LMFDB - Embedded newform 192.9.l.a.175.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [192,9,Mod(79,192)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(192, base_ring=CyclotomicField(4))

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

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

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

chi := DirichletCharacter("192.79");

S:= CuspForms(chi, 9);

N := Newforms(S);

Level:	$ N $	$=$	$ 192 = 2^{6} \cdot 3 $
Weight:	$ k $	$=$	$ 9 $
Character orbit:	$[\chi]$	$=$	192.l (of order $4$, 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:	$78.2166931317$
Analytic rank:	$0$
Dimension:	$64$
Relative dimension:	$32$ over $\Q(i)$
Twist minimal:	no (minimal twist has level 48)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			175.5
Character	$\chi$	$=$	192.175
Dual form			192.9.l.a.79.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-33.0681 + 33.0681i) q^{3} +(-384.834 + 384.834i) q^{5} -1641.15 q^{7} -2187.00i q^{9} +O(q^{10})$	\(q+(-33.0681 + 33.0681i) q^{3} +(-384.834 + 384.834i) q^{5} -1641.15 q^{7} -2187.00i q^{9} +(-5395.29 - 5395.29i) q^{11} +(31216.1 + 31216.1i) q^{13} -25451.5i q^{15} -103035. q^{17} +(-143933. + 143933. i) q^{19} +(54269.7 - 54269.7i) q^{21} -322047. q^{23} +94430.7i q^{25} +(72320.0 + 72320.0i) q^{27} +(-645577. - 645577. i) q^{29} -611529. i q^{31} +356824. q^{33} +(631570. - 631570. i) q^{35} +(-486387. + 486387. i) q^{37} -2.06451e6 q^{39} +852590. i q^{41} +(821316. + 821316. i) q^{43} +(841632. + 841632. i) q^{45} +2.87783e6i q^{47} -3.07143e6 q^{49} +(3.40717e6 - 3.40717e6i) q^{51} +(4.13734e6 - 4.13734e6i) q^{53} +4.15258e6 q^{55} -9.51920e6i q^{57} +(1.34276e7 + 1.34276e7i) q^{59} +(-1.49089e7 - 1.49089e7i) q^{61} +3.58919e6i q^{63} -2.40260e7 q^{65} +(2.88490e6 - 2.88490e6i) q^{67} +(1.06495e7 - 1.06495e7i) q^{69} +2.41039e7 q^{71} +7.84105e6i q^{73} +(-3.12264e6 - 3.12264e6i) q^{75} +(8.85448e6 + 8.85448e6i) q^{77} +5.93662e7i q^{79} -4.78297e6 q^{81} +(6.14005e7 - 6.14005e7i) q^{83} +(3.96514e7 - 3.96514e7i) q^{85} +4.26961e7 q^{87} -7.56364e7i q^{89} +(-5.12302e7 - 5.12302e7i) q^{91} +(2.02221e7 + 2.02221e7i) q^{93} -1.10781e8i q^{95} +1.26587e8 q^{97} +(-1.17995e7 + 1.17995e7i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 64 q+O(q^{10}) $ 64 * q	$ 64 q - 39552 q^{11} + 167552 q^{19} - 1691136 q^{23} - 2132352 q^{29} + 2415744 q^{35} - 4720512 q^{37} + 7244672 q^{43} + 52706752 q^{49} - 13862016 q^{51} - 5358720 q^{53} + 46326784 q^{55} - 44938752 q^{59} + 24476032 q^{61} + 29941632 q^{65} + 44244736 q^{67} - 8636544 q^{69} - 159664128 q^{71} - 12918528 q^{75} - 94964352 q^{77} - 306110016 q^{81} - 209328000 q^{83} + 106960000 q^{85} + 45401472 q^{91} - 86500224 q^{99}+O(q^{100}) $ 64 * q - 39552 * q^11 + 167552 * q^19 - 1691136 * q^23 - 2132352 * q^29 + 2415744 * q^35 - 4720512 * q^37 + 7244672 * q^43 + 52706752 * q^49 - 13862016 * q^51 - 5358720 * q^53 + 46326784 * q^55 - 44938752 * q^59 + 24476032 * q^61 + 29941632 * q^65 + 44244736 * q^67 - 8636544 * q^69 - 159664128 * q^71 - 12918528 * q^75 - 94964352 * q^77 - 306110016 * q^81 - 209328000 * q^83 + 106960000 * q^85 + 45401472 * q^91 - 86500224 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/192\mathbb{Z}\right)^\times$.

$n$	$65$	$127$	$133$
$\chi(n)$	$1$	$-1$	$e\left(\frac{3}{4}\right)$

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
$3$	−33.0681	+	33.0681i	−0.408248	+	0.408248i
$3$	−33.0681	+	33.0681i	−0.408248	+	0.408248i
$4$		0			0
$5$	−384.834	+	384.834i	−0.615734	+	0.615734i	−0.944434	−	0.328700i	$-0.893389\pi$
$5$	−384.834	+	384.834i	−0.615734	+	0.615734i	0.328700	+	0.944434i	$0.393389\pi$
$6$		0			0
$7$	−1641.15			−0.683528			−0.341764	−	0.939786i	$-0.611024\pi$
$7$	−1641.15			−0.683528			−0.341764	+	0.939786i	$0.611024\pi$
$8$		0			0
$9$		−	2187.00i		−	0.333333i
$10$		0			0
$11$	−5395.29	−	5395.29i	−0.368506	−	0.368506i	0.498426	−	0.866932i	$-0.333911\pi$
$11$	−5395.29	−	5395.29i	−0.368506	−	0.368506i	−0.866932	+	0.498426i	$0.833911\pi$
$12$		0			0
$13$	31216.1	+	31216.1i	1.09296	+	1.09296i	0.995211	+	0.0977498i	$0.0311645\pi$
$13$	31216.1	+	31216.1i	1.09296	+	1.09296i	0.0977498	+	0.995211i	$0.468836\pi$
$14$		0			0
$15$		−	25451.5i		−	0.502745i
$16$		0			0
$17$	−103035.			−1.23364			−0.616821	−	0.787103i	$-0.711580\pi$
$17$	−103035.			−1.23364			−0.616821	+	0.787103i	$0.711580\pi$
$18$		0			0
$19$	−143933.	+	143933.i	−1.10445	+	1.10445i	−0.110584	+	0.993867i	$0.535272\pi$
$19$	−143933.	+	143933.i	−1.10445	+	1.10445i	−0.993867	+	0.110584i	$0.964728\pi$
$20$		0			0
$21$	54269.7	−	54269.7i	0.279049	−	0.279049i
$22$		0			0
$23$	−322047.			−1.15082			−0.575410	−	0.817865i	$-0.695158\pi$
$23$	−322047.			−1.15082			−0.575410	+	0.817865i	$0.695158\pi$
$24$		0			0
$25$			94430.7i			0.241743i
$26$		0			0
$27$	72320.0	+	72320.0i	0.136083	+	0.136083i
$28$		0			0
$29$	−645577.	−	645577.i	−0.912759	−	0.912759i	0.0837291	−	0.996489i	$-0.473317\pi$
$29$	−645577.	−	645577.i	−0.912759	−	0.912759i	−0.996489	+	0.0837291i	$0.973317\pi$
$30$		0			0
$31$		−	611529.i		−	0.662171i	−0.943601	−	0.331086i	$-0.892585\pi$
$31$		−	611529.i		−	0.662171i	0.943601	−	0.331086i	$-0.107415\pi$
$32$		0			0
$33$	356824.			0.300884
$34$		0			0
$35$	631570.	−	631570.i	0.420871	−	0.420871i
$36$		0			0
$37$	−486387.	+	486387.i	−0.259523	+	0.259523i	−0.824860	−	0.565337i	$-0.808746\pi$
$37$	−486387.	+	486387.i	−0.259523	+	0.259523i	0.565337	+	0.824860i	$0.308746\pi$
$38$		0			0
$39$	−2.06451e6			−0.892399
$40$		0			0
$41$			852590.i			0.301720i	0.988555	+	0.150860i	$0.0482043\pi$
$41$			852590.i			0.301720i	−0.988555	+	0.150860i	$0.951796\pi$
$42$		0			0
$43$	821316.	+	821316.i	0.240235	+	0.240235i	0.816947	−	0.576712i	$-0.195665\pi$
$43$	821316.	+	821316.i	0.240235	+	0.240235i	−0.576712	+	0.816947i	$0.695665\pi$
$44$		0			0
$45$	841632.	+	841632.i	0.205245	+	0.205245i
$46$		0			0
$47$			2.87783e6i			0.589758i	0.955535	+	0.294879i	$0.0952794\pi$
$47$			2.87783e6i			0.589758i	−0.955535	+	0.294879i	$0.904721\pi$
$48$		0			0
$49$	−3.07143e6			−0.532790
$50$		0			0
$51$	3.40717e6	−	3.40717e6i	0.503632	−	0.503632i
$52$		0			0
$53$	4.13734e6	−	4.13734e6i	0.524345	−	0.524345i	−0.394536	−	0.918881i	$-0.629094\pi$
$53$	4.13734e6	−	4.13734e6i	0.524345	−	0.524345i	0.918881	+	0.394536i	$0.129094\pi$
$54$		0			0
$55$	4.15258e6			0.453803
$56$		0			0
$57$		−	9.51920e6i		−	0.901781i
$58$		0			0
$59$	1.34276e7	+	1.34276e7i	1.10813	+	1.10813i	0.993396	+	0.114733i	$0.0366013\pi$
$59$	1.34276e7	+	1.34276e7i	1.10813	+	1.10813i	0.114733	+	0.993396i	$0.463399\pi$
$60$		0			0
