LMFDB - Embedded newform 36.23.d.c.19.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [36,23,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, 23, names="a")

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

chi := DirichletCharacter("36.19");

S:= CuspForms(chi, 23);

N := Newforms(S);

Level:	$ N $	$=$	$ 36 = 2^{2} \cdot 3^{2} $
Weight:	$ k $	$=$	$ 23 $
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:	$110.414676543$
Analytic rank:	$0$
Dimension:	$10$
Coefficient field:	$\mathbb{Q}[x]/(x^{10} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{10} - 5 x^{9} - 63342 x^{8} - 45742928 x^{7} + 34835133568 x^{6} + 12622768560288 x^{5} + \cdots + 11\!\cdots\!40 $ x^10 - 5x^9 - 63342x^8 - 45742928x^7 + 34835133568x^6 + 12622768560288x^5 + 13335465927292608x^4 - 404504858109047040x^3 - 95573988251584922880x^2 - 1820809561188275535801600*x + 1168838172864011361183920640
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{90}\cdot 3^{16} $
Twist minimal:	no (minimal twist has level 4)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			19.2
Root			$408.476 + 250.605i$ of defining polynomial
Character	$\chi$	$=$	36.19
Dual form			36.23.d.c.19.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1785.90 + 1002.42i) q^{2} +(2.18461e6 - 3.58046e6i) q^{4} +6.52379e7 q^{5} -3.27904e9i q^{7} +(-3.12381e8 + 8.58425e9i) q^{8} +O(q^{10})$	\(q+(-1785.90 + 1002.42i) q^{2} +(2.18461e6 - 3.58046e6i) q^{4} +6.52379e7 q^{5} -3.27904e9i q^{7} +(-3.12381e8 + 8.58425e9i) q^{8} +(-1.16509e11 + 6.53958e10i) q^{10} +2.30540e11i q^{11} -1.19775e12 q^{13} +(3.28698e12 + 5.85606e12i) q^{14} +(-8.04715e12 - 1.56438e13i) q^{16} +2.07597e13 q^{17} -6.48196e12i q^{19} +(1.42519e14 - 2.33581e14i) q^{20} +(-2.31098e14 - 4.11722e14i) q^{22} -1.02386e15i q^{23} +1.87179e15 q^{25} +(2.13907e15 - 1.20065e15i) q^{26} +(-1.17405e16 - 7.16343e15i) q^{28} -1.56390e16 q^{29} -2.85873e16i q^{31} +(3.00531e16 + 1.98717e16i) q^{32} +(-3.70748e16 + 2.08100e16i) q^{34} -2.13918e17i q^{35} +2.10744e17 q^{37} +(6.49765e15 + 1.15762e16i) q^{38} +(-2.03791e16 + 5.60018e17i) q^{40} +5.57168e17 q^{41} -8.07417e17i q^{43} +(8.25438e17 + 5.03639e17i) q^{44} +(1.02634e18 + 1.82852e18i) q^{46} +8.59587e17i q^{47} -6.84231e18 q^{49} +(-3.34285e18 + 1.87632e18i) q^{50} +(-2.61662e18 + 4.28850e18i) q^{52} -1.56480e19 q^{53} +1.50399e19i q^{55} +(2.81481e19 + 1.02431e18i) q^{56} +(2.79297e19 - 1.56768e19i) q^{58} -7.82838e18i q^{59} +1.24317e19 q^{61} +(2.86565e19 + 5.10542e19i) q^{62} +(-7.35918e19 - 5.36311e18i) q^{64} -7.81387e19 q^{65} +1.36610e20i q^{67} +(4.53518e19 - 7.43292e19i) q^{68} +(2.14436e20 + 3.82037e20i) q^{70} +2.01190e20i q^{71} +2.57734e19 q^{73} +(-3.76369e20 + 2.11254e20i) q^{74} +(-2.32084e19 - 1.41606e19i) q^{76} +7.55950e20 q^{77} -8.27585e20i q^{79} +(-5.24979e20 - 1.02057e21i) q^{80} +(-9.95050e20 + 5.58517e20i) q^{82} +6.46586e20i q^{83} +1.35432e21 q^{85} +(8.09371e20 + 1.44197e21i) q^{86} +(-1.97901e21 - 7.20162e19i) q^{88} -1.96738e21 q^{89} +3.92748e21i q^{91} +(-3.66590e21 - 2.23674e21i) q^{92} +(-8.61668e20 - 1.53514e21i) q^{94} -4.22869e20i q^{95} -3.08304e21 q^{97} +(1.22197e22 - 6.85887e21i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q - 1540 q^{2} + 2264464 q^{4} + 17091100 q^{5} - 9804431680 q^{8}+O(q^{10}) $ 10 * q - 1540 * q^2 + 2264464 * q^4 + 17091100 * q^5 - 9804431680 * q^8	$ 10 q - 1540 q^{2} + 2264464 q^{4} + 17091100 q^{5} - 9804431680 q^{8} + 159414035240 q^{10} - 531230356540 q^{13} + 5894008940736 q^{14} - 27717620084480 q^{16} - 14058178115540 q^{17} - 233643631625120 q^{20} + 120589650366240 q^{22} + 77\!\cdots\!70 q^{25}+ \cdots + 23\!\cdots\!20 q^{98}+O(q^{100}) $ 10 * q - 1540 * q^2 + 2264464 * q^4 + 17091100 * q^5 - 9804431680 * q^8 + 159414035240 * q^10 - 531230356540 * q^13 + 5894008940736 * q^14 - 27717620084480 * q^16 - 14058178115540 * q^17 - 233643631625120 * q^20 + 120589650366240 * q^22 + 7710175817606670 * q^25 + 3953973318046744 * q^26 + 1177952265288960 * q^28 + 14464474185570172 * q^29 + 73831192092953600 * q^32 - 26625976920357496 * q^34 + 324587767823538020 * q^37 - 369140808808591200 * q^38 - 1158049295468479360 * q^40 + 1355457345814233100 * q^41 + 1919761520625210240 * q^44 + 6132624002565203904 * q^46 + 183553700661552298 * q^49 - 29084394113996178540 * q^50 - 38492433127521128800 * q^52 + 11424344766226018780 * q^53 + 102844865827678657536 * q^56 + 173059696836432320360 * q^58 + 58241718146183220740 * q^61 - 317897221476923285760 * q^62 - 412080172429987966976 * q^64 + 121531695066047433560 * q^65 + 667890522330713878240 * q^68 + 1014396282552321513600 * q^70 + 83030422224875883380 * q^73 - 801906083011176262184 * q^74 + 286747421140990627200 * q^76 + 704201825495570814720 * q^77 - 1509611955050789726720 * q^80 - 2389572513290905036600 * q^82 - 1796890366112110859960 * q^85 + 8221838255181360278496 * q^86 + 11178210842814940531200 * q^88 - 3420669206528505615668 * q^89 - 21476264197983864733440 * q^92 - 20874543047091388369536 * q^94 - 20429910746446196146540 * q^97 + 23110416876469762175420 * 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 $

$2$	−1785.90	+	1002.42i	−0.872024	+	0.489463i
$2$	−1785.90	+	1002.42i	−0.872024	+	0.489463i
$3$		0			0
$3$		0			0
$4$	2.18461e6	−	3.58046e6i	0.520851	−	0.853647i
$5$	6.52379e7			1.33607			0.668036	−	0.744129i	$-0.267135\pi$
$5$	6.52379e7			1.33607			0.668036	+	0.744129i	$0.267135\pi$
$6$		0			0
$7$		−	3.27904e9i		−	1.65832i	−0.559010	−	0.829161i	$-0.688819\pi$
$7$		−	3.27904e9i		−	1.65832i	0.559010	−	0.829161i	$-0.311181\pi$
$8$	−3.12381e8	+	8.58425e9i	−0.0363659	+	0.999339i
$9$		0			0
$10$	−1.16509e11	+	6.53958e10i	−1.16509	+	0.653958i
$11$			2.30540e11i			0.808028i	0.914753	+	0.404014i	$0.132385\pi$
$11$			2.30540e11i			0.808028i	−0.914753	+	0.404014i	$0.867615\pi$
$12$		0			0
$13$	−1.19775e12			−0.668328			−0.334164	−	0.942515i	$-0.608454\pi$
$13$	−1.19775e12			−0.668328			−0.334164	+	0.942515i	$0.608454\pi$
$14$	3.28698e12	+	5.85606e12i	0.811688	+	1.44610i
$15$		0			0
$16$	−8.04715e12	−	1.56438e13i	−0.457428	−	0.889247i
$17$	2.07597e13			0.605735			0.302868	−	0.953033i	$-0.402056\pi$
$17$	2.07597e13			0.605735			0.302868	+	0.953033i	$0.402056\pi$
$18$		0			0
$19$		−	6.48196e12i		−	0.0556438i	−0.999613	−	0.0278219i	$-0.991143\pi$
$19$		−	6.48196e12i		−	0.0556438i	0.999613	−	0.0278219i	$-0.00885713\pi$
$20$	1.42519e14	−	2.33581e14i	0.695895	−	1.14053i
$21$		0			0
$22$	−2.31098e14	−	4.11722e14i	−0.395500	−	0.704620i
$23$		−	1.02386e15i		−	1.07457i	−0.843400	−	0.537286i	$-0.819450\pi$
$23$		−	1.02386e15i		−	1.07457i	0.843400	−	0.537286i	$-0.180550\pi$
$24$		0			0
$25$	1.87179e15			0.785087
$26$	2.13907e15	−	1.20065e15i	0.582798	−	0.327122i
$27$		0			0
$28$	−1.17405e16	−	7.16343e15i	−1.41562	−	0.863739i
$29$	−1.56390e16			−1.28183			−0.640914	−	0.767613i	$-0.721444\pi$
$29$	−1.56390e16			−1.28183			−0.640914	+	0.767613i	$0.721444\pi$
$30$		0			0
$31$		−	2.85873e16i		−	1.12511i	−0.826760	−	0.562554i	$-0.809819\pi$
$31$		−	2.85873e16i		−	1.12511i	0.826760	−	0.562554i	$-0.190181\pi$
$32$	3.00531e16	+	1.98717e16i	0.834141	+	0.551551i
$33$		0			0
$34$	−3.70748e16	+	2.08100e16i	−0.528216	+	0.296485i
$35$		−	2.13918e17i		−	2.21564i
$36$		0			0
$37$	2.10744e17			1.18450			0.592252	−	0.805753i	$-0.298239\pi$
$37$	2.10744e17			1.18450			0.592252	+	0.805753i	$0.298239\pi$
$38$	6.49765e15	+	1.15762e16i	0.0272356	+	0.0485227i
$39$		0			0
$40$	−2.03791e16	+	5.60018e17i	−0.0485874	+	1.33519i
