LMFDB - Embedded newform 546.2.q.j.335.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [546,2,Mod(251,546)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(546, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 3, 1]))

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

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

chi := DirichletCharacter("546.251");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 546 = 2 \cdot 3 \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	546.q (of order $6$, degree $2$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$4.35983195036$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$12$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			335.1
Character	$\chi$	$=$	546.335
Dual form			546.2.q.j.251.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.500000 + 0.866025i) q^{2} +(-1.68382 + 0.405895i) q^{3} +(-0.500000 + 0.866025i) q^{4} +0.465645i q^{5} +(-1.19343 - 1.25528i) q^{6} +(2.62938 - 0.293915i) q^{7} -1.00000 q^{8} +(2.67050 - 1.36691i) q^{9} +O(q^{10})$	\(q+(0.500000 + 0.866025i) q^{2} +(-1.68382 + 0.405895i) q^{3} +(-0.500000 + 0.866025i) q^{4} +0.465645i q^{5} +(-1.19343 - 1.25528i) q^{6} +(2.62938 - 0.293915i) q^{7} -1.00000 q^{8} +(2.67050 - 1.36691i) q^{9} +(-0.403261 + 0.232823i) q^{10} +(1.39698 + 2.41964i) q^{11} +(0.490394 - 1.66118i) q^{12} +(-0.799665 + 3.51576i) q^{13} +(1.56923 + 2.13015i) q^{14} +(-0.189003 - 0.784062i) q^{15} +(-0.500000 - 0.866025i) q^{16} +(0.508355 - 0.880496i) q^{17} +(2.51903 + 1.62927i) q^{18} +(-0.817625 + 1.41617i) q^{19} +(-0.403261 - 0.232823i) q^{20} +(-4.30810 + 1.56215i) q^{21} +(-1.39698 + 2.41964i) q^{22} +(-7.14652 + 4.12605i) q^{23} +(1.68382 - 0.405895i) q^{24} +4.78317 q^{25} +(-3.44457 + 1.06535i) q^{26} +(-3.94182 + 3.38557i) q^{27} +(-1.06015 + 2.42406i) q^{28} +(-4.01364 + 2.31727i) q^{29} +(0.584516 - 0.555713i) q^{30} +1.94747 q^{31} +(0.500000 - 0.866025i) q^{32} +(-3.33438 - 3.50721i) q^{33} +1.01671 q^{34} +(0.136860 + 1.22436i) q^{35} +(-0.151472 + 2.99617i) q^{36} +(4.51505 - 2.60676i) q^{37} -1.63525 q^{38} +(-0.0805363 - 6.24448i) q^{39} -0.465645i q^{40} +(-9.35517 + 5.40121i) q^{41} +(-3.50691 - 2.94984i) q^{42} +(-3.24949 + 5.62828i) q^{43} -2.79396 q^{44} +(0.636494 + 1.24350i) q^{45} +(-7.14652 - 4.12605i) q^{46} -0.277466i q^{47} +(1.19343 + 1.25528i) q^{48} +(6.82723 - 1.54563i) q^{49} +(2.39159 + 4.14235i) q^{50} +(-0.498589 + 1.68894i) q^{51} +(-2.64490 - 2.45041i) q^{52} -8.99975i q^{53} +(-4.90290 - 1.72093i) q^{54} +(-1.12669 + 0.650496i) q^{55} +(-2.62938 + 0.293915i) q^{56} +(0.801918 - 2.71644i) q^{57} +(-4.01364 - 2.31727i) q^{58} +(8.80951 + 5.08617i) q^{59} +(0.773520 + 0.228350i) q^{60} +(11.2444 + 6.49197i) q^{61} +(0.973737 + 1.68656i) q^{62} +(6.61999 - 4.37901i) q^{63} +1.00000 q^{64} +(-1.63709 - 0.372360i) q^{65} +(1.37014 - 4.64126i) q^{66} +(-0.308335 + 0.178017i) q^{67} +(0.508355 + 0.880496i) q^{68} +(10.3587 - 9.84825i) q^{69} +(-0.991893 + 0.730702i) q^{70} +(5.01505 - 8.68632i) q^{71} +(-2.67050 + 1.36691i) q^{72} +1.46098 q^{73} +(4.51505 + 2.60676i) q^{74} +(-8.05400 + 1.94147i) q^{75} +(-0.817625 - 1.41617i) q^{76} +(4.38435 + 5.95154i) q^{77} +(5.36761 - 3.19199i) q^{78} -4.98126 q^{79} +(0.403261 - 0.232823i) q^{80} +(5.26312 - 7.30065i) q^{81} +(-9.35517 - 5.40121i) q^{82} +12.2750i q^{83} +(0.801186 - 4.51200i) q^{84} +(0.409999 + 0.236713i) q^{85} -6.49897 q^{86} +(5.81767 - 5.53099i) q^{87} +(-1.39698 - 2.41964i) q^{88} +(10.1441 - 5.85671i) q^{89} +(-0.758659 + 1.17297i) q^{90} +(-1.06929 + 9.47927i) q^{91} -8.25209i q^{92} +(-3.27919 + 0.790470i) q^{93} +(0.240293 - 0.138733i) q^{94} +(-0.659432 - 0.380723i) q^{95} +(-0.490394 + 1.66118i) q^{96} +(7.82871 - 13.5597i) q^{97} +(4.75217 + 5.13974i) q^{98} +(7.03805 + 4.55210i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 12 q^{2} - 12 q^{4} - 18 q^{7} - 24 q^{8} + 6 q^{9}+O(q^{10}) $ 24 * q + 12 * q^2 - 12 * q^4 - 18 * q^7 - 24 * q^8 + 6 * q^9	$ 24 q + 12 q^{2} - 12 q^{4} - 18 q^{7} - 24 q^{8} + 6 q^{9} + 12 q^{15} - 12 q^{16} - 6 q^{18} + 12 q^{21} - 36 q^{23} - 12 q^{25} + 18 q^{28} + 6 q^{30} + 12 q^{32} - 36 q^{35} - 12 q^{36} + 36 q^{37} + 12 q^{39} - 12 q^{42} - 42 q^{43} - 36 q^{46} - 6 q^{50} + 12 q^{51} + 18 q^{56} - 36 q^{57} - 6 q^{60} + 66 q^{63} + 24 q^{64} + 66 q^{65} - 54 q^{67} + 48 q^{71} - 6 q^{72} + 36 q^{74} - 12 q^{78} - 48 q^{79} - 6 q^{81} - 24 q^{84} - 84 q^{86} + 36 q^{91} + 54 q^{93} - 36 q^{95} + 36 q^{99}+O(q^{100}) $ 24 * q + 12 * q^2 - 12 * q^4 - 18 * q^7 - 24 * q^8 + 6 * q^9 + 12 * q^15 - 12 * q^16 - 6 * q^18 + 12 * q^21 - 36 * q^23 - 12 * q^25 + 18 * q^28 + 6 * q^30 + 12 * q^32 - 36 * q^35 - 12 * q^36 + 36 * q^37 + 12 * q^39 - 12 * q^42 - 42 * q^43 - 36 * q^46 - 6 * q^50 + 12 * q^51 + 18 * q^56 - 36 * q^57 - 6 * q^60 + 66 * q^63 + 24 * q^64 + 66 * q^65 - 54 * q^67 + 48 * q^71 - 6 * q^72 + 36 * q^74 - 12 * q^78 - 48 * q^79 - 6 * q^81 - 24 * q^84 - 84 * q^86 + 36 * q^91 + 54 * q^93 - 36 * q^95 + 36 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/546\mathbb{Z}\right)^\times$.

$n$	$157$	$365$	$379$
$\chi(n)$	$-1$	$-1$	$e\left(\frac{5}{6}\right)$

Coefficient data

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

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

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

$2$	0.500000	+	0.866025i	0.353553	+	0.612372i
$2$	0.500000	+	0.866025i	0.353553	+	0.612372i
$3$	−1.68382	+	0.405895i	−0.972154	+	0.234344i
$3$	−1.68382	+	0.405895i	−0.972154	+	0.234344i
$4$	−0.500000	+	0.866025i	−0.250000	+	0.433013i
$5$			0.465645i			0.208243i	0.994565	+	0.104121i	$0.0332031\pi$
$5$			0.465645i			0.208243i	−0.994565	+	0.104121i	$0.966797\pi$
$6$	−1.19343	−	1.25528i	−0.487214	−	0.512467i
$7$	2.62938	−	0.293915i	0.993810	−	0.111089i
$7$	2.62938	−	0.293915i	0.993810	−	0.111089i
$8$	−1.00000			−0.353553
$9$	2.67050	−	1.36691i	0.890166	−	0.455636i
$10$	−0.403261	+	0.232823i	−0.127522	+	0.0736250i
$11$	1.39698	+	2.41964i	0.421205	+	0.729548i	0.996058	−	0.0887086i	$-0.0282740\pi$
$11$	1.39698	+	2.41964i	0.421205	+	0.729548i	−0.574853	+	0.818257i	$0.694941\pi$
$12$	0.490394	−	1.66118i	0.141565	−	0.479541i
$13$	−0.799665	+	3.51576i	−0.221787	+	0.975095i
$13$	−0.799665	+	3.51576i	−0.221787	+	0.975095i
$14$	1.56923	+	2.13015i	0.419393	+	0.569306i
$15$	−0.189003	−	0.784062i	−0.0488004	−	0.202444i
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	0.508355	−	0.880496i	0.123294	−	0.213552i	−0.797771	−	0.602961i	$-0.793987\pi$
$17$	0.508355	−	0.880496i	0.123294	−	0.213552i	0.921065	+	0.389409i	$0.127321\pi$
$18$	2.51903	+	1.62927i	0.593740	+	0.384021i
$19$	−0.817625	+	1.41617i	−0.187576	+	0.324891i	−0.944442	−	0.328679i	$-0.893396\pi$
$19$	−0.817625	+	1.41617i	−0.187576	+	0.324891i	0.756865	+	0.653571i	$0.226730\pi$
$20$	−0.403261	−	0.232823i	−0.0901718	−	0.0520607i
$21$	−4.30810	+	1.56215i	−0.940103	+	0.340889i
$22$	−1.39698	+	2.41964i	−0.297837	+	0.515869i
$23$	−7.14652	+	4.12605i	−1.49015	+	0.860340i	−0.999937	−	0.0112612i	$-0.996415\pi$
$23$	−7.14652	+	4.12605i	−1.49015	+	0.860340i	−0.490216	+	0.871601i	$0.663082\pi$
$24$	1.68382	−	0.405895i	0.343708	−	0.0828530i
$25$	4.78317			0.956635
$26$	−3.44457	+	1.06535i	−0.675535	+	0.208932i
$27$	−3.94182	+	3.38557i	−0.758603	+	0.651553i
$28$	−1.06015	+	2.42406i	−0.200349	+	0.458105i
$29$	−4.01364	+	2.31727i	−0.745313	+	0.430307i	−0.823998	−	0.566593i	$-0.808261\pi$
$29$	−4.01364	+	2.31727i	−0.745313	+	0.430307i	0.0786847	+	0.996900i	$0.474928\pi$
$30$	0.584516	−	0.555713i	0.106718	−	0.101459i
$31$	1.94747			0.349777			0.174888	−	0.984588i	$-0.444044\pi$
$31$	1.94747			0.349777			0.174888	+	0.984588i	$0.444044\pi$
$32$	0.500000	−	0.866025i	0.0883883	−	0.153093i
$33$	−3.33438	−	3.50721i	−0.580441	−	0.610527i
$34$	1.01671			0.174364
$35$	0.136860	+	1.22436i	0.0231336	+	0.206954i
$36$	−0.151472	+	2.99617i	−0.0252453	+	0.499362i
$37$	4.51505	−	2.60676i	0.742269	−	0.428549i	−0.0806247	−	0.996745i	$-0.525692\pi$
$37$	4.51505	−	2.60676i	0.742269	−	0.428549i	0.822894	+	0.568195i	$0.192358\pi$
$38$	−1.63525			−0.265273
$39$	−0.0805363	−	6.24448i	−0.0128961	−	0.999917i
$40$		−	0.465645i		−	0.0736250i
$41$	−9.35517	+	5.40121i	−1.46103	+	0.843527i	−0.999059	−	0.0433672i	$-0.986191\pi$
$41$	−9.35517	+	5.40121i	−1.46103	+	0.843527i	−0.461973	+	0.886894i	$0.652858\pi$
$42$	−3.50691	−	2.94984i	−0.541128	−	0.455171i
$43$	−3.24949	+	5.62828i	−0.495542	+	0.858304i	−0.999987	−	0.00513985i	$-0.998364\pi$
$43$	−3.24949	+	5.62828i	−0.495542	+	0.858304i	0.504445	+	0.863444i	$0.331697\pi$
$44$	−2.79396			−0.421205
$45$	0.636494	+	1.24350i	0.0948830	+	0.185371i
$46$	−7.14652	−	4.12605i	−1.05370	−	0.608352i
$47$		−	0.277466i		−	0.0404726i	−0.999795	−	0.0202363i	$-0.993558\pi$
$47$		−	0.277466i		−	0.0404726i	0.999795	−	0.0202363i	$-0.00644186\pi$
$48$	1.19343	+	1.25528i	0.172256	+	0.181185i
$49$	6.82723	−	1.54563i	0.975318	−	0.220804i
$50$	2.39159	+	4.14235i	0.338222	+	0.585817i
$51$	−0.498589	+	1.68894i	−0.0698164	+	0.236498i
$52$	−2.64490	−	2.45041i	−0.366782	−	0.339810i
$53$		−	8.99975i		−	1.23621i	−0.786095	−	0.618105i	$-0.787901\pi$
$53$		−	8.99975i		−	1.23621i	0.786095	−	0.618105i	$-0.212099\pi$
$54$	−4.90290	−	1.72093i	−0.667200	−	0.234189i
$55$	−1.12669	+	0.650496i	−0.151923	+	0.0877129i
