LMFDB - Embedded newform 36.33.d.b.19.14

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			19.14
Root			$4.04243e9 + 6.98294e11i$ of defining polynomial
Character	$\chi$	$=$	36.19
Dual form			36.33.d.b.19.13

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(61401.1 + 22910.1i) q^{2} +(3.24522e9 + 2.81341e9i) q^{4} -1.39224e11 q^{5} -2.23454e13i q^{7} +(1.34805e14 + 2.47095e14i) q^{8} +O(q^{10})$	\(q+(61401.1 + 22910.1i) q^{2} +(3.24522e9 + 2.81341e9i) q^{4} -1.39224e11 q^{5} -2.23454e13i q^{7} +(1.34805e14 + 2.47095e14i) q^{8} +(-8.54848e15 - 3.18962e15i) q^{10} +1.78893e16i q^{11} +2.16497e17 q^{13} +(5.11935e17 - 1.37203e18i) q^{14} +(2.61621e18 + 1.82603e19i) q^{16} +6.14938e19 q^{17} -4.44940e20i q^{19} +(-4.51812e20 - 3.91693e20i) q^{20} +(-4.09845e20 + 1.09842e21i) q^{22} +8.74399e21i q^{23} -3.89986e21 q^{25} +(1.32931e22 + 4.95995e21i) q^{26} +(6.28668e22 - 7.25159e22i) q^{28} -4.53622e23 q^{29} -1.07502e24i q^{31} +(-2.57706e23 + 1.18114e24i) q^{32} +(3.77579e24 + 1.40883e24i) q^{34} +3.11101e24i q^{35} -9.58490e23 q^{37} +(1.01936e25 - 2.73198e25i) q^{38} +(-1.87680e25 - 3.44014e25i) q^{40} +1.42325e25 q^{41} +1.36563e26i q^{43} +(-5.03298e25 + 5.80547e25i) q^{44} +(-2.00325e26 + 5.36891e26i) q^{46} +1.63099e26i q^{47} +6.05110e26 q^{49} +(-2.39456e26 - 8.93461e25i) q^{50} +(7.02580e26 + 6.09093e26i) q^{52} -6.59943e27 q^{53} -2.49061e27i q^{55} +(5.52143e27 - 3.01227e27i) q^{56} +(-2.78529e28 - 1.03925e28i) q^{58} -2.05929e26i q^{59} +1.66456e28 q^{61} +(2.46288e28 - 6.60074e28i) q^{62} +(-4.28834e28 + 6.66192e28i) q^{64} -3.01414e28 q^{65} -2.31454e29i q^{67} +(1.99561e29 + 1.73007e29i) q^{68} +(-7.12735e28 + 1.91019e29i) q^{70} -3.68248e29i q^{71} +2.79454e29 q^{73} +(-5.88523e28 - 2.19591e28i) q^{74} +(1.25180e30 - 1.44393e30i) q^{76} +3.99743e29 q^{77} -2.19129e30i q^{79} +(-3.64239e29 - 2.54226e30i) q^{80} +(8.73891e29 + 3.26068e29i) q^{82} -3.91771e30i q^{83} -8.56139e30 q^{85} +(-3.12866e30 + 8.38511e30i) q^{86} +(-4.42035e30 + 2.41156e30i) q^{88} +2.76276e31 q^{89} -4.83771e30i q^{91} +(-2.46004e31 + 2.83762e31i) q^{92} +(-3.73660e30 + 1.00144e31i) q^{94} +6.19462e31i q^{95} +2.89803e30 q^{97} +(3.71544e31 + 1.38631e31i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	61401.1	+	22910.1i	0.936907	+	0.349580i
$2$	61401.1	+	22910.1i	0.936907	+	0.349580i
$3$		0			0
$3$		0			0
$4$	3.24522e9	+	2.81341e9i	0.755588	+	0.655048i
$5$	−1.39224e11			−0.912416			−0.456208	−	0.889873i	$-0.650793\pi$
$5$	−1.39224e11			−0.912416			−0.456208	+	0.889873i	$0.650793\pi$
$6$		0			0
$7$		−	2.23454e13i		−	0.672388i	−0.941793	−	0.336194i	$-0.890860\pi$
$7$		−	2.23454e13i		−	0.672388i	0.941793	−	0.336194i	$-0.109140\pi$
$8$	1.34805e14	+	2.47095e14i	0.478923	+	0.877857i
$9$		0			0
$10$	−8.54848e15	−	3.18962e15i	−0.854848	−	0.318962i
$11$			1.78893e16i			0.389323i	0.980870	+	0.194661i	$0.0623608\pi$
$11$			1.78893e16i			0.389323i	−0.980870	+	0.194661i	$0.937639\pi$
$12$		0			0
$13$	2.16497e17			0.325355			0.162677	−	0.986679i	$-0.447987\pi$
$13$	2.16497e17			0.325355			0.162677	+	0.986679i	$0.447987\pi$
$14$	5.11935e17	−	1.37203e18i	0.235053	−	0.629965i
$15$		0			0
$16$	2.61621e18	+	1.82603e19i	0.141825	+	0.989892i
$17$	6.14938e19			1.26371			0.631857	−	0.775085i	$-0.282293\pi$
$17$	6.14938e19			1.26371			0.631857	+	0.775085i	$0.282293\pi$
$18$		0			0
$19$		−	4.44940e20i		−	1.54257i	−0.636492	−	0.771283i	$-0.719615\pi$
$19$		−	4.44940e20i		−	1.54257i	0.636492	−	0.771283i	$-0.280385\pi$
$20$	−4.51812e20	−	3.91693e20i	−0.689410	−	0.597676i
$21$		0			0
$22$	−4.09845e20	+	1.09842e21i	−0.136100	+	0.364759i
$23$			8.74399e21i			1.42582i	0.701256	+	0.712909i	$0.252623\pi$
$23$			8.74399e21i			1.42582i	−0.701256	+	0.712909i	$0.747377\pi$
$24$		0			0
$25$	−3.89986e21			−0.167498
$26$	1.32931e22	+	4.95995e21i	0.304827	+	0.113738i
$27$		0			0
$28$	6.28668e22	−	7.25159e22i	0.440446	−	0.508048i
$29$	−4.53622e23			−1.81270			−0.906351	−	0.422526i	$-0.861144\pi$
$29$	−4.53622e23			−1.81270			−0.906351	+	0.422526i	$0.861144\pi$
$30$		0			0
$31$		−	1.07502e24i		−	1.47785i	−0.673789	−	0.738924i	$-0.735334\pi$
$31$		−	1.07502e24i		−	1.47785i	0.673789	−	0.738924i	$-0.264666\pi$
$32$	−2.57706e23	+	1.18114e24i	−0.213169	+	0.977015i
$33$		0			0
$34$	3.77579e24	+	1.40883e24i	1.18398	+	0.441769i
$35$			3.11101e24i			0.613497i
$36$		0			0
$37$	−9.58490e23			−0.0776891			−0.0388445	−	0.999245i	$-0.512368\pi$
$37$	−9.58490e23			−0.0776891			−0.0388445	+	0.999245i	$0.512368\pi$
$38$	1.01936e25	−	2.73198e25i	0.539251	−	1.44524i
$39$		0			0
$40$	−1.87680e25	−	3.44014e25i	−0.436977	−	0.800970i
$41$	1.42325e25			0.223223			0.111612	−	0.993752i	$-0.464399\pi$
$41$	1.42325e25			0.223223			0.111612	+	0.993752i	$0.464399\pi$
$42$		0			0
$43$			1.36563e26i			0.999625i	0.866134	+	0.499813i	$0.166598\pi$
$43$			1.36563e26i			0.999625i	−0.866134	+	0.499813i	$0.833402\pi$
$44$	−5.03298e25	+	5.80547e25i	−0.255025	+	0.294168i
$45$		0			0
$46$	−2.00325e26	+	5.36891e26i	−0.498438	+	1.33586i
$47$			1.63099e26i			0.287663i	0.989602	+	0.143832i	$0.0459424\pi$
$47$			1.63099e26i			0.287663i	−0.989602	+	0.143832i	$0.954058\pi$
$48$		0			0
$49$	6.05110e26			0.547895
$50$	−2.39456e26	−	8.93461e25i	−0.156930	−	0.0585539i
$51$		0			0
$52$	7.02580e26	+	6.09093e26i	0.245834	+	0.213123i
$53$	−6.59943e27			−1.70252			−0.851261	−	0.524743i	$-0.824162\pi$
$53$	−6.59943e27			−1.70252			−0.851261	+	0.524743i	$0.824162\pi$
$54$		0			0
$55$		−	2.49061e27i		−	0.355224i
$56$	5.52143e27	−	3.01227e27i	0.590260	−	0.322022i
$57$		0			0
$58$	−2.78529e28	−	1.03925e28i	−1.69833	−	0.633684i
$59$		−	2.05929e26i		−	0.00955181i	−0.999989	−	0.00477590i	$-0.998480\pi$
$59$		−	2.05929e26i		−	0.00955181i	0.999989	−	0.00477590i	$-0.00152022\pi$
$60$		0			0
$61$	1.66456e28			0.452919			0.226460	−	0.974021i	$-0.427285\pi$
$61$	1.66456e28			0.452919			0.226460	+	0.974021i	$0.427285\pi$
$62$	2.46288e28	−	6.60074e28i	0.516626	−	1.38460i
$63$		0			0
$64$	−4.28834e28	+	6.66192e28i	−0.541265	+	0.840852i
$65$	−3.01414e28			−0.296859
$66$		0			0
$67$		−	2.31454e29i		−	1.40368i	−0.712336	−	0.701839i	$-0.752363\pi$
$67$		−	2.31454e29i		−	1.40368i	0.712336	−	0.701839i	$-0.247637\pi$
$68$	1.99561e29	+	1.73007e29i	0.954847	+	0.827793i
$69$		0			0
$70$	−7.12735e28	+	1.91019e29i	−0.214466	+	0.574789i
$71$		−	3.68248e29i		−	0.883095i	−0.897238	−	0.441547i	$-0.854430\pi$
$71$		−	3.68248e29i		−	0.883095i	0.897238	−	0.441547i	$-0.145570\pi$
$72$		0			0
$73$	2.79454e29			0.429679			0.214840	−	0.976649i	$-0.431077\pi$
$73$	2.79454e29			0.429679			0.214840	+	0.976649i	$0.431077\pi$
$74$	−5.88523e28	−	2.19591e28i	−0.0727874	−	0.0271585i
$75$		0			0
$76$	1.25180e30	−	1.44393e30i	1.01045	−	1.16554i
$77$	3.99743e29			0.261776
$78$		0			0
$79$		−	2.19129e30i		−	0.952063i	−0.879428	−	0.476032i	$-0.842075\pi$
$79$		−	2.19129e30i		−	0.952063i	0.879428	−	0.476032i	$-0.157925\pi$
