LMFDB - Embedded newform 99.8.f.c.91.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [99,8,Mod(37,99)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(99, base_ring=CyclotomicField(10))

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

N = Newforms(chi, 8, names="a")

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

chi := DirichletCharacter("99.37");

S:= CuspForms(chi, 8);

N := Newforms(S);

Level:	$ N $	$=$	$ 99 = 3^{2} \cdot 11 $
Weight:	$ k $	$=$	$ 8 $
Character orbit:	$[\chi]$	$=$	99.f (of order $5$, degree $4$, 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:	$30.9261175229$
Analytic rank:	$0$
Dimension:	$28$
Relative dimension:	$7$ over $\Q(\zeta_{5})$
Twist minimal:	no (minimal twist has level 33)
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			91.2
Character	$\chi$	$=$	99.91
Dual form			99.8.f.c.37.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-8.90518 + 6.46999i) q^{2} +(-2.11276 + 6.50241i) q^{4} +(328.988 + 239.024i) q^{5} +(-385.790 + 1187.34i) q^{7} +(-458.645 - 1411.56i) q^{8} +O(q^{10})$	\(q+(-8.90518 + 6.46999i) q^{2} +(-2.11276 + 6.50241i) q^{4} +(328.988 + 239.024i) q^{5} +(-385.790 + 1187.34i) q^{7} +(-458.645 - 1411.56i) q^{8} -4476.18 q^{10} +(447.136 + 4391.72i) q^{11} +(-4560.85 + 3313.65i) q^{13} +(-4246.55 - 13069.5i) q^{14} +(12509.1 + 9088.40i) q^{16} +(18725.3 + 13604.8i) q^{17} +(3333.74 + 10260.2i) q^{19} +(-2249.30 + 1634.21i) q^{20} +(-32396.2 - 36216.1i) q^{22} +89435.3 q^{23} +(26958.8 + 82970.5i) q^{25} +(19175.9 - 59017.4i) q^{26} +(-6905.49 - 5017.13i) q^{28} +(-59656.9 + 183605. i) q^{29} +(-92009.9 + 66849.1i) q^{31} +19780.6 q^{32} -254775. q^{34} +(-410723. + 298407. i) q^{35} +(139953. - 430730. i) q^{37} +(-96070.8 - 69799.5i) q^{38} +(186509. - 574014. i) q^{40} +(-58573.8 - 180272. i) q^{41} +104890. q^{43} +(-29501.5 - 6371.20i) q^{44} +(-796438. + 578646. i) q^{46} +(-149679. - 460664. i) q^{47} +(-594681. - 432061. i) q^{49} +(-776891. - 564444. i) q^{50} +(-11910.7 - 36657.5i) q^{52} +(-595854. + 432913. i) q^{53} +(-902624. + 1.55170e6i) q^{55} +1.85295e6 q^{56} +(-656667. - 2.02101e6i) q^{58} +(774654. - 2.38414e6i) q^{59} +(-1.01031e6 - 734032. i) q^{61} +(386851. - 1.19061e6i) q^{62} +(-1.77732e6 + 1.29130e6i) q^{64} -2.29251e6 q^{65} -2.01460e6 q^{67} +(-128026. + 93016.3i) q^{68} +(1.72686e6 - 5.31474e6i) q^{70} +(-3.92548e6 - 2.85203e6i) q^{71} +(-1.72601e6 + 5.31212e6i) q^{73} +(1.54052e6 + 4.74122e6i) q^{74} -73759.3 q^{76} +(-5.38697e6 - 1.16338e6i) q^{77} +(5.30364e6 - 3.85332e6i) q^{79} +(1.94300e6 + 5.97995e6i) q^{80} +(1.68797e6 + 1.22638e6i) q^{82} +(4.63362e6 + 3.36652e6i) q^{83} +(2.90855e6 + 8.95160e6i) q^{85} +(-934067. + 678640. i) q^{86} +(5.99412e6 - 2.64540e6i) q^{88} +8.34195e6 q^{89} +(-2.17490e6 - 6.69366e6i) q^{91} +(-188956. + 581545. i) q^{92} +(4.31341e6 + 3.13387e6i) q^{94} +(-1.35567e6 + 4.17232e6i) q^{95} +(-4.98820e6 + 3.62414e6i) q^{97} +8.09117e6 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 28 q + 22 q^{2} - 692 q^{4} + 777 q^{5} - 83 q^{7} - 3568 q^{8}+O(q^{10}) $ 28 * q + 22 * q^2 - 692 * q^4 + 777 * q^5 - 83 * q^7 - 3568 * q^8	\( 28 q + 22 q^{2} - 692 q^{4} + 777 q^{5} - 83 q^{7} - 3568 q^{8} - 1352 q^{10} + 18851 q^{11} + 14635 q^{13} - 62912 q^{14} - 36148 q^{16} + 10338 q^{17} + 90342 q^{19} + 289719 q^{20} - 202339 q^{22} - 138508 q^{23} - 174068 q^{25} - 466130 q^{26} - 640233 q^{28} + 487290 q^{29} - 388352 q^{31} - 2726322 q^{32} - 1543708 q^{34} - 742659 q^{35} + 670209 q^{37} - 2282072 q^{38} + 4641741 q^{40} + 2721357 q^{41} - 199784 q^{43} + 5887437 q^{44} + 3389447 q^{46} - 2112053 q^{47} + 3927748 q^{49} + 3663090 q^{50} - 4343053 q^{52} + 1743854 q^{53} - 8387710 q^{55} + 6307818 q^{56} + 546605 q^{58} + 218820 q^{59} - 743157 q^{61} - 3996183 q^{62} - 21725666 q^{64} - 4895794 q^{65} - 3235686 q^{67} - 961671 q^{68} + 31155916 q^{70} - 9848757 q^{71} - 6667768 q^{73} + 31115192 q^{74} - 6535748 q^{76} - 8320585 q^{77} - 10121851 q^{79} - 44592526 q^{80} + 24927115 q^{82} - 13288897 q^{83} - 28050005 q^{85} - 20937351 q^{86} + 39687014 q^{88} + 40241460 q^{89} + 8733043 q^{91} - 11607651 q^{92} - 7877385 q^{94} - 14371097 q^{95} + 30518151 q^{97} + 16954218 q^{98}+O(q^{100}) \) 28 * q + 22 * q^2 - 692 * q^4 + 777 * q^5 - 83 * q^7 - 3568 * q^8 - 1352 * q^10 + 18851 * q^11 + 14635 * q^13 - 62912 * q^14 - 36148 * q^16 + 10338 * q^17 + 90342 * q^19 + 289719 * q^20 - 202339 * q^22 - 138508 * q^23 - 174068 * q^25 - 466130 * q^26 - 640233 * q^28 + 487290 * q^29 - 388352 * q^31 - 2726322 * q^32 - 1543708 * q^34 - 742659 * q^35 + 670209 * q^37 - 2282072 * q^38 + 4641741 * q^40 + 2721357 * q^41 - 199784 * q^43 + 5887437 * q^44 + 3389447 * q^46 - 2112053 * q^47 + 3927748 * q^49 + 3663090 * q^50 - 4343053 * q^52 + 1743854 * q^53 - 8387710 * q^55 + 6307818 * q^56 + 546605 * q^58 + 218820 * q^59 - 743157 * q^61 - 3996183 * q^62 - 21725666 * q^64 - 4895794 * q^65 - 3235686 * q^67 - 961671 * q^68 + 31155916 * q^70 - 9848757 * q^71 - 6667768 * q^73 + 31115192 * q^74 - 6535748 * q^76 - 8320585 * q^77 - 10121851 * q^79 - 44592526 * q^80 + 24927115 * q^82 - 13288897 * q^83 - 28050005 * q^85 - 20937351 * q^86 + 39687014 * q^88 + 40241460 * q^89 + 8733043 * q^91 - 11607651 * q^92 - 7877385 * q^94 - 14371097 * q^95 + 30518151 * q^97 + 16954218 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/99\mathbb{Z}\right)^\times$.

