LMFDB - Embedded newform 99.11.k.a.46.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [99,11,Mod(19,99)]

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, 3]))

N = Newforms(chi, 11, names="a")

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

chi := DirichletCharacter("99.19");

S:= CuspForms(chi, 11);

N := Newforms(S);

Level:	$ N $	$=$	$ 99 = 3^{2} \cdot 11 $
Weight:	$ k $	$=$	$ 11 $
Character orbit:	$[\chi]$	$=$	99.k (of order $10$, 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:	$62.9003680147$
Analytic rank:	$0$
Dimension:	$36$
Relative dimension:	$9$ over $\Q(\zeta_{10})$
Twist minimal:	no (minimal twist has level 11)
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			46.1
Character	$\chi$	$=$	99.46
Dual form			99.11.k.a.28.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-48.9033 - 15.8897i) q^{2} +(1310.62 + 952.222i) q^{4} +(-259.656 - 799.138i) q^{5} +(6472.97 - 8909.28i) q^{7} +(-18014.0 - 24794.1i) q^{8} +O(q^{10})$	\(q+(-48.9033 - 15.8897i) q^{2} +(1310.62 + 952.222i) q^{4} +(-259.656 - 799.138i) q^{5} +(6472.97 - 8909.28i) q^{7} +(-18014.0 - 24794.1i) q^{8} +43206.3i q^{10} +(160863. - 7773.63i) q^{11} +(317694. + 103225. i) q^{13} +(-458115. + 332840. i) q^{14} +(-25653.8 - 78954.2i) q^{16} +(1.58896e6 - 516284. i) q^{17} +(-1.68812e6 - 2.32350e6i) q^{19} +(420647. - 1.29462e6i) q^{20} +(-7.99027e6 - 2.17591e6i) q^{22} +6.17837e6 q^{23} +(7.32936e6 - 5.32509e6i) q^{25} +(-1.38961e7 - 1.00961e7i) q^{26} +(1.69672e7 - 5.51299e6i) q^{28} +(-8.83955e6 + 1.21666e7i) q^{29} +(-4.09149e6 + 1.25923e7i) q^{31} +3.56515e7i q^{32} -8.59090e7 q^{34} +(-8.80048e6 - 2.85945e6i) q^{35} +(8.78268e7 + 6.38099e7i) q^{37} +(4.56352e7 + 1.40451e8i) q^{38} +(-1.51365e7 + 2.08336e7i) q^{40} +(-5.72523e7 - 7.88010e7i) q^{41} +1.88418e8i q^{43} +(2.18233e8 + 1.42989e8i) q^{44} +(-3.02143e8 - 9.81722e7i) q^{46} +(-5.83203e7 + 4.23722e7i) q^{47} +(4.98137e7 + 1.53311e8i) q^{49} +(-4.43044e8 + 1.43954e8i) q^{50} +(3.18084e8 + 4.37805e8i) q^{52} +(-2.41473e8 + 7.43178e8i) q^{53} +(-4.79812e7 - 1.26533e8i) q^{55} -3.37502e8 q^{56} +(6.25607e8 - 4.54530e8i) q^{58} +(6.58470e7 + 4.78406e7i) q^{59} +(4.32363e8 - 1.40483e8i) q^{61} +(4.00175e8 - 5.50794e8i) q^{62} +(5.40221e8 - 1.66263e9i) q^{64} -2.80684e8i q^{65} -1.82676e9 q^{67} +(2.57414e9 + 8.36389e8i) q^{68} +(3.84937e8 + 2.79673e8i) q^{70} +(-1.08996e8 - 3.35454e8i) q^{71} +(1.85130e9 - 2.54810e9i) q^{73} +(-3.28110e9 - 4.51605e9i) q^{74} -4.65270e9i q^{76} +(9.72006e8 - 1.48349e9i) q^{77} +(2.23582e9 + 7.26461e8i) q^{79} +(-5.64341e7 + 4.10018e7i) q^{80} +(1.54771e9 + 4.76335e9i) q^{82} +(1.62134e9 - 5.26804e8i) q^{83} +(-8.25164e8 - 1.13574e9i) q^{85} +(2.99390e9 - 9.21429e9i) q^{86} +(-3.09053e9 - 3.84843e9i) q^{88} +4.54171e9 q^{89} +(2.97609e9 - 2.16225e9i) q^{91} +(8.09750e9 + 5.88318e9i) q^{92} +(3.52533e9 - 1.14545e9i) q^{94} +(-1.41847e9 + 1.95235e9i) q^{95} +(-1.54774e9 + 4.76346e9i) q^{97} -8.28894e9i q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 36 q + 5 q^{2} + 2839 q^{4} - 566 q^{5} - 9740 q^{7} + 56325 q^{8}+O(q^{10}) $ 36 * q + 5 * q^2 + 2839 * q^4 - 566 * q^5 - 9740 * q^7 + 56325 * q^8	\( 36 q + 5 q^{2} + 2839 q^{4} - 566 q^{5} - 9740 q^{7} + 56325 q^{8} + 124277 q^{11} + 516610 q^{13} + 256990 q^{14} + 1558071 q^{16} + 1563930 q^{17} + 6441265 q^{19} - 11846024 q^{20} - 38364515 q^{22} - 2991652 q^{23} + 53140199 q^{25} - 53101970 q^{26} - 158441860 q^{28} + 30773770 q^{29} + 63499996 q^{31} + 8404770 q^{34} - 93755030 q^{35} - 20015352 q^{37} - 222215700 q^{38} + 66388740 q^{40} - 168755230 q^{41} - 1092554652 q^{44} - 843022850 q^{46} + 1466232 q^{47} - 247720591 q^{49} - 1888812255 q^{50} - 1016067090 q^{52} + 1574434638 q^{53} + 1667070934 q^{55} - 464386660 q^{56} - 5738108180 q^{58} + 3108186601 q^{59} + 4185015940 q^{61} - 8028589520 q^{62} - 568398521 q^{64} - 6673767122 q^{67} + 12578329400 q^{68} - 10858899380 q^{70} - 5532218182 q^{71} + 6815310530 q^{73} - 27099775830 q^{74} + 17322154610 q^{77} - 28511789960 q^{79} - 9512354316 q^{80} + 4251999505 q^{82} - 6078874665 q^{83} + 52883120010 q^{85} + 11116561805 q^{86} - 35103955205 q^{88} + 19181286322 q^{89} - 22561214930 q^{91} + 78730839752 q^{92} + 94886813720 q^{94} - 79444332050 q^{95} - 7866178077 q^{97}+O(q^{100}) \) 36 * q + 5 * q^2 + 2839 * q^4 - 566 * q^5 - 9740 * q^7 + 56325 * q^8 + 124277 * q^11 + 516610 * q^13 + 256990 * q^14 + 1558071 * q^16 + 1563930 * q^17 + 6441265 * q^19 - 11846024 * q^20 - 38364515 * q^22 - 2991652 * q^23 + 53140199 * q^25 - 53101970 * q^26 - 158441860 * q^28 + 30773770 * q^29 + 63499996 * q^31 + 8404770 * q^34 - 93755030 * q^35 - 20015352 * q^37 - 222215700 * q^38 + 66388740 * q^40 - 168755230 * q^41 - 1092554652 * q^44 - 843022850 * q^46 + 1466232 * q^47 - 247720591 * q^49 - 1888812255 * q^50 - 1016067090 * q^52 + 1574434638 * q^53 + 1667070934 * q^55 - 464386660 * q^56 - 5738108180 * q^58 + 3108186601 * q^59 + 4185015940 * q^61 - 8028589520 * q^62 - 568398521 * q^64 - 6673767122 * q^67 + 12578329400 * q^68 - 10858899380 * q^70 - 5532218182 * q^71 + 6815310530 * q^73 - 27099775830 * q^74 + 17322154610 * q^77 - 28511789960 * q^79 - 9512354316 * q^80 + 4251999505 * q^82 - 6078874665 * q^83 + 52883120010 * q^85 + 11116561805 * q^86 - 35103955205 * q^88 + 19181286322 * q^89 - 22561214930 * q^91 + 78730839752 * q^92 + 94886813720 * q^94 - 79444332050 * q^95 - 7866178077 * q^97

