LMFDB - Embedded newform 36.33.d.b.19.11

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			19.11
Root			$-7.09569e9 - 8.80649e10i$ of defining polynomial
Character	$\chi$	$=$	36.19
Dual form			36.33.d.b.19.12

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(56022.2 - 34007.1i) q^{2} +(1.98200e9 - 3.81031e9i) q^{4} +2.17196e11 q^{5} +2.81808e12i q^{7} +(-1.85418e13 - 2.80864e14i) q^{8} +O(q^{10})$	\(q+(56022.2 - 34007.1i) q^{2} +(1.98200e9 - 3.81031e9i) q^{4} +2.17196e11 q^{5} +2.81808e12i q^{7} +(-1.85418e13 - 2.80864e14i) q^{8} +(1.21678e16 - 7.38622e15i) q^{10} +6.95526e16i q^{11} -7.08184e17 q^{13} +(9.58347e16 + 1.57875e17i) q^{14} +(-1.05901e19 - 1.51040e19i) q^{16} -6.55998e19 q^{17} -1.83995e20i q^{19} +(4.30482e20 - 8.27584e20i) q^{20} +(2.36528e21 + 3.89649e21i) q^{22} -7.92873e20i q^{23} +2.38911e22 q^{25} +(-3.96740e22 + 2.40833e22i) q^{26} +(1.07377e22 + 5.58542e21i) q^{28} +1.45523e23 q^{29} +1.34887e24i q^{31} +(-1.10693e24 - 4.86021e23i) q^{32} +(-3.67504e24 + 2.23086e24i) q^{34} +6.12075e23i q^{35} -2.62567e24 q^{37} +(-6.25715e24 - 1.03078e25i) q^{38} +(-4.02721e24 - 6.10025e25i) q^{40} +1.80745e25 q^{41} +1.56149e26i q^{43} +(2.65017e26 + 1.37853e26i) q^{44} +(-2.69633e25 - 4.44185e25i) q^{46} +8.64218e26i q^{47} +1.09649e27 q^{49} +(1.33843e27 - 8.12470e26i) q^{50} +(-1.40362e27 + 2.69840e27i) q^{52} -5.50243e27 q^{53} +1.51066e28i q^{55} +(7.91495e26 - 5.22522e25i) q^{56} +(8.15252e27 - 4.94882e27i) q^{58} +9.48554e27i q^{59} +3.04221e28 q^{61} +(4.58712e28 + 7.55666e28i) q^{62} +(-7.85406e28 + 1.04154e28i) q^{64} -1.53815e29 q^{65} +7.40203e28i q^{67} +(-1.30019e29 + 2.49955e29i) q^{68} +(2.08149e28 + 3.42898e28i) q^{70} -2.60149e29i q^{71} +3.70906e29 q^{73} +(-1.47095e29 + 8.92914e28i) q^{74} +(-7.01078e29 - 3.64678e29i) q^{76} -1.96004e29 q^{77} -2.10671e30i q^{79} +(-2.30013e30 - 3.28054e30i) q^{80} +(1.01257e30 - 6.14660e29i) q^{82} +6.24724e30i q^{83} -1.42480e31 q^{85} +(5.31019e30 + 8.74783e30i) q^{86} +(1.95348e31 - 1.28963e30i) q^{88} -1.03445e31 q^{89} -1.99572e30i q^{91} +(-3.02109e30 - 1.57147e30i) q^{92} +(2.93896e31 + 4.84153e31i) q^{94} -3.99630e31i q^{95} +1.05656e32 q^{97} +(6.14275e31 - 3.72883e31i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	56022.2	−	34007.1i	0.854830	−	0.518908i
$2$	56022.2	−	34007.1i	0.854830	−	0.518908i
$3$		0			0
$3$		0			0
$4$	1.98200e9	−	3.81031e9i	0.461470	−	0.887156i
$5$	2.17196e11			1.42342			0.711709	−	0.702475i	$-0.247922\pi$
$5$	2.17196e11			1.42342			0.711709	+	0.702475i	$0.247922\pi$
$6$		0			0
$7$			2.81808e12i			0.0847977i	0.999101	+	0.0423988i	$0.0135000\pi$
$7$			2.81808e12i			0.0847977i	−0.999101	+	0.0423988i	$0.986500\pi$
$8$	−1.85418e13	−	2.80864e14i	−0.0658738	−	0.997828i
$9$		0			0
$10$	1.21678e16	−	7.38622e15i	1.21678	−	0.738622i
$11$			6.95526e16i			1.51367i	0.653607	+	0.756834i	$0.273255\pi$
$11$			6.95526e16i			1.51367i	−0.653607	+	0.756834i	$0.726745\pi$
$12$		0			0
$13$	−7.08184e17			−1.06427			−0.532136	−	0.846659i	$-0.678610\pi$
$13$	−7.08184e17			−1.06427			−0.532136	+	0.846659i	$0.678610\pi$
$14$	9.58347e16	+	1.57875e17i	0.0440022	+	0.0724876i
$15$		0			0
$16$	−1.05901e19	−	1.51040e19i	−0.574091	−	0.818791i
$17$	−6.55998e19			−1.34809			−0.674046	−	0.738689i	$-0.735445\pi$
$17$	−6.55998e19			−1.34809			−0.674046	+	0.738689i	$0.735445\pi$
$18$		0			0
$19$		−	1.83995e20i		−	0.637894i	−0.947773	−	0.318947i	$-0.896671\pi$
$19$		−	1.83995e20i		−	0.637894i	0.947773	−	0.318947i	$-0.103329\pi$
$20$	4.30482e20	−	8.27584e20i	0.656864	−	1.26279i
$21$		0			0
$22$	2.36528e21	+	3.89649e21i	0.785454	+	1.29393i
$23$		−	7.92873e20i		−	0.129288i	−0.997908	−	0.0646440i	$-0.979409\pi$
$23$		−	7.92873e20i		−	0.129288i	0.997908	−	0.0646440i	$-0.0205912\pi$
$24$		0			0
$25$	2.38911e22			1.02612
$26$	−3.96740e22	+	2.40833e22i	−0.909771	+	0.552259i
$27$		0			0
$28$	1.07377e22	+	5.58542e21i	0.0752288	+	0.0391316i
$29$	1.45523e23			0.581519			0.290760	−	0.956796i	$-0.406092\pi$
$29$	1.45523e23			0.581519			0.290760	+	0.956796i	$0.406092\pi$
$30$		0			0
$31$			1.34887e24i			1.85431i	0.374673	+	0.927157i	$0.377755\pi$
$31$			1.34887e24i			1.85431i	−0.374673	+	0.927157i	$0.622245\pi$
$32$	−1.10693e24	−	4.86021e23i	−0.915628	−	0.402027i
$33$		0			0
$34$	−3.67504e24	+	2.23086e24i	−1.15239	+	0.699535i
$35$			6.12075e23i			0.120702i
$36$		0			0
$37$	−2.62567e24			−0.212820			−0.106410	−	0.994322i	$-0.533936\pi$
$37$	−2.62567e24			−0.212820			−0.106410	+	0.994322i	$0.533936\pi$
$38$	−6.25715e24	−	1.03078e25i	−0.331008	−	0.545291i
$39$		0			0
$40$	−4.02721e24	−	6.10025e25i	−0.0937659	−	1.42033i
$41$	1.80745e25			0.283481			0.141740	−	0.989904i	$-0.454730\pi$
$41$	1.80745e25			0.283481			0.141740	+	0.989904i	$0.454730\pi$
$42$		0			0
$43$			1.56149e26i			1.14300i	0.820603	+	0.571498i	$0.193638\pi$
$43$			1.56149e26i			1.14300i	−0.820603	+	0.571498i	$0.806362\pi$
$44$	2.65017e26	+	1.37853e26i	1.34286	+	0.698512i
$45$		0			0
$46$	−2.69633e25	−	4.44185e25i	−0.0670885	−	0.110519i
$47$			8.64218e26i			1.52425i	0.647427	+	0.762127i	$0.275845\pi$
$47$			8.64218e26i			1.52425i	−0.647427	+	0.762127i	$0.724155\pi$
$48$		0			0
$49$	1.09649e27			0.992809
$50$	1.33843e27	−	8.12470e26i	0.877156	−	0.532460i
$51$		0			0
$52$	−1.40362e27	+	2.69840e27i	−0.491129	+	0.944175i
$53$	−5.50243e27			−1.41952			−0.709759	−	0.704444i	$-0.751196\pi$
$53$	−5.50243e27			−1.41952			−0.709759	+	0.704444i	$0.751196\pi$
$54$		0			0
$55$			1.51066e28i			2.15458i
$56$	7.91495e26	−	5.22522e25i	0.0846135	−	0.00558594i
$57$		0			0
$58$	8.15252e27	−	4.94882e27i	0.497100	−	0.301755i
$59$			9.48554e27i			0.439977i	0.975502	+	0.219988i	$0.0706020\pi$
$59$			9.48554e27i			0.439977i	−0.975502	+	0.219988i	$0.929398\pi$
$60$		0			0
$61$	3.04221e28			0.827774			0.413887	−	0.910328i	$-0.364171\pi$
$61$	3.04221e28			0.827774			0.413887	+	0.910328i	$0.364171\pi$
$62$	4.58712e28	+	7.55666e28i	0.962218	+	1.58512i
$63$		0			0
$64$	−7.85406e28	+	1.04154e28i	−0.991321	+	0.131461i
$65$	−1.53815e29			−1.51490
$66$		0			0
$67$			7.40203e28i			0.448905i	0.974485	+	0.224452i	$0.0720593\pi$
$67$			7.40203e28i			0.448905i	−0.974485	+	0.224452i	$0.927941\pi$
$68$	−1.30019e29	+	2.49955e29i	−0.622103	+	1.19597i
$69$		0			0
$70$	2.08149e28	+	3.42898e28i	0.0626334	+	0.103180i
$71$		−	2.60149e29i		−	0.623863i	−0.950105	−	0.311932i	$-0.899024\pi$
$71$		−	2.60149e29i		−	0.623863i	0.950105	−	0.311932i	$-0.100976\pi$
$72$		0			0
$73$	3.70906e29			0.570293			0.285147	−	0.958484i	$-0.407958\pi$
$73$	3.70906e29			0.570293			0.285147	+	0.958484i	$0.407958\pi$
$74$	−1.47095e29	+	8.92914e28i	−0.181925	+	0.110434i
$75$		0			0
$76$	−7.01078e29	−	3.64678e29i	−0.565912	−	0.294369i
$77$	−1.96004e29			−0.128355
$78$		0			0
$79$		−	2.10671e30i		−	0.915317i	−0.889128	−	0.457659i	$-0.848688\pi$
$79$		−	2.10671e30i		−	0.915317i	0.889128	−	0.457659i	$-0.151312\pi$
$80$	−2.30013e30	−	3.28054e30i	−0.817172	−	1.16548i
