LMFDB - Embedded newform 720.2.bd.g.307.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [720,2,Mod(307,720)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(720, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([2, 3, 0, 1]))

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

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

chi := DirichletCharacter("720.307");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 720 = 2^{4} \cdot 3^{2} \cdot 5 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	720.bd (of order $4$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$5.74922894553$
Analytic rank:	$0$
Dimension:	$18$
Relative dimension:	$9$ over $\Q(i)$
Coefficient field:	$\mathbb{Q}[x]/(x^{18} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{18} + 2 x^{16} - 4 x^{15} - 5 x^{14} - 14 x^{13} - 10 x^{12} + 6 x^{11} + 37 x^{10} + 70 x^{9} + \cdots + 512 $ x^18 + 2x^16 - 4x^15 - 5x^14 - 14x^13 - 10x^12 + 6x^11 + 37x^10 + 70x^9 + 74x^8 + 24x^7 - 80x^6 - 224x^5 - 160x^4 - 256x^3 + 256*x^2 + 512
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{6} $
Twist minimal:	no (minimal twist has level 80)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			307.5
Root			$-0.480367 + 1.33013i$ of defining polynomial
Character	$\chi$	$=$	720.307
Dual form			720.2.bd.g.523.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.307817 + 1.38031i) q^{2} +(-1.81050 + 0.849763i) q^{4} +(-1.43498 - 1.71489i) q^{5} +(-0.458895 - 0.458895i) q^{7} +(-1.73024 - 2.23747i) q^{8} +(1.92536 - 2.50858i) q^{10} +(0.492763 + 0.492763i) q^{11} +4.52109 q^{13} +(0.492160 - 0.774671i) q^{14} +(2.55581 - 3.07699i) q^{16} +(3.12823 + 3.12823i) q^{17} +(4.04508 + 4.04508i) q^{19} +(4.05527 + 1.88541i) q^{20} +(-0.528484 + 0.831845i) q^{22} +(1.80660 - 1.80660i) q^{23} +(-0.881683 + 4.92165i) q^{25} +(1.39167 + 6.24050i) q^{26} +(1.22078 + 0.440876i) q^{28} +(3.83926 - 3.83926i) q^{29} +0.139949i q^{31} +(5.03391 + 2.58065i) q^{32} +(-3.35500 + 5.28085i) q^{34} +(-0.128450 + 1.44546i) q^{35} +5.84330 q^{37} +(-4.33831 + 6.82860i) q^{38} +(-1.35417 + 6.17788i) q^{40} -4.55648i q^{41} -7.49928 q^{43} +(-1.31088 - 0.473414i) q^{44} +(3.04976 + 1.93756i) q^{46} +(4.14073 - 4.14073i) q^{47} -6.57883i q^{49} +(-7.06479 + 0.297972i) q^{50} +(-8.18543 + 3.84186i) q^{52} +2.75773i q^{53} +(0.137930 - 1.55214i) q^{55} +(-0.232768 + 1.82076i) q^{56} +(6.48115 + 4.11757i) q^{58} +(3.62521 - 3.62521i) q^{59} +(3.72781 + 3.72781i) q^{61} +(-0.193173 + 0.0430787i) q^{62} +(-2.01257 + 7.74271i) q^{64} +(-6.48766 - 7.75317i) q^{65} +3.32677 q^{67} +(-8.32192 - 3.00540i) q^{68} +(-2.03471 + 0.267635i) q^{70} -1.37056 q^{71} +(-2.55028 - 2.55028i) q^{73} +(1.79867 + 8.06556i) q^{74} +(-10.7610 - 3.88625i) q^{76} -0.452252i q^{77} -3.86426 q^{79} +(-8.94421 + 0.0324871i) q^{80} +(6.28934 - 1.40256i) q^{82} +14.4698i q^{83} +(0.875628 - 9.85351i) q^{85} +(-2.30840 - 10.3513i) q^{86} +(0.249948 - 1.95514i) q^{88} +3.35011 q^{89} +(-2.07470 - 2.07470i) q^{91} +(-1.73566 + 4.80602i) q^{92} +(6.99006 + 4.44089i) q^{94} +(1.13226 - 12.7415i) q^{95} +(-4.95582 - 4.95582i) q^{97} +(9.08081 - 2.02507i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 18 q + 4 q^{2} - 4 q^{4} + 4 q^{5} + 2 q^{7} + 4 q^{8} - 12 q^{10} + 2 q^{11} - 12 q^{14} + 6 q^{17} + 2 q^{19} + 4 q^{20} + 4 q^{22} + 2 q^{23} + 6 q^{25} + 16 q^{26} - 4 q^{28} + 14 q^{29} + 4 q^{32}+ \cdots - 32 q^{98}+O(q^{100}) $ 18 * q + 4 * q^2 - 4 * q^4 + 4 * q^5 + 2 * q^7 + 4 * q^8 - 12 * q^10 + 2 * q^11 - 12 * q^14 + 6 * q^17 + 2 * q^19 + 4 * q^20 + 4 * q^22 + 2 * q^23 + 6 * q^25 + 16 * q^26 - 4 * q^28 + 14 * q^29 + 4 * q^32 - 28 * q^34 + 6 * q^35 + 8 * q^37 - 16 * q^38 + 20 * q^40 - 44 * q^43 - 44 * q^44 + 12 * q^46 + 38 * q^47 - 20 * q^50 - 40 * q^52 - 6 * q^55 - 20 * q^56 - 20 * q^58 + 10 * q^59 + 14 * q^61 - 16 * q^64 + 12 * q^67 - 36 * q^68 - 36 * q^70 - 24 * q^71 + 14 * q^73 - 48 * q^74 - 16 * q^76 + 16 * q^79 + 20 * q^80 - 28 * q^82 - 10 * q^85 + 36 * q^86 - 96 * q^88 + 12 * q^89 - 52 * q^92 + 28 * q^94 + 34 * q^95 + 18 * q^97 - 32 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/720\mathbb{Z}\right)^\times$.

$n$	$181$	$271$	$577$	$641$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$-1$	$e\left(\frac{1}{4}\right)$	$1$

Coefficient data

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

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

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

$2$	0.307817	+	1.38031i	0.217659	+	0.976025i
$2$	0.307817	+	1.38031i	0.217659	+	0.976025i
$3$		0			0
$3$		0			0
$4$	−1.81050	+	0.849763i	−0.905249	+	0.424882i
$5$	−1.43498	−	1.71489i	−0.641741	−	0.766921i
$5$	−1.43498	−	1.71489i	−0.641741	−	0.766921i
$6$		0			0
$7$	−0.458895	−	0.458895i	−0.173446	−	0.173446i	0.615046	−	0.788491i	$-0.289138\pi$
$7$	−0.458895	−	0.458895i	−0.173446	−	0.173446i	−0.788491	+	0.615046i	$0.789138\pi$
$8$	−1.73024	−	2.23747i	−0.611731	−	0.791066i
$9$		0			0
$10$	1.92536	−	2.50858i	0.608853	−	0.793283i
$11$	0.492763	+	0.492763i	0.148574	+	0.148574i	0.777481	−	0.628907i	$-0.216497\pi$
$11$	0.492763	+	0.492763i	0.148574	+	0.148574i	−0.628907	+	0.777481i	$0.716497\pi$
$12$		0			0
$13$	4.52109			1.25393			0.626963	−	0.779049i	$-0.284298\pi$
$13$	4.52109			1.25393			0.626963	+	0.779049i	$0.284298\pi$
$14$	0.492160	−	0.774671i	0.131535	−	0.207040i
$15$		0			0
$16$	2.55581	−	3.07699i	0.638951	−	0.769247i
$17$	3.12823	+	3.12823i	0.758708	+	0.758708i	0.976087	−	0.217379i	$-0.0697508\pi$
$17$	3.12823	+	3.12823i	0.758708	+	0.758708i	−0.217379	+	0.976087i	$0.569751\pi$
$18$		0			0
$19$	4.04508	+	4.04508i	0.928005	+	0.928005i	0.997577	−	0.0695721i	$-0.0221634\pi$
$19$	4.04508	+	4.04508i	0.928005	+	0.928005i	−0.0695721	+	0.997577i	$0.522163\pi$
$20$	4.05527	+	1.88541i	0.906786	+	0.421591i
$21$		0			0
$22$	−0.528484	+	0.831845i	−0.112673	+	0.177350i
$23$	1.80660	−	1.80660i	0.376701	−	0.376701i	−0.493209	−	0.869911i	$-0.664176\pi$
$23$	1.80660	−	1.80660i	0.376701	−	0.376701i	0.869911	+	0.493209i	$0.164176\pi$
$24$		0			0
$25$	−0.881683	+	4.92165i	−0.176337	+	0.984330i
$26$	1.39167	+	6.24050i	0.272928	+	1.22386i
$27$		0			0
$28$	1.22078	+	0.440876i	0.230706	+	0.0833177i
$29$	3.83926	−	3.83926i	0.712932	−	0.712932i	−0.254215	−	0.967148i	$-0.581817\pi$
$29$	3.83926	−	3.83926i	0.712932	−	0.712932i	0.967148	+	0.254215i	$0.0818172\pi$
$30$		0			0
$31$			0.139949i			0.0251356i	0.999921	+	0.0125678i	$0.00400057\pi$
$31$			0.139949i			0.0251356i	−0.999921	+	0.0125678i	$0.995999\pi$
$32$	5.03391	+	2.58065i	0.889878	+	0.456199i
$33$		0			0
$34$	−3.35500	+	5.28085i	−0.575378	+	0.905658i
$35$	−0.128450	+	1.44546i	−0.0217120	+	0.244327i
$36$		0			0
$37$	5.84330			0.960633			0.480317	−	0.877095i	$-0.340522\pi$
$37$	5.84330			0.960633			0.480317	+	0.877095i	$0.340522\pi$
$38$	−4.33831	+	6.82860i	−0.703767	+	1.10774i
$39$		0			0
$40$	−1.35417	+	6.17788i	−0.214113	+	0.976809i
$41$		−	4.55648i		−	0.711602i	−0.934562	−	0.355801i	$-0.884208\pi$
$41$		−	4.55648i		−	0.711602i	0.934562	−	0.355801i	$-0.115792\pi$
$42$		0			0
$43$	−7.49928			−1.14363			−0.571815	−	0.820383i	$-0.693760\pi$
$43$	−7.49928			−1.14363			−0.571815	+	0.820383i	$0.693760\pi$
$44$	−1.31088	−	0.473414i	−0.197622	−	0.0713699i
$45$		0			0
$46$	3.04976	+	1.93756i	0.449662	+	0.285677i
$47$	4.14073	−	4.14073i	0.603987	−	0.603987i	−0.337381	−	0.941368i	$-0.609541\pi$
$47$	4.14073	−	4.14073i	0.603987	−	0.603987i	0.941368	+	0.337381i	$0.109541\pi$
$48$		0			0
$49$		−	6.57883i		−	0.939833i
$50$	−7.06479	+	0.297972i	−0.999112	+	0.0421396i
$51$		0			0
$52$	−8.18543	+	3.84186i	−1.13511	+	0.532770i
$53$			2.75773i			0.378803i	0.981900	+	0.189402i	$0.0606548\pi$
