LMFDB - Embedded newform 72.11.b.b.19.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [72,11,Mod(19,72)]

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([1, 1, 0]))

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

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

chi := DirichletCharacter("72.19");

S:= CuspForms(chi, 11);

N := Newforms(S);

Level:	$ N $	$=$	$ 72 = 2^{3} \cdot 3^{2} $
Weight:	$ k $	$=$	$ 11 $
Character orbit:	$[\chi]$	$=$	72.b (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:	$45.7457221925$
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} - 3x^{7} + 5x^{6} - 51x^{5} + 30855x^{4} - 121569x^{3} + 12144527x^{2} + 279415575x + 3348211684 $ x^8 - 3x^7 + 5x^6 - 51x^5 + 30855x^4 - 121569x^3 + 12144527x^2 + 279415575*x + 3348211684
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{28}\cdot 3^{3} $
Twist minimal:	no (minimal twist has level 8)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			19.1
Root			$-11.4287 - 6.91461i$ of defining polynomial
Character	$\chi$	$=$	72.19
Dual form			72.11.b.b.19.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-28.8575 - 13.8292i) q^{2} +(641.505 + 798.152i) q^{4} -5381.00i q^{5} -6613.83i q^{7} +(-7474.38 - 31904.2i) q^{8} +O(q^{10})$	\(q+(-28.8575 - 13.8292i) q^{2} +(641.505 + 798.152i) q^{4} -5381.00i q^{5} -6613.83i q^{7} +(-7474.38 - 31904.2i) q^{8} +(-74415.0 + 155282. i) q^{10} -221096. q^{11} -361689. i q^{13} +(-91464.1 + 190858. i) q^{14} +(-225518. + 1.02404e6i) q^{16} -776217. q^{17} +1.46186e6 q^{19} +(4.29486e6 - 3.45194e6i) q^{20} +(6.38025e6 + 3.05758e6i) q^{22} -2.34458e6i q^{23} -1.91895e7 q^{25} +(-5.00188e6 + 1.04374e7i) q^{26} +(5.27884e6 - 4.24281e6i) q^{28} -2.88750e7i q^{29} -3.00762e7i q^{31} +(2.06695e7 - 2.64324e7i) q^{32} +(2.23996e7 + 1.07345e7i) q^{34} -3.55890e7 q^{35} -1.16919e7i q^{37} +(-4.21857e7 - 2.02164e7i) q^{38} +(-1.71676e8 + 4.02196e7i) q^{40} -4.70330e7 q^{41} +3.52427e7 q^{43} +(-1.41834e8 - 1.76468e8i) q^{44} +(-3.24238e7 + 6.76587e7i) q^{46} +4.23068e8i q^{47} +2.38733e8 q^{49} +(5.53761e8 + 2.65376e8i) q^{50} +(2.88683e8 - 2.32025e8i) q^{52} -9.16056e6i q^{53} +1.18971e9i q^{55} +(-2.11009e8 + 4.94343e7i) q^{56} +(-3.99319e8 + 8.33260e8i) q^{58} +1.03098e9 q^{59} +1.37140e8i q^{61} +(-4.15930e8 + 8.67921e8i) q^{62} +(-9.62009e8 + 4.76928e8i) q^{64} -1.94625e9 q^{65} -7.94671e8 q^{67} +(-4.97947e8 - 6.19539e8i) q^{68} +(1.02701e9 + 4.92168e8i) q^{70} +2.04858e9i q^{71} -1.88707e9 q^{73} +(-1.61690e8 + 3.37399e8i) q^{74} +(9.37794e8 + 1.16679e9i) q^{76} +1.46229e9i q^{77} +1.04965e9i q^{79} +(5.51035e9 + 1.21351e9i) q^{80} +(1.35725e9 + 6.50430e8i) q^{82} -3.77162e9 q^{83} +4.17682e9i q^{85} +(-1.01702e9 - 4.87380e8i) q^{86} +(1.65255e9 + 7.05387e9i) q^{88} +4.07338e9 q^{89} -2.39215e9 q^{91} +(1.87133e9 - 1.50406e9i) q^{92} +(5.85070e9 - 1.22087e10i) q^{94} -7.86629e9i q^{95} +1.76770e9 q^{97} +(-6.88921e9 - 3.30149e9i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 42 q^{2} + 212 q^{4} + 72 q^{8}+O(q^{10}) $ 8 * q - 42 * q^2 + 212 * q^4 + 72 * q^8	$ 8 q - 42 q^{2} + 212 q^{4} + 72 q^{8} + 9120 q^{10} - 143328 q^{11} + 400320 q^{14} - 1987312 q^{16} + 370800 q^{17} + 1753312 q^{19} - 2557440 q^{20} + 1549180 q^{22} - 18792760 q^{25} - 1891680 q^{26} + 18286080 q^{28} + 64016928 q^{32} - 115705388 q^{34} - 53736960 q^{35} - 375128220 q^{38} - 357584640 q^{40} - 92669328 q^{41} - 10190624 q^{43} - 727831512 q^{44} + 851947200 q^{46} - 80432248 q^{49} + 1669361190 q^{50} + 2420759040 q^{52} + 2928529920 q^{56} - 3245264160 q^{58} + 965642016 q^{59} - 4060980480 q^{62} - 5804705728 q^{64} + 839028480 q^{65} - 1225582880 q^{67} - 5258111400 q^{68} + 7723829760 q^{70} + 2800072720 q^{73} + 7669373280 q^{74} + 3753451288 q^{76} + 6408629760 q^{80} - 3638778380 q^{82} - 1853422560 q^{83} - 3022180476 q^{86} + 5815578640 q^{88} - 6162596112 q^{89} + 7645985280 q^{91} + 8903892480 q^{92} - 14182177920 q^{94} - 9697863536 q^{97} - 34759868298 q^{98}+O(q^{100}) $ 8 * q - 42 * q^2 + 212 * q^4 + 72 * q^8 + 9120 * q^10 - 143328 * q^11 + 400320 * q^14 - 1987312 * q^16 + 370800 * q^17 + 1753312 * q^19 - 2557440 * q^20 + 1549180 * q^22 - 18792760 * q^25 - 1891680 * q^26 + 18286080 * q^28 + 64016928 * q^32 - 115705388 * q^34 - 53736960 * q^35 - 375128220 * q^38 - 357584640 * q^40 - 92669328 * q^41 - 10190624 * q^43 - 727831512 * q^44 + 851947200 * q^46 - 80432248 * q^49 + 1669361190 * q^50 + 2420759040 * q^52 + 2928529920 * q^56 - 3245264160 * q^58 + 965642016 * q^59 - 4060980480 * q^62 - 5804705728 * q^64 + 839028480 * q^65 - 1225582880 * q^67 - 5258111400 * q^68 + 7723829760 * q^70 + 2800072720 * q^73 + 7669373280 * q^74 + 3753451288 * q^76 + 6408629760 * q^80 - 3638778380 * q^82 - 1853422560 * q^83 - 3022180476 * q^86 + 5815578640 * q^88 - 6162596112 * q^89 + 7645985280 * q^91 + 8903892480 * q^92 - 14182177920 * q^94 - 9697863536 * q^97 - 34759868298 * 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 $

$2$	−28.8575	−	13.8292i	−0.901795	−	0.432163i
$2$	−28.8575	−	13.8292i	−0.901795	−	0.432163i
$3$		0			0
$3$		0			0
$4$	641.505	+	798.152i	0.626470	+	0.779446i
$5$		−	5381.00i		−	1.72192i	−0.508673	−	0.860960i	$-0.669864\pi$
$5$		−	5381.00i		−	1.72192i	0.508673	−	0.860960i	$-0.330136\pi$
$6$		0			0
$7$		−	6613.83i		−	0.393516i	−0.980452	−	0.196758i	$-0.936959\pi$
$7$		−	6613.83i		−	0.393516i	0.980452	−	0.196758i	$-0.0630414\pi$
$8$	−7474.38	−	31904.2i	−0.228100	−	0.973638i
$9$		0			0
$10$	−74415.0	+	155282.i	−0.744150	+	1.55282i
$11$	−221096.			−1.37283			−0.686415	−	0.727210i	$-0.740816\pi$
$11$	−221096.			−1.37283			−0.686415	+	0.727210i	$0.740816\pi$
$12$		0			0
$13$		−	361689.i		−	0.974134i	−0.873365	−	0.487067i	$-0.838067\pi$
$13$		−	361689.i		−	0.974134i	0.873365	−	0.487067i	$-0.161933\pi$
$14$	−91464.1	+	190858.i	−0.170063	+	0.354871i
$15$		0			0
$16$	−225518.	+	1.02404e6i	−0.215071	+	0.976598i
$17$	−776217.			−0.546687			−0.273343	−	0.961917i	$-0.588130\pi$
$17$	−776217.			−0.546687			−0.273343	+	0.961917i	$0.588130\pi$
$18$		0			0
$19$	1.46186e6			0.590390			0.295195	−	0.955437i	$-0.404615\pi$
$19$	1.46186e6			0.590390			0.295195	+	0.955437i	$0.404615\pi$
$20$	4.29486e6	−	3.45194e6i	1.34214	−	1.07873i
$21$		0			0
$22$	6.38025e6	+	3.05758e6i	1.23801	+	0.593286i
$23$		−	2.34458e6i		−	0.364273i	−0.983273	−	0.182136i	$-0.941699\pi$
$23$		−	2.34458e6i		−	0.364273i	0.983273	−	0.182136i	$-0.0583012\pi$
$24$		0			0
$25$	−1.91895e7			−1.96501
$26$	−5.00188e6	+	1.04374e7i	−0.420985	+	0.878469i
$27$		0			0
$28$	5.27884e6	−	4.24281e6i	0.306725	−	0.246526i
$29$		−	2.88750e7i		−	1.40777i	−0.710313	−	0.703886i	$-0.751446\pi$
$29$		−	2.88750e7i		−	1.40777i	0.710313	−	0.703886i	$-0.248554\pi$
$30$		0			0
$31$		−	3.00762e7i		−	1.05054i	−0.850935	−	0.525272i	$-0.823964\pi$
$31$		−	3.00762e7i		−	1.05054i	0.850935	−	0.525272i	$-0.176036\pi$
$32$	2.06695e7	−	2.64324e7i	0.616000	−	0.787746i
$33$		0			0
$34$	2.23996e7	+	1.07345e7i	0.493000	+	0.236258i
$35$	−3.55890e7			−0.677604
$36$		0			0
$37$		−	1.16919e7i		−	0.168607i	−0.996440	−	0.0843037i	$-0.973133\pi$
$37$		−	1.16919e7i		−	0.168607i	0.996440	−	0.0843037i	$-0.0268666\pi$
$38$	−4.21857e7	−	2.02164e7i	−0.532411	−	0.255145i
$39$		0			0
$40$	−1.71676e8	+	4.02196e7i	−1.67653	+	0.392770i
$41$	−4.70330e7			−0.405960			−0.202980	−	0.979183i	$-0.565063\pi$
$41$	−4.70330e7			−0.405960			−0.202980	+	0.979183i	$0.565063\pi$
$42$		0			0
$43$	3.52427e7			0.239733			0.119866	−	0.992790i	$-0.461753\pi$
