LMFDB - Embedded newform 72.8.d.b.37.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [72,8,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, 8, names="a")

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

chi := DirichletCharacter("72.37");

S:= CuspForms(chi, 8);

N := Newforms(S);

Level:	$ N $	$=$	$ 72 = 2^{3} \cdot 3^{2} $
Weight:	$ k $	$=$	$ 8 $
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:	$22.4917218349$
Analytic rank:	$0$
Dimension:	$6$
Coefficient field:	$\mathbb{Q}[x]/(x^{6} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - 3x^{5} - 10x^{4} - 24x^{3} - 320x^{2} - 3072x + 32768 $ x^6 - 3x^5 - 10x^4 - 24x^3 - 320x^2 - 3072*x + 32768
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{15} $
Twist minimal:	no (minimal twist has level 8)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			37.6
Root			$-4.85268 + 2.90715i$ of defining polynomial
Character	$\chi$	$=$	72.37
Dual form			72.8.d.b.37.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(9.70536 + 5.81430i) q^{2} +(60.3879 + 112.860i) q^{4} -324.492i q^{5} -956.960 q^{7} +(-70.1132 + 1446.46i) q^{8} +O(q^{10})$	\(q+(9.70536 + 5.81430i) q^{2} +(60.3879 + 112.860i) q^{4} -324.492i q^{5} -956.960 q^{7} +(-70.1132 + 1446.46i) q^{8} +(1886.69 - 3149.31i) q^{10} -5452.20i q^{11} -6289.38i q^{13} +(-9287.64 - 5564.05i) q^{14} +(-9090.60 + 13630.7i) q^{16} -34587.3 q^{17} -14595.6i q^{19} +(36622.0 - 19595.4i) q^{20} +(31700.7 - 52915.6i) q^{22} +24667.5 q^{23} -27169.8 q^{25} +(36568.3 - 61040.6i) q^{26} +(-57788.8 - 108002. i) q^{28} -171116. i q^{29} +111688. q^{31} +(-167481. + 79435.5i) q^{32} +(-335682. - 201101. i) q^{34} +310526. i q^{35} -103636. i q^{37} +(84863.4 - 141656. i) q^{38} +(469363. + 22751.1i) q^{40} -71691.3 q^{41} -328419. i q^{43} +(615334. - 329247. i) q^{44} +(239406. + 143424. i) q^{46} -119043. q^{47} +92230.3 q^{49} +(-263693. - 157973. i) q^{50} +(709817. - 379802. i) q^{52} +1.04011e6i q^{53} -1.76919e6 q^{55} +(67095.6 - 1.38420e6i) q^{56} +(994918. - 1.66074e6i) q^{58} +225984. i q^{59} +1.55268e6i q^{61} +(1.08398e6 + 649390. i) q^{62} +(-2.08732e6 - 202831. i) q^{64} -2.04085e6 q^{65} +316375. i q^{67} +(-2.08865e6 - 3.90351e6i) q^{68} +(-1.80549e6 + 3.01376e6i) q^{70} -538965. q^{71} -2.68512e6 q^{73} +(602570. - 1.00582e6i) q^{74} +(1.64726e6 - 881400. i) q^{76} +5.21754e6i q^{77} +8.22632e6 q^{79} +(4.42305e6 + 2.94982e6i) q^{80} +(-695790. - 416834. i) q^{82} +5.89510e6i q^{83} +1.12233e7i q^{85} +(1.90952e6 - 3.18742e6i) q^{86} +(7.88638e6 + 382271. i) q^{88} -437005. q^{89} +6.01868e6i q^{91} +(1.48962e6 + 2.78396e6i) q^{92} +(-1.15536e6 - 692152. i) q^{94} -4.73616e6 q^{95} -7.84322e6 q^{97} +(895128. + 536254. i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q - 6 q^{2} + 116 q^{4} - 688 q^{7} - 1512 q^{8}+O(q^{10}) $ 6 * q - 6 * q^2 + 116 * q^4 - 688 * q^7 - 1512 * q^8	$ 6 q - 6 q^{2} + 116 q^{4} - 688 q^{7} - 1512 q^{8} - 1656 q^{10} - 12048 q^{14} + 35344 q^{16} - 1452 q^{17} + 114768 q^{20} + 152860 q^{22} + 1296 q^{23} - 39314 q^{25} + 316968 q^{26} - 480800 q^{28} - 89280 q^{31} - 817056 q^{32} - 1009108 q^{34} - 974124 q^{38} + 954464 q^{40} - 521244 q^{41} + 1096344 q^{44} + 929840 q^{46} - 1566432 q^{47} - 511050 q^{49} + 148626 q^{50} + 823952 q^{52} - 3270256 q^{55} + 2468928 q^{56} + 3130744 q^{58} + 7055808 q^{62} - 4792768 q^{64} - 1416480 q^{65} - 6608040 q^{68} - 7406912 q^{70} + 7597104 q^{71} + 2089564 q^{73} - 7744200 q^{74} + 9241288 q^{76} + 16015904 q^{79} + 12600384 q^{80} + 10715932 q^{82} + 5639076 q^{86} + 1541200 q^{88} - 2169084 q^{89} - 669600 q^{92} + 15503712 q^{94} - 48537936 q^{95} - 1088308 q^{97} + 14983242 q^{98}+O(q^{100}) $ 6 * q - 6 * q^2 + 116 * q^4 - 688 * q^7 - 1512 * q^8 - 1656 * q^10 - 12048 * q^14 + 35344 * q^16 - 1452 * q^17 + 114768 * q^20 + 152860 * q^22 + 1296 * q^23 - 39314 * q^25 + 316968 * q^26 - 480800 * q^28 - 89280 * q^31 - 817056 * q^32 - 1009108 * q^34 - 974124 * q^38 + 954464 * q^40 - 521244 * q^41 + 1096344 * q^44 + 929840 * q^46 - 1566432 * q^47 - 511050 * q^49 + 148626 * q^50 + 823952 * q^52 - 3270256 * q^55 + 2468928 * q^56 + 3130744 * q^58 + 7055808 * q^62 - 4792768 * q^64 - 1416480 * q^65 - 6608040 * q^68 - 7406912 * q^70 + 7597104 * q^71 + 2089564 * q^73 - 7744200 * q^74 + 9241288 * q^76 + 16015904 * q^79 + 12600384 * q^80 + 10715932 * q^82 + 5639076 * q^86 + 1541200 * q^88 - 2169084 * q^89 - 669600 * q^92 + 15503712 * q^94 - 48537936 * q^95 - 1088308 * q^97 + 14983242 * 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 $

$2$	9.70536	+	5.81430i	0.857840	+	0.513916i
$2$	9.70536	+	5.81430i	0.857840	+	0.513916i
$3$		0			0
$3$		0			0
$4$	60.3879	+	112.860i	0.471781	+	0.881716i
$5$		−	324.492i		−	1.16094i	−0.814283	−	0.580468i	$-0.802870\pi$
$5$		−	324.492i		−	1.16094i	0.814283	−	0.580468i	$-0.197130\pi$
$6$		0			0
$7$	−956.960			−1.05451			−0.527255	−	0.849707i	$-0.676779\pi$
$7$	−956.960			−1.05451			−0.527255	+	0.849707i	$0.676779\pi$
$8$	−70.1132	+	1446.46i	−0.0484155	+	0.998827i
$9$		0			0
$10$	1886.69	−	3149.31i	0.596624	−	0.995898i
$11$		−	5452.20i		−	1.23509i	−0.786537	−	0.617544i	$-0.788128\pi$
$11$		−	5452.20i		−	1.23509i	0.786537	−	0.617544i	$-0.211872\pi$
$12$		0			0
$13$		−	6289.38i		−	0.793973i	−0.917824	−	0.396987i	$-0.870056\pi$
$13$		−	6289.38i		−	0.793973i	0.917824	−	0.396987i	$-0.129944\pi$
$14$	−9287.64	−	5564.05i	−0.904602	−	0.541930i
$15$		0			0
$16$	−9090.60	+	13630.7i	−0.554846	+	0.831953i
$17$	−34587.3			−1.70744			−0.853720	−	0.520733i	$-0.825659\pi$
$17$	−34587.3			−1.70744			−0.853720	+	0.520733i	$0.825659\pi$
$18$		0			0
$19$		−	14595.6i		−	0.488186i	−0.969752	−	0.244093i	$-0.921510\pi$
$19$		−	14595.6i		−	0.488186i	0.969752	−	0.244093i	$-0.0784903\pi$
$20$	36622.0	−	19595.4i	1.02362	−	0.547707i
$21$		0			0
$22$	31700.7	−	52915.6i	0.634731	−	1.05951i
$23$	24667.5			0.422743			0.211372	−	0.977406i	$-0.432207\pi$
$23$	24667.5			0.422743			0.211372	+	0.977406i	$0.432207\pi$
$24$		0			0
$25$	−27169.8			−0.347774
$26$	36568.3	−	61040.6i	0.408036	−	0.681102i
$27$		0			0
$28$	−57788.8	−	108002.i	−0.497497	−	0.929779i
$29$		−	171116.i		−	1.30286i	−0.758710	−	0.651429i	$-0.774170\pi$
$29$		−	171116.i		−	1.30286i	0.758710	−	0.651429i	$-0.225830\pi$
$30$		0			0
$31$	111688.			0.673352			0.336676	−	0.941620i	$-0.390697\pi$
$31$	111688.			0.673352			0.336676	+	0.941620i	$0.390697\pi$
$32$	−167481.	+	79435.5i	−0.903524	+	0.428539i
$33$		0			0
$34$	−335682.	−	201101.i	−1.46471	−	0.877480i
$35$			310526.i			1.22422i
$36$		0			0
$37$		−	103636.i		−	0.336360i	−0.985756	−	0.168180i	$-0.946211\pi$
$37$		−	103636.i		−	0.336360i	0.985756	−	0.168180i	$-0.0537890\pi$
$38$	84863.4	−	141656.i	0.250887	−	0.418786i
$39$		0			0
$40$	469363.	+	22751.1i	1.15958	+	0.0562074i
$41$	−71691.3			−0.162451			−0.0812256	−	0.996696i	$-0.525883\pi$
$41$	−71691.3			−0.162451			−0.0812256	+	0.996696i	$0.525883\pi$
$42$		0			0
$43$		−	328419.i		−	0.629925i	−0.949104	−	0.314962i	$-0.898008\pi$
$43$		−	328419.i		−	0.629925i	0.949104	−	0.314962i	$-0.101992\pi$
$44$	615334.	−	329247.i	1.08900	−	0.582690i
$45$		0			0
$46$	239406.	+	143424.i	0.362646	+	0.217255i
$47$	−119043.			−0.167248			−0.0836241	−	0.996497i	$-0.526650\pi$
$47$	−119043.			−0.167248			−0.0836241	+	0.996497i	$0.526650\pi$
