LMFDB - Embedded newform 720.2.bm.h.109.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [720,2,Mod(109,720)]

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([0, 3, 0, 2]))

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

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

chi := DirichletCharacter("720.109");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 720 = 2^{4} \cdot 3^{2} \cdot 5 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	720.bm (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:	$48$
Relative dimension:	$24$ over $\Q(i)$
Twist minimal:	no (minimal twist has level 240)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			109.1
Character	$\chi$	$=$	720.109
Dual form			720.2.bm.h.469.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.40976 - 0.112110i) q^{2} +(1.97486 + 0.316097i) q^{4} +(0.466917 + 2.18678i) q^{5} -1.00010 q^{7} +(-2.74865 - 0.667024i) q^{8} +O(q^{10})$	\(q+(-1.40976 - 0.112110i) q^{2} +(1.97486 + 0.316097i) q^{4} +(0.466917 + 2.18678i) q^{5} -1.00010 q^{7} +(-2.74865 - 0.667024i) q^{8} +(-0.413083 - 3.13518i) q^{10} +(1.89490 - 1.89490i) q^{11} +(-2.65915 + 2.65915i) q^{13} +(1.40991 + 0.112121i) q^{14} +(3.80016 + 1.24850i) q^{16} +1.73836i q^{17} +(5.33902 + 5.33902i) q^{19} +(0.230863 + 4.46617i) q^{20} +(-2.88380 + 2.45892i) q^{22} +0.160230 q^{23} +(-4.56398 + 2.04209i) q^{25} +(4.04689 - 3.45065i) q^{26} +(-1.97506 - 0.316129i) q^{28} +(-2.70291 - 2.70291i) q^{29} -4.64288 q^{31} +(-5.21736 - 2.18612i) q^{32} +(0.194888 - 2.45068i) q^{34} +(-0.466965 - 2.18700i) q^{35} +(-5.35773 - 5.35773i) q^{37} +(-6.92819 - 8.12530i) q^{38} +(0.175241 - 6.32213i) q^{40} +9.89786i q^{41} +(7.23165 + 7.23165i) q^{43} +(4.34114 - 3.14320i) q^{44} +(-0.225886 - 0.0179634i) q^{46} +4.79583i q^{47} -5.99980 q^{49} +(6.66306 - 2.36719i) q^{50} +(-6.09201 + 4.41091i) q^{52} +(3.44618 + 3.44618i) q^{53} +(5.02849 + 3.25896i) q^{55} +(2.74893 + 0.667092i) q^{56} +(3.50744 + 4.11349i) q^{58} +(-0.101729 + 0.101729i) q^{59} +(-6.01811 - 6.01811i) q^{61} +(6.54535 + 0.520513i) q^{62} +(7.11016 + 3.66683i) q^{64} +(-7.05657 - 4.57336i) q^{65} +(-9.04430 + 9.04430i) q^{67} +(-0.549491 + 3.43302i) q^{68} +(0.413125 + 3.13550i) q^{70} +4.60679i q^{71} +12.1920 q^{73} +(6.95248 + 8.15379i) q^{74} +(8.85617 + 12.2315i) q^{76} +(-1.89509 + 1.89509i) q^{77} -5.73529 q^{79} +(-0.955822 + 8.89305i) q^{80} +(1.10965 - 13.9536i) q^{82} +(2.04924 - 2.04924i) q^{83} +(-3.80140 + 0.811670i) q^{85} +(-9.38417 - 11.0057i) q^{86} +(-6.47237 + 3.94448i) q^{88} +15.0386i q^{89} +(2.65942 - 2.65942i) q^{91} +(0.316432 + 0.0506483i) q^{92} +(0.537662 - 6.76099i) q^{94} +(-9.18235 + 14.1681i) q^{95} -3.84735i q^{97} +(8.45829 + 0.672638i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q+O(q^{10}) $ 48 * q	$ 48 q + 12 q^{10} + 16 q^{14} - 4 q^{16} + 8 q^{19} + 40 q^{26} - 48 q^{31} - 28 q^{34} - 24 q^{35} - 16 q^{40} + 40 q^{44} - 4 q^{46} + 48 q^{49} + 32 q^{50} - 48 q^{56} + 32 q^{59} + 16 q^{61} + 48 q^{64} - 16 q^{65} - 40 q^{74} + 60 q^{76} - 96 q^{79} - 72 q^{80} - 16 q^{86} - 32 q^{91} + 44 q^{94} + 48 q^{95}+O(q^{100}) $ 48 * q + 12 * q^10 + 16 * q^14 - 4 * q^16 + 8 * q^19 + 40 * q^26 - 48 * q^31 - 28 * q^34 - 24 * q^35 - 16 * q^40 + 40 * q^44 - 4 * q^46 + 48 * q^49 + 32 * q^50 - 48 * q^56 + 32 * q^59 + 16 * q^61 + 48 * q^64 - 16 * q^65 - 40 * q^74 + 60 * q^76 - 96 * q^79 - 72 * q^80 - 16 * q^86 - 32 * q^91 + 44 * q^94 + 48 * q^95

Display 100 coefficients 10 coefficients

Character values

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

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

Coefficient data

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

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

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

$2$	−1.40976	−	0.112110i	−0.996853	−	0.0792738i
$2$	−1.40976	−	0.112110i	−0.996853	−	0.0792738i
$3$		0			0
$3$		0			0
$4$	1.97486	+	0.316097i	0.987431	+	0.158049i
$5$	0.466917	+	2.18678i	0.208812	+	0.977956i
$5$	0.466917	+	2.18678i	0.208812	+	0.977956i
$6$		0			0
$7$	−1.00010			−0.378003			−0.189001	−	0.981977i	$-0.560525\pi$
$7$	−1.00010			−0.378003			−0.189001	+	0.981977i	$0.560525\pi$
$8$	−2.74865	−	0.667024i	−0.971795	−	0.235829i
$9$		0			0
$10$	−0.413083	−	3.13518i	−0.130628	−	0.991431i
$11$	1.89490	−	1.89490i	0.571334	−	0.571334i	−0.361167	−	0.932501i	$-0.617622\pi$
$11$	1.89490	−	1.89490i	0.571334	−	0.571334i	0.932501	+	0.361167i	$0.117622\pi$
$12$		0			0
$13$	−2.65915	+	2.65915i	−0.737515	+	0.737515i	−0.972097	−	0.234581i	$-0.924628\pi$
$13$	−2.65915	+	2.65915i	−0.737515	+	0.737515i	0.234581	+	0.972097i	$0.424628\pi$
$14$	1.40991	+	0.112121i	0.376813	+	0.0299657i
$15$		0			0
$16$	3.80016	+	1.24850i	0.950041	+	0.312124i
$17$			1.73836i			0.421614i	0.977528	+	0.210807i	$0.0676092\pi$
$17$			1.73836i			0.421614i	−0.977528	+	0.210807i	$0.932391\pi$
$18$		0			0
$19$	5.33902	+	5.33902i	1.22485	+	1.22485i	0.965886	+	0.258968i	$0.0833826\pi$
$19$	5.33902	+	5.33902i	1.22485	+	1.22485i	0.258968	+	0.965886i	$0.416617\pi$
$20$	0.230863	+	4.46617i	0.0516226	+	0.998667i
$21$		0			0
$22$	−2.88380	+	2.45892i	−0.614828	+	0.524244i
$23$	0.160230			0.0334103			0.0167051	−	0.999860i	$-0.494682\pi$
$23$	0.160230			0.0334103			0.0167051	+	0.999860i	$0.494682\pi$
$24$		0			0
$25$	−4.56398	+	2.04209i	−0.912795	+	0.408417i
$26$	4.04689	−	3.45065i	0.793660	−	0.676729i
$27$		0			0
$28$	−1.97506	−	0.316129i	−0.373252	−	0.0597428i
$29$	−2.70291	−	2.70291i	−0.501918	−	0.501918i	0.410116	−	0.912034i	$-0.365488\pi$
$29$	−2.70291	−	2.70291i	−0.501918	−	0.501918i	−0.912034	+	0.410116i	$0.865488\pi$
$30$		0			0
$31$	−4.64288			−0.833885			−0.416943	−	0.908933i	$-0.636898\pi$
$31$	−4.64288			−0.833885			−0.416943	+	0.908933i	$0.636898\pi$
$32$	−5.21736	−	2.18612i	−0.922308	−	0.386456i
$33$		0			0
$34$	0.194888	−	2.45068i	0.0334230	−	0.420287i
$35$	−0.466965	−	2.18700i	−0.0789314	−	0.369670i
$36$		0			0
$37$	−5.35773	−	5.35773i	−0.880806	−	0.880806i	0.112811	−	0.993616i	$-0.464015\pi$
$37$	−5.35773	−	5.35773i	−0.880806	−	0.880806i	−0.993616	+	0.112811i	$0.964015\pi$
$38$	−6.92819	−	8.12530i	−1.12390	−	1.31810i
$39$		0			0
$40$	0.175241	−	6.32213i	0.0277080	−	0.999616i
$41$			9.89786i			1.54579i	0.634536	+	0.772893i	$0.281191\pi$
$41$			9.89786i			1.54579i	−0.634536	+	0.772893i	$0.718809\pi$
$42$		0			0
$43$	7.23165	+	7.23165i	1.10282	+	1.10282i	0.994069	+	0.108747i	$0.0346838\pi$
$43$	7.23165	+	7.23165i	1.10282	+	1.10282i	0.108747	+	0.994069i	$0.465316\pi$
$44$	4.34114	−	3.14320i	0.654452	−	0.473855i
$45$		0			0
$46$	−0.225886	−	0.0179634i	−0.0333051	−	0.00264856i
$47$			4.79583i			0.699544i	0.936835	+	0.349772i	$0.113741\pi$
$47$			4.79583i			0.699544i	−0.936835	+	0.349772i	$0.886259\pi$
$48$		0			0
$49$	−5.99980			−0.857114
$50$	6.66306	−	2.36719i	0.942299	−	0.334771i
$51$		0			0
$52$	−6.09201	+	4.41091i	−0.844809	+	0.611683i
$53$	3.44618	+	3.44618i	0.473369	+	0.473369i	0.903003	−	0.429634i	$-0.141357\pi$
$53$	3.44618	+	3.44618i	0.473369	+	0.473369i	−0.429634	+	0.903003i	$0.641357\pi$
$54$		0			0
$55$	5.02849	+	3.25896i	0.678041	+	0.439438i
$56$	2.74893	+	0.667092i	0.367341	+	0.0891439i
$57$		0			0
$58$	3.50744	+	4.11349i	0.460549	+	0.540127i
$59$	−0.101729	+	0.101729i	−0.0132440	+	0.0132440i	−0.713698	−	0.700454i	$-0.752981\pi$
$59$	−0.101729	+	0.101729i	−0.0132440	+	0.0132440i	0.700454	+	0.713698i	$0.252981\pi$
$60$		0			0
$61$	−6.01811	−	6.01811i	−0.770540	−	0.770540i	0.207661	−	0.978201i	$-0.433415\pi$