$56$	−2.62938	+	0.293915i	−0.351365	+	0.0392760i
$57$	0.801918	−	2.71644i	0.106217	−	0.359802i
$58$	−4.01364	−	2.31727i	−0.527016	−	0.304273i
$59$	8.80951	+	5.08617i	1.14690	+	0.662163i	0.948130	−	0.317883i	$-0.102972\pi$
$59$	8.80951	+	5.08617i	1.14690	+	0.662163i	0.198770	+	0.980046i	$0.436305\pi$
$60$	0.773520	+	0.228350i	0.0998609	+	0.0294798i
$61$	11.2444	+	6.49197i	1.43970	+	0.831211i	0.997828	−	0.0658671i	$-0.0209813\pi$
$61$	11.2444	+	6.49197i	1.43970	+	0.831211i	0.441872	+	0.897078i	$0.354315\pi$
$62$	0.973737	+	1.68656i	0.123665	+	0.214194i
$63$	6.61999	−	4.37901i	0.834040	−	0.551704i
$64$	1.00000			0.125000
$65$	−1.63709	−	0.372360i	−0.203057	−	0.0461856i
$66$	1.37014	−	4.64126i	0.168653	−	0.571300i
$67$	−0.308335	+	0.178017i	−0.0376691	+	0.0217483i	−0.518716	−	0.854946i	$-0.673590\pi$
$67$	−0.308335	+	0.178017i	−0.0376691	+	0.0217483i	0.481047	+	0.876695i	$0.340257\pi$
$68$	0.508355	+	0.880496i	0.0616471	+	0.106776i
$69$	10.3587	−	9.84825i	1.24704	−	1.18559i
$70$	−0.991893	+	0.730702i	−0.118554	+	0.0873356i
$71$	5.01505	−	8.68632i	0.595177	−	1.03088i	−0.398345	−	0.917235i	$-0.630415\pi$
$71$	5.01505	−	8.68632i	0.595177	−	1.03088i	0.993522	−	0.113640i	$-0.0362512\pi$
$72$	−2.67050	+	1.36691i	−0.314721	+	0.161092i
$73$	1.46098			0.170995			0.0854975	−	0.996338i	$-0.472752\pi$
$73$	1.46098			0.170995			0.0854975	+	0.996338i	$0.472752\pi$
$74$	4.51505	+	2.60676i	0.524863	+	0.303030i
$75$	−8.05400	+	1.94147i	−0.929996	+	0.224181i
$76$	−0.817625	−	1.41617i	−0.0937881	−	0.162446i
$77$	4.38435	+	5.95154i	0.499643	+	0.678241i
$78$	5.36761	−	3.19199i	0.607762	−	0.361421i
$79$	−4.98126			−0.560435			−0.280218	−	0.959937i	$-0.590407\pi$
$79$	−4.98126			−0.560435			−0.280218	+	0.959937i	$0.590407\pi$
$80$	0.403261	−	0.232823i	0.0450859	−	0.0260304i
$81$	5.26312	−	7.30065i	0.584791	−	0.811184i
$82$	−9.35517	−	5.40121i	−1.03311	−	0.596464i
$83$			12.2750i			1.34736i	0.739024	+	0.673679i	$0.235287\pi$
$83$			12.2750i			1.34736i	−0.739024	+	0.673679i	$0.764713\pi$
$84$	0.801186	−	4.51200i	0.0874165	−	0.492299i
$85$	0.409999	+	0.236713i	0.0444706	+	0.0256751i
$86$	−6.49897			−0.700802
$87$	5.81767	−	5.53099i	0.623720	−	0.592984i
$88$	−1.39698	−	2.41964i	−0.148918	−	0.257934i
$89$	10.1441	−	5.85671i	1.07527	−	0.620810i	0.145657	−	0.989335i	$-0.453470\pi$
$89$	10.1441	−	5.85671i	1.07527	−	0.620810i	0.929618	+	0.368525i	$0.120137\pi$
$90$	−0.758659	+	1.17297i	−0.0799697	+	0.123642i
$91$	−1.06929	+	9.47927i	−0.112092	+	0.993698i
$92$		−	8.25209i		−	0.860340i
$93$	−3.27919	+	0.790470i	−0.340037	+	0.0819679i
$94$	0.240293	−	0.138733i	0.0247843	−	0.0143092i
$95$	−0.659432	−	0.380723i	−0.0676563	−	0.0390614i
$96$	−0.490394	+	1.66118i	−0.0500507	+	0.169543i
$97$	7.82871	−	13.5597i	0.794885	−	1.37678i	−0.128027	−	0.991771i	$-0.540864\pi$
$97$	7.82871	−	13.5597i	0.794885	−	1.37678i	0.922912	−	0.385011i	$-0.125802\pi$
$98$	4.75217	+	5.13974i	0.480041	+	0.519192i
$99$	7.03805	+	4.55210i	0.707351	+	0.457503i
$100$	−2.39159	+	4.14235i	−0.239159	+	0.414235i
$101$	−2.03145	−	3.51858i	−0.202137	−	0.350112i	0.747080	−	0.664734i	$-0.231455\pi$
$101$	−2.03145	−	3.51858i	−0.202137	−	0.350112i	−0.949217	+	0.314623i	$0.898122\pi$
$102$	−1.71196	+	0.412677i	−0.169509	+	0.0408612i
$103$		−	3.03761i		−	0.299305i	−0.988739	−	0.149652i	$-0.952185\pi$
$103$		−	3.03761i		−	0.299305i	0.988739	−	0.149652i	$-0.0478154\pi$
$104$	0.799665	−	3.51576i	0.0784136	−	0.344748i
$105$	−0.727408	−	2.00604i	−0.0709877	−	0.195770i
$106$	7.79401	−	4.49987i	0.757021	−	0.437066i
$107$	−11.3525	+	6.55437i	−1.09749	+	0.633635i	−0.935560	−	0.353168i	$-0.885105\pi$
$107$	−11.3525	+	6.55437i	−1.09749	+	0.633635i	−0.161928	+	0.986803i	$0.551771\pi$
$108$	−0.961081	−	5.10650i	−0.0924801	−	0.491373i
$109$		−	10.8172i		−	1.03610i	−0.855350	−	0.518051i	$-0.826658\pi$
$109$		−	10.8172i		−	1.03610i	0.855350	−	0.518051i	$-0.173342\pi$
$110$	−1.12669	−	0.650496i	−0.107426	−	0.0620224i
$111$	−6.54445	+	6.22195i	−0.621172	+	0.590562i
$112$	−1.56923	−	2.13015i	−0.148278	−	0.201280i
$113$	0.251978	+	0.145480i	0.0237041	+	0.0136856i	0.511805	−	0.859102i	$-0.328977\pi$
$113$	0.251978	+	0.145480i	0.0237041	+	0.0136856i	−0.488101	+	0.872787i	$0.662310\pi$
$114$	2.75347	−	0.663740i	0.257886	−	0.0621650i
$115$	−1.92127	−	3.32774i	−0.179160	−	0.310314i
$116$		−	4.63455i		−	0.430307i
$117$	2.67021	+	10.4819i	0.246861	+	0.969051i
$118$			10.1723i			0.936440i
$119$	1.07786	−	2.46457i	0.0988077	−	0.225927i
$120$	0.189003	+	0.784062i	0.0172535	+	0.0715748i
$121$	1.59690	−	2.76591i	0.145173	−	0.251447i
$122$			12.9839i			1.17551i
$123$	13.5601	−	12.8919i	1.22267	−	1.16242i
$124$	−0.973737	+	1.68656i	−0.0874441	+	0.151458i
$125$			4.55549i			0.407455i
$126$	7.10233	+	3.54357i	0.632726	+	0.315686i
$127$	−1.89703	−	3.28576i	−0.168334	−	0.291564i	0.769500	−	0.638647i	$-0.220506\pi$
$127$	−1.89703	−	3.28576i	−0.168334	−	0.291564i	−0.937834	+	0.347083i	$0.887172\pi$
$128$	0.500000	+	0.866025i	0.0441942	+	0.0765466i
$129$	3.18706	−	10.7960i	0.280605	−	0.950531i
$130$	−0.496074	−	1.60395i	−0.0435086	−	0.140675i
$131$	8.80601			0.769384			0.384692	−	0.923045i	$-0.374308\pi$
$131$	8.80601			0.769384			0.384692	+	0.923045i	$0.374308\pi$
$132$	4.70452	−	1.13405i	0.409476	−	0.0987067i
$133$	−1.73361	+	3.96395i	−0.150323	+	0.343718i
$134$	−0.308335	−	0.178017i	−0.0266361	−	0.0153783i
$135$	−1.57647	−	1.83549i	−0.135681	−	0.157974i
$136$	−0.508355	+	0.880496i	−0.0435911	+	0.0755019i
$137$	8.51407	−	14.7468i	0.727407	−	1.25991i	−0.230569	−	0.973056i	$-0.574059\pi$
$137$	8.51407	−	14.7468i	0.727407	−	1.25991i	0.957976	−	0.286849i	$-0.0926078\pi$
$138$	13.7082	+	4.04678i	1.16692	+	0.344485i
$139$	−17.3730	−	10.0303i	−1.47356	−	0.850757i	−0.473998	−	0.880526i	$-0.657190\pi$
$139$	−17.3730	−	10.0303i	−1.47356	−	0.850757i	−0.999557	+	0.0297682i	$0.990523\pi$
$140$	−1.12875	−	0.493654i	−0.0953971	−	0.0417213i
$141$	0.112622	+	0.467203i	0.00948451	+	0.0393456i
$142$	10.0301			0.841707
$143$	−9.62397	+	2.97654i	−0.804797	+	0.248910i
$144$	−2.51903	−	1.62927i	−0.209919	−	0.135772i
$145$	−1.07903	−	1.86893i	−0.0896083	−	0.155206i
$146$	0.730491	+	1.26525i	0.0604559	+	0.104713i
$147$	−10.8685	+	5.37369i	−0.896415	+	0.443215i
$148$			5.21353i			0.428549i
$149$	1.91703	−	3.32040i	0.157049	−	0.272017i	−0.776754	−	0.629804i	$-0.783135\pi$
$149$	1.91703	−	3.32040i	0.157049	−	0.272017i	0.933803	+	0.357787i	$0.116469\pi$
$150$	−5.70836	−	6.00424i	−0.466086	−	0.490244i
$151$			20.7448i			1.68819i	0.536197	+	0.844093i	$0.319860\pi$
$151$			20.7448i			1.68819i	−0.536197	+	0.844093i	$0.680140\pi$
$152$	0.817625	−	1.41617i	0.0663182	−	0.114866i
$153$	0.154003	−	3.04624i	0.0124504	−	0.246274i
$154$	−2.96201	+	6.77273i	−0.238686	+	0.545762i
$155$			0.906832i			0.0728385i
$156$	5.44815	+	3.05249i	0.436201	+	0.244395i
$157$			6.10387i			0.487142i	0.969883	+	0.243571i	$0.0783189\pi$
$157$			6.10387i			0.487142i	−0.969883	+	0.243571i	$0.921681\pi$
$158$	−2.49063	−	4.31389i	−0.198144	−	0.343195i
$159$	3.65295	+	15.1540i	0.289698	+	1.20179i
$160$	0.403261	+	0.232823i	0.0318805	+	0.0184062i
$161$	−17.5782	+	12.9494i	−1.38535	+	1.02055i
$162$	8.95411	+	0.907671i	0.703502	+	0.0713134i
$163$	−4.36215	−	2.51849i	−0.341670	−	0.197263i	0.319340	−	0.947640i	$-0.396539\pi$
$163$	−4.36215	−	2.51849i	−0.341670	−	0.197263i	−0.661010	+	0.750377i	$0.729872\pi$
$164$		−	10.8024i		−	0.843527i
$165$	1.63311	−	1.55264i	0.127138	−	0.120873i
$166$	−10.6305	+	6.13751i	−0.825085	+	0.476363i
$167$	0.975840	−	0.563401i	0.0755128	−	0.0435973i	−0.461768	−	0.887001i	$-0.652785\pi$
$167$	0.975840	−	0.563401i	0.0755128	−	0.0435973i	0.537281	+	0.843403i	$0.319451\pi$
$168$	4.30810	−	1.56215i	0.332377	−	0.120523i
$169$	−11.7211	−	5.62285i	−0.901621	−	0.432527i
$170$			0.473426i			0.0363101i
$171$	−0.247694	+	4.89949i	−0.0189416	+	0.374674i
$172$	−3.24949	−	5.62828i	−0.247771	−	0.429152i
$173$	3.84077	−	6.65242i	0.292009	−	0.505774i	−0.682276	−	0.731095i	$-0.739010\pi$
$173$	3.84077	−	6.65242i	0.292009	−	0.505774i	0.974285	+	0.225321i	$0.0723431\pi$
$174$	7.69881	+	2.27276i	0.583645	+	0.172297i
$175$	12.5768	−	1.40585i	0.950714	−	0.106272i
$176$	1.39698	−	2.41964i	0.105301	−	0.182387i
$177$	−16.8981	−	4.98846i	−1.27014	−	0.374956i
$178$	10.1441	+	5.85671i	0.760334	+	0.438979i
$179$	22.0237	−	12.7154i	1.64613	−	0.950393i	0.667540	−	0.744574i	$-0.267348\pi$
$179$	22.0237	−	12.7154i	1.64613	−	0.950393i	0.978590	−	0.205819i	$-0.0659858\pi$
$180$	−1.39515	−	0.0705321i	−0.103989	−	0.00525715i
$181$		−	0.270132i		−	0.0200788i	−0.999950	−	0.0100394i	$-0.996804\pi$
$181$		−	0.270132i		−	0.0200788i	0.999950	−	0.0100394i	$-0.00319569\pi$
$182$	−8.74393	+	3.81361i	−0.648144	+	0.282683i
$183$	−21.5686	−	6.36725i	−1.59440	−	0.470681i
$184$	7.14652	−	4.12605i	0.526848	−	0.304176i
$185$	1.21383	+	2.10241i	0.0892423	+	0.154572i
$186$	−2.32416	−	2.44463i	−0.170416	−	0.179249i
$187$	2.84064			0.207728
$188$	0.240293	+	0.138733i	0.0175252	+	0.0101182i
$189$	−9.36944	+	10.0605i	−0.681527	+	0.731793i
$190$		−	0.761446i		−	0.0552411i
$191$	5.43711	+	3.13912i	0.393415	+	0.227138i	0.683639	−	0.729820i	$-0.260396\pi$
$191$	5.43711	+	3.13912i	0.393415	+	0.227138i	−0.290224	+	0.956959i	$0.593730\pi$
$192$	−1.68382	+	0.405895i	−0.121519	+	0.0292930i
