LMFDB - Embedded newform 288.3.t.b.79.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [288,3,Mod(79,288)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(288, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 3, 4]))

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

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

chi := DirichletCharacter("288.79");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 288 = 2^{5} \cdot 3^{2} $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	288.t (of order $6$, degree $2$, not 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:	$7.84743161358$
Analytic rank:	$0$
Dimension:	$40$
Relative dimension:	$20$ over $\Q(\zeta_{6})$
Twist minimal:	no (minimal twist has level 72)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			79.4
Character	$\chi$	$=$	288.79
Dual form			288.3.t.b.175.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.66358 - 1.38035i) q^{3} +(8.07964 - 4.66478i) q^{5} +(4.91220 + 2.83606i) q^{7} +(5.18928 + 7.35333i) q^{9} +O(q^{10})$	\(q+(-2.66358 - 1.38035i) q^{3} +(8.07964 - 4.66478i) q^{5} +(4.91220 + 2.83606i) q^{7} +(5.18928 + 7.35333i) q^{9} +(1.85519 - 3.21328i) q^{11} +(-11.0919 + 6.40390i) q^{13} +(-27.9598 + 1.27229i) q^{15} +11.1817 q^{17} +13.1532 q^{19} +(-9.16928 - 14.3346i) q^{21} +(20.2104 - 11.6685i) q^{23} +(31.0204 - 53.7288i) q^{25} +(-3.67189 - 26.7492i) q^{27} +(-14.6837 - 8.47767i) q^{29} +(-3.32057 + 1.91713i) q^{31} +(-9.37688 + 5.99801i) q^{33} +52.9184 q^{35} -13.8029i q^{37} +(38.3837 - 1.74662i) q^{39} +(3.05861 + 5.29766i) q^{41} +(11.3997 - 19.7448i) q^{43} +(76.2291 + 35.2054i) q^{45} +(-49.8977 - 28.8084i) q^{47} +(-8.41350 - 14.5726i) q^{49} +(-29.7834 - 15.4347i) q^{51} +60.0402i q^{53} -34.6162i q^{55} +(-35.0344 - 18.1559i) q^{57} +(55.3504 + 95.8696i) q^{59} +(-73.2932 - 42.3159i) q^{61} +(4.63630 + 50.8382i) q^{63} +(-59.7456 + 103.482i) q^{65} +(-16.0918 - 27.8718i) q^{67} +(-69.9385 + 3.18250i) q^{69} +38.7881i q^{71} -13.6313 q^{73} +(-156.790 + 100.292i) q^{75} +(18.2261 - 10.5229i) q^{77} +(-4.14976 - 2.39586i) q^{79} +(-27.1428 + 76.3169i) q^{81} +(2.70708 - 4.68879i) q^{83} +(90.3444 - 52.1604i) q^{85} +(27.4092 + 42.8496i) q^{87} +98.2333 q^{89} -72.6474 q^{91} +(11.4909 - 0.522884i) q^{93} +(106.273 - 61.3566i) q^{95} +(42.1665 - 73.0345i) q^{97} +(33.2554 - 3.03280i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q + 6 q^{3} - 18 q^{9}+O(q^{10}) $ 40 * q + 6 * q^3 - 18 * q^9	$ 40 q + 6 q^{3} - 18 q^{9} + 16 q^{11} - 4 q^{17} + 76 q^{19} + 118 q^{25} + 144 q^{27} + 156 q^{33} + 108 q^{35} + 20 q^{41} + 16 q^{43} + 166 q^{49} - 330 q^{51} - 258 q^{57} + 64 q^{59} - 102 q^{65} + 64 q^{67} - 292 q^{73} - 138 q^{75} - 42 q^{81} - 554 q^{83} - 688 q^{89} + 204 q^{91} + 92 q^{97} - 90 q^{99}+O(q^{100}) $ 40 * q + 6 * q^3 - 18 * q^9 + 16 * q^11 - 4 * q^17 + 76 * q^19 + 118 * q^25 + 144 * q^27 + 156 * q^33 + 108 * q^35 + 20 * q^41 + 16 * q^43 + 166 * q^49 - 330 * q^51 - 258 * q^57 + 64 * q^59 - 102 * q^65 + 64 * q^67 - 292 * q^73 - 138 * q^75 - 42 * q^81 - 554 * q^83 - 688 * q^89 + 204 * q^91 + 92 * q^97 - 90 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/288\mathbb{Z}\right)^\times$.

$n$	$37$	$65$	$127$
$\chi(n)$	$-1$	$e\left(\frac{2}{3}\right)$	$-1$

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
$3$	−2.66358	−	1.38035i	−0.887859	−	0.460116i
$3$	−2.66358	−	1.38035i	−0.887859	−	0.460116i
$4$		0			0
$5$	8.07964	−	4.66478i	1.61593	−	0.932956i	0.627969	−	0.778239i	$-0.283887\pi$
$5$	8.07964	−	4.66478i	1.61593	−	0.932956i	0.987959	−	0.154718i	$-0.0494468\pi$
$6$		0			0
$7$	4.91220	+	2.83606i	0.701744	+	0.405152i	0.807996	−	0.589187i	$-0.200552\pi$
$7$	4.91220	+	2.83606i	0.701744	+	0.405152i	−0.106253	+	0.994339i	$0.533885\pi$
$8$		0			0
$9$	5.18928	+	7.35333i	0.576586	+	0.817036i
$10$		0			0
$11$	1.85519	−	3.21328i	0.168654	−	0.292116i	−0.769293	−	0.638896i	$-0.779391\pi$
$11$	1.85519	−	3.21328i	0.168654	−	0.292116i	0.937947	+	0.346779i	$0.112725\pi$
$12$		0			0
$13$	−11.0919	+	6.40390i	−0.853221	+	0.492608i	−0.861736	−	0.507356i	$-0.830623\pi$
$13$	−11.0919	+	6.40390i	−0.853221	+	0.492608i	0.00851505	+	0.999964i	$0.497290\pi$
$14$		0			0
$15$	−27.9598	+	1.27229i	−1.86398	+	0.0848191i
$16$		0			0
$17$	11.1817			0.657749			0.328875	−	0.944374i	$-0.393331\pi$
$17$	11.1817			0.657749			0.328875	+	0.944374i	$0.393331\pi$
$18$		0			0
$19$	13.1532			0.692271			0.346136	−	0.938185i	$-0.387494\pi$
$19$	13.1532			0.692271			0.346136	+	0.938185i	$0.387494\pi$
$20$		0			0
$21$	−9.16928	−	14.3346i	−0.436632	−	0.682601i
$22$		0			0
$23$	20.2104	−	11.6685i	0.878713	−	0.507325i	0.00847922	−	0.999964i	$-0.497301\pi$
$23$	20.2104	−	11.6685i	0.878713	−	0.507325i	0.870234	+	0.492639i	$0.163968\pi$
$24$		0			0
$25$	31.0204	−	53.7288i	1.24081	−	2.14915i
$26$		0			0
$27$	−3.67189	−	26.7492i	−0.135996	−	0.990709i
$28$		0			0
$29$	−14.6837	−	8.47767i	−0.506336	−	0.292333i	0.224990	−	0.974361i	$-0.427765\pi$
$29$	−14.6837	−	8.47767i	−0.506336	−	0.292333i	−0.731326	+	0.682028i	$0.761098\pi$
$30$		0			0
$31$	−3.32057	+	1.91713i	−0.107115	+	0.0618429i	−0.552600	−	0.833446i	$-0.686364\pi$
$31$	−3.32057	+	1.91713i	−0.107115	+	0.0618429i	0.445485	+	0.895289i	$0.353031\pi$
$32$		0			0
$33$	−9.37688	+	5.99801i	−0.284148	+	0.181758i
$34$		0			0
$35$	52.9184			1.51196
$36$		0			0
$37$		−	13.8029i		−	0.373052i	−0.982450	−	0.186526i	$-0.940277\pi$
$37$		−	13.8029i		−	0.373052i	0.982450	−	0.186526i	$-0.0597229\pi$
$38$		0			0
$39$	38.3837	−	1.74662i	0.984197	−	0.0447851i
$40$		0			0
$41$	3.05861	+	5.29766i	0.0746001	+	0.129211i	0.900912	−	0.434001i	$-0.142899\pi$
$41$	3.05861	+	5.29766i	0.0746001	+	0.129211i	−0.826312	+	0.563212i	$0.809565\pi$
$42$		0			0
$43$	11.3997	−	19.7448i	0.265109	−	0.459182i	−0.702483	−	0.711700i	$-0.747926\pi$
$43$	11.3997	−	19.7448i	0.265109	−	0.459182i	0.967592	+	0.252518i	$0.0812588\pi$
$44$		0			0
$45$	76.2291	+	35.2054i	1.69398	+	0.782341i
$46$		0			0
$47$	−49.8977	−	28.8084i	−1.06165	−	0.612945i	−0.135764	−	0.990741i	$-0.543349\pi$
$47$	−49.8977	−	28.8084i	−1.06165	−	0.612945i	−0.925889	+	0.377796i	$0.876682\pi$
$48$		0			0
$49$	−8.41350	−	14.5726i	−0.171704	−	0.297400i
$50$		0			0
$51$	−29.7834	−	15.4347i	−0.583988	−	0.302641i
$52$		0			0
$53$			60.0402i			1.13283i	0.824119	+	0.566417i	$0.191671\pi$
$53$			60.0402i			1.13283i	−0.824119	+	0.566417i	$0.808329\pi$
$54$		0			0
$55$		−	34.6162i		−	0.629385i
$56$		0			0
$57$	−35.0344	−	18.1559i	−0.614639	−	0.318525i
$58$		0			0
$59$	55.3504	+	95.8696i	0.938142	+	1.62491i	0.768933	+	0.639329i	$0.220788\pi$
$59$	55.3504	+	95.8696i	0.938142	+	1.62491i	0.169208	+	0.985580i	$0.445879\pi$
$60$		0			0
$61$	−73.2932	−	42.3159i	−1.20153	−	0.693703i	−0.240633	−	0.970616i	$-0.577355\pi$
$61$	−73.2932	−	42.3159i	−1.20153	−	0.693703i	−0.960895	+	0.276913i	$0.910688\pi$
