LMFDB - Embedded newform 252.9.z.d.73.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [252,9,Mod(73,252)]

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, 0, 1]))

N = Newforms(chi, 9, names="a")

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

chi := DirichletCharacter("252.73");

S:= CuspForms(chi, 9);

N := Newforms(S);

Level:	$ N $	$=$	$ 252 = 2^{2} \cdot 3^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 9 $
Character orbit:	$[\chi]$	$=$	252.z (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:	$102.659409735$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$6$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 3 x^{11} + 148097 x^{10} + 46071824 x^{9} + 21578502553 x^{8} + 3561445462121 x^{7} + \cdots + 45\!\cdots\!96 $ x^12 - 3x^11 + 148097x^10 + 46071824x^9 + 21578502553x^8 + 3561445462121x^7 + 576413321817541x^6 + 47217566733462528x^5 + 5214056955297543333x^4 + 358752845334081085965x^3 + 30962072851910211245661x^2 + 1221542968331193193318500*x + 45396580558961892385326096
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 2^{20}\cdot 3^{10}\cdot 7^{4} $
Twist minimal:	no (minimal twist has level 84)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			73.3
Root			$-122.377 + 211.963i$ of defining polynomial
Character	$\chi$	$=$	252.73
Dual form			252.9.z.d.145.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(133.903 - 77.3091i) q^{5} +(-2234.88 - 877.558i) q^{7} +O(q^{10})$	$q+(133.903 - 77.3091i) q^{5} +(-2234.88 - 877.558i) q^{7} +(-3950.92 + 6843.20i) q^{11} -4177.64i q^{13} +(-110620. - 63866.3i) q^{17} +(139247. - 80394.4i) q^{19} +(16422.4 + 28444.4i) q^{23} +(-183359. + 317587. i) q^{25} -659560. q^{29} +(-5163.53 - 2981.17i) q^{31} +(-367101. + 55268.8i) q^{35} +(329534. + 570770. i) q^{37} -1.10208e6i q^{41} +4.57153e6 q^{43} +(1.35905e6 - 784649. i) q^{47} +(4.22459e6 + 3.92247e6i) q^{49} +(-4.31027e6 + 7.46560e6i) q^{53} +1.22177e6i q^{55} +(-1.85511e7 - 1.07105e7i) q^{59} +(2.16597e7 - 1.25052e7i) q^{61} +(-322970. - 559400. i) q^{65} +(-9.65705e6 + 1.67265e7i) q^{67} -9.50918e6 q^{71} +(6.91695e6 + 3.99350e6i) q^{73} +(1.48351e7 - 1.18266e7i) q^{77} +(-1.32777e6 - 2.29977e6i) q^{79} +5.37421e7i q^{83} -1.97498e7 q^{85} +(3.33121e7 - 1.92328e7i) q^{89} +(-3.66612e6 + 9.33654e6i) q^{91} +(1.24304e7 - 2.15302e7i) q^{95} -2.56754e7i q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 285 q^{5} + 198 q^{7}+O(q^{10}) $ 12 * q - 285 * q^5 + 198 * q^7	$ 12 q - 285 q^{5} + 198 q^{7} + 17919 q^{11} + 205782 q^{17} + 74313 q^{19} + 62832 q^{23} + 878679 q^{25} + 575454 q^{29} + 1442952 q^{31} + 3989514 q^{35} - 2058621 q^{37} + 7721322 q^{43} - 12088194 q^{47} - 16964694 q^{49} + 5506743 q^{53} - 7511901 q^{59} - 37215576 q^{61} - 5047122 q^{65} - 36824553 q^{67} + 30011556 q^{71} + 95080185 q^{73} + 38333727 q^{77} + 8514456 q^{79} + 20121540 q^{85} - 83038554 q^{89} - 198538635 q^{91} + 221605224 q^{95}+O(q^{100}) $ 12 * q - 285 * q^5 + 198 * q^7 + 17919 * q^11 + 205782 * q^17 + 74313 * q^19 + 62832 * q^23 + 878679 * q^25 + 575454 * q^29 + 1442952 * q^31 + 3989514 * q^35 - 2058621 * q^37 + 7721322 * q^43 - 12088194 * q^47 - 16964694 * q^49 + 5506743 * q^53 - 7511901 * q^59 - 37215576 * q^61 - 5047122 * q^65 - 36824553 * q^67 + 30011556 * q^71 + 95080185 * q^73 + 38333727 * q^77 + 8514456 * q^79 + 20121540 * q^85 - 83038554 * q^89 - 198538635 * q^91 + 221605224 * q^95