$n$	$46$	$56$
$\chi(n)$	$e\left(\frac{4}{5}\right)$	$1$

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 $

$2$	−8.90518	+	6.46999i	−0.787114	+	0.571872i	−0.907106	−	0.420903i	$-0.861713\pi$
$2$	−8.90518	+	6.46999i	−0.787114	+	0.571872i	0.119992	+	0.992775i	$0.461713\pi$
$3$		0			0
$3$		0			0
$4$	−2.11276	+	6.50241i	−0.0165059	+	0.0508001i
$5$	328.988	+	239.024i	1.17702	+	0.855157i	0.991833	−	0.127545i	$-0.0407099\pi$
$5$	328.988	+	239.024i	1.17702	+	0.855157i	0.185190	+	0.982703i	$0.440710\pi$
$6$		0			0
$7$	−385.790	+	1187.34i	−0.425116	+	1.30837i	0.477766	+	0.878487i	$0.341447\pi$
$7$	−385.790	+	1187.34i	−0.425116	+	1.30837i	−0.902883	+	0.429887i	$0.858553\pi$
$8$	−458.645	−	1411.56i	−0.316710	−	0.974733i
$9$		0			0
$10$	−4476.18			−1.41549
$11$	447.136	+	4391.72i	0.101290	+	0.994857i
$11$	447.136	+	4391.72i	0.101290	+	0.994857i
$12$		0			0
$13$	−4560.85	+	3313.65i	−0.575764	+	0.418317i	−0.837194	−	0.546905i	$-0.815806\pi$
$13$	−4560.85	+	3313.65i	−0.575764	+	0.418317i	0.261431	+	0.965222i	$0.415806\pi$
$14$	−4246.55	−	13069.5i	−0.413607	−	1.27295i
$15$		0			0
$16$	12509.1	+	9088.40i	0.763496	+	0.554712i
$17$	18725.3	+	13604.8i	0.924397	+	0.671614i	0.944615	−	0.328182i	$-0.106436\pi$
$17$	18725.3	+	13604.8i	0.924397	+	0.671614i	−0.0202175	+	0.999796i	$0.506436\pi$
$18$		0			0
$19$	3333.74	+	10260.2i	0.111505	+	0.343177i	0.991202	−	0.132358i	$-0.0422548\pi$
$19$	3333.74	+	10260.2i	0.111505	+	0.343177i	−0.879697	+	0.475534i	$0.842255\pi$
$20$	−2249.30	+	1634.21i	−0.0628699	+	0.0456777i
$21$		0			0
$22$	−32396.2	−	36216.1i	−0.648657	−	0.725141i
$23$	89435.3			1.53272			0.766358	−	0.642414i	$-0.222067\pi$
$23$	89435.3			1.53272			0.766358	+	0.642414i	$0.222067\pi$
$24$		0			0
$25$	26958.8	+	82970.5i	0.345072	+	1.06202i
$26$	19175.9	−	59017.4i	0.213968	−	0.658526i
$27$		0			0
$28$	−6905.49	−	5017.13i	−0.0594486	−	0.0431919i
$29$	−59656.9	+	183605.i	−0.454221	+	1.39795i	0.417826	+	0.908527i	$0.362792\pi$
$29$	−59656.9	+	183605.i	−0.454221	+	1.39795i	−0.872047	+	0.489422i	$0.837208\pi$
$30$		0			0
$31$	−92009.9	+	66849.1i	−0.554713	+	0.403023i	−0.829520	−	0.558477i	$-0.811386\pi$
$31$	−92009.9	+	66849.1i	−0.554713	+	0.403023i	0.274807	+	0.961499i	$0.411386\pi$
$32$	19780.6			0.106712
$33$		0			0
$34$	−254775.			−1.11168
$35$	−410723.	+	298407.i	−1.61924	+	1.17644i
$36$		0			0
$37$	139953.	−	430730.i	0.454229	−	1.39797i	−0.417809	−	0.908535i	$-0.637202\pi$
$37$	139953.	−	430730.i	0.454229	−	1.39797i	0.872038	−	0.489439i	$-0.162798\pi$
$38$	−96070.8	−	69799.5i	−0.284020	−	0.206353i
$39$		0			0
$40$	186509.	−	574014.i	0.460775	−	1.41812i
$41$	−58573.8	−	180272.i	−0.132727	−	0.408492i	0.862502	−	0.506053i	$-0.168896\pi$
$41$	−58573.8	−	180272.i	−0.132727	−	0.408492i	−0.995230	+	0.0975606i	$0.968896\pi$
$42$		0			0
$43$	104890.			0.201185			0.100593	−	0.994928i	$-0.467926\pi$
$43$	104890.			0.201185			0.100593	+	0.994928i	$0.467926\pi$
$44$	−29501.5	−	6371.20i	−0.0522107	−	0.0112755i
$45$		0			0
$46$	−796438.	+	578646.i	−1.20642	+	0.876517i
$47$	−149679.	−	460664.i	−0.210290	−	0.647205i	−0.999455	−	0.0330235i	$-0.989486\pi$
$47$	−149679.	−	460664.i	−0.210290	−	0.647205i	0.789165	−	0.614181i	$-0.210514\pi$
$48$		0			0
$49$	−594681.	−	432061.i	−0.722101	−	0.524637i
$50$	−776891.	−	564444.i	−0.878952	−	0.638596i
$51$		0			0
$52$	−11910.7	−	36657.5i	−0.0117470	−	0.0361536i
$53$	−595854.	+	432913.i	−0.549762	+	0.399425i	−0.827698	−	0.561174i	$-0.810350\pi$
$53$	−595854.	+	432913.i	−0.549762	+	0.399425i	0.277936	+	0.960600i	$0.410350\pi$
$54$		0			0
$55$	−902624.	+	1.55170e6i	−0.731539	+	1.25759i
$56$	1.85295e6			1.40995
$57$		0			0
$58$	−656667.	−	2.02101e6i	−0.441924	−	1.36010i
$59$	774654.	−	2.38414e6i	0.491050	−	1.51130i	−0.331974	−	0.943289i	$-0.607715\pi$
$59$	774654.	−	2.38414e6i	0.491050	−	1.51130i	0.823024	−	0.568007i	$-0.192285\pi$
$60$		0			0
$61$	−1.01031e6	−	734032.i	−0.569901	−	0.414057i	0.265168	−	0.964202i	$-0.414572\pi$
$61$	−1.01031e6	−	734032.i	−0.569901	−	0.414057i	−0.835069	+	0.550145i	$0.814572\pi$
$62$	386851.	−	1.19061e6i	0.206145	−	0.634450i
$63$		0			0
$64$	−1.77732e6	+	1.29130e6i	−0.847490	+	0.615738i
$65$	−2.29251e6			−1.03541
$66$		0			0
$67$	−2.01460e6			−0.818326			−0.409163	−	0.912461i	$-0.634179\pi$
$67$	−2.01460e6			−0.818326			−0.409163	+	0.912461i	$0.634179\pi$
$68$	−128026.	+	93016.3i	−0.0493761	+	0.0358738i
$69$		0			0
$70$	1.72686e6	−	5.31474e6i	0.601749	−	1.85199i
$71$	−3.92548e6	−	2.85203e6i	−1.30163	−	0.945692i	−0.301663	−	0.953415i	$-0.597542\pi$
$71$	−3.92548e6	−	2.85203e6i	−1.30163	−	0.945692i	−0.999970	+	0.00772249i	$0.997542\pi$
$72$		0			0
$73$	−1.72601e6	+	5.31212e6i	−0.519295	+	1.59823i	0.256034	+	0.966668i	$0.417584\pi$
$73$	−1.72601e6	+	5.31212e6i	−0.519295	+	1.59823i	−0.775329	+	0.631558i	$0.782416\pi$
$74$	1.54052e6	+	4.74122e6i	0.441932	+	1.36013i
$75$		0			0
$76$	−73759.3			−0.0192739
$77$	−5.38697e6	−	1.16338e6i	−1.34470	−	0.290405i
$78$		0			0
$79$	5.30364e6	−	3.85332e6i	1.21026	−	0.879306i	0.215007	−	0.976613i	$-0.431023\pi$
$79$	5.30364e6	−	3.85332e6i	1.21026	−	0.879306i	0.995254	+	0.0973061i	$0.0310226\pi$
$80$	1.94300e6	+	5.97995e6i	0.424286	+	1.30582i
$81$		0			0
$82$	1.68797e6	+	1.22638e6i	0.338077	+	0.245627i
$83$	4.63362e6	+	3.36652e6i	0.889503	+	0.646261i	0.935748	−	0.352669i	$-0.114726\pi$
$83$	4.63362e6	+	3.36652e6i	0.889503	+	0.646261i	−0.0462457	+	0.998930i	$0.514726\pi$
$84$		0			0
$85$	2.90855e6	+	8.95160e6i	0.513701	+	1.58101i
$86$	−934067.	+	678640.i	−0.158356	+	0.115052i
$87$		0			0
$88$	5.99412e6	−	2.64540e6i	0.937640	−	0.413811i
$89$	8.34195e6			1.25430			0.627151	−	0.778897i	$-0.284221\pi$
$89$	8.34195e6			1.25430			0.627151	+	0.778897i	$0.284221\pi$
$90$		0			0
$91$	−2.17490e6	−	6.69366e6i	−0.302548	−	0.931148i
$92$	−188956.	+	581545.i	−0.0252989	+	0.0778621i
$93$		0			0
$94$	4.31341e6	+	3.13387e6i	0.535640	+	0.389165i
$95$	−1.35567e6	+	4.17232e6i	−0.162226	+	0.499281i
$96$		0			0
$97$	−4.98820e6	+	3.62414e6i	−0.554936	+	0.403185i	−0.829602	−	0.558355i	$-0.811433\pi$
$97$	−4.98820e6	+	3.62414e6i	−0.554936	+	0.403185i	0.274666	+	0.961540i	$0.411433\pi$
$98$	8.09117e6			0.868401
$99$		0			0
$100$	−596466.			−0.0596466
$101$	40788.3	−	29634.4i	0.00393922	−	0.00286201i	−0.585814	−	0.810446i	$-0.699225\pi$
$101$	40788.3	−	29634.4i	0.00393922	−	0.00286201i	0.589753	+	0.807584i	$0.299225\pi$
$102$		0			0
$103$	1.60099e6	−	4.92734e6i	0.144364	−	0.444306i	−0.852565	−	0.522622i	$-0.824954\pi$
$103$	1.60099e6	−	4.92734e6i	0.144364	−	0.444306i	0.996929	+	0.0783152i	$0.0249540\pi$
$104$	6.76925e6	+	4.91814e6i	0.590097	+	0.428731i
$105$		0			0
$106$	2.50524e6	−	7.71034e6i	0.204305	−	0.628786i
$107$	−97911.1	−	301339.i	−0.00772660	−	0.0237800i	0.947119	−	0.320883i	$-0.103980\pi$
$107$	−97911.1	−	301339.i	−0.00772660	−	0.0237800i	−0.954845	+	0.297103i	$0.903980\pi$
$108$		0			0
$109$	1.53104e7			1.13238			0.566191	−	0.824274i	$-0.308417\pi$
$109$	1.53104e7			1.13238			0.566191	+	0.824274i	$0.308417\pi$
$110$	−2.00146e6	−	1.96581e7i	−0.143375	−	1.40821i
$111$		0			0
$112$	−1.56169e7	+	1.13463e7i	−1.05035	+	0.763120i
$113$	−2.17277e6	−	6.68709e6i	−0.141657	−	0.435976i	0.854909	−	0.518778i	$-0.173613\pi$
$113$	−2.17277e6	−	6.68709e6i	−0.141657	−	0.435976i	−0.996566	+	0.0828022i	$0.973613\pi$
$114$		0			0
$115$	2.94231e7	+	2.13772e7i	1.80404	+	1.31071i
$116$	−1.06783e6	−	775827.i	−0.0635186	−	0.0461490i
$117$		0			0
$118$	8.52692e6	+	2.62432e7i	0.477755	+	1.47038i
$119$	−2.33775e7	+	1.69848e7i	−1.27170	+	0.923943i
$120$		0			0
$121$	−1.90873e7	+	3.92740e6i	−0.979481	+	0.201537i
$122$	1.37461e7			0.685364
$123$		0			0
$124$	−240285.	−	739522.i	−0.0113175	−	0.0348318i
$125$	−1.14546e6	+	3.52536e6i	−0.0524560	+	0.161443i
$126$		0			0
$127$	−2.82858e7	−	2.05509e7i	−1.22534	−	0.890260i	−0.228807	−	0.973472i	$-0.573482\pi$
$127$	−2.82858e7	−	2.05509e7i	−1.22534	−	0.890260i	−0.996532	+	0.0832114i	$0.973482\pi$
$128$	6.69024e6	−	2.05904e7i	0.281973	−	0.867822i
$129$		0			0
$130$	2.04152e7	−	1.48325e7i	0.814989	−	0.592124i
$131$	−1.13361e7			−0.440568			−0.220284	−	0.975436i	$-0.570698\pi$
$131$	−1.13361e7			−0.440568			−0.220284	+	0.975436i	$0.570698\pi$
$132$		0			0
$133$	−1.34684e7			−0.496406
$134$	1.79403e7	−	1.30344e7i	0.644116	−	0.467978i
$135$		0			0
$136$	1.06157e7	−	3.26718e7i	0.361878	−	1.11375i
$137$	2.81547e7	+	2.04556e7i	0.935468	+	0.679658i	0.947326	−	0.320272i	$-0.103774\pi$
$137$	2.81547e7	+	2.04556e7i	0.935468	+	0.679658i	−0.0118572	+	0.999930i	$0.503774\pi$
$138$		0			0
$139$	4.89344e6	−	1.50605e7i	0.154548	−	0.475649i	−0.843567	−	0.537024i	$-0.819548\pi$
$139$	4.89344e6	−	1.50605e7i	0.154548	−	0.475649i	0.998115	+	0.0613748i	$0.0195485\pi$
$140$	−1.07261e6	−	3.30115e6i	−0.0330364	−	0.101676i
$141$		0			0
$142$	5.34097e7			1.56535
$143$	−1.65920e7	−	1.85484e7i	−0.474484	−	0.530431i
$144$		0			0
$145$	−6.35123e7	+	4.61444e7i	−1.73010	+	1.25699i
$146$	−1.89989e7	−	5.84727e7i	−0.505236	−	1.55496i
$147$		0			0
$148$	2.50510e6	+	1.82006e6i	0.0635197	+	0.0461498i
$149$	3.83384e7	+	2.78545e7i	0.949472	+	0.689832i	0.950682	−	0.310167i	$-0.100385\pi$
$149$	3.83384e7	+	2.78545e7i	0.949472	+	0.689832i	−0.00120982	+	0.999999i	$0.500385\pi$
$150$		0			0
$151$	−7.59611e6	−	2.33784e7i	−0.179544	−	0.552581i	0.820267	−	0.571980i	$-0.193825\pi$
$151$	−7.59611e6	−	2.33784e7i	−0.179544	−	0.552581i	−0.999812	+	0.0193993i	$0.993825\pi$