$62$		0			0
$63$	4.63630	+	50.8382i	0.0735921	+	0.806955i
$64$		0			0
$65$	−59.7456	+	103.482i	−0.919163	+	1.59204i
$66$		0			0
$67$	−16.0918	−	27.8718i	−0.240176	−	0.415997i	0.720588	−	0.693363i	$-0.243872\pi$
$67$	−16.0918	−	27.8718i	−0.240176	−	0.415997i	−0.960764	+	0.277366i	$0.910538\pi$
$68$		0			0
$69$	−69.9385	+	3.18250i	−1.01360	+	0.0461231i
$70$		0			0
$71$			38.7881i			0.546311i	0.961970	+	0.273156i	$0.0880674\pi$
$71$			38.7881i			0.546311i	−0.961970	+	0.273156i	$0.911933\pi$
$72$		0			0
$73$	−13.6313			−0.186730			−0.0933652	−	0.995632i	$-0.529762\pi$
$73$	−13.6313			−0.186730			−0.0933652	+	0.995632i	$0.529762\pi$
$74$		0			0
$75$	−156.790	+	100.292i	−2.09053	+	1.33723i
$76$		0			0
$77$	18.2261	−	10.5229i	0.236703	−	0.136661i
$78$		0			0
$79$	−4.14976	−	2.39586i	−0.0525286	−	0.0303274i	0.473506	−	0.880791i	$-0.342988\pi$
$79$	−4.14976	−	2.39586i	−0.0525286	−	0.0303274i	−0.526034	+	0.850463i	$0.676322\pi$
$80$		0			0
$81$	−27.1428	+	76.3169i	−0.335096	+	0.942184i
$82$		0			0
$83$	2.70708	−	4.68879i	0.0326154	−	0.0564915i	−0.849257	−	0.527980i	$-0.822950\pi$
$83$	2.70708	−	4.68879i	0.0326154	−	0.0564915i	0.881872	+	0.471488i	$0.156283\pi$
$84$		0			0
$85$	90.3444	−	52.1604i	1.06288	−	0.613651i
$86$		0			0
$87$	27.4092	+	42.8496i	0.315048	+	0.492524i
$88$		0			0
$89$	98.2333			1.10374			0.551872	−	0.833929i	$-0.313914\pi$
$89$	98.2333			1.10374			0.551872	+	0.833929i	$0.313914\pi$
$90$		0			0
$91$	−72.6474			−0.798323
$92$		0			0
$93$	11.4909	−	0.522884i	0.123558	−	0.00562241i
$94$		0			0
$95$	106.273	−	61.3566i	1.11866	−	0.645859i
$96$		0			0
$97$	42.1665	−	73.0345i	0.434706	−	0.752932i	−0.562566	−	0.826753i	$-0.690186\pi$
$97$	42.1665	−	73.0345i	0.434706	−	0.752932i	0.997272	+	0.0738200i	$0.0235190\pi$
$98$		0			0
$99$	33.2554	−	3.03280i	0.335913	−	0.0306343i
$100$		0			0
$101$	92.9603	+	53.6706i	0.920399	+	0.531393i	0.883762	−	0.467936i	$-0.155002\pi$
$101$	92.9603	+	53.6706i	0.920399	+	0.531393i	0.0366366	+	0.999329i	$0.488336\pi$
$102$		0			0
$103$	−75.2912	+	43.4694i	−0.730983	+	0.422033i	−0.818782	−	0.574105i	$-0.805350\pi$
$103$	−75.2912	+	43.4694i	−0.730983	+	0.422033i	0.0877989	+	0.996138i	$0.472017\pi$
$104$		0			0
$105$	−140.952	−	73.0459i	−1.34240	−	0.695675i
$106$		0			0
$107$	−168.670			−1.57636			−0.788179	−	0.615446i	$-0.788976\pi$
$107$	−168.670			−1.57636			−0.788179	+	0.615446i	$0.788976\pi$
$108$		0			0
$109$			162.909i			1.49458i	0.664497	+	0.747291i	$0.268646\pi$
$109$			162.909i			1.49458i	−0.664497	+	0.747291i	$0.731354\pi$
$110$		0			0
$111$	−19.0528	+	36.7651i	−0.171647	+	0.331218i
$112$		0			0
$113$	30.8328	+	53.4040i	0.272857	+	0.472602i	0.969592	−	0.244727i	$-0.0786982\pi$
$113$	30.8328	+	53.4040i	0.272857	+	0.472602i	−0.696736	+	0.717328i	$0.745365\pi$
$114$		0			0
$115$	108.862	−	188.554i	0.946624	−	1.63960i
$116$		0			0
$117$	−104.649	−	48.3306i	−0.894434	−	0.413082i
$118$		0			0
$119$	54.9270	+	31.7121i	0.461571	+	0.266488i
$120$		0			0
$121$	53.6166	+	92.8666i	0.443112	+	0.767492i
$122$		0			0
$123$	−0.834213	−	18.3327i	−0.00678222	−	0.149046i
$124$		0			0
$125$		−	345.574i		−	2.76459i
$126$		0			0
$127$			108.522i			0.854507i	0.904132	+	0.427254i	$0.140519\pi$
$127$			108.522i			0.854507i	−0.904132	+	0.427254i	$0.859481\pi$
$128$		0			0
$129$	−57.6186	+	36.8563i	−0.446656	+	0.285708i
$130$		0			0
$131$	32.6404	+	56.5348i	0.249163	+	0.431563i	0.963294	−	0.268449i	$-0.0865111\pi$
$131$	32.6404	+	56.5348i	0.249163	+	0.431563i	−0.714131	+	0.700012i	$0.753178\pi$
$132$		0			0
$133$	64.6110	+	37.3032i	0.485797	+	0.280475i
$134$		0			0
$135$	−154.446	−	198.995i	−1.14405	−	1.47404i
$136$		0			0
$137$	35.6297	−	61.7125i	0.260071	−	0.450456i	−0.706190	−	0.708023i	$-0.749587\pi$
$137$	35.6297	−	61.7125i	0.260071	−	0.450456i	0.966261	+	0.257567i	$0.0829207\pi$
$138$		0			0
$139$	38.9742	+	67.5054i	0.280390	+	0.485650i	0.971481	−	0.237118i	$-0.0762028\pi$
$139$	38.9742	+	67.5054i	0.280390	+	0.485650i	−0.691091	+	0.722768i	$0.742869\pi$
$140$		0			0
$141$	93.1406	+	145.610i	0.660572	+	1.03269i
$142$		0			0
$143$			47.5218i			0.332320i
$144$		0			0
$145$	−158.186			−1.09094
$146$		0			0
$147$	2.29472	+	50.4288i	0.0156104	+	0.343053i
$148$		0			0
$149$	−127.047	+	73.3505i	−0.852664	+	0.492286i	−0.861549	−	0.507675i	$-0.830505\pi$
$149$	−127.047	+	73.3505i	−0.852664	+	0.492286i	0.00888514	+	0.999961i	$0.497172\pi$
$150$		0			0
$151$	−91.4191	−	52.7808i	−0.605424	−	0.349542i	0.165748	−	0.986168i	$-0.446996\pi$
$151$	−91.4191	−	52.7808i	−0.605424	−	0.349542i	−0.771173	+	0.636626i	$0.780329\pi$
$152$		0			0
$153$	58.0251	+	82.2230i	0.379249	+	0.537405i
$154$		0			0
$155$	−17.8860	+	30.9794i	−0.115393	+	0.199867i
$156$		0			0
$157$	−148.874	+	85.9525i	−0.948243	+	0.547468i	−0.892535	−	0.450979i	$-0.851075\pi$
$157$	−148.874	+	85.9525i	−0.948243	+	0.547468i	−0.0557082	+	0.998447i	$0.517742\pi$
$158$		0			0
$159$	82.8764	−	159.922i	0.521235	−	1.00580i
$160$		0			0
$161$	132.370			0.822175
$162$		0			0
$163$	83.1474			0.510107			0.255053	−	0.966927i	$-0.417907\pi$
$163$	83.1474			0.510107			0.255053	+	0.966927i	$0.417907\pi$
$164$		0			0
$165$	−47.7824	+	92.2029i	−0.289590	+	0.558805i
$166$		0			0
$167$	−202.139	+	116.705i	−1.21041	+	0.698831i	−0.962849	−	0.270041i	$-0.912963\pi$
$167$	−202.139	+	116.705i	−1.21041	+	0.698831i	−0.247562	+	0.968872i	$0.579630\pi$
$168$		0			0
$169$	−2.48015	+	4.29575i	−0.0146755	+	0.0254186i
$170$		0			0
$171$	68.2554	+	96.7194i	0.399154	+	0.565611i
$172$		0			0
$173$	38.5845	+	22.2768i	0.223032	+	0.128767i	0.607353	−	0.794432i	$-0.292231\pi$
$173$	38.5845	+	22.2768i	0.223032	+	0.128767i	−0.384322	+	0.923199i	$0.625565\pi$
$174$		0			0
$175$	304.757	−	175.951i	1.74147	−	1.00544i
$176$		0			0
$177$	−15.0964	−	331.759i	−0.0852905	−	1.87434i
$178$		0			0
$179$	15.3758			0.0858984			0.0429492	−	0.999077i	$-0.486325\pi$
$179$	15.3758			0.0858984			0.0429492	+	0.999077i	$0.486325\pi$
$180$		0			0
$181$		−	240.627i		−	1.32943i	−0.747096	−	0.664716i	$-0.768553\pi$
$181$		−	240.627i		−	1.32943i	0.747096	−	0.664716i	$-0.231447\pi$
$182$		0			0
$183$	136.811	+	213.882i	0.747604	+	1.16875i
$184$		0			0
$185$	−64.3876	−	111.523i	−0.348041	−	0.602825i
$186$		0			0
$187$	20.7442	−	35.9301i	0.110932	−	0.192139i
$188$		0			0
$189$	57.8252	−	141.811i	0.305954	−	0.750323i
$190$		0			0
$191$	68.8601	+	39.7564i	0.360524	+	0.208149i	0.669311	−	0.742983i	$-0.266590\pi$
$191$	68.8601	+	39.7564i	0.360524	+	0.208149i	−0.308787	+	0.951131i	$0.599923\pi$
$192$		0			0
$193$	16.7549	+	29.0203i	0.0868128	+	0.150364i	0.906162	−	0.422930i	$-0.138998\pi$
$193$	16.7549	+	29.0203i	0.0868128	+	0.150364i	−0.819349	+	0.573294i	$0.805665\pi$
$194$		0			0
$195$	301.979	−	193.163i	1.54861	−	0.990582i
$196$		0			0
$197$			183.151i			0.929699i	0.885390	+	0.464849i	$0.153892\pi$
$197$			183.151i			0.929699i	−0.885390	+	0.464849i	$0.846108\pi$