$80$	−3.64239e29	−	2.54226e30i	−0.129404	−	0.903193i
$81$		0			0
$82$	8.73891e29	+	3.26068e29i	0.209139	+	0.0780344i
$83$		−	3.91771e30i		−	0.772294i	−0.922437	−	0.386147i	$-0.873806\pi$
$83$		−	3.91771e30i		−	0.772294i	0.922437	−	0.386147i	$-0.126194\pi$
$84$		0			0
$85$	−8.56139e30			−1.15303
$86$	−3.12866e30	+	8.38511e30i	−0.349449	+	0.936555i
$87$		0			0
$88$	−4.42035e30	+	2.41156e30i	−0.341770	+	0.186456i
$89$	2.76276e31			1.78280			0.891400	−	0.453217i	$-0.149724\pi$
$89$	2.76276e31			1.78280			0.891400	+	0.453217i	$0.149724\pi$
$90$		0			0
$91$		−	4.83771e30i		−	0.218765i
$92$	−2.46004e31	+	2.83762e31i	−0.933979	+	1.07733i
$93$		0			0
$94$	−3.73660e30	+	1.00144e31i	−0.100561	+	0.269514i
$95$			6.19462e31i			1.40746i
$96$		0			0
$97$	2.89803e30			0.0471798			0.0235899	−	0.999722i	$-0.492490\pi$
$97$	2.89803e30			0.0471798			0.0235899	+	0.999722i	$0.492490\pi$
$98$	3.71544e31	+	1.38631e31i	0.513326	+	0.191533i
$99$		0			0
$100$	−1.26559e31	−	1.09719e31i	−0.126559	−	0.109719i
$101$	−2.75294e31			−0.234777			−0.117388	−	0.993086i	$-0.537452\pi$
$101$	−2.75294e31			−0.234777			−0.117388	+	0.993086i	$0.537452\pi$
$102$		0			0
$103$		−	6.01350e30i		−	0.0374742i	−0.999824	−	0.0187371i	$-0.994035\pi$
$103$		−	6.01350e30i		−	0.0374742i	0.999824	−	0.0187371i	$-0.00596455\pi$
$104$	2.91848e31	+	5.34952e31i	0.155820	+	0.285615i
$105$		0			0
$106$	−4.05212e32	−	1.51194e32i	−1.59510	−	0.595168i
$107$		−	1.74148e32i		−	0.589900i	−0.955513	−	0.294950i	$-0.904697\pi$
$107$		−	1.74148e32i		−	0.589900i	0.955513	−	0.294950i	$-0.0953030\pi$
$108$		0			0
$109$	5.59935e32			1.41031			0.705153	−	0.709055i	$-0.250878\pi$
$109$	5.59935e32			1.41031			0.705153	+	0.709055i	$0.250878\pi$
$110$	5.70601e31	−	1.52926e32i	0.124179	−	0.332812i
$111$		0			0
$112$	4.08034e32	−	5.84604e31i	0.665591	−	0.0953616i
$113$	7.28604e32			1.03095			0.515474	−	0.856905i	$-0.327616\pi$
$113$	7.28604e32			1.03095			0.515474	+	0.856905i	$0.327616\pi$
$114$		0			0
$115$		−	1.21737e33i		−	1.30094i
$116$	−1.47211e33	−	1.27622e33i	−1.36966	−	1.18741i
$117$		0			0
$118$	4.71785e30	−	1.26443e31i	0.00333912	−	0.00894915i
$119$		−	1.37411e33i		−	0.849706i
$120$		0			0
$121$	1.79135e33			0.848428
$122$	1.02206e33	+	3.81351e32i	0.424343	+	0.158332i
$123$		0			0
$124$	3.02447e33	−	3.48868e33i	0.968060	−	1.11664i
$125$	3.78450e33			1.06524
$126$		0			0
$127$			1.27122e33i			0.277563i	0.990323	+	0.138781i	$0.0443185\pi$
$127$			1.27122e33i			0.277563i	−0.990323	+	0.138781i	$0.955681\pi$
$128$	−4.15934e33	+	3.10803e33i	−0.801060	+	0.598585i
$129$		0			0
$130$	−1.85072e33	−	6.90543e32i	−0.278129	−	0.103776i
$131$		−	5.79109e33i		−	0.769874i	−0.922943	−	0.384937i	$-0.874223\pi$
$131$		−	5.79109e33i		−	0.769874i	0.922943	−	0.384937i	$-0.125777\pi$
$132$		0			0
$133$	−9.94237e33			−1.03720
$134$	5.30262e33	−	1.42115e34i	0.490697	−	1.31511i
$135$		0			0
$136$	8.28967e33	+	1.51948e34i	0.605222	+	1.10936i
$137$	−5.24158e33			−0.340356			−0.170178	−	0.985413i	$-0.554434\pi$
$137$	−5.24158e33			−0.340356			−0.170178	+	0.985413i	$0.554434\pi$
$138$		0			0
$139$		−	3.31449e34i		−	1.70679i	−0.521267	−	0.853394i	$-0.674540\pi$
$139$		−	3.31449e34i		−	1.70679i	0.521267	−	0.853394i	$-0.325460\pi$
$140$	−8.75254e33	+	1.00959e34i	−0.401870	+	0.463551i
$141$		0			0
$142$	8.43660e33	−	2.26109e34i	0.308712	−	0.827377i
$143$			3.87297e33i			0.126668i
$144$		0			0
$145$	6.31549e34			1.65394
$146$	1.71588e34	+	6.40231e33i	0.402569	+	0.150207i
$147$		0			0
$148$	−3.11051e33	−	2.69662e33i	−0.0587009	−	0.0508900i
$149$	−5.60725e34			−0.950100			−0.475050	−	0.879959i	$-0.657570\pi$
$149$	−5.60725e34			−0.950100			−0.475050	+	0.879959i	$0.657570\pi$
$150$		0			0
$151$		−	2.77124e34i		−	0.379353i	−0.981847	−	0.189676i	$-0.939256\pi$
$151$		−	2.77124e34i		−	0.379353i	0.981847	−	0.189676i	$-0.0607439\pi$
$152$	1.09942e35	−	5.99801e34i	1.35415	−	0.738771i
$153$		0			0
$154$	2.45447e34	+	9.15815e33i	0.245260	+	0.0915117i
$155$			1.49668e35i			1.34841i
$156$		0			0
$157$	−8.55727e34			−0.627973			−0.313986	−	0.949428i	$-0.601665\pi$
$157$	−8.55727e34			−0.627973			−0.313986	+	0.949428i	$0.601665\pi$
$158$	5.02025e34	−	1.34547e35i	0.332822	−	0.891994i
$159$		0			0
$160$	3.58787e34	−	1.64442e35i	0.194499	−	0.891444i
$161$	1.95388e35			0.958703
$162$		0			0
$163$		−	1.94005e35i		−	0.781287i	−0.920542	−	0.390644i	$-0.872252\pi$
$163$		−	1.94005e35i		−	0.781287i	0.920542	−	0.390644i	$-0.127748\pi$
$164$	4.61876e34	+	4.00418e34i	0.168665	+	0.146222i
$165$		0			0
$166$	8.97550e34	−	2.40552e35i	0.269979	−	0.723567i
$167$		−	3.97663e35i		−	1.08655i	−0.839553	−	0.543277i	$-0.817183\pi$
$167$		−	3.97663e35i		−	1.08655i	0.839553	−	0.543277i	$-0.182817\pi$
$168$		0			0
$169$	−3.95908e35			−0.894144
$170$	−5.25679e35	−	1.96142e35i	−1.08028	−	0.403077i
$171$		0			0
$172$	−3.84207e35	+	4.43177e35i	−0.654802	+	0.755304i
$173$	1.09919e35			0.170740			0.0853698	−	0.996349i	$-0.472793\pi$
$173$	1.09919e35			0.170740			0.0853698	+	0.996349i	$0.472793\pi$
$174$		0			0
$175$			8.71440e34i			0.112623i
$176$	−3.26663e35	+	4.68022e34i	−0.385388	+	0.0552158i
$177$		0			0
$178$	1.69636e36	+	6.32950e35i	1.67032	+	0.623231i
$179$			1.77396e36i			1.59696i	0.602021	+	0.798480i	$0.294362\pi$
$179$			1.77396e36i			1.59696i	−0.602021	+	0.798480i	$0.705638\pi$
$180$		0			0
$181$	7.69778e34			0.0580107			0.0290054	−	0.999579i	$-0.490766\pi$
$181$	7.69778e34			0.0580107			0.0290054	+	0.999579i	$0.490766\pi$
$182$	1.10832e35	−	2.97041e35i	0.0764758	−	0.204962i
$183$		0			0
$184$	−2.16059e36	+	1.17873e36i	−1.25166	+	0.682858i
$185$	1.33444e35			0.0708847
$186$		0			0
$187$			1.10008e36i			0.491993i
$188$	−4.58863e35	+	5.29291e35i	−0.188433	+	0.217355i
$189$		0			0
$190$	−1.41919e36	+	3.80356e36i	−0.492021	+	1.31866i
$191$		−	1.79749e36i		−	0.572971i	−0.958085	−	0.286486i	$-0.907513\pi$
$191$		−	1.79749e36i		−	0.572971i	0.958085	−	0.286486i	$-0.0924871\pi$
$192$		0			0
$193$	2.10472e36			0.567908			0.283954	−	0.958838i	$-0.408354\pi$
$193$	2.10472e36			0.567908			0.283954	+	0.958838i	$0.408354\pi$
$194$	1.77942e35	+	6.63942e34i	0.0442030	+	0.0164931i
$195$		0			0
$196$	1.96372e36	+	1.70242e36i	0.413982	+	0.358897i
$197$	1.10393e36			0.214528			0.107264	−	0.994231i	$-0.465791\pi$
$197$	1.10393e36			0.214528			0.107264	+	0.994231i	$0.465791\pi$
$198$		0			0
$199$		−	8.49051e36i		−	1.40373i	−0.712309	−	0.701866i	$-0.752350\pi$
$199$		−	8.49051e36i		−	1.40373i	0.712309	−	0.701866i	$-0.247650\pi$
$200$	−5.25721e35	−	9.63635e35i	−0.0802186	−	0.147039i
$201$		0			0
$202$	−1.69034e36	−	6.30701e35i	−0.219964	−	0.0820732i
$203$			1.01364e37i			1.21884i
$204$		0			0
$205$	−1.98150e36			−0.203672
$206$	1.37770e35	−	3.69236e35i	0.0131002	−	0.0351098i
$207$		0			0
$208$	5.66401e35	+	3.95329e36i	0.0461436	+	0.322066i
$209$	7.95966e36			0.600557
$210$		0			0
$211$			2.37381e37i			1.53790i	0.639312	+	0.768948i	$0.279219\pi$
$211$			2.37381e37i			1.53790i	−0.639312	+	0.768948i	$0.720781\pi$