$61$	−6.01811	−	6.01811i	−0.770540	−	0.770540i	−0.978201	+	0.207661i	$0.933415\pi$
$62$	6.54535	+	0.520513i	0.831261	+	0.0661053i
$63$		0			0
$64$	7.11016	+	3.66683i	0.888770	+	0.458354i
$65$	−7.05657	−	4.57336i	−0.875259	−	0.567256i
$66$		0			0
$67$	−9.04430	+	9.04430i	−1.10494	+	1.10494i	−0.111131	+	0.993806i	$0.535447\pi$
$67$	−9.04430	+	9.04430i	−1.10494	+	1.10494i	−0.993806	+	0.111131i	$0.964553\pi$
$68$	−0.549491	+	3.43302i	−0.0666356	+	0.416315i
$69$		0			0
$70$	0.413125	+	3.13550i	0.0493778	+	0.374764i
$71$			4.60679i			0.546726i	0.961911	+	0.273363i	$0.0881360\pi$
$71$			4.60679i			0.546726i	−0.961911	+	0.273363i	$0.911864\pi$
$72$		0			0
$73$	12.1920			1.42697			0.713485	−	0.700671i	$-0.247116\pi$
$73$	12.1920			1.42697			0.713485	+	0.700671i	$0.247116\pi$
$74$	6.95248	+	8.15379i	0.808209	+	0.947858i
$75$		0			0
$76$	8.85617	+	12.2315i	1.01587	+	1.40305i
$77$	−1.89509	+	1.89509i	−0.215966	+	0.215966i
$78$		0			0
$79$	−5.73529			−0.645271			−0.322635	−	0.946523i	$-0.604569\pi$
$79$	−5.73529			−0.645271			−0.322635	+	0.946523i	$0.604569\pi$
$80$	−0.955822	+	8.89305i	−0.106864	+	0.994274i
$81$		0			0
$82$	1.10965	−	13.9536i	0.122540	−	1.54092i
$83$	2.04924	−	2.04924i	0.224934	−	0.224934i	−0.585639	−	0.810572i	$-0.699156\pi$
$83$	2.04924	−	2.04924i	0.224934	−	0.224934i	0.810572	+	0.585639i	$0.199156\pi$
$84$		0			0
$85$	−3.80140	+	0.811670i	−0.412320	+	0.0880380i
$86$	−9.38417	−	11.0057i	−1.01192	−	1.18677i
$87$		0			0
$88$	−6.47237	+	3.94448i	−0.689957	+	0.420483i
$89$			15.0386i			1.59409i	0.603922	+	0.797044i	$0.293604\pi$
$89$			15.0386i			1.59409i	−0.603922	+	0.797044i	$0.706396\pi$
$90$		0			0
$91$	2.65942	−	2.65942i	0.278783	−	0.278783i
$92$	0.316432	+	0.0506483i	0.0329903	+	0.00528045i
$93$		0			0
$94$	0.537662	−	6.76099i	0.0554556	−	0.697343i
$95$	−9.18235	+	14.1681i	−0.942089	+	1.45362i
$96$		0			0
$97$		−	3.84735i		−	0.390639i	−0.980740	−	0.195320i	$-0.937426\pi$
$97$		−	3.84735i		−	0.390639i	0.980740	−	0.195320i	$-0.0625744\pi$
$98$	8.45829	+	0.672638i	0.854416	+	0.0679467i
$99$		0			0
$100$	−9.65873	+	2.59018i	−0.965873	+	0.259018i
$101$	−5.60917	+	5.60917i	−0.558133	+	0.558133i	−0.928776	−	0.370642i	$-0.879138\pi$
$101$	−5.60917	+	5.60917i	−0.558133	+	0.558133i	0.370642	+	0.928776i	$0.379138\pi$
$102$		0			0
$103$	14.9978			1.47778			0.738888	−	0.673828i	$-0.235351\pi$
$103$	14.9978			1.47778			0.738888	+	0.673828i	$0.235351\pi$
$104$	9.08279	−	5.53536i	0.890641	−	0.542786i
$105$		0			0
$106$	−4.47195	−	5.24465i	−0.434354	−	0.509406i
$107$	−1.22436	−	1.22436i	−0.118363	−	0.118363i	0.645444	−	0.763807i	$-0.276672\pi$
$107$	−1.22436	−	1.22436i	−0.118363	−	0.118363i	−0.763807	+	0.645444i	$0.776672\pi$
$108$		0			0
$109$	5.31222	+	5.31222i	0.508819	+	0.508819i	0.914164	−	0.405345i	$-0.132849\pi$
$109$	5.31222	+	5.31222i	0.508819	+	0.508819i	−0.405345	+	0.914164i	$0.632849\pi$
$110$	−6.72361	−	5.15811i	−0.641071	−	0.491806i
$111$		0			0
$112$	−3.80055	−	1.24862i	−0.359118	−	0.117984i
$113$		−	10.5478i		−	0.992249i	−0.868251	−	0.496125i	$-0.834756\pi$
$113$		−	10.5478i		−	0.992249i	0.868251	−	0.496125i	$-0.165244\pi$
$114$		0			0
$115$	0.0748141	+	0.350387i	0.00697645	+	0.0326738i
$116$	−4.48349	−	6.19226i	−0.416282	−	0.574937i
$117$		0			0
$118$	0.154819	−	0.132009i	0.0142523	−	0.0121524i
$119$		−	1.73854i		−	0.159371i
$120$		0			0
$121$			3.81870i			0.347154i
$122$	7.80942	+	9.15880i	0.707031	+	0.829199i
$123$		0			0
$124$	−9.16904	−	1.46760i	−0.823404	−	0.131794i
$125$	−6.59658	−	9.02691i	−0.590016	−	0.807391i
$126$		0			0
$127$			5.78563i			0.513391i	0.966492	+	0.256696i	$0.0826338\pi$
$127$			5.78563i			0.513391i	−0.966492	+	0.256696i	$0.917366\pi$
$128$	−9.61255	−	5.96649i	−0.849637	−	0.527368i
$129$		0			0
$130$	9.43537	+	7.23847i	0.827536	+	0.634856i
$131$	1.01902	+	1.01902i	0.0890321	+	0.0890321i	0.750220	−	0.661188i	$-0.229947\pi$
$131$	1.01902	+	1.01902i	0.0890321	+	0.0890321i	−0.661188	+	0.750220i	$0.729947\pi$
$132$		0			0
$133$	−5.33956	−	5.33956i	−0.462998	−	0.462998i
$134$	13.7643	−	11.7364i	1.18905	−	1.01387i
$135$		0			0
$136$	1.15953	−	4.77814i	0.0994287	−	0.409722i
$137$	−11.1576			−0.953260			−0.476630	−	0.879104i	$-0.658142\pi$
$137$	−11.1576			−0.953260			−0.476630	+	0.879104i	$0.658142\pi$
$138$		0			0
$139$	15.9657	−	15.9657i	1.35419	−	1.35419i	0.473277	−	0.880914i	$-0.343071\pi$
$139$	15.9657	−	15.9657i	1.35419	−	1.35419i	0.880914	−	0.473277i	$-0.156929\pi$
$140$	−0.230887	−	4.46663i	−0.0195135	−	0.377499i
$141$		0			0
$142$	0.516468	−	6.49449i	0.0433411	−	0.545005i
$143$			10.0777i			0.842736i
$144$		0			0
$145$	4.64862	−	7.17270i	0.386047	−	0.595660i
$146$	−17.1879	−	1.36685i	−1.42248	−	0.113121i
$147$		0			0
$148$	−8.88722	−	12.2743i	−0.730525	−	1.00895i
$149$	14.5202	−	14.5202i	1.18954	−	1.18954i	0.212342	−	0.977195i	$-0.431891\pi$
$149$	14.5202	−	14.5202i	1.18954	−	1.18954i	0.977195	−	0.212342i	$-0.0681090\pi$
$150$		0			0
$151$		−	14.7230i		−	1.19814i	−0.800695	−	0.599072i	$-0.795536\pi$
$151$		−	14.7230i		−	1.19814i	0.800695	−	0.599072i	$-0.204464\pi$
$152$	−11.1138	−	18.2363i	−0.901451	−	1.47916i
$153$		0			0
$154$	2.88409	−	2.45917i	0.232407	−	0.198166i
$155$	−2.16784	−	10.1529i	−0.174125	−	0.815503i
$156$		0			0
$157$	9.44726	−	9.44726i	0.753974	−	0.753974i	−0.221245	−	0.975218i	$-0.571012\pi$
$157$	9.44726	−	9.44726i	0.753974	−	0.753974i	0.975218	+	0.221245i	$0.0710119\pi$
$158$	8.08540	+	0.642984i	0.643240	+	0.0511531i
$159$		0			0
$160$	2.34448	−	12.4299i	0.185348	−	0.982673i
$161$	−0.160246			−0.0126292
$162$		0			0
$163$	7.66138	−	7.66138i	0.600086	−	0.600086i	−0.340250	−	0.940335i	$-0.610512\pi$
$163$	7.66138	−	7.66138i	0.600086	−	0.600086i	0.940335	+	0.340250i	$0.110512\pi$
$164$	−3.12869	+	19.5469i	−0.244310	+	1.52636i
$165$		0			0
$166$	−3.11869	+	2.65921i	−0.242057	+	0.206394i
$167$	14.4195			1.11581			0.557906	−	0.829904i	$-0.311605\pi$
$167$	14.4195			1.11581			0.557906	+	0.829904i	$0.311605\pi$
$168$		0			0
$169$		−	1.14216i		−	0.0878581i
$170$	5.45007	−	0.718086i	0.418002	−	0.0550747i
$171$		0			0
$172$	11.9956	+	16.5674i	0.914657	+	1.26325i
$173$	0.942572	−	0.942572i	0.0716624	−	0.0716624i	−0.670367	−	0.742030i	$-0.733863\pi$
$173$	0.942572	−	0.942572i	0.0716624	−	0.0716624i	0.742030	+	0.670367i	$0.233863\pi$
$174$		0			0
$175$	4.56444	−	2.04229i	0.345039	−	0.154383i
$176$	9.56672	−	4.83516i	0.721119	−	0.364464i
$177$		0			0
$178$	1.68598	−	21.2008i	0.126369	−	1.58907i
$179$	3.23789	+	3.23789i	0.242011	+	0.242011i	0.817682	−	0.575671i	$-0.195259\pi$
$179$	3.23789	+	3.23789i	0.242011	+	0.242011i	−0.575671	+	0.817682i	$0.695259\pi$
$180$		0			0
$181$	−13.0914	+	13.0914i	−0.973076	+	0.973076i	−0.999647	−	0.0265713i	$-0.991541\pi$
$181$	−13.0914	+	13.0914i	−0.973076	+	0.973076i	0.0265713	+	0.999647i	$0.491541\pi$
$182$	−4.04730	+	3.45100i	−0.300006	+	0.255805i
$183$		0			0
$184$	−0.440416	−	0.106877i	−0.0324679	−	0.00787910i
$185$	9.21454	−	14.2178i	0.677467	−	1.04531i
$186$		0			0
$187$	3.29402	+	3.29402i	0.240883	+	0.240883i
$188$	−1.51595	+	9.47111i	−0.110562	+	0.690752i
$189$		0			0
$190$	14.5333	−	18.9442i	1.05436	−	1.37436i
$191$	−9.80663			−0.709583			−0.354791	−	0.934946i	$-0.615448\pi$
$191$	−9.80663			−0.709583			−0.354791	+	0.934946i	$0.615448\pi$
$192$		0			0
$193$		−	6.82164i		−	0.491033i	−0.969392	−	0.245516i	$-0.921043\pi$
$193$		−	6.82164i		−	0.491033i	0.969392	−	0.245516i	$-0.0789575\pi$
$194$	−0.431327	+	5.42385i	−0.0309675	+	0.389410i
$195$		0			0
$196$	−11.8488	−	1.89652i	−0.846341	−	0.135466i
$197$	−15.5142	−	15.5142i	−1.10534	−	1.10534i	−0.993755	−	0.111587i	$-0.964407\pi$
