LMFDB - Embedded newform 570.2.bc.b.139.2

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			139.2
Character	$\chi$	$=$	570.139
Dual form			570.2.bc.b.529.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.642788 - 0.766044i) q^{2} +(0.342020 - 0.939693i) q^{3} +(-0.173648 + 0.984808i) q^{4} +(-1.66564 + 1.49186i) q^{5} +(-0.939693 + 0.342020i) q^{6} +(-0.828729 - 0.478467i) q^{7} +(0.866025 - 0.500000i) q^{8} +(-0.766044 - 0.642788i) q^{9} +O(q^{10})$	\(q+(-0.642788 - 0.766044i) q^{2} +(0.342020 - 0.939693i) q^{3} +(-0.173648 + 0.984808i) q^{4} +(-1.66564 + 1.49186i) q^{5} +(-0.939693 + 0.342020i) q^{6} +(-0.828729 - 0.478467i) q^{7} +(0.866025 - 0.500000i) q^{8} +(-0.766044 - 0.642788i) q^{9} +(2.21348 + 0.317005i) q^{10} +(1.79706 + 3.11260i) q^{11} +(0.866025 + 0.500000i) q^{12} +(-0.293194 - 0.805545i) q^{13} +(0.166170 + 0.942396i) q^{14} +(0.832208 + 2.07544i) q^{15} +(-0.939693 - 0.342020i) q^{16} +(2.71478 + 3.23535i) q^{17} +1.00000i q^{18} +(3.57816 - 2.48934i) q^{19} +(-1.17996 - 1.89939i) q^{20} +(-0.733054 + 0.615105i) q^{21} +(1.22926 - 3.37737i) q^{22} +(6.02668 + 1.06267i) q^{23} +(-0.173648 - 0.984808i) q^{24} +(0.548708 - 4.96980i) q^{25} +(-0.428621 + 0.742394i) q^{26} +(-0.866025 + 0.500000i) q^{27} +(0.615105 - 0.733054i) q^{28} +(7.47236 + 6.27006i) q^{29} +(1.05494 - 1.97157i) q^{30} +(-3.10990 + 5.38650i) q^{31} +(0.342020 + 0.939693i) q^{32} +(3.53951 - 0.624112i) q^{33} +(0.733394 - 4.15928i) q^{34} +(2.09417 - 0.439394i) q^{35} +(0.766044 - 0.642788i) q^{36} +6.43571i q^{37} +(-4.20694 - 1.14091i) q^{38} -0.857243 q^{39} +(-0.696556 + 2.12481i) q^{40} +(-3.92076 - 1.42704i) q^{41} +(0.942396 + 0.166170i) q^{42} +(9.38098 - 1.65412i) q^{43} +(-3.37737 + 1.22926i) q^{44} +(2.23490 - 0.0721787i) q^{45} +(-3.05983 - 5.29978i) q^{46} +(-0.672390 + 0.801323i) q^{47} +(-0.642788 + 0.766044i) q^{48} +(-3.04214 - 5.26914i) q^{49} +(-4.15979 + 2.77419i) q^{50} +(3.96874 - 1.44450i) q^{51} +(0.844219 - 0.148859i) q^{52} +(-2.67225 - 0.471190i) q^{53} +(0.939693 + 0.342020i) q^{54} +(-7.63681 - 2.50350i) q^{55} -0.956934 q^{56} +(-1.11541 - 4.21377i) q^{57} -9.75447i q^{58} +(1.26742 - 1.06349i) q^{59} +(-2.18842 + 0.459169i) q^{60} +(2.27719 - 12.9146i) q^{61} +(6.12531 - 1.08006i) q^{62} +(0.327291 + 0.899224i) q^{63} +(0.500000 - 0.866025i) q^{64} +(1.69012 + 0.904342i) q^{65} +(-2.75325 - 2.31025i) q^{66} +(-6.94544 + 8.27725i) q^{67} +(-3.65761 + 2.11172i) q^{68} +(3.05983 - 5.29978i) q^{69} +(-1.68270 - 1.32179i) q^{70} +(2.29879 + 13.0371i) q^{71} +(-0.984808 - 0.173648i) q^{72} +(-0.157011 + 0.431384i) q^{73} +(4.93004 - 4.13679i) q^{74} +(-4.48242 - 2.21539i) q^{75} +(1.83018 + 3.95606i) q^{76} -3.43933i q^{77} +(0.551025 + 0.656686i) q^{78} +(9.80313 + 3.56805i) q^{79} +(2.07544 - 0.832208i) q^{80} +(0.173648 + 0.984808i) q^{81} +(1.42704 + 3.92076i) q^{82} +(-6.94130 - 4.00756i) q^{83} +(-0.478467 - 0.828729i) q^{84} +(-9.34853 - 1.33885i) q^{85} +(-7.29711 - 6.12300i) q^{86} +(8.44762 - 4.87724i) q^{87} +(3.11260 + 1.79706i) q^{88} +(8.66974 - 3.15553i) q^{89} +(-1.49186 - 1.66564i) q^{90} +(-0.142448 + 0.807862i) q^{91} +(-2.09305 + 5.75059i) q^{92} +(3.99801 + 4.76464i) q^{93} +1.04605 q^{94} +(-2.24617 + 9.48445i) q^{95} +1.00000 q^{96} +(4.92542 + 5.86989i) q^{97} +(-2.08095 + 5.71735i) q^{98} +(0.624112 - 3.53951i) 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
$5$	−1.66564	+	1.49186i	−0.744897	+	0.667180i
$5$	−1.66564	+	1.49186i	−0.744897	+	0.667180i
$6$	−0.939693	+	0.342020i	−0.383628	+	0.139629i
$7$	−0.828729	−	0.478467i	−0.313230	−	0.180844i	0.335141	−	0.942168i	$-0.391216\pi$
$7$	−0.828729	−	0.478467i	−0.313230	−	0.180844i	−0.648371	+	0.761325i	$0.724549\pi$
$8$	0.866025	−	0.500000i	0.306186	−	0.176777i
$9$	−0.766044	−	0.642788i	−0.255348	−	0.214263i
$10$	2.21348	+	0.317005i	0.699965	+	0.100246i
$11$	1.79706	+	3.11260i	0.541834	+	0.938483i	0.998799	+	0.0489987i	$0.0156030\pi$
$11$	1.79706	+	3.11260i	0.541834	+	0.938483i	−0.456965	+	0.889485i	$0.651064\pi$
$12$	0.866025	+	0.500000i	0.250000	+	0.144338i
$13$	−0.293194	−	0.805545i	−0.0813174	−	0.223418i	0.892370	−	0.451304i	$-0.149041\pi$
$13$	−0.293194	−	0.805545i	−0.0813174	−	0.223418i	−0.973688	+	0.227886i	$0.926819\pi$
$14$	0.166170	+	0.942396i	0.0444108	+	0.251866i
$15$	0.832208	+	2.07544i	0.214875	+	0.535875i
$16$	−0.939693	−	0.342020i	−0.234923	−	0.0855050i
$17$	2.71478	+	3.23535i	0.658431	+	0.784687i	0.987160	−	0.159737i	$-0.0510646\pi$
$17$	2.71478	+	3.23535i	0.658431	+	0.784687i	−0.328729	+	0.944424i	$0.606620\pi$
$18$			1.00000i			0.235702i
$19$	3.57816	−	2.48934i	0.820885	−	0.571093i
$19$	3.57816	−	2.48934i	0.820885	−	0.571093i
$20$	−1.17996	−	1.89939i	−0.263847	−	0.424717i
$21$	−0.733054	+	0.615105i	−0.159965	+	0.134227i
$22$	1.22926	−	3.37737i	0.262079	−	0.720057i
$23$	6.02668	+	1.06267i	1.25665	+	0.221581i	0.762038	−	0.647532i	$-0.224199\pi$
$23$	6.02668	+	1.06267i	1.25665	+	0.221581i	0.494612	+	0.869114i	$0.335310\pi$
$24$	−0.173648	−	0.984808i	−0.0354458	−	0.201023i
$25$	0.548708	−	4.96980i	0.109742	−	0.993960i
$26$	−0.428621	+	0.742394i	−0.0840596	+	0.145595i
$27$	−0.866025	+	0.500000i	−0.166667	+	0.0962250i
$28$	0.615105	−	0.733054i	0.116244	−	0.138534i
$29$	7.47236	+	6.27006i	1.38758	+	1.16432i	0.966308	+	0.257387i	$0.0828614\pi$
$29$	7.47236	+	6.27006i	1.38758	+	1.16432i	0.421274	+	0.906933i	$0.361583\pi$
$30$	1.05494	−	1.97157i	0.192605	−	0.359958i
$31$	−3.10990	+	5.38650i	−0.558554	+	0.967445i	0.439063	+	0.898456i	$0.355310\pi$
$31$	−3.10990	+	5.38650i	−0.558554	+	0.967445i	−0.997617	+	0.0689883i	$0.978023\pi$
$32$	0.342020	+	0.939693i	0.0604612	+	0.166116i
$33$	3.53951	−	0.624112i	0.616150	−	0.108644i
$34$	0.733394	−	4.15928i	0.125776	−	0.713311i
$35$	2.09417	−	0.439394i	0.353979	−	0.0742712i
$36$	0.766044	−	0.642788i	0.127674	−	0.107131i
$37$			6.43571i			1.05802i	0.848614	+	0.529012i	$0.177437\pi$
$37$			6.43571i			1.05802i	−0.848614	+	0.529012i	$0.822563\pi$
$38$	−4.20694	−	1.14091i	−0.682455	−	0.185080i
$39$	−0.857243			−0.137269
$40$	−0.696556	+	2.12481i	−0.110135	+	0.335962i
$41$	−3.92076	−	1.42704i	−0.612321	−	0.222866i	0.0171977	−	0.999852i	$-0.494526\pi$
$41$	−3.92076	−	1.42704i	−0.612321	−	0.222866i	−0.629518	+	0.776986i	$0.716748\pi$
$42$	0.942396	+	0.166170i	0.145415	+	0.0256406i
$43$	9.38098	−	1.65412i	1.43059	−	0.252251i	0.595936	−	0.803032i	$-0.296781\pi$
$43$	9.38098	−	1.65412i	1.43059	−	0.252251i	0.834650	+	0.550781i	$0.185670\pi$
$44$	−3.37737	+	1.22926i	−0.509157	+	0.185318i
$45$	2.23490	−	0.0721787i	0.333160	−	0.0107598i
$46$	−3.05983	−	5.29978i	−0.451147	−	0.781409i
$47$	−0.672390	+	0.801323i	−0.0980781	+	0.116885i	−0.812851	−	0.582472i	$-0.802086\pi$
$47$	−0.672390	+	0.801323i	−0.0980781	+	0.116885i	0.714773	+	0.699357i	$0.246530\pi$
$48$	−0.642788	+	0.766044i	−0.0927784	+	0.110569i
$49$	−3.04214	−	5.26914i	−0.434591	−	0.752734i
$50$	−4.15979	+	2.77419i	−0.588283	+	0.392330i
$51$	3.96874	−	1.44450i	0.555735	−	0.202271i
$52$	0.844219	−	0.148859i	0.117072	−	0.0206430i
$53$	−2.67225	−	0.471190i	−0.367062	−	0.0647229i	−0.0129249	−	0.999916i	$-0.504114\pi$
$53$	−2.67225	−	0.471190i	−0.367062	−	0.0647229i	−0.354137	+	0.935194i	$0.615225\pi$
$54$	0.939693	+	0.342020i	0.127876	+	0.0465430i
$55$	−7.63681	−	2.50350i	−1.02975	−	0.337572i
$56$	−0.956934			−0.127876
$57$	−1.11541	−	4.21377i	−0.147740	−	0.558127i
$58$		−	9.75447i		−	1.28083i
$59$	1.26742	−	1.06349i	0.165004	−	0.138455i	−0.556547	−	0.830816i	$-0.687874\pi$
$59$	1.26742	−	1.06349i	0.165004	−	0.138455i	0.721551	+	0.692361i	$0.243429\pi$
$60$	−2.18842	+	0.459169i	−0.282523	+	0.0592785i
$61$	2.27719	−	12.9146i	0.291565	−	1.65355i	−0.389281	−	0.921119i	$-0.627276\pi$
$61$	2.27719	−	12.9146i	0.291565	−	1.65355i	0.680845	−	0.732427i	$-0.261613\pi$
$62$	6.12531	−	1.08006i	0.777915	−	0.137167i
$63$	0.327291	+	0.899224i	0.0412348	+	0.113292i
$64$	0.500000	−	0.866025i	0.0625000	−	0.108253i
$65$	1.69012	+	0.904342i	0.209633	+	0.112170i
$66$	−2.75325	−	2.31025i	−0.338902	−	0.284373i
$67$	−6.94544	+	8.27725i	−0.848520	+	1.01123i	0.151222	+	0.988500i	$0.451679\pi$
$67$	−6.94544	+	8.27725i	−0.848520	+	1.01123i	−0.999742	+	0.0227270i	$0.992765\pi$
$68$	−3.65761	+	2.11172i	−0.443551	+	0.256084i
$69$	3.05983	−	5.29978i	0.368360	−	0.638018i
$70$	−1.68270	−	1.32179i	−0.201121	−	0.157984i
$71$	2.29879	+	13.0371i	0.272816	+	1.54722i	0.745815	+	0.666153i	$0.232060\pi$
$71$	2.29879	+	13.0371i	0.272816	+	1.54722i	−0.472999	+	0.881063i	$0.656829\pi$
$72$	−0.984808	−	0.173648i	−0.116061	−	0.0204646i
$73$	−0.157011	+	0.431384i	−0.0183768	+	0.0504897i	−0.948542	−	0.316652i	$-0.897441\pi$
$73$	−0.157011	+	0.431384i	−0.0183768	+	0.0504897i	0.930165	+	0.367142i	$0.119664\pi$
$74$	4.93004	−	4.13679i	0.573105	−	0.480893i
$75$	−4.48242	−	2.21539i	−0.517585	−	0.255811i
$76$	1.83018	+	3.95606i	0.209936	+	0.453792i
$77$		−	3.43933i		−	0.391948i
$78$	0.551025	+	0.656686i	0.0623913	+	0.0743550i
$79$	9.80313	+	3.56805i	1.10294	+	0.401437i	0.828399	−	0.560139i	$-0.189252\pi$
$79$	9.80313	+	3.56805i	1.10294	+	0.401437i	0.274540	+	0.961576i	$0.411475\pi$
$80$	2.07544	−	0.832208i	0.232041	−	0.0930436i
