LMFDB - Embedded newform 72.22.f.a.35.78

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [72,22,Mod(35,72)]

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, 1]))

N = Newforms(chi, 22, names="a")

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

chi := DirichletCharacter("72.35");

S:= CuspForms(chi, 22);

N := Newforms(S);

Level:	$ N $	$=$	$ 72 = 2^{3} \cdot 3^{2} $
Weight:	$ k $	$=$	$ 22 $
Character orbit:	$[\chi]$	$=$	72.f (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:	$201.223687887$
Analytic rank:	$0$
Dimension:	$84$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			35.78
Character	$\chi$	$=$	72.35
Dual form			72.22.f.a.35.77

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1383.40 + 428.211i) q^{2} +(1.73042e6 + 1.18477e6i) q^{4} -4.14728e7 q^{5} +2.70660e8i q^{7} +(1.88653e9 + 2.38000e9i) q^{8} +O(q^{10})$	\(q+(1383.40 + 428.211i) q^{2} +(1.73042e6 + 1.18477e6i) q^{4} -4.14728e7 q^{5} +2.70660e8i q^{7} +(1.88653e9 + 2.38000e9i) q^{8} +(-5.73733e10 - 1.77591e10i) q^{10} +1.22616e11i q^{11} -9.13395e10i q^{13} +(-1.15899e11 + 3.74430e11i) q^{14} +(1.59068e12 + 4.10031e12i) q^{16} +1.30428e13i q^{17} +4.42830e13 q^{19} +(-7.17654e13 - 4.91358e13i) q^{20} +(-5.25056e13 + 1.69627e14i) q^{22} +1.64232e14 q^{23} +1.24315e15 q^{25} +(3.91126e13 - 1.26359e14i) q^{26} +(-3.20670e14 + 4.68356e14i) q^{28} -2.31284e15 q^{29} +1.58177e15i q^{31} +(4.44741e14 + 6.35350e15i) q^{32} +(-5.58508e15 + 1.80434e16i) q^{34} -1.12250e16i q^{35} -3.81093e16i q^{37} +(6.12609e16 + 1.89625e16i) q^{38} +(-7.82396e16 - 9.87050e16i) q^{40} +1.05875e17i q^{41} +2.64492e16 q^{43} +(-1.45272e17 + 2.12178e17i) q^{44} +(2.27197e17 + 7.03258e16i) q^{46} +3.60142e17 q^{47} +4.85289e17 q^{49} +(1.71977e18 + 5.32332e17i) q^{50} +(1.08216e17 - 1.58056e17i) q^{52} +7.43815e17 q^{53} -5.08523e18i q^{55} +(-6.44169e17 + 5.10608e17i) q^{56} +(-3.19958e18 - 9.90385e17i) q^{58} +3.96701e18i q^{59} +4.70909e18i q^{61} +(-6.77329e17 + 2.18821e18i) q^{62} +(-2.10539e18 + 8.97986e18i) q^{64} +3.78810e18i q^{65} -2.46007e19 q^{67} +(-1.54528e19 + 2.25696e19i) q^{68} +(4.80667e18 - 1.55286e19i) q^{70} -1.80477e19 q^{71} -6.21935e19 q^{73} +(1.63188e19 - 5.27203e19i) q^{74} +(7.66282e19 + 5.24652e19i) q^{76} -3.31872e19 q^{77} +1.17050e20i q^{79} +(-6.59698e19 - 1.70051e20i) q^{80} +(-4.53369e19 + 1.46467e20i) q^{82} +2.71098e19i q^{83} -5.40922e20i q^{85} +(3.65897e19 + 1.13258e19i) q^{86} +(-2.91826e20 + 2.31319e20i) q^{88} -1.51004e20i q^{89} +2.47219e19 q^{91} +(2.84190e20 + 1.94577e20i) q^{92} +(4.98219e20 + 1.54217e20i) q^{94} -1.83654e21 q^{95} -3.99303e19 q^{97} +(6.71348e20 + 2.07806e20i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 84 q + 2424084 q^{4}+O(q^{10}) $ 84 * q + 2424084 * q^4	$ 84 q + 2424084 q^{4} + 17057181612 q^{10} - 4099708064904 q^{16} + 92015527242864 q^{19} - 236011369239528 q^{22} + 80\!\cdots\!00 q^{25}+ \cdots - 16\!\cdots\!12 q^{97}+O(q^{100}) $ 84 * q + 2424084 * q^4 + 17057181612 * q^10 - 4099708064904 * q^16 + 92015527242864 * q^19 - 236011369239528 * q^22 + 8010864257812500 * q^25 - 3042238700022024 * q^28 + 74414158327329924 * q^34 + 75018327243317184 * q^40 + 707788847336454432 * q^43 - 162639476543943288 * q^46 - 5423745715136249124 * q^49 - 70566629446202808 * q^52 - 14491558288019904108 * q^58 - 28749968749508108064 * q^64 - 13653811098426494352 * q^67 + 140256684870035374392 * q^70 - 71781309378863778384 * q^73 + 376055720386305092400 * q^76 - 368362114062816367548 * q^82 - 592572120184082106720 * q^88 - 522206955652189957200 * q^91 - 528772551789914644488 * q^94 - 1686050813935078492512 * q^97

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 $

$2$	1383.40	+	428.211i	0.955283	+	0.295694i
$2$	1383.40	+	428.211i	0.955283	+	0.295694i
$3$		0			0
$3$		0			0
$4$	1.73042e6	+	1.18477e6i	0.825130	+	0.564943i
$5$	−4.14728e7			−1.89923			−0.949616	−	0.313416i	$-0.898527\pi$
$5$	−4.14728e7			−1.89923			−0.949616	+	0.313416i	$0.898527\pi$
$6$		0			0
$7$			2.70660e8i			0.362155i	0.983469	+	0.181077i	$0.0579585\pi$
$7$			2.70660e8i			0.362155i	−0.983469	+	0.181077i	$0.942042\pi$
$8$	1.88653e9	+	2.38000e9i	0.621182	+	0.783667i
$9$		0			0
$10$	−5.73733e10	−	1.77591e10i	−1.81430	−	0.561592i
$11$			1.22616e11i			1.42536i	0.701490	+	0.712680i	$0.252519\pi$
$11$			1.22616e11i			1.42536i	−0.701490	+	0.712680i	$0.747481\pi$
$12$		0			0
$13$		−	9.13395e10i		−	0.183761i	−0.995770	−	0.0918805i	$-0.970712\pi$
$13$		−	9.13395e10i		−	0.183761i	0.995770	−	0.0918805i	$-0.0292878\pi$
$14$	−1.15899e11	+	3.74430e11i	−0.107087	+	0.345960i
$15$		0			0
$16$	1.59068e12	+	4.10031e12i	0.361678	+	0.932303i
$17$			1.30428e13i			1.56913i	0.620048	+	0.784564i	$0.287113\pi$
$17$			1.30428e13i			1.56913i	−0.620048	+	0.784564i	$0.712887\pi$
