LMFDB - Embedded newform 300.2.w.a.223.17

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [300,2,Mod(67,300)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(300, base_ring=CyclotomicField(20))

chi = DirichletCharacter(H, H._module([10, 0, 13]))

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

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

chi := DirichletCharacter("300.67");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 300 = 2^{2} \cdot 3 \cdot 5^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	300.w (of order $20$, degree $8$, 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:	$2.39551206064$
Analytic rank:	$0$
Dimension:	$240$
Relative dimension:	$30$ over $\Q(\zeta_{20})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{20}]$

Embedding invariants

Embedding label			223.17
Character	$\chi$	$=$	300.223
Dual form			300.2.w.a.187.17

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.152118 + 1.40601i) q^{2} +(-0.453990 - 0.891007i) q^{3} +(-1.95372 + 0.427760i) q^{4} +(1.07461 - 1.96092i) q^{5} +(1.18370 - 0.773853i) q^{6} +(-0.868967 - 0.868967i) q^{7} +(-0.898631 - 2.68188i) q^{8} +(-0.587785 + 0.809017i) q^{9} +(2.92054 + 1.21262i) q^{10} +(-2.63624 - 3.62847i) q^{11} +(1.26811 + 1.54658i) q^{12} +(-0.530391 - 3.34876i) q^{13} +(1.08959 - 1.35396i) q^{14} +(-2.23506 - 0.0672487i) q^{15} +(3.63404 - 1.67145i) q^{16} +(5.52269 + 2.81395i) q^{17} +(-1.22690 - 0.703365i) q^{18} +(-1.47067 - 4.52625i) q^{19} +(-1.26069 + 4.29076i) q^{20} +(-0.379753 + 1.16876i) q^{21} +(4.70064 - 4.25853i) q^{22} +(-0.748674 + 4.72694i) q^{23} +(-1.98160 + 2.01823i) q^{24} +(-2.69041 - 4.21446i) q^{25} +(4.62770 - 1.25514i) q^{26} +(0.987688 + 0.156434i) q^{27} +(2.06943 + 1.32601i) q^{28} +(2.21880 + 0.720931i) q^{29} +(-0.245441 - 3.15274i) q^{30} +(9.32059 - 3.02844i) q^{31} +(2.90287 + 4.85524i) q^{32} +(-2.03617 + 3.99620i) q^{33} +(-3.11633 + 8.19300i) q^{34} +(-2.63778 + 0.770171i) q^{35} +(0.802303 - 1.83202i) q^{36} +(-8.45865 + 1.33972i) q^{37} +(6.14023 - 2.75630i) q^{38} +(-2.74297 + 1.99289i) q^{39} +(-6.22463 - 1.11984i) q^{40} +(2.25676 + 1.63963i) q^{41} +(-1.70105 - 0.356146i) q^{42} +(-5.74249 + 5.74249i) q^{43} +(6.70259 + 5.96134i) q^{44} +(0.954775 + 2.02198i) q^{45} +(-6.76001 - 0.333587i) q^{46} +(-4.24551 + 2.16319i) q^{47} +(-3.13909 - 2.47914i) q^{48} -5.48979i q^{49} +(5.51631 - 4.42384i) q^{50} -6.19825i q^{51} +(2.46870 + 6.31566i) q^{52} +(0.643686 - 0.327974i) q^{53} +(-0.0697026 + 1.41249i) q^{54} +(-9.94808 + 1.27025i) q^{55} +(-1.54958 + 3.11134i) q^{56} +(-3.36525 + 3.36525i) q^{57} +(-0.676115 + 3.22932i) q^{58} +(0.305784 + 0.222165i) q^{59} +(4.39544 - 0.824682i) q^{60} +(2.68715 - 1.95233i) q^{61} +(5.67585 + 12.6441i) q^{62} +(1.21378 - 0.192243i) q^{63} +(-6.38493 + 4.82003i) q^{64} +(-7.13661 - 2.55857i) q^{65} +(-5.92843 - 2.25497i) q^{66} +(3.01843 - 5.92399i) q^{67} +(-11.9935 - 3.13529i) q^{68} +(4.55163 - 1.47891i) q^{69} +(-1.48412 - 3.59158i) q^{70} +(4.75445 + 1.54481i) q^{71} +(2.69789 + 0.849360i) q^{72} +(3.39138 + 0.537142i) q^{73} +(-3.17037 - 11.6891i) q^{74} +(-2.53369 + 4.31050i) q^{75} +(4.80942 + 8.21394i) q^{76} +(-0.862218 + 5.44383i) q^{77} +(-3.21927 - 3.55349i) q^{78} +(0.521056 - 1.60364i) q^{79} +(0.627622 - 8.92222i) q^{80} +(-0.309017 - 0.951057i) q^{81} +(-1.96204 + 3.42244i) q^{82} +(13.5881 + 6.92350i) q^{83} +(0.241983 - 2.44587i) q^{84} +(11.4527 - 7.80563i) q^{85} +(-8.94753 - 7.20045i) q^{86} +(-0.364959 - 2.30426i) q^{87} +(-7.36211 + 10.3307i) q^{88} +(-0.948617 - 1.30566i) q^{89} +(-2.69768 + 1.65000i) q^{90} +(-2.44907 + 3.37085i) q^{91} +(-0.559295 - 9.55537i) q^{92} +(-6.92982 - 6.92982i) q^{93} +(-3.68729 - 5.64016i) q^{94} +(-10.4560 - 1.98011i) q^{95} +(3.00817 - 4.79071i) q^{96} +(-5.55806 - 10.9083i) q^{97} +(7.71870 - 0.835099i) q^{98} +4.48504 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 240 q + 12 q^{8} + 8 q^{10} + 8 q^{12} + 4 q^{13} + 20 q^{17} - 20 q^{20} - 12 q^{22} + 20 q^{25} + 4 q^{28} - 8 q^{30} - 20 q^{32} - 8 q^{33} - 4 q^{37} - 76 q^{38} - 92 q^{40} - 20 q^{42} - 140 q^{44}+ \cdots + 256 q^{98}+O(q^{100}) $ 240 * q + 12 * q^8 + 8 * q^10 + 8 * q^12 + 4 * q^13 + 20 * q^17 - 20 * q^20 - 12 * q^22 + 20 * q^25 + 4 * q^28 - 8 * q^30 - 20 * q^32 - 8 * q^33 - 4 * q^37 - 76 * q^38 - 92 * q^40 - 20 * q^42 - 140 * q^44 - 4 * q^45 - 16 * q^48 - 164 * q^50 - 172 * q^52 - 4 * q^53 - 120 * q^58 + 20 * q^60 - 44 * q^62 - 60 * q^64 - 20 * q^65 + 16 * q^68 - 44 * q^70 + 12 * q^72 - 44 * q^73 - 48 * q^77 + 24 * q^78 - 4 * q^80 + 60 * q^81 + 24 * q^82 + 80 * q^84 - 64 * q^85 + 60 * q^88 - 260 * q^89 + 48 * q^90 + 144 * q^92 - 64 * q^93 + 40 * q^94 - 20 * q^96 - 180 * q^97 + 256 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/300\mathbb{Z}\right)^\times$.