$53$			2.75773i			0.378803i	−0.981900	+	0.189402i	$0.939345\pi$
$54$		0			0
$55$	0.137930	−	1.55214i	0.0185985	−	0.209290i
$56$	−0.232768	+	1.82076i	−0.0311050	+	0.243309i
$57$		0			0
$58$	6.48115	+	4.11757i	0.851016	+	0.540663i
$59$	3.62521	−	3.62521i	0.471962	−	0.471962i	−0.430587	−	0.902549i	$-0.641694\pi$
$59$	3.62521	−	3.62521i	0.471962	−	0.471962i	0.902549	+	0.430587i	$0.141694\pi$
$60$		0			0
$61$	3.72781	+	3.72781i	0.477298	+	0.477298i	0.904266	−	0.426969i	$-0.140419\pi$
$61$	3.72781	+	3.72781i	0.477298	+	0.477298i	−0.426969	+	0.904266i	$0.640419\pi$
$62$	−0.193173	+	0.0430787i	−0.0245330	+	0.00547100i
$63$		0			0
$64$	−2.01257	+	7.74271i	−0.251571	+	0.967839i
$65$	−6.48766	−	7.75317i	−0.804696	−	0.961662i
$66$		0			0
$67$	3.32677			0.406430			0.203215	−	0.979134i	$-0.434861\pi$
$67$	3.32677			0.406430			0.203215	+	0.979134i	$0.434861\pi$
$68$	−8.32192	−	3.00540i	−1.00918	−	0.364459i
$69$		0			0
$70$	−2.03471	+	0.267635i	−0.243195	+	0.0319885i
$71$	−1.37056			−0.162655			−0.0813275	−	0.996687i	$-0.525916\pi$
$71$	−1.37056			−0.162655			−0.0813275	+	0.996687i	$0.525916\pi$
$72$		0			0
$73$	−2.55028	−	2.55028i	−0.298488	−	0.298488i	0.541933	−	0.840422i	$-0.317693\pi$
$73$	−2.55028	−	2.55028i	−0.298488	−	0.298488i	−0.840422	+	0.541933i	$0.817693\pi$
$74$	1.79867	+	8.06556i	0.209091	+	0.937602i
$75$		0			0
$76$	−10.7610	−	3.88625i	−1.23437	−	0.445783i
$77$		−	0.452252i		−	0.0515389i
$78$		0			0
$79$	−3.86426			−0.434763			−0.217382	−	0.976087i	$-0.569752\pi$
$79$	−3.86426			−0.434763			−0.217382	+	0.976087i	$0.569752\pi$
$80$	−8.94421	+	0.0324871i	−0.999993	+	0.00363216i
$81$		0			0
$82$	6.28934	−	1.40256i	0.694541	−	0.154887i
$83$			14.4698i			1.58827i	0.607744	+	0.794133i	$0.292075\pi$
$83$			14.4698i			1.58827i	−0.607744	+	0.794133i	$0.707925\pi$
$84$		0			0
$85$	0.875628	−	9.85351i	0.0949752	−	1.06876i
$86$	−2.30840	−	10.3513i	−0.248922	−	1.11621i
$87$		0			0
$88$	0.249948	−	1.95514i	0.0266445	−	0.208419i
$89$	3.35011			0.355111			0.177556	−	0.984111i	$-0.443181\pi$
$89$	3.35011			0.355111			0.177556	+	0.984111i	$0.443181\pi$
$90$		0			0
$91$	−2.07470	−	2.07470i	−0.217488	−	0.217488i
$92$	−1.73566	+	4.80602i	−0.180955	+	0.501062i
$93$		0			0
$94$	6.99006	+	4.44089i	0.720970	+	0.458043i
$95$	1.13226	−	12.7415i	0.116168	−	1.30725i
$96$		0			0
$97$	−4.95582	−	4.95582i	−0.503187	−	0.503187i	0.409240	−	0.912427i	$-0.365794\pi$
$97$	−4.95582	−	4.95582i	−0.503187	−	0.503187i	−0.912427	+	0.409240i	$0.865794\pi$
$98$	9.08081	−	2.02507i	0.917300	−	0.204563i
$99$		0			0
$100$	−2.58595	−	9.65986i	−0.258595	−	0.965986i
$101$	1.84536	−	1.84536i	0.183621	−	0.183621i	−0.609311	−	0.792931i	$-0.708554\pi$
$101$	1.84536	−	1.84536i	0.183621	−	0.183621i	0.792931	+	0.609311i	$0.208554\pi$
$102$		0			0
$103$	−11.6655	+	11.6655i	−1.14944	+	1.14944i	−0.162773	+	0.986664i	$0.552044\pi$
$103$	−11.6655	+	11.6655i	−1.14944	+	1.14944i	−0.986664	+	0.162773i	$0.947956\pi$
$104$	−7.82256	−	10.1158i	−0.767065	−	0.991938i
$105$		0			0
$106$	−3.80651	+	0.848874i	−0.369721	+	0.0824500i
$107$			15.3106i			1.48013i	0.672534	+	0.740067i	$0.265206\pi$
$107$			15.3106i			1.48013i	−0.672534	+	0.740067i	$0.734794\pi$
$108$		0			0
$109$	12.4798	−	12.4798i	1.19535	−	1.19535i	0.219803	−	0.975544i	$-0.429458\pi$
$109$	12.4798	−	12.4798i	1.19535	−	1.19535i	0.975544	−	0.219803i	$-0.0705416\pi$
$110$	2.18488	−	0.287388i	0.208320	−	0.0274013i
$111$		0			0
$112$	−2.58486	+	0.239168i	−0.244246	+	0.0225993i
$113$	−2.53557	+	2.53557i	−0.238526	+	0.238526i	−0.816240	−	0.577713i	$-0.803945\pi$
$113$	−2.53557	+	2.53557i	−0.238526	+	0.238526i	0.577713	+	0.816240i	$0.303945\pi$
$114$		0			0
$115$	−5.69053	−	0.505686i	−0.530645	−	0.0471555i
$116$	−3.68851	+	10.2134i	−0.342470	+	0.948293i
$117$		0			0
$118$	6.11980	+	3.88800i	0.563373	+	0.357919i
$119$		−	2.87106i		−	0.263189i
$120$		0			0
$121$		−	10.5144i		−	0.955852i
$122$	−3.99805	+	6.29301i	−0.361966	+	0.569743i
$123$		0			0
$124$	−0.118924	−	0.253378i	−0.0106797	−	0.0227540i
$125$	9.70527	−	5.55047i	0.868066	−	0.496449i
$126$		0			0
$127$	−0.615790	+	0.615790i	−0.0546426	+	0.0546426i	−0.733900	−	0.679257i	$-0.762302\pi$
$127$	−0.615790	+	0.615790i	−0.0546426	+	0.0546426i	0.679257	+	0.733900i	$0.262302\pi$
$128$	−11.3068	−	0.394630i	−0.999391	−	0.0348807i
$129$		0			0
$130$	8.70475	−	11.3415i	0.763457	−	0.994718i
$131$	−9.55413	+	9.55413i	−0.834748	+	0.834748i	−0.988162	−	0.153414i	$-0.950973\pi$
$131$	−9.55413	+	9.55413i	−0.834748	+	0.834748i	0.153414	+	0.988162i	$0.450973\pi$
$132$		0			0
$133$		−	3.71253i		−	0.321917i
$134$	1.02404	+	4.59197i	0.0884632	+	0.396686i
$135$		0			0
$136$	1.58676	−	12.4119i	0.136063	−	1.06431i
$137$	3.70277	−	3.70277i	0.316349	−	0.316349i	−0.531014	−	0.847363i	$-0.678189\pi$
$137$	3.70277	−	3.70277i	0.316349	−	0.316349i	0.847363	+	0.531014i	$0.178189\pi$
$138$		0			0
$139$	5.46761	−	5.46761i	0.463756	−	0.463756i	−0.436128	−	0.899885i	$-0.643651\pi$
$139$	5.46761	−	5.46761i	0.463756	−	0.463756i	0.899885	+	0.436128i	$0.143651\pi$
$140$	−0.995737	−	2.72615i	−0.0841551	−	0.230401i
$141$		0			0
$142$	−0.421880	−	1.89179i	−0.0354034	−	0.158755i
$143$	2.22783	+	2.22783i	0.186300	+	0.186300i
$144$		0			0
$145$	−12.0931	−	1.07465i	−1.00428	−	0.0892450i
$146$	2.73516	−	4.30520i	0.226363	−	0.356301i
$147$		0			0
$148$	−10.5793	+	4.96542i	−0.869612	+	0.408155i
$149$	−4.21561	−	4.21561i	−0.345356	−	0.345356i	0.513021	−	0.858376i	$-0.328526\pi$
$149$	−4.21561	−	4.21561i	−0.345356	−	0.345356i	−0.858376	+	0.513021i	$0.828526\pi$
$150$		0			0
$151$	12.4417			1.01249			0.506244	−	0.862390i	$-0.331034\pi$
$151$	12.4417			1.01249			0.506244	+	0.862390i	$0.331034\pi$
$152$	2.05181	−	16.0497i	0.166424	−	1.30180i
$153$		0			0
$154$	0.624247	−	0.139211i	0.0503033	−	0.0112179i
$155$	0.239997	−	0.200824i	0.0192771	−	0.0161306i
$156$		0			0
$157$			7.50500i			0.598964i	0.954102	+	0.299482i	$0.0968138\pi$
$157$			7.50500i			0.598964i	−0.954102	+	0.299482i	$0.903186\pi$
$158$	−1.18948	−	5.33387i	−0.0946302	−	0.424340i
$159$		0			0
$160$	−2.79802	−	12.3358i	−0.221203	−	0.975228i
$161$	−1.65807			−0.130675
$162$		0			0
$163$			23.7284i			1.85855i	0.369383	+	0.929277i	$0.379569\pi$
$163$			23.7284i			1.85855i	−0.369383	+	0.929277i	$0.620431\pi$
$164$	3.87193	+	8.24949i	0.302347	+	0.644177i
$165$		0			0
$166$	−19.9728	+	4.45404i	−1.55019	+	0.345701i
$167$	0.402976	+	0.402976i	0.0311832	+	0.0311832i	0.722526	−	0.691343i	$-0.242981\pi$
$167$	0.402976	+	0.402976i	0.0311832	+	0.0311832i	−0.691343	+	0.722526i	$0.742981\pi$
$168$		0			0
$169$	7.44028			0.572330
$170$	13.8704	−	1.82444i	1.06381	−	0.139928i
$171$		0			0
$172$	13.5774	−	6.37261i	1.03527	−	0.485907i
$173$	15.4500			1.17464			0.587320	−	0.809355i	$-0.300183\pi$
$173$	15.4500			1.17464			0.587320	+	0.809355i	$0.300183\pi$
$174$		0			0
$175$	2.66312	−	1.85392i	0.201313	−	0.140143i
$176$	2.77563	−	0.256820i	0.209221	−	0.0193585i
$177$		0			0
$178$	1.03122	+	4.62419i	0.0772932	+	0.346597i
$179$	−5.20444	−	5.20444i	−0.388998	−	0.388998i	0.485332	−	0.874330i	$-0.338699\pi$
$179$	−5.20444	−	5.20444i	−0.388998	−	0.388998i	−0.874330	+	0.485332i	$0.838699\pi$
$180$		0			0
$181$	−9.08925	+	9.08925i	−0.675599	+	0.675599i	−0.959001	−	0.283402i	$-0.908537\pi$
$181$	−9.08925	+	9.08925i	−0.675599	+	0.675599i	0.283402	+	0.959001i	$0.408537\pi$
$182$	2.22510	−	3.50236i	0.164936	−	0.259612i
$183$		0			0
$184$	−7.16804	−	0.916372i	−0.528435	−	0.0675559i
$185$	−8.38500	−	10.0206i	−0.616478	−	0.736730i
$186$		0			0
$187$			3.08295i			0.225448i
$188$	−3.97814	+	11.0154i	−0.290136	+	0.803382i
$189$		0			0
$190$	17.9357	−	2.35916i	1.30119	−	0.171151i
$191$		−	15.1075i		−	1.09314i	−0.837413	−	0.546571i	$-0.815933\pi$
$191$		−	15.1075i		−	1.09314i	0.837413	−	0.546571i	$-0.184067\pi$
