LMFDB - Embedded newform 36.33.d.b.19.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [36,33,Mod(19,36)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(36, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 33, names="a")

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

chi := DirichletCharacter("36.19");

S:= CuspForms(chi, 33);

N := Newforms(S);

Level:	$ N $	$=$	$ 36 = 2^{2} \cdot 3^{2} $
Weight:	$ k $	$=$	$ 33 $
Character orbit:	$[\chi]$	$=$	36.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:	$233.519958512$
Analytic rank:	$0$
Dimension:	$14$
Coefficient field:	$\mathbb{Q}[x]/(x^{14} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{14} - 2 x^{13} + \cdots + 14\!\cdots\!00 $ x^14 - 2x^13 + 9908582210366388423701407x^12 - 8086811312184504416198453608163876x^11 + 37405696613034355742044961924532536232196387188631x^10 - 23967245486347359096340195260317848310298537718567913502866x^9 + 66242167963727172731981497199893034024106297462627614478569459875355082433x^8 + 26083342528284667843809328930901913280380991116670007441644373018174057471562657304x^7 + 53211111349226757955236284041675612414616879072055733957779796413942354982120453658633802959840248x^6 + 130568052823388987480787282317472440860477934857615337860200410718075575507010323142108374100462635255939232x^5 + 14218633454594290381653882162061992351310214926866457046465831121598124876878342861858935466706714610876614837654091632784x^4 + 95128576135542061922951273389005694868240523677280496503718751132181580640597603192233724288211402324629649228698495463742310120064x^3 + 106659529774879839046874897450256163097463871227896597630135686097797297816051233796716344513792743013061728191822414438633304079884586605034240x^2 - 748136622941085299881986954907550052585975638698845524851040659174207772383986632947990765215720398283397111840494569827815481257242194462879461396633600*x + 1412553279760522403662278831384374862593416871748973473283212732072617708021143367724549193323116564646691593364247878015385748132738933779314492941420657045504000
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{182}\cdot 3^{29}\cdot 5^{6} $
Twist minimal:	no (minimal twist has level 4)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			19.7
Root			$-4.89209e9 + 1.78639e12i$ of defining polynomial
Character	$\chi$	$=$	36.19
Dual form			36.33.d.b.19.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(15224.0 - 63743.2i) q^{2} +(-3.83143e9 - 1.94085e9i) q^{4} +1.46681e11 q^{5} -5.71644e13i q^{7} +(-1.82046e14 + 2.14680e14i) q^{8} +O(q^{10})$	\(q+(15224.0 - 63743.2i) q^{2} +(-3.83143e9 - 1.94085e9i) q^{4} +1.46681e11 q^{5} -5.71644e13i q^{7} +(-1.82046e14 + 2.14680e14i) q^{8} +(2.23307e15 - 9.34993e15i) q^{10} +6.39967e16i q^{11} +3.82332e17 q^{13} +(-3.64385e18 - 8.70272e17i) q^{14} +(1.09129e19 + 1.48725e19i) q^{16} +4.07694e19 q^{17} +6.13984e19i q^{19} +(-5.61998e20 - 2.84687e20i) q^{20} +(4.07936e21 + 9.74287e20i) q^{22} -2.81087e20i q^{23} -1.76771e21 q^{25} +(5.82063e21 - 2.43711e22i) q^{26} +(-1.10948e23 + 2.19021e23i) q^{28} -9.24035e22 q^{29} -4.23845e23i q^{31} +(1.11416e24 - 4.69206e23i) q^{32} +(6.20674e23 - 2.59877e24i) q^{34} -8.38495e24i q^{35} -4.96114e23 q^{37} +(3.91373e24 + 9.34729e23i) q^{38} +(-2.67027e25 + 3.14895e25i) q^{40} -7.78015e25 q^{41} -5.67810e24i q^{43} +(1.24208e26 - 2.45199e26i) q^{44} +(-1.79174e25 - 4.27927e24i) q^{46} -2.70622e26i q^{47} -2.16335e27 q^{49} +(-2.69116e25 + 1.12679e26i) q^{50} +(-1.46488e27 - 7.42051e26i) q^{52} -1.23036e27 q^{53} +9.38712e27i q^{55} +(1.22721e28 + 1.04066e28i) q^{56} +(-1.40675e27 + 5.89010e27i) q^{58} -3.43224e27i q^{59} +4.92044e28 q^{61} +(-2.70172e28 - 6.45261e27i) q^{62} +(-1.29467e28 - 7.81632e28i) q^{64} +5.60809e28 q^{65} -1.86282e29i q^{67} +(-1.56205e29 - 7.91275e28i) q^{68} +(-5.34483e29 - 1.27652e29i) q^{70} -7.39887e29i q^{71} +1.01270e30 q^{73} +(-7.55284e27 + 3.16239e28i) q^{74} +(1.19165e29 - 2.35243e29i) q^{76} +3.65834e30 q^{77} -2.63707e30i q^{79} +(1.60072e30 + 2.18151e30i) q^{80} +(-1.18445e30 + 4.95932e30i) q^{82} +5.56904e30i q^{83} +5.98011e30 q^{85} +(-3.61940e29 - 8.64434e28i) q^{86} +(-1.37388e31 - 1.16503e31i) q^{88} -1.36383e31 q^{89} -2.18558e31i q^{91} +(-5.45549e29 + 1.07697e30i) q^{92} +(-1.72503e31 - 4.11995e30i) q^{94} +9.00598e30i q^{95} -9.37964e31 q^{97} +(-3.29348e31 + 1.37899e32i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 14 q + 23780 q^{2} - 2922848368 q^{4} - 138121491740 q^{5} + 191366550113600 q^{8}+O(q^{10}) $ 14 * q + 23780 * q^2 - 2922848368 * q^4 - 138121491740 * q^5 + 191366550113600 * q^8	$ 14 q + 23780 q^{2} - 2922848368 q^{4} - 138121491740 q^{5} + 191366550113600 q^{8} + 31\!\cdots\!00 q^{10}+ \cdots + 46\!\cdots\!00 q^{98}+O(q^{100}) $ 14 * q + 23780 * q^2 - 2922848368 * q^4 - 138121491740 * q^5 + 191366550113600 * q^8 + 31775605694457400 * q^10 - 1640418469677858020 * q^13 - 7731597686180285568 * q^14 - 30570843123186593536 * q^16 - 31570967905797256220 * q^17 - 2022222335397731344160 * q^20 + 5453282318362187158080 * q^22 + 10252879651857697291050 * q^25 + 100487287286439222842824 * q^26 + 287406099989137745118720 * q^28 + 383350228001906510553316 * q^29 + 3049085458330908760601600 * q^32 + 2968198158688225453161016 * q^34 - 10743727036349878681805540 * q^37 + 23674230631082905997232960 * q^38 + 46284510399605997225174400 * q^40 - 36301708465641824663518748 * q^41 + 341183497187317069095824640 * q^44 - 292611965791335032977170048 * q^46 - 4831123780514350255580603890 * q^49 + 510591072029103065039587500 * q^50 - 9698318635805895955111735520 * q^52 - 18428895934780252746021636380 * q^53 - 6374003242890184756165527552 * q^56 - 38529567312130296955877295560 * q^58 + 106402038936127775684939892508 * q^61 - 21568431972603200921875622400 * q^62 - 196737301243248539525687308288 * q^64 - 113178238686492542374351007800 * q^65 - 354271480525935415641826176800 * q^68 - 514873634674652910315035354880 * q^70 + 1432707125192338982920850898460 * q^73 + 984194129445064624850959434184 * q^74 - 782627770945775078204519980800 * q^76 + 3080015547766001613074070589440 * q^77 - 6279147555674556254006737379840 * q^80 - 4557892929168088074284564686280 * q^82 + 6758108895547933966316548575800 * q^85 + 23458263349697798020331664550848 * q^86 + 11102138256776653733497151431680 * q^88 + 18473812211636703183423448507876 * q^89 - 60798444498044060215697222361600 * q^92 - 130643574777689548682138472237312 * q^94 - 201795139515948373218799959195620 * q^97 + 460006462884606019803763245136100 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/36\mathbb{Z}\right)^\times$.

$n$	$19$	$29$
$\chi(n)$	$-1$	$1$

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 $

$2$	15224.0	−	63743.2i	0.232300	−	0.972644i
$2$	15224.0	−	63743.2i	0.232300	−	0.972644i
$3$		0			0
$3$		0			0
$4$	−3.83143e9	−	1.94085e9i	−0.892074	−	0.451890i
$5$	1.46681e11			0.961290			0.480645	−	0.876915i	$-0.340403\pi$
$5$	1.46681e11			0.961290			0.480645	+	0.876915i	$0.340403\pi$
$6$		0			0
$7$		−	5.71644e13i		−	1.72011i	−0.510198	−	0.860057i	$-0.670428\pi$
$7$		−	5.71644e13i		−	1.72011i	0.510198	−	0.860057i	$-0.329572\pi$
$8$	−1.82046e14	+	2.14680e14i	−0.646757	+	0.762696i
$9$		0			0
$10$	2.23307e15	−	9.34993e15i	0.223307	−	0.934993i
$11$			6.39967e16i			1.39276i	0.717675	+	0.696378i	$0.245206\pi$
$11$			6.39967e16i			1.39276i	−0.717675	+	0.696378i	$0.754794\pi$
$12$		0			0
$13$	3.82332e17			0.574576			0.287288	−	0.957844i	$-0.407246\pi$
$13$	3.82332e17			0.574576			0.287288	+	0.957844i	$0.407246\pi$
$14$	−3.64385e18	−	8.70272e17i	−1.67306	−	0.399582i
$15$		0			0
$16$	1.09129e19	+	1.48725e19i	0.591590	+	0.806239i
$17$	4.07694e19			0.837822			0.418911	−	0.908027i	$-0.362412\pi$