$41$	5.57168e17			1.01243			0.506214	−	0.862408i	$-0.331045\pi$
$41$	5.57168e17			1.01243			0.506214	+	0.862408i	$0.331045\pi$
$42$		0			0
$43$		−	8.07417e17i		−	0.868850i	−0.900708	−	0.434425i	$-0.856952\pi$
$43$		−	8.07417e17i		−	0.868850i	0.900708	−	0.434425i	$-0.143048\pi$
$44$	8.25438e17	+	5.03639e17i	0.689771	+	0.420862i
$45$		0			0
$46$	1.02634e18	+	1.82852e18i	0.525964	+	0.937053i
$47$			8.59587e17i			0.347707i	0.984772	+	0.173854i	$0.0556219\pi$
$47$			8.59587e17i			0.347707i	−0.984772	+	0.173854i	$0.944378\pi$
$48$		0			0
$49$	−6.84231e18			−1.75003
$50$	−3.34285e18	+	1.87632e18i	−0.684615	+	0.384271i
$51$		0			0
$52$	−2.61662e18	+	4.28850e18i	−0.348100	+	0.570517i
$53$	−1.56480e19			−1.68821			−0.844103	−	0.536181i	$-0.819867\pi$
$53$	−1.56480e19			−1.68821			−0.844103	+	0.536181i	$0.819867\pi$
$54$		0			0
$55$			1.50399e19i			1.07958i
$56$	2.81481e19	+	1.02431e18i	1.65722	+	0.0603064i
$57$		0			0
$58$	2.79297e19	−	1.56768e19i	1.11778	−	0.627408i
$59$		−	7.82838e18i		−	0.259597i	−0.991540	−	0.129799i	$-0.958567\pi$
$59$		−	7.82838e18i		−	0.259597i	0.991540	−	0.129799i	$-0.0414331\pi$
$60$		0			0
$61$	1.24317e19			0.285694			0.142847	−	0.989745i	$-0.454374\pi$
$61$	1.24317e19			0.285694			0.142847	+	0.989745i	$0.454374\pi$
$62$	2.86565e19	+	5.10542e19i	0.550699	+	0.981121i
$63$		0			0
$64$	−7.35918e19	−	5.36311e18i	−0.997355	−	0.0726837i
$65$	−7.81387e19			−0.892934
$66$		0			0
$67$			1.36610e20i			1.11856i	0.828979	+	0.559279i	$0.188922\pi$
$67$			1.36610e20i			1.11856i	−0.828979	+	0.559279i	$0.811078\pi$
$68$	4.53518e19	−	7.43292e19i	0.315498	−	0.517084i
$69$		0			0
$70$	2.14436e20	+	3.82037e20i	1.08447	+	1.93209i
$71$			2.01190e20i			0.870492i	0.900312	+	0.435246i	$0.143339\pi$
$71$			2.01190e20i			0.870492i	−0.900312	+	0.435246i	$0.856661\pi$
$72$		0			0
$73$	2.57734e19			0.0821524			0.0410762	−	0.999156i	$-0.486921\pi$
$73$	2.57734e19			0.0821524			0.0410762	+	0.999156i	$0.486921\pi$
$74$	−3.76369e20	+	2.11254e20i	−1.03292	+	0.579771i
$75$		0			0
$76$	−2.32084e19	−	1.41606e19i	−0.0475002	−	0.0289822i
$77$	7.55950e20			1.33997
$78$		0			0
$79$		−	8.27585e20i		−	1.10641i	−0.833046	−	0.553203i	$-0.813405\pi$
$79$		−	8.27585e20i		−	1.10641i	0.833046	−	0.553203i	$-0.186595\pi$
$80$	−5.24979e20	−	1.02057e21i	−0.611156	−	1.18810i
$81$		0			0
$82$	−9.95050e20	+	5.58517e20i	−0.882861	+	0.495546i
$83$			6.46586e20i			0.502074i	0.967978	+	0.251037i	$0.0807715\pi$
$83$			6.46586e20i			0.502074i	−0.967978	+	0.251037i	$0.919228\pi$
$84$		0			0
$85$	1.35432e21			0.809306
$86$	8.09371e20	+	1.44197e21i	0.425270	+	0.757658i
$87$		0			0
$88$	−1.97901e21	−	7.20162e19i	−0.807493	−	0.0293847i
$89$	−1.96738e21			−0.708923			−0.354461	−	0.935071i	$-0.615336\pi$
$89$	−1.96738e21			−0.708923			−0.354461	+	0.935071i	$0.615336\pi$
$90$		0			0
$91$			3.92748e21i			1.10830i
$92$	−3.66590e21	−	2.23674e21i	−0.917306	−	0.559693i
$93$		0			0
$94$	−8.61668e20	−	1.53514e21i	−0.170190	−	0.303209i
$95$		−	4.22869e20i		−	0.0743441i
$96$		0			0
$97$	−3.08304e21			−0.431013			−0.215506	−	0.976502i	$-0.569140\pi$
$97$	−3.08304e21			−0.431013			−0.215506	+	0.976502i	$0.569140\pi$
$98$	1.22197e22	−	6.85887e21i	1.52607	−	0.856576i
$99$		0			0
$100$	4.08914e21	−	6.70187e21i	0.408914	−	0.670187i
$101$	−1.90013e21			−0.170313			−0.0851565	−	0.996368i	$-0.527139\pi$
$101$	−1.90013e21			−0.170313			−0.0851565	+	0.996368i	$0.527139\pi$
$102$		0			0
$103$		−	2.69990e22i		−	1.95046i	−0.221184	−	0.975232i	$-0.570992\pi$
$103$		−	2.69990e22i		−	1.95046i	0.221184	−	0.975232i	$-0.429008\pi$
$104$	3.74154e20	−	1.02818e22i	0.0243044	−	0.667886i
$105$		0			0
$106$	2.79459e22	−	1.56859e22i	1.47216	−	0.826315i
$107$		−	2.37790e22i		−	1.12973i	−0.825185	−	0.564863i	$-0.808929\pi$
$107$		−	2.37790e22i		−	1.12973i	0.825185	−	0.564863i	$-0.191071\pi$
$108$		0			0
$109$	−1.54276e22			−0.597872			−0.298936	−	0.954273i	$-0.596632\pi$
$109$	−1.54276e22			−0.597872			−0.298936	+	0.954273i	$0.596632\pi$
$110$	−1.50763e22	−	2.68599e22i	−0.528416	−	0.941422i
$111$		0			0
$112$	−5.12967e22	+	2.63870e22i	−1.47466	+	0.758562i
$113$	−4.91614e22			−1.28162			−0.640812	−	0.767697i	$-0.721402\pi$
$113$	−4.91614e22			−1.28162			−0.640812	+	0.767697i	$0.721402\pi$
$114$		0			0
$115$		−	6.67946e22i		−	1.43571i
$116$	−3.41650e22	+	5.59946e22i	−0.667642	+	1.09423i
$117$		0			0
$118$	7.84733e21	+	1.39807e22i	0.127063	+	0.226375i
$119$		−	6.80720e22i		−	1.00450i
$120$		0			0
$121$	2.82542e22			0.347091
$122$	−2.22018e22	+	1.24618e22i	−0.249132	+	0.139837i
$123$		0			0
$124$	−1.02356e23	−	6.24521e22i	−0.960446	−	0.586014i
$125$	−3.34274e22			−0.287139
$126$		0			0
$127$			1.68835e23i			1.21793i	0.793198	+	0.608964i	$0.208414\pi$
$127$			1.68835e23i			1.21793i	−0.793198	+	0.608964i	$0.791586\pi$
$128$	1.36804e23	−	6.41920e22i	0.905293	−	0.424787i
$129$		0			0
$130$	1.39548e23	−	7.83279e22i	0.778660	−	0.437058i
$131$		−	3.80646e22i		−	0.195226i	−0.995224	−	0.0976129i	$-0.968879\pi$
$131$		−	3.80646e22i		−	0.195226i	0.995224	−	0.0976129i	$-0.0311207\pi$
$132$		0			0
$133$	−2.12546e22			−0.0922754
$134$	−1.36940e23	−	2.43972e23i	−0.547493	−	0.975410i
$135$		0			0
$136$	−6.48493e21	+	1.78206e23i	−0.0220281	+	0.605335i
$137$	1.78768e23			0.560226			0.280113	−	0.959967i	$-0.409628\pi$
$137$	1.78768e23			0.560226			0.280113	+	0.959967i	$0.409628\pi$
$138$		0			0
$139$			3.00886e23i			0.803970i	0.915646	+	0.401985i	$0.131680\pi$
$139$			3.00886e23i			0.803970i	−0.915646	+	0.401985i	$0.868320\pi$
$140$	−7.65924e23	−	4.67327e23i	−1.89137	−	1.15402i
$141$		0			0
$142$	−2.01677e23	−	3.59306e23i	−0.426074	−	0.759090i
$143$		−	2.76129e23i		−	0.540028i
$144$		0			0
$145$	−1.02025e24			−1.71261
$146$	−4.60288e22	+	2.58358e22i	−0.0716389	+	0.0402106i
$147$		0			0
$148$	4.60393e23	−	7.54560e23i	0.616950	−	1.01115i
$149$	−1.60515e23			−0.199740			−0.0998701	−	0.995000i	$-0.531843\pi$
$149$	−1.60515e23			−0.199740			−0.0998701	+	0.995000i	$0.531843\pi$
$150$		0			0
$151$		−	1.36960e24i		−	1.47180i	−0.677091	−	0.735900i	$-0.736759\pi$
$151$		−	1.36960e24i		−	1.47180i	0.677091	−	0.735900i	$-0.263241\pi$
$152$	5.56428e22	+	2.02484e21i	0.0556070	+	0.00202354i
$153$		0			0
$154$	−1.35005e24	+	7.57780e23i	−1.16849	+	0.655866i
$155$		−	1.86497e24i		−	1.50323i
$156$		0			0
$157$	1.70659e24			1.19463			0.597315	−	0.802007i	$-0.296234\pi$
$157$	1.70659e24			1.19463			0.597315	+	0.802007i	$0.296234\pi$
$158$	8.29589e23	+	1.47799e24i	0.541545	+	0.964813i
$159$		0			0
$160$	1.96060e24	+	1.29639e24i	1.11447	+	0.736911i
$161$	−3.35729e24			−1.78199
$162$		0			0
$163$		−	2.89527e23i		−	0.134161i	−0.997748	−	0.0670805i	$-0.978632\pi$
$163$		−	2.89527e23i		−	0.134161i	0.997748	−	0.0670805i	$-0.0213684\pi$
$164$	1.21720e24	−	1.99492e24i	0.527324	−	0.864256i
$165$		0			0
$166$	−6.48151e23	−	1.15474e24i	−0.245747	−	0.437820i
$167$		−	6.70501e23i		−	0.237968i	−0.992896	−	0.118984i	$-0.962036\pi$
$167$		−	6.70501e23i		−	0.237968i	0.992896	−	0.118984i	$-0.0379637\pi$
$168$		0			0
$169$	−1.77723e24			−0.553338
$170$	−2.41868e24	+	1.35760e24i	−0.705734	+	0.396125i
$171$		0			0
$172$	−2.89092e24	−	1.76389e24i	−0.741691	−	0.452542i
$173$	−1.20344e24			−0.289680			−0.144840	−	0.989455i	$-0.546267\pi$
$173$	−1.20344e24			−0.289680			−0.144840	+	0.989455i	$0.546267\pi$
$174$		0			0
$175$		−	6.13769e24i		−	1.30193i
$176$	3.60652e24	−	1.85519e24i	0.718536	−	0.369614i
$177$		0			0
$178$	3.51356e24	−	1.97215e24i	0.618198	−	0.346992i
$179$			2.09363e24i			0.346351i	0.984891	+	0.173175i	$0.0554027\pi$
