LMFDB - Embedded newform 252.4.bm.a.173.20

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [252,4,Mod(173,252)]

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, 1, 5]))

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

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

chi := DirichletCharacter("252.173");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 252 = 2^{2} \cdot 3^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	252.bm (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			173.20
Character	$\chi$	$=$	252.173
Dual form			252.4.bm.a.185.20

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(4.25643 + 2.98040i) q^{3} +13.0880 q^{5} +(15.3663 - 10.3381i) q^{7} +(9.23438 + 25.3718i) q^{9} +O(q^{10})$	\(q+(4.25643 + 2.98040i) q^{3} +13.0880 q^{5} +(15.3663 - 10.3381i) q^{7} +(9.23438 + 25.3718i) q^{9} -52.7281i q^{11} +(31.8581 - 18.3933i) q^{13} +(55.7082 + 39.0076i) q^{15} +(20.4867 + 35.4840i) q^{17} +(-108.800 - 62.8157i) q^{19} +(96.2174 + 1.79470i) q^{21} -2.29807i q^{23} +46.2960 q^{25} +(-36.3127 + 135.515i) q^{27} +(-151.695 - 87.5813i) q^{29} +(232.713 + 134.357i) q^{31} +(157.151 - 224.434i) q^{33} +(201.115 - 135.305i) q^{35} +(-191.441 + 331.586i) q^{37} +(190.421 + 16.6604i) q^{39} +(75.5046 + 130.778i) q^{41} +(23.2485 - 40.2676i) q^{43} +(120.860 + 332.066i) q^{45} +(186.330 + 322.734i) q^{47} +(129.249 - 317.716i) q^{49} +(-18.5565 + 212.094i) q^{51} +(-539.634 + 311.558i) q^{53} -690.107i q^{55} +(-275.883 - 591.639i) q^{57} +(2.00904 - 3.47975i) q^{59} +(675.337 - 389.906i) q^{61} +(404.193 + 294.406i) q^{63} +(416.960 - 240.732i) q^{65} +(219.894 - 380.868i) q^{67} +(6.84917 - 9.78156i) q^{69} +800.222i q^{71} +(-428.450 + 247.366i) q^{73} +(197.056 + 137.981i) q^{75} +(-545.107 - 810.239i) q^{77} +(-70.1113 - 121.436i) q^{79} +(-558.453 + 468.585i) q^{81} +(-506.825 + 877.846i) q^{83} +(268.130 + 464.416i) q^{85} +(-384.652 - 824.897i) q^{87} +(-211.792 + 366.834i) q^{89} +(299.392 - 611.989i) q^{91} +(590.089 + 1265.46i) q^{93} +(-1423.98 - 822.133i) q^{95} +(264.560 + 152.744i) q^{97} +(1337.81 - 486.911i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q + 6 q^{7} - 30 q^{9}+O(q^{10}) $ 48 * q + 6 * q^7 - 30 * q^9	$ 48 q + 6 q^{7} - 30 q^{9} + 36 q^{13} + 66 q^{15} + 72 q^{17} + 126 q^{21} + 1200 q^{25} + 396 q^{27} + 42 q^{29} - 90 q^{31} + 108 q^{33} - 390 q^{35} + 84 q^{37} + 1014 q^{39} + 618 q^{41} - 42 q^{43} - 1014 q^{45} + 198 q^{47} - 276 q^{49} + 408 q^{51} + 1620 q^{53} + 492 q^{57} + 750 q^{59} - 1314 q^{61} + 1542 q^{63} + 564 q^{65} + 294 q^{67} + 924 q^{69} - 1410 q^{75} - 2448 q^{77} - 804 q^{79} - 666 q^{81} - 360 q^{85} + 1788 q^{87} - 1722 q^{89} + 540 q^{91} + 1128 q^{93} - 2946 q^{95} + 792 q^{97} - 54 q^{99}+O(q^{100}) $ 48 * q + 6 * q^7 - 30 * q^9 + 36 * q^13 + 66 * q^15 + 72 * q^17 + 126 * q^21 + 1200 * q^25 + 396 * q^27 + 42 * q^29 - 90 * q^31 + 108 * q^33 - 390 * q^35 + 84 * q^37 + 1014 * q^39 + 618 * q^41 - 42 * q^43 - 1014 * q^45 + 198 * q^47 - 276 * q^49 + 408 * q^51 + 1620 * q^53 + 492 * q^57 + 750 * q^59 - 1314 * q^61 + 1542 * q^63 + 564 * q^65 + 294 * q^67 + 924 * q^69 - 1410 * q^75 - 2448 * q^77 - 804 * q^79 - 666 * q^81 - 360 * q^85 + 1788 * q^87 - 1722 * q^89 + 540 * q^91 + 1128 * q^93 - 2946 * q^95 + 792 * q^97 - 54 * q^99

Display 100 coefficients 10 coefficients

Character values

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

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

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
$3$	4.25643	+	2.98040i	0.819150	+	0.573579i
$3$	4.25643	+	2.98040i	0.819150	+	0.573579i
$4$		0			0
$5$	13.0880			1.17063			0.585314	−	0.810807i	$-0.300971\pi$
$5$	13.0880			1.17063			0.585314	+	0.810807i	$0.300971\pi$
$6$		0			0
$7$	15.3663	−	10.3381i	0.829705	−	0.558203i
$7$	15.3663	−	10.3381i	0.829705	−	0.558203i
$8$		0			0
$9$	9.23438	+	25.3718i	0.342014	+	0.939695i
$10$		0			0
$11$		−	52.7281i		−	1.44528i	−0.691222	−	0.722642i	$-0.742927\pi$
$11$		−	52.7281i		−	1.44528i	0.691222	−	0.722642i	$-0.257073\pi$
$12$		0			0
$13$	31.8581	−	18.3933i	0.679681	−	0.392414i	−0.120054	−	0.992767i	$-0.538307\pi$
$13$	31.8581	−	18.3933i	0.679681	−	0.392414i	0.799735	+	0.600353i	$0.204973\pi$
$14$		0			0
$15$	55.7082	+	39.0076i	0.958920	+	0.671447i
$16$		0			0
$17$	20.4867	+	35.4840i	0.292280	+	0.506244i	0.974348	−	0.225045i	$-0.0722528\pi$
$17$	20.4867	+	35.4840i	0.292280	+	0.506244i	−0.682069	+	0.731288i	$0.738919\pi$
$18$		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
$21$	96.2174	+	1.79470i	0.999826	+	0.0186493i
$22$		0			0
$23$		−	2.29807i		−	0.0208339i	−0.999946	−	0.0104170i	$-0.996684\pi$
$23$		−	2.29807i		−	0.0208339i	0.999946	−	0.0104170i	$-0.00331588\pi$
$24$		0			0
$25$	46.2960			0.370368
$26$		0			0
$27$	−36.3127	+	135.515i	−0.258829	+	0.965923i
$28$		0			0
$29$	−151.695	−	87.5813i	−0.971348	−	0.560808i	−0.0717014	−	0.997426i	$-0.522843\pi$
$29$	−151.695	−	87.5813i	−0.971348	−	0.560808i	−0.899647	+	0.436618i	$0.856176\pi$
$30$		0			0
$31$	232.713	+	134.357i	1.34827	+	0.778427i	0.988005	−	0.154421i	$-0.0493513\pi$
$31$	232.713	+	134.357i	1.34827	+	0.778427i	0.360270	+	0.932848i	$0.382685\pi$
$32$		0			0
$33$	157.151	−	224.434i	0.828985	−	1.18391i
$34$		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
$39$	190.421	+	16.6604i	0.781842	+	0.0684049i
$40$		0			0
$41$	75.5046	+	130.778i	0.287606	+	0.498148i	0.973238	−	0.229801i	$-0.0738074\pi$
$41$	75.5046	+	130.778i	0.287606	+	0.498148i	−0.685632	+	0.727948i	$0.740474\pi$
$42$		0			0
$43$	23.2485	−	40.2676i	0.0824504	−	0.142808i	−0.821852	−	0.569702i	$-0.807059\pi$
$43$	23.2485	−	40.2676i	0.0824504	−	0.142808i	0.904302	+	0.426893i	$0.140392\pi$
$44$		0			0
$45$	120.860	+	332.066i	0.400371	+	1.10003i
$46$		0			0
$47$	186.330	+	322.734i	0.578278	+	1.00161i	0.995677	+	0.0928836i	$0.0296084\pi$