$152$	1.29539e7	−	9.41156e6i	0.299191	−	0.217375i
$153$		0			0
$154$	5.54990e7	−	2.44935e7i	1.22451	−	0.540417i
$155$	−4.62487e7			−0.997558
$156$		0			0
$157$	−6.21290e6	−	1.91213e7i	−0.128128	−	0.394339i	0.866330	−	0.499473i	$-0.166473\pi$
$157$	−6.21290e6	−	1.91213e7i	−0.128128	−	0.394339i	−0.994458	+	0.105134i	$0.966473\pi$
$158$	−2.22989e7	+	6.86290e7i	−0.449763	+	1.38423i
$159$		0			0
$160$	6.50758e6	+	4.72803e6i	0.125603	+	0.0912558i
$161$	−3.45033e7	+	1.06190e8i	−0.651583	+	2.00537i
$162$		0			0
$163$	1.52129e7	−	1.10528e7i	0.275141	−	0.199902i	−0.441654	−	0.897185i	$-0.645608\pi$
$163$	1.52129e7	−	1.10528e7i	0.275141	−	0.199902i	0.716795	+	0.697283i	$0.245608\pi$
$164$	1.29595e6			0.0229422
$165$		0			0
$166$	−6.30446e7			−1.06972
$167$	−9.34426e6	+	6.78900e6i	−0.155252	+	0.112797i	−0.662699	−	0.748886i	$-0.730589\pi$
$167$	−9.34426e6	+	6.78900e6i	−0.155252	+	0.112797i	0.507447	+	0.861683i	$0.330589\pi$
$168$		0			0
$169$	−9.56928e6	+	2.94512e7i	−0.152502	+	0.469353i
$170$	−8.38180e7	−	6.08973e7i	−1.30848	−	0.950664i
$171$		0			0
$172$	−221608.	+	682040.i	−0.00332075	+	0.0102202i
$173$	−806588.	−	2.48242e6i	−0.0118438	−	0.0364514i	0.944960	−	0.327186i	$-0.106100\pi$
$173$	−806588.	−	2.48242e6i	−0.0118438	−	0.0364514i	−0.956804	+	0.290735i	$0.906100\pi$
$174$		0			0
$175$	−1.08915e8			−1.53622
$176$	−3.43205e7	+	5.90003e7i	−0.474525	+	0.815756i
$177$		0			0
$178$	−7.42865e7	+	5.39723e7i	−0.987279	+	0.717300i
$179$	−1.67924e7	−	5.16818e7i	−0.218840	−	0.673522i	−0.998859	−	0.0477648i	$-0.984790\pi$
$179$	−1.67924e7	−	5.16818e7i	−0.218840	−	0.673522i	0.780018	−	0.625757i	$-0.215210\pi$
$180$		0			0
$181$	7.14030e7	+	5.18773e7i	0.895038	+	0.650283i	0.937187	−	0.348828i	$-0.113420\pi$
$181$	7.14030e7	+	5.18773e7i	0.895038	+	0.650283i	−0.0421485	+	0.999111i	$0.513420\pi$
$182$	6.26758e7	+	4.55366e7i	0.770637	+	0.559901i
$183$		0			0
$184$	−4.10191e7	−	1.26244e8i	−0.485426	−	1.49399i
$185$	1.48997e8	−	1.08253e8i	1.73013	−	1.25701i
$186$		0			0
$187$	−5.13756e7	+	8.83197e7i	−0.574528	+	0.987670i
$188$	3.31166e6			0.0363491
$189$		0			0
$190$	−1.49224e7	−	4.59264e7i	−0.157834	−	0.485763i
$191$	−1.11505e7	+	3.43177e7i	−0.115792	+	0.356370i	−0.992111	−	0.125360i	$-0.959991\pi$
$191$	−1.11505e7	+	3.43177e7i	−0.115792	+	0.356370i	0.876320	+	0.481730i	$0.159991\pi$
$192$		0			0
$193$	1.96019e6	+	1.42416e6i	0.0196267	+	0.0142597i	0.597555	−	0.801828i	$-0.296139\pi$
$193$	1.96019e6	+	1.42416e6i	0.0196267	+	0.0142597i	−0.577929	+	0.816087i	$0.696139\pi$
$194$	2.09727e7	−	6.45472e7i	0.206228	−	0.634705i
$195$		0			0
$196$	4.06586e6	−	2.95402e6i	0.0385706	−	0.0280232i
$197$	1.64970e8			1.53735			0.768676	−	0.639639i	$-0.220916\pi$
$197$	1.64970e8			1.53735			0.768676	+	0.639639i	$0.220916\pi$
$198$		0			0
$199$	8.76155e7			0.788125			0.394063	−	0.919084i	$-0.371069\pi$
$199$	8.76155e7			0.788125			0.394063	+	0.919084i	$0.371069\pi$
$200$	1.04754e8	−	7.61080e7i	0.925901	−	0.672706i
$201$		0			0
$202$	−171492.	+	527799.i	−0.00146391	+	0.00450546i
$203$	−1.94986e8	−	1.41666e8i	−1.63594	−	1.18858i
$204$		0			0
$205$	2.38191e7	−	7.33077e7i	0.193102	−	0.594308i
$206$	1.76228e7	+	5.42373e7i	0.140455	+	0.432277i
$207$		0			0
$208$	−8.71681e7			−0.671639
$209$	−4.35693e7	+	1.92285e7i	−0.330117	+	0.145692i
$210$		0			0
$211$	−1.30313e8	+	9.46779e7i	−0.954991	+	0.693841i	−0.951982	−	0.306154i	$-0.900958\pi$
$211$	−1.30313e8	+	9.46779e7i	−0.954991	+	0.693841i	−0.00300860	+	0.999995i	$0.500958\pi$
$212$	−1.55608e6	−	4.78913e6i	−0.0112165	−	0.0345208i
$213$		0			0
$214$	2.82158e6	+	2.05000e6i	0.0196808	+	0.0142990i
$215$	3.45077e7	+	2.50713e7i	0.236800	+	0.172045i
$216$		0			0
$217$	−4.38761e7	−	1.35037e8i	−0.291487	−	0.897104i
$218$	−1.36342e8	+	9.90579e7i	−0.891313	+	0.647577i
$219$		0			0
$220$	−8.18276e6	−	9.14760e6i	−0.0518108	−	0.0579199i
$221$	−1.30485e8			−0.813182
$222$		0			0
$223$	6.38017e7	+	1.96362e8i	0.385270	+	1.18574i	0.936284	+	0.351244i	$0.114241\pi$
$223$	6.38017e7	+	1.96362e8i	0.385270	+	1.18574i	−0.551014	+	0.834496i	$0.685759\pi$
$224$	−7.63116e6	+	2.34863e7i	−0.0453652	+	0.139620i
$225$		0			0
$226$	6.26143e7	+	4.54920e7i	0.360823	+	0.262153i
$227$	−7.18734e7	+	2.21204e8i	−0.407829	+	1.25517i	0.510682	+	0.859770i	$0.329393\pi$
$227$	−7.18734e7	+	2.21204e8i	−0.407829	+	1.25517i	−0.918510	+	0.395397i	$0.870607\pi$
$228$		0			0
$229$	5.67892e7	−	4.12598e7i	0.312494	−	0.227040i	−0.420472	−	0.907306i	$-0.638135\pi$
$229$	5.67892e7	−	4.12598e7i	0.312494	−	0.227040i	0.732966	+	0.680265i	$0.238135\pi$
$230$	−4.00328e8			−2.16955
$231$		0			0
$232$	2.86531e8			1.50648
$233$	7.12030e7	−	5.17320e7i	0.368767	−	0.267925i	−0.387932	−	0.921688i	$-0.626811\pi$
$233$	7.12030e7	−	5.17320e7i	0.368767	−	0.267925i	0.756700	+	0.653763i	$0.226811\pi$
$234$		0			0
$235$	6.08671e7	−	1.87330e8i	0.305946	−	0.941605i
$236$	1.38660e7	+	1.00742e7i	0.0686687	+	0.0498907i
$237$		0			0
$238$	9.82897e7	−	3.02505e8i	0.472595	−	1.45450i
$239$	1.31843e7	+	4.05772e7i	0.0624691	+	0.192260i	0.977420	−	0.211304i	$-0.0677711\pi$
$239$	1.31843e7	+	4.05772e7i	0.0624691	+	0.192260i	−0.914951	+	0.403564i	$0.867771\pi$
$240$		0			0
$241$	−6.76250e7			−0.311206			−0.155603	−	0.987820i	$-0.549732\pi$
$241$	−6.76250e7			−0.311206			−0.155603	+	0.987820i	$0.549732\pi$
$242$	1.44566e8	−	1.58469e8i	0.655709	−	0.718770i
$243$		0			0
$244$	6.90751e6	−	5.01860e6i	0.0304409	−	0.0221166i
$245$	−9.23700e7	−	2.84286e8i	−0.401282	−	1.23502i
$246$		0			0
$247$	−4.92034e7	−	3.57484e7i	−0.207757	−	0.150944i
$248$	1.36562e8	+	9.92178e7i	0.568523	+	0.413056i
$249$		0			0
$250$	−1.26085e7	−	3.88051e7i	−0.0510358	−	0.157072i
$251$	2.73826e8	−	1.98946e8i	1.09299	−	0.794105i	0.113090	−	0.993585i	$-0.463925\pi$
$251$	2.73826e8	−	1.98946e8i	1.09299	−	0.794105i	0.979902	+	0.199479i	$0.0639250\pi$
$252$		0			0
$253$	3.99898e7	+	3.92775e8i	0.155248	+	1.52483i
$254$	3.84854e8			1.47360
$255$		0			0
$256$	−1.32537e7	−	4.07908e7i	−0.0493741	−	0.151958i
$257$	−3.79953e7	+	1.16937e8i	−0.139625	+	0.429722i	−0.996281	−	0.0861667i	$-0.972538\pi$
$257$	−3.79953e7	+	1.16937e8i	−0.139625	+	0.429722i	0.856656	+	0.515889i	$0.172538\pi$
$258$		0			0
$259$	4.57430e8	+	3.32343e8i	1.63597	+	1.18860i
$260$	4.84352e6	−	1.49068e7i	0.0170905	−	0.0525991i
$261$		0			0
$262$	1.00950e8	−	7.33442e7i	0.346777	−	0.251948i
$263$	−2.50356e8			−0.848618			−0.424309	−	0.905518i	$-0.639483\pi$
$263$	−2.50356e8			−0.848618			−0.424309	+	0.905518i	$0.639483\pi$
$264$		0			0
$265$	−2.99505e8			−0.988654
$266$	1.19939e8	−	8.71407e7i	0.390728	−	0.283880i
$267$		0			0
$268$	4.25636e6	−	1.30997e7i	0.0135072	−	0.0415710i
$269$	4.59086e8	+	3.33545e8i	1.43801	+	1.04477i	0.988455	+	0.151518i	$0.0484161\pi$
$269$	4.59086e8	+	3.33545e8i	1.43801	+	1.04477i	0.449551	+	0.893255i	$0.351584\pi$
$270$		0			0
$271$	7.56453e7	−	2.32812e8i	0.230882	−	0.710581i	−0.766759	−	0.641935i	$-0.778132\pi$
$271$	7.56453e7	−	2.32812e8i	0.230882	−	0.710581i	0.997641	−	0.0686460i	$-0.0218679\pi$
$272$	1.10592e8	+	3.40367e8i	0.333221	+	1.02555i
$273$		0			0
$274$	−3.83070e8			−1.12500
$275$	−3.52329e8	+	1.55495e8i	−1.02161	+	0.450869i
$276$		0			0
$277$	−3.45039e8	+	2.50686e8i	−0.975414	+	0.708680i	−0.956679	−	0.291144i	$-0.905964\pi$
$277$	−3.45039e8	+	2.50686e8i	−0.975414	+	0.708680i	−0.0187353	+	0.999824i	$0.505964\pi$
$278$	5.38641e7	+	1.65777e8i	0.150364	+	0.462771i
$279$		0			0
$280$	6.09597e8	+	4.42898e8i	1.65955	+	1.20573i
$281$	3.10681e8	+	2.25723e8i	0.835301	+	0.606882i	0.921054	−	0.389435i	$-0.127330\pi$
$281$	3.10681e8	+	2.25723e8i	0.835301	+	0.606882i	−0.0857528	+	0.996316i	$0.527330\pi$
$282$		0			0
$283$	1.85246e8	+	5.70127e8i	0.485842	+	1.49527i	0.830757	+	0.556635i	$0.187908\pi$
$283$	1.85246e8	+	5.70127e8i	0.485842	+	1.49527i	−0.344915	+	0.938634i	$0.612092\pi$
$284$	2.68387e7	−	1.94994e7i	0.0695259	−	0.0505136i
$285$		0			0
$286$	2.67762e8	+	5.78265e7i	0.676812	+	0.146166i
$287$	2.36641e8			0.590885
$288$		0			0
$289$	3.87474e7	+	1.19252e8i	0.0944279	+	0.290619i
$290$	2.67035e8	−	8.21848e8i	0.642946	−	1.97879i
$291$		0			0
$292$	−3.08950e7	−	2.24465e7i	−0.0726186	−	0.0527605i
$293$	1.25987e8	−	3.87747e8i	0.292609	−	0.900557i	−0.691405	−	0.722467i	$-0.743008\pi$
$293$	1.25987e8	−	3.87747e8i	0.292609	−	0.900557i	0.984014	−	0.178090i	$-0.0569919\pi$
$294$		0			0
$295$	8.24717e8	−	5.99192e8i	1.87037	−	1.35890i
$296$	−6.72191e8			−1.50651
$297$		0			0
$298$	−5.21629e8			−1.14184
$299$	−4.07901e8	+	2.96358e8i	−0.882482	+	0.641161i
$300$		0			0
$301$	−4.04657e7	+	1.24540e8i	−0.0855271	+	0.263225i
$302$	2.18903e8	+	1.59042e8i	0.457327	+	0.332268i
$303$		0			0
$304$	−5.15466e7	+	1.58644e8i	−0.105231	+	0.323867i
$305$	−1.56928e8	−	4.82975e8i	−0.316702	−	0.974710i
$306$		0			0
$307$	−6.58510e8			−1.29891			−0.649453	−	0.760401i	$-0.725002\pi$
$307$	−6.58510e8			−1.29891			−0.649453	+	0.760401i	$0.725002\pi$
$308$	1.89462e7	−	3.25703e7i	0.0369482	−	0.0635177i
$309$		0			0
$310$	4.11852e8	−	2.99228e8i	0.785192	−	0.570475i
$311$	2.37012e8	+	7.29449e8i	0.446796	+	1.37510i	0.880502	+	0.474043i	$0.157206\pi$
$311$	2.37012e8	+	7.29449e8i	0.446796	+	1.37510i	−0.433705	+	0.901055i	$0.642794\pi$
$312$		0			0
$313$	−8.08592e7	−	5.87476e7i	−0.149047	−	0.108289i	0.510762	−	0.859722i	$-0.329363\pi$
$313$	−8.08592e7	−	5.87476e7i	−0.149047	−	0.108289i	−0.659810	+	0.751433i	$0.729363\pi$
$314$	1.79042e8	+	1.30081e8i	0.326363	+	0.237116i
