LMFDB - Embedded newform 416.2.bf.a.53.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [416,2,Mod(53,416)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(416, base_ring=CyclotomicField(8))

chi = DirichletCharacter(H, H._module([0, 5, 0]))

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

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

chi := DirichletCharacter("416.53");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 416 = 2^{5} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	416.bf (of order $8$, degree $4$, 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:	$3.32177672409$
Analytic rank:	$0$
Dimension:	$192$
Relative dimension:	$48$ over $\Q(\zeta_{8})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{8}]$

Embedding invariants

Embedding label			53.6
Character	$\chi$	$=$	416.53
Dual form			416.2.bf.a.157.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.30913 + 0.534951i) q^{2} +(-2.18213 + 0.903868i) q^{3} +(1.42765 - 1.40064i) q^{4} +(-0.245375 + 0.592388i) q^{5} +(2.37317 - 2.35062i) q^{6} +(-0.0561050 - 0.0561050i) q^{7} +(-1.11971 + 2.59735i) q^{8} +(1.82339 - 1.82339i) q^{9} +(0.00432984 - 0.906777i) q^{10} +(-3.91635 - 1.62221i) q^{11} +(-1.84933 + 4.34680i) q^{12} +(0.382683 + 0.923880i) q^{13} +(0.103462 + 0.0434354i) q^{14} -1.51445i q^{15} +(0.0763944 - 3.99927i) q^{16} +1.12749i q^{17} +(-1.41164 + 3.36249i) q^{18} +(-2.51373 - 6.06867i) q^{19} +(0.479413 + 1.18941i) q^{20} +(0.173140 + 0.0717169i) q^{21} +(5.99482 + 0.0286251i) q^{22} +(1.07931 - 1.07931i) q^{23} +(0.0956940 - 6.67984i) q^{24} +(3.24482 + 3.24482i) q^{25} +(-0.995214 - 1.00476i) q^{26} +(0.380827 - 0.919398i) q^{27} +(-0.158682 - 0.00151544i) q^{28} +(0.936042 - 0.387721i) q^{29} +(0.810159 + 1.98262i) q^{30} +6.40551 q^{31} +(2.03940 + 5.27644i) q^{32} +10.0122 q^{33} +(-0.603150 - 1.47603i) q^{34} +(0.0470026 - 0.0194691i) q^{35} +(0.0492512 - 5.15710i) q^{36} +(3.65943 - 8.83465i) q^{37} +(6.53724 + 6.59997i) q^{38} +(-1.67013 - 1.67013i) q^{39} +(-1.26389 - 1.30063i) q^{40} +(4.29726 - 4.29726i) q^{41} +(-0.265028 - 0.00126550i) q^{42} +(3.00252 + 1.24369i) q^{43} +(-7.86333 + 3.16946i) q^{44} +(0.632741 + 1.52757i) q^{45} +(-0.835583 + 1.99034i) q^{46} +1.39908i q^{47} +(3.44811 + 8.79598i) q^{48} -6.99370i q^{49} +(-5.98372 - 2.51208i) q^{50} +(-1.01910 - 2.46032i) q^{51} +(1.84037 + 0.782978i) q^{52} +(-1.35454 - 0.561067i) q^{53} +(-0.00672001 + 1.40734i) q^{54} +(1.92195 - 1.92195i) q^{55} +(0.208546 - 0.0829030i) q^{56} +(10.9706 + 10.9706i) q^{57} +(-1.01799 + 1.00832i) q^{58} +(0.487735 - 1.17750i) q^{59} +(-2.12121 - 2.16212i) q^{60} +(-2.48250 + 1.02829i) q^{61} +(-8.38566 + 3.42664i) q^{62} -0.204603 q^{63} +(-5.49249 - 5.81658i) q^{64} -0.641196 q^{65} +(-13.1074 + 5.35606i) q^{66} +(-5.72975 + 2.37334i) q^{67} +(1.57921 + 1.60966i) q^{68} +(-1.37964 + 3.33076i) q^{69} +(-0.0511176 + 0.0506318i) q^{70} +(-8.71943 - 8.71943i) q^{71} +(2.69432 + 6.77768i) q^{72} +(9.50101 - 9.50101i) q^{73} +(-0.0645737 + 13.5233i) q^{74} +(-10.0135 - 4.14773i) q^{75} +(-12.0888 - 5.14313i) q^{76} +(0.128713 + 0.310741i) q^{77} +(3.07986 + 1.29298i) q^{78} +1.14559i q^{79} +(2.35037 + 1.02658i) q^{80} +10.0865i q^{81} +(-3.32685 + 7.92450i) q^{82} +(2.85267 + 6.88695i) q^{83} +(0.347634 - 0.140120i) q^{84} +(-0.667908 - 0.276657i) q^{85} +(-4.59601 - 0.0219459i) q^{86} +(-1.69212 + 1.69212i) q^{87} +(8.59863 - 8.35574i) q^{88} +(-9.25342 - 9.25342i) q^{89} +(-1.64552 - 1.66131i) q^{90} +(0.0303638 - 0.0733047i) q^{91} +(0.0291530 - 3.05262i) q^{92} +(-13.9777 + 5.78974i) q^{93} +(-0.748440 - 1.83158i) q^{94} +4.21181 q^{95} +(-9.21945 - 9.67053i) q^{96} -7.62258 q^{97} +(3.74129 + 9.15568i) q^{98} +(-10.0990 + 4.18313i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 192 q - 16 q^{10} - 16 q^{12} - 40 q^{16} - 40 q^{18} - 8 q^{22} - 16 q^{23} + 24 q^{24} + 80 q^{30} - 48 q^{31} - 48 q^{35} + 80 q^{36} - 56 q^{38} - 64 q^{40} - 16 q^{43} - 80 q^{44} + 24 q^{50} + 32 q^{51}+ \cdots + 56 q^{98}+O(q^{100}) $ 192 * q - 16 * q^10 - 16 * q^12 - 40 * q^16 - 40 * q^18 - 8 * q^22 - 16 * q^23 + 24 * q^24 + 80 * q^30 - 48 * q^31 - 48 * q^35 + 80 * q^36 - 56 * q^38 - 64 * q^40 - 16 * q^43 - 80 * q^44 + 24 * q^50 + 32 * q^51 - 32 * q^53 - 24 * q^54 + 32 * q^55 + 16 * q^56 - 64 * q^58 - 56 * q^60 - 64 * q^61 + 24 * q^62 + 80 * q^63 + 72 * q^64 + 96 * q^66 + 80 * q^67 - 32 * q^68 - 64 * q^69 - 120 * q^72 - 32 * q^74 + 32 * q^75 + 64 * q^76 - 32 * q^77 - 56 * q^80 - 80 * q^82 - 80 * q^83 + 112 * q^84 - 112 * q^87 - 88 * q^88 - 120 * q^90 + 144 * q^92 + 40 * q^94 + 136 * q^96 + 56 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/416\mathbb{Z}\right)^\times$.

$n$	$261$	$287$	$353$
$\chi(n)$	$e\left(\frac{5}{8}\right)$	$1$	$1$

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 $

$2$	−1.30913	+	0.534951i	−0.925696	+	0.378268i
$2$	−1.30913	+	0.534951i	−0.925696	+	0.378268i
$3$	−2.18213	+	0.903868i	−1.25985	+	0.521848i	−0.909865	−	0.414905i	$-0.863815\pi$
$3$	−2.18213	+	0.903868i	−1.25985	+	0.521848i	−0.349989	+	0.936754i	$0.613815\pi$
$4$	1.42765	−	1.40064i	0.713827	−	0.700322i
$5$	−0.245375	+	0.592388i	−0.109735	+	0.264924i	−0.969202	−	0.246268i	$-0.920796\pi$
$5$	−0.245375	+	0.592388i	−0.109735	+	0.264924i	0.859467	+	0.511192i	$0.170796\pi$
$6$	2.37317	−	2.35062i	0.968843	−	0.959635i
$7$	−0.0561050	−	0.0561050i	−0.0212057	−	0.0212057i	0.696424	−	0.717630i	$-0.254773\pi$
$7$	−0.0561050	−	0.0561050i	−0.0212057	−	0.0212057i	−0.717630	+	0.696424i	$0.754773\pi$
$8$	−1.11971	+	2.59735i	−0.395878	+	0.918303i
$9$	1.82339	−	1.82339i	0.607798	−	0.607798i
$10$	0.00432984	−	0.906777i	0.00136922	−	0.286748i
$11$	−3.91635	−	1.62221i	−1.18082	−	0.489113i	−0.296068	−	0.955167i	$-0.595675\pi$
$11$	−3.91635	−	1.62221i	−1.18082	−	0.489113i	−0.884757	+	0.466053i	$0.845675\pi$
$12$	−1.84933	+	4.34680i	−0.533856	+	1.25481i
$13$	0.382683	+	0.923880i	0.106137	+	0.256238i
$13$	0.382683	+	0.923880i	0.106137	+	0.256238i
$14$	0.103462	+	0.0434354i	0.0276514	+	0.0116086i
$15$		−	1.51445i		−	0.391030i
$16$	0.0763944	−	3.99927i	0.0190986	−	0.999818i
$17$			1.12749i			0.273455i	0.990609	+	0.136728i	$0.0436585\pi$
$17$			1.12749i			0.273455i	−0.990609	+	0.136728i	$0.956341\pi$
$18$	−1.41164	+	3.36249i	−0.332726	+	0.792547i
$19$	−2.51373	−	6.06867i	−0.576688	−	1.39225i	−0.895769	−	0.444521i	$-0.853374\pi$
$19$	−2.51373	−	6.06867i	−0.576688	−	1.39225i	0.319080	−	0.947728i	$-0.396626\pi$
$20$	0.479413	+	1.18941i	0.107200	+	0.265960i
$21$	0.173140	+	0.0717169i	0.0377822	+	0.0156499i
$22$	5.99482	+	0.0286251i	1.27810	+	0.00610290i
$23$	1.07931	−	1.07931i	0.225052	−	0.225052i	−0.585570	−	0.810622i	$-0.699129\pi$
$23$	1.07931	−	1.07931i	0.225052	−	0.225052i	0.810622	+	0.585570i	$0.199129\pi$
$24$	0.0956940	−	6.67984i	0.0195335	−	1.36352i
$25$	3.24482	+	3.24482i	0.648964	+	0.648964i
$26$	−0.995214	−	1.00476i	−0.195177	−	0.197050i
$27$	0.380827	−	0.919398i	0.0732902	−	0.176938i
$28$	−0.158682	−	0.00151544i	−0.0299880	−	0.000286391i
$29$	0.936042	−	0.387721i	0.173819	−	0.0719980i	−0.294077	−	0.955782i	$-0.595012\pi$
$29$	0.936042	−	0.387721i	0.173819	−	0.0719980i	0.467896	+	0.883784i	$0.345012\pi$
$30$	0.810159	+	1.98262i	0.147914	+	0.361975i
$31$	6.40551			1.15046			0.575232	−	0.817990i	$-0.304912\pi$
$31$	6.40551			1.15046			0.575232	+	0.817990i	$0.304912\pi$
$32$	2.03940	+	5.27644i	0.360519	+	0.932752i
$33$	10.0122			1.74291
$34$	−0.603150	−	1.47603i	−0.103439	−	0.253137i
$35$	0.0470026	−	0.0194691i	0.00794490	−	0.00329088i
$36$	0.0492512	−	5.15710i	0.00820854	−	0.859517i
$37$	3.65943	−	8.83465i	0.601607	−	1.45241i	−0.270319	−	0.962771i	$-0.587129\pi$
$37$	3.65943	−	8.83465i	0.601607	−	1.45241i	0.871926	−	0.489637i	$-0.162871\pi$
$38$	6.53724	+	6.59997i	1.06048	+	1.07066i
$39$	−1.67013	−	1.67013i	−0.267435	−	0.267435i
$40$	−1.26389	−	1.30063i	−0.199839	−	0.205648i
$41$	4.29726	−	4.29726i	0.671119	−	0.671119i	−0.286855	−	0.957974i	$-0.592610\pi$
$41$	4.29726	−	4.29726i	0.671119	−	0.671119i	0.957974	+	0.286855i	$0.0926099\pi$
$42$	−0.265028	−	0.00126550i	−0.0408947	−	0.000195271i
$43$	3.00252	+	1.24369i	0.457881	+	0.189660i	0.599688	−	0.800234i	$-0.295291\pi$
$43$	3.00252	+	1.24369i	0.457881	+	0.189660i	−0.141807	+	0.989894i	$0.545291\pi$
$44$	−7.86333	+	3.16946i	−1.18544	+	0.477815i
$45$	0.632741	+	1.52757i	0.0943235	+	0.227717i
$46$	−0.835583	+	1.99034i	−0.123200	+	0.293460i
$47$			1.39908i			0.204077i	0.994780	+	0.102039i	$0.0325365\pi$
$47$			1.39908i			0.204077i	−0.994780	+	0.102039i	$0.967463\pi$
$48$	3.44811	+	8.79598i	0.497692	+	1.26959i
$49$		−	6.99370i		−	0.999101i
$50$	−5.98372	−	2.51208i	−0.846226	−	0.355261i
$51$	−1.01910	−	2.46032i	−0.142702	−	0.344514i
$52$	1.84037	+	0.782978i	0.255213	+	0.108579i
$53$	−1.35454	−	0.561067i	−0.186060	−	0.0770685i	0.287709	−	0.957718i	$-0.407107\pi$
$53$	−1.35454	−	0.561067i	−0.186060	−	0.0770685i	−0.473768	+	0.880650i	$0.657107\pi$
$54$	−0.00672001	+	1.40734i	−0.000914477	+	0.191514i
$55$	1.92195	−	1.92195i	0.259156	−	0.259156i
$56$	0.208546	−	0.0829030i	0.0278681	−	0.0110784i
$57$	10.9706	+	10.9706i	1.45309	+	1.45309i
$58$	−1.01799	+	1.00832i	−0.133669	+	0.132398i
$59$	0.487735	−	1.17750i	0.0634977	−	0.153297i	−0.888946	−	0.458013i	$-0.848561\pi$
$59$	0.487735	−	1.17750i	0.0634977	−	0.153297i	0.952443	+	0.304716i	$0.0985614\pi$
