LMFDB - Embedded newform 72.19.b.b.19.16

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			19.16
Root			$434599. i$ of defining polynomial
Character	$\chi$	$=$	72.19
Dual form			72.19.b.b.19.15

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(426.398 + 283.424i) q^{2} +(101486. + 241703. i) q^{4} +3.47680e6i q^{5} +1.08296e7i q^{7} +(-2.52310e7 + 1.31825e8i) q^{8} +O(q^{10})$	\(q+(426.398 + 283.424i) q^{2} +(101486. + 241703. i) q^{4} +3.47680e6i q^{5} +1.08296e7i q^{7} +(-2.52310e7 + 1.31825e8i) q^{8} +(-9.85407e8 + 1.48250e9i) q^{10} +1.36275e8 q^{11} -2.80141e9i q^{13} +(-3.06936e9 + 4.61771e9i) q^{14} +(-4.81207e10 + 4.90587e10i) q^{16} -2.99849e10 q^{17} -5.03309e10 q^{19} +(-8.40350e11 + 3.52845e11i) q^{20} +(5.81073e10 + 3.86236e10i) q^{22} +1.64351e12i q^{23} -8.27341e12 q^{25} +(7.93988e11 - 1.19452e12i) q^{26} +(-2.61754e12 + 1.09905e12i) q^{28} +5.13731e12i q^{29} -3.37595e13i q^{31} +(-3.44230e13 + 7.27996e12i) q^{32} +(-1.27855e13 - 8.49843e12i) q^{34} -3.76523e13 q^{35} +1.22733e14i q^{37} +(-2.14610e13 - 1.42650e13i) q^{38} +(-4.58328e14 - 8.77229e13i) q^{40} -4.29547e14 q^{41} -5.15040e14 q^{43} +(1.38300e13 + 3.29380e13i) q^{44} +(-4.65809e14 + 7.00787e14i) q^{46} +4.52697e14i q^{47} +1.51113e15 q^{49} +(-3.52776e15 - 2.34488e15i) q^{50} +(6.77109e14 - 2.84304e14i) q^{52} -3.85227e15i q^{53} +4.73800e14i q^{55} +(-1.42761e15 - 2.73241e14i) q^{56} +(-1.45604e15 + 2.19054e15i) q^{58} +8.14938e15 q^{59} +1.63847e16i q^{61} +(9.56825e15 - 1.43950e16i) q^{62} +(-1.67412e16 - 6.65214e15i) q^{64} +9.73995e15 q^{65} +3.10380e16 q^{67} +(-3.04304e15 - 7.24742e15i) q^{68} +(-1.60548e16 - 1.06716e16i) q^{70} -4.98018e16i q^{71} +7.59692e16 q^{73} +(-3.47854e16 + 5.23330e16i) q^{74} +(-5.10788e15 - 1.21651e16i) q^{76} +1.47580e15i q^{77} +1.64362e17i q^{79} +(-1.70567e17 - 1.67306e17i) q^{80} +(-1.83158e17 - 1.21744e17i) q^{82} -4.04293e16 q^{83} -1.04251e17i q^{85} +(-2.19612e17 - 1.45975e17i) q^{86} +(-3.43835e15 + 1.79644e16i) q^{88} -1.65081e17 q^{89} +3.03382e16 q^{91} +(-3.97240e17 + 1.66793e17i) q^{92} +(-1.28305e17 + 1.93029e17i) q^{94} -1.74990e17i q^{95} -4.02901e17 q^{97} +(6.44344e17 + 4.28291e17i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	426.398	+	283.424i	0.832808	+	0.553562i
$2$	426.398	+	283.424i	0.832808	+	0.553562i
$3$		0			0
$3$		0			0
$4$	101486.	+	241703.i	0.387138	+	0.922022i
$5$			3.47680e6i			1.78012i	0.455844	+	0.890060i	$0.349337\pi$
$5$			3.47680e6i			1.78012i	−0.455844	+	0.890060i	$0.650663\pi$
$6$		0			0
$7$			1.08296e7i			0.268367i	0.990956	+	0.134184i	$0.0428412\pi$
$7$			1.08296e7i			0.268367i	−0.990956	+	0.134184i	$0.957159\pi$
$8$	−2.52310e7	+	1.31825e8i	−0.187985	+	0.982172i
$9$		0			0
$10$	−9.85407e8	+	1.48250e9i	−0.985407	+	1.48250i
$11$	1.36275e8			0.0577939			0.0288970	−	0.999582i	$-0.490801\pi$
$11$	1.36275e8			0.0577939			0.0288970	+	0.999582i	$0.490801\pi$
$12$		0			0
$13$		−	2.80141e9i		−	0.264172i	−0.991238	−	0.132086i	$-0.957832\pi$
$13$		−	2.80141e9i		−	0.264172i	0.991238	−	0.132086i	$-0.0421675\pi$
$14$	−3.06936e9	+	4.61771e9i	−0.148558	+	0.223498i
$15$		0			0
$16$	−4.81207e10	+	4.90587e10i	−0.700249	+	0.713899i
$17$	−2.99849e10			−0.252849			−0.126425	−	0.991976i	$-0.540350\pi$
$17$	−2.99849e10			−0.252849			−0.126425	+	0.991976i	$0.540350\pi$
$18$		0			0
$19$	−5.03309e10			−0.155974			−0.0779871	−	0.996954i	$-0.524849\pi$
$19$	−5.03309e10			−0.155974			−0.0779871	+	0.996954i	$0.524849\pi$
$20$	−8.40350e11	+	3.52845e11i	−1.64131	+	0.689151i
$21$		0			0
$22$	5.81073e10	+	3.86236e10i	0.0481312	+	0.0319925i
$23$			1.64351e12i			0.912475i	0.889858	+	0.456237i	$0.150803\pi$
$23$			1.64351e12i			0.912475i	−0.889858	+	0.456237i	$0.849197\pi$
$24$		0			0
$25$	−8.27341e12			−2.16883
$26$	7.93988e11	−	1.19452e12i	0.146236	−	0.220005i
$27$		0			0
$28$	−2.61754e12	+	1.09905e12i	−0.247441	+	0.103895i
$29$			5.13731e12i			0.354123i	0.984200	+	0.177061i	$0.0566591\pi$
$29$			5.13731e12i			0.354123i	−0.984200	+	0.177061i	$0.943341\pi$
$30$		0			0
$31$		−	3.37595e13i		−	1.27685i	−0.769683	−	0.638426i	$-0.779586\pi$
$31$		−	3.37595e13i		−	1.27685i	0.769683	−	0.638426i	$-0.220414\pi$
$32$	−3.44230e13	+	7.27996e12i	−0.978360	+	0.206909i
$33$		0			0
$34$	−1.27855e13	−	8.49843e12i	−0.210575	−	0.139968i
$35$	−3.76523e13			−0.477726
$36$		0			0
$37$			1.22733e14i			0.944376i	0.881498	+	0.472188i	$0.156536\pi$
$37$			1.22733e14i			0.944376i	−0.881498	+	0.472188i	$0.843464\pi$
$38$	−2.14610e13	−	1.42650e13i	−0.129896	−	0.0863414i
$39$		0			0
$40$	−4.58328e14	−	8.77229e13i	−1.74838	−	0.334636i
$41$	−4.29547e14			−1.31207			−0.656033	−	0.754732i	$-0.727767\pi$
$41$	−4.29547e14			−1.31207			−0.656033	+	0.754732i	$0.727767\pi$
$42$		0			0
$43$	−5.15040e14			−1.02477			−0.512383	−	0.858757i	$-0.671237\pi$
$43$	−5.15040e14			−1.02477			−0.512383	+	0.858757i	$0.671237\pi$
$44$	1.38300e13	+	3.29380e13i	0.0223742	+	0.0532873i
$45$		0			0
$46$	−4.65809e14	+	7.00787e14i	−0.505112	+	0.759916i
$47$			4.52697e14i			0.404508i	0.979333	+	0.202254i	$0.0648266\pi$
$47$			4.52697e14i			0.404508i	−0.979333	+	0.202254i	$0.935173\pi$
$48$		0			0
$49$	1.51113e15			0.927979
$50$	−3.52776e15	−	2.34488e15i	−1.80621	−	1.20058i
$51$		0			0
$52$	6.77109e14	−	2.84304e14i	0.243573	−	0.102271i
$53$		−	3.85227e15i		−	1.16744i	−0.811956	−	0.583719i	$-0.801597\pi$
$53$		−	3.85227e15i		−	1.16744i	0.811956	−	0.583719i	$-0.198403\pi$
$54$		0			0
$55$			4.73800e14i			0.102880i
$56$	−1.42761e15	−	2.73241e14i	−0.263583	−	0.0504492i
$57$		0			0
$58$	−1.45604e15	+	2.19054e15i	−0.196029	+	0.294916i
$59$	8.14938e15			0.940711			0.470356	−	0.882477i	$-0.344126\pi$
$59$	8.14938e15			0.940711			0.470356	+	0.882477i	$0.344126\pi$
$60$		0			0
$61$			1.63847e16i			1.40110i	0.713603	+	0.700551i	$0.247062\pi$
$61$			1.63847e16i			1.40110i	−0.713603	+	0.700551i	$0.752938\pi$
$62$	9.56825e15	−	1.43950e16i	0.706817	−	1.06337i
$63$		0			0
$64$	−1.67412e16	−	6.65214e15i	−0.929323	−	0.369268i
$65$	9.73995e15			0.470258
$66$		0			0
$67$	3.10380e16			1.14083			0.570414	−	0.821357i	$-0.306783\pi$
$67$	3.10380e16			1.14083			0.570414	+	0.821357i	$0.306783\pi$
$68$	−3.04304e15	−	7.24742e15i	−0.0978875	−	0.233133i
$69$		0			0
$70$	−1.60548e16	−	1.06716e16i	−0.397854	−	0.264451i
$71$		−	4.98018e16i		−	1.08623i	−0.839660	−	0.543113i	$-0.817245\pi$
$71$		−	4.98018e16i		−	1.08623i	0.839660	−	0.543113i	$-0.182755\pi$
$72$		0			0
$73$	7.59692e16			1.29042			0.645211	−	0.764005i	$-0.276770\pi$
$73$	7.59692e16			1.29042			0.645211	+	0.764005i	$0.276770\pi$
$74$	−3.47854e16	+	5.23330e16i	−0.522771	+	0.786484i
$75$		0			0
$76$	−5.10788e15	−	1.21651e16i	−0.0603835	−	0.143812i
$77$			1.47580e15i			0.0155100i
$78$		0			0
$79$			1.64362e17i			1.37138i	0.727893	+	0.685690i	$0.240500\pi$
$79$			1.64362e17i			1.37138i	−0.727893	+	0.685690i	$0.759500\pi$
$80$	−1.70567e17	−	1.67306e17i	−1.27082	−	1.24653i
$81$		0			0