$17$	4.07694e19			0.837822			0.418911	+	0.908027i	$0.362412\pi$
$18$		0			0
$19$			6.13984e19i			0.212863i	0.994320	+	0.106431i	$0.0339424\pi$
$19$			6.13984e19i			0.212863i	−0.994320	+	0.106431i	$0.966058\pi$
$20$	−5.61998e20	−	2.84687e20i	−0.857541	−	0.434397i
$21$		0			0
$22$	4.07936e21	+	9.74287e20i	1.35466	+	0.323537i
$23$		−	2.81087e20i		−	0.0458348i	−0.999737	−	0.0229174i	$-0.992705\pi$
$23$		−	2.81087e20i		−	0.0458348i	0.999737	−	0.0229174i	$-0.00729548\pi$
$24$		0			0
$25$	−1.76771e21			−0.0759224
$26$	5.82063e21	−	2.43711e22i	0.133474	−	0.558858i
$27$		0			0
$28$	−1.10948e23	+	2.19021e23i	−0.777303	+	1.53447i
$29$	−9.24035e22			−0.369250			−0.184625	−	0.982809i	$-0.559107\pi$
$29$	−9.24035e22			−0.369250			−0.184625	+	0.982809i	$0.559107\pi$
$30$		0			0
$31$		−	4.23845e23i		−	0.582666i	−0.956622	−	0.291333i	$-0.905901\pi$
$31$		−	4.23845e23i		−	0.582666i	0.956622	−	0.291333i	$-0.0940987\pi$
$32$	1.11416e24	−	4.69206e23i	0.921610	−	0.388118i
$33$		0			0
$34$	6.20674e23	−	2.59877e24i	0.194626	−	0.814903i
$35$		−	8.38495e24i		−	1.65353i
$36$		0			0
$37$	−4.96114e23			−0.0402118			−0.0201059	−	0.999798i	$-0.506400\pi$
$37$	−4.96114e23			−0.0402118			−0.0201059	+	0.999798i	$0.506400\pi$
$38$	3.91373e24	+	9.34729e23i	0.207040	+	0.0494480i
$39$		0			0
$40$	−2.67027e25	+	3.14895e25i	−0.621721	+	0.733172i
$41$	−7.78015e25			−1.22024			−0.610121	−	0.792308i	$-0.708879\pi$
$41$	−7.78015e25			−1.22024			−0.610121	+	0.792308i	$0.708879\pi$
$42$		0			0
$43$		−	5.67810e24i		−	0.0415631i	−0.999784	−	0.0207815i	$-0.993385\pi$
$43$		−	5.67810e24i		−	0.0415631i	0.999784	−	0.0207815i	$-0.00661544\pi$
$44$	1.24208e26	−	2.45199e26i	0.629373	−	1.24244i
$45$		0			0
$46$	−1.79174e25	−	4.27927e24i	−0.0445810	−	0.0106474i
$47$		−	2.70622e26i		−	0.477307i	−0.971105	−	0.238653i	$-0.923294\pi$
$47$		−	2.70622e26i		−	0.477307i	0.971105	−	0.238653i	$-0.0767059\pi$
$48$		0			0
$49$	−2.16335e27			−1.95879
$50$	−2.69116e25	+	1.12679e26i	−0.0176368	+	0.0738454i
$51$		0			0
$52$	−1.46488e27	−	7.42051e26i	−0.512564	−	0.259645i
$53$	−1.23036e27			−0.317408			−0.158704	−	0.987326i	$-0.550732\pi$
$53$	−1.23036e27			−0.317408			−0.158704	+	0.987326i	$0.550732\pi$
$54$		0			0
$55$			9.38712e27i			1.33884i
$56$	1.22721e28	+	1.04066e28i	1.31192	+	1.11250i
$57$		0			0
$58$	−1.40675e27	+	5.89010e27i	−0.0857768	+	0.359149i
$59$		−	3.43224e27i		−	0.159201i	−0.996827	−	0.0796005i	$-0.974636\pi$
$59$		−	3.43224e27i		−	0.159201i	0.996827	−	0.0796005i	$-0.0253645\pi$
$60$		0			0
$61$	4.92044e28			1.33883			0.669416	−	0.742888i	$-0.266544\pi$
$61$	4.92044e28			1.33883			0.669416	+	0.742888i	$0.266544\pi$
$62$	−2.70172e28	−	6.45261e27i	−0.566726	−	0.135353i
$63$		0			0
$64$	−1.29467e28	−	7.81632e28i	−0.163411	−	0.986558i
$65$	5.60809e28			0.552333
$66$		0			0
$67$		−	1.86282e29i		−	1.12973i	−0.825184	−	0.564864i	$-0.808929\pi$
$67$		−	1.86282e29i		−	1.12973i	0.825184	−	0.564864i	$-0.191071\pi$
$68$	−1.56205e29	−	7.91275e28i	−0.747399	−	0.378604i
$69$		0			0
$70$	−5.34483e29	−	1.27652e29i	−1.60829	−	0.384114i
$71$		−	7.39887e29i		−	1.77432i	−0.461463	−	0.887159i	$-0.652675\pi$
$71$		−	7.39887e29i		−	1.77432i	0.461463	−	0.887159i	$-0.347325\pi$
$72$		0			0
$73$	1.01270e30			1.55710			0.778549	−	0.627583i	$-0.215956\pi$
$73$	1.01270e30			1.55710			0.778549	+	0.627583i	$0.215956\pi$
$74$	−7.55284e27	+	3.16239e28i	−0.00934120	+	0.0391118i
$75$		0			0
$76$	1.19165e29	−	2.35243e29i	0.0961905	−	0.189889i
$77$	3.65834e30			2.39570
$78$		0			0
$79$		−	2.63707e30i		−	1.14575i	−0.819644	−	0.572874i	$-0.805829\pi$
$79$		−	2.63707e30i		−	1.14575i	0.819644	−	0.572874i	$-0.194171\pi$
$80$	1.60072e30	+	2.18151e30i	0.568690	+	0.775029i
$81$		0			0
$82$	−1.18445e30	+	4.95932e30i	−0.283462	+	1.18686i
$83$			5.56904e30i			1.09782i	0.835882	+	0.548910i	$0.184957\pi$
$83$			5.56904e30i			1.09782i	−0.835882	+	0.548910i	$0.815043\pi$
$84$		0			0
$85$	5.98011e30			0.805390
$86$	−3.61940e29	−	8.64434e28i	−0.0404261	−	0.00965510i
$87$		0			0
$88$	−1.37388e31	−	1.16503e31i	−1.06225	−	0.900775i
$89$	−1.36383e31			−0.880073			−0.440037	−	0.897980i	$-0.645035\pi$
$89$	−1.36383e31			−0.880073			−0.440037	+	0.897980i	$0.645035\pi$
$90$		0			0
$91$		−	2.18558e31i		−	0.988336i
$92$	−5.45549e29	+	1.07697e30i	−0.0207123	+	0.0408880i
$93$		0			0
$94$	−1.72503e31	−	4.11995e30i	−0.464249	−	0.110878i
$95$			9.00598e30i			0.204623i
$96$		0			0
$97$	−9.37964e31			−1.52700			−0.763499	−	0.645809i	$-0.776520\pi$
$97$	−9.37964e31			−1.52700			−0.763499	+	0.645809i	$0.776520\pi$
$98$	−3.29348e31	+	1.37899e32i	−0.455028	+	1.90521i
$99$		0			0
$100$	6.77283e30	+	3.43086e30i	0.0677283	+	0.0343086i
$101$	−5.72813e30			−0.0488507			−0.0244253	−	0.999702i	$-0.507776\pi$
$101$	−5.72813e30			−0.0488507			−0.0244253	+	0.999702i	$0.507776\pi$
$102$		0			0
$103$		−	9.76491e31i		−	0.608517i	−0.952590	−	0.304258i	$-0.901591\pi$
$103$		−	9.76491e31i		−	0.608517i	0.952590	−	0.304258i	$-0.0984087\pi$
$104$	−6.96020e31	+	8.20790e31i	−0.371611	+	0.438227i
$105$		0			0
$106$	−1.87310e31	+	7.84271e31i	−0.0737339	+	0.308725i
$107$		−	2.83419e32i		−	0.960038i	−0.877258	−	0.480019i	$-0.840630\pi$
$107$		−	2.83419e32i		−	0.960038i	0.877258	−	0.480019i	$-0.159370\pi$
$108$		0			0
$109$	−2.57765e32			−0.649232			−0.324616	−	0.945846i	$-0.605235\pi$
$109$	−2.57765e32			−0.649232			−0.324616	+	0.945846i	$0.605235\pi$
$110$	5.98365e32	+	1.42910e32i	1.30222	+	0.311013i
$111$		0			0
$112$	8.50177e32	−	6.23831e32i	1.38682	−	1.01760i
$113$	−2.01143e32			−0.284610			−0.142305	−	0.989823i	$-0.545451\pi$
$113$	−2.01143e32			−0.284610			−0.142305	+	0.989823i	$0.545451\pi$
$114$		0			0
$115$		−	4.12302e31i		−	0.0440606i
$116$	3.54037e32	+	1.79342e32i	0.329398	+	0.166861i
$117$		0			0
$118$	−2.18782e32	−	5.22525e31i	−0.154846	−	0.0369824i
$119$		−	2.33056e33i		−	1.44115i
$120$		0			0
$121$	−1.98421e33			−0.939768
$122$	7.49087e32	−	3.13644e33i	0.311011	−	1.30221i
$123$		0			0
$124$	−8.22620e32	+	1.62393e33i	−0.263301	+	0.519781i
$125$	−3.67448e33			−1.03427
$126$		0			0
$127$		−	7.58615e33i		−	1.65639i	−0.560442	−	0.828194i	$-0.689369\pi$
$127$		−	7.58615e33i		−	1.65639i	0.560442	−	0.828194i	$-0.310631\pi$
$128$	−5.17947e33	−	3.64691e32i	−0.997530	−	0.0702370i
$129$		0			0
$130$	8.53776e32	−	3.57478e33i	0.128307	−	0.537224i
$131$		−	7.08226e33i		−	0.941523i	−0.882261	−	0.470761i	$-0.843979\pi$
$131$		−	7.08226e33i		−	0.941523i	0.882261	−	0.470761i	$-0.156021\pi$
$132$		0			0
$133$	3.50980e33			0.366148
$134$	−1.18742e34	−	2.83596e33i	−1.09882	−	0.262436i
$135$		0			0
$136$	−7.42191e33	+	8.75238e33i	−0.541868	+	0.639004i
$137$	1.56966e34			1.01924			0.509620	−	0.860399i	$-0.329786\pi$
$137$	1.56966e34			1.01924			0.509620	+	0.860399i	$0.329786\pi$
$138$		0			0
$139$			1.66363e34i			0.856680i	0.903618	+	0.428340i	$0.140901\pi$
$139$			1.66363e34i			0.856680i	−0.903618	+	0.428340i	$0.859099\pi$
$140$	−1.62740e34	+	3.21263e34i	−0.747213	+	1.47507i
$141$		0			0
$142$	−4.71628e34	−	1.12640e34i	−1.72578	−	0.412174i
$143$			2.44680e34i			0.800243i
$144$		0			0
$145$	−1.35539e34			−0.354956
$146$	1.54174e34	−	6.45529e34i	0.361714	−	1.51450i
$147$		0			0
$148$	1.90082e33	+	9.62884e32i	0.0358719	+	0.0181713i
$149$	−3.15083e33			−0.0533881			−0.0266941	−	0.999644i	$-0.508498\pi$
$149$	−3.15083e33			−0.0533881			−0.0266941	+	0.999644i	$0.508498\pi$
$150$		0			0
$151$		−	6.49171e34i		−	0.888644i	−0.895867	−	0.444322i	$-0.853445\pi$
$151$		−	6.49171e34i		−	0.888644i	0.895867	−	0.444322i	$-0.146555\pi$
$152$	−1.31810e34	−	1.11773e34i	−0.162349	−	0.137670i
$153$		0			0
$154$	5.56946e34	−	2.33194e35i	0.556521	−	2.33016i
$155$		−	6.21700e34i		−	0.560111i
$156$		0			0
$157$	−2.59905e35			−1.90731			−0.953653	−	0.300908i	$-0.902710\pi$
