LMFDB - Embedded newform 120.2.m.b.59.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [120,2,Mod(59,120)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(120, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("120.59");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 120 = 2^{3} \cdot 3 \cdot 5 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	120.m (of order $2$, degree $1$, 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:	$0.958204824255$
Analytic rank:	$0$
Dimension:	$16$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} + 24x^{14} + 192x^{12} + 672x^{10} + 1092x^{8} + 880x^{6} + 352x^{4} + 64x^{2} + 4 $ x^16 + 24x^14 + 192x^12 + 672x^10 + 1092x^8 + 880x^6 + 352x^4 + 64*x^2 + 4
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{13} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			59.10
Root			$-0.528036i$ of defining polynomial
Character	$\chi$	$=$	120.59
Dual form			120.2.m.b.59.11

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.541196 - 1.30656i) q^{2} +(1.30656 + 1.13705i) q^{3} +(-1.41421 - 1.41421i) q^{4} +(2.10100 + 0.765367i) q^{5} +(2.19274 - 1.09174i) q^{6} -2.27411 q^{7} +(-2.61313 + 1.08239i) q^{8} +(0.414214 + 2.97127i) q^{9} +O(q^{10})$	\(q+(0.541196 - 1.30656i) q^{2} +(1.30656 + 1.13705i) q^{3} +(-1.41421 - 1.41421i) q^{4} +(2.10100 + 0.765367i) q^{5} +(2.19274 - 1.09174i) q^{6} -2.27411 q^{7} +(-2.61313 + 1.08239i) q^{8} +(0.414214 + 2.97127i) q^{9} +(2.13705 - 2.33088i) q^{10} -4.20201i q^{11} +(-0.239721 - 3.45580i) q^{12} -3.21608 q^{13} +(-1.23074 + 2.97127i) q^{14} +(1.87483 + 3.38896i) q^{15} +4.00000i q^{16} +1.53073 q^{17} +(4.10632 + 1.06684i) q^{18} -4.82843 q^{19} +(-1.88887 - 4.05366i) q^{20} +(-2.97127 - 2.58579i) q^{21} +(-5.49019 - 2.27411i) q^{22} -1.08239i q^{23} +(-4.64495 - 1.55705i) q^{24} +(3.82843 + 3.21608i) q^{25} +(-1.74053 + 4.20201i) q^{26} +(-2.83730 + 4.35313i) q^{27} +(3.21608 + 3.21608i) q^{28} +1.74053 q^{29} +(5.44253 - 0.615493i) q^{30} +6.82843i q^{31} +(5.22625 + 2.16478i) q^{32} +(4.77791 - 5.49019i) q^{33} +(0.828427 - 2.00000i) q^{34} +(-4.77791 - 1.74053i) q^{35} +(3.61622 - 4.78779i) q^{36} +7.76429 q^{37} +(-2.61313 + 6.30864i) q^{38} +(-4.20201 - 3.65685i) q^{39} +(-6.31861 + 0.274109i) q^{40} +2.46148i q^{41} +(-4.98653 + 2.48273i) q^{42} -8.70626i q^{43} +(-5.94253 + 5.94253i) q^{44} +(-1.40385 + 6.55967i) q^{45} +(-1.41421 - 0.585786i) q^{46} +1.08239i q^{47} +(-4.54822 + 5.22625i) q^{48} -1.82843 q^{49} +(6.27394 - 3.26155i) q^{50} +(2.00000 + 1.74053i) q^{51} +(4.54822 + 4.54822i) q^{52} -11.0866i q^{53} +(4.15211 + 6.06300i) q^{54} +(3.21608 - 8.82843i) q^{55} +(5.94253 - 2.46148i) q^{56} +(-6.30864 - 5.49019i) q^{57} +(0.941967 - 2.27411i) q^{58} +4.20201i q^{59} +(2.14130 - 7.44411i) q^{60} -8.48528i q^{61} +(8.92177 + 3.69552i) q^{62} +(-0.941967 - 6.75699i) q^{63} +(5.65685 - 5.65685i) q^{64} +(-6.75699 - 2.46148i) q^{65} +(-4.58749 - 9.21391i) q^{66} -2.27411i q^{67} +(-2.16478 - 2.16478i) q^{68} +(1.23074 - 1.41421i) q^{69} +(-4.85990 + 5.30067i) q^{70} +11.8851 q^{71} +(-4.29847 - 7.31595i) q^{72} +4.54822i q^{73} +(4.20201 - 10.1445i) q^{74} +(1.34523 + 8.55514i) q^{75} +(6.82843 + 6.82843i) q^{76} +9.55582i q^{77} +(-7.05202 + 3.51111i) q^{78} +0.485281i q^{79} +(-3.06147 + 8.40401i) q^{80} +(-8.65685 + 2.46148i) q^{81} +(3.21608 + 1.33214i) q^{82} +6.94269 q^{83} +(0.545152 + 7.85886i) q^{84} +(3.21608 + 1.17157i) q^{85} +(-11.3753 - 4.71179i) q^{86} +(2.27411 + 1.97908i) q^{87} +(4.54822 + 10.9804i) q^{88} -8.40401i q^{89} +(7.81086 + 5.38428i) q^{90} +7.31371 q^{91} +(-1.53073 + 1.53073i) q^{92} +(-7.76429 + 8.92177i) q^{93} +(1.41421 + 0.585786i) q^{94} +(-10.1445 - 3.69552i) q^{95} +(4.36695 + 8.77096i) q^{96} +10.9804i q^{97} +(-0.989538 + 2.38896i) q^{98} +(12.4853 - 1.74053i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 16 q^{9}+O(q^{10}) $ 16 * q - 16 * q^9	$ 16 q - 16 q^{9} + 16 q^{10} - 32 q^{19} - 32 q^{24} + 16 q^{25} + 16 q^{30} - 32 q^{34} - 32 q^{36} + 32 q^{40} + 16 q^{49} + 32 q^{51} + 32 q^{54} + 64 q^{66} - 64 q^{70} + 32 q^{75} + 64 q^{76} - 48 q^{81} + 32 q^{84} - 16 q^{90} - 64 q^{91} + 64 q^{96} + 64 q^{99}+O(q^{100}) $ 16 * q - 16 * q^9 + 16 * q^10 - 32 * q^19 - 32 * q^24 + 16 * q^25 + 16 * q^30 - 32 * q^34 - 32 * q^36 + 32 * q^40 + 16 * q^49 + 32 * q^51 + 32 * q^54 + 64 * q^66 - 64 * q^70 + 32 * q^75 + 64 * q^76 - 48 * q^81 + 32 * q^84 - 16 * q^90 - 64 * q^91 + 64 * q^96 + 64 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/120\mathbb{Z}\right)^\times$.

$n$	$31$	$41$	$61$	$97$
$\chi(n)$	$-1$	$-1$	$-1$	$-1$

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 $

$2$	0.541196	−	1.30656i	0.382683	−	0.923880i
$2$	0.541196	−	1.30656i	0.382683	−	0.923880i
$3$	1.30656	+	1.13705i	0.754344	+	0.656479i
$3$	1.30656	+	1.13705i	0.754344	+	0.656479i
$4$	−1.41421	−	1.41421i	−0.707107	−	0.707107i
$5$	2.10100	+	0.765367i	0.939597	+	0.342282i
$5$	2.10100	+	0.765367i	0.939597	+	0.342282i
$6$	2.19274	−	1.09174i	0.895182	−	0.445700i
$7$	−2.27411			−0.859533			−0.429766	−	0.902940i	$-0.641404\pi$
$7$	−2.27411			−0.859533			−0.429766	+	0.902940i	$0.641404\pi$
$8$	−2.61313	+	1.08239i	−0.923880	+	0.382683i
$9$	0.414214	+	2.97127i	0.138071	+	0.990422i
$10$	2.13705	−	2.33088i	0.675796	−	0.737089i
$11$		−	4.20201i		−	1.26695i	−0.773762	−	0.633476i	$-0.781627\pi$
$11$		−	4.20201i		−	1.26695i	0.773762	−	0.633476i	$-0.218373\pi$
$12$	−0.239721	−	3.45580i	−0.0692015	−	0.997603i
$13$	−3.21608			−0.891979			−0.445990	−	0.895038i	$-0.647148\pi$
$13$	−3.21608			−0.891979			−0.445990	+	0.895038i	$0.647148\pi$
$14$	−1.23074	+	2.97127i	−0.328929	+	0.794104i
$15$	1.87483	+	3.38896i	0.484079	+	0.875024i
$16$			4.00000i			1.00000i
$17$	1.53073			0.371257			0.185629	−	0.982620i	$-0.440568\pi$
$17$	1.53073			0.371257			0.185629	+	0.982620i	$0.440568\pi$
$18$	4.10632	+	1.06684i	0.967868	+	0.251457i
$19$	−4.82843			−1.10772			−0.553859	−	0.832611i	$-0.686845\pi$
$19$	−4.82843			−1.10772			−0.553859	+	0.832611i	$0.686845\pi$
$20$	−1.88887	−	4.05366i	−0.422365	−	0.906426i
$21$	−2.97127	−	2.58579i	−0.648384	−	0.564265i
$22$	−5.49019	−	2.27411i	−1.17051	−	0.484842i
$23$		−	1.08239i		−	0.225694i	−0.993612	−	0.112847i	$-0.964003\pi$
$23$		−	1.08239i		−	0.225694i	0.993612	−	0.112847i	$-0.0359971\pi$
$24$	−4.64495	−	1.55705i	−0.948147	−	0.317832i
$25$	3.82843	+	3.21608i	0.765685	+	0.643215i
$26$	−1.74053	+	4.20201i	−0.341346	+	0.824081i
$27$	−2.83730	+	4.35313i	−0.546038	+	0.837760i
$28$	3.21608	+	3.21608i	0.607781	+	0.607781i
$29$	1.74053			0.323208			0.161604	−	0.986856i	$-0.448333\pi$
$29$	1.74053			0.323208			0.161604	+	0.986856i	$0.448333\pi$
$30$	5.44253	−	0.615493i	0.993666	−	0.112373i
$31$			6.82843i			1.22642i	0.789919	+	0.613211i	$0.210122\pi$
$31$			6.82843i			1.22642i	−0.789919	+	0.613211i	$0.789878\pi$
$32$	5.22625	+	2.16478i	0.923880	+	0.382683i
$33$	4.77791	−	5.49019i	0.831727	−	0.955719i
$34$	0.828427	−	2.00000i	0.142074	−	0.342997i
$35$	−4.77791	−	1.74053i	−0.807614	−	0.294203i
$36$	3.61622	−	4.78779i	0.602703	−	0.797965i
$37$	7.76429			1.27644			0.638221	−	0.769853i	$-0.279671\pi$
$37$	7.76429			1.27644			0.638221	+	0.769853i	$0.279671\pi$
$38$	−2.61313	+	6.30864i	−0.423905	+	1.02340i
$39$	−4.20201	−	3.65685i	−0.672859	−	0.585565i
$40$	−6.31861	+	0.274109i	−0.999060	+	0.0433405i
$41$			2.46148i			0.384418i	0.981354	+	0.192209i	$0.0615652\pi$
$41$			2.46148i			0.384418i	−0.981354	+	0.192209i	$0.938435\pi$
$42$	−4.98653	+	2.48273i	−0.769438	+	0.383094i
$43$		−	8.70626i		−	1.32769i	−0.747869	−	0.663846i	$-0.768923\pi$
$43$		−	8.70626i		−	1.32769i	0.747869	−	0.663846i	$-0.231077\pi$
$44$	−5.94253	+	5.94253i	−0.895871	+	0.895871i
$45$	−1.40385	+	6.55967i	−0.209273	+	0.977857i
$46$	−1.41421	−	0.585786i	−0.208514	−	0.0863695i
$47$			1.08239i			0.157883i	0.996879	+	0.0789416i	$0.0251541\pi$
$47$			1.08239i			0.157883i	−0.996879	+	0.0789416i	$0.974846\pi$
$48$	−4.54822	+	5.22625i	−0.656479	+	0.754344i
$49$	−1.82843			−0.261204
$50$	6.27394	−	3.26155i	0.887269	−	0.461253i
$51$	2.00000	+	1.74053i	0.280056	+	0.243723i
$52$	4.54822	+	4.54822i	0.630724	+	0.630724i
$53$		−	11.0866i		−	1.52286i	−0.648250	−	0.761428i	$-0.724499\pi$
$53$		−	11.0866i		−	1.52286i	0.648250	−	0.761428i	$-0.275501\pi$
$54$	4.15211	+	6.06300i	0.565030	+	0.825070i
$55$	3.21608	−	8.82843i	0.433656	−	1.19042i
$56$	5.94253	−	2.46148i	0.794104	−	0.328929i
$57$	−6.30864	−	5.49019i	−0.835600	−	0.727193i
$58$	0.941967	−	2.27411i	0.123686	−	0.298605i
$59$			4.20201i			0.547055i	0.961864	+	0.273527i	$0.0881904\pi$
$59$			4.20201i			0.547055i	−0.961864	+	0.273527i	$0.911810\pi$
$60$	2.14130	−	7.44411i	0.276440	−	0.961031i
$61$		−	8.48528i		−	1.08643i	−0.839594	−	0.543214i	$-0.817207\pi$