$47$	186.330	+	322.734i	0.578278	+	1.00161i	−0.417399	+	0.908723i	$0.637058\pi$
$48$		0			0
$49$	129.249	−	317.716i	0.376819	−	0.926287i
$50$		0			0
$51$	−18.5565	+	212.094i	−0.0509497	+	0.582335i
$52$		0			0
$53$	−539.634	+	311.558i	−1.39857	+	0.807467i	−0.994243	−	0.107146i	$-0.965829\pi$
$53$	−539.634	+	311.558i	−1.39857	+	0.807467i	−0.404330	+	0.914613i	$0.632495\pi$
$54$		0			0
$55$		−	690.107i		−	1.69189i
$56$		0			0
$57$	−275.883	−	591.639i	−0.641081	−	1.37482i
$58$		0			0
$59$	2.00904	−	3.47975i	0.00443312	−	0.00767839i	−0.863800	−	0.503834i	$-0.831922\pi$
$59$	2.00904	−	3.47975i	0.00443312	−	0.00767839i	0.868233	+	0.496156i	$0.165256\pi$
$60$		0			0
$61$	675.337	−	389.906i	1.41751	−	0.818400i	0.421430	−	0.906861i	$-0.361528\pi$
$61$	675.337	−	389.906i	1.41751	−	0.818400i	0.996080	+	0.0884612i	$0.0281949\pi$
$62$		0			0
$63$	404.193	+	294.406i	0.808311	+	0.588756i
$64$		0			0
$65$	416.960	−	240.732i	0.795654	−	0.459371i
$66$		0			0
$67$	219.894	−	380.868i	0.400961	−	0.694485i	−0.592881	−	0.805290i	$-0.702010\pi$
$67$	219.894	−	380.868i	0.400961	−	0.694485i	0.993842	+	0.110805i	$0.0353430\pi$
$68$		0			0
$69$	6.84917	−	9.78156i	0.0119499	−	0.0170661i
$70$		0			0
$71$			800.222i			1.33759i	0.743447	+	0.668795i	$0.233190\pi$
$71$			800.222i			1.33759i	−0.743447	+	0.668795i	$0.766810\pi$
$72$		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
$75$	197.056	+	137.981i	0.303387	+	0.212436i
$76$		0			0
$77$	−545.107	−	810.239i	−0.806762	−	1.19916i
$78$		0			0
$79$	−70.1113	−	121.436i	−0.0998498	−	0.172945i	0.811773	−	0.583974i	$-0.198503\pi$
$79$	−70.1113	−	121.436i	−0.0998498	−	0.172945i	−0.911622	+	0.411029i	$0.865170\pi$
$80$		0			0
$81$	−558.453	+	468.585i	−0.766053	+	0.642777i
$82$		0			0
$83$	−506.825	+	877.846i	−0.670256	+	1.16092i	0.307575	+	0.951524i	$0.400482\pi$
$83$	−506.825	+	877.846i	−0.670256	+	1.16092i	−0.977831	+	0.209394i	$0.932851\pi$
$84$		0			0
$85$	268.130	+	464.416i	0.342151	+	0.592623i
$86$		0			0
$87$	−384.652	−	824.897i	−0.474012	−	1.01653i
$88$		0			0
$89$	−211.792	+	366.834i	−0.252246	+	0.436902i	−0.964144	−	0.265380i	$-0.914502\pi$
$89$	−211.792	+	366.834i	−0.252246	+	0.436902i	0.711898	+	0.702283i	$0.247836\pi$
$90$		0			0
$91$	299.392	−	611.989i	0.344888	−	0.704988i
$92$		0			0
$93$	590.089	+	1265.46i	0.657950	+	1.41099i
$94$		0			0
$95$	−1423.98	−	822.133i	−1.53786	−	0.887885i
$96$		0			0
$97$	264.560	+	152.744i	0.276928	+	0.159884i	0.632032	−	0.774942i	$-0.282221\pi$
$97$	264.560	+	152.744i	0.276928	+	0.159884i	−0.355104	+	0.934827i	$0.615555\pi$
$98$		0			0
$99$	1337.81	−	486.911i	1.35813	−	0.494307i
$100$		0			0
$101$	−829.087			−0.816804			−0.408402	−	0.912802i	$-0.633914\pi$
$101$	−829.087			−0.816804			−0.408402	+	0.912802i	$0.633914\pi$
$102$		0			0
$103$		−	1503.41i		−	1.43821i	−0.694904	−	0.719103i	$-0.744553\pi$
$103$		−	1503.41i		−	1.43821i	0.694904	−	0.719103i	$-0.255447\pi$
$104$		0			0
$105$	1259.29	+	23.4890i	1.17042	+	0.0218314i
$106$		0			0
$107$	−1429.35	−	825.235i	−1.29141	−	0.745593i	−0.312502	−	0.949917i	$-0.601167\pi$
$107$	−1429.35	−	825.235i	−1.29141	−	0.745593i	−0.978903	+	0.204324i	$0.934500\pi$
$108$		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	−0.900694	−	0.434454i	$-0.856942\pi$
$113$	−1170.93	+	676.036i	−0.974794	+	0.562797i	−0.0740993	+	0.997251i	$0.523608\pi$
$114$		0			0
$115$		−	30.0771i		−	0.0243888i
$116$		0			0
$117$	760.860	+	638.446i	0.601210	+	0.504482i
$118$		0			0
$119$	681.642	+	333.467i	0.525093	+	0.256881i
$120$		0			0
$121$	−1449.26			−1.08885
$122$		0			0
$123$	−68.3908	+	781.680i	−0.0501349	+	0.573022i
$124$		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
$129$	218.969	−	102.106i	0.149451	−	0.0696896i
$130$		0			0
$131$	100.267			0.0668728			0.0334364	−	0.999441i	$-0.489355\pi$
$131$	100.267			0.0668728			0.0334364	+	0.999441i	$0.489355\pi$
$132$		0			0
$133$	−2321.25	+	159.533i	−1.51337	+	0.104010i
$134$		0			0
$135$	−475.260	+	1773.63i	−0.302992	+	1.13074i
$136$		0			0
$137$			474.479i			0.295894i	0.988995	+	0.147947i	$0.0472665\pi$
$137$			474.479i			0.295894i	−0.988995	+	0.147947i	$0.952734\pi$
$138$		0			0
$139$	746.967	−	431.261i	0.455805	−	0.263159i	−0.254474	−	0.967080i	$-0.581902\pi$
$139$	746.967	−	431.261i	0.455805	−	0.263159i	0.710279	+	0.703921i	$0.248569\pi$
$140$		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
$147$	1497.06	−	967.123i	0.839970	−	0.542632i
$148$		0			0
$149$			510.180i			0.280507i	0.990116	+	0.140254i	$0.0447918\pi$
$149$			510.180i			0.280507i	−0.990116	+	0.140254i	$0.955208\pi$
$150$		0			0
$151$	479.043			0.258172			0.129086	−	0.991633i	$-0.458796\pi$
$151$	479.043			0.258172			0.129086	+	0.991633i	$0.458796\pi$
$152$		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
$157$	719.374	+	415.331i	0.365683	+	0.211127i	0.671571	−	0.740940i	$-0.265620\pi$
$157$	719.374	+	415.331i	0.365683	+	0.211127i	−0.305888	+	0.952068i	$0.598953\pi$
$158$		0			0
$159$	−3225.48	−	282.204i	−1.60879	−	0.140756i
$160$		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
$165$	2056.80	−	2937.39i	0.970433	−	1.38591i
$166$		0			0
$167$	−1718.66	−	2976.81i	−0.796371	−	1.37935i	−0.921965	−	0.387273i	$-0.873417\pi$
$167$	−1718.66	−	2976.81i	−0.796371	−	1.37935i	0.125595	−	0.992082i	$-0.459916\pi$
$168$		0			0
$169$	−421.873	+	730.705i	−0.192022	+	0.332592i
$170$		0			0
$171$	589.045	−	3340.51i	0.263424	−	1.49389i
$172$		0			0
$173$	367.325	+	636.225i	0.161429	+	0.279603i	0.935381	−	0.353641i	$-0.115056\pi$
$173$	367.325	+	636.225i	0.161429	+	0.279603i	−0.773952	+	0.633244i	$0.781723\pi$
$174$		0			0
$175$	711.401	−	478.611i	0.307296	−	0.206741i
$176$		0			0
$177$	18.9224	−	8.82358i	0.00803556	−	0.00374701i
$178$		0			0
$179$	2865.41	−	1654.34i	1.19648	−	0.690790i	0.236714	−	0.971579i	$-0.423929\pi$
$179$	2865.41	−	1654.34i	1.19648	−	0.690790i	0.959769	+	0.280789i	$0.0905962\pi$
