LMFDB - Embedded newform 72.20.d.b.37.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [72,20,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, 20, names="a")

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

chi := DirichletCharacter("72.37");

S:= CuspForms(chi, 20);

N := Newforms(S);

Level:	$ N $	$=$	$ 72 = 2^{3} \cdot 3^{2} $
Weight:	$ k $	$=$	$ 20 $
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:	$164.748021521$
Analytic rank:	$0$
Dimension:	$18$
Coefficient field:	$\mathbb{Q}[x]/(x^{18} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{18} - 9 x^{17} + 3029197094710 x^{16} - 24233576757476 x^{15} + \cdots + 11\!\cdots\!52 $ x^18 - 9x^17 + 3029197094710x^16 - 24233576757476x^15 + 3666373385397631772951150x^14 - 25664613697359334817402934x^13 + 2288558813400943515734688691172794536x^12 - 13731352880072021116343563422152991580x^11 + 797347137448451076604305820722674456768802005609x^10 - 3986735687116384648288147250006673795452858783225x^9 + 156816961995505010413790628590969656223945140307497061835402x^8 - 627267847958099627532615251355829485045232096457337309552248x^7 + 16729139446039926524800568668372570271935699643494450209774686790214560x^6 - 50187418335924342106565101598639295206702826260054714153668963065467152x^5 + 876106553890603967004320494333017909256417720590701905735688948342294947287783200x^4 - 1752213107697562236782832230977703791942517176383291832316055640309688411664317952x^3 + 18678677257259690524211679657602301764724302346110904809324415405979874812173320788961484288x^2 - 18678677256383583970371263108933435161611886146488870124597927742419621444385686885600890880*x + 113751286079151332076181426449135809801643053652804434109440434519249339410833533987328023600682237952
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	multiple of $ 2^{153}\cdot 3^{22}\cdot 5^{4}\cdot 7 $
Twist minimal:	no (minimal twist has level 8)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			37.6
Root			$0.500000 - 921862. i$ of defining polynomial
Character	$\chi$	$=$	72.37
Dual form			72.20.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)

$f(q)$	$=$	\(q+(-424.854 + 586.333i) q^{2} +(-163286. - 498212. i) q^{4} +7.37490e6i q^{5} +5.30965e7 q^{7} +(3.61491e8 + 1.15928e8i) q^{8} +(-4.32415e9 - 3.13326e9i) q^{10} -8.12973e8i q^{11} -1.03661e10i q^{13} +(-2.25583e10 + 3.11322e10i) q^{14} +(-2.21553e11 + 1.62702e11i) q^{16} -5.21391e11 q^{17} +1.67441e12i q^{19} +(3.67427e12 - 1.20422e12i) q^{20} +(4.76673e11 + 3.45395e11i) q^{22} +1.06368e13 q^{23} -3.53156e13 q^{25} +(6.07802e12 + 4.40410e12i) q^{26} +(-8.66989e12 - 2.64533e13i) q^{28} -7.99511e13i q^{29} +2.82112e14 q^{31} +(-1.26965e12 - 1.99029e14i) q^{32} +(2.21515e14 - 3.05709e14i) q^{34} +3.91581e14i q^{35} -1.12989e15i q^{37} +(-9.81761e14 - 7.11379e14i) q^{38} +(-8.54956e14 + 2.66596e15i) q^{40} -2.42038e15 q^{41} -2.17667e15i q^{43} +(-4.05033e14 + 1.32747e14i) q^{44} +(-4.51910e15 + 6.23672e15i) q^{46} -1.03125e15 q^{47} -8.57966e15 q^{49} +(1.50040e16 - 2.07067e16i) q^{50} +(-5.16454e15 + 1.69264e15i) q^{52} +1.92963e16i q^{53} +5.99559e15 q^{55} +(1.91939e16 + 6.15536e15i) q^{56} +(4.68780e16 + 3.39676e16i) q^{58} -1.72226e16i q^{59} -5.82188e16i q^{61} +(-1.19857e17 + 1.65412e17i) q^{62} +(1.17237e17 + 8.38138e16i) q^{64} +7.64493e16 q^{65} +1.51600e17i q^{67} +(8.51358e16 + 2.59764e17i) q^{68} +(-2.29597e17 - 1.66365e17i) q^{70} -4.29045e17 q^{71} -8.38419e17 q^{73} +(6.62491e17 + 4.80037e17i) q^{74} +(8.34211e17 - 2.73407e17i) q^{76} -4.31660e16i q^{77} -1.06444e18 q^{79} +(-1.19991e18 - 1.63393e18i) q^{80} +(1.02831e18 - 1.41915e18i) q^{82} -2.96065e18i q^{83} -3.84521e18i q^{85} +(1.27625e18 + 9.24766e17i) q^{86} +(9.42462e16 - 2.93883e17i) q^{88} -2.03527e18 q^{89} -5.50405e17i q^{91} +(-1.73684e18 - 5.29940e18i) q^{92} +(4.38133e17 - 6.04659e17i) q^{94} -1.23486e19 q^{95} -1.22385e19 q^{97} +(3.64511e18 - 5.03054e18i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 18 q + 458 q^{2} - 412108 q^{4} - 80707216 q^{7} + 173313752 q^{8} + 758800104 q^{10} + 122453668784 q^{14} - 696212072432 q^{16} - 14121426692 q^{17} - 6517087595632 q^{20} - 11074654117412 q^{22} - 2177121583952 q^{23}+ \cdots - 88\!\cdots\!22 q^{98}+O(q^{100}) $ 18 * q + 458 * q^2 - 412108 * q^4 - 80707216 * q^7 + 173313752 * q^8 + 758800104 * q^10 + 122453668784 * q^14 - 696212072432 * q^16 - 14121426692 * q^17 - 6517087595632 * q^20 - 11074654117412 * q^22 - 2177121583952 * q^23 - 44414474211734 * q^25 - 26782030269304 * q^26 - 97002327802784 * q^28 + 428505770260416 * q^31 - 122449430282912 * q^32 - 478448330325748 * q^34 + 486194587539796 * q^38 - 1697818250610976 * q^40 - 1200260021141524 * q^41 - 7031781193616424 * q^44 - 14917443628457488 * q^46 + 1134160959992928 * q^47 + 31570092936329058 * q^49 + 34734151321861826 * q^50 - 26877456911772208 * q^52 - 51757047863478736 * q^55 - 52858270161183424 * q^56 - 20470056808312424 * q^58 - 93766686763697984 * q^62 - 253721318369185216 * q^64 + 184007586011668640 * q^65 - 201388986348307752 * q^68 - 340698473416023872 * q^70 + 1599477989199799056 * q^71 - 93004298989809068 * q^73 + 93558253821761240 * q^74 - 1090379619519933176 * q^76 + 1813975801025264480 * q^79 - 3057120301750869696 * q^80 - 2418785089528546244 * q^82 - 1332333723895598620 * q^86 - 3097741184498130608 * q^88 - 4470509771045743540 * q^89 + 2965990502259463392 * q^92 - 3533635112749329696 * q^94 - 23809730986995679856 * q^95 + 8246429789464117220 * q^97 - 8841667592735478822 * q^98

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 $

$2$	−424.854	+	586.333i	−0.586753	+	0.809766i
$2$	−424.854	+	586.333i	−0.586753	+	0.809766i
$3$		0			0
$3$		0			0
$4$	−163286.	−	498212.i	−0.311443	−	0.950265i
$5$			7.37490e6i			1.68866i	0.535827	+	0.844328i	$0.320000\pi$
$5$			7.37490e6i			1.68866i	−0.535827	+	0.844328i	$0.680000\pi$
$6$		0			0
$7$	5.30965e7			0.497318			0.248659	−	0.968591i	$-0.420010\pi$
$7$	5.30965e7			0.497318			0.248659	+	0.968591i	$0.420010\pi$
$8$	3.61491e8	+	1.15928e8i	0.952232	+	0.305375i
$9$		0			0
$10$	−4.32415e9	−	3.13326e9i	−1.36742	−	0.990823i
$11$		−	8.12973e8i		−	0.103955i	−0.998648	−	0.0519775i	$-0.983448\pi$
$11$		−	8.12973e8i		−	0.103955i	0.998648	−	0.0519775i	$-0.0165524\pi$
$12$		0			0
$13$		−	1.03661e10i		−	0.271116i	−0.990769	−	0.135558i	$-0.956717\pi$
$13$		−	1.03661e10i		−	0.271116i	0.990769	−	0.135558i	$-0.0432827\pi$
$14$	−2.25583e10	+	3.11322e10i	−0.291803	+	0.402711i
$15$		0			0
$16$	−2.21553e11	+	1.62702e11i	−0.806007	+	0.591906i
$17$	−5.21391e11			−1.06635			−0.533174	−	0.846005i	$-0.679001\pi$
$17$	−5.21391e11			−1.06635			−0.533174	+	0.846005i	$0.679001\pi$
$18$		0			0
$19$			1.67441e12i			1.19042i	0.803568	+	0.595212i	$0.202932\pi$
$19$			1.67441e12i			1.19042i	−0.803568	+	0.595212i	$0.797068\pi$
$20$	3.67427e12	−	1.20422e12i	1.60467	−	0.525919i
$21$		0			0
$22$	4.76673e11	+	3.45395e11i	0.0841793	+	0.0609959i
$23$	1.06368e13			1.23139			0.615697	−	0.787983i	$-0.288874\pi$
$23$	1.06368e13			1.23139			0.615697	+	0.787983i	$0.288874\pi$
$24$		0			0
$25$	−3.53156e13			−1.85156
$26$	6.07802e12	+	4.40410e12i	0.219541	+	0.159078i
$27$		0			0
$28$	−8.66989e12	−	2.64533e13i	−0.154886	−	0.472584i
$29$		−	7.99511e13i		−	1.02340i	−0.859165	−	0.511698i	$-0.829017\pi$
$29$		−	7.99511e13i		−	1.02340i	0.859165	−	0.511698i	$-0.170983\pi$
$30$		0			0
$31$	2.82112e14			1.91640			0.958200	−	0.286100i	$-0.0923591\pi$
$31$	2.82112e14			1.91640			0.958200	+	0.286100i	$0.0923591\pi$