$81$		0			0
$82$	1.01257e30	−	6.14660e29i	0.242328	−	0.147100i
$83$			6.24724e30i			1.23151i	0.787937	+	0.615756i	$0.211149\pi$
$83$			6.24724e30i			1.23151i	−0.787937	+	0.615756i	$0.788851\pi$
$84$		0			0
$85$	−1.42480e31			−1.91890
$86$	5.31019e30	+	8.74783e30i	0.593110	+	0.977068i
$87$		0			0
$88$	1.95348e31	−	1.28963e30i	1.51038	−	0.0997110i
$89$	−1.03445e31			−0.667526			−0.333763	−	0.942657i	$-0.608318\pi$
$89$	−1.03445e31			−0.667526			−0.333763	+	0.942657i	$0.608318\pi$
$90$		0			0
$91$		−	1.99572e30i		−	0.0902477i
$92$	−3.02109e30	−	1.57147e30i	−0.114699	−	0.0596625i
$93$		0			0
$94$	2.93896e31	+	4.84153e31i	0.790947	+	1.30298i
$95$		−	3.99630e31i		−	0.907990i
$96$		0			0
$97$	1.05656e32			1.72007			0.860036	−	0.510233i	$-0.170441\pi$
$97$	1.05656e32			1.72007			0.860036	+	0.510233i	$0.170441\pi$
$98$	6.14275e31	−	3.72883e31i	0.848684	−	0.515176i
$99$		0			0
$100$	4.73522e31	−	9.10326e31i	0.473522	−	0.910326i
$101$	−9.75597e31			−0.832010			−0.416005	−	0.909362i	$-0.636570\pi$
$101$	−9.75597e31			−0.832010			−0.416005	+	0.909362i	$0.636570\pi$
$102$		0			0
$103$			1.75898e31i			0.109614i	0.998497	+	0.0548068i	$0.0174543\pi$
$103$			1.75898e31i			0.109614i	−0.998497	+	0.0548068i	$0.982546\pi$
$104$	1.31310e31	+	1.98903e32i	0.0701076	+	1.06196i
$105$		0			0
$106$	−3.08258e32	+	1.87122e32i	−1.21345	+	0.736599i
$107$		−	2.30757e32i		−	0.781653i	−0.920464	−	0.390827i	$-0.872189\pi$
$107$		−	2.30757e32i		−	0.781653i	0.920464	−	0.390827i	$-0.127811\pi$
$108$		0			0
$109$	−3.17192e32			−0.798910			−0.399455	−	0.916753i	$-0.630801\pi$
$109$	−3.17192e32			−0.798910			−0.399455	+	0.916753i	$0.630801\pi$
$110$	5.13731e32	+	8.46302e32i	1.11803	+	1.84180i
$111$		0			0
$112$	4.25643e31	−	2.98438e31i	0.0694316	−	0.0486816i
$113$	−1.38155e33			−1.95485			−0.977424	−	0.211288i	$-0.932234\pi$
$113$	−1.38155e33			−1.95485			−0.977424	+	0.211288i	$0.932234\pi$
$114$		0			0
$115$		−	1.72209e32i		−	0.184031i
$116$	2.88426e32	−	5.54488e32i	0.268353	−	0.515898i
$117$		0			0
$118$	3.22576e32	+	5.31400e32i	0.228307	+	0.376105i
$119$		−	1.84865e32i		−	0.114315i
$120$		0			0
$121$	−2.72619e33			−1.29119
$122$	1.70431e33	−	1.03457e33i	0.707606	−	0.429538i
$123$		0			0
$124$	5.13961e33	+	2.67346e33i	1.64507	+	0.855710i
$125$	1.32074e32			0.0371755
$126$		0			0
$127$			5.38941e33i			1.17674i	0.808590	+	0.588372i	$0.200231\pi$
$127$			5.38941e33i			1.17674i	−0.808590	+	0.588372i	$0.799769\pi$
$128$	−4.04581e33	+	3.25444e33i	−0.779195	+	0.626781i
$129$		0			0
$130$	−8.61704e33	+	5.23080e33i	−1.29498	+	0.786094i
$131$			1.38685e34i			1.84370i	0.387550	+	0.921849i	$0.373321\pi$
$131$			1.38685e34i			1.84370i	−0.387550	+	0.921849i	$0.626679\pi$
$132$		0			0
$133$	5.18512e32			0.0540919
$134$	2.51722e33	+	4.14678e33i	0.232940	+	0.383737i
$135$		0			0
$136$	1.21634e33	+	1.84246e34i	0.0888039	+	1.34516i
$137$	1.41446e34			0.918461			0.459231	−	0.888317i	$-0.348125\pi$
$137$	1.41446e34			0.918461			0.459231	+	0.888317i	$0.348125\pi$
$138$		0			0
$139$			1.36246e34i			0.701596i	0.936451	+	0.350798i	$0.114090\pi$
$139$			1.36246e34i			0.701596i	−0.936451	+	0.350798i	$0.885910\pi$
$140$	2.33219e33	+	1.21313e33i	0.107082	+	0.0557005i
$141$		0			0
$142$	−8.84694e33	−	1.45741e34i	−0.323727	−	0.533297i
$143$		−	4.92560e34i		−	1.61095i
$144$		0			0
$145$	3.16071e34			0.827745
$146$	2.07790e34	−	1.26134e34i	0.487504	−	0.295929i
$147$		0			0
$148$	−5.20406e33	+	1.00046e34i	−0.0982098	+	0.188804i
$149$	−1.20034e34			−0.203388			−0.101694	−	0.994816i	$-0.532426\pi$
$149$	−1.20034e34			−0.203388			−0.101694	+	0.994816i	$0.532426\pi$
$150$		0			0
$151$			4.78649e34i			0.655219i	0.944813	+	0.327609i	$0.106243\pi$
$151$			4.78649e34i			0.655219i	−0.944813	+	0.327609i	$0.893757\pi$
$152$	−5.16775e34	+	3.41160e33i	−0.636509	+	0.0420205i
$153$		0			0
$154$	−1.09806e34	+	6.66555e33i	−0.109722	+	0.0666046i
$155$			2.92970e35i			2.63946i
$156$		0			0
$157$	7.13932e34			0.523917			0.261959	−	0.965079i	$-0.415632\pi$
$157$	7.13932e34			0.523917			0.261959	+	0.965079i	$0.415632\pi$
$158$	−7.16432e34	−	1.18023e35i	−0.474965	−	0.782441i
$159$		0			0
$160$	−2.40420e35	−	1.05562e35i	−1.30332	−	0.572252i
$161$	2.23438e33			0.0109633
$162$		0			0
$163$		−	9.56621e34i		−	0.385246i	−0.981273	−	0.192623i	$-0.938301\pi$
$163$		−	9.56621e34i		−	0.385246i	0.981273	−	0.192623i	$-0.0616995\pi$
$164$	3.58235e34	−	6.88692e34i	0.130818	−	0.251492i
$165$		0			0
$166$	2.12451e35	+	3.49984e35i	0.639041	+	1.05273i
$167$			1.85412e35i			0.506609i	0.967387	+	0.253305i	$0.0815175\pi$
$167$			1.85412e35i			0.506609i	−0.967387	+	0.253305i	$0.918482\pi$
$168$		0			0
$169$	5.87451e34			0.132674
$170$	−7.98205e35	+	4.84534e35i	−1.64033	+	0.995731i
$171$		0			0
$172$	5.94977e35	+	3.09488e35i	1.01402	+	0.527458i
$173$	2.05267e35			0.318846			0.159423	−	0.987210i	$-0.449037\pi$
$173$	2.05267e35			0.318846			0.159423	+	0.987210i	$0.449037\pi$
$174$		0			0
$175$			6.73271e34i			0.0870123i
$176$	1.05052e36	−	7.36570e35i	1.23938	−	0.868984i
$177$		0			0
$178$	−5.79519e35	+	3.51786e35i	−0.570621	+	0.346384i
$179$		−	1.25998e35i		−	0.113426i	−0.998391	−	0.0567132i	$-0.981938\pi$
$179$		−	1.25998e35i		−	0.113426i	0.998391	−	0.0567132i	$-0.0180621\pi$
$180$		0			0
$181$	−1.20858e35			−0.0910789			−0.0455394	−	0.998963i	$-0.514501\pi$
$181$	−1.20858e35			−0.0910789			−0.0455394	+	0.998963i	$0.514501\pi$
$182$	−6.78686e34	−	1.11804e35i	−0.0468302	−	0.0771465i
$183$		0			0
$184$	−2.22689e35	+	1.47013e34i	−0.129007	+	0.00851669i
$185$	−5.70285e35			−0.302931
$186$		0			0
$187$		−	4.56263e36i		−	2.04056i
$188$	3.29293e36	+	1.71288e36i	1.35225	+	0.703397i
$189$		0			0
$190$	−1.35903e36	−	2.23882e36i	−0.471163	−	0.776177i
$191$		−	2.97958e36i		−	0.949776i	−0.880046	−	0.474888i	$-0.842489\pi$
$191$		−	2.97958e36i		−	0.949776i	0.880046	−	0.474888i	$-0.157511\pi$
$192$		0			0
$193$	−1.00262e35			−0.0270532			−0.0135266	−	0.999909i	$-0.504306\pi$
$193$	−1.00262e35			−0.0270532			−0.0135266	+	0.999909i	$0.504306\pi$
$194$	5.91908e36	−	3.59306e36i	1.47037	−	0.892559i
$195$		0			0
$196$	2.17323e36	−	4.17795e36i	0.458151	−	0.880777i
$197$	−9.62694e36			−1.87081			−0.935403	−	0.353585i	$-0.884963\pi$
$197$	−9.62694e36			−1.87081			−0.935403	+	0.353585i	$0.884963\pi$
$198$		0			0
$199$		−	1.60787e36i		−	0.265828i	−0.991128	−	0.132914i	$-0.957567\pi$
$199$		−	1.60787e36i		−	0.265828i	0.991128	−	0.132914i	$-0.0424335\pi$
$200$	−4.42985e35	−	6.71015e36i	−0.0675942	−	1.02389i
$201$		0			0
$202$	−5.46551e36	+	3.31773e36i	−0.711228	+	0.431736i
$203$			4.10095e35i			0.0493115i
$204$		0			0
$205$	3.92570e36			0.403511
$206$	5.98178e35	+	9.85417e35i	0.0568794	+	0.0937011i
$207$		0			0
$208$	7.49975e36	+	1.06964e37i	0.610989	+	0.871416i
$209$	1.27973e37			0.965560
$210$		0			0
$211$			3.10011e36i			0.200843i	0.994945	+	0.100422i	$0.0320192\pi$