$n$	$101$	$151$	$277$
$\chi(n)$	$1$	$-1$	$e\left(\frac{11}{20}\right)$

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 $

$2$	0.152118	+	1.40601i	0.107564	+	0.994198i
$2$	0.152118	+	1.40601i	0.107564	+	0.994198i
$3$	−0.453990	−	0.891007i	−0.262112	−	0.514423i
$3$	−0.453990	−	0.891007i	−0.262112	−	0.514423i
$4$	−1.95372	+	0.427760i	−0.976860	+	0.213880i
$5$	1.07461	−	1.96092i	0.480582	−	0.876950i
$5$	1.07461	−	1.96092i	0.480582	−	0.876950i
$6$	1.18370	−	0.773853i	0.483244	−	0.315924i
$7$	−0.868967	−	0.868967i	−0.328439	−	0.328439i	0.523554	−	0.851993i	$-0.324606\pi$
$7$	−0.868967	−	0.868967i	−0.328439	−	0.328439i	−0.851993	+	0.523554i	$0.824606\pi$
$8$	−0.898631	−	2.68188i	−0.317714	−	0.948187i
$9$	−0.587785	+	0.809017i	−0.195928	+	0.269672i
$10$	2.92054	+	1.21262i	0.923555	+	0.383465i
$11$	−2.63624	−	3.62847i	−0.794856	−	1.09403i	−0.993486	−	0.113951i	$-0.963649\pi$
$11$	−2.63624	−	3.62847i	−0.794856	−	1.09403i	0.198630	−	0.980075i	$-0.436351\pi$
$12$	1.26811	+	1.54658i	0.366071	+	0.446459i
$13$	−0.530391	−	3.34876i	−0.147104	−	0.928778i	−0.945258	−	0.326325i	$-0.894190\pi$
$13$	−0.530391	−	3.34876i	−0.147104	−	0.928778i	0.798154	−	0.602454i	$-0.205810\pi$
$14$	1.08959	−	1.35396i	0.291205	−	0.361861i
$15$	−2.23506	−	0.0672487i	−0.577089	−	0.0173635i
$16$	3.63404	−	1.67145i	0.908511	−	0.417861i
$17$	5.52269	+	2.81395i	1.33945	+	0.682483i	0.969160	−	0.246434i	$-0.0792589\pi$
$17$	5.52269	+	2.81395i	1.33945	+	0.682483i	0.370288	+	0.928917i	$0.379259\pi$
$18$	−1.22690	−	0.703365i	−0.289183	−	0.165785i
$19$	−1.47067	−	4.52625i	−0.337394	−	1.03839i	−0.965531	−	0.260290i	$-0.916182\pi$
$19$	−1.47067	−	4.52625i	−0.337394	−	1.03839i	0.628136	−	0.778103i	$-0.283818\pi$
$20$	−1.26069	+	4.29076i	−0.281899	+	0.959444i
$21$	−0.379753	+	1.16876i	−0.0828688	+	0.255044i
$22$	4.70064	−	4.25853i	1.00218	−	0.907922i
$23$	−0.748674	+	4.72694i	−0.156109	+	0.985635i	0.777900	+	0.628388i	$0.216285\pi$
$23$	−0.748674	+	4.72694i	−0.156109	+	0.985635i	−0.934010	+	0.357248i	$0.883715\pi$
$24$	−1.98160	+	2.01823i	−0.404492	+	0.411970i
$25$	−2.69041	−	4.21446i	−0.538082	−	0.842892i
$26$	4.62770	−	1.25514i	0.907567	−	0.246154i
$27$	0.987688	+	0.156434i	0.190081	+	0.0301058i
$28$	2.06943	+	1.32601i	0.391085	+	0.250592i
$29$	2.21880	+	0.720931i	0.412020	+	0.133874i	0.507690	−	0.861540i	$-0.330499\pi$
$29$	2.21880	+	0.720931i	0.412020	+	0.133874i	−0.0956700	+	0.995413i	$0.530499\pi$
$30$	−0.245441	−	3.15274i	−0.0448112	−	0.575609i
$31$	9.32059	−	3.02844i	1.67403	−	0.543925i	0.690289	−	0.723533i	$-0.257483\pi$
$31$	9.32059	−	3.02844i	1.67403	−	0.543925i	0.983738	+	0.179609i	$0.0574832\pi$
$32$	2.90287	+	4.85524i	0.513160	+	0.858293i
$33$	−2.03617	+	3.99620i	−0.354451	+	0.695649i
$34$	−3.11633	+	8.19300i	−0.534447	+	1.40509i
$35$	−2.63778	+	0.770171i	−0.445866	+	0.130183i
$36$	0.802303	−	1.83202i	0.133717	−	0.305337i
$37$	−8.45865	+	1.33972i	−1.39059	+	0.220248i	−0.806402	−	0.591368i	$-0.798588\pi$
$37$	−8.45865	+	1.33972i	−1.39059	+	0.220248i	−0.584191	+	0.811616i	$0.698588\pi$
$38$	6.14023	−	2.75630i	0.996077	−	0.447131i
$39$	−2.74297	+	1.99289i	−0.439227	+	0.319117i
$40$	−6.22463	−	1.11984i	−0.984200	−	0.177062i
$41$	2.25676	+	1.63963i	0.352447	+	0.256067i	0.749895	−	0.661557i	$-0.230104\pi$
$41$	2.25676	+	1.63963i	0.352447	+	0.256067i	−0.397448	+	0.917625i	$0.630104\pi$
$42$	−1.70105	−	0.356146i	−0.262478	−	0.0549545i
$43$	−5.74249	+	5.74249i	−0.875722	+	0.875722i	−0.993089	−	0.117367i	$-0.962555\pi$
$43$	−5.74249	+	5.74249i	−0.875722	+	0.875722i	0.117367	+	0.993089i	$0.462555\pi$
$44$	6.70259	+	5.96134i	1.01045	+	0.898706i
$45$	0.954775	+	2.02198i	0.142330	+	0.301419i
$46$	−6.76001	−	0.333587i	−0.996708	−	0.0491847i
$47$	−4.24551	+	2.16319i	−0.619271	+	0.315534i	−0.735331	−	0.677708i	$-0.762973\pi$
$47$	−4.24551	+	2.16319i	−0.619271	+	0.315534i	0.116061	+	0.993242i	$0.462973\pi$
$48$	−3.13909	−	2.47914i	−0.453089	−	0.357832i
$49$		−	5.48979i		−	0.784256i
$50$	5.51631	−	4.42384i	0.780124	−	0.625625i
$51$		−	6.19825i		−	0.867929i
$52$	2.46870	+	6.31566i	0.342347	+	0.875824i
$53$	0.643686	−	0.327974i	0.0884171	−	0.0450507i	−0.409223	−	0.912434i	$-0.634200\pi$
$53$	0.643686	−	0.327974i	0.0884171	−	0.0450507i	0.497640	+	0.867384i	$0.334200\pi$
$54$	−0.0697026	+	1.41249i	−0.00948532	+	0.192216i
$55$	−9.94808	+	1.27025i	−1.34140	+	0.171280i
$56$	−1.54958	+	3.11134i	−0.207072	+	0.415771i
$57$	−3.36525	+	3.36525i	−0.445738	+	0.445738i
$58$	−0.676115	+	3.22932i	−0.0887783	+	0.424030i
$59$	0.305784	+	0.222165i	0.0398097	+	0.0289234i	0.607512	−	0.794310i	$-0.292168\pi$
$59$	0.305784	+	0.222165i	0.0398097	+	0.0289234i	−0.567702	+	0.823234i	$0.692168\pi$
$60$	4.39544	−	0.824682i	0.567449	−	0.106466i
$61$	2.68715	−	1.95233i	0.344054	−	0.249970i	−0.402316	−	0.915501i	$-0.631795\pi$
$61$	2.68715	−	1.95233i	0.344054	−	0.249970i	0.746370	+	0.665531i	$0.231795\pi$
$62$	5.67585	+	12.6441i	0.720834	+	1.60581i
$63$	1.21378	−	0.192243i	0.152921	−	0.0242204i
$64$	−6.38493	+	4.82003i	−0.798116	+	0.602504i
$65$	−7.13661	−	2.55857i	−0.885188	−	0.317351i
$66$	−5.92843	−	2.25497i	−0.729739	−	0.277568i
$67$	3.01843	−	5.92399i	0.368759	−	0.723731i	−0.629835	−	0.776729i	$-0.716878\pi$
$67$	3.01843	−	5.92399i	0.368759	−	0.723731i	0.998595	+	0.0529977i	$0.0168776\pi$
$68$	−11.9935	−	3.13529i	−1.45442	−	0.380209i
$69$	4.55163	−	1.47891i	0.547951	−	0.178040i
$70$	−1.48412	−	3.59158i	−0.177386	−	0.429276i
$71$	4.75445	+	1.54481i	0.564249	+	0.183336i	0.577232	−	0.816580i	$-0.304133\pi$
$71$	4.75445	+	1.54481i	0.564249	+	0.183336i	−0.0129832	+	0.999916i	$0.504133\pi$
$72$	2.69789	+	0.849360i	0.317949	+	0.100098i
$73$	3.39138	+	0.537142i	0.396931	+	0.0628677i	0.351709	−	0.936109i	$-0.385601\pi$
$73$	3.39138	+	0.537142i	0.396931	+	0.0628677i	0.0452218	+	0.998977i	$0.485601\pi$
$74$	−3.17037	−	11.6891i	−0.368548	−	1.35883i
$75$	−2.53369	+	4.31050i	−0.292565	+	0.497734i
$76$	4.80942	+	8.21394i	0.551678	+	0.942203i
$77$	−0.862218	+	5.44383i	−0.0982588	+	0.620382i
$78$	−3.21927	−	3.55349i	−0.364511	−	0.402353i
$79$	0.521056	−	1.60364i	0.0586234	−	0.180424i	−0.917457	−	0.397836i	$-0.869761\pi$
$79$	0.521056	−	1.60364i	0.0586234	−	0.180424i	0.976080	+	0.217412i	$0.0697614\pi$
$80$	0.627622	−	8.92222i	0.0701703	−	0.997535i
$81$	−0.309017	−	0.951057i	−0.0343352	−	0.105673i
$82$	−1.96204	+	3.42244i	−0.216671	+	0.377945i
$83$	13.5881	+	6.92350i	1.49149	+	0.759953i	0.994192	−	0.107625i	$-0.0343247\pi$
$83$	13.5881	+	6.92350i	1.49149	+	0.759953i	0.497300	+	0.867578i	$0.334325\pi$
$84$	0.241983	−	2.44587i	0.0264025	−	0.266866i
$85$	11.4527	−	7.80563i	1.24222	−	0.846640i
$86$	−8.94753	−	7.20045i	−0.964837	−	0.776445i
$87$	−0.364959	−	2.30426i	−0.0391277	−	0.247043i
$88$	−7.36211	+	10.3307i	−0.784804	+	1.10126i
$89$	−0.948617	−	1.30566i	−0.100553	−	0.138400i	0.755775	−	0.654831i	$-0.227260\pi$
$89$	−0.948617	−	1.30566i	−0.100553	−	0.138400i	−0.856329	+	0.516431i	$0.827260\pi$
$90$	−2.69768	+	1.65000i	−0.284361	+	0.173926i
$91$	−2.44907	+	3.37085i	−0.256732	+	0.353361i
$92$	−0.559295	−	9.55537i	−0.0583106	−	0.996216i
$93$	−6.92982	−	6.92982i	−0.718589	−	0.718589i
$94$	−3.68729	−	5.64016i	−0.380315	−	0.581738i
$95$	−10.4560	−	1.98011i	−1.07276	−	0.203155i
$96$	3.00817	−	4.79071i	0.307020	−	0.488950i
$97$	−5.55806	−	10.9083i	−0.564336	−	1.10757i	−0.980175	−	0.198133i	$-0.936512\pi$
$97$	−5.55806	−	10.9083i	−0.564336	−	1.10757i	0.415840	−	0.909438i	$-0.363488\pi$
$98$	7.71870	−	0.835099i	0.779706	−	0.0843577i
$99$	4.48504			0.450763
$100$	7.05909	+	7.08303i	0.705909	+	0.708303i
$101$	−7.90808			−0.786884			−0.393442	−	0.919350i	$-0.628716\pi$
$101$	−7.90808			−0.786884			−0.393442	+	0.919350i	$0.628716\pi$
$102$	8.71480	−	0.942869i	0.862894	−	0.0933579i
$103$	7.63035	+	14.9754i	0.751841	+	1.47557i	0.875485	+	0.483245i	$0.160542\pi$
$103$	7.63035	+	14.9754i	0.751841	+	1.47557i	−0.123644	+	0.992327i	$0.539458\pi$
$104$	−8.50433	+	4.43174i	−0.833918	+	0.434568i
$105$	1.88375	+	2.00063i	0.183836	+	0.195241i
$106$	0.559051	+	0.855137i	0.0542999	+	0.0830582i
$107$	0.756931	+	0.756931i	0.0731753	+	0.0731753i	0.742747	−	0.669572i	$-0.233522\pi$
$107$	0.756931	+	0.756931i	0.0731753	+	0.0731753i	−0.669572	+	0.742747i	$0.733522\pi$
$108$	−1.99658	+	0.116864i	−0.192121	+	0.0112453i
$109$	−3.37095	+	4.63972i	−0.322879	+	0.444404i	−0.939343	−	0.342978i	$-0.888564\pi$
$109$	−3.37095	+	4.63972i	−0.322879	+	0.444404i	0.616465	+	0.787383i	$0.288564\pi$
$110$	−3.29927	−	13.7939i	−0.314573	−	1.31519i
$111$	5.03384	+	6.92849i	0.477791	+	0.657623i
$112$	−4.61029	−	1.70543i	−0.435632	−	0.161148i
$113$	2.86561	+	18.0927i	0.269574	+	1.70202i	0.636095	+	0.771611i	$0.280549\pi$
$113$	2.86561	+	18.0927i	0.269574	+	1.70202i	−0.366522	+	0.930410i	$0.619451\pi$
$114$	−5.24349	−	4.21965i	−0.491098	−	0.395207i
$115$	8.46461	+	6.54772i	0.789329	+	0.610578i
$116$	−4.64329	−	0.459385i	−0.431119	−	0.0426529i
$117$	3.02096	+	1.53926i	0.279288	+	0.142304i
$118$	−0.265851	+	0.463730i	−0.0244735	+	0.0426898i
$119$	−2.35380	−	7.24426i	−0.215773	−	0.664080i
$120$	1.82814	+	6.05458i	0.166885	+	0.552705i
$121$	−2.81687	+	8.66943i	−0.256079	+	0.788130i
$122$	3.15375	+	3.48117i	0.285527	+	0.315170i
$123$	0.436375	−	2.75516i	0.0393466	−	0.248425i
$124$	−16.9144	+	9.90370i	−1.51896	+	0.889379i
$125$	−11.1554	+	0.746764i	−0.997767	+	0.0667926i
$126$	0.454933	+	1.67733i	0.0405287	+	0.149429i
$127$	2.29897	+	0.364120i	0.204000	+	0.0323105i	0.257598	−	0.966252i	$-0.417069\pi$
$127$	2.29897	+	0.364120i	0.204000	+	0.0323105i	−0.0535979	+	0.998563i	$0.517069\pi$
$128$	−7.74827	−	8.24404i	−0.684857	−	0.728678i
$129$	7.72364	+	2.50956i	0.680028	+	0.220955i
$130$	2.51176	−	10.4233i	0.220296	−	0.914188i
$131$	21.3803	−	6.94688i	1.86801	−	0.606952i	0.875746	−	0.482772i	$-0.160370\pi$
$131$	21.3803	−	6.94688i	1.86801	−	0.606952i	0.992260	−	0.124180i	$-0.0396300\pi$
$132$	2.26868	−	8.67844i	0.197464	−	0.755361i
$133$	−2.65520	+	5.21113i	−0.230235	+	0.451862i
$134$	8.78834	+	3.34278i	0.759197	+	0.288773i
$135$	1.36814	−	1.76867i	0.117751	−	0.152223i
$136$	2.58381	−	17.3399i	0.221560	−	1.48688i
$137$	20.2164	−	3.20196i	1.72720	−	0.273562i	0.787690	−	0.616072i	$-0.211277\pi$
$137$	20.2164	−	3.20196i	1.72720	−	0.273562i	0.939514	+	0.342510i	$0.111277\pi$
$138$	2.77175	+	6.17465i	0.235947	+	0.525621i
$139$	7.81703	−	5.67941i	0.663032	−	0.481721i	−0.204653	−	0.978834i	$-0.565607\pi$
$139$	7.81703	−	5.67941i	0.663032	−	0.481721i	0.867686	+	0.497114i	$0.165607\pi$
$140$	4.82403	−	2.63303i	0.407705	−	0.222532i
$141$	3.85484	+	2.80070i	0.324636	+	0.235862i
$142$	−1.44878	+	6.91978i	−0.121579	+	0.580695i
$143$	−10.7526	+	10.7526i	−0.899181	+	0.899181i
$144$	−0.783810	+	3.92245i	−0.0653175	+	0.326871i
$145$	3.79804	−	3.57616i	0.315410	−	0.296984i
$146$	−0.239335	+	4.85002i	−0.0198075	+	0.401391i
$147$	−4.89144	+	2.49231i	−0.403439	+	0.205563i
$148$	15.9528	−	6.23570i	1.31131	−	0.512572i
$149$		−	8.40173i		−	0.688296i	−0.938915	−	0.344148i	$-0.888168\pi$
$149$		−	8.40173i		−	0.688296i	0.938915	−	0.344148i	$-0.111832\pi$
$150$	−6.44602	−	2.90668i	−0.526315	−	0.237330i
$151$		−	0.959977i		−	0.0781219i	−0.999237	−	0.0390609i	$-0.987563\pi$
$151$		−	0.959977i		−	0.0781219i	0.999237	−	0.0390609i	$-0.0124366\pi$