$179$			2.09363e24i			0.346351i	−0.984891	+	0.173175i	$0.944597\pi$
$180$		0			0
$181$	−6.07098e24			−0.888780			−0.444390	−	0.895833i	$-0.646580\pi$
$181$	−6.07098e24			−0.888780			−0.444390	+	0.895833i	$0.646580\pi$
$182$	−3.93699e24	−	7.01410e24i	−0.542474	−	0.966467i
$183$		0			0
$184$	8.78910e24	+	3.19835e23i	1.07386	+	0.0390778i
$185$	1.37485e25			1.58258
$186$		0			0
$187$			4.78594e24i			0.489451i
$188$	3.07772e24	+	1.87786e24i	0.296819	+	0.181104i
$189$		0			0
$190$	4.23893e23	+	7.55205e23i	0.0363887	+	0.0648298i
$191$			3.81076e24i			0.308777i	0.988010	+	0.154388i	$0.0493407\pi$
$191$			3.81076e24i			0.308777i	−0.988010	+	0.154388i	$0.950659\pi$
$192$		0			0
$193$	1.79870e24			0.129965			0.0649827	−	0.997886i	$-0.479301\pi$
$193$	1.79870e24			0.129965			0.0649827	+	0.997886i	$0.479301\pi$
$194$	5.50601e24	−	3.09050e24i	0.375853	−	0.210965i
$195$		0			0
$196$	−1.49478e25	+	2.44986e25i	−0.911506	+	1.49391i
$197$	−7.75126e24			−0.446934			−0.223467	−	0.974711i	$-0.571738\pi$
$197$	−7.75126e24			−0.446934			−0.223467	+	0.974711i	$0.571738\pi$
$198$		0			0
$199$			1.90298e25i			0.981860i	0.871199	+	0.490930i	$0.163343\pi$
$199$			1.90298e25i			0.981860i	−0.871199	+	0.490930i	$0.836657\pi$
$200$	−5.84712e23	+	1.60679e25i	−0.0285504	+	0.784568i
$201$		0			0
$202$	3.39345e24	−	1.90473e24i	0.148517	−	0.0833620i
$203$			5.12808e25i			2.12568i
$204$		0			0
$205$	3.63485e25			1.35268
$206$	2.70643e25	+	4.82176e25i	0.954681	+	1.70085i
$207$		0			0
$208$	9.63848e24	+	1.87374e25i	0.305712	+	0.594309i
$209$	1.49435e24			0.0449617
$210$		0			0
$211$			1.37490e25i			0.372532i	0.982499	+	0.186266i	$0.0596386\pi$
$211$			1.37490e25i			0.372532i	−0.982499	+	0.186266i	$0.940361\pi$
$212$	−3.41849e25	+	5.60272e25i	−0.879305	+	1.44113i
$213$		0			0
$214$	2.38366e25	+	4.24671e25i	0.552959	+	0.985147i
$215$		−	5.26741e25i		−	1.16085i
$216$		0			0
$217$	−9.37390e25			−1.86579
$218$	2.75523e25	−	1.54650e25i	0.521358	−	0.292636i
$219$		0			0
$220$	5.38498e25	+	3.28563e25i	0.921583	+	0.562302i
$221$	−2.48650e25			−0.404830
$222$		0			0
$223$		−	1.07103e26i		−	1.57923i	−0.613600	−	0.789617i	$-0.710279\pi$
$223$		−	1.07103e26i		−	1.57923i	0.613600	−	0.789617i	$-0.289721\pi$
$224$	6.51602e25	−	9.85455e25i	0.914648	−	1.38328i
$225$		0			0
$226$	8.77975e25	−	4.92804e25i	1.11761	−	0.627308i
$227$		−	1.17534e25i		−	0.142521i	−0.997458	−	0.0712607i	$-0.977298\pi$
$227$		−	1.17534e25i		−	0.142521i	0.997458	−	0.0712607i	$-0.0227022\pi$
$228$		0			0
$229$	−9.48445e25			−1.04429			−0.522146	−	0.852856i	$-0.674868\pi$
$229$	−9.48445e25			−1.04429			−0.522146	+	0.852856i	$0.674868\pi$
$230$	6.69563e25	+	1.19289e26i	0.702725	+	1.25197i
$231$		0			0
$232$	4.88531e24	−	1.34249e26i	0.0466148	−	1.28098i
$233$	8.11776e25			0.738790			0.369395	−	0.929273i	$-0.379565\pi$
$233$	8.11776e25			0.738790			0.369395	+	0.929273i	$0.379565\pi$
$234$		0			0
$235$			5.60776e25i			0.464562i
$236$	−2.80292e25	−	1.71020e25i	−0.221604	−	0.135212i
$237$		0			0
$238$	6.82367e25	+	1.21570e26i	0.491668	+	0.875952i
$239$		−	1.56047e25i		−	0.107369i	−0.998558	−	0.0536845i	$-0.982903\pi$
$239$		−	1.56047e25i		−	0.107369i	0.998558	−	0.0536845i	$-0.0170965\pi$
$240$		0			0
$241$	−1.58806e26			−0.996964			−0.498482	−	0.866900i	$-0.666109\pi$
$241$	−1.58806e26			−0.996964			−0.498482	+	0.866900i	$0.666109\pi$
$242$	−5.04593e25	+	2.83226e25i	−0.302672	+	0.169888i
$243$		0			0
$244$	2.71584e25	−	4.45111e25i	0.148804	−	0.243882i
$245$	−4.46378e26			−2.33817
$246$		0			0
$247$			7.76378e24i			0.0371883i
$248$	2.45401e26	+	8.93012e24i	1.12436	+	0.0409156i
$249$		0			0
$250$	5.96981e25	−	3.35083e25i	0.250392	−	0.140544i
$251$		−	1.35006e26i		−	0.541929i	−0.962589	−	0.270965i	$-0.912657\pi$
$251$		−	1.35006e26i		−	0.541929i	0.962589	−	0.270965i	$-0.0873426\pi$
$252$		0			0
$253$	2.36041e26			0.868284
$254$	−1.69244e26	−	3.01523e26i	−0.596131	−	1.06206i
$255$		0			0
$256$	−1.79972e26	+	2.51776e26i	−0.581520	+	0.813532i
$257$	4.06306e26			1.25773			0.628867	−	0.777513i	$-0.283519\pi$
$257$	4.06306e26			1.25773			0.628867	+	0.777513i	$0.283519\pi$
$258$		0			0
$259$		−	6.91039e26i		−	1.96429i
$260$	−1.70703e26	+	2.79772e26i	−0.465086	+	0.762251i
$261$		0			0
$262$	3.81568e25	+	6.79798e25i	0.0955559	+	0.170242i
$263$		−	4.30318e26i		−	1.03342i	−0.856161	−	0.516709i	$-0.827157\pi$
$263$		−	4.30318e26i		−	1.03342i	0.856161	−	0.516709i	$-0.172843\pi$
$264$		0			0
$265$	−1.02085e27			−2.25556
$266$	3.79588e25	−	2.13061e25i	0.0804663	−	0.0451654i
$267$		0			0
$268$	4.89125e26	+	2.98439e26i	0.954854	+	0.582603i
$269$	−4.75629e26			−0.891237			−0.445619	−	0.895223i	$-0.647016\pi$
$269$	−4.75629e26			−0.891237			−0.445619	+	0.895223i	$0.647016\pi$
$270$		0			0
$271$		−	9.39071e26i		−	1.62194i	−0.585085	−	0.810972i	$-0.698939\pi$
$271$		−	9.39071e26i		−	1.62194i	0.585085	−	0.810972i	$-0.301061\pi$
$272$	−1.67056e26	−	3.24760e26i	−0.277080	−	0.538648i
$273$		0			0
$274$	−3.19262e26	+	1.79201e26i	−0.488530	+	0.274210i
$275$			4.31523e26i			0.634372i
$276$		0			0
$277$	−5.11627e26			−0.694505			−0.347253	−	0.937772i	$-0.612885\pi$
$277$	−5.11627e26			−0.694505			−0.347253	+	0.937772i	$0.612885\pi$
$278$	−3.01615e26	−	5.37354e26i	−0.393514	−	0.701081i
$279$		0			0
$280$	1.83632e27	+	6.68238e25i	2.21417	+	0.0805736i
$281$	−1.13838e27			−1.31983			−0.659917	−	0.751339i	$-0.729408\pi$
$281$	−1.13838e27			−1.31983			−0.659917	+	0.751339i	$0.729408\pi$
$282$		0			0
$283$			1.28612e27i			1.37922i	0.724183	+	0.689608i	$0.242217\pi$
$283$			1.28612e27i			1.37922i	−0.724183	+	0.689608i	$0.757783\pi$
$284$	7.20352e26	+	4.39522e26i	0.743093	+	0.453397i
$285$		0			0
$286$	2.76798e26	+	4.93141e26i	0.264324	+	0.470917i
$287$		−	1.82698e27i		−	1.67893i
$288$		0			0
$289$	−7.43598e26			−0.633085
$290$	1.82207e27	−	1.02272e27i	1.49344	−	0.838261i
$291$		0			0
$292$	5.63048e25	−	9.22805e25i	0.0427892	−	0.0701292i
$293$	−2.23679e27			−1.63712			−0.818560	−	0.574421i	$-0.805227\pi$
$293$	−2.23679e27			−1.63712			−0.818560	+	0.574421i	$0.805227\pi$
$294$		0			0
$295$		−	5.10707e26i		−	0.346840i
$296$	−6.58324e25	+	1.80908e27i	−0.0430755	+	1.18372i
$297$		0			0
$298$	2.86664e26	−	1.60903e26i	0.174178	−	0.0977655i
$299$			1.22633e27i			0.718167i
$300$		0			0
$301$	−2.64756e27			−1.44083
$302$	1.37292e27	+	2.44598e27i	0.720392	+	1.28344i
$303$		0			0
$304$	−1.01403e26	+	5.21613e25i	−0.0494811	+	0.0254530i
$305$	8.11016e26			0.381708
$306$		0			0
$307$		−	2.10997e27i		−	0.924175i	−0.886834	−	0.462088i	$-0.847101\pi$
$307$		−	2.10997e27i		−	0.924175i	0.886834	−	0.462088i	$-0.152899\pi$
$308$	1.65146e27	−	2.70665e27i	0.697925	−	1.14386i
$309$		0			0
$310$	1.86949e27	+	3.33067e27i	0.735774	+	1.31085i
$311$		−	2.95432e27i		−	1.12226i	−0.827727	−	0.561130i	$-0.810367\pi$
$311$		−	2.95432e27i		−	1.12226i	0.827727	−	0.561130i	$-0.189633\pi$
$312$		0			0
$313$	−2.10744e26			−0.0746050			−0.0373025	−	0.999304i	$-0.511877\pi$
$313$	−2.10744e26			−0.0746050			−0.0373025	+	0.999304i	$0.511877\pi$
$314$	−3.04781e27	+	1.71072e27i	−1.04175	+	0.584727i
$315$		0			0
$316$	−2.96313e27	−	1.80795e27i	−0.944481	−	0.576274i
$317$	2.00178e27			0.616260			0.308130	−	0.951344i	$-0.400297\pi$
$317$	2.00178e27			0.616260			0.308130	+	0.951344i	$0.400297\pi$
$318$		0			0
$319$		−	3.60540e27i		−	1.03575i
$320$	−4.80097e27	−	3.49878e26i	−1.33254	−	0.0971106i
$321$		0			0
$322$	5.99580e27	−	3.36542e27i	1.55394	−	0.872217i
$323$		−	1.34564e26i		−	0.0337054i
$324$		0			0