$18$		0			0
$19$	4.42830e13			1.65701			0.828503	−	0.559985i	$-0.189193\pi$
$19$	4.42830e13			1.65701			0.828503	+	0.559985i	$0.189193\pi$
$20$	−7.17654e13	−	4.91358e13i	−1.56711	−	1.07296i
$21$		0			0
$22$	−5.25056e13	+	1.69627e14i	−0.421471	+	1.36162i
$23$	1.64232e14			0.826636			0.413318	−	0.910587i	$-0.364370\pi$
$23$	1.64232e14			0.826636			0.413318	+	0.910587i	$0.364370\pi$
$24$		0			0
$25$	1.24315e15			2.60708
$26$	3.91126e13	−	1.26359e14i	0.0543371	−	0.175544i
$27$		0			0
$28$	−3.20670e14	+	4.68356e14i	−0.204597	+	0.298825i
$29$	−2.31284e15			−1.02086			−0.510431	−	0.859919i	$-0.670514\pi$
$29$	−2.31284e15			−1.02086			−0.510431	+	0.859919i	$0.670514\pi$
$30$		0			0
$31$			1.58177e15i			0.346612i	0.984868	+	0.173306i	$0.0554450\pi$
$31$			1.58177e15i			0.346612i	−0.984868	+	0.173306i	$0.944555\pi$
$32$	4.44741e14	+	6.35350e15i	0.0698285	+	0.997559i
$33$		0			0
$34$	−5.58508e15	+	1.80434e16i	−0.463982	+	1.49896i
$35$		−	1.12250e16i		−	0.687816i
$36$		0			0
$37$		−	3.81093e16i		−	1.30291i	−0.758689	−	0.651453i	$-0.774160\pi$
$37$		−	3.81093e16i		−	1.30291i	0.758689	−	0.651453i	$-0.225840\pi$
$38$	6.12609e16	+	1.89625e16i	1.58291	+	0.489967i
$39$		0			0
$40$	−7.82396e16	−	9.87050e16i	−1.17977	−	1.48836i
$41$			1.05875e17i			1.23186i	0.787799	+	0.615932i	$0.211221\pi$
$41$			1.05875e17i			1.23186i	−0.787799	+	0.615932i	$0.788779\pi$
$42$		0			0
$43$	2.64492e16			0.186635			0.0933176	−	0.995636i	$-0.470253\pi$
$43$	2.64492e16			0.186635			0.0933176	+	0.995636i	$0.470253\pi$
$44$	−1.45272e17	+	2.12178e17i	−0.805247	+	1.17611i
$45$		0			0
$46$	2.27197e17	+	7.03258e16i	0.789671	+	0.244432i
$47$	3.60142e17			0.998725			0.499362	−	0.866393i	$-0.333568\pi$
$47$	3.60142e17			0.998725			0.499362	+	0.866393i	$0.333568\pi$
$48$		0			0
$49$	4.85289e17			0.868844
$50$	1.71977e18	+	5.32332e17i	2.49050	+	0.770899i
$51$		0			0
$52$	1.08216e17	−	1.58056e17i	0.103815	−	0.151627i
$53$	7.43815e17			0.584209			0.292104	−	0.956386i	$-0.405645\pi$
$53$	7.43815e17			0.584209			0.292104	+	0.956386i	$0.405645\pi$
$54$		0			0
$55$		−	5.08523e18i		−	2.70709i
$56$	−6.44169e17	+	5.10608e17i	−0.283809	+	0.224964i
$57$		0			0
$58$	−3.19958e18	−	9.90385e17i	−0.975212	−	0.301863i
$59$			3.96701e18i			1.01046i	0.862986	+	0.505228i	$0.168592\pi$
$59$			3.96701e18i			1.01046i	−0.862986	+	0.505228i	$0.831408\pi$
$60$		0			0
$61$			4.70909e18i			0.845228i	0.906310	+	0.422614i	$0.138887\pi$
$61$			4.70909e18i			0.845228i	−0.906310	+	0.422614i	$0.861113\pi$
$62$	−6.77329e17	+	2.18821e18i	−0.102491	+	0.331113i
$63$		0			0
$64$	−2.10539e18	+	8.97986e18i	−0.228267	+	0.973599i
$65$			3.78810e18i			0.349005i
$66$		0			0
$67$	−2.46007e19			−1.64878			−0.824390	−	0.566022i	$-0.808482\pi$
$67$	−2.46007e19			−1.64878			−0.824390	+	0.566022i	$0.808482\pi$
$68$	−1.54528e19	+	2.25696e19i	−0.886468	+	1.29473i
$69$		0			0
$70$	4.80667e18	−	1.55286e19i	0.203383	−	0.657059i
$71$	−1.80477e19			−0.657974			−0.328987	−	0.944334i	$-0.606707\pi$
$71$	−1.80477e19			−0.657974			−0.328987	+	0.944334i	$0.606707\pi$
$72$		0			0
$73$	−6.21935e19			−1.69377			−0.846885	−	0.531775i	$-0.821525\pi$
$73$	−6.21935e19			−1.69377			−0.846885	+	0.531775i	$0.821525\pi$
$74$	1.63188e19	−	5.27203e19i	0.385262	−	1.24464i
$75$		0			0
$76$	7.66282e19	+	5.24652e19i	1.36724	+	0.936114i
$77$	−3.31872e19			−0.516201
$78$		0			0
$79$			1.17050e20i			1.39087i	0.718590	+	0.695434i	$0.244788\pi$
$79$			1.17050e20i			1.39087i	−0.718590	+	0.695434i	$0.755212\pi$
$80$	−6.59698e19	−	1.70051e20i	−0.686911	−	1.77066i
$81$		0			0
$82$	−4.53369e19	+	1.46467e20i	−0.364255	+	1.17678i
$83$			2.71098e19i			0.191781i	0.995392	+	0.0958907i	$0.0305699\pi$
$83$			2.71098e19i			0.191781i	−0.995392	+	0.0958907i	$0.969430\pi$
$84$		0			0
$85$		−	5.40922e20i		−	2.98014i
$86$	3.65897e19	+	1.13258e19i	0.178289	+	0.0551870i
$87$		0			0
$88$	−2.91826e20	+	2.31319e20i	−1.11701	+	0.885407i
$89$		−	1.51004e20i		−	0.513326i	−0.966501	−	0.256663i	$-0.917377\pi$
$89$		−	1.51004e20i		−	0.513326i	0.966501	−	0.256663i	$-0.0826231\pi$
$90$		0			0
$91$	2.47219e19			0.0665500
$92$	2.84190e20	+	1.94577e20i	0.682082	+	0.467002i
$93$		0			0
$94$	4.98219e20	+	1.54217e20i	0.954064	+	0.295317i
$95$	−1.83654e21			−3.14704
$96$		0			0
$97$	−3.99303e19			−0.0549793			−0.0274897	−	0.999622i	$-0.508751\pi$
$97$	−3.99303e19			−0.0549793			−0.0274897	+	0.999622i	$0.508751\pi$
$98$	6.71348e20	+	2.07806e20i	0.829991	+	0.256912i
$99$		0			0
$100$	2.15118e21	+	1.47285e21i	2.15118	+	1.47285i
$101$	6.46427e20			0.582298			0.291149	−	0.956678i	$-0.405963\pi$
$101$	6.46427e20			0.582298			0.291149	+	0.956678i	$0.405963\pi$
$102$		0			0
$103$		−	1.63829e21i		−	1.20116i	−0.799564	−	0.600581i	$-0.794936\pi$
$103$		−	1.63829e21i		−	1.20116i	0.799564	−	0.600581i	$-0.205064\pi$