Display 100 coefficients 10 coefficients

Character values

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

$n$	$46$	$56$
$\chi(n)$	$e\left(\frac{1}{10}\right)$	$1$

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 $

$2$	−48.9033	−	15.8897i	−1.52823	−	0.496552i	−0.580129	−	0.814524i	$-0.696998\pi$
$2$	−48.9033	−	15.8897i	−1.52823	−	0.496552i	−0.948100	+	0.317973i	$0.896998\pi$
$3$		0			0
$3$		0			0
$4$	1310.62	+	952.222i	1.27990	+	0.929905i
$5$	−259.656	−	799.138i	−0.0830898	−	0.255724i	0.900877	−	0.434074i	$-0.142924\pi$
$5$	−259.656	−	799.138i	−0.0830898	−	0.255724i	−0.983967	+	0.178350i	$0.942924\pi$
$6$		0			0
$7$	6472.97	−	8909.28i	0.385135	−	0.530093i	−0.571800	−	0.820393i	$-0.693755\pi$
$7$	6472.97	−	8909.28i	0.385135	−	0.530093i	0.956936	+	0.290299i	$0.0937549\pi$
$8$	−18014.0	−	24794.1i	−0.549743	−	0.756657i
$9$		0			0
$10$			43206.3i			0.432063i
$11$	160863.	−	7773.63i	0.998834	−	0.0482681i
$11$	160863.	−	7773.63i	0.998834	−	0.0482681i
$12$		0			0
$13$	317694.	+	103225.i	0.855643	+	0.278015i	0.703808	−	0.710390i	$-0.251482\pi$
$13$	317694.	+	103225.i	0.855643	+	0.278015i	0.151835	+	0.988406i	$0.451482\pi$
$14$	−458115.	+	332840.i	−0.851794	+	0.618865i
$15$		0			0
$16$	−25653.8	−	78954.2i	−0.0244653	−	0.0752966i
$17$	1.58896e6	−	516284.i	1.11910	−	0.363617i	0.309675	−	0.950843i	$-0.399780\pi$
$17$	1.58896e6	−	516284.i	1.11910	−	0.363617i	0.809423	+	0.587225i	$0.199780\pi$
$18$		0			0
$19$	−1.68812e6	−	2.32350e6i	−0.681767	−	0.938371i	0.318187	−	0.948028i	$-0.396926\pi$
$19$	−1.68812e6	−	2.32350e6i	−0.681767	−	0.938371i	−0.999953	+	0.00965664i	$0.996926\pi$
$20$	420647.	−	1.29462e6i	0.131452	−	0.404568i
$21$		0			0
$22$	−7.99027e6	−	2.17591e6i	−1.55042	−	0.422208i
$23$	6.17837e6			0.959919			0.479960	−	0.877291i	$-0.340651\pi$
$23$	6.17837e6			0.959919			0.479960	+	0.877291i	$0.340651\pi$
$24$		0			0
$25$	7.32936e6	−	5.32509e6i	0.750526	−	0.545289i
$26$	−1.38961e7	−	1.00961e7i	−1.16957	−	0.849742i
$27$		0			0
$28$	1.69672e7	−	5.51299e6i	0.985873	−	0.320329i
$29$	−8.83955e6	+	1.21666e7i	−0.430963	+	0.593170i	−0.968174	−	0.250278i	$-0.919478\pi$
$29$	−8.83955e6	+	1.21666e7i	−0.430963	+	0.593170i	0.537211	+	0.843448i	$0.319478\pi$
$30$		0			0
$31$	−4.09149e6	+	1.25923e7i	−0.142914	+	0.439843i	−0.996737	−	0.0807203i	$-0.974278\pi$
$31$	−4.09149e6	+	1.25923e7i	−0.142914	+	0.439843i	0.853823	+	0.520563i	$0.174278\pi$
$32$			3.56515e7i			1.06250i
$33$		0			0
$34$	−8.59090e7			−1.89079
$35$	−8.80048e6	−	2.85945e6i	−0.167558	−	0.0544430i
$36$		0			0
$37$	8.78268e7	+	6.38099e7i	1.26654	+	0.920194i	0.999059	−	0.0433700i	$-0.0138094\pi$
$37$	8.78268e7	+	6.38099e7i	1.26654	+	0.920194i	0.267479	+	0.963564i	$0.413809\pi$
$38$	4.56352e7	+	1.40451e8i	0.575946	+	1.77258i
$39$		0			0
$40$	−1.51365e7	+	2.08336e7i	−0.147817	+	0.203453i
$41$	−5.72523e7	−	7.88010e7i	−0.494167	−	0.680162i	0.486983	−	0.873411i	$-0.338097\pi$
$41$	−5.72523e7	−	7.88010e7i	−0.494167	−	0.680162i	−0.981150	+	0.193249i	$0.938097\pi$
$42$		0			0
$43$			1.88418e8i			1.28168i	0.767673	+	0.640842i	$0.221415\pi$
$43$			1.88418e8i			1.28168i	−0.767673	+	0.640842i	$0.778585\pi$
$44$	2.18233e8	+	1.42989e8i	1.32330	+	0.867042i
$45$		0			0
$46$	−3.02143e8	−	9.81722e7i	−1.46698	−	0.476650i
$47$	−5.83203e7	+	4.23722e7i	−0.254291	+	0.184753i	−0.707626	−	0.706587i	$-0.750234\pi$
$47$	−5.83203e7	+	4.23722e7i	−0.254291	+	0.184753i	0.453336	+	0.891340i	$0.350234\pi$
$48$		0			0
$49$	4.98137e7	+	1.53311e8i	0.176347	+	0.542741i
$50$	−4.43044e8	+	1.43954e8i	−1.41774	+	0.460652i
$51$		0			0
$52$	3.18084e8	+	4.37805e8i	0.836613	+	1.15150i
$53$	−2.41473e8	+	7.43178e8i	−0.577417	+	1.77711i	0.0503810	+	0.998730i	$0.483956\pi$
$53$	−2.41473e8	+	7.43178e8i	−0.577417	+	1.77711i	−0.627798	+	0.778376i	$0.716044\pi$
$54$		0			0
$55$	−4.79812e7	−	1.26533e8i	−0.0953362	−	0.251415i
$56$	−3.37502e8			−0.612824
$57$		0			0
$58$	6.25607e8	−	4.54530e8i	0.953150	−	0.692504i
$59$	6.58470e7	+	4.78406e7i	0.0921034	+	0.0669170i	0.632884	−	0.774247i	$-0.281871\pi$
$59$	6.58470e7	+	4.78406e7i	0.0921034	+	0.0669170i	−0.540780	+	0.841164i	$0.681871\pi$
$60$		0			0
$61$	4.32363e8	−	1.40483e8i	0.511917	−	0.166332i	−0.0416569	−	0.999132i	$-0.513264\pi$
$61$	4.32363e8	−	1.40483e8i	0.511917	−	0.166332i	0.553574	+	0.832800i	$0.313264\pi$
$62$	4.00175e8	−	5.50794e8i	0.436809	−	0.601217i
$63$		0			0
$64$	5.40221e8	−	1.66263e9i	0.503120	−	1.54844i
$65$		−	2.80684e8i		−	0.241909i
$66$		0			0
$67$	−1.82676e9			−1.35303			−0.676516	−	0.736428i	$-0.736511\pi$
$67$	−1.82676e9			−1.35303			−0.676516	+	0.736428i	$0.736511\pi$
$68$	2.57414e9	+	8.36389e8i	1.77047	+	0.575260i
$69$		0			0
$70$	3.84937e8	+	2.79673e8i	0.229034	+	0.166403i
$71$	−1.08996e8	−	3.35454e8i	−0.0604112	−	0.185926i	0.916297	−	0.400500i	$-0.131164\pi$
$71$	−1.08996e8	−	3.35454e8i	−0.0604112	−	0.185926i	−0.976708	+	0.214574i	$0.931164\pi$
$72$		0			0
$73$	1.85130e9	−	2.54810e9i	0.893024	−	1.22914i	−0.0796158	−	0.996826i	$-0.525369\pi$
$73$	1.85130e9	−	2.54810e9i	0.893024	−	1.22914i	0.972640	−	0.232317i	$-0.0746306\pi$
$74$	−3.28110e9	−	4.51605e9i	−1.47864	−	2.03517i
$75$		0			0
$76$		−	4.65270e9i		−	1.83500i
$77$	9.72006e8	−	1.48349e9i	0.359100	−	0.548065i
$78$		0			0
$79$	2.23582e9	+	7.26461e8i	0.726609	+	0.236090i	0.648886	−	0.760885i	$-0.275235\pi$
$79$	2.23582e9	+	7.26461e8i	0.726609	+	0.236090i	0.0777230	+	0.996975i	$0.475235\pi$
$80$	−5.64341e7	+	4.10018e7i	−0.0172223	+	0.0125128i
$81$		0			0
$82$	1.54771e9	+	4.76335e9i	0.417464	+	1.28482i
$83$	1.62134e9	−	5.26804e8i	0.411607	−	0.133739i	−0.0958917	−	0.995392i	$-0.530570\pi$
$83$	1.62134e9	−	5.26804e8i	0.411607	−	0.133739i	0.507499	+	0.861653i	$0.330570\pi$
$84$		0			0
$85$	−8.25164e8	−	1.13574e9i	−0.185971	−	0.255967i
$86$	2.99390e9	−	9.21429e9i	0.636422	−	1.95871i
$87$		0			0
$88$	−3.09053e9	−	3.84843e9i	−0.585625	−	0.729240i
$89$	4.54171e9			0.813334			0.406667	−	0.913576i	$-0.366691\pi$
$89$	4.54171e9			0.813334			0.406667	+	0.913576i	$0.366691\pi$
$90$		0			0
$91$	2.97609e9	−	2.16225e9i	0.476913	−	0.346497i
$92$	8.09750e9	+	5.88318e9i	1.22860	+	0.892633i
$93$		0			0
$94$	3.52533e9	−	1.14545e9i	0.480354	−	0.156076i
$95$	−1.41847e9	+	1.95235e9i	−0.183316	+	0.252313i
$96$		0			0
$97$	−1.54774e9	+	4.76346e9i	−0.180235	+	0.554708i	−0.999834	−	0.0182309i	$-0.994197\pi$
$97$	−1.54774e9	+	4.76346e9i	−0.180235	+	0.554708i	0.819598	+	0.572938i	$0.194197\pi$
$98$		−	8.28894e9i		−	0.916998i
$99$		0			0
$100$	1.46767e10			1.46767
$101$	−2.33386e9	−	7.58316e8i	−0.222058	−	0.0721512i	0.195875	−	0.980629i	$-0.437245\pi$
$101$	−2.33386e9	−	7.58316e8i	−0.222058	−	0.0721512i	−0.417933	+	0.908478i	$0.637245\pi$
$102$		0			0
$103$	−1.57616e10	−	1.14515e10i	−1.35961	−	0.987812i	−0.998470	−	0.0552995i	$-0.982389\pi$
$103$	−1.57616e10	−	1.14515e10i	−1.35961	−	0.987812i	−0.361137	−	0.932513i	$-0.617611\pi$
$104$	−3.16356e9	−	9.73645e9i	−0.260022	−	0.800265i
$105$		0			0
$106$	2.36177e10	−	3.25070e10i	1.76485	−	2.42911i
$107$	7.03811e8	+	9.68712e8i	0.0501807	+	0.0690678i	0.833370	−	0.552716i	$-0.186408\pi$
$107$	7.03811e8	+	9.68712e8i	0.0501807	+	0.0690678i	−0.783189	+	0.621783i	$0.786408\pi$
$108$		0			0
$109$			9.65634e9i			0.627596i	0.949490	+	0.313798i	$0.101601\pi$
$109$			9.65634e9i			0.627596i	−0.949490	+	0.313798i	$0.898399\pi$
$110$	3.35870e8	+	6.95031e9i	0.0208549	+	0.431560i
$111$		0			0
$112$	−8.69481e8	−	2.82512e8i	−0.0493367	−	0.0160305i
$113$	2.43305e10	−	1.76771e10i	1.32056	−	0.959444i	0.320636	−	0.947203i	$-0.396104\pi$
$113$	2.43305e10	−	1.76771e10i	1.32056	−	0.959444i	0.999925	−	0.0122409i	$-0.00389650\pi$
$114$		0			0
$115$	−1.60425e9	−	4.93737e9i	−0.0797595	−	0.245474i
$116$	−2.31706e10	+	7.52859e9i	−1.10318	+	0.358446i
$117$		0			0
$118$	−2.45996e9	−	3.38585e9i	−0.107527	−	0.147999i
$119$	5.68557e9	−	1.74984e10i	0.238253	−	0.733268i
$120$		0			0
$121$	2.58166e10	−	2.50098e9i	0.995340	−	0.0964237i
$122$	−2.33762e10			−0.864919
$123$		0			0
$124$	−1.73531e10	+	1.26078e10i	−0.591927	+	0.430060i
$125$	−1.27971e10	−	9.29766e9i	−0.419336	−	0.304666i
$126$		0			0
$127$	1.91531e10	−	6.22323e9i	0.579724	−	0.188364i	−0.00445277	−	0.999990i	$-0.501417\pi$
$127$	1.91531e10	−	6.22323e9i	0.579724	−	0.188364i	0.584177	+	0.811626i	$0.301417\pi$
$128$	−3.13788e10	+	4.31893e10i	−0.913244	+	1.25697i
$129$		0			0
$130$	−4.45998e9	+	1.37264e10i	−0.120120	+	0.369692i
$131$			7.07549e10i			1.83400i	0.398883	+	0.917002i	$0.369398\pi$
$131$			7.07549e10i			1.83400i	−0.398883	+	0.917002i	$0.630602\pi$
$132$		0			0
$133$	−3.16279e10			−0.759997
$134$	8.93347e10	+	2.90266e10i	2.06774	+	0.671850i
$135$		0			0
$136$	−4.14243e10	−	3.00965e10i	−0.890350	−	0.646877i
$137$	−1.20231e10	−	3.70032e10i	−0.249122	−	0.766719i	−0.994931	−	0.100559i	$-0.967937\pi$
$137$	−1.20231e10	−	3.70032e10i	−0.249122	−	0.766719i	0.745809	−	0.666160i	$-0.232063\pi$
$138$		0			0
$139$	−5.87511e9	+	8.08640e9i	−0.113225	+	0.155841i	−0.861868	−	0.507132i	$-0.830706\pi$
$139$	−5.87511e9	+	8.08640e9i	−0.113225	+	0.155841i	0.748643	+	0.662973i	$0.230706\pi$
$140$	−8.81127e9	−	1.21277e10i	−0.163832	−	0.225495i
$141$		0			0
$142$			1.81367e10i			0.314136i
$143$	5.19078e10	+	1.41355e10i	0.868065	+	0.236391i
$144$		0			0
$145$	1.20180e10	+	3.90489e9i	0.187497	+	0.0609213i
$146$	−1.31023e11	+	9.51940e10i	−1.97508	+	1.43498i
$147$		0			0
$148$	5.43465e10	+	1.67261e11i	0.765355	+	2.35552i
$149$	3.57822e8	−	1.16263e8i	0.00487231	−	0.00158311i	−0.306580	−	0.951845i	$-0.599185\pi$
$149$	3.57822e8	−	1.16263e8i	0.00487231	−	0.00158311i	0.311452	+	0.950262i	$0.399185\pi$
$150$		0			0
$151$	3.29963e10	+	4.54155e10i	0.420320	+	0.578521i	0.965697	−	0.259670i	$-0.0836137\pi$
