LMFDB - Embedded newform 252.4.w.a.5.12

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [252,4,Mod(5,252)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(252, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 5, 5]))

N = Newforms(chi, 4, names="a")

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

chi := DirichletCharacter("252.5");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 252 = 2^{2} \cdot 3^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	252.w (of order $6$, 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:	$14.8684813214$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$24$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			5.12
Character	$\chi$	$=$	252.5
Dual form			252.4.w.a.101.12

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.452892 - 5.17638i) q^{3} +(6.54401 + 11.3346i) q^{5} +(1.26985 + 18.4767i) q^{7} +(-26.5898 + 4.68868i) q^{9} +O(q^{10})$	\(q+(-0.452892 - 5.17638i) q^{3} +(6.54401 + 11.3346i) q^{5} +(1.26985 + 18.4767i) q^{7} +(-26.5898 + 4.68868i) q^{9} +(-45.6639 - 26.3641i) q^{11} +(-31.8581 - 18.3933i) q^{13} +(55.7082 - 39.0076i) q^{15} +(-20.4867 - 35.4840i) q^{17} +(-108.800 - 62.8157i) q^{19} +(95.0671 - 14.9412i) q^{21} +(1.99019 - 1.14903i) q^{23} +(-23.1480 + 40.0935i) q^{25} +(36.3127 + 135.515i) q^{27} +(-151.695 + 87.5813i) q^{29} -268.714i q^{31} +(-115.790 + 248.314i) q^{33} +(-201.115 + 135.305i) q^{35} +(-191.441 + 331.586i) q^{37} +(-80.7824 + 173.240i) q^{39} +(-75.5046 + 130.778i) q^{41} +(23.2485 + 40.2676i) q^{43} +(-227.148 - 270.700i) q^{45} +372.661 q^{47} +(-339.775 + 46.9253i) q^{49} +(-174.401 + 122.117i) q^{51} +(539.634 - 311.558i) q^{53} -690.107i q^{55} +(-275.883 + 591.639i) q^{57} +4.01807 q^{59} +779.812i q^{61} +(-120.396 - 485.337i) q^{63} -481.464i q^{65} -439.789 q^{67} +(-6.84917 - 9.78156i) q^{69} -800.222i q^{71} +(-428.450 + 247.366i) q^{73} +(218.023 + 101.665i) q^{75} +(429.134 - 877.196i) q^{77} +140.223 q^{79} +(685.033 - 249.342i) q^{81} +(506.825 + 877.846i) q^{83} +(268.130 - 464.416i) q^{85} +(522.056 + 745.567i) q^{87} +(211.792 - 366.834i) q^{89} +(299.392 - 611.989i) q^{91} +(-1390.97 + 121.698i) q^{93} -1644.27i q^{95} +(-264.560 + 152.744i) q^{97} +(1337.81 + 486.911i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q + 6 q^{7} + 12 q^{9}+O(q^{10}) $ 48 * q + 6 * q^7 + 12 * q^9	$ 48 q + 6 q^{7} + 12 q^{9} + 12 q^{11} - 36 q^{13} + 66 q^{15} - 72 q^{17} + 24 q^{21} + 30 q^{23} - 600 q^{25} - 396 q^{27} + 42 q^{29} + 390 q^{35} + 84 q^{37} - 840 q^{39} - 618 q^{41} - 42 q^{43} + 366 q^{45} + 396 q^{47} + 318 q^{49} - 738 q^{51} - 1620 q^{53} + 492 q^{57} + 1500 q^{59} + 672 q^{63} - 588 q^{67} - 924 q^{69} + 564 q^{75} - 2472 q^{77} + 1608 q^{79} + 2592 q^{81} - 360 q^{85} + 2640 q^{87} + 1722 q^{89} + 540 q^{91} + 660 q^{93} - 792 q^{97} - 54 q^{99}+O(q^{100}) $ 48 * q + 6 * q^7 + 12 * q^9 + 12 * q^11 - 36 * q^13 + 66 * q^15 - 72 * q^17 + 24 * q^21 + 30 * q^23 - 600 * q^25 - 396 * q^27 + 42 * q^29 + 390 * q^35 + 84 * q^37 - 840 * q^39 - 618 * q^41 - 42 * q^43 + 366 * q^45 + 396 * q^47 + 318 * q^49 - 738 * q^51 - 1620 * q^53 + 492 * q^57 + 1500 * q^59 + 672 * q^63 - 588 * q^67 - 924 * q^69 + 564 * q^75 - 2472 * q^77 + 1608 * q^79 + 2592 * q^81 - 360 * q^85 + 2640 * q^87 + 1722 * q^89 + 540 * q^91 + 660 * q^93 - 792 * q^97 - 54 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/252\mathbb{Z}\right)^\times$.

$n$	$29$	$73$	$127$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{5}{6}\right)$	$1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	−0.452892	−	5.17638i	−0.0871591	−	0.996194i
$3$	−0.452892	−	5.17638i	−0.0871591	−	0.996194i
$4$		0			0
$5$	6.54401	+	11.3346i	0.585314	+	1.01379i	0.994836	+	0.101493i	$0.0323620\pi$
$5$	6.54401	+	11.3346i	0.585314	+	1.01379i	−0.409523	+	0.912300i	$0.634305\pi$
$6$		0			0
$7$	1.26985	+	18.4767i	0.0685656	+	0.997647i
$7$	1.26985	+	18.4767i	0.0685656	+	0.997647i
$8$		0			0
$9$	−26.5898	+	4.68868i	−0.984807	+	0.173655i
$10$		0			0
$11$	−45.6639	−	26.3641i	−1.25165	−	0.722642i	−0.280216	−	0.959937i	$-0.590406\pi$
$11$	−45.6639	−	26.3641i	−1.25165	−	0.722642i	−0.971438	+	0.237295i	$0.923739\pi$
$12$		0			0
$13$	−31.8581	−	18.3933i	−0.679681	−	0.392414i	0.120054	−	0.992767i	$-0.461693\pi$
$13$	−31.8581	−	18.3933i	−0.679681	−	0.392414i	−0.799735	+	0.600353i	$0.795027\pi$
$14$		0			0
$15$	55.7082	−	39.0076i	0.958920	−	0.671447i
$16$		0			0
$17$	−20.4867	−	35.4840i	−0.292280	−	0.506244i	0.682069	−	0.731288i	$-0.261081\pi$
$17$	−20.4867	−	35.4840i	−0.292280	−	0.506244i	−0.974348	+	0.225045i	$0.927747\pi$
$18$		0			0
$19$	−108.800	−	62.8157i	−1.31371	−	0.758469i	−0.330999	−	0.943631i	$-0.607386\pi$
$19$	−108.800	−	62.8157i	−1.31371	−	0.758469i	−0.982708	+	0.185162i	$0.940719\pi$
$20$		0			0
$21$	95.0671	−	14.9412i	0.987874	−	0.155259i
$22$		0			0
$23$	1.99019	−	1.14903i	0.0180427	−	0.0104170i	−0.490952	−	0.871187i	$-0.663351\pi$
$23$	1.99019	−	1.14903i	0.0180427	−	0.0104170i	0.508994	+	0.860770i	$0.330017\pi$
$24$		0			0
$25$	−23.1480	+	40.0935i	−0.185184	+	0.320748i
$26$		0			0
$27$	36.3127	+	135.515i	0.258829	+	0.965923i
$28$		0			0
$29$	−151.695	+	87.5813i	−0.971348	+	0.560808i	−0.899647	−	0.436618i	$-0.856176\pi$
$29$	−151.695	+	87.5813i	−0.971348	+	0.560808i	−0.0717014	+	0.997426i	$0.522843\pi$
$30$		0			0
$31$		−	268.714i		−	1.55685i	−0.627735	−	0.778427i	$-0.716018\pi$
$31$		−	268.714i		−	1.55685i	0.627735	−	0.778427i	$-0.283982\pi$
$32$		0			0
$33$	−115.790	+	248.314i	−0.610799	+	1.30987i
$34$		0			0
$35$	−201.115	+	135.305i	−0.971275	+	0.653447i
$36$		0			0
$37$	−191.441	+	331.586i	−0.850615	+	1.47331i	0.0300387	+	0.999549i	$0.490437\pi$
$37$	−191.441	+	331.586i	−0.850615	+	1.47331i	−0.880654	+	0.473760i	$0.842896\pi$
$38$		0			0
$39$	−80.7824	+	173.240i	−0.331680	+	0.711297i
$40$		0			0
$41$	−75.5046	+	130.778i	−0.287606	+	0.498148i	−0.973238	−	0.229801i	$-0.926193\pi$
$41$	−75.5046	+	130.778i	−0.287606	+	0.498148i	0.685632	+	0.727948i	$0.259526\pi$
$42$		0			0
$43$	23.2485	+	40.2676i	0.0824504	+	0.142808i	0.904302	−	0.426893i	$-0.140392\pi$
$43$	23.2485	+	40.2676i	0.0824504	+	0.142808i	−0.821852	+	0.569702i	$0.807059\pi$
$44$		0			0
$45$	−227.148	−	270.700i	−0.752471	−	0.896748i
$46$		0			0
$47$	372.661			1.15656			0.578278	−	0.815840i	$-0.303725\pi$
$47$	372.661			1.15656			0.578278	+	0.815840i	$0.303725\pi$
$48$		0			0
$49$	−339.775	+	46.9253i	−0.990598	+	0.136808i
$50$		0			0
$51$	−174.401	+	122.117i	−0.478842	+	0.335291i
$52$		0			0
$53$	539.634	−	311.558i	1.39857	−	0.807467i	0.404330	−	0.914613i	$-0.367505\pi$
$53$	539.634	−	311.558i	1.39857	−	0.807467i	0.994243	+	0.107146i	$0.0341714\pi$
$54$		0			0
$55$		−	690.107i		−	1.69189i
$56$		0			0
$57$	−275.883	+	591.639i	−0.641081	+	1.37482i
$58$		0			0
$59$	4.01807			0.00886624			0.00443312	−	0.999990i	$-0.498589\pi$