$43$	3.52427e7			0.239733			0.119866	+	0.992790i	$0.461753\pi$
$44$	−1.41834e8	−	1.76468e8i	−0.860036	−	1.07005i
$45$		0			0
$46$	−3.24238e7	+	6.76587e7i	−0.157425	+	0.328499i
$47$			4.23068e8i			1.84468i	0.386380	+	0.922340i	$0.373725\pi$
$47$			4.23068e8i			1.84468i	−0.386380	+	0.922340i	$0.626275\pi$
$48$		0			0
$49$	2.38733e8			0.845145
$50$	5.53761e8	+	2.65376e8i	1.77203	+	0.849204i
$51$		0			0
$52$	2.88683e8	−	2.32025e8i	0.759284	−	0.610265i
$53$		−	9.16056e6i		−	0.0219050i	−0.999940	−	0.0109525i	$-0.996514\pi$
$53$		−	9.16056e6i		−	0.0219050i	0.999940	−	0.0109525i	$-0.00348635\pi$
$54$		0			0
$55$			1.18971e9i			2.36390i
$56$	−2.11009e8	+	4.94343e7i	−0.383142	+	0.0897611i
$57$		0			0
$58$	−3.99319e8	+	8.33260e8i	−0.608388	+	1.26952i
$59$	1.03098e9			1.44209			0.721044	−	0.692890i	$-0.243663\pi$
$59$	1.03098e9			1.44209			0.721044	+	0.692890i	$0.243663\pi$
$60$		0			0
$61$			1.37140e8i			0.162374i	0.996699	+	0.0811869i	$0.0258711\pi$
$61$			1.37140e8i			0.162374i	−0.996699	+	0.0811869i	$0.974129\pi$
$62$	−4.15930e8	+	8.67921e8i	−0.454006	+	0.947375i
$63$		0			0
$64$	−9.62009e8	+	4.76928e8i	−0.895941	+	0.444173i
$65$	−1.94625e9			−1.67738
$66$		0			0
$67$	−7.94671e8			−0.588591			−0.294295	−	0.955715i	$-0.595085\pi$
$67$	−7.94671e8			−0.588591			−0.294295	+	0.955715i	$0.595085\pi$
$68$	−4.97947e8	−	6.19539e8i	−0.342483	−	0.426113i
$69$		0			0
$70$	1.02701e9	+	4.92168e8i	0.611060	+	0.292835i
$71$			2.04858e9i			1.13543i	0.823225	+	0.567716i	$0.192173\pi$
$71$			2.04858e9i			1.13543i	−0.823225	+	0.567716i	$0.807827\pi$
$72$		0			0
$73$	−1.88707e9			−0.910277			−0.455139	−	0.890421i	$-0.650410\pi$
$73$	−1.88707e9			−0.910277			−0.455139	+	0.890421i	$0.650410\pi$
$74$	−1.61690e8	+	3.37399e8i	−0.0728659	+	0.152049i
$75$		0			0
$76$	9.37794e8	+	1.16679e9i	0.369862	+	0.460177i
$77$			1.46229e9i			0.540231i
$78$		0			0
$79$			1.04965e9i			0.341120i	0.985347	+	0.170560i	$0.0545577\pi$
$79$			1.04965e9i			0.341120i	−0.985347	+	0.170560i	$0.945442\pi$
$80$	5.51035e9	+	1.21351e9i	1.68162	+	0.370335i
$81$		0			0
$82$	1.35725e9	+	6.50430e8i	0.366093	+	0.175441i
$83$	−3.77162e9			−0.957496			−0.478748	−	0.877952i	$-0.658909\pi$
$83$	−3.77162e9			−0.957496			−0.478748	+	0.877952i	$0.658909\pi$
$84$		0			0
$85$			4.17682e9i			0.941351i
$86$	−1.01702e9	−	4.87380e8i	−0.216190	−	0.103604i
$87$		0			0
$88$	1.65255e9	+	7.05387e9i	0.313142	+	1.33664i
$89$	4.07338e9			0.729465			0.364733	−	0.931112i	$-0.381160\pi$
$89$	4.07338e9			0.729465			0.364733	+	0.931112i	$0.381160\pi$
$90$		0			0
$91$	−2.39215e9			−0.383337
$92$	1.87133e9	−	1.50406e9i	0.283931	−	0.228206i
$93$		0			0
$94$	5.85070e9	−	1.22087e10i	0.797203	−	1.66352i
$95$		−	7.86629e9i		−	1.01660i
$96$		0			0
$97$	1.76770e9			0.205850			0.102925	−	0.994689i	$-0.467180\pi$
$97$	1.76770e9			0.205850			0.102925	+	0.994689i	$0.467180\pi$
$98$	−6.88921e9	−	3.30149e9i	−0.762148	−	0.365241i
$99$		0			0
$100$	−1.23102e10	−	1.53162e10i	−1.23102	−	1.53162i
$101$			1.09549e10i			1.04232i	0.853459	+	0.521160i	$0.174500\pi$
$101$			1.09549e10i			1.04232i	−0.853459	+	0.521160i	$0.825500\pi$
$102$		0			0
$103$			2.37007e8i			0.0204444i	0.999948	+	0.0102222i	$0.00325389\pi$
$103$			2.37007e8i			0.0204444i	−0.999948	+	0.0102222i	$0.996746\pi$
$104$	−1.15394e10	+	2.70340e9i	−0.948453	+	0.222200i
$105$		0			0
$106$	−1.26683e8	+	2.64350e8i	−0.00946652	+	0.0197538i
$107$	−4.29761e9			−0.306414			−0.153207	−	0.988194i	$-0.548960\pi$
$107$	−4.29761e9			−0.306414			−0.153207	+	0.988194i	$0.548960\pi$
$108$		0			0
$109$			2.92292e9i			0.189970i	0.995479	+	0.0949849i	$0.0302803\pi$
$109$			2.92292e9i			0.189970i	−0.995479	+	0.0949849i	$0.969720\pi$
$110$	1.64528e10	−	3.43321e10i	1.02159	−	2.13176i
$111$		0			0
$112$	6.77281e9	+	1.49154e9i	0.384307	+	0.0846339i
$113$	−2.48941e10			−1.35115			−0.675575	−	0.737291i	$-0.736105\pi$
$113$	−2.48941e10			−1.35115			−0.675575	+	0.737291i	$0.736105\pi$
$114$		0			0
$115$	−1.26162e10			−0.627248
$116$	2.30467e10	−	1.85235e10i	1.09728	−	0.881927i
$117$		0			0
$118$	−2.97516e10	−	1.42577e10i	−1.30047	−	0.623217i
$119$			5.13377e9i			0.215130i
$120$		0			0
$121$	2.29458e10			0.884661
$122$	1.89654e9	−	3.95752e9i	0.0701720	−	0.146428i
$123$		0			0
$124$	2.40054e10	−	1.92940e10i	0.818841	−	0.658134i
$125$			5.07100e10i			1.66167i
$126$		0			0
$127$		−	1.86927e10i		−	0.565788i	−0.959151	−	0.282894i	$-0.908706\pi$
$127$		−	1.86927e10i		−	0.565788i	0.959151	−	0.282894i	$-0.0912945\pi$
$128$	3.43567e10	−	4.59074e8i	0.999911	−	0.0133608i
$129$		0			0
$130$	5.61638e10	+	2.69151e10i	1.51265	+	0.724902i
$131$	1.62805e10			0.421998			0.210999	−	0.977486i	$-0.432328\pi$
$131$	1.62805e10			0.421998			0.210999	+	0.977486i	$0.432328\pi$
$132$		0			0
$133$		−	9.66852e9i		−	0.232328i
$134$	2.29322e10	+	1.09897e10i	0.530788	+	0.254367i
$135$		0			0
$136$	5.80174e9	+	2.47646e10i	0.124699	+	0.532275i
$137$	−3.24700e10			−0.672791			−0.336395	−	0.941721i	$-0.609208\pi$
$137$	−3.24700e10			−0.672791			−0.336395	+	0.941721i	$0.609208\pi$
$138$		0			0
$139$	3.25763e10			0.627809			0.313905	−	0.949455i	$-0.398363\pi$
$139$	3.25763e10			0.627809			0.313905	+	0.949455i	$0.398363\pi$
$140$	−2.28305e10	−	2.84055e10i	−0.424498	−	0.528155i
$141$		0			0
$142$	2.83302e10	−	5.91168e10i	0.490692	−	1.02393i
$143$			7.99678e10i			1.33732i
$144$		0			0
$145$	−1.55377e11			−2.42407
$146$	5.44560e10	+	2.60967e10i	0.820884	+	0.393388i
$147$		0			0
$148$	9.33192e9	−	7.50042e9i	0.131420	−	0.105627i
$149$		−	9.28139e10i		−	1.26381i	−0.775046	−	0.631905i	$-0.782273\pi$
$149$		−	9.28139e10i		−	1.26381i	0.775046	−	0.631905i	$-0.217727\pi$
$150$		0			0
$151$			1.62055e10i			0.206432i	0.994659	+	0.103216i	$0.0329133\pi$
$151$			1.62055e10i			0.206432i	−0.994659	+	0.103216i	$0.967087\pi$
$152$	−1.09265e10	−	4.66396e10i	−0.134668	−	0.574826i
$153$		0			0
$154$	2.02223e10	−	4.21979e10i	0.233468	−	0.487178i
$155$	−1.61840e11			−1.80895
$156$		0			0
$157$		−	2.39468e10i		−	0.251043i	−0.992091	−	0.125522i	$-0.959940\pi$
$157$		−	2.39468e10i		−	0.251043i	0.992091	−	0.125522i	$-0.0400605\pi$
$158$	1.45158e10	−	3.02901e10i	0.147420	−	0.307621i
$159$		0			0
$160$	−1.42233e11	−	1.11223e11i	−1.35644	−	1.06070i
$161$	−1.55067e10			−0.143347
$162$		0			0
$163$	7.89570e10			0.686203			0.343101	−	0.939298i	$-0.388523\pi$
$163$	7.89570e10			0.686203			0.343101	+	0.939298i	$0.388523\pi$
$164$	−3.01719e10	−	3.75395e10i	−0.254322	−	0.316424i
$165$		0			0
$166$	1.08839e11	+	5.21585e10i	0.863466	+	0.413795i
$167$			1.85927e11i			1.43140i	0.698408	+	0.715700i	$0.253892\pi$
$167$			1.85927e11i			1.43140i	−0.698408	+	0.715700i	$0.746108\pi$
$168$		0			0
$169$	7.03958e9			0.0510638
$170$	5.77622e10	−	1.20532e11i	0.406817	−	0.848906i
$171$		0			0
$172$	2.26084e10	+	2.81291e10i	0.150185	+	0.186859i
$173$			7.40712e9i			0.0477990i	0.999714	+	0.0238995i	$0.00760817\pi$
$173$			7.40712e9i			0.0477990i	−0.999714	+	0.0238995i	$0.992392\pi$
$174$		0			0
$175$			1.26916e11i			0.773263i
$176$	4.98611e10	−	2.26410e11i	0.295256	−	1.34070i
$177$		0			0
$178$	−1.17547e11	−	5.63317e10i	−0.657829	−	0.315248i
$179$	3.09505e11			1.68423			0.842117	−	0.539295i	$-0.181309\pi$
$179$	3.09505e11			1.68423			0.842117	+	0.539295i	$0.181309\pi$
$180$		0			0
$181$			3.52000e11i			1.81196i	0.423316	+	0.905982i	$0.360866\pi$
$181$			3.52000e11i			1.81196i	−0.423316	+	0.905982i	$0.639134\pi$
$182$	6.90313e10	+	3.30816e10i	0.345692	+	0.165664i
$183$		0			0
$184$	−7.48020e10	+	1.75243e10i	−0.354670	+	0.0830906i
