LMFDB - Embedded newform 72.19.b.b.19.12

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [72,19,Mod(19,72)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(72, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 19, names="a")

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

chi := DirichletCharacter("72.19");

S:= CuspForms(chi, 19);

N := Newforms(S);

Level:	$ N $	$=$	$ 72 = 2^{3} \cdot 3^{2} $
Weight:	$ k $	$=$	$ 19 $
Character orbit:	$[\chi]$	$=$	72.b (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:	$147.878019151$
Analytic rank:	$0$
Dimension:	$16$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} + 596528635860 x^{14} + \cdots + 10\!\cdots\!00 $ x^16 + 596528635860x^14 + 138779834279766656473350x^12 + 15929648761783167648276226991833500x^10 + 933523590560757897979237259108548418050400625x^8 + 25644573975450247397592798233489377096637438971735125000x^6 + 248699290390053747845725741341783912036325565894332832183906250000x^4 + 571314919513523940667592109743659078499903982727661487427097929687500000000*x^2 + 104537110830703973784435514554213400615593028192885557279787723664062500000000000000
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{120}\cdot 3^{15}\cdot 5^{2} $
Twist minimal:	no (minimal twist has level 8)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			19.12
Root			$-285196. i$ of defining polynomial
Character	$\chi$	$=$	72.19
Dual form			72.19.b.b.19.11

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(299.623 + 415.174i) q^{2} +(-82595.7 + 248792. i) q^{4} -2.28157e6i q^{5} -3.15838e7i q^{7} +(-1.28040e8 + 4.02522e7i) q^{8} +O(q^{10})$	\(q+(299.623 + 415.174i) q^{2} +(-82595.7 + 248792. i) q^{4} -2.28157e6i q^{5} -3.15838e7i q^{7} +(-1.28040e8 + 4.02522e7i) q^{8} +(9.47248e8 - 6.83611e8i) q^{10} -2.35396e9 q^{11} -1.20623e10i q^{13} +(1.31128e10 - 9.46323e9i) q^{14} +(-5.50754e10 - 4.10983e10i) q^{16} +1.97418e11 q^{17} -1.48691e11 q^{19} +(5.67635e11 + 1.88448e11i) q^{20} +(-7.05302e11 - 9.77305e11i) q^{22} +1.21145e12i q^{23} -1.39085e12 q^{25} +(5.00794e12 - 3.61413e12i) q^{26} +(7.85778e12 + 2.60868e12i) q^{28} -1.97751e12i q^{29} -2.27392e13i q^{31} +(5.61095e11 - 3.51799e13i) q^{32} +(5.91511e13 + 8.19629e13i) q^{34} -7.20605e13 q^{35} -1.66947e14i q^{37} +(-4.45513e13 - 6.17327e13i) q^{38} +(9.18382e13 + 2.92131e14i) q^{40} +2.66745e14 q^{41} -7.20962e14 q^{43} +(1.94427e14 - 5.85647e14i) q^{44} +(-5.02962e14 + 3.62978e14i) q^{46} +1.62833e15i q^{47} +6.30880e14 q^{49} +(-4.16731e14 - 5.77445e14i) q^{50} +(3.00099e15 + 9.96290e14i) q^{52} +2.17325e15i q^{53} +5.37072e15i q^{55} +(1.27132e15 + 4.04397e15i) q^{56} +(8.21010e14 - 5.92507e14i) q^{58} -1.10087e16 q^{59} +6.26095e15i q^{61} +(9.44075e15 - 6.81320e15i) q^{62} +(1.47739e16 - 1.03078e16i) q^{64} -2.75208e16 q^{65} -4.55298e16 q^{67} +(-1.63059e16 + 4.91160e16i) q^{68} +(-2.15910e16 - 2.99177e16i) q^{70} -5.40107e16i q^{71} +4.71784e14 q^{73} +(6.93122e16 - 5.00213e16i) q^{74} +(1.22812e16 - 3.69931e16i) q^{76} +7.43470e16i q^{77} +1.72873e17i q^{79} +(-9.37685e16 + 1.25658e17i) q^{80} +(7.99229e16 + 1.10746e17i) q^{82} +8.17983e16 q^{83} -4.50422e17i q^{85} +(-2.16017e17 - 2.99325e17i) q^{86} +(3.01400e17 - 9.47522e16i) q^{88} -4.18502e17 q^{89} -3.80971e17 q^{91} +(-3.01399e17 - 1.00060e17i) q^{92} +(-6.76042e17 + 4.87886e17i) q^{94} +3.39248e17i q^{95} -5.20072e17 q^{97} +(1.89026e17 + 2.61925e17i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 426 q^{2} - 444332 q^{4} - 304914744 q^{8}+O(q^{10}) $ 16 * q - 426 * q^2 - 444332 * q^4 - 304914744 * q^8	$ 16 q - 426 q^{2} - 444332 q^{4} - 304914744 q^{8} - 1569837600 q^{10} + 2471571264 q^{11} - 26163923904 q^{14} - 192320075504 q^{16} + 176439301344 q^{17} - 833365634368 q^{19} - 1256486405760 q^{20} + 59927319356 q^{22} - 15320509140080 q^{25} - 4184514840864 q^{26} - 12301604294400 q^{28} - 141481742931936 q^{32} + 80653465357268 q^{34} - 20487495736320 q^{35} - 493456694265564 q^{38} - 519930573603840 q^{40} + 594931562445024 q^{41} - 25\!\cdots\!92 q^{43}+ \cdots + 81\!\cdots\!66 q^{98}+O(q^{100}) $ 16 * q - 426 * q^2 - 444332 * q^4 - 304914744 * q^8 - 1569837600 * q^10 + 2471571264 * q^11 - 26163923904 * q^14 - 192320075504 * q^16 + 176439301344 * q^17 - 833365634368 * q^19 - 1256486405760 * q^20 + 59927319356 * q^22 - 15320509140080 * q^25 - 4184514840864 * q^26 - 12301604294400 * q^28 - 141481742931936 * q^32 + 80653465357268 * q^34 - 20487495736320 * q^35 - 493456694265564 * q^38 - 519930573603840 * q^40 + 594931562445024 * q^41 - 2540155017577792 * q^43 - 73781630442072 * q^44 + 153882272211264 * q^46 - 3186415704132848 * q^49 - 5668141028706330 * q^50 - 4594372123628160 * q^52 - 8184134137073664 * q^56 - 10505700099162720 * q^58 - 556807886314176 * q^59 - 6212402633091840 * q^62 - 56432885385732032 * q^64 + 21153177930524160 * q^65 + 162428574934613696 * q^67 + 70717864614203736 * q^68 + 4248100663257600 * q^70 - 7655712852492256 * q^73 - 9613779604149984 * q^74 - 151130166278324584 * q^76 - 26870186366192640 * q^80 + 329788507250077556 * q^82 - 866357336138514624 * q^83 - 1269201398006865468 * q^86 - 758460699051663856 * q^88 + 883646550464284128 * q^89 - 379834560933460992 * q^91 - 1413121475102841600 * q^92 + 671428514272869504 * q^94 - 2614894858526780128 * q^97 + 81635840192738166 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/72\mathbb{Z}\right)^\times$.

$n$	$37$	$55$	$65$
$\chi(n)$	$-1$	$-1$	$1$

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 $

$2$	299.623	+	415.174i	0.585202	+	0.810888i
$2$	299.623	+	415.174i	0.585202	+	0.810888i
$3$		0			0
$3$		0			0
$4$	−82595.7	+	248792.i	−0.315078	+	0.949066i
$5$		−	2.28157e6i		−	1.16816i	−0.811695	−	0.584081i	$-0.801455\pi$
$5$		−	2.28157e6i		−	1.16816i	0.811695	−	0.584081i	$-0.198545\pi$
$6$		0			0
$7$		−	3.15838e7i		−	0.782675i	−0.920247	−	0.391337i	$-0.872013\pi$
$7$		−	3.15838e7i		−	0.782675i	0.920247	−	0.391337i	$-0.127987\pi$
$8$	−1.28040e8	+	4.02522e7i	−0.953970	+	0.299903i
$9$		0			0
$10$	9.47248e8	−	6.83611e8i	0.947248	−	0.683611i
$11$	−2.35396e9			−0.998309			−0.499155	−	0.866513i	$-0.666356\pi$
$11$	−2.35396e9			−0.998309			−0.499155	+	0.866513i	$0.666356\pi$
$12$		0			0
$13$		−	1.20623e10i		−	1.13747i	−0.822522	−	0.568733i	$-0.807434\pi$
$13$		−	1.20623e10i		−	1.13747i	0.822522	−	0.568733i	$-0.192566\pi$
$14$	1.31128e10	−	9.46323e9i	0.634661	−	0.458023i
$15$		0			0
$16$	−5.50754e10	−	4.10983e10i	−0.801452	−	0.598059i
$17$	1.97418e11			1.66474			0.832370	−	0.554220i	$-0.186983\pi$
$17$	1.97418e11			1.66474			0.832370	+	0.554220i	$0.186983\pi$
$18$		0			0
$19$	−1.48691e11			−0.460789			−0.230395	−	0.973097i	$-0.574002\pi$
$19$	−1.48691e11			−0.460789			−0.230395	+	0.973097i	$0.574002\pi$
$20$	5.67635e11	+	1.88448e11i	1.10866	+	0.368062i
$21$		0			0
$22$	−7.05302e11	−	9.77305e11i	−0.584213	−	0.809517i
$23$			1.21145e12i			0.672596i	0.941756	+	0.336298i	$0.109175\pi$
$23$			1.21145e12i			0.672596i	−0.941756	+	0.336298i	$0.890825\pi$
$24$		0			0
$25$	−1.39085e12			−0.364603
$26$	5.00794e12	−	3.61413e12i	0.922357	−	0.665647i
$27$		0			0
$28$	7.85778e12	+	2.60868e12i	0.742810	+	0.246603i
$29$		−	1.97751e12i		−	0.136313i	−0.997675	−	0.0681563i	$-0.978288\pi$
$29$		−	1.97751e12i		−	0.136313i	0.997675	−	0.0681563i	$-0.0217117\pi$
$30$		0			0
$31$		−	2.27392e13i		−	0.860044i	−0.902819	−	0.430022i	$-0.858506\pi$
$31$		−	2.27392e13i		−	0.860044i	0.902819	−	0.430022i	$-0.141494\pi$
$32$	5.61095e11	−	3.51799e13i	0.0159473	−	0.999873i
$33$		0			0