$81$	0.173648	+	0.984808i	0.0192942	+	0.109423i
$82$	1.42704	+	3.92076i	0.157590	+	0.432976i
$83$	−6.94130	−	4.00756i	−0.761906	−	0.439887i	0.0680734	−	0.997680i	$-0.478315\pi$
$83$	−6.94130	−	4.00756i	−0.761906	−	0.439887i	−0.829980	+	0.557793i	$0.811648\pi$
$84$	−0.478467	−	0.828729i	−0.0522050	−	0.0904218i
$85$	−9.34853	−	1.33885i	−1.01399	−	0.145219i
$86$	−7.29711	−	6.12300i	−0.786867	−	0.660260i
$87$	8.44762	−	4.87724i	0.905680	−	0.522895i
$88$	3.11260	+	1.79706i	0.331804	+	0.191567i
$89$	8.66974	−	3.15553i	0.918991	−	0.334485i	0.161154	−	0.986929i	$-0.448479\pi$
$89$	8.66974	−	3.15553i	0.918991	−	0.334485i	0.757837	+	0.652444i	$0.226256\pi$
$90$	−1.49186	−	1.66564i	−0.157256	−	0.175574i
$91$	−0.142448	+	0.807862i	−0.0149326	+	0.0846870i
$92$	−2.09305	+	5.75059i	−0.218215	+	0.599541i
$93$	3.99801	+	4.76464i	0.414574	+	0.494070i
$94$	1.04605			0.107892
$95$	−2.24617	+	9.48445i	−0.230453	+	0.973084i
$96$	1.00000			0.102062
$97$	4.92542	+	5.86989i	0.500101	+	0.595997i	0.955756	−	0.294159i	$-0.0950397\pi$
$97$	4.92542	+	5.86989i	0.500101	+	0.595997i	−0.455656	+	0.890156i	$0.650595\pi$
$98$	−2.08095	+	5.71735i	−0.210207	+	0.577540i
$99$	0.624112	−	3.53951i	0.0627256	−	0.355735i
$100$	4.79902	+	1.40337i	0.479902	+	0.140337i
$101$	−1.09007	+	0.396753i	−0.108466	+	0.0394784i	−0.395683	−	0.918387i	$-0.629492\pi$
$101$	−1.09007	+	0.396753i	−0.108466	+	0.0394784i	0.287217	+	0.957866i	$0.407270\pi$
$102$	−3.65761	−	2.11172i	−0.362158	−	0.209092i
$103$	−8.34850	+	4.82001i	−0.822602	+	0.474929i	−0.851313	−	0.524658i	$-0.824193\pi$
$103$	−8.34850	+	4.82001i	−0.822602	+	0.474929i	0.0287111	+	0.999588i	$0.490860\pi$
$104$	−0.656686	−	0.551025i	−0.0643934	−	0.0540324i
$105$	0.303353	−	2.11816i	0.0296042	−	0.206711i
$106$	1.35674	+	2.34994i	0.131778	+	0.228246i
$107$	−14.6608	−	8.46443i	−1.41732	−	0.818287i	−0.421253	−	0.906943i	$-0.638410\pi$
$107$	−14.6608	−	8.46443i	−1.41732	−	0.818287i	−0.996062	+	0.0886558i	$0.971743\pi$
$108$	−0.342020	−	0.939693i	−0.0329109	−	0.0904220i
$109$	−2.49553	−	14.1528i	−0.239028	−	1.35560i	−0.833962	−	0.551821i	$-0.813933\pi$
$109$	−2.49553	−	14.1528i	−0.239028	−	1.35560i	0.594934	−	0.803774i	$-0.297178\pi$
$110$	2.99105	+	7.45936i	0.285186	+	0.711222i
$111$	6.04759	+	2.20114i	0.574012	+	0.208923i
$112$	0.615105	+	0.733054i	0.0581220	+	0.0692671i
$113$			14.3066i			1.34586i	0.739708	+	0.672928i	$0.234963\pi$
$113$			14.3066i			1.34586i	−0.739708	+	0.672928i	$0.765037\pi$
$114$	−2.51096	+	3.56301i	−0.235173	+	0.333707i
$115$	−11.6236	+	7.22095i	−1.08391	+	0.673357i
$116$	−7.47236	+	6.27006i	−0.693791	+	0.582160i
$117$	−0.293194	+	0.805545i	−0.0271058	+	0.0744726i
$118$	−1.62937	−	0.287302i	−0.149995	−	0.0264482i
$119$	−0.701810	−	3.98016i	−0.0643348	−	0.364861i
$120$	1.75843	+	1.38128i	0.160522	+	0.126093i
$121$	−0.958839	+	1.66076i	−0.0871671	+	0.150978i
$122$	−11.3569	+	6.55692i	−1.02821	+	0.593636i
$123$	−2.68196	+	3.19624i	−0.241824	+	0.288195i
$124$	−4.76464	−	3.99801i	−0.427877	−	0.359032i
$125$	6.50030	+	9.09649i	0.581404	+	0.813615i
$126$	0.478467	−	0.828729i	0.0426252	−	0.0738291i
$127$	5.11047	+	14.0409i	0.453481	+	1.24593i	0.930259	+	0.366905i	$0.119583\pi$
$127$	5.11047	+	14.0409i	0.453481	+	1.24593i	−0.476778	+	0.879024i	$0.658195\pi$
$128$	−0.984808	+	0.173648i	−0.0870455	+	0.0153485i
$129$	1.65412	−	9.38098i	0.145637	−	0.825949i
$130$	−0.393619	−	1.87600i	−0.0345227	−	0.164536i
$131$	−5.92629	+	4.97275i	−0.517783	+	0.434471i	−0.863858	−	0.503735i	$-0.831959\pi$
$131$	−5.92629	+	4.97275i	−0.517783	+	0.434471i	0.346075	+	0.938207i	$0.387514\pi$
$132$			3.59412i			0.312828i
$133$	−4.15639	+	0.350957i	−0.360405	+	0.0304318i
$134$	10.8052			0.933425
$135$	0.696556	−	2.12481i	0.0599500	−	0.182874i
$136$	3.96874	+	1.44450i	0.340317	+	0.123865i
$137$	−11.7288	−	2.06811i	−1.00206	−	0.176690i	−0.351535	−	0.936175i	$-0.614340\pi$
$137$	−11.7288	−	2.06811i	−1.00206	−	0.176690i	−0.650526	+	0.759484i	$0.725451\pi$
$138$	−6.02668	+	1.06267i	−0.513025	+	0.0904602i
$139$	4.32553	−	1.57437i	0.366887	−	0.133536i	−0.151996	−	0.988381i	$-0.548570\pi$
$139$	4.32553	−	1.57437i	0.366887	−	0.133536i	0.518883	+	0.854845i	$0.326348\pi$
$140$	0.0690702	+	2.13865i	0.00583750	+	0.180749i
$141$	0.523026	+	0.905908i	0.0440468	+	0.0762912i
$142$	8.50934	−	10.1410i	0.714088	−	0.851017i
$143$	1.98045	−	2.36021i	0.165613	−	0.197370i
$144$	0.500000	+	0.866025i	0.0416667	+	0.0721688i
$145$	−21.8003	+	0.704065i	−1.81042	+	0.0584694i
$146$	0.431384	−	0.157011i	0.0357016	−	0.0129943i
$147$	−5.99184	+	1.05652i	−0.494199	+	0.0871406i
$148$	−6.33794	−	1.11755i	−0.520975	−	0.0918620i
$149$	−8.49778	−	3.09294i	−0.696165	−	0.253383i	−0.0303924	−	0.999538i	$-0.509676\pi$
$149$	−8.49778	−	3.09294i	−0.696165	−	0.253383i	−0.665773	+	0.746155i	$0.731898\pi$
$150$	1.18415	+	4.85775i	0.0966858	+	0.396634i
$151$	−11.6272			−0.946209			−0.473104	−	0.881006i	$-0.656867\pi$
$151$	−11.6272			−0.946209			−0.473104	+	0.881006i	$0.656867\pi$
$152$	1.85411	−	3.94491i	0.150388	−	0.319974i
$153$		−	4.22345i		−	0.341446i
$154$	−2.63468	+	2.21076i	−0.212309	+	0.178148i
$155$	−2.85594	−	13.6115i	−0.229394	−	1.09330i
$156$	0.148859	−	0.844219i	0.0119182	−	0.0675916i
$157$	7.25008	−	1.27838i	0.578619	−	0.102026i	0.123324	−	0.992366i	$-0.460645\pi$
$157$	7.25008	−	1.27838i	0.578619	−	0.102026i	0.455296	+	0.890340i	$0.349534\pi$
$158$	−3.56805	−	9.80313i	−0.283859	−	0.779895i
$159$	−1.35674	+	2.34994i	−0.107596	+	0.186362i
$160$	−1.97157	−	1.05494i	−0.155866	−	0.0834006i
$161$	−4.48604	−	3.76423i	−0.353549	−	0.296663i
$162$	0.642788	−	0.766044i	0.0505022	−	0.0601861i
$163$	12.6717	−	7.31602i	0.992525	−	0.573035i	0.0864972	−	0.996252i	$-0.472433\pi$
$163$	12.6717	−	7.31602i	0.992525	−	0.573035i	0.906028	+	0.423217i	$0.139099\pi$
$164$	2.08620	−	3.61340i	0.162904	−	0.282159i
$165$	−4.96447	+	6.32000i	−0.386483	+	0.492012i
$166$	1.39181	+	7.89335i	0.108025	+	0.612643i
$167$	−0.575171	−	0.101418i	−0.0445081	−	0.00784797i	0.151350	−	0.988480i	$-0.451638\pi$
$167$	−0.575171	−	0.101418i	−0.0445081	−	0.00784797i	−0.195858	+	0.980632i	$0.562749\pi$
$168$	−0.327291	+	0.899224i	−0.0252510	+	0.0693766i
$169$	9.39564	−	7.88388i	0.722741	−	0.606452i
$170$	4.98350	+	8.02199i	0.382217	+	0.615258i
$171$	−4.34114	−	0.393051i	−0.331975	−	0.0300574i
$172$			9.52570i			0.726328i
$173$	5.35997	+	6.38777i	0.407511	+	0.485653i	0.930295	−	0.366812i	$-0.119551\pi$
$173$	5.35997	+	6.38777i	0.407511	+	0.485653i	−0.522784	+	0.852465i	$0.675106\pi$
$174$	−9.16621	−	3.33623i	−0.694888	−	0.252919i
$175$	−2.83262	+	3.85608i	−0.214126	+	0.291492i
$176$	−0.624112	−	3.53951i	−0.0470442	−	0.266801i
$177$	−0.565874	−	1.55472i	−0.0425337	−	0.116860i
$178$	−7.99008	−	4.61307i	−0.598881	−	0.345764i
$179$	−0.887971	−	1.53801i	−0.0663701	−	0.114956i	0.830931	−	0.556376i	$-0.187808\pi$
$179$	−0.887971	−	1.53801i	−0.0663701	−	0.114956i	−0.897301	+	0.441419i	$0.854475\pi$
$180$	−0.317005	+	2.21348i	−0.0236281	+	0.164983i
$181$	14.6717	+	12.3110i	1.09054	+	0.915071i	0.996753	−	0.0805216i	$-0.0256586\pi$
$181$	14.6717	+	12.3110i	1.09054	+	0.915071i	0.0937861	+	0.995592i	$0.470103\pi$
$182$	0.710422	−	0.410162i	0.0526600	−	0.0304033i
$183$	−11.3569	−	6.55692i	−0.839528	−	0.484701i
$184$	5.75059	−	2.09305i	0.423939	−	0.154301i
$185$	−9.60118	−	10.7196i	−0.705892	−	0.788118i
$186$	1.08006	−	6.12531i	0.0791936	−	0.449129i
$187$	−5.19172	+	14.2641i	−0.379656	+	1.04310i
$188$	−0.672390	−	0.801323i	−0.0490391	−	0.0584425i
$189$	0.956934			0.0696067
$190$	8.70932	−	4.37581i	0.631840	−	0.317455i
$191$	−13.2154			−0.956234			−0.478117	−	0.878296i	$-0.658681\pi$
$191$	−13.2154			−0.956234			−0.478117	+	0.878296i	$0.658681\pi$
$192$	−0.642788	−	0.766044i	−0.0463892	−	0.0552845i
$193$	5.30060	−	14.5633i	0.381545	−	1.04829i	−0.589160	−	0.808016i	$-0.700541\pi$
$193$	5.30060	−	14.5633i	0.381545	−	1.04829i	0.970706	−	0.240271i	$-0.0772364\pi$
$194$	1.33060	−	7.54618i	0.0955312	−	0.541784i
$195$	1.42786	−	1.27889i	0.102251	−	0.0915829i
$196$	5.71735	−	2.08095i	0.408382	−	0.148639i
$197$	3.14012	+	1.81295i	0.223725	+	0.129167i	0.607674	−	0.794187i	$-0.292103\pi$
$197$	3.14012	+	1.81295i	0.223725	+	0.129167i	−0.383949	+	0.923354i	$0.625436\pi$
$198$	−3.11260	+	1.79706i	−0.221203	+	0.127711i
$199$	−12.0899	−	10.1447i	−0.857033	−	0.719136i	0.104294	−	0.994546i	$-0.466742\pi$
$199$	−12.0899	−	10.1447i	−0.857033	−	0.719136i	−0.961327	+	0.275411i	$0.911186\pi$
$200$	−2.00971	−	4.57833i	−0.142108	−	0.323737i
$201$	5.40259	+	9.35756i	0.381069	+	0.660031i
$202$	1.00461	+	0.580013i	0.0706843	+	0.0408096i
$203$	−3.19255	−	8.77146i	−0.224073	−	0.615636i
$204$	0.733394	+	4.15928i	0.0513479	+	0.291208i
$205$	8.65953	−	3.47230i	0.604808	−	0.242516i
$206$	9.05865	+	3.29708i	0.631146	+	0.229718i
$207$	−3.93364	−	4.68793i	−0.273407	−	0.325833i
$208$			0.857243i			0.0594391i
$209$	14.1785	+	6.66387i	0.980744	+	0.460950i
$210$	−1.81759	+	1.12914i	−0.125426	+	0.0779183i
$211$	−16.6397	+	13.9624i	−1.14553	+	0.961211i	−0.999606	−	0.0280849i	$-0.991059\pi$
$211$	−16.6397	+	13.9624i	−1.14553	+	0.961211i	−0.145921	+	0.989296i	$0.546615\pi$
$212$	0.928063	−	2.54983i	0.0637396	−	0.175123i
$213$	13.0371	+	2.29879i	0.893285	+	0.157510i