$61$		−	8.48528i		−	1.08643i	0.839594	−	0.543214i	$-0.182793\pi$
$62$	8.92177	+	3.69552i	1.13307	+	0.469331i
$63$	−0.941967	−	6.75699i	−0.118677	−	0.851300i
$64$	5.65685	−	5.65685i	0.707107	−	0.707107i
$65$	−6.75699	−	2.46148i	−0.838101	−	0.305309i
$66$	−4.58749	−	9.21391i	−0.564681	−	1.13415i
$67$		−	2.27411i		−	0.277827i	−0.990305	−	0.138913i	$-0.955639\pi$
$67$		−	2.27411i		−	0.277827i	0.990305	−	0.138913i	$-0.0443609\pi$
$68$	−2.16478	−	2.16478i	−0.262519	−	0.262519i
$69$	1.23074	−	1.41421i	0.148164	−	0.170251i
$70$	−4.85990	+	5.30067i	−0.580869	+	0.633552i
$71$	11.8851			1.41050			0.705249	−	0.708960i	$-0.250835\pi$
$71$	11.8851			1.41050			0.705249	+	0.708960i	$0.250835\pi$
$72$	−4.29847	−	7.31595i	−0.506579	−	0.862193i
$73$			4.54822i			0.532329i	0.963928	+	0.266164i	$0.0857564\pi$
$73$			4.54822i			0.532329i	−0.963928	+	0.266164i	$0.914244\pi$
$74$	4.20201	−	10.1445i	0.488473	−	1.17928i
$75$	1.34523	+	8.55514i	0.155333	+	0.987862i
$76$	6.82843	+	6.82843i	0.783274	+	0.783274i
$77$			9.55582i			1.08899i
$78$	−7.05202	+	3.51111i	−0.798484	+	0.397555i
$79$			0.485281i			0.0545984i	0.999627	+	0.0272992i	$0.00869069\pi$
$79$			0.485281i			0.0545984i	−0.999627	+	0.0272992i	$0.991309\pi$
$80$	−3.06147	+	8.40401i	−0.342282	+	0.939597i
$81$	−8.65685	+	2.46148i	−0.961873	+	0.273498i
$82$	3.21608	+	1.33214i	0.355156	+	0.147111i
$83$	6.94269			0.762060			0.381030	−	0.924563i	$-0.375569\pi$
$83$	6.94269			0.762060			0.381030	+	0.924563i	$0.375569\pi$
$84$	0.545152	+	7.85886i	0.0594809	+	0.857472i
$85$	3.21608	+	1.17157i	0.348832	+	0.127075i
$86$	−11.3753	−	4.71179i	−1.22663	−	0.508086i
$87$	2.27411	+	1.97908i	0.243810	+	0.212179i
$88$	4.54822	+	10.9804i	0.484842	+	1.17051i
$89$		−	8.40401i		−	0.890823i	−0.895326	−	0.445412i	$-0.853057\pi$
$89$		−	8.40401i		−	0.890823i	0.895326	−	0.445412i	$-0.146943\pi$
$90$	7.81086	+	5.38428i	0.823337	+	0.567553i
$91$	7.31371			0.766685
$92$	−1.53073	+	1.53073i	−0.159590	+	0.159590i
$93$	−7.76429	+	8.92177i	−0.805120	+	0.925144i
$94$	1.41421	+	0.585786i	0.145865	+	0.0604193i
$95$	−10.1445	−	3.69552i	−1.04081	−	0.379152i
$96$	4.36695	+	8.77096i	0.445700	+	0.895182i
$97$			10.9804i			1.11489i	0.830215	+	0.557444i	$0.188218\pi$
$97$			10.9804i			1.11489i	−0.830215	+	0.557444i	$0.811782\pi$
$98$	−0.989538	+	2.38896i	−0.0999584	+	0.241321i
$99$	12.4853	−	1.74053i	1.25482	−	0.174930i
$100$	−0.865995	−	9.96243i	−0.0865995	−	0.996243i
$101$	−13.6256			−1.35580			−0.677899	−	0.735155i	$-0.737109\pi$
$101$	−13.6256			−1.35580			−0.677899	+	0.735155i	$0.737109\pi$
$102$	3.35650	−	1.67116i	0.332343	−	0.165469i
$103$	−8.70626			−0.857853			−0.428927	−	0.903339i	$-0.641108\pi$
$103$	−8.70626			−0.857853			−0.428927	+	0.903339i	$0.641108\pi$
$104$	8.40401	−	3.48106i	0.824081	−	0.341346i
$105$	−4.26357	−	7.70685i	−0.416081	−	0.752112i
$106$	−14.4853	−	6.00000i	−1.40693	−	0.582772i
$107$	5.67459			0.548584			0.274292	−	0.961647i	$-0.411557\pi$
$107$	5.67459			0.548584			0.274292	+	0.961647i	$0.411557\pi$
$108$	10.1688	−	2.14371i	0.978493	−	0.206279i
$109$			16.4853i			1.57900i	0.613748	+	0.789502i	$0.289661\pi$
$109$			16.4853i			1.57900i	−0.613748	+	0.789502i	$0.710339\pi$
$110$	−9.79437	−	8.97992i	−0.933856	−	0.856201i
$111$	10.1445	+	8.82843i	0.962877	+	0.837957i
$112$		−	9.09644i		−	0.859533i
$113$	−0.634051			−0.0596465			−0.0298232	−	0.999555i	$-0.509494\pi$
$113$	−0.634051			−0.0596465			−0.0298232	+	0.999555i	$0.509494\pi$
$114$	−10.5875	+	5.27137i	−0.991609	+	0.493709i
$115$	0.828427	−	2.27411i	0.0772512	−	0.212062i
$116$	−2.46148	−	2.46148i	−0.228543	−	0.228543i
$117$	−1.33214	−	9.55582i	−0.123157	−	0.883436i
$118$	5.49019	+	2.27411i	0.505413	+	0.209349i
$119$	−3.48106			−0.319108
$120$	−8.56734	−	6.82647i	−0.782088	−	0.623168i
$121$	−6.65685			−0.605169
$122$	−11.0866	−	4.59220i	−1.00373	−	0.415758i
$123$	−2.79884	+	3.21608i	−0.252362	+	0.289984i
$124$	9.65685	−	9.65685i	0.867211	−	0.867211i
$125$	5.58206	+	9.68714i	0.499275	+	0.866444i
$126$	−9.33822	−	2.42612i	−0.831914	−	0.216136i
$127$	2.27411			0.201795			0.100897	−	0.994897i	$-0.467829\pi$
$127$	2.27411			0.201795			0.100897	+	0.994897i	$0.467829\pi$
$128$	−4.32957	−	10.4525i	−0.382683	−	0.923880i
$129$	9.89949	−	11.3753i	0.871602	−	1.00154i
$130$	−6.87293	+	7.49628i	−0.602796	+	0.657468i
$131$			11.1641i			0.975413i	0.873008	+	0.487707i	$0.162166\pi$
$131$			11.1641i			0.975413i	−0.873008	+	0.487707i	$0.837834\pi$
$132$	−14.5213	+	1.00731i	−1.26392	+	0.0876750i
$133$	10.9804			0.952119
$134$	−2.97127	−	1.23074i	−0.256678	−	0.106320i
$135$	−9.29291	+	6.97437i	−0.799806	+	0.600258i
$136$	−4.00000	+	1.65685i	−0.342997	+	0.142074i
$137$	8.02509			0.685629			0.342815	−	0.939403i	$-0.388620\pi$
$137$	8.02509			0.685629			0.342815	+	0.939403i	$0.388620\pi$
$138$	−1.18169	−	2.37340i	−0.100592	−	0.202038i
$139$	−2.48528			−0.210799			−0.105399	−	0.994430i	$-0.533612\pi$
$139$	−2.48528			−0.210799			−0.105399	+	0.994430i	$0.533612\pi$
$140$	4.29551	+	9.21846i	0.363037	+	0.779102i
$141$	−1.23074	+	1.41421i	−0.103647	+	0.119098i
$142$	6.43215	−	15.5286i	0.539774	−	1.30313i
$143$			13.5140i			1.13010i
$144$	−11.8851	+	1.65685i	−0.990422	+	0.138071i
$145$	3.65685	+	1.33214i	0.303685	+	0.110628i
$146$	5.94253	+	2.46148i	0.491808	+	0.203713i
$147$	−2.38896	−	2.07902i	−0.197038	−	0.171475i
$148$	−10.9804	−	10.9804i	−0.902581	−	0.902581i
$149$	0.720950			0.0590625			0.0295313	−	0.999564i	$-0.490599\pi$
$149$	0.720950			0.0590625			0.0295313	+	0.999564i	$0.490599\pi$
$150$	11.9059	+	2.87238i	0.972109	+	0.234529i
$151$			2.82843i			0.230174i	0.993355	+	0.115087i	$0.0367147\pi$
$151$			2.82843i			0.230174i	−0.993355	+	0.115087i	$0.963285\pi$
$152$	12.6173	−	5.22625i	1.02340	−	0.423905i
$153$	0.634051	+	4.54822i	0.0512600	+	0.367702i
$154$	12.4853	+	5.17157i	1.00609	+	0.416737i
$155$	−5.22625	+	14.3465i	−0.419783	+	1.15234i
$156$	0.770961	+	11.1141i	0.0617263	+	0.889841i
$157$	−23.2929			−1.85897			−0.929487	−	0.368854i	$-0.879750\pi$
$157$	−23.2929			−1.85897			−0.929487	+	0.368854i	$0.879750\pi$
$158$	0.634051	+	0.262632i	0.0504424	+	0.0208939i
$159$	12.6060	−	14.4853i	0.999722	−	1.14876i
$160$	9.32352	+	8.54822i	0.737089	+	0.675796i
$161$			2.46148i			0.193992i
$162$	−1.46898	+	12.6429i	−0.115414	+	0.993317i
$163$			8.70626i			0.681927i	0.940077	+	0.340964i	$0.110753\pi$
$163$			8.70626i			0.681927i	−0.940077	+	0.340964i	$0.889247\pi$
$164$	3.48106	−	3.48106i	0.271825	−	0.271825i
$165$	14.2404	−	7.87804i	1.10861	−	0.613305i
$166$	3.75736	−	9.07107i	0.291628	−	0.704051i
$167$		−	5.04054i		−	0.390049i	−0.980798	−	0.195024i	$-0.937521\pi$
$167$		−	5.04054i		−	0.390049i	0.980798	−	0.195024i	$-0.0624786\pi$
$168$	10.5631	+	3.54091i	0.814963	+	0.273187i
$169$	−2.65685			−0.204373
$170$	3.27126	−	3.56796i	0.250894	−	0.273650i
$171$	−2.00000	−	14.3465i	−0.152944	−	1.09711i
$172$	−12.3125	+	12.3125i	−0.938820	+	0.938820i
$173$		−	0.262632i		−	0.0199676i	−0.999950	−	0.00998379i	$-0.996822\pi$
$173$		−	0.262632i		−	0.0199676i	0.999950	−	0.00998379i	$-0.00317799\pi$
$174$	3.81653	−	1.90020i	0.289330	−	0.144054i
$175$	−8.70626	−	7.31371i	−0.658132	−	0.552864i
$176$	16.8080			1.26695
$177$	−4.77791	+	5.49019i	−0.359130	+	0.412668i
$178$	−10.9804	−	4.54822i	−0.823014	−	0.340903i
$179$		−	7.68306i		−	0.574259i	−0.957892	−	0.287129i	$-0.907299\pi$
$179$		−	7.68306i		−	0.574259i	0.957892	−	0.287129i	$-0.0927010\pi$
$180$	11.2621	−	7.29143i	0.839428	−	0.543471i
$181$		−	21.6569i		−	1.60974i	−0.593450	−	0.804871i	$-0.702235\pi$
$181$		−	21.6569i		−	1.60974i	0.593450	−	0.804871i	$-0.297765\pi$
$182$	3.95815	−	9.55582i	0.293398	−	0.708325i
$183$	9.64823	−	11.0866i	0.713218	−	0.819542i
$184$	1.17157	+	2.82843i	0.0863695	+	0.208514i
$185$	16.3128	+	5.94253i	1.19934	+	0.436904i
$186$	7.45485	+	14.9730i	0.546616	+	1.09787i
$187$		−	6.43215i		−	0.470366i
$188$	1.53073	−	1.53073i	0.111640	−	0.111640i
$189$	6.45232	−	9.89949i	0.469337	−	0.720082i
$190$	−10.3186	+	11.2545i	−0.748591	+	0.816486i
$191$	−8.40401			−0.608093			−0.304046	−	0.952657i	$-0.598338\pi$
$191$	−8.40401			−0.608093			−0.304046	+	0.952657i	$0.598338\pi$
$192$	13.8232	−	0.958884i	0.997603	−	0.0692015i
$193$		−	13.6447i		−	0.982164i	−0.871113	−	0.491082i	$-0.836602\pi$
$193$		−	13.6447i		−	0.982164i	0.871113	−	0.491082i	$-0.163398\pi$
$194$	14.3465	+	5.94253i	1.03002	+	0.426649i
$195$	−6.02959	−	10.8991i	−0.431788	−	0.780503i
$196$	2.58579	+	2.58579i	0.184699	+	0.184699i
$197$		−	8.02509i		−	0.571764i	−0.958265	−	0.285882i	$-0.907713\pi$
$197$		−	8.02509i		−	0.571764i	0.958265	−	0.285882i	$-0.0922865\pi$
$198$	4.48288	−	17.2548i	0.318584	−	1.22624i
$199$			14.8284i			1.05116i	0.850744	+	0.525580i	$0.176152\pi$
$199$			14.8284i			1.05116i	−0.850744	+	0.525580i	$0.823848\pi$