$212$	−2.14166e37	−	1.85669e37i	−1.28640	−	1.11523i
$213$		0			0
$214$	3.98975e36	−	1.06929e37i	0.206217	−	0.552681i
$215$		−	1.90128e37i		−	0.912074i
$216$		0			0
$217$	−2.40218e37			−0.993687
$218$	3.43806e37	+	1.28282e37i	1.32133	+	0.493015i
$219$		0			0
$220$	7.00710e36	−	8.08259e36i	0.232689	−	0.268403i
$221$	1.33132e37			0.411156
$222$		0			0
$223$		−	5.19320e37i		−	1.38854i	−0.719716	−	0.694268i	$-0.755728\pi$
$223$		−	5.19320e37i		−	1.38854i	0.719716	−	0.694268i	$-0.244272\pi$
$224$	2.63930e37	+	5.75855e36i	0.656933	+	0.143333i
$225$		0			0
$226$	4.47371e37	+	1.66924e37i	0.965902	+	0.360399i
$227$		−	2.16268e37i		−	0.435090i	−0.976050	−	0.217545i	$-0.930195\pi$
$227$		−	2.16268e37i		−	0.435090i	0.976050	−	0.217545i	$-0.0698049\pi$
$228$		0			0
$229$	3.92200e37			0.685709			0.342854	−	0.939389i	$-0.388606\pi$
$229$	3.92200e37			0.685709			0.342854	+	0.939389i	$0.388606\pi$
$230$	2.78900e37	−	7.47478e37i	0.454782	−	1.21886i
$231$		0			0
$232$	−6.11505e37	−	1.12088e38i	−0.868145	−	1.59129i
$233$	1.54117e37			0.204247			0.102124	−	0.994772i	$-0.467436\pi$
$233$	1.54117e37			0.204247			0.102124	+	0.994772i	$0.467436\pi$
$234$		0			0
$235$		−	2.27072e37i		−	0.262468i
$236$	5.79363e35	−	6.68286e35i	0.00625689	−	0.00721723i
$237$		0			0
$238$	3.14809e37	−	8.43716e37i	0.297040	−	0.796095i
$239$			2.42617e37i			0.214070i	0.994255	+	0.107035i	$0.0341357\pi$
$239$			2.42617e37i			0.214070i	−0.994255	+	0.107035i	$0.965864\pi$
$240$		0			0
$241$	1.91142e38			1.47599			0.737996	−	0.674805i	$-0.235772\pi$
$241$	1.91142e38			1.47599			0.737996	+	0.674805i	$0.235772\pi$
$242$	1.09991e38	+	4.10400e37i	0.794897	+	0.296593i
$243$		0			0
$244$	5.40185e37	+	4.68307e37i	0.342220	+	0.296684i
$245$	−8.42456e37			−0.499908
$246$		0			0
$247$		−	9.63280e37i		−	0.501882i
$248$	2.65632e38	−	1.44918e38i	1.29734	−	0.707776i
$249$		0			0
$250$	2.32373e38	+	8.67033e37i	0.998033	+	0.372388i
$251$		−	4.00964e38i		−	1.61557i	−0.589477	−	0.807785i	$-0.700666\pi$
$251$		−	4.00964e38i		−	1.61557i	0.589477	−	0.807785i	$-0.299334\pi$
$252$		0			0
$253$	−1.56424e38			−0.555104
$254$	−2.91238e37	+	7.80543e37i	−0.0970304	+	0.260050i
$255$		0			0
$256$	−3.26593e38	+	9.55456e37i	−0.959771	+	0.280783i
$257$	5.30332e38			1.46426			0.732129	−	0.681166i	$-0.238527\pi$
$257$	5.30332e38			1.46426			0.732129	+	0.681166i	$0.238527\pi$
$258$		0			0
$259$			2.14179e37i			0.0522372i
$260$	−9.78157e37	−	8.48001e37i	−0.224303	−	0.194457i
$261$		0			0
$262$	1.32674e38	−	3.55579e38i	0.269133	−	0.721300i
$263$		−	9.05669e38i		−	1.72853i	−0.503034	−	0.864267i	$-0.667783\pi$
$263$		−	9.05669e38i		−	1.72853i	0.503034	−	0.864267i	$-0.332217\pi$
$264$		0			0
$265$	9.18797e38			1.55341
$266$	−6.10473e38	−	2.27781e38i	−0.971762	−	0.362586i
$267$		0			0
$268$	6.51174e38	−	7.51119e38i	0.919475	−	1.06060i
$269$	7.91984e38			1.05361			0.526805	−	0.849986i	$-0.323390\pi$
$269$	7.91984e38			1.05361			0.526805	+	0.849986i	$0.323390\pi$
$270$		0			0
$271$			7.17026e38i			0.847278i	0.905831	+	0.423639i	$0.139248\pi$
$271$			7.17026e38i			0.847278i	−0.905831	+	0.423639i	$0.860752\pi$
$272$	1.60881e38	+	1.12289e39i	0.179227	+	1.25094i
$273$		0			0
$274$	−3.21839e38	−	1.20085e38i	−0.318881	−	0.118982i
$275$		−	6.97657e37i		−	0.0652107i
$276$		0			0
$277$	−1.07006e39			−0.890698			−0.445349	−	0.895357i	$-0.646920\pi$
$277$	−1.07006e39			−0.890698			−0.445349	+	0.895357i	$0.646920\pi$
$278$	7.59352e38	−	2.03513e39i	0.596659	−	1.59910i
$279$		0			0
$280$	−7.68714e38	+	4.19379e38i	−0.538563	+	0.293818i
$281$	9.83963e38			0.651145			0.325573	−	0.945517i	$-0.394443\pi$
$281$	9.83963e38			0.651145			0.325573	+	0.945517i	$0.394443\pi$
$282$		0			0
$283$		−	8.98302e38i		−	0.530688i	−0.964154	−	0.265344i	$-0.914514\pi$
$283$		−	8.98302e38i		−	0.530688i	0.964154	−	0.265344i	$-0.0854855\pi$
$284$	1.03603e39	−	1.19505e39i	0.578469	−	0.667256i
$285$		0			0
$286$	−8.87300e37	+	2.37805e38i	−0.0442807	+	0.118676i
$287$		−	3.18031e38i		−	0.150093i
$288$		0			0
$289$	1.41358e39			0.596973
$290$	3.87778e39	+	1.44688e39i	1.54958	+	0.578184i
$291$		0			0
$292$	9.06890e38	+	7.86218e38i	0.324660	+	0.281460i
$293$	3.27044e38			0.110847			0.0554235	−	0.998463i	$-0.482349\pi$
$293$	3.27044e38			0.110847			0.0554235	+	0.998463i	$0.482349\pi$
$294$		0			0
$295$			2.86702e37i			0.00871522i
$296$	−1.29209e38	−	2.36838e38i	−0.0372071	−	0.0681999i
$297$		0			0
$298$	−3.44291e39	−	1.28462e39i	−0.890155	−	0.332136i
$299$			1.89304e39i			0.463897i
$300$		0			0
$301$	3.05155e39			0.672136
$302$	6.34894e38	−	1.70157e39i	0.132614	−	0.355418i
$303$		0			0
$304$	8.12473e39	−	1.16406e39i	1.52697	−	0.218775i
$305$	−2.31745e39			−0.413251
$306$		0			0
$307$		−	1.67228e39i		−	0.268592i	−0.990941	−	0.134296i	$-0.957123\pi$
$307$		−	1.67228e39i		−	0.268592i	0.990941	−	0.134296i	$-0.0428774\pi$
$308$	1.29726e39	+	1.12464e39i	0.197795	+	0.171476i
$309$		0			0
$310$	−3.42891e39	+	9.18979e39i	−0.471378	+	1.26334i
$311$			1.74120e39i			0.227344i	0.993518	+	0.113672i	$0.0362613\pi$
$311$			1.74120e39i			0.227344i	−0.993518	+	0.113672i	$0.963739\pi$
$312$		0			0
$313$	−1.14924e40			−1.35426			−0.677128	−	0.735866i	$-0.736776\pi$
$313$	−1.14924e40			−1.35426			−0.677128	+	0.735866i	$0.736776\pi$
$314$	−5.25426e39	−	1.96048e39i	−0.588352	−	0.219527i
$315$		0			0
$316$	6.16498e39	−	7.11122e39i	0.623647	−	0.719367i
$317$	1.00613e40			0.967623			0.483811	−	0.875172i	$-0.339252\pi$
$317$	1.00613e40			0.967623			0.483811	+	0.875172i	$0.339252\pi$
$318$		0			0
$319$		−	8.11498e39i		−	0.705726i
$320$	5.97038e39	−	9.27496e39i	0.493858	−	0.767207i
$321$		0			0
$322$	1.19970e40	+	4.47636e39i	0.898215	+	0.335143i
$323$		−	2.73611e40i		−	1.94936i
$324$		0			0
$325$	−8.44307e38			−0.0544962
$326$	4.44467e39	−	1.19121e40i	0.273122	−	0.731993i
$327$		0			0
$328$	1.91861e39	+	3.51677e39i	0.106907	+	0.195958i
$329$	3.64451e39			0.193421
$330$		0			0
$331$		−	4.73509e39i		−	0.228076i	−0.993476	−	0.114038i	$-0.963621\pi$
$331$		−	4.73509e39i		−	0.228076i	0.993476	−	0.114038i	$-0.0363786\pi$
$332$	1.10221e40	−	1.27138e40i	0.505889	−	0.583536i
$333$		0			0
$334$	9.11049e39	−	2.44169e40i	0.379838	−	1.01800i
$335$			3.22238e40i			1.28074i
$336$		0			0
$337$	3.62976e40			1.31159			0.655797	−	0.754937i	$-0.272333\pi$
$337$	3.62976e40			1.31159			0.655797	+	0.754937i	$0.272333\pi$
$338$	−2.43092e40	−	9.07029e39i	−0.837729	−	0.312575i
$339$		0			0
$340$	−2.77836e40	−	2.40867e40i	−0.871217	−	0.755291i
$341$	1.92313e40			0.575360
$342$		0			0
$343$		−	3.82003e40i		−	1.04079i
$344$	−3.37439e40	+	1.84093e40i	−0.877528	+	0.478744i
$345$		0			0
$346$	6.74913e39	+	2.51825e39i	0.159967	+	0.0596871i
$347$		−	2.25109e40i		−	0.509473i	−0.967011	−	0.254736i	$-0.918011\pi$
$347$		−	2.25109e40i		−	0.509473i	0.967011	−	0.254736i	$-0.0819887\pi$
$348$		0			0
$349$	3.78768e40			0.781928			0.390964	−	0.920406i	$-0.372142\pi$