$157$	−2.59905e35			−1.90731			−0.953653	+	0.300908i	$0.902710\pi$
$158$	−1.68096e35	−	4.01468e34i	−1.11440	−	0.266157i
$159$		0			0
$160$	1.63426e35	−	6.88236e34i	0.885934	−	0.373093i
$161$	−1.60682e34			−0.0788412
$162$		0			0
$163$			1.38465e34i			0.0557619i	0.999611	+	0.0278809i	$0.00887593\pi$
$163$			1.38465e34i			0.0557619i	−0.999611	+	0.0278809i	$0.991124\pi$
$164$	2.98091e35	+	1.51001e35i	1.08855	+	0.551416i
$165$		0			0
$166$	3.54989e35	+	8.47831e34i	1.06779	+	0.255023i
$167$			6.26917e35i			1.71296i	0.516182	+	0.856479i	$0.327353\pi$
$167$			6.26917e35i			1.71296i	−0.516182	+	0.856479i	$0.672647\pi$
$168$		0			0
$169$	−2.96601e35			−0.669863
$170$	9.10412e34	−	3.81191e35i	0.187092	−	0.783358i
$171$		0			0
$172$	−1.10204e34	+	2.17552e34i	−0.0187819	+	0.0370773i
$173$	1.09058e36			1.69403			0.847014	−	0.531570i	$-0.178398\pi$
$173$	1.09058e36			1.69403			0.847014	+	0.531570i	$0.178398\pi$
$174$		0			0
$175$			1.01050e35i			0.130595i
$176$	−9.51790e35	+	6.98391e35i	−1.12289	+	0.823941i
$177$		0			0
$178$	−2.07629e35	+	8.69346e35i	−0.204441	+	0.855998i
$179$		−	1.61896e36i		−	1.45743i	−0.684815	−	0.728717i	$-0.740117\pi$
$179$		−	1.61896e36i		−	1.45743i	0.684815	−	0.728717i	$-0.259883\pi$
$180$		0			0
$181$	−8.32130e35			−0.627096			−0.313548	−	0.949572i	$-0.601518\pi$
$181$	−8.32130e35			−0.627096			−0.313548	+	0.949572i	$0.601518\pi$
$182$	−1.39316e36	−	3.32733e35i	−0.961299	−	0.229590i
$183$		0			0
$184$	6.03438e34	+	5.11708e34i	0.0349581	+	0.0296440i
$185$	−7.27705e34			−0.0386552
$186$		0			0
$187$			2.60911e36i			1.16688i
$188$	−5.25238e35	+	1.03687e36i	−0.215690	+	0.425793i
$189$		0			0
$190$	5.74070e35	+	1.37107e35i	0.199025	+	0.0475338i
$191$		−	2.12110e36i		−	0.676127i	−0.941123	−	0.338063i	$-0.890228\pi$
$191$		−	2.12110e36i		−	0.676127i	0.941123	−	0.338063i	$-0.109772\pi$
$192$		0			0
$193$	5.32606e36			1.43711			0.718553	−	0.695472i	$-0.244805\pi$
$193$	5.32606e36			1.43711			0.718553	+	0.695472i	$0.244805\pi$
$194$	−1.42796e36	+	5.97888e36i	−0.354721	+	1.48523i
$195$		0			0
$196$	8.28870e36	+	4.19874e36i	1.74739	+	0.885160i
$197$	3.57225e36			0.694195			0.347098	−	0.937829i	$-0.387167\pi$
$197$	3.57225e36			0.694195			0.347098	+	0.937829i	$0.387167\pi$
$198$		0			0
$199$			2.75249e36i			0.455069i	0.973770	+	0.227534i	$0.0730664\pi$
$199$			2.75249e36i			0.455069i	−0.973770	+	0.227534i	$0.926934\pi$
$200$	3.21804e35	−	3.79491e35i	0.0491033	−	0.0579057i
$201$		0			0
$202$	−8.72050e34	+	3.65129e35i	−0.0113480	+	0.0475143i
$203$			5.28220e36i			0.635152i
$204$		0			0
$205$	−1.14120e37			−1.17301
$206$	−6.22447e36	−	1.48661e36i	−0.591871	−	0.141358i
$207$		0			0
$208$	4.17236e36	+	5.68623e36i	0.339913	+	0.463245i
$209$	−3.92930e36			−0.296466
$210$		0			0
$211$		−	2.17197e36i		−	0.140713i	−0.997522	−	0.0703567i	$-0.977586\pi$
$211$		−	2.17197e36i		−	0.140713i	0.997522	−	0.0703567i	$-0.0224137\pi$
$212$	4.71403e36	+	2.38795e36i	0.283151	+	0.143434i
$213$		0			0
$214$	−1.80660e37	−	4.31477e36i	−0.933775	−	0.223017i
$215$		−	8.32870e35i		−	0.0399541i
$216$		0			0
$217$	−2.42288e37			−1.00225
$218$	−3.92422e36	+	1.64308e37i	−0.150817	+	0.631472i
$219$		0			0
$220$	1.82190e37	−	3.59660e37i	0.605009	−	1.19434i
$221$	1.55875e37			0.481392
$222$		0			0
$223$			2.64062e36i			0.0706038i	0.999377	+	0.0353019i	$0.0112393\pi$
$223$			2.64062e36i			0.0706038i	−0.999377	+	0.0353019i	$0.988761\pi$
$224$	−2.68219e37	−	6.36902e37i	−0.667607	−	1.58527i
$225$		0			0
$226$	−3.06220e36	+	1.28215e37i	−0.0661148	+	0.276824i
$227$			4.82575e37i			0.970847i	0.874279	+	0.485423i	$0.161335\pi$
$227$			4.82575e37i			0.970847i	−0.874279	+	0.485423i	$0.838665\pi$
$228$		0			0
$229$	−6.43637e37			−1.12531			−0.562656	−	0.826691i	$-0.690221\pi$
$229$	−6.43637e37			−1.12531			−0.562656	+	0.826691i	$0.690221\pi$
$230$	−2.62815e36	−	6.27689e35i	−0.0428552	−	0.0102353i
$231$		0			0
$232$	1.68217e37	−	1.98372e37i	0.238815	−	0.281626i
$233$	−9.66736e37			−1.28119			−0.640594	−	0.767880i	$-0.721312\pi$
$233$	−9.66736e37			−1.28119			−0.640594	+	0.767880i	$0.721312\pi$
$234$		0			0
$235$		−	3.96951e37i		−	0.458830i
$236$	−6.66148e36	+	1.31504e37i	−0.0719414	+	0.142019i
$237$		0			0
$238$	−1.48558e38	−	3.54805e37i	−1.40173	−	0.334779i
$239$			9.30138e37i			0.820694i	0.911930	+	0.410347i	$0.134592\pi$
$239$			9.30138e37i			0.820694i	−0.911930	+	0.410347i	$0.865408\pi$
$240$		0			0
$241$	1.83413e38			1.41631			0.708155	−	0.706057i	$-0.249528\pi$
$241$	1.83413e38			1.41631			0.708155	+	0.706057i	$0.249528\pi$
$242$	−3.02076e37	+	1.26480e38i	−0.218308	+	0.914060i
$243$		0			0
$244$	−1.88523e38	−	9.54985e37i	−1.19434	−	0.605005i
$245$	−3.17322e38			−1.88297
$246$		0			0
$247$			2.34746e37i			0.122306i
$248$	9.09909e37	+	7.71592e37i	0.444397	+	0.376843i
$249$		0			0
$250$	−5.59402e37	+	2.34223e38i	−0.240262	+	1.00598i
$251$		−	1.81978e38i		−	0.733229i	−0.930373	−	0.366614i	$-0.880517\pi$
$251$		−	1.81978e38i		−	0.733229i	0.930373	−	0.366614i	$-0.119483\pi$
$252$		0			0
$253$	1.79887e37			0.0638367
$254$	−4.83566e38	−	1.15492e38i	−1.61108	−	0.384779i
$255$		0			0
$256$	−1.02099e38	+	3.24604e38i	−0.300042	+	0.953926i
$257$	−1.81708e38			−0.501700			−0.250850	−	0.968026i	$-0.580710\pi$
$257$	−1.81708e38			−0.501700			−0.250850	+	0.968026i	$0.580710\pi$
$258$		0			0
$259$			2.83601e37i			0.0691689i
$260$	−2.14870e38	−	1.08845e38i	−0.492722	−	0.249594i
$261$		0			0
$262$	−4.51446e38	−	1.07820e38i	−0.915767	−	0.218716i
$263$			1.03099e38i			0.196772i	0.995148	+	0.0983859i	$0.0313680\pi$
$263$			1.03099e38i			0.196772i	−0.995148	+	0.0983859i	$0.968632\pi$
$264$		0			0
$265$	−1.80471e38			−0.305121
$266$	5.34333e37	−	2.23726e38i	0.0850561	−	0.356132i
$267$		0			0
$268$	−3.61546e38	+	7.13726e38i	−0.510513	+	1.00780i
$269$	−7.79655e38			−1.03721			−0.518604	−	0.855014i	$-0.673548\pi$
$269$	−7.79655e38			−1.03721			−0.518604	+	0.855014i	$0.673548\pi$
$270$		0			0
$271$		−	1.53349e38i		−	0.181206i	−0.995887	−	0.0906032i	$-0.971121\pi$
$271$		−	1.53349e38i		−	0.181206i	0.995887	−	0.0906032i	$-0.0288795\pi$
$272$	4.44913e38	+	6.06343e38i	0.495648	+	0.675485i
$273$		0			0
$274$	2.38965e38	−	1.00055e39i	0.236770	−	0.991359i
$275$		−	1.13127e38i		−	0.105741i
$276$		0			0
$277$	−4.47583e38			−0.372561			−0.186280	−	0.982497i	$-0.559643\pi$
$277$	−4.47583e38			−0.372561			−0.186280	+	0.982497i	$0.559643\pi$
$278$	1.06045e39	+	2.53270e38i	0.833245	+	0.199007i
$279$		0			0
$280$	1.80008e39	+	1.52645e39i	1.26114	+	1.06943i
$281$	−2.40210e39			−1.58961			−0.794804	−	0.606867i	$-0.792426\pi$
$281$	−2.40210e39			−1.58961			−0.794804	+	0.606867i	$0.792426\pi$
$282$		0			0
$283$			1.34695e39i			0.795736i	0.917443	+	0.397868i	$0.130250\pi$
$283$			1.34695e39i			0.795736i	−0.917443	+	0.397868i	$0.869750\pi$
$284$	−1.43601e39	+	2.83482e39i	−0.801798	+	1.58282i
$285$		0			0
$286$	1.55967e39	+	3.72501e38i	0.778352	+	0.185896i
$287$			4.44748e39i			2.09896i
$288$		0			0
$289$	−7.05765e38			−0.298054
$290$	−2.06344e38	+	8.63966e38i	−0.0824563	+	0.345246i
$291$		0			0
$292$	−3.88010e39	−	1.96551e39i	−1.38905	−	0.703638i
$293$	−1.19107e39			−0.403696			−0.201848	−	0.979417i	$-0.564695\pi$
$293$	−1.19107e39			−0.403696			−0.201848	+	0.979417i	$0.564695\pi$
$294$		0			0
$295$		−	5.03445e38i		−	0.153038i
$296$	9.03155e37	−	1.06506e38i	0.0260073	−	0.0306694i
$297$		0			0
$298$	−4.79683e37	+	2.00844e38i	−0.0124021	+	0.0519276i
$299$		−	1.07469e38i		−	0.0263356i
$300$		0			0
$301$	−3.24585e38			−0.0714932
$302$	−4.13802e39	−	9.88298e38i	−0.864335	−	0.206432i
$303$		0			0
$304$	−9.13146e38	+	6.70035e38i	−0.171618	+	0.125927i
$305$	7.21735e39			1.28701
$306$		0			0
$307$			9.61787e39i			1.54477i	0.635152	+	0.772387i	$0.280937\pi$
$307$			9.61787e39i			1.54477i	−0.635152	+	0.772387i	$0.719063\pi$
