LMFDB - Embedded newform 570.2.bc.b.139.10

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			139.10
Character	$\chi$	$=$	570.139
Dual form			570.2.bc.b.529.10

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.642788 + 0.766044i) q^{2} +(-0.342020 + 0.939693i) q^{3} +(-0.173648 + 0.984808i) q^{4} +(2.07544 + 0.832208i) q^{5} +(-0.939693 + 0.342020i) q^{6} +(0.828729 + 0.478467i) q^{7} +(-0.866025 + 0.500000i) q^{8} +(-0.766044 - 0.642788i) q^{9} +O(q^{10})$	\(q+(0.642788 + 0.766044i) q^{2} +(-0.342020 + 0.939693i) q^{3} +(-0.173648 + 0.984808i) q^{4} +(2.07544 + 0.832208i) 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} +(0.696556 + 2.12481i) 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} +(-1.49186 + 1.66564i) 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} +(3.61486 + 3.45439i) 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} +(-2.23490 - 0.0721787i) 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} +(1.32179 + 1.68270i) q^{35} +(0.766044 - 0.642788i) q^{36} -6.43571i q^{37} +(4.20694 + 1.14091i) q^{38} -0.857243 q^{39} +(-2.21348 + 0.317005i) 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} +(-1.05494 - 1.97157i) 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} +(-0.322625 + 4.98958i) 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} +(1.13935 + 7.95552i) q^{55} -0.956934 q^{56} +(1.11541 + 4.21377i) q^{57} +9.75447i q^{58} +(1.26742 - 1.06349i) q^{59} +(-1.38128 - 1.75843i) 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} +(-0.0618746 + 1.91585i) 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} +(-0.439394 + 2.09417i) 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} +(-1.66564 - 1.49186i) 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} +(-2.94187 - 8.97402i) 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} +(0.832208 - 2.07544i) q^{90} +(-0.142448 + 0.807862i) q^{91} +(2.09305 - 5.75059i) q^{92} +(-3.99801 - 4.76464i) q^{93} +1.04605 q^{94} +(9.49788 - 2.18869i) 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
$5$	2.07544	+	0.832208i	0.928163	+	0.372175i
$5$	2.07544	+	0.832208i	0.928163	+	0.372175i
$6$	−0.939693	+	0.342020i	−0.383628	+	0.139629i
$7$	0.828729	+	0.478467i	0.313230	+	0.180844i	0.648371	−	0.761325i	$-0.275451\pi$
$7$	0.828729	+	0.478467i	0.313230	+	0.180844i	−0.335141	+	0.942168i	$0.608784\pi$
$8$	−0.866025	+	0.500000i	−0.306186	+	0.176777i
$9$	−0.766044	−	0.642788i	−0.255348	−	0.214263i
$10$	0.696556	+	2.12481i	0.220270	+	0.671923i
$11$	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	0.973688	−	0.227886i	$-0.0731813\pi$
$13$	0.293194	+	0.805545i	0.0813174	+	0.223418i	−0.892370	+	0.451304i	$0.850959\pi$
$14$	0.166170	+	0.942396i	0.0444108	+	0.251866i
$15$	−1.49186	+	1.66564i	−0.385197	+	0.430066i
$16$	−0.939693	−	0.342020i	−0.234923	−	0.0855050i
$17$	−2.71478	−	3.23535i	−0.658431	−	0.784687i	0.328729	−	0.944424i	$-0.393380\pi$
$17$	−2.71478	−	3.23535i	−0.658431	−	0.784687i	−0.987160	+	0.159737i	$0.948935\pi$
$18$		−	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	−0.494612	−	0.869114i	$-0.664690\pi$
$23$	−6.02668	−	1.06267i	−1.25665	−	0.221581i	−0.762038	+	0.647532i	$0.775801\pi$
$24$	−0.173648	−	0.984808i	−0.0354458	−	0.201023i
$25$	3.61486	+	3.45439i	0.722972	+	0.690877i
$26$	−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	$0.361583\pi$
$30$	−2.23490	−	0.0721787i	−0.408036	−	0.0131780i
$31$	−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
$35$	1.32179	+	1.68270i	0.223423	+	0.284429i
$36$	0.766044	−	0.642788i	0.127674	−	0.107131i
$37$		−	6.43571i		−	1.05802i	−0.848614	−	0.529012i	$-0.822563\pi$
$37$		−	6.43571i		−	1.05802i	0.848614	−	0.529012i	$-0.177437\pi$
$38$	4.20694	+	1.14091i	0.682455	+	0.185080i
$39$	−0.857243			−0.137269
$40$	−2.21348	+	0.317005i	−0.349982	+	0.0501228i
$41$	−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	−0.834650	−	0.550781i	$-0.814330\pi$
$43$	−9.38098	+	1.65412i	−1.43059	+	0.252251i	−0.595936	+	0.803032i	$0.703219\pi$
$44$	−3.37737	+	1.22926i	−0.509157	+	0.185318i
$45$	−1.05494	−	1.97157i	−0.157262	−	0.293905i
$46$	−3.05983	−	5.29978i	−0.451147	−	0.781409i
$47$	0.672390	−	0.801323i	0.0980781	−	0.116885i	−0.714773	−	0.699357i	$-0.753470\pi$
$47$	0.672390	−	0.801323i	0.0980781	−	0.116885i	0.812851	+	0.582472i	$0.197914\pi$
$48$	0.642788	−	0.766044i	0.0927784	−	0.110569i
$49$	−3.04214	−	5.26914i	−0.434591	−	0.752734i
$50$	−0.322625	+	4.98958i	−0.0456260	+	0.705633i
$51$	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	0.354137	−	0.935194i	$-0.384775\pi$
$53$	2.67225	+	0.471190i	0.367062	+	0.0647229i	0.0129249	+	0.999916i	$0.495886\pi$
$54$	0.939693	+	0.342020i	0.127876	+	0.0465430i
$55$	1.13935	+	7.95552i	0.153630	+	1.07272i
$56$	−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	$0.243429\pi$
$60$	−1.38128	−	1.75843i	−0.178322	−	0.227012i
$61$	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
$65$	−0.0618746	+	1.91585i	−0.00767461	+	0.237632i
$66$	−2.75325	−	2.31025i	−0.338902	−	0.284373i
$67$	6.94544	−	8.27725i	0.848520	−	1.01123i	−0.151222	−	0.988500i	$-0.548321\pi$
$67$	6.94544	−	8.27725i	0.848520	−	1.01123i	0.999742	−	0.0227270i	$-0.00723484\pi$