$211$			3.10011e36i			0.200843i	−0.994945	+	0.100422i	$0.967981\pi$
$212$	−1.09058e37	+	2.09660e37i	−0.655065	+	1.25933i
$213$		0			0
$214$	−7.84738e36	−	1.29275e37i	−0.405606	−	0.668181i
$215$			3.39151e37i			1.62696i
$216$		0			0
$217$	−3.80122e36			−0.157242
$218$	−1.77698e37	+	1.07868e37i	−0.682933	+	0.414561i
$219$		0			0
$220$	5.75606e37	+	2.99412e37i	1.91145	+	0.994274i
$221$	4.64567e37			1.43474
$222$		0			0
$223$		−	1.15242e37i		−	0.308129i	−0.988061	−	0.154065i	$-0.950764\pi$
$223$		−	1.15242e37i		−	0.308129i	0.988061	−	0.154065i	$-0.0492364\pi$
$224$	1.36964e36	−	3.11940e36i	0.0340910	−	0.0776431i
$225$		0			0
$226$	−7.73977e37	+	4.69827e37i	−1.67106	+	1.01439i
$227$			4.61854e37i			0.929160i	0.885531	+	0.464580i	$0.153795\pi$
$227$			4.61854e37i			0.929160i	−0.885531	+	0.464580i	$0.846205\pi$
$228$		0			0
$229$	3.72281e37			0.650883			0.325441	−	0.945562i	$-0.394487\pi$
$229$	3.72281e37			0.650883			0.325441	+	0.945562i	$0.394487\pi$
$230$	−5.85634e36	−	9.64752e36i	−0.0954950	−	0.157315i
$231$		0			0
$232$	−2.69826e36	−	4.08722e37i	−0.0383069	−	0.580256i
$233$	−7.06883e37			−0.936813			−0.468407	−	0.883513i	$-0.655172\pi$
$233$	−7.06883e37			−0.936813			−0.468407	+	0.883513i	$0.655172\pi$
$234$		0			0
$235$			1.87705e38i			2.16965i
$236$	3.61428e37	+	1.88003e37i	0.390328	+	0.203036i
$237$		0			0
$238$	−6.28673e36	−	1.03565e37i	−0.0593190	−	0.0977200i
$239$			1.27048e37i			0.112099i	0.998428	+	0.0560493i	$0.0178504\pi$
$239$			1.27048e37i			0.112099i	−0.998428	+	0.0560493i	$0.982150\pi$
$240$		0			0
$241$	4.54592e37			0.351034			0.175517	−	0.984476i	$-0.443840\pi$
$241$	4.54592e37			0.351034			0.175517	+	0.984476i	$0.443840\pi$
$242$	−1.52727e38	+	9.27098e37i	−1.10375	+	0.670008i
$243$		0			0
$244$	6.02965e37	−	1.15917e38i	0.381993	−	0.734365i
$245$	2.38153e38			1.41318
$246$		0			0
$247$			1.30302e38i			0.678892i
$248$	3.78849e38	−	2.50105e37i	1.85029	−	0.122151i
$249$		0			0
$250$	7.39907e36	−	4.49146e36i	0.0317787	−	0.0192907i
$251$			1.86541e38i			0.751612i	0.926698	+	0.375806i	$0.122634\pi$
$251$			1.86541e38i			0.751612i	−0.926698	+	0.375806i	$0.877366\pi$
$252$		0			0
$253$	5.51464e37			0.195699
$254$	1.83279e38	+	3.01927e38i	0.610622	+	1.00592i
$255$		0			0
$256$	−1.15981e38	+	3.19907e38i	−0.340838	+	0.940122i
$257$	1.69751e38			0.468687			0.234344	−	0.972154i	$-0.424706\pi$
$257$	1.69751e38			0.468687			0.234344	+	0.972154i	$0.424706\pi$
$258$		0			0
$259$		−	7.39932e36i		−	0.0180466i
$260$	−3.04861e38	+	5.86082e38i	−0.699082	+	1.34395i
$261$		0			0
$262$	4.71629e38	+	7.76945e38i	0.956709	+	1.57605i
$263$		−	2.65236e38i		−	0.506221i	−0.967437	−	0.253110i	$-0.918546\pi$
$263$		−	2.65236e38i		−	0.506221i	0.967437	−	0.253110i	$-0.0814536\pi$
$264$		0			0
$265$	−1.19511e39			−2.02057
$266$	2.90482e37	−	1.76331e37i	0.0462394	−	0.0280687i
$267$		0			0
$268$	2.82040e38	+	1.46708e38i	0.398249	+	0.207156i
$269$	−1.81625e38			−0.241624			−0.120812	−	0.992675i	$-0.538550\pi$
$269$	−1.81625e38			−0.241624			−0.120812	+	0.992675i	$0.538550\pi$
$270$		0			0
$271$			1.02031e39i			1.20566i	0.797870	+	0.602829i	$0.205960\pi$
$271$			1.02031e39i			1.20566i	−0.797870	+	0.602829i	$0.794040\pi$
$272$	6.94709e38	+	9.90821e38i	0.773928	+	1.10381i
$273$		0			0
$274$	7.92410e38	−	4.81017e38i	0.785129	−	0.476597i
$275$			1.66169e39i			1.55320i
$276$		0			0
$277$	1.47642e39			1.22895			0.614475	−	0.788937i	$-0.289368\pi$
$277$	1.47642e39			1.22895			0.614475	+	0.788937i	$0.289368\pi$
$278$	4.63334e38	+	7.63280e38i	0.364064	+	0.599745i
$279$		0			0
$280$	1.71910e38	−	1.13490e37i	0.120440	−	0.00795113i
$281$	5.86616e38			0.388197			0.194099	−	0.980982i	$-0.437822\pi$
$281$	5.86616e38			0.388197			0.194099	+	0.980982i	$0.437822\pi$
$282$		0			0
$283$		−	2.31347e39i		−	1.36673i	−0.730078	−	0.683363i	$-0.760516\pi$
$283$		−	2.31347e39i		−	1.36673i	0.730078	−	0.683363i	$-0.239484\pi$
$284$	−9.91249e38	−	5.15615e38i	−0.553464	−	0.287894i
$285$		0			0
$286$	−1.67506e39	−	2.75943e39i	−0.835936	−	1.37709i
$287$			5.09352e37i			0.0240385i
$288$		0			0
$289$	1.93542e39			0.817351
$290$	1.77070e39	−	1.07487e39i	0.707581	−	0.429523i
$291$		0			0
$292$	7.35135e38	−	1.41327e39i	0.263173	−	0.505939i
$293$	−9.55731e38			−0.323932			−0.161966	−	0.986796i	$-0.551783\pi$
$293$	−9.55731e38			−0.323932			−0.161966	+	0.986796i	$0.551783\pi$
$294$		0			0
$295$			2.06022e39i			0.626271i
$296$	4.86846e37	+	7.37454e38i	0.0140192	+	0.212357i
$297$		0			0
$298$	−6.72457e38	+	4.08202e38i	−0.173862	+	0.105539i
$299$			5.61500e38i			0.137598i
$300$		0			0
$301$	−4.40041e38			−0.0969235
$302$	1.62775e39	+	2.68150e39i	0.339998	+	0.560101i
$303$		0			0
$304$	−2.77907e39	+	1.94853e39i	−0.522302	+	0.366210i
$305$	6.60756e39			1.17827
$306$		0			0
$307$		−	1.81430e39i		−	0.291404i	−0.989329	−	0.145702i	$-0.953456\pi$
$307$		−	1.81430e39i		−	0.291404i	0.989329	−	0.145702i	$-0.0465440\pi$
$308$	−3.88480e38	+	7.46837e38i	−0.0592322	+	0.113871i
$309$		0			0
$310$	9.96306e39	+	1.64128e40i	1.36964	+	2.25629i
$311$			1.20307e40i			1.57082i	0.618976	+	0.785410i	$0.287548\pi$
$311$			1.20307e40i			1.57082i	−0.618976	+	0.785410i	$0.712452\pi$
$312$		0			0
$313$	9.36962e39			1.10411			0.552055	−	0.833808i	$-0.313844\pi$
$313$	9.36962e39			1.10411			0.552055	+	0.833808i	$0.313844\pi$
$314$	3.99960e39	−	2.42788e39i	0.447860	−	0.271865i
$315$		0			0
$316$	−8.02722e39	−	4.17550e39i	−0.812029	−	0.422391i
$317$	1.26999e40			1.22138			0.610692	−	0.791868i	$-0.290891\pi$
$317$	1.26999e40			1.22138			0.610692	+	0.791868i	$0.290891\pi$
$318$		0			0
$319$			1.01215e40i			0.880227i
$320$	−1.70587e40	+	2.26220e39i	−1.41106	+	0.187124i
$321$		0			0
$322$	1.25175e38	−	7.59847e37i	0.00937178	−	0.00568895i
$323$			1.20700e40i			0.859940i
$324$		0			0
$325$	−1.69193e40			−1.09207
$326$	−3.25320e39	−	5.35920e39i	−0.199907	−	0.329320i
$327$		0			0
$328$	−3.35133e38	−	5.07646e39i	−0.0186739	−	0.282865i
$329$	−2.43543e39			−0.129253
$330$		0			0
$331$			1.76393e39i			0.0849637i	0.999097	+	0.0424818i	$0.0135265\pi$
$331$			1.76393e39i			0.0849637i	−0.999097	+	0.0424818i	$0.986474\pi$
$332$	2.38039e40	+	1.23820e40i	1.09254	+	0.568305i
$333$		0			0
$334$	6.30531e39	+	1.03872e40i	0.262883	+	0.433065i
$335$			1.60769e40i			0.638979i
$336$		0			0
$337$	8.12789e38			0.0293697			0.0146848	−	0.999892i	$-0.495326\pi$
$337$	8.12789e38			0.0293697			0.0146848	+	0.999892i	$0.495326\pi$
$338$	3.29103e39	−	1.99775e39i	0.113413	−	0.0688453i
$339$		0			0
$340$	−2.82395e40	+	5.42893e40i	−0.885513	+	1.70236i
$341$	−9.38175e40			−2.80681
$342$		0			0
$343$			6.20234e39i			0.168986i
$344$	4.38567e40	−	2.89529e39i	1.14051	−	0.0752935i
$345$		0			0
$346$	1.14995e40	−	6.98054e39i	0.272559	−	0.165452i
$347$		−	7.06291e40i		−	1.59850i	−0.601000	−	0.799249i	$-0.705231\pi$
$347$		−	7.06291e40i		−	1.59850i	0.601000	−	0.799249i	$-0.294769\pi$
$348$		0			0
$349$	−1.82205e40			−0.376143			−0.188071	−	0.982155i	$-0.560224\pi$