$325$	−2.24194e27			−0.524696
$326$	2.90228e26	+	5.17069e26i	0.0656669	+	0.116992i
$327$		0			0
$328$	−1.74049e26	+	4.78287e27i	−0.0368178	+	1.01176i
$329$	2.81862e27			0.576610
$330$		0			0
$331$		−	9.42339e25i		−	0.0180343i	−0.999959	−	0.00901715i	$-0.997130\pi$
$331$		−	9.42339e25i		−	0.0180343i	0.999959	−	0.00901715i	$-0.00287029\pi$
$332$	2.31507e27	+	1.41254e27i	0.428594	+	0.261506i
$333$		0			0
$334$	6.72124e26	+	1.19745e27i	0.116476	+	0.207513i
$335$			8.91212e27i			1.49447i
$336$		0			0
$337$	5.66099e27			0.889126			0.444563	−	0.895748i	$-0.353359\pi$
$337$	5.66099e27			0.889126			0.444563	+	0.895748i	$0.353359\pi$
$338$	3.17397e27	−	1.78153e27i	0.482524	−	0.270838i
$339$		0			0
$340$	2.95866e27	−	4.84908e27i	0.421528	−	0.690862i
$341$	6.59051e27			0.909119
$342$		0			0
$343$			9.61576e27i			1.24379i
$344$	6.93107e27	+	2.52221e26i	0.868275	+	0.0315965i
$345$		0			0
$346$	2.14924e27	−	1.20636e27i	0.252608	−	0.141788i
$347$			4.71029e27i			0.536319i	0.963375	+	0.268159i	$0.0864154\pi$
$347$			4.71029e27i			0.536319i	−0.963375	+	0.268159i	$0.913585\pi$
$348$		0			0
$349$	−5.26090e27			−0.562315			−0.281158	−	0.959662i	$-0.590718\pi$
$349$	−5.26090e27			−0.562315			−0.281158	+	0.959662i	$0.590718\pi$
$350$	6.15255e27	+	1.09613e28i	0.637245	+	1.13531i
$351$		0			0
$352$	−4.58122e27	+	6.92844e27i	−0.445668	+	0.674009i
$353$	−1.91623e28			−1.80686			−0.903431	−	0.428733i	$-0.858960\pi$
$353$	−1.91623e28			−1.80686			−0.903431	+	0.428733i	$0.858960\pi$
$354$		0			0
$355$			1.31252e28i			1.16304i
$356$	−4.29797e27	+	7.04413e27i	−0.369244	+	0.605170i
$357$		0			0
$358$	−2.09870e27	−	3.73902e27i	−0.169526	−	0.302026i
$359$		−	1.89213e28i		−	1.48222i	−0.671384	−	0.741109i	$-0.734300\pi$
$359$		−	1.89213e28i		−	1.48222i	0.671384	−	0.741109i	$-0.265700\pi$
$360$		0			0
$361$	1.35280e28			0.996904
$362$	1.08422e28	−	6.08567e27i	0.775037	−	0.435025i
$363$		0			0
$364$	1.40622e28	+	8.58001e27i	0.946100	+	0.577261i
$365$	1.68140e27			0.109761
$366$		0			0
$367$		−	1.27013e28i		−	0.780766i	−0.920653	−	0.390383i	$-0.872343\pi$
$367$		−	1.27013e28i		−	0.780766i	0.920653	−	0.390383i	$-0.127657\pi$
$368$	−1.60171e28	+	8.23918e27i	−0.955560	+	0.491539i
$369$		0			0
$370$	−2.45535e28	+	1.37818e28i	−1.38005	+	0.774615i
$371$			5.13106e28i			2.79959i
$372$		0			0
$373$	−2.94227e28			−1.51316			−0.756582	−	0.653899i	$-0.773132\pi$
$373$	−2.94227e28			−1.51316			−0.756582	+	0.653899i	$0.773132\pi$
$374$	−4.79752e27	−	8.54723e27i	−0.239568	−	0.426813i
$375$		0			0
$376$	−7.37892e27	−	2.68519e26i	−0.347477	−	0.0126447i
$377$	1.87316e28			0.856682
$378$		0			0
$379$			8.36564e25i			0.00360967i	0.999998	+	0.00180484i	$0.000574498\pi$
$379$			8.36564e25i			0.00360967i	−0.999998	+	0.00180484i	$0.999426\pi$
$380$	−1.51407e27	−	9.23804e26i	−0.0634637	−	0.0387222i
$381$		0			0
$382$	−3.81998e27	−	6.80565e27i	−0.151135	−	0.269261i
$383$		−	3.20966e28i		−	1.23388i	−0.787011	−	0.616939i	$-0.788373\pi$
$383$		−	3.20966e28i		−	1.23388i	0.787011	−	0.616939i	$-0.211627\pi$
$384$		0			0
$385$	4.93166e28			1.79030
$386$	−3.21230e27	+	1.80305e27i	−0.113333	+	0.0636133i
$387$		0			0
$388$	−6.73523e27	+	1.10387e28i	−0.224493	+	0.367933i
$389$	1.31115e28			0.424820			0.212410	−	0.977181i	$-0.431869\pi$
$389$	1.31115e28			0.424820			0.212410	+	0.977181i	$0.431869\pi$
$390$		0			0
$391$		−	2.12551e28i		−	0.650906i
$392$	2.13741e27	−	5.87361e28i	0.0636415	−	1.74887i
$393$		0			0
$394$	1.38430e28	−	7.77002e27i	0.389737	−	0.218758i
$395$		−	5.39899e28i		−	1.47824i
$396$		0			0
$397$	4.02852e28			1.04340			0.521699	−	0.853130i	$-0.325298\pi$
$397$	4.02852e28			1.04340			0.521699	+	0.853130i	$0.325298\pi$
$398$	−1.90758e28	−	3.39853e28i	−0.480584	−	0.856205i
$399$		0			0
$400$	−1.50626e28	−	2.92820e28i	−0.359120	−	0.698136i
$401$	1.55924e27			0.0361679			0.0180840	−	0.999836i	$-0.494243\pi$
$401$	1.55924e27			0.0361679			0.0180840	+	0.999836i	$0.494243\pi$
$402$		0			0
$403$			3.42405e28i			0.751942i
$404$	−4.15104e27	+	6.80333e27i	−0.0887078	+	0.145387i
$405$		0			0
$406$	−5.14050e28	−	9.15827e28i	−1.04044	−	1.85365i
$407$			4.85849e28i			0.957112i
$408$		0			0
$409$	4.83341e28			0.902189			0.451095	−	0.892476i	$-0.351034\pi$
$409$	4.83341e28			0.902189			0.451095	+	0.892476i	$0.351034\pi$
$410$	−6.49149e28	+	3.64365e28i	−1.17957	+	0.662085i
$411$		0			0
$412$	−9.66687e28	−	5.89822e28i	−1.66501	−	1.01590i
$413$	−2.56696e28			−0.430496
$414$		0			0
$415$			4.21819e28i			0.670806i
$416$	−3.59962e28	−	2.38014e28i	−0.557480	−	0.368617i
$417$		0			0
$418$	−2.66877e27	+	1.49797e27i	−0.0392077	+	0.0220071i
$419$		−	2.67025e28i		−	0.382119i	−0.981578	−	0.191059i	$-0.938808\pi$
$419$		−	2.67025e28i		−	0.382119i	0.981578	−	0.191059i	$-0.0611923\pi$
$420$		0			0
$421$	−9.08309e28			−1.23348			−0.616738	−	0.787168i	$-0.711546\pi$
$421$	−9.08309e28			−1.23348			−0.616738	+	0.787168i	$0.711546\pi$
$422$	−1.37823e28	−	2.45544e28i	−0.182341	−	0.324857i
$423$		0			0
$424$	4.88815e27	−	1.34327e29i	0.0613932	−	1.68709i
$425$	3.88579e28			0.475555
$426$		0			0
$427$		−	4.07640e28i		−	0.473773i
$428$	−8.51398e28	−	5.19479e28i	−0.964387	−	0.588419i
$429$		0			0
$430$	5.28017e28	+	9.40710e28i	0.568191	+	1.01229i
$431$			1.37308e28i			0.144028i	0.997404	+	0.0720138i	$0.0229426\pi$
$431$			1.37308e28i			0.144028i	−0.997404	+	0.0720138i	$0.977057\pi$
$432$		0			0
$433$	1.64110e29			1.63595			0.817973	−	0.575256i	$-0.195098\pi$
$433$	1.64110e29			1.63595			0.817973	+	0.575256i	$0.195098\pi$
$434$	1.67409e29	−	9.39659e28i	1.62702	−	0.913237i
$435$		0			0
$436$	−3.37034e28	+	5.52380e28i	−0.311402	+	0.510372i
$437$	−6.63664e27			−0.0597933
$438$		0			0
$439$			4.23898e28i			0.363205i	0.983372	+	0.181602i	$0.0581284\pi$
$439$			4.23898e28i			0.363205i	−0.983372	+	0.181602i	$0.941872\pi$
$440$	−1.29106e29	−	4.69818e27i	−1.07887	−	0.0392600i
$441$		0			0
$442$	4.44064e28	−	2.49251e28i	0.353021	−	0.198149i
$443$		−	1.30441e29i		−	1.01152i	−0.862675	−	0.505758i	$-0.831213\pi$
$443$		−	1.30441e29i		−	1.01152i	0.862675	−	0.505758i	$-0.168787\pi$
$444$		0			0
$445$	−1.28348e29			−0.947172
$446$	1.07362e29	+	1.91275e29i	0.772977	+	1.37713i
$447$		0			0
$448$	−1.75859e28	+	2.41311e29i	−0.120533	+	1.65394i
$449$	1.82786e29			1.22246			0.611229	−	0.791454i	$-0.290675\pi$
$449$	1.82786e29			1.22246			0.611229	+	0.791454i	$0.290675\pi$
$450$		0			0
$451$			1.28449e29i			0.818070i
$452$	−1.07398e29	+	1.76020e29i	−0.667536	+	1.09406i
$453$		0			0
$454$	1.17819e28	+	2.09905e28i	0.0697590	+	0.124282i
$455$			2.56220e29i			1.48077i
$456$		0			0
$457$	1.35905e29			0.748441			0.374220	−	0.927340i	$-0.377910\pi$
$457$	1.35905e29			0.748441			0.374220	+	0.927340i	$0.377910\pi$
$458$	1.69383e29	−	9.50741e28i	0.910648	−	0.511143i
$459$		0			0
$460$	−2.39155e29	−	1.45920e29i	−1.22559	−	0.747789i
$461$	−1.93686e29			−0.969145			−0.484572	−	0.874751i	$-0.661025\pi$
$461$	−1.93686e29			−0.969145			−0.484572	+	0.874751i	$0.661025\pi$
$462$		0			0
$463$			4.24549e28i			0.202552i	0.994858	+	0.101276i	$0.0322926\pi$
$463$			4.24549e28i			0.202552i	−0.994858	+	0.101276i	$0.967707\pi$
$464$	1.25849e29	+	2.44653e29i	0.586343	+	1.13986i
$465$		0			0
$466$	−1.44975e29	+	8.13741e28i	−0.644242	+	0.361610i
$467$		−	9.50103e28i		−	0.412368i	−0.978513	−	0.206184i	$-0.933895\pi$
$467$		−	9.50103e28i		−	0.412368i	0.978513	−	0.206184i	$-0.0661045\pi$
$468$		0			0
$469$	4.47949e29			1.85493
$470$	−5.62134e28	−	1.00149e29i	−0.227386	−	0.405109i
$471$		0			0