Display 100 coefficients 10 coefficients

Character values

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

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

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			0
$3$		0			0
$4$		0			0
$5$	133.903	−	77.3091i	0.214245	−	0.123695i	−0.389037	−	0.921222i	$-0.627192\pi$
$5$	133.903	−	77.3091i	0.214245	−	0.123695i	0.603283	+	0.797527i	$0.293859\pi$
$6$		0			0
$7$	−2234.88	−	877.558i	−0.930813	−	0.365497i
$7$	−2234.88	−	877.558i	−0.930813	−	0.365497i
$8$		0			0
$9$		0			0
$10$		0			0
$11$	−3950.92	+	6843.20i	−0.269853	+	0.467400i	−0.968824	−	0.247751i	$-0.920309\pi$
$11$	−3950.92	+	6843.20i	−0.269853	+	0.467400i	0.698970	+	0.715151i	$0.253642\pi$
$12$		0			0
$13$		−	4177.64i		−	0.146271i	−0.997322	−	0.0731354i	$-0.976699\pi$
$13$		−	4177.64i		−	0.146271i	0.997322	−	0.0731354i	$-0.0233005\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	−110620.	−	63866.3i	−1.32445	−	0.764674i	−0.340019	−	0.940419i	$-0.610433\pi$
$17$	−110620.	−	63866.3i	−1.32445	−	0.764674i	−0.984436	+	0.175745i	$0.943767\pi$
$18$		0			0
$19$	139247.	−	80394.4i	1.06849	−	0.616895i	0.140724	−	0.990049i	$-0.455057\pi$
$19$	139247.	−	80394.4i	1.06849	−	0.616895i	0.927769	+	0.373154i	$0.121724\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	16422.4	+	28444.4i	0.0586847	+	0.101645i	0.893875	−	0.448316i	$-0.147976\pi$
$23$	16422.4	+	28444.4i	0.0586847	+	0.101645i	−0.835191	+	0.549961i	$0.814643\pi$
$24$		0			0
$25$	−183359.	+	317587.i	−0.469399	+	0.813023i
$26$		0			0
$27$		0			0
$28$		0			0
$29$	−659560.			−0.932528			−0.466264	−	0.884646i	$-0.654400\pi$
$29$	−659560.			−0.932528			−0.466264	+	0.884646i	$0.654400\pi$
$30$		0			0
$31$	−5163.53	−	2981.17i	−0.00559114	−	0.00322804i	0.497202	−	0.867635i	$-0.334361\pi$
$31$	−5163.53	−	2981.17i	−0.00559114	−	0.00322804i	−0.502793	+	0.864407i	$0.667694\pi$
$32$		0			0
$33$		0			0
$34$		0			0
$35$	−367101.	+	55268.8i	−0.244632	+	0.0368305i
$36$		0			0
$37$	329534.	+	570770.i	0.175830	+	0.304547i	0.940448	−	0.339937i	$-0.110406\pi$
$37$	329534.	+	570770.i	0.175830	+	0.304547i	−0.764618	+	0.644484i	$0.777072\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$		−	1.10208e6i		−	0.390013i	−0.980802	−	0.195007i	$-0.937527\pi$
$41$		−	1.10208e6i		−	0.390013i	0.980802	−	0.195007i	$-0.0624728\pi$
$42$		0			0
$43$	4.57153e6			1.33717			0.668586	−	0.743635i	$-0.266900\pi$
$43$	4.57153e6			1.33717			0.668586	+	0.743635i	$0.266900\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	1.35905e6	−	784649.i	0.278512	−	0.160799i	−0.354237	−	0.935156i	$-0.615260\pi$
$47$	1.35905e6	−	784649.i	0.278512	−	0.160799i	0.632750	+	0.774356i	$0.281926\pi$
$48$		0			0
$49$	4.22459e6	+	3.92247e6i	0.732824	+	0.680418i
$50$		0			0
$51$		0			0
$52$		0			0
$53$	−4.31027e6	+	7.46560e6i	−0.546262	+	0.946153i	0.452265	+	0.891884i	$0.350616\pi$
$53$	−4.31027e6	+	7.46560e6i	−0.546262	+	0.946153i	−0.998526	+	0.0542691i	$0.982717\pi$
$54$		0			0
$55$			1.22177e6i			0.133518i
$56$		0			0
$57$		0			0
$58$		0			0
$59$	−1.85511e7	−	1.07105e7i	−1.53095	−	0.883895i	−0.999318	−	0.0369211i	$-0.988245\pi$
$59$	−1.85511e7	−	1.07105e7i	−1.53095	−	0.883895i	−0.531634	−	0.846974i	$-0.678422\pi$
$60$		0			0
$61$	2.16597e7	−	1.25052e7i	1.56435	−	0.903177i	0.567539	−	0.823346i	$-0.307896\pi$
$61$	2.16597e7	−	1.25052e7i	1.56435	−	0.903177i	0.996808	−	0.0798301i	$-0.0254378\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	−322970.	−	559400.i	−0.0180929	−	0.0313379i
$66$		0			0
$67$	−9.65705e6	+	1.67265e7i	−0.479231	+	0.830053i	−0.999716	−	0.0238177i	$-0.992418\pi$
$67$	−9.65705e6	+	1.67265e7i	−0.479231	+	0.830053i	0.520485	+	0.853871i	$0.325751\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$	−9.50918e6			−0.374205			−0.187103	−	0.982340i	$-0.559910\pi$
$71$	−9.50918e6			−0.374205			−0.187103	+	0.982340i	$0.559910\pi$
$72$		0			0
$73$	6.91695e6	+	3.99350e6i	0.243570	+	0.140625i	0.616816	−	0.787107i	$-0.288422\pi$
$73$	6.91695e6	+	3.99350e6i	0.243570	+	0.140625i	−0.373247	+	0.927732i	$0.621755\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	1.48351e7	−	1.18266e7i	0.422016	−	0.336431i
$78$		0			0
$79$	−1.32777e6	−	2.29977e6i	−0.0340891	−	0.0590441i	0.848478	−	0.529231i	$-0.177520\pi$
$79$	−1.32777e6	−	2.29977e6i	−0.0340891	−	0.0590441i	−0.882567	+	0.470187i	$0.844186\pi$
$80$		0			0
$81$		0			0
$82$		0			0
$83$			5.37421e7i			1.13241i	0.824266	+	0.566203i	$0.191588\pi$
$83$			5.37421e7i			1.13241i	−0.824266	+	0.566203i	$0.808412\pi$
$84$		0			0
$85$	−1.97498e7			−0.378344
$86$		0			0
$87$		0			0
$88$		0			0
$89$	3.33121e7	−	1.92328e7i	0.530936	−	0.306536i	−0.210461	−	0.977602i	$-0.567497\pi$
$89$	3.33121e7	−	1.92328e7i	0.530936	−	0.306536i	0.741398	+	0.671066i	$0.234163\pi$
$90$		0			0
$91$	−3.66612e6	+	9.33654e6i	−0.0534615	+	0.136151i
$92$		0			0
$93$		0			0
$94$		0			0
$95$	1.24304e7	−	2.15302e7i	0.152613	−	0.264334i
$96$		0			0
$97$		−	2.56754e7i		−	0.290021i	−0.989430	−	0.145011i	$-0.953678\pi$
$97$		−	2.56754e7i		−	0.290021i	0.989430	−	0.145011i	$-0.0463216\pi$
$98$		0			0
$99$		0			0
$100$		0			0
$101$	1.37265e8	+	7.92500e7i	1.31909	+	0.761577i	0.983582	−	0.180461i	$-0.0577589\pi$
$101$	1.37265e8	+	7.92500e7i	1.31909	+	0.761577i	0.335507	+	0.942038i	$0.391092\pi$
$102$		0			0
$103$	−2.36862e7	+	1.36753e7i	−0.210449	+	0.121503i	−0.601520	−	0.798858i	$-0.705438\pi$
$103$	−2.36862e7	+	1.36753e7i	−0.210449	+	0.121503i	0.391071	+	0.920361i	$0.372105\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	8.08597e7	+	1.40053e8i	0.616875	+	1.06846i	0.990053	+	0.140698i	$0.0449348\pi$
$107$	8.08597e7	+	1.40053e8i	0.616875	+	1.06846i	−0.373178	+	0.927760i	$0.621732\pi$
$108$		0			0
$109$	−2.95165e7	+	5.11241e7i	−0.209102	+	0.362176i	−0.951432	−	0.307859i	$-0.900388\pi$
$109$	−2.95165e7	+	5.11241e7i	−0.209102	+	0.362176i	0.742330	+	0.670035i	$0.233721\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	1.64113e8			1.00654			0.503268	−	0.864131i	$-0.332131\pi$
$113$	1.64113e8			1.00654			0.503268	+	0.864131i	$0.332131\pi$
$114$		0			0
$115$	4.39802e6	+	2.53920e6i	0.0251458	+	0.0145180i
$116$		0			0
$117$		0			0
$118$		0			0
$119$	1.91176e8	+	2.39809e8i	0.953333	+	1.19585i
$120$		0			0
$121$	7.59599e7	+	1.31566e8i	0.354358	+	0.613767i
$122$		0			0
$123$		0			0
$124$		0			0
$125$			1.17099e8i			0.479638i
$126$		0			0
$127$	1.21072e8			0.465403			0.232702	−	0.972548i	$-0.425243\pi$
$127$	1.21072e8			0.465403			0.232702	+	0.972548i	$0.425243\pi$
$128$		0			0
$129$		0			0
$130$		0			0
$131$	−5.54093e7	+	3.19906e7i	−0.188147	+	0.108627i	−0.591115	−	0.806587i	$-0.701312\pi$
$131$	−5.54093e7	+	3.19906e7i	−0.188147	+	0.108627i	0.402968	+	0.915214i	$0.367979\pi$
$132$		0			0
$133$	−3.81751e8	+	5.74744e7i	−1.22004	+	0.183683i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	1.56859e8	−	2.71688e8i	0.445274	−	0.771237i	−0.552797	−	0.833316i	$-0.686440\pi$
$137$	1.56859e8	−	2.71688e8i	0.445274	−	0.771237i	0.998071	+	0.0620787i	$0.0197730\pi$
$138$		0			0
$139$		−	2.04519e8i		−	0.547867i	−0.961749	−	0.273934i	$-0.911675\pi$
$139$		−	2.04519e8i		−	0.547867i	0.961749	−	0.273934i	$-0.0883248\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$	2.85884e7	+	1.65055e7i	0.0683670	+	0.0394717i
$144$		0			0
$145$	−8.83172e7	+	5.09900e7i	−0.199790	+	0.115349i
$146$		0			0
$147$		0			0
$148$		0			0
$149$	3.34340e8	+	5.79093e8i	0.678333	+	1.17491i	0.975483	+	0.220076i	$0.0706306\pi$