$32$	−1.26965e12	−	1.99029e14i	−0.00637908	−	0.999980i
$33$		0			0
$34$	2.21515e14	−	3.05709e14i	0.625683	−	0.863493i
$35$			3.91581e14i			0.839799i
$36$		0			0
$37$		−	1.12989e15i		−	1.42928i	−0.699490	−	0.714642i	$-0.746589\pi$
$37$		−	1.12989e15i		−	1.42928i	0.699490	−	0.714642i	$-0.253411\pi$
$38$	−9.81761e14	−	7.11379e14i	−0.963966	−	0.698485i
$39$		0			0
$40$	−8.54956e14	+	2.66596e15i	−0.515672	+	1.60799i
$41$	−2.42038e15			−1.15461			−0.577306	−	0.816528i	$-0.695896\pi$
$41$	−2.42038e15			−1.15461			−0.577306	+	0.816528i	$0.695896\pi$
$42$		0			0
$43$		−	2.17667e15i		−	0.660453i	−0.943902	−	0.330226i	$-0.892875\pi$
$43$		−	2.17667e15i		−	0.660453i	0.943902	−	0.330226i	$-0.107125\pi$
$44$	−4.05033e14	+	1.32747e14i	−0.0987848	+	0.0323760i
$45$		0			0
$46$	−4.51910e15	+	6.23672e15i	−0.722524	+	0.997142i
$47$	−1.03125e15			−0.134411			−0.0672057	−	0.997739i	$-0.521408\pi$
$47$	−1.03125e15			−0.134411			−0.0672057	+	0.997739i	$0.521408\pi$
$48$		0			0
$49$	−8.57966e15			−0.752675
$50$	1.50040e16	−	2.07067e16i	1.08641	−	1.49933i
$51$		0			0
$52$	−5.16454e15	+	1.69264e15i	−0.257632	+	0.0844371i
$53$			1.92963e16i			0.803254i	0.915803	+	0.401627i	$0.131555\pi$
$53$			1.92963e16i			0.803254i	−0.915803	+	0.401627i	$0.868445\pi$
$54$		0			0
$55$	5.99559e15			0.175544
$56$	1.91939e16	+	6.15536e15i	0.473562	+	0.151868i
$57$		0			0
$58$	4.68780e16	+	3.39676e16i	0.828711	+	0.600480i
$59$		−	1.72226e16i		−	0.258824i	−0.991591	−	0.129412i	$-0.958691\pi$
$59$		−	1.72226e16i		−	0.258824i	0.991591	−	0.129412i	$-0.0413090\pi$
$60$		0			0
$61$		−	5.82188e16i		−	0.637427i	−0.947851	−	0.318713i	$-0.896749\pi$
$61$		−	5.82188e16i		−	0.637427i	0.947851	−	0.318713i	$-0.103251\pi$
$62$	−1.19857e17	+	1.65412e17i	−1.12445	+	1.55184i
$63$		0			0
$64$	1.17237e17	+	8.38138e16i	0.813493	+	0.581575i
$65$	7.64493e16			0.457822
$66$		0			0
$67$			1.51600e17i			0.680749i	0.940290	+	0.340375i	$0.110554\pi$
$67$			1.51600e17i			0.680749i	−0.940290	+	0.340375i	$0.889446\pi$
$68$	8.51358e16	+	2.59764e17i	0.332107	+	1.01331i
$69$		0			0
$70$	−2.29597e17	−	1.66365e17i	−0.680041	−	0.492754i
$71$	−4.29045e17			−1.11058			−0.555288	−	0.831658i	$-0.687392\pi$
$71$	−4.29045e17			−1.11058			−0.555288	+	0.831658i	$0.687392\pi$
$72$		0			0
$73$	−8.38419e17			−1.66684			−0.833420	−	0.552639i	$-0.813621\pi$
$73$	−8.38419e17			−1.66684			−0.833420	+	0.552639i	$0.813621\pi$
$74$	6.62491e17	+	4.80037e17i	1.15739	+	0.838636i
$75$		0			0
$76$	8.34211e17	−	2.73407e17i	1.13122	−	0.370749i
$77$		−	4.31660e16i		−	0.0516987i
$78$		0			0
$79$	−1.06444e18			−0.999223			−0.499612	−	0.866250i	$-0.666524\pi$
$79$	−1.06444e18			−0.999223			−0.499612	+	0.866250i	$0.666524\pi$
$80$	−1.19991e18	−	1.63393e18i	−0.999526	−	1.36107i
$81$		0			0
$82$	1.02831e18	−	1.41915e18i	0.677472	−	0.934966i
$83$		−	2.96065e18i		−	1.73838i	−0.494475	−	0.869192i	$-0.664640\pi$
$83$		−	2.96065e18i		−	1.73838i	0.494475	−	0.869192i	$-0.335360\pi$
$84$		0			0
$85$		−	3.84521e18i		−	1.80070i
$86$	1.27625e18	+	9.24766e17i	0.534812	+	0.387522i
$87$		0			0
$88$	9.42462e16	−	2.93883e17i	0.0317452	−	0.0989894i
$89$	−2.03527e18			−0.615767			−0.307884	−	0.951424i	$-0.599621\pi$
$89$	−2.03527e18			−0.615767			−0.307884	+	0.951424i	$0.599621\pi$
$90$		0			0
$91$		−	5.50405e17i		−	0.134831i
$92$	−1.73684e18	−	5.29940e18i	−0.383509	−	1.17015i
$93$		0			0
$94$	4.38133e17	−	6.04659e17i	0.0788662	−	0.108842i
$95$	−1.23486e19			−2.01022
$96$		0			0
$97$	−1.22385e19			−1.63454			−0.817269	−	0.576257i	$-0.804513\pi$
$97$	−1.22385e19			−1.63454			−0.817269	+	0.576257i	$0.804513\pi$
$98$	3.64511e18	−	5.03054e18i	0.441634	−	0.609491i
$99$		0			0
$100$	5.76654e18	+	1.75947e19i	0.576654	+	1.75947i
$101$			4.77647e18i			0.434564i	0.976109	+	0.217282i	$0.0697192\pi$
$101$			4.77647e18i			0.434564i	−0.976109	+	0.217282i	$0.930281\pi$
$102$		0			0
$103$	6.83745e18			0.516346			0.258173	−	0.966099i	$-0.416880\pi$
$103$	6.83745e18			0.516346			0.258173	+	0.966099i	$0.416880\pi$
$104$	1.20172e18	−	3.74727e18i	0.0827920	−	0.258166i
$105$		0			0
$106$	−1.13141e19	−	8.19811e18i	−0.650448	−	0.471312i
$107$			9.18352e17i			0.0482907i	0.999708	+	0.0241453i	$0.00768645\pi$
$107$			9.18352e17i			0.0482907i	−0.999708	+	0.0241453i	$0.992314\pi$
$108$		0			0
$109$		−	2.43225e19i		−	1.07265i	−0.844012	−	0.536324i	$-0.819813\pi$
$109$		−	2.43225e19i		−	1.07265i	0.844012	−	0.536324i	$-0.180187\pi$
$110$	−2.54725e18	+	3.51542e18i	−0.103001	+	0.142150i
$111$		0			0
$112$	−1.17637e19	+	8.63890e18i	−0.400842	+	0.294366i
$113$	5.50211e18			0.172300			0.0861498	−	0.996282i	$-0.472544\pi$
$113$	5.50211e18			0.172300			0.0861498	+	0.996282i	$0.472544\pi$
$114$		0			0
$115$			7.84455e19i			2.07940i
$116$	−3.98327e19	+	1.30549e19i	−0.972497	+	0.318729i
$117$		0			0
$118$	1.00982e19	+	7.31711e18i	0.209587	+	0.151866i
$119$	−2.76840e19			−0.530314
$120$		0			0
$121$	6.04982e19			0.989193
$122$	3.41357e19	+	2.47345e19i	0.516167	+	0.374012i
$123$		0			0
$124$	−4.60649e19	−	1.40552e20i	−0.596849	−	1.82109i
$125$		−	1.19784e20i		−	1.43799i
$126$		0			0
$127$	4.69956e19			0.485202			0.242601	−	0.970126i	$-0.421999\pi$
$127$	4.69956e19			0.485202			0.242601	+	0.970126i	$0.421999\pi$
$128$	−9.89513e19	+	3.31311e19i	−0.948259	+	0.317498i
$129$		0			0
$130$	−3.24798e19	+	4.48247e19i	−0.268628	+	0.370729i
$131$		−	5.15638e19i		−	0.396522i	−0.980149	−	0.198261i	$-0.936471\pi$
$131$		−	5.15638e19i		−	0.396522i	0.980149	−	0.198261i	$-0.0635294\pi$
$132$		0			0
$133$			8.89051e19i			0.592020i
$134$	−8.88879e19	−	6.44077e19i	−0.551248	−	0.399432i
$135$		0			0
$136$	−1.88478e20	−	6.04438e19i	−1.01541	−	0.325636i
$137$	1.26213e20			0.634247			0.317124	−	0.948384i	$-0.397283\pi$
$137$	1.26213e20			0.634247			0.317124	+	0.948384i	$0.397283\pi$
$138$		0			0
$139$		−	3.53665e20i		−	1.54864i	−0.632791	−	0.774322i	$-0.718091\pi$
$139$		−	3.53665e20i		−	1.54864i	0.632791	−	0.774322i	$-0.281909\pi$
$140$	1.95091e20	−	6.39396e19i	0.798031	−	0.261549i
$141$		0			0
$142$	1.82281e20	−	2.51563e20i	0.651633	−	0.899307i
$143$	−8.42739e18			−0.0281839
$144$		0			0
$145$	5.89631e20			1.72816
$146$	3.56206e20	−	4.91593e20i	0.978023	−	1.34975i
$147$		0			0
$148$	−5.62924e20	+	1.84494e20i	−1.35820	+	0.445140i
$149$		−	3.87883e20i		−	0.877871i	−0.898518	−	0.438936i	$-0.855356\pi$
$149$		−	3.87883e20i		−	0.877871i	0.898518	−	0.438936i	$-0.144644\pi$
$150$		0			0
$151$	1.24861e20			0.248970			0.124485	−	0.992222i	$-0.460272\pi$
$151$	1.24861e20			0.248970			0.124485	+	0.992222i	$0.460272\pi$
$152$	−1.94110e20	+	6.05284e20i	−0.363525	+	1.13356i
$153$		0			0
$154$	2.53097e19	+	1.83393e19i	0.0418639	+	0.0303344i
$155$			2.08055e21i			3.23614i
$156$		0			0
$157$		−	3.26809e20i		−	0.450036i	−0.974355	−	0.225018i	$-0.927756\pi$
$157$		−	3.26809e20i		−	0.450036i	0.974355	−	0.225018i	$-0.0722441\pi$
$158$	4.52231e20	−	6.24115e20i	0.586297	−	0.809137i
$159$		0			0
$160$	1.46782e21	−	9.36352e18i	1.68862	−	0.0107721i
$161$	5.64777e20			0.612395
$162$		0			0
$163$			9.64660e20i			0.930234i	0.885249	+	0.465117i	$0.153988\pi$
$163$			9.64660e20i			0.930234i	−0.885249	+	0.465117i	$0.846012\pi$
$164$	3.95213e20	+	1.20586e21i	0.359596	+	1.09719i
$165$		0			0
$166$	1.73593e21	+	1.25785e21i	1.40768	+	1.02000i
$167$	−6.67061e20			−0.510928			−0.255464	−	0.966819i	$-0.582228\pi$
$167$	−6.67061e20			−0.510928			−0.255464	+	0.966819i	$0.582228\pi$
$168$		0			0
$169$	1.35446e21			0.926496
$170$	2.25457e21	+	1.63365e21i	1.45814	+	1.05656i
