LMFDB - Embedded newform 720.2.bd.g.523.5

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			523.5
Root			$-0.480367 - 1.33013i$ of defining polynomial
Character	$\chi$	$=$	720.523
Dual form			720.2.bd.g.307.5

$q$-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 $\left(\mathbb{Z}/720\mathbb{Z}\right)^\times$.

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

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	−0.788491	−	0.615046i	$-0.789138\pi$
$7$	−0.458895	+	0.458895i	−0.173446	+	0.173446i	0.615046	+	0.788491i	$0.289138\pi$
$8$	−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	−0.628907	−	0.777481i	$-0.716497\pi$
$11$	0.492763	−	0.492763i	0.148574	−	0.148574i	0.777481	+	0.628907i	$0.216497\pi$
$12$		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	−0.217379	−	0.976087i	$-0.569751\pi$
$17$	3.12823	−	3.12823i	0.758708	−	0.758708i	0.976087	+	0.217379i	$0.0697508\pi$
$18$		0			0
$19$	4.04508	−	4.04508i	0.928005	−	0.928005i	−0.0695721	−	0.997577i	$-0.522163\pi$
$19$	4.04508	−	4.04508i	0.928005	−	0.928005i	0.997577	+	0.0695721i	$0.0221634\pi$
$20$	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	0.869911	−	0.493209i	$-0.164176\pi$
$23$	1.80660	+	1.80660i	0.376701	+	0.376701i	−0.493209	+	0.869911i	$0.664176\pi$
$24$		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	0.967148	−	0.254215i	$-0.0818172\pi$
$29$	3.83926	+	3.83926i	0.712932	+	0.712932i	−0.254215	+	0.967148i	$0.581817\pi$
$30$		0			0
$31$		−	0.139949i		−	0.0251356i	−0.999921	−	0.0125678i	$-0.995999\pi$
$31$		−	0.139949i		−	0.0251356i	0.999921	−	0.0125678i	$-0.00400057\pi$
$32$	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	$0.115792\pi$
$41$			4.55648i			0.711602i	−0.934562	+	0.355801i	$0.884208\pi$
$42$		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	0.941368	−	0.337381i	$-0.109541\pi$
$47$	4.14073	+	4.14073i	0.603987	+	0.603987i	−0.337381	+	0.941368i	$0.609541\pi$
$48$		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	$-0.939345\pi$
$53$		−	2.75773i		−	0.378803i	0.981900	−	0.189402i	$-0.0606548\pi$
$54$		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	0.902549	−	0.430587i	$-0.141694\pi$
$59$	3.62521	+	3.62521i	0.471962	+	0.471962i	−0.430587	+	0.902549i	$0.641694\pi$
$60$		0			0
$61$	3.72781	−	3.72781i	0.477298	−	0.477298i	−0.426969	−	0.904266i	$-0.640419\pi$
$61$	3.72781	−	3.72781i	0.477298	−	0.477298i	0.904266	+	0.426969i	$0.140419\pi$
$62$	−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	−0.840422	−	0.541933i	$-0.817693\pi$
$73$	−2.55028	+	2.55028i	−0.298488	+	0.298488i	0.541933	+	0.840422i	$0.317693\pi$
$74$	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	$-0.707925\pi$
$83$		−	14.4698i		−	1.58827i	0.607744	−	0.794133i	$-0.292075\pi$
$84$		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	−0.912427	−	0.409240i	$-0.865794\pi$
$97$	−4.95582	+	4.95582i	−0.503187	+	0.503187i	0.409240	+	0.912427i	$0.365794\pi$
$98$	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	0.792931	−	0.609311i	$-0.208554\pi$
$101$	1.84536	+	1.84536i	0.183621	+	0.183621i	−0.609311	+	0.792931i	$0.708554\pi$
$102$		0			0
$103$	−11.6655	−	11.6655i	−1.14944	−	1.14944i	−0.986664	−	0.162773i	$-0.947956\pi$
$103$	−11.6655	−	11.6655i	−1.14944	−	1.14944i	−0.162773	−	0.986664i	$-0.552044\pi$
$104$	−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	$-0.734794\pi$
$107$		−	15.3106i		−	1.48013i	0.672534	−	0.740067i	$-0.265206\pi$