$149$	3.34340e8	+	5.79093e8i	0.678333	+	1.17491i	−0.297150	+	0.954831i	$0.596036\pi$
$150$		0			0
$151$	1.10149e8	−	1.90784e8i	0.211872	−	0.366973i	−0.740428	−	0.672135i	$-0.765377\pi$
$151$	1.10149e8	−	1.90784e8i	0.211872	−	0.366973i	0.952300	+	0.305162i	$0.0987107\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$	−921886.			−0.00159717
$156$		0			0
$157$	7.29270e8	+	4.21044e8i	1.20030	+	0.692994i	0.960622	−	0.277859i	$-0.0896247\pi$
$157$	7.29270e8	+	4.21044e8i	1.20030	+	0.692994i	0.239678	+	0.970852i	$0.422958\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$	−1.17405e7	−	7.79814e7i	−0.0174736	−	0.116061i
$162$		0			0
$163$	5.08666e8	+	8.81036e8i	0.720581	+	1.24808i	0.960767	+	0.277355i	$0.0894580\pi$
$163$	5.08666e8	+	8.81036e8i	0.720581	+	1.24808i	−0.240187	+	0.970727i	$0.577209\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$			7.85051e8i			1.00933i	0.863316	+	0.504664i	$0.168383\pi$
$167$			7.85051e8i			1.00933i	−0.863316	+	0.504664i	$0.831617\pi$
$168$		0			0
$169$	7.98278e8			0.978605
$170$		0			0
$171$		0			0
$172$		0			0
$173$	4.30544e8	−	2.48575e8i	0.480655	−	0.277506i	−0.240035	−	0.970764i	$-0.577159\pi$
$173$	4.30544e8	−	2.48575e8i	0.480655	−	0.277506i	0.720689	+	0.693258i	$0.243825\pi$
$174$		0			0
$175$	6.88487e8	−	5.48862e8i	0.734080	−	0.585208i
$176$		0			0
$177$		0			0
$178$		0			0
$179$	−8.80361e8	+	1.52483e9i	−0.857529	+	1.48528i	0.0167496	+	0.999860i	$0.494668\pi$
$179$	−8.80361e8	+	1.52483e9i	−0.857529	+	1.48528i	−0.874279	+	0.485424i	$0.838665\pi$
$180$		0			0
$181$			1.40594e9i			1.30994i	0.755653	+	0.654972i	$0.227320\pi$
$181$			1.40594e9i			1.30994i	−0.755653	+	0.654972i	$0.772680\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$	8.82515e7	+	5.09520e7i	0.0753417	+	0.0434985i
$186$		0			0
$187$	8.74100e8	−	5.04662e8i	0.714817	−	0.412700i
$188$		0			0
$189$		0			0
$190$		0			0
$191$	−3.46452e8	−	6.00072e8i	−0.260321	−	0.450889i	0.706006	−	0.708206i	$-0.250495\pi$
$191$	−3.46452e8	−	6.00072e8i	−0.260321	−	0.450889i	−0.966327	+	0.257317i	$0.917162\pi$
$192$		0			0
$193$	−5.17803e8	+	8.96861e8i	−0.373195	+	0.646392i	−0.990055	−	0.140680i	$-0.955071\pi$
$193$	−5.17803e8	+	8.96861e8i	−0.373195	+	0.646392i	0.616860	+	0.787073i	$0.288404\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	1.58650e9			1.05335			0.526676	−	0.850066i	$-0.323438\pi$
$197$	1.58650e9			1.05335			0.526676	+	0.850066i	$0.323438\pi$
$198$		0			0
$199$	4.38090e8	+	2.52932e8i	0.279352	+	0.161284i	0.633130	−	0.774046i	$-0.281770\pi$
$199$	4.38090e8	+	2.52932e8i	0.279352	+	0.161284i	−0.353778	+	0.935329i	$0.615103\pi$
$200$		0			0
$201$		0			0
$202$		0			0
$203$	1.47404e9	+	5.78802e8i	0.868009	+	0.340836i
$204$		0			0
$205$	−8.52012e7	−	1.47573e8i	−0.0482425	−	0.0835585i
$206$		0			0
$207$		0			0
$208$		0			0
$209$			1.27053e9i			0.665885i
$210$		0			0
$211$	8.53493e8			0.430596			0.215298	−	0.976548i	$-0.430928\pi$
$211$	8.53493e8			0.430596			0.215298	+	0.976548i	$0.430928\pi$
$212$		0			0
$213$		0			0
$214$		0			0
$215$	6.12143e8	−	3.53421e8i	0.286483	−	0.165401i
$216$		0			0
$217$	8.92373e6	+	1.11939e7i	0.00402446	+	0.00504825i
$218$		0			0
$219$		0			0
$220$		0			0
$221$	−2.66811e8	+	4.62130e8i	−0.111850	+	0.193729i
$222$		0			0
$223$		−	1.19055e9i		−	0.481426i	−0.970596	−	0.240713i	$-0.922619\pi$
$223$		−	1.19055e9i		−	0.481426i	0.970596	−	0.240713i	$-0.0773812\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	1.55248e9	+	8.96322e8i	0.584684	+	0.337567i	0.762993	−	0.646407i	$-0.223729\pi$
$227$	1.55248e9	+	8.96322e8i	0.584684	+	0.337567i	−0.178309	+	0.983975i	$0.557063\pi$
$228$		0			0
$229$	−3.51985e9	+	2.03219e9i	−1.27992	+	0.738961i	−0.976833	−	0.214003i	$-0.931350\pi$
$229$	−3.51985e9	+	2.03219e9i	−1.27992	+	0.738961i	−0.303085	+	0.952964i	$0.598016\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	−4.96945e8	−	8.60734e8i	−0.168610	−	0.292042i	0.769321	−	0.638862i	$-0.220595\pi$
$233$	−4.96945e8	−	8.60734e8i	−0.168610	−	0.292042i	−0.937932	+	0.346820i	$0.887261\pi$
$234$		0			0
$235$	1.21321e8	−	2.10134e8i	0.0397800	−	0.0689010i
$236$		0			0
$237$		0			0
$238$		0			0
$239$	−1.71719e9			−0.526291			−0.263145	−	0.964756i	$-0.584760\pi$
$239$	−1.71719e9			−0.526291			−0.263145	+	0.964756i	$0.584760\pi$
$240$		0			0
$241$	−3.95118e9	−	2.28121e9i	−1.17127	−	0.676235i	−0.217293	−	0.976106i	$-0.569723\pi$
$241$	−3.95118e9	−	2.28121e9i	−1.17127	−	0.676235i	−0.953980	+	0.299872i	$0.903056\pi$
$242$		0			0
$243$		0			0
$244$		0			0
$245$	8.68929e8	+	1.98633e8i	0.241168	+	0.0551300i
$246$		0			0
$247$	−3.35859e8	−	5.81725e8i	−0.0902338	−	0.156289i
$248$		0			0
$249$		0			0
$250$		0			0
$251$			1.49784e8i			0.0377373i	0.999822	+	0.0188687i	$0.00600644\pi$
$251$			1.49784e8i			0.0377373i	−0.999822	+	0.0188687i	$0.993994\pi$
$252$		0			0
$253$	−2.59534e8			−0.0633450
$254$		0			0
$255$		0			0
$256$		0			0
$257$	6.35751e9	−	3.67051e9i	1.45732	−	0.841384i	0.458440	−	0.888725i	$-0.348408\pi$
$257$	6.35751e9	−	3.67051e9i	1.45732	−	0.841384i	0.998879	+	0.0473414i	$0.0150749\pi$
$258$		0			0
$259$	−2.35586e8	−	1.56479e9i	−0.0523541	−	0.347742i
$260$		0			0
$261$		0			0
$262$		0			0
$263$	−2.40019e9	+	4.15725e9i	−0.501675	+	0.868926i	0.498323	+	0.866991i	$0.333949\pi$
$263$	−2.40019e9	+	4.15725e9i	−0.501675	+	0.868926i	−0.999998	+	0.00193513i	$0.999384\pi$
$264$		0			0
$265$			1.33289e9i			0.270278i
$266$		0			0
$267$		0			0
$268$		0			0
$269$	2.69474e9	+	1.55581e9i	0.514645	+	0.297131i	0.734741	−	0.678348i	$-0.237304\pi$
$269$	2.69474e9	+	1.55581e9i	0.514645	+	0.297131i	−0.220096	+	0.975478i	$0.570637\pi$
$270$		0			0
$271$	−3.16838e9	+	1.82927e9i	−0.587436	+	0.339156i	−0.764083	−	0.645118i	$-0.776808\pi$
$271$	−3.16838e9	+	1.82927e9i	−0.587436	+	0.339156i	0.176647	+	0.984274i	$0.443475\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	−1.44888e9	−	2.50953e9i	−0.253338	−	0.438794i
$276$		0			0
$277$	5.24448e9	−	9.08370e9i	0.890806	−	1.54292i	0.0518958	−	0.998653i	$-0.483474\pi$
$277$	5.24448e9	−	9.08370e9i	0.890806	−	1.54292i	0.838911	−	0.544269i	$-0.183193\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$	−1.88553e9			−0.302419			−0.151210	−	0.988502i	$-0.548317\pi$
$281$	−1.88553e9			−0.302419			−0.151210	+	0.988502i	$0.548317\pi$
$282$		0			0
$283$	1.50968e9	+	8.71616e8i	0.235364	+	0.135887i	0.613044	−	0.790049i	$-0.289945\pi$
$283$	1.50968e9	+	8.71616e8i	0.235364	+	0.135887i	−0.377680	+	0.925936i	$0.623278\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	−9.67143e8	+	2.46303e9i	−0.142549	+	0.363029i
$288$		0			0
$289$	4.66994e9	+	8.08857e9i	0.669453	+	1.15953i
$290$		0			0
$291$		0			0
$292$		0			0
$293$		−	7.68210e9i		−	1.04234i	−0.853453	−	0.521170i	$-0.825496\pi$
$293$		−	7.68210e9i		−	1.04234i	0.853453	−	0.521170i	$-0.174504\pi$
$294$		0			0
$295$	−3.31207e9			−0.437333
$296$		0			0
$297$		0			0
$298$		0			0
$299$	1.18831e8	−	6.86068e7i	0.0148677	−	0.00858386i
$300$		0			0
$301$	−1.02168e10	−	4.01178e9i	−1.24466	−	0.488732i
$302$		0			0
$303$		0			0
$304$		0			0
$305$	1.93354e9	−	3.34899e9i	0.223436	−	0.387003i
$306$		0			0
$307$		−	8.93846e9i		−	1.00626i	−0.864211	−	0.503129i	$-0.832182\pi$
$307$		−	8.93846e9i		−	1.00626i	0.864211	−	0.503129i	$-0.167818\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$	−1.36754e10	−	7.89550e9i	−1.46184	−	0.843992i	−0.462740	−	0.886494i	$-0.653134\pi$
$311$	−1.36754e10	−	7.89550e9i	−1.46184	−	0.843992i	−0.999096	+	0.0425024i	$0.986467\pi$
$312$		0			0