$34$	5.91511e13	+	8.19629e13i	0.974209	+	1.34992i
$35$	−7.20605e13			−0.914291
$36$		0			0
$37$		−	1.66947e14i		−	1.28459i	−0.766459	−	0.642294i	$-0.777983\pi$
$37$		−	1.66947e14i		−	1.28459i	0.766459	−	0.642294i	$-0.222017\pi$
$38$	−4.45513e13	−	6.17327e13i	−0.269655	−	0.373648i
$39$		0			0
$40$	9.18382e13	+	2.92131e14i	0.350335	+	1.11439i
$41$	2.66745e14			0.814781			0.407390	−	0.913254i	$-0.366439\pi$
$41$	2.66745e14			0.814781			0.407390	+	0.913254i	$0.366439\pi$
$42$		0			0
$43$	−7.20962e14			−1.43449			−0.717243	−	0.696824i	$-0.754596\pi$
$43$	−7.20962e14			−1.43449			−0.717243	+	0.696824i	$0.754596\pi$
$44$	1.94427e14	−	5.85647e14i	0.314545	−	0.947461i
$45$		0			0
$46$	−5.02962e14	+	3.62978e14i	−0.545400	+	0.393604i
$47$			1.62833e15i			1.45500i	0.686109	+	0.727498i	$0.259317\pi$
$47$			1.62833e15i			1.45500i	−0.686109	+	0.727498i	$0.740683\pi$
$48$		0			0
$49$	6.30880e14			0.387420
$50$	−4.16731e14	−	5.77445e14i	−0.213366	−	0.295652i
$51$		0			0
$52$	3.00099e15	+	9.96290e14i	1.07953	+	0.358390i
$53$			2.17325e15i			0.658608i	0.944224	+	0.329304i	$0.106814\pi$
$53$			2.17325e15i			0.658608i	−0.944224	+	0.329304i	$0.893186\pi$
$54$		0			0
$55$			5.37072e15i			1.16619i
$56$	1.27132e15	+	4.04397e15i	0.234726	+	0.746648i
$57$		0			0
$58$	8.21010e14	−	5.92507e14i	0.110534	−	0.0797704i
$59$	−1.10087e16			−1.27077			−0.635386	−	0.772195i	$-0.719159\pi$
$59$	−1.10087e16			−1.27077			−0.635386	+	0.772195i	$0.719159\pi$
$60$		0			0
$61$			6.26095e15i			0.535392i	0.963503	+	0.267696i	$0.0862623\pi$
$61$			6.26095e15i			0.535392i	−0.963503	+	0.267696i	$0.913738\pi$
$62$	9.44075e15	−	6.81320e15i	0.697399	−	0.503299i
$63$		0			0
$64$	1.47739e16	−	1.03078e16i	0.820117	−	0.572196i
$65$	−2.75208e16			−1.32874
$66$		0			0
$67$	−4.55298e16			−1.67349			−0.836744	−	0.547595i	$-0.815544\pi$
$67$	−4.55298e16			−1.67349			−0.836744	+	0.547595i	$0.815544\pi$
$68$	−1.63059e16	+	4.91160e16i	−0.524523	+	1.57995i
$69$		0			0
$70$	−2.15910e16	−	2.99177e16i	−0.535045	−	0.741388i
$71$		−	5.40107e16i		−	1.17803i	−0.808123	−	0.589013i	$-0.799517\pi$
$71$		−	5.40107e16i		−	1.17803i	0.808123	−	0.589013i	$-0.200483\pi$
$72$		0			0
$73$	4.71784e14			0.00801378			0.00400689	−	0.999992i	$-0.498725\pi$
$73$	4.71784e14			0.00801378			0.00400689	+	0.999992i	$0.498725\pi$
$74$	6.93122e16	−	5.00213e16i	1.04166	−	0.751743i
$75$		0			0
$76$	1.22812e16	−	3.69931e16i	0.145184	−	0.437319i
$77$			7.43470e16i			0.781352i
$78$		0			0
$79$			1.72873e17i			1.44240i	0.692729	+	0.721198i	$0.256408\pi$
$79$			1.72873e17i			1.44240i	−0.692729	+	0.721198i	$0.743592\pi$
$80$	−9.37685e16	+	1.25658e17i	−0.698630	+	0.936226i
$81$		0			0
$82$	7.99229e16	+	1.10746e17i	0.476811	+	0.660696i
$83$	8.17983e16			0.437564			0.218782	−	0.975774i	$-0.429792\pi$
$83$	8.17983e16			0.437564			0.218782	+	0.975774i	$0.429792\pi$
$84$		0			0
$85$		−	4.50422e17i		−	1.94469i
$86$	−2.16017e17	−	2.99325e17i	−0.839463	−	1.16321i
$87$		0			0
$88$	3.01400e17	−	9.47522e16i	0.952357	−	0.299396i
$89$	−4.18502e17			−1.19450			−0.597252	−	0.802053i	$-0.703741\pi$
$89$	−4.18502e17			−1.19450			−0.597252	+	0.802053i	$0.703741\pi$
$90$		0			0
$91$	−3.80971e17			−0.890266
$92$	−3.01399e17	−	1.00060e17i	−0.638338	−	0.211920i
$93$		0			0
$94$	−6.76042e17	+	4.87886e17i	−1.17984	+	0.851467i
$95$			3.39248e17i			0.538276i
$96$		0			0
$97$	−5.20072e17			−0.684097			−0.342048	−	0.939682i	$-0.611121\pi$
$97$	−5.20072e17			−0.684097			−0.342048	+	0.939682i	$0.611121\pi$
$98$	1.89026e17	+	2.61925e17i	0.226719	+	0.314154i
$99$		0			0
$100$	1.14878e17	−	3.46032e17i	0.114878	−	0.346032i
$101$			1.51822e18i			1.38817i	0.719892	+	0.694086i	$0.244191\pi$
$101$			1.51822e18i			1.38817i	−0.719892	+	0.694086i	$0.755809\pi$
$102$		0			0
$103$			1.83823e18i			1.40885i	0.709776	+	0.704427i	$0.248796\pi$
$103$			1.83823e18i			1.40885i	−0.709776	+	0.704427i	$0.751204\pi$
$104$	4.85533e17	+	1.54445e18i	0.341129	+	1.08511i
$105$		0			0
$106$	−9.02278e17	+	6.51156e17i	−0.534057	+	0.385418i
$107$	−6.17561e17			−0.335913			−0.167956	−	0.985794i	$-0.553717\pi$
$107$	−6.17561e17			−0.335913			−0.167956	+	0.985794i	$0.553717\pi$
$108$		0			0
$109$			1.49091e18i			0.686458i	0.939252	+	0.343229i	$0.111521\pi$
$109$			1.49091e18i			0.686458i	−0.939252	+	0.343229i	$0.888479\pi$
$110$	−2.22979e18	+	1.60919e18i	−0.945647	+	0.682455i
$111$		0			0
$112$	−1.29804e18	+	1.73949e18i	−0.468086	+	0.627277i
$113$	−1.52525e18			−0.507734			−0.253867	−	0.967239i	$-0.581703\pi$
$113$	−1.52525e18			−0.507734			−0.253867	+	0.967239i	$0.581703\pi$
$114$		0			0
$115$	2.76400e18			0.785701
$116$	4.91988e17	+	1.63334e17i	0.129370	+	0.0429491i
$117$		0			0
$118$	−3.29846e18	−	4.57053e18i	−0.743658	−	1.03045i
$119$		−	6.23520e18i		−	1.30295i
$120$		0			0
$121$	−1.87828e16			−0.00337826
$122$	−2.59939e18	+	1.87593e18i	−0.434143	+	0.313312i
$123$		0			0
$124$	5.65734e18	+	1.87816e18i	0.816238	+	0.270980i
$125$		−	5.53017e18i		−	0.742247i
$126$		0			0
$127$		−	1.57929e19i		−	1.83750i	−0.394836	−	0.918751i	$-0.629199\pi$
$127$		−	1.57929e19i		−	1.83750i	0.394836	−	0.918751i	$-0.370801\pi$
$128$	8.70613e18	+	3.04530e18i	0.943921	+	0.330173i
$129$		0			0
$130$	−8.24588e18	−	1.14259e19i	−0.777583	−	1.07746i
$131$	−1.13035e19			−0.994884			−0.497442	−	0.867497i	$-0.665727\pi$
$131$	−1.13035e19			−0.994884			−0.497442	+	0.867497i	$0.665727\pi$
$132$		0			0
$133$			4.69622e18i			0.360648i
$134$	−1.36418e19	−	1.89028e19i	−0.979328	−	1.35701i
$135$		0			0
$136$	−2.52773e19	+	7.94652e18i	−1.58811	+	0.499260i
$137$	3.18491e19			1.87332			0.936661	−	0.350237i	$-0.113899\pi$
$137$	3.18491e19			1.87332			0.936661	+	0.350237i	$0.113899\pi$
$138$		0			0
$139$	−3.62220e18			−0.186999			−0.0934996	−	0.995619i	$-0.529805\pi$
$139$	−3.62220e18			−0.186999			−0.0934996	+	0.995619i	$0.529805\pi$
$140$	5.95188e18	−	1.79281e19i	0.288073	−	0.867723i
$141$		0			0
$142$	2.24239e19	−	1.61829e19i	0.955247	−	0.689383i
$143$			2.83941e19i			1.13554i
$144$		0			0
$145$	−4.51181e18			−0.159235
$146$	1.41357e17	+	1.95873e17i	0.00468968	+	0.00649827i
$147$		0			0
$148$	4.15351e19	+	1.37891e19i	1.21916	+	0.404745i
$149$		−	1.37566e19i		−	0.380046i	−0.981780	−	0.190023i	$-0.939144\pi$
$149$		−	1.37566e19i		−	0.380046i	0.981780	−	0.190023i	$-0.0608563\pi$
$150$		0			0
$151$		−	2.58894e18i		−	0.0634351i	−0.999497	−	0.0317176i	$-0.989902\pi$
$151$		−	2.58894e18i		−	0.0634351i	0.999497	−	0.0317176i	$-0.0100977\pi$
$152$	1.90383e19	−	5.98514e18i	0.439579	−	0.138192i
$153$		0			0
$154$	−3.08670e19	+	2.22761e19i	−0.633589	+	0.457249i
$155$	−5.18811e19			−1.00467
$156$		0			0
$157$			3.57853e18i			0.0617458i	0.999523	+	0.0308729i	$0.00982871\pi$
$157$			3.57853e18i			0.0617458i	−0.999523	+	0.0308729i	$0.990171\pi$
$158$	−7.17726e19	+	5.17969e19i	−1.16962	+	0.844092i
$159$		0			0
$160$	−8.02653e19	−	1.28018e18i	−1.16801	−	0.0186290i
$161$	3.82621e19			0.526424
$162$		0			0
$163$	−1.25921e20			−1.55028			−0.775142	−	0.631787i	$-0.782322\pi$
$163$	−1.25921e20			−1.55028			−0.775142	+	0.631787i	$0.782322\pi$
$164$	−2.20320e19	+	6.63639e19i	−0.256719	+	0.773281i
$165$		0			0
$166$	2.45087e19	+	3.39606e19i	0.256063	+	0.354815i
$167$		−	2.01076e20i		−	1.99027i	−0.0985377	−	0.995133i	$-0.531416\pi$
$167$		−	2.01076e20i		−	1.99027i	0.0985377	−	0.995133i	$-0.468584\pi$
$168$		0			0
$169$	−3.30425e19			−0.293828
$170$	1.87004e20	−	1.34957e20i	1.57692	−	1.13803i
$171$		0			0
$172$	5.95483e19	−	1.79369e20i	0.451974	−	1.36142i
$173$			1.31482e20i			0.947218i	0.880735	+	0.473609i	$0.157049\pi$