$48$		0			0
$49$	92230.3			0.111992
$50$	−263693.	−	157973.i	−0.298334	−	0.178727i
$51$		0			0
$52$	709817.	−	379802.i	0.700059	−	0.374581i
$53$			1.04011e6i			0.959648i	0.877365	+	0.479824i	$0.159300\pi$
$53$			1.04011e6i			0.959648i	−0.877365	+	0.479824i	$0.840700\pi$
$54$		0			0
$55$	−1.76919e6			−1.43386
$56$	67095.6	−	1.38420e6i	0.0510547	−	1.05327i
$57$		0			0
$58$	994918.	−	1.66074e6i	0.669559	−	1.11764i
$59$			225984.i			0.143250i	0.997432	+	0.0716250i	$0.0228185\pi$
$59$			225984.i			0.143250i	−0.997432	+	0.0716250i	$0.977182\pi$
$60$		0			0
$61$			1.55268e6i			0.875843i	0.899013	+	0.437922i	$0.144285\pi$
$61$			1.55268e6i			0.875843i	−0.899013	+	0.437922i	$0.855715\pi$
$62$	1.08398e6	+	649390.i	0.577629	+	0.346047i
$63$		0			0
$64$	−2.08732e6	−	202831.i	−0.995312	−	0.0967175i
$65$	−2.04085e6			−0.921753
$66$		0			0
$67$			316375.i			0.128511i	0.997933	+	0.0642555i	$0.0204673\pi$
$67$			316375.i			0.128511i	−0.997933	+	0.0642555i	$0.979533\pi$
$68$	−2.08865e6	−	3.90351e6i	−0.805537	−	1.50548i
$69$		0			0
$70$	−1.80549e6	+	3.01376e6i	−0.629146	+	1.05019i
$71$	−538965.			−0.178713			−0.0893566	−	0.996000i	$-0.528481\pi$
$71$	−538965.			−0.178713			−0.0893566	+	0.996000i	$0.528481\pi$
$72$		0			0
$73$	−2.68512e6			−0.807856			−0.403928	−	0.914791i	$-0.632355\pi$
$73$	−2.68512e6			−0.807856			−0.403928	+	0.914791i	$0.632355\pi$
$74$	602570.	−	1.00582e6i	0.172861	−	0.288543i
$75$		0			0
$76$	1.64726e6	−	881400.i	0.430442	−	0.230317i
$77$			5.21754e6i			1.30241i
$78$		0			0
$79$	8.22632e6			1.87720			0.938600	−	0.345007i	$-0.112123\pi$
$79$	8.22632e6			1.87720			0.938600	+	0.345007i	$0.112123\pi$
$80$	4.42305e6	+	2.94982e6i	0.965845	+	0.644141i
$81$		0			0
$82$	−695790.	−	416834.i	−0.139357	−	0.0834863i
$83$			5.89510e6i			1.13167i	0.824520	+	0.565833i	$0.191445\pi$
$83$			5.89510e6i			1.13167i	−0.824520	+	0.565833i	$0.808555\pi$
$84$		0			0
$85$			1.12233e7i			1.98223i
$86$	1.90952e6	−	3.18742e6i	0.323728	−	0.540375i
$87$		0			0
$88$	7.88638e6	+	382271.i	1.23364	+	0.0597974i
$89$	−437005.			−0.0657085			−0.0328542	−	0.999460i	$-0.510460\pi$
$89$	−437005.			−0.0657085			−0.0328542	+	0.999460i	$0.510460\pi$
$90$		0			0
$91$			6.01868e6i			0.837253i
$92$	1.48962e6	+	2.78396e6i	0.199442	+	0.372740i
$93$		0			0
$94$	−1.15536e6	−	692152.i	−0.143472	−	0.0859516i
$95$	−4.73616e6			−0.566753
$96$		0			0
$97$	−7.84322e6			−0.872556			−0.436278	−	0.899812i	$-0.643704\pi$
$97$	−7.84322e6			−0.872556			−0.436278	+	0.899812i	$0.643704\pi$
$98$	895128.	+	536254.i	0.0960713	+	0.0575545i
$99$		0			0
$100$	−1.64073e6	−	3.06638e6i	−0.164073	−	0.306638i
$101$			6.19757e6i			0.598545i	0.954168	+	0.299272i	$0.0967439\pi$
$101$			6.19757e6i			0.598545i	−0.954168	+	0.299272i	$0.903256\pi$
$102$		0			0
$103$	−6.59816e6			−0.594966			−0.297483	−	0.954727i	$-0.596147\pi$
$103$	−6.59816e6			−0.594966			−0.297483	+	0.954727i	$0.596147\pi$
$104$	9.09731e6	+	440968.i	0.793042	+	0.0384406i
$105$		0			0
$106$	−6.04748e6	+	1.00946e7i	−0.493179	+	0.823225i
$107$		−	512845.i		−	0.0404709i	−0.999795	−	0.0202354i	$-0.993558\pi$
$107$		−	512845.i		−	0.0404709i	0.999795	−	0.0202354i	$-0.00644158\pi$
$108$		0			0
$109$		−	1.95882e7i		−	1.44878i	−0.689393	−	0.724388i	$-0.742123\pi$
$109$		−	1.95882e7i		−	1.44878i	0.689393	−	0.724388i	$-0.257877\pi$
$110$	−1.71707e7	−	1.02866e7i	−1.23002	−	0.736883i
$111$		0			0
$112$	8.69934e6	−	1.30441e7i	0.585091	−	0.877303i
$113$	−1.88876e7			−1.23141			−0.615705	−	0.787977i	$-0.711129\pi$
$113$	−1.88876e7			−1.23141			−0.615705	+	0.787977i	$0.711129\pi$
$114$		0			0
$115$		−	8.00438e6i		−	0.490778i
$116$	1.93121e7	−	1.03333e7i	1.14875	−	0.614663i
$117$		0			0
$118$	−1.31394e6	+	2.19325e6i	−0.0736185	+	0.122886i
$119$	3.30987e7			1.80051
$120$		0			0
$121$	−1.02394e7			−0.525441
$122$	−9.02772e6	+	1.50693e7i	−0.450110	+	0.751334i
$123$		0			0
$124$	6.74463e6	+	1.26051e7i	0.317675	+	0.593706i
$125$		−	1.65345e7i		−	0.757193i
$126$		0			0
$127$	3.96314e7			1.71683			0.858413	−	0.512959i	$-0.171451\pi$
$127$	3.96314e7			1.71683			0.858413	+	0.512959i	$0.171451\pi$
$128$	−1.90789e7	−	1.41048e7i	−0.804114	−	0.594475i
$129$		0			0
$130$	−1.98072e7	−	1.18661e7i	−0.790717	−	0.473703i
$131$		−	3.65337e7i		−	1.41986i	−0.704274	−	0.709928i	$-0.748727\pi$
$131$		−	3.65337e7i		−	1.41986i	0.704274	−	0.709928i	$-0.251273\pi$
$132$		0			0
$133$			1.39675e7i			0.514797i
$134$	−1.83950e6	+	3.07053e6i	−0.0660439	+	0.110242i
$135$		0			0
$136$	2.42503e6	−	5.00290e7i	0.0826666	−	1.70544i
$137$	2.56967e7			0.853799			0.426899	−	0.904299i	$-0.359606\pi$
$137$	2.56967e7			0.853799			0.426899	+	0.904299i	$0.359606\pi$
$138$		0			0
$139$		−	5.23001e7i		−	1.65177i	−0.563836	−	0.825886i	$-0.690675\pi$
$139$		−	5.23001e7i		−	1.65177i	0.563836	−	0.825886i	$-0.309325\pi$
$140$	−3.50458e7	+	1.87520e7i	−1.07941	+	0.577563i
$141$		0			0
$142$	−5.23085e6	−	3.13370e6i	−0.153307	−	0.0918436i
$143$	−3.42910e7			−0.980626
$144$		0			0
$145$	−5.55256e7			−1.51254
$146$	−2.60601e7	−	1.56121e7i	−0.693011	−	0.415170i
$147$		0			0
$148$	1.16963e7	−	6.25836e6i	0.296574	−	0.158688i
$149$			1.80406e7i			0.446785i	0.974729	+	0.223392i	$0.0717131\pi$
$149$			1.80406e7i			0.446785i	−0.974729	+	0.223392i	$0.928287\pi$
$150$		0			0
$151$	3.87385e7			0.915637			0.457818	−	0.889046i	$-0.348631\pi$
$151$	3.87385e7			0.915637			0.457818	+	0.889046i	$0.348631\pi$
$152$	2.11120e7	+	1.02335e6i	0.487614	+	0.0236358i
$153$		0			0
$154$	−3.03363e7	+	5.06381e7i	−0.669331	+	1.11726i
$155$		−	3.62420e7i		−	0.781719i
$156$		0			0
$157$			5.12341e7i			1.05660i	0.849058	+	0.528300i	$0.177170\pi$
$157$			5.12341e7i			1.05660i	−0.849058	+	0.528300i	$0.822830\pi$
$158$	7.98393e7	+	4.78302e7i	1.61034	+	0.964723i
$159$		0			0
$160$	2.57762e7	+	5.43460e7i	0.497506	+	1.04893i
$161$	−2.36058e7			−0.445787
$162$		0			0
$163$		−	8.57572e7i		−	1.55101i	−0.631343	−	0.775504i	$-0.717496\pi$
$163$		−	8.57572e7i		−	1.55101i	0.631343	−	0.775504i	$-0.282504\pi$
$164$	−4.32929e6	−	8.09105e6i	−0.0766413	−	0.143236i
$165$		0			0
$166$	−3.42759e7	+	5.72141e7i	−0.581581	+	0.970789i
$167$	1.05871e8			1.75901			0.879503	−	0.475893i	$-0.157875\pi$
$167$	1.05871e8			1.75901			0.879503	+	0.475893i	$0.157875\pi$
$168$		0			0
$169$	2.31923e7			0.369606
$170$	−6.52555e7	+	1.08926e8i	−1.01870	+	1.70044i
$171$		0			0
$172$	3.70652e7	−	1.98325e7i	0.555415	−	0.297186i
$173$		−	1.98148e7i		−	0.290956i	−0.989361	−	0.145478i	$-0.953528\pi$
$173$		−	1.98148e7i		−	0.290956i	0.989361	−	0.145478i	$-0.0464720\pi$
$174$		0			0
$175$	2.60005e7			0.366731
$176$	7.43175e7	+	4.95638e7i	1.02753	+	0.685284i
$177$		0			0
$178$	−4.24129e6	−	2.54088e6i	−0.0563674	−	0.0337686i
$179$		−	2.97800e7i		−	0.388096i	−0.980992	−	0.194048i	$-0.937838\pi$
$179$		−	2.97800e7i		−	0.388096i	0.980992	−	0.194048i	$-0.0621618\pi$
$180$		0			0
$181$			3.96227e6i			0.0496671i	0.999692	+	0.0248335i	$0.00790558\pi$
$181$			3.96227e6i			0.0496671i	−0.999692	+	0.0248335i	$0.992094\pi$
$182$	−3.49944e7	+	5.84135e7i	−0.430278	+	0.718230i
$183$		0			0
$184$	−1.72951e6	+	3.56804e7i	−0.0204674	+	0.422248i
$185$	−3.36290e7			−0.390493
$186$		0			0
$187$			1.88577e8i			2.10884i
$188$	−7.18876e6	−	1.34352e7i	−0.0789045	−	0.147465i
$189$		0			0
