LMFDB - Embedded newform 520.2.ca.b.101.21

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [520,2,Mod(101,520)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(520, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 3, 0, 5]))

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

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

chi := DirichletCharacter("520.101");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 520 = 2^{3} \cdot 5 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	520.ca (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:	$4.15222090511$
Analytic rank:	$0$
Dimension:	$56$
Relative dimension:	$28$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			101.21
Character	$\chi$	$=$	520.101
Dual form			520.2.ca.b.381.21

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.14713 - 0.827103i) q^{2} +(-1.05921 + 0.611534i) q^{3} +(0.631801 - 1.89758i) q^{4} +1.00000 q^{5} +(-0.709244 + 1.57758i) q^{6} +(3.94053 + 2.27507i) q^{7} +(-0.844743 - 2.69934i) q^{8} +(-0.752053 + 1.30259i) q^{9} +(1.14713 - 0.827103i) q^{10} +(0.572114 + 0.990930i) q^{11} +(0.491229 + 2.39630i) q^{12} +(-0.184836 + 3.60081i) q^{13} +(6.40201 - 0.649436i) q^{14} +(-1.05921 + 0.611534i) q^{15} +(-3.20166 - 2.39779i) q^{16} +(0.505178 - 0.874994i) q^{17} +(0.214679 + 2.11626i) q^{18} +(2.97393 - 5.15100i) q^{19} +(0.631801 - 1.89758i) q^{20} -5.56512 q^{21} +(1.47589 + 0.663526i) q^{22} +(-0.586182 - 1.01530i) q^{23} +(2.54549 + 2.34257i) q^{24} +1.00000 q^{25} +(2.76621 + 4.28347i) q^{26} -5.50883i q^{27} +(6.80677 - 6.04011i) q^{28} +(3.04627 - 1.75877i) q^{29} +(-0.709244 + 1.57758i) q^{30} -0.814108i q^{31} +(-5.65593 - 0.102470i) q^{32} +(-1.21198 - 0.699734i) q^{33} +(-0.144207 - 1.42156i) q^{34} +(3.94053 + 2.27507i) q^{35} +(1.99663 + 2.25006i) q^{36} +(3.97121 + 6.87834i) q^{37} +(-0.848931 - 8.36860i) q^{38} +(-2.00624 - 3.92704i) q^{39} +(-0.844743 - 2.69934i) q^{40} +(-7.63515 + 4.40815i) q^{41} +(-6.38390 + 4.60293i) q^{42} +(1.17648 + 0.679243i) q^{43} +(2.24184 - 0.459564i) q^{44} +(-0.752053 + 1.30259i) q^{45} +(-1.51218 - 0.679841i) q^{46} -9.05737i q^{47} +(4.85755 + 0.581837i) q^{48} +(6.85187 + 11.8678i) q^{49} +(1.14713 - 0.827103i) q^{50} +1.23573i q^{51} +(6.71606 + 2.62574i) q^{52} -8.10029i q^{53} +(-4.55637 - 6.31932i) q^{54} +(0.572114 + 0.990930i) q^{55} +(2.81243 - 12.5587i) q^{56} +7.27464i q^{57} +(2.03978 - 4.53711i) q^{58} +(-3.14969 + 5.45542i) q^{59} +(0.491229 + 2.39630i) q^{60} +(-10.5468 - 6.08920i) q^{61} +(-0.673351 - 0.933885i) q^{62} +(-5.92698 + 3.42194i) q^{63} +(-6.57282 + 4.56049i) q^{64} +(-0.184836 + 3.60081i) q^{65} +(-1.96904 + 0.199745i) q^{66} +(-5.23119 - 9.06069i) q^{67} +(-1.34120 - 1.51144i) q^{68} +(1.24178 + 0.716940i) q^{69} +(6.40201 - 0.649436i) q^{70} +(-5.04169 - 2.91082i) q^{71} +(4.15143 + 0.929685i) q^{72} +14.5790i q^{73} +(10.2446 + 4.60573i) q^{74} +(-1.05921 + 0.611534i) q^{75} +(-7.89552 - 8.89769i) q^{76} +5.20639i q^{77} +(-5.54948 - 2.84545i) q^{78} -5.60175 q^{79} +(-3.20166 - 2.39779i) q^{80} +(1.11268 + 1.92721i) q^{81} +(-5.11248 + 11.3718i) q^{82} -2.31651 q^{83} +(-3.51605 + 10.5603i) q^{84} +(0.505178 - 0.874994i) q^{85} +(1.91138 - 0.193895i) q^{86} +(-2.15109 + 3.72580i) q^{87} +(2.19156 - 2.38141i) q^{88} +(-12.1107 + 6.99213i) q^{89} +(0.214679 + 2.11626i) q^{90} +(-8.92044 + 13.7686i) q^{91} +(-2.29696 + 0.470865i) q^{92} +(0.497854 + 0.862309i) q^{93} +(-7.49138 - 10.3899i) q^{94} +(2.97393 - 5.15100i) q^{95} +(6.05347 - 3.35025i) q^{96} +(4.36544 + 2.52039i) q^{97} +(17.6758 + 7.94665i) q^{98} -1.72104 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 56 q + 6 q^{4} + 56 q^{5} - 13 q^{6} + 28 q^{9} - 8 q^{11} + 6 q^{12} - 4 q^{14} + 14 q^{16} + 18 q^{18} - 16 q^{19} + 6 q^{20} - 6 q^{22} + 12 q^{23} + 22 q^{24} + 56 q^{25} - 37 q^{26} - 12 q^{28} - 13 q^{30}+ \cdots - 48 q^{99}+O(q^{100}) $ 56 * q + 6 * q^4 + 56 * q^5 - 13 * q^6 + 28 * q^9 - 8 * q^11 + 6 * q^12 - 4 * q^14 + 14 * q^16 + 18 * q^18 - 16 * q^19 + 6 * q^20 - 6 * q^22 + 12 * q^23 + 22 * q^24 + 56 * q^25 - 37 * q^26 - 12 * q^28 - 13 * q^30 - 30 * q^32 - 16 * q^34 + 15 * q^36 + 4 * q^37 - 24 * q^39 - 61 * q^42 + 24 * q^44 + 28 * q^45 - 19 * q^46 - 51 * q^48 + 20 * q^49 - 64 * q^52 - 5 * q^54 - 8 * q^55 - 23 * q^56 - q^58 - 16 * q^59 + 6 * q^60 + 10 * q^62 - 30 * q^64 + 14 * q^66 - 36 * q^67 - 51 * q^68 - 4 * q^70 - 81 * q^72 + 70 * q^74 - 60 * q^76 + 143 * q^78 + 14 * q^80 - 28 * q^81 + 21 * q^82 + 40 * q^83 + 31 * q^84 - 28 * q^86 - 36 * q^87 - 19 * q^88 + 18 * q^90 + 16 * q^91 - 18 * q^92 + 43 * q^94 - 16 * q^95 - 48 * q^96 + 24 * q^97 + 56 * q^98 - 48 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/520\mathbb{Z}\right)^\times$.

$n$	$41$	$261$	$391$	$417$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$-1$	$1$	$1$

Coefficient data

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

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

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

$2$	1.14713	−	0.827103i	0.811141	−	0.584850i
$2$	1.14713	−	0.827103i	0.811141	−	0.584850i
$3$	−1.05921	+	0.611534i	−0.611534	+	0.353069i	−0.773566	−	0.633716i	$-0.781529\pi$
$3$	−1.05921	+	0.611534i	−0.611534	+	0.353069i	0.162032	+	0.986786i	$0.448195\pi$
$4$	0.631801	−	1.89758i	0.315900	−	0.948792i
$5$	1.00000			0.447214
$5$	1.00000			0.447214
$6$	−0.709244	+	1.57758i	−0.289548	+	0.644045i
$7$	3.94053	+	2.27507i	1.48938	+	0.859895i	0.999926	−	0.0121337i	$-0.00386237\pi$
$7$	3.94053	+	2.27507i	1.48938	+	0.859895i	0.489455	+	0.872029i	$0.337196\pi$
$8$	−0.844743	−	2.69934i	−0.298662	−	0.954359i
$9$	−0.752053	+	1.30259i	−0.250684	+	0.434198i
$10$	1.14713	−	0.827103i	0.362753	−	0.261553i
$11$	0.572114	+	0.990930i	0.172499	+	0.298777i	0.939293	−	0.343116i	$-0.111483\pi$
$11$	0.572114	+	0.990930i	0.172499	+	0.298777i	−0.766794	+	0.641893i	$0.778149\pi$
$12$	0.491229	+	2.39630i	0.141806	+	0.691753i
$13$	−0.184836	+	3.60081i	−0.0512643	+	0.998685i
$13$	−0.184836	+	3.60081i	−0.0512643	+	0.998685i
$14$	6.40201	−	0.649436i	1.71101	−	0.173569i
$15$	−1.05921	+	0.611534i	−0.273486	+	0.157897i
$16$	−3.20166	−	2.39779i	−0.800414	−	0.599448i
$17$	0.505178	−	0.874994i	0.122524	−	0.212217i	−0.798239	−	0.602341i	$-0.794235\pi$
$17$	0.505178	−	0.874994i	0.122524	−	0.212217i	0.920762	+	0.390124i	$0.127568\pi$
$18$	0.214679	+	2.11626i	0.0506004	+	0.498808i
$19$	2.97393	−	5.15100i	0.682266	−	1.18172i	−0.292021	−	0.956412i	$-0.594328\pi$
$19$	2.97393	−	5.15100i	0.682266	−	1.18172i	0.974288	−	0.225308i	$-0.0723389\pi$
$20$	0.631801	−	1.89758i	0.141275	−	0.424313i
$21$	−5.56512			−1.21441
$22$	1.47589	+	0.663526i	0.314661	+	0.141464i
$23$	−0.586182	−	1.01530i	−0.122227	−	0.211704i	0.798418	−	0.602103i	$-0.205670\pi$
$23$	−0.586182	−	1.01530i	−0.122227	−	0.211704i	−0.920646	+	0.390399i	$0.872337\pi$
$24$	2.54549	+	2.34257i	0.519597	+	0.478175i
$25$	1.00000			0.200000
$26$	2.76621	+	4.28347i	0.542499	+	0.840057i
$27$		−	5.50883i		−	1.06017i
$28$	6.80677	−	6.04011i	1.28636	−	1.14147i
$29$	3.04627	−	1.75877i	0.565679	−	0.326595i	−0.189743	−	0.981834i	$-0.560765\pi$
$29$	3.04627	−	1.75877i	0.565679	−	0.326595i	0.755422	+	0.655239i	$0.227432\pi$
$30$	−0.709244	+	1.57758i	−0.129490	+	0.288026i
$31$		−	0.814108i		−	0.146218i	−0.997324	−	0.0731090i	$-0.976708\pi$
$31$		−	0.814108i		−	0.146218i	0.997324	−	0.0731090i	$-0.0232921\pi$
$32$	−5.65593	−	0.102470i	−0.999836	−	0.0181144i
$33$	−1.21198	−	0.699734i	−0.210978	−	0.121808i
$34$	−0.144207	−	1.42156i	−0.0247313	−	0.243796i
$35$	3.94053	+	2.27507i	0.666072	+	0.384557i
$36$	1.99663	+	2.25006i	0.332772	+	0.375010i
$37$	3.97121	+	6.87834i	0.652863	+	1.13079i	0.982425	+	0.186658i	$0.0597655\pi$
$37$	3.97121	+	6.87834i	0.652863	+	1.13079i	−0.329562	+	0.944134i	$0.606901\pi$
$38$	−0.848931	−	8.36860i	−0.137715	−	1.35757i
$39$	−2.00624	−	3.92704i	−0.321255	−	0.628830i
$40$	−0.844743	−	2.69934i	−0.133566	−	0.426802i
$41$	−7.63515	+	4.40815i	−1.19241	+	0.688438i	−0.958852	−	0.283905i	$-0.908370\pi$
$41$	−7.63515	+	4.40815i	−1.19241	+	0.688438i	−0.233557	+	0.972343i	$0.575037\pi$
$42$	−6.38390	+	4.60293i	−0.985058	+	0.710248i
$43$	1.17648	+	0.679243i	0.179412	+	0.103584i	0.587016	−	0.809575i	$-0.300302\pi$
$43$	1.17648	+	0.679243i	0.179412	+	0.103584i	−0.407604	+	0.913159i	$0.633636\pi$
$44$	2.24184	−	0.459564i	0.337970	−	0.0692819i
$45$	−0.752053	+	1.30259i	−0.112109	+	0.194179i
$46$	−1.51218	−	0.679841i	−0.222959	−	0.100237i
$47$		−	9.05737i		−	1.32115i	−0.750759	−	0.660576i	$-0.770312\pi$
$47$		−	9.05737i		−	1.32115i	0.750759	−	0.660576i	$-0.229688\pi$
$48$	4.85755	+	0.581837i	0.701127	+	0.0839810i
$49$	6.85187	+	11.8678i	0.978838	+	1.69540i
$50$	1.14713	−	0.827103i	0.162228	−	0.116970i
$51$			1.23573i			0.173037i
$52$	6.71606	+	2.62574i	0.931350	+	0.364124i
$53$		−	8.10029i		−	1.11266i	−0.830961	−	0.556330i	$-0.812209\pi$
$53$		−	8.10029i		−	1.11266i	0.830961	−	0.556330i	$-0.187791\pi$
$54$	−4.55637	−	6.31932i	−0.620043	−	0.859951i
$55$	0.572114	+	0.990930i	0.0771438	+	0.133617i
$56$	2.81243	−	12.5587i	0.375827	−	1.67822i
$57$			7.27464i			0.963549i
$58$	2.03978	−	4.53711i	0.267836	−	0.595752i