$214$	2.93967	+	16.6717i	0.200951	+	1.13965i
$215$	−13.1576	+	16.7503i	−0.897342	+	1.14236i
$216$	−0.500000	+	0.866025i	−0.0340207	+	0.0589256i
$217$	5.15453	−	2.97597i	0.349912	−	0.202022i
$218$	−9.23760	+	11.0089i	−0.625650	+	0.745620i
$219$	0.351668	+	0.295084i	0.0237635	+	0.0199399i
$220$	3.79159	−	7.08606i	0.255629	−	0.477742i
$221$	1.81026	−	3.13546i	0.121771	−	0.210914i
$222$	−2.20114	−	6.04759i	−0.147731	−	0.405888i
$223$	−3.88894	+	0.685726i	−0.260423	+	0.0459196i	−0.302335	−	0.953202i	$-0.597766\pi$
$223$	−3.88894	+	0.685726i	−0.260423	+	0.0459196i	0.0419121	+	0.999121i	$0.486655\pi$
$224$	0.166170	−	0.942396i	0.0111027	−	0.0629665i
$225$	−3.61486	+	3.45439i	−0.240991	+	0.230292i
$226$	10.9595	−	9.19613i	0.729016	−	0.611717i
$227$		−	12.1413i		−	0.805847i	−0.915234	−	0.402923i	$-0.867994\pi$
$227$		−	12.1413i		−	0.805847i	0.915234	−	0.402923i	$-0.132006\pi$
$228$	4.34344	−	0.366752i	0.287652	−	0.0242887i
$229$	−12.1003			−0.799609			−0.399804	−	0.916600i	$-0.630922\pi$
$229$	−12.1003			−0.799609			−0.399804	+	0.916600i	$0.630922\pi$
$230$	13.0031	+	4.26268i	0.857399	+	0.281073i
$231$	−3.23192	−	1.17632i	−0.212644	−	0.0773962i
$232$	9.60628	+	1.69385i	0.630683	+	0.111206i
$233$	17.5780	−	3.09947i	1.15157	−	0.203053i	0.434910	−	0.900474i	$-0.356780\pi$
$233$	17.5780	−	3.09947i	1.15157	−	0.203053i	0.716662	+	0.697421i	$0.245669\pi$
$234$	0.805545	−	0.293194i	0.0526601	−	0.0191667i
$235$	−0.0755027	−	2.33783i	−0.00492525	−	0.152503i
$236$	0.827252	+	1.43284i	0.0538495	+	0.0932701i
$237$	6.70573	−	7.99158i	0.435584	−	0.519109i
$238$	−2.59787	+	3.09602i	−0.168395	+	0.200685i
$239$	7.57602	+	13.1220i	0.490052	+	0.848795i	0.999934	−	0.0114493i	$-0.00364451\pi$
$239$	7.57602	+	13.1220i	0.490052	+	0.848795i	−0.509883	+	0.860244i	$0.670311\pi$
$240$	−0.0721787	−	2.23490i	−0.00465911	−	0.144262i
$241$	9.28534	−	3.37959i	0.598121	−	0.217698i	−0.0251763	−	0.999683i	$-0.508015\pi$
$241$	9.28534	−	3.37959i	0.598121	−	0.217698i	0.623298	+	0.781985i	$0.285792\pi$
$242$	1.88854	−	0.333001i	0.121400	−	0.0214061i
$243$	0.984808	+	0.173648i	0.0631754	+	0.0111395i
$244$	12.3230	+	4.48520i	0.788898	+	0.287135i
$245$	12.9279	+	4.23804i	0.825935	+	0.270758i
$246$	4.17239			0.266022
$247$	−3.05437	−	2.15250i	−0.194345	−	0.136961i
$248$			6.21980i			0.394958i
$249$	−6.13994	+	5.15202i	−0.389103	+	0.326496i
$250$	2.79001	−	10.8266i	0.176456	−	0.684736i
$251$	3.81087	−	21.6125i	0.240540	−	1.36417i	−0.590087	−	0.807340i	$-0.700906\pi$
$251$	3.81087	−	21.6125i	0.240540	−	1.36417i	0.830627	−	0.556830i	$-0.187982\pi$
$252$	−0.942396	+	0.166170i	−0.0593654	+	0.0104677i
$253$	7.52265	+	20.6683i	0.472945	+	1.29941i
$254$	7.47101	−	12.9402i	0.468773	−	0.811938i
$255$	−4.45550	+	8.32683i	−0.279014	+	0.521446i
$256$	0.766044	+	0.642788i	0.0478778	+	0.0401742i
$257$	9.96799	−	11.8794i	0.621786	−	0.741016i	−0.359590	−	0.933110i	$-0.617084\pi$
$257$	9.96799	−	11.8794i	0.621786	−	0.741016i	0.981376	+	0.192094i	$0.0615280\pi$
$258$	−8.24950	+	4.76285i	−0.513591	+	0.296522i
$259$	3.07927	−	5.33346i	0.191337	−	0.331405i
$260$	−1.18409	+	1.50740i	−0.0734340	+	0.0934851i
$261$	−1.69385	−	9.60628i	−0.104846	−	0.594614i
$262$	7.61870	+	1.34338i	0.470685	+	0.0829944i
$263$	3.83608	−	10.5395i	0.236543	−	0.649896i	−0.763449	−	0.645868i	$-0.776496\pi$
$263$	3.83608	−	10.5395i	0.236543	−	0.649896i	0.999992	−	0.00402808i	$-0.00128218\pi$
$264$	2.75325	−	2.31025i	0.169451	−	0.142186i
$265$	5.15396	−	3.20179i	0.316605	−	0.196684i
$266$	2.94052	+	2.95839i	0.180295	+	0.181390i
$267$		−	9.22614i		−	0.564631i
$268$	−6.94544	−	8.27725i	−0.424260	−	0.505613i
$269$	−6.35360	−	2.31252i	−0.387386	−	0.140997i	0.140983	−	0.990012i	$-0.454974\pi$
$269$	−6.35360	−	2.31252i	−0.387386	−	0.140997i	−0.528368	+	0.849015i	$0.677196\pi$
$270$	−2.07544	+	0.832208i	−0.126307	+	0.0506465i
$271$	1.37524	+	7.79935i	0.0835397	+	0.473777i	0.997662	+	0.0683389i	$0.0217699\pi$
$271$	1.37524	+	7.79935i	0.0835397	+	0.473777i	−0.914122	+	0.405438i	$0.867119\pi$
$272$	−1.44450	−	3.96874i	−0.0875859	−	0.240640i
$273$	0.710422	+	0.410162i	0.0429967	+	0.0248242i
$274$	5.95488	+	10.3142i	0.359748	+	0.623101i
$275$	16.4550	−	7.22312i	0.992277	−	0.435570i
$276$	4.68793	+	3.93364i	0.282180	+	0.236777i
$277$	−2.21763	+	1.28035i	−0.133245	+	0.0769288i	−0.565141	−	0.824995i	$-0.691178\pi$
$277$	−2.21763	+	1.28035i	−0.133245	+	0.0769288i	0.431896	+	0.901923i	$0.357845\pi$
$278$	−3.98643	−	2.30157i	−0.239090	−	0.138039i
$279$	5.84470	−	2.12730i	0.349913	−	0.127358i
$280$	1.59391	−	1.42761i	0.0952542	−	0.0853161i
$281$	1.53888	−	8.72743i	0.0918020	−	0.520635i	−0.903879	−	0.427789i	$-0.859293\pi$
$281$	1.53888	−	8.72743i	0.0918020	−	0.520635i	0.995681	−	0.0928457i	$-0.0295963\pi$
$282$	0.357771	−	0.982968i	0.0213050	−	0.0585349i
$283$	−0.412909	−	0.492086i	−0.0245449	−	0.0292515i	0.753632	−	0.657296i	$-0.228300\pi$
$283$	−0.412909	−	0.492086i	−0.0245449	−	0.0292515i	−0.778177	+	0.628045i	$0.783855\pi$
$284$	−13.2382			−0.785542
$285$	8.14423	+	5.35458i	0.482422	+	0.317178i
$286$	−3.08103			−0.182185
$287$	2.56646	+	3.05859i	0.151493	+	0.180543i
$288$	0.342020	−	0.939693i	0.0201537	−	0.0553719i
$289$	−0.145433	+	0.824789i	−0.00855486	+	0.0485170i
$290$	14.5523	+	16.2474i	0.854541	+	0.954082i
$291$	7.20048	−	2.62076i	0.422100	−	0.153632i
$292$	−0.397566	−	0.229535i	−0.0232658	−	0.0134325i
$293$	−1.87026	+	1.07979i	−0.109262	+	0.0630823i	−0.553635	−	0.832759i	$-0.686760\pi$
$293$	−1.87026	+	1.07979i	−0.109262	+	0.0630823i	0.444373	+	0.895842i	$0.353426\pi$
$294$	4.66083	+	3.91090i	0.271825	+	0.228088i
$295$	−0.524485	+	3.66222i	−0.0305367	+	0.213222i
$296$	3.21785	+	5.57349i	0.187034	+	0.323952i
$297$	−3.11260	−	1.79706i	−0.180611	−	0.104276i
$298$	3.09294	+	8.49778i	0.179169	+	0.492263i
$299$	−0.910963	−	5.16633i	−0.0526824	−	0.298777i
$300$	2.96010	−	4.02962i	0.170901	−	0.232650i
$301$	−8.56574	−	3.11767i	−0.493721	−	0.179700i
$302$	7.47382	+	8.90696i	0.430070	+	0.512538i
$303$			1.16003i			0.0666418i
$304$	−4.21377	+	1.11541i	−0.241676	+	0.0639732i
$305$	15.4738	+	24.9083i	0.886027	+	1.42625i
$306$	−3.23535	+	2.71478i	−0.184953	+	0.155194i
$307$	1.94257	−	5.33717i	0.110868	−	0.304608i	−0.871834	−	0.489802i	$-0.837069\pi$
$307$	1.94257	−	5.33717i	0.110868	−	0.304608i	0.982702	+	0.185194i	$0.0592913\pi$
$308$	3.38708	+	0.597234i	0.192997	+	0.0340306i
$309$	1.67397	+	9.49356i	0.0952289	+	0.540070i
$310$	−8.59126	+	10.9371i	−0.487951	+	0.621185i
$311$	6.44093	−	11.1560i	0.365232	−	0.632600i	−0.623582	−	0.781758i	$-0.714323\pi$
$311$	6.44093	−	11.1560i	0.365232	−	0.632600i	0.988813	+	0.149158i	$0.0476564\pi$
$312$	−0.742394	+	0.428621i	−0.0420298	+	0.0242659i
$313$	10.9494	−	13.0490i	0.618897	−	0.737573i	−0.361983	−	0.932185i	$-0.617900\pi$
$313$	10.9494	−	13.0490i	0.618897	−	0.737573i	0.980880	+	0.194612i	$0.0623447\pi$
$314$	−5.63956	−	4.73215i	−0.318259	−	0.267051i
$315$	−1.88666	−	1.00951i	−0.106301	−	0.0568795i
$316$	−5.21614	+	9.03461i	−0.293431	+	0.508237i
$317$	−9.81615	−	26.9696i	−0.551330	−	1.51477i	−0.831896	−	0.554931i	$-0.812744\pi$
$317$	−9.81615	−	26.9696i	−0.551330	−	1.51477i	0.280566	−	0.959835i	$-0.409478\pi$
$318$	2.67225	−	0.471190i	0.149852	−	0.0264230i
$319$	−6.08788	+	34.5261i	−0.340856	+	1.93309i
$320$	0.459169	+	2.18842i	0.0256683	+	0.122336i
$321$	−12.9683	+	10.8817i	−0.723818	+	0.607355i
$322$			5.85611i			0.326348i
$323$	17.7678	+	4.81858i	0.988626	+	0.268113i
$324$	−1.00000			−0.0555556
$325$	−4.16427	+	1.01511i	−0.230992	+	0.0563081i
$326$	−13.7496	−	5.00445i	−0.761521	−	0.277171i
$327$	−14.1528	−	2.49553i	−0.782653	−	0.138003i
$328$	−4.10900	+	0.724528i	−0.226882	+	0.0400054i
$329$	0.940636	−	0.342363i	0.0518589	−	0.0188751i
$330$	8.03250	−	0.259419i	0.442175	−	0.0142805i
$331$	−5.24757	−	9.08905i	−0.288432	−	0.499580i	0.685003	−	0.728540i	$-0.259801\pi$
$331$	−5.24757	−	9.08905i	−0.288432	−	0.499580i	−0.973436	+	0.228960i	$0.926467\pi$
$332$	5.15202	−	6.13994i	0.282754	−	0.336973i
$333$	4.13679	−	4.93004i	0.226695	−	0.270164i
$334$	0.292022	+	0.505797i	0.0159787	+	0.0276760i
$335$	−0.779904	−	24.1485i	−0.0426107	−	1.31937i
$336$	0.899224	−	0.327291i	0.0490567	−	0.0178552i
$337$	11.9959	−	2.11520i	0.653459	−	0.115223i	0.162917	−	0.986640i	$-0.447910\pi$
$337$	11.9959	−	2.11520i	0.653459	−	0.115223i	0.490542	+	0.871417i	$0.336799\pi$
$338$	−12.0788	−	2.12982i	−0.657000	−	0.115847i
$339$	13.4438	+	4.89316i	0.730169	+	0.265760i
$340$	2.94187	−	8.97402i	0.159545	−	0.486684i
$341$	−22.3547			−1.21057
$342$	2.48934	+	3.57816i	0.134608	+	0.193485i
$343$			12.5208i			0.676059i
$344$	7.29711	−	6.12300i	0.393434	−	0.330130i
$345$	2.80996	+	13.3923i	0.151283	+	0.721020i
$346$	1.44799	−	8.21196i	0.0778444	−	0.441477i
$347$	28.1835	−	4.96951i	1.51297	−	0.266777i	0.645304	−	0.763926i	$-0.276731\pi$
$347$	28.1835	−	4.96951i	1.51297	−	0.266777i	0.867666	+	0.497148i	$0.165619\pi$
$348$	3.33623	+	9.16621i	0.178841	+	0.491360i
$349$	2.39370	−	4.14601i	0.128132	−	0.221931i	−0.794821	−	0.606844i	$-0.792435\pi$
$349$	2.39370	−	4.14601i	0.128132	−	0.221931i	0.922953	+	0.384913i	$0.125769\pi$
$350$	4.77470	−	0.308731i	0.255218	−	0.0165023i