$193$	6.96974	−	4.02398i	0.501693	−	0.289653i	−0.227719	−	0.973727i	$-0.573127\pi$
$193$	6.96974	−	4.02398i	0.501693	−	0.289653i	0.729413	+	0.684074i	$0.239794\pi$
$194$	15.6574			1.12414
$195$	2.90771	−	0.0375014i	0.208226	−	0.00268553i
$196$	−2.07506	+	6.68537i	−0.148219	+	0.477526i
$197$	5.68452	+	9.84588i	0.405005	+	0.701490i	0.994322	−	0.106412i	$-0.0339364\pi$
$197$	5.68452	+	9.84588i	0.405005	+	0.701490i	−0.589317	+	0.807902i	$0.700603\pi$
$198$	−0.423205	+	8.37118i	−0.0300759	+	0.594914i
$199$	3.95997	+	2.28629i	0.280715	+	0.162071i	0.633747	−	0.773540i	$-0.281516\pi$
$199$	3.95997	+	2.28629i	0.280715	+	0.162071i	−0.353032	+	0.935611i	$0.614849\pi$
$200$	−4.78317			−0.338222
$201$	0.446924	−	0.424900i	0.0315236	−	0.0299702i
$202$	2.03145	−	3.51858i	0.142932	−	0.247566i
$203$	−9.87227	+	7.27265i	−0.692898	+	0.510440i
$204$	−1.21337	−	1.27626i	−0.0849527	−	0.0893560i
$205$	−2.51505	−	4.35619i	−0.175658	−	0.304249i
$206$	2.63065	−	1.51881i	0.183286	−	0.105820i
$207$	−13.4448	+	20.7872i	−0.934481	+	1.44481i
$208$	3.44457	−	1.06535i	0.238838	−	0.0738686i
$209$	−4.56882			−0.316032
$210$	1.37358	−	1.63298i	0.0947861	−	0.112686i
$211$	5.13457	+	8.89333i	0.353478	+	0.612242i	0.986856	−	0.161600i	$-0.0516655\pi$
$211$	5.13457	+	8.89333i	0.353478	+	0.612242i	−0.633378	+	0.773843i	$0.718332\pi$
$212$	7.79401	+	4.49987i	0.535295	+	0.309053i
$213$	−4.91870	+	16.6618i	−0.337024	+	1.14165i
$214$	−11.3525	−	6.55437i	−0.776041	−	0.448048i
$215$	−2.62078	−	1.51311i	−0.178736	−	0.103193i
$216$	3.94182	−	3.38557i	0.268207	−	0.230359i
$217$	5.12064	−	0.572392i	0.347612	−	0.0388565i
$218$	9.36799	−	5.40861i	0.634481	−	0.366318i
$219$	−2.46003	+	0.593006i	−0.166234	+	0.0400716i
$220$		−	1.30099i		−	0.0877129i
$221$	2.68910	+	2.49135i	0.180888	+	0.167587i
$222$	−8.66060	−	2.55668i	−0.581261	−	0.171593i
$223$	−8.20296	−	14.2079i	−0.549311	−	0.951434i	−0.998322	−	0.0579082i	$-0.981557\pi$
$223$	−8.20296	−	14.2079i	−0.549311	−	0.951434i	0.449011	−	0.893526i	$-0.351776\pi$
$224$	1.06015	−	2.42406i	0.0708342	−	0.161965i
$225$	12.7735	−	6.53816i	0.851564	−	0.435877i
$226$			0.290959i			0.0193543i
$227$	−23.5487	−	13.5958i	−1.56298	−	0.902387i	−0.996953	−	0.0780009i	$-0.975146\pi$
$227$	−23.5487	−	13.5958i	−1.56298	−	0.902387i	−0.566027	−	0.824386i	$-0.691520\pi$
$228$	1.95155	+	2.05270i	0.129245	+	0.135944i
$229$	5.93616			0.392272			0.196136	−	0.980577i	$-0.437161\pi$
$229$	5.93616			0.392272			0.196136	+	0.980577i	$0.437161\pi$
$230$	1.92127	−	3.32774i	0.126685	−	0.219425i
$231$	−9.79816	−	8.24174i	−0.644671	−	0.542267i
$232$	4.01364	−	2.31727i	0.263508	−	0.152136i
$233$			19.9017i			1.30380i	0.758303	+	0.651902i	$0.226029\pi$
$233$			19.9017i			1.30380i	−0.758303	+	0.651902i	$0.773971\pi$
$234$	−7.74247	+	7.55342i	−0.506141	+	0.493782i
$235$	0.129201			0.00842814
$236$	−8.80951	+	5.08617i	−0.573450	+	0.331082i
$237$	8.38754	−	2.02187i	0.544829	−	0.131334i
$238$	2.67331	−	0.298826i	0.173285	−	0.0193700i
$239$	−5.37098			−0.347420			−0.173710	−	0.984797i	$-0.555576\pi$
$239$	−5.37098			−0.347420			−0.173710	+	0.984797i	$0.555576\pi$
$240$	−0.584516	+	0.555713i	−0.0377304	+	0.0358711i
$241$	−4.43996	+	7.69024i	−0.286003	+	0.495372i	−0.972852	−	0.231428i	$-0.925660\pi$
$241$	−4.43996	+	7.69024i	−0.286003	+	0.495372i	0.686849	+	0.726800i	$0.258993\pi$
$242$	3.19380			0.205305
$243$	−5.89885	+	14.4293i	−0.378411	+	0.925638i
$244$	−11.2444	+	6.49197i	−0.719850	+	0.415606i
$245$	0.719713	+	3.17907i	0.0459808	+	0.203103i
$246$	17.9447	+	5.29745i	1.14411	+	0.337753i
$247$	−4.32508	−	4.00703i	−0.275198	−	0.254961i
$248$	−1.94747			−0.123665
$249$	−4.98237	−	20.6689i	−0.315745	−	1.30984i
$250$	−3.94517	+	2.27774i	−0.249514	+	0.144057i
$251$	4.21323	−	7.29753i	0.265937	−	0.460616i	−0.701872	−	0.712303i	$-0.747652\pi$
$251$	4.21323	−	7.29753i	0.265937	−	0.460616i	0.967809	+	0.251687i	$0.0809854\pi$
$252$	0.482345	+	7.92258i	0.0303849	+	0.499076i
$253$	−19.9671	−	11.5280i	−1.25532	−	0.724759i
$254$	1.89703	−	3.28576i	0.119030	−	0.206167i
$255$	−0.786445	−	0.232165i	−0.0492491	−	0.0145388i
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	−11.3361	−	19.6348i	−0.707129	−	1.22478i	−0.965918	−	0.258850i	$-0.916656\pi$
$257$	−11.3361	−	19.6348i	−0.707129	−	1.22478i	0.258788	−	0.965934i	$-0.416677\pi$
$258$	10.9431	−	2.63790i	0.681288	−	0.164229i
$259$	11.1056	−	8.18120i	0.690067	−	0.508355i
$260$	1.14102	−	1.23159i	0.0707631	−	0.0763797i
$261$	−7.55091	+	11.6745i	−0.467389	+	0.722636i
$262$	4.40300	+	7.62623i	0.272018	+	0.471150i
$263$	1.77900	−	1.02711i	0.109698	−	0.0633341i	−0.444147	−	0.895954i	$-0.646493\pi$
$263$	1.77900	−	1.02711i	0.109698	−	0.0633341i	0.553845	+	0.832620i	$0.313160\pi$
$264$	3.33438	+	3.50721i	0.205217	+	0.215854i
$265$	4.19069			0.257432
$266$	−4.29969	+	0.480625i	−0.263631	+	0.0294690i
$267$	−14.7037	+	13.9791i	−0.899850	+	0.855507i
$268$		−	0.356034i		−	0.0217483i
$269$	8.39939	−	14.5482i	0.512120	−	0.887018i	−0.487781	−	0.872966i	$-0.662194\pi$
$269$	8.39939	−	14.5482i	0.512120	−	0.887018i	0.999901	−	0.0140519i	$-0.00447301\pi$
$270$	0.801342	−	2.28301i	0.0487681	−	0.138940i
$271$	−15.4047	−	26.6817i	−0.935767	−	1.62080i	−0.773260	−	0.634089i	$-0.781375\pi$
$271$	−15.4047	−	26.6817i	−0.935767	−	1.62080i	−0.162507	−	0.986707i	$-0.551958\pi$
$272$	−1.01671			−0.0616471
$273$	−2.04711	−	16.3954i	−0.123897	−	0.992295i
$274$	17.0281			1.02871
$275$	6.68199	+	11.5736i	0.402939	+	0.697911i
$276$	3.34948	+	13.8950i	0.201615	+	0.836383i
$277$	5.58729	−	9.67746i	0.335708	−	0.581462i	−0.647913	−	0.761714i	$-0.724358\pi$
$277$	5.58729	−	9.67746i	0.335708	−	0.581462i	0.983620	+	0.180252i	$0.0576913\pi$
$278$		−	20.0606i		−	1.20315i
$279$	5.20072	−	2.66202i	0.311359	−	0.159371i
$280$	−0.136860	−	1.22436i	−0.00817896	−	0.0731693i
$281$	5.68985			0.339428			0.169714	−	0.985493i	$-0.445716\pi$
$281$	5.68985			0.339428			0.169714	+	0.985493i	$0.445716\pi$
$282$	−0.348299	+	0.331135i	−0.0207409	+	0.0197188i
$283$	12.9779	−	7.49278i	0.771455	−	0.445400i	−0.0619386	−	0.998080i	$-0.519728\pi$
$283$	12.9779	−	7.49278i	0.771455	−	0.445400i	0.833393	+	0.552680i	$0.186395\pi$
$284$	5.01505	+	8.68632i	0.297588	+	0.515438i
$285$	1.26490	+	0.373409i	0.0749261	+	0.0221188i
$286$	−7.38974	−	6.84634i	−0.436965	−	0.404832i
$287$	−23.0107	+	16.9514i	−1.35828	+	1.00061i
$288$	0.151472	−	2.99617i	0.00892555	−	0.176551i
$289$	7.98315	+	13.8272i	0.469597	+	0.813366i
$290$	1.07903	−	1.86893i	0.0633626	−	0.109747i
$291$	−7.67831	+	26.0098i	−0.450111	+	1.52472i
$292$	−0.730491	+	1.26525i	−0.0427488	+	0.0740431i
$293$	17.5737	+	10.1462i	1.02667	+	0.592747i	0.916028	−	0.401113i	$-0.131377\pi$
$293$	17.5737	+	10.1462i	1.02667	+	0.592747i	0.110640	+	0.993861i	$0.464710\pi$
$294$	−10.0880	−	6.72552i	−0.588343	−	0.392240i
$295$	−2.36835	+	4.10210i	−0.137891	+	0.238834i
$296$	−4.51505	+	2.60676i	−0.262432	+	0.151515i
$297$	−13.6985	−	4.80820i	−0.794867	−	0.279000i
$298$	3.83406			0.222101
$299$	−8.79134	−	28.4249i	−0.508417	−	1.64385i
$300$	2.34564	−	7.94571i	0.135426	−	0.458746i
$301$	−6.88989	+	15.7539i	−0.397126	+	0.908041i
$302$	−17.9655	+	10.3724i	−1.03380	+	0.596864i
$303$	4.84877	+	5.10009i	0.278555	+	0.292993i
$304$	1.63525			0.0937881
$305$	−3.02295	+	5.23591i	−0.173094	+	0.299807i
$306$	2.71512	−	1.38975i	0.155213	−	0.0794467i
$307$	−11.0362			−0.629869			−0.314935	−	0.949113i	$-0.601983\pi$
$307$	−11.0362			−0.629869			−0.314935	+	0.949113i	$0.601983\pi$
$308$	−7.34636	+	0.821186i	−0.418598	+	0.0467914i
$309$	1.23295	+	5.11479i	0.0701402	+	0.290970i
$310$	−0.785339	+	0.453416i	−0.0446043	+	0.0257523i
$311$	21.6017			1.22492			0.612460	−	0.790502i	$-0.290180\pi$
$311$	21.6017			1.22492			0.612460	+	0.790502i	$0.290180\pi$
$312$	0.0805363	+	6.24448i	0.00455947	+	0.353524i
$313$		−	3.56747i		−	0.201645i	−0.994904	−	0.100823i	$-0.967853\pi$
$313$		−	3.56747i		−	0.201645i	0.994904	−	0.100823i	$-0.0321474\pi$
$314$	−5.28611	+	3.05194i	−0.298312	+	0.172231i
$315$	2.03907	+	3.08256i	0.114888	+	0.173683i
$316$	2.49063	−	4.31389i	0.140109	−	0.242676i
$317$	−21.5505			−1.21040			−0.605199	−	0.796074i	$-0.706907\pi$
$317$	−21.5505			−1.21040			−0.605199	+	0.796074i	$0.706907\pi$
$318$	−11.2972	+	10.7405i	−0.633517	+	0.602299i
$319$	−11.2139	−	6.47436i	−0.627859	−	0.362495i
$320$			0.465645i			0.0260304i
$321$	16.4552	−	15.6443i	0.918439	−	0.873180i
$322$	−20.0036	−	8.74845i	−1.11476	−	0.487532i
$323$	0.831288	+	1.43983i	0.0462541	+	0.0801144i
$324$	3.69099	+	8.20832i	0.205055	+	0.456018i
$325$	−3.82494	+	16.8165i	−0.212169	+	0.932810i
$326$		−	5.03698i		−	0.278973i
$327$	4.39066	+	18.2143i	0.242804	+	1.00725i
$328$	9.35517	−	5.40121i	0.516553	−	0.298232i
$329$	−0.0815515	−	0.729563i	−0.00449608	−	0.0402221i
$330$	2.16118	+	0.638000i	0.118969	+	0.0351207i
$331$	26.3507	+	15.2136i	1.44836	+	0.836214i	0.998384	−	0.0568249i	$-0.0180977\pi$
$331$	26.3507	+	15.2136i	1.44836	+	0.836214i	0.449980	+	0.893039i	$0.351431\pi$
$332$	−10.6305	−	6.13751i	−0.583423	−	0.336839i
$333$	8.49422	−	13.1330i	0.465480	−	0.719685i
$334$	0.975840	+	0.563401i	0.0533956	+	0.0308280i
$335$	−0.0828928	−	0.143575i	−0.00452892	−	0.00784432i
$336$	3.50691	+	2.94984i	0.191318	+	0.160927i
$337$	−19.4209			−1.05793			−0.528963	−	0.848645i	$-0.677419\pi$
$337$	−19.4209			−1.05793			−0.528963	+	0.848645i	$0.677419\pi$