$180$		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
$185$	−2505.59	+	4339.80i	−0.995753	+	1.72470i
$186$		0			0
$187$	1871.01	−	1080.23i	0.731666	−	0.422428i
$188$		0			0
$189$	842.972	+	2457.78i	0.324430	+	0.945910i
$190$		0			0
$191$	3829.99	−	2211.24i	1.45093	−	0.837696i	0.452398	−	0.891816i	$-0.350569\pi$
$191$	3829.99	−	2211.24i	1.45093	−	0.837696i	0.998534	+	0.0541196i	$0.0172352\pi$
$192$		0			0
$193$	2132.01	−	3692.75i	0.795158	−	1.37725i	−0.127581	−	0.991828i	$-0.540721\pi$
$193$	2132.01	−	3692.75i	0.795158	−	1.37725i	0.922739	−	0.385425i	$-0.125945\pi$
$194$		0			0
$195$	2492.24	+	218.051i	0.915245	+	0.0800766i
$196$		0			0
$197$			163.023i			0.0589590i	0.999565	+	0.0294795i	$0.00938498\pi$
$197$			163.023i			0.0589590i	−0.999565	+	0.0294795i	$0.990615\pi$
$198$		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
$201$	2071.11	−	965.764i	0.726789	−	0.338904i
$202$		0			0
$203$	−3236.42	+	222.431i	−1.11898	+	0.0769043i
$204$		0			0
$205$	988.205	+	1711.62i	0.336679	+	0.583145i
$206$		0			0
$207$	58.3060	−	21.2212i	0.0195775	−	0.00712549i
$208$		0			0
$209$	−3312.16	+	5736.82i	−1.09620	+	1.89868i
$210$		0			0
$211$	1330.09	+	2303.78i	0.433967	+	0.751654i	0.997211	−	0.0746375i	$-0.0237800\pi$
$211$	1330.09	+	2303.78i	0.433967	+	0.751654i	−0.563243	+	0.826291i	$0.690447\pi$
$212$		0			0
$213$	−2384.99	+	3406.09i	−0.767214	+	1.09569i
$214$		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
$219$	−2560.92	−	224.060i	−0.790186	−	0.0691350i
$220$		0			0
$221$	1305.34	+	753.637i	0.397314	+	0.229390i
$222$		0			0
$223$	1923.61	+	1110.60i	0.577645	+	0.333503i	0.760197	−	0.649693i	$-0.225103\pi$
$223$	1923.61	+	1110.60i	0.577645	+	0.333503i	−0.182552	+	0.983196i	$0.558436\pi$
$224$		0			0
$225$	427.515	+	1174.61i	0.126671	+	0.348033i
$226$		0			0
$227$	−3511.35			−1.02668			−0.513340	−	0.858185i	$-0.671592\pi$
$227$	−3511.35			−1.02668			−0.513340	+	0.858185i	$0.671592\pi$
$228$		0			0
$229$		−	5031.79i		−	1.45201i	−0.687690	−	0.726004i	$-0.741375\pi$
$229$		−	5031.79i		−	1.45201i	0.687690	−	0.726004i	$-0.258625\pi$
$230$		0			0
$231$	94.6311	−	5073.36i	0.0269535	−	1.44503i
$232$		0			0
$233$	3525.46	+	2035.43i	0.991248	+	0.572297i	0.905647	−	0.424032i	$-0.139386\pi$
$233$	3525.46	+	2035.43i	0.991248	+	0.572297i	0.0856006	+	0.996330i	$0.472719\pi$
$234$		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	0.0664767	−	0.997788i	$-0.478824\pi$
$239$	3561.19	−	2056.05i	0.963825	−	0.556464i	0.897348	+	0.441324i	$0.145491\pi$
$240$		0			0
$241$		−	4980.33i		−	1.33117i	−0.746324	−	0.665583i	$-0.768183\pi$
$241$		−	4980.33i		−	1.33117i	0.746324	−	0.665583i	$-0.231817\pi$
$242$		0			0
$243$	−3773.59	+	330.083i	−0.996196	+	0.0871392i
$244$		0			0
$245$	1691.61	−	4158.28i	0.441115	−	1.08434i
$246$		0			0
$247$	−4621.55			−1.19054
$248$		0			0
$249$	−4773.60	+	2225.95i	−1.21492	+	0.566521i
$250$		0			0
$251$	3477.88			0.874589			0.437294	−	0.899318i	$-0.355937\pi$
$251$	3477.88			0.874589			0.437294	+	0.899318i	$0.355937\pi$
$252$		0			0
$253$	−121.173			−0.0301110
$254$		0			0
$255$	−242.868	+	2775.89i	−0.0596431	+	0.681698i
$256$		0			0
$257$	−2077.30			−0.504195			−0.252097	−	0.967702i	$-0.581120\pi$
$257$	−2077.30			−0.504195			−0.252097	+	0.967702i	$0.581120\pi$
$258$		0			0
$259$	486.204	+	7074.40i	0.116646	+	1.69723i
$260$		0			0
$261$	821.281	−	4657.54i	0.194774	−	1.10458i
$262$		0			0
$263$			1505.64i			0.353011i	0.984300	+	0.176505i	$0.0564793\pi$
$263$			1505.64i			0.353011i	−0.984300	+	0.176505i	$0.943521\pi$
$264$		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	$-0.981049\pi$
$269$	−2429.40	−	4207.85i	−0.550644	−	0.953743i	0.447584	−	0.894242i	$-0.352284\pi$
$270$		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
$273$	3098.32	−	1712.58i	0.686881	−	0.379670i
$274$		0			0
$275$		−	2441.10i		−	0.535288i
$276$		0			0
$277$	−1180.90			−0.256149			−0.128074	−	0.991765i	$-0.540880\pi$
$277$	−1180.90			−0.256149			−0.128074	+	0.991765i	$0.540880\pi$
$278$		0			0
$279$	−1259.91	+	7145.05i	−0.270355	+	1.53320i
$280$		0			0
$281$	4403.68	+	2542.46i	0.934880	+	0.539753i	0.888352	−	0.459164i	$-0.151851\pi$
$281$	4403.68	+	2542.46i	0.934880	+	0.539753i	0.0465286	+	0.998917i	$0.485184\pi$
$282$		0			0
$283$	3627.86	+	2094.55i	0.762029	+	0.439957i	0.830024	−	0.557728i	$-0.188327\pi$
$283$	3627.86	+	2094.55i	0.762029	+	0.439957i	−0.0679951	+	0.997686i	$0.521660\pi$
$284$		0			0
$285$	−3610.76	−	7743.37i	−0.750467	−	1.60940i
$286$		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
$291$	670.842	+	1438.64i	0.135139	+	0.289809i
$292$		0			0
$293$	3061.53	+	5302.72i	0.610431	+	1.05730i	0.991168	+	0.132615i	$0.0423372\pi$
$293$	3061.53	+	5302.72i	0.610431	+	1.05730i	−0.380736	+	0.924684i	$0.624329\pi$
$294$		0			0
$295$	26.2943	−	45.5430i	0.00518953	−	0.00898853i
$296$		0			0
$297$	7145.47	+	1914.70i	1.39603	+	0.374081i
$298$		0			0
$299$	−42.2691	−	73.2122i	−0.00817553	−	0.0141604i
$300$		0			0
$301$	−59.0444	−	859.111i	−0.0113065	−	0.164513i
$302$		0			0
$303$	−3528.95	−	2471.01i	−0.669085	−	0.468502i
$304$		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
$311$	1191.04	−	2062.94i	0.217163	−	0.376137i	−0.736777	−	0.676136i	$-0.763653\pi$
$311$	1191.04	−	2062.94i	0.217163	−	0.376137i	0.953939	+	0.299999i	$0.0969864\pi$
$312$		0			0
$313$	−7017.17	+	4051.37i	−1.26720	+	0.731619i	−0.974458	−	0.224572i	$-0.927902\pi$
$313$	−7017.17	+	4051.37i	−1.26720	+	0.731619i	−0.292744	+	0.956191i	$0.594568\pi$
$314$		0			0
$315$	5290.09	+	3853.18i	0.946231	+	0.689214i
$316$		0			0
$317$	−4369.60	+	2522.79i	−0.774200	+	0.446985i	−0.834371	−	0.551204i	$-0.814169\pi$
$317$	−4369.60	+	2522.79i	−0.774200	+	0.446985i	0.0601709	+	0.998188i	$0.480835\pi$
$318$		0			0
$319$	−4618.00	+	7998.61i	−0.810528	+	1.40388i
$320$		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
