LMFDB - Embedded newform 570.2.bc.b.139.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [570,2,Mod(139,570)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(570, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([0, 9, 14]))

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

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

chi := DirichletCharacter("570.139");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 570 = 2 \cdot 3 \cdot 5 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	570.bc (of order $18$, degree $6$, 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:	$4.55147291521$
Analytic rank:	$0$
Dimension:	$60$
Relative dimension:	$10$ over $\Q(\zeta_{18})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			139.8
Character	$\chi$	$=$	570.139
Dual form			570.2.bc.b.529.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.642788 + 0.766044i) q^{2} +(-0.342020 + 0.939693i) q^{3} +(-0.173648 + 0.984808i) q^{4} +(-0.329815 + 2.21161i) q^{5} +(-0.939693 + 0.342020i) q^{6} +(4.20443 + 2.42743i) q^{7} +(-0.866025 + 0.500000i) q^{8} +(-0.766044 - 0.642788i) q^{9} +O(q^{10})$	\(q+(0.642788 + 0.766044i) q^{2} +(-0.342020 + 0.939693i) q^{3} +(-0.173648 + 0.984808i) q^{4} +(-0.329815 + 2.21161i) q^{5} +(-0.939693 + 0.342020i) q^{6} +(4.20443 + 2.42743i) q^{7} +(-0.866025 + 0.500000i) q^{8} +(-0.766044 - 0.642788i) q^{9} +(-1.90619 + 1.16894i) q^{10} +(-0.496192 - 0.859430i) q^{11} +(-0.866025 - 0.500000i) q^{12} +(-0.932074 - 2.56085i) q^{13} +(0.843036 + 4.78110i) q^{14} +(-1.96543 - 1.06634i) q^{15} +(-0.939693 - 0.342020i) q^{16} +(4.91232 + 5.85427i) q^{17} -1.00000i q^{18} +(-3.24353 - 2.91196i) q^{19} +(-2.12074 - 0.708846i) q^{20} +(-3.71903 + 3.12064i) q^{21} +(0.339416 - 0.932536i) q^{22} +(1.05975 + 0.186863i) q^{23} +(-0.173648 - 0.984808i) q^{24} +(-4.78244 - 1.45884i) q^{25} +(1.36260 - 2.36009i) q^{26} +(0.866025 - 0.500000i) q^{27} +(-3.12064 + 3.71903i) q^{28} +(-4.00615 - 3.36156i) q^{29} +(-0.446491 - 2.19104i) q^{30} +(2.03521 - 3.52509i) q^{31} +(-0.342020 - 0.939693i) q^{32} +(0.977308 - 0.172326i) q^{33} +(-1.32706 + 7.52611i) q^{34} +(-6.75521 + 8.49795i) q^{35} +(0.766044 - 0.642788i) q^{36} -2.64356i q^{37} +(0.145792 - 4.35646i) q^{38} +2.72520 q^{39} +(-0.820177 - 2.08022i) q^{40} +(-2.15250 - 0.783445i) q^{41} +(-4.78110 - 0.843036i) q^{42} +(2.72639 - 0.480736i) q^{43} +(0.932536 - 0.339416i) q^{44} +(1.67425 - 1.48219i) q^{45} +(0.538052 + 0.931933i) q^{46} +(-8.16833 + 9.73464i) q^{47} +(0.642788 - 0.766044i) q^{48} +(8.28480 + 14.3497i) q^{49} +(-1.95656 - 4.60129i) q^{50} +(-7.18133 + 2.61379i) q^{51} +(2.68380 - 0.473226i) q^{52} +(6.59945 + 1.16366i) q^{53} +(0.939693 + 0.342020i) q^{54} +(2.06438 - 0.813931i) q^{55} -4.85485 q^{56} +(3.84570 - 2.05197i) q^{57} -5.22965i q^{58} +(-3.56022 + 2.98738i) q^{59} +(1.39143 - 1.75040i) q^{60} +(-0.552763 + 3.13487i) q^{61} +(4.00859 - 0.706822i) q^{62} +(-1.66046 - 4.56207i) q^{63} +(0.500000 - 0.866025i) q^{64} +(5.97102 - 1.21678i) q^{65} +(0.760211 + 0.637893i) q^{66} +(7.09299 - 8.45309i) q^{67} +(-6.61835 + 3.82110i) q^{68} +(-0.538052 + 0.931933i) q^{69} +(-10.8520 + 0.287591i) q^{70} +(-0.784877 - 4.45126i) q^{71} +(0.984808 + 0.173648i) q^{72} +(5.24705 - 14.4161i) q^{73} +(2.02509 - 1.69925i) q^{74} +(3.00656 - 3.99507i) q^{75} +(3.43096 - 2.68860i) q^{76} -4.81788i q^{77} +(1.75173 + 2.08763i) q^{78} +(11.4523 + 4.16831i) q^{79} +(1.06634 - 1.96543i) q^{80} +(0.173648 + 0.984808i) q^{81} +(-0.783445 - 2.15250i) q^{82} +(6.69976 + 3.86811i) q^{83} +(-2.42743 - 4.20443i) q^{84} +(-14.5675 + 8.93331i) q^{85} +(2.12075 + 1.77952i) q^{86} +(4.52901 - 2.61483i) q^{87} +(0.859430 + 0.496192i) q^{88} +(16.0990 - 5.85955i) q^{89} +(2.21161 + 0.329815i) q^{90} +(2.29745 - 13.0295i) q^{91} +(-0.368049 + 1.01121i) q^{92} +(2.61642 + 3.11813i) q^{93} -12.7077 q^{94} +(7.50989 - 6.21301i) q^{95} +1.00000 q^{96} +(-0.384987 - 0.458809i) q^{97} +(-5.66714 + 15.5703i) q^{98} +(-0.172326 + 0.977308i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 60 q + 6 q^{5}+O(q^{10}) $ 60 * q + 6 * q^5	$ 60 q + 6 q^{5} + 6 q^{10} - 12 q^{11} + 12 q^{15} + 24 q^{19} + 12 q^{20} - 18 q^{21} - 6 q^{25} - 6 q^{26} + 12 q^{29} + 6 q^{30} - 36 q^{31} - 6 q^{35} - 12 q^{39} - 6 q^{40} - 30 q^{41} - 6 q^{44} - 6 q^{45} - 36 q^{46} + 18 q^{49} - 90 q^{55} + 24 q^{56} + 60 q^{59} + 6 q^{60} + 36 q^{61} + 30 q^{64} + 24 q^{65} - 12 q^{66} + 36 q^{69} - 72 q^{70} - 72 q^{71} + 6 q^{74} + 6 q^{76} + 6 q^{80} + 12 q^{84} + 18 q^{85} - 12 q^{86} + 60 q^{89} + 12 q^{90} - 48 q^{91} - 156 q^{94} - 84 q^{95} + 60 q^{96} - 6 q^{99}+O(q^{100}) $ 60 * q + 6 * q^5 + 6 * q^10 - 12 * q^11 + 12 * q^15 + 24 * q^19 + 12 * q^20 - 18 * q^21 - 6 * q^25 - 6 * q^26 + 12 * q^29 + 6 * q^30 - 36 * q^31 - 6 * q^35 - 12 * q^39 - 6 * q^40 - 30 * q^41 - 6 * q^44 - 6 * q^45 - 36 * q^46 + 18 * q^49 - 90 * q^55 + 24 * q^56 + 60 * q^59 + 6 * q^60 + 36 * q^61 + 30 * q^64 + 24 * q^65 - 12 * q^66 + 36 * q^69 - 72 * q^70 - 72 * q^71 + 6 * q^74 + 6 * q^76 + 6 * q^80 + 12 * q^84 + 18 * q^85 - 12 * q^86 + 60 * q^89 + 12 * q^90 - 48 * q^91 - 156 * q^94 - 84 * q^95 + 60 * q^96 - 6 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/570\mathbb{Z}\right)^\times$.

$n$	$191$	$211$	$457$
$\chi(n)$	$1$	$e\left(\frac{7}{9}\right)$	$-1$

Coefficient data

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

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

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

$2$	0.642788	+	0.766044i	0.454519	+	0.541675i
$2$	0.642788	+	0.766044i	0.454519	+	0.541675i
$3$	−0.342020	+	0.939693i	−0.197465	+	0.542532i
$3$	−0.342020	+	0.939693i	−0.197465	+	0.542532i
$4$	−0.173648	+	0.984808i	−0.0868241	+	0.492404i
$5$	−0.329815	+	2.21161i	−0.147498	+	0.989062i
$5$	−0.329815	+	2.21161i	−0.147498	+	0.989062i
$6$	−0.939693	+	0.342020i	−0.383628	+	0.139629i
$7$	4.20443	+	2.42743i	1.58912	+	0.917481i	0.993452	+	0.114253i	$0.0364475\pi$
$7$	4.20443	+	2.42743i	1.58912	+	0.917481i	0.595672	+	0.803228i	$0.296886\pi$
$8$	−0.866025	+	0.500000i	−0.306186	+	0.176777i
$9$	−0.766044	−	0.642788i	−0.255348	−	0.214263i
$10$	−1.90619	+	1.16894i	−0.602791	+	0.369652i
$11$	−0.496192	−	0.859430i	−0.149608	−	0.259128i	0.781475	−	0.623937i	$-0.214468\pi$
$11$	−0.496192	−	0.859430i	−0.149608	−	0.259128i	−0.931082	+	0.364809i	$0.881134\pi$
$12$	−0.866025	−	0.500000i	−0.250000	−	0.144338i
$13$	−0.932074	−	2.56085i	−0.258511	−	0.710253i	−0.999260	−	0.0384707i	$-0.987751\pi$
$13$	−0.932074	−	2.56085i	−0.258511	−	0.710253i	0.740749	−	0.671782i	$-0.234471\pi$
$14$	0.843036	+	4.78110i	0.225311	+	1.27780i
$15$	−1.96543	−	1.06634i	−0.507472	−	0.275328i
$16$	−0.939693	−	0.342020i	−0.234923	−	0.0855050i
$17$	4.91232	+	5.85427i	1.19141	+	1.41987i	0.883485	+	0.468459i	$0.155191\pi$
$17$	4.91232	+	5.85427i	1.19141	+	1.41987i	0.307927	+	0.951410i	$0.400365\pi$
$18$		−	1.00000i		−	0.235702i
$19$	−3.24353	−	2.91196i	−0.744116	−	0.668050i
$19$	−3.24353	−	2.91196i	−0.744116	−	0.668050i
$20$	−2.12074	−	0.708846i	−0.474212	−	0.158503i
$21$	−3.71903	+	3.12064i	−0.811560	+	0.680979i
$22$	0.339416	−	0.932536i	0.0723636	−	0.198817i
$23$	1.05975	+	0.186863i	0.220974	+	0.0389637i	0.283039	−	0.959108i	$-0.408657\pi$
$23$	1.05975	+	0.186863i	0.220974	+	0.0389637i	−0.0620648	+	0.998072i	$0.519769\pi$
$24$	−0.173648	−	0.984808i	−0.0354458	−	0.201023i
$25$	−4.78244	−	1.45884i	−0.956489	−	0.291769i
$26$	1.36260	−	2.36009i	0.267228	−	0.462853i
$27$	0.866025	−	0.500000i	0.166667	−	0.0962250i
$28$	−3.12064	+	3.71903i	−0.589745	+	0.702831i
$29$	−4.00615	−	3.36156i	−0.743923	−	0.624225i	0.189965	−	0.981791i	$-0.439162\pi$
$29$	−4.00615	−	3.36156i	−0.743923	−	0.624225i	−0.933888	+	0.357566i	$0.883607\pi$
$30$	−0.446491	−	2.19104i	−0.0815177	−	0.400027i
$31$	2.03521	−	3.52509i	0.365535	−	0.633125i	−0.623327	−	0.781962i	$-0.714219\pi$
$31$	2.03521	−	3.52509i	0.365535	−	0.633125i	0.988862	+	0.148836i	$0.0475527\pi$
$32$	−0.342020	−	0.939693i	−0.0604612	−	0.166116i
$33$	0.977308	−	0.172326i	0.170127	−	0.0299981i
$34$	−1.32706	+	7.52611i	−0.227588	+	1.29072i
$35$	−6.75521	+	8.49795i	−1.14184	+	1.43642i
$36$	0.766044	−	0.642788i	0.127674	−	0.107131i
$37$		−	2.64356i		−	0.434599i	−0.976105	−	0.217299i	$-0.930275\pi$
$37$		−	2.64356i		−	0.434599i	0.976105	−	0.217299i	$-0.0697248\pi$
$38$	0.145792	−	4.35646i	0.0236506	−	0.706711i
$39$	2.72520			0.436382
$40$	−0.820177	−	2.08022i	−0.129681	−	0.328911i
$41$	−2.15250	−	0.783445i	−0.336164	−	0.122354i	0.168423	−	0.985715i	$-0.446133\pi$
$41$	−2.15250	−	0.783445i	−0.336164	−	0.122354i	−0.504586	+	0.863361i	$0.668355\pi$
$42$	−4.78110	−	0.843036i	−0.737739	−	0.130083i
$43$	2.72639	−	0.480736i	0.415771	−	0.0733116i	0.0381501	−	0.999272i	$-0.487854\pi$
$43$	2.72639	−	0.480736i	0.415771	−	0.0733116i	0.377620	+	0.925960i	$0.376742\pi$
$44$	0.932536	−	0.339416i	0.140585	−	0.0511688i
$45$	1.67425	−	1.48219i	0.249582	−	0.220952i
$46$	0.538052	+	0.931933i	0.0793314	+	0.137406i
$47$	−8.16833	+	9.73464i	−1.19147	+	1.41994i	−0.308049	+	0.951370i	$0.599676\pi$
$47$	−8.16833	+	9.73464i	−1.19147	+	1.41994i	−0.883425	+	0.468573i	$0.844768\pi$
$48$	0.642788	−	0.766044i	0.0927784	−	0.110569i
$49$	8.28480	+	14.3497i	1.18354	+	2.04996i
$50$	−1.95656	−	4.60129i	−0.276699	−	0.650721i
$51$	−7.18133	+	2.61379i	−1.00559	+	0.366004i
$52$	2.68380	−	0.473226i	0.372176	−	0.0656247i
$53$	6.59945	+	1.16366i	0.906505	+	0.159841i	0.607416	−	0.794384i	$-0.292206\pi$
$53$	6.59945	+	1.16366i	0.906505	+	0.159841i	0.299089	+	0.954225i	$0.403317\pi$
$54$	0.939693	+	0.342020i	0.127876	+	0.0465430i