$61$	−1.49089e7	−	1.49089e7i	−1.07678	−	1.07678i	−0.996796	−	0.0799824i	$-0.974514\pi$
$61$	−1.49089e7	−	1.49089e7i	−1.07678	−	1.07678i	−0.0799824	−	0.996796i	$-0.525486\pi$
$62$		0			0
$63$			3.58919e6i			0.227843i
$64$		0			0
$65$	−2.40260e7			−1.34595
$66$		0			0
$67$	2.88490e6	−	2.88490e6i	0.143163	−	0.143163i	−0.631893	−	0.775056i	$-0.717722\pi$
$67$	2.88490e6	−	2.88490e6i	0.143163	−	0.143163i	0.775056	+	0.631893i	$0.217722\pi$
$68$		0			0
$69$	1.06495e7	−	1.06495e7i	0.469820	−	0.469820i
$70$		0			0
$71$	2.41039e7			0.948535			0.474267	−	0.880381i	$-0.342713\pi$
$71$	2.41039e7			0.948535			0.474267	+	0.880381i	$0.342713\pi$
$72$		0			0
$73$			7.84105e6i			0.276111i	0.990425	+	0.138055i	$0.0440852\pi$
$73$			7.84105e6i			0.276111i	−0.990425	+	0.138055i	$0.955915\pi$
$74$		0			0
$75$	−3.12264e6	−	3.12264e6i	−0.0986910	−	0.0986910i
$76$		0			0
$77$	8.85448e6	+	8.85448e6i	0.251884	+	0.251884i
$78$		0			0
$79$			5.93662e7i			1.52416i	0.647482	+	0.762081i	$0.275822\pi$
$79$			5.93662e7i			1.52416i	−0.647482	+	0.762081i	$0.724178\pi$
$80$		0			0
$81$	−4.78297e6			−0.111111
$82$		0			0
$83$	6.14005e7	−	6.14005e7i	1.29378	−	1.29378i	0.361346	−	0.932432i	$-0.382317\pi$
$83$	6.14005e7	−	6.14005e7i	1.29378	−	1.29378i	0.932432	−	0.361346i	$-0.117683\pi$
$84$		0			0
$85$	3.96514e7	−	3.96514e7i	0.759596	−	0.759596i
$86$		0			0
$87$	4.26961e7			0.745265
$88$		0			0
$89$		−	7.56364e7i		−	1.20551i	−0.797926	−	0.602755i	$-0.794070\pi$
$89$		−	7.56364e7i		−	1.20551i	0.797926	−	0.602755i	$-0.205930\pi$
$90$		0			0
$91$	−5.12302e7	−	5.12302e7i	−0.747069	−	0.747069i
$92$		0			0
$93$	2.02221e7	+	2.02221e7i	0.270330	+	0.270330i
$94$		0			0
$95$		−	1.10781e8i		−	1.36010i
$96$		0			0
$97$	1.26587e8			1.42989			0.714943	−	0.699183i	$-0.246453\pi$
$97$	1.26587e8			1.42989			0.714943	+	0.699183i	$0.246453\pi$
$98$		0			0
$99$	−1.17995e7	+	1.17995e7i	−0.122835	+	0.122835i
$100$		0			0
$101$	−1.95367e7	+	1.95367e7i	−0.187744	+	0.187744i	−0.794720	−	0.606976i	$-0.792382\pi$
$101$	−1.95367e7	+	1.95367e7i	−0.187744	+	0.187744i	0.606976	+	0.794720i	$0.292382\pi$
$102$		0			0
$103$	−9.15906e7			−0.813771			−0.406885	−	0.913479i	$-0.633385\pi$
$103$	−9.15906e7			−0.813771			−0.406885	+	0.913479i	$0.633385\pi$
$104$		0			0
$105$			4.17697e7i			0.343640i
$106$		0			0
$107$	3.10695e7	+	3.10695e7i	0.237028	+	0.237028i	0.815618	−	0.578590i	$-0.196397\pi$
$107$	3.10695e7	+	3.10695e7i	0.237028	+	0.237028i	−0.578590	+	0.815618i	$0.696397\pi$
$108$		0			0
$109$	1.58824e8	+	1.58824e8i	1.12515	+	1.12515i	0.990955	+	0.134197i	$0.0428455\pi$
$109$	1.58824e8	+	1.58824e8i	1.12515	+	1.12515i	0.134197	+	0.990955i	$0.457154\pi$
$110$		0			0
$111$		−	3.21678e7i		−	0.211899i
$112$		0			0
$113$	1.60534e8			0.984586			0.492293	−	0.870430i	$-0.336159\pi$
$113$	1.60534e8			0.984586			0.492293	+	0.870430i	$0.336159\pi$
$114$		0			0
$115$	1.23934e8	−	1.23934e8i	0.708599	−	0.708599i
$116$		0			0
$117$	6.82695e7	−	6.82695e7i	0.364320	−	0.364320i
$118$		0			0
$119$	1.69096e8			0.843228
$120$		0			0
$121$		−	1.56140e8i		−	0.728407i
$122$		0			0
$123$	−2.81935e7	−	2.81935e7i	−0.123177	−	0.123177i
$124$		0			0
$125$	−1.86666e8	−	1.86666e8i	−0.764583	−	0.764583i
$126$		0			0
$127$		−	3.99089e7i		−	0.153411i	−0.997054	−	0.0767053i	$-0.975560\pi$
$127$		−	3.99089e7i		−	0.153411i	0.997054	−	0.0767053i	$-0.0244401\pi$
$128$		0			0
$129$	−5.43187e7			−0.196151
$130$		0			0
$131$	1.54455e8	−	1.54455e8i	0.524464	−	0.524464i	−0.394453	−	0.918916i	$-0.629066\pi$
$131$	1.54455e8	−	1.54455e8i	0.524464	−	0.524464i	0.918916	+	0.394453i	$0.129066\pi$
$132$		0			0
$133$	2.36216e8	−	2.36216e8i	0.754923	−	0.754923i
$134$		0			0
$135$	−5.56623e7			−0.167582
$136$		0			0
$137$			1.36175e8i			0.386557i	0.981144	+	0.193279i	$0.0619121\pi$
$137$			1.36175e8i			0.386557i	−0.981144	+	0.193279i	$0.938088\pi$
$138$		0			0
$139$	−1.58060e8	−	1.58060e8i	−0.423412	−	0.423412i	0.462965	−	0.886377i	$-0.346786\pi$
$139$	−1.58060e8	−	1.58060e8i	−0.423412	−	0.423412i	−0.886377	+	0.462965i	$0.846786\pi$
$140$		0			0
$141$	−9.51645e7	−	9.51645e7i	−0.240768	−	0.240768i
$142$		0			0
$143$		−	3.36840e8i		−	0.805525i
$144$		0			0
$145$	4.96880e8			1.12403
$146$		0			0
$147$	1.01566e8	−	1.01566e8i	0.217511	−	0.217511i
$148$		0			0
$149$	8.48839e7	−	8.48839e7i	0.172219	−	0.172219i	−0.615735	−	0.787953i	$-0.711141\pi$
$149$	8.48839e7	−	8.48839e7i	0.172219	−	0.172219i	0.787953	+	0.615735i	$0.211141\pi$
$150$		0			0
$151$	−2.18564e8			−0.420407			−0.210204	−	0.977658i	$-0.567413\pi$
$151$	−2.18564e8			−0.420407			−0.210204	+	0.977658i	$0.567413\pi$
$152$		0			0
$153$			2.25338e8i			0.411214i
$154$		0			0
$155$	2.35337e8	+	2.35337e8i	0.407722	+	0.407722i
$156$		0			0
$157$	−4.95758e8	−	4.95758e8i	−0.815964	−	0.815964i	0.169557	−	0.985520i	$-0.445766\pi$
$157$	−4.95758e8	−	4.95758e8i	−0.815964	−	0.815964i	−0.985520	+	0.169557i	$0.945766\pi$
$158$		0			0
$159$			2.73628e8i			0.428126i
$160$		0			0
$161$	5.28527e8			0.786617
$162$		0			0
$163$	4.97042e8	−	4.97042e8i	0.704113	−	0.704113i	−0.261178	−	0.965291i	$-0.584111\pi$
$163$	4.97042e8	−	4.97042e8i	0.704113	−	0.704113i	0.965291	+	0.261178i	$0.0841109\pi$
$164$		0			0
$165$	−1.37318e8	+	1.37318e8i	−0.185264	+	0.185264i
$166$		0			0
$167$	−9.42688e8			−1.21200			−0.605999	−	0.795465i	$-0.707226\pi$
$167$	−9.42688e8			−1.21200			−0.605999	+	0.795465i	$0.707226\pi$
$168$		0			0
$169$			1.13315e9i			1.38913i
$170$		0			0
$171$	3.14782e8	+	3.14782e8i	0.368150	+	0.368150i
$172$		0			0
$173$	−3.41416e8	−	3.41416e8i	−0.381153	−	0.381153i	0.490364	−	0.871518i	$-0.336864\pi$
$173$	−3.41416e8	−	3.41416e8i	−0.381153	−	0.381153i	−0.871518	+	0.490364i	$0.836864\pi$
$174$		0			0
$175$		−	1.54975e8i		−	0.165238i
$176$		0			0
$177$	−8.88051e8			−0.904784
$178$		0			0
$179$	3.79686e8	−	3.79686e8i	0.369839	−	0.369839i	−0.497580	−	0.867418i	$-0.665778\pi$
$179$	3.79686e8	−	3.79686e8i	0.369839	−	0.369839i	0.867418	+	0.497580i	$0.165778\pi$
$180$		0			0
$181$	1.22061e9	−	1.22061e9i	1.13727	−	1.13727i	0.148334	−	0.988937i	$-0.452609\pi$
$181$	1.22061e9	−	1.22061e9i	1.13727	−	1.13727i	0.988937	−	0.148334i	$-0.0473910\pi$
$182$		0			0
$183$	9.86019e8			0.879186
$184$		0			0
$185$		−	3.74357e8i		−	0.319594i
$186$		0			0
$187$	5.55904e8	+	5.55904e8i	0.454604	+	0.454604i
$188$		0			0
$189$	−1.18688e8	−	1.18688e8i	−0.0930163	−	0.0930163i
$190$		0			0
$191$			1.77560e8i			0.133417i	0.997773	+	0.0667086i	$0.0212498\pi$
$191$			1.77560e8i			0.133417i	−0.997773	+	0.0667086i	$0.978750\pi$
$192$		0			0
$193$	1.45722e9			1.05026			0.525128	−	0.851023i	$-0.324017\pi$
$193$	1.45722e9			1.05026			0.525128	+	0.851023i	$0.324017\pi$