$313$	−8.18174e9	+	4.72373e9i	−0.852449	+	0.492162i	−0.861476	−	0.507798i	$-0.830460\pi$
$313$	−8.18174e9	+	4.72373e9i	−0.852449	+	0.492162i	0.00902752	+	0.999959i	$0.497126\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	−8.46257e9	−	1.46576e10i	−0.838041	−	1.45153i	−0.891530	−	0.452961i	$-0.850368\pi$
$317$	−8.46257e9	−	1.46576e10i	−0.838041	−	1.45153i	0.0534897	−	0.998568i	$-0.482966\pi$
$318$		0			0
$319$	2.60587e9	−	4.51350e9i	0.251646	−	0.435863i
$320$		0			0
$321$		0			0
$322$		0			0
$323$	−2.05380e10			−1.88689
$324$		0			0
$325$	1.32677e9	+	7.66009e8i	0.118922	+	0.0686595i
$326$		0			0
$327$		0			0
$328$		0			0
$329$	−3.72589e9	+	5.60950e8i	−0.318014	+	0.0478785i
$330$		0			0
$331$	1.02406e10	+	1.77372e10i	0.853123	+	1.47765i	0.878375	+	0.477972i	$0.158628\pi$
$331$	1.02406e10	+	1.77372e10i	0.853123	+	1.47765i	−0.0252519	+	0.999681i	$0.508039\pi$
$332$		0			0
$333$		0			0
$334$		0			0
$335$			2.98631e9i			0.237113i
$336$		0			0
$337$	2.14997e10			1.66691			0.833456	−	0.552586i	$-0.186359\pi$
$337$	2.14997e10			1.66691			0.833456	+	0.552586i	$0.186359\pi$
$338$		0			0
$339$		0			0
$340$		0			0
$341$	4.08014e7	−	2.35567e7i	0.00301757	−	0.00174220i
$342$		0			0
$343$	−5.99925e9	−	1.24736e10i	−0.433431	−	0.901187i
$344$		0			0
$345$		0			0
$346$		0			0
$347$	−7.58609e9	+	1.31395e10i	−0.523239	+	0.906277i	0.476395	+	0.879231i	$0.341943\pi$
$347$	−7.58609e9	+	1.31395e10i	−0.523239	+	0.906277i	−0.999634	+	0.0270456i	$0.991390\pi$
$348$		0			0
$349$		−	1.30313e9i		−	0.0878387i	−0.999035	−	0.0439194i	$-0.986016\pi$
$349$		−	1.30313e9i		−	0.0878387i	0.999035	−	0.0439194i	$-0.0139845\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	−1.83413e10	−	1.05893e10i	−1.18122	−	0.681978i	−0.224924	−	0.974376i	$-0.572213\pi$
$353$	−1.83413e10	−	1.05893e10i	−1.18122	−	0.681978i	−0.956297	+	0.292399i	$0.905547\pi$
$354$		0			0
$355$	−1.27331e9	+	7.35147e8i	−0.0801717	+	0.0462872i
$356$		0			0
$357$		0			0
$358$		0			0
$359$	−1.50520e10	−	2.60708e10i	−0.906184	−	1.56956i	−0.819320	−	0.573337i	$-0.805649\pi$
$359$	−1.50520e10	−	2.60708e10i	−0.906184	−	1.56956i	−0.0868642	−	0.996220i	$-0.527685\pi$
$360$		0			0
$361$	4.43472e9	−	7.68117e9i	0.261119	−	0.452271i
$362$		0			0
$363$		0			0
$364$		0			0
$365$	1.23494e9			0.0695783
$366$		0			0
$367$	−5.68403e9	−	3.28168e9i	−0.313323	−	0.180897i	0.335090	−	0.942186i	$-0.391233\pi$
$367$	−5.68403e9	−	3.28168e9i	−0.313323	−	0.180897i	−0.648412	+	0.761289i	$0.724567\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$	1.61844e10	−	1.29022e10i	0.854283	−	0.681034i
$372$		0			0
$373$	−6.45827e9	−	1.11861e10i	−0.333642	−	0.577885i	0.649581	−	0.760293i	$-0.274944\pi$
$373$	−6.45827e9	−	1.11861e10i	−0.333642	−	0.577885i	−0.983223	+	0.182407i	$0.941611\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$			2.75540e9i			0.136402i
$378$		0			0
$379$	−2.24358e10			−1.08739			−0.543694	−	0.839283i	$-0.682975\pi$
$379$	−2.24358e10			−1.08739			−0.543694	+	0.839283i	$0.682975\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$	2.40505e10	−	1.38855e10i	1.11771	−	0.645309i	0.176894	−	0.984230i	$-0.443395\pi$
$383$	2.40505e10	−	1.38855e10i	1.11771	−	0.645309i	0.940815	+	0.338921i	$0.110062\pi$
$384$		0			0
$385$	1.07217e9	−	2.73051e9i	0.0488003	−	0.124280i
$386$		0			0
$387$		0			0
$388$		0			0
$389$	−8.31848e9	+	1.44080e10i	−0.363284	+	0.629226i	−0.988499	−	0.151226i	$-0.951678\pi$
$389$	−8.31848e9	+	1.44080e10i	−0.363284	+	0.629226i	0.625216	+	0.780452i	$0.285011\pi$
$390$		0			0
$391$		−	4.19535e9i		−	0.179499i
$392$		0			0
$393$		0			0
$394$		0			0
$395$	−3.55587e8	−	2.05298e8i	−0.0146069	−	0.00843329i
$396$		0			0
$397$	−1.08327e10	+	6.25426e9i	−0.436088	+	0.251776i	−0.701937	−	0.712239i	$-0.747681\pi$
$397$	−1.08327e10	+	6.25426e9i	−0.436088	+	0.251776i	0.265849	+	0.964015i	$0.414348\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	8.27309e8	+	1.43294e9i	0.0319956	+	0.0554180i	0.881580	−	0.472035i	$-0.156480\pi$
$401$	8.27309e8	+	1.43294e9i	0.0319956	+	0.0554180i	−0.849584	+	0.527453i	$0.823147\pi$
$402$		0			0
$403$	−1.24543e7	+	2.15714e7i	−0.000472169	+	0.000817821i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	−5.20786e9			−0.189794
$408$		0			0
$409$	1.00393e10	+	5.79619e9i	0.358765	+	0.207133i	0.668539	−	0.743677i	$-0.266920\pi$
$409$	1.00393e10	+	5.79619e9i	0.358765	+	0.207133i	−0.309774	+	0.950810i	$0.600253\pi$
$410$		0			0
$411$		0			0
$412$		0			0
$413$	3.20604e10	+	4.02163e10i	1.10197	+	1.38230i
$414$		0			0
$415$	4.15476e9	+	7.19625e9i	0.140073	+	0.242613i
$416$		0			0
$417$		0			0
$418$		0			0
$419$			2.35810e10i			0.765079i	0.923939	+	0.382540i	$0.124950\pi$
$419$			2.35810e10i			0.765079i	−0.923939	+	0.382540i	$0.875050\pi$
$420$		0			0
$421$	8.62676e9			0.274612			0.137306	−	0.990529i	$-0.456156\pi$
$421$	8.62676e9			0.274612			0.137306	+	0.990529i	$0.456156\pi$
$422$		0			0
$423$		0			0
$424$		0			0
$425$	4.05663e10	−	2.34209e10i	1.24340	−	0.717875i
$426$		0			0
$427$	−5.93809e10	+	8.94007e9i	−1.78622	+	0.268924i
$428$		0			0
$429$		0			0
$430$		0			0
$431$	1.28994e10	−	2.23424e10i	0.373818	−	0.647472i	−0.616331	−	0.787487i	$-0.711382\pi$
$431$	1.28994e10	−	2.23424e10i	0.373818	−	0.647472i	0.990149	+	0.140015i	$0.0447152\pi$
$432$		0			0
$433$		−	4.11174e10i		−	1.16970i	−0.811142	−	0.584849i	$-0.801154\pi$
$433$		−	4.11174e10i		−	1.16970i	0.811142	−	0.584849i	$-0.198846\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	4.57354e9	+	2.64053e9i	0.125408	+	0.0724046i
$438$		0			0
$439$	−3.33223e10	+	1.92386e10i	−0.897174	+	0.517983i	−0.876282	−	0.481798i	$-0.839984\pi$
$439$	−3.33223e10	+	1.92386e10i	−0.897174	+	0.517983i	−0.0208914	+	0.999782i	$0.506650\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	−6.20399e9	−	1.07456e10i	−0.161085	−	0.279008i	0.774173	−	0.632974i	$-0.218166\pi$
$443$	−6.20399e9	−	1.07456e10i	−0.161085	−	0.279008i	−0.935258	+	0.353966i	$0.884833\pi$
$444$		0			0
$445$	2.97374e9	−	5.15067e9i	0.0758338	−	0.131348i
$446$		0			0
$447$		0			0
$448$		0			0
$449$	−3.45902e10			−0.851076			−0.425538	−	0.904941i	$-0.639915\pi$
$449$	−3.45902e10			−0.851076			−0.425538	+	0.904941i	$0.639915\pi$
$450$		0			0
$451$	7.54178e9	+	4.35425e9i	0.182292	+	0.105246i
$452$		0			0
$453$		0			0
$454$		0			0
$455$	2.30893e8	+	1.53362e9i	0.00538723	+	0.0357826i
$456$		0			0
$457$	−2.64356e9	−	4.57878e9i	−0.0606072	−	0.104975i	0.834130	−	0.551568i	$-0.185970\pi$
$457$	−2.64356e9	−	4.57878e9i	−0.0606072	−	0.104975i	−0.894737	+	0.446593i	$0.852637\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$			3.55209e10i			0.786466i	0.919439	+	0.393233i	$0.128643\pi$
$461$			3.55209e10i			0.786466i	−0.919439	+	0.393233i	$0.871357\pi$
$462$		0			0
$463$	5.68452e8			0.0123700			0.00618500	−	0.999981i	$-0.498031\pi$
$463$	5.68452e8			0.0123700			0.00618500	+	0.999981i	$0.498031\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	−1.20351e9	+	6.94848e8i	−0.0253036	+	0.0146091i	−0.512598	−	0.858628i	$-0.671317\pi$
$467$	−1.20351e9	+	6.94848e8i	−0.0253036	+	0.0146091i	0.487295	+	0.873238i	$0.337984\pi$
$468$		0			0
$469$	3.62608e10	−	2.89071e10i	0.749456	−	0.597466i
$470$		0			0
$471$		0			0
$472$		0			0
$473$	−1.80617e10	+	3.12839e10i	−0.360840	+	0.624994i
$474$		0			0
$475$			5.89641e10i			1.15828i
$476$		0			0
$477$		0			0
$478$		0			0
$479$	4.91139e10	+	2.83559e10i	0.932958	+	0.538644i	0.887746	−	0.460334i	$-0.152270\pi$
$479$	4.91139e10	+	2.83559e10i	0.932958	+	0.538644i	0.0452122	+	0.998977i	$0.485604\pi$
$480$		0			0