$59$	−3.14969	+	5.45542i	−0.410055	+	0.710235i	−0.994895	−	0.100913i	$-0.967824\pi$
$59$	−3.14969	+	5.45542i	−0.410055	+	0.710235i	0.584841	+	0.811148i	$0.301157\pi$
$60$	0.491229	+	2.39630i	0.0634174	+	0.309362i
$61$	−10.5468	−	6.08920i	−1.35038	−	0.779643i	−0.362078	−	0.932148i	$-0.617933\pi$
$61$	−10.5468	−	6.08920i	−1.35038	−	0.779643i	−0.988303	+	0.152505i	$0.951266\pi$
$62$	−0.673351	−	0.933885i	−0.0855157	−	0.118604i
$63$	−5.92698	+	3.42194i	−0.746729	+	0.431124i
$64$	−6.57282	+	4.56049i	−0.821602	+	0.570061i
$65$	−0.184836	+	3.60081i	−0.0229261	+	0.446626i
$66$	−1.96904	+	0.199745i	−0.242372	+	0.0245869i
$67$	−5.23119	−	9.06069i	−0.639092	−	1.10694i	−0.985632	−	0.168905i	$-0.945977\pi$
$67$	−5.23119	−	9.06069i	−0.639092	−	1.10694i	0.346540	−	0.938035i	$-0.387356\pi$
$68$	−1.34120	−	1.51144i	−0.162645	−	0.183289i
$69$	1.24178	+	0.716940i	0.149492	+	0.0863094i
$70$	6.40201	−	0.649436i	0.765186	−	0.0776224i
$71$	−5.04169	−	2.91082i	−0.598339	−	0.345451i	0.170049	−	0.985436i	$-0.445607\pi$
$71$	−5.04169	−	2.91082i	−0.598339	−	0.345451i	−0.768388	+	0.639985i	$0.778941\pi$
$72$	4.15143	+	0.929685i	0.489250	+	0.109564i
$73$			14.5790i			1.70635i	0.521628	+	0.853173i	$0.325325\pi$
$73$			14.5790i			1.70635i	−0.521628	+	0.853173i	$0.674675\pi$
$74$	10.2446	+	4.60573i	1.19091	+	0.535405i
$75$	−1.05921	+	0.611534i	−0.122307	+	0.0706139i
$76$	−7.89552	−	8.89769i	−0.905679	−	1.02063i
$77$			5.20639i			0.593323i
$78$	−5.54948	−	2.84545i	−0.628355	−	0.322184i
$79$	−5.60175			−0.630246			−0.315123	−	0.949051i	$-0.602046\pi$
$79$	−5.60175			−0.630246			−0.315123	+	0.949051i	$0.602046\pi$
$80$	−3.20166	−	2.39779i	−0.357956	−	0.268081i
$81$	1.11268	+	1.92721i	0.123631	+	0.214135i
$82$	−5.11248	+	11.3718i	−0.564579	+	1.25580i
$83$	−2.31651			−0.254270			−0.127135	−	0.991885i	$-0.540578\pi$
$83$	−2.31651			−0.254270			−0.127135	+	0.991885i	$0.540578\pi$
$84$	−3.51605	+	10.5603i	−0.383632	+	1.15222i
$85$	0.505178	−	0.874994i	0.0547943	−	0.0949064i
$86$	1.91138	−	0.193895i	0.206109	−	0.0209082i
$87$	−2.15109	+	3.72580i	−0.230621	+	0.399448i
$88$	2.19156	−	2.38141i	0.233622	−	0.253859i
$89$	−12.1107	+	6.99213i	−1.28373	+	0.741164i	−0.977529	−	0.210802i	$-0.932393\pi$
$89$	−12.1107	+	6.99213i	−1.28373	+	0.741164i	−0.306205	+	0.951966i	$0.599059\pi$
$90$	0.214679	+	2.11626i	0.0226292	+	0.223074i
$91$	−8.92044	+	13.7686i	−0.935116	+	1.44334i
$92$	−2.29696	+	0.470865i	−0.239475	+	0.0490910i
$93$	0.497854	+	0.862309i	0.0516251	+	0.0894173i
$94$	−7.49138	−	10.3899i	−0.772677	−	1.07164i
$95$	2.97393	−	5.15100i	0.305119	−	0.528481i
$96$	6.05347	−	3.35025i	0.617829	−	0.341934i
$97$	4.36544	+	2.52039i	0.443243	+	0.255906i	0.704972	−	0.709235i	$-0.250959\pi$
$97$	4.36544	+	2.52039i	0.443243	+	0.255906i	−0.261729	+	0.965141i	$0.584293\pi$
$98$	17.6758	+	7.94665i	1.78553	+	0.802733i
$99$	−1.72104			−0.172971
$100$	0.631801	−	1.89758i	0.0631801	−	0.189758i
$101$	−6.95428	+	4.01506i	−0.691977	+	0.399513i	−0.804352	−	0.594153i	$-0.797487\pi$
$101$	−6.95428	+	4.01506i	−0.691977	+	0.399513i	0.112375	+	0.993666i	$0.464154\pi$
$102$	1.02208	+	1.41754i	0.101201	+	0.140358i
$103$	6.09755			0.600809			0.300405	−	0.953812i	$-0.402878\pi$
$103$	6.09755			0.600809			0.300405	+	0.953812i	$0.402878\pi$
$104$	9.87593	−	2.54282i	0.968415	−	0.249344i
$105$	−5.56512			−0.543101
$106$	−6.69977	−	9.29206i	−0.650740	−	0.902525i
$107$	8.69066	−	5.01756i	0.840158	−	0.485065i	−0.0171600	−	0.999853i	$-0.505462\pi$
$107$	8.69066	−	5.01756i	0.840158	−	0.485065i	0.857318	+	0.514787i	$0.172129\pi$
$108$	−10.4535	−	3.48048i	−1.00589	−	0.334909i
$109$	−8.28364			−0.793429			−0.396714	−	0.917942i	$-0.629850\pi$
$109$	−8.28364			−0.793429			−0.396714	+	0.917942i	$0.629850\pi$
$110$	1.47589	+	0.663526i	0.140721	+	0.0632647i
$111$	−8.41267	−	4.85706i	−0.798495	−	0.461012i
$112$	−7.16109	−	16.7326i	−0.676660	−	1.58108i
$113$	5.45926	−	9.45571i	0.513564	−	0.889519i	−0.486312	−	0.873785i	$-0.661658\pi$
$113$	5.45926	−	9.45571i	0.513564	−	0.889519i	0.999876	−	0.0157336i	$-0.00500837\pi$
$114$	6.01687	+	8.34493i	0.563532	+	0.781574i
$115$	−0.586182	−	1.01530i	−0.0546617	−	0.0946769i
$116$	−1.41277	−	6.89175i	−0.131173	−	0.639883i
$117$	−4.55138	−	2.94876i	−0.420776	−	0.272613i
$118$	0.899103	+	8.86318i	0.0827692	+	0.815922i
$119$	3.98134	−	2.29863i	0.364969	−	0.210715i
$120$	2.54549	+	2.34257i	0.232371	+	0.213846i
$121$	4.84537	−	8.39243i	0.440488	−	0.762948i
$122$	−17.1349	+	1.73821i	−1.55132	+	0.157370i
$123$	5.39147	−	9.33830i	0.486133	−	0.842006i
$124$	−1.54484	−	0.514354i	−0.138731	−	0.0461903i
$125$	1.00000			0.0894427
$126$	−3.96870	+	8.82762i	−0.353559	+	0.786427i
$127$	−4.34447	−	7.52484i	−0.385509	−	0.667722i	0.606330	−	0.795213i	$-0.292641\pi$
$127$	−4.34447	−	7.52484i	−0.385509	−	0.667722i	−0.991840	+	0.127491i	$0.959308\pi$
$128$	−3.76786	+	10.6679i	−0.333035	+	0.942914i
$129$	−1.66152			−0.146289
$130$	2.76621	+	4.28347i	0.242613	+	0.375685i
$131$			18.5123i			1.61743i	0.588201	+	0.808715i	$0.299836\pi$
$131$			18.5123i			1.61743i	−0.588201	+	0.808715i	$0.700164\pi$
$132$	−2.09353	+	1.85773i	−0.182219	+	0.161695i
$133$	23.4377	−	13.5318i	2.03231	−	1.17335i
$134$	−13.4950	−	6.06703i	−1.16579	−	0.524111i
$135$		−	5.50883i		−	0.474124i
$136$	−2.78865	−	0.624500i	−0.239125	−	0.0535504i
$137$	−1.42212	−	0.821060i	−0.121500	−	0.0701479i	0.438018	−	0.898966i	$-0.355680\pi$
$137$	−1.42212	−	0.821060i	−0.121500	−	0.0701479i	−0.559518	+	0.828818i	$0.689014\pi$
$138$	2.01746	−	0.204656i	0.171738	−	0.0174215i
$139$	14.6180	+	8.43972i	1.23988	+	0.715848i	0.969070	−	0.246784i	$-0.0793739\pi$
$139$	14.6180	+	8.43972i	1.23988	+	0.715848i	0.270814	+	0.962632i	$0.412707\pi$
$140$	6.80677	−	6.04011i	0.575277	−	0.510482i
$141$	5.53889	+	9.59363i	0.466458	+	0.807930i
$142$	−8.19101	+	0.830917i	−0.687375	+	0.0697290i
$143$	−3.67390	+	1.87691i	−0.307227	+	0.156955i
$144$	5.53116	−	2.36719i	0.460930	−	0.197266i
$145$	3.04627	−	1.75877i	0.252979	−	0.146058i
$146$	12.0584	+	16.7240i	0.997957	+	1.38409i
$147$	−14.5151	−	8.38030i	−1.19719	−	0.691195i
$148$	15.5612	−	3.18997i	1.27913	−	0.262214i
$149$	7.39536	−	12.8091i	0.605852	−	1.04937i	−0.386065	−	0.922472i	$-0.626166\pi$
$149$	7.39536	−	12.8091i	0.605852	−	1.04937i	0.991916	−	0.126894i	$-0.0405008\pi$
$150$	−0.709244	+	1.57758i	−0.0579095	+	0.128809i
$151$			7.24626i			0.589692i	0.955545	+	0.294846i	$0.0952683\pi$
$151$			7.24626i			0.589692i	−0.955545	+	0.294846i	$0.904732\pi$
$152$	−16.4165	−	3.67636i	−1.33155	−	0.298193i
$153$	0.759841	+	1.31608i	0.0614295	+	0.106399i
$154$	4.30622	+	5.97239i	0.347005	+	0.481269i
$155$		−	0.814108i		−	0.0653907i
$156$	−8.71943	+	1.32590i	−0.698113	+	0.106157i
$157$		−	8.00548i		−	0.638907i	−0.947602	−	0.319453i	$-0.896501\pi$
$157$		−	8.00548i		−	0.638907i	0.947602	−	0.319453i	$-0.103499\pi$
$158$	−6.42592	+	4.63323i	−0.511219	+	0.368600i
$159$	4.95360	+	8.57989i	0.392846	+	0.680430i
$160$	−5.65593	−	0.102470i	−0.447140	−	0.00810099i
$161$		−	5.33441i		−	0.420411i
$162$	2.87038	+	1.29046i	0.225519	+	0.101388i
$163$	1.57351	−	2.72541i	0.123247	−	0.213470i	−0.797799	−	0.602923i	$-0.794003\pi$
$163$	1.57351	−	2.72541i	0.123247	−	0.213470i	0.921046	+	0.389453i	$0.127336\pi$
$164$	3.54096	+	17.2734i	0.276502	+	1.34883i
$165$	−1.21198	−	0.699734i	−0.0943521	−	0.0544742i
$166$	−2.65733	+	1.91599i	−0.206249	+	0.148710i
$167$	9.82233	−	5.67093i	0.760075	−	0.438829i	−0.0692478	−	0.997599i	$-0.522060\pi$
$167$	9.82233	−	5.67093i	0.760075	−	0.438829i	0.829323	+	0.558770i	$0.188727\pi$
$168$	4.70110	+	15.0221i	0.362698	+	1.15898i
$169$	−12.9317	−	1.33112i	−0.994744	−	0.102394i
$170$	−0.144207	−	1.42156i	−0.0110602	−	0.109029i
$171$	4.47310	+	7.74764i	0.342067	+	0.592477i
$172$	2.03222	−	1.80333i	0.154956	−	0.137503i
$173$	−17.0348	−	9.83505i	−1.29513	−	0.747745i	−0.315573	−	0.948901i	$-0.602197\pi$
$173$	−17.0348	−	9.83505i	−1.29513	−	0.747745i	−0.979559	+	0.201157i	$0.935530\pi$
$174$	0.614046	+	6.05314i	0.0465507	+	0.458887i
$175$	3.94053	+	2.27507i	0.297876	+	0.171979i
$176$	0.544332	−	4.54443i	0.0410305	−	0.342549i
$177$		−	7.70457i		−	0.579111i
$178$	−8.10932	+	18.0377i	−0.607819	+	1.35198i
$179$	−2.69851	+	1.55798i	−0.201696	+	0.116449i	−0.597446	−	0.801909i	$-0.703818\pi$
$179$	−2.69851	+	1.55798i	−0.201696	+	0.116449i	0.395750	+	0.918358i	$0.370485\pi$
$180$	1.99663	+	2.25006i	0.148820	+	0.167710i
$181$			24.7399i			1.83891i	0.393200	+	0.919453i	$0.371368\pi$
$181$			24.7399i			1.83891i	−0.393200	+	0.919453i	$0.628632\pi$
$182$	1.15517	+	23.1725i	0.0856271	+	1.71766i
$183$	14.8950			1.10107
$184$	−2.24545	+	2.43997i	−0.165537	+	0.179877i
$185$	3.97121	+	6.87834i	0.291969	+	0.505705i
$186$	1.28432	+	0.577401i	0.0941710	+	0.0423371i
$187$	1.15608			0.0845408
$188$	−17.1871	−	5.72245i	−1.25350	−	0.417353i
$189$	12.5330	−	21.7077i	0.911638	−	1.57900i
$190$	−0.848931	−	8.36860i	−0.0615880	−	0.607122i
$191$	1.36233	−	2.35962i	0.0985744	−	0.170736i	−0.812520	−	0.582933i	$-0.801905\pi$
$191$	1.36233	−	2.35962i	0.0985744	−	0.170736i	0.911095	+	0.412197i	$0.135238\pi$
$192$	4.17309	−	8.85001i	0.301167	−	0.638694i
$193$	3.88542	−	2.24325i	0.279679	−	0.161472i	−0.353599	−	0.935397i	$-0.615042\pi$