$315$		0			0
$316$	1.38505e7	+	4.26276e7i	0.0246923	+	0.0759952i
$317$	−2.89982e8	+	2.10685e8i	−0.511286	+	0.371471i	−0.813311	−	0.581829i	$-0.802337\pi$
$317$	−2.89982e8	+	2.10685e8i	−0.511286	+	0.371471i	0.302025	+	0.953300i	$0.402337\pi$
$318$		0			0
$319$	−8.33017e8	−	1.79900e8i	−1.43677	−	0.310287i
$320$	−8.93366e8			−1.52407
$321$		0			0
$322$	−3.79791e8	−	1.16888e9i	−0.633942	−	1.95107i
$323$	−7.71620e7	+	2.37480e8i	−0.127407	+	0.392120i
$324$		0			0
$325$	−3.97891e8	−	2.89084e8i	−0.642942	−	0.467125i
$326$	−6.39620e7	+	1.96855e8i	−0.102249	+	0.314691i
$327$		0			0
$328$	−2.27600e8	+	1.65361e8i	−0.356135	+	0.258747i
$329$	6.04709e8			0.936183
$330$		0			0
$331$	8.36902e8			1.26846			0.634230	−	0.773145i	$-0.281317\pi$
$331$	8.36902e8			1.26846			0.634230	+	0.773145i	$0.281317\pi$
$332$	−3.16803e7	+	2.30171e7i	−0.0475122	+	0.0345197i
$333$		0			0
$334$	3.92875e7	−	1.20914e8i	0.0576955	−	0.177568i
$335$	−6.62778e8	−	4.81536e8i	−0.963189	−	0.699797i
$336$		0			0
$337$	−2.16073e8	+	6.65004e8i	−0.307536	+	0.946498i	0.671183	+	0.741292i	$0.265786\pi$
$337$	−2.16073e8	+	6.65004e8i	−0.307536	+	0.946498i	−0.978719	+	0.205206i	$0.934214\pi$
$338$	−1.05333e8	−	3.24181e8i	−0.148373	−	0.456646i
$339$		0			0
$340$	−6.43521e7			−0.0887946
$341$	−3.34724e8	−	3.74191e8i	−0.457137	−	0.511038i
$342$		0			0
$343$	−8.93625e7	+	6.49257e7i	−0.119571	+	0.0868735i
$344$	−4.81074e7	−	1.48059e8i	−0.0637173	−	0.196102i
$345$		0			0
$346$	2.32441e7	+	1.68878e7i	0.0301679	+	0.0219183i
$347$	2.84516e7	+	2.06713e7i	0.0365556	+	0.0265592i	0.605913	−	0.795531i	$-0.292808\pi$
$347$	2.84516e7	+	2.06713e7i	0.0365556	+	0.0265592i	−0.569357	+	0.822090i	$0.692808\pi$
$348$		0			0
$349$	−9.05378e6	−	2.78647e7i	−0.0114009	−	0.0350885i	0.945194	−	0.326509i	$-0.105872\pi$
$349$	−9.05378e6	−	2.78647e7i	−0.0114009	−	0.0350885i	−0.956595	+	0.291420i	$0.905872\pi$
$350$	9.69904e8	−	7.04677e8i	1.20918	−	0.878520i
$351$		0			0
$352$	8.84462e6	+	8.68710e7i	0.0108089	+	0.106164i
$353$	1.53446e8			0.185670			0.0928352	−	0.995681i	$-0.470407\pi$
$353$	1.53446e8			0.185670			0.0928352	+	0.995681i	$0.470407\pi$
$354$		0			0
$355$	−6.09733e8	−	1.87657e9i	−0.723337	−	2.22620i
$356$	−1.76245e7	+	5.42428e7i	−0.0207035	+	0.0637187i
$357$		0			0
$358$	4.83920e8	+	3.51588e8i	0.557420	+	0.404990i
$359$	1.55029e8	−	4.77131e8i	0.176841	−	0.544260i	−0.822872	−	0.568227i	$-0.807630\pi$
$359$	1.55029e8	−	4.77131e8i	0.176841	−	0.544260i	0.999713	+	0.0239667i	$0.00762957\pi$
$360$		0			0
$361$	6.29000e8	−	4.56995e8i	0.703680	−	0.511254i
$362$	−9.71502e8			−1.07638
$363$		0			0
$364$	4.81200e7			0.0522962
$365$	−1.83756e9	+	1.33507e9i	−1.97796	+	1.43707i
$366$		0			0
$367$	4.22220e7	−	1.29946e8i	0.0445869	−	0.137224i	−0.926285	−	0.376824i	$-0.877016\pi$
$367$	4.22220e7	−	1.29946e8i	0.0445869	−	0.137224i	0.970872	+	0.239600i	$0.0770162\pi$
$368$	1.11876e9	+	8.12824e8i	1.17022	+	0.850216i
$369$		0			0
$370$	−6.26453e8	+	1.92802e9i	−0.642957	+	1.97882i
$371$	−2.84141e8	−	8.74495e8i	−0.288885	−	0.889096i
$372$		0			0
$373$	3.36463e8			0.335704			0.167852	−	0.985812i	$-0.446317\pi$
$373$	3.36463e8			0.335704			0.167852	+	0.985812i	$0.446317\pi$
$374$	−1.13919e8	−	1.11890e9i	−0.112602	−	1.10597i
$375$		0			0
$376$	−5.81607e8	+	4.22562e8i	−0.564251	+	0.409952i
$377$	−3.36317e8	−	1.03508e9i	−0.323262	−	0.994897i
$378$		0			0
$379$	−1.62131e9	−	1.17795e9i	−1.52978	−	1.11145i	−0.956360	−	0.292190i	$-0.905616\pi$
$379$	−1.62131e9	−	1.17795e9i	−1.52978	−	1.11145i	−0.573420	−	0.819261i	$-0.694384\pi$
$380$	−2.42659e7	−	1.76302e7i	−0.0226858	−	0.0164822i
$381$		0			0
$382$	−1.22738e8	−	3.77748e8i	−0.112657	−	0.346722i
$383$	−4.15888e8	+	3.02161e8i	−0.378252	+	0.274816i	−0.760624	−	0.649192i	$-0.775107\pi$
$383$	−4.15888e8	+	3.02161e8i	−0.378252	+	0.274816i	0.382373	+	0.924008i	$0.375107\pi$
$384$		0			0
$385$	−1.49417e9	−	1.67035e9i	−1.33441	−	1.49175i
$386$	−2.66702e7			−0.0236032
$387$		0			0
$388$	−1.30268e7	−	4.00923e7i	−0.0113221	−	0.0348458i
$389$	4.19134e8	−	1.28996e9i	0.361018	−	1.11110i	−0.591419	−	0.806365i	$-0.701432\pi$
$389$	4.19134e8	−	1.28996e9i	0.361018	−	1.11110i	0.952437	−	0.304736i	$-0.0985681\pi$
$390$		0			0
$391$	1.67471e9	+	1.21675e9i	1.41684	+	1.02939i
$392$	−3.37134e8	+	1.03759e9i	−0.282684	+	0.870013i
$393$		0			0
$394$	−1.46909e9	+	1.06735e9i	−1.21007	+	0.879168i
$395$	2.66587e9			2.17645
$396$		0			0
$397$	−1.69759e9			−1.36165			−0.680827	−	0.732445i	$-0.738379\pi$
$397$	−1.69759e9			−1.36165			−0.680827	+	0.732445i	$0.738379\pi$
$398$	−7.80231e8	+	5.66871e8i	−0.620344	+	0.450706i
$399$		0			0
$400$	−4.16839e8	+	1.28290e9i	−0.325656	+	1.00227i
$401$	−8.97197e8	−	6.51852e8i	−0.694836	−	0.504828i	0.183410	−	0.983037i	$-0.441286\pi$
$401$	−8.97197e8	−	6.51852e8i	−0.694836	−	0.504828i	−0.878246	+	0.478208i	$0.841286\pi$
$402$		0			0
$403$	1.98129e8	−	6.09778e8i	0.150793	−	0.464092i
$404$	106519.	+	327833.i	8.03699e−5	+	0.000247353i
$405$		0			0
$406$	2.65297e9			1.96739
$407$	1.95422e9	+	4.22039e8i	1.43679	+	0.310293i
$408$		0			0
$409$	8.31630e7	−	6.04214e7i	0.0601033	−	0.0436676i	−0.557328	−	0.830292i	$-0.688173\pi$
$409$	8.31630e7	−	6.04214e7i	0.0601033	−	0.0436676i	0.617431	+	0.786625i	$0.288173\pi$
$410$	2.62187e8	+	8.06928e8i	0.187874	+	0.578218i
$411$		0			0
$412$	2.86571e7	+	2.08206e7i	0.0201879	+	0.0146674i
$413$	2.53193e9	+	1.83955e9i	1.76859	+	1.28495i
$414$		0			0
$415$	7.19727e8	+	2.21509e9i	0.494310	+	1.52133i
$416$	−9.02165e7	+	6.55461e7i	−0.0614411	+	0.0446396i
$417$		0			0
$418$	2.63584e8	−	4.53126e8i	0.176523	−	0.303461i
$419$	−2.94726e9			−1.95736			−0.978678	−	0.205401i	$-0.934150\pi$
$419$	−2.94726e9			−1.95736			−0.978678	+	0.205401i	$0.934150\pi$
$420$		0			0
$421$	6.99099e8	+	2.15161e9i	0.456616	+	1.40532i	0.869227	+	0.494413i	$0.164617\pi$
$421$	6.99099e8	+	2.15161e9i	0.456616	+	1.40532i	−0.412611	+	0.910907i	$0.635383\pi$
$422$	5.47895e8	−	1.68625e9i	0.354898	−	1.09226i
$423$		0			0
$424$	8.84370e8	+	6.42533e8i	0.563448	+	0.409369i
$425$	−6.23982e8	+	1.92042e9i	−0.394286	+	1.21349i
$426$		0			0
$427$	1.26131e9	−	9.16396e8i	0.784016	−	0.569621i
$428$	2.16629e6			0.00133556
$429$		0			0
$430$	−4.69508e8			−0.284776
$431$	−7.77287e8	+	5.64732e8i	−0.467639	+	0.339760i	−0.796520	−	0.604612i	$-0.793328\pi$
$431$	−7.77287e8	+	5.64732e8i	−0.467639	+	0.339760i	0.328881	+	0.944371i	$0.393328\pi$
$432$		0			0
$433$	6.38212e8	−	1.96421e9i	0.377796	−	1.16274i	−0.563777	−	0.825927i	$-0.690652\pi$
$433$	6.38212e8	−	1.96421e9i	0.377796	−	1.16274i	0.941573	−	0.336809i	$-0.109348\pi$
$434$	1.26441e9	+	9.18648e8i	0.742462	+	0.539430i
$435$		0			0
$436$	−3.23472e7	+	9.95543e7i	−0.0186910	+	0.0575251i
$437$	2.98154e8	+	9.17623e8i	0.170905	+	0.525992i
$438$		0			0
$439$	6.16532e8			0.347800			0.173900	−	0.984763i	$-0.444363\pi$
$439$	6.16532e8			0.347800			0.173900	+	0.984763i	$0.444363\pi$
$440$	2.60431e9	+	5.62432e8i	1.45750	+	0.314764i
$441$		0			0
$442$	1.16199e9	−	8.44237e8i	0.640067	−	0.465036i
$443$	3.27657e8	+	1.00842e9i	0.179063	+	0.551100i	0.999796	−	0.0202129i	$-0.00643439\pi$
$443$	3.27657e8	+	1.00842e9i	0.179063	+	0.551100i	−0.820733	+	0.571313i	$0.806434\pi$
$444$		0			0
$445$	2.74440e9	+	1.99392e9i	1.47634	+	1.07263i
$446$	−1.83862e9	−	1.33584e9i	−0.981343	−	0.712987i
$447$		0			0
$448$	−8.47536e8	−	2.60845e9i	−0.445333	−	1.37059i
$449$	2.28063e9	−	1.65697e9i	1.18903	−	0.863879i	0.195866	−	0.980631i	$-0.437248\pi$
$449$	2.28063e9	−	1.65697e9i	1.18903	−	0.863879i	0.993161	+	0.116752i	$0.0372482\pi$
$450$		0			0
$451$	7.65513e8	−	3.37846e8i	0.392948	−	0.173421i
$452$	4.80728e7			0.0244858
$453$		0			0
$454$	−7.91140e8	−	2.43488e9i	−0.396787	−	1.22119i
$455$	8.84427e8	−	2.72199e9i	0.440171	−	1.35471i
$456$		0			0
$457$	1.38277e9	+	1.00464e9i	0.677710	+	0.492385i	0.872597	−	0.488441i	$-0.162434\pi$
$457$	1.38277e9	+	1.00464e9i	0.677710	+	0.492385i	−0.194888	+	0.980826i	$0.562434\pi$
$458$	−2.38768e8	+	7.34852e8i	−0.116131	+	0.357413i
$459$		0			0
$460$	−2.01167e8	+	1.46157e8i	−0.0963618	+	0.0700109i
$461$	−3.96255e9			−1.88374			−0.941871	−	0.335975i	$-0.890934\pi$
$461$	−3.96255e9			−1.88374			−0.941871	+	0.335975i	$0.890934\pi$
$462$		0			0
$463$	3.09364e9			1.44856			0.724281	−	0.689505i	$-0.242172\pi$
$463$	3.09364e9			1.44856			0.724281	+	0.689505i	$0.242172\pi$
$464$	−2.41493e9	+	1.75455e9i	−1.12226	+	0.815366i
$465$		0			0
$466$	−2.99370e8	+	9.21365e8i	−0.137043	+	0.421775i
$467$	6.33971e8	+	4.60607e8i	0.288045	+	0.209277i	0.722419	−	0.691456i	$-0.243030\pi$
$467$	6.33971e8	+	4.60607e8i	0.288045	+	0.209277i	−0.434374	+	0.900733i	$0.643030\pi$
$468$		0			0
$469$	7.77211e8	−	2.39201e9i	0.347884	−	1.07068i
$470$	6.69989e8	+	2.06201e9i	0.297663	+	0.916113i
$471$		0			0
$472$	−3.72065e9			−1.62863
$473$	4.69003e7	+	4.60650e8i	0.0203780	+	0.200150i
$474$		0			0
$475$	−7.61420e8	+	5.53204e8i	−0.325984	+	0.236841i
$476$	−6.10508e7	−	1.87895e8i	−0.0259458	−	0.0798529i
$477$		0			0
$478$	−3.79943e8	−	2.76045e8i	−0.159118	−	0.115606i
$479$	5.70443e8	+	4.14451e8i	0.237158	+	0.172305i	0.700016	−	0.714127i	$-0.253176\pi$
$479$	5.70443e8	+	4.14451e8i	0.237158	+	0.172305i	−0.462858	+	0.886432i	$0.653176\pi$
$480$		0			0
$481$	7.88986e8	+	2.42825e9i	0.323267	+	0.994914i
$482$	6.02213e8	−	4.37533e8i	0.244955	−	0.177970i
$483$		0			0
$484$	1.47894e7	−	1.32411e8i	0.00592914	−	0.0530843i
$485$	−2.50731e9			−0.997959