$68$	3.65761	−	2.11172i	0.443551	−	0.256084i
$69$	3.05983	−	5.29978i	0.368360	−	0.638018i
$70$	−0.439394	+	2.09417i	−0.0525177	+	0.250301i
$71$	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	−0.930165	−	0.367142i	$-0.880336\pi$
$73$	0.157011	−	0.431384i	0.0183768	−	0.0504897i	0.948542	+	0.316652i	$0.102559\pi$
$74$	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	$0.411475\pi$
$80$	−1.66564	−	1.49186i	−0.186224	−	0.166795i
$81$	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	0.829980	−	0.557793i	$-0.188352\pi$
$83$	6.94130	+	4.00756i	0.761906	+	0.439887i	−0.0680734	+	0.997680i	$0.521685\pi$
$84$	−0.478467	−	0.828729i	−0.0522050	−	0.0904218i
$85$	−2.94187	−	8.97402i	−0.319090	−	0.973369i
$86$	−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	$0.226256\pi$
$90$	0.832208	−	2.07544i	0.0877224	−	0.218770i
$91$	−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
$95$	9.49788	−	2.18869i	0.974461	−	0.224555i
$96$	1.00000			0.102062
$97$	−4.92542	−	5.86989i	−0.500101	−	0.595997i	0.455656	−	0.890156i	$-0.349405\pi$
$97$	−4.92542	−	5.86989i	−0.500101	−	0.595997i	−0.955756	+	0.294159i	$0.904960\pi$
$98$	2.08095	−	5.71735i	0.210207	−	0.577540i
$99$	0.624112	−	3.53951i	0.0627256	−	0.355735i
$100$	−4.02962	+	2.96010i	−0.402962	+	0.296010i
$101$	−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	−0.0287111	−	0.999588i	$-0.509140\pi$
$103$	8.34850	−	4.82001i	0.822602	−	0.474929i	0.851313	+	0.524658i	$0.175807\pi$
$104$	−0.656686	−	0.551025i	−0.0643934	−	0.0540324i
$105$	−2.03330	+	0.666558i	−0.198430	+	0.0650494i
$106$	1.35674	+	2.34994i	0.131778	+	0.228246i
$107$	14.6608	+	8.46443i	1.41732	+	0.818287i	0.996062	−	0.0886558i	$-0.0282571\pi$
$107$	14.6608	+	8.46443i	1.41732	+	0.818287i	0.421253	+	0.906943i	$0.361590\pi$
$108$	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	$-0.297178\pi$
$110$	−5.36192	+	5.98650i	−0.511239	+	0.570791i
$111$	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	$-0.765037\pi$
$113$		−	14.3066i		−	1.34586i	0.739708	−	0.672928i	$-0.234963\pi$
$114$	−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
$120$	0.459169	−	2.18842i	0.0419162	−	0.199774i
$121$	−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
$125$	4.62764	+	10.1777i	0.413909	+	0.910318i
$126$	0.478467	−	0.828729i	0.0426252	−	0.0738291i
$127$	−5.11047	−	14.0409i	−0.453481	−	1.24593i	−0.930259	−	0.366905i	$-0.880417\pi$
$127$	−5.11047	−	14.0409i	−0.453481	−	1.24593i	0.476778	−	0.879024i	$-0.341805\pi$
$128$	0.984808	−	0.173648i	0.0870455	−	0.0153485i
$129$	1.65412	−	9.38098i	0.145637	−	0.825949i
$130$	−1.50740	+	1.18409i	−0.132208	+	0.103851i
$131$	−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
$135$	2.21348	−	0.317005i	0.190506	−	0.0272834i
$136$	3.96874	+	1.44450i	0.340317	+	0.123865i
$137$	11.7288	+	2.06811i	1.00206	+	0.176690i	0.650526	−	0.759484i	$-0.274549\pi$
$137$	11.7288	+	2.06811i	1.00206	+	0.176690i	0.351535	+	0.936175i	$0.385660\pi$
$138$	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	$0.326348\pi$
$140$	−1.88666	+	1.00951i	−0.159452	+	0.0853192i
$141$	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
$145$	10.2904	+	19.2316i	0.854572	+	1.59710i
$146$	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	$0.731898\pi$
$150$	−4.57833	−	2.00971i	−0.373819	−	0.164092i
$151$	−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
$155$	−10.9371	+	8.59126i	−0.878488	+	0.690066i
$156$	0.148859	−	0.844219i	0.0119182	−	0.0675916i
$157$	−7.25008	+	1.27838i	−0.578619	+	0.102026i	−0.455296	−	0.890340i	$-0.650466\pi$
$157$	−7.25008	+	1.27838i	−0.578619	+	0.102026i	−0.123324	+	0.992366i	$0.539355\pi$
$158$	3.56805	+	9.80313i	0.283859	+	0.779895i
$159$	−1.35674	+	2.34994i	−0.107596	+	0.186362i
$160$	0.0721787	−	2.23490i	0.00570623	−	0.176685i
$161$	−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	−0.906028	−	0.423217i	$-0.860901\pi$
$163$	−12.6717	+	7.31602i	−0.992525	+	0.573035i	−0.0864972	+	0.996252i	$0.527567\pi$
$164$	2.08620	−	3.61340i	0.162904	−	0.282159i
$165$	−7.86542	−	1.65031i	−0.612322	−	0.128476i
$166$	1.39181	+	7.89335i	0.108025	+	0.612643i
$167$	0.575171	+	0.101418i	0.0445081	+	0.00784797i	0.195858	−	0.980632i	$-0.437251\pi$
$167$	0.575171	+	0.101418i	0.0445081	+	0.00784797i	−0.151350	+	0.988480i	$0.548362\pi$
$168$	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	0.522784	−	0.852465i	$-0.324894\pi$
$173$	−5.35997	−	6.38777i	−0.407511	−	0.485653i	−0.930295	+	0.366812i	$0.880449\pi$
$174$	−9.16621	−	3.33623i	−0.694888	−	0.252919i
$175$	1.34293	+	4.59234i	0.101516	+	0.347148i
$176$	−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	$0.854475\pi$
$180$	2.12481	−	0.696556i	0.158374	−	0.0519182i
$181$	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
$185$	5.35585	−	13.3569i	0.393770	−	0.982018i
$186$	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
$190$	7.78175	+	5.86893i	0.564548	+	0.425777i
$191$	−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	$0.299459\pi$
$193$	−5.30060	+	14.5633i	−0.381545	+	1.04829i	−0.970706	+	0.240271i	$0.922764\pi$
$194$	1.33060	−	7.54618i	0.0955312	−	0.541784i
$195$	−1.77915	−	0.713404i	−0.127408	−	0.0510879i
$196$	5.71735	−	2.08095i	0.408382	−	0.148639i