$481$	2.38447e9	−	1.37668e9i	0.0445464	−	0.0257189i
$482$		0			0
$483$		0			0
$484$		0			0
$485$	−1.98494e9	−	3.43802e9i	−0.0358741	−	0.0621357i
$486$		0			0
$487$	2.00673e10	−	3.47576e10i	0.356758	−	0.617923i	−0.630659	−	0.776060i	$-0.717215\pi$
$487$	2.00673e10	−	3.47576e10i	0.356758	−	0.617923i	0.987417	+	0.158137i	$0.0505487\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$	6.70262e8			0.0115324			0.00576619	−	0.999983i	$-0.498165\pi$
$491$	6.70262e8			0.0115324			0.00576619	+	0.999983i	$0.498165\pi$
$492$		0			0
$493$	7.29603e10	+	4.21237e10i	1.23509	+	0.713080i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	2.12519e10	+	8.34486e9i	0.348315	+	0.136771i
$498$		0			0
$499$	4.56562e10	+	7.90788e10i	0.736372	+	1.27543i	0.954119	+	0.299428i	$0.0967959\pi$
$499$	4.56562e10	+	7.90788e10i	0.736372	+	1.27543i	−0.217747	+	0.976005i	$0.569871\pi$
$500$		0			0
$501$		0			0
$502$		0			0
$503$			4.38153e10i			0.684468i	0.939615	+	0.342234i	$0.111184\pi$
$503$			4.38153e10i			0.684468i	−0.939615	+	0.342234i	$0.888816\pi$
$504$		0			0
$505$	2.45070e10			0.376812
$506$		0			0
$507$		0			0
$508$		0			0
$509$	5.28346e10	−	3.05041e10i	0.787132	−	0.454451i	−0.0518199	−	0.998656i	$-0.516502\pi$
$509$	5.28346e10	−	3.05041e10i	0.787132	−	0.454451i	0.838952	+	0.544206i	$0.183169\pi$
$510$		0			0
$511$	−1.19540e10	−	1.49950e10i	−0.175320	−	0.219920i
$512$		0			0
$513$		0			0
$514$		0			0
$515$	−2.11444e9	+	3.66232e9i	−0.0300585	+	0.0520628i
$516$		0			0
$517$			1.24004e10i			0.173569i
$518$		0			0
$519$		0			0
$520$		0			0
$521$	9.04455e10	+	5.22187e10i	1.22754	+	0.708721i	0.966515	−	0.256611i	$-0.0826058\pi$
$521$	9.04455e10	+	5.22187e10i	1.22754	+	0.708721i	0.261026	+	0.965332i	$0.415939\pi$
$522$		0			0
$523$	−6.17123e10	+	3.56296e10i	−0.824831	+	0.476216i	−0.852079	−	0.523413i	$-0.824659\pi$
$523$	−6.17123e10	+	3.56296e10i	−0.824831	+	0.476216i	0.0272488	+	0.999629i	$0.491325\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	3.80792e8	+	6.59552e8i	0.00493680	+	0.00855079i
$528$		0			0
$529$	3.86161e10	−	6.68851e10i	0.493112	−	0.854095i
$530$		0			0
$531$		0			0
$532$		0			0
$533$	−4.60411e9			−0.0570476
$534$		0			0
$535$	2.16548e10	+	1.25024e10i	0.264325	+	0.152608i
$536$		0			0
$537$		0			0
$538$		0			0
$539$	−4.35333e10	+	1.34123e10i	−0.515782	+	0.158909i
$540$		0			0
$541$	5.99851e10	+	1.03897e11i	0.700251	+	1.21287i	0.968378	+	0.249487i	$0.0802621\pi$
$541$	5.99851e10	+	1.03897e11i	0.700251	+	1.21287i	−0.268127	+	0.963384i	$0.586405\pi$
$542$		0			0
$543$		0			0
$544$		0			0
$545$			9.12759e9i			0.103459i
$546$		0			0
$547$	7.67882e10			0.857720			0.428860	−	0.903371i	$-0.358915\pi$
$547$	7.67882e10			0.857720			0.428860	+	0.903371i	$0.358915\pi$
$548$		0			0
$549$		0			0
$550$		0			0
$551$	−9.18418e10	+	5.30249e10i	−0.996400	+	0.575272i
$552$		0			0
$553$	9.49234e8	+	6.30492e9i	0.0101502	+	0.0674185i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	6.00412e9	−	1.03994e10i	0.0623775	−	0.108041i	−0.833150	−	0.553047i	$-0.813465\pi$
$557$	6.00412e9	−	1.03994e10i	0.0623775	−	0.108041i	0.895528	+	0.445006i	$0.146798\pi$
$558$		0			0
$559$		−	1.90982e10i		−	0.195589i
$560$		0			0
$561$		0			0
$562$		0			0
$563$	−7.79826e10	−	4.50233e10i	−0.776183	−	0.448129i	0.0588931	−	0.998264i	$-0.481243\pi$
$563$	−7.79826e10	−	4.50233e10i	−0.776183	−	0.448129i	−0.835076	+	0.550135i	$0.814576\pi$
$564$		0			0
$565$	2.19753e10	−	1.26874e10i	0.215645	−	0.124503i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	5.50444e10	+	9.53398e10i	0.525127	+	0.909547i	0.999572	+	0.0292615i	$0.00931555\pi$
$569$	5.50444e10	+	9.53398e10i	0.525127	+	0.909547i	−0.474445	+	0.880285i	$0.657351\pi$
$570$		0			0
$571$	2.27688e9	−	3.94367e9i	0.0214188	−	0.0370985i	−0.855117	−	0.518435i	$-0.826515\pi$
$571$	2.27688e9	−	3.94367e9i	0.0214188	−	0.0370985i	0.876536	+	0.481336i	$0.159848\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$	−1.20448e10			−0.110186
$576$		0			0
$577$	2.58023e10	+	1.48969e10i	0.232785	+	0.134398i	0.611856	−	0.790969i	$-0.290423\pi$
$577$	2.58023e10	+	1.48969e10i	0.232785	+	0.134398i	−0.379071	+	0.925367i	$0.623757\pi$
$578$		0			0
$579$		0			0
$580$		0			0
$581$	4.71618e10	−	1.20107e11i	0.413891	−	1.05406i
$582$		0			0
$583$	−3.40591e10	−	5.89920e10i	−0.294821	−	0.510645i
$584$		0			0
$585$		0			0
$586$		0			0
$587$			4.87063e10i			0.410235i	0.978737	+	0.205118i	$0.0657577\pi$
$587$			4.87063e10i			0.410235i	−0.978737	+	0.205118i	$0.934242\pi$
$588$		0			0
$589$	−9.58676e8			−0.00796546
$590$		0			0
$591$		0			0
$592$		0			0
$593$	1.48606e11	−	8.57978e10i	1.20176	−	0.693837i	0.240815	−	0.970571i	$-0.422585\pi$
$593$	1.48606e11	−	8.57978e10i	1.20176	−	0.693837i	0.960947	+	0.276734i	$0.0892520\pi$
$594$		0			0
$595$	4.41385e10	+	1.73316e10i	0.352168	+	0.138284i
$596$		0			0
$597$		0			0
$598$		0			0
$599$	−1.22733e11	+	2.12580e11i	−0.953355	+	1.65126i	−0.215268	+	0.976555i	$0.569063\pi$
$599$	−1.22733e11	+	2.12580e11i	−0.953355	+	1.65126i	−0.738087	+	0.674705i	$0.764271\pi$
$600$		0			0
$601$			6.97408e10i			0.534551i	0.963620	+	0.267275i	$0.0861233\pi$
$601$			6.97408e10i			0.534551i	−0.963620	+	0.267275i	$0.913877\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$	2.03426e10	+	1.17448e10i	0.151839	+	0.0876644i
$606$		0			0
$607$	8.32636e10	−	4.80723e10i	0.613339	−	0.354111i	−0.160932	−	0.986965i	$-0.551450\pi$
$607$	8.32636e10	−	4.80723e10i	0.613339	−	0.354111i	0.774271	+	0.632854i	$0.218117\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	−3.27798e9	−	5.67763e9i	−0.0235202	−	0.0407383i
$612$		0			0
$613$	−5.64299e10	+	9.77394e10i	−0.399638	+	0.692194i	−0.993681	−	0.112239i	$-0.964198\pi$
$613$	−5.64299e10	+	9.77394e10i	−0.399638	+	0.692194i	0.594043	+	0.804433i	$0.297531\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	1.66934e11			1.15187			0.575936	−	0.817495i	$-0.304638\pi$
$617$	1.66934e11			1.15187			0.575936	+	0.817495i	$0.304638\pi$
$618$		0			0
$619$	−2.13512e11	−	1.23271e11i	−1.45432	−	0.839650i	−0.455595	−	0.890187i	$-0.650573\pi$
$619$	−2.13512e11	−	1.23271e11i	−1.45432	−	0.839650i	−0.998722	+	0.0505371i	$0.983907\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$	−9.13266e10	+	1.37496e10i	−0.606240	+	0.0912723i
$624$		0			0
$625$	−6.25718e10	−	1.08378e11i	−0.410071	−	0.710263i
$626$		0			0
$627$		0			0
$628$		0			0
$629$		−	8.41846e10i		−	0.537811i
$630$		0			0
$631$	−2.85012e11			−1.79782			−0.898910	−	0.438133i	$-0.855640\pi$
$631$	−2.85012e11			−1.79782			−0.898910	+	0.438133i	$0.855640\pi$
$632$		0			0
$633$		0			0
$634$		0			0
$635$	1.62120e10	−	9.35998e9i	0.0997104	−	0.0575679i
$636$		0			0
$637$	1.63867e10	−	1.76488e10i	0.0995254	−	0.107191i
$638$		0			0
$639$		0			0
$640$		0			0
$641$	1.12062e11	−	1.94098e11i	0.663785	−	1.14971i	−0.315828	−	0.948816i	$-0.602282\pi$
$641$	1.12062e11	−	1.94098e11i	0.663785	−	1.14971i	0.979613	−	0.200893i	$-0.0643844\pi$
$642$		0			0
$643$			2.37170e11i			1.38745i	0.720241	+	0.693724i	$0.244031\pi$
$643$			2.37170e11i			1.38745i	−0.720241	+	0.693724i	$0.755969\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	1.95163e11	+	1.12678e11i	1.11373	+	0.643014i	0.939794	−	0.341742i	$-0.111017\pi$
$647$	1.95163e11	+	1.12678e11i	1.11373	+	0.643014i	0.173940	+	0.984756i	$0.444350\pi$
$648$		0			0
$649$	1.46588e11	−	8.46326e10i	0.826265	−	0.477044i
$650$		0			0
$651$		0			0
$652$		0			0
$653$	9.06390e10	+	1.56991e11i	0.498497	+	0.863422i	0.999998	−	0.00173469i	$-0.000552168\pi$