$190$	−4.59662e7	−	2.75375e7i	−0.486184	−	0.291264i
$191$	4.80105e7			0.498562			0.249281	−	0.968431i	$-0.419806\pi$
$191$	4.80105e7			0.498562			0.249281	+	0.968431i	$0.419806\pi$
$192$		0			0
$193$	−4.72502e6			−0.0473100			−0.0236550	−	0.999720i	$-0.507530\pi$
$193$	−4.72502e6			−0.0473100			−0.0236550	+	0.999720i	$0.507530\pi$
$194$	−7.61212e7	−	4.56028e7i	−0.748514	−	0.448420i
$195$		0			0
$196$	5.56959e6	+	1.04091e7i	0.0528357	+	0.0987452i
$197$		−	1.14882e8i		−	1.07058i	−0.844668	−	0.535290i	$-0.820202\pi$
$197$		−	1.14882e8i		−	1.07058i	0.844668	−	0.535290i	$-0.179798\pi$
$198$		0			0
$199$	1.20933e7			0.108782			0.0543911	−	0.998520i	$-0.482678\pi$
$199$	1.20933e7			0.108782			0.0543911	+	0.998520i	$0.482678\pi$
$200$	1.90496e6	−	3.93000e7i	0.0168377	−	0.347366i
$201$		0			0
$202$	−3.60345e7	+	6.01496e7i	−0.307602	+	0.513456i
$203$			1.63751e8i			1.37388i
$204$		0			0
$205$			2.32632e7i			0.188596i
$206$	−6.40375e7	−	3.83636e7i	−0.510386	−	0.305763i
$207$		0			0
$208$	8.57287e7	+	5.71742e7i	0.660548	+	0.440533i
$209$	−7.95784e7			−0.602953
$210$		0			0
$211$		−	1.95850e8i		−	1.43527i	−0.696418	−	0.717636i	$-0.745224\pi$
$211$		−	1.95850e8i		−	1.43527i	0.696418	−	0.717636i	$-0.254776\pi$
$212$	−1.17386e8	+	6.28098e7i	−0.846137	+	0.452743i
$213$		0			0
$214$	2.98183e6	−	4.97734e6i	0.0207986	−	0.0347176i
$215$	−1.06569e8			−0.731302
$216$		0			0
$217$	−1.06881e8			−0.710057
$218$	1.13891e8	−	1.90110e8i	0.744549	−	1.24282i
$219$		0			0
$220$	−1.06838e8	−	1.99671e8i	−0.676466	−	1.26426i
$221$			2.17532e8i			1.35566i
$222$		0			0
$223$	1.08024e8			0.652311			0.326156	−	0.945316i	$-0.394247\pi$
$223$	1.08024e8			0.652311			0.326156	+	0.945316i	$0.394247\pi$
$224$	1.60272e8	−	7.60167e7i	0.952775	−	0.451898i
$225$		0			0
$226$	−1.83311e8	−	1.09818e8i	−1.05635	−	0.632841i
$227$		−	1.61144e8i		−	0.914374i	−0.889371	−	0.457187i	$-0.848857\pi$
$227$		−	1.61144e8i		−	0.914374i	0.889371	−	0.457187i	$-0.151143\pi$
$228$		0			0
$229$			5.27173e7i			0.290088i	0.989425	+	0.145044i	$0.0463323\pi$
$229$			5.27173e7i			0.290088i	−0.989425	+	0.145044i	$0.953668\pi$
$230$	4.65399e7	−	7.76854e7i	0.252219	−	0.421010i
$231$		0			0
$232$	2.47511e8	+	1.19975e7i	1.30133	+	0.0630786i
$233$	1.79423e8			0.929249			0.464625	−	0.885508i	$-0.346189\pi$
$233$	1.79423e8			0.929249			0.464625	+	0.885508i	$0.346189\pi$
$234$		0			0
$235$			3.86285e7i			0.194165i
$236$	−2.55044e7	+	1.36467e7i	−0.126306	+	0.0675826i
$237$		0			0
$238$	3.21234e8	+	1.92445e8i	1.54455	+	0.925312i
$239$	8.42441e7			0.399160			0.199580	−	0.979882i	$-0.436042\pi$
$239$	8.42441e7			0.399160			0.199580	+	0.979882i	$0.436042\pi$
$240$		0			0
$241$	−2.12302e8			−0.977000			−0.488500	−	0.872564i	$-0.662456\pi$
$241$	−2.12302e8			−0.977000			−0.488500	+	0.872564i	$0.662456\pi$
$242$	−9.93766e7	−	5.95347e7i	−0.450745	−	0.270033i
$243$		0			0
$244$	−1.75234e8	+	9.37629e7i	−0.772245	+	0.413206i
$245$		−	2.99280e7i		−	0.130016i
$246$		0			0
$247$	−9.17975e7			−0.387607
$248$	−7.83083e6	+	1.61552e8i	−0.0326007	+	0.672563i
$249$		0			0
$250$	9.61366e7	−	1.60473e8i	0.389134	−	0.649551i
$251$			1.18102e8i			0.471411i	0.971825	+	0.235706i	$0.0757401\pi$
$251$			1.18102e8i			0.471411i	−0.971825	+	0.235706i	$0.924260\pi$
$252$		0			0
$253$		−	1.34492e8i		−	0.522125i
$254$	3.84637e8	+	2.30429e8i	1.47276	+	0.882304i
$255$		0			0
$256$	−1.03157e8	−	2.47823e8i	−0.384291	−	0.923212i
$257$	−1.27463e8			−0.468402			−0.234201	−	0.972188i	$-0.575247\pi$
$257$	−1.27463e8			−0.468402			−0.234201	+	0.972188i	$0.575247\pi$
$258$		0			0
$259$			9.91755e7i			0.354695i
$260$	−1.23243e8	−	2.30330e8i	−0.434865	−	0.812724i
$261$		0			0
$262$	2.12418e8	−	3.54573e8i	0.729687	−	1.21801i
$263$	−4.33125e8			−1.46814			−0.734071	−	0.679073i	$-0.762382\pi$
$263$	−4.33125e8			−1.46814			−0.734071	+	0.679073i	$0.762382\pi$
$264$		0			0
$265$	3.37506e8			1.11409
$266$	−8.12109e7	+	1.35559e8i	−0.264563	+	0.441614i
$267$		0			0
$268$	−3.57060e7	+	1.91052e7i	−0.113310	+	0.0606290i
$269$			3.44748e8i			1.07986i	0.841709	+	0.539931i	$0.181550\pi$
$269$			3.44748e8i			1.07986i	−0.841709	+	0.539931i	$0.818450\pi$
$270$		0			0
$271$	−4.42513e8			−1.35062			−0.675311	−	0.737533i	$-0.735990\pi$
$271$	−4.42513e8			−1.35062			−0.675311	+	0.737533i	$0.735990\pi$
$272$	3.14419e8	−	4.71450e8i	0.947366	−	1.42051i
$273$		0			0
$274$	2.49396e8	+	1.49408e8i	0.732423	+	0.438781i
$275$			1.48135e8i			0.429531i
$276$		0			0
$277$		−	3.18148e8i		−	0.899395i	−0.893181	−	0.449697i	$-0.851532\pi$
$277$		−	3.18148e8i		−	0.899395i	0.893181	−	0.449697i	$-0.148468\pi$
$278$	3.04088e8	−	5.07591e8i	0.848873	−	1.41696i
$279$		0			0
$280$	−4.49162e8	−	2.17719e7i	−1.22278	−	0.0592713i
$281$	−1.28497e8			−0.345478			−0.172739	−	0.984968i	$-0.555262\pi$
$281$	−1.28497e8			−0.345478			−0.172739	+	0.984968i	$0.555262\pi$
$282$		0			0
$283$			3.98970e8i			1.04637i	0.852218	+	0.523187i	$0.175257\pi$
$283$			3.98970e8i			1.04637i	−0.852218	+	0.523187i	$0.824743\pi$
$284$	−3.25470e7	−	6.08274e7i	−0.0843134	−	0.157574i
$285$		0			0
$286$	−3.32806e8	−	1.99378e8i	−0.841221	−	0.503960i
$287$	6.86057e7			0.171306
$288$		0			0
$289$	7.85942e8			1.91535
$290$	−5.38896e8	−	3.22842e8i	−1.29751	−	0.777316i
$291$		0			0
$292$	−1.62149e8	−	3.03042e8i	−0.381131	−	0.712299i
$293$			2.00958e8i			0.466732i	0.972389	+	0.233366i	$0.0749741\pi$
$293$			2.00958e8i			0.466732i	−0.972389	+	0.233366i	$0.925026\pi$
$294$		0			0
$295$	7.33298e7			0.166304
$296$	1.49905e8	+	7.26625e6i	0.335965	+	0.0162850i
$297$		0			0
$298$	−1.04893e8	+	1.75090e8i	−0.229610	+	0.383270i
$299$		−	1.55143e8i		−	0.335647i
$300$		0			0
$301$			3.14284e8i			0.664262i
$302$	3.75971e8	+	2.25237e8i	0.785470	+	0.470560i
$303$		0			0
$304$	1.98949e8	+	1.32683e8i	0.406148	+	0.270868i
$305$	5.03830e8			1.01680
$306$		0			0
$307$		−	1.58918e7i		−	0.0313465i	−0.999877	−	0.0156733i	$-0.995011\pi$
$307$		−	1.58918e7i		−	0.0313465i	0.999877	−	0.0156733i	$-0.00498916\pi$
$308$	−5.88850e8	+	3.15077e8i	−1.14836	+	0.614453i
$309$		0			0
$310$	2.10722e8	−	3.51741e8i	0.401738	−	0.670591i
$311$	−4.87710e8			−0.919391			−0.459695	−	0.888077i	$-0.652041\pi$
$311$	−4.87710e8			−0.919391			−0.459695	+	0.888077i	$0.652041\pi$
$312$		0			0
$313$	−3.24731e8			−0.598576			−0.299288	−	0.954163i	$-0.596749\pi$
$313$	−3.24731e8			−0.598576			−0.299288	+	0.954163i	$0.596749\pi$
$314$	−2.97890e8	+	4.97245e8i	−0.543003	+	0.906394i
$315$		0			0
$316$	4.96770e8	+	9.28419e8i	0.885627	+	1.65516i
$317$		−	1.06084e9i		−	1.87043i	−0.354086	−	0.935213i	$-0.615208\pi$
$317$		−	1.06084e9i		−	1.87043i	0.354086	−	0.935213i	$-0.384792\pi$
$318$		0			0
$319$	−9.32958e8			−1.60914
$320$	−6.58171e7	+	6.77318e8i	−0.112283	+	1.15549i
$321$		0			0
$322$	−2.29102e8	−	1.37251e8i	−0.382414	−	0.229097i
$323$			5.04824e8i			0.833548i
$324$		0			0
$325$			1.70881e8i			0.276123i
$326$	4.98618e8	−	8.32304e8i	0.797088	−	1.33052i
$327$		0			0
$328$	5.02651e6	−	1.03698e8i	0.00786516	−	0.162261i
$329$	1.13919e8			0.176365
$330$		0			0
$331$			2.88487e8i			0.437249i	0.975809	+	0.218624i	$0.0701569\pi$
$331$			2.88487e8i			0.437249i	−0.975809	+	0.218624i	$0.929843\pi$
$332$	−6.65319e8	+	3.55993e8i	−0.997808	+	0.533898i
$333$		0			0
$334$	1.02751e9	+	6.15563e8i	1.50895	+	0.903982i
$335$	1.02661e8			0.149193
$336$		0			0