$351$	0.656686	+	0.551025i	0.0350513	+	0.0294115i
$352$	−2.31025	+	2.75325i	−0.123137	+	0.146749i
$353$	25.9492	−	14.9818i	1.38114	−	0.797401i	0.388844	−	0.921303i	$-0.372874\pi$
$353$	25.9492	−	14.9818i	1.38114	−	0.797401i	0.992294	+	0.123903i	$0.0395410\pi$
$354$	−0.827252	+	1.43284i	−0.0439679	+	0.0761547i
$355$	−23.2784	−	18.2856i	−1.23549	−	0.970498i
$356$	1.60210	+	9.08598i	0.0849113	+	0.481556i
$357$	−3.98016	−	0.701810i	−0.210652	−	0.0371437i
$358$	−0.607408	+	1.66884i	−0.0321025	+	0.0882009i
$359$	0.707571	−	0.593723i	0.0373442	−	0.0313355i	−0.623925	−	0.781485i	$-0.714463\pi$
$359$	0.707571	−	0.593723i	0.0373442	−	0.0313355i	0.661269	+	0.750149i	$0.270018\pi$
$360$	1.89939	−	1.17996i	0.100107	−	0.0621893i
$361$	6.60640	−	17.8145i	0.347705	−	0.937604i
$362$		−	19.1525i		−	1.00664i
$363$	1.23266	+	1.46903i	0.0646978	+	0.0771039i
$364$	−0.770853	−	0.280568i	−0.0404037	−	0.0147057i
$365$	−0.382041	−	0.952769i	−0.0199969	−	0.0498702i
$366$	2.27719	+	12.9146i	0.119031	+	0.675058i
$367$	6.84841	+	18.8159i	0.357484	+	0.982180i	0.979899	+	0.199492i	$0.0639293\pi$
$367$	6.84841	+	18.8159i	0.357484	+	0.982180i	−0.622415	+	0.782687i	$0.713848\pi$
$368$	−5.29978	−	3.05983i	−0.276270	−	0.159505i
$369$	2.08620	+	3.61340i	0.108603	+	0.188106i
$370$	−2.04015	+	14.2453i	−0.106062	+	0.740580i
$371$	1.98912	+	1.66907i	0.103270	+	0.0866539i
$372$	−5.38650	+	3.10990i	−0.279277	+	0.161241i
$373$	−24.1310	−	13.9320i	−1.24946	−	0.721373i	−0.278454	−	0.960449i	$-0.589822\pi$
$373$	−24.1310	−	13.9320i	−1.24946	−	0.721373i	−0.971001	+	0.239076i	$0.923155\pi$
$374$	14.2641	−	5.19172i	0.737580	−	0.268457i
$375$	10.7711	−	2.99710i	0.556219	−	0.154769i
$376$	−0.181645	+	1.03016i	−0.00936763	+	0.0531265i
$377$	2.85996	−	7.85766i	0.147295	−	0.404690i
$378$	−0.615105	−	0.733054i	−0.0316376	−	0.0377042i
$379$	−13.7008			−0.703765			−0.351883	−	0.936044i	$-0.614458\pi$
$379$	−13.7008			−0.703765			−0.351883	+	0.936044i	$0.614458\pi$
$380$	−8.95031	−	3.85901i	−0.459141	−	0.197963i
$381$	14.9420			0.765503
$382$	8.49471	+	10.1236i	0.434627	+	0.517968i
$383$	0.636953	−	1.75001i	0.0325468	−	0.0894216i	−0.922355	−	0.386344i	$-0.873738\pi$
$383$	0.636953	−	1.75001i	0.0325468	−	0.0894216i	0.954902	+	0.296922i	$0.0959601\pi$
$384$	−0.173648	+	0.984808i	−0.00886145	+	0.0502558i
$385$	5.13100	+	5.72869i	0.261500	+	0.291961i
$386$	−14.5633	+	5.30060i	−0.741251	+	0.269793i
$387$	−8.24950	−	4.76285i	−0.419346	−	0.242109i
$388$	−6.63600	+	3.83130i	−0.336892	+	0.194505i
$389$	−21.5804	−	18.1081i	−1.09417	−	0.918117i	−0.0971501	−	0.995270i	$-0.530973\pi$
$389$	−21.5804	−	18.1081i	−1.09417	−	0.918117i	−0.997019	+	0.0771526i	$0.975417\pi$
$390$	−1.89749	−	0.271750i	−0.0960832	−	0.0137606i
$391$	12.9230	+	22.3833i	0.653545	+	1.13197i
$392$	−5.26914	−	3.04214i	−0.266132	−	0.153651i
$393$	2.64595	+	7.26968i	0.133470	+	0.366707i
$394$	−0.629632	−	3.57082i	−0.0317204	−	0.179895i
$395$	−21.6515	+	8.68181i	−1.08941	+	0.436829i
$396$	3.37737	+	1.22926i	0.169719	+	0.0617727i
$397$	−24.2135	−	28.8565i	−1.21524	−	1.44826i	−0.857532	−	0.514430i	$-0.828003\pi$
$397$	−24.2135	−	28.8565i	−1.21524	−	1.44826i	−0.357706	−	0.933834i	$-0.616441\pi$
$398$			15.7823i			0.791094i
$399$	−1.09178	+	4.02576i	−0.0546572	+	0.201540i
$400$	−2.21539	+	4.48242i	−0.110769	+	0.224121i
$401$	−3.96562	+	3.32755i	−0.198034	+	0.166170i	−0.736412	−	0.676533i	$-0.763482\pi$
$401$	−3.96562	+	3.32755i	−0.198034	+	0.166170i	0.538379	+	0.842703i	$0.319037\pi$
$402$	3.69559	−	10.1535i	0.184319	−	0.506413i
$403$	5.25087	+	0.925871i	0.261565	+	0.0461209i
$404$	−0.201437	−	1.14240i	−0.0100218	−	0.0568367i
$405$	−1.75843	−	1.38128i	−0.0873771	−	0.0686361i
$406$	−4.66719	+	8.08382i	−0.231629	+	0.401193i
$407$	−20.0318	+	11.5653i	−0.992938	+	0.573273i
$408$	2.71478	−	3.23535i	0.134402	−	0.160174i
$409$	−9.39401	−	7.88251i	−0.464504	−	0.389765i	0.380281	−	0.924871i	$-0.375827\pi$
$409$	−9.39401	−	7.88251i	−0.464504	−	0.389765i	−0.844785	+	0.535106i	$0.820272\pi$
$410$	−8.22617	−	4.40163i	−0.406262	−	0.217381i
$411$	−5.95488	+	10.3142i	−0.293733	+	0.508760i
$412$	−3.29708	−	9.05865i	−0.162435	−	0.446288i
$413$	−1.55920	+	0.274929i	−0.0767231	+	0.0135284i
$414$	−1.06267	+	6.02668i	−0.0522272	+	0.296195i
$415$	17.5404	−	3.68029i	0.861025	−	0.180659i
$416$	0.656686	−	0.551025i	0.0321967	−	0.0270162i
$417$		−	4.60314i		−	0.225417i
$418$	−4.00892	−	15.1448i	−0.196083	−	0.740756i
$419$	−6.42349			−0.313808			−0.156904	−	0.987614i	$-0.550151\pi$
$419$	−6.42349			−0.313808			−0.156904	+	0.987614i	$0.550151\pi$
$420$	2.03330	+	0.666558i	0.0992149	+	0.0325247i
$421$	24.5894	+	8.94981i	1.19841	+	0.436187i	0.862671	−	0.505766i	$-0.168790\pi$
$421$	24.5894	+	8.94981i	1.19841	+	0.436187i	0.335744	+	0.941953i	$0.391012\pi$
$422$	21.3916	+	3.77192i	1.04133	+	0.183614i
$423$	1.03016	−	0.181645i	0.0500881	−	0.00883189i
$424$	−2.54983	+	0.928063i	−0.123831	+	0.0450707i
$425$	17.5687	−	11.7167i	0.852205	−	0.568341i
$426$	−6.61909	−	11.4646i	−0.320696	−	0.555462i
$427$	−8.06639	+	9.61315i	−0.390360	+	0.465213i
$428$	10.8817	−	12.9683i	0.525985	−	0.626844i
$429$	−1.54052	−	2.66825i	−0.0743768	−	0.128824i
$430$	21.2890	−	0.687552i	1.02665	−	0.0331567i
$431$	7.79953	−	2.83880i	0.375690	−	0.136740i	−0.147272	−	0.989096i	$-0.547049\pi$
$431$	7.79953	−	2.83880i	0.375690	−	0.136740i	0.522962	+	0.852356i	$0.324827\pi$
$432$	0.984808	−	0.173648i	0.0473816	−	0.00835465i
$433$	−25.3840	−	4.47589i	−1.21988	−	0.215097i	−0.473605	−	0.880737i	$-0.657048\pi$
$433$	−25.3840	−	4.47589i	−1.21988	−	0.215097i	−0.746273	+	0.665640i	$0.768159\pi$
$434$	−5.59299	−	2.03568i	−0.268472	−	0.0977159i
$435$	−6.79454	+	20.7264i	−0.325773	+	0.993754i
$436$	14.3712			0.688254
$437$	24.2097	−	11.2001i	1.15811	−	0.535772i
$438$		−	0.459070i		−	0.0219352i
$439$	16.3190	−	13.6932i	0.778861	−	0.653542i	−0.164100	−	0.986444i	$-0.552472\pi$
$439$	16.3190	−	13.6932i	0.778861	−	0.653542i	0.942962	+	0.332901i	$0.108028\pi$
$440$	−7.86542	+	1.65031i	−0.374969	+	0.0786753i
$441$	−1.05652	+	5.99184i	−0.0503107	+	0.285326i
$442$	−3.56552	+	0.628697i	−0.169594	+	0.0299040i
$443$	7.43353	+	20.4235i	0.353178	+	0.970348i	0.981343	+	0.192268i	$0.0615842\pi$
$443$	7.43353	+	20.4235i	0.353178	+	0.970348i	−0.628165	+	0.778080i	$0.716194\pi$
$444$	−3.21785	+	5.57349i	−0.152713	+	0.264506i
$445$	−9.73305	+	18.1900i	−0.461391	+	0.862289i
$446$	3.02506	+	2.53833i	0.143241	+	0.120193i
$447$	−5.81282	+	6.92745i	−0.274937	+	0.327657i
$448$	−0.828729	+	0.478467i	−0.0391538	+	0.0226054i
$449$	−13.2162	+	22.8911i	−0.623710	+	1.08030i	0.365078	+	0.930977i	$0.381042\pi$
$449$	−13.2162	+	22.8911i	−0.623710	+	1.08030i	−0.988789	+	0.149321i	$0.952291\pi$
$450$	4.96980	+	0.548708i	0.234279	+	0.0258664i
$451$	−2.60404	−	14.7682i	−0.122619	−	0.695409i
$452$	−14.0893	−	2.48432i	−0.662704	−	0.116853i
$453$	−3.97674	+	10.9260i	−0.186844	+	0.513348i
$454$	−9.30078	+	7.80428i	−0.436507	+	0.366273i
$455$	−0.967950	−	1.55812i	−0.0453782	−	0.0730457i
$456$	−3.07286	−	3.09153i	−0.143900	−	0.144774i
$457$			27.2209i			1.27334i	0.771136	+	0.636671i	$0.219689\pi$
$457$			27.2209i			1.27334i	−0.771136	+	0.636671i	$0.780311\pi$
$458$	7.77791	+	9.26935i	0.363438	+	0.433128i
$459$	−3.96874	−	1.44450i	−0.185245	−	0.0674237i
$460$	−5.09282	−	12.7009i	−0.237454	−	0.592185i
$461$	−3.88684	−	22.0433i	−0.181028	−	1.02666i	−0.930953	−	0.365138i	$-0.881022\pi$
$461$	−3.88684	−	22.0433i	−0.181028	−	1.02666i	0.749925	−	0.661522i	$-0.230089\pi$
$462$	1.17632	+	3.23192i	0.0547274	+	0.150362i
$463$	−11.8940	−	6.86699i	−0.552760	−	0.319136i	0.197475	−	0.980308i	$-0.436726\pi$
$463$	−11.8940	−	6.86699i	−0.552760	−	0.319136i	−0.750234	+	0.661172i	$0.770059\pi$
$464$	−4.87724	−	8.44762i	−0.226420	−	0.392171i
$465$	−13.7674	−	1.97171i	−0.638449	−	0.0914356i
$466$	−13.6732	−	11.4732i	−0.633400	−	0.531486i
$467$	−30.3376	+	17.5154i	−1.40385	+	0.810516i	−0.994786	−	0.101988i	$-0.967480\pi$
$467$	−30.3376	+	17.5154i	−1.40385	+	0.810516i	−0.409069	+	0.912503i	$0.634146\pi$
$468$	−0.742394	−	0.428621i	−0.0343172	−	0.0198130i
$469$	9.71628	−	3.53644i	0.448656	−	0.163297i
$470$	−1.74235	+	1.56056i	−0.0803685	+	0.0719835i
$471$	1.27838	−	7.25008i	0.0589049	−	0.334066i
$472$	0.565874	−	1.55472i	0.0260464	−	0.0715620i
$473$	22.0068	+	26.2267i	1.01187	+	1.20590i
$474$	−10.4323			−0.479170
$475$	−10.4081	−	19.1486i	−0.477559	−	0.878600i
$476$	4.04156			0.185245
$477$	1.74419	+	2.07864i	0.0798609	+	0.0951745i
$478$	5.18230	−	14.2383i	0.237033	−	0.651243i
$479$	−6.44330	+	36.5418i	−0.294402	+	1.66964i	0.375220	+	0.926936i	$0.377567\pi$
$479$	−6.44330	+	36.5418i	−0.294402	+	1.66964i	−0.669622	+	0.742702i	$0.733544\pi$
$480$	−1.66564	+	1.49186i	−0.0760257	+	0.0680938i
$481$	5.18425	−	1.88691i	0.236381	−	0.0860358i
$482$	−8.55742	−	4.94063i	−0.389780	−	0.225039i
$483$	−5.07154	+	2.92805i	−0.230763	+	0.133231i
$484$	−1.46903	−	1.23266i	−0.0667739	−	0.0560300i
$485$	−16.9610	−	2.42908i	−0.770160	−	0.110299i
$486$	−0.500000	−	0.866025i	−0.0226805	−	0.0392837i
$487$	14.2194	+	8.20959i	0.644344	+	0.372012i	0.786286	−	0.617863i	$-0.212001\pi$
$487$	14.2194	+	8.20959i	0.644344	+	0.372012i	−0.141942	+	0.989875i	$0.545335\pi$
