LMFDB - Embedded newform 72.10.d.b.37.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [72,10,Mod(37,72)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(72, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 10, names="a")

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

chi := DirichletCharacter("72.37");

S:= CuspForms(chi, 10);

N := Newforms(S);

Level:	$ N $	$=$	$ 72 = 2^{3} \cdot 3^{2} $
Weight:	$ k $	$=$	$ 10 $
Character orbit:	$[\chi]$	$=$	72.d (of order $2$, degree $1$, 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:	$37.0825802038$
Analytic rank:	$0$
Dimension:	$8$
Coefficient field:	$\mathbb{Q}[x]/(x^{8} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - x^{7} + 59x^{6} - 313x^{5} - 315x^{4} - 92091x^{3} + 1261649x^{2} - 16074123x + 251007534 $ x^8 - x^7 + 59x^6 - 313x^5 - 315x^4 - 92091x^3 + 1261649x^2 - 16074123x + 251007534
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{28}\cdot 3^{2} $
Twist minimal:	no (minimal twist has level 8)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			37.8
Root			$9.73909 + 3.55976i$ of defining polynomial
Character	$\chi$	$=$	72.37
Dual form			72.10.d.b.37.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(21.4782 + 7.11952i) q^{2} +(410.625 + 305.829i) q^{4} +2583.09i q^{5} +6967.65 q^{7} +(6642.12 + 9492.10i) q^{8} +O(q^{10})$	\(q+(21.4782 + 7.11952i) q^{2} +(410.625 + 305.829i) q^{4} +2583.09i q^{5} +6967.65 q^{7} +(6642.12 + 9492.10i) q^{8} +(-18390.4 + 55480.1i) q^{10} +25054.5i q^{11} -29701.4i q^{13} +(149652. + 49606.3i) q^{14} +(75081.4 + 251162. i) q^{16} +138527. q^{17} -489569. i q^{19} +(-789984. + 1.06068e6i) q^{20} +(-178376. + 538124. i) q^{22} -847079. q^{23} -4.71924e6 q^{25} +(211460. - 637933. i) q^{26} +(2.86109e6 + 2.13091e6i) q^{28} -1.13646e6i q^{29} +4.35747e6 q^{31} +(-175542. + 5.92904e6i) q^{32} +(2.97532e6 + 986249. i) q^{34} +1.79981e7i q^{35} -535315. i q^{37} +(3.48550e6 - 1.05151e7i) q^{38} +(-2.45190e7 + 1.71572e7i) q^{40} -1.45816e7 q^{41} +3.96441e7i q^{43} +(-7.66238e6 + 1.02880e7i) q^{44} +(-1.81937e7 - 6.03080e6i) q^{46} +4.48997e7 q^{47} +8.19448e6 q^{49} +(-1.01361e8 - 3.35988e7i) q^{50} +(9.08355e6 - 1.21961e7i) q^{52} -4.85666e7i q^{53} -6.47180e7 q^{55} +(4.62799e7 + 6.61376e7i) q^{56} +(8.09108e6 - 2.44092e7i) q^{58} -4.19685e6i q^{59} -6.38659e7i q^{61} +(9.35906e7 + 3.10231e7i) q^{62} +(-4.59823e7 + 1.26095e8i) q^{64} +7.67215e7 q^{65} +5.79621e7i q^{67} +(5.68828e7 + 4.23657e7i) q^{68} +(-1.28138e8 + 3.86566e8i) q^{70} -2.74912e8 q^{71} -9.16969e7 q^{73} +(3.81119e6 - 1.14976e7i) q^{74} +(1.49724e8 - 2.01029e8i) q^{76} +1.74571e8i q^{77} +2.02396e8 q^{79} +(-6.48774e8 + 1.93942e8i) q^{80} +(-3.13186e8 - 1.03814e8i) q^{82} -6.11053e8i q^{83} +3.57829e8i q^{85} +(-2.82247e8 + 8.51483e8i) q^{86} +(-2.37819e8 + 1.66415e8i) q^{88} +7.71588e8 q^{89} -2.06949e8i q^{91} +(-3.47831e8 - 2.59061e8i) q^{92} +(9.64363e8 + 3.19664e8i) q^{94} +1.26460e9 q^{95} +1.08292e9 q^{97} +(1.76003e8 + 5.83408e7i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 18 q^{2} - 428 q^{4} + 4800 q^{7} + 3384 q^{8}+O(q^{10}) $ 8 * q + 18 * q^2 - 428 * q^4 + 4800 * q^7 + 3384 * q^8	$ 8 q + 18 q^{2} - 428 q^{4} + 4800 q^{7} + 3384 q^{8} + 26392 q^{10} + 72336 q^{14} + 185616 q^{16} + 102000 q^{17} - 1245264 q^{20} - 2373124 q^{22} - 3412032 q^{23} - 2423384 q^{25} - 4551240 q^{26} + 7509920 q^{28} + 803584 q^{31} + 14113248 q^{32} + 27757244 q^{34} + 63661140 q^{38} - 93063648 q^{40} + 2180784 q^{41} - 114013320 q^{44} - 131840944 q^{46} - 7432320 q^{47} + 24436680 q^{49} - 231784902 q^{50} + 219270896 q^{52} + 7056832 q^{55} + 358503360 q^{56} + 375425192 q^{58} + 344291904 q^{62} - 316815296 q^{64} + 146501760 q^{65} - 79875048 q^{68} - 56202048 q^{70} - 560234688 q^{71} - 523987120 q^{73} + 65773608 q^{74} - 87532760 q^{76} - 248943744 q^{79} - 890441280 q^{80} - 1051981172 q^{82} - 1492810428 q^{86} + 1544767952 q^{88} - 744827856 q^{89} + 2959012128 q^{92} + 3068552352 q^{94} + 1465245504 q^{95} - 9932784 q^{97} + 3062604162 q^{98}+O(q^{100}) $ 8 * q + 18 * q^2 - 428 * q^4 + 4800 * q^7 + 3384 * q^8 + 26392 * q^10 + 72336 * q^14 + 185616 * q^16 + 102000 * q^17 - 1245264 * q^20 - 2373124 * q^22 - 3412032 * q^23 - 2423384 * q^25 - 4551240 * q^26 + 7509920 * q^28 + 803584 * q^31 + 14113248 * q^32 + 27757244 * q^34 + 63661140 * q^38 - 93063648 * q^40 + 2180784 * q^41 - 114013320 * q^44 - 131840944 * q^46 - 7432320 * q^47 + 24436680 * q^49 - 231784902 * q^50 + 219270896 * q^52 + 7056832 * q^55 + 358503360 * q^56 + 375425192 * q^58 + 344291904 * q^62 - 316815296 * q^64 + 146501760 * q^65 - 79875048 * q^68 - 56202048 * q^70 - 560234688 * q^71 - 523987120 * q^73 + 65773608 * q^74 - 87532760 * q^76 - 248943744 * q^79 - 890441280 * q^80 - 1051981172 * q^82 - 1492810428 * q^86 + 1544767952 * q^88 - 744827856 * q^89 + 2959012128 * q^92 + 3068552352 * q^94 + 1465245504 * q^95 - 9932784 * q^97 + 3062604162 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/72\mathbb{Z}\right)^\times$.

$n$	$37$	$55$	$65$
$\chi(n)$	$-1$	$1$	$1$

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 $

$2$	21.4782	+	7.11952i	0.949211	+	0.314642i
$2$	21.4782	+	7.11952i	0.949211	+	0.314642i
$3$		0			0
$3$		0			0
$4$	410.625	+	305.829i	0.802001	+	0.597322i
$5$			2583.09i			1.84831i	0.382017	+	0.924155i	$0.375230\pi$
$5$			2583.09i			1.84831i	−0.382017	+	0.924155i	$0.624770\pi$
$6$		0			0
$7$	6967.65			1.09684			0.548422	−	0.836202i	$-0.315229\pi$
$7$	6967.65			1.09684			0.548422	+	0.836202i	$0.315229\pi$
$8$	6642.12	+	9492.10i	0.573326	+	0.819327i
$9$		0			0
$10$	−18390.4	+	55480.1i	−0.581555	+	1.75444i
$11$			25054.5i			0.515962i	0.966150	+	0.257981i	$0.0830572\pi$
$11$			25054.5i			0.515962i	−0.966150	+	0.257981i	$0.916943\pi$
$12$		0			0
$13$		−	29701.4i		−	0.288425i	−0.989547	−	0.144212i	$-0.953935\pi$
$13$		−	29701.4i		−	0.288425i	0.989547	−	0.144212i	$-0.0460648\pi$
$14$	149652.	+	49606.3i	1.04114	+	0.345113i
$15$		0			0
$16$	75081.4	+	251162.i	0.286413	+	0.958106i
$17$	138527.			0.402268			0.201134	−	0.979564i	$-0.435537\pi$
$17$	138527.			0.402268			0.201134	+	0.979564i	$0.435537\pi$
$18$		0			0
$19$		−	489569.i		−	0.861832i	−0.902392	−	0.430916i	$-0.858191\pi$
$19$		−	489569.i		−	0.861832i	0.902392	−	0.430916i	$-0.141809\pi$
$20$	−789984.	+	1.06068e6i	−1.10404	+	1.48235i
$21$		0			0
$22$	−178376.	+	538124.i	−0.162343	+	0.489757i
$23$	−847079.			−0.631173			−0.315587	−	0.948897i	$-0.602201\pi$
$23$	−847079.			−0.631173			−0.315587	+	0.948897i	$0.602201\pi$
$24$		0			0
$25$	−4.71924e6			−2.41625
$26$	211460.	−	637933.i	0.0907503	−	0.273776i
$27$		0			0
$28$	2.86109e6	+	2.13091e6i	0.879671	+	0.655169i
$29$		−	1.13646e6i		−	0.298376i	−0.988809	−	0.149188i	$-0.952334\pi$
$29$		−	1.13646e6i		−	0.298376i	0.988809	−	0.149188i	$-0.0476660\pi$
$30$		0			0
$31$	4.35747e6			0.847436			0.423718	−	0.905794i	$-0.360725\pi$
$31$	4.35747e6			0.847436			0.423718	+	0.905794i	$0.360725\pi$
$32$	−175542.	+	5.92904e6i	−0.0295941	+	0.999562i
$33$		0			0
$34$	2.97532e6	+	986249.i	0.381837	+	0.126570i
$35$			1.79981e7i			2.02731i
$36$		0			0
$37$		−	535315.i		−	0.0469571i	−0.999724	−	0.0234786i	$-0.992526\pi$
$37$		−	535315.i		−	0.0469571i	0.999724	−	0.0234786i	$-0.00747415\pi$
$38$	3.48550e6	−	1.05151e7i	0.271168	−	0.818060i
$39$		0			0
$40$	−2.45190e7	+	1.71572e7i	−1.51437	+	1.05968i
$41$	−1.45816e7			−0.805894			−0.402947	−	0.915223i	$-0.632014\pi$
$41$	−1.45816e7			−0.805894			−0.402947	+	0.915223i	$0.632014\pi$