$308$	−1.40167e40	−	7.10030e39i	−2.13714	−	1.08259i
$309$		0			0
$310$	−3.96292e39	−	9.46477e38i	−0.544788	−	0.130114i
$311$			1.94296e39i			0.253687i	0.991923	+	0.126844i	$0.0404846\pi$
$311$			1.94296e39i			0.253687i	−0.991923	+	0.126844i	$0.959515\pi$
$312$		0			0
$313$	−5.24329e39			−0.617866			−0.308933	−	0.951084i	$-0.599972\pi$
$313$	−5.24329e39			−0.617866			−0.308933	+	0.951084i	$0.599972\pi$
$314$	−3.95680e39	+	1.65672e40i	−0.443067	+	1.85513i
$315$		0			0
$316$	−5.11818e39	+	1.01038e40i	−0.517752	+	1.02209i
$317$	−3.19617e39			−0.307384			−0.153692	−	0.988119i	$-0.549116\pi$
$317$	−3.19617e39			−0.307384			−0.153692	+	0.988119i	$0.549116\pi$
$318$		0			0
$319$		−	5.91353e39i		−	0.514275i
$320$	−1.89904e39	−	1.14651e40i	−0.157085	−	0.948368i
$321$		0			0
$322$	−2.44622e38	+	1.02424e39i	−0.0183148	+	0.0766844i
$323$			2.50318e39i			0.178341i
$324$		0			0
$325$	−6.75851e38			−0.0436231
$326$	8.82619e38	+	2.10799e38i	0.0542365	+	0.0129535i
$327$		0			0
$328$	1.41634e40	−	1.67024e40i	0.789201	−	0.930674i
$329$	−1.54700e40			−0.821022
$330$		0			0
$331$		−	3.13828e40i		−	1.51163i	−0.654788	−	0.755813i	$-0.727242\pi$
$331$		−	3.13828e40i		−	1.51163i	0.654788	−	0.755813i	$-0.272758\pi$
$332$	1.08087e40	−	2.13374e40i	0.496094	−	0.979336i
$333$		0			0
$334$	3.99617e40	+	9.54419e39i	1.66610	+	0.397920i
$335$		−	2.73240e40i		−	1.08600i
$336$		0			0
$337$	−4.25178e40			−1.53636			−0.768178	−	0.640236i	$-0.778836\pi$
$337$	−4.25178e40			−1.53636			−0.768178	+	0.640236i	$0.778836\pi$
$338$	−4.51546e39	+	1.89063e40i	−0.155609	+	0.651538i
$339$		0			0
$340$	−2.29123e40	−	1.16065e40i	−0.718467	−	0.363948i
$341$	2.71247e40			0.811511
$342$		0			0
$343$			6.05325e40i			1.64923i
$344$	1.21897e39	+	1.03367e39i	0.0317000	+	0.0268812i
$345$		0			0
$346$	1.66030e40	−	6.95172e40i	0.393523	−	1.64769i
$347$		−	6.07154e40i		−	1.37413i	−0.726597	−	0.687064i	$-0.758899\pi$
$347$		−	6.07154e40i		−	1.37413i	0.726597	−	0.687064i	$-0.241101\pi$
$348$		0			0
$349$	−1.47031e40			−0.303530			−0.151765	−	0.988417i	$-0.548496\pi$
$349$	−1.47031e40			−0.303530			−0.151765	+	0.988417i	$0.548496\pi$
$350$	6.44124e39	+	1.53838e39i	0.127023	+	0.0303372i
$351$		0			0
$352$	3.00276e40	+	7.13025e40i	0.540553	+	1.28358i
$353$	−4.72487e40			−0.812821			−0.406410	−	0.913691i	$-0.633220\pi$
$353$	−4.72487e40			−0.812821			−0.406410	+	0.913691i	$0.633220\pi$
$354$		0			0
$355$		−	1.08527e41i		−	1.70563i
$356$	5.22540e40	+	2.64699e40i	0.785090	+	0.397697i
$357$		0			0
$358$	−1.03198e41	−	2.46471e40i	−1.41756	−	0.338562i
$359$			7.34931e40i			0.965463i	0.875769	+	0.482731i	$0.160355\pi$
$359$			7.34931e40i			0.965463i	−0.875769	+	0.482731i	$0.839645\pi$
$360$		0			0
$361$	7.94287e40			0.954690
$362$	−1.26684e40	+	5.30427e40i	−0.145674	+	0.609941i
$363$		0			0
$364$	−4.24189e40	+	8.37389e40i	−0.446619	+	0.881668i
$365$	1.48544e41			1.49682
$366$		0			0
$367$		−	2.06487e40i		−	0.190649i	−0.995446	−	0.0953245i	$-0.969611\pi$
$367$		−	2.06487e40i		−	0.190649i	0.995446	−	0.0953245i	$-0.0303889\pi$
$368$	4.18046e39	−	3.06748e39i	0.0369538	−	0.0271154i
$369$		0			0
$370$	−1.10786e39	+	4.63863e39i	−0.00897959	+	0.0375977i
$371$			7.03328e40i			0.545979i
$372$		0			0
$373$	1.13423e41			0.807907			0.403954	−	0.914780i	$-0.367636\pi$
$373$	1.13423e41			0.807907			0.403954	+	0.914780i	$0.367636\pi$
$374$	1.66313e41	+	3.97211e40i	1.13496	+	0.271067i
$375$		0			0
$376$	5.80971e40	+	4.92656e40i	0.364040	+	0.308701i
$377$	−3.53288e40			−0.212162
$378$		0			0
$379$			3.63335e40i			0.200484i	0.994963	+	0.100242i	$0.0319617\pi$
$379$			3.63335e40i			0.200484i	−0.994963	+	0.100242i	$0.968038\pi$
$380$	1.74793e40	−	3.45058e40i	0.0924670	−	0.182538i
$381$		0			0
$382$	−1.35206e41	−	3.22917e40i	−0.657631	−	0.157064i
$383$		−	1.98232e40i		−	0.0924686i	−0.998931	−	0.0462343i	$-0.985278\pi$
$383$		−	1.98232e40i		−	0.0924686i	0.998931	−	0.0462343i	$-0.0147221\pi$
$384$		0			0
$385$	5.36609e41			2.30296
$386$	8.10839e40	−	3.39500e41i	0.333840	−	1.39779i
$387$		0			0
$388$	3.59374e41	+	1.82045e41i	1.36219	+	0.690035i
$389$	1.68951e41			0.614563			0.307282	−	0.951619i	$-0.400581\pi$
$389$	1.68951e41			0.614563			0.307282	+	0.951619i	$0.400581\pi$
$390$		0			0
$391$		−	1.14598e40i		−	0.0384015i
$392$	3.93828e41	−	4.64427e41i	1.26686	−	1.49396i
$393$		0			0
$394$	5.43839e40	−	2.27706e41i	0.161262	−	0.675205i
$395$		−	3.86809e41i		−	1.10139i
$396$		0			0
$397$	2.48937e40			0.0653794			0.0326897	−	0.999466i	$-0.489593\pi$
$397$	2.48937e40			0.0653794			0.0326897	+	0.999466i	$0.489593\pi$
$398$	1.75453e41	+	4.19040e40i	0.442620	+	0.105712i
$399$		0			0
$400$	−1.92908e40	−	2.62902e40i	−0.0449149	−	0.0612116i
$401$	1.93121e41			0.432035			0.216017	−	0.976389i	$-0.430693\pi$
$401$	1.93121e41			0.432035			0.216017	+	0.976389i	$0.430693\pi$
$402$		0			0
$403$		−	1.62049e41i		−	0.334786i
$404$	2.19469e40	+	1.11175e40i	0.0435784	+	0.0220751i
$405$		0			0
$406$	3.36704e41	+	8.04162e40i	0.617777	+	0.147546i
$407$		−	3.17496e40i		−	0.0560052i
$408$		0			0
$409$	−6.28224e41			−1.02457			−0.512285	−	0.858816i	$-0.671201\pi$
$409$	−6.28224e41			−1.02457			−0.512285	+	0.858816i	$0.671201\pi$
$410$	−1.73737e41	+	7.27438e41i	−0.272489	+	1.14092i
$411$		0			0
$412$	−1.89523e41	+	3.74135e41i	−0.274983	+	0.542842i
$413$	−1.96202e41			−0.273844
$414$		0			0
$415$			8.16874e41i			1.05532i
$416$	4.25978e41	−	1.79392e41i	0.529534	−	0.223003i
$417$		0			0
$418$	−5.98196e40	+	2.50466e41i	−0.0688689	+	0.288355i
$419$		−	5.12219e41i		−	0.567586i	−0.958886	−	0.283793i	$-0.908407\pi$
$419$		−	5.12219e41i		−	0.567586i	0.958886	−	0.283793i	$-0.0915928\pi$
$420$		0			0
$421$	1.70891e41			0.175471			0.0877355	−	0.996144i	$-0.472037\pi$
$421$	1.70891e41			0.175471			0.0877355	+	0.996144i	$0.472037\pi$
$422$	−1.38449e41	−	3.30661e40i	−0.136864	−	0.0326877i
$423$		0			0
$424$	2.23982e41	−	2.64133e41i	0.205286	−	0.242086i
$425$	−7.20683e40			−0.0636095
$426$		0			0
$427$		−	2.81274e42i		−	2.30294i
$428$	−5.50075e41	+	1.08590e42i	−0.433832	+	0.856424i
$429$		0			0
$430$	−5.30898e40	−	1.26796e40i	−0.0388612	−	0.00928134i
$431$			2.81567e41i			0.198584i	0.995058	+	0.0992922i	$0.0316579\pi$
$431$			2.81567e41i			0.198584i	−0.995058	+	0.0992922i	$0.968342\pi$
$432$		0			0
$433$	−2.65364e42			−1.73795			−0.868973	−	0.494859i	$-0.835220\pi$
$433$	−2.65364e42			−1.73795			−0.868973	+	0.494859i	$0.835220\pi$
$434$	−3.68860e41	+	1.54442e42i	−0.232823	+	0.974834i
$435$		0			0
$436$	9.87608e41	+	5.00284e41i	0.579163	+	0.293382i
$437$	1.72583e40			0.00975652
$438$		0			0
$439$		−	1.28733e42i		−	0.676482i	−0.941059	−	0.338241i	$-0.890168\pi$
$439$		−	1.28733e42i		−	0.676482i	0.941059	−	0.338241i	$-0.109832\pi$
$440$	−2.01522e42	−	1.70889e42i	−1.02113	−	0.865905i
$441$		0			0
$442$	2.37304e41	−	9.93595e41i	0.111827	−	0.468223i
$443$		−	1.10165e42i		−	0.500708i	−0.968154	−	0.250354i	$-0.919453\pi$
$443$		−	1.10165e42i		−	0.500708i	0.968154	−	0.250354i	$-0.0805471\pi$
$444$		0			0
$445$	−2.00048e42			−0.846005
$446$	1.68322e41	+	4.02008e40i	0.0686724	+	0.0164013i
$447$		0			0
$448$	−4.46816e42	+	7.40092e41i	−1.69699	+	0.281085i
$449$	1.09716e42			0.402093			0.201047	−	0.979582i	$-0.435566\pi$
$449$	1.09716e42			0.402093			0.201047	+	0.979582i	$0.435566\pi$
$450$		0			0
$451$		−	4.97904e42i		−	1.69950i
$452$	7.70664e41	+	3.90389e41i	0.253893	+	0.128612i
$453$		0			0
$454$	3.07609e42	+	7.34672e41i	0.944289	+	0.225528i
$455$		−	3.20583e42i		−	0.950077i
$456$		0			0
$457$	6.91623e42			1.91078			0.955389	−	0.295351i	$-0.0954364\pi$
$457$	6.91623e42			1.91078			0.955389	+	0.295351i	$0.0954364\pi$
$458$	−9.79873e41	+	4.10275e42i	−0.261410	+	1.09453i
$459$		0			0
$460$	−8.00218e40	+	1.57970e41i	−0.0199105	+	0.0393053i