$194$		0			0
$195$	7.94494e8	−	7.94494e8i	0.549481	−	0.549481i
$196$		0			0
$197$	−4.53284e8	+	4.53284e8i	−0.300958	+	0.300958i	−0.841388	−	0.540431i	$-0.818261\pi$
$197$	−4.53284e8	+	4.53284e8i	−0.300958	+	0.300958i	0.540431	+	0.841388i	$0.318261\pi$
$198$		0			0
$199$	−5.22382e8			−0.333101			−0.166551	−	0.986033i	$-0.553263\pi$
$199$	−5.22382e8			−0.333101			−0.166551	+	0.986033i	$0.553263\pi$
$200$		0			0
$201$			1.90796e8i			0.116892i
$202$		0			0
$203$	1.05949e9	+	1.05949e9i	0.623896	+	0.623896i
$204$		0			0
$205$	−3.28106e8	−	3.28106e8i	−0.185780	−	0.185780i
$206$		0			0
$207$			7.04316e8i			0.383607i
$208$		0			0
$209$	1.55312e9			0.813993
$210$		0			0
$211$	−2.04066e9	+	2.04066e9i	−1.02954	+	1.02954i	−0.0299864	+	0.999550i	$0.509546\pi$
$211$	−2.04066e9	+	2.04066e9i	−1.02954	+	1.02954i	−0.999550	+	0.0299864i	$0.990454\pi$
$212$		0			0
$213$	−7.97069e8	+	7.97069e8i	−0.387238	+	0.387238i
$214$		0			0
$215$	−6.32141e8			−0.295842
$216$		0			0
$217$			1.00361e9i			0.452612i
$218$		0			0
$219$	−2.59289e8	−	2.59289e8i	−0.112722	−	0.112722i
$220$		0			0
$221$	−3.21635e9	−	3.21635e9i	−1.34832	−	1.34832i
$222$		0			0
$223$			3.77778e9i			1.52763i	0.645437	+	0.763814i	$0.276675\pi$
$223$			3.77778e9i			1.52763i	−0.645437	+	0.763814i	$0.723325\pi$
$224$		0			0
$225$	2.06520e8			0.0805809
$226$		0			0
$227$	2.90321e9	−	2.90321e9i	1.09339	−	1.09339i	0.0982251	−	0.995164i	$-0.468683\pi$
$227$	2.90321e9	−	2.90321e9i	1.09339	−	1.09339i	0.995164	−	0.0982251i	$-0.0313165\pi$
$228$		0			0
$229$	−3.11959e9	+	3.11959e9i	−1.13437	+	1.13437i	−0.144932	+	0.989442i	$0.546296\pi$
$229$	−3.11959e9	+	3.11959e9i	−1.13437	+	1.13437i	−0.989442	+	0.144932i	$0.953704\pi$
$230$		0			0
$231$	−5.85602e8			−0.205662
$232$		0			0
$233$			8.02496e8i			0.272282i	0.990689	+	0.136141i	$0.0434700\pi$
$233$			8.02496e8i			0.272282i	−0.990689	+	0.136141i	$0.956530\pi$
$234$		0			0
$235$	−1.10749e9	−	1.10749e9i	−0.363134	−	0.363134i
$236$		0			0
$237$	−1.96313e9	−	1.96313e9i	−0.622237	−	0.622237i
$238$		0			0
$239$			1.81741e9i			0.557009i	0.960435	+	0.278504i	$0.0898386\pi$
$239$			1.81741e9i			0.557009i	−0.960435	+	0.278504i	$0.910161\pi$
$240$		0			0
$241$	−3.03588e9			−0.899945			−0.449972	−	0.893042i	$-0.648566\pi$
$241$	−3.03588e9			−0.899945			−0.449972	+	0.893042i	$0.648566\pi$
$242$		0			0
$243$	1.58164e8	−	1.58164e8i	0.0453609	−	0.0453609i
$244$		0			0
$245$	1.18199e9	−	1.18199e9i	0.328057	−	0.328057i
$246$		0			0
$247$	−8.98605e9			−2.41424
$248$		0			0
$249$			4.06080e9i			1.05637i
$250$		0			0
$251$	−2.76988e9	−	2.76988e9i	−0.697856	−	0.697856i	0.266092	−	0.963948i	$-0.414267\pi$
$251$	−2.76988e9	−	2.76988e9i	−0.697856	−	0.697856i	−0.963948	+	0.266092i	$0.914267\pi$
$252$		0			0
$253$	1.73754e9	+	1.73754e9i	0.424084	+	0.424084i
$254$		0			0
$255$			2.62239e9i			0.620207i
$256$		0			0
$257$	−7.22766e9			−1.65678			−0.828391	−	0.560151i	$-0.810743\pi$
$257$	−7.22766e9			−1.65678			−0.828391	+	0.560151i	$0.810743\pi$
$258$		0			0
$259$	7.98234e8	−	7.98234e8i	0.177391	−	0.177391i
$260$		0			0
$261$	−1.41188e9	+	1.41188e9i	−0.304253	+	0.304253i
$262$		0			0
$263$	−2.44090e9			−0.510183			−0.255092	−	0.966917i	$-0.582106\pi$
$263$	−2.44090e9			−0.510183			−0.255092	+	0.966917i	$0.582106\pi$
$264$		0			0
$265$			3.18437e9i			0.645715i
$266$		0			0
$267$	2.50115e9	+	2.50115e9i	0.492148	+	0.492148i
$268$		0			0
$269$	−2.52011e9	−	2.52011e9i	−0.481294	−	0.481294i	0.424251	−	0.905545i	$-0.360538\pi$
$269$	−2.52011e9	−	2.52011e9i	−0.481294	−	0.481294i	−0.905545	+	0.424251i	$0.860538\pi$
$270$		0			0
$271$			3.26633e9i			0.605596i	0.953055	+	0.302798i	$0.0979208\pi$
$271$			3.26633e9i			0.605596i	−0.953055	+	0.302798i	$0.902079\pi$
$272$		0			0
$273$	3.38817e9			0.609979
$274$		0			0
$275$	5.09481e8	−	5.09481e8i	0.0890835	−	0.0890835i
$276$		0			0
$277$	−1.51461e8	+	1.51461e8i	−0.0257266	+	0.0257266i	−0.719853	−	0.694126i	$-0.755791\pi$
$277$	−1.51461e8	+	1.51461e8i	−0.0257266	+	0.0257266i	0.694126	+	0.719853i	$0.255791\pi$
$278$		0			0
$279$	−1.33741e9			−0.220724
$280$		0			0
$281$			8.66129e9i			1.38918i	0.719408	+	0.694588i	$0.244413\pi$
$281$			8.66129e9i			1.38918i	−0.719408	+	0.694588i	$0.755587\pi$
$282$		0			0
$283$	4.50915e9	+	4.50915e9i	0.702990	+	0.702990i	0.965051	−	0.262061i	$-0.0844023\pi$
$283$	4.50915e9	+	4.50915e9i	0.702990	+	0.702990i	−0.262061	+	0.965051i	$0.584402\pi$
$284$		0			0
$285$	3.66331e9	+	3.66331e9i	0.555257	+	0.555257i
$286$		0			0
$287$		−	1.39923e9i		−	0.206234i
$288$		0			0
$289$	3.64046e9			0.521873
$290$		0			0
$291$	−4.18598e9	+	4.18598e9i	−0.583748	+	0.583748i
$292$		0			0
$293$	7.35696e9	−	7.35696e9i	0.998224	−	0.998224i	−0.00177487	−	0.999998i	$-0.500565\pi$
$293$	7.35696e9	−	7.35696e9i	0.998224	−	0.998224i	0.999998	+	0.00177487i	$0.000564961\pi$
$294$		0			0
$295$	−1.03348e10			−1.36463
$296$		0			0
$297$		−	7.80375e8i		−	0.100295i
$298$		0			0
$299$	−1.00530e10	−	1.00530e10i	−1.25780	−	1.25780i
$300$		0			0
$301$	−1.34790e9	−	1.34790e9i	−0.164207	−	0.164207i
$302$		0			0
$303$		−	1.29208e9i		−	0.153292i
$304$		0			0
$305$	1.14749e10			1.32602
$306$		0			0
$307$	1.00075e10	−	1.00075e10i	1.12660	−	1.12660i	0.135878	−	0.990726i	$-0.456614\pi$
$307$	1.00075e10	−	1.00075e10i	1.12660	−	1.12660i	0.990726	−	0.135878i	$-0.0433856\pi$
$308$		0			0
$309$	3.02873e9	−	3.02873e9i	0.332220	−	0.332220i
$310$		0			0
$311$	−3.28626e9			−0.351286			−0.175643	−	0.984454i	$-0.556200\pi$
$311$	−3.28626e9			−0.351286			−0.175643	+	0.984454i	$0.556200\pi$
$312$		0			0
$313$			1.64826e10i			1.71731i	0.512558	+	0.858653i	$0.328698\pi$
$313$			1.64826e10i			1.71731i	−0.512558	+	0.858653i	$0.671302\pi$
$314$		0			0
$315$	−1.38124e9	−	1.38124e9i	−0.140290	−	0.140290i
$316$		0			0
$317$	−3.61075e9	−	3.61075e9i	−0.357569	−	0.357569i	0.505347	−	0.862916i	$-0.331365\pi$
$317$	−3.61075e9	−	3.61075e9i	−0.357569	−	0.357569i	−0.862916	+	0.505347i	$0.831365\pi$
$318$		0			0
$319$			6.96616e9i			0.672714i
$320$		0			0
$321$	−2.05482e9			−0.193533
$322$		0			0
$323$	1.48302e10	−	1.48302e10i	1.36250	−	1.36250i
$324$		0			0
$325$	−2.94775e9	+	2.94775e9i	−0.264215	+	0.264215i
$326$		0			0
$327$	−1.05040e10			−0.918683
$328$		0			0
$329$		−	4.72295e9i		−	0.403116i
$330$		0			0
$331$	5.14455e9	+	5.14455e9i	0.428584	+	0.428584i	0.888146	−	0.459562i	$-0.151994\pi$
$331$	5.14455e9	+	5.14455e9i	0.428584	+	0.428584i	−0.459562	+	0.888146i	$0.651994\pi$
$332$		0			0
$333$	1.06373e9	+	1.06373e9i	0.0865075	+	0.0865075i
$334$		0			0
$335$			2.22041e9i			0.176301i
$336$		0			0
$337$	1.55489e10			1.20553			0.602767	−	0.797917i	$-0.294065\pi$