$193$	3.88542	−	2.24325i	0.279679	−	0.161472i	0.633278	+	0.773924i	$0.281709\pi$
$194$	7.09233	−	0.719464i	0.509200	−	0.0516545i
$195$	−2.00624	−	3.92704i	−0.143670	−	0.281221i
$196$	26.8491	−	5.50393i	1.91780	−	0.393138i
$197$	11.1395	+	19.2942i	0.793658	+	1.37466i	0.923688	+	0.383146i	$0.125159\pi$
$197$	11.1395	+	19.2942i	0.793658	+	1.37466i	−0.130029	+	0.991510i	$0.541507\pi$
$198$	−1.97425	+	1.42348i	−0.140304	+	0.101162i
$199$	11.7148	−	20.2907i	0.830443	−	1.43837i	−0.0672446	−	0.997737i	$-0.521421\pi$
$199$	11.7148	−	20.2907i	0.830443	−	1.43837i	0.897687	−	0.440633i	$-0.145246\pi$
$200$	−0.844743	−	2.69934i	−0.0597323	−	0.190872i
$201$	11.0818	+	6.39810i	0.781653	+	0.451287i
$202$	−4.65658	+	10.3577i	−0.327636	+	0.728765i
$203$	16.0053			1.12335
$204$	2.34491	+	0.780738i	0.164177	+	0.0546626i
$205$	−7.63515	+	4.40815i	−0.533262	+	0.307879i
$206$	6.99466	−	5.04330i	0.487341	−	0.351383i
$207$	1.76336			0.122562
$208$	9.22577	−	11.0854i	0.639692	−	0.768631i
$209$	6.80571			0.470761
$210$	−6.38390	+	4.60293i	−0.440531	+	0.317633i
$211$	−10.7239	+	6.19145i	−0.738264	+	0.426237i	−0.821438	−	0.570298i	$-0.806828\pi$
$211$	−10.7239	+	6.19145i	−0.738264	+	0.426237i	0.0831739	+	0.996535i	$0.473494\pi$
$212$	−15.3710	−	5.11777i	−1.05568	−	0.351490i
$213$	7.12027			0.487873
$214$	5.81926	−	12.9438i	0.397796	−	0.884823i
$215$	1.17648	+	0.679243i	0.0802355	+	0.0463240i
$216$	−14.8702	+	4.65354i	−1.01179	+	0.316633i
$217$	1.85215	−	3.20802i	0.125732	−	0.217774i
$218$	−9.50238	+	6.85142i	−0.643583	+	0.464037i
$219$	−8.91557	−	15.4422i	−0.602458	−	1.04349i
$220$	2.24184	−	0.459564i	0.151145	−	0.0309838i
$221$	3.05731	+	1.98078i	0.205657	+	0.133242i
$222$	−13.6677	+	1.38649i	−0.917315	+	0.0930548i
$223$	−19.5063	+	11.2620i	−1.30624	+	0.754159i	−0.981467	−	0.191632i	$-0.938622\pi$
$223$	−19.5063	+	11.2620i	−1.30624	+	0.754159i	−0.324775	+	0.945791i	$0.605289\pi$
$224$	−22.0542	−	13.2714i	−1.47356	−	0.886733i
$225$	−0.752053	+	1.30259i	−0.0501368	+	0.0868395i
$226$	−1.55839	−	15.3623i	−0.103662	−	1.02188i
$227$	8.13510	−	14.0904i	0.539946	−	0.935214i	−0.458960	−	0.888457i	$-0.651778\pi$
$227$	8.13510	−	14.0904i	0.539946	−	0.935214i	0.998906	−	0.0467570i	$-0.0148886\pi$
$228$	13.8042	+	4.59612i	0.914208	+	0.304385i
$229$	−5.90333			−0.390103			−0.195051	−	0.980793i	$-0.562487\pi$
$229$	−5.90333			−0.390103			−0.195051	+	0.980793i	$0.562487\pi$
$230$	−1.51218	−	0.679841i	−0.0997102	−	0.0448274i
$231$	−3.18389	−	5.51465i	−0.209484	−	0.362837i
$232$	−7.32082	−	6.73721i	−0.480635	−	0.442319i
$233$	−0.205797			−0.0134822			−0.00674110	−	0.999977i	$-0.502146\pi$
$233$	−0.205797			−0.0134822			−0.00674110	+	0.999977i	$0.502146\pi$
$234$	−7.65995	+	0.381857i	−0.500747	+	0.0249628i
$235$		−	9.05737i		−	0.590837i
$236$	8.36215	+	9.42354i	0.544330	+	0.613420i
$237$	5.93342	−	3.42566i	0.385417	−	0.222521i
$238$	2.66590	−	5.92980i	0.172805	−	0.384372i
$239$		−	22.3457i		−	1.44542i	−0.691150	−	0.722711i	$-0.742896\pi$
$239$		−	22.3457i		−	1.44542i	0.691150	−	0.722711i	$-0.257104\pi$
$240$	4.85755	+	0.581837i	0.313553	+	0.0375574i
$241$	−5.21726	−	3.01218i	−0.336073	−	0.194032i	0.322461	−	0.946583i	$-0.395490\pi$
$241$	−5.21726	−	3.01218i	−0.336073	−	0.194032i	−0.658534	+	0.752551i	$0.728823\pi$
$242$	−1.38315	−	13.6348i	−0.0889122	−	0.876478i
$243$	11.9552	+	6.90236i	0.766929	+	0.442787i
$244$	−18.2183	+	16.1663i	−1.16630	+	1.03494i
$245$	6.85187	+	11.8678i	0.437750	+	0.758205i
$246$	−1.53904	−	15.1715i	−0.0981254	−	0.967301i
$247$	17.9981	+	11.6606i	1.14519	+	0.741949i
$248$	−2.19755	+	0.687712i	−0.139545	+	0.0436697i
$249$	2.45366	−	1.41662i	0.155495	−	0.0897749i
$250$	1.14713	−	0.827103i	0.0725507	−	0.0523106i
$251$	−18.0416	−	10.4163i	−1.13878	−	0.657472i	−0.192648	−	0.981268i	$-0.561708\pi$
$251$	−18.0416	−	10.4163i	−1.13878	−	0.657472i	−0.946127	+	0.323796i	$0.895041\pi$
$252$	2.74876	+	13.4089i	0.173155	+	0.844683i
$253$	0.670726	−	1.16173i	0.0421682	−	0.0730374i
$254$	−11.2075	−	5.03863i	−0.703220	−	0.316151i
$255$			1.23573i			0.0773847i
$256$	4.50120	+	15.3538i	0.281325	+	0.959613i
$257$	−0.0721456	−	0.124960i	−0.00450032	−	0.00779478i	0.863766	−	0.503892i	$-0.168099\pi$
$257$	−0.0721456	−	0.124960i	−0.00450032	−	0.00779478i	−0.868267	+	0.496098i	$0.834766\pi$
$258$	−1.90597	+	1.37425i	−0.118661	+	0.0855570i
$259$			36.1391i			2.24557i
$260$	6.71606	+	2.62574i	0.416513	+	0.162841i
$261$			5.29074i			0.327489i
$262$	15.3116	+	21.2360i	0.945954	+	1.31196i
$263$	−12.7246	−	22.0397i	−0.784632	−	1.35902i	−0.929218	−	0.369531i	$-0.879518\pi$
$263$	−12.7246	−	22.0397i	−0.784632	−	1.35902i	0.144586	−	0.989492i	$-0.453815\pi$
$264$	−0.865010	+	3.86262i	−0.0532377	+	0.237728i
$265$		−	8.10029i		−	0.497597i
$266$	15.6939	−	34.9081i	0.962254	−	2.14035i
$267$	8.55184	−	14.8122i	0.523364	−	0.906494i
$268$	−20.4985	+	4.20208i	−1.25215	+	0.256683i
$269$	−19.4744	−	11.2436i	−1.18738	−	0.685533i	−0.229668	−	0.973269i	$-0.573764\pi$
$269$	−19.4744	−	11.2436i	−1.18738	−	0.685533i	−0.957710	+	0.287736i	$0.907097\pi$
$270$	−4.55637	−	6.31932i	−0.277292	−	0.384582i
$271$	10.8229	−	6.24860i	0.657444	−	0.379575i	−0.133859	−	0.991000i	$-0.542737\pi$
$271$	10.8229	−	6.24860i	0.657444	−	0.379575i	0.791302	+	0.611425i	$0.209403\pi$
$272$	−3.71546	+	1.59012i	−0.225283	+	0.0964151i
$273$	1.02864	−	20.0390i	0.0622559	−	1.21281i
$274$	−2.31045	+	0.234378i	−0.139579	+	0.0141593i
$275$	0.572114	+	0.990930i	0.0344998	+	0.0597554i
$276$	2.14501	−	1.90341i	0.129114	−	0.114572i
$277$	−12.5777	−	7.26175i	−0.755722	−	0.436316i	0.0720355	−	0.997402i	$-0.477051\pi$
$277$	−12.5777	−	7.26175i	−0.755722	−	0.436316i	−0.827758	+	0.561086i	$0.810384\pi$
$278$	23.7492	−	2.40918i	1.42438	−	0.144493i
$279$	1.06045	+	0.612252i	0.0634875	+	0.0366546i
$280$	2.81243	−	12.5587i	0.168075	−	0.750524i
$281$		−	9.66247i		−	0.576414i	−0.957568	−	0.288207i	$-0.906941\pi$
$281$		−	9.66247i		−	0.576414i	0.957568	−	0.288207i	$-0.0930592\pi$
$282$	14.2887	+	6.42388i	0.850882	+	0.382537i
$283$	−12.9189	+	7.45873i	−0.767949	+	0.443376i	−0.832143	−	0.554562i	$-0.812886\pi$
$283$	−12.9189	+	7.45873i	−0.767949	+	0.443376i	0.0641934	+	0.997937i	$0.479553\pi$
$284$	−8.70888	+	7.72798i	−0.516777	+	0.458571i
$285$			7.27464i			0.430912i
$286$	−2.66203	+	5.19175i	−0.157409	+	0.306995i
$287$	−40.1154			−2.36794
$288$	4.38703	−	7.29031i	0.258508	−	0.429585i
$289$	7.98959	+	13.8384i	0.469976	+	0.814022i
$290$	2.03978	−	4.53711i	0.119780	−	0.266428i
$291$	−6.16521			−0.361411
$292$	27.6649	+	9.21104i	1.61897	+	0.539035i
$293$	−0.439423	+	0.761103i	−0.0256714	+	0.0444641i	−0.878576	−	0.477603i	$-0.841506\pi$
$293$	−0.439423	+	0.761103i	−0.0256714	+	0.0444641i	0.852904	+	0.522067i	$0.174839\pi$
$294$	−23.5820	+	2.39222i	−1.37533	+	0.139517i
$295$	−3.14969	+	5.45542i	−0.183382	+	0.317627i
$296$	15.2123	−	16.5300i	0.884196	−	0.960790i
$297$	5.45886	−	3.15168i	0.316755	−	0.182879i
$298$	−2.11106	−	20.8104i	−0.122291	−	1.20552i
$299$	3.76424	−	1.92307i	0.217692	−	0.111214i
$300$	0.491229	+	2.39630i	0.0283611	+	0.138351i
$301$	3.09065	+	5.35316i	0.178142	+	0.308551i
$302$	5.99340	+	8.31238i	0.344882	+	0.478323i
$303$	4.91069	−	8.50556i	0.282112	−	0.488632i
$304$	−21.8725	+	9.36086i	−1.25447	+	0.536882i
$305$	−10.5468	−	6.08920i	−0.603909	−	0.348667i
$306$	1.96017	+	0.881248i	0.112055	+	0.0503776i
$307$	18.9672			1.08251			0.541257	−	0.840857i	$-0.317948\pi$
$307$	18.9672			1.08251			0.541257	+	0.840857i	$0.317948\pi$
$308$	9.87957	+	3.28940i	0.562941	+	0.187431i
$309$	−6.45857	+	3.72886i	−0.367415	+	0.212127i
$310$	−0.673351	−	0.933885i	−0.0382438	−	0.0530411i
$311$	7.42874			0.421245			0.210623	−	0.977567i	$-0.432451\pi$
$311$	7.42874			0.421245			0.210623	+	0.977567i	$0.432451\pi$
$312$	−8.90564	+	8.73285i	−0.504183	+	0.494400i
$313$	18.3767			1.03871			0.519356	−	0.854558i	$-0.326172\pi$
$313$	18.3767			1.03871			0.519356	+	0.854558i	$0.326172\pi$
$314$	−6.62136	−	9.18330i	−0.373665	−	0.518244i
$315$	−5.92698	+	3.42194i	−0.333947	+	0.192805i
$316$	−3.53919	+	10.6298i	−0.199095	+	0.597973i
$317$	9.12947			0.512762			0.256381	−	0.966576i	$-0.417470\pi$
$317$	9.12947			0.512762			0.256381	+	0.966576i	$0.417470\pi$
$318$	12.7789	+	5.74508i	0.716603	+	0.322168i
$319$	3.48563	+	2.01243i	0.195158	+	0.112674i
$320$	−6.57282	+	4.56049i	−0.367432	+	0.254939i
$321$	−6.13681	+	10.6293i	−0.342523	+	0.593268i
$322$	−4.41211	−	6.11925i	−0.245877	−	0.341012i
$323$	−3.00473	−	5.20434i	−0.167188	−	0.289577i
$324$	4.36004	−	0.893784i	0.242224	−	0.0496547i
$325$	−0.184836	+	3.60081i	−0.0102529	+	0.199737i
$326$	−0.449172	−	4.42785i	−0.0248773	−	0.245236i
$327$	8.77409	−	5.06573i	0.485208	−	0.280135i
$328$	18.3488	+	16.8861i	1.01314	+	0.932377i
$329$	20.6061	−	35.6909i	1.13605	−	1.96770i
$330$	−1.96904	+	0.199745i	−0.108392	+	0.0109956i
$331$	−0.660141	+	1.14340i	−0.0362846	+	0.0628468i	−0.883597	−	0.468247i	$-0.844886\pi$
$331$	−0.660141	+	1.14340i	−0.0362846	+	0.0628468i	0.847313	+	0.531094i	$0.178219\pi$
$332$	−1.46357	+	4.39577i	−0.0803239	+	0.241249i
$333$	−11.9462			−0.654649
$334$	6.57702	−	14.6294i	0.359879	−	0.800483i
$335$	−5.23119	−	9.06069i	−0.285811	−	0.495038i
$336$	17.8176	+	13.3440i	0.972031	+	0.727975i
$337$	−8.88371			−0.483926			−0.241963	−	0.970285i	$-0.577791\pi$