$200$	−13.4852	−	4.26015i	−0.953549	−	0.301238i
$201$	2.58579	−	2.97127i	0.182387	−	0.209577i
$202$	−7.37412	+	17.8027i	−0.518841	+	1.25259i
$203$	−3.95815			−0.277808
$204$	−0.366949	−	5.28991i	−0.0256916	−	0.370367i
$205$	−1.88393	+	5.17157i	−0.131580	+	0.361198i
$206$	−4.71179	+	11.3753i	−0.328286	+	0.792553i
$207$	3.21608	−	0.448342i	0.223533	−	0.0311619i
$208$		−	12.8643i		−	0.891979i
$209$			20.2891i			1.40342i
$210$	−12.3769	+	1.39970i	−0.854088	+	0.0965883i
$211$	1.51472			0.104278			0.0521388	−	0.998640i	$-0.483396\pi$
$211$	1.51472			0.104278			0.0521388	+	0.998640i	$0.483396\pi$
$212$	−15.6788	+	15.6788i	−1.07682	+	1.07682i
$213$	15.5286	+	13.5140i	1.06400	+	0.925962i
$214$	3.07107	−	7.41421i	0.209934	−	0.506825i
$215$	6.66348	−	18.2919i	0.454446	−	1.24750i
$216$	2.70242	−	14.4463i	0.183876	−	0.982949i
$217$		−	15.5286i		−	1.05415i
$218$	21.5391	+	8.92177i	1.45881	+	0.604259i
$219$	−5.17157	+	5.94253i	−0.349463	+	0.401559i
$220$	−17.0335	+	7.93706i	−1.14840	+	0.535117i
$221$	−4.92296			−0.331154
$222$	17.0251	−	8.47657i	1.14265	−	0.568910i
$223$	10.5902			0.709172			0.354586	−	0.935023i	$-0.384622\pi$
$223$	10.5902			0.709172			0.354586	+	0.935023i	$0.384622\pi$
$224$	−11.8851	−	4.92296i	−0.794104	−	0.328929i
$225$	−7.97003	+	12.7074i	−0.531336	+	0.847161i
$226$	−0.343146	+	0.828427i	−0.0228257	+	0.0551062i
$227$	−4.77791			−0.317121			−0.158561	−	0.987349i	$-0.550685\pi$
$227$	−4.77791			−0.317121			−0.158561	+	0.987349i	$0.550685\pi$
$228$	1.15748	+	16.6861i	0.0766557	+	1.10506i
$229$			3.31371i			0.218976i	0.993988	+	0.109488i	$0.0349211\pi$
$229$			3.31371i			0.218976i	−0.993988	+	0.109488i	$0.965079\pi$
$230$	−2.52293	−	2.31313i	−0.166357	−	0.152523i
$231$	−10.8655	+	12.4853i	−0.714897	+	0.821471i
$232$	−4.54822	+	1.88393i	−0.298605	+	0.123686i
$233$	−28.0334			−1.83653			−0.918265	−	0.395967i	$-0.870410\pi$
$233$	−28.0334			−1.83653			−0.918265	+	0.395967i	$0.870410\pi$
$234$	−13.2062	−	3.43105i	−0.863318	−	0.224294i
$235$	−0.828427	+	2.27411i	−0.0540406	+	0.148347i
$236$	5.94253	−	5.94253i	0.386826	−	0.386826i
$237$	−0.551791	+	0.634051i	−0.0358427	+	0.0411860i
$238$	−1.88393	+	4.54822i	−0.122117	+	0.294817i
$239$	−13.3270			−0.862050			−0.431025	−	0.902340i	$-0.641848\pi$
$239$	−13.3270			−0.862050			−0.431025	+	0.902340i	$0.641848\pi$
$240$	−13.5558	+	7.49932i	−0.875024	+	0.484079i
$241$	10.4853			0.675416			0.337708	−	0.941251i	$-0.390348\pi$
$241$	10.4853			0.675416			0.337708	+	0.941251i	$0.390348\pi$
$242$	−3.60266	+	8.69760i	−0.231588	+	0.559103i
$243$	−14.1096	−	6.62724i	−0.905129	−	0.425138i
$244$	−12.0000	+	12.0000i	−0.768221	+	0.768221i
$245$	−3.84153	−	1.39942i	−0.245426	−	0.0894055i
$246$	2.68729	+	5.39738i	0.171335	+	0.344125i
$247$	15.5286			0.988060
$248$	−7.39104	−	17.8435i	−0.469331	−	1.13307i
$249$	9.07107	+	7.89422i	0.574856	+	0.500276i
$250$	15.6778	−	2.05067i	0.991554	−	0.129696i
$251$		−	27.9721i		−	1.76559i	−0.469762	−	0.882793i	$-0.655660\pi$
$251$		−	27.9721i		−	1.76559i	0.469762	−	0.882793i	$-0.344340\pi$
$252$	−8.22368	+	10.8880i	−0.518043	+	0.685877i
$253$	−4.54822			−0.285944
$254$	1.23074	−	2.97127i	0.0772234	−	0.186434i
$255$	2.86986	+	5.18759i	0.179718	+	0.324859i
$256$	−16.0000			−1.00000
$257$	−2.42742			−0.151418			−0.0757090	−	0.997130i	$-0.524122\pi$
$257$	−2.42742			−0.151418			−0.0757090	+	0.997130i	$0.524122\pi$
$258$	−9.50495	−	19.0906i	−0.591752	−	1.18853i
$259$	−17.6569			−1.09714
$260$	6.07476	+	13.0369i	0.376741	+	0.808513i
$261$	0.720950	+	5.17157i	0.0446257	+	0.320112i
$262$	14.5866	+	6.04198i	0.901165	+	0.373275i
$263$			27.5851i			1.70097i	0.526001	+	0.850484i	$0.323691\pi$
$263$			27.5851i			1.70097i	−0.526001	+	0.850484i	$0.676309\pi$
$264$	−6.54275	+	19.5181i	−0.402678	+	1.20126i
$265$	8.48528	−	23.2929i	0.521247	−	1.43087i
$266$	5.94253	−	14.3465i	0.364360	−	0.879643i
$267$	9.55582	−	10.9804i	0.584807	−	0.671988i
$268$	−3.21608	+	3.21608i	−0.196453	+	0.196453i
$269$	7.68306			0.468445			0.234222	−	0.972183i	$-0.424746\pi$
$269$	7.68306			0.468445			0.234222	+	0.972183i	$0.424746\pi$
$270$	4.08316	+	15.9163i	0.248493	+	0.968634i
$271$		−	14.1421i		−	0.859074i	−0.903049	−	0.429537i	$-0.858677\pi$
$271$		−	14.1421i		−	0.859074i	0.903049	−	0.429537i	$-0.141323\pi$
$272$			6.12293i			0.371257i
$273$	9.55582	+	8.31609i	0.578345	+	0.503312i
$274$	4.34315	−	10.4853i	0.262379	−	0.633439i
$275$	13.5140	−	16.0871i	0.814923	−	0.970087i
$276$	−3.74053	+	0.259472i	−0.225153	+	0.0156184i
$277$	16.8607			1.01306			0.506532	−	0.862221i	$-0.330927\pi$
$277$	16.8607			1.01306			0.506532	+	0.862221i	$0.330927\pi$
$278$	−1.34502	+	3.24718i	−0.0806692	+	0.194753i
$279$	−20.2891	+	2.82843i	−1.21468	+	0.169334i
$280$	14.3692	−	0.623354i	0.858725	−	0.0372525i
$281$			5.94253i			0.354502i	0.984166	+	0.177251i	$0.0567204\pi$
$281$			5.94253i			0.354502i	−0.984166	+	0.177251i	$0.943280\pi$
$282$	1.18169	+	2.37340i	0.0703685	+	0.141334i
$283$			26.1188i			1.55260i	0.630363	+	0.776300i	$0.282906\pi$
$283$			26.1188i			1.55260i	−0.630363	+	0.776300i	$0.717094\pi$
$284$	−16.8080	−	16.8080i	−0.997373	−	0.997373i
$285$	−9.05247	−	16.3633i	−0.536222	−	0.969280i
$286$	17.6569	+	7.31371i	1.04407	+	0.432469i
$287$		−	5.59767i		−	0.330420i
$288$	−4.26737	+	16.4253i	−0.251457	+	0.967868i
$289$	−14.6569			−0.862168
$290$	3.71960	−	4.05696i	0.218423	−	0.238233i
$291$	−12.4853	+	14.3465i	−0.731900	+	0.841009i
$292$	6.43215	−	6.43215i	0.376413	−	0.376413i
$293$		−	16.3128i		−	0.953004i	−0.879173	−	0.476502i	$-0.841904\pi$
$293$		−	16.3128i		−	0.953004i	0.879173	−	0.476502i	$-0.158096\pi$
$294$	−4.00927	+	1.99616i	−0.233825	+	0.116419i
$295$	−3.21608	+	8.82843i	−0.187247	+	0.514011i
$296$	−20.2891	+	8.40401i	−1.17928	+	0.488473i
$297$	18.2919	+	11.9223i	1.06140	+	0.691804i
$298$	0.390175	−	0.941967i	0.0226023	−	0.0545667i
$299$			3.48106i			0.201315i
$300$	10.1964	−	14.0012i	0.588687	−	0.808361i
$301$			19.7990i			1.14119i
$302$	3.69552	+	1.53073i	0.212653	+	0.0880838i
$303$	−17.8027	−	15.4930i	−1.02274	−	0.890052i
$304$		−	19.3137i		−	1.10772i
$305$	6.49435	−	17.8276i	0.371866	−	1.02081i
$306$	6.28568	+	1.63305i	0.359328	+	0.0933553i
$307$			17.8027i			1.01605i	0.861341	+	0.508027i	$0.169625\pi$
$307$			17.8027i			1.01605i	−0.861341	+	0.508027i	$0.830375\pi$
$308$	13.5140	−	13.5140i	0.770030	−	0.770030i
$309$	−11.3753	−	9.89949i	−0.647117	−	0.563163i
$310$	15.9162	+	14.5927i	0.903982	+	0.828811i
$311$	9.84591			0.558310			0.279155	−	0.960246i	$-0.409946\pi$
$311$	9.84591			0.558310			0.279155	+	0.960246i	$0.409946\pi$
$312$	14.9385	+	5.00760i	0.845727	+	0.283500i
$313$			24.6250i			1.39189i	0.718096	+	0.695944i	$0.245014\pi$
$313$			24.6250i			1.39189i	−0.718096	+	0.695944i	$0.754986\pi$
$314$	−12.6060	+	30.4336i	−0.711399	+	1.71747i
$315$	3.19250	−	14.9174i	0.179877	−	0.840500i
$316$	0.686292	−	0.686292i	0.0386069	−	0.0386069i
$317$			9.81845i			0.551459i	0.961235	+	0.275730i	$0.0889194\pi$
$317$			9.81845i			0.551459i	−0.961235	+	0.275730i	$0.911081\pi$
$318$	−12.1036	−	24.3099i	−0.678736	−	1.36323i
$319$		−	7.31371i		−	0.409489i
$320$	16.2146	−	7.55550i	0.906426	−	0.422365i
$321$	7.41421	+	6.45232i	0.413821	+	0.360134i
$322$	3.21608	+	1.33214i	0.179225	+	0.0742374i
$323$	−7.39104			−0.411248
$324$	15.7237	+	8.76158i	0.873539	+	0.486755i
$325$	−12.3125	−	10.3431i	−0.682975	−	0.573734i
$326$	11.3753	+	4.71179i	0.630018	+	0.260962i
$327$	−18.7447	+	21.5391i	−1.03658	+	1.19111i
$328$	−2.66428	−	6.43215i	−0.147111	−	0.355156i
$329$		−	2.46148i		−	0.135706i
$330$	−2.58630	−	22.8696i	−0.142371	−	1.25893i
$331$	−1.51472			−0.0832565			−0.0416282	−	0.999133i	$-0.513255\pi$
$331$	−1.51472			−0.0832565			−0.0416282	+	0.999133i	$0.513255\pi$
$332$	−9.81845	−	9.81845i	−0.538858	−	0.538858i
$333$	3.21608	+	23.0698i	0.176240	+	1.26422i
$334$	−6.58579	−	2.72792i	−0.360358	−	0.149265i
$335$	1.74053	−	4.77791i	0.0950952	−	0.261045i
$336$	10.3431	−	11.8851i	0.564265	−	0.648384i
$337$		−	19.2965i		−	1.05114i	−0.850749	−	0.525572i	$-0.823851\pi$
$337$		−	19.2965i		−	1.05114i	0.850749	−	0.525572i	$-0.176149\pi$
$338$	−1.43788	+	3.47135i	−0.0782103	+	0.188816i
$339$	−0.828427	−	0.720950i	−0.0449940	−	0.0391566i
$340$	−2.89136	−	6.20507i	−0.156806	−	0.336517i
$341$	28.6931			1.55382
$342$	−19.8271	−	5.15117i	−1.07212	−	0.278543i
$343$	20.0768			1.08405
$344$	9.42359	+	22.7506i	0.508086	+	1.22663i
$345$	3.66818	−	2.02930i	0.197488	−	0.109254i
$346$	−0.343146	−	0.142136i	−0.0184476	−	0.00764126i
$347$	−15.2304			−0.817611			−0.408806	−	0.912621i	$-0.634055\pi$
$347$	−15.2304			−0.817611			−0.408806	+	0.912621i	$0.634055\pi$
$348$	−0.417241	−	6.01491i	−0.0223665	−	0.322433i
$349$		−	13.6569i		−	0.731035i	−0.930805	−	0.365517i	$-0.880892\pi$