$171$		0			0
$172$	−1.08444e21	+	3.55419e20i	−0.627605	+	0.205693i
$173$		−	1.05036e21i		−	0.575310i	−0.957734	−	0.287655i	$-0.907124\pi$
$173$		−	1.05036e21i		−	0.575310i	0.957734	−	0.287655i	$-0.0928757\pi$
$174$		0			0
$175$	−1.87514e21			−0.920812
$176$	1.32272e20	+	1.80117e20i	0.0615316	+	0.0837885i
$177$		0			0
$178$	8.64693e20	−	1.19335e21i	0.361303	−	0.498628i
$179$		−	3.05446e21i		−	1.21012i	−0.796178	−	0.605062i	$-0.793148\pi$
$179$		−	3.05446e21i		−	1.21012i	0.796178	−	0.605062i	$-0.206852\pi$
$180$		0			0
$181$			4.09335e20i			0.145926i	0.997335	+	0.0729629i	$0.0232455\pi$
$181$			4.09335e20i			0.145926i	−0.997335	+	0.0729629i	$0.976755\pi$
$182$	3.22721e20	+	2.33842e20i	0.109182	+	0.0791124i
$183$		0			0
$184$	3.84512e21	+	1.23310e21i	1.17257	+	0.376037i
$185$	8.33280e21			2.41357
$186$		0			0
$187$			4.23877e20i			0.110852i
$188$	1.68389e20	+	5.13784e20i	0.0418614	+	0.127726i
$189$		0			0
$190$	5.24635e21	−	7.24039e21i	1.17950	−	1.62781i
$191$	−8.05271e21			−1.72236			−0.861182	−	0.508297i	$-0.830275\pi$
$191$	−8.05271e21			−1.72236			−0.861182	+	0.508297i	$0.830275\pi$
$192$		0			0
$193$	−2.34435e20			−0.0454181			−0.0227090	−	0.999742i	$-0.507229\pi$
$193$	−2.34435e20			−0.0454181			−0.0227090	+	0.999742i	$0.507229\pi$
$194$	5.19956e21	−	7.17581e21i	0.959069	−	1.32359i
$195$		0			0
$196$	1.40094e21	+	4.27449e21i	0.234415	+	0.715241i
$197$		−	1.68777e21i		−	0.269082i	−0.990908	−	0.134541i	$-0.957044\pi$
$197$		−	1.68777e21i		−	0.269082i	0.990908	−	0.134541i	$-0.0429560\pi$
$198$		0			0
$199$	9.56331e21			1.38517			0.692586	−	0.721335i	$-0.256471\pi$
$199$	9.56331e21			1.38517			0.692586	+	0.721335i	$0.256471\pi$
$200$	−1.27663e22	−	4.09407e21i	−1.76311	−	0.565418i
$201$		0			0
$202$	−2.80060e21	−	2.02930e21i	−0.351896	−	0.254982i
$203$		−	4.24512e21i		−	0.508953i
$204$		0			0
$205$		−	1.78500e22i		−	1.94974i
$206$	−2.90492e21	+	4.00902e21i	−0.302967	+	0.418119i
$207$		0			0
$208$	1.68659e21	+	2.29665e21i	0.160475	+	0.218521i
$209$	1.36125e21			0.123751
$210$		0			0
$211$		−	8.14897e21i		−	0.676736i	−0.941014	−	0.338368i	$-0.890125\pi$
$211$		−	8.14897e21i		−	0.676736i	0.941014	−	0.338368i	$-0.109875\pi$
$212$	9.61365e21	−	3.15081e21i	0.763305	−	0.250168i
$213$		0			0
$214$	−5.38460e20	−	3.90166e20i	−0.0391042	−	0.0283347i
$215$	1.60527e22			1.11528
$216$		0			0
$217$	1.49792e22			0.953060
$218$	1.42611e22	+	1.03335e22i	0.868594	+	0.629379i
$219$		0			0
$220$	−9.78995e20	−	2.98708e21i	−0.0546720	−	0.166814i
$221$			5.40482e21i			0.289104i
$222$		0			0
$223$	1.64188e22			0.806204			0.403102	−	0.915155i	$-0.367932\pi$
$223$	1.64188e22			0.806204			0.403102	+	0.915155i	$0.367932\pi$
$224$	−6.74137e19	−	1.05677e22i	−0.00317243	−	0.497308i
$225$		0			0
$226$	−2.33760e21	+	3.22607e21i	−0.101097	+	0.139522i
$227$			3.07665e22i			1.27595i	0.770059	+	0.637973i	$0.220227\pi$
$227$			3.07665e22i			1.27595i	−0.770059	+	0.637973i	$0.779773\pi$
$228$		0			0
$229$			3.68234e22i			1.40503i	0.711667	+	0.702517i	$0.247941\pi$
$229$			3.68234e22i			1.40503i	−0.711667	+	0.702517i	$0.752059\pi$
$230$	−4.59952e22	−	3.33279e22i	−1.68383	−	1.22009i
$231$		0			0
$232$	9.26856e21	−	2.89016e22i	0.312519	−	0.974511i
$233$	1.13563e22			0.367585			0.183792	−	0.982965i	$-0.441163\pi$
$233$	1.13563e22			0.367585			0.183792	+	0.982965i	$0.441163\pi$
$234$		0			0
$235$		−	7.60539e21i		−	0.226974i
$236$	−8.58053e21	+	2.81221e21i	−0.245952	+	0.0806090i
$237$		0			0
$238$	1.17617e22	−	1.62321e22i	0.311163	−	0.429431i
$239$	1.71615e22			0.436289			0.218144	−	0.975916i	$-0.430000\pi$
$239$	1.71615e22			0.436289			0.218144	+	0.975916i	$0.430000\pi$
$240$		0			0
$241$	2.01060e22			0.472241			0.236120	−	0.971724i	$-0.424124\pi$
$241$	2.01060e22			0.472241			0.236120	+	0.971724i	$0.424124\pi$
$242$	−2.57029e22	+	3.54721e22i	−0.580412	+	0.801015i
$243$		0			0
$244$	−2.90054e22	+	9.50631e21i	−0.605724	+	0.198522i
$245$		−	6.32741e22i		−	1.27101i
$246$		0			0
$247$	1.73571e22			0.322743
$248$	1.01981e23	+	3.27047e22i	1.82486	+	0.585220i
$249$		0			0
$250$	7.02335e22	+	5.08909e22i	1.16443	+	0.843742i
$251$		−	9.14531e22i		−	1.45982i	−0.683546	−	0.729908i	$-0.739563\pi$
$251$		−	9.14531e22i		−	1.45982i	0.683546	−	0.729908i	$-0.260437\pi$
$252$		0			0
$253$		−	8.64745e21i		−	0.128010i
$254$	−1.99663e22	+	2.75551e22i	−0.284693	+	0.392900i
$255$		0			0
$256$	2.26140e22	−	7.20944e22i	0.299294	−	0.954161i
$257$	−7.33268e22			−0.935186			−0.467593	−	0.883944i	$-0.654879\pi$
$257$	−7.33268e22			−0.935186			−0.467593	+	0.883944i	$0.654879\pi$
$258$		0			0
$259$		−	5.99930e22i		−	0.710809i
$260$	−1.24831e22	−	3.80880e22i	−0.142585	−	0.435052i
$261$		0			0
$262$	3.02336e22	+	2.19071e22i	0.321090	+	0.232660i
$263$	1.28147e23			1.31259			0.656293	−	0.754506i	$-0.272124\pi$
$263$	1.28147e23			1.31259			0.656293	+	0.754506i	$0.272124\pi$
$264$		0			0
$265$	−1.42308e23			−1.35642
$266$	−5.21280e22	−	3.77717e22i	−0.479397	−	0.347369i
$267$		0			0
$268$	7.55288e22	−	2.47540e22i	0.646892	−	0.212014i
$269$			6.95977e22i			0.575371i	0.957725	+	0.287686i	$0.0928858\pi$
$269$			6.95977e22i			0.575371i	−0.957725	+	0.287686i	$0.907114\pi$
$270$		0			0
$271$	7.81978e22			0.602541			0.301270	−	0.953539i	$-0.402589\pi$
$271$	7.81978e22			0.602541			0.301270	+	0.953539i	$0.402589\pi$
$272$	1.15516e23	−	8.48314e22i	0.859484	−	0.631178i
$273$		0			0
$274$	−5.36221e22	+	7.40029e22i	−0.372146	+	0.513592i
$275$			2.87107e22i			0.192479i
$276$		0			0
$277$			4.00035e22i			0.250346i	0.992135	+	0.125173i	$0.0399485\pi$
$277$			4.00035e22i			0.250346i	−0.992135	+	0.125173i	$0.960051\pi$
$278$	2.07366e23	+	1.50256e23i	1.25404	+	0.908671i
$279$		0			0
$280$	−4.53951e22	+	1.41553e23i	−0.256453	+	0.799683i
$281$	−8.39766e22			−0.458615			−0.229308	−	0.973354i	$-0.573646\pi$
$281$	−8.39766e22			−0.458615			−0.229308	+	0.973354i	$0.573646\pi$
$282$		0			0
$283$		−	2.12048e23i		−	1.08259i	−0.840833	−	0.541294i	$-0.817935\pi$
$283$		−	2.12048e23i		−	1.08259i	0.840833	−	0.541294i	$-0.182065\pi$
$284$	7.00568e22	+	2.13755e23i	0.345881	+	1.05534i
$285$		0			0
$286$	3.58041e21	−	4.94126e21i	0.0165370	−	0.0228224i
$287$	−1.28513e23			−0.574210
$288$		0			0
$289$	3.27766e22			0.137099
$290$	−2.50507e23	+	3.45721e23i	−1.01400	+	1.39941i
$291$		0			0
$292$	1.36902e23	+	4.17711e23i	0.519126	+	1.58394i
$293$			1.22310e23i			0.448974i	0.974477	+	0.224487i	$0.0720706\pi$
$293$			1.22310e23i			0.448974i	−0.974477	+	0.224487i	$0.927929\pi$
$294$		0			0
$295$	1.27015e23			0.437065
$296$	1.30985e23	−	4.08444e23i	0.436467	−	1.36101i
$297$		0			0
$298$	2.27429e23	+	1.64794e23i	0.710871	+	0.515093i
$299$		−	1.10263e23i		−	0.333851i
$300$		0			0
$301$		−	1.15573e23i		−	0.328455i
$302$	−5.30478e22	+	7.32103e22i	−0.146084	+	0.201607i
$303$		0			0
$304$	−2.72429e23	−	3.70971e23i	−0.704620	−	0.959491i
$305$	4.29358e23			1.07639
$306$		0			0
$307$			6.44871e23i			1.51935i	0.650302	+	0.759675i	$0.274642\pi$
$307$			6.44871e23i			1.51935i	−0.650302	+	0.759675i	$0.725358\pi$
$308$	−2.15058e22	+	7.04839e21i	−0.0491275	+	0.0161012i
$309$		0			0
$310$	−1.21990e24	−	8.83931e23i	−2.62052	−	1.89881i
$311$	−1.39658e23			−0.290966			−0.145483	−	0.989361i	$-0.546474\pi$
$311$	−1.39658e23			−0.290966			−0.145483	+	0.989361i	$0.546474\pi$
$312$		0			0
$313$	−5.89594e23			−1.15580			−0.577899	−	0.816108i	$-0.696127\pi$
$313$	−5.89594e23			−1.15580			−0.577899	+	0.816108i	$0.696127\pi$
$314$	1.91619e23	+	1.38846e23i	0.364424	+	0.264060i
$315$		0			0
$316$	1.73807e23	+	5.30316e23i	0.311201	+	0.949527i