$461$	−2.42051e40			−0.00581690			−0.00290845	−	0.999996i	$-0.500926\pi$
$461$	−2.42051e40			−0.00581690			−0.00290845	+	0.999996i	$0.500926\pi$
$462$		0			0
$463$			7.32467e42i			1.64245i	0.570604	+	0.821225i	$0.306709\pi$
$463$			7.32467e42i			1.64245i	−0.570604	+	0.821225i	$0.693291\pi$
$464$	−1.00839e42	−	1.37427e42i	−0.218445	−	0.297704i
$465$		0			0
$466$	−1.47176e42	+	6.16228e42i	−0.297620	+	1.24614i
$467$			5.77631e41i			0.112870i	0.998406	+	0.0564352i	$0.0179734\pi$
$467$			5.77631e41i			0.112870i	−0.998406	+	0.0564352i	$0.982027\pi$
$468$		0			0
$469$	−1.06487e43			−1.94326
$470$	−2.53030e42	−	6.04319e41i	−0.446278	−	0.106586i
$471$		0			0
$472$	7.36834e41	+	6.24826e41i	0.121422	+	0.102964i
$473$	3.63380e41			0.0578872
$474$		0			0
$475$		−	1.08534e41i		−	0.0161610i
$476$	−4.52328e42	+	8.92938e42i	−0.651242	+	1.28561i
$477$		0			0
$478$	5.92900e42	+	1.41604e42i	0.798243	+	0.190647i
$479$			9.75812e42i			1.27057i	0.772278	+	0.635284i	$0.219117\pi$
$479$			9.75812e42i			1.27057i	−0.772278	+	0.635284i	$0.780883\pi$
$480$		0			0
$481$	−1.89680e41			−0.0231047
$482$	2.79229e42	−	1.16914e43i	0.329009	−	1.37757i
$483$		0			0
$484$	7.60234e42	+	3.85105e42i	0.838342	+	0.424672i
$485$	−1.37582e43			−1.46789
$486$		0			0
$487$		−	8.73926e42i		−	0.872994i	−0.899706	−	0.436497i	$-0.856219\pi$
$487$		−	8.73926e42i		−	0.872994i	0.899706	−	0.436497i	$-0.143781\pi$
$488$	−8.95745e42	+	1.05632e43i	−0.865899	+	1.02112i
$489$		0			0
$490$	−4.83091e42	+	2.02271e43i	−0.437413	+	1.83146i
$491$		−	6.41960e42i		−	0.562606i	−0.959619	−	0.281303i	$-0.909233\pi$
$491$		−	6.41960e42i		−	0.562606i	0.959619	−	0.281303i	$-0.0907665\pi$
$492$		0			0
$493$	−3.76724e42			−0.309366
$494$	1.49634e42	+	3.57377e41i	0.118960	+	0.0284116i
$495$		0			0
$496$	6.30362e42	−	4.62538e42i	0.469768	−	0.344699i
$497$	−4.22952e43			−3.05203
$498$		0			0
$499$			1.60910e43i			1.08886i	0.838805	+	0.544432i	$0.183255\pi$
$499$			1.60910e43i			1.08886i	−0.838805	+	0.544432i	$0.816745\pi$
$500$	1.40785e43	+	7.13162e42i	0.922647	+	0.467378i
$501$		0			0
$502$	−1.15999e43	−	2.77043e42i	−0.713171	−	0.170329i
$503$			9.65906e42i			0.575238i	0.957745	+	0.287619i	$0.0928636\pi$
$503$			9.65906e42i			0.575238i	−0.957745	+	0.287619i	$0.907136\pi$
$504$		0			0
$505$	−8.40208e41			−0.0469597
$506$	2.73860e41	−	1.14666e42i	0.0148293	−	0.0620904i
$507$		0			0
$508$	−1.47236e43	+	2.90658e43i	−0.748506	+	1.47762i
$509$	3.22003e43			1.58626			0.793132	−	0.609050i	$-0.208449\pi$
$509$	3.22003e43			1.58626			0.793132	+	0.609050i	$0.208449\pi$
$510$		0			0
$511$		−	5.78906e43i		−	2.67839i
$512$	1.91370e43	+	1.14499e43i	0.858131	+	0.513431i
$513$		0			0
$514$	−2.76633e42	+	1.15827e43i	−0.116545	+	0.487976i
$515$		−	1.43233e43i		−	0.584961i
$516$		0			0
$517$	1.73189e43			0.664771
$518$	1.80776e42	+	4.31754e41i	0.0672767	+	0.0160679i
$519$		0			0
$520$	−1.02093e43	+	1.20394e43i	−0.357226	+	0.421263i
$521$	2.63327e43			0.893494			0.446747	−	0.894660i	$-0.352582\pi$
$521$	2.63327e43			0.893494			0.446747	+	0.894660i	$0.352582\pi$
$522$		0			0
$523$		−	5.37407e43i		−	1.71505i	−0.514444	−	0.857524i	$-0.672002\pi$
$523$		−	5.37407e43i		−	1.71505i	0.514444	−	0.857524i	$-0.327998\pi$
$524$	−1.37456e43	+	2.71351e43i	−0.425465	+	0.839908i
$525$		0			0
$526$	6.57187e42	+	1.56958e42i	0.191389	+	0.0457101i
$527$		−	1.72799e43i		−	0.488170i
$528$		0			0
$529$	3.75299e43			0.997899
$530$	−2.74749e42	+	1.15038e43i	−0.0708796	+	0.296774i
$531$		0			0
$532$	−1.34476e43	−	6.81202e42i	−0.326631	−	0.165459i
$533$	−2.97460e43			−0.701122
$534$		0			0
$535$		−	4.15722e43i		−	0.922874i
$536$	3.99910e43	+	3.39119e43i	0.861639	+	0.730660i
$537$		0			0
$538$	−1.18695e43	+	4.96977e43i	−0.240943	+	1.00883i
$539$		−	1.38447e44i		−	2.72812i
$540$		0			0
$541$	−4.14984e43			−0.770682			−0.385341	−	0.922774i	$-0.625916\pi$
$541$	−4.14984e43			−0.770682			−0.385341	+	0.922774i	$0.625916\pi$
$542$	−9.77498e42	−	2.33459e42i	−0.176249	−	0.0420942i
$543$		0			0
$544$	4.54236e43	−	1.91292e43i	0.772145	−	0.325174i
$545$	−3.78093e43			−0.624100
$546$		0			0
$547$		−	8.89957e43i		−	1.38539i	−0.721231	−	0.692694i	$-0.756424\pi$
$547$		−	8.89957e43i		−	1.38539i	0.721231	−	0.692694i	$-0.243576\pi$
$548$	−6.01404e43	−	3.04648e43i	−0.909238	−	0.460585i
$549$		0			0
$550$	−7.21110e42	−	1.72225e42i	−0.102849	−	0.0245637i
$551$		−	5.67343e42i		−	0.0785995i
$552$		0			0
$553$	−1.50747e44			−1.97082
$554$	−6.81401e42	+	2.85304e43i	−0.0865459	+	0.362369i
$555$		0			0
$556$	3.22885e43	−	6.37406e43i	0.387125	−	0.764222i
$557$	4.03548e43			0.470123			0.235062	−	0.971980i	$-0.424471\pi$
$557$	4.03548e43			0.470123			0.235062	+	0.971980i	$0.424471\pi$
$558$		0			0
$559$		−	2.17092e42i		−	0.0238811i
$560$	1.24705e44	−	9.15042e43i	1.33314	−	0.978211i
$561$		0			0
$562$	−3.65696e43	+	1.53118e44i	−0.369266	+	1.54612i
$563$			5.34292e43i			0.524378i	0.965017	+	0.262189i	$0.0844444\pi$
$563$			5.34292e43i			0.524378i	−0.965017	+	0.262189i	$0.915556\pi$
$564$		0			0
$565$	−2.95039e43			−0.273592
$566$	8.58590e43	+	2.05060e43i	0.773968	+	0.184849i
$567$		0			0
$568$	1.58839e44	+	1.34693e44i	1.35327	+	1.14755i
$569$	−9.27836e42			−0.0768555			−0.0384277	−	0.999261i	$-0.512235\pi$
$569$	−9.27836e42			−0.0768555			−0.0384277	+	0.999261i	$0.512235\pi$
$570$		0			0
$571$		−	2.36677e43i		−	0.185344i	−0.995697	−	0.0926719i	$-0.970459\pi$
$571$		−	2.36677e43i		−	0.185344i	0.995697	−	0.0926719i	$-0.0295408\pi$
$572$	4.74888e43	−	9.37474e43i	0.361622	−	0.713876i
$573$		0			0
$574$	2.83497e44	+	6.77084e43i	2.04154	+	0.487588i
$575$			4.96879e41i			0.00347989i
$576$		0			0
$577$	1.03883e44			0.688225			0.344113	−	0.938928i	$-0.388180\pi$
$577$	1.03883e44			0.688225			0.344113	+	0.938928i	$0.388180\pi$
$578$	−1.07446e43	+	4.49877e43i	−0.0692379	+	0.289900i
$579$		0			0
$580$	5.19306e43	+	2.63061e43i	0.316647	+	0.160401i
$581$	3.18351e44			1.88838
$582$		0			0
$583$		−	7.87390e43i		−	0.442072i
$584$	−1.84358e44	+	2.17407e44i	−1.00706	+	1.18759i
$585$		0			0
$586$	−1.81328e43	+	7.59224e43i	−0.0937785	+	0.392652i
$587$		−	2.34372e44i		−	1.17949i	−0.807588	−	0.589747i	$-0.799228\pi$
$587$		−	2.34372e44i		−	1.17949i	0.807588	−	0.589747i	$-0.200772\pi$
$588$		0			0
$589$	2.60234e43			0.124028
$590$	−3.20912e43	−	7.66446e42i	−0.148852	−	0.0355508i
$591$		0			0
$592$	−5.41404e42	−	7.37844e42i	−0.0237889	−	0.0324203i
$593$	3.76769e44			1.61139			0.805695	−	0.592331i	$-0.201792\pi$
$593$	3.76769e44			1.61139			0.805695	+	0.592331i	$0.201792\pi$
$594$		0			0
$595$		−	3.41850e44i		−	1.38536i
$596$	1.20722e43	+	6.11530e42i	0.0476261	+	0.0241256i
$597$		0			0
$598$	−6.85040e42	−	1.63610e42i	−0.0256151	−	0.00611775i
$599$		−	3.22426e44i		−	1.17382i	−0.809652	−	0.586910i	$-0.800344\pi$
$599$		−	3.22426e44i		−	1.17382i	0.809652	−	0.586910i	$-0.199656\pi$
$600$		0			0
$601$	−2.80517e43			−0.0968206			−0.0484103	−	0.998828i	$-0.515416\pi$
$601$	−2.80517e43			−0.0968206			−0.0484103	+	0.998828i	$0.515416\pi$
$602$	−4.94149e42	+	2.06901e43i	−0.0166079	+	0.0695375i
$603$		0			0
$604$	−1.25995e44	+	2.48725e44i	−0.401570	+	0.792736i
$605$	−2.91046e44			−0.903389
$606$		0			0
$607$		−	3.35287e44i		−	0.987184i	−0.869694	−	0.493592i	$-0.835684\pi$
$607$		−	3.35287e44i		−	0.987184i	0.869694	−	0.493592i	$-0.164316\pi$
$608$	2.88085e43	+	6.84075e43i	0.0826157	+	0.196176i
$609$		0			0
$610$	1.09877e44	−	4.60057e44i	0.298971	−	1.25180i
$611$		−	1.03467e44i		−	0.274249i
$612$		0			0
$613$	5.01061e44			1.26044			0.630221	−	0.776416i	$-0.282964\pi$
$613$	5.01061e44			1.26044			0.630221	+	0.776416i	$0.282964\pi$
$614$	6.13074e44	+	1.46423e44i	1.50252	+	0.358851i
$615$		0			0
$616$	−6.65986e44	+	7.85372e44i	−1.54944	+	1.82719i
$617$	−9.93241e43			−0.225161			−0.112580	−	0.993643i	$-0.535912\pi$
