LMFDB - Embedded newform 36.33.d.b.19.2

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			19.2
Root			$7.49079e9 - 1.45317e12i$ of defining polynomial
Character	$\chi$	$=$	36.19
Dual form			36.33.d.b.19.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-60712.0 + 24678.5i) q^{2} +(3.07691e9 - 2.99655e9i) q^{4} -2.49571e11 q^{5} +4.65014e13i q^{7} +(-1.12855e14 + 2.57860e14i) q^{8} +O(q^{10})$	\(q+(-60712.0 + 24678.5i) q^{2} +(3.07691e9 - 2.99655e9i) q^{4} -2.49571e11 q^{5} +4.65014e13i q^{7} +(-1.12855e14 + 2.57860e14i) q^{8} +(1.51520e16 - 6.15903e15i) q^{10} +4.19273e16i q^{11} -6.87705e17 q^{13} +(-1.14758e18 - 2.82319e18i) q^{14} +(4.88063e17 - 1.84403e19i) q^{16} -4.91747e19 q^{17} +3.14168e20i q^{19} +(-7.67909e20 + 7.47854e20i) q^{20} +(-1.03470e21 - 2.54549e21i) q^{22} -4.04400e21i q^{23} +3.90027e22 q^{25} +(4.17519e22 - 1.69715e22i) q^{26} +(1.39344e23 + 1.43081e23i) q^{28} -1.16515e23 q^{29} -3.53780e23i q^{31} +(4.25447e23 + 1.13159e24i) q^{32} +(2.98549e24 - 1.21356e24i) q^{34} -1.16054e25i q^{35} -7.58489e24 q^{37} +(-7.75318e24 - 1.90737e25i) q^{38} +(2.81654e25 - 6.43545e25i) q^{40} +2.78643e25 q^{41} -1.82822e26i q^{43} +(1.25637e26 + 1.29007e26i) q^{44} +(9.97996e25 + 2.45519e26i) q^{46} -6.77015e25i q^{47} -1.05795e27 q^{49} +(-2.36793e27 + 9.62526e26i) q^{50} +(-2.11601e27 + 2.06075e27i) q^{52} -1.13783e27 q^{53} -1.04638e28i q^{55} +(-1.19909e28 - 5.24792e27i) q^{56} +(7.07388e27 - 2.87542e27i) q^{58} +5.33270e27i q^{59} -5.47348e28 q^{61} +(8.73075e27 + 2.14787e28i) q^{62} +(-5.37556e28 - 5.82017e28i) q^{64} +1.71631e29 q^{65} -6.20754e28i q^{67} +(-1.51306e29 + 1.47355e29i) q^{68} +(2.86403e29 + 7.04587e29i) q^{70} +4.47902e29i q^{71} +5.03491e29 q^{73} +(4.60494e29 - 1.87183e29i) q^{74} +(9.41421e29 + 9.66668e29i) q^{76} -1.94968e30 q^{77} -1.79837e30i q^{79} +(-1.21806e29 + 4.60216e30i) q^{80} +(-1.69170e30 + 6.87649e29i) q^{82} -2.17738e30i q^{83} +1.22726e31 q^{85} +(4.51175e30 + 1.10995e31i) q^{86} +(-1.08114e31 - 4.73171e30i) q^{88} -1.19112e31 q^{89} -3.19792e31i q^{91} +(-1.21181e31 - 1.24430e31i) q^{92} +(1.67077e30 + 4.11029e30i) q^{94} -7.84072e31i q^{95} -9.02666e31 q^{97} +(6.42303e31 - 2.61086e31i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−60712.0	+	24678.5i	−0.926391	+	0.376563i
$2$	−60712.0	+	24678.5i	−0.926391	+	0.376563i
$3$		0			0
$3$		0			0
$4$	3.07691e9	−	2.99655e9i	0.716400	−	0.697690i
$5$	−2.49571e11			−1.63559			−0.817795	−	0.575510i	$-0.804804\pi$
$5$	−2.49571e11			−1.63559			−0.817795	+	0.575510i	$0.804804\pi$
$6$		0			0
$7$			4.65014e13i			1.39926i	0.714507	+	0.699628i	$0.246651\pi$
$7$			4.65014e13i			1.39926i	−0.714507	+	0.699628i	$0.753349\pi$
$8$	−1.12855e14	+	2.57860e14i	−0.400942	+	0.916103i
$9$		0			0
$10$	1.51520e16	−	6.15903e15i	1.51520	−	0.615903i
$11$			4.19273e16i			0.912461i	0.889862	+	0.456230i	$0.150801\pi$
$11$			4.19273e16i			0.912461i	−0.889862	+	0.456230i	$0.849199\pi$
$12$		0			0
$13$	−6.87705e17			−1.03350			−0.516748	−	0.856138i	$-0.672857\pi$
$13$	−6.87705e17			−1.03350			−0.516748	+	0.856138i	$0.672857\pi$
$14$	−1.14758e18	−	2.82319e18i	−0.526909	−	1.29626i
$15$		0			0
$16$	4.88063e17	−	1.84403e19i	0.0264580	−	0.999650i
$17$	−4.91747e19			−1.01055			−0.505277	−	0.862957i	$-0.668610\pi$
$17$	−4.91747e19			−1.01055			−0.505277	+	0.862957i	$0.668610\pi$
$18$		0			0
$19$			3.14168e20i			1.08919i	0.838699	+	0.544596i	$0.183317\pi$
$19$			3.14168e20i			1.08919i	−0.838699	+	0.544596i	$0.816683\pi$
$20$	−7.67909e20	+	7.47854e20i	−1.17174	+	1.14113i
$21$		0			0
$22$	−1.03470e21	−	2.54549e21i	−0.343599	−	0.845295i
$23$		−	4.04400e21i		−	0.659425i	−0.944081	−	0.329713i	$-0.893048\pi$
$23$		−	4.04400e21i		−	0.659425i	0.944081	−	0.329713i	$-0.106952\pi$
$24$		0			0
$25$	3.90027e22			1.67515
$26$	4.17519e22	−	1.69715e22i	0.957420	−	0.389176i
$27$		0			0
$28$	1.39344e23	+	1.43081e23i	0.976247	+	1.00243i
$29$	−1.16515e23			−0.465603			−0.232801	−	0.972524i	$-0.574789\pi$
$29$	−1.16515e23			−0.465603			−0.232801	+	0.972524i	$0.574789\pi$
$30$		0			0
$31$		−	3.53780e23i		−	0.486347i	−0.969983	−	0.243174i	$-0.921812\pi$
$31$		−	3.53780e23i		−	0.486347i	0.969983	−	0.243174i	$-0.0781885\pi$
$32$	4.25447e23	+	1.13159e24i	0.351921	+	0.936030i
$33$		0			0
$34$	2.98549e24	−	1.21356e24i	0.936167	−	0.380537i
$35$		−	1.16054e25i		−	2.28861i
$36$		0			0
$37$	−7.58489e24			−0.614783			−0.307392	−	0.951583i	$-0.599456\pi$
$37$	−7.58489e24			−0.614783			−0.307392	+	0.951583i	$0.599456\pi$
$38$	−7.75318e24	−	1.90737e25i	−0.410150	−	1.00902i
$39$		0			0
$40$	2.81654e25	−	6.43545e25i	0.655776	−	1.49837i
$41$	2.78643e25			0.437026			0.218513	−	0.975834i	$-0.429879\pi$
$41$	2.78643e25			0.437026			0.218513	+	0.975834i	$0.429879\pi$
$42$		0			0
$43$		−	1.82822e26i		−	1.33823i	−0.743157	−	0.669117i	$-0.766672\pi$
$43$		−	1.82822e26i		−	1.33823i	0.743157	−	0.669117i	$-0.233328\pi$
$44$	1.25637e26	+	1.29007e26i	0.636614	+	0.653687i
$45$		0			0
$46$	9.97996e25	+	2.45519e26i	0.248315	+	0.610885i
$47$		−	6.77015e25i		−	0.119408i	−0.998216	−	0.0597039i	$-0.980984\pi$
$47$		−	6.77015e25i		−	0.119408i	0.998216	−	0.0597039i	$-0.0190157\pi$
$48$		0			0
$49$	−1.05795e27			−0.957918
$50$	−2.36793e27	+	9.62526e26i	−1.55185	+	0.630801i
$51$		0			0
$52$	−2.11601e27	+	2.06075e27i	−0.740396	+	0.721059i
$53$	−1.13783e27			−0.293537			−0.146769	−	0.989171i	$-0.546887\pi$
$53$	−1.13783e27			−0.293537			−0.146769	+	0.989171i	$0.546887\pi$
$54$		0			0
$55$		−	1.04638e28i		−	1.49241i
$56$	−1.19909e28	−	5.24792e27i	−1.28186	−	0.561021i
$57$		0			0
$58$	7.07388e27	−	2.87542e27i	0.431330	−	0.175329i
$59$			5.33270e27i			0.247352i	0.992323	+	0.123676i	$0.0394683\pi$
$59$			5.33270e27i			0.247352i	−0.992323	+	0.123676i	$0.960532\pi$
$60$		0			0
$61$	−5.47348e28			−1.48931			−0.744657	−	0.667448i	$-0.767387\pi$
$61$	−5.47348e28			−1.48931			−0.744657	+	0.667448i	$0.767387\pi$
$62$	8.73075e27	+	2.14787e28i	0.183141	+	0.450548i
$63$		0			0
$64$	−5.37556e28	−	5.82017e28i	−0.678491	−	0.734609i
$65$	1.71631e29			1.69037
$66$		0			0
$67$		−	6.20754e28i		−	0.376464i	−0.982125	−	0.188232i	$-0.939724\pi$
$67$		−	6.20754e28i		−	0.376464i	0.982125	−	0.188232i	$-0.0602756\pi$
$68$	−1.51306e29	+	1.47355e29i	−0.723960	+	0.705053i
$69$		0			0
$70$	2.86403e29	+	7.04587e29i	0.861806	+	2.12015i
$71$			4.47902e29i			1.07411i	0.843546	+	0.537056i	$0.180464\pi$
$71$			4.47902e29i			1.07411i	−0.843546	+	0.537056i	$0.819536\pi$
$72$		0			0
$73$	5.03491e29			0.774151			0.387076	−	0.922048i	$-0.373485\pi$
$73$	5.03491e29			0.774151			0.387076	+	0.922048i	$0.373485\pi$
$74$	4.60494e29	−	1.87183e29i	0.569529	−	0.231505i
$75$		0			0
$76$	9.41421e29	+	9.66668e29i	0.759918	+	0.780297i
$77$	−1.94968e30			−1.27677
$78$		0			0
$79$		−	1.79837e30i		−	0.781349i	−0.920529	−	0.390674i	$-0.872242\pi$
$79$		−	1.79837e30i		−	0.781349i	0.920529	−	0.390674i	$-0.127758\pi$