$185$	−6.29141e10			−0.290328
$186$		0			0
$187$	1.71618e11			0.750508
$188$	−3.37673e11	+	2.71400e11i	−1.43783	+	1.15564i
$189$		0			0
$190$	−1.08785e11	+	2.27001e11i	−0.439339	+	0.916769i
$191$		−	4.23512e11i		−	1.66609i	−0.553205	−	0.833045i	$-0.686595\pi$
$191$		−	4.23512e11i		−	1.66609i	0.553205	−	0.833045i	$-0.313405\pi$
$192$		0			0
$193$	−2.50051e11			−0.933774			−0.466887	−	0.884317i	$-0.654625\pi$
$193$	−2.50051e11			−0.933774			−0.466887	+	0.884317i	$0.654625\pi$
$194$	−5.10114e10	−	2.44459e10i	−0.185634	−	0.0889607i
$195$		0			0
$196$	1.53148e11	+	1.90545e11i	0.529458	+	0.658744i
$197$			4.85950e11i			1.63780i	0.573937	+	0.818899i	$0.305415\pi$
$197$			4.85950e11i			1.63780i	−0.573937	+	0.818899i	$0.694585\pi$
$198$		0			0
$199$		−	1.41021e11i		−	0.451876i	−0.974142	−	0.225938i	$-0.927455\pi$
$199$		−	1.41021e11i		−	0.451876i	0.974142	−	0.225938i	$-0.0725447\pi$
$200$	1.43430e11	+	6.12226e11i	0.448218	+	1.91321i
$201$		0			0
$202$	1.51498e11	−	3.16130e11i	0.450452	−	0.939959i
$203$	−1.90975e11			−0.553982
$204$		0			0
$205$			2.53085e11i			0.699031i
$206$	3.27762e9	−	6.83941e9i	0.00883532	−	0.0184367i
$207$		0			0
$208$	3.70383e11	+	8.15675e10i	0.951337	+	0.209508i
$209$	−3.23212e11			−0.810505
$210$		0			0
$211$	−4.54045e11			−1.08564			−0.542821	−	0.839848i	$-0.682644\pi$
$211$	−4.54045e11			−1.08564			−0.542821	+	0.839848i	$0.682644\pi$
$212$	7.31152e9	−	5.87655e9i	0.0170737	−	0.0137228i
$213$		0			0
$214$	1.24018e11	+	5.94327e10i	0.276323	+	0.132421i
$215$		−	1.89641e11i		−	0.412801i
$216$		0			0
$217$	−1.98919e11			−0.413406
$218$	4.04217e10	−	8.43480e10i	0.0820979	−	0.171314i
$219$		0			0
$220$	−9.49574e11	+	7.63208e11i	−1.84253	+	1.48091i
$221$			2.80749e11i			0.532546i
$222$		0			0
$223$		−	7.10192e11i		−	1.28781i	−0.765106	−	0.643905i	$-0.777313\pi$
$223$		−	7.10192e11i		−	1.28781i	0.765106	−	0.643905i	$-0.222687\pi$
$224$	−1.74819e11	−	1.36705e11i	−0.309991	−	0.242406i
$225$		0			0
$226$	7.18380e11	+	3.44266e11i	1.21846	+	0.583918i
$227$	1.75996e11			0.291994			0.145997	−	0.989285i	$-0.453361\pi$
$227$	1.75996e11			0.291994			0.145997	+	0.989285i	$0.453361\pi$
$228$		0			0
$229$		−	3.96342e11i		−	0.629351i	−0.949199	−	0.314676i	$-0.898104\pi$
$229$		−	3.96342e11i		−	0.629351i	0.949199	−	0.314676i	$-0.101896\pi$
$230$	3.64071e11	+	1.74472e11i	0.565650	+	0.271074i
$231$		0			0
$232$	−9.21234e11	+	2.15823e11i	−1.37066	+	0.321113i
$233$	9.14879e11			1.33225			0.666123	−	0.745842i	$-0.267953\pi$
$233$	9.14879e11			1.33225			0.666123	+	0.745842i	$0.267953\pi$
$234$		0			0
$235$	2.27653e12			3.17639
$236$	6.61381e11	+	8.22882e11i	0.903424	+	1.12403i
$237$		0			0
$238$	7.09960e10	−	1.48147e11i	0.0929714	−	0.194003i
$239$			1.99248e11i			0.255508i	0.991806	+	0.127754i	$0.0407768\pi$
$239$			1.99248e11i			0.255508i	−0.991806	+	0.127754i	$0.959223\pi$
$240$		0			0
$241$	−5.21033e11			−0.640885			−0.320442	−	0.947268i	$-0.603832\pi$
$241$	−5.21033e11			−0.640885			−0.320442	+	0.947268i	$0.603832\pi$
$242$	−6.62158e11	−	3.17323e11i	−0.797783	−	0.382318i
$243$		0			0
$244$	−1.09459e11	+	8.79762e10i	−0.126561	+	0.101722i
$245$		−	1.28462e12i		−	1.45527i
$246$		0			0
$247$		−	5.28740e11i		−	0.575119i
$248$	−9.59555e11	+	2.24801e11i	−1.02285	+	0.239629i
$249$		0			0
$250$	7.01280e11	−	1.46336e12i	0.718111	−	1.49848i
$251$	8.76908e11			0.880209			0.440104	−	0.897947i	$-0.354941\pi$
$251$	8.76908e11			0.880209			0.440104	+	0.897947i	$0.354941\pi$
$252$		0			0
$253$			5.18377e11i			0.500084i
$254$	−2.58506e11	+	5.39424e11i	−0.244513	+	0.510225i
$255$		0			0
$256$	−9.97795e11	−	4.61878e11i	−0.907489	−	0.420076i
$257$	−6.77292e11			−0.604102			−0.302051	−	0.953292i	$-0.597671\pi$
$257$	−6.77292e11			−0.604102			−0.302051	+	0.953292i	$0.597671\pi$
$258$		0			0
$259$	−7.73283e10			−0.0663498
$260$	−1.24853e12	−	1.55340e12i	−1.05083	−	1.30743i
$261$		0			0
$262$	−4.69813e11	−	2.25146e11i	−0.380556	−	0.182372i
$263$		−	2.38906e12i		−	1.89867i	−0.314269	−	0.949334i	$-0.601759\pi$
$263$		−	2.38906e12i		−	1.89867i	0.314269	−	0.949334i	$-0.398241\pi$
$264$		0			0
$265$	−4.92930e10			−0.0377186
$266$	−1.33708e11	+	2.79009e11i	−0.100404	+	0.209512i
$267$		0			0
$268$	−5.09786e11	−	6.34269e11i	−0.368734	−	0.458774i
$269$		−	9.15425e11i		−	0.649922i	−0.945727	−	0.324961i	$-0.894649\pi$
$269$		−	9.15425e11i		−	0.649922i	0.945727	−	0.324961i	$-0.105351\pi$
$270$		0			0
$271$			7.01162e11i			0.479702i	0.970810	+	0.239851i	$0.0770986\pi$
$271$			7.01162e11i			0.479702i	−0.970810	+	0.239851i	$0.922901\pi$
$272$	1.75051e11	−	7.94875e11i	0.117576	−	0.533893i
$273$		0			0
$274$	9.37003e11	+	4.49035e11i	0.606720	+	0.290755i
$275$	4.24272e12			2.69762
$276$		0			0
$277$		−	2.10823e12i		−	1.29276i	−0.763014	−	0.646382i	$-0.776281\pi$
$277$		−	2.10823e12i		−	1.29276i	0.763014	−	0.646382i	$-0.223719\pi$
$278$	−9.40069e11	−	4.50505e11i	−0.566155	−	0.271316i
$279$		0			0
$280$	2.66006e11	+	1.13544e12i	0.154561	+	0.659740i
$281$	−2.87581e12			−1.64145			−0.820727	−	0.571320i	$-0.806431\pi$
$281$	−2.87581e12			−1.64145			−0.820727	+	0.571320i	$0.806431\pi$
$282$		0			0
$283$	2.12641e12			1.17142			0.585712	−	0.810519i	$-0.300815\pi$
$283$	2.12641e12			1.17142			0.585712	+	0.810519i	$0.300815\pi$
$284$	−1.63508e12	+	1.31417e12i	−0.885007	+	0.711313i
$285$		0			0
$286$	1.10589e12	−	2.30767e12i	0.577940	−	1.20599i
$287$			3.11068e11i			0.159752i
$288$		0			0
$289$	−1.41348e12			−0.701134
$290$	4.48377e12	+	2.14874e12i	2.18602	+	1.04759i
$291$		0			0
$292$	−1.21057e12	−	1.50617e12i	−0.570261	−	0.709512i
$293$		−	6.04754e11i		−	0.280053i	−0.990148	−	0.140027i	$-0.955281\pi$
$293$		−	6.04754e11i		−	0.280053i	0.990148	−	0.140027i	$-0.0447188\pi$
$294$		0			0
$295$		−	5.54772e12i		−	2.48316i
$296$	−3.73021e11	+	8.73897e10i	−0.164163	+	0.0384593i
$297$		0			0
$298$	−1.28354e12	+	2.67837e12i	−0.546172	+	1.13970i
$299$	−8.48010e11			−0.354850
$300$		0			0
$301$		−	2.33090e11i		−	0.0943388i
$302$	2.24109e11	−	4.67648e11i	0.0892122	−	0.186159i
$303$		0			0
$304$	−3.29677e11	+	1.49700e12i	−0.126976	+	0.576574i
$305$	7.37952e11			0.279595
$306$		0			0
$307$	−3.39388e11			−0.124453			−0.0622264	−	0.998062i	$-0.519820\pi$
$307$	−3.39388e11			−0.124453			−0.0622264	+	0.998062i	$0.519820\pi$
$308$	−1.16713e12	+	9.38065e11i	−0.421081	+	0.338438i
$309$		0			0
$310$	4.67028e12	+	2.23812e12i	1.63130	+	0.781762i
$311$		−	4.79193e11i		−	0.164706i	−0.996603	−	0.0823528i	$-0.973757\pi$
$311$		−	4.79193e11i		−	0.164706i	0.996603	−	0.0823528i	$-0.0262434\pi$
$312$		0			0
$313$	−3.15123e12			−1.04896			−0.524479	−	0.851423i	$-0.675740\pi$
$313$	−3.15123e12			−1.04896			−0.524479	+	0.851423i	$0.675740\pi$
$314$	−3.31165e11	+	6.91043e11i	−0.108492	+	0.226390i
$315$		0			0
$316$	−8.37778e11	+	6.73354e11i	−0.265885	+	0.213702i
$317$			7.24188e11i			0.226232i	0.993582	+	0.113116i	$0.0360832\pi$
$317$			7.24188e11i			0.226232i	−0.993582	+	0.113116i	$0.963917\pi$
$318$		0			0
$319$			6.38414e12i			1.93263i
$320$	2.56635e12	+	5.17657e12i	0.764831	+	1.54274i
$321$		0			0
$322$	4.47483e11	+	2.14445e11i	0.129270	+	0.0619494i
$323$	−1.13472e12			−0.322758
$324$		0			0
$325$			6.94064e12i			1.91418i
$326$	−2.27850e12	−	1.09191e12i	−0.618815	−	0.296552i
$327$		0			0
$328$	3.51542e11	+	1.50055e12i	0.0925995	+	0.395258i
$329$	2.79810e12			0.725911
$330$		0			0
$331$	1.89023e12			0.475745			0.237872	−	0.971296i	$-0.423550\pi$
$331$	1.89023e12			0.475745			0.237872	+	0.971296i	$0.423550\pi$