$617$	−9.93241e43			−0.225161			−0.112580	+	0.993643i	$0.535912\pi$
$618$		0			0
$619$		−	1.77023e44i		−	0.381048i	−0.981683	−	0.190524i	$-0.938981\pi$
$619$		−	1.77023e44i		−	0.381048i	0.981683	−	0.190524i	$-0.0610187\pi$
$620$	−1.20663e44	+	2.38200e44i	−0.253109	+	0.499660i
$621$		0			0
$622$	1.23851e44	+	2.95797e43i	0.246747	+	0.0589315i
$623$			7.79624e44i			1.51383i
$624$		0			0
$625$	−4.97819e44			−0.918313
$626$	−7.98239e43	+	3.34224e44i	−0.143530	+	0.600964i
$627$		0			0
$628$	9.95808e44	+	5.04438e44i	1.70146	+	0.861893i
$629$	−2.02263e43			−0.0336903
$630$		0			0
$631$			4.90233e44i			0.776128i	0.921633	+	0.388064i	$0.126856\pi$
$631$			4.90233e44i			0.776128i	−0.921633	+	0.388064i	$0.873144\pi$
$632$	5.66127e44	+	4.80069e44i	0.873857	+	0.741020i
$633$		0			0
$634$	−4.86585e43	+	2.03734e44i	−0.0714054	+	0.298976i
$635$		−	1.11275e45i		−	1.59227i
$636$		0			0
$637$	−8.27117e44			−1.12548
$638$	−3.76947e44	−	9.00276e43i	−0.500207	−	0.119466i
$639$		0			0
$640$	−7.59731e44	−	5.34934e43i	−0.958916	−	0.0675181i
$641$	−1.44698e45			−1.78128			−0.890641	−	0.454706i	$-0.849744\pi$
$641$	−1.44698e45			−1.78128			−0.890641	+	0.454706i	$0.849744\pi$
$642$		0			0
$643$		−	1.18107e45i		−	1.38325i	−0.722258	−	0.691623i	$-0.756896\pi$
$643$		−	1.18107e45i		−	1.38325i	0.722258	−	0.691623i	$-0.243104\pi$
$644$	6.15641e43	+	3.11860e43i	0.0703321	+	0.0356276i
$645$		0			0
$646$	1.59561e44	+	3.81084e43i	0.173462	+	0.0414286i
$647$			4.17210e44i			0.442472i	0.975220	+	0.221236i	$0.0710091\pi$
$647$			4.17210e44i			0.442472i	−0.975220	+	0.221236i	$0.928991\pi$
$648$		0			0
$649$	2.19652e44			0.221728
$650$	−1.02892e43	+	4.30809e43i	−0.0101336	+	0.0424298i
$651$		0			0
$652$	2.68740e43	−	5.30517e43i	0.0251983	−	0.0497437i
$653$	−1.61773e45			−1.48011			−0.740057	−	0.672544i	$-0.765201\pi$
$653$	−1.61773e45			−1.48011			−0.740057	+	0.672544i	$0.765201\pi$
$654$		0			0
$655$		−	1.03883e45i		−	0.905076i
$656$	−8.49041e44	−	1.15710e45i	−0.721884	−	0.983807i
$657$		0			0
$658$	−2.35515e44	+	9.86105e44i	−0.190723	+	0.798562i
$659$		−	9.04904e44i		−	0.715214i	−0.933872	−	0.357607i	$-0.883593\pi$
$659$		−	9.04904e44i		−	0.715214i	0.933872	−	0.357607i	$-0.116407\pi$
$660$		0			0
$661$	−5.46004e44			−0.411124			−0.205562	−	0.978644i	$-0.565902\pi$
$661$	−5.46004e44			−0.411124			−0.205562	+	0.978644i	$0.565902\pi$
$662$	−2.00044e45	−	4.77772e44i	−1.47027	−	0.351150i
$663$		0			0
$664$	−1.19556e45	−	1.01382e45i	−0.837303	−	0.710023i
$665$	5.14822e44			0.351974
$666$		0			0
$667$			2.59735e43i			0.0169245i
$668$	1.21675e45	−	2.40199e45i	0.774069	−	1.52808i
$669$		0			0
$670$	−1.74172e45	−	4.15981e44i	−1.05629	−	0.252277i
$671$			3.14892e45i			1.86467i
$672$		0			0
$673$	6.50078e44			0.367050			0.183525	−	0.983015i	$-0.441249\pi$
$673$	6.50078e44			0.367050			0.183525	+	0.983015i	$0.441249\pi$
$674$	−6.47291e44	+	2.71022e45i	−0.356895	+	1.49433i
$675$		0			0
$676$	1.13641e45	+	5.75660e44i	0.597567	+	0.302705i
$677$	−1.51141e45			−0.776181			−0.388091	−	0.921621i	$-0.626865\pi$
$677$	−1.51141e45			−0.776181			−0.388091	+	0.921621i	$0.626865\pi$
$678$		0			0
$679$			5.36182e45i			2.62661i
$680$	−1.08865e45	+	1.28381e45i	−0.520892	+	0.614268i
$681$		0			0
$682$	4.12946e44	−	1.72901e45i	0.188514	−	0.789311i
$683$		−	1.57870e45i		−	0.703992i	−0.936001	−	0.351996i	$-0.885503\pi$
$683$		−	1.57870e45i		−	0.703992i	0.936001	−	0.351996i	$-0.114497\pi$
$684$		0			0
$685$	2.30240e45			0.979786
$686$	3.85853e45	+	9.21547e44i	1.60412	+	0.383117i
$687$		0			0
$688$	8.44474e43	−	6.19646e43i	0.0335098	−	0.0245883i
$689$	−4.70406e44			−0.182375
$690$		0			0
$691$		−	2.81812e45i		−	1.04306i	−0.853232	−	0.521532i	$-0.825361\pi$
$691$		−	2.81812e45i		−	1.04306i	0.853232	−	0.521532i	$-0.174639\pi$
$692$	−4.17848e45	−	2.11666e45i	−1.51120	−	0.765515i
$693$		0			0
$694$	−3.87019e45	−	9.24332e44i	−1.33654	−	0.319210i
$695$			2.44022e45i			0.823518i
$696$		0			0
$697$	−3.17192e45			−1.02235
$698$	−2.23840e44	+	9.37223e44i	−0.0705101	+	0.295227i
$699$		0			0
$700$	1.96123e44	−	3.87165e44i	0.0590147	−	0.116500i
$701$	5.77620e45			1.69884			0.849422	−	0.527714i	$-0.176951\pi$
$701$	5.77620e45			1.69884			0.849422	+	0.527714i	$0.176951\pi$
$702$		0			0
$703$		−	3.04606e43i		−	0.00855959i
$704$	5.00219e45	−	8.28548e44i	1.37403	−	0.227591i
$705$		0			0
$706$	−7.19315e44	+	3.01179e45i	−0.188818	+	0.790585i
$707$			3.27445e44i			0.0840288i
$708$		0			0
$709$	3.05399e44			0.0749080			0.0374540	−	0.999298i	$-0.488075\pi$
$709$	3.05399e44			0.0749080			0.0374540	+	0.999298i	$0.488075\pi$
$710$	−6.91789e45	−	1.65222e45i	−1.65898	−	0.396219i
$711$		0			0
$712$	2.48279e45	−	2.92786e45i	0.569194	−	0.671228i
$713$	−1.19137e44			−0.0267064
$714$		0			0
$715$			3.58900e45i			0.769266i
$716$	−3.14217e45	+	6.20294e45i	−0.658600	+	1.30014i
$717$		0			0
$718$	4.68469e45	+	1.11886e45i	0.939052	+	0.224277i
$719$			2.10378e45i			0.412418i	0.978508	+	0.206209i	$0.0661127\pi$
$719$			2.10378e45i			0.412418i	−0.978508	+	0.206209i	$0.933887\pi$
$720$		0			0
$721$	−5.58206e45			−1.04672
$722$	1.20922e45	−	5.06304e45i	0.221774	−	0.928573i
$723$		0			0
$724$	3.18825e45	+	1.61504e45i	0.559416	+	0.283379i
$725$	1.63342e44			0.0280343
$726$		0			0
$727$			5.93359e45i			0.974466i	0.873272	+	0.487233i	$0.161994\pi$
$727$			5.93359e45i			0.974466i	−0.873272	+	0.487233i	$0.838006\pi$
$728$	4.69200e45	+	3.97876e45i	0.753800	+	0.639213i
$729$		0			0
$730$	2.26144e45	−	9.46869e45i	0.347712	−	1.45588i
$731$		−	2.31493e44i		−	0.0348225i
$732$		0			0
$733$	1.14451e46			1.64800			0.824000	−	0.566590i	$-0.191738\pi$
$733$	1.14451e46			1.64800			0.824000	+	0.566590i	$0.191738\pi$
$734$	−1.31621e45	−	3.14355e44i	−0.185434	−	0.0442878i
$735$		0			0
$736$	−1.31888e44	−	3.13176e44i	−0.0177893	−	0.0422418i
$737$	1.19214e46			1.57343
$738$		0			0
$739$			2.33426e45i			0.295011i	0.989061	+	0.147505i	$0.0471244\pi$
$739$			2.33426e45i			0.295011i	−0.989061	+	0.147505i	$0.952876\pi$
$740$	2.78815e44	+	1.41237e44i	0.0344833	+	0.0174679i
$741$		0			0
$742$	4.48324e45	+	1.07075e45i	0.531043	+	0.126831i
$743$			2.99487e45i			0.347182i	0.984818	+	0.173591i	$0.0555371\pi$
$743$			2.99487e45i			0.347182i	−0.984818	+	0.173591i	$0.944463\pi$
$744$		0			0
$745$	−4.62167e44			−0.0513214
$746$	1.72676e45	−	7.22997e45i	0.187677	−	0.785806i
$747$		0			0
$748$	5.06390e45	−	9.99662e45i	0.527303	−	1.04094i
$749$	−1.62015e46			−1.65138
$750$		0			0
$751$			1.07059e46i			1.04564i	0.852442	+	0.522822i	$0.175121\pi$
$751$			1.07059e46i			1.04564i	−0.852442	+	0.522822i	$0.824879\pi$
$752$	4.02482e45	−	2.95327e45i	0.384823	−	0.282370i
$753$		0			0
$754$	−5.37847e44	+	2.25197e45i	−0.0492852	+	0.206358i
$755$		−	9.52211e45i		−	0.854244i
$756$		0			0
$757$	−9.65089e45			−0.829915			−0.414957	−	0.909841i	$-0.636203\pi$
$757$	−9.65089e45			−0.829915			−0.414957	+	0.909841i	$0.636203\pi$
$758$	2.31601e45	+	5.53141e44i	0.195000	+	0.0465724i
$759$		0			0
$760$	−1.93340e45	−	1.63950e45i	−0.156065	−	0.132341i
$761$	1.39608e46			1.10346			0.551729	−	0.834023i	$-0.313968\pi$
$761$	1.39608e46			1.10346			0.551729	+	0.834023i	$0.313968\pi$
$762$		0			0
$763$			1.47350e46i			1.11675i
$764$	−4.11675e45	+	8.12686e45i	−0.305535	+	0.603155i
$765$		0			0
$766$	−1.26360e45	−	3.01789e44i	−0.0899391	−	0.0214804i
$767$		−	1.31226e45i		−	0.0914730i
$768$		0			0
$769$	−1.40709e45			−0.0940808			−0.0470404	−	0.998893i	$-0.514979\pi$
$769$	−1.40709e45			−0.0940808			−0.0470404	+	0.998893i	$0.514979\pi$
$770$	8.16934e45	−	3.42052e46i	0.534977	−	2.23996i
$771$		0			0
$772$	−2.04064e46	−	1.03371e46i	−1.28200	−	0.649414i
$773$	2.99265e46			1.84155			0.920775	−	0.390093i	$-0.127557\pi$
$773$	2.99265e46			1.84155			0.920775	+	0.390093i	$0.127557\pi$
