LMFDB - Embedded newform 720.2.bm.h.109.7

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			109.7
Character	$\chi$	$=$	720.109
Dual form			720.2.bm.h.469.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.903247 + 1.08818i) q^{2} +(-0.368289 - 1.96580i) q^{4} +(2.09919 + 0.770325i) q^{5} +3.05002 q^{7} +(2.47181 + 1.37484i) q^{8} +O(q^{10})$	\(q+(-0.903247 + 1.08818i) q^{2} +(-0.368289 - 1.96580i) q^{4} +(2.09919 + 0.770325i) q^{5} +3.05002 q^{7} +(2.47181 + 1.37484i) q^{8} +(-2.73434 + 1.58851i) q^{10} +(1.80989 - 1.80989i) q^{11} +(2.47057 - 2.47057i) q^{13} +(-2.75492 + 3.31898i) q^{14} +(-3.72873 + 1.44796i) q^{16} -3.66653i q^{17} +(-2.31596 - 2.31596i) q^{19} +(0.741196 - 4.41029i) q^{20} +(0.334715 + 3.60427i) q^{22} -4.86336 q^{23} +(3.81320 + 3.23412i) q^{25} +(0.456900 + 4.91998i) q^{26} +(-1.12329 - 5.99573i) q^{28} +(-4.74672 - 4.74672i) q^{29} +1.86172 q^{31} +(1.79231 - 5.36541i) q^{32} +(3.98986 + 3.31179i) q^{34} +(6.40257 + 2.34951i) q^{35} +(5.40092 + 5.40092i) q^{37} +(4.61208 - 0.428306i) q^{38} +(4.12972 + 4.79014i) q^{40} -6.47424i q^{41} +(-4.19382 - 4.19382i) q^{43} +(-4.22444 - 2.89131i) q^{44} +(4.39282 - 5.29223i) q^{46} +8.24387i q^{47} +2.30263 q^{49} +(-6.96358 + 1.22825i) q^{50} +(-5.76653 - 3.94676i) q^{52} +(9.99761 + 9.99761i) q^{53} +(5.19350 - 2.40510i) q^{55} +(7.53906 + 4.19328i) q^{56} +(9.45277 - 0.877843i) q^{58} +(2.47155 - 2.47155i) q^{59} +(8.01822 + 8.01822i) q^{61} +(-1.68160 + 2.02590i) q^{62} +(4.21965 + 6.79666i) q^{64} +(7.08935 - 3.28306i) q^{65} +(-8.60064 + 8.60064i) q^{67} +(-7.20766 + 1.35034i) q^{68} +(-8.33981 + 4.84499i) q^{70} -6.63653i q^{71} +2.70041 q^{73} +(-10.7556 + 0.998828i) q^{74} +(-3.69977 + 5.40565i) q^{76} +(5.52020 - 5.52020i) q^{77} -10.9690 q^{79} +(-8.94271 + 0.167218i) q^{80} +(7.04516 + 5.84784i) q^{82} +(-3.65688 + 3.65688i) q^{83} +(2.82442 - 7.69675i) q^{85} +(8.35170 - 0.775591i) q^{86} +(6.96199 - 1.98539i) q^{88} +13.1530i q^{89} +(7.53530 - 7.53530i) q^{91} +(1.79112 + 9.56038i) q^{92} +(-8.97085 - 7.44625i) q^{94} +(-3.07760 - 6.64569i) q^{95} +12.4932i q^{97} +(-2.07985 + 2.50569i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−0.903247	+	1.08818i	−0.638692	+	0.769462i
$2$	−0.903247	+	1.08818i	−0.638692	+	0.769462i
$3$		0			0
$3$		0			0
$4$	−0.368289	−	1.96580i	−0.184144	−	0.982899i
$5$	2.09919	+	0.770325i	0.938786	+	0.344500i
$5$	2.09919	+	0.770325i	0.938786	+	0.344500i
$6$		0			0
$7$	3.05002			1.15280			0.576400	−	0.817168i	$-0.304457\pi$
$7$	3.05002			1.15280			0.576400	+	0.817168i	$0.304457\pi$
$8$	2.47181	+	1.37484i	0.873915	+	0.486078i
$9$		0			0
$10$	−2.73434	+	1.58851i	−0.864675	+	0.502331i
$11$	1.80989	−	1.80989i	0.545702	−	0.545702i	−0.379493	−	0.925195i	$-0.623901\pi$
$11$	1.80989	−	1.80989i	0.545702	−	0.545702i	0.925195	+	0.379493i	$0.123901\pi$
$12$		0			0
$13$	2.47057	−	2.47057i	0.685214	−	0.685214i	−0.275956	−	0.961170i	$-0.588995\pi$
$13$	2.47057	−	2.47057i	0.685214	−	0.685214i	0.961170	+	0.275956i	$0.0889946\pi$
$14$	−2.75492	+	3.31898i	−0.736284	+	0.887036i
$15$		0			0
$16$	−3.72873	+	1.44796i	−0.932182	+	0.361991i
$17$		−	3.66653i		−	0.889265i	−0.895713	−	0.444632i	$-0.853334\pi$
$17$		−	3.66653i		−	0.889265i	0.895713	−	0.444632i	$-0.146666\pi$
$18$		0			0
$19$	−2.31596	−	2.31596i	−0.531318	−	0.531318i	0.389647	−	0.920964i	$-0.372597\pi$
$19$	−2.31596	−	2.31596i	−0.531318	−	0.531318i	−0.920964	+	0.389647i	$0.872597\pi$
$20$	0.741196	−	4.41029i	0.165736	−	0.986170i
$21$		0			0
$22$	0.334715	+	3.60427i	0.0713615	+	0.768433i
$23$	−4.86336			−1.01408			−0.507040	−	0.861922i	$-0.669260\pi$
$23$	−4.86336			−1.01408			−0.507040	+	0.861922i	$0.669260\pi$
$24$		0			0
$25$	3.81320	+	3.23412i	0.762640	+	0.646824i
$26$	0.456900	+	4.91998i	0.0896054	+	0.964887i
$27$		0			0
$28$	−1.12329	−	5.99573i	−0.212282	−	1.13309i
$29$	−4.74672	−	4.74672i	−0.881444	−	0.881444i	0.112237	−	0.993681i	$-0.464198\pi$
$29$	−4.74672	−	4.74672i	−0.881444	−	0.881444i	−0.993681	+	0.112237i	$0.964198\pi$
$30$		0			0
$31$	1.86172			0.334375			0.167188	−	0.985925i	$-0.446531\pi$
$31$	1.86172			0.334375			0.167188	+	0.985925i	$0.446531\pi$
$32$	1.79231	−	5.36541i	0.316839	−	0.948479i
$33$		0			0
$34$	3.98986	+	3.31179i	0.684256	+	0.567966i
$35$	6.40257	+	2.34951i	1.08223	+	0.397139i
$36$		0			0
$37$	5.40092	+	5.40092i	0.887905	+	0.887905i	0.994322	−	0.106416i	$-0.0339376\pi$
$37$	5.40092	+	5.40092i	0.887905	+	0.887905i	−0.106416	+	0.994322i	$0.533938\pi$
$38$	4.61208	−	0.428306i	0.748178	−	0.0694804i
$39$		0			0
$40$	4.12972	+	4.79014i	0.652966	+	0.757387i
$41$		−	6.47424i		−	1.01111i	−0.862796	−	0.505553i	$-0.831288\pi$
$41$		−	6.47424i		−	1.01111i	0.862796	−	0.505553i	$-0.168712\pi$
$42$		0			0
$43$	−4.19382	−	4.19382i	−0.639551	−	0.639551i	0.310893	−	0.950445i	$-0.399372\pi$
$43$	−4.19382	−	4.19382i	−0.639551	−	0.639551i	−0.950445	+	0.310893i	$0.899372\pi$
$44$	−4.22444	−	2.89131i	−0.636858	−	0.435882i
$45$		0			0
$46$	4.39282	−	5.29223i	0.647685	−	0.780297i
$47$			8.24387i			1.20249i	0.799064	+	0.601246i	$0.205329\pi$
$47$			8.24387i			1.20249i	−0.799064	+	0.601246i	$0.794671\pi$
$48$		0			0
$49$	2.30263			0.328947
$50$	−6.96358	+	1.22825i	−0.984798	+	0.173701i
$51$		0			0
$52$	−5.76653	−	3.94676i	−0.799674	−	0.547318i
$53$	9.99761	+	9.99761i	1.37328	+	1.37328i	0.855539	+	0.517739i	$0.173226\pi$
$53$	9.99761	+	9.99761i	1.37328	+	1.37328i	0.517739	+	0.855539i	$0.326774\pi$
$54$		0			0
$55$	5.19350	−	2.40510i	0.700292	−	0.324303i
$56$	7.53906	+	4.19328i	1.00745	+	0.560351i
$57$		0			0
$58$	9.45277	−	0.877843i	1.24121	−	0.115266i
$59$	2.47155	−	2.47155i	0.321769	−	0.321769i	−0.527676	−	0.849445i	$-0.676937\pi$
$59$	2.47155	−	2.47155i	0.321769	−	0.321769i	0.849445	+	0.527676i	$0.176937\pi$
$60$		0			0
$61$	8.01822	+	8.01822i	1.02663	+	1.02663i	0.999636	+	0.0269927i	$0.00859310\pi$
$61$	8.01822	+	8.01822i	1.02663	+	1.02663i	0.0269927	+	0.999636i	$0.491407\pi$
$62$	−1.68160	+	2.02590i	−0.213563	+	0.257289i
$63$		0			0
$64$	4.21965	+	6.79666i	0.527456	+	0.849582i
$65$	7.08935	−	3.28306i	0.879325	−	0.407213i
$66$		0			0
$67$	−8.60064	+	8.60064i	−1.05074	+	1.05074i	−0.0520936	+	0.998642i	$0.516589\pi$
$67$	−8.60064	+	8.60064i	−1.05074	+	1.05074i	−0.998642	+	0.0520936i	$0.983411\pi$
$68$	−7.20766	+	1.35034i	−0.874058	+	0.163753i
$69$		0			0
$70$	−8.33981	+	4.84499i	−0.996797	+	0.579087i
$71$		−	6.63653i		−	0.787611i	−0.919194	−	0.393806i	$-0.871158\pi$
$71$		−	6.63653i		−	0.787611i	0.919194	−	0.393806i	$-0.128842\pi$
$72$		0			0
$73$	2.70041			0.316059			0.158030	−	0.987434i	$-0.449486\pi$
$73$	2.70041			0.316059			0.158030	+	0.987434i	$0.449486\pi$
$74$	−10.7556	+	0.998828i	−1.25031	+	0.116111i
$75$		0			0
$76$	−3.69977	+	5.40565i	−0.424393	+	0.620071i
$77$	5.52020	−	5.52020i	0.629085	−	0.629085i
$78$		0			0
$79$	−10.9690			−1.23411			−0.617054	−	0.786921i	$-0.711674\pi$
$79$	−10.9690			−1.23411			−0.617054	+	0.786921i	$0.711674\pi$
$80$	−8.94271	+	0.167218i	−0.999825	+	0.0186955i
$81$		0			0
$82$	7.04516	+	5.84784i	0.778008	+	0.645786i
$83$	−3.65688	+	3.65688i	−0.401395	+	0.401395i	−0.878724	−	0.477330i	$-0.841605\pi$
$83$	−3.65688	+	3.65688i	−0.401395	+	0.401395i	0.477330	+	0.878724i	$0.341605\pi$
$84$		0			0
$85$	2.82442	−	7.69675i	0.306352	−	0.834830i