$80$	−1.21806e29	+	4.60216e30i	−0.0432743	+	1.63502i
$81$		0			0
$82$	−1.69170e30	+	6.87649e29i	−0.404857	+	0.164568i
$83$		−	2.17738e30i		−	0.429224i	−0.976699	−	0.214612i	$-0.931151\pi$
$83$		−	2.17738e30i		−	0.429224i	0.976699	−	0.214612i	$-0.0688487\pi$
$84$		0			0
$85$	1.22726e31			1.65285
$86$	4.51175e30	+	1.10995e31i	0.503930	+	1.23973i
$87$		0			0
$88$	−1.08114e31	−	4.73171e30i	−0.835908	−	0.365844i
$89$	−1.19112e31			−0.768627			−0.384314	−	0.923203i	$-0.625562\pi$
$89$	−1.19112e31			−0.768627			−0.384314	+	0.923203i	$0.625562\pi$
$90$		0			0
$91$		−	3.19792e31i		−	1.44612i
$92$	−1.21181e31	−	1.24430e31i	−0.460074	−	0.472412i
$93$		0			0
$94$	1.67077e30	+	4.11029e30i	0.0449646	+	0.110618i
$95$		−	7.84072e31i		−	1.78147i
$96$		0			0
$97$	−9.02666e31			−1.46953			−0.734767	−	0.678320i	$-0.762708\pi$
$97$	−9.02666e31			−1.46953			−0.734767	+	0.678320i	$0.762708\pi$
$98$	6.42303e31	−	2.61086e31i	0.887406	−	0.360717i
$99$		0			0
$100$	1.20008e32	−	1.16874e32i	1.20008	−	1.16874i
$101$	−2.25353e32			−1.92186			−0.960929	−	0.276794i	$-0.910728\pi$
$101$	−2.25353e32			−1.92186			−0.960929	+	0.276794i	$0.910728\pi$
$102$		0			0
$103$		−	1.26169e32i		−	0.786242i	−0.919487	−	0.393121i	$-0.871395\pi$
$103$		−	1.26169e32i		−	0.786242i	0.919487	−	0.393121i	$-0.128605\pi$
$104$	7.76110e31	−	1.77332e32i	0.414372	−	0.946788i
$105$		0			0
$106$	6.90799e31	−	2.80799e31i	0.271930	−	0.110535i
$107$			4.06321e32i			1.37635i	0.725545	+	0.688175i	$0.241588\pi$
$107$			4.06321e32i			1.37635i	−0.725545	+	0.688175i	$0.758412\pi$
$108$		0			0
$109$	−5.20609e32			−1.31126			−0.655629	−	0.755083i	$-0.727596\pi$
$109$	−5.20609e32			−1.31126			−0.655629	+	0.755083i	$0.727596\pi$
$110$	2.58232e32	+	6.35281e32i	0.561987	+	1.38256i
$111$		0			0
$112$	8.57499e32	+	2.26956e31i	1.39877	+	0.0370215i
$113$	−4.51919e32			−0.639448			−0.319724	−	0.947511i	$-0.603590\pi$
$113$	−4.51919e32			−0.639448			−0.319724	+	0.947511i	$0.603590\pi$
$114$		0			0
$115$			1.00927e33i			1.07855i
$116$	−3.58508e32	+	3.49145e32i	−0.333558	+	0.324846i
$117$		0			0
$118$	−1.31603e32	−	3.23759e32i	−0.0931436	−	0.229144i
$119$		−	2.28669e33i		−	1.41402i
$120$		0			0
$121$	3.53478e32			0.167416
$122$	3.32306e33	−	1.35077e33i	1.37969	−	0.560821i
$123$		0			0
$124$	−1.06012e33	−	1.08855e33i	−0.339320	−	0.348419i
$125$	−3.92316e33			−1.10427
$126$		0			0
$127$		−	5.08881e33i		−	1.11111i	−0.831480	−	0.555555i	$-0.812506\pi$
$127$		−	5.08881e33i		−	1.11111i	0.831480	−	0.555555i	$-0.187494\pi$
$128$	4.69994e33	+	2.20693e33i	0.905175	+	0.425040i
$129$		0			0
$130$	−1.04201e34	+	4.23560e33i	−1.56595	+	0.636533i
$131$		−	7.19059e33i		−	0.955925i	−0.878380	−	0.477962i	$-0.841376\pi$
$131$		−	7.19059e33i		−	0.955925i	0.878380	−	0.477962i	$-0.158624\pi$
$132$		0			0
$133$	−1.46092e34			−1.52406
$134$	1.53193e33	+	3.76872e33i	0.141762	+	0.348752i
$135$		0			0
$136$	5.54962e33	−	1.26802e34i	0.405173	−	0.925771i
$137$	2.68810e33			0.174548			0.0872741	−	0.996184i	$-0.472184\pi$
$137$	2.68810e33			0.174548			0.0872741	+	0.996184i	$0.472184\pi$
$138$		0			0
$139$		−	3.58167e34i		−	1.84437i	−0.386744	−	0.922187i	$-0.626400\pi$
$139$		−	3.58167e34i		−	1.84437i	0.386744	−	0.922187i	$-0.373600\pi$
$140$	−3.47762e34	−	3.57088e34i	−1.59674	−	1.63956i
$141$		0			0
$142$	−1.10535e34	−	2.71930e34i	−0.404471	−	0.995048i
$143$		−	2.88336e34i		−	0.943024i
$144$		0			0
$145$	2.90789e34			0.761535
$146$	−3.05679e34	+	1.24254e34i	−0.717167	+	0.291517i
$147$		0			0
$148$	−2.33381e34	+	2.27285e34i	−0.440431	+	0.428928i
$149$	8.57097e34			1.45228			0.726139	−	0.687548i	$-0.241313\pi$
$149$	8.57097e34			1.45228			0.726139	+	0.687548i	$0.241313\pi$
$150$		0			0
$151$			7.17265e34i			0.981857i	0.871200	+	0.490929i	$0.163342\pi$
$151$			7.17265e34i			0.981857i	−0.871200	+	0.490929i	$0.836658\pi$
$152$	−8.10114e34	−	3.54555e34i	−0.997812	−	0.436702i
$153$		0			0
$154$	1.18369e35	−	4.81151e34i	1.18278	−	0.480783i
$155$			8.82933e34i			0.795464i
$156$		0			0
$157$	−1.95517e33			−0.0143480			−0.00717399	−	0.999974i	$-0.502284\pi$
$157$	−1.95517e33			−0.0143480			−0.00717399	+	0.999974i	$0.502284\pi$
$158$	4.43809e34	+	1.09182e35i	0.294227	+	0.723835i
$159$		0			0
$160$	−1.06179e35	−	2.82412e35i	−0.575599	−	1.53096i
$161$	1.88052e35			0.922705
$162$		0			0
$163$		−	8.07068e34i		−	0.325019i	−0.986707	−	0.162509i	$-0.948041\pi$
$163$		−	8.07068e34i		−	0.325019i	0.986707	−	0.162509i	$-0.0519588\pi$
$164$	8.57362e34	−	8.34970e34i	0.313085	−	0.304908i
$165$		0			0
$166$	5.37343e34	+	1.32193e35i	0.161630	+	0.397629i
$167$		−	6.85162e33i		−	0.0187210i	−0.999956	−	0.00936052i	$-0.997020\pi$
$167$		−	6.85162e33i		−	0.0187210i	0.999956	−	0.00936052i	$-0.00297959\pi$
$168$		0			0
$169$	3.01587e34			0.0681123
$170$	−7.45093e35	+	3.02869e35i	−1.53119	+	0.622403i
$171$		0			0
$172$	−5.47835e35	−	5.62526e35i	−0.933672	−	0.958711i
$173$	−9.99732e35			−1.55291			−0.776454	−	0.630174i	$-0.782984\pi$
$173$	−9.99732e35			−1.55291			−0.776454	+	0.630174i	$0.782984\pi$
$174$		0			0
$175$			1.81368e36i			2.34397i
$176$	7.73152e35	+	2.04632e34i	0.912141	+	0.0241418i
$177$		0			0
$178$	7.23153e35	−	2.93950e35i	0.712049	−	0.289437i
$179$		−	4.70514e35i		−	0.423569i	−0.977316	−	0.211785i	$-0.932072\pi$
$179$		−	4.70514e35i		−	0.423569i	0.977316	−	0.211785i	$-0.0679275\pi$
$180$		0			0
$181$	−7.45049e35			−0.561471			−0.280736	−	0.959785i	$-0.590578\pi$
$181$	−7.45049e35			−0.561471			−0.280736	+	0.959785i	$0.590578\pi$
$182$	7.89198e35	+	1.94152e36i	0.544558	+	1.33968i
$183$		0			0
$184$	1.04279e36	+	4.56386e35i	0.604102	+	0.264391i
$185$	1.89297e36			1.00553
$186$		0			0
$187$		−	2.06176e36i		−	0.922090i
$188$	−2.02871e35	−	2.08312e35i	−0.0833096	−	0.0855438i
$189$		0			0
$190$	1.93497e36	+	4.76026e36i	0.670836	+	1.65034i
$191$		−	3.68249e36i		−	1.17384i	−0.809646	−	0.586919i	$-0.800341\pi$
$191$		−	3.68249e36i		−	1.17384i	0.809646	−	0.586919i	$-0.199659\pi$
$192$		0			0
$193$	8.17250e35			0.220515			0.110258	−	0.993903i	$-0.464832\pi$
$193$	8.17250e35			0.220515			0.110258	+	0.993903i	$0.464832\pi$
$194$	5.48026e36	−	2.22764e36i	1.36136	−	0.553372i
$195$		0			0
$196$	−3.25523e36	+	3.17021e36i	−0.686252	+	0.668330i
$197$	3.31320e36			0.643855			0.321928	−	0.946764i	$-0.395669\pi$
$197$	3.31320e36			0.643855			0.321928	+	0.946764i	$0.395669\pi$
$198$		0			0
$199$			6.72031e36i			1.11107i	0.831495	+	0.555533i	$0.187486\pi$
$199$			6.72031e36i			1.11107i	−0.831495	+	0.555533i	$0.812514\pi$
$200$	−4.40165e36	+	1.00572e37i	−0.671639	+	1.53461i
$201$		0			0
$202$	1.36816e37	−	5.56137e36i	1.78039	−	0.723702i
$203$		−	5.41813e36i		−	0.651498i
$204$		0			0
$205$	−6.95414e36			−0.714795
$206$	3.11365e36	+	7.65995e36i	0.296070	+	0.728367i
$207$		0			0
$208$	−3.35643e35	+	1.26815e37i	−0.0273442	+	1.03313i
$209$	−1.31722e37			−0.993844
$210$		0			0
$211$			2.52226e37i			1.63407i	0.576586	+	0.817036i	$0.304385\pi$