$108$		0			0
$109$	12.4798	+	12.4798i	1.19535	+	1.19535i	0.975544	+	0.219803i	$0.0705416\pi$
$109$	12.4798	+	12.4798i	1.19535	+	1.19535i	0.219803	+	0.975544i	$0.429458\pi$
$110$	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	0.577713	−	0.816240i	$-0.303945\pi$
$113$	−2.53557	−	2.53557i	−0.238526	−	0.238526i	−0.816240	+	0.577713i	$0.803945\pi$
$114$		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	0.679257	−	0.733900i	$-0.262302\pi$
$127$	−0.615790	−	0.615790i	−0.0546426	−	0.0546426i	−0.733900	+	0.679257i	$0.762302\pi$
$128$	−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	0.153414	−	0.988162i	$-0.450973\pi$
$131$	−9.55413	−	9.55413i	−0.834748	−	0.834748i	−0.988162	+	0.153414i	$0.950973\pi$
$132$		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	0.847363	−	0.531014i	$-0.178189\pi$
$137$	3.70277	+	3.70277i	0.316349	+	0.316349i	−0.531014	+	0.847363i	$0.678189\pi$
$138$		0			0
$139$	5.46761	+	5.46761i	0.463756	+	0.463756i	0.899885	−	0.436128i	$-0.143651\pi$
$139$	5.46761	+	5.46761i	0.463756	+	0.463756i	−0.436128	+	0.899885i	$0.643651\pi$
$140$	−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	−0.858376	−	0.513021i	$-0.828526\pi$
$149$	−4.21561	+	4.21561i	−0.345356	+	0.345356i	0.513021	+	0.858376i	$0.328526\pi$
$150$		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	$-0.903186\pi$
$157$		−	7.50500i		−	0.598964i	0.954102	−	0.299482i	$-0.0968138\pi$
$158$	−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	$-0.620431\pi$
$163$		−	23.7284i		−	1.85855i	0.369383	−	0.929277i	$-0.379569\pi$
$164$	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	−0.691343	−	0.722526i	$-0.742981\pi$
$167$	0.402976	−	0.402976i	0.0311832	−	0.0311832i	0.722526	+	0.691343i	$0.242981\pi$
$168$		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	−0.874330	−	0.485332i	$-0.838699\pi$
$179$	−5.20444	+	5.20444i	−0.388998	+	0.388998i	0.485332	+	0.874330i	$0.338699\pi$
$180$		0			0
$181$	−9.08925	−	9.08925i	−0.675599	−	0.675599i	0.283402	−	0.959001i	$-0.408537\pi$
$181$	−9.08925	−	9.08925i	−0.675599	−	0.675599i	−0.959001	+	0.283402i	$0.908537\pi$
$182$	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	$0.184067\pi$
$191$			15.1075i			1.09314i	−0.837413	+	0.546571i	$0.815933\pi$
$192$		0			0
$193$	4.19166	+	4.19166i	0.301722	+	0.301722i	0.841687	−	0.539965i	$-0.181563\pi$
$193$	4.19166	+	4.19166i	0.301722	+	0.301722i	−0.539965	+	0.841687i	$0.681563\pi$
$194$	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	$0.0616533\pi$
$199$			5.43055i			0.384961i	−0.981301	+	0.192481i	$0.938347\pi$
$200$	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	0.809498	−	0.587122i	$-0.199739\pi$
$211$	3.23020	+	3.23020i	0.222376	+	0.222376i	−0.587122	+	0.809498i	$0.699739\pi$
$212$	−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	−0.925664	−	0.378347i	$-0.876493\pi$
$223$	−8.17319	+	8.17319i	−0.547317	+	0.547317i	0.378347	+	0.925664i	$0.376493\pi$
$224$	−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	−0.176378	+	0.984322i	$0.556438\pi$
$229$	−17.5646	+	17.5646i	−1.16070	+	1.16070i	−0.984322	+	0.176378i	$0.943562\pi$
$230$	−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	−0.954068	−	0.299590i	$-0.903150\pi$
$233$	−9.99018	+	9.99018i	−0.654479	+	0.654479i	0.299590	+	0.954068i	$0.403150\pi$
$234$		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	−0.243339	+	0.969941i	$0.578243\pi$
