−	1.19469i
$957$	−3.62779	+	17.2645i	−0.117270	+	0.558082i
$958$	−4.90458	+	0.435974i	−0.158460	+	0.0140857i
$959$	6.01477	−	10.4179i	0.194227	−	0.336411i
$960$	−12.7772	+	14.4988i	−0.412383	+	0.467946i
$961$	6.98727	−	12.1023i	0.225396	−	0.390397i
$962$	−7.90070	+	20.3901i	−0.254729	+	0.657402i
$963$	−5.14931	−	46.8957i	−0.165934	−	1.51119i
$964$	−11.0283	−	13.0689i	−0.355197	−	0.420922i
$965$			4.13692i			0.133172i
$966$	0.430080	−	3.61364i	0.0138376	−	0.116267i
$967$	−12.8743	+	7.43300i	−0.414011	+	0.239029i	−0.692511	−	0.721407i	$-0.743496\pi$
$967$	−12.8743	+	7.43300i	−0.414011	+	0.239029i	0.278501	+	0.960436i	$0.410162\pi$
$968$	16.1661	−	4.40413i	0.519600	−	0.141554i
$969$	4.25122	+	12.9812i	0.136569	+	0.417018i
$970$	−22.6822	−	10.5385i	−0.728281	−	0.338370i
$971$	−17.2331	+	29.8487i	−0.553038	+	0.957890i	0.445015	+	0.895523i	$0.353198\pi$
$971$	−17.2331	+	29.8487i	−0.553038	+	0.957890i	−0.998053	+	0.0623668i	$0.980135\pi$
$972$	20.3819	+	23.5919i	0.653749	+	0.756711i
$973$	−5.28287	−	9.15020i	−0.169361	−	0.293342i
$974$	−51.5639	−	23.9573i	−1.65221	−	0.767643i
$975$	−18.8859	−	2.69690i	−0.604831	−	0.0863700i
$976$	−23.7552	−	19.7087i	−0.760385	−	0.630859i
$977$	−46.2902	−	26.7256i	−1.48095	−	0.855029i	−0.481186	−	0.876618i	$-0.659794\pi$
$977$	−46.2902	−	26.7256i	−1.48095	−	0.855029i	−0.999767	+	0.0215897i	$0.993127\pi$
$978$	−47.1143	−	35.2296i	−1.50655	−	1.12652i
$979$	17.8369	−	10.2981i	0.570070	−	0.329130i
$980$	−3.30017	−	18.4163i	−0.105420	−	0.588287i
$981$	−47.2386	−	20.7696i	−1.50821	−	0.663121i
$982$	22.9392	−	49.3725i	0.732018	−	1.57554i
$983$	29.1582	−	50.5035i	0.930003	−	1.61081i	0.146692	−	0.989182i	$-0.453137\pi$
$983$	29.1582	−	50.5035i	0.930003	−	1.61081i	0.783311	−	0.621630i	$-0.213529\pi$
$984$	−15.3867	−	7.71439i	−0.490510	−	0.245926i
$985$	1.67900	−	2.90811i	0.0534973	−	0.0926601i
$986$	−17.5527	+	37.7790i	−0.558991	+	1.20313i
$987$	−0.581431	+	2.76701i	−0.0185072	+	0.0880748i
$988$	2.09662	+	8.47238i	0.0667024	+	0.269542i
$989$		−	8.99850i		−	0.286136i
$990$	−13.0710	+	2.62273i	−0.415423	+	0.0833559i
$991$	34.9555	−	20.1816i	1.11040	−	0.641088i	0.171465	−	0.985190i	$-0.445150\pi$
$991$	34.9555	−	20.1816i	1.11040	−	0.641088i	0.938932	+	0.344102i	$0.111816\pi$
$992$	−21.5428	+	31.2265i	−0.683984	+	0.991442i
$993$	17.0977	−	5.59931i	0.542578	−	0.177689i
$994$	−0.644371	−	7.24899i	−0.0204382	−	0.229924i
$995$	−9.14692			−0.289977
$996$	10.0718	−	16.3029i	0.319138	−	0.516578i
$997$	16.2627	+	28.1678i	0.515045	+	0.892084i	0.999848	+	0.0174605i	$0.00555815\pi$
$997$	16.2627	+	28.1678i	0.515045	+	0.892084i	−0.484803	+	0.874624i	$0.661109\pi$
$998$	−39.6164	+	27.8219i	−1.25403	+	0.880688i
$999$	2.17481	−	22.1774i	0.0688079	−	0.701662i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	468.2.bm.a.263.2	yes	160
4.3	odd	2	inner	468.2.bm.a.263.79	yes	160