$338$	−0.991003	−	12.9622i	−0.0539035	−	0.705049i
$339$	−0.483335	−	0.142685i	−0.0262512	−	0.00774957i
$340$	−0.409999	+	0.236713i	−0.0222353	+	0.0128376i
$341$	2.72058	+	4.71218i	0.147328	+	0.255179i
$342$	−4.36693	+	2.23524i	−0.236137	+	0.120868i
$343$	17.4971	−	6.07065i	0.944753	−	0.327785i
$344$	3.24949	−	5.62828i	0.175201	−	0.303456i
$345$	4.58579	+	4.82348i	0.246891	+	0.259688i
$346$	7.68155			0.412963
$347$	13.6612	+	7.88727i	0.733369	+	0.423411i	0.819654	−	0.572860i	$-0.194166\pi$
$347$	13.6612	+	7.88727i	0.733369	+	0.423411i	−0.0862842	+	0.996271i	$0.527499\pi$
$348$	1.88114	+	7.80374i	0.100840	+	0.418324i
$349$	2.93182	+	5.07806i	0.156937	+	0.271822i	0.933762	−	0.357893i	$-0.116505\pi$
$349$	2.93182	+	5.07806i	0.156937	+	0.271822i	−0.776826	+	0.629715i	$0.783172\pi$
$350$	7.50588	+	10.1889i	0.401206	+	0.544618i
$351$	−8.75070	−	16.5658i	−0.467078	−	0.884216i
$352$	2.79396			0.148918
$353$	−27.1942	+	15.7006i	−1.44740	+	0.835657i	−0.998326	−	0.0578380i	$-0.981579\pi$
$353$	−27.1942	+	15.7006i	−1.44740	+	0.835657i	−0.449074	+	0.893495i	$0.648246\pi$
$354$	−4.12890	−	17.1284i	−0.219449	−	0.910364i
$355$	4.04474	+	2.33523i	0.214673	+	0.123941i
$356$			11.7134i			0.620810i
$357$	−0.814573	+	4.58739i	−0.0431118	+	0.242790i
$358$	22.0237	+	12.7154i	1.16399	+	0.672030i
$359$	8.80708			0.464820			0.232410	−	0.972618i	$-0.425339\pi$
$359$	8.80708			0.464820			0.232410	+	0.972618i	$0.425339\pi$
$360$	−0.636494	−	1.24350i	−0.0335462	−	0.0655384i
$361$	8.16298	+	14.1387i	0.429630	+	0.744142i
$362$	0.233942	−	0.135066i	0.0122957	−	0.00709892i
$363$	−1.56622	+	5.30547i	−0.0822054	+	0.278465i
$364$	−7.67465	−	5.66567i	−0.402261	−	0.296962i
$365$			0.680300i			0.0356085i
$366$	−5.27012	−	21.8626i	−0.275473	−	1.14278i
$367$	3.96802	−	2.29094i	0.207129	−	0.119586i	−0.392847	−	0.919604i	$-0.628510\pi$
$367$	3.96802	−	2.29094i	0.207129	−	0.119586i	0.599977	+	0.800018i	$0.295177\pi$
$368$	7.14652	+	4.12605i	0.372538	+	0.215085i
$369$	−17.6000	+	27.2116i	−0.916219	+	1.41658i
$370$	−1.21383	+	2.10241i	−0.0631038	+	0.109299i
$371$	−2.64516	−	23.6637i	−0.137330	−	1.22856i
$372$	0.955030	−	3.23510i	0.0495160	−	0.167732i
$373$	−13.5242	+	23.4245i	−0.700254	+	1.21288i	0.268123	+	0.963385i	$0.413597\pi$
$373$	−13.5242	+	23.4245i	−0.700254	+	1.21288i	−0.968377	+	0.249491i	$0.919737\pi$
$374$	1.42032	+	2.46007i	0.0734431	+	0.127207i
$375$	−1.84905	−	7.67062i	−0.0954845	−	0.396109i
$376$			0.277466i			0.0143092i
$377$	−4.93740	−	15.9640i	−0.254289	−	0.822188i
$378$	−13.3974	−	3.08393i	−0.689086	−	0.158620i
$379$	5.46704	−	3.15640i	0.280823	−	0.162133i	−0.352973	−	0.935634i	$-0.614829\pi$
$379$	5.46704	−	3.15640i	0.280823	−	0.162133i	0.633796	+	0.773500i	$0.281496\pi$
$380$	0.659432	−	0.380723i	0.0338281	−	0.0195307i
$381$	4.52793	+	4.76263i	0.231973	+	0.243997i
$382$			6.27823i			0.321222i
$383$	−9.19749	−	5.31017i	−0.469970	−	0.271337i	0.246257	−	0.969205i	$-0.420799\pi$
$383$	−9.19749	−	5.31017i	−0.469970	−	0.271337i	−0.716227	+	0.697867i	$0.754133\pi$
$384$	−1.19343	−	1.25528i	−0.0609017	−	0.0640584i
$385$	−2.77131	+	2.04155i	−0.141239	+	0.104047i
$386$	6.96974	+	4.02398i	0.354751	+	0.204815i
$387$	−0.984411	+	19.4721i	−0.0500404	+	0.989820i
$388$	7.82871	+	13.5597i	0.397443	+	0.688391i
$389$		−	9.76203i		−	0.494955i	−0.968894	−	0.247477i	$-0.920398\pi$
$389$		−	9.76203i		−	0.494955i	0.968894	−	0.247477i	$-0.0796016\pi$
$390$	1.48633	+	2.49940i	0.0752634	+	0.126562i
$391$			8.38998i			0.424300i
$392$	−6.82723	+	1.54563i	−0.344827	+	0.0780659i
$393$	−14.8277	+	3.57432i	−0.747960	+	0.180300i
$394$	−5.68452	+	9.84588i	−0.286382	+	0.496028i
$395$		−	2.31950i		−	0.116707i
$396$	−7.46126	+	3.81908i	−0.374942	+	0.191916i
$397$	−0.0876790	+	0.151865i	−0.00440048	+	0.00762186i	−0.868217	−	0.496184i	$-0.834734\pi$
$397$	−0.0876790	+	0.151865i	−0.00440048	+	0.00762186i	0.863817	+	0.503806i	$0.168067\pi$
$398$			4.57258i			0.229203i
$399$	1.31014	−	7.37824i	0.0655890	−	0.369374i
$400$	−2.39159	−	4.14235i	−0.119579	−	0.207118i
$401$	−1.96794	−	3.40858i	−0.0982743	−	0.170216i	0.812696	−	0.582688i	$-0.197999\pi$
$401$	−1.96794	−	3.40858i	−0.0982743	−	0.170216i	−0.910970	+	0.412472i	$0.864666\pi$
$402$	0.591437	+	0.174597i	0.0294982	+	0.00870812i
$403$	−1.55733	+	6.84684i	−0.0775759	+	0.341065i
$404$	4.06290			0.202137
$405$	3.39951	+	2.45075i	0.168923	+	0.121779i
$406$	−11.2344	−	4.91331i	−0.557556	−	0.243844i
$407$	12.6148	+	7.28319i	0.625295	+	0.361014i
$408$	0.498589	−	1.68894i	0.0246838	−	0.0836148i
$409$	−11.5132	+	19.9414i	−0.569290	+	0.986038i	0.427347	+	0.904088i	$0.359448\pi$
$409$	−11.5132	+	19.9414i	−0.569290	+	0.986038i	−0.996636	+	0.0819507i	$0.973885\pi$
$410$	2.51505	−	4.35619i	0.124209	−	0.215137i
$411$	−8.35051	+	28.2868i	−0.411900	+	1.39528i
$412$	2.63065	+	1.51881i	0.129603	+	0.0748262i
$413$	24.6584	+	10.7842i	1.21336	+	0.530656i
$414$	−24.7247	−	1.24996i	−1.21515	−	0.0614321i
$415$	−5.71580			−0.280578
$416$	2.64490	+	2.45041i	0.129677	+	0.120141i
$417$	33.3242	+	9.83759i	1.63189	+	0.481749i
$418$	−2.28441	−	3.95671i	−0.111734	−	0.193529i
$419$	12.5535	+	21.7434i	0.613280	+	1.06223i	0.990684	+	0.136184i	$0.0434837\pi$
$419$	12.5535	+	21.7434i	0.613280	+	1.06223i	−0.377403	+	0.926049i	$0.623183\pi$
$420$	2.10099	+	0.373068i	0.102518	+	0.0182039i
$421$		−	22.3849i		−	1.09097i	−0.838120	−	0.545486i	$-0.816345\pi$
$421$		−	22.3849i		−	1.09097i	0.838120	−	0.545486i	$-0.183655\pi$
$422$	−5.13457	+	8.89333i	−0.249947	+	0.432921i
$423$	−0.379271	−	0.740974i	−0.0184408	−	0.0360274i
$424$			8.99975i			0.437066i
$425$	2.43155	−	4.21157i	0.117947	−	0.204291i
$426$	−16.8889	+	4.07117i	−0.818268	+	0.197249i
$427$	31.4739	+	13.7649i	1.52313	+	0.666131i
$428$		−	13.1087i		−	0.633635i
$429$	14.9969	−	8.91827i	0.724056	−	0.430578i
$430$		−	3.02622i		−	0.145937i
$431$	−10.8170	−	18.7355i	−0.521035	−	0.902459i	−0.999701	−	0.0244617i	$-0.992213\pi$
$431$	−10.8170	−	18.7355i	−0.521035	−	0.902459i	0.478666	−	0.877997i	$-0.341121\pi$
$432$	4.90290	+	1.72093i	0.235891	+	0.0827982i
$433$	9.15166	+	5.28372i	0.439801	+	0.253919i	0.703513	−	0.710682i	$-0.251614\pi$
$433$	9.15166	+	5.28372i	0.439801	+	0.253919i	−0.263712	+	0.964601i	$0.584947\pi$
$434$	3.05603	+	4.14841i	0.146694	+	0.199130i
$435$	2.57548	+	2.70897i	0.123485	+	0.129885i
$436$	9.36799	+	5.40861i	0.448646	+	0.259026i
$437$		−	13.4942i		−	0.645517i
$438$	−1.74357	−	1.83395i	−0.0833112	−	0.0876294i
$439$	28.4269	−	16.4123i	1.35674	−	0.783316i	0.367560	−	0.930000i	$-0.380193\pi$
$439$	28.4269	−	16.4123i	1.35674	−	0.783316i	0.989183	+	0.146684i	$0.0468600\pi$
$440$	1.12669	−	0.650496i	0.0537130	−	0.0310112i
$441$	16.1194	−	13.4598i	0.767589	−	0.640942i
$442$	−0.813027	+	3.57450i	−0.0386718	+	0.170022i
$443$		−	32.8664i		−	1.56153i	−0.624826	−	0.780764i	$-0.714830\pi$
$443$		−	32.8664i		−	1.56153i	0.624826	−	0.780764i	$-0.285170\pi$
$444$	−2.11614	−	8.77864i	−0.100428	−	0.416616i
$445$	2.72715	+	4.72356i	0.129279	+	0.223918i
$446$	8.20296	−	14.2079i	0.388421	−	0.672766i
$447$	−1.88020	+	6.36906i	−0.0889305	+	0.301246i
$448$	2.62938	−	0.293915i	0.124226	−	0.0138862i
$449$	2.61300	−	4.52584i	0.123315	−	0.213588i	−0.797758	−	0.602978i	$-0.793981\pi$
$449$	2.61300	−	4.52584i	0.123315	−	0.213588i	0.921073	+	0.389390i	$0.127314\pi$
$450$	12.0489	+	7.79306i	0.567993	+	0.367368i
$451$	−26.1379	−	15.0907i	−1.23079	−	0.710596i
$452$	−0.251978	+	0.145480i	−0.0118521	+	0.00684279i
$453$	−8.42020	−	34.9305i	−0.395616	−	1.64118i
$454$		−	27.1917i		−	1.27617i
$455$	−4.41398	−	0.497908i	−0.206930	−	0.0233423i
$456$	−0.801918	+	2.71644i	−0.0375532	+	0.127209i
$457$	−30.3072	+	17.4979i	−1.41771	+	0.818517i	−0.996098	−	0.0882584i	$-0.971870\pi$
$457$	−30.3072	+	17.4979i	−1.41771	+	0.818517i	−0.421615	+	0.906775i	$0.638537\pi$
$458$	2.96808	+	5.14086i	0.138689	+	0.240217i
$459$	0.977141	+	5.19183i	0.0456090	+	0.242334i
$460$	3.84255			0.179160
$461$	−19.3938	−	11.1970i	−0.903260	−	0.521498i	−0.0250037	−	0.999687i	$-0.507960\pi$
$461$	−19.3938	−	11.1970i	−0.903260	−	0.521498i	−0.878256	+	0.478190i	$0.841293\pi$
$462$	2.23848	−	12.6063i	0.104143	−	0.586499i
$463$		−	16.1024i		−	0.748340i	−0.927360	−	0.374170i	$-0.877928\pi$
$463$		−	16.1024i		−	0.748340i	0.927360	−	0.374170i	$-0.122072\pi$
$464$	4.01364	+	2.31727i	0.186328	+	0.107577i
$465$	−0.368078	−	1.52694i	−0.0170692	−	0.0708102i
$466$	−17.2354	+	9.95086i	−0.798414	+	0.460965i
$467$	32.1440			1.48745			0.743723	−	0.668488i	$-0.233058\pi$
$467$	32.1440			1.48745			0.743723	+	0.668488i	$0.233058\pi$
$468$	−10.4127	−	2.92847i	−0.481327	−	0.135369i
$469$	−0.758406	+	0.558698i	−0.0350199	+	0.0257983i
$470$	0.0646004	+	0.111891i	0.00297980	+	0.00516116i
$471$	−2.47753	−	10.2778i	−0.114159	−	0.473577i
$472$	−8.80951	−	5.08617i	−0.405490	−	0.234110i
$473$	−18.1579			−0.834899
$474$	5.94476	+	6.25289i	0.273052	+	0.287205i
$475$	−3.91084	+	6.77378i	−0.179442	+	0.310802i
$476$	1.59545	+	2.16574i	0.0731272	+	0.0992666i
$477$	−12.3018	−	24.0338i	−0.563262	−	1.10043i
$478$	−2.68549	−	4.65141i	−0.122831	−	0.212750i
$479$	−0.698448	+	0.403249i	−0.0319129	+	0.0184249i	−0.515872	−	0.856666i	$-0.672532\pi$
$479$	−0.698448	+	0.403249i	−0.0319129	+	0.0184249i	0.483959	+	0.875091i	$0.339198\pi$
$480$	−0.773520	−	0.228350i	−0.0353062	−	0.0104227i
$481$	5.55422	+	17.9583i	0.253251	+	0.818830i