$251$	−19.2220	+	19.2220i	−1.21328	+	1.21328i	−0.969941	+	0.243339i	$0.921757\pi$
$252$		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	−0.683077	−	0.730347i	$-0.739358\pi$
$257$	0.757800	−	0.757800i	0.0472703	−	0.0472703i	0.730347	+	0.683077i	$0.239358\pi$
$258$		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	0.508012	−	0.861350i	$-0.330380\pi$
$263$	−5.73017	−	5.73017i	−0.353338	−	0.353338i	−0.861350	+	0.508012i	$0.830380\pi$
$264$		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	0.342635	−	0.939468i	$-0.388680\pi$
$269$	−9.78879	−	9.78879i	−0.596833	−	0.596833i	−0.939468	+	0.342635i	$0.888680\pi$
$270$		0			0
$271$		−	4.10159i		−	0.249154i	−0.992210	−	0.124577i	$-0.960243\pi$
$271$		−	4.10159i		−	0.249154i	0.992210	−	0.124577i	$-0.0397574\pi$
$272$	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	$-0.750506\pi$
$281$		−	23.6688i		−	1.41196i	0.708230	−	0.705981i	$-0.249494\pi$
$282$		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	$0.376087\pi$
$293$			31.6731i			1.85036i	−0.379526	+	0.925181i	$0.623913\pi$
$294$		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	−0.980205	−	0.197988i	$-0.936559\pi$
$313$	−13.8388	+	13.8388i	−0.782217	+	0.782217i	0.197988	+	0.980205i	$0.436559\pi$
$314$	−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	$-0.558505\pi$
$317$		−	35.0092i		−	1.96631i	0.182766	−	0.983156i	$-0.441495\pi$
$318$		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	−0.0727709	−	0.997349i	$-0.523184\pi$
$331$	16.8212	−	16.8212i	0.924578	−	0.924578i	0.997349	+	0.0727709i	$0.0231842\pi$
$332$	−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	−0.191680	−	0.981457i	$-0.561394\pi$
$337$	14.4984	−	14.4984i	0.789777	−	0.789777i	0.981457	+	0.191680i	$0.0613937\pi$
$338$	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	$-0.851373\pi$
$347$		−	16.7705i		−	0.900286i	0.892956	−	0.450143i	$-0.148627\pi$
$348$		0			0
$349$	1.86337	+	1.86337i	0.0997439	+	0.0997439i	0.755218	−	0.655474i	$-0.227531\pi$
$349$	1.86337	+	1.86337i	0.0997439	+	0.0997439i	−0.655474	+	0.755218i	$0.727531\pi$
$350$	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	−0.937998	−	0.346642i	$-0.887322\pi$
$353$	−24.1362	−	24.1362i	−1.28464	−	1.28464i	−0.346642	−	0.937998i	$-0.612678\pi$
$354$		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	$0.104781\pi$
$359$			12.2500i			0.646532i	−0.946308	+	0.323266i	$0.895219\pi$
$360$		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	0.774363	−	0.632742i	$-0.218071\pi$
$367$	2.71307	+	2.71307i	0.141621	+	0.141621i	−0.632742	+	0.774363i	$0.718071\pi$
$368$	−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	$0.140349\pi$
$373$			16.4846i			0.853541i	−0.904360	+	0.426771i	$0.859651\pi$
$374$	−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	0.258587	−	0.965988i	$-0.416743\pi$
$379$	−13.7716	−	13.7716i	−0.707401	−	0.707401i	−0.965988	+	0.258587i	$0.916743\pi$
$380$	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	−0.937721	−	0.347389i	$-0.887068\pi$
$383$	−11.5530	+	11.5530i	−0.590332	+	0.590332i	0.347389	+	0.937721i	$0.387068\pi$
$384$		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	−0.183338	−	0.983050i	$-0.558690\pi$
$389$	15.7728	−	15.7728i	0.799712	−	0.799712i	0.983050	+	0.183338i	$0.0586903\pi$
$390$		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	$-0.729225\pi$
$397$		−	29.9558i		−	1.50344i	0.659483	−	0.751720i	$-0.270775\pi$