$86$	8.35170	−	0.775591i	0.900587	−	0.0836341i
$87$		0			0
$88$	6.96199	−	1.98539i	0.742151	−	0.211644i
$89$			13.1530i			1.39421i	0.716968	+	0.697106i	$0.245529\pi$
$89$			13.1530i			1.39421i	−0.716968	+	0.697106i	$0.754471\pi$
$90$		0			0
$91$	7.53530	−	7.53530i	0.789914	−	0.789914i
$92$	1.79112	+	9.56038i	0.186737	+	0.996739i
$93$		0			0
$94$	−8.97085	−	7.44625i	−0.925272	−	0.768022i
$95$	−3.07760	−	6.64569i	−0.315755	−	0.681833i
$96$		0			0
$97$			12.4932i			1.26849i	0.773131	+	0.634247i	$0.218690\pi$
$97$			12.4932i			1.26849i	−0.773131	+	0.634247i	$0.781310\pi$
$98$	−2.07985	+	2.50569i	−0.210096	+	0.253113i
$99$		0			0
$100$	4.95327	−	8.68707i	0.495327	−	0.868707i
$101$	−0.569518	+	0.569518i	−0.0566692	+	0.0566692i	−0.734873	−	0.678204i	$-0.762758\pi$
$101$	−0.569518	+	0.569518i	−0.0566692	+	0.0566692i	0.678204	+	0.734873i	$0.262758\pi$
$102$		0			0
$103$	−12.2060			−1.20269			−0.601345	−	0.798989i	$-0.705368\pi$
$103$	−12.2060			−1.20269			−0.601345	+	0.798989i	$0.705368\pi$
$104$	9.50341	−	2.71014i	0.931886	−	0.265752i
$105$		0			0
$106$	−19.9096	+	1.84893i	−1.93379	+	0.179584i
$107$	7.99550	+	7.99550i	0.772955	+	0.772955i	0.978622	−	0.205667i	$-0.0659365\pi$
$107$	7.99550	+	7.99550i	0.772955	+	0.772955i	−0.205667	+	0.978622i	$0.565937\pi$
$108$		0			0
$109$	−7.07511	−	7.07511i	−0.677672	−	0.677672i	0.281801	−	0.959473i	$-0.409068\pi$
$109$	−7.07511	−	7.07511i	−0.677672	−	0.677672i	−0.959473	+	0.281801i	$0.909068\pi$
$110$	−2.07383	+	7.82388i	−0.197732	+	0.745978i
$111$		0			0
$112$	−11.3727	+	4.41632i	−1.07462	+	0.417303i
$113$		−	6.25105i		−	0.588050i	−0.955798	−	0.294025i	$-0.905005\pi$
$113$		−	6.25105i		−	0.588050i	0.955798	−	0.294025i	$-0.0949948\pi$
$114$		0			0
$115$	−10.2091	−	3.74637i	−0.952005	−	0.349351i
$116$	−7.58293	+	11.0793i	−0.704058	+	1.02868i
$117$		0			0
$118$	0.457081	+	4.92193i	0.0420777	+	0.453100i
$119$		−	11.1830i		−	1.02514i
$120$		0			0
$121$			4.44861i			0.404419i
$122$	−15.9677	+	1.48286i	−1.44565	+	0.134252i
$123$		0			0
$124$	−0.685652	−	3.65977i	−0.0615734	−	0.328657i
$125$	5.51331	+	9.72643i	0.493125	+	0.869958i
$126$		0			0
$127$		−	14.1884i		−	1.25902i	−0.776993	−	0.629509i	$-0.783256\pi$
$127$		−	14.1884i		−	1.25902i	0.776993	−	0.629509i	$-0.216744\pi$
$128$	−11.2074	−	1.54730i	−0.990604	−	0.136764i
$129$		0			0
$130$	−2.83086	+	10.6799i	−0.248283	+	0.936692i
$131$	12.5522	+	12.5522i	1.09669	+	1.09669i	0.994795	+	0.101896i	$0.0324909\pi$
$131$	12.5522	+	12.5522i	1.09669	+	1.09669i	0.101896	+	0.994795i	$0.467509\pi$
$132$		0			0
$133$	−7.06373	−	7.06373i	−0.612503	−	0.612503i
$134$	−1.59057	−	17.1276i	−0.137405	−	1.47960i
$135$		0			0
$136$	5.04088	−	9.06296i	0.432252	−	0.777142i
$137$	−4.88336			−0.417214			−0.208607	−	0.978000i	$-0.566893\pi$
$137$	−4.88336			−0.417214			−0.208607	+	0.978000i	$0.566893\pi$
$138$		0			0
$139$	5.84556	−	5.84556i	0.495814	−	0.495814i	−0.414318	−	0.910132i	$-0.635980\pi$
$139$	5.84556	−	5.84556i	0.495814	−	0.495814i	0.910132	+	0.414318i	$0.135980\pi$
$140$	2.26066	−	13.4515i	0.191061	−	1.13686i
$141$		0			0
$142$	7.22177	+	5.99443i	0.606037	+	0.503041i
$143$		−	8.94292i		−	0.747845i
$144$		0			0
$145$	−6.30775	−	13.6208i	−0.523830	−	1.13115i
$146$	−2.43914	+	2.93855i	−0.201865	+	0.243196i
$147$		0			0
$148$	8.62802	−	12.6062i	0.709219	−	1.03622i
$149$	15.1483	−	15.1483i	1.24100	−	1.24100i	0.281412	−	0.959587i	$-0.409197\pi$
$149$	15.1483	−	15.1483i	1.24100	−	1.24100i	0.959587	−	0.281412i	$-0.0908029\pi$
$150$		0			0
$151$			4.02031i			0.327168i	0.986529	+	0.163584i	$0.0523056\pi$
$151$			4.02031i			0.327168i	−0.986529	+	0.163584i	$0.947694\pi$
$152$	−2.54054	−	8.90867i	−0.206065	−	0.722589i
$153$		0			0
$154$	1.02089	+	10.9931i	0.0822655	+	0.885849i
$155$	3.90811	+	1.43413i	0.313907	+	0.115192i
$156$		0			0
$157$	9.86041	−	9.86041i	0.786946	−	0.786946i	−0.194046	−	0.980992i	$-0.562161\pi$
$157$	9.86041	−	9.86041i	0.786946	−	0.786946i	0.980992	+	0.194046i	$0.0621612\pi$
$158$	9.90771	−	11.9363i	0.788215	−	0.949600i
$159$		0			0
$160$	7.89551	−	9.88235i	0.624195	−	0.781268i
$161$	−14.8333			−1.16903
$162$		0			0
$163$	−13.1713	+	13.1713i	−1.03165	+	1.03165i	−0.0321718	+	0.999482i	$0.510242\pi$
$163$	−13.1713	+	13.1713i	−1.03165	+	1.03165i	−0.999482	+	0.0321718i	$0.989758\pi$
$164$	−12.7270	+	2.38439i	−0.993815	+	0.186190i
$165$		0			0
$166$	−0.676291	−	7.28242i	−0.0524904	−	0.565226i
$167$	−0.0610761			−0.00472621			−0.00236311	−	0.999997i	$-0.500752\pi$
$167$	−0.0610761			−0.00472621			−0.00236311	+	0.999997i	$0.500752\pi$
$168$		0			0
$169$			0.792537i			0.0609644i
$170$	5.82433	+	10.0256i	0.446705	+	0.768925i
$171$		0			0
$172$	−6.69966	+	9.78874i	−0.510845	+	0.746384i
$173$	−8.01622	+	8.01622i	−0.609462	+	0.609462i	−0.942805	−	0.333343i	$-0.891823\pi$
$173$	−8.01622	+	8.01622i	−0.609462	+	0.609462i	0.333343	+	0.942805i	$0.391823\pi$
$174$		0			0
$175$	11.6303	+	9.86413i	0.879171	+	0.745658i
$176$	−4.12793	+	9.36923i	−0.311154	+	0.706232i
$177$		0			0
$178$	−14.3128	−	11.8804i	−1.07279	−	0.890472i
$179$	−11.8352	−	11.8352i	−0.884607	−	0.884607i	0.109392	−	0.993999i	$-0.465110\pi$
$179$	−11.8352	−	11.8352i	−0.884607	−	0.884607i	−0.993999	+	0.109392i	$0.965110\pi$
$180$		0			0
$181$	3.63391	−	3.63391i	0.270106	−	0.270106i	−0.559037	−	0.829143i	$-0.688829\pi$
$181$	3.63391	−	3.63391i	0.270106	−	0.270106i	0.829143	+	0.559037i	$0.188829\pi$
$182$	1.39355	+	15.0060i	0.103297	+	1.11232i
$183$		0			0
$184$	−12.0213	−	6.68632i	−0.886221	−	0.492922i
$185$	7.17709	+	15.4980i	0.527670	+	1.13944i
$186$		0			0
$187$	−6.63602	−	6.63602i	−0.485274	−	0.485274i
$188$	16.2058	−	3.03612i	1.18193	−	0.221432i
$189$		0			0
$190$	10.0116	+	2.65370i	0.726315	+	0.192520i
$191$	−19.0823			−1.38074			−0.690372	−	0.723455i	$-0.742553\pi$
$191$	−19.0823			−1.38074			−0.690372	+	0.723455i	$0.742553\pi$
$192$		0			0
$193$			2.99015i			0.215236i	0.994192	+	0.107618i	$0.0343223\pi$
$193$			2.99015i			0.215236i	−0.994192	+	0.107618i	$0.965678\pi$
$194$	−13.5949	−	11.2845i	−0.976058	−	0.810177i
$195$		0			0
$196$	−0.848033	−	4.52651i	−0.0605738	−	0.323322i
$197$	−1.37271	−	1.37271i	−0.0978016	−	0.0978016i	0.656513	−	0.754315i	$-0.272031\pi$
$197$	−1.37271	−	1.37271i	−0.0978016	−	0.0978016i	−0.754315	+	0.656513i	$0.772031\pi$
$198$		0			0
$199$		−	15.7129i		−	1.11386i	−0.830560	−	0.556930i	$-0.811979\pi$
$199$		−	15.7129i		−	1.11386i	0.830560	−	0.556930i	$-0.188021\pi$
$200$	4.97911	+	13.2366i	0.352076	+	0.935971i
$201$		0			0
$202$	−0.105325	−	1.13416i	−0.00741063	−	0.0797989i
$203$	−14.4776	−	14.4776i	−1.01613	−	1.01613i
$204$		0			0
$205$	4.98727	−	13.5907i	0.348326	−	0.949213i
$206$	11.0250	−	13.2823i	0.768149	−	0.925425i
$207$		0			0
$208$	−5.63479	+	12.7894i	−0.390703	+	0.886785i
$209$	−8.38326			−0.579882
$210$		0			0
$211$	16.8391	+	16.8391i	1.15925	+	1.15925i	0.984637	+	0.174614i	$0.0558679\pi$
$211$	16.8391	+	16.8391i	1.15925	+	1.15925i	0.174614	+	0.984637i	$0.444132\pi$
$212$	15.9713	−	23.3353i	1.09691	−	1.60267i
$213$		0			0
$214$	−15.9225	+	1.47866i	−1.08844	+	0.101079i
$215$	−5.57302	−	12.0342i	−0.380077	−	0.820727i
$216$		0			0
$217$	5.67830			0.385468
$218$	14.0896	−	1.30845i	0.954267	−	0.0886192i
$219$		0			0
$220$	−6.64065	−	9.32361i	−0.447712	−	0.628598i