$192$		0			0
$193$	4.19166	−	4.19166i	0.301722	−	0.301722i	−0.539965	−	0.841687i	$-0.681563\pi$
$193$	4.19166	−	4.19166i	0.301722	−	0.301722i	0.841687	+	0.539965i	$0.181563\pi$
$194$	5.31507	−	8.36604i	0.381600	−	0.600647i
$195$		0			0
$196$	5.59045	+	11.9110i	0.399318	+	0.850783i
$197$	4.03184			0.287256			0.143628	−	0.989632i	$-0.454123\pi$
$197$	4.03184			0.287256			0.143628	+	0.989632i	$0.454123\pi$
$198$		0			0
$199$		−	5.43055i		−	0.384961i	−0.981301	−	0.192481i	$-0.938347\pi$
$199$		−	5.43055i		−	0.384961i	0.981301	−	0.192481i	$-0.0616533\pi$
$200$	12.5376	−	6.54287i	0.886541	−	0.462651i
$201$		0			0
$202$	3.11520	+	1.97914i	0.219185	+	0.139252i
$203$	−3.52363			−0.247310
$204$		0			0
$205$	−7.81385	+	6.53844i	−0.545743	+	0.456664i
$206$	−19.6928	−	12.5111i	−1.37206	−	0.871693i
$207$		0			0
$208$	11.5550	−	13.9114i	0.801197	−	0.964579i
$209$			3.98653i			0.275754i
$210$		0			0
$211$	3.23020	−	3.23020i	0.222376	−	0.222376i	−0.587122	−	0.809498i	$-0.699739\pi$
$211$	3.23020	−	3.23020i	0.222376	−	0.222376i	0.809498	+	0.587122i	$0.199739\pi$
$212$	−2.34342	−	4.99286i	−0.160946	−	0.342911i
$213$		0			0
$214$	−21.1334	+	4.71286i	−1.44465	+	0.322165i
$215$	10.7613	+	12.8604i	0.733914	+	0.877074i
$216$		0			0
$217$	0.0642220	−	0.0642220i	0.00435967	−	0.00435967i
$218$	21.0674	+	13.3845i	1.42687	+	0.906511i
$219$		0			0
$220$	1.06923	+	2.92735i	0.0720872	+	0.197362i
$221$	14.1430	+	14.1430i	0.951363	+	0.951363i
$222$		0			0
$223$	−8.17319	−	8.17319i	−0.547317	−	0.547317i	0.378347	−	0.925664i	$-0.376493\pi$
$223$	−8.17319	−	8.17319i	−0.547317	−	0.547317i	−0.925664	+	0.378347i	$0.876493\pi$
$224$	−1.12579	−	3.49428i	−0.0752199	−	0.233471i
$225$		0			0
$226$	−4.28035	−	2.71937i	−0.284725	−	0.180890i
$227$	1.54068			0.102258			0.0511292	−	0.998692i	$-0.483718\pi$
$227$	1.54068			0.102258			0.0511292	+	0.998692i	$0.483718\pi$
$228$		0			0
$229$	−17.5646	−	17.5646i	−1.16070	−	1.16070i	−0.984322	−	0.176378i	$-0.943562\pi$
$229$	−17.5646	−	17.5646i	−1.16070	−	1.16070i	−0.176378	−	0.984322i	$-0.556438\pi$
$230$	−1.05364	−	8.01034i	−0.0694748	−	0.528186i
$231$		0			0
$232$	−15.2331	−	1.94741i	−1.00010	−	0.127854i
$233$	−9.99018	−	9.99018i	−0.654479	−	0.654479i	0.299590	−	0.954068i	$-0.403150\pi$
$233$	−9.99018	−	9.99018i	−0.654479	−	0.654479i	−0.954068	+	0.299590i	$0.903150\pi$
$234$		0			0
$235$	−13.0427	−	1.15904i	−0.850814	−	0.0756072i
$236$	−3.48286	+	9.64399i	−0.226715	+	0.627771i
$237$		0			0
$238$	3.96294	−	0.883759i	0.256879	−	0.0572856i
$239$	−26.2762			−1.69967			−0.849833	−	0.527052i	$-0.823297\pi$
$239$	−26.2762			−1.69967			−0.849833	+	0.527052i	$0.823297\pi$
$240$		0			0
$241$	−0.113242			−0.00729456			−0.00364728	−	0.999993i	$-0.501161\pi$
$241$	−0.113242			−0.00729456			−0.00364728	+	0.999993i	$0.501161\pi$
$242$	14.5131	−	3.23650i	0.932935	−	0.208050i
$243$		0			0
$244$	−9.91696	−	3.58144i	−0.634868	−	0.229278i
$245$	−11.2820	+	9.44047i	−0.720778	+	0.603130i
$246$		0			0
$247$	18.2882	+	18.2882i	1.16365	+	1.16365i
$248$	0.313133	−	0.242145i	0.0198840	−	0.0153762i
$249$		0			0
$250$	10.6488	+	11.6877i	0.673489	+	0.739197i
$251$	−19.2220	−	19.2220i	−1.21328	−	1.21328i	−0.969941	−	0.243339i	$-0.921757\pi$
$251$	−19.2220	−	19.2220i	−1.21328	−	1.21328i	−0.243339	−	0.969941i	$-0.578243\pi$
$252$		0			0
$253$	1.78045			0.111936
$254$	−1.03953	−	0.660430i	−0.0652260	−	0.0414390i
$255$		0			0
$256$	−2.93572	−	15.7284i	−0.183482	−	0.983023i
$257$	0.757800	+	0.757800i	0.0472703	+	0.0472703i	0.730347	−	0.683077i	$-0.239358\pi$
$257$	0.757800	+	0.757800i	0.0472703	+	0.0472703i	−0.683077	+	0.730347i	$0.739358\pi$
$258$		0			0
$259$	−2.68146	−	2.68146i	−0.166618	−	0.166618i
$260$	18.3343	+	8.52412i	1.13704	+	0.528643i
$261$		0			0
$262$	−16.1286	−	10.2467i	−0.996425	−	0.633044i
$263$	−5.73017	+	5.73017i	−0.353338	+	0.353338i	−0.861350	−	0.508012i	$-0.830380\pi$
$263$	−5.73017	+	5.73017i	−0.353338	+	0.353338i	0.508012	+	0.861350i	$0.330380\pi$
$264$		0			0
$265$	4.72919	−	3.95728i	0.290512	−	0.243094i
$266$	5.12443	−	1.14278i	0.314199	−	0.0700682i
$267$		0			0
$268$	−6.02311	+	2.82697i	−0.367920	+	0.172685i
$269$	−9.78879	+	9.78879i	−0.596833	+	0.596833i	−0.939468	−	0.342635i	$-0.888680\pi$
$269$	−9.78879	+	9.78879i	−0.596833	+	0.596833i	0.342635	+	0.939468i	$0.388680\pi$
$270$		0			0
$271$			4.10159i			0.249154i	0.992210	+	0.124577i	$0.0397574\pi$
$271$			4.10159i			0.249154i	−0.992210	+	0.124577i	$0.960243\pi$
$272$	17.6207	−	1.63038i	1.06841	−	0.0988565i
$273$		0			0
$274$	6.25074	+	3.97119i	0.377621	+	0.239908i
$275$	−2.85967	+	1.99075i	−0.172444	+	0.120046i
$276$		0			0
$277$	24.6755			1.48261			0.741305	−	0.671169i	$-0.234207\pi$
$277$	24.6755			1.48261			0.741305	+	0.671169i	$0.234207\pi$
$278$	9.23000	+	5.86396i	0.553578	+	0.351697i
$279$		0			0
$280$	3.45642	−	2.21358i	0.206560	−	0.132286i
$281$			23.6688i			1.41196i	0.708230	+	0.705981i	$0.249494\pi$
$281$			23.6688i			1.41196i	−0.708230	+	0.705981i	$0.750506\pi$
$282$		0			0
$283$	13.0492			0.775694			0.387847	−	0.921724i	$-0.373219\pi$
$283$	13.0492			0.775694			0.387847	+	0.921724i	$0.373219\pi$
$284$	2.48139	−	1.16465i	0.147243	−	0.0691091i
$285$		0			0
$286$	−2.38932	+	3.76085i	−0.141284	+	0.222384i
$287$	−2.09094	+	2.09094i	−0.123424	+	0.123424i
$288$		0			0
$289$			2.57168i			0.151275i
$290$	−2.23912	−	17.0231i	−0.131486	−	0.999628i
$291$		0			0
$292$	6.78442	+	2.45015i	0.397028	+	0.143384i
$293$		−	31.6731i		−	1.85036i	−0.379526	−	0.925181i	$-0.623913\pi$
$293$		−	31.6731i		−	1.85036i	0.379526	−	0.925181i	$-0.376087\pi$
$294$		0			0
$295$	−11.4189	−	1.01474i	−0.664835	−	0.0590802i
$296$	−10.1103	−	13.0742i	−0.587649	−	0.759924i
$297$		0			0
$298$	4.52120	−	7.11646i	0.261906	−	0.412246i
$299$	8.16779	−	8.16779i	0.472355	−	0.472355i
$300$		0			0
$301$	3.44138	+	3.44138i	0.198358	+	0.198358i
$302$	3.82975	+	17.1733i	0.220377	+	0.988213i
$303$		0			0
$304$	22.7851	−	2.10823i	1.30682	−	0.120915i
$305$	1.04346	−	11.7421i	0.0597482	−	0.672351i
$306$		0			0
$307$	−27.3597			−1.56150			−0.780751	−	0.624843i	$-0.785163\pi$
$307$	−27.3597			−1.56150			−0.780751	+	0.624843i	$0.785163\pi$
$308$	0.384307	+	0.818802i	0.0218979	+	0.0466556i
$309$		0			0
$310$	0.351074	+	0.269453i	0.0199397	+	0.0153039i
$311$	15.8076			0.896368			0.448184	−	0.893941i	$-0.352071\pi$
$311$	15.8076			0.896368			0.448184	+	0.893941i	$0.352071\pi$
$312$		0			0
$313$	−13.8388	−	13.8388i	−0.782217	−	0.782217i	0.197988	−	0.980205i	$-0.436559\pi$
$313$	−13.8388	−	13.8388i	−0.782217	−	0.782217i	−0.980205	+	0.197988i	$0.936559\pi$
$314$	−10.3592	+	2.31016i	−0.584604	+	0.130370i
$315$		0			0
$316$	6.99624	−	3.28371i	0.393569	−	0.184723i
$317$			35.0092i			1.96631i	0.182766	+	0.983156i	$0.441495\pi$
$317$			35.0092i			1.96631i	−0.182766	+	0.983156i	$0.558505\pi$
$318$		0			0
$319$	3.78369			0.211846
$320$	16.1659	−	7.65928i	0.903700	−	0.428167i
$321$		0			0
$322$	−0.510383	−	2.28865i	−0.0284425	−	0.127542i
$323$			25.3079i			1.40817i
$324$		0			0
$325$	−3.98617	+	22.2512i	−0.221113	+	1.23428i
$326$	−32.7525	+	7.30401i	−1.81400	+	0.404532i
$327$		0			0
$328$	−10.1950	+	7.88378i	−0.562924	+	0.435309i
$329$	−3.80032			−0.209518
$330$		0			0
$331$	16.8212	+	16.8212i	0.924578	+	0.924578i	0.997349	−	0.0727709i	$-0.0231842\pi$
$331$	16.8212	+	16.8212i	0.924578	+	0.924578i	−0.0727709	+	0.997349i	$0.523184\pi$
$332$	−12.2959	−	26.1975i	−0.674825	−	1.43778i
$333$		0			0
$334$	−0.432188	+	0.680273i	−0.0236483	+	0.0372229i
$335$	−4.77384	−	5.70504i	−0.260823	−	0.311700i
$336$		0			0
$337$	14.4984	+	14.4984i	0.789777	+	0.789777i	0.981457	−	0.191680i	$-0.0613937\pi$
$337$	14.4984	+	14.4984i	0.789777	+	0.789777i	−0.191680	+	0.981457i	$0.561394\pi$