$151$	3.29963e10	+	4.54155e10i	0.420320	+	0.578521i	−0.545378	+	0.838191i	$0.683614\pi$
$152$	−2.71994e10	+	8.37110e10i	−0.335228	+	1.03173i
$153$		0			0
$154$	−7.11066e10	+	5.71030e10i	−0.820930	+	0.659258i
$155$	1.11254e10			0.124353
$156$		0			0
$157$	−3.85540e10	+	2.80111e10i	−0.404177	+	0.293652i	−0.771240	−	0.636544i	$-0.780363\pi$
$157$	−3.85540e10	+	2.80111e10i	−0.404177	+	0.293652i	0.367063	+	0.930196i	$0.380363\pi$
$158$	−9.77958e10	−	7.10528e10i	−0.993195	−	0.721598i
$159$		0			0
$160$	2.84905e10	−	9.25711e9i	0.271706	−	0.0882827i
$161$	3.99924e10	−	5.50448e10i	0.369699	−	0.508847i
$162$		0			0
$163$	5.05819e10	−	1.55675e11i	0.439599	−	1.35295i	−0.448701	−	0.893682i	$-0.648113\pi$
$163$	5.05819e10	−	1.55675e11i	0.439599	−	1.35295i	0.888300	−	0.459264i	$-0.151887\pi$
$164$		−	1.57795e11i		−	1.33007i
$165$		0			0
$166$	−8.76595e10			−0.695438
$167$	2.33212e11	+	7.57750e10i	1.79543	+	0.583370i	0.999750	−	0.0223517i	$-0.00711535\pi$
$167$	2.33212e11	+	7.57750e10i	1.79543	+	0.583370i	0.795677	+	0.605721i	$0.207115\pi$
$168$		0			0
$169$	−2.12556e10	−	1.54431e10i	−0.154184	−	0.112021i
$170$	2.23067e10	+	6.86531e10i	0.157106	+	0.483521i
$171$		0			0
$172$	−1.79416e11	+	2.46945e11i	−1.19184	+	1.64043i
$173$	−5.03347e10	−	6.92797e10i	−0.324816	−	0.447070i	0.615114	−	0.788438i	$-0.289110\pi$
$173$	−5.03347e10	−	6.92797e10i	−0.324816	−	0.447070i	−0.939930	+	0.341368i	$0.889110\pi$
$174$		0			0
$175$		−	9.97684e10i		−	0.607859i
$176$	−4.74051e9	−	1.25014e10i	−0.0280713	−	0.0740279i
$177$		0			0
$178$	−2.22105e11	−	7.21661e10i	−1.24296	−	0.403862i
$179$	1.66075e11	−	1.20661e11i	0.903731	−	0.656599i	−0.0356904	−	0.999363i	$-0.511363\pi$
$179$	1.66075e11	−	1.20661e11i	0.903731	−	0.656599i	0.939422	+	0.342764i	$0.111363\pi$
$180$		0			0
$181$	3.40584e9	+	1.04821e10i	0.0175320	+	0.0539579i	0.959440	−	0.281914i	$-0.0909692\pi$
$181$	3.40584e9	+	1.04821e10i	0.0175320	+	0.0539579i	−0.941908	+	0.335872i	$0.890969\pi$
$182$	−1.79898e11	+	5.84524e10i	−0.900886	+	0.292716i
$183$		0			0
$184$	−1.11297e11	−	1.53187e11i	−0.527709	−	0.726329i
$185$	2.81882e10	−	8.67542e10i	0.130079	−	0.400343i
$186$		0			0
$187$	2.51592e11	−	9.54032e10i	1.10024	−	0.417210i
$188$	−1.16784e11			−0.497270
$189$		0			0
$190$	1.00390e11	−	7.29376e10i	0.405436	−	0.294566i
$191$	−1.61198e11	−	1.17117e11i	−0.634151	−	0.460738i	0.223685	−	0.974662i	$-0.428191\pi$
$191$	−1.61198e11	−	1.17117e11i	−0.634151	−	0.460738i	−0.857836	+	0.513924i	$0.828191\pi$
$192$		0			0
$193$	2.24719e11	−	7.30157e10i	0.839177	−	0.272665i	0.142271	−	0.989828i	$-0.454560\pi$
$193$	2.24719e11	−	7.30157e10i	0.839177	−	0.272665i	0.696906	+	0.717163i	$0.254560\pi$
$194$	1.51380e11	−	2.08356e11i	0.550882	−	0.758224i
$195$		0			0
$196$	−8.06991e10	+	2.48366e11i	−0.278990	+	0.858642i
$197$		−	3.09846e11i		−	1.04427i	−0.852862	−	0.522137i	$-0.825135\pi$
$197$		−	3.09846e11i		−	1.04427i	0.852862	−	0.522137i	$-0.174865\pi$
$198$		0			0
$199$	−1.92515e11			−0.616876			−0.308438	−	0.951244i	$-0.599806\pi$
$199$	−1.92515e11			−0.616876			−0.308438	+	0.951244i	$0.599806\pi$
$200$	−2.64062e11	−	8.57989e10i	−0.825193	−	0.268122i
$201$		0			0
$202$	1.02084e11	+	7.41684e10i	0.303529	+	0.220527i
$203$	5.11775e10	+	1.57508e11i	0.148456	+	0.456902i
$204$		0			0
$205$	−4.81070e10	+	6.62136e10i	−0.132874	+	0.182885i
$206$	5.88834e11	+	8.10460e11i	1.58729	+	2.18472i
$207$		0			0
$208$		−	2.77314e10i		−	0.0712288i
$209$	−2.89619e11	−	3.60643e11i	−0.726266	−	0.904370i
$210$		0			0
$211$	7.03219e11	+	2.28490e11i	1.68143	+	0.546329i	0.985188	−	0.171479i	$-0.0548545\pi$
$211$	7.03219e11	+	2.28490e11i	1.68143	+	0.546329i	0.696241	+	0.717808i	$0.254854\pi$
$212$	−1.02415e12	+	7.44089e11i	−2.39158	+	1.73758i
$213$		0			0
$214$	−1.90262e10	−	5.85566e10i	−0.0423919	−	0.130469i
$215$	1.50572e11	−	4.89239e10i	0.327757	−	0.106495i
$216$		0			0
$217$	8.57044e10	+	1.17962e11i	0.178117	+	0.245157i
$218$	1.53436e11	−	4.72227e11i	0.311634	−	0.959110i
$219$		0			0
$220$	5.76027e10	−	2.11526e11i	0.111771	−	0.410441i
$221$	5.58097e11			1.05864
$222$		0			0
$223$	−4.25851e11	+	3.09399e11i	−0.772206	+	0.561040i	−0.902630	−	0.430418i	$-0.858366\pi$
$223$	−4.25851e11	+	3.09399e11i	−0.772206	+	0.561040i	0.130424	+	0.991458i	$0.458366\pi$
$224$	3.17629e11	+	2.30771e11i	0.563223	+	0.409206i
$225$		0			0
$226$	−1.47072e12	+	4.77867e11i	−2.49453	+	0.810523i
$227$	−5.98367e11	+	8.23582e11i	−0.992747	+	1.36640i	−0.0630761	+	0.998009i	$0.520091\pi$
$227$	−5.98367e11	+	8.23582e11i	−0.992747	+	1.36640i	−0.929671	+	0.368391i	$0.879909\pi$
$228$		0			0
$229$	−1.86554e11	+	5.74155e11i	−0.296229	+	0.911699i	0.686577	+	0.727057i	$0.259113\pi$
$229$	−1.86554e11	+	5.74155e11i	−0.296229	+	0.911699i	−0.982806	+	0.184642i	$0.940887\pi$
$230$			2.66945e11i			0.414746i
$231$		0			0
$232$	4.60896e11			0.685745
$233$	1.01025e12	+	3.28251e11i	1.47113	+	0.477998i	0.931449	−	0.363873i	$-0.118546\pi$
$233$	1.01025e12	+	3.28251e11i	1.47113	+	0.477998i	0.539678	+	0.841871i	$0.318546\pi$
$234$		0			0
$235$	4.90044e10	+	3.56038e10i	0.0683747	+	0.0496771i
$236$	4.07455e10	+	1.25402e11i	0.0556570	+	0.171295i
$237$		0			0
$238$	−5.56086e11	+	7.65387e11i	−0.728212	+	1.00230i
$239$	1.14369e11	+	1.57415e11i	0.146662	+	0.201863i	0.876027	−	0.482261i	$-0.160184\pi$
$239$	1.14369e11	+	1.57415e11i	0.146662	+	0.201863i	−0.729365	+	0.684125i	$0.760184\pi$
$240$		0			0
$241$		−	1.38360e12i		−	1.70187i	−0.525269	−	0.850936i	$-0.676035\pi$
$241$		−	1.38360e12i		−	1.70187i	0.525269	−	0.850936i	$-0.323965\pi$
$242$	−1.30226e12	−	2.87910e11i	−1.56899	−	0.346880i
$243$		0			0
$244$	7.00436e11	+	2.27585e11i	0.809877	+	0.263145i
$245$	1.09582e11	−	7.96160e10i	0.124139	−	0.0901925i
$246$		0			0
$247$	−2.96463e11	−	9.12420e11i	−0.322467	−	0.992453i
$248$	3.85920e11	−	1.25393e11i	0.411376	−	0.133664i
$249$		0			0
$250$	4.78086e11	+	6.58029e11i	0.489560	+	0.673821i
$251$	2.37026e11	−	7.29491e11i	0.237918	−	0.732237i	−0.758803	−	0.651320i	$-0.774215\pi$
$251$	2.37026e11	−	7.29491e11i	0.237918	−	0.732237i	0.996721	−	0.0809162i	$-0.0257846\pi$
$252$		0			0
$253$	9.93873e11	−	4.80284e10i	0.958800	−	0.0463335i
$254$	−1.03554e12			−0.979484
$255$		0			0
$256$	7.72532e11	−	5.61278e11i	0.702614	−	0.510479i
$257$	−7.09884e11	−	5.15761e11i	−0.633172	−	0.460026i	0.224326	−	0.974514i	$-0.427982\pi$
$257$	−7.09884e11	−	5.15761e11i	−0.633172	−	0.460026i	−0.857498	+	0.514488i	$0.827982\pi$
$258$		0			0
$259$	1.13700e12	−	3.69434e11i	0.975577	−	0.316984i
$260$	2.67274e11	−	3.67871e11i	0.224952	−	0.309620i
$261$		0			0
$262$	1.12427e12	−	3.46015e12i	0.910678	−	2.80278i
$263$		−	1.73051e12i		−	1.37529i	−0.726047	−	0.687645i	$-0.758645\pi$
$263$		−	1.73051e12i		−	1.37529i	0.726047	−	0.687645i	$-0.241355\pi$
$264$		0			0
$265$	6.56601e11			0.502426
$266$	1.54671e12	+	5.02556e11i	1.16145	+	0.377378i
$267$		0			0
$268$	−2.39419e12	−	1.73948e12i	−1.73175	−	1.25819i
$269$	7.37486e11	+	2.26975e12i	0.523591	+	1.61145i	0.767086	+	0.641545i	$0.221706\pi$
$269$	7.37486e11	+	2.26975e12i	0.523591	+	1.61145i	−0.243495	+	0.969902i	$0.578294\pi$
$270$		0			0
$271$	−4.49960e11	+	6.19316e11i	−0.307841	+	0.423707i	−0.934707	−	0.355420i	$-0.884338\pi$
$271$	−4.49960e11	+	6.19316e11i	−0.307841	+	0.423707i	0.626865	+	0.779128i	$0.284338\pi$
$272$	−8.15256e10	−	1.12210e11i	−0.0547583	−	0.0753683i
$273$		0			0
$274$			2.00062e12i			1.29542i
$275$	1.13763e12	−	9.13587e11i	0.723331	−	0.580880i
$276$		0			0
$277$	−8.53975e11	−	2.77473e11i	−0.523656	−	0.170146i	0.0352478	−	0.999379i	$-0.488778\pi$
$277$	−8.53975e11	−	2.77473e11i	−0.523656	−	0.170146i	−0.558904	+	0.829232i	$0.688778\pi$
$278$	4.15803e11	−	3.02098e11i	0.250417	−	0.181938i
$279$		0			0
$280$	8.76342e10	+	2.69710e11i	0.0509194	+	0.156714i
$281$	−2.34922e11	+	7.63309e10i	−0.134089	+	0.0435681i	−0.375293	−	0.926906i	$-0.622458\pi$
$281$	−2.34922e11	+	7.63309e10i	−0.134089	+	0.0435681i	0.241204	+	0.970475i	$0.422458\pi$
$282$		0			0
$283$	5.91705e11	+	8.14413e11i	0.325967	+	0.448655i	0.940277	−	0.340410i	$-0.110566\pi$
$283$	5.91705e11	+	8.14413e11i	0.325967	+	0.448655i	−0.614310	+	0.789064i	$0.710566\pi$
$284$	1.76575e11	−	5.43441e11i	0.0955734	−	0.294145i
$285$		0			0
$286$	−2.31386e12	−	1.51607e12i	−1.20922	−	0.792299i
$287$	−1.07265e12			−0.550871
$288$		0			0
$289$	6.27270e11	−	4.55738e11i	0.311147	−	0.226061i
$290$	−5.25674e11	−	3.81925e11i	−0.256287	−	0.186203i
$291$		0			0
$292$	4.85272e12	−	1.57674e12i	2.28597	−	0.742757i
$293$	−9.13332e11	+	1.25709e12i	−0.422952	+	0.582143i	−0.966317	−	0.257353i	$-0.917150\pi$
$293$	−9.13332e11	+	1.25709e12i	−0.422952	+	0.582143i	0.543366	+	0.839496i	$0.317150\pi$
$294$		0			0
$295$	2.11337e10	−	6.50429e10i	0.00945944	−	0.0291132i
$296$		−	3.32706e12i		−	1.46420i
$297$		0			0
$298$	−1.93461e10			−0.00823211
$299$	1.96283e12	+	6.37763e11i	0.821348	+	0.266872i
$300$		0			0
$301$	1.67867e12	+	1.21963e12i	0.679412	+	0.493622i
$302$	−8.91991e11	−	2.74527e12i	−0.355080	−	1.09282i
$303$		0			0
$304$	−1.40143e11	+	1.92891e11i	−0.0539765	+	0.0742923i
$305$	−2.24531e11	−	3.09040e11i	−0.0850701	−	0.117089i
$306$		0			0
$307$		−	6.56191e11i		−	0.240624i	−0.992736	−	0.120312i	$-0.961611\pi$
$307$		−	6.56191e11i		−	0.240624i	0.992736	−	0.120312i	$-0.0383894\pi$
$308$	2.68655e12	−	1.01873e12i	0.969262	−	0.367542i
$309$		0			0
$310$	−5.44068e11	−	1.76778e11i	−0.190040	−	0.0617477i
$311$	5.24312e11	−	3.80935e11i	0.180214	−	0.130933i	−0.494021	−	0.869450i	$-0.664473\pi$
$311$	5.24312e11	−	3.80935e11i	0.180214	−	0.130933i	0.674235	+	0.738517i	$0.264473\pi$
$312$		0			0
$313$	−5.12349e11	−	1.57685e12i	−0.170547	−	0.524889i	0.828855	−	0.559463i	$-0.188993\pi$
$313$	−5.12349e11	−	1.57685e12i	−0.170547	−	0.524889i	−0.999402	+	0.0345737i	$0.988993\pi$