$221$	−9.05844	−	9.05844i	−0.609336	−	0.609336i
$222$		0			0
$223$			10.6893i			0.715809i	0.933758	+	0.357905i	$0.116509\pi$
$223$			10.6893i			0.715809i	−0.933758	+	0.357905i	$0.883491\pi$
$224$	5.46659	−	16.3646i	0.365252	−	1.09341i
$225$		0			0
$226$	6.80230	+	5.64625i	0.452482	+	0.375583i
$227$	−15.0722	+	15.0722i	−1.00037	+	1.00037i	−0.000374434		1.00000i	$0.500119\pi$
$227$	−15.0722	+	15.0722i	−1.00037	+	1.00037i	−1.00000		0.000374434i	$0.999881\pi$
$228$		0			0
$229$	−3.23629	+	3.23629i	−0.213860	+	0.213860i	−0.805905	−	0.592045i	$-0.798321\pi$
$229$	−3.23629	+	3.23629i	−0.213860	+	0.213860i	0.592045	+	0.805905i	$0.298321\pi$
$230$	13.2981	−	7.72550i	0.876850	−	0.509404i
$231$		0			0
$232$	−5.20701	−	18.2589i	−0.341857	−	1.19876i
$233$	−4.75428			−0.311463			−0.155732	−	0.987799i	$-0.549773\pi$
$233$	−4.75428			−0.311463			−0.155732	+	0.987799i	$0.549773\pi$
$234$		0			0
$235$	−6.35046	+	17.3054i	−0.414258	+	1.12888i
$236$	−5.76882	−	3.94833i	−0.375518	−	0.257015i
$237$		0			0
$238$	12.1692	+	10.1010i	0.788810	+	0.654752i
$239$	−11.9224			−0.771196			−0.385598	−	0.922667i	$-0.626005\pi$
$239$	−11.9224			−0.771196			−0.385598	+	0.922667i	$0.626005\pi$
$240$		0			0
$241$	−28.2991			−1.82291			−0.911453	−	0.411403i	$-0.865039\pi$
$241$	−28.2991			−1.82291			−0.911453	+	0.411403i	$0.865039\pi$
$242$	−4.84090	−	4.01819i	−0.311185	−	0.258299i
$243$		0			0
$244$	12.8092	−	18.7152i	0.820024	−	1.19812i
$245$	4.83366	+	1.77377i	0.308811	+	0.113322i
$246$		0			0
$247$	−11.4435			−0.728133
$248$	4.60182	+	2.55956i	0.292216	+	0.162533i
$249$		0			0
$250$	−15.5640	−	2.78588i	−0.984355	−	0.176195i
$251$	4.39215	−	4.39215i	0.277230	−	0.277230i	−0.554772	−	0.832002i	$-0.687195\pi$
$251$	4.39215	−	4.39215i	0.277230	−	0.277230i	0.832002	+	0.554772i	$0.187195\pi$
$252$		0			0
$253$	−8.80214	+	8.80214i	−0.553386	+	0.553386i
$254$	15.4396	+	12.8156i	0.968767	+	0.804125i
$255$		0			0
$256$	11.8068	−	10.7981i	0.737925	−	0.674882i
$257$		−	2.53050i		−	0.157849i	−0.996881	−	0.0789243i	$-0.974851\pi$
$257$		−	2.53050i		−	0.157849i	0.996881	−	0.0789243i	$-0.0251485\pi$
$258$		0			0
$259$	16.4729	+	16.4729i	1.02358	+	1.02358i
$260$	−9.06476	−	12.7271i	−0.562172	−	0.789302i
$261$		0			0
$262$	−24.9969	+	2.32136i	−1.54431	+	0.143414i
$263$	0.540983			0.0333584			0.0166792	−	0.999861i	$-0.494691\pi$
$263$	0.540983			0.0333584			0.0166792	+	0.999861i	$0.494691\pi$
$264$		0			0
$265$	13.2855	+	28.6883i	0.816120	+	1.76231i
$266$	14.0669	−	1.30634i	0.862499	−	0.0800970i
$267$		0			0
$268$	20.0747	+	13.7396i	1.22625	+	0.839280i
$269$	3.00188	+	3.00188i	0.183028	+	0.183028i	0.792674	−	0.609646i	$-0.208688\pi$
$269$	3.00188	+	3.00188i	0.183028	+	0.183028i	−0.609646	+	0.792674i	$0.708688\pi$
$270$		0			0
$271$	−8.44312			−0.512883			−0.256442	−	0.966560i	$-0.582550\pi$
$271$	−8.44312			−0.512883			−0.256442	+	0.966560i	$0.582550\pi$
$272$	5.30900	+	13.6715i	0.321906	+	0.828956i
$273$		0			0
$274$	4.41089	−	5.31400i	0.266471	−	0.321030i
$275$	12.7549	−	1.04807i	0.769147	−	0.0632011i
$276$		0			0
$277$	12.2494	+	12.2494i	0.735992	+	0.735992i	0.971800	−	0.235807i	$-0.0757735\pi$
$277$	12.2494	+	12.2494i	0.735992	+	0.735992i	−0.235807	+	0.971800i	$0.575773\pi$
$278$	1.08106	+	11.6410i	0.0648376	+	0.698182i
$279$		0			0
$280$	12.5957	+	14.6100i	0.752739	+	0.873116i
$281$			16.6912i			0.995715i	0.867259	+	0.497857i	$0.165880\pi$
$281$			16.6912i			0.995715i	−0.867259	+	0.497857i	$0.834120\pi$
$282$		0			0
$283$	1.25800	+	1.25800i	0.0747802	+	0.0747802i	0.743508	−	0.668727i	$-0.233161\pi$
$283$	1.25800	+	1.25800i	0.0747802	+	0.0747802i	−0.668727	+	0.743508i	$0.733161\pi$
$284$	−13.0461	+	2.44416i	−0.774143	+	0.145034i
$285$		0			0
$286$	9.73155	+	8.07767i	0.575438	+	0.477643i
$287$		−	19.7466i		−	1.16560i
$288$		0			0
$289$	3.55654			0.209208
$290$	20.5194	+	5.43895i	1.20494	+	0.319386i
$291$		0			0
$292$	−0.994532	−	5.30847i	−0.0582006	−	0.310655i
$293$	−12.4197	−	12.4197i	−0.725564	−	0.725564i	0.244169	−	0.969733i	$-0.421485\pi$
$293$	−12.4197	−	12.4197i	−0.725564	−	0.725564i	−0.969733	+	0.244169i	$0.921485\pi$
$294$		0			0
$295$	7.09216	−	3.28436i	0.412922	−	0.191223i
$296$	5.92464	+	20.7754i	0.344363	+	1.20755i
$297$		0			0
$298$	2.80148	+	30.1669i	0.162285	+	1.74752i
$299$	−12.0153	+	12.0153i	−0.694862	+	0.694862i
$300$		0			0
$301$	−12.7912	−	12.7912i	−0.737275	−	0.737275i
$302$	−4.37484	−	3.63134i	−0.251744	−	0.208960i
$303$		0			0
$304$	11.9890	+	5.28216i	0.687617	+	0.302953i
$305$	10.6551	+	23.0084i	0.610111	+	1.31746i
$306$		0			0
$307$	21.6994	−	21.6994i	1.23845	−	1.23845i	0.277816	−	0.960634i	$-0.410389\pi$
$307$	21.6994	−	21.6994i	1.23845	−	1.23845i	0.960634	−	0.277816i	$-0.0896107\pi$
$308$	−12.8846	−	8.81857i	−0.734170	−	0.502485i
$309$		0			0
$310$	−5.09059	+	2.95737i	−0.289126	+	0.167967i
$311$			13.6575i			0.774447i	0.921986	+	0.387224i	$0.126566\pi$
$311$			13.6575i			0.774447i	−0.921986	+	0.387224i	$0.873434\pi$
$312$		0			0
$313$	−13.7537			−0.777403			−0.388701	−	0.921364i	$-0.627076\pi$
$313$	−13.7537			−0.777403			−0.388701	+	0.921364i	$0.627076\pi$
$314$	1.82355	+	19.6363i	0.102909	+	1.10814i
$315$		0			0
$316$	4.03976	+	21.5628i	0.227254	+	1.21300i
$317$	16.5311	−	16.5311i	0.928477	−	0.928477i	−0.0691306	−	0.997608i	$-0.522023\pi$
$317$	16.5311	−	16.5311i	0.928477	−	0.928477i	0.997608	+	0.0691306i	$0.0220225\pi$
$318$		0			0
$319$	−17.1821			−0.962012
$320$	3.62222	+	17.5180i	0.202488	+	0.979285i
$321$		0			0
$322$	13.3982	−	16.1414i	0.746651	−	0.899526i
$323$	−8.49155	+	8.49155i	−0.472482	+	0.472482i
$324$		0			0
$325$	17.4109	−	1.43066i	0.965784	−	0.0793588i
$326$	−2.43585	−	26.2297i	−0.134909	−	1.45273i
$327$		0			0
$328$	8.90102	−	16.0031i	0.491476	−	0.883621i
$329$			25.1440i			1.38623i
$330$		0			0
$331$	−8.05179	+	8.05179i	−0.442566	+	0.442566i	−0.892874	−	0.450307i	$-0.851314\pi$
$331$	−8.05179	+	8.05179i	−0.442566	+	0.442566i	0.450307	+	0.892874i	$0.351314\pi$
$332$	8.53547	+	5.84190i	0.468445	+	0.320616i
$333$		0			0
$334$	0.0551668	−	0.0664621i	0.00301859	−	0.00363664i
$335$	−24.6797	+	11.4291i	−1.34839	+	0.624438i
$336$		0			0
$337$		−	4.77730i		−	0.260236i	−0.991499	−	0.130118i	$-0.958464\pi$
$337$		−	4.77730i		−	0.260236i	0.991499	−	0.130118i	$-0.0415356\pi$
$338$	−0.862426	−	0.715857i	−0.0469098	−	0.0389375i
$339$		0			0
$340$	−16.1705	−	2.71762i	−0.876966	−	0.147384i
$341$	3.36951	−	3.36951i	0.182469	−	0.182469i
$342$		0			0
$343$	−14.3271			−0.773589
$344$	−4.60049	−	16.1321i	−0.248042	−	0.869785i
$345$		0			0
$346$	−1.48249	−	15.9638i	−0.0796994	−	0.858217i
$347$	3.32673	+	3.32673i	0.178588	+	0.178588i	0.790740	−	0.612152i	$-0.209696\pi$
$347$	3.32673	+	3.32673i	0.178588	+	0.178588i	−0.612152	+	0.790740i	$0.709696\pi$
$348$		0			0
$349$	21.8586	+	21.8586i	1.17007	+	1.17007i	0.982194	+	0.187872i	$0.0601590\pi$
$349$	21.8586	+	21.8586i	1.17007	+	1.17007i	0.187872	+	0.982194i	$0.439841\pi$
$350$	−21.2391	+	3.74620i	−1.13528	+	0.200243i
$351$		0			0
$352$	−6.46691	−	12.9547i	−0.344687	−	0.690487i
$353$			5.19436i			0.276468i	0.990400	+	0.138234i	$0.0441426\pi$
$353$			5.19436i			0.276468i	−0.990400	+	0.138234i	$0.955857\pi$
$354$		0			0
$355$	5.11229	−	13.9313i	0.271332	−	0.739399i