$197$	−3.14012	−	1.81295i	−0.223725	−	0.129167i	0.383949	−	0.923354i	$-0.374564\pi$
$197$	−3.14012	−	1.81295i	−0.223725	−	0.129167i	−0.607674	+	0.794187i	$0.707897\pi$
$198$	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	$0.911186\pi$
$200$	−4.85775	−	1.18415i	−0.343495	−	0.0837324i
$201$	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
$205$	−6.94970	−	6.22462i	−0.485388	−	0.434746i
$206$	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
$215$	−20.8462	−	4.37390i	−1.42170	−	0.298298i
$216$	−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
$220$	−8.03250	−	0.259419i	−0.541551	−	0.0174900i
$221$	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	−0.0419121	−	0.999121i	$-0.513345\pi$
$223$	3.88894	−	0.685726i	0.260423	−	0.0459196i	0.302335	+	0.953202i	$0.402234\pi$
$224$	0.166170	−	0.942396i	0.0111027	−	0.0629665i
$225$	−0.548708	−	4.96980i	−0.0365806	−	0.331320i
$226$	10.9595	−	9.19613i	0.729016	−	0.611717i
$227$			12.1413i			0.805847i	0.915234	+	0.402923i	$0.132006\pi$
$227$			12.1413i			0.805847i	−0.915234	+	0.402923i	$0.867994\pi$
$228$	−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	$0.630922\pi$
$230$	−1.93996	−	13.5458i	−0.127917	−	0.893181i
$231$	−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	−0.716662	−	0.697421i	$-0.754331\pi$
$233$	−17.5780	+	3.09947i	−1.15157	+	0.203053i	−0.434910	+	0.900474i	$0.643220\pi$
$234$	0.805545	−	0.293194i	0.0526601	−	0.0191667i
$235$	2.06237	−	1.10353i	0.134534	−	0.0719861i
$236$	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	$0.670311\pi$
$240$	1.97157	−	1.05494i	0.127264	−	0.0680963i
$241$	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
$245$	−1.92874	−	13.4674i	−0.123223	−	0.860404i
$246$	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
$250$	−4.82195	+	10.0871i	−0.304967	+	0.637962i
$251$	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
$255$	9.43900	+	0.304843i	0.591093	+	0.0190900i
$256$	0.766044	+	0.642788i	0.0478778	+	0.0401742i
$257$	−9.96799	+	11.8794i	−0.621786	+	0.741016i	−0.981376	−	0.192094i	$-0.938472\pi$
$257$	−9.96799	+	11.8794i	−0.621786	+	0.741016i	0.359590	+	0.933110i	$0.382916\pi$
$258$	8.24950	−	4.76285i	0.513591	−	0.296522i
$259$	3.07927	−	5.33346i	0.191337	−	0.331405i
$260$	−1.87600	−	0.393619i	−0.116345	−	0.0244112i
$261$	−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	$0.223504\pi$
$263$	−3.83608	+	10.5395i	−0.236543	+	0.649896i	−0.999992	+	0.00402808i	$0.998718\pi$
$264$	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	$0.677196\pi$
$270$	1.66564	+	1.49186i	0.101368	+	0.0907917i
$271$	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
$275$	−4.25599	+	17.4593i	−0.256646	+	1.05284i
$276$	4.68793	+	3.93364i	0.282180	+	0.236777i
$277$	2.21763	−	1.28035i	0.133245	−	0.0769288i	−0.431896	−	0.901923i	$-0.642155\pi$
$277$	2.21763	−	1.28035i	0.133245	−	0.0769288i	0.565141	+	0.824995i	$0.308822\pi$
$278$	3.98643	+	2.30157i	0.239090	+	0.138039i
$279$	5.84470	−	2.12730i	0.349913	−	0.127358i
$280$	−1.98605	−	0.796368i	−0.118689	−	0.0475921i
$281$	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	0.778177	−	0.628045i	$-0.216145\pi$
$283$	0.412909	+	0.492086i	0.0245449	+	0.0292515i	−0.753632	+	0.657296i	$0.771700\pi$
$284$	−13.2382			−0.785542
$285$	−1.19177	+	9.67366i	−0.0705943	+	0.573018i
$286$	−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
$290$	−8.11775	+	20.2448i	−0.476691	+	1.18881i
$291$	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	−0.444373	−	0.895842i	$-0.646574\pi$
$293$	1.87026	−	1.07979i	0.109262	−	0.0630823i	0.553635	+	0.832759i	$0.313240\pi$
$294$	4.66083	+	3.91090i	0.271825	+	0.228088i
$295$	3.51550	−	1.15245i	0.204680	−	0.0670985i
$296$	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
$300$	−1.40337	−	4.79902i	−0.0810235	−	0.277071i
$301$	−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	−0.982702	−	0.185194i	$-0.940709\pi$
$307$	−1.94257	+	5.33717i	−0.110868	+	0.304608i	0.871834	+	0.489802i	$0.162931\pi$
$308$	−3.38708	−	0.597234i	−0.192997	−	0.0340306i
$309$	1.67397	+	9.49356i	0.0952289	+	0.540070i
$310$	−13.6115	−	2.85594i	−0.773082	−	0.162206i
$311$	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	−0.980880	−	0.194612i	$-0.937655\pi$
$313$	−10.9494	+	13.0490i	−0.618897	+	0.737573i	0.361983	+	0.932185i	$0.382100\pi$
$314$	−5.63956	−	4.73215i	−0.318259	−	0.267051i
$315$	0.0690702	−	2.13865i	0.00389167	−	0.120500i
$316$	−5.21614	+	9.03461i	−0.293431	+	0.508237i
$317$	9.81615	+	26.9696i	0.551330	+	1.51477i	0.831896	+	0.554931i	$0.187256\pi$
$317$	9.81615	+	26.9696i	0.551330	+	1.51477i	−0.280566	+	0.959835i	$0.590522\pi$
$318$	−2.67225	+	0.471190i	−0.149852	+	0.0264230i
$319$	−6.08788	+	34.5261i	−0.340856	+	1.93309i
$320$	1.75843	−	1.38128i	0.0982992	−	0.0772157i
$321$	−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
$325$	−1.72280	+	3.92474i	−0.0955640	+	0.217705i
$326$	−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
$330$	−3.79159	−	7.08606i	−0.208720	−	0.390075i
$331$	−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
$335$	21.3032	−	11.3988i	1.16392	−	0.622786i
$336$	0.899224	−	0.327291i	0.0490567	−	0.0178552i