$198$		0			0
$199$		−	86.2656i		−	0.433496i	−0.976228	−	0.216748i	$-0.930455\pi$
$199$		−	86.2656i		−	0.433496i	0.976228	−	0.216748i	$-0.0695449\pi$
$200$		0			0
$201$	4.38892	+	96.4509i	0.0218354	+	0.479855i
$202$		0			0
$203$	−48.0864	−	83.2881i	−0.236879	−	0.410286i
$204$		0			0
$205$	49.4249	+	28.5355i	0.241097	+	0.139197i
$206$		0			0
$207$	190.680	+	88.0627i	0.921157	+	0.425424i
$208$		0			0
$209$	24.4016	−	42.2648i	0.116754	−	0.202224i
$210$		0			0
$211$	115.005	+	199.195i	0.545049	+	0.944053i	0.998604	+	0.0528247i	$0.0168224\pi$
$211$	115.005	+	199.195i	0.545049	+	0.944053i	−0.453554	+	0.891229i	$0.649844\pi$
$212$		0			0
$213$	53.5411	−	103.315i	0.251367	−	0.485047i
$214$		0			0
$215$		−	212.708i		−	0.989339i
$216$		0			0
$217$	−21.7484			−0.100223
$218$		0			0
$219$	36.3081	+	18.8160i	0.165790	+	0.0859176i
$220$		0			0
$221$	−124.026	+	71.6067i	−0.561206	+	0.324012i
$222$		0			0
$223$	−327.758	−	189.231i	−1.46977	−	0.848570i	−0.470342	−	0.882484i	$-0.655869\pi$
$223$	−327.758	−	189.231i	−1.46977	−	0.848570i	−0.999425	+	0.0339138i	$0.989203\pi$
$224$		0			0
$225$	556.059	−	50.7110i	2.47137	−	0.225382i
$226$		0			0
$227$	208.237	−	360.677i	0.917343	−	1.58889i	0.113910	−	0.993491i	$-0.463663\pi$
$227$	208.237	−	360.677i	0.917343	−	1.58889i	0.803434	−	0.595394i	$-0.203004\pi$
$228$		0			0
$229$	153.319	−	88.5187i	0.669515	−	0.386545i	−0.126378	−	0.991982i	$-0.540335\pi$
$229$	153.319	−	88.5187i	0.669515	−	0.386545i	0.795893	+	0.605438i	$0.207002\pi$
$230$		0			0
$231$	−63.0719	+	2.87004i	−0.273039	+	0.0124244i
$232$		0			0
$233$	−144.457			−0.619987			−0.309993	−	0.950739i	$-0.600327\pi$
$233$	−144.457			−0.619987			−0.309993	+	0.950739i	$0.600327\pi$
$234$		0			0
$235$	−537.540			−2.28740
$236$		0			0
$237$	7.74607	+	12.1097i	0.0326839	+	0.0510957i
$238$		0			0
$239$	−157.611	+	90.9966i	−0.659459	+	0.380739i	−0.792071	−	0.610429i	$-0.790997\pi$
$239$	−157.611	+	90.9966i	−0.659459	+	0.380739i	0.132612	+	0.991168i	$0.457664\pi$
$240$		0			0
$241$	70.3168	−	121.792i	0.291771	−	0.505362i	−0.682458	−	0.730925i	$-0.739089\pi$
$241$	70.3168	−	121.792i	0.291771	−	0.505362i	0.974229	+	0.225563i	$0.0724222\pi$
$242$		0			0
$243$	177.641	−	165.809i	0.731032	−	0.682343i
$244$		0			0
$245$	−135.956	−	78.4942i	−0.554922	−	0.320385i
$246$		0			0
$247$	−145.893	+	84.2315i	−0.590661	+	0.341018i
$248$		0			0
$249$	−13.6827	+	8.75225i	−0.0549505	+	0.0351496i
$250$		0			0
$251$	−38.7781			−0.154494			−0.0772471	−	0.997012i	$-0.524613\pi$
$251$	−38.7781			−0.154494			−0.0772471	+	0.997012i	$0.524613\pi$
$252$		0			0
$253$		−	86.5889i		−	0.342249i
$254$		0			0
$255$	−312.639	+	14.2264i	−1.22603	+	0.0557897i
$256$		0			0
$257$	−74.9268	−	129.777i	−0.291544	−	0.504969i	0.682631	−	0.730763i	$-0.260836\pi$
$257$	−74.9268	−	129.777i	−0.291544	−	0.504969i	−0.974175	+	0.225794i	$0.927502\pi$
$258$		0			0
$259$	39.1460	−	67.8028i	0.151143	−	0.261787i
$260$		0			0
$261$	−13.8590	−	151.967i	−0.0530996	−	0.582250i
$262$		0			0
$263$	−67.5653	−	39.0088i	−0.256902	−	0.148323i	0.366018	−	0.930608i	$-0.380721\pi$
$263$	−67.5653	−	39.0088i	−0.256902	−	0.148323i	−0.622921	+	0.782285i	$0.714054\pi$
$264$		0			0
$265$	280.074	+	485.103i	1.05688	+	1.83058i
$266$		0			0
$267$	−261.652	−	135.596i	−0.979969	−	0.507851i
$268$		0			0
$269$			240.267i			0.893187i	0.894737	+	0.446594i	$0.147363\pi$
$269$			240.267i			0.893187i	−0.894737	+	0.446594i	$0.852637\pi$
$270$		0			0
$271$			440.449i			1.62527i	0.582772	+	0.812636i	$0.301968\pi$
$271$			440.449i			1.62527i	−0.582772	+	0.812636i	$0.698032\pi$
$272$		0			0
$273$	193.502	+	100.279i	0.708799	+	0.367321i
$274$		0			0
$275$	−115.097	−	199.354i	−0.418535	−	0.724925i
$276$		0			0
$277$	−111.638	−	64.4543i	−0.403026	−	0.232687i	0.284763	−	0.958598i	$-0.408085\pi$
$277$	−111.638	−	64.4543i	−0.403026	−	0.232687i	−0.687789	+	0.725911i	$0.741418\pi$
$278$		0			0
$279$	−31.3286	−	14.4687i	−0.112289	−	0.0518591i
$280$		0			0
$281$	70.2020	−	121.593i	0.249829	−	0.432717i	−0.713649	−	0.700503i	$-0.752959\pi$
$281$	70.2020	−	121.593i	0.249829	−	0.432717i	0.963478	+	0.267787i	$0.0862922\pi$
$282$		0			0
$283$	209.786	+	363.361i	0.741295	+	1.28396i	0.951906	+	0.306390i	$0.0991213\pi$
$283$	209.786	+	363.361i	0.741295	+	1.28396i	−0.210611	+	0.977570i	$0.567545\pi$
$284$		0			0
$285$	−367.759	+	16.7346i	−1.29038	+	0.0587178i
$286$		0			0
$287$			34.6976i			0.120898i
$288$		0			0
$289$	−163.969			−0.567366
$290$		0			0
$291$	−213.127	+	136.328i	−0.732394	+	0.468483i
$292$		0			0
$293$	329.166	−	190.044i	1.12343	−	0.648615i	0.181158	−	0.983454i	$-0.442015\pi$
$293$	329.166	−	190.044i	1.12343	−	0.648615i	0.942275	+	0.334839i	$0.108682\pi$
$294$		0			0
$295$	894.422	+	516.395i	3.03194	+	1.75049i
$296$		0			0
$297$	−92.7646	−	37.8259i	−0.312339	−	0.127360i
$298$		0			0
$299$	−149.448	+	258.851i	−0.499825	+	0.865722i
$300$		0			0
$301$	111.995	−	64.6604i	0.372077	−	0.214819i
$302$		0			0
$303$	−173.523	−	271.273i	−0.572682	−	0.895292i
$304$		0			0
$305$	−789.577			−2.58878
$306$		0			0
$307$	−306.165			−0.997281			−0.498640	−	0.866809i	$-0.666167\pi$
$307$	−306.165			−0.997281			−0.498640	+	0.866809i	$0.666167\pi$
$308$		0			0
$309$	260.547	−	11.8560i	0.843194	−	0.0383689i
$310$		0			0
$311$	492.156	−	284.146i	1.58249	−	0.913654i	0.588000	−	0.808861i	$-0.299915\pi$
$311$	492.156	−	284.146i	1.58249	−	0.913654i	0.994494	−	0.104793i	$-0.0334179\pi$
$312$		0			0
$313$	−156.683	+	271.382i	−0.500583	+	0.867036i	0.499417	+	0.866362i	$0.333548\pi$
$313$	−156.683	+	271.382i	−0.500583	+	0.867036i	−1.00000		0.000673622i	$0.999786\pi$
$314$		0			0
$315$	274.608	+	389.127i	0.871773	+	1.23532i
$316$		0			0
$317$	133.136	+	76.8660i	0.419987	+	0.242480i	0.695072	−	0.718940i	$-0.255373\pi$
$317$	133.136	+	76.8660i	0.419987	+	0.242480i	−0.275085	+	0.961420i	$0.588706\pi$
$318$		0			0
$319$	−54.4822	+	31.4553i	−0.170791	+	0.0986061i
$320$		0			0
$321$	449.266	+	232.824i	1.39958	+	0.725308i
$322$		0			0
$323$	147.075			0.455341
$324$		0			0
$325$			794.605i			2.44494i
$326$		0			0
$327$	224.872	−	433.922i	0.687681	−	1.32698i
$328$		0			0
$329$	−163.405	−	283.026i	−0.496672	−	0.860261i
$330$		0			0
$331$	−306.335	+	530.588i	−0.925484	+	1.60299i	−0.134704	+	0.990886i	$0.543008\pi$
$331$	−306.335	+	530.588i	−0.925484	+	1.60299i	−0.790780	+	0.612100i	$0.790325\pi$
$332$		0			0
$333$	101.497	−	71.6272i	0.304797	−	0.215097i
$334$		0			0
$335$	−260.031	−	150.129i	−0.776213	−	0.448147i
$336$		0			0
$337$	−233.237	−	403.978i	−0.692098	−	1.19875i	−0.971149	−	0.238473i	$-0.923353\pi$
$337$	−233.237	−	403.978i	−0.692098	−	1.19875i	0.279051	−	0.960276i	$-0.409980\pi$
$338$		0			0
$339$	−8.40943	−	184.806i	−0.0248066	−	0.545149i
$340$		0			0
$341$			14.2266i			0.0417201i
$342$		0			0
$343$		−	373.379i		−	1.08857i
$344$		0			0
$345$	−550.232	+	351.961i	−1.59488	+	1.02018i