$349$	−1.82205e40			−0.376143			−0.188071	+	0.982155i	$0.560224\pi$
$350$	2.28960e39	+	3.77181e39i	0.0451514	+	0.0743808i
$351$		0			0
$352$	3.38040e40	−	7.69896e40i	0.608535	−	1.38596i
$353$	2.49744e40			0.429636			0.214818	−	0.976654i	$-0.431084\pi$
$353$	2.49744e40			0.429636			0.214818	+	0.976654i	$0.431084\pi$
$354$		0			0
$355$		−	5.65035e40i		−	0.888018i
$356$	−2.05027e40	+	3.94156e40i	−0.308043	+	0.592199i
$357$		0			0
$358$	−4.28482e39	−	7.05866e39i	−0.0588578	−	0.0969603i
$359$		−	8.95589e40i		−	1.17651i	−0.808674	−	0.588257i	$-0.799814\pi$
$359$		−	8.95589e40i		−	1.17651i	0.808674	−	0.588257i	$-0.200186\pi$
$360$		0			0
$361$	4.93443e40			0.593091
$362$	−6.77072e39	+	4.11003e39i	−0.0778570	+	0.0472615i
$363$		0			0
$364$	−7.60429e39	−	3.95550e39i	−0.0800638	−	0.0416466i
$365$	8.05594e40			0.811765
$366$		0			0
$367$		−	1.14387e40i		−	0.105614i	−0.998605	−	0.0528069i	$-0.983183\pi$
$367$		−	1.14387e40i		−	0.105614i	0.998605	−	0.0528069i	$-0.0168168\pi$
$368$	−1.19756e40	+	8.39662e39i	−0.105860	+	0.0742232i
$369$		0			0
$370$	−3.19486e40	+	1.93937e40i	−0.258955	+	0.157193i
$371$		−	1.55063e40i		−	0.120372i
$372$		0			0
$373$	−1.08315e41			−0.771519			−0.385760	−	0.922599i	$-0.626061\pi$
$373$	−1.08315e41			−0.771519			−0.385760	+	0.922599i	$0.626061\pi$
$374$	−1.55162e41	−	2.55609e41i	−1.05886	−	1.74433i
$375$		0			0
$376$	2.42727e41	−	1.60242e40i	1.52094	−	0.100408i
$377$	−1.03057e41			−0.618894
$378$		0			0
$379$		−	9.31410e40i		−	0.513941i	−0.966419	−	0.256971i	$-0.917276\pi$
$379$		−	9.31410e40i		−	0.513941i	0.966419	−	0.256971i	$-0.0827244\pi$
$380$	−1.52271e41	−	7.92066e40i	−0.805528	−	0.419010i
$381$		0			0
$382$	−1.01327e41	−	1.66923e41i	−0.492846	−	0.811897i
$383$		−	7.96910e39i		−	0.0371731i	−0.999827	−	0.0185866i	$-0.994083\pi$
$383$		−	7.96910e39i		−	0.0371731i	0.999827	−	0.0185866i	$-0.00591663\pi$
$384$		0			0
$385$	−4.25714e40			−0.182703
$386$	−5.61688e39	+	3.40962e39i	−0.0231259	+	0.0140381i
$387$		0			0
$388$	2.09410e41	−	4.02582e41i	0.793761	−	1.52597i
$389$	−9.70371e39			−0.0352975			−0.0176488	−	0.999844i	$-0.505618\pi$
$389$	−9.70371e39			−0.0352975			−0.0176488	+	0.999844i	$0.505618\pi$
$390$		0			0
$391$			5.20123e40i			0.174292i
$392$	−2.03308e40	−	3.07963e41i	−0.0654001	−	0.990653i
$393$		0			0
$394$	−5.39322e41	+	3.27385e41i	−1.59922	+	0.970775i
$395$		−	4.57570e41i		−	1.30288i
$396$		0			0
$397$	−5.94309e41			−1.56086			−0.780430	−	0.625243i	$-0.785000\pi$
$397$	−5.94309e41			−1.56086			−0.780430	+	0.625243i	$0.785000\pi$
$398$	−5.46790e40	−	9.00762e40i	−0.137940	−	0.227238i
$399$		0			0
$400$	−2.53010e41	−	3.60853e41i	−0.589085	−	0.840176i
$401$	8.19907e40			0.183423			0.0917117	−	0.995786i	$-0.470766\pi$
$401$	8.19907e40			0.183423			0.0917117	+	0.995786i	$0.470766\pi$
$402$		0			0
$403$		−	9.55248e41i		−	1.97349i
$404$	−1.93363e41	+	3.71732e41i	−0.383947	+	0.738123i
$405$		0			0
$406$	1.39462e40	+	2.29744e40i	0.0255881	+	0.0421529i
$407$		−	1.82622e41i		−	0.322138i
$408$		0			0
$409$	7.15084e41			1.16623			0.583115	−	0.812390i	$-0.301834\pi$
$409$	7.15084e41			1.16623			0.583115	+	0.812390i	$0.301834\pi$
$410$	2.19926e41	−	1.33502e41i	0.344934	−	0.209385i
$411$		0			0
$412$	6.70224e40	+	3.48629e40i	0.0972444	+	0.0505834i
$413$	−2.67310e40			−0.0373090
$414$		0			0
$415$			1.35688e42i			1.75296i
$416$	7.83907e41	+	3.44192e41i	0.974476	+	0.427866i
$417$		0			0
$418$	7.16935e41	−	4.35201e41i	0.825390	−	0.501036i
$419$		−	1.14174e42i		−	1.26515i	−0.774498	−	0.632576i	$-0.781997\pi$
$419$		−	1.14174e42i		−	1.26515i	0.774498	−	0.632576i	$-0.218003\pi$
$420$		0			0
$421$	2.75721e39			0.00283110			0.00141555	−	0.999999i	$-0.499549\pi$
$421$	2.75721e39			0.00283110			0.00141555	+	0.999999i	$0.499549\pi$
$422$	1.05426e41	+	1.73675e41i	0.104219	+	0.171687i
$423$		0			0
$424$	1.02025e41	+	1.54543e42i	0.0935090	+	1.41644i
$425$	−1.56725e42			−1.38330
$426$		0			0
$427$			8.57317e40i			0.0701933i
$428$	−8.79254e41	−	4.57359e41i	−0.693448	−	0.360709i
$429$		0			0
$430$	1.15335e42	+	1.89999e42i	0.844243	+	1.39078i
$431$			1.37954e42i			0.972967i	0.873690	+	0.486484i	$0.161721\pi$
$431$			1.37954e42i			0.972967i	−0.873690	+	0.486484i	$0.838279\pi$
$432$		0			0
$433$	−1.83219e42			−1.19995			−0.599976	−	0.800018i	$-0.704823\pi$
$433$	−1.83219e42			−1.19995			−0.599976	+	0.800018i	$0.704823\pi$
$434$	−2.12953e41	+	1.29269e41i	−0.134415	+	0.0815938i
$435$		0			0
$436$	−6.28673e41	+	1.20860e42i	−0.368673	+	0.708758i
$437$	−1.45885e41			−0.0824721
$438$		0			0
$439$		−	3.54955e42i		−	1.86527i	−0.360827	−	0.932633i	$-0.617506\pi$
$439$		−	3.54955e42i		−	1.86527i	0.360827	−	0.932633i	$-0.382494\pi$
$440$	4.24288e42	−	2.80103e41i	2.14990	−	0.141930i
$441$		0			0
$442$	2.60260e42	−	1.57986e42i	1.22646	−	0.744495i
$443$			3.06452e42i			1.39285i	0.717631	+	0.696423i	$0.245226\pi$
$443$			3.06452e42i			1.39285i	−0.717631	+	0.696423i	$0.754774\pi$
$444$		0			0
$445$	−2.24678e42			−0.950168
$446$	−3.91905e41	−	6.45610e41i	−0.159890	−	0.263398i
$447$		0			0
$448$	−2.93515e40	−	2.21333e41i	−0.0111476	−	0.0840617i
$449$	−2.68427e42			−0.983749			−0.491875	−	0.870666i	$-0.663688\pi$
$449$	−2.68427e42			−0.983749			−0.491875	+	0.870666i	$0.663688\pi$
$450$		0			0
$451$			1.25713e42i			0.429095i
$452$	−2.73824e42	+	5.26415e42i	−0.902103	+	1.73425i
$453$		0			0
$454$	1.57063e42	+	2.58740e42i	0.482148	+	0.794274i
$455$		−	4.33462e41i		−	0.128460i
$456$		0			0
$457$	1.28397e42			0.354729			0.177365	−	0.984145i	$-0.443243\pi$
$457$	1.28397e42			0.354729			0.177365	+	0.984145i	$0.443243\pi$
$458$	2.08560e42	−	1.26602e42i	0.556394	−	0.337748i
$459$		0			0
$460$	−6.56169e41	−	3.41318e41i	−0.163264	−	0.0849246i
$461$	5.93149e42			1.42544			0.712721	−	0.701448i	$-0.247463\pi$
$461$	5.93149e42			1.42544			0.712721	+	0.701448i	$0.247463\pi$
$462$		0			0
$463$			2.14282e42i			0.480495i	0.970712	+	0.240248i	$0.0772286\pi$
$463$			2.14282e42i			0.480495i	−0.970712	+	0.240248i	$0.922771\pi$
$464$	−1.54111e42	−	2.19799e42i	−0.333845	−	0.476143i
$465$		0			0
$466$	−3.96011e42	+	2.40391e42i	−0.800816	+	0.486120i
$467$		−	2.77518e42i		−	0.542278i	−0.962540	−	0.271139i	$-0.912600\pi$
$467$		−	2.77518e42i		−	0.542278i	0.962540	−	0.271139i	$-0.0874003\pi$
$468$		0			0
$469$	−2.08595e41			−0.0380661
$470$	6.38330e42	+	1.05156e43i	1.12585	+	1.85468i
$471$		0			0
$472$	2.66414e42	−	1.75879e41i	0.439021	−	0.0289829i
$473$	−1.08606e43			−1.73012
$474$		0			0
$475$		−	4.39585e42i		−	0.654554i
$476$	−7.04392e41	−	3.66402e41i	−0.101415	−	0.0527529i
$477$		0			0
$478$	4.32052e41	+	7.11748e41i	0.0581688	+	0.0958252i
$479$			9.77483e42i			1.27274i	0.771383	+	0.636372i	$0.219566\pi$
$479$			9.77483e42i			1.27274i	−0.771383	+	0.636372i	$0.780434\pi$
$480$		0			0
$481$	1.85945e42			0.226498
$482$	2.54672e42	−	1.54594e42i	0.300074	−	0.182154i
$483$		0			0
$484$	−5.40330e42	+	1.03876e43i	−0.595845	+	1.14549i