$42$		0			0
$43$			3.96441e7i			1.76836i	0.467148	+	0.884179i	$0.345281\pi$
$43$			3.96441e7i			1.76836i	−0.467148	+	0.884179i	$0.654719\pi$
$44$	−7.66238e6	+	1.02880e7i	−0.308196	+	0.413802i
$45$		0			0
$46$	−1.81937e7	−	6.03080e6i	−0.599116	−	0.198593i
$47$	4.48997e7			1.34216			0.671078	−	0.741387i	$-0.265832\pi$
$47$	4.48997e7			1.34216			0.671078	+	0.741387i	$0.265832\pi$
$48$		0			0
$49$	8.19448e6			0.203067
$50$	−1.01361e8	−	3.35988e7i	−2.29353	−	0.760253i
$51$		0			0
$52$	9.08355e6	−	1.21961e7i	0.172282	−	0.231317i
$53$		−	4.85666e7i		−	0.845466i	−0.906254	−	0.422733i	$-0.861071\pi$
$53$		−	4.85666e7i		−	0.845466i	0.906254	−	0.422733i	$-0.138929\pi$
$54$		0			0
$55$	−6.47180e7			−0.953658
$56$	4.62799e7	+	6.61376e7i	0.628849	+	0.898674i
$57$		0			0
$58$	8.09108e6	−	2.44092e7i	0.0938816	−	0.283222i
$59$		−	4.19685e6i		−	0.0450910i	−0.999746	−	0.0225455i	$-0.992823\pi$
$59$		−	4.19685e6i		−	0.0450910i	0.999746	−	0.0225455i	$-0.00717706\pi$
$60$		0			0
$61$		−	6.38659e7i		−	0.590588i	−0.955406	−	0.295294i	$-0.904582\pi$
$61$		−	6.38659e7i		−	0.590588i	0.955406	−	0.295294i	$-0.0954176\pi$
$62$	9.35906e7	+	3.10231e7i	0.804395	+	0.266638i
$63$		0			0
$64$	−4.59823e7	+	1.26095e8i	−0.342595	+	0.939483i
$65$	7.67215e7			0.533098
$66$		0			0
$67$			5.79621e7i			0.351404i	0.984443	+	0.175702i	$0.0562196\pi$
$67$			5.79621e7i			0.351404i	−0.984443	+	0.175702i	$0.943780\pi$
$68$	5.68828e7	+	4.23657e7i	0.322619	+	0.240284i
$69$		0			0
$70$	−1.28138e8	+	3.86566e8i	−0.637875	+	1.92434i
$71$	−2.74912e8			−1.28390			−0.641950	−	0.766746i	$-0.721875\pi$
$71$	−2.74912e8			−1.28390			−0.641950	+	0.766746i	$0.721875\pi$
$72$		0			0
$73$	−9.16969e7			−0.377921			−0.188961	−	0.981985i	$-0.560512\pi$
$73$	−9.16969e7			−0.377921			−0.188961	+	0.981985i	$0.560512\pi$
$74$	3.81119e6	−	1.14976e7i	0.0147747	−	0.0445722i
$75$		0			0
$76$	1.49724e8	−	2.01029e8i	0.514791	−	0.691191i
$77$			1.74571e8i			0.565930i
$78$		0			0
$79$	2.02396e8			0.584627			0.292314	−	0.956322i	$-0.405575\pi$
$79$	2.02396e8			0.584627			0.292314	+	0.956322i	$0.405575\pi$
$80$	−6.48774e8	+	1.93942e8i	−1.77088	+	0.529379i
$81$		0			0
$82$	−3.13186e8	−	1.03814e8i	−0.764963	−	0.253568i
$83$		−	6.11053e8i		−	1.41328i	−0.707574	−	0.706639i	$-0.750210\pi$
$83$		−	6.11053e8i		−	1.41328i	0.707574	−	0.706639i	$-0.249790\pi$
$84$		0			0
$85$			3.57829e8i			0.743516i
$86$	−2.82247e8	+	8.51483e8i	−0.556399	+	1.67854i
$87$		0			0
$88$	−2.37819e8	+	1.66415e8i	−0.422742	+	0.295814i
$89$	7.71588e8			1.30356			0.651779	−	0.758409i	$-0.274023\pi$
$89$	7.71588e8			1.30356			0.651779	+	0.758409i	$0.274023\pi$
$90$		0			0
$91$		−	2.06949e8i		−	0.316357i
$92$	−3.47831e8	−	2.59061e8i	−0.506202	−	0.377014i
$93$		0			0
$94$	9.64363e8	+	3.19664e8i	1.27399	+	0.422298i
$95$	1.26460e9			1.59293
$96$		0			0
$97$	1.08292e9			1.24200			0.621001	−	0.783810i	$-0.286726\pi$
$97$	1.08292e9			1.24200			0.621001	+	0.783810i	$0.286726\pi$
$98$	1.76003e8	+	5.83408e7i	0.192753	+	0.0638933i
$99$		0			0
$100$	−1.93784e9	−	1.44328e9i	−1.93784	−	1.44328i
$101$			6.22244e8i			0.594996i	0.954722	+	0.297498i	$0.0961522\pi$
$101$			6.22244e8i			0.594996i	−0.954722	+	0.297498i	$0.903848\pi$
$102$		0			0
$103$	6.34170e8			0.555186			0.277593	−	0.960699i	$-0.410463\pi$
$103$	6.34170e8			0.555186			0.277593	+	0.960699i	$0.410463\pi$
$104$	2.81929e8	−	1.97280e8i	0.236314	−	0.165361i
$105$		0			0
$106$	3.45771e8	−	1.04312e9i	0.266019	−	0.802526i
$107$		−	1.54145e9i		−	1.13685i	−0.822735	−	0.568425i	$-0.807553\pi$
$107$		−	1.54145e9i		−	1.13685i	0.822735	−	0.568425i	$-0.192447\pi$
$108$		0			0
$109$		−	2.19786e9i		−	1.49135i	−0.666309	−	0.745676i	$-0.732127\pi$
$109$		−	2.19786e9i		−	1.49135i	0.666309	−	0.745676i	$-0.267873\pi$
$110$	−1.39002e9	−	4.60761e8i	−0.905222	−	0.300060i
$111$		0			0
$112$	5.23140e8	+	1.75001e9i	0.314150	+	1.05089i
$113$	5.43476e8			0.313565			0.156782	−	0.987633i	$-0.449888\pi$
$113$	5.43476e8			0.313565			0.156782	+	0.987633i	$0.449888\pi$
$114$		0			0
$115$		−	2.18808e9i		−	1.16660i
$116$	3.47563e8	−	4.66660e8i	0.178227	−	0.239298i
$117$		0			0
$118$	2.98796e7	−	9.01407e7i	0.0141875	−	0.0428008i
$119$	9.65210e8			0.441225
$120$		0			0
$121$	1.73022e9			0.733783
$122$	4.54695e8	−	1.37172e9i	0.185823	−	0.560592i
$123$		0			0
$124$	1.78929e9	+	1.33264e9i	0.679645	+	0.506192i
$125$		−	7.14513e9i		−	2.61767i
$126$		0			0
$127$	−2.41305e9			−0.823093			−0.411547	−	0.911389i	$-0.635011\pi$
$127$	−2.41305e9			−0.823093			−0.411547	+	0.911389i	$0.635011\pi$
$128$	−1.88535e9	+	2.38093e9i	−0.620795	+	0.783973i
$129$		0			0
$130$	1.64784e9	+	5.46221e8i	0.506022	+	0.167735i
$131$			1.57746e9i			0.467990i	0.972238	+	0.233995i	$0.0751799\pi$
$131$			1.57746e9i			0.467990i	−0.972238	+	0.233995i	$0.924820\pi$
$132$		0			0
$133$		−	3.41114e9i		−	0.945295i
$134$	−4.12662e8	+	1.24492e9i	−0.110566	+	0.333557i
$135$		0			0
$136$	9.20115e8	+	1.31492e9i	0.230631	+	0.329589i
$137$	6.39076e9			1.54992			0.774961	−	0.632009i	$-0.217769\pi$
$137$	6.39076e9			1.54992			0.774961	+	0.632009i	$0.217769\pi$
$138$		0			0
$139$			2.45897e9i			0.558710i	0.960188	+	0.279355i	$0.0901206\pi$
$139$			2.45897e9i			0.558710i	−0.960188	+	0.279355i	$0.909879\pi$
$140$	−5.50433e9	+	7.39045e9i	−1.21096	+	1.62590i
$141$		0			0
$142$	−5.90462e9	−	1.95724e9i	−1.21869	−	0.403969i
$143$	7.44153e8			0.148816
$144$		0			0
$145$	2.93559e9			0.551492
$146$	−1.96948e9	−	6.52838e8i	−0.358727	−	0.118910i
$147$		0			0
$148$	1.63715e8	−	2.19814e8i	0.0280485	−	0.0376597i
$149$		−	3.84540e9i		−	0.639150i	−0.947561	−	0.319575i	$-0.896460\pi$
$149$		−	3.84540e9i		−	0.639150i	0.947561	−	0.319575i	$-0.103540\pi$
$150$		0			0
$151$	4.07627e9			0.638067			0.319034	−	0.947743i	$-0.396642\pi$
$151$	4.07627e9			0.638067			0.319034	+	0.947743i	$0.396642\pi$
$152$	4.64704e9	−	3.25177e9i	0.706123	−	0.494111i
$153$		0			0
$154$	−1.24286e9	+	3.74946e9i	−0.178065	+	0.537187i
$155$			1.12557e10i			1.56632i
$156$		0			0
$157$			7.59409e9i			0.997533i	0.866736	+	0.498767i	$0.166214\pi$
$157$			7.59409e9i			0.997533i	−0.866736	+	0.498767i	$0.833786\pi$
$158$	4.34709e9	+	1.44096e9i	0.554935	+	0.183948i
$159$		0			0
$160$	−1.53153e10	−	4.53441e8i	−1.84750	−	0.0546991i
$161$	−5.90214e9			−0.692298
$162$		0			0
$163$			7.71277e9i			0.855788i	0.903829	+	0.427894i	$0.140744\pi$
$163$			7.71277e9i			0.855788i	−0.903829	+	0.427894i	$0.859256\pi$
$164$	−5.98757e9	−	4.45948e9i	−0.646328	−	0.481378i
$165$		0			0
$166$	4.35041e9	−	1.31243e10i	0.444676	−	1.34150i
$167$	−1.01170e10			−1.00653			−0.503265	−	0.864132i	$-0.667868\pi$
$167$	−1.01170e10			−1.00653			−0.503265	+	0.864132i	$0.667868\pi$
$168$		0			0
$169$	9.72232e9			0.916811
$170$	−2.54757e9	+	7.68552e9i	−0.233941	+	0.705753i
$171$		0			0
$172$	−1.21243e10	+	1.62788e10i	−1.05628	+	1.41823i
$173$			1.89724e10i			1.61033i	0.593053	+	0.805164i	$0.297922\pi$
$173$			1.89724e10i			1.61033i	−0.593053	+	0.805164i	$0.702078\pi$
$174$		0			0
$175$	−3.28820e10			−2.65025
$176$	−6.29272e9	+	1.88112e9i	−0.494347	+	0.147778i
$177$		0			0
$178$	1.65723e10	+	5.49334e9i	1.23735	+	0.410153i
$179$		−	1.72674e10i		−	1.25716i	−0.777746	−	0.628578i	$-0.783637\pi$
$179$		−	1.72674e10i		−	1.25716i	0.777746	−	0.628578i	$-0.216363\pi$
$180$		0			0
$181$			1.03363e10i			0.715830i	0.933754	+	0.357915i	$0.116512\pi$
$181$			1.03363e10i			0.715830i	−0.933754	+	0.357915i	$0.883488\pi$
$182$	1.47338e9	−	4.44489e9i	0.0995390	−	0.300289i
$183$		0			0