$332$	−2.41951e12	−	3.01033e12i	−0.599843	−	0.746316i
$333$		0			0
$334$	2.57123e12	−	5.36539e12i	0.618599	−	1.29083i
$335$			4.27612e12i			1.01351i
$336$		0			0
$337$	−2.44837e12			−0.563285			−0.281643	−	0.959519i	$-0.590879\pi$
$337$	−2.44837e12			−0.563285			−0.281643	+	0.959519i	$0.590879\pi$
$338$	−2.03144e11	−	9.73520e10i	−0.0460491	−	0.0220679i
$339$		0			0
$340$	−3.33374e12	+	2.67945e12i	−0.733732	+	0.589728i
$341$			6.64971e12i			1.44222i
$342$		0			0
$343$		−	3.44718e12i		−	0.726095i
$344$	−2.63418e11	−	1.12439e12i	−0.0546830	−	0.233413i
$345$		0			0
$346$	1.02435e11	−	2.13750e11i	0.0206570	−	0.0431049i
$347$	−5.66030e12			−1.12510			−0.562551	−	0.826762i	$-0.690180\pi$
$347$	−5.66030e12			−1.12510			−0.562551	+	0.826762i	$0.690180\pi$
$348$		0			0
$349$			8.20588e12i			1.58489i	0.609946	+	0.792443i	$0.291191\pi$
$349$			8.20588e12i			1.58489i	−0.609946	+	0.792443i	$0.708809\pi$
$350$	1.75515e12	−	3.66248e12i	0.334176	−	0.697325i
$351$		0			0
$352$	−4.56994e12	+	5.84408e12i	−0.845663	+	1.08144i
$353$	7.02465e11			0.128160			0.0640798	−	0.997945i	$-0.479589\pi$
$353$	7.02465e11			0.128160			0.0640798	+	0.997945i	$0.479589\pi$
$354$		0			0
$355$	1.10234e13			1.95512
$356$	2.61309e12	+	3.25118e12i	0.456988	+	0.568579i
$357$		0			0
$358$	−8.93153e12	−	4.28021e12i	−1.51883	−	0.727864i
$359$		−	5.97852e12i		−	1.00259i	−0.865278	−	0.501293i	$-0.832858\pi$
$359$		−	5.97852e12i		−	1.00259i	0.865278	−	0.501293i	$-0.167142\pi$
$360$		0			0
$361$	−3.99402e12			−0.651440
$362$	4.86788e12	−	1.01578e13i	0.783064	−	1.63402i
$363$		0			0
$364$	−1.53458e12	−	1.90930e12i	−0.240149	−	0.298791i
$365$			1.01543e13i			1.56742i
$366$		0			0
$367$		−	1.90765e12i		−	0.286530i	−0.989684	−	0.143265i	$-0.954240\pi$
$367$		−	1.90765e12i		−	0.286530i	0.989684	−	0.143265i	$-0.0457601\pi$
$368$	2.40094e12	+	5.28746e11i	0.355748	+	0.0783445i
$369$		0			0
$370$	1.81554e12	+	8.70054e11i	0.261817	+	0.125469i
$371$	−6.05864e10			−0.00861996
$372$		0			0
$373$		−	4.41936e12i		−	0.612090i	−0.952017	−	0.306045i	$-0.900994\pi$
$373$		−	4.41936e12i		−	0.612090i	0.952017	−	0.306045i	$-0.0990058\pi$
$374$	−4.95246e12	−	2.37335e12i	−0.676804	−	0.324342i
$375$		0			0
$376$	1.34976e13	−	3.16217e12i	1.79605	−	0.420771i
$377$	−1.04438e13			−1.37136
$378$		0			0
$379$	−1.15746e13			−1.48017			−0.740083	−	0.672516i	$-0.765214\pi$
$379$	−1.15746e13			−1.48017			−0.740083	+	0.672516i	$0.765214\pi$
$380$	6.27850e12	−	5.04627e12i	0.792388	−	0.636872i
$381$		0			0
$382$	−5.85684e12	+	1.22215e13i	−0.720023	+	1.50247i
$383$			7.38843e12i			0.896517i	0.893904	+	0.448259i	$0.147956\pi$
$383$			7.38843e12i			0.896517i	−0.893904	+	0.448259i	$0.852044\pi$
$384$		0			0
$385$	7.86857e12			0.930234
$386$	7.21583e12	+	3.45801e12i	0.842073	+	0.403543i
$387$		0			0
$388$	1.13399e12	+	1.41090e12i	0.128959	+	0.160449i
$389$		−	8.41928e12i		−	0.945207i	−0.881275	−	0.472603i	$-0.843314\pi$
$389$		−	8.41928e12i		−	0.945207i	0.881275	−	0.472603i	$-0.156686\pi$
$390$		0			0
$391$			1.81991e12i			0.199143i
$392$	−1.78438e12	−	7.61656e12i	−0.192777	−	0.822865i
$393$		0			0
$394$	6.72031e12	−	1.40233e13i	0.707796	−	1.47696i
$395$	5.64815e12			0.587382
$396$		0			0
$397$		−	7.62252e12i		−	0.772940i	−0.922302	−	0.386470i	$-0.873694\pi$
$397$		−	7.62252e12i		−	0.772940i	0.922302	−	0.386470i	$-0.126306\pi$
$398$	−1.95022e12	+	4.06952e12i	−0.195284	+	0.407500i
$399$		0			0
$400$	4.32759e12	−	1.96508e13i	0.422616	−	1.91902i
$401$	−1.08466e13			−1.04610			−0.523050	−	0.852302i	$-0.675206\pi$
$401$	−1.08466e13			−1.04610			−0.523050	+	0.852302i	$0.675206\pi$
$402$		0			0
$403$	−1.08782e13			−1.02337
$404$	−8.74366e12	+	7.02761e12i	−0.812431	+	0.652982i
$405$		0			0
$406$	5.51104e12	+	2.64103e12i	0.499578	+	0.239410i
$407$			2.58503e12i			0.231469i
$408$		0			0
$409$	−1.74748e13			−1.52685			−0.763425	−	0.645897i	$-0.776484\pi$
$409$	−1.74748e13			−1.52685			−0.763425	+	0.645897i	$0.776484\pi$
$410$	3.49996e12	−	7.30338e12i	0.302095	−	0.630383i
$411$		0			0
$412$	−1.89167e11	+	1.52041e11i	−0.0159353	+	0.0128078i
$413$		−	6.81875e12i		−	0.567485i
$414$		0			0
$415$			2.02951e13i			1.64873i
$416$	−9.56030e12	−	7.47594e12i	−0.767370	−	0.600066i
$417$		0			0
$418$	9.32707e12	+	4.46977e12i	0.730910	+	0.350270i
$419$	−1.67775e13			−1.29914			−0.649572	−	0.760300i	$-0.725052\pi$
$419$	−1.67775e13			−1.29914			−0.649572	+	0.760300i	$0.725052\pi$
$420$		0			0
$421$			4.09777e12i			0.309840i	0.987927	+	0.154920i	$0.0495120\pi$
$421$			4.09777e12i			0.309840i	−0.987927	+	0.154920i	$0.950488\pi$
$422$	1.31026e13	+	6.27909e12i	0.979027	+	0.469175i
$423$		0			0
$424$	−2.92260e11	+	6.84695e10i	−0.0213275	+	0.00499652i
$425$	1.48952e13			1.07424
$426$		0			0
$427$	9.07022e11			0.0638967
$428$	−2.75694e12	−	3.43015e12i	−0.191959	−	0.238833i
$429$		0			0
$430$	−2.62259e12	+	5.47256e12i	−0.178397	+	0.372262i
$431$			1.03214e13i			0.693985i	0.937868	+	0.346993i	$0.112797\pi$
$431$			1.03214e13i			0.693985i	−0.937868	+	0.346993i	$0.887203\pi$
$432$		0			0
$433$	2.17422e13			1.42844			0.714222	−	0.699919i	$-0.246781\pi$
$433$	2.17422e13			1.42844			0.714222	+	0.699919i	$0.246781\pi$
$434$	5.74028e12	+	2.75089e12i	0.372808	+	0.178659i
$435$		0			0
$436$	−2.33294e12	+	1.87507e12i	−0.148071	+	0.119010i
$437$		−	3.42746e12i		−	0.215063i
$438$		0			0
$439$		−	3.10509e13i		−	1.90437i	−0.305524	−	0.952184i	$-0.598832\pi$
$439$		−	3.10509e13i		−	1.90437i	0.305524	−	0.952184i	$-0.401168\pi$
$440$	3.79569e13	−	8.89238e12i	2.30158	−	0.539206i
$441$		0			0
$442$	3.88254e12	−	8.10170e12i	0.230147	−	0.480247i
$443$	2.32225e13			1.36110			0.680552	−	0.732700i	$-0.261740\pi$
$443$	2.32225e13			1.36110			0.680552	+	0.732700i	$0.261740\pi$
$444$		0			0
$445$		−	2.19188e13i		−	1.25608i
$446$	−9.82141e12	+	2.04943e13i	−0.556544	+	1.16134i
$447$		0			0
$448$	3.15432e12	+	6.36256e12i	0.174789	+	0.352567i
$449$	1.05020e13			0.575493			0.287747	−	0.957707i	$-0.407094\pi$
$449$	1.05020e13			0.575493			0.287747	+	0.957707i	$0.407094\pi$
$450$		0			0
$451$	1.03988e13			0.557314
$452$	−1.59697e13	−	1.98693e13i	−0.846455	−	1.05315i
$453$		0			0
$454$	−5.07880e12	−	2.43389e12i	−0.263319	−	0.126189i
$455$			1.28722e13i			0.660076i
$456$		0			0
$457$	1.72386e13			0.864813			0.432407	−	0.901679i	$-0.357665\pi$
$457$	1.72386e13			0.864813			0.432407	+	0.901679i	$0.357665\pi$
$458$	−5.48111e12	+	1.14374e13i	−0.271982	+	0.567546i
$459$		0			0
$460$	−8.09336e12	−	1.00697e13i	−0.392952	−	0.488906i
$461$			8.78179e11i			0.0421773i	0.999778	+	0.0210886i	$0.00671322\pi$
$461$			8.78179e11i			0.0421773i	−0.999778	+	0.0210886i	$0.993287\pi$
$462$		0			0
$463$			3.73576e13i			1.75579i	0.478849	+	0.877897i	$0.341054\pi$
$463$			3.73576e13i			1.75579i	−0.478849	+	0.877897i	$0.658946\pi$
$464$	2.95691e13	+	6.51185e12i	1.37483	+	0.302771i
$465$		0			0
$466$	−2.64011e13	−	1.26521e13i	−1.20141	−	0.575748i
$467$	−3.05749e13			−1.37652			−0.688258	−	0.725466i	$-0.741624\pi$
$467$	−3.05749e13			−1.37652			−0.688258	+	0.725466i	$0.741624\pi$
$468$		0			0
$469$			5.25582e12i			0.231620i
$470$	−6.56948e13	−	3.14826e13i	−2.86445	−	1.37272i
$471$		0			0
$472$	−7.70596e12	−	3.28927e13i	−0.328940	−	1.40407i
$473$	−7.79201e12			−0.329112
$474$		0			0
$475$	−2.80525e13			−1.16012
$476$	−4.09753e12	+	3.29334e12i	−0.167682	+	0.134773i
$477$		0			0
$478$	2.75545e12	−	5.74979e12i	0.110421	−	0.230416i
$479$		−	2.02856e13i		−	0.804470i	−0.915536	−	0.402235i	$-0.868233\pi$
$479$		−	2.02856e13i		−	0.804470i	0.915536	−	0.402235i	$-0.131767\pi$