$173$			1.31482e20i			0.947218i	−0.880735	+	0.473609i	$0.842951\pi$
$174$		0			0
$175$			4.39283e19i			0.285366i
$176$	1.29645e20	+	9.67438e19i	0.800097	+	0.597048i
$177$		0			0
$178$	−1.25393e20	−	1.73751e20i	−0.699026	−	0.968609i
$179$	−6.48527e19			−0.343756			−0.171878	−	0.985118i	$-0.554984\pi$
$179$	−6.48527e19			−0.343756			−0.171878	+	0.985118i	$0.554984\pi$
$180$		0			0
$181$		−	2.49257e19i		−	0.119547i	−0.998212	−	0.0597736i	$-0.980962\pi$
$181$		−	2.49257e19i		−	0.119547i	0.998212	−	0.0597736i	$-0.0190379\pi$
$182$	−1.14148e20	−	1.58170e20i	−0.520985	−	0.721906i
$183$		0			0
$184$	−4.87635e19	−	1.55113e20i	−0.201713	−	0.641636i
$185$	−3.80901e20			−1.50061
$186$		0			0
$187$	−4.64715e20			−1.66193
$188$	−4.05116e20	−	1.34493e20i	−1.38089	−	0.458437i
$189$		0			0
$190$	−1.40847e20	+	1.01647e20i	−0.436482	+	0.315000i
$191$		−	2.45881e20i		−	0.726817i	−0.931630	−	0.363408i	$-0.881613\pi$
$191$		−	2.45881e20i		−	0.726817i	0.931630	−	0.363408i	$-0.118387\pi$
$192$		0			0
$193$	2.94564e19			0.0792800			0.0396400	−	0.999214i	$-0.487379\pi$
$193$	2.94564e19			0.0792800			0.0396400	+	0.999214i	$0.487379\pi$
$194$	−1.55826e20	−	2.15920e20i	−0.400335	−	0.554726i
$195$		0			0
$196$	−5.21080e19	+	1.56958e20i	−0.122067	+	0.367687i
$197$			7.48850e20i			1.67571i	0.545892	+	0.837855i	$0.316191\pi$
$197$			7.48850e20i			1.67571i	−0.545892	+	0.837855i	$0.683809\pi$
$198$		0			0
$199$		−	4.33087e20i		−	0.884906i	−0.896792	−	0.442453i	$-0.854108\pi$
$199$		−	4.33087e20i		−	0.884906i	0.896792	−	0.442453i	$-0.145892\pi$
$200$	1.78084e20	−	5.59848e19i	0.347820	−	0.109345i
$201$		0			0
$202$	−6.30328e20	+	4.54895e20i	−1.12565	+	0.812361i
$203$	−6.24571e19			−0.106688
$204$		0			0
$205$		−	6.08595e20i		−	0.951796i
$206$	−7.63188e20	+	5.50778e20i	−1.14242	+	0.824464i
$207$		0			0
$208$	−4.95738e20	+	6.64333e20i	−0.680271	+	0.911624i
$209$	3.50013e20			0.460010
$210$		0			0
$211$	−2.15183e20			−0.259577			−0.129789	−	0.991542i	$-0.541430\pi$
$211$	−2.15183e20			−0.259577			−0.129789	+	0.991542i	$0.541430\pi$
$212$	−5.40687e20	−	1.79501e20i	−0.625062	−	0.207513i
$213$		0			0
$214$	−1.85036e20	−	2.56396e20i	−0.196577	−	0.272387i
$215$			1.64492e21i			1.67571i
$216$		0			0
$217$	−7.18190e20			−0.673135
$218$	−6.18990e20	+	4.46713e20i	−0.556641	+	0.401717i
$219$		0			0
$220$	−1.33619e21	−	4.43598e20i	−1.10679	−	0.367440i
$221$		−	2.38131e21i		−	1.89359i
$222$		0			0
$223$			7.77856e20i			0.570369i	0.958473	+	0.285184i	$0.0920548\pi$
$223$			7.77856e20i			0.570369i	−0.958473	+	0.285184i	$0.907945\pi$
$224$	−1.11111e21	−	1.77215e19i	−0.782575	−	0.0124815i
$225$		0			0
$226$	−4.57002e20	−	6.33247e20i	−0.297127	−	0.411715i
$227$	−4.74764e20			−0.296650			−0.148325	−	0.988939i	$-0.547388\pi$
$227$	−4.74764e20			−0.296650			−0.148325	+	0.988939i	$0.547388\pi$
$228$		0			0
$229$			1.42048e21i			0.820192i	0.912042	+	0.410096i	$0.134505\pi$
$229$			1.42048e21i			0.820192i	−0.912042	+	0.410096i	$0.865495\pi$
$230$	8.28159e20	+	1.14754e21i	0.459794	+	0.637115i
$231$		0			0
$232$	7.95991e19	+	2.53199e20i	0.0408805	+	0.130038i
$233$	−1.81736e21			−0.897920			−0.448960	−	0.893552i	$-0.648205\pi$
$233$	−1.81736e21			−0.897920			−0.448960	+	0.893552i	$0.648205\pi$
$234$		0			0
$235$	3.71515e21			1.69967
$236$	9.09271e20	−	2.73887e21i	0.400392	−	1.20605i
$237$		0			0
$238$	2.58870e21	−	1.86821e21i	1.05655	−	0.762489i
$239$			8.68263e20i			0.341248i	0.985336	+	0.170624i	$0.0545783\pi$
$239$			8.68263e20i			0.341248i	−0.985336	+	0.170624i	$0.945422\pi$
$240$		0			0
$241$	−4.45834e21			−1.62562			−0.812811	−	0.582527i	$-0.802064\pi$
$241$	−4.45834e21			−1.62562			−0.812811	+	0.582527i	$0.802064\pi$
$242$	−5.62777e18	−	7.79815e18i	−0.00197696	−	0.00273939i
$243$		0			0
$244$	−1.55767e21	−	5.17128e20i	−0.508122	−	0.168690i
$245$		−	1.43939e21i		−	0.452569i
$246$		0			0
$247$			1.79355e21i			0.524132i
$248$	9.15305e20	+	2.91152e21i	0.257929	+	0.820456i
$249$		0			0
$250$	2.29599e21	−	1.65697e21i	0.601879	−	0.434364i
$251$	4.99327e21			1.26276			0.631382	−	0.775472i	$-0.282488\pi$
$251$	4.99327e21			1.26276			0.631382	+	0.775472i	$0.282488\pi$
$252$		0			0
$253$		−	2.85170e21i		−	0.671459i
$254$	6.55680e21	−	4.73192e21i	1.49001	−	1.07531i
$255$		0			0
$256$	1.34423e21	+	4.52701e21i	0.284651	+	0.958631i
$257$	−3.92398e20			−0.0802285			−0.0401143	−	0.999195i	$-0.512772\pi$
$257$	−3.92398e20			−0.0802285			−0.0401143	+	0.999195i	$0.512772\pi$
$258$		0			0
$259$	−5.27282e21			−1.00541
$260$	2.27310e21	−	6.84696e21i	0.418658	−	1.26107i
$261$		0			0
$262$	−3.38680e21	−	4.69294e21i	−0.582208	−	0.806739i
$263$			2.33587e21i			0.388014i	0.981000	+	0.194007i	$0.0621485\pi$
$263$			2.33587e21i			0.388014i	−0.981000	+	0.194007i	$0.937852\pi$
$264$		0			0
$265$	4.95841e21			0.769360
$266$	−1.94975e21	+	1.40710e21i	−0.292445	+	0.211052i
$267$		0			0
$268$	3.76057e21	−	1.13274e22i	0.527278	−	1.58825i
$269$			9.87480e21i			1.33893i	0.742844	+	0.669465i	$0.233477\pi$
$269$			9.87480e21i			1.33893i	−0.742844	+	0.669465i	$0.766523\pi$
$270$		0			0
$271$		−	2.00043e21i		−	0.253746i	−0.991919	−	0.126873i	$-0.959506\pi$
$271$		−	2.00043e21i		−	0.253746i	0.991919	−	0.126873i	$-0.0404941\pi$
$272$	−1.08729e22	−	8.11355e21i	−1.33421	−	0.995613i
$273$		0			0
$274$	9.54274e21	+	1.32229e22i	1.09627	+	1.51905i
$275$	3.27401e21			0.363986
$276$		0			0
$277$		−	1.56250e21i		−	0.162743i	−0.996684	−	0.0813713i	$-0.974070\pi$
$277$		−	1.56250e21i		−	0.162743i	0.996684	−	0.0813713i	$-0.0259300\pi$
$278$	−1.08530e21	−	1.50385e21i	−0.109432	−	0.151635i
$279$		0			0
$280$	9.22660e21	−	2.90059e21i	0.872206	−	0.274198i
$281$	1.34574e21			0.123198			0.0615991	−	0.998101i	$-0.480380\pi$
$281$	1.34574e21			0.123198			0.0615991	+	0.998101i	$0.480380\pi$
$282$		0			0
$283$	4.08841e21			0.351137			0.175569	−	0.984467i	$-0.443824\pi$
$283$	4.08841e21			0.351137			0.175569	+	0.984467i	$0.443824\pi$
$284$	1.34374e22	+	4.46106e21i	1.11802	+	0.371170i
$285$		0			0
$286$	−1.17885e22	+	8.50753e21i	−0.920797	+	0.664522i
$287$		−	8.42480e21i		−	0.637709i
$288$		0			0
$289$	2.49108e22			1.77136
$290$	−1.35184e21	−	1.87319e21i	−0.0931848	−	0.129122i
$291$		0			0
$292$	−3.89673e19	+	1.17376e20i	−0.00252496	+	0.00760560i
$293$			1.32334e22i			0.831503i	0.909478	+	0.415752i	$0.136481\pi$
$293$			1.32334e22i			0.831503i	−0.909478	+	0.415752i	$0.863519\pi$
$294$		0			0
$295$			2.51171e22i			1.48447i
$296$	6.72000e21	+	2.13759e22i	0.385251	+	1.22546i
$297$		0			0
$298$	5.71141e21	−	4.12181e21i	0.308175	−	0.222404i
$299$	1.46128e22			0.765055
$300$		0			0
$301$			2.27707e22i			1.12274i
$302$	1.07486e21	−	7.75707e20i	0.0514387	−	0.0371223i
$303$		0			0
$304$	8.18921e21	+	6.11095e21i	0.369300	+	0.275579i
$305$	1.42848e22			0.625425
$306$		0			0
$307$	9.21006e21			0.380204			0.190102	−	0.981764i	$-0.439118\pi$
$307$	9.21006e21			0.380204			0.190102	+	0.981764i	$0.439118\pi$
$308$	−1.84969e22	−	6.14074e21i	−0.741554	−	0.246186i
$309$		0			0
$310$	−1.55448e22	−	2.15397e22i	−0.587935	−	0.814675i
$311$			2.22406e21i			0.0817151i	0.999165	+	0.0408576i	$0.0130090\pi$
$311$			2.22406e21i			0.0817151i	−0.999165	+	0.0408576i	$0.986991\pi$
$312$		0			0
$313$	3.00302e22			1.04150			0.520751	−	0.853709i	$-0.325652\pi$
$313$	3.00302e22			1.04150			0.520751	+	0.853709i	$0.325652\pi$
$314$	−1.48571e21	+	1.07221e21i	−0.0500689	+	0.0361338i
$315$		0			0
$316$	−4.30095e22	−	1.42786e22i	−1.36893	−	0.454466i
$317$			2.62622e22i			0.812453i	0.913772	+	0.406227i	$0.133156\pi$
$317$			2.62622e22i			0.812453i	−0.913772	+	0.406227i	$0.866844\pi$
$318$		0			0