$197$	−15.5142	−	15.5142i	−1.10534	−	1.10534i	−0.111587	−	0.993755i	$-0.535593\pi$
$198$		0			0
$199$			7.92050i			0.561469i	0.959785	+	0.280735i	$0.0905781\pi$
$199$			7.92050i			0.561469i	−0.959785	+	0.280735i	$0.909422\pi$
$200$	13.9069	−	2.56870i	0.983366	−	0.181634i
$201$		0			0
$202$	8.53645	−	7.27876i	0.600622	−	0.512132i
$203$	2.70319	+	2.70319i	0.189726	+	0.189726i
$204$		0			0
$205$	−21.6444	+	4.62148i	−1.51171	+	0.322778i
$206$	−21.1433	−	1.68140i	−1.47313	−	0.117149i
$207$		0			0
$208$	−13.4252	+	6.78527i	−0.930867	+	0.470474i
$209$	20.2338			1.39960
$210$		0			0
$211$	−10.2008	−	10.2008i	−0.702253	−	0.702253i	0.262641	−	0.964894i	$-0.415406\pi$
$211$	−10.2008	−	10.2008i	−0.702253	−	0.702253i	−0.964894	+	0.262641i	$0.915406\pi$
$212$	5.71641	+	7.89506i	0.392604	+	0.542235i
$213$		0			0
$214$	1.58879	+	1.86332i	0.108608	+	0.127374i
$215$	−12.4374	+	19.1906i	−0.848225	+	1.30879i
$216$		0			0
$217$	4.64335			0.315211
$218$	−6.89342	−	8.08453i	−0.466881	−	0.547553i
$219$		0			0
$220$	8.90042	+	8.02550i	0.600066	+	0.541079i
$221$	−4.62256	−	4.62256i	−0.310947	−	0.310947i
$222$		0			0
$223$			13.8689i			0.928732i	0.885643	+	0.464366i	$0.153718\pi$
$223$			13.8689i			0.928732i	−0.885643	+	0.464366i	$0.846282\pi$
$224$	5.21789	+	2.18634i	0.348635	+	0.146081i
$225$		0			0
$226$	−1.18251	+	14.8698i	−0.0786594	+	0.989126i
$227$	17.9180	−	17.9180i	1.18926	−	1.18926i	0.211987	−	0.977273i	$-0.432007\pi$
$227$	17.9180	−	17.9180i	1.18926	−	1.18926i	0.977273	−	0.211987i	$-0.0679934\pi$
$228$		0			0
$229$	−2.04384	+	2.04384i	−0.135061	+	0.135061i	−0.771405	−	0.636344i	$-0.780446\pi$
$229$	−2.04384	+	2.04384i	−0.135061	+	0.135061i	0.636344	+	0.771405i	$0.280446\pi$
$230$	−0.0661883	−	0.502350i	−0.00436432	−	0.0331240i
$231$		0			0
$232$	5.62645	+	9.23226i	0.369394	+	0.606128i
$233$	11.1084			0.727733			0.363867	−	0.931451i	$-0.381456\pi$
$233$	11.1084			0.727733			0.363867	+	0.931451i	$0.381456\pi$
$234$		0			0
$235$	−10.4874	+	2.23926i	−0.684123	+	0.146073i
$236$	−0.233058	+	0.168745i	−0.0151708	+	0.0109844i
$237$		0			0
$238$	−0.194908	+	2.45092i	−0.0126340	+	0.158870i
$239$	19.1106			1.23616			0.618080	−	0.786115i	$-0.287911\pi$
$239$	19.1106			1.23616			0.618080	+	0.786115i	$0.287911\pi$
$240$		0			0
$241$	−5.95102			−0.383339			−0.191669	−	0.981460i	$-0.561390\pi$
$241$	−5.95102			−0.383339			−0.191669	+	0.981460i	$0.561390\pi$
$242$	0.428114	−	5.38346i	0.0275202	−	0.346062i
$243$		0			0
$244$	−9.98263	−	13.7873i	−0.639073	−	0.882638i
$245$	−2.80141	−	13.1202i	−0.178975	−	0.838220i
$246$		0			0
$247$	−28.3945			−1.80670
$248$	12.7616	+	3.09691i	0.810365	+	0.196654i
$249$		0			0
$250$	8.28761	+	13.4653i	0.524155	+	0.851623i
$251$	20.8714	−	20.8714i	1.31739	−	1.31739i	0.401552	−	0.915836i	$-0.368471\pi$
$251$	20.8714	−	20.8714i	1.31739	−	1.31739i	0.915836	−	0.401552i	$-0.131529\pi$
$252$		0			0
$253$	0.303620	−	0.303620i	0.0190884	−	0.0190884i
$254$	0.648627	−	8.15636i	0.0406985	−	0.511776i
$255$		0			0
$256$	12.8825	+	9.48899i	0.805157	+	0.593062i
$257$			9.30565i			0.580470i	0.956955	+	0.290235i	$0.0937335\pi$
$257$			9.30565i			0.580470i	−0.956955	+	0.290235i	$0.906266\pi$
$258$		0			0
$259$	5.35828	+	5.35828i	0.332947	+	0.332947i
$260$	−12.4901	−	11.2623i	−0.774605	−	0.698460i
$261$		0			0
$262$	−1.32233	−	1.55082i	−0.0816940	−	0.0958098i
$263$	20.0922			1.23894			0.619469	−	0.785021i	$-0.287348\pi$
$263$	20.0922			1.23894			0.619469	+	0.785021i	$0.287348\pi$
$264$		0			0
$265$	−5.92695	+	9.14511i	−0.364089	+	0.561780i
$266$	6.92889	+	8.12613i	0.424838	+	0.498245i
$267$		0			0
$268$	−20.7201	+	15.0024i	−1.26568	+	0.916415i
$269$	−21.1446	−	21.1446i	−1.28921	−	1.28921i	−0.935268	−	0.353941i	$-0.884841\pi$
$269$	−21.1446	−	21.1446i	−1.28921	−	1.28921i	−0.353941	−	0.935268i	$-0.615159\pi$
$270$		0			0
$271$	21.4729			1.30438			0.652192	−	0.758053i	$-0.273849\pi$
$271$	21.4729			1.30438			0.652192	+	0.758053i	$0.273849\pi$
$272$	−2.17034	+	6.60605i	−0.131596	+	0.400551i
$273$		0			0
$274$	15.7296	+	1.25088i	0.950260	+	0.0755685i
$275$	−4.77873	+	12.5178i	−0.288169	+	0.754854i
$276$		0			0
$277$	−4.23508	−	4.23508i	−0.254461	−	0.254461i	0.568336	−	0.822797i	$-0.307588\pi$
$277$	−4.23508	−	4.23508i	−0.254461	−	0.254461i	−0.822797	+	0.568336i	$0.807588\pi$
$278$	−24.2977	+	20.7179i	−1.45728	+	1.24258i
$279$		0			0
$280$	−0.175259	+	6.32277i	−0.0104737	+	0.377858i
$281$			13.5822i			0.810248i	0.914262	+	0.405124i	$0.132772\pi$
$281$			13.5822i			0.810248i	−0.914262	+	0.405124i	$0.867228\pi$
$282$		0			0
$283$	−15.9090	−	15.9090i	−0.945692	−	0.945692i	0.0529078	−	0.998599i	$-0.483151\pi$
$283$	−15.9090	−	15.9090i	−0.945692	−	0.945692i	−0.998599	+	0.0529078i	$0.983151\pi$
$284$	−1.45620	+	9.09779i	−0.0864093	+	0.539854i
$285$		0			0
$286$	1.12981	−	14.2071i	0.0668069	−	0.840084i
$287$		−	9.89887i		−	0.584312i
$288$		0			0
$289$	13.9781			0.822241
$290$	−7.35759	+	9.59064i	−0.432053	+	0.563182i
$291$		0			0
$292$	24.0776	+	3.85387i	1.40903	+	0.225531i
$293$	6.55813	+	6.55813i	0.383130	+	0.383130i	0.872229	−	0.489098i	$-0.162674\pi$
$293$	6.55813	+	6.55813i	0.383130	+	0.383130i	−0.489098	+	0.872229i	$0.662674\pi$
$294$		0			0
$295$	−0.269958	−	0.174960i	−0.0157176	−	0.0101866i
$296$	11.1528	+	18.3003i	0.648243	+	1.06368i
$297$		0			0
$298$	−22.0978	+	18.8421i	−1.28009	+	1.09149i
$299$	−0.426076	+	0.426076i	−0.0246406	+	0.0246406i
$300$		0			0
$301$	−7.23238	−	7.23238i	−0.416868	−	0.416868i
$302$	−1.65060	+	20.7560i	−0.0949814	+	1.19437i
$303$		0			0
$304$	13.6234	+	26.9549i	0.781355	+	1.54597i
$305$	10.3503	−	15.9702i	0.592656	−	0.914452i
$306$		0			0
$307$	6.02585	−	6.02585i	0.343913	−	0.343913i	−0.513923	−	0.857836i	$-0.671808\pi$
$307$	6.02585	−	6.02585i	0.343913	−	0.343913i	0.857836	+	0.513923i	$0.171808\pi$
$308$	−4.34158	+	3.14352i	−0.247385	+	0.179118i
$309$		0			0
$310$	1.91789	+	14.5563i	0.108929	+	0.826740i
$311$		−	21.1776i		−	1.20087i	−0.799673	−	0.600436i	$-0.794994\pi$
$311$		−	21.1776i		−	1.20087i	0.799673	−	0.600436i	$-0.205006\pi$
$312$		0			0
$313$	−4.30438			−0.243298			−0.121649	−	0.992573i	$-0.538818\pi$
$313$	−4.30438			−0.243298			−0.121649	+	0.992573i	$0.538818\pi$
$314$	−14.3775	+	12.2593i	−0.811371	+	0.691830i
$315$		0			0
$316$	−11.3264	−	1.81291i	−0.637161	−	0.101984i
$317$	−23.4323	+	23.4323i	−1.31609	+	1.31609i	−0.399242	+	0.916845i	$0.630727\pi$
$317$	−23.4323	+	23.4323i	−1.31609	+	1.31609i	−0.916845	+	0.399242i	$0.869273\pi$
$318$		0			0
$319$	−10.2435			−0.573526
$320$	−4.69869	+	17.2604i	−0.262665	+	0.964887i
$321$		0			0
$322$	0.225909	+	0.0179652i	0.0125894	+	0.00100116i
$323$	−9.28113	+	9.28113i	−0.516416	+	0.516416i
$324$		0			0
$325$	6.70608	−	17.5665i	0.371987	−	0.974415i
$326$	−11.6596	+	9.94181i	−0.645768	+	0.550626i
$327$		0			0
$328$	6.60212	−	27.2058i	0.364541	−	1.50219i
$329$		−	4.79632i		−	0.264430i
$330$		0			0
$331$	5.03806	−	5.03806i	0.276917	−	0.276917i	−0.554960	−	0.831877i	$-0.687267\pi$
$331$	5.03806	−	5.03806i	0.276917	−	0.276917i	0.831877	+	0.554960i	$0.187267\pi$
$332$	4.69473	−	3.39921i	0.257657	−	0.186556i
$333$		0			0
$334$	−20.3280	−	1.61657i	−1.11230	−	0.0884547i
$335$	−24.0008	−	15.5549i	−1.31130	−	0.849856i
$336$		0			0
$337$			11.5659i			0.630037i	0.949086	+	0.315018i	$0.102011\pi$
$337$			11.5659i			0.630037i	−0.949086	+	0.315018i	$0.897989\pi$
$338$	−0.128047	+	1.61017i	−0.00696485	+	0.0875816i
$339$		0			0
$340$	−7.76382	+	0.401323i	−0.421052	+	0.0217648i
$341$	−8.79779	+	8.79779i	−0.476427	+	0.476427i
$342$		0			0
$343$	13.0011			0.701994