$314$	2.33051e12	−	7.57228e11i	0.763488	−	0.248072i
$315$		0			0
$316$	2.23856e12	+	3.08111e12i	0.710449	+	0.977850i
$317$	5.34886e11	−	1.64621e12i	0.167095	−	0.514267i	−0.832089	−	0.554642i	$-0.812855\pi$
$317$	5.34886e11	−	1.64621e12i	0.167095	−	0.514267i	0.999185	+	0.0403750i	$0.0128553\pi$
$318$		0			0
$319$	−1.32738e12	+	2.02587e12i	−0.401830	+	0.613281i
$320$	−1.46894e12			−0.437778
$321$		0			0
$322$	−2.83041e12	+	2.05641e12i	−0.817654	+	0.594060i
$323$	−3.88194e12	−	2.82040e12i	−1.10417	−	0.802228i
$324$		0			0
$325$	2.87818e12	−	9.35177e11i	0.793781	−	0.257915i
$326$	−4.94724e12	+	6.80930e12i	−1.34362	+	1.84933i
$327$		0			0
$328$	−9.22460e11	+	2.83904e12i	−0.242984	+	0.747829i
$329$			7.93865e11i			0.205953i
$330$		0			0
$331$	3.53130e11			0.0888781			0.0444390	−	0.999012i	$-0.485850\pi$
$331$	3.53130e11			0.0888781			0.0444390	+	0.999012i	$0.485850\pi$
$332$	2.62659e12	+	8.53432e11i	0.651182	+	0.211582i
$333$		0			0
$334$	−1.02008e13	−	7.41130e12i	−2.45415	−	1.78305i
$335$	4.74329e11	+	1.45983e12i	0.112423	+	0.346003i
$336$		0			0
$337$	5.90465e11	−	8.12705e11i	0.135845	−	0.186975i	−0.735675	−	0.677335i	$-0.763135\pi$
$337$	5.90465e11	−	8.12705e11i	0.135845	−	0.186975i	0.871520	+	0.490360i	$0.163135\pi$
$338$	7.94084e11	+	1.09296e12i	0.180004	+	0.247755i
$339$		0			0
$340$		−	2.27427e12i		−	0.500549i
$341$	−5.60283e11	+	2.05745e12i	−0.121517	+	0.446228i
$342$		0			0
$343$	4.64683e12	+	1.50985e12i	0.978783	+	0.318026i
$344$	4.67167e12	−	3.39417e12i	0.969795	−	0.704597i
$345$		0			0
$346$	1.36070e12	+	4.18781e12i	0.274399	+	0.844514i
$347$	−2.43226e11	+	7.90290e10i	−0.0483463	+	0.0157087i	−0.333090	−	0.942895i	$-0.608091\pi$
$347$	−2.43226e11	+	7.90290e10i	−0.0483463	+	0.0157087i	0.284744	+	0.958604i	$0.408091\pi$
$348$		0			0
$349$	−2.36216e12	−	3.25123e12i	−0.456228	−	0.627944i	0.517493	−	0.855687i	$-0.326865\pi$
$349$	−2.36216e12	−	3.25123e12i	−0.456228	−	0.627944i	−0.973721	+	0.227743i	$0.926865\pi$
$350$	−1.58529e12	+	4.87901e12i	−0.301834	+	0.928948i
$351$		0			0
$352$	2.77142e11	+	5.73502e12i	0.0512848	+	1.06126i
$353$	−6.05587e12			−1.10485			−0.552425	−	0.833563i	$-0.686297\pi$
$353$	−6.05587e12			−1.10485			−0.552425	+	0.833563i	$0.686297\pi$
$354$		0			0
$355$	−2.39773e11	+	1.74205e11i	−0.0425263	+	0.0308972i
$356$	5.95246e12	+	4.32471e12i	1.04099	+	0.756323i
$357$		0			0
$358$	−1.00389e13	+	3.26183e12i	−1.70714	+	0.554685i
$359$	−3.68033e11	+	5.06554e11i	−0.0617183	+	0.0849480i	−0.838760	−	0.544501i	$-0.816719\pi$
$359$	−3.68033e11	+	5.06554e11i	−0.0617183	+	0.0849480i	0.777042	+	0.629449i	$0.216719\pi$
$360$		0			0
$361$	−6.54296e11	+	2.01371e12i	−0.106718	+	0.328444i
$362$		−	5.66727e11i		−	0.0911656i
$363$		0			0
$364$	5.95947e12			0.932612
$365$	−2.51698e12	−	8.17818e11i	−0.388522	−	0.126239i
$366$		0			0
$367$	−7.04813e12	−	5.12077e12i	−1.05863	−	0.769139i	−0.0847944	−	0.996398i	$-0.527023\pi$
$367$	−7.04813e12	−	5.12077e12i	−1.05863	−	0.769139i	−0.973834	+	0.227260i	$0.927023\pi$
$368$	−1.58499e11	−	4.87808e11i	−0.0234848	−	0.0722787i
$369$		0			0
$370$	−2.75699e12	+	3.79467e12i	−0.397582	+	0.547225i
$371$	5.05813e12	+	6.96192e12i	0.719649	+	0.990512i
$372$		0			0
$373$			1.07207e13i			1.48483i	0.669938	+	0.742417i	$0.266321\pi$
$373$			1.07207e13i			1.48483i	−0.669938	+	0.742417i	$0.733679\pi$
$374$	−1.38196e13	+	6.67825e11i	−1.88859	+	0.0912651i
$375$		0			0
$376$	2.10116e12	+	6.82709e11i	0.279589	+	0.0908440i
$377$	−4.06418e12	+	2.95280e12i	−0.533661	+	0.387728i
$378$		0			0
$379$	9.24126e10	+	2.84417e11i	0.0118178	+	0.0363713i	0.956792	−	0.290775i	$-0.0939131\pi$
$379$	9.24126e10	+	2.84417e11i	0.0118178	+	0.0363713i	−0.944974	+	0.327146i	$0.893913\pi$
$380$	−3.71815e12	+	1.20810e12i	−0.469254	+	0.152470i
$381$		0			0
$382$	6.02217e12	+	8.28880e12i	0.740348	+	1.01900i
$383$	−1.08587e12	+	3.34196e12i	−0.131760	+	0.405515i	−0.995072	−	0.0991554i	$-0.968386\pi$
$383$	−1.08587e12	+	3.34196e12i	−0.131760	+	0.405515i	0.863312	+	0.504670i	$0.168386\pi$
$384$		0			0
$385$	−1.43790e12	−	3.91569e11i	−0.169991	−	0.0462919i
$386$	−1.21497e13			−1.41785
$387$		0			0
$388$	−6.56438e12	+	4.76930e12i	−0.746509	+	0.542371i
$389$	8.46992e12	+	6.15376e12i	0.950893	+	0.690864i	0.951018	−	0.309136i	$-0.100040\pi$
$389$	8.46992e12	+	6.15376e12i	0.950893	+	0.690864i	−0.000125210		1.00000i	$0.500040\pi$
$390$		0			0
$391$	9.81718e12	−	3.18979e12i	1.07424	−	0.349043i
$392$	2.90387e12	−	3.99683e12i	0.313723	−	0.431802i
$393$		0			0
$394$	−4.92334e12	+	1.51525e13i	−0.518536	+	1.59589i
$395$		−	1.97536e12i		−	0.205428i
$396$		0			0
$397$	−1.72874e13			−1.75298			−0.876492	−	0.481416i	$-0.840123\pi$
$397$	−1.72874e13			−1.75298			−0.876492	+	0.481416i	$0.840123\pi$
$398$	9.41460e12	+	3.05899e12i	0.942729	+	0.306311i
$399$		0			0
$400$	−6.08464e11	−	4.42075e11i	−0.0594203	−	0.0431714i
$401$	1.26528e12	+	3.89412e12i	0.122029	+	0.375567i	0.993348	−	0.115150i	$-0.0367349\pi$
$401$	1.26528e12	+	3.89412e12i	0.122029	+	0.375567i	−0.871319	+	0.490717i	$0.836735\pi$
$402$		0			0
$403$	−2.59969e12	+	3.57817e12i	−0.244566	+	0.336616i
$404$	−2.33672e12	−	3.21622e12i	−0.217120	−	0.298840i
$405$		0			0
$406$		−	8.51587e12i		−	0.771967i
$407$	1.46241e13	+	9.58193e12i	1.30948	+	0.857988i
$408$		0			0
$409$	1.65960e13	+	5.39237e12i	1.45006	+	0.471155i	0.925019	−	0.379920i	$-0.124048\pi$
$409$	1.65960e13	+	5.39237e12i	1.45006	+	0.471155i	0.525045	+	0.851074i	$0.324048\pi$
$410$	3.40470e12	−	2.47366e12i	0.293873	−	0.213511i
$411$		0			0
$412$	−9.75313e12	−	3.00170e13i	−0.821595	−	2.52861i
$413$	8.52451e11	−	2.76978e11i	0.0709446	−	0.0230513i
$414$		0			0
$415$	−8.41978e11	−	1.15888e12i	−0.0684007	−	0.0941454i
$416$	−3.68013e12	+	1.13263e13i	−0.295391	+	0.909119i
$417$		0			0
$418$	8.43283e12	+	2.22386e13i	0.660834	+	1.74271i
$419$	8.69601e12			0.673364			0.336682	−	0.941618i	$-0.390695\pi$
$419$	8.69601e12			0.673364			0.336682	+	0.941618i	$0.390695\pi$
$420$		0			0
$421$	1.73698e13	−	1.26199e13i	1.31336	−	0.954215i	0.313375	−	0.949630i	$-0.398540\pi$
$421$	1.73698e13	−	1.26199e13i	1.31336	−	0.954215i	0.999989	−	0.00458541i	$-0.00145959\pi$
$422$	−3.07591e13	−	2.23478e13i	−2.29833	−	1.66983i
$423$		0			0
$424$	2.27763e13	−	7.40048e12i	1.66209	−	0.540046i
$425$	8.89679e12	−	1.22454e13i	0.641636	−	0.883136i
$426$		0			0
$427$	1.54707e12	−	4.76139e12i	0.108986	−	0.335424i
$428$			1.93980e12i			0.135063i
$429$		0			0
$430$	−8.14087e12			−0.553769
$431$	−1.97081e13	−	6.40356e12i	−1.32513	−	0.430561i	−0.440878	−	0.897567i	$-0.645333\pi$
$431$	−1.97081e13	−	6.40356e12i	−1.32513	−	0.430561i	−0.884254	+	0.467006i	$0.845333\pi$
$432$		0			0
$433$	7.02019e12	+	5.10047e12i	0.461222	+	0.335097i	0.794010	−	0.607904i	$-0.207990\pi$
$433$	7.02019e12	+	5.10047e12i	0.461222	+	0.335097i	−0.332789	+	0.943001i	$0.607990\pi$
$434$	−2.31686e12	−	7.13055e12i	−0.150470	−	0.463100i
$435$		0			0
$436$	−9.19498e12	+	1.26558e13i	−0.583604	+	0.803262i
$437$	−1.04298e13	−	1.43554e13i	−0.654441	−	0.900761i
$438$		0			0
$439$		−	4.19959e12i		−	0.257564i	−0.991673	−	0.128782i	$-0.958893\pi$
$439$		−	4.19959e12i		−	0.257564i	0.991673	−	0.128782i	$-0.0411067\pi$
$440$	−2.27295e12	+	3.46902e12i	−0.137825	+	0.210351i
$441$		0			0
$442$	−2.72928e13	−	8.86797e12i	−1.61784	−	0.525670i
$443$	2.32598e12	−	1.68992e12i	0.136328	−	0.0990484i	−0.517531	−	0.855664i	$-0.673149\pi$
$443$	2.32598e12	−	1.68992e12i	0.136328	−	0.0990484i	0.653859	+	0.756616i	$0.273149\pi$
$444$		0			0
$445$	−1.17928e12	−	3.62945e12i	−0.0675797	−	0.207989i
$446$	2.57418e13	−	8.36400e12i	1.45869	−	0.473958i
$447$		0			0
$448$	−1.13160e13	−	1.55751e13i	−0.627051	−	0.863061i
$449$	1.02593e12	−	3.15750e12i	0.0562196	−	0.173026i	−0.919004	−	0.394249i	$-0.871005\pi$
$449$	1.02593e12	−	3.15750e12i	0.0562196	−	0.173026i	0.975223	+	0.221223i	$0.0710048\pi$
$450$		0			0
$451$	−9.82236e12	−	1.22311e13i	−0.526421	−	0.655517i
$452$	4.87206e13			2.58238
$453$		0			0
$454$	4.23486e13	−	3.07681e13i	2.19563	−	1.59522i
$455$	−2.50070e12	−	1.81686e12i	−0.128234	−	0.0931676i
$456$		0			0
$457$	2.12756e13	−	6.91285e12i	1.06733	−	0.346798i	0.277885	−	0.960614i	$-0.410367\pi$
$457$	2.12756e13	−	6.91285e12i	1.06733	−	0.346798i	0.789449	+	0.613817i	$0.210367\pi$
$458$	1.82462e13	−	2.51138e13i	0.905412	−	1.24619i
$459$		0			0
$460$	2.59891e12	−	7.99862e12i	0.126183	−	0.388352i
$461$		−	3.55379e13i		−	1.70682i	−0.521242	−	0.853409i	$-0.674531\pi$
$461$		−	3.55379e13i		−	1.70682i	0.521242	−	0.853409i	$-0.325469\pi$
$462$		0			0
$463$	2.97354e13			1.39755			0.698776	−	0.715340i	$-0.253728\pi$
$463$	2.97354e13			1.39755			0.698776	+	0.715340i	$0.253728\pi$
$464$	1.18737e12	+	3.85801e11i	0.0552074	+	0.0179380i
$465$		0			0
$466$	−4.41889e13	−	3.21051e13i	−2.01087	−	1.46098i
$467$	−7.14379e12	−	2.19863e13i	−0.321621	−	0.989847i	−0.972943	−	0.231046i	$-0.925785\pi$
$467$	−7.14379e12	−	2.19863e13i	−0.321621	−	0.989847i	0.651322	−	0.758802i	$-0.274215\pi$
$468$		0			0
$469$	−1.18246e13	+	1.62751e13i	−0.521100	+	0.717233i
$470$	−1.83075e12	−	2.51981e12i	−0.0798250	−	0.109870i
$471$		0			0
$472$		−	2.49442e12i		−	0.106478i
$473$	1.46469e12	+	3.03096e13i	0.0618645	+	1.28019i
$474$		0			0
$475$	−2.47457e13	−	8.04036e12i	−1.02337	−	0.332512i
$476$	2.41140e13	−	1.75198e13i	0.986811	−	0.716960i
$477$		0			0
$478$	−3.09174e12	−	9.51541e12i	−0.123898	−	0.381319i
$479$	−8.37932e12	+	2.72260e12i	−0.332301	+	0.107971i	−0.470415	−	0.882445i	$-0.655896\pi$
$479$	−8.37932e12	+	2.72260e12i	−0.332301	+	0.107971i	0.138115	+	0.990416i	$0.455896\pi$
$480$		0			0
$481$	2.13153e13	+	2.93380e13i	0.827877	+	1.13947i
$482$	−2.19850e13	+	6.76629e13i	−0.845068	+	2.60085i