9.5	odd	6		468.2.bd.a.419.30	yes	160
13.9	even	3		468.2.bd.a.191.57	yes	160
36.23	even	6		468.2.bd.a.419.57	yes	160
52.35	odd	6		468.2.bd.a.191.30	✓	160
117.113	odd	6	inner	468.2.bm.a.347.79	yes	160
468.347	even	6	inner	468.2.bm.a.347.2	yes	160

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
468.2.bd.a.191.30	✓	160	52.35	odd	6
468.2.bd.a.191.57	yes	160	13.9	even	3
468.2.bd.a.419.30	yes	160	9.5	odd	6
468.2.bd.a.419.57	yes	160	36.23	even	6
468.2.bm.a.263.2	yes	160	1.1	even	1	trivial
468.2.bm.a.263.79	yes	160	4.3	odd	2	inner
468.2.bm.a.347.2	yes	160	468.347	even	6	inner
468.2.bm.a.347.79	yes	160	117.113	odd	6	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:	\( N \)	\(=\)	\( 468 = 2^{2} \cdot 3^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	468.bm (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.40866 + 0.125217i) q^{2} +(1.69503 + 0.356177i) q^{3} +(1.96864 - 0.352777i) q^{4} +(-1.20784 + 0.697346i) q^{5} +(-2.43232 - 0.289485i) q^{6} +(0.468412 - 0.270438i) q^{7} +(-2.72897 + 0.743451i) q^{8} +(2.74628 + 1.20747i) q^{9} +O(q^{10})\)	\(q+(-1.40866 + 0.125217i) q^{2} +(1.69503 + 0.356177i) q^{3} +(1.96864 - 0.352777i) q^{4} +(-1.20784 + 0.697346i) q^{5} +(-2.43232 - 0.289485i) q^{6} +(0.468412 - 0.270438i) q^{7} +(-2.72897 + 0.743451i) q^{8} +(2.74628 + 1.20747i) q^{9} +(1.61411 - 1.13356i) q^{10} -2.25302 q^{11} +(3.46256 + 0.103217i) q^{12} +(2.00261 + 2.99826i) q^{13} +(-0.625969 + 0.439608i) q^{14} +(-2.29571 + 0.751820i) q^{15} +(3.75110 - 1.38898i) q^{16} +(5.64286 + 3.25790i) q^{17} +(-4.01976 - 1.35703i) q^{18} +(1.04819 + 0.605174i) q^{19} +(-2.13179 + 1.79892i) q^{20} +(0.890298 - 0.291563i) q^{21} +(3.17374 - 0.282117i) q^{22} +(-1.37340 + 2.37879i) q^{23} +(-4.89050 + 0.288176i) q^{24} +(-1.52742 + 2.64556i) q^{25} +(-3.19643 - 3.97276i) q^{26} +(4.22496 + 3.02486i) q^{27} +(0.826731 - 0.697640i) q^{28} -4.52075i q^{29} +(3.13973 - 1.34652i) q^{30} +(5.80783 - 3.35315i) q^{31} +(-5.11009 + 2.42631i) q^{32} +(-3.81894 - 0.802475i) q^{33} +(-8.35681 - 3.88269i) q^{34} +(-0.377177 + 0.653290i) q^{35} +(5.83240 + 1.40824i) q^{36} +(-2.14426 - 3.71396i) q^{37} +(-1.55232 - 0.721232i) q^{38} +(2.32659 + 5.79543i) q^{39} +(2.77771 - 2.80100i) q^{40} +(3.04273 + 1.75672i) q^{41} +(-1.21762 + 0.522194i) q^{42} +(-2.83710 + 1.63800i) q^{43} +(-4.43539 + 0.794814i) q^{44} +(-4.15908 + 0.456681i) q^{45} +(1.63678 - 3.52288i) q^{46} +(-1.50905 + 2.61376i) q^{47} +(6.85296 - 1.01832i) q^{48} +(-3.35373 + 5.80883i) q^{49} +(1.82034 - 3.91796i) q^{50} +(8.40444 + 7.53211i) q^{51} +(5.00015 + 5.19601i) q^{52} -4.45322i q^{53} +(-6.33029 - 3.73195i) q^{54} +(2.72128 - 1.57113i) q^{55} +(-1.07723 + 1.08626i) q^{56} +(1.56117 + 1.39913i) q^{57} +(0.566076 + 6.36820i) q^{58} +7.57000 q^{59} +(-4.25420 + 2.28994i) q^{60} +(-3.85831 - 6.68279i) q^{61} +(-7.76138 + 5.45069i) q^{62} +(1.61293 - 0.177105i) q^{63} +(6.89456 - 4.05771i) q^{64} +(-4.50966 - 2.22489i) q^{65} +(5.48007 + 0.652216i) q^{66} +(4.52780 + 2.61412i) q^{67} +(12.2581 + 4.42297i) q^{68} +(-3.17523 + 3.54296i) q^{69} +(0.449511 - 0.967493i) q^{70} +(-4.75712 + 8.23957i) q^{71} +(-8.39220 - 1.25342i) q^{72} +8.09409 q^{73} +(3.48558 + 4.96321i) q^{74} +(-3.53131 + 3.94029i) q^{75} +(2.27701 + 0.821592i) q^{76} +(-1.05534 + 0.609302i) q^{77} +(-4.00306 - 7.87245i) q^{78} +(-3.22560 - 1.86230i) q^{79} +(-3.56212 + 4.29348i) q^{80} +(6.08406 + 6.63206i) q^{81} +(-4.50614 - 2.09362i) q^{82} +(2.76597 - 4.79079i) q^{83} +(1.64982 - 0.888060i) q^{84} -9.08754 q^{85} +(3.79140 - 2.66264i) q^{86} +(1.61019 - 7.66282i) q^{87} +(6.14843 - 1.67501i) q^{88} +(-7.91688 + 4.57081i) q^{89} +(5.80154 - 1.16410i) q^{90} +(1.74889 + 0.862836i) q^{91} +(-1.86454 + 5.16749i) q^{92} +(11.0388 - 3.61509i) q^{93} +(1.79845 - 3.87085i) q^{94} -1.68806 q^{95} +(-9.52597 + 2.29257i) q^{96} +(-6.34022 - 10.9816i) q^{97} +(3.99689 - 8.60260i) q^{98} +(-6.18741 - 2.72044i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 160 q - 2 q^{4} - 12 q^{5} - 6 q^{6} - 2 q^{9}+O(q^{10}) \) 160 * q - 2 * q^4 - 12 * q^5 - 6 * q^6 - 2 * q^9	\( 160 q - 2 q^{4} - 12 q^{5} - 6 q^{6} - 2 q^{9} - 4 q^{10} - 7 q^{12} - 2 q^{13} - 6 q^{14} - 2 q^{16} + 4 q^{18} - 3 q^{20} - 2 q^{21} - 18 q^{22} + 12 q^{24} + 60 q^{25} - 18 q^{26} + 6 q^{28} - 18 q^{30} - 26 q^{33} - 4 q^{34} - 2 q^{36} - 4 q^{37} - 42 q^{38} + 8 q^{40} - 6 q^{41} + 5 q^{42} + 8 q^{45} - 6 q^{46} + 33 q^{48} + 58 q^{49} - 96 q^{50} - 8 q^{52} + 7 q^{54} - 24 q^{56} - 12 q^{57} - 22 q^{58} - 39 q^{60} + 2 q^{61} + 3 q^{62} - 26 q^{64} - 6 q^{65} + 30 q^{66} - 66 q^{68} + 2 q^{69} - 27 q^{70} + 48 q^{72} - 16 q^{73} - 33 q^{74} + 9 q^{76} + 12 q^{77} - 26 q^{78} + 90 q^{80} - 10 q^{81} + 11 q^{82} - 13 q^{84} + 16 q^{85} - 60 q^{86} + 6 q^{88} - 57 q^{90} - 36 q^{92} - 102 q^{93} - 33 q^{94} + 93 q^{96} + 2 q^{97} - 9 q^{98}+O(q^{100}) \) 160 * q - 2 * q^4 - 12 * q^5 - 6 * q^6 - 2 * q^9 - 4 * q^10 - 7 * q^12 - 2 * q^13 - 6 * q^14 - 2 * q^16 + 4 * q^18 - 3 * q^20 - 2 * q^21 - 18 * q^22 + 12 * q^24 + 60 * q^25 - 18 * q^26 + 6 * q^28 - 18 * q^30 - 26 * q^33 - 4 * q^34 - 2 * q^36 - 4 * q^37 - 42 * q^38 + 8 * q^40 - 6 * q^41 + 5 * q^42 + 8 * q^45 - 6 * q^46 + 33 * q^48 + 58 * q^49 - 96 * q^50 - 8 * q^52 + 7 * q^54 - 24 * q^56 - 12 * q^57 - 22 * q^58 - 39 * q^60 + 2 * q^61 + 3 * q^62 - 26 * q^64 - 6 * q^65 + 30 * q^66 - 66 * q^68 + 2 * q^69 - 27 * q^70 + 48 * q^72 - 16 * q^73 - 33 * q^74 + 9 * q^76 + 12 * q^77 - 26 * q^78 + 90 * q^80 - 10 * q^81 + 11 * q^82 - 13 * q^84 + 16 * q^85 - 60 * q^86 + 6 * q^88 - 57 * q^90 - 36 * q^92 - 102 * q^93 - 33 * q^94 + 93 * q^96 + 2 * q^97 - 9 * q^98

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