$337$	−1.10595e8			−0.157410			−0.0787051	−	0.996898i	$-0.525079\pi$
$337$	−1.10595e8			−0.157410			−0.0787051	+	0.996898i	$0.525079\pi$
$338$	2.25089e8	+	1.34847e8i	0.317063	+	0.189947i
$339$		0			0
$340$	−1.26666e9	+	6.77751e8i	−1.74776	+	0.935177i
$341$		−	6.08948e8i		−	0.831649i
$342$		0			0
$343$	6.99837e8			0.936414
$344$	4.75044e8	+	2.30265e7i	0.629186	+	0.0304981i
$345$		0			0
$346$	1.15209e8	−	1.92309e8i	0.149527	−	0.249594i
$347$			1.10651e9i			1.42168i	0.703352	+	0.710841i	$0.251686\pi$
$347$			1.10651e9i			1.42168i	−0.703352	+	0.710841i	$0.748314\pi$
$348$		0			0
$349$		−	1.38337e9i		−	1.74201i	−0.491278	−	0.871003i	$-0.663470\pi$
$349$		−	1.38337e9i		−	1.74201i	0.491278	−	0.871003i	$-0.336530\pi$
$350$	2.52344e8	+	1.51174e8i	0.314597	+	0.188469i
$351$		0			0
$352$	4.33099e8	+	9.13138e8i	0.529283	+	1.11593i
$353$	2.47617e8			0.299618			0.149809	−	0.988715i	$-0.452134\pi$
$353$	2.47617e8			0.299618			0.149809	+	0.988715i	$0.452134\pi$
$354$		0			0
$355$			1.74890e8i			0.207475i
$356$	−2.63898e7	−	4.93202e7i	−0.0310000	−	0.0579362i
$357$		0			0
$358$	1.73150e8	−	2.89026e8i	0.199449	−	0.332925i
$359$	1.38641e9			1.58148			0.790738	−	0.612155i	$-0.209697\pi$
$359$	1.38641e9			1.58148			0.790738	+	0.612155i	$0.209697\pi$
$360$		0			0
$361$	6.80839e8			0.761674
$362$	−2.30378e7	+	3.84552e7i	−0.0255247	+	0.0426064i
$363$		0			0
$364$	−6.79267e8	+	3.63456e8i	−0.738219	+	0.395000i
$365$			8.71299e8i			0.937869i
$366$		0			0
$367$	−7.49367e8			−0.791341			−0.395670	−	0.918393i	$-0.629488\pi$
$367$	−7.49367e8			−0.791341			−0.395670	+	0.918393i	$0.629488\pi$
$368$	−2.24242e8	+	3.36235e8i	−0.234558	+	0.351703i
$369$		0			0
$370$	−3.26381e8	−	1.95529e8i	−0.334980	−	0.200680i
$371$		−	9.95340e8i		−	1.01196i
$372$		0			0
$373$			1.49519e9i			1.49181i	0.666051	+	0.745906i	$0.267983\pi$
$373$			1.49519e9i			1.49181i	−0.666051	+	0.745906i	$0.732017\pi$
$374$	−1.09644e9	+	1.83021e9i	−1.08377	+	1.80905i
$375$		0			0
$376$	8.34649e6	−	1.72191e8i	0.00809741	−	0.167052i
$377$	−1.07621e9			−1.03443
$378$		0			0
$379$		−	7.92096e7i		−	0.0747379i	−0.999302	−	0.0373689i	$-0.988102\pi$
$379$		−	7.92096e7i		−	0.0747379i	0.999302	−	0.0373689i	$-0.0118977\pi$
$380$	−2.86007e8	−	5.34522e8i	−0.267383	−	0.499715i
$381$		0			0
$382$	4.65959e8	+	2.79147e8i	0.427687	+	0.256219i
$383$	−4.80285e8			−0.436820			−0.218410	−	0.975857i	$-0.570087\pi$
$383$	−4.80285e8			−0.436820			−0.218410	+	0.975857i	$0.570087\pi$
$384$		0			0
$385$	1.69305e9			1.51202
$386$	−4.58580e7	−	2.74726e7i	−0.0405844	−	0.0243134i
$387$		0			0
$388$	−4.73636e8	−	8.85183e8i	−0.411655	−	0.769346i
$389$		−	1.07150e9i		−	0.922928i	−0.887159	−	0.461464i	$-0.847324\pi$
$389$		−	1.07150e9i		−	0.922928i	0.887159	−	0.461464i	$-0.152676\pi$
$390$		0			0
$391$	−8.53180e8			−0.721809
$392$	−6.46656e6	+	1.33407e8i	−0.00542216	+	0.111861i
$393$		0			0
$394$	6.67957e8	−	1.11497e9i	0.550189	−	0.918387i
$395$		−	2.66937e9i		−	2.17931i
$396$		0			0
$397$		−	2.03185e9i		−	1.62976i	−0.579627	−	0.814882i	$-0.696802\pi$
$397$		−	2.03185e9i		−	1.62976i	0.579627	−	0.814882i	$-0.303198\pi$
$398$	1.17369e8	+	7.03138e7i	0.0933178	+	0.0559049i
$399$		0			0
$400$	2.46990e8	−	3.70344e8i	0.192961	−	0.289331i
$401$	2.57759e9			1.99622			0.998111	−	0.0614301i	$-0.0195661\pi$
$401$	2.57759e9			1.99622			0.998111	+	0.0614301i	$0.0195661\pi$
$402$		0			0
$403$		−	7.02451e8i		−	0.534624i
$404$	−6.99455e8	+	3.74258e8i	−0.527746	+	0.282382i
$405$		0			0
$406$	−9.52097e8	+	1.58926e9i	−0.706057	+	1.17857i
$407$	−5.65044e8			−0.415434
$408$		0			0
$409$	3.30242e8			0.238672			0.119336	−	0.992854i	$-0.461923\pi$
$409$	3.30242e8			0.238672			0.119336	+	0.992854i	$0.461923\pi$
$410$	−1.35259e8	+	2.25778e8i	−0.0969223	+	0.161785i
$411$		0			0
$412$	−3.98449e8	−	7.44666e8i	−0.280693	−	0.524591i
$413$		−	2.16257e8i		−	0.151059i
$414$		0			0
$415$	1.91291e9			1.31379
$416$	4.99600e8	+	1.05335e9i	0.340248	+	0.717374i
$417$		0			0
$418$	−7.72337e8	−	4.62692e8i	−0.517237	−	0.309867i
$419$			5.80021e7i			0.0385207i	0.999815	+	0.0192604i	$0.00613114\pi$
$419$			5.80021e7i			0.0385207i	−0.999815	+	0.0192604i	$0.993869\pi$
$420$		0			0
$421$		−	1.90609e8i		−	0.124496i	−0.998061	−	0.0622480i	$-0.980173\pi$
$421$		−	1.90609e8i		−	0.124496i	0.998061	−	0.0622480i	$-0.0198270\pi$
$422$	1.13873e9	−	1.90079e9i	0.737610	−	1.23123i
$423$		0			0
$424$	−1.50447e9	−	7.29251e7i	−0.958523	−	0.0464619i
$425$	9.39731e8			0.593803
$426$		0			0
$427$		−	1.48585e9i		−	0.923586i
$428$	5.78795e7	−	3.09696e7i	0.0356838	−	0.0190934i
$429$		0			0
$430$	−1.03429e9	−	6.19625e8i	−0.627341	−	0.375828i
$431$	−2.42923e9			−1.46150			−0.730749	−	0.682646i	$-0.760829\pi$
$431$	−2.42923e9			−1.46150			−0.730749	+	0.682646i	$0.760829\pi$
$432$		0			0
$433$	−2.37902e9			−1.40828			−0.704141	−	0.710060i	$-0.748668\pi$
$433$	−2.37902e9			−1.40828			−0.704141	+	0.710060i	$0.748668\pi$
$434$	−1.03732e9	−	6.21440e8i	−0.609116	−	0.364910i
$435$		0			0
$436$	2.21071e9	−	1.18289e9i	1.27741	−	0.683504i
$437$		−	3.60037e8i		−	0.206378i
$438$		0			0
$439$	−1.33161e9			−0.751194			−0.375597	−	0.926783i	$-0.622562\pi$
$439$	−1.33161e9			−0.751194			−0.375597	+	0.926783i	$0.622562\pi$
$440$	1.24044e8	−	2.55906e9i	0.0694210	−	1.43218i
$441$		0			0
$442$	−1.26480e9	+	2.11123e9i	−0.696696	+	1.16294i
$443$			5.02643e8i			0.274692i	0.990523	+	0.137346i	$0.0438573\pi$
$443$			5.02643e8i			0.274692i	−0.990523	+	0.137346i	$0.956143\pi$
$444$		0			0
$445$			1.41805e8i			0.0762834i
$446$	1.04842e9	+	6.28086e8i	0.559579	+	0.335233i
$447$		0			0
$448$	1.99748e9	+	1.94102e8i	1.04957	+	0.101990i
$449$	−3.14785e9			−1.64116			−0.820580	−	0.571531i	$-0.806350\pi$
$449$	−3.14785e9			−1.64116			−0.820580	+	0.571531i	$0.806350\pi$
$450$		0			0
$451$			3.90876e8i			0.200641i
$452$	−1.14058e9	−	2.13165e9i	−0.580955	−	1.08575i
$453$		0			0
$454$	9.36939e8	−	1.56396e9i	0.469911	−	0.784387i
$455$	1.95301e9			0.971998
$456$		0			0
$457$	−2.68422e9			−1.31556			−0.657782	−	0.753209i	$-0.728505\pi$
$457$	−2.68422e9			−1.31556			−0.657782	+	0.753209i	$0.728505\pi$
$458$	−3.06514e8	+	5.11641e8i	−0.149081	+	0.248849i
$459$		0			0
$460$	9.03372e8	−	4.83368e8i	0.432727	−	0.231540i
$461$			1.30434e9i			0.620065i	0.950726	+	0.310033i	$0.100340\pi$
$461$			1.30434e9i			0.620065i	−0.950726	+	0.310033i	$0.899660\pi$
$462$		0			0
$463$	2.86853e9			1.34315			0.671577	−	0.740934i	$-0.265617\pi$
$463$	2.86853e9			1.34315			0.671577	+	0.740934i	$0.265617\pi$
$464$	2.33243e9	+	1.55554e9i	1.08392	+	0.722886i
$465$		0			0
$466$	1.74136e9	+	1.04322e9i	0.797148	+	0.477556i
$467$			5.96519e8i			0.271029i	0.990775	+	0.135514i	$0.0432687\pi$
$467$			5.96519e8i			0.271029i	−0.990775	+	0.135514i	$0.956731\pi$
$468$		0			0
$469$		−	3.02758e8i		−	0.135516i
$470$	−2.24597e8	+	3.74903e8i	−0.0997843	+	0.166562i
$471$		0			0
$472$	−3.26875e8	−	1.58444e7i	−0.143082	−	0.00693553i
$473$	−1.79061e9			−0.778012
$474$		0			0
$475$			3.96561e8i			0.169778i
$476$	1.99876e9	+	3.73550e9i	0.849447	+	1.58754i
$477$		0			0
$478$	8.17619e8	+	4.89820e8i	0.342416	+	0.205135i
$479$	2.16068e9			0.898289			0.449144	−	0.893459i	$-0.351729\pi$
$479$	2.16068e9			0.898289			0.449144	+	0.893459i	$0.351729\pi$
$480$		0			0
$481$	−6.51805e8			−0.267061
$482$	−2.06047e9	−	1.23439e9i	−0.838110	−	0.502096i