$338$	2.29024	+	10.2699i	0.124573	+	0.558608i
$339$		0			0
$340$	6.78783	+	18.5838i	0.368122	+	1.00785i
$341$	−0.0689618	+	0.0689618i	−0.00373449	+	0.00373449i
$342$		0			0
$343$	−6.23125	+	6.23125i	−0.336456	+	0.336456i
$344$	12.9755	+	16.7794i	0.699593	+	0.904687i
$345$		0			0
$346$	4.75576	+	21.3257i	0.255671	+	1.14648i
$347$			16.7705i			0.900286i	0.892956	+	0.450143i	$0.148627\pi$
$347$			16.7705i			0.900286i	−0.892956	+	0.450143i	$0.851373\pi$
$348$		0			0
$349$	1.86337	−	1.86337i	0.0997439	−	0.0997439i	−0.655474	−	0.755218i	$-0.727531\pi$
$349$	1.86337	−	1.86337i	0.0997439	−	0.0997439i	0.755218	+	0.655474i	$0.227531\pi$
$350$	3.37873	+	3.10525i	0.180601	+	0.165983i
$351$		0			0
$352$	1.20888	+	3.75217i	0.0644333	+	0.199991i
$353$	−24.1362	+	24.1362i	−1.28464	+	1.28464i	−0.346642	+	0.937998i	$0.612678\pi$
$353$	−24.1362	+	24.1362i	−1.28464	+	1.28464i	−0.937998	+	0.346642i	$0.887322\pi$
$354$		0			0
$355$	1.96672	+	2.35035i	0.104382	+	0.124744i
$356$	−6.06537	+	2.84680i	−0.321464	+	0.150880i
$357$		0			0
$358$	5.58171	−	8.78574i	0.295003	−	0.464341i
$359$		−	12.2500i		−	0.646532i	−0.946308	−	0.323266i	$-0.895219\pi$
$359$		−	12.2500i		−	0.646532i	0.946308	−	0.323266i	$-0.104781\pi$
$360$		0			0
$361$			13.7253i			0.722386i
$362$	−15.3438	−	9.74814i	−0.806451	−	0.512351i
$363$		0			0
$364$	5.51926	+	1.99324i	0.289288	+	0.104474i
$365$	−0.713853	+	8.03305i	−0.0373648	+	0.420469i
$366$		0			0
$367$	2.71307	−	2.71307i	0.141621	−	0.141621i	−0.632742	−	0.774363i	$-0.718071\pi$
$367$	2.71307	−	2.71307i	0.141621	−	0.141621i	0.774363	+	0.632742i	$0.218071\pi$
$368$	−0.941567	−	10.1762i	−0.0490826	−	0.530470i
$369$		0			0
$370$	11.2505	−	14.6584i	0.584885	−	0.762054i
$371$	1.26551	−	1.26551i	0.0657018	−	0.0657018i
$372$		0			0
$373$		−	16.4846i		−	0.853541i	−0.904360	−	0.426771i	$-0.859651\pi$
$373$		−	16.4846i		−	0.853541i	0.904360	−	0.426771i	$-0.140349\pi$
$374$	−4.25542	+	0.948984i	−0.220043	+	0.0490708i
$375$		0			0
$376$	−16.4292	−	2.10033i	−0.847272	−	0.108316i
$377$	17.3576	−	17.3576i	0.893964	−	0.893964i
$378$		0			0
$379$	−13.7716	+	13.7716i	−0.707401	+	0.707401i	−0.965988	−	0.258587i	$-0.916743\pi$
$379$	−13.7716	+	13.7716i	−0.707401	+	0.707401i	0.258587	+	0.965988i	$0.416743\pi$
$380$	8.77726	+	24.0305i	0.450264	+	1.23274i
$381$		0			0
$382$	20.8530	−	4.65034i	1.06693	−	0.237932i
$383$	−11.5530	−	11.5530i	−0.590332	−	0.590332i	0.347389	−	0.937721i	$-0.387068\pi$
$383$	−11.5530	−	11.5530i	−0.590332	−	0.590332i	−0.937721	+	0.347389i	$0.887068\pi$
$384$		0			0
$385$	−0.775562	+	0.648972i	−0.0395263	+	0.0330747i
$386$	7.07604	+	4.49552i	0.360161	+	0.228816i
$387$		0			0
$388$	13.1838	+	4.76123i	0.669305	+	0.241715i
$389$	15.7728	+	15.7728i	0.799712	+	0.799712i	0.983050	−	0.183338i	$-0.0586903\pi$
$389$	15.7728	+	15.7728i	0.799712	+	0.799712i	−0.183338	+	0.983050i	$0.558690\pi$
$390$		0			0
$391$	11.3029			0.571612
$392$	−14.7200	+	11.3829i	−0.743470	+	0.574925i
$393$		0			0
$394$	1.24107	+	5.56517i	0.0625240	+	0.280369i
$395$	5.54512	+	6.62677i	0.279006	+	0.333429i
$396$		0			0
$397$			29.9558i			1.50344i	0.659483	+	0.751720i	$0.270775\pi$
$397$			29.9558i			1.50344i	−0.659483	+	0.751720i	$0.729225\pi$
$398$	7.49583	−	1.67161i	0.375732	−	0.0837904i
$399$		0			0
$400$	12.8905	+	15.2917i	0.644523	+	0.764585i
$401$	−19.9241			−0.994963			−0.497481	−	0.867475i	$-0.665742\pi$
$401$	−19.9241			−0.994963			−0.497481	+	0.867475i	$0.665742\pi$
$402$		0			0
$403$			0.632724i			0.0315182i
$404$	−1.77291	+	4.90915i	−0.0882054	+	0.244239i
$405$		0			0
$406$	−1.08463	−	4.86369i	−0.0538294	−	0.241381i
$407$	2.87936	+	2.87936i	0.142725	+	0.142725i
$408$		0			0
$409$	5.89856			0.291665			0.145832	−	0.989309i	$-0.453414\pi$
$409$	5.89856			0.291665			0.145832	+	0.989309i	$0.453414\pi$
$410$	−11.4303	−	8.77287i	−0.564502	−	0.433261i
$411$		0			0
$412$	11.2075	−	31.0333i	0.552152	−	1.52890i
$413$	−3.32717			−0.163720
$414$		0			0
$415$	24.8141	−	20.7638i	1.21808	−	1.01926i
$416$	22.7588	+	11.6674i	1.11584	+	0.572039i
$417$		0			0
$418$	−5.50264	+	1.22712i	−0.269143	+	0.0600204i
$419$	−8.24430	−	8.24430i	−0.402760	−	0.402760i	0.476444	−	0.879205i	$-0.341925\pi$
$419$	−8.24430	−	8.24430i	−0.402760	−	0.402760i	−0.879205	+	0.476444i	$0.841925\pi$
$420$		0			0
$421$	−17.1776	+	17.1776i	−0.837184	+	0.837184i	−0.988487	−	0.151304i	$-0.951653\pi$
$421$	−17.1776	+	17.1776i	−0.837184	+	0.837184i	0.151304	+	0.988487i	$0.451653\pi$
$422$	5.45297	+	3.46436i	0.265447	+	0.168642i
$423$		0			0
$424$	6.17034	−	4.77152i	0.299658	−	0.231725i
$425$	−18.1542	+	12.6380i	−0.880607	+	0.613031i
$426$		0			0
$427$		−	3.42135i		−	0.165571i
$428$	−13.0104	−	27.7198i	−0.628881	−	1.33989i
$429$		0			0
$430$	−14.4388	+	18.8126i	−0.696303	+	0.907222i
$431$			32.1769i			1.54990i	0.632020	+	0.774952i	$0.282226\pi$
$431$			32.1769i			1.54990i	−0.632020	+	0.774952i	$0.717774\pi$
$432$		0			0
$433$	−20.3383	+	20.3383i	−0.977396	+	0.977396i	−0.999750	−	0.0223540i	$-0.992884\pi$
$433$	−20.3383	+	20.3383i	−0.977396	+	0.977396i	0.0223540	+	0.999750i	$0.492884\pi$
$434$	0.108415	+	0.0688775i	0.00520407	+	0.00330623i
$435$		0			0
$436$	−11.9898	+	33.1995i	−0.574206	+	1.58997i
$437$	14.6156			0.699161
$438$		0			0
$439$		−	35.4180i		−	1.69041i	−0.534444	−	0.845204i	$-0.679479\pi$
$439$		−	35.4180i		−	1.69041i	0.534444	−	0.845204i	$-0.320521\pi$
$440$	−3.71151	+	2.37695i	−0.176940	+	0.113317i
$441$		0			0
$442$	−15.1683	+	23.8752i	−0.721481	+	1.13563i
$443$	3.03787			0.144333			0.0721667	−	0.997393i	$-0.477009\pi$
$443$	3.03787			0.144333			0.0721667	+	0.997393i	$0.477009\pi$
$444$		0			0
$445$	−4.80733	−	5.74507i	−0.227890	−	0.272342i
$446$	8.76567	−	13.7974i	0.415067	−	0.653324i
$447$		0			0
$448$	4.47664	−	2.62953i	0.211502	−	0.124234i
$449$			8.65559i			0.408483i	0.978921	+	0.204241i	$0.0654727\pi$
$449$			8.65559i			0.408483i	−0.978921	+	0.204241i	$0.934527\pi$
$450$		0			0
$451$	2.24526	−	2.24526i	0.105725	−	0.105725i
$452$	2.43601	−	6.74527i	0.114580	−	0.317271i
$453$		0			0
$454$	0.474247	+	2.12661i	0.0222575	+	0.0998068i
$455$	−0.580733	+	6.53504i	−0.0272252	+	0.306367i
$456$		0			0
$457$	−13.5575	+	13.5575i	−0.634193	+	0.634193i	−0.949117	−	0.314924i	$-0.898021\pi$
$457$	−13.5575	+	13.5575i	−0.634193	+	0.634193i	0.314924	+	0.949117i	$0.398021\pi$
$458$	18.8379	−	29.6512i	0.880236	−	1.38551i
$459$		0			0
$460$	10.7324	−	3.92006i	0.500401	−	0.182774i
$461$	1.19682	+	1.19682i	0.0557416	+	0.0557416i	0.734428	−	0.678687i	$-0.237450\pi$
$461$	1.19682	+	1.19682i	0.0557416	+	0.0557416i	−0.678687	+	0.734428i	$0.737450\pi$
$462$		0			0
$463$	−21.1815	−	21.1815i	−0.984390	−	0.984390i	0.0154904	−	0.999880i	$-0.495069\pi$
$463$	−21.1815	−	21.1815i	−0.984390	−	0.984390i	−0.999880	+	0.0154904i	$0.995069\pi$
$464$	−2.00096	−	21.6258i	−0.0928921	−	1.00395i
$465$		0			0
$466$	10.7144	−	16.8647i	0.496334	−	0.781241i
$467$	−24.8448			−1.14968			−0.574840	−	0.818266i	$-0.694936\pi$
$467$	−24.8448			−1.14968			−0.574840	+	0.818266i	$0.694936\pi$
$468$		0			0
$469$	−1.52664	−	1.52664i	−0.0704936	−	0.0704936i
$470$	−2.41494	−	18.3598i	−0.111393	−	0.846873i
$471$		0			0
$472$	−14.3838	−	1.83884i	−0.662066	−	0.0846394i
$473$	−3.69537	−	3.69537i	−0.169913	−	0.169913i
$474$		0			0
$475$	−23.4749	+	16.3420i	−1.07710	+	0.749822i
$476$	2.43972	+	5.19804i	0.111824	+	0.238252i
$477$		0			0
$478$	−8.08825	−	36.2692i	−0.369948	−	1.65892i
$479$	23.5766			1.07724			0.538621	−	0.842548i	$-0.318946\pi$
$479$	23.5766			1.07724			0.538621	+	0.842548i	$0.318946\pi$
$480$		0			0
$481$	26.4181			1.20456
$482$	−0.0348578	−	0.156309i	−0.00158773	−	0.00711967i
$483$		0			0
$484$	8.93472	+	19.0362i	0.406124	+	0.865284i
$485$	−1.38719	+	15.6102i	−0.0629891	+	0.708821i
$486$		0			0