$59$	4.01807			0.00886624			0.00443312	+	0.999990i	$0.498589\pi$
$60$		0			0
$61$			779.812i			1.63680i	0.574649	+	0.818400i	$0.305138\pi$
$61$			779.812i			1.63680i	−0.574649	+	0.818400i	$0.694862\pi$
$62$		0			0
$63$	−120.396	−	485.337i	−0.240770	−	0.970582i
$64$		0			0
$65$		−	481.464i		−	0.918742i
$66$		0			0
$67$	−439.789			−0.801922			−0.400961	−	0.916095i	$-0.631324\pi$
$67$	−439.789			−0.801922			−0.400961	+	0.916095i	$0.631324\pi$
$68$		0			0
$69$	−6.84917	−	9.78156i	−0.0119499	−	0.0170661i
$70$		0			0
$71$		−	800.222i		−	1.33759i	−0.743447	−	0.668795i	$-0.766810\pi$
$71$		−	800.222i		−	1.33759i	0.743447	−	0.668795i	$-0.233190\pi$
$72$		0			0
$73$	−428.450	+	247.366i	−0.686936	+	0.396603i	−0.802463	−	0.596702i	$-0.796478\pi$
$73$	−428.450	+	247.366i	−0.686936	+	0.396603i	0.115527	+	0.993304i	$0.463144\pi$
$74$		0			0
$75$	218.023	+	101.665i	0.335668	+	0.156523i
$76$		0			0
$77$	429.134	−	877.196i	0.635121	−	1.29826i
$78$		0			0
$79$	140.223			0.199700			0.0998498	−	0.995003i	$-0.468164\pi$
$79$	140.223			0.199700			0.0998498	+	0.995003i	$0.468164\pi$
$80$		0			0
$81$	685.033	−	249.342i	0.939688	−	0.342033i
$82$		0			0
$83$	506.825	+	877.846i	0.670256	+	1.16092i	0.977831	+	0.209394i	$0.0671491\pi$
$83$	506.825	+	877.846i	0.670256	+	1.16092i	−0.307575	+	0.951524i	$0.599518\pi$
$84$		0			0
$85$	268.130	−	464.416i	0.342151	−	0.592623i
$86$		0			0
$87$	522.056	+	745.567i	0.643336	+	0.918772i
$88$		0			0
$89$	211.792	−	366.834i	0.252246	−	0.436902i	−0.711898	−	0.702283i	$-0.752164\pi$
$89$	211.792	−	366.834i	0.252246	−	0.436902i	0.964144	+	0.265380i	$0.0854975\pi$
$90$		0			0
$91$	299.392	−	611.989i	0.344888	−	0.704988i
$92$		0			0
$93$	−1390.97	+	121.698i	−1.55093	+	0.135694i
$94$		0			0
$95$		−	1644.27i		−	1.77577i
$96$		0			0
$97$	−264.560	+	152.744i	−0.276928	+	0.159884i	−0.632032	−	0.774942i	$-0.717779\pi$
$97$	−264.560	+	152.744i	−0.276928	+	0.159884i	0.355104	+	0.934827i	$0.384445\pi$
$98$		0			0
$99$	1337.81	+	486.911i	1.35813	+	0.494307i
$100$		0			0
$101$	−414.543	+	718.010i	−0.408402	+	0.707373i	−0.994711	−	0.102714i	$-0.967247\pi$
$101$	−414.543	+	718.010i	−0.408402	+	0.707373i	0.586309	+	0.810088i	$0.300581\pi$
$102$		0			0
$103$	−1301.99	+	751.704i	−1.24552	+	0.719103i	−0.970213	−	0.242253i	$-0.922114\pi$
$103$	−1301.99	+	751.704i	−1.24552	+	0.719103i	−0.275309	+	0.961356i	$0.588780\pi$
$104$		0			0
$105$	791.471	+	979.768i	0.735616	+	0.910625i
$106$		0			0
$107$	1429.35	+	825.235i	1.29141	+	0.745593i	0.978903	−	0.204324i	$-0.0654995\pi$
$107$	1429.35	+	825.235i	1.29141	+	0.745593i	0.312502	+	0.949917i	$0.398833\pi$
$108$		0			0
$109$	−561.132	−	971.909i	−0.493089	−	0.854055i	0.506879	−	0.862017i	$-0.330799\pi$
$109$	−561.132	−	971.909i	−0.493089	−	0.854055i	−0.999968	+	0.00796189i	$0.997466\pi$
$110$		0			0
$111$	1803.12	+	840.800i	1.54184	+	0.718966i
$112$		0			0
$113$	−1170.93	−	676.036i	−0.974794	−	0.562797i	−0.0740993	−	0.997251i	$-0.523608\pi$
$113$	−1170.93	−	676.036i	−0.974794	−	0.562797i	−0.900694	+	0.434454i	$0.856942\pi$
$114$		0			0
$115$	26.0476	+	15.0386i	0.0211213	+	0.0121944i
$116$		0			0
$117$	933.341	+	339.701i	0.737499	+	0.268422i
$118$		0			0
$119$	629.612	−	423.586i	0.485012	−	0.326303i
$120$		0			0
$121$	724.628	+	1255.09i	0.544424	+	0.942970i
$122$		0			0
$123$	711.151	+	331.612i	0.521319	+	0.243093i
$124$		0			0
$125$	1030.08			0.737064
$126$		0			0
$127$	−214.982			−0.150209			−0.0751045	−	0.997176i	$-0.523929\pi$
$127$	−214.982			−0.150209			−0.0751045	+	0.997176i	$0.523929\pi$
$128$		0			0
$129$	197.911	−	138.580i	0.135078	−	0.0945836i
$130$		0			0
$131$	50.1333	+	86.8334i	0.0334364	+	0.0579135i	0.882259	−	0.470764i	$-0.156022\pi$
$131$	50.1333	+	86.8334i	0.0334364	+	0.0579135i	−0.848823	+	0.528677i	$0.822688\pi$
$132$		0			0
$133$	1022.47	−	2090.03i	0.666609	−	1.36262i
$134$		0			0
$135$	−1298.37	+	1298.40i	−0.827750	+	0.827767i
$136$		0			0
$137$	410.910	+	237.239i	0.256251	+	0.147947i	0.622623	−	0.782522i	$-0.286067\pi$
$137$	410.910	+	237.239i	0.256251	+	0.147947i	−0.366372	+	0.930468i	$0.619400\pi$
$138$		0			0
$139$	−746.967	−	431.261i	−0.455805	−	0.263159i	0.254474	−	0.967080i	$-0.418098\pi$
$139$	−746.967	−	431.261i	−0.455805	−	0.263159i	−0.710279	+	0.703921i	$0.751431\pi$
$140$		0			0
$141$	−168.775	−	1929.03i	−0.100804	−	1.15215i
$142$		0			0
$143$	969.845	+	1679.82i	0.567150	+	0.982333i
$144$		0			0
$145$	−1985.39	−	1146.27i	−1.13709	−	0.656498i
$146$		0			0
$147$	396.784	+	1737.55i	0.222627	+	0.974904i
$148$		0			0
$149$	−441.829	+	255.090i	−0.242926	+	0.140254i	−0.616521	−	0.787338i	$-0.711458\pi$
$149$	−441.829	+	255.090i	−0.242926	+	0.140254i	0.373595	+	0.927592i	$0.378125\pi$
$150$		0			0
$151$	−239.521	+	414.863i	−0.129086	+	0.223583i	−0.923323	−	0.384025i	$-0.874538\pi$
$151$	−239.521	+	414.863i	−0.129086	+	0.223583i	0.794237	+	0.607608i	$0.207871\pi$
$152$		0			0
$153$	711.111	+	847.457i	0.375751	+	0.447796i
$154$		0			0
$155$	3045.75	−	1758.47i	1.57833	−	0.911248i
$156$		0			0
$157$		−	830.662i		−	0.422255i	−0.977459	−	0.211127i	$-0.932287\pi$
$157$		−	830.662i		−	0.422255i	0.977459	−	0.211127i	$-0.0677135\pi$
$158$		0			0
$159$	−1857.14	−	2652.25i	−0.926292	−	1.32287i
$160$		0			0
$161$	23.7576	+	35.3129i	0.0116296	+	0.0172860i
$162$		0			0
$163$	764.572	−	1324.28i	0.367398	−	0.636352i	−0.621760	−	0.783208i	$-0.713582\pi$
$163$	764.572	−	1324.28i	0.367398	−	0.636352i	0.989158	+	0.146856i	$0.0469153\pi$
$164$		0			0
$165$	−3572.25	+	312.544i	−1.68545	+	0.147464i
$166$		0			0
$167$	1718.66	−	2976.81i	0.796371	−	1.37935i	−0.125595	−	0.992082i	$-0.540084\pi$
$167$	1718.66	−	2976.81i	0.796371	−	1.37935i	0.921965	−	0.387273i	$-0.126583\pi$
$168$		0			0
$169$	−421.873	−	730.705i	−0.192022	−	0.332592i
$170$		0			0
$171$	3187.49	+	1160.13i	1.42546	+	0.518814i
$172$		0			0
$173$	734.650			0.322858			0.161429	−	0.986884i	$-0.448390\pi$
$173$	734.650			0.322858			0.161429	+	0.986884i	$0.448390\pi$
$174$		0			0
$175$	−770.190	−	376.786i	−0.332691	−	0.162756i
$176$		0			0
$177$	−1.81975	−	20.7991i	−0.000772773	−	0.00883250i
$178$		0			0
$179$	−2865.41	+	1654.34i	−1.19648	+	0.690790i	−0.959769	−	0.280789i	$-0.909404\pi$
$179$	−2865.41	+	1654.34i	−1.19648	+	0.690790i	−0.236714	+	0.971579i	$0.576071\pi$
$180$		0			0
$181$			2891.26i			1.18732i	0.804715	+	0.593662i	$0.202318\pi$
$181$			2891.26i			1.18732i	−0.804715	+	0.593662i	$0.797682\pi$
$182$		0			0
$183$	4036.60	−	353.171i	1.63057	−	0.142662i
$184$		0			0
$185$	−5011.17			−1.99151
$186$		0			0
$187$			2160.45i			0.844856i
$188$		0			0
$189$	−2457.76	+	843.022i	−0.945903	+	0.324449i
$190$		0			0
$191$		−	4422.49i		−	1.67539i	−0.546136	−	0.837696i	$-0.683902\pi$
$191$		−	4422.49i		−	1.67539i	0.546136	−	0.837696i	$-0.316098\pi$
$192$		0			0
$193$	−4264.02			−1.59032			−0.795158	−	0.606403i	$-0.792612\pi$