$483$		0			0
$484$	3.62172e13	+	2.13053e13i	1.36360	+	0.802159i
$485$	4.20854e12			0.156828
$486$		0			0
$487$	2.84053e13	−	2.06377e13i	1.03694	−	0.753384i	0.0672572	−	0.997736i	$-0.478575\pi$
$487$	2.84053e13	−	2.06377e13i	1.03694	−	0.753384i	0.969687	+	0.244352i	$0.0785752\pi$
$488$	−1.12717e13	−	8.18940e12i	−0.407279	−	0.295906i
$489$		0			0
$490$	−6.62400e12	+	2.15227e12i	−0.234498	+	0.0761932i
$491$	1.06722e13	−	1.46891e13i	0.373979	−	0.514738i	−0.579998	−	0.814618i	$-0.696947\pi$
$491$	1.06722e13	−	1.46891e13i	0.373979	−	0.514738i	0.953977	+	0.299880i	$0.0969466\pi$
$492$		0			0
$493$	−7.76427e12	+	2.38960e13i	−0.266604	+	0.820521i
$494$			4.93311e13i			1.67682i
$495$		0			0
$496$	1.09918e12			0.0366151
$497$	−3.69418e12	−	1.20031e12i	−0.121825	−	0.0395833i
$498$		0			0
$499$	−1.12576e13	−	8.17913e12i	−0.363867	−	0.264365i	0.390796	−	0.920477i	$-0.372200\pi$
$499$	−1.12576e13	−	8.17913e12i	−0.363867	−	0.264365i	−0.754663	+	0.656112i	$0.772200\pi$
$500$	−7.91876e12	−	2.43714e13i	−0.253400	−	0.779886i
$501$		0			0
$502$	−2.31827e13	+	3.19083e13i	−0.727187	+	1.00089i
$503$	3.43743e13	+	4.73121e13i	1.06756	+	1.46937i	0.872519	+	0.488580i	$0.162485\pi$
$503$	3.43743e13	+	4.73121e13i	1.06756	+	1.46937i	0.195044	+	0.980795i	$0.437515\pi$
$504$		0			0
$505$			2.06197e12i			0.0627807i
$506$	−4.93668e13	−	1.34436e13i	−1.48827	−	0.405286i
$507$		0			0
$508$	3.10284e13	+	1.00817e13i	0.917152	+	0.298001i
$509$	3.73531e13	−	2.71386e13i	1.09330	−	0.794326i	0.113344	−	0.993556i	$-0.463844\pi$
$509$	3.73531e13	−	2.71386e13i	1.09330	−	0.794326i	0.979953	+	0.199229i	$0.0638439\pi$
$510$		0			0
$511$	−1.07183e13	−	3.29876e13i	−0.307625	−	0.946773i
$512$	5.29264e12	−	1.71968e12i	0.150426	−	0.0488763i
$513$		0			0
$514$	2.65204e13	+	3.65022e13i	0.739205	+	1.01743i
$515$	−5.05871e12	+	1.55691e13i	−0.139638	+	0.429761i
$516$		0			0
$517$	−9.05220e12	+	7.26948e12i	−0.245076	+	0.196812i
$518$	−6.14733e13			−1.64830
$519$		0			0
$520$	−6.95933e12	+	5.05625e12i	−0.183042	+	0.132988i
$521$	−8.31906e12	−	6.04415e12i	−0.216713	−	0.157452i	0.474133	−	0.880453i	$-0.342762\pi$
$521$	−8.31906e12	−	6.04415e12i	−0.216713	−	0.157452i	−0.690846	+	0.723002i	$0.742762\pi$
$522$		0			0
$523$	6.41826e13	−	2.08542e13i	1.64025	−	0.532948i	0.663652	−	0.748041i	$-0.269005\pi$
$523$	6.41826e13	−	2.08542e13i	1.64025	−	0.532948i	0.976594	+	0.215093i	$0.0690054\pi$
$524$	−6.73744e13	+	9.27330e13i	−1.70545	+	2.34735i
$525$		0			0
$526$	−2.74971e13	+	8.46275e13i	−0.682903	+	2.10176i
$527$			2.21211e13i			0.544193i
$528$		0			0
$529$	−3.25426e12			−0.0785550
$530$	−3.21100e13	−	1.04332e13i	−0.767823	−	0.249481i
$531$		0			0
$532$	−4.14522e13	−	3.01168e13i	−0.972723	−	0.706725i
$533$	−1.00545e13	−	3.09445e13i	−0.233735	−	0.719362i
$534$		0			0
$535$	5.91386e11	−	8.13973e11i	0.0134928	−	0.0185712i
$536$	3.29073e13	+	4.52930e13i	0.743820	+	1.02378i
$537$		0			0
$538$		−	1.22717e14i		−	2.72265i
$539$	9.20498e12	+	2.42749e13i	0.202339	+	0.533596i
$540$		0			0
$541$	3.43288e12	+	1.11541e12i	0.0740751	+	0.0240685i	0.345820	−	0.938301i	$-0.387601\pi$
$541$	3.43288e12	+	1.11541e12i	0.0740751	+	0.0240685i	−0.271745	+	0.962369i	$0.587601\pi$
$542$	3.18452e13	−	2.31369e13i	0.680845	−	0.494663i
$543$		0			0
$544$	1.84063e13	+	5.66488e13i	0.386342	+	1.18904i
$545$	7.71674e12	−	2.50732e12i	0.160491	−	0.0521468i
$546$		0			0
$547$	−1.52390e13	−	2.09747e13i	−0.311186	−	0.428311i	0.624565	−	0.780973i	$-0.285276\pi$
$547$	−1.52390e13	−	2.09747e13i	−0.311186	−	0.428311i	−0.935751	+	0.352662i	$0.885276\pi$
$548$	1.94776e13	−	5.99458e13i	0.394123	−	1.21299i
$549$		0			0
$550$	−7.01504e13	+	2.66009e13i	−1.39385	+	0.528546i
$551$	4.31914e13			0.850430
$552$		0			0
$553$	2.09446e13	−	1.52172e13i	0.404993	−	0.294244i
$554$	3.73533e13	+	2.71387e13i	0.715780	+	0.520045i
$555$		0			0
$556$	−1.54001e13	+	5.00380e12i	−0.289834	+	0.0941728i
$557$	−4.06274e12	+	5.59189e12i	−0.0757780	+	0.104300i	−0.845223	−	0.534413i	$-0.820533\pi$
$557$	−4.06274e12	+	5.59189e12i	−0.0757780	+	0.104300i	0.769445	+	0.638713i	$0.220533\pi$
$558$		0			0
$559$	−1.94495e13	+	5.98594e13i	−0.356328	+	1.09666i
$560$			7.68191e11i			0.0139485i
$561$		0			0
$562$	1.27014e13			0.226552
$563$	−3.54065e13	−	1.15043e13i	−0.625952	−	0.203384i	−0.0211708	−	0.999776i	$-0.506739\pi$
$563$	−3.54065e13	−	1.15043e13i	−0.625952	−	0.203384i	−0.604781	+	0.796392i	$0.706739\pi$
$564$		0			0
$565$	−2.04440e13	−	1.48534e13i	−0.355078	−	0.257979i
$566$	−1.59956e13	−	4.92295e13i	−0.275372	−	0.847507i
$567$		0			0
$568$	−6.35384e12	+	8.74531e12i	−0.107472	+	0.147922i
$569$	8.51221e12	+	1.17161e13i	0.142719	+	0.196436i	0.874392	−	0.485220i	$-0.161260\pi$
$569$	8.51221e12	+	1.17161e13i	0.142719	+	0.196436i	−0.731673	+	0.681655i	$0.761260\pi$
$570$		0			0
$571$		−	1.02782e13i		−	0.169330i	−0.996409	−	0.0846652i	$-0.973018\pi$
$571$		−	1.02782e13i		−	0.169330i	0.996409	−	0.0846652i	$-0.0269821\pi$
$572$	5.45713e13	+	6.79540e13i	0.891219	+	1.10978i
$573$		0			0
$574$	5.24563e13	+	1.70441e13i	0.841857	+	0.273536i
$575$	4.52835e13	−	3.29004e13i	0.720444	−	0.523434i
$576$		0			0
$577$	−2.23416e13	−	6.87603e13i	−0.349329	−	1.07512i	−0.959225	−	0.282643i	$-0.908789\pi$
$577$	−2.23416e13	−	6.87603e13i	−0.349329	−	1.07512i	0.609896	−	0.792481i	$-0.291211\pi$
$578$	−3.79171e13	+	1.23200e13i	−0.587754	+	0.190973i
$579$		0			0
$580$	1.20328e13	+	1.65617e13i	0.183327	+	0.252327i
$581$	5.80142e12	−	1.78549e13i	0.0876301	−	0.269698i
$582$		0			0
$583$	−3.30670e13	+	1.21427e14i	−0.490966	+	1.80291i
$584$	−9.65273e13			−1.42097
$585$		0			0
$586$	6.46398e13	−	4.69636e13i	0.935431	−	0.679630i
$587$	−6.47188e13	−	4.70210e13i	−0.928624	−	0.674685i	0.0170316	−	0.999855i	$-0.494578\pi$
$587$	−6.47188e13	−	4.70210e13i	−0.928624	−	0.674685i	−0.945656	+	0.325170i	$0.894578\pi$
$588$		0			0
$589$	3.61652e13	−	1.17508e13i	0.510170	−	0.165764i
$590$	−2.06702e12	+	2.84501e12i	−0.0289124	+	0.0397945i
$591$		0			0
$592$	2.78497e12	−	8.57126e12i	0.0383012	−	0.117879i
$593$		−	2.33053e13i		−	0.317820i	−0.987293	−	0.158910i	$-0.949202\pi$
$593$		−	2.33053e13i		−	0.317820i	0.987293	−	0.158910i	$-0.0507980\pi$
$594$		0			0
$595$	−1.54599e13			−0.207311
$596$	5.79677e11	+	1.88349e11i	0.00770824	+	0.00250456i
$597$		0			0
$598$	−8.58552e13	−	6.23775e13i	−1.12269	−	0.815684i
$599$	7.53121e12	+	2.31787e13i	0.0976631	+	0.300576i	0.987939	−	0.154846i	$-0.0494882\pi$
$599$	7.53121e12	+	2.31787e13i	0.0976631	+	0.300576i	−0.890275	+	0.455422i	$0.849488\pi$
$600$		0			0
$601$	4.80361e13	−	6.61161e13i	0.612627	−	0.843208i	−0.384164	−	0.923265i	$-0.625510\pi$
$601$	4.80361e13	−	6.61161e13i	0.612627	−	0.843208i	0.996790	+	0.0800569i	$0.0255102\pi$
$602$	−6.27132e13	−	8.63173e13i	−0.793189	−	1.09173i
$603$		0			0
$604$			9.09423e13i			1.13131i
$605$	−8.70204e12	−	1.99816e13i	−0.107360	−	0.246521i
$606$		0			0
$607$	−8.41378e13	−	2.73380e13i	−1.02105	−	0.331760i	−0.249805	−	0.968296i	$-0.580367\pi$
$607$	−8.41378e13	−	2.73380e13i	−1.02105	−	0.331760i	−0.771247	+	0.636536i	$0.780367\pi$
$608$	8.28363e13	−	6.01841e13i	0.997018	−	0.724376i
$609$		0			0
$610$	6.06977e12	+	1.86808e13i	0.0718659	+	0.221181i
$611$	−2.29019e13	+	7.44128e12i	−0.268946	+	0.0873859i
$612$		0			0
$613$	4.18720e13	+	5.76318e13i	0.483750	+	0.665825i	0.979220	−	0.202800i	$-0.0650041\pi$
$613$	4.18720e13	+	5.76318e13i	0.483750	+	0.665825i	−0.495470	+	0.868625i	$0.665004\pi$
$614$	−1.04266e13	+	3.20899e13i	−0.119482	+	0.367728i
$615$		0			0
$616$	−5.42917e13	+	2.62361e12i	−0.612110	+	0.0295799i
$617$	6.17669e13			0.690764			0.345382	−	0.938462i	$-0.387749\pi$
$617$	6.17669e13			0.690764			0.345382	+	0.938462i	$0.387749\pi$
$618$		0			0
$619$	−1.23298e14	+	8.95812e13i	−1.35676	+	0.985743i	−0.358115	+	0.933677i	$0.616580\pi$
$619$	−1.23298e14	+	8.95812e13i	−1.35676	+	0.985743i	−0.998644	+	0.0520655i	$0.983420\pi$
$620$	1.45812e13	+	1.05938e13i	0.159160	+	0.115636i
$621$		0			0
$622$	−3.16935e13	+	1.02979e13i	−0.340423	+	0.110610i
$623$	2.93983e13	−	4.04633e13i	0.313244	−	0.431143i
$624$		0			0
$625$	2.32322e13	−	7.15015e13i	0.243608	−	0.749747i
$626$			8.52541e13i			0.886837i
$627$		0			0
$628$	−7.72025e13			−0.790375
$629$	1.72497e14	+	5.60477e13i	1.75198	+	0.569252i
$630$		0			0
$631$	−1.34606e13	−	9.77967e12i	−0.134560	−	0.0977636i	0.518469	−	0.855096i	$-0.326502\pi$
$631$	−1.34606e13	−	9.77967e12i	−0.134560	−	0.0977636i	−0.653029	+	0.757333i	$0.726502\pi$
$632$	−2.22640e13	−	6.85216e13i	−0.220810	−	0.679583i
$633$		0			0
$634$	−5.23154e13	+	7.20059e13i	−0.510720	+	0.702946i
$635$	−9.94644e12	−	1.36901e13i	−0.0963383	−	0.132598i
$636$		0			0
$637$			5.38480e13i			0.513420i
$638$	9.71038e13	−	7.79804e13i	0.918614	−	0.737704i
$639$		0			0
$640$	4.26619e13	+	1.38617e13i	0.397319	+	0.129097i
$641$	−1.73128e14	+	1.25785e14i	−1.59984	+	1.16235i	−0.712033	+	0.702146i	$0.752225\pi$
$641$	−1.73128e14	+	1.25785e14i	−1.59984	+	1.16235i	−0.887811	+	0.460208i	$0.847775\pi$
$642$		0			0
$643$	1.18502e13	+	3.64713e13i	0.107813	+	0.331815i	0.990380	−	0.138371i	$-0.0441867\pi$
$643$	1.18502e13	+	3.64713e13i	0.107813	+	0.331815i	−0.882567	+	0.470186i	$0.844187\pi$
$644$	1.04830e14	−	3.40613e13i	0.946358	−	0.307490i
$645$		0			0
$646$	1.45025e14	+	1.99610e14i	1.28908	+	1.77427i
$647$	−1.83688e13	+	5.65334e13i	−0.162017	+	0.498636i	−0.998804	−	0.0488918i	$-0.984431\pi$
$647$	−1.83688e13	+	5.65334e13i	−0.162017	+	0.498636i	0.836787	+	0.547528i	$0.184431\pi$
$648$		0			0
$649$	1.09643e13	+	7.18393e12i	0.0952260	+	0.0623934i
$650$	−1.55612e14			−1.34115
$651$		0			0
$652$	2.14531e14	−	1.55866e14i	1.82076	−	1.32286i
$653$	−1.13489e14	−	8.24549e13i	−0.955849	−	0.694465i	−0.00366602	−	0.999993i	$-0.501167\pi$