$488$	−4.48520	−	12.3230i	−0.203035	−	0.557835i
$489$	−2.54083	−	14.4097i	−0.114900	−	0.651631i
$490$	−5.06338	−	12.6275i	−0.228740	−	0.570453i
$491$	−31.8673	−	11.5987i	−1.43815	−	0.523444i	−0.498895	−	0.866662i	$-0.666261\pi$
$491$	−31.8673	−	11.5987i	−1.43815	−	0.523444i	−0.939256	+	0.343218i	$0.888483\pi$
$492$	−2.68196	−	3.19624i	−0.120912	−	0.144097i
$493$			41.1975i			1.85544i
$494$	0.314395	+	3.72338i	0.0141453	+	0.167523i
$495$	4.24091	+	6.82664i	0.190615	+	0.306835i
$496$	4.76464	−	3.99801i	0.213939	−	0.179516i
$497$	4.33274	−	11.9041i	0.194350	−	0.533972i
$498$	7.89335	+	1.39181i	0.353710	+	0.0623685i
$499$	3.88666	+	22.0424i	0.173991	+	0.986752i	0.939302	+	0.343091i	$0.111474\pi$
$499$	3.88666	+	22.0424i	0.173991	+	0.986752i	−0.765311	+	0.643661i	$0.777415\pi$
$500$	−10.0871	+	4.82195i	−0.451107	+	0.215644i
$501$	−0.292022	+	0.505797i	−0.0130466	+	0.0225973i
$502$	−19.0057	+	10.9730i	−0.848267	+	0.489747i
$503$	−14.0274	+	16.7173i	−0.625453	+	0.745386i	−0.981998	−	0.188892i	$-0.939510\pi$
$503$	−14.0274	+	16.7173i	−0.625453	+	0.745386i	0.356545	+	0.934278i	$0.383955\pi$
$504$	0.733054	+	0.615105i	0.0326528	+	0.0273990i
$505$	1.22376	−	2.28708i	0.0544567	−	0.101774i
$506$	10.9974	−	19.0480i	0.488893	−	0.846788i
$507$	−4.19492	−	11.5255i	−0.186303	−	0.511864i
$508$	−14.7150	+	2.59465i	−0.652873	+	0.115119i
$509$	−5.20362	+	29.5112i	−0.230646	+	1.30806i	0.620945	+	0.783854i	$0.286749\pi$
$509$	−5.20362	+	29.5112i	−0.230646	+	1.30806i	−0.851591	+	0.524206i	$0.824362\pi$
$510$	9.24266	−	1.93928i	0.409272	−	0.0858726i
$511$	0.336523	−	0.282376i	0.0148869	−	0.0124916i
$512$		−	1.00000i		−	0.0441942i
$513$	−1.85411	+	3.94491i	−0.0818607	+	0.174172i
$514$	−15.5074			−0.684004
$515$	6.71481	−	20.4832i	0.295890	−	0.902597i
$516$	8.95123	+	3.25798i	0.394056	+	0.143425i
$517$	−3.70252	−	0.652854i	−0.162837	−	0.0287125i
$518$	−6.06499	+	1.06942i	−0.266480	+	0.0469876i
$519$	7.83576	−	2.85198i	0.343952	−	0.125188i
$520$	1.91585	−	0.0618746i	0.0840157	−	0.00271338i
$521$	−13.8357	−	23.9642i	−0.606155	−	1.04989i	−0.991868	−	0.127272i	$-0.959378\pi$
$521$	−13.8357	−	23.9642i	−0.606155	−	1.04989i	0.385713	−	0.922619i	$-0.373955\pi$
$522$	−6.27006	+	7.47236i	−0.274433	+	0.327056i
$523$	21.5971	−	25.7384i	0.944375	−	1.12546i	−0.0475799	−	0.998867i	$-0.515151\pi$
$523$	21.5971	−	25.7384i	0.944375	−	1.12546i	0.991955	−	0.126594i	$-0.0404047\pi$
$524$	−3.86811	−	6.69977i	−0.168979	−	0.292681i
$525$	2.65472	+	3.98065i	0.115861	+	0.173730i
$526$	−10.5395	+	3.83608i	−0.459546	+	0.167261i
$527$	−25.8699	+	4.56156i	−1.12691	+	0.198705i
$528$	−3.53951	−	0.624112i	−0.154038	−	0.0271610i
$529$	13.5787	+	4.94225i	0.590379	+	0.214881i
$530$	−5.76561	−	1.89009i	−0.250442	−	0.0821001i
$531$	−1.65450			−0.0717993
$532$	0.376124	−	4.15419i	0.0163070	−	0.180107i
$533$			3.57675i			0.154926i
$534$	−7.06764	+	5.93045i	−0.305847	+	0.256636i
$535$	37.0474	−	7.77321i	1.60170	−	0.336065i
$536$	−1.87630	+	10.6410i	−0.0810438	+	0.459622i
$537$	−1.74896	+	0.308389i	−0.0754733	+	0.0133080i
$538$	2.31252	+	6.35360i	0.0996998	+	0.273923i
$539$	10.9338	−	18.9379i	0.470952	−	0.815713i
$540$	1.97157	+	1.05494i	0.0848429	+	0.0453975i
$541$	0.799947	+	0.671235i	0.0343924	+	0.0288586i	0.659822	−	0.751422i	$-0.270632\pi$
$541$	0.799947	+	0.671235i	0.0343924	+	0.0288586i	−0.625429	+	0.780281i	$0.715076\pi$
$542$	5.09067	−	6.06682i	0.218663	−	0.260592i
$543$	16.5866	−	9.57627i	0.711799	−	0.410957i
$544$	−2.11172	+	3.65761i	−0.0905394	+	0.156819i
$545$	25.2707	+	19.8505i	1.08248	+	0.850304i
$546$	−0.142448	−	0.807862i	−0.00609621	−	0.0345733i
$547$	23.1807	+	4.08738i	0.991136	+	0.174764i	0.645628	−	0.763652i	$-0.276596\pi$
$547$	23.1807	+	4.08738i	0.991136	+	0.174764i	0.345508	+	0.938416i	$0.387707\pi$
$548$	4.07338	−	11.1915i	0.174006	−	0.478078i
$549$	−10.0458	+	8.42941i	−0.428744	+	0.359759i
$550$	−16.1103	−	7.96237i	−0.686947	−	0.339516i
$551$	42.3456	+	3.83401i	1.80398	+	0.163334i
$552$		−	6.11965i		−	0.260470i
$553$	−6.41695	−	7.64742i	−0.272876	−	0.325201i
$554$	2.40627	+	0.875812i	0.102233	+	0.0372097i
$555$	−13.3569	+	5.35585i	−0.566969	+	0.227343i
$556$	0.799326	+	4.53320i	0.0338990	+	0.192251i
$557$	11.8539	+	32.5682i	0.502264	+	1.37996i	0.889059	+	0.457793i	$0.151360\pi$
$557$	11.8539	+	32.5682i	0.502264	+	1.37996i	−0.386795	+	0.922166i	$0.626418\pi$
$558$	−5.38650	−	3.10990i	−0.228029	−	0.131653i
$559$	−4.08292	−	7.07182i	−0.172689	−	0.299106i
$560$	−2.11816	−	0.303353i	−0.0895085	−	0.0128190i
$561$	11.6282	+	9.75724i	0.490944	+	0.411951i
$562$	−7.67477	+	4.43103i	−0.323741	+	0.186912i
$563$	6.75311	+	3.89891i	0.284610	+	0.164319i	0.635508	−	0.772094i	$-0.280791\pi$
$563$	6.75311	+	3.89891i	0.284610	+	0.164319i	−0.350899	+	0.936413i	$0.614124\pi$
$564$	−0.982968	+	0.357771i	−0.0413904	+	0.0150649i
$565$	−21.3435	−	23.8297i	−0.897928	−	1.00252i
$566$	−0.111547	+	0.632613i	−0.00468866	+	0.0265907i
$567$	0.327291	−	0.899224i	0.0137449	−	0.0377639i
$568$	8.50934	+	10.1410i	0.357044	+	0.425509i
$569$	−23.6188			−0.990150			−0.495075	−	0.868850i	$-0.664860\pi$
$569$	−23.6188			−0.990150			−0.495075	+	0.868850i	$0.664860\pi$
$570$	−1.13316	−	9.68070i	−0.0474628	−	0.405480i
$571$	−29.3288			−1.22737			−0.613686	−	0.789551i	$-0.710314\pi$
$571$	−29.3288			−1.22737			−0.613686	+	0.789551i	$0.710314\pi$
$572$	1.98045	+	2.36021i	0.0828067	+	0.0986852i
$573$	−4.51994	+	12.4184i	−0.188823	+	0.518787i
$574$	0.693326	−	3.93204i	0.0289388	−	0.164120i
$575$	8.58813	−	29.3683i	0.358150	−	1.22474i
$576$	−0.939693	+	0.342020i	−0.0391539	+	0.0142508i
$577$	−25.4072	−	14.6688i	−1.05771	−	0.610671i	−0.132915	−	0.991127i	$-0.542434\pi$
$577$	−25.4072	−	14.6688i	−1.05771	−	0.610671i	−0.924799	+	0.380456i	$0.875767\pi$
$578$	0.725307	−	0.418756i	0.0301688	−	0.0174180i
$579$	−11.8721	−	9.96186i	−0.493387	−	0.414001i
$580$	3.09221	−	21.5914i	0.128397	−	0.896533i
$581$	3.83497	+	6.64236i	0.159101	+	0.275572i
$582$	−6.63600	−	3.83130i	−0.275071	−	0.158812i
$583$	−3.33557	−	9.16440i	−0.138145	−	0.379550i
$584$	0.0797166	+	0.452095i	0.00329870	+	0.0187078i
$585$	−0.713404	−	1.77915i	−0.0294956	−	0.0735589i
$586$	2.02935	+	0.738623i	0.0838317	+	0.0305122i
$587$	0.144491	+	0.172198i	0.00596380	+	0.00710738i	0.769018	−	0.639227i	$-0.220746\pi$
$587$	0.144491	+	0.172198i	0.00596380	+	0.00710738i	−0.763054	+	0.646334i	$0.776301\pi$
$588$		−	6.08428i		−	0.250911i
$589$	2.28112	+	27.0153i	0.0939919	+	1.11315i
$590$	3.14255	−	1.95225i	0.129377	−	0.0803728i
$591$	2.77760	−	2.33069i	0.114255	−	0.0958716i
$592$	2.20114	−	6.04759i	0.0904664	−	0.248554i
$593$	−32.1895	−	5.67587i	−1.32186	−	0.233080i	−0.532199	−	0.846619i	$-0.678634\pi$
$593$	−32.1895	−	5.67587i	−1.32186	−	0.233080i	−0.789664	+	0.613539i	$0.789745\pi$
$594$	0.624112	+	3.53951i	0.0256076	+	0.145228i
$595$	7.10680	+	5.58251i	0.291351	+	0.228861i
$596$	4.52157	−	7.83159i	0.185211	−	0.320795i
$597$	−13.6679	+	7.89114i	−0.559388	+	0.322963i
$598$	−3.37208	+	4.01869i	−0.137895	+	0.164337i
$599$	28.5536	+	23.9594i	1.16667	+	0.978953i	0.999975	−	0.00705583i	$-0.00224596\pi$
$599$	28.5536	+	23.9594i	1.16667	+	0.978953i	0.166695	+	0.986008i	$0.446690\pi$
$600$	−4.98958	+	0.322625i	−0.203699	+	0.0131711i
$601$	1.83917	−	3.18553i	0.0750212	−	0.129940i	−0.826074	−	0.563561i	$-0.809431\pi$
$601$	1.83917	−	3.18553i	0.0750212	−	0.129940i	0.901095	+	0.433621i	$0.142764\pi$
$602$	3.11767	+	8.56574i	0.127067	+	0.349113i
$603$	10.6410	−	1.87630i	0.433336	−	0.0764088i
$604$	2.01904	−	11.4506i	0.0821537	−	0.465917i
$605$	−0.880538	−	4.19667i	−0.0357989	−	0.170619i
$606$	0.888632	−	0.745651i	0.0360982	−	0.0302900i
$607$			48.0175i			1.94897i	0.224454	+	0.974485i	$0.427940\pi$
$607$			48.0175i			1.94897i	−0.224454	+	0.974485i	$0.572060\pi$
$608$	3.56301	+	2.51096i	0.144499	+	0.101833i
$609$	−9.33439			−0.378249
$610$	9.13452	−	27.8644i	0.369846	−	1.12820i
$611$	0.842642	+	0.306697i	0.0340897	+	0.0124076i
$612$	4.15928	+	0.733394i	0.168129	+	0.0296457i
$613$	−7.42725	+	1.30962i	−0.299984	+	0.0528952i	−0.321614	−	0.946871i	$-0.604225\pi$
$613$	−7.42725	+	1.30962i	−0.299984	+	0.0528952i	0.0216304	+	0.999766i	$0.493114\pi$
$614$	−5.33717	+	1.94257i	−0.215391	+	0.0783957i
$615$	−0.301158	−	9.32489i	−0.0121439	−	0.376016i
$616$	−1.71967	−	2.97855i	−0.0692873	−	0.120009i
$617$	−1.17874	+	1.40477i	−0.0474544	+	0.0565539i	−0.789250	−	0.614073i	$-0.789530\pi$
$617$	−1.17874	+	1.40477i	−0.0474544	+	0.0565539i	0.741795	+	0.670627i	$0.233975\pi$
$618$	6.19648	−	7.38468i	0.249259	−	0.297055i
$619$	−10.6591	−	18.4621i	−0.428425	−	0.742054i	0.568308	−	0.822816i	$-0.307598\pi$
$619$	−10.6591	−	18.4621i	−0.428425	−	0.742054i	−0.996733	+	0.0807616i	$0.974265\pi$
$620$	13.9006	−	0.448937i	0.558263	−	0.0180297i
$621$	−5.75059	+	2.09305i	−0.230763	+	0.0839910i
$622$	−12.6862	+	2.23691i	−0.508669	+	0.0896920i
$623$	−8.69468	−	1.53311i	−0.348345	−	0.0614226i
$624$	0.805545	+	0.293194i	0.0322476	+	0.0117372i
$625$	−24.3978	−	5.45394i	−0.975914	−	0.218158i
$626$	−17.0343			−0.680826
$627$	11.1113	−	11.0442i	0.443743	−	0.441063i
$628$			7.36192i			0.293773i
$629$	−20.8218	+	17.4715i	−0.830218	+	0.696636i