$337$	−11.9959	+	2.11520i	−0.653459	+	0.115223i	−0.490542	−	0.871417i	$-0.663201\pi$
$337$	−11.9959	+	2.11520i	−0.653459	+	0.115223i	−0.162917	+	0.986640i	$0.552090\pi$
$338$	12.0788	+	2.12982i	0.657000	+	0.115847i
$339$	13.4438	+	4.89316i	0.730169	+	0.265760i
$340$	9.34853	−	1.33885i	0.506995	−	0.0726095i
$341$	−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
$345$	10.7610	−	8.45293i	0.579352	−	0.455090i
$346$	1.44799	−	8.21196i	0.0778444	−	0.441477i
$347$	−28.1835	+	4.96951i	−1.51297	+	0.266777i	−0.867666	−	0.497148i	$-0.834381\pi$
$347$	−28.1835	+	4.96951i	−1.51297	+	0.266777i	−0.645304	+	0.763926i	$0.723269\pi$
$348$	−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	$0.125769\pi$
$350$	−2.65472	+	3.98065i	−0.141901	+	0.212774i
$351$	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	−0.992294	−	0.123903i	$-0.960459\pi$
$353$	−25.9492	+	14.9818i	−1.38114	+	0.797401i	−0.388844	+	0.921303i	$0.627126\pi$
$354$	−0.827252	+	1.43284i	−0.0439679	+	0.0761547i
$355$	−6.07856	+	28.9707i	−0.322617	+	1.53760i
$356$	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
$365$	0.684867	−	0.764644i	0.0358476	−	0.0400233i
$366$	2.27719	+	12.9146i	0.119031	+	0.675058i
$367$	−6.84841	−	18.8159i	−0.357484	−	0.982180i	−0.979899	−	0.199492i	$-0.936071\pi$
$367$	−6.84841	−	18.8159i	−0.357484	−	0.982180i	0.622415	−	0.782687i	$-0.286152\pi$
$368$	5.29978	+	3.05983i	0.276270	+	0.159505i
$369$	2.08620	+	3.61340i	0.108603	+	0.188106i
$370$	13.6746	−	4.48283i	0.710911	−	0.233051i
$371$	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	0.971001	−	0.239076i	$-0.0768446\pi$
$373$	24.1310	+	13.9320i	1.24946	+	0.721373i	0.278454	+	0.960449i	$0.410178\pi$
$374$	14.2641	−	5.19172i	0.737580	−	0.268457i
$375$	−11.1466	+	0.867596i	−0.575609	+	0.0448025i
$376$	−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	$0.614458\pi$
$380$	0.506150	+	9.73364i	0.0259649	+	0.499325i
$381$	14.9420			0.765503
$382$	−8.49471	−	10.1236i	−0.434627	−	0.517968i
$383$	−0.636953	+	1.75001i	−0.0325468	+	0.0894216i	−0.954902	−	0.296922i	$-0.904040\pi$
$383$	−0.636953	+	1.75001i	−0.0325468	+	0.0894216i	0.922355	+	0.386344i	$0.126262\pi$
$384$	−0.173648	+	0.984808i	−0.00886145	+	0.0502558i
$385$	−2.86224	+	7.13811i	−0.145873	+	0.363792i
$386$	−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	$0.975417\pi$
$390$	−0.597117	−	1.82148i	−0.0302362	−	0.0922340i
$391$	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
$395$	17.3764	+	15.5635i	0.874302	+	0.783084i
$396$	3.37737	+	1.22926i	0.169719	+	0.0617727i
$397$	24.2135	+	28.8565i	1.21524	+	1.44826i	0.857532	+	0.514430i	$0.171997\pi$
$397$	24.2135	+	28.8565i	1.21524	+	1.44826i	0.357706	+	0.933834i	$0.383559\pi$
$398$		−	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
$405$	−0.459169	+	2.18842i	−0.0228163	+	0.108743i
$406$	−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	$0.820272\pi$
$410$	0.301158	−	9.32489i	0.0148731	−	0.460523i
$411$	−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
$415$	11.0711	+	14.0940i	0.543458	+	0.691849i
$416$	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	$0.550151\pi$
$420$	−0.303353	−	2.11816i	−0.0148021	−	0.103355i
$421$	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
$425$	1.36259	−	21.0732i	0.0660953	−	1.02220i
$426$	−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
$430$	−10.0491	−	18.7806i	−0.484609	−	0.905681i
$431$	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	0.746273	−	0.665640i	$-0.231841\pi$
$433$	25.3840	+	4.47589i	1.21988	+	0.215097i	0.473605	+	0.880737i	$0.342952\pi$
$434$	−5.59299	−	2.03568i	−0.268472	−	0.0977159i
$435$	−21.5914	+	3.09221i	−1.03523	+	0.148260i
$436$	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	$0.108028\pi$
$440$	−4.96447	−	6.32000i	−0.236672	−	0.301294i
$441$	−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	$-0.938416\pi$
$443$	−7.43353	−	20.4235i	−0.353178	−	0.970348i	0.628165	−	0.778080i	$-0.283806\pi$
$444$	−3.21785	+	5.57349i	−0.152713	+	0.264506i
$445$	20.6195	+	0.665931i	0.977460	+	0.0315682i
$446$	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	$0.952291\pi$
$450$	3.45439	−	3.61486i	0.162841	−	0.170406i
$451$	−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	$-0.780311\pi$
$457$		−	27.2209i		−	1.27334i	0.771136	−	0.636671i	$-0.219689\pi$
$458$	−7.77791	−	9.26935i	−0.363438	−	0.433128i
$459$	−3.96874	−	1.44450i	−0.185245	−	0.0674237i
$460$	9.12967	−	10.1931i	0.425673	−	0.475257i
$461$	−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	0.750234	−	0.661172i	$-0.229941\pi$
$463$	11.8940	+	6.86699i	0.552760	+	0.319136i	−0.197475	+	0.980308i	$0.563274\pi$
$464$	−4.87724	−	8.44762i	−0.226420	−	0.392171i
$465$	−4.33244	−	13.2159i	−0.200912	−	0.612872i
$466$	−13.6732	−	11.4732i	−0.633400	−	0.531486i
$467$	30.3376	−	17.5154i	1.40385	−	0.810516i	0.409069	−	0.912503i	$-0.365854\pi$
$467$	30.3376	−	17.5154i	1.40385	−	0.810516i	0.994786	+	0.101988i	$0.0325202\pi$
$468$	0.742394	+	0.428621i	0.0343172	+	0.0198130i
$469$	9.71628	−	3.53644i	0.448656	−	0.163297i
$470$	2.17101	+	0.870533i	0.100141	+	0.0401547i
$471$	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
$475$	21.5337	+	3.36172i	0.988032	+	0.154246i