$82$	−1.83158e17	−	1.21744e17i	−1.09270	−	0.726310i
$83$	−4.04293e16			−0.216268			−0.108134	−	0.994136i	$-0.534488\pi$
$83$	−4.04293e16			−0.216268			−0.108134	+	0.994136i	$0.534488\pi$
$84$		0			0
$85$		−	1.04251e17i		−	0.450102i
$86$	−2.19612e17	−	1.45975e17i	−0.853433	−	0.567272i
$87$		0			0
$88$	−3.43835e15	+	1.79644e16i	−0.0108644	+	0.0567636i
$89$	−1.65081e17			−0.471182			−0.235591	−	0.971852i	$-0.575702\pi$
$89$	−1.65081e17			−0.471182			−0.235591	+	0.971852i	$0.575702\pi$
$90$		0			0
$91$	3.03382e16			0.0708952
$92$	−3.97240e17	+	1.66793e17i	−0.841322	+	0.353253i
$93$		0			0
$94$	−1.28305e17	+	1.93029e17i	−0.223920	+	0.336877i
$95$		−	1.74990e17i		−	0.277653i
$96$		0			0
$97$	−4.02901e17			−0.529972			−0.264986	−	0.964252i	$-0.585367\pi$
$97$	−4.02901e17			−0.529972			−0.264986	+	0.964252i	$0.585367\pi$
$98$	6.44344e17	+	4.28291e17i	0.772828	+	0.513694i
$99$		0			0
$100$	−8.39634e17	−	1.99970e18i	−0.839634	−	1.99970i
$101$		−	1.24060e18i		−	1.13433i	−0.823606	−	0.567163i	$-0.808041\pi$
$101$		−	1.24060e18i		−	1.13433i	0.823606	−	0.567163i	$-0.191959\pi$
$102$		0			0
$103$		−	1.12022e18i		−	0.858556i	−0.903172	−	0.429278i	$-0.858768\pi$
$103$		−	1.12022e18i		−	0.858556i	0.903172	−	0.429278i	$-0.141232\pi$
$104$	3.69296e17	+	7.06824e16i	0.259463	+	0.0496605i
$105$		0			0
$106$	1.09183e18	−	1.64260e18i	0.646250	−	0.972252i
$107$	1.14037e18			0.620287			0.310144	−	0.950690i	$-0.399623\pi$
$107$	1.14037e18			0.620287			0.310144	+	0.950690i	$0.399623\pi$
$108$		0			0
$109$			2.82963e16i			0.0130284i	0.999979	+	0.00651419i	$0.00207355\pi$
$109$			2.82963e16i			0.0130284i	−0.999979	+	0.00651419i	$0.997926\pi$
$110$	−1.34286e17	+	2.02027e17i	−0.0569505	+	0.0856793i
$111$		0			0
$112$	−5.31286e17	−	5.21128e17i	−0.191587	−	0.187924i
$113$	−2.32500e18			−0.773956			−0.386978	−	0.922089i	$-0.626481\pi$
$113$	−2.32500e18			−0.773956			−0.386978	+	0.922089i	$0.626481\pi$
$114$		0			0
$115$	−5.71413e18			−1.62431
$116$	−1.24170e18	+	5.21364e17i	−0.326509	+	0.137094i
$117$		0			0
$118$	3.47487e18	+	2.30973e18i	0.783432	+	0.520742i
$119$		−	3.24724e17i		−	0.0678565i
$120$		0			0
$121$	−5.54135e18			−0.996660
$122$	−4.64381e18	+	6.98639e18i	−0.775597	+	1.16685i
$123$		0			0
$124$	8.15975e18	−	3.42611e18i	1.17729	−	0.494317i
$125$		−	1.55020e19i		−	2.08065i
$126$		0			0
$127$			9.14710e18i			1.06427i	0.846661	+	0.532133i	$0.178609\pi$
$127$			9.14710e18i			1.06427i	−0.846661	+	0.532133i	$0.821391\pi$
$128$	−5.25303e18	−	7.58131e18i	−0.569535	−	0.821967i
$129$		0			0
$130$	4.15309e18	+	2.76053e18i	0.391635	+	0.260317i
$131$	−1.00187e18			−0.0881796			−0.0440898	−	0.999028i	$-0.514039\pi$
$131$	−1.00187e18			−0.0881796			−0.0440898	+	0.999028i	$0.514039\pi$
$132$		0			0
$133$		−	5.45064e17i		−	0.0418584i
$134$	1.32345e19	+	8.79691e18i	0.950091	+	0.631520i
$135$		0			0
$136$	7.56548e17	−	3.95275e18i	0.0475320	−	0.248342i
$137$	−3.46626e18			−0.203881			−0.101940	−	0.994791i	$-0.532505\pi$
$137$	−3.46626e18			−0.203881			−0.101940	+	0.994791i	$0.532505\pi$
$138$		0			0
$139$	2.01094e19			1.03817			0.519083	−	0.854724i	$-0.326274\pi$
$139$	2.01094e19			1.03817			0.519083	+	0.854724i	$0.326274\pi$
$140$	−3.82117e18	−	9.10065e18i	−0.184946	−	0.440474i
$141$		0			0
$142$	1.41150e19	−	2.12354e19i	0.601294	−	0.904618i
$143$		−	3.81763e17i		−	0.0152675i
$144$		0			0
$145$	−1.78614e19			−0.630381
$146$	3.23931e19	+	2.15315e19i	1.07467	+	0.714329i
$147$		0			0
$148$	−2.96648e19	+	1.24556e19i	−0.870736	+	0.365604i
$149$		−	2.79939e19i		−	0.773369i	−0.922212	−	0.386684i	$-0.873620\pi$
$149$		−	2.79939e19i		−	0.773369i	0.922212	−	0.386684i	$-0.126380\pi$
$150$		0			0
$151$			3.64407e19i			0.892882i	0.894813	+	0.446441i	$0.147309\pi$
$151$			3.64407e19i			0.892882i	−0.894813	+	0.446441i	$0.852691\pi$
$152$	1.26990e18	−	6.63487e18i	0.0293209	−	0.153193i
$153$		0			0
$154$	−4.18278e17	+	6.29279e17i	−0.00858575	+	0.0129168i
$155$	1.17375e20			2.27295
$156$		0			0
$157$		−	5.65222e19i		−	0.975264i	−0.873049	−	0.487632i	$-0.837861\pi$
$157$		−	5.65222e19i		−	0.975264i	0.873049	−	0.487632i	$-0.162139\pi$
$158$	−4.65842e19	+	7.00836e19i	−0.759145	+	1.14210i
$159$		0			0
$160$	−2.53109e19	−	1.19682e20i	−0.368323	−	1.74160i
$161$	−1.77985e19			−0.244878
$162$		0			0
$163$	2.32565e18			0.0286323			0.0143161	−	0.999898i	$-0.495443\pi$
$163$	2.32565e18			0.0286323			0.0143161	+	0.999898i	$0.495443\pi$
$164$	−4.35929e19	−	1.03823e20i	−0.507950	−	1.20975i
$165$		0			0
$166$	−1.72389e19	−	1.14586e19i	−0.180110	−	0.119718i
$167$			1.78856e20i			1.77033i	0.465274	+	0.885167i	$0.345956\pi$
$167$			1.78856e20i			1.77033i	−0.465274	+	0.885167i	$0.654044\pi$
$168$		0			0
$169$	1.04607e20			0.930213
$170$	2.95473e19	−	4.44525e19i	0.249160	−	0.374849i
$171$		0			0
$172$	−5.22692e19	−	1.24486e20i	−0.396725	−	0.944857i
$173$		−	1.63126e20i		−	1.17519i	−0.809154	−	0.587597i	$-0.800074\pi$
$173$		−	1.63126e20i		−	1.17519i	0.809154	−	0.587597i	$-0.199926\pi$
$174$		0			0
$175$		−	8.95977e19i		−	0.582042i
$176$	−6.55766e18	+	6.68548e18i	−0.0404701	+	0.0412590i
$177$		0			0
$178$	−7.03903e19	−	4.67880e19i	−0.392404	−	0.260828i
$179$	2.69767e19			0.142992			0.0714961	−	0.997441i	$-0.477223\pi$
$179$	2.69767e19			0.142992			0.0714961	+	0.997441i	$0.477223\pi$
$180$		0			0
$181$		−	2.69695e20i		−	1.29350i	−0.762703	−	0.646749i	$-0.776128\pi$
$181$		−	2.69695e20i		−	1.29350i	0.762703	−	0.646749i	$-0.223872\pi$
$182$	1.29361e19	+	8.59856e18i	0.0590421	+	0.0392449i
$183$		0			0
$184$	−2.16655e20	−	4.14673e19i	−0.896207	−	0.171532i
$185$	−4.26717e20			−1.68110
$186$		0			0
$187$	−4.08619e18			−0.0146132
$188$	−1.09418e20	+	4.59423e19i	−0.372965	+	0.156600i
$189$		0			0
$190$	4.95965e19	−	7.46155e19i	0.153698	−	0.231231i
$191$		−	1.48397e20i		−	0.438658i	−0.975651	−	0.219329i	$-0.929613\pi$
$191$		−	1.48397e20i		−	0.438658i	0.975651	−	0.219329i	$-0.0703867\pi$
$192$		0			0
$193$	−1.72513e20			−0.464309			−0.232154	−	0.972679i	$-0.574577\pi$
$193$	−1.72513e20			−0.464309			−0.232154	+	0.972679i	$0.574577\pi$
$194$	−1.71796e20	−	1.14192e20i	−0.441365	−	0.293372i
$195$		0			0
$196$	1.53359e20	+	3.65245e20i	0.359256	+	0.855617i
$197$			3.97468e20i			0.889418i	0.895675	+	0.444709i	$0.146693\pi$
$197$			3.97468e20i			0.889418i	−0.895675	+	0.444709i	$0.853307\pi$
$198$		0			0
$199$		−	3.99187e20i		−	0.815640i	−0.913062	−	0.407820i	$-0.866289\pi$
$199$		−	3.99187e20i		−	0.815640i	0.913062	−	0.407820i	$-0.133711\pi$
$200$	2.08746e20	−	1.09064e21i	0.407707	−	2.13016i
$201$		0			0
$202$	3.51614e20	−	5.28987e20i	0.627920	−	0.944675i
$203$	−5.56350e19			−0.0950350
$204$		0			0
$205$		−	1.49345e21i		−	2.33563i
$206$	3.17497e20	−	4.77660e20i	0.475264	−	0.715012i
$207$		0			0
$208$	1.37434e20	+	1.34806e20i	0.188592	+	0.184986i
$209$	−6.85885e18			−0.00901436
$210$		0			0
$211$	−1.19555e21			−1.44220			−0.721100	−	0.692831i	$-0.756363\pi$
$211$	−1.19555e21			−1.44220			−0.721100	+	0.692831i	$0.756363\pi$
