LMFDB - Embedded newform 120.2.m.b.59.8

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			59.8
Root			$-0.886177i$ of defining polynomial
Character	$\chi$	$=$	120.59
Dual form			120.2.m.b.59.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.541196 + 1.30656i) q^{2} +(-1.30656 + 1.13705i) q^{3} +(-1.41421 - 1.41421i) q^{4} +(-2.10100 - 0.765367i) q^{5} +(-0.778527 - 2.32248i) q^{6} -2.27411 q^{7} +(2.61313 - 1.08239i) q^{8} +(0.414214 - 2.97127i) q^{9} +O(q^{10})$	\(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} +(-0.778527 - 2.32248i) 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} +(3.45580 + 0.239721i) q^{12} -3.21608 q^{13} +(1.23074 - 2.97127i) q^{14} +(3.61536 - 1.38896i) q^{15} +4.00000i q^{16} -1.53073 q^{17} +(3.65798 + 2.14923i) 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} +(-2.18347 + 4.38548i) 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} +(-0.141860 + 5.47539i) 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} +(-4.78779 + 3.61622i) 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} +(1.77045 + 5.28156i) q^{42} -8.70626i q^{43} +(5.94253 - 5.94253i) q^{44} +(-3.14437 + 5.92562i) 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} +(-7.22317 + 1.35121i) 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} +(-7.07717 - 3.14861i) 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} +(9.75906 - 3.27137i) 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} +(-2.13368 - 8.21264i) q^{72} +4.54822i q^{73} +(-4.20201 + 10.1445i) q^{74} +(-8.65894 + 0.151125i) q^{75} +(6.82843 + 6.82843i) q^{76} -9.55582i q^{77} +(2.50380 + 7.46926i) 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} +(-7.85886 - 0.545152i) 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} +(-6.04047 - 7.31524i) 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} +(9.28991 - 3.11411i) 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
$6$	−0.778527	−	2.32248i	−0.317832	−	0.948147i
$7$	−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	$0.218373\pi$
$11$			4.20201i			1.26695i	−0.773762	+	0.633476i	$0.781627\pi$
$12$	3.45580	+	0.239721i	0.997603	+	0.0692015i
$13$	−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
$15$	3.61536	−	1.38896i	0.933481	−	0.358627i
$16$			4.00000i			1.00000i
$17$	−1.53073			−0.371257			−0.185629	−	0.982620i	$-0.559432\pi$
$17$	−1.53073			−0.371257			−0.185629	+	0.982620i	$0.559432\pi$
$18$	3.65798	+	2.14923i	0.862193	+	0.506579i
$19$	−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	$0.0359971\pi$
$23$			1.08239i			0.225694i	−0.993612	+	0.112847i	$0.964003\pi$
$24$	−2.18347	+	4.38548i	−0.445700	+	0.895182i
$25$	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	$-0.551667\pi$
$29$	−1.74053			−0.323208			−0.161604	+	0.986856i	$0.551667\pi$
$30$	−0.141860	+	5.47539i	−0.0258999	+	0.999665i
$31$			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
$36$	−4.78779	+	3.61622i	−0.797965	+	0.602703i
$37$	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	$-0.938435\pi$
$41$		−	2.46148i		−	0.384418i	0.981354	−	0.192209i	$-0.0615652\pi$
$42$	1.77045	+	5.28156i	0.273187	+	0.814963i
$43$		−	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
$45$	−3.14437	+	5.92562i	−0.468735	+	0.883339i
$46$	−1.41421	−	0.585786i	−0.208514	−	0.0863695i
$47$		−	1.08239i		−	0.157883i	−0.996879	−	0.0789416i	$-0.974846\pi$
$47$		−	1.08239i		−	0.157883i	0.996879	−	0.0789416i	$-0.0251541\pi$
$48$	−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	$0.275501\pi$
$53$			11.0866i			1.52286i	−0.648250	+	0.761428i	$0.724499\pi$
$54$	−7.22317	+	1.35121i	−0.982949	+	0.183876i
$55$	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	$-0.911810\pi$