$356$	25.8561	−	4.84409i	1.37037	−	0.256736i
$357$		0			0
$358$	23.5691	−	2.18877i	1.24566	−	0.115680i
$359$			21.0115i			1.10894i	0.832203	+	0.554472i	$0.187080\pi$
$359$			21.0115i			1.10894i	−0.832203	+	0.554472i	$0.812920\pi$
$360$		0			0
$361$		−	8.27265i		−	0.435403i
$362$	0.672044	+	7.23668i	0.0353218	+	0.380352i
$363$		0			0
$364$	−17.5880	−	12.0377i	−0.921864	−	0.630948i
$365$	5.66868	+	2.08020i	0.296712	+	0.108882i
$366$		0			0
$367$		−	24.5855i		−	1.28335i	−0.766976	−	0.641676i	$-0.778240\pi$
$367$		−	24.5855i		−	1.28335i	0.766976	−	0.641676i	$-0.221760\pi$
$368$	18.1341	−	7.04196i	0.945307	−	0.367088i
$369$		0			0
$370$	−23.3474	−	6.18854i	−1.21377	−	0.321727i
$371$	30.4929	+	30.4929i	1.58311	+	1.58311i
$372$		0			0
$373$	−1.00389	−	1.00389i	−0.0519795	−	0.0519795i	0.680639	−	0.732619i	$-0.261702\pi$
$373$	−1.00389	−	1.00389i	−0.0519795	−	0.0519795i	−0.732619	+	0.680639i	$0.761702\pi$
$374$	13.2152	−	1.22724i	0.683340	−	0.0634592i
$375$		0			0
$376$	−11.3340	+	20.3772i	−0.584505	+	1.05088i
$377$	−23.4542			−1.20796
$378$		0			0
$379$	−4.93721	+	4.93721i	−0.253607	+	0.253607i	−0.822448	−	0.568841i	$-0.807392\pi$
$379$	−4.93721	+	4.93721i	−0.253607	+	0.253607i	0.568841	+	0.822448i	$0.307392\pi$
$380$	−11.9306	+	8.49747i	−0.612029	+	0.435911i
$381$		0			0
$382$	17.2360	−	20.7650i	0.881870	−	1.06243i
$383$		−	4.25312i		−	0.217324i	−0.994079	−	0.108662i	$-0.965343\pi$
$383$		−	4.25312i		−	0.217324i	0.994079	−	0.108662i	$-0.0346566\pi$
$384$		0			0
$385$	15.8403	−	7.33560i	0.807296	−	0.373857i
$386$	−3.25383	−	2.70085i	−0.165616	−	0.137469i
$387$		0			0
$388$	24.5591	−	4.60111i	1.24680	−	0.233586i
$389$	15.1555	−	15.1555i	0.768414	−	0.768414i	−0.209413	−	0.977827i	$-0.567155\pi$
$389$	15.1555	−	15.1555i	0.768414	−	0.768414i	0.977827	+	0.209413i	$0.0671553\pi$
$390$		0			0
$391$			17.8317i			0.901786i
$392$	5.69166	+	3.16574i	0.287472	+	0.159894i
$393$		0			0
$394$	2.73366	−	0.253865i	0.137720	−	0.0127895i
$395$	−23.0260	−	8.44969i	−1.15856	−	0.425150i
$396$		0			0
$397$	2.06126	−	2.06126i	0.103451	−	0.103451i	−0.653487	−	0.756938i	$-0.726694\pi$
$397$	2.06126	−	2.06126i	0.103451	−	0.103451i	0.756938	+	0.653487i	$0.226694\pi$
$398$	17.0985	+	14.1927i	0.857073	+	0.711413i
$399$		0			0
$400$	−18.9013	−	6.53777i	−0.945063	−	0.326889i
$401$	−10.1012			−0.504431			−0.252215	−	0.967671i	$-0.581159\pi$
$401$	−10.1012			−0.504431			−0.252215	+	0.967671i	$0.581159\pi$
$402$		0			0
$403$	4.59952	−	4.59952i	0.229119	−	0.229119i
$404$	1.32930	+	0.909811i	0.0661354	+	0.0452648i
$405$		0			0
$406$	28.8312	−	2.67744i	1.43087	−	0.132879i
$407$	19.5501			0.969063
$408$		0			0
$409$		−	15.5464i		−	0.768720i	−0.923183	−	0.384360i	$-0.874422\pi$
$409$		−	15.5464i		−	0.768720i	0.923183	−	0.384360i	$-0.125578\pi$
$410$	10.2844	+	17.7028i	0.507910	+	0.874278i
$411$		0			0
$412$	4.49532	+	23.9945i	0.221469	+	1.18212i
$413$	7.53829	−	7.53829i	0.370935	−	0.370935i
$414$		0			0
$415$	−10.4935	+	4.85950i	−0.515104	+	0.238543i
$416$	−8.82760	−	17.6837i	−0.432809	−	0.867013i
$417$		0			0
$418$	7.57216	−	9.12253i	0.370366	−	0.446198i
$419$	−0.811206	−	0.811206i	−0.0396300	−	0.0396300i	0.687014	−	0.726644i	$-0.258921\pi$
$419$	−0.811206	−	0.811206i	−0.0396300	−	0.0396300i	−0.726644	+	0.687014i	$0.758921\pi$
$420$		0			0
$421$	6.67755	−	6.67755i	0.325444	−	0.325444i	−0.525407	−	0.850851i	$-0.676087\pi$
$421$	6.67755	−	6.67755i	0.325444	−	0.325444i	0.850851	+	0.525407i	$0.176087\pi$
$422$	−33.5339	+	3.11417i	−1.63241	+	0.151595i
$423$		0			0
$424$	10.9671	+	38.4572i	0.532609	+	1.86765i
$425$	11.8580	−	13.9812i	0.575197	−	0.678189i
$426$		0			0
$427$	24.4558	+	24.4558i	1.18350	+	1.18350i
$428$	12.7729	−	18.6622i	0.617401	−	0.902072i
$429$		0			0
$430$	18.1293	+	4.80541i	0.874271	+	0.231738i
$431$	20.8900			1.00623			0.503117	−	0.864218i	$-0.332186\pi$
$431$	20.8900			1.00623			0.503117	+	0.864218i	$0.332186\pi$
$432$		0			0
$433$		−	21.0344i		−	1.01085i	−0.862870	−	0.505426i	$-0.831336\pi$
$433$		−	21.0344i		−	1.01085i	0.862870	−	0.505426i	$-0.168664\pi$
$434$	−5.12891	+	6.17903i	−0.246195	+	0.296603i
$435$		0			0
$436$	−11.3025	+	16.5139i	−0.541294	+	0.790873i
$437$	11.2633	+	11.2633i	0.538799	+	0.538799i
$438$		0			0
$439$		−	27.5268i		−	1.31378i	−0.753986	−	0.656891i	$-0.771871\pi$
$439$		−	27.5268i		−	1.31378i	0.753986	−	0.656891i	$-0.228129\pi$
$440$	16.1439	+	1.19528i	0.769633	+	0.0569827i
$441$		0			0
$442$	18.0393	−	1.67524i	0.858040	−	0.0796829i
$443$	15.3577	+	15.3577i	0.729667	+	0.729667i	0.970553	−	0.240886i	$-0.0774381\pi$
$443$	15.3577	+	15.3577i	0.729667	+	0.729667i	−0.240886	+	0.970553i	$0.577438\pi$
$444$		0			0
$445$	−10.1321	+	27.6106i	−0.480306	+	1.30887i
$446$	−11.6319	−	9.65509i	−0.550788	−	0.457182i
$447$		0			0
$448$	12.8700	+	20.7299i	0.608052	+	0.979398i
$449$	−34.2343			−1.61562			−0.807808	−	0.589445i	$-0.799346\pi$
$449$	−34.2343			−1.61562			−0.807808	+	0.589445i	$0.799346\pi$
$450$		0			0
$451$	−11.7177	−	11.7177i	−0.551763	−	0.551763i
$452$	−12.2883	+	2.30219i	−0.577993	+	0.108286i
$453$		0			0
$454$	−2.78740	−	30.0152i	−0.130819	−	1.40868i
$455$	21.6227	−	10.0134i	1.01369	−	0.469435i
$456$		0			0
$457$	−37.3287			−1.74616			−0.873081	−	0.487575i	$-0.837881\pi$
$457$	−37.3287			−1.74616			−0.873081	+	0.487575i	$0.837881\pi$
$458$	−0.598509	−	6.44485i	−0.0279665	−	0.301148i
$459$		0			0
$460$	−3.60470	+	21.4488i	−0.168070	+	1.00006i
$461$	−4.31480	−	4.31480i	−0.200960	−	0.200960i	0.599451	−	0.800411i	$-0.295386\pi$
$461$	−4.31480	−	4.31480i	−0.200960	−	0.200960i	−0.800411	+	0.599451i	$0.795386\pi$
$462$		0			0
$463$			12.6151i			0.586272i	0.956071	+	0.293136i	$0.0946988\pi$
$463$			12.6151i			0.586272i	−0.956071	+	0.293136i	$0.905301\pi$
$464$	24.5723	+	10.8262i	1.14074	+	0.502591i
$465$		0			0
$466$	4.29429	−	5.17353i	0.198929	−	0.239659i
$467$	3.20222	−	3.20222i	0.148181	−	0.148181i	−0.629124	−	0.777305i	$-0.716586\pi$
$467$	3.20222	−	3.20222i	0.148181	−	0.148181i	0.777305	+	0.629124i	$0.216586\pi$
$468$		0			0
$469$	−26.2321	+	26.2321i	−1.21129	+	1.21129i
$470$	−13.0955	−	22.5416i	−0.604049	−	1.03977i
$471$		0			0
$472$	9.50719	−	2.71122i	0.437604	−	0.124794i
$473$	−15.1807			−0.698009
$474$		0			0
$475$	−1.34113	−	16.3213i	−0.0615352	−	0.748873i
$476$	−21.9835	+	4.11857i	−1.00761	+	0.188775i
$477$		0			0
$478$	10.7689	−	12.9738i	0.492557	−	0.593406i
$479$	9.07562			0.414676			0.207338	−	0.978269i	$-0.433520\pi$
$479$	9.07562			0.414676			0.207338	+	0.978269i	$0.433520\pi$
$480$		0			0
$481$	26.6867			1.21681
$482$	25.5611	−	30.7947i	1.16428	−	1.40266i
$483$		0			0
$484$	8.74506	−	1.63837i	0.397503	−	0.0744714i
$485$	−9.62383	+	26.2256i	−0.436996	+	1.19084i
$486$		0			0
$487$	−1.02703			−0.0465390			−0.0232695	−	0.999729i	$-0.507408\pi$
$487$	−1.02703			−0.0465390			−0.0232695	+	0.999729i	$0.507408\pi$
$488$	8.79575	+	30.8432i	0.398165	+	1.39621i
$489$		0			0
$490$	−6.29618	+	3.65775i	−0.284433	+	0.165241i
$491$	20.0654	−	20.0654i	0.905539	−	0.905539i	−0.0903689	−	0.995908i	$-0.528805\pi$
$491$	20.0654	−	20.0654i	0.905539	−	0.905539i	0.995908	+	0.0903689i	$0.0288046\pi$
$492$		0			0
$493$	−17.4040	+	17.4040i	−0.783837	+	0.783837i
$494$	10.3363	−	12.4526i	0.465053	−	0.560271i
$495$		0			0
$496$	−6.94186	+	2.69571i	−0.311699	+	0.121041i