$346$		0			0
$347$	−178.207	−	308.664i	−0.513565	−	0.889520i	−0.999876	−	0.0157348i	$-0.994991\pi$
$347$	−178.207	−	308.664i	−0.513565	−	0.889520i	0.486311	−	0.873786i	$-0.338342\pi$
$348$		0			0
$349$	125.660	+	72.5496i	0.360056	+	0.207878i	0.669105	−	0.743168i	$-0.266677\pi$
$349$	125.660	+	72.5496i	0.360056	+	0.207878i	−0.309049	+	0.951046i	$0.600011\pi$
$350$		0			0
$351$	212.027	+	273.184i	0.604066	+	0.778302i
$352$		0			0
$353$	−209.033	+	362.055i	−0.592160	+	1.02565i	0.401780	+	0.915736i	$0.368392\pi$
$353$	−209.033	+	362.055i	−0.592160	+	1.02565i	−0.993941	+	0.109916i	$0.964942\pi$
$354$		0			0
$355$	180.938	+	313.394i	0.509684	+	0.882799i
$356$		0			0
$357$	−102.528	−	160.286i	−0.287195	−	0.448980i
$358$		0			0
$359$			291.137i			0.810968i	0.914102	+	0.405484i	$0.132897\pi$
$359$			291.137i			0.810968i	−0.914102	+	0.405484i	$0.867103\pi$
$360$		0			0
$361$	−187.995			−0.520761
$362$		0			0
$363$	−14.6235	−	321.367i	−0.0402852	−	0.885308i
$364$		0			0
$365$	−110.136	+	63.5871i	−0.301743	+	0.174211i
$366$		0			0
$367$	−321.962	−	185.885i	−0.877281	−	0.506499i	−0.00752022	−	0.999972i	$-0.502394\pi$
$367$	−321.962	−	185.885i	−0.877281	−	0.506499i	−0.869761	+	0.493473i	$0.835727\pi$
$368$		0			0
$369$	−23.0835	+	49.9820i	−0.0625568	+	0.135452i
$370$		0			0
$371$	−170.278	+	294.930i	−0.458970	+	0.794959i
$372$		0			0
$373$	−424.454	+	245.059i	−1.13795	+	0.656994i	−0.945921	−	0.324396i	$-0.894839\pi$
$373$	−424.454	+	245.059i	−1.13795	+	0.656994i	−0.192025	+	0.981390i	$0.561506\pi$
$374$		0			0
$375$	−477.012	+	920.462i	−1.27203	+	2.45457i
$376$		0			0
$377$	217.160			0.576022
$378$		0			0
$379$	249.848			0.659230			0.329615	−	0.944115i	$-0.393081\pi$
$379$	249.848			0.659230			0.329615	+	0.944115i	$0.393081\pi$
$380$		0			0
$381$	149.799	−	289.058i	0.393172	−	0.758682i
$382$		0			0
$383$	−42.3609	+	24.4571i	−0.110603	+	0.0638566i	−0.554281	−	0.832330i	$-0.687007\pi$
$383$	−42.3609	+	24.4571i	−0.110603	+	0.0638566i	0.443678	+	0.896186i	$0.353673\pi$
$384$		0			0
$385$	98.1737	−	170.042i	0.254997	−	0.441667i
$386$		0			0
$387$	204.346	−	18.6358i	0.528026	−	0.0481545i
$388$		0			0
$389$	−446.299	−	257.671i	−1.14730	−	0.662393i	−0.199071	−	0.979985i	$-0.563792\pi$
$389$	−446.299	−	257.671i	−1.14730	−	0.662393i	−0.948228	+	0.317592i	$0.897126\pi$
$390$		0			0
$391$	225.987	−	130.474i	0.577973	−	0.333693i
$392$		0			0
$393$	−8.90243	−	195.640i	−0.0226525	−	0.497811i
$394$		0			0
$395$	−44.7047			−0.113177
$396$		0			0
$397$		−	560.274i		−	1.41127i	−0.708576	−	0.705634i	$-0.750662\pi$
$397$		−	560.274i		−	1.41127i	0.708576	−	0.705634i	$-0.249338\pi$
$398$		0			0
$399$	−120.605	−	188.545i	−0.302268	−	0.472545i
$400$		0			0
$401$	226.974	+	393.131i	0.566021	+	0.980377i	0.996954	+	0.0779928i	$0.0248511\pi$
$401$	226.974	+	393.131i	0.566021	+	0.980377i	−0.430933	+	0.902384i	$0.641816\pi$
$402$		0			0
$403$	24.5542	−	42.5292i	0.0609286	−	0.105531i
$404$		0			0
$405$	136.698	+	743.228i	0.337525	+	1.83513i
$406$		0			0
$407$	−44.3527	−	25.6070i	−0.108975	−	0.0629165i
$408$		0			0
$409$	233.772	+	404.905i	0.571570	+	0.989988i	0.996405	+	0.0847172i	$0.0269987\pi$
$409$	233.772	+	404.905i	0.571570	+	0.989988i	−0.424835	+	0.905271i	$0.639668\pi$
$410$		0			0
$411$	−180.087	+	115.194i	−0.438168	+	0.280278i
$412$		0			0
$413$			627.908i			1.52036i
$414$		0			0
$415$		−	50.5117i		−	0.121715i
$416$		0			0
$417$	−10.6300	−	233.604i	−0.0254915	−	0.560201i
$418$		0			0
$419$	−92.4411	−	160.113i	−0.220623	−	0.382131i	0.734374	−	0.678745i	$-0.237476\pi$
$419$	−92.4411	−	160.113i	−0.220623	−	0.382131i	−0.954997	+	0.296614i	$0.904142\pi$
$420$		0			0
$421$	−326.113	−	188.282i	−0.774616	−	0.447225i	0.0599029	−	0.998204i	$-0.480921\pi$
$421$	−326.113	−	188.282i	−0.774616	−	0.447225i	−0.834519	+	0.550980i	$0.814254\pi$
$422$		0			0
$423$	−47.0951	−	516.409i	−0.111336	−	1.22082i
$424$		0			0
$425$	346.862	−	600.782i	0.816145	−	1.41360i
$426$		0			0
$427$	−240.021	−	415.728i	−0.562110	−	0.973603i
$428$		0			0
$429$	65.5966	−	126.578i	0.152906	−	0.295053i
$430$		0			0
$431$			300.981i			0.698332i	0.937061	+	0.349166i	$0.113535\pi$
$431$			300.981i			0.698332i	−0.937061	+	0.349166i	$0.886465\pi$
$432$		0			0
$433$	−670.846			−1.54930			−0.774649	−	0.632391i	$-0.782074\pi$
$433$	−670.846			−1.54930			−0.774649	+	0.632391i	$0.782074\pi$
$434$		0			0
$435$	421.340	+	218.352i	0.968598	+	0.501958i
$436$		0			0
$437$	265.830	−	153.477i	0.608308	−	0.351207i
$438$		0			0
$439$	−513.168	−	296.277i	−1.16895	−	0.674892i	−0.215515	−	0.976501i	$-0.569143\pi$
$439$	−513.168	−	296.277i	−1.16895	−	0.674892i	−0.953432	+	0.301609i	$0.902476\pi$
$440$		0			0
$441$	63.4971	−	137.488i	0.143984	−	0.311765i
$442$		0			0
$443$	106.548	−	184.547i	0.240515	−	0.416584i	−0.720346	−	0.693615i	$-0.756017\pi$
$443$	106.548	−	184.547i	0.240515	−	0.416584i	0.960861	+	0.277031i	$0.0893503\pi$
$444$		0			0
$445$	793.689	−	458.237i	1.78357	−	1.02975i
$446$		0			0
$447$	439.648	−	20.0058i	0.983553	−	0.0447558i
$448$		0			0
$449$	574.593			1.27972			0.639858	−	0.768493i	$-0.278993\pi$
$449$	574.593			1.27972			0.639858	+	0.768493i	$0.278993\pi$
$450$		0			0
$451$	22.6972			0.0503263
$452$		0			0
$453$	170.646	+	266.776i	0.376701	+	0.588909i
$454$		0			0
$455$	−586.965	+	338.884i	−1.29003	+	0.744801i
$456$		0			0
$457$	200.997	−	348.138i	0.439819	−	0.761789i	−0.557856	−	0.829938i	$-0.688376\pi$
$457$	200.997	−	348.138i	0.439819	−	0.761789i	0.997675	+	0.0681485i	$0.0217092\pi$
$458$		0			0
$459$	−41.0581	−	299.102i	−0.0894511	−	0.651638i
$460$		0			0
$461$	−126.646	−	73.1191i	−0.274720	−	0.158610i	0.356311	−	0.934368i	$-0.384034\pi$
$461$	−126.646	−	73.1191i	−0.274720	−	0.158610i	−0.631031	+	0.775758i	$0.717368\pi$
$462$		0			0
$463$	443.882	−	256.275i	0.958708	−	0.553510i	0.0629326	−	0.998018i	$-0.479955\pi$
$463$	443.882	−	256.275i	0.958708	−	0.553510i	0.895775	+	0.444508i	$0.146621\pi$
$464$		0			0
$465$	90.4031	−	57.8272i	0.194415	−	0.124360i
$466$		0			0
$467$	294.463			0.630543			0.315271	−	0.949002i	$-0.397904\pi$
$467$	294.463			0.630543			0.315271	+	0.949002i	$0.397904\pi$
$468$		0			0
$469$		−	182.549i		−	0.389231i
$470$		0			0
$471$	515.182	−	23.4429i	1.09380	−	0.0497727i
$472$		0			0
$473$	−42.2971	−	73.2607i	−0.0894230	−	0.154885i
$474$		0			0
$475$	408.016	−	706.704i	0.858980	−	1.48780i
$476$		0			0
$477$	−441.495	+	311.565i	−0.925566	+	0.653176i
$478$		0			0
$479$	648.588	+	374.462i	1.35405	+	0.781758i	0.988813	−	0.149158i	$-0.0476564\pi$
$479$	648.588	+	374.462i	1.35405	+	0.781758i	0.365232	+	0.930917i	$0.380990\pi$
$480$		0			0
$481$	88.3925	+	153.100i	0.183768	+	0.318296i
$482$		0			0
$483$	−352.578	−	182.717i	−0.729975	−	0.378296i
$484$		0			0
$485$		−	786.789i		−	1.62225i
$486$		0			0
$487$			81.6059i			0.167569i	0.996484	+	0.0837843i	$0.0267007\pi$
