LMFDB - Embedded newform 144.3.j.a.125.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [144,3,Mod(53,144)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(144, base_ring=CyclotomicField(4))

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

N = Newforms(chi, 3, names="a")

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

chi := DirichletCharacter("144.53");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 144 = 2^{4} \cdot 3^{2} $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	144.j (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:	$3.92371580679$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$16$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			125.1
Character	$\chi$	$=$	144.125
Dual form			144.3.j.a.53.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.99710 + 0.107698i) q^{2} +(3.97680 - 0.430168i) q^{4} +(-1.92848 - 1.92848i) q^{5} -2.43162i q^{7} +(-7.89574 + 1.28738i) q^{8} +O(q^{10})$	\(q+(-1.99710 + 0.107698i) q^{2} +(3.97680 - 0.430168i) q^{4} +(-1.92848 - 1.92848i) q^{5} -2.43162i q^{7} +(-7.89574 + 1.28738i) q^{8} +(4.05906 + 3.64367i) q^{10} +(-2.79147 - 2.79147i) q^{11} +(-1.54064 - 1.54064i) q^{13} +(0.261881 + 4.85619i) q^{14} +(15.6299 - 3.42138i) q^{16} -20.3746i q^{17} +(-25.0179 - 25.0179i) q^{19} +(-8.49876 - 6.83962i) q^{20} +(5.87548 + 5.27421i) q^{22} -3.55894 q^{23} -17.5619i q^{25} +(3.24273 + 2.91088i) q^{26} +(-1.04601 - 9.67008i) q^{28} +(23.4539 - 23.4539i) q^{29} -13.3241 q^{31} +(-30.8460 + 8.51615i) q^{32} +(2.19430 + 40.6900i) q^{34} +(-4.68934 + 4.68934i) q^{35} +(-25.4406 + 25.4406i) q^{37} +(52.6575 + 47.2687i) q^{38} +(17.7095 + 12.7441i) q^{40} +64.0726 q^{41} +(-24.6791 + 24.6791i) q^{43} +(-12.3019 - 9.90033i) q^{44} +(7.10756 - 0.383292i) q^{46} +79.5718i q^{47} +43.0872 q^{49} +(1.89139 + 35.0729i) q^{50} +(-6.78954 - 5.46408i) q^{52} +(-39.8061 - 39.8061i) q^{53} +10.7666i q^{55} +(3.13043 + 19.1994i) q^{56} +(-44.3138 + 49.3657i) q^{58} +(19.2371 + 19.2371i) q^{59} +(63.5441 + 63.5441i) q^{61} +(26.6094 - 1.43498i) q^{62} +(60.6853 - 20.3297i) q^{64} +5.94218i q^{65} +(-65.1837 - 65.1837i) q^{67} +(-8.76448 - 81.0256i) q^{68} +(8.86003 - 9.87010i) q^{70} -84.6981 q^{71} -39.7473i q^{73} +(48.0675 - 53.5473i) q^{74} +(-110.253 - 88.7292i) q^{76} +(-6.78781 + 6.78781i) q^{77} +109.386 q^{79} +(-36.7401 - 23.5439i) q^{80} +(-127.959 + 6.90050i) q^{82} +(14.7433 - 14.7433i) q^{83} +(-39.2920 + 39.2920i) q^{85} +(46.6287 - 51.9444i) q^{86} +(25.6344 + 18.4470i) q^{88} +32.3085 q^{89} +(-3.74625 + 3.74625i) q^{91} +(-14.1532 + 1.53094i) q^{92} +(-8.56974 - 158.913i) q^{94} +96.4929i q^{95} +123.467 q^{97} +(-86.0494 + 4.64042i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q+O(q^{10}) $ 32 * q	$ 32 q + 40 q^{10} + 48 q^{16} + 64 q^{19} - 88 q^{22} - 120 q^{28} - 248 q^{34} - 184 q^{40} + 128 q^{43} + 24 q^{46} - 224 q^{49} + 632 q^{52} + 456 q^{58} + 64 q^{61} - 48 q^{64} - 64 q^{67} - 312 q^{70} - 576 q^{76} - 512 q^{79} - 720 q^{82} + 320 q^{85} - 400 q^{88} - 192 q^{91} + 696 q^{94}+O(q^{100}) $ 32 * q + 40 * q^10 + 48 * q^16 + 64 * q^19 - 88 * q^22 - 120 * q^28 - 248 * q^34 - 184 * q^40 + 128 * q^43 + 24 * q^46 - 224 * q^49 + 632 * q^52 + 456 * q^58 + 64 * q^61 - 48 * q^64 - 64 * q^67 - 312 * q^70 - 576 * q^76 - 512 * q^79 - 720 * q^82 + 320 * q^85 - 400 * q^88 - 192 * q^91 + 696 * q^94

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/144\mathbb{Z}\right)^\times$.

$n$	$37$	$65$	$127$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$-1$	$1$

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 $

$2$	−1.99710	+	0.107698i	−0.998549	+	0.0538491i
$2$	−1.99710	+	0.107698i	−0.998549	+	0.0538491i
$3$		0			0
$3$		0			0
$4$	3.97680	−	0.430168i	0.994201	−	0.107542i
$5$	−1.92848	−	1.92848i	−0.385696	−	0.385696i	0.487453	−	0.873149i	$-0.337926\pi$
$5$	−1.92848	−	1.92848i	−0.385696	−	0.385696i	−0.873149	+	0.487453i	$0.837926\pi$
$6$		0			0
$7$		−	2.43162i		−	0.347375i	−0.984801	−	0.173687i	$-0.944432\pi$
$7$		−	2.43162i		−	0.347375i	0.984801	−	0.173687i	$-0.0555682\pi$
$8$	−7.89574	+	1.28738i	−0.986967	+	0.160923i
$9$		0			0
$10$	4.05906	+	3.64367i	0.405906	+	0.364367i
$11$	−2.79147	−	2.79147i	−0.253770	−	0.253770i	0.568744	−	0.822514i	$-0.307429\pi$
$11$	−2.79147	−	2.79147i	−0.253770	−	0.253770i	−0.822514	+	0.568744i	$0.807429\pi$
$12$		0			0
$13$	−1.54064	−	1.54064i	−0.118511	−	0.118511i	0.645364	−	0.763875i	$-0.276706\pi$
$13$	−1.54064	−	1.54064i	−0.118511	−	0.118511i	−0.763875	+	0.645364i	$0.776706\pi$
$14$	0.261881	+	4.85619i	0.0187058	+	0.346871i
$15$		0			0
$16$	15.6299	−	3.42138i	0.976869	−	0.213837i
$17$		−	20.3746i		−	1.19850i	−0.800561	−	0.599252i	$-0.795465\pi$
$17$		−	20.3746i		−	1.19850i	0.800561	−	0.599252i	$-0.204535\pi$
$18$		0			0
$19$	−25.0179	−	25.0179i	−1.31673	−	1.31673i	−0.916349	−	0.400380i	$-0.868878\pi$
$19$	−25.0179	−	25.0179i	−1.31673	−	1.31673i	−0.400380	−	0.916349i	$-0.631122\pi$
$20$	−8.49876	−	6.83962i	−0.424938	−	0.341981i
$21$		0			0
$22$	5.87548	+	5.27421i	0.267067	+	0.239737i
$23$	−3.55894			−0.154737			−0.0773683	−	0.997003i	$-0.524652\pi$
$23$	−3.55894			−0.154737			−0.0773683	+	0.997003i	$0.524652\pi$
$24$		0			0
$25$		−	17.5619i		−	0.702477i
$26$	3.24273	+	2.91088i	0.124720	+	0.111957i
$27$		0			0
$28$	−1.04601	−	9.67008i	−0.0373573	−	0.345360i
$29$	23.4539	−	23.4539i	0.808756	−	0.808756i	−0.175690	−	0.984446i	$-0.556216\pi$
$29$	23.4539	−	23.4539i	0.808756	−	0.808756i	0.984446	+	0.175690i	$0.0562156\pi$
$30$		0			0
$31$	−13.3241			−0.429808			−0.214904	−	0.976635i	$-0.568944\pi$
$31$	−13.3241			−0.429808			−0.214904	+	0.976635i	$0.568944\pi$
$32$	−30.8460	+	8.51615i	−0.963937	+	0.266130i
$33$		0			0
$34$	2.19430	+	40.6900i	0.0645384	+	1.19676i
$35$	−4.68934	+	4.68934i	−0.133981	+	0.133981i
$36$		0			0
$37$	−25.4406	+	25.4406i	−0.687584	+	0.687584i	−0.961697	−	0.274113i	$-0.911616\pi$
$37$	−25.4406	+	25.4406i	−0.687584	+	0.687584i	0.274113	+	0.961697i	$0.411616\pi$
$38$	52.6575	+	47.2687i	1.38572	+	1.24391i
$39$		0			0
$40$	17.7095	+	12.7441i	0.442737	+	0.318602i
$41$	64.0726			1.56275			0.781373	−	0.624064i	$-0.214520\pi$
$41$	64.0726			1.56275			0.781373	+	0.624064i	$0.214520\pi$
$42$		0			0
$43$	−24.6791	+	24.6791i	−0.573932	+	0.573932i	−0.933225	−	0.359293i	$-0.883018\pi$
$43$	−24.6791	+	24.6791i	−0.573932	+	0.573932i	0.359293	+	0.933225i	$0.383018\pi$
$44$	−12.3019	−	9.90033i	−0.279589	−	0.225008i
$45$		0			0
$46$	7.10756	−	0.383292i	0.154512	−	0.00833243i
$47$			79.5718i			1.69302i	0.532375	+	0.846508i	$0.321299\pi$
$47$			79.5718i			1.69302i	−0.532375	+	0.846508i	$0.678701\pi$
$48$		0			0
$49$	43.0872			0.879331
$50$	1.89139	+	35.0729i	0.0378277	+	0.701457i
$51$		0			0
$52$	−6.78954	−	5.46408i	−0.130568	−	0.105078i
$53$	−39.8061	−	39.8061i	−0.751058	−	0.751058i	0.223619	−	0.974677i	$-0.428213\pi$
$53$	−39.8061	−	39.8061i	−0.751058	−	0.751058i	−0.974677	+	0.223619i	$0.928213\pi$
$54$		0			0
$55$			10.7666i			0.195757i
$56$	3.13043	+	19.1994i	0.0559005	+	0.342847i
$57$		0			0
$58$	−44.3138	+	49.3657i	−0.764031	+	0.851133i
$59$	19.2371	+	19.2371i	0.326053	+	0.326053i	0.851083	−	0.525030i	$-0.175946\pi$
$59$	19.2371	+	19.2371i	0.326053	+	0.326053i	−0.525030	+	0.851083i	$0.675946\pi$
$60$		0			0
$61$	63.5441	+	63.5441i	1.04171	+	1.04171i	0.999092	+	0.0426158i	$0.0135691\pi$
$61$	63.5441	+	63.5441i	1.04171	+	1.04171i	0.0426158	+	0.999092i	$0.486431\pi$