$193$	−4264.02			−1.59032			−0.795158	+	0.606403i	$0.792612\pi$
$194$		0			0
$195$	−2492.24	+	218.051i	−0.915245	+	0.0800766i
$196$		0			0
$197$		−	163.023i		−	0.0589590i	−0.999565	−	0.0294795i	$-0.990615\pi$
$197$		−	163.023i		−	0.0589590i	0.999565	−	0.0294795i	$-0.00938498\pi$
$198$		0			0
$199$	239.024	−	138.000i	0.0851455	−	0.0491588i	−0.456823	−	0.889558i	$-0.651013\pi$
$199$	239.024	−	138.000i	0.0851455	−	0.0491588i	0.541968	+	0.840399i	$0.317679\pi$
$200$		0			0
$201$	199.177	+	2276.51i	0.0698947	+	0.798870i
$202$		0			0
$203$	−1810.84	−	2691.61i	−0.626090	−	0.930610i
$204$		0			0
$205$	−1976.41			−0.673358
$206$		0			0
$207$	−47.5311	+	39.8839i	−0.0159596	+	0.0133919i
$208$		0			0
$209$	3312.16	+	5736.82i	1.09620	+	1.89868i
$210$		0			0
$211$	1330.09	−	2303.78i	0.433967	−	0.751654i	−0.563243	−	0.826291i	$-0.690447\pi$
$211$	1330.09	−	2303.78i	0.433967	−	0.751654i	0.997211	+	0.0746375i	$0.0237800\pi$
$212$		0			0
$213$	−4142.25	+	362.414i	−1.33250	+	0.116583i
$214$		0			0
$215$	−304.277	+	527.023i	−0.0965186	+	0.167175i
$216$		0			0
$217$	4964.94	−	341.227i	1.55319	−	0.106747i
$218$		0			0
$219$	1474.50	+	2105.79i	0.454966	+	0.649754i
$220$		0			0
$221$			1507.27i			0.458779i
$222$		0			0
$223$	−1923.61	+	1110.60i	−0.577645	+	0.333503i	−0.760197	−	0.649693i	$-0.774897\pi$
$223$	−1923.61	+	1110.60i	−0.577645	+	0.333503i	0.182552	+	0.983196i	$0.441564\pi$
$224$		0			0
$225$	427.515	−	1174.61i	0.126671	−	0.348033i
$226$		0			0
$227$	−1755.67	+	3040.92i	−0.513340	+	0.889131i	0.486540	+	0.873658i	$0.338259\pi$
$227$	−1755.67	+	3040.92i	−0.513340	+	0.889131i	−0.999880	+	0.0154731i	$0.995075\pi$
$228$		0			0
$229$	−4357.66	+	2515.89i	−1.25748	+	0.726004i	−0.972583	−	0.232555i	$-0.925291\pi$
$229$	−4357.66	+	2515.89i	−1.25748	+	0.726004i	−0.284893	+	0.958559i	$0.591958\pi$
$230$		0			0
$231$	−4735.05	−	1824.08i	−1.34867	−	0.519550i
$232$		0			0
$233$	−3525.46	−	2035.43i	−0.991248	−	0.572297i	−0.0856006	−	0.996330i	$-0.527281\pi$
$233$	−3525.46	−	2035.43i	−0.991248	−	0.572297i	−0.905647	+	0.424032i	$0.860614\pi$
$234$		0			0
$235$	2438.69	+	4223.94i	0.676948	+	1.17251i
$236$		0			0
$237$	−63.5056	−	725.845i	−0.0174056	−	0.198940i
$238$		0			0
$239$	3561.19	+	2056.05i	0.963825	+	0.556464i	0.897348	−	0.441324i	$-0.145491\pi$
$239$	3561.19	+	2056.05i	0.963825	+	0.556464i	0.0664767	+	0.997788i	$0.478824\pi$
$240$		0			0
$241$	4313.09	+	2490.16i	1.15282	+	0.665583i	0.949574	−	0.313544i	$-0.101516\pi$
$241$	4313.09	+	2490.16i	1.15282	+	0.665583i	0.203250	+	0.979127i	$0.434850\pi$
$242$		0			0
$243$	−1600.93	−	3433.06i	−0.422633	−	0.906301i
$244$		0			0
$245$	−2755.37	−	3544.12i	−0.718506	−	0.924185i
$246$		0			0
$247$	2310.78	+	4002.38i	0.595268	+	1.03103i
$248$		0			0
$249$	4314.53	−	3021.09i	1.09808	−	0.768890i
$250$		0			0
$251$	−3477.88			−0.874589			−0.437294	−	0.899318i	$-0.644063\pi$
$251$	−3477.88			−0.874589			−0.437294	+	0.899318i	$0.644063\pi$
$252$		0			0
$253$	−121.173			−0.0301110
$254$		0			0
$255$	−2525.42	−	1177.61i	−0.620189	−	0.289196i
$256$		0			0
$257$	−1038.65	−	1798.99i	−0.252097	−	0.436646i	0.712006	−	0.702174i	$-0.247787\pi$
$257$	−1038.65	−	1798.99i	−0.252097	−	0.436646i	−0.964103	+	0.265528i	$0.914454\pi$
$258$		0			0
$259$	−6369.71	−	3116.13i	−1.52816	−	0.747595i
$260$		0			0
$261$	3622.90	−	3040.02i	0.859203	−	0.720967i
$262$		0			0
$263$	1303.92	+	752.820i	0.305716	+	0.176505i	0.645008	−	0.764176i	$-0.276854\pi$
$263$	1303.92	+	752.820i	0.305716	+	0.176505i	−0.339292	+	0.940681i	$0.610187\pi$
$264$		0			0
$265$	7062.73	+	4077.67i	1.63721	+	0.945243i
$266$		0			0
$267$	−1994.79	−	930.177i	−0.457225	−	0.213206i
$268$		0			0
$269$	2429.40	+	4207.85i	0.550644	+	0.953743i	0.998228	+	0.0595016i	$0.0189511\pi$
$269$	2429.40	+	4207.85i	0.550644	+	0.953743i	−0.447584	+	0.894242i	$0.647716\pi$
$270$		0			0
$271$	−3442.24	−	1987.38i	−0.771591	−	0.445478i	0.0618508	−	0.998085i	$-0.480300\pi$
$271$	−3442.24	−	1987.38i	−0.771591	−	0.445478i	−0.833442	+	0.552607i	$0.813633\pi$
$272$		0			0
$273$	−3303.48	−	1272.60i	−0.732365	−	0.282129i
$274$		0			0
$275$	2114.06	−	1220.55i	0.463573	−	0.267644i
$276$		0			0
$277$	590.449	−	1022.69i	0.128074	−	0.221832i	−0.794856	−	0.606798i	$-0.792454\pi$
$277$	590.449	−	1022.69i	0.128074	−	0.221832i	0.922931	+	0.384967i	$0.125787\pi$
$278$		0			0
$279$	1259.91	+	7145.05i	0.270355	+	1.53320i
$280$		0			0
$281$	4403.68	−	2542.46i	0.934880	−	0.539753i	0.0465286	−	0.998917i	$-0.485184\pi$
$281$	4403.68	−	2542.46i	0.934880	−	0.539753i	0.888352	+	0.459164i	$0.151851\pi$
$282$		0			0
$283$		−	4189.10i		−	0.879915i	−0.898019	−	0.439957i	$-0.854994\pi$
$283$		−	4189.10i		−	0.879915i	0.898019	−	0.439957i	$-0.145006\pi$
$284$		0			0
$285$	−8511.34	+	744.674i	−1.76901	+	0.154774i
$286$		0			0
$287$	−2512.22	−	1229.01i	−0.516695	−	0.252773i
$288$		0			0
$289$	1617.09	−	2800.88i	0.329145	−	0.570096i
$290$		0			0
$291$	910.476	+	1300.29i	0.183413	+	0.261939i
$292$		0			0
$293$	−3061.53	+	5302.72i	−0.610431	+	1.05730i	0.380736	+	0.924684i	$0.375671\pi$
$293$	−3061.53	+	5302.72i	−0.610431	+	1.05730i	−0.991168	+	0.132615i	$0.957663\pi$
$294$		0			0
$295$	26.2943	+	45.5430i	0.00518953	+	0.00898853i
$296$		0			0
$297$	1914.56	−	7145.51i	0.374053	−	1.39604i
$298$		0			0
$299$	−84.5381			−0.0163511
$300$		0			0
$301$	−714.489	+	480.689i	−0.136819	+	0.0920481i
$302$		0			0
$303$	3904.44	+	1820.65i	0.740277	+	0.345194i
$304$		0			0
$305$	−8838.82	+	5103.10i	−1.65938	+	0.958041i
$306$		0			0
$307$			5711.99i			1.06189i	0.847406	+	0.530946i	$0.178163\pi$
$307$			5711.99i			1.06189i	−0.847406	+	0.530946i	$0.821837\pi$
$308$		0			0
$309$	4480.76	+	6399.15i	0.824925	+	1.17811i
$310$		0			0
$311$	2382.08			0.434326			0.217163	−	0.976135i	$-0.430320\pi$
$311$	2382.08			0.434326			0.217163	+	0.976135i	$0.430320\pi$
$312$		0			0
$313$		−	8102.73i		−	1.46324i	−0.681714	−	0.731619i	$-0.738765\pi$
$313$		−	8102.73i		−	1.46324i	0.681714	−	0.731619i	$-0.261235\pi$
$314$		0			0
$315$	4713.20	−	4540.68i	0.843044	−	0.812186i
$316$		0			0
$317$			5045.58i			0.893969i	0.894542	+	0.446985i	$0.147502\pi$
$317$			5045.58i			0.893969i	−0.894542	+	0.446985i	$0.852498\pi$
$318$		0			0
$319$	9236.00			1.62106
$320$		0			0
$321$	3624.39	−	7772.59i	0.630198	−	1.35148i
$322$		0			0
$323$			5147.55i			0.886741i
$324$		0			0
$325$	1474.91	−	851.537i	0.251732	−	0.145338i
$326$		0			0
$327$	−4776.84	+	3344.80i	−0.807828	+	0.565651i
$328$		0			0
$329$	473.224	+	6885.53i	0.0792999	+	1.15383i
$330$		0			0
$331$	−105.530			−0.0175240			−0.00876198	−	0.999962i	$-0.502789\pi$
$331$	−105.530			−0.0175240			−0.00876198	+	0.999962i	$0.502789\pi$
$332$		0			0
$333$	3535.68	−	9714.41i	0.581844	−	1.59864i
$334$		0			0
$335$	−2877.98	−	4984.81i	−0.469376	−	0.812983i
$336$		0			0
$337$	4390.05	−	7603.79i	0.709618	−	1.22909i	−0.255381	−	0.966841i	$-0.582201\pi$
