LMFDB - Embedded newform 720.2.z.g.667.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [720,2,Mod(163,720)]

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, 3]))

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

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

chi := DirichletCharacter("720.163");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 720 = 2^{4} \cdot 3^{2} \cdot 5 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	720.z (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			667.9
Root			$-0.480367 - 1.33013i$ of defining polynomial
Character	$\chi$	$=$	720.667
Dual form			720.2.z.g.163.9

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.38031 + 0.307817i) q^{2} +(1.81050 + 0.849763i) q^{4} +(1.71489 - 1.43498i) q^{5} +(-0.458895 - 0.458895i) q^{7} +(2.23747 + 1.73024i) q^{8} +(2.80878 - 1.45284i) q^{10} +(0.492763 - 0.492763i) q^{11} -4.52109i q^{13} +(-0.492160 - 0.774671i) q^{14} +(2.55581 + 3.07699i) q^{16} +(3.12823 + 3.12823i) q^{17} +(-4.04508 + 4.04508i) q^{19} +(4.32419 - 1.14077i) q^{20} +(0.831845 - 0.528484i) q^{22} +(1.80660 - 1.80660i) q^{23} +(0.881683 - 4.92165i) q^{25} +(1.39167 - 6.24050i) q^{26} +(-0.440876 - 1.22078i) q^{28} +(-3.83926 - 3.83926i) q^{29} -0.139949i q^{31} +(2.58065 + 5.03391i) q^{32} +(3.35500 + 5.28085i) q^{34} +(-1.44546 - 0.128450i) q^{35} +5.84330i q^{37} +(-6.82860 + 4.33831i) q^{38} +(6.31986 - 0.243561i) q^{40} +4.55648i q^{41} +7.49928i q^{43} +(1.31088 - 0.473414i) q^{44} +(3.04976 - 1.93756i) q^{46} +(-4.14073 + 4.14073i) q^{47} -6.57883i q^{49} +(2.73196 - 6.52199i) q^{50} +(3.84186 - 8.18543i) q^{52} -2.75773 q^{53} +(0.137930 - 1.55214i) q^{55} +(-0.232768 - 1.82076i) q^{56} +(-4.11757 - 6.48115i) q^{58} +(-3.62521 - 3.62521i) q^{59} +(3.72781 - 3.72781i) q^{61} +(0.0430787 - 0.193173i) q^{62} +(2.01257 + 7.74271i) q^{64} +(-6.48766 - 7.75317i) q^{65} +3.32677i q^{67} +(3.00540 + 8.32192i) q^{68} +(-1.95563 - 0.622235i) q^{70} -1.37056 q^{71} +(2.55028 + 2.55028i) q^{73} +(-1.79867 + 8.06556i) q^{74} +(-10.7610 + 3.88625i) q^{76} -0.452252 q^{77} +3.86426 q^{79} +(8.79833 + 1.60917i) q^{80} +(-1.40256 + 6.28934i) q^{82} -14.4698 q^{83} +(9.85351 + 0.875628i) q^{85} +(-2.30840 + 10.3513i) q^{86} +(1.95514 - 0.249948i) q^{88} -3.35011 q^{89} +(-2.07470 + 2.07470i) q^{91} +(4.80602 - 1.73566i) q^{92} +(-6.99006 + 4.44089i) q^{94} +(-1.13226 + 12.7415i) q^{95} +(-4.95582 - 4.95582i) q^{97} +(2.02507 - 9.08081i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 18 q + 4 q^{4} - 2 q^{5} + 2 q^{7} + 12 q^{8} + 2 q^{11} + 12 q^{14} + 6 q^{17} - 2 q^{19} + 12 q^{20} + 12 q^{22} + 2 q^{23} - 6 q^{25} + 16 q^{26} + 40 q^{28} - 14 q^{29} - 20 q^{32} + 28 q^{34} - 2 q^{35}+ \cdots + 56 q^{98}+O(q^{100}) $ 18 * q + 4 * q^4 - 2 * q^5 + 2 * q^7 + 12 * q^8 + 2 * q^11 + 12 * q^14 + 6 * q^17 - 2 * q^19 + 12 * q^20 + 12 * q^22 + 2 * q^23 - 6 * q^25 + 16 * q^26 + 40 * q^28 - 14 * q^29 - 20 * q^32 + 28 * q^34 - 2 * q^35 - 24 * q^38 + 44 * q^40 + 44 * q^44 + 12 * q^46 - 38 * q^47 + 8 * q^50 + 8 * q^52 - 12 * q^53 - 6 * q^55 - 20 * q^56 + 20 * q^58 - 10 * q^59 + 14 * q^61 + 40 * q^62 + 16 * q^64 + 60 * q^68 - 28 * q^70 - 24 * q^71 - 14 * q^73 + 48 * q^74 - 16 * q^76 + 44 * q^77 - 16 * q^79 + 92 * q^80 + 48 * q^82 - 40 * q^83 + 14 * q^85 + 36 * q^86 - 8 * q^88 - 12 * q^89 + 8 * q^92 - 28 * q^94 - 34 * q^95 + 18 * q^97 + 56 * q^98