$317$		−	5.35459e23i		−	0.930386i	−0.885209	−	0.465193i	$-0.845985\pi$
$317$		−	5.35459e23i		−	0.930386i	0.885209	−	0.465193i	$-0.154015\pi$
$318$		0			0
$319$	−6.49981e22			−0.106387
$320$	−6.18118e23	+	8.64608e23i	−0.982080	+	1.37371i
$321$		0			0
$322$	−2.39948e23	+	3.31148e23i	−0.359324	+	0.495897i
$323$		−	8.73022e23i		−	1.26941i
$324$		0			0
$325$			3.66087e23i			0.501987i
$326$	−5.65612e23	−	4.09840e23i	−0.753272	−	0.545817i
$327$		0			0
$328$	−8.74945e23	−	2.80589e23i	−1.09946	−	0.352589i
$329$	−5.47559e22			−0.0668452
$330$		0			0
$331$		−	1.94456e23i		−	0.224107i	−0.993702	−	0.112054i	$-0.964257\pi$
$331$		−	1.94456e23i		−	0.224107i	0.993702	−	0.112054i	$-0.0357429\pi$
$332$	−1.47503e24	+	4.83432e23i	−1.65193	+	0.541407i
$333$		0			0
$334$	2.83404e23	−	3.91120e23i	0.299788	−	0.413732i
$335$	−1.11803e24			−1.14955
$336$		0			0
$337$	1.03103e24			1.00182			0.500909	−	0.865500i	$-0.332999\pi$
$337$	1.03103e24			1.00182			0.500909	+	0.865500i	$0.332999\pi$
$338$	−5.75450e23	+	7.94167e23i	−0.543624	+	0.750245i
$339$		0			0
$340$	−1.91573e24	+	6.27868e23i	−1.71114	+	0.560813i
$341$		−	2.29350e23i		−	0.199219i
$342$		0			0
$343$	−1.06079e24			−0.871637
$344$	2.52336e23	−	7.86846e23i	0.201685	−	0.628904i
$345$		0			0
$346$	6.15864e23	+	4.46252e23i	0.465867	+	0.337565i
$347$			1.26415e24i			0.930398i	0.885206	+	0.465199i	$0.154017\pi$
$347$			1.26415e24i			0.930398i	−0.885206	+	0.465199i	$0.845983\pi$
$348$		0			0
$349$		−	6.37817e23i		−	0.444483i	−0.974992	−	0.222241i	$-0.928663\pi$
$349$		−	6.37817e23i		−	0.444483i	0.974992	−	0.222241i	$-0.0713373\pi$
$350$	7.96659e23	−	1.09945e24i	0.540289	−	0.745643i
$351$		0			0
$352$	−1.61805e23	+	1.03219e21i	−0.103953	+	0.000663138i
$353$	1.44725e24			0.905073			0.452537	−	0.891746i	$-0.350519\pi$
$353$	1.44725e24			0.905073			0.452537	+	0.891746i	$0.350519\pi$
$354$		0			0
$355$		−	3.16416e24i		−	1.87538i
$356$	3.32330e23	+	1.01400e24i	0.191776	+	0.585142i
$357$		0			0
$358$	1.79093e24	+	1.29770e24i	0.979918	+	0.710044i
$359$	−8.77525e23			−0.467587			−0.233793	−	0.972286i	$-0.575114\pi$
$359$	−8.77525e23			−0.467587			−0.233793	+	0.972286i	$0.575114\pi$
$360$		0			0
$361$	−8.25221e23			−0.417111
$362$	−2.40007e23	−	1.73908e23i	−0.118166	−	0.0856224i
$363$		0			0
$364$	−2.74219e23	+	8.98733e22i	−0.128125	+	0.0419921i
$365$		−	6.18326e24i		−	2.81472i
$366$		0			0
$367$	−1.73781e24			−0.751061			−0.375531	−	0.926810i	$-0.622540\pi$
$367$	−1.73781e24			−0.751061			−0.375531	+	0.926810i	$0.622540\pi$
$368$	−2.35662e24	+	1.73063e24i	−0.992513	+	0.728870i
$369$		0			0
$370$	−3.54023e24	+	4.88580e24i	−1.41617	+	1.95443i
$371$			1.02456e24i			0.399473i
$372$		0			0
$373$		−	1.93757e24i		−	0.717834i	−0.933369	−	0.358917i	$-0.883146\pi$
$373$		−	1.93757e24i		−	0.717834i	0.933369	−	0.358917i	$-0.116854\pi$
$374$	−2.48533e23	−	1.80086e23i	−0.0897645	−	0.0650429i
$375$		0			0
$376$	−3.72789e23	−	1.19551e23i	−0.127991	−	0.0410458i
$377$	−8.28785e23			−0.277459
$378$		0			0
$379$			3.31679e24i			1.05595i	0.849258	+	0.527977i	$0.177049\pi$
$379$			3.31679e24i			1.05595i	−0.849258	+	0.527977i	$0.822951\pi$
$380$	2.01635e24	+	6.15222e24i	0.626068	+	1.91024i
$381$		0			0
$382$	3.42123e24	−	4.72157e24i	1.01060	−	1.39471i
$383$	3.92182e24			1.13005			0.565027	−	0.825073i	$-0.308866\pi$
$383$	3.92182e24			1.13005			0.565027	+	0.825073i	$0.308866\pi$
$384$		0			0
$385$	3.18345e23			0.0873013
$386$	9.96008e22	−	1.37457e23i	0.0266492	−	0.0367780i
$387$		0			0
$388$	1.99836e24	+	6.09735e24i	0.509065	+	1.55324i
$389$		−	1.76592e23i		−	0.0438986i	−0.999759	−	0.0219493i	$-0.993013\pi$
$389$		−	1.76592e23i		−	0.0438986i	0.999759	−	0.0219493i	$-0.00698724\pi$
$390$		0			0
$391$	−5.54595e24			−1.31310
$392$	−3.10147e24	−	9.94622e23i	−0.716721	−	0.229848i
$393$		0			0
$394$	9.89598e23	+	7.17058e23i	0.217894	+	0.157885i
$395$		−	7.85011e24i		−	1.68734i
$396$		0			0
$397$		−	1.57919e22i		−	0.00323538i	−0.999999	−	0.00161769i	$-0.999485\pi$
$397$		−	1.57919e22i		−	0.00323538i	0.999999	−	0.00161769i	$-0.000514927\pi$
$398$	−4.06301e24	+	5.60729e24i	−0.812754	+	1.12167i
$399$		0			0
$400$	7.82430e24	−	5.74592e24i	1.49237	−	1.09595i
$401$	−2.59856e23			−0.0484018			−0.0242009	−	0.999707i	$-0.507704\pi$
$401$	−2.59856e23			−0.0484018			−0.0242009	+	0.999707i	$0.507704\pi$
$402$		0			0
$403$		−	2.92442e24i		−	0.519567i
$404$	2.37970e24	−	7.79930e23i	0.412951	−	0.135342i
$405$		0			0
$406$	2.48906e24	+	1.80356e24i	0.412133	+	0.298630i
$407$	−9.18568e23			−0.148581
$408$		0			0
$409$	1.46776e23			0.0226612			0.0113306	−	0.999936i	$-0.496393\pi$
$409$	1.46776e23			0.0226612			0.0113306	+	0.999936i	$0.496393\pi$
$410$	1.04661e25	+	7.58366e24i	1.57884	+	1.14402i
$411$		0			0
$412$	−1.11646e24	−	3.40650e24i	−0.160812	−	0.490665i
$413$		−	9.14460e23i		−	0.128718i
$414$		0			0
$415$	2.18345e25			2.93553
$416$	−2.06316e24	+	1.31613e22i	−0.271111	+	0.00172947i
$417$		0			0
$418$	−5.78332e23	+	7.98145e23i	−0.0726110	+	0.100209i
$419$		−	7.63206e24i		−	0.936717i	−0.883538	−	0.468359i	$-0.844846\pi$
$419$		−	7.63206e24i		−	0.936717i	0.883538	−	0.468359i	$-0.155154\pi$
$420$		0			0
$421$		−	5.87918e24i		−	0.689663i	−0.938665	−	0.344831i	$-0.887936\pi$
$421$		−	5.87918e24i		−	0.689663i	0.938665	−	0.344831i	$-0.112064\pi$
$422$	4.77801e24	+	3.46212e24i	0.547998	+	0.397077i
$423$		0			0
$424$	−2.23698e24	+	6.97544e24i	−0.245294	+	0.764885i
$425$	1.84133e25			1.97441
$426$		0			0
$427$		−	3.09121e24i		−	0.317004i
$428$	4.57534e23	−	1.49954e23i	0.0458889	−	0.0150398i
$429$		0			0
$430$	−6.82006e24	+	9.41223e24i	−0.654392	+	0.903114i
$431$	1.90683e25			1.78969			0.894843	−	0.446380i	$-0.147287\pi$
$431$	1.90683e25			1.78969			0.894843	+	0.446380i	$0.147287\pi$
$432$		0			0
$433$	6.62807e24			0.595322			0.297661	−	0.954672i	$-0.403794\pi$
$433$	6.62807e24			0.595322			0.297661	+	0.954672i	$0.403794\pi$
$434$	−6.36396e24	+	8.78278e24i	−0.559210	+	0.771756i
$435$		0			0
$436$	−1.21178e25	+	3.97152e24i	−1.01930	+	0.334068i
$437$			1.78104e25i			1.46588i
$438$		0			0
$439$	3.89484e24			0.306956			0.153478	−	0.988152i	$-0.450953\pi$
$439$	3.89484e24			0.306956			0.153478	+	0.988152i	$0.450953\pi$
$440$	2.16735e24	+	6.95056e23i	0.167159	+	0.0536068i
$441$		0			0
$442$	−3.16903e24	−	2.29626e24i	−0.234107	−	0.169633i
$443$		−	1.78700e25i		−	1.29208i	−0.763304	−	0.646039i	$-0.776424\pi$
$443$		−	1.78700e25i		−	1.29208i	0.763304	−	0.646039i	$-0.223576\pi$
$444$		0			0
$445$		−	1.50099e25i		−	1.03982i
$446$	−6.97559e24	+	9.62689e24i	−0.473042	+	0.652837i
$447$		0			0
$448$	6.22485e24	+	4.45022e24i	0.404565	+	0.289228i
$449$	−2.66924e25			−1.69843			−0.849215	−	0.528047i	$-0.822925\pi$
$449$	−2.66924e25			−1.69843			−0.849215	+	0.528047i	$0.822925\pi$
$450$		0			0
$451$			1.96770e24i			0.120028i
$452$	−8.98416e23	−	2.74122e24i	−0.0536614	−	0.163730i
$453$		0			0
$454$	−1.80394e25	−	1.30713e25i	−1.03322	−	0.748664i
$455$	4.05918e24			0.227683
$456$		0			0
$457$	3.50613e25			1.88636			0.943180	−	0.332283i	$-0.107819\pi$
$457$	3.50613e25			1.88636			0.943180	+	0.332283i	$0.107819\pi$
$458$	−2.15908e25	−	1.56446e25i	−1.13775	−	0.824408i
$459$		0			0
$460$	3.90825e25	−	1.28090e25i	1.97598	−	0.647615i
$461$		−	2.18646e25i		−	1.08289i	−0.840737	−	0.541443i	$-0.817878\pi$
$461$		−	2.18646e25i		−	1.08289i	0.840737	−	0.541443i	$-0.182122\pi$
$462$		0			0
$463$	1.52250e25			0.723666			0.361833	−	0.932243i	$-0.382151\pi$
$463$	1.52250e25			0.723666			0.361833	+	0.932243i	$0.382151\pi$