$349$		−	13.6569i		−	0.731035i	0.930805	−	0.365517i	$-0.119108\pi$
$350$	−14.2676	+	7.41713i	−0.762636	+	0.396462i
$351$	9.12496	−	14.0000i	0.487054	−	0.747265i
$352$	9.09644	−	21.9607i	0.484842	−	1.17051i
$353$	26.3939			1.40481			0.702403	−	0.711780i	$-0.252111\pi$
$353$	26.3939			1.40481			0.702403	+	0.711780i	$0.252111\pi$
$354$	4.58749	+	9.21391i	0.243822	+	0.489714i
$355$	24.9706	+	9.09644i	1.32530	+	0.482789i
$356$	−11.8851	+	11.8851i	−0.629907	+	0.629907i
$357$	−4.54822	−	3.95815i	−0.240717	−	0.209488i
$358$	−10.0384	−	4.15804i	−0.530546	−	0.219759i
$359$	32.1741			1.69809			0.849043	−	0.528323i	$-0.177179\pi$
$359$	32.1741			1.69809			0.849043	+	0.528323i	$0.177179\pi$
$360$	−3.43171	−	18.6607i	−0.180867	−	0.983508i
$361$	4.31371			0.227037
$362$	−28.2960	−	11.7206i	−1.48721	−	0.616021i
$363$	−8.69760	−	7.56921i	−0.456506	−	0.397280i
$364$	−10.3431	−	10.3431i	−0.542128	−	0.542128i
$365$	−3.48106	+	9.55582i	−0.182207	+	0.500175i
$366$	−9.26370	−	18.6060i	−0.484221	−	0.972552i
$367$	−24.2349			−1.26505			−0.632524	−	0.774540i	$-0.717981\pi$
$367$	−24.2349			−1.26505			−0.632524	+	0.774540i	$0.717981\pi$
$368$	4.32957			0.225694
$369$	−7.31371	+	1.01958i	−0.380736	+	0.0530771i
$370$	16.5927	−	18.0976i	0.862615	−	0.940851i
$371$			25.2120i			1.30894i
$372$	23.5977	−	1.63692i	1.22348	−	0.0848702i
$373$	−10.4286			−0.539971			−0.269986	−	0.962864i	$-0.587019\pi$
$373$	−10.4286			−0.539971			−0.269986	+	0.962864i	$0.587019\pi$
$374$	−8.40401	−	3.48106i	−0.434561	−	0.180001i
$375$	−3.72149	+	19.0040i	−0.192177	+	0.981360i
$376$	−1.17157	−	2.82843i	−0.0604193	−	0.145865i
$377$	−5.59767			−0.288295
$378$	−9.44234	−	13.7879i	−0.485662	−	0.709175i
$379$	15.1716			0.779311			0.389656	−	0.920961i	$-0.372594\pi$
$379$	15.1716			0.779311			0.389656	+	0.920961i	$0.372594\pi$
$380$	9.12029	+	19.5728i	0.467861	+	1.00406i
$381$	2.97127	+	2.58579i	0.152223	+	0.132474i
$382$	−4.54822	+	10.9804i	−0.232707	+	0.561805i
$383$			18.5545i			0.948091i	0.880500	+	0.474046i	$0.157207\pi$
$383$			18.5545i			0.948091i	−0.880500	+	0.474046i	$0.842793\pi$
$384$	6.22821	−	18.5798i	0.317832	−	0.948147i
$385$	−7.31371	+	20.0768i	−0.372741	+	1.02321i
$386$	−17.8276	−	7.38443i	−0.907401	−	0.375858i
$387$	25.8686	−	3.60625i	1.31498	−	0.183316i
$388$	15.5286	−	15.5286i	0.788345	−	0.788345i
$389$	−12.6060			−0.639150			−0.319575	−	0.947561i	$-0.603540\pi$
$389$	−12.6060			−0.639150			−0.319575	+	0.947561i	$0.603540\pi$
$390$	−17.5036	+	1.97947i	−0.886329	+	0.100234i
$391$		−	1.65685i		−	0.0837907i
$392$	4.77791	−	1.97908i	0.241321	−	0.0999584i
$393$	−12.6942	+	14.5866i	−0.640338	+	0.735798i
$394$	−10.4853	−	4.34315i	−0.528241	−	0.218805i
$395$	−0.371418	+	1.01958i	−0.0186881	+	0.0513005i
$396$	−20.1183	−	15.1954i	−1.01098	−	0.763596i
$397$	0.551791			0.0276936			0.0138468	−	0.999904i	$-0.495592\pi$
$397$	0.551791			0.0276936			0.0138468	+	0.999904i	$0.495592\pi$
$398$	19.3743	+	8.02509i	0.971145	+	0.402261i
$399$	14.3465	+	12.4853i	0.718226	+	0.625046i
$400$	−12.8643	+	15.3137i	−0.643215	+	0.765685i
$401$		−	25.2120i		−	1.25903i	−0.776989	−	0.629514i	$-0.783254\pi$
$401$		−	25.2120i		−	1.25903i	0.776989	−	0.629514i	$-0.216746\pi$
$402$	−2.48273	−	4.98653i	−0.123827	−	0.248706i
$403$		−	21.9607i		−	1.09394i
$404$	19.2695	+	19.2695i	0.958694	+	0.958694i
$405$	−20.0720	−	1.45410i	−0.997386	−	0.0722546i
$406$	−2.14214	+	5.17157i	−0.106312	+	0.256661i
$407$		−	32.6256i		−	1.61719i
$408$	−7.11019	−	2.38343i	−0.352007	−	0.117998i
$409$	−7.17157			−0.354611			−0.177306	−	0.984156i	$-0.556738\pi$
$409$	−7.17157			−0.354611			−0.177306	+	0.984156i	$0.556738\pi$
$410$	5.73741	+	5.26031i	0.283350	+	0.259788i
$411$	10.4853	+	9.12496i	0.517201	+	0.450101i
$412$	12.3125	+	12.3125i	0.606594	+	0.606594i
$413$		−	9.55582i		−	0.470211i
$414$	1.15474	−	4.44465i	0.0567524	−	0.218442i
$415$	14.5866	+	5.31371i	0.716029	+	0.260840i
$416$	−16.8080	−	6.96211i	−0.824081	−	0.341346i
$417$	−3.24718	−	2.82590i	−0.159015	−	0.138385i
$418$	26.5090	+	10.9804i	1.29660	+	0.537067i
$419$		−	4.20201i		−	0.205281i	−0.994718	−	0.102641i	$-0.967271\pi$
$419$		−	4.20201i		−	0.205281i	0.994718	−	0.102641i	$-0.0327292\pi$
$420$	−4.86955	+	16.9287i	−0.237610	+	0.826037i
$421$			29.1716i			1.42174i	0.703326	+	0.710868i	$0.251698\pi$
$421$			29.1716i			1.42174i	−0.703326	+	0.710868i	$0.748302\pi$
$422$	0.819760	−	1.97908i	0.0399053	−	0.0963399i
$423$	−3.21608	+	0.448342i	−0.156371	+	0.0217991i
$424$	12.0000	+	28.9706i	0.582772	+	1.40693i
$425$	5.86030	+	4.92296i	0.284266	+	0.238798i
$426$	26.0609	−	12.9754i	1.26265	−	0.628659i
$427$			19.2965i			0.933821i
$428$	−8.02509	−	8.02509i	−0.387907	−	0.387907i
$429$	−15.3661	+	17.6569i	−0.741883	+	0.852481i
$430$	−20.2932	−	18.6058i	−0.978627	−	0.897249i
$431$	−21.7310			−1.04674			−0.523372	−	0.852104i	$-0.675326\pi$
$431$	−21.7310			−1.04674			−0.523372	+	0.852104i	$0.675326\pi$
$432$	−17.4125	−	11.3492i	−0.837760	−	0.546038i
$433$		−	29.1732i		−	1.40198i	−0.713173	−	0.700988i	$-0.752742\pi$
$433$		−	29.1732i		−	1.40198i	0.713173	−	0.700988i	$-0.247258\pi$
$434$	−20.2891	−	8.40401i	−0.973907	−	0.403405i
$435$	3.26319	+	5.89857i	0.156458	+	0.282815i
$436$	23.3137	−	23.3137i	1.11652	−	1.11652i
$437$			5.22625i			0.250006i
$438$	4.96546	+	9.97306i	0.237259	+	0.476531i
$439$		−	11.5147i		−	0.549568i	−0.961506	−	0.274784i	$-0.911394\pi$
$439$		−	11.5147i		−	0.549568i	0.961506	−	0.274784i	$-0.0886063\pi$
$440$	1.15181	+	26.5508i	0.0549103	+	1.26576i
$441$	−0.757359	−	5.43275i	−0.0360647	−	0.258702i
$442$	−2.66428	+	6.43215i	−0.126727	+	0.305946i
$443$	40.4650			1.92255			0.961275	−	0.275591i	$-0.0888737\pi$
$443$	40.4650			1.92255			0.961275	+	0.275591i	$0.0888737\pi$
$444$	−1.86126	−	26.8318i	−0.0883317	−	1.27338i
$445$	6.43215	−	17.6569i	0.304913	−	0.837015i
$446$	5.73137	−	13.8368i	0.271388	−	0.655189i
$447$	0.941967	+	0.819760i	0.0445535	+	0.0387733i
$448$	−12.8643	+	12.8643i	−0.607781	+	0.607781i
$449$		−	24.7897i		−	1.16990i	−0.811070	−	0.584949i	$-0.801114\pi$
$449$		−	24.7897i		−	1.16990i	0.811070	−	0.584949i	$-0.198886\pi$
$450$	12.2897	+	17.2906i	0.579342	+	0.815085i
$451$	10.3431			0.487040
$452$	0.896683	+	0.896683i	0.0421764	+	0.0421764i
$453$	−3.21608	+	3.69552i	−0.151104	+	0.173631i
$454$	−2.58579	+	6.24264i	−0.121357	+	0.292982i
$455$	15.3661	+	5.59767i	0.720375	+	0.262423i
$456$	22.4278	+	7.51812i	1.05028	+	0.352068i
$457$			12.8643i			0.601767i	0.953661	+	0.300883i	$0.0972815\pi$
$457$			12.8643i			0.601767i	−0.953661	+	0.300883i	$0.902719\pi$
$458$	4.32957	+	1.79337i	0.202307	+	0.0837985i
$459$	−4.34315	+	6.66348i	−0.202721	+	0.311025i
$460$	−4.38765	+	2.04450i	−0.204575	+	0.0953255i
$461$	18.5486			0.863892			0.431946	−	0.901899i	$-0.357827\pi$
$461$	18.5486			0.863892			0.431946	+	0.901899i	$0.357827\pi$
$462$	10.4324	+	20.9534i	0.485361	+	0.974842i
$463$	4.93839			0.229507			0.114753	−	0.993394i	$-0.463392\pi$
$463$	4.93839			0.229507			0.114753	+	0.993394i	$0.463392\pi$
$464$			6.96211i			0.323208i
$465$	−23.1412	+	12.8021i	−1.07315	+	0.593685i
$466$	−15.1716	+	36.6274i	−0.702810	+	1.69673i
$467$	−8.73606			−0.404257			−0.202128	−	0.979359i	$-0.564786\pi$
$467$	−8.73606			−0.404257			−0.202128	+	0.979359i	$0.564786\pi$
$468$	−11.6300	+	15.3979i	−0.537599	+	0.711768i
$469$			5.17157i			0.238801i
$470$	2.52293	+	2.31313i	0.116374	+	0.106697i
$471$	−30.4336	−	26.4853i	−1.40231	−	1.22038i
$472$	−4.54822	−	10.9804i	−0.209349	−	0.505413i
$473$	−36.5838			−1.68212
$474$	0.529800	+	1.06410i	0.0243345	+	0.0488755i
$475$	−18.4853	−	15.5286i	−0.848163	−	0.712501i
$476$	4.92296	+	4.92296i	0.225643	+	0.225643i
$477$	32.9411	−	4.59220i	1.50827	−	0.210262i
$478$	−7.21250	+	17.4125i	−0.329892	+	0.796430i
$479$	−15.3661			−0.702096			−0.351048	−	0.936357i	$-0.614175\pi$
$479$	−15.3661			−0.702096			−0.351048	+	0.936357i	$0.614175\pi$
$480$	2.46197	+	21.7701i	0.112373	+	0.993666i
$481$	−24.9706			−1.13856
$482$	5.67459	−	13.6997i	0.258471	−	0.624003i
$483$	−2.79884	+	3.21608i	−0.127351	+	0.146337i
$484$	9.41421	+	9.41421i	0.427919	+	0.427919i
$485$	−8.40401	+	23.0698i	−0.381607	+	1.04755i
$486$	−16.2949	+	14.8484i	−0.739154	+	0.673537i
$487$	−19.6866			−0.892086			−0.446043	−	0.895011i	$-0.647167\pi$
$487$	−19.6866			−0.892086			−0.446043	+	0.895011i	$0.647167\pi$
$488$	9.18440	+	22.1731i	0.415758	+	1.00373i
$489$	−9.89949	+	11.3753i	−0.447671	+	0.514408i
$490$	−3.90745	+	4.26184i	−0.176521	+	0.192530i
$491$			14.0479i			0.633974i	0.948430	+	0.316987i	$0.102671\pi$
$491$			14.0479i			0.633974i	−0.948430	+	0.316987i	$0.897329\pi$
$492$	8.50637	−	0.590068i	0.383497	−	0.0266023i
$493$	2.66428			0.119993
$494$	8.40401	−	20.2891i	0.378114	−	0.912849i
$495$	27.5638	+	5.89897i	1.23890	+	0.265139i
$496$	−27.3137			−1.22642
$497$	−27.0279			−1.21237