$55$	2.06438	−	0.813931i	0.278361	−	0.109750i
$56$	−4.85485			−0.648757
$57$	3.84570	−	2.05197i	0.509376	−	0.271790i
$58$		−	5.22965i		−	0.686687i
$59$	−3.56022	+	2.98738i	−0.463501	+	0.388923i	−0.844417	−	0.535686i	$-0.820053\pi$
$59$	−3.56022	+	2.98738i	−0.463501	+	0.388923i	0.380916	+	0.924609i	$0.375609\pi$
$60$	1.39143	−	1.75040i	0.179633	−	0.225976i
$61$	−0.552763	+	3.13487i	−0.0707740	+	0.401379i	0.928755	+	0.370694i	$0.120880\pi$
$61$	−0.552763	+	3.13487i	−0.0707740	+	0.401379i	−0.999529	+	0.0306854i	$0.990231\pi$
$62$	4.00859	−	0.706822i	0.509091	−	0.0897665i
$63$	−1.66046	−	4.56207i	−0.209198	−	0.574767i
$64$	0.500000	−	0.866025i	0.0625000	−	0.108253i
$65$	5.97102	−	1.21678i	0.740614	−	0.150923i
$66$	0.760211	+	0.637893i	0.0935755	+	0.0785191i
$67$	7.09299	−	8.45309i	0.866546	−	1.03271i	−0.132591	−	0.991171i	$-0.542330\pi$
$67$	7.09299	−	8.45309i	0.866546	−	1.03271i	0.999137	−	0.0415388i	$-0.0132260\pi$
$68$	−6.61835	+	3.82110i	−0.802592	+	0.463377i
$69$	−0.538052	+	0.931933i	−0.0647738	+	0.112192i
$70$	−10.8520	+	0.287591i	−1.29706	+	0.0343737i
$71$	−0.784877	−	4.45126i	−0.0931478	−	0.528267i	−0.995299	−	0.0968477i	$-0.969124\pi$
$71$	−0.784877	−	4.45126i	−0.0931478	−	0.528267i	0.902151	−	0.431419i	$-0.141987\pi$
$72$	0.984808	+	0.173648i	0.116061	+	0.0204646i
$73$	5.24705	−	14.4161i	0.614120	−	1.68728i	−0.106814	−	0.994279i	$-0.534065\pi$
$73$	5.24705	−	14.4161i	0.614120	−	1.68728i	0.720935	−	0.693003i	$-0.243713\pi$
$74$	2.02509	−	1.69925i	0.235411	−	0.197534i
$75$	3.00656	−	3.99507i	0.347167	−	0.461311i
$76$	3.43096	−	2.68860i	0.393558	−	0.308403i
$77$		−	4.81788i		−	0.549049i
$78$	1.75173	+	2.08763i	0.198344	+	0.236377i
$79$	11.4523	+	4.16831i	1.28849	+	0.468972i	0.893231	−	0.449599i	$-0.148433\pi$
$79$	11.4523	+	4.16831i	1.28849	+	0.468972i	0.395258	+	0.918570i	$0.370655\pi$
$80$	1.06634	−	1.96543i	0.119220	−	0.219742i
$81$	0.173648	+	0.984808i	0.0192942	+	0.109423i
$82$	−0.783445	−	2.15250i	−0.0865170	−	0.237704i
$83$	6.69976	+	3.86811i	0.735394	+	0.424580i	0.820392	−	0.571801i	$-0.193755\pi$
$83$	6.69976	+	3.86811i	0.735394	+	0.424580i	−0.0849984	+	0.996381i	$0.527089\pi$
$84$	−2.42743	−	4.20443i	−0.264854	−	0.458741i
$85$	−14.5675	+	8.93331i	−1.58007	+	0.968953i
$86$	2.12075	+	1.77952i	0.228687	+	0.191891i
$87$	4.52901	−	2.61483i	0.485561	−	0.280339i
$88$	0.859430	+	0.496192i	0.0916156	+	0.0528943i
$89$	16.0990	−	5.85955i	1.70649	−	0.621111i	0.709952	−	0.704250i	$-0.248717\pi$
$89$	16.0990	−	5.85955i	1.70649	−	0.621111i	0.996538	+	0.0831388i	$0.0264945\pi$
$90$	2.21161	+	0.329815i	0.233124	+	0.0347655i
$91$	2.29745	−	13.0295i	0.240838	−	1.36586i
$92$	−0.368049	+	1.01121i	−0.0383718	+	0.105426i
$93$	2.61642	+	3.11813i	0.271310	+	0.323335i
$94$	−12.7077			−1.31070
$95$	7.50989	−	6.21301i	0.770499	−	0.637442i
$96$	1.00000			0.102062
$97$	−0.384987	−	0.458809i	−0.0390895	−	0.0465850i	0.746146	−	0.665783i	$-0.231902\pi$
$97$	−0.384987	−	0.458809i	−0.0390895	−	0.0465850i	−0.785235	+	0.619198i	$0.787458\pi$
$98$	−5.66714	+	15.5703i	−0.572467	+	1.57284i
$99$	−0.172326	+	0.977308i	−0.0173194	+	0.0982232i
$100$	2.26714	−	4.45646i	0.226714	−	0.445646i
$101$	8.75683	−	3.18723i	0.871337	−	0.317141i	0.132629	−	0.991166i	$-0.457658\pi$
$101$	8.75683	−	3.18723i	0.871337	−	0.317141i	0.738709	+	0.674025i	$0.235436\pi$
$102$	−6.61835	−	3.82110i	−0.655314	−	0.378346i
$103$	−15.3842	+	8.88207i	−1.51585	+	0.875176i	−0.516023	+	0.856575i	$0.672588\pi$
$103$	−15.3842	+	8.88207i	−1.51585	+	0.875176i	−0.999827	+	0.0186016i	$0.994079\pi$
$104$	2.08763	+	1.75173i	0.204709	+	0.171771i
$105$	−5.67505	−	9.25429i	−0.553828	−	0.903126i
$106$	3.35063	+	5.80346i	0.325442	+	0.563682i
$107$	−0.799741	−	0.461731i	−0.0773139	−	0.0446372i	0.460845	−	0.887481i	$-0.347547\pi$
$107$	−0.799741	−	0.461731i	−0.0773139	−	0.0446372i	−0.538159	+	0.842844i	$0.680880\pi$
$108$	0.342020	+	0.939693i	0.0329109	+	0.0904220i
$109$	−1.72974	−	9.80982i	−0.165679	−	0.939610i	−0.948362	−	0.317190i	$-0.897261\pi$
$109$	−1.72974	−	9.80982i	−0.165679	−	0.939610i	0.782683	−	0.622420i	$-0.213850\pi$
$110$	1.95046	+	1.05822i	0.185969	+	0.100897i
$111$	2.48413	+	0.904151i	0.235784	+	0.0858182i
$112$	−3.12064	−	3.71903i	−0.294873	−	0.351416i
$113$			3.27169i			0.307775i	0.988088	+	0.153887i	$0.0491793\pi$
$113$			3.27169i			0.307775i	−0.988088	+	0.153887i	$0.950821\pi$
$114$	4.04387	+	1.62700i	0.378743	+	0.152382i
$115$	−0.762792	+	2.28213i	−0.0711307	+	0.212810i
$116$	4.00615	−	3.36156i	0.371961	−	0.312113i
$117$	−0.932074	+	2.56085i	−0.0861703	+	0.236751i
$118$	−4.57693	−	0.807035i	−0.421340	−	0.0742936i
$119$	6.44266	+	36.5381i	0.590598	+	3.34945i
$120$	2.23528	−	0.0592379i	0.204053	−	0.00540766i
$121$	5.00759	−	8.67339i	0.455235	−	0.788490i
$122$	−2.75676	+	1.59162i	−0.249585	+	0.144098i
$123$	1.47240	−	1.75473i	0.132761	−	0.158219i
$124$	3.11813	+	2.61642i	0.280016	+	0.234961i
$125$	4.80372	−	10.0958i	0.429658	−	0.902992i
$126$	2.42743	−	4.20443i	0.216252	−	0.374560i
$127$	6.44588	+	17.7099i	0.571979	+	1.57150i	0.801372	+	0.598166i	$0.204104\pi$
$127$	6.44588	+	17.7099i	0.571979	+	1.57150i	−0.229393	+	0.973334i	$0.573674\pi$
$128$	0.984808	−	0.173648i	0.0870455	−	0.0153485i
$129$	−0.480736	+	2.72639i	−0.0423265	+	0.240045i
$130$	4.77020	+	3.79194i	0.418375	+	0.332575i
$131$	−7.11162	+	5.96736i	−0.621345	+	0.521370i	−0.898226	−	0.439534i	$-0.855144\pi$
$131$	−7.11162	+	5.96736i	−0.621345	+	0.521370i	0.276881	+	0.960904i	$0.410699\pi$
$132$			0.992385i			0.0863760i
$133$	−6.56860	−	20.1166i	−0.569570	−	1.74433i
$134$	11.0347			0.953255
$135$	0.820177	+	2.08022i	0.0705896	+	0.179037i
$136$	−7.18133	−	2.61379i	−0.615794	−	0.224131i
$137$	−18.8558	−	3.32478i	−1.61096	−	0.284055i	−0.705569	−	0.708641i	$-0.749308\pi$
$137$	−18.8558	−	3.32478i	−1.61096	−	0.284055i	−0.905387	+	0.424586i	$0.860420\pi$
$138$	−1.05975	+	0.186863i	−0.0902123	+	0.0159069i
$139$	8.65349	−	3.14961i	0.733980	−	0.267147i	0.0521313	−	0.998640i	$-0.483399\pi$
$139$	8.65349	−	3.14961i	0.733980	−	0.267147i	0.681848	+	0.731493i	$0.261176\pi$
$140$	−7.19582	−	8.12823i	−0.608158	−	0.686961i
$141$	−6.35384	−	11.0052i	−0.535090	−	0.926802i
$142$	2.90535	−	3.46246i	0.243812	−	0.290564i
$143$	−1.73839	+	2.07173i	−0.145371	+	0.173247i
$144$	0.500000	+	0.866025i	0.0416667	+	0.0721688i
$145$	8.75574	−	7.75134i	0.727125	−	0.643714i
$146$	14.4161	−	5.24705i	1.19309	−	0.434249i
$147$	−16.3179	+	2.87728i	−1.34588	+	0.237314i
$148$	2.60340	+	0.459050i	0.213998	+	0.0377336i
$149$	−4.94451	−	1.79965i	−0.405070	−	0.147433i	0.131446	−	0.991323i	$-0.458038\pi$
$149$	−4.94451	−	1.79965i	−0.405070	−	0.147433i	−0.536516	+	0.843890i	$0.680260\pi$
$150$	4.99298	−	0.264827i	0.407675	−	0.0216230i
$151$	−11.6204			−0.945656			−0.472828	−	0.881155i	$-0.656767\pi$
$151$	−11.6204			−0.945656			−0.472828	+	0.881155i	$0.656767\pi$
$152$	4.26496	+	0.900069i	0.345934	+	0.0730052i
$153$		−	7.64221i		−	0.617836i
$154$	3.69071	−	3.09687i	0.297406	−	0.249553i
$155$	7.12489	+	5.66373i	0.572285	+	0.454922i
$156$	−0.473226	+	2.68380i	−0.0378884	+	0.214876i
$157$	11.5460	−	2.03586i	0.921468	−	0.162480i	0.307262	−	0.951625i	$-0.400587\pi$
$157$	11.5460	−	2.03586i	0.921468	−	0.162480i	0.614206	+	0.789145i	$0.289476\pi$
$158$	4.16831	+	11.4523i	0.331613	+	0.911099i
$159$	−3.35063	+	5.80346i	−0.265722	+	0.460244i
$160$	2.19104	−	0.446491i	0.173217	−	0.0352982i
$161$	4.00206	+	3.35813i	0.315407	+	0.264658i
$162$	−0.642788	+	0.766044i	−0.0505022	+	0.0601861i
$163$	−2.31209	+	1.33488i	−0.181097	+	0.104556i	−0.587808	−	0.809001i	$-0.700009\pi$
$163$	−2.31209	+	1.33488i	−0.181097	+	0.104556i	0.406711	+	0.913557i	$0.366676\pi$
$164$	1.14532	−	1.98375i	0.0894345	−	0.154905i
$165$	0.0587868	+	2.21826i	0.00457654	+	0.172691i
$166$	1.34338	+	7.61868i	0.104266	+	0.591324i
$167$	5.99852	+	1.05770i	0.464180	+	0.0818474i	0.400847	−	0.916145i	$-0.368716\pi$
$167$	5.99852	+	1.05770i	0.464180	+	0.0818474i	0.0633328	+	0.997992i	$0.479827\pi$
$168$	1.66046	−	4.56207i	0.128107	−	0.351971i
$169$	4.26937	−	3.58243i	0.328413	−	0.275571i
$170$	−16.2071	−	5.41715i	−1.24303	−	0.415477i
$171$	0.612914	+	4.31559i	0.0468707	+	0.330022i
$172$			2.76845i			0.211092i
$173$	7.13002	+	8.49722i	0.542085	+	0.646032i	0.965654	−	0.259832i	$-0.0836672\pi$
$173$	7.13002	+	8.49722i	0.542085	+	0.646032i	−0.423569	+	0.905864i	$0.639223\pi$
$174$	4.91427	+	1.78865i	0.372550	+	0.135597i
$175$	−16.5662	−	17.7426i	−1.25229	−	1.34122i
$176$	0.172326	+	0.977308i	0.0129895	+	0.0736674i
$177$	−1.58955	−	4.36725i	−0.119478	−	0.328263i
$178$	14.8369	+	8.56610i	1.11207	+	0.642056i
$179$	2.51784	+	4.36102i	0.188192	+	0.325958i	0.944647	−	0.328087i	$-0.106404\pi$
$179$	2.51784	+	4.36102i	0.188192	+	0.325958i	−0.756456	+	0.654045i	$0.773071\pi$
$180$	1.16894	+	1.90619i	0.0871279	+	0.142079i
$181$	1.49147	+	1.25149i	0.110860	+	0.0930227i	0.696533	−	0.717525i	$-0.254725\pi$
$181$	1.49147	+	1.25149i	0.110860	+	0.0930227i	−0.585673	+	0.810548i	$0.699170\pi$
$182$	11.4579	−	6.61523i	0.849317	−	0.490353i
$183$	−2.75676	−	1.59162i	−0.203786	−	0.117656i
$184$	−1.01121	+	0.368049i	−0.0745471	+	0.0271329i
$185$	5.84653	+	0.871886i	0.429845	+	0.0641023i
$186$	−0.706822	+	4.00859i	−0.0518267	+	0.293924i
$187$	2.59388	−	7.12664i	0.189684	−	0.521151i
$188$	−8.16833	−	9.73464i	−0.595737	−	0.709972i
$189$	4.85485			0.353139
$190$	9.58671	+	1.75926i	0.695493	+	0.127630i
$191$	−8.70671			−0.629995			−0.314998	−	0.949092i	$-0.602004\pi$
$191$	−8.70671			−0.629995			−0.314998	+	0.949092i	$0.602004\pi$
$192$	0.642788	+	0.766044i	0.0463892	+	0.0552845i