$485$	2.29481e43			2.44838
$486$		0			0
$487$			4.78815e42i			0.478304i	0.970982	+	0.239152i	$0.0768695\pi$
$487$			4.78815e42i			0.478304i	−0.970982	+	0.239152i	$0.923131\pi$
$488$	−5.64081e41	−	8.54446e42i	−0.0545286	−	0.825976i
$489$		0			0
$490$	1.33418e43	−	8.09889e42i	1.20803	−	0.733311i
$491$		−	4.17934e42i		−	0.366272i	−0.983088	−	0.183136i	$-0.941375\pi$
$491$		−	4.17934e42i		−	0.366272i	0.983088	−	0.183136i	$-0.0586248\pi$
$492$		0			0
$493$	−9.54628e42			−0.783941
$494$	4.43121e42	+	7.29982e42i	0.352283	+	0.580338i
$495$		0			0
$496$	2.03734e43	−	1.42847e43i	1.51830	−	1.06455i
$497$	7.33121e41			0.0529021
$498$		0			0
$499$		−	2.18612e43i		−	1.47933i	−0.672975	−	0.739665i	$-0.734984\pi$
$499$		−	2.18612e43i		−	1.47933i	0.672975	−	0.739665i	$-0.265016\pi$
$500$	2.61770e41	−	5.03242e41i	0.0171554	−	0.0329805i
$501$		0			0
$502$	6.34371e42	+	1.04504e43i	0.390017	+	0.642501i
$503$		−	8.88151e41i		−	0.0528931i	−0.999650	−	0.0264466i	$-0.991581\pi$
$503$		−	8.88151e41i		−	0.0528931i	0.999650	−	0.0264466i	$-0.00841918\pi$
$504$		0			0
$505$	−2.11896e43			−1.18430
$506$	3.08942e42	−	1.87537e42i	0.167289	−	0.101550i
$507$		0			0
$508$	2.05353e43	+	1.06818e43i	1.04396	+	0.543032i
$509$	−1.41679e43			−0.697946			−0.348973	−	0.937133i	$-0.613470\pi$
$509$	−1.41679e43			−0.697946			−0.348973	+	0.937133i	$0.613470\pi$
$510$		0			0
$511$			1.04524e42i			0.0483595i
$512$	4.38160e42	+	2.18661e43i	0.196478	+	0.980508i
$513$		0			0
$514$	9.50984e42	−	5.77276e42i	0.400648	−	0.243205i
$515$			3.82043e42i			0.156026i
$516$		0			0
$517$	−6.01086e43			−2.30721
$518$	−2.51630e41	−	4.14526e41i	−0.00936453	−	0.0154268i
$519$		0			0
$520$	2.85201e42	+	4.32010e43i	0.0997923	+	1.51161i
$521$	−4.87247e43			−1.65328			−0.826639	−	0.562733i	$-0.809750\pi$
$521$	−4.87247e43			−1.65328			−0.826639	+	0.562733i	$0.809750\pi$
$522$		0			0
$523$		−	1.24274e42i		−	0.0396601i	−0.999803	−	0.0198300i	$-0.993687\pi$
$523$		−	1.24274e42i		−	0.0396601i	0.999803	−	0.0198300i	$-0.00631251\pi$
$524$	5.28433e43	+	2.74874e43i	1.63565	+	0.850810i
$525$		0			0
$526$	−9.01990e42	−	1.48591e43i	−0.262682	−	0.432733i
$527$		−	8.84856e43i		−	2.49979i
$528$		0			0
$529$	3.69803e43			0.983285
$530$	−6.69525e43	+	4.06422e43i	−1.72724	+	1.04849i
$531$		0			0
$532$	1.02769e42	−	1.97569e42i	0.0249618	−	0.0479880i
$533$	−1.28000e43			−0.301700
$534$		0			0
$535$		−	5.01195e43i		−	1.11262i
$536$	2.07896e43	−	1.37247e42i	0.447930	−	0.0295710i
$537$		0			0
$538$	−1.01750e43	+	6.17656e42i	−0.206548	+	0.125381i
$539$			7.62635e43i			1.50278i
$540$		0			0
$541$	−5.93941e43			−1.10303			−0.551515	−	0.834165i	$-0.685950\pi$
$541$	−5.93941e43			−1.10303			−0.551515	+	0.834165i	$0.685950\pi$
$542$	3.46979e43	+	5.71601e43i	0.625625	+	1.03063i
$543$		0			0
$544$	7.26141e43	+	3.18828e43i	1.23435	+	0.541969i
$545$	−6.88929e43			−1.13718
$546$		0			0
$547$			1.03500e44i			1.61118i	0.592476	+	0.805588i	$0.298150\pi$
$547$			1.03500e44i			1.61118i	−0.592476	+	0.805588i	$0.701850\pi$
$548$	2.80345e43	−	5.38952e43i	0.423842	−	0.814819i
$549$		0			0
$550$	5.65094e43	+	9.30916e43i	0.805967	+	1.32772i
$551$		−	2.67755e43i		−	0.370948i
$552$		0			0
$553$	5.93687e42			0.0776168
$554$	8.27123e43	−	5.02089e43i	1.05054	−	0.637711i
$555$		0			0
$556$	5.19139e43	+	2.70039e43i	0.622425	+	0.323765i
$557$	−3.46931e43			−0.404166			−0.202083	−	0.979368i	$-0.564771\pi$
$557$	−3.46931e43			−0.404166			−0.202083	+	0.979368i	$0.564771\pi$
$558$		0			0
$559$		−	1.10582e44i		−	1.21646i
$560$	9.24481e42	−	6.48195e42i	0.0988301	−	0.0692943i
$561$		0			0
$562$	3.28635e43	−	1.99491e43i	0.331843	−	0.201439i
$563$		−	1.44724e44i		−	1.42038i	−0.704008	−	0.710192i	$-0.748608\pi$
$563$		−	1.44724e44i		−	1.42038i	0.704008	−	0.710192i	$-0.251392\pi$
$564$		0			0
$565$	−3.00068e44			−2.78256
$566$	−7.86746e43	−	1.29606e44i	−0.709205	−	1.16832i
$567$		0			0
$568$	−7.30665e43	+	4.82364e42i	−0.622508	+	0.0410962i
$569$	8.69359e43			0.720117			0.360059	−	0.932930i	$-0.382757\pi$
$569$	8.69359e43			0.720117			0.360059	+	0.932930i	$0.382757\pi$
$570$		0			0
$571$		−	1.65234e44i		−	1.29396i	−0.762506	−	0.646981i	$-0.776031\pi$
$571$		−	1.65234e44i		−	1.29396i	0.762506	−	0.646981i	$-0.223969\pi$
$572$	−1.87681e44	−	9.76253e43i	−1.42917	−	0.743406i
$573$		0			0
$574$	1.73216e42	+	2.85350e42i	0.0124738	+	0.0205488i
$575$		−	1.89426e43i		−	0.132665i
$576$		0			0
$577$	−8.34544e43			−0.552887			−0.276443	−	0.961030i	$-0.589156\pi$
$577$	−8.34544e43			−0.552887			−0.276443	+	0.961030i	$0.589156\pi$
$578$	1.08426e44	−	6.58180e43i	0.698697	−	0.424130i
$579$		0			0
$580$	6.26451e43	−	1.20433e44i	0.381979	−	0.734339i
$581$	−1.76052e43			−0.104429
$582$		0			0
$583$		−	3.82709e44i		−	2.14868i
$584$	−6.87727e42	−	1.04174e44i	−0.0375674	−	0.569054i
$585$		0			0
$586$	−5.35421e43	+	3.25017e43i	−0.276907	+	0.168091i
$587$		−	6.43456e42i		−	0.0323824i	−0.999869	−	0.0161912i	$-0.994846\pi$
$587$		−	6.43456e42i		−	0.0323824i	0.999869	−	0.0161912i	$-0.00515405\pi$
$588$		0			0
$589$	2.48186e44			1.18286
$590$	7.00623e43	+	1.15418e44i	0.324977	+	0.535355i
$591$		0			0
$592$	2.78061e43	+	3.96581e43i	0.122178	+	0.174255i
$593$	−6.27744e43			−0.268477			−0.134239	−	0.990949i	$-0.542859\pi$
$593$	−6.27744e43			−0.268477			−0.134239	+	0.990949i	$0.542859\pi$
$594$		0			0
$595$		−	4.01520e43i		−	0.162718i
$596$	−2.37907e43	+	4.57367e43i	−0.0938572	+	0.180437i
$597$		0			0
$598$	1.90950e43	+	3.14564e43i	0.0714004	+	0.117623i
$599$		−	5.41478e43i		−	0.197129i	−0.995131	−	0.0985647i	$-0.968575\pi$
$599$		−	5.41478e43i		−	0.197129i	0.995131	−	0.0985647i	$-0.0314251\pi$
$600$		0			0
$601$	−4.48094e44			−1.54660			−0.773299	−	0.634042i	$-0.781395\pi$
$601$	−4.48094e44			−1.54660			−0.773299	+	0.634042i	$0.781395\pi$
$602$	−2.46520e43	+	1.49645e43i	−0.0828531	+	0.0502943i
$603$		0			0
$604$	1.82380e44	+	9.48682e43i	0.581281	+	0.302364i
$605$	−5.92118e44			−1.83790
$606$		0			0
$607$		−	1.09513e44i		−	0.322440i	−0.986919	−	0.161220i	$-0.948457\pi$
$607$		−	1.09513e44i		−	0.322440i	0.986919	−	0.161220i	$-0.0515428\pi$
$608$	−8.94255e43	+	2.03669e44i	−0.256451	+	0.584074i
$609$		0			0
$610$	3.70170e44	−	2.24704e44i	1.00722	−	0.611412i
$611$		−	6.12025e44i		−	1.62222i
$612$		0			0
$613$	1.27103e44			0.319734			0.159867	−	0.987139i	$-0.448894\pi$
$613$	1.27103e44			0.319734			0.159867	+	0.987139i	$0.448894\pi$
$614$	−6.16991e43	−	1.01641e44i	−0.151212	−	0.249101i
$615$		0			0
$616$	3.63428e42	+	5.50505e43i	0.00845526	+	0.128077i
$617$	−6.26067e44			−1.41925			−0.709624	−	0.704581i	$-0.751135\pi$
$617$	−6.26067e44			−1.41925			−0.709624	+	0.704581i	$0.751135\pi$
$618$		0			0
$619$			2.94769e44i			0.634500i	0.948342	+	0.317250i	$0.102759\pi$
$619$			2.94769e44i			0.634500i	−0.948342	+	0.317250i	$0.897241\pi$
$620$	1.11630e45	+	5.80665e44i	2.34161	+	1.21803i
$621$		0			0
$622$	4.09131e44	+	6.73989e44i	0.815111	+	1.34278i