$337$	1.55489e10			1.20553			0.602767	+	0.797917i	$0.294065\pi$
$338$		0			0
$339$	−5.30856e9	+	5.30856e9i	−0.401955	+	0.401955i
$340$		0			0
$341$	−3.29938e9	+	3.29938e9i	−0.244014	+	0.244014i
$342$		0			0
$343$	1.45016e10			1.04770
$344$		0			0
$345$			8.19656e9i			0.578569i
$346$		0			0
$347$	1.31648e10	+	1.31648e10i	0.908019	+	0.908019i	0.996112	−	0.0880935i	$-0.0280774\pi$
$347$	1.31648e10	+	1.31648e10i	0.908019	+	0.908019i	−0.0880935	+	0.996112i	$0.528077\pi$
$348$		0			0
$349$	−1.71698e10	−	1.71698e10i	−1.15735	−	1.15735i	−0.985044	−	0.172301i	$-0.944880\pi$
$349$	−1.71698e10	−	1.71698e10i	−1.15735	−	1.15735i	−0.172301	−	0.985044i	$-0.555120\pi$
$350$		0			0
$351$			4.51509e9i			0.297466i
$352$		0			0
$353$	−1.92630e10			−1.24058			−0.620291	−	0.784372i	$-0.712985\pi$
$353$	−1.92630e10			−1.24058			−0.620291	+	0.784372i	$0.712985\pi$
$354$		0			0
$355$	−9.27599e9	+	9.27599e9i	−0.584045	+	0.584045i
$356$		0			0
$357$	−5.59168e9	+	5.59168e9i	−0.344247	+	0.344247i
$358$		0			0
$359$	1.02815e10			0.618981			0.309491	−	0.950903i	$-0.399842\pi$
$359$	1.02815e10			0.618981			0.309491	+	0.950903i	$0.399842\pi$
$360$		0			0
$361$		−	2.44500e10i		−	1.43962i
$362$		0			0
$363$	5.16327e9	+	5.16327e9i	0.297371	+	0.297371i
$364$		0			0
$365$	−3.01750e9	−	3.01750e9i	−0.170011	−	0.170011i
$366$		0			0
$367$		−	2.39423e10i		−	1.31978i	−0.751361	−	0.659891i	$-0.770602\pi$
$367$		−	2.39423e10i		−	1.31978i	0.751361	−	0.659891i	$-0.229398\pi$
$368$		0			0
$369$	1.86461e9			0.100573
$370$		0			0
$371$	−6.78999e9	+	6.78999e9i	−0.358404	+	0.358404i
$372$		0			0
$373$	−5.92293e9	+	5.92293e9i	−0.305986	+	0.305986i	−0.843350	−	0.537364i	$-0.819420\pi$
$373$	−5.92293e9	+	5.92293e9i	−0.305986	+	0.305986i	0.537364	+	0.843350i	$0.319420\pi$
$374$		0			0
$375$	1.23454e10			0.624280
$376$		0			0
$377$		−	4.03048e10i		−	1.99522i
$378$		0			0
$379$	1.10426e10	+	1.10426e10i	0.535200	+	0.535200i	0.922115	−	0.386916i	$-0.126460\pi$
$379$	1.10426e10	+	1.10426e10i	0.535200	+	0.535200i	−0.386916	+	0.922115i	$0.626460\pi$
$380$		0			0
$381$	1.31971e9	+	1.31971e9i	0.0626296	+	0.0626296i
$382$		0			0
$383$		−	3.10277e10i		−	1.44196i	−0.692954	−	0.720982i	$-0.743691\pi$
$383$		−	3.10277e10i		−	1.44196i	0.692954	−	0.720982i	$-0.256309\pi$
$384$		0			0
$385$	−6.81501e9			−0.310187
$386$		0			0
$387$	1.79622e9	−	1.79622e9i	0.0800784	−	0.0800784i
$388$		0			0
$389$	3.10968e10	−	3.10968e10i	1.35805	−	1.35805i	0.481738	−	0.876315i	$-0.340006\pi$
$389$	3.10968e10	−	3.10968e10i	1.35805	−	1.35805i	0.876315	−	0.481738i	$-0.159994\pi$
$390$		0			0
$391$	3.31821e10			1.41970
$392$		0			0
$393$			1.02150e10i			0.428223i
$394$		0			0
$395$	−2.28461e10	−	2.28461e10i	−0.938479	−	0.938479i
$396$		0			0
$397$	1.64482e10	+	1.64482e10i	0.662151	+	0.662151i	0.955887	−	0.293736i	$-0.0948985\pi$
$397$	1.64482e10	+	1.64482e10i	0.662151	+	0.662151i	−0.293736	+	0.955887i	$0.594899\pi$
$398$		0			0
$399$			1.56224e10i			0.616392i
$400$		0			0
$401$	3.28798e10			1.27160			0.635802	−	0.771852i	$-0.280670\pi$
$401$	3.28798e10			1.27160			0.635802	+	0.771852i	$0.280670\pi$
$402$		0			0
$403$	1.90895e10	−	1.90895e10i	0.723727	−	0.723727i
$404$		0			0
$405$	1.84065e9	−	1.84065e9i	0.0684149	−	0.0684149i
$406$		0			0
$407$	5.24840e9			0.191271
$408$		0			0
$409$		−	6.27386e9i		−	0.224203i	−0.993697	−	0.112102i	$-0.964242\pi$
$409$		−	6.27386e9i		−	0.224203i	0.993697	−	0.112102i	$-0.0357582\pi$
$410$		0			0
$411$	−4.50304e9	−	4.50304e9i	−0.157811	−	0.157811i
$412$		0			0
$413$	−2.20367e10	−	2.20367e10i	−0.757437	−	0.757437i
$414$		0			0
$415$			4.72580e10i			1.59325i
$416$		0			0
$417$	1.04535e10			0.345714
$418$		0			0
$419$	7.37482e9	−	7.37482e9i	0.239274	−	0.239274i	−0.577276	−	0.816549i	$-0.695884\pi$
$419$	7.37482e9	−	7.37482e9i	0.239274	−	0.239274i	0.816549	+	0.577276i	$0.195884\pi$
$420$		0			0
$421$	−3.59972e10	+	3.59972e10i	−1.14588	+	1.14588i	−0.158529	+	0.987354i	$0.550675\pi$
$421$	−3.59972e10	+	3.59972e10i	−1.14588	+	1.14588i	−0.987354	+	0.158529i	$0.949325\pi$
$422$		0			0
$423$	6.29382e9			0.196586
$424$		0			0
$425$		−	9.72967e9i		−	0.298224i
$426$		0			0
$427$	2.44677e10	+	2.44677e10i	0.736008	+	0.736008i
$428$		0			0
$429$	1.11386e10	+	1.11386e10i	0.328854	+	0.328854i
$430$		0			0
$431$		−	4.58757e10i		−	1.32946i	−0.747086	−	0.664728i	$-0.768548\pi$
$431$		−	4.58757e10i		−	1.32946i	0.747086	−	0.664728i	$-0.231452\pi$
$432$		0			0
$433$	−4.70715e10			−1.33908			−0.669540	−	0.742776i	$-0.733509\pi$
$433$	−4.70715e10			−1.33908			−0.669540	+	0.742776i	$0.733509\pi$
$434$		0			0
$435$	−1.64309e10	+	1.64309e10i	−0.458885	+	0.458885i
$436$		0			0
$437$	4.63532e10	−	4.63532e10i	1.27102	−	1.27102i
$438$		0			0
$439$	−1.94691e10			−0.524188			−0.262094	−	0.965042i	$-0.584413\pi$
$439$	−1.94691e10			−0.524188			−0.262094	+	0.965042i	$0.584413\pi$
$440$		0			0
$441$			6.71721e9i			0.177597i
$442$		0			0
$443$	−4.47090e10	−	4.47090e10i	−1.16086	−	1.16086i	−0.984288	−	0.176573i	$-0.943499\pi$
$443$	−4.47090e10	−	4.47090e10i	−1.16086	−	1.16086i	−0.176573	−	0.984288i	$-0.556501\pi$
$444$		0			0
$445$	2.91075e10	+	2.91075e10i	0.742274	+	0.742274i
$446$		0			0
$447$			5.61390e9i			0.140616i
$448$		0			0
$449$	4.98537e10			1.22663			0.613313	−	0.789840i	$-0.289837\pi$
$449$	4.98537e10			1.22663			0.613313	+	0.789840i	$0.289837\pi$
$450$		0			0
$451$	4.59997e9	−	4.59997e9i	0.111186	−	0.111186i
$452$		0			0
$453$	7.22749e9	−	7.22749e9i	0.171631	−	0.171631i
$454$		0			0
$455$	3.94303e10			0.919992
$456$		0			0
$457$		−	2.08818e10i		−	0.478743i	−0.970928	−	0.239372i	$-0.923059\pi$
$457$		−	2.08818e10i		−	0.478743i	0.970928	−	0.239372i	$-0.0769415\pi$
$458$		0			0
$459$	−7.45149e9	−	7.45149e9i	−0.167877	−	0.167877i
$460$		0			0
$461$	4.14710e10	+	4.14710e10i	0.918206	+	0.918206i	0.996899	−	0.0786924i	$-0.0250745\pi$
$461$	4.14710e10	+	4.14710e10i	0.918206	+	0.918206i	−0.0786924	+	0.996899i	$0.525075\pi$
$462$		0			0
$463$		−	5.47650e10i		−	1.19173i	−0.803083	−	0.595867i	$-0.796809\pi$
$463$		−	5.47650e10i		−	1.19173i	0.803083	−	0.595867i	$-0.203191\pi$
$464$		0			0
$465$	−1.55643e10			−0.332903
$466$		0			0
$467$	−3.98156e10	+	3.98156e10i	−0.837117	+	0.837117i	−0.988478	−	0.151362i	$-0.951634\pi$
$467$	−3.98156e10	+	3.98156e10i	−0.837117	+	0.837117i	0.151362	+	0.988478i	$0.451634\pi$
$468$		0			0
$469$	−4.73455e9	+	4.73455e9i	−0.0978560	+	0.0978560i
$470$		0			0
$471$	3.27875e10			0.666232
$472$		0			0
$473$		−	8.86248e9i		−	0.177056i
$474$		0			0
$475$	−1.35917e10	−	1.35917e10i	−0.266993	−	0.266993i
$476$		0			0
$477$	−9.04835e9	−	9.04835e9i	−0.174782	−	0.174782i
$478$		0			0
