LMFDB - Embedded newform 310.2.s.a.263.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [310,2,Mod(23,310)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(310, base_ring=CyclotomicField(20))

chi = DirichletCharacter(H, H._module([15, 18]))

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

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

chi := DirichletCharacter("310.23");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 310 = 2 \cdot 5 \cdot 31 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	310.s (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:	$2.47536246266$
Analytic rank:	$0$
Dimension:	$128$
Relative dimension:	$16$ over $\Q(\zeta_{20})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{20}]$

Embedding invariants

Embedding label			263.10
Character	$\chi$	$=$	310.263
Dual form			310.2.s.a.277.10

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.156434 - 0.987688i) q^{2} +(-1.90681 + 0.302009i) q^{3} +(-0.951057 - 0.309017i) q^{4} +(1.36063 + 1.77445i) q^{5} +1.93058i q^{6} +(-1.19249 - 2.34039i) q^{7} +(-0.453990 + 0.891007i) q^{8} +(0.691555 - 0.224700i) q^{9} +O(q^{10})$	\(q+(0.156434 - 0.987688i) q^{2} +(-1.90681 + 0.302009i) q^{3} +(-0.951057 - 0.309017i) q^{4} +(1.36063 + 1.77445i) q^{5} +1.93058i q^{6} +(-1.19249 - 2.34039i) q^{7} +(-0.453990 + 0.891007i) q^{8} +(0.691555 - 0.224700i) q^{9} +(1.96546 - 1.06629i) q^{10} +(-4.23123 - 1.37481i) q^{11} +(1.90681 + 0.302009i) q^{12} +(-3.81581 + 0.604364i) q^{13} +(-2.49812 + 0.811688i) q^{14} +(-3.13037 - 2.97263i) q^{15} +(0.809017 + 0.587785i) q^{16} +(-2.07435 + 4.07115i) q^{17} +(-0.113750 - 0.718192i) q^{18} +(2.55296 + 3.51385i) q^{19} +(-0.745699 - 2.10806i) q^{20} +(2.98067 + 4.10253i) q^{21} +(-2.01980 + 3.96407i) q^{22} +(-7.78045 - 3.96434i) q^{23} +(0.596582 - 1.83609i) q^{24} +(-1.29738 + 4.82875i) q^{25} +3.86337i q^{26} +(3.90968 - 1.99208i) q^{27} +(0.410903 + 2.59434i) q^{28} +(1.79620 - 1.30501i) q^{29} +(-3.42573 + 2.62681i) q^{30} +(1.44818 + 5.37613i) q^{31} +(0.707107 - 0.707107i) q^{32} +(8.48338 + 1.34364i) q^{33} +(3.69652 + 2.68568i) q^{34} +(2.53038 - 5.30041i) q^{35} -0.727144 q^{36} +(-7.74107 - 7.74107i) q^{37} +(3.86996 - 1.97184i) q^{38} +(7.09351 - 2.30482i) q^{39} +(-2.19876 + 0.406744i) q^{40} +(-4.11628 + 2.99065i) q^{41} +(4.51830 - 2.30219i) q^{42} +(1.16786 - 7.37359i) q^{43} +(3.59930 + 2.61505i) q^{44} +(1.33967 + 0.921400i) q^{45} +(-5.13266 + 7.06450i) q^{46} +(-6.48865 + 1.02770i) q^{47} +(-1.72016 - 0.876466i) q^{48} +(0.0591151 - 0.0813649i) q^{49} +(4.56634 + 2.03679i) q^{50} +(2.72588 - 8.38939i) q^{51} +(3.81581 + 0.604364i) q^{52} +(11.6942 + 5.95847i) q^{53} +(-1.35595 - 4.17317i) q^{54} +(-3.31760 - 9.37874i) q^{55} +2.62668 q^{56} +(-5.92923 - 5.92923i) q^{57} +(-1.00796 - 1.97823i) q^{58} +(-0.0738602 + 0.101660i) q^{59} +(2.05856 + 3.79447i) q^{60} -9.39553i q^{61} +(5.53649 - 0.589341i) q^{62} +(-1.35055 - 1.35055i) q^{63} +(-0.587785 - 0.809017i) q^{64} +(-6.26432 - 5.94866i) q^{65} +(2.65419 - 8.16874i) q^{66} +(5.18685 - 5.18685i) q^{67} +(3.23088 - 3.23088i) q^{68} +(16.0331 + 5.20948i) q^{69} +(-4.83931 - 3.32839i) q^{70} +(1.93309 + 5.94943i) q^{71} +(-0.113750 + 0.718192i) q^{72} +(2.70715 + 5.31308i) q^{73} +(-8.85673 + 6.43479i) q^{74} +(1.01552 - 9.59934i) q^{75} +(-1.34217 - 4.13077i) q^{76} +(1.82810 + 11.5422i) q^{77} +(-1.16677 - 7.36673i) q^{78} +(0.279023 + 0.858743i) q^{79} +(0.0577743 + 2.23532i) q^{80} +(-8.61821 + 6.26150i) q^{81} +(2.30991 + 4.53345i) q^{82} +(-1.25537 + 7.92610i) q^{83} +(-1.56703 - 4.82282i) q^{84} +(-10.0465 + 1.85848i) q^{85} +(-7.10011 - 2.30697i) q^{86} +(-3.03088 + 3.03088i) q^{87} +(3.14591 - 3.14591i) q^{88} +(2.51071 - 7.72717i) q^{89} +(1.11963 - 1.17904i) q^{90} +(5.96474 + 8.20976i) q^{91} +(6.17460 + 6.17460i) q^{92} +(-4.38505 - 9.81391i) q^{93} +6.56953i q^{94} +(-2.76153 + 9.31115i) q^{95} +(-1.13477 + 1.56187i) q^{96} +(-3.19263 - 6.26588i) q^{97} +(-0.0711155 - 0.0711155i) q^{98} -3.23505 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 128 q + 12 q^{7}+O(q^{10}) $ 128 * q + 12 * q^7	$ 128 q + 12 q^{7} + 8 q^{10} + 32 q^{16} + 8 q^{20} - 80 q^{21} - 20 q^{22} - 20 q^{23} + 40 q^{25} + 8 q^{28} - 32 q^{31} + 20 q^{33} - 48 q^{35} - 128 q^{36} + 52 q^{38} + 8 q^{41} - 20 q^{42} + 64 q^{45} - 40 q^{46} - 20 q^{47} - 20 q^{48} + 24 q^{50} - 16 q^{51} - 40 q^{53} - 40 q^{55} + 20 q^{60} - 8 q^{62} + 256 q^{63} - 160 q^{65} + 56 q^{66} + 8 q^{67} - 32 q^{70} + 56 q^{71} - 80 q^{73} - 160 q^{75} + 48 q^{76} - 20 q^{77} + 4 q^{78} - 96 q^{81} + 16 q^{82} - 240 q^{83} + 120 q^{85} + 40 q^{87} - 64 q^{90} + 80 q^{91} - 160 q^{93} + 32 q^{95} - 56 q^{97} - 176 q^{98}+O(q^{100}) $ 128 * q + 12 * q^7 + 8 * q^10 + 32 * q^16 + 8 * q^20 - 80 * q^21 - 20 * q^22 - 20 * q^23 + 40 * q^25 + 8 * q^28 - 32 * q^31 + 20 * q^33 - 48 * q^35 - 128 * q^36 + 52 * q^38 + 8 * q^41 - 20 * q^42 + 64 * q^45 - 40 * q^46 - 20 * q^47 - 20 * q^48 + 24 * q^50 - 16 * q^51 - 40 * q^53 - 40 * q^55 + 20 * q^60 - 8 * q^62 + 256 * q^63 - 160 * q^65 + 56 * q^66 + 8 * q^67 - 32 * q^70 + 56 * q^71 - 80 * q^73 - 160 * q^75 + 48 * q^76 - 20 * q^77 + 4 * q^78 - 96 * q^81 + 16 * q^82 - 240 * q^83 + 120 * q^85 + 40 * q^87 - 64 * q^90 + 80 * q^91 - 160 * q^93 + 32 * q^95 - 56 * q^97 - 176 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/310\mathbb{Z}\right)^\times$.

$n$	$187$	$251$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$e\left(\frac{7}{10}\right)$