$476$	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	$0.733544\pi$
$480$	2.07544	+	0.832208i	0.0947302	+	0.0379849i
$481$	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
$485$	−5.33742	−	16.2815i	−0.242360	−	0.739307i
$486$	−0.500000	−	0.866025i	−0.0226805	−	0.0392837i
$487$	−14.2194	−	8.20959i	−0.644344	−	0.372012i	0.141942	−	0.989875i	$-0.454665\pi$
$487$	−14.2194	−	8.20959i	−0.644344	−	0.372012i	−0.786286	+	0.617863i	$0.787999\pi$
$488$	4.48520	+	12.3230i	0.203035	+	0.557835i
$489$	−2.54083	−	14.4097i	−0.114900	−	0.651631i
$490$	9.07689	−	10.1342i	0.410052	−	0.457817i
$491$	−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	$0.777415\pi$
$500$	−10.8266	+	2.79001i	−0.484182	+	0.124773i
$501$	−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	−0.356545	−	0.934278i	$-0.616045\pi$
$503$	14.0274	−	16.7173i	0.625453	−	0.745386i	0.981998	+	0.188892i	$0.0604898\pi$
$504$	0.733054	+	0.615105i	0.0326528	+	0.0273990i
$505$	−2.59255	−	0.0837292i	−0.115367	−	0.00372590i
$506$	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	$0.824362\pi$
$510$	5.83375	+	7.42664i	0.258323	+	0.328857i
$511$	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
$515$	21.3380	−	3.05593i	0.940265	−	0.134660i
$516$	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
$520$	−0.904342	−	1.69012i	−0.0396580	−	0.0741165i
$521$	−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	$0.484849\pi$
$523$	−21.5971	+	25.7384i	−0.944375	+	1.12546i	−0.991955	+	0.126594i	$0.959595\pi$
$524$	−3.86811	−	6.69977i	−0.168979	−	0.292681i
$525$	−4.77470	−	0.308731i	−0.208385	−	0.0134741i
$526$	−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
$530$	0.860184	+	6.00623i	0.0373640	+	0.260894i
$531$	−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
$535$	23.3834	+	29.7682i	1.01095	+	1.28699i
$536$	−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
$540$	−0.0721787	+	2.23490i	−0.00310608	+	0.0961749i
$541$	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
$545$	6.59879	−	31.4501i	0.282661	−	1.34717i
$546$	−0.142448	−	0.807862i	−0.00609621	−	0.0345733i
$547$	−23.1807	−	4.08738i	−0.991136	−	0.174764i	−0.345508	−	0.938416i	$-0.612293\pi$
$547$	−23.1807	−	4.08738i	−0.991136	−	0.174764i	−0.645628	+	0.763652i	$0.723404\pi$
$548$	−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
$555$	10.7196	+	9.60118i	0.455020	+	0.407547i
$556$	0.799326	+	4.53320i	0.0338990	+	0.192251i
$557$	−11.8539	−	32.5682i	−0.502264	−	1.37996i	−0.889059	−	0.457793i	$-0.848640\pi$
$557$	−11.8539	−	32.5682i	−0.502264	−	1.37996i	0.386795	−	0.922166i	$-0.373582\pi$
$558$	5.38650	+	3.10990i	0.228029	+	0.131653i
$559$	−4.08292	−	7.07182i	−0.172689	−	0.299106i
$560$	−0.666558	−	2.03330i	−0.0281672	−	0.0859227i
$561$	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	0.350899	−	0.936413i	$-0.385876\pi$
$563$	−6.75311	−	3.89891i	−0.284610	−	0.164319i	−0.635508	+	0.772094i	$0.719209\pi$
$564$	−0.982968	+	0.357771i	−0.0413904	+	0.0150649i
$565$	11.9061	−	29.6925i	0.500893	−	1.24917i
$566$	−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	$0.664860\pi$
$570$	−8.17651	+	5.30516i	−0.342476	+	0.222209i
$571$	−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
$575$	−18.1148	−	24.6599i	−0.755438	−	1.02839i
$576$	−0.939693	+	0.342020i	−0.0391539	+	0.0142508i
$577$	25.4072	+	14.6688i	1.05771	+	0.610671i	0.924799	−	0.380456i	$-0.124233\pi$
$577$	25.4072	+	14.6688i	1.05771	+	0.610671i	0.132915	+	0.991127i	$0.457566\pi$
$578$	−0.725307	+	0.418756i	−0.0301688	+	0.0174180i
$579$	−11.8721	−	9.96186i	−0.493387	−	0.414001i
$580$	−20.7264	+	6.79454i	−0.860616	+	0.282128i
$581$	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
$585$	1.27889	−	1.42786i	0.0528754	−	0.0590346i
$586$	2.02935	+	0.738623i	0.0838317	+	0.0305122i
$587$	−0.144491	−	0.172198i	−0.00596380	−	0.00710738i	0.763054	−	0.646334i	$-0.223699\pi$
$587$	−0.144491	−	0.172198i	−0.00596380	−	0.00710738i	−0.769018	+	0.639227i	$0.779254\pi$
$588$			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	0.789664	−	0.613539i	$-0.210255\pi$
$593$	32.1895	+	5.67587i	1.32186	+	0.233080i	0.532199	+	0.846619i	$0.321366\pi$
$594$	0.624112	+	3.53951i	0.0256076	+	0.145228i
$595$	1.85576	−	8.84462i	0.0760787	−	0.362594i
$596$	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	$0.446690\pi$
$600$	2.77419	−	4.15979i	0.113256	−	0.169823i
$601$	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
$605$	−3.37210	+	2.64884i	−0.137095	+	0.107691i
$606$	0.888632	−	0.745651i	0.0360982	−	0.0302900i
$607$		−	48.0175i		−	1.94897i	−0.224454	−	0.974485i	$-0.572060\pi$
$607$		−	48.0175i		−	1.94897i	0.224454	−	0.974485i	$-0.427940\pi$
$608$	−3.56301	−	2.51096i	−0.144499	−	0.101833i
$609$	−9.33439			−0.378249
$610$	29.0273	−	4.15715i	1.17528	−	0.168318i
$611$	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	−0.0216304	−	0.999766i	$-0.506886\pi$
$613$	7.42725	−	1.30962i	0.299984	−	0.0528952i	0.321614	+	0.946871i	$0.395775\pi$
$614$	−5.33717	+	1.94257i	−0.215391	+	0.0783957i
$615$	8.22617	−	4.40163i	0.331711	−	0.177491i
$616$	−1.71967	−	2.97855i	−0.0692873	−	0.120009i
$617$	1.17874	−	1.40477i	0.0474544	−	0.0565539i	−0.741795	−	0.670627i	$-0.766025\pi$