$152$	−10.8173	+	8.01158i	−0.877396	+	0.649825i
$153$	−5.52269	+	2.81395i	−0.446483	+	0.227494i
$154$	−7.78523	−	0.384179i	−0.627352	−	0.0309580i
$155$	4.07750	−	21.5313i	0.327513	−	1.72944i
$156$	4.50652	−	5.06688i	0.360811	−	0.405675i
$157$	8.31117	−	8.31117i	0.663303	−	0.663303i	−0.292854	−	0.956157i	$-0.594605\pi$
$157$	8.31117	−	8.31117i	0.663303	−	0.663303i	0.956157	+	0.292854i	$0.0946049\pi$
$158$	2.33400	+	0.488665i	0.185683	+	0.0388761i
$159$	−0.584455	−	0.424631i	−0.0463503	−	0.0336754i
$160$	12.6402	−	0.474792i	0.999295	−	0.0375356i
$161$	4.75813	−	3.45698i	0.374993	−	0.272448i
$162$	1.29019	−	0.579154i	0.101367	−	0.0455026i
$163$	22.0465	−	3.49183i	1.72682	−	0.273501i	0.787442	−	0.616389i	$-0.211405\pi$
$163$	22.0465	−	3.49183i	1.72682	−	0.273501i	0.939376	+	0.342888i	$0.111405\pi$
$164$	−5.11044	−	2.23803i	−0.399059	−	0.174761i
$165$	5.64813	+	8.28713i	0.439707	+	0.645152i
$166$	−7.66750	+	20.1582i	−0.595113	+	1.56458i
$167$	−0.816203	+	1.60189i	−0.0631597	+	0.123958i	−0.920428	−	0.390912i	$-0.872160\pi$
$167$	−0.816203	+	1.60189i	−0.0631597	+	0.123958i	0.857268	+	0.514870i	$0.172160\pi$
$168$	3.47572	−	0.0318322i	0.268158	−	0.00245591i
$169$	1.43087	−	0.464917i	0.110067	−	0.0357628i
$170$	12.7170	+	14.9152i	0.975346	+	1.14394i
$171$	4.52625	+	1.47067i	0.346131	+	0.112465i
$172$	8.76282	−	13.6756i	0.668158	−	1.04276i
$173$	−8.78515	−	1.39143i	−0.667923	−	0.105789i	−0.186741	−	0.982409i	$-0.559792\pi$
$173$	−8.78515	−	1.39143i	−0.667923	−	0.105789i	−0.481182	+	0.876621i	$0.659792\pi$
$174$	3.18429	−	0.863656i	0.241400	−	0.0654736i
$175$	−1.32435	+	6.00011i	−0.100111	+	0.453565i
$176$	−15.6450	−	8.77970i	−1.17929	−	0.661795i
$177$	0.0591275	−	0.373316i	0.00444430	−	0.0280602i
$178$	1.69147	−	1.53238i	0.126781	−	0.114857i
$179$	2.58378	−	7.95205i	0.193120	−	0.594364i	−0.806873	−	0.590725i	$-0.798842\pi$
$179$	2.58378	−	7.95205i	0.193120	−	0.594364i	0.999993	−	0.00363866i	$-0.00115822\pi$
$180$	−2.73029	−	3.54197i	−0.203503	−	0.264003i
$181$	6.98134	+	21.4863i	0.518919	+	1.59707i	0.776037	+	0.630688i	$0.217227\pi$
$181$	6.98134	+	21.4863i	0.518919	+	1.59707i	−0.257118	+	0.966380i	$0.582773\pi$
$182$	−5.11200	−	2.93064i	−0.378926	−	0.217234i
$183$	−2.95948	−	1.50793i	−0.218771	−	0.111469i
$184$	13.3499	−	2.23992i	0.984164	−	0.165129i
$185$	−6.46270	+	18.0264i	−0.475147	+	1.32533i
$186$	8.68924	−	10.7975i	0.637126	−	0.791714i
$187$	−4.34879	−	27.4572i	−0.318015	−	2.00787i
$188$	7.36920	−	6.04233i	0.537454	−	0.440682i
$189$	−0.722332	−	0.994205i	−0.0525419	−	0.0723178i
$190$	1.19350	−	15.0025i	0.0865854	−	1.08839i
$191$	−3.77520	+	5.19612i	−0.273164	+	0.375978i	−0.923455	−	0.383707i	$-0.874647\pi$
$191$	−3.77520	+	5.19612i	−0.273164	+	0.375978i	0.650291	+	0.759686i	$0.274647\pi$
$192$	7.19338	+	3.50076i	0.519137	+	0.252646i
$193$	−11.6325	−	11.6325i	−0.837323	−	0.837323i	0.151183	−	0.988506i	$-0.451692\pi$
$193$	−11.6325	−	11.6325i	−0.837323	−	0.837323i	−0.988506	+	0.151183i	$0.951692\pi$
$194$	14.4917	−	9.47404i	1.04044	−	0.680196i
$195$	0.960255	+	7.52033i	0.0687653	+	0.538542i
$196$	2.34831	+	10.7255i	0.167737	+	0.766108i
$197$	−0.611842	−	1.20081i	−0.0435919	−	0.0855540i	0.868183	−	0.496244i	$-0.165288\pi$
$197$	−0.611842	−	1.20081i	−0.0435919	−	0.0855540i	−0.911775	+	0.410690i	$0.865288\pi$
$198$	0.682257	+	6.30600i	0.0484859	+	0.448148i
$199$	−20.5955			−1.45997			−0.729987	−	0.683461i	$-0.760474\pi$
$199$	−20.5955			−1.45997			−0.729987	+	0.683461i	$0.760474\pi$
$200$	−8.88498	+	11.0026i	−0.628263	+	0.778001i
$201$	−6.64865			−0.468960
$202$	−1.20297	−	11.1188i	−0.0846403	−	0.782318i
$203$	−1.30160	−	2.55453i	−0.0913542	−	0.179293i
$204$	2.65136	+	12.1097i	0.185633	+	0.847845i
$205$	5.64033	−	2.66335i	0.393938	−	0.186017i
$206$	−19.8948	+	13.0064i	−1.38614	+	0.906197i
$207$	−3.38412	−	3.38412i	−0.235212	−	0.235212i
$208$	−7.52473	−	11.2830i	−0.521746	−	0.782336i
$209$	−12.5463	+	17.2686i	−0.867849	+	1.19449i
$210$	−2.52635	+	2.95291i	−0.174334	+	0.203770i
$211$	3.36303	+	4.62882i	0.231521	+	0.318661i	0.908933	−	0.416943i	$-0.136899\pi$
$211$	3.36303	+	4.62882i	0.231521	+	0.318661i	−0.677412	+	0.735604i	$0.736899\pi$
$212$	−1.11729	+	0.916113i	−0.0767356	+	0.0629189i
$213$	−0.782035	−	4.93757i	−0.0535841	−	0.338317i
$214$	−0.949108	+	1.17939i	−0.0648797	+	0.0806218i
$215$	5.08961	+	17.4315i	0.347108	+	1.18882i
$216$	−0.468029	−	2.78944i	−0.0318453	−	0.189797i
$217$	−10.7309	−	5.46767i	−0.728461	−	0.371170i
$218$	−7.03627	−	4.03380i	−0.476556	−	0.273204i
$219$	−1.06106	−	3.26560i	−0.0716996	−	0.220669i
$220$	18.8924	−	6.73710i	1.27373	−	0.454215i
$221$	6.49405	−	19.9866i	0.436837	−	1.34445i
$222$	−8.97578	+	8.13158i	−0.602415	+	0.545756i
$223$	0.323229	−	2.04079i	0.0216450	−	0.136661i	−0.974499	−	0.224390i	$-0.927961\pi$
$223$	0.323229	−	2.04079i	0.0216450	−	0.136661i	0.996144	+	0.0877290i	$0.0279609\pi$
$224$	1.69654	−	6.74154i	0.113355	−	0.450438i
$225$	4.99096	+	0.300609i	0.332730	+	0.0200406i
$226$	−25.0026	+	6.78130i	−1.66315	+	0.451086i
$227$	−21.4739	−	3.40114i	−1.42528	−	0.225741i	−0.604323	−	0.796739i	$-0.706557\pi$
$227$	−21.4739	−	3.40114i	−1.42528	−	0.225741i	−0.820952	+	0.570998i	$0.806557\pi$
$228$	5.13524	−	8.01427i	0.340089	−	0.530758i
$229$	−9.11712	−	2.96233i	−0.602476	−	0.195756i	−0.00813172	−	0.999967i	$-0.502588\pi$
$229$	−9.11712	−	2.96233i	−0.602476	−	0.195756i	−0.594345	+	0.804211i	$0.702588\pi$
$230$	−7.91853	+	12.8974i	−0.522132	+	0.850426i
$231$	5.24193	−	1.70320i	0.344893	−	0.112063i
$232$	−0.0604311	−	6.59839i	−0.00396749	−	0.433206i
$233$	3.34038	−	6.55586i	0.218835	−	0.429488i	−0.755324	−	0.655352i	$-0.772520\pi$
$233$	3.34038	−	6.55586i	0.218835	−	0.429488i	0.974159	+	0.225864i	$0.0725203\pi$
$234$	−1.70466	+	4.48164i	−0.111437	+	0.292974i
$235$	−0.320430	+	10.6497i	−0.0209025	+	0.694709i
$236$	−0.692450	−	0.303246i	−0.0450746	−	0.0197397i
$237$	−1.66541	+	0.263775i	−0.108180	+	0.0171341i
$238$	9.82743	−	4.41145i	0.637018	−	0.285952i
$239$	9.18160	−	6.67082i	0.593908	−	0.431500i	−0.249803	−	0.968297i	$-0.580366\pi$
$239$	9.18160	−	6.67082i	0.593908	−	0.431500i	0.843711	+	0.536797i	$0.180366\pi$
$240$	−8.23469	+	3.49139i	−0.531547	+	0.225368i
$241$	−4.36910	−	3.17434i	−0.281438	−	0.204477i	0.438106	−	0.898923i	$-0.355649\pi$
$241$	−4.36910	−	3.17434i	−0.281438	−	0.204477i	−0.719545	+	0.694446i	$0.755649\pi$
$242$	−12.6178	−	2.64176i	−0.811102	−	0.169819i
$243$	−0.707107	+	0.707107i	−0.0453609	+	0.0453609i
$244$	−4.41481	+	4.96375i	−0.282629	+	0.317772i
$245$	−10.7650	−	5.89941i	−0.687753	−	0.376899i
$246$	3.94016	+	0.194436i	0.251216	+	0.0123968i
$247$	−14.3773	+	7.32560i	−0.914805	+	0.466117i
$248$	−16.4977	−	22.2752i	−1.04760	−	1.41448i
$249$		−	15.2503i		−	0.966450i
$250$	−2.74689	−	15.5710i	−0.173729	−	0.984794i
$251$			12.4891i			0.788307i	0.919045	+	0.394153i	$0.128962\pi$
$251$			12.4891i			0.788307i	−0.919045	+	0.394153i	$0.871038\pi$
$252$	−2.28914	+	0.894793i	−0.144202	+	0.0563667i
$253$	19.1253	−	9.74480i	1.20239	−	0.612651i
$254$	−0.162241	+	3.28775i	−0.0101799	+	0.206292i
$255$	−12.1543	−	6.66073i	−0.761130	−	0.417111i
$256$	10.4125	−	12.1482i	0.650784	−	0.759263i
$257$	12.3554	−	12.3554i	0.770711	−	0.770711i	−0.207520	−	0.978231i	$-0.566539\pi$
$257$	12.3554	−	12.3554i	0.770711	−	0.770711i	0.978231	+	0.207520i	$0.0665392\pi$
$258$	−2.35356	+	11.2412i	−0.146526	+	0.699850i
$259$	8.51446	+	6.18612i	0.529063	+	0.384387i
$260$	15.0374	+	1.94597i	0.932579	+	0.120684i
$261$	−1.88742	+	1.37129i	−0.116829	+	0.0848809i
$262$	13.0197	+	29.0041i	0.804361	+	1.79188i
$263$	−6.03239	+	0.955437i	−0.371973	+	0.0589148i	−0.339623	−	0.940562i	$-0.610299\pi$
$263$	−6.03239	+	0.955437i	−0.371973	+	0.0589148i	−0.0323506	+	0.999477i	$0.510299\pi$
$264$	12.5471	+	1.86964i	0.772219	+	0.115068i
$265$	0.0485822	−	1.61466i	0.00298438	−	0.0991879i
$266$	−7.73079	−	2.94053i	−0.474005	−	0.180295i
$267$	−0.732688	+	1.43798i	−0.0448398	+	0.0880030i
$268$	−3.36311	+	12.8650i	−0.205435	+	0.785854i
$269$	−15.3432	+	4.98530i	−0.935490	+	0.303959i	−0.736806	−	0.676105i	$-0.763667\pi$
$269$	−15.3432	+	4.98530i	−0.935490	+	0.303959i	−0.198684	+	0.980064i	$0.563667\pi$
$270$	2.69489	+	1.65457i	0.164006	+	0.100694i
$271$	−13.5467	−	4.40159i	−0.822904	−	0.267378i	−0.132850	−	0.991136i	$-0.542413\pi$
$271$	−13.5467	−	4.40159i	−0.822904	−	0.267378i	−0.690053	+	0.723758i	$0.742413\pi$
$272$	24.7730	+	0.995146i	1.50209	+	0.0603396i
$273$	4.11531	+	0.651800i	0.249070	+	0.0394488i
$274$	7.57728	+	27.9374i	0.457760	+	1.68776i
$275$	−8.19949	+	20.8724i	−0.494448	+	1.25865i
$276$	−8.25998	+	4.83638i	−0.497192	+	0.291116i
$277$	−2.25919	+	14.2640i	−0.135742	+	0.857040i	0.822016	+	0.569464i	$0.192849\pi$
$277$	−2.25919	+	14.2640i	−0.135742	+	0.857040i	−0.957758	+	0.287576i	$0.907151\pi$
$278$	9.17441	+	10.1269i	0.550244	+	0.607369i
$279$	−3.02844	+	9.32059i	−0.181308	+	0.558009i
$280$	4.43589	+	6.38210i	0.265095	+	0.381403i
$281$	−0.729043	−	2.24376i	−0.0434911	−	0.133852i	0.926953	−	0.375177i	$-0.122418\pi$
$281$	−0.729043	−	2.24376i	−0.0434911	−	0.133852i	−0.970444	+	0.241325i	$0.922418\pi$
$282$	−3.35142	+	5.84597i	−0.199574	+	0.348123i
$283$	−12.0621	−	6.14594i	−0.717016	−	0.365338i	0.0571112	−	0.998368i	$-0.481811\pi$
$283$	−12.0621	−	6.14594i	−0.717016	−	0.365338i	−0.774127	+	0.633030i	$0.781811\pi$
$284$	−9.94966	−	0.984372i	−0.590404	−	0.0584117i
$285$	2.98264	+	10.2153i	0.176676	+	0.605104i
$286$	−16.7540	−	13.4826i	−0.990683	−	0.797245i
$287$	−0.536263	−	3.38583i	−0.0316546	−	0.199859i
$288$	−5.63424	−	0.505365i	−0.332000	−	0.0297789i
$289$	12.5894	+	17.3278i	0.740553	+	1.01928i
$290$	5.60587	+	4.79607i	0.329188	+	0.281635i
$291$	−7.19607	+	9.90454i	−0.421841	+	0.580614i
$292$	−6.85558	+	0.401271i	−0.401192	+	0.0234826i
$293$	13.5220	+	13.5220i	0.789964	+	0.789964i	0.981488	−	0.191524i	$-0.0613430\pi$
$293$	13.5220	+	13.5220i	0.789964	+	0.789964i	−0.191524	+	0.981488i	$0.561343\pi$
$294$	−4.24829	−	6.49828i	−0.247765	−	0.378987i
$295$	0.764247	−	0.360876i	0.0444962	−	0.0210110i
$296$	11.1942	+	21.4811i	0.650647	+	1.24857i
$297$	−2.03617	−	3.99620i	−0.118150	−	0.231883i
$298$	11.8129	−	1.27806i	0.684303	−	0.0740359i
$299$	16.2265			0.938401
$300$	3.10627	−	9.50532i	0.179340	−	0.548790i
$301$	9.98007			0.575242
$302$	1.34974	−	0.146030i	0.0776686	−	0.00840310i
$303$	3.59019	+	7.04615i	0.206251	+	0.404791i
$304$	−12.9099	−	13.9905i	−0.740431	−	0.802407i
$305$	−0.940711	−	7.36728i	−0.0538650	−	0.421849i
$306$	−4.79654	−	7.33689i	−0.274200	−	0.419422i
$307$	11.3516	+	11.3516i	0.647873	+	0.647873i	0.952479	−	0.304606i	$-0.0985247\pi$
$307$	11.3516	+	11.3516i	0.647873	+	0.647873i	−0.304606	+	0.952479i	$0.598525\pi$
$308$	−0.644118	−	11.0045i	−0.0367020	−	0.627042i
$309$	9.87908	−	13.5974i	0.562001	−	0.773528i
$310$	30.8935	+	2.45768i	1.75463	+	0.139587i
$311$	−7.06216	−	9.72023i	−0.400458	−	0.551183i	0.560401	−	0.828222i	$-0.310647\pi$
$311$	−7.06216	−	9.72023i	−0.400458	−	0.551183i	−0.960859	+	0.277038i	$0.910647\pi$
$312$	7.80960	+	5.56545i	0.442131	+	0.315081i
$313$	0.0322523	+	0.203633i	0.00182301	+	0.0115100i	0.988583	−	0.150677i	$-0.0481453\pi$
$313$	0.0322523	+	0.203633i	0.00182301	+	0.0115100i	−0.986760	+	0.162187i	$0.948145\pi$