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 $

$2$	0.156434	−	0.987688i	0.110616	−	0.698401i
$2$	0.156434	−	0.987688i	0.110616	−	0.698401i
$3$	−1.90681	+	0.302009i	−1.10090	+	0.174365i	−0.680338	−	0.732899i	$-0.738167\pi$
$3$	−1.90681	+	0.302009i	−1.10090	+	0.174365i	−0.420561	+	0.907264i	$0.638167\pi$
$4$	−0.951057	−	0.309017i	−0.475528	−	0.154508i
$5$	1.36063	+	1.77445i	0.608492	+	0.793560i
$5$	1.36063	+	1.77445i	0.608492	+	0.793560i
$6$			1.93058i			0.788157i
$7$	−1.19249	−	2.34039i	−0.450717	−	0.884583i	−0.998838	−	0.0481836i	$-0.984657\pi$
$7$	−1.19249	−	2.34039i	−0.450717	−	0.884583i	0.548121	−	0.836399i	$-0.315343\pi$
$8$	−0.453990	+	0.891007i	−0.160510	+	0.315018i
$9$	0.691555	−	0.224700i	0.230518	−	0.0749000i
$10$	1.96546	−	1.06629i	0.621532	−	0.337191i
$11$	−4.23123	−	1.37481i	−1.27577	−	0.414521i	−0.408679	−	0.912678i	$-0.634010\pi$
$11$	−4.23123	−	1.37481i	−1.27577	−	0.414521i	−0.867087	+	0.498157i	$0.834010\pi$
$12$	1.90681	+	0.302009i	0.550449	+	0.0871826i
$13$	−3.81581	+	0.604364i	−1.05831	+	0.167621i	−0.661247	−	0.750169i	$-0.729972\pi$
$13$	−3.81581	+	0.604364i	−1.05831	+	0.167621i	−0.397068	+	0.917789i	$0.629972\pi$
$14$	−2.49812	+	0.811688i	−0.667650	+	0.216933i
$15$	−3.13037	−	2.97263i	−0.808257	−	0.767529i
$16$	0.809017	+	0.587785i	0.202254	+	0.146946i
$17$	−2.07435	+	4.07115i	−0.503105	+	0.987398i	0.490171	+	0.871626i	$0.336934\pi$
$17$	−2.07435	+	4.07115i	−0.503105	+	0.987398i	−0.993276	+	0.115772i	$0.963066\pi$
$18$	−0.113750	−	0.718192i	−0.0268112	−	0.169279i
$19$	2.55296	+	3.51385i	0.585689	+	0.806132i	0.994305	−	0.106575i	$-0.0339884\pi$
$19$	2.55296	+	3.51385i	0.585689	+	0.806132i	−0.408616	+	0.912706i	$0.633988\pi$
$20$	−0.745699	−	2.10806i	−0.166743	−	0.471377i
$21$	2.98067	+	4.10253i	0.650435	+	0.895246i
$22$	−2.01980	+	3.96407i	−0.430622	+	0.845143i
$23$	−7.78045	−	3.96434i	−1.62234	−	0.826621i	−0.999002	−	0.0446653i	$-0.985778\pi$
$23$	−7.78045	−	3.96434i	−1.62234	−	0.826621i	−0.623334	−	0.781956i	$-0.714222\pi$
$24$	0.596582	−	1.83609i	0.121777	−	0.374791i
$25$	−1.29738	+	4.82875i	−0.259475	+	0.965750i
$26$			3.86337i			0.757670i
$27$	3.90968	−	1.99208i	0.752418	−	0.383376i
$28$	0.410903	+	2.59434i	0.0776533	+	0.490284i
$29$	1.79620	−	1.30501i	0.333545	−	0.242335i	−0.408388	−	0.912808i	$-0.633909\pi$
$29$	1.79620	−	1.30501i	0.333545	−	0.242335i	0.741933	+	0.670474i	$0.233909\pi$
$30$	−3.42573	+	2.62681i	−0.625450	+	0.479587i
$31$	1.44818	+	5.37613i	0.260101	+	0.965581i
$31$	1.44818	+	5.37613i	0.260101	+	0.965581i
$32$	0.707107	−	0.707107i	0.125000	−	0.125000i
$33$	8.48338	+	1.34364i	1.47677	+	0.233897i
$34$	3.69652	+	2.68568i	0.633949	+	0.460591i
$35$	2.53038	−	5.30041i	0.427712	−	0.895933i
$36$	−0.727144			−0.121191
$37$	−7.74107	−	7.74107i	−1.27262	−	1.27262i	−0.944706	−	0.327917i	$-0.893653\pi$
$37$	−7.74107	−	7.74107i	−1.27262	−	1.27262i	−0.327917	−	0.944706i	$-0.606347\pi$
$38$	3.86996	−	1.97184i	0.627790	−	0.319875i
$39$	7.09351	−	2.30482i	1.13587	−	0.369067i
$40$	−2.19876	+	0.406744i	−0.347655	+	0.0643119i
$41$	−4.11628	+	2.99065i	−0.642855	+	0.467062i	−0.860830	−	0.508893i	$-0.830055\pi$
$41$	−4.11628	+	2.99065i	−0.642855	+	0.467062i	0.217975	+	0.975954i	$0.430055\pi$
$42$	4.51830	−	2.30219i	0.697190	−	0.355236i
$43$	1.16786	−	7.37359i	0.178097	−	1.12446i	−0.723001	−	0.690847i	$-0.757238\pi$
$43$	1.16786	−	7.37359i	0.178097	−	1.12446i	0.901098	−	0.433615i	$-0.142762\pi$
$44$	3.59930	+	2.61505i	0.542615	+	0.394233i
$45$	1.33967	+	0.921400i	0.199706	+	0.137354i
$46$	−5.13266	+	7.06450i	−0.756769	+	1.04160i
$47$	−6.48865	+	1.02770i	−0.946467	+	0.149906i	−0.610543	−	0.791983i	$-0.709049\pi$
$47$	−6.48865	+	1.02770i	−0.946467	+	0.149906i	−0.335924	+	0.941889i	$0.609049\pi$
$48$	−1.72016	−	0.876466i	−0.248284	−	0.126507i
$49$	0.0591151	−	0.0813649i	0.00844501	−	0.0116236i
$50$	4.56634	+	2.03679i	0.645779	+	0.288045i
$51$	2.72588	−	8.38939i	0.381699	−	1.17475i
$52$	3.81581	+	0.604364i	0.529157	+	0.0838103i
$53$	11.6942	+	5.95847i	1.60632	+	0.818459i	0.999725	+	0.0234442i	$0.00746320\pi$
$53$	11.6942	+	5.95847i	1.60632	+	0.818459i	0.606590	+	0.795014i	$0.292537\pi$
$54$	−1.35595	−	4.17317i	−0.184521	−	0.567897i
$55$	−3.31760	−	9.37874i	−0.447345	−	1.26463i
$56$	2.62668			0.351004
$57$	−5.92923	−	5.92923i	−0.785345	−	0.785345i
$58$	−1.00796	−	1.97823i	−0.132352	−	0.259754i
$59$	−0.0738602	+	0.101660i	−0.00961578	+	0.0132350i	−0.813798	−	0.581148i	$-0.802604\pi$
$59$	−0.0738602	+	0.101660i	−0.00961578	+	0.0132350i	0.804182	+	0.594383i	$0.202604\pi$
$60$	2.05856	+	3.79447i	0.265759	+	0.489865i
$61$		−	9.39553i		−	1.20297i	−0.798883	−	0.601487i	$-0.794575\pi$
$61$		−	9.39553i		−	1.20297i	0.798883	−	0.601487i	$-0.205425\pi$
$62$	5.53649	−	0.589341i	0.703134	−	0.0748464i
$63$	−1.35055	−	1.35055i	−0.170154	−	0.170154i
$64$	−0.587785	−	0.809017i	−0.0734732	−	0.101127i
$65$	−6.26432	−	5.94866i	−0.776993	−	0.737840i
$66$	2.65419	−	8.16874i	0.326708	−	1.00550i
$67$	5.18685	−	5.18685i	0.633675	−	0.633675i	−0.315313	−	0.948988i	$-0.602109\pi$
$67$	5.18685	−	5.18685i	0.633675	−	0.633675i	0.948988	+	0.315313i	$0.102109\pi$
$68$	3.23088	−	3.23088i	0.391802	−	0.391802i
$69$	16.0331	+	5.20948i	1.93016	+	0.627147i
$70$	−4.83931	−	3.32839i	−0.578409	−	0.397819i
$71$	1.93309	+	5.94943i	0.229415	+	0.706068i	0.997813	+	0.0660953i	$0.0210541\pi$
$71$	1.93309	+	5.94943i	0.229415	+	0.706068i	−0.768398	+	0.639972i	$0.778946\pi$
$72$	−0.113750	+	0.718192i	−0.0134056	+	0.0846397i
$73$	2.70715	+	5.31308i	0.316848	+	0.621849i	0.993420	−	0.114528i	$-0.0365354\pi$
$73$	2.70715	+	5.31308i	0.316848	+	0.621849i	−0.676572	+	0.736376i	$0.736535\pi$
$74$	−8.85673	+	6.43479i	−1.02957	+	0.748029i
$75$	1.01552	−	9.59934i	0.117263	−	1.10844i
$76$	−1.34217	−	4.13077i	−0.153957	−	0.473832i
$77$	1.82810	+	11.5422i	0.208331	+	1.31535i
$78$	−1.16677	−	7.36673i	−0.132111	−	0.834117i
$79$	0.279023	+	0.858743i	0.0313925	+	0.0966162i	0.965525	−	0.260310i	$-0.0838248\pi$
$79$	0.279023	+	0.858743i	0.0313925	+	0.0966162i	−0.934133	+	0.356926i	$0.883825\pi$
$80$	0.0577743	+	2.23532i	0.00645937	+	0.249917i
$81$	−8.61821	+	6.26150i	−0.957579	+	0.695722i
$82$	2.30991	+	4.53345i	0.255086	+	0.500635i
$83$	−1.25537	+	7.92610i	−0.137795	+	0.870002i	0.817839	+	0.575446i	$0.195172\pi$
$83$	−1.25537	+	7.92610i	−0.137795	+	0.870002i	−0.955634	+	0.294556i	$0.904828\pi$
$84$	−1.56703	−	4.82282i	−0.170977	−	0.526213i
$85$	−10.0465	+	1.85848i	−1.08969	+	0.201580i
$86$	−7.10011	−	2.30697i	−0.765625	−	0.248767i
$87$	−3.03088	+	3.03088i	−0.324945	+	0.324945i
$88$	3.14591	−	3.14591i	0.335355	−	0.335355i
$89$	2.51071	−	7.72717i	0.266135	−	0.819079i	−0.725295	−	0.688438i	$-0.758297\pi$
$89$	2.51071	−	7.72717i	0.266135	−	0.819079i	0.991430	−	0.130640i	$-0.0417034\pi$
$90$	1.11963	−	1.17904i	0.118019	−	0.124281i
$91$	5.96474	+	8.20976i	0.625275	+	0.860617i
$92$	6.17460	+	6.17460i	0.643746	+	0.643746i
$93$	−4.38505	−	9.81391i	−0.454709	−	1.01765i
$94$			6.56953i			0.677596i
$95$	−2.76153	+	9.31115i	−0.283327	+	0.955304i
$96$	−1.13477	+	1.56187i	−0.115817	+	0.159408i
$97$	−3.19263	−	6.26588i	−0.324162	−	0.636204i	0.670207	−	0.742174i	$-0.266205\pi$
$97$	−3.19263	−	6.26588i	−0.324162	−	0.636204i	−0.994369	+	0.105970i	$0.966205\pi$
$98$	−0.0711155	−	0.0711155i	−0.00718375	−	0.00718375i
$99$	−3.23505			−0.325135
$100$	2.72604	−	4.19150i	0.272604	−	0.419150i
$101$	3.13592	+	9.65137i	0.312036	+	0.960348i	0.976957	+	0.213434i	$0.0684649\pi$
$101$	3.13592	+	9.65137i	0.312036	+	0.960348i	−0.664922	+	0.746913i	$0.731535\pi$
$102$	−7.85968	−	4.00471i	−0.778224	−	0.396525i
$103$	−4.95186	−	0.784297i	−0.487921	−	0.0772791i	−0.0923732	−	0.995724i	$-0.529445\pi$
$103$	−4.95186	−	0.784297i	−0.487921	−	0.0772791i	−0.395548	+	0.918445i	$0.629445\pi$
$104$	1.19385	−	3.67428i	0.117066	−	0.360293i
$105$	−3.22418	+	10.8711i	−0.314648	+	1.06091i
$106$	7.71448	−	10.6181i	0.749296	−	1.03132i
$107$	−2.49031	−	1.26888i	−0.240747	−	0.122667i	0.329455	−	0.944171i	$-0.393135\pi$
$107$	−2.49031	−	1.26888i	−0.240747	−	0.122667i	−0.570202	+	0.821504i	$0.693135\pi$
$108$	−4.33391	+	0.686424i	−0.417031	+	0.0660512i
$109$	0.536680	−	0.738677i	0.0514047	−	0.0707525i	−0.782541	−	0.622599i	$-0.786077\pi$
$109$	0.536680	−	0.738677i	0.0514047	−	0.0707525i	0.833946	+	0.551847i	$0.186077\pi$
$110$	−9.78226	+	1.80960i	−0.932702	+	0.172538i
$111$	17.0986	+	12.4229i	1.62293	+	1.17913i
$112$	0.410903	−	2.59434i	0.0388267	−	0.245142i
$113$	1.35127	−	0.688508i	0.127117	−	0.0647694i	−0.389275	−	0.921121i	$-0.627275\pi$
$113$	1.35127	−	0.688508i	0.127117	−	0.0647694i	0.516393	+	0.856352i	$0.327275\pi$
$114$	−6.78376	+	4.92869i	−0.635358	+	0.461614i
$115$	−3.55177	−	19.2000i	−0.331205	−	1.79041i
$116$	−2.11156	+	0.686086i	−0.196053	+	0.0637015i
$117$	−2.50304	+	1.27536i	−0.231406	+	0.117907i
$118$	0.0888540	+	0.0888540i	0.00817967	+	0.00817967i
$119$	12.0017			1.10019
$120$	4.06979	−	1.43963i	0.371519	−	0.131420i
$121$	7.11405	+	5.16866i	0.646732	+	0.469878i
$122$	−9.27985	−	1.46978i	−0.840158	−	0.133068i
$123$	6.94577	−	6.94577i	0.626279	−	0.626279i
$124$	0.284012	−	5.56052i	0.0255051	−	0.499349i
$125$	−10.3336	+	4.26801i	−0.924269	+	0.381742i
$126$	−1.54520	+	1.12265i	−0.137657	+	0.100014i
$127$	1.33154	+	8.40703i	0.118155	+	0.746003i	0.973626	+	0.228151i	$0.0732681\pi$
$127$	1.33154	+	8.40703i	0.118155	+	0.746003i	−0.855470	+	0.517852i	$0.826732\pi$
$128$	−0.891007	+	0.453990i	−0.0787546	+	0.0401275i
$129$			14.4128i			1.26897i
$130$	−6.85538	+	5.25662i	−0.601256	+	0.461036i
$131$	1.41655	−	4.35969i	0.123765	−	0.380908i	−0.869909	−	0.493212i	$-0.835823\pi$
$131$	1.41655	−	4.35969i	0.123765	−	0.380908i	0.993674	+	0.112303i	$0.0358229\pi$
$132$	−7.65297	−	3.89938i	−0.666105	−	0.339398i
$133$	5.17939	−	10.1651i	0.449110	−	0.881428i
$134$	−4.31159	−	5.93440i	−0.372465	−	0.512654i
$135$	8.85448	+	4.22706i	0.762072	+	0.363807i
$136$	−2.68568	−	3.69652i	−0.230295	−	0.316974i
$137$	2.18212	+	13.7773i	0.186431	+	1.17708i	0.886405	+	0.462910i	$0.153195\pi$
$137$	2.18212	+	13.7773i	0.186431	+	1.17708i	−0.699974	+	0.714168i	$0.746805\pi$
$138$	7.65347	−	15.0208i	0.651507	−	1.27865i
$139$	−12.2549	−	8.90371i	−1.03945	−	0.755203i	−0.0692696	−	0.997598i	$-0.522067\pi$
$139$	−12.2549	−	8.90371i	−1.03945	−	0.755203i	−0.970178	+	0.242395i	$0.922067\pi$
$140$	−4.04445	+	4.25906i	−0.341818	+	0.359956i
$141$	12.0623	−	3.91927i	1.01583	−	0.330062i
$142$	6.17858	−	0.978592i	0.518495	−	0.0821216i
$143$	16.9765	+	2.68881i	1.41964	+	0.224849i
$144$	0.691555	+	0.224700i	0.0576296	+	0.0187250i
$145$	4.75964	+	1.41163i	0.395267	+	0.117229i
$146$	5.67116	−	1.84267i	0.469348	−	0.152500i
$147$	−0.0881484	+	0.173001i	−0.00727035	+	0.0142689i
$148$	4.97007	+	9.75431i	0.408537	+	0.801800i
$149$		−	6.50075i		−	0.532562i	−0.963895	−	0.266281i	$-0.914205\pi$
$149$		−	6.50075i		−	0.532562i	0.963895	−	0.266281i	$-0.0857949\pi$
$150$	−9.32229	−	2.50469i	−0.761162	−	0.204507i
$151$	−14.6783	−	4.76926i	−1.19450	−	0.388117i	−0.356766	−	0.934194i	$-0.616121\pi$
$151$	−14.6783	−	4.76926i	−1.19450	−	0.388117i	−0.837735	+	0.546076i	$0.816121\pi$