$630$	0.439394	+	2.09417i	0.0175059	+	0.0834337i
$631$	−1.86492	+	10.5765i	−0.0742411	+	0.421042i	0.924923	+	0.380155i	$0.124129\pi$
$631$	−1.86492	+	10.5765i	−0.0742411	+	0.421042i	−0.999164	+	0.0408870i	$0.986982\pi$
$632$	10.2738	−	1.81154i	0.408669	−	0.0720594i
$633$	7.42924	+	20.4117i	0.295286	+	0.811291i
$634$	−14.3502	+	24.8554i	−0.569921	+	0.987132i
$635$	−29.4593	−	15.7630i	−1.16906	−	0.625535i
$636$	−2.07864	−	1.74419i	−0.0824235	−	0.0691616i
$637$	−3.35259	+	3.99546i	−0.132834	+	0.158306i
$638$	30.3617	−	17.5294i	1.20203	−	0.693994i
$639$	6.61909	−	11.4646i	0.261847	−	0.453533i
$640$	1.38128	−	1.75843i	0.0545997	−	0.0695081i
$641$	6.93225	+	39.3148i	0.273807	+	1.55284i	0.742724	+	0.669597i	$0.233533\pi$
$641$	6.93225	+	39.3148i	0.273807	+	1.55284i	−0.468917	+	0.883242i	$0.655356\pi$
$642$	16.6717	+	2.93967i	0.657978	+	0.116019i
$643$	−1.70868	+	4.69457i	−0.0673839	+	0.185136i	−0.968814	−	0.247789i	$-0.920296\pi$
$643$	−1.70868	+	4.69457i	−0.0673839	+	0.185136i	0.901430	+	0.432924i	$0.142518\pi$
$644$	4.48604	−	3.76423i	0.176775	−	0.148332i
$645$	11.2399	+	18.0930i	0.442572	+	0.712413i
$646$	−7.72966	−	16.7082i	−0.304120	−	0.657377i
$647$			4.05424i			0.159389i	0.996819	+	0.0796944i	$0.0253944\pi$
$647$			4.05424i			0.159389i	−0.996819	+	0.0796944i	$0.974606\pi$
$648$	0.642788	+	0.766044i	0.0252511	+	0.0300931i
$649$	5.58786	+	2.03382i	0.219343	+	0.0798342i
$650$	3.45436	+	2.53752i	0.135491	+	0.0995297i
$651$	−1.03354	−	5.86151i	−0.0405077	−	0.229731i
$652$	5.00445	+	13.7496i	0.195989	+	0.538477i
$653$	−7.04516	−	4.06753i	−0.275699	−	0.159175i	0.355776	−	0.934571i	$-0.384217\pi$
$653$	−7.04516	−	4.06753i	−0.275699	−	0.159175i	−0.631475	+	0.775397i	$0.717550\pi$
$654$	7.18558	+	12.4458i	0.280978	+	0.486669i
$655$	2.45242	−	17.1240i	0.0958240	−	0.669090i
$656$	3.19624	+	2.68196i	0.124792	+	0.104713i
$657$	0.397566	−	0.229535i	0.0155105	−	0.00895500i
$658$	−0.866894	−	0.500502i	−0.0337951	−	0.0195116i
$659$	−19.8476	+	7.22392i	−0.773151	+	0.281404i	−0.698314	−	0.715792i	$-0.746066\pi$
$659$	−19.8476	+	7.22392i	−0.773151	+	0.281404i	−0.0748372	+	0.997196i	$0.523844\pi$
$660$	−5.36192	−	5.98650i	−0.208712	−	0.233024i
$661$	7.03660	−	39.9066i	0.273692	−	1.55218i	−0.469394	−	0.882989i	$-0.655528\pi$
$661$	7.03660	−	39.9066i	0.273692	−	1.55218i	0.743086	−	0.669196i	$-0.233361\pi$
$662$	−3.58955	+	9.86220i	−0.139512	+	0.383305i
$663$	−2.32723	−	2.77348i	−0.0903819	−	0.107713i
$664$	−8.01512			−0.311047
$665$	6.39946	−	6.78532i	0.248161	−	0.263123i
$666$	−6.43571			−0.249379
$667$	38.3706	+	45.7283i	1.48571	+	1.77061i
$668$	0.199755	−	0.548822i	0.00772874	−	0.0212345i
$669$	−0.685726	+	3.88894i	−0.0265117	+	0.150355i
$670$	−17.9975	+	16.1198i	−0.695305	+	0.622763i
$671$	44.2902	−	16.1203i	1.70981	−	0.622318i
$672$	−0.828729	−	0.478467i	−0.0319689	−	0.0184573i
$673$	41.0512	−	23.7009i	1.58241	−	0.913604i	0.587901	−	0.808933i	$-0.299955\pi$
$673$	41.0512	−	23.7009i	1.58241	−	0.913604i	0.994507	−	0.104671i	$-0.0333788\pi$
$674$	−9.33117	−	7.82978i	−0.359423	−	0.301592i
$675$	2.00971	+	4.57833i	0.0773536	+	0.176220i
$676$	6.13257	+	10.6219i	0.235868	+	0.408535i
$677$	−11.3954	−	6.57915i	−0.437961	−	0.252857i	0.264771	−	0.964311i	$-0.414704\pi$
$677$	−11.3954	−	6.57915i	−0.437961	−	0.252857i	−0.702733	+	0.711454i	$0.748037\pi$
$678$	−4.89316	−	13.4438i	−0.187921	−	0.516308i
$679$	−1.27329	−	7.22120i	−0.0488645	−	0.277124i
$680$	−8.76549	+	3.51479i	−0.336141	+	0.134786i
$681$	−11.4091	−	4.15257i	−0.437197	−	0.159127i
$682$	14.3693	+	17.1247i	0.550229	+	0.655738i
$683$		−	32.5004i		−	1.24359i	−0.783179	−	0.621797i	$-0.786403\pi$
$683$		−	32.5004i		−	1.24359i	0.783179	−	0.621797i	$-0.213597\pi$
$684$	1.14091	−	4.20694i	0.0436238	−	0.160856i
$685$	22.6213	−	14.0530i	0.864316	−	0.536939i
$686$	9.59148	−	8.04821i	0.366204	−	0.307282i
$687$	−4.13854	+	11.3705i	−0.157895	+	0.433813i
$688$	−9.38098	−	1.65412i	−0.357647	−	0.0630627i
$689$	0.403924	+	2.29077i	0.0153883	+	0.0872713i
$690$	8.45293	−	10.7610i	0.321798	−	0.409664i
$691$	15.3191	−	26.5335i	0.582766	−	1.00938i	−0.412384	−	0.911010i	$-0.635304\pi$
$691$	15.3191	−	26.5335i	0.582766	−	1.00938i	0.995150	−	0.0983700i	$-0.0313629\pi$
$692$	−7.22147	+	4.16932i	−0.274519	+	0.158494i
$693$	−2.21076	+	2.63468i	−0.0839798	+	0.100083i
$694$	−21.9229	−	18.3955i	−0.832181	−	0.698283i
$695$	−4.85605	+	9.07542i	−0.184200	+	0.344250i
$696$	4.87724	−	8.44762i	0.184871	−	0.320206i
$697$	−6.02704	−	16.5591i	−0.228290	−	0.627222i
$698$	−4.71467	+	0.831323i	−0.178453	+	0.0314660i
$699$	3.09947	−	17.5780i	0.117233	−	0.664860i
$700$	−3.30562	−	3.45918i	−0.124941	−	0.130745i
$701$	30.2770	−	25.4054i	1.14355	−	0.959549i	0.143997	−	0.989578i	$-0.454005\pi$
$701$	30.2770	−	25.4054i	1.14355	−	0.959549i	0.999549	+	0.0300294i	$0.00956010\pi$
$702$		−	0.857243i		−	0.0323545i
$703$	16.0207	+	23.0280i	0.604230	+	0.868516i
$704$	3.59412			0.135458
$705$	−2.22266	−	0.728634i	−0.0837103	−	0.0274420i
$706$	−28.1566	−	10.2482i	−1.05969	−	0.385694i
$707$	1.09320	+	0.192761i	0.0411142	+	0.00724954i
$708$	1.62937	−	0.287302i	0.0612354	−	0.0107975i
$709$	−21.5186	+	7.83212i	−0.808147	+	0.294141i	−0.712858	−	0.701308i	$-0.752600\pi$
$709$	−21.5186	+	7.83212i	−0.808147	+	0.294141i	−0.0952886	+	0.995450i	$0.530377\pi$
$710$	0.955515	+	29.5861i	0.0358598	+	1.11035i
$711$	−5.21614	−	9.03461i	−0.195620	−	0.338824i
$712$	5.93045	−	7.06764i	0.222253	−	0.264871i
$713$	−24.4664	+	29.1580i	−0.916275	+	1.09197i
$714$	2.02078	+	3.50009i	0.0756258	+	0.130988i
$715$	0.222385	+	6.88580i	0.00831672	+	0.257514i
$716$	1.66884	−	0.607408i	0.0623675	−	0.0226999i
$717$	14.9218	−	2.63112i	0.557266	−	0.0982611i
$718$	−0.909636	−	0.160393i	−0.0339473	−	0.00598583i
$719$	−40.1646	−	14.6187i	−1.49789	−	0.545186i	−0.542374	−	0.840137i	$-0.682474\pi$
$719$	−40.1646	−	14.6187i	−1.49789	−	0.545186i	−0.955512	+	0.294951i	$0.904697\pi$
$720$	−2.12481	−	0.696556i	−0.0791869	−	0.0259591i
$721$	9.22486			0.343552
$722$	−17.8932	+	6.39013i	−0.665916	+	0.237816i
$723$		−	9.88125i		−	0.367488i
$724$	−14.6717	+	12.3110i	−0.545269	+	0.457535i
$725$	35.2611	−	33.6957i	1.30956	−	1.25143i
$726$	0.333001	−	1.88854i	0.0123588	−	0.0700904i
$727$	35.8982	−	6.32982i	1.33139	−	0.234760i	0.537728	−	0.843119i	$-0.319283\pi$
$727$	35.8982	−	6.32982i	1.33139	−	0.234760i	0.793662	+	0.608358i	$0.208172\pi$
$728$	0.280568	+	0.770853i	0.0103985	+	0.0285697i
$729$	0.500000	−	0.866025i	0.0185185	−	0.0320750i
$730$	−0.484292	+	0.905089i	−0.0179245	+	0.0334988i
$731$	30.8190	+	25.8602i	1.13988	+	0.956473i
$732$	8.42941	−	10.0458i	0.311560	−	0.371303i
$733$	2.05356	−	1.18562i	0.0758500	−	0.0437920i	−0.461595	−	0.887091i	$-0.652723\pi$
$733$	2.05356	−	1.18562i	0.0758500	−	0.0437920i	0.537445	+	0.843299i	$0.319389\pi$
$734$	10.0117	−	17.3408i	0.369539	−	0.640060i
$735$	8.40406	−	10.6988i	0.309989	−	0.394630i
$736$	1.06267	+	6.02668i	0.0391704	+	0.222147i
$737$	−38.2451	−	6.74364i	−1.40878	−	0.248405i
$738$	1.42704	−	3.92076i	0.0525301	−	0.144325i
$739$	−14.3841	+	12.0697i	−0.529128	+	0.443991i	−0.867800	−	0.496914i	$-0.834467\pi$
$739$	−14.3841	+	12.0697i	−0.529128	+	0.443991i	0.338672	+	0.940904i	$0.390022\pi$
$740$	12.2239	−	7.59388i	0.449361	−	0.279157i
$741$	−3.06735	+	2.13397i	−0.112682	+	0.0783932i
$742$		−	2.59662i		−	0.0953248i
$743$	−13.2172	−	15.7517i	−0.484893	−	0.577873i	0.467018	−	0.884248i	$-0.345328\pi$
$743$	−13.2172	−	15.7517i	−0.484893	−	0.577873i	−0.951911	+	0.306375i	$0.900884\pi$
$744$	5.84470	+	2.12730i	0.214277	+	0.0779905i
$745$	18.7685	−	7.52577i	0.687623	−	0.275723i
$746$	4.83854	+	27.4407i	0.177152	+	1.00468i
$747$	2.74133	+	7.53175i	0.100300	+	0.275572i
$748$	−13.1459	−	7.58978i	−0.480661	−	0.277510i
$749$	8.09990	+	14.0294i	0.295964	+	0.512625i
$750$	−9.21946	−	6.32467i	−0.336647	−	0.230944i
$751$	8.12411	+	6.81694i	0.296453	+	0.248754i	0.778866	−	0.627190i	$-0.215795\pi$
$751$	8.12411	+	6.81694i	0.296453	+	0.248754i	−0.482413	+	0.875944i	$0.660240\pi$
$752$	0.905908	−	0.523026i	0.0330351	−	0.0190728i
$753$	−19.0057	−	10.9730i	−0.692607	−	0.399877i
$754$	−7.85766	+	2.85996i	−0.286159	+	0.104153i
$755$	19.3667	−	17.3462i	0.704828	−	0.631292i
$756$	−0.166170	+	0.942396i	−0.00604354	+	0.0342746i
$757$	6.99034	−	19.2058i	0.254068	−	0.698047i	−0.745436	−	0.666577i	$-0.767759\pi$
$757$	6.99034	−	19.2058i	0.254068	−	0.698047i	0.999505	−	0.0314702i	$-0.0100189\pi$
$758$	8.80674	+	10.4955i	0.319875	+	0.381212i
$759$	21.9948			0.798359
$760$	2.79698	+	9.33686i	0.101457	+	0.338683i
$761$	25.5098			0.924729			0.462365	−	0.886690i	$-0.347001\pi$
$761$	25.5098			0.924729			0.462365	+	0.886690i	$0.347001\pi$
$762$	−9.60454	−	11.4462i	−0.347936	−	0.414654i
$763$	−4.70355	+	12.9229i	−0.170280	+	0.467840i
$764$	2.29483	−	13.0146i	0.0830241	−	0.470853i
$765$	6.30079	+	7.03474i	0.227806	+	0.254342i
$766$	−1.75001	+	0.636953i	−0.0632306	+	0.0230141i
$767$	−1.22829	−	0.709155i	−0.0443511	−	0.0256061i
$768$	0.866025	−	0.500000i	0.0312500	−	0.0180422i
$769$	29.7445	+	24.9586i	1.07261	+	0.900030i	0.995287	−	0.0969754i	$-0.0309168\pi$
$769$	29.7445	+	24.9586i	1.07261	+	0.900030i	0.0773276	+	0.997006i	$0.475361\pi$
$770$	1.09028	−	7.61291i	0.0392911	−	0.274350i