$653$	9.06390e10	+	1.56991e11i	0.498497	+	0.863422i	−0.501502	+	0.865157i	$0.667219\pi$
$654$		0			0
$655$	−4.94632e9	+	8.56729e9i	−0.0268731	+	0.0465455i
$656$		0			0
$657$		0			0
$658$		0			0
$659$	−2.00364e11			−1.06238			−0.531189	−	0.847253i	$-0.678255\pi$
$659$	−2.00364e11			−1.06238			−0.531189	+	0.847253i	$0.678255\pi$
$660$		0			0
$661$	−8.46518e10	−	4.88737e10i	−0.443435	−	0.256017i	0.261618	−	0.965171i	$-0.415744\pi$
$661$	−8.46518e10	−	4.88737e10i	−0.443435	−	0.256017i	−0.705054	+	0.709154i	$0.749077\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$	−4.66745e10	+	3.72089e10i	−0.238667	+	0.190266i
$666$		0			0
$667$	−1.08315e10	−	1.87608e10i	−0.0547251	−	0.0947867i
$668$		0			0
$669$		0			0
$670$		0			0
$671$			1.97629e11i			0.974901i
$672$		0			0
$673$	−2.14833e11			−1.04723			−0.523614	−	0.851956i	$-0.675416\pi$
$673$	−2.14833e11			−1.04723			−0.523614	+	0.851956i	$0.675416\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	2.10418e11	−	1.21485e11i	1.00168	−	0.578320i	0.0929348	−	0.995672i	$-0.470375\pi$
$677$	2.10418e11	−	1.21485e11i	1.00168	−	0.578320i	0.908745	+	0.417352i	$0.137042\pi$
$678$		0			0
$679$	−2.25316e10	+	5.73814e10i	−0.106002	+	0.269955i
$680$		0			0
$681$		0			0
$682$		0			0
$683$	1.78386e11	−	3.08973e11i	0.819742	−	1.41984i	−0.0861296	−	0.996284i	$-0.527450\pi$
$683$	1.78386e11	−	3.08973e11i	0.819742	−	1.41984i	0.905872	−	0.423552i	$-0.139217\pi$
$684$		0			0
$685$		−	4.85065e10i		−	0.220312i
$686$		0			0
$687$		0			0
$688$		0			0
$689$	3.11886e10	+	1.80068e10i	0.138395	+	0.0799022i
$690$		0			0
$691$	3.06169e11	−	1.76767e11i	1.34291	−	0.775332i	0.355680	−	0.934608i	$-0.384249\pi$
$691$	3.06169e11	−	1.76767e11i	1.34291	−	0.775332i	0.987234	+	0.159275i	$0.0509158\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	−1.58112e10	−	2.73858e10i	−0.0677682	−	0.117378i
$696$		0			0
$697$	−7.03861e10	+	1.21912e11i	−0.298233	+	0.516555i
$698$		0			0
$699$		0			0
$700$		0			0
$701$	−3.14132e11			−1.30089			−0.650445	−	0.759553i	$-0.725418\pi$
$701$	−3.14132e11			−1.30089			−0.650445	+	0.759553i	$0.725418\pi$
$702$		0			0
$703$	9.17734e10	+	5.29854e10i	0.375747	+	0.216938i
$704$		0			0
$705$		0			0
$706$		0			0
$707$	−2.37224e11	−	2.97572e11i	−0.949471	−	1.19101i
$708$		0			0
$709$	−1.40578e11	−	2.43487e11i	−0.556328	−	0.963589i	−0.997799	−	0.0663130i	$-0.978876\pi$
$709$	−1.40578e11	−	2.43487e11i	−0.556328	−	0.963589i	0.441471	−	0.897276i	$-0.354457\pi$
$710$		0			0
$711$		0			0
$712$		0			0
$713$		−	1.95831e8i		−	0.000757747i
$714$		0			0
$715$	5.10412e9			0.0195297
$716$		0			0
$717$		0			0
$718$		0			0
$719$	−4.14076e11	+	2.39067e11i	−1.54940	+	0.894548i	−0.551215	+	0.834363i	$0.685836\pi$
$719$	−4.14076e11	+	2.39067e11i	−1.54940	+	0.894548i	−0.998187	+	0.0601845i	$0.980831\pi$
$720$		0			0
$721$	6.49367e10	−	9.77652e9i	0.240298	−	0.0361779i
$722$		0			0
$723$		0			0
$724$		0			0
$725$	1.20936e11	−	2.09468e11i	0.437728	−	0.758167i
$726$		0			0
$727$		−	5.00817e11i		−	1.79284i	−0.443206	−	0.896420i	$-0.646159\pi$
$727$		−	5.00817e11i		−	1.79284i	0.443206	−	0.896420i	$-0.353841\pi$
$728$		0			0
$729$		0			0
$730$		0			0
$731$	−5.05701e11	−	2.91967e11i	−1.77102	−	1.02250i
$732$		0			0
$733$	−8.44252e10	+	4.87429e10i	−0.292453	+	0.168848i	−0.639048	−	0.769167i	$-0.720671\pi$
$733$	−8.44252e10	+	4.87429e10i	−0.292453	+	0.168848i	0.346594	+	0.938015i	$0.387338\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	−7.63085e10	−	1.32170e11i	−0.258644	−	0.447985i
$738$		0			0
$739$	−1.10837e11	+	1.91976e11i	−0.371628	+	0.643678i	−0.989816	−	0.142352i	$-0.954534\pi$
$739$	−1.10837e11	+	1.91976e11i	−0.371628	+	0.643678i	0.618188	+	0.786030i	$0.287867\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	−2.62831e11			−0.862426			−0.431213	−	0.902250i	$-0.641914\pi$
$743$	−2.62831e11			−0.862426			−0.431213	+	0.902250i	$0.641914\pi$
$744$		0			0
$745$	8.95384e10	+	5.16950e10i	0.290659	+	0.167812i
$746$		0			0
$747$		0			0
$748$		0			0
$749$	−5.78071e10	−	3.83961e11i	−0.183677	−	1.22000i
$750$		0			0
$751$	−1.37391e11	−	2.37969e11i	−0.431917	−	0.748102i	0.565122	−	0.825008i	$-0.308829\pi$
$751$	−1.37391e11	−	2.37969e11i	−0.431917	−	0.748102i	−0.997038	+	0.0769059i	$0.975496\pi$
$752$		0			0
$753$		0			0
$754$		0			0
$755$		−	3.40622e10i		−	0.104830i
$756$		0			0
$757$	1.73327e11			0.527817			0.263909	−	0.964548i	$-0.414988\pi$
$757$	1.73327e11			0.527817			0.263909	+	0.964548i	$0.414988\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	−3.50804e11	+	2.02537e11i	−1.04599	+	0.603901i	−0.921523	−	0.388323i	$-0.873054\pi$
$761$	−3.50804e11	+	2.02537e11i	−1.04599	+	0.603901i	−0.124464	+	0.992224i	$0.539721\pi$
$762$		0			0
$763$	1.10830e11	−	8.83538e10i	0.327009	−	0.260692i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	−4.47446e10	+	7.74999e10i	−0.129288	+	0.223934i
$768$		0			0
$769$			6.69043e11i			1.91315i	0.291488	+	0.956574i	$0.405850\pi$
$769$			6.69043e11i			1.91315i	−0.291488	+	0.956574i	$0.594150\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$	7.11009e10	+	4.10502e10i	0.199140	+	0.114973i	0.596254	−	0.802796i	$-0.296655\pi$
$773$	7.11009e10	+	4.10502e10i	0.199140	+	0.114973i	−0.397115	+	0.917769i	$0.629988\pi$
$774$		0			0
$775$	1.89356e9	−	1.09325e9i	0.00524895	−	0.00303048i
$776$		0			0
$777$		0			0
$778$		0			0
$779$	−8.86014e10	−	1.53462e11i	−0.240597	−	0.416727i
$780$		0			0
$781$	3.75701e10	−	6.50732e10i	0.100981	−	0.174903i
$782$		0			0
$783$		0			0
$784$		0			0
$785$	1.30202e11			0.342878
$786$		0			0
$787$	1.30594e11	+	7.53983e10i	0.340427	+	0.196545i	0.660461	−	0.750861i	$-0.270361\pi$
$787$	1.30594e11	+	7.53983e10i	0.340427	+	0.196545i	−0.320034	+	0.947406i	$0.603694\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$	−3.66773e11	−	1.44019e11i	−0.936896	−	0.367885i
$792$		0			0
$793$	−5.22424e10	−	9.04865e10i	−0.132108	−	0.228819i
$794$		0			0
$795$		0			0
$796$		0			0
$797$		−	2.07975e11i		−	0.515439i	−0.966220	−	0.257720i	$-0.917029\pi$
$797$		−	2.07975e11i		−	0.515439i	0.966220	−	0.257720i	$-0.0829711\pi$
$798$		0			0
$799$	−2.00451e11			−0.491836
$800$		0			0
$801$		0			0
$802$		0			0
$803$	−5.46567e10	+	3.15561e10i	−0.131456	+	0.0758963i
$804$		0			0
$805$	−7.60077e9	−	9.53433e9i	−0.0180998	−	0.0227042i
$806$		0			0
$807$		0			0
$808$		0			0
$809$	3.44290e11	−	5.96328e11i	0.803768	−	1.39217i	−0.113352	−	0.993555i	$-0.536159\pi$
$809$	3.44290e11	−	5.96328e11i	0.803768	−	1.39217i	0.917120	−	0.398612i	$-0.130508\pi$
$810$		0			0
$811$			1.52097e10i			0.0351591i	0.999845	+	0.0175795i	$0.00559603\pi$
$811$			1.52097e10i			0.0351591i	−0.999845	+	0.0175795i	$0.994404\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$	1.36224e11	+	7.86491e10i	0.308762	+	0.178264i
$816$		0			0
$817$	6.36572e11	−	3.67525e11i	1.42876	−	0.824895i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	3.67890e11	+	6.37204e11i	0.809740	+	1.40251i	0.913044	+	0.407860i	$0.133725\pi$
$821$	3.67890e11	+	6.37204e11i	0.809740	+	1.40251i	−0.103305	+	0.994650i	$0.532942\pi$
$822$		0			0
$823$	−9.71200e10	+	1.68217e11i	−0.211694	+	0.366665i	−0.952245	−	0.305335i	$-0.901231\pi$
$823$	−9.71200e10	+	1.68217e11i	−0.211694	+	0.366665i	0.740551	+	0.672001i	$0.234565\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	−5.50782e11			−1.17749			−0.588746	−	0.808318i	$-0.700378\pi$
$827$	−5.50782e11			−1.17749			−0.588746	+	0.808318i	$0.700378\pi$
$828$		0			0