$152$	−4.28988	+	0.679450i	−0.347955	+	0.0551107i
$153$	−0.519743	+	3.28153i	−0.0420188	+	0.265296i
$154$	11.6860			0.941688
$155$	−7.56926	+	9.88465i	−0.607977	+	0.793954i
$156$	−7.45855			−0.597162
$157$	1.99908	−	12.6217i	0.159544	−	1.00732i	−0.769849	−	0.638226i	$-0.779668\pi$
$157$	1.99908	−	12.6217i	0.159544	−	1.00732i	0.929393	−	0.369093i	$-0.120332\pi$
$158$	0.891820	−	0.141250i	0.0709494	−	0.0112373i
$159$	−24.0981	−	7.82994i	−1.91110	−	0.620955i
$160$	2.21684	+	0.292618i	0.175257	+	0.0231335i
$161$			22.9367i			1.80766i
$162$	4.83622	+	9.49162i	0.379969	+	0.745732i
$163$	−10.2934	+	20.2019i	−0.806239	+	1.58233i	0.00669514	+	0.999978i	$0.497869\pi$
$163$	−10.2934	+	20.2019i	−0.806239	+	1.58233i	−0.812934	+	0.582356i	$0.802131\pi$
$164$	4.83898	−	1.57228i	0.377861	−	0.122774i
$165$	9.15851	+	16.8816i	0.712989	+	1.31423i
$166$	7.63213	+	2.47983i	0.592368	+	0.192472i
$167$	−9.50248	−	1.50505i	−0.735324	−	0.116464i	−0.222470	−	0.974940i	$-0.571412\pi$
$167$	−9.50248	−	1.50505i	−0.735324	−	0.116464i	−0.512854	+	0.858476i	$0.671412\pi$
$168$	−5.00858	+	0.793281i	−0.386420	+	0.0612030i
$169$	1.83139	−	0.595056i	0.140876	−	0.0457735i
$170$	0.263980	+	10.2135i	0.0202463	+	0.783342i
$171$	2.55507	+	1.85637i	0.195391	+	0.141960i
$172$	−3.38927	+	6.65181i	−0.258429	+	0.507196i
$173$	1.94977	+	12.3104i	0.148238	+	0.935939i	0.943908	+	0.330209i	$0.107119\pi$
$173$	1.94977	+	12.3104i	0.148238	+	0.935939i	−0.795670	+	0.605731i	$0.792881\pi$
$174$	2.51943	+	3.46770i	0.190998	+	0.262886i
$175$	12.8482	−	2.72186i	0.971235	−	0.205753i
$176$	−2.61505	−	3.59930i	−0.197117	−	0.271308i
$177$	0.110135	−	0.216153i	0.00827828	−	0.0162470i
$178$	−7.23928	−	3.68860i	−0.542607	−	0.276472i
$179$	−3.49929	+	10.7697i	−0.261549	+	0.804966i	0.730919	+	0.682464i	$0.239092\pi$
$179$	−3.49929	+	10.7697i	−0.261549	+	0.804966i	−0.992468	+	0.122502i	$0.960908\pi$
$180$	−0.989374	−	1.29028i	−0.0737436	−	0.0961721i
$181$		−	5.17427i		−	0.384600i	−0.981336	−	0.192300i	$-0.938405\pi$
$181$		−	5.17427i		−	0.384600i	0.981336	−	0.192300i	$-0.0615947\pi$
$182$	9.04178	−	4.60702i	0.670221	−	0.341495i
$183$	2.83754	+	17.9155i	0.209757	+	1.32435i
$184$	7.06450	−	5.13266i	0.520802	−	0.378385i
$185$	3.20345	−	24.2689i	0.235522	−	1.78428i
$186$	−10.3791	+	2.79583i	−0.761029	+	0.205000i
$187$	14.3741	−	14.3741i	1.05114	−	1.05114i
$188$	6.48865	+	1.02770i	0.473234	+	0.0749528i
$189$	−9.32447	−	6.77462i	−0.678255	−	0.492781i
$190$	8.76452	+	4.18411i	0.635845	+	0.303548i
$191$	−15.4029			−1.11452			−0.557258	−	0.830339i	$-0.688147\pi$
$191$	−15.4029			−1.11452			−0.557258	+	0.830339i	$0.688147\pi$
$192$	1.36513	+	1.36513i	0.0985196	+	0.0985196i
$193$	−8.04885	+	4.10109i	−0.579369	+	0.295203i	−0.719011	−	0.694999i	$-0.755405\pi$
$193$	−8.04885	+	4.10109i	−0.579369	+	0.295203i	0.139642	+	0.990202i	$0.455405\pi$
$194$	−6.68818	+	2.17312i	−0.480183	+	0.156021i
$195$	13.7414	+	9.45110i	0.984044	+	0.676807i
$196$	−0.0813649	+	0.0591151i	−0.00581178	+	0.00422250i
$197$	−17.6832	+	9.01003i	−1.25987	+	0.641938i	−0.951008	−	0.309167i	$-0.899950\pi$
$197$	−17.6832	+	9.01003i	−1.25987	+	0.641938i	−0.308867	+	0.951105i	$0.599950\pi$
$198$	−0.506074	+	3.19522i	−0.0359651	+	0.227075i
$199$	−3.97012	−	2.88446i	−0.281434	−	0.204474i	0.438108	−	0.898922i	$-0.355649\pi$
$199$	−3.97012	−	2.88446i	−0.281434	−	0.204474i	−0.719543	+	0.694448i	$0.755649\pi$
$200$	−3.71345	−	3.34818i	−0.262581	−	0.236752i
$201$	−8.32388	+	11.4568i	−0.587121	+	0.808103i
$202$	10.0231	−	1.58751i	0.705224	−	0.111696i
$203$	−5.19617	−	2.64758i	−0.364700	−	0.185824i
$204$	−5.18493	+	7.13644i	−0.363018	+	0.499651i
$205$	−10.9075	−	3.23498i	−0.761814	−	0.225941i
$206$	−1.54928	+	4.76820i	−0.107944	+	0.332216i
$207$	−6.27139	−	0.993291i	−0.435892	−	0.0690385i
$208$	−3.44229	−	1.75393i	−0.238680	−	0.121613i
$209$	−5.97129	−	18.3777i	−0.413043	−	1.27122i
$210$	10.2329	+	4.88510i	0.706135	+	0.337104i
$211$	−11.6956			−0.805161			−0.402581	−	0.915385i	$-0.631887\pi$
$211$	−11.6956			−0.805161			−0.402581	+	0.915385i	$0.631887\pi$
$212$	−9.28053	−	9.28053i	−0.637390	−	0.637390i
$213$	−5.48282	−	10.7606i	−0.375677	−	0.737307i
$214$	−1.64282	+	2.26115i	−0.112301	+	0.154569i
$215$	14.6731	−	7.96040i	1.00070	−	0.542895i
$216$			4.38793i			0.298561i
$217$	10.8553	−	9.80026i	0.736904	−	0.665285i
$218$	−0.645628	−	0.645628i	−0.0437274	−	0.0437274i
$219$	−6.76662	−	9.31346i	−0.457246	−	0.629345i
$220$	0.257037	+	9.94491i	0.0173294	+	0.670486i
$221$	5.45488	−	16.7884i	0.366935	−	1.12931i
$222$	14.9448	−	14.9448i	1.00303	−	1.00303i
$223$	−7.28958	+	7.28958i	−0.488146	+	0.488146i	−0.907721	−	0.419574i	$-0.862179\pi$
$223$	−7.28958	+	7.28958i	−0.488146	+	0.488146i	0.419574	+	0.907721i	$0.362179\pi$
$224$	−2.49812	−	0.811688i	−0.166912	−	0.0542332i
$225$	0.187813	+	3.63087i	0.0125209	+	0.242058i
$226$	−0.468646	−	1.44234i	−0.0311738	−	0.0959432i
$227$	−1.25443	+	7.92016i	−0.0832595	+	0.525680i	0.910444	+	0.413633i	$0.135740\pi$
$227$	−1.25443	+	7.92016i	−0.0832595	+	0.525680i	−0.993703	+	0.112046i	$0.964260\pi$
$228$	3.80680	+	7.47126i	0.252111	+	0.494796i
$229$	1.71330	−	1.24478i	0.113218	−	0.0822577i	−0.529736	−	0.848163i	$-0.677709\pi$
$229$	1.71330	−	1.24478i	0.113218	−	0.0822577i	0.642954	+	0.765905i	$0.277709\pi$
$230$	−19.5193	+	0.504497i	−1.28706	+	0.0332656i
$231$	−6.97169	−	21.4566i	−0.458703	−	1.41174i
$232$	0.347319	+	2.19289i	0.0228026	+	0.143970i
$233$	−2.16304	−	13.6569i	−0.141705	−	0.894693i	−0.951426	−	0.307877i	$-0.900381\pi$
$233$	−2.16304	−	13.6569i	−0.141705	−	0.894693i	0.809721	−	0.586815i	$-0.199619\pi$
$234$	0.868099	+	2.67173i	0.0567494	+	0.174657i
$235$	−10.6523	−	10.1155i	−0.694877	−	0.659862i
$236$	0.101660	−	0.0738602i	0.00661749	−	0.00480789i
$237$	−0.791393	−	1.55320i	−0.0514065	−	0.100891i
$238$	1.87748	−	11.8539i	0.121699	−	0.768376i
$239$	2.14533	+	6.60263i	0.138770	+	0.427089i	0.996157	−	0.0875822i	$-0.0279140\pi$
$239$	2.14533	+	6.60263i	0.138770	+	0.427089i	−0.857388	+	0.514671i	$0.827914\pi$
$240$	−0.785253	−	4.24489i	−0.0506879	−	0.274007i
$241$	7.39496	+	2.40277i	0.476351	+	0.154776i	0.537345	−	0.843362i	$-0.319427\pi$
$241$	7.39496	+	2.40277i	0.476351	+	0.154776i	−0.0609944	+	0.998138i	$0.519427\pi$
$242$	6.21791	−	6.21791i	0.399702	−	0.399702i
$243$	5.23407	−	5.23407i	0.335766	−	0.335766i
$244$	−2.90338	+	8.93568i	−0.185870	+	0.572048i
$245$	0.224812	−	0.00581051i	0.0143627	−	0.000371220i
$246$	−5.77370	−	7.94682i	−0.368118	−	0.506671i
$247$	−11.8652	−	11.8652i	−0.754967	−	0.754967i
$248$	−5.44763	−	1.15037i	−0.345925	−	0.0730487i
$249$		−	15.4927i		−	0.981811i
$250$	2.59892	+	10.8741i	0.164370	+	0.687737i
$251$	1.32605	−	1.82515i	0.0836996	−	0.115203i	−0.765114	−	0.643895i	$-0.777317\pi$
$251$	1.32605	−	1.82515i	0.0836996	−	0.115203i	0.848814	+	0.528692i	$0.177317\pi$
$252$	0.867109	+	1.70180i	0.0546227	+	0.107203i
$253$	27.4707	+	27.4707i	1.72707	+	1.72707i
$254$	8.51182			0.534079
$255$	18.5955	−	6.57790i	1.16450	−	0.411924i
$256$	0.309017	+	0.951057i	0.0193136	+	0.0594410i
$257$	6.58971	+	3.35763i	0.411055	+	0.209443i	0.647275	−	0.762257i	$-0.275909\pi$
$257$	6.58971	+	3.35763i	0.411055	+	0.209443i	−0.236220	+	0.971700i	$0.575909\pi$
$258$	14.2353	+	2.25465i	0.886251	+	0.140368i
$259$	−8.88597	+	27.3482i	−0.552147	+	1.69933i
$260$	4.11948	+	7.59329i	0.255479	+	0.470916i
$261$	0.948932	−	1.30609i	0.0587374	−	0.0808452i
$262$	−4.08442	−	2.08112i	−0.252336	−	0.128572i
$263$	−14.2528	+	2.25742i	−0.878864	+	0.139198i	−0.579531	−	0.814950i	$-0.696764\pi$
$263$	−14.2528	+	2.25742i	−0.878864	+	0.139198i	−0.299333	+	0.954149i	$0.596764\pi$
$264$	−5.04856	+	6.94875i	−0.310717	+	0.427666i
$265$	5.33838	+	28.8580i	0.327934	+	1.77273i
$266$	−9.22973	−	6.70579i	−0.565911	−	0.411159i
$267$	−2.45378	+	15.4925i	−0.150169	+	0.948127i
$268$	−6.53582	+	3.33017i	−0.399239	+	0.203422i
$269$	−3.24900	+	2.36053i	−0.198095	+	0.143924i	−0.682411	−	0.730969i	$-0.739068\pi$
$269$	−3.24900	+	2.36053i	−0.198095	+	0.143924i	0.484316	+	0.874893i	$0.339068\pi$
$270$	5.56016	−	8.08420i	0.338381	−	0.491989i
$271$	7.84933	−	2.55040i	0.476813	−	0.154926i	−0.0607441	−	0.998153i	$-0.519347\pi$
$271$	7.84933	−	2.55040i	0.476813	−	0.154926i	0.537557	+	0.843228i	$0.319347\pi$
$272$	−4.07115	+	2.07435i	−0.246850	+	0.125776i
$273$	−13.8531	−	13.8531i	−0.838426	−	0.838426i
$274$	13.9491			0.842695
$275$	12.1281	−	18.6479i	0.731353	−	1.12451i
$276$	−13.6386	−	9.90902i	−0.820947	−	0.596453i
$277$	21.6318	+	3.42614i	1.29973	+	0.205857i	0.767667	−	0.640849i	$-0.221418\pi$
$277$	21.6318	+	3.42614i	1.29973	+	0.205857i	0.532061	+	0.846706i	$0.321418\pi$
$278$	−10.7112	+	10.7112i	−0.642414	+	0.642414i
$279$	2.20951	+	3.39248i	0.132280	+	0.203103i
$280$	3.57393	+	4.66092i	0.213583	+	0.278543i
$281$	10.7756	−	7.82893i	0.642818	−	0.467035i	−0.217999	−	0.975949i	$-0.569953\pi$
$281$	10.7756	−	7.82893i	0.642818	−	0.467035i	0.860817	+	0.508914i	$0.169953\pi$
$282$	−1.98406	−	12.5269i	−0.118149	−	0.745964i
$283$	16.0791	−	8.19270i	0.955802	−	0.487005i	0.0947379	−	0.995502i	$-0.469799\pi$
$283$	16.0791	−	8.19270i	0.955802	−	0.487005i	0.861064	+	0.508497i	$0.169799\pi$
$284$		−	6.25560i		−	0.371202i
$285$	2.45366	−	18.5886i	0.145342	−	1.10110i
$286$	5.31141	−	16.3468i	0.314070	−	0.966608i
$287$	11.9079	+	6.06738i	0.702901	+	0.358146i
$288$	0.330117	−	0.647890i	0.0194523	−	0.0381773i
$289$	−2.27895	−	3.13671i	−0.134056	−	0.184512i
$290$	2.13882	−	4.48022i	0.125596	−	0.263087i
$291$	7.98010	+	10.9837i	0.467802	+	0.643874i
$292$	−0.932820	−	5.88959i	−0.0545891	−	0.344662i
$293$	8.65481	−	16.9860i	0.505619	−	0.992334i	−0.487265	−	0.873254i	$-0.662006\pi$
$293$	8.65481	−	16.9860i	0.505619	−	0.992334i	0.992885	−	0.119080i	$-0.0379945\pi$
$294$	0.157082	+	0.114126i	0.00916118	+	0.00665599i
$295$	−0.280887	+	0.00725983i	−0.0163539	+	0.000422684i
$296$	10.4117	−	3.38297i	0.605169	−	0.196631i
$297$	−19.2815	+	3.05389i	−1.11883	+	0.177205i
$298$	−6.42071	−	1.01694i	−0.371942	−	0.0589098i
$299$	32.0846	+	10.4249i	1.85550	+	0.602889i
$300$	−3.93218	+	8.81570i	−0.227024	+	0.508975i
$301$	−18.6497	+	6.05965i	−1.07495	+	0.349273i
$302$	−7.00674	+	13.7515i	−0.403192	+	0.791309i
$303$	−8.89442	−	17.4563i	−0.510971	−	1.00284i
$304$			4.34335i			0.249108i
$305$	16.6719	−	12.7838i	0.954632	−	0.732000i
$306$	3.15982	+	1.02669i	0.180635	+	0.0586919i
$307$	24.3554	−	3.85752i	1.39004	−	0.220160i	0.583869	−	0.811848i	$-0.301538\pi$
$307$	24.3554	−	3.85752i	1.39004	−	0.220160i	0.806167	+	0.591688i	$0.201538\pi$
$308$	1.82810	−	11.5422i	0.104166	−	0.657676i
$309$	9.67913			0.550627
$310$	8.57886	+	9.02237i	0.487247	+	0.512436i
$311$	−13.6508			−0.774066			−0.387033	−	0.922066i	$-0.626500\pi$
$311$	−13.6508			−0.774066			−0.387033	+	0.922066i	$0.626500\pi$
$312$	−1.16677	+	7.36673i	−0.0660556	+	0.417059i
$313$	14.0005	−	2.21746i	0.791355	−	0.125338i	0.252344	−	0.967637i	$-0.418798\pi$
$313$	14.0005	−	2.21746i	0.791355	−	0.125338i	0.539010	+	0.842299i	$0.318798\pi$
$314$	−12.1536	−	3.94893i	−0.685865	−	0.222851i
$315$	0.558893	−	4.23410i	0.0314900	−	0.238565i
$316$		−	0.902936i		−	0.0507941i