$653$	−1.13489e14	−	8.24549e13i	−0.955849	−	0.694465i	−0.952183	+	0.305528i	$0.901167\pi$
$654$		0			0
$655$	5.65429e13	−	1.83719e13i	0.468999	−	0.152387i
$656$	−4.75293e12	+	6.54185e12i	−0.0391239	+	0.0538495i
$657$		0			0
$658$	1.26142e13	−	3.88227e13i	0.102266	−	0.314743i
$659$		−	3.84162e13i		−	0.309092i	−0.987986	−	0.154546i	$-0.950609\pi$
$659$		−	3.84162e13i		−	0.309092i	0.987986	−	0.154546i	$-0.0493914\pi$
$660$		0			0
$661$	−2.10584e14			−1.66885			−0.834427	−	0.551118i	$-0.814201\pi$
$661$	−2.10584e14			−1.66885			−0.834427	+	0.551118i	$0.814201\pi$
$662$	−1.72692e13	−	5.61111e12i	−0.135826	−	0.0441326i
$663$		0			0
$664$	−4.22684e13	−	3.07098e13i	−0.327473	−	0.237923i
$665$	8.21236e12	+	2.52750e13i	0.0631480	+	0.194350i
$666$		0			0
$667$	−5.46140e13	+	7.51698e13i	−0.413690	+	0.569395i
$668$	2.33497e14	+	3.21382e14i	1.75550	+	2.41623i
$669$		0			0
$670$		−	7.89277e13i		−	0.584595i
$671$	6.84593e13	−	2.59596e13i	0.503292	−	0.190847i
$672$		0			0
$673$	1.09076e14	+	3.54408e13i	0.790046	+	0.256702i	0.676124	−	0.736788i	$-0.263658\pi$
$673$	1.09076e14	+	3.54408e13i	0.790046	+	0.256702i	0.113923	+	0.993490i	$0.463658\pi$
$674$	−4.17893e13	+	3.03617e13i	−0.300445	+	0.218286i
$675$		0			0
$676$	−1.31528e13	−	4.04801e13i	−0.0931717	−	0.286753i
$677$	7.13999e13	−	2.31992e13i	0.502058	−	0.163129i	−0.0470292	−	0.998894i	$-0.514975\pi$
$677$	7.13999e13	−	2.31992e13i	0.502058	−	0.163129i	0.549087	+	0.835765i	$0.314975\pi$
$678$		0			0
$679$	3.24205e13	+	4.46230e13i	0.224632	+	0.309179i
$680$	−1.32952e13	+	4.09185e13i	−0.0914430	+	0.281433i
$681$		0			0
$682$	6.00919e13	−	9.17134e13i	0.407281	−	0.621600i
$683$	−2.09453e14			−1.40924			−0.704618	−	0.709587i	$-0.748882\pi$
$683$	−2.09453e14			−1.40924			−0.704618	+	0.709587i	$0.748882\pi$
$684$		0			0
$685$	−2.64488e13	+	1.92162e13i	−0.175369	+	0.127413i
$686$	−2.03255e14	−	1.47673e14i	−1.33789	−	0.972033i
$687$		0			0
$688$	1.48764e13	−	4.83364e12i	0.0965064	−	0.0313568i
$689$	−1.53429e14	+	2.11177e14i	−0.988126	+	1.36004i
$690$		0			0
$691$	−1.61632e13	+	4.97451e13i	−0.102597	+	0.315762i	−0.989159	−	0.146848i	$-0.953087\pi$
$691$	−1.61632e13	+	4.97451e13i	−0.102597	+	0.315762i	0.886562	+	0.462610i	$0.153087\pi$
$692$		−	1.38729e14i		−	0.874254i
$693$		0			0
$694$	1.31503e13			0.0816843
$695$	7.98765e12	+	2.59535e12i	0.0492601	+	0.0160056i
$696$		0			0
$697$	−1.31655e14	−	9.56532e13i	−0.800340	−	0.581481i
$698$	6.38565e13	+	1.96530e14i	0.385414	+	1.18618i
$699$		0			0
$700$	9.50017e13	−	1.30759e14i	0.565251	−	0.778001i
$701$	−7.64905e13	−	1.05280e14i	−0.451874	−	0.621952i	0.520925	−	0.853603i	$-0.325587\pi$
$701$	−7.64905e13	−	1.05280e14i	−0.451874	−	0.621952i	−0.972799	+	0.231651i	$0.925587\pi$
$702$		0			0
$703$		−	3.11784e14i		−	1.81584i
$704$	7.39770e13	−	2.71655e14i	0.427793	−	1.57092i
$705$		0			0
$706$	2.96152e14	+	9.62257e13i	1.68846	+	0.548615i
$707$	−2.18630e13	+	1.58844e13i	−0.123769	+	0.0899238i
$708$		0			0
$709$	−2.27631e13	−	7.00577e13i	−0.127058	−	0.391043i	0.867213	−	0.497938i	$-0.165909\pi$
$709$	−2.27631e13	−	7.00577e13i	−0.127058	−	0.391043i	−0.994270	+	0.106895i	$0.965909\pi$
$710$	1.44937e13	−	4.70930e12i	0.0803320	−	0.0261015i
$711$		0			0
$712$	−8.18142e13	−	1.12608e14i	−0.447125	−	0.615415i
$713$	−2.52788e13	+	7.78000e13i	−0.137185	+	0.422214i
$714$		0			0
$715$	−2.18194e12	−	4.51518e13i	−0.0116765	−	0.241627i
$716$	3.32557e14			1.76726
$717$		0			0
$718$	2.60470e13	−	1.89242e13i	0.136501	−	0.0991737i
$719$	−5.87141e13	−	4.26583e13i	−0.305561	−	0.222003i	0.424428	−	0.905462i	$-0.360475\pi$
$719$	−5.87141e13	−	4.26583e13i	−0.305561	−	0.222003i	−0.729989	+	0.683458i	$0.760475\pi$
$720$		0			0
$721$	−2.04048e14	+	6.62993e13i	−1.04727	+	0.340277i
$722$	6.39945e13	−	8.80808e13i	0.326179	−	0.448947i
$723$		0			0
$724$	−5.51752e12	+	1.69812e13i	−0.0277365	+	0.0853641i
$725$			1.36245e14i			0.680189i
$726$		0			0
$727$	8.09116e12			0.0398418			0.0199209	−	0.999802i	$-0.493659\pi$
$727$	8.09116e12			0.0398418			0.0199209	+	0.999802i	$0.493659\pi$
$728$	−1.07222e14	−	3.48387e13i	−0.524359	−	0.170375i
$729$		0			0
$730$	1.10094e14	+	7.99880e13i	0.531067	+	0.385843i
$731$	9.72774e13	+	2.99389e14i	0.466042	+	1.43433i
$732$		0			0
$733$	−1.64098e14	+	2.25861e14i	−0.775502	+	1.06739i	0.220261	+	0.975441i	$0.429309\pi$
$733$	−1.64098e14	+	2.25861e14i	−0.775502	+	1.06739i	−0.995764	+	0.0919467i	$0.970691\pi$
$734$	2.63310e14	+	3.62415e14i	1.23591	+	1.70108i
$735$		0			0
$736$			2.20268e14i			1.01991i
$737$	−2.93859e14	+	1.42006e13i	−1.35145	+	0.0653083i
$738$		0			0
$739$	−4.66433e12	−	1.51553e12i	−0.0211625	−	0.00687611i	0.298417	−	0.954436i	$-0.403542\pi$
$739$	−4.66433e12	−	1.51553e12i	−0.0211625	−	0.00687611i	−0.319579	+	0.947560i	$0.603542\pi$
$740$	1.19553e14	−	8.68606e13i	0.538770	−	0.391439i
$741$		0			0
$742$	−1.36737e14	−	4.20833e14i	−0.607948	−	1.87107i
$743$	−1.66179e14	+	5.39948e13i	−0.733892	+	0.238456i	−0.652036	−	0.758188i	$-0.726085\pi$
$743$	−1.66179e14	+	5.39948e13i	−0.733892	+	0.238456i	−0.0818560	+	0.996644i	$0.526085\pi$
$744$		0			0
$745$	−1.85821e11	−	2.55760e11i	−0.000809679	−	0.00111443i
$746$	1.70348e14	−	5.24277e14i	0.737297	−	2.26917i
$747$		0			0
$748$	4.20587e14	+	1.14534e14i	1.79617	+	0.489132i
$749$	1.31863e13			0.0559388
$750$		0			0
$751$	−1.23758e14	+	8.99154e13i	−0.518052	+	0.376387i	−0.815870	−	0.578236i	$-0.803741\pi$
$751$	−1.23758e14	+	8.99154e13i	−0.518052	+	0.376387i	0.297818	+	0.954623i	$0.403741\pi$
$752$	4.84160e12	+	3.51762e12i	0.0201326	+	0.0146272i
$753$		0			0
$754$	2.45671e14	−	7.98232e13i	1.00808	−	0.327546i
$755$	2.77255e13	−	3.81609e13i	0.113017	−	0.155555i
$756$		0			0
$757$	−3.48323e13	+	1.07203e14i	−0.140121	+	0.431247i	−0.996351	−	0.0853467i	$-0.972800\pi$
$757$	−3.48323e13	+	1.07203e14i	−0.140121	+	0.431247i	0.856231	+	0.516594i	$0.172800\pi$
$758$		−	1.53773e13i		−	0.0614519i
$759$		0			0
$760$	7.39591e13			0.291691
$761$	5.76404e13	+	1.87285e13i	0.225841	+	0.0733803i	0.419752	−	0.907639i	$-0.362117\pi$
$761$	5.76404e13	+	1.87285e13i	0.225841	+	0.0733803i	−0.193910	+	0.981019i	$0.562117\pi$
$762$		0			0
$763$	8.60310e13	+	6.25052e13i	0.332684	+	0.241709i
$764$	−9.97479e13	−	3.06993e14i	−0.383210	−	1.17940i
$765$		0			0
$766$	1.06205e14	−	1.46179e14i	0.402718	−	0.554294i
$767$	1.59809e13	+	2.19958e13i	0.0602037	+	0.0828633i
$768$		0			0
$769$			1.11982e14i			0.416406i	0.978086	+	0.208203i	$0.0667615\pi$
$769$			1.11982e14i			0.416406i	−0.978086	+	0.208203i	$0.933239\pi$
$770$	6.40964e13	+	4.19968e13i	0.236799	+	0.155154i
$771$		0			0
$772$	3.64049e14	+	1.18287e14i	1.32762	+	0.431369i
$773$	4.47527e13	−	3.25147e13i	0.162152	−	0.117810i	−0.503750	−	0.863849i	$-0.668047\pi$
$773$	4.47527e13	−	3.25147e13i	0.162152	−	0.117810i	0.665902	+	0.746039i	$0.268047\pi$
$774$		0			0
$775$	3.70672e13	+	1.14081e14i	0.132581	+	0.408043i
$776$	1.45987e14	−	4.74340e13i	0.518806	−	0.168570i
$777$		0			0
$778$	−3.16426e14	−	4.35524e14i	−1.11013	−	1.52797i
$779$	−8.64454e13	+	2.66051e14i	−0.301338	+	0.927424i
$780$		0			0
$781$	−2.01411e13	−	5.31149e13i	−0.0693151	−	0.182794i
$782$	−5.30778e14			−1.81501
$783$		0			0
$784$	1.08266e13	−	7.86601e12i	0.0365522	−	0.0265567i
$785$	3.23955e13	+	2.35367e13i	0.108677	+	0.0789583i
$786$		0			0
$787$	−3.08376e14	+	1.00197e14i	−1.02143	+	0.331882i	−0.771395	−	0.636356i	$-0.780441\pi$
$787$	−3.08376e14	+	1.00197e14i	−1.02143	+	0.331882i	−0.250031	+	0.968238i	$0.580441\pi$
$788$	2.95042e14	−	4.06091e14i	0.971075	−	1.33657i
$789$		0			0
$790$	−3.13877e13	+	9.66015e13i	−0.102006	+	0.313941i
$791$		−	3.31191e14i		−	1.06954i
$792$		0			0
$793$	1.51861e14			0.484261
$794$	8.45413e14	+	2.74691e14i	2.67896	+	0.870448i
$795$		0			0
$796$	−2.52314e14	−	1.83317e14i	−0.789542	−	0.573636i
$797$	−1.63547e14	−	5.03346e14i	−0.508571	−	1.56522i	−0.794684	−	0.607023i	$-0.792363\pi$
$797$	−1.63547e14	−	5.03346e14i	−0.508571	−	1.56522i	0.286113	−	0.958196i	$-0.407637\pi$
$798$		0			0
$799$	−7.07925e13	+	9.74375e13i	−0.217397	+	0.299221i
$800$	1.89847e14	+	2.61303e14i	0.579369	+	0.797432i
$801$		0			0
$802$		−	2.10540e14i		−	0.634546i
$803$	2.77999e14	−	4.24287e14i	0.832655	−	1.27081i
$804$		0			0
$805$	−5.43726e13	−	1.76667e13i	−0.160843	−	0.0522609i
$806$	1.83989e14	−	1.33676e14i	0.540900	−	0.392987i
$807$		0			0
$808$	2.32403e13	+	7.15262e13i	0.0674815	+	0.207687i
$809$	−3.79028e13	+	1.23154e13i	−0.109378	+	0.0355390i	−0.363195	−	0.931713i	$-0.618314\pi$
$809$	−3.79028e13	+	1.23154e13i	−0.109378	+	0.0355390i	0.253817	+	0.967252i	$0.418314\pi$
$810$		0			0
$811$	1.10787e14	+	1.52485e14i	0.315780	+	0.434634i	0.937173	−	0.348865i	$-0.113433\pi$
$811$	1.10787e14	+	1.52485e14i	0.315780	+	0.434634i	−0.621393	+	0.783499i	$0.713433\pi$
$812$	−8.29084e13	+	2.55166e14i	−0.234865	+	0.722841i
$813$		0			0
$814$	−5.62915e14	−	7.00961e14i	−1.57515	−	1.96143i
$815$	−1.37540e14			−0.382507
$816$		0			0
$817$	4.37790e14	−	3.18073e14i	1.20270	−	0.873810i
$818$	−7.25918e14	−	5.27410e14i	−1.98208	−	1.44006i
$819$		0			0
$820$	−1.26100e14	+	4.09724e13i	−0.340131	+	0.110515i
$821$	1.29425e14	−	1.78138e14i	0.346978	−	0.477574i	−0.599485	−	0.800386i	$-0.704628\pi$
$821$	1.29425e14	−	1.78138e14i	0.346978	−	0.477574i	0.946463	+	0.322812i	$0.104628\pi$
$822$		0			0
$823$	1.56118e14	−	4.80483e14i	0.413480	−	1.27256i	−0.500123	−	0.865954i	$-0.666712\pi$
$823$	1.56118e14	−	4.80483e14i	0.413480	−	1.27256i	0.913603	−	0.406607i	$-0.133288\pi$
$824$			5.97081e14i			1.57180i
$825$		0			0
$826$	−4.60888e13			−0.119866
$827$	−2.97177e14	−	9.65588e13i	−0.768225	−	0.249611i	−0.101420	−	0.994844i	$-0.532339\pi$