$480$		0			0
$481$	−4.22883e12			−0.164246
$482$	1.50357e13	+	7.20548e12i	0.577947	+	0.276967i
$483$		0			0
$484$	1.47199e13	+	1.83143e13i	0.554213	+	0.689545i
$485$		−	9.51200e12i		−	0.354457i
$486$		0			0
$487$		−	2.31802e13i		−	0.846199i	−0.906083	−	0.423100i	$-0.860942\pi$
$487$		−	2.31802e13i		−	0.846199i	0.906083	−	0.423100i	$-0.139058\pi$
$488$	4.37534e12	−	1.02504e12i	0.158093	−	0.0370374i
$489$		0			0
$490$	−1.77653e13	+	3.70708e13i	−0.628915	+	1.31236i
$491$	2.54719e13			0.892593			0.446296	−	0.894885i	$-0.352743\pi$
$491$	2.54719e13			0.892593			0.446296	+	0.894885i	$0.352743\pi$
$492$		0			0
$493$			2.24133e13i			0.769611i
$494$	−7.31207e12	+	1.52581e13i	−0.248545	+	0.518639i
$495$		0			0
$496$	3.07991e13	+	6.78272e12i	1.02596	+	0.225941i
$497$	1.35489e13			0.446811
$498$		0			0
$499$	−6.30694e12			−0.203852			−0.101926	−	0.994792i	$-0.532501\pi$
$499$	−6.30694e12			−0.203852			−0.101926	+	0.994792i	$0.532501\pi$
$500$	−4.04743e13	+	3.25307e13i	−1.29518	+	1.04098i
$501$		0			0
$502$	−2.53053e13	−	1.21270e13i	−0.793768	−	0.380394i
$503$		−	5.04100e13i		−	1.56559i	−0.622283	−	0.782793i	$-0.713795\pi$
$503$		−	5.04100e13i		−	1.56559i	0.622283	−	0.782793i	$-0.286205\pi$
$504$		0			0
$505$	5.89482e13			1.79479
$506$	7.16875e12	−	1.49590e13i	0.216118	−	0.450974i
$507$		0			0
$508$	1.49196e13	−	1.19915e13i	0.441001	−	0.354449i
$509$			6.42360e12i			0.188014i	0.995572	+	0.0940068i	$0.0299676\pi$
$509$			6.42360e12i			0.188014i	−0.995572	+	0.0940068i	$0.970032\pi$
$510$		0			0
$511$			1.24808e13i			0.358209i
$512$	2.24064e13	+	2.71274e13i	0.636828	+	0.771006i
$513$		0			0
$514$	1.95449e13	+	9.36642e12i	0.544776	+	0.261071i
$515$	1.27533e12			0.0352036
$516$		0			0
$517$		−	9.35384e13i		−	2.53243i
$518$	2.23150e12	+	1.06939e12i	0.0598339	+	0.0286739i
$519$		0			0
$520$	1.45470e13	+	6.20934e13i	0.382610	+	1.63316i
$521$	2.69887e13			0.703063			0.351531	−	0.936176i	$-0.385661\pi$
$521$	2.69887e13			0.703063			0.351531	+	0.936176i	$0.385661\pi$
$522$		0			0
$523$	−6.68036e13			−1.70723			−0.853613	−	0.520907i	$-0.825594\pi$
$523$	−6.68036e13			−1.70723			−0.853613	+	0.520907i	$0.825594\pi$
$524$	1.04440e13	+	1.29943e13i	0.264369	+	0.328924i
$525$		0			0
$526$	−3.30389e13	+	6.89423e13i	−0.820534	+	1.71221i
$527$			2.33456e13i			0.574318i
$528$		0			0
$529$	3.59294e13			0.867305
$530$	1.42247e12	+	6.81683e11i	0.0340145	+	0.0163006i
$531$		0			0
$532$	7.71695e12	−	6.20241e12i	0.181087	−	0.145547i
$533$			1.70113e13i			0.395459i
$534$		0			0
$535$			2.31255e13i			0.527620i
$536$	5.93967e12	+	2.53533e13i	0.134257	+	0.573074i
$537$		0			0
$538$	−1.26596e13	+	2.64168e13i	−0.280873	+	0.586097i
$539$	−5.27827e13			−1.16024
$540$		0			0
$541$		−	1.02428e11i		−	0.00221021i	−0.999999	−	0.00110511i	$-0.999648\pi$
$541$		−	1.02428e11i		−	0.00221021i	0.999999	−	0.00110511i	$-0.000351766\pi$
$542$	9.69652e12	−	2.02337e13i	0.207310	−	0.432593i
$543$		0			0
$544$	−1.60440e13	+	2.05173e13i	−0.336759	+	0.430650i
$545$	1.57282e13			0.327113
$546$		0			0
$547$	−1.84176e13			−0.376094			−0.188047	−	0.982160i	$-0.560216\pi$
$547$	−1.84176e13			−0.376094			−0.188047	+	0.982160i	$0.560216\pi$
$548$	−2.08297e13	−	2.59160e13i	−0.421483	−	0.524404i
$549$		0			0
$550$	−1.22434e14	−	5.86735e13i	−2.43270	−	1.16581i
$551$		−	4.22114e13i		−	0.831135i
$552$		0			0
$553$	6.94218e12			0.134236
$554$	−2.91552e13	+	6.08382e13i	−0.558685	+	1.16581i
$555$		0			0
$556$	2.08979e13	+	2.60008e13i	0.393303	+	0.489343i
$557$		−	7.26795e13i		−	1.35561i	−0.735240	−	0.677807i	$-0.762931\pi$
$557$		−	7.26795e13i		−	1.35561i	0.735240	−	0.677807i	$-0.237069\pi$
$558$		0			0
$559$		−	1.27469e13i		−	0.233532i
$560$	8.02597e12	−	3.64445e13i	0.145733	−	0.661747i
$561$		0			0
$562$	8.29886e13	+	3.97702e13i	1.48026	+	0.709376i
$563$	−1.23522e13			−0.218376			−0.109188	−	0.994021i	$-0.534825\pi$
$563$	−1.23522e13			−0.218376			−0.109188	+	0.994021i	$0.534825\pi$
$564$		0			0
$565$			1.33955e14i			2.32657i
$566$	−6.13627e13	−	2.94066e13i	−1.05638	−	0.506246i
$567$		0			0
$568$	6.53582e13	−	1.53118e13i	1.10550	−	0.258992i
$569$	9.79422e13			1.64213			0.821067	−	0.570832i	$-0.193379\pi$
$569$	9.79422e13			1.64213			0.821067	+	0.570832i	$0.193379\pi$
$570$		0			0
$571$	4.63676e13			0.763895			0.381948	−	0.924184i	$-0.375254\pi$
$571$	4.63676e13			0.763895			0.381948	+	0.924184i	$0.375254\pi$
$572$	−6.38265e13	+	5.12998e13i	−1.04237	+	0.837790i
$573$		0			0
$574$	4.30183e12	−	8.97664e12i	0.0690389	−	0.144064i
$575$			4.49914e13i			0.715798i
$576$		0			0
$577$	−7.69976e13			−1.20392			−0.601961	−	0.798526i	$-0.705614\pi$
$577$	−7.69976e13			−1.20392			−0.601961	+	0.798526i	$0.705614\pi$
$578$	4.07895e13	+	1.95473e13i	0.632279	+	0.303004i
$579$		0			0
$580$	−9.96748e13	−	1.24014e14i	−1.51861	−	1.88943i
$581$			2.49448e13i			0.376791i
$582$		0			0
$583$			2.02536e12i			0.0300718i
$584$	1.41047e13	+	6.02054e13i	0.207634	+	0.886280i
$585$		0			0
$586$	−8.36328e12	+	1.74517e13i	−0.121029	+	0.252551i
$587$	−2.22966e12			−0.0319926			−0.0159963	−	0.999872i	$-0.505092\pi$
$587$	−2.22966e12			−0.0319926			−0.0159963	+	0.999872i	$0.505092\pi$
$588$		0			0
$589$		−	4.39673e13i		−	0.620230i
$590$	−7.67207e13	+	1.60093e14i	−1.07313	+	2.23930i
$591$		0			0
$592$	1.19730e13	+	2.63674e12i	0.164662	+	0.0362626i
$593$	−4.14340e13			−0.565045			−0.282523	−	0.959261i	$-0.591171\pi$
$593$	−4.14340e13			−0.565045			−0.282523	+	0.959261i	$0.591171\pi$
$594$		0			0
$595$	2.76248e13			0.370437
$596$	7.40796e13	−	5.95406e13i	0.985071	−	0.791738i
$597$		0			0
$598$	2.44714e13	+	1.17273e13i	0.320002	+	0.153353i
$599$			1.30467e14i			1.69187i	0.533290	+	0.845933i	$0.320955\pi$
$599$			1.30467e14i			1.69187i	−0.533290	+	0.845933i	$0.679045\pi$
$600$		0			0
$601$	6.20993e13			0.791980			0.395990	−	0.918255i	$-0.370401\pi$
$601$	6.20993e13			0.791980			0.395990	+	0.918255i	$0.370401\pi$
$602$	−3.22345e12	+	6.72637e12i	−0.0407698	+	0.0850743i
$603$		0			0
$604$	−1.29344e13	+	1.03959e13i	−0.160902	+	0.129323i
$605$		−	1.23471e14i		−	1.52331i
$606$		0			0
$607$			9.56403e13i			1.16064i	0.814389	+	0.580320i	$0.197072\pi$
$607$			9.56403e13i			1.16064i	−0.814389	+	0.580320i	$0.802928\pi$
$608$	3.02160e13	−	3.86405e13i	0.363680	−	0.465078i
$609$		0			0
$610$	−2.12954e13	−	1.02053e13i	−0.252137	−	0.120830i
$611$	1.53019e14			1.79696
$612$		0			0
$613$		−	7.01720e13i		−	0.810702i	−0.914161	−	0.405351i	$-0.867149\pi$
$613$		−	7.01720e13i		−	0.810702i	0.914161	−	0.405351i	$-0.132851\pi$
$614$	9.79388e12	+	4.69347e12i	0.112231	+	0.0537839i
$615$		0			0
$616$	4.66531e13	−	1.09297e13i	0.525989	−	0.123227i
$617$	4.75331e13			0.531582			0.265791	−	0.964031i	$-0.414367\pi$
$617$	4.75331e13			0.531582			0.265791	+	0.964031i	$0.414367\pi$
$618$		0			0
$619$	7.55113e13			0.830919			0.415459	−	0.909612i	$-0.363621\pi$
$619$	7.55113e13			0.830919			0.415459	+	0.909612i	$0.363621\pi$
$620$	−1.03821e14	−	1.29173e14i	−1.13325	−	1.40998i
$621$		0			0
$622$	−6.62686e12	+	1.38283e13i	−0.0711797	+	0.148531i
$623$		−	2.69406e13i		−	0.287057i
$624$		0			0
$625$	8.54727e13			0.896247
$626$	9.09365e13	+	4.35791e13i	0.945946	+	0.453321i
$627$		0			0
$628$	1.91132e13	−	1.53620e13i	0.195675	−	0.157271i
$629$			9.07546e12i			0.0921755i
$630$		0			0
$631$		−	7.50751e13i		−	0.750498i	−0.926924	−	0.375249i	$-0.877557\pi$
$631$		−	7.50751e13i		−	0.750498i	0.926924	−	0.375249i	$-0.122443\pi$
$632$	3.34881e13	−	7.84546e12i	0.332128	−	0.0778095i
$633$		0			0
$634$	1.00150e13	−	2.08982e13i	0.0977694	−	0.204015i