$349$	3.78768e40			0.781928			0.390964	+	0.920406i	$0.372142\pi$
$350$	−1.99648e39	+	5.35074e39i	−0.0393709	+	0.105518i
$351$		0			0
$352$	−2.11297e40	−	4.61017e39i	−0.380374	−	0.0829917i
$353$	−4.87419e40			−0.838508			−0.419254	−	0.907869i	$-0.637708\pi$
$353$	−4.87419e40			−0.838508			−0.419254	+	0.907869i	$0.637708\pi$
$354$		0			0
$355$			5.12689e40i			0.805750i
$356$	8.96577e40	+	7.77276e40i	1.34706	+	1.16782i
$357$		0			0
$358$	−4.06414e40	+	1.08923e41i	−0.558265	+	1.49620i
$359$			5.11945e40i			0.672531i	0.941767	+	0.336265i	$0.109164\pi$
$359$			5.11945e40i			0.672531i	−0.941767	+	0.336265i	$0.890836\pi$
$360$		0			0
$361$	−1.14773e41			−1.37951
$362$	4.72652e39	+	1.76357e39i	0.0543506	+	0.0202794i
$363$		0			0
$364$	1.36104e40	−	1.56994e40i	0.143301	−	0.165296i
$365$	−3.89066e40			−0.392046
$366$		0			0
$367$			1.13981e41i			1.05239i	0.850364	+	0.526196i	$0.176382\pi$
$367$			1.13981e41i			1.05239i	−0.850364	+	0.526196i	$0.823618\pi$
$368$	−1.59668e41	+	2.28761e40i	−1.41141	+	0.202217i
$369$		0			0
$370$	8.19363e39	+	3.05722e39i	0.0664124	+	0.0247799i
$371$			1.47467e41i			1.14476i
$372$		0			0
$373$	−1.95796e41			−1.39464			−0.697319	−	0.716761i	$-0.745624\pi$
$373$	−1.95796e41			−1.39464			−0.697319	+	0.716761i	$0.745624\pi$
$374$	−2.52029e40	+	6.75462e40i	−0.171991	+	0.460951i
$375$		0			0
$376$	−4.03008e40	+	2.19865e40i	−0.252527	+	0.137769i
$377$	−9.82077e40			−0.589772
$378$		0			0
$379$		−	1.25171e40i		−	0.0690679i	−0.999404	−	0.0345339i	$-0.989005\pi$
$379$		−	1.25171e40i		−	0.0690679i	0.999404	−	0.0345339i	$-0.0109947\pi$
$380$	−1.74280e41	+	2.01029e41i	−0.921955	+	1.06346i
$381$		0			0
$382$	4.11807e40	−	1.10368e41i	0.200299	−	0.536821i
$383$		−	2.07290e41i		−	0.966938i	−0.875362	−	0.483469i	$-0.839377\pi$
$383$		−	2.07290e41i		−	0.966938i	0.875362	−	0.483469i	$-0.160623\pi$
$384$		0			0
$385$	−5.56537e40			−0.238848
$386$	1.29232e41	+	4.82194e40i	0.532077	+	0.198529i
$387$		0			0
$388$	9.40477e39	+	8.15335e39i	0.0356484	+	0.0309050i
$389$	−2.02435e41			−0.736361			−0.368181	−	0.929754i	$-0.620019\pi$
$389$	−2.02435e41			−0.736361			−0.368181	+	0.929754i	$0.620019\pi$
$390$		0			0
$391$			5.37701e41i			1.80183i
$392$	8.15718e40	+	1.49519e41i	0.262400	+	0.480973i
$393$		0			0
$394$	6.77827e40	+	2.52912e40i	0.200992	+	0.0749946i
$395$			3.05079e41i			0.868677i
$396$		0			0
$397$	1.88519e40			0.0495115			0.0247558	−	0.999694i	$-0.492119\pi$
$397$	1.88519e40			0.0495115			0.0247558	+	0.999694i	$0.492119\pi$
$398$	1.94518e41	−	5.21327e41i	0.490717	−	1.31517i
$399$		0			0
$400$	−1.02029e40	−	7.12125e40i	−0.0237554	−	0.165805i
$401$	−7.93687e41			−1.77558			−0.887788	−	0.460252i	$-0.847759\pi$
$401$	−7.93687e41			−1.77558			−0.887788	+	0.460252i	$0.847759\pi$
$402$		0			0
$403$		−	2.32738e41i		−	0.480825i
$404$	−8.93391e40	−	7.74515e40i	−0.177394	−	0.153790i
$405$		0			0
$406$	−2.32225e41	+	6.22385e41i	−0.426082	+	1.14194i
$407$		−	1.71467e40i		−	0.0302461i
$408$		0			0
$409$	1.31441e41			0.214367			0.107183	−	0.994239i	$-0.465817\pi$
$409$	1.31441e41			0.214367			0.107183	+	0.994239i	$0.465817\pi$
$410$	−1.21666e41	−	4.53963e40i	−0.190822	−	0.0711998i
$411$		0			0
$412$	1.69184e40	−	1.95152e40i	0.0245474	−	0.0283150i
$413$	−4.60157e39			−0.00642252
$414$		0			0
$415$			5.45437e41i			0.704653i
$416$	−5.57925e40	+	2.55713e41i	−0.0693557	+	0.317877i
$417$		0			0
$418$	4.88732e41	+	1.82356e41i	0.562665	+	0.209943i
$419$			7.01171e41i			0.776961i	0.921457	+	0.388481i	$0.127000\pi$
$419$			7.01171e41i			0.776961i	−0.921457	+	0.388481i	$0.873000\pi$
$420$		0			0
$421$	−8.56023e41			−0.878966			−0.439483	−	0.898251i	$-0.644838\pi$
$421$	−8.56023e41			−0.878966			−0.439483	+	0.898251i	$0.644838\pi$
$422$	−5.43842e41	+	1.45755e42i	−0.537618	+	1.44086i
$423$		0			0
$424$	−8.89636e41	−	1.63068e42i	−0.815378	−	1.49457i
$425$	−2.39817e41			−0.211669
$426$		0			0
$427$		−	3.71952e41i		−	0.304537i
$428$	4.89950e41	−	5.65150e41i	0.386413	−	0.445721i
$429$		0			0
$430$	4.35584e41	−	1.16740e42i	0.318843	−	0.854528i
$431$			5.29035e41i			0.373120i	0.982444	+	0.186560i	$0.0597338\pi$
$431$			5.29035e41i			0.373120i	−0.982444	+	0.186560i	$0.940266\pi$
$432$		0			0
$433$	2.07497e41			0.135896			0.0679478	−	0.997689i	$-0.478355\pi$
$433$	2.07497e41			0.135896			0.0679478	+	0.997689i	$0.478355\pi$
$434$	−1.47496e42	−	5.50341e41i	−0.930991	−	0.347373i
$435$		0			0
$436$	1.81711e42	+	1.57533e42i	1.06561	+	0.923818i
$437$	3.89055e42			2.19942
$438$		0			0
$439$		−	2.85946e42i		−	1.50263i	−0.659944	−	0.751315i	$-0.729420\pi$
$439$		−	2.85946e42i		−	1.50263i	0.659944	−	0.751315i	$-0.270580\pi$
$440$	6.15416e41	−	3.35747e41i	0.311836	−	0.170125i
$441$		0			0
$442$	8.17446e41	+	3.05007e41i	0.385214	+	0.143732i
$443$		−	2.21579e42i		−	1.00709i	−0.863969	−	0.503545i	$-0.832029\pi$
$443$		−	2.21579e42i		−	1.00709i	0.863969	−	0.503545i	$-0.167971\pi$
$444$		0			0
$445$	−3.84641e42			−1.62665
$446$	1.18977e42	−	3.18868e42i	0.485405	−	1.30093i
$447$		0			0
$448$	1.48863e42	+	9.58248e41i	0.565379	+	0.363940i
$449$	−8.69610e40			−0.0318701			−0.0159350	−	0.999873i	$-0.505072\pi$
$449$	−8.69610e40			−0.0318701			−0.0159350	+	0.999873i	$0.505072\pi$
$450$		0			0
$451$			2.54609e41i			0.0869059i
$452$	2.36448e42	+	2.04986e42i	0.778971	+	0.675320i
$453$		0			0
$454$	4.95473e41	−	1.32791e42i	0.152099	−	0.407639i
$455$			6.73523e41i			0.199604i
$456$		0			0
$457$	4.54305e42			1.25513			0.627565	−	0.778564i	$-0.284052\pi$
$457$	4.54305e42			1.25513			0.627565	+	0.778564i	$0.284052\pi$
$458$	2.40815e42	+	8.98533e41i	0.642445	+	0.239710i
$459$		0			0
$460$	3.42496e42	−	3.95064e42i	0.852177	−	0.982973i
$461$	−4.18043e42			−1.00463			−0.502315	−	0.864684i	$-0.667518\pi$
$461$	−4.18043e42			−1.00463			−0.502315	+	0.864684i	$0.667518\pi$
$462$		0			0
$463$		−	1.57491e42i		−	0.353150i	−0.984287	−	0.176575i	$-0.943498\pi$
$463$		−	1.57491e42i		−	0.353150i	0.984287	−	0.176575i	$-0.0565018\pi$
$464$	−1.18677e42	−	8.28327e42i	−0.257087	−	1.79438i
$465$		0			0
$466$	9.46297e41	+	3.53084e41i	0.191361	+	0.0714008i
$467$		−	3.22443e42i		−	0.630061i	−0.949082	−	0.315031i	$-0.897985\pi$
$467$		−	3.22443e42i		−	0.630061i	0.949082	−	0.315031i	$-0.102015\pi$
$468$		0			0
$469$	−5.17193e42			−0.943815
$470$	5.20223e41	−	1.39425e42i	0.0917537	−	0.245908i
$471$		0			0
$472$	5.08840e40	−	2.77603e40i	0.00838512	−	0.00457458i
$473$	−2.44301e42			−0.389177
$474$		0			0
$475$			1.73520e42i			0.258376i
$476$	3.86592e42	−	4.45928e42i	0.556598	−	0.642027i
$477$		0			0
$478$	−5.55838e41	+	1.48970e42i	−0.0748346	+	0.200563i
$479$			6.21903e42i			0.809756i	0.914371	+	0.404878i	$0.132686\pi$
$479$			6.21903e42i			0.809756i	−0.914371	+	0.404878i	$0.867314\pi$
$480$		0			0
$481$	−2.07510e41			−0.0252765
$482$	1.17363e43	+	4.37908e42i	1.38287	+	0.515977i
$483$		0			0
$484$	5.81334e42	+	5.03980e42i	0.641061	+	0.555761i
$485$	−4.03475e41			−0.0430475
$486$		0			0