$60$	−2.12121	−	2.16212i	−0.273847	−	0.279128i
$61$	−2.48250	+	1.02829i	−0.317852	+	0.131658i	−0.535905	−	0.844278i	$-0.680029\pi$
$61$	−2.48250	+	1.02829i	−0.317852	+	0.131658i	0.218053	+	0.975937i	$0.430029\pi$
$62$	−8.38566	+	3.42664i	−1.06498	+	0.435183i
$63$	−0.204603			−0.0257776
$64$	−5.49249	−	5.81658i	−0.686561	−	0.727072i
$65$	−0.641196			−0.0795305
$66$	−13.1074	+	5.35606i	−1.61340	+	0.659286i
$67$	−5.72975	+	2.37334i	−0.700001	+	0.289950i	−0.704160	−	0.710042i	$-0.748676\pi$
$67$	−5.72975	+	2.37334i	−0.700001	+	0.289950i	0.00415906	+	0.999991i	$0.498676\pi$
$68$	1.57921	+	1.60966i	0.191507	+	0.195200i
$69$	−1.37964	+	3.33076i	−0.166090	+	0.400976i
$70$	−0.0511176	+	0.0506318i	−0.00610973	+	0.00605166i
$71$	−8.71943	−	8.71943i	−1.03481	−	1.03481i	−0.999372	−	0.0354345i	$-0.988718\pi$
$71$	−8.71943	−	8.71943i	−1.03481	−	1.03481i	−0.0354345	−	0.999372i	$-0.511282\pi$
$72$	2.69432	+	6.77768i	0.317529	+	0.798757i
$73$	9.50101	−	9.50101i	1.11201	−	1.11201i	0.119131	−	0.992879i	$-0.461989\pi$
$73$	9.50101	−	9.50101i	1.11201	−	1.11201i	0.992879	−	0.119131i	$-0.0380108\pi$
$74$	−0.0645737	+	13.5233i	−0.00750654	+	1.57206i
$75$	−10.0135	−	4.14773i	−1.15626	−	0.478939i
$76$	−12.0888	−	5.14313i	−1.38668	−	0.589957i
$77$	0.128713	+	0.310741i	0.0146682	+	0.0354122i
$78$	3.07986	+	1.29298i	0.348725	+	0.146402i
$79$			1.14559i			0.128889i	0.997921	+	0.0644447i	$0.0205276\pi$
$79$			1.14559i			0.128889i	−0.997921	+	0.0644447i	$0.979472\pi$
$80$	2.35037	+	1.02658i	0.262780	+	0.114775i
$81$			10.0865i			1.12072i
$82$	−3.32685	+	7.92450i	−0.367390	+	0.875115i
$83$	2.85267	+	6.88695i	0.313121	+	0.755941i	0.999586	+	0.0287780i	$0.00916158\pi$
$83$	2.85267	+	6.88695i	0.313121	+	0.755941i	−0.686465	+	0.727163i	$0.740838\pi$
$84$	0.347634	−	0.140120i	0.0379299	−	0.0152884i
$85$	−0.667908	−	0.276657i	−0.0724448	−	0.0300076i
$86$	−4.59601	−	0.0219459i	−0.495601	−	0.00236648i
$87$	−1.69212	+	1.69212i	−0.181414	+	0.181414i
$88$	8.59863	−	8.35574i	0.916617	−	0.890725i
$89$	−9.25342	−	9.25342i	−0.980860	−	0.980860i	0.0189600	−	0.999820i	$-0.493964\pi$
$89$	−9.25342	−	9.25342i	−0.980860	−	0.980860i	−0.999820	+	0.0189600i	$0.993964\pi$
$90$	−1.64552	−	1.66131i	−0.173453	−	0.175117i
$91$	0.0303638	−	0.0733047i	0.00318299	−	0.00768442i
$92$	0.0291530	−	3.05262i	0.00303941	−	0.318257i
$93$	−13.9777	+	5.78974i	−1.44942	+	0.600368i
$94$	−0.748440	−	1.83158i	−0.0771957	−	0.188913i
$95$	4.21181			0.432123
$96$	−9.21945	−	9.67053i	−0.940956	−	0.986994i
$97$	−7.62258			−0.773956			−0.386978	−	0.922089i	$-0.626481\pi$
$97$	−7.62258			−0.773956			−0.386978	+	0.922089i	$0.626481\pi$
$98$	3.74129	+	9.15568i	0.377927	+	0.924864i
$99$	−10.0990	+	4.18313i	−1.01499	+	0.420421i
$100$	9.17732	+	0.0876450i	0.917732	+	0.00876450i
$101$	2.04349	−	4.93341i	0.203335	−	0.490893i	−0.789012	−	0.614378i	$-0.789407\pi$
$101$	2.04349	−	4.93341i	0.203335	−	0.490893i	0.992346	+	0.123485i	$0.0394070\pi$
$102$	2.65029	+	2.67572i	0.262417	+	0.264935i
$103$	−13.1754	−	13.1754i	−1.29821	−	1.29821i	−0.929575	−	0.368633i	$-0.879826\pi$
$103$	−13.1754	−	13.1754i	−1.29821	−	1.29821i	−0.368633	−	0.929575i	$-0.620174\pi$
$104$	−2.82814	−	0.0405153i	−0.277322	−	0.00397286i
$105$	−0.0849684	+	0.0849684i	−0.00829206	+	0.00829206i
$106$	2.07341	+	0.00990048i	0.201387	+	0.000961620i
$107$	0.135180	+	0.0559933i	0.0130683	+	0.00541308i	0.389208	−	0.921150i	$-0.372749\pi$
$107$	0.135180	+	0.0559933i	0.0130683	+	0.00541308i	−0.376140	+	0.926563i	$0.622749\pi$
$108$	−0.744060	−	1.84599i	−0.0715972	−	0.177630i
$109$	1.12145	+	2.70742i	0.107415	+	0.259324i	0.968443	−	0.249234i	$-0.0801789\pi$
$109$	1.12145	+	2.70742i	0.107415	+	0.259324i	−0.861028	+	0.508558i	$0.830179\pi$
$110$	−1.48794	+	3.54423i	−0.141869	+	0.337930i
$111$			22.5860i			2.14377i
$112$	−0.228665	+	0.220093i	−0.0216068	+	0.0207968i
$113$			17.0763i			1.60640i	0.595708	+	0.803201i	$0.296871\pi$
$113$			17.0763i			1.60640i	−0.595708	+	0.803201i	$0.703129\pi$
$114$	−20.2306	−	8.49319i	−1.89477	−	0.795460i
$115$	0.374535	+	0.904208i	0.0349256	+	0.0843178i
$116$	0.793285	−	1.86459i	0.0736547	−	0.173123i
$117$	2.38238	+	0.986814i	0.220251	+	0.0912310i
$118$	−0.00860648	+	1.80241i	−0.000792290	+	0.165925i
$119$	0.0632575	−	0.0632575i	0.00579881	−	0.00579881i
$120$	3.93357	+	1.69575i	0.359084	+	0.154800i
$121$	4.92808	+	4.92808i	0.448007	+	0.448007i
$122$	2.69984	−	2.67418i	0.244432	−	0.242109i
$123$	−5.49302	+	13.2613i	−0.495289	+	1.19573i
$124$	9.14485	−	8.97184i	0.821232	−	0.805695i
$125$	−5.68033	+	2.35287i	−0.508064	+	0.210447i
$126$	0.267852	−	0.109453i	0.0238622	−	0.00975081i
$127$	15.0751			1.33770			0.668848	−	0.743399i	$-0.266788\pi$
$127$	15.0751			1.33770			0.668848	+	0.743399i	$0.266788\pi$
$128$	10.3020	+	4.67646i	0.910575	+	0.413344i
$129$	−7.67603			−0.675837
$130$	0.839410	−	0.343008i	0.0736211	−	0.0300838i
$131$	6.78546	−	2.81063i	0.592848	−	0.245566i	−0.0660273	−	0.997818i	$-0.521032\pi$
$131$	6.78546	−	2.81063i	0.592848	−	0.245566i	0.658875	+	0.752252i	$0.271032\pi$
$132$	14.2940	−	14.0236i	1.24414	−	1.22060i
$133$	−0.199450	+	0.481515i	−0.0172945	+	0.0417526i
$134$	6.23138	−	6.17216i	0.538309	−	0.533193i
$135$	0.451195	+	0.451195i	0.0388327	+	0.0388327i
$136$	−2.92848	−	1.26246i	−0.251115	−	0.108255i
$137$	9.05065	−	9.05065i	0.773249	−	0.773249i	−0.205424	−	0.978673i	$-0.565857\pi$
$137$	9.05065	−	9.05065i	0.773249	−	0.773249i	0.978673	+	0.205424i	$0.0658573\pi$
$138$	0.0243449	−	5.09844i	0.00207238	−	0.434008i
$139$	−1.32970	−	0.550778i	−0.112783	−	0.0467164i	0.325578	−	0.945515i	$-0.394441\pi$
$139$	−1.32970	−	0.550778i	−0.112783	−	0.0467164i	−0.438362	+	0.898799i	$0.644441\pi$
$140$	0.0398342	−	0.0936291i	0.00336661	−	0.00791311i
$141$	−1.26459	−	3.05298i	−0.106497	−	0.257107i
$142$	16.0794	+	6.75042i	1.34935	+	0.566483i
$143$		−	4.23903i		−	0.354485i
$144$	−7.15295	−	7.43155i	−0.596079	−	0.619295i
$145$			0.649637i			0.0539494i
$146$	−7.35550	+	17.5207i	−0.608746	+	1.45002i
$147$	6.32139	+	15.2612i	0.521379	+	1.25872i
$148$	−7.14980	−	17.7384i	−0.587710	−	1.45809i
$149$	−18.4558	−	7.64465i	−1.51196	−	0.626274i	−0.535998	−	0.844219i	$-0.680065\pi$
$149$	−18.4558	−	7.64465i	−1.51196	−	0.626274i	−0.975961	+	0.217945i	$0.930065\pi$
$150$	15.3278	+	0.0731901i	1.25151	+	0.00597595i
$151$	1.20680	−	1.20680i	0.0982077	−	0.0982077i	−0.656296	−	0.754504i	$-0.727878\pi$
$151$	1.20680	−	1.20680i	0.0982077	−	0.0982077i	0.754504	+	0.656296i	$0.227878\pi$
$152$	18.5771	+	0.266132i	1.50680	+	0.0215862i
$153$	2.05585	+	2.05585i	0.166206	+	0.166206i
$154$	−0.334733	−	0.337945i	−0.0269736	−	0.0272324i
$155$	−1.57175	+	3.79454i	−0.126246	+	0.304785i
$156$	−4.72363	−	0.0451114i	−0.378193	−	0.00361181i
$157$	2.43590	−	1.00898i	0.194406	−	0.0805257i	−0.283356	−	0.959015i	$-0.591448\pi$
$157$	2.43590	−	1.00898i	0.194406	−	0.0805257i	0.477763	+	0.878489i	$0.341448\pi$
$158$	−0.612837	−	1.49973i	−0.0487547	−	0.119312i
$159$	3.46290			0.274626
$160$	−3.62612	−	0.0865889i	−0.286670	−	0.00684546i
$161$	−0.121110			−0.00954477
$162$	−5.39577	−	13.2045i	−0.423932	−	1.03745i
$163$	−1.68592	+	0.698331i	−0.132052	+	0.0546975i	−0.447731	−	0.894168i	$-0.647768\pi$
$163$	−1.68592	+	0.698331i	−0.132052	+	0.0546975i	0.315679	+	0.948866i	$0.397768\pi$
$164$	0.116072	−	12.1539i	0.00906370	−	0.949062i
$165$	−2.45676	+	5.93113i	−0.191258	+	0.461738i
$166$	−7.41870	−	7.48989i	−0.575803	−	0.581328i
$167$	−3.37263	−	3.37263i	−0.260982	−	0.260982i	0.564471	−	0.825453i	$-0.309080\pi$
$167$	−3.37263	−	3.37263i	−0.260982	−	0.260982i	−0.825453	+	0.564471i	$0.809080\pi$
$168$	−0.380141	+	0.369403i	−0.0293285	+	0.0285001i
$169$	−0.707107	+	0.707107i	−0.0543928	+	0.0543928i
$170$	1.02238	+	0.00488183i	0.0784128	+	0.000374420i
$171$	−15.6491	−	6.48207i	−1.19672	−	0.495696i
$172$	6.02853	−	2.42991i	0.459671	−	0.185279i
$173$	−4.96431	−	11.9849i	−0.377429	−	0.911195i	−0.992446	−	0.122681i	$-0.960851\pi$
$173$	−4.96431	−	11.9849i	−0.377429	−	0.911195i	0.615017	−	0.788514i	$-0.289149\pi$
$174$	1.31000	−	3.12040i	0.0993112	−	0.236557i
$175$		−	0.364101i		−	0.0275234i
$176$	−6.78683	+	15.5386i	−0.511576	+	1.17127i
$177$			3.01030i			0.226268i
$178$	17.0641	+	7.16382i	1.27901	+	0.536951i
$179$	9.62151	+	23.2284i	0.719146	+	1.73617i	0.675770	+	0.737113i	$0.263811\pi$
$179$	9.62151	+	23.2284i	0.719146	+	1.73617i	0.0433760	+	0.999059i	$0.486189\pi$
$180$	3.04292	+	1.29460i	0.226806	+	0.0964938i
$181$	−5.92141	−	2.45273i	−0.440135	−	0.182310i	0.151601	−	0.988442i	$-0.451557\pi$
$181$	−5.92141	−	2.45273i	−0.440135	−	0.182310i	−0.591736	+	0.806132i	$0.701557\pi$
$182$	−0.000535794		0.112209i	−3.97157e−5		0.00831746i
$183$	4.48770	−	4.48770i	0.331741	−	0.331741i
$184$	1.59484	+	4.01188i	0.117573	+	0.295759i
$185$	4.33561	+	4.33561i	0.318760	+	0.318760i
$186$	15.2014	−	15.0569i	1.11462	−	1.10402i
$187$	1.82901	−	4.41563i	0.133751	−	0.322903i
$188$	1.95962	+	1.99741i	0.142920	+	0.145676i
$189$	−0.0729491	+	0.0302165i	−0.00530627	+	0.00219793i
$190$	−5.51382	+	2.25311i	−0.400014	+	0.163458i
$191$	19.4101			1.40447			0.702234	−	0.711947i	$-0.252186\pi$
$191$	19.4101			1.40447			0.702234	+	0.711947i	$0.252186\pi$
$192$	17.2427	+	7.72805i	1.24439	+	0.557724i
$193$	−19.0783			−1.37329			−0.686643	−	0.726995i	$-0.740916\pi$
$193$	−19.0783			−1.37329			−0.686643	+	0.726995i	$0.740916\pi$
$194$	9.97897	−	4.07771i	0.716448	−	0.292763i