$193$	−1.61628	+	4.44070i	−0.116342	+	0.319648i	−0.984173	−	0.177213i	$-0.943292\pi$
$193$	−1.61628	+	4.44070i	−0.116342	+	0.319648i	0.867830	+	0.496861i	$0.165514\pi$
$194$	0.104004	−	0.589834i	0.00746702	−	0.0423476i
$195$	−0.898812	+	6.02709i	−0.0643653	+	0.431609i
$196$	−15.5703	+	5.66714i	−1.11217	+	0.404795i
$197$	−11.4098	−	6.58746i	−0.812916	−	0.469337i	0.0350516	−	0.999386i	$-0.488840\pi$
$197$	−11.4098	−	6.58746i	−0.812916	−	0.469337i	−0.847967	+	0.530048i	$0.822174\pi$
$198$	−0.859430	+	0.496192i	−0.0610770	+	0.0352629i
$199$	3.35137	+	2.81213i	0.237572	+	0.199347i	0.753799	−	0.657105i	$-0.228219\pi$
$199$	3.35137	+	2.81213i	0.237572	+	0.199347i	−0.516227	+	0.856452i	$0.672664\pi$
$200$	4.87114	−	1.12783i	0.344442	−	0.0797493i
$201$	5.51736	+	9.55636i	0.389165	+	0.674053i
$202$	8.07034	+	4.65941i	0.567827	+	0.327835i
$203$	−8.68362	−	23.8580i	−0.609470	−	1.67451i
$204$	−1.32706	−	7.52611i	−0.0929125	−	0.526933i
$205$	2.44260	−	4.50210i	0.170599	−	0.314440i
$206$	−16.6928	−	6.07569i	−1.16304	−	0.423314i
$207$	−0.691706	−	0.824343i	−0.0480769	−	0.0572958i
$208$			2.72520i			0.188959i
$209$	−0.893214	+	4.23248i	−0.0617849	+	0.292767i
$210$	3.44135	−	10.2959i	0.237475	−	0.710483i
$211$	−18.8967	+	15.8562i	−1.30090	+	1.09158i	−0.310912	+	0.950439i	$0.600634\pi$
$211$	−18.8967	+	15.8562i	−1.30090	+	1.09158i	−0.989989	+	0.141146i	$0.954921\pi$
$212$	−2.29197	+	6.29712i	−0.157413	+	0.432488i
$213$	4.45126	+	0.784877i	0.304995	+	0.0537789i
$214$	−0.160357	−	0.909432i	−0.0109618	−	0.0621675i
$215$	0.163997	+	6.18827i	0.0111845	+	0.422036i
$216$	−0.500000	+	0.866025i	−0.0340207	+	0.0589256i
$217$	17.1138	−	9.88066i	1.16176	−	0.670743i
$218$	6.40290	−	7.63068i	0.433659	−	0.516815i
$219$	11.7521	+	9.86122i	0.794137	+	0.666360i
$220$	0.443091	+	2.17435i	0.0298732	+	0.146595i
$221$	10.4133	−	18.0363i	0.700473	−	1.21326i
$222$	0.904151	+	2.48413i	0.0606826	+	0.166724i
$223$	−10.0261	+	1.76787i	−0.671396	+	0.118385i	−0.498946	−	0.866633i	$-0.666279\pi$
$223$	−10.0261	+	1.76787i	−0.671396	+	0.118385i	−0.172450	+	0.985018i	$0.555168\pi$
$224$	0.843036	−	4.78110i	0.0563277	−	0.319450i
$225$	2.72584	+	4.19164i	0.181723	+	0.279442i
$226$	−2.50626	+	2.10300i	−0.166714	+	0.139890i
$227$			23.2830i			1.54535i	0.634804	+	0.772673i	$0.281081\pi$
$227$			23.2830i			1.54535i	−0.634804	+	0.772673i	$0.718919\pi$
$228$	1.35300	+	4.14360i	0.0896044	+	0.274416i
$229$	−4.74400			−0.313492			−0.156746	−	0.987639i	$-0.550100\pi$
$229$	−4.74400			−0.313492			−0.156746	+	0.987639i	$0.550100\pi$
$230$	−2.23853	+	0.882595i	−0.147604	+	0.0581966i
$231$	4.52733	+	1.64781i	0.297876	+	0.108418i
$232$	5.15020	+	0.908120i	0.338127	+	0.0596210i
$233$	−7.71216	+	1.35986i	−0.505240	+	0.0890875i	−0.420458	−	0.907312i	$-0.638131\pi$
$233$	−7.71216	+	1.35986i	−0.505240	+	0.0890875i	−0.0847824	+	0.996399i	$0.527020\pi$
$234$	−2.56085	+	0.932074i	−0.167408	+	0.0609316i
$235$	−18.8352	−	21.2758i	−1.22867	−	1.38788i
$236$	−2.32377	−	4.02488i	−0.151264	−	0.261997i
$237$	−7.83386	+	9.33603i	−0.508864	+	0.606440i
$238$	−23.8486	+	28.4216i	−1.54587	+	1.84230i
$239$	−7.17445	−	12.4265i	−0.464077	−	0.803805i	0.535082	−	0.844800i	$-0.320281\pi$
$239$	−7.17445	−	12.4265i	−0.464077	−	0.803805i	−0.999159	+	0.0409951i	$0.986947\pi$
$240$	1.48219	+	1.67425i	0.0956750	+	0.108072i
$241$	−10.9526	+	3.98641i	−0.705518	+	0.256787i	−0.669765	−	0.742573i	$-0.733605\pi$
$241$	−10.9526	+	3.98641i	−0.705518	+	0.256787i	−0.0357528	+	0.999361i	$0.511383\pi$
$242$	9.86302	−	1.73912i	0.634019	−	0.111795i
$243$	−0.984808	−	0.173648i	−0.0631754	−	0.0111395i
$244$	−2.99126	−	1.08873i	−0.191496	−	0.0696988i
$245$	−34.4684	+	13.5900i	−2.20210	+	0.868234i
$246$	2.29064			0.146046
$247$	−4.43390	+	11.0204i	−0.282122	+	0.701209i
$248$			4.07043i			0.258472i
$249$	−5.92628	+	4.97274i	−0.375563	+	0.315135i
$250$	10.8216	−	2.80957i	0.684416	−	0.177693i
$251$	2.46487	−	13.9790i	0.155581	−	0.882346i	−0.802671	−	0.596422i	$-0.796588\pi$
$251$	2.46487	−	13.9790i	0.155581	−	0.882346i	0.958252	−	0.285924i	$-0.0923005\pi$
$252$	4.78110	−	0.843036i	0.301181	−	0.0531063i
$253$	−0.365246	−	1.00351i	−0.0229628	−	0.0630899i
$254$	−9.42324	+	16.3215i	−0.591267	+	1.02410i
$255$	−3.41218	−	16.7444i	−0.213679	−	1.04857i
$256$	0.766044	+	0.642788i	0.0478778	+	0.0401742i
$257$	2.99006	−	3.56342i	0.186515	−	0.222280i	−0.664682	−	0.747127i	$-0.731433\pi$
$257$	2.99006	−	3.56342i	0.186515	−	0.222280i	0.851197	+	0.524847i	$0.175877\pi$
$258$	−2.39755	+	1.38422i	−0.149265	+	0.0861780i
$259$	6.41705	−	11.1147i	0.398736	−	0.690631i
$260$	0.161435	+	6.09160i	0.0100118	+	0.377785i
$261$	0.908120	+	5.15020i	0.0562112	+	0.318790i
$262$	−9.14252	−	1.61207i	−0.564827	−	0.0995942i
$263$	2.80285	−	7.70076i	0.172831	−	0.474849i	−0.822788	−	0.568348i	$-0.807583\pi$
$263$	2.80285	−	7.70076i	0.172831	−	0.474849i	0.995619	+	0.0934986i	$0.0298051\pi$
$264$	−0.760211	+	0.637893i	−0.0467877	+	0.0392596i
$265$	−4.75016	+	14.2116i	−0.291800	+	0.873013i
$266$	11.1880	−	17.9625i	0.685978	−	1.10135i
$267$			17.1322i			1.04847i
$268$	7.09299	+	8.45309i	0.433273	+	0.516355i
$269$	−3.64108	−	1.32524i	−0.222001	−	0.0808016i	0.228625	−	0.973514i	$-0.426577\pi$
$269$	−3.64108	−	1.32524i	−0.222001	−	0.0808016i	−0.450626	+	0.892713i	$0.648799\pi$
$270$	−1.06634	+	1.96543i	−0.0648954	+	0.119612i
$271$	2.92179	+	16.5703i	0.177486	+	1.00657i	0.935235	+	0.354027i	$0.115188\pi$
$271$	2.92179	+	16.5703i	0.177486	+	1.00657i	−0.757749	+	0.652546i	$0.773701\pi$
$272$	−2.61379	−	7.18133i	−0.158484	−	0.435432i
$273$	11.4579	+	6.61523i	0.693464	+	0.400372i
$274$	−9.57332	−	16.5815i	−0.578345	−	1.00172i
$275$	1.11924	+	4.83404i	0.0674925	+	0.291504i
$276$	−0.824343	−	0.691706i	−0.0496196	−	0.0416358i
$277$	5.57553	−	3.21904i	0.335001	−	0.193413i	−0.323058	−	0.946379i	$-0.604711\pi$
$277$	5.57553	−	3.21904i	0.335001	−	0.193413i	0.658059	+	0.752966i	$0.271378\pi$
$278$	7.97510	+	4.60443i	0.478315	+	0.276155i
$279$	−3.82495	+	1.39217i	−0.228994	+	0.0833469i
$280$	1.60120	−	10.7370i	0.0956902	−	0.641661i
$281$	2.75540	−	15.6266i	0.164373	−	0.932206i	−0.785335	−	0.619071i	$-0.787509\pi$
$281$	2.75540	−	15.6266i	0.164373	−	0.932206i	0.949708	−	0.313136i	$-0.101379\pi$
$282$	4.34628	−	11.9413i	0.258817	−	0.711094i
$283$	−7.02832	−	8.37602i	−0.417790	−	0.497903i	0.515568	−	0.856848i	$-0.327581\pi$
$283$	−7.02832	−	8.37602i	−0.417790	−	0.497903i	−0.933358	+	0.358946i	$0.883136\pi$
$284$	4.51993			0.268208
$285$	3.26979	+	9.18196i	0.193686	+	0.543893i
$286$	−2.70445			−0.159917
$287$	−7.14826	−	8.51897i	−0.421949	−	0.502859i
$288$	−0.342020	+	0.939693i	−0.0201537	+	0.0553719i
$289$	−7.18962	+	40.7743i	−0.422919	+	2.39849i
$290$	11.5660	+	1.72482i	0.679176	+	0.101285i
$291$	0.562813	−	0.204847i	0.0329927	−	0.0120083i
$292$	13.2860	+	7.67067i	0.777504	+	0.448892i
$293$	15.5846	−	8.99775i	0.910460	−	0.525654i	0.0298806	−	0.999553i	$-0.490487\pi$
$293$	15.5846	−	8.99775i	0.910460	−	0.525654i	0.880579	+	0.473899i	$0.157154\pi$
$294$	−12.6930	−	10.6507i	−0.740274	−	0.621163i
$295$	−5.43270	−	8.85909i	−0.316304	−	0.515796i
$296$	1.32178	+	2.28939i	0.0768269	+	0.133068i
$297$	−0.859430	−	0.496192i	−0.0498692	−	0.0287920i
$298$	−1.79965	−	4.94451i	−0.104251	−	0.286428i
$299$	−0.509241	−	2.88805i	−0.0294501	−	0.167020i
$300$	3.41230	+	3.65462i	0.197009	+	0.210999i
$301$	12.6299	+	4.59689i	0.727973	+	0.264960i
$302$	−7.46946	−	8.90175i	−0.429819	−	0.512238i
$303$			9.31882i			0.535353i
$304$	2.05197	+	3.84570i	0.117689	+	0.220566i
$305$	−6.75081	−	2.25642i	−0.386550	−	0.129202i
$306$	5.85427	−	4.91232i	0.334666	−	0.280818i
$307$	7.88289	−	21.6581i	0.449900	−	1.23609i	−0.482893	−	0.875679i	$-0.660414\pi$
$307$	7.88289	−	21.6581i	0.449900	−	1.23609i	0.932793	−	0.360411i	$-0.117364\pi$
$308$	4.74469	+	0.836616i	0.270354	+	0.0476706i
$309$	−3.08471	−	17.4943i	−0.175483	−	0.995214i
$310$	0.241124	+	9.09856i	0.0136949	+	0.516763i
$311$	−3.73403	+	6.46752i	−0.211737	+	0.366740i	−0.952258	−	0.305294i	$-0.901245\pi$
$311$	−3.73403	+	6.46752i	−0.211737	+	0.366740i	0.740521	+	0.672033i	$0.234579\pi$
$312$	−2.36009	+	1.36260i	−0.133614	+	0.0771421i
$313$	12.2375	−	14.5841i	0.691703	−	0.824340i	−0.299858	−	0.953984i	$-0.596939\pi$
$313$	12.2375	−	14.5841i	0.691703	−	0.824340i	0.991561	+	0.129644i	$0.0413836\pi$
$314$	8.98116	+	7.53609i	0.506836	+	0.425286i
$315$	10.6372	−	2.16765i	0.599336	−	0.122133i
$316$	−6.09366	+	10.5545i	−0.342795	+	0.593739i
$317$	−8.30467	−	22.8169i	−0.466436	−	1.28152i	−0.920566	−	0.390588i	$-0.872272\pi$
$317$	−8.30467	−	22.8169i	−0.466436	−	1.28152i	0.454129	−	0.890936i	$-0.349950\pi$
$318$	−6.59945	+	1.16366i	−0.370079	+	0.0652549i
$319$	−0.901204	+	5.11098i	−0.0504577	+	0.286160i
$320$	1.75040	+	1.39143i	0.0978505	+	0.0777835i
$321$	0.707412	−	0.593589i	0.0394839	−	0.0331309i
$322$			5.22432i			0.291140i
$323$	1.11418	−	33.2930i	0.0619944	−	1.85247i
$324$	−1.00000			−0.0555556
$325$	0.721707	+	13.6069i	0.0400331	+	0.754774i
$326$	−2.50876	−	0.913115i	−0.138947	−	0.0505727i
$327$	9.80982	+	1.72974i	0.542484	+	0.0956546i
$328$	2.25584	−	0.397766i	0.124558	−	0.0219629i
$329$	−57.9733	+	21.1006i	−3.19617	+	1.16331i
$330$	−1.66150	+	1.47090i	−0.0914625	+	0.0809706i
$331$	−14.2374	−	24.6600i	−0.782560	−	1.35543i	−0.930446	−	0.366430i	$-0.880580\pi$
$331$	−14.2374	−	24.6600i	−0.782560	−	1.35543i	0.147885	−	0.989005i	$-0.452753\pi$
$332$	−4.97274	+	5.92628i	−0.272915	+	0.325247i
$333$	−1.69925	+	2.02509i	−0.0931182	+	0.110974i
$334$	3.04553	+	5.27501i	0.166644	+	0.288636i
$335$	16.3556	+	18.4749i	0.893601	+	1.00939i
$336$	4.56207	−	1.66046i	0.248881	−	0.0905854i