$487$			81.6059i			0.167569i	−0.996484	+	0.0837843i	$0.973299\pi$
$488$		0			0
$489$	−221.469	−	114.772i	−0.452903	−	0.234708i
$490$		0			0
$491$	345.383	+	598.220i	0.703427	+	1.21837i	0.967256	+	0.253802i	$0.0816811\pi$
$491$	345.383	+	598.220i	0.703427	+	1.21837i	−0.263829	+	0.964569i	$0.584986\pi$
$492$		0			0
$493$	−164.190	−	94.7950i	−0.333042	−	0.192282i
$494$		0			0
$495$	254.544	−	179.633i	0.514231	−	0.362895i
$496$		0			0
$497$	−110.005	+	190.535i	−0.221339	+	0.383370i
$498$		0			0
$499$	−432.927	−	749.851i	−0.867588	−	1.50271i	−0.864454	−	0.502712i	$-0.832336\pi$
$499$	−432.927	−	749.851i	−0.867588	−	1.50271i	−0.00313444	−	0.999995i	$-0.500998\pi$
$500$		0			0
$501$	699.505	−	31.8304i	1.39622	−	0.0635338i
$502$		0			0
$503$		−	349.624i		−	0.695077i	−0.937666	−	0.347539i	$-0.887018\pi$
$503$		−	349.624i		−	0.695077i	0.937666	−	0.347539i	$-0.112982\pi$
$504$		0			0
$505$	1001.45			1.98306
$506$		0			0
$507$	12.5357	−	8.01858i	0.0247253	−	0.0158157i
$508$		0			0
$509$	12.5795	−	7.26280i	0.0247142	−	0.0142688i	−0.487592	−	0.873072i	$-0.662125\pi$
$509$	12.5795	−	7.26280i	0.0247142	−	0.0142688i	0.512306	+	0.858803i	$0.328791\pi$
$510$		0			0
$511$	−66.9598	−	38.6593i	−0.131037	−	0.0756542i
$512$		0			0
$513$	−48.2969	−	351.836i	−0.0941460	−	0.685840i
$514$		0			0
$515$	−405.550	+	702.434i	−0.787477	+	1.36395i
$516$		0			0
$517$	−185.139	+	106.890i	−0.358103	+	0.206751i
$518$		0			0
$519$	−72.0230	−	112.596i	−0.138773	−	0.216948i
$520$		0			0
$521$	219.308			0.420936			0.210468	−	0.977601i	$-0.432501\pi$
$521$	219.308			0.420936			0.210468	+	0.977601i	$0.432501\pi$
$522$		0			0
$523$	802.128			1.53371			0.766853	−	0.641823i	$-0.221821\pi$
$523$	802.128			1.53371			0.766853	+	0.641823i	$0.221821\pi$
$524$		0			0
$525$	−1054.62	+	47.9895i	−2.00879	+	0.0914086i
$526$		0			0
$527$	−37.1297	+	21.4369i	−0.0704549	+	0.0406771i
$528$		0			0
$529$	7.80688	−	13.5219i	0.0147578	−	0.0255613i
$530$		0			0
$531$	−417.732	+	904.503i	−0.786690	+	1.70340i
$532$		0			0
$533$	−67.8514	−	39.1740i	−0.127301	−	0.0734972i
$534$		0			0
$535$	−1362.80	+	786.810i	−2.54728	+	1.47067i
$536$		0			0
$537$	−40.9547	−	21.2240i	−0.0762656	−	0.0395232i
$538$		0			0
$539$	−62.4345			−0.115834
$540$		0			0
$541$			780.008i			1.44179i	0.693045	+	0.720895i	$0.256269\pi$
$541$			780.008i			1.44179i	−0.693045	+	0.720895i	$0.743731\pi$
$542$		0			0
$543$	−332.149	+	640.929i	−0.611693	+	1.18035i
$544$		0			0
$545$	759.937	+	1316.25i	1.39438	+	2.41514i
$546$		0			0
$547$	19.8872	−	34.4456i	0.0363568	−	0.0629718i	−0.847274	−	0.531155i	$-0.821758\pi$
$547$	19.8872	−	34.4456i	0.0363568	−	0.0629718i	0.883631	+	0.468184i	$0.155091\pi$
$548$		0			0
$549$	−69.1766	−	758.538i	−0.126005	−	1.38167i
$550$		0			0
$551$	−193.138	−	111.508i	−0.350522	−	0.202374i
$552$		0			0
$553$	−13.5896	−	23.5380i	−0.0245744	−	0.0425641i
$554$		0			0
$555$	17.5613	+	385.926i	0.0316419	+	0.695363i
$556$		0			0
$557$		−	87.9243i		−	0.157853i	−0.996880	−	0.0789266i	$-0.974851\pi$
$557$		−	87.9243i		−	0.157853i	0.996880	−	0.0789266i	$-0.0251493\pi$
$558$		0			0
$559$			292.009i			0.522378i
$560$		0			0
$561$	−104.850	+	67.0682i	−0.186898	+	0.119551i
$562$		0			0
$563$	−263.524	−	456.436i	−0.468071	−	0.810722i	0.531264	−	0.847207i	$-0.321717\pi$
$563$	−263.524	−	456.436i	−0.468071	−	0.810722i	−0.999334	+	0.0364845i	$0.988384\pi$
$564$		0			0
$565$	498.236	+	287.656i	0.881833	+	0.509127i
$566$		0			0
$567$	−349.770	+	297.906i	−0.616879	+	0.525407i
$568$		0			0
$569$	464.624	−	804.752i	0.816562	−	1.41433i	−0.0916393	−	0.995792i	$-0.529211\pi$
$569$	464.624	−	804.752i	0.816562	−	1.41433i	0.908201	−	0.418534i	$-0.137456\pi$
$570$		0			0
$571$	−198.535	−	343.873i	−0.347698	−	0.602230i	0.638142	−	0.769918i	$-0.279703\pi$
$571$	−198.535	−	343.873i	−0.347698	−	0.602230i	−0.985840	+	0.167688i	$0.946370\pi$
$572$		0			0
$573$	−128.536	−	200.945i	−0.224322	−	0.350689i
$574$		0			0
$575$		−	1447.84i		−	2.51799i
$576$		0			0
$577$	351.123			0.608531			0.304266	−	0.952587i	$-0.401589\pi$
$577$	351.123			0.608531			0.304266	+	0.952587i	$0.401589\pi$
$578$		0			0
$579$	−4.56977	−	100.425i	−0.00789253	−	0.173446i
$580$		0			0
$581$	26.5954	−	15.3549i	0.0457753	−	0.0264284i
$582$		0			0
$583$	192.926	+	111.386i	0.330919	+	0.191056i
$584$		0			0
$585$	−1070.98	+	97.6701i	−1.83073	+	0.166957i
$586$		0			0
$587$	466.965	−	808.807i	0.795511	−	1.37787i	−0.127003	−	0.991902i	$-0.540536\pi$
$587$	466.965	−	808.807i	0.795511	−	1.37787i	0.922514	−	0.385964i	$-0.126131\pi$
$588$		0			0
$589$	−43.6759	+	25.2163i	−0.0741527	+	0.0428121i
$590$		0			0
$591$	252.812	−	487.836i	0.427769	−	0.825441i
$592$		0			0
$593$	−743.820			−1.25433			−0.627167	−	0.778885i	$-0.715786\pi$
$593$	−743.820			−1.25433			−0.627167	+	0.778885i	$0.715786\pi$
$594$		0			0
$595$	591.720			0.994488
$596$		0			0
$597$	−119.077	+	229.775i	−0.199458	+	0.384883i
$598$		0			0
$599$	519.915	−	300.173i	0.867971	−	0.501124i	0.00129781	−	0.999999i	$-0.499587\pi$
$599$	519.915	−	300.173i	0.867971	−	0.501124i	0.866674	+	0.498876i	$0.166254\pi$
$600$		0			0
$601$	−47.0344	+	81.4660i	−0.0782603	+	0.135551i	−0.902499	−	0.430691i	$-0.858270\pi$
$601$	−47.0344	+	81.4660i	−0.0782603	+	0.135551i	0.824239	+	0.566242i	$0.191603\pi$
$602$		0			0
$603$	121.446	−	262.962i	0.201402	−	0.436090i
$604$		0			0
$605$	866.405	+	500.219i	1.43207	+	0.826808i
$606$		0			0
$607$	107.746	−	62.2074i	0.177506	−	0.102483i	−0.408614	−	0.912707i	$-0.633988\pi$
$607$	107.746	−	62.2074i	0.177506	−	0.102483i	0.586121	+	0.810224i	$0.300654\pi$
$608$		0			0
$609$	13.1152	+	288.220i	0.0215357	+	0.473268i
$610$		0			0
$611$	737.945			1.20777
$612$		0			0
$613$		−	196.037i		−	0.319799i	−0.987133	−	0.159899i	$-0.948883\pi$
$613$		−	196.037i		−	0.319799i	0.987133	−	0.159899i	$-0.0511170\pi$
$614$		0			0
$615$	−92.2580	−	144.230i	−0.150013	−	0.234520i
$616$		0			0
$617$	−21.0476	−	36.4555i	−0.0341128	−	0.0590850i	0.848465	−	0.529252i	$-0.177527\pi$
$617$	−21.0476	−	36.4555i	−0.0341128	−	0.0590850i	−0.882578	+	0.470166i	$0.844194\pi$
$618$		0			0
$619$	304.862	−	528.036i	0.492507	−	0.853047i	−0.507456	−	0.861678i	$-0.669414\pi$
$619$	304.862	−	528.036i	0.492507	−	0.853047i	0.999963	+	0.00863088i	$0.00274733\pi$
$620$		0			0
$621$	−386.332	−	497.766i	−0.622113	−	0.801555i
$622$		0			0
$623$	482.542	+	278.596i	0.774546	+	0.447184i
$624$		0			0
$625$	−836.517	−	1448.89i	−1.33843	−	2.31822i
$626$		0			0
$627$	−123.336	+	78.8928i	−0.196707	+	0.125826i
$628$		0			0
$629$		−	154.341i		−	0.245375i
$630$		0			0
$631$		−	897.433i		−	1.42224i	−0.703071	−	0.711120i	$-0.748188\pi$
$631$		−	897.433i		−	1.42224i	0.703071	−	0.711120i	$-0.251812\pi$
$632$		0			0
$633$	−31.3669	−	689.319i	−0.0495528	−	1.08897i
$634$		0			0
$635$	506.233	+	876.822i	0.797218	+	1.38082i
$636$		0			0
$637$	186.643	+	107.758i	0.293003	+	0.169165i
$638$		0			0