$314$	12.9499	+	10.4213i	0.730803	+	0.588108i
$315$	0.927366	−	2.58670i	0.0522511	−	0.145744i
$316$	−0.332023	+	3.35596i	−0.0186777	+	0.188787i
$317$	−0.800165	−	0.407705i	−0.0449418	−	0.0228990i	0.431375	−	0.902173i	$-0.358029\pi$
$317$	−0.800165	−	0.407705i	−0.0449418	−	0.0228990i	−0.476317	+	0.879274i	$0.658029\pi$
$318$	0.508129	−	0.886342i	0.0284944	−	0.0497036i
$319$	−3.23340	−	9.95139i	−0.181036	−	0.557171i
$320$	2.59037	+	17.7000i	0.144806	+	0.989460i
$321$	0.330791	−	1.01807i	0.0184630	−	0.0568231i
$322$	5.58435	+	6.16410i	0.311203	+	0.343512i
$323$	4.61460	−	29.1354i	0.256763	−	1.62114i
$324$	1.01056	+	1.72591i	0.0561420	+	0.0958841i
$325$	−12.6862	+	11.2449i	−0.703706	+	0.623752i
$326$	8.26323	+	30.4665i	0.457658	+	1.68738i
$327$	5.66440	+	0.897153i	0.313242	+	0.0496127i
$328$	2.36930	−	7.52577i	0.130823	−	0.415541i
$329$	5.56895	+	1.80946i	0.307026	+	0.0997588i
$330$	−10.7926	+	9.20195i	−0.594112	+	0.506551i
$331$	−8.52303	+	2.76930i	−0.468468	+	0.152214i	−0.533732	−	0.845654i	$-0.679211\pi$
$331$	−8.52303	+	2.76930i	−0.468468	+	0.152214i	0.0652642	+	0.997868i	$0.479211\pi$
$332$	−29.5090	−	7.71413i	−1.61952	−	0.423368i
$333$	3.88801	−	7.63066i	0.213062	−	0.418157i
$334$	−2.37643	−	0.903912i	−0.130032	−	0.0494599i
$335$	−8.37284	−	12.2849i	−0.457457	−	0.671195i
$336$	0.573478	+	4.88205i	0.0312858	+	0.266338i
$337$	−7.67391	+	1.21543i	−0.418024	+	0.0662085i	−0.361904	−	0.932215i	$-0.617873\pi$
$337$	−7.67391	+	1.21543i	−0.418024	+	0.0662085i	−0.0561205	+	0.998424i	$0.517873\pi$
$338$	0.871339	+	1.94109i	0.0473946	+	0.105581i
$339$	14.8198	−	10.7672i	0.804900	−	0.584794i
$340$	−19.0364	+	20.1490i	−1.03239	+	1.09273i
$341$	−35.5599	−	25.8358i	−1.92568	−	1.39909i
$342$	−1.37925	+	6.58766i	−0.0745811	+	0.356220i
$343$	−10.8532	+	10.8532i	−0.586019	+	0.586019i
$344$	20.5610	+	10.2403i	1.10858	+	0.552119i
$345$	1.99121	−	10.5146i	0.107203	−	0.566089i
$346$	0.619981	−	12.5637i	0.0333304	−	0.675427i
$347$	−19.3079	+	9.83786i	−1.03650	+	0.528124i	−0.887546	−	0.460720i	$-0.847591\pi$
$347$	−19.3079	+	9.83786i	−1.03650	+	0.528124i	−0.148956	+	0.988844i	$0.547591\pi$
$348$	1.69870	+	4.34576i	0.0910597	+	0.232957i
$349$			23.0418i			1.23340i	0.787198	+	0.616701i	$0.211531\pi$
$349$			23.0418i			1.23340i	−0.787198	+	0.616701i	$0.788469\pi$
$350$	−8.63766	−	0.949319i	−0.461702	−	0.0507432i
$351$		−	3.39050i		−	0.180972i
$352$	9.96444	−	23.3326i	0.531106	−	1.24363i
$353$	−13.7543	+	7.00816i	−0.732066	+	0.373006i	−0.779946	−	0.625847i	$-0.784754\pi$
$353$	−13.7543	+	7.00816i	−0.732066	+	0.373006i	0.0478797	+	0.998853i	$0.484754\pi$
$354$	0.533880	+	0.0263455i	0.0283754	+	0.00140025i
$355$	8.13844	−	7.66301i	0.431944	−	0.406710i
$356$	2.41184	+	2.14511i	0.127827	+	0.113691i
$357$	−5.38608	+	5.38608i	−0.285062	+	0.285062i
$358$	11.5737	+	2.42316i	0.611688	+	0.128068i
$359$	−18.1516	−	13.1879i	−0.958007	−	0.696033i	−0.00532016	−	0.999986i	$-0.501693\pi$
$359$	−18.1516	−	13.1879i	−0.958007	−	0.696033i	−0.952687	+	0.303953i	$0.901693\pi$
$360$	4.56471	−	4.37760i	0.240581	−	0.230720i
$361$	−2.95276	+	2.14531i	−0.155409	+	0.112911i
$362$	−29.1480	+	13.0843i	−1.53198	+	0.687695i
$363$	9.00335	−	1.42599i	0.472553	−	0.0748451i
$364$	3.34288	−	7.63332i	0.175214	−	0.400094i
$365$	4.69772	−	6.07301i	0.245890	−	0.317876i
$366$	1.66997	−	4.39043i	0.0872907	−	0.229492i
$367$	−7.37062	+	14.4657i	−0.384743	+	0.755101i	−0.999433	−	0.0336676i	$-0.989281\pi$
$367$	−7.37062	+	14.4657i	−0.384743	+	0.755101i	0.614690	+	0.788769i	$0.289281\pi$
$368$	5.18011	+	18.4293i	0.270032	+	0.960692i
$369$	−2.65298	+	0.862005i	−0.138109	+	0.0448742i
$370$	−26.3284	−	6.34446i	−1.36875	−	0.329833i
$371$	−0.844341	−	0.274343i	−0.0438360	−	0.0142432i
$372$	16.5032	+	10.5746i	0.855653	+	0.548269i
$373$	8.67472	+	1.37394i	0.449160	+	0.0711400i	0.376917	−	0.926247i	$-0.376984\pi$
$373$	8.67472	+	1.37394i	0.449160	+	0.0711400i	0.0722432	+	0.997387i	$0.476984\pi$
$374$	37.9435	−	10.2912i	1.96201	−	0.532144i
$375$	5.72981	+	9.60049i	0.295886	+	0.495767i
$376$	9.61656	+	9.44201i	0.495936	+	0.486935i
$377$	1.23739	−	7.81259i	0.0637290	−	0.402369i
$378$	1.28798	−	1.16684i	0.0662466	−	0.0600159i
$379$	4.77015	−	14.6810i	0.245026	−	0.754112i	−0.750606	−	0.660750i	$-0.770238\pi$
$379$	4.77015	−	14.6810i	0.245026	−	0.754112i	0.995632	−	0.0933626i	$-0.0297616\pi$
$380$	21.2751	−	0.604084i	1.09139	−	0.0309888i
$381$	−0.719275	−	2.21370i	−0.0368496	−	0.113411i
$382$	−7.88007	−	4.51754i	−0.403180	−	0.231138i
$383$	−19.5086	−	9.94011i	−0.996841	−	0.507916i	−0.122106	−	0.992517i	$-0.538965\pi$
$383$	−19.5086	−	9.94011i	−0.996841	−	0.507916i	−0.874735	+	0.484601i	$0.838965\pi$
$384$	−3.82786	+	10.6465i	−0.195339	+	0.543301i
$385$	9.74836	+	7.54075i	0.496822	+	0.384312i
$386$	14.5858	−	18.1249i	0.742399	−	0.922531i
$387$	−1.27042	−	8.02113i	−0.0645792	−	0.407737i
$388$	15.5250	+	18.9343i	0.788164	+	0.961242i
$389$	19.3223	+	26.5948i	0.979678	+	1.34841i	0.937002	+	0.349323i	$0.113588\pi$
$389$	19.3223	+	26.5948i	0.979678	+	1.34841i	0.0426759	+	0.999089i	$0.486412\pi$
$390$	−10.4276	+	2.49411i	−0.528021	+	0.126294i
$391$	−17.4361	+	23.9987i	−0.881779	+	1.21367i
$392$	−14.7229	+	4.93330i	−0.743621	+	0.249169i
$393$	−15.8962	−	15.8962i	−0.801856	−	0.801856i
$394$	1.59527	−	1.04292i	0.0803687	−	0.0525415i
$395$	−2.58468	−	2.74505i	−0.130050	−	0.138118i
$396$	−8.76251	+	1.91852i	−0.440333	+	0.0964092i
$397$	−4.68709	−	9.19893i	−0.235238	−	0.461681i	0.742965	−	0.669330i	$-0.233419\pi$
$397$	−4.68709	−	9.19893i	−0.235238	−	0.461681i	−0.978203	+	0.207649i	$0.933419\pi$
$398$	−3.13295	−	28.9574i	−0.157041	−	1.45150i
$399$	5.84858			0.292795
$400$	−16.8213	−	10.8187i	−0.841066	−	0.540933i
$401$	19.3269			0.965137			0.482569	−	0.875858i	$-0.339704\pi$
$401$	19.3269			0.965137			0.482569	+	0.875858i	$0.339704\pi$
$402$	−1.01138	−	9.34806i	−0.0504432	−	0.466239i
$403$	−15.0851	−	29.6061i	−0.751442	−	1.47479i
$404$	15.4502	−	3.38276i	0.768675	−	0.168299i
$405$	−2.19702	−	0.416061i	−0.109171	−	0.0206742i
$406$	3.39369	−	2.21865i	0.168426	−	0.110110i
$407$	27.1602	+	27.1602i	1.34628	+	1.34628i
$408$	−16.6230	+	5.56994i	−0.822959	+	0.275753i
$409$	20.5429	−	28.2749i	1.01578	−	1.39810i	0.100661	−	0.994921i	$-0.467904\pi$
$409$	20.5429	−	28.2749i	1.01578	−	1.39810i	0.915120	−	0.403182i	$-0.132096\pi$
$410$	4.60269	+	7.52520i	0.227311	+	0.371643i
$411$	−12.0310	−	16.5593i	−0.593447	−	0.816809i
$412$	−21.3135	−	25.9938i	−1.05004	−	1.28062i
$413$	−0.0726621	−	0.458770i	−0.00357547	−	0.0225746i
$414$	4.24331	−	5.27288i	0.208547	−	0.259148i
$415$	28.1784	−	19.2052i	1.38322	−	0.942744i
$416$	14.7194	−	12.2962i	0.721676	−	0.602870i
$417$	−8.60925	−	4.38663i	−0.421597	−	0.214814i
$418$	−26.1883	−	15.0134i	−1.28091	−	0.734329i
$419$	5.52699	+	17.0103i	0.270011	+	0.831010i	0.990496	+	0.137539i	$0.0439192\pi$
$419$	5.52699	+	17.0103i	0.270011	+	0.831010i	−0.720485	+	0.693471i	$0.756081\pi$
$420$	−4.53611	−	3.10287i	−0.221340	−	0.151405i
$421$	−11.1963	+	34.4588i	−0.545676	+	1.67942i	0.173703	+	0.984798i	$0.444427\pi$
$421$	−11.1963	+	34.4588i	−0.545676	+	1.67942i	−0.719378	+	0.694619i	$0.755573\pi$
$422$	−5.99658	+	5.43258i	−0.291909	+	0.264454i
$423$	0.745386	−	4.70618i	0.0362419	−	0.228822i
$424$	−1.45802	−	1.43156i	−0.0708078	−	0.0695226i
$425$	−2.99902	−	30.8458i	−0.145474	−	1.49624i
$426$	6.82331	−	1.85064i	0.330590	−	0.0896639i
$427$	−4.03155	−	0.638535i	−0.195100	−	0.0309009i
$428$	−1.80262	−	1.15505i	−0.0871327	−	0.0558313i
$429$	14.4623	+	4.69908i	0.698245	+	0.226874i
$430$	−23.7347	+	9.80769i	−1.14459	+	0.472969i
$431$	32.9891	−	10.7188i	1.58903	−	0.516307i	0.624666	−	0.780892i	$-0.285235\pi$
$431$	32.9891	−	10.7188i	1.58903	−	0.516307i	0.964362	+	0.264586i	$0.0852352\pi$
$432$	3.85077	−	1.08238i	0.185270	−	0.0520759i
$433$	−0.342596	+	0.672382i	−0.0164641	+	0.0323126i	−0.899092	−	0.437760i	$-0.855772\pi$
$433$	−0.342596	+	0.672382i	−0.0164641	+	0.0323126i	0.882628	+	0.470072i	$0.155772\pi$
$434$	6.05522	−	15.9195i	0.290660	−	0.764159i
$435$	−4.91066	−	1.76053i	−0.235448	−	0.0844111i
$436$	4.60121	−	10.5067i	0.220358	−	0.503178i
$437$	22.4964	−	3.56308i	1.07615	−	0.170445i
$438$	4.43006	−	1.98861i	0.211676	−	0.0950197i
$439$	−6.65831	+	4.83755i	−0.317784	+	0.230883i	−0.735229	−	0.677819i	$-0.762925\pi$
$439$	−6.65831	+	4.83755i	−0.317784	+	0.230883i	0.417445	+	0.908702i	$0.362925\pi$
$440$	12.3463	+	25.5380i	0.588587	+	1.21748i
$441$	4.44134	+	3.22682i	0.211492	+	0.153658i
$442$	29.0892	+	6.09035i	1.38363	+	0.289689i
$443$	5.05289	−	5.05289i	0.240070	−	0.240070i	−0.576809	−	0.816879i	$-0.695702\pi$
$443$	5.05289	−	5.05289i	0.240070	−	0.240070i	0.816879	+	0.576809i	$0.195702\pi$
$444$	−12.7985	−	11.3831i	−0.607388	−	0.540216i
$445$	−3.57969	+	0.457083i	−0.169694	+	0.0216678i
$446$	2.91854	+	0.144021i	0.138197	+	0.00681961i
$447$	−7.48599	+	3.81430i	−0.354075	+	0.180410i
$448$	9.73674	+	1.35984i	0.460018	+	0.0642464i
$449$		−	3.96534i		−	0.187136i	−0.995613	−	0.0935679i	$-0.970173\pi$
$449$		−	3.96534i		−	0.187136i	0.995613	−	0.0935679i	$-0.0298272\pi$
$450$	0.336557	+	7.06305i	0.0158654	+	0.332956i
$451$		−	12.5110i		−	0.589122i
$452$	−13.3379	−	34.1223i	−0.627363	−	1.60498i
$453$	−0.855346	+	0.435821i	−0.0401877	+	0.0204766i
$454$	1.51545	−	30.7099i	0.0711234	−	1.44129i
$455$	3.97817	+	8.42479i	0.186500	+	0.394960i
$456$	12.0493	+	6.00107i	0.564260	+	0.281026i
$457$	−28.6276	+	28.6276i	−1.33914	+	1.33914i	−0.442252	+	0.896891i	$0.645820\pi$
$457$	−28.6276	+	28.6276i	−1.33914	+	1.33914i	−0.896891	+	0.442252i	$0.854180\pi$
$458$	2.77818	−	13.2694i	0.129816	−	0.620037i
$459$	5.01449	+	3.64324i	0.234057	+	0.170052i
$460$	−19.3383	−	9.17160i	−0.901655	−	0.427628i
$461$	19.5894	−	14.2325i	0.912367	−	0.662874i	−0.0292451	−	0.999572i	$-0.509310\pi$
$461$	19.5894	−	14.2325i	0.912367	−	0.662874i	0.941613	+	0.336699i	$0.109310\pi$
$462$	3.19211	+	7.11110i	0.148511	+	0.330838i
$463$	−2.56198	+	0.405779i	−0.119066	+	0.0188581i	−0.215683	−	0.976463i	$-0.569198\pi$
$463$	−2.56198	+	0.405779i	−0.119066	+	0.0188581i	0.0966173	+	0.995322i	$0.469198\pi$
$464$	9.26820	−	1.08870i	0.430266	−	0.0505418i
$465$	−21.0357	+	6.14194i	−0.975508	+	0.284826i
$466$	9.72572	+	3.69933i	0.450535	+	0.171368i
$467$	15.4035	−	30.2311i	0.712789	−	1.39893i	−0.195550	−	0.980694i	$-0.562649\pi$
$467$	15.4035	−	30.2311i	0.712789	−	1.39893i	0.908339	−	0.418234i	$-0.137351\pi$
$468$	−6.56054	−	1.71503i	−0.303261	−	0.0792773i
$469$	−7.77067	+	2.52484i	−0.358816	+	0.116586i
$470$	−15.0223	+	1.16949i	−0.692927	+	0.0539444i
$471$	−11.1785	−	3.63211i	−0.515078	−	0.167359i
$472$	0.321033	−	1.01972i	0.0147767	−	0.0469364i
$473$	35.9751	+	5.69789i	1.65414	+	0.261989i
$474$	−0.624210	−	2.30146i	−0.0286709	−	0.105710i
$475$	−15.1190	+	18.3756i	−0.693708	+	0.843128i
$476$	7.69747	+	13.1464i	0.352813	+	0.602564i
$477$	−0.113012	+	0.713531i	−0.00517448	+	0.0326704i
$478$	10.7759	+	11.8947i	0.492879	+	0.544049i
$479$	−9.51698	+	29.2903i	−0.434842	+	1.33831i	0.458406	+	0.888743i	$0.348421\pi$
$479$	−9.51698	+	29.2903i	−0.434842	+	1.33831i	−0.893248	+	0.449564i	$0.851579\pi$
$480$	−6.16157	−	11.0469i	−0.281236	−	0.504222i
$481$	8.97279	+	27.6154i	0.409124	+	1.25915i