$104$	2.17388e20	−	1.72315e20i	0.144007	−	0.114149i
$105$		0			0
$106$	1.02899e21	+	3.18510e20i	0.558085	+	0.172747i
$107$			2.14616e21i			1.05471i	0.849645	+	0.527355i	$0.176816\pi$
$107$			2.14616e21i			1.05471i	−0.849645	+	0.527355i	$0.823184\pi$
$108$		0			0
$109$		−	2.23991e20i		−	0.0906260i	−0.998973	−	0.0453130i	$-0.985571\pi$
$109$		−	2.23991e20i		−	0.0906260i	0.998973	−	0.0453130i	$-0.0144285\pi$
$110$	2.17755e21	−	7.03489e21i	0.800470	−	2.58603i
$111$		0			0
$112$	−1.10979e21	+	4.30533e20i	−0.337638	+	0.130984i
$113$			2.30205e21i			0.637957i	0.947762	+	0.318978i	$0.103340\pi$
$113$			2.30205e21i			0.637957i	−0.947762	+	0.318978i	$0.896660\pi$
$114$		0			0
$115$	−6.81114e21			−1.56997
$116$	−4.00220e21	−	2.74019e21i	−0.842344	−	0.576729i
$117$		0			0
$118$	−1.69872e21	+	5.48796e21i	−0.298786	+	0.965272i
$119$	−3.53017e21			−0.568267
$120$		0			0
$121$	−7.63446e21			−1.03165
$122$	−2.01648e21	+	6.51454e21i	−0.249929	+	0.807432i
$123$		0			0
$124$	−1.87403e21	+	2.73712e21i	−0.195816	+	0.286000i
$125$	−3.17813e22			−3.05222
$126$		0			0
$127$			1.13165e22i			0.919965i	0.887928	+	0.459982i	$0.152144\pi$
$127$			1.13165e22i			0.919965i	−0.887928	+	0.459982i	$0.847856\pi$
$128$	−6.75786e21	+	1.15212e22i	−0.505947	+	0.862565i
$129$		0			0
$130$	−1.62211e21	+	5.24045e21i	−0.103199	+	0.333398i
$131$		−	2.41878e22i		−	1.41987i	−0.704267	−	0.709935i	$-0.748724\pi$
$131$		−	2.41878e22i		−	1.41987i	0.704267	−	0.709935i	$-0.251276\pi$
$132$		0			0
$133$			1.19856e22i			0.600092i
$134$	−3.40326e22	−	1.05343e22i	−1.57505	−	0.487535i
$135$		0			0
$136$	−3.10419e22	+	2.46057e22i	−1.22967	+	0.974713i
$137$			6.73944e20i			0.0247205i	0.999924	+	0.0123603i	$0.00393450\pi$
$137$			6.73944e20i			0.0247205i	−0.999924	+	0.0123603i	$0.996066\pi$
$138$		0			0
$139$	−2.20391e22			−0.694287			−0.347144	−	0.937812i	$-0.612848\pi$
$139$	−2.20391e22			−0.694287			−0.347144	+	0.937812i	$0.612848\pi$
$140$	1.32991e22	−	1.94240e22i	0.388577	−	0.567538i
$141$		0			0
$142$	−2.49671e22	−	7.72822e21i	−0.628551	−	0.194559i
$143$	1.11997e22			0.261926
$144$		0			0
$145$	9.59200e22			1.93885
$146$	−8.60382e22	−	2.66319e22i	−1.61803	−	0.500838i
$147$		0			0
$148$	4.51509e22	−	6.59452e22i	0.736068	−	1.07507i
$149$	1.02771e23			1.56104			0.780519	−	0.625132i	$-0.214955\pi$
$149$	1.02771e23			1.56104			0.780519	+	0.625132i	$0.214955\pi$
$150$		0			0
$151$			3.07511e22i			0.406072i	0.979171	+	0.203036i	$0.0650809\pi$
$151$			3.07511e22i			0.406072i	−0.979171	+	0.203036i	$0.934919\pi$
$152$	8.35411e22	+	1.05393e23i	1.02930	+	1.29854i
$153$		0			0
$154$	−4.59111e22	−	1.42111e22i	−0.493118	−	0.152638i
$155$		−	6.56002e22i		−	0.658297i
$156$		0			0
$157$			9.32560e22i			0.817957i	0.912544	+	0.408978i	$0.134115\pi$
$157$			9.32560e22i			0.817957i	−0.912544	+	0.408978i	$0.865885\pi$
$158$	−5.01219e22	+	1.61926e23i	−0.411271	+	1.32867i
$159$		0			0
$160$	−1.84447e22	−	2.63497e23i	−0.132621	−	1.89460i
$161$			4.44509e22i			0.299370i
$162$		0			0
$163$	−2.96490e22			−0.175404			−0.0877021	−	0.996147i	$-0.527952\pi$
$163$	−2.96490e22			−0.175404			−0.0877021	+	0.996147i	$0.527952\pi$
$164$	−1.25438e23	+	1.83209e23i	−0.695934	+	1.01645i
$165$		0			0
$166$	−1.16087e22	+	3.75036e22i	−0.0567086	+	0.183205i
$167$	2.62512e22			0.120400			0.0601999	−	0.998186i	$-0.480826\pi$
$167$	2.62512e22			0.120400			0.0601999	+	0.998186i	$0.480826\pi$
$168$		0			0
$169$	2.38722e23			0.966232
$170$	2.31629e23	−	7.48310e23i	0.881209	−	2.84687i
$171$		0			0
$172$	4.57683e22	+	3.13363e22i	0.153998	+	0.105438i
$173$	5.81627e22			0.184145			0.0920726	−	0.995752i	$-0.470651\pi$
$173$	5.81627e22			0.184145			0.0920726	+	0.995752i	$0.470651\pi$
$174$		0			0
$175$			3.36472e23i			0.944167i
$176$	−5.02764e23	+	1.95043e23i	−1.32887	+	0.515522i
$177$		0			0
$178$	6.46616e22	−	2.08899e23i	0.151788	−	0.490372i
$179$		−	5.75206e23i		−	1.27311i	−0.771231	−	0.636556i	$-0.780358\pi$
$179$		−	5.75206e23i		−	1.27311i	0.771231	−	0.636556i	$-0.219642\pi$
$180$		0			0
$181$		−	6.95825e23i		−	1.37049i	−0.728314	−	0.685243i	$-0.759696\pi$
$181$		−	6.95825e23i		−	1.37049i	0.728314	−	0.685243i	$-0.240304\pi$
$182$	3.42002e22	+	1.05862e22i	0.0635740	+	0.0196784i
$183$		0			0
$184$	3.09828e23	+	3.90870e23i	0.513491	+	0.647807i
$185$			1.58050e24i			2.47452i
$186$		0			0
$187$	−1.59926e24			−2.23657
$188$	6.23197e23	+	4.26686e23i	0.824077	+	0.564223i
$189$		0			0
$190$	−2.54066e24	−	7.86425e23i	−3.00631	−	0.930561i
$191$	−1.32712e24			−1.48614			−0.743070	−	0.669214i	$-0.766631\pi$
$191$	−1.32712e24			−1.48614			−0.743070	+	0.669214i	$0.766631\pi$
$192$		0			0
$193$	2.40826e22			0.0241742			0.0120871	−	0.999927i	$-0.496152\pi$
$193$	2.40826e22			0.0241742			0.0120871	+	0.999927i	$0.496152\pi$