$337$	−22.1507	+	3.90576i	−1.20662	+	0.212761i	−0.740560	−	0.671990i	$-0.765440\pi$
$337$	−22.1507	+	3.90576i	−1.20662	+	0.212761i	−0.466065	+	0.884751i	$0.654329\pi$
$338$	5.48860	+	0.967788i	0.298540	+	0.0526407i
$339$	−3.07438	−	1.11898i	−0.166978	−	0.0607749i
$340$	−6.26797	−	15.8975i	−0.339928	−	0.862161i
$341$	−4.03943			−0.218747
$342$	−2.91196	+	3.24353i	−0.157461	+	0.175390i
$343$			46.4590i			2.50855i
$344$	−2.12075	+	1.77952i	−0.114343	+	0.0959455i
$345$	−1.88362	−	1.49733i	−0.101410	−	0.0806133i
$346$	−1.92616	+	10.9238i	−0.103551	+	0.587268i
$347$	−29.8339	+	5.26051i	−1.60157	+	0.282399i	−0.901859	−	0.432031i	$-0.857797\pi$
$347$	−29.8339	+	5.26051i	−1.60157	+	0.282399i	−0.699707	+	0.714430i	$0.746686\pi$
$348$	1.78865	+	4.91427i	0.0958815	+	0.263432i
$349$	14.5202	−	25.1497i	0.777247	−	1.34623i	−0.156276	−	0.987714i	$-0.549949\pi$
$349$	14.5202	−	25.1497i	0.777247	−	1.34623i	0.933523	−	0.358518i	$-0.116718\pi$
$350$	2.94310	−	24.0952i	0.157315	−	1.28794i
$351$	−2.08763	−	1.75173i	−0.111429	−	0.0935002i
$352$	−0.637893	+	0.760211i	−0.0339998	+	0.0405194i
$353$	10.2697	−	5.92921i	0.546601	−	0.315580i	−0.201149	−	0.979561i	$-0.564468\pi$
$353$	10.2697	−	5.92921i	0.546601	−	0.315580i	0.747750	+	0.663980i	$0.231134\pi$
$354$	2.32377	−	4.02488i	0.123507	−	0.213920i
$355$	10.1033	−	0.267751i	0.536228	−	0.0142107i
$356$	2.97497	+	16.8719i	0.157673	+	0.894210i
$357$	−36.5381	−	6.44266i	−1.93380	−	0.340982i
$358$	−1.72230	+	4.73198i	−0.0910264	+	0.250093i
$359$	8.03014	−	6.73809i	0.423815	−	0.355623i	−0.405797	−	0.913963i	$-0.633006\pi$
$359$	8.03014	−	6.73809i	0.423815	−	0.355623i	0.829612	+	0.558340i	$0.188562\pi$
$360$	−0.708846	+	2.12074i	−0.0373595	+	0.111773i
$361$	2.04095	+	18.8901i	0.107419	+	0.994214i
$362$			1.94698i			0.102331i
$363$	6.43763	+	7.67207i	0.337888	+	0.402679i
$364$	12.4326	+	4.52508i	0.651643	+	0.237179i
$365$	30.1523	+	16.3591i	1.57825	+	0.856274i
$366$	−0.552763	−	3.13487i	−0.0288934	−	0.163862i
$367$	−0.735015	−	2.01944i	−0.0383675	−	0.105414i	0.919030	−	0.394189i	$-0.128974\pi$
$367$	−0.735015	−	2.01944i	−0.0383675	−	0.105414i	−0.957397	+	0.288775i	$0.906752\pi$
$368$	−0.931933	−	0.538052i	−0.0485804	−	0.0280479i
$369$	1.14532	+	1.98375i	0.0596230	+	0.103270i
$370$	3.09017	+	5.03914i	0.160650	+	0.261972i
$371$	24.9222	+	20.9122i	1.29390	+	1.08571i
$372$	−3.52509	+	2.03521i	−0.182768	+	0.105521i
$373$	13.2589	+	7.65503i	0.686520	+	0.396362i	0.802307	−	0.596912i	$-0.203606\pi$
$373$	13.2589	+	7.65503i	0.686520	+	0.396362i	−0.115787	+	0.993274i	$0.536939\pi$
$374$	7.12664	−	2.59388i	0.368510	−	0.134127i
$375$	7.84394	+	7.96697i	0.405059	+	0.411413i
$376$	2.20666	−	12.5146i	0.113800	−	0.645392i
$377$	−4.87442	+	13.3924i	−0.251046	+	0.689742i
$378$	3.12064	+	3.71903i	0.160508	+	0.191286i
$379$	−17.7234			−0.910388			−0.455194	−	0.890392i	$-0.650430\pi$
$379$	−17.7234			−0.910388			−0.455194	+	0.890392i	$0.650430\pi$
$380$	4.81455	+	8.47468i	0.246981	+	0.434742i
$381$	−18.8465			−0.965535
$382$	−5.59656	−	6.66972i	−0.286345	−	0.341253i
$383$	−2.11873	+	5.82117i	−0.108262	+	0.297448i	−0.981980	−	0.188986i	$-0.939480\pi$
$383$	−2.11873	+	5.82117i	−0.108262	+	0.297448i	0.873718	+	0.486433i	$0.161702\pi$
$384$	−0.173648	+	0.984808i	−0.00886145	+	0.0502558i
$385$	10.6553	+	1.58901i	0.543043	+	0.0809834i
$386$	−4.44070	+	1.61628i	−0.226025	+	0.0822665i
$387$	−2.39755	−	1.38422i	−0.121874	−	0.0703641i
$388$	0.518691	−	0.299466i	0.0263325	−	0.0152031i
$389$	−14.7772	−	12.3996i	−0.749234	−	0.628682i	0.186066	−	0.982537i	$-0.440426\pi$
$389$	−14.7772	−	12.3996i	−0.749234	−	0.628682i	−0.935300	+	0.353855i	$0.884871\pi$
$390$	−5.19476	+	3.18561i	−0.263047	+	0.161309i
$391$	4.11190	+	7.12202i	0.207948	+	0.360176i
$392$	−14.3497	−	8.28480i	−0.724769	−	0.418446i
$393$	−3.17516	−	8.72369i	−0.160166	−	0.440052i
$394$	−2.28780	−	12.9748i	−0.115258	−	0.653659i
$395$	−12.9958	+	23.9533i	−0.653891	+	1.20522i
$396$	−0.932536	−	0.339416i	−0.0468617	−	0.0170563i
$397$	−0.347445	−	0.414068i	−0.0174377	−	0.0207815i	0.757255	−	0.653119i	$-0.226540\pi$
$397$	−0.347445	−	0.414068i	−0.0174377	−	0.0207815i	−0.774693	+	0.632338i	$0.782096\pi$
$398$			4.37490i			0.219294i
$399$	21.1500	+	0.707801i	1.05882	+	0.0354343i
$400$	3.99507	+	3.00656i	0.199754	+	0.150328i
$401$	−3.17447	+	2.66369i	−0.158525	+	0.133019i	−0.718600	−	0.695423i	$-0.755217\pi$
$401$	−3.17447	+	2.66369i	−0.158525	+	0.133019i	0.560075	+	0.828442i	$0.310772\pi$
$402$	−3.77410	+	10.3693i	−0.188235	+	0.517171i
$403$	−10.9242	−	1.92623i	−0.544174	−	0.0959526i
$404$	1.61820	+	9.17725i	0.0805083	+	0.456585i
$405$	−2.23528	+	0.0592379i	−0.111072	+	0.00294356i
$406$	12.6946	−	21.9877i	0.630022	−	1.09123i
$407$	−2.27196	+	1.31171i	−0.112617	+	0.0650193i
$408$	4.91232	−	5.85427i	0.243196	−	0.289830i
$409$	−5.55853	−	4.66416i	−0.274851	−	0.230628i	0.494934	−	0.868931i	$-0.335192\pi$
$409$	−5.55853	−	4.66416i	−0.274851	−	0.230628i	−0.769785	+	0.638303i	$0.779637\pi$
$410$	5.01888	−	1.02275i	0.247865	−	0.0505100i
$411$	9.57332	−	16.5815i	0.472217	−	0.817904i
$412$	−6.07569	−	16.6928i	−0.299328	−	0.822397i
$413$	−22.2203	+	3.91804i	−1.09339	+	0.192794i
$414$	0.186863	−	1.05975i	0.00918383	−	0.0520841i
$415$	−10.7644	+	13.5415i	−0.528405	+	0.664726i
$416$	−2.08763	+	1.75173i	−0.102354	+	0.0858855i
$417$			9.20886i			0.450960i
$418$	−3.81641	+	2.03634i	−0.186667	+	0.0996008i
$419$	−13.4568			−0.657406			−0.328703	−	0.944433i	$-0.606612\pi$
$419$	−13.4568			−0.657406			−0.328703	+	0.944433i	$0.606612\pi$
$420$	10.0992	−	3.98184i	0.492788	−	0.194294i
$421$	9.66702	+	3.51851i	0.471142	+	0.171482i	0.566670	−	0.823945i	$-0.308232\pi$
$421$	9.66702	+	3.51851i	0.471142	+	0.171482i	−0.0955277	+	0.995427i	$0.530454\pi$
$422$	−24.2931	−	4.28353i	−1.18257	−	0.208519i
$423$	12.5146	−	2.20666i	0.608481	−	0.107292i
$424$	−6.29712	+	2.29197i	−0.305815	+	0.111308i
$425$	−14.9524	−	35.1640i	−0.725298	−	1.70571i
$426$	2.25996	+	3.91437i	0.109496	+	0.189652i
$427$	−9.93372	+	11.8386i	−0.480727	+	0.572908i
$428$	0.593589	−	0.707412i	0.0286922	−	0.0341941i
$429$	−1.35222	−	2.34212i	−0.0652860	−	0.113079i
$430$	−4.63507	+	4.10337i	−0.223523	+	0.197882i
$431$	7.47124	−	2.71931i	0.359877	−	0.130984i	−0.155753	−	0.987796i	$-0.549780\pi$
$431$	7.47124	−	2.71931i	0.359877	−	0.130984i	0.515630	+	0.856812i	$0.327558\pi$
$432$	−0.984808	+	0.173648i	−0.0473816	+	0.00835465i
$433$	16.7302	+	2.94998i	0.804000	+	0.141767i	0.560522	−	0.828139i	$-0.310600\pi$
$433$	16.7302	+	2.94998i	0.804000	+	0.141767i	0.243478	+	0.969906i	$0.421712\pi$
$434$	18.5696	+	6.75877i	0.891368	+	0.324431i
$435$	4.28924	+	10.8788i	0.205653	+	0.521600i
$436$	9.96115			0.477053
$437$	−2.89321	−	3.69206i	−0.138401	−	0.176615i
$438$			15.3413i			0.733038i
$439$	−9.60410	+	8.05879i	−0.458379	+	0.384625i	−0.842534	−	0.538643i	$-0.818937\pi$
$439$	−9.60410	+	8.05879i	−0.458379	+	0.384625i	0.384155	+	0.923268i	$0.374493\pi$
$440$	−1.38084	+	1.73707i	−0.0658288	+	0.0828117i
$441$	2.87728	−	16.3179i	0.137013	−	0.777041i
$442$	20.5102	−	3.61650i	0.975569	−	0.172019i
$443$	−1.10875	−	3.04626i	−0.0526781	−	0.144732i	0.910563	−	0.413370i	$-0.135649\pi$
$443$	−1.10875	−	3.04626i	−0.0526781	−	0.144732i	−0.963241	+	0.268638i	$0.913426\pi$
$444$	−1.32178	+	2.28939i	−0.0627289	+	0.108650i
$445$	7.64937	+	37.5373i	0.362615	+	1.77944i
$446$	−7.79891	−	6.54406i	−0.369289	−	0.309870i
$447$	3.38224	−	4.03080i	0.159975	−	0.190650i
$448$	4.20443	−	2.42743i	0.198640	−	0.114685i
$449$	18.8518	−	32.6523i	0.889673	−	1.54096i	0.0494117	−	0.998778i	$-0.484265\pi$
$449$	18.8518	−	32.6523i	0.889673	−	1.54096i	0.840262	−	0.542181i	$-0.182401\pi$
$450$	−1.45884	+	4.78244i	−0.0687706	+	0.225447i
$451$	0.394736	+	2.23866i	0.0185874	+	0.105414i
$452$	−3.22199	−	0.568123i	−0.151550	−	0.0267223i
$453$	3.97441	−	10.9196i	0.186734	−	0.513048i
$454$	−17.8358	+	14.9660i	−0.837076	+	0.702390i
$455$	28.0584	+	9.37836i	1.31540	+	0.439664i
$456$	−2.30449	+	3.69991i	−0.107918	+	0.173264i
$457$			14.2488i			0.666529i	0.942833	+	0.333265i	$0.108150\pi$
$457$			14.2488i			0.666529i	−0.942833	+	0.333265i	$0.891850\pi$
$458$	−3.04938	−	3.63411i	−0.142488	−	0.169811i
$459$	7.18133	+	2.61379i	0.335196	+	0.122001i
$460$	−2.11501	−	1.14749i	−0.0986127	−	0.0535021i
$461$	5.33648	+	30.2647i	0.248545	+	1.40957i	0.812114	+	0.583499i	$0.198317\pi$
$461$	5.33648	+	30.2647i	0.248545	+	1.40957i	−0.563569	+	0.826069i	$0.690572\pi$
$462$	1.64781	+	4.52733i	0.0766632	+	0.210630i
$463$	−7.88150	−	4.55038i	−0.366284	−	0.211474i	0.305550	−	0.952176i	$-0.401160\pi$
$463$	−7.88150	−	4.55038i	−0.366284	−	0.211474i	−0.671834	+	0.740702i	$0.734493\pi$
$464$	2.61483	+	4.52901i	0.121390	+	0.210254i
$465$	−7.75902	+	4.75810i	−0.359816	+	0.220652i
$466$	−5.99900	−	5.03376i	−0.277898	−	0.233184i
$467$	8.34488	−	4.81792i	0.386155	−	0.222947i	−0.294338	−	0.955701i	$-0.595099\pi$
$467$	8.34488	−	4.81792i	0.386155	−	0.222947i	0.680493	+	0.732755i	$0.261766\pi$
$468$	−2.36009	−	1.36260i	−0.109095	−	0.0629863i
$469$	50.3412	−	18.3227i	2.32454	−	0.846064i
$470$	4.19118	−	28.1044i	0.193325	−	1.29636i
$471$	−2.03586	+	11.5460i	−0.0938077	+	0.532010i
$472$	1.58955	−	4.36725i	0.0731650	−	0.201019i
$473$	−1.76597	−	2.10460i	−0.0811995	−	0.0967698i
$474$	−12.1873			−0.559782
$475$	11.2639	+	18.6581i	0.516823	+	0.856092i
$476$	−37.1018			−1.70056
$477$	−4.30749	−	5.13346i	−0.197226	−	0.235045i
$478$	4.90762	−	13.4836i	0.224469	−	0.616724i
$479$	7.41875	−	42.0738i	0.338972	−	1.92240i	−0.0448451	−	0.998994i	$-0.514279\pi$
$479$	7.41875	−	42.0738i	0.338972	−	1.92240i	0.383817	−	0.923409i	$-0.374609\pi$