$464$	1.30082e25	+	1.77135e25i	0.605754	+	0.824864i
$465$		0			0
$466$	−4.82479e24	+	6.65861e24i	−0.215681	+	0.297658i
$467$		−	3.40954e25i		−	1.49343i	−0.665144	−	0.746715i	$-0.731630\pi$
$467$		−	3.40954e25i		−	1.49343i	0.665144	−	0.746715i	$-0.268370\pi$
$468$		0			0
$469$			8.04940e24i			0.338549i
$470$	4.45930e24	+	3.23118e24i	0.183796	+	0.133178i
$471$		0			0
$472$	1.99658e24	−	6.22583e24i	0.0790384	−	0.246461i
$473$	−1.76957e24			−0.0686574
$474$		0			0
$475$		−	5.91328e25i		−	2.20414i
$476$	4.52041e24	+	1.37925e25i	0.165163	+	0.503939i
$477$		0			0
$478$	−7.29112e24	+	1.00623e25i	−0.255994	+	0.353292i
$479$	1.65943e25			0.571177			0.285589	−	0.958352i	$-0.407811\pi$
$479$	1.65943e25			0.571177			0.285589	+	0.958352i	$0.407811\pi$
$480$		0			0
$481$	−1.17126e25			−0.387502
$482$	−8.54211e24	+	1.17888e25i	−0.277088	+	0.382404i
$483$		0			0
$484$	−9.87849e24	−	3.01409e25i	−0.308077	−	0.939996i
$485$		−	9.02573e25i		−	2.76017i
$486$		0			0
$487$	−4.18125e25			−1.22965			−0.614824	−	0.788664i	$-0.710773\pi$
$487$	−4.18125e25			−1.22965			−0.614824	+	0.788664i	$0.710773\pi$
$488$	6.74919e24	−	2.10456e25i	0.194654	−	0.606978i
$489$		0			0
$490$	3.70997e25	+	2.68823e25i	1.02922	+	0.745768i
$491$		−	1.21005e25i		−	0.329253i	−0.986356	−	0.164626i	$-0.947358\pi$
$491$		−	1.21005e25i		−	0.329253i	0.986356	−	0.164626i	$-0.0526419\pi$
$492$		0			0
$493$			4.16858e25i			1.09130i
$494$	−7.37426e24	+	1.01771e25i	−0.189370	+	0.261347i
$495$		0			0
$496$	−6.25030e25	+	4.59002e25i	−1.54463	+	1.13433i
$497$	−2.27807e25			−0.552309
$498$		0			0
$499$			2.17124e25i			0.506703i	0.967374	+	0.253351i	$0.0815329\pi$
$499$			2.17124e25i			0.506703i	−0.967374	+	0.253351i	$0.918467\pi$
$500$	−5.96780e25	+	1.95591e25i	−1.36647	+	0.447850i
$501$		0			0
$502$	5.36220e25	+	3.88542e25i	1.18211	+	0.856550i
$503$	9.72377e24			0.210348			0.105174	−	0.994454i	$-0.466460\pi$
$503$	9.72377e24			0.210348			0.105174	+	0.994454i	$0.466460\pi$
$504$		0			0
$505$	−3.52260e25			−0.733830
$506$	5.07029e24	+	3.67391e24i	0.103658	+	0.0751100i
$507$		0			0
$508$	−7.67372e24	−	2.34138e25i	−0.151113	−	0.461070i
$509$			7.14540e25i			1.38104i	0.723311	+	0.690522i	$0.242619\pi$
$509$			7.14540e25i			1.38104i	−0.723311	+	0.690522i	$0.757381\pi$
$510$		0			0
$511$	−4.45171e25			−0.828950
$512$	3.26637e25	+	4.38890e25i	0.597036	+	0.802215i
$513$		0			0
$514$	3.11532e25	−	4.29939e25i	0.548723	−	0.757282i
$515$			5.04255e25i			0.871930i
$516$		0			0
$517$			8.38382e23i			0.0139727i
$518$	3.51759e25	+	2.54883e25i	0.575589	+	0.417069i
$519$		0			0
$520$	2.76357e25	+	8.86260e24i	0.435953	+	0.139807i
$521$	2.53391e25			0.392494			0.196247	−	0.980554i	$-0.437125\pi$
$521$	2.53391e25			0.392494			0.196247	+	0.980554i	$0.437125\pi$
$522$		0			0
$523$		−	2.71691e25i		−	0.405798i	−0.979200	−	0.202899i	$-0.934964\pi$
$523$		−	2.71691e25i		−	0.405798i	0.979200	−	0.202899i	$-0.0650362\pi$
$524$	−2.56897e25	+	8.41963e24i	−0.376801	+	0.123494i
$525$		0			0
$526$	−5.44437e25	+	7.51367e25i	−0.770163	+	1.06289i
$527$	−1.47091e26			−2.04355
$528$		0			0
$529$	3.85265e25			0.516333
$530$	6.04603e25	−	8.34401e25i	0.795883	−	1.09838i
$531$		0			0
$532$	4.42936e25	−	1.45169e25i	0.562575	−	0.184380i
$533$			2.50900e25i			0.313034i
$534$		0			0
$535$	−6.77275e24			−0.0815463
$536$	−1.75746e25	+	5.48019e25i	−0.207884	+	0.648232i
$537$		0			0
$538$	−4.08074e25	−	2.95689e25i	−0.465916	−	0.337600i
$539$			6.97503e24i			0.0782444i
$540$		0			0
$541$		−	1.69248e26i		−	1.83295i	−0.400095	−	0.916474i	$-0.631023\pi$
$541$		−	1.69248e26i		−	1.83295i	0.400095	−	0.916474i	$-0.368977\pi$
$542$	−3.32227e25	+	4.58500e25i	−0.353542	+	0.487917i
$543$		0			0
$544$	6.61983e23	+	1.03772e26i	0.00680232	+	1.06633i
$545$	1.79376e26			1.81133
$546$		0			0
$547$			1.60559e25i			0.156586i	0.996930	+	0.0782932i	$0.0249470\pi$
$547$			1.60559e25i			0.156586i	−0.996930	+	0.0782932i	$0.975053\pi$
$548$	−2.06088e25	−	6.28809e25i	−0.197532	−	0.602703i
$549$		0			0
$550$	−1.68340e25	−	1.21978e25i	−0.155863	−	0.112937i
$551$	1.33871e26			1.21828
$552$		0			0
$553$	−5.65178e25			−0.496932
$554$	−2.34554e25	−	1.69957e25i	−0.202721	−	0.146891i
$555$		0			0
$556$	−1.76200e26	+	5.77485e25i	−1.47162	+	0.482314i
$557$		−	1.81361e25i		−	0.148909i	−0.997224	−	0.0744544i	$-0.976278\pi$
$557$		−	1.81361e25i		−	0.148909i	0.997224	−	0.0744544i	$-0.0237215\pi$
$558$		0			0
$559$	−2.25636e25			−0.179059
$560$	−6.37110e25	−	8.67561e25i	−0.497082	−	0.676883i
$561$		0			0
$562$	3.56778e25	−	4.92383e25i	0.269094	−	0.371371i
$563$			7.15020e25i			0.530260i	0.964213	+	0.265130i	$0.0854148\pi$
$563$			7.15020e25i			0.530260i	−0.964213	+	0.265130i	$0.914585\pi$
$564$		0			0
$565$			4.05775e25i			0.290955i
$566$	1.24331e26	+	9.00895e25i	0.876643	+	0.635211i
$567$		0			0
$568$	−1.55096e26	−	4.97382e25i	−1.05753	−	0.339142i
$569$	8.69099e25			0.582778			0.291389	−	0.956605i	$-0.405883\pi$
$569$	8.69099e25			0.582778			0.291389	+	0.956605i	$0.405883\pi$
$570$		0			0
$571$			2.62084e26i			1.69980i	0.526946	+	0.849899i	$0.323337\pi$
$571$			2.62084e26i			1.69980i	−0.526946	+	0.849899i	$0.676663\pi$
$572$	1.37607e24	+	4.19863e24i	0.00877767	+	0.0267822i
$573$		0			0
$574$	5.45995e25	−	7.53517e25i	0.336919	−	0.464976i
$575$	−3.75646e26			−2.28000
$576$		0			0
$577$	3.26333e25			0.191642			0.0958210	−	0.995399i	$-0.469452\pi$
$577$	3.26333e25			0.191642			0.0958210	+	0.995399i	$0.469452\pi$
$578$	−1.39253e25	+	1.92180e25i	−0.0804433	+	0.111018i
$579$		0			0
$580$	−9.62784e25	−	2.93762e26i	−0.538224	−	1.64221i
$581$		−	1.57200e26i		−	0.864530i
$582$		0			0
$583$	1.56874e25			0.0835024
$584$	−3.03081e26	−	9.71962e25i	−1.58722	−	0.509011i
$585$		0			0
$586$	−7.17146e25	−	5.19641e25i	−0.363564	−	0.263436i
$587$		−	6.88215e24i		−	0.0343291i	−0.999853	−	0.0171645i	$-0.994536\pi$
$587$		−	6.88215e24i		−	0.0343291i	0.999853	−	0.0171645i	$-0.00546391\pi$
$588$		0			0
$589$			4.72371e26i			2.28133i
$590$	−5.39629e25	+	7.44732e25i	−0.256449	+	0.353921i
$591$		0			0
$592$	1.83835e26	+	2.50330e26i	0.846002	+	1.15201i
$593$	2.74812e25			0.124456			0.0622281	−	0.998062i	$-0.480179\pi$
$593$	2.74812e25			0.124456			0.0622281	+	0.998062i	$0.480179\pi$
$594$		0			0
$595$		−	2.04167e26i		−	0.895518i
$596$	−1.93248e26	+	6.33357e25i	−0.834210	+	0.273407i
$597$		0			0
$598$	6.46508e25	+	4.68456e25i	0.270341	+	0.195888i
$599$	2.05361e26			0.845207			0.422604	−	0.906315i	$-0.361116\pi$
$599$	2.05361e26			0.845207			0.422604	+	0.906315i	$0.361116\pi$
$600$		0			0
$601$	−1.15717e26			−0.461414			−0.230707	−	0.973023i	$-0.574104\pi$
$601$	−1.15717e26			−0.461414			−0.230707	+	0.973023i	$0.574104\pi$
$602$	6.77645e25	+	4.91018e25i	0.265972	+	0.192722i
$603$		0			0
$604$	−2.03880e25	−	6.22074e25i	−0.0775398	−	0.236587i
$605$			4.46168e26i			1.67041i
$606$		0			0
$607$	−2.75446e25			−0.0999411			−0.0499705	−	0.998751i	$-0.515913\pi$
$607$	−2.75446e25			−0.0999411			−0.0499705	+	0.998751i	$0.515913\pi$
$608$	3.33255e26	−	2.12591e24i	1.19040	−	0.00759382i
$609$		0			0
$610$	−1.82415e26	+	2.51747e26i	−0.631577	+	0.871627i
$611$			1.06901e25i			0.0364411i
$612$		0			0
$613$			2.06636e26i			0.682860i	0.939907	+	0.341430i	$0.110911\pi$
$613$			2.06636e26i			0.682860i	−0.939907	+	0.341430i	$0.889089\pi$
$614$	−3.78109e26	−	2.73976e26i	−1.23032	−	0.891483i
$615$		0			0
$616$	5.00414e24	−	1.56041e25i	0.0157875	−	0.0492292i
$617$	−5.57410e26			−1.73167			−0.865837	−	0.500327i	$-0.833213\pi$
$617$	−5.57410e26			−1.73167			−0.865837	+	0.500327i	$0.833213\pi$