$486$		0			0
$487$	3.92474e8	+	1.20791e9i	0.153978	+	0.473897i	0.998056	−	0.0623244i	$-0.0198513\pi$
$487$	3.92474e8	+	1.20791e9i	0.153978	+	0.473897i	−0.844078	+	0.536221i	$0.819851\pi$
$488$	−5.72760e8	+	1.76277e9i	−0.223102	+	0.686637i
$489$		0			0
$490$	2.66190e9	+	1.93398e9i	1.02213	+	0.742619i
$491$	1.07262e9	−	3.30120e9i	0.408943	−	1.25860i	−0.508615	−	0.860994i	$-0.669842\pi$
$491$	1.07262e9	−	3.30120e9i	0.408943	−	1.25860i	0.917558	−	0.397602i	$-0.130158\pi$
$492$		0			0
$493$	−3.61500e9	+	2.62645e9i	−1.35876	+	0.987199i
$494$	6.69456e8			0.249849
$495$		0			0
$496$	−1.75851e9			−0.647083
$497$	4.90074e9	−	3.56060e9i	1.79066	−	1.30099i
$498$		0			0
$499$	1.73510e8	−	5.34007e8i	0.0625132	−	0.192396i	−0.914922	−	0.403630i	$-0.867748\pi$
$499$	1.73510e8	−	5.34007e8i	0.0625132	−	0.192396i	0.977435	+	0.211234i	$0.0677483\pi$
$500$	−2.05033e7	−	1.48965e7i	−0.00733547	−	0.00532953i
$501$		0			0
$502$	−1.15129e9	+	3.54331e9i	−0.406183	+	1.25010i
$503$	−9.52238e8	−	2.93069e9i	−0.333624	−	1.02679i	−0.967396	−	0.253270i	$-0.918494\pi$
$503$	−9.52238e8	−	2.93069e9i	−0.333624	−	1.02679i	0.633771	−	0.773520i	$-0.281506\pi$
$504$		0			0
$505$	2.05022e7			0.00708403
$506$	−2.89737e9	−	3.23900e9i	−0.994207	−	1.11144i
$507$		0			0
$508$	1.93391e8	−	1.40507e8i	0.0654507	−	0.0475527i
$509$	3.12184e8	+	9.60803e8i	0.104930	+	0.322940i	0.989714	−	0.143061i	$-0.0456944\pi$
$509$	3.12184e8	+	9.60803e8i	0.104930	+	0.322940i	−0.884784	+	0.466001i	$0.845694\pi$
$510$		0			0
$511$	−5.64142e9	−	4.09873e9i	−1.87032	−	1.35886i
$512$	2.62390e9	+	1.90637e9i	0.863977	+	0.627716i
$513$		0			0
$514$	−4.18229e8	−	1.28718e9i	−0.135845	−	0.418088i
$515$	1.70446e9	−	1.23836e9i	0.549872	−	0.399505i
$516$		0			0
$517$	1.95618e9	−	8.63327e8i	0.622576	−	0.274763i
$518$	−6.22375e9			−1.96742
$519$		0			0
$520$	1.05145e9	+	3.23602e9i	0.327926	+	1.00925i
$521$	4.42903e8	−	1.36312e9i	0.137207	−	0.422280i	−0.858720	−	0.512446i	$-0.828740\pi$
$521$	4.42903e8	−	1.36312e9i	0.137207	−	0.422280i	0.995927	+	0.0901655i	$0.0287396\pi$
$522$		0			0
$523$	−3.37964e9	−	2.45546e9i	−1.03304	−	0.750544i	−0.0641213	−	0.997942i	$-0.520424\pi$
$523$	−3.37964e9	−	2.45546e9i	−1.03304	−	0.750544i	−0.968914	+	0.247398i	$0.920424\pi$
$524$	2.39504e7	−	7.37117e7i	0.00727199	−	0.0223809i
$525$		0			0
$526$	2.22946e9	−	1.61980e9i	0.667959	−	0.485300i
$527$	−2.63238e9			−0.783451
$528$		0			0
$529$	4.59385e9			1.34922
$530$	2.66715e9	−	1.93780e9i	0.778183	−	0.565383i
$531$		0			0
$532$	2.84556e7	−	8.75774e7i	0.00819365	−	0.0252175i
$533$	8.64505e8	+	6.28099e8i	0.247299	+	0.179673i
$534$		0			0
$535$	3.98157e7	−	1.22540e8i	0.0112413	−	0.0345971i
$536$	9.23985e8	+	2.84373e9i	0.259172	+	0.797649i
$537$		0			0
$538$	−6.24627e9			−1.72935
$539$	1.63159e9	−	2.80487e9i	0.448797	−	0.771527i
$540$		0			0
$541$	4.79206e9	−	3.48163e9i	1.30116	−	0.945350i	0.301197	−	0.953562i	$-0.402614\pi$
$541$	4.79206e9	−	3.48163e9i	1.30116	−	0.945350i	0.999966	+	0.00821196i	$0.00261398\pi$
$542$	8.32658e8	+	2.56266e9i	0.224631	+	0.691342i
$543$		0			0
$544$	3.70399e8	+	2.69110e8i	0.0986446	+	0.0716695i
$545$	5.03692e9	+	3.65954e9i	1.33284	+	0.968364i
$546$		0			0
$547$	−1.63082e9	−	5.01916e9i	−0.426041	−	1.31122i	−0.901994	−	0.431749i	$-0.857897\pi$
$547$	−1.63082e9	−	5.01916e9i	−0.426041	−	1.31122i	0.475953	−	0.879471i	$-0.342103\pi$
$548$	−1.92495e8	+	1.39856e8i	−0.0499675	+	0.0363035i
$549$		0			0
$550$	2.13151e9	−	3.66427e9i	0.546283	−	0.939115i
$551$	−2.08270e9			−0.530391
$552$		0			0
$553$	2.52911e9	+	7.78379e9i	0.635959	+	1.95728i
$554$	1.45070e9	−	4.46480e9i	0.362488	−	1.11562i
$555$		0			0
$556$	8.75907e7	+	6.36384e7i	0.0216121	+	0.0157021i
$557$	−1.07704e9	+	3.31479e9i	−0.264082	+	0.812762i	0.727821	+	0.685767i	$0.240533\pi$
$557$	−1.07704e9	+	3.31479e9i	−0.264082	+	0.812762i	−0.991903	+	0.126995i	$0.959467\pi$
$558$		0			0
$559$	−4.78390e8	+	3.47570e8i	−0.115835	+	0.0841592i
$560$	−7.84982e9			−1.88887
$561$		0			0
$562$	−4.22710e9			−1.00454
$563$	−2.59569e9	+	1.88588e9i	−0.613019	+	0.445384i	−0.850476	−	0.526014i	$-0.823686\pi$
$563$	−2.59569e9	+	1.88588e9i	−0.613019	+	0.445384i	0.237457	+	0.971398i	$0.423686\pi$
$564$		0			0
$565$	8.83559e8	−	2.71932e9i	0.206094	−	0.634293i
$566$	−5.33836e9	−	3.87855e9i	−1.23751	−	0.899107i
$567$		0			0
$568$	−2.22542e9	+	6.84914e9i	−0.509557	+	1.56825i
$569$	1.83641e8	+	5.65188e8i	0.0417904	+	0.128618i	0.969775	−	0.244001i	$-0.0784600\pi$
$569$	1.83641e8	+	5.65188e8i	0.0417904	+	0.128618i	−0.927985	+	0.372618i	$0.878460\pi$
$570$		0			0
$571$	−1.48637e9			−0.334119			−0.167059	−	0.985947i	$-0.553427\pi$
$571$	−1.48637e9			−0.334119			−0.167059	+	0.985947i	$0.553427\pi$
$572$	1.55664e8	−	6.86996e7i	0.0347778	−	0.0153486i
$573$		0			0
$574$	−2.10733e9	+	1.53106e9i	−0.465094	+	0.337911i
$575$	2.41107e9	+	7.42050e9i	0.528898	+	1.62778i
$576$		0			0
$577$	−3.36319e9	−	2.44350e9i	−0.728846	−	0.529538i	0.160352	−	0.987060i	$-0.448737\pi$
$577$	−3.36319e9	−	2.44350e9i	−0.728846	−	0.529538i	−0.889198	+	0.457522i	$0.848737\pi$
$578$	−1.11661e9	−	8.11267e8i	−0.240522	−	0.174750i
$579$		0			0
$580$	−1.65864e8	−	5.10476e8i	−0.0352982	−	0.108637i
$581$	−5.78481e9	+	4.20291e9i	−1.22369	+	0.889065i
$582$		0			0
$583$	−2.16766e9	−	2.42326e9i	−0.453056	−	0.506477i
$584$	8.29003e9			1.72231
$585$		0			0
$586$	1.38678e9	+	4.26808e9i	0.284687	+	0.876176i
$587$	1.78035e9	−	5.47935e9i	0.363305	−	1.11814i	−0.587731	−	0.809057i	$-0.699979\pi$
$587$	1.78035e9	−	5.47935e9i	0.363305	−	1.11814i	0.951036	−	0.309081i	$-0.100021\pi$
$588$		0			0
$589$	−9.92621e8	−	7.21181e8i	−0.200161	−	0.145426i
$590$	−3.46749e9	+	1.06718e10i	−0.695077	+	2.13923i
$591$		0			0
$592$	5.66533e9	−	4.11610e9i	1.12227	−	0.815380i
$593$	1.34021e9			0.263925			0.131962	−	0.991255i	$-0.457872\pi$
$593$	1.34021e9			0.263925			0.131962	+	0.991255i	$0.457872\pi$
$594$		0			0
$595$	−1.17507e10			−2.28693
$596$	−2.62121e8	+	1.90442e8i	−0.0507155	+	0.0368469i
$597$		0			0
$598$	1.71500e9	−	5.27824e9i	0.327952	−	1.00933i
$599$	7.81900e8	+	5.68084e8i	0.148647	+	0.107999i	0.659623	−	0.751596i	$-0.270716\pi$
$599$	7.81900e8	+	5.68084e8i	0.148647	+	0.107999i	−0.510976	+	0.859595i	$0.670716\pi$
$600$		0			0
$601$	2.37401e9	−	7.30644e9i	0.446089	−	1.37292i	−0.435197	−	0.900335i	$-0.643321\pi$
$601$	2.37401e9	−	7.30644e9i	0.446089	−	1.37292i	0.881285	−	0.472584i	$-0.156679\pi$
$602$	−4.45422e8	−	1.37087e9i	−0.0832116	−	0.256099i
$603$		0			0
$604$	1.68065e8			0.0310347
$605$	−7.21824e9	−	3.27025e9i	−1.32522	−	0.600396i
$606$		0			0
$607$	−3.62453e9	+	2.63338e9i	−0.657796	+	0.477917i	−0.865918	−	0.500186i	$-0.833265\pi$
$607$	−3.62453e9	+	2.63338e9i	−0.657796	+	0.477917i	0.208122	+	0.978103i	$0.433265\pi$
$608$	6.59433e7	+	2.02953e8i	0.0118989	+	0.0366212i
$609$		0			0
$610$	4.52232e9	+	3.28566e9i	0.806690	+	0.586094i
$611$	2.20914e9	+	1.60504e9i	0.391814	+	0.284669i
$612$		0			0
$613$	2.16870e9	+	6.67456e9i	0.380266	+	1.17034i	0.939857	+	0.341568i	$0.110958\pi$
$613$	2.16870e9	+	6.67456e9i	0.380266	+	1.17034i	−0.559591	+	0.828769i	$0.689042\pi$
$614$	5.86415e9	−	4.26055e9i	1.02239	−	0.742808i
$615$		0			0
$616$	8.28519e8	+	8.13763e9i	0.142814	+	1.40270i
$617$	−7.09558e7			−0.0121616			−0.00608079	−	0.999982i	$-0.501936\pi$
$617$	−7.09558e7			−0.0121616			−0.00608079	+	0.999982i	$0.501936\pi$
$618$		0			0
$619$	2.34153e8	+	7.20650e8i	0.0396810	+	0.122126i	0.968935	−	0.247317i	$-0.0795488\pi$
$619$	2.34153e8	+	7.20650e8i	0.0396810	+	0.122126i	−0.929254	+	0.369442i	$0.879549\pi$
$620$	9.77124e7	−	3.00728e8i	0.0164656	−	0.0506760i
$621$		0			0
$622$	−6.83016e9	−	4.96240e9i	−1.13806	−	0.826848i
$623$	−3.21824e9	+	9.90472e9i	−0.533225	+	1.64110i
$624$		0			0
$625$	4.29449e9	−	3.12013e9i	0.703610	−	0.511202i
$626$	1.10016e9			0.179245
$627$		0			0
$628$	1.37461e8			0.0221473
$629$	8.48064e9	−	6.16154e9i	1.35879	−	0.987216i
$630$		0			0
$631$	−1.68252e9	+	5.17826e9i	−0.266598	+	0.820506i	0.724722	+	0.689041i	$0.241968\pi$
$631$	−1.68252e9	+	5.17826e9i	−0.266598	+	0.820506i	−0.991321	+	0.131465i	$0.958032\pi$
$632$	−7.87169e9	−	5.71912e9i	−1.24039	−	0.901196i
$633$		0			0
$634$	1.21922e9	−	3.75237e9i	0.190007	−	0.584781i
$635$	−4.39356e9	−	1.35220e10i	−0.680939	−	2.09571i
$636$		0			0
$637$	4.14395e9			0.635224
$638$	8.58212e9	−	3.78757e9i	1.30834	−	0.577415i
$639$		0			0
$640$	7.12261e9	−	5.17488e9i	1.07401	−	0.780316i
$641$	1.76222e9	+	5.42354e9i	0.264275	+	0.813354i	0.991860	+	0.127336i	$0.0406428\pi$
$641$	1.76222e9	+	5.42354e9i	0.264275	+	0.813354i	−0.727585	+	0.686018i	$0.759357\pi$
$642$		0			0
$643$	−2.88868e8	−	2.09875e8i	−0.0428510	−	0.0311331i	0.566154	−	0.824300i	$-0.308431\pi$
$643$	−2.88868e8	−	2.09875e8i	−0.0428510	−	0.0311331i	−0.609005	+	0.793167i	$0.708431\pi$
$644$	−6.17595e8	−	4.48709e8i	−0.0911177	−	0.0662009i
$645$		0			0
$646$	−8.49353e8	−	2.61404e9i	−0.123958	−	0.381503i
$647$	2.09335e8	−	1.52091e8i	0.0303863	−	0.0220769i	−0.572488	−	0.819913i	$-0.694022\pi$
$647$	2.09335e8	−	1.52091e8i	0.0303863	−	0.0220769i	0.602875	+	0.797836i	$0.294022\pi$
$648$		0			0
$649$	1.08169e10	+	2.33603e9i	1.55326	+	0.335446i
$650$	5.41366e9			0.773204
$651$		0			0
$652$	3.97288e7	+	1.22273e8i	0.00561357	+	0.0172768i
$653$	−2.03439e9	+	6.26121e9i	−0.285916	+	0.879958i	0.700207	+	0.713940i	$0.253091\pi$
$653$	−2.03439e9	+	6.26121e9i	−0.285916	+	0.879958i	−0.986123	+	0.166018i	$0.946909\pi$
$654$		0			0