$59$		−	4.20201i		−	0.547055i	0.961864	−	0.273527i	$-0.0881904\pi$
$60$	−7.07717	−	3.14861i	−0.913658	−	0.406483i
$61$		−	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
$66$	9.75906	−	3.27137i	1.20126	−	0.402678i
$67$		−	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	$-0.749165\pi$
$71$	−11.8851			−1.41050			−0.705249	+	0.708960i	$0.749165\pi$
$72$	−2.13368	−	8.21264i	−0.251457	−	0.967868i
$73$			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
$75$	−8.65894	+	0.151125i	−0.999848	+	0.0174504i
$76$	6.82843	+	6.82843i	0.783274	+	0.783274i
$77$		−	9.55582i		−	1.08899i
$78$	2.50380	+	7.46926i	0.283500	+	0.845727i
$79$			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	$-0.624431\pi$
$83$	−6.94269			−0.762060			−0.381030	+	0.924563i	$0.624431\pi$
$84$	−7.85886	−	0.545152i	−0.857472	−	0.0594809i
$85$	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	$0.146943\pi$
$89$			8.40401i			0.890823i	−0.895326	+	0.445412i	$0.853057\pi$
$90$	−6.04047	−	7.31524i	−0.636721	−	0.771094i
$91$	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
$96$	9.28991	−	3.11411i	0.948147	−	0.317832i
$97$			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	$-0.262891\pi$
$101$	13.6256			1.35580			0.677899	+	0.735155i	$0.262891\pi$
$102$	1.19172	+	3.55509i	0.117998	+	0.352007i
$103$	−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
$105$	−8.22172	+	3.15864i	−0.802357	+	0.308251i
$106$	−14.4853	−	6.00000i	−1.40693	−	0.582772i
$107$	−5.67459			−0.548584			−0.274292	−	0.961647i	$-0.588443\pi$
$107$	−5.67459			−0.548584			−0.274292	+	0.961647i	$0.588443\pi$
$108$	2.14371	−	10.1688i	0.206279	−	0.978493i
$109$			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	$-0.490506\pi$
$113$	0.634051			0.0596465			0.0298232	+	0.999555i	$0.490506\pi$
$114$	3.75906	+	11.2139i	0.352068	+	1.05028i
$115$	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
$120$	7.94399	−	7.54275i	0.725184	−	0.688556i
$121$	−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
$126$	−8.31864	−	4.88759i	−0.741083	−	0.435421i
$127$	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	$-0.837834\pi$
$131$		−	11.1641i		−	0.975413i	0.873008	−	0.487707i	$-0.162166\pi$
$132$	−1.00731	+	14.5213i	−0.0876750	+	1.26392i
$133$	10.9804			0.952119
$134$	2.97127	+	1.23074i	0.256678	+	0.106320i
$135$	−2.62943	−	11.3175i	−0.226305	−	0.974056i
$136$	−4.00000	+	1.65685i	−0.342997	+	0.142074i
$137$	−8.02509			−0.685629			−0.342815	−	0.939403i	$-0.611380\pi$
$137$	−8.02509			−0.685629			−0.342815	+	0.939403i	$0.611380\pi$
$138$	2.51383	−	0.842671i	0.213991	−	0.0717329i
$139$	−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	$-0.509401\pi$
$149$	−0.720950			−0.0590625			−0.0295313	+	0.999564i	$0.509401\pi$
$150$	4.48873	−	11.3952i	0.366503	−	0.930417i
$151$			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
$156$	−11.1141	−	0.770961i	−0.889841	−	0.0617263i
$157$	−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
$162$	7.90113	−	9.97858i	0.620772	−	0.783992i
$163$			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
$165$	5.83640	+	15.1918i	0.454363	+	1.18268i
$166$	3.75736	−	9.07107i	0.291628	−	0.704051i
$167$			5.04054i			0.390049i	0.980798	+	0.195024i	$0.0624786\pi$
$167$			5.04054i			0.390049i	−0.980798	+	0.195024i	$0.937521\pi$
$168$	4.96546	−	9.97306i	0.383094	−	0.769438i
$169$	−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	$0.00317799\pi$
$173$			0.262632i			0.0199676i	−0.999950	+	0.00998379i	$0.996822\pi$
$174$	1.35505	+	4.04233i	0.102726	+	0.306449i
$175$	−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	$0.0927010\pi$
$179$			7.68306i			0.574259i	−0.957892	+	0.287129i	$0.907299\pi$
$180$	12.8269	−	3.93327i	0.956061	−	0.293169i