$317$	−2.36546	−	4.64248i	−0.132858	−	0.260748i	0.814988	−	0.579478i	$-0.196744\pi$
$317$	−2.36546	−	4.64248i	−0.132858	−	0.260748i	−0.947845	+	0.318730i	$0.896744\pi$
$318$	−11.5033	+	22.5765i	−0.645074	+	1.26603i
$319$	−9.39427	+	3.05238i	−0.525978	+	0.170901i
$320$	0.635806	−	2.14377i	0.0355426	−	0.119840i
$321$	5.13177	+	1.66741i	0.286427	+	0.0930659i
$322$	22.6543	+	3.58808i	1.26247	+	0.199956i
$323$	−19.6011	+	3.10451i	−1.09064	+	0.172740i
$324$	10.1313	−	3.29186i	0.562851	−	0.182881i
$325$	2.03221	−	19.2097i	0.112727	−	1.06556i
$326$	18.3429	+	13.3269i	1.01592	+	0.738109i
$327$	−0.800262	+	1.57060i	−0.0442546	+	0.0868545i
$328$	−0.795939	−	5.02536i	−0.0439484	−	0.277479i
$329$	10.1428	+	13.9604i	0.559193	+	0.769663i
$330$	18.1064	−	6.40490i	0.996726	−	0.352578i
$331$	−11.8804	−	16.3520i	−0.653006	−	0.898785i	0.346219	−	0.938154i	$-0.387465\pi$
$331$	−11.8804	−	16.3520i	−0.653006	−	0.898785i	−0.999225	+	0.0393685i	$0.987465\pi$
$332$	3.64323	−	7.15024i	0.199948	−	0.392420i
$333$	−7.09279	−	3.61396i	−0.388683	−	0.198044i
$334$	−2.97303	+	9.15005i	−0.162677	+	0.500668i
$335$	16.2612	+	2.14645i	0.888445	+	0.117273i
$336$			5.07101i			0.276646i
$337$	−9.05749	+	4.61502i	−0.493393	+	0.251396i	−0.682939	−	0.730476i	$-0.739298\pi$
$337$	−9.05749	+	4.61502i	−0.493393	+	0.251396i	0.189546	+	0.981872i	$0.439298\pi$
$338$	−0.301237	−	1.90193i	−0.0163851	−	0.103452i
$339$	−2.36869	+	1.72095i	−0.128649	+	0.0934693i
$340$	10.1291	+	1.33702i	0.549327	+	0.0725100i
$341$	1.26357	−	24.7386i	0.0684259	−	1.33967i
$342$	2.23322	−	2.23322i	0.120758	−	0.120758i
$343$	−18.4213	−	2.91764i	−0.994656	−	0.157538i
$344$	6.03971	+	4.38811i	0.325640	+	0.236591i
$345$	12.5712	+	35.5382i	0.676809	+	1.91331i
$346$	12.4638			0.670059
$347$	−16.5824	−	16.5824i	−0.890187	−	0.890187i	0.104353	−	0.994540i	$-0.466723\pi$
$347$	−16.5824	−	16.5824i	−0.890187	−	0.890187i	−0.994540	+	0.104353i	$0.966723\pi$
$348$	3.81914	−	1.94595i	0.204727	−	0.104314i
$349$	−9.68610	+	3.14720i	−0.518485	+	0.168466i	−0.556558	−	0.830809i	$-0.687878\pi$
$349$	−9.68610	+	3.14720i	−0.518485	+	0.168466i	0.0380727	+	0.999275i	$0.487878\pi$
$350$	−0.678440	−	13.1158i	−0.0362641	−	0.701071i
$351$	−13.7146	+	9.96426i	−0.732033	+	0.531853i
$352$	−3.96407	+	2.01980i	−0.211286	+	0.107656i
$353$	−4.15559	+	26.2373i	−0.221180	+	1.39647i	0.587976	+	0.808878i	$0.299925\pi$
$353$	−4.15559	+	26.2373i	−0.221180	+	1.39647i	−0.809156	+	0.587594i	$0.800075\pi$
$354$	−0.196263	−	0.142593i	−0.0104312	−	0.00757874i
$355$	−7.92678	+	11.5251i	−0.420710	+	0.611691i
$356$	−4.77566	+	6.57313i	−0.253109	+	0.348375i
$357$	−22.8850	+	3.62462i	−1.21120	+	0.191835i
$358$	10.0897	+	5.14097i	0.533258	+	0.271709i
$359$	15.7436	−	21.6691i	0.830913	−	1.14365i	−0.156839	−	0.987624i	$-0.550130\pi$
$359$	15.7436	−	21.6691i	0.830913	−	1.14365i	0.987752	−	0.156030i	$-0.0498695\pi$
$360$	−1.42917	+	0.775348i	−0.0753239	+	0.0408644i
$361$	0.0418072	−	0.128669i	0.00220038	−	0.00677207i
$362$	−5.11056	−	0.809434i	−0.268605	−	0.0425429i
$363$	−15.1262	−	7.70716i	−0.793917	−	0.404521i
$364$	−3.13585	−	9.65116i	−0.164363	−	0.505858i
$365$	−5.74439	+	12.0328i	−0.300675	+	0.629828i
$366$	18.1388			0.948132
$367$	9.59040	+	9.59040i	0.500615	+	0.500615i	0.911629	−	0.411014i	$-0.134825\pi$
$367$	9.59040	+	9.59040i	0.500615	+	0.500615i	−0.411014	+	0.911629i	$0.634825\pi$
$368$	−3.96434	−	7.78045i	−0.206655	−	0.405584i
$369$	−2.17464	+	2.99313i	−0.113207	+	0.155816i
$370$	−23.4690	−	6.96050i	−1.22009	−	0.361859i
$371$		−	34.4742i		−	1.78981i
$372$	1.13777	+	10.6886i	0.0589906	+	0.554180i
$373$	−16.5127	−	16.5127i	−0.854996	−	0.854996i	0.135748	−	0.990743i	$-0.456656\pi$
$373$	−16.5127	−	16.5127i	−0.854996	−	0.854996i	−0.990743	+	0.135748i	$0.956656\pi$
$374$	−11.9486	−	16.4458i	−0.617845	−	0.850391i
$375$	18.4153	−	11.2591i	0.950964	−	0.581420i
$376$	2.03010	−	6.24800i	0.104694	−	0.322216i
$377$	−6.06523	+	6.06523i	−0.312375	+	0.312375i
$378$	−8.14989	+	8.14989i	−0.419185	+	0.419185i
$379$	23.4989	+	7.63526i	1.20706	+	0.392197i	0.842353	−	0.538926i	$-0.181170\pi$
$379$	23.4989	+	7.63526i	1.20706	+	0.392197i	0.364705	+	0.931123i	$0.381170\pi$
$380$	5.50367	−	8.00207i	0.282332	−	0.410498i
$381$	−5.07800	−	15.6285i	−0.260154	−	0.800672i
$382$	−2.40955	+	15.2133i	−0.123283	+	0.778379i
$383$	14.5572	+	28.5700i	0.743836	+	1.45986i	0.882892	+	0.469576i	$0.155593\pi$
$383$	14.5572	+	28.5700i	0.743836	+	1.45986i	−0.139056	+	0.990284i	$0.544407\pi$
$384$	1.56187	−	1.13477i	0.0797040	−	0.0579083i
$385$	−17.9937	+	18.9485i	−0.917043	+	0.965704i
$386$	2.79148	+	8.59131i	0.142083	+	0.437286i
$387$	−0.849203	−	5.36166i	−0.0431674	−	0.272548i
$388$	1.10010	+	6.94579i	0.0558493	+	0.352619i
$389$	0.826251	+	2.54294i	0.0418926	+	0.128932i	0.969815	−	0.243840i	$-0.0784072\pi$
$389$	0.826251	+	2.54294i	0.0418926	+	0.128932i	−0.927923	+	0.372772i	$0.878407\pi$
$390$	11.4844	−	12.0938i	0.581534	−	0.612392i
$391$	32.2788	−	23.4519i	1.63241	−	1.18601i
$392$	0.0456590	+	0.0896108i	0.00230613	+	0.00452603i
$393$	−1.38443	+	8.74093i	−0.0698351	+	0.440921i
$394$	6.13284	+	18.8749i	0.308968	+	0.950906i
$395$	−1.14415	+	1.66354i	−0.0575687	+	0.0837020i
$396$	3.07672	+	0.999686i	0.154611	+	0.0502361i
$397$	25.7349	−	25.7349i	1.29160	−	1.29160i	0.357798	−	0.933799i	$-0.383528\pi$
$397$	25.7349	−	25.7349i	1.29160	−	1.29160i	0.933799	−	0.357798i	$-0.116472\pi$
$398$	−3.47001	+	3.47001i	−0.173936	+	0.173936i
$399$	−6.80616	+	20.9472i	−0.340734	+	1.04867i
$400$	−3.88787	+	3.14396i	−0.194393	+	0.157198i
$401$	13.1436	+	18.0907i	0.656362	+	0.903405i	0.999354	−	0.0359334i	$-0.0114404\pi$
$401$	13.1436	+	18.0907i	0.656362	+	0.903405i	−0.342992	+	0.939338i	$0.611440\pi$
$402$	10.0136	+	10.0136i	0.499435	+	0.499435i
$403$	−8.77513	−	19.6390i	−0.437120	−	0.978290i
$404$		−	10.1481i		−	0.504885i
$405$	−22.8369	−	6.77304i	−1.13478	−	0.336555i
$406$	−3.42785	+	4.71803i	−0.170121	+	0.234152i
$407$	22.1118	+	43.3968i	1.09604	+	2.15110i
$408$	6.23748	+	6.23748i	0.308801	+	0.308801i
$409$	−20.4147			−1.00944			−0.504721	−	0.863282i	$-0.668405\pi$
$409$	−20.4147			−1.00944			−0.504721	+	0.863282i	$0.668405\pi$
$410$	−4.90147	+	10.2672i	−0.242066	+	0.507059i
$411$	−8.32178	−	25.6118i	−0.410483	−	1.26334i
$412$	4.46714	+	2.27612i	0.220080	+	0.112136i
$413$	0.326000	+	0.0516334i	0.0160414	+	0.00254071i
$414$	−1.96212	+	6.03880i	−0.0964332	+	0.296791i
$415$	−15.7726	+	8.55688i	−0.774246	+	0.420041i
$416$	−2.27083	+	3.12553i	−0.111337	+	0.153242i
$417$	26.0568	+	13.2766i	1.27601	+	0.650158i
$418$	−19.0856	+	3.02286i	−0.933507	+	0.147853i
$419$	−3.61465	+	4.97515i	−0.176587	+	0.243052i	−0.888131	−	0.459590i	$-0.847996\pi$
$419$	−3.61465	+	4.97515i	−0.176587	+	0.243052i	0.711544	+	0.702642i	$0.247996\pi$
$420$	6.42573	−	9.34269i	0.313543	−	0.455877i
$421$	−18.4622	−	13.4135i	−0.899790	−	0.653736i	0.0386217	−	0.999254i	$-0.487703\pi$
$421$	−18.4622	−	13.4135i	−0.899790	−	0.653736i	−0.938412	+	0.345518i	$0.887703\pi$
$422$	−1.82960	+	11.5517i	−0.0890636	+	0.562326i
$423$	−4.25634	+	2.16871i	−0.206950	+	0.105446i
$424$	−10.6181	+	7.71448i	−0.515659	+	0.374648i
$425$	−16.9673	−	15.2983i	−0.823037	−	0.742078i
$426$	−11.4859	+	3.73198i	−0.556492	+	0.180815i
$427$	−21.9892	+	11.2040i	−1.06413	+	0.542201i
$428$	1.97632	+	1.97632i	0.0955291	+	0.0955291i
$429$	−33.1830			−1.60209
$430$	−5.56701	−	15.7377i	−0.268465	−	0.758942i
$431$	6.51372	+	4.73250i	0.313755	+	0.227956i	0.733506	−	0.679683i	$-0.237883\pi$
$431$	6.51372	+	4.73250i	0.313755	+	0.227956i	−0.419751	+	0.907639i	$0.637883\pi$
$432$	4.33391	+	0.686424i	0.208515	+	0.0330256i
$433$	−25.6061	+	25.6061i	−1.23055	+	1.23055i	−0.266795	+	0.963753i	$0.585965\pi$
$433$	−25.6061	+	25.6061i	−1.23055	+	1.23055i	−0.963753	+	0.266795i	$0.914035\pi$
$434$	−7.98147	−	12.2547i	−0.383123	−	0.588246i
$435$	−9.50207	−	1.25425i	−0.455590	−	0.0601369i
$436$	−0.738677	+	0.536680i	−0.0353762	+	0.0257023i
$437$	−5.93309	−	37.4601i	−0.283818	−	1.79196i
$438$	−10.2573	+	5.22637i	−0.490114	+	0.249726i
$439$		−	24.7667i		−	1.18205i	−0.806653	−	0.591025i	$-0.798723\pi$
$439$		−	24.7667i		−	1.18205i	0.806653	−	0.591025i	$-0.201277\pi$
$440$	9.86268	+	1.30185i	0.470185	+	0.0620635i
$441$	0.0225986	−	0.0695515i	0.00107613	−	0.00331197i
$442$	−15.7284	−	8.01400i	−0.748122	−	0.381187i
$443$	−14.5094	+	28.4763i	−0.689362	+	1.35295i	0.235210	+	0.971944i	$0.424422\pi$
$443$	−14.5094	+	28.4763i	−0.689362	+	1.35295i	−0.924573	+	0.381005i	$0.875578\pi$
$444$	−12.4229	−	17.0986i	−0.589564	−	0.811466i
$445$	17.1277	−	6.05868i	0.811929	−	0.287209i
$446$	6.05949	+	8.34018i	0.286925	+	0.394919i
$447$	1.96329	+	12.3957i	0.0928603	+	0.586297i
$448$	−1.19249	+	2.34039i	−0.0563397	+	0.110573i
$449$	−11.7204	−	8.51536i	−0.553119	−	0.401865i	0.275815	−	0.961211i	$-0.411052\pi$
$449$	−11.7204	−	8.51536i	−0.553119	−	0.401865i	−0.828934	+	0.559346i	$0.811052\pi$
$450$	3.61554	+	0.382492i	0.170438	+	0.0180308i
$451$	21.5285	−	6.99505i	1.01374	−	0.329384i
$452$	−1.49790	+	0.237244i	−0.0704552	+	0.0111590i
$453$	29.4291	+	4.66111i	1.38270	+	0.218998i
$454$	7.62641	+	2.47797i	0.357925	+	0.116297i
$455$	−6.45205	+	21.7546i	−0.302477	+	1.01987i
$456$	7.97479	−	2.59117i	0.373454	−	0.121343i
$457$	2.23960	−	4.39547i	0.104764	−	0.205611i	−0.832674	−	0.553764i	$-0.813191\pi$
$457$	2.23960	−	4.39547i	0.104764	−	0.205611i	0.937438	+	0.348153i	$0.113191\pi$
$458$	−0.961440	−	1.88693i	−0.0449252	−	0.0881706i
$459$			20.0491i			0.935814i
$460$	−2.55520	+	19.3579i	−0.119137	+	0.902566i
$461$	−24.0118	−	7.80190i	−1.11834	−	0.363371i	−0.309206	−	0.950995i	$-0.600063\pi$
$461$	−24.0118	−	7.80190i	−1.11834	−	0.363371i	−0.809134	+	0.587624i	$0.800063\pi$
$462$	−22.2831	+	3.52929i	−1.03670	+	0.164198i
$463$	2.23072	−	14.0842i	0.103671	−	0.654550i	−0.880055	−	0.474872i	$-0.842494\pi$
$463$	2.23072	−	14.0842i	0.103671	−	0.654550i	0.983725	−	0.179678i	$-0.0575056\pi$
$464$	2.22022			0.103071
$465$	11.4479	−	21.1342i	0.530883	−	0.980074i
$466$	−13.8271			−0.640529
$467$	−0.759205	+	4.79343i	−0.0351318	+	0.221814i	−0.999008	−	0.0445383i	$-0.985818\pi$
$467$	−0.759205	+	4.79343i	−0.0351318	+	0.221814i	0.963876	+	0.266352i	$0.0858183\pi$
$468$	2.77464	−	0.439460i	0.128258	−	0.0203140i
$469$	−18.3245	−	5.95399i	−0.846146	−	0.274930i
$470$	−11.6573	+	8.93870i	−0.537713	+	0.412312i
$471$			24.6709i			1.13677i
$472$	−0.0570478	−	0.111963i	−0.00262584	−	0.00515349i
$473$	−15.0788	+	29.5938i	−0.693323	+	1.36072i
$474$	−1.65787	+	0.538676i	−0.0761487	+	0.0247422i
$475$	−20.2796	+	7.76882i	−0.930493	+	0.356458i
$476$	−11.4143	−	3.70873i	−0.523173	−	0.169989i
$477$	9.42602	+	1.49293i	0.431588	+	0.0683568i
$478$	6.85695	−	1.08603i	0.313629	−	0.0496740i
$479$	−19.7013	+	6.40133i	−0.900174	+	0.292484i	−0.722309	−	0.691571i	$-0.756919\pi$
$479$	−19.7013	+	6.40133i	−0.900174	+	0.292484i	−0.177865	+	0.984055i	$0.556919\pi$
$480$	−4.31547	+	0.111538i	−0.196973	+	0.00509099i
$481$	34.2168	+	24.8600i	1.56015	+	1.13352i
$482$	3.53001	−	6.92804i	0.160788	−	0.315563i
$483$	−6.92709	−	43.7359i	−0.315193	−	1.99005i