$618$		0			0
$619$		−	2.05924e26i		−	0.620363i	−0.950677	−	0.310182i	$-0.899610\pi$
$619$		−	2.05924e26i		−	0.620363i	0.950677	−	0.310182i	$-0.100390\pi$
$620$	1.03656e27	−	3.39724e26i	3.07519	−	1.00787i
$621$		0			0
$622$	5.93344e25	−	8.18863e25i	0.170725	−	0.235615i
$623$	−1.08066e26			−0.306232
$624$		0			0
$625$	2.09804e26			0.576706
$626$	2.50492e26	−	3.45699e26i	0.678167	−	0.935926i
$627$		0			0
$628$	−1.62820e26	+	5.33632e25i	−0.427653	+	0.140160i
$629$			5.89114e26i			1.52412i
$630$		0			0
$631$	−5.57503e26			−1.39948			−0.699742	−	0.714396i	$-0.746702\pi$
$631$	−5.57503e26			−1.39948			−0.699742	+	0.714396i	$0.746702\pi$
$632$	−3.84785e26	−	1.23398e26i	−0.951493	−	0.305137i
$633$		0			0
$634$	3.13958e26	+	2.27492e26i	0.753396	+	0.545907i
$635$			3.46588e26i			0.819338i
$636$		0			0
$637$			8.89380e25i			0.204062i
$638$	2.76147e25	−	3.81106e25i	0.0624230	−	0.0861487i
$639$		0			0
$640$	−2.44339e26	−	7.29756e26i	−0.536145	−	1.60128i
$641$	−7.78879e25			−0.168391			−0.0841955	−	0.996449i	$-0.526832\pi$
$641$	−7.78879e25			−0.168391			−0.0841955	+	0.996449i	$0.526832\pi$
$642$		0			0
$643$		−	6.65702e26i		−	1.39725i	−0.715486	−	0.698627i	$-0.753794\pi$
$643$		−	6.65702e26i		−	1.39725i	0.715486	−	0.698627i	$-0.246206\pi$
$644$	−9.22201e25	−	2.81379e26i	−0.190726	−	0.581937i
$645$		0			0
$646$	5.11882e26	+	3.70907e26i	1.02792	+	0.744828i
$647$	−3.44957e26			−0.682614			−0.341307	−	0.939952i	$-0.610870\pi$
$647$	−3.44957e26			−0.682614			−0.341307	+	0.939952i	$0.610870\pi$
$648$		0			0
$649$	−1.40015e25			−0.0269061
$650$	−2.14649e26	−	1.55534e26i	−0.406492	−	0.294542i
$651$		0			0
$652$	4.80606e26	−	1.57515e26i	0.883968	−	0.289715i
$653$		−	6.00601e26i		−	1.08871i	−0.838856	−	0.544354i	$-0.816775\pi$
$653$		−	6.00601e26i		−	1.08871i	0.838856	−	0.544354i	$-0.183225\pi$
$654$		0			0
$655$	3.80278e26			0.669589
$656$	5.36243e26	−	3.93800e26i	0.930626	−	0.683423i
$657$		0			0
$658$	2.32633e25	−	3.21052e25i	0.0392216	−	0.0541290i
$659$		−	2.01544e26i		−	0.334933i	−0.985878	−	0.167466i	$-0.946441\pi$
$659$		−	2.01544e26i		−	0.334933i	0.985878	−	0.167466i	$-0.0535585\pi$
$660$		0			0
$661$			3.42807e26i			0.553523i	0.960939	+	0.276761i	$0.0892611\pi$
$661$			3.42807e26i			0.553523i	−0.960939	+	0.276761i	$0.910739\pi$
$662$	1.14016e26	+	8.26156e25i	0.181475	+	0.131496i
$663$		0			0
$664$	3.43222e26	−	1.07025e27i	0.530858	−	1.65535i
$665$	−6.55666e26			−0.999717
$666$		0			0
$667$		−	8.50426e26i		−	1.26020i
$668$	1.08922e26	+	3.32338e26i	0.159125	+	0.485517i
$669$		0			0
$670$	4.75000e26	−	6.55539e26i	0.674502	−	0.930868i
$671$	−4.73304e25			−0.0662637
$672$		0			0
$673$	9.95640e25			0.135506			0.0677531	−	0.997702i	$-0.478417\pi$
$673$	9.95640e25			0.135506			0.0677531	+	0.997702i	$0.478417\pi$
$674$	−4.38039e26	+	6.04530e26i	−0.587820	+	0.811239i
$675$		0			0
$676$	−2.21164e26	−	6.74811e26i	−0.288550	−	0.880417i
$677$			8.97633e26i			1.15480i	0.816462	+	0.577400i	$0.195933\pi$
$677$			8.97633e26i			1.15480i	−0.816462	+	0.577400i	$0.804067\pi$
$678$		0			0
$679$	−6.49818e26			−0.812885
$680$	4.45767e26	−	1.39001e27i	0.549887	−	1.71468i
$681$		0			0
$682$	1.34475e26	+	9.74402e25i	0.161321	+	0.116893i
$683$		−	6.48900e26i		−	0.767681i	−0.923399	−	0.383841i	$-0.874601\pi$
$683$		−	6.48900e26i		−	0.767681i	0.923399	−	0.383841i	$-0.125399\pi$
$684$		0			0
$685$			9.30808e26i			1.07103i
$686$	4.50681e26	−	6.21977e26i	0.511435	−	0.705822i
$687$		0			0
$688$	3.54148e26	+	4.82248e26i	0.390926	+	0.532329i
$689$	2.00028e26			0.217775
$690$		0			0
$691$			1.77349e27i			1.87840i	0.343372	+	0.939200i	$0.388431\pi$
$691$			1.77349e27i			1.87840i	−0.343372	+	0.939200i	$0.611569\pi$
$692$	−5.23305e26	+	1.71510e26i	−0.546697	+	0.179176i
$693$		0			0
$694$	−7.41214e26	−	5.37080e26i	−0.753405	−	0.545914i
$695$	2.60825e27			2.61513
$696$		0			0
$697$	1.26196e27			1.23122
$698$	3.73974e26	+	2.70979e26i	0.359927	+	0.260801i
$699$		0			0
$700$	3.06183e26	+	9.34216e26i	0.286780	+	0.875016i
$701$			1.23835e27i			1.14425i	0.820166	+	0.572125i	$0.193881\pi$
$701$			1.23835e27i			1.14425i	−0.820166	+	0.572125i	$0.806119\pi$
$702$		0			0
$703$	1.89189e27			1.70146
$704$	6.81384e25	−	9.53102e25i	0.0604577	−	0.0845667i
$705$		0			0
$706$	−6.14870e26	+	8.48571e26i	−0.531054	+	0.732898i
$707$			2.53614e26i			0.216117i
$708$		0			0
$709$			4.11828e26i			0.341646i	0.985302	+	0.170823i	$0.0546427\pi$
$709$			4.11828e26i			0.341646i	−0.985302	+	0.170823i	$0.945357\pi$
$710$	1.85525e27	+	1.34431e27i	1.51862	+	1.10038i
$711$		0			0
$712$	−7.35732e26	−	2.35944e26i	−0.586354	−	0.188040i
$713$	3.00078e27			2.35984
$714$		0			0
$715$		−	6.21512e25i		−	0.0475929i
$716$	−1.52177e27	+	4.98749e26i	−1.14994	+	0.376885i
$717$		0			0
$718$	3.72820e26	−	5.14522e26i	0.274358	−	0.378636i
$719$	−2.65339e27			−1.92698			−0.963488	−	0.267753i	$-0.913719\pi$
$719$	−2.65339e27			−1.92698			−0.963488	+	0.267753i	$0.913719\pi$
$720$		0			0
$721$	3.63044e26			0.256788
$722$	3.50599e26	−	4.83855e26i	0.244741	−	0.337763i
$723$		0			0
$724$	2.03936e26	−	6.68385e25i	0.138668	−	0.0454476i
$725$			2.82353e27i			1.89488i
$726$		0			0
$727$	−5.35591e26			−0.350152			−0.175076	−	0.984555i	$-0.556017\pi$
$727$	−5.35591e26			−0.350152			−0.175076	+	0.984555i	$0.556017\pi$
$728$	6.38073e25	−	1.98967e26i	0.0411739	−	0.128390i
$729$		0			0
$730$	3.62545e27	+	2.62698e27i	2.27927	+	1.65154i
$731$			1.13490e27i			0.704273i
$732$		0			0
$733$		−	3.45816e26i		−	0.209102i	−0.994520	−	0.104551i	$-0.966659\pi$
$733$		−	3.45816e26i		−	0.209102i	0.994520	−	0.104551i	$-0.0333405\pi$
$734$	7.38317e26	−	1.01894e27i	0.440687	−	0.608184i
$735$		0			0
$736$	−1.35050e25	−	2.11703e27i	−0.00785517	−	1.23137i
$737$	1.23246e26			0.0707674
$738$		0			0
$739$		−	6.39162e26i		−	0.357675i	−0.983879	−	0.178838i	$-0.942766\pi$
$739$		−	6.39162e26i		−	0.357675i	0.983879	−	0.178838i	$-0.0572337\pi$
$740$	−1.36063e27	−	4.15151e27i	−0.751689	−	2.29353i
$741$		0			0
$742$	−6.00737e26	−	4.35291e26i	−0.323480	−	0.234392i
$743$	−1.77477e27			−0.943514			−0.471757	−	0.881729i	$-0.656380\pi$
$743$	−1.77477e27			−0.943514			−0.471757	+	0.881729i	$0.656380\pi$
$744$		0			0
$745$	2.86060e27			1.48242
$746$	1.13606e27	+	8.23186e26i	0.581278	+	0.421191i
$747$		0			0
$748$	2.11181e26	−	6.92131e25i	0.105339	−	0.0345242i
$749$			4.87612e25i			0.0240158i
$750$		0			0
$751$	−1.12256e27			−0.539050			−0.269525	−	0.962993i	$-0.586867\pi$
$751$	−1.12256e27			−0.539050			−0.269525	+	0.962993i	$0.586867\pi$
$752$	2.28478e26	−	1.67787e26i	0.108336	−	0.0795589i
$753$		0			0
$754$	3.52113e26	−	4.85944e26i	0.162800	−	0.224677i
$755$			9.20838e26i			0.420424i
$756$		0			0
$757$			1.11106e27i			0.494684i	0.968928	+	0.247342i	$0.0795571\pi$
$757$			1.11106e27i			0.494684i	−0.968928	+	0.247342i	$0.920443\pi$
$758$	−1.94474e27	−	1.40915e27i	−0.855076	−	0.619584i
$759$		0			0
$760$	−4.46391e27	−	1.43155e27i	−1.91419	−	0.613869i
$761$	−5.48843e26			−0.232431			−0.116215	−	0.993224i	$-0.537076\pi$
$761$	−5.48843e26			−0.232431			−0.116215	+	0.993224i	$0.537076\pi$
$762$		0			0
$763$		−	1.29144e27i		−	0.533447i
$764$	1.31489e27	+	4.01196e27i	0.536418	+	1.63670i
$765$		0			0
$766$	−1.66620e27	+	2.29949e27i	−0.663062	+	0.915079i
$767$	−1.78532e26			−0.0701715
$768$		0			0
$769$	−1.02318e27			−0.392331			−0.196166	−	0.980571i	$-0.562849\pi$
$769$	−1.02318e27			−0.392331			−0.196166	+	0.980571i	$0.562849\pi$
$770$	−1.35250e26	+	1.86656e26i	−0.0512243	+	0.0706937i
$771$		0			0