$212$	9.31104e20	−	3.90951e20i	1.07640	−	0.451959i
$213$		0			0
$214$	4.86252e20	+	3.23209e20i	0.516580	+	0.343368i
$215$		−	1.79069e21i		−	1.82421i
$216$		0			0
$217$	3.65601e20			0.342665
$218$	−8.01984e18	+	1.20655e19i	−0.00721202	+	0.0108501i
$219$		0			0
$220$	−1.14519e20	+	4.80840e19i	−0.0948577	+	0.0398287i
$221$			8.40001e19i			0.0667958i
$222$		0			0
$223$		−	9.47274e20i		−	0.694595i	−0.937755	−	0.347298i	$-0.887099\pi$
$223$		−	9.47274e20i		−	0.694595i	0.937755	−	0.347298i	$-0.112901\pi$
$224$	−7.88390e19	−	3.72787e20i	−0.0555276	−	0.262560i
$225$		0			0
$226$	−9.91373e20	−	6.58960e20i	−0.644557	−	0.428433i
$227$	−2.11701e21			−1.32279			−0.661395	−	0.750038i	$-0.730035\pi$
$227$	−2.11701e21			−1.32279			−0.661395	+	0.750038i	$0.730035\pi$
$228$		0			0
$229$			1.70342e21i			0.983561i	0.870719	+	0.491781i	$0.163654\pi$
$229$			1.70342e21i			0.983561i	−0.870719	+	0.491781i	$0.836346\pi$
$230$	−2.43649e21	−	1.61952e21i	−1.35274	−	0.899159i
$231$		0			0
$232$	−6.77225e20	−	1.29619e20i	−0.347809	−	0.0665699i
$233$	−2.47054e21			−1.22064			−0.610321	−	0.792154i	$-0.708960\pi$
$233$	−2.47054e21			−1.22064			−0.610321	+	0.792154i	$0.708960\pi$
$234$		0			0
$235$	−1.57393e21			−0.720072
$236$	8.27046e20	+	1.96973e21i	0.364185	+	0.867356i
$237$		0			0
$238$	9.20345e19	−	1.38462e20i	0.0375628	−	0.0565115i
$239$			2.48664e20i			0.0977307i	0.998805	+	0.0488654i	$0.0155605\pi$
$239$			2.48664e20i			0.0977307i	−0.998805	+	0.0488654i	$0.984439\pi$
$240$		0			0
$241$	1.90611e21			0.695016			0.347508	−	0.937677i	$-0.387028\pi$
$241$	1.90611e21			0.695016			0.347508	+	0.937677i	$0.387028\pi$
$242$	−2.36282e21	−	1.57055e21i	−0.830026	−	0.551713i
$243$		0			0
$244$	−3.96022e21	+	1.66281e21i	−1.29185	+	0.542419i
$245$			5.25390e21i			1.65191i
$246$		0			0
$247$			1.40998e20i			0.0412040i
$248$	4.45034e21	+	8.51785e20i	1.25409	+	0.240030i
$249$		0			0
$250$	4.39365e21	−	6.61003e21i	1.15177	−	1.73278i
$251$	7.71308e21			1.95058			0.975292	−	0.220921i	$-0.0709063\pi$
$251$	7.71308e21			1.95058			0.975292	+	0.220921i	$0.0709063\pi$
$252$		0			0
$253$			2.23969e20i			0.0527355i
$254$	−2.59251e21	+	3.90030e21i	−0.589137	+	0.886329i
$255$		0			0
$256$	−9.11542e19	−	4.72149e21i	−0.0193027	−	0.999814i
$257$	7.58318e21			1.55043			0.775217	−	0.631695i	$-0.217641\pi$
$257$	7.58318e21			1.55043			0.775217	+	0.631695i	$0.217641\pi$
$258$		0			0
$259$	−1.32915e21			−0.253440
$260$	9.88466e20	+	2.35417e21i	0.182055	+	0.433588i
$261$		0			0
$262$	−4.27193e20	−	2.83953e20i	−0.0734366	−	0.0488129i
$263$		−	3.30248e21i		−	0.548578i	−0.961647	−	0.274289i	$-0.911558\pi$
$263$		−	3.30248e21i		−	0.548578i	0.961647	−	0.274289i	$-0.0884425\pi$
$264$		0			0
$265$	1.33936e22			2.07818
$266$	1.54484e20	−	2.32414e20i	0.0231712	−	0.0348600i
$267$		0			0
$268$	3.14992e21	+	7.50196e21i	0.441658	+	1.05187i
$269$			1.42430e22i			1.93122i	0.259994	+	0.965610i	$0.416279\pi$
$269$			1.42430e22i			1.93122i	−0.259994	+	0.965610i	$0.583721\pi$
$270$		0			0
$271$			1.37402e22i			1.74289i	0.490491	+	0.871446i	$0.336817\pi$
$271$			1.37402e22i			1.74289i	−0.490491	+	0.871446i	$0.663183\pi$
$272$	1.44289e21	−	1.47102e21i	0.177058	−	0.180509i
$273$		0			0
$274$	−1.47801e21	−	9.82422e20i	−0.169794	−	0.112861i
$275$	−1.12746e21			−0.125345
$276$		0			0
$277$			9.97314e21i			1.03876i	0.854544	+	0.519379i	$0.173837\pi$
$277$			9.97314e21i			1.03876i	−0.854544	+	0.519379i	$0.826163\pi$
$278$	8.57461e21	+	5.69949e21i	0.864592	+	0.574689i
$279$		0			0
$280$	9.50004e20	−	4.96351e21i	0.0898055	−	0.469209i
$281$	−4.87172e21			−0.445990			−0.222995	−	0.974820i	$-0.571583\pi$
$281$	−4.87172e21			−0.445990			−0.222995	+	0.974820i	$0.571583\pi$
$282$		0			0
$283$	−2.09871e21			−0.180249			−0.0901247	−	0.995930i	$-0.528727\pi$
$283$	−2.09871e21			−0.180249			−0.0901247	+	0.995930i	$0.528727\pi$
$284$	1.20372e22	−	5.05418e21i	1.00152	−	0.420519i
$285$		0			0
$286$	1.08201e20	−	1.62783e20i	0.00845154	−	0.0127149i
$287$		−	4.65181e21i		−	0.352116i
$288$		0			0
$289$	−1.31640e22			−0.936067
$290$	−7.61605e21	−	5.06234e21i	−0.524986	−	0.348955i
$291$		0			0
$292$	7.70979e21	+	1.83619e22i	0.499571	+	1.18980i
$293$		−	1.17383e22i		−	0.737557i	−0.929517	−	0.368779i	$-0.879776\pi$
$293$		−	1.17383e22i		−	0.737557i	0.929517	−	0.368779i	$-0.120224\pi$
$294$		0			0
$295$			2.83337e22i			1.67458i
$296$	−1.61792e22	−	3.09667e21i	−0.927540	−	0.177529i
$297$		0			0
$298$	7.93413e21	−	1.19365e22i	0.428108	−	0.644068i
$299$	4.60414e21			0.241050
$300$		0			0
$301$		−	5.57767e21i		−	0.275014i
$302$	−1.03282e22	+	1.55382e22i	−0.494266	+	0.743599i
$303$		0			0
$304$	2.42196e21	−	2.46917e21i	0.109221	−	0.111350i
$305$	−5.69662e22			−2.49413
$306$		0			0
$307$	−3.79319e22			−1.56588			−0.782941	−	0.622096i	$-0.786282\pi$
$307$	−3.79319e22			−1.56588			−0.782941	+	0.622096i	$0.786282\pi$
$308$	−3.56705e20	+	1.49773e20i	−0.0143006	+	0.00600450i
$309$		0			0
$310$	5.00484e22	+	3.32668e22i	1.89293	+	1.25822i
$311$			3.70263e22i			1.36040i	0.733026	+	0.680201i	$0.238107\pi$
$311$			3.70263e22i			1.36040i	−0.733026	+	0.680201i	$0.761893\pi$
$312$		0			0
$313$	−2.78803e22			−0.966938			−0.483469	−	0.875361i	$-0.660623\pi$
$313$	−2.78803e22			−0.966938			−0.483469	+	0.875361i	$0.660623\pi$
$314$	1.60197e22	−	2.41009e22i	0.539870	−	0.812208i
$315$		0			0
$316$	−3.97268e22	+	1.66804e22i	−1.26444	+	0.530913i
$317$			8.83287e21i			0.273255i	0.990622	+	0.136628i	$0.0436264\pi$
$317$			8.83287e21i			0.273255i	−0.990622	+	0.136628i	$0.956374\pi$
$318$		0			0
$319$			7.00087e20i			0.0204661i
$320$	2.31281e22	−	5.82057e22i	0.657341	−	1.65431i
$321$		0			0
$322$	−7.58924e21	−	5.04452e21i	−0.203937	−	0.135555i
$323$	1.50917e21			0.0394380
$324$		0			0
$325$			2.31773e22i			0.572943i
$326$	9.91651e20	+	6.59144e20i	0.0238452	+	0.0158497i
$327$		0			0
$328$	1.08379e22	−	5.66249e22i	0.246649	−	1.28867i
$329$	−4.90252e21			−0.108557
$330$		0			0
$331$	2.27336e22			0.476669			0.238335	−	0.971183i	$-0.423399\pi$
$331$	2.27336e22			0.476669			0.238335	+	0.971183i	$0.423399\pi$
$332$	−4.10300e21	−	9.77186e21i	−0.0837256	−	0.199404i
$333$		0			0
$334$	−5.06920e22	+	7.62637e22i	−0.979990	+	1.47435i
$335$			1.07913e23i			2.03081i
$336$		0			0
$337$	6.91628e22			1.23368			0.616842	−	0.787087i	$-0.288412\pi$
$337$	6.91628e22			1.23368			0.616842	+	0.787087i	$0.288412\pi$
$338$	4.46044e22	+	2.96483e22i	0.774689	+	0.514931i
$339$		0			0
$340$	2.51978e22	−	1.05800e22i	0.415004	−	0.174251i
$341$		−	4.60058e21i		−	0.0737943i
$342$		0			0
$343$			3.40000e22i			0.517407i
$344$	1.29950e22	−	6.78950e22i	0.192641	−	1.00650i
$345$		0			0
$346$	4.62339e22	−	6.95567e22i	0.650543	−	0.978710i
$347$	−3.56633e22			−0.488941			−0.244471	−	0.969657i	$-0.578614\pi$
$347$	−3.56633e22			−0.488941			−0.244471	+	0.969657i	$0.578614\pi$
$348$		0			0
$349$		−	6.57517e22i		−	0.856008i	−0.903777	−	0.428004i	$-0.859217\pi$