$62$	26.6094	−	1.43498i	0.429185	−	0.0231448i
$63$		0			0
$64$	60.6853	−	20.3297i	0.948208	−	0.317651i
$65$			5.94218i			0.0914182i
$66$		0			0
$67$	−65.1837	−	65.1837i	−0.972891	−	0.972891i	0.0267514	−	0.999642i	$-0.491484\pi$
$67$	−65.1837	−	65.1837i	−0.972891	−	0.972891i	−0.999642	+	0.0267514i	$0.991484\pi$
$68$	−8.76448	−	81.0256i	−0.128889	−	1.19155i
$69$		0			0
$70$	8.86003	−	9.87010i	0.126572	−	0.141001i
$71$	−84.6981			−1.19293			−0.596466	−	0.802639i	$-0.703429\pi$
$71$	−84.6981			−1.19293			−0.596466	+	0.802639i	$0.703429\pi$
$72$		0			0
$73$		−	39.7473i		−	0.544483i	−0.962229	−	0.272242i	$-0.912235\pi$
$73$		−	39.7473i		−	0.544483i	0.962229	−	0.272242i	$-0.0877650\pi$
$74$	48.0675	−	53.5473i	0.649561	−	0.723612i
$75$		0			0
$76$	−110.253	−	88.7292i	−1.45070	−	1.16749i
$77$	−6.78781	+	6.78781i	−0.0881533	+	0.0881533i
$78$		0			0
$79$	109.386			1.38463			0.692317	−	0.721593i	$-0.256590\pi$
$79$	109.386			1.38463			0.692317	+	0.721593i	$0.256590\pi$
$80$	−36.7401	−	23.5439i	−0.459251	−	0.294299i
$81$		0			0
$82$	−127.959	+	6.90050i	−1.56048	+	0.0841525i
$83$	14.7433	−	14.7433i	0.177630	−	0.177630i	−0.612692	−	0.790322i	$-0.709913\pi$
$83$	14.7433	−	14.7433i	0.177630	−	0.177630i	0.790322	+	0.612692i	$0.209913\pi$
$84$		0			0
$85$	−39.2920	+	39.2920i	−0.462258	+	0.462258i
$86$	46.6287	−	51.9444i	0.542194	−	0.604005i
$87$		0			0
$88$	25.6344	+	18.4470i	0.291300	+	0.209625i
$89$	32.3085			0.363017			0.181508	−	0.983389i	$-0.441902\pi$
$89$	32.3085			0.363017			0.181508	+	0.983389i	$0.441902\pi$
$90$		0			0
$91$	−3.74625	+	3.74625i	−0.0411676	+	0.0411676i
$92$	−14.1532	+	1.53094i	−0.153839	+	0.0166407i
$93$		0			0
$94$	−8.56974	−	158.913i	−0.0911674	−	1.69056i
$95$			96.4929i			1.01572i
$96$		0			0
$97$	123.467			1.27286			0.636428	−	0.771336i	$-0.280411\pi$
$97$	123.467			1.27286			0.636428	+	0.771336i	$0.280411\pi$
$98$	−86.0494	+	4.64042i	−0.878055	+	0.0473512i
$99$		0			0
$100$	−7.55457	−	69.8403i	−0.0755457	−	0.698403i
$101$	−83.5696	−	83.5696i	−0.827422	−	0.827422i	0.159737	−	0.987160i	$-0.448935\pi$
$101$	−83.5696	−	83.5696i	−0.827422	−	0.827422i	−0.987160	+	0.159737i	$0.948935\pi$
$102$		0			0
$103$			38.0120i			0.369049i	0.982828	+	0.184524i	$0.0590744\pi$
$103$			38.0120i			0.369049i	−0.982828	+	0.184524i	$0.940926\pi$
$104$	14.1479	+	10.1811i	0.136037	+	0.0978950i
$105$		0			0
$106$	83.7837	+	75.2096i	0.790412	+	0.709524i
$107$	−69.3864	−	69.3864i	−0.648471	−	0.648471i	0.304153	−	0.952623i	$-0.401627\pi$
$107$	−69.3864	−	69.3864i	−0.648471	−	0.648471i	−0.952623	+	0.304153i	$0.901627\pi$
$108$		0			0
$109$	46.2338	+	46.2338i	0.424163	+	0.424163i	0.886634	−	0.462471i	$-0.153037\pi$
$109$	46.2338	+	46.2338i	0.424163	+	0.424163i	−0.462471	+	0.886634i	$0.653037\pi$
$110$	−1.15954	−	21.5020i	−0.0105413	−	0.195472i
$111$		0			0
$112$	−8.31951	−	38.0060i	−0.0742814	−	0.339340i
$113$			97.1603i			0.859826i	0.902870	+	0.429913i	$0.141456\pi$
$113$			97.1603i			0.859826i	−0.902870	+	0.429913i	$0.858544\pi$
$114$		0			0
$115$	6.86335	+	6.86335i	0.0596813	+	0.0596813i
$116$	83.1825	−	103.361i	0.717090	−	0.891040i
$117$		0			0
$118$	−40.4902	−	36.3466i	−0.343138	−	0.308022i
$119$	−49.5432			−0.416330
$120$		0			0
$121$		−	105.415i		−	0.871201i
$122$	−133.747	−	120.060i	−1.09629	−	0.984101i
$123$		0			0
$124$	−52.9871	+	5.73158i	−0.427316	+	0.0462224i
$125$	−82.0799	+	82.0799i	−0.656639	+	0.656639i
$126$		0			0
$127$	187.433			1.47585			0.737926	−	0.674881i	$-0.235805\pi$
$127$	187.433			1.47585			0.737926	+	0.674881i	$0.235805\pi$
$128$	−119.005	+	47.1360i	−0.929727	+	0.368250i
$129$		0			0
$130$	−0.639962	−	11.8671i	−0.00492279	−	0.0912855i
$131$	79.2297	−	79.2297i	0.604807	−	0.604807i	−0.336778	−	0.941584i	$-0.609337\pi$
$131$	79.2297	−	79.2297i	0.604807	−	0.604807i	0.941584	+	0.336778i	$0.109337\pi$
$132$		0			0
$133$	−60.8340	+	60.8340i	−0.457398	+	0.457398i
$134$	137.198	+	123.158i	1.02387	+	0.919090i
$135$		0			0
$136$	26.2298	+	160.872i	0.192866	+	1.18288i
$137$	3.46186			0.0252691			0.0126345	−	0.999920i	$-0.495978\pi$
$137$	3.46186			0.0252691			0.0126345	+	0.999920i	$0.495978\pi$
$138$		0			0
$139$	−14.1054	+	14.1054i	−0.101478	+	0.101478i	−0.756023	−	0.654545i	$-0.772860\pi$
$139$	−14.1054	+	14.1054i	−0.101478	+	0.101478i	0.654545	+	0.756023i	$0.272860\pi$
$140$	−16.6314	+	20.6658i	−0.118795	+	0.147613i
$141$		0			0
$142$	169.150	−	9.12183i	1.19120	−	0.0642383i
$143$			8.60130i			0.0601489i
$144$		0			0
$145$	−90.4609			−0.623868
$146$	4.28071	+	79.3793i	0.0293200	+	0.543693i
$147$		0			0
$148$	−90.2285	+	112.116i	−0.609652	+	0.757541i
$149$	85.7760	+	85.7760i	0.575678	+	0.575678i	0.933709	−	0.358032i	$-0.116552\pi$
$149$	85.7760	+	85.7760i	0.575678	+	0.575678i	−0.358032	+	0.933709i	$0.616552\pi$
$150$		0			0
$151$			221.163i			1.46465i	0.680953	+	0.732327i	$0.261566\pi$
$151$			221.163i			1.46465i	−0.680953	+	0.732327i	$0.738434\pi$
$152$	229.742	+	165.327i	1.51146	+	1.08768i
$153$		0			0
$154$	12.8249	−	14.2870i	0.0832784	−	0.0927724i
$155$	25.6952	+	25.6952i	0.165775	+	0.165775i
$156$		0			0
$157$	−114.407	−	114.407i	−0.728709	−	0.728709i	0.241654	−	0.970363i	$-0.422310\pi$
$157$	−114.407	−	114.407i	−0.728709	−	0.728709i	−0.970363	+	0.241654i	$0.922310\pi$
$158$	−218.455	+	11.7807i	−1.38263	+	0.0745613i
$159$		0			0
$160$	75.9092	+	43.0627i	0.474432	+	0.269142i
$161$			8.65400i			0.0537516i
$162$		0			0
$163$	−124.266	−	124.266i	−0.762366	−	0.762366i	0.214383	−	0.976750i	$-0.431226\pi$
$163$	−124.266	−	124.266i	−0.762366	−	0.762366i	−0.976750	+	0.214383i	$0.931226\pi$
$164$	254.804	−	27.5620i	1.55368	−	0.168061i
$165$		0			0
$166$	−27.8559	+	31.0316i	−0.167807	+	0.186937i
$167$	230.474			1.38008			0.690041	−	0.723770i	$-0.257592\pi$
$167$	230.474			1.38008			0.690041	+	0.723770i	$0.257592\pi$
$168$		0			0
$169$		−	164.253i		−	0.971910i
$170$	74.2382	−	82.7016i	0.436696	−	0.486480i
$171$		0			0
$172$	−87.5277	+	108.760i	−0.508882	+	0.632325i
$173$	−43.4882	+	43.4882i	−0.251377	+	0.251377i	−0.821535	−	0.570158i	$-0.806882\pi$
$173$	−43.4882	+	43.4882i	−0.251377	+	0.251377i	0.570158	+	0.821535i	$0.306882\pi$
$174$		0			0
$175$	−42.7039			−0.244023
$176$	−53.1812	−	34.0798i	−0.302166	−	0.193635i
$177$		0			0
$178$	−64.5233	+	3.47957i	−0.362490	+	0.0195481i
$179$	145.904	−	145.904i	0.815104	−	0.815104i	−0.170290	−	0.985394i	$-0.554470\pi$
$179$	145.904	−	145.904i	0.815104	−	0.815104i	0.985394	+	0.170290i	$0.0544704\pi$
$180$		0			0
$181$	−184.775	+	184.775i	−1.02085	+	1.02085i	−0.0210758	+	0.999778i	$0.506709\pi$
$181$	−184.775	+	184.775i	−1.02085	+	1.02085i	−0.999778	+	0.0210758i	$0.993291\pi$
$182$	7.07816	−	7.88509i	0.0388910	−	0.0433247i
$183$		0			0
$184$	28.1005	−	4.58172i	0.152720	−	0.0249006i
$185$	98.1235			0.530397
$186$		0			0
$187$	−56.8750	+	56.8750i	−0.304145	+	0.304145i
$188$	34.2292	+	316.441i	0.182070	+	1.68320i
$189$		0			0
$190$	−10.3921	−	192.706i	−0.0546954	−	1.01424i
$191$		−	352.205i		−	1.84401i	−0.387182	−	0.922003i	$-0.626551\pi$
$191$		−	352.205i		−	1.84401i	0.387182	−	0.922003i	$-0.373449\pi$
$192$		0			0
$193$	−145.660			−0.754715			−0.377357	−	0.926068i	$-0.623167\pi$
$193$	−145.660			−0.754715			−0.377357	+	0.926068i	$0.623167\pi$
$194$	−246.576	+	13.2972i	−1.27101	+	0.0685422i
$195$		0			0
$196$	171.349	−	18.5347i	0.874231	−	0.0945650i
$197$	−18.7746	−	18.7746i	−0.0953027	−	0.0953027i	0.657848	−	0.753151i	$-0.271467\pi$