$344$	−15.0536	−	24.7010i	−0.811635	−	1.33179i
$345$		0			0
$346$	−1.43448	+	1.22313i	−0.0771179	+	0.0657560i
$347$	−1.64106	−	1.64106i	−0.0880968	−	0.0880968i	0.661685	−	0.749782i	$-0.269842\pi$
$347$	−1.64106	−	1.64106i	−0.0880968	−	0.0880968i	−0.749782	+	0.661685i	$0.769842\pi$
$348$		0			0
$349$	13.8252	+	13.8252i	0.740045	+	0.740045i	0.972586	−	0.232542i	$-0.0747042\pi$
$349$	13.8252	+	13.8252i	0.740045	+	0.740045i	−0.232542	+	0.972586i	$0.574704\pi$
$350$	−6.66374	+	2.36743i	−0.356192	+	0.126544i
$351$		0			0
$352$	−14.0289	+	5.74390i	−0.747742	+	0.306151i
$353$			3.70491i			0.197193i	0.995128	+	0.0985964i	$0.0314353\pi$
$353$			3.70491i			0.197193i	−0.995128	+	0.0985964i	$0.968565\pi$
$354$		0			0
$355$	−10.0740	+	2.15099i	−0.534674	+	0.114163i
$356$	−4.75366	+	29.6992i	−0.251943	+	1.57405i
$357$		0			0
$358$	−4.20166	−	4.92766i	−0.222064	−	0.260435i
$359$			12.9673i			0.684387i	0.939630	+	0.342194i	$0.111170\pi$
$359$			12.9673i			0.684387i	−0.939630	+	0.342194i	$0.888830\pi$
$360$		0			0
$361$			38.0102i			2.00054i
$362$	19.9234	−	16.9881i	1.04715	−	0.892874i
$363$		0			0
$364$	6.09262	−	4.41135i	0.319340	−	0.231218i
$365$	5.69267	+	26.6612i	0.297968	+	1.39551i
$366$		0			0
$367$			3.12457i			0.163101i	0.996669	+	0.0815507i	$0.0259873\pi$
$367$			3.12457i			0.163101i	−0.996669	+	0.0815507i	$0.974013\pi$
$368$	0.608900	+	0.200047i	0.0317411	+	0.0104282i
$369$		0			0
$370$	−14.5843	+	19.0106i	−0.758200	+	0.988316i
$371$	−3.44653	−	3.44653i	−0.178935	−	0.178935i
$372$		0			0
$373$	21.1651	+	21.1651i	1.09589	+	1.09589i	0.994886	+	0.101002i	$0.0322050\pi$
$373$	21.1651	+	21.1651i	1.09589	+	1.09589i	0.101002	+	0.994886i	$0.467795\pi$
$374$	−4.27450	−	5.01308i	−0.221029	−	0.259220i
$375$		0			0
$376$	3.19894	−	13.1821i	0.164973	−	0.679813i
$377$	14.3749			0.740344
$378$		0			0
$379$	2.37189	−	2.37189i	0.121836	−	0.121836i	−0.643560	−	0.765396i	$-0.722543\pi$
$379$	2.37189	−	2.37189i	0.121836	−	0.121836i	0.765396	+	0.643560i	$0.222543\pi$
$380$	−22.6124	+	25.0776i	−1.15999	+	1.28645i
$381$		0			0
$382$	13.8250	+	1.09942i	0.707350	+	0.0562513i
$383$			3.48238i			0.177942i	0.996034	+	0.0889708i	$0.0283578\pi$
$383$			3.48238i			0.177942i	−0.996034	+	0.0889708i	$0.971642\pi$
$384$		0			0
$385$	−5.02900	−	3.25929i	−0.256301	−	0.166109i
$386$	−0.764775	+	9.61690i	−0.0389260	+	0.489487i
$387$		0			0
$388$	1.21614	−	7.59799i	0.0617400	−	0.385730i
$389$	−5.90261	+	5.90261i	−0.299274	+	0.299274i	−0.840730	−	0.541455i	$-0.817874\pi$
$389$	−5.90261	+	5.90261i	−0.299274	+	0.299274i	0.541455	+	0.840730i	$0.317874\pi$
$390$		0			0
$391$			0.278537i			0.0140862i
$392$	16.4913	+	4.00201i	0.832939	+	0.202132i
$393$		0			0
$394$	20.1321	+	23.6106i	1.01424	+	1.18949i
$395$	−2.67791	−	12.5418i	−0.134740	−	0.631046i
$396$		0			0
$397$	9.12810	−	9.12810i	0.458126	−	0.458126i	−0.439914	−	0.898040i	$-0.644991\pi$
$397$	9.12810	−	9.12810i	0.458126	−	0.458126i	0.898040	+	0.439914i	$0.144991\pi$
$398$	0.887968	−	11.1660i	0.0445098	−	0.559702i
$399$		0			0
$400$	−19.8934	+	2.06215i	−0.994670	+	0.103107i
$401$	0.825205			0.0412088			0.0206044	−	0.999788i	$-0.493441\pi$
$401$	0.825205			0.0412088			0.0206044	+	0.999788i	$0.493441\pi$
$402$		0			0
$403$	12.3461	−	12.3461i	0.615003	−	0.615003i
$404$	−12.8504	+	9.30430i	−0.639331	+	0.462906i
$405$		0			0
$406$	−3.50780	−	4.11390i	−0.174089	−	0.204170i
$407$	−20.3047			−1.00647
$408$		0			0
$409$		−	35.3312i		−	1.74702i	−0.486809	−	0.873508i	$-0.661839\pi$
$409$		−	35.3312i		−	1.74702i	0.486809	−	0.873508i	$-0.338161\pi$
$410$	31.0316	−	4.08864i	1.53254	−	0.201923i
$411$		0			0
$412$	29.6186	+	4.74076i	1.45920	+	0.233561i
$413$	0.101740	−	0.101740i	0.00500628	−	0.00500628i
$414$		0			0
$415$	5.43806	+	3.52441i	0.266944	+	0.173006i
$416$	19.6870	−	8.06052i	0.965233	−	0.395200i
$417$		0			0
$418$	−28.5249	−	2.26842i	−1.39520	−	0.110952i
$419$	11.7984	+	11.7984i	0.576392	+	0.576392i	0.933907	−	0.357516i	$-0.116376\pi$
$419$	11.7984	+	11.7984i	0.576392	+	0.576392i	−0.357516	+	0.933907i	$0.616376\pi$
$420$		0			0
$421$	24.9466	−	24.9466i	1.21582	−	1.21582i	0.246739	−	0.969082i	$-0.420641\pi$
$421$	24.9466	−	24.9466i	1.21582	−	1.21582i	0.969082	−	0.246739i	$-0.0793590\pi$
$422$	13.2371	+	15.5243i	0.644372	+	0.755713i
$423$		0			0
$424$	−7.17366	−	11.7710i	−0.348384	−	0.571652i
$425$	−3.54988	−	7.93383i	−0.172195	−	0.384847i
$426$		0			0
$427$	6.01872	+	6.01872i	0.291266	+	0.291266i
$428$	−2.03093	−	2.80496i	−0.0981685	−	0.135583i
$429$		0			0
$430$	19.6853	−	25.6598i	0.949308	−	1.23743i
$431$	−10.8925			−0.524672			−0.262336	−	0.964977i	$-0.584493\pi$
$431$	−10.8925			−0.524672			−0.262336	+	0.964977i	$0.584493\pi$
$432$		0			0
$433$			3.09561i			0.148765i	0.997230	+	0.0743827i	$0.0236986\pi$
$433$			3.09561i			0.148765i	−0.997230	+	0.0743827i	$0.976301\pi$
$434$	−6.54602	−	0.520566i	−0.314219	−	0.0249880i
$435$		0			0
$436$	8.81173	+	12.1701i	0.422005	+	0.582842i
$437$	0.855471	+	0.855471i	0.0409227	+	0.0409227i
$438$		0			0
$439$			26.4374i			1.26179i	0.775869	+	0.630894i	$0.217312\pi$
$439$			26.4374i			1.26179i	−0.775869	+	0.630894i	$0.782688\pi$
$440$	−11.6477	−	12.3119i	−0.555284	−	0.586946i
$441$		0			0
$442$	5.99848	+	7.03495i	0.285318	+	0.334618i
$443$	−18.8131	−	18.8131i	−0.893840	−	0.893840i	0.101042	−	0.994882i	$-0.467782\pi$
$443$	−18.8131	−	18.8131i	−0.893840	−	0.893840i	−0.994882	+	0.101042i	$0.967782\pi$
$444$		0			0
$445$	−32.8860	+	7.02178i	−1.55895	+	0.332864i
$446$	1.55485	−	19.5519i	0.0736241	−	0.925809i
$447$		0			0
$448$	−7.11088	−	3.66721i	−0.335957	−	0.173259i
$449$	16.9583			0.800310			0.400155	−	0.916447i	$-0.368956\pi$
$449$	16.9583			0.800310			0.400155	+	0.916447i	$0.368956\pi$
$450$		0			0
$451$	18.7555	+	18.7555i	0.883161	+	0.883161i
$452$	3.33412	−	20.8304i	0.156824	−	0.979778i
$453$		0			0
$454$	−27.2689	+	23.2513i	−1.27979	+	1.09124i
$455$	7.05728	+	4.57383i	0.330851	+	0.214424i
$456$		0			0
$457$	−5.71266			−0.267227			−0.133614	−	0.991034i	$-0.542658\pi$
$457$	−5.71266			−0.267227			−0.133614	+	0.991034i	$0.542658\pi$
$458$	3.11047	−	2.65220i	0.145343	−	0.123929i
$459$		0			0
$460$	0.0369912	+	0.715615i	0.00172472	+	0.0333657i
$461$	23.4428	+	23.4428i	1.09184	+	1.09184i	0.995332	+	0.0965077i	$0.0307672\pi$
$461$	23.4428	+	23.4428i	1.09184	+	1.09184i	0.0965077	+	0.995332i	$0.469233\pi$
$462$		0			0
$463$			16.7093i			0.776547i	0.921544	+	0.388273i	$0.126928\pi$
$463$			16.7093i			0.776547i	−0.921544	+	0.388273i	$0.873072\pi$
$464$	−6.89693	−	13.6461i	−0.320182	−	0.633504i
$465$		0			0
$466$	−15.6602	−	1.24536i	−0.725443	−	0.0576902i
$467$	−14.3258	+	14.3258i	−0.662918	+	0.662918i	−0.956067	−	0.293149i	$-0.905297\pi$
$467$	−14.3258	+	14.3258i	−0.662918	+	0.662918i	0.293149	+	0.956067i	$0.405297\pi$
$468$		0			0
$469$	9.04522	−	9.04522i	0.417669	−	0.417669i
$470$	15.0358	−	1.98108i	0.693550	−	0.0913802i
$471$		0			0
$472$	0.347474	−	0.211762i	0.0159938	−	0.00974716i
$473$	27.4065			1.26015
$474$		0			0
$475$	−35.2699	−	13.4644i	−1.61829	−	0.617790i
$476$	0.549547	−	3.43337i	0.0251884	−	0.157368i
$477$		0			0
$478$	−26.9414	−	2.14249i	−1.23227	−	0.0979951i
$479$	−11.2464			−0.513860			−0.256930	−	0.966430i	$-0.582711\pi$
$479$	−11.2464			−0.513860			−0.256930	+	0.966430i	$0.582711\pi$
$480$		0			0
$481$	28.4940			1.29922
$482$	8.38952	+	0.667169i	0.382132	+	0.0303887i
$483$		0			0
$484$	−1.20708	+	7.54140i	−0.0548673	+	0.342791i
$485$	8.41330	−	1.79639i	0.382028	−	0.0815701i
$486$		0			0
$487$	−6.82860			−0.309434			−0.154717	−	0.987959i	$-0.549447\pi$