$398$	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	−0.879205	−	0.476444i	$-0.841925\pi$
$419$	−8.24430	+	8.24430i	−0.402760	+	0.402760i	0.476444	+	0.879205i	$0.341925\pi$
$420$		0			0
$421$	−17.1776	−	17.1776i	−0.837184	−	0.837184i	0.151304	−	0.988487i	$-0.451653\pi$
$421$	−17.1776	−	17.1776i	−0.837184	−	0.837184i	−0.988487	+	0.151304i	$0.951653\pi$
$422$	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	$-0.717774\pi$
$431$		−	32.1769i		−	1.54990i	0.632020	−	0.774952i	$-0.282226\pi$
$432$		0			0
$433$	−20.3383	−	20.3383i	−0.977396	−	0.977396i	0.0223540	−	0.999750i	$-0.492884\pi$
$433$	−20.3383	−	20.3383i	−0.977396	−	0.977396i	−0.999750	+	0.0223540i	$0.992884\pi$
$434$	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	$0.320521\pi$
$439$			35.4180i			1.69041i	−0.534444	+	0.845204i	$0.679479\pi$
$440$	−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	$-0.934527\pi$
$449$		−	8.65559i		−	0.408483i	0.978921	−	0.204241i	$-0.0654727\pi$
$450$		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	0.314924	−	0.949117i	$-0.398021\pi$
$457$	−13.5575	−	13.5575i	−0.634193	−	0.634193i	−0.949117	+	0.314924i	$0.898021\pi$
$458$	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	−0.678687	−	0.734428i	$-0.737450\pi$
$461$	1.19682	−	1.19682i	0.0557416	−	0.0557416i	0.734428	+	0.678687i	$0.237450\pi$
$462$		0			0
$463$	−21.1815	+	21.1815i	−0.984390	+	0.984390i	−0.999880	−	0.0154904i	$-0.995069\pi$
$463$	−21.1815	+	21.1815i	−0.984390	+	0.984390i	0.0154904	+	0.999880i	$0.495069\pi$
$464$	−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	−0.764182	−	0.645001i	$-0.776857\pi$
$487$	−2.63011	+	2.63011i	−0.119182	+	0.119182i	0.645001	+	0.764182i	$0.276857\pi$
$488$	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	−0.145843	−	0.989308i	$-0.546589\pi$
$491$	18.6899	−	18.6899i	0.843465	−	0.843465i	0.989308	+	0.145843i	$0.0465894\pi$
$492$		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	−0.889965	−	0.456028i	$-0.849272\pi$
$499$	−9.69342	+	9.69342i	−0.433937	+	0.433937i	0.456028	+	0.889965i	$0.349272\pi$
$500$	−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	0.935336	−	0.353759i	$-0.115097\pi$
$503$	13.0434	+	13.0434i	0.581577	+	0.581577i	−0.353759	+	0.935336i	$0.615097\pi$
$504$		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	0.987341	+	0.158611i	$0.0507016\pi$
$509$	25.8539	+	25.8539i	1.14595	+	1.14595i	0.158611	+	0.987341i	$0.449298\pi$
$510$		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	$0.184912\pi$
$521$			25.0528i			1.09758i	−0.835959	+	0.548792i	$0.815088\pi$
$522$		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	−0.0660360	+	0.997817i	$0.521035\pi$
$541$	−24.7446	+	24.7446i	−1.06385	+	1.06385i	−0.997817	+	0.0660360i	$0.978965\pi$
$542$	−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	$0.227640\pi$
$557$			30.9517i			1.31146i	−0.754993	+	0.655732i	$0.772360\pi$
$558$		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	$-0.976486\pi$
$563$		−	3.50238i		−	0.147608i	0.997273	−	0.0738039i	$-0.0235139\pi$
$564$		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	−0.902155	−	0.431412i	$-0.858016\pi$
$571$	−11.2487	+	11.2487i	−0.470743	+	0.470743i	0.431412	+	0.902155i	$0.358016\pi$
$572$	−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	−0.765438	−	0.643509i	$-0.777478\pi$
$577$	−2.92884	+	2.92884i	−0.121929	+	0.121929i	0.643509	+	0.765438i	$0.277478\pi$