$774$		0			0
$775$			7.49232e44i			0.0442374i
$776$	1.70752e46	−	2.01362e46i	0.987596	−	1.16463i
$777$		0			0
$778$	2.57211e45	−	1.07695e46i	0.142763	−	0.597751i
$779$		−	4.77689e45i		−	0.259744i
$780$		0			0
$781$	4.73503e46			2.47119
$782$	−7.30482e44	−	1.74464e44i	−0.0373510	−	0.00892065i
$783$		0			0
$784$	−2.36084e46	−	3.21743e46i	−1.15880	−	1.57926i
$785$	−3.81232e46			−1.83347
$786$		0			0
$787$		−	1.65954e46i		−	0.766290i	−0.923688	−	0.383145i	$-0.874841\pi$
$787$		−	1.65954e46i		−	0.766290i	0.923688	−	0.383145i	$-0.125159\pi$
$788$	−1.36868e46	−	6.93321e45i	−0.619273	−	0.313700i
$789$		0			0
$790$	−2.46564e46	−	5.88878e45i	−1.07127	−	0.255854i
$791$			1.14982e46i			0.489561i
$792$		0			0
$793$	1.88124e46			0.769260
$794$	3.78981e44	−	1.58680e45i	0.0151876	−	0.0635909i
$795$		0			0
$796$	5.34219e45	−	1.05460e46i	0.205641	−	0.405955i
$797$	2.40047e46			0.905655			0.452827	−	0.891598i	$-0.350415\pi$
$797$	2.40047e46			0.905655			0.452827	+	0.891598i	$0.350415\pi$
$798$		0			0
$799$		−	1.10331e46i		−	0.399898i
$800$	−1.96950e45	+	8.29417e44i	−0.0699708	+	0.0294668i
$801$		0			0
$802$	2.94007e45	−	1.23101e46i	0.100362	−	0.420216i
$803$			6.48097e46i			2.16866i
$804$		0			0
$805$	−2.35690e45			−0.0757892
$806$	−1.03295e46	−	2.46704e45i	−0.325627	−	0.0777706i
$807$		0			0
$808$	1.04278e45	−	1.22971e45i	0.0315945	−	0.0372582i
$809$	1.46290e45			0.0434549			0.0217275	−	0.999764i	$-0.493083\pi$
$809$	1.46290e45			0.0434549			0.0217275	+	0.999764i	$0.493083\pi$
$810$		0			0
$811$			6.60062e46i			1.88474i	0.334574	+	0.942369i	$0.391408\pi$
$811$			6.60062e46i			1.88474i	−0.334574	+	0.942369i	$0.608592\pi$
$812$	1.02520e46	−	2.02384e46i	0.287019	−	0.566603i
$813$		0			0
$814$	−2.02382e45	−	4.83357e44i	−0.0544731	−	0.0130100i
$815$			2.03102e45i			0.0536033i
$816$		0			0
$817$	3.48626e44			0.00884722
$818$	−9.56409e45	+	4.00450e46i	−0.238008	+	0.996542i
$819$		0			0
$820$	4.37243e46	+	2.21490e46i	1.04641	+	0.530070i
$821$	8.81734e45			0.206941			0.103471	−	0.994633i	$-0.467005\pi$
$821$	8.81734e45			0.206941			0.103471	+	0.994633i	$0.467005\pi$
$822$		0			0
$823$		−	3.84058e46i		−	0.866961i	−0.901163	−	0.433480i	$-0.857285\pi$
$823$		−	3.84058e46i		−	0.866961i	0.901163	−	0.433480i	$-0.142715\pi$
$824$	2.09633e46	+	1.77766e46i	0.464113	+	0.393563i
$825$		0			0
$826$	−2.98698e45	+	1.25066e46i	−0.0636139	+	0.266353i
$827$			5.40170e46i			1.12835i	0.825656	+	0.564174i	$0.190805\pi$
$827$			5.40170e46i			1.12835i	−0.825656	+	0.564174i	$0.809195\pi$
$828$		0			0
$829$	−5.31805e46			−1.06876			−0.534380	−	0.845244i	$-0.679455\pi$
$829$	−5.31805e46			−1.06876			−0.534380	+	0.845244i	$0.679455\pi$
$830$	5.20701e46	+	1.24361e46i	1.02645	+	0.245151i
$831$		0			0
$832$	−4.94995e45	−	2.98843e46i	−0.0938917	−	0.566852i
$833$	−8.81984e46			−1.64112
$834$		0			0
$835$			9.19569e46i			1.64665i
$836$	1.50548e46	+	7.62619e45i	0.264469	+	0.133970i
$837$		0			0
$838$	−3.26505e46	−	7.79803e45i	−0.552059	−	0.131850i
$839$		−	1.08388e47i		−	1.79801i	−0.437943	−	0.899003i	$-0.644293\pi$
$839$		−	1.08388e47i		−	1.79801i	0.437943	−	0.899003i	$-0.355707\pi$
$840$		0			0
$841$	−5.40849e46			−0.863654
$842$	2.60164e45	−	1.08931e46i	0.0407619	−	0.170671i
$843$		0			0
$844$	−4.21548e45	+	8.32176e45i	−0.0635870	+	0.125527i
$845$	−4.35058e46			−0.643932
$846$		0			0
$847$			1.13426e47i			1.61651i
$848$	−1.34268e46	−	1.82985e46i	−0.187776	−	0.255907i
$849$		0			0
$850$	−1.09717e45	+	4.59387e45i	−0.0147765	+	0.0618694i
$851$			1.39451e44i			0.00184310i
$852$		0			0
$853$	−3.06780e46			−0.390520			−0.195260	−	0.980752i	$-0.562555\pi$
$853$	−3.06780e46			−0.390520			−0.195260	+	0.980752i	$0.562555\pi$
$854$	−1.79293e47	−	4.28212e46i	−2.23995	−	0.534974i
$855$		0			0
$856$	6.08443e46	+	5.15953e46i	0.732217	+	0.620911i
$857$	−1.81471e46			−0.214345			−0.107172	−	0.994240i	$-0.534180\pi$
$857$	−1.81471e46			−0.214345			−0.107172	+	0.994240i	$0.534180\pi$
$858$		0			0
$859$		−	1.25824e47i		−	1.43177i	−0.698216	−	0.715887i	$-0.746023\pi$
$859$		−	1.25824e47i		−	1.43177i	0.698216	−	0.715887i	$-0.253977\pi$
$860$	−1.61648e45	+	3.19108e45i	−0.0180549	+	0.0356420i
$861$		0			0
$862$	1.79480e46	+	4.28658e45i	0.193152	+	0.0461311i
$863$		−	1.26832e47i		−	1.33984i	−0.742431	−	0.669922i	$-0.766327\pi$
$863$		−	1.26832e47i		−	1.33984i	0.742431	−	0.669922i	$-0.233673\pi$
$864$		0			0
$865$	1.59968e47			1.62845
$866$	−4.03991e46	+	1.69152e47i	−0.403725	+	1.69040i
$867$		0			0
$868$	9.28310e46	+	4.70246e46i	0.894082	+	0.452908i
$869$	1.68764e47			1.59575
$870$		0			0
$871$		−	7.12216e46i		−	0.649114i
$872$	4.69251e46	−	5.53370e46i	0.419896	−	0.495167i
$873$		0			0
$874$	2.62740e44	−	1.10010e45i	0.00226644	−	0.00948962i
$875$			2.10049e47i			1.77907i
$876$		0			0
$877$	1.96939e47			1.60820			0.804098	−	0.594497i	$-0.202649\pi$
$877$	1.96939e47			1.60820			0.804098	+	0.594497i	$0.202649\pi$
$878$	−8.20584e46	−	1.95983e46i	−0.657977	−	0.157147i
$879$		0			0
$880$	−1.39610e47	+	1.02441e47i	−1.07943	+	0.792046i
$881$	2.44488e46			0.185628			0.0928141	−	0.995683i	$-0.470414\pi$
$881$	2.44488e46			0.185628			0.0928141	+	0.995683i	$0.470414\pi$
$882$		0			0
$883$			2.15626e47i			1.57881i	0.613874	+	0.789404i	$0.289610\pi$
$883$			2.15626e47i			1.57881i	−0.613874	+	0.789404i	$0.710390\pi$
$884$	−5.97222e46	−	3.02530e46i	−0.429437	−	0.217536i
$885$		0			0
$886$	−7.02228e46	−	1.67716e46i	−0.487011	−	0.116315i
$887$			3.56722e46i			0.242970i	0.992593	+	0.121485i	$0.0387656\pi$
$887$			3.56722e46i			0.242970i	−0.992593	+	0.121485i	$0.961234\pi$
$888$		0			0
$889$	−4.33658e47			−2.84918
$890$	−3.04553e46	+	1.27517e47i	−0.196527	+	0.822862i
$891$		0			0
$892$	5.12506e45	−	1.01173e46i	0.0319052	−	0.0629838i
$893$	1.66158e46			0.101601
$894$		0			0
$895$		−	2.37471e47i		−	1.40102i
$896$	−2.08474e46	+	2.96082e47i	−0.120816	+	1.71587i
$897$		0			0
$898$	1.67031e46	−	6.99362e46i	0.0934062	−	0.391094i
$899$			3.91647e46i			0.215149i
$900$		0			0
$901$	−5.01611e46			−0.265932
$902$	−3.17380e47	−	7.58010e46i	−1.65301	−	0.394794i
$903$		0			0
$904$	3.66172e46	−	4.31813e46i	0.184073	−	0.217071i
$905$	−1.22058e47			−0.602821
$906$		0			0
$907$		−	1.18540e47i		−	0.565129i	−0.959248	−	0.282565i	$-0.908815\pi$
$907$		−	1.18540e47i		−	0.565129i	0.959248	−	0.282565i	$-0.0911851\pi$
$908$	9.36607e46	−	1.84895e47i	0.438716	−	0.866067i
$909$		0			0
$910$	−2.04350e47	−	4.88056e46i	−0.924087	−	0.220703i
$911$		−	2.37322e46i		−	0.105450i	−0.998609	−	0.0527248i	$-0.983209\pi$
$911$		−	2.37322e46i		−	0.105450i	0.998609	−	0.0527248i	$-0.0167906\pi$
$912$		0			0
$913$	−3.56401e47			−1.52899
$914$	1.05293e47	−	4.40863e47i	0.443874	−	1.85851i
$915$		0			0
$916$	2.46605e47	+	1.24921e47i	1.00386	+	0.508518i
$917$	−4.04853e47			−1.61953
$918$		0			0
$919$		−	3.14225e47i		−	1.21393i	−0.794730	−	0.606963i	$-0.792388\pi$
$919$		−	3.14225e47i		−	1.21393i	0.794730	−	0.606963i	$-0.207612\pi$
$920$	8.85129e45	+	7.50579e45i	0.0336048	+	0.0284965i
$921$		0			0
$922$	−3.68498e44	+	1.54291e45i	−0.00135127	+	0.00565777i
$923$		−	2.82882e47i		−	1.01948i
$924$		0			0
$925$	8.76983e44			0.00305297
$926$	4.66898e47	+	1.11511e47i	1.59752	+	0.381541i
$927$		0			0
$928$	−1.02952e47	+	4.33563e46i	−0.340305	+	0.143313i
$929$	2.38969e46			0.0776409			0.0388205	−	0.999246i	$-0.487640\pi$
$929$	2.38969e46			0.0776409			0.0388205	+	0.999246i	$0.487640\pi$
$930$		0			0
$931$		−	1.32826e47i		−	0.416954i
$932$	3.70398e47	+	1.87629e47i	1.14291	+	0.578957i
$933$		0			0
$934$	3.68200e46	+	8.79385e45i	0.109783	+	0.0262198i
$935$			3.82707e47i			1.12171i
$936$		0			0
$937$	5.26937e46			0.149254			0.0746268	−	0.997212i	$-0.476223\pi$
$937$	5.26937e46			0.149254			0.0746268	+	0.997212i	$0.476223\pi$