$184$	−5.62640e9	−	8.04056e9i	−0.361868	−	0.517137i
$185$	1.38277e9			0.0867913
$186$		0			0
$187$			3.47073e9i			0.207555i
$188$	1.84369e10	+	1.37316e10i	1.07641	+	0.801699i
$189$		0			0
$190$	2.71613e10	+	9.00336e9i	1.51203	+	0.501203i
$191$	9.14299e9			0.497094			0.248547	−	0.968620i	$-0.420047\pi$
$191$	9.14299e9			0.497094			0.248547	+	0.968620i	$0.420047\pi$
$192$		0			0
$193$	8.45502e8			0.0438639			0.0219319	−	0.999759i	$-0.493018\pi$
$193$	8.45502e8			0.0438639			0.0219319	+	0.999759i	$0.493018\pi$
$194$	2.32591e10	+	7.70985e9i	1.17892	+	0.390785i
$195$		0			0
$196$	3.36486e9	+	2.50611e9i	0.162860	+	0.121296i
$197$			2.12407e9i			0.100478i	0.998737	+	0.0502390i	$0.0159983\pi$
$197$			2.12407e9i			0.100478i	−0.998737	+	0.0502390i	$0.984002\pi$
$198$		0			0
$199$	−2.92879e9			−0.132388			−0.0661941	−	0.997807i	$-0.521086\pi$
$199$	−2.92879e9			−0.132388			−0.0661941	+	0.997807i	$0.521086\pi$
$200$	−3.13458e10	−	4.47955e10i	−1.38530	−	1.97970i
$201$		0			0
$202$	−4.43008e9	+	1.33647e10i	−0.187211	+	0.564777i
$203$		−	7.91848e9i		−	0.327272i
$204$		0			0
$205$		−	3.76656e10i		−	1.48954i
$206$	1.36208e10	+	4.51499e9i	0.526988	+	0.174684i
$207$		0			0
$208$	7.45986e9	−	2.23002e9i	0.276341	−	0.0826084i
$209$	1.22659e10			0.444673
$210$		0			0
$211$		−	3.16571e10i		−	1.09951i	−0.835325	−	0.549757i	$-0.814720\pi$
$211$		−	3.16571e10i		−	1.09951i	0.835325	−	0.549757i	$-0.185280\pi$
$212$	1.48531e10	−	1.99427e10i	0.505016	−	0.678065i
$213$		0			0
$214$	1.09744e10	−	3.31076e10i	0.357700	−	1.07911i
$215$	−1.02404e11			−3.26847
$216$		0			0
$217$	3.03613e10			0.929505
$218$	1.56477e10	−	4.72059e10i	0.469241	−	1.41561i
$219$		0			0
$220$	−2.65748e10	−	1.97926e10i	−0.764835	−	0.569641i
$221$		−	4.11446e9i		−	0.116024i
$222$		0			0
$223$	−4.92453e10			−1.33350			−0.666750	−	0.745282i	$-0.732315\pi$
$223$	−4.92453e10			−1.33350			−0.666750	+	0.745282i	$0.732315\pi$
$224$	−1.22311e9	+	4.13115e10i	−0.0324601	+	1.09636i
$225$		0			0
$226$	1.16729e10	+	3.86929e9i	0.297639	+	0.0986605i
$227$			5.67209e10i			1.41784i	0.705290	+	0.708919i	$0.250817\pi$
$227$			5.67209e10i			1.41784i	−0.705290	+	0.708919i	$0.749183\pi$
$228$		0			0
$229$			3.33645e9i			0.0801723i	0.999196	+	0.0400862i	$0.0127632\pi$
$229$			3.33645e9i			0.0801723i	−0.999196	+	0.0400862i	$0.987237\pi$
$230$	1.55781e10	−	4.69960e10i	0.367062	−	1.10735i
$231$		0			0
$232$	1.07874e10	−	7.54852e9i	0.244468	−	0.171067i
$233$	4.60006e10			1.02250			0.511249	−	0.859433i	$-0.329183\pi$
$233$	4.60006e10			1.02250			0.511249	+	0.859433i	$0.329183\pi$
$234$		0			0
$235$			1.15980e11i			2.48072i
$236$	1.28352e9	−	1.72333e9i	0.0269338	−	0.0361630i
$237$		0			0
$238$	2.07310e10	+	6.87183e9i	0.418816	+	0.138828i
$239$	4.05955e10			0.804798			0.402399	−	0.915464i	$-0.368176\pi$
$239$	4.05955e10			0.804798			0.402399	+	0.915464i	$0.368176\pi$
$240$		0			0
$241$	3.45208e10			0.659181			0.329590	−	0.944124i	$-0.393089\pi$
$241$	3.45208e10			0.659181			0.329590	+	0.944124i	$0.393089\pi$
$242$	3.71620e10	+	1.23184e10i	0.696515	+	0.230879i
$243$		0			0
$244$	1.95320e10	−	2.62249e10i	0.352771	−	0.473652i
$245$			2.11671e10i			0.375331i
$246$		0			0
$247$	−1.45409e10			−0.248573
$248$	2.89428e10	+	4.13616e10i	0.485857	+	0.694327i
$249$		0			0
$250$	5.08700e10	−	1.53465e11i	0.823629	−	2.48472i
$251$			7.83857e10i			1.24654i	0.782008	+	0.623268i	$0.214196\pi$
$251$			7.83857e10i			1.24654i	−0.782008	+	0.623268i	$0.785804\pi$
$252$		0			0
$253$		−	2.12231e10i		−	0.325661i
$254$	−5.18279e10	−	1.71797e10i	−0.781289	−	0.258979i
$255$		0			0
$256$	−5.74451e10	+	3.77151e10i	−0.835936	+	0.548828i
$257$	−1.06489e11			−1.52267			−0.761337	−	0.648356i	$-0.775457\pi$
$257$	−1.06489e11			−1.52267			−0.761337	+	0.648356i	$0.775457\pi$
$258$		0			0
$259$		−	3.72988e9i		−	0.0515046i
$260$	3.15038e10	+	2.34637e10i	0.427545	+	0.318431i
$261$		0			0
$262$	−1.12307e10	+	3.38809e10i	−0.147249	+	0.444221i
$263$	6.39865e8			0.00824684			0.00412342	−	0.999991i	$-0.498687\pi$
$263$	6.39865e8			0.00824684			0.00412342	+	0.999991i	$0.498687\pi$
$264$		0			0
$265$	1.25452e11			1.56268
$266$	2.42857e10	−	7.32652e10i	0.297429	−	0.897284i
$267$		0			0
$268$	−1.77265e10	+	2.38007e10i	−0.209902	+	0.281827i
$269$		−	9.60820e10i		−	1.11881i	−0.828894	−	0.559406i	$-0.811029\pi$
$269$		−	9.60820e10i		−	1.11881i	0.828894	−	0.559406i	$-0.188971\pi$
$270$		0			0
$271$	−9.78435e10			−1.10197			−0.550986	−	0.834515i	$-0.685748\pi$
$271$	−9.78435e10			−1.10197			−0.550986	+	0.834515i	$0.685748\pi$
$272$	1.04008e10	+	3.47928e10i	0.115215	+	0.385416i
$273$		0			0
$274$	1.37262e11	+	4.54992e10i	1.47120	+	0.487670i
$275$		−	1.18238e11i		−	1.24669i
$276$		0			0
$277$		−	1.61396e11i		−	1.64716i	−0.567202	−	0.823579i	$-0.691974\pi$
$277$		−	1.61396e11i		−	1.64716i	0.567202	−	0.823579i	$-0.308026\pi$
$278$	−1.75067e10	+	5.28142e10i	−0.175793	+	0.530333i
$279$		0			0
$280$	−1.70840e11	+	1.19545e11i	−1.66103	+	1.16231i
$281$	2.71451e10			0.259724			0.129862	−	0.991532i	$-0.458547\pi$
$281$	2.71451e10			0.259724			0.129862	+	0.991532i	$0.458547\pi$
$282$		0			0
$283$		−	2.80153e10i		−	0.259631i	−0.991538	−	0.129815i	$-0.958562\pi$
$283$		−	2.80153e10i		−	0.259631i	0.991538	−	0.129815i	$-0.0414385\pi$
$284$	−1.12886e11	−	8.40761e10i	−1.02969	−	0.766902i
$285$		0			0
$286$	1.59831e10	+	5.29801e9i	0.141258	+	0.0468237i
$287$	−1.01599e11			−0.883940
$288$		0			0
$289$	−9.93980e10			−0.838180
$290$	6.30511e10	+	2.09000e10i	0.523482	+	0.173522i
$291$		0			0
$292$	−3.76530e10	−	2.80435e10i	−0.303094	−	0.225741i
$293$		−	2.49001e10i		−	0.197377i	−0.995118	−	0.0986884i	$-0.968535\pi$
$293$		−	2.49001e10i		−	0.197377i	0.995118	−	0.0986884i	$-0.0314647\pi$
$294$		0			0
$295$	1.08409e10			0.0833421
$296$	5.08126e9	−	3.55562e9i	0.0384733	−	0.0269217i
$297$		0			0
$298$	2.73774e10	−	8.25921e10i	0.201103	−	0.606688i
$299$			2.51594e10i			0.182046i
$300$		0			0
$301$			2.76226e11i			1.93961i
$302$	8.75508e10	+	2.90211e10i	0.605660	+	0.200762i
$303$		0			0
$304$	1.22961e11	−	3.67575e10i	0.825727	−	0.246840i
$305$	1.64971e11			1.09159
$306$		0			0
$307$		−	1.71738e11i		−	1.10343i	−0.834034	−	0.551713i	$-0.813974\pi$
$307$		−	1.71738e11i		−	1.10343i	0.834034	−	0.551713i	$-0.186026\pi$
$308$	−5.33887e10	+	7.16830e10i	−0.338042	+	0.453877i
$309$		0			0
$310$	−8.01356e10	+	2.41753e11i	−0.492831	+	1.48677i
$311$	1.24783e11			0.756371			0.378185	−	0.925730i	$-0.376548\pi$
$311$	1.24783e11			0.756371			0.378185	+	0.925730i	$0.376548\pi$
$312$		0			0
$313$	−2.95278e10			−0.173893			−0.0869463	−	0.996213i	$-0.527711\pi$
$313$	−2.95278e10			−0.173893			−0.0869463	+	0.996213i	$0.527711\pi$
$314$	−5.40663e10	+	1.63107e11i	−0.313865	+	0.946869i
$315$		0			0
$316$	8.31087e10	+	6.18984e10i	0.468872	+	0.349211i
$317$			1.20582e11i			0.670678i	0.942098	+	0.335339i	$0.108851\pi$
$317$			1.20582e11i			0.670678i	−0.942098	+	0.335339i	$0.891149\pi$
$318$		0			0
$319$	2.84735e10			0.153951
$320$	−3.25716e11	−	1.18777e11i	−1.73646	−	0.633221i
$321$		0			0
$322$	−1.26767e11	−	4.20205e10i	−0.657137	−	0.217826i
$323$		−	6.78187e10i		−	0.346687i
$324$		0			0
$325$			1.40168e11i			0.696906i
$326$	−5.49112e10	+	1.65656e11i	−0.269266	+	0.812323i
$327$		0			0
$328$	−9.68527e10	−	1.38410e11i	−0.462040	−	0.660291i
$329$	3.12845e11			1.47214
$330$		0			0
$331$			4.18670e11i			1.91711i	0.284913	+	0.958553i	$0.408035\pi$
$331$			4.18670e11i			1.91711i	−0.284913	+	0.958553i	$0.591965\pi$
$332$	1.86878e11	−	2.50914e11i	0.844182	−	1.13345i