$487$	−6.82860			−0.309434			−0.154717	+	0.987959i	$0.549447\pi$
$488$	12.5275	+	20.5559i	0.567091	+	0.930522i
$489$		0			0
$490$	2.47841	+	18.8105i	0.111963	+	0.849770i
$491$	26.3274	−	26.3274i	1.18814	−	1.18814i	0.210560	−	0.977581i	$-0.432471\pi$
$491$	26.3274	−	26.3274i	1.18814	−	1.18814i	0.977581	−	0.210560i	$-0.0675287\pi$
$492$		0			0
$493$	4.69863	−	4.69863i	0.211616	−	0.211616i
$494$	40.0295	+	3.18331i	1.80101	+	0.143224i
$495$		0			0
$496$	−17.6437	−	5.79662i	−0.792225	−	0.260276i
$497$		−	4.60726i		−	0.206664i
$498$		0			0
$499$	−16.9896	−	16.9896i	−0.760558	−	0.760558i	0.215865	−	0.976423i	$-0.430743\pi$
$499$	−16.9896	−	16.9896i	−0.760558	−	0.760558i	−0.976423	+	0.215865i	$0.930743\pi$
$500$	−10.1740	−	19.9121i	−0.454994	−	0.890495i
$501$		0			0
$502$	−31.7635	+	27.0838i	−1.41768	+	1.20881i
$503$	−12.7938			−0.570447			−0.285223	−	0.958461i	$-0.592068\pi$
$503$	−12.7938			−0.570447			−0.285223	+	0.958461i	$0.592068\pi$
$504$		0			0
$505$	−14.8850	−	9.64698i	−0.662375	−	0.429285i
$506$	−0.462071	+	0.393993i	−0.0205416	+	0.0175151i
$507$		0			0
$508$	−1.82882	+	11.4258i	−0.0811408	+	0.506939i
$509$	−15.4048	−	15.4048i	−0.682807	−	0.682807i	0.277825	−	0.960632i	$-0.410387\pi$
$509$	−15.4048	−	15.4048i	−0.682807	−	0.682807i	−0.960632	+	0.277825i	$0.910387\pi$
$510$		0			0
$511$	−12.1933			−0.539398
$512$	−17.0975	−	14.8215i	−0.755608	−	0.655024i
$513$		0			0
$514$	1.04326	−	13.1188i	0.0460161	−	0.578643i
$515$	7.00273	+	32.7968i	0.308577	+	1.44520i
$516$		0			0
$517$	9.08763	+	9.08763i	0.399674	+	0.399674i
$518$	−6.95318	−	8.15461i	−0.305505	−	0.358293i
$519$		0			0
$520$	16.3455	+	17.2775i	0.716797	+	0.757667i
$521$		−	2.66408i		−	0.116715i	−0.998296	−	0.0583577i	$-0.981414\pi$
$521$		−	2.66408i		−	0.116715i	0.998296	−	0.0583577i	$-0.0185864\pi$
$522$		0			0
$523$	10.1050	+	10.1050i	0.441861	+	0.441861i	0.892637	−	0.450776i	$-0.148853\pi$
$523$	10.1050	+	10.1050i	0.441861	+	0.441861i	−0.450776	+	0.892637i	$0.648853\pi$
$524$	1.69031	+	2.33453i	0.0738417	+	0.101985i
$525$		0			0
$526$	−28.3252	−	2.25254i	−1.23504	−	0.0982154i
$527$		−	8.07099i		−	0.351578i
$528$		0			0
$529$	−22.9743			−0.998884
$530$	9.38085	−	12.2280i	0.407478	−	0.531149i
$531$		0			0
$532$	−8.85707	−	12.2327i	−0.384003	−	0.530355i
$533$	−26.3199	−	26.3199i	−1.14004	−	1.14004i
$534$		0			0
$535$	2.10573	−	3.24907i	0.0910385	−	0.140470i
$536$	30.8924	−	18.8268i	1.33435	−	0.813196i
$537$		0			0
$538$	27.4383	+	32.1794i	1.18295	+	1.38735i
$539$	−11.3690	+	11.3690i	−0.489699	+	0.489699i
$540$		0			0
$541$	14.4482	+	14.4482i	0.621177	+	0.621177i	0.945832	−	0.324656i	$-0.105248\pi$
$541$	14.4482	+	14.4482i	0.621177	+	0.621177i	−0.324656	+	0.945832i	$0.605248\pi$
$542$	−30.2717	−	2.40733i	−1.30028	−	0.103404i
$543$		0			0
$544$	3.80027	−	9.06965i	0.162935	−	0.388858i
$545$	−9.13627	+	14.0970i	−0.391355	+	0.603850i
$546$		0			0
$547$	18.9410	−	18.9410i	0.809860	−	0.809860i	−0.174753	−	0.984612i	$-0.555913\pi$
$547$	18.9410	−	18.9410i	0.809860	−	0.809860i	0.984612	+	0.174753i	$0.0559125\pi$
$548$	−22.0348	−	3.52689i	−0.941278	−	0.150661i
$549$		0			0
$550$	8.14026	−	17.1114i	0.347102	−	0.729634i
$551$		−	28.8618i		−	1.22955i
$552$		0			0
$553$	5.73588			0.243914
$554$	5.49566	+	6.44525i	0.233488	+	0.273833i
$555$		0			0
$556$	36.5767	−	26.4833i	1.55120	−	1.12314i
$557$	29.6116	−	29.6116i	1.25468	−	1.25468i	0.301086	−	0.953597i	$-0.402651\pi$
$557$	29.6116	−	29.6116i	1.25468	−	1.25468i	0.953597	−	0.301086i	$-0.0973492\pi$
$558$		0			0
$559$	−38.4601			−1.62669
$560$	0.955919	−	8.89396i	0.0403950	−	0.375838i
$561$		0			0
$562$	1.52271	−	19.1477i	0.0642314	−	0.807698i
$563$	4.19738	−	4.19738i	0.176898	−	0.176898i	−0.613104	−	0.790002i	$-0.710079\pi$
$563$	4.19738	−	4.19738i	0.176898	−	0.176898i	0.790002	+	0.613104i	$0.210079\pi$
$564$		0			0
$565$	23.0656	−	4.92493i	0.970376	−	0.207193i
$566$	20.6444	+	24.2115i	0.867747	+	1.01768i
$567$		0			0
$568$	3.07284	−	12.6625i	0.128934	−	0.531305i
$569$			41.7953i			1.75215i	0.482173	+	0.876076i	$0.339848\pi$
$569$			41.7953i			1.75215i	−0.482173	+	0.876076i	$0.660152\pi$
$570$		0			0
$571$	−10.7600	+	10.7600i	−0.450290	+	0.450290i	−0.895451	−	0.445160i	$-0.853147\pi$
$571$	−10.7600	+	10.7600i	−0.450290	+	0.450290i	0.445160	+	0.895451i	$0.353147\pi$
$572$	−3.18552	+	19.9020i	−0.133193	+	0.832144i
$573$		0			0
$574$	−1.10976	+	13.9551i	−0.0463206	+	0.582473i
$575$	−0.731286	+	0.327204i	−0.0304967	+	0.0136453i
$576$		0			0
$577$			10.6682i			0.444124i	0.975032	+	0.222062i	$0.0712788\pi$
$577$			10.6682i			0.444124i	−0.975032	+	0.222062i	$0.928721\pi$
$578$	−19.7058	−	1.56709i	−0.819654	−	0.0651822i
$579$		0			0
$580$	11.4477	−	12.6957i	0.475338	−	0.527159i
$581$	−2.04945	+	2.04945i	−0.0850256	+	0.0850256i
$582$		0			0
$583$	13.0604			0.540904
$584$	−33.5116	−	8.13238i	−1.38672	−	0.336520i
$585$		0			0
$586$	−8.51018	−	9.98065i	−0.351552	−	0.412297i
$587$	17.6711	+	17.6711i	0.729365	+	0.729365i	0.970493	−	0.241128i	$-0.0775175\pi$
$587$	17.6711	+	17.6711i	0.729365	+	0.729365i	−0.241128	+	0.970493i	$0.577518\pi$
$588$		0			0
$589$	−24.7884	−	24.7884i	−1.02139	−	1.02139i
$590$	0.360963	+	0.276917i	0.0148606	+	0.0114005i
$591$		0			0
$592$	−13.6711	−	27.0494i	−0.561881	−	1.11172i
$593$			4.79734i			0.197003i	0.995137	+	0.0985016i	$0.0314050\pi$
$593$			4.79734i			0.197003i	−0.995137	+	0.0985016i	$0.968595\pi$
$594$		0			0
$595$	3.80179	−	0.811752i	0.155858	−	0.0332786i
$596$	33.2651	−	24.0855i	1.36259	−	0.986582i
$597$		0			0
$598$	0.648433	−	0.552898i	0.0265164	−	0.0226097i
$599$		−	1.03944i		−	0.0424705i	−0.999775	−	0.0212353i	$-0.993240\pi$
$599$		−	1.03944i		−	0.0424705i	0.999775	−	0.0212353i	$-0.00675991\pi$
$600$		0			0
$601$			6.22752i			0.254026i	0.991901	+	0.127013i	$0.0405390\pi$
$601$			6.22752i			0.254026i	−0.991901	+	0.127013i	$0.959461\pi$
$602$	9.38512	+	11.0068i	0.382509	+	0.448602i
$603$		0			0
$604$	4.65391	−	29.0760i	0.189365	−	1.18308i
$605$	−8.35063	+	1.78301i	−0.339501	+	0.0724898i
$606$		0			0
$607$		−	25.3718i		−	1.02981i	−0.857247	−	0.514905i	$-0.827827\pi$
$607$		−	25.3718i		−	1.02981i	0.857247	−	0.514905i	$-0.172173\pi$
$608$	−16.1838	−	39.5273i	−0.656341	−	1.60304i
$609$		0			0
$610$	−16.3819	+	21.3538i	−0.663283	+	0.864592i
$611$	−12.7528	−	12.7528i	−0.515925	−	0.515925i
$612$		0			0
$613$	17.1175	+	17.1175i	0.691369	+	0.691369i	0.962533	−	0.271164i	$-0.0874086\pi$
$613$	17.1175	+	17.1175i	0.691369	+	0.691369i	−0.271164	+	0.962533i	$0.587409\pi$
$614$	−9.17058	+	7.81946i	−0.370094	+	0.315568i
$615$		0			0
$616$	6.47302	−	3.94488i	0.260806	−	0.158944i
$617$	8.28793			0.333659			0.166830	−	0.985986i	$-0.446647\pi$
$617$	8.28793			0.333659			0.166830	+	0.985986i	$0.446647\pi$
$618$		0			0
$619$	2.23506	−	2.23506i	0.0898348	−	0.0898348i	−0.660761	−	0.750596i	$-0.729766\pi$
$619$	2.23506	−	2.23506i	0.0898348	−	0.0898348i	0.750596	+	0.660761i	$0.229766\pi$
$620$	−1.07187	−	20.7359i	−0.0430473	−	0.832773i
$621$		0			0
$622$	−2.37422	+	29.8554i	−0.0951977	+	1.19709i
$623$		−	15.0401i		−	0.602570i
$624$		0			0
$625$	16.6598	−	18.6401i	0.666391	−	0.745603i
$626$	6.06815	+	0.482564i	0.242532	+	0.0192872i
$627$		0			0
$628$	21.6433	−	15.6708i	0.863662	−	0.625333i
$629$	9.31367	−	9.31367i	0.371360	−	0.371360i
$630$		0			0
$631$			17.2372i			0.686201i	0.939299	+	0.343100i	$0.111477\pi$
$631$			17.2372i			0.686201i	−0.939299	+	0.343100i	$0.888523\pi$
$632$	15.7643	+	3.82558i	0.627071	+	0.152173i
$633$		0			0
$634$	35.6609	−	30.4070i	1.41628	−	1.20761i
$635$	−12.6519	+	2.70141i	−0.502074	+	0.107202i
$636$		0			0