$480$	−0.329815	+	2.21161i	−0.0150539	+	0.100946i
$481$	−6.76977	+	2.46399i	−0.308675	+	0.112348i
$482$	−10.0940	−	5.82775i	−0.459767	−	0.265447i
$483$	−4.52440	+	2.61216i	−0.205867	+	0.118857i
$484$	7.67207	+	6.43763i	0.348730	+	0.292620i
$485$	1.14168	−	0.700118i	0.0518411	−	0.0317907i
$486$	−0.500000	−	0.866025i	−0.0226805	−	0.0392837i
$487$	26.2715	+	15.1678i	1.19047	+	0.687320i	0.958414	−	0.285382i	$-0.0921203\pi$
$487$	26.2715	+	15.1678i	1.19047	+	0.687320i	0.232059	+	0.972702i	$0.425454\pi$
$488$	−1.08873	−	2.99126i	−0.0492845	−	0.135408i
$489$	−0.463600	−	2.62921i	−0.0209647	−	0.118897i
$490$	−32.5664	−	17.6688i	−1.47120	−	0.798196i
$491$	−13.9882	−	5.09131i	−0.631281	−	0.229767i	0.00650786	−	0.999979i	$-0.497928\pi$
$491$	−13.9882	−	5.09131i	−0.631281	−	0.229767i	−0.637789	+	0.770211i	$0.720151\pi$
$492$	1.47240	+	1.75473i	0.0663807	+	0.0791094i
$493$		−	39.9661i		−	1.79998i
$494$	−11.2921	+	3.68719i	−0.508058	+	0.165895i
$495$	−2.10459	−	0.703448i	−0.0945943	−	0.0316176i
$496$	−3.11813	+	2.61642i	−0.140008	+	0.117481i
$497$	7.50515	−	20.6202i	0.336652	−	0.924943i
$498$	−7.61868	−	1.34338i	−0.341401	−	0.0601983i
$499$	1.33264	+	7.55777i	0.0596571	+	0.338332i	0.999998	−	0.00190101i	$-0.000605110\pi$
$499$	1.33264	+	7.55777i	0.0596571	+	0.338332i	−0.940341	+	0.340233i	$0.889494\pi$
$500$	9.10822	+	6.48385i	0.407332	+	0.289966i
$501$	−3.04553	+	5.27501i	−0.136064	+	0.235670i
$502$	12.2929	−	7.09732i	0.548660	−	0.316769i
$503$	13.4434	−	16.0212i	0.599411	−	0.714350i	−0.377974	−	0.925816i	$-0.623379\pi$
$503$	13.4434	−	16.0212i	0.599411	−	0.714350i	0.977385	+	0.211466i	$0.0678236\pi$
$504$	3.71903	+	3.12064i	0.165659	+	0.139004i
$505$	4.16077	+	20.4179i	0.185152	+	0.908584i
$506$	0.533954	−	0.924836i	0.0237372	−	0.0411140i
$507$	1.90617	+	5.23716i	0.0846560	+	0.232590i
$508$	−18.5602	+	3.27266i	−0.823474	+	0.145201i
$509$	2.64896	−	15.0230i	0.117413	−	0.665882i	−0.868114	−	0.496364i	$-0.834668\pi$
$509$	2.64896	−	15.0230i	0.117413	−	0.665882i	0.985527	−	0.169517i	$-0.0542209\pi$
$510$	10.6336	−	13.3769i	0.470865	−	0.592341i
$511$	57.0550	−	47.8748i	2.52396	−	2.11786i
$512$			1.00000i			0.0441942i
$513$	−4.26496	−	0.900069i	−0.188303	−	0.0397390i
$514$	4.65171			0.205178
$515$	−14.5697	−	36.9533i	−0.642020	−	1.62836i
$516$	−2.60149	−	0.946865i	−0.114524	−	0.0416834i
$517$	12.4193	+	2.18986i	0.546201	+	0.0963099i
$518$	12.6391	−	2.22862i	0.555331	−	0.0979199i
$519$	−10.4234	+	3.79380i	−0.457536	+	0.166529i
$520$	−4.56267	+	4.03927i	−0.200086	+	0.177134i
$521$	−19.6661	−	34.0627i	−0.861587	−	1.49231i	−0.870396	−	0.492352i	$-0.836137\pi$
$521$	−19.6661	−	34.0627i	−0.861587	−	1.49231i	0.00880862	−	0.999961i	$-0.497196\pi$
$522$	−3.36156	+	4.00615i	−0.147131	+	0.175344i
$523$	17.4872	−	20.8404i	0.764661	−	0.911287i	−0.233472	−	0.972363i	$-0.575009\pi$
$523$	17.4872	−	20.8404i	0.764661	−	0.911287i	0.998133	+	0.0610764i	$0.0194533\pi$
$524$	−4.64178	−	8.03980i	−0.202777	−	0.351220i
$525$	22.3386	−	9.49879i	0.974936	−	0.414561i
$526$	7.70076	−	2.80285i	0.335769	−	0.122210i
$527$	30.6345	−	5.40168i	1.33446	−	0.235301i
$528$	−0.977308	−	0.172326i	−0.0425319	−	0.00749952i
$529$	−20.5248	−	7.47040i	−0.892381	−	0.324800i
$530$	−13.9401	+	5.49622i	−0.605519	+	0.238741i
$531$	4.64753			0.201686
$532$	20.9516	−	2.97561i	0.908366	−	0.129009i
$533$			6.24246i			0.270391i
$534$	−13.1240	+	11.0124i	−0.567932	+	0.476551i
$535$	1.28493	−	1.61643i	0.0555526	−	0.0698844i
$536$	−1.91616	+	10.8671i	−0.0827655	+	0.469387i
$537$	−4.95917	+	0.874435i	−0.214004	+	0.0377347i
$538$	−1.32524	−	3.64108i	−0.0571353	−	0.156978i
$539$	8.22171	−	14.2404i	0.354134	−	0.613378i
$540$	−2.19104	+	0.446491i	−0.0942872	+	0.0192139i
$541$	19.7084	+	16.5373i	0.847331	+	0.710995i	0.959200	−	0.282728i	$-0.0912392\pi$
$541$	19.7084	+	16.5373i	0.847331	+	0.710995i	−0.111869	+	0.993723i	$0.535684\pi$
$542$	−10.8155	+	12.8894i	−0.464565	+	0.553647i
$543$	−1.68613	+	0.973488i	−0.0723588	+	0.0417764i
$544$	3.82110	−	6.61835i	0.163828	−	0.283759i
$545$	22.2660	−	0.590078i	0.953770	−	0.0252761i
$546$	2.29745	+	13.0295i	0.0983216	+	0.557609i
$547$	20.9575	+	3.69538i	0.896079	+	0.158003i	0.602676	−	0.797986i	$-0.294101\pi$
$547$	20.9575	+	3.69538i	0.896079	+	0.158003i	0.293403	+	0.955989i	$0.405212\pi$
$548$	6.54854	−	17.9920i	0.279740	−	0.768578i
$549$	2.43850	−	2.04614i	0.104073	−	0.0873273i
$550$	−2.98366	+	3.96465i	−0.127224	+	0.169053i
$551$	3.20533	+	22.5690i	0.136552	+	0.961474i
$552$		−	1.07610i		−	0.0458020i
$553$	38.0322	+	45.3251i	1.61730	+	1.92742i
$554$	6.04981	+	2.20195i	0.257032	+	0.0935519i
$555$	−2.81893	+	5.19574i	−0.119657	+	0.220547i
$556$	1.59910	+	9.06895i	0.0678170	+	0.384609i
$557$	13.4753	+	37.0230i	0.570965	+	1.56871i	0.802983	+	0.596002i	$0.203245\pi$
$557$	13.4753	+	37.0230i	0.570965	+	1.56871i	−0.232018	+	0.972711i	$0.574533\pi$
$558$	−3.52509	−	2.03521i	−0.149229	−	0.0861575i
$559$	−3.77229	−	6.53380i	−0.159551	−	0.276350i
$560$	9.25429	−	5.67505i	0.391065	−	0.239815i
$561$	5.80969	+	4.87491i	0.245285	+	0.205819i
$562$	13.7418	−	7.93385i	0.579664	−	0.334669i
$563$	−19.0576	−	11.0029i	−0.803180	−	0.463716i	0.0414018	−	0.999143i	$-0.486818\pi$
$563$	−19.0576	−	11.0029i	−0.803180	−	0.463716i	−0.844582	+	0.535426i	$0.820151\pi$
$564$	11.9413	−	4.34628i	0.502820	−	0.183011i
$565$	−7.23571	−	1.07905i	−0.304408	−	0.0453961i
$566$	1.89869	−	10.7680i	0.0798079	−	0.452613i
$567$	−1.66046	+	4.56207i	−0.0697327	+	0.191589i
$568$	2.90535	+	3.46246i	0.121906	+	0.145282i
$569$	−29.9856			−1.25706			−0.628532	−	0.777784i	$-0.716344\pi$
$569$	−29.9856			−1.25706			−0.628532	+	0.777784i	$0.716344\pi$
$570$	−4.93201	+	8.40686i	−0.206579	+	0.352125i
$571$	4.61925			0.193310			0.0966548	−	0.995318i	$-0.469186\pi$
$571$	4.61925			0.193310			0.0966548	+	0.995318i	$0.469186\pi$
$572$	−1.73839	−	2.07173i	−0.0726856	−	0.0866233i
$573$	2.97787	−	8.18163i	0.124402	−	0.341792i
$574$	1.93109	−	10.9518i	0.0806023	−	0.457118i
$575$	−4.79561	−	2.43968i	−0.199991	−	0.101742i
$576$	−0.939693	+	0.342020i	−0.0391539	+	0.0142508i
$577$	−8.45472	−	4.88133i	−0.351974	−	0.203213i	0.313580	−	0.949562i	$-0.398472\pi$
$577$	−8.45472	−	4.88133i	−0.351974	−	0.203213i	−0.665555	+	0.746349i	$0.731805\pi$
$578$	−35.8563	+	20.7017i	−1.49143	+	0.861076i
$579$	−3.62009	−	3.03761i	−0.150446	−	0.126239i
$580$	6.11317	+	9.96873i	0.253835	+	0.413929i
$581$	18.7791	+	32.5263i	0.779088	+	1.34942i
$582$	0.518691	+	0.299466i	0.0215004	+	0.0124133i
$583$	−2.27451	−	6.24917i	−0.0942006	−	0.258814i
$584$	2.66400	+	15.1083i	0.110237	+	0.625185i
$585$	−5.35620	−	2.90599i	−0.221452	−	0.120148i
$586$	16.9102	+	6.15482i	0.698555	+	0.254253i
$587$	19.4154	+	23.1384i	0.801360	+	0.955024i	0.999685	−	0.0251125i	$-0.00799439\pi$
$587$	19.4154	+	23.1384i	0.801360	+	0.955024i	−0.198324	+	0.980136i	$0.563550\pi$
$588$		−	16.5696i		−	0.683319i
$589$	−16.8662	+	5.50728i	−0.694960	+	0.226923i
$590$	3.29439	−	9.85621i	0.135628	−	0.405774i
$591$	10.0926	−	8.46868i	0.415153	−	0.348355i
$592$	−0.904151	+	2.48413i	−0.0371604	+	0.102097i
$593$	−30.4057	−	5.36135i	−1.24861	−	0.220164i	−0.490010	−	0.871717i	$-0.663007\pi$
$593$	−30.4057	−	5.36135i	−1.24861	−	0.220164i	−0.758603	+	0.651553i	$0.774118\pi$
$594$	−0.172326	−	0.977308i	−0.00707061	−	0.0400994i
$595$	−82.9330	+	2.19783i	−3.39992	+	0.0901024i
$596$	2.63092	−	4.55688i	0.107767	−	0.186657i
$597$	−3.78877	+	2.18745i	−0.155064	+	0.0895263i
$598$	1.88504	−	2.24650i	0.0770850	−	0.0918663i
$599$	−20.5933	−	17.2798i	−0.841419	−	0.706035i	0.116463	−	0.993195i	$-0.462844\pi$
$599$	−20.5933	−	17.2798i	−0.841419	−	0.706035i	−0.957882	+	0.287160i	$0.907289\pi$
$600$	−0.606219	+	4.96311i	−0.0247488	+	0.202618i
$601$	−7.87768	+	13.6445i	−0.321337	+	0.556572i	−0.980764	−	0.195196i	$-0.937466\pi$
$601$	−7.87768	+	13.6445i	−0.321337	+	0.556572i	0.659427	+	0.751769i	$0.270799\pi$
$602$	4.59689	+	12.6299i	0.187355	+	0.514755i
$603$	−10.8671	+	1.91616i	−0.442542	+	0.0780321i
$604$	2.01786	−	11.4439i	0.0821057	−	0.465645i
$605$	17.5306	+	13.9354i	0.712720	+	0.566556i
$606$	−7.13863	+	5.99003i	−0.289987	+	0.243328i
$607$			11.3852i			0.462111i	0.972941	+	0.231056i	$0.0742180\pi$
$607$			11.3852i			0.462111i	−0.972941	+	0.231056i	$0.925782\pi$
$608$	−1.62700	+	4.04387i	−0.0659834	+	0.164001i
$609$	25.3892			1.02882
$610$	−2.61082	−	6.62182i	−0.105709	−	0.268110i
$611$	32.5425	+	11.8445i	1.31653	+	0.479177i
$612$	7.52611	+	1.32706i	0.304225	+	0.0536430i
$613$	−30.5074	+	5.37927i	−1.23218	+	0.217267i	−0.751562	−	0.659663i	$-0.770699\pi$
$613$	−30.5074	+	5.37927i	−1.23218	+	0.217267i	−0.480619	+	0.876930i	$0.659588\pi$
$614$	21.6581	−	7.88289i	0.874048	−	0.318127i
$615$	3.39517	+	3.83510i	0.136906	+	0.154646i
$616$	2.40894	+	4.17241i	0.0970590	+	0.168111i
$617$	4.26769	−	5.08603i	0.171811	−	0.204756i	−0.673267	−	0.739399i	$-0.735110\pi$
$617$	4.26769	−	5.08603i	0.171811	−	0.204756i	0.845078	+	0.534643i	$0.179554\pi$
$618$	11.4186	−	13.6081i	0.459322	−	0.547399i
$619$	−13.5209	−	23.4189i	−0.543452	−	0.941286i	−0.998703	−	0.0509230i	$-0.983784\pi$
$619$	−13.5209	−	23.4189i	−0.543452	−	0.941286i	0.455251	−	0.890363i	$-0.349550\pi$
$620$	−6.81491	+	6.03315i	−0.273693	+	0.242297i
$621$	1.01121	−	0.368049i	0.0405783	−	0.0147693i
$622$	−7.35460	+	1.29681i	−0.294892	+	0.0519975i
$623$	81.9107	+	14.4431i	3.28168	+	0.578649i
$624$	−2.56085	−	0.932074i	−0.102516	−	0.0373128i
$625$	20.7435	+	13.9537i	0.829742	+	0.558147i
$626$	19.0381			0.760917
$627$	−3.67173	−	2.28694i	−0.146635	−	0.0913316i
$628$			11.7241i			0.467842i
$629$	15.4761	−	12.9860i	0.617073	−	0.517786i