$829$	−9.83589e10	−	5.67875e10i	−0.208255	−	0.120236i	0.392245	−	0.919861i	$-0.371698\pi$
$829$	−9.83589e10	−	5.67875e10i	−0.208255	−	0.120236i	−0.600500	+	0.799625i	$0.705032\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$	−2.16808e11	−	7.03712e11i	−0.450294	−	1.46155i
$834$		0			0
$835$	6.06916e10	+	1.05121e11i	0.124848	+	0.216244i
$836$		0			0
$837$		0			0
$838$		0			0
$839$			5.71368e11i			1.15310i	0.817061	+	0.576551i	$0.195602\pi$
$839$			5.71368e11i			1.15310i	−0.817061	+	0.576551i	$0.804398\pi$
$840$		0			0
$841$	−6.52276e10			−0.130391
$842$		0			0
$843$		0			0
$844$		0			0
$845$	1.06892e11	−	6.17142e10i	0.209662	−	0.121048i
$846$		0			0
$847$	−5.43042e10	−	3.60694e11i	−0.105511	−	0.700819i
$848$		0			0
$849$		0			0
$850$		0			0
$851$	−1.08235e10	+	1.87468e10i	−0.0206371	+	0.0357445i
$852$		0			0
$853$			1.61864e11i			0.305742i	0.988246	+	0.152871i	$0.0488519\pi$
$853$			1.61864e11i			0.305742i	−0.988246	+	0.152871i	$0.951148\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	1.38704e11	+	8.00810e10i	0.257138	+	0.148459i	0.623028	−	0.782199i	$-0.285902\pi$
$857$	1.38704e11	+	8.00810e10i	0.257138	+	0.148459i	−0.365890	+	0.930658i	$0.619235\pi$
$858$		0			0
$859$	−2.45231e11	+	1.41584e11i	−0.450405	+	0.260042i	−0.708001	−	0.706211i	$-0.750403\pi$
$859$	−2.45231e11	+	1.41584e11i	−0.450405	+	0.260042i	0.257596	+	0.966253i	$0.417070\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	3.89609e11	+	6.74823e11i	0.702402	+	1.21660i	0.967621	+	0.252408i	$0.0812224\pi$
$863$	3.89609e11	+	6.74823e11i	0.702402	+	1.21660i	−0.265219	+	0.964188i	$0.585444\pi$
$864$		0			0
$865$	3.84342e10	−	6.65700e10i	0.0686520	−	0.118909i
$866$		0			0
$867$		0			0
$868$		0			0
$869$	2.09837e10			0.0367963
$870$		0			0
$871$	6.98774e10	+	4.03437e10i	0.121413	+	0.0700976i
$872$		0			0
$873$		0			0
$874$		0			0
$875$	1.02761e11	−	2.61703e11i	0.175306	−	0.446453i
$876$		0			0
$877$	−3.57632e10	−	6.19436e10i	−0.0604557	−	0.104712i	0.834213	−	0.551442i	$-0.185922\pi$
$877$	−3.57632e10	−	6.19436e10i	−0.0604557	−	0.104712i	−0.894669	+	0.446729i	$0.852589\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$			8.68861e11i			1.44227i	0.692795	+	0.721135i	$0.256379\pi$
$881$			8.68861e11i			1.44227i	−0.692795	+	0.721135i	$0.743621\pi$
$882$		0			0
$883$	−8.82118e11			−1.45105			−0.725527	−	0.688194i	$-0.758404\pi$
$883$	−8.82118e11			−1.45105			−0.725527	+	0.688194i	$0.758404\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	7.26589e11	−	4.19496e11i	1.17380	−	0.677694i	0.219229	−	0.975674i	$-0.429646\pi$
$887$	7.26589e11	−	4.19496e11i	1.17380	−	0.677694i	0.954572	+	0.297979i	$0.0963126\pi$
$888$		0			0
$889$	−2.70582e11	−	1.06248e11i	−0.433203	−	0.170103i
$890$		0			0
$891$		0			0
$892$		0			0
$893$	1.26163e11	−	2.18520e11i	0.198392	−	0.343626i
$894$		0			0
$895$			2.72240e11i			0.424287i
$896$		0			0
$897$		0			0
$898$		0			0
$899$	3.40566e9	+	1.96626e9i	0.00521389	+	0.00301024i
$900$		0			0
$901$	9.53601e11	−	5.50562e11i	1.44700	−	0.835424i
$902$		0			0
$903$		0			0
$904$		0			0
$905$	1.08692e11	+	1.88260e11i	0.162033	+	0.280649i
$906$		0			0
$907$	−4.38453e11	+	7.59423e11i	−0.647879	+	1.12216i	0.335749	+	0.941951i	$0.391011\pi$
$907$	−4.38453e11	+	7.59423e11i	−0.647879	+	1.12216i	−0.983628	+	0.180208i	$0.942323\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$	−1.09312e10			−0.0158706			−0.00793529	−	0.999969i	$-0.502526\pi$
$911$	−1.09312e10			−0.0158706			−0.00793529	+	0.999969i	$0.502526\pi$
$912$		0			0
$913$	−3.67768e11	−	2.12331e11i	−0.529287	−	0.305584i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	1.51907e11	−	2.28702e10i	0.214832	−	0.0323440i
$918$		0			0
$919$	−3.27143e11	−	5.66628e11i	−0.458643	−	0.794394i	0.540246	−	0.841507i	$-0.318331\pi$
$919$	−3.27143e11	−	5.66628e11i	−0.458643	−	0.794394i	−0.998890	+	0.0471134i	$0.984998\pi$
$920$		0			0
$921$		0			0
$922$		0			0
$923$			3.97260e10i			0.0547353i
$924$		0			0
$925$	−2.41692e11			−0.330138
$926$		0			0
$927$		0			0
$928$		0			0
$929$	1.55844e11	−	8.99765e10i	0.209231	−	0.120800i	−0.391723	−	0.920083i	$-0.628121\pi$
$929$	1.55844e11	−	8.99765e10i	0.209231	−	0.120800i	0.600954	+	0.799283i	$0.294787\pi$
$930$		0			0
$931$	9.03606e11	+	2.06560e11i	1.20276	+	0.274947i
$932$		0			0
$933$		0			0
$934$		0			0
$935$	7.80300e10	−	1.35152e11i	0.102097	−	0.176838i
$936$		0			0
$937$			7.66845e11i			0.994831i	0.867512	+	0.497415i	$0.165718\pi$
$937$			7.66845e11i			0.994831i	−0.867512	+	0.497415i	$0.834282\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$	1.22218e12	+	7.05627e11i	1.55875	+	0.899946i	0.997377	+	0.0723858i	$0.0230613\pi$
$941$	1.22218e12	+	7.05627e11i	1.55875	+	0.899946i	0.561376	+	0.827561i	$0.310272\pi$
$942$		0			0
$943$	3.13481e10	−	1.80988e10i	0.0396428	−	0.0228878i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	−1.03071e10	−	1.78523e10i	−0.0128155	−	0.0221971i	0.859547	−	0.511057i	$-0.170746\pi$
$947$	−1.03071e10	−	1.78523e10i	−0.0128155	−	0.0221971i	−0.872362	+	0.488860i	$0.837413\pi$
$948$		0			0
$949$	1.66834e10	−	2.88966e10i	0.0205694	−	0.0356272i
$950$		0			0
$951$		0			0
$952$		0			0
$953$	−2.06006e10			−0.0249752			−0.0124876	−	0.999922i	$-0.503975\pi$
$953$	−2.06006e10			−0.0249752			−0.0124876	+	0.999922i	$0.503975\pi$
$954$		0			0
$955$	−9.27821e10	−	5.35677e10i	−0.111545	−	0.0644006i
$956$		0			0
$957$		0			0
$958$		0			0
$959$	−5.88983e11	+	4.69537e11i	−0.696351	+	0.555131i
$960$		0			0
$961$	−4.26428e11	−	7.38595e11i	−0.499979	−	0.865989i
$962$		0			0
$963$		0			0
$964$		0			0
$965$			1.60124e11i			0.184649i
$966$		0			0
$967$	−1.50116e12			−1.71681			−0.858405	−	0.512973i	$-0.828544\pi$
$967$	−1.50116e12			−1.71681			−0.858405	+	0.512973i	$0.828544\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$	6.65121e11	−	3.84008e11i	0.748210	−	0.431979i	−0.0768368	−	0.997044i	$-0.524482\pi$
$971$	6.65121e11	−	3.84008e11i	0.748210	−	0.431979i	0.825047	+	0.565064i	$0.191149\pi$
$972$		0			0
$973$	−1.79478e11	+	4.57076e11i	−0.200244	+	0.509962i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	−5.61187e11	+	9.72004e11i	−0.615927	+	1.06682i	0.374294	+	0.927310i	$0.377885\pi$
$977$	−5.61187e11	+	9.72004e11i	−0.615927	+	1.06682i	−0.990221	+	0.139507i	$0.955448\pi$
$978$		0			0
$979$			3.03949e11i			0.330879i
$980$		0			0
$981$		0			0
$982$		0			0
$983$	1.27850e12	+	7.38145e11i	1.36927	+	0.790546i	0.990834	−	0.135083i	$-0.0431300\pi$
$983$	1.27850e12	+	7.38145e11i	1.36927	+	0.790546i	0.378432	+	0.925629i	$0.376463\pi$
$984$		0			0
$985$	2.12437e11	−	1.22651e11i	0.225676	−	0.130294i
$986$		0			0
$987$		0			0
$988$		0			0
$989$	7.50753e10	+	1.30034e11i	0.0784715	+	0.135917i
$990$		0			0
$991$	7.05075e11	−	1.22123e12i	0.731039	−	1.26620i	−0.225400	−	0.974266i	$-0.572369\pi$
$991$	7.05075e11	−	1.22123e12i	0.731039	−	1.26620i	0.956439	−	0.291931i	$-0.0942978\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$	7.82157e10			0.0797998
$996$		0			0
$997$	9.23084e11	+	5.32943e11i	0.934244	+	0.539386i	0.888151	−	0.459551i	$-0.151990\pi$
$997$	9.23084e11	+	5.32943e11i	0.934244	+	0.539386i	0.0460928	+	0.998937i	$0.485323\pi$
$998$		0			0
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	252.9.z.d.73.3		12
3.2	odd	2		84.9.m.b.73.4	yes	12
7.5	odd	6	inner	252.9.z.d.145.3		12
21.5	even	6		84.9.m.b.61.4	✓	12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
84.9.m.b.61.4	✓	12	21.5	even	6
84.9.m.b.73.4	yes	12	3.2	odd	2
252.9.z.d.73.3		12	1.1	even	1	trivial
252.9.z.d.145.3		12	7.5	odd	6	inner