$337$	−8.88371			−0.483926			−0.241963	+	0.970285i	$0.577791\pi$
$338$	−15.9352	+	9.16886i	−0.866763	+	0.498720i
$339$			13.3541i			0.725294i
$340$	−1.34120	−	1.51144i	−0.0727370	−	0.0819693i
$341$	0.806724	−	0.465762i	0.0436866	−	0.0252224i
$342$	11.5393	+	5.18781i	0.623975	+	0.280525i
$343$			30.5029i			1.64700i
$344$	0.839678	−	3.74951i	0.0452724	−	0.202160i
$345$	1.24178	+	0.716940i	0.0668550	+	0.0385988i
$346$	−27.6757	+	2.80749i	−1.48785	+	0.150932i
$347$	11.9243	+	6.88451i	0.640131	+	0.369580i	0.784665	−	0.619920i	$-0.212835\pi$
$347$	11.9243	+	6.88451i	0.640131	+	0.369580i	−0.144534	+	0.989500i	$0.546168\pi$
$348$	5.71096	+	6.43584i	0.306139	+	0.344997i
$349$	−3.90021	−	6.75535i	−0.208773	−	0.361606i	0.742555	−	0.669785i	$-0.233614\pi$
$349$	−3.90021	−	6.75535i	−0.208773	−	0.361606i	−0.951328	+	0.308179i	$0.900280\pi$
$350$	6.40201	−	0.649436i	0.342202	−	0.0347138i
$351$	19.8362	+	1.01823i	1.05878	+	0.0543491i
$352$	−3.13429	−	5.66325i	−0.167058	−	0.301852i
$353$	11.9984	−	6.92729i	0.638611	−	0.368702i	−0.145468	−	0.989363i	$-0.546469\pi$
$353$	11.9984	−	6.92729i	0.638611	−	0.368702i	0.784079	+	0.620660i	$0.213135\pi$
$354$	−6.37247	−	8.83812i	−0.338693	−	0.469741i
$355$	−5.04169	−	2.91082i	−0.267585	−	0.154490i
$356$	5.61659	+	27.3987i	0.297679	+	1.45213i
$357$	−2.81138	+	4.86945i	−0.148794	+	0.257719i
$358$	−1.80692	+	4.01915i	−0.0954986	+	0.212419i
$359$		−	8.80624i		−	0.464775i	−0.972623	−	0.232388i	$-0.925346\pi$
$359$		−	8.80624i		−	0.464775i	0.972623	−	0.232388i	$-0.0746538\pi$
$360$	4.15143	+	0.929685i	0.218799	+	0.0489987i
$361$	−8.18852	−	14.1829i	−0.430975	−	0.746470i
$362$	20.4625	+	28.3799i	1.07548	+	1.49161i
$363$			11.8524i			0.622092i
$364$	20.4911	+	25.6263i	1.07403	+	1.34318i
$365$			14.5790i			0.763101i
$366$	17.0865	−	12.3197i	0.893124	−	0.643962i
$367$	10.6973	+	18.5283i	0.558397	+	0.967172i	0.997631	+	0.0687988i	$0.0219166\pi$
$367$	10.6973	+	18.5283i	0.558397	+	0.967172i	−0.439234	+	0.898373i	$0.644750\pi$
$368$	−0.557716	+	4.65617i	−0.0290730	+	0.242720i
$369$		−	13.2607i		−	0.690322i
$370$	10.2446	+	4.60573i	0.532590	+	0.239440i
$371$	18.4287	−	31.9195i	0.956771	−	1.65718i
$372$	1.95085	−	0.399914i	0.101147	−	0.0207346i
$373$	24.6923	+	14.2561i	1.27852	+	0.738154i	0.976576	−	0.215171i	$-0.0690309\pi$
$373$	24.6923	+	14.2561i	1.27852	+	0.738154i	0.301945	+	0.953325i	$0.402364\pi$
$374$	1.32617	−	0.956196i	0.0685745	−	0.0494437i
$375$	−1.05921	+	0.611534i	−0.0546973	+	0.0315795i
$376$	−24.4489	+	7.65115i	−1.26085	+	0.394578i
$377$	5.76992	+	11.2941i	0.297166	+	0.581678i
$378$	−3.57763	−	35.2675i	−0.184013	−	1.81397i
$379$	1.37039	+	2.37358i	0.0703921	+	0.121923i	0.899073	−	0.437798i	$-0.144242\pi$
$379$	1.37039	+	2.37358i	0.0703921	+	0.121923i	−0.828681	+	0.559721i	$0.810908\pi$
$380$	−7.89552	−	8.89769i	−0.405032	−	0.456442i
$381$	9.20339	+	5.31358i	0.471504	+	0.272223i
$382$	−0.388886	−	3.83356i	−0.0198972	−	0.196142i
$383$	26.2337	+	15.1460i	1.34048	+	0.773926i	0.986878	−	0.161470i	$-0.0516236\pi$
$383$	26.2337	+	15.1460i	1.34048	+	0.773926i	0.353601	+	0.935396i	$0.384957\pi$
$384$	−2.53281	−	13.6037i	−0.129252	−	0.694209i
$385$			5.20639i			0.265342i
$386$	2.60167	−	5.78693i	0.132422	−	0.294547i
$387$	−1.76955	+	1.02165i	−0.0899515	+	0.0519335i
$388$	7.54073	−	6.69141i	0.382823	−	0.339705i
$389$		−	2.87672i		−	0.145856i	−0.997337	−	0.0729278i	$-0.976766\pi$
$389$		−	2.87672i		−	0.145856i	0.997337	−	0.0729278i	$-0.0232343\pi$
$390$	−5.54948	−	2.84545i	−0.281009	−	0.144085i
$391$	−1.18450			−0.0599030
$392$	26.2471	−	28.5207i	1.32568	−	1.44051i
$393$	−11.3209	−	19.6084i	−0.571065	−	0.989113i
$394$	28.7368	+	12.9194i	1.44774	+	0.650869i
$395$	−5.60175			−0.281855
$396$	−1.08735	+	3.26582i	−0.0546416	+	0.164113i
$397$	1.96447	−	3.40257i	0.0985941	−	0.170770i	−0.812509	−	0.582949i	$-0.801899\pi$
$397$	1.96447	−	3.40257i	0.0985941	−	0.170770i	0.911103	+	0.412179i	$0.135232\pi$
$398$	−3.34409	−	32.9654i	−0.167624	−	1.65241i
$399$	−16.5503	+	28.6659i	−0.828551	+	1.43509i
$400$	−3.20166	−	2.39779i	−0.160083	−	0.119890i
$401$	12.3010	−	7.10197i	0.614281	−	0.354655i	−0.160358	−	0.987059i	$-0.551265\pi$
$401$	12.3010	−	7.10197i	0.614281	−	0.354655i	0.774639	+	0.632404i	$0.217932\pi$
$402$	18.0042	−	1.82639i	0.897966	−	0.0910920i
$403$	2.93145	+	0.150477i	0.146026	+	0.00749577i
$404$	3.22519	+	15.7331i	0.160459	+	0.782749i
$405$	1.11268	+	1.92721i	0.0552893	+	0.0957639i
$406$	18.3601	−	13.2380i	0.911194	−	0.656991i
$407$	−4.54397	+	7.87038i	−0.225236	+	0.390120i
$408$	3.33566	−	1.04388i	0.165140	−	0.0516796i
$409$	1.48633	+	0.858133i	0.0734943	+	0.0424319i	0.536297	−	0.844029i	$-0.319823\pi$
$409$	1.48633	+	0.858133i	0.0734943	+	0.0424319i	−0.462803	+	0.886461i	$0.653156\pi$
$410$	−5.11248	+	11.3718i	−0.252488	+	0.561611i
$411$	2.00842			0.0990683
$412$	3.85243	−	11.5706i	0.189796	−	0.570043i
$413$	−24.8229	+	14.3315i	−1.22146	+	0.705208i
$414$	2.02280	−	1.45848i	0.0994150	−	0.0716803i
$415$	−2.31651			−0.113713
$416$	1.41440	−	20.3470i	0.0693465	−	0.997593i
$417$	−20.6447			−1.01098
$418$	7.80701	−	5.62902i	0.381853	−	0.275324i
$419$	−7.27337	+	4.19928i	−0.355327	+	0.205148i	−0.667029	−	0.745032i	$-0.732434\pi$
$419$	−7.27337	+	4.19928i	−0.355327	+	0.205148i	0.311702	+	0.950180i	$0.399101\pi$
$420$	−3.51605	+	10.5603i	−0.171566	+	0.515290i
$421$	−7.41738			−0.361501			−0.180750	−	0.983529i	$-0.557853\pi$
$421$	−7.41738			−0.361501			−0.180750	+	0.983529i	$0.557853\pi$
$422$	−7.18071	+	15.9721i	−0.349551	+	0.777512i
$423$	11.7981	+	6.81162i	0.573641	+	0.331192i
$424$	−21.8654	+	6.84266i	−1.06188	+	0.332309i
$425$	0.505178	−	0.874994i	0.0245047	−	0.0424434i
$426$	8.16785	−	5.88920i	0.395734	−	0.285332i
$427$	−27.7067	−	47.9894i	−1.34082	−	2.32237i
$428$	−4.03047	−	19.6614i	−0.194820	−	0.950368i
$429$	2.74363	−	4.23476i	0.132464	−	0.204456i
$430$	1.91138	−	0.193895i	0.0921749	−	0.00935045i
$431$	−26.0610	+	15.0463i	−1.25531	+	0.724755i	−0.972160	−	0.234320i	$-0.924714\pi$
$431$	−26.0610	+	15.0463i	−1.25531	+	0.724755i	−0.283153	+	0.959075i	$0.591380\pi$
$432$	−13.2090	+	17.6374i	−0.635519	+	0.848578i
$433$	−20.6058	+	35.6904i	−0.990254	+	1.71517i	−0.374510	+	0.927223i	$0.622189\pi$
$433$	−20.6058	+	35.6904i	−0.990254	+	1.71517i	−0.615744	+	0.787947i	$0.711144\pi$
$434$	−0.528711	−	5.21192i	−0.0253789	−	0.250180i
$435$	−2.15109	+	3.72580i	−0.103137	+	0.178638i
$436$	−5.23361	+	15.7189i	−0.250644	+	0.752799i
$437$	−6.97305			−0.333566
$438$	−22.9996	−	10.3401i	−1.09896	−	0.494069i
$439$	16.9420	+	29.3445i	0.808599	+	1.40053i	0.913834	+	0.406088i	$0.133107\pi$
$439$	16.9420	+	29.3445i	0.808599	+	1.40053i	−0.105235	+	0.994447i	$0.533559\pi$
$440$	2.19156	−	2.38141i	0.104479	−	0.113529i
$441$	−20.6119			−0.981517
$442$	5.14544	−	0.256506i	0.244743	−	0.0122007i
$443$			36.2565i			1.72260i	0.508098	+	0.861299i	$0.330349\pi$
$443$			36.2565i			1.72260i	−0.508098	+	0.861299i	$0.669651\pi$
$444$	−14.5318	+	12.8951i	−0.689649	+	0.611973i
$445$	−12.1107	+	6.99213i	−0.574103	+	0.331459i
$446$	−13.0614	+	29.0527i	−0.618477	+	1.37569i
$447$			18.0901i			0.855630i
$448$	−36.2758	+	3.01714i	−1.71387	+	0.142547i
$449$	1.59884	+	0.923091i	0.0754539	+	0.0435633i	0.537252	−	0.843422i	$-0.319462\pi$
$449$	1.59884	+	0.923091i	0.0754539	+	0.0435633i	−0.461798	+	0.886985i	$0.652796\pi$
$450$	0.214679	+	2.11626i	0.0101201	+	0.0997617i
$451$	−8.73635	−	5.04393i	−0.411379	−	0.237510i
$452$	−14.4939	−	16.3335i	−0.681734	−	0.768265i
$453$	−4.43133	−	7.67529i	−0.208202	−	0.360617i
$454$	−2.32223	−	22.8921i	−0.108988	−	1.07438i
$455$	−8.92044	+	13.7686i	−0.418197	+	0.645482i
$456$	19.6367	−	6.14520i	0.919572	−	0.287775i
$457$	−3.05167	+	1.76189i	−0.142751	+	0.0824175i	−0.569675	−	0.821870i	$-0.692931\pi$
$457$	−3.05167	+	1.76189i	−0.142751	+	0.0824175i	0.426923	+	0.904288i	$0.359597\pi$
$458$	−6.77187	+	4.88266i	−0.316429	+	0.228152i
$459$	−4.82019	−	2.78294i	−0.224987	−	0.129896i
$460$	−2.29696	+	0.470865i	−0.107096	+	0.0219542i
$461$	18.8888	−	32.7164i	0.879740	−	1.52375i	0.0281134	−	0.999605i	$-0.491050\pi$
$461$	18.8888	−	32.7164i	0.879740	−	1.52375i	0.851626	−	0.524149i	$-0.175617\pi$
$462$	−8.21351	−	3.69260i	−0.382127	−	0.171795i
$463$		−	0.0534854i		−	0.00248568i	−0.999999	−	0.00124284i	$-0.999604\pi$
$463$		−	0.0534854i		−	0.00248568i	0.999999	−	0.00124284i	$-0.000395608\pi$
$464$	−13.9703	−	1.67336i	−0.648554	−	0.0776837i
$465$	0.497854	+	0.862309i	0.0230874	+	0.0399886i
$466$	−0.236075	+	0.170215i	−0.0109360	+	0.00788507i
$467$			1.74333i			0.0806719i	0.999186	+	0.0403360i	$0.0128428\pi$
$467$			1.74333i			0.0806719i	−0.999186	+	0.0403360i	$0.987157\pi$
$468$	−8.47110	+	6.77361i	−0.391577	+	0.313110i
$469$		−	47.6053i		−	2.19821i
$470$	−7.49138	−	10.3899i	−0.345551	−	0.479253i
$471$	4.89562	+	8.47947i	0.225578	+	0.390713i
$472$	17.3867	+	3.89364i	0.800287	+	0.179219i
$473$			1.55442i			0.0714722i
$474$	3.97301	−	8.83722i	0.182486	−	0.405907i
$475$	2.97393	−	5.15100i	0.136453	−	0.236344i
$476$	−1.84643	−	9.00721i	−0.0846309	−	0.412845i
$477$	10.5514	+	6.09184i	0.483115	+	0.278926i
$478$	−18.4822	−	25.6334i	−0.845356	−	1.17244i
$479$	−35.5001	+	20.4960i	−1.62204	+	0.936485i	−0.635666	+	0.771964i	$0.719274\pi$