Character values

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

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

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 $

$2$	1.38031	+	0.307817i	0.976025	+	0.217659i
$2$	1.38031	+	0.307817i	0.976025	+	0.217659i
$3$		0			0
$3$		0			0
$4$	1.81050	+	0.849763i	0.905249	+	0.424882i
$5$	1.71489	−	1.43498i	0.766921	−	0.641741i
$5$	1.71489	−	1.43498i	0.766921	−	0.641741i
$6$		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	$0.789138\pi$
$8$	2.23747	+	1.73024i	0.791066	+	0.611731i
$9$		0			0
$10$	2.80878	−	1.45284i	0.888215	−	0.459428i
$11$	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
$13$		−	4.52109i		−	1.25393i	−0.779049	−	0.626963i	$-0.784298\pi$
$13$		−	4.52109i		−	1.25393i	0.779049	−	0.626963i	$-0.215702\pi$
$14$	−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	$-0.977837\pi$
$19$	−4.04508	+	4.04508i	−0.928005	+	0.928005i	0.0695721	+	0.997577i	$0.477837\pi$
$20$	4.32419	−	1.14077i	0.966919	−	0.255085i
$21$		0			0
$22$	0.831845	−	0.528484i	0.177350	−	0.112673i
$23$	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
$28$	−0.440876	−	1.22078i	−0.0833177	−	0.230706i
$29$	−3.83926	−	3.83926i	−0.712932	−	0.712932i	0.254215	−	0.967148i	$-0.418183\pi$
$29$	−3.83926	−	3.83926i	−0.712932	−	0.712932i	−0.967148	+	0.254215i	$0.918183\pi$
$30$		0			0
$31$		−	0.139949i		−	0.0251356i	−0.999921	−	0.0125678i	$-0.995999\pi$
$31$		−	0.139949i		−	0.0251356i	0.999921	−	0.0125678i	$-0.00400057\pi$
$32$	2.58065	+	5.03391i	0.456199	+	0.889878i
$33$		0			0
$34$	3.35500	+	5.28085i	0.575378	+	0.905658i
$35$	−1.44546	−	0.128450i	−0.244327	−	0.0217120i
$36$		0			0
$37$			5.84330i			0.960633i	0.877095	+	0.480317i	$0.159478\pi$
$37$			5.84330i			0.960633i	−0.877095	+	0.480317i	$0.840522\pi$
$38$	−6.82860	+	4.33831i	−1.10774	+	0.703767i
$39$		0			0
$40$	6.31986	−	0.243561i	0.999258	−	0.0385104i
$41$			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
$43$			7.49928i			1.14363i	0.820383	+	0.571815i	$0.193760\pi$
$43$			7.49928i			1.14363i	−0.820383	+	0.571815i	$0.806240\pi$
$44$	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	$-0.890459\pi$
$47$	−4.14073	+	4.14073i	−0.603987	+	0.603987i	0.337381	+	0.941368i	$0.390459\pi$
$48$		0			0
$49$		−	6.57883i		−	0.939833i
$50$	2.73196	−	6.52199i	0.386357	−	0.922349i
$51$		0			0
$52$	3.84186	−	8.18543i	0.532770	−	1.13511i
$53$	−2.75773			−0.378803			−0.189402	−	0.981900i	$-0.560655\pi$
$53$	−2.75773			−0.378803			−0.189402	+	0.981900i	$0.560655\pi$
$54$		0			0
$55$	0.137930	−	1.55214i	0.0185985	−	0.209290i
$56$	−0.232768	−	1.82076i	−0.0311050	−	0.243309i
$57$		0			0
$58$	−4.11757	−	6.48115i	−0.540663	−	0.851016i
$59$	−3.62521	−	3.62521i	−0.471962	−	0.471962i	0.430587	−	0.902549i	$-0.358306\pi$
$59$	−3.62521	−	3.62521i	−0.471962	−	0.471962i	−0.902549	+	0.430587i	$0.858306\pi$
$60$		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	$0.140419\pi$
$62$	0.0430787	−	0.193173i	0.00547100	−	0.0245330i
$63$		0			0
$64$	2.01257	+	7.74271i	0.251571	+	0.967839i
$65$	−6.48766	−	7.75317i	−0.804696	−	0.961662i
$66$		0			0
$67$			3.32677i			0.406430i	0.979134	+	0.203215i	$0.0651390\pi$
$67$			3.32677i			0.406430i	−0.979134	+	0.203215i	$0.934861\pi$
$68$	3.00540	+	8.32192i	0.364459	+	1.00918i
$69$		0			0
$70$	−1.95563	−	0.622235i	−0.233743	−	0.0743714i
$71$	−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	$-0.182307\pi$
$73$	2.55028	+	2.55028i	0.298488	+	0.298488i	−0.541933	+	0.840422i	$0.682307\pi$
$74$	−1.79867	+	8.06556i	−0.209091	+	0.937602i
$75$		0			0
$76$	−10.7610	+	3.88625i	−1.23437	+	0.445783i
$77$	−0.452252			−0.0515389
$78$		0			0
$79$	3.86426			0.434763			0.217382	−	0.976087i	$-0.430248\pi$
$79$	3.86426			0.434763			0.217382	+	0.976087i	$0.430248\pi$
$80$	8.79833	+	1.60917i	0.983683	+	0.179911i
$81$		0			0
$82$	−1.40256	+	6.28934i	−0.154887	+	0.694541i
$83$	−14.4698			−1.58827			−0.794133	−	0.607744i	$-0.792075\pi$
$83$	−14.4698			−1.58827			−0.794133	+	0.607744i	$0.792075\pi$
$84$		0			0
$85$	9.85351	+	0.875628i	1.06876	+	0.0949752i
$86$	−2.30840	+	10.3513i	−0.248922	+	1.11621i
$87$		0			0
$88$	1.95514	−	0.249948i	0.208419	−	0.0266445i
$89$	−3.35011			−0.355111			−0.177556	−	0.984111i	$-0.556819\pi$
$89$	−3.35011			−0.355111			−0.177556	+	0.984111i	$0.556819\pi$
$90$		0			0
$91$	−2.07470	+	2.07470i	−0.217488	+	0.217488i
$92$	4.80602	−	1.73566i	0.501062	−	0.180955i
$93$		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	$0.865794\pi$
$98$	2.02507	−	9.08081i	0.204563	−	0.917300i
$99$		0			0
$100$	5.77852	−	8.16142i	0.577852	−	0.816142i
$101$	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	−0.162773	+	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
$107$	15.3106			1.48013			0.740067	−	0.672534i	$-0.234794\pi$
$107$	15.3106			1.48013			0.740067	+	0.672534i	$0.234794\pi$
$108$		0			0
$109$	−12.4798	−	12.4798i	−1.19535	−	1.19535i	−0.975544	−	0.219803i	$-0.929458\pi$
$109$	−12.4798	−	12.4798i	−1.19535	−	1.19535i	−0.219803	−	0.975544i	$-0.570542\pi$
$110$	0.668159	−	2.09997i	0.0637065	−	0.200224i
$111$		0			0
$112$	0.239168	−	2.58486i	0.0225993	−	0.244246i
$113$	−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
$115$	0.505686	−	5.69053i	0.0471555	−	0.530645i
$116$	−3.68851	−	10.2134i	−0.342470	−	0.948293i
$117$		0			0
$118$	−3.88800	−	6.11980i	−0.357919	−	0.563373i
$119$		−	2.87106i		−	0.263189i
$120$		0			0
$121$			10.5144i			0.955852i
$122$	6.29301	−	3.99805i	0.569743	−	0.361966i
$123$		0			0
$124$	0.118924	−	0.253378i	0.0106797	−	0.0227540i
$125$	−5.55047	−	9.70527i	−0.496449	−	0.868066i
$126$		0			0
$127$	0.615790	−	0.615790i	0.0546426	−	0.0546426i	−0.679257	−	0.733900i	$-0.737698\pi$
$127$	0.615790	−	0.615790i	0.0546426	−	0.0546426i	0.733900	+	0.679257i	$0.237698\pi$
$128$	0.394630	+	11.3068i	0.0348807	+	0.999391i
$129$		0			0
$130$	−6.56842	−	12.6988i	−0.576088	−	1.11376i
$131$	−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
$133$	3.71253			0.321917
$134$	−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	$-0.821811\pi$
$137$	−3.70277	+	3.70277i	−0.316349	+	0.316349i	0.531014	+	0.847363i	$0.321811\pi$
$138$		0			0
$139$	−5.46761	−	5.46761i	−0.463756	−	0.463756i	0.436128	−	0.899885i	$-0.356349\pi$
$139$	−5.46761	−	5.46761i	−0.463756	−	0.463756i	−0.899885	+	0.436128i	$0.856349\pi$
$140$	−2.50784	−	1.46085i	−0.211951	−	0.123465i
$141$		0			0
$142$	−1.89179	−	0.421880i	−0.158755	−	0.0354034i
$143$	−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
$148$	−4.96542	+	10.5793i	−0.408155	+	0.869612i
$149$	4.21561	−	4.21561i	0.345356	−	0.345356i	−0.513021	−	0.858376i	$-0.671474\pi$
$149$	4.21561	−	4.21561i	0.345356	−	0.345356i	0.858376	+	0.513021i	$0.171474\pi$
$150$		0			0
$151$	12.4417			1.01249			0.506244	−	0.862390i	$-0.331034\pi$
$151$	12.4417			1.01249			0.506244	+	0.862390i	$0.331034\pi$
$152$	−16.0497	+	2.05181i	−1.30180	+	0.166424i
$153$		0			0
$154$	−0.624247	−	0.139211i	−0.0503033	−	0.0112179i
$155$	−0.200824	−	0.239997i	−0.0161306	−	0.0192771i
$156$		0			0
$157$	7.50500			0.598964			0.299482	−	0.954102i	$-0.403186\pi$
$157$	7.50500			0.598964			0.299482	+	0.954102i	$0.403186\pi$
$158$	5.33387	+	1.18948i	0.424340	+	0.0946302i
$159$		0			0
$160$	11.6491	+	4.92942i	0.920940	+	0.389705i
$161$	−1.65807			−0.130675
$162$		0			0
$163$	−23.7284			−1.85855			−0.929277	−	0.369383i	$-0.879569\pi$
$163$	−23.7284			−1.85855			−0.929277	+	0.369383i	$0.879569\pi$
$164$	−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
$170$	13.3313	+	4.24171i	1.02247	+	0.325324i
$171$		0			0
$172$	−6.37261	+	13.5774i	−0.485907	+	1.03527i
$173$		−	15.4500i		−	1.17464i	−0.809355	−	0.587320i	$-0.800183\pi$
$173$		−	15.4500i		−	1.17464i	0.809355	−	0.587320i	$-0.199817\pi$
$174$		0			0
$175$	−2.66312	+	1.85392i	−0.201313	+	0.140143i
$176$	2.77563	+	0.256820i	0.209221	+	0.0193585i