$484$	−5.16866	−	7.11405i	−0.234939	−	0.323366i
$485$	6.77454	−	14.1907i	0.307616	−	0.644367i
$486$	−4.35084	−	5.98842i	−0.197358	−	0.271640i
$487$	−14.6705	+	28.7926i	−0.664786	+	1.30472i	0.274503	+	0.961586i	$0.411487\pi$
$487$	−14.6705	+	28.7926i	−0.664786	+	1.30472i	−0.939288	+	0.343129i	$0.888513\pi$
$488$	8.37148	+	4.26548i	0.378959	+	0.193089i
$489$	13.5264	−	41.6299i	0.611684	−	1.88257i
$490$	0.0294294	−	0.222953i	0.00132948	−	0.0100720i
$491$			14.1609i			0.639072i	0.947574	+	0.319536i	$0.103527\pi$
$491$			14.1609i			0.639072i	−0.947574	+	0.319536i	$0.896473\pi$
$492$	−8.75219	+	4.45946i	−0.394579	+	0.201048i
$493$	1.58695	+	10.0196i	0.0714728	+	0.451262i
$494$	−13.5753	+	9.86303i	−0.610781	+	0.443759i
$495$	−4.40171	−	5.74045i	−0.197842	−	0.258014i
$496$	−1.98841	+	5.20060i	−0.0892820	+	0.233514i
$497$	11.6188	−	11.6188i	0.521174	−	0.521174i
$498$	−15.3020	−	2.42359i	−0.685698	−	0.108604i
$499$	30.6216	+	22.2479i	1.37081	+	0.995951i	0.997673	+	0.0681744i	$0.0217174\pi$
$499$	30.6216	+	22.2479i	1.37081	+	0.995951i	0.373136	+	0.927777i	$0.378283\pi$
$500$	11.1468	−	0.865844i	0.498498	−	0.0387217i
$501$	18.5740			0.829825
$502$	−1.59524	−	1.59524i	−0.0711991	−	0.0711991i
$503$	32.3930	−	16.5050i	1.44433	−	0.735924i	0.456250	−	0.889852i	$-0.349192\pi$
$503$	32.3930	−	16.5050i	1.44433	−	0.735924i	0.988082	+	0.153928i	$0.0491924\pi$
$504$	1.81649	−	0.590214i	0.0809130	−	0.0262902i
$505$	−12.8591	+	18.6965i	−0.572222	+	0.831983i
$506$	31.4298	−	22.8351i	1.39723	−	1.01514i
$507$	−3.31241	+	1.68776i	−0.147109	+	0.0749560i
$508$	1.33154	−	8.40703i	0.0590776	−	0.373001i
$509$	−33.1422	−	24.0792i	−1.46900	−	1.06729i	−0.980901	−	0.194508i	$-0.937689\pi$
$509$	−33.1422	−	24.0792i	−1.46900	−	1.06729i	−0.488103	−	0.872786i	$-0.662311\pi$
$510$	−3.58794	−	19.3956i	−0.158877	−	0.858850i
$511$	9.20641	−	12.6715i	0.407268	−	0.560556i
$512$	0.987688	−	0.156434i	0.0436501	−	0.00691349i
$513$	16.9811	+	8.65230i	0.749734	+	0.382009i
$514$	4.34715	−	5.98333i	0.191744	−	0.263914i
$515$	−5.34594	−	9.85398i	−0.235570	−	0.434218i
$516$	4.45378	−	13.7073i	0.196067	−	0.603432i
$517$	28.8679	+	4.57223i	1.26961	+	0.201086i
$518$	25.6214	+	13.0548i	1.12574	+	0.573594i
$519$	−7.43569	−	22.8847i	−0.326391	−	1.00453i
$520$	8.14423	−	2.88091i	0.357148	−	0.126336i
$521$	−38.5655			−1.68958			−0.844792	−	0.535095i	$-0.820276\pi$
$521$	−38.5655			−1.68958			−0.844792	+	0.535095i	$0.820276\pi$
$522$	−1.14157	−	1.14157i	−0.0499651	−	0.0499651i
$523$	13.2554	+	26.0153i	0.579620	+	1.13757i	0.975651	+	0.219331i	$0.0703874\pi$
$523$	13.2554	+	26.0153i	0.579620	+	1.13757i	−0.396031	+	0.918237i	$0.629613\pi$
$524$	−2.69444	+	3.70858i	−0.117707	+	0.162010i
$525$	−23.6772	+	9.07036i	−1.03336	+	0.395863i
$526$			14.4304i			0.629197i
$527$	−24.8911	−	5.25623i	−1.08427	−	0.228965i
$528$	6.07343	+	6.07343i	0.264312	+	0.264312i
$529$	31.3004	+	43.0812i	1.36088	+	1.87310i
$530$	29.3378	−	0.758268i	1.27435	−	0.0329371i
$531$	−0.0282354	+	0.0868998i	−0.00122531	+	0.00377113i
$532$	−8.06708	+	8.06708i	−0.349752	+	0.349752i
$533$	13.8995	−	13.8995i	0.602054	−	0.602054i
$534$	14.9179	+	4.84713i	0.645562	+	0.209756i
$535$	−1.13683	−	6.14541i	−0.0491493	−	0.265689i
$536$	2.26674	+	6.97630i	0.0979082	+	0.301330i
$537$	3.41994	−	21.5927i	0.147581	−	0.931792i
$538$	1.82322	+	3.57827i	0.0786045	+	0.154270i
$539$	−0.361991	+	0.263002i	−0.0155921	+	0.0113283i
$540$	−7.11487	−	6.75636i	−0.306175	−	0.290747i
$541$	−2.70656	−	8.32994i	−0.116364	−	0.358132i	0.875865	−	0.482556i	$-0.160292\pi$
$541$	−2.70656	−	8.32994i	−0.116364	−	0.358132i	−0.992229	+	0.124424i	$0.960292\pi$
$542$	−1.29110	−	8.15166i	−0.0554573	−	0.350144i
$543$	1.56268	+	9.86636i	0.0670609	+	0.423406i
$544$	1.41195	+	4.34553i	0.0605367	+	0.186313i
$545$	2.04097	−	0.0527512i	0.0874256	−	0.00225961i
$546$	−15.8496	+	11.5154i	−0.678301	+	0.492815i
$547$	−13.3744	−	26.2488i	−0.571850	−	1.12232i	−0.978018	−	0.208520i	$-0.933135\pi$
$547$	−13.3744	−	26.2488i	−0.571850	−	1.12232i	0.406169	−	0.913798i	$-0.366865\pi$
$548$	2.18212	−	13.7773i	0.0932155	−	0.588539i
$549$	−2.11117	−	6.49752i	−0.0901027	−	0.277308i
$550$	−16.5211	−	14.8960i	−0.704461	−	0.635167i
$551$	9.17123	+	2.97991i	0.390707	+	0.126949i
$552$	−11.9206	+	11.9206i	−0.507373	+	0.507373i
$553$	1.67706	−	1.67706i	0.0713159	−	0.0713159i
$554$	6.76791	−	20.8295i	0.287541	−	0.884961i
$555$	1.22107	+	47.2437i	0.0518313	+	2.00538i
$556$	8.90371	+	12.2549i	0.377601	+	0.519724i
$557$	26.7550	+	26.7550i	1.13365	+	1.13365i	0.989566	+	0.144081i	$0.0460225\pi$
$557$	26.7550	+	26.7550i	1.13365	+	1.13365i	0.144081	+	0.989566i	$0.453977\pi$
$558$	3.69636	−	1.65161i	0.156479	−	0.0699182i
$559$			28.8420i			1.21989i
$560$	5.16262	−	2.80080i	0.218160	−	0.118356i
$561$	−23.0677	+	31.7499i	−0.973917	+	1.34048i
$562$	−6.04687	−	11.8676i	−0.255072	−	0.500606i
$563$	9.14233	+	9.14233i	0.385303	+	0.385303i	0.873008	−	0.487705i	$-0.162166\pi$
$563$	9.14233	+	9.14233i	0.385303	+	0.385303i	−0.487705	+	0.873008i	$0.662166\pi$
$564$	−12.6830			−0.534052
$565$	3.06031	+	1.46097i	0.128748	+	0.0614634i
$566$	−5.57651	−	17.1627i	−0.234398	−	0.721403i
$567$	24.9314	+	12.7032i	1.04702	+	0.533484i
$568$	−6.17858	−	0.978592i	−0.259248	−	0.0410608i
$569$	3.70597	−	11.4058i	0.155363	−	0.478157i	−0.842835	−	0.538172i	$-0.819115\pi$
$569$	3.70597	−	11.4058i	0.155363	−	0.478157i	0.998197	+	0.0600155i	$0.0191150\pi$
$570$	−17.9759	−	5.33135i	−0.752929	−	0.223306i
$571$	−20.2473	+	27.8681i	−0.847325	+	1.16624i	0.137121	+	0.990554i	$0.456215\pi$
$571$	−20.2473	+	27.8681i	−0.847325	+	1.16624i	−0.984446	+	0.175688i	$0.943785\pi$
$572$	−15.3147	−	7.80322i	−0.640339	−	0.326269i
$573$	29.3705	−	4.65183i	1.22697	−	0.194333i
$574$	7.85548	−	10.8121i	0.327881	−	0.451290i
$575$	29.2369	−	32.4266i	1.21926	−	1.35228i
$576$	−0.588272	−	0.427405i	−0.0245113	−	0.0178085i
$577$	0.428051	−	2.70261i	0.0178200	−	0.112511i	−0.977175	−	0.212436i	$-0.931860\pi$
$577$	0.428051	−	2.70261i	0.0178200	−	0.112511i	0.994995	+	0.0999250i	$0.0318603\pi$
$578$	−3.45460	+	1.76020i	−0.143692	+	0.0732149i
$579$	14.1091	−	10.2508i	0.586353	−	0.426011i
$580$	−4.09047	−	2.81335i	−0.169848	−	0.116818i
$581$	20.0471	−	6.51371i	0.831695	−	0.270234i
$582$	12.0968	−	6.16363i	0.501428	−	0.255491i
$583$	−41.2889	−	41.2889i	−1.71001	−	1.71001i
$584$	−5.96301			−0.246751
$585$	−5.66878	−	2.70623i	−0.234375	−	0.111889i
$586$	−15.4230	−	11.2055i	−0.637118	−	0.462893i
$587$	−19.6931	−	3.11908i	−0.812821	−	0.128738i	−0.263833	−	0.964568i	$-0.584987\pi$
$587$	−19.6931	−	3.11908i	−0.812821	−	0.128738i	−0.548988	+	0.835830i	$0.684987\pi$
$588$	0.137294	−	0.137294i	0.00566192	−	0.00566192i
$589$	−15.1937	+	18.8137i	−0.626047	+	0.775206i
$590$	−0.0367700	+	0.278565i	−0.00151380	+	0.0114683i
$591$	30.9974	−	22.5209i	1.27506	−	0.926387i
$592$	−1.71257	−	10.8127i	−0.0703862	−	0.444401i
$593$	−31.3695	+	15.9836i	−1.28819	+	0.656367i	−0.957789	−	0.287473i	$-0.907185\pi$
$593$	−31.3695	+	15.9836i	−1.28819	+	0.656367i	−0.330404	+	0.943840i	$0.607185\pi$
$594$			19.5218i			0.800991i
$595$	16.3299	+	21.2965i	0.669459	+	0.873069i
$596$	−2.00884	+	6.18258i	−0.0822853	+	0.253248i
$597$	8.44141	+	4.30112i	0.345484	+	0.176033i
$598$	15.3157	−	30.0588i	0.626306	−	1.22919i
$599$	9.84252	+	13.5471i	0.402154	+	0.553518i	0.961283	−	0.275563i	$-0.0888642\pi$
$599$	9.84252	+	13.5471i	0.402154	+	0.553518i	−0.559129	+	0.829081i	$0.688864\pi$
$600$	8.09204	+	5.26285i	0.330356	+	0.214855i
$601$	−8.04717	−	11.0760i	−0.328251	−	0.451798i	0.612713	−	0.790305i	$-0.290078\pi$
$601$	−8.04717	−	11.0760i	−0.328251	−	0.451798i	−0.940964	+	0.338507i	$0.890078\pi$
$602$	3.06759	+	19.3680i	0.125026	+	0.789382i
$603$	2.42151	−	4.75248i	0.0986115	−	0.193536i
$604$	12.4861	+	9.07168i	0.508052	+	0.369121i
$605$	0.508036	+	19.6562i	0.0206546	+	0.799138i
$606$	−18.6328	+	6.05415i	−0.756904	+	0.245933i
$607$	−39.1391	+	6.19903i	−1.58861	+	0.251611i	−0.887281	−	0.461229i	$-0.847409\pi$
$607$	−39.1391	+	6.19903i	−1.58861	+	0.251611i	−0.701327	+	0.712840i	$0.747409\pi$
$608$	4.28988	+	0.679450i	0.173978	+	0.0275553i
$609$	10.7077	+	3.47915i	0.433899	+	0.140982i
$610$	−10.0184	−	18.4665i	−0.405632	−	0.747687i
$611$	24.1383	−	7.84302i	0.976533	−	0.317295i
$612$	1.50835	−	2.96031i	0.0609716	−	0.119663i
$613$	−19.3343	−	37.9457i	−0.780904	−	1.53261i	−0.845060	−	0.534671i	$-0.820436\pi$
$613$	−19.3343	−	37.9457i	−0.780904	−	1.53261i	0.0641563	−	0.997940i	$-0.479564\pi$
$614$		−	24.6590i		−	0.995156i
$615$	21.7756	+	2.87433i	0.878076	+	0.115904i
$616$	−11.1141	−	3.61118i	−0.447799	−	0.145499i
$617$	30.1413	−	4.77392i	1.21344	−	0.192191i	0.483282	−	0.875465i	$-0.339445\pi$
$617$	30.1413	−	4.77392i	1.21344	−	0.192191i	0.730162	+	0.683274i	$0.239445\pi$
$618$	1.51415	−	9.55997i	0.0609080	−	0.384558i
$619$	31.1836			1.25337			0.626687	−	0.779271i	$-0.284411\pi$
$619$	31.1836			1.25337			0.626687	+	0.779271i	$0.284411\pi$
$620$	10.2533	−	7.06183i	0.411783	−	0.283610i
$621$	−38.3163			−1.53758
$622$	−2.13545	+	13.4827i	−0.0856239	+	0.540608i
$623$	−21.0786	+	3.33851i	−0.844494	+	0.133755i
$624$	7.09351	+	2.30482i	0.283967	+	0.0922666i
$625$	−21.6336	−	12.5294i	−0.865345	−	0.501176i
$626$		−	14.1750i		−	0.566547i
$627$	16.9364	+	33.2395i	0.676374	+	1.32746i
$628$	−5.80154	+	11.3862i	−0.231507	+	0.454358i
$629$	47.5727	−	15.4573i	1.89685	−	0.616324i
$630$	−4.09454	−	1.21437i	−0.163130	−	0.0483817i
$631$	10.3107	+	3.35016i	0.410464	+	0.133368i	0.506968	−	0.861965i	$-0.330766\pi$
$631$	10.3107	+	3.35016i	0.410464	+	0.133368i	−0.0965043	+	0.995333i	$0.530766\pi$
$632$	−0.891820	−	0.141250i	−0.0354747	−	0.00561864i
$633$	22.3014	−	3.53220i	0.886401	−	0.140392i
$634$	−4.95537	+	1.61010i	−0.196803	+	0.0639451i
$635$	−13.1061	+	13.8016i	−0.520102	+	0.547700i
$636$	20.4990	+	14.8934i	0.812840	+	0.590563i
$637$	−0.176398	+	0.346200i	−0.00698913	+	0.0137169i
$638$	1.54522	+	9.75611i	0.0611757	+	0.386248i
$639$	2.67367	+	3.67999i	0.105769	+	0.145578i
$640$	−2.01792	−	0.963337i	−0.0797651	−	0.0380793i
$641$	−17.2763	−	23.7788i	−0.682374	−	0.939208i	0.317585	−	0.948230i	$-0.397128\pi$
$641$	−17.2763	−	23.7788i	−0.682374	−	0.939208i	−0.999959	+	0.00902223i	$0.997128\pi$
$642$	2.44967	−	4.80775i	0.0966807	−	0.189747i
$643$	9.88631	+	5.03733i	0.389878	+	0.198653i	0.637931	−	0.770094i	$-0.279791\pi$
$643$	9.88631	+	5.03733i	0.389878	+	0.198653i	−0.248053	+	0.968747i	$0.579791\pi$
$644$	7.08782	−	21.8141i	0.279299	−	0.859595i
$645$	−25.5748	+	19.6104i	−1.00701	+	0.772159i
$646$			19.8455i			0.780809i
$647$	23.0930	−	11.7665i	0.907879	−	0.462587i	0.0632854	−	0.997995i	$-0.479842\pi$
$647$	23.0930	−	11.7665i	0.907879	−	0.462587i	0.844594	+	0.535408i	$0.179842\pi$
$648$	−1.66645	−	10.5215i	−0.0654643	−	0.413325i
$649$	0.452283	−	0.328603i	0.0177537	−	0.0128988i
$650$	−18.6553	−	5.01224i	−0.731719	−	0.196596i
$651$	−17.7392	+	21.9657i	−0.695254	+	0.860902i
$652$	16.0323	−	16.0323i	0.627873	−	0.627873i
$653$	36.9919	+	5.85894i	1.44760	+	0.229278i	0.830243	−	0.557402i	$-0.188202\pi$
$653$	36.9919	+	5.85894i	1.44760	+	0.229278i	0.617361	+	0.786680i	$0.288202\pi$