$472$	6.72008e28	+	2.44544e27i	0.259425	+	0.00944048i
$473$	1.86142e29			0.702055
$474$		0			0
$475$		−	1.21329e28i		−	0.0436852i
$476$	−2.43729e29	−	1.48711e29i	−0.857492	−	0.523197i
$477$		0			0
$478$	1.56425e28	+	2.78685e28i	0.0525532	+	0.0936283i
$479$			1.57564e29i			0.517329i	0.965967	+	0.258664i	$0.0832824\pi$
$479$			1.57564e29i			0.517329i	−0.965967	+	0.258664i	$0.916718\pi$
$480$		0			0
$481$	−2.52419e29			−0.791637
$482$	2.83612e29	−	1.59190e29i	0.869376	−	0.487977i
$483$		0			0
$484$	6.17243e28	−	1.01163e29i	0.180783	−	0.296293i
$485$	−2.01131e29			−0.575864
$486$		0			0
$487$			5.04059e29i			1.37931i	0.724137	+	0.689656i	$0.242238\pi$
$487$			5.04059e29i			1.37931i	−0.724137	+	0.689656i	$0.757762\pi$
$488$	−3.88342e27	+	1.06717e29i	−0.0103895	+	0.285505i
$489$		0			0
$490$	7.97188e29	−	4.47458e29i	2.03894	−	1.14445i
$491$			7.75458e29i			1.93938i	0.244348	+	0.969688i	$0.421426\pi$
$491$			7.75458e29i			1.93938i	−0.244348	+	0.969688i	$0.578574\pi$
$492$		0			0
$493$	−3.24660e29			−0.776448
$494$	−7.78257e27	−	1.38654e28i	−0.0182023	−	0.0324291i
$495$		0			0
$496$	−4.47214e29	+	2.30046e29i	−1.00050	+	0.514656i
$497$	6.59711e29			1.44356
$498$		0			0
$499$		−	9.28584e29i		−	1.94408i	−0.234805	−	0.972042i	$-0.575445\pi$
$499$		−	9.28584e29i		−	1.94408i	0.234805	−	0.972042i	$-0.424555\pi$
$500$	−7.30258e28	+	1.19685e29i	−0.149557	+	0.245116i
$501$		0			0
$502$	1.35333e29	+	2.41108e29i	0.265254	+	0.472575i
$503$			5.16238e29i			0.989925i	0.868914	+	0.494963i	$0.164818\pi$
$503$			5.16238e29i			0.989925i	−0.868914	+	0.494963i	$0.835182\pi$
$504$		0			0
$505$	−1.23960e29			−0.227550
$506$	−4.21547e29	+	2.36613e29i	−0.757165	+	0.424993i
$507$		0			0
$508$	6.04506e29	+	3.68838e29i	1.03968	+	0.634359i
$509$	−4.57096e28			−0.0769328			−0.0384664	−	0.999260i	$-0.512247\pi$
$509$	−4.57096e28			−0.0769328			−0.0384664	+	0.999260i	$0.512247\pi$
$510$		0			0
$511$		−	8.45121e28i		−	0.136235i
$512$	6.90270e28	−	6.30055e29i	0.108905	−	0.994052i
$513$		0			0
$514$	−7.25624e29	+	4.07290e29i	−1.09677	+	0.615615i
$515$		−	1.76136e30i		−	2.60596i
$516$		0			0
$517$	−1.98169e29			−0.280957
$518$	6.92712e29	+	1.23413e30i	0.961447	+	1.71291i
$519$		0			0
$520$	2.44090e28	−	6.70763e29i	0.0324724	−	0.892344i
$521$	−8.14119e29			−1.06041			−0.530204	−	0.847870i	$-0.677885\pi$
$521$	−8.14119e29			−1.06041			−0.530204	+	0.847870i	$0.677885\pi$
$522$		0			0
$523$		−	1.37304e29i		−	0.171461i	−0.996318	−	0.0857303i	$-0.972678\pi$
$523$		−	1.37304e29i		−	0.171461i	0.996318	−	0.0857303i	$-0.0273224\pi$
$524$	−1.36289e29	−	8.31563e28i	−0.166654	−	0.101684i
$525$		0			0
$526$	4.31360e29	+	7.68507e29i	0.505820	+	0.901166i
$527$		−	5.93463e29i		−	0.681518i
$528$		0			0
$529$	−1.40449e29			−0.154706
$530$	1.82313e30	−	1.02332e30i	1.96691	−	1.10402i
$531$		0			0
$532$	−4.64331e28	+	7.61013e28i	−0.0480618	+	0.0787706i
$533$	−6.67349e29			−0.676634
$534$		0			0
$535$		−	1.55129e30i		−	1.50939i
$536$	−1.17269e30	−	4.26742e28i	−1.11782	−	0.0406774i
$537$		0			0
$538$	8.49428e29	−	4.76780e29i	0.777180	−	0.436228i
$539$		−	1.57742e30i		−	1.41407i
$540$		0			0
$541$	−7.37739e29			−0.634940			−0.317470	−	0.948268i	$-0.602833\pi$
$541$	−7.37739e29			−0.634940			−0.317470	+	0.948268i	$0.602833\pi$
$542$	9.41344e29	+	1.67709e30i	0.793882	+	1.41437i
$543$		0			0
$544$	6.23894e29	+	4.12531e29i	0.505269	+	0.334094i
$545$	−1.00647e30			−0.798799
$546$		0			0
$547$			5.34377e29i			0.407368i	0.979037	+	0.203684i	$0.0652915\pi$
$547$			5.34377e29i			0.407368i	−0.979037	+	0.203684i	$0.934708\pi$
$548$	3.90538e29	−	6.40070e29i	0.291794	−	0.478235i
$549$		0			0
$550$	−4.32567e29	−	7.70659e29i	−0.310502	−	0.553188i
$551$			1.01371e29i			0.0713258i
$552$		0			0
$553$	−2.71369e30			−1.83478
$554$	9.13717e29	−	5.12865e29i	0.605625	−	0.339935i
$555$		0			0
$556$	1.07731e30	+	6.57319e29i	0.686306	+	0.418749i
$557$	−1.04477e30			−0.652552			−0.326276	−	0.945275i	$-0.605794\pi$
$557$	−1.04477e30			−0.652552			−0.326276	+	0.945275i	$0.605794\pi$
$558$		0			0
$559$			9.67084e29i			0.580677i
$560$	−3.34649e30	+	1.72143e30i	−1.97025	+	1.01349i
$561$		0			0
$562$	2.03304e30	−	1.14114e30i	1.15093	−	0.646010i
$563$			3.25171e30i			1.80518i	0.430506	+	0.902588i	$0.358335\pi$
$563$			3.25171e30i			1.80518i	−0.430506	+	0.902588i	$0.641665\pi$
$564$		0			0
$565$	−3.20718e30			−1.71234
$566$	−1.28924e30	−	2.29690e30i	−0.675075	−	1.20271i
$567$		0			0
$568$	−1.72707e30	−	6.28479e28i	−0.869916	−	0.0316562i
$569$	4.71831e28			0.0233105			0.0116552	−	0.999932i	$-0.496290\pi$
$569$	4.71831e28			0.0233105			0.0116552	+	0.999932i	$0.496290\pi$
$570$		0			0
$571$			2.23338e30i			1.06161i	0.847494	+	0.530805i	$0.178110\pi$
$571$			2.23338e30i			1.06161i	−0.847494	+	0.530805i	$0.821890\pi$
$572$	−9.88669e29	−	6.03235e29i	−0.460993	−	0.281274i
$573$		0			0
$574$	1.83140e30	+	3.26281e30i	0.821775	+	1.46407i
$575$		−	1.91646e30i		−	0.843633i
$576$		0			0
$577$	4.12783e30			1.74899			0.874496	−	0.485033i	$-0.161192\pi$
$577$	4.12783e30			1.74899			0.874496	+	0.485033i	$0.161192\pi$
$578$	1.32800e30	−	7.45398e29i	0.552065	−	0.309872i
$579$		0			0
$580$	−2.22885e30	+	3.65297e30i	−0.892017	+	1.46197i
$581$	2.12018e30			0.832600
$582$		0			0
$583$		−	3.60750e30i		−	1.36412i
$584$	−8.05111e27	+	2.21245e29i	−0.00298755	+	0.0820981i
$585$		0			0
$586$	3.99469e30	−	2.24220e30i	1.42761	−	0.801310i
$587$		−	9.89293e29i		−	0.346981i	−0.984836	−	0.173491i	$-0.944495\pi$
$587$		−	9.89293e29i		−	0.346981i	0.984836	−	0.173491i	$-0.0555046\pi$
$588$		0			0
$589$	−1.85302e29			−0.0626053
$590$	5.11943e29	+	9.12074e29i	0.169766	+	0.302453i
$591$		0			0
$592$	−1.69589e30	−	3.29684e30i	−0.541824	−	1.05332i
$593$	−9.95491e29			−0.312202			−0.156101	−	0.987741i	$-0.549893\pi$
$593$	−9.95491e29			−0.312202			−0.156101	+	0.987741i	$0.549893\pi$
$594$		0			0
$595$		−	4.44087e30i		−	1.34209i
$596$	−3.50662e29	+	5.74716e29i	−0.104035	+	0.170508i
$597$		0			0
$598$	−1.22930e30	−	2.19011e30i	−0.351516	−	0.626259i
$599$		−	3.75250e30i		−	1.05348i	−0.850027	−	0.526739i	$-0.823414\pi$
$599$		−	3.75250e30i		−	1.05348i	0.850027	−	0.526739i	$-0.176586\pi$
$600$		0			0
$601$	1.84318e30			0.498825			0.249413	−	0.968397i	$-0.419762\pi$
$601$	1.84318e30			0.498825			0.249413	+	0.968397i	$0.419762\pi$
$602$	4.72828e30	−	2.65396e30i	1.25644	−	0.705235i
$603$		0			0
$604$	−4.90381e30	−	2.99205e30i	−1.25640	−	0.766589i
$605$	1.84324e30			0.463739
$606$		0			0
$607$		−	2.22364e30i		−	0.539497i	−0.962931	−	0.269748i	$-0.913059\pi$
$607$		−	2.22364e30i		−	0.539497i	0.962931	−	0.269748i	$-0.0869405\pi$
$608$	1.28808e29	−	1.94803e29i	0.0306904	−	0.0464148i
$609$		0			0
$610$	−1.44840e30	+	8.12980e29i	−0.332859	+	0.186832i
$611$		−	1.02957e30i		−	0.232382i
$612$		0			0
$613$	1.39971e29			0.0304771			0.0152386	−	0.999884i	$-0.495149\pi$
$613$	1.39971e29			0.0304771			0.0152386	+	0.999884i	$0.495149\pi$
$614$	2.11508e30	+	3.76821e30i	0.452350	+	0.805903i
$615$		0			0
$616$	−2.36144e29	+	6.48927e30i	−0.0487292	+	1.33908i
$617$	−8.02739e30			−1.62719			−0.813593	−	0.581434i	$-0.802492\pi$
$617$	−8.02739e30			−1.62719			−0.813593	+	0.581434i	$0.802492\pi$
$618$		0			0
$619$			3.49783e30i			0.684229i	0.939658	+	0.342114i	$0.111143\pi$
$619$			3.49783e30i			0.684229i	−0.939658	+	0.342114i	$0.888857\pi$
$620$	−6.67746e30	−	4.07424e30i	−1.28322	−	0.782957i
$621$		0			0
$622$	2.96148e30	+	5.27614e30i	0.549305	+	0.978638i
$623$			6.45114e30i			1.17562i
$624$		0			0
$625$	−6.64343e30			−1.16873
$626$	3.76369e29	−	2.11254e29i	0.0650573	−	0.0365164i