$177$		0			0
$178$	−4.62419	−	1.03122i	−0.346597	−	0.0772932i
$179$	5.20444	−	5.20444i	0.388998	−	0.388998i	−0.485332	−	0.874330i	$-0.661301\pi$
$179$	5.20444	−	5.20444i	0.388998	−	0.388998i	0.874330	+	0.485332i	$0.161301\pi$
$180$		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	$0.908537\pi$
$182$	−3.50236	+	2.22510i	−0.259612	+	0.164936i
$183$		0			0
$184$	7.16804	−	0.916372i	0.528435	−	0.0675559i
$185$	8.38500	+	10.0206i	0.616478	+	0.736730i
$186$		0			0
$187$	3.08295			0.225448
$188$	−11.0154	+	3.97814i	−0.803382	+	0.290136i
$189$		0			0
$190$	−5.48490	+	17.2386i	−0.397917	+	1.25062i
$191$			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	−0.539965	−	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
$197$			4.03184i			0.287256i	0.989632	+	0.143628i	$0.0458769\pi$
$197$			4.03184i			0.287256i	−0.989632	+	0.143628i	$0.954123\pi$
$198$		0			0
$199$		−	5.43055i		−	0.384961i	−0.981301	−	0.192481i	$-0.938347\pi$
$199$		−	5.43055i		−	0.384961i	0.981301	−	0.192481i	$-0.0616533\pi$
$200$	10.4884	−	9.48654i	0.741639	−	0.670800i
$201$		0			0
$202$	1.97914	+	3.11520i	0.139252	+	0.219185i
$203$			3.52363i			0.247310i
$204$		0			0
$205$	6.53844	+	7.81385i	0.456664	+	0.545743i
$206$	−19.6928	+	12.5111i	−1.37206	+	0.871693i
$207$		0			0
$208$	13.9114	−	11.5550i	0.964579	−	0.801197i
$209$			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	$0.699739\pi$
$212$	−4.99286	−	2.34342i	−0.342911	−	0.160946i
$213$		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
$218$	−13.3845	−	21.0674i	−0.906511	−	1.42687i
$219$		0			0
$220$	1.56867	−	2.69293i	0.105760	−	0.181557i
$221$	14.1430	−	14.1430i	0.951363	−	0.951363i
$222$		0			0
$223$	8.17319	+	8.17319i	0.547317	+	0.547317i	0.925664	−	0.378347i	$-0.123507\pi$
$223$	8.17319	+	8.17319i	0.547317	+	0.547317i	−0.378347	+	0.925664i	$0.623507\pi$
$224$	1.12579	−	3.49428i	0.0752199	−	0.233471i
$225$		0			0
$226$	−4.28035	+	2.71937i	−0.284725	+	0.180890i
$227$			1.54068i			0.102258i	0.998692	+	0.0511292i	$0.0162820\pi$
$227$			1.54068i			0.102258i	−0.998692	+	0.0511292i	$0.983718\pi$
$228$		0			0
$229$	17.5646	−	17.5646i	1.16070	−	1.16070i	0.176378	−	0.984322i	$-0.443562\pi$
$229$	17.5646	−	17.5646i	1.16070	−	1.16070i	0.984322	−	0.176378i	$-0.0564382\pi$
$230$	2.44964	−	7.69903i	0.161525	−	0.507659i
$231$		0			0
$232$	−1.94741	−	15.2331i	−0.127854	−	1.00010i
$233$	9.99018	+	9.99018i	0.654479	+	0.654479i	0.954068	−	0.299590i	$-0.0968498\pi$
$233$	9.99018	+	9.99018i	0.654479	+	0.654479i	−0.299590	+	0.954068i	$0.596850\pi$
$234$		0			0
$235$	−1.15904	+	13.0427i	−0.0756072	+	0.850814i
$236$	−3.48286	−	9.64399i	−0.226715	−	0.627771i
$237$		0			0
$238$	0.883759	−	3.96294i	0.0572856	−	0.256879i
$239$	26.2762			1.69967			0.849833	−	0.527052i	$-0.176703\pi$
$239$	26.2762			1.69967			0.849833	+	0.527052i	$0.176703\pi$
$240$		0			0
$241$	−0.113242			−0.00729456			−0.00364728	−	0.999993i	$-0.501161\pi$
$241$	−0.113242			−0.00729456			−0.00364728	+	0.999993i	$0.501161\pi$
$242$	−3.23650	+	14.5131i	−0.208050	+	0.932935i
$243$		0			0
$244$	9.91696	−	3.58144i	0.634868	−	0.229278i
$245$	−9.44047	−	11.2820i	−0.603130	−	0.720778i
$246$		0			0
$247$	18.2882	+	18.2882i	1.16365	+	1.16365i
$248$	0.242145	−	0.313133i	0.0153762	−	0.0198840i
$249$		0			0
$250$	−4.67391	−	15.1048i	−0.295604	−	0.955311i
$251$	−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
$253$		−	1.78045i		−	0.111936i
$254$	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
$260$	−5.15755	−	19.5501i	−0.319857	−	1.21244i
$261$		0			0
$262$	−10.2467	−	16.1286i	−0.633044	−	0.996425i
$263$	−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
$268$	−2.82697	+	6.02311i	−0.172685	+	0.367920i
$269$	9.78879	+	9.78879i	0.596833	+	0.596833i	0.939468	−	0.342635i	$-0.111320\pi$
$269$	9.78879	+	9.78879i	0.596833	+	0.596833i	−0.342635	+	0.939468i	$0.611320\pi$
$270$		0			0
$271$		−	4.10159i		−	0.249154i	−0.992210	−	0.124577i	$-0.960243\pi$
$271$		−	4.10159i		−	0.249154i	0.992210	−	0.124577i	$-0.0397574\pi$
$272$	−1.63038	+	17.6207i	−0.0988565	+	1.06841i
$273$		0			0
$274$	−6.25074	+	3.97119i	−0.377621	+	0.239908i
$275$	−1.99075	−	2.85967i	−0.120046	−	0.172444i
$276$		0			0
$277$			24.6755i			1.48261i	0.671169	+	0.741305i	$0.265793\pi$
$277$			24.6755i			1.48261i	−0.671169	+	0.741305i	$0.734207\pi$
$278$	−5.86396	−	9.23000i	−0.351697	−	0.553578i
$279$		0			0
$280$	−3.01192	−	2.78838i	−0.179997	−	0.166638i
$281$		−	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
$283$		−	13.0492i		−	0.775694i	−0.921724	−	0.387847i	$-0.873219\pi$
$283$		−	13.0492i		−	0.775694i	0.921724	−	0.387847i	$-0.126781\pi$
$284$	−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
$290$	−16.3615	−	5.20582i	−0.960778	−	0.305696i
$291$		0			0
$292$	2.45015	+	6.78442i	0.143384	+	0.397028i
$293$	31.6731			1.85036			0.925181	−	0.379526i	$-0.123913\pi$
$293$	31.6731			1.85036			0.925181	+	0.379526i	$0.123913\pi$
$294$		0			0
$295$	−11.4189	−	1.01474i	−0.664835	−	0.0590802i
$296$	−10.1103	+	13.0742i	−0.587649	+	0.759924i
$297$		0			0
$298$	7.11646	−	4.52120i	0.412246	−	0.261906i
$299$	−8.16779	−	8.16779i	−0.472355	−	0.472355i
$300$		0			0
$301$	3.44138	−	3.44138i	0.198358	−	0.198358i
$302$	17.1733	+	3.82975i	0.988213	+	0.220377i
$303$		0			0
$304$	−22.7851	−	2.10823i	−1.30682	−	0.120915i
$305$	1.04346	−	11.7421i	0.0597482	−	0.672351i
$306$		0			0
$307$		−	27.3597i		−	1.56150i	−0.624843	−	0.780751i	$-0.714837\pi$
$307$		−	27.3597i		−	1.56150i	0.624843	−	0.780751i	$-0.285163\pi$
$308$	−0.818802	−	0.384307i	−0.0466556	−	0.0218979i
$309$		0			0
$310$	−0.203324	−	0.393087i	−0.0115480	−	0.0223259i
$311$	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	$-0.0634406\pi$
$313$	13.8388	+	13.8388i	0.782217	+	0.782217i	−0.197988	+	0.980205i	$0.563441\pi$
$314$	10.3592	+	2.31016i	0.584604	+	0.130370i
$315$		0			0
$316$	6.99624	+	3.28371i	0.393569	+	0.184723i
$317$	35.0092			1.96631			0.983156	−	0.182766i	$-0.0585051\pi$
$317$	35.0092			1.96631			0.983156	+	0.182766i	$0.0585051\pi$
$318$		0			0
$319$	−3.78369			−0.211846
$320$	14.5619	+	10.3899i	0.814037	+	0.580813i
$321$		0			0
$322$	−2.28865	−	0.510383i	−0.127542	−	0.0284425i
$323$	−25.3079			−1.40817
$324$		0			0
$325$	−22.2512	−	3.98617i	−1.23428	−	0.221113i
$326$	−32.7525	−	7.30401i	−1.81400	−	0.404532i
$327$		0			0
$328$	−7.88378	+	10.1950i	−0.435309	+	0.562924i
$329$	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	$0.0231842\pi$
$332$	−26.1975	−	12.2959i	−1.43778	−	0.674825i
$333$		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	$0.561394\pi$
$338$	−10.2699	−	2.29024i	−0.558608	−	0.124573i
$339$		0			0
$340$	17.0957	+	9.95847i	0.927144	+	0.540074i
$341$	−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
$347$	16.7705			0.900286			0.450143	−	0.892956i	$-0.351373\pi$
$347$	16.7705			0.900286			0.450143	+	0.892956i	$0.351373\pi$
$348$		0			0
$349$	−1.86337	−	1.86337i	−0.0997439	−	0.0997439i	0.655474	−	0.755218i	$-0.272469\pi$
$349$	−1.86337	−	1.86337i	−0.0997439	−	0.0997439i	−0.755218	+	0.655474i	$0.772469\pi$
$350$	−4.24659	+	1.73923i	−0.226990	+	0.0929656i
$351$		0			0
$352$	3.75217	+	1.20888i	0.199991	+	0.0644333i
$353$	−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
$355$	−2.35035	+	1.96672i	−0.124744	+	0.104382i
$356$	−6.06537	−	2.84680i	−0.321464	−	0.150880i
$357$		0			0
$358$	8.78574	−	5.58171i	0.464341	−	0.295003i
$359$		−	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
$362$	−9.74814	−	15.3438i	−0.512351	−	0.806451i
$363$		0			0
$364$	−5.51926	+	1.99324i	−0.289288	+	0.104474i
$365$	8.03305	+	0.713853i	0.420469	+	0.0373648i
$366$		0			0
$367$	−2.71307	+	2.71307i	−0.141621	+	0.141621i	−0.774363	−	0.632742i	$-0.781929\pi$
$367$	−2.71307	+	2.71307i	−0.141621	+	0.141621i	0.632742	+	0.774363i	$0.281929\pi$