$630$	8.49795	+	6.75521i	0.338567	+	0.269134i
$631$	5.75894	−	32.6606i	0.229260	−	1.30020i	−0.625112	−	0.780535i	$-0.714947\pi$
$631$	5.75894	−	32.6606i	0.229260	−	1.30020i	0.854372	−	0.519662i	$-0.173942\pi$
$632$	−12.0022	+	2.11631i	−0.477421	+	0.0841822i
$633$	−8.43690	−	23.1802i	−0.335337	−	0.921330i
$634$	12.1406	−	21.0282i	0.482165	−	0.835135i
$635$	−41.2934	+	8.41478i	−1.63868	+	0.333930i
$636$	−5.13346	−	4.30749i	−0.203555	−	0.170803i
$637$	29.0254	−	34.5911i	1.15003	−	1.37055i
$638$	−4.49452	+	2.59491i	−0.177940	+	0.102734i
$639$	−2.25996	+	3.91437i	−0.0894028	+	0.154850i
$640$	0.0592379	+	2.23528i	0.00234158	+	0.0883573i
$641$	−3.47751	−	19.7219i	−0.137353	−	0.778969i	−0.973192	−	0.229994i	$-0.926129\pi$
$641$	−3.47751	−	19.7219i	−0.137353	−	0.778969i	0.835839	−	0.548975i	$-0.184982\pi$
$642$	0.909432	+	0.160357i	0.0358924	+	0.00632880i
$643$	−3.64631	+	10.0182i	−0.143796	+	0.395078i	−0.990593	−	0.136839i	$-0.956306\pi$
$643$	−3.64631	+	10.0182i	−0.143796	+	0.395078i	0.846797	+	0.531916i	$0.178528\pi$
$644$	−4.00206	+	3.35813i	−0.157703	+	0.132329i
$645$	−5.87116	−	1.96241i	−0.231177	−	0.0772696i
$646$	26.2201	−	20.5468i	1.03162	−	0.808403i
$647$		−	19.9413i		−	0.783972i	−0.919971	−	0.391986i	$-0.871788\pi$
$647$		−	19.9413i		−	0.783972i	0.919971	−	0.391986i	$-0.128212\pi$
$648$	−0.642788	−	0.766044i	−0.0252511	−	0.0300931i
$649$	4.33399	+	1.57744i	0.170124	+	0.0619201i
$650$	−9.95958	+	9.29920i	−0.390647	+	0.364745i
$651$	3.43152	+	19.4611i	0.134492	+	0.762741i
$652$	−0.913115	−	2.50876i	−0.0357603	−	0.0982507i
$653$	−4.41581	−	2.54947i	−0.172804	−	0.0997684i	0.411103	−	0.911589i	$-0.365144\pi$
$653$	−4.41581	−	2.54947i	−0.172804	−	0.0997684i	−0.583907	+	0.811820i	$0.698477\pi$
$654$	4.98058	+	8.62661i	0.194756	+	0.337327i
$655$	−10.8520	−	17.6963i	−0.424021	−	0.691450i
$656$	1.75473	+	1.47240i	0.0685108	+	0.0574874i
$657$	−13.2860	+	7.67067i	−0.518336	+	0.299261i
$658$	−53.4285	−	30.8469i	−2.08286	−	1.20254i
$659$	−42.1914	+	15.3564i	−1.64354	+	0.598201i	−0.987653	−	0.156655i	$-0.949929\pi$
$659$	−42.1914	+	15.3564i	−1.64354	+	0.598201i	−0.655891	+	0.754856i	$0.727707\pi$
$660$	−2.19477	−	0.327303i	−0.0854312	−	0.0127403i
$661$	5.61905	−	31.8672i	0.218556	−	1.23949i	−0.656073	−	0.754698i	$-0.727783\pi$
$661$	5.61905	−	31.8672i	0.218556	−	1.23949i	0.874628	−	0.484794i	$-0.161105\pi$
$662$	9.73898	−	26.7576i	0.378516	−	1.03997i
$663$	13.3871	+	15.9541i	0.519910	+	0.619605i
$664$	−7.73621			−0.300223
$665$	46.6564	−	7.89245i	1.80926	−	0.306056i
$666$	−2.64356			−0.102436
$667$	−3.61738	−	4.31103i	−0.140066	−	0.166924i
$668$	−2.08327	+	5.72373i	−0.0806040	+	0.221458i
$669$	1.76787	−	10.0261i	0.0683497	−	0.387631i
$670$	−3.63942	+	24.4045i	−0.140603	+	0.942829i
$671$	2.96848	−	1.08044i	0.114597	−	0.0417099i
$672$	4.20443	+	2.42743i	0.162189	+	0.0936400i
$673$	−17.9761	+	10.3785i	−0.692929	+	0.400063i	−0.804709	−	0.593670i	$-0.797678\pi$
$673$	−17.9761	+	10.3785i	−0.692929	+	0.400063i	0.111779	+	0.993733i	$0.464345\pi$
$674$	−17.2302	−	14.4578i	−0.663682	−	0.556895i
$675$	−4.87114	+	1.12783i	−0.187490	+	0.0434100i
$676$	2.78664	+	4.82659i	0.107178	+	0.185638i
$677$	−13.2558	−	7.65325i	−0.509462	−	0.294138i	0.223150	−	0.974784i	$-0.428366\pi$
$677$	−13.2558	−	7.65325i	−0.509462	−	0.294138i	−0.732613	+	0.680646i	$0.761699\pi$
$678$	−1.11898	−	3.07438i	−0.0429743	−	0.118071i
$679$	−0.504922	−	2.86356i	−0.0193771	−	0.109893i
$680$	8.14919	−	15.0202i	0.312507	−	0.576000i
$681$	−21.8789	−	7.96325i	−0.838399	−	0.305152i
$682$	−2.59650	−	3.09438i	−0.0994249	−	0.118490i
$683$		−	15.2033i		−	0.581739i	−0.956763	−	0.290870i	$-0.906055\pi$
$683$		−	15.2033i		−	0.581739i	0.956763	−	0.290870i	$-0.0939445\pi$
$684$	−4.35646	−	0.145792i	−0.166573	−	0.00557451i
$685$	13.5720	−	40.6050i	0.518561	−	1.55144i
$686$	−35.5897	+	29.8633i	−1.35882	+	1.14018i
$687$	1.62254	−	4.45790i	0.0619039	−	0.170080i
$688$	−2.72639	−	0.480736i	−0.103943	−	0.0183279i
$689$	−3.17121	−	17.9848i	−0.120814	−	0.685168i
$690$	−0.0637461	−	2.40540i	−0.00242677	−	0.0915718i
$691$	−22.1966	+	38.4456i	−0.844398	+	1.46254i	0.0417447	+	0.999128i	$0.486708\pi$
$691$	−22.1966	+	38.4456i	−0.844398	+	1.46254i	−0.886143	+	0.463412i	$0.846625\pi$
$692$	−9.60625	+	5.54617i	−0.365175	+	0.210834i
$693$	−3.09687	+	3.69071i	−0.117641	+	0.140199i
$694$	−23.2066	−	19.4727i	−0.880911	−	0.739172i
$695$	4.11167	+	20.1769i	0.155965	+	0.765355i
$696$	−2.61483	+	4.52901i	−0.0991147	+	0.171672i
$697$	−5.98725	−	16.4498i	−0.226783	−	0.623082i
$698$	28.5992	−	5.04280i	1.08249	−	0.190873i
$699$	1.35986	−	7.71216i	0.0514347	−	0.291701i
$700$	20.3498	−	13.2335i	0.769149	−	0.500181i
$701$	−22.8945	+	19.2108i	−0.864714	+	0.725581i	−0.962978	−	0.269579i	$-0.913115\pi$
$701$	−22.8945	+	19.2108i	−0.864714	+	0.725581i	0.0982645	+	0.995160i	$0.468671\pi$
$702$		−	2.72520i		−	0.102856i
$703$	−7.69795	+	8.57447i	−0.290334	+	0.323392i
$704$	−0.992385			−0.0374019
$705$	26.4347	−	10.4225i	0.995590	−	0.392536i
$706$	11.1433	+	4.05582i	0.419383	+	0.152643i
$707$	44.5542	+	7.85611i	1.67563	+	0.295459i
$708$	4.57693	−	0.807035i	0.172011	−	0.0303303i
$709$	13.8515	−	5.04155i	0.520206	−	0.189339i	−0.0685542	−	0.997647i	$-0.521839\pi$
$709$	13.8515	−	5.04155i	0.520206	−	0.189339i	0.588760	+	0.808308i	$0.299616\pi$
$710$	6.69939	+	7.56748i	0.251424	+	0.284003i
$711$	−6.09366	−	10.5545i	−0.228530	−	0.395826i
$712$	−11.0124	+	13.1240i	−0.412706	+	0.491843i
$713$	2.81554	−	3.35543i	0.105443	−	0.125662i
$714$	−18.5509	−	32.1311i	−0.694250	−	1.20248i
$715$	−4.00851	−	4.52792i	−0.149910	−	0.169335i
$716$	−4.73198	+	1.72230i	−0.176842	+	0.0643654i
$717$	14.1309	−	2.49166i	0.527729	−	0.0930528i
$718$	10.3233	+	1.82029i	0.385264	+	0.0679324i
$719$	47.4478	+	17.2696i	1.76950	+	0.644047i	0.999985	+	0.00542130i	$0.00172566\pi$
$719$	47.4478	+	17.2696i	1.76950	+	0.644047i	0.769518	+	0.638625i	$0.220497\pi$
$720$	−2.08022	+	0.820177i	−0.0775252	+	0.0305662i
$721$	−86.2423			−3.21183
$722$	−13.1587	+	13.7058i	−0.489717	+	0.510076i
$723$		−	11.6555i		−	0.433472i
$724$	−1.49147	+	1.25149i	−0.0554300	+	0.0465113i
$725$	14.2552	+	21.9208i	0.529424	+	0.814118i
$726$	−1.73912	+	9.86302i	−0.0645447	+	0.366051i
$727$	29.8525	−	5.26381i	1.10717	−	0.195224i	0.409969	−	0.912100i	$-0.365540\pi$
$727$	29.8525	−	5.26381i	1.10717	−	0.195224i	0.697201	+	0.716876i	$0.254429\pi$
$728$	4.52508	+	12.4326i	0.167711	+	0.460782i
$729$	0.500000	−	0.866025i	0.0185185	−	0.0320750i
$730$	6.84977	+	33.6135i	0.253521	+	1.24409i
$731$	16.2072	+	13.5995i	0.599447	+	0.502996i
$732$	2.04614	−	2.43850i	0.0756276	−	0.0901295i
$733$	−43.9021	+	25.3469i	−1.62156	+	0.936210i	−0.635061	+	0.772462i	$0.719025\pi$
$733$	−43.9021	+	25.3469i	−1.62156	+	0.936210i	−0.986502	+	0.163747i	$0.947642\pi$
$734$	1.07452	−	1.86112i	0.0396613	−	0.0686953i
$735$	−0.981548	−	37.0377i	−0.0362050	−	1.36616i
$736$	−0.186863	−	1.05975i	−0.00688788	−	0.0390631i
$737$	−10.7843	−	1.90157i	−0.397246	−	0.0700452i
$738$	−0.783445	+	2.15250i	−0.0288390	+	0.0792345i
$739$	−13.9019	+	11.6651i	−0.511389	+	0.429106i	−0.861618	−	0.507558i	$-0.830548\pi$
$739$	−13.9019	+	11.6651i	−0.511389	+	0.429106i	0.350229	+	0.936664i	$0.386104\pi$
$740$	−1.87388	+	5.60630i	−0.0688852	+	0.206092i
$741$	−8.83927	−	7.93569i	−0.324719	−	0.291525i
$742$			32.5336i			1.19435i
$743$	−8.24819	−	9.82982i	−0.302597	−	0.360621i	0.593223	−	0.805038i	$-0.297855\pi$
$743$	−8.24819	−	9.82982i	−0.302597	−	0.360621i	−0.895820	+	0.444417i	$0.853411\pi$
$744$	−3.82495	−	1.39217i	−0.140229	−	0.0510394i
$745$	5.61091	−	10.3418i	0.205568	−	0.378893i
$746$	2.65856	+	15.0775i	0.0973369	+	0.552025i
$747$	−2.64594	−	7.26966i	−0.0968099	−	0.265983i
$748$	6.56794	+	3.79200i	0.240148	+	0.138649i
$749$	−2.24163	−	3.88262i	−0.0819075	−	0.141868i
$750$	−1.06107	+	11.1299i	−0.0387446	+	0.406406i
$751$	20.8619	+	17.5052i	0.761262	+	0.638774i	0.938455	−	0.345402i	$-0.112257\pi$
$751$	20.8619	+	17.5052i	0.761262	+	0.638774i	−0.177193	+	0.984176i	$0.556702\pi$
$752$	11.0052	−	6.35384i	0.401317	−	0.231701i
$753$	12.2929	+	7.09732i	0.447979	+	0.258641i
$754$	−13.3924	+	4.87442i	−0.487721	+	0.177516i
$755$	3.83258	−	25.6998i	0.139482	−	0.935312i
$756$	−0.843036	+	4.78110i	−0.0306609	+	0.173887i
$757$	1.06586	−	2.92843i	0.0387394	−	0.106436i	−0.918815	−	0.394689i	$-0.870852\pi$
$757$	1.06586	−	2.92843i	0.0387394	−	0.106436i	0.957554	+	0.288253i	$0.0930745\pi$
$758$	−11.3924	−	13.5769i	−0.413789	−	0.493135i
$759$	1.06791			0.0387626
$760$	−3.39725	+	9.13557i	−0.123231	+	0.331382i
$761$	19.5367			0.708204			0.354102	−	0.935207i	$-0.384787\pi$
$761$	19.5367			0.708204			0.354102	+	0.935207i	$0.384787\pi$
$762$	−12.1143	−	14.4372i	−0.438854	−	0.523006i
$763$	16.5401	−	45.4435i	0.598791	−	1.64516i
$764$	1.51190	−	8.57443i	0.0546988	−	0.310212i
$765$	16.9016	+	2.52051i	0.611078	+	0.0911294i
$766$	−5.82117	+	2.11873i	−0.210327	+	0.0765529i
$767$	10.9686	+	6.33273i	0.396054	+	0.228662i
$768$	−0.866025	+	0.500000i	−0.0312500	+	0.0180422i
$769$	25.3400	+	21.2628i	0.913785	+	0.766757i	0.972835	−	0.231498i	$-0.0743627\pi$
$769$	25.3400	+	21.2628i	0.913785	+	0.766757i	−0.0590501	+	0.998255i	$0.518807\pi$
$770$	5.63183	+	9.18381i	0.202957	+	0.330962i
$771$	2.32586	+	4.02850i	0.0837637	+	0.145083i
$772$	−4.09257	−	2.36284i	−0.147295	−	0.0850406i
$773$	16.8208	+	46.2148i	0.605002	+	1.66223i	0.740987	+	0.671519i	$0.234358\pi$
$773$	16.8208	+	46.2148i	0.605002	+	1.66223i	−0.135985	+	0.990711i	$0.543420\pi$
$774$	−0.480736	−	2.72639i	−0.0172797	−	0.0979981i
$775$	−14.8759	+	13.8895i	−0.534357	+	0.498926i
$776$	0.562813	+	0.204847i	0.0202038	+	0.00735358i