$197$	−18.7746	−	18.7746i	−0.0953027	−	0.0953027i	−0.753151	+	0.657848i	$0.771467\pi$
$198$		0			0
$199$		−	260.124i		−	1.30716i	−0.756858	−	0.653579i	$-0.773267\pi$
$199$		−	260.124i		−	1.30716i	0.756858	−	0.653579i	$-0.226733\pi$
$200$	22.6089	+	138.664i	0.113044	+	0.693321i
$201$		0			0
$202$	175.897	+	157.896i	0.870778	+	0.781666i
$203$	−57.0310	−	57.0310i	−0.280941	−	0.280941i
$204$		0			0
$205$	−123.563	−	123.563i	−0.602745	−	0.602745i
$206$	−4.09382	−	75.9137i	−0.0198729	−	0.368513i
$207$		0			0
$208$	−29.3511	−	18.8089i	−0.141111	−	0.0904275i
$209$			139.673i			0.668293i
$210$		0			0
$211$	127.020	+	127.020i	0.601991	+	0.601991i	0.940840	−	0.338850i	$-0.110038\pi$
$211$	127.020	+	127.020i	0.601991	+	0.601991i	−0.338850	+	0.940840i	$0.610038\pi$
$212$	−175.424	−	141.178i	−0.827472	−	0.665932i
$213$		0			0
$214$	146.044	+	131.099i	0.682449	+	0.612610i
$215$	95.1863			0.442727
$216$		0			0
$217$			32.3991i			0.149304i
$218$	−97.3127	−	87.3541i	−0.446388	−	0.400707i
$219$		0			0
$220$	4.63145	+	42.8167i	0.0210520	+	0.194621i
$221$	−31.3898	+	31.3898i	−0.142035	+	0.142035i
$222$		0			0
$223$	−70.2119			−0.314852			−0.157426	−	0.987531i	$-0.550320\pi$
$223$	−70.2119			−0.314852			−0.157426	+	0.987531i	$0.550320\pi$
$224$	20.7081	+	75.0058i	0.0924467	+	0.334847i
$225$		0			0
$226$	−10.4640	−	194.039i	−0.0463009	−	0.858579i
$227$	57.6438	−	57.6438i	0.253938	−	0.253938i	−0.568645	−	0.822583i	$-0.692532\pi$
$227$	57.6438	−	57.6438i	0.253938	−	0.253938i	0.822583	+	0.568645i	$0.192532\pi$
$228$		0			0
$229$	136.406	−	136.406i	0.595660	−	0.595660i	−0.343495	−	0.939155i	$-0.611611\pi$
$229$	136.406	−	136.406i	0.595660	−	0.595660i	0.939155	+	0.343495i	$0.111611\pi$
$230$	−14.4460	−	12.9676i	−0.0628085	−	0.0563810i
$231$		0			0
$232$	−154.992	+	215.380i	−0.668068	+	0.928362i
$233$	−171.152			−0.734556			−0.367278	−	0.930111i	$-0.619710\pi$
$233$	−171.152			−0.734556			−0.367278	+	0.930111i	$0.619710\pi$
$234$		0			0
$235$	153.453	−	153.453i	0.652990	−	0.652990i
$236$	84.7774	+	68.2270i	0.359226	+	0.289098i
$237$		0			0
$238$	98.9427	−	5.33572i	0.415726	−	0.0224190i
$239$			79.7138i			0.333531i	0.985997	+	0.166765i	$0.0533322\pi$
$239$			79.7138i			0.333531i	−0.985997	+	0.166765i	$0.946668\pi$
$240$		0			0
$241$	−68.5687			−0.284517			−0.142259	−	0.989830i	$-0.545436\pi$
$241$	−68.5687			−0.284517			−0.142259	+	0.989830i	$0.545436\pi$
$242$	11.3530	+	210.525i	0.0469134	+	0.869937i
$243$		0			0
$244$	280.037	+	225.368i	1.14769	+	0.923639i
$245$	−83.0929	−	83.0929i	−0.339155	−	0.339155i
$246$		0			0
$247$			77.0869i			0.312093i
$248$	105.203	−	17.1531i	0.424207	−	0.0691659i
$249$		0			0
$250$	155.082	−	172.761i	0.620327	−	0.691046i
$251$	−11.6232	−	11.6232i	−0.0463074	−	0.0463074i	0.683574	−	0.729881i	$-0.260425\pi$
$251$	−11.6232	−	11.6232i	−0.0463074	−	0.0463074i	−0.729881	+	0.683574i	$0.760425\pi$
$252$		0			0
$253$	9.93469	+	9.93469i	0.0392675	+	0.0392675i
$254$	−374.323	+	20.1862i	−1.47371	+	0.0794733i
$255$		0			0
$256$	232.588	−	106.952i	0.908548	−	0.417781i
$257$		−	44.8750i		−	0.174611i	−0.996182	−	0.0873055i	$-0.972174\pi$
$257$		−	44.8750i		−	0.174611i	0.996182	−	0.0873055i	$-0.0278256\pi$
$258$		0			0
$259$	61.8619	+	61.8619i	0.238849	+	0.238849i
$260$	2.55614	+	23.6309i	0.00983129	+	0.0908880i
$261$		0			0
$262$	−149.697	+	166.762i	−0.571361	+	0.636498i
$263$	−384.441			−1.46175			−0.730876	−	0.682510i	$-0.760888\pi$
$263$	−384.441			−1.46175			−0.730876	+	0.682510i	$0.760888\pi$
$264$		0			0
$265$			153.531i			0.579360i
$266$	114.940	−	128.043i	0.432104	−	0.481365i
$267$		0			0
$268$	−287.263	−	231.183i	−1.07188	−	0.862622i
$269$	−0.844060	+	0.844060i	−0.00313777	+	0.00313777i	−0.708674	−	0.705536i	$-0.750706\pi$
$269$	−0.844060	+	0.844060i	−0.00313777	+	0.00313777i	0.705536	+	0.708674i	$0.250706\pi$
$270$		0			0
$271$	−37.3816			−0.137939			−0.0689697	−	0.997619i	$-0.521971\pi$
$271$	−37.3816			−0.137939			−0.0689697	+	0.997619i	$0.521971\pi$
$272$	−69.7092	−	318.453i	−0.256284	−	1.17078i
$273$		0			0
$274$	−6.91368	+	0.372837i	−0.0252324	+	0.00136072i
$275$	−49.0236	+	49.0236i	−0.178268	+	0.178268i
$276$		0			0
$277$	342.799	−	342.799i	1.23754	−	1.23754i	0.276541	−	0.961002i	$-0.410812\pi$
$277$	342.799	−	342.799i	1.23754	−	1.23754i	0.961002	−	0.276541i	$-0.0891882\pi$
$278$	26.6507	−	29.6890i	0.0958659	−	0.106795i
$279$		0			0
$280$	30.9888	−	43.0627i	0.110674	−	0.153796i
$281$	−303.846			−1.08130			−0.540651	−	0.841247i	$-0.681822\pi$
$281$	−303.846			−1.08130			−0.540651	+	0.841247i	$0.681822\pi$
$282$		0			0
$283$	−10.3395	+	10.3395i	−0.0365354	+	0.0365354i	−0.725138	−	0.688603i	$-0.758224\pi$
$283$	−10.3395	+	10.3395i	−0.0365354	+	0.0365354i	0.688603	+	0.725138i	$0.258224\pi$
$284$	−336.828	+	36.4344i	−1.18601	+	0.128290i
$285$		0			0
$286$	−0.926344	−	17.1776i	−0.00323897	−	0.0600617i
$287$		−	155.800i		−	0.542858i
$288$		0			0
$289$	−126.123			−0.436411
$290$	180.659	−	9.74248i	0.622963	−	0.0335947i
$291$		0			0
$292$	−17.0980	−	158.067i	−0.0585548	−	0.541326i
$293$	230.634	+	230.634i	0.787148	+	0.787148i	0.981026	−	0.193877i	$-0.0621064\pi$
$293$	230.634	+	230.634i	0.787148	+	0.787148i	−0.193877	+	0.981026i	$0.562106\pi$
$294$		0			0
$295$		−	74.1969i		−	0.251515i
$296$	168.121	−	233.624i	0.567975	−	0.789271i
$297$		0			0
$298$	−180.541	−	162.065i	−0.605842	−	0.543843i
$299$	5.48304	+	5.48304i	0.0183379	+	0.0183379i
$300$		0			0
$301$	60.0102	+	60.0102i	0.199369	+	0.199369i
$302$	−23.8188	−	441.684i	−0.0788703	−	1.46253i
$303$		0			0
$304$	−476.623	−	305.431i	−1.56784	−	1.00471i
$305$		−	245.087i		−	0.803565i
$306$		0			0
$307$	255.002	+	255.002i	0.830625	+	0.830625i	0.987602	−	0.156978i	$-0.0501750\pi$
$307$	255.002	+	255.002i	0.830625	+	0.830625i	−0.156978	+	0.987602i	$0.550175\pi$
$308$	−24.0739	+	29.9137i	−0.0781619	+	0.0971223i
$309$		0			0
$310$	−54.0831	−	48.5485i	−0.174462	−	0.156608i
$311$	333.987			1.07391			0.536957	−	0.843610i	$-0.319574\pi$
$311$	333.987			1.07391			0.536957	+	0.843610i	$0.319574\pi$
$312$		0			0
$313$			159.757i			0.510405i	0.966888	+	0.255203i	$0.0821421\pi$
$313$			159.757i			0.510405i	−0.966888	+	0.255203i	$0.917858\pi$
$314$	240.804	+	216.161i	0.766892	+	0.688411i
$315$		0			0
$316$	435.007	−	47.0544i	1.37660	−	0.148906i
$317$	265.214	−	265.214i	0.836637	−	0.836637i	−0.151778	−	0.988415i	$-0.548500\pi$
$317$	265.214	−	265.214i	0.836637	−	0.836637i	0.988415	+	0.151778i	$0.0484998\pi$
$318$		0			0
$319$	−130.942			−0.410476
$320$	−156.236	−	77.8251i	−0.488237	−	0.243203i
$321$		0			0
$322$	−0.932020	−	17.2829i	−0.00289447	−	0.0536736i
$323$	−509.728	+	509.728i	−1.57810	+	1.57810i
$324$		0			0
$325$	−27.0566	+	27.0566i	−0.0832509	+	0.0832509i
$326$	261.554	+	234.788i	0.802313	+	0.720207i
$327$		0			0
$328$	−505.900	+	82.4859i	−1.54238	+	0.251481i
$329$	193.488			0.588111
$330$		0			0
$331$	−83.6950	+	83.6950i	−0.252855	+	0.252855i	−0.822140	−	0.569285i	$-0.807220\pi$
$331$	−83.6950	+	83.6950i	−0.252855	+	0.252855i	0.569285	+	0.822140i	$0.307220\pi$
$332$	52.2890	−	64.9731i	0.157497	−	0.195702i
$333$		0			0
$334$	−460.279	+	24.8216i	−1.37808	+	0.0743162i
$335$			251.411i			0.750481i
$336$		0			0
$337$	346.530			1.02828			0.514140	−	0.857706i	$-0.328111\pi$
$337$	346.530			1.02828			0.514140	+	0.857706i	$0.328111\pi$
$338$	17.6897	+	328.029i	0.0523365	+	0.970500i
$339$		0			0
$340$	−139.354	+	173.159i	−0.409865	+	0.509290i