$333$		0			0
$334$	−2.17294e11	−	7.20281e10i	−0.955409	−	0.316696i
$335$	−1.49721e11			−0.649504
$336$		0			0
$337$	2.95362e11			1.24744			0.623721	−	0.781647i	$-0.285620\pi$
$337$	2.95362e11			1.24744			0.623721	+	0.781647i	$0.285620\pi$
$338$	2.08818e11	+	6.92183e10i	0.870247	+	0.288467i
$339$		0			0
$340$	−1.09434e11	+	1.46933e11i	−0.444119	+	0.596301i
$341$			1.09174e11i			0.437245i
$342$		0			0
$343$	−2.24073e11			−0.874111
$344$	−3.76306e11	+	2.63321e11i	−1.44886	+	1.01385i
$345$		0			0
$346$	−1.35074e11	+	4.07492e11i	−0.506676	+	1.52854i
$347$			1.55047e10i			0.0574093i	0.999588	+	0.0287046i	$0.00913822\pi$
$347$			1.55047e10i			0.0574093i	−0.999588	+	0.0287046i	$0.990862\pi$
$348$		0			0
$349$		−	3.06969e11i		−	1.10759i	−0.832652	−	0.553797i	$-0.813178\pi$
$349$		−	3.06969e11i		−	1.10759i	0.832652	−	0.553797i	$-0.186822\pi$
$350$	−7.06246e11	−	2.34104e11i	−2.51565	−	0.833879i
$351$		0			0
$352$	−1.48549e11	−	4.39810e9i	−0.515736	−	0.0152694i
$353$	−2.99671e11			−1.02721			−0.513604	−	0.858028i	$-0.671690\pi$
$353$	−2.99671e11			−1.02721			−0.513604	+	0.858028i	$0.671690\pi$
$354$		0			0
$355$		−	7.10124e11i		−	2.37305i
$356$	3.16833e11	+	2.35974e11i	1.04546	+	0.778644i
$357$		0			0
$358$	1.22936e11	−	3.70873e11i	0.395554	−	1.19331i
$359$	4.04368e11			1.28485			0.642424	−	0.766349i	$-0.277929\pi$
$359$	4.04368e11			1.28485			0.642424	+	0.766349i	$0.277929\pi$
$360$		0			0
$361$	8.30100e10			0.257246
$362$	−7.35893e10	+	2.22004e11i	−0.225230	+	0.679474i
$363$		0			0
$364$	6.32910e10	−	8.49784e10i	0.188967	−	0.253719i
$365$		−	2.36861e11i		−	0.698516i
$366$		0			0
$367$	5.07965e11			1.46163			0.730813	−	0.682578i	$-0.239141\pi$
$367$	5.07965e11			1.46163			0.730813	+	0.682578i	$0.239141\pi$
$368$	−6.35998e10	−	2.12754e11i	−0.180776	−	0.604731i
$369$		0			0
$370$	2.96993e10	+	9.84465e9i	0.0823833	+	0.0273082i
$371$		−	3.38395e11i		−	0.927345i
$372$		0			0
$373$			6.94617e10i			0.185804i	0.995675	+	0.0929022i	$0.0296144\pi$
$373$			6.94617e10i			0.185804i	−0.995675	+	0.0929022i	$0.970386\pi$
$374$	−2.47099e10	+	7.45449e10i	−0.0653054	+	0.197013i
$375$		0			0
$376$	2.98229e11	+	4.26192e11i	0.769493	+	1.09966i
$377$	−3.37546e10			−0.0860591
$378$		0			0
$379$			4.45070e11i			1.10803i	0.832507	+	0.554015i	$0.186905\pi$
$379$			4.45070e11i			1.10803i	−0.832507	+	0.554015i	$0.813095\pi$
$380$	5.19277e11	+	3.86752e11i	1.27753	+	0.951494i
$381$		0			0
$382$	1.96375e11	+	6.50938e10i	0.471847	+	0.156406i
$383$	4.50375e11			1.06950			0.534749	−	0.845011i	$-0.320406\pi$
$383$	4.50375e11			1.06950			0.534749	+	0.845011i	$0.320406\pi$
$384$		0			0
$385$	−4.50932e11			−1.04601
$386$	1.81598e10	+	6.01957e9i	0.0416360	+	0.0138014i
$387$		0			0
$388$	4.44672e11	+	3.31187e11i	0.996087	+	0.741875i
$389$		−	5.76192e11i		−	1.27583i	−0.770106	−	0.637916i	$-0.779797\pi$
$389$		−	5.76192e11i		−	1.27583i	0.770106	−	0.637916i	$-0.220203\pi$
$390$		0			0
$391$	−1.17344e11			−0.253901
$392$	5.44287e10	+	7.77829e10i	0.116424	+	0.166378i
$393$		0			0
$394$	−1.51224e10	+	4.56212e10i	−0.0316145	+	0.0953748i
$395$			5.22807e11i			1.08057i
$396$		0			0
$397$		−	3.22788e11i		−	0.652169i	−0.945341	−	0.326084i	$-0.894271\pi$
$397$		−	3.22788e11i		−	0.652169i	0.945341	−	0.326084i	$-0.105729\pi$
$398$	−6.29051e10	−	2.08516e10i	−0.125664	−	0.0416548i
$399$		0			0
$400$	−3.54327e11	−	1.18529e12i	−0.692045	−	2.31503i
$401$	−1.47838e11			−0.285520			−0.142760	−	0.989757i	$-0.545598\pi$
$401$	−1.47838e11			−0.285520			−0.142760	+	0.989757i	$0.545598\pi$
$402$		0			0
$403$		−	1.29423e11i		−	0.244421i
$404$	−1.90300e11	+	2.55509e11i	−0.355404	+	0.477188i
$405$		0			0
$406$	5.63758e10	−	1.70074e11i	0.102973	−	0.310650i
$407$	1.34120e10			0.0242281
$408$		0			0
$409$	−7.24078e11			−1.27947			−0.639735	−	0.768595i	$-0.720956\pi$
$409$	−7.24078e11			−1.27947			−0.639735	+	0.768595i	$0.720956\pi$
$410$	2.68161e11	−	8.08990e11i	0.468672	−	1.41389i
$411$		0			0
$412$	2.60406e11	+	1.93948e11i	0.445260	+	0.331625i
$413$		−	2.92422e10i		−	0.0494578i
$414$		0			0
$415$	1.57841e12			2.61218
$416$	1.76101e11	+	5.21384e9i	0.288298	+	0.00853567i
$417$		0			0
$418$	2.63449e11	+	8.73272e10i	0.422088	+	0.139912i
$419$		−	6.10316e11i		−	0.967368i	−0.875243	−	0.483684i	$-0.839298\pi$
$419$		−	6.10316e11i		−	0.967368i	0.875243	−	0.483684i	$-0.160702\pi$
$420$		0			0
$421$		−	7.16040e11i		−	1.11088i	−0.831556	−	0.555441i	$-0.812550\pi$
$421$		−	7.16040e11i		−	1.11088i	0.831556	−	0.555441i	$-0.187450\pi$
$422$	2.25384e11	−	6.79938e11i	0.345953	−	1.04367i
$423$		0			0
$424$	4.60999e11	−	3.22585e11i	0.692714	−	0.484728i
$425$	−6.53744e11			−0.971981
$426$		0			0
$427$		−	4.44995e11i		−	0.647783i
$428$	4.71421e11	−	6.32959e11i	0.679066	−	0.911756i
$429$		0			0
$430$	−2.19946e12	−	7.29070e11i	−3.10247	−	1.02840i
$431$	−4.78823e11			−0.668385			−0.334193	−	0.942505i	$-0.608464\pi$
$431$	−4.78823e11			−0.668385			−0.334193	+	0.942505i	$0.608464\pi$
$432$		0			0
$433$	−3.13312e11			−0.428334			−0.214167	−	0.976797i	$-0.568704\pi$
$433$	−3.13312e11			−0.428334			−0.214167	+	0.976797i	$0.568704\pi$
$434$	6.52106e11	+	2.16158e11i	0.882296	+	0.292461i
$435$		0			0
$436$	6.72168e11	−	9.02494e11i	0.890817	−	1.19607i
$437$			4.14703e11i			0.543965i
$438$		0			0
$439$	6.95985e11			0.894354			0.447177	−	0.894445i	$-0.352429\pi$
$439$	6.95985e11			0.894354			0.447177	+	0.894445i	$0.352429\pi$
$440$	−4.29864e11	−	6.14310e11i	−0.546757	−	0.781358i
$441$		0			0
$442$	2.92930e10	−	8.83711e10i	0.0365059	−	0.110131i
$443$			3.55482e11i			0.438531i	0.975665	+	0.219266i	$0.0703661\pi$
$443$			3.55482e11i			0.438531i	−0.975665	+	0.219266i	$0.929634\pi$
$444$		0			0
$445$			1.99308e12i			2.40938i
$446$	−1.05770e12	−	3.50603e11i	−1.26577	−	0.419574i
$447$		0			0
$448$	−3.20388e11	+	8.78587e11i	−0.375773	+	1.03047i
$449$	8.15188e11			0.946562			0.473281	−	0.880911i	$-0.343069\pi$
$449$	8.15188e11			0.946562			0.473281	+	0.880911i	$0.343069\pi$
$450$		0			0
$451$		−	3.65334e11i		−	0.415811i
$452$	2.23165e11	+	1.66211e11i	0.251479	+	0.187299i
$453$		0			0
$454$	−4.03826e11	+	1.21826e12i	−0.446111	+	1.34583i
$455$	5.34568e11			0.584725
$456$		0			0
$457$	−5.94548e11			−0.637623			−0.318811	−	0.947818i	$-0.603284\pi$
$457$	−5.94548e11			−0.637623			−0.318811	+	0.947818i	$0.603284\pi$
$458$	−2.37539e10	+	7.16608e10i	−0.0252255	+	0.0761004i
$459$		0			0
$460$	6.69179e11	−	8.98481e11i	0.696838	−	0.935618i
$461$			1.42516e12i			1.46964i	0.678265	+	0.734818i	$0.262732\pi$
$461$			1.42516e12i			1.46964i	−0.678265	+	0.734818i	$0.737268\pi$
$462$		0			0
$463$	−1.04996e12			−1.06183			−0.530917	−	0.847424i	$-0.678153\pi$
$463$	−1.04996e12			−1.06183			−0.530917	+	0.847424i	$0.678153\pi$
$464$	2.85436e11	−	8.53272e10i	0.285876	−	0.0854588i
$465$		0			0
$466$	9.88010e11	+	3.27503e11i	0.970565	+	0.321720i
$467$		−	1.15656e11i		−	0.112523i	−0.998416	−	0.0562616i	$-0.982082\pi$
$467$		−	1.15656e11i		−	0.112523i	0.998416	−	0.0562616i	$-0.0179181\pi$
$468$		0			0
$469$			4.03859e11i			0.385436i
$470$	−8.25722e11	+	2.49104e12i	−0.780537	+	2.35473i
$471$		0			0
$472$	3.98369e10	−	2.78760e10i	0.0369443	−	0.0258518i
$473$	−9.93261e11			−0.912406
$474$		0			0
$475$			2.31039e12i			2.08240i
$476$	3.96339e11	+	2.95189e11i	0.353863	+	0.263554i
$477$		0			0
$478$	8.71917e11	+	2.89020e11i	0.763923	+	0.253223i
$479$	−1.37302e12			−1.19170			−0.595849	−	0.803096i	$-0.703184\pi$
$479$	−1.37302e12			−1.19170			−0.595849	+	0.803096i	$0.703184\pi$
$480$		0			0