$497$		−	20.2416i		−	0.907958i
$498$		0			0
$499$	15.1622	+	15.1622i	0.678752	+	0.678752i	0.959718	−	0.280966i	$-0.0906547\pi$
$499$	15.1622	+	15.1622i	0.678752	+	0.678752i	−0.280966	+	0.959718i	$0.590655\pi$
$500$	17.0897	−	14.4202i	0.764275	−	0.644890i
$501$		0			0
$502$	0.812271	+	8.74667i	0.0362534	+	0.390383i
$503$	15.6071			0.695885			0.347942	−	0.937516i	$-0.386880\pi$
$503$	15.6071			0.695885			0.347942	+	0.937516i	$0.386880\pi$
$504$		0			0
$505$	−1.63424	+	0.756813i	−0.0727228	+	0.0336777i
$506$	−1.62784	−	17.5289i	−0.0723663	−	0.779253i
$507$		0			0
$508$	−27.8916	+	5.22543i	−1.23749	+	0.231841i
$509$	−10.8076	−	10.8076i	−0.479040	−	0.479040i	0.425785	−	0.904824i	$-0.359998\pi$
$509$	−10.8076	−	10.8076i	−0.479040	−	0.479040i	−0.904824	+	0.425785i	$0.859998\pi$
$510$		0			0
$511$	8.23632			0.364353
$512$	1.08587	+	22.6013i	0.0479893	+	0.998848i
$513$		0			0
$514$	2.75365	+	2.28567i	0.121458	+	0.100817i
$515$	−25.6227	−	9.40257i	−1.12907	−	0.414327i
$516$		0			0
$517$	14.9205	+	14.9205i	0.656202	+	0.656202i
$518$	−32.8047	+	3.04645i	−1.44135	+	0.133853i
$519$		0			0
$520$	22.0372	+	1.63161i	0.966393	+	0.0715507i
$521$		−	32.1238i		−	1.40737i	−0.710513	−	0.703684i	$-0.751537\pi$
$521$		−	32.1238i		−	1.40737i	0.710513	−	0.703684i	$-0.248463\pi$
$522$		0			0
$523$	−3.26553	−	3.26553i	−0.142792	−	0.142792i	0.632097	−	0.774889i	$-0.282194\pi$
$523$	−3.26553	−	3.26553i	−0.142792	−	0.142792i	−0.774889	+	0.632097i	$0.782194\pi$
$524$	20.0523	−	29.2979i	0.875987	−	1.27989i
$525$		0			0
$526$	−0.488641	+	0.588689i	−0.0213058	+	0.0256681i
$527$		−	6.82607i		−	0.297348i
$528$		0			0
$529$	0.652259			0.0283591
$530$	−43.2182	−	11.4556i	−1.87728	−	0.497599i
$531$		0			0
$532$	−11.2844	+	16.4874i	−0.489240	+	0.714818i
$533$	−15.9951	−	15.9951i	−0.692824	−	0.692824i
$534$		0			0
$535$	10.6249	+	22.9432i	0.459356	+	0.991922i
$536$	−33.0836	+	9.43465i	−1.42899	+	0.407515i
$537$		0			0
$538$	−5.97805	+	0.555159i	−0.257732	+	0.0239346i
$539$	4.16751	−	4.16751i	0.179507	−	0.179507i
$540$		0			0
$541$	−25.5767	−	25.5767i	−1.09963	−	1.09963i	−0.994454	−	0.105176i	$-0.966459\pi$
$541$	−25.5767	−	25.5767i	−1.09963	−	1.09963i	−0.105176	−	0.994454i	$-0.533541\pi$
$542$	7.62623	−	9.18767i	0.327574	−	0.394644i
$543$		0			0
$544$	−19.6724	−	6.57157i	−0.843449	−	0.281754i
$545$	−9.40186	−	20.3021i	−0.402731	−	0.869647i
$546$		0			0
$547$	−6.44163	+	6.44163i	−0.275424	+	0.275424i	−0.831279	−	0.555855i	$-0.812391\pi$
$547$	−6.44163	+	6.44163i	−0.275424	+	0.275424i	0.555855	+	0.831279i	$0.312391\pi$
$548$	1.79849	+	9.59971i	0.0768276	+	0.410079i
$549$		0			0
$550$	−10.3803	+	14.8263i	−0.442617	+	0.632196i
$551$			21.9864i			0.936654i
$552$		0			0
$553$	−33.4557			−1.42268
$554$	−24.3937	+	2.26536i	−1.03639	+	0.0962457i
$555$		0			0
$556$	−13.6440	−	9.33833i	−0.578636	−	0.396033i
$557$	−1.38276	+	1.38276i	−0.0585893	+	0.0585893i	−0.735794	−	0.677205i	$-0.763191\pi$
$557$	−1.38276	+	1.38276i	−0.0585893	+	0.0585893i	0.677205	+	0.735794i	$0.263191\pi$
$558$		0			0
$559$	−20.7223			−0.876459
$560$	−27.2755	+	0.510018i	−1.15260	+	0.0215522i
$561$		0			0
$562$	−18.1631	−	15.0763i	−0.766165	−	0.635955i
$563$	4.13198	−	4.13198i	0.174142	−	0.174142i	−0.614654	−	0.788797i	$-0.710704\pi$
$563$	4.13198	−	4.13198i	0.174142	−	0.174142i	0.788797	+	0.614654i	$0.210704\pi$
$564$		0			0
$565$	4.81534	−	13.1221i	0.202583	−	0.552053i
$566$	−2.50522	+	0.232650i	−0.105302	+	0.00977900i
$567$		0			0
$568$	9.12414	−	16.4042i	0.382840	−	0.688306i
$569$			14.2348i			0.596755i	0.954448	+	0.298378i	$0.0964455\pi$
$569$			14.2348i			0.596755i	−0.954448	+	0.298378i	$0.903554\pi$
$570$		0			0
$571$	14.6986	−	14.6986i	0.615116	−	0.615116i	−0.329158	−	0.944275i	$-0.606765\pi$
$571$	14.6986	−	14.6986i	0.615116	−	0.615116i	0.944275	+	0.329158i	$0.106765\pi$
$572$	−17.5800	+	3.29358i	−0.735056	+	0.137711i
$573$		0			0
$574$	21.4879	+	17.8360i	0.896887	+	0.744462i
$575$	−18.5450	−	15.7287i	−0.773378	−	0.655931i
$576$		0			0
$577$		−	8.52221i		−	0.354784i	−0.984140	−	0.177392i	$-0.943234\pi$
$577$		−	8.52221i		−	0.354784i	0.984140	−	0.177392i	$-0.0567661\pi$
$578$	−3.21244	+	3.87017i	−0.133620	+	0.160978i
$579$		0			0
$580$	−24.4527	+	17.4162i	−1.01534	+	0.723167i
$581$	−11.1536	+	11.1536i	−0.462728	+	0.462728i
$582$		0			0
$583$	36.1891			1.49880
$584$	6.67490	+	3.71263i	0.276209	+	0.153630i
$585$		0			0
$586$	24.7329	−	2.29685i	1.02171	−	0.0948820i
$587$	13.9568	+	13.9568i	0.576057	+	0.576057i	0.933815	−	0.357757i	$-0.116459\pi$
$587$	13.9568	+	13.9568i	0.576057	+	0.576057i	−0.357757	+	0.933815i	$0.616459\pi$
$588$		0			0
$589$	−4.31168	−	4.31168i	−0.177660	−	0.177660i
$590$	−2.83199	+	10.6842i	−0.116591	+	0.439860i
$591$		0			0
$592$	−27.9589	−	12.3182i	−1.14910	−	0.506276i
$593$			22.9285i			0.941561i	0.882250	+	0.470781i	$0.156028\pi$
$593$			22.9285i			0.941561i	−0.882250	+	0.470781i	$0.843972\pi$
$594$		0			0
$595$	8.61455	−	23.4752i	0.353162	−	0.962391i
$596$	−35.3575	−	24.1996i	−1.44830	−	0.991254i
$597$		0			0
$598$	−2.22207	−	23.9276i	−0.0908671	−	0.978473i
$599$		−	15.8822i		−	0.648928i	−0.945898	−	0.324464i	$-0.894816\pi$
$599$		−	15.8822i		−	0.648928i	0.945898	−	0.324464i	$-0.105184\pi$
$600$		0			0
$601$			4.12190i			0.168136i	0.996460	+	0.0840680i	$0.0267913\pi$
$601$			4.12190i			0.168136i	−0.996460	+	0.0840680i	$0.973209\pi$
$602$	25.4729	−	2.36557i	1.03820	−	0.0964134i
$603$		0			0
$604$	7.90313	−	1.48064i	0.321574	−	0.0602462i
$605$	−3.42687	+	9.33847i	−0.139322	+	0.379663i
$606$		0			0
$607$		−	26.7142i		−	1.08429i	−0.840283	−	0.542147i	$-0.817611\pi$
$607$		−	26.7142i		−	1.08429i	0.840283	−	0.542147i	$-0.182389\pi$
$608$	−16.5770	+	8.27515i	−0.672286	+	0.335602i
$609$		0			0
$610$	−34.6616	−	9.18754i	−1.40341	−	0.371993i
$611$	20.3671	+	20.3671i	0.823964	+	0.823964i
$612$		0			0
$613$	−10.0253	−	10.0253i	−0.404918	−	0.404918i	0.475044	−	0.879962i	$-0.342432\pi$
$613$	−10.0253	−	10.0253i	−0.404918	−	0.404918i	−0.879962	+	0.475044i	$0.842432\pi$
$614$	4.01302	+	43.2129i	0.161952	+	1.74393i
$615$		0			0
$616$	21.2342	−	6.05549i	0.855552	−	0.243983i
$617$	26.3757			1.06185			0.530923	−	0.847420i	$-0.321845\pi$
$617$	26.3757			1.06185			0.530923	+	0.847420i	$0.321845\pi$
$618$		0			0
$619$	−7.39439	+	7.39439i	−0.297206	+	0.297206i	−0.839918	−	0.542713i	$-0.817397\pi$
$619$	−7.39439	+	7.39439i	−0.297206	+	0.297206i	0.542713	+	0.839918i	$0.317397\pi$
$620$	1.37990	−	8.21073i	0.0554182	−	0.329751i
$621$		0			0
$622$	−14.8619	−	12.3361i	−0.595908	−	0.494634i
$623$			40.1168i			1.60725i
$624$		0			0
$625$	4.08096	+	24.6647i	0.163239	+	0.986587i
$626$	12.4230	−	14.9665i	0.496521	−	0.598182i
$627$		0			0
$628$	−23.0150	−	15.7521i	−0.918400	−	0.628577i
$629$	19.8026	−	19.8026i	0.789583	−	0.789583i
$630$		0			0
$631$		−	34.8730i		−	1.38827i	−0.719844	−	0.694136i	$-0.755787\pi$
$631$		−	34.8730i		−	1.38827i	0.719844	−	0.694136i	$-0.244213\pi$
$632$	−27.1132	−	15.0806i	−1.07851	−	0.599873i
$633$		0			0
$634$	3.05720	+	32.9205i	0.121417	+	1.30744i
$635$	10.9297	−	29.7842i	0.433732	−	1.18195i
$636$		0			0
$637$	5.68882	−	5.68882i	0.225399	−	0.225399i
$638$	15.5197	−	18.6973i	0.614429	−	0.740232i
$639$		0			0
$640$	−22.3345	−	11.8814i	−0.882850	−	0.469655i