$578$	−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	$0.158604\pi$
$587$			23.1574i			0.955809i	−0.878412	+	0.477905i	$0.841396\pi$
$588$		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	0.932726	−	0.360585i	$-0.117423\pi$
$593$	13.9325	+	13.9325i	0.572141	+	0.572141i	−0.360585	+	0.932726i	$0.617423\pi$
$594$		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	$0.240207\pi$
$599$			33.5311i			1.37004i	−0.728523	+	0.685021i	$0.759793\pi$
$600$		0			0
$601$			19.4164i			0.792011i	0.918248	+	0.396005i	$0.129604\pi$
$601$			19.4164i			0.792011i	−0.918248	+	0.396005i	$0.870396\pi$
$602$	−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	0.487130	−	0.873330i	$-0.338044\pi$
$607$	−9.51495	−	9.51495i	−0.386200	−	0.386200i	−0.873330	+	0.487130i	$0.838044\pi$
$608$	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	$-0.939340\pi$
$613$		−	9.37947i		−	0.378833i	0.981897	−	0.189417i	$-0.0606597\pi$
$614$	−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	0.774904	−	0.632079i	$-0.217798\pi$
$617$	3.54768	+	3.54768i	0.142824	+	0.142824i	−0.632079	+	0.774904i	$0.717798\pi$
$618$		0			0
$619$	24.6158	+	24.6158i	0.989392	+	0.989392i	0.999944	−	0.0105527i	$-0.00335910\pi$
$619$	24.6158	+	24.6158i	0.989392	+	0.989392i	−0.0105527	+	0.999944i	$0.503359\pi$
$620$	−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	$-0.967149\pi$
$643$		−	5.22468i		−	0.206041i	0.994679	−	0.103021i	$-0.0328507\pi$
$644$	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	−0.990418	−	0.138100i	$-0.955900\pi$
$647$	−21.6797	+	21.6797i	−0.852318	+	0.852318i	0.138100	+	0.990418i	$0.455900\pi$
$648$		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	−0.673994	−	0.738737i	$-0.735423\pi$
$659$	1.66201	−	1.66201i	0.0647427	−	0.0647427i	0.738737	+	0.673994i	$0.235423\pi$
$660$		0			0
$661$	−5.62818	−	5.62818i	−0.218911	−	0.218911i	0.589129	−	0.808039i	$-0.299471\pi$
$661$	−5.62818	−	5.62818i	−0.218911	−	0.218911i	−0.808039	+	0.589129i	$0.799471\pi$
$662$	−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	0.712449	−	0.701724i	$-0.247586\pi$
$673$	0.278251	+	0.278251i	0.0107258	+	0.0107258i	−0.701724	+	0.712449i	$0.747586\pi$
$674$	−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	0.989354	−	0.145529i	$-0.0464884\pi$
$691$	22.1815	+	22.1815i	0.843825	+	0.843825i	−0.145529	+	0.989354i	$0.546488\pi$
$692$	−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	−0.943691	−	0.330828i	$-0.892672\pi$
$701$	−16.2264	+	16.2264i	−0.612864	+	0.612864i	0.330828	+	0.943691i	$0.392672\pi$
$702$		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	−0.0465856	−	0.998914i	$-0.514834\pi$
$709$	25.3577	−	25.3577i	0.952329	−	0.952329i	0.998914	+	0.0465856i	$0.0148340\pi$
$710$	−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	−0.992493	−	0.122300i	$-0.960973\pi$
$727$	−23.4630	+	23.4630i	−0.870193	+	0.870193i	0.122300	+	0.992493i	$0.460973\pi$
$728$	−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	−0.724801	−	0.688959i	$-0.758068\pi$
$739$	−0.974343	+	0.974343i	−0.0358418	+	0.0358418i	0.688959	+	0.724801i	$0.258068\pi$
$740$	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	−0.997573	−	0.0696259i	$-0.977819\pi$
$743$	−29.0897	−	29.0897i	−1.06720	−	1.06720i	−0.0696259	−	0.997573i	$-0.522181\pi$
$744$		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	$0.0453193\pi$
$751$			7.77705i			0.283789i	−0.989882	+	0.141894i	$0.954681\pi$