$195$	1.39917	−	0.579556i	0.100197	−	0.0415029i
$196$	−9.79569	−	9.98459i	−0.699692	−	0.713185i
$197$	1.93413	−	4.66941i	0.137801	−	0.332682i	−0.839881	−	0.542770i	$-0.817375\pi$
$197$	1.93413	−	4.66941i	0.137801	−	0.332682i	0.977682	+	0.210089i	$0.0673753\pi$
$198$	10.9831	−	10.8787i	0.780537	−	0.773118i
$199$	−2.54683	−	2.54683i	−0.180540	−	0.180540i	0.611051	−	0.791591i	$-0.290747\pi$
$199$	−2.54683	−	2.54683i	−0.180540	−	0.180540i	−0.791591	+	0.611051i	$0.790747\pi$
$200$	−12.0612	+	4.79468i	−0.852856	+	0.339035i
$201$	10.3579	−	10.3579i	0.730588	−	0.730588i
$202$	−0.0360590	+	7.55166i	−0.00253710	+	0.531333i
$203$	−0.0742697	−	0.0307635i	−0.00521271	−	0.00215918i
$204$	−4.90095	−	2.08509i	−0.343135	−	0.145986i
$205$	1.49120	+	3.60008i	0.104150	+	0.251441i
$206$	24.2965	+	10.2001i	1.69282	+	0.710676i
$207$		−	3.93603i		−	0.273573i
$208$	3.72408	−	1.45988i	0.258218	−	0.101224i
$209$			27.8448i			1.92607i
$210$	0.0657809	−	0.156689i	0.00453931	−	0.0108126i
$211$	0.894728	+	2.16006i	0.0615956	+	0.148705i	0.951681	−	0.307090i	$-0.0993552\pi$
$211$	0.894728	+	2.16006i	0.0615956	+	0.148705i	−0.890085	+	0.455795i	$0.849355\pi$
$212$	−2.71966	+	1.09621i	−0.186787	+	0.0752881i
$213$	26.9082	+	11.1457i	1.84372	+	0.763692i
$214$	−0.206922		0.000988048i	−0.0141449		6.75416e-5i
$215$	−1.47349	+	1.47349i	−0.100491	+	0.100491i
$216$	1.96159	+	2.01860i	0.133469	+	0.137349i
$217$	−0.359381	−	0.359381i	−0.0243964	−	0.0243964i
$218$	−2.91646	−	2.94445i	−0.197528	−	0.199423i
$219$	−12.1448	+	29.3201i	−0.820669	+	1.98127i
$220$	0.0519133	−	5.43585i	0.00349999	−	0.366485i
$221$	−1.04166	+	0.431470i	−0.0700697	+	0.0290238i
$222$	−12.0824	−	29.5681i	−0.810918	−	1.98448i
$223$	−20.5592			−1.37674			−0.688372	−	0.725358i	$-0.741674\pi$
$223$	−20.5592			−1.37674			−0.688372	+	0.725358i	$0.741674\pi$
$224$	0.181614	−	0.410455i	0.0121346	−	0.0274247i
$225$	11.8332			0.788878
$226$	−9.13498	−	22.3551i	−0.607650	−	1.48704i
$227$	10.3971	−	4.30664i	0.690083	−	0.285842i	−0.00995180	−	0.999950i	$-0.503168\pi$
$227$	10.3971	−	4.30664i	0.690083	−	0.285842i	0.700035	+	0.714109i	$0.253168\pi$
$228$	31.0280	+	0.296323i	2.05488	+	0.0196244i
$229$	10.5973	−	25.5841i	0.700289	−	1.69065i	−0.0226564	−	0.999743i	$-0.507212\pi$
$229$	10.5973	−	25.5841i	0.700289	−	1.69065i	0.722946	−	0.690905i	$-0.242788\pi$
$230$	−0.974023	−	0.983369i	−0.0642252	−	0.0648415i
$231$	−0.561737	−	0.561737i	−0.0369596	−	0.0369596i
$232$	−0.0410487	+	2.86537i	−0.00269498	+	0.188121i
$233$	−9.23553	+	9.23553i	−0.605040	+	0.605040i	−0.941646	−	0.336606i	$-0.890721\pi$
$233$	−9.23553	+	9.23553i	−0.605040	+	0.605040i	0.336606	+	0.941646i	$0.390721\pi$
$234$	−3.64675	−	0.0174131i	−0.238395	−	0.00113833i
$235$	−0.828799	−	0.343300i	−0.0540649	−	0.0223944i
$236$	−0.952936	−	2.36420i	−0.0620308	−	0.153896i
$237$	−1.03547	−	2.49984i	−0.0672607	−	0.162382i
$238$	−0.0489728	+	0.116652i	−0.00317443	+	0.00756144i
$239$		−	18.3309i		−	1.18573i	−0.805302	−	0.592865i	$-0.797997\pi$
$239$		−	18.3309i		−	1.18573i	0.805302	−	0.592865i	$-0.202003\pi$
$240$	−6.05671	−	0.115696i	−0.390959	−	0.00746813i
$241$			13.5408i			0.872240i	0.899888	+	0.436120i	$0.143648\pi$
$241$			13.5408i			0.872240i	−0.899888	+	0.436120i	$0.856352\pi$
$242$	−9.08779	−	3.81523i	−0.584185	−	0.245252i
$243$	−7.97436	−	19.2518i	−0.511555	−	1.23500i
$244$	−2.10389	+	4.94513i	−0.134688	+	0.316580i
$245$	4.14298	+	1.71608i	0.264686	+	0.109636i
$246$	0.0969288	−	20.2993i	0.00617996	−	1.29424i
$247$	4.64476	−	4.64476i	0.295539	−	0.295539i
$248$	−7.17233	+	16.6374i	−0.455443	+	1.05647i
$249$	−12.4498	−	12.4498i	−0.788973	−	0.788973i
$250$	6.17763	−	6.11891i	0.390708	−	0.386994i
$251$	1.32598	−	3.20119i	0.0836949	−	0.202057i	−0.876492	−	0.481417i	$-0.840122\pi$
$251$	1.32598	−	3.20119i	0.0836949	−	0.202057i	0.960187	+	0.279360i	$0.0901222\pi$
$252$	−0.292102	+	0.286576i	−0.0184007	+	0.0180526i
$253$	−5.97783	+	2.47610i	−0.375823	+	0.155671i
$254$	−19.7353	+	8.06443i	−1.23830	+	0.506007i
$255$	1.70752			0.106929
$256$	−15.9883	−	0.611044i	−0.999270	−	0.0381902i
$257$	7.54279			0.470507			0.235253	−	0.971934i	$-0.424408\pi$
$257$	7.54279			0.470507			0.235253	+	0.971934i	$0.424408\pi$
$258$	10.0489	−	4.10630i	0.625619	−	0.255647i
$259$	−0.700980	+	0.290356i	−0.0435568	+	0.0180418i
$260$	−0.915406	+	0.898087i	−0.0567711	+	0.0556970i
$261$	0.999805	−	2.41374i	0.0618864	−	0.149407i
$262$	−7.37951	+	7.30937i	−0.455908	+	0.451574i
$263$	−18.7532	−	18.7532i	−1.15637	−	1.15637i	−0.985249	−	0.171125i	$-0.945260\pi$
$263$	−18.7532	−	18.7532i	−1.15637	−	1.15637i	−0.171125	−	0.985249i	$-0.554740\pi$
$264$	−11.2108	+	26.0053i	−0.689979	+	1.60052i
$265$	0.664738	−	0.664738i	0.0408345	−	0.0408345i
$266$	0.00351946	−	0.737063i	0.000215792	−	0.0451922i
$267$	28.5560	+	11.8283i	1.74760	+	0.723880i
$268$	−4.85590	+	11.4137i	−0.296621	+	0.697200i
$269$	−7.26788	−	17.5462i	−0.443130	−	1.06981i	−0.974844	−	0.222887i	$-0.928452\pi$
$269$	−7.26788	−	17.5462i	−0.443130	−	1.06981i	0.531714	−	0.846924i	$-0.321548\pi$
$270$	−0.832041	−	0.349306i	−0.0506364	−	0.0212581i
$271$		−	4.23969i		−	0.257543i	−0.991674	−	0.128772i	$-0.958897\pi$
$271$		−	4.23969i		−	0.257543i	0.991674	−	0.128772i	$-0.0411034\pi$
$272$	4.50912	+	0.0861336i	0.273406	+	0.00522262i
$273$			0.187405i			0.0113423i
$274$	−7.00684	+	16.6902i	−0.423299	+	1.00829i
$275$	−7.44409	−	17.9716i	−0.448895	−	1.08373i
$276$	2.69555	+	6.68756i	0.162253	+	0.402544i
$277$	10.9664	+	4.54242i	0.658906	+	0.272928i	0.686978	−	0.726678i	$-0.258937\pi$
$277$	10.9664	+	4.54242i	0.658906	+	0.272928i	−0.0280721	+	0.999606i	$0.508937\pi$
$278$	2.03539	+	0.00971893i	0.122074	+	0.000582903i
$279$	11.6798	−	11.6798i	0.699250	−	0.699250i
$280$	−0.00206123	+	0.143882i	−0.000123182	+	0.00859861i
$281$	−8.02546	−	8.02546i	−0.478759	−	0.478759i	0.425976	−	0.904735i	$-0.359931\pi$
$281$	−8.02546	−	8.02546i	−0.478759	−	0.478759i	−0.904735	+	0.425976i	$0.859931\pi$
$282$	3.28870	+	3.32026i	0.195839	+	0.197719i
$283$	−7.53261	+	18.1853i	−0.447767	+	1.08101i	0.525390	+	0.850862i	$0.323920\pi$
$283$	−7.53261	+	18.1853i	−0.447767	+	1.08101i	−0.973157	+	0.230143i	$0.926080\pi$
$284$	−24.6612	−	0.235518i	−1.46337	−	0.0139754i
$285$	−9.19072	+	3.80692i	−0.544411	+	0.225502i
$286$	2.26767	+	5.54945i	0.134090	+	0.328146i
$287$	−0.482195			−0.0284631
$288$	13.3397	+	5.90240i	0.786048	+	0.347802i
$289$	15.7288			0.925222
$290$	−0.347524	−	0.850461i	−0.0204073	−	0.0499408i
$291$	16.6335	−	6.88981i	0.975071	−	0.403888i
$292$	0.256629	−	26.8717i	0.0150181	−	1.57255i
$293$	−2.42331	+	5.85039i	−0.141571	+	0.341784i	−0.978723	−	0.205188i	$-0.934219\pi$
$293$	−2.42331	+	5.85039i	−0.141571	+	0.341784i	0.837151	+	0.546972i	$0.184219\pi$
$294$	−16.4395	−	16.5973i	−0.958772	−	0.967972i
$295$	0.577856	+	0.577856i	0.0336441	+	0.0336441i
$296$	18.8492	+	19.3971i	1.09559	+	1.12743i
$297$	−2.98291	+	2.98291i	−0.173086	+	0.173086i
$298$	28.2506	+	0.134896i	1.63651	+	0.00781432i
$299$	1.41019	+	0.584120i	0.0815534	+	0.0337805i
$300$	−20.1053	+	8.10383i	−1.16078	+	0.467875i
$301$	−0.0986796	−	0.238234i	−0.00568780	−	0.0137316i
$302$	−0.934279	+	2.22543i	−0.0537617	+	0.128059i
$303$			12.6124i			0.724563i
$304$	−24.4623	+	9.58945i	−1.40301	+	0.549993i
$305$		−	1.72292i		−	0.0986540i
$306$	−3.79116	−	1.59160i	−0.216726	−	0.0909858i
$307$	11.3008	+	27.2825i	0.644970	+	1.55709i	0.819895	+	0.572513i	$0.194031\pi$
$307$	11.3008	+	27.2825i	0.644970	+	1.55709i	−0.174926	+	0.984582i	$0.555969\pi$
$308$	0.618994	+	0.263349i	0.0352705	+	0.0150057i
$309$	40.6592	+	16.8416i	2.31302	+	0.958084i
$310$	0.0277348	−	5.80837i	0.00157523	−	0.329893i
$311$	14.6768	−	14.6768i	0.832247	−	0.832247i	−0.155577	−	0.987824i	$-0.549724\pi$
$311$	14.6768	−	14.6768i	0.832247	−	0.832247i	0.987824	+	0.155577i	$0.0497237\pi$
$312$	6.20798	−	2.46785i	0.351458	−	0.139715i
$313$	6.51503	+	6.51503i	0.368251	+	0.368251i	0.866839	−	0.498588i	$-0.166148\pi$
$313$	6.51503	+	6.51503i	0.368251	+	0.368251i	−0.498588	+	0.866839i	$0.666148\pi$
$314$	−2.64916	+	2.62398i	−0.149501	+	0.148080i
$315$	0.0502045	−	0.121204i	0.00282870	−	0.00682909i
$316$	1.60457	+	1.63551i	0.0902641	+	0.0920048i
$317$	−14.7707	+	6.11822i	−0.829605	+	0.343633i	−0.756746	−	0.653709i	$-0.773212\pi$
$317$	−14.7707	+	6.11822i	−0.829605	+	0.343633i	−0.0728584	+	0.997342i	$0.523212\pi$
$318$	−4.53340	+	1.85248i	−0.254220	+	0.103882i
$319$	−4.29483			−0.240465
$320$	4.79339	−	1.82644i	0.267959	−	0.102101i
$321$	−0.345591			−0.0192890
$322$	0.158548	−	0.0647877i	0.00883556	−	0.00361048i
$323$	6.84234	−	2.83419i	0.380718	−	0.157698i
$324$	14.1276	+	14.4000i	0.784864	+	0.800000i
$325$	−1.75608	+	4.23956i	−0.0974100	+	0.235169i
$326$	1.83352	−	1.81609i	0.101549	−	0.100584i
$327$	−4.89429	−	4.89429i	−0.270655	−	0.270655i
$328$	6.34980	+	15.9732i	0.350609	+	0.881972i
$329$	0.0784954	−	0.0784954i	0.00432759	−	0.00432759i
$330$	0.0433514	−	9.07888i	0.00238642	−	0.499776i
$331$	9.35521	+	3.87506i	0.514209	+	0.212992i	0.624671	−	0.780888i	$-0.285233\pi$
$331$	9.35521	+	3.87506i	0.514209	+	0.212992i	−0.110462	+	0.993880i	$0.535233\pi$
$332$	13.7188	+	5.83661i	0.752916	+	0.320326i
$333$	−9.43647	−	22.7816i	−0.517115	−	1.24843i
$334$	6.21940	+	2.61102i	0.340311	+	0.142869i
$335$		−	3.97659i		−	0.217264i
$336$	0.300042	−	0.686954i	0.0163686	−	0.0374764i