$483$		0			0
$484$	−6.18334e8	−	1.15561e9i	−0.247893	−	0.463290i
$485$			2.54506e9i			1.01298i
$486$		0			0
$487$	1.41934e8			0.0556847			0.0278424	−	0.999612i	$-0.491136\pi$
$487$	1.41934e8			0.0556847			0.0278424	+	0.999612i	$0.491136\pi$
$488$	−2.24588e9	−	1.08863e8i	−0.874816	−	0.0424044i
$489$		0			0
$490$	1.74010e8	−	2.90462e8i	0.0668172	−	0.111533i
$491$			2.38677e9i			0.909966i	0.890500	+	0.454983i	$0.150355\pi$
$491$			2.38677e9i			0.909966i	−0.890500	+	0.454983i	$0.849645\pi$
$492$		0			0
$493$			5.91843e9i			2.22455i
$494$	−8.90927e8	−	5.33738e8i	−0.332505	−	0.199197i
$495$		0			0
$496$	−1.01532e9	+	1.52239e9i	−0.373607	+	0.560197i
$497$	5.15769e8			0.188455
$498$		0			0
$499$			5.23900e9i			1.88754i	0.330601	+	0.943771i	$0.392749\pi$
$499$			5.23900e9i			1.88754i	−0.330601	+	0.943771i	$0.607251\pi$
$500$	1.86608e9	−	9.98486e8i	0.667629	−	0.357229i
$501$		0			0
$502$	−6.86681e8	+	1.14622e9i	−0.242266	+	0.404396i
$503$	3.63292e9			1.27282			0.636411	−	0.771350i	$-0.280418\pi$
$503$	3.63292e9			1.27282			0.636411	+	0.771350i	$0.280418\pi$
$504$		0			0
$505$	2.01106e9			0.694872
$506$	7.81976e8	−	1.30529e9i	0.268328	−	0.447900i
$507$		0			0
$508$	2.39326e9	+	4.47278e9i	0.809965	+	1.51375i
$509$			2.58693e9i			0.869505i	0.900550	+	0.434753i	$0.143164\pi$
$509$			2.58693e9i			0.869505i	−0.900550	+	0.434753i	$0.856836\pi$
$510$		0			0
$511$	2.56955e9			0.851892
$512$	4.39735e8	−	3.00500e9i	0.144793	−	0.989462i
$513$		0			0
$514$	−1.23708e9	−	7.41108e8i	−0.401814	−	0.240719i
$515$			2.14105e9i			0.690718i
$516$		0			0
$517$			6.49047e8i			0.206566i
$518$	−5.76636e8	+	9.62533e8i	−0.182283	+	0.304272i
$519$		0			0
$520$	1.43091e8	−	2.95200e9i	0.0446272	−	0.920672i
$521$	−1.08542e8			−0.0336253			−0.0168127	−	0.999859i	$-0.505352\pi$
$521$	−1.08542e8			−0.0336253			−0.0168127	+	0.999859i	$0.505352\pi$
$522$		0			0
$523$		−	6.10725e9i		−	1.86676i	−0.358884	−	0.933382i	$-0.616843\pi$
$523$		−	6.10725e9i		−	1.86676i	0.358884	−	0.933382i	$-0.383157\pi$
$524$	4.12318e9	−	2.20620e9i	1.25191	−	0.669861i
$525$		0			0
$526$	−4.20363e9	−	2.51832e9i	−1.25943	−	0.754502i
$527$	−3.86300e9			−1.14971
$528$		0			0
$529$	−2.79634e9			−0.821288
$530$	3.27561e9	+	1.96236e9i	0.955712	+	0.572549i
$531$		0			0
$532$	−1.57636e9	+	8.43465e8i	−0.453905	+	0.242871i
$533$			4.50894e8i			0.128982i
$534$		0			0
$535$	−1.66414e8			−0.0469841
$536$	−4.57623e8	−	2.21821e7i	−0.128360	−	0.00622193i
$537$		0			0
$538$	−2.00446e9	+	3.34590e9i	−0.554958	+	0.926349i
$539$		−	5.02858e8i		−	0.138320i
$540$		0			0
$541$		−	5.39345e8i		−	0.146445i	−0.997316	−	0.0732227i	$-0.976672\pi$
$541$		−	5.39345e8i		−	0.146445i	0.997316	−	0.0732227i	$-0.0233284\pi$
$542$	−4.29475e9	−	2.57290e9i	−1.15862	−	0.694106i
$543$		0			0
$544$	5.79270e9	−	2.74746e9i	1.54271	−	0.731704i
$545$	−6.35620e9			−1.68194
$546$		0			0
$547$		−	8.82287e7i		−	0.0230491i	−0.999934	−	0.0115246i	$-0.996332\pi$
$547$		−	8.82287e7i		−	0.0230491i	0.999934	−	0.0115246i	$-0.00366846\pi$
$548$	1.55177e9	+	2.90012e9i	0.402806	+	0.752808i
$549$		0			0
$550$	−8.61304e8	+	1.43771e9i	−0.220743	+	0.368469i
$551$	−2.49754e9			−0.636037
$552$		0			0
$553$	−7.87226e9			−1.97953
$554$	1.84981e9	−	3.08774e9i	0.462213	−	0.771537i
$555$		0			0
$556$	5.90257e9	−	3.15829e9i	1.45639	−	0.779274i
$557$		−	5.57233e8i		−	0.136629i	−0.997664	−	0.0683147i	$-0.978238\pi$
$557$		−	5.57233e8i		−	0.136629i	0.997664	−	0.0683147i	$-0.0217622\pi$
$558$		0			0
$559$	−2.06555e9			−0.500143
$560$	−4.23269e9	−	2.82286e9i	−1.01849	−	0.679254i
$561$		0			0
$562$	−1.24711e9	−	7.47119e8i	−0.296365	−	0.177547i
$563$		−	1.17012e9i		−	0.276344i	−0.990408	−	0.138172i	$-0.955877\pi$
$563$		−	1.17012e9i		−	0.276344i	0.990408	−	0.138172i	$-0.0441227\pi$
$564$		0			0
$565$			6.12887e9i			1.42959i
$566$	−2.31973e9	+	3.87214e9i	−0.537749	+	0.897623i
$567$		0			0
$568$	3.77886e7	−	7.79590e8i	0.00865250	−	0.178504i
$569$	2.39181e9			0.544295			0.272147	−	0.962256i	$-0.412266\pi$
$569$	2.39181e9			0.544295			0.272147	+	0.962256i	$0.412266\pi$
$570$		0			0
$571$			3.15823e9i			0.709933i	0.934879	+	0.354966i	$0.115508\pi$
$571$			3.15823e9i			0.709933i	−0.934879	+	0.354966i	$0.884492\pi$
$572$	−2.07076e9	−	3.87007e9i	−0.462640	−	0.864634i
$573$		0			0
$574$	6.65843e8	+	3.98894e8i	0.146954	+	0.0880371i
$575$	−6.70211e8			−0.147019
$576$		0			0
$577$	4.03435e9			0.874296			0.437148	−	0.899390i	$-0.355989\pi$
$577$	4.03435e9			0.874296			0.437148	+	0.899390i	$0.355989\pi$
$578$	7.62785e9	+	4.56970e9i	1.64306	+	0.984329i
$579$		0			0
$580$	−3.35308e9	−	6.26660e9i	−0.713585	−	1.33363i
$581$		−	5.64138e9i		−	1.19335i
$582$		0			0
$583$	5.67087e9			1.18525
$584$	1.88262e8	−	3.88391e9i	0.0391128	−	0.806908i
$585$		0			0
$586$	−1.16843e9	+	1.95037e9i	−0.239861	+	0.400382i
$587$		−	2.72240e9i		−	0.555544i	−0.960647	−	0.277772i	$-0.910404\pi$
$587$		−	2.72240e9i		−	0.555544i	0.960647	−	0.277772i	$-0.0895960\pi$
$588$		0			0
$589$		−	1.63016e9i		−	0.328721i
$590$	7.11692e8	+	4.26361e8i	0.142662	+	0.0854664i
$591$		0			0
$592$	1.41263e9	+	9.42113e8i	0.279836	+	0.186628i
$593$	2.29251e9			0.451460			0.225730	−	0.974190i	$-0.427523\pi$
$593$	2.29251e9			0.451460			0.225730	+	0.974190i	$0.427523\pi$
$594$		0			0
$595$		−	1.07402e10i		−	2.09028i
$596$	−2.03605e9	+	1.08943e9i	−0.393937	+	0.210784i
$597$		0			0
$598$	9.02047e8	−	1.50572e9i	0.172494	−	0.287932i
$599$	3.58734e9			0.681991			0.340995	−	0.940065i	$-0.389236\pi$
$599$	3.58734e9			0.681991			0.340995	+	0.940065i	$0.389236\pi$
$600$		0			0
$601$	8.20369e9			1.54152			0.770759	−	0.637127i	$-0.219877\pi$
$601$	8.20369e9			1.54152			0.770759	+	0.637127i	$0.219877\pi$
$602$	−1.82734e9	+	3.05024e9i	−0.341375	+	0.569831i
$603$		0			0
$604$	2.33934e9	+	4.37201e9i	0.431980	+	0.807332i
$605$			3.32259e9i			0.610004i
$606$		0			0
$607$	−4.60087e9			−0.834986			−0.417493	−	0.908680i	$-0.637091\pi$
$607$	−4.60087e9			−0.834986			−0.417493	+	0.908680i	$0.637091\pi$
$608$	1.15941e9	+	2.44449e9i	0.209207	+	0.441088i
$609$		0			0
$610$	4.88985e9	+	2.92942e9i	0.872251	+	0.522549i
$611$			7.48707e8i			0.132791i
$612$		0			0
$613$		−	8.55728e9i		−	1.50046i	−0.661178	−	0.750229i	$-0.729943\pi$
$613$		−	8.55728e9i		−	1.50046i	0.661178	−	0.750229i	$-0.270057\pi$
$614$	9.23998e7	−	1.54236e8i	0.0161095	−	0.0268903i
$615$		0			0
$616$	−7.54695e9	−	3.65819e8i	−1.30089	−	0.0630570i
$617$	2.58089e9			0.442355			0.221178	−	0.975234i	$-0.429010\pi$
$617$	2.58089e9			0.442355			0.221178	+	0.975234i	$0.429010\pi$
$618$		0			0
$619$		−	5.26641e9i		−	0.892478i	−0.894914	−	0.446239i	$-0.852763\pi$
$619$		−	5.26641e9i		−	0.892478i	0.894914	−	0.446239i	$-0.147237\pi$
$620$	4.09026e9	−	2.18858e9i	0.689255	−	0.368800i
$621$		0			0
$622$	−4.73340e9	−	2.83569e9i	−0.788690	−	0.472490i
$623$	4.18197e8			0.0692903
$624$		0			0
$625$	−7.48796e9			−1.22683
$626$	−3.15164e9	−	1.88809e9i	−0.513483	−	0.307618i
$627$		0			0
$628$	−5.78226e9	+	3.09392e9i	−0.931621	+	0.498483i
$629$			3.58449e9i			0.574314i
$630$		0			0
$631$	8.32515e9			1.31914			0.659568	−	0.751645i	$-0.270739\pi$
$631$	8.32515e9			1.31914			0.659568	+	0.751645i	$0.270739\pi$
$632$	−5.76773e8	+	1.18990e10i	−0.0908857	+	1.87500i
$633$		0			0
$634$	6.16801e9	−	1.02958e10i	0.961242	−	1.60453i