$479$	−35.5001	+	20.4960i	−1.62204	+	0.936485i	−0.986374	+	0.164521i	$0.947392\pi$
$480$	6.05347	−	3.35025i	0.276302	−	0.152917i
$481$	−25.5016	+	13.0282i	−1.16277	+	0.594035i
$482$	−8.47624	+	0.859851i	−0.386082	+	0.0391652i
$483$	3.26217	+	5.65025i	0.148434	+	0.257095i
$484$	−12.8640	−	14.4968i	−0.584729	−	0.658947i
$485$	4.36544	+	2.52039i	0.198224	+	0.114445i
$486$	19.4231	−	1.97033i	0.881052	−	0.0893761i
$487$	9.82918	+	5.67488i	0.445402	+	0.257153i	0.705887	−	0.708325i	$-0.250549\pi$
$487$	9.82918	+	5.67488i	0.445402	+	0.257153i	−0.260484	+	0.965478i	$0.583882\pi$
$488$	−7.52746	+	33.6132i	−0.340752	+	1.52160i
$489$			3.84903i			0.174059i
$490$	17.6758	+	7.94665i	0.798513	+	0.358993i
$491$	3.97077	−	2.29253i	0.179198	−	0.103460i	−0.407718	−	0.913108i	$-0.633675\pi$
$491$	3.97077	−	2.29253i	0.179198	−	0.103460i	0.586916	+	0.809648i	$0.300342\pi$
$492$	−14.3139	−	16.1307i	−0.645320	−	0.727229i
$493$		−	3.55396i		−	0.160062i
$494$	30.2906	−	1.51002i	1.36284	−	0.0679391i
$495$	−1.72104			−0.0773550
$496$	−1.95206	+	2.60649i	−0.0876501	+	0.117035i
$497$	−13.2446	−	22.9404i	−0.594103	−	1.02902i
$498$	1.64297	−	3.65448i	0.0736233	−	0.163761i
$499$	26.8211			1.20068			0.600338	−	0.799746i	$-0.295033\pi$
$499$	26.8211			1.20068			0.600338	+	0.799746i	$0.295033\pi$
$500$	0.631801	−	1.89758i	0.0282550	−	0.0848626i
$501$	−6.93593	+	12.0134i	−0.309874	+	0.536718i
$502$	−29.3114	+	2.97342i	−1.30823	+	0.132710i
$503$	1.88459	−	3.26420i	0.0840296	−	0.145543i	−0.820948	−	0.571003i	$-0.806554\pi$
$503$	1.88459	−	3.26420i	0.0840296	−	0.145543i	0.904977	+	0.425460i	$0.139888\pi$
$504$	14.2437	+	13.1082i	0.634466	+	0.583887i
$505$	−6.95428	+	4.01506i	−0.309462	+	0.178668i
$506$	−0.191464	−	1.88741i	−0.00851161	−	0.0839057i
$507$	14.5114	−	6.49822i	0.644472	−	0.288596i
$508$	−17.0239	+	3.48980i	−0.755312	+	0.154835i
$509$	8.23498	+	14.2634i	0.365009	+	0.632214i	0.988778	−	0.149395i	$-0.0477325\pi$
$509$	8.23498	+	14.2634i	0.365009	+	0.632214i	−0.623769	+	0.781609i	$0.714399\pi$
$510$	1.02208	+	1.41754i	0.0452584	+	0.0627699i
$511$	−33.1683	+	57.4491i	−1.46728	+	2.54140i
$512$	17.8626	+	13.8898i	0.789424	+	0.613848i
$513$	−28.3760	−	16.3829i	−1.25283	−	0.723321i
$514$	−0.186115	−	0.0836730i	−0.00820918	−	0.00369066i
$515$	6.09755			0.268690
$516$	−1.04975	+	3.15288i	−0.0462126	+	0.138798i
$517$	8.97522	−	5.18185i	0.394730	−	0.227897i
$518$	29.8907	+	41.4561i	1.31332	+	1.82148i
$519$	24.0579			1.05602
$520$	9.87593	−	2.54282i	0.433088	−	0.111510i
$521$	31.9015			1.39763			0.698815	−	0.715302i	$-0.253711\pi$
$521$	31.9015			1.39763			0.698815	+	0.715302i	$0.253711\pi$
$522$	4.37599	+	6.06915i	0.191532	+	0.265639i
$523$	−30.2068	+	17.4399i	−1.32085	+	0.762594i	−0.983865	−	0.178915i	$-0.942741\pi$
$523$	−30.2068	+	17.4399i	−1.32085	+	0.762594i	−0.336988	+	0.941509i	$0.609408\pi$
$524$	35.1287	+	11.6961i	1.53460	+	0.510946i
$525$	−5.56512			−0.242882
$526$	−32.8258	−	14.7577i	−1.43127	−	0.643467i
$527$	−0.712339	−	0.411269i	−0.0310300	−	0.0179152i
$528$	2.20251	+	5.14637i	0.0958520	+	0.223967i
$529$	10.8128	−	18.7283i	0.470121	−	0.814273i
$530$	−6.69977	−	9.29206i	−0.291020	−	0.403621i
$531$	−4.73746	−	8.20553i	−0.205588	−	0.356090i
$532$	−10.8697	−	53.0245i	−0.471263	−	2.29890i
$533$	−14.4617	−	28.3075i	−0.626405	−	1.22613i
$534$	−2.44119	−	24.0648i	−0.105641	−	1.04138i
$535$	8.69066	−	5.01756i	0.375730	−	0.216928i
$536$	−20.0388	+	21.7747i	−0.865546	+	0.940524i
$537$	1.90552	−	3.30046i	0.0822293	−	0.142425i
$538$	−31.6393	+	3.20957i	−1.36407	+	0.138374i
$539$	−7.84010	+	13.5794i	−0.337697	+	0.584908i
$540$	−10.4535	−	3.48048i	−0.449845	−	0.149776i
$541$	17.8535			0.767582			0.383791	−	0.923420i	$-0.374618\pi$
$541$	17.8535			0.767582			0.383791	+	0.923420i	$0.374618\pi$
$542$	7.24699	−	16.1196i	0.311285	−	0.692395i
$543$	−15.1293	−	26.2047i	−0.649261	−	1.12455i
$544$	−2.94691	+	4.89714i	−0.126348	+	0.209963i
$545$	−8.28364			−0.354832
$546$	−15.3943	−	23.8380i	−0.658816	−	1.02017i
$547$		−	45.5394i		−	1.94712i	−0.228424	−	0.973562i	$-0.573357\pi$
$547$		−	45.5394i		−	1.94712i	0.228424	−	0.973562i	$-0.426643\pi$
$548$	−2.45653	+	2.17984i	−0.104938	+	0.0931183i
$549$	15.8635	−	9.15880i	0.677038	−	0.390888i
$550$	1.47589	+	0.663526i	0.0629321	+	0.0282928i
$551$		−	20.9218i		−	0.891298i
$552$	0.886279	−	3.95760i	0.0377226	−	0.168447i
$553$	−22.0739	−	12.7444i	−0.938677	−	0.541946i
$554$	−20.4345	+	2.07292i	−0.868177	+	0.0880701i
$555$	−8.41267	−	4.85706i	−0.357098	−	0.206171i
$556$	25.2508	−	22.4067i	1.07087	−	0.950256i
$557$	6.58799	+	11.4107i	0.279142	+	0.483488i	0.971172	−	0.238381i	$-0.0766166\pi$
$557$	6.58799	+	11.4107i	0.279142	+	0.483488i	−0.692030	+	0.721869i	$0.743283\pi$
$558$	1.72287	−	0.174772i	0.0729348	−	0.00739869i
$559$	−2.66328	+	4.11074i	−0.112645	+	0.173866i
$560$	−7.16109	−	16.7326i	−0.302611	−	0.707080i
$561$	−1.22453	+	0.706981i	−0.0516996	+	0.0298488i
$562$	−7.99186	−	11.0841i	−0.337116	−	0.467554i
$563$	−36.2657	−	20.9380i	−1.52842	−	0.882431i	−0.999429	−	0.0338006i	$-0.989239\pi$
$563$	−36.2657	−	20.9380i	−1.52842	−	0.882431i	−0.528986	−	0.848630i	$-0.677428\pi$
$564$	21.7042	−	4.44924i	0.913912	−	0.187347i
$565$	5.45926	−	9.45571i	0.229673	−	0.397805i
$566$	−8.65048	+	19.2414i	−0.363607	+	0.808776i
$567$			10.1257i			0.425238i
$568$	−3.59835	+	16.0681i	−0.150983	+	0.674203i
$569$	2.92320	+	5.06313i	0.122547	+	0.212257i	0.920771	−	0.390103i	$-0.127560\pi$
$569$	2.92320	+	5.06313i	0.122547	+	0.212257i	−0.798225	+	0.602360i	$0.794227\pi$
$570$	6.01687	+	8.34493i	0.252019	+	0.349531i
$571$			27.1617i			1.13668i	0.822794	+	0.568340i	$0.192414\pi$
$571$			27.1617i			1.13668i	−0.822794	+	0.568340i	$0.807586\pi$
$572$	1.24043	+	8.15737i	0.0518650	+	0.341077i
$573$			3.33243i			0.139214i
$574$	−46.0175	+	33.1796i	−1.92073	+	1.38489i
$575$	−0.586182	−	1.01530i	−0.0244455	−	0.0423408i
$576$	−0.997356	−	11.9914i	−0.0415565	−	0.499643i
$577$			18.6263i			0.775423i	0.921781	+	0.387711i	$0.126734\pi$
$577$			18.6263i			0.775423i	−0.921781	+	0.387711i	$0.873266\pi$
$578$	20.6108	+	9.26616i	0.857298	+	0.385421i
$579$	−2.74364	+	4.75213i	−0.114022	+	0.197492i
$580$	−1.41277	−	6.89175i	−0.0586621	−	0.286164i
$581$	−9.12828	−	5.27021i	−0.378705	−	0.218645i
$582$	−7.07228	+	5.09926i	−0.293155	+	0.211371i
$583$	8.02682	−	4.63429i	0.332437	−	0.191933i
$584$	39.3537	−	12.3155i	1.62847	−	0.509620i
$585$	−4.55138	−	2.94876i	−0.188177	−	0.121916i
$586$	0.125437	+	1.23653i	0.00518174	+	0.0510806i
$587$	5.08980	+	8.81578i	0.210078	+	0.363866i	0.951739	−	0.306909i	$-0.0992948\pi$
$587$	5.08980	+	8.81578i	0.210078	+	0.363866i	−0.741660	+	0.670775i	$0.765961\pi$
$588$	−25.0730	+	22.2490i	−1.03399	+	0.917532i
$589$	−4.19347	−	2.42110i	−0.172789	−	0.0997597i
$590$	0.899103	+	8.86318i	0.0370155	+	0.364891i
$591$	−23.5981	−	13.6244i	−0.970698	−	0.560433i
$592$	3.77836	−	31.5442i	0.155290	−	1.29646i
$593$			36.1001i			1.48246i	0.671254	+	0.741228i	$0.265756\pi$
$593$			36.1001i			1.48246i	−0.671254	+	0.741228i	$0.734244\pi$
$594$	3.65525	−	8.13042i	0.149977	−	0.333595i
$595$	3.98134	−	2.29863i	0.163219	−	0.0942346i
$596$	−19.6340	−	22.1262i	−0.804242	−	0.906322i
$597$			28.6561i			1.17282i
$598$	2.72749	−	5.31941i	0.111535	−	0.217527i
$599$	−36.0020			−1.47100			−0.735500	−	0.677524i	$-0.763053\pi$
$599$	−36.0020			−1.47100			−0.735500	+	0.677524i	$0.763053\pi$
$600$	2.54549	+	2.34257i	0.103919	+	0.0956349i
$601$	−7.83301	−	13.5672i	−0.319515	−	0.553416i	0.660872	−	0.750499i	$-0.270187\pi$
$601$	−7.83301	−	13.5672i	−0.319515	−	0.553416i	−0.980387	+	0.197082i	$0.936853\pi$
$602$	7.97298	+	3.58447i	0.324954	+	0.146092i
$603$	15.7365			0.640841
$604$	13.7504	+	4.57819i	0.559495	+	0.186284i
$605$	4.84537	−	8.39243i	0.196992	−	0.341201i
$606$	−1.40179	−	13.8186i	−0.0569440	−	0.561342i
$607$	7.69440	−	13.3271i	0.312306	−	0.540930i	−0.666555	−	0.745456i	$-0.732232\pi$
$607$	7.69440	−	13.3271i	0.312306	−	0.540930i	0.978861	+	0.204526i	$0.0655652\pi$
$608$	−17.3482	+	28.8289i	−0.703560	+	1.16917i
$609$	−16.9529	+	9.78775i	−0.686966	+	0.396620i
$610$	−17.1349	+	1.73821i	−0.693773	+	0.0703781i
$611$	32.6139	+	1.67413i	1.31942	+	0.0677280i
$612$	2.97745	−	0.610360i	0.120356	−	0.0246724i
$613$	2.05756	+	3.56380i	0.0831040	+	0.143940i	0.904582	−	0.426300i	$-0.140183\pi$
$613$	2.05756	+	3.56380i	0.0831040	+	0.143940i	−0.821478	+	0.570241i	$0.806850\pi$
$614$	21.7578	−	15.6878i	0.878072	−	0.633109i
$615$	5.39147	−	9.33830i	0.217405	−	0.376557i
$616$	14.0538	−	4.39806i	0.566244	−	0.177203i
$617$	41.2096	+	23.7924i	1.65904	+	0.957845i	0.973160	+	0.230128i	$0.0739143\pi$
$617$	41.2096	+	23.7924i	1.65904	+	0.957845i	0.685877	+	0.727718i	$0.259419\pi$
$618$	−4.32465	+	9.61938i	−0.173963	+	0.386948i
$619$	19.3757			0.778775			0.389387	−	0.921074i	$-0.372687\pi$
$619$	19.3757			0.778775			0.389387	+	0.921074i	$0.372687\pi$
$620$	−1.54484	−	0.514354i	−0.0620422	−	0.0206569i
$621$	−5.59309	+	3.22917i	−0.224443	+	0.129582i
$622$	8.52171	−	6.14434i	0.341690	−	0.246365i
$623$	−63.6302			−2.54929
$624$	−2.99294	+	17.3836i	−0.119813	+	0.695900i
$625$	1.00000			0.0400000
$626$	21.0804	−	15.1994i	0.842543	−	0.607491i