$482$	−8.87993			−0.404470
$483$	24.3424	−	28.9393i	1.10762	−	1.31679i
$484$	1.59690	+	2.76591i	0.0725864	+	0.125723i
$485$	6.31402	+	3.64540i	0.286705	+	0.165529i
$486$	−15.4455	+	2.10608i	−0.700624	+	0.0955336i
$487$	7.32472	+	4.22893i	0.331915	+	0.191631i	0.656691	−	0.754160i	$-0.271956\pi$
$487$	7.32472	+	4.22893i	0.331915	+	0.191631i	−0.324776	+	0.945791i	$0.605289\pi$
$488$	−11.2444	−	6.49197i	−0.509011	−	0.293878i
$489$	8.36732	+	2.47011i	0.378383	+	0.111702i
$490$	−2.39329	+	2.21282i	−0.108118	+	0.0999651i
$491$	4.29055	−	2.47715i	0.193630	−	0.111792i	−0.400051	−	0.916493i	$-0.631008\pi$
$491$	4.29055	−	2.47715i	0.193630	−	0.111792i	0.593681	+	0.804701i	$0.297674\pi$
$492$	4.38465	+	18.1893i	0.197675	+	0.820038i
$493$			4.71199i			0.212217i
$494$	1.30765	−	5.74914i	0.0588341	−	0.258666i
$495$	−2.11966	+	3.27724i	−0.0952717	+	0.147301i
$496$	−0.973737	−	1.68656i	−0.0437221	−	0.0757288i
$497$	10.6334	−	24.3136i	0.476973	−	1.09061i
$498$	15.4086	−	14.6493i	0.690477	−	0.656451i
$499$			10.4075i			0.465906i	0.972488	+	0.232953i	$0.0748388\pi$
$499$			10.4075i			0.465906i	−0.972488	+	0.232953i	$0.925161\pi$
$500$	−3.94517	−	2.27774i	−0.176433	−	0.101864i
$501$	−1.41446	+	1.34476i	−0.0631933	+	0.0600792i
$502$	8.42646			0.376091
$503$	2.19872	−	3.80829i	0.0980359	−	0.169803i	−0.812836	−	0.582493i	$-0.802077\pi$
$503$	2.19872	−	3.80829i	0.0980359	−	0.169803i	0.910872	+	0.412690i	$0.135411\pi$
$504$	−6.61999	+	4.37901i	−0.294878	+	0.195057i
$505$	1.63841	−	0.945936i	0.0729082	−	0.0420936i
$506$		−	23.0560i		−	1.02496i
$507$	22.0185	+	4.71034i	0.977874	+	0.209194i
$508$	3.79407			0.168334
$509$	14.7836	−	8.53531i	0.655271	−	0.378321i	−0.135202	−	0.990818i	$-0.543168\pi$
$509$	14.7836	−	8.53531i	0.655271	−	0.378321i	0.790473	+	0.612497i	$0.209835\pi$
$510$	−0.192161	−	0.797164i	−0.00850904	−	0.0352990i
$511$	3.84147	−	0.429405i	0.169937	−	0.0189957i
$512$	−1.00000			−0.0441942
$513$	−1.57161	−	8.35040i	−0.0693882	−	0.368679i
$514$	11.3361	−	19.6348i	0.500016	−	0.866053i
$515$	1.41445			0.0623281
$516$	7.75604	+	8.15805i	0.341441	+	0.359138i
$517$	0.671368	−	0.387615i	0.0295267	−	0.0170473i
$518$	12.6379	+	5.52712i	0.555278	+	0.242848i
$519$	−3.76699	+	12.7604i	−0.165352	+	0.560120i
$520$	1.63709	+	0.372360i	0.0717913	+	0.0163291i
$521$	36.0935			1.58128			0.790642	−	0.612279i	$-0.209747\pi$
$521$	36.0935			1.58128			0.790642	+	0.612279i	$0.209747\pi$
$522$	−13.8859	−	0.702003i	−0.607770	−	0.0307258i
$523$	−17.5784	+	10.1489i	−0.768648	+	0.443779i	−0.832392	−	0.554187i	$-0.813029\pi$
$523$	−17.5784	+	10.1489i	−0.768648	+	0.443779i	0.0637443	+	0.997966i	$0.479696\pi$
$524$	−4.40300	+	7.62623i	−0.192346	+	0.333153i
$525$	−20.6064	+	7.47204i	−0.899336	+	0.326107i
$526$	1.77900	+	1.02711i	0.0775681	+	0.0447840i
$527$	0.990008	−	1.71474i	0.0431254	−	0.0746954i
$528$	−1.37014	+	4.64126i	−0.0596277	+	0.201985i
$529$	22.5485	−	39.0551i	0.980370	−	1.69805i
$530$	2.09534	+	3.62924i	0.0910160	+	0.157644i
$531$	30.4781	+	1.54082i	1.32264	+	0.0668660i
$532$	−2.56608	−	3.48333i	−0.111254	−	0.151021i
$533$	−11.5083	−	37.2096i	−0.498481	−	1.61173i
$534$	−19.4581	−	5.74420i	−0.842034	−	0.248576i
$535$	−3.05201	−	5.28624i	−0.131950	−	0.228544i
$536$	0.308335	−	0.178017i	0.0133180	−	0.00768917i
$537$	−31.9228	+	30.3498i	−1.37757	+	1.30969i
$538$	16.7988			0.724247
$539$	13.2773	+	14.3602i	0.571896	+	0.618538i
$540$	2.37782	−	0.447523i	0.102325	−	0.0192583i
$541$		−	27.0224i		−	1.16178i	−0.813981	−	0.580892i	$-0.802704\pi$
$541$		−	27.0224i		−	1.16178i	0.813981	−	0.580892i	$-0.197296\pi$
$542$	15.4047	−	26.6817i	0.661687	−	1.14608i
$543$	0.109645	+	0.454854i	0.00470534	+	0.0195197i
$544$	−0.508355	−	0.880496i	−0.0217955	−	0.0377510i
$545$	5.03699			0.215761
$546$	13.1753	−	9.97055i	0.563850	−	0.426700i
$547$	−9.23401			−0.394818			−0.197409	−	0.980321i	$-0.563253\pi$
$547$	−9.23401			−0.394818			−0.197409	+	0.980321i	$0.563253\pi$
$548$	8.51407	+	14.7468i	0.363703	+	0.629953i
$549$	38.9021	+	1.96670i	1.66030	+	0.0839366i
$550$	−6.68199	+	11.5736i	−0.284921	+	0.493498i
$551$		−	7.57865i		−	0.322861i
$552$	−10.3587	+	9.84825i	−0.440896	+	0.419170i
$553$	−13.0976	+	1.46407i	−0.556966	+	0.0622584i
$554$	11.1746			0.474762
$555$	−2.89722	−	3.04739i	−0.122980	−	0.129355i
$556$	17.3730	−	10.0303i	0.736778	−	0.425379i
$557$	18.5481	+	32.1263i	0.785910	+	1.36124i	0.928454	+	0.371447i	$0.121138\pi$
$557$	18.5481	+	32.1263i	0.785910	+	1.36124i	−0.142544	+	0.989788i	$0.545528\pi$
$558$	4.90574	+	3.17295i	0.207676	+	0.134322i
$559$	−17.1891	−	15.9251i	−0.727023	−	0.673562i
$560$	0.991893	−	0.730702i	0.0419151	−	0.0308778i
$561$	−4.78313	+	1.15300i	−0.201944	+	0.0486798i
$562$	2.84492	+	4.92755i	0.120006	+	0.207856i
$563$	10.9911	−	19.0372i	0.463220	−	0.802321i	−0.535899	−	0.844282i	$-0.680027\pi$
$563$	10.9911	−	19.0372i	0.463220	−	0.802321i	0.999119	+	0.0419612i	$0.0133606\pi$
$564$	−0.460921	−	0.136068i	−0.0194083	−	0.00572950i
$565$	−0.0677419	+	0.117332i	−0.00284992	+	0.00493621i
$566$	12.9779	+	7.49278i	0.545501	+	0.314945i
$567$	11.6930	−	20.7431i	0.491058	−	0.871127i
$568$	−5.01505	+	8.68632i	−0.210427	+	0.364470i
$569$	38.0392	−	21.9620i	1.59469	−	0.920693i	0.602200	−	0.798345i	$-0.294291\pi$
$569$	38.0392	−	21.9620i	1.59469	−	0.920693i	0.992487	−	0.122348i	$-0.0390425\pi$
$570$	0.309067	+	1.28214i	0.0129454	+	0.0537029i
$571$	7.22333			0.302287			0.151143	−	0.988512i	$-0.451704\pi$
$571$	7.22333			0.302287			0.151143	+	0.988512i	$0.451704\pi$
$572$	2.23423	−	9.82287i	0.0934178	−	0.410715i
$573$	−10.4293	−	3.07881i	−0.435689	−	0.128619i
$574$	−26.1857	−	11.4522i	−1.09297	−	0.478005i
$575$	−34.1831	+	19.7356i	−1.42553	+	0.823031i
$576$	2.67050	−	1.36691i	0.111271	−	0.0569545i
$577$	4.24210			0.176601			0.0883004	−	0.996094i	$-0.471856\pi$
$577$	4.24210			0.176601			0.0883004	+	0.996094i	$0.471856\pi$
$578$	−7.98315	+	13.8272i	−0.332055	+	0.575137i
$579$	−10.1025	+	9.60465i	−0.419845	+	0.399156i
$580$	2.15805			0.0896083
$581$	3.60781	+	32.2756i	0.149677	+	1.33902i
$582$	−26.3643	+	6.35527i	−1.09283	+	0.263435i
$583$	21.7761	−	12.5725i	0.901875	−	0.520698i
$584$	−1.46098			−0.0604559
$585$	−4.88084	+	1.24337i	−0.201798	+	0.0514071i
$586$			20.2924i			0.838271i
$587$	−34.2636	+	19.7821i	−1.41421	+	0.816494i	−0.995782	−	0.0917557i	$-0.970752\pi$
$587$	−34.2636	+	19.7821i	−1.41421	+	0.816494i	−0.418428	+	0.908250i	$0.637419\pi$
$588$	0.780475	−	12.0992i	0.0321862	−	0.498963i
$589$	−1.59230	+	2.75795i	−0.0656097	+	0.113639i
$590$	−4.73670			−0.195007
$591$	−13.5681	−	14.2714i	−0.558117	−	0.587045i
$592$	−4.51505	−	2.60676i	−0.185567	−	0.107137i
$593$		−	0.231641i		−	0.00951238i	−0.999989	−	0.00475619i	$-0.998486\pi$
$593$		−	0.231641i		−	0.00951238i	0.999989	−	0.00475619i	$-0.00151395\pi$
$594$	−2.68522	−	14.2673i	−0.110176	−	0.585396i
$595$	1.14761	+	0.501902i	0.0470476	+	0.0205760i
$596$	1.91703	+	3.32040i	0.0785246	+	0.136009i
$597$	−7.59588	−	2.24237i	−0.310878	−	0.0917741i
$598$	20.2210	−	21.8260i	0.826898	−	0.892530i
$599$			1.45949i			0.0596333i	0.999555	+	0.0298167i	$0.00949235\pi$
$599$			1.45949i			0.0596333i	−0.999555	+	0.0298167i	$0.990508\pi$
$600$	8.05400	−	1.94147i	0.328803	−	0.0792601i
$601$	14.1862	−	8.19043i	0.578669	−	0.334095i	−0.181935	−	0.983311i	$-0.558236\pi$
$601$	14.1862	−	8.19043i	0.578669	−	0.334095i	0.760604	+	0.649216i	$0.224903\pi$
$602$	−17.0882	+	1.91015i	−0.696465	+	0.0778517i
$603$	−0.580074	+	0.896860i	−0.0236225	+	0.0365230i
$604$	−17.9655	−	10.3724i	−0.731006	−	0.422046i
$605$	1.28793	+	0.743589i	0.0523620	+	0.0302312i
$606$	−1.99243	+	6.74921i	−0.0809367	+	0.274168i
$607$	−15.9865	−	9.22984i	−0.648874	−	0.374627i	0.139151	−	0.990271i	$-0.455563\pi$
$607$	−15.9865	−	9.22984i	−0.648874	−	0.374627i	−0.788025	+	0.615644i	$0.788896\pi$
$608$	0.817625	+	1.41617i	0.0331591	+	0.0574332i
$609$	13.6712	−	16.2529i	0.553985	−	0.658602i
$610$	−6.04591			−0.244792
$611$	0.975504	+	0.221880i	0.0394647	+	0.00897631i
$612$	2.56112	+	1.65649i	0.103527	+	0.0669596i
$613$	−19.8455	+	11.4578i	−0.801554	+	0.462777i	−0.844014	−	0.536321i	$-0.819814\pi$
$613$	−19.8455	+	11.4578i	−0.801554	+	0.462777i	0.0424606	+	0.999098i	$0.486480\pi$
$614$	−5.51810	−	9.55763i	−0.222692	−	0.385715i
$615$	6.00304	+	6.31419i	0.242066	+	0.254613i
$616$	−4.38435	−	5.95154i	−0.176650	−	0.239795i
$617$	−11.9139	+	20.6355i	−0.479636	+	0.830754i	−0.999727	−	0.0233564i	$-0.992565\pi$
$617$	−11.9139	+	20.6355i	−0.479636	+	0.830754i	0.520091	+	0.854111i	$0.325898\pi$
$618$	−3.81306	+	3.62516i	−0.153384	+	0.145825i
$619$	−24.6008			−0.988789			−0.494394	−	0.869238i	$-0.664610\pi$
$619$	−24.6008			−0.988789			−0.494394	+	0.869238i	$0.664610\pi$
$620$	−0.785339	−	0.453416i	−0.0315400	−	0.0182096i
$621$	14.2013	−	40.4592i	0.569877	−	1.62357i
$622$	10.8008	+	18.7076i	0.433074	+	0.750107i
$623$	24.9513	−	18.3810i	0.999654	−	0.736419i
$624$	−5.36761	+	3.19199i	−0.214876	+	0.127782i
$625$	21.7946			0.871785
$626$	3.08952	−	1.78373i	0.123482	−	0.0712923i
$627$	7.69307	−	1.85446i	0.307232	−	0.0740601i
$628$	−5.28611	−	3.05194i	−0.210939	−	0.121786i
$629$		−	5.30064i		−	0.211350i
$630$	−1.65005	+	3.30717i	−0.0657394	+	0.131761i
$631$	−18.8984	−	10.9110i	−0.752332	−	0.434359i	0.0742037	−	0.997243i	$-0.476358\pi$
$631$	−18.8984	−	10.9110i	−0.752332	−	0.434359i	−0.826536	+	0.562884i	$0.809692\pi$