$635$		−	1.28601e10i		−	1.99313i
$636$		0			0
$637$		−	5.80071e8i		−	0.0889187i
$638$	−9.05469e9	−	5.42449e9i	−1.38039	−	0.826965i
$639$		0			0
$640$	−4.57691e9	+	6.19093e9i	−0.690148	+	0.933526i
$641$	−4.26190e9			−0.639146			−0.319573	−	0.947562i	$-0.603540\pi$
$641$	−4.26190e9			−0.639146			−0.319573	+	0.947562i	$0.603540\pi$
$642$		0			0
$643$			1.26588e10i			1.87782i	0.344167	+	0.938908i	$0.388161\pi$
$643$			1.26588e10i			1.87782i	−0.344167	+	0.938908i	$0.611839\pi$
$644$	−1.42550e9	−	2.66414e9i	−0.210314	−	0.393058i
$645$		0			0
$646$	−2.93519e9	+	4.89949e9i	−0.428374	+	0.715052i
$647$	7.38061e9			1.07134			0.535670	−	0.844427i	$-0.320059\pi$
$647$	7.38061e9			1.07134			0.535670	+	0.844427i	$0.320059\pi$
$648$		0			0
$649$	1.23211e9			0.176926
$650$	−9.93555e8	+	1.65846e9i	−0.141904	+	0.236870i
$651$		0			0
$652$	9.67853e9	−	5.17870e9i	1.36755	−	0.731735i
$653$		−	3.21579e9i		−	0.451951i	−0.974133	−	0.225975i	$-0.927443\pi$
$653$		−	3.21579e9i		−	0.451951i	0.974133	−	0.225975i	$-0.0725569\pi$
$654$		0			0
$655$	−1.18549e10			−1.64836
$656$	6.51717e8	−	9.77204e8i	0.0901354	−	0.135152i
$657$		0			0
$658$	1.10563e9	+	6.62362e8i	0.151293	+	0.0906368i
$659$			5.17004e9i			0.703711i	0.936054	+	0.351856i	$0.114449\pi$
$659$			5.17004e9i			0.703711i	−0.936054	+	0.351856i	$0.885551\pi$
$660$		0			0
$661$			1.95604e9i			0.263435i	0.991287	+	0.131717i	$0.0420491\pi$
$661$			1.95604e9i			0.263435i	−0.991287	+	0.131717i	$0.957951\pi$
$662$	−1.67735e9	+	2.79987e9i	−0.224709	+	0.375090i
$663$		0			0
$664$	−8.52701e9	−	4.13325e8i	−1.13034	−	0.0547902i
$665$	4.53232e9			0.597647
$666$		0			0
$667$		−	4.22099e9i		−	0.550775i
$668$	6.39330e9	+	1.19485e10i	0.829865	+	1.55094i
$669$		0			0
$670$	9.96362e8	+	5.96902e8i	0.127984	+	0.0766727i
$671$	8.46551e9			1.08174
$672$		0			0
$673$	1.54679e9			0.195605			0.0978024	−	0.995206i	$-0.468819\pi$
$673$	1.54679e9			0.195605			0.0978024	+	0.995206i	$0.468819\pi$
$674$	−1.07337e9	−	6.43035e8i	−0.135033	−	0.0808956i
$675$		0			0
$676$	1.40053e9	+	2.61747e9i	0.174373	+	0.325888i
$677$		−	8.55209e9i		−	1.05928i	−0.848222	−	0.529642i	$-0.822326\pi$
$677$		−	8.55209e9i		−	1.05928i	0.848222	−	0.529642i	$-0.177674\pi$
$678$		0			0
$679$	7.50565e9			0.920119
$680$	−1.62340e10	−	7.86900e8i	−1.97990	−	0.0959707i
$681$		0			0
$682$	3.54061e9	−	5.91006e9i	0.427398	−	0.713422i
$683$			7.26976e9i			0.873067i	0.899688	+	0.436534i	$0.143794\pi$
$683$			7.26976e9i			0.873067i	−0.899688	+	0.436534i	$0.856206\pi$
$684$		0			0
$685$		−	8.33837e9i		−	0.991206i
$686$	6.79217e9	+	4.06906e9i	0.803293	+	0.481238i
$687$		0			0
$688$	4.47658e9	+	2.98552e9i	0.524068	+	0.349511i
$689$	6.54162e9			0.761935
$690$		0			0
$691$			5.19893e9i			0.599434i	0.954028	+	0.299717i	$0.0968922\pi$
$691$			5.19893e9i			0.599434i	−0.954028	+	0.299717i	$0.903108\pi$
$692$	2.23629e9	−	1.19657e9i	0.256541	−	0.137268i
$693$		0			0
$694$	−6.43358e9	+	1.07391e10i	−0.730626	+	1.21958i
$695$	−1.69709e10			−1.91760
$696$		0			0
$697$	2.47961e9			0.277376
$698$	8.04333e9	−	1.34261e10i	0.895245	−	1.49436i
$699$		0			0
$700$	1.57011e9	+	2.93440e9i	0.173017	+	0.323353i
$701$		−	1.35221e10i		−	1.48262i	−0.671163	−	0.741310i	$-0.734205\pi$
$701$		−	1.35221e10i		−	1.48262i	0.671163	−	0.741310i	$-0.265795\pi$
$702$		0			0
$703$	−1.51263e9			−0.164206
$704$	−1.10588e9	+	1.13805e10i	−0.119455	+	1.22930i
$705$		0			0
$706$	2.40321e9	+	1.43972e9i	0.257025	+	0.153979i
$707$		−	5.93083e9i		−	0.631172i
$708$		0			0
$709$		−	1.05901e10i		−	1.11594i	−0.829862	−	0.557969i	$-0.811581\pi$
$709$		−	1.05901e10i		−	1.11594i	0.829862	−	0.557969i	$-0.188419\pi$
$710$	−1.01686e9	+	1.69737e9i	−0.106625	+	0.177980i
$711$		0			0
$712$	3.06398e7	−	6.32109e8i	0.00318131	−	0.0656314i
$713$	2.75507e9			0.284655
$714$		0			0
$715$			1.11271e10i			1.13845i
$716$	3.36096e9	−	1.79835e9i	0.342191	−	0.183096i
$717$		0			0
$718$	1.34556e10	+	8.06102e9i	1.35665	+	0.812746i
$719$	−1.49161e10			−1.49659			−0.748297	−	0.663363i	$-0.769128\pi$
$719$	−1.49161e10			−1.49659			−0.748297	+	0.663363i	$0.769128\pi$
$720$		0			0
$721$	6.31417e9			0.627398
$722$	6.60779e9	+	3.95860e9i	0.653395	+	0.391437i
$723$		0			0
$724$	−4.47180e8	+	2.39273e8i	−0.0437923	+	0.0234320i
$725$			4.64919e9i			0.453100i
$726$		0			0
$727$	−8.90159e9			−0.859206			−0.429603	−	0.903018i	$-0.641346\pi$
$727$	−8.90159e9			−0.859206			−0.429603	+	0.903018i	$0.641346\pi$
$728$	−8.70577e9	−	4.21989e8i	−0.836271	−	0.0405361i
$729$		0			0
$730$	−5.06599e9	+	8.45627e9i	−0.481986	+	0.804542i
$731$			1.13591e10i			1.07556i
$732$		0			0
$733$			7.99792e9i			0.750090i	0.927007	+	0.375045i	$0.122373\pi$
$733$			7.99792e9i			0.750090i	−0.927007	+	0.375045i	$0.877627\pi$
$734$	−7.27288e9	−	4.35704e9i	−0.678844	−	0.406683i
$735$		0			0
$736$	−4.13132e9	+	1.95947e9i	−0.381959	+	0.181162i
$737$	1.72494e9			0.158722
$738$		0			0
$739$		−	1.03852e10i		−	0.946588i	−0.880905	−	0.473294i	$-0.843065\pi$
$739$		−	1.03852e10i		−	0.946588i	0.880905	−	0.473294i	$-0.156935\pi$
$740$	−2.03078e9	−	3.79536e9i	−0.184227	−	0.344304i
$741$		0			0
$742$	5.78720e9	−	9.66013e9i	0.520062	−	0.868099i
$743$	3.73477e9			0.334044			0.167022	−	0.985953i	$-0.446585\pi$
$743$	3.73477e9			0.334044			0.167022	+	0.985953i	$0.446585\pi$
$744$		0			0
$745$	5.85402e9			0.518689
$746$	−8.69345e9	+	1.45113e10i	−0.766666	+	1.27974i
$747$		0			0
$748$	−2.12827e10	+	1.13878e10i	−1.85940	+	0.994908i
$749$			4.90772e8i			0.0426770i
$750$		0			0
$751$	−1.34330e10			−1.15726			−0.578631	−	0.815589i	$-0.696413\pi$
$751$	−1.34330e10			−1.15726			−0.578631	+	0.815589i	$0.696413\pi$
$752$	1.08217e9	−	1.62264e9i	0.0927970	−	0.139143i
$753$		0			0
$754$	−1.04450e10	−	6.25741e9i	−0.887379	−	0.531612i
$755$		−	1.25703e10i		−	1.06300i
$756$		0			0
$757$			6.78007e9i			0.568065i	0.958815	+	0.284033i	$0.0916724\pi$
$757$			6.78007e9i			0.568065i	−0.958815	+	0.284033i	$0.908328\pi$
$758$	4.60548e8	−	7.68758e8i	0.0384090	−	0.0641132i
$759$		0			0
$760$	3.32068e8	−	6.85065e9i	0.0274397	−	0.566089i
$761$	−8.01137e9			−0.658962			−0.329481	−	0.944162i	$-0.606874\pi$
$761$	−8.01137e9			−0.658962			−0.329481	+	0.944162i	$0.606874\pi$
$762$		0			0
$763$			1.87451e10i			1.52775i
$764$	2.89925e9	+	5.41845e9i	0.235212	+	0.439590i
$765$		0			0
$766$	−4.66133e9	−	2.79252e9i	−0.374722	−	0.224489i
$767$	1.42130e9			0.113737
$768$		0			0
$769$	1.46553e10			1.16213			0.581063	−	0.813858i	$-0.302637\pi$
$769$	1.46553e10			1.16213			0.581063	+	0.813858i	$0.302637\pi$
$770$	1.64316e10	+	9.84389e9i	1.29707	+	0.777051i
$771$		0			0
$772$	−2.85334e8	−	5.33264e8i	−0.0223199	−	0.0417140i
$773$			2.33296e10i			1.81668i	0.418233	+	0.908340i	$0.362650\pi$
$773$			2.33296e10i			1.81668i	−0.418233	+	0.908340i	$0.637350\pi$
$774$		0			0
$775$	−3.03456e9			−0.234174
$776$	5.49913e8	−	1.13449e10i	0.0422453	−	0.871533i
$777$		0			0
$778$	6.23001e9	−	1.03993e10i	0.474307	−	0.791725i
$779$			1.04638e9i			0.0793064i
$780$		0			0
$781$			2.93855e9i			0.220726i
$782$	−8.28042e9	−	4.96064e9i	−0.619197	−	0.370949i
$783$		0			0
$784$	−8.38429e8	+	1.25716e9i	−0.0621384	+	0.0931721i
$785$	1.66250e10			1.22664
$786$		0			0
$787$			5.27740e8i			0.0385930i	0.999814	+	0.0192965i	$0.00614264\pi$
$787$			5.27740e8i			0.0385930i	−0.999814	+	0.0192965i	$0.993857\pi$