$498$	15.2235	−	7.57960i	0.682183	−	0.339650i
$499$	25.1127			1.12420			0.562099	−	0.827070i	$-0.309994\pi$
$499$	25.1127			1.12420			0.562099	+	0.827070i	$0.309994\pi$
$500$	5.80546	−	21.5939i	0.259628	−	0.965709i
$501$	5.73137	−	6.58579i	0.256059	−	0.294231i
$502$	−36.5474	−	15.1384i	−1.63119	−	0.675660i
$503$		−	28.4818i		−	1.26994i	−0.772537	−	0.634969i	$-0.781013\pi$
$503$		−	28.4818i		−	1.26994i	0.772537	−	0.634969i	$-0.218987\pi$
$504$	9.77519	+	16.6373i	0.435421	+	0.741083i
$505$	−28.6274	−	10.4286i	−1.27390	−	0.464066i
$506$	−2.46148	+	5.94253i	−0.109426	+	0.264178i
$507$	−3.47135	−	3.02099i	−0.154168	−	0.134167i
$508$	−3.21608	−	3.21608i	−0.142690	−	0.142690i
$509$	−13.6256			−0.603944			−0.301972	−	0.953317i	$-0.597645\pi$
$509$	−13.6256			−0.603944			−0.301972	+	0.953317i	$0.597645\pi$
$510$	8.33107	−	0.942155i	0.368906	−	0.0417193i
$511$		−	10.3431i		−	0.457554i
$512$	−8.65914	+	20.9050i	−0.382683	+	0.923880i
$513$	13.6997	−	21.0188i	0.604856	−	0.928002i
$514$	−1.31371	+	3.17157i	−0.0579452	+	0.139892i
$515$	−18.2919	−	6.66348i	−0.806037	−	0.293628i
$516$	−30.0871	+	2.08707i	−1.32451	+	0.0918783i
$517$	4.54822			0.200030
$518$	−9.55582	+	23.0698i	−0.419859	+	1.01363i
$519$	0.298627	−	0.343146i	0.0131083	−	0.0150624i
$520$	20.3211	−	0.881556i	0.891141	−	0.0386588i
$521$		−	9.84591i		−	0.431357i	−0.976464	−	0.215679i	$-0.930804\pi$
$521$		−	9.84591i		−	0.431357i	0.976464	−	0.215679i	$-0.0691964\pi$
$522$	7.14716	+	1.85687i	0.312823	+	0.0812729i
$523$		−	4.15804i		−	0.181819i	−0.995859	−	0.0909093i	$-0.971023\pi$
$523$		−	4.15804i		−	0.181819i	0.995859	−	0.0909093i	$-0.0289773\pi$
$524$	15.7884	−	15.7884i	0.689721	−	0.689721i
$525$	−3.05919	−	19.4553i	−0.133514	−	0.849100i
$526$	36.0416	+	14.9289i	1.57149	+	0.650932i
$527$			10.4525i			0.455318i
$528$	21.9607	+	19.1116i	0.955719	+	0.831727i
$529$	21.8284			0.949062
$530$	−25.8414	−	23.6926i	−1.12248	−	1.02914i
$531$	−12.4853	+	1.74053i	−0.541815	+	0.0755325i
$532$	−15.5286	−	15.5286i	−0.673250	−	0.673250i
$533$		−	7.91630i		−	0.342893i
$534$	−9.17497	−	18.4278i	−0.397040	−	0.797450i
$535$	11.9223	+	4.34315i	0.515448	+	0.187771i
$536$	2.46148	+	5.94253i	0.106320	+	0.256678i
$537$	8.73606	−	10.0384i	0.376989	−	0.433189i
$538$	4.15804	−	10.0384i	0.179266	−	0.432786i
$539$			7.68306i			0.330933i
$540$	23.0054	+	3.27891i	0.989995	+	0.141102i
$541$			16.0000i			0.687894i	0.938989	+	0.343947i	$0.111764\pi$
$541$			16.0000i			0.687894i	−0.938989	+	0.343947i	$0.888236\pi$
$542$	−18.4776	−	7.65367i	−0.793680	−	0.328753i
$543$	24.6250	−	28.2960i	1.05676	−	1.21430i
$544$	8.00000	+	3.31371i	0.342997	+	0.142074i
$545$	−12.6173	+	34.6356i	−0.540465	+	1.48363i
$546$	16.0371	−	7.98465i	0.686323	−	0.341711i
$547$		−	33.3313i		−	1.42514i	−0.701600	−	0.712571i	$-0.747530\pi$
$547$		−	33.3313i		−	1.42514i	0.701600	−	0.712571i	$-0.252470\pi$
$548$	−11.3492	−	11.3492i	−0.484813	−	0.484813i
$549$	25.2120	−	3.51472i	1.07602	−	0.150005i
$550$	−13.7051	−	26.3631i	−0.584386	−	1.12413i
$551$	−8.40401			−0.358023
$552$	−1.68534	+	5.02766i	−0.0717329	+	0.213991i
$553$		−	1.10358i		−	0.0469291i
$554$	9.12496	−	22.0296i	0.387682	−	0.935948i
$555$	14.5567	+	26.3128i	0.617898	+	1.11692i
$556$	3.51472	+	3.51472i	0.149057	+	0.149057i
$557$		−	19.3743i		−	0.820914i	−0.911880	−	0.410457i	$-0.865369\pi$
$557$		−	19.3743i		−	0.820914i	0.911880	−	0.410457i	$-0.134631\pi$
$558$	−7.28485	+	28.0397i	−0.308392	+	1.18701i
$559$			28.0000i			1.18427i
$560$	6.96211	−	19.1116i	0.294203	−	0.807614i
$561$	7.31371	−	8.40401i	0.308785	−	0.354818i
$562$	7.76429	+	3.21608i	0.327517	+	0.135662i
$563$	6.04601			0.254809			0.127405	−	0.991851i	$-0.459335\pi$
$563$	6.04601			0.254809			0.127405	+	0.991851i	$0.459335\pi$
$564$	3.74053	−	0.259472i	0.157505	−	0.0109257i
$565$	−1.33214	−	0.485281i	−0.0560437	−	0.0204159i
$566$	34.1258	+	14.1354i	1.43442	+	0.594155i
$567$	19.6866	−	5.59767i	0.826761	−	0.235080i
$568$	−31.0572	+	12.8643i	−1.30313	+	0.539774i
$569$		−	9.42359i		−	0.395057i	−0.980297	−	0.197529i	$-0.936708\pi$
$569$		−	9.42359i		−	0.395057i	0.980297	−	0.197529i	$-0.0632916\pi$
$570$	−26.2789	+	2.97186i	−1.10070	+	0.124478i
$571$	−41.1127			−1.72051			−0.860256	−	0.509862i	$-0.829697\pi$
$571$	−41.1127			−1.72051			−0.860256	+	0.509862i	$0.829697\pi$
$572$	19.1116	−	19.1116i	0.799098	−	0.799098i
$573$	−10.9804	−	9.55582i	−0.458712	−	0.399200i
$574$	−7.31371	−	3.02944i	−0.305268	−	0.126446i
$575$	3.48106	−	4.14386i	0.145170	−	0.172811i
$576$	19.1512	+	14.4649i	0.797965	+	0.602703i
$577$			15.5286i			0.646464i	0.946320	+	0.323232i	$0.104769\pi$
$577$			15.5286i			0.646464i	−0.946320	+	0.323232i	$0.895231\pi$
$578$	−7.93223	+	19.1501i	−0.329937	+	0.796539i
$579$	15.5147	−	17.8276i	0.644770	−	0.740890i
$580$	−3.28764	−	7.05551i	−0.136512	−	0.292964i
$581$	−15.7884			−0.655015
$582$	11.9877	+	24.0771i	0.496905	+	0.998028i
$583$	−46.5858			−1.92939
$584$	−4.92296	−	11.8851i	−0.203713	−	0.491808i
$585$	4.51487	−	21.0964i	0.186667	−	0.872228i
$586$	−21.3137	−	8.82843i	−0.880461	−	0.364699i
$587$	−12.1689			−0.502266			−0.251133	−	0.967953i	$-0.580803\pi$
$587$	−12.1689			−0.502266			−0.251133	+	0.967953i	$0.580803\pi$
$588$	0.438312	+	6.31867i	0.0180757	+	0.260578i
$589$		−	32.9706i		−	1.35853i
$590$	9.79437	+	8.97992i	0.403228	+	0.369697i
$591$	9.12496	−	10.4853i	0.375351	−	0.431307i
$592$			31.0572i			1.27644i
$593$	39.3826			1.61725			0.808625	−	0.588325i	$-0.200212\pi$
$593$	39.3826			1.61725			0.808625	+	0.588325i	$0.200212\pi$
$594$	25.4768	−	17.4472i	1.04532	−	0.715866i
$595$	−7.31371	−	2.66428i	−0.299833	−	0.109225i
$596$	−1.01958	−	1.01958i	−0.0417635	−	0.0417635i
$597$	−16.8607	+	19.3743i	−0.690064	+	0.792936i
$598$	4.54822	+	1.88393i	0.185990	+	0.0770398i
$599$	30.1350			1.23128			0.615641	−	0.788027i	$-0.288897\pi$
$599$	30.1350			1.23128			0.615641	+	0.788027i	$0.288897\pi$
$600$	−12.7753	−	20.8996i	−0.521548	−	0.853222i
$601$	30.4853			1.24352			0.621760	−	0.783208i	$-0.286418\pi$
$601$	30.4853			1.24352			0.621760	+	0.783208i	$0.286418\pi$
$602$	25.8686	+	10.7151i	1.05433	+	0.436716i
$603$	6.75699	−	0.941967i	0.275166	−	0.0383599i
$604$	4.00000	−	4.00000i	0.162758	−	0.162758i
$605$	−13.9861	−	5.09494i	−0.568615	−	0.207139i
$606$	−29.8774	+	14.8756i	−1.21369	+	0.604279i
$607$	35.2152			1.42934			0.714671	−	0.699461i	$-0.246576\pi$
$607$	35.2152			1.42934			0.714671	+	0.699461i	$0.246576\pi$
$608$	−25.2346	−	10.4525i	−1.02340	−	0.423905i
$609$	−5.17157	−	4.50063i	−0.209563	−	0.182375i
$610$	−19.7782	−	18.1335i	−0.800795	−	0.734204i
$611$		−	3.48106i		−	0.140828i
$612$	5.53547	−	7.32884i	0.223758	−	0.296251i
$613$	−16.0804			−0.649480			−0.324740	−	0.945803i	$-0.605277\pi$
$613$	−16.0804			−0.649480			−0.324740	+	0.945803i	$0.605277\pi$
$614$	23.2603	+	9.63475i	0.938711	+	0.388827i
$615$	−8.34184	+	4.61485i	−0.336375	+	0.186089i
$616$	−10.3431	−	24.9706i	−0.416737	−	1.00609i
$617$	31.0949			1.25183			0.625916	−	0.779890i	$-0.284725\pi$
$617$	31.0949			1.25183			0.625916	+	0.779890i	$0.284725\pi$
$618$	−19.0906	+	9.50495i	−0.767935	+	0.382345i
$619$	14.4853			0.582213			0.291106	−	0.956691i	$-0.405977\pi$
$619$	14.4853			0.582213			0.291106	+	0.956691i	$0.405977\pi$
$620$	27.6801	−	12.8980i	1.11166	−	0.517998i
$621$	4.71179	+	3.07107i	0.189078	+	0.123238i
$622$	5.32857	−	12.8643i	0.213656	−	0.515812i
$623$			19.1116i			0.765692i
$624$	14.6274	−	16.8080i	0.585565	−	0.672859i
$625$	4.31371	+	24.6250i	0.172548	+	0.985001i
$626$	32.1741	+	13.3270i	1.28594	+	0.532653i
$627$	−23.0698	+	26.5090i	−0.921319	+	1.05867i
$628$	32.9411	+	32.9411i	1.31449	+	1.31449i
$629$	11.8851			0.473889
$630$	−17.7628	−	12.2444i	−0.707685	−	0.487830i
$631$		−	26.1421i		−	1.04070i	−0.853952	−	0.520351i	$-0.825801\pi$
$631$		−	26.1421i		−	1.04070i	0.853952	−	0.520351i	$-0.174199\pi$
$632$	−0.525265	−	1.26810i	−0.0208939	−	0.0504424i
$633$	1.97908	+	1.72232i	0.0786612	+	0.0684560i
$634$	12.8284	+	5.31371i	0.509482	+	0.211034i
$635$	4.77791	+	1.74053i	0.189606	+	0.0690707i
$636$	−38.3129	+	2.65768i	−1.51920	+	0.105384i
$637$	5.88036			0.232988
$638$	−9.55582	−	3.95815i	−0.378319	−	0.156705i
$639$	4.92296	+	35.3137i	0.194749	+	1.39699i
$640$	−1.09644	−	25.2745i	−0.0433405	−	0.999060i
$641$			24.7897i			0.979135i	0.871965	+	0.489567i	$0.162845\pi$
$641$			24.7897i			0.979135i	−0.871965	+	0.489567i	$0.837155\pi$
$642$	12.4429	−	6.19516i	0.491082	−	0.244504i
$643$		−	1.49376i		−	0.0589081i	−0.999566	−	0.0294540i	$-0.990623\pi$
$643$		−	1.49376i		−	0.0589081i	0.999566	−	0.0294540i	$-0.00937687\pi$
$644$	3.48106	−	3.48106i	0.137173	−	0.137173i
$645$	29.5051	−	16.3227i	1.16176	−	0.642708i
$646$	−4.00000	+	9.65685i	−0.157378	+	0.379944i
$647$			42.3671i			1.66562i	0.553556	+	0.832812i	$0.313271\pi$