$482$	3.79852	−	6.62587i	0.173018	−	0.301800i
$483$	−5.24034	−	2.67009i	−0.238444	−	0.121493i
$484$	1.79494	−	18.1426i	0.0815881	−	0.824662i
$485$	−27.3631	−	0.823305i	−1.24249	−	0.0373843i
$486$	−1.10176	−	0.886634i	−0.0499769	−	0.0402185i
$487$	−4.00267	−	25.2719i	−0.181378	−	1.14518i	−0.895469	−	0.445124i	$-0.853159\pi$
$487$	−4.00267	−	25.2719i	−0.181378	−	1.14518i	0.714090	−	0.700053i	$-0.246841\pi$
$488$	−7.65065	−	5.45218i	−0.346329	−	0.246809i
$489$	−13.1202	−	18.0584i	−0.593314	−	0.816627i
$490$	6.65705	−	16.0331i	0.300735	−	0.724304i
$491$	−21.3712	+	29.4149i	−0.964467	+	1.32748i	−0.0196748	+	0.999806i	$0.506263\pi$
$491$	−21.3712	+	29.4149i	−0.964467	+	1.32748i	−0.944793	+	0.327669i	$0.893737\pi$
$492$	0.325993	+	5.56948i	0.0146969	+	0.251092i
$493$	10.2251	+	10.2251i	0.460513	+	0.460513i
$494$	−12.4869	−	19.1002i	−0.561812	−	0.859360i
$495$	4.81968	−	8.79480i	0.216629	−	0.395297i
$496$	28.8096	−	26.5844i	1.29359	−	1.19367i
$497$	−2.78906	−	5.47385i	−0.125107	−	0.245536i
$498$	21.4421	−	2.31986i	0.960843	−	0.103955i
$499$	21.4166			0.958738			0.479369	−	0.877613i	$-0.340866\pi$
$499$	21.4166			0.958738			0.479369	+	0.877613i	$0.340866\pi$
$500$	21.4750	−	6.23079i	0.960393	−	0.278649i
$501$	1.79784			0.0803217
$502$	−17.5598	+	1.89983i	−0.783733	+	0.0847934i
$503$	2.54246	+	4.98985i	0.113362	+	0.222486i	0.940716	−	0.339195i	$-0.110155\pi$
$503$	2.54246	+	4.98985i	0.113362	+	0.222486i	−0.827354	+	0.561681i	$0.810155\pi$
$504$	−1.60631	−	3.08244i	−0.0715506	−	0.137303i
$505$	−8.49813	+	15.5071i	−0.378162	+	0.690058i
$506$	16.6106	+	25.4079i	0.738430	+	1.12952i
$507$	−1.06384	−	1.06384i	−0.0472470	−	0.0472470i
$508$	−4.64729	+	0.272015i	−0.206190	+	0.0120687i
$509$	−14.8244	+	20.4041i	−0.657082	+	0.904395i	−0.999380	−	0.0351958i	$-0.988795\pi$
$509$	−14.8244	+	20.4041i	−0.657082	+	0.904395i	0.342299	+	0.939591i	$0.388795\pi$
$510$	7.51615	−	18.1022i	0.332821	−	0.801581i
$511$	−2.48024	−	3.41376i	−0.109719	−	0.151016i
$512$	18.6644	+	12.7922i	0.824859	+	0.565339i
$513$	−0.744500	−	4.70059i	−0.0328705	−	0.207536i
$514$	19.2513	+	15.4924i	0.849140	+	0.683339i
$515$	37.5653	+	1.13027i	1.65532	+	0.0498056i
$516$	−16.1633	−	1.59912i	−0.711550	−	0.0703974i
$517$	19.0413	+	9.70200i	0.837433	+	0.426694i
$518$	−7.40253	+	12.9124i	−0.325248	+	0.567339i
$519$	2.74860	+	8.45932i	0.120650	+	0.371323i
$520$	−0.448582	+	21.4387i	−0.0196716	+	0.940150i
$521$	10.5745	−	32.5450i	0.463278	−	1.42582i	−0.397858	−	0.917447i	$-0.630246\pi$
$521$	10.5745	−	32.5450i	0.463278	−	1.42582i	0.861136	−	0.508375i	$-0.169754\pi$
$522$	−2.21516	−	2.44513i	−0.0969549	−	0.107021i
$523$	−2.99899	+	18.9349i	−0.131137	+	0.827966i	0.831174	+	0.556013i	$0.187669\pi$
$523$	−2.99899	+	18.9349i	−0.131137	+	0.827966i	−0.962311	+	0.271953i	$0.912331\pi$
$524$	−38.7995	+	22.7179i	−1.69497	+	0.992436i
$525$	5.94738	−	1.54399i	0.259565	−	0.0673852i
$526$	−2.26099	−	8.33625i	−0.0985839	−	0.363478i
$527$	59.9966	+	9.50252i	2.61349	+	0.413936i
$528$	−0.720085	+	17.9257i	−0.0313377	+	0.780116i
$529$	0.0908487	+	0.0295185i	0.00394994	+	0.00128341i
$530$	2.27762	−	0.177313i	0.0989334	−	0.00770198i
$531$	−0.359471	+	0.116799i	−0.0155997	+	0.00506865i
$532$	2.95841	−	11.3169i	0.128263	−	0.490648i
$533$	4.29376	−	8.42699i	0.185984	−	0.365013i
$534$	−2.13327	−	0.811422i	−0.0923156	−	0.0351137i
$535$	2.29769	−	0.670873i	0.0993378	−	0.0290044i
$536$	−18.5999	−	2.77156i	−0.803392	−	0.119713i
$537$	−8.25833	+	1.30799i	−0.356373	+	0.0564440i
$538$	−9.34335	−	20.8143i	−0.402820	−	0.897367i
$539$	−19.9196	+	14.4724i	−0.857996	+	0.623371i
$540$	−1.91639	+	4.04072i	−0.0824685	+	0.173885i
$541$	−29.5454	−	21.4660i	−1.27026	−	0.922895i	−0.271043	−	0.962567i	$-0.587369\pi$
$541$	−29.5454	−	21.4660i	−1.27026	−	0.922895i	−0.999213	+	0.0396722i	$0.987369\pi$
$542$	4.12797	−	19.7164i	0.177312	−	0.846890i
$543$	15.9750	−	15.9750i	0.685553	−	0.685553i
$544$	2.36925	+	34.9825i	0.101581	+	1.49986i
$545$	5.47564	+	11.5961i	0.234551	+	0.496721i
$546$	−0.290423	+	5.88531i	−0.0124290	+	0.251868i
$547$	−3.73686	+	1.90403i	−0.159777	+	0.0814103i	−0.532050	−	0.846713i	$-0.678578\pi$
$547$	−3.73686	+	1.90403i	−0.159777	+	0.0814103i	0.372274	+	0.928123i	$0.378578\pi$
$548$	−38.1275	+	14.9035i	−1.62873	+	0.636646i
$549$			3.32150i			0.141758i
$550$	−30.5941	−	8.35347i	−1.30454	−	0.356193i
$551$		−	11.1031i		−	0.473007i
$552$	−8.05649	−	10.8779i	−0.342907	−	0.462994i
$553$	−1.84629	+	0.940734i	−0.0785124	+	0.0400041i
$554$	−20.3990	−	1.00663i	−0.866668	−	0.0427676i
$555$	18.9957	−	2.42551i	0.806321	−	0.102957i
$556$	−12.8429	+	14.4398i	−0.544659	+	0.612383i
$557$	−9.53036	+	9.53036i	−0.403814	+	0.403814i	−0.879575	−	0.475761i	$-0.842173\pi$
$557$	−9.53036	+	9.53036i	−0.403814	+	0.403814i	0.475761	+	0.879575i	$0.342173\pi$
$558$	−13.5655	−	2.84018i	−0.574274	−	0.120235i
$559$	22.2760	+	16.1845i	0.942174	+	0.684529i
$560$	−8.29850	+	7.20774i	−0.350676	+	0.304582i
$561$	−22.4902	+	16.3401i	−0.949537	+	0.689879i
$562$	3.04385	−	1.36636i	0.128397	−	0.0576364i
$563$	−7.44681	+	1.17946i	−0.313846	+	0.0497083i	−0.311370	−	0.950289i	$-0.600788\pi$
$563$	−7.44681	+	1.17946i	−0.313846	+	0.0497083i	−0.00247542	+	0.999997i	$0.500788\pi$
$564$	−8.72930	−	3.82285i	−0.367570	−	0.160971i
$565$	38.5578	+	13.8235i	1.62214	+	0.581557i
$566$	6.80638	−	17.8943i	0.286093	−	0.752153i
$567$	−0.557911	+	1.09496i	−0.0234301	+	0.0459841i
$568$	−0.129492	−	14.1391i	−0.00543336	−	0.593261i
$569$	19.9781	−	6.49127i	0.837524	−	0.272128i	0.141313	−	0.989965i	$-0.454868\pi$
$569$	19.9781	−	6.49127i	0.837524	−	0.272128i	0.696211	+	0.717837i	$0.254868\pi$
$570$	−13.9091	+	5.74756i	−0.582589	+	0.240739i
$571$	−16.6846	−	5.42116i	−0.698230	−	0.226869i	−0.0616706	−	0.998097i	$-0.519643\pi$
$571$	−16.6846	−	5.42116i	−0.698230	−	0.226869i	−0.636559	+	0.771228i	$0.719643\pi$
$572$	16.4081	−	25.6072i	0.686057	−	1.07069i
$573$	6.34369	+	1.00474i	0.265011	+	0.0419737i
$574$	4.67894	−	1.26904i	0.195295	−	0.0529687i
$575$	21.9357	−	9.56216i	0.914784	−	0.398770i
$576$	−0.146523	−	7.99866i	−0.00610512	−	0.333277i
$577$	0.710623	−	4.48670i	0.0295836	−	0.186784i	−0.968471	−	0.249125i	$-0.919857\pi$
$577$	0.710623	−	4.48670i	0.0295836	−	0.186784i	0.998055	+	0.0623417i	$0.0198569\pi$
$578$	−22.4480	+	20.3367i	−0.933713	+	0.845894i
$579$	−5.08357	+	15.6456i	−0.211266	+	0.650210i
$580$	−5.89057	+	8.61147i	−0.244592	+	0.357572i
$581$	−5.79135	−	17.8239i	−0.240266	−	0.739462i
$582$	−15.0205	−	8.61107i	−0.622620	−	0.356940i
$583$	−2.88696	−	1.47098i	−0.119566	−	0.0609217i
$584$	−1.60705	−	9.57796i	−0.0665002	−	0.396339i
$585$	6.26472	−	4.26975i	0.259014	−	0.176533i
$586$	−16.9551	+	21.0690i	−0.700409	+	0.870352i
$587$	−0.853147	−	5.38656i	−0.0352131	−	0.222327i	0.963806	−	0.266604i	$-0.0859016\pi$
$587$	−0.853147	−	5.38656i	−0.0352131	−	0.222327i	−0.999019	+	0.0442770i	$0.985902\pi$
$588$	8.49039	−	6.96164i	0.350138	−	0.287093i
$589$	−27.4150	−	37.7335i	−1.12962	−	1.55478i
$590$	0.623651	+	1.01964i	0.0256753	+	0.0419780i
$591$	−0.792157	+	1.09031i	−0.0325850	+	0.0448494i
$592$	−28.4998	+	19.0068i	−1.17134	+	0.781173i
$593$	10.2013	+	10.2013i	0.418916	+	0.418916i	0.884830	−	0.465914i	$-0.154274\pi$
$593$	10.2013	+	10.2013i	0.418916	+	0.418916i	−0.465914	+	0.884830i	$0.654274\pi$
$594$	5.30895	−	3.47076i	0.217829	−	0.142407i
$595$	−16.7348	−	3.16916i	−0.686062	−	0.129923i
$596$	3.59392	+	16.4146i	0.147213	+	0.672369i
$597$	9.35014	+	18.3507i	0.382676	+	0.751044i
$598$	2.46835	+	22.8146i	0.100938	+	0.932957i
$599$	−16.3953			−0.669893			−0.334947	−	0.942237i	$-0.608718\pi$
$599$	−16.3953			−0.669893			−0.334947	+	0.942237i	$0.608718\pi$
$600$	13.8371	+	2.92150i	0.564896	+	0.119270i
$601$	−12.3492			−0.503736			−0.251868	−	0.967762i	$-0.581045\pi$
$601$	−12.3492			−0.503736			−0.251868	+	0.967762i	$0.581045\pi$
$602$	1.51815	+	14.0321i	0.0618753	+	0.571904i
$603$	3.01843	+	5.92399i	0.122920	+	0.241244i
$604$	0.410640	+	1.87553i	0.0167087	+	0.0763141i
$605$	13.9730	+	14.8399i	0.568083	+	0.603329i
$606$	−9.36082	+	6.11969i	−0.380257	+	0.248596i
$607$	29.6207	+	29.6207i	1.20227	+	1.20227i	0.973476	+	0.228791i	$0.0734771\pi$
$607$	29.6207	+	29.6207i	1.20227	+	1.20227i	0.228791	+	0.973476i	$0.426523\pi$
$608$	17.7069	−	20.2796i	0.718108	−	0.822445i
$609$	−1.68519	+	2.31946i	−0.0682873	+	0.0939894i
$610$	10.2154	−	2.44335i	0.413608	−	0.0989282i
$611$	9.49579	+	13.0698i	0.384159	+	0.528749i
$612$	9.58609	−	7.86005i	0.387495	−	0.317724i
$613$	−0.513499	−	3.24210i	−0.0207400	−	0.130947i	0.975146	−	0.221564i	$-0.0711162\pi$
$613$	−0.513499	−	3.24210i	−0.0207400	−	0.130947i	−0.995886	+	0.0906167i	$0.971116\pi$
$614$	−14.2337	+	17.6873i	−0.574426	+	0.713802i
$615$	−4.93372	−	3.81643i	−0.198947	−	0.153893i
$616$	15.3745	−	2.57963i	0.619456	−	0.103936i
$617$	18.7804	+	9.56911i	0.756072	+	0.385238i	0.789138	−	0.614215i	$-0.210527\pi$
$617$	18.7804	+	9.56911i	0.756072	+	0.385238i	−0.0330668	+	0.999453i	$0.510527\pi$
$618$	20.6208	+	11.8217i	0.829492	+	0.475537i
$619$	6.78934	+	20.8954i	0.272887	+	0.839859i	0.989771	+	0.142667i	$0.0455677\pi$
$619$	6.78934	+	20.8954i	0.272887	+	0.839859i	−0.716884	+	0.697192i	$0.754432\pi$
$620$	1.24395	+	43.8104i	0.0499581	+	1.75947i
$621$	−1.47891	+	4.55163i	−0.0593467	+	0.182650i
$622$	12.5924	−	11.4081i	0.504911	−	0.457422i
$623$	−0.310258	+	1.95889i	−0.0124302	+	0.0784813i
$624$	−6.63708	+	11.8270i	−0.265696	+	0.473458i
$625$	−10.5234	+	22.6773i	−0.420935	+	0.907091i
$626$	−0.281404	+	0.0763234i	−0.0112472	+	0.00305050i
$627$	21.0823	+	3.33911i	0.841947	+	0.133351i
$628$	−12.6825	+	19.7929i	−0.506087	+	0.789822i
$629$	−50.4844	−	16.4034i	−2.01294	−	0.654045i
$630$	3.77800	+	0.910399i	0.150519	+	0.0362712i
$631$	41.0489	−	13.3376i	1.63413	−	0.530962i	0.658916	−	0.752217i	$-0.271015\pi$
$631$	41.0489	−	13.3376i	1.63413	−	0.530962i	0.975216	+	0.221255i	$0.0710153\pi$
$632$	−4.76901	+	0.0436768i	−0.189701	+	0.00173737i
$633$	2.59752	−	5.09792i	0.103242	−	0.202624i
$634$	0.451516	−	1.18706i	0.0179320	−	0.0471441i
$635$	3.18451	−	4.11680i	0.126373	−	0.163370i
$636$	1.32350	+	0.579604i	0.0524802	+	0.0229828i
$637$	−18.3840	+	2.91174i	−0.728400	+	0.115367i
$638$	13.4999	−	6.05998i	0.534466	−	0.239917i
$639$	−4.04437	+	2.93841i	−0.159993	+	0.116242i
$640$	−24.4923	+	6.33458i	−0.968143	+	0.250396i
$641$	23.0054	+	16.7144i	0.908660	+	0.660180i	0.940676	−	0.339307i	$-0.110193\pi$
$641$	23.0054	+	16.7144i	0.908660	+	0.660180i	−0.0320157	+	0.999487i	$0.510193\pi$
$642$	1.48173	+	0.310228i	0.0584794	+	0.0122437i
$643$	31.2213	−	31.2213i	1.23125	−	1.23125i	0.267763	−	0.963485i	$-0.413716\pi$
$643$	31.2213	−	31.2213i	1.23125	−	1.23125i	0.963485	−	0.267763i	$-0.0862843\pi$
$644$	−7.81729	+	8.78931i	−0.308044	+	0.346347i
$645$	13.2210	−	12.4486i	0.520575	−	0.490164i
$646$	41.6667	+	2.05613i	1.63935	+	0.0808974i
$647$	−32.1671	+	16.3899i	−1.26462	+	0.644355i	−0.952167	−	0.305578i	$-0.901150\pi$
$647$	−32.1671	+	16.3899i	−1.26462	+	0.644355i	−0.312452	+	0.949934i	$0.601150\pi$
$648$	−2.27292	+	1.68339i	−0.0892889	+	0.0661300i
$649$		−	1.69521i		−	0.0665428i
$650$	−17.7402	−	16.1264i	−0.695827	−	0.632530i
$651$			12.0436i			0.472025i
$652$	−41.5791	+	16.2527i	−1.62836	+	0.636504i