$752$	−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	$-0.839380\pi$
$761$		−	26.6737i		−	0.966921i	0.875366	−	0.483460i	$-0.160620\pi$
$762$		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	$-0.690513\pi$
$769$		−	45.8210i		−	1.65235i	0.563415	−	0.826174i	$-0.309487\pi$
$770$	−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	$0.108247\pi$
$773$			18.5473i			0.667101i	−0.942732	+	0.333550i	$0.891753\pi$
$774$		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	$-0.986722\pi$
$797$		−	2.35457i		−	0.0834033i	0.999130	−	0.0417016i	$-0.0132779\pi$
$798$		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	−0.730073	−	0.683369i	$-0.760514\pi$
$811$	−1.33006	+	1.33006i	−0.0467048	+	0.0467048i	0.683369	+	0.730073i	$0.260514\pi$
$812$	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	−0.944651	−	0.328076i	$-0.893600\pi$
$821$	−36.4676	−	36.4676i	−1.27273	−	1.27273i	−0.328076	−	0.944651i	$-0.606400\pi$
$822$		0			0
$823$	26.3978	+	26.3978i	0.920170	+	0.920170i	0.997041	−	0.0768712i	$-0.0244930\pi$
$823$	26.3978	+	26.3978i	0.920170	+	0.920170i	−0.0768712	+	0.997041i	$0.524493\pi$
$824$	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	$-0.988938\pi$
$827$		−	1.99830i		−	0.0694878i	0.999396	−	0.0347439i	$-0.0110616\pi$
$828$		0			0
$829$	−13.0376	−	13.0376i	−0.452813	−	0.452813i	0.443474	−	0.896287i	$-0.353746\pi$
$829$	−13.0376	−	13.0376i	−0.452813	−	0.452813i	−0.896287	+	0.443474i	$0.853746\pi$
$830$	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	$-0.914295\pi$
$839$		−	15.4102i		−	0.532018i	0.963971	−	0.266009i	$-0.0857050\pi$
$840$		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	$0.0435353\pi$
$853$			7.96419i			0.272689i	−0.990662	+	0.136344i	$0.956465\pi$
$854$	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	0.609723	−	0.792615i	$-0.291281\pi$
$857$	−5.35407	−	5.35407i	−0.182891	−	0.182891i	−0.792615	+	0.609723i	$0.791281\pi$
$858$		0			0
$859$	35.0058	+	35.0058i	1.19438	+	1.19438i	0.975824	+	0.218559i	$0.0701355\pi$
$859$	35.0058	+	35.0058i	1.19438	+	1.19438i	0.218559	+	0.975824i	$0.429864\pi$
$860$	−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	0.293923	−	0.955829i	$-0.405039\pi$
$863$	36.7138	−	36.7138i	1.24975	−	1.24975i	0.955829	−	0.293923i	$-0.0949610\pi$
$864$		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	$0.0778463\pi$
$877$			14.3410i			0.484262i	−0.970244	+	0.242131i	$0.922154\pi$
$878$	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	$0.0328672\pi$
$883$			6.12563i			0.206144i	−0.994674	+	0.103072i	$0.967133\pi$
$884$	−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	−0.990964	−	0.134130i	$-0.957176\pi$
$887$	−25.5187	+	25.5187i	−0.856834	+	0.856834i	0.134130	+	0.990964i	$0.457176\pi$
$888$		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	$-0.820581\pi$
$907$		−	32.1815i		−	1.06857i	0.845305	−	0.534284i	$-0.179419\pi$
$908$	−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	$0.221026\pi$
$911$			38.6282i			1.27981i	−0.768455	+	0.639904i	$0.778974\pi$
$912$		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	$-0.897476\pi$
$919$		−	19.1924i		−	0.633099i	0.948576	−	0.316550i	$-0.102524\pi$
$920$	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	$-0.910812\pi$
$929$		−	16.8576i		−	0.553081i	0.961002	−	0.276541i	$-0.0891880\pi$
$930$		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	0.197795	−	0.980243i	$-0.436622\pi$