$827$	−2.97177e14	−	9.65588e13i	−0.768225	−	0.249611i	−0.666805	+	0.745232i	$0.732339\pi$
$828$		0			0
$829$	4.24894e14	+	3.08703e14i	1.08519	+	0.788440i	0.978581	−	0.205860i	$-0.0659993\pi$
$829$	4.24894e14	+	3.08703e14i	1.08519	+	0.788440i	0.106613	+	0.994301i	$0.465999\pi$
$830$	2.27613e13	+	7.00520e13i	0.0577838	+	0.177840i
$831$		0			0
$832$	3.43250e14	−	4.72443e14i	0.860982	−	1.18504i
$833$	1.58304e14	+	2.17887e14i	0.394700	+	0.543258i
$834$		0			0
$835$		−	2.06044e14i		−	0.507606i
$836$	−3.61684e13	−	7.48448e14i	−0.0885722	−	1.83286i
$837$		0			0
$838$	−4.25264e14	−	1.38177e14i	−1.02905	−	0.334360i
$839$	−3.85247e14	+	2.79899e14i	−0.926680	+	0.673272i	−0.945178	−	0.326557i	$-0.894112\pi$
$839$	−3.85247e14	+	2.79899e14i	−0.926680	+	0.673272i	0.0184978	+	0.999829i	$0.494112\pi$
$840$		0			0
$841$	6.01172e13	+	1.85022e14i	0.142896	+	0.439787i
$842$	−1.04997e15	+	3.41156e14i	−2.48094	+	0.806106i
$843$		0			0
$844$	7.04081e14	+	9.69085e14i	1.64403	+	2.26282i
$845$	−6.82202e12	+	2.09960e13i	−0.0158354	+	0.0487364i
$846$		0			0
$847$	1.44828e14	−	2.46196e14i	0.332227	−	0.564760i
$848$	6.48717e13			0.147937
$849$		0			0
$850$	−6.29658e14	+	4.57473e14i	−1.41909	+	1.03103i
$851$	5.42626e14	+	3.94241e14i	1.21577	+	0.883312i
$852$		0			0
$853$	−4.55794e14	+	1.48097e14i	−1.00931	+	0.327944i	−0.766579	−	0.642150i	$-0.778043\pi$
$853$	−4.55794e14	+	1.48097e14i	−1.00931	+	0.327944i	−0.242729	+	0.970094i	$0.578043\pi$
$854$	−1.51314e14	+	2.08265e14i	−0.333111	+	0.458488i
$855$		0			0
$856$	1.13399e13	−	3.49007e13i	0.0246741	−	0.0759392i
$857$			3.50986e14i			0.759251i	0.925140	+	0.379625i	$0.123947\pi$
$857$			3.50986e14i			0.759251i	−0.925140	+	0.379625i	$0.876053\pi$
$858$		0			0
$859$	−5.55923e14			−1.18864			−0.594318	−	0.804230i	$-0.702578\pi$
$859$	−5.55923e14			−1.18864			−0.594318	+	0.804230i	$0.702578\pi$
$860$	2.43930e14	+	7.92575e13i	0.518528	+	0.168480i
$861$		0			0
$862$	8.62043e14	+	6.26311e14i	1.81131	+	1.31599i
$863$	−1.15037e14	−	3.54046e14i	−0.240316	−	0.739616i	−0.996372	−	0.0851087i	$-0.972876\pi$
$863$	−1.15037e14	−	3.54046e14i	−0.240316	−	0.739616i	0.756056	−	0.654507i	$-0.227124\pi$
$864$		0			0
$865$	−4.22944e13	+	5.82132e13i	−0.0873378	+	0.120210i
$866$	−2.62266e14	−	3.60978e14i	−0.538459	−	0.741126i
$867$		0			0
$868$			2.36213e14i			0.479408i
$869$	3.65308e14	+	9.94805e13i	0.737158	+	0.200742i
$870$		0			0
$871$	−5.80352e14	−	1.88568e14i	−1.15771	−	0.376163i
$872$	2.39420e14	−	1.73949e14i	0.474874	−	0.345016i
$873$		0			0
$874$	2.81951e14	+	8.67756e14i	0.552862	+	1.70153i
$875$	−1.65671e14	+	5.38298e13i	−0.323003	+	0.104950i
$876$		0			0
$877$	−1.14158e14	−	1.57124e14i	−0.220043	−	0.302863i	0.684697	−	0.728828i	$-0.259935\pi$
$877$	−1.14158e14	−	1.57124e14i	−0.220043	−	0.302863i	−0.904739	+	0.425965i	$0.859935\pi$
$878$	−6.67301e13	+	2.05374e14i	−0.127894	+	0.393616i
$879$		0			0
$880$	−8.75945e12	+	7.03438e12i	−0.0165983	+	0.0133295i
$881$	−1.12274e14			−0.211543			−0.105772	−	0.994390i	$-0.533731\pi$
$881$	−1.12274e14			−0.211543			−0.105772	+	0.994390i	$0.533731\pi$
$882$		0			0
$883$	1.75326e13	−	1.27382e13i	0.0326620	−	0.0237303i	−0.571334	−	0.820717i	$-0.693574\pi$
$883$	1.75326e13	−	1.27382e13i	0.0326620	−	0.0237303i	0.603996	+	0.796987i	$0.293574\pi$
$884$	7.31454e14	+	5.31432e14i	1.35496	+	0.984434i
$885$		0			0
$886$	−1.40600e14	+	4.56838e13i	−0.257524	+	0.0836746i
$887$	6.47327e13	−	8.90969e13i	0.117898	−	0.162272i	−0.745989	−	0.665958i	$-0.768023\pi$
$887$	6.47327e13	−	8.90969e13i	0.117898	−	0.162272i	0.863887	+	0.503686i	$0.168023\pi$
$888$		0			0
$889$	6.85332e13	−	2.10924e14i	0.123422	−	0.379854i
$890$			1.96230e14i			0.351412i
$891$		0			0
$892$	−8.52745e14			−1.51006
$893$	1.96903e14	+	6.39778e13i	0.346734	+	0.112661i
$894$		0			0
$895$	−1.39547e14	−	1.01387e14i	−0.242999	−	0.176549i
$896$	1.81671e14	+	5.59126e14i	0.314590	+	0.968210i
$897$		0			0
$898$	−1.00343e14	+	1.38111e14i	−0.171833	+	0.236508i
$899$	−1.17039e14	−	1.61090e14i	−0.199311	−	0.274328i
$900$		0			0
$901$			1.30555e15i			2.19872i
$902$	2.85998e14	+	7.54217e14i	0.478994	+	1.26318i
$903$		0			0
$904$	−8.76578e14	−	2.84817e14i	−1.45194	−	0.471763i
$905$	7.49229e12	−	5.44347e12i	0.0123416	−	0.00896671i
$906$		0			0
$907$	9.41286e13	+	2.89698e14i	0.153350	+	0.471964i	0.997990	−	0.0633713i	$-0.0201852\pi$
$907$	9.41286e13	+	2.89698e14i	0.153350	+	0.471964i	−0.844640	+	0.535335i	$0.820185\pi$
$908$	−1.56847e15	+	5.09626e14i	−2.54124	+	0.825700i
$909$		0			0
$910$	9.34231e13	+	1.28586e14i	0.149709	+	0.206056i
$911$	−1.82724e14	+	5.62366e14i	−0.291208	+	0.896245i	0.693261	+	0.720686i	$0.256173\pi$
$911$	−1.82724e14	+	5.62366e14i	−0.291208	+	0.896245i	−0.984469	+	0.175559i	$0.943827\pi$
$912$		0			0
$913$	2.56718e14	−	9.73471e13i	0.404672	−	0.153451i
$914$	−1.15029e15			−1.80333
$915$		0			0
$916$	−7.91225e14	+	5.74859e14i	−1.22694	+	0.891423i
$917$	6.30376e14	+	4.57995e14i	0.972194	+	0.706340i
$918$		0			0
$919$	2.03432e14	−	6.60989e13i	0.310342	−	0.100836i	−0.149705	−	0.988731i	$-0.547832\pi$
$919$	2.03432e14	−	6.60989e13i	0.310342	−	0.100836i	0.460047	+	0.887894i	$0.347832\pi$
$920$	−9.35188e13	+	1.28718e14i	−0.141893	+	0.195298i
$921$		0			0
$922$	−5.64685e14	+	1.73792e15i	−0.847523	+	2.60841i
$923$		−	1.17823e14i		−	0.175882i
$924$		0			0
$925$	9.83507e14			1.45234
$926$	−1.45416e15	−	4.72485e14i	−2.13578	−	0.693957i
$927$		0			0
$928$	−4.33758e14	−	3.15143e14i	−0.630242	−	0.457898i
$929$	2.81145e12	+	8.65276e12i	0.00406305	+	0.0125048i	0.953067	−	0.302758i	$-0.0979074\pi$
$929$	2.81145e12	+	8.65276e12i	0.00406305	+	0.0125048i	−0.949004	+	0.315263i	$0.897907\pi$
$930$		0			0
$931$	2.72126e14	−	3.74550e14i	0.389065	−	0.535502i
$932$	1.01149e15	+	1.39220e15i	1.43841	+	1.97980i
$933$		0			0
$934$			1.18872e15i			1.67242i
$935$	−1.41567e14	−	1.76285e14i	−0.198110	−	0.246693i
$936$		0			0
$937$	−6.41613e14	−	2.08473e14i	−0.888332	−	0.288636i	−0.170919	−	0.985285i	$-0.554674\pi$
$937$	−6.41613e14	−	2.08473e14i	−0.888332	−	0.288636i	−0.717413	+	0.696649i	$0.754674\pi$
$938$	8.36867e14	−	6.08020e14i	1.15250	−	0.837343i
$939$		0			0
$940$	3.03235e13	+	9.33261e13i	0.0413181	+	0.127164i
$941$	7.32159e14	−	2.37893e14i	0.992332	−	0.322428i	0.232535	−	0.972588i	$-0.425298\pi$
$941$	7.32159e14	−	2.37893e14i	0.992332	−	0.322428i	0.759797	+	0.650160i	$0.225298\pi$
$942$		0			0
$943$	−3.53726e14	−	4.86862e14i	−0.474360	−	0.652901i
$944$	2.08799e12	−	6.42619e12i	0.00278528	−	0.00857222i
$945$		0			0
$946$	4.09981e14	−	1.50551e15i	0.541138	−	1.98714i
$947$	−5.88390e13			−0.0772530			−0.0386265	−	0.999254i	$-0.512298\pi$
$947$	−5.88390e13			−0.0772530			−0.0386265	+	0.999254i	$0.512298\pi$
$948$		0			0
$949$	8.51177e14	−	6.18416e14i	1.10583	−	0.803433i
$950$	1.08239e15	+	7.86401e14i	1.39883	+	1.01631i
$951$		0			0
$952$	−5.36277e14	+	1.74247e14i	−0.685811	+	0.222833i
$953$	2.79753e14	−	3.85047e14i	0.355885	−	0.489834i	−0.593111	−	0.805121i	$-0.702101\pi$
$953$	2.79753e14	−	3.85047e14i	0.355885	−	0.489834i	0.948997	+	0.315286i	$0.102101\pi$
$954$		0			0
$955$	−5.17368e13	+	1.59229e14i	−0.0651302	+	0.200450i
$956$			3.15216e14i			0.394747i
$957$		0			0
$958$	4.53038e14			0.561445
$959$	−4.07497e14	−	1.32404e14i	−0.502378	−	0.163233i
$960$		0			0
$961$	5.21267e14	+	3.78723e14i	0.635980	+	0.462066i
$962$	−5.76218e14	−	1.77342e15i	−0.699377	−	2.15246i
$963$		0			0
$964$	1.31750e15	−	1.81338e15i	1.58258	−	2.17823i
$965$	−1.16699e14	−	1.60623e14i	−0.139454	−	0.191942i
$966$		0			0
$967$		−	1.21859e14i		−	0.144121i	−0.997400	−	0.0720604i	$-0.977043\pi$
$967$		−	1.21859e14i		−	0.144121i	0.997400	−	0.0720604i	$-0.0229574\pi$
$968$	−5.27069e14	−	5.95046e14i	−0.620141	−	0.700123i
$969$		0			0
$970$	−2.05812e14	−	6.68723e13i	−0.239669	−	0.0778731i
$971$	4.09216e14	−	2.97313e14i	0.474085	−	0.344443i	−0.324946	−	0.945733i	$-0.605346\pi$
$971$	4.09216e14	−	2.97313e14i	0.474085	−	0.344443i	0.799031	+	0.601290i	$0.205346\pi$
$972$		0			0
$973$	3.40146e13	+	1.04686e14i	0.0390032	+	0.120040i
$974$	−1.71704e15	+	5.57901e14i	−1.95878	+	0.636447i
$975$		0			0
$976$	−2.21835e13	−	3.05330e13i	−0.0250485	−	0.0344762i
$977$	3.97744e14	−	1.22413e15i	0.446818	−	1.37517i	−0.433659	−	0.901077i	$-0.642778\pi$
$977$	3.97744e14	−	1.22413e15i	0.446818	−	1.37517i	0.880477	−	0.474089i	$-0.157222\pi$
$978$		0			0
$979$	7.30594e14	−	3.53055e13i	0.812386	−	0.0392581i
$980$	2.19433e14			0.242757
$981$		0			0
$982$	−7.55311e14	+	5.48766e14i	−0.827120	+	0.600938i
$983$	−6.79664e14	−	4.93805e14i	−0.740503	−	0.538007i	0.152366	−	0.988324i	$-0.451311\pi$
$983$	−6.79664e14	−	4.93805e14i	−0.740503	−	0.538007i	−0.892869	+	0.450317i	$0.851311\pi$
$984$		0			0
$985$	−2.47609e14	+	8.04532e13i	−0.267046	+	0.0867685i
$986$	7.59397e14	−	1.04522e15i	0.814863	−	1.12156i
$987$		0			0
$988$	4.80275e14	−	1.47814e15i	0.510159	−	1.57011i
$989$			1.16412e15i			1.23031i
$990$		0			0
$991$	−6.54919e12			−0.00685203			−0.00342602	−	0.999994i	$-0.501091\pi$
$991$	−6.54919e12			−0.00685203			−0.00342602	+	0.999994i	$0.501091\pi$
$992$	−4.48935e14	−	1.45868e14i	−0.467332	−	0.151845i
$993$		0			0
$994$	1.61585e14	+	1.17398e14i	0.166521	+	0.120985i
$995$	4.99875e13	+	1.53846e14i	0.0512561	+	0.157750i
$996$		0			0
$997$	4.80429e14	−	6.61254e14i	0.487701	−	0.671263i	−0.492261	−	0.870448i	$-0.663829\pi$
$997$	4.80429e14	−	6.61254e14i	0.487701	−	0.671263i	0.979962	+	0.199185i	$0.0638294\pi$
$998$	4.20571e14	+	5.78866e14i	0.424802	+	0.584690i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	99.11.k.a.46.1		36
3.2	odd	2		11.11.d.a.2.9	✓	36
11.6	odd	10	inner	99.11.k.a.28.1		36
33.17	even	10		11.11.d.a.6.9	yes	36
33.26	odd	10		121.11.b.c.120.33		36
33.29	even	10		121.11.b.c.120.4		36