$319$			4.65498e21i			0.136082i
$320$	−2.35179e22	−	3.37077e22i	−0.668418	−	0.958030i
$321$		0			0
$322$	1.14642e22	+	1.58854e22i	0.308064	+	0.426871i
$323$	−2.93543e22			−0.767094
$324$		0			0
$325$			1.67768e22i			0.414723i
$326$	−3.77290e22	−	5.22794e22i	−0.907229	−	1.25711i
$327$		0			0
$328$	−3.41539e22	+	1.07371e22i	−0.777276	+	0.244355i
$329$	5.14288e22			1.13879
$330$		0			0
$331$	4.90686e22			1.02885			0.514425	−	0.857535i	$-0.328005\pi$
$331$	4.90686e22			1.02885			0.514425	+	0.857535i	$0.328005\pi$
$332$	−6.75619e21	+	2.03508e22i	−0.137867	+	0.415277i
$333$		0			0
$334$	8.34815e22	−	6.02470e22i	1.61388	−	1.16471i
$335$			1.03879e23i			1.95490i
$336$		0			0
$337$	−3.64989e22			−0.651044			−0.325522	−	0.945535i	$-0.605540\pi$
$337$	−3.64989e22			−0.651044			−0.325522	+	0.945535i	$0.605540\pi$
$338$	−9.90031e21	−	1.37184e22i	−0.171949	−	0.238261i
$339$		0			0
$340$	1.12061e23	+	3.72030e22i	1.84564	+	0.612727i
$341$			5.35273e22i			0.858590i
$342$		0			0
$343$		−	7.13570e22i		−	1.08590i
$344$	9.23117e22	−	2.90203e22i	1.36846	−	0.430206i
$345$		0			0
$346$	−5.45878e22	+	3.93949e22i	−0.768087	+	0.554313i
$347$	−5.72256e22			−0.784558			−0.392279	−	0.919846i	$-0.628313\pi$
$347$	−5.72256e22			−0.784558			−0.392279	+	0.919846i	$0.628313\pi$
$348$		0			0
$349$			1.68448e22i			0.219300i	0.993970	+	0.109650i	$0.0349729\pi$
$349$			1.68448e22i			0.219300i	−0.993970	+	0.109650i	$0.965027\pi$
$350$	−1.82379e22	+	1.31619e22i	−0.231399	+	0.166996i
$351$		0			0
$352$	−1.32080e21	+	8.28121e22i	−0.0159203	+	0.998182i
$353$	3.65726e22			0.429718			0.214859	−	0.976645i	$-0.431071\pi$
$353$	3.65726e22			0.429718			0.214859	+	0.976645i	$0.431071\pi$
$354$		0			0
$355$	−1.23229e23			−1.37613
$356$	3.45665e22	−	1.04120e23i	0.376362	−	1.13366i
$357$		0			0
$358$	−1.94314e22	−	2.69252e22i	−0.201167	−	0.278748i
$359$			1.53519e23i			1.54993i	0.632001	+	0.774967i	$0.282234\pi$
$359$			1.53519e23i			1.54993i	−0.632001	+	0.774967i	$0.717766\pi$
$360$		0			0
$361$	−8.20183e22			−0.787673
$362$	1.03485e22	−	7.46831e21i	0.0969394	−	0.0699593i
$363$		0			0
$364$	3.14666e22	−	9.47826e22i	0.280503	−	0.844921i
$365$		−	1.07641e21i		−	0.00936139i
$366$		0			0
$367$			1.28235e23i			1.06172i	0.847458	+	0.530862i	$0.178132\pi$
$367$			1.28235e23i			1.06172i	−0.847458	+	0.530862i	$0.821868\pi$
$368$	4.97884e22	−	6.67210e22i	0.402252	−	0.539054i
$369$		0			0
$370$	−1.14127e23	−	1.58140e23i	−0.878158	−	1.21682i
$371$	6.86394e22			0.515476
$372$		0			0
$373$			1.23697e23i			0.885078i	0.896749	+	0.442539i	$0.145922\pi$
$373$			1.23697e23i			0.885078i	−0.896749	+	0.442539i	$0.854078\pi$
$374$	−1.39239e23	−	1.92938e23i	−0.972562	−	1.34764i
$375$		0			0
$376$	−6.55440e22	−	2.08491e23i	−0.436357	−	1.38802i
$377$	−2.38532e22			−0.155051
$378$		0			0
$379$	1.99505e23			1.23652			0.618261	−	0.785973i	$-0.287837\pi$
$379$	1.99505e23			1.23652			0.618261	+	0.785973i	$0.287837\pi$
$380$	−8.44023e22	−	2.80205e22i	−0.510860	−	0.169599i
$381$		0			0
$382$	1.02084e23	−	7.36717e22i	0.589367	−	0.425335i
$383$		−	2.81741e23i		−	1.58877i	−0.607414	−	0.794385i	$-0.707793\pi$
$383$		−	2.81741e23i		−	1.58877i	0.607414	−	0.794385i	$-0.292207\pi$
$384$		0			0
$385$	1.69628e23			0.912746
$386$	8.82582e21	+	1.22295e22i	0.0463948	+	0.0642872i
$387$		0			0
$388$	4.29557e22	−	1.29390e23i	0.215544	−	0.649253i
$389$			1.39106e23i			0.682025i	0.940059	+	0.341013i	$0.110770\pi$
$389$			1.39106e23i			0.682025i	−0.940059	+	0.341013i	$0.889230\pi$
$390$		0			0
$391$			2.39162e23i			1.11970i
$392$	−8.07776e22	+	2.53943e22i	−0.369587	+	0.116188i
$393$		0			0
$394$	−3.10904e23	+	2.24373e23i	−1.35881	+	0.980629i
$395$	3.94422e23			1.68495
$396$		0			0
$397$		−	7.33153e22i		−	0.299282i	−0.988740	−	0.149641i	$-0.952188\pi$
$397$		−	7.33153e22i		−	0.299282i	0.988740	−	0.149641i	$-0.0478118\pi$
$398$	1.79806e23	−	1.29763e23i	0.717559	−	0.517848i
$399$		0			0
$400$	7.66015e22	+	5.71615e22i	0.292212	+	0.218054i
$401$	−8.73430e22			−0.325783			−0.162892	−	0.986644i	$-0.552082\pi$
$401$	−8.73430e22			−0.325783			−0.162892	+	0.986644i	$0.552082\pi$
$402$		0			0
$403$	−2.74286e23			−0.978270
$404$	−3.77722e23	−	1.25399e23i	−1.31747	−	0.437382i
$405$		0			0
$406$	−1.87136e22	−	2.59306e22i	−0.0624343	−	0.0865124i
$407$			3.92987e23i			1.28242i
$408$		0			0
$409$	−1.40850e23			−0.439792			−0.219896	−	0.975523i	$-0.570572\pi$
$409$	−1.40850e23			−0.439792			−0.219896	+	0.975523i	$0.570572\pi$
$410$	2.52673e23	−	1.82349e23i	0.771800	−	0.556993i
$411$		0			0
$412$	−4.57338e23	−	1.51830e23i	−1.33710	−	0.443898i
$413$			3.47696e23i			0.994602i
$414$		0			0
$415$		−	1.86628e23i		−	0.511146i
$416$	−4.24349e23	−	6.76807e21i	−1.13732	−	0.0181395i
$417$		0			0
$418$	1.04872e23	+	1.45316e23i	0.269199	+	0.373017i
$419$	5.27955e22			0.132639			0.0663194	−	0.997798i	$-0.478874\pi$
$419$	5.27955e22			0.132639			0.0663194	+	0.997798i	$0.478874\pi$
$420$		0			0
$421$		−	6.84254e23i		−	1.64694i	−0.567358	−	0.823471i	$-0.692034\pi$
$421$		−	6.84254e23i		−	1.64694i	0.567358	−	0.823471i	$-0.307966\pi$
$422$	−6.44739e22	−	8.93386e22i	−0.151905	−	0.210488i
$423$		0			0
$424$	−8.74781e22	−	2.78262e23i	−0.197518	−	0.628292i
$425$	−2.74579e23			−0.606969
$426$		0			0
$427$	1.97744e23			0.419038
$428$	5.10079e22	−	1.53644e23i	0.105839	−	0.318803i
$429$		0			0
$430$	−6.82930e23	+	4.92857e23i	−1.35881	+	0.980629i
$431$			7.07267e23i			1.37812i	0.724703	+	0.689062i	$0.241977\pi$
$431$			7.07267e23i			1.37812i	−0.724703	+	0.689062i	$0.758023\pi$
$432$		0			0
$433$	−4.41534e23			−0.825227			−0.412614	−	0.910906i	$-0.635384\pi$
$433$	−4.41534e23			−0.825227			−0.412614	+	0.910906i	$0.635384\pi$
$434$	−2.15187e23	−	2.98174e23i	−0.393920	−	0.545837i
$435$		0			0
$436$	−3.70927e23	−	1.23143e23i	−0.651494	−	0.216288i
$437$		−	1.80131e23i		−	0.309925i
$438$		0			0
$439$			5.68846e23i			0.939321i	0.882847	+	0.469660i	$0.155624\pi$
$439$			5.68846e23i			0.939321i	−0.882847	+	0.469660i	$0.844376\pi$
$440$	−2.16183e23	−	6.87665e23i	−0.349743	−	1.11251i
$441$		0			0
$442$	9.88658e23	−	7.13495e23i	1.53548	−	1.10813i
$443$	−7.74459e23			−1.17860			−0.589298	−	0.807916i	$-0.700595\pi$
$443$	−7.74459e23			−1.17860			−0.589298	+	0.807916i	$0.700595\pi$
$444$		0			0
$445$			9.54841e23i			1.39537i
$446$	−3.22946e23	+	2.33064e23i	−0.462505	+	0.333781i
$447$		0			0
$448$	−3.25558e23	−	4.66616e23i	−0.447843	−	0.641885i
$449$	1.71986e23			0.231886			0.115943	−	0.993256i	$-0.463011\pi$
$449$	1.71986e23			0.231886			0.115943	+	0.993256i	$0.463011\pi$
$450$		0			0
$451$	−6.27906e23			−0.813403
$452$	1.25979e23	−	3.79471e23i	0.159976	−	0.481873i
$453$		0			0
$454$	−1.42250e23	−	1.97110e23i	−0.173600	−	0.240550i
$455$			8.69211e23i			1.03997i
$456$		0			0
$457$	1.16332e24			1.33799			0.668994	−	0.743268i	$-0.266725\pi$
$457$	1.16332e24			1.33799			0.668994	+	0.743268i	$0.266725\pi$
$458$	−5.89747e23	+	4.25609e23i	−0.665084	+	0.479978i
$459$		0			0
$460$	−2.28295e23	+	6.87661e23i	−0.247557	+	0.745682i
$461$		−	7.56568e23i		−	0.804525i	−0.915524	−	0.402262i	$-0.868224\pi$
$461$		−	7.56568e23i		−	0.804525i	0.915524	−	0.402262i	$-0.131776\pi$
$462$		0			0
$463$		−	5.36371e23i		−	0.548575i	−0.961648	−	0.274288i	$-0.911558\pi$
$463$		−	5.36371e23i		−	0.548575i	0.961648	−	0.274288i	$-0.0884420\pi$
$464$	−8.12722e22	+	1.08912e23i	−0.0815230	+	0.109248i
$465$		0			0
$466$	−5.44523e23	−	7.54521e23i	−0.525464	−	0.728112i
$467$	−6.57507e22			−0.0622370			−0.0311185	−	0.999516i	$-0.509907\pi$
$467$	−6.57507e22			−0.0622370			−0.0311185	+	0.999516i	$0.509907\pi$