$641$	−6.05015			−0.238966			−0.119483	−	0.992836i	$-0.538124\pi$
$641$	−6.05015			−0.238966			−0.119483	+	0.992836i	$0.538124\pi$
$642$		0			0
$643$	7.52447	−	7.52447i	0.296736	−	0.296736i	−0.542998	−	0.839734i	$-0.682711\pi$
$643$	7.52447	−	7.52447i	0.296736	−	0.296736i	0.839734	+	0.542998i	$0.182711\pi$
$644$	5.46296	+	29.1594i	0.215271	+	1.14904i
$645$		0			0
$646$	−1.57040	−	16.9103i	−0.0617865	−	0.665328i
$647$	−24.8356			−0.976389			−0.488194	−	0.872735i	$-0.662344\pi$
$647$	−24.8356			−0.976389			−0.488194	+	0.872735i	$0.662344\pi$
$648$		0			0
$649$		−	8.94648i		−	0.351180i
$650$	−14.1695	+	20.2385i	−0.555775	+	0.793820i
$651$		0			0
$652$	30.7429	+	21.0412i	1.20399	+	0.824039i
$653$	−20.0550	+	20.0550i	−0.784813	+	0.784813i	−0.980639	−	0.195826i	$-0.937261\pi$
$653$	−20.0550	+	20.0550i	−0.784813	+	0.784813i	0.195826	+	0.980639i	$0.437261\pi$
$654$		0			0
$655$	16.6802	+	36.0187i	0.651749	+	1.40737i
$656$	9.37446	+	24.1407i	0.366011	+	0.942535i
$657$		0			0
$658$	−27.3613	−	22.7112i	−1.06665	−	0.885376i
$659$	−20.7719	−	20.7719i	−0.809158	−	0.809158i	0.175349	−	0.984506i	$-0.443895\pi$
$659$	−20.7719	−	20.7719i	−0.809158	−	0.809158i	−0.984506	+	0.175349i	$0.943895\pi$
$660$		0			0
$661$	−11.2908	+	11.2908i	−0.439161	+	0.439161i	−0.891730	−	0.452568i	$-0.850508\pi$
$661$	−11.2908	+	11.2908i	−0.439161	+	0.439161i	0.452568	+	0.891730i	$0.350508\pi$
$662$	−1.48907	−	16.0346i	−0.0578744	−	0.623202i
$663$		0			0
$664$	−14.0667	+	4.01149i	−0.545894	+	0.155676i
$665$	−9.38674	−	20.2695i	−0.364002	−	0.786017i
$666$		0			0
$667$	23.0850	+	23.0850i	0.893855	+	0.893855i
$668$	0.0224936	+	0.120063i	0.000870305	+	0.00464539i
$669$		0			0
$670$	9.85489	−	37.1793i	0.380728	−	1.43636i
$671$	29.0242			1.12047
$672$		0			0
$673$		−	1.03722i		−	0.0399820i	−0.999800	−	0.0199910i	$-0.993636\pi$
$673$		−	1.03722i		−	0.0399820i	0.999800	−	0.0199910i	$-0.00636376\pi$
$674$	5.19858	+	4.31508i	0.200242	+	0.166211i
$675$		0			0
$676$	1.55797	−	0.291882i	0.0599218	−	0.0112262i
$677$	−18.4431	−	18.4431i	−0.708825	−	0.708825i	0.257463	−	0.966288i	$-0.417113\pi$
$677$	−18.4431	−	18.4431i	−0.708825	−	0.708825i	−0.966288	+	0.257463i	$0.917113\pi$
$678$		0			0
$679$			38.1046i			1.46232i
$680$	17.5632	−	15.1418i	0.673518	−	0.580660i
$681$		0			0
$682$	0.623147	+	6.71015i	0.0238615	+	0.256945i
$683$	−0.922102	−	0.922102i	−0.0352833	−	0.0352833i	0.689245	−	0.724528i	$-0.257942\pi$
$683$	−0.922102	−	0.922102i	−0.0352833	−	0.0352833i	−0.724528	+	0.689245i	$0.757942\pi$
$684$		0			0
$685$	−10.2511	−	3.76178i	−0.391675	−	0.143730i
$686$	12.9409	−	15.5905i	0.494086	−	0.595248i
$687$		0			0
$688$	21.7101	+	9.56511i	0.827690	+	0.364666i
$689$	49.3997			1.88198
$690$		0			0
$691$	−7.34104	−	7.34104i	−0.279266	−	0.279266i	0.553550	−	0.832816i	$-0.313273\pi$
$691$	−7.34104	−	7.34104i	−0.279266	−	0.279266i	−0.832816	+	0.553550i	$0.813273\pi$
$692$	18.7106	+	12.8060i	0.711269	+	0.486811i
$693$		0			0
$694$	−6.62495	+	0.615235i	−0.251480	+	0.0233540i
$695$	16.7739	−	7.76795i	0.636271	−	0.294655i
$696$		0			0
$697$	−23.7380			−0.899141
$698$	−43.5300	+	4.04246i	−1.64763	+	0.153009i
$699$		0			0
$700$	15.1076	−	26.4957i	0.571012	−	1.00145i
$701$	−25.7637	−	25.7637i	−0.973080	−	0.973080i	0.0265667	−	0.999647i	$-0.491543\pi$
$701$	−25.7637	−	25.7637i	−0.973080	−	0.973080i	−0.999647	+	0.0265667i	$0.991543\pi$
$702$		0			0
$703$		−	25.0166i		−	0.943520i
$704$	19.9383	+	4.66409i	0.751453	+	0.175785i
$705$		0			0
$706$	−5.65242	−	4.69179i	−0.212732	−	0.176578i
$707$	−1.73704	+	1.73704i	−0.0653282	+	0.0653282i
$708$		0			0
$709$	18.8691	−	18.8691i	0.708645	−	0.708645i	−0.257605	−	0.966250i	$-0.582933\pi$
$709$	18.8691	−	18.8691i	0.708645	−	0.708645i	0.966250	+	0.257605i	$0.0829335\pi$
$710$	10.5422	+	18.1466i	0.395642	+	0.681028i
$711$		0			0
$712$	−18.0832	+	32.5116i	−0.677695	+	1.21842i
$713$	−9.05423			−0.339084
$714$		0			0
$715$	6.88896	−	18.7729i	0.257632	−	0.702067i
$716$	−18.9069	+	27.6245i	−0.706584	+	1.03237i
$717$		0			0
$718$	−22.8644	−	18.9786i	−0.853290	−	0.708274i
$719$	48.8119			1.82038			0.910189	−	0.414194i	$-0.135937\pi$
$719$	48.8119			1.82038			0.910189	+	0.414194i	$0.135937\pi$
$720$		0			0
$721$	−37.2285			−1.38646
$722$	9.00217	+	7.47225i	0.335026	+	0.278088i
$723$		0			0
$724$	−8.48187	−	5.80521i	−0.315226	−	0.215749i
$725$	−2.74873	−	33.4517i	−0.102085	−	1.24236i
$726$		0			0
$727$	20.2737			0.751908			0.375954	−	0.926638i	$-0.377315\pi$
$727$	20.2737			0.751908			0.375954	+	0.926638i	$0.377315\pi$
$728$	28.9856	−	8.26600i	1.07428	−	0.306358i
$729$		0			0
$730$	−7.38386	+	4.28964i	−0.273289	+	0.158767i
$731$	−15.3768	+	15.3768i	−0.568730	+	0.568730i
$732$		0			0
$733$	−21.1889	+	21.1889i	−0.782631	+	0.782631i	−0.980274	−	0.197643i	$-0.936671\pi$
$733$	−21.1889	+	21.1889i	−0.782631	+	0.782631i	0.197643	+	0.980274i	$0.436671\pi$
$734$	26.7535	+	22.2068i	0.987490	+	0.819666i
$735$		0			0
$736$	−8.71666	+	26.0939i	−0.321300	+	0.961834i
$737$			31.1324i			1.14678i
$738$		0			0
$739$	−3.65840	−	3.65840i	−0.134576	−	0.134576i	0.636610	−	0.771186i	$-0.280336\pi$
$739$	−3.65840	−	3.65840i	−0.134576	−	0.134576i	−0.771186	+	0.636610i	$0.780336\pi$
$740$	27.8227	−	19.8165i	1.02278	−	0.728467i
$741$		0			0
$742$	−60.7246	+	5.63926i	−2.22927	+	0.207024i
$743$	4.42017			0.162160			0.0810802	−	0.996708i	$-0.474163\pi$
$743$	4.42017			0.162160			0.0810802	+	0.996708i	$0.474163\pi$
$744$		0			0
$745$	43.4684	−	20.1301i	1.59256	−	0.737509i
$746$	1.99918	−	0.185656i	0.0731952	−	0.00679736i
$747$		0			0
$748$	−10.6011	+	15.4890i	−0.387615	+	0.566335i
$749$	24.3865	+	24.3865i	0.891062	+	0.891062i
$750$		0			0
$751$	30.4414			1.11082			0.555411	−	0.831576i	$-0.312561\pi$
$751$	30.4414			1.11082			0.555411	+	0.831576i	$0.312561\pi$
$752$	−11.9368	−	30.7391i	−0.435291	−	1.12094i
$753$		0			0
$754$	21.1850	−	25.5225i	0.771512	−	0.929476i
$755$	−3.09695	+	8.43940i	−0.112710	+	0.307141i
$756$		0			0
$757$	−18.5016	−	18.5016i	−0.672454	−	0.672454i	0.285828	−	0.958281i	$-0.407732\pi$
$757$	−18.5016	−	18.5016i	−0.672454	−	0.672454i	−0.958281	+	0.285828i	$0.907732\pi$
$758$	−0.913071	−	9.83211i	−0.0331642	−	0.357118i
$759$		0			0
$760$	1.52950	−	20.6580i	0.0554807	−	0.749346i
$761$		−	11.9248i		−	0.432273i	−0.976363	−	0.216137i	$-0.930654\pi$
$761$		−	11.9248i		−	0.432273i	0.976363	−	0.216137i	$-0.0693456\pi$
$762$		0			0
$763$	−21.5792	−	21.5792i	−0.781220	−	0.781220i
$764$	7.02778	+	37.5119i	0.254256	+	1.35713i
$765$		0			0
$766$	4.62817	+	3.84161i	0.167223	+	0.138803i
$767$		−	12.2123i		−	0.440961i
$768$		0			0
$769$	51.5679			1.85958			0.929792	−	0.368085i	$-0.119986\pi$
$769$	51.5679			1.85958			0.929792	+	0.368085i	$0.119986\pi$
$770$	−6.32522	+	23.8630i	−0.227945	+	0.859963i
$771$		0			0
$772$	5.87803	−	1.10124i	0.211555	−	0.0396345i
$773$	13.7126	+	13.7126i	0.493209	+	0.493209i	0.909316	−	0.416107i	$-0.136606\pi$
$773$	13.7126	+	13.7126i	0.493209	+	0.493209i	−0.416107	+	0.909316i	$0.636606\pi$
$774$		0			0
$775$	7.09912	+	6.02103i	0.255008	+	0.216282i
$776$	−17.1761	+	30.8808i	−0.616586	+	1.10856i
$777$		0			0
$778$	2.80281	+	30.1811i	0.100486	+	1.08205i
$779$	−14.9941	+	14.9941i	−0.537219	+	0.537219i
$780$		0			0
$781$	−12.0114	−	12.0114i	−0.429801	−	0.429801i