$181$		−	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
$186$	15.8589	−	5.31611i	1.16283	−	0.389796i
$187$		−	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	$-0.401662\pi$
$191$	8.40401			0.608093			0.304046	+	0.952657i	$0.401662\pi$
$192$	−0.958884	+	13.8232i	−0.0692015	+	0.997603i
$193$		−	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
$195$	−11.6273	+	4.46699i	−0.832646	+	0.319887i
$196$	2.58579	+	2.58579i	0.184699	+	0.184699i
$197$			8.02509i			0.571764i	0.958265	+	0.285882i	$0.0922865\pi$
$197$			8.02509i			0.571764i	−0.958265	+	0.285882i	$0.907713\pi$
$198$	−9.03109	+	15.3708i	−0.641812	+	1.09236i
$199$			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
$204$	−5.28991	−	0.366949i	−0.370367	−	0.0256916i
$205$	−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
$210$	0.322604	−	12.4516i	0.0222618	−	0.859244i
$211$	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
$216$	12.1260	+	8.30421i	0.825070	+	0.565030i
$217$		−	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
$222$	−6.04471	−	18.0324i	−0.405694	−	1.21025i
$223$	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
$225$	11.1416	−	10.0431i	0.742774	−	0.669542i
$226$	−0.343146	+	0.828427i	−0.0228257	+	0.0551062i
$227$	4.77791			0.317121			0.158561	−	0.987349i	$-0.449315\pi$
$227$	4.77791			0.317121			0.158561	+	0.987349i	$0.449315\pi$
$228$	−16.6861	−	1.15748i	−1.10506	−	0.0766557i
$229$			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	$-0.129590\pi$
$233$	28.0334			1.83653			0.918265	+	0.395967i	$0.129590\pi$
$234$	−11.7643	−	6.91210i	−0.769058	−	0.451858i
$235$	−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	$-0.358152\pi$
$239$	13.3270			0.862050			0.431025	+	0.902340i	$0.358152\pi$
$240$	5.55582	+	14.4614i	0.358627	+	0.933481i
$241$	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
$246$	−5.71672	+	1.91633i	−0.364485	+	0.122181i
$247$	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	$0.344340\pi$
$251$			27.9721i			1.76559i	−0.469762	+	0.882793i	$0.655660\pi$
$252$	10.8880	−	8.22368i	0.685877	−	0.518043i
$253$	−4.54822			−0.285944
$254$	−1.23074	+	2.97127i	−0.0772234	+	0.186434i
$255$	−5.53415	+	2.12612i	−0.346562	+	0.133143i
$256$	−16.0000			−1.00000
$257$	2.42742			0.151418			0.0757090	−	0.997130i	$-0.475878\pi$
$257$	2.42742			0.151418			0.0757090	+	0.997130i	$0.475878\pi$
$258$	−20.2201	+	6.77806i	−1.25885	+	0.421983i
$259$	−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	$-0.676309\pi$
$263$		−	27.5851i		−	1.70097i	0.526001	−	0.850484i	$-0.323691\pi$
$264$	−18.4278	−	9.17497i	−1.13415	−	0.564681i
$265$	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	$-0.575254\pi$
$269$	−7.68306			−0.468445			−0.234222	+	0.972183i	$0.575254\pi$
$270$	16.2101	+	2.68948i	0.986514	+	0.163677i
$271$		−	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
$276$	−0.259472	+	3.74053i	−0.0156184	+	0.225153i
$277$	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	$-0.943280\pi$
$281$		−	5.94253i		−	0.354502i	0.984166	−	0.177251i	$-0.0567204\pi$
$282$	−2.51383	+	0.842671i	−0.149696	+	0.0501803i
$283$			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
$285$	−17.4565	+	6.70647i	−1.03403	+	0.397257i
$286$	17.6569	+	7.31371i	1.04407	+	0.432469i
$287$			5.59767i			0.330420i
$288$	−8.59694	+	14.6319i	−0.506579	+	0.862193i
$289$	−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	$0.158096\pi$
$293$			16.3128i			0.953004i	−0.879173	+	0.476502i	$0.841904\pi$
$294$	1.42348	+	4.24648i	0.0830190	+	0.247660i
$295$	−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
$300$	12.4593	+	12.0319i	0.719338	+	0.694660i
$301$			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
$306$	−5.59939	−	3.28991i	−0.320096	−	0.188071i