$194$	−5.52395e22	−	1.70986e22i	−0.0525208	−	0.0162571i
$195$		0			0
$196$	8.39755e23	+	5.74957e23i	0.716909	+	0.490847i
$197$	9.07905e23			0.734760			0.367380	−	0.930071i	$-0.380255\pi$
$197$	9.07905e23			0.734760			0.367380	+	0.930071i	$0.380255\pi$
$198$		0			0
$199$		−	2.32341e24i		−	1.69110i	−0.533899	−	0.845548i	$-0.679274\pi$
$199$		−	2.32341e24i		−	1.69110i	0.533899	−	0.845548i	$-0.320726\pi$
$200$	2.34525e24	+	2.95870e24i	1.61947	+	2.04308i
$201$		0			0
$202$	8.94265e23	+	2.76807e23i	0.556259	+	0.172182i
$203$		−	6.25993e23i		−	0.369710i
$204$		0			0
$205$		−	4.39093e24i		−	2.33960i
$206$	7.01536e23	−	2.26641e24i	0.355176	−	1.14745i
$207$		0			0
$208$	3.74520e23	−	1.45292e23i	0.171321	−	0.0664624i
$209$			5.42981e24i			2.36183i
$210$		0			0
$211$	−2.18515e24			−0.860033			−0.430017	−	0.902821i	$-0.641492\pi$
$211$	−2.18515e24			−0.860033			−0.430017	+	0.902821i	$0.641492\pi$
$212$	1.28711e24	+	8.81251e23i	0.482048	+	0.330045i
$213$		0			0
$214$	−9.19011e23	+	2.96900e24i	−0.311872	+	1.00755i
$215$	−1.09692e24			−0.354464
$216$		0			0
$217$	−4.28120e23			−0.125527
$218$	9.59155e22	−	3.09869e23i	0.0267976	−	0.0865734i
$219$		0			0
$220$	6.02484e24	−	8.79960e24i	1.52935	−	2.23370i
$221$	1.19133e24			0.288344
$222$		0			0
$223$		−	7.96264e23i		−	0.175330i	−0.996150	−	0.0876650i	$-0.972060\pi$
$223$		−	7.96264e23i		−	0.175330i	0.996150	−	0.0876650i	$-0.0279405\pi$
$224$	−1.71964e24	+	1.20374e23i	−0.361271	+	0.0252887i
$225$		0			0
$226$	−9.85764e23	+	3.18465e24i	−0.188640	+	0.609429i
$227$		−	4.28227e24i		−	0.782353i	−0.920316	−	0.391176i	$-0.872068\pi$
$227$		−	4.28227e24i		−	0.782353i	0.920316	−	0.391176i	$-0.127932\pi$
$228$		0			0
$229$			1.71312e24i			0.285440i	0.989763	+	0.142720i	$0.0455848\pi$
$229$			1.71312e24i			0.285440i	−0.989763	+	0.142720i	$0.954415\pi$
$230$	−9.42251e24	−	2.91660e24i	−1.49977	−	0.464232i
$231$		0			0
$232$	−4.36325e24	−	5.50456e24i	−0.634141	−	0.800016i
$233$			9.50214e24i			1.32003i	0.751252	+	0.660016i	$0.229450\pi$
$233$			9.50214e24i			1.32003i	−0.751252	+	0.660016i	$0.770550\pi$
$234$		0			0
$235$	−1.49361e25			−1.89681
$236$	−4.70001e24	+	6.86461e24i	−0.570851	+	0.833758i
$237$		0			0
$238$	−4.88363e24	−	1.51166e24i	−0.542856	−	0.168033i
$239$	−3.34184e24			−0.355474			−0.177737	−	0.984078i	$-0.556878\pi$
$239$	−3.34184e24			−0.355474			−0.177737	+	0.984078i	$0.556878\pi$
$240$		0			0
$241$	6.78257e24			0.661021			0.330511	−	0.943802i	$-0.392779\pi$
$241$	6.78257e24			0.661021			0.330511	+	0.943802i	$0.392779\pi$
$242$	−1.05615e25	−	3.26916e24i	−0.985517	−	0.305053i
$243$		0			0
$244$	−5.57920e24	+	8.14872e24i	−0.477506	+	0.697423i
$245$	−2.01263e25			−1.65014
$246$		0			0
$247$		−	4.04478e24i		−	0.304493i
$248$	−3.76459e24	+	2.98405e24i	−0.271629	+	0.215309i
$249$		0			0
$250$	−4.39661e25	−	1.36091e25i	−2.91573	−	0.902524i
$251$		−	2.69968e25i		−	1.71687i	−0.512919	−	0.858437i	$-0.671436\pi$
$251$		−	2.69968e25i		−	1.71687i	0.512919	−	0.858437i	$-0.328564\pi$
$252$		0			0
$253$			2.01374e25i			1.17825i
$254$	−4.84583e24	+	1.56551e25i	−0.272028	+	0.878826i
$255$		0			0
$256$	−1.42823e25	+	1.30446e25i	−0.738377	+	0.674388i
$257$		−	5.63292e24i		−	0.279535i	−0.990184	−	0.139767i	$-0.955365\pi$
$257$		−	5.63292e24i		−	0.279535i	0.990184	−	0.139767i	$-0.0446355\pi$
$258$		0			0
$259$	1.03147e25			0.471854
$260$	−4.48804e24	+	6.55502e24i	−0.197168	+	0.287974i
$261$		0			0
$262$	1.03575e25	−	3.34614e25i	0.419847	−	1.35638i
$263$	−8.78848e24			−0.342278			−0.171139	−	0.985247i	$-0.554745\pi$
$263$	−8.78848e24			−0.342278			−0.171139	+	0.985247i	$0.554745\pi$
$264$		0			0
$265$	−3.08481e25			−1.10955
$266$	−5.13237e24	+	1.65809e25i	−0.177444	+	0.573258i
$267$		0			0
$268$	−4.25697e25	−	2.91463e25i	−1.36046	−	0.931467i
$269$	6.12733e24			0.188310			0.0941548	−	0.995558i	$-0.469985\pi$
$269$	6.12733e24			0.188310			0.0941548	+	0.995558i	$0.469985\pi$
$270$		0			0
$271$			4.42193e25i			1.25729i	0.777694	+	0.628643i	$0.216389\pi$
$271$			4.42193e25i			1.25729i	−0.777694	+	0.628643i	$0.783611\pi$
$272$	−5.34797e25	+	2.07469e25i	−1.46290	+	0.567519i
$273$		0			0
$274$	−2.88590e23	+	9.32332e23i	−0.00730972	+	0.0236151i
$275$			1.52431e26i			3.71603i
$276$		0			0
$277$		−	8.60294e25i		−	1.94361i	−0.235784	−	0.971806i	$-0.575766\pi$
$277$		−	8.60294e25i		−	1.94361i	0.235784	−	0.971806i	$-0.424234\pi$
$278$	−3.04889e25	−	9.43740e24i	−0.663241	−	0.205297i
$279$		0			0
$280$	2.67155e25	−	2.11763e25i	0.539018	−	0.427259i
$281$			5.51814e24i			0.107245i	0.998561	+	0.0536224i	$0.0170767\pi$
$281$			5.51814e24i			0.107245i	−0.998561	+	0.0536224i	$0.982923\pi$
$282$		0			0
$283$	−2.73234e25			−0.492920			−0.246460	−	0.969153i	$-0.579267\pi$
$283$	−2.73234e25			−0.492920			−0.246460	+	0.969153i	$0.579267\pi$
$284$	−3.12301e25	−	2.13824e25i	−0.542914	−	0.371718i