$777$	8.24960	+	9.83149i	0.295953	+	0.352703i
$778$		−	19.2903i		−	0.691590i
$779$	4.70033	+	8.80912i	0.168407	+	0.315619i
$780$	−5.77945	−	1.93175i	−0.206937	−	0.0691678i
$781$	−3.43610	+	2.88323i	−0.122953	+	0.103170i
$782$	−2.81271	+	7.72785i	−0.100582	+	0.276347i
$783$	−5.15020	−	0.908120i	−0.184053	−	0.0324535i
$784$	−2.87728	−	16.3179i	−0.102760	−	0.582781i
$785$	0.694510	+	26.2066i	0.0247881	+	0.935355i
$786$	4.64178	−	8.03980i	0.165567	−	0.286770i
$787$	−25.7029	+	14.8396i	−0.916208	+	0.528973i	−0.882423	−	0.470456i	$-0.844089\pi$
$787$	−25.7029	+	14.8396i	−0.916208	+	0.528973i	−0.0337846	+	0.999429i	$0.510756\pi$
$788$	8.46868	−	10.0926i	0.301684	−	0.359533i
$789$	6.27772	+	5.26763i	0.223493	+	0.187533i
$790$	−26.7029	+	5.44153i	−0.950046	+	0.193601i
$791$	−7.94179	+	13.7556i	−0.282378	+	0.489092i
$792$	−0.339416	−	0.932536i	−0.0120606	−	0.0331362i
$793$	8.54316	−	1.50639i	0.303377	−	0.0534935i
$794$	0.0938617	−	0.532316i	0.00333103	−	0.0188912i
$795$	−11.7299	−	9.32436i	−0.416017	−	0.330701i
$796$	−3.35137	+	2.81213i	−0.118786	+	0.0996733i
$797$			24.6102i			0.871739i	0.900010	+	0.435870i	$0.143559\pi$
$797$			24.6102i			0.871739i	−0.900010	+	0.435870i	$0.856441\pi$
$798$	13.0527	+	16.6568i	0.462062	+	0.589644i
$799$	−97.1147			−3.43567
$800$	0.264827	+	4.99298i	0.00936305	+	0.176529i
$801$	−16.0990	−	5.85955i	−0.568830	−	0.207037i
$802$	−4.08102	−	0.719593i	−0.144106	−	0.0254097i
$803$	−14.9932	+	2.64371i	−0.529099	+	0.0932944i
$804$	−10.3693	+	3.77410i	−0.365695	+	0.133102i
$805$	−8.74682	+	7.74345i	−0.308285	+	0.272921i
$806$	−5.54637	−	9.60659i	−0.195363	−	0.338378i
$807$	2.49065	−	2.96824i	0.0876749	−	0.104487i
$808$	−5.99003	+	7.13863i	−0.210728	+	0.251136i
$809$	8.39480	+	14.5402i	0.295145	+	0.511207i	0.975019	−	0.222123i	$-0.0712986\pi$
$809$	8.39480	+	14.5402i	0.295145	+	0.511207i	−0.679873	+	0.733330i	$0.737965\pi$
$810$	−1.48219	−	1.67425i	−0.0520789	−	0.0588271i
$811$	−4.90498	+	1.78527i	−0.172237	+	0.0626892i	−0.426699	−	0.904394i	$-0.640324\pi$
$811$	−4.90498	+	1.78527i	−0.172237	+	0.0626892i	0.254462	+	0.967083i	$0.418102\pi$
$812$	25.0035	−	4.40879i	0.877450	−	0.154718i
$813$	−16.5703	−	2.92179i	−0.581146	−	0.102472i
$814$	−2.46522	−	0.897266i	−0.0864058	−	0.0314491i
$815$	−2.18968	−	5.55370i	−0.0767013	−	0.194538i
$816$	7.64221			0.267531
$817$	−10.2430	−	6.37986i	−0.358358	−	0.223203i
$818$		−	7.25614i		−	0.253705i
$819$	−10.1351	+	8.50438i	−0.354150	+	0.297167i
$820$	4.00955	+	3.18727i	0.140019	+	0.111304i
$821$	0.613324	−	3.47833i	0.0214051	−	0.121395i	−0.972233	−	0.234015i	$-0.924813\pi$
$821$	0.613324	−	3.47833i	0.0214051	−	0.121395i	0.993638	+	0.112621i	$0.0359245\pi$
$822$	18.8558	−	3.32478i	0.657670	−	0.115965i
$823$	−1.41005	−	3.87407i	−0.0491512	−	0.135042i	0.912688	−	0.408657i	$-0.134003\pi$
$823$	−1.41005	−	3.87407i	−0.0491512	−	0.135042i	−0.961839	+	0.273615i	$0.911781\pi$
$824$	8.88207	−	15.3842i	0.309422	−	0.535934i
$825$	−4.92532	−	0.601602i	−0.171478	−	0.0209451i
$826$	−17.2843	−	14.5033i	−0.601399	−	0.504633i
$827$	0.995651	−	1.18657i	0.0346222	−	0.0412611i	−0.748456	−	0.663185i	$-0.769204\pi$
$827$	0.995651	−	1.18657i	0.0346222	−	0.0412611i	0.783078	+	0.621924i	$0.213649\pi$
$828$	0.931933	−	0.538052i	0.0323869	−	0.0186986i
$829$	12.4045	−	21.4853i	0.430827	−	0.746214i	−0.566118	−	0.824324i	$-0.691555\pi$
$829$	12.4045	−	21.4853i	0.430827	−	0.746214i	0.996945	+	0.0781105i	$0.0248887\pi$
$830$	−17.2926	+	0.458277i	−0.600236	+	0.0159070i
$831$	1.11796	+	6.34026i	0.0387816	+	0.219941i
$832$	−2.68380	−	0.473226i	−0.0930441	−	0.0164062i
$833$	−43.3094	+	118.992i	−1.50058	+	4.12282i
$834$	−7.05439	+	5.91934i	−0.244274	+	0.204970i
$835$	−4.31763	+	12.9176i	−0.149418	+	0.447030i
$836$	−4.01307	−	1.61461i	−0.138795	−	0.0558423i
$837$		−	4.07043i		−	0.140695i
$838$	−8.64984	−	10.3085i	−0.298804	−	0.356101i
$839$	10.4628	+	3.80814i	0.361215	+	0.131472i	0.516251	−	0.856437i	$-0.327327\pi$
$839$	10.4628	+	3.80814i	0.361215	+	0.131472i	−0.155036	+	0.987909i	$0.549549\pi$
$840$	9.54188	+	5.17692i	0.329226	+	0.178621i
$841$	−0.286647	−	1.62566i	−0.00988438	−	0.0560571i
$842$	3.51851	+	9.66702i	0.121256	+	0.333148i
$843$	13.7418	+	7.93385i	0.473294	+	0.273256i
$844$	−12.3339	−	21.3630i	−0.424551	−	0.735344i
$845$	6.51484	+	10.6237i	0.224117	+	0.365467i
$846$	9.73464	+	8.16833i	0.334684	+	0.280833i
$847$	42.1081	−	24.3111i	1.44685	−	0.835339i
$848$	−5.80346	−	3.35063i	−0.199292	−	0.115061i
$849$	10.2747	−	3.73969i	0.352627	−	0.128346i
$850$	17.3260	−	34.0572i	0.594276	−	1.16815i
$851$	0.493985	−	2.80153i	0.0169336	−	0.0960351i
$852$	−1.54591	+	4.24734i	−0.0529619	+	0.145512i
$853$	20.1245	+	23.9834i	0.689050	+	0.821177i	0.991240	−	0.132070i	$-0.0421624\pi$
$853$	20.1245	+	23.9834i	0.689050	+	0.821177i	−0.302191	+	0.953247i	$0.597718\pi$
$854$	−15.4541			−0.528829
$855$	−9.74656	−	0.0678197i	−0.333325	−	0.00231938i
$856$	0.923461			0.0315633
$857$	−11.1871	−	13.3323i	−0.382145	−	0.455422i	0.540345	−	0.841443i	$-0.318294\pi$
$857$	−11.1871	−	13.3323i	−0.382145	−	0.455422i	−0.922490	+	0.386021i	$0.873849\pi$
$858$	0.924976	−	2.54135i	0.0315782	−	0.0867603i
$859$	−7.69192	+	43.6231i	−0.262445	+	1.48840i	0.513768	+	0.857929i	$0.328249\pi$
$859$	−7.69192	+	43.6231i	−0.262445	+	1.48840i	−0.776213	+	0.630471i	$0.782862\pi$
$860$	−6.12273	−	0.913076i	−0.208783	−	0.0311356i
$861$	10.4501	−	3.80351i	0.356137	−	0.129623i
$862$	6.88553	+	3.97536i	0.234522	+	0.135401i
$863$	−34.8713	+	20.1330i	−1.18703	+	0.685334i	−0.957631	−	0.287997i	$-0.907011\pi$
$863$	−34.8713	+	20.1330i	−1.18703	+	0.685334i	−0.229403	+	0.973332i	$0.573677\pi$
$864$	−0.766044	−	0.642788i	−0.0260614	−	0.0218681i
$865$	−21.1441	+	12.9663i	−0.718922	+	0.440868i
$866$	8.49413	+	14.7123i	0.288642	+	0.499943i
$867$	−35.8563	−	20.7017i	−1.21775	−	0.703066i
$868$	6.75877	+	18.5696i	0.229408	+	0.630292i
$869$	−2.10019	−	11.9108i	−0.0712441	−	0.404045i
$870$	−5.57659	+	10.2785i	−0.189064	+	0.348474i
$871$	−28.2583	−	10.2852i	−0.957497	−	0.348500i
$872$	6.40290	+	7.63068i	0.216830	+	0.258408i
$873$			0.598933i			0.0202708i
$874$	0.968567	−	4.58954i	0.0327623	−	0.155243i
$875$	44.7036	−	30.7862i	1.51126	−	1.04076i
$876$	−11.7521	+	9.86122i	−0.397068	+	0.333180i
$877$	−9.16997	+	25.1943i	−0.309648	+	0.850750i	0.683077	+	0.730346i	$0.260641\pi$
$877$	−9.16997	+	25.1943i	−0.309648	+	0.850750i	−0.992725	+	0.120404i	$0.961581\pi$
$878$	−12.3468	−	2.17707i	−0.416684	−	0.0734726i
$879$	3.12489	+	17.7221i	0.105400	+	0.597752i
$880$	−2.21826	+	0.0587868i	−0.0747775	+	0.00198170i
$881$	−7.67648	+	13.2960i	−0.258627	+	0.447955i	−0.965874	−	0.259011i	$-0.916603\pi$
$881$	−7.67648	+	13.2960i	−0.258627	+	0.447955i	0.707247	+	0.706966i	$0.249937\pi$
$882$	14.3497	−	8.28480i	0.483179	−	0.278964i
$883$	−17.2033	+	20.5021i	−0.578937	+	0.689950i	−0.973439	−	0.228945i	$-0.926473\pi$
$883$	−17.2033	+	20.5021i	−0.578937	+	0.689950i	0.394502	+	0.918895i	$0.370917\pi$
$884$	15.9541	+	13.3871i	0.536594	+	0.450256i
$885$	10.1829	−	2.07508i	0.342295	−	0.0697531i
$886$	1.62088	−	2.80744i	0.0544545	−	0.0943179i
$887$	3.29880	+	9.06339i	0.110763	+	0.304319i	0.982673	−	0.185347i	$-0.0593410\pi$
$887$	3.29880	+	9.06339i	0.110763	+	0.304319i	−0.871910	+	0.489666i	$0.837119\pi$
$888$	−2.60340	+	0.459050i	−0.0873644	+	0.0154047i
$889$	−15.8883	+	90.1069i	−0.532876	+	3.02209i
$890$	−23.8383	+	29.9882i	−0.799062	+	1.00521i
$891$	0.760211	−	0.637893i	0.0254680	−	0.0213702i
$892$		−	10.1807i		−	0.340877i
$893$	54.8411	−	7.78871i	1.83519	−	0.260639i
$894$	5.26184			0.175982
$895$	−10.4753	+	4.13014i	−0.350151	+	0.138055i
$896$	4.56207	+	1.66046i	0.152408	+	0.0554720i
$897$	2.88805	+	0.509241i	0.0964291	+	0.0170030i
$898$	37.1309	−	6.54718i	1.23907	−	0.218482i
$899$	−20.0032	+	7.28056i	−0.667143	+	0.242820i
$900$	−4.60129	+	1.95656i	−0.153376	+	0.0652185i
$901$	25.6062	+	44.3513i	0.853067	+	1.47755i
$902$	−1.46118	+	1.74137i	−0.0486520	+	0.0579813i
$903$	−8.63933	+	10.2960i	−0.287499	+	0.342628i
$904$	−1.63585	−	2.83337i	−0.0544074	−	0.0942364i
$905$	−3.25972	+	2.88579i	−0.108357	+	0.0959269i
$906$	10.9196	−	3.97441i	0.362780	−	0.132041i
$907$	−0.885204	+	0.156085i	−0.0293927	+	0.00518273i	−0.188325	−	0.982107i	$-0.560306\pi$
$907$	−0.885204	+	0.156085i	−0.0293927	+	0.00518273i	0.158932	+	0.987289i	$0.449195\pi$
$908$	−22.9293	−	4.04305i	−0.760935	−	0.134173i
$909$	−8.75683	−	3.18723i	−0.290446	−	0.105714i
$910$	10.8513	+	27.5222i	0.359718	+	0.912354i
$911$	−11.8867			−0.393823			−0.196911	−	0.980421i	$-0.563091\pi$
$911$	−11.8867			−0.393823			−0.196911	+	0.980421i	$0.563091\pi$
$912$	−4.31559	+	0.612914i	−0.142904	+	0.0202956i
$913$		−	7.67730i		−	0.254081i
$914$	−10.9152	+	9.15893i	−0.361042	+	0.302950i
$915$	4.42926	−	5.57194i	0.146427	−	0.184203i
$916$	0.823787	−	4.67193i	0.0272187	−	0.154365i
$917$	−44.3856	+	7.82638i	−1.46574	+	0.258450i
$918$	2.61379	+	7.18133i	0.0862679	+	0.237019i
$919$	29.4964	−	51.0893i	0.972998	−	1.68528i	0.286608	−	0.958048i	$-0.407472\pi$
$919$	29.4964	−	51.0893i	0.972998	−	1.68528i	0.686390	−	0.727234i	$-0.259194\pi$
$920$	−0.480470	−	2.35778i	−0.0158406	−	0.0777338i
$921$	17.6558	+	14.8150i	0.581779	+	0.488170i
$922$	−19.7539	+	23.5417i	−0.650559	+	0.775306i
$923$	−10.6675	+	6.15886i	−0.351124	+	0.202721i
$924$	−2.40894	+	4.17241i	−0.0792483	+	0.137262i
$925$	−3.85654	+	12.6427i	−0.126802	+	0.415689i
$926$	−1.58033	−	8.96251i	−0.0519329	−	0.294526i
$927$	17.4943	+	3.08471i	0.574587	+	0.101315i
$928$	−1.78865	+	4.91427i	−0.0587152	+	0.161319i
$929$	25.0580	−	21.0261i	0.822125	−	0.689845i	−0.131344	−	0.991337i	$-0.541929\pi$