$307$			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	$-0.590054\pi$
$311$	−9.84591			−0.558310			−0.279155	+	0.960246i	$0.590054\pi$
$312$	7.02222	−	14.1040i	0.397555	−	0.798484i
$313$			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
$315$	7.15065	−	13.4755i	0.402893	−	0.759258i
$316$	0.686292	−	0.686292i	0.0386069	−	0.0386069i
$317$		−	9.81845i		−	0.551459i	−0.961235	−	0.275730i	$-0.911081\pi$
$317$		−	9.81845i		−	0.551459i	0.961235	−	0.275730i	$-0.0889194\pi$
$318$	25.7483	−	8.63118i	1.44389	−	0.484012i
$319$		−	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
$324$	8.76158	+	15.7237i	0.486755	+	0.873539i
$325$	−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
$330$	−23.0076	−	0.596095i	−1.26653	−	0.0328139i
$331$	−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
$342$	−17.6623	−	10.3774i	−0.955066	−	0.561147i
$343$	20.0768			1.08405
$344$	−9.42359	−	22.7506i	−0.508086	−	1.22663i
$345$	1.50339	+	3.91323i	0.0809400	+	0.210681i
$346$	−0.343146	−	0.142136i	−0.0184476	−	0.00764126i
$347$	15.2304			0.817611			0.408806	−	0.912621i	$-0.365945\pi$
$347$	15.2304			0.817611			0.408806	+	0.912621i	$0.365945\pi$
$348$	−6.01491	−	0.417241i	−0.322433	−	0.0223665i
$349$		−	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	$-0.747889\pi$
$353$	−26.3939			−1.40481			−0.702403	+	0.711780i	$0.747889\pi$
$354$	−9.75906	+	3.27137i	−0.518688	+	0.173872i
$355$	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	$-0.822821\pi$
$359$	−32.1741			−1.69809			−0.849043	+	0.528323i	$0.822821\pi$
$360$	−1.80280	+	18.8878i	−0.0950161	+	0.995476i
$361$	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
$366$	−19.7069	+	6.60602i	−1.03009	+	0.345302i
$367$	−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
$372$	−1.63692	+	23.5977i	−0.0848702	+	1.22348i
$373$	−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
$375$	18.3081	+	6.30975i	0.945427	+	0.325834i
$376$	−1.17157	−	2.82843i	−0.0604193	−	0.145865i
$377$	5.59767			0.288295
$378$	16.4263	−	3.07280i	0.844877	−	0.158048i
$379$	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	$-0.842793\pi$
$383$		−	18.5545i		−	0.948091i	0.880500	−	0.474046i	$-0.157207\pi$
$384$	−17.5419	−	8.73390i	−0.895182	−	0.445700i
$385$	−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	$-0.396460\pi$
$389$	12.6060			0.639150			0.319575	+	0.947561i	$0.396460\pi$
$390$	0.456231	−	17.6093i	0.0231022	−	0.891680i
$391$		−	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
$396$	−15.1954	−	20.1183i	−0.763596	−	1.01098i
$397$	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	$0.216746\pi$
$401$			25.2120i			1.25903i	−0.776989	+	0.629514i	$0.783254\pi$
$402$	−5.28156	+	1.77045i	−0.263421	+	0.0883023i
$403$		−	21.9607i		−	1.09394i
$404$	−19.2695	−	19.2695i	−0.958694	−	0.958694i
$405$	16.3041	+	11.7972i	0.810159	+	0.586210i
$406$	−2.14214	+	5.17157i	−0.106312	+	0.256661i
$407$			32.6256i			1.61719i
$408$	3.34232	−	6.71300i	0.165469	−	0.332343i
$409$	−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
$414$	−2.32631	+	3.95937i	−0.114332	+	0.194592i
$415$	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	$0.0327292\pi$
$419$			4.20201i			0.205281i	−0.994718	+	0.102641i	$0.967271\pi$
$420$	16.0942	+	7.16028i	0.785319	+	0.349386i
$421$			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
$426$	9.25284	+	27.6028i	0.448302	+	1.33736i
$427$			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	$-0.324674\pi$
$431$	21.7310			1.04674			0.523372	+	0.852104i	$0.324674\pi$
$432$	−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
$435$	−6.29263	+	2.41752i	−0.301708	+	0.115911i
$436$	23.3137	−	23.3137i	1.11652	−	1.11652i
$437$		−	5.22625i		−	0.250006i