$349$		−	6.57517e22i		−	0.856008i	0.903777	−	0.428004i	$-0.140783\pi$
$350$	2.53941e22	−	3.82042e22i	0.322196	−	0.484729i
$351$		0			0
$352$	−4.69099e21	+	9.92077e20i	−0.0565433	+	0.0119581i
$353$	2.20900e22			0.259552			0.129776	−	0.991543i	$-0.458574\pi$
$353$	2.20900e22			0.259552			0.129776	+	0.991543i	$0.458574\pi$
$354$		0			0
$355$	1.73151e23			1.93361
$356$	−1.67534e22	−	3.99006e22i	−0.182412	−	0.434440i
$357$		0			0
$358$	1.15028e22	+	7.64585e21i	0.119085	+	0.0791551i
$359$			1.38349e23i			1.39678i	0.715719	+	0.698389i	$0.246099\pi$
$359$			1.38349e23i			1.39678i	−0.715719	+	0.698389i	$0.753901\pi$
$360$		0			0
$361$	−1.01594e23			−0.975672
$362$	7.64380e22	−	1.14997e23i	0.716032	−	1.07723i
$363$		0			0
$364$	3.07889e21	+	7.33281e21i	0.0274462	+	0.0653669i
$365$			2.64129e23i			2.29710i
$366$		0			0
$367$		−	2.17842e22i		−	0.180363i	−0.995925	−	0.0901813i	$-0.971255\pi$
$367$		−	2.17842e22i		−	0.180363i	0.995925	−	0.0901813i	$-0.0287447\pi$
$368$	−8.06283e22	−	7.90867e22i	−0.651414	−	0.638959i
$369$		0			0
$370$	−1.81951e23	−	1.20942e23i	−1.40004	−	0.930595i
$371$	4.17185e22			0.313302
$372$		0			0
$373$			1.59981e23i			1.14469i	0.820013	+	0.572345i	$0.193966\pi$
$373$			1.59981e23i			1.14469i	−0.820013	+	0.572345i	$0.806034\pi$
$374$	−1.74234e21	−	1.15812e21i	−0.0121700	−	0.00808929i
$375$		0			0
$376$	−5.96767e22	−	1.14220e22i	−0.397296	−	0.0760415i
$377$	1.43917e22			0.0935494
$378$		0			0
$379$	−1.69897e23			−1.05301			−0.526506	−	0.850171i	$-0.676498\pi$
$379$	−1.69897e23			−1.05301			−0.526506	+	0.850171i	$0.676498\pi$
$380$	4.22956e22	−	1.77590e22i	0.256002	−	0.107490i
$381$		0			0
$382$	4.20593e22	−	6.32762e22i	0.242824	−	0.365317i
$383$			1.52269e22i			0.0858665i	0.999078	+	0.0429333i	$0.0136703\pi$
$383$			1.52269e22i			0.0858665i	−0.999078	+	0.0429333i	$0.986330\pi$
$384$		0			0
$385$	−5.13106e21			−0.0276097
$386$	−7.35593e22	−	4.88944e22i	−0.386680	−	0.257024i
$387$		0			0
$388$	−4.08887e22	−	9.73822e22i	−0.205172	−	0.488646i
$389$		−	8.21497e22i		−	0.402772i	−0.979512	−	0.201386i	$-0.935455\pi$
$389$		−	8.21497e22i		−	0.402772i	0.979512	−	0.201386i	$-0.0645446\pi$
$390$		0			0
$391$		−	4.92803e22i		−	0.230719i
$392$	−3.81274e22	+	1.99205e23i	−0.174447	+	0.911435i
$393$		0			0
$394$	−1.12652e23	+	1.69479e23i	−0.492348	+	0.740714i
$395$	−5.71454e23			−2.44122
$396$		0			0
$397$			7.33206e22i			0.299303i	0.988739	+	0.149652i	$0.0478152\pi$
$397$			7.33206e22i			0.299303i	−0.988739	+	0.149652i	$0.952185\pi$
$398$	1.13139e23	−	1.70212e23i	0.451508	−	0.679272i
$399$		0			0
$400$	3.98123e23	−	4.05883e23i	1.51872	−	1.54832i
$401$	1.38921e23			0.518167			0.259083	−	0.965855i	$-0.416580\pi$
$401$	1.38921e23			0.518167			0.259083	+	0.965855i	$0.416580\pi$
$402$		0			0
$403$	−9.45743e22			−0.337309
$404$	2.99855e23	−	1.25903e23i	1.04587	−	0.439140i
$405$		0			0
$406$	−2.37226e22	−	1.57683e22i	−0.0791459	−	0.0526078i
$407$			1.67254e22i			0.0545792i
$408$		0			0
$409$	−9.61573e22			−0.300243			−0.150121	−	0.988668i	$-0.547966\pi$
$409$	−9.61573e22			−0.300243			−0.150121	+	0.988668i	$0.547966\pi$
$410$	4.23278e23	−	6.36802e23i	1.29292	−	1.94513i
$411$		0			0
$412$	2.70760e23	−	1.13687e23i	0.791608	−	0.332379i
$413$			8.82544e22i			0.252456i
$414$		0			0
$415$		−	1.40564e23i		−	0.384984i
$416$	2.03942e22	+	9.64331e22i	0.0546596	+	0.258456i
$417$		0			0
$418$	−2.92460e21	−	1.94396e21i	−0.00750723	−	0.00499001i
$419$	3.85125e22			0.0967554			0.0483777	−	0.998829i	$-0.484595\pi$
$419$	3.85125e22			0.0967554			0.0483777	+	0.998829i	$0.484595\pi$
$420$		0			0
$421$			4.63719e23i			1.11613i	0.829796	+	0.558066i	$0.188457\pi$
$421$			4.63719e23i			1.11613i	−0.829796	+	0.558066i	$0.811543\pi$
$422$	−5.09780e23	−	3.38847e23i	−1.20108	−	0.798348i
$423$		0			0
$424$	5.07825e23	+	9.71966e22i	1.14663	+	0.219461i
$425$	2.48077e23			0.548386
$426$		0			0
$427$	−1.77439e23			−0.376010
$428$	1.15732e23	+	2.75631e23i	0.240137	+	0.571919i
$429$		0			0
$430$	5.07524e23	−	7.63545e23i	1.00981	−	1.51921i
$431$		−	2.54794e23i		−	0.496471i	−0.968700	−	0.248235i	$-0.920149\pi$
$431$		−	2.54794e23i		−	0.496471i	0.968700	−	0.248235i	$-0.0798507\pi$
$432$		0			0
$433$	−5.45490e23			−1.01952			−0.509760	−	0.860316i	$-0.670266\pi$
$433$	−5.45490e23			−1.01952			−0.509760	+	0.860316i	$0.670266\pi$
$434$	1.55892e23	+	1.03620e23i	0.285374	+	0.189687i
$435$		0			0
$436$	−6.83928e21	+	2.87167e21i	−0.0120125	+	0.00504378i
$437$		−	8.27192e22i		−	0.142322i
$438$		0			0
$439$		−	3.40557e23i		−	0.562352i	−0.959656	−	0.281176i	$-0.909275\pi$
$439$		−	3.40557e23i		−	0.562352i	0.959656	−	0.281176i	$-0.0907245\pi$
$440$	−6.24587e22	−	1.19544e22i	−0.101046	−	0.0193400i
$441$		0			0
$442$	−2.38076e22	+	3.58174e22i	−0.0369756	+	0.0556281i
$443$	−3.64770e23			−0.555118			−0.277559	−	0.960709i	$-0.589525\pi$
$443$	−3.64770e23			−0.555118			−0.277559	+	0.960709i	$0.589525\pi$
$444$		0			0
$445$		−	5.73955e23i		−	0.838759i
$446$	2.68480e23	−	4.03915e23i	0.384502	−	0.578465i
$447$		0			0
$448$	7.20400e22	−	1.81300e23i	0.0990995	−	0.249400i
$449$	−1.21112e23			−0.163294			−0.0816468	−	0.996661i	$-0.526018\pi$
$449$	−1.21112e23			−0.163294			−0.0816468	+	0.996661i	$0.526018\pi$
$450$		0			0
$451$	−5.85365e22			−0.0758294
$452$	−2.35954e23	−	5.61958e23i	−0.299628	−	0.713605i
$453$		0			0
$454$	−9.02689e23	−	6.00012e23i	−1.10163	−	0.732246i
$455$			1.05480e23i			0.126202i
$456$		0			0
$457$	−1.16172e23			−0.133615			−0.0668077	−	0.997766i	$-0.521281\pi$
$457$	−1.16172e23			−0.133615			−0.0668077	+	0.997766i	$0.521281\pi$
$458$	−4.82789e23	+	7.26332e23i	−0.544462	+	0.819117i
$459$		0			0
$460$	−5.79904e23	−	1.38112e24i	−0.628833	−	1.49765i
$461$			1.17462e24i			1.24908i	0.780992	+	0.624541i	$0.214714\pi$
$461$			1.17462e24i			1.24908i	−0.780992	+	0.624541i	$0.785286\pi$
$462$		0			0
$463$			7.75697e23i			0.793347i	0.917960	+	0.396673i	$0.129835\pi$
$463$			7.75697e23i			0.793347i	−0.917960	+	0.396673i	$0.870165\pi$
$464$	−2.52030e23	−	2.47211e23i	−0.252808	−	0.247974i
$465$		0			0
$466$	−1.05343e24	−	7.00210e23i	−1.01656	−	0.675701i
$467$	−1.68463e24			−1.59460			−0.797300	−	0.603584i	$-0.793739\pi$
$467$	−1.68463e24			−1.59460			−0.797300	+	0.603584i	$0.793739\pi$
$468$		0			0
$469$			3.36129e23i			0.306161i
$470$	−6.71122e23	−	4.46091e23i	−0.599681	−	0.398605i
$471$		0			0
$472$	−2.05617e23	+	1.07429e24i	−0.176840	+	0.923940i
$473$	−7.01871e22			−0.0592252
$474$		0			0
$475$	4.16409e23			0.338281
$476$	7.84866e22	−	3.29549e22i	0.0625652	−	0.0262698i
$477$		0			0
$478$	−7.04772e22	+	1.06030e23i	−0.0541000	+	0.0813909i
$479$			1.30173e24i			0.980619i	0.871548	+	0.490310i	$0.163116\pi$
$479$			1.30173e24i			0.980619i	−0.871548	+	0.490310i	$0.836884\pi$
$480$		0			0
$481$	3.43825e23			0.249478
$482$	8.12761e23	+	5.40237e23i	0.578814	+	0.384734i
$483$		0			0
$484$	−5.62368e23	−	1.33936e24i	−0.385844	−	0.918942i
$485$		−	1.40080e24i		−	0.943413i