$468$		0			0
$469$			1.43800e24i			1.30980i
$470$	1.11314e24	+	1.54243e24i	0.994651	+	1.37824i
$471$		0			0
$472$	1.40955e24	−	4.43125e23i	1.21228	−	0.381108i
$473$	1.69712e24			1.43206
$474$		0			0
$475$	2.06807e23			0.168005
$476$	1.55127e24	+	5.15001e23i	1.23659	+	0.410531i
$477$		0			0
$478$	−3.60481e23	+	2.60152e23i	−0.276714	+	0.199699i
$479$		−	5.93035e23i		−	0.446746i	−0.974733	−	0.223373i	$-0.928293\pi$
$479$		−	5.93035e23i		−	0.446746i	0.974733	−	0.223373i	$-0.0717067\pi$
$480$		0			0
$481$	−2.01376e24			−1.46117
$482$	−1.33582e24	−	1.85099e24i	−0.951317	−	1.31820i
$483$		0			0
$484$	1.55138e21	−	4.67301e21i	0.00106441	−	0.00320619i
$485$			1.18658e24i			0.799136i
$486$		0			0
$487$			7.87024e23i			0.510773i	0.966839	+	0.255386i	$0.0822026\pi$
$487$			7.87024e23i			0.510773i	−0.966839	+	0.255386i	$0.917797\pi$
$488$	−2.52017e23	−	8.01650e23i	−0.160565	−	0.510748i
$489$		0			0
$490$	5.97600e23	−	4.31276e23i	0.366983	−	0.264844i
$491$	−1.18812e24			−0.716352			−0.358176	−	0.933654i	$-0.616601\pi$
$491$	−1.18812e24			−0.716352			−0.358176	+	0.933654i	$0.616601\pi$
$492$		0			0
$493$		−	3.90396e23i		−	0.226925i
$494$	−7.44635e23	+	5.37389e23i	−0.425012	+	0.306723i
$495$		0			0
$496$	−9.34543e23	+	1.25237e24i	−0.514357	+	0.689284i
$497$	−1.70586e24			−0.922012
$498$		0			0
$499$	2.13800e23			0.111456			0.0557280	−	0.998446i	$-0.482252\pi$
$499$	2.13800e23			0.111456			0.0557280	+	0.998446i	$0.482252\pi$
$500$	1.37586e24	+	4.56768e23i	0.704441	+	0.233865i
$501$		0			0
$502$	1.49610e24	+	2.07308e24i	0.738971	+	1.02396i
$503$			4.77628e23i			0.231728i	0.993265	+	0.115864i	$0.0369637\pi$
$503$			4.77628e23i			0.231728i	−0.993265	+	0.115864i	$0.963036\pi$
$504$		0			0
$505$	3.46393e24			1.62161
$506$	1.18395e24	−	8.54436e23i	0.544478	−	0.392939i
$507$		0			0
$508$	3.92914e24	+	1.30442e24i	1.74391	+	0.578956i
$509$			2.94342e24i			1.28349i	0.766918	+	0.641745i	$0.221789\pi$
$509$			2.94342e24i			1.28349i	−0.766918	+	0.641745i	$0.778211\pi$
$510$		0			0
$511$		−	1.49007e22i		−	0.00627218i
$512$	−1.47674e24	+	1.91449e24i	−0.610764	+	0.791813i
$513$		0			0
$514$	−1.17572e23	−	1.62914e23i	−0.0469499	−	0.0650563i
$515$	4.19406e24			1.64577
$516$		0			0
$517$		−	3.83303e24i		−	1.45254i
$518$	−1.57986e24	−	2.18914e24i	−0.588370	−	0.815278i
$519$		0			0
$520$	3.52376e24	−	1.10778e24i	1.26758	−	0.398494i
$521$	2.63387e24			0.931225			0.465613	−	0.884989i	$-0.345834\pi$
$521$	2.63387e24			0.931225			0.465613	+	0.884989i	$0.345834\pi$
$522$		0			0
$523$	1.34682e24			0.460040			0.230020	−	0.973186i	$-0.426121\pi$
$523$	1.34682e24			0.460040			0.230020	+	0.973186i	$0.426121\pi$
$524$	9.33623e23	−	2.81223e24i	0.313466	−	0.944211i
$525$		0			0
$526$	−9.69795e23	+	6.99882e23i	−0.314636	+	0.227067i
$527$		−	4.48913e24i		−	1.43175i
$528$		0			0
$529$	1.77654e24			0.547615
$530$	1.48566e24	+	2.05861e24i	0.450231	+	0.623865i
$531$		0			0
$532$	−1.16838e24	−	3.87888e23i	−0.342279	−	0.113632i
$533$		−	3.21754e24i		−	0.926785i
$534$		0			0
$535$			1.40901e24i			0.392400i
$536$	5.82962e24	−	1.83268e24i	1.59646	−	0.501883i
$537$		0			0
$538$	−4.09976e24	+	2.95872e24i	−1.08572	+	0.783544i
$539$	−1.48507e24			−0.386765
$540$		0			0
$541$		−	6.78202e24i		−	1.70838i	−0.519964	−	0.854188i	$-0.674055\pi$
$541$		−	6.78202e24i		−	1.70838i	0.519964	−	0.854188i	$-0.325945\pi$
$542$	8.30527e23	−	5.99375e23i	0.205760	−	0.148493i
$543$		0			0
$544$	1.10770e23	−	6.94515e24i	0.0265481	−	1.66453i
$545$	3.40162e24			0.801895
$546$		0			0
$547$	−7.61034e23			−0.173587			−0.0867937	−	0.996226i	$-0.527662\pi$
$547$	−7.61034e23			−0.173587			−0.0867937	+	0.996226i	$0.527662\pi$
$548$	−2.63060e24	+	7.92381e24i	−0.590242	+	1.77791i
$549$		0			0
$550$	9.80969e23	+	1.35928e24i	0.213006	+	0.295152i
$551$			2.94037e23i			0.0628114i
$552$		0			0
$553$	5.45999e24			1.12893
$554$	6.48709e23	−	4.68160e23i	0.131966	−	0.0952373i
$555$		0			0
$556$	2.99178e23	−	9.01175e23i	0.0589193	−	0.177475i
$557$		−	7.01797e24i		−	1.35993i	−0.733247	−	0.679963i	$-0.761996\pi$
$557$		−	7.01797e24i		−	1.35993i	0.733247	−	0.679963i	$-0.238004\pi$
$558$		0			0
$559$			8.69642e24i			1.63168i
$560$	3.96876e24	+	2.96156e24i	0.732761	+	0.546800i
$561$		0			0
$562$	4.03215e23	+	5.58717e23i	0.0720958	+	0.0998999i
$563$	−5.94509e23			−0.104612			−0.0523061	−	0.998631i	$-0.516657\pi$
$563$	−5.94509e23			−0.104612			−0.0523061	+	0.998631i	$0.516657\pi$
$564$		0			0
$565$			3.47997e24i			0.593116i
$566$	1.22498e24	+	1.69740e24i	0.205486	+	0.284733i
$567$		0			0
$568$	2.17405e24	+	6.91552e24i	0.353293	+	1.12380i
$569$	−5.55373e24			−0.888330			−0.444165	−	0.895945i	$-0.646500\pi$
$569$	−5.55373e24			−0.888330			−0.444165	+	0.895945i	$0.646500\pi$
$570$		0			0
$571$	−2.47515e24			−0.383598			−0.191799	−	0.981434i	$-0.561432\pi$
$571$	−2.47515e24			−0.383598			−0.191799	+	0.981434i	$0.561432\pi$
$572$	−7.06422e24	−	2.34523e24i	−1.07770	−	0.357784i
$573$		0			0
$574$	3.49776e24	−	2.52427e24i	0.517110	−	0.373188i
$575$		−	1.68494e24i		−	0.245230i
$576$		0			0
$577$	4.72502e24			0.666532			0.333266	−	0.942833i	$-0.391849\pi$
$577$	4.72502e24			0.666532			0.333266	+	0.942833i	$0.391849\pi$
$578$	7.46386e24	+	1.03423e25i	1.03660	+	1.43638i
$579$		0			0
$580$	3.72656e23	−	1.12250e24i	0.0501715	−	0.151125i
$581$		−	2.58350e24i		−	0.342470i
$582$		0			0
$583$		−	5.11574e24i		−	0.657494i
$584$	−6.04070e22	+	1.89903e22i	−0.00764490	+	0.00240335i
$585$		0			0
$586$	−5.49418e24	+	3.96504e24i	−0.674256	+	0.486597i
$587$	−1.57029e25			−1.89774			−0.948868	−	0.315673i	$-0.897770\pi$
$587$	−1.57029e25			−1.89774			−0.948868	+	0.315673i	$0.897770\pi$
$588$		0			0
$589$			3.38112e24i			0.396299i
$590$	−1.04280e25	+	7.52566e24i	−1.20374	+	0.868713i
$591$		0			0
$592$	−6.86124e24	+	9.19468e24i	−0.768259	+	1.02954i
$593$	−3.27442e24			−0.361112			−0.180556	−	0.983565i	$-0.557790\pi$
$593$	−3.27442e24			−0.361112			−0.180556	+	0.983565i	$0.557790\pi$
$594$		0			0
$595$	−1.42260e25			−1.52206
$596$	3.42254e24	+	1.13624e24i	0.360689	+	0.119744i
$597$		0			0
$598$	4.37833e24	+	6.06686e24i	0.447711	+	0.620373i
$599$			1.49219e24i			0.150308i	0.997172	+	0.0751539i	$0.0239448\pi$
$599$			1.49219e24i			0.150308i	−0.997172	+	0.0751539i	$0.976055\pi$
$600$		0			0
$601$	−1.53036e25			−1.49597			−0.747986	−	0.663715i	$-0.768979\pi$
$601$	−1.53036e25			−1.49597			−0.747986	+	0.663715i	$0.768979\pi$
$602$	−9.45380e24	+	6.82263e24i	−0.910412	+	0.657027i
$603$		0			0
$604$	6.44108e23	+	2.13835e23i	0.0602041	+	0.0199870i
$605$			4.28543e22i			0.00394635i
$606$		0			0
$607$		−	1.56235e25i		−	1.39663i	−0.715792	−	0.698314i	$-0.753934\pi$
$607$		−	1.56235e25i		−	1.39663i	0.715792	−	0.698314i	$-0.246066\pi$
$608$	−8.34298e22	+	5.23093e24i	−0.00734833	+	0.460731i
$609$		0			0
$610$	4.28005e24	+	5.93068e24i	0.366000	+	0.507149i
$611$	1.96413e25			1.65501
$612$		0			0
$613$		−	1.88084e25i		−	1.53889i	−0.638712	−	0.769446i	$-0.720533\pi$
$613$		−	1.88084e25i		−	1.53889i	0.638712	−	0.769446i	$-0.279467\pi$
$614$	2.75955e24	+	3.82378e24i	0.222496	+	0.308303i
$615$		0			0
$616$	−2.99263e24	−	9.51936e24i	−0.234329	−	0.745386i
$617$	5.11620e24			0.394804			0.197402	−	0.980323i	$-0.436750\pi$
$617$	5.11620e24			0.394804			0.197402	+	0.980323i	$0.436750\pi$
$618$		0			0
$619$	5.65819e24			0.424094			0.212047	−	0.977259i	$-0.431987\pi$
$619$	5.65819e24			0.424094			0.212047	+	0.977259i	$0.431987\pi$
$620$	4.28515e24	−	1.29076e25i	0.316549	−	0.953498i
$621$		0			0
$622$	−9.23372e23	+	6.66380e23i	−0.0662618	+	0.0478199i
$623$			1.32179e25i			0.934909i