$782$	−19.4041	−	16.1064i	−0.693890	−	0.575964i
$783$		0			0
$784$	−8.58588	+	3.33412i	−0.306639	+	0.119076i
$785$	28.2946	−	13.1031i	1.00988	−	0.467671i
$786$		0			0
$787$	−31.1247	+	31.1247i	−1.10948	+	1.10948i	−0.116257	+	0.993219i	$0.537090\pi$
$787$	−31.1247	+	31.1247i	−1.10948	+	1.10948i	−0.993219	+	0.116257i	$0.962910\pi$
$788$	−2.19292	+	3.20403i	−0.0781195	+	0.114139i
$789$		0			0
$790$	29.9930	−	17.4244i	1.06710	−	0.619931i
$791$		−	19.0658i		−	0.677903i
$792$		0			0
$793$	39.6192			1.40692
$794$	0.381202	+	4.10485i	0.0135283	+	0.145676i
$795$		0			0
$796$	−30.8884	+	5.78689i	−1.09481	+	0.205111i
$797$	−33.0578	+	33.0578i	−1.17097	+	1.17097i	−0.188987	+	0.981980i	$0.560521\pi$
$797$	−33.0578	+	33.0578i	−1.17097	+	1.17097i	−0.981980	+	0.188987i	$0.939479\pi$
$798$		0			0
$799$	30.2264			1.06933
$800$	24.1868	−	14.6628i	0.855133	−	0.518409i
$801$		0			0
$802$	9.12390	−	10.9920i	0.322176	−	0.388140i
$803$	4.88745	−	4.88745i	0.172474	−	0.172474i
$804$		0			0
$805$	−31.1380	−	11.4265i	−1.09747	−	0.402731i
$806$	0.850621	+	9.15964i	0.0299618	+	0.322634i
$807$		0			0
$808$	−2.19073	+	0.624744i	−0.0770697	+	0.0219784i
$809$		−	2.77525i		−	0.0975726i	−0.998809	−	0.0487863i	$-0.984465\pi$
$809$		−	2.77525i		−	0.0975726i	0.998809	−	0.0487863i	$-0.0155353\pi$
$810$		0			0
$811$	−21.8766	+	21.8766i	−0.768192	+	0.768192i	−0.977788	−	0.209596i	$-0.932785\pi$
$811$	−21.8766	+	21.8766i	−0.768192	+	0.768192i	0.209596	+	0.977788i	$0.432785\pi$
$812$	−23.1281	+	33.7920i	−0.811638	+	1.18587i
$813$		0			0
$814$	−17.6586	+	21.2741i	−0.618933	+	0.745658i
$815$	−37.7952	+	17.5029i	−1.32391	+	0.613098i
$816$		0			0
$817$			19.4254i			0.679610i
$818$	16.9173	+	14.0422i	0.591501	+	0.490975i
$819$		0			0
$820$	−28.5532	−	4.79868i	−0.997123	−	0.167577i
$821$	15.1782	−	15.1782i	0.529722	−	0.529722i	−0.390767	−	0.920490i	$-0.627790\pi$
$821$	15.1782	−	15.1782i	0.529722	−	0.529722i	0.920490	+	0.390767i	$0.127790\pi$
$822$		0			0
$823$	−5.51325			−0.192180			−0.0960900	−	0.995373i	$-0.530634\pi$
$823$	−5.51325			−0.192180			−0.0960900	+	0.995373i	$0.530634\pi$
$824$	−30.1708	−	16.7812i	−1.05105	−	0.584601i
$825$		0			0
$826$	1.39411	+	15.0120i	0.0485072	+	0.522334i
$827$	−6.06405	−	6.06405i	−0.210868	−	0.210868i	0.593768	−	0.804636i	$-0.297640\pi$
$827$	−6.06405	−	6.06405i	−0.210868	−	0.210868i	−0.804636	+	0.593768i	$0.797640\pi$
$828$		0			0
$829$	6.12109	+	6.12109i	0.212594	+	0.212594i	0.805369	−	0.592774i	$-0.201967\pi$
$829$	6.12109	+	6.12109i	0.212594	+	0.212594i	−0.592774	+	0.805369i	$0.701967\pi$
$830$	4.19017	−	15.8082i	0.145443	−	0.548709i
$831$		0			0
$832$	27.2166	+	6.36668i	0.943566	+	0.220725i
$833$		−	8.44267i		−	0.292521i
$834$		0			0
$835$	−0.128210	−	0.0470485i	−0.00443690	−	0.00162818i
$836$	3.08746	+	16.4798i	0.106782	+	0.569966i
$837$		0			0
$838$	1.61546	−	0.150022i	0.0558052	−	0.00518242i
$839$			17.2421i			0.595265i	0.954681	+	0.297632i	$0.0961970\pi$
$839$			17.2421i			0.595265i	−0.954681	+	0.297632i	$0.903803\pi$
$840$		0			0
$841$			16.0627i			0.553888i
$842$	1.23492	+	13.2979i	0.0425583	+	0.458275i
$843$		0			0
$844$	26.9006	−	39.3039i	0.925958	−	1.35290i
$845$	−0.610511	+	1.66369i	−0.0210022	+	0.0572325i
$846$		0			0
$847$			13.5683i			0.466214i
$848$	−51.7545	−	22.8022i	−1.77726	−	0.783030i
$849$		0			0
$850$	4.50343	+	25.5322i	0.154466	+	0.875746i
$851$	−26.2666	−	26.2666i	−0.900407	−	0.900407i
$852$		0			0
$853$	3.60897	+	3.60897i	0.123569	+	0.123569i	0.766187	−	0.642618i	$-0.222152\pi$
$853$	3.60897	+	3.60897i	0.123569	+	0.123569i	−0.642618	+	0.766187i	$0.722152\pi$
$854$	−48.7020	+	4.52277i	−1.66655	+	0.154766i
$855$		0			0
$856$	8.77083	+	30.7558i	0.299781	+	1.05121i
$857$	−31.6802			−1.08217			−0.541087	−	0.840966i	$-0.681987\pi$
$857$	−31.6802			−1.08217			−0.541087	+	0.840966i	$0.681987\pi$
$858$		0			0
$859$	14.9872	−	14.9872i	0.511358	−	0.511358i	−0.403585	−	0.914942i	$-0.632236\pi$
$859$	14.9872	−	14.9872i	0.511358	−	0.511358i	0.914942	+	0.403585i	$0.132236\pi$
$860$	−21.6044	+	15.3875i	−0.736703	+	0.524709i
$861$		0			0
$862$	−18.8688	+	22.7321i	−0.642674	+	0.774259i
$863$		−	17.4922i		−	0.595440i	−0.954653	−	0.297720i	$-0.903774\pi$
$863$		−	17.4922i		−	0.595440i	0.954653	−	0.297720i	$-0.0962262\pi$
$864$		0			0
$865$	−23.0027	+	10.6525i	−0.782114	+	0.362195i
$866$	22.8893	+	18.9993i	0.777812	+	0.645623i
$867$		0			0
$868$	−2.09125	−	11.1624i	−0.0709817	−	0.378876i
$869$	−19.8527	+	19.8527i	−0.673455	+	0.673455i
$870$		0			0
$871$			42.4970i			1.43996i
$872$	−7.76118	−	27.2154i	−0.262827	−	0.921630i
$873$		0			0
$874$	−22.4302	+	2.08301i	−0.758712	+	0.0704588i
$875$	16.8157	+	29.6658i	0.568475	+	1.00289i
$876$		0			0
$877$	30.4741	−	30.4741i	1.02904	−	1.02904i	0.0294719	−	0.999566i	$-0.490617\pi$
$877$	30.4741	−	30.4741i	1.02904	−	1.02904i	0.999566	−	0.0294719i	$-0.00938257\pi$
$878$	29.9542	+	24.8635i	1.01091	+	0.839102i
$879$		0			0
$880$	−15.8827	+	16.4880i	−0.535404	+	0.555809i
$881$	3.45819			0.116509			0.0582547	−	0.998302i	$-0.481446\pi$
$881$	3.45819			0.116509			0.0582547	+	0.998302i	$0.481446\pi$
$882$		0			0
$883$	16.7282	−	16.7282i	0.562949	−	0.562949i	−0.367195	−	0.930144i	$-0.619682\pi$
$883$	16.7282	−	16.7282i	0.562949	−	0.562949i	0.930144	+	0.367195i	$0.119682\pi$
$884$	−14.4709	+	21.1432i	−0.486710	+	0.711122i
$885$		0			0
$886$	−30.5838	+	2.84021i	−1.02748	+	0.0954186i
$887$	−2.56980			−0.0862855			−0.0431428	−	0.999069i	$-0.513737\pi$
$887$	−2.56980			−0.0862855			−0.0431428	+	0.999069i	$0.513737\pi$
$888$		0			0
$889$		−	43.2750i		−	1.45140i
$890$	−20.8936	−	35.9647i	−0.700356	−	1.20554i
$891$		0			0
$892$	21.0130	−	3.93675i	0.703569	−	0.131812i
$893$	19.0925	−	19.0925i	0.638905	−	0.638905i
$894$		0			0
$895$	−15.7274	−	33.9614i	−0.525710	−	1.13520i
$896$	−34.1828	−	4.71931i	−1.14197	−	0.157661i
$897$		0			0
$898$	30.9220	−	37.2532i	1.03188	−	1.24316i
$899$	−8.83708	−	8.83708i	−0.294733	−	0.294733i
$900$		0			0
$901$	36.6566	−	36.6566i	1.22121	−	1.22121i
$902$	23.3349	−	2.16702i	0.776967	−	0.0721540i
$903$		0			0
$904$	8.59417	−	15.4514i	0.285838	−	0.513906i
$905$	10.4276	−	4.82898i	0.346624	−	0.160521i
$906$		0			0
$907$	35.2994	+	35.2994i	1.17210	+	1.17210i	0.981709	+	0.190388i	$0.0609745\pi$
$907$	35.2994	+	35.2994i	1.17210	+	1.17210i	0.190388	+	0.981709i	$0.439026\pi$
$908$	35.1797	+	24.0779i	1.16748	+	0.799054i
$909$		0			0
$910$	−8.63419	+	32.5740i	−0.286221	+	1.07982i
$911$	17.3104			0.573518			0.286759	−	0.958003i	$-0.407422\pi$
$911$	17.3104			0.573518			0.286759	+	0.958003i	$0.407422\pi$
$912$		0			0
$913$			13.2371i			0.438084i
$914$	33.7170	−	40.6205i	1.11526	−	1.34361i
$915$		0			0
$916$	7.55379	+	5.17001i	0.249584	+	0.170822i
$917$	38.2845	+	38.2845i	1.26427	+	1.26427i
$918$		0			0
$919$			16.7668i			0.553085i	0.961002	+	0.276543i	$0.0891887\pi$
$919$			16.7668i			0.553085i	−0.961002	+	0.276543i	$0.910811\pi$
$920$	−20.0843	−	23.2962i	−0.662160	−	0.768051i
$921$		0			0
$922$	8.59263	−	0.797966i	0.282983	−	0.0262796i
$923$	−16.3960	−	16.3960i	−0.539682	−	0.539682i
$924$		0			0
$925$	3.12757	+	38.0620i	0.102834	+	1.25147i
$926$	−13.7275	−	11.3945i	−0.451114	−	0.374447i
$927$		0			0
$928$	−33.9757	+	16.9605i	−1.11531	+	0.556756i
$929$	29.1505			0.956396			0.478198	−	0.878252i	$-0.341290\pi$