$486$		0			0
$487$			1.08221e24i			0.702348i	0.936310	+	0.351174i	$0.114217\pi$
$487$			1.08221e24i			0.702348i	−0.936310	+	0.351174i	$0.885783\pi$
$488$	−2.15991e24	−	4.13402e23i	−1.37612	−	0.263387i
$489$		0			0
$490$	−1.48908e24	+	2.24025e24i	−0.914437	+	1.37573i
$491$	2.27518e24			1.37177			0.685887	−	0.727708i	$-0.259414\pi$
$491$	2.27518e24			1.37177			0.685887	+	0.727708i	$0.259414\pi$
$492$		0			0
$493$		−	1.54042e23i		−	0.0895398i
$494$	−3.99622e22	+	6.01211e22i	−0.0228090	+	0.0343150i
$495$		0			0
$496$	1.65620e24	+	1.62453e24i	0.911543	+	0.894115i
$497$	5.39334e23			0.291508
$498$		0			0
$499$	−7.54183e23			−0.393162			−0.196581	−	0.980488i	$-0.562984\pi$
$499$	−7.54183e23			−0.393162			−0.196581	+	0.980488i	$0.562984\pi$
$500$	3.74688e24	−	1.57324e24i	1.91840	−	0.805497i
$501$		0			0
$502$	3.28884e24	+	2.18607e24i	1.62446	+	1.07977i
$503$			2.48165e24i			1.20401i	0.798494	+	0.602003i	$0.205630\pi$
$503$			2.48165e24i			1.20401i	−0.798494	+	0.602003i	$0.794370\pi$
$504$		0			0
$505$	4.31330e24			2.01923
$506$	−6.34781e22	+	9.54998e22i	−0.0291924	+	0.0439185i
$507$		0			0
$508$	−2.21088e24	+	9.28301e23i	−0.981276	+	0.412017i
$509$		−	2.65070e23i		−	0.115585i	−0.998329	−	0.0577925i	$-0.981594\pi$
$509$		−	2.65070e23i		−	0.115585i	0.998329	−	0.0577925i	$-0.0184062\pi$
$510$		0			0
$511$			8.22715e23i			0.346307i
$512$	1.29931e24	−	2.03907e24i	0.537384	−	0.843338i
$513$		0			0
$514$	3.23345e24	+	2.14925e24i	1.29121	+	0.858262i
$515$	3.89478e24			1.52833
$516$		0			0
$517$			6.16913e22i			0.0233781i
$518$	−5.66745e23	−	3.76712e23i	−0.211067	−	0.140295i
$519$		0			0
$520$	−2.45748e23	+	1.28397e24i	−0.0884017	+	0.461874i
$521$	−4.48105e24			−1.58431			−0.792155	−	0.610320i	$-0.791041\pi$
$521$	−4.48105e24			−1.58431			−0.792155	+	0.610320i	$0.791041\pi$
$522$		0			0
$523$	1.94656e24			0.664895			0.332448	−	0.943122i	$-0.392126\pi$
$523$	1.94656e24			0.664895			0.332448	+	0.943122i	$0.392126\pi$
$524$	−1.01675e23	−	2.42154e23i	−0.0341376	−	0.0813035i
$525$		0			0
$526$	9.36002e23	−	1.40817e24i	0.303672	−	0.456860i
$527$			1.01227e24i			0.322851i
$528$		0			0
$529$	5.43039e23			0.167390
$530$	5.71098e24	+	3.79605e24i	1.73072	+	1.15040i
$531$		0			0
$532$	1.31743e23	−	5.53162e22i	0.0385943	−	0.0162049i
$533$			1.20334e24i			0.346611i
$534$		0			0
$535$			3.96484e24i			1.10419i
$536$	−7.83119e23	+	4.09158e24i	−0.214459	+	1.12049i
$537$		0			0
$538$	−4.03681e24	+	6.07319e24i	−1.06905	+	1.60834i
$539$	2.05930e23			0.0536315
$540$		0			0
$541$		−	3.82714e24i		−	0.964050i	−0.876158	−	0.482025i	$-0.839901\pi$
$541$		−	3.82714e24i		−	0.964050i	0.876158	−	0.482025i	$-0.160099\pi$
$542$	−3.89431e24	+	5.85880e24i	−0.964799	+	1.45149i
$543$		0			0
$544$	1.03217e24	−	2.18289e23i	0.247378	−	0.0523168i
$545$	−9.83803e22			−0.0231921
$546$		0			0
$547$	−8.31133e24			−1.89577			−0.947883	−	0.318620i	$-0.896781\pi$
$547$	−8.31133e24			−1.89577			−0.947883	+	0.318620i	$0.896781\pi$
$548$	−3.51777e23	−	8.37805e23i	−0.0789300	−	0.187983i
$549$		0			0
$550$	−4.80746e23	−	3.19549e23i	−0.104388	−	0.0693862i
$551$		−	2.58566e23i		−	0.0552340i
$552$		0			0
$553$	−1.77998e24			−0.368034
$554$	−2.82663e24	+	4.25252e24i	−0.575017	+	0.865085i
$555$		0			0
$556$	2.04082e24	+	4.86050e24i	0.401913	+	0.957211i
$557$		−	8.43060e23i		−	0.163366i	−0.996658	−	0.0816830i	$-0.973970\pi$
$557$		−	8.43060e23i		−	0.163366i	0.996658	−	0.0816830i	$-0.0260295\pi$
$558$		0			0
$559$			1.44284e24i			0.270715i
$560$	1.81186e24	−	1.84717e24i	0.334527	−	0.341048i
$561$		0			0
$562$	−2.07729e24	−	1.38076e24i	−0.371424	−	0.246883i
$563$	−5.66512e24			−0.996858			−0.498429	−	0.866930i	$-0.666090\pi$
$563$	−5.66512e24			−0.996858			−0.498429	+	0.866930i	$0.666090\pi$
$564$		0			0
$565$		−	8.08354e24i		−	1.37773i
$566$	−8.94884e23	−	5.94824e23i	−0.150113	−	0.0997793i
$567$		0			0
$568$	6.56512e24	+	1.25655e24i	1.06686	+	0.204195i
$569$	7.57789e24			1.21210			0.606049	−	0.795427i	$-0.292754\pi$
$569$	7.57789e24			1.21210			0.606049	+	0.795427i	$0.292754\pi$
$570$		0			0
$571$	−5.34260e24			−0.827995			−0.413997	−	0.910278i	$-0.635868\pi$
$571$	−5.34260e24			−0.827995			−0.413997	+	0.910278i	$0.635868\pi$
$572$	9.22730e22	−	3.87435e22i	0.0140770	−	0.00591064i
$573$		0			0
$574$	1.31844e24	−	1.98352e24i	0.194918	−	0.293245i
$575$		−	1.35974e25i		−	1.97900i
$576$		0			0
$577$	8.76279e24			1.23612			0.618059	−	0.786132i	$-0.287919\pi$
$577$	8.76279e24			1.23612			0.618059	+	0.786132i	$0.287919\pi$
$578$	−5.61309e24	−	3.73099e24i	−0.779564	−	0.518171i
$579$		0			0
$580$	−1.81268e24	−	4.31714e24i	−0.244044	−	0.581225i
$581$		−	4.37833e23i		−	0.0580394i
$582$		0			0
$583$		−	5.24968e23i		−	0.0674708i
$584$	−1.91678e24	+	1.00146e25i	−0.242580	+	1.26742i
$585$		0			0
$586$	3.32691e24	−	5.00517e24i	0.408284	−	0.614244i
$587$	7.96895e24			0.963071			0.481535	−	0.876427i	$-0.340079\pi$
$587$	7.96895e24			0.963071			0.481535	+	0.876427i	$0.340079\pi$
$588$		0			0
$589$			1.69915e24i			0.199156i
$590$	−8.03045e24	+	1.20814e25i	−0.926983	+	1.39460i
$591$		0			0
$592$	−6.02112e24	−	5.90599e24i	−0.674189	−	0.661299i
$593$	−3.11221e24			−0.343224			−0.171612	−	0.985165i	$-0.554897\pi$
$593$	−3.11221e24			−0.343224			−0.171612	+	0.985165i	$0.554897\pi$
$594$		0			0
$595$	1.12900e24			0.120793
$596$	6.76619e24	−	2.84098e24i	0.713063	−	0.299400i
$597$		0			0
$598$	1.96319e24	+	1.30492e24i	0.200749	+	0.133436i
$599$		−	1.18101e25i		−	1.18963i	−0.803864	−	0.594814i	$-0.797226\pi$
$599$		−	1.18101e25i		−	1.18963i	0.803864	−	0.594814i	$-0.202774\pi$
$600$		0			0
$601$	4.63978e24			0.453552			0.226776	−	0.973947i	$-0.427182\pi$
$601$	4.63978e24			0.453552			0.226776	+	0.973947i	$0.427182\pi$
$602$	1.58084e24	−	2.37830e24i	0.152237	−	0.229034i
$603$		0			0
$604$	−8.80781e24	+	3.69821e24i	−0.823257	+	0.345668i
$605$		−	1.92661e25i		−	1.77417i
$606$		0			0
$607$		−	7.64084e24i		−	0.683035i	−0.939875	−	0.341518i	$-0.889059\pi$
$607$		−	7.64084e24i		−	0.683035i	0.939875	−	0.341518i	$-0.110941\pi$
$608$	1.73254e24	−	3.66407e23i	0.152599	−	0.0322724i
$609$		0			0
$610$	−2.42903e25	−	1.61456e25i	−2.07713	−	1.38066i
$611$	1.26819e24			0.106860
$612$		0			0
$613$			1.33533e24i			0.109255i	0.998507	+	0.0546277i	$0.0173972\pi$
$613$			1.33533e24i			0.109255i	−0.998507	+	0.0546277i	$0.982603\pi$
$614$	−1.61741e25	−	1.07508e25i	−1.30408	−	0.866814i
$615$		0			0
$616$	−1.94548e23	−	3.72359e22i	−0.0152335	−	0.00291565i
$617$	1.43061e25			1.10396			0.551982	−	0.833856i	$-0.313872\pi$
$617$	1.43061e25			1.10396			0.551982	+	0.833856i	$0.313872\pi$
$618$		0			0
$619$	−7.11980e24			−0.533644			−0.266822	−	0.963746i	$-0.585974\pi$
$619$	−7.11980e24			−0.533644			−0.266822	+	0.963746i	$0.585974\pi$
$620$	1.19119e25	+	2.83698e25i	0.879944	+	2.09571i
$621$		0			0
$622$	−1.04941e25	+	1.57879e25i	−0.753067	+	1.13295i
$623$		−	1.78776e24i		−	0.126450i
$624$		0			0
$625$	2.23369e25			1.53498