$487$	−2.63011	−	2.63011i	−0.119182	−	0.119182i	0.645001	−	0.764182i	$-0.276857\pi$
$487$	−2.63011	−	2.63011i	−0.119182	−	0.119182i	−0.764182	+	0.645001i	$0.776857\pi$
$488$	1.89089	−	14.7909i	0.0855964	−	0.669552i
$489$		0			0
$490$	−16.5035	−	12.6666i	−0.745553	−	0.572221i
$491$	18.6899	+	18.6899i	0.843465	+	0.843465i	0.989308	−	0.145843i	$-0.0465894\pi$
$491$	18.6899	+	18.6899i	0.843465	+	0.843465i	−0.145843	+	0.989308i	$0.546589\pi$
$492$		0			0
$493$	24.0202			1.08182
$494$	−19.6139	+	30.8727i	−0.882472	+	1.38903i
$495$		0			0
$496$	0.430623	+	0.357683i	0.0193355	+	0.0160605i
$497$	0.628940	+	0.628940i	0.0282118	+	0.0282118i
$498$		0			0
$499$	−9.69342	−	9.69342i	−0.433937	−	0.433937i	0.456028	−	0.889965i	$-0.349272\pi$
$499$	−9.69342	−	9.69342i	−0.433937	−	0.433937i	−0.889965	+	0.456028i	$0.849272\pi$
$500$	−12.8548	+	18.2963i	−0.574884	+	0.818235i
$501$		0			0
$502$	20.6154	−	32.4491i	0.920110	−	1.44827i
$503$	13.0434	−	13.0434i	0.581577	−	0.581577i	−0.353759	−	0.935336i	$-0.615097\pi$
$503$	13.0434	−	13.0434i	0.581577	−	0.581577i	0.935336	+	0.353759i	$0.115097\pi$
$504$		0			0
$505$	−5.81265	−	0.516538i	−0.258659	−	0.0229856i
$506$	0.548051	+	2.45756i	0.0243638	+	0.109252i
$507$		0			0
$508$	0.591611	−	1.63816i	0.0262485	−	0.0726817i
$509$	25.8539	−	25.8539i	1.14595	−	1.14595i	0.158611	−	0.987341i	$-0.449298\pi$
$509$	25.8539	−	25.8539i	1.14595	−	1.14595i	0.987341	−	0.158611i	$-0.0507016\pi$
$510$		0			0
$511$			2.34062i			0.103543i
$512$	20.8063	−	8.89365i	0.919518	−	0.393047i
$513$		0			0
$514$	−0.812734	+	1.27926i	−0.0358481	+	0.0564258i
$515$	36.7448	+	3.26531i	1.61917	+	0.143887i
$516$		0			0
$517$	4.08080			0.179473
$518$	2.87584	−	4.52664i	0.126357	−	0.198889i
$519$		0			0
$520$	−6.12232	+	27.9308i	−0.268481	+	1.22485i
$521$		−	25.0528i		−	1.09758i	−0.835959	−	0.548792i	$-0.815088\pi$
$521$		−	25.0528i		−	1.09758i	0.835959	−	0.548792i	$-0.184912\pi$
$522$		0			0
$523$	40.3434			1.76410			0.882048	−	0.471160i	$-0.156165\pi$
$523$	40.3434			1.76410			0.882048	+	0.471160i	$0.156165\pi$
$524$	9.17898	−	25.4165i	0.400986	−	1.11032i
$525$		0			0
$526$	−9.67325	−	6.14556i	−0.421774	−	0.267959i
$527$	−0.437794	+	0.437794i	−0.0190706	+	0.0190706i
$528$		0			0
$529$			16.4724i			0.716192i
$530$	6.91798	+	5.30963i	0.300498	+	0.230636i
$531$		0			0
$532$	3.15477	+	6.72153i	0.136777	+	0.291415i
$533$		−	20.6003i		−	0.892296i
$534$		0			0
$535$	26.2560	−	21.9704i	1.13515	−	0.949862i
$536$	−5.75610	−	7.44356i	−0.248626	−	0.321513i
$537$		0			0
$538$	−16.5247	−	10.4984i	−0.712430	−	0.452618i
$539$	3.24180	−	3.24180i	0.139634	−	0.139634i
$540$		0			0
$541$	−24.7446	−	24.7446i	−1.06385	−	1.06385i	−0.997817	−	0.0660360i	$-0.978965\pi$
$541$	−24.7446	−	24.7446i	−1.06385	−	1.06385i	−0.0660360	−	0.997817i	$-0.521035\pi$
$542$	−5.66146	+	1.26254i	−0.243181	+	0.0542307i
$543$		0			0
$544$	7.67437	+	23.8201i	0.329036	+	1.02128i
$545$	−39.3097	−	3.49324i	−1.68384	−	0.149634i
$546$		0			0
$547$	19.0254			0.813465			0.406733	−	0.913547i	$-0.366668\pi$
$547$	19.0254			0.813465			0.406733	+	0.913547i	$0.366668\pi$
$548$	−3.55738	+	9.85034i	−0.151964	+	0.420786i
$549$		0			0
$550$	−3.62809	−	3.33444i	−0.154702	−	0.142181i
$551$	31.0602			1.32321
$552$		0			0
$553$	1.77329	+	1.77329i	0.0754079	+	0.0754079i
$554$	7.59554	+	34.0598i	0.322704	+	1.44706i
$555$		0			0
$556$	−5.25292	+	14.5453i	−0.222773	+	0.616856i
$557$		−	30.9517i		−	1.31146i	−0.754993	−	0.655732i	$-0.772360\pi$
$557$		−	30.9517i		−	1.31146i	0.754993	−	0.655732i	$-0.227640\pi$
$558$		0			0
$559$	−33.9050			−1.43403
$560$	4.11936	+	4.08954i	0.174075	+	0.172815i
$561$		0			0
$562$	−32.6702	+	7.28565i	−1.37811	+	0.307327i
$563$			3.50238i			0.147608i	0.997273	+	0.0738039i	$0.0235139\pi$
$563$			3.50238i			0.147608i	−0.997273	+	0.0738039i	$0.976486\pi$
$564$		0			0
$565$	7.98670	+	0.709734i	0.336003	+	0.0298587i
$566$	4.01676	+	18.0119i	0.168837	+	0.757097i
$567$		0			0
$568$	2.37138	+	3.06658i	0.0995011	+	0.128671i
$569$	0.525780			0.0220418			0.0110209	−	0.999939i	$-0.496492\pi$
$569$	0.525780			0.0220418			0.0110209	+	0.999939i	$0.496492\pi$
$570$		0			0
$571$	−11.2487	−	11.2487i	−0.470743	−	0.470743i	0.431412	−	0.902155i	$-0.358016\pi$
$571$	−11.2487	−	11.2487i	−0.470743	−	0.470743i	−0.902155	+	0.431412i	$0.858016\pi$
$572$	−5.92660	−	2.14035i	−0.247804	−	0.0894926i
$573$		0			0
$574$	−3.52977	−	2.24252i	−0.147330	−	0.0936008i
$575$	7.29859	+	10.4843i	0.304372	+	0.437224i
$576$		0			0
$577$	−2.92884	−	2.92884i	−0.121929	−	0.121929i	0.643509	−	0.765438i	$-0.277478\pi$
$577$	−2.92884	−	2.92884i	−0.121929	−	0.121929i	−0.765438	+	0.643509i	$0.777478\pi$
$578$	−3.54971	+	0.791607i	−0.147649	+	0.0329265i
$579$		0			0
$580$	22.8078	−	8.33065i	0.947043	−	0.345912i
$581$	6.64011	−	6.64011i	0.275478	−	0.275478i
$582$		0			0
$583$	−1.35891	+	1.35891i	−0.0562801	+	0.0562801i
$584$	−1.29360	+	10.1188i	−0.0535295	+	0.418718i
$585$		0			0
$586$	43.7186	−	9.74951i	1.80600	−	0.402748i
$587$		−	23.1574i		−	0.955809i	−0.878412	−	0.477905i	$-0.841396\pi$
$587$		−	23.1574i		−	0.955809i	0.878412	−	0.477905i	$-0.158604\pi$
$588$		0			0
$589$	−0.566106	+	0.566106i	−0.0233260	+	0.0233260i
$590$	−2.11428	−	16.0740i	−0.0870436	−	0.661754i
$591$		0			0
$592$	14.9343	−	17.9798i	0.613798	−	0.738964i
$593$	13.9325	−	13.9325i	0.572141	−	0.572141i	−0.360585	−	0.932726i	$-0.617423\pi$
$593$	13.9325	−	13.9325i	0.572141	−	0.572141i	0.932726	+	0.360585i	$0.117423\pi$
$594$		0			0
$595$	−4.92354	+	4.11990i	−0.201846	+	0.168900i
$596$	11.2146	+	4.05008i	0.459368	+	0.165898i
$597$		0			0
$598$	13.7882	+	8.75988i	0.563843	+	0.358218i
$599$		−	33.5311i		−	1.37004i	−0.728523	−	0.685021i	$-0.759793\pi$
$599$		−	33.5311i		−	1.37004i	0.728523	−	0.685021i	$-0.240207\pi$
$600$		0			0
$601$		−	19.4164i		−	0.792011i	−0.918248	−	0.396005i	$-0.870396\pi$
$601$		−	19.4164i		−	0.792011i	0.918248	−	0.396005i	$-0.129604\pi$
$602$	−3.69085	+	5.80948i	−0.150428	+	0.236777i
$603$		0			0
$604$	−22.5256	+	10.5725i	−0.916554	+	0.430187i
$605$	−18.0310	+	15.0879i	−0.733063	+	0.613409i
$606$		0			0
$607$	−9.51495	+	9.51495i	−0.386200	+	0.386200i	−0.873330	−	0.487130i	$-0.838044\pi$
$607$	−9.51495	+	9.51495i	−0.386200	+	0.386200i	0.487130	+	0.873330i	$0.338044\pi$
$608$	9.92363	+	30.8015i	0.402456	+	1.24917i
$609$		0			0
$610$	16.5289	−	2.17412i	0.669236	−	0.0880277i
$611$	18.7206	−	18.7206i	0.757355	−	0.757355i
$612$		0			0
$613$			9.37947i			0.378833i	0.981897	+	0.189417i	$0.0606597\pi$
$613$			9.37947i			0.378833i	−0.981897	+	0.189417i	$0.939340\pi$
$614$	−8.42177	−	37.7648i	−0.339875	−	1.52406i
$615$		0			0
$616$	−1.01190	+	0.782503i	−0.0407707	+	0.0315280i
$617$	3.54768	−	3.54768i	0.142824	−	0.142824i	−0.632079	−	0.774904i	$-0.717798\pi$
$617$	3.54768	−	3.54768i	0.142824	−	0.142824i	0.774904	+	0.632079i	$0.217798\pi$
$618$		0			0
$619$	24.6158	−	24.6158i	0.989392	−	0.989392i	−0.0105527	−	0.999944i	$-0.503359\pi$
$619$	24.6158	−	24.6158i	0.989392	−	0.989392i	0.999944	+	0.0105527i	$0.00335910\pi$
$620$	−0.263862	+	0.567533i	−0.0105970	+	0.0227927i
$621$		0			0
$622$	4.86585	+	21.8194i	0.195103	+	0.874877i
$623$	−1.53735	−	1.53735i	−0.0615926	−	0.0615926i
$624$		0			0
$625$	−23.4453	−	8.67867i	−0.937811	−	0.347147i
$626$	14.8420	−	23.3617i	0.593206	−	0.933720i
$627$		0			0
$628$	−6.37747	−	13.5878i	−0.254489	−	0.542211i
$629$	18.2792	+	18.2792i	0.728840	+	0.728840i
$630$		0			0
$631$	−28.8921			−1.15018			−0.575088	−	0.818092i	$-0.695032\pi$
$631$	−28.8921			−1.15018			−0.575088	+	0.818092i	$0.695032\pi$
$632$	6.68608	+	8.64618i	0.265958	+	0.343927i
$633$		0			0
$634$	−48.3235	+	10.7764i	−1.91917	+	0.427986i
$635$	1.93966	+	0.172367i	0.0769729	+	0.00684016i
$636$		0			0
$637$		−	29.7435i		−	1.17848i