$654$	1.42608	+	1.03611i	0.0557640	+	0.0405149i
$655$	9.66347	−	3.41832i	0.377583	−	0.133565i
$656$	−5.08801			−0.198653
$657$	3.06599	+	3.06599i	0.119616	+	0.119616i
$658$	15.3752	−	7.83408i	0.599389	−	0.305404i
$659$	−15.8052	+	5.13543i	−0.615684	+	0.200048i	−0.600223	−	0.799833i	$-0.704922\pi$
$659$	−15.8052	+	5.13543i	−0.615684	+	0.200048i	−0.0154609	+	0.999880i	$0.504922\pi$
$660$	−3.49358	−	18.8854i	−0.135987	−	0.735115i
$661$	−9.48140	+	6.88864i	−0.368784	+	0.267937i	−0.756706	−	0.653755i	$-0.773193\pi$
$661$	−9.48140	+	6.88864i	−0.368784	+	0.267937i	0.387923	+	0.921692i	$0.373193\pi$
$662$	−18.0091	+	9.17612i	−0.699945	+	0.356640i
$663$	−5.33118	+	33.6597i	−0.207046	+	1.30724i
$664$	−6.49228	−	4.71692i	−0.251949	−	0.183052i
$665$	25.0848	−	4.64038i	0.972745	−	0.179946i
$666$	−4.67902	+	6.44012i	−0.181308	+	0.249550i
$667$	−19.1487	+	3.03286i	−0.741441	+	0.117433i
$668$	8.57231	+	4.36781i	0.331673	+	0.168996i
$669$	11.6983	−	16.1014i	0.452284	−	0.622516i
$670$	4.66384	−	15.7252i	0.180180	−	0.607519i
$671$	−12.9171	+	39.7547i	−0.498658	+	1.53471i
$672$	5.00858	+	0.793281i	0.193210	+	0.0306015i
$673$	7.06379	+	3.59918i	0.272289	+	0.138738i	0.584804	−	0.811175i	$-0.301171\pi$
$673$	7.06379	+	3.59918i	0.272289	+	0.138738i	−0.312515	+	0.949913i	$0.601171\pi$
$674$	3.14130	+	9.66793i	0.120998	+	0.372395i
$675$	4.54694	+	21.4633i	0.175012	+	0.826124i
$676$	−1.92564			−0.0740631
$677$	−19.1727	−	19.1727i	−0.736868	−	0.736868i	0.235103	−	0.971970i	$-0.424457\pi$
$677$	−19.1727	−	19.1727i	−0.736868	−	0.736868i	−0.971970	+	0.235103i	$0.924457\pi$
$678$	1.32922	+	2.60874i	0.0510484	+	0.100188i
$679$	−10.8574	+	14.9440i	−0.416670	+	0.573497i
$680$	2.90510	−	9.79522i	0.111405	−	0.375630i
$681$		−	15.4811i		−	0.593238i
$682$	−24.2364	−	5.11799i	−0.928060	−	0.195978i
$683$	9.02078	+	9.02078i	0.345170	+	0.345170i	0.858307	−	0.513137i	$-0.171517\pi$
$683$	9.02078	+	9.02078i	0.345170	+	0.345170i	−0.513137	+	0.858307i	$0.671517\pi$
$684$	−1.85637	−	2.55507i	−0.0709800	−	0.0976956i
$685$	−21.4782	+	22.6179i	−0.820641	+	0.864187i
$686$	−5.76345	+	17.7381i	−0.220049	+	0.677242i
$687$	−2.89100	+	2.89100i	−0.110299	+	0.110299i
$688$	5.27890	−	5.27890i	0.201256	−	0.201256i
$689$	−48.2237	−	15.6688i	−1.83718	−	0.596935i
$690$	37.0672	−	6.85699i	1.41113	−	0.261041i
$691$	−5.71534	−	17.5900i	−0.217422	−	0.669155i	−0.998973	−	0.0453140i	$-0.985571\pi$
$691$	−5.71534	−	17.5900i	−0.217422	−	0.669155i	0.781551	−	0.623841i	$-0.214429\pi$
$692$	1.94977	−	12.3104i	0.0741191	−	0.467970i
$693$	3.85775	+	7.57127i	0.146544	+	0.287609i
$694$	−18.9722	+	13.7841i	−0.720177	+	0.523239i
$695$	−0.875159	−	33.8604i	−0.0331967	−	1.28440i
$696$	−1.32454	−	4.07653i	−0.0502067	−	0.154520i
$697$	−3.63677	−	22.9617i	−0.137753	−	0.869735i
$698$	1.59322	+	10.0592i	0.0603042	+	0.380745i
$699$	8.24902	+	25.3879i	0.312007	+	0.960258i
$700$	−13.0605	−	1.38168i	−0.493640	−	0.0522227i
$701$	8.06671	−	5.86081i	0.304675	−	0.221360i	−0.424933	−	0.905225i	$-0.639702\pi$
$701$	8.06671	−	5.86081i	0.304675	−	0.221360i	0.729608	+	0.683865i	$0.239702\pi$
$702$	7.69615	+	15.1045i	0.290472	+	0.570084i
$703$	7.43829	−	46.9635i	0.280541	−	1.77126i
$704$	1.37481	+	4.23123i	0.0518152	+	0.159471i
$705$	23.3668	+	16.0713i	0.880046	+	0.605279i
$706$	25.2642	+	8.20885i	0.950832	+	0.308944i
$707$	18.8484	−	18.8484i	0.708867	−	0.708867i
$708$	−0.171540	+	0.171540i	−0.00644686	+	0.00644686i
$709$	0.885054	−	2.72392i	0.0332389	−	0.102299i	−0.933061	−	0.359719i	$-0.882873\pi$
$709$	0.885054	−	2.72392i	0.0332389	−	0.102299i	0.966300	+	0.257420i	$0.0828725\pi$
$710$	10.1432	+	9.63212i	0.380669	+	0.361487i
$711$	0.385919	+	0.531172i	0.0144731	+	0.0199205i
$712$	5.74512	+	5.74512i	0.215308	+	0.215308i
$713$	10.0453	−	47.5698i	0.376199	−	1.78150i
$714$			23.1702i			0.867125i
$715$	18.3275	+	33.7824i	0.685410	+	1.26339i
$716$	6.65605	−	9.16127i	0.248748	−	0.342373i
$717$	−6.08479	−	11.9421i	−0.227241	−	0.445985i
$718$	−18.9395	−	18.9395i	−0.706817	−	0.706817i
$719$	22.0379			0.821876			0.410938	−	0.911663i	$-0.365201\pi$
$719$	22.0379			0.821876			0.410938	+	0.911663i	$0.365201\pi$
$720$	0.542231	+	1.53287i	0.0202077	+	0.0571265i
$721$	4.06946	+	12.5245i	0.151555	+	0.466438i
$722$	−0.120545	−	0.0614208i	−0.00448623	−	0.00228585i
$723$	−14.8265	−	2.34828i	−0.551402	−	0.0873335i
$724$	−1.59894	+	4.92102i	−0.0594240	+	0.182888i
$725$	3.97124	+	10.3665i	0.147488	+	0.385001i
$726$	−9.97852	+	13.7343i	−0.370338	+	0.509726i
$727$	−1.37255	−	0.699348i	−0.0509050	−	0.0259374i	0.428353	−	0.903612i	$-0.359094\pi$
$727$	−1.37255	−	0.699348i	−0.0509050	−	0.0259374i	−0.479258	+	0.877674i	$0.659094\pi$
$728$	−10.0229	+	1.58747i	−0.371473	+	0.0588355i
$729$	10.3848	−	14.2935i	0.384624	−	0.529389i
$730$	10.9861	+	7.55601i	0.406613	+	0.279661i
$731$	27.5964	+	20.0500i	1.02069	+	0.741574i
$732$	2.83754	−	17.9155i	0.104878	−	0.662176i
$733$	21.6566	−	11.0346i	0.799904	−	0.407572i	−0.00573076	−	0.999984i	$-0.501824\pi$
$733$	21.6566	−	11.0346i	0.799904	−	0.407572i	0.805635	+	0.592412i	$0.201824\pi$
$734$	10.9726	−	7.97206i	0.405006	−	0.294254i
$735$	−0.426919	+	0.0789749i	−0.0157472	+	0.00291303i
$736$	−8.30482	+	2.69840i	−0.306120	+	0.0994643i
$737$	−29.0777	+	14.8159i	−1.07109	+	0.545749i
$738$	2.61609	+	2.61609i	0.0962997	+	0.0962997i
$739$	28.8534			1.06139			0.530695	−	0.847563i	$-0.321931\pi$
$739$	28.8534			1.06139			0.530695	+	0.847563i	$0.321931\pi$
$740$	−10.5462	+	22.0912i	−0.387684	+	0.812088i
$741$	26.2082	+	19.0414i	0.962782	+	0.699502i
$742$	−34.0498	−	5.39296i	−1.25001	−	0.197982i
$743$	22.3703	−	22.3703i	0.820688	−	0.820688i	−0.165519	−	0.986207i	$-0.552930\pi$
$743$	22.3703	−	22.3703i	0.820688	−	0.820688i	0.986207	+	0.165519i	$0.0529299\pi$
$744$	10.7350	+	0.548309i	0.393565	+	0.0201020i
$745$	11.5353	−	8.84511i	0.422620	−	0.324060i
$746$	−18.8926	+	13.7263i	−0.691706	+	0.502554i
$747$	0.912835	+	5.76341i	0.0333989	+	0.210872i
$748$	−18.1125	+	9.22876i	−0.662257	+	0.337437i
$749$			7.34140i			0.268249i
$750$	−8.23973	−	19.9499i	−0.300872	−	0.728469i
$751$	5.37651	−	16.5472i	0.196192	−	0.603816i	−0.803769	−	0.594942i	$-0.797175\pi$
$751$	5.37651	−	16.5472i	0.196192	−	0.603816i	0.999961	−	0.00887445i	$-0.00282486\pi$
$752$	−5.85350	−	2.98251i	−0.213455	−	0.108761i
$753$	−1.97732	+	3.88070i	−0.0720575	+	0.141421i
$754$	5.04175	+	6.93937i	0.183610	+	0.252717i
$755$	−11.5089	−	32.5351i	−0.418850	−	1.18407i
$756$	6.77462	+	9.32447i	0.246391	+	0.339128i
$757$	−4.84982	−	30.6206i	−0.176270	−	1.11292i	−0.904149	−	0.427218i	$-0.859494\pi$
$757$	−4.84982	−	30.6206i	−0.176270	−	1.11292i	0.727879	−	0.685706i	$-0.240506\pi$
$758$	11.2173	−	22.0152i	0.407430	−	0.799627i
$759$	−60.6779	−	44.0850i	−2.20247	−	1.60019i
$760$	−7.04259	−	6.68771i	−0.255462	−	0.242589i
$761$	19.4661	−	6.32492i	0.705645	−	0.229278i	0.0658569	−	0.997829i	$-0.479022\pi$
$761$	19.4661	−	6.32492i	0.705645	−	0.229278i	0.639789	+	0.768551i	$0.279022\pi$
$762$	−16.2304	+	2.57065i	−0.587967	+	0.0931248i
$763$	−2.36877	−	0.375177i	−0.0857554	−	0.0135823i
$764$	14.6490	+	4.75976i	0.529984	+	0.172202i
$765$	−6.53010	+	3.54269i	−0.236096	+	0.128086i
$766$	30.4955	−	9.90860i	1.10185	−	0.358012i
$767$	0.220397	−	0.432553i	0.00795806	−	0.0156186i
$768$	−0.876466	−	1.72016i	−0.0316267	−	0.0620709i
$769$			32.4949i			1.17179i	0.810385	+	0.585897i	$0.199258\pi$
$769$			32.4949i			1.17179i	−0.810385	+	0.585897i	$0.800742\pi$
$770$	15.9004	+	20.7363i	0.573009	+	0.747286i
$771$	−13.5794	−	4.41221i	−0.489050	−	0.158902i
$772$	8.92222	−	1.41314i	0.321118	−	0.0508600i
$773$	3.47077	−	21.9136i	0.124835	−	0.788177i	−0.843244	−	0.537531i	$-0.819357\pi$
$773$	3.47077	−	21.9136i	0.124835	−	0.788177i	0.968079	−	0.250646i	$-0.0806430\pi$
$774$	−5.42849			−0.195123
$775$	−27.8388	+	0.0180516i	−1.00000	+	0.000648433i
$776$	7.03237			0.252447
$777$	8.68446	−	54.8315i	0.311553	−	1.96707i
$778$	2.64089	−	0.418275i	0.0946804	−	0.0149959i
$779$	−21.0174	−	6.82897i	−0.753026	−	0.244673i
$780$	−10.1483	−	13.2349i	−0.363368	−	0.473884i
$781$		−	27.8311i		−	0.995874i
$782$	−18.1137	−	35.5501i	−0.647744	−	1.27127i
$783$	4.42286	−	8.68035i	0.158060	−	0.310210i
$784$	0.0956502	−	0.0310786i	0.00341608	−	0.00110995i
$785$	25.1166	−	13.6261i	0.896449	−	0.486338i
$786$	8.41674	+	2.73476i	0.300215	+	0.0975458i
$787$	15.5731	+	2.46654i	0.555121	+	0.0879225i	0.427691	−	0.903925i	$-0.359327\pi$
$787$	15.5731	+	2.46654i	0.555121	+	0.0879225i	0.127430	+	0.991848i	$0.459327\pi$
$788$	19.6020	−	3.10464i	0.698291	−	0.110598i
$789$	26.4956	−	8.60895i	0.943269	−	0.306487i
$790$	1.46408	+	1.39030i	0.0520896	+	0.0494648i
$791$	−3.22275	−	2.34146i	−0.114588	−	0.0832529i
$792$	1.46868	−	2.88245i	0.0521874	−	0.102423i
$793$	5.67832	+	35.8515i	0.201643	+	1.27312i
$794$	−21.3922	−	29.4439i	−0.759182	−	1.04492i
$795$	−18.8947	−	53.4146i	−0.670125	−	1.89442i
$796$	2.88446	+	3.97012i	0.102237	+	0.140717i
$797$	−5.79166	+	11.3668i	−0.205151	+	0.402632i	−0.970541	−	0.240935i	$-0.922546\pi$
$797$	−5.79166	+	11.3668i	−0.205151	+	0.402632i	0.765390	+	0.643566i	$0.222546\pi$
$798$	19.6246	+	9.99923i	0.694703	+	0.353969i
$799$	9.27583	−	28.5481i	0.328155	−	1.00996i
$800$	2.49706	+	4.33182i	0.0882843	+	0.153153i
$801$		−	5.90792i		−	0.208746i
$802$	19.9241	−	10.1518i	0.703543	−	0.358473i
$803$	−4.15010	−	26.2027i	−0.146454	−	0.924673i
$804$	11.4568	−	8.32388i	0.404052	−	0.293561i
$805$	−40.7001	+	31.2083i	−1.43449	+	1.09995i
$806$	−20.7700	+	5.59487i	−0.731592	+	0.197071i
$807$	5.48232	−	5.48232i	0.192987	−	0.192987i
$808$	−10.0231	−	1.58751i	−0.352612	−	0.0558482i
$809$	−10.5587	−	7.67132i	−0.371223	−	0.269709i	0.386495	−	0.922291i	$-0.373686\pi$
$809$	−10.5587	−	7.67132i	−0.371223	−	0.269709i	−0.757718	+	0.652582i	$0.773686\pi$
$810$	−10.2621	+	21.4962i	−0.360575	+	0.755301i
$811$	−21.1095			−0.741254			−0.370627	−	0.928782i	$-0.620857\pi$
$811$	−21.1095			−0.741254			−0.370627	+	0.928782i	$0.620857\pi$
$812$	4.12371	+	4.12371i	0.144714	+	0.144714i
$813$	−14.1970	+	7.23371i	−0.497909	+	0.253697i
$814$	46.3215	−	15.0508i	1.62357	−	0.527530i
$815$	−49.8528	+	9.22215i	−1.74627	+	0.323038i
$816$	7.13644	−	5.18493i	0.249825	−	0.181509i
$817$	28.8911	−	14.7208i	1.01077	−	0.515015i
$818$	−3.19356	+	20.1634i	−0.111660	+	0.704996i
$819$	5.96968	+	4.33723i	0.208598	+	0.151555i
$820$	9.37400	+	6.44726i	0.327354	+	0.225148i
$821$	10.3380	−	14.2290i	0.360798	−	0.496596i	−0.589573	−	0.807715i	$-0.700704\pi$
$821$	10.3380	−	14.2290i	0.360798	−	0.496596i	0.950371	+	0.311119i	$0.100704\pi$
$822$	−26.5983	+	4.21276i	−0.927722	+	0.146937i
$823$	−18.1765	−	9.26138i	−0.633592	−	0.322831i	0.107530	−	0.994202i	$-0.465706\pi$
$823$	−18.1765	−	9.26138i	−0.633592	−	0.322831i	−0.741122	+	0.671371i	$0.765706\pi$
$824$	2.94691	−	4.05607i	0.102660	−	0.141300i
$825$	−17.4942	+	39.2209i	−0.609070	+	1.36550i
$826$	0.101995	−	0.313910i	0.00354887	−	0.0109223i
$827$	14.5826	+	2.30965i	0.507085	+	0.0803144i	0.404735	−	0.914434i	$-0.367364\pi$
$827$	14.5826	+	2.30965i	0.507085	+	0.0803144i	0.102350	+	0.994748i	$0.467364\pi$