$368$	10.1762	+	0.941567i	0.530470	+	0.0490826i
$369$		0			0
$370$	8.48938	+	16.4126i	0.441342	+	0.853249i
$371$	1.26551	+	1.26551i	0.0657018	+	0.0657018i
$372$		0			0
$373$	16.4846			0.853541			0.426771	−	0.904360i	$-0.359651\pi$
$373$	16.4846			0.853541			0.426771	+	0.904360i	$0.359651\pi$
$374$	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	$-0.0832568\pi$
$379$	13.7716	+	13.7716i	0.707401	+	0.707401i	−0.258587	+	0.965988i	$0.583257\pi$
$380$	−12.8772	+	22.1062i	−0.660585	+	1.13403i
$381$		0			0
$382$	−4.65034	+	20.8530i	−0.237932	+	1.06693i
$383$	11.5530	+	11.5530i	0.590332	+	0.590332i	0.937721	−	0.347389i	$-0.112932\pi$
$383$	11.5530	+	11.5530i	0.590332	+	0.590332i	−0.347389	+	0.937721i	$0.612932\pi$
$384$		0			0
$385$	−0.775562	+	0.648972i	−0.0395263	+	0.0330747i
$386$	7.07604	−	4.49552i	0.360161	−	0.228816i
$387$		0			0
$388$	−4.76123	−	13.1838i	−0.241715	−	0.669305i
$389$	−15.7728	+	15.7728i	−0.799712	+	0.799712i	−0.983050	−	0.183338i	$-0.941310\pi$
$389$	−15.7728	+	15.7728i	−0.799712	+	0.799712i	0.183338	+	0.983050i	$0.441310\pi$
$390$		0			0
$391$	11.3029			0.571612
$392$	11.3829	−	14.7200i	0.574925	−	0.743470i
$393$		0			0
$394$	−1.24107	+	5.56517i	−0.0625240	+	0.280369i
$395$	6.62677	−	5.54512i	0.333429	−	0.279006i
$396$		0			0
$397$	29.9558			1.50344			0.751720	−	0.659483i	$-0.229225\pi$
$397$	29.9558			1.50344			0.751720	+	0.659483i	$0.229225\pi$
$398$	1.67161	−	7.49583i	0.0837904	−	0.375732i
$399$		0			0
$400$	17.3973	−	9.86585i	0.869863	−	0.493293i
$401$	−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
$403$	−0.632724			−0.0315182
$404$	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	$-0.546586\pi$
$409$	−5.89856			−0.291665			−0.145832	+	0.989309i	$0.546586\pi$
$410$	6.61982	+	12.7982i	0.326930	+	0.632056i
$411$		0			0
$412$	−31.0333	+	11.2075i	−1.52890	+	0.552152i
$413$			3.32717i			0.163720i
$414$		0			0
$415$	−24.8141	+	20.7638i	−1.21808	+	1.01926i
$416$	22.7588	−	11.6674i	1.11584	−	0.572039i
$417$		0			0
$418$	−1.22712	+	5.50264i	−0.0600204	+	0.269143i
$419$	8.24430	−	8.24430i	0.402760	−	0.402760i	−0.476444	−	0.879205i	$-0.658075\pi$
$419$	8.24430	−	8.24430i	0.402760	−	0.402760i	0.879205	+	0.476444i	$0.158075\pi$
$420$		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	$0.951653\pi$
$422$	3.46436	+	5.45297i	0.168642	+	0.265447i
$423$		0			0
$424$	−6.17034	−	4.77152i	−0.299658	−	0.231725i
$425$	18.1542	−	12.6380i	0.880607	−	0.613031i
$426$		0			0
$427$	−3.42135			−0.165571
$428$	27.7198	+	13.0104i	1.33989	+	0.628881i
$429$		0			0
$430$	10.8952	+	21.0639i	0.525415	+	1.01579i
$431$		−	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	−0.999750	−	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
$437$			14.6156i			0.699161i
$438$		0			0
$439$		−	35.4180i		−	1.69041i	−0.534444	−	0.845204i	$-0.679479\pi$
$439$		−	35.4180i		−	1.69041i	0.534444	−	0.845204i	$-0.320521\pi$
$440$	2.99418	−	3.23421i	0.142742	−	0.154185i
$441$		0			0
$442$	23.8752	−	15.1683i	1.13563	−	0.721481i
$443$		−	3.03787i		−	0.144333i	−0.997393	−	0.0721667i	$-0.977009\pi$
$443$		−	3.03787i		−	0.144333i	0.997393	−	0.0721667i	$-0.0229913\pi$
$444$		0			0
$445$	−5.74507	+	4.80733i	−0.272342	+	0.227890i
$446$	8.76567	+	13.7974i	0.415067	+	0.653324i
$447$		0			0
$448$	2.62953	−	4.47664i	0.124234	−	0.211502i
$449$			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
$452$	−6.74527	+	2.43601i	−0.317271	+	0.114580i
$453$		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	$-0.601979\pi$
$457$	13.5575	−	13.5575i	0.634193	−	0.634193i	0.949117	+	0.314924i	$0.101979\pi$
$458$	29.6512	−	18.8379i	1.38551	−	0.880236i
$459$		0			0
$460$	5.75115	−	9.87298i	0.268149	−	0.460330i
$461$	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	$-0.00493096\pi$
$463$	21.1815	+	21.1815i	0.984390	+	0.984390i	−0.0154904	+	0.999880i	$0.504931\pi$
$464$	2.00096	−	21.6258i	0.0928921	−	1.00395i
$465$		0			0
$466$	10.7144	+	16.8647i	0.496334	+	0.781241i
$467$		−	24.8448i		−	1.14968i	−0.818266	−	0.574840i	$-0.805064\pi$
$467$		−	24.8448i		−	1.14968i	0.818266	−	0.574840i	$-0.194936\pi$
$468$		0			0
$469$	1.52664	−	1.52664i	0.0704936	−	0.0704936i
$470$	−5.61460	+	17.6462i	−0.258982	+	0.813959i
$471$		0			0
$472$	−1.83884	−	14.3838i	−0.0846394	−	0.662066i
$473$	3.69537	+	3.69537i	0.169913	+	0.169913i
$474$		0			0
$475$	16.3420	+	23.4749i	0.749822	+	1.07710i
$476$	2.43972	−	5.19804i	0.111824	−	0.238252i
$477$		0			0
$478$	36.2692	+	8.08825i	1.65892	+	0.369948i
$479$	−23.5766			−1.07724			−0.538621	−	0.842548i	$-0.681054\pi$
$479$	−23.5766			−1.07724			−0.538621	+	0.842548i	$0.681054\pi$
$480$		0			0
$481$	26.4181			1.20456
$482$	−0.156309	−	0.0348578i	−0.00711967	−	0.00158773i
$483$		0			0
$484$	−8.93472	+	19.0362i	−0.406124	+	0.865284i
$485$	−15.6102	−	1.38719i	−0.708821	−	0.0629891i
$486$		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	$0.776857\pi$
$488$	14.7909	−	1.89089i	0.669552	−	0.0855964i
$489$		0			0
$490$	−9.55798	−	18.4785i	−0.431786	−	0.834774i
$491$	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
$493$		−	24.0202i		−	1.08182i
$494$	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	$-0.650728\pi$
$499$	9.69342	−	9.69342i	0.433937	−	0.433937i	0.889965	+	0.456028i	$0.150728\pi$
$500$	−1.80192	−	22.2880i	−0.0805845	−	0.996748i
$501$		0			0
$502$	−32.4491	+	20.6154i	−1.44827	+	0.920110i
$503$	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
$508$	1.63816	−	0.591611i	0.0726817	−	0.0262485i
$509$	−25.8539	−	25.8539i	−1.14595	−	1.14595i	−0.987341	−	0.158611i	$-0.949298\pi$
$509$	−25.8539	−	25.8539i	−1.14595	−	1.14595i	−0.158611	−	0.987341i	$-0.550702\pi$
$510$		0			0
$511$		−	2.34062i		−	0.103543i
$512$	−8.89365	+	20.8063i	−0.393047	+	0.919518i
$513$		0			0
$514$	0.812734	+	1.27926i	0.0358481	+	0.0564258i
$515$	−3.26531	+	36.7448i	−0.143887	+	1.61917i
$516$		0			0
$517$			4.08080i			0.179473i
$518$	4.52664	−	2.87584i	0.198889	−	0.126357i
$519$		0			0
$520$	−1.10116	−	28.5727i	−0.0482892	−	1.25300i
$521$			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
$523$		−	40.3434i		−	1.76410i	−0.471160	−	0.882048i	$-0.656165\pi$
$523$		−	40.3434i		−	1.76410i	0.471160	−	0.882048i	$-0.343835\pi$
$524$	−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
$530$	−7.74586	+	4.00653i	−0.336459	+	0.174033i
$531$		0			0
$532$	6.72153	+	3.15477i	0.291415	+	0.136777i
$533$	20.6003			0.892296
$534$		0			0
$535$	26.2560	−	21.9704i	1.13515	−	0.949862i
$536$	−5.75610	+	7.44356i	−0.248626	+	0.321513i
$537$		0			0
$538$	10.4984	+	16.5247i	0.452618	+	0.712430i
$539$	−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	$0.978965\pi$
$542$	1.26254	−	5.66146i	0.0542307	−	0.243181i
$543$		0			0
$544$	−7.67437	+	23.8201i	−0.329036	+	1.02128i
$545$	−39.3097	−	3.49324i	−1.68384	−	0.149634i
$546$		0			0
$547$			19.0254i			0.813465i	0.913547	+	0.406733i	$0.133332\pi$
$547$			19.0254i			0.813465i	−0.913547	+	0.406733i	$0.866668\pi$
$548$	−9.85034	+	3.55738i	−0.420786	+	0.151964i
$549$		0			0
$550$	−1.86759	−	4.56000i	−0.0796342	−	0.194439i
$551$	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
$557$	−30.9517			−1.31146			−0.655732	−	0.754993i	$-0.727640\pi$
$557$	−30.9517			−1.31146			−0.655732	+	0.754993i	$0.727640\pi$
$558$		0			0
$559$	33.9050			1.43403
$560$	−3.29907	−	4.77594i	−0.139411	−	0.201820i
$561$		0			0
$562$	7.28565	−	32.6702i	0.307327	−	1.37811i
$563$	−3.50238			−0.147608			−0.0738039	−	0.997273i	$-0.523514\pi$
$563$	−3.50238			−0.147608			−0.0738039	+	0.997273i	$0.523514\pi$
$564$		0			0
$565$	−0.709734	+	7.98670i	−0.0298587	+	0.336003i
$566$	4.01676	−	18.0119i	0.168837	−	0.757097i
$567$		0			0
$568$	−3.06658	−	2.37138i	−0.128671	−	0.0995011i
$569$	−0.525780			−0.0220418			−0.0110209	−	0.999939i	$-0.503508\pi$
$569$	−0.525780			−0.0220418			−0.0110209	+	0.999939i	$0.503508\pi$