$771$	−7.75372	−	13.4298i	−0.279243	−	0.483664i
$772$	13.4216	+	7.74895i	0.483053	+	0.278891i
$773$	−4.55481	−	12.5142i	−0.163825	−	0.450105i	0.830433	−	0.557119i	$-0.188093\pi$
$773$	−4.55481	−	12.5142i	−0.163825	−	0.450105i	−0.994258	+	0.107014i	$0.965871\pi$
$774$	1.65412	+	9.38098i	0.0594561	+	0.337192i
$775$	25.0634	+	18.4112i	0.900305	+	0.661350i
$776$	7.20048	+	2.62076i	0.258482	+	0.0940798i
$777$	−3.95864	−	4.71772i	−0.142015	−	0.169247i
$778$			28.1712i			1.00999i
$779$	−17.5815	+	4.65393i	−0.629922	+	0.166744i
$780$	1.01151	+	1.62824i	0.0362179	+	0.0583004i
$781$	−36.4481	+	30.5836i	−1.30422	+	1.09437i
$782$	8.83987	−	24.2873i	0.316113	−	0.868513i
$783$	−9.60628	−	1.69385i	−0.343301	−	0.0605331i
$784$	1.05652	+	5.99184i	0.0377330	+	0.213994i
$785$	−10.1688	+	12.9454i	−0.362942	+	0.462042i
$786$	3.86811	−	6.69977i	0.137971	−	0.238973i
$787$	0.957295	−	0.552694i	0.0341239	−	0.0197014i	−0.482841	−	0.875708i	$-0.660395\pi$
$787$	0.957295	−	0.552694i	0.0341239	−	0.0197014i	0.516965	+	0.856007i	$0.327062\pi$
$788$	−2.33069	+	2.77760i	−0.0830272	+	0.0989480i
$789$	−8.59192	−	7.20947i	−0.305880	−	0.256664i
$790$	20.5680	+	11.0054i	0.731776	+	0.391556i
$791$	6.84525	−	11.8563i	0.243389	−	0.421562i
$792$	−1.22926	−	3.37737i	−0.0436799	−	0.120009i
$793$	−11.0710	+	1.95211i	−0.393141	+	0.0693214i
$794$	−6.54123	+	37.0972i	−0.232140	+	1.31653i
$795$	−1.24594	−	5.93821i	−0.0441891	−	0.210607i
$796$	12.0899	−	10.1447i	0.428516	−	0.359568i
$797$		−	14.0789i		−	0.498700i	−0.968413	−	0.249350i	$-0.919783\pi$
$797$		−	14.0789i		−	0.498700i	0.968413	−	0.249350i	$-0.0802170\pi$
$798$	3.78569	−	1.75136i	0.134012	−	0.0619975i
$799$	−4.41795			−0.156296
$800$	4.85775	−	1.18415i	0.171748	−	0.0418662i
$801$	−8.66974	−	3.15553i	−0.306330	−	0.111495i
$802$	5.09810	+	0.898933i	0.180020	+	0.0317424i
$803$	−1.62488	+	0.286511i	−0.0573409	+	0.0101107i
$804$	−10.1535	+	3.69559i	−0.358088	+	0.130333i
$805$	13.0878	−	0.422686i	0.461285	−	0.0148977i
$806$	−2.66594	−	4.61754i	−0.0939037	−	0.162646i
$807$	−4.34612	+	5.17950i	−0.152991	+	0.182327i
$808$	−0.745651	+	0.888632i	−0.0262319	+	0.0312620i
$809$	−10.9372	−	18.9438i	−0.384532	−	0.666029i	0.607172	−	0.794570i	$-0.292304\pi$
$809$	−10.9372	−	18.9438i	−0.384532	−	0.666029i	−0.991704	+	0.128541i	$0.958970\pi$
$810$	0.0721787	+	2.23490i	0.00253610	+	0.0785265i
$811$	−4.70678	+	1.71313i	−0.165278	+	0.0601561i	−0.423334	−	0.905974i	$-0.639140\pi$
$811$	−4.70678	+	1.71313i	−0.165278	+	0.0601561i	0.258056	+	0.966130i	$0.416918\pi$
$812$	9.19258	−	1.62090i	0.322596	−	0.0568824i
$813$	7.79935	+	1.37524i	0.273535	+	0.0482317i
$814$	21.7357	+	7.91116i	0.761837	+	0.277286i
$815$	−10.1920	+	31.0903i	−0.357011	+	1.08904i
$816$	−4.22345			−0.147850
$817$	29.4490	−	29.2711i	1.03029	−	1.02407i
$818$			12.2630i			0.428766i
$819$	0.628405	−	0.527294i	0.0219583	−	0.0184252i
$820$	1.91583	+	9.13093i	0.0669038	+	0.318866i
$821$	−2.34620	+	13.3060i	−0.0818831	+	0.464382i	0.916103	+	0.400944i	$0.131318\pi$
$821$	−2.34620	+	13.3060i	−0.0818831	+	0.464382i	−0.997986	+	0.0634382i	$0.979793\pi$
$822$	11.7288	−	2.06811i	0.409090	−	0.0721336i
$823$	−6.36947	−	17.5000i	−0.222026	−	0.610010i	0.777803	−	0.628508i	$-0.216334\pi$
$823$	−6.36947	−	17.5000i	−0.222026	−	0.610010i	−0.999829	+	0.0184974i	$0.994112\pi$
$824$	−4.82001	+	8.34850i	−0.167913	+	0.290834i
$825$	−1.15955	−	17.9331i	−0.0403704	−	0.624352i
$826$	1.21284	+	1.01769i	0.0422001	+	0.0354101i
$827$	−21.8779	+	26.0731i	−0.760770	+	0.906651i	−0.997896	−	0.0648281i	$-0.979350\pi$
$827$	−21.8779	+	26.0731i	−0.760770	+	0.906651i	0.237126	+	0.971479i	$0.423795\pi$
$828$	5.29978	−	3.05983i	0.184180	−	0.106336i
$829$	9.55073	−	16.5423i	0.331710	−	0.574539i	−0.651137	−	0.758960i	$-0.725708\pi$
$829$	9.55073	−	16.5423i	0.331710	−	0.574539i	0.982847	+	0.184421i	$0.0590410\pi$
$830$	−14.0940	−	11.0711i	−0.489211	−	0.384283i
$831$	0.444661	+	2.52180i	0.0154251	+	0.0874802i
$832$	−0.844219	−	0.148859i	−0.0292680	−	0.00516074i
$833$	8.78876	−	24.1469i	0.304513	−	0.836642i
$834$	−3.52621	+	2.95884i	−0.122103	+	0.102456i
$835$	1.10933	−	0.689148i	0.0383899	−	0.0238490i
$836$	−9.02470	+	12.8059i	−0.312126	+	0.442901i
$837$		−	6.21980i		−	0.214988i
$838$	4.12894	+	4.92068i	0.142632	+	0.169982i
$839$	40.1567	+	14.6158i	1.38636	+	0.504595i	0.924101	−	0.382148i	$-0.124816\pi$
$839$	40.1567	+	14.6158i	1.38636	+	0.504595i	0.462263	+	0.886743i	$0.347038\pi$
$840$	−0.796368	−	1.98605i	−0.0274773	−	0.0685254i
$841$	11.4868	+	65.1448i	0.396096	+	2.24637i
$842$	−8.94981	−	24.5894i	−0.308431	−	0.847407i
$843$	−7.67477	−	4.43103i	−0.264333	−	0.152613i
$844$	−10.8608	−	18.8115i	−0.373845	−	0.647518i
$845$	−3.88810	+	27.1487i	−0.133755	+	0.933943i
$846$	−0.801323	−	0.672390i	−0.0275501	−	0.0231172i
$847$	1.58923	−	0.917545i	0.0546068	−	0.0315272i
$848$	2.34994	+	1.35674i	0.0806972	+	0.0465906i
$849$	−0.603632	+	0.219704i	−0.0207166	+	0.00754023i
$850$	−20.2684	−	5.92706i	−0.695200	−	0.203296i
$851$	−6.83901	+	38.7860i	−0.234438	+	1.32957i
$852$	−4.52773	+	12.4398i	−0.155117	+	0.426181i
$853$	−24.4755	−	29.1688i	−0.838026	−	0.998721i	−0.999929	−	0.0119141i	$-0.996208\pi$
$853$	−24.4755	−	29.1688i	−0.838026	−	0.998721i	0.161903	−	0.986807i	$-0.448237\pi$
$854$	12.5491			0.429421
$855$	7.81715	−	5.82169i	0.267341	−	0.199098i
$856$	−16.9289			−0.578617
$857$	21.7554	+	25.9271i	0.743150	+	0.885652i	0.996658	−	0.0816813i	$-0.0260290\pi$
$857$	21.7554	+	25.9271i	0.743150	+	0.885652i	−0.253508	+	0.967333i	$0.581585\pi$
$858$	−1.05377	+	2.89522i	−0.0359753	+	0.0988412i
$859$	−5.33481	+	30.2552i	−0.182021	+	1.03229i	0.747702	+	0.664035i	$0.231157\pi$
$859$	−5.33481	+	30.2552i	−0.182021	+	1.03229i	−0.929723	+	0.368260i	$0.879954\pi$
$860$	−14.2110	−	15.8664i	−0.484591	−	0.541039i
$861$	3.75191	−	1.36558i	0.127865	−	0.0465390i
$862$	−7.18808	−	4.15004i	−0.244827	−	0.141351i
$863$	16.8725	−	9.74133i	0.574346	−	0.331599i	−0.184538	−	0.982825i	$-0.559079\pi$
$863$	16.8725	−	9.74133i	0.574346	−	0.331599i	0.758883	+	0.651227i	$0.225745\pi$
$864$	−0.766044	−	0.642788i	−0.0260614	−	0.0218681i
$865$	−18.4574	−	2.64339i	−0.627572	−	0.0898779i
$866$	12.8878	+	22.3223i	0.437945	+	0.758544i
$867$	0.725307	+	0.418756i	0.0246327	+	0.0142217i
$868$	2.03568	+	5.59299i	0.0690956	+	0.189838i
$869$	6.51090	+	36.9252i	0.220867	+	1.25260i
$870$	20.2448	−	8.11775i	0.686362	−	0.275217i
$871$	8.70405	+	3.16802i	0.294926	+	0.107344i
$872$	−9.23760	−	11.0089i	−0.312825	−	0.372810i
$873$		−	7.66259i		−	0.259339i
$874$	−24.1415	−	11.3465i	−0.816597	−	0.383801i
$875$	−1.03461	−	10.6487i	−0.0349763	−	0.359992i
$876$	−0.351668	+	0.295084i	−0.0118817	+	0.00996997i
$877$	2.76345	−	7.59251i	0.0933150	−	0.256381i	−0.884250	−	0.467013i	$-0.845330\pi$
$877$	2.76345	−	7.59251i	0.0933150	−	0.256381i	0.977565	+	0.210632i	$0.0675523\pi$
$878$	−20.9793	−	3.69921i	−0.708015	−	0.124842i
$879$	0.375009	+	2.12678i	0.0126487	+	0.0717345i
$880$	6.32000	+	4.96447i	0.213047	+	0.167352i
$881$	−18.8992	+	32.7343i	−0.636729	+	1.10285i	0.349417	+	0.936967i	$0.386380\pi$
$881$	−18.8992	+	32.7343i	−0.636729	+	1.10285i	−0.986146	+	0.165880i	$0.946954\pi$
$882$	5.26914	−	3.04214i	0.177421	−	0.102434i
$883$	35.3835	−	42.1684i	1.19075	−	1.41908i	0.306623	−	0.951831i	$-0.400801\pi$
$883$	35.3835	−	42.1684i	1.19075	−	1.41908i	0.884126	−	0.467248i	$-0.154755\pi$
$884$	2.77348	+	2.32723i	0.0932822	+	0.0782730i
$885$	3.26197	+	1.74541i	0.109650	+	0.0586712i
$886$	10.8671	−	18.8224i	0.365087	−	0.632350i
$887$	7.64207	+	20.9964i	0.256595	+	0.704990i	0.999371	+	0.0354502i	$0.0112865\pi$
$887$	7.64207	+	20.9964i	0.256595	+	0.704990i	−0.742776	+	0.669540i	$0.766491\pi$
$888$	6.33794	−	1.11755i	0.212687	−	0.0375025i
$889$	2.48291	−	14.0813i	0.0832742	−	0.472272i
$890$	20.1906	−	4.23636i	0.676792	−	0.142003i
$891$	−2.75325	+	2.31025i	−0.0922375	+	0.0773964i
$892$		−	3.94894i		−	0.132220i
$893$	−0.411152	+	4.54106i	−0.0137587	+	0.151961i
$894$	9.04314			0.302448
$895$	3.77354	+	1.23704i	0.126135	+	0.0413498i
$896$	0.899224	+	0.327291i	0.0300410	+	0.0109340i
$897$	−5.16633	−	0.910963i	−0.172499	−	0.0304162i
$898$	26.0308	−	4.58993i	0.868659	−	0.153168i
$899$	−57.0120	+	20.7507i	−1.90146	+	0.692073i
$900$	−2.77419	−	4.15979i	−0.0924730	−	0.138660i
$901$	−5.73011	−	9.92484i	−0.190898	−	0.330644i
$902$	−9.63928	+	11.4876i	−0.320953	+	0.382497i
$903$	−5.85931	+	6.98285i	−0.194986	+	0.232375i
$904$	7.15332	+	12.3899i	0.237916	+	0.412082i
$905$	−42.8041	+	1.38241i	−1.42286	+	0.0459527i
$906$	10.9260	−	3.97674i	0.362992	−	0.132118i
$907$	23.5670	−	4.15550i	0.782531	−	0.137981i	0.231910	−	0.972737i	$-0.425502\pi$
$907$	23.5670	−	4.15550i	0.782531	−	0.137981i	0.550620	+	0.834756i	$0.314391\pi$
$908$	11.9568	+	2.10832i	0.396802	+	0.0699669i
$909$	1.09007	+	0.396753i	0.0361553	+	0.0131595i
$910$	−0.571402	+	1.74303i	−0.0189418	+	0.0577810i
$911$	−1.39188			−0.0461150			−0.0230575	−	0.999734i	$-0.507340\pi$
$911$	−1.39188			−0.0461150			−0.0230575	+	0.999734i	$0.507340\pi$
$912$	−0.393051	+	4.34114i	−0.0130152	+	0.143750i
$913$		−	28.8073i		−	0.953382i
$914$	20.8524	−	17.4973i	0.689738	−	0.578759i
$915$	28.6985	−	6.02147i	0.948744	−	0.199064i