$487$			1.91998e43i			1.91793i	0.283517	+	0.958967i	$0.408499\pi$
$487$			1.91998e43i			1.91793i	−0.283517	+	0.958967i	$0.591501\pi$
$488$	2.24390e42	+	4.11303e42i	0.216914	+	0.397598i
$489$		0			0
$490$	−5.17277e42	−	1.93007e42i	−0.468367	−	0.174758i
$491$		−	4.78448e42i		−	0.419306i	−0.977776	−	0.209653i	$-0.932767\pi$
$491$		−	4.78448e42i		−	0.419306i	0.977776	−	0.209653i	$-0.0672334\pi$
$492$		0			0
$493$	−2.78950e43			−2.29074
$494$	2.20688e42	−	5.91465e42i	0.175448	−	0.470216i
$495$		0			0
$496$	1.96302e43	−	2.81248e42i	1.46291	−	0.209596i
$497$	−8.22867e42			−0.593782
$498$		0			0
$499$			1.53323e43i			1.03752i	0.854919	+	0.518762i	$0.173607\pi$
$499$			1.53323e43i			1.03752i	−0.854919	+	0.518762i	$0.826393\pi$
$500$	1.22816e43	+	1.06474e43i	0.804885	+	0.697785i
$501$		0			0
$502$	9.18612e42	−	2.46196e43i	0.564771	−	1.51364i
$503$			2.93216e42i			0.174623i	0.996181	+	0.0873113i	$0.0278275\pi$
$503$			2.93216e42i			0.174623i	−0.996181	+	0.0873113i	$0.972173\pi$
$504$		0			0
$505$	3.83274e42			0.214214
$506$	−9.60459e42	−	3.58368e42i	−0.520080	−	0.194053i
$507$		0			0
$508$	−3.57646e42	+	4.12539e42i	−0.181817	+	0.209723i
$509$	2.81958e43			1.38899			0.694496	−	0.719497i	$-0.255627\pi$
$509$	2.81958e43			1.38899			0.694496	+	0.719497i	$0.255627\pi$
$510$		0			0
$511$		−	6.24451e42i		−	0.288911i
$512$	−2.22421e43	−	1.61567e42i	−0.997372	−	0.0724492i
$513$		0			0
$514$	3.25630e43	+	1.21499e43i	1.37187	+	0.511876i
$515$			8.37221e41i			0.0341920i
$516$		0			0
$517$	−2.91772e42			−0.111994
$518$	−4.90685e41	+	1.31508e42i	−0.0182611	+	0.0489414i
$519$		0			0
$520$	−4.06321e42	−	7.44779e42i	−0.142173	−	0.260600i
$521$	−3.53836e43			−1.20060			−0.600300	−	0.799775i	$-0.704952\pi$
$521$	−3.53836e43			−1.20060			−0.600300	+	0.799775i	$0.704952\pi$
$522$		0			0
$523$		−	4.38521e43i		−	1.39947i	−0.714402	−	0.699735i	$-0.753301\pi$
$523$		−	4.38521e43i		−	1.39947i	0.714402	−	0.699735i	$-0.246699\pi$
$524$	1.62927e43	−	1.87934e43i	0.504304	−	0.581707i
$525$		0			0
$526$	2.07490e43	−	5.56091e43i	0.604261	−	1.61947i
$527$		−	6.61071e43i		−	1.86758i
$528$		0			0
$529$	−3.88484e43			−1.03296
$530$	5.64151e43	+	2.10497e43i	1.45540	+	0.543040i
$531$		0			0
$532$	−3.22652e43	−	2.79720e43i	−0.783698	−	0.679417i
$533$	3.08129e42			0.0726268
$534$		0			0
$535$			2.42455e43i			0.538234i
$536$	5.71910e43	−	3.12011e43i	1.23223	−	0.672254i
$537$		0			0
$538$	4.86287e43	+	1.81444e43i	0.987135	+	0.368321i
$539$			1.08250e43i			0.213308i
$540$		0			0
$541$	−3.92683e43			−0.729266			−0.364633	−	0.931151i	$-0.618805\pi$
$541$	−3.92683e43			−0.729266			−0.364633	+	0.931151i	$0.618805\pi$
$542$	−1.64271e43	+	4.40262e43i	−0.296192	+	0.793821i
$543$		0			0
$544$	−1.58473e43	+	7.26328e43i	−0.269385	+	1.23467i
$545$	−7.79561e43			−1.28679
$546$		0			0
$547$			4.32555e43i			0.673356i	0.941620	+	0.336678i	$0.109303\pi$
$547$			4.32555e43i			0.673356i	−0.941620	+	0.336678i	$0.890697\pi$
$548$	−1.70101e43	−	1.47467e43i	−0.257168	−	0.222949i
$549$		0			0
$550$	1.59834e42	−	4.28369e42i	0.0227964	−	0.0610963i
$551$			2.01835e44i			2.79621i
$552$		0			0
$553$	−4.89652e43			−0.640156
$554$	−6.57026e43	−	2.45151e43i	−0.834500	−	0.311370i
$555$		0			0
$556$	9.32500e43	−	1.07563e44i	1.11803	−	1.28963i
$557$	−4.56437e43			−0.531738			−0.265869	−	0.964009i	$-0.585659\pi$
$557$	−4.56437e43			−0.531738			−0.265869	+	0.964009i	$0.585659\pi$
$558$		0			0
$559$			2.95654e43i			0.325233i
$560$	−5.68079e43	+	8.13907e42i	−0.607296	+	0.0870094i
$561$		0			0
$562$	6.04164e43	+	2.25427e43i	0.610062	+	0.227627i
$563$			1.65440e42i			0.0162370i	0.999967	+	0.00811850i	$0.00258423\pi$
$563$			1.65440e42i			0.0162370i	−0.999967	+	0.00811850i	$0.997416\pi$
$564$		0			0
$565$	−1.01439e44			−0.940653
$566$	2.05802e43	−	5.51567e43i	0.185518	−	0.497205i
$567$		0			0
$568$	9.09922e43	−	4.96417e43i	0.775231	−	0.422935i
$569$	−1.25234e44			−1.03735			−0.518676	−	0.854971i	$-0.673575\pi$
$569$	−1.25234e44			−1.03735			−0.518676	+	0.854971i	$0.673575\pi$
$570$		0			0
$571$			1.77620e44i			1.39096i	0.718546	+	0.695479i	$0.244808\pi$
$571$			1.77620e44i			1.39096i	−0.718546	+	0.695479i	$0.755192\pi$
$572$	−1.08962e43	+	1.25687e43i	−0.0829737	+	0.0957089i
$573$		0			0
$574$	7.28612e42	−	1.95275e43i	0.0524694	−	0.140623i
$575$		−	3.41003e43i		−	0.238821i
$576$		0			0
$577$	−2.47656e44			−1.64072			−0.820361	−	0.571845i	$-0.806228\pi$
$577$	−2.47656e44			−1.64072			−0.820361	+	0.571845i	$0.806228\pi$
$578$	8.67954e43	+	3.23852e43i	0.559308	+	0.208690i
$579$		0			0
$580$	2.04952e44	+	1.77681e44i	1.24969	+	1.08341i
$581$	−8.75429e43			−0.519281
$582$		0			0
$583$		−	1.18059e44i		−	0.662831i
$584$	3.76718e43	+	6.90515e43i	0.205783	+	0.377197i
$585$		0			0
$586$	2.00808e43	+	7.49260e42i	0.103853	+	0.0387499i
$587$			1.66894e44i			0.839909i	0.907545	+	0.419954i	$0.137954\pi$
$587$			1.66894e44i			0.839909i	−0.907545	+	0.419954i	$0.862046\pi$
$588$		0			0
$589$	−4.78320e44			−2.27968
$590$	−6.56836e41	+	1.76038e42i	−0.00304667	+	0.00816535i
$591$		0			0
$592$	−2.50761e42	−	1.75023e43i	−0.0110183	−	0.0769038i
$593$	−2.26180e44			−0.967338			−0.483669	−	0.875251i	$-0.660696\pi$
$593$	−2.26180e44			−0.967338			−0.483669	+	0.875251i	$0.660696\pi$
$594$		0			0
$595$			1.91308e44i			0.775285i
$596$	−1.81968e44	−	1.57755e44i	−0.717884	−	0.622361i
$597$		0			0
$598$	−4.33698e43	+	1.16235e44i	−0.162169	+	0.434628i
$599$			3.91427e44i			1.42502i	0.701661	+	0.712510i	$0.252442\pi$
$599$			3.91427e44i			1.42502i	−0.701661	+	0.712510i	$0.747558\pi$
$600$		0			0
$601$	2.39574e44			0.826891			0.413446	−	0.910529i	$-0.364325\pi$
$601$	2.39574e44			0.826891			0.413446	+	0.910529i	$0.364325\pi$
$602$	1.87369e44	+	6.99113e43i	0.629728	+	0.234965i
$603$		0			0
$604$	7.79663e43	−	8.99330e43i	0.248494	−	0.286634i
$605$	−2.49398e44			−0.774119
$606$		0			0
$607$			3.33012e44i			0.980486i	0.871586	+	0.490243i	$0.163092\pi$
$607$			3.33012e44i			0.980486i	−0.871586	+	0.490243i	$0.836908\pi$
$608$	5.25536e44	+	1.14664e44i	1.50711	+	0.328828i
$609$		0			0
$610$	−1.42294e44	−	5.30930e43i	−0.387177	−	0.144464i
$611$			3.53103e43i			0.0935927i
$612$		0			0
$613$	−2.76813e44			−0.696337			−0.348169	−	0.937432i	$-0.613196\pi$
$613$	−2.76813e44			−0.696337			−0.348169	+	0.937432i	$0.613196\pi$
$614$	3.83120e43	−	1.02680e44i	0.0938945	−	0.251646i
$615$		0			0
$616$	5.38874e43	+	9.87745e43i	0.125371	+	0.229802i
$617$	2.34450e44			0.531481			0.265741	−	0.964045i	$-0.414384\pi$
$617$	2.34450e44			0.531481			0.265741	+	0.964045i	$0.414384\pi$
$618$		0			0
$619$		−	7.46890e44i		−	1.60771i	−0.594828	−	0.803853i	$-0.702780\pi$
$619$		−	7.46890e44i		−	1.60771i	0.594828	−	0.803853i	$-0.297220\pi$
$620$	−4.21078e44	+	4.85707e44i	−0.883273	+	1.01884i
$621$		0			0
$622$	−3.98911e43	+	1.06912e44i	−0.0794749	+	0.213000i
$623$		−	6.17350e44i		−	1.19873i
$624$		0			0
$625$	−4.36091e44			−0.804447
$626$	−7.05645e44	−	2.63291e44i	−1.26881	−	0.473421i