$211$			2.52226e37i			1.63407i	−0.576586	+	0.817036i	$0.695615\pi$
$212$	−3.50100e36	+	3.40957e36i	−0.210290	+	0.204798i
$213$		0			0
$214$	−1.00274e37	−	2.46685e37i	−0.518283	−	1.27504i
$215$			4.56270e37i			2.18880i
$216$		0			0
$217$	1.64513e37			0.680524
$218$	3.16072e37	−	1.28478e37i	1.21474	−	0.493771i
$219$		0			0
$220$	−3.13555e37	−	3.21964e37i	−1.04124	−	1.06916i
$221$	3.38177e37			1.04440
$222$		0			0
$223$		−	3.57438e37i		−	0.955703i	−0.878441	−	0.477851i	$-0.841416\pi$
$223$		−	3.57438e37i		−	0.955703i	0.878441	−	0.477851i	$-0.158584\pi$
$224$	−5.26205e37	+	1.97839e37i	−1.30975	+	0.492428i
$225$		0			0
$226$	2.74369e37	−	1.11527e37i	0.592379	−	0.240793i
$227$		−	2.14630e37i		−	0.431794i	−0.976416	−	0.215897i	$-0.930733\pi$
$227$		−	2.14630e37i		−	0.431794i	0.976416	−	0.215897i	$-0.0692675\pi$
$228$		0			0
$229$	6.83961e37			1.19581			0.597907	−	0.801565i	$-0.295999\pi$
$229$	6.83961e37			1.19581			0.597907	+	0.801565i	$0.295999\pi$
$230$	−2.49071e37	−	6.12745e37i	−0.406142	−	0.999158i
$231$		0			0
$232$	1.31494e37	−	3.00447e37i	0.186680	−	0.426540i
$233$	5.97446e37			0.791778			0.395889	−	0.918298i	$-0.370436\pi$
$233$	5.97446e37			0.791778			0.395889	+	0.918298i	$0.370436\pi$
$234$		0			0
$235$			1.68964e37i			0.195302i
$236$	1.59797e37	+	1.64083e37i	0.172575	+	0.177203i
$237$		0			0
$238$	5.64321e37	+	1.38830e38i	0.532469	+	1.30994i
$239$			1.48844e38i			1.31330i	0.754195	+	0.656651i	$0.228027\pi$
$239$			1.48844e38i			1.31330i	−0.754195	+	0.656651i	$0.771973\pi$
$240$		0			0
$241$	−1.20182e38			−0.928040			−0.464020	−	0.885825i	$-0.653593\pi$
$241$	−1.20182e38			−0.928040			−0.464020	+	0.885825i	$0.653593\pi$
$242$	−2.14603e37	+	8.72329e36i	−0.155092	+	0.0630427i
$243$		0			0
$244$	−1.68414e38	+	1.64016e38i	−1.06694	+	1.03908i
$245$	2.64034e38			1.56676
$246$		0			0
$247$		−	2.16055e38i		−	1.12567i
$248$	9.12258e37	+	3.99259e37i	0.445544	+	0.194997i
$249$		0			0
$250$	2.38183e38	−	9.68176e37i	1.02299	−	0.415829i
$251$		−	2.24908e38i		−	0.906201i	−0.891459	−	0.453100i	$-0.850318\pi$
$251$		−	2.24908e38i		−	0.906201i	0.891459	−	0.453100i	$-0.149682\pi$
$252$		0			0
$253$	1.69554e38			0.601699
$254$	1.25584e38	+	3.08952e38i	0.418403	+	1.02932i
$255$		0			0
$256$	−3.39806e38	−	1.80000e37i	−0.998600	−	0.0528974i
$257$	−3.64164e38			−1.00547			−0.502733	−	0.864442i	$-0.667672\pi$
$257$	−3.64164e38			−1.00547			−0.502733	+	0.864442i	$0.667672\pi$
$258$		0			0
$259$		−	3.52708e38i		−	0.860239i
$260$	5.28095e38	−	5.14303e38i	1.21098	−	1.17936i
$261$		0			0
$262$	1.77453e38	+	4.36555e38i	0.359966	+	0.885560i
$263$			6.65323e38i			1.26981i	0.772588	+	0.634907i	$0.218962\pi$
$263$			6.65323e38i			1.26981i	−0.772588	+	0.634907i	$0.781038\pi$
$264$		0			0
$265$	2.83969e38			0.480107
$266$	8.86955e38	−	3.60534e38i	1.41187	−	0.573904i
$267$		0			0
$268$	−1.86012e38	−	1.91001e38i	−0.262655	−	0.269699i
$269$	−4.52066e38			−0.601403			−0.300701	−	0.953718i	$-0.597221\pi$
$269$	−4.52066e38			−0.601403			−0.300701	+	0.953718i	$0.597221\pi$
$270$		0			0
$271$			1.41567e39i			1.67284i	0.548092	+	0.836418i	$0.315354\pi$
$271$			1.41567e39i			1.67284i	−0.548092	+	0.836418i	$0.684646\pi$
$272$	−2.40004e37	+	9.06796e38i	−0.0267372	+	1.01020i
$273$		0			0
$274$	−1.63199e38	+	6.63380e37i	−0.161700	+	0.0657285i
$275$			1.63528e39i			1.52851i
$276$		0			0
$277$	−3.33834e36			−0.00277878			−0.00138939	−	0.999999i	$-0.500442\pi$
$277$	−3.33834e36			−0.00277878			−0.00138939	+	0.999999i	$0.500442\pi$
$278$	8.83902e38	+	2.17450e39i	0.694524	+	1.70861i
$279$		0			0
$280$	2.99257e39	+	1.30973e39i	2.09660	+	0.917599i
$281$	1.77763e39			1.17636			0.588179	−	0.808731i	$-0.299845\pi$
$281$	1.77763e39			1.17636			0.588179	+	0.808731i	$0.299845\pi$
$282$		0			0
$283$			1.97454e39i			1.16650i	0.812294	+	0.583248i	$0.198218\pi$
$283$			1.97454e39i			1.16650i	−0.812294	+	0.583248i	$0.801782\pi$
$284$	1.34216e39	+	1.37816e39i	0.749397	+	0.769494i
$285$		0			0
$286$	7.11569e38	+	1.75055e39i	0.355108	+	0.873608i
$287$			1.29573e39i			0.611511i
$288$		0			0
$289$	5.02422e37			0.0212179
$290$	−1.76544e39	+	7.17622e38i	−0.705479	+	0.286766i
$291$		0			0
$292$	1.54920e39	−	1.50874e39i	0.554602	−	0.540117i
$293$	2.15799e39			0.731422			0.365711	−	0.930729i	$-0.380826\pi$
$293$	2.15799e39			0.731422			0.365711	+	0.930729i	$0.380826\pi$
$294$		0			0
$295$		−	1.33089e39i		−	0.404566i
$296$	8.55994e38	−	1.95584e39i	0.246492	−	0.563205i
$297$		0			0
$298$	−5.20360e39	+	2.11518e39i	−1.34538	+	0.546874i
$299$			2.78108e39i			0.681513i
$300$		0			0
$301$	8.50145e39			1.87253
$302$	−1.77010e39	−	4.35466e39i	−0.369732	−	0.909584i
$303$		0			0
$304$	5.79335e39	+	1.53334e38i	1.08881	+	0.0288178i
$305$	1.36602e40			2.43591
$306$		0			0
$307$			4.21465e39i			0.676936i	0.940978	+	0.338468i	$0.109909\pi$
$307$			4.21465e39i			0.676936i	−0.940978	+	0.338468i	$0.890091\pi$
$308$	−5.99899e39	+	5.84232e39i	−0.914675	+	0.890787i
$309$		0			0
$310$	−2.17894e39	−	5.36046e39i	−0.299543	−	0.736911i
$311$		−	8.06001e38i		−	0.105237i	−0.998615	−	0.0526186i	$-0.983243\pi$
$311$		−	8.06001e38i		−	0.105237i	0.998615	−	0.0526186i	$-0.0167568\pi$
$312$		0			0
$313$	9.82093e38			0.115729			0.0578646	−	0.998324i	$-0.481571\pi$
$313$	9.82093e38			0.115729			0.0578646	+	0.998324i	$0.481571\pi$
$314$	1.18702e38	−	4.82506e37i	0.0132918	−	0.00540292i
$315$		0			0
$316$	−5.38891e39	−	5.53342e39i	−0.545139	−	0.559758i
$317$	−9.87696e39			−0.949894			−0.474947	−	0.880014i	$-0.657533\pi$
$317$	−9.87696e39			−0.949894			−0.474947	+	0.880014i	$0.657533\pi$
$318$		0			0
$319$		−	4.88518e39i		−	0.424844i
$320$	1.34158e40	+	1.45255e40i	1.10973	+	1.20152i
$321$		0			0
$322$	−1.14170e40	+	4.64082e39i	−0.854785	+	0.347457i
$323$		−	1.54491e40i		−	1.10069i
$324$		0			0
$325$	−2.68223e40			−1.73126
$326$	1.99172e39	+	4.89987e39i	0.122390	+	0.301094i
$327$		0			0
$328$	−3.14463e39	+	7.18510e39i	−0.175222	+	0.400361i
$329$	3.14822e39			0.167082
$330$		0			0
$331$			2.26441e40i			1.09071i	0.838207	+	0.545353i	$0.183604\pi$
$331$			2.26441e40i			1.09071i	−0.838207	+	0.545353i	$0.816396\pi$
$332$	−6.52463e39	−	6.69960e39i	−0.299465	−	0.307496i
$333$		0			0
$334$	1.69087e38	+	4.15975e38i	0.00704966	+	0.0173430i
$335$			1.54922e40i			0.615740i
$336$		0			0
$337$	2.83693e40			1.02511			0.512555	−	0.858655i	$-0.328699\pi$
$337$	2.83693e40			1.02511			0.512555	+	0.858655i	$0.328699\pi$
$338$	−1.83099e39	+	7.44270e38i	−0.0630986	+	0.0256486i
$339$		0			0
$340$	3.77617e40	−	3.67755e40i	1.18410	−	1.15318i
$341$	1.48331e40			0.443773
$342$		0			0
$343$			2.16122e39i			0.0588835i
$344$	4.71424e40	+	2.06323e40i	1.22596	+	0.536554i
$345$		0			0
$346$	6.06957e40	−	2.46718e40i	1.43860	−	0.584768i
$347$		−	3.40376e40i		−	0.770349i	−0.922844	−	0.385175i	$-0.874141\pi$
$347$		−	3.40376e40i		−	0.770349i	0.922844	−	0.385175i	$-0.125859\pi$
$348$		0			0