$570$		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	$0.358016\pi$
$572$	−2.14035	−	5.92660i	−0.0894926	−	0.247804i
$573$		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	$0.777478\pi$
$578$	−0.791607	+	3.54971i	−0.0329265	+	0.147649i
$579$		0			0
$580$	−20.9814	−	12.2220i	−0.871206	−	0.507489i
$581$	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
$587$	−23.1574			−0.955809			−0.477905	−	0.878412i	$-0.658604\pi$
$587$	−23.1574			−0.955809			−0.477905	+	0.878412i	$0.658604\pi$
$588$		0			0
$589$	0.566106	+	0.566106i	0.0233260	+	0.0233260i
$590$	−15.4493	−	4.91558i	−0.636036	−	0.202371i
$591$		0			0
$592$	−17.9798	+	14.9343i	−0.738964	+	0.613798i
$593$	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
$595$	−4.11990	−	4.92354i	−0.168900	−	0.201846i
$596$	11.2146	−	4.05008i	0.459368	−	0.165898i
$597$		0			0
$598$	−8.75988	−	13.7882i	−0.358218	−	0.563843i
$599$		−	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	$0.129604\pi$
$601$			19.4164i			0.792011i	−0.918248	+	0.396005i	$0.870396\pi$
$602$	5.80948	−	3.69085i	0.236777	−	0.150428i
$603$		0			0
$604$	22.5256	+	10.5725i	0.916554	+	0.430187i
$605$	15.0879	+	18.0310i	0.613409	+	0.733063i
$606$		0			0
$607$	9.51495	−	9.51495i	0.386200	−	0.386200i	−0.487130	−	0.873330i	$-0.661956\pi$
$607$	9.51495	−	9.51495i	0.386200	−	0.386200i	0.873330	+	0.487130i	$0.161956\pi$
$608$	−30.8015	−	9.92363i	−1.24917	−	0.402456i
$609$		0			0
$610$	5.05471	−	15.8865i	0.204659	−	0.643227i
$611$	18.7206	+	18.7206i	0.757355	+	0.757355i
$612$		0			0
$613$	−9.37947			−0.378833			−0.189417	−	0.981897i	$-0.560660\pi$
$613$	−9.37947			−0.378833			−0.189417	+	0.981897i	$0.560660\pi$
$614$	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	$-0.782202\pi$
$617$	−3.54768	+	3.54768i	−0.142824	+	0.142824i	0.632079	+	0.774904i	$0.282202\pi$
$618$		0			0
$619$	−24.6158	−	24.6158i	−0.989392	−	0.989392i	0.0105527	−	0.999944i	$-0.496641\pi$
$619$	−24.6158	−	24.6158i	−0.989392	−	0.989392i	−0.999944	+	0.0105527i	$0.996641\pi$
$620$	−0.159651	−	0.605168i	−0.00641172	−	0.0243041i
$621$		0			0
$622$	21.8194	+	4.86585i	0.874877	+	0.195103i
$623$	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
$628$	13.5878	+	6.37747i	0.542211	+	0.254489i
$629$	−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	$0.695032\pi$
$632$	8.64618	+	6.68608i	0.343927	+	0.265958i
$633$		0			0
$634$	48.3235	+	10.7764i	1.91917	+	0.427986i
$635$	0.172367	−	1.93966i	0.00684016	−	0.0769729i
$636$		0			0
$637$	−29.7435			−1.17848
$638$	−5.22265	−	1.16468i	−0.206767	−	0.0461102i
$639$		0			0
$640$	16.9018	+	18.8237i	0.668101	+	0.744070i
$641$	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
$643$	−5.22468			−0.206041			−0.103021	−	0.994679i	$-0.532851\pi$
$643$	−5.22468			−0.206041			−0.103021	+	0.994679i	$0.532851\pi$
$644$	−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
$650$	−29.4865	−	12.3514i	−1.15656	−	0.484463i
$651$		0			0
$652$	−42.9603	−	20.1636i	−1.68245	−	0.789666i
$653$			22.7642i			0.890833i	0.895323	+	0.445417i	$0.146944\pi$
$653$			22.7642i			0.890833i	−0.895323	+	0.445417i	$0.853056\pi$
$654$		0			0
$655$	−30.0942	−	2.67431i	−1.17588	−	0.104494i
$656$	−14.0202	+	11.6455i	−0.547398	+	0.454679i
$657$		0			0
$658$	5.24560	+	1.16980i	0.204495	+	0.0456036i
$659$	−1.66201	+	1.66201i	−0.0647427	+	0.0647427i	−0.738737	−	0.673994i	$-0.764577\pi$
$659$	−1.66201	+	1.66201i	−0.0647427	+	0.0647427i	0.673994	+	0.738737i	$0.264577\pi$
$660$		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	$0.799471\pi$
$662$	28.3963	−	18.0406i	1.10365	−	0.701168i
$663$		0			0
$664$	−32.3758	−	25.0362i	−1.25642	−	0.971591i
$665$	6.36657	−	5.32739i	0.246885	−	0.206587i
$666$		0			0
$667$	−13.8720			−0.537125
$668$	0.387153	+	1.07202i	0.0149794	+	0.0414777i
$669$		0			0
$670$	4.83326	+	9.34418i	0.186725	+	0.360997i
$671$		−	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
$677$		−	26.3591i		−	1.01306i	−0.862222	−	0.506531i	$-0.830928\pi$
$677$		−	26.3591i		−	1.01306i	0.862222	−	0.506531i	$-0.169072\pi$
$678$		0			0
$679$			4.54840i			0.174551i
$680$	20.5319	+	19.0081i	0.787363	+	0.728927i
$681$		0			0
$682$	−0.0739609	−	0.116416i	−0.00283211	−	0.00445780i
$683$		−	2.83023i		−	0.108296i	−0.998533	−	0.0541479i	$-0.982756\pi$
$683$		−	2.83023i		−	0.108296i	0.998533	−	0.0541479i	$-0.0172442\pi$
$684$		0			0
$685$	−1.03645	+	11.6632i	−0.0396006	+	0.445629i
$686$	−10.5191	+	6.68296i	−0.401622	+	0.255157i
$687$		0			0
$688$	−23.0752	+	19.1667i	−0.879734	+	0.730724i
$689$			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	$0.546488\pi$
$692$	13.1288	−	27.9721i	0.499083	−	1.06334i
$693$		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
$698$	−1.99845	−	3.14560i	−0.0756423	−	0.119063i
$699$		0			0
$700$	−6.39696	+	1.09350i	−0.241782	+	0.0413303i
$701$	−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
$707$		−	1.69365i		−	0.0636965i
$708$		0			0
$709$	−25.3577	+	25.3577i	−0.952329	+	0.952329i	−0.998914	−	0.0465856i	$-0.985166\pi$
$709$	−25.3577	+	25.3577i	−0.952329	+	0.952329i	0.0465856	+	0.998914i	$0.485166\pi$
$710$	−3.84959	+	1.99120i	−0.144473	+	0.0747282i
$711$		0			0
$712$	−7.49579	−	5.79648i	−0.280916	−	0.217232i
$713$	−0.252832	−	0.252832i	−0.00946863	−	0.00946863i
$714$		0			0
$715$	−7.01735	−	0.623594i	−0.262434	−	0.0233211i
$716$	13.8452	−	5.00009i	0.517418	−	0.186862i
$717$		0			0
$718$	3.77076	−	16.9088i	0.140724	−	0.631031i
$719$	41.3374			1.54163			0.770813	−	0.637061i	$-0.219850\pi$
$719$	41.3374			1.54163			0.770813	+	0.637061i	$0.219850\pi$
$720$		0			0
$721$	10.7065			0.398730
$722$	4.22489	−	18.9452i	0.157234	−	0.705067i
$723$		0			0
$724$	−8.73236	−	24.1798i	−0.324536	−	0.898635i
$725$	−22.2805	+	15.5105i	−0.827477	+	0.576045i
$726$		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	$0.960973\pi$
$728$	−8.23182	+	1.05237i	−0.305092	+	0.0390033i
$729$		0			0
$730$	10.8683	+	3.45804i	0.402256	+	0.127988i
$731$	−23.4595	+	23.4595i	−0.867681	+	0.867681i
$732$		0			0
$733$			15.1628i			0.560051i	0.959993	+	0.280025i	$0.0903429\pi$
$733$			15.1628i			0.560051i	−0.959993	+	0.280025i	$0.909657\pi$
$734$	−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	$-0.741932\pi$
$739$	0.974343	−	0.974343i	0.0358418	−	0.0358418i	0.724801	+	0.688959i	$0.241932\pi$
$740$	6.66589	+	25.2676i	0.245043	+	0.928854i
$741$		0			0
$742$	1.35724	+	2.13633i	0.0498260	+	0.0784272i
$743$	−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
$748$	5.58168	+	2.61978i	0.204087	+	0.0957887i
$749$	−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	$0.954681\pi$
$752$	−23.3239	−	2.15808i	−0.850534	−	0.0786970i
$753$		0			0
$754$	−29.3019	+	18.6159i	−1.06711	+	0.677952i
$755$	21.3361	−	17.8535i	0.776498	−	0.649755i
$756$		0			0
$757$			1.42073i			0.0516372i	0.999667	+	0.0258186i	$0.00821923\pi$
$757$			1.42073i			0.0516372i	−0.999667	+	0.0258186i	$0.991781\pi$
$758$	14.7699	+	23.2482i	0.536469	+	0.844413i
$759$		0			0
$760$	−24.5791	+	26.5496i	−0.891579	+	0.963054i
$761$		−	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
$763$			11.4538i			0.414656i
$764$	−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	$0.690513\pi$
$770$	−1.27028	+	0.657050i	−0.0457777	+	0.0236784i
$771$		0			0
$772$	11.1509	−	4.02707i	0.401330	−	0.144937i
$773$	18.5473			0.667101			0.333550	−	0.942732i	$-0.391753\pi$
$773$	18.5473			0.667101			0.333550	+	0.942732i	$0.391753\pi$
$774$		0			0
$775$	−0.688782	−	0.123391i	−0.0247418	−	0.00443233i
$776$	−2.51378	−	19.6633i	−0.0902393	−	0.705870i
$777$		0			0
$778$	−26.6264	+	16.9162i	−0.954603	+	0.606474i
$779$	−18.4313	−	18.4313i	−0.660370	−	0.660370i
$780$		0			0
$781$	−0.675359	+	0.675359i	−0.0241662	+	0.0241662i
$782$	15.6015	+	3.47922i	0.557908	+	0.124417i
$783$		0			0
$784$	20.2430	−	16.8142i	0.722964	−	0.600508i