$623$		−	2.91515e43i		−	0.0566046i
$624$		0			0
$625$	−5.27573e44			−0.973201
$626$	5.24906e44	−	3.18634e44i	0.943827	−	0.572931i
$627$		0			0
$628$	1.41501e44	−	2.72030e44i	0.241772	−	0.464796i
$629$	1.72243e44			0.286900
$630$		0			0
$631$		−	3.61763e44i		−	0.572736i	−0.958120	−	0.286368i	$-0.907552\pi$
$631$		−	3.61763e44i		−	0.572736i	0.958120	−	0.286368i	$-0.0924479\pi$
$632$	−5.91699e44	+	3.90623e43i	−0.913329	+	0.0602954i
$633$		0			0
$634$	7.11476e44	−	4.31887e44i	1.04408	−	0.633786i
$635$			1.17056e45i			1.67500i
$636$		0			0
$637$	−7.76514e44			−1.05662
$638$	3.44204e44	+	5.67029e44i	0.456756	+	0.752444i
$639$		0			0
$640$	−8.78735e44	+	7.06851e44i	−1.10912	+	0.892172i
$641$	7.60593e44			0.936319			0.468159	−	0.883644i	$-0.344917\pi$
$641$	7.60593e44			0.936319			0.468159	+	0.883644i	$0.344917\pi$
$642$		0			0
$643$		−	1.05982e45i		−	1.24124i	−0.784112	−	0.620619i	$-0.786881\pi$
$643$		−	1.05982e45i		−	1.24124i	0.784112	−	0.620619i	$-0.213119\pi$
$644$	4.42853e42	−	8.51366e42i	0.00505924	−	0.00972618i
$645$		0			0
$646$	4.10467e44	+	6.76189e44i	0.446229	+	0.735103i
$647$		−	4.77969e44i		−	0.506911i	−0.967347	−	0.253455i	$-0.918433\pi$
$647$		−	4.77969e44i		−	0.506911i	0.967347	−	0.253455i	$-0.0815671\pi$
$648$		0			0
$649$	−6.59744e44			−0.665979
$650$	−9.47857e44	+	5.75378e44i	−0.933532	+	0.566682i
$651$		0			0
$652$	−3.64502e44	−	1.89602e44i	−0.341774	−	0.177779i
$653$	1.50534e45			1.37729			0.688643	−	0.725101i	$-0.258207\pi$
$653$	1.50534e45			1.37729			0.688643	+	0.725101i	$0.258207\pi$
$654$		0			0
$655$			3.01219e45i			2.62435i
$656$	−1.91411e44	−	2.72997e44i	−0.162744	−	0.232111i
$657$		0			0
$658$	−1.36438e44	+	8.28220e43i	−0.110490	+	0.0670705i
$659$		−	1.35593e45i		−	1.07169i	−0.844315	−	0.535847i	$-0.819992\pi$
$659$		−	1.35593e45i		−	1.07169i	0.844315	−	0.535847i	$-0.180008\pi$
$660$		0			0
$661$	1.79337e45			1.35035			0.675176	−	0.737657i	$-0.264068\pi$
$661$	1.79337e45			1.35035			0.675176	+	0.737657i	$0.264068\pi$
$662$	5.99862e43	+	9.88191e43i	0.0440883	+	0.0726295i
$663$		0			0
$664$	1.75462e45	−	1.15835e44i	1.22884	−	0.0811243i
$665$	1.12619e44			0.0769954
$666$		0			0
$667$		−	1.15381e44i		−	0.0751835i
$668$	7.06475e44	+	3.67485e44i	0.449441	+	0.233785i
$669$		0			0
$670$	5.46731e44	+	9.00665e44i	0.331571	+	0.546218i
$671$			2.11594e45i			1.25297i
$672$		0			0
$673$	−1.07392e45			−0.606361			−0.303181	−	0.952933i	$-0.598049\pi$
$673$	−1.07392e45			−0.606361			−0.303181	+	0.952933i	$0.598049\pi$
$674$	4.55342e43	−	2.76406e43i	0.0251061	−	0.0152401i
$675$		0			0
$676$	1.16433e44	−	2.23837e44i	0.0612248	−	0.117702i
$677$	−1.73726e45			−0.892165			−0.446083	−	0.894992i	$-0.647181\pi$
$677$	−1.73726e45			−0.892165			−0.446083	+	0.894992i	$0.647181\pi$
$678$		0			0
$679$			2.97747e44i			0.145858i
$680$	2.64184e44	+	4.00175e45i	0.126405	+	1.91473i
$681$		0			0
$682$	−5.25586e45	+	3.19046e45i	−2.39935	+	1.45648i
$683$			3.65073e45i			1.62798i	0.580882	+	0.813988i	$0.302708\pi$
$683$			3.65073e45i			1.62798i	−0.580882	+	0.813988i	$0.697292\pi$
$684$		0			0
$685$	3.07215e45			1.30735
$686$	2.10924e44	+	3.47469e44i	0.0876879	+	0.144454i
$687$		0			0
$688$	2.35849e45	−	1.65364e45i	0.935876	−	0.656185i
$689$	3.89674e45			1.51075
$690$		0			0
$691$			4.60791e45i			1.70551i	0.522309	+	0.852756i	$0.325071\pi$
$691$			4.60791e45i			1.70551i	−0.522309	+	0.852756i	$0.674929\pi$
$692$	4.06838e44	−	7.82130e44i	0.147138	−	0.282866i
$693$		0			0
$694$	−2.40189e45	−	3.95680e45i	−0.829473	−	1.36644i
$695$			2.95921e45i			0.998664i
$696$		0			0
$697$	−1.18568e45			−0.382158
$698$	−1.02075e45	+	6.19626e44i	−0.321538	+	0.195183i
$699$		0			0
$700$	2.56537e44	+	1.33442e44i	0.0771935	+	0.0401536i
$701$	−2.86431e45			−0.842425			−0.421212	−	0.906962i	$-0.638395\pi$
$701$	−2.86431e45			−0.842425			−0.421212	+	0.906962i	$0.638395\pi$
$702$		0			0
$703$			4.83110e44i			0.135756i
$704$	−7.24421e44	−	5.46270e45i	−0.198989	−	1.50053i
$705$		0			0
$706$	1.39912e45	−	8.49309e44i	0.367265	−	0.222941i
$707$		−	2.74931e44i		−	0.0705525i
$708$		0			0
$709$	6.73611e45			1.65223			0.826113	−	0.563504i	$-0.190547\pi$
$709$	6.73611e45			1.65223			0.826113	+	0.563504i	$0.190547\pi$
$710$	−1.92152e45	−	3.16545e45i	−0.460799	−	0.759104i
$711$		0			0
$712$	1.91805e44	+	2.90538e45i	0.0439724	+	0.666076i
$713$	1.06948e45			0.239741
$714$		0			0
$715$		−	1.06982e46i		−	2.29306i
$716$	−4.80090e44	−	2.49727e44i	−0.100627	−	0.0523428i
$717$		0			0
$718$	−3.04564e45	−	5.01728e45i	−0.610502	−	1.00572i
$719$		−	6.36501e45i		−	1.24778i	−0.781514	−	0.623888i	$-0.785552\pi$
$719$		−	6.36501e45i		−	1.24778i	0.781514	−	0.623888i	$-0.214448\pi$
$720$		0			0
$721$	−4.95693e43			−0.00929498
$722$	2.76437e45	−	1.67806e45i	0.506992	−	0.307760i
$723$		0			0
$724$	−2.39540e44	+	4.60505e44i	−0.0420301	+	0.0808012i
$725$	3.47672e45			0.596707
$726$		0			0
$727$		−	8.93864e45i		−	1.46798i	−0.679159	−	0.733991i	$-0.737655\pi$
$727$		−	8.93864e45i		−	1.46798i	0.679159	−	0.733991i	$-0.262345\pi$
$728$	−5.60524e44	+	3.70042e43i	−0.0900517	+	0.00594496i
$729$		0			0
$730$	4.51311e45	−	2.73959e45i	0.693921	−	0.421231i
$731$		−	1.02434e46i		−	1.54086i
$732$		0			0
$733$	−3.50667e45			−0.504930			−0.252465	−	0.967606i	$-0.581241\pi$
$733$	−3.50667e45			−0.504930			−0.252465	+	0.967606i	$0.581241\pi$
$734$	−3.88998e44	−	6.40822e44i	−0.0548038	−	0.0902818i
$735$		0			0
$736$	−3.85353e44	+	8.77652e44i	−0.0519773	+	0.118380i
$737$	−5.14831e45			−0.679492
$738$		0			0
$739$			3.33091e45i			0.420971i	0.977597	+	0.210486i	$0.0675045\pi$
$739$			3.33091e45i			0.420971i	−0.977597	+	0.210486i	$0.932496\pi$
$740$	−1.13030e45	+	2.17296e45i	−0.139794	+	0.268747i
$741$		0			0
$742$	−5.27324e44	−	8.68695e44i	−0.0624619	−	0.102898i
$743$			5.60428e45i			0.649679i	0.945769	+	0.324840i	$0.105310\pi$
$743$			5.60428e45i			0.649679i	−0.945769	+	0.324840i	$0.894690\pi$
$744$		0			0
$745$	−2.60710e45			−0.289505
$746$	−6.06803e45	+	3.68348e45i	−0.659518	+	0.400347i
$747$		0			0
$748$	−1.73850e46	−	9.04313e45i	−1.81030	−	0.941658i
$749$	6.50290e44			0.0662824
$750$		0			0
$751$			1.89091e46i			1.84685i	0.383775	+	0.923427i	$0.374624\pi$
$751$			1.89091e46i			1.84685i	−0.383775	+	0.923427i	$0.625376\pi$
$752$	1.30532e46	−	9.15217e45i	1.24805	−	0.875061i
$753$		0			0
$754$	−5.77348e45	+	3.50468e45i	−0.529050	+	0.321149i
$755$			1.03961e46i			0.932650i
$756$		0			0
$757$	2.00538e46			1.72450			0.862250	−	0.506483i	$-0.169055\pi$
$757$	2.00538e46			1.72450			0.862250	+	0.506483i	$0.169055\pi$
$758$	−3.16746e45	−	5.21796e45i	−0.266688	−	0.439333i
$759$		0			0
$760$	−1.12242e46	+	7.40987e44i	−0.906017	+	0.0598127i
$761$	−1.36781e46			−1.08112			−0.540558	−	0.841307i	$-0.681787\pi$
$761$	−1.36781e46			−1.08112			−0.540558	+	0.841307i	$0.681787\pi$
$762$		0			0
$763$		−	8.93871e44i		−	0.0677457i
$764$	−1.13531e46	−	5.90552e45i	−0.842600	−	0.438293i
$765$		0			0