$626$	−1.18881e25	−	7.90195e24i	−0.805273	−	0.535260i
$627$		0			0
$628$	1.36616e25	−	5.73620e24i	0.899215	−	0.377561i
$629$		−	3.68013e24i		−	0.238785i
$630$		0			0
$631$			4.13788e23i			0.0260924i	0.999915	+	0.0130462i	$0.00415285\pi$
$631$			4.13788e23i			0.0260924i	−0.999915	+	0.0130462i	$0.995847\pi$
$632$	−2.16670e25	−	4.14702e24i	−1.34693	−	0.257800i
$633$		0			0
$634$	−2.50345e24	+	3.76632e24i	−0.151264	+	0.227569i
$635$	−3.18026e25			−1.89452
$636$		0			0
$637$		−	4.23331e24i		−	0.245146i
$638$	−1.98421e23	+	2.98515e23i	−0.0113293	+	0.0170444i
$639$		0			0
$640$	2.63587e25	−	1.82637e25i	1.46320	−	1.01384i
$641$	2.79818e25			1.53163			0.765815	−	0.643061i	$-0.222336\pi$
$641$	2.79818e25			1.53163			0.765815	+	0.643061i	$0.222336\pi$
$642$		0			0
$643$	−6.06624e24			−0.322865			−0.161432	−	0.986884i	$-0.551611\pi$
$643$	−6.06624e24			−0.322865			−0.161432	+	0.986884i	$0.551611\pi$
$644$	−1.80629e24	−	4.30194e24i	−0.0948016	−	0.225783i
$645$		0			0
$646$	6.43505e23	+	4.27734e23i	0.0328443	+	0.0218314i
$647$		−	2.42292e25i		−	1.21955i	−0.792574	−	0.609775i	$-0.791260\pi$
$647$		−	2.42292e25i		−	1.21955i	0.792574	−	0.609775i	$-0.208740\pi$
$648$		0			0
$649$	1.11056e24			0.0543674
$650$	−6.56899e24	+	9.88272e24i	−0.317160	+	0.477152i
$651$		0			0
$652$	2.36020e23	+	5.62115e23i	0.0110846	+	0.0263996i
$653$		−	2.57769e25i		−	1.19402i	−0.802233	−	0.597011i	$-0.796355\pi$
$653$		−	2.57769e25i		−	1.19402i	0.802233	−	0.597011i	$-0.203645\pi$
$654$		0			0
$655$		−	3.48328e24i		−	0.156970i
$656$	2.06701e25	−	2.10730e25i	0.918773	−	0.936682i
$657$		0			0
$658$	−2.09042e24	−	1.38949e24i	−0.0904068	−	0.0600929i
$659$	2.16127e25			0.922021			0.461010	−	0.887395i	$-0.347487\pi$
$659$	2.16127e25			0.922021			0.461010	+	0.887395i	$0.347487\pi$
$660$		0			0
$661$		−	3.80929e25i		−	1.58136i	−0.612230	−	0.790680i	$-0.709727\pi$
$661$		−	3.80929e25i		−	1.58136i	0.612230	−	0.790680i	$-0.290273\pi$
$662$	9.69357e24	+	6.44326e24i	0.396974	+	0.263866i
$663$		0			0
$664$	1.02007e24	−	5.32958e24i	0.0406553	−	0.212413i
$665$	1.89507e24			0.0745129
$666$		0			0
$667$	−8.44320e24			−0.323128
$668$	−4.32299e25	+	1.81513e25i	−1.63229	+	0.685362i
$669$		0			0
$670$	−3.05851e25	+	4.60137e25i	−1.12418	+	1.69128i
$671$			2.23282e24i			0.0809751i
$672$		0			0
$673$	−1.42553e25			−0.503317			−0.251658	−	0.967816i	$-0.580976\pi$
$673$	−1.42553e25			−0.503317			−0.251658	+	0.967816i	$0.580976\pi$
$674$	2.94909e25	+	1.96024e25i	1.02742	+	0.682920i
$675$		0			0
$676$	1.06162e25	+	2.52839e25i	0.360120	+	0.857677i
$677$			3.50982e25i			1.17486i	0.809275	+	0.587430i	$0.199860\pi$
$677$			3.50982e25i			1.17486i	−0.809275	+	0.587430i	$0.800140\pi$
$678$		0			0
$679$		−	4.36325e24i		−	0.142227i
$680$	1.37429e25	+	2.63036e24i	0.442078	+	0.0846127i
$681$		0			0
$682$	1.30391e24	−	1.96167e24i	0.0408497	−	0.0614565i
$683$	−5.18583e25			−1.60336			−0.801681	−	0.597752i	$-0.796061\pi$
$683$	−5.18583e25			−1.60336			−0.801681	+	0.597752i	$0.796061\pi$
$684$		0			0
$685$		−	1.20515e25i		−	0.362932i
$686$	−9.63642e24	+	1.44975e25i	−0.286417	+	0.430900i
$687$		0			0
$688$	2.47841e25	−	2.52672e25i	0.717591	−	0.731579i
$689$	−1.07918e25			−0.308405
$690$		0			0
$691$	−1.96292e25			−0.546513			−0.273256	−	0.961941i	$-0.588101\pi$
$691$	−1.96292e25			−0.546513			−0.273256	+	0.961941i	$0.588101\pi$
$692$	3.94281e25	−	1.65550e25i	1.08355	−	0.454961i
$693$		0			0
$694$	−1.52068e25	−	1.01078e25i	−0.407194	−	0.270659i
$695$			6.99164e25i			1.84806i
$696$		0			0
$697$	1.28799e25			0.331755
$698$	1.86356e25	−	2.80363e25i	0.473854	−	0.712890i
$699$		0			0
$700$	2.16560e25	−	9.09289e24i	0.536655	−	0.225330i
$701$		−	5.39698e25i		−	1.32035i	−0.751112	−	0.660174i	$-0.770482\pi$
$701$		−	5.39698e25i		−	1.32035i	0.751112	−	0.660174i	$-0.229518\pi$
$702$		0			0
$703$		−	6.17726e24i		−	0.147298i
$704$	−2.28141e24	−	9.06521e23i	−0.0537092	−	0.0213414i
$705$		0			0
$706$	9.41914e24	+	6.26084e24i	0.216157	+	0.143678i
$707$	1.34351e25			0.304416
$708$		0			0
$709$		−	6.68291e25i		−	1.47622i	−0.674683	−	0.738108i	$-0.735720\pi$
$709$		−	6.68291e25i		−	1.47622i	0.674683	−	0.738108i	$-0.264280\pi$
$710$	7.38311e25	+	4.90751e25i	1.61033	+	1.07037i
$711$		0			0
$712$	4.16517e24	−	2.17618e25i	0.0885753	−	0.462781i
$713$	5.54839e25			1.16510
$714$		0			0
$715$	1.32731e24			0.0271781
$716$	2.73776e24	+	6.52035e24i	0.0553576	+	0.131842i
$717$		0			0
$718$	−3.92115e25	+	5.89919e25i	−0.773204	+	1.16325i
$719$			9.75703e25i			1.90002i	0.312222	+	0.950009i	$0.398927\pi$
$719$			9.75703e25i			1.90002i	−0.312222	+	0.950009i	$0.601073\pi$
$720$		0			0
$721$	1.21315e25			0.230408
$722$	−4.33195e25	−	2.87942e25i	−0.812547	−	0.540095i
$723$		0			0
$724$	6.51860e25	−	2.73702e25i	1.19263	−	0.500762i
$725$		−	4.25031e25i		−	0.768030i
$726$		0			0
$727$		−	3.21406e24i		−	0.0566558i	−0.999599	−	0.0283279i	$-0.990982\pi$
$727$		−	3.21406e24i		−	0.0566558i	0.999599	−	0.0283279i	$-0.00901825\pi$
$728$	−7.65462e23	+	3.99933e24i	−0.0133273	+	0.0696313i
$729$		0			0
$730$	−7.48606e25	+	1.12624e26i	−1.27159	+	1.91305i
$731$	1.54434e25			0.259112
$732$		0			0
$733$			3.47572e25i			0.568996i	0.958677	+	0.284498i	$0.0918270\pi$
$733$			3.47572e25i			0.568996i	−0.958677	+	0.284498i	$0.908173\pi$
$734$	6.17415e24	−	9.28872e24i	0.0998419	−	0.150207i
$735$		0			0
$736$	−1.19647e25	−	5.65744e25i	−0.188799	−	0.892729i
$737$	4.22970e24			0.0659330
$738$		0			0
$739$	−3.36930e25			−0.512554			−0.256277	−	0.966603i	$-0.582496\pi$
$739$	−3.36930e25			−0.512554			−0.256277	+	0.966603i	$0.582496\pi$
$740$	−4.33057e25	−	1.03139e26i	−0.650818	−	1.55001i
$741$		0			0
$742$	1.77887e25	+	1.18240e25i	0.260921	+	0.173432i
$743$			6.47870e25i			0.938833i	0.882977	+	0.469416i	$0.155536\pi$
$743$			6.47870e25i			0.938833i	−0.882977	+	0.469416i	$0.844464\pi$
$744$		0			0
$745$	9.73290e25			1.37669
$746$	−4.53423e25	+	6.82153e25i	−0.633657	+	0.953307i
$747$		0			0
$748$	−4.14690e23	−	9.87643e23i	−0.00565730	−	0.0134737i
$749$			1.23498e25i			0.166465i
$750$		0			0
$751$			1.29075e26i			1.69856i	0.527939	+	0.849282i	$0.322965\pi$
$751$			1.29075e26i			1.69856i	−0.527939	+	0.849282i	$0.677035\pi$
$752$	−2.22087e25	−	2.17841e25i	−0.288777	−	0.283256i
$753$		0			0
$754$	6.13660e24	+	4.07896e24i	0.0779087	+	0.0517854i
$755$	−1.26697e26			−1.58944
$756$		0			0
$757$			8.91927e25i			1.09261i	0.837585	+	0.546306i	$0.183967\pi$
$757$			8.91927e25i			1.09261i	−0.837585	+	0.546306i	$0.816033\pi$
$758$	−7.24438e25	−	4.81530e25i	−0.876957	−	0.582908i
$759$		0			0
$760$	2.30681e25	+	4.41518e24i	0.272703	+	0.0521946i
$761$	−1.25661e26			−1.46804			−0.734022	−	0.679125i	$-0.762359\pi$
$761$	−1.25661e26			−1.46804			−0.734022	+	0.679125i	$0.762359\pi$
$762$		0			0
$763$	−3.06437e23			−0.00349639
$764$	3.58680e25	−	1.50602e25i	0.404452	−	0.169821i
$765$		0			0
$766$	−4.31568e24	+	6.49273e24i	−0.0475325	+	0.0715103i
$767$		−	2.28298e25i		−	0.248510i