$341$	37.1937	+	37.1937i	0.109073	+	0.109073i
$342$		0			0
$343$		−	223.921i		−	0.652832i
$344$	163.088	−	226.631i	0.474093	−	0.658811i
$345$		0			0
$346$	82.1665	−	91.5337i	0.237475	−	0.264548i
$347$	394.994	+	394.994i	1.13831	+	1.13831i	0.988753	+	0.149559i	$0.0477855\pi$
$347$	394.994	+	394.994i	1.13831	+	1.13831i	0.149559	+	0.988753i	$0.452214\pi$
$348$		0			0
$349$	100.763	+	100.763i	0.288719	+	0.288719i	0.836574	−	0.547854i	$-0.184555\pi$
$349$	100.763	+	100.763i	0.288719	+	0.288719i	−0.547854	+	0.836574i	$0.684555\pi$
$350$	85.2840	−	4.59914i	0.243668	−	0.0131404i
$351$		0			0
$352$	109.878	+	62.3331i	0.312154	+	0.177083i
$353$			211.250i			0.598442i	0.954184	+	0.299221i	$0.0967268\pi$
$353$			211.250i			0.598442i	−0.954184	+	0.299221i	$0.903273\pi$
$354$		0			0
$355$	163.339	+	163.339i	0.460109	+	0.460109i
$356$	128.485	−	13.8981i	0.360912	−	0.0390396i
$357$		0			0
$358$	−275.670	+	307.097i	−0.770029	+	0.857814i
$359$	−180.058			−0.501555			−0.250777	−	0.968045i	$-0.580686\pi$
$359$	−180.058			−0.501555			−0.250777	+	0.968045i	$0.580686\pi$
$360$		0			0
$361$			890.786i			2.46755i
$362$	349.113	−	388.913i	0.964400	−	1.07434i
$363$		0			0
$364$	−13.2866	+	16.5096i	−0.0365016	+	0.0453561i
$365$	−76.6519	+	76.6519i	−0.210005	+	0.210005i
$366$		0			0
$367$	−611.746			−1.66688			−0.833442	−	0.552608i	$-0.813633\pi$
$367$	−611.746			−1.66688			−0.833442	+	0.552608i	$0.813633\pi$
$368$	−55.6259	+	12.1765i	−0.151157	+	0.0330883i
$369$		0			0
$370$	−195.962	+	10.5677i	−0.529628	+	0.0285614i
$371$	−96.7933	+	96.7933i	−0.260898	+	0.260898i
$372$		0			0
$373$	250.082	−	250.082i	0.670462	−	0.670462i	−0.287360	−	0.957823i	$-0.592778\pi$
$373$	250.082	−	250.082i	0.670462	−	0.670462i	0.957823	+	0.287360i	$0.0927777\pi$
$374$	107.460	−	119.710i	0.287325	−	0.320081i
$375$		0			0
$376$	−102.439	−	628.278i	−0.272445	−	1.67095i
$377$	−72.2680			−0.191692
$378$		0			0
$379$	196.949	−	196.949i	0.519655	−	0.519655i	−0.397812	−	0.917467i	$-0.630230\pi$
$379$	196.949	−	196.949i	0.519655	−	0.519655i	0.917467	+	0.397812i	$0.130230\pi$
$380$	41.5082	+	383.733i	0.109232	+	1.00982i
$381$		0			0
$382$	37.9319	+	703.389i	0.0992981	+	1.84133i
$383$			27.7580i			0.0724752i	0.999343	+	0.0362376i	$0.0115373\pi$
$383$			27.7580i			0.0724752i	−0.999343	+	0.0362376i	$0.988463\pi$
$384$		0			0
$385$	26.1803			0.0680008
$386$	290.897	−	15.6873i	0.753620	−	0.0406407i
$387$		0			0
$388$	491.004	−	53.1115i	1.26547	−	0.136885i
$389$	250.685	+	250.685i	0.644434	+	0.644434i	0.951642	−	0.307208i	$-0.0993947\pi$
$389$	250.685	+	250.685i	0.644434	+	0.644434i	−0.307208	+	0.951642i	$0.599395\pi$
$390$		0			0
$391$			72.5119i			0.185452i
$392$	−340.205	+	55.4697i	−0.867871	+	0.141504i
$393$		0			0
$394$	39.5168	+	35.4728i	0.100296	+	0.0900324i
$395$	−210.949	−	210.949i	−0.534048	−	0.534048i
$396$		0			0
$397$	211.973	+	211.973i	0.533936	+	0.533936i	0.921741	−	0.387805i	$-0.126767\pi$
$397$	211.973	+	211.973i	0.533936	+	0.533936i	−0.387805	+	0.921741i	$0.626767\pi$
$398$	28.0149	+	519.494i	0.0703893	+	1.30526i
$399$		0			0
$400$	−60.0861	−	274.491i	−0.150215	−	0.686228i
$401$		−	603.861i		−	1.50589i	−0.658085	−	0.752944i	$-0.728633\pi$
$401$		−	603.861i		−	1.50589i	0.658085	−	0.752944i	$-0.271367\pi$
$402$		0			0
$403$	20.5275	+	20.5275i	0.0509368	+	0.0509368i
$404$	−368.289	−	296.391i	−0.911606	−	0.733641i
$405$		0			0
$406$	120.039	+	107.754i	0.295662	+	0.265405i
$407$	142.034			0.348977
$408$		0			0
$409$			229.079i			0.560094i	0.959986	+	0.280047i	$0.0903501\pi$
$409$			229.079i			0.560094i	−0.959986	+	0.280047i	$0.909650\pi$
$410$	260.075	+	233.460i	0.634328	+	0.569414i
$411$		0			0
$412$	16.3515	+	151.166i	0.0396882	+	0.366908i
$413$	46.7774	−	46.7774i	0.113262	−	0.113262i
$414$		0			0
$415$	−56.8642			−0.137022
$416$	60.6428	+	34.4022i	0.145776	+	0.0826976i
$417$		0			0
$418$	−15.0426	−	278.941i	−0.0359870	−	0.667324i
$419$	−581.441	+	581.441i	−1.38769	+	1.38769i	−0.557531	+	0.830156i	$0.688251\pi$
$419$	−581.441	+	581.441i	−1.38769	+	1.38769i	−0.830156	+	0.557531i	$0.811749\pi$
$420$		0			0
$421$	212.037	−	212.037i	0.503650	−	0.503650i	−0.408920	−	0.912570i	$-0.634095\pi$
$421$	212.037	−	212.037i	0.503650	−	0.503650i	0.912570	+	0.408920i	$0.134095\pi$
$422$	−267.351	−	239.992i	−0.633534	−	0.568700i
$423$		0			0
$424$	365.544	+	263.053i	0.862132	+	0.620407i
$425$	−357.816			−0.841921
$426$		0			0
$427$	154.515	−	154.515i	0.361863	−	0.361863i
$428$	−305.784	−	246.088i	−0.714448	−	0.574972i
$429$		0			0
$430$	−190.096	+	10.2514i	−0.442085	+	0.0238405i
$431$			71.0623i			0.164878i	0.996596	+	0.0824388i	$0.0262709\pi$
$431$			71.0623i			0.164878i	−0.996596	+	0.0824388i	$0.973729\pi$
$432$		0			0
$433$	−71.8456			−0.165925			−0.0829626	−	0.996553i	$-0.526438\pi$
$433$	−71.8456			−0.165925			−0.0829626	+	0.996553i	$0.526438\pi$
$434$	−3.48932	−	64.7041i	−0.00803991	−	0.149088i
$435$		0			0
$436$	203.751	+	163.974i	0.467318	+	0.376088i
$437$	89.0371	+	89.0371i	0.203746	+	0.203746i
$438$		0			0
$439$		−	75.0323i		−	0.170916i	−0.996342	−	0.0854582i	$-0.972765\pi$
$439$		−	75.0323i		−	0.170916i	0.996342	−	0.0854582i	$-0.0272354\pi$
$440$	−13.8607	−	85.0103i	−0.0315017	−	0.193205i
$441$		0			0
$442$	59.3079	−	66.0692i	0.134181	−	0.149478i
$443$	407.393	+	407.393i	0.919623	+	0.919623i	0.997002	−	0.0773783i	$-0.0246549\pi$
$443$	407.393	+	407.393i	0.919623	+	0.919623i	−0.0773783	+	0.997002i	$0.524655\pi$
$444$		0			0
$445$	−62.3064	−	62.3064i	−0.140014	−	0.140014i
$446$	140.220	−	7.56170i	0.314395	−	0.0169545i
$447$		0			0
$448$	−49.4340	−	147.564i	−0.110344	−	0.329383i
$449$		−	537.780i		−	1.19773i	−0.800851	−	0.598864i	$-0.795619\pi$
$449$		−	537.780i		−	1.19773i	0.800851	−	0.598864i	$-0.204381\pi$
$450$		0			0
$451$	−178.857	−	178.857i	−0.396578	−	0.396578i
$452$	41.7953	+	386.387i	0.0924674	+	0.854840i
$453$		0			0
$454$	−108.912	+	121.329i	−0.239895	+	0.267244i
$455$	14.4491			0.0317564
$456$		0			0
$457$		−	670.548i		−	1.46728i	−0.679537	−	0.733641i	$-0.737820\pi$
$457$		−	670.548i		−	1.46728i	0.679537	−	0.733641i	$-0.262180\pi$
$458$	−257.726	+	287.107i	−0.562720	+	0.626871i
$459$		0			0
$460$	30.2466	+	24.3418i	0.0657535	+	0.0529170i
$461$	624.560	−	624.560i	1.35479	−	1.35479i	0.474584	−	0.880210i	$-0.342599\pi$
$461$	624.560	−	624.560i	1.35479	−	1.35479i	0.880210	−	0.474584i	$-0.157401\pi$
$462$		0			0
$463$	−556.663			−1.20230			−0.601148	−	0.799138i	$-0.705290\pi$
$463$	−556.663			−1.20230			−0.601148	+	0.799138i	$0.705290\pi$
$464$	286.338	−	446.827i	0.617107	−	0.962990i
$465$		0			0
$466$	341.807	−	18.4327i	0.733491	−	0.0395552i
$467$	135.903	−	135.903i	0.291013	−	0.291013i	−0.546468	−	0.837480i	$-0.684028\pi$
$467$	135.903	−	135.903i	0.291013	−	0.291013i	0.837480	+	0.546468i	$0.184028\pi$
$468$		0			0
$469$	−158.502	+	158.502i	−0.337957	+	0.337957i
$470$	−289.934	+	322.987i	−0.616880	+	0.687206i
$471$		0			0
$472$	−176.657	−	127.126i	−0.374273	−	0.269334i
$473$	137.782			0.291294
$474$		0			0
$475$	−439.362	+	439.362i	−0.924972	+	0.924972i
$476$	−197.024	+	21.3119i	−0.413915	+	0.0447729i
$477$		0			0
$478$	−8.58504	−	159.196i	−0.0179603	−	0.333047i
$479$		−	754.590i		−	1.57534i	−0.616095	−	0.787672i	$-0.711286\pi$
$479$		−	754.590i		−	1.57534i	0.616095	−	0.787672i	$-0.288714\pi$
$480$		0			0
$481$	78.3895			0.162972
$482$	136.938	−	7.38472i	0.284104	−	0.0153210i
$483$		0			0
$484$	−45.3463	−	419.216i	−0.0936907	−	0.866149i