$349$	−5.22160e40			−1.07795			−0.538973	−	0.842323i	$-0.681187\pi$
$349$	−5.22160e40			−1.07795			−0.538973	+	0.842323i	$0.681187\pi$
$350$	−4.47588e40	−	1.10112e41i	−0.882652	−	2.17143i
$351$		0			0
$352$	−4.74445e40	+	1.78378e40i	−0.854090	+	0.321114i
$353$	−8.73532e40			−1.50274			−0.751369	−	0.659882i	$-0.770606\pi$
$353$	−8.73532e40			−1.50274			−0.751369	+	0.659882i	$0.770606\pi$
$354$		0			0
$355$		−	1.11783e41i		−	1.75681i
$356$	−3.66498e40	+	3.56926e40i	−0.550645	+	0.536264i
$357$		0			0
$358$	1.16116e40	+	2.85658e40i	0.159501	+	0.392391i
$359$			1.80854e39i			0.0237584i	0.999929	+	0.0118792i	$0.00378135\pi$
$359$			1.80854e39i			0.0237584i	−0.999929	+	0.0118792i	$0.996219\pi$
$360$		0			0
$361$	−1.55030e40			−0.186337
$362$	4.52334e40	−	1.83867e40i	0.520142	−	0.211430i
$363$		0			0
$364$	−9.58275e40	−	9.83974e40i	−1.00895	−	1.03600i
$365$	−1.25657e41			−1.26619
$366$		0			0
$367$			4.27904e40i			0.395084i	0.980294	+	0.197542i	$0.0632959\pi$
$367$			4.27904e40i			0.395084i	−0.980294	+	0.197542i	$0.936704\pi$
$368$	−7.45725e40	−	1.97373e39i	−0.659194	−	0.0174470i
$369$		0			0
$370$	−1.14926e41	+	4.67156e40i	−0.931516	+	0.378647i
$371$		−	5.29107e40i		−	0.410734i
$372$		0			0
$373$	2.44105e40			0.173875			0.0869373	−	0.996214i	$-0.472292\pi$
$373$	2.44105e40			0.173875			0.0869373	+	0.996214i	$0.472292\pi$
$374$	5.08812e40	+	1.25174e41i	0.347225	+	0.854216i
$375$		0			0
$376$	1.74575e40	+	7.64047e39i	0.109390	+	0.0478756i
$377$	8.01282e40			0.481198
$378$		0			0
$379$		−	1.39770e41i		−	0.771236i	−0.922658	−	0.385618i	$-0.873988\pi$
$379$		−	1.39770e41i		−	0.771236i	0.922658	−	0.385618i	$-0.126012\pi$
$380$	−2.34952e41	−	2.41252e41i	−1.24291	−	1.27624i
$381$		0			0
$382$	9.08782e40	+	2.23571e41i	0.442024	+	1.08743i
$383$		−	4.23797e40i		−	0.197687i	−0.995103	−	0.0988433i	$-0.968486\pi$
$383$		−	4.23797e40i		−	0.197687i	0.995103	−	0.0988433i	$-0.0315143\pi$
$384$		0			0
$385$	4.86583e41			2.08827
$386$	−4.96169e40	+	2.01685e40i	−0.204283	+	0.0830379i
$387$		0			0
$388$	−2.77743e41	+	2.70489e41i	−1.05277	+	1.02528i
$389$	1.85666e41			0.675366			0.337683	−	0.941260i	$-0.390357\pi$
$389$	1.85666e41			0.675366			0.337683	+	0.941260i	$0.390357\pi$
$390$		0			0
$391$			1.98862e41i			0.666384i
$392$	1.19395e41	−	2.72803e41i	0.384070	−	0.877552i
$393$		0			0
$394$	−2.01151e41	+	8.17647e40i	−0.596462	+	0.242452i
$395$			4.48821e41i			1.27797i
$396$		0			0
$397$	−7.51305e40			−0.197319			−0.0986594	−	0.995121i	$-0.531455\pi$
$397$	−7.51305e40			−0.197319			−0.0986594	+	0.995121i	$0.531455\pi$
$398$	−1.65847e41	−	4.08003e41i	−0.418387	−	1.02928i
$399$		0			0
$400$	1.90358e40	−	7.19221e41i	0.0443211	−	1.67457i
$401$	1.59206e41			0.356164			0.178082	−	0.984016i	$-0.443011\pi$
$401$	1.59206e41			0.356164			0.178082	+	0.984016i	$0.443011\pi$
$402$		0			0
$403$			2.43296e41i			0.502638i
$404$	−6.93392e41	+	6.75283e41i	−1.37682	+	1.34086i
$405$		0			0
$406$	1.33711e41	+	3.28945e41i	0.245330	+	0.603541i
$407$		−	3.18014e41i		−	0.560965i
$408$		0			0
$409$	−5.39300e41			−0.879543			−0.439772	−	0.898110i	$-0.644941\pi$
$409$	−5.39300e41			−0.879543			−0.439772	+	0.898110i	$0.644941\pi$
$410$	4.22199e41	−	1.71617e41i	0.662179	−	0.269166i
$411$		0			0
$412$	−3.78071e41	−	3.88210e41i	−0.548553	−	0.563263i
$413$	−2.47978e41			−0.346109
$414$		0			0
$415$			5.43411e41i			0.702035i
$416$	−2.92582e41	−	7.78200e41i	−0.363709	−	0.967382i
$417$		0			0
$418$	7.99711e41	−	3.25070e41i	0.920688	−	0.374245i
$419$		−	2.11602e41i		−	0.234474i	−0.993104	−	0.117237i	$-0.962596\pi$
$419$		−	2.11602e41i		−	0.234474i	0.993104	−	0.117237i	$-0.0374037\pi$
$420$		0			0
$421$	−1.06108e42			−1.08951			−0.544757	−	0.838594i	$-0.683378\pi$
$421$	−1.06108e42			−1.08951			−0.544757	+	0.838594i	$0.683378\pi$
$422$	−6.22456e41	−	1.53132e42i	−0.615332	−	1.51379i
$423$		0			0
$424$	1.28410e41	−	2.93401e41i	0.117691	−	0.268911i
$425$	−1.91795e42			−1.69283
$426$		0			0
$427$		−	2.54524e42i		−	2.08393i
$428$	1.21756e42	+	1.25021e42i	0.960265	+	0.986016i
$429$		0			0
$430$	−1.12600e42	−	2.77010e42i	−0.824222	−	2.02769i
$431$		−	1.51417e42i		−	1.06792i	−0.845510	−	0.533960i	$-0.820703\pi$
$431$		−	1.51417e42i		−	1.06792i	0.845510	−	0.533960i	$-0.179297\pi$
$432$		0			0
$433$	1.62637e42			1.06516			0.532579	−	0.846380i	$-0.321223\pi$
$433$	1.62637e42			1.06516			0.532579	+	0.846380i	$0.321223\pi$
$434$	−9.98789e41	+	4.05992e41i	−0.630432	+	0.256261i
$435$		0			0
$436$	−1.60187e42	+	1.56003e42i	−0.939385	+	0.914851i
$437$	1.27049e42			0.718240
$438$		0			0
$439$			5.61498e41i			0.295064i	0.989057	+	0.147532i	$0.0471329\pi$
$439$			5.61498e41i			0.295064i	−0.989057	+	0.147532i	$0.952867\pi$
$440$	2.69821e42	+	1.18090e42i	1.36720	+	0.598370i
$441$		0			0
$442$	−2.05314e42	+	8.34569e41i	−0.967524	+	0.393284i
$443$		−	3.65040e42i		−	1.65913i	−0.558408	−	0.829566i	$-0.688588\pi$
$443$		−	3.65040e42i		−	1.65913i	0.558408	−	0.829566i	$-0.311412\pi$
$444$		0			0
$445$	2.97269e42			1.25716
$446$	8.82102e41	+	2.17008e42i	0.359883	+	0.885354i
$447$		0			0
$448$	2.70646e42	−	2.49971e42i	1.02791	−	0.949383i
$449$	1.04369e41			0.0382500			0.0191250	−	0.999817i	$-0.493912\pi$
$449$	1.04369e41			0.0382500			0.0191250	+	0.999817i	$0.493912\pi$
$450$		0			0
$451$			1.16828e42i			0.398769i
$452$	−1.39052e42	+	1.35420e42i	−0.458101	+	0.446137i
$453$		0			0
$454$	5.29673e41	+	1.30306e42i	0.162598	+	0.400010i
$455$			7.98109e42i			2.36527i
$456$		0			0
$457$	1.25344e42			0.346293			0.173147	−	0.984896i	$-0.444607\pi$
$457$	1.25344e42			0.346293			0.173147	+	0.984896i	$0.444607\pi$
$458$	−4.15246e42	+	1.68791e42i	−1.10779	+	0.450300i
$459$		0			0
$460$	3.02432e42	+	3.10542e42i	0.752493	+	0.772672i
$461$	5.99142e42			1.43984			0.719921	−	0.694056i	$-0.244178\pi$
$461$	5.99142e42			1.43984			0.719921	+	0.694056i	$0.244178\pi$
$462$		0			0
$463$			5.84792e42i			1.31131i	0.755060	+	0.655656i	$0.227608\pi$
$463$			5.84792e42i			1.31131i	−0.755060	+	0.655656i	$0.772392\pi$
$464$	−5.68669e40	+	2.14858e42i	−0.0123189	+	0.465440i
$465$		0			0
$466$	−3.62721e42	+	1.47440e42i	−0.733496	+	0.298155i
$467$			6.14480e42i			1.20071i	0.799734	+	0.600354i	$0.204974\pi$
$467$			6.14480e42i			1.20071i	−0.799734	+	0.600354i	$0.795026\pi$
$468$		0			0
$469$	2.88659e42			0.526769
$470$	−4.16976e41	−	1.02581e42i	−0.0735437	−	0.180926i
$471$		0			0
$472$	−1.37509e42	−	6.01823e41i	−0.226600	−	0.0991737i
$473$	7.66522e42			1.22109
$474$		0			0
$475$			1.22534e43i			1.82456i
$476$	−6.85220e42	−	7.03596e42i	−0.986549	−	1.01301i
$477$		0			0
$478$	−3.67324e42	−	9.03660e42i	−0.494541	−	1.21663i
$479$		−	3.58791e42i		−	0.467168i	−0.972337	−	0.233584i	$-0.924955\pi$
$479$		−	3.58791e42i		−	0.467168i	0.972337	−	0.233584i	$-0.0750454\pi$
$480$		0			0
$481$	5.21617e42			0.635375
$482$	7.29648e42	−	2.96591e42i	0.859728	−	0.349466i
$483$		0			0
$484$	1.08762e42	−	1.05922e42i	0.119937	−	0.116804i