$655$	−3.72943e9	−	2.70959e9i	−0.518558	−	0.376755i
$656$	9.05675e8	−	2.78738e9i	0.125259	−	0.385508i
$657$		0			0
$658$	−5.38504e9	+	3.91246e9i	−0.736883	+	0.535377i
$659$	2.79910e9			0.380995			0.190498	−	0.981688i	$-0.438990\pi$
$659$	2.79910e9			0.380995			0.190498	+	0.981688i	$0.438990\pi$
$660$		0			0
$661$	−1.38506e10			−1.86536			−0.932681	−	0.360703i	$-0.882537\pi$
$661$	−1.38506e10			−1.86536			−0.932681	+	0.360703i	$0.882537\pi$
$662$	−7.45276e9	+	5.41475e9i	−0.998422	+	0.725396i
$663$		0			0
$664$	2.62687e9	−	8.08469e9i	0.348218	−	1.07170i
$665$	−4.43096e9	−	3.21928e9i	−0.584281	−	0.424505i
$666$		0			0
$667$	−5.33543e9	+	1.64208e10i	−0.696192	+	2.14266i
$668$	−2.44027e7	−	7.51037e7i	−0.00316752	−	0.00974864i
$669$		0			0
$670$	9.01769e9			1.15833
$671$	2.77192e9	−	4.76520e9i	0.354203	−	0.608909i
$672$		0			0
$673$	−7.29819e9	+	5.30244e9i	−0.922916	+	0.670538i	−0.944248	−	0.329234i	$-0.893209\pi$
$673$	−7.29819e9	+	5.30244e9i	−0.922916	+	0.670538i	0.0213319	+	0.999772i	$0.493209\pi$
$674$	−2.37840e9	−	7.31997e9i	−0.299210	−	0.920873i
$675$		0			0
$676$	−1.71286e8	−	1.24447e8i	−0.0213260	−	0.0154942i
$677$	1.00307e10	+	7.28770e9i	1.24242	+	0.902673i	0.997757	−	0.0669350i	$-0.0213220\pi$
$677$	1.00307e10	+	7.28770e9i	1.24242	+	0.902673i	0.244665	+	0.969608i	$0.421322\pi$
$678$		0			0
$679$	−2.37869e9	−	7.32085e9i	−0.291604	−	0.897464i
$680$	1.13018e10	−	8.21121e9i	1.37837	−	1.00144i
$681$		0			0
$682$	5.40179e9	+	1.16658e9i	0.652067	+	0.140822i
$683$	−1.54540e10			−1.85595			−0.927977	−	0.372637i	$-0.878454\pi$
$683$	−1.54540e10			−1.85595			−0.927977	+	0.372637i	$0.878454\pi$
$684$		0			0
$685$	4.37319e9	+	1.34593e10i	0.519854	+	1.59995i
$686$	3.75721e8	−	1.15635e9i	0.0444356	−	0.136759i
$687$		0			0
$688$	1.31209e9	+	9.53286e8i	0.153604	+	0.111600i
$689$	1.28308e9	−	3.94891e9i	0.149447	−	0.459949i
$690$		0			0
$691$	3.76231e9	−	2.73348e9i	0.433792	−	0.315168i	−0.349371	−	0.936984i	$-0.613605\pi$
$691$	3.76231e9	−	2.73348e9i	0.433792	−	0.315168i	0.783163	+	0.621816i	$0.213605\pi$
$692$	1.78459e7			0.00204723
$693$		0			0
$694$	−3.87110e8			−0.0439618
$695$	5.20969e9	−	3.78506e9i	0.588661	−	0.427687i
$696$		0			0
$697$	1.35574e9	−	4.17253e9i	0.151657	−	0.466751i
$698$	2.60910e8	+	1.89562e8i	0.0290400	+	0.0210988i
$699$		0			0
$700$	2.30111e8	−	7.08208e8i	0.0253567	−	0.0780400i
$701$	2.91754e9	+	8.97927e9i	0.319893	+	0.984528i	0.973694	+	0.227862i	$0.0731734\pi$
$701$	2.91754e9	+	8.97927e9i	0.319893	+	0.984528i	−0.653801	+	0.756667i	$0.726827\pi$
$702$		0			0
$703$	4.88593e9			0.530401
$704$	−6.46572e9	−	7.22810e9i	−0.698413	−	0.780764i
$705$		0			0
$706$	−1.36646e9	+	9.92791e8i	−0.146144	+	0.106180i
$707$	1.94504e7	+	5.98622e7i	0.00206995	+	0.00637066i
$708$		0			0
$709$	9.39990e9	+	6.82943e9i	0.990516	+	0.719652i	0.960034	−	0.279883i	$-0.0902958\pi$
$709$	9.39990e9	+	6.82943e9i	0.990516	+	0.719652i	0.0304820	+	0.999535i	$0.490296\pi$
$710$	1.75711e10	+	1.27662e10i	1.84245	+	1.33862i
$711$		0			0
$712$	−3.82599e9	−	1.17752e10i	−0.397250	−	1.22261i
$713$	−8.22893e9	+	5.97867e9i	−0.850218	+	0.617719i
$714$		0			0
$715$	−1.02506e9	−	1.00681e10i	−0.104877	−	1.03009i
$716$	3.71534e8			0.0378271
$717$		0			0
$718$	1.70647e9	+	5.25197e9i	0.172053	+	0.529525i
$719$	−4.78280e9	+	1.47200e10i	−0.479879	+	1.47691i	0.359385	+	0.933189i	$0.382987\pi$
$719$	−4.78280e9	+	1.47200e10i	−0.479879	+	1.47691i	−0.839263	+	0.543725i	$0.817013\pi$
$720$		0			0
$721$	5.23278e9	+	3.80184e9i	0.519947	+	0.377764i
$722$	−2.64460e9	+	8.13925e9i	−0.261505	+	0.804830i
$723$		0			0
$724$	−4.88185e8	+	3.54687e8i	−0.0478079	+	0.0347345i
$725$	−1.68421e10			−1.64139
$726$		0			0
$727$	6.63192e9			0.640131			0.320065	−	0.947395i	$-0.396295\pi$
$727$	6.63192e9			0.640131			0.320065	+	0.947395i	$0.396295\pi$
$728$	−8.45102e9	+	6.14002e9i	−0.811800	+	0.589807i
$729$		0			0
$730$	7.72594e9	−	2.37780e10i	0.735058	−	2.26227i
$731$	1.96411e9	+	1.42701e9i	0.185975	+	0.135119i
$732$		0			0
$733$	−1.65578e9	+	5.09595e9i	−0.155288	+	0.477927i	−0.998190	−	0.0601401i	$-0.980845\pi$
$733$	−1.65578e9	+	5.09595e9i	−0.155288	+	0.477927i	0.842902	+	0.538067i	$0.180845\pi$
$734$	4.64755e8	+	1.43037e9i	0.0433798	+	0.133509i
$735$		0			0
$736$	1.76909e9			0.163560
$737$	−9.00799e8	−	8.84755e9i	−0.0828880	−	0.814117i
$738$		0			0
$739$	2.92332e9	−	2.12392e9i	0.266454	−	0.193590i	−0.446534	−	0.894767i	$-0.647342\pi$
$739$	2.92332e9	−	2.12392e9i	0.266454	−	0.193590i	0.712987	+	0.701177i	$0.247342\pi$
$740$	3.89109e8	+	1.19755e9i	0.0352988	+	0.108639i
$741$		0			0
$742$	8.18830e9	+	5.94915e9i	0.735834	+	0.534615i
$743$	−1.48556e9	−	1.07932e9i	−0.132870	−	0.0965360i	0.519365	−	0.854553i	$-0.326169\pi$
$743$	−1.48556e9	−	1.07932e9i	−0.132870	−	0.0965360i	−0.652235	+	0.758017i	$0.726169\pi$
$744$		0			0
$745$	5.95499e9	+	1.83276e10i	0.527636	+	1.62390i
$746$	−2.99626e9	+	2.17691e9i	−0.264237	+	0.191980i
$747$		0			0
$748$	−4.65747e8	−	5.20664e8i	−0.0406906	−	0.0454885i
$749$	3.95565e8			0.0343979
$750$		0			0
$751$	−5.88934e9	−	1.81255e10i	−0.507372	−	1.56153i	−0.796746	−	0.604315i	$-0.793447\pi$
$751$	−5.88934e9	−	1.81255e10i	−0.507372	−	1.56153i	0.289374	−	0.957216i	$-0.406553\pi$
$752$	2.31435e9	−	7.12284e9i	0.198457	−	0.610788i
$753$		0			0
$754$	9.69191e9	+	7.04158e9i	0.823397	+	0.598233i
$755$	3.08897e9	−	9.50687e9i	0.261216	−	0.803939i
$756$		0			0
$757$	−6.01045e9	+	4.36685e9i	−0.503584	+	0.365875i	−0.810384	−	0.585899i	$-0.800742\pi$
$757$	−6.01045e9	+	4.36685e9i	−0.503584	+	0.365875i	0.306800	+	0.951774i	$0.400742\pi$
$758$	2.20594e10			1.83972
$759$		0			0
$760$	6.51126e9			0.538044
$761$	−9.18696e8	+	6.67472e8i	−0.0755659	+	0.0549018i	−0.624927	−	0.780683i	$-0.714871\pi$
$761$	−9.18696e8	+	6.67472e8i	−0.0755659	+	0.0549018i	0.549361	+	0.835585i	$0.314871\pi$
$762$		0			0
$763$	−5.90659e9	+	1.81786e10i	−0.481394	+	1.48158i
$764$	−1.99589e8	−	1.45010e8i	−0.0161924	−	0.0117644i
$765$		0			0
$766$	1.74858e9	−	5.38159e9i	0.140568	−	0.432623i
$767$	4.36713e9	+	1.34406e10i	0.349472	+	1.07556i
$768$		0			0
$769$	−1.23476e10			−0.979129			−0.489564	−	0.871967i	$-0.662844\pi$
$769$	−1.23476e10			−0.979129			−0.489564	+	0.871967i	$0.662844\pi$
$770$	2.41130e10	+	5.20750e9i	1.90342	+	0.411066i
$771$		0			0
$772$	−1.34019e7	+	9.73706e6i	−0.00104835	+	0.000761671i
$773$	−1.60537e9	−	4.94082e9i	−0.125011	−	0.384743i	0.868892	−	0.495001i	$-0.164832\pi$
$773$	−1.60537e9	−	4.94082e9i	−0.125011	−	0.384743i	−0.993903	+	0.110258i	$0.964832\pi$
$774$		0			0
$775$	−8.02698e9	−	5.83194e9i	−0.619435	−	0.450046i
$776$	7.40352e9	+	5.37897e9i	0.568751	+	0.413222i
$777$		0			0
$778$	4.61358e9	+	1.41991e10i	0.351244	+	1.08102i
$779$	1.65435e9	−	1.20196e9i	0.125385	−	0.0910978i
$780$		0			0
$781$	1.07701e10	−	1.85149e10i	0.808986	−	1.39073i
$782$	−2.27859e10			−1.70389
$783$		0			0
$784$	−3.51219e9	−	1.08094e10i	−0.260298	−	0.801116i
$785$	2.52648e9	−	7.77571e9i	0.186411	−	0.573715i
$786$		0			0
$787$	3.90762e9	+	2.83905e9i	0.285759	+	0.207616i	0.721426	−	0.692492i	$-0.243487\pi$
$787$	3.90762e9	+	2.83905e9i	0.285759	+	0.207616i	−0.435666	+	0.900108i	$0.643487\pi$
$788$	−3.48542e8	+	1.07270e9i	−0.0253754	+	0.0780976i
$789$		0			0
$790$	−2.37400e10	+	1.72481e10i	−1.71311	+	1.24465i
$791$	8.77808e9			0.630641
$792$		0			0
$793$	7.04019e9			0.501335
$794$	1.51174e10	−	1.09834e10i	1.07178	−	0.778691i
$795$		0			0
$796$	−1.85111e8	+	5.69712e8i	−0.0130088	+	0.0400368i
$797$	1.23821e10	+	8.99615e9i	0.866347	+	0.629438i	0.929604	−	0.368560i	$-0.120149\pi$
$797$	1.23821e10	+	8.99615e9i	0.866347	+	0.629438i	−0.0632575	+	0.997997i	$0.520149\pi$
$798$		0			0
$799$	3.46443e9	−	1.06624e10i	0.240281	−	0.739507i
$800$	5.33261e8	+	1.64121e9i	0.0368235	+	0.113331i
$801$		0			0
$802$	1.22072e10			0.835612
$803$	−2.41011e10	−	5.20493e9i	−1.64261	−	0.354740i
$804$		0			0
$805$	−3.67331e10	+	2.66882e10i	−2.48183	+	1.80316i
$806$	2.18088e9	+	6.71207e9i	0.146710	+	0.451527i
$807$		0			0
$808$	−6.05382e7	−	4.39836e7i	−0.00403729	−	0.00293326i
$809$	−9.08077e9	−	6.59757e9i	−0.602980	−	0.438091i	0.243955	−	0.969786i	$-0.421555\pi$
$809$	−9.08077e9	−	6.59757e9i	−0.602980	−	0.438091i	−0.846935	+	0.531696i	$0.821555\pi$
$810$		0			0
$811$	−2.68983e9	−	8.27844e9i	−0.177073	−	0.544974i	0.822649	−	0.568549i	$-0.192495\pi$
$811$	−2.68983e9	−	8.27844e9i	−0.177073	−	0.544974i	−0.999722	+	0.0235754i	$0.992495\pi$
$812$	1.33313e9	−	9.68576e8i	0.0873829	−	0.0634874i
$813$		0			0
$814$	−2.01333e10	+	8.88549e9i	−1.30837	+	0.577425i
$815$	7.64676e9			0.494795
$816$		0			0
$817$	3.49677e8	+	1.07619e9i	0.0224331	+	0.0690420i
$818$	−3.49655e8	+	1.07613e9i	−0.0223359	+	0.0687428i
$819$		0			0
$820$	4.26353e8	+	3.09764e8i	0.0270035	+	0.0196192i
$821$	−4.82969e9	+	1.48642e10i	−0.304592	+	0.937436i	0.675238	+	0.737600i	$0.264041\pi$
$821$	−4.82969e9	+	1.48642e10i	−0.304592	+	0.937436i	−0.979829	+	0.199836i	$0.935959\pi$
$822$		0			0
$823$	−6.86697e9	+	4.98915e9i	−0.429404	+	0.311980i	−0.781410	−	0.624017i	$-0.785499\pi$
$823$	−6.86697e9	+	4.98915e9i	−0.429404	+	0.311980i	0.352007	+	0.935997i	$0.385499\pi$
$824$	−7.68955e9			−0.478802
$825$		0			0
$826$	−3.44492e10			−2.12691
$827$	−5.23730e9	+	3.80512e9i	−0.321987	+	0.233937i	−0.737023	−	0.675868i	$-0.763769\pi$
$827$	−5.23730e9	+	3.80512e9i	−0.321987	+	0.233937i	0.415036	+	0.909805i	$0.363769\pi$
$828$		0			0