$624$		0			0
$625$	−1.79231e25			−1.23167
$626$	8.99776e24	+	1.24678e25i	0.609489	+	0.844541i
$627$		0			0
$628$	−8.90309e23	−	2.95571e23i	−0.0586009	−	0.0194547i
$629$		−	3.29584e25i		−	2.13850i
$630$		0			0
$631$			1.37960e25i			0.869940i	0.900445	+	0.434970i	$0.143241\pi$
$631$			1.37960e25i			0.869940i	−0.900445	+	0.434970i	$0.856759\pi$
$632$	−6.95854e24	−	2.21346e25i	−0.432578	−	1.37600i
$633$		0			0
$634$	−1.09034e25	+	7.86878e24i	−0.658808	+	0.475449i
$635$	−3.60325e25			−2.14650
$636$		0			0
$637$		−	7.60983e24i		−	0.440677i
$638$	−1.93263e24	+	1.39474e24i	−0.110347	+	0.0796355i
$639$		0			0
$640$	6.94807e24	−	1.98636e25i	0.385695	−	1.10265i
$641$	−2.98207e25			−1.63228			−0.816142	−	0.577852i	$-0.803891\pi$
$641$	−2.98207e25			−1.63228			−0.816142	+	0.577852i	$0.803891\pi$
$642$		0			0
$643$	−2.25277e25			−1.19899			−0.599497	−	0.800377i	$-0.704633\pi$
$643$	−2.25277e25			−1.19899			−0.599497	+	0.800377i	$0.704633\pi$
$644$	−3.16028e24	+	9.51930e24i	−0.165864	+	0.499611i
$645$		0			0
$646$	−8.79523e24	−	1.21871e25i	−0.448905	−	0.622027i
$647$		−	2.02021e25i		−	1.01685i	−0.861105	−	0.508427i	$-0.830227\pi$
$647$		−	2.02021e25i		−	1.01685i	0.861105	−	0.508427i	$-0.169773\pi$
$648$		0			0
$649$	2.59140e25			1.26862
$650$	−6.96529e24	+	5.02671e24i	−0.336294	+	0.242697i
$651$		0			0
$652$	1.04006e25	−	3.13282e25i	0.488460	−	1.47132i
$653$		−	2.21111e25i		−	1.02422i	−0.858921	−	0.512109i	$-0.828865\pi$
$653$		−	2.21111e25i		−	1.02422i	0.858921	−	0.512109i	$-0.171135\pi$
$654$		0			0
$655$			2.57898e25i			1.16219i
$656$	−1.46911e25	−	1.09627e25i	−0.653008	−	0.487287i
$657$		0			0
$658$	1.54093e25	+	2.13519e25i	0.666422	+	0.923431i
$659$	6.18455e24			0.263839			0.131920	−	0.991260i	$-0.457886\pi$
$659$	6.18455e24			0.263839			0.131920	+	0.991260i	$0.457886\pi$
$660$		0			0
$661$		−	2.01390e25i		−	0.836035i	−0.908439	−	0.418018i	$-0.862725\pi$
$661$		−	2.01390e25i		−	0.836035i	0.908439	−	0.418018i	$-0.137275\pi$
$662$	1.47021e25	+	2.03720e25i	0.602085	+	0.834282i
$663$		0			0
$664$	−1.04734e25	+	3.29257e24i	−0.417423	+	0.131227i
$665$	1.07147e25			0.421295
$666$		0			0
$667$	2.39565e24			0.0916833
$668$	5.00260e25	+	1.66080e25i	1.88889	+	0.627088i
$669$		0			0
$670$	−4.31280e25	+	3.11247e25i	−1.58521	+	1.14401i
$671$		−	1.47380e25i		−	0.534487i
$672$		0			0
$673$	−3.96508e24			−0.139996			−0.0699980	−	0.997547i	$-0.522299\pi$
$673$	−3.96508e24			−0.139996			−0.0699980	+	0.997547i	$0.522299\pi$
$674$	−1.09359e25	−	1.51534e25i	−0.380992	−	0.527923i
$675$		0			0
$676$	2.72917e24	−	8.22071e24i	0.0925785	−	0.278862i
$677$			1.33836e24i			0.0447997i	0.999749	+	0.0223999i	$0.00713070\pi$
$677$			1.33836e24i			0.0447997i	−0.999749	+	0.0223999i	$0.992869\pi$
$678$		0			0
$679$			1.64258e25i			0.535425i
$680$	1.81305e25	+	5.76719e25i	0.583217	+	1.85517i
$681$		0			0
$682$	−2.22232e25	+	1.60380e25i	−0.696220	+	0.502448i
$683$	5.65250e24			0.174765			0.0873825	−	0.996175i	$-0.472150\pi$
$683$	5.65250e24			0.174765			0.0873825	+	0.996175i	$0.472150\pi$
$684$		0			0
$685$		−	7.26659e25i		−	2.18834i
$686$	2.96256e25	−	2.13802e25i	0.880542	−	0.635470i
$687$		0			0
$688$	3.97072e25	+	2.96303e25i	1.14967	+	0.857907i
$689$	2.62143e25			0.749143
$690$		0			0
$691$	−6.02349e25			−1.67705			−0.838525	−	0.544864i	$-0.816581\pi$
$691$	−6.02349e25			−1.67705			−0.838525	+	0.544864i	$0.816581\pi$
$692$	−3.27115e25	−	1.08598e25i	−0.898972	−	0.298447i
$693$		0			0
$694$	−1.71461e25	−	2.37586e25i	−0.459125	−	0.636188i
$695$			8.26430e24i			0.218445i
$696$		0			0
$697$	5.26602e25			1.35640
$698$	−6.99354e24	+	5.04710e24i	−0.177827	+	0.128334i
$699$		0			0
$700$	−1.09290e25	−	3.62829e24i	−0.270831	−	0.0899123i
$701$			1.73501e25i			0.424463i	0.977219	+	0.212231i	$0.0680731\pi$
$701$			1.73501e25i			0.424463i	−0.977219	+	0.212231i	$0.931927\pi$
$702$		0			0
$703$			2.48235e25i			0.591924i
$704$	−3.47772e25	+	2.42641e25i	−0.818730	+	0.571229i
$705$		0			0
$706$	1.09580e25	+	1.51840e25i	0.251472	+	0.348453i
$707$	4.79512e25			1.08649
$708$		0			0
$709$		−	8.74520e24i		−	0.193176i	−0.995324	−	0.0965881i	$-0.969207\pi$
$709$		−	8.74520e24i		−	0.193176i	0.995324	−	0.0965881i	$-0.0307930\pi$
$710$	−3.69223e25	−	5.11616e25i	−0.805311	−	1.11588i
$711$		0			0
$712$	5.35849e25	−	1.68457e25i	1.13952	−	0.358235i
$713$	2.75474e25			0.578462
$714$		0			0
$715$	6.47830e25			1.32650
$716$	5.35655e24	−	1.61348e25i	0.108310	−	0.326247i
$717$		0			0
$718$	−6.37374e25	+	4.59980e25i	−1.25682	+	0.907025i
$719$			3.39963e25i			0.662021i	0.943627	+	0.331011i	$0.107390\pi$
$719$			3.39963e25i			0.662021i	−0.943627	+	0.331011i	$0.892610\pi$
$720$		0			0
$721$	5.80584e25			1.10267
$722$	−2.45746e25	−	3.40519e25i	−0.460948	−	0.638715i
$723$		0			0
$724$	6.20130e24	+	2.05875e24i	0.113458	+	0.0376667i
$725$			2.75041e24i			0.0497000i
$726$		0			0
$727$		−	2.19781e25i		−	0.387419i	−0.981059	−	0.193710i	$-0.937948\pi$
$727$		−	2.19781e25i		−	0.387419i	0.981059	−	0.193710i	$-0.0620519\pi$
$728$	4.87794e25	−	1.53349e25i	0.849287	−	0.266993i
$729$		0			0
$730$	4.46896e23	−	3.22516e23i	0.00759104	−	0.00547830i
$731$	−1.42331e26			−2.38805
$732$		0			0
$733$			4.81569e25i			0.788357i	0.919034	+	0.394179i	$0.128971\pi$
$733$			4.81569e25i			0.788357i	−0.919034	+	0.394179i	$0.871029\pi$
$734$	−5.32398e25	+	3.84222e25i	−0.860939	+	0.621323i
$735$		0			0
$736$	4.26186e25	+	6.79738e23i	0.672510	+	0.0107261i
$737$	1.07175e26			1.67066
$738$		0			0
$739$	−1.08279e26			−1.64719			−0.823596	−	0.567176i	$-0.808036\pi$
$739$	−1.08279e26			−1.64719			−0.823596	+	0.567176i	$0.808036\pi$
$740$	3.14608e25	−	9.47651e25i	0.472807	−	1.42417i
$741$		0			0
$742$	2.05660e25	+	2.84973e25i	0.301657	+	0.417993i
$743$			2.25860e25i			0.327296i	0.986519	+	0.163648i	$0.0523261\pi$
$743$			2.25860e25i			0.327296i	−0.986519	+	0.163648i	$0.947674\pi$
$744$		0			0
$745$	−3.13867e25			−0.443955
$746$	−5.13560e25	+	3.70627e25i	−0.717699	+	0.517949i
$747$		0			0
$748$	3.83834e25	−	1.15617e26i	0.523636	−	1.57728i
$749$			1.95049e25i			0.262910i
$750$		0			0
$751$			7.67021e25i			1.00936i	0.863305	+	0.504682i	$0.168390\pi$
$751$			7.67021e25i			1.00936i	−0.863305	+	0.504682i	$0.831610\pi$
$752$	6.69216e25	−	8.96810e25i	0.870174	−	1.16611i
$753$		0			0
$754$	−7.14697e24	−	9.90323e24i	−0.0907361	−	0.125729i
$755$	−5.90684e24			−0.0741025
$756$		0			0
$757$		−	6.00705e25i		−	0.735865i	−0.929852	−	0.367933i	$-0.880066\pi$
$757$		−	6.00705e25i		−	0.735865i	0.929852	−	0.367933i	$-0.119934\pi$
$758$	5.97765e25	+	8.28296e25i	0.723615	+	1.00268i
$759$		0			0
$760$	−1.36555e25	−	4.34372e25i	−0.161430	−	0.513499i
$761$	−2.68948e25			−0.314200			−0.157100	−	0.987583i	$-0.550215\pi$
$761$	−2.68948e25			−0.314200			−0.157100	+	0.987583i	$0.550215\pi$
$762$		0			0
$763$	4.70887e25			0.537274
$764$	6.11732e25	+	2.03087e25i	0.689797	+	0.229004i
$765$		0			0
$766$	1.16972e26	−	8.44162e25i	1.28831	−	0.929752i
$767$			1.32790e26i			1.44546i
$768$		0			0
$769$	7.48604e25			0.796004			0.398002	−	0.917385i	$-0.369704\pi$
$769$	7.48604e25			0.796004			0.398002	+	0.917385i	$0.369704\pi$
$770$	5.08244e25	+	7.04250e25i	0.534140	+	0.740134i
$771$		0			0
$772$	−2.43297e24	+	7.32851e24i	−0.0249794	+	0.0752419i
$773$		−	1.49818e26i		−	1.52037i	−0.649706	−	0.760186i	$-0.725108\pi$
$773$		−	1.49818e26i		−	1.52037i	0.649706	−	0.760186i	$-0.274892\pi$
$774$		0			0
$775$			3.16268e25i			0.313574i
$776$	6.65898e25	−	2.09340e25i	0.652608	−	0.205162i
$777$		0			0
$778$	−5.77534e25	+	4.16795e25i	−0.553046	+	0.399122i
$779$	−3.96625e25			−0.375442