$638$	1.16468	+	5.22265i	0.0461102	+	0.206767i
$639$		0			0
$640$	15.5483	+	19.9562i	0.614600	+	0.788839i
$641$	16.6914			0.659271			0.329636	−	0.944108i	$-0.393074\pi$
$641$	16.6914			0.659271			0.329636	+	0.944108i	$0.393074\pi$
$642$		0			0
$643$			5.22468i			0.206041i	0.994679	+	0.103021i	$0.0328507\pi$
$643$			5.22468i			0.206041i	−0.994679	+	0.103021i	$0.967149\pi$
$644$	3.00194	−	1.40897i	0.118293	−	0.0555212i
$645$		0			0
$646$	−34.9327	+	7.79019i	−1.37441	+	0.306501i
$647$	−21.6797	−	21.6797i	−0.852318	−	0.852318i	0.138100	−	0.990418i	$-0.455900\pi$
$647$	−21.6797	−	21.6797i	−0.852318	−	0.852318i	−0.990418	+	0.138100i	$0.955900\pi$
$648$		0			0
$649$	3.57273			0.140242
$650$	−31.9406	+	1.34716i	−1.25281	+	0.0528399i
$651$		0			0
$652$	−20.1636	−	42.9603i	−0.789666	−	1.68245i
$653$	−22.7642			−0.890833			−0.445417	−	0.895323i	$-0.646944\pi$
$653$	−22.7642			−0.890833			−0.445417	+	0.895323i	$0.646944\pi$
$654$		0			0
$655$	30.0942	+	2.67431i	1.17588	+	0.104494i
$656$	−14.0202	−	11.6455i	−0.547398	−	0.454679i
$657$		0			0
$658$	−1.16980	−	5.24560i	−0.0456036	−	0.204495i
$659$	1.66201	+	1.66201i	0.0647427	+	0.0647427i	0.738737	−	0.673994i	$-0.235423\pi$
$659$	1.66201	+	1.66201i	0.0647427	+	0.0647427i	−0.673994	+	0.738737i	$0.735423\pi$
$660$		0			0
$661$	−5.62818	+	5.62818i	−0.218911	+	0.218911i	−0.808039	−	0.589129i	$-0.799471\pi$
$661$	−5.62818	+	5.62818i	−0.218911	+	0.218911i	0.589129	+	0.808039i	$0.299471\pi$
$662$	−18.0406	+	28.3963i	−0.701168	+	1.10365i
$663$		0			0
$664$	32.3758	−	25.0362i	1.25642	−	0.971591i
$665$	−6.36657	+	5.32739i	−0.246885	+	0.206587i
$666$		0			0
$667$		−	13.8720i		−	0.537125i
$668$	−1.07202	−	0.387153i	−0.0414777	−	0.0149794i
$669$		0			0
$670$	6.40525	−	8.34548i	0.247456	−	0.322414i
$671$			3.67386i			0.141828i
$672$		0			0
$673$	0.278251	−	0.278251i	0.0107258	−	0.0107258i	−0.701724	−	0.712449i	$-0.747586\pi$
$673$	0.278251	−	0.278251i	0.0107258	−	0.0107258i	0.712449	+	0.701724i	$0.247586\pi$
$674$	−15.5494	+	24.4751i	−0.598940	+	0.942744i
$675$		0			0
$676$	−13.4706	+	6.32248i	−0.518101	+	0.243172i
$677$	−26.3591			−1.01306			−0.506531	−	0.862222i	$-0.669072\pi$
$677$	−26.3591			−1.01306			−0.506531	+	0.862222i	$0.669072\pi$
$678$		0			0
$679$			4.54840i			0.174551i
$680$	−23.5620	+	15.0897i	−0.903562	+	0.578664i
$681$		0			0
$682$	−0.116416	−	0.0739609i	−0.00445780	−	0.00283211i
$683$	2.83023			0.108296			0.0541479	−	0.998533i	$-0.482756\pi$
$683$	2.83023			0.108296			0.0541479	+	0.998533i	$0.482756\pi$
$684$		0			0
$685$	−11.6632	−	1.03645i	−0.445629	−	0.0396006i
$686$	−10.5191	−	6.68296i	−0.401622	−	0.255157i
$687$		0			0
$688$	−19.1667	+	23.0752i	−0.730724	+	0.879734i
$689$			12.4679i			0.474991i
$690$		0			0
$691$	22.1815	−	22.1815i	0.843825	−	0.843825i	−0.145529	−	0.989354i	$-0.546488\pi$
$691$	22.1815	−	22.1815i	0.843825	−	0.843825i	0.989354	+	0.145529i	$0.0464884\pi$
$692$	−27.9721	+	13.1288i	−1.06334	+	0.499083i
$693$		0			0
$694$	−23.1484	+	5.16223i	−0.878702	+	0.195956i
$695$	−17.2222	−	1.53044i	−0.653276	−	0.0580531i
$696$		0			0
$697$	14.2537	−	14.2537i	0.539898	−	0.539898i
$698$	3.14560	+	1.99845i	0.119063	+	0.0756423i
$699$		0			0
$700$	−3.24618	+	5.61953i	−0.122694	+	0.212398i
$701$	−16.2264	−	16.2264i	−0.612864	−	0.612864i	0.330828	−	0.943691i	$-0.392672\pi$
$701$	−16.2264	−	16.2264i	−0.612864	−	0.612864i	−0.943691	+	0.330828i	$0.892672\pi$
$702$		0			0
$703$	23.6366	+	23.6366i	0.891472	+	0.891472i
$704$	−4.80704	+	2.82360i	−0.181172	+	0.106418i
$705$		0			0
$706$	−40.7449	−	25.8858i	−1.53345	−	0.974226i
$707$	−1.69365			−0.0636965
$708$		0			0
$709$	25.3577	+	25.3577i	0.952329	+	0.952329i	0.998914	−	0.0465856i	$-0.0148340\pi$
$709$	25.3577	+	25.3577i	0.952329	+	0.952329i	−0.0465856	+	0.998914i	$0.514834\pi$
$710$	−2.63882	+	3.43815i	−0.0990331	+	0.129031i
$711$		0			0
$712$	−5.79648	−	7.49579i	−0.217232	−	0.280916i
$713$	0.252832	+	0.252832i	0.00946863	+	0.00946863i
$714$		0			0
$715$	0.623594	−	7.01735i	0.0233211	−	0.262434i
$716$	13.8452	+	5.00009i	0.517418	+	0.186862i
$717$		0			0
$718$	16.9088	−	3.77076i	0.631031	−	0.140724i
$719$	−41.3374			−1.54163			−0.770813	−	0.637061i	$-0.780150\pi$
$719$	−41.3374			−1.54163			−0.770813	+	0.637061i	$0.780150\pi$
$720$		0			0
$721$	10.7065			0.398730
$722$	−18.9452	+	4.22489i	−0.705067	+	0.157234i
$723$		0			0
$724$	8.73236	−	24.1798i	0.324536	−	0.898635i
$725$	15.5105	+	22.2805i	0.576045	+	0.827477i
$726$		0			0
$727$	−23.4630	−	23.4630i	−0.870193	−	0.870193i	0.122300	−	0.992493i	$-0.460973\pi$
$727$	−23.4630	−	23.4630i	−0.870193	−	0.870193i	−0.992493	+	0.122300i	$0.960973\pi$
$728$	−1.05237	+	8.23182i	−0.0390033	+	0.305092i
$729$		0			0
$730$	−11.3078	+	1.48737i	−0.418521	+	0.0550500i
$731$	−23.4595	−	23.4595i	−0.867681	−	0.867681i
$732$		0			0
$733$	−15.1628			−0.560051			−0.280025	−	0.959993i	$-0.590343\pi$
$733$	−15.1628			−0.560051			−0.280025	+	0.959993i	$0.590343\pi$
$734$	4.58000	+	2.90975i	0.169051	+	0.107401i
$735$		0			0
$736$	13.7564	−	4.43205i	0.507069	−	0.163368i
$737$	1.63931	+	1.63931i	0.0603848	+	0.0603848i
$738$		0			0
$739$	−0.974343	−	0.974343i	−0.0358418	−	0.0358418i	0.688959	−	0.724801i	$-0.258068\pi$
$739$	−0.974343	−	0.974343i	−0.0358418	−	0.0358418i	−0.724801	+	0.688959i	$0.758068\pi$
$740$	23.6962	+	11.0170i	0.871089	+	0.404994i
$741$		0			0
$742$	2.13633	+	1.35724i	0.0784272	+	0.0498260i
$743$	−29.0897	+	29.0897i	−1.06720	+	1.06720i	−0.0696259	+	0.997573i	$0.522181\pi$
$743$	−29.0897	+	29.0897i	−1.06720	+	1.06720i	−0.997573	+	0.0696259i	$0.977819\pi$
$744$		0			0
$745$	−1.18000	+	13.2786i	−0.0432317	+	0.486490i
$746$	22.7538	−	5.07424i	0.833078	−	0.185781i
$747$		0			0
$748$	−2.61978	−	5.58168i	−0.0957887	−	0.204087i
$749$	7.02596	−	7.02596i	0.256723	−	0.256723i
$750$		0			0
$751$		−	7.77705i		−	0.283789i	−0.989882	−	0.141894i	$-0.954681\pi$
$751$		−	7.77705i		−	0.283789i	0.989882	−	0.141894i	$-0.0453193\pi$
$752$	−2.15808	−	23.3239i	−0.0786970	−	0.850534i
$753$		0			0
$754$	29.3019	+	18.6159i	1.06711	+	0.677952i
$755$	−17.8535	−	21.3361i	−0.649755	−	0.776498i
$756$		0			0
$757$	1.42073			0.0516372			0.0258186	−	0.999667i	$-0.491781\pi$
$757$	1.42073			0.0516372			0.0258186	+	0.999667i	$0.491781\pi$
$758$	−23.2482	−	14.7699i	−0.844413	−	0.536469i
$759$		0			0
$760$	−30.4677	+	19.5123i	−1.10518	+	0.707786i
$761$			26.6737i			0.966921i	0.875366	+	0.483460i	$0.160620\pi$
$761$			26.6737i			0.966921i	−0.875366	+	0.483460i	$0.839380\pi$
$762$		0			0
$763$	−11.4538			−0.414656
$764$	12.8378	+	27.3521i	0.464456	+	0.989565i
$765$		0			0
$766$	12.3905	−	19.5029i	0.447687	−	0.704669i
$767$	16.3899	−	16.3899i	0.591805	−	0.591805i
$768$		0			0
$769$			45.8210i			1.65235i	0.563415	+	0.826174i	$0.309487\pi$
$769$			45.8210i			1.65235i	−0.563415	+	0.826174i	$0.690513\pi$
$770$	−1.13451	−	0.870750i	−0.0408850	−	0.0313797i
$771$		0			0
$772$	−4.02707	+	11.1509i	−0.144937	+	0.401330i
$773$		−	18.5473i		−	0.667101i	−0.942732	−	0.333550i	$-0.891753\pi$
$773$		−	18.5473i		−	0.667101i	0.942732	−	0.333550i	$-0.108247\pi$
$774$		0			0
$775$	−0.688782	−	0.123391i	−0.0247418	−	0.00443233i
$776$	−2.51378	+	19.6633i	−0.0902393	+	0.705870i
$777$		0			0
$778$	−16.9162	+	26.6264i	−0.606474	+	0.954603i
$779$	18.4313	−	18.4313i	0.660370	−	0.660370i
$780$		0			0
$781$	−0.675359	−	0.675359i	−0.0241662	−	0.0241662i
$782$	3.47922	+	15.6015i	0.124417	+	0.557908i
$783$		0			0
$784$	−20.2430	−	16.8142i	−0.722964	−	0.600508i
$785$	12.8702	−	10.7695i	0.459358	−	0.384380i
$786$		0			0
$787$	−21.3016			−0.759319			−0.379659	−	0.925126i	$-0.623959\pi$
$787$	−21.3016			−0.759319			−0.379659	+	0.925126i	$0.623959\pi$
$788$	−7.29963	+	3.42610i	−0.260039	+	0.122050i
$789$		0			0