$785$	12.8702	−	10.7695i	0.459358	−	0.384380i
$786$		0			0
$787$		−	21.3016i		−	0.759319i	−0.925126	−	0.379659i	$-0.876041\pi$
$787$		−	21.3016i		−	0.759319i	0.925126	−	0.379659i	$-0.123959\pi$
$788$	−3.42610	+	7.29963i	−0.122050	+	0.260039i
$789$		0			0
$790$	10.8539	−	5.61415i	0.386163	−	0.199742i
$791$	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
$797$	2.35457			0.0834033			0.0417016	−	0.999130i	$-0.486722\pi$
$797$	2.35457			0.0834033			0.0417016	+	0.999130i	$0.486722\pi$
$798$		0			0
$799$	−25.9063			−0.916500
$800$	27.0505	−	8.26274i	0.956378	−	0.292132i
$801$		0			0
$802$	−27.5014	−	6.13297i	−0.971108	−	0.216563i
$803$	2.51337			0.0886949
$804$		0			0
$805$	−2.84341	+	2.37930i	−0.100217	+	0.0838592i
$806$	−0.873354	−	0.194763i	−0.0307626	−	0.00686023i
$807$		0			0
$808$	0.936037	+	7.32187i	0.0329297	+	0.257582i
$809$	−23.9476			−0.841952			−0.420976	−	0.907072i	$-0.638312\pi$
$809$	−23.9476			−0.841952			−0.420976	+	0.907072i	$0.638312\pi$
$810$		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	$0.260514\pi$
$812$	−2.99425	+	6.37952i	−0.105078	+	0.223877i
$813$		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
$818$	−8.14182	−	1.81567i	−0.284672	−	0.0634836i
$819$		0			0
$820$	5.19791	+	19.7031i	0.181519	+	0.688061i
$821$	−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	−0.0768712	−	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
$827$	1.99830			0.0694878			0.0347439	−	0.999396i	$-0.488938\pi$
$827$	1.99830			0.0694878			0.0347439	+	0.999396i	$0.488938\pi$
$828$		0			0
$829$	13.0376	+	13.0376i	0.452813	+	0.452813i	0.896287	−	0.443474i	$-0.146254\pi$
$829$	13.0376	+	13.0376i	0.452813	+	0.452813i	−0.443474	+	0.896287i	$0.646254\pi$
$830$	−40.6425	+	21.0223i	−1.41072	+	0.729694i
$831$		0			0
$832$	35.0055	−	9.09901i	1.21360	−	0.315451i
$833$	20.5801	−	20.5801i	0.713059	−	0.713059i
$834$		0			0
$835$	1.26932	+	0.112797i	0.0439266	+	0.00390352i
$836$	−3.38761	+	7.21760i	−0.117163	+	0.249626i
$837$		0			0
$838$	13.9174	−	8.84194i	0.480769	−	0.305440i
$839$			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
$842$	−18.4228	−	28.9979i	−0.634891	−	0.999333i
$843$		0			0
$844$	3.10336	+	8.59317i	0.106822	+	0.295789i
$845$	−12.7593	+	10.6766i	−0.438932	+	0.367287i
$846$		0			0
$847$	4.82499	−	4.82499i	0.165789	−	0.165789i
$848$	−7.04822	−	8.48550i	−0.242037	−	0.291393i
$849$		0			0
$850$	28.9485	−	11.8561i	0.992926	−	0.406661i
$851$	10.5565	+	10.5565i	0.361872	+	0.361872i
$852$		0			0
$853$	7.96419			0.272689			0.136344	−	0.990662i	$-0.456465\pi$
$853$	7.96419			0.272689			0.136344	+	0.990662i	$0.456465\pi$
$854$	−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	$-0.708719\pi$
$857$	5.35407	−	5.35407i	0.182891	−	0.182891i	0.792615	+	0.609723i	$0.208719\pi$
$858$		0			0
$859$	−35.0058	−	35.0058i	−1.19438	−	1.19438i	−0.975824	−	0.218559i	$-0.929864\pi$
$859$	−35.0058	−	35.0058i	−1.19438	−	1.19438i	−0.218559	−	0.975824i	$-0.570136\pi$
$860$	8.55499	+	32.4283i	0.291723	+	1.10580i
$861$		0			0
$862$	9.90457	−	44.4140i	0.337351	−	1.51275i
$863$	−36.7138	−	36.7138i	−1.24975	−	1.24975i	−0.955829	−	0.293923i	$-0.905039\pi$
$863$	−36.7138	−	36.7138i	−1.24975	−	1.24975i	−0.293923	−	0.955829i	$-0.594961\pi$
$864$		0			0
$865$	−22.1703	−	26.4950i	−0.753814	−	0.900856i
$866$	−34.3336	+	21.8126i	−1.16670	+	0.741224i
$867$		0			0
$868$	−0.170847	+	0.0617003i	−0.00579893	+	0.00209424i
$869$	1.90416	−	1.90416i	0.0645943	−	0.0645943i
$870$		0			0
$871$	15.0406			0.509633
$872$	−6.33022	−	49.5162i	−0.214368	−	1.67683i
$873$		0			0
$874$	−4.49894	+	20.1741i	−0.152179	+	0.682399i
$875$	−1.90662	+	7.00078i	−0.0644555	+	0.236669i
$876$		0			0
$877$	−14.3410			−0.484262			−0.242131	−	0.970244i	$-0.577846\pi$
$877$	−14.3410			−0.484262			−0.242131	+	0.970244i	$0.577846\pi$
$878$	10.9022	−	48.8877i	0.367933	−	1.64988i
$879$		0			0
$880$	5.12843	−	3.54255i	0.172879	−	0.119419i
$881$	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
$883$	6.12563			0.206144			0.103072	−	0.994674i	$-0.467133\pi$
$883$	6.12563			0.206144			0.103072	+	0.994674i	$0.467133\pi$
$884$	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
$890$	−9.40974	+	4.86717i	−0.315415	+	0.163148i
$891$		0			0
$892$	7.85227	+	21.7428i	0.262913	+	0.728003i
$893$		−	33.4992i		−	1.12101i
$894$		0			0
$895$	1.45678	−	16.3933i	0.0486948	−	0.547967i
$896$	5.00755	−	5.36973i	0.167290	−	0.179390i
$897$		0			0
$898$	−2.66433	+	11.9474i	−0.0889100	+	0.398689i
$899$	−0.537302	+	0.537302i	−0.0179200	+	0.0179200i
$900$		0			0
$901$	−8.62682	−	8.62682i	−0.287401	−	0.287401i
$902$	2.40802	+	3.79028i	0.0801784	+	0.126203i
$903$		0			0
$904$	−10.0604	+	1.28613i	−0.334604	+	0.0427762i
$905$	−28.6299	−	2.54418i	−0.951691	−	0.0845715i
$906$		0			0
$907$	32.1815			1.06857			0.534284	−	0.845305i	$-0.320581\pi$
$907$	32.1815			1.06857			0.534284	+	0.845305i	$0.320581\pi$
$908$	−1.30921	+	2.78940i	−0.0434477	+	0.0925694i
$909$		0			0
$910$	−2.81318	+	8.84161i	−0.0932562	+	0.293096i
$911$			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
$917$			8.76867i			0.289567i
$918$		0			0
$919$			19.1924i			0.633099i	0.948576	+	0.316550i	$0.102524\pi$
$919$			19.1924i			0.633099i	−0.948576	+	0.316550i	$0.897476\pi$
$920$	10.9774	−	11.8575i	0.361915	−	0.390929i
$921$		0			0
$922$	2.02038	−	1.28358i	0.0665378	−	0.0422725i
$923$			6.19641i			0.203957i
$924$		0			0
$925$	28.7587	+	5.15194i	0.945580	+	0.169395i
$926$	22.7170	+	35.7571i	0.746527	+	1.17505i
$927$		0			0
$928$	9.41870	−	29.2343i	0.309184	−	0.959662i
$929$			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
$932$	9.59792	+	26.5765i	0.314390	+	0.870542i
$933$		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	$-0.563378\pi$
$937$	23.9511	−	23.9511i	0.782449	−	0.782449i	0.980243	+	0.197795i	$0.0633779\pi$
$938$	2.57715	−	1.63730i	0.0841470	−	0.0534599i
$939$		0			0
$940$	−13.1817	+	22.6289i	−0.429939	+	0.738075i
$941$	−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
$947$		−	20.2943i		−	0.659477i	−0.944072	−	0.329738i	$-0.893039\pi$
$947$		−	20.2943i		−	0.659477i	0.944072	−	0.329738i	$-0.106961\pi$
$948$		0			0
$949$	11.5301	−	11.5301i	0.374282	−	0.374282i
$950$	15.3310	+	37.4330i	0.497403	+	1.21449i
$951$		0			0
$952$	4.96761	−	6.42391i	0.161001	−	0.208200i
$953$	−10.9257	−	10.9257i	−0.353919	−	0.353919i	0.507647	−	0.861565i	$-0.330516\pi$
$953$	−10.9257	−	10.9257i	−0.353919	−	0.353919i	−0.861565	+	0.507647i	$0.830516\pi$
$954$		0			0
$955$	21.6789	+	25.9077i	0.701514	+	0.838353i
$956$	47.5730	+	22.3285i	1.53862	+	0.722157i
$957$		0			0
$958$	−32.5429	−	7.25726i	−1.05141	−	0.234471i
$959$	3.39836			0.109739
$960$		0			0
$961$	30.9804			0.999368
$962$	36.4651	+	8.13193i	1.17568	+	0.262184i
$963$		0			0
$964$	−0.205024	−	0.0962289i	−0.00660339	−	0.00309932i
$965$	1.17329	−	13.2032i	0.0377696	−	0.425025i
$966$		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	$0.671343\pi$
$968$	−18.1923	+	23.5256i	−0.584724	+	0.756142i
$969$		0			0
$970$	−21.1198	−	6.71982i	−0.678117	−	0.215760i
$971$	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
$973$			5.01811i			0.160873i
$974$	−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
$980$	−7.50496	−	28.4481i	−0.239737	−	0.908742i
$981$		0			0
$982$	31.5509	−	20.0448i	1.00683	−	0.639655i
$983$	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
$988$	17.5701	+	48.6513i	0.558979	+	1.54781i
$989$	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	$-0.424776\pi$
$992$	0.704492	−	0.361160i	0.0223677	−	0.0114668i
$993$		0			0
$994$	0.674533	+	1.06173i	0.0213949	+	0.0336760i
$995$	−7.79271	−	9.31279i	−0.247046	−	0.295235i
$996$		0			0
$997$			39.1082i			1.23857i	0.785167	+	0.619284i	$0.212577\pi$
$997$			39.1082i			1.23857i	−0.785167	+	0.619284i	$0.787423\pi$
$998$	16.3637	−	10.3961i	0.517984	−	0.329083i
$999$		0			0