$485$	−238.104	−	238.104i	−0.490936	−	0.490936i
$486$		0			0
$487$		−	752.536i		−	1.54525i	−0.634863	−	0.772624i	$-0.718944\pi$
$487$		−	752.536i		−	1.54525i	0.634863	−	0.772624i	$-0.281056\pi$
$488$	−583.533	−	419.922i	−1.19577	−	0.860496i
$489$		0			0
$490$	174.894	+	156.996i	0.356926	+	0.320399i
$491$	−577.864	−	577.864i	−1.17691	−	1.17691i	−0.980527	−	0.196387i	$-0.937079\pi$
$491$	−577.864	−	577.864i	−1.17691	−	1.17691i	−0.196387	−	0.980527i	$-0.562921\pi$
$492$		0			0
$493$	−477.863	−	477.863i	−0.969297	−	0.969297i
$494$	−8.30212	−	153.950i	−0.0168059	−	0.311640i
$495$		0			0
$496$	−208.254	+	45.5867i	−0.419866	+	0.0919087i
$497$			205.954i			0.414394i
$498$		0			0
$499$	46.1997	+	46.1997i	0.0925846	+	0.0925846i	0.751882	−	0.659298i	$-0.229146\pi$
$499$	46.1997	+	46.1997i	0.0925846	+	0.0925846i	−0.659298	+	0.751882i	$0.729146\pi$
$500$	−291.107	+	361.724i	−0.582215	+	0.723447i
$501$		0			0
$502$	24.4644	+	21.9608i	0.0487339	+	0.0437466i
$503$	442.969			0.880655			0.440327	−	0.897837i	$-0.354862\pi$
$503$	442.969			0.880655			0.440327	+	0.897837i	$0.354862\pi$
$504$		0			0
$505$			322.325i			0.638267i
$506$	−20.9105	−	18.7706i	−0.0413251	−	0.0370960i
$507$		0			0
$508$	745.385	−	80.6278i	1.46729	−	0.158716i
$509$	−166.024	+	166.024i	−0.326178	+	0.326178i	−0.851131	−	0.524953i	$-0.824083\pi$
$509$	−166.024	+	166.024i	−0.326178	+	0.326178i	0.524953	+	0.851131i	$0.324083\pi$
$510$		0			0
$511$	−96.6504			−0.189140
$512$	−452.983	+	238.643i	−0.884733	+	0.466099i
$513$		0			0
$514$	4.83296	+	89.6198i	0.00940264	+	0.174358i
$515$	73.3054	−	73.3054i	0.142341	−	0.142341i
$516$		0			0
$517$	222.122	−	222.122i	0.429637	−	0.429637i
$518$	−130.207	−	116.882i	−0.251364	−	0.225641i
$519$		0			0
$520$	−7.64986	−	46.9179i	−0.0147113	−	0.0902267i
$521$	7.42117			0.0142441			0.00712204	−	0.999975i	$-0.497733\pi$
$521$	7.42117			0.0142441			0.00712204	+	0.999975i	$0.497733\pi$
$522$		0			0
$523$	653.700	−	653.700i	1.24990	−	1.24990i	0.294143	−	0.955761i	$-0.404966\pi$
$523$	653.700	−	653.700i	1.24990	−	1.24990i	0.955761	−	0.294143i	$-0.0950343\pi$
$524$	280.999	−	349.163i	0.536257	−	0.666341i
$525$		0			0
$526$	767.766	−	41.4036i	1.45963	−	0.0787140i
$527$			271.472i			0.515127i
$528$		0			0
$529$	−516.334			−0.976057
$530$	−16.5350	−	306.616i	−0.0311980	−	0.578520i
$531$		0			0
$532$	−215.756	+	268.093i	−0.405556	+	0.503935i
$533$	−98.7126	−	98.7126i	−0.185202	−	0.185202i
$534$		0			0
$535$			267.621i			0.500226i
$536$	598.589	+	430.757i	1.11677	+	0.803651i
$537$		0			0
$538$	1.59477	−	1.77657i	0.00296425	−	0.00330218i
$539$	−120.277	−	120.277i	−0.223148	−	0.223148i
$540$		0			0
$541$	−192.630	−	192.630i	−0.356063	−	0.356063i	0.506296	−	0.862360i	$-0.331014\pi$
$541$	−192.630	−	192.630i	−0.356063	−	0.356063i	−0.862360	+	0.506296i	$0.831014\pi$
$542$	74.6547	−	4.02593i	0.137739	−	0.00742792i
$543$		0			0
$544$	173.513	+	628.474i	0.318958	+	1.15528i
$545$		−	178.322i		−	0.327196i
$546$		0			0
$547$	−131.598	−	131.598i	−0.240582	−	0.240582i	0.576509	−	0.817091i	$-0.304415\pi$
$547$	−131.598	−	131.598i	−0.240582	−	0.240582i	−0.817091	+	0.576509i	$0.804415\pi$
$548$	13.7671	−	1.48918i	0.0251225	−	0.00271749i
$549$		0			0
$550$	92.6252	−	103.185i	0.168409	−	0.187609i
$551$	−1173.53			−2.12982
$552$		0			0
$553$		−	265.986i		−	0.480987i
$554$	−647.685	+	721.523i	−1.16911	+	1.30239i
$555$		0			0
$556$	−50.0266	+	62.1620i	−0.0899760	+	0.111802i
$557$	−109.222	+	109.222i	−0.196090	+	0.196090i	−0.798322	−	0.602231i	$-0.794278\pi$
$557$	−109.222	+	109.222i	−0.196090	+	0.196090i	0.602231	+	0.798322i	$0.294278\pi$
$558$		0			0
$559$	76.0430			0.136034
$560$	−57.2499	+	89.3380i	−0.102232	+	0.159532i
$561$		0			0
$562$	606.810	−	32.7236i	1.07973	−	0.0582271i
$563$	640.646	−	640.646i	1.13791	−	1.13791i	0.149090	−	0.988824i	$-0.452365\pi$
$563$	640.646	−	640.646i	1.13791	−	1.13791i	0.988824	−	0.149090i	$-0.0476346\pi$
$564$		0			0
$565$	187.372	−	187.372i	0.331632	−	0.331632i
$566$	19.5355	−	21.7626i	0.0345150	−	0.0384498i
$567$		0			0
$568$	668.754	−	109.039i	1.17738	−	0.191970i
$569$	273.069			0.479911			0.239955	−	0.970784i	$-0.422867\pi$
$569$	273.069			0.479911			0.239955	+	0.970784i	$0.422867\pi$
$570$		0			0
$571$	−663.916	+	663.916i	−1.16273	+	1.16273i	−0.178849	+	0.983877i	$0.557237\pi$
$571$	−663.916	+	663.916i	−1.16273	+	1.16273i	−0.983877	+	0.178849i	$0.942763\pi$
$572$	3.70000	+	34.2057i	0.00646853	+	0.0598001i
$573$		0			0
$574$	16.7794	+	311.149i	0.0292324	+	0.542071i
$575$			62.5018i			0.108699i
$576$		0			0
$577$	−403.711			−0.699672			−0.349836	−	0.936811i	$-0.613763\pi$
$577$	−403.711			−0.699672			−0.349836	+	0.936811i	$0.613763\pi$
$578$	251.880	−	13.5832i	0.435778	−	0.0235003i
$579$		0			0
$580$	−359.745	+	38.9134i	−0.620250	+	0.0670920i
$581$	−35.8501	−	35.8501i	−0.0617041	−	0.0617041i
$582$		0			0
$583$			222.235i			0.381192i
$584$	51.1699	+	313.834i	0.0876198	+	0.537387i
$585$		0			0
$586$	−485.439	−	435.761i	−0.828394	−	0.743619i
$587$	703.189	+	703.189i	1.19794	+	1.19794i	0.974783	+	0.223154i	$0.0716353\pi$
$587$	703.189	+	703.189i	1.19794	+	1.19794i	0.223154	+	0.974783i	$0.428365\pi$
$588$		0			0
$589$	333.339	+	333.339i	0.565941	+	0.565941i
$590$	7.99087	+	148.178i	0.0135438	+	0.251150i
$591$		0			0
$592$	−310.592	+	484.677i	−0.524649	+	0.818710i
$593$			668.046i			1.12655i	0.826268	+	0.563277i	$0.190460\pi$
$593$			668.046i			1.12655i	−0.826268	+	0.563277i	$0.809540\pi$
$594$		0			0
$595$	95.5432	+	95.5432i	0.160577	+	0.160577i
$596$	378.012	+	304.216i	0.634248	+	0.510429i
$597$		0			0
$598$	−11.5407	−	10.3597i	−0.0192988	−	0.0173238i
$599$	677.684			1.13136			0.565679	−	0.824625i	$-0.308614\pi$
$599$	677.684			1.13136			0.565679	+	0.824625i	$0.308614\pi$
$600$		0			0
$601$			170.941i			0.284427i	0.989836	+	0.142214i	$0.0454220\pi$
$601$			170.941i			0.284427i	−0.989836	+	0.142214i	$0.954578\pi$
$602$	−126.309	−	113.383i	−0.209816	−	0.188344i
$603$		0			0
$604$	95.1371	+	879.520i	0.157512	+	1.45616i
$605$	−203.292	+	203.292i	−0.336019	+	0.336019i
$606$		0			0
$607$	1112.69			1.83310			0.916548	−	0.399925i	$-0.130964\pi$
$607$	1112.69			1.83310			0.916548	+	0.399925i	$0.130964\pi$
$608$	984.756	+	558.645i	1.61967	+	0.918823i
$609$		0			0
$610$	26.3955	+	489.464i	0.0432713	+	0.802399i
$611$	122.591	−	122.591i	0.200640	−	0.200640i
$612$		0			0
$613$	−455.272	+	455.272i	−0.742696	+	0.742696i	−0.973096	−	0.230400i	$-0.925996\pi$
$613$	−455.272	+	455.272i	−0.742696	+	0.742696i	0.230400	+	0.973096i	$0.425996\pi$
$614$	−536.727	−	481.800i	−0.874148	−	0.784691i
$615$		0			0
$616$	44.8562	−	62.3332i	0.0728186	−	0.101190i
$617$	−229.336			−0.371695			−0.185847	−	0.982579i	$-0.559503\pi$
$617$	−229.336			−0.371695			−0.185847	+	0.982579i	$0.559503\pi$
$618$		0			0
$619$	163.423	−	163.423i	0.264011	−	0.264011i	−0.562670	−	0.826681i	$-0.690226\pi$
$619$	163.423	−	163.423i	0.264011	−	0.264011i	0.826681	+	0.562670i	$0.190226\pi$
$620$	113.238	+	91.1315i	0.182642	+	0.146986i
$621$		0			0
$622$	−667.005	+	35.9698i	−1.07235	+	0.0578293i
$623$		−	78.5621i		−	0.126103i
$624$		0			0
$625$	−122.469			−0.195950
$626$	−17.2055	−	319.050i	−0.0274849	−	0.509664i
$627$		0			0
$628$	−504.190	−	405.761i	−0.802850	−	0.646116i
$629$	518.341	+	518.341i	0.824072	+	0.824072i
$630$		0			0
$631$			555.849i			0.880902i	0.897777	+	0.440451i	$0.145181\pi$
$631$			555.849i			0.880902i	−0.897777	+	0.440451i	$0.854819\pi$