$929$	29.1505			0.956396			0.478198	+	0.878252i	$0.341290\pi$
$930$		0			0
$931$	−5.33280	−	5.33280i	−0.174776	−	0.174776i
$932$	1.75095	+	9.34595i	0.0573542	+	0.306137i
$933$		0			0
$934$	0.592209	+	6.37701i	0.0193777	+	0.208662i
$935$	−8.81837	−	19.0421i	−0.288391	−	0.622745i
$936$		0			0
$937$	−44.3671			−1.44941			−0.724705	−	0.689059i	$-0.758024\pi$
$937$	−44.3671			−1.44941			−0.724705	+	0.689059i	$0.758024\pi$
$938$	−4.85129	−	52.2395i	−0.158400	−	1.70568i
$939$		0			0
$940$	36.3578	+	6.11032i	1.18586	+	0.199297i
$941$	0.969738	+	0.969738i	0.0316125	+	0.0316125i	0.722736	−	0.691124i	$-0.242884\pi$
$941$	0.969738	+	0.969738i	0.0316125	+	0.0316125i	−0.691124	+	0.722736i	$0.742884\pi$
$942$		0			0
$943$			31.4865i			1.02534i
$944$	−5.63703	+	12.7945i	−0.183470	+	0.416425i
$945$		0			0
$946$	13.7119	−	16.5194i	0.445813	−	0.537091i
$947$	29.4598	−	29.4598i	0.957316	−	0.957316i	−0.0418099	−	0.999126i	$-0.513312\pi$
$947$	29.4598	−	29.4598i	0.957316	−	0.957316i	0.999126	+	0.0418099i	$0.0133124\pi$
$948$		0			0
$949$	6.67157	−	6.67157i	0.216568	−	0.216568i
$950$	18.9720	+	13.2828i	0.615532	+	0.430950i
$951$		0			0
$952$	15.3748	−	27.6422i	0.498300	−	0.895889i
$953$	57.8116			1.87270			0.936351	−	0.351065i	$-0.114180\pi$
$953$	57.8116			1.87270			0.936351	+	0.351065i	$0.114180\pi$
$954$		0			0
$955$	−40.0573	−	14.6995i	−1.29622	−	0.475666i
$956$	4.39088	+	23.4370i	0.142011	+	0.758008i
$957$		0			0
$958$	−8.19753	+	9.87595i	−0.264850	+	0.319077i
$959$	−14.8944			−0.480964
$960$		0			0
$961$	−27.5340			−0.888193
$962$	−24.1047	+	29.0401i	−0.777167	+	0.936289i
$963$		0			0
$964$	10.4223	+	55.6304i	0.335678	+	1.79173i
$965$	−2.30339	+	6.27689i	−0.0741487	+	0.202060i
$966$		0			0
$967$	−8.69630			−0.279654			−0.139827	−	0.990176i	$-0.544655\pi$
$967$	−8.69630			−0.279654			−0.139827	+	0.990176i	$0.544655\pi$
$968$	−6.11610	+	10.9961i	−0.196579	+	0.353428i
$969$		0			0
$970$	−19.8456	−	34.1607i	−0.637204	−	1.09683i
$971$	−15.8418	+	15.8418i	−0.508388	+	0.508388i	−0.914031	−	0.405643i	$-0.867048\pi$
$971$	−15.8418	+	15.8418i	−0.508388	+	0.508388i	0.405643	+	0.914031i	$0.367048\pi$
$972$		0			0
$973$	17.8291	−	17.8291i	0.571574	−	0.571574i
$974$	0.927660	−	1.11759i	0.0297241	−	0.0358100i
$975$		0			0
$976$	−41.5079	−	18.2877i	−1.32863	−	0.585374i
$977$			59.1087i			1.89106i	0.325541	+	0.945528i	$0.394454\pi$
$977$			59.1087i			1.89106i	−0.325541	+	0.945528i	$0.605546\pi$
$978$		0			0
$979$	23.8054	+	23.8054i	0.760824	+	0.760824i
$980$	1.70670	−	10.1553i	0.0545185	−	0.324398i
$981$		0			0
$982$	3.71083	+	39.9589i	0.118417	+	1.27514i
$983$	−49.7311			−1.58618			−0.793088	−	0.609107i	$-0.791528\pi$
$983$	−49.7311			−1.58618			−0.793088	+	0.609107i	$0.791528\pi$
$984$		0			0
$985$	−1.82415	−	3.93901i	−0.0581222	−	0.125507i
$986$	−3.21864	−	34.6589i	−0.102502	−	1.10376i
$987$		0			0
$988$	4.21451	+	22.4956i	0.134082	+	0.715681i
$989$	20.3960	+	20.3960i	0.648556	+	0.648556i
$990$		0			0
$991$	54.8832			1.74342			0.871710	−	0.490021i	$-0.163011\pi$
$991$	54.8832			1.74342			0.871710	+	0.490021i	$0.163011\pi$
$992$	3.33679	−	9.98891i	0.105943	−	0.317148i
$993$		0			0
$994$	22.0265	+	18.2831i	0.698640	+	0.579906i
$995$	12.1041	−	32.9844i	0.383724	−	1.04568i
$996$		0			0
$997$	−2.92958	−	2.92958i	−0.0927806	−	0.0927806i	0.659193	−	0.751974i	$-0.270898\pi$
$997$	−2.92958	−	2.92958i	−0.0927806	−	0.0927806i	−0.751974	+	0.659193i	$0.770898\pi$
$998$	−30.1944	+	2.80404i	−0.955788	+	0.0887604i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	720.2.bm.h.109.7		48
3.2	odd	2		240.2.bl.a.109.18	yes	48
5.4	even	2	inner	720.2.bm.h.109.18		48
12.11	even	2		960.2.bl.a.529.1		48
15.14	odd	2		240.2.bl.a.109.7	✓	48
16.5	even	4	inner	720.2.bm.h.469.18		48
24.5	odd	2		1920.2.bl.a.289.10		48
24.11	even	2		1920.2.bl.b.289.15		48
48.5	odd	4		240.2.bl.a.229.7	yes	48
48.11	even	4		960.2.bl.a.49.19		48
48.29	odd	4		1920.2.bl.a.1249.15		48
48.35	even	4		1920.2.bl.b.1249.10		48
60.59	even	2		960.2.bl.a.529.19		48
80.69	even	4	inner	720.2.bm.h.469.7		48
120.29	odd	2		1920.2.bl.a.289.15		48
120.59	even	2		1920.2.bl.b.289.10		48
240.29	odd	4		1920.2.bl.a.1249.10		48
240.59	even	4		960.2.bl.a.49.1		48
240.149	odd	4		240.2.bl.a.229.18	yes	48
240.179	even	4		1920.2.bl.b.1249.15		48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
240.2.bl.a.109.7	✓	48	15.14	odd	2
240.2.bl.a.109.18	yes	48	3.2	odd	2
240.2.bl.a.229.7	yes	48	48.5	odd	4
240.2.bl.a.229.18	yes	48	240.149	odd	4
720.2.bm.h.109.7		48	1.1	even	1	trivial
720.2.bm.h.109.18		48	5.4	even	2	inner
720.2.bm.h.469.7		48	80.69	even	4	inner
720.2.bm.h.469.18		48	16.5	even	4	inner
960.2.bl.a.49.1		48	240.59	even	4
960.2.bl.a.49.19		48	48.11	even	4
960.2.bl.a.529.1		48	12.11	even	2
960.2.bl.a.529.19		48	60.59	even	2
1920.2.bl.a.289.10		48	24.5	odd	2
1920.2.bl.a.289.15		48	120.29	odd	2
1920.2.bl.a.1249.10		48	240.29	odd	4
1920.2.bl.a.1249.15		48	48.29	odd	4
1920.2.bl.b.289.10		48	120.59	even	2
1920.2.bl.b.289.15		48	24.11	even	2
1920.2.bl.b.1249.10		48	48.35	even	4
1920.2.bl.b.1249.15		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)

\(f(q)\)	\(=\)	\(q+(-0.903247 + 1.08818i) q^{2} +(-0.368289 - 1.96580i) q^{4} +(2.09919 + 0.770325i) q^{5} +3.05002 q^{7} +(2.47181 + 1.37484i) q^{8} +O(q^{10})\)	\(q+(-0.903247 + 1.08818i) q^{2} +(-0.368289 - 1.96580i) q^{4} +(2.09919 + 0.770325i) q^{5} +3.05002 q^{7} +(2.47181 + 1.37484i) q^{8} +(-2.73434 + 1.58851i) q^{10} +(1.80989 - 1.80989i) q^{11} +(2.47057 - 2.47057i) q^{13} +(-2.75492 + 3.31898i) q^{14} +(-3.72873 + 1.44796i) q^{16} -3.66653i q^{17} +(-2.31596 - 2.31596i) q^{19} +(0.741196 - 4.41029i) q^{20} +(0.334715 + 3.60427i) q^{22} -4.86336 q^{23} +(3.81320 + 3.23412i) q^{25} +(0.456900 + 4.91998i) q^{26} +(-1.12329 - 5.99573i) q^{28} +(-4.74672 - 4.74672i) q^{29} +1.86172 q^{31} +(1.79231 - 5.36541i) q^{32} +(3.98986 + 3.31179i) q^{34} +(6.40257 + 2.34951i) q^{35} +(5.40092 + 5.40092i) q^{37} +(4.61208 - 0.428306i) q^{38} +(4.12972 + 4.79014i) q^{40} -6.47424i q^{41} +(-4.19382 - 4.19382i) q^{43} +(-4.22444 - 2.89131i) q^{44} +(4.39282 - 5.29223i) q^{46} +8.24387i q^{47} +2.30263 q^{49} +(-6.96358 + 1.22825i) q^{50} +(-5.76653 - 3.94676i) q^{52} +(9.99761 + 9.99761i) q^{53} +(5.19350 - 2.40510i) q^{55} +(7.53906 + 4.19328i) q^{56} +(9.45277 - 0.877843i) q^{58} +(2.47155 - 2.47155i) q^{59} +(8.01822 + 8.01822i) q^{61} +(-1.68160 + 2.02590i) q^{62} +(4.21965 + 6.79666i) q^{64} +(7.08935 - 3.28306i) q^{65} +(-8.60064 + 8.60064i) q^{67} +(-7.20766 + 1.35034i) q^{68} +(-8.33981 + 4.84499i) q^{70} -6.63653i q^{71} +2.70041 q^{73} +(-10.7556 + 0.998828i) q^{74} +(-3.69977 + 5.40565i) q^{76} +(5.52020 - 5.52020i) q^{77} -10.9690 q^{79} +(-8.94271 + 0.167218i) q^{80} +(7.04516 + 5.84784i) q^{82} +(-3.65688 + 3.65688i) q^{83} +(2.82442 - 7.69675i) q^{85} +(8.35170 - 0.775591i) q^{86} +(6.96199 - 1.98539i) q^{88} +13.1530i q^{89} +(7.53530 - 7.53530i) q^{91} +(1.79112 + 9.56038i) q^{92} +(-8.97085 - 7.44625i) q^{94} +(-3.07760 - 6.64569i) q^{95} +12.4932i q^{97} +(-2.07985 + 2.50569i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q+O(q^{10}) \) 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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