$788$	1.29655e10	−	6.93747e9i	0.943948	−	0.505079i
$789$		0			0
$790$	1.55205e10	−	2.59072e10i	1.11998	−	1.86950i
$791$	1.80747e10			1.29853
$792$		0			0
$793$	9.76536e9			0.695396
$794$	1.18138e10	−	1.97198e10i	0.837562	−	1.39808i
$795$		0			0
$796$	7.30287e8	+	1.36484e9i	0.0513213	+	0.0959150i
$797$			2.41514e9i			0.168981i	0.996424	+	0.0844907i	$0.0269263\pi$
$797$			2.41514e9i			0.168981i	−0.996424	+	0.0844907i	$0.973074\pi$
$798$		0			0
$799$	4.11738e9			0.285566
$800$	4.55042e9	−	2.15825e9i	0.314222	−	0.149034i
$801$		0			0
$802$	2.50165e10	+	1.49869e10i	1.71244	+	1.02589i
$803$			1.46398e10i			0.997773i
$804$		0			0
$805$			7.65988e9i			0.517531i
$806$	4.08426e9	−	6.81754e9i	0.274752	−	0.458622i
$807$		0			0
$808$	−8.96451e9	−	4.34531e8i	−0.597843	−	0.0289789i
$809$	−1.16364e10			−0.772679			−0.386340	−	0.922357i	$-0.626261\pi$
$809$	−1.16364e10			−0.772679			−0.386340	+	0.922357i	$0.626261\pi$
$810$		0			0
$811$			1.44359e10i			0.950320i	0.879899	+	0.475160i	$0.157610\pi$
$811$			1.44359e10i			0.950320i	−0.879899	+	0.475160i	$0.842390\pi$
$812$	−1.84809e10	+	9.88858e9i	−1.21137	+	0.648168i
$813$		0			0
$814$	−5.48396e9	−	3.28533e9i	−0.356376	−	0.213498i
$815$	−2.78275e10			−1.80062
$816$		0			0
$817$	−4.79348e9			−0.307521
$818$	3.20512e9	+	1.92013e9i	0.204742	+	0.122657i
$819$		0			0
$820$	−2.62548e9	+	1.40482e9i	−0.166288	+	0.0889757i
$821$			7.63805e9i			0.481706i	0.970562	+	0.240853i	$0.0774271\pi$
$821$			7.63805e9i			0.481706i	−0.970562	+	0.240853i	$0.922573\pi$
$822$		0			0
$823$	−2.16446e10			−1.35348			−0.676738	−	0.736224i	$-0.736607\pi$
$823$	−2.16446e10			−1.35348			−0.676738	+	0.736224i	$0.736607\pi$
$824$	4.62618e8	−	9.54395e9i	0.0288056	−	0.594268i
$825$		0			0
$826$	1.25738e9	−	2.09885e9i	0.0776315	−	0.129584i
$827$			1.57823e10i			0.970288i	0.874434	+	0.485144i	$0.161233\pi$
$827$			1.57823e10i			0.970288i	−0.874434	+	0.485144i	$0.838767\pi$
$828$		0			0
$829$		−	2.63296e10i		−	1.60510i	−0.596582	−	0.802552i	$-0.703475\pi$
$829$		−	2.63296e10i		−	1.60510i	0.596582	−	0.802552i	$-0.296525\pi$
$830$	1.85655e10	+	1.11222e10i	1.12702	+	0.675179i
$831$		0			0
$832$	−1.27568e9	+	1.31279e10i	−0.0767911	+	0.790251i
$833$	−3.19000e9			−0.191220
$834$		0			0
$835$		−	3.43541e10i		−	2.04210i
$836$	−4.80557e9	−	8.98119e9i	−0.284461	−	0.531633i
$837$		0			0
$838$	−3.37241e8	+	5.62931e8i	−0.0197964	+	0.0330446i
$839$	1.84995e9			0.108142			0.0540710	−	0.998537i	$-0.482780\pi$
$839$	1.84995e9			0.108142			0.0540710	+	0.998537i	$0.482780\pi$
$840$		0			0
$841$	−1.20307e10			−0.697438
$842$	1.10826e9	−	1.84993e9i	0.0639805	−	0.106798i
$843$		0			0
$844$	2.21035e10	−	1.18270e10i	1.26550	−	0.677134i
$845$		−	7.52569e9i		−	0.429090i
$846$		0			0
$847$	9.79866e9			0.554083
$848$	−1.41774e10	−	9.45519e9i	−0.798382	−	0.532457i
$849$		0			0
$850$	9.12042e9	+	5.46387e9i	0.509388	+	0.305165i
$851$		−	2.55643e9i		−	0.142194i
$852$		0			0
$853$		−	6.28088e7i		−	0.00346496i	−0.999998	−	0.00173248i	$-0.999449\pi$
$853$		−	6.28088e7i		−	0.00346496i	0.999998	−	0.00173248i	$-0.000551466\pi$
$854$	8.63917e9	−	1.44207e10i	0.474646	−	0.792289i
$855$		0			0
$856$	7.41808e8	+	3.59572e7i	0.0404234	+	0.00195942i
$857$	6.25595e9			0.339516			0.169758	−	0.985486i	$-0.445701\pi$
$857$	6.25595e9			0.339516			0.169758	+	0.985486i	$0.445701\pi$
$858$		0			0
$859$		−	2.48119e10i		−	1.33562i	−0.744331	−	0.667811i	$-0.767231\pi$
$859$		−	2.48119e10i		−	1.33562i	0.744331	−	0.667811i	$-0.232769\pi$
$860$	−6.43549e9	−	1.20274e10i	−0.345014	−	0.644801i
$861$		0			0
$862$	−2.35765e10	−	1.41243e10i	−1.25373	−	0.751087i
$863$	−1.28944e10			−0.682909			−0.341455	−	0.939898i	$-0.610920\pi$
$863$	−1.28944e10			−0.682909			−0.341455	+	0.939898i	$0.610920\pi$
$864$		0			0
$865$	−6.42973e9			−0.337782
$866$	−2.30892e10	−	1.38323e10i	−1.20808	−	0.723739i
$867$		0			0
$868$	−6.45435e9	−	1.20626e10i	−0.334991	−	0.626069i
$869$		−	4.48516e10i		−	2.31851i
$870$		0			0
$871$	1.98980e9			0.102034
$872$	2.83334e10	+	1.37339e9i	1.44708	+	0.0701432i
$873$		0			0
$874$	2.09336e9	−	3.49429e9i	0.106061	−	0.177039i
$875$			1.58229e10i			0.798468i
$876$		0			0
$877$			2.75670e10i			1.38004i	0.723792	+	0.690018i	$0.242397\pi$
$877$			2.75670e10i			1.38004i	−0.723792	+	0.690018i	$0.757603\pi$
$878$	−1.29238e10	−	7.74239e9i	−0.644404	−	0.386051i
$879$		0			0
$880$	1.60830e10	−	2.41154e10i	0.795571	−	1.19290i
$881$	−2.74343e10			−1.35169			−0.675847	−	0.737042i	$-0.736222\pi$
$881$	−2.74343e10			−1.35169			−0.675847	+	0.737042i	$0.736222\pi$
$882$		0			0
$883$			2.09906e10i			1.02604i	0.858378	+	0.513018i	$0.171473\pi$
$883$			2.09906e10i			1.02604i	−0.858378	+	0.513018i	$0.828527\pi$
$884$	−2.45506e10	+	1.31363e10i	−1.19531	+	0.639575i
$885$		0			0
$886$	−2.92251e9	+	4.87833e9i	−0.141169	+	0.235642i
$887$	2.39134e10			1.15056			0.575280	−	0.817957i	$-0.304893\pi$
$887$	2.39134e10			1.15056			0.575280	+	0.817957i	$0.304893\pi$
$888$		0			0
$889$	−3.79257e10			−1.81041
$890$	−8.24493e8	+	1.37626e9i	−0.0392033	+	0.0654390i
$891$		0			0
$892$	6.52337e9	+	1.21916e10i	0.307748	+	0.575153i
$893$			1.73751e9i			0.0816483i
$894$		0			0
$895$	−9.66337e9			−0.450555
$896$	1.82577e10	+	1.34978e10i	0.847947	+	0.626880i
$897$		0			0
$898$	−3.05510e10	−	1.83025e10i	−1.40785	−	0.843419i
$899$		−	1.91117e10i		−	0.877282i
$900$		0			0
$901$		−	3.59744e10i		−	1.63854i
$902$	−2.27267e9	+	3.79359e9i	−0.103113	+	0.172118i
$903$		0			0
$904$	1.32427e9	−	2.73201e10i	0.0596194	−	1.22997i
$905$	1.28572e9			0.0576603
$906$		0			0
$907$			3.84425e10i			1.71075i	0.518012	+	0.855373i	$0.326672\pi$
$907$			3.84425e10i			1.71075i	−0.518012	+	0.855373i	$0.673328\pi$
$908$	1.81867e10	−	9.73115e9i	0.806218	−	0.431384i
$909$		0			0
$910$	1.89547e10	+	1.13554e10i	0.833819	+	0.499525i
$911$	−3.64507e10			−1.59732			−0.798660	−	0.601783i	$-0.794457\pi$
$911$	−3.64507e10			−1.59732			−0.798660	+	0.601783i	$0.794457\pi$
$912$		0			0
$913$	3.21413e10			1.39771
$914$	−2.60513e10	−	1.56069e10i	−1.12854	−	0.676089i
$915$		0			0
$916$	−5.94966e9	+	3.18349e9i	−0.255775	+	0.136858i
$917$			3.49613e10i			1.49725i
$918$		0			0
$919$	2.37343e10			1.00872			0.504361	−	0.863493i	$-0.331728\pi$
$919$	2.37343e10			1.00872			0.504361	+	0.863493i	$0.331728\pi$
$920$	1.15780e10	+	5.61213e8i	0.490203	+	0.0237613i
$921$		0			0
$922$	−7.58382e9	+	1.26591e10i	−0.318662	+	0.531917i
$923$			3.38976e9i			0.141894i
$924$		0			0
$925$			2.81577e9i			0.116977i
$926$	2.78401e10	+	1.66785e10i	1.15221	+	0.690269i
$927$		0			0
$928$	1.35927e10	+	2.86586e10i	0.558325	+	1.17716i
$929$	4.23952e10			1.73485			0.867424	−	0.497570i	$-0.165774\pi$
$929$	4.23952e10			1.73485			0.867424	+	0.497570i	$0.165774\pi$
$930$		0			0
$931$		−	1.34616e9i		−	0.0546730i
$932$	1.08350e10	+	2.02496e10i	0.438402	+	0.819334i
$933$		0			0
$934$	−3.46834e9	+	5.78943e9i	−0.139286	+	0.232499i
$935$	6.11916e10			2.44823
$936$		0			0
$937$	3.70014e10			1.46937			0.734683	−	0.678411i	$-0.237331\pi$
$937$	3.70014e10			1.46937			0.734683	+	0.678411i	$0.237331\pi$
$938$	1.76033e9	−	2.93838e9i	0.0696439	−	0.116251i
$939$		0			0
$940$	−4.35960e9	+	2.33269e9i	−0.171198	+	0.0916031i
$941$			2.10617e10i			0.824005i	0.911183	+	0.412003i	$0.135171\pi$
$941$			2.10617e10i			0.824005i	−0.911183	+	0.412003i	$0.864829\pi$