$639$	−285.221	+	201.282i	−0.446356	+	0.314996i
$640$		0			0
$641$	−478.777	+	829.266i	−0.746922	+	1.29371i	0.202370	+	0.979309i	$0.435136\pi$
$641$	−478.777	+	829.266i	−0.746922	+	1.29371i	−0.949292	+	0.314397i	$0.898198\pi$
$642$		0			0
$643$	96.6408	+	167.387i	0.150297	+	0.260321i	0.931337	−	0.364160i	$-0.118644\pi$
$643$	96.6408	+	167.387i	0.150297	+	0.260321i	−0.781040	+	0.624481i	$0.785310\pi$
$644$		0			0
$645$	−293.611	+	566.564i	−0.455211	+	0.878393i
$646$		0			0
$647$			462.896i			0.715450i	0.933827	+	0.357725i	$0.116447\pi$
$647$			462.896i			0.715450i	−0.933827	+	0.357725i	$0.883553\pi$
$648$		0			0
$649$	410.741			0.632884
$650$		0			0
$651$	57.9286	+	30.0204i	0.0889840	+	0.0461143i
$652$		0			0
$653$	175.738	−	101.463i	0.269125	−	0.155379i	−0.359365	−	0.933197i	$-0.617007\pi$
$653$	175.738	−	101.463i	0.269125	−	0.155379i	0.628490	+	0.777818i	$0.283673\pi$
$654$		0			0
$655$	527.445	+	304.520i	0.805259	+	0.464917i
$656$		0			0
$657$	−70.7367	−	100.236i	−0.107666	−	0.152565i
$658$		0			0
$659$	−423.773	+	733.996i	−0.643054	+	1.11380i	0.341693	+	0.939812i	$0.389000\pi$
$659$	−423.773	+	733.996i	−0.643054	+	1.11380i	−0.984747	+	0.173991i	$0.944334\pi$
$660$		0			0
$661$	−552.689	+	319.095i	−0.836141	+	0.482746i	−0.855951	−	0.517058i	$-0.827027\pi$
$661$	−552.689	+	319.095i	−0.836141	+	0.482746i	0.0198096	+	0.999804i	$0.493694\pi$
$662$		0			0
$663$	429.196	−	19.5302i	0.647355	−	0.0294574i
$664$		0			0
$665$	696.044			1.04668
$666$		0			0
$667$	−395.686			−0.593232
$668$		0			0
$669$	611.804	+	956.452i	0.914505	+	1.42967i
$670$		0			0
$671$	−271.946	+	157.008i	−0.405284	+	0.233991i
$672$		0			0
$673$	216.850	−	375.595i	0.322214	−	0.558091i	−0.658730	−	0.752379i	$-0.728906\pi$
$673$	216.850	−	375.595i	0.322214	−	0.558091i	0.980945	+	0.194288i	$0.0622396\pi$
$674$		0			0
$675$	−1551.10	−	632.482i	−2.29793	−	0.937011i
$676$		0			0
$677$	304.392	+	175.741i	0.449619	+	0.259588i	0.707669	−	0.706544i	$-0.249747\pi$
$677$	304.392	+	175.741i	0.449619	+	0.259588i	−0.258050	+	0.966131i	$0.583080\pi$
$678$		0			0
$679$	414.261	−	239.173i	0.610104	−	0.352244i
$680$		0			0
$681$	−1052.51	+	673.251i	−1.54554	+	0.988621i
$682$		0			0
$683$	−174.129			−0.254948			−0.127474	−	0.991842i	$-0.540687\pi$
$683$	−174.129			−0.254948			−0.127474	+	0.991842i	$0.540687\pi$
$684$		0			0
$685$		−	664.819i		−	0.970539i
$686$		0			0
$687$	−530.563	+	24.1429i	−0.772290	+	0.0351424i
$688$		0			0
$689$	−384.491	−	665.958i	−0.558043	−	0.966558i
$690$		0			0
$691$	−147.131	+	254.838i	−0.212925	+	0.368796i	−0.952629	−	0.304136i	$-0.901632\pi$
$691$	−147.131	+	254.838i	−0.212925	+	0.368796i	0.739704	+	0.672932i	$0.234966\pi$
$692$		0			0
$693$	171.958	+	79.4166i	0.248136	+	0.114598i
$694$		0			0
$695$	629.796	+	363.613i	0.906181	+	0.523184i
$696$		0			0
$697$	34.2005	+	59.2370i	0.0490682	+	0.0849886i
$698$		0			0
$699$	384.772	+	199.401i	0.550461	+	0.285266i
$700$		0			0
$701$		−	579.128i		−	0.826146i	−0.910698	−	0.413073i	$-0.864455\pi$
$701$		−	579.128i		−	0.826146i	0.910698	−	0.413073i	$-0.135545\pi$
$702$		0			0
$703$		−	181.552i		−	0.258253i
$704$		0			0
$705$	1431.78	+	741.993i	2.03089	+	1.05247i
$706$		0			0
$707$	304.427	+	527.282i	0.430589	+	0.745803i
$708$		0			0
$709$	−702.992	−	405.872i	−0.991526	−	0.572458i	−0.0857956	−	0.996313i	$-0.527343\pi$
$709$	−702.992	−	405.872i	−0.991526	−	0.572458i	−0.905730	+	0.423855i	$0.860677\pi$
$710$		0			0
$711$	−3.91668	−	42.9473i	−0.00550869	−	0.0604041i
$712$		0			0
$713$	−44.7400	+	77.4920i	−0.0627490	+	0.108684i
$714$		0			0
$715$	221.679	+	383.959i	0.310040	+	0.537005i
$716$		0			0
$717$	545.415	−	24.8187i	0.760690	−	0.0346146i
$718$		0			0
$719$			441.412i			0.613924i	0.951722	+	0.306962i	$0.0993125\pi$
$719$			441.412i			0.613924i	−0.951722	+	0.306962i	$0.900687\pi$
$720$		0			0
$721$	−493.128			−0.683950
$722$		0			0
$723$	−355.410	+	227.341i	−0.491576	+	0.314442i
$724$		0			0
$725$	−910.990	+	525.961i	−1.25654	+	0.725463i
$726$		0			0
$727$	30.1778	+	17.4232i	0.0415101	+	0.0239658i	0.520611	−	0.853794i	$-0.325704\pi$
$727$	30.1778	+	17.4232i	0.0415101	+	0.0239658i	−0.479101	+	0.877760i	$0.659037\pi$
$728$		0			0
$729$	−702.035	+	196.440i	−0.963010	+	0.269465i
$730$		0			0
$731$	127.468	−	220.781i	0.174375	−	0.302026i
$732$		0			0
$733$	−889.135	+	513.342i	−1.21301	+	0.700331i	−0.963413	−	0.268020i	$-0.913631\pi$
$733$	−889.135	+	513.342i	−1.21301	+	0.700331i	−0.249595	+	0.968350i	$0.580297\pi$
$734$		0			0
$735$	253.780	+	396.742i	0.345279	+	0.539785i
$736$		0			0
$737$	−119.413			−0.162026
$738$		0			0
$739$	−1155.74			−1.56393			−0.781963	−	0.623324i	$-0.785782\pi$
$739$	−1155.74			−1.56393			−0.781963	+	0.623324i	$0.785782\pi$
$740$		0			0
$741$	504.866	−	22.9735i	0.681331	−	0.0310034i
$742$		0			0
$743$	−703.173	+	405.977i	−0.946397	+	0.546403i	−0.891960	−	0.452115i	$-0.850670\pi$
$743$	−703.173	+	405.977i	−0.946397	+	0.546403i	−0.0544372	+	0.998517i	$0.517336\pi$
$744$		0			0
$745$	−684.328	+	1185.29i	−0.918562	+	1.59100i
$746$		0			0
$747$	48.5260	−	4.42544i	0.0649612	−	0.00592428i
$748$		0			0
$749$	−828.543	−	478.360i	−1.10620	−	0.638665i
$750$		0			0
$751$	−189.525	+	109.422i	−0.252363	+	0.145702i	−0.620846	−	0.783933i	$-0.713211\pi$
$751$	−189.525	+	109.422i	−0.252363	+	0.145702i	0.368483	+	0.929635i	$0.379877\pi$
$752$		0			0
$753$	103.288	+	53.5272i	0.137169	+	0.0710853i
$754$		0			0
$755$	−984.844			−1.30443
$756$		0			0
$757$		−	985.851i		−	1.30231i	−0.758944	−	0.651156i	$-0.774284\pi$
$757$		−	985.851i		−	1.30231i	0.758944	−	0.651156i	$-0.225716\pi$
$758$		0			0
$759$	−119.523	+	230.636i	−0.157474	+	0.303869i
$760$		0			0
$761$	216.932	+	375.738i	0.285062	+	0.493742i	0.972624	−	0.232384i	$-0.0746525\pi$
$761$	216.932	+	375.738i	0.285062	+	0.493742i	−0.687562	+	0.726125i	$0.741319\pi$
$762$		0			0
$763$	−462.022	+	800.245i	−0.605533	+	1.04881i
$764$		0			0
$765$	852.374	+	393.657i	1.11421	+	0.514584i
$766$		0			0
$767$	−1227.88	−	708.916i	−1.60089	−	0.924272i
$768$		0			0
$769$	−318.366	−	551.425i	−0.414000	−	0.717068i	0.581323	−	0.813673i	$-0.302535\pi$
$769$	−318.366	−	551.425i	−0.414000	−	0.717068i	−0.995323	+	0.0966044i	$0.969202\pi$
$770$		0			0
$771$	20.4358	+	449.096i	0.0265055	+	0.582485i
$772$		0			0
$773$			815.596i			1.05510i	0.849523	+	0.527552i	$0.176890\pi$
$773$			815.596i			1.05510i	−0.849523	+	0.527552i	$0.823110\pi$
$774$		0			0
$775$			237.880i			0.306942i
$776$		0			0
$777$	−197.860	+	126.563i	−0.254646	+	0.162887i
$778$		0			0
$779$	40.2303	+	69.6809i	0.0516435	+	0.0894492i
$780$		0			0
$781$	124.637	+	71.9592i	0.159586	+	0.0921373i
$782$		0			0
$783$	−172.853	+	423.907i	−0.220758	+	0.541388i
$784$		0			0
$785$	−801.899	+	1388.93i	−1.02153	+	1.76934i
$786$		0			0
$787$	−22.2735	−	38.5788i	−0.0283017	−	0.0490201i	0.851528	−	0.524310i	$-0.175677\pi$