$337$			18.1621i			0.989351i	0.869078	+	0.494675i	$0.164713\pi$
$337$			18.1621i			0.989351i	−0.869078	+	0.494675i	$0.835287\pi$
$338$	0.547429	−	1.30396i	0.0297762	−	0.0709263i
$339$	−15.4347	−	37.2627i	−0.838298	−	2.02383i
$340$	−1.34104	+	0.540532i	−0.0727281	+	0.0293144i
$341$	−25.0862	−	10.3911i	−1.35850	−	0.562707i
$342$	23.9543	+	0.114381i	1.29530	+	0.00618503i
$343$	−0.785116	+	0.785116i	−0.0423923	+	0.0423923i
$344$	−6.59226	+	6.40605i	−0.355431	+	0.345391i
$345$	−1.63457	−	1.63457i	−0.0880022	−	0.0880022i
$346$	12.9103	+	13.0342i	0.694060	+	0.700720i
$347$	6.69243	−	16.1569i	0.359268	−	0.867350i	−0.636135	−	0.771578i	$-0.719468\pi$
$347$	6.69243	−	16.1569i	0.359268	−	0.867350i	0.995403	−	0.0957724i	$-0.0305321\pi$
$348$	−0.0457053	+	4.78581i	−0.00245006	+	0.256546i
$349$	18.9966	−	7.86867i	1.01687	−	0.421200i	0.188912	−	0.981994i	$-0.439504\pi$
$349$	18.9966	−	7.86867i	1.01687	−	0.421200i	0.827955	+	0.560794i	$0.189504\pi$
$350$	0.194776	+	0.476656i	0.0104112	+	0.0254784i
$351$	0.995149			0.0531171
$352$	0.572451	−	23.9727i	0.0305117	−	1.27775i
$353$	−30.6889			−1.63340			−0.816702	−	0.577059i	$-0.804200\pi$
$353$	−30.6889			−1.63340			−0.816702	+	0.577059i	$0.804200\pi$
$354$	−1.61036	−	3.94088i	−0.0855898	−	0.209455i
$355$	7.30482	−	3.02575i	0.387699	−	0.160590i
$356$	−26.1714	−	0.249942i	−1.38708	−	0.0132469i
$357$	−0.0808597	+	0.195213i	−0.00427955	+	0.0103317i
$358$	−25.0219	−	25.2620i	−1.32245	−	1.33514i
$359$	23.2614	+	23.2614i	1.22769	+	1.22769i	0.964835	+	0.262857i	$0.0846648\pi$
$359$	23.2614	+	23.2614i	1.22769	+	1.22769i	0.262857	+	0.964835i	$0.415335\pi$
$360$	−4.67613	−	0.0669893i	−0.246454	−	0.00353065i
$361$	−17.0749	+	17.0749i	−0.898679	+	0.898679i
$362$	9.06400	+	0.0432804i	0.476393	+	0.00227477i
$363$	−15.2080	−	6.29938i	−0.798215	−	0.330632i
$364$	−0.0593247	−	0.147183i	−0.00310946	−	0.00771446i
$365$	3.29697	+	7.95959i	0.172571	+	0.416624i
$366$	−3.47430	+	8.27570i	−0.181604	+	0.432578i
$367$			32.2583i			1.68387i	0.539578	+	0.841936i	$0.318584\pi$
$367$			32.2583i			1.68387i	−0.539578	+	0.841936i	$0.681416\pi$
$368$	−4.23401	−	4.39892i	−0.220713	−	0.229309i
$369$		−	15.6712i		−	0.815810i
$370$	−7.99522	−	3.35654i	−0.415652	−	0.174498i
$371$	0.0445175	+	0.107475i	0.00231123	+	0.00557981i
$372$	−11.8459	+	27.8435i	−0.614182	+	1.44362i
$373$	6.72655	+	2.78623i	0.348288	+	0.144266i	0.549968	−	0.835186i	$-0.314640\pi$
$373$	6.72655	+	2.78623i	0.348288	+	0.144266i	−0.201680	+	0.979451i	$0.564640\pi$
$374$	−0.0322744	+	6.75908i	−0.00166887	+	0.349503i
$375$	10.2685	−	10.2685i	0.530265	−	0.530265i
$376$	−3.63391	−	1.56657i	−0.187405	−	0.0807896i
$377$	0.716416	+	0.716416i	0.0368973	+	0.0368973i
$378$	0.0793357	−	0.0785816i	0.00408059	−	0.00404180i
$379$	−7.93549	+	19.1580i	−0.407619	+	0.984079i	0.578144	+	0.815935i	$0.303777\pi$
$379$	−7.93549	+	19.1580i	−0.407619	+	0.984079i	−0.985762	+	0.168144i	$0.946223\pi$
$380$	6.01301	−	5.89925i	0.308461	−	0.302625i
$381$	−32.8958	+	13.6259i	−1.68530	+	0.698075i
$382$	−25.4104	+	10.3835i	−1.30011	+	0.531264i
$383$	−36.8525			−1.88307			−0.941537	−	0.336911i	$-0.890618\pi$
$383$	−36.8525			−1.88307			−0.941537	+	0.336911i	$0.890618\pi$
$384$	−26.7072	−	0.893008i	−1.36289	−	0.0455711i
$385$	−0.215662			−0.0109911
$386$	24.9760	−	10.2060i	1.27125	−	0.519470i
$387$	7.74252	−	3.20706i	0.393574	−	0.163024i
$388$	−10.8824	+	10.6765i	−0.552471	+	0.542018i
$389$	−5.31642	+	12.8350i	−0.269553	+	0.650759i	−0.999462	−	0.0327850i	$-0.989562\pi$
$389$	−5.31642	+	12.8350i	−0.269553	+	0.650759i	0.729909	+	0.683544i	$0.239562\pi$
$390$	−1.52167	+	1.50720i	−0.0770526	+	0.0763203i
$391$	1.21691	+	1.21691i	0.0615417	+	0.0615417i
$392$	18.1651	+	7.83094i	0.917477	+	0.395522i
$393$	−12.2663	+	12.2663i	−0.618754	+	0.618754i
$394$	−0.0341293	+	7.14754i	−0.00171941	+	0.360088i
$395$	−0.678636	−	0.281100i	−0.0341459	−	0.0141437i
$396$	−8.55877	+	20.1171i	−0.430094	+	1.01092i
$397$	−14.8215	−	35.7822i	−0.743869	−	1.79586i	−0.589368	−	0.807865i	$-0.700623\pi$
$397$	−14.8215	−	35.7822i	−0.743869	−	1.79586i	−0.154501	−	0.987993i	$-0.549377\pi$
$398$	4.69658	+	1.97171i	0.235418	+	0.0988330i
$399$		−	1.23100i		−	0.0616273i
$400$	13.2248	−	12.7290i	0.661240	−	0.636451i
$401$		−	16.5997i		−	0.828951i	−0.910060	−	0.414476i	$-0.863965\pi$
$401$		−	16.5997i		−	0.828951i	0.910060	−	0.414476i	$-0.136035\pi$
$402$	−8.01887	+	19.1008i	−0.399945	+	0.952661i
$403$	2.45128	+	5.91792i	0.122107	+	0.294793i
$404$	−3.99256	−	9.90541i	−0.198637	−	0.492812i
$405$	−5.97510	−	2.47497i	−0.296905	−	0.122982i
$406$	0.113686		0.000542847i	0.00564213		2.69411e-5i
$407$	−28.6633	+	28.6633i	−1.42078	+	1.42078i
$408$	7.53142	+	0.107894i	0.372861	+	0.00534153i
$409$	−16.7973	−	16.7973i	−0.830573	−	0.830573i	0.157022	−	0.987595i	$-0.449811\pi$
$409$	−16.7973	−	16.7973i	−0.830573	−	0.830573i	−0.987595	+	0.157022i	$0.949811\pi$
$410$	−3.87805	−	3.91526i	−0.191523	−	0.193361i
$411$	−11.5691	+	27.9303i	−0.570662	+	1.37770i
$412$	−37.2639	−	0.355877i	−1.83586	−	0.0175328i
$413$	−0.0934277	+	0.0386990i	−0.00459728	+	0.00190425i
$414$	2.10558	+	5.15278i	0.103484	+	0.253245i
$415$	−4.77972			−0.234627
$416$	−4.09435	+	3.90337i	−0.200742	+	0.191378i
$417$	3.39940			0.166469
$418$	−14.8956	−	36.4526i	−0.728569	−	1.78295i
$419$	31.8417	−	13.1893i	1.55557	−	0.644337i	0.571256	−	0.820772i	$-0.306456\pi$
$419$	31.8417	−	13.1893i	1.55557	−	0.644337i	0.984312	+	0.176435i	$0.0564565\pi$
$420$	−0.00229506	+	0.240316i	−0.000111987	+	0.0117262i
$421$	−7.24402	+	17.4886i	−0.353052	+	0.852342i	0.643188	+	0.765708i	$0.277611\pi$
$421$	−7.24402	+	17.4886i	−0.353052	+	0.852342i	−0.996240	+	0.0866344i	$0.972389\pi$
$422$	−2.32685	−	2.34917i	−0.113269	−	0.114356i
$423$	2.55108	+	2.55108i	0.124038	+	0.124038i
$424$	2.97398	−	2.88997i	0.144429	−	0.140350i
$425$	−3.65849	+	3.65849i	−0.177463	+	0.177463i
$426$	−41.1888	−	0.196675i	−1.99560	−	0.00952895i
$427$	0.196972	+	0.0815887i	0.00953217	+	0.00394835i
$428$	0.271417	−	0.109400i	0.0131194	−	0.00528803i
$429$	3.83152	+	9.25011i	0.184988	+	0.446600i
$430$	1.14075	−	2.71724i	0.0550117	−	0.131037i
$431$		−	31.7410i		−	1.52891i	−0.644677	−	0.764455i	$-0.723008\pi$
$431$		−	31.7410i		−	1.52891i	0.644677	−	0.764455i	$-0.276992\pi$
$432$	−3.64783	−	1.59327i	−0.175506	−	0.0766561i
$433$		−	26.4466i		−	1.27094i	−0.772124	−	0.635472i	$-0.780806\pi$
$433$		−	26.4466i		−	1.27094i	0.772124	−	0.635472i	$-0.219194\pi$
$434$	0.662728	+	0.278226i	0.0318120	+	0.0133553i
$435$	−0.587186	−	1.41759i	−0.0281534	−	0.0679683i
$436$	5.39317	+	2.29451i	0.258286	+	0.109887i
$437$	−9.26309	−	3.83690i	−0.443114	−	0.183544i
$438$	0.214305	−	44.8808i	0.0102399	−	2.14449i
$439$	−3.97939	+	3.97939i	−0.189926	+	0.189926i	−0.795664	−	0.605738i	$-0.792878\pi$
$439$	−3.97939	+	3.97939i	−0.189926	+	0.189926i	0.605738	+	0.795664i	$0.292878\pi$
$440$	2.83995	+	7.14401i	0.135389	+	0.340577i
$441$	−12.7523	−	12.7523i	−0.607252	−	0.607252i
$442$	1.13286	−	1.12209i	0.0538845	−	0.0533723i
$443$	5.36090	−	12.9424i	0.254704	−	0.614910i	−0.743868	−	0.668326i	$-0.767011\pi$
$443$	5.36090	−	12.9424i	0.254704	−	0.614910i	0.998572	+	0.0534164i	$0.0170111\pi$
$444$	31.6349	+	32.2450i	1.50133	+	1.53028i
$445$	7.75217	−	3.21105i	0.367488	−	0.152218i
$446$	26.9147	−	10.9982i	1.27445	−	0.520778i
$447$	47.1827			2.23167
$448$	−0.0181830	+	0.634495i	−0.000859067	+	0.0299771i
$449$	30.7010			1.44887			0.724434	−	0.689344i	$-0.242101\pi$
$449$	30.7010			1.44887			0.724434	+	0.689344i	$0.242101\pi$
$450$	−15.4912	+	6.33017i	−0.730262	+	0.298407i
$451$	−23.8006	+	9.85853i	−1.12073	+	0.464220i
$452$	23.9178	+	24.3790i	1.12500	+	1.14669i
$453$	−1.54260	+	3.72417i	−0.0724778	+	0.174977i
$454$	−11.3074	+	11.1999i	−0.530683	+	0.525639i
$455$	0.0359743	+	0.0359743i	0.00168650	+	0.00168650i
$456$	−40.7783	+	16.2105i	−1.90962	+	0.759128i
$457$	12.1155	−	12.1155i	0.566740	−	0.566740i	−0.364474	−	0.931214i	$-0.618751\pi$
$457$	12.1155	−	12.1155i	0.566740	−	0.566740i	0.931214	+	0.364474i	$0.118751\pi$
$458$	−0.186998	+	39.1621i	−0.00873784	+	1.82992i
$459$	1.03661	+	0.429377i	0.0483847	+	0.0200416i
$460$	1.80118	+	0.766306i	0.0839804	+	0.0357292i
$461$	1.83990	+	4.44192i	0.0856929	+	0.206881i	0.960917	−	0.276837i	$-0.0892861\pi$
$461$	1.83990	+	4.44192i	0.0856929	+	0.206881i	−0.875224	+	0.483718i	$0.839286\pi$
$462$	1.03589	+	0.434886i	0.0481939	+	0.0202327i
$463$			20.4660i			0.951134i	0.879679	+	0.475567i	$0.157757\pi$
$463$			20.4660i			0.951134i	−0.879679	+	0.475567i	$0.842243\pi$
$464$	−1.47909	−	3.77311i	−0.0686652	−	0.175162i
$465$		−	9.70085i		−	0.449866i
$466$	7.14997	−	17.0311i	0.331216	−	0.788950i
$467$	−4.07703	−	9.84283i	−0.188663	−	0.455472i	0.801040	−	0.598611i	$-0.204280\pi$
$467$	−4.07703	−	9.84283i	−0.188663	−	0.455472i	−0.989703	+	0.143139i	$0.954280\pi$
$468$	4.78339	−	1.92804i	0.221112	−	0.0891235i
$469$	0.454624	+	0.188311i	0.0209926	+	0.00869541i
$470$	1.26866	+	0.00605780i	0.0585187	+	0.000279426i
$471$	−4.40347	+	4.40347i	−0.202901	+	0.202901i
$472$	2.51225	+	2.58528i	0.115636	+	0.118997i
$473$	−9.74143	−	9.74143i	−0.447911	−	0.447911i
$474$	2.69285	+	2.71869i	0.123687	+	0.124874i
$475$	11.5352	−	27.8483i	0.529269	−	1.27777i
$476$	0.00170863	−	0.178911i	7.83150e−5	−	0.00820038i
$477$	−3.49290	+	1.44681i	−0.159929	+	0.0662447i
$478$	9.80615	+	23.9976i	0.448523	+	1.09763i