$479$		−	4.13653e10i		−	0.785767i	−0.919588	−	0.392884i	$-0.871478\pi$
$479$		−	4.13653e10i		−	0.785767i	0.919588	−	0.392884i	$-0.128522\pi$
$480$		0			0
$481$	−3.03662e10			−0.567296
$482$		0			0
$483$	−1.74774e10	+	1.74774e10i	−0.321135	+	0.321135i
$484$		0			0
$485$	−4.87149e10	+	4.87149e10i	−0.880430	+	0.880430i
$486$		0			0
$487$	−3.75043e10			−0.666753			−0.333377	−	0.942794i	$-0.608188\pi$
$487$	−3.75043e10			−0.666753			−0.333377	+	0.942794i	$0.608188\pi$
$488$		0			0
$489$			3.28725e10i			0.574906i
$490$		0			0
$491$	3.37271e10	+	3.37271e10i	0.580300	+	0.580300i	0.934986	−	0.354686i	$-0.115412\pi$
$491$	3.37271e10	+	3.37271e10i	0.580300	+	0.580300i	−0.354686	+	0.934986i	$0.615412\pi$
$492$		0			0
$493$	6.65171e10	+	6.65171e10i	1.12602	+	1.12602i
$494$		0			0
$495$		−	9.08170e9i		−	0.151268i
$496$		0			0
$497$	−3.95581e10			−0.648350
$498$		0			0
$499$	−2.51104e10	+	2.51104e10i	−0.404997	+	0.404997i	−0.879990	−	0.474992i	$-0.842451\pi$
$499$	−2.51104e10	+	2.51104e10i	−0.404997	+	0.404997i	0.474992	+	0.879990i	$0.342451\pi$
$500$		0			0
$501$	3.11729e10	−	3.11729e10i	0.494796	−	0.494796i
$502$		0			0
$503$	−6.44447e10			−1.00673			−0.503367	−	0.864073i	$-0.667906\pi$
$503$	−6.44447e10			−1.00673			−0.503367	+	0.864073i	$0.667906\pi$
$504$		0			0
$505$		−	1.50368e10i		−	0.231201i
$506$		0			0
$507$	−3.74712e10	−	3.74712e10i	−0.567109	−	0.567109i
$508$		0			0
$509$	1.53752e10	+	1.53752e10i	0.229061	+	0.229061i	0.812300	−	0.583240i	$-0.198215\pi$
$509$	1.53752e10	+	1.53752e10i	0.229061	+	0.229061i	−0.583240	+	0.812300i	$0.698215\pi$
$510$		0			0
$511$		−	1.28683e10i		−	0.188729i
$512$		0			0
$513$	−2.08185e10			−0.300594
$514$		0			0
$515$	3.52472e10	−	3.52472e10i	0.501066	−	0.501066i
$516$		0			0
$517$	1.55268e10	−	1.55268e10i	0.217329	−	0.217329i
$518$		0			0
$519$	2.25800e10			0.311210
$520$		0			0
$521$		−	9.02387e10i		−	1.22473i	−0.790574	−	0.612367i	$-0.790218\pi$
$521$		−	9.02387e10i		−	1.22473i	0.790574	−	0.612367i	$-0.209782\pi$
$522$		0			0
$523$	4.84379e10	+	4.84379e10i	0.647409	+	0.647409i	0.952366	−	0.304957i	$-0.0986421\pi$
$523$	4.84379e10	+	4.84379e10i	0.647409	+	0.647409i	−0.304957	+	0.952366i	$0.598642\pi$
$524$		0			0
$525$	5.12473e9	+	5.12473e9i	0.0674580	+	0.0674580i
$526$		0			0
$527$			6.30089e10i			0.816883i
$528$		0			0
$529$	2.54030e10			0.324387
$530$		0			0
$531$	2.93662e10	−	2.93662e10i	0.369376	−	0.369376i
$532$		0			0
$533$	−2.66145e10	+	2.66145e10i	−0.329769	+	0.329769i
$534$		0			0
$535$	−2.39132e10			−0.291893
$536$		0			0
$537$			2.51110e10i			0.301972i
$538$		0			0
$539$	1.65713e10	+	1.65713e10i	0.196336	+	0.196336i
$540$		0			0
$541$	3.79797e10	+	3.79797e10i	0.443367	+	0.443367i	0.893142	−	0.449775i	$-0.148496\pi$
$541$	3.79797e10	+	3.79797e10i	0.443367	+	0.443367i	−0.449775	+	0.893142i	$0.648496\pi$
$542$		0			0
$543$			8.07268e10i			0.928578i
$544$		0			0
$545$	−1.22242e11			−1.38559
$546$		0			0
$547$	−1.14985e11	+	1.14985e11i	−1.28438	+	1.28438i	−0.346230	+	0.938150i	$0.612538\pi$
$547$	−1.14985e11	+	1.14985e11i	−1.28438	+	1.28438i	−0.938150	+	0.346230i	$0.887462\pi$
$548$		0			0
$549$	−3.26058e10	+	3.26058e10i	−0.358926	+	0.358926i
$550$		0			0
$551$	1.85840e11			2.01620
$552$		0			0
$553$		−	9.74289e10i		−	1.04181i
$554$		0			0
$555$	1.23793e10	+	1.23793e10i	0.130474	+	0.130474i
$556$		0			0
$557$	−6.72576e10	−	6.72576e10i	−0.698748	−	0.698748i	0.265392	−	0.964141i	$-0.414499\pi$
$557$	−6.72576e10	−	6.72576e10i	−0.698748	−	0.698748i	−0.964141	+	0.265392i	$0.914499\pi$
$558$		0			0
$559$			5.12765e10i			0.525135i
$560$		0			0
$561$	−3.67654e10			−0.371183
$562$		0			0
$563$	−7.11194e10	+	7.11194e10i	−0.707872	+	0.707872i	−0.966087	−	0.258216i	$-0.916866\pi$
$563$	−7.11194e10	+	7.11194e10i	−0.707872	+	0.707872i	0.258216	+	0.966087i	$0.416866\pi$
$564$		0			0
$565$	−6.17790e10	+	6.17790e10i	−0.606243	+	0.606243i
$566$		0			0
$567$	7.84957e9			0.0759475
$568$		0			0
$569$			1.10524e11i			1.05440i	0.849740	+	0.527202i	$0.176759\pi$
$569$			1.10524e11i			1.05440i	−0.849740	+	0.527202i	$0.823241\pi$
$570$		0			0
$571$	−1.00791e11	−	1.00791e11i	−0.948153	−	0.948153i	0.0505672	−	0.998721i	$-0.483897\pi$
$571$	−1.00791e11	−	1.00791e11i	−0.948153	−	0.948153i	−0.998721	+	0.0505672i	$0.983897\pi$
$572$		0			0
$573$	−5.87158e9	−	5.87158e9i	−0.0544673	−	0.0544673i
$574$		0			0
$575$		−	3.04111e10i		−	0.278202i
$576$		0			0
$577$	3.37265e10			0.304276			0.152138	−	0.988359i	$-0.451384\pi$
$577$	3.37265e10			0.304276			0.152138	+	0.988359i	$0.451384\pi$
$578$		0			0
$579$	−4.81874e10	+	4.81874e10i	−0.428765	+	0.428765i
$580$		0			0
$581$	−1.00767e11	+	1.00767e11i	−0.884333	+	0.884333i
$582$		0			0
$583$	−4.46443e10			−0.386448
$584$		0			0
$585$			5.25448e10i			0.448649i
$586$		0			0
$587$	−1.03937e11	−	1.03937e11i	−0.875424	−	0.875424i	0.117633	−	0.993057i	$-0.462469\pi$
$587$	−1.03937e11	−	1.03937e11i	−0.875424	−	0.875424i	−0.993057	+	0.117633i	$0.962469\pi$
$588$		0			0
$589$	8.80193e10	+	8.80193e10i	0.731336	+	0.731336i
$590$		0			0
$591$		−	2.99785e10i		−	0.245731i
$592$		0			0
$593$	−1.66969e11			−1.35026			−0.675131	−	0.737698i	$-0.735913\pi$
$593$	−1.66969e11			−1.35026			−0.675131	+	0.737698i	$0.735913\pi$
$594$		0			0
$595$	−6.50738e10	+	6.50738e10i	−0.519205	+	0.519205i
$596$		0			0
$597$	1.72742e10	−	1.72742e10i	0.135988	−	0.135988i
$598$		0			0
$599$	6.70800e10			0.521058			0.260529	−	0.965466i	$-0.416103\pi$
$599$	6.70800e10			0.521058			0.260529	+	0.965466i	$0.416103\pi$
$600$		0			0
$601$		−	1.69694e11i		−	1.30067i	−0.759646	−	0.650337i	$-0.774628\pi$
$601$		−	1.69694e11i		−	1.30067i	0.759646	−	0.650337i	$-0.225372\pi$
$602$		0			0
$603$	−6.30927e9	−	6.30927e9i	−0.0477211	−	0.0477211i
$604$		0			0
$605$	6.00882e10	+	6.00882e10i	0.448505	+	0.448505i
$606$		0			0
$607$		−	1.42708e11i		−	1.05122i	−0.850725	−	0.525611i	$-0.823837\pi$
$607$		−	1.42708e11i		−	1.05122i	0.850725	−	0.525611i	$-0.176163\pi$
$608$		0			0
$609$	−7.00706e10			−0.509409
$610$		0			0
$611$	−8.98346e10	+	8.98346e10i	−0.644583	+	0.644583i
$612$		0			0
$613$	−1.31736e10	+	1.31736e10i	−0.0932957	+	0.0932957i	−0.752214	−	0.658919i	$-0.771014\pi$
$613$	−1.31736e10	+	1.31736e10i	−0.0932957	+	0.0932957i	0.658919	+	0.752214i	$0.271014\pi$
$614$		0			0
$615$	2.16997e10			0.151688
$616$		0			0
$617$			1.15813e11i			0.799130i	0.916705	+	0.399565i	$0.130839\pi$
$617$			1.15813e11i			0.799130i	−0.916705	+	0.399565i	$0.869161\pi$
$618$		0			0
$619$	1.00573e11	+	1.00573e11i	0.685047	+	0.685047i	0.961133	−	0.276086i	$-0.0890374\pi$
$619$	1.00573e11	+	1.00573e11i	0.685047	+	0.685047i	−0.276086	+	0.961133i	$0.589037\pi$