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
11.11.d.a.2.9	✓	36	3.2	odd	2
11.11.d.a.6.9	yes	36	33.17	even	10
99.11.k.a.28.1		36	11.6	odd	10	inner
99.11.k.a.46.1		36	1.1	even	1	trivial
121.11.b.c.120.4		36	33.29	even	10
121.11.b.c.120.33		36	33.26	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:	\( k \)	\(=\)	\( 11 \)
Character orbit:	\([\chi]\)	\(=\)	99.k (of order \(10\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-48.9033 - 15.8897i) q^{2} +(1310.62 + 952.222i) q^{4} +(-259.656 - 799.138i) q^{5} +(6472.97 - 8909.28i) q^{7} +(-18014.0 - 24794.1i) q^{8} +O(q^{10})\)	\(q+(-48.9033 - 15.8897i) q^{2} +(1310.62 + 952.222i) q^{4} +(-259.656 - 799.138i) q^{5} +(6472.97 - 8909.28i) q^{7} +(-18014.0 - 24794.1i) q^{8} +43206.3i q^{10} +(160863. - 7773.63i) q^{11} +(317694. + 103225. i) q^{13} +(-458115. + 332840. i) q^{14} +(-25653.8 - 78954.2i) q^{16} +(1.58896e6 - 516284. i) q^{17} +(-1.68812e6 - 2.32350e6i) q^{19} +(420647. - 1.29462e6i) q^{20} +(-7.99027e6 - 2.17591e6i) q^{22} +6.17837e6 q^{23} +(7.32936e6 - 5.32509e6i) q^{25} +(-1.38961e7 - 1.00961e7i) q^{26} +(1.69672e7 - 5.51299e6i) q^{28} +(-8.83955e6 + 1.21666e7i) q^{29} +(-4.09149e6 + 1.25923e7i) q^{31} +3.56515e7i q^{32} -8.59090e7 q^{34} +(-8.80048e6 - 2.85945e6i) q^{35} +(8.78268e7 + 6.38099e7i) q^{37} +(4.56352e7 + 1.40451e8i) q^{38} +(-1.51365e7 + 2.08336e7i) q^{40} +(-5.72523e7 - 7.88010e7i) q^{41} +1.88418e8i q^{43} +(2.18233e8 + 1.42989e8i) q^{44} +(-3.02143e8 - 9.81722e7i) q^{46} +(-5.83203e7 + 4.23722e7i) q^{47} +(4.98137e7 + 1.53311e8i) q^{49} +(-4.43044e8 + 1.43954e8i) q^{50} +(3.18084e8 + 4.37805e8i) q^{52} +(-2.41473e8 + 7.43178e8i) q^{53} +(-4.79812e7 - 1.26533e8i) q^{55} -3.37502e8 q^{56} +(6.25607e8 - 4.54530e8i) q^{58} +(6.58470e7 + 4.78406e7i) q^{59} +(4.32363e8 - 1.40483e8i) q^{61} +(4.00175e8 - 5.50794e8i) q^{62} +(5.40221e8 - 1.66263e9i) q^{64} -2.80684e8i q^{65} -1.82676e9 q^{67} +(2.57414e9 + 8.36389e8i) q^{68} +(3.84937e8 + 2.79673e8i) q^{70} +(-1.08996e8 - 3.35454e8i) q^{71} +(1.85130e9 - 2.54810e9i) q^{73} +(-3.28110e9 - 4.51605e9i) q^{74} -4.65270e9i q^{76} +(9.72006e8 - 1.48349e9i) q^{77} +(2.23582e9 + 7.26461e8i) q^{79} +(-5.64341e7 + 4.10018e7i) q^{80} +(1.54771e9 + 4.76335e9i) q^{82} +(1.62134e9 - 5.26804e8i) q^{83} +(-8.25164e8 - 1.13574e9i) q^{85} +(2.99390e9 - 9.21429e9i) q^{86} +(-3.09053e9 - 3.84843e9i) q^{88} +4.54171e9 q^{89} +(2.97609e9 - 2.16225e9i) q^{91} +(8.09750e9 + 5.88318e9i) q^{92} +(3.52533e9 - 1.14545e9i) q^{94} +(-1.41847e9 + 1.95235e9i) q^{95} +(-1.54774e9 + 4.76346e9i) q^{97} -8.28894e9i q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 36 q + 5 q^{2} + 2839 q^{4} - 566 q^{5} - 9740 q^{7} + 56325 q^{8}+O(q^{10}) \) 36 * q + 5 * q^2 + 2839 * q^4 - 566 * q^5 - 9740 * q^7 + 56325 * q^8	\( 36 q + 5 q^{2} + 2839 q^{4} - 566 q^{5} - 9740 q^{7} + 56325 q^{8} + 124277 q^{11} + 516610 q^{13} + 256990 q^{14} + 1558071 q^{16} + 1563930 q^{17} + 6441265 q^{19} - 11846024 q^{20} - 38364515 q^{22} - 2991652 q^{23} + 53140199 q^{25} - 53101970 q^{26} - 158441860 q^{28} + 30773770 q^{29} + 63499996 q^{31} + 8404770 q^{34} - 93755030 q^{35} - 20015352 q^{37} - 222215700 q^{38} + 66388740 q^{40} - 168755230 q^{41} - 1092554652 q^{44} - 843022850 q^{46} + 1466232 q^{47} - 247720591 q^{49} - 1888812255 q^{50} - 1016067090 q^{52} + 1574434638 q^{53} + 1667070934 q^{55} - 464386660 q^{56} - 5738108180 q^{58} + 3108186601 q^{59} + 4185015940 q^{61} - 8028589520 q^{62} - 568398521 q^{64} - 6673767122 q^{67} + 12578329400 q^{68} - 10858899380 q^{70} - 5532218182 q^{71} + 6815310530 q^{73} - 27099775830 q^{74} + 17322154610 q^{77} - 28511789960 q^{79} - 9512354316 q^{80} + 4251999505 q^{82} - 6078874665 q^{83} + 52883120010 q^{85} + 11116561805 q^{86} - 35103955205 q^{88} + 19181286322 q^{89} - 22561214930 q^{91} + 78730839752 q^{92} + 94886813720 q^{94} - 79444332050 q^{95} - 7866178077 q^{97}+O(q^{100}) \) 36 * q + 5 * q^2 + 2839 * q^4 - 566 * q^5 - 9740 * q^7 + 56325 * q^8 + 124277 * q^11 + 516610 * q^13 + 256990 * q^14 + 1558071 * q^16 + 1563930 * q^17 + 6441265 * q^19 - 11846024 * q^20 - 38364515 * q^22 - 2991652 * q^23 + 53140199 * q^25 - 53101970 * q^26 - 158441860 * q^28 + 30773770 * q^29 + 63499996 * q^31 + 8404770 * q^34 - 93755030 * q^35 - 20015352 * q^37 - 222215700 * q^38 + 66388740 * q^40 - 168755230 * q^41 - 1092554652 * q^44 - 843022850 * q^46 + 1466232 * q^47 - 247720591 * q^49 - 1888812255 * q^50 - 1016067090 * q^52 + 1574434638 * q^53 + 1667070934 * q^55 - 464386660 * q^56 - 5738108180 * q^58 + 3108186601 * q^59 + 4185015940 * q^61 - 8028589520 * q^62 - 568398521 * q^64 - 6673767122 * q^67 + 12578329400 * q^68 - 10858899380 * q^70 - 5532218182 * q^71 + 6815310530 * q^73 - 27099775830 * q^74 + 17322154610 * q^77 - 28511789960 * q^79 - 9512354316 * q^80 + 4251999505 * q^82 - 6078874665 * q^83 + 52883120010 * q^85 + 11116561805 * q^86 - 35103955205 * q^88 + 19181286322 * q^89 - 22561214930 * q^91 + 78730839752 * q^92 + 94886813720 * q^94 - 79444332050 * q^95 - 7866178077 * q^97

Introduction

L-functions

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