$479$	30.0166			1.37150			0.685748	−	0.727839i	$-0.259475\pi$
$479$	30.0166			1.37150			0.685748	+	0.727839i	$0.259475\pi$
$480$	7.99092	−	3.08858i	0.364734	−	0.140974i
$481$	9.56256			0.436015
$482$	−7.24367	−	17.7267i	−0.329940	−	0.807430i
$483$	0.264277	−	0.109467i	0.0120250	−	0.00498092i
$484$	13.9381	+	0.133111i	0.633549	+	0.00605050i
$485$	1.87039	−	4.51552i	0.0849301	−	0.205039i
$486$	20.7383	+	20.9373i	0.940707	+	0.949733i
$487$	25.6858	+	25.6858i	1.16394	+	1.16394i	0.983606	+	0.180329i	$0.0577161\pi$
$487$	25.6858	+	25.6858i	1.16394	+	1.16394i	0.180329	+	0.983606i	$0.442284\pi$
$488$	0.108866	−	7.59931i	0.00492814	−	0.344005i
$489$	3.04770	−	3.04770i	0.137822	−	0.137822i
$490$	−6.34173	−	0.0302816i	−0.286490	−	0.00136798i
$491$	−2.50158	−	1.03619i	−0.112895	−	0.0467625i	0.325521	−	0.945535i	$-0.394460\pi$
$491$	−2.50158	−	1.03619i	−0.112895	−	0.0467625i	−0.438416	+	0.898772i	$0.644460\pi$
$492$	10.7323	+	26.6264i	0.483847	+	1.20041i
$493$	0.437150	+	1.05537i	0.0196883	+	0.0475316i
$494$	−3.59588	+	8.56532i	−0.161786	+	0.385372i
$495$		−	7.00894i		−	0.315029i
$496$	0.489345	−	25.6174i	0.0219722	−	1.15025i
$497$			0.978407i			0.0438876i
$498$	22.9584	+	9.63839i	1.02879	+	0.431907i
$499$	0.230320	+	0.556043i	0.0103106	+	0.0248919i	0.928951	−	0.370203i	$-0.120712\pi$
$499$	0.230320	+	0.556043i	0.0103106	+	0.0248919i	−0.918640	+	0.395095i	$0.870712\pi$
$500$	−4.81401	+	11.3152i	−0.215289	+	0.506031i
$501$	10.4079	+	4.31110i	0.464991	+	0.192606i
$502$	−0.0233979	+	4.90012i	−0.00104430	+	0.218703i
$503$	17.3151	−	17.3151i	0.772040	−	0.772040i	−0.206423	−	0.978463i	$-0.566182\pi$
$503$	17.3151	−	17.3151i	0.772040	−	0.772040i	0.978463	+	0.206423i	$0.0661822\pi$
$504$	0.229097	−	0.531426i	0.0102048	−	0.0236716i
$505$	2.42107	+	2.42107i	0.107736	+	0.107736i
$506$	6.50118	−	6.43939i	0.289013	−	0.286266i
$507$	0.903868	−	2.18213i	0.0401422	−	0.0969118i
$508$	21.5220	−	21.1148i	0.954884	−	0.936818i
$509$	−1.53882	+	0.637402i	−0.0682072	+	0.0282523i	−0.416526	−	0.909124i	$-0.636753\pi$
$509$	−1.53882	+	0.637402i	−0.0682072	+	0.0282523i	0.348319	+	0.937376i	$0.386753\pi$
$510$	−2.23538	+	0.913442i	−0.0989841	+	0.0404479i
$511$	−1.06611			−0.0471618
$512$	21.2577	−	7.75304i	0.939467	−	0.342639i
$513$	−6.53682			−0.288608
$514$	−9.87452	+	4.03503i	−0.435546	+	0.177977i
$515$	11.0378	−	4.57202i	0.486385	−	0.201467i
$516$	−10.9587	+	10.7514i	−0.482431	+	0.473303i
$517$	2.26960	−	5.47930i	0.0998168	−	0.240979i
$518$	0.762350	−	0.755104i	0.0334957	−	0.0331774i
$519$	21.6655	+	21.6655i	0.951011	+	0.951011i
$520$	0.717955	−	1.66541i	0.0314844	−	0.0730331i
$521$	21.9161	−	21.9161i	0.960163	−	0.960163i	−0.0390729	−	0.999236i	$-0.512440\pi$
$521$	21.9161	−	21.9161i	0.960163	−	0.960163i	0.999236	+	0.0390729i	$0.0124404\pi$
$522$	−0.0176424	+	3.69476i	−0.000772186	+	0.161715i
$523$	−35.0977	−	14.5379i	−1.53471	−	0.635699i	−0.554241	−	0.832356i	$-0.686991\pi$
$523$	−35.0977	−	14.5379i	−1.53471	−	0.635699i	−0.980472	+	0.196657i	$0.936991\pi$
$524$	5.75060	−	13.5166i	0.251216	−	0.590476i
$525$	0.329099	+	0.794516i	0.0143631	+	0.0346755i
$526$	34.5825	+	14.5184i	1.50787	+	0.633032i
$527$			7.22212i			0.314600i
$528$	0.764880	−	40.0417i	0.0332871	−	1.74259i
$529$			20.6702i			0.898703i
$530$	−0.514628	+	1.22583i	−0.0223540	+	0.0532468i
$531$	−1.25771	−	3.03637i	−0.0545798	−	0.131767i
$532$	0.389685	+	0.966795i	0.0168950	+	0.0419159i
$533$	5.61464	+	2.32566i	0.243197	+	0.100735i
$534$	−43.7112	−	0.208720i	−1.89157	−	0.00903219i
$535$	−0.0663395	+	0.0663395i	−0.00286811	+	0.00286811i
$536$	0.251270	−	17.5397i	0.0108532	−	0.757598i
$537$	−41.9908	−	41.9908i	−1.81204	−	1.81204i
$538$	18.9010	+	19.0824i	0.814879	+	0.822699i
$539$	−11.3452	+	27.3898i	−0.488674	+	1.17976i
$540$	1.27611	+	0.0121871i	0.0549152	+	0.000524449i
$541$	36.6629	−	15.1863i	1.57626	−	0.652909i	0.588446	−	0.808537i	$-0.299740\pi$
$541$	36.6629	−	15.1863i	1.57626	−	0.652909i	0.987816	+	0.155627i	$0.0497399\pi$
$542$	2.26803	+	5.55032i	0.0974202	+	0.238407i
$543$	15.1382			0.649644
$544$	−5.94911	+	2.29940i	−0.255066	+	0.0985859i
$545$	−1.87902			−0.0804882
$546$	−0.100253	−	0.245338i	−0.00429042	−	0.0104995i
$547$	37.9329	−	15.7123i	1.62189	−	0.671811i	0.627606	−	0.778531i	$-0.284035\pi$
$547$	37.9329	−	15.7123i	1.62189	−	0.671811i	0.994289	+	0.106721i	$0.0340350\pi$
$548$	0.244465	−	25.5979i	0.0104430	−	1.09349i
$549$	−2.65161	+	6.40155i	−0.113168	+	0.273211i
$550$	19.3592	+	19.5450i	0.825481	+	0.833402i
$551$	−4.70591	−	4.70591i	−0.200478	−	0.200478i
$552$	−7.10635	−	7.31291i	−0.302466	−	0.311258i
$553$	0.0642735	−	0.0642735i	0.00273319	−	0.00273319i
$554$	−16.7864	−	0.0801548i	−0.713187	−	0.00340545i
$555$	−13.3797	−	5.54204i	−0.567935	−	0.235247i
$556$	−2.66979	+	1.07611i	−0.113224	+	0.0456372i
$557$	13.4337	+	32.4319i	0.569205	+	1.37418i	0.902226	+	0.431263i	$0.141932\pi$
$557$	13.4337	+	32.4319i	0.569205	+	1.37418i	−0.333022	+	0.942919i	$0.608068\pi$
$558$	−9.04226	+	21.5385i	−0.382789	+	0.911796i
$559$			3.24991i			0.137457i
$560$	−0.0742716	−	0.189464i	−0.00313855	−	0.00800630i
$561$			11.2887i			0.476608i
$562$	14.7996	+	6.21316i	0.624285	+	0.262086i
$563$	3.08761	+	7.45415i	0.130127	+	0.314155i	0.975492	−	0.220034i	$-0.0706170\pi$
$563$	3.08761	+	7.45415i	0.130127	+	0.314155i	−0.845365	+	0.534189i	$0.820617\pi$
$564$	−6.08153	−	2.58737i	−0.256078	−	0.108948i
$565$	−10.1158	−	4.19009i	−0.425574	−	0.176279i
$566$	0.132919	−	27.8366i	0.00558700	−	1.17006i
$567$	0.565901	−	0.565901i	0.0237656	−	0.0237656i
$568$	32.4107	−	12.8842i	1.35992	−	0.540609i
$569$	−16.4371	−	16.4371i	−0.689079	−	0.689079i	0.272950	−	0.962028i	$-0.412001\pi$
$569$	−16.4371	−	16.4371i	−0.689079	−	0.689079i	−0.962028	+	0.272950i	$0.912001\pi$
$570$	9.99535	−	9.90035i	0.418659	−	0.414680i
$571$	14.4397	−	34.8606i	0.604284	−	1.45887i	−0.264847	−	0.964290i	$-0.585322\pi$
$571$	14.4397	−	34.8606i	0.604284	−	1.45887i	0.869132	−	0.494581i	$-0.164678\pi$
$572$	−5.93737	−	6.05187i	−0.248254	−	0.253041i
$573$	−42.3554	+	17.5442i	−1.76942	+	0.732919i
$574$	0.631257	−	0.257951i	0.0263482	−	0.0107667i
$575$	7.00435			0.292102
$576$	−20.6209	−	0.590943i	−0.859204	−	0.0246226i
$577$	−0.0235122			−0.000978825			−0.000489412	−	1.00000i	$-0.500156\pi$
$577$	−0.0235122			−0.000978825			−0.000489412		1.00000i	$0.500156\pi$
$578$	−20.5910	+	8.41413i	−0.856475	+	0.349982i
$579$	41.6313	−	17.2443i	1.73014	−	0.716647i
$580$	0.909910	+	0.927457i	0.0377819	+	0.0385106i
$581$	0.226343	−	0.546441i	0.00939030	−	0.0226702i
$582$	−18.0897	+	17.9178i	−0.749842	+	0.742715i
$583$	4.39467	+	4.39467i	0.182009	+	0.182009i
$584$	14.0391	+	35.3159i	0.580941	+	1.46138i
$585$	−1.16915	+	1.16915i	−0.0483385	+	0.0483385i
$586$	0.0427613	−	8.95529i	0.00176645	−	0.369940i
$587$	24.3079	+	10.0687i	1.00329	+	0.415578i	0.823004	−	0.568036i	$-0.192297\pi$
$587$	24.3079	+	10.0687i	1.00329	+	0.415578i	0.180290	+	0.983614i	$0.442297\pi$
$588$	30.4002	+	12.9337i	1.25368	+	0.533376i
$589$	−16.1017	−	38.8729i	−0.663459	−	1.60173i
$590$	−1.06561	−	0.447365i	−0.0438707	−	0.0184177i
$591$			11.9375i			0.491041i
$592$	−35.0526	−	15.3100i	−1.44065	−	0.629236i
$593$		−	0.804547i		−	0.0330388i	−0.999864	−	0.0165194i	$-0.994741\pi$
$593$		−	0.804547i		−	0.0330388i	0.999864	−	0.0165194i	$-0.00525853\pi$
$594$	2.30931	−	5.50073i	0.0947521	−	0.225698i
$595$	0.0219512	+	0.0529948i	0.000899910	+	0.00217257i
$596$	−37.0560	+	14.9361i	−1.51787	+	0.611807i
$597$	7.85953	+	3.25552i	0.321669	+	0.133240i
$598$	−2.15860	−	0.0103073i	−0.0882717	−	0.000421496i
$599$	6.97412	−	6.97412i	0.284955	−	0.284955i	−0.550127	−	0.835081i	$-0.685421\pi$
$599$	6.97412	−	6.97412i	0.284955	−	0.284955i	0.835081	+	0.550127i	$0.185421\pi$
$600$	21.9854	−	21.3644i	0.897549	−	0.872196i
$601$	28.9382	+	28.9382i	1.18042	+	1.18042i	0.979637	+	0.200779i	$0.0643473\pi$
$601$	28.9382	+	28.9382i	1.18042	+	1.18042i	0.200779	+	0.979637i	$0.435653\pi$
$602$	0.256628	+	0.259090i	0.0104594	+	0.0105597i
$603$	−6.12006	+	14.7751i	−0.249228	+	0.601690i
$604$	0.0325965	−	3.41318i	0.00132633	−	0.138880i
$605$	−4.12856	+	1.71011i	−0.167850	+	0.0695257i
$606$	−6.74702	−	16.5113i	−0.274079	−	0.670725i
$607$	−6.71786			−0.272669			−0.136335	−	0.990663i	$-0.543532\pi$
$607$	−6.71786			−0.272669			−0.136335	+	0.990663i	$0.543532\pi$
$608$	26.8945	−	25.6400i	1.09072	−	1.03984i
$609$	0.189872			0.00769401
$610$	0.921677	+	2.25553i	0.0373176	+	0.0913236i
$611$	−1.29258	+	0.535405i	−0.0522923	+	0.0216602i
$612$	5.81456	+	0.0555300i	0.235040	+	0.00224467i
$613$	−13.8181	+	33.3599i	−0.558109	+	1.34740i	0.353152	+	0.935566i	$0.385110\pi$
$613$	−13.8181	+	33.3599i	−0.558109	+	1.34740i	−0.911261	+	0.411829i	$0.864890\pi$
$614$	−29.3890	−	29.6710i	−1.18604	−	1.19743i
$615$	−6.50800	−	6.50800i	−0.262428	−	0.262428i
$616$	−0.951224	−	0.0136271i	−0.0383259	−	0.000549050i
$617$	29.0044	−	29.0044i	1.16767	−	1.16767i	0.184920	−	0.982754i	$-0.440797\pi$
$617$	29.0044	−	29.0044i	1.16767	−	1.16767i	0.982754	−	0.184920i	$-0.0592026\pi$
$618$	−62.2377	−	0.297183i	−2.50357	−	0.0119545i
$619$	−1.75263	−	0.725965i	−0.0704443	−	0.0291790i	0.347183	−	0.937797i	$-0.387138\pi$
$619$	−1.75263	−	0.725965i	−0.0704443	−	0.0291790i	−0.417627	+	0.908618i	$0.637138\pi$
$620$	3.07089	+	7.61876i	0.123330	+	0.305977i
$621$	−0.581286	−	1.40335i	−0.0233262	−	0.0563145i
$622$	−11.3625	+	27.0653i	−0.455596	+	1.08522i