$828$	5.65751	+	2.88264i	0.196612	+	0.100179i
$829$	−7.62366	−	23.4632i	−0.264781	−	0.814911i	−0.991744	−	0.128235i	$-0.959069\pi$
$829$	−7.62366	−	23.4632i	−0.264781	−	0.814911i	0.726963	−	0.686676i	$-0.240931\pi$
$830$	5.98416	+	16.9170i	0.207713	+	0.587197i
$831$	−42.2825			−1.46676
$832$	2.73182	+	2.73182i	0.0947087	+	0.0947087i
$833$	0.208623	+	0.409446i	0.00722836	+	0.0141865i
$834$	17.1893	−	23.6591i	0.595218	−	0.819247i
$835$	−10.2587	−	18.9095i	−0.355018	−	0.654391i
$836$			19.3235i			0.668317i
$837$	16.3716	+	18.1340i	0.565885	+	0.626804i
$838$	4.34844	+	4.34844i	0.150214	+	0.150214i
$839$	5.50513	+	7.57716i	0.190058	+	0.261592i	0.893403	−	0.449256i	$-0.148311\pi$
$839$	5.50513	+	7.57716i	0.190058	+	0.261592i	−0.703345	+	0.710849i	$0.748311\pi$
$840$	−8.22246	−	7.80813i	−0.283702	−	0.269406i
$841$	−7.43823	+	22.8925i	−0.256491	+	0.789397i
$842$	−16.1365	+	16.1365i	−0.556101	+	0.556101i
$843$	−18.1826	+	18.1826i	−0.626243	+	0.626243i
$844$	11.1232	+	3.61415i	0.382877	+	0.124404i
$845$	3.54775	+	2.44007i	0.122046	+	0.0839411i
$846$	1.47617	+	4.54320i	0.0507519	+	0.156198i
$847$	3.61325	−	22.8132i	0.124153	−	0.783870i
$848$	5.95847	+	11.6942i	0.204615	+	0.401579i
$849$	−28.1855	+	20.4780i	−0.967324	+	0.702802i
$850$	−17.7643	+	14.3653i	−0.609309	+	0.492724i
$851$	29.5408	+	90.9172i	1.01264	+	3.11660i
$852$	1.88925	+	11.9283i	0.0647247	+	0.408655i
$853$	−2.26271	−	14.2862i	−0.0774739	−	0.489151i	−0.995665	−	0.0930129i	$-0.970350\pi$
$853$	−2.26271	−	14.2862i	−0.0774739	−	0.489151i	0.918191	−	0.396138i	$-0.129650\pi$
$854$	7.62623	+	23.4711i	0.260964	+	0.803166i
$855$	0.182465	+	7.05969i	0.00624018	+	0.241436i
$856$	2.26115	−	1.64282i	0.0772847	−	0.0561506i
$857$	−3.19321	−	6.26702i	−0.109078	−	0.214077i	0.830015	−	0.557741i	$-0.188332\pi$
$857$	−3.19321	−	6.26702i	−0.109078	−	0.214077i	−0.939093	+	0.343664i	$0.888332\pi$
$858$	−5.19096	+	32.7744i	−0.177217	+	1.11890i
$859$	16.7549	+	51.5662i	0.571669	+	1.75942i	0.647251	+	0.762277i	$0.275919\pi$
$859$	16.7549	+	51.5662i	0.571669	+	1.75942i	−0.0755815	+	0.997140i	$0.524081\pi$
$860$	−16.4149	+	3.03655i	−0.559742	+	0.103545i
$861$	−24.5385	−	7.97305i	−0.836271	−	0.271721i
$862$	5.69320	−	5.69320i	0.193911	−	0.193911i
$863$	−19.2053	+	19.2053i	−0.653755	+	0.653755i	−0.953895	−	0.300140i	$-0.902967\pi$
$863$	−19.2053	+	19.2053i	−0.653755	+	0.653755i	0.300140	+	0.953895i	$0.402967\pi$
$864$	1.35595	−	4.17317i	0.0461302	−	0.141974i
$865$	−19.1913	+	20.2096i	−0.652522	+	0.687148i
$866$	21.2851	+	29.2965i	0.723298	+	0.995534i
$867$	5.29285	+	5.29285i	0.179755	+	0.179755i
$868$	−13.3524	+	5.96614i	−0.453211	+	0.202504i
$869$		−	4.01715i		−	0.136272i
$870$	−2.72526	+	9.18888i	−0.0923951	+	0.311532i
$871$	−16.6573	+	22.9268i	−0.564411	+	0.776845i
$872$	0.414518	+	0.813538i	0.0140374	+	0.0275499i
$873$	−3.61582	−	3.61582i	−0.122377	−	0.122377i
$874$	−37.9270			−1.28290
$875$	22.3115	+	19.0952i	0.754266	+	0.645534i
$876$	3.55742	+	10.9486i	0.120194	+	0.369920i
$877$	3.39128	+	1.72794i	0.114515	+	0.0583484i	0.510310	−	0.859991i	$-0.329531\pi$
$877$	3.39128	+	1.72794i	0.114515	+	0.0583484i	−0.395795	+	0.918339i	$0.629531\pi$
$878$	−24.4618	−	3.87436i	−0.825545	−	0.130753i
$879$	−11.3732	+	35.0030i	−0.383607	+	1.18062i
$880$	2.82869	−	9.53760i	0.0953551	−	0.321512i
$881$	−15.3781	+	21.1661i	−0.518100	+	0.713103i	−0.985259	−	0.171070i	$-0.945278\pi$
$881$	−15.3781	+	21.1661i	−0.518100	+	0.713103i	0.467159	+	0.884173i	$0.345278\pi$
$882$	−0.0651600	−	0.0332007i	−0.00219405	−	0.00111792i
$883$	19.5594	−	3.09791i	0.658228	−	0.104253i	0.181620	−	0.983369i	$-0.441866\pi$
$883$	19.5594	−	3.09791i	0.658228	−	0.104253i	0.476608	+	0.879116i	$0.341866\pi$
$884$	−10.3758	+	14.2810i	−0.348976	+	0.480324i
$885$	0.533407	−	0.0986737i	0.0179303	−	0.00331688i
$886$	25.8559	+	18.7854i	0.868647	+	0.631109i
$887$	7.25826	−	45.8269i	0.243709	−	1.53872i	−0.497514	−	0.867456i	$-0.665754\pi$
$887$	7.25826	−	45.8269i	0.243709	−	1.53872i	0.741223	−	0.671259i	$-0.234246\pi$
$888$	−18.8315	+	9.59513i	−0.631944	+	0.321991i
$889$	18.0878	−	13.1416i	0.606647	−	0.440755i
$890$	−3.30473	−	17.8646i	−0.110775	−	0.598822i
$891$	45.0740	−	14.6454i	1.51004	−	0.490641i
$892$	9.18541	−	4.68020i	0.307550	−	0.156705i
$893$	−20.1764	−	20.1764i	−0.675179	−	0.675179i
$894$	12.5502			0.419742
$895$	−23.8716	+	8.44426i	−0.797940	+	0.282260i
$896$	2.12503	+	1.54392i	0.0709921	+	0.0515788i
$897$	−64.3277	−	10.1885i	−2.14784	−	0.340185i
$898$	−10.2440	+	10.2440i	−0.341846	+	0.341846i
$899$	9.61714	+	7.76669i	0.320750	+	0.259034i
$900$	0.943379	−	3.51120i	0.0314460	−	0.117040i
$901$	−48.5156	+	35.2487i	−1.61629	+	1.17430i
$902$	−3.54112	−	22.3578i	−0.117906	−	0.744432i
$903$	33.7314	−	17.1870i	1.12251	−	0.571948i
$904$			1.51657i			0.0504403i
$905$	9.18150	−	7.04026i	0.305203	−	0.234026i
$906$	9.20745	−	28.3376i	0.305897	−	0.941454i
$907$	−12.4396	−	6.33832i	−0.413052	−	0.210460i	0.235101	−	0.971971i	$-0.424458\pi$
$907$	−12.4396	−	6.33832i	−0.413052	−	0.210460i	−0.648152	+	0.761511i	$0.724458\pi$
$908$	3.64050	−	7.14488i	0.120814	−	0.237111i
$909$	4.33732	+	5.96982i	0.143860	+	0.198006i
$910$	20.4775	+	9.77578i	0.678821	+	0.324064i
$911$	5.98560	+	8.23847i	0.198312	+	0.272953i	0.896578	−	0.442885i	$-0.146045\pi$
$911$	5.98560	+	8.23847i	0.198312	+	0.272953i	−0.698267	+	0.715838i	$0.746045\pi$
$912$	−1.31173	−	8.28196i	−0.0434358	−	0.274243i
$913$	16.2087	−	31.8113i	0.536428	−	1.05280i
$914$	−3.99100	−	2.89963i	−0.132011	−	0.0959113i
$915$	−27.9294	+	29.4114i	−0.923318	+	0.972313i
$916$	−2.01410	+	0.654422i	−0.0665479	+	0.0216227i
$917$	−11.8926	+	1.88360i	−0.392727	+	0.0622019i
$918$	19.8023	+	3.13638i	0.653574	+	0.103516i
$919$	−2.02145	−	0.656809i	−0.0666815	−	0.0216661i	0.275486	−	0.961305i	$-0.411161\pi$
$919$	−2.02145	−	0.656809i	−0.0666815	−	0.0216661i	−0.342168	+	0.939639i	$0.611161\pi$
$920$	18.7198	+	5.55198i	0.617175	+	0.183043i
$921$	−45.2762	+	14.7111i	−1.49190	+	0.484748i
$922$	−11.4621	+	22.4957i	−0.377485	+	0.740855i
$923$	−10.9719	−	21.5336i	−0.361145	−	0.708787i
$924$			22.5608i			0.742197i
$925$	47.4227	−	27.3366i	1.55925	−	0.898822i
$926$	−13.5619	−	4.40652i	−0.445671	−	0.144807i
$927$	−3.60071	+	0.570297i	−0.118263	+	0.0187310i
$928$	0.347319	−	2.19289i	0.0114013	−	0.0719850i
$929$	−11.2368			−0.368669			−0.184335	−	0.982864i	$-0.559013\pi$
$929$	−11.2368			−0.368669			−0.184335	+	0.982864i	$0.559013\pi$
$930$	−19.0831	−	14.6131i	−0.625760	−	0.479181i
$931$	0.436822			0.0143163
$932$	−2.16304	+	13.6569i	−0.0708527	+	0.447346i
$933$	26.0295	−	4.12267i	0.852168	−	0.134970i
$934$	4.61565	+	1.49972i	0.151029	+	0.0490722i
$935$	45.0641	+	5.94837i	1.47375	+	0.194533i
$936$		−	2.80923i		−	0.0918225i
$937$	11.2220	+	22.0244i	0.366606	+	0.719506i	0.998454	−	0.0555872i	$-0.0177031\pi$
$937$	11.2220	+	22.0244i	0.366606	+	0.719506i	−0.631847	+	0.775093i	$0.717703\pi$
$938$	−8.74727	+	17.1675i	−0.285608	+	0.560538i
$939$	−26.0266	+	8.45656i	−0.849347	+	0.275969i
$940$	7.00504	+	12.9121i	0.228479	+	0.421148i
$941$	−17.2964	−	5.61995i	−0.563847	−	0.183205i	0.0132043	−	0.999913i	$-0.495797\pi$
$941$	−17.2964	−	5.61995i	−0.563847	−	0.183205i	−0.577051	+	0.816708i	$0.695797\pi$
$942$	24.3672	+	3.85938i	0.793925	+	0.125745i
$943$	43.8825	−	6.95030i	1.42901	−	0.226333i
$944$	−0.119508	+	0.0388306i	−0.00388966	+	0.00126383i
$945$	−0.665888	−	25.7636i	−0.0216614	−	0.838090i
$946$	26.8706	+	19.5226i	0.873638	+	0.634735i
$947$	−13.2802	+	26.0639i	−0.431549	+	0.846963i	0.568162	+	0.822917i	$0.307655\pi$
$947$	−13.2802	+	26.0639i	−0.431549	+	0.846963i	−0.999711	+	0.0240457i	$0.992345\pi$
$948$	0.272695	+	1.72173i	0.00885673	+	0.0559192i
$949$	−13.5410	−	18.6376i	−0.439559	−	0.605001i
$950$	4.50074	+	21.2453i	0.146023	+	0.689287i
$951$	5.91257	+	8.13795i	0.191728	+	0.263891i
$952$	−5.44865	+	10.6936i	−0.176592	+	0.346581i
$953$	−7.61322	−	3.87913i	−0.246616	−	0.125657i	0.326314	−	0.945262i	$-0.394193\pi$
$953$	−7.61322	−	3.87913i	−0.246616	−	0.125657i	−0.572930	+	0.819604i	$0.694193\pi$
$954$	2.94911	−	9.07642i	0.0954809	−	0.293860i
$955$	−20.9577	−	27.3318i	−0.678174	−	0.884435i
$956$		−	6.94242i		−	0.224534i
$957$	16.9913	−	8.65749i	0.549250	−	0.279857i
$958$	3.24056	+	20.4601i	0.104698	+	0.661036i
$959$	29.6422	−	21.5363i	0.957195	−	0.695443i
$960$	−0.564923	+	4.27979i	−0.0182328	+	0.138130i
$961$	−26.8055	+	15.5712i	−0.864695	+	0.502298i
$962$	29.9066	−	29.9066i	0.964228	−	0.964228i
$963$	−2.00730	−	0.317926i	−0.0646844	−	0.0102450i
$964$	−6.29053	−	4.57033i	−0.202604	−	0.147201i
$965$	−18.2287	−	8.70225i	−0.586803	−	0.280135i
$966$	−44.2811			−1.42472
$967$	11.8631	+	11.8631i	0.381492	+	0.381492i	0.871640	−	0.490147i	$-0.163057\pi$
$967$	11.8631	+	11.8631i	0.381492	+	0.381492i	−0.490147	+	0.871640i	$0.663057\pi$
$968$	−7.83503	+	3.99214i	−0.251827	+	0.128312i
$969$	36.4381	−	11.8394i	1.17056	−	0.380338i
$970$	−12.9562	−	8.91105i	−0.416000	−	0.286117i
$971$	−16.4129	+	11.9247i	−0.526714	+	0.382680i	−0.819127	−	0.573612i	$-0.805542\pi$
$971$	−16.4129	+	11.9247i	−0.526714	+	0.382680i	0.292413	+	0.956292i	$0.405542\pi$
$972$	−6.59531	+	3.36048i	−0.211545	+	0.107787i
$973$	−6.22431	+	39.2987i	−0.199542	+	1.25986i
$974$	26.1431	+	18.9941i	0.837679	+	0.608609i
$975$	1.92646	+	37.2430i	0.0616960	+	1.19273i
$976$	5.52255	−	7.60114i	0.176773	−	0.243307i
$977$	13.6614	−	2.16375i	0.437065	−	0.0692244i	0.0659754	−	0.997821i	$-0.478984\pi$
$977$	13.6614	−	2.16375i	0.437065	−	0.0692244i	0.371090	+	0.928597i	$0.378984\pi$
$978$	−39.0014	−	19.8722i	−1.24713	−	0.635443i
$979$	−21.2468	+	29.2437i	−0.679051	+	0.934634i
$980$	−0.215604	−	0.0639446i	−0.00688723	−	0.00204264i
$981$	0.205163	−	0.631428i	0.00655036	−	0.0201599i
$982$	13.9866	+	2.21525i	0.446329	+	0.0706915i
$983$	−11.9950	−	6.11178i	−0.382582	−	0.194935i	0.252113	−	0.967698i	$-0.418874\pi$
$983$	−11.9950	−	6.11178i	−0.382582	−	0.194935i	−0.634696	+	0.772762i	$0.718874\pi$
$984$	3.03541	+	9.34205i	0.0967655	+	0.297814i
$985$	−40.0481	−	19.1187i	−1.27604	−	0.609172i
$986$	10.1445			0.323068
$987$	−23.5567	−	23.5567i	−0.749818	−	0.749818i
$988$	7.61795	+	14.9511i	0.242359	+	0.475657i
$989$	−38.3179	+	52.7400i	−1.21844	+	1.67703i
$990$	−6.35836	+	3.44951i	−0.202082	+	0.109633i
$991$			4.11801i			0.130813i	0.997859	+	0.0654065i	$0.0208344\pi$
$991$			4.11801i			0.130813i	−0.997859	+	0.0654065i	$0.979166\pi$
$992$	4.82552	+	2.77748i	0.153210	+	0.0881850i
$993$	27.5921	+	27.5921i	0.875610	+	0.875610i
$994$	−9.65816	−	13.2933i	−0.306338	−	0.421638i
$995$	−0.283518	−	10.9695i	−0.00898813	−	0.347756i
$996$	−4.78751	+	14.7344i	−0.151698	+	0.466879i
$997$	−15.4275	+	15.4275i	−0.488595	+	0.488595i	−0.907863	−	0.419268i	$-0.862287\pi$
$997$	−15.4275	+	15.4275i	−0.488595	+	0.488595i	0.419268	+	0.907863i	$0.362287\pi$
$998$	26.7642	−	26.7642i	0.847207	−	0.847207i
$999$	−45.6859	−	14.8442i	−1.44544	−	0.469651i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	310.2.s.a.263.10	yes	128
5.2	odd	4	inner	310.2.s.a.77.15	✓	128
31.29	odd	10	inner	310.2.s.a.153.15	yes	128
155.122	even	20	inner	310.2.s.a.277.10	yes	128