$653$	−34.2761	+	17.4646i	−1.34133	+	0.683441i	−0.969553	−	0.244882i	$-0.921251\pi$
$653$	−34.2761	+	17.4646i	−1.34133	+	0.683441i	−0.371775	+	0.928323i	$0.621251\pi$
$654$	−0.399745	+	8.10067i	−0.0156313	+	0.316761i
$655$	9.35329	−	49.3903i	0.365463	−	1.92984i
$656$	10.9417	+	2.18644i	0.427202	+	0.0853662i
$657$	−2.42796	+	2.42796i	−0.0947238	+	0.0947238i
$658$	−1.69698	+	8.10524i	−0.0661551	+	0.315975i
$659$	−9.74331	−	7.07893i	−0.379545	−	0.275756i	0.381613	−	0.924322i	$-0.375369\pi$
$659$	−9.74331	−	7.07893i	−0.379545	−	0.275756i	−0.761158	+	0.648566i	$0.775369\pi$
$660$	−14.5798	−	13.7747i	−0.567517	−	0.536179i
$661$	31.6245	−	22.9765i	1.23005	−	0.893683i	0.233155	−	0.972440i	$-0.425095\pi$
$661$	31.6245	−	22.9765i	1.23005	−	0.893683i	0.996894	+	0.0787568i	$0.0250951\pi$
$662$	−5.19017	−	11.5622i	−0.201722	−	0.449377i
$663$	−20.7565	+	3.28750i	−0.806114	+	0.127676i
$664$	6.35726	−	42.6634i	0.246710	−	1.65566i
$665$	7.36528	+	10.8066i	0.285613	+	0.419061i
$666$	11.3202	+	4.30582i	0.438649	+	0.166847i
$667$	−5.06895	+	9.94838i	−0.196271	+	0.385203i
$668$	0.909409	−	3.47878i	0.0351861	−	0.134598i
$669$	−1.96510	+	0.638500i	−0.0759751	+	0.0246858i
$670$	15.9990	−	13.6410i	0.618095	−	0.526999i
$671$	−14.1679	−	4.60344i	−0.546947	−	0.177714i
$672$	−6.77697	+	1.54896i	−0.261427	+	0.0597526i
$673$	−34.7952	−	5.51101i	−1.34126	−	0.212434i	−0.555781	−	0.831329i	$-0.687581\pi$
$673$	−34.7952	−	5.51101i	−1.34126	−	0.212434i	−0.785474	+	0.618895i	$0.787581\pi$
$674$	−2.87624	−	10.6047i	−0.110789	−	0.408477i
$675$	−1.99800	−	4.58345i	−0.0769031	−	0.176417i
$676$	−2.59664	+	1.52039i	−0.0998708	+	0.0584763i
$677$	3.20219	−	20.2178i	0.123070	−	0.777035i	−0.846530	−	0.532341i	$-0.821313\pi$
$677$	3.20219	−	20.2178i	0.123070	−	0.777035i	0.969600	−	0.244694i	$-0.0786875\pi$
$678$	17.3931	+	19.1988i	0.667979	+	0.737327i
$679$	−4.64919	+	14.3087i	−0.178419	+	0.549119i
$680$	−31.2255	−	23.7003i	−1.19744	−	0.908865i
$681$	6.71853	+	20.6775i	0.257455	+	0.792364i
$682$	30.9160	−	53.9277i	1.18384	−	2.06500i
$683$	0.181468	+	0.0924627i	0.00694369	+	0.00353799i	0.457459	−	0.889231i	$-0.348760\pi$
$683$	0.181468	+	0.0924627i	0.00694369	+	0.00353799i	−0.450515	+	0.892769i	$0.648760\pi$
$684$	−9.47212	−	0.937126i	−0.362176	−	0.0358319i
$685$	15.4460	−	43.0836i	0.590162	−	1.64614i
$686$	−16.9107	−	13.6087i	−0.645653	−	0.519584i
$687$	1.49963	+	9.46828i	0.0572144	+	0.361238i
$688$	−11.2702	+	30.4667i	−0.429673	+	1.16153i
$689$	−1.43971	−	1.98159i	−0.0548487	−	0.0754927i
$690$	15.0866	+	1.20019i	0.574336	+	0.0456904i
$691$	−11.4692	+	15.7860i	−0.436309	+	0.600528i	−0.969387	−	0.245538i	$-0.921035\pi$
$691$	−11.4692	+	15.7860i	−0.436309	+	0.600528i	0.533078	+	0.846066i	$0.321035\pi$
$692$	17.7589	−	1.03947i	0.675093	−	0.0395146i
$693$	−3.89735	−	3.89735i	−0.148048	−	0.148048i
$694$	−16.7692	−	25.6505i	−0.636550	−	0.973681i
$695$	−2.73657	−	21.4317i	−0.103804	−	0.812952i
$696$	−5.85178	+	3.04945i	−0.221811	+	0.115589i
$697$	7.84953	+	15.4056i	0.297322	+	0.583528i
$698$	−32.3970	+	3.50509i	−1.22625	+	0.132670i
$699$	−7.35781			−0.278298
$700$	0.0208031	−	12.2890i	0.000786285	−	0.464482i
$701$	−10.3544			−0.391080			−0.195540	−	0.980696i	$-0.562646\pi$
$701$	−10.3544			−0.391080			−0.195540	+	0.980696i	$0.562646\pi$
$702$	4.76707	−	0.515758i	0.179922	−	0.0194660i
$703$	18.5038	+	36.3157i	0.697883	+	1.36967i
$704$	34.3216	+	10.4608i	1.29354	+	0.394255i
$705$	9.63442	−	4.54935i	0.362853	−	0.171339i
$706$	−11.9458	−	18.2726i	−0.449586	−	0.687697i
$707$	6.87186	+	6.87186i	0.258443	+	0.258443i
$708$	0.0441711	+	0.754648i	0.00166005	+	0.0283614i
$709$	15.3330	−	21.1040i	0.575841	−	0.792578i	−0.417390	−	0.908727i	$-0.637055\pi$
$709$	15.3330	−	21.1040i	0.575841	−	0.792578i	0.993232	+	0.116150i	$0.0370552\pi$
$710$	12.0123	+	10.2770i	0.450812	+	0.385690i
$711$	0.991107	+	1.36414i	0.0371694	+	0.0511593i
$712$	−2.64916	+	3.71738i	−0.0992815	+	0.139315i
$713$	7.33719	+	46.3252i	0.274780	+	1.73489i
$714$	−8.39219	−	6.75355i	−0.314070	−	0.252745i
$715$	9.53013	+	32.6400i	0.356407	+	1.22067i
$716$	−1.64641	+	16.6413i	−0.0615293	+	0.621915i
$717$	−10.1121	−	5.15238i	−0.377644	−	0.192419i
$718$	15.7812	−	27.5275i	0.588948	−	1.02732i
$719$	−0.0165289	−	0.0508707i	−0.000616424	−	0.00189716i	0.950748	−	0.309965i	$-0.100317\pi$
$719$	−0.0165289	−	0.0508707i	−0.000616424	−	0.00189716i	−0.951364	+	0.308068i	$0.900317\pi$
$720$	6.84932	+	5.75211i	0.255259	+	0.214368i
$721$	6.38261	−	19.6437i	0.237701	−	0.731568i
$722$	−3.46549	−	3.82527i	−0.128972	−	0.142362i
$723$	−0.844825	+	5.33401i	−0.0314194	+	0.198374i
$724$	−22.8306	−	38.9920i	−0.848491	−	1.44913i
$725$	−2.93114	−	11.2906i	−0.108860	−	0.419324i
$726$	3.37453	+	12.4419i	0.125241	+	0.461761i
$727$	30.0813	+	4.76440i	1.11565	+	0.176702i	0.686922	−	0.726731i	$-0.258961\pi$
$727$	30.0813	+	4.76440i	1.11565	+	0.176702i	0.428730	+	0.903433i	$0.358961\pi$
$728$	11.2410	+	3.53895i	0.416620	+	0.131162i
$729$	0.951057	+	0.309017i	0.0352243	+	0.0114451i
$730$	9.25331	+	5.68121i	0.342480	+	0.210271i
$731$	−47.8731	+	15.5549i	−1.77065	+	0.575319i
$732$	6.42702	+	1.68013i	0.237549	+	0.0620992i
$733$	1.86449	−	3.65926i	0.0688664	−	0.135158i	−0.854007	−	0.520262i	$-0.825834\pi$
$733$	1.86449	−	3.65926i	0.0688664	−	0.135158i	0.922873	+	0.385104i	$0.125834\pi$
$734$	−21.4601	−	8.16266i	−0.792105	−	0.301289i
$735$	−0.369182	+	12.2700i	−0.0136175	+	0.452586i
$736$	−25.1237	+	10.0867i	−0.926073	+	0.371801i
$737$	−29.4523	+	4.66479i	−1.08489	+	0.171830i
$738$	−1.61555	−	3.59898i	−0.0594693	−	0.132480i
$739$	−37.0386	+	26.9101i	−1.36249	+	0.989905i	−0.364205	+	0.931319i	$0.618659\pi$
$739$	−37.0386	+	26.9101i	−1.36249	+	0.989905i	−0.998282	+	0.0585867i	$0.981341\pi$
$740$	4.91533	−	37.9830i	0.180691	−	1.39628i
$741$	13.0543	+	9.48451i	0.479562	+	0.348422i
$742$	0.257289	−	1.22888i	0.00944537	−	0.0451137i
$743$	−20.4738	+	20.4738i	−0.751110	+	0.751110i	−0.974686	−	0.223576i	$-0.928227\pi$
$743$	−20.4738	+	20.4738i	−0.751110	+	0.751110i	0.223576	+	0.974686i	$0.428227\pi$
$744$	−12.3576	+	24.8123i	−0.453051	+	0.909662i
$745$	−16.4751	−	9.02861i	−0.603601	−	0.330783i
$746$	−0.612188	+	12.4057i	−0.0224138	+	0.454206i
$747$	−13.5881	+	6.92350i	−0.497164	+	0.253318i
$748$	20.2414	+	51.7834i	0.740098	+	1.89339i
$749$		−	1.31550i		−	0.0480672i
$750$	−12.6268	+	9.51657i	−0.461064	+	0.347496i
$751$		−	11.0553i		−	0.403414i	−0.979446	−	0.201707i	$-0.935351\pi$
$751$		−	11.0553i		−	0.403414i	0.979446	−	0.201707i	$-0.0646489\pi$
$752$	−11.8127	+	14.9573i	−0.430765	+	0.545435i
$753$	11.1279	−	5.66994i	0.405523	−	0.206624i
$754$	11.1728	+	0.551346i	0.406889	+	0.0200788i
$755$	−1.88244	−	1.03160i	−0.0685090	−	0.0375439i
$756$	1.83652	+	1.63341i	0.0667934	+	0.0594067i
$757$	13.0048	−	13.0048i	0.472669	−	0.472669i	−0.430109	−	0.902777i	$-0.641525\pi$
$757$	13.0048	−	13.0048i	0.472669	−	0.472669i	0.902777	+	0.430109i	$0.141525\pi$
$758$	21.3672	+	4.47362i	0.776093	+	0.162489i
$759$	−17.3654	−	12.6167i	−0.630323	−	0.457956i
$760$	4.08569	+	29.8211i	0.148203	+	1.08173i
$761$	−43.5067	+	31.6095i	−1.57712	+	1.14584i	−0.657209	+	0.753709i	$0.728263\pi$
$761$	−43.5067	+	31.6095i	−1.57712	+	1.14584i	−0.919908	+	0.392134i	$0.871737\pi$
$762$	3.00307	−	1.34805i	0.108790	−	0.0488347i
$763$	6.96101	−	1.10252i	0.252005	−	0.0399137i
$764$	5.15300	−	11.7667i	0.186429	−	0.425702i
$765$	−0.416825	+	13.8534i	−0.0150703	+	0.500873i
$766$	11.0083	−	28.9413i	0.397745	−	1.04569i
$767$	0.581792	−	1.14183i	0.0210073	−	0.0412291i
$768$	−15.5513	−	3.76247i	−0.561160	−	0.135767i
$769$	−0.181257	+	0.0588941i	−0.00653631	+	0.00212377i	−0.312283	−	0.949989i	$-0.601094\pi$
$769$	−0.181257	+	0.0588941i	−0.00653631	+	0.00212377i	0.305747	+	0.952113i	$0.401094\pi$
$770$	−9.11945	+	14.8534i	−0.328642	+	0.535278i
$771$	−16.6180	−	5.39952i	−0.598483	−	0.194459i
$772$	27.7025	+	17.7507i	0.997034	+	0.638861i
$773$	−19.0875	−	3.02316i	−0.686528	−	0.108735i	−0.196581	−	0.980488i	$-0.562984\pi$
$773$	−19.0875	−	3.02316i	−0.686528	−	0.108735i	−0.489947	+	0.871752i	$0.662984\pi$
$774$	11.0845	−	3.00638i	0.398425	−	0.108062i
$775$	−37.8395	−	31.1335i	−1.35923	−	1.11835i
$776$	−24.2601	+	24.7086i	−0.870887	+	0.886986i
$777$	1.64639	−	10.3949i	0.0590638	−	0.372914i
$778$	−34.4533	+	31.2129i	−1.23521	+	1.11903i
$779$	4.10244	−	12.6260i	0.146985	−	0.452374i
$780$	−5.09296	−	14.2819i	−0.182357	−	0.511373i
$781$	−6.92855	−	21.3239i	−0.247923	−	0.763028i
$782$	−36.3947	−	20.8646i	−1.30147	−	0.746117i
$783$	2.07870	+	1.05915i	0.0742868	+	0.0378510i
$784$	−9.17589	−	19.9501i	−0.327710	−	0.712505i
$785$	−7.36624	−	25.2288i	−0.262912	−	0.900455i
$786$	19.9321	−	24.7683i	0.710953	−	0.883454i
$787$	−1.63251	−	10.3073i	−0.0581927	−	0.367414i	−0.999550	−	0.0300023i	$-0.990449\pi$
$787$	−1.63251	−	10.3073i	−0.0581927	−	0.367414i	0.941357	−	0.337412i	$-0.109551\pi$
$788$	1.70902	+	2.08432i	0.0608815	+	0.0742508i
$789$	3.58995	+	4.94114i	0.127806	+	0.175909i
$790$	3.46638	−	4.05166i	0.123328	−	0.144152i
$791$	13.2319	−	18.2121i	0.470471	−	0.647548i
$792$	−4.03039	−	12.0283i	−0.143214	−	0.427408i
$793$	−7.96311	−	7.96311i	−0.282778	−	0.282778i
$794$	12.2208	−	7.98941i	0.433699	−	0.283534i
$795$	−1.46073	+	0.689754i	−0.0518068	+	0.0244631i
$796$	40.2378	−	8.80991i	1.42619	−	0.312259i
$797$	9.74336	+	19.1224i	0.345127	+	0.677351i	0.996695	−	0.0812404i	$-0.0258881\pi$
$797$	9.74336	+	19.1224i	0.345127	+	0.677351i	−0.651567	+	0.758591i	$0.725888\pi$
$798$	0.889677	+	8.22316i	0.0314942	+	0.291097i
$799$	−29.5337			−1.04483
$800$	12.6523	−	25.2966i	0.447326	−	0.894371i
$801$	1.61388			0.0570238
$802$	2.93997	+	27.1737i	0.103814	+	0.959538i
$803$	−6.99149	−	13.7216i	−0.246724	−	0.484224i
$804$	12.9896	−	2.84403i	0.458108	−	0.100301i
$805$	−1.66572	−	13.0452i	−0.0587088	−	0.459784i
$806$	39.3318	−	25.7134i	1.38540	−	0.905716i
$807$	11.4076	+	11.4076i	0.401566	+	0.401566i
$808$	7.10644	+	21.2085i	0.250004	+	0.746113i
$809$	−20.9545	+	28.8414i	−0.736720	+	1.01401i	0.262081	+	0.965046i	$0.415591\pi$
$809$	−20.9545	+	28.8414i	−0.736720	+	1.01401i	−0.998801	+	0.0489622i	$0.984409\pi$
$810$	0.250778	−	3.15232i	0.00881143	−	0.110761i
$811$	−3.52375	−	4.85003i	−0.123736	−	0.170308i	0.742655	−	0.669674i	$-0.233566\pi$
$811$	−3.52375	−	4.85003i	−0.123736	−	0.170308i	−0.866391	+	0.499366i	$0.833566\pi$
$812$	3.63568	+	4.43406i	0.127587	+	0.155605i
$813$	2.22823	+	14.0685i	0.0781474	+	0.493403i
$814$	−34.0559	+	42.3190i	−1.19366	+	1.48328i
$815$	16.8443	−	46.9839i	0.590031	−	1.64577i
$816$	−10.3600	−	22.5247i	−0.362674	−	0.788523i
$817$	34.4373	+	17.5467i	1.20481	+	0.613880i
$818$	42.8797	+	24.5824i	1.49925	+	0.859502i
$819$	−1.28755	−	3.96268i	−0.0449907	−	0.138467i
$820$	−9.88035	+	7.61615i	−0.345037	+	0.265968i
$821$	−3.94578	+	12.1439i	−0.137709	+	0.423824i	−0.996002	−	0.0893362i	$-0.971525\pi$
$821$	−3.94578	+	12.1439i	−0.137709	+	0.423824i	0.858293	+	0.513160i	$0.171525\pi$
$822$	21.4524	−	19.4347i	0.748237	−	0.677863i
$823$	7.94099	−	50.1375i	0.276806	−	1.74768i	−0.321956	−	0.946755i	$-0.604340\pi$
$823$	7.94099	−	50.1375i	0.276806	−	1.74768i	0.598761	−	0.800927i	$-0.295660\pi$
$824$	33.3053	−	33.9210i	1.16025	−	1.18170i
$825$	22.3199	−	2.17008i	0.777081	−	0.0755525i