$627$		0			0
$628$	3.72823e30	−	6.11037e30i	0.622225	−	1.01979i
$629$	4.37498e30			0.717495
$630$		0			0
$631$			9.52513e28i			0.0150851i	0.999972	+	0.00754254i	$0.00240089\pi$
$631$			9.52513e28i			0.0150851i	−0.999972	+	0.00754254i	$0.997599\pi$
$632$	7.10420e30	+	2.58522e29i	1.10567	+	0.0402355i
$633$		0			0
$634$	−3.57498e30	+	2.00662e30i	−0.537393	+	0.301636i
$635$			1.10144e31i			1.62724i
$636$		0			0
$637$	8.19538e30			1.16960
$638$	3.61413e30	+	6.43890e30i	0.506963	+	0.903201i
$639$		0			0
$640$	8.92481e30	−	4.18775e30i	1.20954	−	0.567545i
$641$	8.21339e30			1.09417			0.547084	−	0.837077i	$-0.315738\pi$
$641$	8.21339e30			1.09417			0.547084	+	0.837077i	$0.315738\pi$
$642$		0			0
$643$			1.43951e31i			1.85308i	0.376201	+	0.926538i	$0.377230\pi$
$643$			1.43951e31i			1.85308i	−0.376201	+	0.926538i	$0.622770\pi$
$644$	−7.33437e30	+	1.20206e31i	−0.928150	+	1.52119i
$645$		0			0
$646$	1.34889e29	+	2.40318e29i	0.0164976	+	0.0293919i
$647$		−	4.12645e30i		−	0.496169i	−0.968738	−	0.248084i	$-0.920199\pi$
$647$		−	4.12645e30i		−	0.496169i	0.968738	−	0.248084i	$-0.0798010\pi$
$648$		0			0
$649$	1.80475e30			0.209762
$650$	4.00390e30	−	2.24737e30i	0.457547	−	0.256819i
$651$		0			0
$652$	−1.03664e30	−	6.32504e29i	−0.114526	−	0.0698779i
$653$	7.02751e30			0.763408			0.381704	−	0.924285i	$-0.375337\pi$
$653$	7.02751e30			0.763408			0.381704	+	0.924285i	$0.375337\pi$
$654$		0			0
$655$		−	2.48325e30i		−	0.260836i
$656$	−4.48362e30	−	8.71623e30i	−0.463112	−	0.900298i
$657$		0			0
$658$	−5.03380e30	+	2.82545e30i	−0.502818	+	0.282230i
$659$			1.07907e31i			1.06001i	0.847994	+	0.530006i	$0.177810\pi$
$659$			1.07907e31i			1.06001i	−0.847994	+	0.530006i	$0.822190\pi$
$660$		0			0
$661$	1.30479e31			1.23973			0.619863	−	0.784710i	$-0.287188\pi$
$661$	1.30479e31			1.23973			0.619863	+	0.784710i	$0.287188\pi$
$662$	9.44620e28	+	1.68293e29i	0.00882713	+	0.0157263i
$663$		0			0
$664$	−5.55046e30	−	2.01981e29i	−0.501742	−	0.0182584i
$665$	−1.38661e30			−0.123286
$666$		0			0
$667$			1.60121e31i			1.37742i
$668$	−2.40070e30	−	1.46478e30i	−0.203140	−	0.123946i
$669$		0			0
$670$	−8.93370e30	−	1.59162e31i	−0.731490	−	1.30322i
$671$			2.86600e30i			0.230849i
$672$		0			0
$673$	6.04617e30			0.471319			0.235659	−	0.971836i	$-0.424275\pi$
$673$	6.04617e30			0.471319			0.235659	+	0.971836i	$0.424275\pi$
$674$	−1.01100e31	+	5.67469e30i	−0.775339	+	0.435195i
$675$		0			0
$676$	−3.88256e30	+	6.36330e30i	−0.288207	+	0.472355i
$677$	−6.59036e30			−0.481320			−0.240660	−	0.970609i	$-0.577364\pi$
$677$	−6.59036e30			−0.481320			−0.240660	+	0.970609i	$0.577364\pi$
$678$		0			0
$679$			1.01094e31i			0.714758i
$680$	−4.23063e29	+	1.16258e31i	−0.0294311	+	0.808770i
$681$		0			0
$682$	−1.17700e31	+	6.60646e30i	−0.792773	+	0.444980i
$683$		−	2.51024e31i		−	1.66375i	−0.554965	−	0.831874i	$-0.687268\pi$
$683$		−	2.51024e31i		−	1.66375i	0.554965	−	0.831874i	$-0.312732\pi$
$684$		0			0
$685$	1.16624e31			0.748501
$686$	−9.63904e30	−	1.71728e31i	−0.608791	−	1.08462i
$687$		0			0
$688$	−1.26311e31	+	6.49740e30i	−0.772622	+	0.397436i
$689$	1.87425e31			1.12828
$690$		0			0
$691$		−	1.46330e31i		−	0.853250i	−0.904429	−	0.426625i	$-0.859702\pi$
$691$		−	1.46330e31i		−	0.853250i	0.904429	−	0.426625i	$-0.140298\pi$
$692$	−2.62905e30	+	4.30888e30i	−0.150880	+	0.247285i
$693$		0			0
$694$	−4.72169e30	−	8.41213e30i	−0.262508	−	0.467683i
$695$			1.96292e31i			1.07416i
$696$		0			0
$697$	1.15666e31			0.613263
$698$	9.39546e30	−	5.27363e30i	0.490353	−	0.275233i
$699$		0			0
$700$	−2.19757e31	−	1.34085e31i	−1.11139	−	0.678111i
$701$	3.75758e31			1.87073			0.935363	−	0.353689i	$-0.115073\pi$
$701$	3.75758e31			1.87073			0.935363	+	0.353689i	$0.115073\pi$
$702$		0			0
$703$		−	1.36603e30i		−	0.0659103i
$704$	1.23641e30	−	1.69658e31i	0.0587304	−	0.805891i
$705$		0			0
$706$	3.42220e31	−	1.92087e31i	1.57563	−	0.884393i
$707$			6.23060e30i			0.282434i
$708$		0			0
$709$	1.52222e31			0.668914			0.334457	−	0.942411i	$-0.391447\pi$
$709$	1.52222e31			0.668914			0.334457	+	0.942411i	$0.391447\pi$
$710$	−1.31570e31	−	2.34404e31i	−0.569265	−	1.01420i
$711$		0			0
$712$	6.14573e29	−	1.68885e31i	0.0257806	−	0.708454i
$713$	−2.92695e31			−1.20901
$714$		0			0
$715$		−	1.80141e31i		−	0.721516i
$716$	7.49614e30	+	4.57376e30i	0.295661	+	0.180397i
$717$		0			0
$718$	1.89671e31	+	3.37917e31i	0.725492	+	1.29253i
$719$		−	3.45942e31i		−	1.30312i	−0.758595	−	0.651562i	$-0.774114\pi$
$719$		−	3.45942e31i		−	1.30312i	0.758595	−	0.651562i	$-0.225886\pi$
$720$		0			0
$721$	−8.85309e31			−3.23450
$722$	−2.41597e31	+	1.35607e31i	−0.869324	+	0.487948i
$723$		0			0
$724$	−1.32627e31	+	2.17369e31i	−0.462922	+	0.758705i
$725$	−2.92729e31			−1.00635
$726$		0			0
$727$			4.78687e31i			1.59652i	0.602316	+	0.798258i	$0.294245\pi$
$727$			4.78687e31i			1.59652i	−0.602316	+	0.798258i	$0.705755\pi$
$728$	−3.37145e31	−	1.22687e30i	−1.10757	−	0.0403044i
$729$		0			0
$730$	−3.00282e30	+	1.68547e30i	−0.0957146	+	0.0537242i
$731$		−	1.67617e31i		−	0.526293i
$732$		0			0
$733$	6.29217e31			1.91715			0.958577	−	0.284835i	$-0.0919387\pi$
$733$	6.29217e31			1.91715			0.958577	+	0.284835i	$0.0919387\pi$
$734$	1.27320e31	+	2.26833e31i	0.382156	+	0.680846i
$735$		0			0
$736$	2.03459e31	−	3.07703e31i	0.592681	−	0.896345i
$737$	−3.14940e31			−0.903826
$738$		0			0
$739$		−	4.80915e31i		−	1.33961i	−0.742535	−	0.669807i	$-0.766377\pi$
$739$		−	4.80915e31i		−	1.33961i	0.742535	−	0.669807i	$-0.233623\pi$
$740$	3.00351e31	−	4.92259e31i	0.824290	−	1.35097i
$741$		0			0
$742$	−5.14348e31	−	9.16359e31i	−1.37030	−	2.44131i
$743$			4.82491e31i			1.26652i	0.773939	+	0.633260i	$0.218284\pi$
$743$			4.82491e31i			1.26652i	−0.773939	+	0.633260i	$0.781716\pi$
$744$		0			0
$745$	−1.04716e31			−0.266867
$746$	5.25462e31	−	2.94940e31i	1.31951	−	0.740638i
$747$		0			0
$748$	1.71358e31	+	1.04554e31i	0.417818	+	0.254931i
$749$	−7.79725e31			−1.87345
$750$		0			0
$751$		−	7.60469e31i		−	1.77436i	−0.461422	−	0.887181i	$-0.652661\pi$
$751$		−	7.60469e31i		−	1.77436i	0.461422	−	0.887181i	$-0.347339\pi$
$752$	1.34472e31	−	6.91723e30i	0.309197	−	0.159051i
$753$		0			0
$754$	−3.34528e31	+	1.87769e31i	−0.747047	+	0.419314i
$755$		−	8.93500e31i		−	1.96643i
$756$		0			0
$757$	−2.48369e31			−0.530936			−0.265468	−	0.964120i	$-0.585527\pi$
$757$	−2.48369e31			−0.530936			−0.265468	+	0.964120i	$0.585527\pi$
$758$	−8.38589e28	−	1.49402e29i	−0.00176680	−	0.00314772i
$759$		0			0
$760$	3.63002e30	+	1.32096e29i	0.0742949	+	0.00270359i
$761$	8.17239e31			1.64861			0.824305	−	0.566146i	$-0.191566\pi$
$761$	8.17239e31			1.64861			0.824305	+	0.566146i	$0.191566\pi$
$762$		0			0
$763$			5.05879e31i			0.991464i
$764$	1.36443e31	+	8.32502e30i	0.263586	+	0.160827i
$765$		0			0
$766$	3.21743e31	+	5.73214e31i	0.603938	+	1.07597i
$767$			9.37645e30i			0.173496i
$768$		0			0
$769$	7.16587e31			1.28848			0.644242	−	0.764821i	$-0.277173\pi$
$769$	7.16587e31			1.28848			0.644242	+	0.764821i	$0.277173\pi$
$770$	−8.80747e31	+	4.94359e31i	−1.56118	+	0.876284i
$771$		0			0
$772$	3.92945e30	−	6.44016e30i	0.0676927	−	0.110945i
$773$	2.38900e31			0.405734			0.202867	−	0.979206i	$-0.434974\pi$
$773$	2.38900e31			0.405734			0.202867	+	0.979206i	$0.434974\pi$
$774$		0			0
$775$		−	5.35095e31i		−	0.883308i
$776$	9.63082e29	−	2.64656e31i	0.0156742	−	0.430727i
$777$		0			0
$778$	−2.34158e31	+	1.31432e31i	−0.370454	+	0.207934i
$779$		−	3.61154e30i		−	0.0563353i
$780$		0			0
$781$	−4.63823e31			−0.703382