$635$	−1.00585e14			−0.974241
$636$		0			0
$637$		−	8.63469e13i		−	0.823284i
$638$	8.82877e13	−	1.84230e14i	0.835212	−	1.74284i
$639$		0			0
$640$	−2.47028e12	−	1.84873e14i	−0.0230063	−	1.72177i
$641$	−1.92038e14			−1.77458			−0.887291	−	0.461210i	$-0.847416\pi$
$641$	−1.92038e14			−1.77458			−0.887291	+	0.461210i	$0.847416\pi$
$642$		0			0
$643$	−1.14745e14			−1.04395			−0.521975	−	0.852961i	$-0.674805\pi$
$643$	−1.14745e14			−1.04395			−0.521975	+	0.852961i	$0.674805\pi$
$644$	−9.94761e12	−	1.23767e13i	−0.0898027	−	0.111731i
$645$		0			0
$646$	3.27452e13	+	1.56924e13i	0.291062	+	0.139484i
$647$		−	5.82025e13i		−	0.513358i	−0.966497	−	0.256679i	$-0.917372\pi$
$647$		−	5.82025e13i		−	0.513358i	0.966497	−	0.256679i	$-0.0826284\pi$
$648$		0			0
$649$	−2.27946e14			−1.97974
$650$	9.59837e13	−	2.00289e14i	0.827238	−	1.72620i
$651$		0			0
$652$	5.06513e13	+	6.30197e13i	0.429885	+	0.534858i
$653$			1.62553e14i			1.36908i	0.728974	+	0.684542i	$0.239998\pi$
$653$			1.62553e14i			1.36908i	−0.728974	+	0.684542i	$0.760002\pi$
$654$		0			0
$655$		−	8.76052e13i		−	0.726647i
$656$	1.06068e13	−	4.81636e13i	0.0873102	−	0.396460i
$657$		0			0
$658$	−8.07460e13	−	3.86955e13i	−0.654624	−	0.313712i
$659$	−1.20273e14			−0.967704			−0.483852	−	0.875150i	$-0.660763\pi$
$659$	−1.20273e14			−0.967704			−0.483852	+	0.875150i	$0.660763\pi$
$660$		0			0
$661$		−	1.23883e14i		−	0.981758i	−0.871228	−	0.490879i	$-0.836676\pi$
$661$		−	1.23883e14i		−	0.981758i	0.871228	−	0.490879i	$-0.163324\pi$
$662$	−5.45471e13	−	2.61404e13i	−0.429024	−	0.205599i
$663$		0			0
$664$	2.81905e13	+	1.20330e14i	0.218405	+	0.932255i
$665$	−5.20263e13			−0.400050
$666$		0			0
$667$	−6.76999e13			−0.512813
$668$	−1.48398e14	+	1.19273e14i	−1.11570	+	0.896729i
$669$		0			0
$670$	5.91355e13	−	1.23398e14i	0.438000	−	0.913975i
$671$		−	3.03211e13i		−	0.222911i
$672$		0			0
$673$	7.76604e13			0.562502			0.281251	−	0.959634i	$-0.409251\pi$
$673$	7.76604e13			0.562502			0.281251	+	0.959634i	$0.409251\pi$
$674$	7.06538e13	+	3.38591e13i	0.507968	+	0.243431i
$675$		0			0
$676$	4.51593e12	+	5.61866e12i	0.0319900	+	0.0398015i
$677$		−	1.79880e14i		−	1.26485i	−0.774621	−	0.632426i	$-0.782059\pi$
$677$		−	1.79880e14i		−	1.26485i	0.774621	−	0.632426i	$-0.217941\pi$
$678$		0			0
$679$		−	1.16913e13i		−	0.0810053i
$680$	1.33258e14	−	3.12192e13i	0.916535	−	0.214722i
$681$		0			0
$682$	9.19603e13	−	1.91894e14i	0.623273	−	1.30058i
$683$	1.46057e13			0.0982698			0.0491349	−	0.998792i	$-0.484354\pi$
$683$	1.46057e13			0.0982698			0.0491349	+	0.998792i	$0.484354\pi$
$684$		0			0
$685$			1.74721e14i			1.15849i
$686$	−4.76718e13	+	9.94768e13i	−0.313791	+	0.654789i
$687$		0			0
$688$	−7.94788e12	+	3.60899e13i	−0.0515596	+	0.234123i
$689$	−3.31327e12			−0.0213384
$690$		0			0
$691$	−1.80286e14			−1.14438			−0.572191	−	0.820120i	$-0.693906\pi$
$691$	−1.80286e14			−1.14438			−0.572191	+	0.820120i	$0.693906\pi$
$692$	−5.91201e12	+	4.75170e12i	−0.0372567	+	0.0299446i
$693$		0			0
$694$	1.63342e14	+	7.82776e13i	1.01461	+	0.486228i
$695$		−	1.75293e14i		−	1.08104i
$696$		0			0
$697$	3.65078e13			0.221933
$698$	1.13481e14	−	2.36801e14i	0.684929	−	1.42924i
$699$		0			0
$700$	−1.01298e14	+	8.14174e13i	−0.602716	+	0.484426i
$701$			2.61562e14i			1.54520i	0.634895	+	0.772598i	$0.281043\pi$
$701$			2.61562e14i			1.54520i	−0.634895	+	0.772598i	$0.718957\pi$
$702$		0			0
$703$		−	1.70920e13i		−	0.0995442i
$704$	2.12696e14	−	1.05447e14i	1.22997	−	0.609774i
$705$		0			0
$706$	−2.02714e13	−	9.71455e12i	−0.115574	−	0.0553859i
$707$	7.24537e13			0.410170
$708$		0			0
$709$			2.37281e14i			1.32444i	0.749310	+	0.662219i	$0.230385\pi$
$709$			2.37281e14i			1.32444i	−0.749310	+	0.662219i	$0.769615\pi$
$710$	−3.18107e14	−	1.52445e14i	−1.76312	−	0.844932i
$711$		0			0
$712$	−3.04460e13	−	1.29958e14i	−0.166391	−	0.710235i
$713$	−7.05161e13			−0.382684
$714$		0			0
$715$	4.30307e14			2.30276
$716$	1.98549e14	+	2.47032e14i	1.05512	+	1.31277i
$717$		0			0
$718$	−8.26783e13	+	1.72525e14i	−0.433280	+	0.904127i
$719$			2.61945e14i			1.36322i	0.731717	+	0.681609i	$0.238719\pi$
$719$			2.61945e14i			1.36322i	−0.731717	+	0.681609i	$0.761281\pi$
$720$		0			0
$721$	1.56752e12			0.00804521
$722$	1.15257e14	+	5.52342e13i	0.587465	+	0.281528i
$723$		0			0
$724$	−2.80949e14	+	2.25810e14i	−1.41233	+	1.13514i
$725$			5.54098e14i			2.76628i
$726$		0			0
$727$			1.58213e14i			0.779058i	0.921014	+	0.389529i	$0.127362\pi$
$727$			1.58213e14i			0.779058i	−0.921014	+	0.389529i	$0.872638\pi$
$728$	1.78798e13	+	7.63195e13i	0.0874393	+	0.373232i
$729$		0			0
$730$	1.40426e14	−	2.93028e14i	0.677383	−	1.41350i
$731$	−2.73560e13			−0.131059
$732$		0			0
$733$			2.50230e14i			1.18255i	0.806469	+	0.591276i	$0.201376\pi$
$733$			2.50230e14i			1.18255i	−0.806469	+	0.591276i	$0.798624\pi$
$734$	−2.63814e13	+	5.50501e13i	−0.123828	+	0.258391i
$735$		0			0
$736$	−6.19729e13	−	4.84614e13i	−0.286954	−	0.224392i
$737$	1.75698e14			0.808035
$738$		0			0
$739$	3.08452e14			1.39948			0.699738	−	0.714400i	$-0.253300\pi$
$739$	3.08452e14			1.39948			0.699738	+	0.714400i	$0.253300\pi$
$740$	−4.03597e13	−	5.02151e13i	−0.181882	−	0.226295i
$741$		0			0
$742$	1.74837e12	+	8.37863e11i	0.00777344	+	0.00372523i
$743$			2.42121e14i			1.06927i	0.845082	+	0.534637i	$0.179552\pi$
$743$			2.42121e14i			1.06927i	−0.845082	+	0.534637i	$0.820448\pi$
$744$		0			0
$745$	−4.99431e14			−2.17618
$746$	−6.11163e13	+	1.27531e14i	−0.264523	+	0.551980i
$747$		0			0
$748$	1.10094e14	+	1.36977e14i	0.470170	+	0.584980i
$749$			2.84237e13i			0.120579i
$750$		0			0
$751$		−	2.94510e14i		−	1.23282i	−0.787424	−	0.616412i	$-0.788586\pi$
$751$		−	2.94510e14i		−	1.23282i	0.787424	−	0.616412i	$-0.211414\pi$
$752$	−4.33238e14	−	9.54095e13i	−1.80151	−	0.396737i
$753$		0			0
$754$	3.01381e14	+	1.44429e14i	1.23668	+	0.592651i
$755$	8.72015e13			0.355459
$756$		0			0
$757$			2.90155e14i			1.16721i	0.812036	+	0.583607i	$0.198359\pi$
$757$			2.90155e14i			1.16721i	−0.812036	+	0.583607i	$0.801641\pi$
$758$	3.34014e14	+	1.60068e14i	1.33481	+	0.639673i
$759$		0			0
$760$	−2.50967e14	+	5.87956e13i	−0.989804	+	0.231887i
$761$	−4.11236e14			−1.61127			−0.805635	−	0.592412i	$-0.798176\pi$
$761$	−4.11236e14			−1.61127			−0.805635	+	0.592412i	$0.798176\pi$
$762$		0			0
$763$	1.93317e13			0.0747562
$764$	3.38027e14	−	2.71685e14i	1.29863	−	1.04376i
$765$		0			0
$766$	1.02176e14	−	2.13211e14i	0.387442	−	0.808475i
$767$		−	3.72895e14i		−	1.40479i
$768$		0			0
$769$	−1.42100e14			−0.528400			−0.264200	−	0.964468i	$-0.585108\pi$
$769$	−1.42100e14			−0.528400			−0.264200	+	0.964468i	$0.585108\pi$
$770$	−2.27067e14	−	1.08816e14i	−0.838881	−	0.402013i
$771$		0			0
$772$	−1.60409e14	−	1.99579e14i	−0.584981	−	0.727826i
$773$		−	2.58504e14i		−	0.936635i	−0.883560	−	0.468317i	$-0.844860\pi$
$773$		−	2.58504e14i		−	0.936635i	0.883560	−	0.468317i	$-0.155140\pi$
$774$		0			0
$775$			5.77147e14i			2.06433i
$776$	−1.32125e13	−	5.63970e13i	−0.0469543	−	0.200423i
$777$		0			0
$778$	−1.16432e14	+	2.42959e14i	−0.408484	+	0.852383i
$779$	−6.87559e13			−0.239675
$780$		0			0
$781$		−	4.52932e14i		−	1.55875i
$782$	2.51679e13	−	5.25178e13i	0.0860623	−	0.179586i
$783$		0			0
$784$	−5.38385e13	+	2.44471e14i	−0.181766	+	0.825367i
$785$	−1.28858e14			−0.432277
$786$		0			0
$787$	−4.24394e14			−1.40571			−0.702855	−	0.711333i	$-0.748092\pi$
$787$	−4.24394e14			−1.40571			−0.702855	+	0.711333i	$0.748092\pi$
$788$	−3.87862e14	+	3.11739e14i	−1.27657	+	1.02603i