$337$	4390.05	−	7603.79i	0.709618	−	1.22909i	0.964999	−	0.262254i	$-0.0844658\pi$
$338$		0			0
$339$	−2969.11	+	6367.34i	−0.475693	+	1.02014i
$340$		0			0
$341$	−7084.39	+	12270.5i	−1.12505	+	1.94864i
$342$		0			0
$343$	−1298.49	−	6218.32i	−0.204407	−	0.978886i
$344$		0			0
$345$	66.0486	−	141.643i	0.0103071	−	0.0221038i
$346$		0			0
$347$		−	9530.18i		−	1.47437i	−0.675691	−	0.737185i	$-0.736154\pi$
$347$		−	9530.18i		−	1.47437i	0.675691	−	0.737185i	$-0.263846\pi$
$348$		0			0
$349$	8832.94	−	5099.70i	1.35477	−	0.782179i	0.365861	−	0.930670i	$-0.380775\pi$
$349$	8832.94	−	5099.70i	1.35477	−	0.782179i	0.988914	+	0.148490i	$0.0474414\pi$
$350$		0			0
$351$	1335.72	−	4985.17i	0.203121	−	0.758088i
$352$		0			0
$353$	1761.84	−	3051.59i	0.265646	−	0.460112i	−0.702087	−	0.712092i	$-0.747748\pi$
$353$	1761.84	−	3051.59i	0.265646	−	0.460112i	0.967733	+	0.251979i	$0.0810814\pi$
$354$		0			0
$355$	9070.16	−	5236.66i	1.35604	−	0.782910i
$356$		0			0
$357$	−2477.79	−	3067.27i	−0.367334	−	0.454726i
$358$		0			0
$359$	4002.21	+	2310.68i	0.588381	+	0.339702i	0.764457	−	0.644675i	$-0.223007\pi$
$359$	4002.21	+	2310.68i	0.588381	+	0.339702i	−0.176076	+	0.984377i	$0.556341\pi$
$360$		0			0
$361$	4462.13	+	7728.63i	0.650551	+	1.12679i
$362$		0			0
$363$	6168.66	−	4319.37i	0.891930	−	0.624541i
$364$		0			0
$365$	−5607.56	−	3237.53i	−0.804146	−	0.464274i
$366$		0			0
$367$	−1173.43	−	677.480i	−0.166901	−	0.0963601i	0.414223	−	0.910175i	$-0.364053\pi$
$367$	−1173.43	−	677.480i	−0.166901	−	0.0963601i	−0.581124	+	0.813815i	$0.697387\pi$
$368$		0			0
$369$	1394.48	−	3831.37i	0.196730	−	0.540523i
$370$		0			0
$371$	6441.80	+	9575.00i	0.901460	+	1.33992i
$372$		0			0
$373$	2733.76	+	4735.01i	0.379487	+	0.657291i	0.990988	−	0.133953i	$-0.0427671\pi$
$373$	2733.76	+	4735.01i	0.379487	+	0.657291i	−0.611501	+	0.791244i	$0.709434\pi$
$374$		0			0
$375$	−466.514	−	5332.07i	−0.0642418	−	0.734259i
$376$		0			0
$377$	6443.64			0.880277
$378$		0			0
$379$	−6733.99			−0.912670			−0.456335	−	0.889808i	$-0.650838\pi$
$379$	−6733.99			−0.912670			−0.456335	+	0.889808i	$0.650838\pi$
$380$		0			0
$381$	97.3634	+	1112.83i	0.0130921	+	0.149637i
$382$		0			0
$383$	−4748.40	−	8224.47i	−0.633504	−	1.09726i	−0.986830	−	0.161761i	$-0.948283\pi$
$383$	−4748.40	−	8224.47i	−0.633504	−	1.09726i	0.353326	−	0.935500i	$-0.385051\pi$
$384$		0			0
$385$	12750.9	−	876.333i	1.68791	−	0.116005i
$386$		0			0
$387$	−806.975	−	961.702i	−0.105997	−	0.126321i
$388$		0			0
$389$	−5277.80	−	3047.14i	−0.687906	−	0.397163i	0.114921	−	0.993375i	$-0.463338\pi$
$389$	−5277.80	−	3047.14i	−0.687906	−	0.397163i	−0.802827	+	0.596212i	$0.796672\pi$
$390$		0			0
$391$	−81.5447	−	47.0799i	−0.0105470	−	0.00608934i
$392$		0			0
$393$	426.778	−	298.835i	0.0547788	−	0.0383568i
$394$		0			0
$395$	917.617	+	1589.36i	0.116887	+	0.202454i
$396$		0			0
$397$	2477.41	+	1430.33i	0.313193	+	0.180822i	0.648355	−	0.761339i	$-0.275457\pi$
$397$	2477.41	+	1430.33i	0.313193	+	0.180822i	−0.335161	+	0.942161i	$0.608791\pi$
$398$		0			0
$399$	−11281.8	−	4346.11i	−1.41554	−	0.545308i
$400$		0			0
$401$	−3269.15	+	1887.45i	−0.407116	+	0.235049i	−0.689550	−	0.724238i	$-0.742192\pi$
$401$	−3269.15	+	1887.45i	−0.407116	+	0.235049i	0.282434	+	0.959287i	$0.408858\pi$
$402$		0			0
$403$	−4942.54	+	8560.73i	−0.610931	+	1.05816i
$404$		0			0
$405$	7309.03	+	6132.84i	0.896763	+	0.752453i
$406$		0			0
$407$	17483.9	−	10094.3i	2.12935	−	1.22938i
$408$		0			0
$409$			8606.94i			1.04055i	0.853998	+	0.520276i	$0.174171\pi$
$409$			8606.94i			1.04055i	−0.853998	+	0.520276i	$0.825829\pi$
$410$		0			0
$411$	1041.94	−	2234.47i	0.125049	−	0.268171i
$412$		0			0
$413$	5.10236	+	74.2406i	0.000607919	+	0.00884538i
$414$		0			0
$415$	−6633.33	+	11489.3i	−0.784620	+	1.35900i
$416$		0			0
$417$	−1894.08	+	4061.90i	−0.222430	+	0.477007i
$418$		0			0
$419$	−3204.64	+	5550.60i	−0.373644	+	0.647171i	−0.990123	−	0.140201i	$-0.955225\pi$
$419$	−3204.64	+	5550.60i	−0.373644	+	0.647171i	0.616479	+	0.787371i	$0.288559\pi$
$420$		0			0
$421$	5420.73	+	9388.98i	0.627530	+	1.08691i	0.988046	+	0.154161i	$0.0492675\pi$
$421$	5420.73	+	9388.98i	0.627530	+	1.08691i	−0.360515	+	0.932753i	$0.617399\pi$
$422$		0			0
$423$	−9908.96	+	1747.29i	−1.13898	+	0.200841i
$424$		0			0
$425$	1896.91			0.216502
$426$		0			0
$427$	−14408.3	+	990.247i	−1.63295	+	0.112228i
$428$		0			0
$429$	8256.15	−	5781.06i	0.929162	−	0.650611i
$430$		0			0
$431$	−5999.82	+	3464.00i	−0.670537	+	0.387135i	−0.796280	−	0.604928i	$-0.793202\pi$
$431$	−5999.82	+	3464.00i	−0.670537	+	0.387135i	0.125743	+	0.992063i	$0.459868\pi$
$432$		0			0
$433$			10405.0i			1.15481i	0.816457	+	0.577406i	$0.195935\pi$
$433$			10405.0i			1.15481i	−0.816457	+	0.577406i	$0.804065\pi$
$434$		0			0
$435$	−5034.34	+	10796.3i	−0.554892	+	1.18998i
$436$		0			0
$437$	−288.710			−0.0316038
$438$		0			0
$439$			12717.9i			1.38267i	0.722533	+	0.691337i	$0.242978\pi$
$439$			12717.9i			1.38267i	−0.722533	+	0.691337i	$0.757022\pi$
$440$		0			0
$441$	8814.52	−	2840.83i	0.951790	−	0.306752i
$442$		0			0
$443$		−	1161.09i		−	0.124526i	−0.998060	−	0.0622631i	$-0.980168\pi$
$443$		−	1161.09i		−	0.124526i	0.998060	−	0.0622631i	$-0.0198318\pi$
$444$		0			0
$445$	5543.86			0.590571
$446$		0			0
$447$	1520.54	+	2171.54i	0.160893	+	0.229778i
$448$		0			0
$449$		−	10066.4i		−	1.05804i	−0.848609	−	0.529021i	$-0.822559\pi$
$449$		−	10066.4i		−	1.05804i	0.848609	−	0.529021i	$-0.177441\pi$
$450$		0			0
$451$	6895.67	−	3981.22i	0.719965	−	0.415672i
$452$		0			0
$453$	2255.97	+	1051.97i	0.233984	+	0.109107i
$454$		0			0
$455$	8895.84	−	611.388i	0.916579	−	0.0629940i
$456$		0			0
$457$	−8687.04			−0.889197			−0.444598	−	0.895730i	$-0.646654\pi$
$457$	−8687.04			−0.889197			−0.444598	+	0.895730i	$0.646654\pi$
$458$		0			0
$459$	4064.70	−	4064.78i	0.413342	−	0.413350i
$460$		0			0
$461$	1569.09	+	2717.75i	0.158525	+	0.274573i	0.934337	−	0.356391i	$-0.115993\pi$
$461$	1569.09	+	2717.75i	0.158525	+	0.274573i	−0.775812	+	0.630964i	$0.782660\pi$
$462$		0			0
$463$	7155.71	−	12394.0i	0.718259	−	1.24406i	−0.243430	−	0.969918i	$-0.578273\pi$
$463$	7155.71	−	12394.0i	0.718259	−	1.24406i	0.961689	−	0.274142i	$-0.0883939\pi$
$464$		0			0
$465$	−10481.9	−	14969.6i	−1.04535	−	1.49290i
$466$		0			0
$467$	−4129.97	+	7153.32i	−0.409234	+	0.708814i	−0.994804	−	0.101807i	$-0.967537\pi$
$467$	−4129.97	+	7153.32i	−0.409234	+	0.708814i	0.585570	+	0.810622i	$0.300871\pi$
$468$		0			0
$469$	−558.467	−	8125.83i	−0.0549842	−	0.800034i
$470$		0			0
$471$	−4299.82	+	376.200i	−0.420648	+	0.0368033i
$472$		0			0
$473$		−	2451.70i		−	0.238329i
$474$		0			0
$475$	5037.01	−	2908.12i	0.486555	−	0.280913i
$476$		0			0
$477$	−12887.9	+	10814.4i	−1.23710	+	1.03807i
$478$		0			0
$479$	−7094.66	+	12288.3i	−0.676750	+	1.17217i	0.299203	+	0.954189i	$0.403279\pi$