$632$	−863.684	+	140.822i	−1.36659	+	0.222819i
$633$		0			0
$634$	−501.095	+	558.221i	−0.790371	+	0.880475i
$635$	−361.462	−	361.462i	−0.569231	−	0.569231i
$636$		0			0
$637$	−66.3818	−	66.3818i	−0.104210	−	0.104210i
$638$	261.504	−	14.1022i	0.409881	−	0.0221038i
$639$		0			0
$640$	320.400	+	138.598i	0.500625	+	0.216559i
$641$			982.994i			1.53353i	0.641927	+	0.766766i	$0.278135\pi$
$641$			982.994i			1.53353i	−0.641927	+	0.766766i	$0.721865\pi$
$642$		0			0
$643$	−163.762	−	163.762i	−0.254684	−	0.254684i	0.568204	−	0.822888i	$-0.307639\pi$
$643$	−163.762	−	163.762i	−0.254684	−	0.254684i	−0.822888	+	0.568204i	$0.807639\pi$
$644$	3.72267	+	34.4152i	0.00578055	+	0.0534398i
$645$		0			0
$646$	963.080	−	1072.87i	1.49084	−	1.66079i
$647$	655.404			1.01299			0.506495	−	0.862243i	$-0.330941\pi$
$647$	655.404			1.01299			0.506495	+	0.862243i	$0.330941\pi$
$648$		0			0
$649$		−	107.400i		−	0.165485i
$650$	51.1206	−	56.9485i	0.0786471	−	0.0876131i
$651$		0			0
$652$	−547.635	−	440.725i	−0.839931	−	0.675959i
$653$	−469.752	+	469.752i	−0.719376	+	0.719376i	−0.968477	−	0.249102i	$-0.919865\pi$
$653$	−469.752	+	469.752i	−0.719376	+	0.719376i	0.249102	+	0.968477i	$0.419865\pi$
$654$		0			0
$655$	−305.586			−0.466543
$656$	1001.45	−	219.217i	1.52660	−	0.334172i
$657$		0			0
$658$	−386.415	+	20.8384i	−0.587258	+	0.0316692i
$659$	576.834	−	576.834i	0.875317	−	0.875317i	−0.117728	−	0.993046i	$-0.537561\pi$
$659$	576.834	−	576.834i	0.875317	−	0.875317i	0.993046	+	0.117728i	$0.0375612\pi$
$660$		0			0
$661$	−679.417	+	679.417i	−1.02786	+	1.02786i	−0.0282616	+	0.999601i	$0.508997\pi$
$661$	−679.417	+	679.417i	−1.02786	+	1.02786i	−0.999601	+	0.0282616i	$0.991003\pi$
$662$	158.133	−	176.161i	0.238872	−	0.266104i
$663$		0			0
$664$	−97.4287	+	135.389i	−0.146730	+	0.203899i
$665$	234.634			0.352834
$666$		0			0
$667$	−83.4711	+	83.4711i	−0.125144	+	0.125144i
$668$	916.549	−	99.1424i	1.37208	−	0.148417i
$669$		0			0
$670$	−27.0765	−	502.093i	−0.0404127	−	0.749392i
$671$		−	354.764i		−	0.528709i
$672$		0			0
$673$	929.909			1.38174			0.690868	−	0.722981i	$-0.257228\pi$
$673$	929.909			1.38174			0.690868	+	0.722981i	$0.257228\pi$
$674$	−692.055	+	37.3207i	−1.02679	+	0.0553720i
$675$		0			0
$676$	−70.6563	−	653.201i	−0.104521	−	0.966274i
$677$	−597.623	−	597.623i	−0.882751	−	0.882751i	0.111062	−	0.993813i	$-0.464575\pi$
$677$	−597.623	−	597.623i	−0.882751	−	0.882751i	−0.993813	+	0.111062i	$0.964575\pi$
$678$		0			0
$679$		−	300.225i		−	0.442158i
$680$	259.655	−	360.823i	0.381846	−	0.530622i
$681$		0			0
$682$	−78.2852	−	70.2738i	−0.114788	−	0.103041i
$683$	−286.314	−	286.314i	−0.419200	−	0.419200i	0.465728	−	0.884928i	$-0.345793\pi$
$683$	−286.314	−	286.314i	−0.419200	−	0.419200i	−0.884928	+	0.465728i	$0.845793\pi$
$684$		0			0
$685$	−6.67614	−	6.67614i	−0.00974619	−	0.00974619i
$686$	24.1159	+	447.193i	0.0351544	+	0.651885i
$687$		0			0
$688$	−301.295	+	470.168i	−0.437929	+	0.683384i
$689$			122.653i			0.178017i
$690$		0			0
$691$	483.066	+	483.066i	0.699083	+	0.699083i	0.964213	−	0.265130i	$-0.0854149\pi$
$691$	483.066	+	483.066i	0.699083	+	0.699083i	−0.265130	+	0.964213i	$0.585415\pi$
$692$	−154.237	+	191.651i	−0.222885	+	0.276952i
$693$		0			0
$694$	−831.383	−	746.302i	−1.19796	−	1.07536i
$695$	54.4039			0.0782790
$696$		0			0
$697$		−	1305.45i		−	1.87296i
$698$	−212.086	−	190.382i	−0.303848	−	0.272753i
$699$		0			0
$700$	−169.825	+	18.3699i	−0.242607	+	0.0262427i
$701$	−349.679	+	349.679i	−0.498829	+	0.498829i	−0.911073	−	0.412244i	$-0.864745\pi$
$701$	−349.679	+	349.679i	−0.498829	+	0.498829i	0.412244	+	0.911073i	$0.364745\pi$
$702$		0			0
$703$	1272.94			1.81072
$704$	−226.151	−	112.652i	−0.321237	−	0.160017i
$705$		0			0
$706$	−22.7512	−	421.887i	−0.0322256	−	0.597574i
$707$	−203.210	+	203.210i	−0.287425	+	0.287425i
$708$		0			0
$709$	−374.404	+	374.404i	−0.528074	+	0.528074i	−0.919998	−	0.391924i	$-0.871810\pi$
$709$	−374.404	+	374.404i	−0.528074	+	0.528074i	0.391924	+	0.919998i	$0.371810\pi$
$710$	−343.795	−	308.612i	−0.484218	−	0.434665i
$711$		0			0
$712$	−255.099	+	41.5934i	−0.358286	+	0.0584177i
$713$	47.4195			0.0665071
$714$		0			0
$715$	16.5874	−	16.5874i	0.0231992	−	0.0231992i
$716$	517.467	−	642.993i	0.722719	−	0.898035i
$717$		0			0
$718$	359.594	−	19.3920i	0.500827	−	0.0270083i
$719$			819.536i			1.13983i	0.821704	+	0.569914i	$0.193024\pi$
$719$			819.536i			1.13983i	−0.821704	+	0.569914i	$0.806976\pi$
$720$		0			0
$721$	92.4308			0.128198
$722$	−95.9361	−	1778.99i	−0.132875	−	2.46397i
$723$		0			0
$724$	−655.328	+	814.296i	−0.905149	+	1.12472i
$725$	−411.896	−	411.896i	−0.568132	−	0.568132i
$726$		0			0
$727$			1089.99i			1.49930i	0.661836	+	0.749649i	$0.269778\pi$
$727$			1089.99i			1.49930i	−0.661836	+	0.749649i	$0.730222\pi$
$728$	24.7565	−	34.4022i	0.0340062	−	0.0472558i
$729$		0			0
$730$	144.826	−	161.337i	0.198392	−	0.221009i
$731$	502.825	+	502.825i	0.687860	+	0.687860i
$732$		0			0
$733$	165.917	+	165.917i	0.226354	+	0.226354i	0.811168	−	0.584814i	$-0.198832\pi$
$733$	165.917	+	165.917i	0.226354	+	0.226354i	−0.584814	+	0.811168i	$0.698832\pi$
$734$	1221.72	−	65.8840i	1.66446	−	0.0897602i
$735$		0			0
$736$	109.779	−	30.3085i	0.149156	−	0.0411800i
$737$			363.917i			0.493781i
$738$		0			0
$739$	−316.451	−	316.451i	−0.428215	−	0.428215i	0.459805	−	0.888020i	$-0.347919\pi$
$739$	−316.451	−	316.451i	−0.428215	−	0.428215i	−0.888020	+	0.459805i	$0.847919\pi$
$740$	390.218	−	42.2096i	0.527321	−	0.0570400i
$741$		0			0
$742$	182.881	−	203.730i	0.246471	−	0.274569i
$743$	−1074.58			−1.44627			−0.723134	−	0.690708i	$-0.757299\pi$
$743$	−1074.58			−1.44627			−0.723134	+	0.690708i	$0.757299\pi$
$744$		0			0
$745$		−	330.835i		−	0.444073i
$746$	−472.506	+	526.372i	−0.633386	+	0.705593i
$747$		0			0
$748$	−201.715	+	250.647i	−0.269672	+	0.335089i
$749$	−168.721	+	168.721i	−0.225262	+	0.225262i
$750$		0			0
$751$	425.307			0.566320			0.283160	−	0.959073i	$-0.408617\pi$
$751$	425.307			0.566320			0.283160	+	0.959073i	$0.408617\pi$
$752$	272.246	+	1243.70i	0.362029	+	1.65386i
$753$		0			0
$754$	144.326	−	7.78313i	0.191414	−	0.0103225i
$755$	426.508	−	426.508i	0.564912	−	0.564912i
$756$		0			0
$757$	93.5146	−	93.5146i	0.123533	−	0.123533i	−0.642637	−	0.766170i	$-0.722160\pi$
$757$	93.5146	−	93.5146i	0.123533	−	0.123533i	0.766170	+	0.642637i	$0.222160\pi$
$758$	−372.116	+	414.538i	−0.490919	+	0.546885i
$759$		0			0
$760$	−124.223	−	761.883i	−0.163452	−	1.00248i
$761$	−430.074			−0.565144			−0.282572	−	0.959246i	$-0.591188\pi$
$761$	−430.074			−0.565144			−0.282572	+	0.959246i	$0.591188\pi$
$762$		0			0
$763$	112.423	−	112.423i	0.147343	−	0.147343i
$764$	−151.507	−	1400.65i	−0.198308	−	1.83331i
$765$		0			0
$766$	−2.98949	−	55.4355i	−0.00390273	−	0.0723701i
$767$		−	59.2749i		−	0.0772814i
$768$		0			0
$769$	−307.931			−0.400430			−0.200215	−	0.979752i	$-0.564164\pi$
$769$	−307.931			−0.400430			−0.200215	+	0.979752i	$0.564164\pi$
$770$	−52.2847	+	2.81957i	−0.0679022	+	0.00366178i
$771$		0			0
$772$	−579.261	+	62.6582i	−0.750338	+	0.0811635i
$773$	531.375	+	531.375i	0.687419	+	0.687419i	0.961661	−	0.274241i	$-0.0884268\pi$
$773$	531.375	+	531.375i	0.687419	+	0.687419i	−0.274241	+	0.961661i	$0.588427\pi$
$774$		0			0
$775$			233.996i			0.301930i
$776$	−974.863	+	158.949i	−1.25627	+	0.204831i
$777$		0			0
$778$	−527.641	−	473.644i	−0.678202	−	0.608797i
$779$	−1602.96	−	1602.96i	−2.05771	−	2.05771i