$627$		0			0
$628$	−2.77702e44	−	2.40751e44i	−0.474488	−	0.411352i
$629$	−5.89412e43			−0.0981768
$630$		0			0
$631$			3.23311e44i			0.511859i	0.966695	+	0.255930i	$0.0823815\pi$
$631$			3.23311e44i			0.511859i	−0.966695	+	0.255930i	$0.917619\pi$
$632$	5.41455e44	−	2.95396e44i	0.835775	−	0.455965i
$633$		0			0
$634$	6.17775e44	+	2.30505e44i	0.906572	+	0.338262i
$635$		−	1.76984e44i		−	0.253253i
$636$		0			0
$637$	1.31004e44			0.178260
$638$	1.85915e44	−	4.98269e44i	0.246708	−	0.661200i
$639$		0			0
$640$	5.79078e44	−	4.32711e44i	0.730899	−	0.546158i
$641$	8.79742e44			1.08300			0.541498	−	0.840702i	$-0.317857\pi$
$641$	8.79742e44			1.08300			0.541498	+	0.840702i	$0.317857\pi$
$642$		0			0
$643$			1.22266e45i			1.43196i	0.698123	+	0.715978i	$0.254019\pi$
$643$			1.22266e45i			1.43196i	−0.698123	+	0.715978i	$0.745981\pi$
$644$	6.34078e44	+	5.49706e44i	0.724384	+	0.627996i
$645$		0			0
$646$	6.26844e44	−	1.68000e45i	0.681458	−	1.82637i
$647$			1.76718e44i			0.187419i	0.995600	+	0.0937094i	$0.0298724\pi$
$647$			1.76718e44i			0.187419i	−0.995600	+	0.0937094i	$0.970128\pi$
$648$		0			0
$649$	3.68392e42			0.00371874
$650$	−5.18414e43	−	1.93431e43i	−0.0510579	−	0.0190508i
$651$		0			0
$652$	5.45815e44	−	6.29589e44i	0.511780	−	0.590331i
$653$	−6.63007e44			−0.606606			−0.303303	−	0.952894i	$-0.598090\pi$
$653$	−6.63007e44			−0.606606			−0.303303	+	0.952894i	$0.598090\pi$
$654$		0			0
$655$			8.06256e44i			0.702445i
$656$	3.72352e43	+	2.59889e44i	0.0316587	+	0.220967i
$657$		0			0
$658$	2.23777e44	+	8.34959e43i	0.181218	+	0.0676162i
$659$		−	1.59975e45i		−	1.26440i	−0.774804	−	0.632202i	$-0.782151\pi$
$659$		−	1.59975e45i		−	1.26440i	0.774804	−	0.632202i	$-0.217849\pi$
$660$		0			0
$661$	2.05812e45			1.54970			0.774850	−	0.632145i	$-0.217825\pi$
$661$	2.05812e45			1.54970			0.774850	+	0.632145i	$0.217825\pi$
$662$	1.08481e44	−	2.90740e44i	0.0797309	−	0.213686i
$663$		0			0
$664$	9.68045e44	−	5.28127e44i	0.677964	−	0.369870i
$665$	1.38421e45			0.946360
$666$		0			0
$667$		−	3.96647e45i		−	2.58458i
$668$	1.11879e45	−	1.29050e45i	0.711745	−	0.820987i
$669$		0			0
$670$	−7.38250e44	+	1.97858e45i	−0.447720	+	1.19993i
$671$			2.97777e44i			0.176332i
$672$		0			0
$673$	−1.30868e45			−0.738911			−0.369455	−	0.929249i	$-0.620456\pi$
$673$	−1.30868e45			−0.738911			−0.369455	+	0.929249i	$0.620456\pi$
$674$	2.22871e45	+	8.31581e44i	1.22884	+	0.458507i
$675$		0			0
$676$	−1.28481e45	−	1.11385e45i	−0.675604	−	0.585707i
$677$	−4.37637e44			−0.224748			−0.112374	−	0.993666i	$-0.535845\pi$
$677$	−4.37637e44			−0.224748			−0.112374	+	0.993666i	$0.535845\pi$
$678$		0			0
$679$		−	6.47578e43i		−	0.0317231i
$680$	−1.15412e45	−	2.11547e45i	−0.552214	−	1.01220i
$681$		0			0
$682$	1.18083e45	+	4.40592e44i	0.539058	+	0.201134i
$683$		−	4.04925e45i		−	1.80569i	−0.429963	−	0.902846i	$-0.641474\pi$
$683$		−	4.04925e45i		−	1.80569i	0.429963	−	0.902846i	$-0.358526\pi$
$684$		0			0
$685$	7.29751e44			0.310546
$686$	8.75173e44	−	2.34554e45i	0.363838	−	0.975119i
$687$		0			0
$688$	−2.49368e45	+	3.57278e44i	−0.989521	+	0.141772i
$689$	−1.42875e45			−0.553924
$690$		0			0
$691$			7.76543e44i			0.287420i	0.989620	+	0.143710i	$0.0459032\pi$
$691$			7.76543e44i			0.287420i	−0.989620	+	0.143710i	$0.954097\pi$
$692$	3.56711e44	+	3.09246e44i	0.129009	+	0.111843i
$693$		0			0
$694$	5.15726e44	−	1.38219e45i	0.178102	−	0.477328i
$695$			4.61455e45i			1.55730i
$696$		0			0
$697$	8.75211e44			0.282090
$698$	2.32568e45	+	8.67761e44i	0.732594	+	0.273346i
$699$		0			0
$700$	−2.45172e44	+	2.82802e44i	−0.0737737	+	0.0850969i
$701$	−1.30382e45			−0.383467			−0.191734	−	0.981447i	$-0.561411\pi$
$701$	−1.30382e45			−0.383467			−0.191734	+	0.981447i	$0.561411\pi$
$702$		0			0
$703$			4.26471e44i			0.119841i
$704$	−1.19177e45	−	7.67154e44i	−0.327363	−	0.210727i
$705$		0			0
$706$	−2.99281e45	−	1.11668e45i	−0.785603	−	0.293126i
$707$			6.15156e44i			0.157861i
$708$		0			0
$709$	6.95799e44			0.170665			0.0853324	−	0.996353i	$-0.472805\pi$
$709$	6.95799e44			0.170665			0.0853324	+	0.996353i	$0.472805\pi$
$710$	−1.17457e45	+	3.14796e45i	−0.281674	+	0.754912i
$711$		0			0
$712$	3.72433e45	+	6.82663e45i	0.853825	+	1.56504i
$713$	9.39997e45			2.10714
$714$		0			0
$715$		−	5.39209e44i		−	0.115574i
$716$	−4.99086e45	+	5.75688e45i	−1.04609	+	1.20664i
$717$		0			0
$718$	−1.17287e45	+	3.14340e45i	−0.235103	+	0.630099i
$719$		−	8.60509e44i		−	0.168692i	−0.996437	−	0.0843458i	$-0.973120\pi$
$719$		−	8.60509e44i		−	0.168692i	0.996437	−	0.0843458i	$-0.0268800\pi$
$720$		0			0
$721$	−1.34374e44			−0.0251972
$722$	−7.04721e45	−	2.62946e45i	−1.29247	−	0.482250i
$723$		0			0
$724$	2.49810e44	+	2.16570e44i	0.0438322	+	0.0379998i
$725$	1.76906e45			0.303623
$726$		0			0
$727$		−	7.29693e45i		−	1.19837i	−0.800612	−	0.599183i	$-0.795492\pi$
$727$		−	7.29693e45i		−	1.19837i	0.800612	−	0.599183i	$-0.204508\pi$
$728$	1.19537e45	−	6.52147e44i	0.192044	−	0.104772i
$729$		0			0
$730$	−2.38891e45	−	8.91352e44i	−0.367310	−	0.137051i
$731$			8.39777e45i			1.26324i
$732$		0			0
$733$	1.38096e45			0.198846			0.0994228	−	0.995045i	$-0.468300\pi$
$733$	1.38096e45			0.198846			0.0994228	+	0.995045i	$0.468300\pi$
$734$	−2.61132e45	+	6.99859e45i	−0.367895	+	0.985992i
$735$		0			0
$736$	−1.03279e46	−	2.25338e45i	−1.39305	−	0.303941i
$737$	4.14054e45			0.546484
$738$		0			0
$739$			1.34106e46i			1.69487i	0.530897	+	0.847437i	$0.321855\pi$
$739$			1.34106e46i			1.69487i	−0.530897	+	0.847437i	$0.678145\pi$
$740$	4.33057e44	+	3.75433e44i	0.0535596	+	0.0464329i
$741$		0			0
$742$	−3.37848e45	+	9.05464e45i	−0.400184	+	1.07253i
$743$		−	6.23466e45i		−	0.722756i	−0.932419	−	0.361378i	$-0.882306\pi$
$743$		−	6.23466e45i		−	0.722756i	0.932419	−	0.361378i	$-0.117694\pi$
$744$		0			0
$745$	7.80661e45			0.866886
$746$	−1.20221e46	−	4.48569e45i	−1.30665	−	0.487538i
$747$		0			0
$748$	−3.09498e45	+	3.57001e45i	−0.322279	+	0.371744i
$749$	−3.89141e45			−0.396642
$750$		0			0
$751$		−	3.87283e45i		−	0.378259i	−0.981952	−	0.189130i	$-0.939433\pi$
$751$		−	3.87283e45i		−	0.378259i	0.981952	−	0.189130i	$-0.0605666\pi$
$752$	−2.97823e45	+	4.26701e44i	−0.284755	+	0.0407979i
$753$		0			0
$754$	−6.03006e45	−	2.24995e45i	−0.552561	−	0.206172i
$755$			3.85822e45i			0.346127i
$756$		0			0
$757$	8.44667e45			0.726359			0.363180	−	0.931719i	$-0.381691\pi$
$757$	8.44667e45			0.726359			0.363180	+	0.931719i	$0.381691\pi$
$758$	2.86767e44	−	7.68563e44i	0.0241447	−	0.0647101i
$759$		0			0
$760$	−1.53066e46	+	8.35065e45i	−1.23555	+	0.674066i
$761$	−1.41451e46			−1.11802			−0.559012	−	0.829160i	$-0.688819\pi$
$761$	−1.41451e46			−1.11802			−0.559012	+	0.829160i	$0.688819\pi$
$762$		0			0
$763$		−	1.25120e46i		−	0.948273i
$764$	5.05708e45	−	5.83326e45i	0.375323	−	0.432930i
$765$		0			0
$766$	4.74904e45	−	1.27278e46i	0.338022	−	0.905930i
$767$		−	4.45830e43i		−	0.00310773i
$768$		0			0