$829$	−6.56312e9	+	2.01992e10i	−0.400101	+	1.23138i	0.524817	+	0.851215i	$0.324134\pi$
$829$	−6.56312e9	+	2.01992e10i	−0.400101	+	1.23138i	−0.924917	+	0.380168i	$0.875866\pi$
$830$	−2.07409e10	−	1.50692e10i	−1.25908	−	0.914778i
$831$		0			0
$832$	3.82717e9	−	1.17788e10i	0.230381	−	0.709039i
$833$	−5.25752e9	−	1.61810e10i	−0.315154	−	0.969946i
$834$		0			0
$835$	−4.69688e9			−0.279194
$836$	−3.29805e7	−	3.23931e8i	−0.00195225	−	0.0191748i
$837$		0			0
$838$	2.62459e10	−	1.90688e10i	1.54066	−	1.11936i
$839$	−7.50243e9	−	2.30901e10i	−0.438566	−	1.34977i	−0.889388	−	0.457153i	$-0.848869\pi$
$839$	−7.50243e9	−	2.30901e10i	−0.438566	−	1.34977i	0.450822	−	0.892614i	$-0.351131\pi$
$840$		0			0
$841$	−1.61964e10	−	1.17674e10i	−0.938929	−	0.682172i
$842$	−2.01465e10	−	1.46373e10i	−1.16307	−	0.845021i
$843$		0			0
$844$	−3.40315e8	−	1.04738e9i	−0.0194842	−	0.0599661i
$845$	−1.01877e10	+	7.40181e9i	−0.580869	+	0.422026i
$846$		0			0
$847$	2.70054e9	−	2.41783e10i	0.152707	−	1.36720i
$848$	−1.13881e10			−0.641307
$849$		0			0
$850$	−6.86842e9	−	2.11388e10i	−0.383611	−	1.18063i
$851$	1.25167e10	−	3.85225e10i	0.696204	−	2.14270i
$852$		0			0
$853$	3.51002e9	+	2.55018e9i	0.193637	+	0.140685i	0.680379	−	0.732860i	$-0.261815\pi$
$853$	3.51002e9	+	2.55018e9i	0.193637	+	0.140685i	−0.486743	+	0.873545i	$0.661815\pi$
$854$	−5.30313e9	+	1.63213e10i	−0.291360	+	0.896713i
$855$		0			0
$856$	−3.80453e8	+	2.76415e8i	−0.0207321	+	0.0150627i
$857$	−1.60588e10			−0.871524			−0.435762	−	0.900062i	$-0.643521\pi$
$857$	−1.60588e10			−0.871524			−0.435762	+	0.900062i	$0.643521\pi$
$858$		0			0
$859$	3.02898e10			1.63050			0.815249	−	0.579111i	$-0.196600\pi$
$859$	3.02898e10			1.63050			0.815249	+	0.579111i	$0.196600\pi$
$860$	−2.35930e8	+	1.71413e8i	−0.0126485	+	0.00918967i
$861$		0			0
$862$	3.26807e9	−	1.00581e10i	0.173786	−	0.534859i
$863$	1.92862e10	+	1.40122e10i	1.02143	+	0.742111i	0.966575	−	0.256383i	$-0.0825308\pi$
$863$	1.92862e10	+	1.40122e10i	1.02143	+	0.742111i	0.0548535	+	0.998494i	$0.482531\pi$
$864$		0			0
$865$	3.28000e8	−	1.00948e9i	0.0172313	−	0.0530325i
$866$	7.02506e9	+	2.16209e10i	0.367568	+	1.13126i
$867$		0			0
$868$	9.70764e8			0.0503842
$869$	1.92942e10	+	2.15692e10i	0.997371	+	1.11497i
$870$		0			0
$871$	9.18828e9	−	6.67568e9i	0.471163	−	0.342320i
$872$	−7.02202e9	−	2.16116e10i	−0.358636	−	1.10377i
$873$		0			0
$874$	−8.59213e9	−	6.24254e9i	−0.435322	−	0.316280i
$875$	−3.74390e9	−	2.72010e9i	−0.188928	−	0.137264i
$876$		0			0
$877$	−3.36337e9	−	1.03514e10i	−0.168374	−	0.518203i	0.830895	−	0.556430i	$-0.187829\pi$
$877$	−3.36337e9	−	1.03514e10i	−0.168374	−	0.518203i	−0.999269	+	0.0382266i	$0.987829\pi$
$878$	−5.49033e9	+	3.98896e9i	−0.273758	+	0.198897i
$879$		0			0
$880$	−2.53935e10	+	1.12070e10i	−1.25613	+	0.554370i
$881$	1.33013e10			0.655356			0.327678	−	0.944789i	$-0.393734\pi$
$881$	1.33013e10			0.655356			0.327678	+	0.944789i	$0.393734\pi$
$882$		0			0
$883$	8.48482e9	+	2.61136e10i	0.414744	+	1.27645i	0.912480	+	0.409122i	$0.134165\pi$
$883$	8.48482e9	+	2.61136e10i	0.414744	+	1.27645i	−0.497735	+	0.867329i	$0.665835\pi$
$884$	2.75684e8	−	8.48467e8i	0.0134223	−	0.0413097i
$885$		0			0
$886$	−9.44234e9	−	6.86026e9i	−0.456101	−	0.331377i
$887$	−9.76767e8	+	3.00618e9i	−0.0469957	+	0.144638i	−0.971801	−	0.235803i	$-0.924228\pi$
$887$	−9.76767e8	+	3.00618e9i	−0.0469957	+	0.144638i	0.924805	+	0.380441i	$0.124228\pi$
$888$		0			0
$889$	3.53133e10	−	2.56566e10i	1.68570	−	1.22474i
$890$	−3.73400e10			−1.77546
$891$		0			0
$892$	−1.41162e9			−0.0665950
$893$	4.22751e9	−	3.07146e9i	0.198657	−	0.144333i
$894$		0			0
$895$	6.82866e9	−	2.10165e10i	0.318387	−	0.979894i
$896$	2.18668e10	+	1.58872e10i	1.01556	+	0.737851i
$897$		0			0
$898$	−9.58879e9	+	2.95113e10i	−0.441872	+	1.35994i
$899$	−6.78480e9	−	2.08815e10i	−0.311443	−	0.958523i
$900$		0			0
$901$	−1.70473e10			−0.776458
$902$	−4.63117e9	+	7.96144e9i	−0.210120	+	0.361218i
$903$		0			0
$904$	−8.44273e9	+	6.13400e9i	−0.380096	+	0.276156i
$905$	1.10908e10	+	3.41340e10i	0.497386	+	1.53080i
$906$		0			0
$907$	−7.50380e8	−	5.45183e8i	−0.0333930	−	0.0242615i	0.570964	−	0.820975i	$-0.306570\pi$
$907$	−7.50380e8	−	5.45183e8i	−0.0333930	−	0.0242615i	−0.604357	+	0.796714i	$0.706570\pi$
$908$	−1.28651e9	−	9.34701e8i	−0.0570310	−	0.0414355i
$909$		0			0
$910$	9.73524e9	+	2.99620e10i	0.428254	+	1.31803i
$911$	1.42113e10	−	1.03251e10i	0.622760	−	0.452461i	−0.231125	−	0.972924i	$-0.574241\pi$
$911$	1.42113e10	−	1.03251e10i	0.622760	−	0.452461i	0.853884	+	0.520463i	$0.174241\pi$
$912$		0			0
$913$	−1.27130e10	+	2.18549e10i	−0.552840	+	0.950387i
$914$	−1.88138e10			−0.815016
$915$		0			0
$916$	1.48306e8	+	4.56439e8i	0.00637565	+	0.0196222i
$917$	4.37334e9	−	1.34598e10i	0.187293	−	0.576427i
$918$		0			0
$919$	−1.75238e10	−	1.27318e10i	−0.744775	−	0.541111i	0.149428	−	0.988773i	$-0.452257\pi$
$919$	−1.75238e10	−	1.27318e10i	−0.744775	−	0.541111i	−0.894203	+	0.447662i	$0.852257\pi$
$920$	1.66805e10	−	5.13372e10i	0.706237	−	2.17357i
$921$		0			0
$922$	3.52872e10	−	2.56377e10i	1.48272	−	1.07726i
$923$	2.73542e10			1.14503
$924$		0			0
$925$	3.95108e10			1.64142
$926$	−2.75495e10	+	2.00158e10i	−1.14018	+	0.828391i
$927$		0			0
$928$	−1.18005e9	+	3.63182e9i	−0.0484710	+	0.149178i
$929$	7.96173e9	+	5.78453e9i	0.325801	+	0.236708i	0.738647	−	0.674093i	$-0.235465\pi$
$929$	7.96173e9	+	5.78453e9i	0.325801	+	0.236708i	−0.412846	+	0.910801i	$0.635465\pi$
$930$		0			0
$931$	2.45052e9	−	7.54192e9i	0.0995254	−	0.306308i
$932$	1.85948e8	+	5.72288e8i	0.00752377	+	0.0231558i
$933$		0			0
$934$	−8.62574e9			−0.346404
$935$	−3.80124e10	+	1.67761e10i	−1.52085	+	0.671199i
$936$		0			0
$937$	−2.57159e10	+	1.86837e10i	−1.02120	+	0.741949i	−0.966529	−	0.256556i	$-0.917412\pi$
$937$	−2.57159e10	+	1.86837e10i	−1.02120	+	0.741949i	−0.0546752	+	0.998504i	$0.517412\pi$
$938$	8.55508e9	+	2.63298e10i	0.338465	+	1.04169i
$939$		0			0
$940$	1.08950e9	+	7.91566e8i	0.0427837	+	0.0310842i
$941$	2.15298e9	+	1.56423e9i	0.0842318	+	0.0611980i	0.629104	−	0.777321i	$-0.283422\pi$
$941$	2.15298e9	+	1.56423e9i	0.0842318	+	0.0611980i	−0.544872	+	0.838519i	$0.683422\pi$
$942$		0			0
$943$	−5.23857e9	−	1.61227e10i	−0.203433	−	0.626103i
$944$	3.13582e10	−	2.27831e10i	1.21325	−	0.881476i
$945$		0			0
$946$	−3.39805e9	−	3.79872e9i	−0.130500	−	0.145888i
$947$	2.30870e10			0.883370			0.441685	−	0.897170i	$-0.354381\pi$
$947$	2.30870e10			0.883370			0.441685	+	0.897170i	$0.354381\pi$
$948$		0			0
$949$	−9.73044e9	−	2.99472e10i	−0.369574	−	1.13743i
$950$	3.20135e9	−	9.85276e9i	0.121144	−	0.372842i
$951$		0			0
$952$	3.46971e10	+	2.52089e10i	1.30336	+	0.946944i
$953$	−3.12083e9	+	9.60492e9i	−0.116800	+	0.359475i	−0.992318	−	0.123711i	$-0.960520\pi$
$953$	−3.12083e9	+	9.60492e9i	−0.116800	+	0.359475i	0.875518	+	0.483186i	$0.160520\pi$
$954$		0			0
$955$	−1.18711e10	+	8.62486e9i	−0.441041	+	0.320435i
$956$	−2.91705e8			−0.0107979
$957$		0			0
$958$	−7.76139e9			−0.285207
$959$	−3.51495e10	+	2.55376e10i	−1.28693	+	0.935009i
$960$		0			0
$961$	−4.50485e9	+	1.38645e10i	−0.163738	+	0.503932i
$962$	−2.27368e10	−	1.65193e10i	−0.823412	−	0.598244i
$963$		0			0
$964$	1.42876e8	−	4.39726e8i	0.00513675	−	0.0158093i
$965$	3.04471e8	+	9.37065e8i	0.0109069	+	0.0335679i
$966$		0			0
$967$	−3.64895e10			−1.29770			−0.648852	−	0.760915i	$-0.724750\pi$
$967$	−3.64895e10			−1.29770			−0.648852	+	0.760915i	$0.724750\pi$
$968$	1.42981e10	+	2.51417e10i	0.506656	+	0.890903i
$969$		0			0
$970$	2.23281e10	−	1.62223e10i	0.785507	−	0.570705i
$971$	5.73616e9	+	1.76541e10i	0.201073	+	0.618839i	0.999852	+	0.0172144i	$0.00547978\pi$
$971$	5.73616e9	+	1.76541e10i	0.201073	+	0.618839i	−0.798779	+	0.601625i	$0.794520\pi$
$972$		0			0
$973$	1.59940e10	+	1.16204e10i	0.556626	+	0.404412i
$974$	−1.13102e10	−	8.21736e9i	−0.392207	−	0.284955i
$975$		0			0
$976$	−5.96688e9	−	1.83642e10i	−0.205434	−	0.632262i
$977$	2.17208e10	−	1.57811e10i	0.745153	−	0.541385i	−0.149168	−	0.988812i	$-0.547660\pi$
$977$	2.17208e10	−	1.57811e10i	0.745153	−	0.541385i	0.894321	+	0.447427i	$0.147660\pi$
$978$		0			0
$979$	3.72998e9	+	3.66355e10i	0.127048	+	1.24785i
$980$	2.04370e9			0.0693626
$981$		0			0
$982$	1.18068e10	+	3.63376e10i	0.397871	+	1.22452i
$983$	−1.07676e10	+	3.31392e10i	−0.361561	+	1.11277i	0.590546	+	0.807004i	$0.298912\pi$
$983$	−1.07676e10	+	3.31392e10i	−0.361561	+	1.11277i	−0.952107	+	0.305765i	$0.901088\pi$
$984$		0			0
$985$	5.42731e10	+	3.94317e10i	1.80950	+	1.31468i
$986$	1.51991e10	−	4.67780e10i	0.504950	−	1.55408i
$987$		0			0
$988$	3.36406e8	−	2.44413e8i	0.0110972	−	0.00806260i
$989$	9.38090e9			0.308360
$990$		0			0
$991$	5.26008e10			1.71686			0.858429	−	0.512932i	$-0.171441\pi$
$991$	5.26008e10			1.71686			0.858429	+	0.512932i	$0.171441\pi$
$992$	−1.82001e9	+	1.32232e9i	−0.0591948	+	0.0430075i
$993$		0			0
$994$	−2.06049e10	+	6.34155e10i	−0.665455	+	2.04806i
$995$	2.88244e10	+	2.09422e10i	0.927641	+	0.673971i
$996$		0			0
$997$	−2.76554e9	+	8.51147e9i	−0.0883787	+	0.272002i	−0.985472	−	0.169840i	$-0.945675\pi$
$997$	−2.76554e9	+	8.51147e9i	−0.0883787	+	0.272002i	0.897093	+	0.441842i	$0.145675\pi$
$998$	1.90989e9	+	5.87804e9i	0.0608207	+	0.187187i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	99.8.f.c.91.2		28
3.2	odd	2		33.8.e.a.25.6	yes	28
11.4	even	5	inner	99.8.f.c.37.2		28
33.2	even	10		363.8.a.p.1.11		14
33.20	odd	10		363.8.a.q.1.4		14
33.26	odd	10		33.8.e.a.4.6	✓	28