$787$	−22.2735	−	38.5788i	−0.0283017	−	0.0490201i	−0.879829	+	0.475290i	$0.842343\pi$
$788$		0			0
$789$	126.119	+	197.167i	0.159847	+	0.249894i
$790$		0			0
$791$			349.775i			0.442193i
$792$		0			0
$793$	1083.95			1.36689
$794$		0			0
$795$	−76.3883	−	1678.71i	−0.0960859	−	2.11158i
$796$		0			0
$797$	−131.223	+	75.7614i	−0.164646	+	0.0950582i	−0.580059	−	0.814575i	$-0.696970\pi$
$797$	−131.223	+	75.7614i	−0.164646	+	0.0950582i	0.415413	+	0.909633i	$0.363637\pi$
$798$		0			0
$799$	−557.943	−	322.128i	−0.698301	−	0.403164i
$800$		0			0
$801$	509.760	+	722.341i	0.636404	+	0.901799i
$802$		0			0
$803$	−25.2887	+	43.8013i	−0.0314927	+	0.0545470i
$804$		0			0
$805$	1069.50	−	617.478i	1.32858	−	0.767053i
$806$		0			0
$807$	331.653	−	639.970i	0.410970	−	0.793024i
$808$		0			0
$809$	−214.614			−0.265284			−0.132642	−	0.991164i	$-0.542346\pi$
$809$	−214.614			−0.265284			−0.132642	+	0.991164i	$0.542346\pi$
$810$		0			0
$811$	958.317			1.18165			0.590824	−	0.806800i	$-0.298803\pi$
$811$	958.317			1.18165			0.590824	+	0.806800i	$0.298803\pi$
$812$		0			0
$813$	607.973	−	1173.17i	0.747814	−	1.44301i
$814$		0			0
$815$	671.801	−	387.864i	0.824295	−	0.475907i
$816$		0			0
$817$	149.942	−	259.706i	0.183527	−	0.317878i
$818$		0			0
$819$	−376.988	−	534.200i	−0.460302	−	0.652259i
$820$		0			0
$821$	980.237	+	565.940i	1.19395	+	0.689330i	0.959201	−	0.282725i	$-0.0912383\pi$
$821$	980.237	+	565.940i	1.19395	+	0.689330i	0.234754	+	0.972055i	$0.424572\pi$
$822$		0			0
$823$	786.212	−	453.920i	0.955300	−	0.551543i	0.0605770	−	0.998164i	$-0.480706\pi$
$823$	786.212	−	453.920i	0.955300	−	0.551543i	0.894723	+	0.446621i	$0.147373\pi$
$824$		0			0
$825$	31.3920	+	689.870i	0.0380509	+	0.836206i
$826$		0			0
$827$	10.7818			0.0130373			0.00651865	−	0.999979i	$-0.497925\pi$
$827$	10.7818			0.0130373			0.00651865	+	0.999979i	$0.497925\pi$
$828$		0			0
$829$			112.915i			0.136206i	0.997678	+	0.0681030i	$0.0216946\pi$
$829$			112.915i			0.136206i	−0.997678	+	0.0681030i	$0.978305\pi$
$830$		0			0
$831$	208.387	+	325.779i	0.250767	+	0.392032i
$832$		0			0
$833$	−94.0775	−	162.947i	−0.112938	−	0.195615i
$834$		0			0
$835$	−1088.80	+	1885.87i	−1.30396	+	2.25852i
$836$		0			0
$837$	63.4744	+	81.7829i	0.0758356	+	0.0977096i
$838$		0			0
$839$	−257.467	−	148.649i	−0.306874	−	0.177174i	0.338653	−	0.940911i	$-0.390029\pi$
$839$	−257.467	−	148.649i	−0.306874	−	0.177174i	−0.645527	+	0.763738i	$0.723362\pi$
$840$		0			0
$841$	−276.758	−	479.360i	−0.329082	−	0.569988i
$842$		0			0
$843$	−354.830	+	226.970i	−0.420913	+	0.269241i
$844$		0			0
$845$			46.2775i			0.0547662i
$846$		0			0
$847$			608.240i			0.718111i
$848$		0			0
$849$	−57.2178	−	1257.42i	−0.0673943	−	1.48106i
$850$		0			0
$851$	−161.059	−	278.963i	−0.189259	−	0.327806i
$852$		0			0
$853$	1353.97	+	781.714i	1.58730	+	0.916429i	0.993749	+	0.111634i	$0.0356083\pi$
$853$	1353.97	+	781.714i	1.58730	+	0.916429i	0.593552	+	0.804795i	$0.297725\pi$
$854$		0			0
$855$	1002.65	+	463.061i	1.17269	+	0.541592i
$856$		0			0
$857$	14.3592	−	24.8709i	0.0167552	−	0.0290208i	−0.857526	−	0.514440i	$-0.828000\pi$
$857$	14.3592	−	24.8709i	0.0167552	−	0.0290208i	0.874281	+	0.485419i	$0.161333\pi$
$858$		0			0
$859$	−602.824	−	1044.12i	−0.701774	−	1.21551i	−0.967843	−	0.251555i	$-0.919058\pi$
$859$	−602.824	−	1044.12i	−0.701774	−	1.21551i	0.266069	−	0.963954i	$-0.414275\pi$
$860$		0			0
$861$	47.8948	−	92.4197i	0.0556269	−	0.107340i
$862$		0			0
$863$			740.816i			0.858419i	0.903205	+	0.429210i	$0.141208\pi$
$863$			740.816i			0.858419i	−0.903205	+	0.429210i	$0.858792\pi$
$864$		0			0
$865$	415.665			0.480537
$866$		0			0
$867$	436.743	+	226.334i	0.503741	+	0.261054i
$868$		0			0
$869$	−15.3972	+	8.88956i	−0.0177183	+	0.0102296i
$870$		0			0
$871$	356.976	+	206.100i	0.409846	+	0.236625i
$872$		0			0
$873$	755.860	−	68.9323i	0.865819	−	0.0789603i
$874$		0			0
$875$	980.069	−	1697.53i	1.12008	−	1.94003i
$876$		0			0
$877$	−1084.73	+	626.268i	−1.23686	+	0.714102i	−0.968451	−	0.249203i	$-0.919832\pi$
$877$	−1084.73	+	626.268i	−1.23686	+	0.714102i	−0.268410	+	0.963305i	$0.586498\pi$
$878$		0			0
$879$	−1139.09	+	51.8332i	−1.29589	+	0.0589684i
$880$		0			0
$881$	814.978			0.925060			0.462530	−	0.886604i	$-0.346942\pi$
$881$	814.978			0.925060			0.462530	+	0.886604i	$0.346942\pi$
$882$		0			0
$883$	895.745			1.01443			0.507217	−	0.861819i	$-0.330674\pi$
$883$	895.745			1.01443			0.507217	+	0.861819i	$0.330674\pi$
$884$		0			0
$885$	−1669.56	−	2610.07i	−1.88650	−	2.94923i
$886$		0			0
$887$	1453.92	−	839.424i	1.63915	−	0.946363i	0.658021	−	0.752999i	$-0.271394\pi$
$887$	1453.92	−	839.424i	1.63915	−	0.946363i	0.981127	−	0.193363i	$-0.0619396\pi$
$888$		0			0
$889$	−307.776	+	533.084i	−0.346205	+	0.599645i
$890$		0			0
$891$	194.873	+	228.800i	0.218712	+	0.256790i
$892$		0			0
$893$	−656.312	−	378.922i	−0.734951	−	0.424324i
$894$		0			0
$895$	124.231	−	71.7248i	0.138806	−	0.0801394i
$896$		0			0
$897$	755.369	−	483.179i	0.842106	−	0.538661i
$898$		0			0
$899$	65.0112			0.0723150
$900$		0			0
$901$			671.354i			0.745121i
$902$		0			0
$903$	−387.561	+	17.6357i	−0.429193	+	0.0195301i
$904$		0			0
$905$	−1122.47	−	1944.18i	−1.24030	−	2.14827i
$906$		0			0
$907$	195.810	−	339.153i	0.215888	−	0.373928i	−0.737659	−	0.675173i	$-0.764069\pi$
$907$	195.810	−	339.153i	0.215888	−	0.373928i	0.953547	+	0.301245i	$0.0974022\pi$
$908$		0			0
$909$	87.7390	+	962.079i	0.0965225	+	1.05839i
$910$		0			0
$911$	−1375.58	−	794.190i	−1.50996	−	0.871778i	−0.999932	−	0.0116223i	$-0.996300\pi$
$911$	−1375.58	−	794.190i	−1.50996	−	0.871778i	−0.510031	−	0.860156i	$-0.670366\pi$
$912$		0			0
$913$	−10.0443	−	17.3972i	−0.0110014	−	0.0190550i
$914$		0			0
$915$	2103.10	+	1089.89i	2.29847	+	1.19114i
$916$		0			0
$917$			370.281i			0.403796i
$918$		0			0
$919$			995.618i			1.08337i	0.840581	+	0.541686i	$0.182214\pi$
$919$			995.618i			1.08337i	−0.840581	+	0.541686i	$0.817786\pi$
$920$		0			0
$921$	815.494	+	422.615i	0.885445	+	0.458865i
$922$		0			0
$923$	−248.395	−	430.233i	−0.269117	−	0.466124i
$924$		0			0
$925$	−741.615	−	428.172i	−0.801746	−	0.462888i
$926$		0			0
$927$	−710.352	−	328.066i	−0.766291	−	0.353901i
$928$		0			0
$929$	729.805	−	1264.06i	0.785581	−	1.36067i	−0.143070	−	0.989713i	$-0.545697\pi$
$929$	729.805	−	1264.06i	0.785581	−	1.36067i	0.928651	−	0.370954i	$-0.120969\pi$
$930$		0			0
$931$	−110.664	−	191.676i	−0.118866	−	0.205881i
$932$		0			0
$933$	−1703.12	+	77.4989i	−1.82542	+	0.0830642i
$934$		0			0
$935$		−	387.069i		−	0.413978i
$936$		0			0
$937$	449.372			0.479585			0.239793	−	0.970824i	$-0.422921\pi$
$937$	449.372			0.479585			0.239793	+	0.970824i	$0.422921\pi$
$938$		0			0
$939$	791.938	−	506.571i	0.843384	−	0.539479i
$940$		0			0
$941$	994.500	−	574.175i	1.05685	−	0.610175i	0.132294	−	0.991211i	$-0.457766\pi$
$941$	994.500	−	574.175i	1.05685	−	0.610175i	0.924561	+	0.381035i	$0.124432\pi$