$789$		0			0
$790$	−1.62991e14	−	7.81095e13i	−0.529698	−	0.253845i
$791$			1.64645e14i			0.531700i
$792$		0			0
$793$	4.96021e13			0.158174
$794$	−1.05413e14	+	2.19966e14i	−0.334036	+	0.697034i
$795$		0			0
$796$	1.12556e14	−	9.04659e13i	0.352213	−	0.283087i
$797$		−	3.84509e14i		−	1.19568i	−0.801616	−	0.597839i	$-0.796026\pi$
$797$		−	3.84509e14i		−	1.19568i	0.801616	−	0.597839i	$-0.203974\pi$
$798$		0			0
$799$		−	3.28393e14i		−	1.00846i
$800$	−3.96638e14	+	5.07225e14i	−1.21044	+	1.54793i
$801$		0			0
$802$	3.13006e14	+	1.50001e14i	0.943369	+	0.452086i
$803$	4.17223e14			1.24966
$804$		0			0
$805$			8.34414e13i			0.246832i
$806$	3.13918e14	+	1.50437e14i	0.922870	+	0.442263i
$807$		0			0
$808$	3.49506e14	−	8.18809e13i	1.01484	−	0.237753i
$809$	2.91643e14			0.841606			0.420803	−	0.907152i	$-0.361748\pi$
$809$	2.91643e14			0.841606			0.420803	+	0.907152i	$0.361748\pi$
$810$		0			0
$811$	−1.84338e14			−0.525424			−0.262712	−	0.964874i	$-0.584617\pi$
$811$	−1.84338e14			−0.525424			−0.262712	+	0.964874i	$0.584617\pi$
$812$	−1.22511e14	−	1.52427e14i	−0.347053	−	0.431799i
$813$		0			0
$814$	3.57489e13	−	7.45973e13i	0.100033	−	0.208738i
$815$		−	4.24867e14i		−	1.18159i
$816$		0			0
$817$	5.15201e13			0.141536
$818$	5.04279e14	+	2.41663e14i	1.37691	+	0.659848i
$819$		0			0
$820$	−2.02000e14	+	1.62355e14i	−0.544856	+	0.437922i
$821$		−	3.88449e14i		−	1.04140i	−0.853740	−	0.520700i	$-0.825671\pi$
$821$		−	3.88449e14i		−	1.04140i	0.853740	−	0.520700i	$-0.174329\pi$
$822$		0			0
$823$		−	2.91752e14i		−	0.772707i	−0.922351	−	0.386354i	$-0.873734\pi$
$823$		−	2.91752e14i		−	0.772707i	0.922351	−	0.386354i	$-0.126266\pi$
$824$	7.56150e12	−	1.77148e12i	0.0199054	−	0.00466337i
$825$		0			0
$826$	−9.42980e13	+	1.96772e14i	−0.245246	+	0.511755i
$827$	2.48060e14			0.641253			0.320626	−	0.947206i	$-0.396107\pi$
$827$	2.48060e14			0.641253			0.320626	+	0.947206i	$0.396107\pi$
$828$		0			0
$829$			1.64039e14i			0.418962i	0.977813	+	0.209481i	$0.0671774\pi$
$829$			1.64039e14i			0.418962i	−0.977813	+	0.209481i	$0.932823\pi$
$830$	2.80665e14	−	5.85664e14i	0.712521	−	1.48682i
$831$		0			0
$832$	1.72499e14	+	3.47948e14i	0.432684	+	0.872766i
$833$	−1.85308e14			−0.462030
$834$		0			0
$835$	1.00048e15			2.46476
$836$	−2.07342e14	−	2.57972e14i	−0.507757	−	0.631744i
$837$		0			0
$838$	4.84156e14	+	2.32020e14i	1.17156	+	0.561443i
$839$			5.19240e14i			1.24899i	0.781030	+	0.624494i	$0.214695\pi$
$839$			5.19240e14i			1.24899i	−0.781030	+	0.624494i	$0.785305\pi$
$840$		0			0
$841$	−4.13060e14			−0.981824
$842$	5.66690e13	−	1.18251e14i	0.133901	−	0.279412i
$843$		0			0
$844$	−2.91272e14	−	3.62397e14i	−0.680122	−	0.846199i
$845$		−	3.78800e13i		−	0.0879278i
$846$		0			0
$847$		−	1.51760e14i		−	0.348128i
$848$	9.38076e12	+	2.06587e12i	0.0213924	+	0.00471112i
$849$		0			0
$850$	−4.29839e14	−	2.05990e14i	−0.968748	−	0.464249i
$851$	−2.74127e13			−0.0614191
$852$		0			0
$853$		−	8.40549e14i		−	1.86131i	−0.365903	−	0.930653i	$-0.619240\pi$
$853$		−	8.40549e14i		−	1.86131i	0.365903	−	0.930653i	$-0.380760\pi$
$854$	−2.61744e13	−	1.25434e13i	−0.0576218	−	0.0276138i
$855$		0			0
$856$	3.21220e13	+	1.37112e14i	0.0698930	+	0.298336i
$857$	−9.08205e13			−0.196463			−0.0982313	−	0.995164i	$-0.531319\pi$
$857$	−9.08205e13			−0.196463			−0.0982313	+	0.995164i	$0.531319\pi$
$858$		0			0
$859$	5.90738e14			1.26307			0.631537	−	0.775346i	$-0.282424\pi$
$859$	5.90738e14			1.26307			0.631537	+	0.775346i	$0.282424\pi$
$860$	1.51363e14	−	1.21656e14i	0.321756	−	0.258607i
$861$		0			0
$862$	1.42736e14	−	2.97848e14i	0.299915	−	0.625833i
$863$		−	5.07805e14i		−	1.06082i	−0.847740	−	0.530411i	$-0.822037\pi$
$863$		−	5.07805e14i		−	1.06082i	0.847740	−	0.530411i	$-0.177963\pi$
$864$		0			0
$865$	3.98577e13			0.0823060
$866$	−6.27424e14	−	3.00677e14i	−1.28816	−	0.617321i
$867$		0			0
$868$	−1.27607e14	−	1.58767e14i	−0.258986	−	0.322227i
$869$		−	2.32072e14i		−	0.468300i
$870$		0			0
$871$			2.87424e14i			0.573366i
$872$	9.32533e13	−	2.18470e13i	0.184962	−	0.0433321i
$873$		0			0
$874$	−4.73992e13	+	9.89079e13i	−0.0929423	+	0.193943i
$875$	3.35387e14			0.653892
$876$		0			0
$877$			2.07322e14i			0.399620i	0.979835	+	0.199810i	$0.0640325\pi$
$877$			2.07322e14i			0.399620i	−0.979835	+	0.199810i	$0.935968\pi$
$878$	−4.29409e14	+	8.96049e14i	−0.822998	+	1.71735i
$879$		0			0
$880$	−1.21831e15	−	2.68302e14i	−2.30858	−	0.508407i
$881$	−3.62994e14			−0.683943			−0.341971	−	0.939710i	$-0.611095\pi$
$881$	−3.62994e14			−0.683943			−0.341971	+	0.939710i	$0.611095\pi$
$882$		0			0
$883$	5.88143e12			0.0109567			0.00547835	−	0.999985i	$-0.498256\pi$
$883$	5.88143e12			0.0109567			0.00547835	+	0.999985i	$0.498256\pi$
$884$	−2.24081e14	+	1.80102e14i	−0.415091	+	0.333624i
$885$		0			0
$886$	−6.70143e14	−	3.21150e14i	−1.22744	−	0.588219i
$887$		−	4.25024e13i		−	0.0774096i	−0.999251	−	0.0387048i	$-0.987677\pi$
$887$		−	4.25024e13i		−	0.0774096i	0.999251	−	0.0387048i	$-0.0123232\pi$
$888$		0			0
$889$	−1.23630e14			−0.222647
$890$	−3.03121e14	+	6.32522e14i	−0.542832	+	1.13273i
$891$		0			0
$892$	5.66841e14	−	4.55592e14i	1.00378	−	0.806774i
$893$			6.18468e14i			1.08908i
$894$		0			0
$895$		−	1.66545e15i		−	2.90012i
$896$	−3.03624e12	−	2.27229e14i	−0.00525770	−	0.393481i
$897$		0			0
$898$	−3.03061e14	−	1.45235e14i	−0.518977	−	0.248707i
$899$	−8.68450e14			−1.47893
$900$		0			0
$901$			7.11058e12i			0.0119752i
$902$	−3.00083e14	−	1.43807e14i	−0.502583	−	0.240851i
$903$		0			0
$904$	1.86068e14	+	7.94225e14i	0.308197	+	1.31553i
$905$	1.89411e15			3.12006
$906$		0			0
$907$	2.03986e14			0.332326			0.166163	−	0.986098i	$-0.446862\pi$
$907$	2.03986e14			0.332326			0.166163	+	0.986098i	$0.446862\pi$
$908$	1.12903e14	+	1.40472e14i	0.182926	+	0.227594i
$909$		0			0
$910$	1.78012e14	−	3.71458e14i	0.285261	−	0.595254i
$911$		−	1.49719e14i		−	0.238608i	−0.992858	−	0.119304i	$-0.961934\pi$
$911$		−	1.49719e14i		−	0.238608i	0.992858	−	0.119304i	$-0.0380664\pi$
$912$		0			0
$913$	8.33888e14			1.31448
$914$	−4.97464e14	−	2.38397e14i	−0.779884	−	0.373740i
$915$		0			0
$916$	3.16342e14	−	2.54256e14i	0.490545	−	0.394270i
$917$		−	1.07676e14i		−	0.166063i
$918$		0			0
$919$			9.31781e14i			1.42146i	0.703463	+	0.710732i	$0.251636\pi$
$919$			9.31781e14i			1.42146i	−0.703463	+	0.710732i	$0.748364\pi$
$920$	9.42983e13	+	4.02509e14i	0.143075	+	0.610713i
$921$		0			0
$922$	1.21445e13	−	2.53420e13i	0.0182275	−	0.0380353i
$923$	7.40948e14			1.10606
$924$		0			0
$925$			2.24362e14i			0.331315i
$926$	5.16626e14	−	1.07804e15i	0.758790	−	1.58337i
$927$		0			0
$928$	−7.63236e14	−	5.96833e14i	−1.10897	−	0.867188i
$929$	9.29163e14			1.34281			0.671403	−	0.741093i	$-0.265692\pi$
$929$	9.29163e14			1.34281			0.671403	+	0.741093i	$0.265692\pi$
$930$		0			0
$931$	3.48995e14			0.498965
$932$	5.86900e14	+	7.30213e14i	0.834612	+	1.03841i
$933$		0			0
$934$	8.82315e14	+	4.22828e14i	1.24134	+	0.594879i
$935$		−	9.23477e14i		−	1.29231i
$936$		0			0
$937$	−3.08132e14			−0.426618			−0.213309	−	0.976985i	$-0.568424\pi$
$937$	−3.08132e14			−0.426618			−0.213309	+	0.976985i	$0.568424\pi$
$938$	7.26839e13	−	1.51670e14i	0.100098	−	0.208874i
$939$		0			0
$940$	1.46040e15	+	1.81702e15i	1.98991	+	2.47582i
$941$		−	6.11614e14i		−	0.828952i	−0.910060	−	0.414476i	$-0.863965\pi$
$941$		−	6.11614e14i		−	0.828952i	0.910060	−	0.414476i	$-0.136035\pi$
$942$		0			0
$943$			1.10273e14i			0.147880i
$944$	−2.32506e14	+	1.05577e15i	−0.310151	+	1.40834i
$945$		0			0
$946$	2.24858e14	+	1.07758e14i	0.296792	+	0.142230i