$766$	−2.71006e44	−	4.46446e44i	−0.0192894	−	0.0317767i
$767$		−	6.71750e45i		−	0.468255i
$768$		0			0
$769$	1.11734e46			0.747071			0.373536	−	0.927616i	$-0.378145\pi$
$769$	1.11734e46			0.747071			0.373536	+	0.927616i	$0.378145\pi$
$770$	−2.38494e45	+	1.44773e45i	−0.156180	+	0.0948062i
$771$		0			0
$772$	−1.98719e44	+	3.82028e44i	−0.0124842	+	0.0240004i
$773$	2.18678e46			1.34565			0.672827	−	0.739800i	$-0.265080\pi$
$773$	2.18678e46			1.34565			0.672827	+	0.739800i	$0.265080\pi$
$774$		0			0
$775$			3.22261e46i			1.90274i
$776$	−1.95906e45	−	2.96749e46i	−0.113308	−	1.71634i
$777$		0			0
$778$	−5.43623e44	+	3.29996e44i	−0.0301734	+	0.0183162i
$779$		−	3.32561e45i		−	0.180831i
$780$		0			0
$781$	1.80941e46			0.944321
$782$	1.76879e45	+	2.91384e45i	0.0904415	+	0.148990i
$783$		0			0
$784$	−1.16119e46	−	1.65614e46i	−0.569963	−	0.812904i
$785$	1.55063e46			0.745753
$786$		0			0
$787$			1.68275e46i			0.777007i	0.921447	+	0.388503i	$0.127008\pi$
$787$			1.68275e46i			0.777007i	−0.921447	+	0.388503i	$0.872992\pi$
$788$	−1.90806e46	+	3.66816e46i	−0.863320	+	1.65970i
$789$		0			0
$790$	−1.55606e46	−	2.56341e46i	−0.676074	−	1.11374i
$791$		−	3.89332e45i		−	0.165767i
$792$		0			0
$793$	−2.15444e46			−0.880976
$794$	−3.32945e46	+	2.02107e46i	−1.33427	+	0.809942i
$795$		0			0
$796$	−6.12647e45	−	3.18679e45i	−0.235831	−	0.122672i
$797$	3.48117e45			0.131339			0.0656693	−	0.997841i	$-0.479082\pi$
$797$	3.48117e45			0.131339			0.0656693	+	0.997841i	$0.479082\pi$
$798$		0			0
$799$		−	5.66925e46i		−	2.05483i
$800$	−2.64457e46	−	1.16116e46i	−0.939541	−	0.412527i
$801$		0			0
$802$	4.59330e45	−	2.78827e45i	0.156796	−	0.0951798i
$803$			2.57975e46i			0.863234i
$804$		0			0
$805$	4.85298e44			0.0156054
$806$	−3.24853e46	−	5.35151e46i	−1.02406	−	1.68700i
$807$		0			0
$808$	1.80893e45	+	2.74010e46i	0.0548076	+	0.830203i
$809$	2.87821e46			0.854961			0.427481	−	0.904025i	$-0.359401\pi$
$809$	2.87821e46			0.854961			0.427481	+	0.904025i	$0.359401\pi$
$810$		0			0
$811$			4.47972e46i			1.27914i	0.768733	+	0.639569i	$0.220887\pi$
$811$			4.47972e46i			1.27914i	−0.768733	+	0.639569i	$0.779113\pi$
$812$	1.56259e45	+	8.12807e44i	0.0437470	+	0.0227558i
$813$		0			0
$814$	−6.21045e45	−	1.02309e46i	−0.167160	−	0.275374i
$815$		−	2.07775e46i		−	0.548366i
$816$		0			0
$817$	2.87307e46			0.729111
$818$	4.00606e46	−	2.43180e46i	0.996929	−	0.605166i
$819$		0			0
$820$	7.78073e45	−	1.49581e46i	0.186208	−	0.357977i
$821$	2.72426e46			0.639378			0.319689	−	0.947523i	$-0.396422\pi$
$821$	2.72426e46			0.639378			0.319689	+	0.947523i	$0.396422\pi$
$822$		0			0
$823$		−	1.08853e46i		−	0.245721i	−0.992424	−	0.122861i	$-0.960793\pi$
$823$		−	1.08853e46i		−	0.245721i	0.992424	−	0.122861i	$-0.0392068\pi$
$824$	4.94033e45	−	3.26146e44i	0.109376	−	0.00722066i
$825$		0			0
$826$	−1.49753e45	+	9.09043e44i	−0.0318929	+	0.0193599i
$827$		−	3.00168e46i		−	0.627013i	−0.949586	−	0.313507i	$-0.898496\pi$
$827$		−	3.00168e46i		−	0.627013i	0.949586	−	0.313507i	$-0.101504\pi$
$828$		0			0
$829$	7.52687e46			1.51266			0.756331	−	0.654189i	$-0.226990\pi$
$829$	7.52687e46			1.51266			0.756331	+	0.654189i	$0.226990\pi$
$830$	4.61435e46	+	7.60152e46i	0.909622	+	1.49848i
$831$		0			0
$832$	5.56212e46	−	7.37605e45i	1.05503	−	0.139911i
$833$	−7.19292e46			−1.33840
$834$		0			0
$835$			4.02707e46i			0.721117i
$836$	2.53643e46	−	4.87618e46i	0.445576	−	0.856602i
$837$		0			0
$838$	−3.88273e46	−	6.39628e46i	−0.656497	−	1.08149i
$839$			5.53407e46i			0.918023i	0.888430	+	0.459011i	$0.151796\pi$
$839$			5.53407e46i			0.918023i	−0.888430	+	0.459011i	$0.848204\pi$
$840$		0			0
$841$	−4.14463e46			−0.661835
$842$	1.54465e44	−	9.37647e43i	0.00242011	−	0.00146908i
$843$		0			0
$844$	1.18124e46	+	6.14440e45i	0.178179	+	0.0926831i
$845$	1.27592e46			0.188850
$846$		0			0
$847$		−	7.68260e45i		−	0.109490i
$848$	5.82714e46	+	8.31089e46i	0.814933	+	1.16229i
$849$		0			0
$850$	−8.78009e46	+	5.32978e46i	−1.18249	+	0.717805i
$851$			2.08182e45i			0.0275150i
$852$		0			0
$853$	−5.02319e45			−0.0639433			−0.0319717	−	0.999489i	$-0.510179\pi$
$853$	−5.02319e45			−0.0639433			−0.0319717	+	0.999489i	$0.510179\pi$
$854$	2.91549e45	+	4.80288e45i	0.0364238	+	0.0600034i
$855$		0			0
$856$	−6.48112e46	+	4.27865e45i	−0.779955	+	0.0514904i
$857$	−9.46054e46			−1.11744			−0.558718	−	0.829357i	$-0.688707\pi$
$857$	−9.46054e46			−1.11744			−0.558718	+	0.829357i	$0.688707\pi$
$858$		0			0
$859$			1.91602e46i			0.218026i	0.994040	+	0.109013i	$0.0347691\pi$
$859$			1.91602e46i			0.218026i	−0.994040	+	0.109013i	$0.965231\pi$
$860$	1.29227e47	+	6.72196e46i	1.44337	+	0.750793i
$861$		0			0
$862$	4.69142e46	+	7.72848e46i	0.504880	+	0.831722i
$863$			9.20747e46i			0.972675i	0.873771	+	0.486338i	$0.161667\pi$
$863$			9.20747e46i			0.972675i	−0.873771	+	0.486338i	$0.838333\pi$
$864$		0			0
$865$	4.45832e46			0.453851
$866$	−1.02643e47	+	6.23075e46i	−1.02575	+	0.622664i
$867$		0			0
$868$	−7.53401e45	+	1.44838e46i	−0.0725622	+	0.139498i
$869$	1.46527e47			1.38549
$870$		0			0
$871$		−	5.24200e46i		−	0.477756i
$872$	5.88131e45	+	8.90876e46i	0.0526272	+	0.797175i
$873$		0			0
$874$	−8.17278e45	+	4.96112e45i	−0.0704996	+	0.0427954i
$875$			3.72194e44i			0.00315240i
$876$		0			0
$877$	−1.63787e47			−1.33748			−0.668739	−	0.743497i	$-0.733166\pi$
$877$	−1.63787e47			−1.33748			−0.668739	+	0.743497i	$0.733166\pi$
$878$	−1.20710e47	−	1.98853e47i	−0.967901	−	1.59449i
$879$		0			0
$880$	2.28170e47	−	1.59980e47i	1.76415	−	1.23693i
$881$	−3.60559e46			−0.273755			−0.136877	−	0.990588i	$-0.543707\pi$
$881$	−3.60559e46			−0.273755			−0.136877	+	0.990588i	$0.543707\pi$
$882$		0			0
$883$		−	1.54388e47i		−	1.13042i	−0.824945	−	0.565212i	$-0.808794\pi$
$883$		−	1.54388e47i		−	1.13042i	0.824945	−	0.565212i	$-0.191206\pi$
$884$	9.20770e46	−	1.77014e47i	0.662087	−	1.27283i
$885$		0			0
$886$	1.04216e47	+	1.71681e47i	0.722759	+	1.19065i
$887$		−	1.06318e47i		−	0.724150i	−0.932149	−	0.362075i	$-0.882068\pi$
$887$		−	1.06318e47i		−	0.724150i	0.932149	−	0.362075i	$-0.117932\pi$
$888$		0			0
$889$	−1.51878e46			−0.0997852
$890$	−1.25869e47	+	7.64065e46i	−0.812232	+	0.493049i
$891$		0			0
$892$	−4.39107e46	−	2.28409e46i	−0.273358	−	0.142192i
$893$	1.59012e47			0.972313
$894$		0			0
$895$		−	2.73662e46i		−	0.161453i
$896$	−9.17124e45	−	1.14014e46i	−0.0531496	−	0.0660739i
$897$		0			0
$898$	−1.50378e47	+	9.12843e46i	−0.840939	+	0.510475i
$899$			1.96292e47i			1.07832i
$900$		0			0
$901$	3.60958e47			1.91364
$902$	4.27512e46	+	7.04269e46i	0.222661	+	0.366804i
$903$		0			0
$904$	2.56165e46	+	3.88028e47i	0.128773	+	1.95060i
$905$	−2.62499e46			−0.129643
$906$		0			0
$907$			1.29696e47i			0.618314i	0.951011	+	0.309157i	$0.100047\pi$
$907$			1.29696e47i			0.618314i	−0.951011	+	0.309157i	$0.899953\pi$
$908$	1.75980e47	+	9.15393e46i	0.824310	+	0.428779i
$909$		0			0
$910$	−1.47408e46	−	2.42835e46i	−0.0666590	−	0.109812i