$479$	−7094.66	+	12288.3i	−0.676750	+	1.17217i	−0.975954	+	0.217977i	$0.930054\pi$
$480$		0			0
$481$	12197.9	−	7042.48i	1.15629	−	0.667587i
$482$		0			0
$483$	172.033	−	138.971i	0.0162066	−	0.0130919i
$484$		0			0
$485$	−3462.56	−	1999.11i	−0.324179	−	0.187165i
$486$		0			0
$487$	−1994.11	−	3453.90i	−0.185548	−	0.321379i	0.758213	−	0.652007i	$-0.226073\pi$
$487$	−1994.11	−	3453.90i	−0.185548	−	0.321379i	−0.943761	+	0.330628i	$0.892739\pi$
$488$		0			0
$489$	−7201.23	−	3357.96i	−0.665953	−	0.310536i
$490$		0			0
$491$	−6900.79	−	3984.18i	−0.634274	−	0.366198i	0.148131	−	0.988968i	$-0.452674\pi$
$491$	−6900.79	−	3984.18i	−0.634274	−	0.366198i	−0.782405	+	0.622769i	$0.786007\pi$
$492$		0			0
$493$	6215.48	+	3588.51i	0.567811	+	0.327826i
$494$		0			0
$495$	3235.69	+	18349.8i	0.293805	+	1.66618i
$496$		0			0
$497$	14785.4	−	1016.16i	1.33444	−	0.0917126i
$498$		0			0
$499$	−9884.84	−	17121.1i	−0.886786	−	1.53596i	−0.843652	−	0.536890i	$-0.819599\pi$
$499$	−9884.84	−	17121.1i	−0.886786	−	1.53596i	−0.0431340	−	0.999069i	$-0.513734\pi$
$500$		0			0
$501$	−16187.4	−	7548.26i	−1.44352	−	0.673117i
$502$		0			0
$503$	−20456.0			−1.81330			−0.906650	−	0.421884i	$-0.861369\pi$
$503$	−20456.0			−1.81330			−0.906650	+	0.421884i	$0.861369\pi$
$504$		0			0
$505$	−10851.1			−0.956173
$506$		0			0
$507$	−3591.34	+	2514.70i	−0.314590	+	0.220280i
$508$		0			0
$509$	−3775.12	−	6538.70i	−0.328741	−	0.569397i	0.653521	−	0.756908i	$-0.273291\pi$
$509$	−3775.12	−	6538.70i	−0.328741	−	0.569397i	−0.982262	+	0.187512i	$0.939958\pi$
$510$		0			0
$511$	−5114.57	−	7602.22i	−0.442769	−	0.658126i
$512$		0			0
$513$	4561.67	−	17025.1i	0.392598	−	1.46525i
$514$		0			0
$515$	−17040.5	−	9838.31i	−1.45804	−	0.841801i
$516$		0			0
$517$	−17017.1	−	9824.85i	−1.44761	−	0.835776i
$518$		0			0
$519$	−332.717	−	3802.82i	−0.0281400	−	0.321629i
$520$		0			0
$521$	4820.98	+	8350.18i	0.405395	+	0.702165i	0.994367	−	0.105988i	$-0.0338006\pi$
$521$	4820.98	+	8350.18i	0.405395	+	0.702165i	−0.588972	+	0.808153i	$0.700467\pi$
$522$		0			0
$523$	−5146.99	−	2971.61i	−0.430329	−	0.248450i	0.269158	−	0.963096i	$-0.413255\pi$
$523$	−5146.99	−	2971.61i	−0.430329	−	0.248450i	−0.699487	+	0.714646i	$0.746588\pi$
$524$		0			0
$525$	−1601.57	+	4157.44i	−0.133140	+	0.345610i
$526$		0			0
$527$	−9535.06	+	5505.07i	−0.788147	+	0.455037i
$528$		0			0
$529$	−6080.86	+	10532.4i	−0.499783	+	0.865650i
$530$		0			0
$531$	−106.840	+	18.8394i	−0.00873153	+	0.00153966i
$532$		0			0
$533$	4810.87	−	2777.56i	0.390960	−	0.225721i
$534$		0			0
$535$			21601.4i			1.74562i
$536$		0			0
$537$	9861.23	+	14083.2i	0.792446	+	1.13172i
$538$		0			0
$539$	16752.6	+	6815.06i	1.33875	+	0.544611i
$540$		0			0
$541$	3335.68	−	5777.58i	0.265087	−	0.459145i	−0.702499	−	0.711685i	$-0.747933\pi$
$541$	3335.68	−	5777.58i	0.265087	−	0.459145i	0.967587	+	0.252540i	$0.0812658\pi$
$542$		0			0
$543$	14966.3	−	1309.43i	1.18281	−	0.103486i
$544$		0			0
$545$	7344.10	−	12720.4i	0.577223	−	0.999780i
$546$		0			0
$547$	−9537.65	−	16519.7i	−0.745522	−	1.29128i	−0.949951	−	0.312400i	$-0.898867\pi$
$547$	−9537.65	−	16519.7i	−0.745522	−	1.29128i	0.204429	−	0.978881i	$-0.434466\pi$
$548$		0			0
$549$	−3656.29	−	20735.0i	−0.284238	−	1.61193i
$550$		0			0
$551$	22005.9			1.70142
$552$		0			0
$553$	178.062	+	2590.85i	0.0136925	+	0.199230i
$554$		0			0
$555$	2269.52	+	25939.7i	0.173578	+	1.98393i
$556$		0			0
$557$	−9248.44	+	5339.59i	−0.703535	+	0.406186i	−0.808663	−	0.588273i	$-0.799808\pi$
$557$	−9248.44	+	5339.59i	−0.703535	+	0.406186i	0.105128	+	0.994459i	$0.466475\pi$
$558$		0			0
$559$		−	1710.47i		−	0.129419i
$560$		0			0
$561$	11183.3	−	978.451i	0.841640	−	0.0736368i
$562$		0			0
$563$	8144.91			0.609711			0.304855	−	0.952399i	$-0.401392\pi$
$563$	8144.91			0.609711			0.304855	+	0.952399i	$0.401392\pi$
$564$		0			0
$565$		−	17695.9i		−	1.31765i
$566$		0			0
$567$	5476.90	+	12340.5i	0.405658	+	0.914025i
$568$		0			0
$569$		−	1105.44i		−	0.0814456i	−0.999170	−	0.0407228i	$-0.987034\pi$
$569$		−	1105.44i		−	0.0814456i	0.999170	−	0.0407228i	$-0.0129661\pi$
$570$		0			0
$571$	48.5292			0.00355671			0.00177836	−	0.999998i	$-0.499434\pi$
$571$	48.5292			0.00355671			0.00177836	+	0.999998i	$0.499434\pi$
$572$		0			0
$573$	−22892.5	+	2002.91i	−1.66902	+	0.146026i
$574$		0			0
$575$			106.391i			0.00771623i
$576$		0			0
$577$	21892.4	−	12639.6i	1.57954	−	0.911946i	0.584613	−	0.811312i	$-0.301246\pi$
$577$	21892.4	−	12639.6i	1.57954	−	0.911946i	0.994924	−	0.100633i	$-0.0320869\pi$
$578$		0			0
$579$	1931.14	+	22072.2i	0.138610	+	1.58426i
$580$		0			0
$581$	−15576.1	+	10479.2i	−1.11223	+	0.748278i
$582$		0			0
$583$	−32855.7			−2.33404
$584$		0			0
$585$	2257.43	+	12802.0i	0.159544	+	0.904783i
$586$		0			0
$587$	−7182.29	−	12440.1i	−0.505016	−	0.874714i	−0.999983	−	0.00580216i	$-0.998153\pi$
$587$	−7182.29	−	12440.1i	−0.505016	−	0.874714i	0.494967	−	0.868912i	$-0.335180\pi$
$588$		0			0
$589$	−16879.5	+	29236.1i	−1.18083	+	2.04525i
$590$		0			0
$591$	−843.870	+	73.8319i	−0.0587346	+	0.00513881i
$592$		0			0
$593$	5430.08	−	9405.18i	0.376032	−	0.651306i	−0.614449	−	0.788956i	$-0.710622\pi$
$593$	5430.08	−	9405.18i	0.376032	−	0.651306i	0.990481	+	0.137650i	$0.0439551\pi$
$594$		0			0
$595$	8921.34	+	4364.42i	0.614688	+	0.300712i
$596$		0			0
$597$	−822.595	−	1174.78i	−0.0563929	−	0.0805368i
$598$		0			0
$599$		−	1627.66i		−	0.111026i	−0.998458	−	0.0555129i	$-0.982321\pi$
$599$		−	1627.66i		−	0.111026i	0.998458	−	0.0555129i	$-0.0176794\pi$
$600$		0			0
$601$	−554.089	+	319.903i	−0.0376069	+	0.0217124i	−0.518686	−	0.854965i	$-0.673578\pi$
$601$	−554.089	+	319.903i	−0.0376069	+	0.0217124i	0.481079	+	0.876677i	$0.340245\pi$
$602$		0			0
$603$	11693.9	−	2062.03i	0.789738	−	0.139257i
$604$		0			0
$605$	−9483.94	+	16426.7i	−0.637318	+	1.10387i
$606$		0			0
$607$	−23114.4	+	13345.1i	−1.54561	+	0.892357i	−0.547138	+	0.837042i	$0.684283\pi$
$607$	−23114.4	+	13345.1i	−1.54561	+	0.892357i	−0.998469	+	0.0553145i	$0.982384\pi$
$608$		0			0
$609$	−13112.7	+	10592.6i	−0.872499	+	0.704818i
$610$		0			0
$611$	−11872.3	−	6854.46i	−0.786090	−	0.453849i
$612$		0			0
$613$	−2906.29	−	5033.84i	−0.191491	−	0.331672i	0.754254	−	0.656583i	$-0.227999\pi$
$613$	−2906.29	−	5033.84i	−0.191491	−	0.331672i	−0.945744	+	0.324911i	$0.894666\pi$
$614$		0			0
$615$	895.100	+	10230.6i	0.0586893	+	0.670796i
$616$		0			0
$617$	9804.86	+	5660.84i	0.639755	+	0.369363i	0.784520	−	0.620103i	$-0.212909\pi$
$617$	9804.86	+	5660.84i	0.639755	+	0.369363i	−0.144765	+	0.989466i	$0.546243\pi$
$618$		0			0
$619$	7044.46	+	4067.12i	0.457416	+	0.264089i	0.710957	−	0.703235i	$-0.248262\pi$
$619$	7044.46	+	4067.12i	0.457416	+	0.264089i	−0.253541	+	0.967325i	$0.581595\pi$
$620$		0			0
$621$	227.981	+	227.976i	0.0147320	+	0.0147317i
$622$		0			0
$623$	7046.81	+	3447.38i	0.453170	+	0.221696i