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
310.2.s.a.77.15	✓	128	5.2	odd	4	inner
310.2.s.a.153.15	yes	128	31.29	odd	10	inner
310.2.s.a.263.10	yes	128	1.1	even	1	trivial
310.2.s.a.277.10	yes	128	155.122	even	20	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:	\( N \)	\(=\)	\( 310 = 2 \cdot 5 \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	310.s (of order \(20\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(0.156434 - 0.987688i) q^{2} +(-1.90681 + 0.302009i) q^{3} +(-0.951057 - 0.309017i) q^{4} +(1.36063 + 1.77445i) q^{5} +1.93058i q^{6} +(-1.19249 - 2.34039i) q^{7} +(-0.453990 + 0.891007i) q^{8} +(0.691555 - 0.224700i) q^{9} +O(q^{10})\)	\(q+(0.156434 - 0.987688i) q^{2} +(-1.90681 + 0.302009i) q^{3} +(-0.951057 - 0.309017i) q^{4} +(1.36063 + 1.77445i) q^{5} +1.93058i q^{6} +(-1.19249 - 2.34039i) q^{7} +(-0.453990 + 0.891007i) q^{8} +(0.691555 - 0.224700i) q^{9} +(1.96546 - 1.06629i) q^{10} +(-4.23123 - 1.37481i) q^{11} +(1.90681 + 0.302009i) q^{12} +(-3.81581 + 0.604364i) q^{13} +(-2.49812 + 0.811688i) q^{14} +(-3.13037 - 2.97263i) q^{15} +(0.809017 + 0.587785i) q^{16} +(-2.07435 + 4.07115i) q^{17} +(-0.113750 - 0.718192i) q^{18} +(2.55296 + 3.51385i) q^{19} +(-0.745699 - 2.10806i) q^{20} +(2.98067 + 4.10253i) q^{21} +(-2.01980 + 3.96407i) q^{22} +(-7.78045 - 3.96434i) q^{23} +(0.596582 - 1.83609i) q^{24} +(-1.29738 + 4.82875i) q^{25} +3.86337i q^{26} +(3.90968 - 1.99208i) q^{27} +(0.410903 + 2.59434i) q^{28} +(1.79620 - 1.30501i) q^{29} +(-3.42573 + 2.62681i) q^{30} +(1.44818 + 5.37613i) q^{31} +(0.707107 - 0.707107i) q^{32} +(8.48338 + 1.34364i) q^{33} +(3.69652 + 2.68568i) q^{34} +(2.53038 - 5.30041i) q^{35} -0.727144 q^{36} +(-7.74107 - 7.74107i) q^{37} +(3.86996 - 1.97184i) q^{38} +(7.09351 - 2.30482i) q^{39} +(-2.19876 + 0.406744i) q^{40} +(-4.11628 + 2.99065i) q^{41} +(4.51830 - 2.30219i) q^{42} +(1.16786 - 7.37359i) q^{43} +(3.59930 + 2.61505i) q^{44} +(1.33967 + 0.921400i) q^{45} +(-5.13266 + 7.06450i) q^{46} +(-6.48865 + 1.02770i) q^{47} +(-1.72016 - 0.876466i) q^{48} +(0.0591151 - 0.0813649i) q^{49} +(4.56634 + 2.03679i) q^{50} +(2.72588 - 8.38939i) q^{51} +(3.81581 + 0.604364i) q^{52} +(11.6942 + 5.95847i) q^{53} +(-1.35595 - 4.17317i) q^{54} +(-3.31760 - 9.37874i) q^{55} +2.62668 q^{56} +(-5.92923 - 5.92923i) q^{57} +(-1.00796 - 1.97823i) q^{58} +(-0.0738602 + 0.101660i) q^{59} +(2.05856 + 3.79447i) q^{60} -9.39553i q^{61} +(5.53649 - 0.589341i) q^{62} +(-1.35055 - 1.35055i) q^{63} +(-0.587785 - 0.809017i) q^{64} +(-6.26432 - 5.94866i) q^{65} +(2.65419 - 8.16874i) q^{66} +(5.18685 - 5.18685i) q^{67} +(3.23088 - 3.23088i) q^{68} +(16.0331 + 5.20948i) q^{69} +(-4.83931 - 3.32839i) q^{70} +(1.93309 + 5.94943i) q^{71} +(-0.113750 + 0.718192i) q^{72} +(2.70715 + 5.31308i) q^{73} +(-8.85673 + 6.43479i) q^{74} +(1.01552 - 9.59934i) q^{75} +(-1.34217 - 4.13077i) q^{76} +(1.82810 + 11.5422i) q^{77} +(-1.16677 - 7.36673i) q^{78} +(0.279023 + 0.858743i) q^{79} +(0.0577743 + 2.23532i) q^{80} +(-8.61821 + 6.26150i) q^{81} +(2.30991 + 4.53345i) q^{82} +(-1.25537 + 7.92610i) q^{83} +(-1.56703 - 4.82282i) q^{84} +(-10.0465 + 1.85848i) q^{85} +(-7.10011 - 2.30697i) q^{86} +(-3.03088 + 3.03088i) q^{87} +(3.14591 - 3.14591i) q^{88} +(2.51071 - 7.72717i) q^{89} +(1.11963 - 1.17904i) q^{90} +(5.96474 + 8.20976i) q^{91} +(6.17460 + 6.17460i) q^{92} +(-4.38505 - 9.81391i) q^{93} +6.56953i q^{94} +(-2.76153 + 9.31115i) q^{95} +(-1.13477 + 1.56187i) q^{96} +(-3.19263 - 6.26588i) q^{97} +(-0.0711155 - 0.0711155i) q^{98} -3.23505 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 128 q + 12 q^{7}+O(q^{10}) \) 128 * q + 12 * q^7	\( 128 q + 12 q^{7} + 8 q^{10} + 32 q^{16} + 8 q^{20} - 80 q^{21} - 20 q^{22} - 20 q^{23} + 40 q^{25} + 8 q^{28} - 32 q^{31} + 20 q^{33} - 48 q^{35} - 128 q^{36} + 52 q^{38} + 8 q^{41} - 20 q^{42} + 64 q^{45} - 40 q^{46} - 20 q^{47} - 20 q^{48} + 24 q^{50} - 16 q^{51} - 40 q^{53} - 40 q^{55} + 20 q^{60} - 8 q^{62} + 256 q^{63} - 160 q^{65} + 56 q^{66} + 8 q^{67} - 32 q^{70} + 56 q^{71} - 80 q^{73} - 160 q^{75} + 48 q^{76} - 20 q^{77} + 4 q^{78} - 96 q^{81} + 16 q^{82} - 240 q^{83} + 120 q^{85} + 40 q^{87} - 64 q^{90} + 80 q^{91} - 160 q^{93} + 32 q^{95} - 56 q^{97} - 176 q^{98}+O(q^{100}) \) 128 * q + 12 * q^7 + 8 * q^10 + 32 * q^16 + 8 * q^20 - 80 * q^21 - 20 * q^22 - 20 * q^23 + 40 * q^25 + 8 * q^28 - 32 * q^31 + 20 * q^33 - 48 * q^35 - 128 * q^36 + 52 * q^38 + 8 * q^41 - 20 * q^42 + 64 * q^45 - 40 * q^46 - 20 * q^47 - 20 * q^48 + 24 * q^50 - 16 * q^51 - 40 * q^53 - 40 * q^55 + 20 * q^60 - 8 * q^62 + 256 * q^63 - 160 * q^65 + 56 * q^66 + 8 * q^67 - 32 * q^70 + 56 * q^71 - 80 * q^73 - 160 * q^75 + 48 * q^76 - 20 * q^77 + 4 * q^78 - 96 * q^81 + 16 * q^82 - 240 * q^83 + 120 * q^85 + 40 * q^87 - 64 * q^90 + 80 * q^91 - 160 * q^93 + 32 * q^95 - 56 * q^97 - 176 * q^98

Introduction

L-functions

Modular forms

Varieties

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Database

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