$780$		0			0
$781$			1.27139e26i			1.17603i
$782$	−9.92938e25	+	7.16584e25i	−0.907949	+	0.655249i
$783$		0			0
$784$	−3.47459e25	−	2.59281e25i	−0.310498	−	0.231700i
$785$	8.16465e24			0.0721291
$786$		0			0
$787$	−8.02440e25			−0.692851			−0.346426	−	0.938077i	$-0.612605\pi$
$787$	−8.02440e25			−0.692851			−0.346426	+	0.938077i	$0.612605\pi$
$788$	−1.86308e26	−	6.18518e25i	−1.59036	−	0.527979i
$789$		0			0
$790$	1.18178e26	+	1.63754e26i	0.986037	+	1.36631i
$791$			4.81733e25i			0.397391i
$792$		0			0
$793$	7.55212e25			0.608990
$794$	3.04387e25	−	2.19670e25i	0.242684	−	0.175140i
$795$		0			0
$796$	1.07748e26	+	3.57711e25i	0.839834	+	0.278814i
$797$			1.67418e26i			1.29026i	0.764073	+	0.645129i	$0.223197\pi$
$797$			1.67418e26i			1.29026i	−0.764073	+	0.645129i	$0.776803\pi$
$798$		0			0
$799$			3.21462e26i			2.42219i
$800$	−7.80399e23	+	4.89299e25i	−0.00581442	+	0.364556i
$801$		0			0
$802$	−2.61700e25	−	3.62626e25i	−0.190649	−	0.264174i
$803$	−1.11056e24			−0.00800023
$804$		0			0
$805$		−	8.72975e25i		−	0.614949i
$806$	−8.21826e25	−	1.13877e26i	−0.572485	−	0.793267i
$807$		0			0
$808$	−6.11119e25	−	1.94393e26i	−0.416317	−	1.32427i
$809$	−2.62973e25			−0.177163			−0.0885816	−	0.996069i	$-0.528233\pi$
$809$	−2.62973e25			−0.177163			−0.0885816	+	0.996069i	$0.528233\pi$
$810$		0			0
$811$	2.21655e26			1.46046			0.730231	−	0.683201i	$-0.239413\pi$
$811$	2.21655e26			1.46046			0.730231	+	0.683201i	$0.239413\pi$
$812$	5.15869e24	−	1.55388e25i	0.0336152	−	0.101254i
$813$		0			0
$814$	−1.63158e26	+	1.17748e26i	−1.03990	+	0.750472i
$815$			2.87298e26i			1.81098i
$816$		0			0
$817$	1.07200e26			0.660995
$818$	−4.22020e25	−	5.84773e25i	−0.257367	−	0.356622i
$819$		0			0
$820$	1.51414e26	+	5.02674e25i	0.903317	+	0.299890i
$821$			1.11156e26i			0.655912i	0.944693	+	0.327956i	$0.106360\pi$
$821$			1.11156e26i			0.655912i	−0.944693	+	0.327956i	$0.893640\pi$
$822$		0			0
$823$			4.27602e25i			0.246854i	0.992354	+	0.123427i	$0.0393885\pi$
$823$			4.27602e25i			0.246854i	−0.992354	+	0.123427i	$0.960611\pi$
$824$	−7.39931e25	−	2.35367e26i	−0.422519	−	1.34400i
$825$		0			0
$826$	−1.44354e26	+	1.04178e26i	−0.806510	+	0.582043i
$827$	2.87229e26			1.58737			0.793686	−	0.608328i	$-0.208160\pi$
$827$	2.87229e26			1.58737			0.793686	+	0.608328i	$0.208160\pi$
$828$		0			0
$829$		−	1.66637e26i		−	0.901114i	−0.892748	−	0.450557i	$-0.851225\pi$
$829$		−	1.66637e26i		−	0.901114i	0.892748	−	0.450557i	$-0.148775\pi$
$830$	7.74833e25	−	5.59182e25i	0.414482	−	0.299123i
$831$		0			0
$832$	−1.24335e26	−	1.78207e26i	−0.650853	−	0.932855i
$833$	1.24547e26			0.644954
$834$		0			0
$835$	−4.58768e26			−2.32495
$836$	−2.89096e25	+	8.70804e25i	−0.144939	+	0.436580i
$837$		0			0
$838$	1.58188e25	+	2.19194e25i	0.0776205	+	0.107555i
$839$		−	1.34302e26i		−	0.651966i	−0.945376	−	0.325983i	$-0.894305\pi$
$839$		−	1.34302e26i		−	0.651966i	0.945376	−	0.325983i	$-0.105695\pi$
$840$		0			0
$841$	2.06547e26			0.981419
$842$	2.84085e26	−	2.05018e26i	1.33549	−	0.963794i
$843$		0			0
$844$	1.77732e25	−	5.35358e25i	0.0817869	−	0.246356i
$845$			7.53887e25i			0.343238i
$846$		0			0
$847$			5.93232e23i			0.00264408i
$848$	8.93168e25	−	1.19693e26i	0.393886	−	0.527842i
$849$		0			0
$850$	−8.22702e25	−	1.13998e26i	−0.355199	−	0.492184i
$851$	2.02248e26			0.864008
$852$		0			0
$853$		−	4.35359e26i		−	1.82099i	−0.413525	−	0.910493i	$-0.635702\pi$
$853$		−	4.35359e26i		−	1.82099i	0.413525	−	0.910493i	$-0.364298\pi$
$854$	5.92488e25	+	8.20984e25i	0.245222	+	0.339793i
$855$		0			0
$856$	7.90724e25	−	2.48582e25i	0.320450	−	0.100741i
$857$	1.71357e26			0.687184			0.343592	−	0.939119i	$-0.388356\pi$
$857$	1.71357e26			0.687184			0.343592	+	0.939119i	$0.388356\pi$
$858$		0			0
$859$	1.21980e25			0.0479016			0.0239508	−	0.999713i	$-0.492375\pi$
$859$	1.21980e25			0.0479016			0.0239508	+	0.999713i	$0.492375\pi$
$860$	−4.09243e26	−	1.35863e26i	−1.59036	−	0.527979i
$861$		0			0
$862$	−2.93639e26	+	2.11914e26i	−1.11750	+	0.806480i
$863$			1.05114e26i			0.395878i	0.980214	+	0.197939i	$0.0634248\pi$
$863$			1.05114e26i			0.395878i	−0.980214	+	0.197939i	$0.936575\pi$
$864$		0			0
$865$	2.99984e26			1.10650
$866$	−1.32294e26	−	1.83314e26i	−0.482924	−	0.669166i
$867$		0			0
$868$	5.93194e25	−	1.78680e26i	0.212090	−	0.638849i
$869$		−	4.06937e26i		−	1.43996i
$870$		0			0
$871$			5.49192e26i			1.90353i
$872$	−6.00126e25	−	1.90896e26i	−0.205871	−	0.654861i
$873$		0			0
$874$	7.47860e25	−	5.39716e25i	0.251314	−	0.181369i
$875$	−1.74664e26			−0.580938
$876$		0			0
$877$		−	3.91748e26i		−	1.27647i	−0.769841	−	0.638235i	$-0.779665\pi$
$877$		−	3.91748e26i		−	1.27647i	0.769841	−	0.638235i	$-0.220335\pi$
$878$	−2.36170e26	+	1.70439e26i	−0.761683	+	0.549692i
$879$		0			0
$880$	2.20727e26	−	2.95794e26i	0.697449	−	0.934643i
$881$	−2.84213e26			−0.888917			−0.444459	−	0.895799i	$-0.646604\pi$
$881$	−2.84213e26			−0.888917			−0.444459	+	0.895799i	$0.646604\pi$
$882$		0			0
$883$	3.72981e26			1.14299			0.571493	−	0.820607i	$-0.306364\pi$
$883$	3.72981e26			1.14299			0.571493	+	0.820607i	$0.306364\pi$
$884$	5.92450e26	+	1.96686e26i	1.79714	+	0.596626i
$885$		0			0
$886$	−2.32046e26	−	3.21535e26i	−0.689716	−	0.955708i
$887$			5.42179e25i			0.159526i	0.996814	+	0.0797628i	$0.0254163\pi$
$887$			5.42179e25i			0.159526i	−0.996814	+	0.0797628i	$0.974584\pi$
$888$		0			0
$889$	−4.98799e26			−1.43817
$890$	−3.96426e26	+	2.86093e26i	−1.13149	+	0.816576i
$891$		0			0
$892$	−1.93524e26	−	6.42476e25i	−0.541317	−	0.179710i
$893$		−	2.42118e26i		−	0.670447i
$894$		0			0
$895$			1.47966e26i			0.401563i
$896$	9.61822e25	−	2.74972e26i	0.258418	−	0.738783i
$897$		0			0
$898$	5.15309e25	+	7.14041e25i	0.135700	+	0.188034i
$899$	−4.49670e25			−0.117235
$900$		0			0
$901$			4.29039e26i			1.09641i
$902$	−1.88135e26	−	2.60691e26i	−0.476005	−	0.659579i
$903$		0			0
$904$	1.95293e26	−	6.13949e25i	0.484363	−	0.152271i
$905$	−5.68696e25			−0.139651
$906$		0			0
$907$	−7.92341e26			−1.90742			−0.953711	−	0.300726i	$-0.902771\pi$
$907$	−7.92341e26			−1.90742			−0.953711	+	0.300726i	$0.902771\pi$
$908$	3.92135e25	−	1.18117e26i	0.0934679	−	0.281541i
$909$		0			0
$910$	−3.60874e26	+	2.60436e26i	−0.843303	+	0.608595i
$911$			6.20038e25i			0.143467i	0.997424	+	0.0717337i	$0.0228532\pi$
$911$			6.20038e25i			0.143467i	−0.997424	+	0.0717337i	$0.977147\pi$
$912$		0			0
$913$	−1.92550e26			−0.436824
$914$	3.48557e26	+	4.82979e26i	0.782993	+	1.08496i
$915$		0			0
$916$	−3.53404e26	−	1.17325e26i	−0.778416	−	0.258424i
$917$			3.57008e26i			0.778671i
$918$		0			0
$919$		−	4.21982e26i		−	0.902515i	−0.892394	−	0.451257i	$-0.850976\pi$
$919$		−	4.21982e26i		−	0.902515i	0.892394	−	0.451257i	$-0.149024\pi$
$920$	−3.53902e26	+	1.11257e26i	−0.749535	+	0.235634i
$921$		0			0
$922$	3.14108e26	−	2.26685e26i	0.652379	−	0.470809i
$923$	−6.51491e26			−1.33996
$924$		0			0
$925$			2.32198e26i			0.468364i
$926$	2.22687e26	−	1.60709e26i	0.444833	−	0.321027i
$927$		0			0
$928$	−6.95685e25	−	1.10957e24i	−0.136295	−	0.00217382i
$929$	2.05506e25			0.0398735			0.0199367	−	0.999801i	$-0.493654\pi$
$929$	2.05506e25			0.0398735			0.0199367	+	0.999801i	$0.493654\pi$
$930$		0			0
$931$	−9.38061e25			−0.178519
$932$	1.50106e26	−	4.52144e26i	0.282914	−	0.852185i
$933$		0			0
$934$	−1.97005e25	−	2.72980e25i	−0.0364212	−	0.0504672i
$935$			1.06028e27i			1.94140i
$936$		0			0
$937$	−6.71887e26			−1.20681			−0.603406	−	0.797434i	$-0.706190\pi$
$937$	−6.71887e26			−1.20681			−0.603406	+	0.797434i	$0.706190\pi$
$938$	−5.97022e26	+	4.30859e26i	−1.06210	+	0.766495i