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
80.2.j.b.43.5	✓	18	15.8	even	4
80.2.j.b.67.5	yes	18	48.35	even	4
80.2.s.b.3.1	yes	18	240.83	odd	4
80.2.s.b.27.1	yes	18	3.2	odd	2
320.2.j.b.47.9		18	48.29	odd	4
320.2.j.b.143.1		18	60.23	odd	4
320.2.s.b.207.1		18	12.11	even	2
320.2.s.b.303.1		18	240.173	even	4
400.2.j.d.43.5		18	15.2	even	4
400.2.j.d.307.5		18	240.179	even	4
400.2.s.d.107.9		18	15.14	odd	2
400.2.s.d.243.9		18	240.227	odd	4
640.2.j.c.543.9		18	120.83	odd	4
640.2.j.c.607.1		18	48.5	odd	4
640.2.j.d.543.1		18	120.53	even	4
640.2.j.d.607.9		18	48.11	even	4
640.2.s.c.223.9		18	240.53	even	4
640.2.s.c.287.9		18	24.11	even	2
640.2.s.d.223.1		18	240.203	odd	4
640.2.s.d.287.1		18	24.5	odd	2
720.2.z.g.163.9		18	80.3	even	4	inner
720.2.z.g.667.9		18	1.1	even	1	trivial
720.2.bd.g.307.5		18	16.3	odd	4
720.2.bd.g.523.5		18	5.3	odd	4
1600.2.j.d.143.9		18	60.47	odd	4
1600.2.j.d.1007.1		18	240.29	odd	4
1600.2.s.d.207.9		18	60.59	even	2
1600.2.s.d.943.9		18	240.77	even	4