$327$	508.264	−	5809.26i	0.0859543	−	0.982425i
$328$		0			0
$329$	6199.65	+	3032.94i	1.03890	+	0.508241i
$330$		0			0
$331$	52.7648	+	91.3913i	0.00876198	+	0.0151762i	0.870373	−	0.492393i	$-0.163878\pi$
$331$	52.7648	+	91.3913i	0.00876198	+	0.0151762i	−0.861611	+	0.507569i	$0.830544\pi$
$332$		0			0
$333$	−10180.8	−	1795.21i	−1.67538	−	0.295427i
$334$		0			0
$335$	2877.98	−	4984.81i	0.469376	−	0.812983i
$336$		0			0
$337$	4390.05	+	7603.79i	0.709618	+	1.22909i	0.964999	+	0.262254i	$0.0844658\pi$
$337$	4390.05	+	7603.79i	0.709618	+	1.22909i	−0.255381	+	0.966841i	$0.582201\pi$
$338$		0			0
$339$	−6998.83	−	612.342i	−1.12131	−	0.0981058i
$340$		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
$345$	89.6420	−	128.021i	0.0139889	−	0.0199781i
$346$		0			0
$347$	−8253.37	−	4765.09i	−1.27684	−	0.737185i	−0.300576	−	0.953758i	$-0.597179\pi$
$347$	−8253.37	−	4765.09i	−1.27684	−	0.737185i	−0.976267	+	0.216573i	$0.930512\pi$
$348$		0			0
$349$	−8832.94	−	5099.70i	−1.35477	−	0.782179i	−0.365861	−	0.930670i	$-0.619225\pi$
$349$	−8832.94	−	5099.70i	−1.35477	−	0.782179i	−0.988914	+	0.148490i	$0.952559\pi$
$350$		0			0
$351$	1335.72	+	4985.17i	0.203121	+	0.758088i
$352$		0			0
$353$	3523.67			0.531292			0.265646	−	0.964071i	$-0.414415\pi$
$353$	3523.67			0.531292			0.265646	+	0.964071i	$0.414415\pi$
$354$		0			0
$355$			10473.3i			1.56582i
$356$		0			0
$357$	1907.49	+	3450.95i	0.282788	+	0.511607i
$358$		0			0
$359$	−4002.21	−	2310.68i	−0.588381	−	0.339702i	0.176076	−	0.984377i	$-0.443659\pi$
$359$	−4002.21	−	2310.68i	−0.588381	−	0.339702i	−0.764457	+	0.644675i	$0.776993\pi$
$360$		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
$367$			1354.96i			0.192720i	0.995347	+	0.0963601i	$0.0307201\pi$
$367$			1354.96i			0.192720i	−0.995347	+	0.0963601i	$0.969280\pi$
$368$		0			0
$369$	−2620.82	+	3123.34i	−0.369742	+	0.440635i
$370$		0			0
$371$	−5071.29	+	10366.3i	−0.709672	+	1.45065i
$372$		0			0
$373$	−5467.52			−0.758974			−0.379487	−	0.925197i	$-0.623900\pi$
$373$	−5467.52			−0.758974			−0.379487	+	0.925197i	$0.623900\pi$
$374$		0			0
$375$	−4384.46	−	3070.05i	−0.603766	−	0.422765i
$376$		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
$381$	−915.054	−	640.732i	−0.123044	−	0.0861567i
$382$		0			0
$383$	−9496.81			−1.26701			−0.633504	−	0.773739i	$-0.718384\pi$
$383$	−9496.81			−1.26701			−0.633504	+	0.773739i	$0.718384\pi$
$384$		0			0
$385$	−7134.36	−	10604.4i	−0.944418	−	1.40377i
$386$		0			0
$387$	1236.35	+	218.010i	0.162395	+	0.0286358i
$388$		0			0
$389$		−	6094.28i		−	0.794325i	−0.917748	−	0.397163i	$-0.869995\pi$
$389$		−	6094.28i		−	0.794325i	0.917748	−	0.397163i	$-0.130005\pi$
$390$		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
$399$	−10355.7	−	6239.23i	−1.29933	−	0.782837i
$400$		0			0
$401$			3774.89i			0.470098i	0.971984	+	0.235049i	$0.0755250\pi$
$401$			3774.89i			0.470098i	−0.971984	+	0.235049i	$0.924475\pi$
$402$		0			0
$403$	9885.08			1.22186
$404$		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
$409$	−7453.82	−	4303.47i	−0.901144	−	0.520276i	−0.0235728	−	0.999722i	$-0.507504\pi$
$409$	−7453.82	−	4303.47i	−0.901144	−	0.520276i	−0.877571	+	0.479446i	$0.840837\pi$
$410$		0			0
$411$	−1414.14	+	2019.58i	−0.169718	+	0.242381i
$412$		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
$417$	4464.74	+	390.629i	0.524315	+	0.0458734i
$418$		0			0
$419$	3204.64	+	5550.60i	0.373644	+	0.647171i	0.990123	−	0.140201i	$-0.0447748\pi$
$419$	3204.64	+	5550.60i	0.373644	+	0.647171i	−0.616479	+	0.787371i	$0.711441\pi$
$420$		0			0
$421$	5420.73	−	9388.98i	0.627530	−	1.08691i	−0.360515	−	0.932753i	$-0.617399\pi$
$421$	5420.73	−	9388.98i	0.627530	−	1.08691i	0.988046	−	0.154161i	$-0.0492675\pi$
$422$		0			0
$423$	−6467.67	+	7707.77i	−0.743426	+	0.885968i
$424$		0			0
$425$	948.454	+	1642.77i	0.108251	+	0.187497i
$426$		0			0
$427$	6346.59	−	12973.1i	0.719281	−	1.47029i
$428$		0			0
$429$	878.469	−	10040.6i	0.0988646	−	1.12998i
$430$		0			0
$431$	5999.82	−	3464.00i	0.670537	−	0.387135i	−0.125743	−	0.992063i	$-0.540132\pi$
$431$	5999.82	−	3464.00i	0.670537	−	0.387135i	0.796280	+	0.604928i	$0.206798\pi$
$432$		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
$437$	−144.355	+	250.030i	−0.0158019	+	0.0273697i
$438$		0			0
$439$	11014.0	−	6358.96i	1.19743	−	0.691337i	0.237449	−	0.971400i	$-0.423689\pi$
$439$	11014.0	−	6358.96i	1.19743	−	0.691337i	0.959982	+	0.280063i	$0.0903555\pi$
$440$		0			0
$441$	9254.56	+	345.362i	0.999304	+	0.0372921i
$442$		0			0
$443$	1005.53	−	580.545i	0.107843	−	0.0622631i	−0.445108	−	0.895477i	$-0.646835\pi$
$443$	1005.53	−	580.545i	0.107843	−	0.0622631i	0.552951	+	0.833214i	$0.313502\pi$
$444$		0			0
$445$	−2771.93	+	4801.13i	−0.295286	+	0.511450i
$446$		0			0
$447$	−1520.54	+	2171.54i	−0.160893	+	0.229778i
$448$		0			0
$449$			10066.4i			1.05804i	0.848609	+	0.529021i	$0.177441\pi$
$449$			10066.4i			1.05804i	−0.848609	+	0.529021i	$0.822559\pi$
$450$		0			0
$451$	6895.67	−	3981.22i	0.719965	−	0.415672i
$452$		0			0
$453$	2039.01	+	1427.74i	0.211482	+	0.148082i
$454$		0			0
$455$	3918.45	−	8009.72i	0.403735	−	0.825278i
$456$		0			0
$457$	4343.52	+	7523.20i	0.444598	+	0.770067i	0.998024	−	0.0628316i	$-0.0200131\pi$
$457$	4343.52	+	7523.20i	0.444598	+	0.770067i	−0.553426	+	0.832898i	$0.686680\pi$
$458$		0			0
$459$	−5552.56	+	1487.74i	−0.564643	+	0.151290i
$460$		0			0
$461$	−1569.09	+	2717.75i	−0.158525	+	0.274573i	−0.934337	−	0.356391i	$-0.884007\pi$
$461$	−1569.09	+	2717.75i	−0.158525	+	0.274573i	0.775812	+	0.630964i	$0.217340\pi$
$462$		0			0
$463$	7155.71	+	12394.0i	0.718259	+	1.24406i	0.961689	+	0.274142i	$0.0883939\pi$
$463$	7155.71	+	12394.0i	0.718259	+	1.24406i	−0.243430	+	0.969918i	$0.578273\pi$
$464$		0			0
$465$	7723.09	+	16562.4i	0.770214	+	1.65174i
$466$		0			0