$790$	−7.44011	+	9.69381i	−0.264707	+	0.344890i
$791$	2.32712			0.0827427
$792$		0			0
$793$	16.8538	+	16.8538i	0.598496	+	0.598496i
$794$	−41.3482	+	9.22090i	−1.46739	+	0.327237i
$795$		0			0
$796$	4.61468	+	9.83200i	0.163563	+	0.348486i
$797$			2.35457i			0.0834033i	0.999130	+	0.0417016i	$0.0132779\pi$
$797$			2.35457i			0.0834033i	−0.999130	+	0.0417016i	$0.986722\pi$
$798$		0			0
$799$	25.9063			0.916500
$800$	−17.1394	+	22.4998i	−0.605968	+	0.795489i
$801$		0			0
$802$	−6.13297	−	27.5014i	−0.216563	−	0.971108i
$803$		−	2.51337i		−	0.0886949i
$804$		0			0
$805$	2.37930	+	2.84341i	0.0838592	+	0.100217i
$806$	−0.873354	+	0.194763i	−0.0307626	+	0.00686023i
$807$		0			0
$808$	−7.32187	−	0.936037i	−0.257582	−	0.0329297i
$809$	23.9476			0.841952			0.420976	−	0.907072i	$-0.361688\pi$
$809$	23.9476			0.841952			0.420976	+	0.907072i	$0.361688\pi$
$810$		0			0
$811$	−1.33006	−	1.33006i	−0.0467048	−	0.0467048i	0.683369	−	0.730073i	$-0.260514\pi$
$811$	−1.33006	−	1.33006i	−0.0467048	−	0.0467048i	−0.730073	+	0.683369i	$0.760514\pi$
$812$	6.37952	−	2.99425i	0.223877	−	0.105078i
$813$		0			0
$814$	−3.08809	+	4.86072i	−0.108238	+	0.170368i
$815$	40.6916	−	34.0498i	1.42537	−	1.19271i
$816$		0			0
$817$	−30.3352	−	30.3352i	−1.06129	−	1.06129i
$818$	1.81567	+	8.14182i	0.0634836	+	0.284672i
$819$		0			0
$820$	8.59083	−	18.4777i	0.300005	−	0.645271i
$821$	−36.4676	+	36.4676i	−1.27273	+	1.27273i	−0.328076	+	0.944651i	$0.606400\pi$
$821$	−36.4676	+	36.4676i	−1.27273	+	1.27273i	−0.944651	+	0.328076i	$0.893600\pi$
$822$		0			0
$823$	26.3978	−	26.3978i	0.920170	−	0.920170i	−0.0768712	−	0.997041i	$-0.524493\pi$
$823$	26.3978	−	26.3978i	0.920170	−	0.920170i	0.997041	+	0.0768712i	$0.0244930\pi$
$824$	46.2853	+	5.91718i	1.61243	+	0.206135i
$825$		0			0
$826$	−1.02416	−	4.59252i	−0.0356351	−	0.159794i
$827$			1.99830i			0.0694878i	0.999396	+	0.0347439i	$0.0110616\pi$
$827$			1.99830i			0.0694878i	−0.999396	+	0.0347439i	$0.988938\pi$
$828$		0			0
$829$	−13.0376	+	13.0376i	−0.452813	+	0.452813i	−0.896287	−	0.443474i	$-0.853746\pi$
$829$	−13.0376	+	13.0376i	−0.452813	+	0.452813i	0.443474	+	0.896287i	$0.353746\pi$
$830$	36.2986	+	27.8596i	1.25994	+	0.967021i
$831$		0			0
$832$	−9.09901	+	35.0055i	−0.315451	+	1.21360i
$833$	20.5801	−	20.5801i	0.713059	−	0.713059i
$834$		0			0
$835$	0.112797	−	1.26932i	0.00390352	−	0.0439266i
$836$	−3.38761	−	7.21760i	−0.117163	−	0.249626i
$837$		0			0
$838$	8.84194	−	13.9174i	0.305440	−	0.480769i
$839$			15.4102i			0.532018i	0.963971	+	0.266009i	$0.0857050\pi$
$839$			15.4102i			0.532018i	−0.963971	+	0.266009i	$0.914295\pi$
$840$		0			0
$841$		−	0.479815i		−	0.0165453i
$842$	−28.9979	−	18.4228i	−0.999333	−	0.634891i
$843$		0			0
$844$	−3.10336	+	8.59317i	−0.106822	+	0.295789i
$845$	−10.6766	−	12.7593i	−0.367287	−	0.438932i
$846$		0			0
$847$	−4.82499	+	4.82499i	−0.165789	+	0.165789i
$848$	8.48550	+	7.04822i	0.291393	+	0.242037i
$849$		0			0
$850$	−23.0324	−	21.1682i	−0.790006	−	0.726062i
$851$	10.5565	−	10.5565i	0.361872	−	0.361872i
$852$		0			0
$853$		−	7.96419i		−	0.272689i	−0.990662	−	0.136344i	$-0.956465\pi$
$853$		−	7.96419i		−	0.272689i	0.990662	−	0.136344i	$-0.0435353\pi$
$854$	4.72251	−	1.05315i	0.161601	−	0.0360380i
$855$		0			0
$856$	34.2571	−	26.4910i	1.17088	−	0.905443i
$857$	−5.35407	+	5.35407i	−0.182891	+	0.182891i	−0.792615	−	0.609723i	$-0.791281\pi$
$857$	−5.35407	+	5.35407i	−0.182891	+	0.182891i	0.609723	+	0.792615i	$0.291281\pi$
$858$		0			0
$859$	35.0058	−	35.0058i	1.19438	−	1.19438i	0.218559	−	0.975824i	$-0.429864\pi$
$859$	35.0058	−	35.0058i	1.19438	−	1.19438i	0.975824	−	0.218559i	$-0.0701355\pi$
$860$	−30.4116	−	14.1392i	−1.03703	−	0.482144i
$861$		0			0
$862$	−44.4140	+	9.90457i	−1.51275	+	0.337351i
$863$	36.7138	+	36.7138i	1.24975	+	1.24975i	0.955829	+	0.293923i	$0.0949610\pi$
$863$	36.7138	+	36.7138i	1.24975	+	1.24975i	0.293923	+	0.955829i	$0.405039\pi$
$864$		0			0
$865$	−22.1703	−	26.4950i	−0.753814	−	0.900856i
$866$	−34.3336	−	21.8126i	−1.16670	−	0.741224i
$867$		0			0
$868$	−0.0617003	+	0.170847i	−0.00209424	+	0.00579893i
$869$	−1.90416	−	1.90416i	−0.0645943	−	0.0645943i
$870$		0			0
$871$	15.0406			0.509633
$872$	−49.5162	−	6.33022i	−1.67683	−	0.214368i
$873$		0			0
$874$	4.49894	+	20.1741i	0.152179	+	0.682399i
$875$	−7.00078	−	1.90662i	−0.236669	−	0.0644555i
$876$		0			0
$877$		−	14.3410i		−	0.484262i	−0.970244	−	0.242131i	$-0.922154\pi$
$877$		−	14.3410i		−	0.484262i	0.970244	−	0.242131i	$-0.0778463\pi$
$878$	48.8877	−	10.9022i	1.64988	−	0.367933i
$879$		0			0
$880$	−4.42338	−	4.39137i	−0.149112	−	0.148033i
$881$	13.6397			0.459533			0.229767	−	0.973246i	$-0.426204\pi$
$881$	13.6397			0.459533			0.229767	+	0.973246i	$0.426204\pi$
$882$		0			0
$883$		−	6.12563i		−	0.206144i	−0.994674	−	0.103072i	$-0.967133\pi$
$883$		−	6.12563i		−	0.206144i	0.994674	−	0.103072i	$-0.0328672\pi$
$884$	−37.6242	−	13.5877i	−1.26544	−	0.457004i
$885$		0			0
$886$	0.935105	+	4.19319i	0.0314155	+	0.140873i
$887$	−25.5187	−	25.5187i	−0.856834	−	0.856834i	0.134130	−	0.990964i	$-0.457176\pi$
$887$	−25.5187	−	25.5187i	−0.856834	−	0.856834i	−0.990964	+	0.134130i	$0.957176\pi$
$888$		0			0
$889$	0.565166			0.0189551
$890$	6.45018	−	8.40403i	0.216211	−	0.281704i
$891$		0			0
$892$	21.7428	+	7.85227i	0.728003	+	0.262913i
$893$	33.4992			1.12101
$894$		0			0
$895$	−1.45678	+	16.3933i	−0.0486948	+	0.547967i
$896$	5.00755	+	5.36973i	0.167290	+	0.179390i
$897$		0			0
$898$	−11.9474	+	2.66433i	−0.398689	+	0.0889100i
$899$	0.537302	+	0.537302i	0.0179200	+	0.0179200i
$900$		0			0
$901$	−8.62682	+	8.62682i	−0.287401	+	0.287401i
$902$	3.79028	+	2.40802i	0.126203	+	0.0801784i
$903$		0			0
$904$	10.0604	+	1.28613i	0.334604	+	0.0427762i
$905$	28.6299	+	2.54418i	0.951691	+	0.0845715i
$906$		0			0
$907$			32.1815i			1.06857i	0.845305	+	0.534284i	$0.179419\pi$
$907$			32.1815i			1.06857i	−0.845305	+	0.534284i	$0.820581\pi$
$908$	−2.78940	+	1.30921i	−0.0925694	+	0.0434477i
$909$		0			0
$910$	−9.19913	+	1.21000i	−0.304948	+	0.0401112i
$911$		−	38.6282i		−	1.27981i	−0.768455	−	0.639904i	$-0.778974\pi$
$911$		−	38.6282i		−	1.27981i	0.768455	−	0.639904i	$-0.221026\pi$
$912$		0			0
$913$	−7.13018	+	7.13018i	−0.235974	+	0.235974i
$914$	−22.8868	−	14.5403i	−0.757027	−	0.480950i
$915$		0			0
$916$	46.7264	+	16.8749i	1.54388	+	0.557563i
$917$	8.76867			0.289567
$918$		0			0
$919$			19.1924i			0.633099i	0.948576	+	0.316550i	$0.102524\pi$
$919$			19.1924i			0.633099i	−0.948576	+	0.316550i	$0.897476\pi$
$920$	8.71450	+	13.6074i	0.287309	+	0.448622i
$921$		0			0
$922$	−1.28358	+	2.02038i	−0.0422725	+	0.0665378i
$923$	−6.19641			−0.203957
$924$		0			0
$925$	−5.15194	+	28.7587i	−0.169395	+	0.945580i
$926$	22.7170	−	35.7571i	0.746527	−	1.17505i
$927$		0			0
$928$	29.2343	−	9.41870i	0.959662	−	0.309184i
$929$			16.8576i			0.553081i	0.961002	+	0.276541i	$0.0891880\pi$
$929$			16.8576i			0.553081i	−0.961002	+	0.276541i	$0.910812\pi$
$930$		0			0
$931$	26.6119	−	26.6119i	0.872170	−	0.872170i
$932$	26.5765	+	9.59792i	0.870542	+	0.314390i
$933$		0			0
$934$	−7.64764	−	34.2935i	−0.250239	−	1.12212i
$935$	5.28692	−	4.42397i	0.172901	−	0.144679i
$936$		0			0
$937$	−23.9511	+	23.9511i	−0.782449	+	0.782449i	−0.980243	−	0.197795i	$-0.936622\pi$
$937$	−23.9511	+	23.9511i	−0.782449	+	0.782449i	0.197795	+	0.980243i	$0.436622\pi$
$938$	1.63730	−	2.57715i	0.0534599	−	0.0841470i
$939$		0			0
$940$	24.5988	−	8.98480i	0.802323	−	0.293052i
$941$	−14.2496	−	14.2496i	−0.464525	−	0.464525i	0.435610	−	0.900135i	$-0.356533\pi$
$941$	−14.2496	−	14.2496i	−0.464525	−	0.464525i	−0.900135	+	0.435610i	$0.856533\pi$
$942$		0			0
$943$	−8.23171	−	8.23171i	−0.268061	−	0.268061i
$944$	−1.88940	−	20.4200i	−0.0614946	−	0.664616i
$945$		0			0