$438$	10.5631	−	3.54091i	0.504726	−	0.169191i
$439$		−	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	$-0.911126\pi$
$443$	−40.4650			−1.92255			−0.961275	+	0.275591i	$0.911126\pi$
$444$	26.8318	+	1.86126i	1.27338	+	0.0883317i
$445$	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	$0.198886\pi$
$449$			24.7897i			1.16990i	−0.811070	+	0.584949i	$0.801114\pi$
$450$	7.09220	+	19.9925i	0.334329	+	0.942456i
$451$	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
$456$	10.5427	−	21.1750i	0.493709	−	0.991609i
$457$			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	$-0.642173\pi$
$461$	−18.5486			−0.863892			−0.431946	+	0.901899i	$0.642173\pi$
$462$	−22.1932	+	7.43946i	−1.03252	+	0.346115i
$463$	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
$465$	9.48438	+	24.6872i	0.439828	+	1.14484i
$466$	−15.1716	+	36.6274i	−0.702810	+	1.69673i
$467$	8.73606			0.404257			0.202128	−	0.979359i	$-0.435214\pi$
$467$	8.73606			0.404257			0.202128	+	0.979359i	$0.435214\pi$
$468$	15.3979	−	11.6300i	0.711768	−	0.537599i
$469$			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
$474$	1.12705	−	0.377804i	0.0517673	−	0.0173531i
$475$	−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	$-0.385825\pi$
$479$	15.3661			0.702096			0.351048	+	0.936357i	$0.385825\pi$
$480$	−21.9016	−	0.567438i	−0.999665	−	0.0258999i
$481$	−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
$486$	1.02287	+	22.0217i	0.0463982	+	0.998923i
$487$	−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	$-0.897329\pi$
$491$		−	14.0479i		−	0.633974i	0.948430	−	0.316987i	$-0.102671\pi$
$492$	0.590068	−	8.50637i	0.0266023	−	0.383497i
$493$	2.66428			0.119993
$494$	−8.40401	+	20.2891i	−0.378114	+	0.912849i
$495$	−24.8995	−	13.2127i	−1.11915	−	0.593866i
$496$	−27.3137			−1.22642
$497$	27.0279			1.21237
$498$	5.40507	+	16.1242i	0.242207	+	0.722545i
$499$	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	$0.218987\pi$
$503$			28.4818i			1.26994i	−0.772537	+	0.634969i	$0.781013\pi$
$504$	4.85223	+	18.6764i	0.216136	+	0.831914i
$505$	−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	$-0.402355\pi$
$509$	13.6256			0.603944			0.301972	+	0.953317i	$0.402355\pi$
$510$	0.217149	−	8.38136i	0.00961553	−	0.371133i
$511$		−	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
$516$	2.08707	−	30.0871i	0.0918783	−	1.32451i
$517$	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	$0.0691964\pi$
$521$			9.84591i			0.431357i	−0.976464	+	0.215679i	$0.930804\pi$
$522$	−6.36681	−	3.74080i	−0.278668	−	0.163730i
$523$		−	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
$525$	19.6914	−	0.343674i	0.859402	−	0.0149992i
$526$	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
$534$	19.5181	−	6.54275i	0.844632	−	0.283132i
$535$	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
$540$	−12.2868	+	19.7240i	−0.528740	+	0.848784i
$541$			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
$546$	−5.69392	−	16.9859i	−0.243677	−	0.726930i
$547$		−	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
$552$	−4.74681	−	2.36338i	−0.202038	−	0.100592i
$553$		−	1.10358i		−	0.0469291i
$554$	−9.12496	+	22.0296i	−0.387682	+	0.935948i
$555$	28.0707	−	10.7843i	1.19153	−	0.457766i
$556$	3.51472	+	3.51472i	0.149057	+	0.149057i
$557$			19.3743i			0.820914i	0.911880	+	0.410457i	$0.134631\pi$
$557$			19.3743i			0.820914i	−0.911880	+	0.410457i	$0.865369\pi$
$558$	−14.6759	+	24.9782i	−0.621280	+	1.05741i
$559$			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	$-0.540665\pi$
$563$	−6.04601			−0.254809			−0.127405	+	0.991851i	$0.540665\pi$
$564$	0.259472	−	3.74053i	0.0109257	−	0.157505i
$565$	−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	$0.0632916\pi$