$627$	−7.20866	+	4.16192i	−0.287886	+	0.166211i
$628$	−15.1911	−	5.05787i	−0.606190	−	0.201831i
$629$	8.02467			0.319965
$630$	−3.96870	+	8.82762i	−0.158117	+	0.351701i
$631$	37.4272	+	21.6086i	1.48996	+	0.860226i	0.999934	−	0.0114845i	$-0.00365572\pi$
$631$	37.4272	+	21.6086i	1.48996	+	0.860226i	0.490021	+	0.871711i	$0.336989\pi$
$632$	4.73204	+	15.1210i	0.188230	+	0.601481i
$633$	7.57256	−	13.1161i	0.300982	−	0.521316i
$634$	10.4727	−	7.55102i	0.415923	−	0.299889i
$635$	−4.34447	−	7.52484i	−0.172405	−	0.298614i
$636$	19.4108	−	3.97910i	0.769687	−	0.157782i
$637$	−44.0001	+	22.4787i	−1.74335	+	0.890638i
$638$	5.66295	−	0.574464i	0.224198	−	0.0227432i
$639$	7.58324	−	4.37818i	0.299988	−	0.173198i
$640$	−3.76786	+	10.6679i	−0.148938	+	0.421684i
$641$	−0.375135	+	0.649753i	−0.0148169	+	0.0256637i	−0.873339	−	0.487113i	$-0.838050\pi$
$641$	−0.375135	+	0.649753i	−0.0148169	+	0.0256637i	0.858522	+	0.512777i	$0.171383\pi$
$642$	1.75180	+	17.2689i	0.0691380	+	0.681549i
$643$	−17.4326	+	30.1942i	−0.687475	+	1.19074i	0.285177	+	0.958475i	$0.407948\pi$
$643$	−17.4326	+	30.1942i	−0.687475	+	1.19074i	−0.972652	+	0.232267i	$0.925386\pi$
$644$	−10.1225	−	3.37029i	−0.398882	−	0.132808i
$645$	−1.66152			−0.0654223
$646$	−7.75133	−	3.48482i	−0.304972	−	0.137108i
$647$	1.16225	+	2.01308i	0.0456928	+	0.0791422i	0.887967	−	0.459907i	$-0.152117\pi$
$647$	1.16225	+	2.01308i	0.0456928	+	0.0791422i	−0.842274	+	0.539049i	$0.818784\pi$
$648$	4.26227	−	4.63149i	0.167438	−	0.181942i
$649$	−7.20792			−0.282936
$650$	2.76621	+	4.28347i	0.108500	+	0.168011i
$651$			4.53061i			0.177569i
$652$	−4.17754	−	4.70779i	−0.163605	−	0.184371i
$653$	−4.47325	+	2.58263i	−0.175052	+	0.101066i	−0.584966	−	0.811058i	$-0.698892\pi$
$653$	−4.47325	+	2.58263i	−0.175052	+	0.101066i	0.409914	+	0.912124i	$0.365559\pi$
$654$	5.87512	−	13.0681i	0.229735	−	0.511004i
$655$			18.5123i			0.723336i
$656$	35.0149	+	4.19409i	1.36710	+	0.163752i
$657$	−18.9905	−	10.9642i	−0.740892	−	0.427754i
$658$	−5.88218	−	57.9853i	−0.229311	−	2.26050i
$659$	−7.64399	−	4.41326i	−0.297767	−	0.171916i	0.343672	−	0.939090i	$-0.388329\pi$
$659$	−7.64399	−	4.41326i	−0.297767	−	0.171916i	−0.641440	+	0.767174i	$0.721662\pi$
$660$	−2.09353	+	1.85773i	−0.0814906	+	0.0723122i
$661$	−7.48609	−	12.9663i	−0.291175	−	0.504330i	0.682913	−	0.730500i	$-0.260713\pi$
$661$	−7.48609	−	12.9663i	−0.291175	−	0.504330i	−0.974088	+	0.226170i	$0.927380\pi$
$662$	0.188442	+	1.85763i	0.00732402	+	0.0721988i
$663$	−4.44964	−	0.228408i	−0.172810	−	0.00887064i
$664$	1.95685	+	6.25303i	0.0759407	+	0.242665i
$665$	23.4377	−	13.5318i	0.908877	−	0.524740i
$666$	−13.7038	+	9.88077i	−0.531013	+	0.382872i
$667$	−3.57134	−	2.06191i	−0.138283	−	0.0798376i
$668$	−4.55531	−	22.2216i	−0.176250	−	0.859780i
$669$	13.7742	−	23.8576i	0.532541	−	0.922388i
$670$	−13.4950	−	6.06703i	−0.521356	−	0.234390i
$671$		−	13.9349i		−	0.537950i
$672$	31.4759	+	0.570260i	1.21421	+	0.0219983i
$673$	13.9440	+	24.1518i	0.537503	+	0.930982i	0.999038	+	0.0438600i	$0.0139656\pi$
$673$	13.9440	+	24.1518i	0.537503	+	0.930982i	−0.461535	+	0.887122i	$0.652701\pi$
$674$	−10.1907	+	7.34774i	−0.392533	+	0.283024i
$675$		−	5.50883i		−	0.212035i
$676$	−10.6962	+	23.6979i	−0.411390	+	0.911459i
$677$			28.4872i			1.09485i	0.836854	+	0.547426i	$0.184392\pi$
$677$			28.4872i			1.09485i	−0.836854	+	0.547426i	$0.815608\pi$
$678$	11.0452	+	15.3188i	0.424189	+	0.588316i
$679$	11.4681	+	19.8633i	0.440105	+	0.762285i
$680$	−2.78865	−	0.624500i	−0.106940	−	0.0239485i
$681$			19.8996i			0.762553i
$682$	0.540181	−	1.20153i	0.0206846	−	0.0460091i
$683$	17.0661	−	29.5594i	0.653017	−	1.13106i	−0.329370	−	0.944201i	$-0.606836\pi$
$683$	17.0661	−	29.5594i	0.653017	−	1.13106i	0.982387	−	0.186858i	$-0.0598304\pi$
$684$	17.5279	−	3.59313i	0.670197	−	0.137387i
$685$	−1.42212	−	0.821060i	−0.0543363	−	0.0313711i
$686$	25.2290	+	34.9907i	0.963249	+	1.33595i
$687$	6.25285	−	3.61009i	0.238561	−	0.137733i
$688$	−2.13801	−	4.99566i	−0.0815109	−	0.190458i
$689$	29.1676	+	1.49723i	1.11120	+	0.0570398i
$690$	2.01746	−	0.204656i	0.0768033	−	0.00779113i
$691$	19.2910	+	33.4129i	0.733863	+	1.27109i	0.955220	+	0.295895i	$0.0956179\pi$
$691$	19.2910	+	33.4129i	0.733863	+	1.27109i	−0.221358	+	0.975193i	$0.571049\pi$
$692$	−29.4254	+	26.1112i	−1.11859	+	0.992598i
$693$	−6.78181	−	3.91548i	−0.257620	−	0.148737i
$694$	19.3729	−	1.96524i	0.735386	−	0.0745994i
$695$	14.6180	+	8.43972i	0.554493	+	0.320137i
$696$	11.8743	+	2.65917i	0.450094	+	0.100796i
$697$			8.90761i			0.337400i
$698$	−10.0614	−	4.52338i	−0.380830	−	0.171212i
$699$	0.217982	−	0.125852i	0.00824482	−	0.00476015i
$700$	6.80677	−	6.04011i	0.257272	−	0.228295i
$701$		−	36.6408i		−	1.38390i	−0.721943	−	0.691952i	$-0.756751\pi$
$701$		−	36.6408i		−	1.38390i	0.721943	−	0.691952i	$-0.243249\pi$
$702$	23.5969	−	15.2386i	0.890606	−	0.575143i
$703$	47.2404			1.78171
$704$	−8.27953	−	3.90409i	−0.312046	−	0.147141i
$705$	5.53889	+	9.59363i	0.208607	+	0.361317i
$706$	8.03413	−	17.8704i	0.302368	−	0.672562i
$707$	−36.5381			−1.37416
$708$	−14.6201	−	4.86775i	−0.549456	−	0.182941i
$709$	−19.5660	+	33.8893i	−0.734816	+	1.27274i	0.219988	+	0.975503i	$0.429398\pi$
$709$	−19.5660	+	33.8893i	−0.734816	+	1.27274i	−0.954804	+	0.297236i	$0.903935\pi$
$710$	−8.19101	+	0.830917i	−0.307403	+	0.0311838i
$711$	4.21281	−	7.29680i	0.157993	−	0.273652i
$712$	29.1045	+	26.7843i	1.09074	+	1.00379i
$713$	−0.826561	+	0.477215i	−0.0309549	+	0.0178718i
$714$	0.802530	+	7.91118i	0.0300339	+	0.296068i
$715$	−3.67390	+	1.87691i	−0.137396	+	0.0701926i
$716$	1.25149	+	6.10498i	0.0467703	+	0.228154i
$717$	13.6652	+	23.6687i	0.510334	+	0.883925i
$718$	−7.28367	−	10.1019i	−0.271824	−	0.376998i
$719$	1.76172	−	3.05139i	0.0657011	−	0.113798i	−0.831304	−	0.555818i	$-0.812405\pi$
$719$	1.76172	−	3.05139i	0.0657011	−	0.113798i	0.897005	+	0.442021i	$0.145738\pi$
$720$	5.53116	−	2.36719i	0.206134	−	0.0882200i
$721$	24.0276	+	13.8723i	0.894834	+	0.516633i
$722$	−21.1240	−	9.49687i	−0.786155	−	0.353437i
$723$	7.36821			0.274027
$724$	46.9461	+	15.6307i	1.74474	+	0.580911i
$725$	3.04627	−	1.75877i	0.113136	−	0.0653189i
$726$	9.80319	+	13.5962i	0.363830	+	0.504604i
$727$	−26.8400			−0.995440			−0.497720	−	0.867338i	$-0.665829\pi$
$727$	−26.8400			−0.995440			−0.497720	+	0.867338i	$0.665829\pi$
$728$	44.7015	+	12.4483i	1.65675	+	0.461366i
$729$	−23.5602			−0.872599
$730$	12.0584	+	16.7240i	0.446300	+	0.618983i
$731$	1.18867	−	0.686277i	0.0439644	−	0.0253829i
$732$	9.41068	−	28.2646i	0.347829	−	1.04469i
$733$	−23.3750			−0.863375			−0.431687	−	0.902023i	$-0.642082\pi$
$733$	−23.3750			−0.863375			−0.431687	+	0.902023i	$0.642082\pi$
$734$	27.5961	+	12.4066i	1.01859	+	0.457934i
$735$	−14.5151	−	8.38030i	−0.535398	−	0.309112i
$736$	3.21136	+	5.80251i	0.118372	+	0.213883i
$737$	5.98568	−	10.3675i	0.220485	−	0.381892i
$738$	−10.9679	−	15.2117i	−0.403735	−	0.559949i
$739$	5.89711	+	10.2141i	0.216929	+	0.375732i	0.953868	−	0.300228i	$-0.0970627\pi$
$739$	5.89711	+	10.2141i	0.216929	+	0.375732i	−0.736939	+	0.675960i	$0.763729\pi$
$740$	15.5612	−	3.18997i	0.572043	−	0.117266i
$741$	−26.1946	−	1.34462i	−0.962282	−	0.0493957i
$742$	−5.26062	−	51.8581i	−0.193123	−	1.90377i
$743$	−1.19902	+	0.692253i	−0.0439877	+	0.0253963i	−0.521833	−	0.853048i	$-0.674751\pi$
$743$	−1.19902	+	0.692253i	−0.0439877	+	0.0253963i	0.477845	+	0.878444i	$0.341418\pi$
$744$	1.90710	−	2.07231i	0.0699178	−	0.0759744i
$745$	7.39536	−	12.8091i	0.270945	−	0.469291i
$746$	40.1165	−	4.06952i	1.46877	−	0.148996i
$747$	1.74214	−	3.01747i	0.0637414	−	0.110403i
$748$	0.730411	−	2.19376i	0.0267065	−	0.0802116i
$749$	45.6611			1.66842
$750$	−0.709244	+	1.57758i	−0.0258979	+	0.0576051i
$751$	−7.32831	−	12.6930i	−0.267414	−	0.463175i	0.700779	−	0.713378i	$-0.252836\pi$
$751$	−7.32831	−	12.6930i	−0.267414	−	0.463175i	−0.968193	+	0.250204i	$0.919502\pi$
$752$	−21.7177	+	28.9986i	−0.791962	+	1.05747i
$753$	25.4797			0.928533
$754$	15.9602	+	8.18348i	0.581238	+	0.298025i
$755$			7.24626i			0.263718i
$756$	−33.2739	−	37.4973i	−1.21016	−	1.36376i
$757$	23.8763	−	13.7850i	0.867797	−	0.501023i	0.00118172	−	0.999999i	$-0.499624\pi$
$757$	23.8763	−	13.7850i	0.867797	−	0.501023i	0.866616	+	0.498976i	$0.166291\pi$
$758$	3.53521	+	1.58935i	0.128404	+	0.0577277i
$759$			1.64069i			0.0595531i
$760$	−16.4165	−	3.67636i	−0.595488	−	0.133356i
$761$	32.0510	+	18.5047i	1.16185	+	0.670794i	0.951746	−	0.306885i	$-0.0992869\pi$
$761$	32.0510	+	18.5047i	1.16185	+	0.670794i	0.210103	+	0.977679i	$0.432620\pi$
$762$	14.9523	−	1.51680i	0.541666	−	0.0549480i
$763$	−32.6419	−	18.8458i	−1.18172	−	0.682265i
$764$	−3.61686	−	4.07594i	−0.130853	−	0.147462i
$765$	0.759841	+	1.31608i	0.0274721	+	0.0475831i
$766$	42.6207	−	4.32355i	1.53995	−	0.156216i
$767$	−19.0618	−	12.3498i	−0.688280	−	0.445925i
$768$	−14.1571	−	13.5102i	−0.510850	−	0.487508i
$769$	−31.5869	+	18.2367i	−1.13905	+	0.657632i	−0.946196	−	0.323595i	$-0.895108\pi$
$769$	−31.5869	+	18.2367i	−1.13905	+	0.657632i	−0.192856	+	0.981227i	$0.561775\pi$
$770$	4.30622	+	5.97239i	0.155186	+	0.215230i
$771$	0.152834	+	0.0882390i	0.00550420	+	0.00317785i
$772$	−1.80194	−	8.79020i	−0.0648533	−	0.316366i