$623$			1.03833i			0.0415996i
$624$	−6.80689	+	6.55171i	−0.272494	+	0.262278i
$625$			19.0020i			0.760082i
$626$	−12.0143	−	5.04382i	−0.480187	−	0.201591i
$627$	−25.1680	−	60.7610i	−1.00511	−	2.42656i
$628$	2.06440	−	4.85231i	0.0823785	−	0.193628i
$629$	9.96094	+	4.12596i	0.397169	+	0.164513i
$630$	−0.000885898		0.185529i	−3.52950e−5		0.00739167i
$631$	−35.3136	+	35.3136i	−1.40581	+	1.40581i	−0.625947	+	0.779866i	$0.715287\pi$
$631$	−35.3136	+	35.3136i	−1.40581	+	1.40581i	−0.779866	+	0.625947i	$0.784713\pi$
$632$	−2.97551	−	1.28274i	−0.118360	−	0.0510245i
$633$	−3.90482	−	3.90482i	−0.155203	−	0.155203i
$634$	16.0638	−	15.9112i	0.637976	−	0.631913i
$635$	−3.69905	+	8.93029i	−0.146792	+	0.354388i
$636$	4.94383	−	4.85029i	0.196036	−	0.192327i
$637$	6.46134	−	2.67637i	0.256008	−	0.106042i
$638$	5.62250	−	2.29753i	0.222597	−	0.0909599i
$639$	−31.7979			−1.25791
$640$	−5.29812	+	4.95528i	−0.209427	+	0.195875i
$641$	−1.43608			−0.0567219			−0.0283609	−	0.999598i	$-0.509029\pi$
$641$	−1.43608			−0.0567219			−0.0283609	+	0.999598i	$0.509029\pi$
$642$	0.452424	−	0.184874i	0.0178557	−	0.00729640i
$643$	3.66119	−	1.51652i	0.144383	−	0.0598055i	−0.309322	−	0.950957i	$-0.600102\pi$
$643$	3.66119	−	1.51652i	0.144383	−	0.0598055i	0.453705	+	0.891152i	$0.350102\pi$
$644$	−0.172903	+	0.169631i	−0.00681332	+	0.00668441i
$645$	1.88351	−	4.54718i	0.0741629	−	0.179045i
$646$	−7.44137	+	7.37064i	−0.292777	+	0.289994i
$647$	−31.9257	−	31.9257i	−1.25513	−	1.25513i	−0.953392	−	0.301735i	$-0.902434\pi$
$647$	−31.9257	−	31.9257i	−1.25513	−	1.25513i	−0.301735	−	0.953392i	$-0.597566\pi$
$648$	−26.1981	−	11.2939i	−1.02916	−	0.443668i
$649$	−3.82028	+	3.82028i	−0.149959	+	0.149959i
$650$	0.0309875	−	6.48957i	0.00121543	−	0.254542i
$651$	1.10905	+	0.459383i	0.0434671	+	0.0180046i
$652$	−1.42880	+	3.35835i	−0.0559561	+	0.131523i
$653$	−10.5649	−	25.5060i	−0.413437	−	0.998126i	−0.984208	−	0.177016i	$-0.943355\pi$
$653$	−10.5649	−	25.5060i	−0.413437	−	0.998126i	0.570771	−	0.821110i	$-0.306645\pi$
$654$	9.02549	+	3.78907i	0.352924	+	0.148164i
$655$			4.70928i			0.184007i
$656$	−16.8576	−	17.5142i	−0.658179	−	0.683814i
$657$		−	34.6482i		−	1.35175i
$658$	−0.0607697	+	0.144752i	−0.00236905	+	0.00564303i
$659$	13.4136	+	32.3833i	0.522520	+	1.26147i	0.936333	+	0.351112i	$0.114197\pi$
$659$	13.4136	+	32.3833i	0.522520	+	1.26147i	−0.413814	+	0.910362i	$0.635803\pi$
$660$	4.80000	+	11.9086i	0.186840	+	0.463543i
$661$	10.4813	+	4.34150i	0.407676	+	0.168865i	0.577091	−	0.816680i	$-0.304188\pi$
$661$	10.4813	+	4.34150i	0.407676	+	0.168865i	−0.169415	+	0.985545i	$0.554188\pi$
$662$	−14.3202	−	0.0683785i	−0.556569	−	0.00265761i
$663$	1.88305	−	1.88305i	0.0731315	−	0.0731315i
$664$	−21.0820	−	0.302017i	−0.818141	−	0.0117205i
$665$	−0.236303	−	0.236303i	−0.00916345	−	0.00916345i
$666$	24.5407	+	24.7761i	0.950931	+	0.960056i
$667$	0.591809	−	1.42875i	0.0229150	−	0.0553216i
$668$	−9.53879	−	0.0910971i	−0.369067	−	0.00352465i
$669$	44.8628	−	18.5828i	1.73450	−	0.718452i
$670$	2.12728	+	5.20589i	0.0821841	+	0.201121i
$671$	11.3904			0.439723
$672$	−0.0253077	+	1.05982i	−0.000976267	+	0.0408835i
$673$	−5.32259			−0.205171			−0.102585	−	0.994724i	$-0.532712\pi$
$673$	−5.32259			−0.205171			−0.102585	+	0.994724i	$0.532712\pi$
$674$	−9.71582	−	23.7765i	−0.374239	−	0.915838i
$675$	4.21900	−	1.74757i	0.162389	−	0.0672638i
$676$	−0.0190995	+	1.99991i	−0.000734595	+	0.0769196i
$677$	7.34347	−	17.7287i	0.282232	−	0.681369i	−0.717655	−	0.696399i	$-0.754784\pi$
$677$	7.34347	−	17.7287i	0.282232	−	0.681369i	0.999887	+	0.0150298i	$0.00478433\pi$
$678$	40.1398	+	40.5250i	1.54156	+	1.55635i
$679$	0.427665	+	0.427665i	0.0164123	+	0.0164123i
$680$	1.46644	−	1.42502i	0.0562354	−	0.0546470i
$681$	−18.7953	+	18.7953i	−0.720237	+	0.720237i
$682$	38.3999	+	0.183359i	1.47041	+	0.00702116i
$683$	−6.38354	−	2.64415i	−0.244259	−	0.101176i	0.257195	−	0.966359i	$-0.417202\pi$
$683$	−6.38354	−	2.64415i	−0.244259	−	0.101176i	−0.501455	+	0.865184i	$0.667202\pi$
$684$	−31.4206	+	12.6647i	−1.20140	+	0.484245i
$685$	3.14069	+	7.58230i	0.120000	+	0.289705i
$686$	0.607822	−	1.44782i	0.0232068	−	0.0552780i
$687$			65.4065i			2.49541i
$688$	5.20321	−	11.9129i	0.198371	−	0.454175i
$689$		−	1.46614i		−	0.0558554i
$690$	3.01428	+	1.26545i	0.114752	+	0.0481749i
$691$	−3.48507	−	8.41369i	−0.132578	−	0.320072i	0.843624	−	0.536934i	$-0.180418\pi$
$691$	−3.48507	−	8.41369i	−0.132578	−	0.320072i	−0.976202	+	0.216862i	$0.930418\pi$
$692$	−23.8739	−	10.1571i	−0.907549	−	0.386114i
$693$	0.801297	+	0.331908i	0.0304388	+	0.0126081i
$694$	−0.118093	+	24.7317i	−0.00448276	+	0.938802i
$695$	0.652549	−	0.652549i	0.0247526	−	0.0247526i
$696$	−2.50034	−	6.28971i	−0.0947752	−	0.238411i
$697$	4.84509	+	4.84509i	0.183521	+	0.183521i
$698$	−20.6598	+	20.4634i	−0.781984	+	0.774551i
$699$	11.8054	−	28.5008i	0.446522	−	1.07800i
$700$	−0.509976	−	0.519810i	−0.0192753	−	0.0196470i
$701$	−19.0349	+	7.88453i	−0.718939	+	0.297794i	−0.711998	−	0.702181i	$-0.752210\pi$
$701$	−19.0349	+	7.88453i	−0.718939	+	0.297794i	−0.00694140	+	0.999976i	$0.502210\pi$
$702$	−1.30278	+	0.532356i	−0.0491703	+	0.0200925i
$703$	−62.8134			−2.36905
$704$	12.0748	+	31.6897i	0.455087	+	1.19435i
$705$	2.11884			0.0798003
$706$	40.1758	−	16.4171i	1.51204	−	0.617864i
$707$	−0.391439	+	0.162139i	−0.0147216	+	0.00609787i
$708$	4.21635	+	4.29766i	0.158460	+	0.161516i
$709$	−7.72468	+	18.6490i	−0.290106	+	0.700379i	−0.999992	−	0.00393799i	$-0.998746\pi$
$709$	−7.72468	+	18.6490i	−0.290106	+	0.700379i	0.709886	+	0.704317i	$0.248746\pi$
$710$	−7.94434	+	7.86883i	−0.298146	+	0.295312i
$711$	2.08887	+	2.08887i	0.0783388	+	0.0783388i
$712$	34.3956	−	13.6732i	1.28903	−	0.512426i
$713$	6.91355	−	6.91355i	0.258914	−	0.258914i
$714$	0.00142684	−	0.298815i	5.33980e−5	−	0.0111829i
$715$	2.51115	+	1.04015i	0.0939116	+	0.0388995i
$716$	46.2709	+	19.6858i	1.72922	+	0.735693i
$717$	16.5687	+	40.0005i	0.618771	+	1.49385i
$718$	−42.8960	−	18.0086i	−1.60087	−	0.672074i
$719$			2.73768i			0.102098i	0.998696	+	0.0510491i	$0.0162565\pi$
$719$			2.73768i			0.102098i	−0.998696	+	0.0510491i	$0.983743\pi$
$720$	6.15751	−	2.41380i	0.229477	−	0.0899572i
$721$			1.47841i			0.0550588i
$722$	13.2191	−	31.4876i	0.491963	−	1.17185i
$723$	−12.2391	−	29.5478i	−0.455177	−	1.09889i
$724$	−11.8891	+	4.79214i	−0.441856	+	0.178098i
$725$	4.29537	+	1.77920i	0.159526	+	0.0660779i
$726$	23.2792	+	0.111158i	0.863972	+	0.00412545i
$727$	−27.9386	+	27.9386i	−1.03619	+	1.03619i	−0.0368652	+	0.999320i	$0.511737\pi$
$727$	−27.9386	+	27.9386i	−1.03619	+	1.03619i	−0.999320	+	0.0368652i	$0.988263\pi$
$728$	0.156399	+	0.160946i	0.00579655	+	0.00596504i
$729$	13.4055	+	13.4055i	0.496501	+	0.496501i
$730$	−8.57417	−	8.65644i	−0.317344	−	0.320389i
$731$	−1.40224	+	3.38530i	−0.0518637	+	0.125210i
$732$	0.121216	−	12.6926i	0.00448028	−	0.469131i
$733$	33.5807	−	13.9096i	1.24033	−	0.513762i	0.336513	−	0.941679i	$-0.390752\pi$
$733$	33.5807	−	13.9096i	1.24033	−	0.513762i	0.903818	+	0.427917i	$0.140752\pi$
$734$	−17.2566	−	42.2304i	−0.636954	−	1.55875i
$735$	−10.5916			−0.390679
$736$	7.89608	+	3.49377i	0.291053	+	0.128782i
$737$	26.2898			0.968396
$738$	8.38332	+	20.5157i	0.308594	+	0.755192i
$739$	−5.64568	+	2.33852i	−0.207680	+	0.0860237i	−0.484098	−	0.875014i	$-0.660852\pi$
$739$	−5.64568	+	2.33852i	−0.207680	+	0.0860237i	0.276419	+	0.961037i	$0.410852\pi$
$740$	12.2624	+	0.117108i	0.450774	+	0.00430497i
$741$	−5.93722	+	14.3337i	−0.218109	+	0.526562i
$742$	−0.115773	−	0.116884i	−0.00425016	−	0.00429095i
$743$	−15.9415	−	15.9415i	−0.584837	−	0.584837i	0.351391	−	0.936229i	$-0.385709\pi$
$743$	−15.9415	−	15.9415i	−0.584837	−	0.584837i	−0.936229	+	0.351391i	$0.885709\pi$
$744$	0.612969	−	42.7878i	0.0224725	−	1.56868i
$745$	9.05719	−	9.05719i	0.331830	−	0.331830i
$746$	−10.2964	−	0.0491653i	−0.376980	−	0.00180007i
$747$	17.7592	+	7.35609i	0.649774	+	0.269145i
$748$	−3.57352	−	8.86579i	−0.130661	−	0.324165i
$749$	−0.00444276	−	0.0107258i	−0.000162335	−	0.000391911i
$750$	−7.94970	+	18.9360i	−0.290282	+	0.691446i
$751$		−	11.7817i		−	0.429922i	−0.976623	−	0.214961i	$-0.931038\pi$
$751$		−	11.7817i		−	0.429922i	0.976623	−	0.214961i	$-0.0689624\pi$
$752$	5.59531	+	0.106882i	0.204040	+	0.00389759i
$753$			8.18393i			0.298239i
$754$	−1.32113	−	0.554635i	−0.0481127	−	0.0201986i
$755$	0.418774	+	1.01101i	0.0152407	+	0.0367944i
$756$	−0.0618235	+	0.145314i	−0.00224850	+	0.00528503i
$757$	−25.0425	−	10.3729i	−0.910183	−	0.377010i	−0.122057	−	0.992523i	$-0.538949\pi$
$757$	−25.0425	−	10.3729i	−0.910183	−	0.377010i	−0.788127	+	0.615513i	$0.788949\pi$
$758$	0.140028	−	29.3254i	0.00508605	−	1.06515i
$759$	10.8063	−	10.8063i	0.392245	−	0.392245i
$760$	−4.71602	+	10.9396i	−0.171068	+	0.396819i
$761$	20.9783	+	20.9783i	0.760464	+	0.760464i	0.976406	−	0.215942i	$-0.0692823\pi$
$761$	20.9783	+	20.9783i	0.760464	+	0.760464i	−0.215942	+	0.976406i	$0.569282\pi$
$762$	35.7757	−	35.4357i	1.29602	−	1.28370i
$763$	0.0889807	−	0.214818i	0.00322132	−	0.00777695i
$764$	27.7109	−	27.1867i	1.00255	−	0.983579i
$765$	−1.72232	+	0.713406i	−0.0622704	+	0.0257933i
$766$	48.2448	−	19.7143i	1.74315	−	0.712306i
$767$	1.27451			0.0460200
$768$	35.4409	−	13.1180i	1.27886	−	0.473354i
$769$	−31.0180			−1.11854			−0.559268	−	0.828987i	$-0.688918\pi$
$769$	−31.0180			−1.11854			−0.559268	+	0.828987i	$0.688918\pi$