$942$		0			0
$943$	123.631	+	71.3786i	0.131104	+	0.0756931i
$944$		0			0
$945$	−194.311	−	1415.52i	−0.205620	−	1.49791i
$946$		0			0
$947$	−162.539	+	281.526i	−0.171636	+	0.297282i	−0.938992	−	0.343939i	$-0.888239\pi$
$947$	−162.539	+	281.526i	−0.171636	+	0.297282i	0.767356	+	0.641221i	$0.221572\pi$
$948$		0			0
$949$	151.197	−	87.2936i	0.159322	−	0.0919848i
$950$		0			0
$951$	−248.516	−	388.512i	−0.261320	−	0.408530i
$952$		0			0
$953$	−1073.20			−1.12613			−0.563064	−	0.826414i	$-0.690377\pi$
$953$	−1073.20			−1.12613			−0.563064	+	0.826414i	$0.690377\pi$
$954$		0			0
$955$	741.819			0.776774
$956$		0			0
$957$	188.537	−	8.57922i	0.197008	−	0.00896471i
$958$		0			0
$959$	350.041	−	202.096i	0.365006	−	0.210736i
$960$		0			0
$961$	−473.149	+	819.518i	−0.492351	+	0.852777i
$962$		0			0
$963$	−875.277	−	1240.29i	−0.908907	−	1.28794i
$964$		0			0
$965$	270.746	+	156.316i	0.280566	+	0.161985i
$966$		0			0
$967$	3.02820	−	1.74833i	0.00313154	−	0.00180800i	−0.498433	−	0.866928i	$-0.666091\pi$
$967$	3.02820	−	1.74833i	0.00313154	−	0.00180800i	0.501565	+	0.865120i	$0.332758\pi$
$968$		0			0
$969$	−391.746	−	203.015i	−0.404278	−	0.209510i
$970$		0			0
$971$	810.426			0.834630			0.417315	−	0.908762i	$-0.362971\pi$
$971$	810.426			0.834630			0.417315	+	0.908762i	$0.362971\pi$
$972$		0			0
$973$			442.134i			0.454402i
$974$		0			0
$975$	1096.83	−	2116.49i	1.12496	−	2.17076i
$976$		0			0
$977$	−546.820	−	947.119i	−0.559692	−	0.969416i	−0.997522	−	0.0703577i	$-0.977586\pi$
$977$	−546.820	−	947.119i	−0.559692	−	0.969416i	0.437829	−	0.899058i	$-0.355747\pi$
$978$		0			0
$979$	182.241	−	315.651i	0.186150	−	0.322422i
$980$		0			0
$981$	−1197.93	+	845.383i	−1.22113	+	0.861756i
$982$		0			0
$983$	−475.171	−	274.340i	−0.483389	−	0.279085i	0.238439	−	0.971158i	$-0.423364\pi$
$983$	−475.171	−	274.340i	−0.483389	−	0.279085i	−0.721828	+	0.692073i	$0.756698\pi$
$984$		0			0
$985$	854.358	+	1479.79i	0.867368	+	1.50233i
$986$		0			0
$987$	44.5676	+	979.417i	0.0451546	+	0.992317i
$988$		0			0
$989$		−	532.067i		−	0.537985i
$990$		0			0
$991$		−	494.677i		−	0.499169i	−0.968353	−	0.249585i	$-0.919706\pi$
$991$		−	494.677i		−	0.499169i	0.968353	−	0.249585i	$-0.0802941\pi$
$992$		0			0
$993$	1548.34	−	990.413i	1.55926	−	0.997395i
$994$		0			0
$995$	−402.410	−	696.995i	−0.404433	−	0.700498i
$996$		0			0
$997$	−112.086	−	64.7128i	−0.112423	−	0.0649075i	0.442734	−	0.896653i	$-0.354009\pi$
$997$	−112.086	−	64.7128i	−0.112423	−	0.0649075i	−0.555157	+	0.831745i	$0.687342\pi$
$998$		0			0
$999$	−369.217	+	50.6828i	−0.369586	+	0.0507335i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	288.3.t.b.79.4		40
3.2	odd	2		864.3.t.b.559.1		40
4.3	odd	2		72.3.p.b.43.7	✓	40
8.3	odd	2	inner	288.3.t.b.79.3		40
8.5	even	2		72.3.p.b.43.10	yes	40
9.2	odd	6		2592.3.b.f.1135.1		20
9.4	even	3	inner	288.3.t.b.175.3		40
9.5	odd	6		864.3.t.b.847.20		40
9.7	even	3		2592.3.b.e.1135.20		20
12.11	even	2		216.3.p.b.19.14		40
24.5	odd	2		216.3.p.b.19.11		40
24.11	even	2		864.3.t.b.559.20		40
36.7	odd	6		648.3.b.f.163.20		20
36.11	even	6		648.3.b.e.163.1		20
36.23	even	6		216.3.p.b.91.11		40
36.31	odd	6		72.3.p.b.67.10	yes	40
72.5	odd	6		216.3.p.b.91.14		40
72.11	even	6		2592.3.b.f.1135.20		20
72.13	even	6		72.3.p.b.67.7	yes	40
72.29	odd	6		648.3.b.e.163.2		20
72.43	odd	6		2592.3.b.e.1135.1		20
72.59	even	6		864.3.t.b.847.1		40
72.61	even	6		648.3.b.f.163.19		20
72.67	odd	6	inner	288.3.t.b.175.4		40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
72.3.p.b.43.7	✓	40	4.3	odd	2
72.3.p.b.43.10	yes	40	8.5	even	2
72.3.p.b.67.7	yes	40	72.13	even	6
72.3.p.b.67.10	yes	40	36.31	odd	6
216.3.p.b.19.11		40	24.5	odd	2
216.3.p.b.19.14		40	12.11	even	2
216.3.p.b.91.11		40	36.23	even	6
216.3.p.b.91.14		40	72.5	odd	6
288.3.t.b.79.3		40	8.3	odd	2	inner
288.3.t.b.79.4		40	1.1	even	1	trivial
288.3.t.b.175.3		40	9.4	even	3	inner
288.3.t.b.175.4		40	72.67	odd	6	inner
648.3.b.e.163.1		20	36.11	even	6
648.3.b.e.163.2		20	72.29	odd	6
648.3.b.f.163.19		20	72.61	even	6
648.3.b.f.163.20		20	36.7	odd	6
864.3.t.b.559.1		40	3.2	odd	2
864.3.t.b.559.20		40	24.11	even	2
864.3.t.b.847.1		40	72.59	even	6
864.3.t.b.847.20		40	9.5	odd	6
2592.3.b.e.1135.1		20	72.43	odd	6
2592.3.b.e.1135.20		20	9.7	even	3
2592.3.b.f.1135.1		20	9.2	odd	6
2592.3.b.f.1135.20		20	72.11	even	6

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:	\( N \)	\(=\)	\( 288 = 2^{5} \cdot 3^{2} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	288.t (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-2.66358 - 1.38035i) q^{3} +(8.07964 - 4.66478i) q^{5} +(4.91220 + 2.83606i) q^{7} +(5.18928 + 7.35333i) q^{9} +O(q^{10})\)	\(q+(-2.66358 - 1.38035i) q^{3} +(8.07964 - 4.66478i) q^{5} +(4.91220 + 2.83606i) q^{7} +(5.18928 + 7.35333i) q^{9} +(1.85519 - 3.21328i) q^{11} +(-11.0919 + 6.40390i) q^{13} +(-27.9598 + 1.27229i) q^{15} +11.1817 q^{17} +13.1532 q^{19} +(-9.16928 - 14.3346i) q^{21} +(20.2104 - 11.6685i) q^{23} +(31.0204 - 53.7288i) q^{25} +(-3.67189 - 26.7492i) q^{27} +(-14.6837 - 8.47767i) q^{29} +(-3.32057 + 1.91713i) q^{31} +(-9.37688 + 5.99801i) q^{33} +52.9184 q^{35} -13.8029i q^{37} +(38.3837 - 1.74662i) q^{39} +(3.05861 + 5.29766i) q^{41} +(11.3997 - 19.7448i) q^{43} +(76.2291 + 35.2054i) q^{45} +(-49.8977 - 28.8084i) q^{47} +(-8.41350 - 14.5726i) q^{49} +(-29.7834 - 15.4347i) q^{51} +60.0402i q^{53} -34.6162i q^{55} +(-35.0344 - 18.1559i) q^{57} +(55.3504 + 95.8696i) q^{59} +(-73.2932 - 42.3159i) q^{61} +(4.63630 + 50.8382i) q^{63} +(-59.7456 + 103.482i) q^{65} +(-16.0918 - 27.8718i) q^{67} +(-69.9385 + 3.18250i) q^{69} +38.7881i q^{71} -13.6313 q^{73} +(-156.790 + 100.292i) q^{75} +(18.2261 - 10.5229i) q^{77} +(-4.14976 - 2.39586i) q^{79} +(-27.1428 + 76.3169i) q^{81} +(2.70708 - 4.68879i) q^{83} +(90.3444 - 52.1604i) q^{85} +(27.4092 + 42.8496i) q^{87} +98.2333 q^{89} -72.6474 q^{91} +(11.4909 - 0.522884i) q^{93} +(106.273 - 61.3566i) q^{95} +(42.1665 - 73.0345i) q^{97} +(33.2554 - 3.03280i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q + 6 q^{3} - 18 q^{9}+O(q^{10}) \) 40 * q + 6 * q^3 - 18 * q^9	\( 40 q + 6 q^{3} - 18 q^{9} + 16 q^{11} - 4 q^{17} + 76 q^{19} + 118 q^{25} + 144 q^{27} + 156 q^{33} + 108 q^{35} + 20 q^{41} + 16 q^{43} + 166 q^{49} - 330 q^{51} - 258 q^{57} + 64 q^{59} - 102 q^{65} + 64 q^{67} - 292 q^{73} - 138 q^{75} - 42 q^{81} - 554 q^{83} - 688 q^{89} + 204 q^{91} + 92 q^{97} - 90 q^{99}+O(q^{100}) \) 40 * q + 6 * q^3 - 18 * q^9 + 16 * q^11 - 4 * q^17 + 76 * q^19 + 118 * q^25 + 144 * q^27 + 156 * q^33 + 108 * q^35 + 20 * q^41 + 16 * q^43 + 166 * q^49 - 330 * q^51 - 258 * q^57 + 64 * q^59 - 102 * q^65 + 64 * q^67 - 292 * q^73 - 138 * q^75 - 42 * q^81 - 554 * q^83 - 688 * q^89 + 204 * q^91 + 92 * q^97 - 90 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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