$624$		0			0
$625$	9634.34	+	16687.2i	0.616598	+	1.06798i
$626$		0			0
$627$	28195.9	−	19743.1i	1.79591	−	1.25752i
$628$		0			0
$629$	15688.0			0.994471
$630$		0			0
$631$	−27693.9			−1.74719			−0.873596	−	0.486651i	$-0.838218\pi$
$631$	−27693.9			−1.74719			−0.873596	+	0.486651i	$0.838218\pi$
$632$		0			0
$633$	−12527.6	−	5841.68i	−0.786617	−	0.366802i
$634$		0			0
$635$	−1406.84	−	2436.72i	−0.0879194	−	0.152281i
$636$		0			0
$637$	11687.7	+	4754.63i	0.726976	+	0.295738i
$638$		0			0
$639$	3751.98	+	21277.7i	0.232279	+	1.31727i
$640$		0			0
$641$	927.855	+	535.697i	0.0571732	+	0.0330090i	0.528314	−	0.849049i	$-0.322824\pi$
$641$	927.855	+	535.697i	0.0571732	+	0.0330090i	−0.471141	+	0.882058i	$0.656158\pi$
$642$		0			0
$643$	−14951.2	−	8632.07i	−0.916978	−	0.529418i	−0.0343083	−	0.999411i	$-0.510923\pi$
$643$	−14951.2	−	8632.07i	−0.916978	−	0.529418i	−0.882670	+	0.469994i	$0.844256\pi$
$644$		0			0
$645$	2865.87	+	1336.37i	0.174951	+	0.0815805i
$646$		0			0
$647$	−1072.86	−	1858.25i	−0.0651910	−	0.112914i	0.831588	−	0.555393i	$-0.187432\pi$
$647$	−1072.86	−	1858.25i	−0.0651910	−	0.112914i	−0.896779	+	0.442479i	$0.854099\pi$
$648$		0			0
$649$	−183.481	−	105.933i	−0.0110975	−	0.00640712i
$650$		0			0
$651$	−4014.90	−	25545.9i	−0.241715	−	1.53797i
$652$		0			0
$653$	5521.01	−	3187.56i	0.330863	−	0.191024i	−0.325361	−	0.945590i	$-0.605486\pi$
$653$	5521.01	−	3187.56i	0.330863	−	0.191024i	0.656224	+	0.754566i	$0.272152\pi$
$654$		0			0
$655$	−656.145	+	1136.48i	−0.0391415	+	0.0677951i
$656$		0			0
$657$	10232.6	−	8586.27i	0.607627	−	0.509866i
$658$		0			0
$659$	−20870.4	+	12049.5i	−1.23368	+	0.712266i	−0.967795	−	0.251738i	$-0.918998\pi$
$659$	−20870.4	+	12049.5i	−1.23368	+	0.712266i	−0.265886	+	0.964004i	$0.585665\pi$
$660$		0			0
$661$		−	23279.8i		−	1.36986i	−0.728608	−	0.684931i	$-0.759832\pi$
$661$		−	23279.8i		−	1.36986i	0.728608	−	0.684931i	$-0.240168\pi$
$662$		0			0
$663$	7802.22	−	682.632i	0.457033	−	0.0399868i
$664$		0			0
$665$	30380.6	−	2087.97i	1.77159	−	0.121757i
$666$		0			0
$667$	−201.268	+	348.606i	−0.0116838	+	0.0202370i
$668$		0			0
$669$	6620.07	+	9454.37i	0.382581	+	0.546379i
$670$		0			0
$671$	20559.0	−	35609.3i	1.18282	−	2.04871i
$672$		0			0
$673$	3779.47	+	6546.24i	0.216475	+	0.374946i	0.953728	−	0.300671i	$-0.0972106\pi$
$673$	3779.47	+	6546.24i	0.216475	+	0.374946i	−0.737253	+	0.675617i	$0.763877\pi$
$674$		0			0
$675$	−6273.85	−	1681.01i	−0.357749	−	0.0958548i
$676$		0			0
$677$	−1824.67			−0.103586			−0.0517931	−	0.998658i	$-0.516494\pi$
$677$	−1824.67			−0.103586			−0.0517931	+	0.998658i	$0.516494\pi$
$678$		0			0
$679$	−3158.15	−	4694.23i	−0.178496	−	0.265313i
$680$		0			0
$681$	16536.1	+	7710.83i	0.930490	+	0.433891i
$682$		0			0
$683$	30780.2	−	17771.0i	1.72441	−	0.995589i	0.815292	−	0.579051i	$-0.196577\pi$
$683$	30780.2	−	17771.0i	1.72441	−	0.995589i	0.909118	−	0.416538i	$-0.136757\pi$
$684$		0			0
$685$			6209.98i			0.346381i
$686$		0			0
$687$	14996.8	+	21417.5i	0.832842	+	1.18941i
$688$		0			0
$689$	−22922.3			−1.26745
$690$		0			0
$691$		−	5482.60i		−	0.301835i	−0.988546	−	0.150917i	$-0.951777\pi$
$691$		−	5482.60i		−	0.301835i	0.988546	−	0.150917i	$-0.0482228\pi$
$692$		0			0
$693$	−7297.69	+	25336.5i	−0.400023	+	1.38882i
$694$		0			0
$695$		−	11288.7i		−	0.616123i
$696$		0			0
$697$	6187.36			0.336246
$698$		0			0
$699$	−8939.48	+	19171.0i	−0.483723	+	1.03736i
$700$		0			0
$701$		−	27379.6i		−	1.47519i	−0.675241	−	0.737597i	$-0.735960\pi$
$701$		−	27379.6i		−	1.47519i	0.675241	−	0.737597i	$-0.264040\pi$
$702$		0			0
$703$	41657.6	−	24051.1i	2.23492	−	1.29033i
$704$		0			0
$705$	20760.2	−	14536.6i	1.10904	−	0.776567i
$706$		0			0
$707$	−13792.9	−	6747.62i	−0.733711	−	0.358940i
$708$		0			0
$709$	12791.0			0.677539			0.338770	−	0.940869i	$-0.389989\pi$
$709$	12791.0			0.677539			0.338770	+	0.940869i	$0.389989\pi$
$710$		0			0
$711$	−3728.49	+	657.458i	−0.196666	+	0.0346788i
$712$		0			0
$713$	−308.761	−	534.791i	−0.0162177	−	0.0280899i
$714$		0			0
$715$	−12693.3	+	21985.5i	−0.663922	+	1.14995i
$716$		0			0
$717$	9030.07	−	19365.2i	0.470341	−	1.00866i
$718$		0			0
$719$	17988.4	−	31156.8i	0.933038	−	1.61607i	0.154943	−	0.987923i	$-0.450481\pi$
$719$	17988.4	−	31156.8i	0.933038	−	1.61607i	0.778096	−	0.628146i	$-0.216186\pi$
$720$		0			0
$721$	−15542.3	−	23101.9i	−0.802810	−	1.19329i
$722$		0			0
$723$	10936.7	−	23454.0i	0.562571	−	1.20645i
$724$		0			0
$725$		−	8109.34i		−	0.415411i
$726$		0			0
$727$	1802.68	−	1040.78i	0.0919636	−	0.0530952i	−0.453313	−	0.891351i	$-0.649758\pi$
$727$	1802.68	−	1040.78i	0.0919636	−	0.0530952i	0.545277	+	0.838256i	$0.316425\pi$
$728$		0			0
$729$	−17045.8	+	9841.84i	−0.866015	+	0.500017i
$730$		0			0
$731$	952.572	−	1649.90i	0.0481972	−	0.0834800i
$732$		0			0
$733$	−2496.76	+	1441.51i	−0.125812	+	0.0726375i	−0.561585	−	0.827419i	$-0.689808\pi$
$733$	−2496.76	+	1441.51i	−0.125812	+	0.0726375i	0.435773	+	0.900056i	$0.356475\pi$
$734$		0			0
$735$	−17097.8	+	15867.9i	−0.858044	+	0.796322i
$736$		0			0
$737$	20082.5	+	11594.6i	1.00373	+	0.579503i
$738$		0			0
$739$	12937.9	+	22409.1i	0.644017	+	1.11547i	0.984528	+	0.175230i	$0.0560669\pi$
$739$	12937.9	+	22409.1i	0.644017	+	1.11547i	−0.340510	+	0.940241i	$0.610600\pi$
$740$		0			0
$741$	19671.3	−	13774.1i	0.975228	−	0.682867i
$742$		0			0
$743$	29937.6	+	17284.5i	1.47820	+	0.853441i	0.999696	−	0.0246423i	$-0.00784468\pi$
$743$	29937.6	+	17284.5i	1.47820	+	0.853441i	0.478507	+	0.878084i	$0.341178\pi$
$744$		0			0
$745$	−5782.66	−	3338.62i	−0.284376	−	0.164185i
$746$		0			0
$747$	−17592.3	−	20965.4i	−0.861671	−	1.02689i
$748$		0			0
$749$	−13432.5	+	27457.5i	−0.655293	+	1.33949i
$750$		0			0
$751$	−6337.57	−	10977.0i	−0.307938	−	0.533364i	0.669973	−	0.742385i	$-0.266306\pi$
$751$	−6337.57	−	10977.0i	−0.307938	−	0.533364i	−0.977911	+	0.209021i	$0.932972\pi$
$752$		0			0
$753$	1575.10	+	18002.8i	0.0762283	+	0.871260i
$754$		0			0
$755$	−6269.72			−0.302223
$756$		0			0
$757$	−36014.0			−1.72913			−0.864565	−	0.502522i	$-0.832406\pi$
$757$	−36014.0			−1.72913			−0.864565	+	0.502522i	$0.832406\pi$
$758$		0			0
$759$	54.8782	+	627.236i	0.00262444	+	0.0299964i
$760$		0			0
$761$	7697.90	+	13333.2i	0.366687	+	0.635120i	0.989045	−	0.147612i	$-0.0471588\pi$
$761$	7697.90	+	13333.2i	0.366687	+	0.635120i	−0.622359	+	0.782732i	$0.713825\pi$
$762$		0			0
$763$	17245.1	−	11602.0i	0.818236	−	0.550487i
$764$		0			0
$765$	−4952.03	+	13605.9i	−0.234041	+	0.643035i
$766$		0			0
$767$	−128.008	−	73.9056i	−0.00602622	−	0.00347924i
$768$		0			0
$769$	4149.23	+	2395.56i	0.194571	+	0.112336i	0.594121	−	0.804376i	$-0.297500\pi$
$769$	4149.23	+	2395.56i	0.194571	+	0.112336i	−0.399550	+	0.916712i	$0.630833\pi$
$770$		0			0
$771$	−8841.86	+	6191.18i	−0.413011	+	0.289196i
$772$		0			0