$647$			42.3671i			1.66562i	−0.553556	+	0.832812i	$0.686729\pi$
$648$	19.9572	−	15.8023i	0.783992	−	0.620772i
$649$	17.6569			0.693092
$650$	−20.1775	+	10.4894i	−0.791425	+	0.411428i
$651$	17.6569	−	20.2891i	0.692027	−	0.795192i
$652$	12.3125	−	12.3125i	0.482195	−	0.482195i
$653$		−	37.5892i		−	1.47098i	−0.677535	−	0.735490i	$-0.736952\pi$
$653$		−	37.5892i		−	1.47098i	0.677535	−	0.735490i	$-0.263048\pi$
$654$	17.9976	+	36.1479i	0.703762	+	1.41350i
$655$	−8.54465	+	23.4558i	−0.333867	+	0.916496i
$656$	−9.84591			−0.384418
$657$	−13.5140	+	1.88393i	−0.527230	+	0.0734993i
$658$	−3.21608	−	1.33214i	−0.125376	−	0.0519323i
$659$		−	0.720950i		−	0.0280842i	−0.999901	−	0.0140421i	$-0.995530\pi$
$659$		−	0.720950i		−	0.0280842i	0.999901	−	0.0140421i	$-0.00446989\pi$
$660$	−31.2802	−	8.99775i	−1.21758	−	0.350237i
$661$			28.7696i			1.11901i	0.828828	+	0.559503i	$0.189008\pi$
$661$			28.7696i			1.11901i	−0.828828	+	0.559503i	$0.810992\pi$
$662$	−0.819760	+	1.97908i	−0.0318609	+	0.0769189i
$663$	−6.43215	−	5.59767i	−0.249804	−	0.217395i
$664$	−18.1421	+	7.51472i	−0.704051	+	0.291628i
$665$	23.0698	+	8.40401i	0.894608	+	0.325894i
$666$	31.8827	+	8.28328i	1.23543	+	0.320970i
$667$		−	1.88393i		−	0.0729462i
$668$	−7.12840	+	7.12840i	−0.275806	+	0.275806i
$669$	13.8368	+	12.0416i	0.534960	+	0.465556i
$670$	−5.30067	−	4.85990i	−0.204783	−	0.187754i
$671$	−35.6552			−1.37645
$672$	−9.93092	−	19.9461i	−0.383094	−	0.769438i
$673$			5.65180i			0.217861i	0.994049	+	0.108930i	$0.0347426\pi$
$673$			5.65180i			0.217861i	−0.994049	+	0.108930i	$0.965257\pi$
$674$	−25.2120	−	10.4432i	−0.971131	−	0.402256i
$675$	−24.8624	+	7.54068i	−0.956954	+	0.290241i
$676$	3.75736	+	3.75736i	0.144514	+	0.144514i
$677$			39.3826i			1.51360i	0.653649	+	0.756798i	$0.273237\pi$
$677$			39.3826i			1.51360i	−0.653649	+	0.756798i	$0.726763\pi$
$678$	−1.39031	+	0.692217i	−0.0533945	+	0.0265844i
$679$		−	24.9706i		−	0.958282i
$680$	−9.67211	+	0.419588i	−0.370909	+	0.0160905i
$681$	−6.24264	−	5.43275i	−0.239219	−	0.208183i
$682$	15.5286	−	37.4893i	0.594620	−	1.43554i
$683$	−21.3533			−0.817063			−0.408532	−	0.912744i	$-0.633959\pi$
$683$	−21.3533			−0.817063			−0.408532	+	0.912744i	$0.633959\pi$
$684$	−17.4607	+	23.1175i	−0.667625	+	0.883920i
$685$	16.8607	+	6.14214i	0.644215	+	0.234679i
$686$	10.8655	−	26.2316i	0.414846	−	1.00153i
$687$	−3.76787	+	4.32957i	−0.143753	+	0.165183i
$688$	34.8250			1.32769
$689$			35.6552i			1.35836i
$690$	−0.666204	−	5.89096i	−0.0253620	−	0.224265i
$691$	−12.8284			−0.488016			−0.244008	−	0.969773i	$-0.578462\pi$
$691$	−12.8284			−0.488016			−0.244008	+	0.969773i	$0.578462\pi$
$692$	−0.371418	+	0.371418i	−0.0141192	+	0.0141192i
$693$	−28.3929	+	3.95815i	−1.07856	+	0.150358i
$694$	−8.24264	+	19.8995i	−0.312886	+	0.755374i
$695$	−5.22158	−	1.90215i	−0.198066	−	0.0721527i
$696$	−8.08467	−	2.71009i	−0.306449	−	0.102726i
$697$			3.76787i			0.142718i
$698$	−17.8435	−	7.39104i	−0.675388	−	0.279755i
$699$	−36.6274	−	31.8755i	−1.38538	−	1.20564i
$700$	1.96937	+	22.6557i	0.0744351	+	0.856303i
$701$	−2.76011			−0.104248			−0.0521239	−	0.998641i	$-0.516599\pi$
$701$	−2.76011			−0.104248			−0.0521239	+	0.998641i	$0.516599\pi$
$702$	−13.3535	−	19.4991i	−0.503995	−	0.735945i
$703$	−37.4893			−1.41394
$704$	−23.7701	−	23.7701i	−0.895871	−	0.895871i
$705$	−3.66818	+	2.02930i	−0.138152	+	0.0764279i
$706$	14.2843	−	34.4853i	0.537596	−	1.29787i
$707$	30.9861			1.16535
$708$	14.5213	−	1.00731i	0.545743	−	0.0378570i
$709$		−	20.2843i		−	0.761792i	−0.924618	−	0.380896i	$-0.875616\pi$
$709$		−	20.2843i		−	0.761792i	0.924618	−	0.380896i	$-0.124384\pi$
$710$	25.3990	−	27.7027i	0.953209	−	1.03966i
$711$	−1.44190	+	0.201010i	−0.0540755	+	0.00753847i
$712$	9.09644	+	21.9607i	0.340903	+	0.823014i
$713$	7.39104			0.276796
$714$	−7.63305	+	3.80040i	−0.285660	+	0.142226i
$715$	−10.3431	+	28.3929i	−0.386812	+	1.06183i
$716$	−10.8655	+	10.8655i	−0.406062	+	0.406062i
$717$	−17.4125	−	15.1535i	−0.650283	−	0.565917i
$718$	17.4125	−	42.0375i	0.649830	−	1.56883i
$719$	−28.6931			−1.07007			−0.535036	−	0.844829i	$-0.679702\pi$
$719$	−28.6931			−1.07007			−0.535036	+	0.844829i	$0.679702\pi$
$720$	−26.2387	−	5.61538i	−0.977857	−	0.209273i
$721$	19.7990			0.737353
$722$	2.33456	−	5.63613i	0.0868834	−	0.209755i
$723$	13.6997	+	11.9223i	0.509497	+	0.443397i
$724$	−30.6274	+	30.6274i	−1.13826	+	1.13826i
$725$	6.66348	+	5.59767i	0.247476	+	0.207892i
$726$	−14.5968	+	7.26754i	−0.541736	+	0.269724i
$727$	18.9063			0.701195			0.350598	−	0.936526i	$-0.385978\pi$
$727$	18.9063			0.701195			0.350598	+	0.936526i	$0.385978\pi$
$728$	−19.1116	+	7.91630i	−0.708325	+	0.293398i
$729$	−10.8995	−	24.7022i	−0.403685	−	0.914898i
$730$	10.6013	+	9.71979i	0.392373	+	0.359746i
$731$		−	13.3270i		−	0.492916i
$732$	−29.3234	+	2.03410i	−1.08382	+	0.0751825i
$733$	38.8215			1.43390			0.716952	−	0.697123i	$-0.245537\pi$
$733$	38.8215			1.43390			0.716952	+	0.697123i	$0.245537\pi$
$734$	−13.1158	+	31.6644i	−0.484113	+	1.16875i
$735$	−3.42799	−	6.19646i	−0.126443	−	0.228560i
$736$	2.34315	−	5.65685i	0.0863695	−	0.208514i
$737$	−9.55582			−0.351993
$738$	−2.62601	+	10.1076i	−0.0966647	+	0.372066i
$739$	−32.8284			−1.20761			−0.603807	−	0.797131i	$-0.706350\pi$
$739$	−32.8284			−1.20761			−0.603807	+	0.797131i	$0.706350\pi$
$740$	−14.6658	−	31.4738i	−0.539125	−	1.15700i
$741$	20.2891	+	17.6569i	0.745338	+	0.648641i
$742$	32.9411	+	13.6447i	1.20931	+	0.500911i
$743$			0.185709i			0.00681301i	0.999994	+	0.00340650i	$0.00108433\pi$
$743$			0.185709i			0.00681301i	−0.999994	+	0.00340650i	$0.998916\pi$
$744$	10.6322	−	31.7177i	0.389796	−	1.16283i
$745$	1.51472	+	0.551791i	0.0554950	+	0.0202161i
$746$	−5.64391	+	13.6256i	−0.206638	+	0.498868i
$747$	2.87576	+	20.6286i	0.105218	+	0.754761i
$748$	−9.09644	+	9.09644i	−0.332599	+	0.332599i
$749$	−12.9046			−0.471525
$750$	22.8158	+	15.1472i	0.833116	+	0.553099i
$751$			27.1127i			0.989356i	0.869076	+	0.494678i	$0.164714\pi$
$751$			27.1127i			0.989356i	−0.869076	+	0.494678i	$0.835286\pi$
$752$	−4.32957			−0.157883
$753$	31.8059	−	36.5474i	1.15907	−	1.33186i
$754$	−3.02944	+	7.31371i	−0.110326	+	0.266350i
$755$	−2.16478	+	5.94253i	−0.0787846	+	0.216271i
$756$	−23.1250	+	4.87504i	−0.841047	+	0.177303i
$757$	−36.1572			−1.31416			−0.657078	−	0.753823i	$-0.728208\pi$
$757$	−36.1572			−1.31416			−0.657078	+	0.753823i	$0.728208\pi$
$758$	8.21080	−	19.8226i	0.298230	−	0.719990i
$759$	−5.94253	−	5.17157i	−0.215700	−	0.187716i
$760$	30.5090	−	1.32352i	1.10668	−	0.0480090i
$761$			4.92296i			0.178457i	0.996011	+	0.0892285i	$0.0284401\pi$
$761$			4.92296i			0.178457i	−0.996011	+	0.0892285i	$0.971560\pi$
$762$	4.98653	−	2.48273i	0.180643	−	0.0899398i
$763$		−	37.4893i		−	1.35720i
$764$	11.8851	+	11.8851i	0.429987	+	0.429987i
$765$	−2.14891	+	10.0411i	−0.0776941	+	0.363037i
$766$	24.2426	+	10.0416i	0.875922	+	0.362819i
$767$		−	13.5140i		−	0.487961i
$768$	−20.9050	−	18.1929i	−0.754344	−	0.656479i
$769$	29.5980			1.06733			0.533665	−	0.845696i	$-0.320814\pi$
$769$	29.5980			1.06733			0.533665	+	0.845696i	$0.320814\pi$
$770$	22.2735	+	20.4213i	0.802680	+	0.735933i
$771$	−3.17157	−	2.76011i	−0.114221	−	0.0994028i
$772$	−19.2965	+	19.2965i	−0.694495	+	0.694495i
$773$			38.1145i			1.37088i	0.728128	+	0.685442i	$0.240391\pi$
$773$			38.1145i			1.37088i	−0.728128	+	0.685442i	$0.759609\pi$
$774$	9.28821	−	35.7507i	0.333858	−	1.28503i
$775$	−21.9607	+	26.1421i	−0.788853	+	0.939053i
$776$	−11.8851	−	28.6931i	−0.426649	−	1.03002i
$777$	−23.0698	−	20.0768i	−0.827624	−	0.720251i
$778$	−6.82233	+	16.4706i	−0.244592	+	0.590498i
$779$		−	11.8851i		−	0.425827i
$780$	−6.88658	+	23.9408i	−0.246579	+	0.857220i
$781$		−	49.9411i		−	1.78703i
$782$	−2.16478	−	0.896683i	−0.0774125	−	0.0320653i
$783$	−4.93839	+	7.57675i	−0.176484	+	0.270771i
$784$		−	7.31371i		−	0.261204i
$785$	−48.9384	−	17.8276i	−1.74669	−	0.636294i
$786$	12.1883	+	24.4800i	0.434742	+	0.873173i
$787$			7.60268i			0.271006i	0.990777	+	0.135503i	$0.0432651\pi$
$787$			7.60268i			0.271006i	−0.990777	+	0.135503i	$0.956735\pi$
$788$	−11.3492	+	11.3492i	−0.404298	+	0.404298i
$789$	−31.3657	+	36.0416i	−1.11665	+	1.28312i
$790$	1.13113	+	1.03707i	0.0402439	+	0.0368974i
$791$	1.44190			0.0512681
$792$	−30.7417	+	18.0622i	−1.09236	+	0.641812i
$793$			27.2893i			0.969072i
$794$	0.298627	−	0.720950i	0.0105979	−	0.0255856i
$795$	37.5718	−	20.7854i	1.33254	−	0.737182i
$796$	20.9706	−	20.9706i	0.743282	−	0.743282i
$797$		−	0.634051i		−	0.0224592i	−0.999937	−	0.0112296i	$-0.996425\pi$
$797$		−	0.634051i		−	0.0224592i	0.999937	−	0.0112296i	$-0.00357457\pi$
$798$	24.0771	−	11.9877i	0.852320	−	0.424359i
$799$			1.65685i			0.0586153i
$800$	13.0462	+	25.0957i	0.461253	+	0.887269i
$801$	24.9706	−	3.48106i	0.882291	−	0.122997i