$768$		0			0
$769$	3.35301e25			0.356531			0.178266	−	0.983982i	$-0.442951\pi$
$769$	3.35301e25			0.356531			0.178266	+	0.983982i	$0.442951\pi$
$770$	−2.18787e24	−	1.45427e24i	−0.0229935	−	0.0152837i
$771$		0			0
$772$	−1.75077e25	−	4.16969e25i	−0.179751	−	0.428103i
$773$		−	6.15259e25i		−	0.624371i	−0.950021	−	0.312185i	$-0.898939\pi$
$773$		−	6.15259e25i		−	0.624371i	0.950021	−	0.312185i	$-0.101061\pi$
$774$		0			0
$775$			2.79306e26i			2.76927i
$776$	1.01656e25	−	5.31124e25i	0.0996270	−	0.520523i
$777$		0			0
$778$	2.32832e25	−	3.50284e25i	0.222960	−	0.335432i
$779$	2.16195e25			0.204648
$780$		0			0
$781$		−	6.78675e24i		−	0.0627773i
$782$	1.39672e25	−	2.10130e25i	0.127717	−	0.192144i
$783$		0			0
$784$	−7.27169e25	+	7.41343e25i	−0.649816	+	0.662483i
$785$	1.96516e26			1.73609
$786$		0			0
$787$	−7.75132e24			−0.0669273			−0.0334636	−	0.999440i	$-0.510654\pi$
$787$	−7.75132e24			−0.0669273			−0.0334636	+	0.999440i	$0.510654\pi$
$788$	−9.60689e25	+	4.03373e25i	−0.820063	+	0.344327i
$789$		0			0
$790$	−2.43666e26	−	1.61964e26i	−2.03307	−	1.35137i
$791$		−	2.51788e25i		−	0.207705i
$792$		0			0
$793$	4.59003e25			0.370132
$794$	−2.07808e25	+	3.12637e25i	−0.165683	+	0.249262i
$795$		0			0
$796$	9.64845e25	−	4.05118e25i	0.752038	−	0.315765i
$797$			1.14334e26i			0.881155i	0.897715	+	0.440578i	$0.145226\pi$
$797$			1.14334e26i			0.881155i	−0.897715	+	0.440578i	$0.854774\pi$
$798$		0			0
$799$		−	1.35741e25i		−	0.102280i
$800$	2.84796e26	−	6.02301e25i	2.12189	−	0.448749i
$801$		0			0
$802$	5.92357e25	+	3.93736e25i	0.431533	+	0.286838i
$803$	1.03527e25			0.0745785
$804$		0			0
$805$		−	6.18817e25i		−	0.435913i
$806$	−4.03263e25	−	2.68046e25i	−0.280914	−	0.186722i
$807$		0			0
$808$	1.63541e26	+	3.13014e25i	1.11410	+	0.213237i
$809$	6.96753e25			0.469399			0.234699	−	0.972068i	$-0.424589\pi$
$809$	6.96753e25			0.469399			0.234699	+	0.972068i	$0.424589\pi$
$810$		0			0
$811$	−2.24307e26			−1.47793			−0.738967	−	0.673741i	$-0.764686\pi$
$811$	−2.24307e26			−1.47793			−0.738967	+	0.673741i	$0.764686\pi$
$812$	−5.64616e24	−	1.34471e25i	−0.0367916	−	0.0876244i
$813$		0			0
$814$	−4.74038e24	+	7.13168e24i	−0.0302130	+	0.0454540i
$815$			8.08580e24i			0.0509688i
$816$		0			0
$817$	2.59224e25			0.159837
$818$	−4.10013e25	−	2.72533e25i	−0.250045	−	0.166203i
$819$		0			0
$820$	3.60970e26	−	1.51564e26i	2.15351	−	0.904212i
$821$			1.51175e26i			0.892055i	0.895019	+	0.446027i	$0.147162\pi$
$821$			1.51175e26i			0.892055i	−0.895019	+	0.446027i	$0.852838\pi$
$822$		0			0
$823$			1.32029e26i			0.762203i	0.924533	+	0.381101i	$0.124455\pi$
$823$			1.32029e26i			0.762203i	−0.924533	+	0.381101i	$0.875545\pi$
$824$	1.47673e26	+	2.82643e25i	0.843250	+	0.161396i
$825$		0			0
$826$	−2.50134e25	+	3.76315e25i	−0.139750	+	0.210247i
$827$	−1.71500e26			−0.947797			−0.473898	−	0.880580i	$-0.657154\pi$
$827$	−1.71500e26			−0.947797			−0.473898	+	0.880580i	$0.657154\pi$
$828$		0			0
$829$		−	1.01192e26i		−	0.547210i	−0.961842	−	0.273605i	$-0.911784\pi$
$829$		−	1.01192e26i		−	0.547210i	0.961842	−	0.273605i	$-0.0882160\pi$
$830$	3.98393e25	−	5.99363e25i	0.213112	−	0.320617i
$831$		0			0
$832$	−1.86354e25	+	4.68990e25i	−0.0975503	+	0.245501i
$833$	−4.53112e25			−0.234639
$834$		0			0
$835$	−6.21845e26			−3.15140
$836$	−6.96076e23	−	1.65780e24i	−0.00348980	−	0.00831144i
$837$		0			0
$838$	1.64216e25	+	1.09154e25i	0.0805787	+	0.0535601i
$839$			1.53518e26i			0.745252i	0.927982	+	0.372626i	$0.121542\pi$
$839$			1.53518e26i			0.745252i	−0.927982	+	0.372626i	$0.878458\pi$
$840$		0			0
$841$	1.84065e26			0.874597
$842$	−1.31429e26	+	1.97729e26i	−0.617849	+	0.929524i
$843$		0			0
$844$	−1.21331e26	−	2.88968e26i	−0.558330	−	1.32974i
$845$			3.63699e26i			1.65589i
$846$		0			0
$847$		−	6.00105e25i		−	0.267471i
$848$	1.88988e26	+	1.85374e26i	0.833433	+	0.817498i
$849$		0			0
$850$	1.05780e26	+	7.03110e25i	0.456700	+	0.303566i
$851$	−2.01712e26			−0.861719
$852$		0			0
$853$			2.05890e26i			0.861178i	0.902548	+	0.430589i	$0.141694\pi$
$853$			2.05890e26i			0.861178i	−0.902548	+	0.430589i	$0.858306\pi$
$854$	−7.56598e25	−	5.02906e25i	−0.313144	−	0.208145i
$855$		0			0
$856$	−2.87727e25	+	1.50330e26i	−0.116605	+	0.609229i
$857$	−1.36020e26			−0.545476			−0.272738	−	0.962088i	$-0.587929\pi$
$857$	−1.36020e26			−0.545476			−0.272738	+	0.962088i	$0.587929\pi$
$858$		0			0
$859$	−1.80946e26			−0.710576			−0.355288	−	0.934757i	$-0.615617\pi$
$859$	−1.80946e26			−0.710576			−0.355288	+	0.934757i	$0.615617\pi$
$860$	4.32814e26	−	1.81729e26i	1.68196	−	0.706219i
$861$		0			0
$862$	7.22147e25	−	1.08644e26i	0.274828	−	0.413465i
$863$		−	2.20461e26i		−	0.830298i	−0.909754	−	0.415149i	$-0.863729\pi$
$863$		−	2.20461e26i		−	0.830298i	0.909754	−	0.415149i	$-0.136271\pi$
$864$		0			0
$865$	5.67157e26			2.09198
$866$	−2.32596e26	−	1.54605e26i	−0.849065	−	0.564368i
$867$		0			0
$868$	3.71034e25	+	8.83668e25i	0.132659	+	0.315945i
$869$			2.23985e25i			0.0792575i
$870$		0			0
$871$		−	8.69503e25i		−	0.301375i
$872$	−3.73015e24	−	7.13943e23i	−0.0127961	−	0.00244915i
$873$		0			0
$874$	2.34446e25	−	3.52713e25i	0.0787844	−	0.118527i
$875$	1.67881e26			0.558378
$876$		0			0
$877$		−	4.77671e26i		−	1.55644i	−0.627991	−	0.778221i	$-0.716123\pi$
$877$		−	4.77671e26i		−	1.55644i	0.627991	−	0.778221i	$-0.283877\pi$
$878$	9.65219e25	−	1.45212e26i	0.311297	−	0.468331i
$879$		0			0
$880$	−2.32441e25	−	2.27996e25i	−0.0734459	−	0.0720417i
$881$	−3.98413e26			−1.24609			−0.623047	−	0.782184i	$-0.714105\pi$
$881$	−3.98413e26			−1.24609			−0.623047	+	0.782184i	$0.714105\pi$
$882$		0			0
$883$	2.83034e26			0.867346			0.433673	−	0.901070i	$-0.357217\pi$
$883$	2.83034e26			0.867346			0.433673	+	0.901070i	$0.357217\pi$
$884$	−2.03030e25	+	8.52481e24i	−0.0615872	+	0.0258592i
$885$		0			0
$886$	−1.55537e26	−	1.03384e26i	−0.462307	−	0.307292i
$887$			1.96588e26i			0.578422i	0.957265	+	0.289211i	$0.0933929\pi$
$887$			1.96588e26i			0.578422i	−0.957265	+	0.289211i	$0.906607\pi$
$888$		0			0
$889$	−9.90594e25			−0.285614
$890$	1.62672e26	−	2.44733e26i	0.464306	−	0.698525i
$891$		0			0
$892$	2.28959e26	−	9.61349e25i	0.640432	−	0.268904i
$893$		−	2.27847e25i		−	0.0630927i
$894$		0			0
$895$			9.37926e25i			0.254543i
$896$	8.21025e25	−	5.68882e25i	0.220589	−	0.152844i
$897$		0			0
$898$	−5.16418e25	−	3.43260e25i	−0.135992	−	0.0903932i
$899$	1.73433e26			0.452162
$900$		0			0
$901$			1.15510e26i			0.295186i
$902$	−2.49598e25	−	1.65906e25i	−0.0631513	−	0.0419763i
$903$		0			0
$904$	5.86619e25	−	3.06492e26i	0.145492	−	0.760158i
$905$	9.37674e26			2.30258
$906$		0			0
$907$	−1.92019e26			−0.462252			−0.231126	−	0.972924i	$-0.574241\pi$
$907$	−1.92019e26			−0.462252			−0.231126	+	0.972924i	$0.574241\pi$
$908$	−2.14847e26	−	5.11687e26i	−0.512102	−	1.21964i
$909$		0			0
$910$	−2.98954e25	+	4.49763e25i	−0.0698606	+	0.105102i
$911$			2.22110e26i			0.513927i	0.966421	+	0.256964i	$0.0827221\pi$