$911$			3.45293e47i			1.53424i	0.641503	+	0.767120i	$0.278311\pi$
$911$			3.45293e47i			1.53424i	−0.641503	+	0.767120i	$0.721689\pi$
$912$		0			0
$913$	−4.34512e47			−1.86410
$914$	7.19310e46	−	4.36643e46i	0.303233	−	0.184072i
$915$		0			0
$916$	7.37859e46	−	1.41850e47i	0.300363	−	0.577434i
$917$	−3.90826e46			−0.156341
$918$		0			0
$919$			4.17823e47i			1.61415i	0.590447	+	0.807076i	$0.298951\pi$
$919$			4.17823e47i			1.61415i	−0.590447	+	0.807076i	$0.701049\pi$
$920$	−4.83673e46	+	3.19307e45i	−0.183631	+	0.0121228i
$921$		0			0
$922$	3.32295e47	−	2.01713e47i	1.21851	−	0.739672i
$923$			1.84234e47i			0.663960i
$924$		0			0
$925$	−6.27302e46			−0.218378
$926$	7.28710e46	+	1.20045e47i	0.249333	+	0.410742i
$927$		0			0
$928$	−1.61083e47	−	7.07273e46i	−0.532455	−	0.233786i
$929$	−1.68290e47			−0.546772			−0.273386	−	0.961904i	$-0.588144\pi$
$929$	−1.68290e47			−0.546772			−0.273386	+	0.961904i	$0.588144\pi$
$930$		0			0
$931$		−	2.01748e47i		−	0.633307i
$932$	−1.40104e47	+	2.69344e47i	−0.432311	+	0.831099i
$933$		0			0
$934$	−9.43761e46	−	1.55472e47i	−0.281392	−	0.463555i
$935$		−	9.90987e47i		−	2.90457i
$936$		0			0
$937$	9.90873e46			0.280663			0.140331	−	0.990105i	$-0.455183\pi$
$937$	9.90873e46			0.280663			0.140331	+	0.990105i	$0.455183\pi$
$938$	−1.16859e46	+	7.09371e45i	−0.0325400	+	0.0197528i
$939$		0			0
$940$	7.15213e47	+	3.72031e47i	1.92482	+	1.00123i
$941$	−1.96858e47			−0.520858			−0.260429	−	0.965493i	$-0.583864\pi$
$941$	−1.96858e47			−0.520858			−0.260429	+	0.965493i	$0.583864\pi$
$942$		0			0
$943$		−	1.43307e46i		−	0.0366507i
$944$	1.43270e47	−	1.00453e47i	0.360249	−	0.252587i
$945$		0			0
$946$	−6.08434e47	+	3.69338e47i	−1.47896	+	0.897771i
$947$		−	3.79998e47i		−	0.908200i	−0.890951	−	0.454100i	$-0.849961\pi$
$947$		−	3.79998e47i		−	0.908200i	0.890951	−	0.454100i	$-0.150039\pi$
$948$		0			0
$949$	−2.62670e47			−0.606947
$950$	−1.49490e47	−	2.46265e47i	−0.339653	−	0.559533i
$951$		0			0
$952$	−5.19219e46	+	3.42773e45i	−0.114067	+	0.00753036i
$953$	−7.54445e47			−1.62982			−0.814912	−	0.579584i	$-0.803215\pi$
$953$	−7.54445e47			−1.62982			−0.814912	+	0.579584i	$0.803215\pi$
$954$		0			0
$955$		−	6.47154e47i		−	1.35193i
$956$	4.84090e46	+	2.51808e46i	0.0994489	+	0.0517301i
$957$		0			0
$958$	3.32414e47	+	5.47607e47i	0.660436	+	1.08798i
$959$			3.98605e46i			0.0778834i
$960$		0			0
$961$	−1.29031e48			−2.43848
$962$	1.04171e47	−	6.32347e46i	0.193617	−	0.117531i
$963$		0			0
$964$	9.00999e46	−	1.73213e47i	0.161991	−	0.311422i
$965$	−2.17765e46			−0.0385080
$966$		0			0
$967$		−	8.33368e47i		−	1.42565i	−0.701342	−	0.712825i	$-0.747415\pi$
$967$		−	8.33368e47i		−	1.42565i	0.701342	−	0.712825i	$-0.252585\pi$
$968$	5.05485e46	+	7.65687e47i	0.0850555	+	1.28838i
$969$		0			0
$970$	1.28560e48	−	7.80399e47i	2.09295	−	1.27048i
$971$		−	8.37495e47i		−	1.34114i	−0.741846	−	0.670571i	$-0.766049\pi$
$971$		−	8.37495e47i		−	1.34114i	0.741846	−	0.670571i	$-0.233951\pi$
$972$		0			0
$973$	−3.83952e46			−0.0594937
$974$	1.62831e47	+	2.68243e47i	0.248196	+	0.408869i
$975$		0			0
$976$	−3.22174e47	−	4.59496e47i	−0.475218	−	0.677774i
$977$	7.41388e45			0.0107580			0.00537901	−	0.999986i	$-0.498288\pi$
$977$	7.41388e45			0.0107580			0.00537901	+	0.999986i	$0.498288\pi$
$978$		0			0
$979$		−	7.19485e47i		−	1.01041i
$980$	4.72018e47	−	9.07435e47i	0.652141	−	1.25371i
$981$		0			0
$982$	−1.42127e47	−	2.34136e47i	−0.190061	−	0.313100i
$983$		−	5.93909e47i		−	0.781382i	−0.920522	−	0.390691i	$-0.872236\pi$
$983$		−	5.93909e47i		−	0.781382i	0.920522	−	0.390691i	$-0.127764\pi$
$984$		0			0
$985$	−2.09093e48			−2.66294
$986$	−5.34803e47	+	3.24642e47i	−0.670137	+	0.406793i
$987$		0			0
$988$	4.96492e47	+	2.58259e47i	0.602284	+	0.313288i
$989$	1.23807e47			0.147776
$990$		0			0
$991$			5.19983e47i			0.600911i	0.953796	+	0.300456i	$0.0971388\pi$
$991$			5.19983e47i			0.600911i	−0.953796	+	0.300456i	$0.902861\pi$
$992$	6.55579e47	−	1.49310e48i	0.745484	−	1.69786i
$993$		0			0
$994$	4.10710e46	−	2.49313e46i	0.0452224	−	0.0274513i
$995$		−	3.49223e47i		−	0.378385i
$996$		0			0
$997$	1.07840e48			1.13150			0.565752	−	0.824575i	$-0.308586\pi$
$997$	1.07840e48			1.13150			0.565752	+	0.824575i	$0.308586\pi$
$998$	−7.43436e47	−	1.22471e48i	−0.767636	−	1.26458i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	36.33.d.b.19.11		14
3.2	odd	2		4.33.b.b.3.4	yes	14
4.3	odd	2	inner	36.33.d.b.19.12		14
12.11	even	2		4.33.b.b.3.3	✓	14

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4.33.b.b.3.3	✓	14	12.11	even	2
4.33.b.b.3.4	yes	14	3.2	odd	2
36.33.d.b.19.11		14	1.1	even	1	trivial
36.33.d.b.19.12		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)

\(f(q)\)	\(=\)	\(q+(56022.2 - 34007.1i) q^{2} +(1.98200e9 - 3.81031e9i) q^{4} +2.17196e11 q^{5} +2.81808e12i q^{7} +(-1.85418e13 - 2.80864e14i) q^{8} +O(q^{10})\)	\(q+(56022.2 - 34007.1i) q^{2} +(1.98200e9 - 3.81031e9i) q^{4} +2.17196e11 q^{5} +2.81808e12i q^{7} +(-1.85418e13 - 2.80864e14i) q^{8} +(1.21678e16 - 7.38622e15i) q^{10} +6.95526e16i q^{11} -7.08184e17 q^{13} +(9.58347e16 + 1.57875e17i) q^{14} +(-1.05901e19 - 1.51040e19i) q^{16} -6.55998e19 q^{17} -1.83995e20i q^{19} +(4.30482e20 - 8.27584e20i) q^{20} +(2.36528e21 + 3.89649e21i) q^{22} -7.92873e20i q^{23} +2.38911e22 q^{25} +(-3.96740e22 + 2.40833e22i) q^{26} +(1.07377e22 + 5.58542e21i) q^{28} +1.45523e23 q^{29} +1.34887e24i q^{31} +(-1.10693e24 - 4.86021e23i) q^{32} +(-3.67504e24 + 2.23086e24i) q^{34} +6.12075e23i q^{35} -2.62567e24 q^{37} +(-6.25715e24 - 1.03078e25i) q^{38} +(-4.02721e24 - 6.10025e25i) q^{40} +1.80745e25 q^{41} +1.56149e26i q^{43} +(2.65017e26 + 1.37853e26i) q^{44} +(-2.69633e25 - 4.44185e25i) q^{46} +8.64218e26i q^{47} +1.09649e27 q^{49} +(1.33843e27 - 8.12470e26i) q^{50} +(-1.40362e27 + 2.69840e27i) q^{52} -5.50243e27 q^{53} +1.51066e28i q^{55} +(7.91495e26 - 5.22522e25i) q^{56} +(8.15252e27 - 4.94882e27i) q^{58} +9.48554e27i q^{59} +3.04221e28 q^{61} +(4.58712e28 + 7.55666e28i) q^{62} +(-7.85406e28 + 1.04154e28i) q^{64} -1.53815e29 q^{65} +7.40203e28i q^{67} +(-1.30019e29 + 2.49955e29i) q^{68} +(2.08149e28 + 3.42898e28i) q^{70} -2.60149e29i q^{71} +3.70906e29 q^{73} +(-1.47095e29 + 8.92914e28i) q^{74} +(-7.01078e29 - 3.64678e29i) q^{76} -1.96004e29 q^{77} -2.10671e30i q^{79} +(-2.30013e30 - 3.28054e30i) q^{80} +(1.01257e30 - 6.14660e29i) q^{82} +6.24724e30i q^{83} -1.42480e31 q^{85} +(5.31019e30 + 8.74783e30i) q^{86} +(1.95348e31 - 1.28963e30i) q^{88} -1.03445e31 q^{89} -1.99572e30i q^{91} +(-3.02109e30 - 1.57147e30i) q^{92} +(2.93896e31 + 4.84153e31i) q^{94} -3.99630e31i q^{95} +1.05656e32 q^{97} +(6.14275e31 - 3.72883e31i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 14 q + 23780 q^{2} - 2922848368 q^{4} - 138121491740 q^{5} + 191366550113600 q^{8}+O(q^{10}) \) 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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