$481$	−1.58996e10			−0.0135436
$482$	7.41444e11	+	2.45772e11i	0.625701	+	0.207406i
$483$		0			0
$484$	7.10472e11	+	5.29152e11i	0.588495	+	0.438305i
$485$			2.79727e12i			2.29561i
$486$		0			0
$487$	−1.53458e12			−1.23626			−0.618131	−	0.786075i	$-0.712110\pi$
$487$	−1.53458e12			−1.23626			−0.618131	+	0.786075i	$0.712110\pi$
$488$	6.06221e11	−	4.24205e11i	0.483885	−	0.338599i
$489$		0			0
$490$	−1.50700e11	+	4.54631e11i	−0.118095	+	0.356268i
$491$		−	5.12475e11i		−	0.397929i	−0.980007	−	0.198965i	$-0.936242\pi$
$491$		−	5.12475e11i		−	0.397929i	0.980007	−	0.198965i	$-0.0637579\pi$
$492$		0			0
$493$		−	1.57431e11i		−	0.120027i
$494$	−3.12312e11	−	1.03524e11i	−0.235949	−	0.0782115i
$495$		0			0
$496$	3.27165e11	+	1.09443e12i	0.242716	+	0.811934i
$497$	−1.91549e12			−1.40824
$498$		0			0
$499$		−	2.45745e12i		−	1.77432i	−0.461463	−	0.887159i	$-0.652675\pi$
$499$		−	2.45745e12i		−	1.77432i	0.461463	−	0.887159i	$-0.347325\pi$
$500$	2.18519e12	−	2.93397e12i	1.56359	−	2.09938i
$501$		0			0
$502$	−5.58069e11	+	1.68358e12i	−0.392212	+	1.18323i
$503$	2.11765e11			0.147502			0.0737512	−	0.997277i	$-0.476503\pi$
$503$	2.11765e11			0.147502			0.0737512	+	0.997277i	$0.476503\pi$
$504$		0			0
$505$	−1.60731e12			−1.09974
$506$	1.51098e11	−	4.55833e11i	0.102467	−	0.309121i
$507$		0			0
$508$	−9.90857e11	−	7.37979e11i	−0.660122	−	0.491652i
$509$		−	2.27707e12i		−	1.50365i	−0.659363	−	0.751824i	$-0.729174\pi$
$509$		−	2.27707e12i		−	1.50365i	0.659363	−	0.751824i	$-0.270826\pi$
$510$		0			0
$511$	−6.38911e11			−0.414521
$512$	−1.50233e12	+	4.01071e11i	−0.966163	+	0.257933i
$513$		0			0
$514$	−2.28720e12	−	7.58153e11i	−1.44534	−	0.479097i
$515$			1.63812e12i			1.02616i
$516$		0			0
$517$			1.12494e12i			0.692501i
$518$	2.65550e10	−	8.01111e10i	0.0162055	−	0.0488888i
$519$		0			0
$520$	5.09593e11	+	7.28249e11i	0.305639	+	0.436782i
$521$	−3.15742e12			−1.87742			−0.938712	−	0.344703i	$-0.887980\pi$
$521$	−3.15742e12			−1.87742			−0.938712	+	0.344703i	$0.887980\pi$
$522$		0			0
$523$		−	6.70464e11i		−	0.391848i	−0.980619	−	0.195924i	$-0.937229\pi$
$523$		−	6.70464e11i		−	0.391848i	0.980619	−	0.195924i	$-0.0627706\pi$
$524$	−4.82431e11	+	6.47742e11i	−0.279541	+	0.375328i
$525$		0			0
$526$	1.37431e10	+	4.55553e9i	0.00782799	+	0.00259480i
$527$	6.03629e11			0.340896
$528$		0			0
$529$	−1.08361e12			−0.601621
$530$	2.69448e12	+	8.93159e11i	1.48332	+	0.491685i
$531$		0			0
$532$	1.04323e12	−	1.40070e12i	0.564646	−	0.758128i
$533$			4.33094e11i			0.232440i
$534$		0			0
$535$	3.98172e12			2.10125
$536$	−5.50182e11	+	3.84991e11i	−0.287915	+	0.201469i
$537$		0			0
$538$	6.84058e11	−	2.06367e12i	0.352025	−	1.06199i
$539$			2.05308e11i			0.104775i
$540$		0			0
$541$		−	6.87645e11i		−	0.345125i	−0.984999	−	0.172562i	$-0.944795\pi$
$541$		−	6.87645e11i		−	0.345125i	0.984999	−	0.172562i	$-0.0552047\pi$
$542$	−2.10150e12	−	6.96599e11i	−1.04600	−	0.346726i
$543$		0			0
$544$	−2.43173e10	+	8.21335e11i	−0.0119048	+	0.402092i
$545$	5.67726e12			2.75648
$546$		0			0
$547$			2.73174e12i			1.30466i	0.757936	+	0.652328i	$0.226208\pi$
$547$			2.73174e12i			1.30466i	−0.757936	+	0.652328i	$0.773792\pi$
$548$	2.62420e12	+	1.95448e12i	1.24304	+	0.925803i
$549$		0			0
$550$	8.41798e11	−	2.53954e12i	0.392262	−	1.18338i
$551$	−5.56377e11			−0.257150
$552$		0			0
$553$	1.41022e12			0.641245
$554$	1.14907e12	−	3.46650e12i	0.518264	−	1.56350i
$555$		0			0
$556$	−7.52024e11	+	1.00971e12i	−0.333730	+	0.448086i
$557$		−	3.59464e12i		−	1.58236i	−0.611580	−	0.791182i	$-0.709466\pi$
$557$		−	3.59464e12i		−	1.58236i	0.611580	−	0.791182i	$-0.290534\pi$
$558$		0			0
$559$	1.17749e12			0.510038
$560$	−4.52043e12	+	1.35132e12i	−1.94238	+	0.580647i
$561$		0			0
$562$	5.83027e11	+	1.93260e11i	0.246533	+	0.0817200i
$563$		−	4.60263e11i		−	0.193072i	−0.995330	−	0.0965358i	$-0.969224\pi$
$563$		−	4.60263e11i		−	0.193072i	0.995330	−	0.0965358i	$-0.0307762\pi$
$564$		0			0
$565$			1.40385e12i			0.579565i
$566$	1.99455e11	−	6.01717e11i	0.0816906	−	0.246444i
$567$		0			0
$568$	−1.82600e12	−	2.60950e12i	−0.736094	−	1.05194i
$569$	1.91911e12			0.767527			0.383764	−	0.923431i	$-0.374628\pi$
$569$	1.91911e12			0.767527			0.383764	+	0.923431i	$0.374628\pi$
$570$		0			0
$571$		−	2.01838e12i		−	0.794586i	−0.917692	−	0.397293i	$-0.869950\pi$
$571$		−	2.01838e12i		−	0.794586i	0.917692	−	0.397293i	$-0.130050\pi$
$572$	3.05568e11	+	2.27583e11i	0.119351	+	0.0888912i
$573$		0			0
$574$	−2.18217e12	−	7.23340e11i	−0.839046	−	0.278124i
$575$	3.99757e12			1.52507
$576$		0			0
$577$	−6.91957e11			−0.259889			−0.129945	−	0.991521i	$-0.541480\pi$
$577$	−6.91957e11			−0.259889			−0.129945	+	0.991521i	$0.541480\pi$
$578$	−2.13489e12	−	7.07667e11i	−0.795610	−	0.263726i
$579$		0			0
$580$	1.20543e12	+	8.97788e11i	0.442298	+	0.329419i
$581$		−	4.25760e12i		−	1.55015i
$582$		0			0
$583$	1.21681e12			0.436229
$584$	−6.09061e11	−	8.70396e11i	−0.216672	−	0.309641i
$585$		0			0
$586$	1.77277e11	−	5.34808e11i	0.0621029	−	0.187352i
$587$			1.99542e12i			0.693686i	0.937923	+	0.346843i	$0.112746\pi$
$587$			1.99542e12i			0.693686i	−0.937923	+	0.346843i	$0.887254\pi$
$588$		0			0
$589$		−	2.13328e12i		−	0.730347i
$590$	2.32842e11	+	7.71817e10i	0.0791092	+	0.0262229i
$591$		0			0
$592$	1.34451e11	−	4.01922e10i	0.0449899	−	0.0134491i
$593$	−5.19417e12			−1.72492			−0.862462	−	0.506121i	$-0.831079\pi$
$593$	−5.19417e12			−1.72492			−0.862462	+	0.506121i	$0.831079\pi$
$594$		0			0
$595$			2.49323e12i			0.815521i
$596$	1.17603e12	−	1.57901e12i	0.381778	−	0.512599i
$597$		0			0
$598$	−1.79123e11	+	5.40379e11i	−0.0572792	+	0.172800i
$599$	−4.47443e12			−1.42010			−0.710048	−	0.704154i	$-0.751327\pi$
$599$	−4.47443e12			−1.42010			−0.710048	+	0.704154i	$0.751327\pi$
$600$		0			0
$601$	3.10552e12			0.970955			0.485477	−	0.874249i	$-0.338646\pi$
$601$	3.10552e12			0.970955			0.485477	+	0.874249i	$0.338646\pi$
$602$	−1.96660e12	+	5.93283e12i	−0.610283	+	1.84110i
$603$		0			0
$604$	1.67382e12	+	1.24664e12i	0.511731	+	0.381132i
$605$			4.46932e12i			1.35626i
$606$		0			0
$607$	−3.79043e12			−1.13329			−0.566643	−	0.823964i	$-0.691758\pi$
$607$	−3.79043e12			−1.13329			−0.566643	+	0.823964i	$0.691758\pi$
$608$	2.90268e12	+	8.59398e10i	0.861455	+	0.0255052i
$609$		0			0
$610$	3.54329e12	+	1.17452e12i	1.03615	+	0.343459i
$611$		−	1.33358e12i		−	0.387111i
$612$		0			0
$613$		−	6.09780e12i		−	1.74422i	−0.489310	−	0.872110i	$-0.662751\pi$
$613$		−	6.09780e12i		−	1.74422i	0.489310	−	0.872110i	$-0.337249\pi$
$614$	1.22269e12	−	3.68862e12i	0.347184	−	1.04738i
$615$		0			0
$616$	−1.65704e12	+	1.15952e12i	−0.463682	+	0.324462i
$617$	2.07665e12			0.576872			0.288436	−	0.957499i	$-0.406865\pi$
$617$	2.07665e12			0.576872			0.288436	+	0.957499i	$0.406865\pi$
$618$		0			0
$619$		−	6.03694e12i		−	1.65276i	−0.563115	−	0.826379i	$-0.690397\pi$
$619$		−	6.03694e12i		−	1.65276i	0.563115	−	0.826379i	$-0.309603\pi$
$620$	−3.44233e12	+	4.62189e12i	−0.935600	+	1.25619i
$621$		0			0
$622$	2.68012e12	+	8.88398e11i	0.717955	+	0.237986i
$623$	5.37615e12			1.42980
$624$		0			0
$625$	9.23927e12			2.42202
$626$	−6.34202e11	−	2.10224e11i	−0.165061	−	0.0547138i
$627$		0			0
$628$	−2.32249e12	+	3.11832e12i	−0.595849	+	0.800023i
$629$		−	7.41558e10i		−	0.0188893i
$630$		0			0
$631$	−7.01879e12			−1.76250			−0.881252	−	0.472648i	$-0.843298\pi$
$631$	−7.01879e12			−1.76250			−0.881252	+	0.472648i	$0.843298\pi$
$632$	1.34434e12	+	1.92116e12i	0.335182	+	0.479001i
$633$		0			0