$285$		0			0
$286$	1.54936e25	+	4.79583e24i	0.250213	+	0.0774499i
$287$	−2.86561e25			−0.446126
$288$		0			0
$289$	−1.01023e26			−1.46216
$290$	1.32695e26	+	4.10740e25i	1.85215	+	0.573308i
$291$		0			0
$292$	−1.07621e26	−	7.36850e25i	−1.39758	−	0.956884i
$293$	6.05146e25			0.758141			0.379070	−	0.925368i	$-0.376244\pi$
$293$	6.05146e25			0.758141			0.379070	+	0.925368i	$0.376244\pi$
$294$		0			0
$295$		−	1.64523e26i		−	1.91909i
$296$	9.07000e25	−	7.18944e25i	1.02104	−	0.809342i
$297$		0			0
$298$	1.42173e26	+	4.40076e25i	1.49123	+	0.461590i
$299$		−	1.50008e25i		−	0.151904i
$300$		0			0
$301$			7.15873e24i			0.0675909i
$302$	−1.31680e25	+	4.25410e25i	−0.120073	+	0.387914i
$303$		0			0
$304$	7.04400e25	+	1.81574e26i	0.599303	+	1.54483i
$305$		−	1.95299e26i		−	1.60528i
$306$		0			0
$307$	7.93773e25			0.609177			0.304588	−	0.952484i	$-0.401481\pi$
$307$	7.93773e25			0.609177			0.304588	+	0.952484i	$0.401481\pi$
$308$	−5.74280e25	−	3.93193e25i	−0.425933	−	0.291624i
$309$		0			0
$310$	2.80907e25	−	9.07511e25i	0.194655	−	0.628860i
$311$	−4.67376e25			−0.313099			−0.156550	−	0.987670i	$-0.550037\pi$
$311$	−4.67376e25			−0.313099			−0.156550	+	0.987670i	$0.550037\pi$
$312$		0			0
$313$	4.43657e24			0.0277864			0.0138932	−	0.999903i	$-0.495578\pi$
$313$	4.43657e24			0.0277864			0.0138932	+	0.999903i	$0.495578\pi$
$314$	−3.99332e25	+	1.29010e26i	−0.241865	+	0.781380i
$315$		0			0
$316$	−1.38677e26	+	2.02545e26i	−0.785761	+	1.14765i
$317$	−3.09298e26			−1.69533			−0.847665	−	0.530532i	$-0.821992\pi$
$317$	−3.09298e26			−1.69533			−0.847665	+	0.530532i	$0.821992\pi$
$318$		0			0
$319$		−	2.83592e26i		−	1.45510i
$320$	8.73162e25	−	3.72420e26i	0.433531	−	1.84909i
$321$		0			0
$322$	−1.90344e25	+	6.14932e25i	−0.0885221	+	0.285983i
$323$			5.77575e26i			2.60005i
$324$		0			0
$325$		−	1.13549e26i		−	0.479080i
$326$	−4.10163e25	−	1.26960e25i	−0.167561	−	0.0518660i
$327$		0			0
$328$	−2.51982e26	+	1.99736e26i	−0.965371	+	0.765212i
$329$			9.74758e25i			0.361693i
$330$		0			0
$331$	1.56291e26			0.544177			0.272089	−	0.962272i	$-0.412286\pi$
$331$	1.56291e26			0.544177			0.272089	+	0.962272i	$0.412286\pi$
$332$	−3.21189e25	+	4.69114e25i	−0.108346	+	0.158245i
$333$		0			0
$334$	3.63158e25	+	1.12410e25i	0.115016	+	0.0356015i
$335$	1.02026e27			3.13141
$336$		0			0
$337$	−3.22884e26			−0.930962			−0.465481	−	0.885058i	$-0.654119\pi$
$337$	−3.22884e26			−0.930962			−0.465481	+	0.885058i	$0.654119\pi$
$338$	3.30247e26	+	1.02223e26i	0.923025	+	0.285709i
$339$		0			0
$340$	6.40869e26	−	9.36024e26i	1.68361	−	2.45900i
$341$	−1.93950e26			−0.494047
$342$		0			0
$343$			2.82524e26i			0.676811i
$344$	4.98972e25	+	6.29490e25i	0.115934	+	0.146260i
$345$		0			0
$346$	8.04621e25	+	2.49059e25i	0.175911	+	0.0544507i
$347$		−	4.52778e26i		−	0.960342i	−0.877175	−	0.480171i	$-0.840575\pi$
$347$		−	4.52778e26i		−	0.960342i	0.877175	−	0.480171i	$-0.159425\pi$
$348$		0			0
$349$			3.27832e26i			0.654612i	0.944918	+	0.327306i	$0.106141\pi$
$349$			3.27832e26i			0.654612i	−0.944918	+	0.327306i	$0.893859\pi$
$350$	−1.44081e26	+	4.65474e26i	−0.279185	+	0.901947i
$351$		0			0
$352$	−7.79042e26	+	5.45325e25i	−1.42188	+	0.0995307i
$353$			5.61843e25i			0.0995362i	0.998761	+	0.0497681i	$0.0158482\pi$
$353$			5.61843e25i			0.0995362i	−0.998761	+	0.0497681i	$0.984152\pi$
$354$		0			0
$355$	7.48488e26			1.24965
$356$	1.78905e26	−	2.61301e26i	0.290000	−	0.423561i
$357$		0			0
$358$	2.46310e26	−	7.95738e26i	0.376452	−	1.21618i
$359$	−3.25539e26			−0.483182			−0.241591	−	0.970378i	$-0.577669\pi$
$359$	−3.25539e26			−0.483182			−0.241591	+	0.970378i	$0.577669\pi$
$360$		0			0
$361$	1.24677e27			1.74567
$362$	2.97960e26	−	9.62602e26i	0.405245	−	1.30920i
$363$		0			0
$364$	4.27794e25	+	2.92898e25i	0.0549124	+	0.0375969i
$365$	2.57933e27			3.21686
$366$		0			0
$367$			6.84892e26i			0.806545i	0.915080	+	0.403272i	$0.132127\pi$
$367$			6.84892e26i			0.806545i	−0.915080	+	0.403272i	$0.867873\pi$
$368$	2.61240e26	+	6.73401e26i	0.298976	+	0.770675i
$369$		0			0
$370$	−6.76787e26	+	2.18646e27i	−0.731702	+	2.36387i
$371$			2.01321e26i			0.211574i
$372$		0			0
$373$			1.33427e27i			1.32526i	0.748945	+	0.662632i	$0.230560\pi$
$373$			1.33427e27i			1.32526i	−0.748945	+	0.662632i	$0.769440\pi$
$374$	−2.21241e27	−	6.84821e26i	−2.13656	−	0.661341i
$375$		0			0
$376$	6.79418e26	+	8.57135e26i	0.620389	+	0.782667i
$377$			2.11254e26i			0.187595i
$378$		0			0
$379$	4.99825e26			0.419862			0.209931	−	0.977716i	$-0.432676\pi$
$379$	4.99825e26			0.419862			0.209931	+	0.977716i	$0.432676\pi$
$380$	−3.17799e27	−	2.17588e27i	−2.59671	−	1.77790i
$381$		0			0
$382$	−1.83593e27	−	5.68287e26i	−1.41968	−	0.439443i
$383$	−2.52990e27			−1.90334			−0.951671	−	0.307121i	$-0.900634\pi$