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:	\( k \)	\(=\)	\( 9 \)
Character orbit:	\([\chi]\)	\(=\)	252.z (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(133.903 - 77.3091i) q^{5} +(-2234.88 - 877.558i) q^{7} +O(q^{10})\)	\(q+(133.903 - 77.3091i) q^{5} +(-2234.88 - 877.558i) q^{7} +(-3950.92 + 6843.20i) q^{11} -4177.64i q^{13} +(-110620. - 63866.3i) q^{17} +(139247. - 80394.4i) q^{19} +(16422.4 + 28444.4i) q^{23} +(-183359. + 317587. i) q^{25} -659560. q^{29} +(-5163.53 - 2981.17i) q^{31} +(-367101. + 55268.8i) q^{35} +(329534. + 570770. i) q^{37} -1.10208e6i q^{41} +4.57153e6 q^{43} +(1.35905e6 - 784649. i) q^{47} +(4.22459e6 + 3.92247e6i) q^{49} +(-4.31027e6 + 7.46560e6i) q^{53} +1.22177e6i q^{55} +(-1.85511e7 - 1.07105e7i) q^{59} +(2.16597e7 - 1.25052e7i) q^{61} +(-322970. - 559400. i) q^{65} +(-9.65705e6 + 1.67265e7i) q^{67} -9.50918e6 q^{71} +(6.91695e6 + 3.99350e6i) q^{73} +(1.48351e7 - 1.18266e7i) q^{77} +(-1.32777e6 - 2.29977e6i) q^{79} +5.37421e7i q^{83} -1.97498e7 q^{85} +(3.33121e7 - 1.92328e7i) q^{89} +(-3.66612e6 + 9.33654e6i) q^{91} +(1.24304e7 - 2.15302e7i) q^{95} -2.56754e7i q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 285 q^{5} + 198 q^{7}+O(q^{10}) \) 12 * q - 285 * q^5 + 198 * q^7	\( 12 q - 285 q^{5} + 198 q^{7} + 17919 q^{11} + 205782 q^{17} + 74313 q^{19} + 62832 q^{23} + 878679 q^{25} + 575454 q^{29} + 1442952 q^{31} + 3989514 q^{35} - 2058621 q^{37} + 7721322 q^{43} - 12088194 q^{47} - 16964694 q^{49} + 5506743 q^{53} - 7511901 q^{59} - 37215576 q^{61} - 5047122 q^{65} - 36824553 q^{67} + 30011556 q^{71} + 95080185 q^{73} + 38333727 q^{77} + 8514456 q^{79} + 20121540 q^{85} - 83038554 q^{89} - 198538635 q^{91} + 221605224 q^{95}+O(q^{100}) \) 12 * q - 285 * q^5 + 198 * q^7 + 17919 * q^11 + 205782 * q^17 + 74313 * q^19 + 62832 * q^23 + 878679 * q^25 + 575454 * q^29 + 1442952 * q^31 + 3989514 * q^35 - 2058621 * q^37 + 7721322 * q^43 - 12088194 * q^47 - 16964694 * q^49 + 5506743 * q^53 - 7511901 * q^59 - 37215576 * q^61 - 5047122 * q^65 - 36824553 * q^67 + 30011556 * q^71 + 95080185 * q^73 + 38333727 * q^77 + 8514456 * q^79 + 20121540 * q^85 - 83038554 * q^89 - 198538635 * q^91 + 221605224 * q^95

Introduction

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