$634$	−8.58483e11	+	2.58987e12i	−0.211023	+	0.636615i
$635$		−	6.23312e12i		−	1.52133i
$636$		0			0
$637$		−	2.43388e11i		−	0.0585695i
$638$	6.11558e11	+	2.02718e11i	0.146132	+	0.0484394i
$639$		0			0
$640$	−6.15015e12	−	4.87005e12i	−1.44903	−	1.14742i
$641$	6.65994e12			1.55815			0.779075	−	0.626931i	$-0.215689\pi$
$641$	6.65994e12			1.55815			0.779075	+	0.626931i	$0.215689\pi$
$642$		0			0
$643$			3.60863e12i			0.832516i	0.909247	+	0.416258i	$0.136659\pi$
$643$			3.60863e12i			0.832516i	−0.909247	+	0.416258i	$0.863341\pi$
$644$	−2.42357e12	−	1.80505e12i	−0.555224	−	0.413525i
$645$		0			0
$646$	4.82837e11	−	1.45662e12i	0.109082	−	0.329079i
$647$	−3.26245e12			−0.731938			−0.365969	−	0.930627i	$-0.619262\pi$
$647$	−3.26245e12			−0.731938			−0.365969	+	0.930627i	$0.619262\pi$
$648$		0			0
$649$	1.05150e11			0.0232652
$650$	−9.97931e11	+	3.01056e12i	−0.219276	+	0.661511i
$651$		0			0
$652$	−2.35879e12	+	3.16705e12i	−0.511181	+	0.686343i
$653$		−	4.35965e11i		−	0.0938302i	−0.998899	−	0.0469151i	$-0.985061\pi$
$653$		−	4.35965e11i		−	0.0938302i	0.998899	−	0.0469151i	$-0.0149390\pi$
$654$		0			0
$655$	−4.07471e12			−0.864990
$656$	−1.09481e12	−	3.66234e12i	−0.230818	−	0.772132i
$657$		0			0
$658$	6.71934e12	+	2.22731e12i	1.39737	+	0.463195i
$659$			2.27883e12i			0.470683i	0.971913	+	0.235341i	$0.0756208\pi$
$659$			2.27883e12i			0.470683i	−0.971913	+	0.235341i	$0.924379\pi$
$660$		0			0
$661$		−	6.28607e12i		−	1.28077i	−0.768052	−	0.640387i	$-0.778774\pi$
$661$		−	6.28607e12i		−	1.28077i	0.768052	−	0.640387i	$-0.221226\pi$
$662$	−2.98073e12	+	8.99228e12i	−0.603201	+	1.81974i
$663$		0			0
$664$	5.80018e12	−	4.05869e12i	1.15794	−	0.810269i
$665$	8.81130e12			1.74720
$666$		0			0
$667$			9.62674e11i			0.188327i
$668$	−4.15428e12	−	3.09407e12i	−0.807239	−	0.601223i
$669$		0			0
$670$	−3.21574e12	−	1.06594e12i	−0.616516	−	0.204361i
$671$	1.60012e12			0.304721
$672$		0			0
$673$	−1.30391e12			−0.245007			−0.122504	−	0.992468i	$-0.539092\pi$
$673$	−1.30391e12			−0.245007			−0.122504	+	0.992468i	$0.539092\pi$
$674$	6.34385e12	+	2.10284e12i	1.18409	+	0.392497i
$675$		0			0
$676$	3.99223e12	+	2.97337e12i	0.735284	+	0.547632i
$677$			3.77662e12i			0.690962i	0.938426	+	0.345481i	$0.112284\pi$
$677$			3.77662e12i			0.690962i	−0.938426	+	0.345481i	$0.887716\pi$
$678$		0			0
$679$	7.54538e12			1.36228
$680$	−3.39655e12	+	2.37674e12i	−0.609183	+	0.426277i
$681$		0			0
$682$	−7.77267e11	+	2.34486e12i	−0.137575	+	0.415037i
$683$		−	8.09351e12i		−	1.42313i	−0.702622	−	0.711563i	$-0.747987\pi$
$683$		−	8.09351e12i		−	1.42313i	0.702622	−	0.711563i	$-0.252013\pi$
$684$		0			0
$685$			1.65079e13i			2.86474i
$686$	−4.81269e12	−	1.59530e12i	−0.829716	−	0.275032i
$687$		0			0
$688$	−9.95708e12	+	2.97653e12i	−1.69428	+	0.506480i
$689$	−1.44250e12			−0.243853
$690$		0			0
$691$			1.04215e12i			0.173891i	0.996213	+	0.0869455i	$0.0277106\pi$
$691$			1.04215e12i			0.173891i	−0.996213	+	0.0869455i	$0.972289\pi$
$692$	−5.80230e12	+	7.79052e12i	−0.961884	+	1.29148i
$693$		0			0
$694$	−1.10386e11	+	3.33014e11i	−0.0180633	+	0.0544935i
$695$	−6.35174e12			−1.03267
$696$		0			0
$697$	−2.01995e12			−0.324185
$698$	2.18548e12	−	6.59315e12i	0.348495	−	1.05134i
$699$		0			0
$700$	−1.35022e13	−	1.00563e13i	−2.12551	−	1.58305i
$701$		−	2.19669e12i		−	0.343587i	−0.985133	−	0.171794i	$-0.945044\pi$
$701$		−	2.19669e12i		−	0.343587i	0.985133	−	0.171794i	$-0.0549562\pi$
$702$		0			0
$703$	−2.62073e11			−0.0404692
$704$	−3.15925e12	−	1.15206e12i	−0.484738	−	0.176766i
$705$		0			0
$706$	−6.43638e12	−	2.13351e12i	−0.975036	−	0.323202i
$707$			4.33557e12i			0.652618i
$708$		0			0
$709$			7.02990e11i			0.104482i	0.998635	+	0.0522410i	$0.0166364\pi$
$709$			7.02990e11i			0.104482i	−0.998635	+	0.0522410i	$0.983364\pi$
$710$	5.05574e12	−	1.52522e13i	0.746659	−	2.25252i
$711$		0			0
$712$	5.12498e12	+	7.32399e12i	0.747363	+	1.06804i
$713$	−3.69112e12			−0.534879
$714$		0			0
$715$			1.92222e12i			0.275058i
$716$	5.28088e12	−	7.09044e12i	0.750927	−	1.00824i
$717$		0			0
$718$	8.68510e12	+	2.87891e12i	1.21959	+	0.404267i
$719$	−1.18349e13			−1.65152			−0.825759	−	0.564022i	$-0.809253\pi$
$719$	−1.18349e13			−1.65152			−0.825759	+	0.564022i	$0.809253\pi$
$720$		0			0
$721$	4.41867e12			0.608952
$722$	1.78290e12	+	5.90992e11i	0.244180	+	0.0809401i
$723$		0			0
$724$	−3.16113e12	+	4.24433e12i	−0.427581	+	0.574097i
$725$			5.36325e12i			0.720953i
$726$		0			0
$727$	−4.66170e12			−0.618927			−0.309464	−	0.950911i	$-0.600150\pi$
$727$	−4.66170e12			−0.618927			−0.309464	+	0.950911i	$0.600150\pi$
$728$	1.96438e12	−	1.37458e12i	0.259200	−	0.181376i
$729$		0			0
$730$	1.68634e12	−	5.08735e12i	0.219782	−	0.663039i
$731$			5.49179e12i			0.711354i
$732$		0			0
$733$		−	1.16839e13i		−	1.49493i	−0.664300	−	0.747466i	$-0.731270\pi$
$733$		−	1.16839e13i		−	1.49493i	0.664300	−	0.747466i	$-0.268730\pi$
$734$	1.09102e13	+	3.61647e12i	1.38739	+	0.459888i
$735$		0			0
$736$	1.48698e11	−	5.02237e12i	0.0186790	−	0.630897i
$737$	−1.45221e12			−0.181311
$738$		0			0
$739$			1.25228e13i			1.54455i	0.635290	+	0.772274i	$0.280881\pi$
$739$			1.25228e13i			1.54455i	−0.635290	+	0.772274i	$0.719119\pi$
$740$	5.67799e11	+	4.22890e11i	0.0696068	+	0.0518424i
$741$		0			0
$742$	2.40921e12	−	7.26811e12i	0.291781	−	0.880246i
$743$	1.10289e13			1.32765			0.663823	−	0.747890i	$-0.268933\pi$
$743$	1.10289e13			1.32765			0.663823	+	0.747890i	$0.268933\pi$
$744$		0			0
$745$	9.93301e12			1.18135
$746$	−4.94534e11	+	1.49191e12i	−0.0584617	+	0.176367i
$747$		0			0
$748$	−1.06145e12	+	1.42517e12i	−0.123977	+	0.166459i
$749$		−	1.07403e13i		−	1.24695i
$750$		0			0
$751$	−6.45522e12			−0.740511			−0.370255	−	0.928930i	$-0.620730\pi$
$751$	−6.45522e12			−0.740511			−0.370255	+	0.928930i	$0.620730\pi$
$752$	3.37113e12	+	1.12771e13i	0.384410	+	1.28593i
$753$		0			0
$754$	−7.24987e11	−	2.40317e11i	−0.0816882	−	0.0270778i
$755$			1.05294e13i			1.17935i
$756$		0			0
$757$			6.48010e12i			0.717217i	0.933488	+	0.358608i	$0.116749\pi$
$757$			6.48010e12i			0.717217i	−0.933488	+	0.358608i	$0.883251\pi$
$758$	−3.16868e12	+	9.55929e12i	−0.348632	+	1.05175i
$759$		0			0
$760$	8.39963e12	+	1.20037e13i	0.913270	+	1.30513i
$761$	−2.62886e12			−0.284142			−0.142071	−	0.989856i	$-0.545376\pi$
$761$	−2.62886e12			−0.284142			−0.142071	+	0.989856i	$0.545376\pi$
$762$		0			0
$763$		−	1.53139e13i		−	1.63578i
$764$	3.75434e12	+	2.79619e12i	0.398670	+	0.296925i
$765$		0			0
$766$	9.67325e12	+	3.20646e12i	1.01518	+	0.336509i
$767$	−1.24652e11			−0.0130053
$768$		0			0
$769$	−1.43517e13			−1.47991			−0.739955	−	0.672656i	$-0.765153\pi$
$769$	−1.43517e13			−1.47991			−0.739955	+	0.672656i	$0.765153\pi$
$770$	−9.68520e12	−	3.21042e12i	−0.992888	−	0.329120i
$771$		0			0
$772$	3.47184e11	+	2.58579e11i	0.0351789	+	0.0262008i
$773$		−	6.56407e12i		−	0.661250i	−0.943762	−	0.330625i	$-0.892740\pi$
$773$		−	6.56407e12i		−	0.661250i	0.943762	−	0.330625i	$-0.107260\pi$
$774$		0			0
$775$	−2.05640e13			−2.04762
$776$	7.19286e12	+	1.02792e13i	0.712072	+	1.01761i
$777$		0			0
$778$	4.10221e12	−	1.23756e13i	0.401430	−	1.21103i
$779$			7.13870e12i			0.694545i
$780$		0			0
$781$		−	6.88778e12i		−	0.662444i
$782$	−2.52033e12	−	8.35431e11i	−0.241005	−	0.0798877i
$783$		0			0
$784$	6.15253e11	+	2.05814e12i	0.0581609	+	0.194560i
$785$	−1.96162e13			−1.84375
$786$		0			0
$787$			1.96637e13i			1.82717i	0.406649	+	0.913584i	$0.366697\pi$
$787$			1.96637e13i			1.82717i	−0.406649	+	0.913584i	$0.633303\pi$