$929$	25.0580	−	21.0261i	0.822125	−	0.689845i	0.953469	+	0.301492i	$0.0974848\pi$
$930$	−8.63232	−	2.88531i	−0.283065	−	0.0946130i
$931$	14.9138	−	70.6687i	0.488779	−	2.31607i
$932$		−	7.83113i		−	0.256517i
$933$	−4.80037	−	5.72086i	−0.157157	−	0.187293i
$934$	9.05472	+	3.29565i	0.296280	+	0.107837i
$935$	14.9058	+	8.08713i	0.487473	+	0.264478i
$936$	−0.473226	−	2.68380i	−0.0154679	−	0.0877228i
$937$	0.00364666	+	0.0100191i	0.000119131	+	0.000327310i	0.939752	−	0.341856i	$-0.111056\pi$
$937$	0.00364666	+	0.0100191i	0.000119131	+	0.000327310i	−0.939633	+	0.342184i	$0.888833\pi$
$938$	46.3947	+	26.7860i	1.51484	+	0.874594i
$939$	9.51907	+	16.4875i	0.310643	+	0.538049i
$940$	24.2233	−	14.8545i	0.790076	−	0.484502i
$941$	−22.3950	−	18.7916i	−0.730055	−	0.612589i	0.200092	−	0.979777i	$-0.435876\pi$
$941$	−22.3950	−	18.7916i	−0.730055	−	0.612589i	−0.930147	+	0.367188i	$0.880320\pi$
$942$	−10.1533	+	5.86204i	−0.330814	+	0.190996i
$943$	−2.13472	−	1.23248i	−0.0695161	−	0.0401352i
$944$	4.36725	−	1.58955i	0.142142	−	0.0517354i
$945$	−1.60120	+	10.7370i	−0.0520871	+	0.349276i
$946$	0.477075	−	2.70563i	0.0155110	−	0.0879675i
$947$	−11.4578	+	31.4800i	−0.372328	+	1.02296i	0.602131	+	0.798397i	$0.294319\pi$
$947$	−11.4578	+	31.4800i	−0.372328	+	1.02296i	−0.974459	+	0.224566i	$0.927904\pi$
$948$	−7.83386	−	9.33603i	−0.254432	−	0.303220i
$949$	−41.8083			−1.35715
$950$	−7.05264	+	20.6218i	−0.228818	+	0.669061i
$951$	24.2812			0.787372
$952$	−23.8486	−	28.4216i	−0.772937	−	0.921150i
$953$	12.0561	−	33.1239i	0.390536	−	1.07299i	−0.576222	−	0.817294i	$-0.695473\pi$
$953$	12.0561	−	33.1239i	0.390536	−	1.07299i	0.966757	−	0.255695i	$-0.0823043\pi$
$954$	1.16366	−	6.59945i	0.0376749	−	0.213665i
$955$	2.87160	−	19.2558i	0.0929229	−	0.623105i
$956$	13.4836	−	4.90762i	0.436090	−	0.158724i
$957$	−4.49452	−	2.59491i	−0.145287	−	0.0838816i
$958$	36.9991	−	21.3615i	1.19539	−	0.690157i
$959$	−71.2070	−	59.7498i	−2.29939	−	1.92942i
$960$	−1.90619	+	1.16894i	−0.0615221	+	0.0377275i
$961$	7.21581	+	12.4982i	0.232768	+	0.403166i
$962$	−6.23905	−	3.60212i	−0.201155	−	0.116137i
$963$	0.315842	+	0.867770i	0.0101779	+	0.0279635i
$964$	−2.02396	−	11.4784i	−0.0651872	−	0.369695i
$965$	−9.28802	−	5.03919i	−0.298992	−	0.162217i
$966$	−4.90926	−	1.78682i	−0.157953	−	0.0574901i
$967$	30.1896	+	35.9785i	0.970831	+	1.15699i	0.987578	+	0.157131i	$0.0502246\pi$
$967$	30.1896	+	35.9785i	0.970831	+	1.15699i	−0.0167468	+	0.999860i	$0.505331\pi$
$968$			10.0152i			0.321900i
$969$	30.9041	+	12.4339i	0.992782	+	0.399433i
$970$	1.27018	+	0.424551i	0.0407830	+	0.0136315i
$971$	−40.4923	+	33.9771i	−1.29946	+	1.09038i	−0.309221	+	0.950990i	$0.600068\pi$
$971$	−40.4923	+	33.9771i	−1.29946	+	1.09038i	−0.990238	+	0.139386i	$0.955487\pi$
$972$	0.342020	−	0.939693i	0.0109703	−	0.0301407i
$973$	44.0284	+	7.76340i	1.41149	+	0.248883i
$974$	5.26773	+	29.8748i	0.168789	+	0.957250i
$975$	−13.0331	−	3.97565i	−0.417394	−	0.127323i
$976$	1.59162	−	2.75676i	0.0509464	−	0.0882418i
$977$	−26.9922	+	15.5839i	−0.863556	+	0.498574i	−0.865201	−	0.501425i	$-0.832809\pi$
$977$	−26.9922	+	15.5839i	−0.863556	+	0.498574i	0.00164569	+	0.999999i	$0.499476\pi$
$978$	1.71609	−	2.04516i	0.0548746	−	0.0653970i
$979$	−13.0241	−	10.9285i	−0.416251	−	0.349276i
$980$	−7.39817	−	36.3046i	−0.236326	−	1.15971i
$981$	−4.98058	+	8.62661i	−0.159018	+	0.275426i
$982$	−5.09131	−	13.9882i	−0.162470	−	0.446383i
$983$	−23.0929	+	4.07191i	−0.736551	+	0.129874i	−0.529325	−	0.848419i	$-0.677555\pi$
$983$	−23.0929	+	4.07191i	−0.736551	+	0.129874i	−0.207226	+	0.978293i	$0.566444\pi$
$984$	−0.397766	+	2.25584i	−0.0126803	+	0.0719136i
$985$	18.3320	−	23.0614i	0.584107	−	0.734798i
$986$	30.6158	−	25.6897i	0.975006	−	0.818127i
$987$		−	61.6939i		−	1.96374i
$988$	−10.0830	−	6.28020i	−0.320783	−	0.199800i
$989$	2.97914			0.0947310
$990$	−0.813931	−	2.06438i	−0.0258684	−	0.0656102i
$991$	−52.2881	−	19.0313i	−1.66099	−	0.604550i	−0.670470	−	0.741937i	$-0.733907\pi$
$991$	−52.2881	−	19.0313i	−1.66099	−	0.604550i	−0.990517	+	0.137387i	$0.956130\pi$
$992$	−4.00859	−	0.706822i	−0.127273	−	0.0224416i
$993$	28.0423	−	4.94461i	0.889895	−	0.156912i
$994$	20.6202	−	7.50515i	0.654034	−	0.238049i
$995$	−7.32467	+	6.48443i	−0.232208	+	0.205570i
$996$	−3.86811	−	6.69976i	−0.122566	−	0.212290i
$997$	6.96661	−	8.30248i	0.220635	−	0.262942i	−0.644361	−	0.764721i	$-0.722877\pi$
$997$	6.96661	−	8.30248i	0.220635	−	0.262942i	0.864996	+	0.501779i	$0.167321\pi$
$998$	−4.93298	+	5.87890i	−0.156151	+	0.186093i
$999$	−1.32178	−	2.28939i	−0.0418193	−	0.0724331i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	570.2.bc.b.139.8	yes	60
5.4	even	2	inner	570.2.bc.b.139.4	✓	60
19.16	even	9	inner	570.2.bc.b.529.4	yes	60
95.54	even	18	inner	570.2.bc.b.529.8	yes	60

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
570.2.bc.b.139.4	✓	60	5.4	even	2	inner
570.2.bc.b.139.8	yes	60	1.1	even	1	trivial
570.2.bc.b.529.4	yes	60	19.16	even	9	inner
570.2.bc.b.529.8	yes	60	95.54	even	18	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:	\( N \)	\(=\)	\( 570 = 2 \cdot 3 \cdot 5 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	570.bc (of order \(18\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(0.642788 + 0.766044i) q^{2} +(-0.342020 + 0.939693i) q^{3} +(-0.173648 + 0.984808i) q^{4} +(-0.329815 + 2.21161i) q^{5} +(-0.939693 + 0.342020i) q^{6} +(4.20443 + 2.42743i) q^{7} +(-0.866025 + 0.500000i) q^{8} +(-0.766044 - 0.642788i) q^{9} +O(q^{10})\)	\(q+(0.642788 + 0.766044i) q^{2} +(-0.342020 + 0.939693i) q^{3} +(-0.173648 + 0.984808i) q^{4} +(-0.329815 + 2.21161i) q^{5} +(-0.939693 + 0.342020i) q^{6} +(4.20443 + 2.42743i) q^{7} +(-0.866025 + 0.500000i) q^{8} +(-0.766044 - 0.642788i) q^{9} +(-1.90619 + 1.16894i) q^{10} +(-0.496192 - 0.859430i) q^{11} +(-0.866025 - 0.500000i) q^{12} +(-0.932074 - 2.56085i) q^{13} +(0.843036 + 4.78110i) q^{14} +(-1.96543 - 1.06634i) q^{15} +(-0.939693 - 0.342020i) q^{16} +(4.91232 + 5.85427i) q^{17} -1.00000i q^{18} +(-3.24353 - 2.91196i) q^{19} +(-2.12074 - 0.708846i) q^{20} +(-3.71903 + 3.12064i) q^{21} +(0.339416 - 0.932536i) q^{22} +(1.05975 + 0.186863i) q^{23} +(-0.173648 - 0.984808i) q^{24} +(-4.78244 - 1.45884i) q^{25} +(1.36260 - 2.36009i) q^{26} +(0.866025 - 0.500000i) q^{27} +(-3.12064 + 3.71903i) q^{28} +(-4.00615 - 3.36156i) q^{29} +(-0.446491 - 2.19104i) q^{30} +(2.03521 - 3.52509i) q^{31} +(-0.342020 - 0.939693i) q^{32} +(0.977308 - 0.172326i) q^{33} +(-1.32706 + 7.52611i) q^{34} +(-6.75521 + 8.49795i) q^{35} +(0.766044 - 0.642788i) q^{36} -2.64356i q^{37} +(0.145792 - 4.35646i) q^{38} +2.72520 q^{39} +(-0.820177 - 2.08022i) q^{40} +(-2.15250 - 0.783445i) q^{41} +(-4.78110 - 0.843036i) q^{42} +(2.72639 - 0.480736i) q^{43} +(0.932536 - 0.339416i) q^{44} +(1.67425 - 1.48219i) q^{45} +(0.538052 + 0.931933i) q^{46} +(-8.16833 + 9.73464i) q^{47} +(0.642788 - 0.766044i) q^{48} +(8.28480 + 14.3497i) q^{49} +(-1.95656 - 4.60129i) q^{50} +(-7.18133 + 2.61379i) q^{51} +(2.68380 - 0.473226i) q^{52} +(6.59945 + 1.16366i) q^{53} +(0.939693 + 0.342020i) q^{54} +(2.06438 - 0.813931i) q^{55} -4.85485 q^{56} +(3.84570 - 2.05197i) q^{57} -5.22965i q^{58} +(-3.56022 + 2.98738i) q^{59} +(1.39143 - 1.75040i) q^{60} +(-0.552763 + 3.13487i) q^{61} +(4.00859 - 0.706822i) q^{62} +(-1.66046 - 4.56207i) q^{63} +(0.500000 - 0.866025i) q^{64} +(5.97102 - 1.21678i) q^{65} +(0.760211 + 0.637893i) q^{66} +(7.09299 - 8.45309i) q^{67} +(-6.61835 + 3.82110i) q^{68} +(-0.538052 + 0.931933i) q^{69} +(-10.8520 + 0.287591i) q^{70} +(-0.784877 - 4.45126i) q^{71} +(0.984808 + 0.173648i) q^{72} +(5.24705 - 14.4161i) q^{73} +(2.02509 - 1.69925i) q^{74} +(3.00656 - 3.99507i) q^{75} +(3.43096 - 2.68860i) q^{76} -4.81788i q^{77} +(1.75173 + 2.08763i) q^{78} +(11.4523 + 4.16831i) q^{79} +(1.06634 - 1.96543i) q^{80} +(0.173648 + 0.984808i) q^{81} +(-0.783445 - 2.15250i) q^{82} +(6.69976 + 3.86811i) q^{83} +(-2.42743 - 4.20443i) q^{84} +(-14.5675 + 8.93331i) q^{85} +(2.12075 + 1.77952i) q^{86} +(4.52901 - 2.61483i) q^{87} +(0.859430 + 0.496192i) q^{88} +(16.0990 - 5.85955i) q^{89} +(2.21161 + 0.329815i) q^{90} +(2.29745 - 13.0295i) q^{91} +(-0.368049 + 1.01121i) q^{92} +(2.61642 + 3.11813i) q^{93} -12.7077 q^{94} +(7.50989 - 6.21301i) q^{95} +1.00000 q^{96} +(-0.384987 - 0.458809i) q^{97} +(-5.66714 + 15.5703i) q^{98} +(-0.172326 + 0.977308i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 60 q + 6 q^{5}+O(q^{10}) \) 60 * q + 6 * q^5	\( 60 q + 6 q^{5} + 6 q^{10} - 12 q^{11} + 12 q^{15} + 24 q^{19} + 12 q^{20} - 18 q^{21} - 6 q^{25} - 6 q^{26} + 12 q^{29} + 6 q^{30} - 36 q^{31} - 6 q^{35} - 12 q^{39} - 6 q^{40} - 30 q^{41} - 6 q^{44} - 6 q^{45} - 36 q^{46} + 18 q^{49} - 90 q^{55} + 24 q^{56} + 60 q^{59} + 6 q^{60} + 36 q^{61} + 30 q^{64} + 24 q^{65} - 12 q^{66} + 36 q^{69} - 72 q^{70} - 72 q^{71} + 6 q^{74} + 6 q^{76} + 6 q^{80} + 12 q^{84} + 18 q^{85} - 12 q^{86} + 60 q^{89} + 12 q^{90} - 48 q^{91} - 156 q^{94} - 84 q^{95} + 60 q^{96} - 6 q^{99}+O(q^{100}) \) 60 * q + 6 * q^5 + 6 * q^10 - 12 * q^11 + 12 * q^15 + 24 * q^19 + 12 * q^20 - 18 * q^21 - 6 * q^25 - 6 * q^26 + 12 * q^29 + 6 * q^30 - 36 * q^31 - 6 * q^35 - 12 * q^39 - 6 * q^40 - 30 * q^41 - 6 * q^44 - 6 * q^45 - 36 * q^46 + 18 * q^49 - 90 * q^55 + 24 * q^56 + 60 * q^59 + 6 * q^60 + 36 * q^61 + 30 * q^64 + 24 * q^65 - 12 * q^66 + 36 * q^69 - 72 * q^70 - 72 * q^71 + 6 * q^74 + 6 * q^76 + 6 * q^80 + 12 * q^84 + 18 * q^85 - 12 * q^86 + 60 * q^89 + 12 * q^90 - 48 * q^91 - 156 * q^94 - 84 * q^95 + 60 * q^96 - 6 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more