$938$	−1.62116e47	+	6.78783e47i	−0.451419	+	1.89010i
$939$		0			0
$940$	−7.70425e46	+	1.52089e47i	−0.207341	+	0.409310i
$941$	1.10297e47			0.291829			0.145915	−	0.989297i	$-0.453388\pi$
$941$	1.10297e47			0.291829			0.145915	+	0.989297i	$0.453388\pi$
$942$		0			0
$943$			2.18690e46i			0.0559296i
$944$	5.10460e46	−	3.74558e46i	0.128354	−	0.0941818i
$945$		0			0
$946$	5.53210e45	−	2.31630e46i	0.0134472	−	0.0563036i
$947$		−	7.59630e47i		−	1.81552i	−0.419485	−	0.907762i	$-0.637789\pi$
$947$		−	7.59630e47i		−	1.81552i	0.419485	−	0.907762i	$-0.362211\pi$
$948$		0			0
$949$	3.87189e47			0.894671
$950$	−6.91832e45	−	1.65233e45i	−0.0157189	−	0.00375421i
$951$		0			0
$952$	5.00325e47	+	4.24269e47i	1.09916	+	0.932074i
$953$	2.69647e47			0.582517			0.291259	−	0.956644i	$-0.405926\pi$
$953$	2.69647e47			0.582517			0.291259	+	0.956644i	$0.405926\pi$
$954$		0			0
$955$		−	3.11126e47i		−	0.649954i
$956$	1.80526e47	−	3.56376e47i	0.370863	−	0.732119i
$957$		0			0
$958$	6.22014e47	+	1.48558e47i	1.23581	+	0.295153i
$959$		−	8.97288e47i		−	1.75321i
$960$		0			0
$961$	3.49500e47			0.660501
$962$	−2.88769e45	+	1.20908e46i	−0.00536722	+	0.0224727i
$963$		0			0
$964$	−7.02735e47	−	3.55979e47i	−1.26345	−	0.640017i
$965$	7.81232e47			1.38148
$966$		0			0
$967$		−	8.68662e47i		−	1.48603i	−0.669276	−	0.743014i	$-0.733396\pi$
$967$		−	8.68662e47i		−	1.48603i	0.669276	−	0.743014i	$-0.266604\pi$
$968$	3.61217e47	−	4.25969e47i	0.607802	−	0.716757i
$969$		0			0
$970$	−2.09454e47	+	8.76989e47i	−0.340990	+	1.42773i
$971$			3.07628e47i			0.492627i	0.969190	+	0.246314i	$0.0792193\pi$
$971$			3.07628e47i			0.492627i	−0.969190	+	0.246314i	$0.920781\pi$
$972$		0			0
$973$	9.51002e47			1.47359
$974$	−5.57069e47	−	1.33047e47i	−0.849113	−	0.202797i
$975$		0			0
$976$	5.36963e47	+	7.31791e47i	0.792040	+	1.07942i
$977$	−1.00138e48			−1.45306			−0.726531	−	0.687134i	$-0.758869\pi$
$977$	−1.00138e48			−1.45306			−0.726531	+	0.687134i	$0.758869\pi$
$978$		0			0
$979$		−	8.72804e47i		−	1.22573i
$980$	1.21580e48	+	6.15876e47i	1.67975	+	0.850895i
$981$		0			0
$982$	−4.09206e47	−	9.77320e46i	−0.547215	−	0.130693i
$983$		−	5.92610e47i		−	0.779674i	−0.920884	−	0.389837i	$-0.872531\pi$
$983$		−	5.92610e47i		−	0.779674i	0.920884	−	0.389837i	$-0.127469\pi$
$984$		0			0
$985$	5.23981e47			0.667323
$986$	−5.73525e46	+	2.40136e47i	−0.0718657	+	0.300903i
$987$		0			0
$988$	4.55607e46	−	8.99411e46i	0.0552687	−	0.109106i
$989$	−1.59604e45			−0.00190504
$990$		0			0
$991$			7.60458e47i			0.878813i	0.898288	+	0.439407i	$0.144811\pi$
$991$			7.60458e47i			0.878813i	−0.898288	+	0.439407i	$0.855189\pi$
$992$	−1.98870e47	−	4.72230e47i	−0.226143	−	0.536991i
$993$		0			0
$994$	−6.43903e47	+	2.69603e48i	−0.708987	+	2.96854i
$995$			4.03739e47i			0.437453i
$996$		0			0
$997$	−4.12064e47			−0.432356			−0.216178	−	0.976354i	$-0.569359\pi$
$997$	−4.12064e47			−0.432356			−0.216178	+	0.976354i	$0.569359\pi$
$998$	1.02569e48	+	2.44969e47i	1.05908	+	0.252943i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	36.33.d.b.19.7		14
3.2	odd	2		4.33.b.b.3.8	yes	14
4.3	odd	2	inner	36.33.d.b.19.8		14
12.11	even	2		4.33.b.b.3.7	✓	14

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4.33.b.b.3.7	✓	14	12.11	even	2
4.33.b.b.3.8	yes	14	3.2	odd	2
36.33.d.b.19.7		14	1.1	even	1	trivial
36.33.d.b.19.8		14	4.3	odd	2	inner

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:	\( N \)	\(=\)	\( 36 = 2^{2} \cdot 3^{2} \)
Weight:	\( k \)	\(=\)	\( 33 \)
Character orbit:	\([\chi]\)	\(=\)	36.d (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(15224.0 - 63743.2i) q^{2} +(-3.83143e9 - 1.94085e9i) q^{4} +1.46681e11 q^{5} -5.71644e13i q^{7} +(-1.82046e14 + 2.14680e14i) q^{8} +O(q^{10})\)	\(q+(15224.0 - 63743.2i) q^{2} +(-3.83143e9 - 1.94085e9i) q^{4} +1.46681e11 q^{5} -5.71644e13i q^{7} +(-1.82046e14 + 2.14680e14i) q^{8} +(2.23307e15 - 9.34993e15i) q^{10} +6.39967e16i q^{11} +3.82332e17 q^{13} +(-3.64385e18 - 8.70272e17i) q^{14} +(1.09129e19 + 1.48725e19i) q^{16} +4.07694e19 q^{17} +6.13984e19i q^{19} +(-5.61998e20 - 2.84687e20i) q^{20} +(4.07936e21 + 9.74287e20i) q^{22} -2.81087e20i q^{23} -1.76771e21 q^{25} +(5.82063e21 - 2.43711e22i) q^{26} +(-1.10948e23 + 2.19021e23i) q^{28} -9.24035e22 q^{29} -4.23845e23i q^{31} +(1.11416e24 - 4.69206e23i) q^{32} +(6.20674e23 - 2.59877e24i) q^{34} -8.38495e24i q^{35} -4.96114e23 q^{37} +(3.91373e24 + 9.34729e23i) q^{38} +(-2.67027e25 + 3.14895e25i) q^{40} -7.78015e25 q^{41} -5.67810e24i q^{43} +(1.24208e26 - 2.45199e26i) q^{44} +(-1.79174e25 - 4.27927e24i) q^{46} -2.70622e26i q^{47} -2.16335e27 q^{49} +(-2.69116e25 + 1.12679e26i) q^{50} +(-1.46488e27 - 7.42051e26i) q^{52} -1.23036e27 q^{53} +9.38712e27i q^{55} +(1.22721e28 + 1.04066e28i) q^{56} +(-1.40675e27 + 5.89010e27i) q^{58} -3.43224e27i q^{59} +4.92044e28 q^{61} +(-2.70172e28 - 6.45261e27i) q^{62} +(-1.29467e28 - 7.81632e28i) q^{64} +5.60809e28 q^{65} -1.86282e29i q^{67} +(-1.56205e29 - 7.91275e28i) q^{68} +(-5.34483e29 - 1.27652e29i) q^{70} -7.39887e29i q^{71} +1.01270e30 q^{73} +(-7.55284e27 + 3.16239e28i) q^{74} +(1.19165e29 - 2.35243e29i) q^{76} +3.65834e30 q^{77} -2.63707e30i q^{79} +(1.60072e30 + 2.18151e30i) q^{80} +(-1.18445e30 + 4.95932e30i) q^{82} +5.56904e30i q^{83} +5.98011e30 q^{85} +(-3.61940e29 - 8.64434e28i) q^{86} +(-1.37388e31 - 1.16503e31i) q^{88} -1.36383e31 q^{89} -2.18558e31i q^{91} +(-5.45549e29 + 1.07697e30i) q^{92} +(-1.72503e31 - 4.11995e30i) q^{94} +9.00598e30i q^{95} -9.37964e31 q^{97} +(-3.29348e31 + 1.37899e32i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 14 q + 23780 q^{2} - 2922848368 q^{4} - 138121491740 q^{5} + 191366550113600 q^{8}+O(q^{10}) \) 14 * q + 23780 * q^2 - 2922848368 * q^4 - 138121491740 * q^5 + 191366550113600 * q^8	\( 14 q + 23780 q^{2} - 2922848368 q^{4} - 138121491740 q^{5} + 191366550113600 q^{8} + 31\!\cdots\!00 q^{10}+ \cdots + 46\!\cdots\!00 q^{98}+O(q^{100}) \) 14 * q + 23780 * q^2 - 2922848368 * q^4 - 138121491740 * q^5 + 191366550113600 * q^8 + 31775605694457400 * q^10 - 1640418469677858020 * q^13 - 7731597686180285568 * q^14 - 30570843123186593536 * q^16 - 31570967905797256220 * q^17 - 2022222335397731344160 * q^20 + 5453282318362187158080 * q^22 + 10252879651857697291050 * q^25 + 100487287286439222842824 * q^26 + 287406099989137745118720 * q^28 + 383350228001906510553316 * q^29 + 3049085458330908760601600 * q^32 + 2968198158688225453161016 * q^34 - 10743727036349878681805540 * q^37 + 23674230631082905997232960 * q^38 + 46284510399605997225174400 * q^40 - 36301708465641824663518748 * q^41 + 341183497187317069095824640 * q^44 - 292611965791335032977170048 * q^46 - 4831123780514350255580603890 * q^49 + 510591072029103065039587500 * q^50 - 9698318635805895955111735520 * q^52 - 18428895934780252746021636380 * q^53 - 6374003242890184756165527552 * q^56 - 38529567312130296955877295560 * q^58 + 106402038936127775684939892508 * q^61 - 21568431972603200921875622400 * q^62 - 196737301243248539525687308288 * q^64 - 113178238686492542374351007800 * q^65 - 354271480525935415641826176800 * q^68 - 514873634674652910315035354880 * q^70 + 1432707125192338982920850898460 * q^73 + 984194129445064624850959434184 * q^74 - 782627770945775078204519980800 * q^76 + 3080015547766001613074070589440 * q^77 - 6279147555674556254006737379840 * q^80 - 4557892929168088074284564686280 * q^82 + 6758108895547933966316548575800 * q^85 + 23458263349697798020331664550848 * q^86 + 11102138256776653733497151431680 * q^88 + 18473812211636703183423448507876 * q^89 - 60798444498044060215697222361600 * q^92 - 130643574777689548682138472237312 * q^94 - 201795139515948373218799959195620 * q^97 + 460006462884606019803763245136100 * q^98

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