$569$			9.42359i			0.395057i	−0.980297	+	0.197529i	$0.936708\pi$
$570$	0.684958	−	26.4375i	0.0286898	−	1.10735i
$571$	−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
$576$	−14.4649	−	19.1512i	−0.602703	−	0.797965i
$577$			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
$582$	25.5017	−	8.54851i	1.05708	−	0.354347i
$583$	−46.5858			−1.92939
$584$	4.92296	+	11.8851i	0.203713	+	0.491808i
$585$	10.1125	−	19.0572i	0.418102	−	0.787919i
$586$	−21.3137	−	8.82843i	−0.880461	−	0.364699i
$587$	12.1689			0.502266			0.251133	−	0.967953i	$-0.419197\pi$
$587$	12.1689			0.502266			0.251133	+	0.967953i	$0.419197\pi$
$588$	−6.31867	−	0.438312i	−0.260578	−	0.0180757i
$589$		−	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	$-0.799788\pi$
$593$	−39.3826			−1.61725			−0.808625	+	0.588325i	$0.799788\pi$
$594$	−5.67779	−	30.3518i	−0.232963	−	1.24535i
$595$	−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	$-0.711103\pi$
$599$	−30.1350			−1.23128			−0.615641	+	0.788027i	$0.711103\pi$
$600$	−22.4633	+	9.76727i	−0.917061	+	0.398747i
$601$	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
$606$	−10.6079	−	31.6451i	−0.430916	−	1.28550i
$607$	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
$612$	7.32884	−	5.53547i	0.296251	−	0.223758i
$613$	−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
$615$	−3.41888	−	8.89912i	−0.137863	−	0.358847i
$616$	−10.3431	−	24.9706i	−0.416737	−	1.00609i
$617$	−31.0949			−1.25183			−0.625916	−	0.779890i	$-0.715275\pi$
$617$	−31.0949			−1.25183			−0.625916	+	0.779890i	$0.715275\pi$
$618$	6.77806	+	20.2201i	0.272653	+	0.813371i
$619$	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
$630$	13.7367	+	16.6357i	0.547283	+	0.662780i
$631$		−	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
$636$	−2.65768	+	38.3129i	−0.105384	+	1.51920i
$637$	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	$-0.837155\pi$
$641$		−	24.7897i		−	0.979135i	0.871965	−	0.489567i	$-0.162845\pi$
$642$	4.41782	+	13.1791i	0.174358	+	0.520138i
$643$		−	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
$645$	−12.0926	−	31.4762i	−0.476146	−	1.23938i
$646$	−4.00000	+	9.65685i	−0.157378	+	0.379944i
$647$		−	42.3671i		−	1.66562i	−0.553556	−	0.832812i	$-0.686729\pi$
$647$		−	42.3671i		−	1.66562i	0.553556	−	0.832812i	$-0.313271\pi$
$648$	−25.2857	+	2.93796i	−0.993317	+	0.115414i
$649$	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	$0.263048\pi$
$653$			37.5892i			1.47098i	−0.677535	+	0.735490i	$0.736952\pi$
$654$	38.2867	−	12.8342i	1.49713	−	0.501858i
$655$	−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	$0.00446989\pi$
$659$			0.720950i			0.0280842i	−0.999901	+	0.0140421i	$0.995530\pi$
$660$	13.2305	−	29.7383i	0.514995	−	1.15756i
$661$			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
$666$	28.4016	+	16.6873i	1.10054	+	0.646619i
$667$		−	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
$672$	−21.1263	+	7.08182i	−0.814963	+	0.273187i
$673$			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
$675$	−3.13762	+	25.7906i	−0.120767	+	0.992681i
$676$	3.75736	+	3.75736i	0.144514	+	0.144514i
$677$		−	39.3826i		−	1.51360i	−0.653649	−	0.756798i	$-0.726763\pi$
$677$		−	39.3826i		−	1.51360i	0.653649	−	0.756798i	$-0.273237\pi$
$678$	−0.493625	−	1.47257i	−0.0189576	−	0.0565536i
$679$		−	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	$-0.366041\pi$
$683$	21.3533			0.817063			0.408532	+	0.912744i	$0.366041\pi$
$684$	23.1175	−	17.4607i	0.883920	−	0.667625i
$685$	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
$690$	−5.92652	−	0.153548i	−0.225619	−	0.00584546i
$691$	−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
$696$	3.80040	−	7.63305i	0.144054	−	0.289330i
$697$			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	$-0.483401\pi$