$617$	1.17874	−	1.40477i	0.0474544	−	0.0565539i	0.789250	+	0.614073i	$0.210470\pi$
$618$	−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	$0.974265\pi$
$620$	−6.56153	−	12.2628i	−0.263517	−	0.492485i
$621$	−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
$625$	1.13444	+	24.9742i	0.0453777	+	0.998970i
$626$	−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
$630$	1.68270	−	1.32179i	0.0670404	−	0.0526614i
$631$	−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
$635$	1.07850	−	33.3940i	0.0427988	−	1.32520i
$636$	−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
$640$	2.18842	+	0.459169i	0.0865047	+	0.0181502i
$641$	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	−0.901430	−	0.432924i	$-0.857482\pi$
$643$	1.70868	−	4.69457i	0.0673839	−	0.185136i	0.968814	+	0.247789i	$0.0797039\pi$
$644$	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	$-0.974606\pi$
$647$		−	4.05424i		−	0.159389i	0.996819	−	0.0796944i	$-0.0253944\pi$
$648$	−0.642788	−	0.766044i	−0.0252511	−	0.0300931i
$649$	5.58786	+	2.03382i	0.219343	+	0.0798342i
$650$	−4.11392	+	1.20303i	−0.161361	+	0.0471866i
$651$	−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	0.631475	−	0.775397i	$-0.282450\pi$
$653$	7.04516	+	4.06753i	0.275699	+	0.159175i	−0.355776	+	0.934571i	$0.615783\pi$
$654$	7.18558	+	12.4458i	0.280978	+	0.486669i
$655$	−16.4380	+	5.38872i	−0.642286	+	0.210555i
$656$	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	$0.523844\pi$
$660$	2.99105	−	7.45936i	0.116427	−	0.290355i
$661$	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
$665$	8.91838	+	2.73059i	0.345840	+	0.105888i
$666$	−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
$670$	22.4255	+	8.99215i	0.866371	+	0.347397i
$671$	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	$0.700045\pi$
$673$	−41.0512	+	23.7009i	−1.58241	+	0.913604i	−0.994507	+	0.104671i	$0.966621\pi$
$674$	−9.33117	−	7.82978i	−0.359423	−	0.301592i
$675$	4.85775	+	1.18415i	0.186975	+	0.0455781i
$676$	6.13257	+	10.6219i	0.235868	+	0.408535i
$677$	11.3954	+	6.57915i	0.437961	+	0.252857i	0.702733	−	0.711454i	$-0.251963\pi$
$677$	11.3954	+	6.57915i	0.437961	+	0.252857i	−0.264771	+	0.964311i	$0.585296\pi$
$678$	4.89316	+	13.4438i	0.187921	+	0.516308i
$679$	−1.27329	−	7.22120i	−0.0488645	−	0.277124i
$680$	7.03474	+	6.30079i	0.269770	+	0.241624i
$681$	−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	$0.213597\pi$
$683$			32.5004i			1.24359i	−0.783179	+	0.621797i	$0.786403\pi$
$684$	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
$690$	13.3923	+	2.80996i	0.509838	+	0.106973i
$691$	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
$695$	10.2876	+	0.332248i	0.390230	+	0.0126029i
$696$	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
$700$	−4.75577	+	0.525078i	−0.179751	+	0.0198461i
$701$	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
$705$	0.331604	+	2.31542i	0.0124889	+	0.0872038i
$706$	−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	$0.530377\pi$
$710$	−26.1000	+	13.9655i	−0.979517	+	0.524117i
$711$	−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
$715$	−6.07447	+	3.25031i	−0.227172	+	0.121555i
$716$	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	$0.904697\pi$
$720$	0.317005	+	2.21348i	0.0118141	+	0.0824916i
$721$	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
$725$	5.35236	+	48.4778i	0.198782	+	1.80042i
$726$	0.333001	−	1.88854i	0.0123588	−	0.0700904i
$727$	−35.8982	+	6.32982i	−1.33139	+	0.234760i	−0.793662	−	0.608358i	$-0.791828\pi$
$727$	−35.8982	+	6.32982i	−1.33139	+	0.234760i	−0.537728	+	0.843119i	$0.680717\pi$
$728$	−0.280568	−	0.770853i	−0.0103985	−	0.0285697i
$729$	0.500000	−	0.866025i	0.0185185	−	0.0320750i
$730$	1.02598	+	0.0331350i	0.0379731	+	0.00122638i
$731$	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	−0.537445	−	0.843299i	$-0.680611\pi$
$733$	−2.05356	+	1.18562i	−0.0758500	+	0.0437920i	0.461595	+	0.887091i	$0.347277\pi$
$734$	10.0117	−	17.3408i	0.369539	−	0.640060i
$735$	13.3149	+	2.79371i	0.491129	+	0.103048i
$736$	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	0.951911	−	0.306375i	$-0.0991162\pi$
$743$	13.2172	+	15.7517i	0.484893	+	0.577873i	−0.467018	+	0.884248i	$0.654672\pi$
$744$	5.84470	+	2.12730i	0.214277	+	0.0779905i
$745$	−15.0626	−	13.4911i	−0.551852	−	0.494276i
$746$	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
$750$	−7.82953	−	7.98113i	−0.285894	−	0.291430i
$751$	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
$755$	−24.1315	−	9.67625i	−0.878236	−	0.352155i
$756$	−0.166170	+	0.942396i	−0.00604354	+	0.0342746i
$757$	−6.99034	+	19.2058i	−0.254068	+	0.698047i	0.745436	+	0.666577i	$0.232241\pi$
$757$	−6.99034	+	19.2058i	−0.254068	+	0.698047i	−0.999505	+	0.0314702i	$0.989981\pi$
$758$	−8.80674	−	10.4955i	−0.319875	−	0.381212i
$759$	21.9948			0.798359
$760$	−7.13106	+	6.64440i	−0.258671	+	0.241018i
$761$	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
$765$	−3.51479	+	8.76549i	−0.127077	+	0.316917i
$766$	−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	$0.475361\pi$
$770$	−7.30792	+	2.39569i	−0.263359	+	0.0863346i
$771$	−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	0.994258	−	0.107014i	$-0.0341289\pi$