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
33.8.e.a.4.6	✓	28	33.26	odd	10
33.8.e.a.25.6	yes	28	3.2	odd	2
99.8.f.c.37.2		28	11.4	even	5	inner
99.8.f.c.91.2		28	1.1	even	1	trivial
363.8.a.p.1.11		14	33.2	even	10
363.8.a.q.1.4		14	33.20	odd	10

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:	\( N \)	\(=\)	\( 99 = 3^{2} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 8 \)
Character orbit:	\([\chi]\)	\(=\)	99.f (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-8.90518 + 6.46999i) q^{2} +(-2.11276 + 6.50241i) q^{4} +(328.988 + 239.024i) q^{5} +(-385.790 + 1187.34i) q^{7} +(-458.645 - 1411.56i) q^{8} +O(q^{10})\)	\(q+(-8.90518 + 6.46999i) q^{2} +(-2.11276 + 6.50241i) q^{4} +(328.988 + 239.024i) q^{5} +(-385.790 + 1187.34i) q^{7} +(-458.645 - 1411.56i) q^{8} -4476.18 q^{10} +(447.136 + 4391.72i) q^{11} +(-4560.85 + 3313.65i) q^{13} +(-4246.55 - 13069.5i) q^{14} +(12509.1 + 9088.40i) q^{16} +(18725.3 + 13604.8i) q^{17} +(3333.74 + 10260.2i) q^{19} +(-2249.30 + 1634.21i) q^{20} +(-32396.2 - 36216.1i) q^{22} +89435.3 q^{23} +(26958.8 + 82970.5i) q^{25} +(19175.9 - 59017.4i) q^{26} +(-6905.49 - 5017.13i) q^{28} +(-59656.9 + 183605. i) q^{29} +(-92009.9 + 66849.1i) q^{31} +19780.6 q^{32} -254775. q^{34} +(-410723. + 298407. i) q^{35} +(139953. - 430730. i) q^{37} +(-96070.8 - 69799.5i) q^{38} +(186509. - 574014. i) q^{40} +(-58573.8 - 180272. i) q^{41} +104890. q^{43} +(-29501.5 - 6371.20i) q^{44} +(-796438. + 578646. i) q^{46} +(-149679. - 460664. i) q^{47} +(-594681. - 432061. i) q^{49} +(-776891. - 564444. i) q^{50} +(-11910.7 - 36657.5i) q^{52} +(-595854. + 432913. i) q^{53} +(-902624. + 1.55170e6i) q^{55} +1.85295e6 q^{56} +(-656667. - 2.02101e6i) q^{58} +(774654. - 2.38414e6i) q^{59} +(-1.01031e6 - 734032. i) q^{61} +(386851. - 1.19061e6i) q^{62} +(-1.77732e6 + 1.29130e6i) q^{64} -2.29251e6 q^{65} -2.01460e6 q^{67} +(-128026. + 93016.3i) q^{68} +(1.72686e6 - 5.31474e6i) q^{70} +(-3.92548e6 - 2.85203e6i) q^{71} +(-1.72601e6 + 5.31212e6i) q^{73} +(1.54052e6 + 4.74122e6i) q^{74} -73759.3 q^{76} +(-5.38697e6 - 1.16338e6i) q^{77} +(5.30364e6 - 3.85332e6i) q^{79} +(1.94300e6 + 5.97995e6i) q^{80} +(1.68797e6 + 1.22638e6i) q^{82} +(4.63362e6 + 3.36652e6i) q^{83} +(2.90855e6 + 8.95160e6i) q^{85} +(-934067. + 678640. i) q^{86} +(5.99412e6 - 2.64540e6i) q^{88} +8.34195e6 q^{89} +(-2.17490e6 - 6.69366e6i) q^{91} +(-188956. + 581545. i) q^{92} +(4.31341e6 + 3.13387e6i) q^{94} +(-1.35567e6 + 4.17232e6i) q^{95} +(-4.98820e6 + 3.62414e6i) q^{97} +8.09117e6 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 28 q + 22 q^{2} - 692 q^{4} + 777 q^{5} - 83 q^{7} - 3568 q^{8}+O(q^{10}) \) 28 * q + 22 * q^2 - 692 * q^4 + 777 * q^5 - 83 * q^7 - 3568 * q^8	\( 28 q + 22 q^{2} - 692 q^{4} + 777 q^{5} - 83 q^{7} - 3568 q^{8} - 1352 q^{10} + 18851 q^{11} + 14635 q^{13} - 62912 q^{14} - 36148 q^{16} + 10338 q^{17} + 90342 q^{19} + 289719 q^{20} - 202339 q^{22} - 138508 q^{23} - 174068 q^{25} - 466130 q^{26} - 640233 q^{28} + 487290 q^{29} - 388352 q^{31} - 2726322 q^{32} - 1543708 q^{34} - 742659 q^{35} + 670209 q^{37} - 2282072 q^{38} + 4641741 q^{40} + 2721357 q^{41} - 199784 q^{43} + 5887437 q^{44} + 3389447 q^{46} - 2112053 q^{47} + 3927748 q^{49} + 3663090 q^{50} - 4343053 q^{52} + 1743854 q^{53} - 8387710 q^{55} + 6307818 q^{56} + 546605 q^{58} + 218820 q^{59} - 743157 q^{61} - 3996183 q^{62} - 21725666 q^{64} - 4895794 q^{65} - 3235686 q^{67} - 961671 q^{68} + 31155916 q^{70} - 9848757 q^{71} - 6667768 q^{73} + 31115192 q^{74} - 6535748 q^{76} - 8320585 q^{77} - 10121851 q^{79} - 44592526 q^{80} + 24927115 q^{82} - 13288897 q^{83} - 28050005 q^{85} - 20937351 q^{86} + 39687014 q^{88} + 40241460 q^{89} + 8733043 q^{91} - 11607651 q^{92} - 7877385 q^{94} - 14371097 q^{95} + 30518151 q^{97} + 16954218 q^{98}+O(q^{100}) \) 28 * q + 22 * q^2 - 692 * q^4 + 777 * q^5 - 83 * q^7 - 3568 * q^8 - 1352 * q^10 + 18851 * q^11 + 14635 * q^13 - 62912 * q^14 - 36148 * q^16 + 10338 * q^17 + 90342 * q^19 + 289719 * q^20 - 202339 * q^22 - 138508 * q^23 - 174068 * q^25 - 466130 * q^26 - 640233 * q^28 + 487290 * q^29 - 388352 * q^31 - 2726322 * q^32 - 1543708 * q^34 - 742659 * q^35 + 670209 * q^37 - 2282072 * q^38 + 4641741 * q^40 + 2721357 * q^41 - 199784 * q^43 + 5887437 * q^44 + 3389447 * q^46 - 2112053 * q^47 + 3927748 * q^49 + 3663090 * q^50 - 4343053 * q^52 + 1743854 * q^53 - 8387710 * q^55 + 6307818 * q^56 + 546605 * q^58 + 218820 * q^59 - 743157 * q^61 - 3996183 * q^62 - 21725666 * q^64 - 4895794 * q^65 - 3235686 * q^67 - 961671 * q^68 + 31155916 * q^70 - 9848757 * q^71 - 6667768 * q^73 + 31115192 * q^74 - 6535748 * q^76 - 8320585 * q^77 - 10121851 * q^79 - 44592526 * q^80 + 24927115 * q^82 - 13288897 * q^83 - 28050005 * q^85 - 20937351 * q^86 + 39687014 * q^88 + 40241460 * q^89 + 8733043 * q^91 - 11607651 * q^92 - 7877385 * q^94 - 14371097 * q^95 + 30518151 * q^97 + 16954218 * q^98

Introduction

L-functions

Modular forms

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