$383$	−2.52990e27			−1.90334			−0.951671	+	0.307121i	$0.900634\pi$
$384$		0			0
$385$	1.37637e27			0.980385
$386$	3.33158e25	+	1.03124e25i	0.0230932	+	0.00714817i
$387$		0			0
$388$	−6.90963e25	−	4.73083e25i	−0.0453651	−	0.0310602i
$389$	−5.83925e26			−0.373153			−0.186576	−	0.982440i	$-0.559739\pi$
$389$	−5.83925e26			−0.373153			−0.186576	+	0.982440i	$0.559739\pi$
$390$		0			0
$391$			2.14204e27i			1.29710i
$392$	9.15512e26	+	1.15499e27i	0.539710	+	0.680884i
$393$		0			0
$394$	1.25599e27	+	3.88775e26i	0.701903	+	0.217264i
$395$		−	4.85437e27i		−	2.64158i
$396$		0			0
$397$		−	1.05478e27i		−	0.544331i	−0.962251	−	0.272165i	$-0.912260\pi$
$397$		−	1.05478e27i		−	0.544331i	0.962251	−	0.272165i	$-0.0877398\pi$
$398$	9.94910e26	−	3.21420e27i	0.500048	−	1.61548i
$399$		0			0
$400$	1.97746e27	+	5.09732e27i	0.942925	+	2.43059i
$401$		−	4.82816e26i		−	0.224267i	−0.993693	−	0.112134i	$-0.964232\pi$
$401$		−	4.82816e26i		−	0.224267i	0.993693	−	0.112134i	$-0.0357685\pi$
$402$		0			0
$403$	1.44478e26			0.0636939
$404$	1.11859e27	+	7.65868e26i	0.480471	+	0.328965i
$405$		0			0
$406$	2.68057e26	−	8.65998e26i	0.109321	−	0.353178i
$407$	4.67282e27			1.85711
$408$		0			0
$409$	3.67932e27			1.38891			0.694453	−	0.719538i	$-0.255646\pi$
$409$	3.67932e27			1.38891			0.694453	+	0.719538i	$0.255646\pi$
$410$	1.88024e27	−	6.07440e27i	0.691805	−	2.23498i
$411$		0			0
$412$	1.94101e27	−	2.83494e27i	0.678588	−	0.991114i
$413$	−1.07371e27			−0.365942
$414$		0			0
$415$		−	1.12432e27i		−	0.364237i
$416$	5.80326e26	−	4.06225e25i	0.183313	−	0.0128318i
$417$		0			0
$418$	−2.32510e27	+	7.51158e27i	−0.698379	+	2.25621i
$419$			2.73787e27i			0.801984i	0.916082	+	0.400992i	$0.131334\pi$
$419$			2.73787e27i			0.801984i	−0.916082	+	0.400992i	$0.868666\pi$
$420$		0			0
$421$		−	6.93173e27i		−	1.93143i	−0.259600	−	0.965716i	$-0.583591\pi$
$421$		−	6.93173e27i		−	1.93143i	0.259600	−	0.965716i	$-0.416409\pi$
$422$	−3.02293e27	−	9.35705e26i	−0.821575	−	0.254307i
$423$		0			0
$424$	1.40323e27	+	1.77028e27i	0.362900	+	0.457825i
$425$			1.62142e28i			4.09084i
$426$		0			0
$427$	−1.27456e27			−0.306103
$428$	−2.54271e27	+	3.71377e27i	−0.595852	+	0.870273i
$429$		0			0
$430$	−1.51748e27	−	4.69714e26i	−0.338613	−	0.104813i
$431$	1.63202e27			0.355398			0.177699	−	0.984085i	$-0.443135\pi$
$431$	1.63202e27			0.355398			0.177699	+	0.984085i	$0.443135\pi$
$432$		0			0
$433$	1.46078e27			0.303013			0.151506	−	0.988456i	$-0.451588\pi$
$433$	1.46078e27			0.303013			0.151506	+	0.988456i	$0.451588\pi$
$434$	−5.92260e26	−	1.83326e26i	−0.119914	−	0.0371177i
$435$		0			0
$436$	2.65378e26	−	3.87599e26i	0.0511985	−	0.0747782i
$437$	7.27266e27			1.36974
$438$		0			0
$439$		−	8.87252e27i		−	1.59283i	−0.604750	−	0.796415i	$-0.706727\pi$
$439$		−	8.87252e27i		−	1.59283i	0.604750	−	0.796415i	$-0.293273\pi$
$440$	1.21028e28	−	9.59343e27i	2.12145	−	1.68159i
$441$		0			0
$442$	1.64808e27	+	5.10139e26i	0.275450	+	0.0852618i
$443$			9.45932e27i			1.54391i	0.635680	+	0.771953i	$0.280720\pi$
$443$			9.45932e27i			1.54391i	−0.635680	+	0.771953i	$0.719280\pi$
$444$		0			0
$445$			6.26256e27i			0.974926i
$446$	3.40969e26	−	1.10155e27i	0.0518441	−	0.167490i
$447$		0			0
$448$	−2.43049e27	−	5.69844e26i	−0.352593	−	0.0826678i
$449$		−	4.72742e27i		−	0.669943i	−0.942228	−	0.334971i	$-0.891273\pi$
$449$		−	4.72742e27i		−	0.669943i	0.942228	−	0.334971i	$-0.108727\pi$
$450$		0			0
$451$	−1.29820e28			−1.75585
$452$	−2.72740e27	+	3.98352e27i	−0.360409	+	0.526397i
$453$		0			0
$454$	1.83372e27	−	5.92408e27i	0.231337	−	0.747368i
$455$	−1.02529e27			−0.126394
$456$		0			0
$457$	9.77342e27			1.15061			0.575303	−	0.817941i	$-0.304884\pi$
$457$	9.77342e27			1.15061			0.575303	+	0.817941i	$0.304884\pi$
$458$	−7.33576e26	+	2.36992e27i	−0.0844029	+	0.272676i
$459$		0			0
$460$	−1.17861e28	−	8.06964e27i	−1.29543	−	0.886946i
$461$	3.52212e27			0.378394			0.189197	−	0.981939i	$-0.439412\pi$
$461$	3.52212e27			0.378394			0.189197	+	0.981939i	$0.439412\pi$
$462$		0			0
$463$		−	6.64319e27i		−	0.681987i	−0.940066	−	0.340993i	$-0.889237\pi$
$463$		−	6.64319e27i		−	0.681987i	0.940066	−	0.340993i	$-0.110763\pi$
$464$	−3.67899e27	−	9.48338e27i	−0.369224	−	0.951753i
$465$		0			0
$466$	−4.06892e27	+	1.31452e28i	−0.390326	+	1.26100i
$467$		−	7.01354e25i		−	0.00657825i	−0.999995	−	0.00328912i	$-0.998953\pi$
$467$		−	7.01354e25i		−	0.00657825i	0.999995	−	0.00328912i	$-0.00104696\pi$
$468$		0			0
$469$		−	6.65843e27i		−	0.597114i
$470$	−2.06625e28	−	6.39579e27i	−1.81199	−	0.560876i
$471$		0			0
$472$	−9.44148e27	+	7.48389e27i	−0.791861	+	0.627677i
$473$			3.24310e27i			0.266022i
$474$		0			0
$475$	5.50505e28			4.31995
$476$	−6.10868e27	−	4.18244e27i	−0.468894	−	0.321039i
$477$		0			0
$478$	−4.62310e27	−	1.43101e27i	−0.339578	−	0.105112i