$772$	3.82799e25	+	1.16799e26i	0.0141451	+	0.0431592i
$773$		−	4.21302e27i		−	1.53776i	−0.639393	−	0.768880i	$-0.720814\pi$
$773$		−	4.21302e27i		−	1.53776i	0.639393	−	0.768880i	$-0.279186\pi$
$774$		0			0
$775$	−9.96298e27			−3.54832
$776$	−4.42409e27	−	1.41878e27i	−1.55646	−	0.499146i
$777$		0			0
$778$	1.03542e26	+	7.50260e25i	0.0355476	+	0.0257576i
$779$		−	4.05270e27i		−	1.37448i
$780$		0			0
$781$			3.48802e26i			0.115450i
$782$	2.35622e27	−	3.25177e27i	0.770463	−	1.06330i
$783$		0			0
$784$	1.90085e27	−	1.39593e27i	0.606661	−	0.445513i
$785$	2.41018e27			0.759956
$786$		0			0
$787$		−	4.46480e27i		−	1.37417i	−0.726575	−	0.687087i	$-0.758889\pi$
$787$		−	4.46480e27i		−	1.37417i	0.726575	−	0.687087i	$-0.241111\pi$
$788$	−8.40870e26	+	2.75589e26i	−0.255699	+	0.0838037i
$789$		0			0
$790$	4.60278e27	+	3.33515e27i	1.36635	+	0.990053i
$791$	2.92143e26			0.0856876
$792$		0			0
$793$	−6.03505e26			−0.172817
$794$	9.25933e24	+	6.70927e24i	0.00261990	+	0.00189837i
$795$		0			0
$796$	−1.56155e27	−	4.76456e27i	−0.431402	−	1.31628i
$797$		−	3.11016e27i		−	0.849042i	−0.905418	−	0.424521i	$-0.860442\pi$
$797$		−	3.11016e27i		−	0.849042i	0.905418	−	0.424521i	$-0.139558\pi$
$798$		0			0
$799$	5.37687e26			0.143329
$800$	4.48384e25	+	7.02883e27i	0.0118112	+	1.85152i
$801$		0			0
$802$	1.10401e26	−	1.52362e26i	0.0283999	−	0.0391941i
$803$			6.81612e26i			0.173277i
$804$		0			0
$805$			4.16518e27i			1.03412i
$806$	1.71468e27	+	1.24245e27i	0.420728	+	0.304857i
$807$		0			0
$808$	−5.53726e26	+	1.72665e27i	−0.132705	+	0.413806i
$809$	−7.90445e27			−1.87224			−0.936118	−	0.351686i	$-0.885608\pi$
$809$	−7.90445e27			−1.87224			−0.936118	+	0.351686i	$0.885608\pi$
$810$		0			0
$811$		−	2.25871e27i		−	0.522593i	−0.965259	−	0.261296i	$-0.915850\pi$
$811$		−	2.25871e27i		−	0.522593i	0.965259	−	0.261296i	$-0.0841500\pi$
$812$	−2.11497e27	+	6.93168e26i	−0.483640	+	0.158510i
$813$		0			0
$814$	3.90257e26	−	5.38587e26i	0.0871805	−	0.120316i
$815$	−7.11427e27			−1.57084
$816$		0			0
$817$	3.64463e27			0.786219
$818$	−6.23584e25	+	8.60596e25i	−0.0132965	+	0.0183503i
$819$		0			0
$820$	−8.89311e27	+	2.91466e27i	−1.85277	+	0.607233i
$821$			9.36979e26i			0.192961i	0.995335	+	0.0964806i	$0.0307586\pi$
$821$			9.36979e26i			0.192961i	−0.995335	+	0.0964806i	$0.969241\pi$
$822$		0			0
$823$	−7.47754e27			−1.50474			−0.752368	−	0.658743i	$-0.771088\pi$
$823$	−7.47754e27			−1.50474			−0.752368	+	0.658743i	$0.771088\pi$
$824$	2.47168e27	+	7.92651e26i	0.491681	+	0.157679i
$825$		0			0
$826$	5.36179e26	+	3.88512e26i	0.104232	+	0.0755256i
$827$		−	8.79290e26i		−	0.168978i	−0.996424	−	0.0844889i	$-0.973074\pi$
$827$		−	8.79290e26i		−	0.168978i	0.996424	−	0.0844889i	$-0.0269258\pi$
$828$		0			0
$829$			6.19276e27i			1.16310i	0.813511	+	0.581549i	$0.197553\pi$
$829$			6.19276e27i			1.16310i	−0.813511	+	0.581549i	$0.802447\pi$
$830$	−9.27649e27	+	1.28023e28i	−1.72243	+	2.37709i
$831$		0			0
$832$	8.68826e26	−	1.21529e27i	0.157674	−	0.220551i
$833$	4.47336e27			0.802614
$834$		0			0
$835$		−	4.91951e27i		−	0.862781i
$836$	−2.22272e26	−	6.78191e26i	−0.0385413	−	0.117596i
$837$		0			0
$838$	4.47493e27	+	3.24251e27i	0.758522	+	0.549621i
$839$	4.04517e27			0.677951			0.338975	−	0.940795i	$-0.389920\pi$
$839$	4.04517e27			0.677951			0.338975	+	0.940795i	$0.389920\pi$
$840$		0			0
$841$	−2.88922e26			−0.0473390
$842$	3.44716e27	+	2.49780e27i	0.558466	+	0.404662i
$843$		0			0
$844$	−4.05992e27	+	1.33061e27i	−0.643079	+	0.210765i
$845$			9.98903e27i			1.56453i
$846$		0			0
$847$	3.21224e27			0.491944
$848$	−3.13954e27	−	4.27516e27i	−0.475451	−	0.647429i
$849$		0			0
$850$	−7.82296e27	+	1.07963e28i	−1.15849	+	1.59881i
$851$		−	1.20184e28i		−	1.76001i
$852$		0			0
$853$			9.99086e27i			1.43083i	0.698701	+	0.715413i	$0.253762\pi$
$853$			9.99086e27i			1.43083i	−0.698701	+	0.715413i	$0.746238\pi$
$854$	1.81248e27	+	1.31332e27i	0.256699	+	0.186003i
$855$		0			0
$856$	−1.06463e26	+	3.31976e26i	−0.0147467	+	0.0459839i
$857$	7.95258e27			1.08941			0.544703	−	0.838629i	$-0.316642\pi$
$857$	7.95258e27			1.08941			0.544703	+	0.838629i	$0.316642\pi$
$858$		0			0
$859$		−	1.08517e28i		−	1.45400i	−0.686640	−	0.726998i	$-0.740915\pi$
$859$		−	1.08517e28i		−	1.45400i	0.686640	−	0.726998i	$-0.259085\pi$
$860$	−2.62118e27	−	7.99766e27i	−0.347345	−	1.05981i
$861$		0			0
$862$	−8.10123e27	+	1.11804e28i	−1.05010	+	1.44923i
$863$	−7.24244e27			−0.928501			−0.464250	−	0.885704i	$-0.653676\pi$
$863$	−7.24244e27			−0.928501			−0.464250	+	0.885704i	$0.653676\pi$
$864$		0			0
$865$	7.74633e27			0.971501
$866$	−2.81596e27	+	3.88626e27i	−0.349307	+	0.482072i
$867$		0			0
$868$	−2.44588e27	−	7.46281e27i	−0.296824	−	0.905659i
$869$			8.65358e26i			0.103874i
$870$		0			0
$871$	1.57150e27			0.184562
$872$	2.81966e27	−	8.79238e27i	0.327559	−	1.02141i
$873$		0			0
$874$	−1.04428e28	−	7.56681e27i	−1.18702	−	0.860111i
$875$		−	6.36012e27i		−	0.715136i
$876$		0			0
$877$		−	1.15489e28i		−	1.27070i	−0.772224	−	0.635350i	$-0.780856\pi$
$877$		−	1.15489e28i		−	1.27070i	0.772224	−	0.635350i	$-0.219144\pi$
$878$	−1.65474e27	+	2.28367e27i	−0.180107	+	0.248563i
$879$		0			0
$880$	−1.32834e27	+	9.75495e26i	−0.141490	+	0.103906i
$881$	−8.19582e26			−0.0863617			−0.0431809	−	0.999067i	$-0.513749\pi$
$881$	−8.19582e26			−0.0863617			−0.0431809	+	0.999067i	$0.513749\pi$
$882$		0			0
$883$			4.66342e27i			0.480926i	0.970658	+	0.240463i	$0.0772992\pi$
$883$			4.66342e27i			0.480926i	−0.970658	+	0.240463i	$0.922701\pi$
$884$	2.69275e27	−	8.82530e26i	0.274726	−	0.0900394i
$885$		0			0
$886$	1.04778e28	+	7.59214e27i	1.04628	+	0.758130i
$887$	1.92404e28			1.90081			0.950407	−	0.311009i	$-0.100667\pi$
$887$	1.92404e28			1.90081			0.950407	+	0.311009i	$0.100667\pi$
$888$		0			0
$889$	2.49530e27			0.241299
$890$	8.80081e27	+	6.37702e27i	0.842010	+	0.610117i
$891$		0			0
$892$	−2.68095e27	−	8.18005e27i	−0.251086	−	0.766107i
$893$		−	1.72674e27i		−	0.160007i
$894$		0			0
$895$	2.25263e28			2.04348
$896$	−5.25396e27	+	1.75914e27i	−0.471586	+	0.157898i
$897$		0			0
$898$	1.13404e28	−	1.56507e28i	0.996559	−	1.37533i
$899$		−	2.25552e28i		−	1.96123i
$900$		0			0
$901$		−	1.00609e28i		−	0.856549i
$902$	−1.15373e27	−	8.35986e26i	−0.0971945	−	0.0704266i
$903$		0			0
$904$	1.98896e27	+	6.37848e26i	0.164069	+	0.0526159i
$905$	−3.01880e27			−0.246419
$906$		0			0
$907$		−	2.50336e27i		−	0.200103i	−0.994982	−	0.100052i	$-0.968099\pi$
$907$		−	2.50336e27i		−	0.200103i	0.994982	−	0.100052i	$-0.0319008\pi$
$908$	1.53282e28	−	5.02372e27i	1.21249	−	0.397384i
$909$		0			0
$910$	−1.72456e27	+	2.38004e27i	−0.133594	+	0.184370i
$911$	−1.70782e27			−0.130923			−0.0654616	−	0.997855i	$-0.520852\pi$
$911$	−1.70782e27			−0.130923			−0.0654616	+	0.997855i	$0.520852\pi$
$912$		0			0
$913$	−2.40693e27			−0.180714
$914$	−1.48960e28	+	2.05576e28i	−1.10683	+	1.52751i
$915$		0			0
$916$	1.83459e28	−	6.01274e27i	1.33516	−	0.437588i
$917$		−	2.73785e27i		−	0.197198i
$918$		0			0
$919$	−3.74442e27			−0.264172			−0.132086	−	0.991238i	$-0.542168\pi$
$919$	−3.74442e27			−0.264172			−0.132086	+	0.991238i	$0.542168\pi$
$920$	−9.09401e27	+	2.83574e28i	−0.634996	+	1.98007i
$921$		0			0
$922$	1.28199e28	+	9.28927e27i	0.876884	+	0.635386i
$923$			4.44754e27i			0.301095i
$924$		0			0
$925$			3.99027e28i			2.64640i
$926$	−6.46841e27	+	8.92693e27i	−0.424613	+	0.586000i
$927$		0			0
$928$	−1.59126e28	+	1.01510e26i	−1.02337	+	0.00652833i
$929$	2.37867e28			1.51421			0.757104	−	0.653294i	$-0.226613\pi$