$467$	4129.97	−	7153.32i	0.409234	−	0.708814i	−0.585570	−	0.810622i	$-0.699129\pi$
$467$	4129.97	−	7153.32i	0.409234	−	0.708814i	0.994804	+	0.101807i	$0.0324626\pi$
$468$		0			0
$469$	−558.467	−	8125.83i	−0.0549842	−	0.800034i
$470$		0			0
$471$	1824.11	+	3911.85i	0.178451	+	0.382693i
$472$		0			0
$473$	−2123.24	−	1225.85i	−0.206399	−	0.119164i
$474$		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
$479$	−14189.3			−1.35350			−0.676750	−	0.736212i	$-0.736612\pi$
$479$	−14189.3			−1.35350			−0.676750	+	0.736212i	$0.736612\pi$
$480$		0			0
$481$			14085.0i			1.33517i
$482$		0			0
$483$	4.12434	−	221.114i	0.000388538	−	0.0208303i
$484$		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	−0.782405	−	0.622769i	$-0.786007\pi$
$491$	−6900.79	+	3984.18i	−0.634274	+	0.366198i	0.148131	+	0.988968i	$0.452674\pi$
$492$		0			0
$493$		−	7177.02i		−	0.655652i
$494$		0			0
$495$	17509.2	−	6372.70i	1.58986	−	0.578650i
$496$		0			0
$497$	8272.74	+	12296.5i	0.746646	+	1.10980i
$498$		0			0
$499$	19769.7			1.77357			0.886786	−	0.462179i	$-0.152932\pi$
$499$	19769.7			1.77357			0.886786	+	0.462179i	$0.152932\pi$
$500$		0			0
$501$	1556.73	−	17792.9i	0.138822	−	1.58668i
$502$		0			0
$503$	20456.0			1.81330			0.906650	−	0.421884i	$-0.138631\pi$
$503$	20456.0			1.81330			0.906650	+	0.421884i	$0.138631\pi$
$504$		0			0
$505$	−10851.1			−0.956173
$506$		0			0
$507$	−3973.47	+	1852.84i	−0.348063	+	0.162303i
$508$		0			0
$509$	−7550.24			−0.657483			−0.328741	−	0.944420i	$-0.606624\pi$
$509$	−7550.24			−0.657483			−0.328741	+	0.944420i	$0.606624\pi$
$510$		0			0
$511$	−4026.43	+	8230.45i	−0.348569	+	0.712512i
$512$		0			0
$513$	12463.3	−	12463.1i	1.07265	−	1.07263i
$514$		0			0
$515$		−	19676.6i		−	1.68360i
$516$		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	0.588972	−	0.808153i	$-0.299533\pi$
$521$	−4820.98	−	8350.18i	−0.405395	−	0.702165i	−0.994367	+	0.105988i	$0.966199\pi$
$522$		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
$525$	4454.48	+	83.0874i	0.370304	+	0.00690711i
$526$		0			0
$527$			11010.1i			0.910074i
$528$		0			0
$529$	12161.7			0.999566
$530$		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
$535$	−18707.3	−	10800.7i	−1.51175	−	0.872812i
$536$		0			0
$537$	17127.0	+	1498.48i	1.37632	+	0.120417i
$538$		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
$543$	−8617.12	+	12306.4i	−0.681024	+	0.972596i
$544$		0			0
$545$	−7344.10	−	12720.4i	−0.577223	−	0.999780i
$546$		0			0
$547$	−9537.65	+	16519.7i	−0.745522	+	1.29128i	0.204429	+	0.978881i	$0.434466\pi$
$547$	−9537.65	+	16519.7i	−0.745522	+	1.29128i	−0.949951	+	0.312400i	$0.898867\pi$
$548$		0			0
$549$	16128.9	+	13534.0i	1.25385	+	1.05212i
$550$		0			0
$551$	11003.0	+	19057.7i	0.850712	+	1.47348i
$552$		0			0
$553$	−2332.77	−	1141.22i	−0.179384	−	0.0877568i
$554$		0			0
$555$	−23599.2	+	11004.4i	−1.80492	+	0.841641i
$556$		0			0
$557$	9248.44	−	5339.59i	0.703535	−	0.406186i	−0.105128	−	0.994459i	$-0.533525\pi$
$557$	9248.44	−	5339.59i	0.703535	−	0.406186i	0.808663	+	0.588273i	$0.200192\pi$
$558$		0			0
$559$		−	1710.47i		−	0.129419i
$560$		0			0
$561$	11183.3	+	978.451i	0.841640	+	0.0736368i
$562$		0			0
$563$	4072.45	−	7053.70i	0.304855	−	0.528025i	−0.672374	−	0.740212i	$-0.734725\pi$
$563$	4072.45	−	7053.70i	0.304855	−	0.528025i	0.977229	+	0.212187i	$0.0680586\pi$
$564$		0			0
$565$	−15325.1	+	8847.96i	−1.14112	+	0.658826i
$566$		0			0
$567$	−3737.12	+	12973.8i	−0.276797	+	0.960928i
$568$		0			0
$569$	957.341	−	552.721i	0.0705340	−	0.0407228i	−0.464318	−	0.885668i	$-0.653701\pi$
$569$	957.341	−	552.721i	0.0705340	−	0.0407228i	0.534852	+	0.844946i	$0.320367\pi$
$570$		0			0
$571$	−24.2646	+	42.0275i	−0.00177836	+	0.00308020i	−0.866913	−	0.498459i	$-0.833899\pi$
$571$	−24.2646	+	42.0275i	−0.00177836	+	0.00308020i	0.865135	+	0.501539i	$0.167233\pi$
$572$		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
$579$	20080.6	−	9363.67i	1.44132	−	0.672091i
$580$		0			0
$581$	1287.19	+	18728.9i	0.0919130	+	1.33736i
$582$		0			0
$583$	16427.9	+	28453.9i	1.16702	+	2.02134i
$584$		0			0
$585$	9958.15	+	8355.99i	0.703793	+	0.590560i
$586$		0			0
$587$	7182.29	−	12440.1i	0.505016	−	0.874714i	−0.494967	−	0.868912i	$-0.664820\pi$
$587$	7182.29	−	12440.1i	0.505016	−	0.874714i	0.999983	−	0.00580216i	$-0.00184690\pi$
$588$		0			0
$589$	−16879.5	−	29236.1i	−1.18083	−	2.04525i
$590$		0			0
$591$	−485.875	+	693.897i	−0.0338177	+	0.0482963i
$592$		0			0
$593$	−5430.08	+	9405.18i	−0.376032	+	0.651306i	−0.990481	−	0.137650i	$-0.956045\pi$
$593$	−5430.08	+	9405.18i	−0.376032	+	0.651306i	0.614449	+	0.788956i	$0.289378\pi$
$594$		0			0
$595$	8921.34	+	4364.42i	0.614688	+	0.300712i
$596$		0			0
$597$	1428.69	+	124.999i	0.0979434	+	0.00856926i
$598$		0			0
$599$	−1409.60	−	813.831i	−0.0961512	−	0.0555129i	0.451153	−	0.892446i	$-0.351013\pi$
$599$	−1409.60	−	813.831i	−0.0961512	−	0.0555129i	−0.547305	+	0.836934i	$0.684346\pi$
$600$		0			0
$601$	554.089	+	319.903i	0.0376069	+	0.0217124i	0.518686	−	0.854965i	$-0.326422\pi$
$601$	554.089	+	319.903i	0.0376069	+	0.0217124i	−0.481079	+	0.876677i	$0.659755\pi$
$602$		0			0
$603$	11693.9	+	2062.03i	0.789738	+	0.139257i
$604$		0			0
$605$	−18967.9			−1.27464
$606$		0			0
$607$		−	26690.2i		−	1.78471i	−0.451331	−	0.892357i	$-0.649051\pi$
$607$		−	26690.2i		−	1.78471i	0.451331	−	0.892357i	$-0.350949\pi$
$608$		0			0
$609$	−14438.5	−	8699.09i	−0.960721	−	0.578826i
$610$		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	−0.144765	−	0.989466i	$-0.546243\pi$
$617$	9804.86	−	5660.84i	0.639755	−	0.369363i	0.784520	+	0.620103i	$0.212909\pi$
$618$		0			0
$619$		−	8134.24i		−	0.528179i	−0.964498	−	0.264089i	$-0.914929\pi$
$619$		−	8134.24i		−	0.528179i	0.964498	−	0.264089i	$-0.0850714\pi$
$620$		0			0
$621$	311.423	+	83.4490i	0.0201240	+	0.00539242i
$622$		0			0
$623$	537.888	+	7826.41i	0.0345907	+	0.503304i
$624$		0			0