$769$	1.81104e46			1.21089			0.605447	−	0.795885i	$-0.292994\pi$
$769$	1.81104e46			1.21089			0.605447	+	0.795885i	$0.292994\pi$
$770$	−3.41720e45	−	1.27503e45i	−0.223779	−	0.0834967i
$771$		0			0
$772$	6.83030e45	+	5.92144e45i	0.429104	+	0.372007i
$773$	−1.38738e46			−0.853738			−0.426869	−	0.904313i	$-0.640384\pi$
$773$	−1.38738e46			−0.853738			−0.426869	+	0.904313i	$0.640384\pi$
$774$		0			0
$775$			4.19243e45i			0.247536i
$776$	3.90669e44	+	7.16089e44i	0.0225955	+	0.0414171i
$777$		0			0
$778$	−1.24297e46	−	4.63779e45i	−0.689902	−	0.257417i
$779$		−	6.33261e45i		−	0.344337i
$780$		0			0
$781$	6.58770e45			0.343809
$782$	−1.23188e46	+	3.30155e46i	−0.629883	+	1.68814i
$783$		0			0
$784$	1.58310e45	+	1.10495e46i	0.0777053	+	0.542356i
$785$	1.19137e46			0.572972
$786$		0			0
$787$		−	2.35867e46i		−	1.08911i	−0.838726	−	0.544554i	$-0.816699\pi$
$787$		−	2.35867e46i		−	1.08911i	0.838726	−	0.544554i	$-0.183301\pi$
$788$	3.58251e45	+	3.10581e45i	0.162094	+	0.140526i
$789$		0			0
$790$	−6.98938e45	+	1.87322e46i	−0.303672	+	0.813869i
$791$		−	1.62810e46i		−	0.693197i
$792$		0			0
$793$	3.60371e45			0.147360
$794$	1.15753e45	+	4.31898e44i	0.0463877	+	0.0173082i
$795$		0			0
$796$	2.38873e46	−	2.75536e46i	0.919512	−	1.06064i
$797$	4.29181e46			1.61923			0.809613	−	0.586964i	$-0.199677\pi$
$797$	4.29181e46			1.61923			0.809613	+	0.586964i	$0.199677\pi$
$798$		0			0
$799$			1.00296e46i			0.363524i
$800$	1.00502e45	−	4.60628e45i	0.0357054	−	0.163648i
$801$		0			0
$802$	−4.87333e46	−	1.81834e46i	−1.66355	−	0.620706i
$803$			4.99923e45i			0.167284i
$804$		0			0
$805$	−2.72026e46			−0.874736
$806$	5.33205e45	−	1.42904e46i	0.168087	−	0.450488i
$807$		0			0
$808$	−3.71110e45	−	6.80237e45i	−0.112440	−	0.206100i
$809$	−1.17845e46			−0.350054			−0.175027	−	0.984564i	$-0.556001\pi$
$809$	−1.17845e46			−0.350054			−0.175027	+	0.984564i	$0.556001\pi$
$810$		0			0
$811$		−	1.09029e46i		−	0.311321i	−0.987811	−	0.155660i	$-0.950249\pi$
$811$		−	1.09029e46i		−	0.311321i	0.987811	−	0.155660i	$-0.0497505\pi$
$812$	−2.85178e46	+	3.28948e46i	−0.798397	+	0.920939i
$813$		0			0
$814$	3.92832e44	−	1.05283e45i	0.0105734	−	0.0283378i
$815$			2.70100e46i			0.712859i
$816$		0			0
$817$	6.07623e46			1.54199
$818$	8.07062e45	+	3.01132e45i	0.200842	+	0.0749384i
$819$		0			0
$820$	−6.43041e45	−	5.57476e45i	−0.153892	−	0.133415i
$821$	−2.63391e46			−0.618173			−0.309087	−	0.951034i	$-0.600023\pi$
$821$	−2.63391e46			−0.618173			−0.309087	+	0.951034i	$0.600023\pi$
$822$		0			0
$823$			1.90934e46i			0.431007i	0.976503	+	0.215504i	$0.0691393\pi$
$823$			1.90934e46i			0.431007i	−0.976503	+	0.215504i	$0.930861\pi$
$824$	1.48590e45	−	8.10650e44i	0.0328969	−	0.0179473i
$825$		0			0
$826$	−2.82542e44	−	1.05422e44i	−0.00601730	−	0.00224518i
$827$		−	2.78507e46i		−	0.581766i	−0.956759	−	0.290883i	$-0.906051\pi$
$827$		−	2.78507e46i		−	0.581766i	0.956759	−	0.290883i	$-0.0939490\pi$
$828$		0			0
$829$	−1.97696e46			−0.397306			−0.198653	−	0.980070i	$-0.563657\pi$
$829$	−1.97696e46			−0.397306			−0.198653	+	0.980070i	$0.563657\pi$
$830$	−1.24960e46	+	3.34905e46i	−0.246333	+	0.660194i
$831$		0			0
$832$	−9.28411e45	+	1.44228e46i	−0.176103	+	0.273575i
$833$	3.72105e46			0.692382
$834$		0			0
$835$			5.53640e46i			0.991389i
$836$	2.58309e46	+	2.23938e46i	0.453773	+	0.393393i
$837$		0			0
$838$	−1.60639e46	+	4.30527e46i	−0.271610	+	0.727940i
$839$		−	7.36571e45i		−	0.122187i	−0.998132	−	0.0610933i	$-0.980541\pi$
$839$		−	7.36571e45i		−	0.122187i	0.998132	−	0.0610933i	$-0.0194587\pi$
$840$		0			0
$841$	1.43150e47			2.28589
$842$	−5.25608e46	−	1.96116e46i	−0.823509	−	0.307269i
$843$		0			0
$844$	−6.67850e46	+	7.70355e46i	−1.00739	+	1.16201i
$845$	5.51198e46			0.815831
$846$		0			0
$847$		−	4.00285e46i		−	0.570472i
$848$	−1.72655e46	−	1.20507e47i	−0.241461	−	1.68531i
$849$		0			0
$850$	−1.47251e46	−	5.49423e45i	−0.198314	−	0.0739953i
$851$		−	8.38102e45i		−	0.110771i
$852$		0			0
$853$	−8.98888e46			−1.14425			−0.572125	−	0.820166i	$-0.693881\pi$
$853$	−8.98888e46			−1.14425			−0.572125	+	0.820166i	$0.693881\pi$
$854$	8.52144e45	−	2.28383e46i	0.106460	−	0.285323i
$855$		0			0
$856$	4.30311e46	−	2.34760e46i	0.517848	−	0.282517i
$857$	8.55308e45			0.101025			0.0505126	−	0.998723i	$-0.483915\pi$
$857$	8.55308e45			0.101025			0.0505126	+	0.998723i	$0.483915\pi$
$858$		0			0
$859$		−	4.31181e46i		−	0.490647i	−0.969441	−	0.245323i	$-0.921106\pi$
$859$		−	4.31181e46i		−	0.490647i	0.969441	−	0.245323i	$-0.0788942\pi$
$860$	5.34907e46	−	6.17007e46i	0.597452	−	0.689151i
$861$		0			0
$862$	−1.21202e46	+	3.24833e46i	−0.130435	+	0.349578i
$863$		−	2.29879e45i		−	0.0242843i	−0.999926	−	0.0121422i	$-0.996135\pi$
$863$		−	2.29879e45i		−	0.0242843i	0.999926	−	0.0121422i	$-0.00386507\pi$
$864$		0			0
$865$	−1.53033e46			−0.155785
$866$	1.27405e46	+	4.75377e45i	0.127322	+	0.0475064i
$867$		0			0
$868$	−7.79561e46	−	6.75831e46i	−0.750817	−	0.650912i
$869$	3.92005e46			0.370660
$870$		0			0
$871$		−	5.01089e46i		−	0.456693i
$872$	7.54820e46	+	1.38357e47i	0.675429	+	1.23805i
$873$		0			0
$874$	2.38884e47	+	8.91328e46i	2.06065	+	0.768873i
$875$		−	8.45663e46i		−	0.716257i
$876$		0			0
$877$	1.35870e46			0.110951			0.0554753	−	0.998460i	$-0.482333\pi$
$877$	1.35870e46			0.110951			0.0554753	+	0.998460i	$0.482333\pi$
$878$	6.55105e46	−	1.75574e47i	0.525289	−	1.40782i
$879$		0			0
$880$	4.54792e46	−	6.51597e45i	0.351634	−	0.0503798i
$881$	1.55064e45			0.0117733			0.00588663	−	0.999983i	$-0.498126\pi$
$881$	1.55064e45			0.0117733			0.00588663	+	0.999983i	$0.498126\pi$
$882$		0			0
$883$			1.25584e46i			0.0919523i	0.998943	+	0.0459761i	$0.0146398\pi$
$883$			1.25584e46i			0.0919523i	−0.998943	+	0.0459761i	$0.985360\pi$
$884$	4.32043e46	+	3.74555e46i	0.310664	+	0.269327i
$885$		0			0
$886$	5.07639e46	−	1.36052e47i	0.352059	−	0.943550i
$887$		−	2.45267e47i		−	1.67056i	−0.549825	−	0.835280i	$-0.685306\pi$
$887$		−	2.45267e47i		−	1.67056i	0.549825	−	0.835280i	$-0.314694\pi$
$888$		0			0
$889$	2.84059e46			0.186630
$890$	−2.36174e47	−	8.81215e46i	−1.52402	−	0.568646i
$891$		0			0
$892$	1.46106e47	−	1.68531e47i	0.909558	−	1.04916i
$893$	7.25691e46			0.443740
$894$		0			0
$895$		−	2.46976e47i		−	1.45709i
$896$	6.94502e46	+	9.29422e46i	0.402481	+	0.538623i
$897$		0			0
$898$	−5.33950e45	−	1.99228e45i	−0.0298593	−	0.0111411i
$899$			4.87653e47i			2.67890i
$900$		0			0
$901$	−4.05824e47			−2.15150
$902$	−5.83311e45	+	1.56333e46i	−0.0303806	+	0.0814227i
$903$		0			0
$904$	9.82195e46	+	1.80034e47i	0.493745	+	0.905025i
$905$	−1.07171e46			−0.0529299
$906$		0			0
$907$			2.67546e47i			1.27550i	0.770242	+	0.637752i	$0.220136\pi$
$907$			2.67546e47i			1.27550i	−0.770242	+	0.637752i	$0.779864\pi$
$908$	6.08451e46	−	7.01840e46i	0.285005	−	0.328749i
$909$		0			0
$910$	−1.54305e46	+	4.13551e46i	−0.0697777	+	0.187011i
$911$			6.22236e46i			0.276478i	0.990399	+	0.138239i	$0.0441443\pi$
$911$			6.22236e46i			0.276478i	−0.990399	+	0.138239i	$0.955856\pi$