$773$	−6124.33	−	10607.7i	−0.284964	−	0.493572i	0.687637	−	0.726055i	$-0.258648\pi$
$773$	−6124.33	−	10607.7i	−0.284964	−	0.493572i	−0.972600	+	0.232483i	$0.925315\pi$
$774$		0			0
$775$	10773.7	+	6220.20i	0.499358	+	0.288305i
$776$		0			0
$777$	−13245.5	+	34383.3i	−0.611557	+	1.58751i
$778$		0			0
$779$	16429.8	−	9485.75i	0.755659	−	0.436280i
$780$		0			0
$781$	−21097.1	+	36541.3i	−0.966599	+	1.67420i
$782$		0			0
$783$	−17377.1	−	17376.7i	−0.793111	−	0.793095i
$784$		0			0
$785$	9415.17	−	5435.85i	0.428079	−	0.247152i
$786$		0			0
$787$		−	9170.36i		−	0.415360i	−0.978197	−	0.207680i	$-0.933409\pi$
$787$		−	9170.36i		−	0.415360i	0.978197	−	0.207680i	$-0.0665912\pi$
$788$		0			0
$789$	3306.35	−	7090.54i	0.149188	−	0.319937i
$790$		0			0
$791$	11004.0	−	22493.3i	0.494636	−	1.01109i
$792$		0			0
$793$	14343.3	−	24843.4i	0.642303	−	1.11250i
$794$		0			0
$795$	17908.9	−	38406.1i	0.798948	−	1.71336i
$796$		0			0
$797$	−7564.68	+	13102.4i	−0.336204	+	0.582323i	−0.983715	−	0.179733i	$-0.942477\pi$
$797$	−7564.68	+	13102.4i	−0.336204	+	0.582323i	0.647511	+	0.762056i	$0.275810\pi$
$798$		0			0
$799$	−7634.59	−	13223.5i	−0.338038	−	0.585499i
$800$		0			0
$801$	−3911.53	+	10747.1i	−0.172543	+	0.474068i
$802$		0			0
$803$	26086.3			1.14641
$804$		0			0
$805$	−244.786	+	500.369i	−0.0107175	+	0.0219077i
$806$		0			0
$807$	20681.2	−	14481.2i	0.902120	−	0.631676i
$808$		0			0
$809$	−30049.2	+	17348.9i	−1.30590	+	0.753962i	−0.981409	−	0.191926i	$-0.938527\pi$
$809$	−30049.2	+	17348.9i	−1.30590	+	0.753962i	−0.324491	+	0.945889i	$0.605193\pi$
$810$		0			0
$811$			2279.77i			0.0987095i	0.998781	+	0.0493548i	$0.0157165\pi$
$811$			2279.77i			0.0987095i	−0.998781	+	0.0493548i	$0.984284\pi$
$812$		0			0
$813$	−8728.46	+	18718.4i	−0.376532	+	0.807482i
$814$		0			0
$815$	20013.5			0.860173
$816$		0			0
$817$		−	5841.49i		−	0.250144i
$818$		0			0
$819$	−5091.35	+	17676.4i	−0.217223	+	0.754168i
$820$		0			0
$821$		−	32163.5i		−	1.36725i	−0.729832	−	0.683626i	$-0.760402\pi$
$821$		−	32163.5i		−	1.36725i	0.729832	−	0.683626i	$-0.239598\pi$
$822$		0			0
$823$	19456.6			0.824077			0.412039	−	0.911166i	$-0.364817\pi$
$823$	19456.6			0.824077			0.412039	+	0.911166i	$0.364817\pi$
$824$		0			0
$825$	−7275.48	−	10390.4i	−0.307030	−	0.438481i
$826$		0			0
$827$			3379.21i			0.142088i	0.997473	+	0.0710440i	$0.0226331\pi$
$827$			3379.21i			0.142088i	−0.997473	+	0.0710440i	$0.977367\pi$
$828$		0			0
$829$	−29193.5	+	16854.9i	−1.22308	+	0.706145i	−0.965573	−	0.260132i	$-0.916234\pi$
$829$	−29193.5	+	16854.9i	−1.22308	+	0.706145i	−0.257505	+	0.966277i	$0.582901\pi$
$830$		0			0
$831$	−5561.23	−	2593.22i	−0.232150	−	0.108252i
$832$		0			0
$833$	8625.97	+	11095.2i	0.358790	+	0.461497i
$834$		0			0
$835$	44987.7			1.86451
$836$		0			0
$837$	36414.9	−	9757.72i	1.50380	−	0.402958i
$838$		0			0
$839$	7164.60	+	12409.5i	0.294815	+	0.510634i	0.974942	−	0.222460i	$-0.0714087\pi$
$839$	7164.60	+	12409.5i	0.294815	+	0.510634i	−0.680127	+	0.733094i	$0.738075\pi$
$840$		0			0
$841$	3146.47	−	5449.85i	0.129012	−	0.223455i
$842$		0			0
$843$	−15155.1	−	21643.6i	−0.619183	−	0.884278i
$844$		0			0
$845$	5521.48	−	9563.48i	0.224786	−	0.389342i
$846$		0			0
$847$	−22269.8	+	14982.5i	−0.903422	+	0.607798i
$848$		0			0
$849$	−21684.3	+	1897.21i	−0.876566	+	0.0766925i
$850$		0			0
$851$			879.890i			0.0354433i
$852$		0			0
$853$	−1244.42	+	718.465i	−0.0499508	+	0.0288391i	−0.524767	−	0.851246i	$-0.675848\pi$
$853$	−1244.42	+	718.465i	−0.0499508	+	0.0288391i	0.474817	+	0.880085i	$0.342514\pi$
$854$		0			0
$855$	7709.43	+	43720.7i	0.308371	+	1.74879i
$856$		0			0
$857$	−13531.0	+	23436.4i	−0.539336	+	0.934157i	0.459604	+	0.888124i	$0.347991\pi$
$857$	−13531.0	+	23436.4i	−0.539336	+	0.934157i	−0.998940	+	0.0460329i	$0.985342\pi$
$858$		0			0
$859$	1138.87	−	657.528i	0.0452361	−	0.0261171i	−0.477211	−	0.878789i	$-0.658352\pi$
$859$	1138.87	−	657.528i	0.0452361	−	0.0261171i	0.522447	+	0.852671i	$0.325019\pi$
$860$		0			0
$861$	−5224.03	+	13560.8i	−0.206776	+	0.536760i
$862$		0			0
$863$	2494.83	+	1440.39i	0.0984068	+	0.0568152i	0.548396	−	0.836219i	$-0.315239\pi$
$863$	2494.83	+	1440.39i	0.0984068	+	0.0568152i	−0.449989	+	0.893034i	$0.648572\pi$
$864$		0			0
$865$	4807.55	+	8326.92i	0.188973	+	0.327311i
$866$		0			0
$867$	−15230.8	−	7102.17i	−0.596614	−	0.278203i
$868$		0			0
$869$	−6403.11	−	3696.84i	−0.249955	−	0.144311i
$870$		0			0
$871$	14010.9	+	8089.17i	0.545051	+	0.314685i
$872$		0			0
$873$	6318.42	−	5301.86i	0.244956	−	0.205545i
$874$		0			0
$875$	1308.05	+	19032.4i	0.0505372	+	0.735329i
$876$		0			0
$877$	14102.1	+	24425.5i	0.542980	+	0.940470i	0.998731	+	0.0503622i	$0.0160376\pi$
$877$	14102.1	+	24425.5i	0.542980	+	0.940470i	−0.455751	+	0.890108i	$0.650629\pi$
$878$		0			0
$879$	28835.4	+	13446.1i	1.10648	+	0.515955i
$880$		0			0
$881$	−14864.0			−0.568423			−0.284211	−	0.958762i	$-0.591732\pi$
$881$	−14864.0			−0.568423			−0.284211	+	0.958762i	$0.591732\pi$
$882$		0			0
$883$	−9762.51			−0.372066			−0.186033	−	0.982543i	$-0.559563\pi$
$883$	−9762.51			−0.372066			−0.186033	+	0.982543i	$0.559563\pi$
$884$		0			0
$885$	223.839	−	156.735i	0.00850201	−	0.00595321i
$886$		0			0
$887$	−3520.54	−	6097.76i	−0.133267	−	0.230826i	0.791667	−	0.610953i	$-0.209214\pi$
$887$	−3520.54	−	6097.76i	−0.133267	−	0.230826i	−0.924934	+	0.380127i	$0.875880\pi$
$888$		0			0
$889$	−272.995	−	3972.15i	−0.0102992	−	0.149855i
$890$		0			0
$891$	−37854.9	−	6674.33i	−1.42333	−	0.250952i
$892$		0			0
$893$	−40545.5	−	23408.9i	−1.51938	−	0.877212i
$894$		0			0
$895$	−37502.5	−	21652.1i	−1.40064	−	0.808658i
$896$		0			0
$897$	38.2866	+	437.601i	0.00142514	+	0.0162888i
$898$		0			0
$899$	23534.3	+	40762.6i	0.873096	+	1.51225i
$900$		0			0
$901$	−22110.6	−	12765.6i	−0.817550	−	0.472013i
$902$		0			0
$903$	2811.82	+	3480.77i	0.103623	+	0.128275i
$904$		0			0
$905$	−32771.1	+	18920.4i	−1.20370	+	0.694957i
$906$		0			0
$907$	−14658.5	+	25389.3i	−0.536635	+	0.929478i	0.462448	+	0.886647i	$0.346971\pi$
$907$	−14658.5	+	25389.3i	−0.536635	+	0.929478i	−0.999082	+	0.0428319i	$0.986362\pi$
$908$		0			0
$909$	7656.10	−	21035.4i	0.279358	−	0.767547i
$910$		0			0
$911$	−38285.3	+	22104.0i	−1.39237	+	0.803885i	−0.993577	−	0.113156i	$-0.963904\pi$
$911$	−38285.3	+	22104.0i	−1.39237	+	0.803885i	−0.398793	+	0.917041i	$0.630571\pi$
$912$		0			0
$913$		−	53447.9i		−	1.93742i
$914$		0			0
$915$	30418.6	+	43441.9i	1.09902	+	1.56956i
$916$		0			0
$917$	−1540.73	+	1036.56i	−0.0554846	+	0.0373286i
$918$		0			0
$919$	−17491.2	+	30295.7i	−0.627837	+	1.08745i	0.360148	+	0.932895i	$0.382726\pi$
$919$	−17491.2	+	30295.7i	−0.627837	+	1.08745i	−0.987985	+	0.154551i	$0.950607\pi$
$920$		0			0
$921$	29567.4	−	2586.91i	1.05785	−	0.0925534i
$922$		0			0
$923$	−14718.7	+	25493.6i	−0.524889	+	0.909135i
$924$		0			0
$925$	−8862.98	−	15351.1i	−0.315041	−	0.545667i