$770$	0.282330	−	0.115369i	0.0101745	−	0.00415759i
$771$	−16.4594	+	6.81769i	−0.592769	+	0.245533i
$772$	−27.2372	+	26.7219i	−0.980289	+	0.961742i
$773$	−1.97461	+	4.76714i	−0.0710219	+	0.171462i	−0.955404	−	0.295301i	$-0.904580\pi$
$773$	−1.97461	+	4.76714i	−0.0710219	+	0.171462i	0.884382	+	0.466763i	$0.154580\pi$
$774$	−8.42036	+	8.34033i	−0.302664	+	0.299787i
$775$	20.7847	+	20.7847i	0.746609	+	0.746609i
$776$	8.53510	−	19.7985i	0.306392	−	0.710726i
$777$	1.26719	−	1.26719i	0.0454601	−	0.0454601i
$778$	0.0938126	−	19.6467i	0.00336334	−	0.704369i
$779$	−36.8808	−	15.2765i	−1.32139	−	0.547338i
$780$	1.18578	−	2.78715i	0.0424578	−	0.0997959i
$781$	20.0037	+	48.2931i	0.715787	+	1.72806i
$782$	−2.24408	−	0.942108i	−0.0802482	−	0.0336897i
$783$		−	1.00825i		−	0.0360319i
$784$	−27.9697	−	0.534280i	−0.998918	−	0.0190814i
$785$			1.69058i			0.0603393i
$786$	9.49635	−	22.6201i	0.338723	−	0.806832i
$787$	5.38323	+	12.9963i	0.191891	+	0.463267i	0.990317	−	0.138827i	$-0.0443333\pi$
$787$	5.38323	+	12.9963i	0.191891	+	0.463267i	−0.798425	+	0.602094i	$0.794333\pi$
$788$	−3.77890	−	9.37533i	−0.134618	−	0.333982i
$789$	57.8725	+	23.9716i	2.06031	+	0.853410i
$790$	1.03880	+	0.00496024i	0.0369588	+	0.000176477i
$791$	0.958064	−	0.958064i	0.0340648	−	0.0340648i
$792$	0.442875	−	30.9145i	0.0157369	−	1.09850i
$793$	−1.90002	−	1.90002i	−0.0674718	−	0.0674718i
$794$	38.5450	+	38.9149i	1.36791	+	1.38104i
$795$	−0.849710	+	2.05138i	−0.0301361	+	0.0727550i
$796$	−7.20321	−	0.0687919i	−0.255311	−	0.00243826i
$797$	−30.3579	+	12.5746i	−1.07533	+	0.445417i	−0.848869	−	0.528603i	$-0.822716\pi$
$797$	−30.3579	+	12.5746i	−1.07533	+	0.445417i	−0.226462	+	0.974020i	$0.572716\pi$
$798$	0.658527	+	1.61155i	0.0233116	+	0.0570482i
$799$	−1.57744			−0.0558060
$800$	−10.5036	+	23.7386i	−0.371358	+	0.839286i
$801$	−33.7453			−1.19233
$802$	8.88005	+	21.7313i	0.313565	+	0.767357i
$803$	−52.6219	+	21.7967i	−1.85699	+	0.769189i
$804$	0.279774	−	29.2952i	0.00986687	−	1.03316i
$805$	0.0297173	−	0.0717438i	0.00104740	−	0.00252864i
$806$	−6.37485	−	6.43602i	−0.224545	−	0.226699i
$807$	31.7189	+	31.7189i	1.11656	+	1.11656i
$808$	10.5257	+	10.8317i	0.370293	+	0.381057i
$809$	−34.3235	+	34.3235i	−1.20675	+	1.20675i	−0.234678	+	0.972073i	$0.575404\pi$
$809$	−34.3235	+	34.3235i	−1.20675	+	1.20675i	−0.972073	+	0.234678i	$0.924596\pi$
$810$	9.14618	+	0.0436728i	0.321364	+	0.00153451i
$811$	−19.8585	−	8.22568i	−0.697328	−	0.288843i	0.00572175	−	0.999984i	$-0.498179\pi$
$811$	−19.8585	−	8.22568i	−0.697328	−	0.288843i	−0.703049	+	0.711141i	$0.748179\pi$
$812$	−0.149120	+	0.0601057i	−0.00523309	+	0.00210930i
$813$	3.83212	+	9.25156i	0.134398	+	0.324466i
$814$	22.1905	−	52.8574i	0.777778	−	1.85265i
$815$		−	1.17007i		−	0.0409858i
$816$	−9.91734	+	3.88769i	−0.347176	+	0.136097i
$817$		−	21.3476i		−	0.746859i
$818$	30.9756	+	13.0042i	1.08304	+	0.454680i
$819$	−0.0782982	−	0.189029i	−0.00273596	−	0.00660519i
$820$	7.17135	+	3.05103i	0.250434	+	0.106547i
$821$	36.4082	+	15.0808i	1.27065	+	0.526322i	0.913163	−	0.407594i	$-0.133632\pi$
$821$	36.4082	+	15.0808i	1.27065	+	0.526322i	0.357491	+	0.933917i	$0.383632\pi$
$822$	0.204146	−	42.7534i	0.00712042	−	1.49119i
$823$	−17.7609	+	17.7609i	−0.619105	+	0.619105i	−0.945302	−	0.326197i	$-0.894233\pi$
$823$	−17.7609	+	17.7609i	−0.619105	+	0.619105i	0.326197	+	0.945302i	$0.394233\pi$
$824$	48.9737	−	19.4685i	1.70608	−	0.678216i
$825$	32.4879	+	32.4879i	1.13108	+	1.13108i
$826$	0.101607	−	0.100641i	0.00353536	−	0.00350176i
$827$	−2.90814	+	7.02088i	−0.101126	+	0.244140i	−0.966343	−	0.257258i	$-0.917181\pi$
$827$	−2.90814	+	7.02088i	−0.101126	+	0.244140i	0.865217	+	0.501398i	$0.167181\pi$
$828$	−5.51297	−	5.61928i	−0.191589	−	0.195284i
$829$	2.90794	−	1.20451i	0.100997	−	0.0418342i	−0.331613	−	0.943416i	$-0.607593\pi$
$829$	2.90794	−	1.20451i	0.100997	−	0.0418342i	0.432610	+	0.901581i	$0.357593\pi$
$830$	6.25728	−	2.55692i	0.217193	−	0.0887518i
$831$	−28.0358			−0.972552
$832$	3.27193	−	7.30031i	0.113434	−	0.253093i
$833$	7.88530			0.273209
$834$	−4.45027	+	1.81851i	−0.154100	+	0.0629700i
$835$	2.82546	−	1.17034i	0.0977791	−	0.0405014i
$836$	39.0007	+	39.7528i	1.34887	+	1.37488i
$837$	2.43939	−	5.88921i	0.0843177	−	0.203561i
$838$	−34.6294	+	34.3002i	−1.19625	+	1.18488i
$839$	−32.9694	−	32.9694i	−1.13823	−	1.13823i	−0.988767	−	0.149463i	$-0.952246\pi$
$839$	−32.9694	−	32.9694i	−1.13823	−	1.13823i	−0.149463	−	0.988767i	$-0.547754\pi$
$840$	−0.125553	−	0.315833i	−0.00433198	−	0.0108973i
$841$	−19.7802	+	19.7802i	−0.682078	+	0.682078i
$842$	0.127827	−	26.7701i	0.00440519	−	0.922558i
$843$	24.7666	+	10.2586i	0.853006	+	0.353327i
$844$	4.30284	+	1.83063i	0.148110	+	0.0630129i
$845$	−0.245375	−	0.592388i	−0.00844116	−	0.0203788i
$846$	−4.70440	−	1.97500i	−0.161741	−	0.0679018i
$847$		−	0.552980i		−	0.0190006i
$848$	−2.34734	+	5.37429i	−0.0806079	+	0.184554i
$849$		−	46.4912i		−	1.59557i
$850$	2.83233	−	6.74656i	0.0971482	−	0.231405i
$851$	−5.58568	−	13.4850i	−0.191475	−	0.462261i
$852$	54.0267	−	21.7765i	1.85093	−	0.746051i
$853$	15.4979	+	6.41946i	0.530639	+	0.219798i	0.631883	−	0.775064i	$-0.282282\pi$
$853$	15.4979	+	6.41946i	0.530639	+	0.219798i	−0.101244	+	0.994862i	$0.532282\pi$
$854$	−0.301509	−	0.00143970i	−0.0103174	−	4.92655e-5i
$855$	7.67979	−	7.67979i	0.262643	−	0.262643i
$856$	−0.296797	+	0.288413i	−0.0101443	+	0.00985777i
$857$	−2.24579	−	2.24579i	−0.0767146	−	0.0767146i	0.667708	−	0.744423i	$-0.267275\pi$
$857$	−2.24579	−	2.24579i	−0.0767146	−	0.0767146i	−0.744423	+	0.667708i	$0.767275\pi$
$858$	−9.96433	−	10.0599i	−0.340176	−	0.343441i
$859$	−1.32852	+	3.20734i	−0.0453287	+	0.109433i	−0.944922	−	0.327295i	$-0.893863\pi$
$859$	−1.32852	+	3.20734i	−0.0453287	+	0.109433i	0.899593	+	0.436728i	$0.143863\pi$
$860$	−0.0398000	+	4.16747i	−0.00135717	+	0.142109i
$861$	1.05221	−	0.435840i	0.0358593	−	0.0148534i
$862$	16.9799	+	41.5531i	0.578337	+	1.41531i
$863$	−27.1964			−0.925777			−0.462889	−	0.886416i	$-0.653187\pi$
$863$	−27.1964			−0.925777			−0.462889	+	0.886416i	$0.653187\pi$
$864$	5.62781	+	0.134388i	0.191462	+	0.00457197i
$865$	8.31782			0.282814
$866$	14.1477	+	34.6221i	0.480757	+	1.17651i
$867$	−34.3222	+	14.2167i	−1.16564	+	0.482826i
$868$	−1.01644	−	0.00970714i	−0.0345001	−	0.000329482i
$869$	1.85839	−	4.48655i	0.0630415	−	0.152196i
$870$	1.52705	+	1.54170i	0.0517717	+	0.0522685i
$871$	−4.38536	−	4.38536i	−0.148592	−	0.148592i
$872$	−8.28782	−	0.118730i	−0.280661	−	0.00402069i
$873$	−13.8990	+	13.8990i	−0.470409	+	0.470409i
$874$	14.1792	+	0.0677052i	0.479617	+	0.00229016i
$875$	0.450702	+	0.186687i	0.0152365	+	0.00631117i
$876$	23.7285	+	58.8695i	0.801711	+	1.98902i
$877$	18.1846	+	43.9015i	0.614051	+	1.48245i	0.858513	+	0.512791i	$0.171389\pi$
$877$	18.1846	+	43.9015i	0.614051	+	1.48245i	−0.244462	+	0.969659i	$0.578611\pi$
$878$	3.08077	−	7.33832i	0.103971	−	0.247656i
$879$		−	14.9567i		−	0.504476i
$880$	−7.53957	−	7.83322i	−0.254159	−	0.264058i
$881$			20.6413i			0.695423i	0.937602	+	0.347711i	$0.113041\pi$
$881$			20.6413i			0.695423i	−0.937602	+	0.347711i	$0.886959\pi$
$882$	23.5163	+	9.87258i	0.791834	+	0.332427i
$883$	−8.10496	−	19.5671i	−0.272754	−	0.658486i	0.726845	−	0.686801i	$-0.240986\pi$
$883$	−8.10496	−	19.5671i	−0.272754	−	0.658486i	−0.999599	+	0.0283155i	$0.990986\pi$
$884$	−0.882796	+	2.07499i	−0.0296916	+	0.0697893i
$885$	−1.78326	−	0.738652i	−0.0599437	−	0.0248295i
$886$	−0.0945974	+	19.8111i	−0.00317806	+	0.665566i
$887$	−26.3959	+	26.3959i	−0.886287	+	0.886287i	−0.994164	−	0.107877i	$-0.965595\pi$
$887$	−26.3959	+	26.3959i	−0.886287	+	0.886287i	0.107877	+	0.994164i	$0.465595\pi$
$888$	−58.6638	−	25.2898i	−1.96863	−	0.848671i
$889$	−0.845787	−	0.845787i	−0.0283668	−	0.0283668i
$890$	−8.43085	+	8.35072i	−0.282603	+	0.279917i
$891$	16.3623	−	39.5022i	0.548159	−	1.32337i
$892$	−29.3514	+	28.7961i	−0.982757	+	0.964164i
$893$	8.49057	−	3.51691i	0.284126	−	0.117689i
$894$	−61.7684	+	25.2405i	−2.06585	+	0.844167i
$895$	−16.1211			−0.538869
$896$	−0.315620	−	0.840365i	−0.0105441	−	0.0280746i
$897$	−3.60518			−0.120374
$898$	−40.1916	+	16.4235i	−1.34121	+	0.548060i
$899$	5.99583	−	2.48355i	0.199972	−	0.0828311i
$900$	16.8937	−	16.5741i	0.563123	−	0.552469i
$901$	0.632595	−	1.52722i	0.0210748	−	0.0508790i
$902$	25.8843	−	25.6383i	0.861853	−	0.853661i
$903$	0.430663	+	0.430663i	0.0143316	+	0.0143316i
$904$	−44.3531	−	19.1205i	−1.47516	−	0.635939i
$905$	2.90593	−	2.90593i	0.0965965	−	0.0965965i
$906$	0.0272205	−	5.70065i	0.000904340	−	0.189391i
$907$	−17.9375	−	7.42997i	−0.595606	−	0.246708i	0.0644543	−	0.997921i	$-0.479469\pi$
$907$	−17.9375	−	7.42997i	−0.595606	−	0.246708i	−0.660060	+	0.751213i	$0.729469\pi$
$908$	8.81147	−	20.7111i	0.292419	−	0.687322i
$909$	−5.26948	−	12.7216i	−0.174778	−	0.421950i
$910$	−0.0663395	−	0.0278506i	−0.00219913	−	0.000923238i
$911$		−	6.78738i		−	0.224876i	−0.993659	−	0.112438i	$-0.964134\pi$
$911$		−	6.78738i		−	0.224876i	0.993659	−	0.112438i	$-0.0358660\pi$
$912$	44.7123	−	43.0361i	1.48057	−	1.42507i
$913$		−	31.5993i		−	1.04579i
$914$	−9.37960	+	22.3420i	−0.310249	+	0.739008i
$915$	1.55729	+	3.75963i	0.0514824	+	0.124290i
$916$	−20.7050	−	51.3684i	−0.684112	−	1.69726i
$917$	−0.538388	−	0.223008i	−0.0177791	−	0.00736436i
$918$	−1.58675	−	0.00757671i	−0.0523707	−	0.000250069i
$919$	−20.8181	+	20.8181i	−0.686725	+	0.686725i	−0.961507	−	0.274781i	$-0.911395\pi$