$788$	−6.49602e11	+	8.72196e11i	−0.0600177	+	0.0805835i
$789$		0			0
$790$	−3.72213e12	+	1.12289e13i	−0.339993	+	1.02569i
$791$	3.78675e12			0.343932
$792$		0			0
$793$	−1.89691e12			−0.170340
$794$	2.29810e12	−	6.93290e12i	0.205199	−	0.619046i
$795$		0			0
$796$	−1.20263e12	−	8.95708e11i	−0.106175	−	0.0790784i
$797$			2.05859e12i			0.180721i	0.995909	+	0.0903603i	$0.0288019\pi$
$797$			2.05859e12i			0.180721i	−0.995909	+	0.0903603i	$0.971198\pi$
$798$		0			0
$799$	6.21983e12			0.539906
$800$	8.28424e11	−	2.79806e13i	0.0715069	−	2.41519i
$801$		0			0
$802$	−3.17530e12	−	1.05254e12i	−0.271019	−	0.0898365i
$803$		−	2.29741e12i		−	0.194993i
$804$		0			0
$805$		−	1.52458e13i		−	1.27958i
$806$	9.21431e11	−	2.77977e12i	0.0769051	−	0.232007i
$807$		0			0
$808$	−5.90640e12	+	4.13302e12i	−0.487497	+	0.341127i
$809$	9.44339e12			0.775103			0.387552	−	0.921848i	$-0.373321\pi$
$809$	9.44339e12			0.775103			0.387552	+	0.921848i	$0.373321\pi$
$810$		0			0
$811$		−	3.40891e12i		−	0.276708i	−0.990383	−	0.138354i	$-0.955819\pi$
$811$		−	3.40891e12i		−	0.276708i	0.990383	−	0.138354i	$-0.0441812\pi$
$812$	2.42170e12	−	3.25152e12i	0.195487	−	0.262473i
$813$		0			0
$814$	2.88066e11	+	9.54872e10i	0.0229976	+	0.00762317i
$815$	−1.99228e13			−1.58176
$816$		0			0
$817$	1.94085e13			1.52403
$818$	−1.55519e13	−	5.15509e12i	−1.21449	−	0.402575i
$819$		0			0
$820$	1.15192e13	−	1.54664e13i	0.889737	−	1.19462i
$821$			1.44900e12i			0.111307i	0.998450	+	0.0556535i	$0.0177242\pi$
$821$			1.44900e12i			0.111307i	−0.998450	+	0.0556535i	$0.982276\pi$
$822$		0			0
$823$	9.50599e12			0.722267			0.361134	−	0.932514i	$-0.382390\pi$
$823$	9.50599e12			0.722267			0.361134	+	0.932514i	$0.382390\pi$
$824$	4.21223e12	+	6.01961e12i	0.318302	+	0.454879i
$825$		0			0
$826$	2.08190e11	−	6.28069e11i	0.0155615	−	0.0469458i
$827$			1.32590e13i			0.985683i	0.870119	+	0.492842i	$0.164042\pi$
$827$			1.32590e13i			0.985683i	−0.870119	+	0.492842i	$0.835958\pi$
$828$		0			0
$829$			1.63326e13i			1.20104i	0.799608	+	0.600522i	$0.205040\pi$
$829$			1.63326e13i			1.20104i	−0.799608	+	0.600522i	$0.794960\pi$
$830$	3.39013e13	+	1.12375e13i	2.47951	+	0.821899i
$831$		0			0
$832$	3.74521e12	+	1.36574e12i	0.270970	+	0.0988127i
$833$	1.13516e12			0.0816873
$834$		0			0
$835$		−	2.61331e13i		−	1.86038i
$836$	5.03667e12	+	3.75126e12i	0.356628	+	0.265613i
$837$		0			0
$838$	4.34516e12	−	1.31085e13i	0.304374	−	0.918236i
$839$	−2.23005e12			−0.155377			−0.0776884	−	0.996978i	$-0.524754\pi$
$839$	−2.23005e12			−0.155377			−0.0776884	+	0.996978i	$0.524754\pi$
$840$		0			0
$841$	1.32156e13			0.910972
$842$	5.09786e12	−	1.53792e13i	0.349529	−	1.05446i
$843$		0			0
$844$	9.68167e12	−	1.29992e13i	0.656764	−	0.881812i
$845$			2.51137e13i			1.69455i
$846$		0			0
$847$	1.20556e13			0.804846
$848$	1.21981e13	−	3.64645e12i	0.810047	−	0.242152i
$849$		0			0
$850$	−1.40412e13	−	4.65435e12i	−0.922614	−	0.305825i
$851$			4.53454e11i			0.0296381i
$852$		0			0
$853$			2.83205e13i			1.83160i	0.401633	+	0.915801i	$0.368443\pi$
$853$			2.83205e13i			1.83160i	−0.401633	+	0.915801i	$0.631557\pi$
$854$	3.16815e12	−	9.55768e12i	0.203819	−	0.614882i
$855$		0			0
$856$	1.46316e13	−	1.02385e13i	0.931453	−	0.651786i
$857$	6.76700e12			0.428531			0.214266	−	0.976775i	$-0.431264\pi$
$857$	6.76700e12			0.428531			0.214266	+	0.976775i	$0.431264\pi$
$858$		0			0
$859$			2.30991e12i			0.144753i	0.997377	+	0.0723763i	$0.0230582\pi$
$859$			2.30991e12i			0.144753i	−0.997377	+	0.0723763i	$0.976942\pi$
$860$	−4.20497e13	−	3.13182e13i	−2.62132	−	1.95233i
$861$		0			0
$862$	−1.02842e13	−	3.40899e12i	−0.634438	−	0.210302i
$863$	1.05303e13			0.646237			0.323119	−	0.946358i	$-0.395269\pi$
$863$	1.05303e13			0.646237			0.323119	+	0.946358i	$0.395269\pi$
$864$		0			0
$865$	−4.90074e13			−2.97638
$866$	−6.72938e12	−	2.23064e12i	−0.406579	−	0.134772i
$867$		0			0
$868$	1.24671e13	+	9.28537e12i	0.745464	+	0.555214i
$869$			5.07091e12i			0.301646i
$870$		0			0
$871$	1.72156e12			0.101354
$872$	2.08623e13	−	1.45984e13i	1.22190	−	0.855030i
$873$		0			0
$874$	−2.95249e12	+	8.90708e12i	−0.171154	+	0.516338i
$875$		−	4.97848e13i		−	2.87118i
$876$		0			0
$877$		−	1.37761e13i		−	0.786373i	−0.919459	−	0.393186i	$-0.871373\pi$
$877$		−	1.37761e13i		−	0.786373i	0.919459	−	0.393186i	$-0.128627\pi$
$878$	1.49485e13	+	4.95508e12i	0.848931	+	0.281401i
$879$		0			0
$880$	−4.85911e12	−	1.62547e13i	−0.273140	−	0.913706i
$881$	1.13133e13			0.632698			0.316349	−	0.948643i	$-0.397543\pi$
$881$	1.13133e13			0.632698			0.316349	+	0.948643i	$0.397543\pi$
$882$		0			0
$883$		−	3.91577e12i		−	0.216768i	−0.994109	−	0.108384i	$-0.965432\pi$
$883$		−	3.91577e12i		−	0.216768i	0.994109	−	0.108384i	$-0.0345675\pi$
$884$	1.25832e12	−	1.68950e12i	0.0693037	−	0.0930514i
$885$		0			0
$886$	−2.53086e12	+	7.63510e12i	−0.137980	+	0.416259i
$887$	1.62707e12			0.0882573			0.0441287	−	0.999026i	$-0.485949\pi$
$887$	1.62707e12			0.0882573			0.0441287	+	0.999026i	$0.485949\pi$
$888$		0			0
$889$	−1.68133e13			−0.902805
$890$	−1.41898e13	+	4.28078e13i	−0.758091	+	2.28701i
$891$		0			0
$892$	−2.02213e13	−	1.50606e13i	−1.06947	−	0.796528i
$893$		−	2.19815e13i		−	1.15671i
$894$		0			0
$895$	4.46034e13			2.32362
$896$	−1.31365e13	+	1.65895e13i	−0.680915	+	0.859896i
$897$		0			0
$898$	1.75088e13	+	5.80375e12i	0.898487	+	0.297828i
$899$		−	4.95211e12i		−	0.252855i
$900$		0			0
$901$		−	6.72780e12i		−	0.340104i
$902$	2.60101e12	−	7.84671e12i	0.130831	−	0.394692i
$903$		0			0
$904$	3.60983e12	+	5.15873e12i	0.179775	+	0.256912i
$905$	−2.66995e13			−1.32308
$906$		0			0
$907$		−	7.72659e12i		−	0.379101i	−0.981871	−	0.189551i	$-0.939297\pi$
$907$		−	7.72659e12i		−	0.379101i	0.981871	−	0.189551i	$-0.0607031\pi$
$908$	−1.73469e13	+	2.32910e13i	−0.846906	+	1.13711i
$909$		0			0
$910$	1.14816e13	+	3.80587e12i	0.555028	+	0.183979i
$911$	1.47051e13			0.707350			0.353675	−	0.935368i	$-0.384932\pi$
$911$	1.47051e13			0.707350			0.353675	+	0.935368i	$0.384932\pi$
$912$		0			0
$913$	1.53096e13			0.729198
$914$	−1.27698e13	−	4.23290e12i	−0.605238	−	0.200623i
$915$		0			0
$916$	−1.02038e12	+	1.37003e12i	−0.0478887	+	0.0642983i
$917$			1.09911e13i			0.513312i
$918$		0			0
$919$	−3.87199e13			−1.79066			−0.895332	−	0.445399i	$-0.853062\pi$
$919$	−3.87199e13			−1.79066			−0.895332	+	0.445399i	$0.853062\pi$
$920$	2.07695e13	−	1.45335e13i	0.955831	−	0.668844i
$921$		0			0
$922$	−1.01465e13	+	3.06099e13i	−0.462408	+	1.39499i
$923$			8.16529e12i			0.370309i
$924$		0			0
$925$			2.52628e12i			0.113460i
$926$	−2.25512e13	−	7.47519e12i	−1.00790	−	0.334097i
$927$		0			0
$928$	6.73814e12	+	1.99497e11i	0.298246	+	0.00883019i
$929$	−7.75866e12			−0.341756			−0.170878	−	0.985292i	$-0.554660\pi$
$929$	−7.75866e12			−0.341756			−0.170878	+	0.985292i	$0.554660\pi$
$930$		0			0
$931$		−	4.01176e12i		−	0.175010i
$932$	1.88890e13	+	1.40683e13i	0.820044	+	0.610760i
$933$		0			0
$934$	8.23415e11	−	2.48408e12i	0.0354045	−	0.106808i
$935$	−8.96521e12			−0.383626
$936$		0			0
$937$	−1.60112e13			−0.678573			−0.339286	−	0.940683i	$-0.610186\pi$
$937$	−1.60112e13			−0.678573			−0.339286	+	0.940683i	$0.610186\pi$
$938$	−2.87528e12	+	8.67416e12i	−0.121274	+	0.365860i
$939$		0			0
$940$	−3.54700e13	+	4.76243e13i	−1.48179	+	1.98954i
$941$			1.55404e13i			0.646115i	0.946379	+	0.323057i	$0.104711\pi$
$941$			1.55404e13i			0.646115i	−0.946379	+	0.323057i	$0.895289\pi$
$942$		0			0
$943$	1.23518e13			0.508659
$944$	1.05409e12	−	3.15105e11i	0.0432019	−	0.0129146i
$945$		0			0