$947$	−7.23883e14			−0.950427			−0.475213	−	0.879871i	$-0.657629\pi$
$947$	−7.23883e14			−0.950427			−0.475213	+	0.879871i	$0.657629\pi$
$948$		0			0
$949$			6.82532e14i			0.886732i
$950$	8.09523e14	+	3.87944e14i	1.04619	+	0.501362i
$951$		0			0
$952$	1.63789e14	−	3.83717e13i	0.209459	−	0.0490712i
$953$	−1.17221e15			−1.49122			−0.745608	−	0.666385i	$-0.767841\pi$
$953$	−1.17221e15			−1.49122			−0.745608	+	0.666385i	$0.767841\pi$
$954$		0			0
$955$	−2.27892e15			−2.86887
$956$	−1.59030e14	+	1.27819e14i	−0.199155	+	0.160068i
$957$		0			0
$958$	−2.80534e14	+	5.85390e14i	−0.347662	+	0.725468i
$959$			2.14751e14i			0.264754i
$960$		0			0
$961$	−8.49472e13			−0.103641
$962$	1.22033e14	+	5.84815e13i	0.148116	+	0.0709812i
$963$		0			0
$964$	−3.34245e14	−	4.15864e14i	−0.401495	−	0.499535i
$965$			1.34552e15i			1.60788i
$966$		0			0
$967$		−	1.04445e15i		−	1.23525i	−0.786471	−	0.617627i	$-0.788094\pi$
$967$		−	1.04445e15i		−	1.23525i	0.786471	−	0.617627i	$-0.211906\pi$
$968$	−1.71506e14	−	7.32067e14i	−0.201791	−	0.861339i
$969$		0			0
$970$	−1.31544e14	+	2.74492e14i	−0.153183	+	0.319647i
$971$	3.97256e13			0.0460230			0.0230115	−	0.999735i	$-0.492675\pi$
$971$	3.97256e13			0.0460230			0.0230115	+	0.999735i	$0.492675\pi$
$972$		0			0
$973$		−	2.15454e14i		−	0.247053i
$974$	−3.20564e14	+	6.68922e14i	−0.365696	+	0.763099i
$975$		0			0
$976$	−1.40437e14	−	3.09276e13i	−0.158574	−	0.0349219i
$977$	−1.61456e15			−1.81377			−0.906884	−	0.421381i	$-0.861546\pi$
$977$	−1.61456e15			−1.81377			−0.906884	+	0.421381i	$0.861546\pi$
$978$		0			0
$979$	−9.00606e14			−1.00143
$980$	1.02532e15	−	8.24090e14i	1.13431	−	0.911684i
$981$		0			0
$982$	−7.35053e14	−	3.52256e14i	−0.804936	−	0.385746i
$983$			1.09516e14i			0.119319i	0.998219	+	0.0596597i	$0.0190016\pi$
$983$			1.09516e14i			0.119319i	−0.998219	+	0.0596597i	$0.980998\pi$
$984$		0			0
$985$	2.61490e15			2.82016
$986$	3.09958e14	−	6.46791e14i	0.332597	−	0.694031i
$987$		0			0
$988$	4.22015e14	−	3.39190e14i	0.448274	−	0.360295i
$989$		−	8.26296e13i		−	0.0873281i
$990$		0			0
$991$			1.73875e15i			1.81915i	0.415536	+	0.909577i	$0.363594\pi$
$991$			1.73875e15i			1.81915i	−0.415536	+	0.909577i	$0.636406\pi$
$992$	−7.94984e14	−	6.21660e14i	−0.827561	−	0.647135i
$993$		0			0
$994$	−3.90988e14	−	1.87371e14i	−0.402932	−	0.193095i
$995$	−7.58836e14			−0.778094
$996$		0			0
$997$		−	1.61791e15i		−	1.64240i	−0.570641	−	0.821200i	$-0.693305\pi$
$997$		−	1.61791e15i		−	1.64240i	0.570641	−	0.821200i	$-0.306695\pi$
$998$	1.82002e14	+	8.72200e13i	0.183833	+	0.0880975i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	72.11.b.b.19.1		8
3.2	odd	2		8.11.d.b.3.8	yes	8
4.3	odd	2		288.11.b.b.271.1		8
8.3	odd	2	inner	72.11.b.b.19.2		8
8.5	even	2		288.11.b.b.271.8		8
12.11	even	2		32.11.d.b.15.8		8
24.5	odd	2		32.11.d.b.15.7		8
24.11	even	2		8.11.d.b.3.7	✓	8
48.5	odd	4		256.11.c.m.255.11		16
48.11	even	4		256.11.c.m.255.5		16
48.29	odd	4		256.11.c.m.255.6		16
48.35	even	4		256.11.c.m.255.12		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8.11.d.b.3.7	✓	8	24.11	even	2
8.11.d.b.3.8	yes	8	3.2	odd	2
32.11.d.b.15.7		8	24.5	odd	2
32.11.d.b.15.8		8	12.11	even	2
72.11.b.b.19.1		8	1.1	even	1	trivial
72.11.b.b.19.2		8	8.3	odd	2	inner
256.11.c.m.255.5		16	48.11	even	4
256.11.c.m.255.6		16	48.29	odd	4
256.11.c.m.255.11		16	48.5	odd	4
256.11.c.m.255.12		16	48.35	even	4
288.11.b.b.271.1		8	4.3	odd	2
288.11.b.b.271.8		8	8.5	even	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:	\( k \)	\(=\)	\( 11 \)
Character orbit:	\([\chi]\)	\(=\)	72.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-28.8575 - 13.8292i) q^{2} +(641.505 + 798.152i) q^{4} -5381.00i q^{5} -6613.83i q^{7} +(-7474.38 - 31904.2i) q^{8} +O(q^{10})\)	\(q+(-28.8575 - 13.8292i) q^{2} +(641.505 + 798.152i) q^{4} -5381.00i q^{5} -6613.83i q^{7} +(-7474.38 - 31904.2i) q^{8} +(-74415.0 + 155282. i) q^{10} -221096. q^{11} -361689. i q^{13} +(-91464.1 + 190858. i) q^{14} +(-225518. + 1.02404e6i) q^{16} -776217. q^{17} +1.46186e6 q^{19} +(4.29486e6 - 3.45194e6i) q^{20} +(6.38025e6 + 3.05758e6i) q^{22} -2.34458e6i q^{23} -1.91895e7 q^{25} +(-5.00188e6 + 1.04374e7i) q^{26} +(5.27884e6 - 4.24281e6i) q^{28} -2.88750e7i q^{29} -3.00762e7i q^{31} +(2.06695e7 - 2.64324e7i) q^{32} +(2.23996e7 + 1.07345e7i) q^{34} -3.55890e7 q^{35} -1.16919e7i q^{37} +(-4.21857e7 - 2.02164e7i) q^{38} +(-1.71676e8 + 4.02196e7i) q^{40} -4.70330e7 q^{41} +3.52427e7 q^{43} +(-1.41834e8 - 1.76468e8i) q^{44} +(-3.24238e7 + 6.76587e7i) q^{46} +4.23068e8i q^{47} +2.38733e8 q^{49} +(5.53761e8 + 2.65376e8i) q^{50} +(2.88683e8 - 2.32025e8i) q^{52} -9.16056e6i q^{53} +1.18971e9i q^{55} +(-2.11009e8 + 4.94343e7i) q^{56} +(-3.99319e8 + 8.33260e8i) q^{58} +1.03098e9 q^{59} +1.37140e8i q^{61} +(-4.15930e8 + 8.67921e8i) q^{62} +(-9.62009e8 + 4.76928e8i) q^{64} -1.94625e9 q^{65} -7.94671e8 q^{67} +(-4.97947e8 - 6.19539e8i) q^{68} +(1.02701e9 + 4.92168e8i) q^{70} +2.04858e9i q^{71} -1.88707e9 q^{73} +(-1.61690e8 + 3.37399e8i) q^{74} +(9.37794e8 + 1.16679e9i) q^{76} +1.46229e9i q^{77} +1.04965e9i q^{79} +(5.51035e9 + 1.21351e9i) q^{80} +(1.35725e9 + 6.50430e8i) q^{82} -3.77162e9 q^{83} +4.17682e9i q^{85} +(-1.01702e9 - 4.87380e8i) q^{86} +(1.65255e9 + 7.05387e9i) q^{88} +4.07338e9 q^{89} -2.39215e9 q^{91} +(1.87133e9 - 1.50406e9i) q^{92} +(5.85070e9 - 1.22087e10i) q^{94} -7.86629e9i q^{95} +1.76770e9 q^{97} +(-6.88921e9 - 3.30149e9i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 42 q^{2} + 212 q^{4} + 72 q^{8}+O(q^{10}) \) 8 * q - 42 * q^2 + 212 * q^4 + 72 * q^8	\( 8 q - 42 q^{2} + 212 q^{4} + 72 q^{8} + 9120 q^{10} - 143328 q^{11} + 400320 q^{14} - 1987312 q^{16} + 370800 q^{17} + 1753312 q^{19} - 2557440 q^{20} + 1549180 q^{22} - 18792760 q^{25} - 1891680 q^{26} + 18286080 q^{28} + 64016928 q^{32} - 115705388 q^{34} - 53736960 q^{35} - 375128220 q^{38} - 357584640 q^{40} - 92669328 q^{41} - 10190624 q^{43} - 727831512 q^{44} + 851947200 q^{46} - 80432248 q^{49} + 1669361190 q^{50} + 2420759040 q^{52} + 2928529920 q^{56} - 3245264160 q^{58} + 965642016 q^{59} - 4060980480 q^{62} - 5804705728 q^{64} + 839028480 q^{65} - 1225582880 q^{67} - 5258111400 q^{68} + 7723829760 q^{70} + 2800072720 q^{73} + 7669373280 q^{74} + 3753451288 q^{76} + 6408629760 q^{80} - 3638778380 q^{82} - 1853422560 q^{83} - 3022180476 q^{86} + 5815578640 q^{88} - 6162596112 q^{89} + 7645985280 q^{91} + 8903892480 q^{92} - 14182177920 q^{94} - 9697863536 q^{97} - 34759868298 q^{98}+O(q^{100}) \) 8 * q - 42 * q^2 + 212 * q^4 + 72 * q^8 + 9120 * q^10 - 143328 * q^11 + 400320 * q^14 - 1987312 * q^16 + 370800 * q^17 + 1753312 * q^19 - 2557440 * q^20 + 1549180 * q^22 - 18792760 * q^25 - 1891680 * q^26 + 18286080 * q^28 + 64016928 * q^32 - 115705388 * q^34 - 53736960 * q^35 - 375128220 * q^38 - 357584640 * q^40 - 92669328 * q^41 - 10190624 * q^43 - 727831512 * q^44 + 851947200 * q^46 - 80432248 * q^49 + 1669361190 * q^50 + 2420759040 * q^52 + 2928529920 * q^56 - 3245264160 * q^58 + 965642016 * q^59 - 4060980480 * q^62 - 5804705728 * q^64 + 839028480 * q^65 - 1225582880 * q^67 - 5258111400 * q^68 + 7723829760 * q^70 + 2800072720 * q^73 + 7669373280 * q^74 + 3753451288 * q^76 + 6408629760 * q^80 - 3638778380 * q^82 - 1853422560 * q^83 - 3022180476 * q^86 + 5815578640 * q^88 - 6162596112 * q^89 + 7645985280 * q^91 + 8903892480 * q^92 - 14182177920 * q^94 - 9697863536 * q^97 - 34759868298 * q^98

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