$782$	2.13065e31	+	3.79596e31i	0.318595	+	0.567606i
$783$		0			0
$784$	5.50611e31	+	1.07040e32i	0.800513	+	1.55621i
$785$	1.11334e32			1.59611
$786$		0			0
$787$			1.19967e32i			1.67240i	0.548426	+	0.836199i	$0.315227\pi$
$787$			1.19967e32i			1.67240i	−0.548426	+	0.836199i	$0.684773\pi$
$788$	−1.69335e31	+	2.77530e31i	−0.232786	+	0.381524i
$789$		0			0
$790$	5.41206e31	+	9.64208e31i	0.723543	+	1.28906i
$791$			1.61202e32i			2.12535i
$792$		0			0
$793$	−1.48901e31			−0.190938
$794$	−7.19456e31	+	4.03827e31i	−0.909868	+	0.510705i
$795$		0			0
$796$	6.81352e31	+	4.15726e31i	0.838162	+	0.511403i
$797$	−6.78264e31			−0.822919			−0.411460	−	0.911428i	$-0.634981\pi$
$797$	−6.78264e31			−0.822919			−0.411460	+	0.911428i	$0.634981\pi$
$798$		0			0
$799$			1.78448e31i			0.210618i
$800$	5.62532e31	+	3.71957e31i	0.654874	+	0.433015i
$801$		0			0
$802$	−2.78465e30	+	1.56301e30i	−0.0315393	+	0.0177029i
$803$			5.94179e30i			0.0663814i
$804$		0			0
$805$	−2.19023e32			−2.38086
$806$	−3.43233e31	−	6.11502e31i	−0.368048	−	0.655711i
$807$		0			0
$808$	5.93563e29	−	1.63112e31i	0.00619359	−	0.170200i
$809$	−1.23186e32			−1.26803			−0.634013	−	0.773322i	$-0.718594\pi$
$809$	−1.23186e32			−1.26803			−0.634013	+	0.773322i	$0.718594\pi$
$810$		0			0
$811$		−	5.06028e31i		−	0.506927i	−0.967345	−	0.253463i	$-0.918430\pi$
$811$		−	5.06028e31i		−	0.506927i	0.967345	−	0.253463i	$-0.0815697\pi$
$812$	1.83609e32	+	1.12029e32i	1.81458	+	1.10717i
$813$		0			0
$814$	−4.87025e31	−	8.67680e31i	−0.468471	−	0.834624i
$815$		−	1.88882e31i		−	0.179249i
$816$		0			0
$817$	−5.23365e30			−0.0483461
$818$	−8.63202e31	+	4.84511e31i	−0.786731	+	0.441588i
$819$		0			0
$820$	7.94072e31	−	1.30144e32i	0.704543	−	1.15471i
$821$	1.58714e32			1.38944			0.694721	−	0.719279i	$-0.255528\pi$
$821$	1.58714e32			1.38944			0.694721	+	0.719279i	$0.255528\pi$
$822$		0			0
$823$			6.75406e31i			0.575661i	0.957681	+	0.287830i	$0.0929339\pi$
$823$			6.75406e31i			0.575661i	−0.957681	+	0.287830i	$0.907066\pi$
$824$	2.31766e32	+	8.43396e30i	1.94917	+	0.0709304i
$825$		0			0
$826$	4.58435e31	−	2.57317e31i	0.375402	−	0.210712i
$827$			4.05763e31i			0.327878i	0.986471	+	0.163939i	$0.0524200\pi$
$827$			4.05763e31i			0.327878i	−0.986471	+	0.163939i	$0.947580\pi$
$828$		0			0
$829$	2.34323e31			0.184381			0.0921905	−	0.995741i	$-0.470613\pi$
$829$	2.34323e31			0.184381			0.0921905	+	0.995741i	$0.470613\pi$
$830$	−4.22840e31	−	7.53329e31i	−0.328335	−	0.584959i
$831$		0			0
$832$	8.81447e31	+	6.42367e30i	0.666560	+	0.0485766i
$833$	−1.42044e32			−1.06006
$834$		0			0
$835$		−	4.37420e31i		−	0.317942i
$836$	3.26457e30	−	5.35046e30i	0.0234184	−	0.0383815i
$837$		0			0
$838$	2.67672e31	+	4.76882e31i	0.187033	+	0.333217i
$839$		−	2.15473e32i		−	1.48597i	−0.669305	−	0.742987i	$-0.733408\pi$
$839$		−	2.15473e32i		−	1.48597i	0.669305	−	0.742987i	$-0.266592\pi$
$840$		0			0
$841$	9.57244e31			0.643082
$842$	1.62215e32	−	9.10508e31i	1.07562	−	0.603741i
$843$		0			0
$844$	4.92276e31	+	3.00361e31i	0.318011	+	0.194034i
$845$	−1.15943e32			−0.739298
$846$		0			0
$847$		−	9.26467e31i		−	0.575589i
$848$	1.25922e32	+	2.44795e32i	0.772232	+	1.50123i
$849$		0			0
$850$	−6.93964e31	+	3.89519e31i	−0.414695	+	0.232767i
$851$		−	2.15773e32i		−	1.27283i
$852$		0			0
$853$	−1.86518e32			−1.07221			−0.536107	−	0.844150i	$-0.680106\pi$
$853$	−1.86518e32			−1.07221			−0.536107	+	0.844150i	$0.680106\pi$
$854$	4.08627e31	+	7.28007e31i	0.231895	+	0.413142i
$855$		0			0
$856$	2.04125e32	+	7.42811e30i	1.12898	+	0.0410835i
$857$	−1.54711e32			−0.844757			−0.422378	−	0.906420i	$-0.638805\pi$
$857$	−1.54711e32			−0.844757			−0.422378	+	0.906420i	$0.638805\pi$
$858$		0			0
$859$		−	2.79101e32i		−	1.48538i	−0.669636	−	0.742689i	$-0.733550\pi$
$859$		−	2.79101e32i		−	1.48538i	0.669636	−	0.742689i	$-0.266450\pi$
$860$	−1.88597e32	−	1.15072e32i	−0.990953	−	0.604628i
$861$		0			0
$862$	−1.37640e31	−	2.45219e31i	−0.0704962	−	0.125595i
$863$			2.40407e32i			1.21570i	0.794050	+	0.607852i	$0.207969\pi$
$863$			2.40407e32i			1.21570i	−0.794050	+	0.607852i	$0.792031\pi$
$864$		0			0
$865$	−7.85101e31			−0.387033
$866$	−2.93085e32	+	1.64508e32i	−1.42658	+	0.800736i
$867$		0			0
$868$	−2.04783e32	+	3.35628e32i	−0.971800	+	1.59273i
$869$	1.90791e32			0.894007
$870$		0			0
$871$		−	1.63624e32i		−	0.747564i
$872$	4.81930e30	−	1.32435e32i	0.0217421	−	0.597476i
$873$		0			0
$874$	1.18524e31	−	6.65271e30i	0.0521412	−	0.0292666i
$875$			1.09610e32i			0.476169i
$876$		0			0
$877$	−9.86957e31			−0.418122			−0.209061	−	0.977903i	$-0.567041\pi$
$877$	−9.86957e31			−0.418122			−0.209061	+	0.977903i	$0.567041\pi$
$878$	−4.24924e31	−	7.57041e31i	−0.177775	−	0.316723i
$879$		0			0
$880$	2.35281e32	−	1.21029e32i	0.960016	−	0.493831i
$881$	2.75102e32			1.10856			0.554279	−	0.832331i	$-0.312994\pi$
$881$	2.75102e32			1.10856			0.554279	+	0.832331i	$0.312994\pi$
$882$		0			0
$883$			1.84640e31i			0.0725703i	0.999341	+	0.0362851i	$0.0115525\pi$
$883$			1.84640e31i			0.0725703i	−0.999341	+	0.0362851i	$0.988448\pi$
$884$	−5.43202e31	+	8.90279e31i	−0.210856	+	0.345582i
$885$		0			0
$886$	1.30757e32	+	2.32955e32i	0.495100	+	0.882066i
$887$		−	1.64137e32i		−	0.613830i	−0.951737	−	0.306915i	$-0.900703\pi$
$887$		−	1.64137e32i		−	0.613830i	0.951737	−	0.306915i	$-0.0992967\pi$
$888$		0			0
$889$	5.53617e32			2.01972
$890$	2.29217e32	−	1.28659e32i	0.825956	−	0.463606i
$891$		0			0
$892$	−3.83476e32	−	2.33977e32i	−1.34811	−	0.822546i
$893$	5.57181e30			0.0193478
$894$		0			0
$895$			1.36584e32i			0.462749i
$896$	−2.10488e32	−	4.48587e32i	−0.704433	−	1.50127i
$897$		0			0
$898$	−3.26439e32	+	1.83229e32i	−1.06601	+	0.598349i
$899$			4.47075e32i			1.44220i
$900$		0			0
$901$	−3.24849e32			−1.02261
$902$	−1.28760e32	−	2.29398e32i	−0.400415	−	0.713376i
$903$		0			0
$904$	1.53571e31	−	4.22013e32i	0.0466074	−	1.28078i
$905$	−3.96058e32			−1.18747
$906$		0			0
$907$			6.26471e32i			1.83324i	0.399754	+	0.916622i	$0.369096\pi$
$907$			6.26471e32i			1.83324i	−0.399754	+	0.916622i	$0.630904\pi$
$908$	−4.20826e31	−	2.56766e31i	−0.121663	−	0.0742325i
$909$		0			0
$910$	−2.56841e32	−	4.57585e32i	−0.724784	−	1.29127i
$911$		−	4.63208e32i		−	1.29144i	−0.763575	−	0.645719i	$-0.776558\pi$
$911$		−	4.63208e32i		−	1.29144i	0.763575	−	0.645719i	$-0.223442\pi$
$912$		0			0
$913$	−1.49064e32			−0.405689
$914$	−2.42714e32	+	1.36234e32i	−0.652658	+	0.366334i
$915$		0			0
$916$	−2.07198e32	+	3.39587e32i	−0.543921	+	0.891457i
$917$	−1.24816e32			−0.323747
$918$		0			0
$919$			1.22010e32i			0.308977i	0.987995	+	0.154489i	$0.0493730\pi$
$919$			1.22010e32i			0.308977i	−0.987995	+	0.154489i	$0.950627\pi$
$920$	5.73382e32	+	2.08654e31i	1.43476	+	0.0522107i
$921$		0			0
$922$	3.45905e32	−	1.94155e32i	0.845117	−	0.474361i
$923$		−	2.40976e32i		−	0.581774i
$924$		0			0
$925$	3.94469e32			0.929938
$926$	−4.25577e31	−	7.58204e31i	−0.0991419	−	0.176630i
$927$		0			0
$928$	−4.69999e32	−	3.10773e32i	−1.06923	−	0.706993i
$929$	3.74937e32			0.842918			0.421459	−	0.906847i	$-0.361518\pi$
$929$	3.74937e32			0.842918			0.421459	+	0.906847i	$0.361518\pi$
$930$		0			0
$931$			4.43516e31i			0.0973784i
$932$	1.77341e32	−	2.90653e32i	0.384800	−	0.630666i
$933$		0			0
$934$	9.52402e31	+	1.69679e32i	0.201839	+	0.359595i
$935$			3.12224e32i			0.653941i
$936$		0			0
$937$	5.17088e32			1.05786			0.528931	−	0.848665i	$-0.322593\pi$
$937$	5.17088e32			1.05786			0.528931	+	0.848665i	$0.322593\pi$
$938$	−7.99995e32	+	4.49034e32i	−1.61754	+	0.907920i
$939$		0			0