$926$		0			0
$927$	31095.1	−	26092.2i	1.10172	−	0.924468i
$928$		0			0
$929$	4809.62			0.169858			0.0849292	−	0.996387i	$-0.472934\pi$
$929$	4809.62			0.169858			0.0849292	+	0.996387i	$0.472934\pi$
$930$		0			0
$931$	39915.2	+	16237.7i	1.40512	+	0.571611i
$932$		0			0
$933$	−1078.82	−	12330.5i	−0.0378554	−	0.432673i
$934$		0			0
$935$	−24487.8	+	14138.0i	−0.856509	+	0.494506i
$936$		0			0
$937$		−	4209.56i		−	0.146767i	−0.997304	−	0.0733834i	$-0.976620\pi$
$937$		−	4209.56i		−	0.146767i	0.997304	−	0.0733834i	$-0.0233797\pi$
$938$		0			0
$939$	−41942.8	+	3669.66i	−1.45767	+	0.127534i
$940$		0			0
$941$	−4775.17			−0.165426			−0.0827131	−	0.996573i	$-0.526359\pi$
$941$	−4775.17			−0.165426			−0.0827131	+	0.996573i	$0.526359\pi$
$942$		0			0
$943$			347.029i			0.0119839i
$944$		0			0
$945$	−25638.9	−	22340.9i	−0.882574	−	0.769046i
$946$		0			0
$947$		−	55680.4i		−	1.91063i	−0.295586	−	0.955316i	$-0.595515\pi$
$947$		−	55680.4i		−	1.91063i	0.295586	−	0.955316i	$-0.404485\pi$
$948$		0			0
$949$	18199.5			0.622530
$950$		0			0
$951$	26117.8	−	2285.10i	0.890567	−	0.0779175i
$952$		0			0
$953$		−	29426.7i		−	1.00023i	−0.865958	−	0.500117i	$-0.833290\pi$
$953$		−	29426.7i		−	1.00023i	0.865958	−	0.500117i	$-0.166710\pi$
$954$		0			0
$955$	50126.9	−	28940.8i	1.69850	−	0.980630i
$956$		0			0
$957$	−4182.91	−	47809.0i	−0.141290	−	1.61489i
$958$		0			0
$959$	−3861.60	+	7893.52i	−0.130029	+	0.265792i
$960$		0			0
$961$	−42416.2			−1.42379
$962$		0			0
$963$	−41875.3	−	15241.1i	−1.40126	−	0.510007i
$964$		0			0
$965$	−27903.8	−	48330.7i	−0.930833	−	1.61225i
$966$		0			0
$967$	6991.64	−	12109.9i	0.232509	−	0.402717i	−0.726037	−	0.687656i	$-0.758640\pi$
$967$	6991.64	−	12109.9i	0.232509	−	0.402717i	0.958546	+	0.284939i	$0.0919732\pi$
$968$		0			0
$969$	26645.7	−	2331.28i	0.883367	−	0.0772875i
$970$		0			0
$971$	−21826.5	+	37804.5i	−0.721364	+	1.24944i	0.239089	+	0.970998i	$0.423151\pi$
$971$	−21826.5	+	37804.5i	−0.721364	+	1.24944i	−0.960453	+	0.278441i	$0.910182\pi$
$972$		0			0
$973$	7019.74	−	14349.1i	0.231287	−	0.472776i
$974$		0			0
$975$	−5075.85	−	7249.01i	−0.166725	−	0.238107i
$976$		0			0
$977$			33590.6i			1.09996i	0.835178	+	0.549979i	$0.185364\pi$
$977$			33590.6i			1.09996i	−0.835178	+	0.549979i	$0.814636\pi$
$978$		0			0
$979$	−19342.5	+	11167.4i	−0.631448	+	0.364567i
$980$		0			0
$981$	19477.3	+	23211.9i	0.633908	+	0.755452i
$982$		0			0
$983$	−23723.1	+	41089.7i	−0.769736	+	1.33322i	0.167969	+	0.985792i	$0.446279\pi$
$983$	−23723.1	+	41089.7i	−0.769736	+	1.33322i	−0.937706	+	0.347430i	$0.887054\pi$
$984$		0			0
$985$	1847.79	−	1066.82i	0.0597722	−	0.0345095i
$986$		0			0
$987$	35427.8	−	5567.98i	1.14253	−	0.179565i
$988$		0			0
$989$	92.5377	+	53.4267i	0.00297526	+	0.00171776i
$990$		0			0
$991$	12360.3	+	21408.6i	0.396203	+	0.686243i	0.993254	−	0.115960i	$-0.0369944\pi$
$991$	12360.3	+	21408.6i	0.396203	+	0.686243i	−0.597051	+	0.802203i	$0.703661\pi$
$992$		0			0
$993$	47.7935	+	546.261i	0.00152737	+	0.0174573i
$994$		0			0
$995$	3128.35	+	1806.15i	0.0996736	+	0.0575466i
$996$		0			0
$997$	843.007	+	486.711i	0.0267786	+	0.0154607i	0.513330	−	0.858192i	$-0.328412\pi$
$997$	843.007	+	486.711i	0.0267786	+	0.0154607i	−0.486551	+	0.873652i	$0.661745\pi$
$998$		0			0
$999$	−51886.7	−	13902.5i	−1.64327	−	0.440294i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	252.4.w.a.5.12	✓	48
3.2	odd	2		756.4.w.a.341.5		48
7.3	odd	6		252.4.bm.a.185.20	yes	48
9.2	odd	6		252.4.bm.a.173.20	yes	48
9.7	even	3		756.4.bm.a.89.5		48
21.17	even	6		756.4.bm.a.17.5		48
63.38	even	6	inner	252.4.w.a.101.12	yes	48
63.52	odd	6		756.4.w.a.521.5		48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
252.4.w.a.5.12	✓	48	1.1	even	1	trivial
252.4.w.a.101.12	yes	48	63.38	even	6	inner
252.4.bm.a.173.20	yes	48	9.2	odd	6
252.4.bm.a.185.20	yes	48	7.3	odd	6
756.4.w.a.341.5		48	3.2	odd	2
756.4.w.a.521.5		48	63.52	odd	6
756.4.bm.a.17.5		48	21.17	even	6
756.4.bm.a.89.5		48	9.7	even	3

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:	\( N \)	\(=\)	\( 252 = 2^{2} \cdot 3^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	252.w (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.452892 - 5.17638i) q^{3} +(6.54401 + 11.3346i) q^{5} +(1.26985 + 18.4767i) q^{7} +(-26.5898 + 4.68868i) q^{9} +O(q^{10})\)	\(q+(-0.452892 - 5.17638i) q^{3} +(6.54401 + 11.3346i) q^{5} +(1.26985 + 18.4767i) q^{7} +(-26.5898 + 4.68868i) q^{9} +(-45.6639 - 26.3641i) q^{11} +(-31.8581 - 18.3933i) q^{13} +(55.7082 - 39.0076i) q^{15} +(-20.4867 - 35.4840i) q^{17} +(-108.800 - 62.8157i) q^{19} +(95.0671 - 14.9412i) q^{21} +(1.99019 - 1.14903i) q^{23} +(-23.1480 + 40.0935i) q^{25} +(36.3127 + 135.515i) q^{27} +(-151.695 + 87.5813i) q^{29} -268.714i q^{31} +(-115.790 + 248.314i) q^{33} +(-201.115 + 135.305i) q^{35} +(-191.441 + 331.586i) q^{37} +(-80.7824 + 173.240i) q^{39} +(-75.5046 + 130.778i) q^{41} +(23.2485 + 40.2676i) q^{43} +(-227.148 - 270.700i) q^{45} +372.661 q^{47} +(-339.775 + 46.9253i) q^{49} +(-174.401 + 122.117i) q^{51} +(539.634 - 311.558i) q^{53} -690.107i q^{55} +(-275.883 + 591.639i) q^{57} +4.01807 q^{59} +779.812i q^{61} +(-120.396 - 485.337i) q^{63} -481.464i q^{65} -439.789 q^{67} +(-6.84917 - 9.78156i) q^{69} -800.222i q^{71} +(-428.450 + 247.366i) q^{73} +(218.023 + 101.665i) q^{75} +(429.134 - 877.196i) q^{77} +140.223 q^{79} +(685.033 - 249.342i) q^{81} +(506.825 + 877.846i) q^{83} +(268.130 - 464.416i) q^{85} +(522.056 + 745.567i) q^{87} +(211.792 - 366.834i) q^{89} +(299.392 - 611.989i) q^{91} +(-1390.97 + 121.698i) q^{93} -1644.27i q^{95} +(-264.560 + 152.744i) q^{97} +(1337.81 + 486.911i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q + 6 q^{7} + 12 q^{9}+O(q^{10}) \) 48 * q + 6 * q^7 + 12 * q^9	\( 48 q + 6 q^{7} + 12 q^{9} + 12 q^{11} - 36 q^{13} + 66 q^{15} - 72 q^{17} + 24 q^{21} + 30 q^{23} - 600 q^{25} - 396 q^{27} + 42 q^{29} + 390 q^{35} + 84 q^{37} - 840 q^{39} - 618 q^{41} - 42 q^{43} + 366 q^{45} + 396 q^{47} + 318 q^{49} - 738 q^{51} - 1620 q^{53} + 492 q^{57} + 1500 q^{59} + 672 q^{63} - 588 q^{67} - 924 q^{69} + 564 q^{75} - 2472 q^{77} + 1608 q^{79} + 2592 q^{81} - 360 q^{85} + 2640 q^{87} + 1722 q^{89} + 540 q^{91} + 660 q^{93} - 792 q^{97} - 54 q^{99}+O(q^{100}) \) 48 * q + 6 * q^7 + 12 * q^9 + 12 * q^11 - 36 * q^13 + 66 * q^15 - 72 * q^17 + 24 * q^21 + 30 * q^23 - 600 * q^25 - 396 * q^27 + 42 * q^29 + 390 * q^35 + 84 * q^37 - 840 * q^39 - 618 * q^41 - 42 * q^43 + 366 * q^45 + 396 * q^47 + 318 * q^49 - 738 * q^51 - 1620 * q^53 + 492 * q^57 + 1500 * q^59 + 672 * q^63 - 588 * q^67 - 924 * q^69 + 564 * q^75 - 2472 * q^77 + 1608 * q^79 + 2592 * q^81 - 360 * q^85 + 2640 * q^87 + 1722 * q^89 + 540 * q^91 + 660 * q^93 - 792 * q^97 - 54 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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