$929$	2.37867e28			1.51421			0.757104	+	0.653294i	$0.226613\pi$
$930$		0			0
$931$		−	1.43659e28i		−	0.896003i
$932$	−1.85433e27	−	5.65787e27i	−0.114482	−	0.349303i
$933$		0			0
$934$	1.99913e28	+	1.44856e28i	1.20933	+	0.876274i
$935$	−3.12605e27			−0.187191
$936$		0			0
$937$	−1.43366e28			−0.841243			−0.420621	−	0.907236i	$-0.638188\pi$
$937$	−1.43366e28			−0.841243			−0.420621	+	0.907236i	$0.638188\pi$
$938$	−4.71963e27	−	3.41982e27i	−0.274145	−	0.198644i
$939$		0			0
$940$	−3.78910e27	+	1.24185e27i	−0.215686	+	0.0706896i
$941$		−	3.81829e27i		−	0.215163i	−0.994196	−	0.107581i	$-0.965689\pi$
$941$		−	3.81829e27i		−	0.215163i	0.994196	−	0.107581i	$-0.0343106\pi$
$942$		0			0
$943$	−2.57451e28			−1.42178
$944$	2.80215e27	+	3.81573e27i	0.153200	+	0.208614i
$945$		0			0
$946$	7.51810e26	−	1.03756e27i	0.0402849	−	0.0555964i
$947$			1.04528e28i			0.554509i	0.960797	+	0.277254i	$0.0894245\pi$
$947$			1.04528e28i			0.554509i	−0.960797	+	0.277254i	$0.910576\pi$
$948$		0			0
$949$			8.69117e27i			0.451907i
$950$	3.46715e28	+	2.51228e28i	1.78484	+	1.29328i
$951$		0			0
$952$	−1.00075e28	−	3.20935e27i	−0.504982	−	0.161944i
$953$	1.43987e28			0.719349			0.359675	−	0.933078i	$-0.382888\pi$
$953$	1.43987e28			0.719349			0.359675	+	0.933078i	$0.382888\pi$
$954$		0			0
$955$		−	5.93879e28i		−	2.90848i
$956$	−2.80222e27	−	8.55005e27i	−0.135879	−	0.414590i
$957$		0			0
$958$	−7.05015e27	+	9.72978e27i	−0.335140	+	0.462520i
$959$	6.70146e27			0.315423
$960$		0			0
$961$	5.79167e28			2.67259
$962$	4.97614e27	−	6.86747e27i	0.227368	−	0.313786i
$963$		0			0
$964$	−3.28302e27	−	1.00170e28i	−0.147076	−	0.448754i
$965$		−	1.72894e27i		−	0.0766954i
$966$		0			0
$967$	−1.33691e28			−0.581500			−0.290750	−	0.956799i	$-0.593905\pi$
$967$	−1.33691e28			−0.581500			−0.290750	+	0.956799i	$0.593905\pi$
$968$	2.18696e28	+	7.01342e27i	0.941942	+	0.302075i
$969$		0			0
$970$	5.29209e28	+	3.83462e28i	2.23509	+	1.61954i
$971$		−	3.44674e28i		−	1.44154i	−0.693176	−	0.720768i	$-0.743789\pi$
$971$		−	3.44674e28i		−	1.44154i	0.693176	−	0.720768i	$-0.256211\pi$
$972$		0			0
$973$		−	1.87784e28i		−	0.770169i
$974$	1.77642e28	−	2.45161e28i	0.721499	−	0.995728i
$975$		0			0
$976$	9.47232e27	+	1.28986e28i	0.377297	+	0.513770i
$977$	−3.40684e28			−1.34386			−0.671930	−	0.740615i	$-0.734534\pi$
$977$	−3.40684e28			−1.34386			−0.671930	+	0.740615i	$0.734534\pi$
$978$		0			0
$979$			1.65462e27i			0.0640121i
$980$	−3.15240e28	+	1.03318e28i	−1.20779	+	0.395846i
$981$		0			0
$982$	7.09494e27	+	5.14096e27i	0.266618	+	0.193190i
$983$	−1.47311e28			−0.548246			−0.274123	−	0.961695i	$-0.588388\pi$
$983$	−1.47311e28			−0.548246			−0.274123	+	0.961695i	$0.588388\pi$
$984$		0			0
$985$	1.24472e28			0.454387
$986$	−2.44418e28	−	1.77104e28i	−0.883695	−	0.640321i
$987$		0			0
$988$	−2.83417e27	−	8.64755e27i	−0.100516	−	0.306692i
$989$		−	2.31528e28i		−	0.813278i
$990$		0			0
$991$	−3.41639e28			−1.17725			−0.588623	−	0.808407i	$-0.700330\pi$
$991$	−3.41639e28			−1.17725			−0.588623	+	0.808407i	$0.700330\pi$
$992$	−3.58183e26	−	5.61485e28i	−0.0122249	−	1.91636i
$993$		0			0
$994$	9.67850e27	−	1.33571e28i	0.324069	−	0.447241i
$995$			7.05284e28i			2.33908i
$996$		0			0
$997$		−	2.85756e28i		−	0.929805i	−0.885362	−	0.464902i	$-0.846089\pi$
$997$		−	2.85756e28i		−	0.929805i	0.885362	−	0.464902i	$-0.153911\pi$
$998$	−1.27307e28	−	9.22462e27i	−0.410311	−	0.297309i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	72.20.d.b.37.6		18
3.2	odd	2		8.20.b.a.5.13	✓	18
8.5	even	2	inner	72.20.d.b.37.5		18
12.11	even	2		32.20.b.a.17.12		18
24.5	odd	2		8.20.b.a.5.14	yes	18
24.11	even	2		32.20.b.a.17.7		18

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8.20.b.a.5.13	✓	18	3.2	odd	2
8.20.b.a.5.14	yes	18	24.5	odd	2
32.20.b.a.17.7		18	24.11	even	2
32.20.b.a.17.12		18	12.11	even	2
72.20.d.b.37.5		18	8.5	even	2	inner
72.20.d.b.37.6		18	1.1	even	1	trivial

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:	\( k \)	\(=\)	\( 20 \)
Character orbit:	\([\chi]\)	\(=\)	72.d (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-424.854 + 586.333i) q^{2} +(-163286. - 498212. i) q^{4} +7.37490e6i q^{5} +5.30965e7 q^{7} +(3.61491e8 + 1.15928e8i) q^{8} +(-4.32415e9 - 3.13326e9i) q^{10} -8.12973e8i q^{11} -1.03661e10i q^{13} +(-2.25583e10 + 3.11322e10i) q^{14} +(-2.21553e11 + 1.62702e11i) q^{16} -5.21391e11 q^{17} +1.67441e12i q^{19} +(3.67427e12 - 1.20422e12i) q^{20} +(4.76673e11 + 3.45395e11i) q^{22} +1.06368e13 q^{23} -3.53156e13 q^{25} +(6.07802e12 + 4.40410e12i) q^{26} +(-8.66989e12 - 2.64533e13i) q^{28} -7.99511e13i q^{29} +2.82112e14 q^{31} +(-1.26965e12 - 1.99029e14i) q^{32} +(2.21515e14 - 3.05709e14i) q^{34} +3.91581e14i q^{35} -1.12989e15i q^{37} +(-9.81761e14 - 7.11379e14i) q^{38} +(-8.54956e14 + 2.66596e15i) q^{40} -2.42038e15 q^{41} -2.17667e15i q^{43} +(-4.05033e14 + 1.32747e14i) q^{44} +(-4.51910e15 + 6.23672e15i) q^{46} -1.03125e15 q^{47} -8.57966e15 q^{49} +(1.50040e16 - 2.07067e16i) q^{50} +(-5.16454e15 + 1.69264e15i) q^{52} +1.92963e16i q^{53} +5.99559e15 q^{55} +(1.91939e16 + 6.15536e15i) q^{56} +(4.68780e16 + 3.39676e16i) q^{58} -1.72226e16i q^{59} -5.82188e16i q^{61} +(-1.19857e17 + 1.65412e17i) q^{62} +(1.17237e17 + 8.38138e16i) q^{64} +7.64493e16 q^{65} +1.51600e17i q^{67} +(8.51358e16 + 2.59764e17i) q^{68} +(-2.29597e17 - 1.66365e17i) q^{70} -4.29045e17 q^{71} -8.38419e17 q^{73} +(6.62491e17 + 4.80037e17i) q^{74} +(8.34211e17 - 2.73407e17i) q^{76} -4.31660e16i q^{77} -1.06444e18 q^{79} +(-1.19991e18 - 1.63393e18i) q^{80} +(1.02831e18 - 1.41915e18i) q^{82} -2.96065e18i q^{83} -3.84521e18i q^{85} +(1.27625e18 + 9.24766e17i) q^{86} +(9.42462e16 - 2.93883e17i) q^{88} -2.03527e18 q^{89} -5.50405e17i q^{91} +(-1.73684e18 - 5.29940e18i) q^{92} +(4.38133e17 - 6.04659e17i) q^{94} -1.23486e19 q^{95} -1.22385e19 q^{97} +(3.64511e18 - 5.03054e18i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 18 q + 458 q^{2} - 412108 q^{4} - 80707216 q^{7} + 173313752 q^{8} + 758800104 q^{10} + 122453668784 q^{14} - 696212072432 q^{16} - 14121426692 q^{17} - 6517087595632 q^{20} - 11074654117412 q^{22} - 2177121583952 q^{23}+ \cdots - 88\!\cdots\!22 q^{98}+O(q^{100}) \) 18 * q + 458 * q^2 - 412108 * q^4 - 80707216 * q^7 + 173313752 * q^8 + 758800104 * q^10 + 122453668784 * q^14 - 696212072432 * q^16 - 14121426692 * q^17 - 6517087595632 * q^20 - 11074654117412 * q^22 - 2177121583952 * q^23 - 44414474211734 * q^25 - 26782030269304 * q^26 - 97002327802784 * q^28 + 428505770260416 * q^31 - 122449430282912 * q^32 - 478448330325748 * q^34 + 486194587539796 * q^38 - 1697818250610976 * q^40 - 1200260021141524 * q^41 - 7031781193616424 * q^44 - 14917443628457488 * q^46 + 1134160959992928 * q^47 + 31570092936329058 * q^49 + 34734151321861826 * q^50 - 26877456911772208 * q^52 - 51757047863478736 * q^55 - 52858270161183424 * q^56 - 20470056808312424 * q^58 - 93766686763697984 * q^62 - 253721318369185216 * q^64 + 184007586011668640 * q^65 - 201388986348307752 * q^68 - 340698473416023872 * q^70 + 1599477989199799056 * q^71 - 93004298989809068 * q^73 + 93558253821761240 * q^74 - 1090379619519933176 * q^76 + 1813975801025264480 * q^79 - 3057120301750869696 * q^80 - 2418785089528546244 * q^82 - 1332333723895598620 * q^86 - 3097741184498130608 * q^88 - 4470509771045743540 * q^89 + 2965990502259463392 * q^92 - 3533635112749329696 * q^94 - 23809730986995679856 * q^95 + 8246429789464117220 * q^97 - 8841667592735478822 * q^98

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