$802$	−32.9411	−	13.6447i	−1.16319	−	0.481810i
$803$	19.1116			0.674435
$804$	−7.85886	+	0.545152i	−0.277161	+	0.0192260i
$805$	−1.88393	+	5.17157i	−0.0663999	+	0.182274i
$806$	−28.6931	−	11.8851i	−1.01067	−	0.418634i
$807$	10.0384	+	8.73606i	0.353369	+	0.307524i
$808$	35.6054	−	14.7482i	1.25259	−	0.518841i
$809$			40.5782i			1.42665i	0.700832	+	0.713326i	$0.252812\pi$
$809$			40.5782i			1.42665i	−0.700832	+	0.713326i	$0.747188\pi$
$810$	−12.7628	+	25.4384i	−0.448438	+	0.893814i
$811$	2.48528			0.0872700			0.0436350	−	0.999048i	$-0.486106\pi$
$811$	2.48528			0.0872700			0.0436350	+	0.999048i	$0.486106\pi$
$812$	5.59767	+	5.59767i	0.196440	+	0.196440i
$813$	16.0804	−	18.4776i	0.563964	−	0.648037i
$814$	−42.6274	−	17.6569i	−1.49409	−	0.618872i
$815$	−6.66348	+	18.2919i	−0.233412	+	0.640737i
$816$	−6.96211	+	8.00000i	−0.243723	+	0.280056i
$817$			42.0375i			1.47071i
$818$	−3.88123	+	9.37011i	−0.135704	+	0.327618i
$819$	3.02944	+	21.7310i	0.105857	+	0.759342i
$820$	9.97799	−	4.64942i	0.348447	−	0.162365i
$821$	31.4532			1.09772			0.548862	−	0.835913i	$-0.315061\pi$
$821$	31.4532			1.09772			0.548862	+	0.835913i	$0.315061\pi$
$822$	17.5969	−	8.76129i	0.613763	−	0.305585i
$823$	48.0795			1.67595			0.837973	−	0.545711i	$-0.183740\pi$
$823$	48.0795			1.67595			0.837973	+	0.545711i	$0.183740\pi$
$824$	22.7506	−	9.42359i	0.792553	−	0.328286i
$825$	35.9487	−	5.65265i	1.25157	−	0.196800i
$826$	−12.4853	−	5.17157i	−0.434418	−	0.179942i
$827$	17.7666			0.617806			0.308903	−	0.951094i	$-0.400038\pi$
$827$	17.7666			0.617806			0.308903	+	0.951094i	$0.400038\pi$
$828$	−5.18227	−	3.91417i	−0.180096	−	0.136027i
$829$			10.8284i			0.376087i	0.982161	+	0.188043i	$0.0602146\pi$
$829$			10.8284i			0.376087i	−0.982161	+	0.188043i	$0.939785\pi$
$830$	14.8369	−	16.1826i	0.514997	−	0.561706i
$831$	22.0296	+	19.1716i	0.764199	+	0.665054i
$832$	−18.1929	+	18.1929i	−0.630724	+	0.630724i
$833$	−2.79884			−0.0969739
$834$	−5.44958	+	2.71327i	−0.188703	+	0.0939530i
$835$	3.85786	−	10.5902i	0.133507	−	0.366489i
$836$	28.6931	−	28.6931i	0.992371	−	0.992371i
$837$	−29.7250	−	19.3743i	−1.02745	−	0.669673i
$838$	−5.49019	−	2.27411i	−0.189655	−	0.0785578i
$839$	5.52021			0.190579			0.0952894	−	0.995450i	$-0.469622\pi$
$839$	5.52021			0.190579			0.0952894	+	0.995450i	$0.469622\pi$
$840$	19.4831	+	15.5241i	0.672230	+	0.535633i
$841$	−25.9706			−0.895537
$842$	38.1145	+	15.7875i	1.31351	+	0.544075i
$843$	−6.75699	+	7.76429i	−0.232723	+	0.267417i
$844$	−2.14214	−	2.14214i	−0.0737353	−	0.0737353i
$845$	−5.58206	−	2.03347i	−0.192029	−	0.0699534i
$846$	−1.15474	+	4.44465i	−0.0397008	+	0.152810i
$847$	15.1384			0.520162
$848$	44.3462			1.52286
$849$	−29.6985	+	34.1258i	−1.01925	+	1.17120i
$850$	9.60373	−	4.99257i	0.329405	−	0.171244i
$851$		−	8.40401i		−	0.288086i
$852$	−2.84910	−	41.0724i	−0.0976086	−	1.40712i
$853$	−6.98394			−0.239126			−0.119563	−	0.992827i	$-0.538149\pi$
$853$	−6.98394			−0.239126			−0.119563	+	0.992827i	$0.538149\pi$
$854$	25.2120	+	10.4432i	0.862738	+	0.357358i
$855$	6.77836	−	31.6729i	0.231815	−	1.08319i
$856$	−14.8284	+	6.14214i	−0.506825	+	0.209934i
$857$	27.1367			0.926973			0.463486	−	0.886104i	$-0.346598\pi$
$857$	27.1367			0.926973			0.463486	+	0.886104i	$0.346598\pi$
$858$	14.7537	+	29.6326i	0.503683	+	1.01164i
$859$	32.1421			1.09668			0.548338	−	0.836257i	$-0.315261\pi$
$859$	32.1421			1.09668			0.548338	+	0.836257i	$0.315261\pi$
$860$	−35.2922	+	16.4450i	−1.20345	+	0.560771i
$861$	6.36486	−	7.31371i	0.216914	−	0.249251i
$862$	−11.7607	+	28.3929i	−0.400572	+	0.967066i
$863$		−	32.8113i		−	1.11691i	−0.829535	−	0.558455i	$-0.811394\pi$
$863$		−	32.8113i		−	1.11691i	0.829535	−	0.558455i	$-0.188606\pi$
$864$	−24.2520	+	16.6084i	−0.825070	+	0.565030i
$865$	0.201010	−	0.551791i	0.00683455	−	0.0187615i
$866$	−38.1167	−	15.7884i	−1.29526	−	0.536513i
$867$	−19.1501	−	16.6656i	−0.650372	−	0.565995i
$868$	−21.9607	+	21.9607i	−0.745396	+	0.745396i
$869$	2.03916			0.0691736
$870$	9.47288	−	1.07128i	0.321161	−	0.0363199i
$871$			7.31371i			0.247816i
$872$	−17.8435	−	43.0781i	−0.604259	−	1.45881i
$873$	−32.6256	+	4.54822i	−1.10421	+	0.153934i
$874$	6.82843	+	2.82843i	0.230975	+	0.0956730i
$875$	−12.6942	−	22.0296i	−0.429143	−	0.744737i
$876$	15.7177	−	1.09030i	0.531053	−	0.0368379i
$877$	33.4929			1.13098			0.565488	−	0.824757i	$-0.308688\pi$
$877$	33.4929			1.13098			0.565488	+	0.824757i	$0.308688\pi$
$878$	−15.0447	−	6.23172i	−0.507734	−	0.210310i
$879$	18.5486	−	21.3137i	0.625627	−	0.718894i
$880$	35.3137	+	12.8643i	1.19042	+	0.433656i
$881$			12.3074i			0.414647i	0.978272	+	0.207323i	$0.0664752\pi$
$881$			12.3074i			0.414647i	−0.978272	+	0.207323i	$0.933525\pi$
$882$	−7.50810	−	1.95064i	−0.252811	−	0.0656816i
$883$			12.4741i			0.419788i	0.977724	+	0.209894i	$0.0673119\pi$
$883$			12.4741i			0.419788i	−0.977724	+	0.209894i	$0.932688\pi$
$884$	6.96211	+	6.96211i	0.234161	+	0.234161i
$885$	−14.2404	+	7.87804i	−0.478686	+	0.264817i
$886$	21.8995	−	52.8701i	0.735728	−	1.77620i
$887$		−	37.6662i		−	1.26471i	−0.774680	−	0.632353i	$-0.782089\pi$
$887$		−	37.6662i		−	1.26471i	0.774680	−	0.632353i	$-0.217911\pi$
$888$	−36.0648	−	12.0894i	−1.21025	−	0.405694i
$889$	−5.17157			−0.173449
$890$	−19.5887	−	17.9598i	−0.656616	−	0.602015i
$891$	10.3431	+	36.3762i	0.346508	+	1.21865i
$892$	−14.9768	−	14.9768i	−0.501460	−	0.501460i
$893$		−	5.22625i		−	0.174890i
$894$	1.58086	−	0.787088i	0.0528718	−	0.0263242i
$895$	5.88036	−	16.1421i	0.196559	−	0.539572i
$896$	9.84591	+	23.7701i	0.328929	+	0.794104i
$897$	−3.95815	+	4.54822i	−0.132159	+	0.151861i
$898$	−32.3893	−	13.4161i	−1.08085	−	0.447701i
$899$			11.8851i			0.396389i
$900$	29.2423	−	6.69968i	0.974745	−	0.223323i
$901$		−	16.9706i		−	0.565371i
$902$	5.59767	−	13.5140i	0.186382	−	0.449966i
$903$	−22.5125	+	25.8686i	−0.749170	+	0.860854i
$904$	1.65685	−	0.686292i	0.0551062	−	0.0228257i
$905$	16.5754	−	45.5011i	0.550986	−	1.51251i
$906$	3.08790	+	6.20201i	0.102589	+	0.206048i
$907$		−	46.1956i		−	1.53390i	−0.641707	−	0.766950i	$-0.721774\pi$
$907$		−	46.1956i		−	1.53390i	0.641707	−	0.766950i	$-0.278226\pi$
$908$	6.75699	+	6.75699i	0.224238	+	0.224238i
$909$	−5.64391	−	40.4853i	−0.187197	−	1.34281i
$910$	15.6298	−	17.0474i	0.518123	−	0.565115i
$911$	28.6931			0.950645			0.475322	−	0.879812i	$-0.342331\pi$
$911$	28.6931			0.950645			0.475322	+	0.879812i	$0.342331\pi$
$912$	21.9607	−	25.2346i	0.727193	−	0.835600i
$913$		−	29.1732i		−	0.965493i
$914$	16.8080	+	6.96211i	0.555960	+	0.230286i
$915$	28.7562	−	15.9084i	0.950652	−	0.525917i
$916$	4.68629	−	4.68629i	0.154839	−	0.154839i
$917$		−	25.3884i		−	0.838400i
$918$	6.35577	+	9.28084i	0.209772	+	0.306314i
$919$		−	22.1421i		−	0.730402i	−0.930929	−	0.365201i	$-0.881000\pi$
$919$		−	22.1421i		−	0.730402i	0.930929	−	0.365201i	$-0.119000\pi$
$920$	0.296694	+	6.83922i	0.00978170	+	0.225482i
$921$	−20.2426	+	23.2603i	−0.667018	+	0.766454i
$922$	10.0384	−	24.2349i	0.330597	−	0.798132i
$923$	−38.2233			−1.25813
$924$	33.0230	−	2.29073i	1.08638	−	0.0753595i
$925$	29.7250	+	24.9706i	0.977353	+	0.821027i
$926$	2.67264	−	6.45232i	0.0878284	−	0.212036i
$927$	−3.60625	−	25.8686i	−0.118445	−	0.849637i
$928$	9.09644	+	3.76787i	0.298605	+	0.123686i
$929$		−	56.3666i		−	1.84933i	−0.380784	−	0.924664i	$-0.624346\pi$
$929$		−	56.3666i		−	1.84933i	0.380784	−	0.924664i	$-0.375654\pi$
$930$	4.20285	+	37.1639i	0.137817	+	1.21865i
$931$	8.82843			0.289340
$932$	39.6452	+	39.6452i	1.29862	+	1.29862i
$933$	12.8643	+	11.1953i	0.421158	+	0.366519i
$934$	−4.72792	+	11.4142i	−0.154702	+	0.373484i
$935$	4.92296	−	13.5140i	0.160998	−	0.441954i
$936$	13.8242	+	23.5287i	0.451858	+	0.769058i
$937$		−	32.9411i		−	1.07614i	−0.842900	−	0.538070i	$-0.819154\pi$
$937$		−	32.9411i		−	1.07614i	0.842900	−	0.538070i	$-0.180846\pi$
$938$	6.75699	+	2.79884i	0.220623	+	0.0913852i
$939$	−28.0000	+	32.1741i	−0.913745	+	1.04996i
$940$	4.38765	−	2.04450i	0.143109	−	0.0666843i
$941$	3.18243			0.103744			0.0518721	−	0.998654i	$-0.483481\pi$
$941$	3.18243			0.103744			0.0518721	+	0.998654i	$0.483481\pi$
$942$	−51.0752	+	25.4297i	−1.66412	+	0.828545i
$943$	2.66428			0.0867610
$944$	−16.8080			−0.547055
$945$	21.1331	−	15.8605i	0.687460	−	0.515941i
$946$	−19.7990	+	47.7990i	−0.643721	+	1.55408i
$947$	−36.5068			−1.18631			−0.593156	−	0.805087i	$-0.702118\pi$
$947$	−36.5068			−1.18631			−0.593156	+	0.805087i	$0.702118\pi$
$948$	1.67703	−	0.116332i	0.0544675	−	0.00377829i
$949$		−	14.6274i		−	0.474826i
$950$	−30.2932	+	15.7482i	−0.982843	+	0.510938i
$951$	−11.1641	+	12.8284i	−0.362021	+	0.415990i
$952$	9.09644	−	3.76787i	0.294817	−	0.122117i
$953$	−39.9079			−1.29274			−0.646371	−	0.763023i	$-0.723714\pi$
$953$	−39.9079			−1.29274			−0.646371	+	0.763023i	$0.723714\pi$