$780$		0			0
$781$	236.432	+	236.432i	0.302730	+	0.302730i
$782$	−7.80940	−	144.813i	−0.00998644	−	0.185183i
$783$		0			0
$784$	673.449	−	147.418i	0.858992	−	0.188033i
$785$			441.265i			0.562121i
$786$		0			0
$787$	−114.817	−	114.817i	−0.145892	−	0.145892i	0.630388	−	0.776280i	$-0.282896\pi$
$787$	−114.817	−	114.817i	−0.145892	−	0.145892i	−0.776280	+	0.630388i	$0.782896\pi$
$788$	−82.7392	−	66.5867i	−0.104999	−	0.0845009i
$789$		0			0
$790$	444.005	+	398.567i	0.562031	+	0.504515i
$791$	236.257			0.298682
$792$		0			0
$793$		−	195.797i		−	0.246907i
$794$	−446.159	−	400.501i	−0.561913	−	0.504409i
$795$		0			0
$796$	−111.897	−	1034.46i	−0.140574	−	1.29958i
$797$	−699.220	+	699.220i	−0.877315	+	0.877315i	−0.993256	−	0.115941i	$-0.963012\pi$
$797$	−699.220	+	699.220i	−0.877315	+	0.877315i	0.115941	+	0.993256i	$0.463012\pi$
$798$		0			0
$799$	1621.24			2.02909
$800$	149.560	+	541.715i	0.186950	+	0.677143i
$801$		0			0
$802$	65.0348	+	1205.97i	0.0810907	+	1.50370i
$803$	−110.953	+	110.953i	−0.138174	+	0.138174i
$804$		0			0
$805$	16.6891	−	16.6891i	0.0207318	−	0.0207318i
$806$	−43.2063	−	38.7847i	−0.0536058	−	0.0481200i
$807$		0			0
$808$	767.430	+	552.258i	0.949789	+	0.683487i
$809$	1160.71			1.43475			0.717376	−	0.696686i	$-0.245343\pi$
$809$	1160.71			1.43475			0.717376	+	0.696686i	$0.245343\pi$
$810$		0			0
$811$	297.004	−	297.004i	0.366220	−	0.366220i	−0.499877	−	0.866097i	$-0.666621\pi$
$811$	297.004	−	297.004i	0.366220	−	0.366220i	0.866097	+	0.499877i	$0.166621\pi$
$812$	−251.334	−	202.268i	−0.309525	−	0.249099i
$813$		0			0
$814$	−283.655	+	15.2968i	−0.348470	+	0.0187921i
$815$			479.288i			0.588084i
$816$		0			0
$817$	1234.84			1.51143
$818$	−24.6714	−	457.492i	−0.0301606	−	0.559282i
$819$		0			0
$820$	−544.538	−	438.232i	−0.664070	−	0.534429i
$821$	−606.627	−	606.627i	−0.738888	−	0.738888i	0.233475	−	0.972363i	$-0.424990\pi$
$821$	−606.627	−	606.627i	−0.738888	−	0.738888i	−0.972363	+	0.233475i	$0.924990\pi$
$822$		0			0
$823$			320.341i			0.389236i	0.980879	+	0.194618i	$0.0623467\pi$
$823$			320.341i			0.389236i	−0.980879	+	0.194618i	$0.937653\pi$
$824$	−48.9360	−	300.133i	−0.0593883	−	0.364239i
$825$		0			0
$826$	−88.3812	+	98.4569i	−0.106999	+	0.119197i
$827$	686.333	+	686.333i	0.829907	+	0.829907i	0.987504	−	0.157597i	$-0.0503746\pi$
$827$	686.333	+	686.333i	0.829907	+	0.829907i	−0.157597	+	0.987504i	$0.550375\pi$
$828$		0			0
$829$	317.721	+	317.721i	0.383258	+	0.383258i	0.872275	−	0.489017i	$-0.162644\pi$
$829$	317.721	+	317.721i	0.383258	+	0.383258i	−0.489017	+	0.872275i	$0.662644\pi$
$830$	113.563	−	6.12418i	0.136823	−	0.00737853i
$831$		0			0
$832$	−124.815	−	62.1734i	−0.150018	−	0.0747277i
$833$		−	877.883i		−	1.05388i
$834$		0			0
$835$	−444.465	−	444.465i	−0.532293	−	0.532293i
$836$	60.0830	+	555.453i	0.0718696	+	0.664418i
$837$		0			0
$838$	1098.57	−	1223.81i	1.31095	−	1.46040i
$839$	−999.424			−1.19121			−0.595605	−	0.803278i	$-0.703087\pi$
$839$	−999.424			−1.19121			−0.595605	+	0.803278i	$0.703087\pi$
$840$		0			0
$841$		−	259.172i		−	0.308171i
$842$	−400.622	+	446.294i	−0.475798	+	0.530040i
$843$		0			0
$844$	559.773	+	450.494i	0.663239	+	0.533760i
$845$	−316.759	+	316.759i	−0.374862	+	0.374862i
$846$		0			0
$847$	−256.330			−0.302633
$848$	−758.357	−	485.973i	−0.894289	−	0.573082i
$849$		0			0
$850$	714.594	−	38.5362i	0.840699	−	0.0453367i
$851$	90.5416	−	90.5416i	0.106394	−	0.106394i
$852$		0			0
$853$	−437.602	+	437.602i	−0.513015	+	0.513015i	−0.915449	−	0.402434i	$-0.868164\pi$
$853$	−437.602	+	437.602i	−0.513015	+	0.513015i	0.402434	+	0.915449i	$0.368164\pi$
$854$	−291.941	+	325.223i	−0.341852	+	0.380824i
$855$		0			0
$856$	637.183	+	458.530i	0.744373	+	0.535666i
$857$	−734.356			−0.856891			−0.428445	−	0.903568i	$-0.640939\pi$
$857$	−734.356			−0.856891			−0.428445	+	0.903568i	$0.640939\pi$
$858$		0			0
$859$	−473.257	+	473.257i	−0.550939	+	0.550939i	−0.926712	−	0.375773i	$-0.877377\pi$
$859$	−473.257	+	473.257i	−0.550939	+	0.550939i	0.375773	+	0.926712i	$0.377377\pi$
$860$	378.537	−	40.9461i	0.440159	−	0.0476117i
$861$		0			0
$862$	−7.65328	−	141.918i	−0.00887851	−	0.164638i
$863$		−	415.374i		−	0.481315i	−0.970610	−	0.240657i	$-0.922637\pi$
$863$		−	415.374i		−	0.481315i	0.970610	−	0.240657i	$-0.0773630\pi$
$864$		0			0
$865$	167.732			0.193910
$866$	143.483	−	7.73765i	0.165684	−	0.00893493i
$867$		0			0
$868$	13.9370	+	128.845i	0.0160565	+	0.148439i
$869$	−305.348	−	305.348i	−0.351379	−	0.351379i
$870$		0			0
$871$			200.849i			0.230596i
$872$	−424.570	−	305.529i	−0.486892	−	0.350377i
$873$		0			0
$874$	−187.405	−	168.227i	−0.214422	−	0.192479i
$875$	199.587	+	199.587i	0.228100	+	0.228100i
$876$		0			0
$877$	−639.234	−	639.234i	−0.728887	−	0.728887i	0.241511	−	0.970398i	$-0.422357\pi$
$877$	−639.234	−	639.234i	−0.728887	−	0.728887i	−0.970398	+	0.241511i	$0.922357\pi$
$878$	8.08084	+	149.847i	0.00920369	+	0.170668i
$879$		0			0
$880$	36.8367	+	168.281i	0.0418599	+	0.191229i
$881$		−	434.503i		−	0.493193i	−0.969118	−	0.246596i	$-0.920688\pi$
$881$		−	434.503i		−	0.493193i	0.969118	−	0.246596i	$-0.0793122\pi$
$882$		0			0
$883$	−597.662	−	597.662i	−0.676854	−	0.676854i	0.282433	−	0.959287i	$-0.408858\pi$
$883$	−597.662	−	597.662i	−0.676854	−	0.676854i	−0.959287	+	0.282433i	$0.908858\pi$
$884$	−111.328	+	138.334i	−0.125937	+	0.156486i
$885$		0			0
$886$	−857.480	−	769.729i	−0.967810	−	0.868768i
$887$	1100.10			1.24025			0.620125	−	0.784503i	$-0.287082\pi$
$887$	1100.10			1.24025			0.620125	+	0.784503i	$0.287082\pi$
$888$		0			0
$889$		−	455.767i		−	0.512674i
$890$	131.142	+	117.722i	0.147351	+	0.132272i
$891$		0			0
$892$	−279.219	+	30.2029i	−0.313026	+	0.0338598i
$893$	1990.72	−	1990.72i	2.22924	−	2.22924i
$894$		0			0
$895$	−562.745			−0.628765
$896$	114.617	+	289.375i	0.127921	+	0.322963i
$897$		0			0
$898$	57.9179	+	1074.00i	0.0644966	+	1.19599i
$899$	−312.501	+	312.501i	−0.347610	+	0.347610i
$900$		0			0
$901$	−811.031	+	811.031i	−0.900146	+	0.900146i
$902$	376.457	+	337.932i	0.417358	+	0.374648i
$903$		0			0
$904$	−125.082	−	767.152i	−0.138366	−	0.848620i
$905$	712.669			0.787479
$906$		0			0
$907$	−344.291	+	344.291i	−0.379593	+	0.379593i	−0.870955	−	0.491362i	$-0.836499\pi$
$907$	−344.291	+	344.291i	−0.379593	+	0.379593i	0.491362	+	0.870955i	$0.336499\pi$
$908$	204.442	−	254.035i	0.225156	−	0.279774i
$909$		0			0
$910$	−28.8564	+	1.55615i	−0.0317103	+	0.00171005i
$911$			803.034i			0.881486i	0.897633	+	0.440743i	$0.145285\pi$
$911$			803.034i			0.881486i	−0.897633	+	0.440743i	$0.854715\pi$
$912$		0			0
$913$	−82.3109			−0.0901543
$914$	72.2168	+	1339.15i	0.0790118	+	1.46515i
$915$		0			0
$916$	483.782	−	601.137i	0.528147	−	0.656264i
$917$	−192.657	−	192.657i	−0.210094	−	0.210094i
$918$		0			0
$919$		−	1119.49i		−	1.21816i	−0.793107	−	0.609082i	$-0.791538\pi$
$919$		−	1119.49i		−	1.21816i	0.793107	−	0.609082i	$-0.208462\pi$
$920$	−63.0270	−	45.3555i	−0.0685076	−	0.0492994i
$921$		0			0
$922$	−1180.04	+	1314.57i	−1.27987	+	1.42578i
$923$	130.489	+	130.489i	0.141375	+	0.141375i
$924$		0			0
$925$	446.786	+	446.786i	0.483012	+	0.483012i
$926$	1111.71	−	59.9516i	1.20055	−	0.0647426i
$927$		0			0
$928$	−523.722	+	923.196i	−0.564356	+	0.994824i
$929$			1069.69i			1.15144i	0.817647	+	0.575721i	$0.195278\pi$
$929$			1069.69i			1.15144i	−0.817647	+	0.575721i	$0.804722\pi$
$930$		0			0
$931$	−1077.95	−	1077.95i	−1.15784	−	1.15784i
$932$	−680.636	+	73.6239i	−0.730296	+	0.0789956i