$479$	1.80345e28			1.29593			0.647966	−	0.761669i	$-0.275620\pi$
$479$	1.80345e28			1.29593			0.647966	+	0.761669i	$0.275620\pi$
$480$		0			0
$481$	−3.48089e27			−0.239423
$482$	9.38299e27	+	2.90437e27i	0.631462	+	0.195460i
$483$		0			0
$484$	−1.32108e28	−	9.04509e27i	−0.851244	−	0.582823i
$485$	1.65602e27			0.104418
$486$		0			0
$487$			1.64624e28i			0.994123i	0.867715	+	0.497062i	$0.165588\pi$
$487$			1.64624e28i			0.994123i	−0.867715	+	0.497062i	$0.834412\pi$
$488$	−1.12076e28	+	8.88384e27i	−0.662377	+	0.525040i
$489$		0			0
$490$	−2.78426e28	−	8.61830e27i	−1.57635	−	0.487936i
$491$			3.10560e28i			1.72104i	0.509421	+	0.860518i	$0.329860\pi$
$491$			3.10560e28i			1.72104i	−0.509421	+	0.860518i	$0.670140\pi$
$492$		0			0
$493$		−	3.01660e28i		−	1.60186i
$494$	1.73202e27	−	5.59554e27i	0.0900368	−	0.290877i
$495$		0			0
$496$	−6.48573e27	+	2.51608e27i	−0.323148	+	0.125362i
$497$		−	4.88478e27i		−	0.238289i
$498$		0			0
$499$	−2.35720e28			−1.10240			−0.551201	−	0.834372i	$-0.685830\pi$
$499$	−2.35720e28			−1.10240			−0.551201	+	0.834372i	$0.685830\pi$
$500$	−5.49950e28	−	3.76535e28i	−2.51848	−	1.72433i
$501$		0			0
$502$	1.15603e28	−	3.73473e28i	0.507670	−	1.64010i
$503$	3.02255e28			1.29990			0.649950	−	0.759977i	$-0.274790\pi$
$503$	3.02255e28			1.29990			0.649950	+	0.759977i	$0.274790\pi$
$504$		0			0
$505$	−2.68091e28			−1.10592
$506$	−8.62307e27	+	2.78581e28i	−0.348403	+	1.12557i
$507$		0			0
$508$	−1.34074e28	+	1.95822e28i	−0.519728	+	0.759090i
$509$	1.04573e28			0.397085			0.198542	−	0.980092i	$-0.436379\pi$
$509$	1.04573e28			0.397085			0.198542	+	0.980092i	$0.436379\pi$
$510$		0			0
$511$		−	1.68333e28i		−	0.613407i
$512$	−2.53439e28	+	1.19300e28i	−0.904772	+	0.425897i
$513$		0			0
$514$	2.41208e27	−	7.79257e27i	0.0826568	−	0.267035i
$515$			6.79446e28i			2.28128i
$516$		0			0
$517$			4.41592e28i			1.42354i
$518$	1.42693e28	+	4.41685e27i	0.450754	+	0.139524i
$519$		0			0
$520$	−9.01567e27	+	7.14637e27i	−0.273503	+	0.216795i
$521$			2.96507e28i			0.881535i	0.897621	+	0.440767i	$0.145294\pi$
$521$			2.96507e28i			0.881535i	−0.897621	+	0.440767i	$0.854706\pi$
$522$		0			0
$523$	5.38670e28			1.53835			0.769174	−	0.639039i	$-0.220668\pi$
$523$	5.38670e28			1.53835			0.769174	+	0.639039i	$0.220668\pi$
$524$	2.86571e28	−	4.18552e28i	0.802146	−	1.17158i
$525$		0			0
$526$	−1.21580e28	−	3.76333e27i	−0.326972	−	0.101210i
$527$	−2.06307e28			−0.543879
$528$		0			0
$529$	−1.24996e28			−0.316673
$530$	−4.26751e28	−	1.32095e28i	−1.05993	−	0.328087i
$531$		0			0
$532$	−1.42002e28	+	2.07402e28i	−0.339018	+	0.495154i
$533$	9.67057e27			0.226369
$534$		0			0
$535$		−	8.90074e28i		−	2.00314i
$536$	−4.64100e28	−	5.85496e28i	−1.02419	−	1.29209i
$537$		0			0
$538$	8.47653e27	+	2.62379e27i	0.179889	+	0.0556821i
$539$			5.95043e28i			1.23841i
$540$		0			0
$541$		−	6.85616e28i		−	1.37249i	−0.727370	−	0.686246i	$-0.759258\pi$
$541$		−	6.85616e28i		−	1.37249i	0.727370	−	0.686246i	$-0.240742\pi$
$542$	−1.89352e28	+	6.11729e28i	−0.371772	+	1.20106i
$543$		0			0
$544$	−8.28677e28	+	5.80069e27i	−1.56530	+	0.109570i
$545$			9.28954e27i			0.172120i
$546$		0			0
$547$	−3.75520e28			−0.669523			−0.334762	−	0.942303i	$-0.608656\pi$
$547$	−3.75520e28			−0.669523			−0.334762	+	0.942303i	$0.608656\pi$
$548$	−7.98470e26	+	1.16621e27i	−0.0139657	+	0.0203976i
$549$		0			0
$550$	−6.52725e28	+	2.10872e29i	−1.09881	+	3.54986i
$551$	−1.02420e29			−1.69157
$552$		0			0
$553$	−3.16806e28			−0.503709
$554$	3.68387e28	−	1.19013e29i	0.574715	−	1.85670i
$555$		0			0
$556$	−3.81370e28	−	2.61114e28i	−0.572877	−	0.392233i
$557$	−9.35504e28			−1.37901			−0.689503	−	0.724283i	$-0.742171\pi$
$557$	−9.35504e28			−1.37901			−0.689503	+	0.724283i	$0.742171\pi$
$558$		0			0
$559$		−	2.41586e27i		−	0.0342963i
$560$	4.60260e28	−	1.78554e28i	0.641253	−	0.248768i
$561$		0			0
$562$	−2.36293e27	+	7.63378e27i	−0.0317117	+	0.102449i
$563$			7.72669e27i			0.101778i	0.998704	+	0.0508892i	$0.0162055\pi$
$563$			7.72669e27i			0.101778i	−0.998704	+	0.0508892i	$0.983794\pi$
$564$		0			0
$565$		−	9.54724e28i		−	1.21163i
$566$	−3.77991e28	−	1.17002e28i	−0.470878	−	0.145754i
$567$		0			0
$568$	−3.40475e28	−	4.29534e28i	−0.408722	−	0.515632i
$569$			8.80243e28i			1.03735i	0.854973	+	0.518673i	$0.173574\pi$
$569$			8.80243e28i			1.03735i	−0.854973	+	0.518673i	$0.826426\pi$
$570$		0			0
$571$	−8.00665e27			−0.0909436			−0.0454718	−	0.998966i	$-0.514479\pi$
$571$	−8.00665e27			−0.0909436			−0.0454718	+	0.998966i	$0.514479\pi$
$572$	1.93802e28	+	1.32691e28i	0.216123	+	0.147973i
$573$		0			0
$574$	−3.96428e28	−	1.22709e28i	−0.426176	−	0.131917i
$575$	2.04165e29			2.15511
$576$		0			0
$577$	1.20011e29			1.22145			0.610723	−	0.791844i	$-0.290879\pi$
$577$	1.20011e29			1.22145			0.610723	+	0.791844i	$0.290879\pi$