$773$	21.9341	−	37.9909i	0.788914	−	1.36644i	−0.137719	−	0.990471i	$-0.543977\pi$
$773$	21.9341	−	37.9909i	0.788914	−	1.36644i	0.926633	−	0.375968i	$-0.122690\pi$
$774$	−1.18489	+	2.63557i	−0.0425900	+	0.0947336i
$775$		−	0.814108i		−	0.0292436i
$776$	3.11570	−	13.9129i	0.111847	−	0.499442i
$777$	−22.1003	−	38.2788i	−0.792843	−	1.37324i
$778$	−2.37935	−	3.29996i	−0.0853037	−	0.118309i
$779$			52.4382i			1.87879i
$780$	−8.71943	+	1.32590i	−0.312206	+	0.0474748i
$781$		−	6.66129i		−	0.238360i
$782$	−1.35878	+	0.979708i	−0.0485898	+	0.0350343i
$783$	−9.68874	−	16.7814i	−0.346247	−	0.599718i
$784$	6.51913	−	54.4259i	0.232826	−	1.94378i
$785$		−	8.00548i		−	0.285728i
$786$	−29.2047	−	13.1298i	−1.04170	−	0.468323i
$787$	−7.49466	+	12.9811i	−0.267156	+	0.462727i	−0.968126	−	0.250463i	$-0.919417\pi$
$787$	−7.49466	+	12.9811i	−0.267156	+	0.462727i	0.700971	+	0.713190i	$0.252750\pi$
$788$	43.6504	−	8.94809i	1.55498	−	0.318762i
$789$	26.9560	+	15.5630i	0.959659	+	0.554059i
$790$	−6.42592	+	4.63323i	−0.228624	+	0.164843i
$791$	43.0248	−	24.8404i	1.52978	−	0.883222i
$792$	1.45384	+	4.64566i	0.0516598	+	0.165076i
$793$	23.8755	−	36.8516i	0.847844	−	1.30864i
$794$	−0.560774	−	5.52800i	−0.0199011	−	0.196181i
$795$	4.95360	+	8.57989i	0.175686	+	0.304297i
$796$	−31.1019	−	35.0496i	−1.10238	−	1.24230i
$797$	34.9581	+	20.1831i	1.23828	+	0.714921i	0.968742	−	0.248069i	$-0.0797958\pi$
$797$	34.9581	+	20.1831i	1.23828	+	0.714921i	0.269538	+	0.962990i	$0.413129\pi$
$798$	4.72441	+	46.5723i	0.167242	+	1.64864i
$799$	−7.92514	−	4.57558i	−0.280371	−	0.161872i
$800$	−5.65593	−	0.102470i	−0.199967	−	0.00362287i
$801$		−	21.0338i		−	0.743192i
$802$	8.23671	−	18.3210i	0.290848	−	0.646938i
$803$	−14.4468	+	8.34086i	−0.509817	+	0.294343i
$804$	19.1425	−	16.9864i	0.675102	−	0.599064i
$805$		−	5.33441i		−	0.188013i
$806$	3.48720	−	2.25199i	0.122831	−	0.0793231i
$807$	27.5033			0.968163
$808$	16.7126	+	15.3803i	0.587946	+	0.541075i
$809$	8.95469	+	15.5100i	0.314830	+	0.545302i	0.979401	−	0.201923i	$-0.0647191\pi$
$809$	8.95469	+	15.5100i	0.314830	+	0.545302i	−0.664571	+	0.747225i	$0.731386\pi$
$810$	2.87038	+	1.29046i	0.100855	+	0.0453421i
$811$	−4.16655			−0.146307			−0.0731536	−	0.997321i	$-0.523306\pi$
$811$	−4.16655			−0.146307			−0.0731536	+	0.997321i	$0.523306\pi$
$812$	10.1121	−	30.3713i	0.354866	−	1.06582i
$813$	−7.64246	+	13.2371i	−0.268033	+	0.464246i
$814$	1.29711	+	12.7867i	0.0454637	+	0.448172i
$815$	1.57351	−	2.72541i	0.0551178	−	0.0954668i
$816$	2.96303	−	3.95640i	0.103727	−	0.138502i
$817$	6.99756	−	4.04004i	0.244813	−	0.141343i
$818$	2.41477	−	0.244961i	0.0844306	−	0.00856485i
$819$	−11.2262	−	21.9744i	−0.392277	−	0.767848i
$820$	3.54096	+	17.2734i	0.123656	+	0.603214i
$821$	0.647798	+	1.12202i	0.0226083	+	0.0391587i	0.877108	−	0.480293i	$-0.159470\pi$
$821$	0.647798	+	1.12202i	0.0226083	+	0.0391587i	−0.854500	+	0.519452i	$0.826136\pi$
$822$	2.30392	−	1.66117i	0.0803584	−	0.0579401i
$823$	15.5669	−	26.9626i	0.542628	−	0.939859i	−0.456124	−	0.889916i	$-0.650763\pi$
$823$	15.5669	−	26.9626i	0.542628	−	0.939859i	0.998752	−	0.0499428i	$-0.0159039\pi$
$824$	−5.15086	−	16.4593i	−0.179439	−	0.573388i
$825$	−1.21198	−	0.699734i	−0.0421956	−	0.0243616i
$826$	−16.6214	+	36.9712i	−0.578332	+	1.28639i
$827$	−5.94622			−0.206770			−0.103385	−	0.994641i	$-0.532967\pi$
$827$	−5.94622			−0.206770			−0.103385	+	0.994641i	$0.532967\pi$
$828$	1.11409	−	3.34612i	0.0387173	−	0.116286i
$829$	−39.5944	+	22.8599i	−1.37517	+	0.793956i	−0.991574	−	0.129544i	$-0.958649\pi$
$829$	−39.5944	+	22.8599i	−1.37517	+	0.793956i	−0.383598	+	0.923500i	$0.625315\pi$
$830$	−2.65733	+	1.91599i	−0.0922373	+	0.0665051i
$831$	17.7632			0.616200
$832$	−15.2066	−	24.5104i	−0.527193	−	0.849746i
$833$	13.8457			0.479723
$834$	−23.6821	+	17.0753i	−0.820044	+	0.591269i
$835$	9.82233	−	5.67093i	0.339916	−	0.196250i
$836$	4.29985	−	12.9144i	0.148713	−	0.446654i
$837$	−4.48478			−0.155017
$838$	−4.87024	+	10.8329i	−0.168240	+	0.374218i
$839$	−1.47495	−	0.851562i	−0.0509209	−	0.0293992i	0.474323	−	0.880351i	$-0.342693\pi$
$839$	−1.47495	−	0.851562i	−0.0509209	−	0.0293992i	−0.525244	+	0.850951i	$0.676026\pi$
$840$	4.70110	+	15.0221i	0.162203	+	0.518313i
$841$	−8.31348	+	14.3994i	−0.286672	+	0.496530i
$842$	−8.50867	+	6.13494i	−0.293228	+	0.211424i
$843$	5.90893	+	10.2346i	0.203514	+	0.352497i
$844$	4.97343	+	24.2613i	0.171192	+	0.835107i
$845$	−12.9317	−	1.33112i	−0.444863	−	0.0457919i
$846$	19.1678	−	1.94443i	0.659002	−	0.0668508i
$847$	38.1867	−	22.0471i	1.31211	−	0.757547i
$848$	−19.4228	+	25.9343i	−0.666982	+	0.890589i
$849$	9.12254	−	15.8007i	0.313085	−	0.542279i
$850$	−0.144207	−	1.42156i	−0.00494626	−	0.0487592i
$851$	4.65570	−	8.06391i	0.159595	−	0.276427i
$852$	4.49859	−	13.5113i	0.154119	−	0.462890i
$853$	20.2265			0.692544			0.346272	−	0.938134i	$-0.387448\pi$
$853$	20.2265			0.692544			0.346272	+	0.938134i	$0.387448\pi$
$854$	−71.4753	−	32.1336i	−2.44583	−	1.09959i
$855$	4.47310	+	7.74764i	0.152977	+	0.264964i
$856$	−20.8854	−	19.2205i	−0.713849	−	0.656942i
$857$	−26.9722			−0.921354			−0.460677	−	0.887568i	$-0.652393\pi$
$857$	−26.9722			−0.921354			−0.460677	+	0.887568i	$0.652393\pi$
$858$	−0.355292	−	7.12707i	−0.0121295	−	0.243314i
$859$		−	5.18933i		−	0.177058i	−0.996074	−	0.0885288i	$-0.971783\pi$
$859$		−	5.18933i		−	0.177058i	0.996074	−	0.0885288i	$-0.0282165\pi$
$860$	2.03222	−	1.80333i	0.0692982	−	0.0614930i
$861$	42.4905	−	24.5319i	1.44807	−	0.836046i
$862$	−17.4504	+	38.8151i	−0.594363	+	1.32205i
$863$			14.0474i			0.478179i	0.970998	+	0.239089i	$0.0768489\pi$
$863$			14.0474i			0.478179i	−0.970998	+	0.239089i	$0.923151\pi$
$864$	−0.564491	+	31.1575i	−0.0192044	+	1.06000i
$865$	−17.0348	−	9.83505i	−0.579201	−	0.334402i
$866$	5.88210	+	57.9845i	0.199882	+	1.97039i
$867$	−16.9253	−	9.77181i	−0.574812	−	0.331868i
$868$	−4.91730	−	5.54144i	−0.166904	−	0.188089i
$869$	−3.20484	−	5.55095i	−0.108717	−	0.188303i
$870$	0.614046	+	6.05314i	0.0208181	+	0.205221i
$871$	33.5927	−	17.1618i	1.13825	−	0.581505i
$872$	6.99754	+	22.3603i	0.236967	+	0.757216i
$873$	−6.56608	+	3.79093i	−0.222228	+	0.128303i
$874$	−7.99898	+	5.76744i	−0.270569	+	0.195086i
$875$	3.94053	+	2.27507i	0.133214	+	0.0769113i
$876$	−34.9358	+	7.16165i	−1.18037	+	0.241970i
$877$	15.2443	−	26.4039i	0.514764	−	0.891598i	−0.485089	−	0.874465i	$-0.661213\pi$
$877$	15.2443	−	26.4039i	0.514764	−	0.891598i	0.999853	−	0.0171330i	$-0.00545387\pi$
$878$	43.7056	+	19.6490i	1.47499	+	0.663122i
$879$		−	1.07489i		−	0.0362551i
$880$	0.544332	−	4.54443i	0.0183494	−	0.153193i
$881$	−13.6820	−	23.6980i	−0.460959	−	0.798404i	0.538050	−	0.842913i	$-0.319161\pi$
$881$	−13.6820	−	23.6980i	−0.460959	−	0.798404i	−0.999009	+	0.0445085i	$0.985828\pi$
$882$	−23.6444	+	17.0481i	−0.796149	+	0.574040i
$883$			15.1443i			0.509647i	0.966988	+	0.254824i	$0.0820174\pi$
$883$			15.1443i			0.509647i	−0.966988	+	0.254824i	$0.917983\pi$
$884$	5.69031	−	4.55005i	0.191386	−	0.153035i
$885$		−	7.70457i		−	0.258986i
$886$	29.9879	+	41.5908i	1.00746	+	1.39727i
$887$	−0.725904	−	1.25730i	−0.0243735	−	0.0422161i	0.853581	−	0.520960i	$-0.174426\pi$
$887$	−0.725904	−	1.25730i	−0.0243735	−	0.0422161i	−0.877955	+	0.478743i	$0.841092\pi$
$888$	−6.00428	+	26.8116i	−0.201491	+	0.899738i
$889$		−	39.5359i		−	1.32599i
$890$	−8.10932	+	18.0377i	−0.271825	+	0.604624i
$891$	−1.27316	+	2.20517i	−0.0426523	+	0.0738760i
$892$	9.04647	+	44.1303i	0.302898	+	1.47759i
$893$	−46.6545	−	26.9360i	−1.56123	−	0.901378i
$894$	14.9623	+	20.7516i	0.500416	+	0.694037i
$895$	−2.69851	+	1.55798i	−0.0902012	+	0.0520777i
$896$	−39.1175	+	33.4649i	−1.30682	+	1.11798i
$897$	−2.81109	+	4.33889i	−0.0938596	+	0.144871i
$898$	2.59756	−	0.263503i	0.0866818	−	0.00879322i
$899$	−1.43183	−	2.47999i	−0.0477540	−	0.0827124i
$900$	1.99663	+	2.25006i	0.0665545	+	0.0750021i
$901$	−7.08770	−	4.09209i	−0.236126	−	0.136327i
$902$	−14.1936	+	1.43983i	−0.472594	+	0.0479411i
$903$	−6.54727	−	3.78007i	−0.217880	−	0.125793i
$904$	−30.1358	−	6.74872i	−1.00230	−	0.224459i
$905$			24.7399i			0.822384i
$906$	−11.4316	−	5.13937i	−0.379788	−	0.170744i
$907$	37.6451	−	21.7344i	1.24999	−	0.721680i	0.278879	−	0.960326i	$-0.410037\pi$
$907$	37.6451	−	21.7344i	1.24999	−	0.721680i	0.971106	+	0.238647i	$0.0767037\pi$
$908$	−21.5980	−	24.3394i	−0.716755	−	0.807731i
$909$		−	12.0781i		−	0.400607i
$910$	1.15517	+	23.1725i	0.0382936	+	0.768159i
$911$	−13.1889			−0.436969			−0.218485	−	0.975840i	$-0.570111\pi$
$911$	−13.1889			−0.436969			−0.218485	+	0.975840i	$0.570111\pi$
$912$	17.4431	−	23.2909i	0.577597	−	0.771238i
$913$	−1.32531	−	2.29550i	−0.0438613	−	0.0759699i
$914$	−2.04340	+	4.54516i	−0.0675896	+	0.150340i
$915$	14.8950			0.492414
$916$	−3.72973	+	11.2021i	−0.123234	+	0.370127i
$917$	−42.1168	+	72.9484i	−1.39082	+	2.40897i
$918$	−7.83115	+	0.794411i	−0.258466	+	0.0262195i
$919$	0.465901	−	0.806964i	0.0153687	−	0.0266193i	−0.858239	−	0.513251i	$-0.828441\pi$
$919$	0.465901	−	0.806964i	0.0153687	−	0.0266193i	0.873607	+	0.486631i	$0.161774\pi$
$920$	−2.24545	+	2.43997i	−0.0740304	+	0.0804433i
$921$	−20.0902	+	11.5991i	−0.661994	+	0.382203i
$922$	−5.39196	−	53.1528i	−0.177575	−	1.75050i
$923$	11.4132	−	17.6162i	0.375670	−	0.579843i