$485$	2.25279e43			2.40355
$486$		0			0
$487$		−	1.26614e43i		−	1.26479i	−0.774644	−	0.632397i	$-0.782071\pi$
$487$		−	1.26614e43i		−	1.26479i	0.774644	−	0.632397i	$-0.217929\pi$
$488$	6.17710e42	−	1.41139e43i	0.597128	−	1.36437i
$489$		0			0
$490$	−1.60300e43	+	6.51595e42i	−1.45143	+	0.589985i
$491$			1.91062e43i			1.67445i	0.546861	+	0.837224i	$0.315823\pi$
$491$			1.91062e43i			1.67445i	−0.546861	+	0.837224i	$0.684177\pi$
$492$		0			0
$493$	5.72961e42			0.470516
$494$	5.33190e42	+	1.31171e43i	0.423888	+	1.04281i
$495$		0			0
$496$	−6.52381e42	−	1.72667e41i	−0.486177	−	0.0128678i
$497$	−2.08281e43			−1.50296
$498$		0			0
$499$			2.27907e43i			1.54223i	0.636695	+	0.771116i	$0.280301\pi$
$499$			2.27907e43i			1.54223i	−0.636695	+	0.771116i	$0.719699\pi$
$500$	−1.20712e43	+	1.17560e43i	−0.791101	+	0.770440i
$501$		0			0
$502$	5.55037e42	+	1.36546e43i	0.341242	+	0.839496i
$503$		−	1.26686e43i		−	0.754465i	−0.926119	−	0.377233i	$-0.876876\pi$
$503$		−	1.26686e43i		−	0.754465i	0.926119	−	0.377233i	$-0.123124\pi$
$504$		0			0
$505$	5.62416e43			3.14337
$506$	−1.02940e43	+	4.18433e42i	−0.557409	+	0.226578i
$507$		0			0
$508$	−1.52489e43	−	1.56578e43i	−0.775210	−	0.795999i
$509$	3.59379e43			1.77039			0.885193	−	0.465224i	$-0.154026\pi$
$509$	3.59379e43			1.77039			0.885193	+	0.465224i	$0.154026\pi$
$510$		0			0
$511$			2.34130e43i			1.08324i
$512$	2.10745e43	−	7.29307e42i	0.945013	−	0.327033i
$513$		0			0
$514$	2.21091e43	−	8.98702e42i	0.931455	−	0.378622i
$515$			3.14881e43i			1.28597i
$516$		0			0
$517$	2.83854e42			0.108955
$518$	8.70429e42	+	2.14136e43i	0.323935	+	0.796918i
$519$		0			0
$520$	−1.93695e43	+	4.42569e43i	−0.677742	+	1.54856i
$521$	−5.25643e43			−1.78356			−0.891778	−	0.452473i	$-0.850542\pi$
$521$	−5.25643e43			−1.78356			−0.891778	+	0.452473i	$0.850542\pi$
$522$		0			0
$523$		−	4.65945e43i		−	1.48699i	−0.668743	−	0.743494i	$-0.733167\pi$
$523$		−	4.65945e43i		−	1.48699i	0.668743	−	0.743494i	$-0.266833\pi$
$524$	−2.15470e43	−	2.21248e43i	−0.666939	−	0.684825i
$525$		0			0
$526$	−1.64191e43	−	4.03930e43i	−0.478166	−	1.17634i
$527$			1.73970e43i			0.491480i
$528$		0			0
$529$	2.12550e43			0.565158
$530$	−1.72403e43	+	7.00793e42i	−0.444766	+	0.180791i
$531$		0			0
$532$	−4.49514e43	+	4.37774e43i	−1.09183	+	1.06332i
$533$	−1.91624e43			−0.451664
$534$		0			0
$535$		−	1.01406e44i		−	2.25114i
$536$	1.60068e43	+	7.00553e42i	0.344880	+	0.150940i
$537$		0			0
$538$	2.74458e43	−	1.11563e43i	0.557134	−	0.226466i
$539$		−	4.43570e43i		−	0.874062i
$540$		0			0
$541$	−6.40627e43			−1.18973			−0.594865	−	0.803825i	$-0.702795\pi$
$541$	−6.40627e43			−1.18973			−0.594865	+	0.803825i	$0.702795\pi$
$542$	−3.49366e43	−	8.59481e43i	−0.629929	−	1.54970i
$543$		0			0
$544$	−2.09212e43	−	5.56456e43i	−0.355635	−	0.945908i
$545$	1.29929e44			2.14468
$546$		0			0
$547$			1.05284e44i			1.63895i	0.573118	+	0.819473i	$0.305734\pi$
$547$			1.05284e44i			1.63895i	−0.573118	+	0.819473i	$0.694266\pi$
$548$	8.27104e42	−	8.05502e42i	0.125046	−	0.121781i
$549$		0			0
$550$	−4.03561e43	−	9.92809e43i	−0.575581	−	1.41600i
$551$		−	3.66054e43i		−	0.507130i
$552$		0			0
$553$	8.36266e43			1.09331
$554$	2.02677e41	−	8.23852e40i	0.00257424	−	0.00104639i
$555$		0			0
$556$	−1.07327e44	−	1.10205e44i	−1.28680	−	1.32131i
$557$	−6.38377e43			−0.743694			−0.371847	−	0.928294i	$-0.621275\pi$
$557$	−6.38377e43			−0.743694			−0.371847	+	0.928294i	$0.621275\pi$
$558$		0			0
$559$			1.25727e44i			1.38306i
$560$	−2.14007e44	−	5.66417e42i	−2.28781	−	0.0605519i
$561$		0			0
$562$	−1.07923e44	+	4.38691e43i	−1.08977	+	0.442974i
$563$		−	5.33900e43i		−	0.523993i	−0.965069	−	0.261997i	$-0.915619\pi$
$563$		−	5.33900e43i		−	0.523993i	0.965069	−	0.261997i	$-0.0843809\pi$
$564$		0			0
$565$	1.12786e44			1.04587
$566$	−4.87286e43	−	1.19878e44i	−0.439260	−	1.08063i
$567$		0			0
$568$	−1.15496e44	−	5.05481e43i	−0.983998	−	0.430657i
$569$	1.24668e43			0.103267			0.0516333	−	0.998666i	$-0.483557\pi$
$569$	1.24668e43			0.103267			0.0516333	+	0.998666i	$0.483557\pi$
$570$		0			0
$571$			4.73606e43i			0.370885i	0.982655	+	0.185443i	$0.0593719\pi$
$571$			4.73606e43i			0.370885i	−0.982655	+	0.185443i	$0.940628\pi$
$572$	−8.64015e43	−	8.87186e43i	−0.657938	−	0.675582i
$573$		0			0
$574$	−3.19766e43	−	7.86663e43i	−0.230273	−	0.566498i
$575$		−	1.57727e44i		−	1.10464i
$576$		0			0
$577$	1.91505e44			1.26872			0.634361	−	0.773037i	$-0.281263\pi$
$577$	1.91505e44			1.26872			0.634361	+	0.773037i	$0.281263\pi$
$578$	−3.05030e42	+	1.23990e42i	−0.0196561	+	0.00798989i
$579$		0			0
$580$	8.94733e43	−	8.71365e43i	0.545564	−	0.531315i
$581$	1.01251e44			0.600595
$582$		0			0
$583$		−	4.77061e43i		−	0.267841i
$584$	−5.68215e43	+	1.29830e44i	−0.310390	+	0.709203i
$585$		0			0
$586$	−1.31016e44	+	5.32559e43i	−0.677582	+	0.275427i
$587$			3.61550e44i			1.81953i	0.415125	+	0.909764i	$0.363738\pi$
$587$			3.61550e44i			1.81953i	−0.415125	+	0.909764i	$0.636262\pi$
$588$		0			0
$589$	1.11146e44			0.529725
$590$	3.28443e43	+	8.08008e43i	0.152345	+	0.374786i
$591$		0			0
$592$	−3.70191e42	+	1.39868e44i	−0.0162659	+	0.614568i
$593$	3.22195e44			1.37798			0.688992	−	0.724769i	$-0.258053\pi$
$593$	3.22195e44			1.37798			0.688992	+	0.724769i	$0.258053\pi$
$594$		0			0
$595$			5.70693e44i			2.31276i
$596$	2.63721e44	−	2.56834e44i	1.04041	−	1.01324i
$597$		0			0
$598$	−6.86327e43	−	1.68845e44i	−0.256633	−	0.631347i
$599$		−	1.11435e44i		−	0.405688i	−0.979211	−	0.202844i	$-0.934982\pi$
$599$		−	1.11435e44i		−	0.405688i	0.979211	−	0.202844i	$-0.0650185\pi$
$600$		0			0
$601$	1.21014e44			0.417679			0.208839	−	0.977950i	$-0.433031\pi$
$601$	1.21014e44			0.417679			0.208839	+	0.977950i	$0.433031\pi$
$602$	−5.16140e44	+	2.09803e44i	−1.73470	+	0.705127i
$603$		0			0
$604$	2.14932e44	+	2.20696e44i	0.685032	+	0.703403i
$605$	−8.82179e43			−0.273824
$606$		0			0
$607$		−	3.55121e44i		−	1.04558i	−0.852462	−	0.522790i	$-0.824891\pi$
$607$		−	3.55121e44i		−	1.04558i	0.852462	−	0.522790i	$-0.175109\pi$
$608$	−3.55509e44	+	1.33662e44i	−1.01952	+	0.383309i
$609$		0			0
$610$	−8.29339e44	+	3.37113e44i	−2.25660	+	0.917273i
$611$			4.65587e43i			0.123407i
$612$		0			0
$613$	1.29016e44			0.324546			0.162273	−	0.986746i	$-0.448118\pi$
$613$	1.29016e44			0.324546			0.162273	+	0.986746i	$0.448118\pi$
$614$	−1.04011e44	−	2.55880e44i	−0.254909	−	0.627107i
$615$		0			0
$616$	2.20031e44	−	5.02744e44i	0.511909	−	1.16965i
$617$	−3.97498e44			−0.901099			−0.450550	−	0.892751i	$-0.648772\pi$
$617$	−3.97498e44			−0.901099			−0.450550	+	0.892751i	$0.648772\pi$
$618$		0			0
$619$		−	4.19604e44i		−	0.903212i	−0.892218	−	0.451606i	$-0.850851\pi$
$619$		−	4.19604e44i		−	0.903212i	0.892218	−	0.451606i	$-0.149149\pi$
$620$	2.64576e44	+	2.71671e44i	0.554987	+	0.569871i
$621$		0			0
$622$	1.98909e43	+	4.89339e43i	0.0396285	+	0.0974908i
$623$		−	5.53888e44i		−	1.07551i
$624$		0			0