$773$	4.55481	+	12.5142i	0.163825	+	0.450105i	−0.830433	+	0.557119i	$0.811907\pi$
$774$	1.65412	+	9.38098i	0.0594561	+	0.337192i
$775$	−29.8489	+	8.72867i	−1.07220	+	0.313543i
$776$	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
$785$	−16.1110	−	3.38037i	−0.575025	−	0.120650i
$786$	3.86811	−	6.69977i	0.137971	−	0.238973i
$787$	−0.957295	+	0.552694i	−0.0341239	+	0.0197014i	−0.516965	−	0.856007i	$-0.672938\pi$
$787$	−0.957295	+	0.552694i	−0.0341239	+	0.0197014i	0.482841	+	0.875708i	$0.339605\pi$
$788$	2.33069	−	2.77760i	0.0830272	−	0.0989480i
$789$	−8.59192	−	7.20947i	−0.305880	−	0.256664i
$790$	−0.752988	+	23.3151i	−0.0267901	+	0.829514i
$791$	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
$795$	−4.77146	+	3.74806i	−0.169226	+	0.132930i
$796$	12.0899	−	10.1447i	0.428516	−	0.359568i
$797$			14.0789i			0.498700i	0.968413	+	0.249350i	$0.0802170\pi$
$797$			14.0789i			0.498700i	−0.968413	+	0.249350i	$0.919783\pi$
$798$	−3.78569	+	1.75136i	−0.134012	+	0.0619975i
$799$	−4.41795			−0.156296
$800$	2.00971	−	4.57833i	0.0710538	−	0.161868i
$801$	−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
$805$	−6.17786	−	11.5457i	−0.217741	−	0.406934i
$806$	−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	$0.958970\pi$
$810$	−1.97157	+	1.05494i	−0.0692740	+	0.0370669i
$811$	−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
$815$	−32.3878	+	4.63842i	−1.13449	+	0.162477i
$816$	−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
$820$	7.33686	−	5.76322i	0.256214	−	0.201260i
$821$	−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	0.999829	−	0.0184974i	$-0.00588825\pi$
$823$	6.36947	+	17.5000i	0.222026	+	0.610010i	−0.777803	+	0.628508i	$0.783666\pi$
$824$	−4.82001	+	8.34850i	−0.167913	+	0.290834i
$825$	−14.9508	−	9.97077i	−0.520519	−	0.347138i
$826$	1.21284	+	1.01769i	0.0422001	+	0.0354101i
$827$	21.8779	−	26.0731i	0.760770	−	0.906651i	−0.237126	−	0.971479i	$-0.576205\pi$
$827$	21.8779	−	26.0731i	0.760770	−	0.906651i	0.997896	+	0.0648281i	$0.0206499\pi$
$828$	−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	$0.0590410\pi$
$830$	−3.68029	+	17.5404i	−0.127745	+	0.608837i
$831$	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	$0.347038\pi$
$840$	1.42761	−	1.59391i	0.0492573	−	0.0549950i
$841$	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
$845$	26.0611	−	8.54335i	0.896528	−	0.293900i
$846$	−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
$850$	17.0189	−	12.5018i	0.583743	−	0.428809i
$851$	−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	$0.00379247\pi$
$853$	24.4755	+	29.1688i	0.838026	+	0.998721i	−0.161903	+	0.986807i	$0.551763\pi$
$854$	12.5491			0.429421
$855$	−8.68266	−	4.42848i	−0.296941	−	0.151451i
$856$	−16.9289			−0.578617
$857$	−21.7554	−	25.9271i	−0.743150	−	0.885652i	0.253508	−	0.967333i	$-0.418415\pi$
$857$	−21.7554	−	25.9271i	−0.743150	−	0.885652i	−0.996658	+	0.0816813i	$0.973971\pi$
$858$	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	$0.879954\pi$
$860$	7.92736	−	19.7700i	0.270321	−	0.674150i
$861$	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	−0.758883	−	0.651227i	$-0.774255\pi$
$863$	−16.8725	+	9.74133i	−0.574346	+	0.331599i	0.184538	+	0.982825i	$0.440921\pi$
$864$	−0.766044	−	0.642788i	−0.0260614	−	0.0218681i
$865$	−5.80833	−	17.7180i	−0.197489	−	0.602430i
$866$	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
$870$	−16.2474	−	14.5523i	−0.550840	−	0.493369i
$871$	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	−0.977565	−	0.210632i	$-0.932448\pi$
$877$	−2.76345	+	7.59251i	−0.0933150	+	0.256381i	0.884250	+	0.467013i	$0.154670\pi$
$878$	20.9793	+	3.69921i	0.708015	+	0.124842i
$879$	0.375009	+	2.12678i	0.0126487	+	0.0717345i
$880$	1.65031	−	7.86542i	0.0556318	−	0.265143i
$881$	−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	$0.599199\pi$
$883$	−35.3835	+	42.1684i	−1.19075	+	1.41908i	−0.884126	+	0.467248i	$0.845245\pi$
$884$	2.77348	+	2.32723i	0.0932822	+	0.0782730i
$885$	−0.119420	+	3.69765i	−0.00401426	+	0.124295i
$886$	10.8671	−	18.8224i	0.365087	−	0.632350i
$887$	−7.64207	−	20.9964i	−0.256595	−	0.704990i	−0.999371	−	0.0354502i	$-0.988713\pi$
$887$	−7.64207	−	20.9964i	−0.256595	−	0.704990i	0.742776	−	0.669540i	$-0.233509\pi$
$888$	−6.33794	+	1.11755i	−0.212687	+	0.0375025i
$889$	2.48291	−	14.0813i	0.0832742	−	0.472272i
$890$	12.7438	+	16.2235i	0.427175	+	0.543814i
$891$	−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
$895$	−0.562982	−	3.93102i	−0.0188184	−	0.131399i
$896$	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
$900$	4.98958	+	0.322625i	0.166319	+	0.0107542i
$901$	−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
$905$	20.2048	+	37.7606i	0.671632	+	1.25521i
$906$	10.9260	−	3.97674i	0.362992	−	0.132118i
$907$	−23.5670	+	4.15550i	−0.782531	+	0.137981i	−0.550620	−	0.834756i	$-0.685609\pi$
$907$	−23.5670	+	4.15550i	−0.782531	+	0.137981i	−0.231910	+	0.972737i	$0.574498\pi$
$908$	−11.9568	−	2.10832i	−0.396802	−	0.0699669i
$909$	1.09007	+	0.396753i	0.0361553	+	0.0131595i
$910$	−1.81577	+	0.260047i	−0.0601923	+	0.00862046i
$911$	−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
$915$	18.1138	+	23.0598i	0.598825	+	0.762333i