$632$	4.98126			0.198144
$633$	−12.2554	−	12.8907i	−0.487110	−	0.512358i
$634$	−10.7753	−	18.6633i	−0.427941	−	0.741215i
$635$	1.53000	−	0.883344i	0.0607161	−	0.0350544i
$636$	−14.9502	−	4.41343i	−0.592814	−	0.175004i
$637$	−0.0254525	+	25.2388i	−0.00100847	+	0.999999i
$638$		−	12.9487i		−	0.512645i
$639$	1.51928	−	30.0519i	0.0601016	−	1.18883i
$640$	−0.403261	+	0.232823i	−0.0159403	+	0.00920312i
$641$	−26.9800	−	15.5769i	−1.06565	−	0.615251i	−0.138658	−	0.990340i	$-0.544279\pi$
$641$	−26.9800	−	15.5769i	−1.06565	−	0.615251i	−0.926989	+	0.375089i	$0.877612\pi$
$642$	21.7760	+	6.42845i	0.859428	+	0.253711i
$643$	−7.10597	+	12.3079i	−0.280232	+	0.485376i	−0.971442	−	0.237278i	$-0.923745\pi$
$643$	−7.10597	+	12.3079i	−0.280232	+	0.485376i	0.691210	+	0.722654i	$0.257078\pi$
$644$	−2.42541	−	21.6978i	−0.0955747	−	0.855015i
$645$	5.02708	+	1.48404i	0.197941	+	0.0584340i
$646$	−0.831288	+	1.43983i	−0.0327066	+	0.0566494i
$647$	12.4757	+	21.6085i	0.490468	+	0.849516i	0.999940	−	0.0109713i	$-0.00349235\pi$
$647$	12.4757	+	21.6085i	0.490468	+	0.849516i	−0.509471	+	0.860488i	$0.670159\pi$
$648$	−5.26312	+	7.30065i	−0.206755	+	0.286797i
$649$			28.4211i			1.11563i
$650$	−16.4760	+	5.09574i	−0.646240	+	0.199872i
$651$	−8.38990	+	3.04225i	−0.328826	+	0.119235i
$652$	4.36215	−	2.51849i	0.170835	−	0.0986317i
$653$	−3.86444	+	2.23114i	−0.151227	+	0.0873111i	−0.573704	−	0.819063i	$-0.694494\pi$
$653$	−3.86444	+	2.23114i	−0.151227	+	0.0873111i	0.422477	+	0.906374i	$0.361161\pi$
$654$	−13.5787	+	12.9096i	−0.530969	+	0.504804i
$655$			4.10047i			0.160219i
$656$	9.35517	+	5.40121i	0.365258	+	0.210882i
$657$	3.90155	−	1.99703i	0.152214	−	0.0779116i
$658$	0.591045	−	0.435407i	0.0230413	−	0.0169739i
$659$	−11.7305	−	6.77262i	−0.456956	−	0.263824i	0.253807	−	0.967255i	$-0.418317\pi$
$659$	−11.7305	−	6.77262i	−0.456956	−	0.263824i	−0.710763	+	0.703431i	$0.751650\pi$
$660$	0.528067	+	2.19064i	0.0205550	+	0.0852704i
$661$	−14.7691	−	25.5809i	−0.574452	−	0.994980i	−0.996101	−	0.0882210i	$-0.971882\pi$
$661$	−14.7691	−	25.5809i	−0.574452	−	0.994980i	0.421649	−	0.906759i	$-0.361452\pi$
$662$			30.4271i			1.18258i
$663$	−5.53918	−	3.10350i	−0.215124	−	0.120530i
$664$		−	12.2750i		−	0.476363i
$665$	−1.84579	−	0.807247i	−0.0715768	−	0.0313037i
$666$	15.6206	+	0.789702i	0.605287	+	0.0306003i
$667$	19.1223	−	33.1209i	0.740420	−	1.28245i
$668$			1.12680i			0.0435973i
$669$	19.5792	+	20.5941i	0.756977	+	0.796213i
$670$	0.0828928	−	0.143575i	0.00320243	−	0.00554677i
$671$			36.2766i			1.40044i
$672$	−0.801186	+	4.51200i	−0.0309064	+	0.174054i
$673$	10.7301	+	18.5850i	0.413614	+	0.716400i	0.995282	−	0.0970262i	$-0.0309331\pi$
$673$	10.7301	+	18.5850i	0.413614	+	0.716400i	−0.581668	+	0.813426i	$0.697600\pi$
$674$	−9.71046	−	16.8190i	−0.374033	−	0.647844i
$675$	−18.8544	+	16.1938i	−0.725706	+	0.623299i
$676$	10.7301	−	7.33932i	0.412695	−	0.282282i
$677$	−43.1118			−1.65692			−0.828461	−	0.560046i	$-0.810783\pi$
$677$	−43.1118			−1.65692			−0.828461	+	0.560046i	$0.810783\pi$
$678$	−0.118099	−	0.489923i	−0.00453556	−	0.0188154i
$679$	16.5992	−	37.9546i	0.637019	−	1.45656i
$680$	−0.409999	−	0.236713i	−0.0157227	−	0.00907753i
$681$	45.1702	+	13.3346i	1.73093	+	0.510985i
$682$	−2.72058	+	4.71218i	−0.104176	+	0.180439i
$683$	−10.3942	+	18.0033i	−0.397724	+	0.688878i	−0.993445	−	0.114314i	$-0.963533\pi$
$683$	−10.3942	+	18.0033i	−0.397724	+	0.688878i	0.595721	+	0.803192i	$0.296866\pi$
$684$	−4.11924	−	2.66426i	−0.157503	−	0.101870i
$685$	6.86678	+	3.96454i	0.262366	+	0.151477i
$686$	14.0059	+	12.1176i	0.534747	+	0.462651i
$687$	−9.99542	+	2.40946i	−0.381349	+	0.0919266i
$688$	6.49897			0.247771
$689$	31.6409	+	7.19678i	1.20542	+	0.274176i
$690$	−1.88436	+	6.38315i	−0.0717365	+	0.243003i
$691$	1.39220	+	2.41136i	0.0529617	+	0.0917323i	0.891291	−	0.453432i	$-0.149801\pi$
$691$	1.39220	+	2.41136i	0.0529617	+	0.0917323i	−0.838329	+	0.545164i	$0.816467\pi$
$692$	3.84077	+	6.65242i	0.146004	+	0.252887i
$693$	19.8436	+	9.90058i	0.753797	+	0.376092i
$694$			15.7745i			0.598794i
$695$	4.67055	−	8.08963i	0.177164	−	0.306857i
$696$	−5.81767	+	5.53099i	−0.220518	+	0.209651i
$697$			10.9829i			0.416008i
$698$	−2.93182	+	5.07806i	−0.110971	+	0.192207i
$699$	−8.07801	−	33.5109i	−0.305538	−	1.26750i
$700$	−5.07088	+	11.5947i	−0.191661	+	0.438239i
$701$			1.61057i			0.0608302i	0.999537	+	0.0304151i	$0.00968292\pi$
$701$			1.61057i			0.0608302i	−0.999537	+	0.0304151i	$0.990317\pi$
$702$	9.97104	−	15.8612i	0.376333	−	0.598643i
$703$			8.52542i			0.321542i
$704$	1.39698	+	2.41964i	0.0526506	+	0.0911935i
$705$	−0.217551	+	0.0524420i	−0.00819344	+	0.00197508i
$706$	−27.1942	−	15.7006i	−1.02347	−	0.590899i
$707$	−6.37561	−	8.65459i	−0.239780	−	0.325489i
$708$	12.7692	−	12.1399i	0.479895	−	0.456247i
$709$	−15.0171	−	8.67010i	−0.563978	−	0.325613i	0.190763	−	0.981636i	$-0.438904\pi$
$709$	−15.0171	−	8.67010i	−0.563978	−	0.325613i	−0.754740	+	0.656024i	$0.772237\pi$
$710$			4.67046i			0.175279i
$711$	−13.3024	+	6.80892i	−0.498880	+	0.255355i
$712$	−10.1441	+	5.85671i	−0.380167	+	0.219490i
$713$	−13.9177	+	8.03536i	−0.521220	+	0.300927i
$714$	−4.38008	+	1.58825i	−0.163920	+	0.0594389i
$715$	−1.38601	−	4.48136i	−0.0518338	−	0.167593i
$716$			25.4308i			0.950393i
$717$	9.04376	−	2.18006i	0.337746	−	0.0814157i
$718$	4.40354	+	7.62715i	0.164339	+	0.284643i
$719$	−1.33248	+	2.30792i	−0.0496931	+	0.0860710i	−0.889802	−	0.456347i	$-0.849158\pi$
$719$	−1.33248	+	2.30792i	−0.0496931	+	0.0860710i	0.840109	+	0.542418i	$0.182491\pi$
$720$	0.758659	−	1.17297i	0.0282736	−	0.0437141i
$721$	−0.892800	−	7.98702i	−0.0332496	−	0.297452i
$722$	−8.16298	+	14.1387i	−0.303795	+	0.526188i
$723$	4.35467	−	14.7511i	0.161952	−	0.548601i
$724$	0.233942	+	0.135066i	0.00869437	+	0.00501970i
$725$	−19.1979	+	11.0839i	−0.712993	+	0.411647i
$726$	−5.37779	+	1.29635i	−0.199588	+	0.0481120i
$727$			42.0015i			1.55775i	0.627180	+	0.778874i	$0.284209\pi$
$727$			42.0015i			1.55775i	−0.627180	+	0.778874i	$0.715791\pi$
$728$	1.06929	−	9.47927i	0.0396304	−	0.351325i
$729$	4.07583	−	26.6906i	0.150957	−	0.988540i
$730$	−0.589157	+	0.340150i	−0.0218057	+	0.0125895i
$731$	3.30378	+	5.72232i	0.122195	+	0.211648i
$732$	16.2985	−	15.4954i	0.602410	−	0.572725i
$733$	0.682575			0.0252115			0.0126057	−	0.999921i	$-0.495987\pi$
$733$	0.682575			0.0252115			0.0126057	+	0.999921i	$0.495987\pi$
$734$	3.96802	+	2.29094i	0.146462	+	0.0845601i
$735$	−2.50223	−	5.06085i	−0.0922963	−	0.186672i
$736$			8.25209i			0.304176i
$737$	−0.861474	−	0.497372i	−0.0317328	−	0.0183209i
$738$	−32.3659	−	1.63626i	−1.19141	−	0.0602316i
$739$	4.21534	−	2.43373i	0.155064	−	0.0895262i	−0.420460	−	0.907311i	$-0.638131\pi$
$739$	4.21534	−	2.43373i	0.155064	−	0.0895262i	0.575524	+	0.817785i	$0.304798\pi$
$740$	−2.42765			−0.0892423
$741$	8.90908	+	4.99159i	0.327283	+	0.183371i
$742$	19.1708	−	14.1226i	0.703782	−	0.518458i
$743$	22.2628	+	38.5603i	0.816743	+	1.41464i	0.908070	+	0.418819i	$0.137556\pi$
$743$	22.2628	+	38.5603i	0.816743	+	1.41464i	−0.0913265	+	0.995821i	$0.529111\pi$
$744$	3.27919	−	0.790470i	0.120221	−	0.0289800i
$745$	1.54613	+	0.892656i	0.0566457	+	0.0327044i
$746$	−27.0483			−0.990309
$747$	16.7788	+	32.7804i	0.613905	+	1.19937i
$748$	−1.42032	+	2.46007i	−0.0519321	+	0.0899490i
$749$	−27.9236	+	20.5706i	−1.02030	+	0.751632i
$750$	5.71843	−	5.43663i	0.208807	−	0.198518i
$751$	−15.0480	−	26.0639i	−0.549108	−	0.951084i	−0.998336	−	0.0576662i	$-0.981634\pi$
$751$	−15.0480	−	26.0639i	−0.549108	−	0.951084i	0.449228	−	0.893417i	$-0.351699\pi$
$752$	−0.240293	+	0.138733i	−0.00876258	+	0.00505908i
$753$	−4.13229	+	13.9979i	−0.150589	+	0.510110i
$754$	11.3565	−	12.2579i	0.413580	−	0.446407i
$755$	−9.65970			−0.351553
$756$	−4.02792	−	13.1444i	−0.146494	−	0.478058i
$757$	20.1948	+	34.9785i	0.733994	+	1.27132i	0.955163	+	0.296080i	$0.0956794\pi$
$757$	20.1948	+	34.9785i	0.733994	+	1.27132i	−0.221169	+	0.975235i	$0.570987\pi$
$758$	5.46704	+	3.15640i	0.198572	+	0.114645i
$759$	38.3001	+	11.3065i	1.39021	+	0.410401i
$760$	0.659432	+	0.380723i	0.0239201	+	0.0138103i
$761$	−8.22094	−	4.74636i	−0.298009	−	0.172056i	0.343539	−	0.939138i	$-0.388374\pi$
$761$	−8.22094	−	4.74636i	−0.298009	−	0.172056i	−0.641548	+	0.767083i	$0.721708\pi$
$762$	−1.86059	+	6.30262i	−0.0674020	+	0.228320i
$763$	−3.17935	−	28.4426i	−0.115100	−	1.02969i
$764$	−5.43711	+	3.13912i	−0.196708	+	0.113569i
$765$	1.41847	+	0.0717106i	0.0512848	+	0.00259270i
$766$		−	10.6203i		−	0.383729i
$767$	−24.9264	+	26.9048i	−0.900040	+	0.971478i
$768$	0.490394	−	1.66118i	0.0176956	−	0.0599426i
$769$	23.9804	+	41.5353i	0.864757	+	1.49780i	0.867289	+	0.497806i	$0.165861\pi$
$769$	23.9804	+	41.5353i	0.864757	+	1.49780i	−0.00253209	+	0.999997i	$0.500806\pi$
$770$	−3.15369	−	1.37925i	−0.113651	−	0.0497046i
$771$	27.0577	+	28.4602i	0.974459	+	1.02497i
$772$			8.04797i			0.289653i
$773$	−36.4656	−	21.0534i	−1.31158	−	0.757239i	−0.329219	−	0.944254i	$-0.606785\pi$
$773$	−36.4656	−	21.0534i	−1.31158	−	0.757239i	−0.982357	+	0.187015i	$0.940119\pi$
$774$	−17.3555	+	8.88350i	−0.623831	+	0.319311i
$775$	9.31511			0.334608
$776$	−7.82871	+	13.5597i	−0.281034	+	0.486766i
$777$	−15.3791	+	18.2834i	−0.551722	+	0.655912i
$778$	8.45417	−	4.88102i	0.303097	−	0.174993i
$779$		−	17.6647i		−	0.632902i