$826$	0.633982	−	0.171951i	0.0220590	−	0.00598294i
$827$	12.9219	+	2.04663i	0.449339	+	0.0711683i	0.377003	−	0.926212i	$-0.376955\pi$
$827$	12.9219	+	2.04663i	0.449339	+	0.0711683i	0.0723358	+	0.997380i	$0.476955\pi$
$828$	8.05920	+	5.16403i	0.280077	+	0.179462i
$829$	29.1547	+	9.47295i	1.01259	+	0.329009i	0.767884	−	0.640589i	$-0.221310\pi$
$829$	29.1547	+	9.47295i	1.01259	+	0.329009i	0.244702	+	0.969598i	$0.421310\pi$
$830$	31.2891	+	36.6977i	1.08606	+	1.27379i
$831$	13.7350	−	4.46276i	0.476460	−	0.154811i
$832$	19.5276	+	18.8251i	0.676999	+	0.652642i
$833$	15.4480	−	30.3184i	0.535241	−	1.05047i
$834$	4.85801	−	12.7720i	0.168219	−	0.442257i
$835$	2.26407	+	3.32192i	0.0783515	+	0.114960i
$836$	17.1253	−	39.1048i	0.592289	−	1.35247i
$837$	9.67959	−	1.53310i	0.334576	−	0.0529916i
$838$	−23.0759	+	10.3586i	−0.797145	+	0.357832i
$839$	−39.5519	+	28.7361i	−1.36548	+	0.992081i	−0.367408	+	0.930060i	$0.619755\pi$
$839$	−39.5519	+	28.7361i	−1.36548	+	0.992081i	−0.998075	+	0.0620209i	$0.980245\pi$
$840$	3.67264	−	6.84982i	0.126718	−	0.236341i
$841$	−19.0582	−	13.8466i	−0.657178	−	0.477468i
$842$	−50.1525	−	10.5003i	−1.72837	−	0.361865i
$843$	−1.66823	+	1.66823i	−0.0574569	+	0.0574569i
$844$	−8.55044	−	7.60484i	−0.294318	−	0.261769i
$845$	0.625965	−	3.30542i	0.0215338	−	0.113710i
$846$	6.73031	+	0.332122i	0.231393	+	0.0114186i
$847$	9.98121	−	5.08568i	0.342958	−	0.174746i
$848$	1.79099	−	2.26776i	0.0615029	−	0.0778752i
$849$			13.5376i			0.464609i
$850$	42.9133	−	8.90887i	1.47191	−	0.305572i
$851$		−	40.9865i		−	1.40500i
$852$	3.63997	+	9.31211i	0.124703	+	0.319028i
$853$	−7.99542	+	4.07387i	−0.273758	+	0.139487i	−0.585480	−	0.810687i	$-0.699094\pi$
$853$	−7.99542	+	4.07387i	−0.273758	+	0.139487i	0.311722	+	0.950173i	$0.399094\pi$
$854$	0.284512	−	5.76553i	0.00973581	−	0.197292i
$855$	7.74783	−	7.29522i	0.264970	−	0.249491i
$856$	1.34979	−	2.71020i	0.0461350	−	0.0926326i
$857$	−0.588621	+	0.588621i	−0.0201069	+	0.0201069i	−0.717089	−	0.696982i	$-0.754526\pi$
$857$	−0.588621	+	0.588621i	−0.0201069	+	0.0201069i	0.696982	+	0.717089i	$0.254526\pi$
$858$	−4.40696	+	21.0489i	−0.150451	+	0.718597i
$859$	8.15543	+	5.92527i	0.278260	+	0.202168i	0.718158	−	0.695880i	$-0.244985\pi$
$859$	8.15543	+	5.92527i	0.278260	+	0.202168i	−0.439898	+	0.898048i	$0.644985\pi$
$860$	−17.4002	−	31.8792i	−0.593341	−	1.08707i
$861$	−2.77334	+	2.01495i	−0.0945152	+	0.0686693i
$862$	20.0890	+	44.7524i	0.684233	+	1.52427i
$863$	28.6065	−	4.53083i	0.973777	−	0.154231i	0.350782	−	0.936457i	$-0.385916\pi$
$863$	28.6065	−	4.53083i	0.973777	−	0.154231i	0.622995	+	0.782226i	$0.285916\pi$
$864$	2.10761	+	5.24957i	0.0717022	+	0.178594i
$865$	−12.1691	+	15.7317i	−0.413763	+	0.534895i
$866$	−0.997490	−	0.379411i	−0.0338961	−	0.0128929i
$867$	9.72373	−	19.0839i	0.330235	−	0.648123i
$868$	23.3040	+	6.09205i	0.790990	+	0.206777i
$869$	−7.19241	+	2.33696i	−0.243986	+	0.0792758i
$870$	1.72832	−	7.17224i	0.0585956	−	0.243162i
$871$	−21.4390	−	6.96594i	−0.726432	−	0.236032i
$872$	15.4724	+	4.87109i	0.523961	+	0.164956i
$873$	12.0920	+	1.91518i	0.409251	+	0.0648189i
$874$	8.43183	+	31.0881i	0.285211	+	1.05157i
$875$	10.3426	+	9.04474i	0.349642	+	0.305768i
$876$	3.46990	+	5.92619i	0.117237	+	0.200227i
$877$	−2.86266	+	18.0741i	−0.0966652	+	0.610320i	0.891032	+	0.453941i	$0.149982\pi$
$877$	−2.86266	+	18.0741i	−0.0966652	+	0.610320i	−0.987697	+	0.156379i	$0.950018\pi$
$878$	−7.81448	−	8.62576i	−0.263726	−	0.291105i
$879$	5.90933	−	18.1871i	0.199317	−	0.613434i
$880$	−34.0286	+	21.2438i	−1.14710	+	0.716129i
$881$	−4.26429	−	13.1241i	−0.143668	−	0.442164i	0.853170	−	0.521634i	$-0.174677\pi$
$881$	−4.26429	−	13.1241i	−0.143668	−	0.442164i	−0.996837	+	0.0794700i	$0.974677\pi$
$882$	−3.86133	+	6.73541i	−0.130018	+	0.226793i
$883$	−30.1105	−	15.3421i	−1.01330	−	0.516301i	−0.133198	−	0.991089i	$-0.542525\pi$
$883$	−30.1105	−	15.3421i	−1.01330	−	0.516301i	−0.880100	+	0.474788i	$0.842525\pi$
$884$	−4.13808	+	41.8262i	−0.139179	+	1.40677i
$885$	−0.668504	−	0.517115i	−0.0224715	−	0.0173826i
$886$	7.87304	+	6.33577i	0.264500	+	0.212854i
$887$	−4.87731	−	30.7941i	−0.163764	−	1.03397i	−0.923462	−	0.383689i	$-0.874653\pi$
$887$	−4.87731	−	30.7941i	−0.163764	−	1.03397i	0.759698	−	0.650276i	$-0.225347\pi$
$888$	14.0578	−	19.7263i	0.471749	−	0.661971i
$889$	−1.68132	−	2.31413i	−0.0563895	−	0.0776136i
$890$	−1.18720	−	4.96354i	−0.0397950	−	0.166378i
$891$	−2.63624	+	3.62847i	−0.0883174	+	0.121558i
$892$	0.241468	+	4.12540i	0.00808494	+	0.138128i
$893$	16.0349	+	16.0349i	0.536587	+	0.536587i
$894$	−6.50170	−	9.94514i	−0.217449	−	0.332615i
$895$	−12.8168	−	13.6120i	−0.428417	−	0.454997i
$896$	−0.430810	+	13.8968i	−0.0143924	+	0.464259i
$897$	−7.36666	−	14.4579i	−0.245966	−	0.482735i
$898$	5.57530	−	0.603201i	0.186050	−	0.0201291i
$899$	22.8638			0.762551
$900$	−9.87952	+	1.54762i	−0.329317	+	0.0515874i
$901$	4.47778			0.149176
$902$	17.5906	−	1.90316i	0.585704	−	0.0633683i
$903$	−4.53086	−	8.89231i	−0.150778	−	0.295918i
$904$	45.9473	−	23.9439i	1.52819	−	0.796361i
$905$	49.6352	+	9.39968i	1.64993	+	0.312456i
$906$	−0.742881	−	1.13633i	−0.0246806	−	0.0377520i
$907$	6.58434	+	6.58434i	0.218629	+	0.218629i	0.807921	−	0.589291i	$-0.200593\pi$
$907$	6.58434	+	6.58434i	0.218629	+	0.218629i	−0.589291	+	0.807921i	$0.700593\pi$
$908$	43.4089	−	2.54081i	1.44058	−	0.0843199i
$909$	4.64825	−	6.39777i	0.154173	−	0.212201i
$910$	−11.2402	+	6.87491i	−0.372608	+	0.227901i
$911$	16.5700	+	22.8067i	0.548990	+	0.755620i	0.989875	−	0.141944i	$-0.0453353\pi$
$911$	16.5700	+	22.8067i	0.548990	+	0.755620i	−0.440885	+	0.897564i	$0.645335\pi$
$912$	−6.60463	+	17.8543i	−0.218701	+	0.591215i
$913$	−10.6999	−	67.5562i	−0.354113	−	2.23578i
$914$	−44.6054	−	35.8959i	−1.47542	−	1.18733i
$915$	−6.13722	+	4.18285i	−0.202890	+	0.138281i
$916$	19.0795	+	1.88763i	0.630403	+	0.0623691i
$917$	−24.6154	−	12.5422i	−0.812872	−	0.414179i
$918$	−4.35963	+	7.60462i	−0.143889	+	0.250990i
$919$	8.14444	+	25.0660i	0.268660	+	0.826852i	0.990827	+	0.135133i	$0.0431461\pi$
$919$	8.14444	+	25.0660i	0.268660	+	0.826852i	−0.722167	+	0.691719i	$0.756854\pi$
$920$	9.95362	−	28.5850i	0.328161	−	0.942421i
$921$	4.96085	−	15.2679i	0.163466	−	0.503096i
$922$	22.9909	+	25.3778i	0.757166	+	0.835773i
$923$	2.65149	−	16.7408i	0.0872748	−	0.551032i
$924$	−9.51269	+	5.56987i	−0.312945	+	0.183235i
$925$	28.4034	+	32.0443i	0.933899	+	1.05361i
$926$	−0.960253	−	3.54045i	−0.0315559	−	0.116346i
$927$	−16.6004	−	2.62924i	−0.545228	−	0.0863556i
$928$	2.94059	+	12.8656i	0.0965297	+	0.422333i
$929$	7.31939	+	2.37821i	0.240141	+	0.0780266i	0.426615	−	0.904433i	$-0.359706\pi$
$929$	7.31939	+	2.37821i	0.240141	+	0.0780266i	−0.186474	+	0.982460i	$0.559706\pi$
$930$	−11.8355	−	28.6421i	−0.388103	−	0.939211i
$931$	−24.8482	+	8.07366i	−0.814366	+	0.264604i
$932$	−3.72183	+	14.2372i	−0.121913	+	0.466354i
$933$	−5.45463	+	10.7053i	−0.178577	+	0.350476i
$934$	44.8483	+	17.0588i	1.46748	+	0.558180i
$935$	−58.5145	−	20.9782i	−1.91363	−	0.686061i
$936$	1.41337	−	9.48506i	0.0461974	−	0.310029i
$937$	41.5344	−	6.57840i	1.35687	−	0.214907i	0.564744	−	0.825266i	$-0.308975\pi$
$937$	41.5344	−	6.57840i	1.35687	−	0.214907i	0.792125	+	0.610359i	$0.208975\pi$
$938$	−4.73201	−	10.5416i	−0.154506	−	0.344194i
$939$	0.166796	−	0.121185i	0.00544319	−	0.00395471i
$940$	−3.92948	−	20.9436i	−0.128165	−	0.683104i
$941$	41.1994	+	29.9331i	1.34306	+	0.975792i	0.999325	+	0.0367262i	$0.0116929\pi$
$941$	41.1994	+	29.9331i	1.34306	+	0.975792i	0.343737	+	0.939066i	$0.388307\pi$
$942$	3.40633	−	16.2696i	0.110984	−	0.530091i
$943$	−9.44001	+	9.44001i	−0.307409	+	0.307409i
$944$	1.48257	+	0.296256i	0.0482535	+	0.00964232i
$945$	−2.72578	+	0.348049i	−0.0886698	+	0.0113220i
$946$	−2.53881	+	51.4480i	−0.0825439	+	1.67272i
$947$	9.51643	−	4.84886i	0.309242	−	0.157567i	−0.292481	−	0.956271i	$-0.594481\pi$
$947$	9.51643	−	4.84886i	0.309242	−	0.157567i	0.601724	+	0.798704i	$0.294481\pi$
$948$	3.14092	−	1.22774i	0.102012	−	0.0398751i
$949$		−	11.6418i		−	0.377909i
$950$	−28.1361	−	18.4622i	−0.912855	−	0.598993i
$951$			0.898046i			0.0291211i
$952$	−17.3130	+	12.8225i	−0.561118	+	0.415580i
$953$	9.54986	−	4.86590i	0.309350	−	0.157622i	−0.292422	−	0.956289i	$-0.594461\pi$
$953$	9.54986	−	4.86590i	0.309350	−	0.157622i	0.601773	+	0.798667i	$0.294461\pi$
$954$	−1.02042	−	0.0503549i	−0.0330374	−	0.00163030i
$955$	6.13229	+	12.9867i	0.198436	+	0.420240i
$956$	−15.0848	+	16.9604i	−0.487876	+	0.548540i
$957$	−7.39882	+	7.39882i	−0.239170	+	0.239170i
$958$	−42.6301	−	8.92537i	−1.37732	−	0.288366i
$959$	−20.3498	−	14.7850i	−0.657129	−	0.477432i
$960$	14.5948	−	10.3437i	0.471046	−	0.333840i
$961$	52.6224	−	38.2324i	1.69750	−	1.23330i
$962$	−37.4626	+	16.8166i	−1.20784	+	0.542190i
$963$	−1.05728	+	0.167457i	−0.0340705	+	0.00539623i
$964$	9.89385	+	4.33284i	0.318659	+	0.139551i
$965$	−35.3107	+	10.3099i	−1.13669	+	0.331888i
$966$	2.95701	−	7.77413i	0.0951403	−	0.250129i
$967$	9.81345	−	19.2600i	0.315579	−	0.619359i	−0.677669	−	0.735367i	$-0.737010\pi$
$967$	9.81345	−	19.2600i	0.315579	−	0.619359i	0.993248	+	0.116008i	$0.0370098\pi$
$968$	25.7817	−	0.236120i	0.828654	−	0.00758918i
$969$	−28.0549	+	9.11558i	−0.901252	+	0.292834i
$970$	−3.00486	−	38.5980i	−0.0964801	−	1.23931i
$971$	−32.1098	−	10.4331i	−1.03045	−	0.334815i	−0.255484	−	0.966813i	$-0.582235\pi$
$971$	−32.1098	−	10.4331i	−1.03045	−	0.334815i	−0.774970	+	0.631998i	$0.782235\pi$
$972$	1.07902	−	1.68396i	0.0346095	−	0.0540131i
$973$	−11.7280	−	1.85753i	−0.375981	−	0.0595496i
$974$	34.9236	−	9.47211i	1.11902	−	0.303506i
$975$	15.7787	+	6.19847i	0.505322	+	0.198510i
$976$	6.50200	−	11.5863i	0.208124	−	0.370867i
$977$	−3.21252	+	20.2830i	−0.102777	+	0.648911i	0.881487	+	0.472209i	$0.156543\pi$
$977$	−3.21252	+	20.2830i	−0.102777	+	0.648911i	−0.984264	+	0.176703i	$0.943457\pi$
$978$	23.3944	−	21.1941i	0.748070	−	0.677712i
$979$	−2.23677	+	6.88406i	−0.0714874	+	0.220016i
$980$	23.5554	+	6.92093i	0.752450	+	0.221081i
$981$	−1.77221	−	5.45432i	−0.0565825	−	0.174143i
$982$	−44.6085	−	25.5735i	−1.42352	−	0.816083i
$983$	9.38458	+	4.78168i	0.299322	+	0.152512i	0.597201	−	0.802092i	$-0.296279\pi$
$983$	9.38458	+	4.78168i	0.299322	+	0.152512i	−0.297880	+	0.954603i	$0.596279\pi$
$984$	−7.78115	+	1.30557i	−0.248054	+	0.0416201i
$985$	−3.01218	−	0.0906309i	−0.0959760	−	0.00288774i
$986$	−12.8211	+	15.9319i	−0.408307	+	0.507376i
$987$	−0.916008	−	5.78345i	−0.0291569	−	0.184089i
$988$	24.9556	−	20.4622i	0.793944	−	0.650989i
$989$	−22.8452	−	31.4437i	−0.726434	−	0.999851i
$990$	13.0987	+	5.43866i	0.416305	+	0.172852i
$991$	32.0318	−	44.0880i	1.01752	−	1.40050i	0.103598	−	0.994619i	$-0.466964\pi$
$991$	32.0318	−	44.0880i	1.01752	−	1.40050i	0.913925	−	0.405882i	$-0.133036\pi$
$992$	41.7603	+	36.4625i	1.32589	+	1.15769i
$993$	6.33684	+	6.33684i	0.201093	+	0.201093i
$994$	7.27201	−	4.75412i	0.230654	−	0.150792i
$995$	−22.1322	+	40.3860i	−0.701637	+	1.28032i
$996$	6.52347	+	29.7949i	0.206704	+	0.944086i
$997$	−25.1191	−	49.2990i	−0.795529	−	1.56131i	−0.827262	−	0.561817i	$-0.810102\pi$
$997$	−25.1191	−	49.2990i	−0.795529	−	1.56131i	0.0317326	−	0.999496i	$-0.489898\pi$
$998$	3.25786	+	30.1119i	0.103126	+	0.953175i
$999$	−8.56409			−0.270956