$916$	2.10119	−	11.9164i	0.0694253	−	0.393730i
$917$	7.29059	−	1.28553i	0.240757	−	0.0424519i
$918$	1.44450	+	3.96874i	0.0476757	+	0.130988i
$919$	11.9283	−	20.6604i	0.393478	−	0.681524i	−0.599428	−	0.800429i	$-0.704605\pi$
$919$	11.9283	−	20.6604i	0.393478	−	0.681524i	0.992906	+	0.118905i	$0.0379384\pi$
$920$	−6.45589	+	12.0653i	−0.212844	+	0.397782i
$921$	−4.35090	−	3.65084i	−0.143367	−	0.120299i
$922$	−14.3878	+	17.1467i	−0.473836	+	0.564696i
$923$	9.82795	−	5.67417i	0.323491	−	0.186768i
$924$	1.71967	−	2.97855i	0.0565729	−	0.0979871i
$925$	31.9842	+	3.53133i	1.05163	+	0.116109i
$926$	2.38488	+	13.5253i	0.0783720	+	0.444470i
$927$	9.49356	+	1.67397i	0.311809	+	0.0549804i
$928$	−3.33623	+	9.16621i	−0.109517	+	0.300896i
$929$	−28.9048	+	24.2540i	−0.948336	+	0.795749i	−0.979017	−	0.203781i	$-0.934677\pi$
$929$	−28.9048	+	24.2540i	−0.948336	+	0.795749i	0.0306803	+	0.999529i	$0.490233\pi$
$930$	7.33911	+	11.8138i	0.240659	+	0.387391i
$931$	−24.0019	−	11.2809i	−0.786631	−	0.369716i
$932$			17.8491i			0.584668i
$933$	−8.28030	−	9.86808i	−0.271085	−	0.323066i
$934$	32.9182	+	11.9812i	1.07712	+	0.392038i
$935$	−12.6325	−	31.5042i	−0.413129	−	1.03030i
$936$	0.148859	+	0.844219i	0.00486560	+	0.0275942i
$937$	−4.28381	−	11.7697i	−0.139946	−	0.384498i	0.849844	−	0.527035i	$-0.176696\pi$
$937$	−4.28381	−	11.7697i	−0.139946	−	0.384498i	−0.989790	+	0.142537i	$0.954474\pi$
$938$	−8.95457	−	5.16992i	−0.292377	−	0.168804i
$939$	−8.51713	−	14.7521i	−0.277946	−	0.481416i
$940$	2.31542	+	0.331604i	0.0755207	+	0.0108157i
$941$	13.4082	+	11.2508i	0.437095	+	0.366766i	0.834621	−	0.550825i	$-0.185687\pi$
$941$	13.4082	+	11.2508i	0.437095	+	0.366766i	−0.397526	+	0.917591i	$0.630131\pi$
$942$	−6.37561	+	3.68096i	−0.207729	+	0.119932i
$943$	−22.1127	−	12.7668i	−0.720090	−	0.415744i
$944$	−1.55472	+	0.565874i	−0.0506020	+	0.0184176i
$945$	−1.59391	+	1.42761i	−0.0518498	+	0.0464402i
$946$	5.94510	−	33.7163i	0.193292	−	1.09621i
$947$	3.16942	−	8.70792i	0.102992	−	0.282969i	−0.877484	−	0.479606i	$-0.840780\pi$
$947$	3.16942	−	8.70792i	0.102992	−	0.282969i	0.980476	+	0.196637i	$0.0630019\pi$
$948$	6.70573	+	7.99158i	0.217792	+	0.259555i
$949$	0.393534			0.0127747
$950$	−7.97848	+	20.2816i	−0.258856	+	0.658022i
$951$	−28.7005			−0.930677
$952$	−2.59787	−	3.09602i	−0.0841973	−	0.100342i
$953$	−13.3052	+	36.5558i	−0.430998	+	1.18416i	0.514203	+	0.857668i	$0.328088\pi$
$953$	−13.3052	+	36.5558i	−0.430998	+	1.18416i	−0.945201	+	0.326489i	$0.894134\pi$
$954$	0.471190	−	2.67225i	0.0152553	−	0.0865173i
$955$	22.0121	−	19.7156i	0.712295	−	0.637980i
$956$	−14.2383	+	5.18230i	−0.460498	+	0.167608i
$957$	30.3617	+	17.5294i	0.981456	+	0.566644i
$958$	32.1343	−	18.5528i	1.03821	−	0.599412i
$959$	8.73050	+	7.32576i	0.281923	+	0.236561i
$960$	2.21348	+	0.317005i	0.0714399	+	0.0102313i
$961$	−3.84295	−	6.65618i	−0.123966	−	0.214715i
$962$	−4.77783	−	2.75848i	−0.154043	−	0.0889370i
$963$	5.79001	+	15.9079i	0.186581	+	0.512626i
$964$	1.71586	+	9.73114i	0.0552642	+	0.313419i
$965$	12.8975	+	32.1649i	0.415184	+	1.03542i
$966$	5.50294	+	2.00291i	0.177054	+	0.0644425i
$967$	−0.708454	−	0.844302i	−0.0227823	−	0.0271509i	0.754533	−	0.656262i	$-0.227863\pi$
$967$	−0.708454	−	0.844302i	−0.0227823	−	0.0271509i	−0.777315	+	0.629111i	$0.783419\pi$
$968$			1.91768i			0.0616365i
$969$	10.6049	−	15.0482i	0.340679	−	0.483418i
$970$	9.04155	+	14.5543i	0.290307	+	0.467310i
$971$	16.0142	−	13.4375i	0.513921	−	0.431231i	−0.348585	−	0.937277i	$-0.613338\pi$
$971$	16.0142	−	13.4375i	0.513921	−	0.431231i	0.862507	+	0.506046i	$0.168893\pi$
$972$	−0.342020	+	0.939693i	−0.0109703	+	0.0301407i
$973$	−4.33798	−	0.764903i	−0.139069	−	0.0245217i
$974$	−2.85116	−	16.1697i	−0.0913571	−	0.518112i
$975$	−0.470376	+	4.26032i	−0.0150641	+	0.136440i
$976$	−6.55692	+	11.3569i	−0.209882	+	0.363526i
$977$	22.3074	−	12.8792i	0.713677	−	0.412042i	−0.0987441	−	0.995113i	$-0.531483\pi$
$977$	22.3074	−	12.8792i	0.713677	−	0.412042i	0.812421	+	0.583071i	$0.198149\pi$
$978$	−9.40529	+	11.2088i	−0.300748	+	0.358418i
$979$	25.4019	+	21.3147i	0.811849	+	0.681222i
$980$	−6.41856	+	11.9956i	−0.205034	+	0.383185i
$981$	−7.18558	+	12.4458i	−0.229418	+	0.397364i
$982$	11.5987	+	31.8673i	0.370131	+	1.01693i
$983$	−47.4575	+	8.36804i	−1.51366	+	0.266899i	−0.867937	−	0.496674i	$-0.834555\pi$
$983$	−47.4575	+	8.36804i	−1.51366	+	0.266899i	−0.645722	+	0.763573i	$0.723444\pi$
$984$	−0.724528	+	4.10900i	−0.0230971	+	0.130990i
$985$	−7.93498	+	1.66490i	−0.252830	+	0.0530482i
$986$	31.5591	−	26.4813i	1.00505	−	0.843335i
$987$		−	1.00100i		−	0.0318623i
$988$	2.65019	−	2.63419i	0.0843137	−	0.0838046i
$989$	58.2940			1.85364
$990$	2.50350	−	7.63681i	0.0795666	−	0.242714i
$991$	−23.9057	−	8.70098i	−0.759391	−	0.276396i	−0.0668391	−	0.997764i	$-0.521291\pi$
$991$	−23.9057	−	8.70098i	−0.759391	−	0.276396i	−0.692552	+	0.721368i	$0.743514\pi$
$992$	−6.12531	−	1.08006i	−0.194479	−	0.0342918i
$993$	−10.3357	+	1.82246i	−0.327993	+	0.0578341i
$994$	−11.9041	+	4.33274i	−0.377575	+	0.137426i
$995$	35.2719	−	1.13914i	1.11819	−	0.0361133i
$996$	−4.00756	−	6.94130i	−0.126984	−	0.219943i
$997$	−16.9815	+	20.2378i	−0.537810	+	0.640937i	−0.964695	−	0.263369i	$-0.915166\pi$
$997$	−16.9815	+	20.2378i	−0.537810	+	0.640937i	0.426885	+	0.904306i	$0.359611\pi$
$998$	14.3871	−	17.1459i	0.455417	−	0.542745i
$999$	−3.21785	−	5.57349i	−0.101808	−	0.176337i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	570.2.bc.b.139.2	✓	60
5.4	even	2	inner	570.2.bc.b.139.10	yes	60
19.16	even	9	inner	570.2.bc.b.529.10	yes	60
95.54	even	18	inner	570.2.bc.b.529.2	yes	60

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
570.2.bc.b.139.2	✓	60	1.1	even	1	trivial
570.2.bc.b.139.10	yes	60	5.4	even	2	inner
570.2.bc.b.529.2	yes	60	95.54	even	18	inner
570.2.bc.b.529.10	yes	60	19.16	even	9	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)

\(f(q)\)	\(=\)	\(q+(-0.642788 - 0.766044i) q^{2} +(0.342020 - 0.939693i) q^{3} +(-0.173648 + 0.984808i) q^{4} +(-1.66564 + 1.49186i) q^{5} +(-0.939693 + 0.342020i) q^{6} +(-0.828729 - 0.478467i) q^{7} +(0.866025 - 0.500000i) q^{8} +(-0.766044 - 0.642788i) q^{9} +O(q^{10})\)	\(q+(-0.642788 - 0.766044i) q^{2} +(0.342020 - 0.939693i) q^{3} +(-0.173648 + 0.984808i) q^{4} +(-1.66564 + 1.49186i) q^{5} +(-0.939693 + 0.342020i) q^{6} +(-0.828729 - 0.478467i) q^{7} +(0.866025 - 0.500000i) q^{8} +(-0.766044 - 0.642788i) q^{9} +(2.21348 + 0.317005i) q^{10} +(1.79706 + 3.11260i) q^{11} +(0.866025 + 0.500000i) q^{12} +(-0.293194 - 0.805545i) q^{13} +(0.166170 + 0.942396i) q^{14} +(0.832208 + 2.07544i) q^{15} +(-0.939693 - 0.342020i) q^{16} +(2.71478 + 3.23535i) q^{17} +1.00000i q^{18} +(3.57816 - 2.48934i) q^{19} +(-1.17996 - 1.89939i) q^{20} +(-0.733054 + 0.615105i) q^{21} +(1.22926 - 3.37737i) q^{22} +(6.02668 + 1.06267i) q^{23} +(-0.173648 - 0.984808i) q^{24} +(0.548708 - 4.96980i) q^{25} +(-0.428621 + 0.742394i) q^{26} +(-0.866025 + 0.500000i) q^{27} +(0.615105 - 0.733054i) q^{28} +(7.47236 + 6.27006i) q^{29} +(1.05494 - 1.97157i) q^{30} +(-3.10990 + 5.38650i) q^{31} +(0.342020 + 0.939693i) q^{32} +(3.53951 - 0.624112i) q^{33} +(0.733394 - 4.15928i) q^{34} +(2.09417 - 0.439394i) q^{35} +(0.766044 - 0.642788i) q^{36} +6.43571i q^{37} +(-4.20694 - 1.14091i) q^{38} -0.857243 q^{39} +(-0.696556 + 2.12481i) q^{40} +(-3.92076 - 1.42704i) q^{41} +(0.942396 + 0.166170i) q^{42} +(9.38098 - 1.65412i) q^{43} +(-3.37737 + 1.22926i) q^{44} +(2.23490 - 0.0721787i) q^{45} +(-3.05983 - 5.29978i) q^{46} +(-0.672390 + 0.801323i) q^{47} +(-0.642788 + 0.766044i) q^{48} +(-3.04214 - 5.26914i) q^{49} +(-4.15979 + 2.77419i) q^{50} +(3.96874 - 1.44450i) q^{51} +(0.844219 - 0.148859i) q^{52} +(-2.67225 - 0.471190i) q^{53} +(0.939693 + 0.342020i) q^{54} +(-7.63681 - 2.50350i) q^{55} -0.956934 q^{56} +(-1.11541 - 4.21377i) q^{57} -9.75447i q^{58} +(1.26742 - 1.06349i) q^{59} +(-2.18842 + 0.459169i) q^{60} +(2.27719 - 12.9146i) q^{61} +(6.12531 - 1.08006i) q^{62} +(0.327291 + 0.899224i) q^{63} +(0.500000 - 0.866025i) q^{64} +(1.69012 + 0.904342i) q^{65} +(-2.75325 - 2.31025i) q^{66} +(-6.94544 + 8.27725i) q^{67} +(-3.65761 + 2.11172i) q^{68} +(3.05983 - 5.29978i) q^{69} +(-1.68270 - 1.32179i) q^{70} +(2.29879 + 13.0371i) q^{71} +(-0.984808 - 0.173648i) q^{72} +(-0.157011 + 0.431384i) q^{73} +(4.93004 - 4.13679i) q^{74} +(-4.48242 - 2.21539i) q^{75} +(1.83018 + 3.95606i) q^{76} -3.43933i q^{77} +(0.551025 + 0.656686i) q^{78} +(9.80313 + 3.56805i) q^{79} +(2.07544 - 0.832208i) q^{80} +(0.173648 + 0.984808i) q^{81} +(1.42704 + 3.92076i) q^{82} +(-6.94130 - 4.00756i) q^{83} +(-0.478467 - 0.828729i) q^{84} +(-9.34853 - 1.33885i) q^{85} +(-7.29711 - 6.12300i) q^{86} +(8.44762 - 4.87724i) q^{87} +(3.11260 + 1.79706i) q^{88} +(8.66974 - 3.15553i) q^{89} +(-1.49186 - 1.66564i) q^{90} +(-0.142448 + 0.807862i) q^{91} +(-2.09305 + 5.75059i) q^{92} +(3.99801 + 4.76464i) q^{93} +1.04605 q^{94} +(-2.24617 + 9.48445i) q^{95} +1.00000 q^{96} +(4.92542 + 5.86989i) q^{97} +(-2.08095 + 5.71735i) q^{98} +(0.624112 - 3.53951i) 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

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