$940$	2.00784e32	+	1.22508e32i	0.396572	+	0.241968i
$941$	−3.96797e32			−0.774610			−0.387305	−	0.921952i	$-0.626594\pi$
$941$	−3.96797e32			−0.774610			−0.387305	+	0.921952i	$0.626594\pi$
$942$		0			0
$943$		−	5.70464e32i		−	1.08793i
$944$	−1.22466e32	+	6.29962e31i	−0.230846	+	0.118747i
$945$		0			0
$946$	−3.32431e32	+	1.86592e32i	−0.612209	+	0.343630i
$947$			7.69103e31i			0.140002i	0.997547	+	0.0700011i	$0.0223003\pi$
$947$			7.69103e31i			0.140002i	−0.997547	+	0.0700011i	$0.977700\pi$
$948$		0			0
$949$	−3.08701e31			−0.0549048
$950$	1.21623e31	+	2.16682e31i	0.0213823	+	0.0380946i
$951$		0			0
$952$	5.84347e32	+	2.12644e31i	1.00384	+	0.0365297i
$953$	3.98077e32			0.675997			0.337999	−	0.941147i	$-0.390250\pi$
$953$	3.98077e32			0.675997			0.337999	+	0.941147i	$0.390250\pi$
$954$		0			0
$955$			2.48606e32i			0.412548i
$956$	−5.58720e31	−	3.40902e31i	−0.0916552	−	0.0559233i
$957$		0			0
$958$	−1.57946e32	−	2.81395e32i	−0.253213	−	0.451123i
$959$		−	5.86187e32i		−	0.929034i
$960$		0			0
$961$	−1.71643e32			−0.265869
$962$	4.50796e32	−	2.53030e32i	0.690326	−	0.387477i
$963$		0			0
$964$	−3.46929e32	+	5.68598e32i	−0.519270	+	0.851056i
$965$	1.17343e32			0.173643
$966$		0			0
$967$			3.16875e32i			0.458349i	0.973385	+	0.229175i	$0.0736027\pi$
$967$			3.16875e32i			0.458349i	−0.973385	+	0.229175i	$0.926397\pi$
$968$	−8.82606e30	+	2.42541e32i	−0.0126223	+	0.346862i
$969$		0			0
$970$	3.59201e32	−	2.01618e32i	0.502167	−	0.281864i
$971$		−	1.32804e32i		−	0.183569i	−0.995779	−	0.0917846i	$-0.970743\pi$
$971$		−	1.32804e32i		−	0.183569i	0.995779	−	0.0917846i	$-0.0292571\pi$
$972$		0			0
$973$	9.86619e32			1.33324
$974$	−5.05279e32	−	9.00201e32i	−0.675122	−	1.20279i
$975$		0			0
$976$	−1.00040e32	−	1.94479e32i	−0.130684	−	0.254053i
$977$	1.31201e33			1.69472			0.847361	−	0.531018i	$-0.178190\pi$
$977$	1.31201e33			1.69472			0.847361	+	0.531018i	$0.178190\pi$
$978$		0			0
$979$		−	4.53560e32i		−	0.572829i
$980$	−9.75161e32	+	1.59824e33i	−1.21784	+	1.99597i
$981$		0			0
$982$	−7.77335e32	−	1.38489e33i	−0.949253	−	1.69118i
$983$			3.40017e32i			0.410593i	0.978700	+	0.205296i	$0.0658159\pi$
$983$			3.40017e32i			0.410593i	−0.978700	+	0.205296i	$0.934184\pi$
$984$		0			0
$985$	−5.05675e32			−0.597136
$986$	5.79812e32	−	3.25446e32i	0.677081	−	0.380043i
$987$		0			0
$988$	2.77979e31	+	1.69608e31i	0.0317457	+	0.0193696i
$989$	−8.26684e32			−0.933642
$990$		0			0
$991$		−	1.23788e32i		−	0.136731i	−0.997660	−	0.0683657i	$-0.978222\pi$
$991$		−	1.23788e32i		−	0.136731i	0.997660	−	0.0683657i	$-0.0217785\pi$
$992$	5.68078e32	−	8.59137e32i	0.620554	−	0.938500i
$993$		0			0
$994$	−1.17818e33	+	6.61308e32i	−1.25882	+	0.706567i
$995$			1.24146e33i			1.31183i
$996$		0			0
$997$	4.21179e32			0.435331			0.217665	−	0.976023i	$-0.430156\pi$
$997$	4.21179e32			0.435331			0.217665	+	0.976023i	$0.430156\pi$
$998$	9.30832e32	+	1.65836e33i	0.951558	+	1.69529i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	36.23.d.c.19.2		10
3.2	odd	2		4.23.b.a.3.9	✓	10
4.3	odd	2	inner	36.23.d.c.19.1		10
12.11	even	2		4.23.b.a.3.10	yes	10
24.5	odd	2		64.23.c.e.63.4		10
24.11	even	2		64.23.c.e.63.7		10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4.23.b.a.3.9	✓	10	3.2	odd	2
4.23.b.a.3.10	yes	10	12.11	even	2
36.23.d.c.19.1		10	4.3	odd	2	inner
36.23.d.c.19.2		10	1.1	even	1	trivial
64.23.c.e.63.4		10	24.5	odd	2
64.23.c.e.63.7		10	24.11	even	2

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:	\( k \)	\(=\)	\( 23 \)
Character orbit:	\([\chi]\)	\(=\)	36.d (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-1785.90 + 1002.42i) q^{2} +(2.18461e6 - 3.58046e6i) q^{4} +6.52379e7 q^{5} -3.27904e9i q^{7} +(-3.12381e8 + 8.58425e9i) q^{8} +O(q^{10})\)	\(q+(-1785.90 + 1002.42i) q^{2} +(2.18461e6 - 3.58046e6i) q^{4} +6.52379e7 q^{5} -3.27904e9i q^{7} +(-3.12381e8 + 8.58425e9i) q^{8} +(-1.16509e11 + 6.53958e10i) q^{10} +2.30540e11i q^{11} -1.19775e12 q^{13} +(3.28698e12 + 5.85606e12i) q^{14} +(-8.04715e12 - 1.56438e13i) q^{16} +2.07597e13 q^{17} -6.48196e12i q^{19} +(1.42519e14 - 2.33581e14i) q^{20} +(-2.31098e14 - 4.11722e14i) q^{22} -1.02386e15i q^{23} +1.87179e15 q^{25} +(2.13907e15 - 1.20065e15i) q^{26} +(-1.17405e16 - 7.16343e15i) q^{28} -1.56390e16 q^{29} -2.85873e16i q^{31} +(3.00531e16 + 1.98717e16i) q^{32} +(-3.70748e16 + 2.08100e16i) q^{34} -2.13918e17i q^{35} +2.10744e17 q^{37} +(6.49765e15 + 1.15762e16i) q^{38} +(-2.03791e16 + 5.60018e17i) q^{40} +5.57168e17 q^{41} -8.07417e17i q^{43} +(8.25438e17 + 5.03639e17i) q^{44} +(1.02634e18 + 1.82852e18i) q^{46} +8.59587e17i q^{47} -6.84231e18 q^{49} +(-3.34285e18 + 1.87632e18i) q^{50} +(-2.61662e18 + 4.28850e18i) q^{52} -1.56480e19 q^{53} +1.50399e19i q^{55} +(2.81481e19 + 1.02431e18i) q^{56} +(2.79297e19 - 1.56768e19i) q^{58} -7.82838e18i q^{59} +1.24317e19 q^{61} +(2.86565e19 + 5.10542e19i) q^{62} +(-7.35918e19 - 5.36311e18i) q^{64} -7.81387e19 q^{65} +1.36610e20i q^{67} +(4.53518e19 - 7.43292e19i) q^{68} +(2.14436e20 + 3.82037e20i) q^{70} +2.01190e20i q^{71} +2.57734e19 q^{73} +(-3.76369e20 + 2.11254e20i) q^{74} +(-2.32084e19 - 1.41606e19i) q^{76} +7.55950e20 q^{77} -8.27585e20i q^{79} +(-5.24979e20 - 1.02057e21i) q^{80} +(-9.95050e20 + 5.58517e20i) q^{82} +6.46586e20i q^{83} +1.35432e21 q^{85} +(8.09371e20 + 1.44197e21i) q^{86} +(-1.97901e21 - 7.20162e19i) q^{88} -1.96738e21 q^{89} +3.92748e21i q^{91} +(-3.66590e21 - 2.23674e21i) q^{92} +(-8.61668e20 - 1.53514e21i) q^{94} -4.22869e20i q^{95} -3.08304e21 q^{97} +(1.22197e22 - 6.85887e21i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q - 1540 q^{2} + 2264464 q^{4} + 17091100 q^{5} - 9804431680 q^{8}+O(q^{10}) \) 10 * q - 1540 * q^2 + 2264464 * q^4 + 17091100 * q^5 - 9804431680 * q^8	\( 10 q - 1540 q^{2} + 2264464 q^{4} + 17091100 q^{5} - 9804431680 q^{8} + 159414035240 q^{10} - 531230356540 q^{13} + 5894008940736 q^{14} - 27717620084480 q^{16} - 14058178115540 q^{17} - 233643631625120 q^{20} + 120589650366240 q^{22} + 77\!\cdots\!70 q^{25}+ \cdots + 23\!\cdots\!20 q^{98}+O(q^{100}) \) 10 * q - 1540 * q^2 + 2264464 * q^4 + 17091100 * q^5 - 9804431680 * q^8 + 159414035240 * q^10 - 531230356540 * q^13 + 5894008940736 * q^14 - 27717620084480 * q^16 - 14058178115540 * q^17 - 233643631625120 * q^20 + 120589650366240 * q^22 + 7710175817606670 * q^25 + 3953973318046744 * q^26 + 1177952265288960 * q^28 + 14464474185570172 * q^29 + 73831192092953600 * q^32 - 26625976920357496 * q^34 + 324587767823538020 * q^37 - 369140808808591200 * q^38 - 1158049295468479360 * q^40 + 1355457345814233100 * q^41 + 1919761520625210240 * q^44 + 6132624002565203904 * q^46 + 183553700661552298 * q^49 - 29084394113996178540 * q^50 - 38492433127521128800 * q^52 + 11424344766226018780 * q^53 + 102844865827678657536 * q^56 + 173059696836432320360 * q^58 + 58241718146183220740 * q^61 - 317897221476923285760 * q^62 - 412080172429987966976 * q^64 + 121531695066047433560 * q^65 + 667890522330713878240 * q^68 + 1014396282552321513600 * q^70 + 83030422224875883380 * q^73 - 801906083011176262184 * q^74 + 286747421140990627200 * q^76 + 704201825495570814720 * q^77 - 1509611955050789726720 * q^80 - 2389572513290905036600 * q^82 - 1796890366112110859960 * q^85 + 8221838255181360278496 * q^86 + 11178210842814940531200 * q^88 - 3420669206528505615668 * q^89 - 21476264197983864733440 * q^92 - 20874543047091388369536 * q^94 - 20429910746446196146540 * q^97 + 23110416876469762175420 * q^98

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