$911$			2.22110e26i			0.513927i	−0.966421	+	0.256964i	$0.917278\pi$
$912$		0			0
$913$	−5.50950e24			−0.0124990
$914$	−4.95355e25	−	3.29260e25i	−0.111276	−	0.0739644i
$915$		0			0
$916$	−4.11720e26	+	1.72873e26i	−0.906865	+	0.380773i
$917$		−	1.08498e25i		−	0.0236645i
$918$		0			0
$919$			4.44214e26i			0.950064i	0.879969	+	0.475032i	$0.157563\pi$
$919$			4.44214e26i			0.950064i	−0.879969	+	0.475032i	$0.842437\pi$
$920$	1.44173e26	−	7.53265e26i	0.305347	−	1.59536i
$921$		0			0
$922$	−3.32917e26	+	5.00857e26i	−0.691445	+	1.04025i
$923$	−1.39516e26			−0.286951
$924$		0			0
$925$		−	1.01542e27i		−	2.04819i
$926$	−2.19851e26	+	3.30755e26i	−0.439167	+	0.660705i
$927$		0			0
$928$	−3.73994e25	−	1.76842e26i	−0.0732712	−	0.346460i
$929$	−9.19897e25			−0.178483			−0.0892417	−	0.996010i	$-0.528444\pi$
$929$	−9.19897e25			−0.178483			−0.0892417	+	0.996010i	$0.528444\pi$
$930$		0			0
$931$	−7.60568e25			−0.144741
$932$	−2.50725e26	−	5.97135e26i	−0.472556	−	1.12546i
$933$		0			0
$934$	−7.18320e26	−	4.77463e26i	−1.32799	−	0.882710i
$935$		−	1.42068e25i		−	0.0260132i
$936$		0			0
$937$	6.97243e26			1.25236			0.626178	−	0.779680i	$-0.284618\pi$
$937$	6.97243e26			1.25236			0.626178	+	0.779680i	$0.284618\pi$
$938$	−9.52669e25	+	1.43325e26i	−0.169479	+	0.254973i
$939$		0			0
$940$	−1.59732e26	−	3.80424e26i	−0.278767	−	0.663922i
$941$		−	7.71125e26i		−	1.33296i	−0.745522	−	0.666481i	$-0.767800\pi$
$941$		−	7.71125e26i		−	1.33296i	0.745522	−	0.666481i	$-0.232200\pi$
$942$		0			0
$943$		−	7.05963e26i		−	1.19723i
$944$	−3.92154e26	+	3.99798e26i	−0.658732	+	0.671573i
$945$		0			0
$946$	−2.99276e25	−	1.98927e25i	−0.0493232	−	0.0327849i
$947$	−5.01052e26			−0.817962			−0.408981	−	0.912543i	$-0.634116\pi$
$947$	−5.01052e26			−0.817962			−0.408981	+	0.912543i	$0.634116\pi$
$948$		0			0
$949$		−	2.12821e26i		−	0.340894i
$950$	1.77556e26	+	1.18020e26i	0.281723	+	0.187259i
$951$		0			0
$952$	4.28067e25	+	8.19310e24i	0.0666468	+	0.0127560i
$953$	−7.95510e26			−1.22690			−0.613451	−	0.789733i	$-0.710219\pi$
$953$	−7.95510e26			−1.22690			−0.613451	+	0.789733i	$0.710219\pi$
$954$		0			0
$955$	5.15947e26			0.780863
$956$	−6.01026e25	+	2.52358e25i	−0.0901099	+	0.0378352i
$957$		0			0
$958$	−3.68941e26	+	5.55053e26i	−0.542834	+	0.816667i
$959$		−	3.75382e25i		−	0.0547150i
$960$		0			0
$961$	−4.40650e26			−0.630352
$962$	1.46606e26	+	9.74483e25i	0.207767	+	0.138102i
$963$		0			0
$964$	1.93443e26	+	4.60712e26i	0.269067	+	0.640820i
$965$		−	5.99794e26i		−	0.826525i
$966$		0			0
$967$			9.39317e26i			1.27050i	0.772307	+	0.635249i	$0.219103\pi$
$967$			9.39317e26i			1.27050i	−0.772307	+	0.635249i	$0.780897\pi$
$968$	1.39814e26	−	7.30487e26i	0.187358	−	0.978891i
$969$		0			0
$970$	3.97022e26	−	5.97300e26i	0.522238	−	0.785682i
$971$	−1.28565e26			−0.167551			−0.0837757	−	0.996485i	$-0.526698\pi$
$971$	−1.28565e26			−0.167551			−0.0837757	+	0.996485i	$0.526698\pi$
$972$		0			0
$973$			2.17777e26i			0.278610i
$974$	−3.06725e26	+	4.61453e26i	−0.388793	+	0.584921i
$975$		0			0
$976$	−8.03812e26	−	7.88443e26i	−1.00024	−	0.981120i
$977$	−3.96171e26			−0.488463			−0.244232	−	0.969717i	$-0.578536\pi$
$977$	−3.96171e26			−0.488463			−0.244232	+	0.969717i	$0.578536\pi$
$978$		0			0
$979$	−2.24965e25			−0.0272314
$980$	−1.26988e27	+	5.33196e26i	−1.52310	+	0.639518i
$981$		0			0
$982$	9.70132e26	+	6.44841e26i	1.14242	+	0.759363i
$983$			3.94343e26i			0.460143i	0.973174	+	0.230071i	$0.0738960\pi$
$983$			3.94343e26i			0.460143i	−0.973174	+	0.230071i	$0.926104\pi$
$984$		0			0
$985$	−1.38191e27			−1.58327
$986$	4.36591e25	−	6.56830e25i	0.0495658	−	0.0745694i
$987$		0			0
$988$	−3.40795e25	+	1.43093e25i	−0.0379910	+	0.0159516i
$989$		−	8.46471e26i		−	0.935073i
$990$		0			0
$991$		−	1.21537e27i		−	1.31840i	−0.751968	−	0.659200i	$-0.770895\pi$
$991$		−	1.21537e27i		−	1.31840i	0.751968	−	0.659200i	$-0.229105\pi$
$992$	2.45768e26	+	1.16210e27i	0.264192	+	1.24922i
$993$		0			0
$994$	2.29971e26	+	1.52860e26i	0.242770	+	0.161368i
$995$	1.38789e27			1.45194
$996$		0			0
$997$			8.41591e25i			0.0864659i	0.999065	+	0.0432330i	$0.0137658\pi$
$997$			8.41591e25i			0.0864659i	−0.999065	+	0.0432330i	$0.986234\pi$
$998$	−3.21582e26	−	2.13753e26i	−0.327429	−	0.217640i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	72.19.b.b.19.16		16
3.2	odd	2		8.19.d.b.3.1	✓	16
8.3	odd	2	inner	72.19.b.b.19.15		16
12.11	even	2		32.19.d.b.15.1		16
24.5	odd	2		32.19.d.b.15.2		16
24.11	even	2		8.19.d.b.3.2	yes	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8.19.d.b.3.1	✓	16	3.2	odd	2
8.19.d.b.3.2	yes	16	24.11	even	2
32.19.d.b.15.1		16	12.11	even	2
32.19.d.b.15.2		16	24.5	odd	2
72.19.b.b.19.15		16	8.3	odd	2	inner
72.19.b.b.19.16		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)

\(f(q)\)	\(=\)	\(q+(426.398 + 283.424i) q^{2} +(101486. + 241703. i) q^{4} +3.47680e6i q^{5} +1.08296e7i q^{7} +(-2.52310e7 + 1.31825e8i) q^{8} +O(q^{10})\)	\(q+(426.398 + 283.424i) q^{2} +(101486. + 241703. i) q^{4} +3.47680e6i q^{5} +1.08296e7i q^{7} +(-2.52310e7 + 1.31825e8i) q^{8} +(-9.85407e8 + 1.48250e9i) q^{10} +1.36275e8 q^{11} -2.80141e9i q^{13} +(-3.06936e9 + 4.61771e9i) q^{14} +(-4.81207e10 + 4.90587e10i) q^{16} -2.99849e10 q^{17} -5.03309e10 q^{19} +(-8.40350e11 + 3.52845e11i) q^{20} +(5.81073e10 + 3.86236e10i) q^{22} +1.64351e12i q^{23} -8.27341e12 q^{25} +(7.93988e11 - 1.19452e12i) q^{26} +(-2.61754e12 + 1.09905e12i) q^{28} +5.13731e12i q^{29} -3.37595e13i q^{31} +(-3.44230e13 + 7.27996e12i) q^{32} +(-1.27855e13 - 8.49843e12i) q^{34} -3.76523e13 q^{35} +1.22733e14i q^{37} +(-2.14610e13 - 1.42650e13i) q^{38} +(-4.58328e14 - 8.77229e13i) q^{40} -4.29547e14 q^{41} -5.15040e14 q^{43} +(1.38300e13 + 3.29380e13i) q^{44} +(-4.65809e14 + 7.00787e14i) q^{46} +4.52697e14i q^{47} +1.51113e15 q^{49} +(-3.52776e15 - 2.34488e15i) q^{50} +(6.77109e14 - 2.84304e14i) q^{52} -3.85227e15i q^{53} +4.73800e14i q^{55} +(-1.42761e15 - 2.73241e14i) q^{56} +(-1.45604e15 + 2.19054e15i) q^{58} +8.14938e15 q^{59} +1.63847e16i q^{61} +(9.56825e15 - 1.43950e16i) q^{62} +(-1.67412e16 - 6.65214e15i) q^{64} +9.73995e15 q^{65} +3.10380e16 q^{67} +(-3.04304e15 - 7.24742e15i) q^{68} +(-1.60548e16 - 1.06716e16i) q^{70} -4.98018e16i q^{71} +7.59692e16 q^{73} +(-3.47854e16 + 5.23330e16i) q^{74} +(-5.10788e15 - 1.21651e16i) q^{76} +1.47580e15i q^{77} +1.64362e17i q^{79} +(-1.70567e17 - 1.67306e17i) q^{80} +(-1.83158e17 - 1.21744e17i) q^{82} -4.04293e16 q^{83} -1.04251e17i q^{85} +(-2.19612e17 - 1.45975e17i) q^{86} +(-3.43835e15 + 1.79644e16i) q^{88} -1.65081e17 q^{89} +3.03382e16 q^{91} +(-3.97240e17 + 1.66793e17i) q^{92} +(-1.28305e17 + 1.93029e17i) q^{94} -1.74990e17i q^{95} -4.02901e17 q^{97} +(6.44344e17 + 4.28291e17i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 426 q^{2} - 444332 q^{4} - 304914744 q^{8}+O(q^{10}) \) 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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