$939$		0			0
$940$	−3.06855e26	+	9.24299e26i	−0.535529	+	1.61310i
$941$			4.67913e26i			0.808833i	0.914575	+	0.404417i	$0.132525\pi$
$941$			4.67913e26i			0.808833i	−0.914575	+	0.404417i	$0.867475\pi$
$942$		0			0
$943$			3.23147e26i			0.548018i
$944$	6.06308e26	+	4.52439e26i	1.01846	+	0.759997i
$945$		0			0
$946$	5.08495e26	+	7.04599e26i	0.838044	+	1.16124i
$947$	−4.93745e26			−0.806033			−0.403017	−	0.915193i	$-0.632038\pi$
$947$	−4.93745e26			−0.806033			−0.403017	+	0.915193i	$0.632038\pi$
$948$		0			0
$949$		−	5.69077e24i		−	0.00911539i
$950$	6.19641e25	+	8.58609e25i	0.0983168	+	0.136233i
$951$		0			0
$952$	2.50981e26	+	7.98353e26i	0.390758	+	1.24298i
$953$	−5.69412e25			−0.0878193			−0.0439097	−	0.999036i	$-0.513981\pi$
$953$	−5.69412e25			−0.0878193			−0.0439097	+	0.999036i	$0.513981\pi$
$954$		0			0
$955$	−5.60994e26			−0.849040
$956$	−2.16017e26	−	7.17148e25i	−0.323867	−	0.107520i
$957$		0			0
$958$	2.46213e26	−	1.77687e26i	0.362261	−	0.261436i
$959$		−	1.00592e27i		−	1.46620i
$960$		0			0
$961$	1.81981e26			0.260325
$962$	−6.03369e26	−	8.36061e26i	−0.855082	−	1.18485i
$963$		0			0
$964$	3.68240e26	−	1.10920e27i	0.512197	−	1.54282i
$965$		−	6.72067e25i		−	0.0926119i
$966$		0			0
$967$		−	1.15434e27i		−	1.56133i	−0.624952	−	0.780663i	$-0.714882\pi$
$967$		−	1.15434e27i		−	1.56133i	0.624952	−	0.780663i	$-0.285118\pi$
$968$	2.40495e24	−	7.56051e23i	0.00322275	−	0.00101315i
$969$		0			0
$970$	−4.92637e26	+	3.55526e26i	−0.648009	+	0.467656i
$971$	−7.22634e25			−0.0941772			−0.0470886	−	0.998891i	$-0.514994\pi$
$971$	−7.22634e25			−0.0941772			−0.0470886	+	0.998891i	$0.514994\pi$
$972$		0			0
$973$			1.14403e26i			0.146360i
$974$	−3.26752e26	+	2.35811e26i	−0.414179	+	0.298905i
$975$		0			0
$976$	2.57314e26	−	3.44824e26i	0.320196	−	0.429091i
$977$	7.87011e26			0.970353			0.485177	−	0.874416i	$-0.338755\pi$
$977$	7.87011e26			0.970353			0.485177	+	0.874416i	$0.338755\pi$
$978$		0			0
$979$	9.85138e26			1.19249
$980$	3.58110e26	+	1.18888e26i	0.429518	+	0.142594i
$981$		0			0
$982$	−3.55988e26	−	4.93277e26i	−0.419211	−	0.580881i
$983$		−	7.96537e26i		−	0.929446i	−0.885456	−	0.464723i	$-0.846154\pi$
$983$		−	7.96537e26i		−	0.929446i	0.885456	−	0.464723i	$-0.153846\pi$
$984$		0			0
$985$	1.70855e27			1.95750
$986$	1.62082e26	−	1.16972e26i	0.184011	−	0.132797i
$987$		0			0
$988$	−4.46220e26	−	1.48139e26i	−0.497436	−	0.165142i
$989$		−	8.73408e26i		−	0.964829i
$990$		0			0
$991$		−	9.86827e25i		−	0.107048i	−0.998567	−	0.0535239i	$-0.982955\pi$
$991$		−	9.86827e25i		−	0.107048i	0.998567	−	0.0535239i	$-0.0170453\pi$
$992$	−7.99964e26	−	1.27589e25i	−0.859934	−	0.0137154i
$993$		0			0
$994$	−5.11116e26	−	7.08230e26i	−0.539563	−	0.747648i
$995$	−9.88116e26			−1.03371
$996$		0			0
$997$		−	1.06974e27i		−	1.09906i	−0.835474	−	0.549530i	$-0.814807\pi$
$997$		−	1.06974e27i		−	1.09906i	0.835474	−	0.549530i	$-0.185193\pi$
$998$	6.40595e25	+	8.87644e25i	0.0652242	+	0.0903782i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	72.19.b.b.19.12		16
3.2	odd	2		8.19.d.b.3.5	✓	16
8.3	odd	2	inner	72.19.b.b.19.11		16
12.11	even	2		32.19.d.b.15.8		16
24.5	odd	2		32.19.d.b.15.7		16
24.11	even	2		8.19.d.b.3.6	yes	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8.19.d.b.3.5	✓	16	3.2	odd	2
8.19.d.b.3.6	yes	16	24.11	even	2
32.19.d.b.15.7		16	24.5	odd	2
32.19.d.b.15.8		16	12.11	even	2
72.19.b.b.19.11		16	8.3	odd	2	inner
72.19.b.b.19.12		16	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:	\( N \)	\(=\)	\( 72 = 2^{3} \cdot 3^{2} \)
Weight:	\( k \)	\(=\)	\( 19 \)
Character orbit:	\([\chi]\)	\(=\)	72.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(299.623 + 415.174i) q^{2} +(-82595.7 + 248792. i) q^{4} -2.28157e6i q^{5} -3.15838e7i q^{7} +(-1.28040e8 + 4.02522e7i) q^{8} +O(q^{10})\)	\(q+(299.623 + 415.174i) q^{2} +(-82595.7 + 248792. i) q^{4} -2.28157e6i q^{5} -3.15838e7i q^{7} +(-1.28040e8 + 4.02522e7i) q^{8} +(9.47248e8 - 6.83611e8i) q^{10} -2.35396e9 q^{11} -1.20623e10i q^{13} +(1.31128e10 - 9.46323e9i) q^{14} +(-5.50754e10 - 4.10983e10i) q^{16} +1.97418e11 q^{17} -1.48691e11 q^{19} +(5.67635e11 + 1.88448e11i) q^{20} +(-7.05302e11 - 9.77305e11i) q^{22} +1.21145e12i q^{23} -1.39085e12 q^{25} +(5.00794e12 - 3.61413e12i) q^{26} +(7.85778e12 + 2.60868e12i) q^{28} -1.97751e12i q^{29} -2.27392e13i q^{31} +(5.61095e11 - 3.51799e13i) q^{32} +(5.91511e13 + 8.19629e13i) q^{34} -7.20605e13 q^{35} -1.66947e14i q^{37} +(-4.45513e13 - 6.17327e13i) q^{38} +(9.18382e13 + 2.92131e14i) q^{40} +2.66745e14 q^{41} -7.20962e14 q^{43} +(1.94427e14 - 5.85647e14i) q^{44} +(-5.02962e14 + 3.62978e14i) q^{46} +1.62833e15i q^{47} +6.30880e14 q^{49} +(-4.16731e14 - 5.77445e14i) q^{50} +(3.00099e15 + 9.96290e14i) q^{52} +2.17325e15i q^{53} +5.37072e15i q^{55} +(1.27132e15 + 4.04397e15i) q^{56} +(8.21010e14 - 5.92507e14i) q^{58} -1.10087e16 q^{59} +6.26095e15i q^{61} +(9.44075e15 - 6.81320e15i) q^{62} +(1.47739e16 - 1.03078e16i) q^{64} -2.75208e16 q^{65} -4.55298e16 q^{67} +(-1.63059e16 + 4.91160e16i) q^{68} +(-2.15910e16 - 2.99177e16i) q^{70} -5.40107e16i q^{71} +4.71784e14 q^{73} +(6.93122e16 - 5.00213e16i) q^{74} +(1.22812e16 - 3.69931e16i) q^{76} +7.43470e16i q^{77} +1.72873e17i q^{79} +(-9.37685e16 + 1.25658e17i) q^{80} +(7.99229e16 + 1.10746e17i) q^{82} +8.17983e16 q^{83} -4.50422e17i q^{85} +(-2.16017e17 - 2.99325e17i) q^{86} +(3.01400e17 - 9.47522e16i) q^{88} -4.18502e17 q^{89} -3.80971e17 q^{91} +(-3.01399e17 - 1.00060e17i) q^{92} +(-6.76042e17 + 4.87886e17i) q^{94} +3.39248e17i q^{95} -5.20072e17 q^{97} +(1.89026e17 + 2.61925e17i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 426 q^{2} - 444332 q^{4} - 304914744 q^{8}+O(q^{10}) \) 16 * q - 426 * q^2 - 444332 * q^4 - 304914744 * q^8	\( 16 q - 426 q^{2} - 444332 q^{4} - 304914744 q^{8} - 1569837600 q^{10} + 2471571264 q^{11} - 26163923904 q^{14} - 192320075504 q^{16} + 176439301344 q^{17} - 833365634368 q^{19} - 1256486405760 q^{20} + 59927319356 q^{22} - 15320509140080 q^{25} - 4184514840864 q^{26} - 12301604294400 q^{28} - 141481742931936 q^{32} + 80653465357268 q^{34} - 20487495736320 q^{35} - 493456694265564 q^{38} - 519930573603840 q^{40} + 594931562445024 q^{41} - 25\!\cdots\!92 q^{43}+ \cdots + 81\!\cdots\!66 q^{98}+O(q^{100}) \) 16 * q - 426 * q^2 - 444332 * q^4 - 304914744 * q^8 - 1569837600 * q^10 + 2471571264 * q^11 - 26163923904 * q^14 - 192320075504 * q^16 + 176439301344 * q^17 - 833365634368 * q^19 - 1256486405760 * q^20 + 59927319356 * q^22 - 15320509140080 * q^25 - 4184514840864 * q^26 - 12301604294400 * q^28 - 141481742931936 * q^32 + 80653465357268 * q^34 - 20487495736320 * q^35 - 493456694265564 * q^38 - 519930573603840 * q^40 + 594931562445024 * q^41 - 2540155017577792 * q^43 - 73781630442072 * q^44 + 153882272211264 * q^46 - 3186415704132848 * q^49 - 5668141028706330 * q^50 - 4594372123628160 * q^52 - 8184134137073664 * q^56 - 10505700099162720 * q^58 - 556807886314176 * q^59 - 6212402633091840 * q^62 - 56432885385732032 * q^64 + 21153177930524160 * q^65 + 162428574934613696 * q^67 + 70717864614203736 * q^68 + 4248100663257600 * q^70 - 7655712852492256 * q^73 - 9613779604149984 * q^74 - 151130166278324584 * q^76 - 26870186366192640 * q^80 + 329788507250077556 * q^82 - 866357336138514624 * q^83 - 1269201398006865468 * q^86 - 758460699051663856 * q^88 + 883646550464284128 * q^89 - 379834560933460992 * q^91 - 1413121475102841600 * q^92 + 671428514272869504 * q^94 - 2614894858526780128 * q^97 + 81635840192738166 * q^98

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