$780$	−1.42138	+	2.53690i	−0.0508935	+	0.0908357i
$781$	28.0237			1.00277
$782$	−7.26594	+	4.19499i	−0.259829	+	0.150013i
$783$	7.97572	−	22.7227i	0.285029	−	0.812043i
$784$	−4.75217	−	5.13974i	−0.169720	−	0.183562i
$785$	−2.84224			−0.101444
$786$	−10.5093	−	11.0540i	−0.374855	−	0.394284i
$787$	4.69267	−	8.12794i	0.167276	−	0.289730i	−0.770185	−	0.637820i	$-0.779836\pi$
$787$	4.69267	−	8.12794i	0.167276	−	0.289730i	0.937461	+	0.348090i	$0.113170\pi$
$788$	−11.3690			−0.405005
$789$	−2.57862	+	2.45155i	−0.0918012	+	0.0872775i
$790$	2.00874	−	1.15975i	0.0714679	−	0.0412620i
$791$	0.705304	+	0.308460i	0.0250777	+	0.0109676i
$792$	−7.03805	−	4.55210i	−0.250086	−	0.161752i
$793$	−31.8159	+	34.3412i	−1.12982	+	1.21949i
$794$	−0.175358			−0.00622322
$795$	−7.05637	+	1.70098i	−0.250264	+	0.0603276i
$796$	−3.95997	+	2.28629i	−0.140358	+	0.0810354i
$797$	9.91670	−	17.1762i	0.351267	−	0.608413i	−0.635204	−	0.772344i	$-0.719084\pi$
$797$	9.91670	−	17.1762i	0.351267	−	0.608413i	0.986472	+	0.163931i	$0.0524175\pi$
$798$	7.04482	−	2.55451i	0.249384	−	0.0904286i
$799$	−0.244308	−	0.141051i	−0.00864300	−	0.00499004i
$800$	2.39159	−	4.14235i	0.0845554	−	0.146454i
$801$	19.0843	−	29.5064i	0.674310	−	1.04256i
$802$	1.96794	−	3.40858i	0.0694905	−	0.120361i
$803$	2.04096	+	3.53505i	0.0720240	+	0.124749i
$804$	0.144513	+	0.599498i	0.00509657	+	0.0211427i
$805$	−6.02982	−	8.18519i	−0.212523	−	0.288490i
$806$	−6.70820	+	2.07474i	−0.236286	+	0.0730795i
$807$	−8.23803	+	27.9058i	−0.289992	+	0.982330i
$808$	2.03145	+	3.51858i	0.0714662	+	0.123783i
$809$	−4.75939	+	2.74783i	−0.167331	+	0.0966087i	−0.581327	−	0.813670i	$-0.697466\pi$
$809$	−4.75939	+	2.74783i	−0.167331	+	0.0966087i	0.413996	+	0.910279i	$0.364133\pi$
$810$	−0.422653	+	4.16944i	−0.0148505	+	0.146499i
$811$	−24.5564			−0.862292			−0.431146	−	0.902282i	$-0.641891\pi$
$811$	−24.5564			−0.862292			−0.431146	+	0.902282i	$0.641891\pi$
$812$	−1.36216	−	12.1860i	−0.0478025	−	0.427643i
$813$	36.7686	+	38.6744i	1.28953	+	1.35637i
$814$			14.5664i			0.510551i
$815$	1.17272	−	2.03121i	0.0410787	−	0.0711504i
$816$	1.71196	−	0.412677i	0.0599304	−	0.0144466i
$817$	−5.31373	−	9.20364i	−0.185904	−	0.321995i
$818$	−23.0263			−0.805097
$819$	10.1018	+	26.7760i	0.352985	+	0.935629i
$820$	5.03009			0.175658
$821$	21.8976	+	37.9278i	0.764233	+	1.32369i	0.940651	+	0.339374i	$0.110215\pi$
$821$	21.8976	+	37.9278i	0.764233	+	1.32369i	−0.176419	+	0.984315i	$0.556451\pi$
$822$	−28.6723	+	6.91164i	−1.00006	+	0.241071i
$823$	−15.4742	+	26.8020i	−0.539395	+	0.934260i	0.459541	+	0.888156i	$0.348014\pi$
$823$	−15.4742	+	26.8020i	−0.539395	+	0.934260i	−0.998937	+	0.0461039i	$0.985319\pi$
$824$			3.03761i			0.105820i
$825$	−15.9489	−	16.7756i	−0.555270	−	0.584051i
$826$	2.98980	+	26.7469i	0.104029	+	0.930644i
$827$	−1.75319			−0.0609644			−0.0304822	−	0.999535i	$-0.509704\pi$
$827$	−1.75319			−0.0609644			−0.0304822	+	0.999535i	$0.509704\pi$
$828$	−11.2799	−	22.0372i	−0.392002	−	0.765845i
$829$	−25.4012	+	14.6654i	−0.882219	+	0.509349i	−0.871389	−	0.490592i	$-0.836781\pi$
$829$	−25.4012	+	14.6654i	−0.882219	+	0.509349i	−0.0108294	+	0.999941i	$0.503447\pi$
$830$	−2.85790	−	4.95003i	−0.0991992	−	0.171818i
$831$	−5.47995	+	18.5630i	−0.190097	+	0.643942i
$832$	−0.799665	+	3.51576i	−0.0277234	+	0.121887i
$833$	2.10974	−	6.79708i	0.0730980	−	0.235505i
$834$	8.14249	+	33.7784i	0.281951	+	1.16965i
$835$	0.262345	+	0.454395i	0.00907883	+	0.0157250i
$836$	2.28441	−	3.95671i	0.0790080	−	0.136846i
$837$	−7.67658	+	6.59331i	−0.265342	+	0.227898i
$838$	−12.5535	+	21.7434i	−0.433655	+	0.751112i
$839$	−13.7040	−	7.91198i	−0.473113	−	0.273152i	0.244429	−	0.969667i	$-0.421399\pi$
$839$	−13.7040	−	7.91198i	−0.473113	−	0.273152i	−0.717542	+	0.696515i	$0.754733\pi$
$840$	0.727408	+	2.00604i	0.0250980	+	0.0692151i
$841$	−3.76049	+	6.51336i	−0.129672	+	0.224599i
$842$	19.3859	−	11.1924i	0.668081	−	0.385717i
$843$	−9.58067	+	2.30948i	−0.329976	+	0.0795427i
$844$	−10.2691			−0.353478
$845$	2.61825	−	5.45786i	0.0900707	−	0.187756i
$846$	0.452066	−	0.698945i	0.0155424	−	0.0240302i
$847$	3.38591	−	7.74198i	0.116341	−	0.266017i
$848$	−7.79401	+	4.49987i	−0.267647	+	0.154526i
$849$	−18.8111	+	17.8841i	−0.645596	+	0.613782i
$850$	4.86310			0.166803
$851$	−21.5112	+	37.2586i	−0.737396	+	1.27721i
$852$	−11.9702	−	12.5906i	−0.410091	−	0.431347i
$853$	−42.9298			−1.46989			−0.734943	−	0.678129i	$-0.762791\pi$
$853$	−42.9298			−1.46989			−0.734943	+	0.678129i	$0.762791\pi$
$854$	3.81617	+	34.1396i	0.130587	+	1.16823i
$855$	−2.28143	−	0.115338i	−0.0780231	−	0.00394446i
$856$	11.3525	−	6.55437i	0.388021	−	0.224024i
$857$	−18.4280			−0.629489			−0.314744	−	0.949176i	$-0.601919\pi$
$857$	−18.4280			−0.629489			−0.314744	+	0.949176i	$0.601919\pi$
$858$	15.2219	+	8.52854i	0.519667	+	0.291159i
$859$			39.0164i			1.33122i	0.746299	+	0.665611i	$0.231829\pi$
$859$			39.0164i			1.33122i	−0.746299	+	0.665611i	$0.768171\pi$
$860$	2.62078	−	1.51311i	0.0893678	−	0.0515966i
$861$	31.8655	−	37.8831i	1.08597	−	1.29105i
$862$	10.8170	−	18.7355i	0.368427	−	0.638135i
$863$	−18.8674			−0.642255			−0.321128	−	0.947036i	$-0.604062\pi$
$863$	−18.8674			−0.642255			−0.321128	+	0.947036i	$0.604062\pi$
$864$	0.961081	+	5.10650i	0.0326966	+	0.173727i
$865$	3.09767	+	1.78844i	0.105324	+	0.0608087i
$866$			10.5674i			0.359096i
$867$	−19.0546	−	20.0422i	−0.647128	−	0.680670i
$868$	−2.06461	+	4.72080i	−0.0700775	+	0.160234i
$869$	−6.95871	−	12.0528i	−0.236058	−	0.408865i
$870$	−1.05830	+	3.58491i	−0.0358797	+	0.121540i
$871$	−0.379300	−	1.22638i	−0.0128521	−	0.0415544i
$872$			10.8172i			0.366318i
$873$	2.37166	−	46.9124i	0.0802684	−	1.58774i
$874$	11.6864	−	6.74712i	0.395297	−	0.228225i
$875$	1.33893	+	11.9781i	0.0452640	+	0.404933i
$876$	0.716458	−	2.42695i	0.0242069	−	0.0819991i
$877$	−23.3402	−	13.4755i	−0.788143	−	0.455034i	0.0511656	−	0.998690i	$-0.483706\pi$
$877$	−23.3402	−	13.4755i	−0.788143	−	0.455034i	−0.839308	+	0.543656i	$0.817040\pi$
$878$	28.4269	+	16.4123i	0.959362	+	0.553888i
$879$	−33.7093	−	9.95128i	−1.13699	−	0.335648i
$880$	1.12669	+	0.650496i	0.0379808	+	0.0219282i
$881$	18.9761	+	32.8676i	0.639321	+	1.10734i	0.985582	+	0.169199i	$0.0541180\pi$
$881$	18.9761	+	32.8676i	0.639321	+	1.10734i	−0.346261	+	0.938138i	$0.612549\pi$
$882$	19.7162	+	7.22989i	0.663879	+	0.243443i
$883$	16.0384			0.539736			0.269868	−	0.962897i	$-0.413020\pi$
$883$	16.0384			0.539736			0.269868	+	0.962897i	$0.413020\pi$
$884$	−3.50212	+	1.08315i	−0.117789	+	0.0364302i
$885$	2.32285	−	7.86851i	0.0780818	−	0.264497i
$886$	28.4631	−	16.4332i	0.956237	−	0.552084i
$887$	−24.2258	−	41.9604i	−0.813424	−	1.40889i	−0.910454	−	0.413610i	$-0.864268\pi$
$887$	−24.2258	−	41.9604i	−0.813424	−	1.40889i	0.0970303	−	0.995281i	$-0.469066\pi$
$888$	6.54445	−	6.22195i	0.219617	−	0.208795i
$889$	−5.95374	−	8.08192i	−0.199682	−	0.271059i
$890$	−2.72715	+	4.72356i	−0.0914143	+	0.158334i
$891$	25.0174	+	2.53599i	0.838115	+	0.0849590i
$892$	16.4059			0.549311
$893$	0.392939	+	0.226864i	0.0131492	+	0.00759170i
$894$	−6.45587	+	1.55623i	−0.215917	+	0.0520480i
$895$	5.92086	+	10.2552i	0.197913	+	0.342795i
$896$	1.56923	+	2.13015i	0.0524241	+	0.0711633i
$897$	26.3406	+	44.2940i	0.879486	+	1.47893i
$898$	5.22599			0.174394
$899$	−7.81645	+	4.51283i	−0.260693	+	0.150511i
$900$	−0.724516	+	14.3312i	−0.0241505	+	0.477707i
$901$	−7.92425	−	4.57507i	−0.263995	−	0.152418i
$902$		−	30.1815i		−	1.00493i
$903$	5.20689	−	29.3233i	0.173274	−	0.975820i
$904$	−0.251978	−	0.145480i	−0.00838067	−	0.00483858i
$905$	0.125786			0.00418126
$906$	26.0406	−	24.7573i	0.865140	−	0.822507i
$907$	15.7893	+	27.3479i	0.524275	+	0.908070i	0.999601	+	0.0282607i	$0.00899685\pi$
$907$	15.7893	+	27.3479i	0.524275	+	0.908070i	−0.475326	+	0.879810i	$0.657670\pi$
$908$	23.5487	−	13.5958i	0.781490	−	0.451194i
$909$	−10.2346	−	6.61955i	−0.339459	−	0.219557i
$910$	−1.77579	−	4.07157i	−0.0588668	−	0.134971i
$911$			9.32478i			0.308944i	0.987997	+	0.154472i	$0.0493676\pi$
$911$			9.32478i			0.308944i	−0.987997	+	0.154472i	$0.950632\pi$
$912$	−2.75347	+	0.663740i	−0.0911764	+	0.0219786i
$913$	−29.7011	+	17.1479i	−0.982963	+	0.567514i
$914$	−30.3072	−	17.4979i	−1.00247	−	0.578779i
$915$	2.96488	−	10.0433i	0.0980159	−	0.332022i
$916$	−2.96808	+	5.14086i	−0.0980681	+	0.169859i
$917$	23.1543	−	2.58822i	0.764622	−	0.0854705i
$918$	−4.00768	+	3.44214i	−0.132273	+	0.113608i
$919$	20.1504	−	34.9016i	0.664701	−	1.15130i	−0.314665	−	0.949203i	$-0.601892\pi$
$919$	20.1504	−	34.9016i	0.664701	−	1.15130i	0.979366	−	0.202094i	$-0.0647745\pi$
$920$	1.92127	+	3.32774i	0.0633425	+	0.109712i
$921$	18.5830	−	4.47954i	0.612330	−	0.147606i
$922$		−	22.3941i		−	0.737509i
$923$	26.5286	+	24.5778i	0.873200	+	0.808989i
$924$	12.0366	−	4.36458i	0.395976	−	0.143584i
$925$	21.5963	−	12.4686i	0.710081	−	0.409965i
$926$	13.9451	−	8.05118i	0.458263	−	0.264578i
$927$	−4.15214	−	8.11194i	−0.136374	−	0.266431i
$928$			4.63455i			0.152136i
$929$	48.3894	+	27.9376i	1.58760	+	0.916604i	0.993701	+	0.112067i	$0.0357472\pi$
$929$	48.3894	+	27.9376i	1.58760	+	0.916604i	0.593903	+	0.804536i	$0.297586\pi$
$930$	1.13833	−	1.08224i	0.0373273	−	0.0354879i
$931$	−3.39325	+	10.9322i	−0.111209	+	0.358290i
$932$	−17.2354	−	9.95086i	−0.564564	−	0.325951i
$933$	−36.3734	+	8.76802i	−1.19081	+	0.287052i