$625$	−19268.7			−1.23320
$626$		0			0
$627$	−31196.0	+	14546.8i	−1.98700	+	0.926545i
$628$		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
$633$	−1204.77	+	13770.1i	−0.0756484	+	0.864632i
$634$		0			0
$635$	−2813.68			−0.175839
$636$		0			0
$637$	−1726.22	−	12499.2i	−0.107371	−	0.777449i
$638$		0			0
$639$	−20303.0	+	7389.55i	−1.25693	+	0.457474i
$640$		0			0
$641$			1071.39i			0.0660180i	0.999455	+	0.0330090i	$0.0105090\pi$
$641$			1071.39i			0.0660180i	−0.999455	+	0.0330090i	$0.989491\pi$
$642$		0			0
$643$	14951.2	−	8632.07i	0.916978	−	0.529418i	0.0343083	−	0.999411i	$-0.489077\pi$
$643$	14951.2	−	8632.07i	0.916978	−	0.529418i	0.882670	+	0.469994i	$0.155744\pi$
$644$		0			0
$645$	2865.87	−	1336.37i	0.174951	−	0.0815805i
$646$		0			0
$647$	1072.86	+	1858.25i	0.0651910	+	0.112914i	0.896779	−	0.442479i	$-0.145901\pi$
$647$	1072.86	+	1858.25i	0.0651910	+	0.112914i	−0.831588	+	0.555393i	$0.812568\pi$
$648$		0			0
$649$	−183.481	−	105.933i	−0.0110975	−	0.00640712i
$650$		0			0
$651$	22149.9	+	13345.1i	1.33352	+	0.803436i
$652$		0			0
$653$		−	6375.11i		−	0.382048i	−0.981585	−	0.191024i	$-0.938819\pi$
$653$		−	6375.11i		−	0.382048i	0.981585	−	0.191024i	$-0.0611808\pi$
$654$		0			0
$655$	1312.29			0.0782831
$656$		0			0
$657$	−10232.6	−	8586.27i	−0.607627	−	0.509866i
$658$		0			0
$659$	−20870.4	−	12049.5i	−1.23368	−	0.712266i	−0.265886	−	0.964004i	$-0.585665\pi$
$659$	−20870.4	−	12049.5i	−1.23368	−	0.712266i	−0.967795	+	0.251738i	$0.918998\pi$
$660$		0			0
$661$	20160.9	+	11639.9i	1.18634	+	0.684931i	0.957472	−	0.288528i	$-0.0931657\pi$
$661$	20160.9	+	11639.9i	1.18634	+	0.684931i	0.228864	+	0.973459i	$0.426499\pi$
$662$		0			0
$663$	3309.93	+	7098.24i	0.193887	+	0.415796i
$664$		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
$669$	4877.69	+	10460.3i	0.281887	+	0.604514i
$670$		0			0
$671$	−20559.0	−	35609.3i	−1.18282	−	2.04871i
$672$		0			0
$673$	3779.47	−	6546.24i	0.216475	−	0.374946i	−0.737253	−	0.675617i	$-0.763877\pi$
$673$	3779.47	−	6546.24i	0.216475	−	0.374946i	0.953728	+	0.300671i	$0.0972106\pi$
$674$		0			0
$675$	−1681.13	+	6273.82i	−0.0958619	+	0.357747i
$676$		0			0
$677$	−912.337	−	1580.21i	−0.0517931	−	0.0897083i	0.838966	−	0.544183i	$-0.183160\pi$
$677$	−912.337	−	1580.21i	−0.0517931	−	0.0897083i	−0.890760	+	0.454475i	$0.849827\pi$
$678$		0			0
$679$	5644.39	−	387.924i	0.319016	−	0.0219251i
$680$		0			0
$681$	−14945.8	−	10465.2i	−0.841005	−	0.588882i
$682$		0			0
$683$	−30780.2	+	17771.0i	−1.72441	+	0.995589i	−0.815292	+	0.579051i	$0.803423\pi$
$683$	−30780.2	+	17771.0i	−1.72441	+	0.995589i	−0.909118	+	0.416538i	$0.863243\pi$
$684$		0			0
$685$			6209.98i			0.346381i
$686$		0			0
$687$	14996.8	−	21417.5i	0.832842	−	1.18941i
$688$		0			0
$689$	−11461.1	+	19851.3i	−0.633723	+	1.09764i
$690$		0			0
$691$	−4748.07	+	2741.30i	−0.261397	+	0.150917i	−0.624972	−	0.780648i	$-0.714889\pi$
$691$	−4748.07	+	2741.30i	−0.261397	+	0.150917i	0.363575	+	0.931565i	$0.381556\pi$
$692$		0			0
$693$	15523.5	−	21312.4i	0.850920	−	1.16824i
$694$		0			0
$695$	9776.31	−	5644.35i	0.533578	−	0.308061i
$696$		0			0
$697$	−3093.68	+	5358.41i	−0.168123	+	0.291197i
$698$		0			0
$699$	8939.48	+	19171.0i	0.483723	+	1.03736i
$700$		0			0
$701$			27379.6i			1.47519i	0.675241	+	0.737597i	$0.264040\pi$
$701$			27379.6i			1.47519i	−0.675241	+	0.737597i	$0.735960\pi$
$702$		0			0
$703$	41657.6	−	24051.1i	2.23492	−	1.29033i
$704$		0			0
$705$	−2208.93	+	25247.2i	−0.118004	+	1.34874i
$706$		0			0
$707$	−12740.0	+	8571.15i	−0.677706	+	0.455942i
$708$		0			0
$709$	−6395.49	−	11077.3i	−0.338770	−	0.586766i	0.645432	−	0.763818i	$-0.276677\pi$
$709$	−6395.49	−	11077.3i	−0.338770	−	0.586766i	−0.984202	+	0.177052i	$0.943344\pi$
$710$		0			0
$711$	2433.62	−	2900.24i	0.128365	−	0.152978i
$712$		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
$717$	21285.8	+	1862.34i	1.10869	+	0.0970018i
$718$		0			0
$719$	−17988.4	+	31156.8i	−0.933038	+	1.61607i	−0.154943	+	0.987923i	$0.549519\pi$
$719$	−17988.4	+	31156.8i	−0.933038	+	1.61607i	−0.778096	+	0.628146i	$0.783814\pi$
$720$		0			0
$721$	−15542.3	−	23101.9i	−0.802810	−	1.19329i
$722$		0			0
$723$	14843.4	−	21198.4i	0.763529	−	1.09042i
$724$		0			0
$725$	−7022.89	−	4054.67i	−0.359757	−	0.207706i
$726$		0			0
$727$	−1802.68	−	1040.78i	−0.0919636	−	0.0530952i	0.453313	−	0.891351i	$-0.350242\pi$
$727$	−1802.68	−	1040.78i	−0.0919636	−	0.0530952i	−0.545277	+	0.838256i	$0.683575\pi$
$728$		0			0
$729$	−17045.8	−	9841.84i	−0.866015	−	0.500017i
$730$		0			0
$731$	1905.14			0.0963944
$732$		0			0
$733$		−	2883.01i		−	0.145275i	−0.997358	−	0.0726375i	$-0.976858\pi$
$733$		−	2883.01i		−	0.145275i	0.997358	−	0.0726375i	$-0.0231416\pi$
$734$		0			0
$735$	19593.6	−	12657.7i	0.983292	−	0.635220i
$736$		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	0.478507	−	0.878084i	$-0.341178\pi$
$743$	29937.6	−	17284.5i	1.47820	−	0.853441i	0.999696	+	0.0246423i	$0.00784468\pi$
$744$		0			0
$745$			6677.24i			0.328369i
$746$		0			0
$747$	−26952.7	−	4752.68i	−1.32015	−	0.232786i
$748$		0			0
$749$	−30495.2	+	2095.85i	−1.48768	+	0.102244i
$750$		0			0
$751$	12675.1			0.615875			0.307938	−	0.951407i	$-0.400361\pi$
$751$	12675.1			0.615875			0.307938	+	0.951407i	$0.400361\pi$
$752$		0			0
$753$	14803.3	+	10365.5i	0.716419	+	0.501646i
$754$		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
$759$	−515.764	−	361.144i	−0.0246654	−	0.0172710i
$760$		0			0
$761$	15395.8			0.733373			0.366687	−	0.930344i	$-0.380492\pi$
$761$	15395.8			0.733373			0.366687	+	0.930344i	$0.380492\pi$
$762$		0			0
$763$	−18670.2	−	9133.67i	−0.885854	−	0.433370i
$764$		0			0
$765$	−9307.02	+	11091.5i	−0.439864	+	0.524203i
$766$		0			0
$767$		−	147.811i		−	0.00695848i
$768$		0			0
$769$	−4149.23	+	2395.56i	−0.194571	+	0.112336i	−0.594121	−	0.804376i	$-0.702500\pi$
$769$	−4149.23	+	2395.56i	−0.194571	+	0.112336i	0.399550	+	0.916712i	$0.369167\pi$