$942$		0			0
$943$	−1.76844e9			−0.0686752
$944$	−3.08032e9	−	2.05433e9i	−0.119177	−	0.0794817i
$945$		0			0
$946$	−1.73785e10	−	1.04111e10i	−0.667410	−	0.399833i
$947$			1.35146e10i			0.517104i	0.965997	+	0.258552i	$0.0832454\pi$
$947$			1.35146e10i			0.517104i	−0.965997	+	0.258552i	$0.916755\pi$
$948$		0			0
$949$			1.68877e10i			0.641416i
$950$	−2.30572e9	+	3.84877e9i	−0.0872519	+	0.145643i
$951$		0			0
$952$	−2.32065e9	+	4.78758e10i	−0.0871728	+	1.79840i
$953$	−4.26831e10			−1.59746			−0.798731	−	0.601688i	$-0.794495\pi$
$953$	−4.26831e10			−1.59746			−0.798731	+	0.601688i	$0.794495\pi$
$954$		0			0
$955$		−	1.55790e10i		−	0.578799i
$956$	5.08733e9	+	9.50776e9i	0.188316	+	0.351946i
$957$		0			0
$958$	2.09702e10	+	1.25628e10i	0.770588	+	0.461645i
$959$	−2.45907e10			−0.900340
$960$		0			0
$961$	−1.50383e10			−0.546597
$962$	−6.32600e9	−	3.78979e9i	−0.229096	−	0.137247i
$963$		0			0
$964$	−1.28205e10	−	2.39603e10i	−0.460930	−	0.861437i
$965$			1.53323e9i			0.0549239i
$966$		0			0
$967$	2.32274e10			0.826053			0.413026	−	0.910719i	$-0.364472\pi$
$967$	2.32274e10			0.826053			0.413026	+	0.910719i	$0.364472\pi$
$968$	7.17914e8	−	1.48108e10i	0.0254395	−	0.524825i
$969$		0			0
$970$	−1.47977e10	+	2.47007e10i	−0.520588	+	0.868977i
$971$		−	4.85678e10i		−	1.70248i	−0.524780	−	0.851238i	$-0.675852\pi$
$971$		−	4.85678e10i		−	1.70248i	0.524780	−	0.851238i	$-0.324148\pi$
$972$		0			0
$973$			5.00491e10i			1.74181i
$974$	1.37752e9	+	8.25248e8i	0.0477686	+	0.0286173i
$975$		0			0
$976$	−2.11641e10	−	1.41148e10i	−0.728660	−	0.485958i
$977$	−1.54549e10			−0.530193			−0.265096	−	0.964222i	$-0.585404\pi$
$977$	−1.54549e10			−0.530193			−0.265096	+	0.964222i	$0.585404\pi$
$978$		0			0
$979$			2.38264e9i			0.0811557i
$980$	3.37766e9	−	1.80729e9i	0.114637	−	0.0613389i
$981$		0			0
$982$	−1.38774e10	+	2.31644e10i	−0.467646	+	0.780606i
$983$	1.59192e10			0.534546			0.267273	−	0.963621i	$-0.413877\pi$
$983$	1.59192e10			0.534546			0.267273	+	0.963621i	$0.413877\pi$
$984$		0			0
$985$	−3.72782e10			−1.24288
$986$	−3.44115e10	+	5.74405e10i	−1.14323	+	1.90831i
$987$		0			0
$988$	−5.54346e9	−	1.03602e10i	−0.182865	−	0.341759i
$989$		−	8.10126e9i		−	0.266296i
$990$		0			0
$991$	1.49883e10			0.489208			0.244604	−	0.969623i	$-0.421342\pi$
$991$	1.49883e10			0.489208			0.244604	+	0.969623i	$0.421342\pi$
$992$	−1.87056e10	+	8.87203e9i	−0.608390	+	0.288557i
$993$		0			0
$994$	5.00572e9	+	2.99883e9i	0.161664	+	0.0968500i
$995$		−	3.92416e9i		−	0.126289i
$996$		0			0
$997$		−	3.44101e10i		−	1.09965i	−0.835281	−	0.549824i	$-0.814695\pi$
$997$		−	3.44101e10i		−	1.09965i	0.835281	−	0.549824i	$-0.185305\pi$
$998$	−3.04611e10	+	5.08464e10i	−0.970038	+	1.61921i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	72.8.d.b.37.6		6
3.2	odd	2		8.8.b.a.5.1	✓	6
4.3	odd	2		288.8.d.b.145.2		6
8.3	odd	2		288.8.d.b.145.5		6
8.5	even	2	inner	72.8.d.b.37.5		6
12.11	even	2		32.8.b.a.17.2		6
24.5	odd	2		8.8.b.a.5.2	yes	6
24.11	even	2		32.8.b.a.17.5		6
48.5	odd	4		256.8.a.r.1.5		6
48.11	even	4		256.8.a.q.1.2		6
48.29	odd	4		256.8.a.r.1.2		6
48.35	even	4		256.8.a.q.1.5		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8.8.b.a.5.1	✓	6	3.2	odd	2
8.8.b.a.5.2	yes	6	24.5	odd	2
32.8.b.a.17.2		6	12.11	even	2
32.8.b.a.17.5		6	24.11	even	2
72.8.d.b.37.5		6	8.5	even	2	inner
72.8.d.b.37.6		6	1.1	even	1	trivial
256.8.a.q.1.2		6	48.11	even	4
256.8.a.q.1.5		6	48.35	even	4
256.8.a.r.1.2		6	48.29	odd	4
256.8.a.r.1.5		6	48.5	odd	4
288.8.d.b.145.2		6	4.3	odd	2
288.8.d.b.145.5		6	8.3	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:	\( k \)	\(=\)	\( 8 \)
Character orbit:	\([\chi]\)	\(=\)	72.d (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(9.70536 + 5.81430i) q^{2} +(60.3879 + 112.860i) q^{4} -324.492i q^{5} -956.960 q^{7} +(-70.1132 + 1446.46i) q^{8} +O(q^{10})\)	\(q+(9.70536 + 5.81430i) q^{2} +(60.3879 + 112.860i) q^{4} -324.492i q^{5} -956.960 q^{7} +(-70.1132 + 1446.46i) q^{8} +(1886.69 - 3149.31i) q^{10} -5452.20i q^{11} -6289.38i q^{13} +(-9287.64 - 5564.05i) q^{14} +(-9090.60 + 13630.7i) q^{16} -34587.3 q^{17} -14595.6i q^{19} +(36622.0 - 19595.4i) q^{20} +(31700.7 - 52915.6i) q^{22} +24667.5 q^{23} -27169.8 q^{25} +(36568.3 - 61040.6i) q^{26} +(-57788.8 - 108002. i) q^{28} -171116. i q^{29} +111688. q^{31} +(-167481. + 79435.5i) q^{32} +(-335682. - 201101. i) q^{34} +310526. i q^{35} -103636. i q^{37} +(84863.4 - 141656. i) q^{38} +(469363. + 22751.1i) q^{40} -71691.3 q^{41} -328419. i q^{43} +(615334. - 329247. i) q^{44} +(239406. + 143424. i) q^{46} -119043. q^{47} +92230.3 q^{49} +(-263693. - 157973. i) q^{50} +(709817. - 379802. i) q^{52} +1.04011e6i q^{53} -1.76919e6 q^{55} +(67095.6 - 1.38420e6i) q^{56} +(994918. - 1.66074e6i) q^{58} +225984. i q^{59} +1.55268e6i q^{61} +(1.08398e6 + 649390. i) q^{62} +(-2.08732e6 - 202831. i) q^{64} -2.04085e6 q^{65} +316375. i q^{67} +(-2.08865e6 - 3.90351e6i) q^{68} +(-1.80549e6 + 3.01376e6i) q^{70} -538965. q^{71} -2.68512e6 q^{73} +(602570. - 1.00582e6i) q^{74} +(1.64726e6 - 881400. i) q^{76} +5.21754e6i q^{77} +8.22632e6 q^{79} +(4.42305e6 + 2.94982e6i) q^{80} +(-695790. - 416834. i) q^{82} +5.89510e6i q^{83} +1.12233e7i q^{85} +(1.90952e6 - 3.18742e6i) q^{86} +(7.88638e6 + 382271. i) q^{88} -437005. q^{89} +6.01868e6i q^{91} +(1.48962e6 + 2.78396e6i) q^{92} +(-1.15536e6 - 692152. i) q^{94} -4.73616e6 q^{95} -7.84322e6 q^{97} +(895128. + 536254. i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - 6 q^{2} + 116 q^{4} - 688 q^{7} - 1512 q^{8}+O(q^{10}) \) 6 * q - 6 * q^2 + 116 * q^4 - 688 * q^7 - 1512 * q^8	\( 6 q - 6 q^{2} + 116 q^{4} - 688 q^{7} - 1512 q^{8} - 1656 q^{10} - 12048 q^{14} + 35344 q^{16} - 1452 q^{17} + 114768 q^{20} + 152860 q^{22} + 1296 q^{23} - 39314 q^{25} + 316968 q^{26} - 480800 q^{28} - 89280 q^{31} - 817056 q^{32} - 1009108 q^{34} - 974124 q^{38} + 954464 q^{40} - 521244 q^{41} + 1096344 q^{44} + 929840 q^{46} - 1566432 q^{47} - 511050 q^{49} + 148626 q^{50} + 823952 q^{52} - 3270256 q^{55} + 2468928 q^{56} + 3130744 q^{58} + 7055808 q^{62} - 4792768 q^{64} - 1416480 q^{65} - 6608040 q^{68} - 7406912 q^{70} + 7597104 q^{71} + 2089564 q^{73} - 7744200 q^{74} + 9241288 q^{76} + 16015904 q^{79} + 12600384 q^{80} + 10715932 q^{82} + 5639076 q^{86} + 1541200 q^{88} - 2169084 q^{89} - 669600 q^{92} + 15503712 q^{94} - 48537936 q^{95} - 1088308 q^{97} + 14983242 q^{98}+O(q^{100}) \) 6 * q - 6 * q^2 + 116 * q^4 - 688 * q^7 - 1512 * q^8 - 1656 * q^10 - 12048 * q^14 + 35344 * q^16 - 1452 * q^17 + 114768 * q^20 + 152860 * q^22 + 1296 * q^23 - 39314 * q^25 + 316968 * q^26 - 480800 * q^28 - 89280 * q^31 - 817056 * q^32 - 1009108 * q^34 - 974124 * q^38 + 954464 * q^40 - 521244 * q^41 + 1096344 * q^44 + 929840 * q^46 - 1566432 * q^47 - 511050 * q^49 + 148626 * q^50 + 823952 * q^52 - 3270256 * q^55 + 2468928 * q^56 + 3130744 * q^58 + 7055808 * q^62 - 4792768 * q^64 - 1416480 * q^65 - 6608040 * q^68 - 7406912 * q^70 + 7597104 * q^71 + 2089564 * q^73 - 7744200 * q^74 + 9241288 * q^76 + 16015904 * q^79 + 12600384 * q^80 + 10715932 * q^82 + 5639076 * q^86 + 1541200 * q^88 - 2169084 * q^89 - 669600 * q^92 + 15503712 * q^94 - 48537936 * q^95 - 1088308 * q^97 + 14983242 * q^98

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