$912$		0			0
$913$	7.00850e46			0.300672
$914$	2.78949e47	+	1.04082e47i	1.17594	+	0.438768i
$915$		0			0
$916$	1.27278e47	+	1.10342e47i	0.518113	+	0.449172i
$917$	−1.29404e47			−0.517654
$918$		0			0
$919$			2.14141e47i			0.827278i	0.910441	+	0.413639i	$0.135742\pi$
$919$			2.14141e47i			0.827278i	−0.910441	+	0.413639i	$0.864258\pi$
$920$	3.00806e47	−	1.64107e47i	1.14204	−	0.623050i
$921$		0			0
$922$	−2.56683e47	−	9.57740e46i	−0.941245	−	0.351199i
$923$		−	7.97245e46i		−	0.287319i
$924$		0			0
$925$	3.73798e45			0.0130127
$926$	3.60812e46	−	9.67010e46i	0.123454	−	0.330868i
$927$		0			0
$928$	1.16901e47	−	5.35791e47i	0.386413	−	1.77104i
$929$	−3.58125e47			−1.16354			−0.581772	−	0.813352i	$-0.697640\pi$
$929$	−3.58125e47			−1.16354			−0.581772	+	0.813352i	$0.697640\pi$
$930$		0			0
$931$		−	2.69238e47i		−	0.845164i
$932$	5.00145e46	+	4.33595e46i	0.154327	+	0.133792i
$933$		0			0
$934$	7.38719e46	−	1.97983e47i	0.220257	−	0.590308i
$935$		−	1.53157e47i		−	0.448902i
$936$		0			0
$937$	−1.81846e47			−0.515074			−0.257537	−	0.966268i	$-0.582911\pi$
$937$	−1.81846e47			−0.515074			−0.257537	+	0.966268i	$0.582911\pi$
$938$	−3.17562e47	−	1.18489e47i	−0.884267	−	0.329939i
$939$		0			0
$940$	6.38845e46	−	7.36898e46i	0.171929	−	0.198318i
$941$	−3.72510e47			−0.985607			−0.492803	−	0.870141i	$-0.664028\pi$
$941$	−3.72510e47			−0.985607			−0.492803	+	0.870141i	$0.664028\pi$
$942$		0			0
$943$			1.24449e47i			0.318276i
$944$	3.76032e45	−	5.38755e44i	0.00945526	−	0.00135469i
$945$		0			0
$946$	−1.50004e47	−	5.59696e46i	−0.364622	−	0.136048i
$947$			2.05570e47i			0.491316i	0.969357	+	0.245658i	$0.0790040\pi$
$947$			2.05570e47i			0.491316i	−0.969357	+	0.245658i	$0.920996\pi$
$948$		0			0
$949$	6.05008e46			0.139798
$950$	−3.97537e46	+	1.06543e47i	−0.0903232	+	0.242075i
$951$		0			0
$952$	3.39534e47	−	1.85236e47i	0.745920	−	0.406944i
$953$	9.72774e46			0.210148			0.105074	−	0.994464i	$-0.466492\pi$
$953$	9.72774e46			0.210148			0.105074	+	0.994464i	$0.466492\pi$
$954$		0			0
$955$			2.50253e47i			0.522788i
$956$	−6.82582e46	+	7.87348e46i	−0.140226	+	0.161749i
$957$		0			0
$958$	−1.42478e47	+	3.81855e47i	−0.283075	+	0.758666i
$959$			1.17125e47i			0.228851i
$960$		0			0
$961$	−6.26524e47			−1.18403
$962$	−1.27413e46	−	4.75407e45i	−0.0236817	−	0.00883617i
$963$		0			0
$964$	6.20299e47	+	5.37761e47i	1.11524	+	0.966845i
$965$	−2.93027e47			−0.518168
$966$		0			0
$967$			4.63298e47i			0.792568i	0.918128	+	0.396284i	$0.129700\pi$
$967$			4.63298e47i			0.792568i	−0.918128	+	0.396284i	$0.870300\pi$
$968$	2.41483e47	+	4.42633e47i	0.406332	+	0.744798i
$969$		0			0
$970$	−2.47738e46	−	9.24364e45i	−0.0403315	−	0.0150486i
$971$		−	8.04985e47i		−	1.28908i	−0.764570	−	0.644540i	$-0.777049\pi$
$971$		−	8.04985e47i		−	1.28908i	0.764570	−	0.644540i	$-0.222951\pi$
$972$		0			0
$973$	−7.40636e47			−1.14762
$974$	−4.39869e47	+	1.17889e48i	−0.670472	+	1.79693i
$975$		0			0
$976$	4.35483e46	+	3.03952e47i	0.0642354	+	0.448341i
$977$	4.45450e47			0.646377			0.323189	−	0.946335i	$-0.395245\pi$
$977$	4.45450e47			0.646377			0.323189	+	0.946335i	$0.395245\pi$
$978$		0			0
$979$			4.94237e47i			0.694085i
$980$	−2.73396e47	−	2.37017e47i	−0.377724	−	0.327463i
$981$		0			0
$982$	1.09613e47	−	2.93773e47i	0.146581	−	0.392851i
$983$			1.72322e47i			0.226718i	0.993554	+	0.113359i	$0.0361610\pi$
$983$			1.72322e47i			0.226718i	−0.993554	+	0.113359i	$0.963839\pi$
$984$		0			0
$985$	−1.53694e47			−0.195738
$986$	−1.71278e48	−	6.39076e47i	−2.14621	−	0.800796i
$987$		0			0
$988$	2.71010e47	−	3.12606e47i	0.328756	−	0.379216i
$989$	−1.19410e48			−1.42528
$990$		0			0
$991$			1.30834e48i			1.51197i	0.654591	+	0.755983i	$0.272841\pi$
$991$			1.30834e48i			1.51197i	−0.654591	+	0.755983i	$0.727159\pi$
$992$	1.26975e48	+	2.77039e47i	1.44388	+	0.315032i
$993$		0			0
$994$	−5.05249e47	−	1.88519e47i	−0.556318	−	0.207574i
$995$			1.18208e48i			1.28079i
$996$		0			0
$997$	−8.48188e47			−0.889958			−0.444979	−	0.895541i	$-0.646789\pi$
$997$	−8.48188e47			−0.889958			−0.444979	+	0.895541i	$0.646789\pi$
$998$	−3.51264e47	+	9.41419e47i	−0.362698	+	0.972063i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	36.33.d.b.19.14		14
3.2	odd	2		4.33.b.b.3.1	✓	14
4.3	odd	2	inner	36.33.d.b.19.13		14
12.11	even	2		4.33.b.b.3.2	yes	14

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4.33.b.b.3.1	✓	14	3.2	odd	2
4.33.b.b.3.2	yes	14	12.11	even	2
36.33.d.b.19.13		14	4.3	odd	2	inner
36.33.d.b.19.14		14	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:	\( N \)	\(=\)	\( 36 = 2^{2} \cdot 3^{2} \)
Weight:	\( k \)	\(=\)	\( 33 \)
Character orbit:	\([\chi]\)	\(=\)	36.d (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(61401.1 + 22910.1i) q^{2} +(3.24522e9 + 2.81341e9i) q^{4} -1.39224e11 q^{5} -2.23454e13i q^{7} +(1.34805e14 + 2.47095e14i) q^{8} +O(q^{10})\)	\(q+(61401.1 + 22910.1i) q^{2} +(3.24522e9 + 2.81341e9i) q^{4} -1.39224e11 q^{5} -2.23454e13i q^{7} +(1.34805e14 + 2.47095e14i) q^{8} +(-8.54848e15 - 3.18962e15i) q^{10} +1.78893e16i q^{11} +2.16497e17 q^{13} +(5.11935e17 - 1.37203e18i) q^{14} +(2.61621e18 + 1.82603e19i) q^{16} +6.14938e19 q^{17} -4.44940e20i q^{19} +(-4.51812e20 - 3.91693e20i) q^{20} +(-4.09845e20 + 1.09842e21i) q^{22} +8.74399e21i q^{23} -3.89986e21 q^{25} +(1.32931e22 + 4.95995e21i) q^{26} +(6.28668e22 - 7.25159e22i) q^{28} -4.53622e23 q^{29} -1.07502e24i q^{31} +(-2.57706e23 + 1.18114e24i) q^{32} +(3.77579e24 + 1.40883e24i) q^{34} +3.11101e24i q^{35} -9.58490e23 q^{37} +(1.01936e25 - 2.73198e25i) q^{38} +(-1.87680e25 - 3.44014e25i) q^{40} +1.42325e25 q^{41} +1.36563e26i q^{43} +(-5.03298e25 + 5.80547e25i) q^{44} +(-2.00325e26 + 5.36891e26i) q^{46} +1.63099e26i q^{47} +6.05110e26 q^{49} +(-2.39456e26 - 8.93461e25i) q^{50} +(7.02580e26 + 6.09093e26i) q^{52} -6.59943e27 q^{53} -2.49061e27i q^{55} +(5.52143e27 - 3.01227e27i) q^{56} +(-2.78529e28 - 1.03925e28i) q^{58} -2.05929e26i q^{59} +1.66456e28 q^{61} +(2.46288e28 - 6.60074e28i) q^{62} +(-4.28834e28 + 6.66192e28i) q^{64} -3.01414e28 q^{65} -2.31454e29i q^{67} +(1.99561e29 + 1.73007e29i) q^{68} +(-7.12735e28 + 1.91019e29i) q^{70} -3.68248e29i q^{71} +2.79454e29 q^{73} +(-5.88523e28 - 2.19591e28i) q^{74} +(1.25180e30 - 1.44393e30i) q^{76} +3.99743e29 q^{77} -2.19129e30i q^{79} +(-3.64239e29 - 2.54226e30i) q^{80} +(8.73891e29 + 3.26068e29i) q^{82} -3.91771e30i q^{83} -8.56139e30 q^{85} +(-3.12866e30 + 8.38511e30i) q^{86} +(-4.42035e30 + 2.41156e30i) q^{88} +2.76276e31 q^{89} -4.83771e30i q^{91} +(-2.46004e31 + 2.83762e31i) q^{92} +(-3.73660e30 + 1.00144e31i) q^{94} +6.19462e31i q^{95} +2.89803e30 q^{97} +(3.71544e31 + 1.38631e31i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 14 q + 23780 q^{2} - 2922848368 q^{4} - 138121491740 q^{5} + 191366550113600 q^{8}+O(q^{10}) \) 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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