$770$		0			0
$771$	−8841.86	−	6191.18i	−0.413011	−	0.289196i
$772$		0			0
$773$	6124.33	+	10607.7i	0.284964	+	0.493572i	0.972600	−	0.232483i	$-0.0746851\pi$
$773$	6124.33	+	10607.7i	0.284964	+	0.493572i	−0.687637	+	0.726055i	$0.741352\pi$
$774$		0			0
$775$	10773.7	+	6220.20i	0.499358	+	0.288305i
$776$		0			0
$777$	−19015.1	+	31560.8i	−0.877944	+	1.45719i
$778$		0			0
$779$		−	18971.5i		−	0.872560i
$780$		0			0
$781$	42194.2			1.93320
$782$		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
$787$	7941.77	+	4585.18i	0.359712	+	0.207680i	0.668954	−	0.743303i	$-0.266742\pi$
$787$	7941.77	+	4585.18i	0.359712	+	0.207680i	−0.309242	+	0.950983i	$0.600075\pi$
$788$		0			0
$789$	−4487.42	+	6408.65i	−0.202479	+	0.289169i
$790$		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
$795$	−42215.1	−	3693.49i	−1.88329	−	0.164773i
$796$		0			0
$797$	7564.68	+	13102.4i	0.336204	+	0.582323i	0.983715	−	0.179733i	$-0.0575234\pi$
$797$	7564.68	+	13102.4i	0.336204	+	0.582323i	−0.647511	+	0.762056i	$0.724190\pi$
$798$		0			0
$799$	−7634.59	+	13223.5i	−0.338038	+	0.585499i
$800$		0			0
$801$	−11263.0	−	1986.05i	−0.496826	−	0.0876073i
$802$		0			0
$803$	13043.1	+	22591.4i	0.573204	+	0.992818i
$804$		0			0
$805$	−310.939	−	462.176i	−0.0136139	−	0.0202355i
$806$		0			0
$807$	2200.51	−	25151.0i	0.0959872	−	1.09710i
$808$		0			0
$809$	30049.2	−	17348.9i	1.30590	−	0.753962i	0.324491	−	0.945889i	$-0.394807\pi$
$809$	30049.2	−	17348.9i	1.30590	−	0.753962i	0.981409	+	0.191926i	$0.0614735\pi$
$810$		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
$815$	10006.7	−	17332.2i	0.430086	−	0.744932i
$816$		0			0
$817$	−5058.88	+	2920.74i	−0.216631	+	0.125072i
$818$		0			0
$819$	18291.9	+	1944.76i	0.780430	+	0.0829738i
$820$		0			0
$821$	27854.4	−	16081.8i	1.18408	−	0.683626i	0.227122	−	0.973866i	$-0.427069\pi$
$821$	27854.4	−	16081.8i	1.18408	−	0.683626i	0.956954	+	0.290240i	$0.0937352\pi$
$822$		0			0
$823$	−9728.32	+	16849.9i	−0.412039	+	0.713672i	−0.995113	−	0.0987473i	$-0.968516\pi$
$823$	−9728.32	+	16849.9i	−0.412039	+	0.713672i	0.583074	+	0.812419i	$0.301850\pi$
$824$		0			0
$825$	7275.48	−	10390.4i	0.307030	−	0.438481i
$826$		0			0
$827$		−	3379.21i		−	0.142088i	−0.997473	−	0.0710440i	$-0.977367\pi$
$827$		−	3379.21i		−	0.142088i	0.997473	−	0.0710440i	$-0.0226331\pi$
$828$		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
$831$	−5026.41	−	3519.55i	−0.209824	−	0.146922i
$832$		0			0
$833$	13921.7	−	1922.69i	0.579064	−	0.0799727i
$834$		0			0
$835$	−22493.8	−	38960.5i	−0.932253	−	1.61471i
$836$		0			0
$837$	−26657.9	+	26657.3i	−1.10087	+	1.10085i
$838$		0			0
$839$	−7164.60	+	12409.5i	−0.294815	+	0.510634i	−0.974942	−	0.222460i	$-0.928591\pi$
$839$	−7164.60	+	12409.5i	−0.294815	+	0.510634i	0.680127	+	0.733094i	$0.261925\pi$
$840$		0			0
$841$	3146.47	+	5449.85i	0.129012	+	0.223455i
$842$		0			0
$843$	11166.4	+	23946.6i	0.456216	+	0.978367i
$844$		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
$849$	9199.14	+	19727.8i	0.371865	+	0.797475i
$850$		0			0
$851$	762.007	+	439.945i	0.0306948	+	0.0177217i
$852$		0			0
$853$	1244.42	+	718.465i	0.0499508	+	0.0288391i	0.524767	−	0.851246i	$-0.324152\pi$
$853$	1244.42	+	718.465i	0.0499508	+	0.0288391i	−0.474817	+	0.880085i	$0.657486\pi$
$854$		0			0
$855$	7709.43	−	43720.7i	0.308371	−	1.74879i
$856$		0			0
$857$	−27062.0			−1.07867			−0.539336	−	0.842091i	$-0.681325\pi$
$857$	−27062.0			−1.07867			−0.539336	+	0.842091i	$0.681325\pi$
$858$		0			0
$859$			1315.06i			0.0522341i	0.999659	+	0.0261171i	$0.00831426\pi$
$859$			1315.06i			0.0522341i	−0.999659	+	0.0261171i	$0.991686\pi$
$860$		0			0
$861$	7030.14	+	12718.6i	0.278266	+	0.503425i
$862$		0			0
$863$	−2494.83	−	1440.39i	−0.0984068	−	0.0568152i	0.449989	−	0.893034i	$-0.351428\pi$
$863$	−2494.83	−	1440.39i	−0.0984068	−	0.0568152i	−0.548396	+	0.836219i	$0.684761\pi$
$864$		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
$871$		−	16178.3i		−	0.629371i
$872$		0			0
$873$	−1432.33	+	8122.85i	−0.0555293	+	0.314910i
$874$		0			0
$875$	−15828.5	+	10649.0i	−0.611545	+	0.411431i
$876$		0			0
$877$	−28204.2			−1.08596			−0.542980	−	0.839745i	$-0.682704\pi$
$877$	−28204.2			−1.08596			−0.542980	+	0.839745i	$0.682704\pi$
$878$		0			0
$879$	−2773.08	+	31695.3i	−0.106409	+	1.21622i
$880$		0			0
$881$	14864.0			0.568423			0.284211	−	0.958762i	$-0.408268\pi$
$881$	14864.0			0.568423			0.284211	+	0.958762i	$0.408268\pi$
$882$		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
$885$	247.656	−	115.483i	0.00940664	−	0.00438635i
$886$		0			0
$887$	−7041.08			−0.266535			−0.133267	−	0.991080i	$-0.542547\pi$
$887$	−7041.08			−0.266535			−0.133267	+	0.991080i	$0.542547\pi$
$888$		0			0
$889$	−3303.48	+	2222.49i	−0.124629	+	0.0838471i
$890$		0			0
$891$	24707.6	+	29446.2i	0.928996	+	1.10716i
$892$		0			0
$893$		−	46817.9i		−	1.75442i
$894$		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
$903$	2309.18	−	3832.72i	0.0850993	−	0.141246i
$904$		0			0
$905$			37840.8i			1.38991i
$906$		0			0
$907$	29317.0			1.07327			0.536635	−	0.843815i	$-0.319695\pi$
$907$	29317.0			1.07327			0.536635	+	0.843815i	$0.319695\pi$
$908$		0			0
$909$	−7656.10	−	21035.4i	−0.279358	−	0.767547i
$910$		0			0
$911$	−38285.3	−	22104.0i	−1.39237	−	0.803885i	−0.398793	−	0.917041i	$-0.630571\pi$
$911$	−38285.3	−	22104.0i	−1.39237	−	0.803885i	−0.993577	+	0.113156i	$0.963904\pi$
$912$		0			0
$913$	46287.2	+	26723.9i	1.67786	+	0.968711i
$914$		0			0
$915$	52831.1	+	4622.30i	1.90879	+	0.167004i
$916$		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
$921$	−17024.0	+	24312.7i	−0.609079	+	0.869848i
$922$		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
$927$	38144.1	−	13883.0i	1.35147	−	0.491886i
$928$		0			0
$929$	2404.81	+	4165.25i	0.0849292	+	0.147102i	0.905361	−	0.424643i	$-0.139600\pi$