$946$	3.96325	−	6.23824i	0.128856	−	0.202823i
$947$	−20.2943			−0.659477			−0.329738	−	0.944072i	$-0.606961\pi$
$947$	−20.2943			−0.659477			−0.329738	+	0.944072i	$0.606961\pi$
$948$		0			0
$949$	−11.5301	−	11.5301i	−0.374282	−	0.374282i
$950$	−29.7829	−	27.3723i	−0.966286	−	0.888075i
$951$		0			0
$952$	−6.42391	+	4.96761i	−0.208200	+	0.161001i
$953$	10.9257	+	10.9257i	0.353919	+	0.353919i	0.861565	−	0.507647i	$-0.169484\pi$
$953$	10.9257	+	10.9257i	0.353919	+	0.353919i	−0.507647	+	0.861565i	$0.669484\pi$
$954$		0			0
$955$	−25.9077	+	21.6789i	−0.838353	+	0.701514i
$956$	47.5730	−	22.3285i	1.53862	−	0.722157i
$957$		0			0
$958$	7.25726	+	32.5429i	0.234471	+	1.05141i
$959$	−3.39836			−0.109739
$960$		0			0
$961$	30.9804			0.999368
$962$	8.13193	+	36.4651i	0.262184	+	1.17568i
$963$		0			0
$964$	0.205024	−	0.0962289i	0.00660339	−	0.00309932i
$965$	−13.2032	−	1.17329i	−0.425025	−	0.0377696i
$966$		0			0
$967$	10.7569	+	10.7569i	0.345918	+	0.345918i	0.858586	−	0.512669i	$-0.171343\pi$
$967$	10.7569	+	10.7569i	0.345918	+	0.345918i	−0.512669	+	0.858586i	$0.671343\pi$
$968$	−23.5256	+	18.1923i	−0.756142	+	0.584724i
$969$		0			0
$970$	−21.9738	+	2.89032i	−0.705537	+	0.0928025i
$971$	18.7456	+	18.7456i	0.601574	+	0.601574i	0.940730	−	0.339156i	$-0.110142\pi$
$971$	18.7456	+	18.7456i	0.601574	+	0.601574i	−0.339156	+	0.940730i	$0.610142\pi$
$972$		0			0
$973$	−5.01811			−0.160873
$974$	2.82077	−	4.43995i	0.0903832	−	0.142265i
$975$		0			0
$976$	20.9980	−	1.94287i	0.672130	−	0.0621899i
$977$	26.3906	+	26.3906i	0.844309	+	0.844309i	0.989416	−	0.145107i	$-0.0463526\pi$
$977$	26.3906	+	26.3906i	0.844309	+	0.844309i	−0.145107	+	0.989416i	$0.546353\pi$
$978$		0			0
$979$	1.65081	+	1.65081i	0.0527602	+	0.0527602i
$980$	12.4038	−	26.6789i	0.396225	−	0.852228i
$981$		0			0
$982$	−20.0448	+	31.5509i	−0.639655	+	1.00683i
$983$	4.87875	−	4.87875i	0.155608	−	0.155608i	−0.625009	−	0.780617i	$-0.714905\pi$
$983$	4.87875	−	4.87875i	0.155608	−	0.155608i	0.780617	+	0.625009i	$0.214905\pi$
$984$		0			0
$985$	−5.78559	−	6.91415i	−0.184344	−	0.220303i
$986$	7.39381	+	33.1553i	0.235467	+	1.05588i
$987$		0			0
$988$	−48.6513	−	17.5701i	−1.54781	−	0.558979i
$989$	−13.5482	+	13.5482i	−0.430807	+	0.430807i
$990$		0			0
$991$			61.2103i			1.94441i	0.234130	+	0.972205i	$0.424776\pi$
$991$			61.2103i			1.94441i	−0.234130	+	0.972205i	$0.575224\pi$
$992$	−0.361160	+	0.704492i	−0.0114668	+	0.0223677i
$993$		0			0
$994$	−0.674533	+	1.06173i	−0.0213949	+	0.0336760i
$995$	−9.31279	+	7.79271i	−0.295235	+	0.247046i
$996$		0			0
$997$	39.1082			1.23857			0.619284	−	0.785167i	$-0.287423\pi$
$997$	39.1082			1.23857			0.619284	+	0.785167i	$0.287423\pi$
$998$	10.3961	−	16.3637i	0.329083	−	0.517984i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	720.2.bd.g.307.5		18
3.2	odd	2		80.2.j.b.67.5	yes	18
5.3	odd	4		720.2.z.g.163.9		18
12.11	even	2		320.2.j.b.47.9		18
15.2	even	4		400.2.s.d.243.9		18
15.8	even	4		80.2.s.b.3.1	yes	18
15.14	odd	2		400.2.j.d.307.5		18
16.11	odd	4		720.2.z.g.667.9		18
24.5	odd	2		640.2.j.d.607.9		18
24.11	even	2		640.2.j.c.607.1		18
48.5	odd	4		320.2.s.b.207.1		18
48.11	even	4		80.2.s.b.27.1	yes	18
48.29	odd	4		640.2.s.c.287.9		18
48.35	even	4		640.2.s.d.287.1		18
60.23	odd	4		320.2.s.b.303.1		18
60.47	odd	4		1600.2.s.d.943.9		18
60.59	even	2		1600.2.j.d.1007.1		18
80.43	even	4	inner	720.2.bd.g.523.5		18
120.53	even	4		640.2.s.d.223.1		18
120.83	odd	4		640.2.s.c.223.9		18
240.53	even	4		320.2.j.b.143.1		18
240.59	even	4		400.2.s.d.107.9		18
240.83	odd	4		640.2.j.d.543.1		18
240.107	odd	4		400.2.j.d.43.5		18
240.149	odd	4		1600.2.s.d.207.9		18
240.173	even	4		640.2.j.c.543.9		18
240.197	even	4		1600.2.j.d.143.9		18
240.203	odd	4		80.2.j.b.43.5	✓	18

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
80.2.j.b.43.5	✓	18	240.203	odd	4
80.2.j.b.67.5	yes	18	3.2	odd	2
80.2.s.b.3.1	yes	18	15.8	even	4
80.2.s.b.27.1	yes	18	48.11	even	4
320.2.j.b.47.9		18	12.11	even	2
320.2.j.b.143.1		18	240.53	even	4
320.2.s.b.207.1		18	48.5	odd	4
320.2.s.b.303.1		18	60.23	odd	4
400.2.j.d.43.5		18	240.107	odd	4
400.2.j.d.307.5		18	15.14	odd	2
400.2.s.d.107.9		18	240.59	even	4
400.2.s.d.243.9		18	15.2	even	4
640.2.j.c.543.9		18	240.173	even	4
640.2.j.c.607.1		18	24.11	even	2
640.2.j.d.543.1		18	240.83	odd	4
640.2.j.d.607.9		18	24.5	odd	2
640.2.s.c.223.9		18	120.83	odd	4
640.2.s.c.287.9		18	48.29	odd	4
640.2.s.d.223.1		18	120.53	even	4
640.2.s.d.287.1		18	48.35	even	4
720.2.z.g.163.9		18	5.3	odd	4
720.2.z.g.667.9		18	16.11	odd	4
720.2.bd.g.307.5		18	1.1	even	1	trivial
720.2.bd.g.523.5		18	80.43	even	4	inner
1600.2.j.d.143.9		18	240.197	even	4
1600.2.j.d.1007.1		18	60.59	even	2
1600.2.s.d.207.9		18	240.149	odd	4
1600.2.s.d.943.9		18	60.47	odd	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:	\( N \)	\(=\)	\( 720 = 2^{4} \cdot 3^{2} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	720.bd (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.307817 + 1.38031i) q^{2} +(-1.81050 + 0.849763i) q^{4} +(-1.43498 - 1.71489i) q^{5} +(-0.458895 - 0.458895i) q^{7} +(-1.73024 - 2.23747i) q^{8} +(1.92536 - 2.50858i) q^{10} +(0.492763 + 0.492763i) q^{11} +4.52109 q^{13} +(0.492160 - 0.774671i) q^{14} +(2.55581 - 3.07699i) q^{16} +(3.12823 + 3.12823i) q^{17} +(4.04508 + 4.04508i) q^{19} +(4.05527 + 1.88541i) q^{20} +(-0.528484 + 0.831845i) q^{22} +(1.80660 - 1.80660i) q^{23} +(-0.881683 + 4.92165i) q^{25} +(1.39167 + 6.24050i) q^{26} +(1.22078 + 0.440876i) q^{28} +(3.83926 - 3.83926i) q^{29} +0.139949i q^{31} +(5.03391 + 2.58065i) q^{32} +(-3.35500 + 5.28085i) q^{34} +(-0.128450 + 1.44546i) q^{35} +5.84330 q^{37} +(-4.33831 + 6.82860i) q^{38} +(-1.35417 + 6.17788i) q^{40} -4.55648i q^{41} -7.49928 q^{43} +(-1.31088 - 0.473414i) q^{44} +(3.04976 + 1.93756i) q^{46} +(4.14073 - 4.14073i) q^{47} -6.57883i q^{49} +(-7.06479 + 0.297972i) q^{50} +(-8.18543 + 3.84186i) q^{52} +2.75773i q^{53} +(0.137930 - 1.55214i) q^{55} +(-0.232768 + 1.82076i) q^{56} +(6.48115 + 4.11757i) q^{58} +(3.62521 - 3.62521i) q^{59} +(3.72781 + 3.72781i) q^{61} +(-0.193173 + 0.0430787i) q^{62} +(-2.01257 + 7.74271i) q^{64} +(-6.48766 - 7.75317i) q^{65} +3.32677 q^{67} +(-8.32192 - 3.00540i) q^{68} +(-2.03471 + 0.267635i) q^{70} -1.37056 q^{71} +(-2.55028 - 2.55028i) q^{73} +(1.79867 + 8.06556i) q^{74} +(-10.7610 - 3.88625i) q^{76} -0.452252i q^{77} -3.86426 q^{79} +(-8.94421 + 0.0324871i) q^{80} +(6.28934 - 1.40256i) q^{82} +14.4698i q^{83} +(0.875628 - 9.85351i) q^{85} +(-2.30840 - 10.3513i) q^{86} +(0.249948 - 1.95514i) q^{88} +3.35011 q^{89} +(-2.07470 - 2.07470i) q^{91} +(-1.73566 + 4.80602i) q^{92} +(6.99006 + 4.44089i) q^{94} +(1.13226 - 12.7415i) q^{95} +(-4.95582 - 4.95582i) q^{97} +(9.08081 - 2.02507i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 18 q + 4 q^{2} - 4 q^{4} + 4 q^{5} + 2 q^{7} + 4 q^{8} - 12 q^{10} + 2 q^{11} - 12 q^{14} + 6 q^{17} + 2 q^{19} + 4 q^{20} + 4 q^{22} + 2 q^{23} + 6 q^{25} + 16 q^{26} - 4 q^{28} + 14 q^{29} + 4 q^{32}+ \cdots - 32 q^{98}+O(q^{100}) \) 18 * q + 4 * q^2 - 4 * q^4 + 4 * q^5 + 2 * q^7 + 4 * q^8 - 12 * q^10 + 2 * q^11 - 12 * q^14 + 6 * q^17 + 2 * q^19 + 4 * q^20 + 4 * q^22 + 2 * q^23 + 6 * q^25 + 16 * q^26 - 4 * q^28 + 14 * q^29 + 4 * q^32 - 28 * q^34 + 6 * q^35 + 8 * q^37 - 16 * q^38 + 20 * q^40 - 44 * q^43 - 44 * q^44 + 12 * q^46 + 38 * q^47 - 20 * q^50 - 40 * q^52 - 6 * q^55 - 20 * q^56 - 20 * q^58 + 10 * q^59 + 14 * q^61 - 16 * q^64 + 12 * q^67 - 36 * q^68 - 36 * q^70 - 24 * q^71 + 14 * q^73 - 48 * q^74 - 16 * q^76 + 16 * q^79 + 20 * q^80 - 28 * q^82 - 10 * q^85 + 36 * q^86 - 96 * q^88 + 12 * q^89 - 52 * q^92 + 28 * q^94 + 34 * q^95 + 18 * q^97 - 32 * q^98

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