$637$	15.9544	−	15.9544i	0.632135	−	0.632135i
$638$	14.4409	+	1.14840i	0.571721	+	0.0454656i
$639$		0			0
$640$	8.55911	−	23.8063i	0.338328	−	0.941028i
$641$	−24.8101			−0.979941			−0.489971	−	0.871739i	$-0.662993\pi$
$641$	−24.8101			−0.979941			−0.489971	+	0.871739i	$0.662993\pi$
$642$		0			0
$643$	−20.7142	+	20.7142i	−0.816887	+	0.816887i	−0.985656	−	0.168769i	$-0.946021\pi$
$643$	−20.7142	+	20.7142i	−0.816887	+	0.816887i	0.168769	+	0.985656i	$0.446021\pi$
$644$	−0.316464	−	0.0506534i	−0.0124704	−	0.00199602i
$645$		0			0
$646$	14.1247	−	12.0437i	0.555729	−	0.473852i
$647$	−14.3607			−0.564577			−0.282289	−	0.959330i	$-0.591094\pi$
$647$	−14.3607			−0.564577			−0.282289	+	0.959330i	$0.591094\pi$
$648$		0			0
$649$			0.385534i			0.0151335i
$650$	−11.4234	+	24.0128i	−0.448062	+	0.941859i
$651$		0			0
$652$	17.5519	−	12.7084i	0.687386	−	0.497701i
$653$	−8.23394	+	8.23394i	−0.322219	+	0.322219i	−0.849618	−	0.527399i	$-0.823167\pi$
$653$	−8.23394	+	8.23394i	−0.322219	+	0.322219i	0.527399	+	0.849618i	$0.323167\pi$
$654$		0			0
$655$	−1.75257	+	2.70416i	−0.0684785	+	0.105660i
$656$	−12.3575	+	37.6135i	−0.482478	+	1.46856i
$657$		0			0
$658$	−0.537716	+	6.76168i	−0.0209624	+	0.263598i
$659$	−32.8934	−	32.8934i	−1.28134	−	1.28134i	−0.939904	−	0.341440i	$-0.889085\pi$
$659$	−32.8934	−	32.8934i	−1.28134	−	1.28134i	−0.341440	−	0.939904i	$-0.610915\pi$
$660$		0			0
$661$	−15.8937	+	15.8937i	−0.618193	+	0.618193i	−0.945068	−	0.326875i	$-0.894004\pi$
$661$	−15.8937	+	15.8937i	−0.618193	+	0.618193i	0.326875	+	0.945068i	$0.394004\pi$
$662$	−7.66728	+	6.53765i	−0.297997	+	0.254093i
$663$		0			0
$664$	−6.99955	+	4.26576i	−0.271635	+	0.165544i
$665$	9.18328	−	14.1695i	0.356113	−	0.549471i
$666$		0			0
$667$	−0.433087	−	0.433087i	−0.0167692	−	0.0167692i
$668$	28.4765	+	4.55796i	1.10179	+	0.176353i
$669$		0			0
$670$	32.0916	+	24.6195i	1.23981	+	0.951133i
$671$	−22.8075			−0.880472
$672$		0			0
$673$		−	1.87365i		−	0.0722238i	−0.999348	−	0.0361119i	$-0.988503\pi$
$673$		−	1.87365i		−	0.0722238i	0.999348	−	0.0361119i	$-0.0114973\pi$
$674$	1.29666	−	16.3052i	0.0499454	−	0.628054i
$675$		0			0
$676$	0.361032	−	2.25560i	0.0138859	−	0.0867538i
$677$	27.7045	+	27.7045i	1.06477	+	1.06477i	0.997752	+	0.0670200i	$0.0213491\pi$
$677$	27.7045	+	27.7045i	1.06477	+	1.06477i	0.0670200	+	0.997752i	$0.478651\pi$
$678$		0			0
$679$			3.84774i			0.147663i
$680$	10.9901	+	0.304632i	0.421452	+	0.0116821i
$681$		0			0
$682$	13.3891	−	11.4165i	0.512696	−	0.437160i
$683$	15.9666	+	15.9666i	0.610945	+	0.610945i	0.943192	−	0.332247i	$-0.107807\pi$
$683$	15.9666	+	15.9666i	0.610945	+	0.610945i	−0.332247	+	0.943192i	$0.607807\pi$
$684$		0			0
$685$	−5.20968	−	24.3992i	−0.199052	−	0.932246i
$686$	−18.3285	−	1.45756i	−0.699785	−	0.0556498i
$687$		0			0
$688$	18.4528	+	36.5102i	0.703505	+	1.39194i
$689$	−18.3278			−0.698235
$690$		0			0
$691$	−8.47128	−	8.47128i	−0.322263	−	0.322263i	0.527372	−	0.849635i	$-0.323177\pi$
$691$	−8.47128	−	8.47128i	−0.322263	−	0.322263i	−0.849635	+	0.527372i	$0.823177\pi$
$692$	2.15940	−	1.56351i	0.0820879	−	0.0594356i
$693$		0			0
$694$	2.12953	+	2.49749i	0.0808358	+	0.0948034i
$695$	42.3680	+	27.4587i	1.60711	+	1.04157i
$696$		0			0
$697$	−17.2061			−0.651726
$698$	−17.9403	−	21.0402i	−0.679050	−	0.796382i
$699$		0			0
$700$	9.65971	−	2.59044i	0.365103	−	0.0979095i
$701$	−12.7252	−	12.7252i	−0.480624	−	0.480624i	0.424707	−	0.905331i	$-0.360377\pi$
$701$	−12.7252	−	12.7252i	−0.480624	−	0.480624i	−0.905331	+	0.424707i	$0.860377\pi$
$702$		0			0
$703$		−	57.2100i		−	2.15772i
$704$	20.4213	−	6.52476i	0.769658	−	0.245911i
$705$		0			0
$706$	0.415358	−	5.22305i	0.0156322	−	0.196572i
$707$	5.60974	−	5.60974i	0.210976	−	0.210976i
$708$		0			0
$709$	−5.12731	+	5.12731i	−0.192560	+	0.192560i	−0.796801	−	0.604241i	$-0.793476\pi$
$709$	−5.12731	+	5.12731i	−0.192560	+	0.192560i	0.604241	+	0.796801i	$0.293476\pi$
$710$	14.4431	−	1.90299i	0.542041	−	0.0714178i
$711$		0			0
$712$	10.0311	−	41.3358i	0.375932	−	1.54913i
$713$	−0.743928			−0.0278603
$714$		0			0
$715$	−22.0376	+	4.70543i	−0.824158	+	0.175973i
$716$	5.37090	+	7.41787i	0.200720	+	0.277219i
$717$		0			0
$718$	1.45376	−	18.2808i	0.0542540	−	0.682233i
$719$	−7.22269			−0.269361			−0.134681	−	0.990889i	$-0.543001\pi$
$719$	−7.22269			−0.269361			−0.134681	+	0.990889i	$0.543001\pi$
$720$		0			0
$721$	−14.9993			−0.558604
$722$	4.26133	−	53.5853i	0.158590	−	1.99424i
$723$		0			0
$724$	−29.9919	+	21.7155i	−1.11464	+	0.807052i
$725$	17.8556	+	6.81645i	0.663140	+	0.253156i
$726$		0			0
$727$	−50.4488			−1.87104			−0.935522	−	0.353268i	$-0.885070\pi$
$727$	−50.4488			−1.87104			−0.935522	+	0.353268i	$0.885070\pi$
$728$	−9.08371	+	5.53592i	−0.336665	+	0.205175i
$729$		0			0
$730$	−5.03632	−	38.2242i	−0.186402	−	1.41474i
$731$	−12.5712	+	12.5712i	−0.464963	+	0.464963i
$732$		0			0
$733$	−9.19912	+	9.19912i	−0.339777	+	0.339777i	−0.856283	−	0.516506i	$-0.827232\pi$
$733$	−9.19912	+	9.19912i	−0.339777	+	0.339777i	0.516506	+	0.856283i	$0.327232\pi$
$734$	0.350296	−	4.40491i	0.0129297	−	0.162588i
$735$		0			0
$736$	−0.835978	−	0.350282i	−0.0308146	−	0.0129116i
$737$			34.2761i			1.26258i
$738$		0			0
$739$	5.53064	+	5.53064i	0.203448	+	0.203448i	0.801476	−	0.598028i	$-0.204049\pi$
$739$	5.53064	+	5.53064i	0.203448	+	0.203448i	−0.598028	+	0.801476i	$0.704049\pi$
$740$	22.6917	−	25.1655i	0.834162	−	0.925101i
$741$		0			0
$742$	4.47240	+	5.24518i	0.164187	+	0.192557i
$743$	7.49683			0.275032			0.137516	−	0.990500i	$-0.456088\pi$
$743$	7.49683			0.275032			0.137516	+	0.990500i	$0.456088\pi$
$744$		0			0
$745$	38.5320	+	24.9726i	1.41170	+	0.914926i
$746$	−27.4650	−	32.2106i	−1.00556	−	1.17931i
$747$		0			0
$748$	5.46401	+	7.54647i	0.199784	+	0.275926i
$749$	1.22448	+	1.22448i	0.0447417	+	0.0447417i
$750$		0			0
$751$	8.92232			0.325580			0.162790	−	0.986661i	$-0.447951\pi$
$751$	8.92232			0.325580			0.162790	+	0.986661i	$0.447951\pi$
$752$	−5.98759	+	18.2250i	−0.218345	+	0.664596i
$753$		0			0
$754$	−20.2652	−	1.61157i	−0.738015	−	0.0586899i
$755$	32.1960	−	6.87444i	1.17173	−	0.250186i
$756$		0			0
$757$	−7.26524	−	7.26524i	−0.264060	−	0.264060i	0.562641	−	0.826701i	$-0.309785\pi$
$757$	−7.26524	−	7.26524i	−0.264060	−	0.264060i	−0.826701	+	0.562641i	$0.809785\pi$
$758$	−3.60971	+	3.07788i	−0.131111	+	0.111794i
$759$		0			0
$760$	34.6895	−	32.8183i	1.25832	−	1.19045i
$761$			21.6817i			0.785963i	0.919546	+	0.392981i	$0.128556\pi$
$761$			21.6817i			0.785963i	−0.919546	+	0.392981i	$0.871444\pi$
$762$		0			0
$763$	−5.31276	−	5.31276i	−0.192335	−	0.192335i
$764$	−19.3667	−	3.09985i	−0.700664	−	0.112149i
$765$		0			0
$766$	0.390410	−	4.90934i	0.0141061	−	0.177382i
$767$		−	0.541027i		−	0.0195354i
$768$		0			0
$769$	0.339883			0.0122565			0.00612824	−	0.999981i	$-0.498049\pi$
$769$	0.339883			0.0122565			0.00612824	+	0.999981i	$0.498049\pi$
$770$	6.72429	+	5.15863i	0.242327	+	0.185904i
$771$		0			0
$772$	2.15630	−	13.4718i	0.0776071	−	0.484861i
$773$	30.8536	+	30.8536i	1.10973	+	1.10973i	0.993186	+	0.116541i	$0.0371806\pi$
$773$	30.8536	+	30.8536i	1.10973	+	1.10973i	0.116541	+	0.993186i	$0.462819\pi$
$774$		0			0
$775$	21.1900	−	9.48115i	0.761167	−	0.340573i
$776$	−2.56628	+	10.5750i	−0.0921240	+	0.379621i
$777$		0			0
$778$	8.98303	−	7.65954i	0.322057	−	0.274608i
$779$	−52.8449	+	52.8449i	−1.89336	+	1.89336i
$780$		0			0
$781$	8.72942	+	8.72942i	0.312363	+	0.312363i
$782$	0.0312269	−	0.392672i	0.00111667	−	0.0140419i
$783$		0			0
$784$	−22.8002	−	7.49073i	−0.814293	−	0.267526i
$785$	25.0701	+	16.2480i	0.894791	+	0.579914i