$625$	7.10064e43			0.130984
$626$	−5.96248e43	+	2.42365e43i	−0.107211	+	0.0435794i
$627$		0			0
$628$	−6.01590e42	+	5.85878e42i	−0.0102789	+	0.0100104i
$629$	3.72985e44			0.621271
$630$		0			0
$631$			4.07277e44i			0.644792i	0.946605	+	0.322396i	$0.104488\pi$
$631$			4.07277e44i			0.644792i	−0.946605	+	0.322396i	$0.895512\pi$
$632$	4.63727e44	+	2.02955e44i	0.715796	+	0.313276i
$633$		0			0
$634$	5.99650e44	−	2.43748e44i	0.879973	−	0.357695i
$635$			1.27002e45i			1.81732i
$636$		0			0
$637$	7.27558e44			0.990004
$638$	1.20559e44	+	2.96589e44i	0.159981	+	0.393572i
$639$		0			0
$640$	−1.17297e45	−	5.50787e44i	−1.48049	−	0.695191i
$641$	−2.63607e44			−0.324510			−0.162255	−	0.986749i	$-0.551877\pi$
$641$	−2.63607e44			−0.324510			−0.162255	+	0.986749i	$0.551877\pi$
$642$		0			0
$643$		−	5.14623e44i		−	0.602717i	−0.953511	−	0.301359i	$-0.902560\pi$
$643$		−	5.14623e44i		−	0.602717i	0.953511	−	0.301359i	$-0.0974401\pi$
$644$	5.78618e44	−	5.63507e44i	0.661026	−	0.643762i
$645$		0			0
$646$	3.81260e44	+	9.37946e44i	0.414478	+	1.01967i
$647$		−	5.16937e44i		−	0.548238i	−0.961696	−	0.274119i	$-0.911614\pi$
$647$		−	5.16937e44i		−	0.548238i	0.961696	−	0.274119i	$-0.0883862\pi$
$648$		0			0
$649$	−2.23586e44			−0.225699
$650$	1.62844e45	−	6.61934e44i	1.60383	−	0.651930i
$651$		0			0
$652$	−2.41842e44	−	2.48328e44i	−0.226762	−	0.232843i
$653$	−1.24102e45			−1.13545			−0.567723	−	0.823220i	$-0.692175\pi$
$653$	−1.24102e45			−1.13545			−0.567723	+	0.823220i	$0.692175\pi$
$654$		0			0
$655$			1.79456e45i			1.56350i
$656$	1.35996e43	−	5.13826e44i	0.0115628	−	0.436873i
$657$		0			0
$658$	−1.91134e44	+	7.76931e43i	−0.154783	+	0.0629170i
$659$			2.03659e45i			1.60967i	0.593499	+	0.804835i	$0.297746\pi$
$659$			2.03659e45i			1.60967i	−0.593499	+	0.804835i	$0.702254\pi$
$660$		0			0
$661$	7.03489e44			0.529705			0.264852	−	0.964289i	$-0.414677\pi$
$661$	7.03489e44			0.529705			0.264852	+	0.964289i	$0.414677\pi$
$662$	−5.58822e44	−	1.37477e45i	−0.410720	−	1.01042i
$663$		0			0
$664$	5.61459e44	+	2.45728e44i	0.393214	+	0.172094i
$665$	3.64604e45			2.49273
$666$		0			0
$667$			4.71188e44i			0.307030i
$668$	−2.05313e43	−	2.10819e43i	−0.0130615	−	0.0134117i
$669$		0			0
$670$	−3.82325e44	−	9.40564e44i	−0.231865	−	0.570416i
$671$		−	2.29488e45i		−	1.35894i
$672$		0			0
$673$	5.51542e44			0.311413			0.155707	−	0.987803i	$-0.450235\pi$
$673$	5.51542e44			0.311413			0.155707	+	0.987803i	$0.450235\pi$
$674$	−1.72236e45	+	7.00111e44i	−0.949652	+	0.386019i
$675$		0			0
$676$	9.27957e43	−	9.03722e43i	0.0487956	−	0.0475212i
$677$	3.04089e45			1.56165			0.780823	−	0.624753i	$-0.214800\pi$
$677$	3.04089e45			1.56165			0.780823	+	0.624753i	$0.214800\pi$
$678$		0			0
$679$		−	4.19752e45i		−	2.05625i
$680$	−1.38503e45	+	3.16461e45i	−0.662697	+	1.51418i
$681$		0			0
$682$	−9.00544e44	+	3.66057e44i	−0.411107	+	0.167109i
$683$			1.65046e45i			0.735993i	0.929827	+	0.367996i	$0.119956\pi$
$683$			1.65046e45i			0.735993i	−0.929827	+	0.367996i	$0.880044\pi$
$684$		0			0
$685$	−6.70871e44			−0.285489
$686$	−5.33357e43	−	1.31212e44i	−0.0221734	−	0.0545492i
$687$		0			0
$688$	−3.37128e45	−	8.92284e43i	−1.33777	−	0.0354069i
$689$	7.82491e44			0.303369
$690$		0			0
$691$			1.42722e45i			0.528252i	0.964488	+	0.264126i	$0.0850834\pi$
$691$			1.42722e45i			0.528252i	−0.964488	+	0.264126i	$0.914917\pi$
$692$	−3.07609e45	+	2.99575e45i	−1.11250	+	1.08345i
$693$		0			0
$694$	8.39996e44	+	2.06649e45i	0.290085	+	0.713645i
$695$			8.93882e45i			3.01664i
$696$		0			0
$697$	−1.37022e45			−0.441638
$698$	3.17014e45	−	1.28861e45i	0.998599	−	0.405915i
$699$		0			0
$700$	5.43479e45	+	5.58054e45i	1.63536	+	1.67922i
$701$	−5.21518e45			−1.53384			−0.766922	−	0.641741i	$-0.778213\pi$
$701$	−5.21518e45			−1.53384			−0.766922	+	0.641741i	$0.778213\pi$
$702$		0			0
$703$		−	2.38293e45i		−	0.669616i
$704$	2.44024e45	−	2.25383e45i	0.670301	−	0.619096i
$705$		0			0
$706$	5.30338e45	−	2.15574e45i	1.39212	−	0.565876i
$707$		−	1.04792e46i		−	2.68917i
$708$		0			0
$709$	−9.80217e44			−0.240426			−0.120213	−	0.992748i	$-0.538358\pi$
$709$	−9.80217e44			−0.240426			−0.120213	+	0.992748i	$0.538358\pi$
$710$	2.75864e45	+	6.78659e45i	0.661549	+	1.62749i
$711$		0			0
$712$	1.34424e45	−	3.07143e45i	0.308175	−	0.704142i
$713$	−1.43069e45			−0.320710
$714$		0			0
$715$			7.19604e45i			1.54240i
$716$	−1.40992e45	−	1.44773e45i	−0.295520	−	0.303445i
$717$		0			0
$718$	−4.46320e43	−	1.09800e44i	−0.00894654	−	0.0220095i
$719$		−	8.51901e45i		−	1.67004i	−0.550220	−	0.835020i	$-0.685456\pi$
$719$		−	8.51901e45i		−	1.67004i	0.550220	−	0.835020i	$-0.314544\pi$
$720$		0			0
$721$	5.86702e45			1.10015
$722$	9.41217e44	−	3.82590e44i	0.172621	−	0.0701679i
$723$		0			0
$724$	−2.29245e45	+	2.23258e45i	−0.402238	+	0.391733i
$725$	−4.54442e45			−0.779956
$726$		0			0
$727$			4.72807e45i			0.776486i	0.921557	+	0.388243i	$0.126918\pi$
$727$			4.72807e45i			0.776486i	−0.921557	+	0.388243i	$0.873082\pi$
$728$	8.24617e45	+	3.60902e45i	1.32480	+	0.579812i
$729$		0			0
$730$	7.62887e45	−	3.10102e45i	1.17299	−	0.476802i
$731$			8.99020e45i			1.35236i
$732$		0			0
$733$	−1.17970e46			−1.69866			−0.849330	−	0.527862i	$-0.822994\pi$
$733$	−1.17970e46			−1.69866			−0.849330	+	0.527862i	$0.822994\pi$
$734$	−1.05600e45	−	2.59789e45i	−0.148774	−	0.366002i
$735$		0			0
$736$	4.57615e45	−	1.72051e45i	0.617242	−	0.232066i
$737$	2.60266e45			0.343508
$738$		0			0
$739$		−	4.15446e45i		−	0.525054i	−0.964925	−	0.262527i	$-0.915444\pi$
$739$		−	4.15446e45i		−	0.525054i	0.964925	−	0.262527i	$-0.0845559\pi$
$740$	5.82451e45	−	5.67239e45i	0.720364	−	0.701550i
$741$		0			0
$742$	1.30575e45	+	3.21231e45i	0.154667	+	0.380500i
$743$		−	3.14116e45i		−	0.364141i	−0.983285	−	0.182070i	$-0.941720\pi$
$743$		−	3.14116e45i		−	0.364141i	0.983285	−	0.182070i	$-0.0582799\pi$
$744$		0			0
$745$	−2.13907e46			−2.37533
$746$	−1.48201e45	+	6.02414e44i	−0.161076	+	0.0654748i
$747$		0			0
$748$	−6.17819e45	−	6.34387e45i	−0.643333	−	0.660585i
$749$	−1.88945e46			−1.92586
$750$		0			0
$751$			6.57015e44i			0.0641707i	0.999485	+	0.0320853i	$0.0102148\pi$
$751$			6.57015e44i			0.0641707i	−0.999485	+	0.0320853i	$0.989785\pi$
$752$	−1.24844e45	−	3.30426e43i	−0.119366	−	0.00315929i
$753$		0			0
$754$	−4.86474e45	+	1.97744e45i	−0.445778	+	0.181202i
$755$		−	1.79009e46i		−	1.60592i
$756$		0			0
$757$	−7.25472e45			−0.623859			−0.311930	−	0.950105i	$-0.600975\pi$
$757$	−7.25472e45			−0.623859			−0.311930	+	0.950105i	$0.600975\pi$
$758$	3.44931e45	+	8.48572e45i	0.290419	+	0.714466i
$759$		0			0
$760$	2.02181e46	+	8.84866e45i	1.63201	+	0.714266i
$761$	−9.43510e45			−0.745748			−0.372874	−	0.927882i	$-0.621628\pi$
$761$	−9.43510e45			−0.745748			−0.372874	+	0.927882i	$0.621628\pi$
$762$		0			0
$763$		−	2.42091e46i		−	1.83478i
$764$	−1.10348e46	−	1.13307e46i	−0.818974	−	0.840937i
$765$		0			0