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

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

\(f(q)\)	\(=\)	\(q+(1.38031 + 0.307817i) q^{2} +(1.81050 + 0.849763i) q^{4} +(1.71489 - 1.43498i) q^{5} +(-0.458895 - 0.458895i) q^{7} +(2.23747 + 1.73024i) q^{8} +(2.80878 - 1.45284i) q^{10} +(0.492763 - 0.492763i) q^{11} -4.52109i q^{13} +(-0.492160 - 0.774671i) q^{14} +(2.55581 + 3.07699i) q^{16} +(3.12823 + 3.12823i) q^{17} +(-4.04508 + 4.04508i) q^{19} +(4.32419 - 1.14077i) q^{20} +(0.831845 - 0.528484i) q^{22} +(1.80660 - 1.80660i) q^{23} +(0.881683 - 4.92165i) q^{25} +(1.39167 - 6.24050i) q^{26} +(-0.440876 - 1.22078i) q^{28} +(-3.83926 - 3.83926i) q^{29} -0.139949i q^{31} +(2.58065 + 5.03391i) q^{32} +(3.35500 + 5.28085i) q^{34} +(-1.44546 - 0.128450i) q^{35} +5.84330i q^{37} +(-6.82860 + 4.33831i) q^{38} +(6.31986 - 0.243561i) q^{40} +4.55648i q^{41} +7.49928i q^{43} +(1.31088 - 0.473414i) q^{44} +(3.04976 - 1.93756i) q^{46} +(-4.14073 + 4.14073i) q^{47} -6.57883i q^{49} +(2.73196 - 6.52199i) q^{50} +(3.84186 - 8.18543i) q^{52} -2.75773 q^{53} +(0.137930 - 1.55214i) q^{55} +(-0.232768 - 1.82076i) q^{56} +(-4.11757 - 6.48115i) q^{58} +(-3.62521 - 3.62521i) q^{59} +(3.72781 - 3.72781i) q^{61} +(0.0430787 - 0.193173i) q^{62} +(2.01257 + 7.74271i) q^{64} +(-6.48766 - 7.75317i) q^{65} +3.32677i q^{67} +(3.00540 + 8.32192i) q^{68} +(-1.95563 - 0.622235i) q^{70} -1.37056 q^{71} +(2.55028 + 2.55028i) q^{73} +(-1.79867 + 8.06556i) q^{74} +(-10.7610 + 3.88625i) q^{76} -0.452252 q^{77} +3.86426 q^{79} +(8.79833 + 1.60917i) q^{80} +(-1.40256 + 6.28934i) q^{82} -14.4698 q^{83} +(9.85351 + 0.875628i) q^{85} +(-2.30840 + 10.3513i) q^{86} +(1.95514 - 0.249948i) q^{88} -3.35011 q^{89} +(-2.07470 + 2.07470i) q^{91} +(4.80602 - 1.73566i) q^{92} +(-6.99006 + 4.44089i) q^{94} +(-1.13226 + 12.7415i) q^{95} +(-4.95582 - 4.95582i) q^{97} +(2.02507 - 9.08081i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 18 q + 4 q^{4} - 2 q^{5} + 2 q^{7} + 12 q^{8} + 2 q^{11} + 12 q^{14} + 6 q^{17} - 2 q^{19} + 12 q^{20} + 12 q^{22} + 2 q^{23} - 6 q^{25} + 16 q^{26} + 40 q^{28} - 14 q^{29} - 20 q^{32} + 28 q^{34} - 2 q^{35}+ \cdots + 56 q^{98}+O(q^{100}) \) 18 * q + 4 * q^4 - 2 * q^5 + 2 * q^7 + 12 * q^8 + 2 * q^11 + 12 * q^14 + 6 * q^17 - 2 * q^19 + 12 * q^20 + 12 * q^22 + 2 * q^23 - 6 * q^25 + 16 * q^26 + 40 * q^28 - 14 * q^29 - 20 * q^32 + 28 * q^34 - 2 * q^35 - 24 * q^38 + 44 * q^40 + 44 * q^44 + 12 * q^46 - 38 * q^47 + 8 * q^50 + 8 * q^52 - 12 * q^53 - 6 * q^55 - 20 * q^56 + 20 * q^58 - 10 * q^59 + 14 * q^61 + 40 * q^62 + 16 * q^64 + 60 * q^68 - 28 * q^70 - 24 * q^71 - 14 * q^73 + 48 * q^74 - 16 * q^76 + 44 * q^77 - 16 * q^79 + 92 * q^80 + 48 * q^82 - 40 * q^83 + 14 * q^85 + 36 * q^86 - 8 * q^88 - 12 * q^89 + 8 * q^92 - 28 * q^94 - 34 * q^95 + 18 * q^97 + 56 * q^98

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