$620$		0			0
$621$	−2.32904e10	−	2.32904e10i	−0.156607	−	0.156607i
$622$		0			0
$623$			1.24131e11i			0.824000i
$624$		0			0
$625$	1.06784e11			0.699818
$626$		0			0
$627$	−5.13589e10	+	5.13589e10i	−0.332311	+	0.332311i
$628$		0			0
$629$	5.01149e10	−	5.01149e10i	0.320158	−	0.320158i
$630$		0			0
$631$	−2.57349e11			−1.62333			−0.811663	−	0.584126i	$-0.801438\pi$
$631$	−2.57349e11			−1.62333			−0.811663	+	0.584126i	$0.801438\pi$
$632$		0			0
$633$		−	1.34962e11i		−	0.840613i
$634$		0			0
$635$	1.53583e10	+	1.53583e10i	0.0944602	+	0.0944602i
$636$		0			0
$637$	−9.58779e10	−	9.58779e10i	−0.582319	−	0.582319i
$638$		0			0
$639$		−	5.27152e10i		−	0.316178i
$640$		0			0
$641$	−5.55257e10			−0.328899			−0.164449	−	0.986386i	$-0.552585\pi$
$641$	−5.55257e10			−0.328899			−0.164449	+	0.986386i	$0.552585\pi$
$642$		0			0
$643$	2.24970e11	−	2.24970e11i	1.31608	−	1.31608i	0.399223	−	0.916854i	$-0.369280\pi$
$643$	2.24970e11	−	2.24970e11i	1.31608	−	1.31608i	0.916854	−	0.399223i	$-0.130720\pi$
$644$		0			0
$645$	2.09037e10	−	2.09037e10i	0.120777	−	0.120777i
$646$		0			0
$647$	7.46421e10			0.425958			0.212979	−	0.977057i	$-0.431683\pi$
$647$	7.46421e10			0.425958			0.212979	+	0.977057i	$0.431683\pi$
$648$		0			0
$649$		−	1.44892e11i		−	0.816704i
$650$		0			0
$651$	−3.31875e10	−	3.31875e10i	−0.184778	−	0.184778i
$652$		0			0
$653$	−1.00441e11	−	1.00441e11i	−0.552407	−	0.552407i	0.374728	−	0.927135i	$-0.377736\pi$
$653$	−1.00441e11	−	1.00441e11i	−0.552407	−	0.552407i	−0.927135	+	0.374728i	$0.877736\pi$
$654$		0			0
$655$			1.18879e11i			0.645861i
$656$		0			0
$657$	1.71484e10			0.0920368
$658$		0			0
$659$	−6.06155e10	+	6.06155e10i	−0.321397	+	0.321397i	−0.849303	−	0.527906i	$-0.822977\pi$
$659$	−6.06155e10	+	6.06155e10i	−0.321397	+	0.321397i	0.527906	+	0.849303i	$0.322977\pi$
$660$		0			0
$661$	−2.53142e11	+	2.53142e11i	−1.32605	+	1.32605i	−0.417258	+	0.908788i	$0.637009\pi$
$661$	−2.53142e11	+	2.53142e11i	−1.32605	+	1.32605i	−0.908788	+	0.417258i	$0.862991\pi$
$662$		0			0
$663$	2.12717e11			1.10090
$664$		0			0
$665$			1.81808e11i			0.929664i
$666$		0			0
$667$	2.07906e11	+	2.07906e11i	1.05042	+	1.05042i
$668$		0			0
$669$	−1.24924e11	−	1.24924e11i	−0.623651	−	0.623651i
$670$		0			0
$671$			1.60876e11i			0.793598i
$672$		0			0
$673$	1.93933e11			0.945347			0.472674	−	0.881238i	$-0.343289\pi$
$673$	1.93933e11			0.945347			0.472674	+	0.881238i	$0.343289\pi$
$674$		0			0
$675$	−6.82922e9	+	6.82922e9i	−0.0328970	+	0.0328970i
$676$		0			0
$677$	2.34311e11	−	2.34311e11i	1.11542	−	1.11542i	0.123015	−	0.992405i	$-0.460744\pi$
$677$	2.34311e11	−	2.34311e11i	1.11542	−	1.11542i	0.992405	−	0.123015i	$-0.0392563\pi$
$678$		0			0
$679$	−2.07748e11			−0.977366
$680$		0			0
$681$			1.92007e11i			0.892749i
$682$		0			0
$683$	1.09474e11	+	1.09474e11i	0.503071	+	0.503071i	0.912391	−	0.409320i	$-0.134234\pi$
$683$	1.09474e11	+	1.09474e11i	0.503071	+	0.503071i	−0.409320	+	0.912391i	$0.634234\pi$
$684$		0			0
$685$	−5.24046e10	−	5.24046e10i	−0.238017	−	0.238017i
$686$		0			0
$687$		−	2.06318e11i		−	0.926212i
$688$		0			0
$689$	2.58303e11			1.14618
$690$		0			0
$691$	1.91786e11	−	1.91786e11i	0.841212	−	0.841212i	−0.147805	−	0.989017i	$-0.547221\pi$
$691$	1.91786e11	−	1.91786e11i	0.841212	−	0.841212i	0.989017	+	0.147805i	$0.0472208\pi$
$692$		0			0
$693$	1.93648e10	−	1.93648e10i	0.0839613	−	0.0839613i
$694$		0			0
$695$	1.21654e11			0.521419
$696$		0			0
$697$		−	8.78466e10i		−	0.372215i
$698$		0			0
$699$	−2.65370e10	−	2.65370e10i	−0.111159	−	0.111159i
$700$		0			0
$701$	6.59629e10	+	6.59629e10i	0.273167	+	0.273167i	0.830374	−	0.557207i	$-0.188127\pi$
$701$	6.59629e10	+	6.59629e10i	0.273167	+	0.273167i	−0.557207	+	0.830374i	$0.688127\pi$
$702$		0			0
$703$		−	1.40014e11i		−	0.573260i
$704$		0			0
$705$	7.32451e10			0.296498
$706$		0			0
$707$	3.20627e10	−	3.20627e10i	0.128328	−	0.128328i
$708$		0			0
$709$	7.04133e10	−	7.04133e10i	0.278657	−	0.278657i	−0.553916	−	0.832573i	$-0.686867\pi$
$709$	7.04133e10	−	7.04133e10i	0.278657	−	0.278657i	0.832573	+	0.553916i	$0.186867\pi$
$710$		0			0
$711$	1.29834e11			0.508054
$712$		0			0
$713$			1.96941e11i			0.762040i
$714$		0			0
$715$	1.29627e11	+	1.29627e11i	0.495989	+	0.495989i
$716$		0			0
$717$	−6.00984e10	−	6.00984e10i	−0.227398	−	0.227398i
$718$		0			0
$719$		−	3.04136e11i		−	1.13803i	−0.822328	−	0.569014i	$-0.807325\pi$
$719$		−	3.04136e11i		−	1.13803i	0.822328	−	0.569014i	$-0.192675\pi$
$720$		0			0
$721$	1.50314e11			0.556235
$722$		0			0
$723$	1.00391e11	−	1.00391e11i	0.367401	−	0.367401i
$724$		0			0
$725$	6.09623e10	−	6.09623e10i	0.220653	−	0.220653i
$726$		0			0
$727$	−3.32769e11			−1.19125			−0.595627	−	0.803261i	$-0.703097\pi$
$727$	−3.32769e11			−1.19125			−0.595627	+	0.803261i	$0.703097\pi$
$728$		0			0
$729$			1.04604e10i			0.0370370i
$730$		0			0
$731$	−8.46243e10	−	8.46243e10i	−0.296364	−	0.296364i
$732$		0			0
$733$	2.26829e11	+	2.26829e11i	0.785748	+	0.785748i	0.980794	−	0.195046i	$-0.0624857\pi$
$733$	2.26829e11	+	2.26829e11i	0.785748	+	0.785748i	−0.195046	+	0.980794i	$0.562486\pi$
$734$		0			0
$735$			7.81723e10i			0.267857i
$736$		0			0
$737$	−3.11298e10			−0.105513
$738$		0			0
$739$	2.61160e11	−	2.61160e11i	0.875646	−	0.875646i	−0.117434	−	0.993081i	$-0.537467\pi$
$739$	2.61160e11	−	2.61160e11i	0.875646	−	0.875646i	0.993081	+	0.117434i	$0.0374669\pi$
$740$		0			0
$741$	2.97152e11	−	2.97152e11i	0.985611	−	0.985611i
$742$		0			0
$743$	−2.26105e11			−0.741918			−0.370959	−	0.928649i	$-0.620971\pi$
$743$	−2.26105e11			−0.741918			−0.370959	+	0.928649i	$0.620971\pi$
$744$		0			0
$745$			6.53324e10i			0.212082i
$746$		0			0
$747$	−1.34283e11	−	1.34283e11i	−0.431259	−	0.431259i
$748$		0			0
$749$	−5.09898e10	−	5.09898e10i	−0.162015	−	0.162015i
$750$		0			0
$751$		−	2.89023e11i		−	0.908599i	−0.890849	−	0.454299i	$-0.849890\pi$
$751$		−	2.89023e11i		−	0.908599i	0.890849	−	0.454299i	$-0.150110\pi$
$752$		0			0
$753$	1.83189e11			0.569797
$754$		0			0
$755$	8.41108e10	−	8.41108e10i	0.258859	−	0.258859i
$756$		0			0
$757$	9.76966e10	−	9.76966e10i	0.297506	−	0.297506i	−0.542530	−	0.840036i	$-0.682534\pi$
$757$	9.76966e10	−	9.76966e10i	0.297506	−	0.297506i	0.840036	+	0.542530i	$0.182534\pi$
$758$		0			0
$759$	−1.14914e11			−0.346263
$760$		0			0
$761$			5.87097e11i			1.75054i	0.483638	+	0.875268i	$0.339315\pi$
$761$			5.87097e11i			1.75054i	−0.483638	+	0.875268i	$0.660685\pi$
$762$		0			0
$763$	−2.60655e11	−	2.60655e11i	−0.769072	−	0.769072i
$764$		0			0
$765$	−8.67175e10	−	8.67175e10i	−0.253199	−	0.253199i
$766$		0			0
$767$			8.38314e11i			2.42228i
$768$		0			0