$766$	1.04587e45	+	2.57295e45i	0.0744415	+	0.183135i
$767$		−	3.66732e45i		−	0.255637i
$768$		0			0
$769$	−8.57108e45			−0.573078			−0.286539	−	0.958069i	$-0.592505\pi$
$769$	−8.57108e45			−0.573078			−0.286539	+	0.958069i	$0.592505\pi$
$770$	−2.95414e46	+	1.20081e46i	−1.93455	+	0.786364i
$771$		0			0
$772$	2.51461e45	−	2.44894e45i	0.157977	−	0.153851i
$773$	9.45230e45			0.581655			0.290828	−	0.956775i	$-0.406069\pi$
$773$	9.45230e45			0.581655			0.290828	+	0.956775i	$0.406069\pi$
$774$		0			0
$775$		−	1.37984e46i		−	0.814706i
$776$	1.01870e46	−	2.32762e46i	0.589197	−	1.34624i
$777$		0			0
$778$	−1.12722e46	+	4.58196e45i	−0.625653	+	0.254318i
$779$			8.75408e45i			0.476005i
$780$		0			0
$781$	−1.87793e46			−0.980085
$782$	−4.90762e45	−	1.20733e46i	−0.250936	−	0.617332i
$783$		0			0
$784$	−5.16347e44	+	1.95089e46i	−0.0253445	+	0.957583i
$785$	4.87955e44			0.0234674
$786$		0			0
$787$		−	3.25122e46i		−	1.50124i	−0.660733	−	0.750621i	$-0.729755\pi$
$787$		−	3.25122e46i		−	1.50124i	0.660733	−	0.750621i	$-0.270245\pi$
$788$	1.01944e46	−	9.92819e45i	0.461258	−	0.449211i
$789$		0			0
$790$	−1.10762e46	−	2.72488e46i	−0.481235	−	1.18390i
$791$		−	2.10149e46i		−	0.894752i
$792$		0			0
$793$	3.76414e46			1.53920
$794$	4.56132e45	−	1.85411e45i	0.182794	−	0.0743030i
$795$		0			0
$796$	2.01378e46	+	2.06778e46i	0.775179	+	0.795968i
$797$	2.94599e45			0.111147			0.0555735	−	0.998455i	$-0.482301\pi$
$797$	2.94599e45			0.111147			0.0555735	+	0.998455i	$0.482301\pi$
$798$		0			0
$799$			3.32920e45i			0.120668i
$800$	1.65936e46	+	4.41351e46i	0.589522	+	1.56799i
$801$		0			0
$802$	−9.66573e45	+	3.92897e45i	−0.329947	+	0.134118i
$803$			2.11100e46i			0.706382i
$804$		0			0
$805$	−4.69322e46			−1.50917
$806$	−6.00418e45	−	1.47710e46i	−0.189275	−	0.465639i
$807$		0			0
$808$	2.54322e46	−	5.81096e46i	0.770554	−	1.76062i
$809$	−3.70181e46			−1.09961			−0.549804	−	0.835294i	$-0.685298\pi$
$809$	−3.70181e46			−1.09961			−0.549804	+	0.835294i	$0.685298\pi$
$810$		0			0
$811$			3.30022e46i			0.942344i	0.882041	+	0.471172i	$0.156169\pi$
$811$			3.30022e46i			0.942344i	−0.882041	+	0.471172i	$0.843831\pi$
$812$	−1.62357e46	−	1.66711e46i	−0.454543	−	0.466733i
$813$		0			0
$814$	7.84810e45	+	1.93073e46i	0.211239	+	0.519673i
$815$			2.01421e46i			0.531597i
$816$		0			0
$817$	5.74366e46			1.45759
$818$	3.27419e46	−	1.33091e46i	0.814801	−	0.331204i
$819$		0			0
$820$	−2.13973e46	+	2.08384e46i	−0.512079	+	0.498705i
$821$	−6.39550e46			−1.50101			−0.750506	−	0.660864i	$-0.770190\pi$
$821$	−6.39550e46			−1.50101			−0.750506	+	0.660864i	$0.770190\pi$
$822$		0			0
$823$		−	3.58417e46i		−	0.809080i	−0.914520	−	0.404540i	$-0.867432\pi$
$823$		−	3.58417e46i		−	0.809080i	0.914520	−	0.404540i	$-0.132568\pi$
$824$	3.25339e46	+	1.42388e46i	0.720279	+	0.315237i
$825$		0			0
$826$	1.50552e46	−	6.11971e45i	0.320632	−	0.130332i
$827$		−	1.31958e46i		−	0.275643i	−0.990457	−	0.137821i	$-0.955990\pi$
$827$		−	1.31958e46i		−	0.275643i	0.990457	−	0.137821i	$-0.0440100\pi$
$828$		0			0
$829$	−7.76124e46			−1.55976			−0.779881	−	0.625927i	$-0.784721\pi$
$829$	−7.76124e46			−1.55976			−0.779881	+	0.625927i	$0.784721\pi$
$830$	−1.34105e46	−	3.29915e46i	−0.264361	−	0.650358i
$831$		0			0
$832$	3.69680e46	+	4.00256e46i	0.701217	+	0.759214i
$833$	5.20245e46			0.968027
$834$		0			0
$835$			1.70997e45i			0.0306199i
$836$	−4.05298e46	+	3.94713e46i	−0.711990	+	0.693395i
$837$		0			0
$838$	5.22201e45	+	1.28468e46i	0.0882944	+	0.217215i
$839$		−	1.83814e46i		−	0.304921i	−0.988310	−	0.152460i	$-0.951280\pi$
$839$		−	1.83814e46i		−	0.304921i	0.988310	−	0.152460i	$-0.0487196\pi$
$840$		0			0
$841$	−4.90474e46			−0.783214
$842$	6.44199e46	−	2.61857e46i	1.00932	−	0.410271i
$843$		0			0
$844$	7.55811e46	+	7.76079e46i	1.14008	+	1.17065i
$845$	−7.52674e45			−0.111404
$846$		0			0
$847$			1.64372e46i			0.234258i
$848$	−5.55333e44	+	2.09819e46i	−0.00776640	+	0.293435i
$849$		0			0
$850$	1.16442e47	−	4.73320e46i	1.56822	−	0.637458i
$851$			3.06733e46i			0.405403i
$852$		0			0
$853$	−1.27256e47			−1.61992			−0.809958	−	0.586488i	$-0.800510\pi$
$853$	−1.27256e47			−1.61992			−0.809958	+	0.586488i	$0.800510\pi$
$854$	6.28127e46	+	1.54527e47i	0.784732	+	1.93054i
$855$		0			0
$856$	−1.04774e47	−	4.58554e46i	−1.26088	−	0.551836i
$857$	8.49613e46			1.00352			0.501762	−	0.865006i	$-0.332685\pi$
$857$	8.49613e46			1.00352			0.501762	+	0.865006i	$0.332685\pi$
$858$		0			0
$859$			1.38903e47i			1.58060i	0.612723	+	0.790298i	$0.290074\pi$
$859$			1.38903e47i			1.58060i	−0.612723	+	0.790298i	$0.709926\pi$
$860$	1.36724e47	+	1.40390e47i	1.52710	+	1.56806i
$861$		0			0
$862$	3.73674e46	+	9.19283e46i	0.402140	+	0.989312i
$863$			1.18295e47i			1.24967i	0.780759	+	0.624833i	$0.214833\pi$
$863$			1.18295e47i			1.24967i	−0.780759	+	0.624833i	$0.785167\pi$
$864$		0			0
$865$	2.49504e47			2.53992
$866$	−9.87403e46	+	4.01364e46i	−0.986753	+	0.401100i
$867$		0			0
$868$	5.06192e46	−	4.92971e46i	0.487528	−	0.474795i
$869$	7.54007e46			0.712950
$870$		0			0
$871$			4.26896e46i			0.389073i
$872$	5.87534e46	−	1.34244e47i	0.525738	−	1.20125i
$873$		0			0
$874$	−7.71342e46	+	3.13538e46i	−0.665371	+	0.270463i
$875$		−	1.82433e47i		−	1.54516i
$876$		0			0
$877$	−1.57931e46			−0.128965			−0.0644827	−	0.997919i	$-0.520540\pi$
$877$	−1.57931e46			−0.128965			−0.0644827	+	0.997919i	$0.520540\pi$
$878$	−1.38569e46	−	3.40896e46i	−0.111110	−	0.273344i
$879$		0			0
$880$	−1.92956e47	−	5.10702e45i	−1.49189	−	0.0394861i
$881$	−2.23327e46			−0.169561			−0.0847806	−	0.996400i	$-0.527019\pi$
$881$	−2.23327e46			−0.169561			−0.0847806	+	0.996400i	$0.527019\pi$
$882$		0			0
$883$		−	5.28087e44i		−	0.00386665i	−0.999998	−	0.00193332i	$-0.999385\pi$
$883$		−	5.28087e44i		−	0.00386665i	0.999998	−	0.00193332i	$-0.000615397\pi$
$884$	1.04054e47	−	1.01337e47i	0.748210	−	0.728669i
$885$		0			0
$886$	9.00863e46	+	2.21623e47i	0.624769	+	1.53701i
$887$			1.36689e47i			0.931011i	0.885045	+	0.465505i	$0.154127\pi$
$887$			1.36689e47i			0.931011i	−0.885045	+	0.465505i	$0.845873\pi$
$888$		0			0
$889$	2.36637e47			1.55473
$890$	−1.80478e47	+	7.33615e46i	−1.16462	+	0.473400i
$891$		0			0
$892$	−1.07108e47	−	1.09981e47i	−0.666784	−	0.684666i
$893$	2.12696e46			0.130058
$894$		0			0
$895$			1.17427e47i			0.692785i
$896$	−1.02625e47	+	2.18554e47i	−0.594740	+	1.26657i
$897$		0			0
$898$	−6.33647e45	+	2.57568e45i	−0.0354345	+	0.0144036i
$899$			4.12209e46i			0.226445i
$900$		0			0
$901$	5.59525e46			0.296635
$902$	−2.88313e46	−	7.09284e46i	−0.150162	−	0.369416i
$903$		0			0
$904$	5.10014e46	−	1.16532e47i	0.256382	−	0.585801i
$905$	1.85943e47			0.918337
$906$		0			0
$907$		−	3.79202e47i		−	1.80782i	−0.427726	−	0.903908i	$-0.640685\pi$
$907$		−	3.79202e47i		−	1.80782i	0.427726	−	0.903908i	$-0.359315\pi$
$908$	−6.43150e46	−	6.60398e46i	−0.301258	−	0.309337i
$909$		0			0
$910$	−1.96961e47	−	4.84548e47i	−0.890673	−	2.19116i