$937$	−23.9511	−	23.9511i	−0.782449	−	0.782449i	−0.980243	+	0.197795i	$0.936622\pi$
$938$	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	−0.900135	−	0.435610i	$-0.856533\pi$
$941$	−14.2496	+	14.2496i	−0.464525	+	0.464525i	0.435610	+	0.900135i	$0.356533\pi$
$942$		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	−0.507647	−	0.861565i	$-0.669484\pi$
$953$	10.9257	−	10.9257i	0.353919	−	0.353919i	0.861565	+	0.507647i	$0.169484\pi$
$954$		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	−0.512669	−	0.858586i	$-0.671343\pi$
$967$	10.7569	−	10.7569i	0.345918	−	0.345918i	0.858586	+	0.512669i	$0.171343\pi$
$968$	−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	−0.339156	−	0.940730i	$-0.610142\pi$
$971$	18.7456	−	18.7456i	0.601574	−	0.601574i	0.940730	+	0.339156i	$0.110142\pi$
$972$		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	−0.145107	−	0.989416i	$-0.546353\pi$
$977$	26.3906	−	26.3906i	0.844309	−	0.844309i	0.989416	+	0.145107i	$0.0463526\pi$
$978$		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	0.780617	−	0.625009i	$-0.214905\pi$
$983$	4.87875	+	4.87875i	0.155608	+	0.155608i	−0.625009	+	0.780617i	$0.714905\pi$
$984$		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	$-0.575224\pi$
$991$		−	61.2103i		−	1.94441i	0.234130	−	0.972205i	$-0.424776\pi$
$992$	−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.523.5		18
3.2	odd	2		80.2.j.b.43.5	✓	18
5.2	odd	4		720.2.z.g.667.9		18
12.11	even	2		320.2.j.b.143.1		18
15.2	even	4		80.2.s.b.27.1	yes	18
15.8	even	4		400.2.s.d.107.9		18
15.14	odd	2		400.2.j.d.43.5		18
16.3	odd	4		720.2.z.g.163.9		18
24.5	odd	2		640.2.j.d.543.1		18
24.11	even	2		640.2.j.c.543.9		18
48.5	odd	4		640.2.s.c.223.9		18
48.11	even	4		640.2.s.d.223.1		18
48.29	odd	4		320.2.s.b.303.1		18
48.35	even	4		80.2.s.b.3.1	yes	18
60.23	odd	4		1600.2.s.d.207.9		18
60.47	odd	4		320.2.s.b.207.1		18
60.59	even	2		1600.2.j.d.143.9		18
80.67	even	4	inner	720.2.bd.g.307.5		18
120.77	even	4		640.2.s.d.287.1		18
120.107	odd	4		640.2.s.c.287.9		18
240.29	odd	4		1600.2.s.d.943.9		18
240.77	even	4		320.2.j.b.47.9		18
240.83	odd	4		400.2.j.d.307.5		18
240.107	odd	4		640.2.j.d.607.9		18
240.173	even	4		1600.2.j.d.1007.1		18
240.179	even	4		400.2.s.d.243.9		18
240.197	even	4		640.2.j.c.607.1		18
240.227	odd	4		80.2.j.b.67.5	yes	18

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
80.2.j.b.43.5	✓	18	3.2	odd	2
80.2.j.b.67.5	yes	18	240.227	odd	4
80.2.s.b.3.1	yes	18	48.35	even	4
80.2.s.b.27.1	yes	18	15.2	even	4
320.2.j.b.47.9		18	240.77	even	4
320.2.j.b.143.1		18	12.11	even	2
320.2.s.b.207.1		18	60.47	odd	4
320.2.s.b.303.1		18	48.29	odd	4
400.2.j.d.43.5		18	15.14	odd	2
400.2.j.d.307.5		18	240.83	odd	4
400.2.s.d.107.9		18	15.8	even	4
400.2.s.d.243.9		18	240.179	even	4
640.2.j.c.543.9		18	24.11	even	2
640.2.j.c.607.1		18	240.197	even	4
640.2.j.d.543.1		18	24.5	odd	2
640.2.j.d.607.9		18	240.107	odd	4
640.2.s.c.223.9		18	48.5	odd	4
640.2.s.c.287.9		18	120.107	odd	4
640.2.s.d.223.1		18	48.11	even	4
640.2.s.d.287.1		18	120.77	even	4
720.2.z.g.163.9		18	16.3	odd	4
720.2.z.g.667.9		18	5.2	odd	4
720.2.bd.g.307.5		18	80.67	even	4	inner
720.2.bd.g.523.5		18	1.1	even	1	trivial
1600.2.j.d.143.9		18	60.59	even	2
1600.2.j.d.1007.1		18	240.173	even	4
1600.2.s.d.207.9		18	60.23	odd	4
1600.2.s.d.943.9		18	240.29	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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