$934$	16.0720	+	27.8375i	0.525892	+	0.910871i
$935$			1.32273i			0.0432580i
$936$	−2.67021	−	10.4819i	−0.0872786	−	0.342611i
$937$		−	47.2565i		−	1.54380i	−0.635742	−	0.771902i	$-0.719306\pi$
$937$		−	47.2565i		−	1.54380i	0.635742	−	0.771902i	$-0.280694\pi$
$938$	−0.863050	−	0.377450i	−0.0281796	−	0.0123242i
$939$	1.44802	+	6.00697i	0.0472543	+	0.196030i
$940$	−0.0646004	+	0.111891i	−0.00210703	+	0.00364949i
$941$			35.6378i			1.16176i	0.813990	+	0.580879i	$0.197291\pi$
$941$			35.6378i			1.16176i	−0.813990	+	0.580879i	$0.802709\pi$
$942$	7.66209	−	7.28452i	0.249644	−	0.237342i
$943$	44.5713	−	77.1997i	1.45144	−	2.51397i
$944$		−	10.1723i		−	0.331082i
$945$	−4.68462	−	4.36284i	−0.152391	−	0.141923i
$946$	−9.07893	−	15.7252i	−0.295181	−	0.511269i
$947$	−4.77969	−	8.27867i	−0.155319	−	0.269021i	0.777856	−	0.628443i	$-0.216307\pi$
$947$	−4.77969	−	8.27867i	−0.155319	−	0.269021i	−0.933175	+	0.359422i	$0.882974\pi$
$948$	−2.44278	+	8.27476i	−0.0793378	+	0.268752i
$949$	−1.16830	+	5.13646i	−0.0379245	+	0.166736i
$950$	−7.82169			−0.253769
$951$	36.2872	−	8.74726i	1.17669	−	0.283649i
$952$	−1.07786	+	2.46457i	−0.0349338	+	0.0798771i
$953$	25.8589	+	14.9297i	0.837653	+	0.483619i	0.856466	−	0.516204i	$-0.172655\pi$
$953$	25.8589	+	14.9297i	0.837653	+	0.483619i	−0.0188130	+	0.999823i	$0.505989\pi$
$954$	14.6630	−	22.6706i	0.474731	−	0.733988i
$955$	−1.46171	+	2.53176i	−0.0472999	+	0.0819259i
$956$	2.68549	−	4.65141i	0.0868550	−	0.150437i
$957$	21.5101	+	6.34998i	0.695324	+	0.205266i
$958$	−0.698448	−	0.403249i	−0.0225658	−	0.0130284i
$959$	18.0524	−	41.2773i	0.582942	−	1.33291i
$960$	−0.189003	−	0.784062i	−0.00610005	−	0.0253055i
$961$	−27.2073			−0.877656
$962$	−12.7753	+	13.7893i	−0.411891	+	0.444584i
$963$	−21.3576	+	33.0213i	−0.688240	+	1.06410i
$964$	−4.43996	−	7.69024i	−0.143002	−	0.247686i
$965$	1.87375	+	3.24543i	0.0603181	+	0.104474i
$966$	37.2334	+	6.61146i	1.19796	+	0.212720i
$967$		−	24.3574i		−	0.783281i	−0.920118	−	0.391640i	$-0.871908\pi$
$967$		−	24.3574i		−	0.783281i	0.920118	−	0.391640i	$-0.128092\pi$
$968$	−1.59690	+	2.76591i	−0.0513263	+	0.0888998i
$969$	−1.98416	−	2.08700i	−0.0637404	−	0.0670442i
$970$			7.29080i			0.234094i
$971$	−21.4689	+	37.1852i	−0.688970	+	1.19333i	0.283201	+	0.959060i	$0.408604\pi$
$971$	−21.4689	+	37.1852i	−0.688970	+	1.19333i	−0.972171	+	0.234271i	$0.924730\pi$
$972$	−9.54668	−	12.3232i	−0.306210	−	0.395266i
$973$	−48.6281	−	21.2672i	−1.55894	−	0.681795i
$974$			8.45786i			0.271007i
$975$	−0.385219	−	29.8684i	−0.0123369	−	0.956555i
$976$		−	12.9839i		−	0.415606i
$977$	11.3672	+	19.6885i	0.363667	+	0.629890i	0.988561	−	0.150819i	$-0.0481911\pi$
$977$	11.3672	+	19.6885i	0.363667	+	0.629890i	−0.624894	+	0.780710i	$0.714858\pi$
$978$	2.04449	+	8.48137i	0.0653754	+	0.271204i
$979$	28.3422	+	16.3634i	0.905822	+	0.522977i
$980$	−3.11301	−	0.966243i	−0.0994414	−	0.0308655i
$981$	−14.7862	−	28.8874i	−0.472086	−	0.922303i
$982$	4.29055	+	2.47715i	0.136917	+	0.0790490i
$983$		−	58.8980i		−	1.87855i	−0.343159	−	0.939277i	$-0.611497\pi$
$983$		−	58.8980i		−	1.87855i	0.343159	−	0.939277i	$-0.388503\pi$
$984$	−13.5601	+	12.8919i	−0.432280	+	0.410978i
$985$	−4.58468	+	2.64697i	−0.146080	+	0.0843394i
$986$	−4.08070	+	2.35599i	−0.129956	+	0.0750301i
$987$	0.433444	+	1.19535i	0.0137967	+	0.0380485i
$988$	5.63273	−	1.74211i	0.179201	−	0.0554239i
$989$		−	53.6301i		−	1.70534i
$990$	−3.89800	−	0.197064i	−0.123887	−	0.00626309i
$991$	−27.7404	−	48.0478i	−0.881204	−	1.52629i	−0.850004	−	0.526777i	$-0.823400\pi$
$991$	−27.7404	−	48.0478i	−0.881204	−	1.52629i	−0.0312004	−	0.999513i	$-0.509933\pi$
$992$	0.973737	−	1.68656i	0.0309162	−	0.0535484i
$993$	−50.5449	−	14.9213i	−1.60399	−	0.473513i
$994$	26.3729	−	2.94799i	0.836497	−	0.0935047i
$995$	−1.06460	+	1.84394i	−0.0337501	+	0.0584569i
$996$	20.3910	+	6.01960i	0.646113	+	0.190738i
$997$	−35.9697	−	20.7671i	−1.13917	−	0.657702i	−0.192947	−	0.981209i	$-0.561805\pi$
$997$	−35.9697	−	20.7671i	−1.13917	−	0.657702i	−0.946226	+	0.323507i	$0.895138\pi$
$998$	−9.01320	+	5.20377i	−0.285308	+	0.164722i
$999$	−8.97211	+	25.5614i	−0.283865	+	0.808727i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	546.2.q.j.335.1	yes	24
3.2	odd	2		546.2.q.i.335.3	yes	24
7.6	odd	2	inner	546.2.q.j.335.12	yes	24
13.4	even	6		546.2.q.i.251.10	yes	24
21.20	even	2		546.2.q.i.335.10	yes	24
39.17	odd	6	inner	546.2.q.j.251.12	yes	24
91.69	odd	6		546.2.q.i.251.3	✓	24
273.251	even	6	inner	546.2.q.j.251.1	yes	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
546.2.q.i.251.3	✓	24	91.69	odd	6
546.2.q.i.251.10	yes	24	13.4	even	6
546.2.q.i.335.3	yes	24	3.2	odd	2
546.2.q.i.335.10	yes	24	21.20	even	2
546.2.q.j.251.1	yes	24	273.251	even	6	inner
546.2.q.j.251.12	yes	24	39.17	odd	6	inner
546.2.q.j.335.1	yes	24	1.1	even	1	trivial
546.2.q.j.335.12	yes	24	7.6	odd	2	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:	\( N \)	\(=\)	\( 546 = 2 \cdot 3 \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	546.q (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.500000 + 0.866025i) q^{2} +(-1.68382 + 0.405895i) q^{3} +(-0.500000 + 0.866025i) q^{4} +0.465645i q^{5} +(-1.19343 - 1.25528i) q^{6} +(2.62938 - 0.293915i) q^{7} -1.00000 q^{8} +(2.67050 - 1.36691i) q^{9} +O(q^{10})\)	\(q+(0.500000 + 0.866025i) q^{2} +(-1.68382 + 0.405895i) q^{3} +(-0.500000 + 0.866025i) q^{4} +0.465645i q^{5} +(-1.19343 - 1.25528i) q^{6} +(2.62938 - 0.293915i) q^{7} -1.00000 q^{8} +(2.67050 - 1.36691i) q^{9} +(-0.403261 + 0.232823i) q^{10} +(1.39698 + 2.41964i) q^{11} +(0.490394 - 1.66118i) q^{12} +(-0.799665 + 3.51576i) q^{13} +(1.56923 + 2.13015i) q^{14} +(-0.189003 - 0.784062i) q^{15} +(-0.500000 - 0.866025i) q^{16} +(0.508355 - 0.880496i) q^{17} +(2.51903 + 1.62927i) q^{18} +(-0.817625 + 1.41617i) q^{19} +(-0.403261 - 0.232823i) q^{20} +(-4.30810 + 1.56215i) q^{21} +(-1.39698 + 2.41964i) q^{22} +(-7.14652 + 4.12605i) q^{23} +(1.68382 - 0.405895i) q^{24} +4.78317 q^{25} +(-3.44457 + 1.06535i) q^{26} +(-3.94182 + 3.38557i) q^{27} +(-1.06015 + 2.42406i) q^{28} +(-4.01364 + 2.31727i) q^{29} +(0.584516 - 0.555713i) q^{30} +1.94747 q^{31} +(0.500000 - 0.866025i) q^{32} +(-3.33438 - 3.50721i) q^{33} +1.01671 q^{34} +(0.136860 + 1.22436i) q^{35} +(-0.151472 + 2.99617i) q^{36} +(4.51505 - 2.60676i) q^{37} -1.63525 q^{38} +(-0.0805363 - 6.24448i) q^{39} -0.465645i q^{40} +(-9.35517 + 5.40121i) q^{41} +(-3.50691 - 2.94984i) q^{42} +(-3.24949 + 5.62828i) q^{43} -2.79396 q^{44} +(0.636494 + 1.24350i) q^{45} +(-7.14652 - 4.12605i) q^{46} -0.277466i q^{47} +(1.19343 + 1.25528i) q^{48} +(6.82723 - 1.54563i) q^{49} +(2.39159 + 4.14235i) q^{50} +(-0.498589 + 1.68894i) q^{51} +(-2.64490 - 2.45041i) q^{52} -8.99975i q^{53} +(-4.90290 - 1.72093i) q^{54} +(-1.12669 + 0.650496i) q^{55} +(-2.62938 + 0.293915i) q^{56} +(0.801918 - 2.71644i) q^{57} +(-4.01364 - 2.31727i) q^{58} +(8.80951 + 5.08617i) q^{59} +(0.773520 + 0.228350i) q^{60} +(11.2444 + 6.49197i) q^{61} +(0.973737 + 1.68656i) q^{62} +(6.61999 - 4.37901i) q^{63} +1.00000 q^{64} +(-1.63709 - 0.372360i) q^{65} +(1.37014 - 4.64126i) q^{66} +(-0.308335 + 0.178017i) q^{67} +(0.508355 + 0.880496i) q^{68} +(10.3587 - 9.84825i) q^{69} +(-0.991893 + 0.730702i) q^{70} +(5.01505 - 8.68632i) q^{71} +(-2.67050 + 1.36691i) q^{72} +1.46098 q^{73} +(4.51505 + 2.60676i) q^{74} +(-8.05400 + 1.94147i) q^{75} +(-0.817625 - 1.41617i) q^{76} +(4.38435 + 5.95154i) q^{77} +(5.36761 - 3.19199i) q^{78} -4.98126 q^{79} +(0.403261 - 0.232823i) q^{80} +(5.26312 - 7.30065i) q^{81} +(-9.35517 - 5.40121i) q^{82} +12.2750i q^{83} +(0.801186 - 4.51200i) q^{84} +(0.409999 + 0.236713i) q^{85} -6.49897 q^{86} +(5.81767 - 5.53099i) q^{87} +(-1.39698 - 2.41964i) q^{88} +(10.1441 - 5.85671i) q^{89} +(-0.758659 + 1.17297i) q^{90} +(-1.06929 + 9.47927i) q^{91} -8.25209i q^{92} +(-3.27919 + 0.790470i) q^{93} +(0.240293 - 0.138733i) q^{94} +(-0.659432 - 0.380723i) q^{95} +(-0.490394 + 1.66118i) q^{96} +(7.82871 - 13.5597i) q^{97} +(4.75217 + 5.13974i) q^{98} +(7.03805 + 4.55210i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 12 q^{2} - 12 q^{4} - 18 q^{7} - 24 q^{8} + 6 q^{9}+O(q^{10}) \) 24 * q + 12 * q^2 - 12 * q^4 - 18 * q^7 - 24 * q^8 + 6 * q^9	\( 24 q + 12 q^{2} - 12 q^{4} - 18 q^{7} - 24 q^{8} + 6 q^{9} + 12 q^{15} - 12 q^{16} - 6 q^{18} + 12 q^{21} - 36 q^{23} - 12 q^{25} + 18 q^{28} + 6 q^{30} + 12 q^{32} - 36 q^{35} - 12 q^{36} + 36 q^{37} + 12 q^{39} - 12 q^{42} - 42 q^{43} - 36 q^{46} - 6 q^{50} + 12 q^{51} + 18 q^{56} - 36 q^{57} - 6 q^{60} + 66 q^{63} + 24 q^{64} + 66 q^{65} - 54 q^{67} + 48 q^{71} - 6 q^{72} + 36 q^{74} - 12 q^{78} - 48 q^{79} - 6 q^{81} - 24 q^{84} - 84 q^{86} + 36 q^{91} + 54 q^{93} - 36 q^{95} + 36 q^{99}+O(q^{100}) \) 24 * q + 12 * q^2 - 12 * q^4 - 18 * q^7 - 24 * q^8 + 6 * q^9 + 12 * q^15 - 12 * q^16 - 6 * q^18 + 12 * q^21 - 36 * q^23 - 12 * q^25 + 18 * q^28 + 6 * q^30 + 12 * q^32 - 36 * q^35 - 12 * q^36 + 36 * q^37 + 12 * q^39 - 12 * q^42 - 42 * q^43 - 36 * q^46 - 6 * q^50 + 12 * q^51 + 18 * q^56 - 36 * q^57 - 6 * q^60 + 66 * q^63 + 24 * q^64 + 66 * q^65 - 54 * q^67 + 48 * q^71 - 6 * q^72 + 36 * q^74 - 12 * q^78 - 48 * q^79 - 6 * q^81 - 24 * q^84 - 84 * q^86 + 36 * q^91 + 54 * q^93 - 36 * q^95 + 36 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more