$946$	−2.13334e13	−	7.07154e12i	−0.866065	−	0.287081i
$947$		−	1.38291e13i		−	0.558750i	−0.960182	−	0.279375i	$-0.909873\pi$
$947$		−	1.38291e13i		−	0.558750i	0.960182	−	0.279375i	$-0.0901273\pi$
$948$		0			0
$949$			2.72353e12i			0.109002i
$950$	−1.64489e13	+	4.96231e13i	−0.655210	+	1.97664i
$951$		0			0
$952$	6.41104e12	+	9.16187e12i	0.252966	+	0.361508i
$953$	1.62441e12			0.0637935			0.0318967	−	0.999491i	$-0.489845\pi$
$953$	1.62441e12			0.0637935			0.0318967	+	0.999491i	$0.489845\pi$
$954$		0			0
$955$			2.36172e13i			0.918784i
$956$	1.66695e13	+	1.24153e13i	0.645449	+	0.480724i
$957$		0			0
$958$	−2.94899e13	−	9.77523e12i	−1.13117	−	0.374958i
$959$	4.45285e13			1.70002
$960$		0			0
$961$	−7.45207e12			−0.281852
$962$	−3.41495e11	−	1.13198e11i	−0.0128557	−	0.00426137i
$963$		0			0
$964$	1.41751e13	+	1.05575e13i	0.528664	+	0.393743i
$965$			2.18401e12i			0.0810740i
$966$		0			0
$967$	2.99781e13			1.10252			0.551259	−	0.834334i	$-0.314148\pi$
$967$	2.99781e13			1.10252			0.551259	+	0.834334i	$0.314148\pi$
$968$	1.14923e13	+	1.64234e13i	0.420697	+	0.601209i
$969$		0			0
$970$	−1.99153e13	+	6.00804e13i	−0.722293	+	2.17901i
$971$			3.61921e13i			1.30655i	0.757119	+	0.653277i	$0.226606\pi$
$971$			3.61921e13i			1.30655i	−0.757119	+	0.653277i	$0.773394\pi$
$972$		0			0
$973$			1.71332e13i			0.612818i
$974$	−3.29601e13	−	1.09255e13i	−1.17347	−	0.388979i
$975$		0			0
$976$	1.60407e13	−	4.79514e12i	0.565846	−	0.169152i
$977$	−2.29688e13			−0.806515			−0.403258	−	0.915087i	$-0.632122\pi$
$977$	−2.29688e13			−0.806515			−0.403258	+	0.915087i	$0.632122\pi$
$978$		0			0
$979$			1.93317e13i			0.672586i
$980$	−6.47351e12	+	8.69174e12i	−0.224193	+	0.301016i
$981$		0			0
$982$	3.64858e12	−	1.10070e13i	0.125205	−	0.377719i
$983$	2.02509e13			0.691758			0.345879	−	0.938279i	$-0.387581\pi$
$983$	2.02509e13			0.691758			0.345879	+	0.938279i	$0.387581\pi$
$984$		0			0
$985$	−5.48667e12			−0.185715
$986$	1.12084e12	−	3.38134e12i	0.0377656	−	0.113931i
$987$		0			0
$988$	−5.97085e12	−	4.44703e12i	−0.199356	−	0.148478i
$989$		−	3.35817e13i		−	1.11614i
$990$		0			0
$991$	−1.63486e12			−0.0538456			−0.0269228	−	0.999638i	$-0.508571\pi$
$991$	−1.63486e12			−0.0538456			−0.0269228	+	0.999638i	$0.508571\pi$
$992$	−7.64918e11	+	2.58356e13i	−0.0250791	+	0.847065i
$993$		0			0
$994$	−4.11413e13	−	1.36374e13i	−1.33672	−	0.443091i
$995$		−	7.56533e12i		−	0.244694i
$996$		0			0
$997$		−	9.91675e12i		−	0.317864i	−0.987290	−	0.158932i	$-0.949195\pi$
$997$		−	9.91675e12i		−	0.317864i	0.987290	−	0.158932i	$-0.0508050\pi$
$998$	1.74959e13	−	5.27815e13i	0.558274	−	1.68420i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	72.10.d.b.37.8		8
3.2	odd	2		8.10.b.a.5.1	✓	8
4.3	odd	2		288.10.d.b.145.8		8
8.3	odd	2		288.10.d.b.145.1		8
8.5	even	2	inner	72.10.d.b.37.7		8
12.11	even	2		32.10.b.a.17.3		8
24.5	odd	2		8.10.b.a.5.2	yes	8
24.11	even	2		32.10.b.a.17.6		8
48.5	odd	4		256.10.a.p.1.6		8
48.11	even	4		256.10.a.s.1.3		8
48.29	odd	4		256.10.a.p.1.3		8
48.35	even	4		256.10.a.s.1.6		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8.10.b.a.5.1	✓	8	3.2	odd	2
8.10.b.a.5.2	yes	8	24.5	odd	2
32.10.b.a.17.3		8	12.11	even	2
32.10.b.a.17.6		8	24.11	even	2
72.10.d.b.37.7		8	8.5	even	2	inner
72.10.d.b.37.8		8	1.1	even	1	trivial
256.10.a.p.1.3		8	48.29	odd	4
256.10.a.p.1.6		8	48.5	odd	4
256.10.a.s.1.3		8	48.11	even	4
256.10.a.s.1.6		8	48.35	even	4
288.10.d.b.145.1		8	8.3	odd	2
288.10.d.b.145.8		8	4.3	odd	2

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:	\( N \)	\(=\)	\( 72 = 2^{3} \cdot 3^{2} \)
Weight:	\( k \)	\(=\)	\( 10 \)
Character orbit:	\([\chi]\)	\(=\)	72.d (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(21.4782 + 7.11952i) q^{2} +(410.625 + 305.829i) q^{4} +2583.09i q^{5} +6967.65 q^{7} +(6642.12 + 9492.10i) q^{8} +O(q^{10})\)	\(q+(21.4782 + 7.11952i) q^{2} +(410.625 + 305.829i) q^{4} +2583.09i q^{5} +6967.65 q^{7} +(6642.12 + 9492.10i) q^{8} +(-18390.4 + 55480.1i) q^{10} +25054.5i q^{11} -29701.4i q^{13} +(149652. + 49606.3i) q^{14} +(75081.4 + 251162. i) q^{16} +138527. q^{17} -489569. i q^{19} +(-789984. + 1.06068e6i) q^{20} +(-178376. + 538124. i) q^{22} -847079. q^{23} -4.71924e6 q^{25} +(211460. - 637933. i) q^{26} +(2.86109e6 + 2.13091e6i) q^{28} -1.13646e6i q^{29} +4.35747e6 q^{31} +(-175542. + 5.92904e6i) q^{32} +(2.97532e6 + 986249. i) q^{34} +1.79981e7i q^{35} -535315. i q^{37} +(3.48550e6 - 1.05151e7i) q^{38} +(-2.45190e7 + 1.71572e7i) q^{40} -1.45816e7 q^{41} +3.96441e7i q^{43} +(-7.66238e6 + 1.02880e7i) q^{44} +(-1.81937e7 - 6.03080e6i) q^{46} +4.48997e7 q^{47} +8.19448e6 q^{49} +(-1.01361e8 - 3.35988e7i) q^{50} +(9.08355e6 - 1.21961e7i) q^{52} -4.85666e7i q^{53} -6.47180e7 q^{55} +(4.62799e7 + 6.61376e7i) q^{56} +(8.09108e6 - 2.44092e7i) q^{58} -4.19685e6i q^{59} -6.38659e7i q^{61} +(9.35906e7 + 3.10231e7i) q^{62} +(-4.59823e7 + 1.26095e8i) q^{64} +7.67215e7 q^{65} +5.79621e7i q^{67} +(5.68828e7 + 4.23657e7i) q^{68} +(-1.28138e8 + 3.86566e8i) q^{70} -2.74912e8 q^{71} -9.16969e7 q^{73} +(3.81119e6 - 1.14976e7i) q^{74} +(1.49724e8 - 2.01029e8i) q^{76} +1.74571e8i q^{77} +2.02396e8 q^{79} +(-6.48774e8 + 1.93942e8i) q^{80} +(-3.13186e8 - 1.03814e8i) q^{82} -6.11053e8i q^{83} +3.57829e8i q^{85} +(-2.82247e8 + 8.51483e8i) q^{86} +(-2.37819e8 + 1.66415e8i) q^{88} +7.71588e8 q^{89} -2.06949e8i q^{91} +(-3.47831e8 - 2.59061e8i) q^{92} +(9.64363e8 + 3.19664e8i) q^{94} +1.26460e9 q^{95} +1.08292e9 q^{97} +(1.76003e8 + 5.83408e7i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 18 q^{2} - 428 q^{4} + 4800 q^{7} + 3384 q^{8}+O(q^{10}) \) 8 * q + 18 * q^2 - 428 * q^4 + 4800 * q^7 + 3384 * q^8	\( 8 q + 18 q^{2} - 428 q^{4} + 4800 q^{7} + 3384 q^{8} + 26392 q^{10} + 72336 q^{14} + 185616 q^{16} + 102000 q^{17} - 1245264 q^{20} - 2373124 q^{22} - 3412032 q^{23} - 2423384 q^{25} - 4551240 q^{26} + 7509920 q^{28} + 803584 q^{31} + 14113248 q^{32} + 27757244 q^{34} + 63661140 q^{38} - 93063648 q^{40} + 2180784 q^{41} - 114013320 q^{44} - 131840944 q^{46} - 7432320 q^{47} + 24436680 q^{49} - 231784902 q^{50} + 219270896 q^{52} + 7056832 q^{55} + 358503360 q^{56} + 375425192 q^{58} + 344291904 q^{62} - 316815296 q^{64} + 146501760 q^{65} - 79875048 q^{68} - 56202048 q^{70} - 560234688 q^{71} - 523987120 q^{73} + 65773608 q^{74} - 87532760 q^{76} - 248943744 q^{79} - 890441280 q^{80} - 1051981172 q^{82} - 1492810428 q^{86} + 1544767952 q^{88} - 744827856 q^{89} + 2959012128 q^{92} + 3068552352 q^{94} + 1465245504 q^{95} - 9932784 q^{97} + 3062604162 q^{98}+O(q^{100}) \) 8 * q + 18 * q^2 - 428 * q^4 + 4800 * q^7 + 3384 * q^8 + 26392 * q^10 + 72336 * q^14 + 185616 * q^16 + 102000 * q^17 - 1245264 * q^20 - 2373124 * q^22 - 3412032 * q^23 - 2423384 * q^25 - 4551240 * q^26 + 7509920 * q^28 + 803584 * q^31 + 14113248 * q^32 + 27757244 * q^34 + 63661140 * q^38 - 93063648 * q^40 + 2180784 * q^41 - 114013320 * q^44 - 131840944 * q^46 - 7432320 * q^47 + 24436680 * q^49 - 231784902 * q^50 + 219270896 * q^52 + 7056832 * q^55 + 358503360 * q^56 + 375425192 * q^58 + 344291904 * q^62 - 316815296 * q^64 + 146501760 * q^65 - 79875048 * q^68 - 56202048 * q^70 - 560234688 * q^71 - 523987120 * q^73 + 65773608 * q^74 - 87532760 * q^76 - 248943744 * q^79 - 890441280 * q^80 - 1051981172 * q^82 - 1492810428 * q^86 + 1544767952 * q^88 - 744827856 * q^89 + 2959012128 * q^92 + 3068552352 * q^94 + 1465245504 * q^95 - 9932784 * q^97 + 3062604162 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more