$786$		0			0
$787$	9.03797	−	9.03797i	0.322169	−	0.322169i	−0.527430	−	0.849599i	$-0.676844\pi$
$787$	9.03797	−	9.03797i	0.322169	−	0.322169i	0.849599	+	0.527430i	$0.176844\pi$
$788$	−25.7344	−	35.5424i	−0.916751	−	1.26615i
$789$		0			0
$790$	2.36915	+	17.9812i	0.0842906	+	0.639742i
$791$			10.5488i			0.375073i
$792$		0			0
$793$	32.0061			1.13657
$794$	−13.8918	+	11.8451i	−0.493002	+	0.420367i
$795$		0			0
$796$	−2.50365	+	15.6419i	−0.0887395	+	0.554412i
$797$	26.5763	−	26.5763i	0.941380	−	0.941380i	−0.0569944	−	0.998374i	$-0.518152\pi$
$797$	26.5763	−	26.5763i	0.941380	−	0.941380i	0.998374	+	0.0569944i	$0.0181517\pi$
$798$		0			0
$799$	−8.33689			−0.294938
$800$	28.2762	−	0.676890i	0.999714	−	0.0239317i
$801$		0			0
$802$	−1.16334	−	0.0925138i	−0.0410791	−	0.00326678i
$803$	23.1027	−	23.1027i	0.815277	−	0.815277i
$804$		0			0
$805$	−0.0748217	−	0.350423i	−0.00263712	−	0.0123508i
$806$	−18.7892	+	16.0210i	−0.661821	+	0.564314i
$807$		0			0
$808$	19.1591	−	11.6762i	0.674015	−	0.410767i
$809$		−	40.1166i		−	1.41043i	−0.708996	−	0.705213i	$-0.750852\pi$
$809$		−	40.1166i		−	1.41043i	0.708996	−	0.705213i	$-0.249148\pi$
$810$		0			0
$811$	−4.55343	+	4.55343i	−0.159893	+	0.159893i	−0.782519	−	0.622627i	$-0.786066\pi$
$811$	−4.55343	+	4.55343i	−0.159893	+	0.159893i	0.622627	+	0.782519i	$0.286066\pi$
$812$	4.48395	+	6.19289i	0.157356	+	0.217328i
$813$		0			0
$814$	28.6249	+	2.27637i	1.00330	+	0.0797866i
$815$	20.3309	+	13.1765i	0.712162	+	0.461552i
$816$		0			0
$817$			77.2198i			2.70158i
$818$	−3.96099	+	49.8087i	−0.138493	+	1.74152i
$819$		0			0
$820$	−44.2056	+	2.28505i	−1.54373	+	0.0797975i
$821$	−15.8058	+	15.8058i	−0.551627	+	0.551627i	−0.926910	−	0.375283i	$-0.877545\pi$
$821$	−15.8058	+	15.8058i	−0.551627	+	0.551627i	0.375283	+	0.926910i	$0.377545\pi$
$822$		0			0
$823$	3.03903			0.105934			0.0529669	−	0.998596i	$-0.483132\pi$
$823$	3.03903			0.105934			0.0529669	+	0.998596i	$0.483132\pi$
$824$	−41.2237	−	10.0039i	−1.43610	−	0.348502i
$825$		0			0
$826$	−0.154835	+	0.132023i	−0.00538739	+	0.00459366i
$827$	1.52610	+	1.52610i	0.0530678	+	0.0530678i	0.733143	−	0.680075i	$-0.238053\pi$
$827$	1.52610	+	1.52610i	0.0530678	+	0.0530678i	−0.680075	+	0.733143i	$0.738053\pi$
$828$		0			0
$829$	28.7055	+	28.7055i	0.996984	+	0.996984i	0.999995	−	0.00301145i	$-0.000958576\pi$
$829$	28.7055	+	28.7055i	0.996984	+	0.996984i	−0.00301145	+	0.999995i	$0.500959\pi$
$830$	−7.27126	−	5.57824i	−0.252389	−	0.193624i
$831$		0			0
$832$	−28.6576	+	9.15631i	−0.993525	+	0.317438i
$833$		−	10.4298i		−	0.361371i
$834$		0			0
$835$	6.73270	+	31.5321i	0.232995	+	1.09121i
$836$	39.9590	+	6.39586i	1.38201	+	0.221205i
$837$		0			0
$838$	−15.3103	−	17.9557i	−0.528885	−	0.620270i
$839$		−	11.9438i		−	0.412346i	−0.978516	−	0.206173i	$-0.933899\pi$
$839$		−	11.9438i		−	0.412346i	0.978516	−	0.206173i	$-0.0661010\pi$
$840$		0			0
$841$		−	14.3885i		−	0.496157i
$842$	−37.9655	+	32.3720i	−1.30838	+	1.11561i
$843$		0			0
$844$	−16.9207	−	23.3696i	−0.582436	−	0.804416i
$845$	2.49764	−	0.533292i	0.0859213	−	0.0183458i
$846$		0			0
$847$		−	3.81908i		−	0.131225i
$848$	8.79351	+	17.3986i	0.301970	+	0.597471i
$849$		0			0
$850$	4.11503	+	11.5828i	0.141144	+	0.397287i
$851$	−0.858469	−	0.858469i	−0.0294280	−	0.0294280i
$852$		0			0
$853$	3.53433	+	3.53433i	0.121013	+	0.121013i	0.765020	−	0.644007i	$-0.222729\pi$
$853$	3.53433	+	3.53433i	0.121013	+	0.121013i	−0.644007	+	0.765020i	$0.722729\pi$
$854$	−7.81021	−	9.15973i	−0.267260	−	0.313440i
$855$		0			0
$856$	2.54866	+	4.18201i	0.0871114	+	0.142938i
$857$	−56.1606			−1.91841			−0.959205	−	0.282710i	$-0.908767\pi$
$857$	−56.1606			−1.91841			−0.959205	+	0.282710i	$0.908767\pi$
$858$		0			0
$859$	−4.66448	+	4.66448i	−0.159150	+	0.159150i	−0.782190	−	0.623040i	$-0.785897\pi$
$859$	−4.66448	+	4.66448i	−0.159150	+	0.159150i	0.623040	+	0.782190i	$0.285897\pi$
$860$	−30.6283	+	33.9673i	−1.04442	+	1.15828i
$861$		0			0
$862$	15.3558	+	1.22116i	0.523021	+	0.0415928i
$863$			12.5882i			0.428507i	0.976778	+	0.214253i	$0.0687319\pi$
$863$			12.5882i			0.428507i	−0.976778	+	0.214253i	$0.931268\pi$
$864$		0			0
$865$	2.50130	+	1.62109i	0.0850467	+	0.0551188i
$866$	0.347049	−	4.36407i	0.0117932	−	0.148297i
$867$		0			0
$868$	9.16997	+	1.46775i	0.311249	+	0.0498187i
$869$	−10.8678	+	10.8678i	−0.368665	+	0.368665i
$870$		0			0
$871$		−	48.1003i		−	1.62982i
$872$	−11.0581	−	18.1448i	−0.374473	−	0.614461i
$873$		0			0
$874$	−1.11010	−	1.30192i	−0.0375498	−	0.0440380i
$875$	6.59725	+	9.02783i	0.223028	+	0.305196i
$876$		0			0
$877$	−23.7329	+	23.7329i	−0.801403	+	0.801403i	−0.983315	−	0.181912i	$-0.941772\pi$
$877$	−23.7329	+	23.7329i	−0.801403	+	0.801403i	0.181912	+	0.983315i	$0.441772\pi$
$878$	2.96390	−	37.2704i	0.100027	−	1.25782i
$879$		0			0
$880$	15.0403	+	18.6627i	0.507007	+	0.629118i
$881$	3.75776			0.126602			0.0633011	−	0.997994i	$-0.479837\pi$
$881$	3.75776			0.126602			0.0633011	+	0.997994i	$0.479837\pi$
$882$		0			0
$883$	−17.1877	+	17.1877i	−0.578413	+	0.578413i	−0.934466	−	0.356053i	$-0.884122\pi$
$883$	−17.1877	+	17.1877i	−0.578413	+	0.578413i	0.356053	+	0.934466i	$0.384122\pi$
$884$	−7.66774	−	10.5901i	−0.257894	−	0.356184i
$885$		0			0
$886$	24.4129	+	28.6312i	0.820169	+	0.961885i
$887$	−49.8359			−1.67333			−0.836663	−	0.547718i	$-0.815497\pi$
$887$	−49.8359			−1.67333			−0.836663	+	0.547718i	$0.815497\pi$
$888$		0			0
$889$		−	5.78621i		−	0.194063i
$890$	47.1487	−	6.21218i	1.58043	−	0.208233i
$891$		0			0
$892$	−4.38393	+	27.3892i	−0.146785	+	0.917059i
$893$	−25.6050	+	25.6050i	−0.856840	+	0.856840i
$894$		0			0
$895$	−5.56871	+	8.59236i	−0.186142	+	0.287211i
$896$	9.61352	+	5.96709i	0.321165	+	0.199347i
$897$		0			0
$898$	−23.9071	−	1.90119i	−0.797792	−	0.0634437i
$899$	12.5493	+	12.5493i	0.418542	+	0.418542i
$900$		0			0
$901$	−5.99070	+	5.99070i	−0.199579	+	0.199579i
$902$	−24.3381	−	28.5435i	−0.810370	−	0.950393i
$903$		0			0
$904$	−7.03561	+	28.9921i	−0.234001	+	0.964262i
$905$	−34.7405	−	22.5153i	−1.15481	−	0.748435i
$906$		0			0
$907$	25.1326	+	25.1326i	0.834515	+	0.834515i	0.988131	−	0.153616i	$-0.0490919\pi$
$907$	25.1326	+	25.1326i	0.834515	+	0.834515i	−0.153616	+	0.988131i	$0.549092\pi$
$908$	41.0494	−	29.7218i	1.36227	−	0.986351i
$909$		0			0
$910$	−9.43632	−	7.23920i	−0.312811	−	0.239977i
$911$	49.4774			1.63926			0.819629	−	0.572894i	$-0.194179\pi$
$911$	49.4774			1.63926			0.819629	+	0.572894i	$0.194179\pi$
$912$		0			0
$913$		−	7.76623i		−	0.257025i
$914$	8.05350	+	0.640447i	0.266386	+	0.0211841i
$915$		0			0
$916$	−4.68236	+	3.39026i	−0.154710	+	0.112017i
$917$	−1.01912	−	1.01912i	−0.0336544	−	0.0336544i
$918$		0			0
$919$		−	4.92570i		−	0.162484i	−0.996694	−	0.0812420i	$-0.974111\pi$
$919$		−	4.92570i		−	0.162484i	0.996694	−	0.0812420i	$-0.0258886\pi$
$920$	0.0280788	−	1.01299i	0.000925732	−	0.0333974i
$921$		0			0
$922$	−30.4206	−	35.6770i	−1.00185	−	1.17496i
$923$	−12.2502	−	12.2502i	−0.403219	−	0.403219i
$924$		0			0
$925$	35.3935	+	13.5116i	1.16373	+	0.444259i
$926$	1.87328	−	23.5561i	0.0615598	−	0.774103i
$927$		0			0
$928$	8.19317	+	20.0110i	0.268954	+	0.656892i
$929$	−15.7829			−0.517822			−0.258911	−	0.965901i	$-0.583364\pi$
$929$	−15.7829			−0.517822			−0.258911	+	0.965901i	$0.583364\pi$
$930$		0			0
$931$	−32.0330	−	32.0330i	−1.04984	−	1.04984i
$932$	21.9375	+	3.51133i	0.718587	+	0.115017i
$933$		0			0
$934$	21.8020	−	18.5899i	0.713384	−	0.608279i
$935$	−5.66525	+	8.74132i	−0.185274	+	0.285872i
$936$		0			0
$937$	−23.6323			−0.772033			−0.386017	−	0.922492i	$-0.626149\pi$