$911$		−	2.01538e46i		−	0.0895493i	−0.998997	−	0.0447746i	$-0.985743\pi$
$911$		−	2.01538e46i		−	0.0895493i	0.998997	−	0.0447746i	$-0.0142570\pi$
$912$		0			0
$913$	9.12916e46			0.391650
$914$	−7.60987e46	+	3.09329e46i	−0.320803	+	0.130401i
$915$		0			0
$916$	2.10449e47	−	2.04953e47i	0.856682	−	0.834308i
$917$	3.34372e47			1.33758
$918$		0			0
$919$			3.04402e47i			1.17598i	0.808869	+	0.587989i	$0.200080\pi$
$919$			3.04402e47i			1.17598i	−0.808869	+	0.587989i	$0.799920\pi$
$920$	−2.60249e47	−	1.13901e47i	−0.988062	−	0.432436i
$921$		0			0
$922$	−3.63751e47	+	1.47859e47i	−1.33386	+	0.542192i
$923$		−	3.08025e47i		−	1.11009i
$924$		0			0
$925$	−2.95831e47			−1.02986
$926$	−1.44318e47	−	3.55039e47i	−0.493792	−	1.21479i
$927$		0			0
$928$	−4.95711e46	−	1.31848e47i	−0.163855	−	0.435818i
$929$	−9.58853e46			−0.311531			−0.155765	−	0.987794i	$-0.549784\pi$
$929$	−9.58853e46			−0.311531			−0.155765	+	0.987794i	$0.549784\pi$
$930$		0			0
$931$		−	3.32374e47i		−	1.04336i
$932$	1.83829e47	−	1.79028e47i	0.567230	−	0.552416i
$933$		0			0
$934$	−1.51644e47	−	3.73063e47i	−0.452143	−	1.11233i
$935$			5.14557e47i			1.50816i
$936$		0			0
$937$	4.66513e47			1.32139			0.660694	−	0.750655i	$-0.270262\pi$
$937$	4.66513e47			1.32139			0.660694	+	0.750655i	$0.270262\pi$
$938$	−1.75251e47	+	7.12367e46i	−0.487994	+	0.198362i
$939$		0			0
$940$	5.06308e46	+	5.19886e46i	0.136260	+	0.139914i
$941$	−5.79901e47			−1.53433			−0.767167	−	0.641447i	$-0.778334\pi$
$941$	−5.79901e47			−1.53433			−0.767167	+	0.641447i	$0.778334\pi$
$942$		0			0
$943$		−	1.12683e47i		−	0.288186i
$944$	9.83365e46	+	2.60269e45i	0.247265	+	0.00654442i
$945$		0			0
$946$	−4.65370e47	+	1.89166e47i	−1.13120	+	0.459816i
$947$		−	4.08962e46i		−	0.0977425i	−0.998805	−	0.0488713i	$-0.984438\pi$
$947$		−	4.08962e46i		−	0.0977425i	0.998805	−	0.0488713i	$-0.0155624\pi$
$948$		0			0
$949$	−3.46253e47			−0.800081
$950$	−3.02395e47	−	7.43927e47i	−0.687063	−	1.69026i
$951$		0			0
$952$	5.89647e47	+	2.58065e47i	1.29539	+	0.566941i
$953$	2.93440e47			0.633917			0.316958	−	0.948439i	$-0.397338\pi$
$953$	2.93440e47			0.633917			0.316958	+	0.948439i	$0.397338\pi$
$954$		0			0
$955$			9.19044e47i			1.91992i
$956$	4.46019e47	+	4.57980e47i	0.916277	+	0.940849i
$957$		0			0
$958$	8.85441e46	+	2.17829e47i	0.175918	+	0.432780i
$959$			1.25000e47i			0.244238i
$960$		0			0
$961$	4.03984e47			0.763466
$962$	−3.16684e47	+	1.28727e47i	−0.588606	+	0.239259i
$963$		0			0
$964$	−3.69790e47	+	3.60132e47i	−0.664848	+	0.647484i
$965$	−2.03962e47			−0.360672
$966$		0			0
$967$			1.52616e47i			0.261081i	0.991443	+	0.130541i	$0.0416713\pi$
$967$			1.52616e47i			0.261081i	−0.991443	+	0.130541i	$0.958329\pi$
$968$	−3.98918e46	+	9.11479e46i	−0.0671240	+	0.153370i
$969$		0			0
$970$	−1.36772e48	+	5.55955e47i	−2.22663	+	0.905090i
$971$			4.62624e47i			0.740833i	0.928866	+	0.370417i	$0.120785\pi$
$971$			4.62624e47i			0.740833i	−0.928866	+	0.370417i	$0.879215\pi$
$972$		0			0
$973$	1.66553e48			2.58075
$974$	3.12465e47	+	7.68701e47i	0.476275	+	1.17169i
$975$		0			0
$976$	−2.67140e46	+	1.00933e48i	−0.0394042	+	1.48879i
$977$	−2.90967e47			−0.422212			−0.211106	−	0.977463i	$-0.567707\pi$
$977$	−2.90967e47			−0.422212			−0.211106	+	0.977463i	$0.567707\pi$
$978$		0			0
$979$		−	4.99405e47i		−	0.701342i
$980$	8.12410e47	−	7.91193e47i	1.12243	−	1.09311i
$981$		0			0
$982$	−4.71513e47	−	1.15998e48i	−0.630535	−	1.55119i
$983$		−	1.04874e48i		−	1.37979i	−0.723909	−	0.689896i	$-0.757656\pi$
$983$		−	1.04874e48i		−	1.37979i	0.723909	−	0.689896i	$-0.242344\pi$
$984$		0			0
$985$	−8.26879e47			−1.05308
$986$	−3.47856e47	+	1.41398e47i	−0.435882	+	0.177179i
$987$		0			0
$988$	−6.47420e47	−	6.64782e47i	−0.785371	−	0.806433i
$989$	−7.39330e47			−0.882465
$990$		0			0
$991$		−	7.53420e47i		−	0.870680i	−0.900266	−	0.435340i	$-0.856628\pi$
$991$		−	7.53420e47i		−	0.870680i	0.900266	−	0.435340i	$-0.143372\pi$
$992$	4.00334e47	−	1.50515e47i	0.455235	−	0.171156i
$993$		0			0
$994$	1.26451e48	−	5.14005e47i	1.39233	−	0.565959i
$995$		−	1.67719e48i		−	1.81725i
$996$		0			0
$997$	−2.59410e47			−0.272185			−0.136092	−	0.990696i	$-0.543454\pi$
$997$	−2.59410e47			−0.272185			−0.136092	+	0.990696i	$0.543454\pi$
$998$	−5.62440e47	−	1.38367e48i	−0.580748	−	1.42871i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	36.33.d.b.19.2		14
3.2	odd	2		4.33.b.b.3.13	✓	14
4.3	odd	2	inner	36.33.d.b.19.1		14
12.11	even	2		4.33.b.b.3.14	yes	14

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4.33.b.b.3.13	✓	14	3.2	odd	2
4.33.b.b.3.14	yes	14	12.11	even	2
36.33.d.b.19.1		14	4.3	odd	2	inner
36.33.d.b.19.2		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)

\(f(q)\)	\(=\)	\(q+(-60712.0 + 24678.5i) q^{2} +(3.07691e9 - 2.99655e9i) q^{4} -2.49571e11 q^{5} +4.65014e13i q^{7} +(-1.12855e14 + 2.57860e14i) q^{8} +O(q^{10})\)	\(q+(-60712.0 + 24678.5i) q^{2} +(3.07691e9 - 2.99655e9i) q^{4} -2.49571e11 q^{5} +4.65014e13i q^{7} +(-1.12855e14 + 2.57860e14i) q^{8} +(1.51520e16 - 6.15903e15i) q^{10} +4.19273e16i q^{11} -6.87705e17 q^{13} +(-1.14758e18 - 2.82319e18i) q^{14} +(4.88063e17 - 1.84403e19i) q^{16} -4.91747e19 q^{17} +3.14168e20i q^{19} +(-7.67909e20 + 7.47854e20i) q^{20} +(-1.03470e21 - 2.54549e21i) q^{22} -4.04400e21i q^{23} +3.90027e22 q^{25} +(4.17519e22 - 1.69715e22i) q^{26} +(1.39344e23 + 1.43081e23i) q^{28} -1.16515e23 q^{29} -3.53780e23i q^{31} +(4.25447e23 + 1.13159e24i) q^{32} +(2.98549e24 - 1.21356e24i) q^{34} -1.16054e25i q^{35} -7.58489e24 q^{37} +(-7.75318e24 - 1.90737e25i) q^{38} +(2.81654e25 - 6.43545e25i) q^{40} +2.78643e25 q^{41} -1.82822e26i q^{43} +(1.25637e26 + 1.29007e26i) q^{44} +(9.97996e25 + 2.45519e26i) q^{46} -6.77015e25i q^{47} -1.05795e27 q^{49} +(-2.36793e27 + 9.62526e26i) q^{50} +(-2.11601e27 + 2.06075e27i) q^{52} -1.13783e27 q^{53} -1.04638e28i q^{55} +(-1.19909e28 - 5.24792e27i) q^{56} +(7.07388e27 - 2.87542e27i) q^{58} +5.33270e27i q^{59} -5.47348e28 q^{61} +(8.73075e27 + 2.14787e28i) q^{62} +(-5.37556e28 - 5.82017e28i) q^{64} +1.71631e29 q^{65} -6.20754e28i q^{67} +(-1.51306e29 + 1.47355e29i) q^{68} +(2.86403e29 + 7.04587e29i) q^{70} +4.47902e29i q^{71} +5.03491e29 q^{73} +(4.60494e29 - 1.87183e29i) q^{74} +(9.41421e29 + 9.66668e29i) q^{76} -1.94968e30 q^{77} -1.79837e30i q^{79} +(-1.21806e29 + 4.60216e30i) q^{80} +(-1.69170e30 + 6.87649e29i) q^{82} -2.17738e30i q^{83} +1.22726e31 q^{85} +(4.51175e30 + 1.10995e31i) q^{86} +(-1.08114e31 - 4.73171e30i) q^{88} -1.19112e31 q^{89} -3.19792e31i q^{91} +(-1.21181e31 - 1.24430e31i) q^{92} +(1.67077e30 + 4.11029e30i) q^{94} -7.84072e31i q^{95} -9.02666e31 q^{97} +(6.42303e31 - 2.61086e31i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 14 q + 23780 q^{2} - 2922848368 q^{4} - 138121491740 q^{5} + 191366550113600 q^{8}+O(q^{10}) \) 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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