$924$	−12.4761	+	2.55753i	−0.410434	+	0.0841366i
$925$	3.97121	+	6.87834i	0.130573	+	0.226158i
$926$	−0.0442380	−	0.0613546i	−0.00145375	−	0.00201624i
$927$	−4.58568	+	7.94262i	−0.150613	+	0.260870i
$928$	−17.4097	+	9.63530i	−0.571502	+	0.316294i
$929$	−3.92370	−	2.26535i	−0.128732	−	0.0743236i	0.434251	−	0.900792i	$-0.357013\pi$
$929$	−3.92370	−	2.26535i	−0.128732	−	0.0743236i	−0.562983	+	0.826468i	$0.690346\pi$
$930$	1.28432	+	0.577401i	0.0421145	+	0.0189337i
$931$	81.5079			2.67131
$932$	−0.130023	+	0.390517i	−0.00425903	+	0.0127918i
$933$	−7.86858	+	4.54293i	−0.257606	+	0.148729i
$934$	1.44192	+	1.99983i	0.0471810	+	0.0654363i
$935$	1.15608			0.0378078
$936$	−4.11495	+	14.7767i	−0.134501	+	0.482990i
$937$	44.1517			1.44237			0.721186	−	0.692741i	$-0.243597\pi$
$937$	44.1517			1.44237			0.721186	+	0.692741i	$0.243597\pi$
$938$	−39.3745	−	54.6093i	−1.28562	−	1.78306i
$939$	−19.4647	+	11.2380i	−0.635208	+	0.366737i
$940$	−17.1871	−	5.72245i	−0.560582	−	0.186646i
$941$	−35.8738			−1.16945			−0.584726	−	0.811231i	$-0.698798\pi$
$941$	−35.8738			−1.16945			−0.584726	+	0.811231i	$0.698798\pi$
$942$	12.6293	+	5.67784i	0.411485	+	0.184994i
$943$	8.95117	+	5.16796i	0.291490	+	0.168292i
$944$	23.1652	−	9.91409i	0.753962	−	0.322676i
$945$	12.5330	−	21.7077i	0.407697	−	0.706152i
$946$	1.28566	+	1.78311i	0.0418005	+	0.0579740i
$947$	−8.27885	−	14.3394i	−0.269026	−	0.465967i	0.699584	−	0.714550i	$-0.253369\pi$
$947$	−8.27885	−	14.3394i	−0.269026	−	0.465967i	−0.968611	+	0.248583i	$0.920035\pi$
$948$	−2.75174	−	13.4235i	−0.0893725	−	0.435975i
$949$	−52.4963	−	2.69473i	−1.70410	−	0.0874747i
$950$	−0.848931	−	8.36860i	−0.0275430	−	0.271513i
$951$	−9.67001	+	5.58298i	−0.313572	+	0.181041i
$952$	−9.56798	−	8.80522i	−0.310100	−	0.285379i
$953$	−22.7172	+	39.3473i	−0.735881	+	1.27458i	0.218454	+	0.975847i	$0.429899\pi$
$953$	−22.7172	+	39.3473i	−0.735881	+	1.27458i	−0.954336	+	0.298737i	$0.903435\pi$
$954$	17.1424	−	1.73896i	0.555004	−	0.0563010i
$955$	1.36233	−	2.35962i	0.0440838	−	0.0763554i
$956$	−42.4029	−	14.1180i	−1.37141	−	0.456610i
$957$	−4.92268			−0.159128
$958$	−23.7708	+	52.8737i	−0.768000	+	1.70827i
$959$	−3.73593	−	6.47083i	−0.120640	−	0.208954i
$960$	4.17309	−	8.85001i	0.134686	−	0.285633i
$961$	30.3372			0.978620
$962$	−18.4779	+	36.0375i	−0.595752	+	1.16189i
$963$			15.0939i			0.486393i
$964$	−9.01214	+	7.99708i	−0.290261	+	0.257569i
$965$	3.88542	−	2.24325i	0.125076	−	0.0722127i
$966$	8.41547	+	3.78340i	0.270763	+	0.121729i
$967$		−	59.6969i		−	1.91972i	−0.280473	−	0.959862i	$-0.590491\pi$
$967$		−	59.6969i		−	1.91972i	0.280473	−	0.959862i	$-0.409509\pi$
$968$	−26.7471	−	5.98984i	−0.859683	−	0.192521i
$969$	6.36526	+	3.67499i	0.204482	+	0.118058i
$970$	7.09233	−	0.719464i	0.227721	−	0.0231006i
$971$	−35.6708	−	20.5945i	−1.14473	−	0.660910i	−0.197132	−	0.980377i	$-0.563163\pi$
$971$	−35.6708	−	20.5945i	−1.14473	−	0.660910i	−0.947597	+	0.319467i	$0.896496\pi$
$972$	20.6511	−	18.3252i	0.662386	−	0.587780i
$973$	38.4019	+	66.5140i	1.23111	+	2.13234i
$974$	15.9690	−	1.61994i	0.511680	−	0.0519062i
$975$	−2.00624	−	3.92704i	−0.0642510	−	0.125766i
$976$	19.1666	+	44.7846i	0.613509	+	1.43352i
$977$	8.75025	−	5.05196i	0.279945	−	0.161627i	−0.353453	−	0.935452i	$-0.614993\pi$
$977$	8.75025	−	5.05196i	0.279945	−	0.161627i	0.633399	+	0.773826i	$0.281659\pi$
$978$	3.18354	+	4.41533i	0.101799	+	0.141187i
$979$	−13.8574	−	8.00059i	−0.442885	−	0.255700i
$980$	26.8491	−	5.50393i	0.857664	−	0.175816i
$981$	6.22973	−	10.7902i	0.198900	−	0.344505i
$982$	2.65882	−	5.91406i	0.0848465	−	0.188725i
$983$		−	36.3609i		−	1.15973i	−0.814712	−	0.579866i	$-0.803105\pi$
$983$		−	36.3609i		−	1.15973i	0.814712	−	0.579866i	$-0.196895\pi$
$984$	−29.7616	−	6.66492i	−0.948766	−	0.212470i
$985$	11.1395	+	19.2942i	0.354935	+	0.614765i
$986$	−2.93949	−	4.07684i	−0.0936125	−	0.129833i
$987$			50.4054i			1.60442i
$988$	33.4983	−	26.7857i	1.06572	−	0.852166i
$989$		−	1.59264i		−	0.0506430i
$990$	−1.97425	+	1.42348i	−0.0627458	+	0.0452411i
$991$	−22.6507	−	39.2322i	−0.719523	−	1.24625i	−0.961189	−	0.275891i	$-0.911027\pi$
$991$	−22.6507	−	39.2322i	−0.719523	−	1.24625i	0.241666	−	0.970360i	$-0.422306\pi$
$992$	−0.0834219	+	4.60453i	−0.00264865	+	0.146194i
$993$		−	1.61480i		−	0.0512440i
$994$	−34.1673	−	15.3609i	−1.08372	−	0.487217i
$995$	11.7148	−	20.2907i	0.371385	−	0.643258i
$996$	−1.13794	−	5.55106i	−0.0360569	−	0.175892i
$997$	9.30515	+	5.37233i	0.294697	+	0.170144i	0.640058	−	0.768326i	$-0.278910\pi$
$997$	9.30515	+	5.37233i	0.294697	+	0.170144i	−0.345361	+	0.938470i	$0.612244\pi$
$998$	30.7672	−	22.1838i	0.973919	−	0.702216i
$999$	37.8916	−	21.8767i	1.19884	−	0.692148i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	520.2.ca.b.101.21	yes	56
8.5	even	2		520.2.ca.a.101.26	✓	56
13.4	even	6		520.2.ca.a.381.26	yes	56
104.69	even	6	inner	520.2.ca.b.381.21	yes	56

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
520.2.ca.a.101.26	✓	56	8.5	even	2
520.2.ca.a.381.26	yes	56	13.4	even	6
520.2.ca.b.101.21	yes	56	1.1	even	1	trivial
520.2.ca.b.381.21	yes	56	104.69	even	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:	\( N \)	\(=\)	\( 520 = 2^{3} \cdot 5 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	520.ca (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.14713 - 0.827103i) q^{2} +(-1.05921 + 0.611534i) q^{3} +(0.631801 - 1.89758i) q^{4} +1.00000 q^{5} +(-0.709244 + 1.57758i) q^{6} +(3.94053 + 2.27507i) q^{7} +(-0.844743 - 2.69934i) q^{8} +(-0.752053 + 1.30259i) q^{9} +(1.14713 - 0.827103i) q^{10} +(0.572114 + 0.990930i) q^{11} +(0.491229 + 2.39630i) q^{12} +(-0.184836 + 3.60081i) q^{13} +(6.40201 - 0.649436i) q^{14} +(-1.05921 + 0.611534i) q^{15} +(-3.20166 - 2.39779i) q^{16} +(0.505178 - 0.874994i) q^{17} +(0.214679 + 2.11626i) q^{18} +(2.97393 - 5.15100i) q^{19} +(0.631801 - 1.89758i) q^{20} -5.56512 q^{21} +(1.47589 + 0.663526i) q^{22} +(-0.586182 - 1.01530i) q^{23} +(2.54549 + 2.34257i) q^{24} +1.00000 q^{25} +(2.76621 + 4.28347i) q^{26} -5.50883i q^{27} +(6.80677 - 6.04011i) q^{28} +(3.04627 - 1.75877i) q^{29} +(-0.709244 + 1.57758i) q^{30} -0.814108i q^{31} +(-5.65593 - 0.102470i) q^{32} +(-1.21198 - 0.699734i) q^{33} +(-0.144207 - 1.42156i) q^{34} +(3.94053 + 2.27507i) q^{35} +(1.99663 + 2.25006i) q^{36} +(3.97121 + 6.87834i) q^{37} +(-0.848931 - 8.36860i) q^{38} +(-2.00624 - 3.92704i) q^{39} +(-0.844743 - 2.69934i) q^{40} +(-7.63515 + 4.40815i) q^{41} +(-6.38390 + 4.60293i) q^{42} +(1.17648 + 0.679243i) q^{43} +(2.24184 - 0.459564i) q^{44} +(-0.752053 + 1.30259i) q^{45} +(-1.51218 - 0.679841i) q^{46} -9.05737i q^{47} +(4.85755 + 0.581837i) q^{48} +(6.85187 + 11.8678i) q^{49} +(1.14713 - 0.827103i) q^{50} +1.23573i q^{51} +(6.71606 + 2.62574i) q^{52} -8.10029i q^{53} +(-4.55637 - 6.31932i) q^{54} +(0.572114 + 0.990930i) q^{55} +(2.81243 - 12.5587i) q^{56} +7.27464i q^{57} +(2.03978 - 4.53711i) q^{58} +(-3.14969 + 5.45542i) q^{59} +(0.491229 + 2.39630i) q^{60} +(-10.5468 - 6.08920i) q^{61} +(-0.673351 - 0.933885i) q^{62} +(-5.92698 + 3.42194i) q^{63} +(-6.57282 + 4.56049i) q^{64} +(-0.184836 + 3.60081i) q^{65} +(-1.96904 + 0.199745i) q^{66} +(-5.23119 - 9.06069i) q^{67} +(-1.34120 - 1.51144i) q^{68} +(1.24178 + 0.716940i) q^{69} +(6.40201 - 0.649436i) q^{70} +(-5.04169 - 2.91082i) q^{71} +(4.15143 + 0.929685i) q^{72} +14.5790i q^{73} +(10.2446 + 4.60573i) q^{74} +(-1.05921 + 0.611534i) q^{75} +(-7.89552 - 8.89769i) q^{76} +5.20639i q^{77} +(-5.54948 - 2.84545i) q^{78} -5.60175 q^{79} +(-3.20166 - 2.39779i) q^{80} +(1.11268 + 1.92721i) q^{81} +(-5.11248 + 11.3718i) q^{82} -2.31651 q^{83} +(-3.51605 + 10.5603i) q^{84} +(0.505178 - 0.874994i) q^{85} +(1.91138 - 0.193895i) q^{86} +(-2.15109 + 3.72580i) q^{87} +(2.19156 - 2.38141i) q^{88} +(-12.1107 + 6.99213i) q^{89} +(0.214679 + 2.11626i) q^{90} +(-8.92044 + 13.7686i) q^{91} +(-2.29696 + 0.470865i) q^{92} +(0.497854 + 0.862309i) q^{93} +(-7.49138 - 10.3899i) q^{94} +(2.97393 - 5.15100i) q^{95} +(6.05347 - 3.35025i) q^{96} +(4.36544 + 2.52039i) q^{97} +(17.6758 + 7.94665i) q^{98} -1.72104 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 56 q + 6 q^{4} + 56 q^{5} - 13 q^{6} + 28 q^{9} - 8 q^{11} + 6 q^{12} - 4 q^{14} + 14 q^{16} + 18 q^{18} - 16 q^{19} + 6 q^{20} - 6 q^{22} + 12 q^{23} + 22 q^{24} + 56 q^{25} - 37 q^{26} - 12 q^{28} - 13 q^{30}+ \cdots - 48 q^{99}+O(q^{100}) \) 56 * q + 6 * q^4 + 56 * q^5 - 13 * q^6 + 28 * q^9 - 8 * q^11 + 6 * q^12 - 4 * q^14 + 14 * q^16 + 18 * q^18 - 16 * q^19 + 6 * q^20 - 6 * q^22 + 12 * q^23 + 22 * q^24 + 56 * q^25 - 37 * q^26 - 12 * q^28 - 13 * q^30 - 30 * q^32 - 16 * q^34 + 15 * q^36 + 4 * q^37 - 24 * q^39 - 61 * q^42 + 24 * q^44 + 28 * q^45 - 19 * q^46 - 51 * q^48 + 20 * q^49 - 64 * q^52 - 5 * q^54 - 8 * q^55 - 23 * q^56 - q^58 - 16 * q^59 + 6 * q^60 + 10 * q^62 - 30 * q^64 + 14 * q^66 - 36 * q^67 - 51 * q^68 - 4 * q^70 - 81 * q^72 + 70 * q^74 - 60 * q^76 + 143 * q^78 + 14 * q^80 - 28 * q^81 + 21 * q^82 + 40 * q^83 + 31 * q^84 - 28 * q^86 - 36 * q^87 - 19 * q^88 + 18 * q^90 + 16 * q^91 - 18 * q^92 + 43 * q^94 - 16 * q^95 - 48 * q^96 + 24 * q^97 + 56 * q^98 - 48 * q^99

Introduction

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