$929$	2404.81	+	4165.25i	0.0849292	+	0.147102i	−0.820432	+	0.571744i	$0.806267\pi$
$930$		0			0
$931$	−34019.9	+	26448.7i	−1.19759	+	0.931064i
$932$		0			0
$933$	11218.0	−	5230.98i	0.393633	−	0.183553i
$934$		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
$941$	−2387.59	+	4135.42i	−0.0827131	+	0.143263i	−0.904414	−	0.426655i	$-0.859692\pi$
$941$	−2387.59	+	4135.42i	−0.0827131	+	0.143263i	0.821701	+	0.569918i	$0.193025\pi$
$942$		0			0
$943$	300.536	−	173.515i	0.0103784	−	0.00599196i
$944$		0			0
$945$	11032.8	+	32167.4i	0.379786	+	1.10731i
$946$		0			0
$947$	48220.6	−	27840.2i	1.65466	−	0.955316i	0.679535	−	0.733643i	$-0.262181\pi$
$947$	48220.6	−	27840.2i	1.65466	−	0.955316i	0.975121	−	0.221673i	$-0.0711519\pi$
$948$		0			0
$949$	−9099.75	+	15761.2i	−0.311265	+	0.539127i
$950$		0			0
$951$	−26117.8	−	2285.10i	−0.890567	−	0.0779175i
$952$		0			0
$953$			29426.7i			1.00023i	0.865958	+	0.500117i	$0.166710\pi$
$953$			29426.7i			1.00023i	−0.865958	+	0.500117i	$0.833290\pi$
$954$		0			0
$955$	50126.9	−	28940.8i	1.69850	−	0.980630i
$956$		0			0
$957$	−43495.3	+	20282.0i	−1.46918	+	0.685083i
$958$		0			0
$959$	4905.19	+	7291.00i	0.165169	+	0.245504i
$960$		0			0
$961$	21208.1	+	36733.5i	0.711896	+	1.23304i
$962$		0			0
$963$	7738.52	−	43885.6i	0.258952	−	1.46853i
$964$		0			0
$965$	27903.8	−	48330.7i	0.930833	−	1.61225i
$966$		0			0
$967$	6991.64	+	12109.9i	0.232509	+	0.402717i	0.958546	−	0.284939i	$-0.0919732\pi$
$967$	6991.64	+	12109.9i	0.232509	+	0.402717i	−0.726037	+	0.687656i	$0.758640\pi$
$968$		0			0
$969$	15341.8	−	21910.2i	0.508616	−	0.726374i
$970$		0			0
$971$	21826.5	−	37804.5i	0.721364	−	1.24944i	−0.239089	−	0.970998i	$-0.576849\pi$
$971$	21826.5	−	37804.5i	0.721364	−	1.24944i	0.960453	−	0.278441i	$-0.0898178\pi$
$972$		0			0
$973$	7019.74	−	14349.1i	0.231287	−	0.472776i
$974$		0			0
$975$	8815.76	+	771.308i	0.289569	+	0.0253350i
$976$		0			0
$977$	29090.3	+	16795.3i	0.952592	+	0.549979i	0.893885	−	0.448296i	$-0.147969\pi$
$977$	29090.3	+	16795.3i	0.952592	+	0.549979i	0.0587071	+	0.998275i	$0.481302\pi$
$978$		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
$983$	−47446.3			−1.53947			−0.769736	−	0.638362i	$-0.779612\pi$
$983$	−47446.3			−1.53947			−0.769736	+	0.638362i	$0.779612\pi$
$984$		0			0
$985$			2133.65i			0.0690190i
$986$		0			0
$987$	17349.0	+	31387.0i	0.559498	+	1.01222i
$988$		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
$997$		−	973.421i		−	0.0309213i	−0.999880	−	0.0154607i	$-0.995079\pi$
$997$		−	973.421i		−	0.0309213i	0.999880	−	0.0154607i	$-0.00492148\pi$
$998$		0			0
$999$	−37983.2	−	37984.0i	−1.20294	−	1.20296i

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
252.4.w.a.5.12	✓	48	9.5	odd	6
252.4.w.a.101.12	yes	48	7.3	odd	6
252.4.bm.a.173.20	yes	48	1.1	even	1	trivial
252.4.bm.a.185.20	yes	48	63.59	even	6	inner
756.4.w.a.341.5		48	9.4	even	3
756.4.w.a.521.5		48	21.17	even	6
756.4.bm.a.17.5		48	63.31	odd	6
756.4.bm.a.89.5		48	3.2	odd	2

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.bm (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(4.25643 + 2.98040i) q^{3} +13.0880 q^{5} +(15.3663 - 10.3381i) q^{7} +(9.23438 + 25.3718i) q^{9} +O(q^{10})\)	\(q+(4.25643 + 2.98040i) q^{3} +13.0880 q^{5} +(15.3663 - 10.3381i) q^{7} +(9.23438 + 25.3718i) q^{9} -52.7281i q^{11} +(31.8581 - 18.3933i) q^{13} +(55.7082 + 39.0076i) q^{15} +(20.4867 + 35.4840i) q^{17} +(-108.800 - 62.8157i) q^{19} +(96.2174 + 1.79470i) q^{21} -2.29807i q^{23} +46.2960 q^{25} +(-36.3127 + 135.515i) q^{27} +(-151.695 - 87.5813i) q^{29} +(232.713 + 134.357i) q^{31} +(157.151 - 224.434i) q^{33} +(201.115 - 135.305i) q^{35} +(-191.441 + 331.586i) q^{37} +(190.421 + 16.6604i) q^{39} +(75.5046 + 130.778i) q^{41} +(23.2485 - 40.2676i) q^{43} +(120.860 + 332.066i) q^{45} +(186.330 + 322.734i) q^{47} +(129.249 - 317.716i) q^{49} +(-18.5565 + 212.094i) q^{51} +(-539.634 + 311.558i) q^{53} -690.107i q^{55} +(-275.883 - 591.639i) q^{57} +(2.00904 - 3.47975i) q^{59} +(675.337 - 389.906i) q^{61} +(404.193 + 294.406i) q^{63} +(416.960 - 240.732i) q^{65} +(219.894 - 380.868i) q^{67} +(6.84917 - 9.78156i) q^{69} +800.222i q^{71} +(-428.450 + 247.366i) q^{73} +(197.056 + 137.981i) q^{75} +(-545.107 - 810.239i) q^{77} +(-70.1113 - 121.436i) q^{79} +(-558.453 + 468.585i) q^{81} +(-506.825 + 877.846i) q^{83} +(268.130 + 464.416i) q^{85} +(-384.652 - 824.897i) q^{87} +(-211.792 + 366.834i) q^{89} +(299.392 - 611.989i) q^{91} +(590.089 + 1265.46i) q^{93} +(-1423.98 - 822.133i) q^{95} +(264.560 + 152.744i) q^{97} +(1337.81 - 486.911i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q + 6 q^{7} - 30 q^{9}+O(q^{10}) \) 48 * q + 6 * q^7 - 30 * q^9	\( 48 q + 6 q^{7} - 30 q^{9} + 36 q^{13} + 66 q^{15} + 72 q^{17} + 126 q^{21} + 1200 q^{25} + 396 q^{27} + 42 q^{29} - 90 q^{31} + 108 q^{33} - 390 q^{35} + 84 q^{37} + 1014 q^{39} + 618 q^{41} - 42 q^{43} - 1014 q^{45} + 198 q^{47} - 276 q^{49} + 408 q^{51} + 1620 q^{53} + 492 q^{57} + 750 q^{59} - 1314 q^{61} + 1542 q^{63} + 564 q^{65} + 294 q^{67} + 924 q^{69} - 1410 q^{75} - 2448 q^{77} - 804 q^{79} - 666 q^{81} - 360 q^{85} + 1788 q^{87} - 1722 q^{89} + 540 q^{91} + 1128 q^{93} - 2946 q^{95} + 792 q^{97} - 54 q^{99}+O(q^{100}) \) 48 * q + 6 * q^7 - 30 * q^9 + 36 * q^13 + 66 * q^15 + 72 * q^17 + 126 * q^21 + 1200 * q^25 + 396 * q^27 + 42 * q^29 - 90 * q^31 + 108 * q^33 - 390 * q^35 + 84 * q^37 + 1014 * q^39 + 618 * q^41 - 42 * q^43 - 1014 * q^45 + 198 * q^47 - 276 * q^49 + 408 * q^51 + 1620 * q^53 + 492 * q^57 + 750 * q^59 - 1314 * q^61 + 1542 * q^63 + 564 * q^65 + 294 * q^67 + 924 * q^69 - 1410 * q^75 - 2448 * q^77 - 804 * q^79 - 666 * q^81 - 360 * q^85 + 1788 * q^87 - 1722 * q^89 + 540 * q^91 + 1128 * q^93 - 2946 * q^95 + 792 * q^97 - 54 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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