$933$		0			0
$934$	−256.775	+	286.048i	−0.274920	+	0.306261i
$935$	219.365			0.234615
$936$		0			0
$937$			61.7823i			0.0659363i	0.999456	+	0.0329682i	$0.0104960\pi$
$937$			61.7823i			0.0659363i	−0.999456	+	0.0329682i	$0.989504\pi$
$938$	299.474	−	333.615i	0.319268	−	0.355666i
$939$		0			0
$940$	544.241	−	676.262i	0.578979	−	0.719427i
$941$	−455.261	+	455.261i	−0.483806	+	0.483806i	−0.906345	−	0.422539i	$-0.861139\pi$
$941$	−455.261	+	455.261i	−0.483806	+	0.483806i	0.422539	+	0.906345i	$0.361139\pi$
$942$		0			0
$943$	−228.031			−0.241814
$944$	366.492	+	234.857i	0.388233	+	0.248789i
$945$		0			0
$946$	−275.164	+	14.8389i	−0.290871	+	0.0156859i
$947$	1145.09	−	1145.09i	1.20918	−	1.20918i	0.237883	−	0.971294i	$-0.423547\pi$
$947$	1145.09	−	1145.09i	1.20918	−	1.20918i	0.971294	−	0.237883i	$-0.0764534\pi$
$948$		0			0
$949$	−61.2362	+	61.2362i	−0.0645271	+	0.0645271i
$950$	830.130	−	924.767i	0.873821	−	0.973438i
$951$		0			0
$952$	391.180	−	63.7811i	0.410904	−	0.0669969i
$953$	1187.58			1.24615			0.623076	−	0.782161i	$-0.285883\pi$
$953$	1187.58			1.24615			0.623076	+	0.782161i	$0.285883\pi$
$954$		0			0
$955$	−679.221	+	679.221i	−0.711227	+	0.711227i
$956$	34.2903	+	317.006i	0.0358685	+	0.331596i
$957$		0			0
$958$	81.2680	+	1506.99i	0.0848309	+	1.57306i
$959$		−	8.41794i		−	0.00877783i
$960$		0			0
$961$	−783.470			−0.815265
$962$	−156.552	+	8.44241i	−0.162736	+	0.00877590i
$963$		0			0
$964$	−272.684	+	29.4960i	−0.282867	+	0.0305975i
$965$	280.903	+	280.903i	0.291091	+	0.291091i
$966$		0			0
$967$		−	464.902i		−	0.480767i	−0.970678	−	0.240384i	$-0.922727\pi$
$967$		−	464.902i		−	0.480767i	0.970678	−	0.240384i	$-0.0772732\pi$
$968$	135.710	+	832.332i	0.140196	+	0.859847i
$969$		0			0
$970$	501.160	+	449.873i	0.516660	+	0.463787i
$971$	−102.522	−	102.522i	−0.105584	−	0.105584i	0.652341	−	0.757925i	$-0.273787\pi$
$971$	−102.522	−	102.522i	−0.105584	−	0.105584i	−0.757925	+	0.652341i	$0.773787\pi$
$972$		0			0
$973$	34.2990	+	34.2990i	0.0352507	+	0.0352507i
$974$	81.0468	+	1502.89i	0.0832103	+	1.54301i
$975$		0			0
$976$	1210.60	+	775.780i	1.24037	+	0.794857i
$977$		−	1273.15i		−	1.30312i	−0.758597	−	0.651560i	$-0.774115\pi$
$977$		−	1273.15i		−	1.30312i	0.758597	−	0.651560i	$-0.225885\pi$
$978$		0			0
$979$	−90.1883	−	90.1883i	−0.0921229	−	0.0921229i
$980$	−366.188	−	294.700i	−0.373661	−	0.300714i
$981$		0			0
$982$	1216.29	+	1091.82i	1.23858	+	1.11183i
$983$	−523.931			−0.532992			−0.266496	−	0.963836i	$-0.585866\pi$
$983$	−523.931			−0.532992			−0.266496	+	0.963836i	$0.585866\pi$
$984$		0			0
$985$			72.4130i			0.0735158i
$986$	1005.80	+	902.875i	1.02009	+	0.915694i
$987$		0			0
$988$	33.1603	+	306.559i	0.0335631	+	0.310283i
$989$	87.8314	−	87.8314i	0.0888083	−	0.0888083i
$990$		0			0
$991$	−1675.46			−1.69067			−0.845336	−	0.534235i	$-0.820600\pi$
$991$	−1675.46			−1.69067			−0.845336	+	0.534235i	$0.820600\pi$
$992$	410.994	−	113.470i	0.414308	−	0.114385i
$993$		0			0
$994$	−22.1809	−	411.310i	−0.0223147	−	0.413793i
$995$	−501.645	+	501.645i	−0.504166	+	0.504166i
$996$		0			0
$997$	911.770	−	911.770i	0.914513	−	0.914513i	−0.0821099	−	0.996623i	$-0.526166\pi$
$997$	911.770	−	911.770i	0.914513	−	0.914513i	0.996623	+	0.0821099i	$0.0261659\pi$
$998$	−97.2410	−	87.2898i	−0.0974359	−	0.0874647i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	144.3.j.a.125.1	yes	32
3.2	odd	2	inner	144.3.j.a.125.16	yes	32
4.3	odd	2		576.3.j.a.17.5		32
8.3	odd	2		1152.3.j.b.161.12		32
8.5	even	2		1152.3.j.a.161.12		32
12.11	even	2		576.3.j.a.17.12		32
16.3	odd	4		1152.3.j.b.737.5		32
16.5	even	4	inner	144.3.j.a.53.16	yes	32
16.11	odd	4		576.3.j.a.305.12		32
16.13	even	4		1152.3.j.a.737.5		32
24.5	odd	2		1152.3.j.a.161.5		32
24.11	even	2		1152.3.j.b.161.5		32
48.5	odd	4	inner	144.3.j.a.53.1	✓	32
48.11	even	4		576.3.j.a.305.5		32
48.29	odd	4		1152.3.j.a.737.12		32
48.35	even	4		1152.3.j.b.737.12		32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
144.3.j.a.53.1	✓	32	48.5	odd	4	inner
144.3.j.a.53.16	yes	32	16.5	even	4	inner
144.3.j.a.125.1	yes	32	1.1	even	1	trivial
144.3.j.a.125.16	yes	32	3.2	odd	2	inner
576.3.j.a.17.5		32	4.3	odd	2
576.3.j.a.17.12		32	12.11	even	2
576.3.j.a.305.5		32	48.11	even	4
576.3.j.a.305.12		32	16.11	odd	4
1152.3.j.a.161.5		32	24.5	odd	2
1152.3.j.a.161.12		32	8.5	even	2
1152.3.j.a.737.5		32	16.13	even	4
1152.3.j.a.737.12		32	48.29	odd	4
1152.3.j.b.161.5		32	24.11	even	2
1152.3.j.b.161.12		32	8.3	odd	2
1152.3.j.b.737.5		32	16.3	odd	4
1152.3.j.b.737.12		32	48.35	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:	\( N \)	\(=\)	\( 144 = 2^{4} \cdot 3^{2} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	144.j (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.99710 + 0.107698i) q^{2} +(3.97680 - 0.430168i) q^{4} +(-1.92848 - 1.92848i) q^{5} -2.43162i q^{7} +(-7.89574 + 1.28738i) q^{8} +O(q^{10})\)	\(q+(-1.99710 + 0.107698i) q^{2} +(3.97680 - 0.430168i) q^{4} +(-1.92848 - 1.92848i) q^{5} -2.43162i q^{7} +(-7.89574 + 1.28738i) q^{8} +(4.05906 + 3.64367i) q^{10} +(-2.79147 - 2.79147i) q^{11} +(-1.54064 - 1.54064i) q^{13} +(0.261881 + 4.85619i) q^{14} +(15.6299 - 3.42138i) q^{16} -20.3746i q^{17} +(-25.0179 - 25.0179i) q^{19} +(-8.49876 - 6.83962i) q^{20} +(5.87548 + 5.27421i) q^{22} -3.55894 q^{23} -17.5619i q^{25} +(3.24273 + 2.91088i) q^{26} +(-1.04601 - 9.67008i) q^{28} +(23.4539 - 23.4539i) q^{29} -13.3241 q^{31} +(-30.8460 + 8.51615i) q^{32} +(2.19430 + 40.6900i) q^{34} +(-4.68934 + 4.68934i) q^{35} +(-25.4406 + 25.4406i) q^{37} +(52.6575 + 47.2687i) q^{38} +(17.7095 + 12.7441i) q^{40} +64.0726 q^{41} +(-24.6791 + 24.6791i) q^{43} +(-12.3019 - 9.90033i) q^{44} +(7.10756 - 0.383292i) q^{46} +79.5718i q^{47} +43.0872 q^{49} +(1.89139 + 35.0729i) q^{50} +(-6.78954 - 5.46408i) q^{52} +(-39.8061 - 39.8061i) q^{53} +10.7666i q^{55} +(3.13043 + 19.1994i) q^{56} +(-44.3138 + 49.3657i) q^{58} +(19.2371 + 19.2371i) q^{59} +(63.5441 + 63.5441i) q^{61} +(26.6094 - 1.43498i) q^{62} +(60.6853 - 20.3297i) q^{64} +5.94218i q^{65} +(-65.1837 - 65.1837i) q^{67} +(-8.76448 - 81.0256i) q^{68} +(8.86003 - 9.87010i) q^{70} -84.6981 q^{71} -39.7473i q^{73} +(48.0675 - 53.5473i) q^{74} +(-110.253 - 88.7292i) q^{76} +(-6.78781 + 6.78781i) q^{77} +109.386 q^{79} +(-36.7401 - 23.5439i) q^{80} +(-127.959 + 6.90050i) q^{82} +(14.7433 - 14.7433i) q^{83} +(-39.2920 + 39.2920i) q^{85} +(46.6287 - 51.9444i) q^{86} +(25.6344 + 18.4470i) q^{88} +32.3085 q^{89} +(-3.74625 + 3.74625i) q^{91} +(-14.1532 + 1.53094i) q^{92} +(-8.56974 - 158.913i) q^{94} +96.4929i q^{95} +123.467 q^{97} +(-86.0494 + 4.64042i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q+O(q^{10}) \) 32 * q	\( 32 q + 40 q^{10} + 48 q^{16} + 64 q^{19} - 88 q^{22} - 120 q^{28} - 248 q^{34} - 184 q^{40} + 128 q^{43} + 24 q^{46} - 224 q^{49} + 632 q^{52} + 456 q^{58} + 64 q^{61} - 48 q^{64} - 64 q^{67} - 312 q^{70} - 576 q^{76} - 512 q^{79} - 720 q^{82} + 320 q^{85} - 400 q^{88} - 192 q^{91} + 696 q^{94}+O(q^{100}) \) 32 * q + 40 * q^10 + 48 * q^16 + 64 * q^19 - 88 * q^22 - 120 * q^28 - 248 * q^34 - 184 * q^40 + 128 * q^43 + 24 * q^46 - 224 * q^49 + 632 * q^52 + 456 * q^58 + 64 * q^61 - 48 * q^64 - 64 * q^67 - 312 * q^70 - 576 * q^76 - 512 * q^79 - 720 * q^82 + 320 * q^85 - 400 * q^88 - 192 * q^91 + 696 * q^94

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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