$919$	−20.8181	+	20.8181i	−0.686725	+	0.686725i	0.274781	+	0.961507i	$0.411395\pi$
$920$	−2.76792	−	0.0396527i	−0.0912556	−	0.00130731i
$921$	−49.3196	−	49.3196i	−1.62513	−	1.62513i
$922$	−4.78489	−	4.83080i	−0.157582	−	0.159094i
$923$	4.71892	−	11.3925i	0.155325	−	0.374988i
$924$	−1.58876	−	0.0151729i	−0.0522663	−	0.000499153i
$925$	40.5411	−	16.7927i	1.33298	−	0.552139i
$926$	−10.9483	−	26.7927i	−0.359783	−	0.880461i
$927$	−48.0478			−1.57810
$928$	3.95476	+	4.14825i	0.129821	+	0.136173i
$929$	−24.4746			−0.802985			−0.401493	−	0.915862i	$-0.631508\pi$
$929$	−24.4746			−0.802985			−0.401493	+	0.915862i	$0.631508\pi$
$930$	5.18948	+	12.6997i	0.170170	+	0.416439i
$931$	−42.4425	+	17.5803i	−1.39100	+	0.576169i
$932$	−0.249459	+	26.1208i	−0.00817129	+	0.855617i
$933$	−18.7608	+	45.2927i	−0.614202	+	1.48282i
$934$	10.6028	+	10.7046i	0.346934	+	0.350264i
$935$	2.16697	+	2.16697i	0.0708675	+	0.0708675i
$936$	−5.23069	+	5.08293i	−0.170970	+	0.166141i
$937$	20.9203	−	20.9203i	0.683437	−	0.683437i	−0.277336	−	0.960773i	$-0.589452\pi$
$937$	20.9203	−	20.9203i	0.683437	−	0.683437i	0.960773	+	0.277336i	$0.0894516\pi$
$938$	−0.695900	−	0.00332291i	−0.0227219	−	0.000108497i
$939$	−20.1054	−	8.32792i	−0.656114	−	0.271771i
$940$	−1.66408	+	0.670738i	−0.0542763	+	0.0218771i
$941$	5.54349	+	13.3832i	0.180713	+	0.436279i	0.988114	−	0.153724i	$-0.0491267\pi$
$941$	5.54349	+	13.3832i	0.180713	+	0.436279i	−0.807401	+	0.590003i	$0.799127\pi$
$942$	3.40908	−	8.12036i	0.111074	−	0.264576i
$943$		−	9.27617i		−	0.302074i
$944$	−4.67186	−	2.04054i	−0.152056	−	0.0664138i
$945$		−	0.0506285i		−	0.00164695i
$946$	17.9640	+	7.54163i	0.584060	+	0.245199i
$947$	16.4509	+	39.7159i	0.534581	+	1.29059i	0.928461	+	0.371430i	$0.121133\pi$
$947$	16.4509	+	39.7159i	0.534581	+	1.29059i	−0.393880	+	0.919162i	$0.628867\pi$
$948$	−4.97967	−	2.11858i	−0.161732	−	0.0688084i
$949$	12.4137	+	5.14191i	0.402965	+	0.166913i
$950$	−0.203547	+	42.6279i	−0.00660394	+	1.38303i
$951$	26.7015	−	26.7015i	0.865856	−	0.865856i
$952$	0.0934719	+	0.235132i	0.00302944	+	0.00762069i
$953$	9.28789	+	9.28789i	0.300864	+	0.300864i	0.841352	−	0.540488i	$-0.181760\pi$
$953$	9.28789	+	9.28789i	0.300864	+	0.300864i	−0.540488	+	0.841352i	$0.681760\pi$
$954$	3.79870	−	3.76259i	0.122987	−	0.121818i
$955$	−4.76276	+	11.4983i	−0.154119	+	0.372077i
$956$	−25.6751	−	26.1702i	−0.830392	−	0.846406i
$957$	9.37189	−	3.88196i	0.302950	−	0.125486i
$958$	−39.2957	+	16.0574i	−1.26959	+	0.518792i
$959$	−1.01557			−0.0327946
$960$	−8.80894	+	8.31812i	−0.284307	+	0.268466i
$961$	10.0306			0.323566
$962$	−12.5187	+	5.11550i	−0.403618	+	0.164930i
$963$	0.348584	−	0.144388i	0.0112330	−	0.00465285i
$964$	18.9659	+	19.3316i	0.610849	+	0.622629i
$965$	4.68134	−	11.3017i	0.150698	−	0.363816i
$966$	−0.287414	+	0.284682i	−0.00924739	+	0.00915950i
$967$	−16.6329	−	16.6329i	−0.534879	−	0.534879i	0.387141	−	0.922020i	$-0.373463\pi$
$967$	−16.6329	−	16.6329i	−0.534879	−	0.534879i	−0.922020	+	0.387141i	$0.873463\pi$
$968$	−18.3180	+	7.28193i	−0.588763	+	0.234050i
$969$	−12.3691	+	12.3691i	−0.397354	+	0.397354i
$970$	−0.0330046	+	6.91199i	−0.00105971	+	0.221931i
$971$	40.4793	+	16.7671i	1.29904	+	0.538081i	0.921668	−	0.387979i	$-0.126827\pi$
$971$	40.4793	+	16.7671i	1.29904	+	0.538081i	0.377375	+	0.926061i	$0.376827\pi$
$972$	−38.3495	−	16.3157i	−1.23006	−	0.523326i
$973$	0.0437012	+	0.105504i	0.00140100	+	0.00338230i
$974$	−47.3668	−	19.8855i	−1.51773	−	0.637171i
$975$		−	10.8385i		−	0.347111i
$976$	3.92274	+	10.0067i	0.125564	+	0.320308i
$977$			20.6403i			0.660343i	0.943921	+	0.330171i	$0.107107\pi$
$977$			20.6403i			0.660343i	−0.943921	+	0.330171i	$0.892893\pi$
$978$	−2.35947	+	5.62021i	−0.0754476	+	0.179715i
$979$	21.2287	+	51.2506i	0.678472	+	1.63798i
$980$	8.31837	−	3.35287i	0.265720	−	0.107104i
$981$	6.98153	+	2.89185i	0.222903	+	0.0923295i
$982$	3.82920	+	0.0182844i	0.122195	+	0.000583477i
$983$	17.7853	−	17.7853i	0.567264	−	0.567264i	−0.364097	−	0.931361i	$-0.618622\pi$
$983$	17.7853	−	17.7853i	0.567264	−	0.567264i	0.931361	+	0.364097i	$0.118622\pi$
$984$	−28.2937	−	29.1162i	−0.901972	−	0.928190i
$985$	2.29151	+	2.29151i	0.0730136	+	0.0730136i
$986$	−1.13686	−	1.14777i	−0.0362050	−	0.0365524i
$987$	−0.100338	+	0.242237i	−0.00319379	+	0.00771048i
$988$	0.125458	−	13.1368i	0.00399136	−	0.417936i
$989$	4.58299	−	1.89834i	0.145731	−	0.0603636i
$990$	3.74944	+	9.17563i	0.119165	+	0.291621i
$991$	36.7127			1.16622			0.583109	−	0.812394i	$-0.301836\pi$
$991$	36.7127			1.16622			0.583109	+	0.812394i	$0.301836\pi$
$992$	13.0634	+	33.7983i	0.414764	+	1.07310i
$993$	−23.9168			−0.758978
$994$	−0.523400	−	1.28086i	−0.0166012	−	0.0406265i
$995$	2.13364	−	0.883784i	0.0676410	−	0.0280178i
$996$	−35.2117	−	0.336278i	−1.11573	−	0.0106554i
$997$	13.0497	−	31.5048i	0.413289	−	0.997768i	−0.570960	−	0.820978i	$-0.693429\pi$
$997$	13.0497	−	31.5048i	0.413289	−	0.997768i	0.984249	−	0.176790i	$-0.0565712\pi$
$998$	−0.598975	−	0.604723i	−0.0189602	−	0.0191422i
$999$	−6.72895	−	6.72895i	−0.212895	−	0.212895i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	416.2.bf.a.53.6	✓	192
32.29	even	8	inner	416.2.bf.a.157.6	yes	192

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
416.2.bf.a.53.6	✓	192	1.1	even	1	trivial
416.2.bf.a.157.6	yes	192	32.29	even	8	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:	\( N \)	\(=\)	\( 416 = 2^{5} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	416.bf (of order \(8\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.30913 + 0.534951i) q^{2} +(-2.18213 + 0.903868i) q^{3} +(1.42765 - 1.40064i) q^{4} +(-0.245375 + 0.592388i) q^{5} +(2.37317 - 2.35062i) q^{6} +(-0.0561050 - 0.0561050i) q^{7} +(-1.11971 + 2.59735i) q^{8} +(1.82339 - 1.82339i) q^{9} +(0.00432984 - 0.906777i) q^{10} +(-3.91635 - 1.62221i) q^{11} +(-1.84933 + 4.34680i) q^{12} +(0.382683 + 0.923880i) q^{13} +(0.103462 + 0.0434354i) q^{14} -1.51445i q^{15} +(0.0763944 - 3.99927i) q^{16} +1.12749i q^{17} +(-1.41164 + 3.36249i) q^{18} +(-2.51373 - 6.06867i) q^{19} +(0.479413 + 1.18941i) q^{20} +(0.173140 + 0.0717169i) q^{21} +(5.99482 + 0.0286251i) q^{22} +(1.07931 - 1.07931i) q^{23} +(0.0956940 - 6.67984i) q^{24} +(3.24482 + 3.24482i) q^{25} +(-0.995214 - 1.00476i) q^{26} +(0.380827 - 0.919398i) q^{27} +(-0.158682 - 0.00151544i) q^{28} +(0.936042 - 0.387721i) q^{29} +(0.810159 + 1.98262i) q^{30} +6.40551 q^{31} +(2.03940 + 5.27644i) q^{32} +10.0122 q^{33} +(-0.603150 - 1.47603i) q^{34} +(0.0470026 - 0.0194691i) q^{35} +(0.0492512 - 5.15710i) q^{36} +(3.65943 - 8.83465i) q^{37} +(6.53724 + 6.59997i) q^{38} +(-1.67013 - 1.67013i) q^{39} +(-1.26389 - 1.30063i) q^{40} +(4.29726 - 4.29726i) q^{41} +(-0.265028 - 0.00126550i) q^{42} +(3.00252 + 1.24369i) q^{43} +(-7.86333 + 3.16946i) q^{44} +(0.632741 + 1.52757i) q^{45} +(-0.835583 + 1.99034i) q^{46} +1.39908i q^{47} +(3.44811 + 8.79598i) q^{48} -6.99370i q^{49} +(-5.98372 - 2.51208i) q^{50} +(-1.01910 - 2.46032i) q^{51} +(1.84037 + 0.782978i) q^{52} +(-1.35454 - 0.561067i) q^{53} +(-0.00672001 + 1.40734i) q^{54} +(1.92195 - 1.92195i) q^{55} +(0.208546 - 0.0829030i) q^{56} +(10.9706 + 10.9706i) q^{57} +(-1.01799 + 1.00832i) q^{58} +(0.487735 - 1.17750i) q^{59} +(-2.12121 - 2.16212i) q^{60} +(-2.48250 + 1.02829i) q^{61} +(-8.38566 + 3.42664i) q^{62} -0.204603 q^{63} +(-5.49249 - 5.81658i) q^{64} -0.641196 q^{65} +(-13.1074 + 5.35606i) q^{66} +(-5.72975 + 2.37334i) q^{67} +(1.57921 + 1.60966i) q^{68} +(-1.37964 + 3.33076i) q^{69} +(-0.0511176 + 0.0506318i) q^{70} +(-8.71943 - 8.71943i) q^{71} +(2.69432 + 6.77768i) q^{72} +(9.50101 - 9.50101i) q^{73} +(-0.0645737 + 13.5233i) q^{74} +(-10.0135 - 4.14773i) q^{75} +(-12.0888 - 5.14313i) q^{76} +(0.128713 + 0.310741i) q^{77} +(3.07986 + 1.29298i) q^{78} +1.14559i q^{79} +(2.35037 + 1.02658i) q^{80} +10.0865i q^{81} +(-3.32685 + 7.92450i) q^{82} +(2.85267 + 6.88695i) q^{83} +(0.347634 - 0.140120i) q^{84} +(-0.667908 - 0.276657i) q^{85} +(-4.59601 - 0.0219459i) q^{86} +(-1.69212 + 1.69212i) q^{87} +(8.59863 - 8.35574i) q^{88} +(-9.25342 - 9.25342i) q^{89} +(-1.64552 - 1.66131i) q^{90} +(0.0303638 - 0.0733047i) q^{91} +(0.0291530 - 3.05262i) q^{92} +(-13.9777 + 5.78974i) q^{93} +(-0.748440 - 1.83158i) q^{94} +4.21181 q^{95} +(-9.21945 - 9.67053i) q^{96} -7.62258 q^{97} +(3.74129 + 9.15568i) q^{98} +(-10.0990 + 4.18313i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 192 q - 16 q^{10} - 16 q^{12} - 40 q^{16} - 40 q^{18} - 8 q^{22} - 16 q^{23} + 24 q^{24} + 80 q^{30} - 48 q^{31} - 48 q^{35} + 80 q^{36} - 56 q^{38} - 64 q^{40} - 16 q^{43} - 80 q^{44} + 24 q^{50} + 32 q^{51}+ \cdots + 56 q^{98}+O(q^{100}) \) 192 * q - 16 * q^10 - 16 * q^12 - 40 * q^16 - 40 * q^18 - 8 * q^22 - 16 * q^23 + 24 * q^24 + 80 * q^30 - 48 * q^31 - 48 * q^35 + 80 * q^36 - 56 * q^38 - 64 * q^40 - 16 * q^43 - 80 * q^44 + 24 * q^50 + 32 * q^51 - 32 * q^53 - 24 * q^54 + 32 * q^55 + 16 * q^56 - 64 * q^58 - 56 * q^60 - 64 * q^61 + 24 * q^62 + 80 * q^63 + 72 * q^64 + 96 * q^66 + 80 * q^67 - 32 * q^68 - 64 * q^69 - 120 * q^72 - 32 * q^74 + 32 * q^75 + 64 * q^76 - 32 * q^77 - 56 * q^80 - 80 * q^82 - 80 * q^83 + 112 * q^84 - 112 * q^87 - 88 * q^88 - 120 * q^90 + 144 * q^92 + 40 * q^94 + 136 * q^96 + 56 * q^98

Introduction

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