$954$	11.8276	−	45.5249i	0.382933	−	1.47392i
$955$	−17.6569	−	6.43215i	−0.571362	−	0.208140i
$956$	18.8472	+	18.8472i	0.609561	+	0.609561i
$957$	8.31609	−	9.55582i	0.268821	−	0.308896i
$958$	−8.31609	+	20.0768i	−0.268681	+	0.648652i
$959$	−18.2499			−0.589321
$960$	29.7765	+	8.56519i	0.961031	+	0.276440i
$961$	−15.6274			−0.504110
$962$	−13.5140	+	32.6256i	−0.435708	+	1.05189i
$963$	2.35049	+	16.8607i	0.0757436	+	0.543329i
$964$	−14.8284	−	14.8284i	−0.477591	−	0.477591i
$965$	10.4432	−	28.6675i	0.336177	−	0.922838i
$966$	2.68729	+	5.39738i	0.0864621	+	0.173658i
$967$	−51.8474			−1.66730			−0.833650	−	0.552293i	$-0.813753\pi$
$967$	−51.8474			−1.66730			−0.833650	+	0.552293i	$0.813753\pi$
$968$	17.3952	−	7.20533i	0.559103	−	0.231588i
$969$	−9.65685	−	8.40401i	−0.310223	−	0.269976i
$970$	25.5939	+	23.4657i	0.821771	+	0.753437i
$971$			48.2612i			1.54878i	0.632711	+	0.774388i	$0.281942\pi$
$971$			48.2612i			1.54878i	−0.632711	+	0.774388i	$0.718058\pi$
$972$	10.5816	+	29.3263i	0.339405	+	0.940640i
$973$	5.65180			0.181188
$974$	−10.6543	+	25.7218i	−0.341387	+	0.824180i
$975$	−4.32635	−	27.5140i	−0.138554	−	0.881152i
$976$	33.9411			1.08643
$977$	13.7766			0.440753			0.220376	−	0.975415i	$-0.429271\pi$
$977$	13.7766			0.440753			0.220376	+	0.975415i	$0.429271\pi$
$978$	9.50495	+	19.0906i	0.303935	+	0.610449i
$979$	−35.3137			−1.12863
$980$	3.45367	+	7.41182i	0.110323	+	0.236762i
$981$	−48.9822	+	6.82843i	−1.56388	+	0.218015i
$982$	18.3545	+	7.60268i	0.585715	+	0.242611i
$983$			1.97908i			0.0631227i	0.999502	+	0.0315613i	$0.0100480\pi$
$983$			1.97908i			0.0631227i	−0.999502	+	0.0315613i	$0.989952\pi$
$984$	3.83265	−	11.4334i	0.122181	−	0.364485i
$985$	6.14214	−	16.8607i	0.195705	−	0.537228i
$986$	1.44190	−	3.48106i	0.0459195	−	0.110859i
$987$	2.79884	−	3.21608i	0.0890879	−	0.102369i
$988$	−21.9607	−	21.9607i	−0.698664	−	0.698664i
$989$	−9.42359			−0.299653
$990$	22.6248	−	32.8213i	0.719062	−	1.04313i
$991$		−	19.7990i		−	0.628936i	−0.949268	−	0.314468i	$-0.898174\pi$
$991$		−	19.7990i		−	0.628936i	0.949268	−	0.314468i	$-0.101826\pi$
$992$	−14.7821	+	35.6871i	−0.469331	+	1.13307i
$993$	−1.97908	−	1.72232i	−0.0628041	−	0.0546561i
$994$	−14.6274	+	35.3137i	−0.463953	+	1.12008i
$995$	−11.3492	+	31.1546i	−0.359793	+	0.987666i
$996$	−1.66431	−	23.9925i	−0.0527357	−	0.760233i
$997$	−12.3125			−0.389941			−0.194971	−	0.980809i	$-0.562461\pi$
$997$	−12.3125			−0.389941			−0.194971	+	0.980809i	$0.562461\pi$
$998$	13.5909	−	32.8113i	0.430212	−	1.03862i
$999$	−22.0296	+	33.7990i	−0.696986	+	1.06935i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	120.2.m.b.59.10	yes	16
3.2	odd	2	inner	120.2.m.b.59.8	yes	16
4.3	odd	2		480.2.m.b.239.2		16
5.2	odd	4		600.2.b.i.251.16		16
5.3	odd	4		600.2.b.i.251.1		16
5.4	even	2	inner	120.2.m.b.59.7	yes	16
8.3	odd	2	inner	120.2.m.b.59.12	yes	16
8.5	even	2		480.2.m.b.239.1		16
12.11	even	2		480.2.m.b.239.13		16
15.2	even	4		600.2.b.i.251.2		16
15.8	even	4		600.2.b.i.251.15		16
15.14	odd	2	inner	120.2.m.b.59.9	yes	16
20.3	even	4		2400.2.b.i.2351.9		16
20.7	even	4		2400.2.b.i.2351.8		16
20.19	odd	2		480.2.m.b.239.16		16
24.5	odd	2		480.2.m.b.239.14		16
24.11	even	2	inner	120.2.m.b.59.6	yes	16
40.3	even	4		600.2.b.i.251.13		16
40.13	odd	4		2400.2.b.i.2351.10		16
40.19	odd	2	inner	120.2.m.b.59.5	✓	16
40.27	even	4		600.2.b.i.251.4		16
40.29	even	2		480.2.m.b.239.15		16
40.37	odd	4		2400.2.b.i.2351.7		16
60.23	odd	4		2400.2.b.i.2351.11		16
60.47	odd	4		2400.2.b.i.2351.6		16
60.59	even	2		480.2.m.b.239.3		16
120.29	odd	2		480.2.m.b.239.4		16
120.53	even	4		2400.2.b.i.2351.12		16
120.59	even	2	inner	120.2.m.b.59.11	yes	16
120.77	even	4		2400.2.b.i.2351.5		16
120.83	odd	4		600.2.b.i.251.3		16
120.107	odd	4		600.2.b.i.251.14		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
120.2.m.b.59.5	✓	16	40.19	odd	2	inner
120.2.m.b.59.6	yes	16	24.11	even	2	inner
120.2.m.b.59.7	yes	16	5.4	even	2	inner
120.2.m.b.59.8	yes	16	3.2	odd	2	inner
120.2.m.b.59.9	yes	16	15.14	odd	2	inner
120.2.m.b.59.10	yes	16	1.1	even	1	trivial
120.2.m.b.59.11	yes	16	120.59	even	2	inner
120.2.m.b.59.12	yes	16	8.3	odd	2	inner
480.2.m.b.239.1		16	8.5	even	2
480.2.m.b.239.2		16	4.3	odd	2
480.2.m.b.239.3		16	60.59	even	2
480.2.m.b.239.4		16	120.29	odd	2
480.2.m.b.239.13		16	12.11	even	2
480.2.m.b.239.14		16	24.5	odd	2
480.2.m.b.239.15		16	40.29	even	2
480.2.m.b.239.16		16	20.19	odd	2
600.2.b.i.251.1		16	5.3	odd	4
600.2.b.i.251.2		16	15.2	even	4
600.2.b.i.251.3		16	120.83	odd	4
600.2.b.i.251.4		16	40.27	even	4
600.2.b.i.251.13		16	40.3	even	4
600.2.b.i.251.14		16	120.107	odd	4
600.2.b.i.251.15		16	15.8	even	4
600.2.b.i.251.16		16	5.2	odd	4
2400.2.b.i.2351.5		16	120.77	even	4
2400.2.b.i.2351.6		16	60.47	odd	4
2400.2.b.i.2351.7		16	40.37	odd	4
2400.2.b.i.2351.8		16	20.7	even	4
2400.2.b.i.2351.9		16	20.3	even	4
2400.2.b.i.2351.10		16	40.13	odd	4
2400.2.b.i.2351.11		16	60.23	odd	4
2400.2.b.i.2351.12		16	120.53	even	4

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:	\( N \)	\(=\)	\( 120 = 2^{3} \cdot 3 \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	120.m (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(0.541196 - 1.30656i) q^{2} +(1.30656 + 1.13705i) q^{3} +(-1.41421 - 1.41421i) q^{4} +(2.10100 + 0.765367i) q^{5} +(2.19274 - 1.09174i) q^{6} -2.27411 q^{7} +(-2.61313 + 1.08239i) q^{8} +(0.414214 + 2.97127i) q^{9} +O(q^{10})\)	\(q+(0.541196 - 1.30656i) q^{2} +(1.30656 + 1.13705i) q^{3} +(-1.41421 - 1.41421i) q^{4} +(2.10100 + 0.765367i) q^{5} +(2.19274 - 1.09174i) q^{6} -2.27411 q^{7} +(-2.61313 + 1.08239i) q^{8} +(0.414214 + 2.97127i) q^{9} +(2.13705 - 2.33088i) q^{10} -4.20201i q^{11} +(-0.239721 - 3.45580i) q^{12} -3.21608 q^{13} +(-1.23074 + 2.97127i) q^{14} +(1.87483 + 3.38896i) q^{15} +4.00000i q^{16} +1.53073 q^{17} +(4.10632 + 1.06684i) q^{18} -4.82843 q^{19} +(-1.88887 - 4.05366i) q^{20} +(-2.97127 - 2.58579i) q^{21} +(-5.49019 - 2.27411i) q^{22} -1.08239i q^{23} +(-4.64495 - 1.55705i) q^{24} +(3.82843 + 3.21608i) q^{25} +(-1.74053 + 4.20201i) q^{26} +(-2.83730 + 4.35313i) q^{27} +(3.21608 + 3.21608i) q^{28} +1.74053 q^{29} +(5.44253 - 0.615493i) q^{30} +6.82843i q^{31} +(5.22625 + 2.16478i) q^{32} +(4.77791 - 5.49019i) q^{33} +(0.828427 - 2.00000i) q^{34} +(-4.77791 - 1.74053i) q^{35} +(3.61622 - 4.78779i) q^{36} +7.76429 q^{37} +(-2.61313 + 6.30864i) q^{38} +(-4.20201 - 3.65685i) q^{39} +(-6.31861 + 0.274109i) q^{40} +2.46148i q^{41} +(-4.98653 + 2.48273i) q^{42} -8.70626i q^{43} +(-5.94253 + 5.94253i) q^{44} +(-1.40385 + 6.55967i) q^{45} +(-1.41421 - 0.585786i) q^{46} +1.08239i q^{47} +(-4.54822 + 5.22625i) q^{48} -1.82843 q^{49} +(6.27394 - 3.26155i) q^{50} +(2.00000 + 1.74053i) q^{51} +(4.54822 + 4.54822i) q^{52} -11.0866i q^{53} +(4.15211 + 6.06300i) q^{54} +(3.21608 - 8.82843i) q^{55} +(5.94253 - 2.46148i) q^{56} +(-6.30864 - 5.49019i) q^{57} +(0.941967 - 2.27411i) q^{58} +4.20201i q^{59} +(2.14130 - 7.44411i) q^{60} -8.48528i q^{61} +(8.92177 + 3.69552i) q^{62} +(-0.941967 - 6.75699i) q^{63} +(5.65685 - 5.65685i) q^{64} +(-6.75699 - 2.46148i) q^{65} +(-4.58749 - 9.21391i) q^{66} -2.27411i q^{67} +(-2.16478 - 2.16478i) q^{68} +(1.23074 - 1.41421i) q^{69} +(-4.85990 + 5.30067i) q^{70} +11.8851 q^{71} +(-4.29847 - 7.31595i) q^{72} +4.54822i q^{73} +(4.20201 - 10.1445i) q^{74} +(1.34523 + 8.55514i) q^{75} +(6.82843 + 6.82843i) q^{76} +9.55582i q^{77} +(-7.05202 + 3.51111i) q^{78} +0.485281i q^{79} +(-3.06147 + 8.40401i) q^{80} +(-8.65685 + 2.46148i) q^{81} +(3.21608 + 1.33214i) q^{82} +6.94269 q^{83} +(0.545152 + 7.85886i) q^{84} +(3.21608 + 1.17157i) q^{85} +(-11.3753 - 4.71179i) q^{86} +(2.27411 + 1.97908i) q^{87} +(4.54822 + 10.9804i) q^{88} -8.40401i q^{89} +(7.81086 + 5.38428i) q^{90} +7.31371 q^{91} +(-1.53073 + 1.53073i) q^{92} +(-7.76429 + 8.92177i) q^{93} +(1.41421 + 0.585786i) q^{94} +(-10.1445 - 3.69552i) q^{95} +(4.36695 + 8.77096i) q^{96} +10.9804i q^{97} +(-0.989538 + 2.38896i) q^{98} +(12.4853 - 1.74053i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 16 q^{9}+O(q^{10}) \) 16 * q - 16 * q^9	\( 16 q - 16 q^{9} + 16 q^{10} - 32 q^{19} - 32 q^{24} + 16 q^{25} + 16 q^{30} - 32 q^{34} - 32 q^{36} + 32 q^{40} + 16 q^{49} + 32 q^{51} + 32 q^{54} + 64 q^{66} - 64 q^{70} + 32 q^{75} + 64 q^{76} - 48 q^{81} + 32 q^{84} - 16 q^{90} - 64 q^{91} + 64 q^{96} + 64 q^{99}+O(q^{100}) \) 16 * q - 16 * q^9 + 16 * q^10 - 32 * q^19 - 32 * q^24 + 16 * q^25 + 16 * q^30 - 32 * q^34 - 32 * q^36 + 32 * q^40 + 16 * q^49 + 32 * q^51 + 32 * q^54 + 64 * q^66 - 64 * q^70 + 32 * q^75 + 64 * q^76 - 48 * q^81 + 32 * q^84 - 16 * q^90 - 64 * q^91 + 64 * q^96 + 64 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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