$769$	−2.78377e10			−0.0796028			−0.0398014	−	0.999208i	$-0.512673\pi$
$769$	−2.78377e10			−0.0796028			−0.0398014	+	0.999208i	$0.512673\pi$
$770$		0			0
$771$	2.39005e11	−	2.39005e11i	0.676378	−	0.676378i
$772$		0			0
$773$	2.61024e11	−	2.61024e11i	0.731075	−	0.731075i	−0.239758	−	0.970833i	$-0.577068\pi$
$773$	2.61024e11	−	2.61024e11i	0.731075	−	0.731075i	0.970833	+	0.239758i	$0.0770680\pi$
$774$		0			0
$775$	5.77471e10			0.160075
$776$		0			0
$777$			5.27922e10i			0.144839i
$778$		0			0
$779$	−1.22716e11	−	1.22716e11i	−0.333235	−	0.333235i
$780$		0			0
$781$	−1.30047e11	−	1.30047e11i	−0.349541	−	0.349541i
$782$		0			0
$783$		−	9.33763e10i		−	0.248422i
$784$		0			0
$785$	3.81569e11			1.00483
$786$		0			0
$787$	1.28668e11	−	1.28668e11i	0.335406	−	0.335406i	−0.519229	−	0.854635i	$-0.673781\pi$
$787$	1.28668e11	−	1.28668e11i	0.335406	−	0.335406i	0.854635	+	0.519229i	$0.173781\pi$
$788$		0			0
$789$	8.07158e10	−	8.07158e10i	0.208282	−	0.208282i
$790$		0			0
$791$	−2.63460e11			−0.672991
$792$		0			0
$793$		−	9.30794e11i		−	2.35375i
$794$		0			0
$795$	−1.05301e11	−	1.05301e11i	−0.263612	−	0.263612i
$796$		0			0
$797$	3.04188e11	+	3.04188e11i	0.753892	+	0.753892i	0.975203	−	0.221311i	$-0.0710336\pi$
$797$	3.04188e11	+	3.04188e11i	0.753892	+	0.753892i	−0.221311	+	0.975203i	$0.571034\pi$
$798$		0			0
$799$		−	2.96518e11i		−	0.727551i
$800$		0			0
$801$	−1.65417e11			−0.401837
$802$		0			0
$803$	4.23048e10	−	4.23048e10i	0.101748	−	0.101748i
$804$		0			0
$805$	−2.03395e11	+	2.03395e11i	−0.484347	+	0.484347i
$806$		0			0
$807$	1.66671e11			0.392975
$808$		0			0
$809$			2.38359e11i			0.556464i	0.960514	+	0.278232i	$0.0897484\pi$
$809$			2.38359e11i			0.556464i	−0.960514	+	0.278232i	$0.910252\pi$
$810$		0			0
$811$	3.90694e11	+	3.90694e11i	0.903137	+	0.903137i	0.995706	−	0.0925691i	$-0.0295079\pi$
$811$	3.90694e11	+	3.90694e11i	0.903137	+	0.903137i	−0.0925691	+	0.995706i	$0.529508\pi$
$812$		0			0
$813$	−1.08011e11	−	1.08011e11i	−0.247234	−	0.247234i
$814$		0			0
$815$			3.82557e11i			0.867093i
$816$		0			0
$817$	−2.36429e11			−0.530656
$818$		0			0
$819$	−1.12040e11	+	1.12040e11i	−0.249023	+	0.249023i
$820$		0			0
$821$	−4.98722e11	+	4.98722e11i	−1.09771	+	1.09771i	−0.103027	+	0.994679i	$0.532853\pi$
$821$	−4.98722e11	+	4.98722e11i	−1.09771	+	1.09771i	−0.994679	+	0.103027i	$0.967147\pi$
$822$		0			0
$823$	−2.41917e11			−0.527311			−0.263656	−	0.964617i	$-0.584928\pi$
$823$	−2.41917e11			−0.527311			−0.263656	+	0.964617i	$0.584928\pi$
$824$		0			0
$825$			3.36952e10i			0.0727364i
$826$		0			0
$827$	−2.56152e11	−	2.56152e11i	−0.547615	−	0.547615i	0.378135	−	0.925750i	$-0.376565\pi$
$827$	−2.56152e11	−	2.56152e11i	−0.547615	−	0.547615i	−0.925750	+	0.378135i	$0.876565\pi$
$828$		0			0
$829$	−5.12961e11	−	5.12961e11i	−1.08609	−	1.08609i	−0.995927	−	0.0901650i	$-0.971261\pi$
$829$	−5.12961e11	−	5.12961e11i	−1.08609	−	1.08609i	−0.0901650	−	0.995927i	$-0.528739\pi$
$830$		0			0
$831$		−	1.00171e10i		−	0.0210057i
$832$		0			0
$833$	3.16465e11			0.657272
$834$		0			0
$835$	3.62778e11	−	3.62778e11i	0.746269	−	0.746269i
$836$		0			0
$837$	4.42258e10	−	4.42258e10i	0.0901101	−	0.0901101i
$838$		0			0
$839$	1.60064e11			0.323032			0.161516	−	0.986870i	$-0.448362\pi$
$839$	1.60064e11			0.323032			0.161516	+	0.986870i	$0.448362\pi$
$840$		0			0
$841$			3.33294e11i			0.666260i
$842$		0			0
$843$	−2.86413e11	−	2.86413e11i	−0.567129	−	0.567129i
$844$		0			0
$845$	−4.36076e11	−	4.36076e11i	−0.855333	−	0.855333i
$846$		0			0
$847$			2.56250e11i			0.497886i
$848$		0			0
$849$	−2.98218e11			−0.573989
$850$		0			0
$851$	1.56639e11	−	1.56639e11i	0.298664	−	0.298664i
$852$		0			0
$853$	9.58588e10	−	9.58588e10i	0.181066	−	0.181066i	−0.610754	−	0.791820i	$-0.709134\pi$
$853$	9.58588e10	−	9.58588e10i	0.181066	−	0.181066i	0.791820	+	0.610754i	$0.209134\pi$
$854$		0			0
$855$	−2.42277e11			−0.453366
$856$		0			0
$857$		−	2.38708e11i		−	0.442531i	−0.975214	−	0.221265i	$-0.928981\pi$
$857$		−	2.38708e11i		−	0.442531i	0.975214	−	0.221265i	$-0.0710187\pi$
$858$		0			0
$859$	3.68287e11	+	3.68287e11i	0.676417	+	0.676417i	0.959187	−	0.282771i	$-0.0912536\pi$
$859$	3.68287e11	+	3.68287e11i	0.676417	+	0.676417i	−0.282771	+	0.959187i	$0.591254\pi$
$860$		0			0
$861$	4.62698e10	+	4.62698e10i	0.0841948	+	0.0841948i
$862$		0			0
$863$			5.95499e11i			1.07359i	0.843713	+	0.536794i	$0.180365\pi$
$863$			5.95499e11i			1.07359i	−0.843713	+	0.536794i	$0.819635\pi$
$864$		0			0
$865$	2.62777e11			0.469378
$866$		0			0
$867$	−1.20383e11	+	1.20383e11i	−0.213054	+	0.213054i
$868$		0			0
$869$	3.20298e11	−	3.20298e11i	0.561663	−	0.561663i
$870$		0			0
$871$	1.80110e11			0.312944
$872$		0			0
$873$		−	2.76845e11i		−	0.476629i
$874$		0			0
$875$	3.06347e11	+	3.06347e11i	0.522614	+	0.522614i
$876$		0			0
$877$	2.72863e11	+	2.72863e11i	0.461260	+	0.461260i	0.899068	−	0.437808i	$-0.144245\pi$
$877$	2.72863e11	+	2.72863e11i	0.461260	+	0.461260i	−0.437808	+	0.899068i	$0.644245\pi$
$878$		0			0
$879$			4.86561e11i			0.815046i
$880$		0			0
$881$	−4.80491e11			−0.797594			−0.398797	−	0.917039i	$-0.630572\pi$
$881$	−4.80491e11			−0.797594			−0.398797	+	0.917039i	$0.630572\pi$
$882$		0			0
$883$	4.86314e11	−	4.86314e11i	0.799970	−	0.799970i	−0.183121	−	0.983090i	$-0.558620\pi$
$883$	4.86314e11	−	4.86314e11i	0.799970	−	0.799970i	0.983090	+	0.183121i	$0.0586199\pi$
$884$		0			0
$885$	3.41752e11	−	3.41752e11i	0.557106	−	0.557106i
$886$		0			0
$887$	4.96631e11			0.802304			0.401152	−	0.916011i	$-0.368610\pi$
$887$	4.96631e11			0.802304			0.401152	+	0.916011i	$0.368610\pi$
$888$		0			0
$889$			6.54966e10i			0.104860i
$890$		0			0
$891$	2.58055e10	+	2.58055e10i	0.0409451	+	0.0409451i
$892$		0			0
$893$	−4.14216e11	−	4.14216e11i	−0.651359	−	0.651359i
$894$		0			0
$895$			2.92232e11i			0.455445i
$896$		0			0
$897$	6.64869e11			1.02699
$898$		0			0
$899$	−3.94789e11	+	3.94789e11i	−0.604403	+	0.604403i
$900$		0			0
$901$	−4.26290e11	+	4.26290e11i	−0.646854	+	0.646854i
$902$		0			0
$903$	8.91452e10			0.134075
$904$		0			0
$905$			9.39467e11i			1.40051i
$906$		0			0
$907$	7.21265e11	+	7.21265e11i	1.06578	+	1.06578i	0.997679	+	0.0680965i	$0.0216926\pi$
$907$	7.21265e11	+	7.21265e11i	1.06578	+	1.06578i	0.0680965	+	0.997679i	$0.478307\pi$
$908$		0			0
$909$	4.27268e10	+	4.27268e10i	0.0625813	+	0.0625813i
$910$		0			0
$911$		−	1.20871e12i		−	1.75489i	−0.479679	−	0.877444i	$-0.659247\pi$
$911$		−	1.20871e12i		−	1.75489i	0.479679	−	0.877444i	$-0.340753\pi$
$912$		0			0
$913$	−6.62548e11			−0.953529
$914$		0			0
$915$	−3.79453e11	+	3.79453e11i	−0.541345	+	0.541345i
$916$		0			0
$917$	−2.53483e11	+	2.53483e11i	−0.358485	+	0.358485i
$918$		0			0