$701$	2.76011			0.104248			0.0521239	+	0.998641i	$0.483401\pi$
$702$	23.2303	−	4.34559i	0.876770	−	0.164014i
$703$	−37.4893			−1.41394
$704$	23.7701	+	23.7701i	0.895871	+	0.895871i
$705$	−1.50339	−	3.91323i	−0.0566211	−	0.147381i
$706$	14.2843	−	34.4853i	0.537596	−	1.29787i
$707$	−30.9861			−1.16535
$708$	1.00731	−	14.5213i	0.0378570	−	0.545743i
$709$		−	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
$714$	−2.71009	−	8.08467i	−0.101423	−	0.302561i
$715$	−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	$-0.320298\pi$
$719$	28.6931			1.07007			0.535036	+	0.844829i	$0.320298\pi$
$720$	−23.7025	−	12.5775i	−0.883339	−	0.468735i
$721$	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
$726$	5.18254	+	15.4604i	0.192342	+	0.573789i
$727$	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
$732$	2.03410	−	29.3234i	0.0751825	−	1.08382i
$733$	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
$735$	−6.61042	+	2.53960i	−0.243829	+	0.0936747i
$736$	2.34315	−	5.65685i	0.0863695	−	0.208514i
$737$	9.55582			0.351993
$738$	5.29029	−	9.00403i	0.194738	−	0.331443i
$739$	−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	$-0.998916\pi$
$743$		−	0.185709i		−	0.00681301i	0.999994	−	0.00340650i	$-0.00108433\pi$
$744$	−29.9459	−	14.9097i	−1.09787	−	0.546616i
$745$	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
$750$	−18.1524	+	20.5059i	−0.662831	+	0.748769i
$751$			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
$756$	−4.87504	+	23.1250i	−0.177303	+	0.841047i
$757$	−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	$-0.971560\pi$
$761$		−	4.92296i		−	0.178457i	0.996011	−	0.0892285i	$-0.0284401\pi$
$762$	−1.77045	−	5.28156i	−0.0641368	−	0.191331i
$763$		−	37.4893i		−	1.35720i
$764$	−11.8851	−	11.8851i	−0.429987	−	0.429987i
$765$	4.81320	−	9.07054i	0.174022	−	0.327946i
$766$	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

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)

\(f(q)\)	\(=\)	\(q+(-0.541196 + 1.30656i) q^{2} +(-1.30656 + 1.13705i) q^{3} +(-1.41421 - 1.41421i) q^{4} +(-2.10100 - 0.765367i) q^{5} +(-0.778527 - 2.32248i) q^{6} -2.27411 q^{7} +(2.61313 - 1.08239i) q^{8} +(0.414214 - 2.97127i) q^{9} +O(q^{10})\)	\(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} +(-0.778527 - 2.32248i) 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} +(3.45580 + 0.239721i) q^{12} -3.21608 q^{13} +(1.23074 - 2.97127i) q^{14} +(3.61536 - 1.38896i) q^{15} +4.00000i q^{16} -1.53073 q^{17} +(3.65798 + 2.14923i) 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} +(-2.18347 + 4.38548i) 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} +(-0.141860 + 5.47539i) 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} +(-4.78779 + 3.61622i) 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} +(1.77045 + 5.28156i) q^{42} -8.70626i q^{43} +(5.94253 - 5.94253i) q^{44} +(-3.14437 + 5.92562i) 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} +(-7.22317 + 1.35121i) 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} +(-7.07717 - 3.14861i) 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} +(9.75906 - 3.27137i) 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} +(-2.13368 - 8.21264i) q^{72} +4.54822i q^{73} +(-4.20201 + 10.1445i) q^{74} +(-8.65894 + 0.151125i) q^{75} +(6.82843 + 6.82843i) q^{76} -9.55582i q^{77} +(2.50380 + 7.46926i) 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} +(-7.85886 - 0.545152i) 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} +(-6.04047 - 7.31524i) 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} +(9.28991 - 3.11411i) 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

Related objects

Downloads

Learn more