$916$	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	$0.0379384\pi$
$920$	13.6768	+	0.441709i	0.450912	+	0.0145627i
$921$	−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
$925$	22.2314	−	23.2642i	0.730965	−	0.764922i
$926$	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
$935$	22.6458	−	25.2837i	0.740596	−	0.826865i
$936$	0.148859	+	0.844219i	0.00486560	+	0.0275942i
$937$	4.28381	+	11.7697i	0.139946	+	0.384498i	0.989790	−	0.142537i	$-0.0455259\pi$
$937$	4.28381	+	11.7697i	0.139946	+	0.384498i	−0.849844	+	0.527035i	$0.823304\pi$
$938$	8.95457	+	5.16992i	0.292377	+	0.168804i
$939$	−8.51713	−	14.7521i	−0.277946	−	0.481416i
$940$	0.728634	+	2.22266i	0.0237654	+	0.0724952i
$941$	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
$945$	1.98605	+	0.796368i	0.0646064	+	0.0259058i
$946$	5.94510	−	33.7163i	0.193292	−	1.09621i
$947$	−3.16942	+	8.70792i	−0.102992	+	0.282969i	−0.980476	−	0.196637i	$-0.936998\pi$
$947$	−3.16942	+	8.70792i	−0.102992	+	0.282969i	0.877484	+	0.479606i	$0.159220\pi$
$948$	−6.70573	−	7.99158i	−0.217792	−	0.259555i
$949$	0.393534			0.0127747
$950$	11.2663	+	18.6566i	0.365529	+	0.605301i
$951$	−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	$-0.671912\pi$
$953$	13.3052	−	36.5558i	0.430998	−	1.18416i	0.945201	−	0.326489i	$-0.105866\pi$
$954$	0.471190	−	2.67225i	0.0152553	−	0.0865173i
$955$	−27.4277	−	10.9980i	−0.887541	−	0.355886i
$956$	−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
$960$	0.696556	+	2.12481i	0.0224812	+	0.0685779i
$961$	−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
$965$	−23.1207	+	25.8139i	−0.744282	+	0.830980i
$966$	5.50294	+	2.00291i	0.177054	+	0.0644425i
$967$	0.708454	+	0.844302i	0.0227823	+	0.0271509i	0.777315	−	0.629111i	$-0.216581\pi$
$967$	0.708454	+	0.844302i	0.0227823	+	0.0271509i	−0.754533	+	0.656262i	$0.772137\pi$
$968$		−	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
$975$	−3.09881	−	2.96125i	−0.0992414	−	0.0948358i
$976$	−6.55692	+	11.3569i	−0.209882	+	0.363526i
$977$	−22.3074	+	12.8792i	−0.713677	+	0.412042i	−0.812421	−	0.583071i	$-0.801851\pi$
$977$	−22.3074	+	12.8792i	−0.713677	+	0.412042i	0.0987441	+	0.995113i	$0.468517\pi$
$978$	9.40529	−	11.2088i	0.300748	−	0.358418i
$979$	25.4019	+	21.3147i	0.811849	+	0.681222i
$980$	13.5978	+	0.439155i	0.434365	+	0.0140283i
$981$	−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	0.645722	−	0.763573i	$-0.276556\pi$
$983$	47.4575	−	8.36804i	1.51366	−	0.266899i	0.867937	+	0.496674i	$0.165445\pi$
$984$	−0.724528	+	4.10900i	−0.0230971	+	0.130990i
$985$	−5.00837	−	6.37590i	−0.159580	−	0.203153i
$986$	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
$990$	7.95552	−	1.13935i	0.252843	−	0.0362110i
$991$	−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
$995$	−16.6494	−	31.1159i	−0.527822	−	0.986441i
$996$	−4.00756	−	6.94130i	−0.126984	−	0.219943i
$997$	16.9815	−	20.2378i	0.537810	−	0.640937i	−0.426885	−	0.904306i	$-0.640389\pi$
$997$	16.9815	−	20.2378i	0.537810	−	0.640937i	0.964695	+	0.263369i	$0.0848336\pi$
$998$	−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.139.10	yes	60
5.4	even	2	inner	570.2.bc.b.139.2	✓	60
19.16	even	9	inner	570.2.bc.b.529.2	yes	60
95.54	even	18	inner	570.2.bc.b.529.10	yes	60

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

\(f(q)\)	\(=\)	\(q+(0.642788 + 0.766044i) q^{2} +(-0.342020 + 0.939693i) q^{3} +(-0.173648 + 0.984808i) q^{4} +(2.07544 + 0.832208i) q^{5} +(-0.939693 + 0.342020i) q^{6} +(0.828729 + 0.478467i) q^{7} +(-0.866025 + 0.500000i) q^{8} +(-0.766044 - 0.642788i) q^{9} +O(q^{10})\)	\(q+(0.642788 + 0.766044i) q^{2} +(-0.342020 + 0.939693i) q^{3} +(-0.173648 + 0.984808i) q^{4} +(2.07544 + 0.832208i) 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} +(0.696556 + 2.12481i) 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} +(-1.49186 + 1.66564i) 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} +(3.61486 + 3.45439i) 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} +(-2.23490 - 0.0721787i) 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} +(1.32179 + 1.68270i) q^{35} +(0.766044 - 0.642788i) q^{36} -6.43571i q^{37} +(4.20694 + 1.14091i) q^{38} -0.857243 q^{39} +(-2.21348 + 0.317005i) 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} +(-1.05494 - 1.97157i) 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} +(-0.322625 + 4.98958i) 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} +(1.13935 + 7.95552i) q^{55} -0.956934 q^{56} +(1.11541 + 4.21377i) q^{57} +9.75447i q^{58} +(1.26742 - 1.06349i) q^{59} +(-1.38128 - 1.75843i) 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} +(-0.0618746 + 1.91585i) 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} +(-0.439394 + 2.09417i) 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} +(-1.66564 - 1.49186i) 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} +(-2.94187 - 8.97402i) 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} +(0.832208 - 2.07544i) q^{90} +(-0.142448 + 0.807862i) q^{91} +(2.09305 - 5.75059i) q^{92} +(-3.99801 - 4.76464i) q^{93} +1.04605 q^{94} +(9.49788 - 2.18869i) 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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