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	300.2.w.a.223.17	yes	240
3.2	odd	2		900.2.bj.f.523.14		240
4.3	odd	2	inner	300.2.w.a.223.12	yes	240
12.11	even	2		900.2.bj.f.523.19		240
25.12	odd	20	inner	300.2.w.a.187.12	✓	240
75.62	even	20		900.2.bj.f.487.19		240
100.87	even	20	inner	300.2.w.a.187.17	yes	240
300.287	odd	20		900.2.bj.f.487.14		240

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
300.2.w.a.187.12	✓	240	25.12	odd	20	inner
300.2.w.a.187.17	yes	240	100.87	even	20	inner
300.2.w.a.223.12	yes	240	4.3	odd	2	inner
300.2.w.a.223.17	yes	240	1.1	even	1	trivial
900.2.bj.f.487.14		240	300.287	odd	20
900.2.bj.f.487.19		240	75.62	even	20
900.2.bj.f.523.14		240	3.2	odd	2
900.2.bj.f.523.19		240	12.11	even	2

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:	\( N \)	\(=\)	\( 300 = 2^{2} \cdot 3 \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	300.w (of order \(20\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(0.152118 + 1.40601i) q^{2} +(-0.453990 - 0.891007i) q^{3} +(-1.95372 + 0.427760i) q^{4} +(1.07461 - 1.96092i) q^{5} +(1.18370 - 0.773853i) q^{6} +(-0.868967 - 0.868967i) q^{7} +(-0.898631 - 2.68188i) q^{8} +(-0.587785 + 0.809017i) q^{9} +(2.92054 + 1.21262i) q^{10} +(-2.63624 - 3.62847i) q^{11} +(1.26811 + 1.54658i) q^{12} +(-0.530391 - 3.34876i) q^{13} +(1.08959 - 1.35396i) q^{14} +(-2.23506 - 0.0672487i) q^{15} +(3.63404 - 1.67145i) q^{16} +(5.52269 + 2.81395i) q^{17} +(-1.22690 - 0.703365i) q^{18} +(-1.47067 - 4.52625i) q^{19} +(-1.26069 + 4.29076i) q^{20} +(-0.379753 + 1.16876i) q^{21} +(4.70064 - 4.25853i) q^{22} +(-0.748674 + 4.72694i) q^{23} +(-1.98160 + 2.01823i) q^{24} +(-2.69041 - 4.21446i) q^{25} +(4.62770 - 1.25514i) q^{26} +(0.987688 + 0.156434i) q^{27} +(2.06943 + 1.32601i) q^{28} +(2.21880 + 0.720931i) q^{29} +(-0.245441 - 3.15274i) q^{30} +(9.32059 - 3.02844i) q^{31} +(2.90287 + 4.85524i) q^{32} +(-2.03617 + 3.99620i) q^{33} +(-3.11633 + 8.19300i) q^{34} +(-2.63778 + 0.770171i) q^{35} +(0.802303 - 1.83202i) q^{36} +(-8.45865 + 1.33972i) q^{37} +(6.14023 - 2.75630i) q^{38} +(-2.74297 + 1.99289i) q^{39} +(-6.22463 - 1.11984i) q^{40} +(2.25676 + 1.63963i) q^{41} +(-1.70105 - 0.356146i) q^{42} +(-5.74249 + 5.74249i) q^{43} +(6.70259 + 5.96134i) q^{44} +(0.954775 + 2.02198i) q^{45} +(-6.76001 - 0.333587i) q^{46} +(-4.24551 + 2.16319i) q^{47} +(-3.13909 - 2.47914i) q^{48} -5.48979i q^{49} +(5.51631 - 4.42384i) q^{50} -6.19825i q^{51} +(2.46870 + 6.31566i) q^{52} +(0.643686 - 0.327974i) q^{53} +(-0.0697026 + 1.41249i) q^{54} +(-9.94808 + 1.27025i) q^{55} +(-1.54958 + 3.11134i) q^{56} +(-3.36525 + 3.36525i) q^{57} +(-0.676115 + 3.22932i) q^{58} +(0.305784 + 0.222165i) q^{59} +(4.39544 - 0.824682i) q^{60} +(2.68715 - 1.95233i) q^{61} +(5.67585 + 12.6441i) q^{62} +(1.21378 - 0.192243i) q^{63} +(-6.38493 + 4.82003i) q^{64} +(-7.13661 - 2.55857i) q^{65} +(-5.92843 - 2.25497i) q^{66} +(3.01843 - 5.92399i) q^{67} +(-11.9935 - 3.13529i) q^{68} +(4.55163 - 1.47891i) q^{69} +(-1.48412 - 3.59158i) q^{70} +(4.75445 + 1.54481i) q^{71} +(2.69789 + 0.849360i) q^{72} +(3.39138 + 0.537142i) q^{73} +(-3.17037 - 11.6891i) q^{74} +(-2.53369 + 4.31050i) q^{75} +(4.80942 + 8.21394i) q^{76} +(-0.862218 + 5.44383i) q^{77} +(-3.21927 - 3.55349i) q^{78} +(0.521056 - 1.60364i) q^{79} +(0.627622 - 8.92222i) q^{80} +(-0.309017 - 0.951057i) q^{81} +(-1.96204 + 3.42244i) q^{82} +(13.5881 + 6.92350i) q^{83} +(0.241983 - 2.44587i) q^{84} +(11.4527 - 7.80563i) q^{85} +(-8.94753 - 7.20045i) q^{86} +(-0.364959 - 2.30426i) q^{87} +(-7.36211 + 10.3307i) q^{88} +(-0.948617 - 1.30566i) q^{89} +(-2.69768 + 1.65000i) q^{90} +(-2.44907 + 3.37085i) q^{91} +(-0.559295 - 9.55537i) q^{92} +(-6.92982 - 6.92982i) q^{93} +(-3.68729 - 5.64016i) q^{94} +(-10.4560 - 1.98011i) q^{95} +(3.00817 - 4.79071i) q^{96} +(-5.55806 - 10.9083i) q^{97} +(7.71870 - 0.835099i) q^{98} +4.48504 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 240 q + 12 q^{8} + 8 q^{10} + 8 q^{12} + 4 q^{13} + 20 q^{17} - 20 q^{20} - 12 q^{22} + 20 q^{25} + 4 q^{28} - 8 q^{30} - 20 q^{32} - 8 q^{33} - 4 q^{37} - 76 q^{38} - 92 q^{40} - 20 q^{42} - 140 q^{44}+ \cdots + 256 q^{98}+O(q^{100}) \) 240 * q + 12 * q^8 + 8 * q^10 + 8 * q^12 + 4 * q^13 + 20 * q^17 - 20 * q^20 - 12 * q^22 + 20 * q^25 + 4 * q^28 - 8 * q^30 - 20 * q^32 - 8 * q^33 - 4 * q^37 - 76 * q^38 - 92 * q^40 - 20 * q^42 - 140 * q^44 - 4 * q^45 - 16 * q^48 - 164 * q^50 - 172 * q^52 - 4 * q^53 - 120 * q^58 + 20 * q^60 - 44 * q^62 - 60 * q^64 - 20 * q^65 + 16 * q^68 - 44 * q^70 + 12 * q^72 - 44 * q^73 - 48 * q^77 + 24 * q^78 - 4 * q^80 + 60 * q^81 + 24 * q^82 + 80 * q^84 - 64 * q^85 + 60 * q^88 - 260 * q^89 + 48 * q^90 + 144 * q^92 - 64 * q^93 + 40 * q^94 - 20 * q^96 - 180 * q^97 + 256 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

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