$919$	−4.04154e11			−0.566610			−0.283305	−	0.959030i	$-0.591431\pi$
$919$	−4.04154e11			−0.566610			−0.283305	+	0.959030i	$0.591431\pi$
$920$		0			0
$921$			6.61857e11i			0.919868i
$922$		0			0
$923$	7.52428e11	+	7.52428e11i	1.03671	+	1.03671i
$924$		0			0
$925$	−4.59299e10	−	4.59299e10i	−0.0627377	−	0.0627377i
$926$		0			0
$927$			2.00309e11i			0.271257i
$928$		0			0
$929$	−3.91794e11			−0.526011			−0.263005	−	0.964794i	$-0.584714\pi$
$929$	−3.91794e11			−0.526011			−0.263005	+	0.964794i	$0.584714\pi$
$930$		0			0
$931$	4.42080e11	−	4.42080e11i	0.588441	−	0.588441i
$932$		0			0
$933$	1.08671e11	−	1.08671e11i	0.143412	−	0.143412i
$934$		0			0
$935$	−4.27862e11			−0.559831
$936$		0			0
$937$		−	8.60556e11i		−	1.11640i	−0.829705	−	0.558201i	$-0.811492\pi$
$937$		−	8.60556e11i		−	1.11640i	0.829705	−	0.558201i	$-0.188508\pi$
$938$		0			0
$939$	−5.45047e11	−	5.45047e11i	−0.701087	−	0.701087i
$940$		0			0
$941$	−1.22516e11	−	1.22516e11i	−0.156256	−	0.156256i	0.624650	−	0.780905i	$-0.285242\pi$
$941$	−1.22516e11	−	1.22516e11i	−0.156256	−	0.156256i	−0.780905	+	0.624650i	$0.785242\pi$
$942$		0			0
$943$		−	2.74574e11i		−	0.347226i
$944$		0			0
$945$	9.13502e10			0.114547
$946$		0			0
$947$	−7.27477e11	+	7.27477e11i	−0.904523	+	0.904523i	−0.995823	−	0.0913008i	$-0.970898\pi$
$947$	−7.27477e11	+	7.27477e11i	−0.904523	+	0.904523i	0.0913008	+	0.995823i	$0.470898\pi$
$948$		0			0
$949$	−2.44767e11	+	2.44767e11i	−0.301778	+	0.301778i
$950$		0			0
$951$	2.38801e11			0.291954
$952$		0			0
$953$		−	8.98115e10i		−	0.108883i	−0.998517	−	0.0544415i	$-0.982662\pi$
$953$		−	8.98115e10i		−	0.108883i	0.998517	−	0.0544415i	$-0.0173378\pi$
$954$		0			0
$955$	−6.83311e10	−	6.83311e10i	−0.0821495	−	0.0821495i
$956$		0			0
$957$	−2.30358e11	−	2.30358e11i	−0.274634	−	0.274634i
$958$		0			0
$959$		−	2.23483e11i		−	0.264223i
$960$		0			0
$961$	4.78923e11			0.561529
$962$		0			0
$963$	6.79491e10	−	6.79491e10i	0.0790093	−	0.0790093i
$964$		0			0
$965$	−5.60787e11	+	5.60787e11i	−0.646679	+	0.646679i
$966$		0			0
$967$	−8.82093e11			−1.00881			−0.504404	−	0.863468i	$-0.668288\pi$
$967$	−8.82093e11			−1.00881			−0.504404	+	0.863468i	$0.668288\pi$
$968$		0			0
$969$			9.80811e11i			1.11247i
$970$		0			0
$971$	−9.08166e10	−	9.08166e10i	−0.102162	−	0.102162i	0.654178	−	0.756340i	$-0.273015\pi$
$971$	−9.08166e10	−	9.08166e10i	−0.102162	−	0.102162i	−0.756340	+	0.654178i	$0.773015\pi$
$972$		0			0
$973$	2.59400e11	+	2.59400e11i	0.289414	+	0.289414i
$974$		0			0
$975$		−	1.94953e11i		−	0.215731i
$976$		0			0
$977$	4.04854e11			0.444345			0.222172	−	0.975007i	$-0.428685\pi$
$977$	4.04854e11			0.444345			0.222172	+	0.975007i	$0.428685\pi$
$978$		0			0
$979$	−4.08081e11	+	4.08081e11i	−0.444238	+	0.444238i
$980$		0			0
$981$	3.47349e11	−	3.47349e11i	0.375051	−	0.375051i
$982$		0			0
$983$	−3.80835e11			−0.407870			−0.203935	−	0.978984i	$-0.565373\pi$
$983$	−3.80835e11			−0.407870			−0.203935	+	0.978984i	$0.565373\pi$
$984$		0			0
$985$		−	3.48878e11i		−	0.370620i
$986$		0			0
$987$	1.56179e11	+	1.56179e11i	0.164571	+	0.164571i
$988$		0			0
$989$	−2.64502e11	−	2.64502e11i	−0.276467	−	0.276467i
$990$		0			0
$991$			4.19820e11i			0.435280i	0.976029	+	0.217640i	$0.0698358\pi$
$991$			4.19820e11i			0.435280i	−0.976029	+	0.217640i	$0.930164\pi$
$992$		0			0
$993$	−3.40241e11			−0.349937
$994$		0			0
$995$	2.01030e11	−	2.01030e11i	0.205102	−	0.205102i
$996$		0			0
$997$	−4.83409e11	+	4.83409e11i	−0.489254	+	0.489254i	−0.908071	−	0.418817i	$-0.862445\pi$
$997$	−4.83409e11	+	4.83409e11i	−0.489254	+	0.489254i	0.418817	+	0.908071i	$0.362445\pi$
$998$		0			0
$999$	−7.03510e10			−0.0706331

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	192.9.l.a.175.5		64
4.3	odd	2		48.9.l.a.19.32	✓	64
16.5	even	4		48.9.l.a.43.32	yes	64
16.11	odd	4	inner	192.9.l.a.79.5		64

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
48.9.l.a.19.32	✓	64	4.3	odd	2
48.9.l.a.43.32	yes	64	16.5	even	4
192.9.l.a.79.5		64	16.11	odd	4	inner
192.9.l.a.175.5		64	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 192 = 2^{6} \cdot 3 \)
Weight:	\( k \)	\(=\)	\( 9 \)
Character orbit:	\([\chi]\)	\(=\)	192.l (of order \(4\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-33.0681 + 33.0681i) q^{3} +(-384.834 + 384.834i) q^{5} -1641.15 q^{7} -2187.00i q^{9} +O(q^{10})\)	\(q+(-33.0681 + 33.0681i) q^{3} +(-384.834 + 384.834i) q^{5} -1641.15 q^{7} -2187.00i q^{9} +(-5395.29 - 5395.29i) q^{11} +(31216.1 + 31216.1i) q^{13} -25451.5i q^{15} -103035. q^{17} +(-143933. + 143933. i) q^{19} +(54269.7 - 54269.7i) q^{21} -322047. q^{23} +94430.7i q^{25} +(72320.0 + 72320.0i) q^{27} +(-645577. - 645577. i) q^{29} -611529. i q^{31} +356824. q^{33} +(631570. - 631570. i) q^{35} +(-486387. + 486387. i) q^{37} -2.06451e6 q^{39} +852590. i q^{41} +(821316. + 821316. i) q^{43} +(841632. + 841632. i) q^{45} +2.87783e6i q^{47} -3.07143e6 q^{49} +(3.40717e6 - 3.40717e6i) q^{51} +(4.13734e6 - 4.13734e6i) q^{53} +4.15258e6 q^{55} -9.51920e6i q^{57} +(1.34276e7 + 1.34276e7i) q^{59} +(-1.49089e7 - 1.49089e7i) q^{61} +3.58919e6i q^{63} -2.40260e7 q^{65} +(2.88490e6 - 2.88490e6i) q^{67} +(1.06495e7 - 1.06495e7i) q^{69} +2.41039e7 q^{71} +7.84105e6i q^{73} +(-3.12264e6 - 3.12264e6i) q^{75} +(8.85448e6 + 8.85448e6i) q^{77} +5.93662e7i q^{79} -4.78297e6 q^{81} +(6.14005e7 - 6.14005e7i) q^{83} +(3.96514e7 - 3.96514e7i) q^{85} +4.26961e7 q^{87} -7.56364e7i q^{89} +(-5.12302e7 - 5.12302e7i) q^{91} +(2.02221e7 + 2.02221e7i) q^{93} -1.10781e8i q^{95} +1.26587e8 q^{97} +(-1.17995e7 + 1.17995e7i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 64 q+O(q^{10}) \) 64 * q	\( 64 q - 39552 q^{11} + 167552 q^{19} - 1691136 q^{23} - 2132352 q^{29} + 2415744 q^{35} - 4720512 q^{37} + 7244672 q^{43} + 52706752 q^{49} - 13862016 q^{51} - 5358720 q^{53} + 46326784 q^{55} - 44938752 q^{59} + 24476032 q^{61} + 29941632 q^{65} + 44244736 q^{67} - 8636544 q^{69} - 159664128 q^{71} - 12918528 q^{75} - 94964352 q^{77} - 306110016 q^{81} - 209328000 q^{83} + 106960000 q^{85} + 45401472 q^{91} - 86500224 q^{99}+O(q^{100}) \) 64 * q - 39552 * q^11 + 167552 * q^19 - 1691136 * q^23 - 2132352 * q^29 + 2415744 * q^35 - 4720512 * q^37 + 7244672 * q^43 + 52706752 * q^49 - 13862016 * q^51 - 5358720 * q^53 + 46326784 * q^55 - 44938752 * q^59 + 24476032 * q^61 + 29941632 * q^65 + 44244736 * q^67 - 8636544 * q^69 - 159664128 * q^71 - 12918528 * q^75 - 94964352 * q^77 - 306110016 * q^81 - 209328000 * q^83 + 106960000 * q^85 + 45401472 * q^91 - 86500224 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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