$937$	−23.6323			−0.772033			−0.386017	+	0.922492i	$0.626149\pi$
$938$	−13.7657	+	11.7375i	−0.449465	+	0.383245i
$939$		0			0
$940$	−21.4190	+	1.10718i	−0.698612	+	0.0361123i
$941$	22.0372	+	22.0372i	0.718391	+	0.718391i	0.968276	−	0.249884i	$-0.0803926\pi$
$941$	22.0372	+	22.0372i	0.718391	+	0.718391i	−0.249884	+	0.968276i	$0.580393\pi$
$942$		0			0
$943$			1.58594i			0.0516452i
$944$	−0.513597	+	0.259579i	−0.0167162	+	0.00844859i
$945$		0			0
$946$	−38.6367	−	3.07255i	−1.25619	−	0.0998972i
$947$	8.89469	−	8.89469i	0.289039	−	0.289039i	−0.547661	−	0.836700i	$-0.684482\pi$
$947$	8.89469	−	8.89469i	0.289039	−	0.289039i	0.836700	+	0.547661i	$0.184482\pi$
$948$		0			0
$949$	−32.4204	+	32.4204i	−1.05241	+	1.05241i
$950$	48.2127	+	22.9357i	1.56423	+	0.744134i
$951$		0			0
$952$	−1.15965	+	4.77863i	−0.0375843	+	0.154876i
$953$	−24.1239			−0.781450			−0.390725	−	0.920507i	$-0.627776\pi$
$953$	−24.1239			−0.781450			−0.390725	+	0.920507i	$0.627776\pi$
$954$		0			0
$955$	−4.57888	−	21.4449i	−0.148169	−	0.693941i
$956$	37.7407	+	6.04080i	1.22062	+	0.195373i
$957$		0			0
$958$	15.8547	+	1.26083i	0.512243	+	0.0407356i
$959$	11.1588			0.360335
$960$		0			0
$961$	−9.44370			−0.304636
$962$	−40.1698	−	3.19447i	−1.29513	−	0.102994i
$963$		0			0
$964$	−11.7524	−	1.88110i	−0.378521	−	0.0605862i
$965$	14.9174	−	3.18514i	0.480208	−	0.102533i
$966$		0			0
$967$	17.5889			0.565620			0.282810	−	0.959176i	$-0.408733\pi$
$967$	17.5889			0.565620			0.282810	+	0.959176i	$0.408733\pi$
$968$	2.54716	−	10.4963i	0.0818689	−	0.337363i
$969$		0			0
$970$	−12.0621	+	1.58927i	−0.387292	+	0.0510285i
$971$	−4.45325	+	4.45325i	−0.142911	+	0.142911i	−0.774943	−	0.632031i	$-0.782221\pi$
$971$	−4.45325	+	4.45325i	−0.142911	+	0.142911i	0.632031	+	0.774943i	$0.282221\pi$
$972$		0			0
$973$	−15.9673	+	15.9673i	−0.511888	+	0.511888i
$974$	9.62671	+	0.765556i	0.308460	+	0.0245300i
$975$		0			0
$976$	−15.3562	−	30.3834i	−0.491540	−	0.972549i
$977$		−	33.1408i		−	1.06027i	−0.847914	−	0.530134i	$-0.822142\pi$
$977$		−	33.1408i		−	1.06027i	0.847914	−	0.530134i	$-0.177858\pi$
$978$		0			0
$979$	28.4967	+	28.4967i	0.910757	+	0.910757i
$980$	−1.38513	−	26.7961i	−0.0442464	−	0.855971i
$981$		0			0
$982$	−40.0670	+	34.1639i	−1.27859	+	1.09021i
$983$	27.3732			0.873070			0.436535	−	0.899687i	$-0.356206\pi$
$983$	27.3732			0.873070			0.436535	+	0.899687i	$0.356206\pi$
$984$		0			0
$985$	26.6822	−	41.1699i	0.850167	−	1.31178i
$986$	−7.15072	+	6.09719i	−0.227725	+	0.194174i
$987$		0			0
$988$	−56.0752	−	8.97542i	−1.78399	−	0.285546i
$989$	1.15873	+	1.15873i	0.0368454	+	0.0368454i
$990$		0			0
$991$	−11.5423			−0.366653			−0.183327	−	0.983052i	$-0.558687\pi$
$991$	−11.5423			−0.366653			−0.183327	+	0.983052i	$0.558687\pi$
$992$	24.2236	+	10.1499i	0.769099	+	0.322260i
$993$		0			0
$994$	−0.516521	+	6.49515i	−0.0163830	+	0.206014i
$995$	−17.3204	+	3.69822i	−0.549092	+	0.117241i
$996$		0			0
$997$	−28.5401	−	28.5401i	−0.903874	−	0.903874i	0.0918946	−	0.995769i	$-0.470708\pi$
$997$	−28.5401	−	28.5401i	−0.903874	−	0.903874i	−0.995769	+	0.0918946i	$0.970708\pi$
$998$	22.0466	+	25.8560i	0.697872	+	0.818456i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	720.2.bm.h.109.1		48
3.2	odd	2		240.2.bl.a.109.24	yes	48
5.4	even	2	inner	720.2.bm.h.109.24		48
12.11	even	2		960.2.bl.a.529.5		48
15.14	odd	2		240.2.bl.a.109.1	✓	48
16.5	even	4	inner	720.2.bm.h.469.24		48
24.5	odd	2		1920.2.bl.a.289.6		48
24.11	even	2		1920.2.bl.b.289.19		48
48.5	odd	4		240.2.bl.a.229.1	yes	48
48.11	even	4		960.2.bl.a.49.23		48
48.29	odd	4		1920.2.bl.a.1249.19		48
48.35	even	4		1920.2.bl.b.1249.6		48
60.59	even	2		960.2.bl.a.529.23		48
80.69	even	4	inner	720.2.bm.h.469.1		48
120.29	odd	2		1920.2.bl.a.289.19		48
120.59	even	2		1920.2.bl.b.289.6		48
240.29	odd	4		1920.2.bl.a.1249.6		48
240.59	even	4		960.2.bl.a.49.5		48
240.149	odd	4		240.2.bl.a.229.24	yes	48
240.179	even	4		1920.2.bl.b.1249.19		48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
240.2.bl.a.109.1	✓	48	15.14	odd	2
240.2.bl.a.109.24	yes	48	3.2	odd	2
240.2.bl.a.229.1	yes	48	48.5	odd	4
240.2.bl.a.229.24	yes	48	240.149	odd	4
720.2.bm.h.109.1		48	1.1	even	1	trivial
720.2.bm.h.109.24		48	5.4	even	2	inner
720.2.bm.h.469.1		48	80.69	even	4	inner
720.2.bm.h.469.24		48	16.5	even	4	inner
960.2.bl.a.49.5		48	240.59	even	4
960.2.bl.a.49.23		48	48.11	even	4
960.2.bl.a.529.5		48	12.11	even	2
960.2.bl.a.529.23		48	60.59	even	2
1920.2.bl.a.289.6		48	24.5	odd	2
1920.2.bl.a.289.19		48	120.29	odd	2
1920.2.bl.a.1249.6		48	240.29	odd	4
1920.2.bl.a.1249.19		48	48.29	odd	4
1920.2.bl.b.289.6		48	120.59	even	2
1920.2.bl.b.289.19		48	24.11	even	2
1920.2.bl.b.1249.6		48	48.35	even	4
1920.2.bl.b.1249.19		48	240.179	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.bm (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.40976 - 0.112110i) q^{2} +(1.97486 + 0.316097i) q^{4} +(0.466917 + 2.18678i) q^{5} -1.00010 q^{7} +(-2.74865 - 0.667024i) q^{8} +O(q^{10})\)	\(q+(-1.40976 - 0.112110i) q^{2} +(1.97486 + 0.316097i) q^{4} +(0.466917 + 2.18678i) q^{5} -1.00010 q^{7} +(-2.74865 - 0.667024i) q^{8} +(-0.413083 - 3.13518i) q^{10} +(1.89490 - 1.89490i) q^{11} +(-2.65915 + 2.65915i) q^{13} +(1.40991 + 0.112121i) q^{14} +(3.80016 + 1.24850i) q^{16} +1.73836i q^{17} +(5.33902 + 5.33902i) q^{19} +(0.230863 + 4.46617i) q^{20} +(-2.88380 + 2.45892i) q^{22} +0.160230 q^{23} +(-4.56398 + 2.04209i) q^{25} +(4.04689 - 3.45065i) q^{26} +(-1.97506 - 0.316129i) q^{28} +(-2.70291 - 2.70291i) q^{29} -4.64288 q^{31} +(-5.21736 - 2.18612i) q^{32} +(0.194888 - 2.45068i) q^{34} +(-0.466965 - 2.18700i) q^{35} +(-5.35773 - 5.35773i) q^{37} +(-6.92819 - 8.12530i) q^{38} +(0.175241 - 6.32213i) q^{40} +9.89786i q^{41} +(7.23165 + 7.23165i) q^{43} +(4.34114 - 3.14320i) q^{44} +(-0.225886 - 0.0179634i) q^{46} +4.79583i q^{47} -5.99980 q^{49} +(6.66306 - 2.36719i) q^{50} +(-6.09201 + 4.41091i) q^{52} +(3.44618 + 3.44618i) q^{53} +(5.02849 + 3.25896i) q^{55} +(2.74893 + 0.667092i) q^{56} +(3.50744 + 4.11349i) q^{58} +(-0.101729 + 0.101729i) q^{59} +(-6.01811 - 6.01811i) q^{61} +(6.54535 + 0.520513i) q^{62} +(7.11016 + 3.66683i) q^{64} +(-7.05657 - 4.57336i) q^{65} +(-9.04430 + 9.04430i) q^{67} +(-0.549491 + 3.43302i) q^{68} +(0.413125 + 3.13550i) q^{70} +4.60679i q^{71} +12.1920 q^{73} +(6.95248 + 8.15379i) q^{74} +(8.85617 + 12.2315i) q^{76} +(-1.89509 + 1.89509i) q^{77} -5.73529 q^{79} +(-0.955822 + 8.89305i) q^{80} +(1.10965 - 13.9536i) q^{82} +(2.04924 - 2.04924i) q^{83} +(-3.80140 + 0.811670i) q^{85} +(-9.38417 - 11.0057i) q^{86} +(-6.47237 + 3.94448i) q^{88} +15.0386i q^{89} +(2.65942 - 2.65942i) q^{91} +(0.316432 + 0.0506483i) q^{92} +(0.537662 - 6.76099i) q^{94} +(-9.18235 + 14.1681i) q^{95} -3.84735i q^{97} +(8.45829 + 0.672638i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q+O(q^{10}) \) 48 * q	\( 48 q + 12 q^{10} + 16 q^{14} - 4 q^{16} + 8 q^{19} + 40 q^{26} - 48 q^{31} - 28 q^{34} - 24 q^{35} - 16 q^{40} + 40 q^{44} - 4 q^{46} + 48 q^{49} + 32 q^{50} - 48 q^{56} + 32 q^{59} + 16 q^{61} + 48 q^{64} - 16 q^{65} - 40 q^{74} + 60 q^{76} - 96 q^{79} - 72 q^{80} - 16 q^{86} - 32 q^{91} + 44 q^{94} + 48 q^{95}+O(q^{100}) \) 48 * q + 12 * q^10 + 16 * q^14 - 4 * q^16 + 8 * q^19 + 40 * q^26 - 48 * q^31 - 28 * q^34 - 24 * q^35 - 16 * q^40 + 40 * q^44 - 4 * q^46 + 48 * q^49 + 32 * q^50 - 48 * q^56 + 32 * q^59 + 16 * q^61 + 48 * q^64 - 16 * q^65 - 40 * q^74 + 60 * q^76 - 96 * q^79 - 72 * q^80 - 16 * q^86 - 32 * q^91 + 44 * q^94 + 48 * q^95

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