$578$	−1.39756e29	−	4.32593e28i	−1.39678	−	0.432352i
$579$		0			0
$580$	1.65982e29	+	1.13643e29i	1.59981	+	1.09534i
$581$	−7.33753e27			−0.0694545
$582$		0			0
$583$			9.12037e28i			0.832708i
$584$	−1.17330e29	−	1.48020e29i	−1.05214	−	1.32735i
$585$		0			0
$586$	8.37157e28	+	2.59130e28i	0.724239	+	0.224178i
$587$		−	8.61883e28i		−	0.732400i	−0.930536	−	0.366200i	$-0.880659\pi$
$587$		−	8.61883e28i		−	0.732400i	0.930536	−	0.366200i	$-0.119341\pi$
$588$		0			0
$589$			7.00452e28i			0.574339i
$590$	7.04506e28	−	2.27601e29i	0.567464	−	1.83327i
$591$		0			0
$592$	1.56260e29	−	6.06197e28i	1.21470	−	0.471233i
$593$			1.67847e29i			1.28185i	0.767602	+	0.640926i	$0.221450\pi$
$593$			1.67847e29i			1.28185i	−0.767602	+	0.640926i	$0.778550\pi$
$594$		0			0
$595$	1.46406e29			1.07927
$596$	1.77837e29	+	1.21760e29i	1.28806	+	0.881898i
$597$		0			0
$598$	6.42352e27	−	2.07521e28i	0.0449170	−	0.145111i
$599$	1.96423e29			1.34961			0.674807	−	0.737994i	$-0.264227\pi$
$599$	1.96423e29			1.34961			0.674807	+	0.737994i	$0.264227\pi$
$600$		0			0
$601$	1.35958e29			0.902036			0.451018	−	0.892515i	$-0.351061\pi$
$601$	1.35958e29			0.902036			0.451018	+	0.892515i	$0.351061\pi$
$602$	−3.06545e27	+	9.90337e27i	−0.0199862	+	0.0645684i
$603$		0			0
$604$	−3.64331e28	+	5.32125e28i	−0.229408	+	0.335062i
$605$	3.16622e29			1.95934
$606$		0			0
$607$		−	8.83550e28i		−	0.528141i	−0.964503	−	0.264071i	$-0.914935\pi$
$607$		−	8.83550e28i		−	0.528141i	0.964503	−	0.264071i	$-0.0850652\pi$
$608$	1.96945e28	+	2.81352e29i	0.115706	+	1.65296i
$609$		0			0
$610$	8.36292e28	−	2.70176e29i	0.474673	−	1.53350i
$611$		−	3.28952e28i		−	0.183527i
$612$		0			0
$613$		−	5.84775e28i		−	0.315249i	−0.987499	−	0.157625i	$-0.949616\pi$
$613$		−	5.84775e28i		−	0.315249i	0.987499	−	0.157625i	$-0.0503836\pi$
$614$	1.09810e29	+	3.39902e28i	0.581936	+	0.180130i
$615$		0			0
$616$	−6.26087e28	−	7.89855e28i	−0.320654	−	0.404529i
$617$			1.01413e29i			0.510622i	0.966859	+	0.255311i	$0.0821779\pi$
$617$			1.01413e29i			0.510622i	−0.966859	+	0.255311i	$0.917822\pi$
$618$		0			0
$619$	−1.75640e29			−0.854812			−0.427406	−	0.904060i	$-0.640572\pi$
$619$	−1.75640e29			−0.854812			−0.427406	+	0.904060i	$0.640572\pi$
$620$	7.77212e28	−	1.13516e29i	0.371901	−	0.543181i
$621$		0			0
$622$	−6.46566e28	−	2.00135e28i	−0.299098	−	0.0925817i
$623$	4.08707e28			0.185904
$624$		0			0
$625$	7.25275e29			3.18979
$626$	6.13754e27	+	1.89979e27i	0.0265438	+	0.00821627i
$627$		0			0
$628$	−1.10487e29	+	1.61372e29i	−0.462099	+	0.674921i
$629$	4.97053e29			2.04443
$630$		0			0
$631$			1.72251e29i			0.685259i	0.939471	+	0.342629i	$0.111318\pi$
$631$			1.72251e29i			0.685259i	−0.939471	+	0.342629i	$0.888682\pi$
$632$	−2.78578e29	+	2.20818e29i	−1.08998	+	0.863981i
$633$		0			0
$634$	−4.27881e29	−	1.32445e29i	−1.61952	−	0.501299i
$635$		−	4.69325e29i		−	1.74723i
$636$		0			0
$637$		−	4.43261e28i		−	0.159660i
$638$	1.21437e29	−	3.92320e29i	0.430263	−	1.39003i
$639$		0			0
$640$	2.80267e29	−	4.77815e29i	0.960910	−	1.63821i
$641$			3.56547e28i			0.120256i	0.998191	+	0.0601282i	$0.0191509\pi$
$641$			3.56547e28i			0.120256i	−0.998191	+	0.0601282i	$0.980849\pi$
$642$		0			0
$643$	3.85976e29			1.25993			0.629963	−	0.776625i	$-0.283070\pi$
$643$	3.85976e29			1.25993			0.629963	+	0.776625i	$0.283070\pi$
$644$	−5.26642e28	+	7.69188e28i	−0.169127	+	0.247019i
$645$		0			0
$646$	−2.47324e29	+	7.99016e29i	−0.768820	+	2.48378i
$647$	−1.60078e29			−0.489594			−0.244797	−	0.969574i	$-0.578721\pi$
$647$	−1.60078e29			−0.489594			−0.244797	+	0.969574i	$0.578721\pi$
$648$		0			0
$649$	−4.86420e29			−1.44026
$650$	4.86229e28	−	1.57083e29i	0.141661	−	0.457657i
$651$		0			0
$652$	−5.13053e28	−	3.51273e28i	−0.144731	−	0.0990934i
$653$	−2.00046e29			−0.555318			−0.277659	−	0.960680i	$-0.589559\pi$
$653$	−2.00046e29			−0.555318			−0.277659	+	0.960680i	$0.589559\pi$
$654$		0			0
$655$			1.00314e30i			2.69666i
$656$	−4.34121e29	+	1.68413e29i	−1.14847	+	0.445539i
$657$		0			0
$658$	−4.17402e28	+	1.34848e29i	−0.106951	+	0.345519i
$659$			7.02306e28i			0.177105i	0.996072	+	0.0885523i	$0.0282240\pi$
$659$			7.02306e28i			0.177105i	−0.996072	+	0.0885523i	$0.971776\pi$
$660$		0			0
$661$			5.38617e28i			0.131572i	0.997834	+	0.0657862i	$0.0209555\pi$
$661$			5.38617e28i			0.131572i	−0.997834	+	0.0657862i	$0.979044\pi$
$662$	2.16213e29	+	6.69256e28i	0.519843	+	0.160910i
$663$		0			0
$664$	−6.45212e28	+	5.11434e28i	−0.150293	+	0.119131i
$665$		−	4.97077e29i		−	1.13971i
$666$		0			0
$667$	−3.79842e29			−0.843882
$668$	4.54256e28	+	3.11016e28i	0.0993454	+	0.0680190i
$669$		0			0
$670$	1.41143e30	+	4.36887e29i	2.99139	+	0.925941i
$671$	−5.77410e29			−1.20475
$672$		0			0
$673$	2.06107e28			0.0416806			0.0208403	−	0.999783i	$-0.493366\pi$
$673$	2.06107e28			0.0416806			0.0208403	+	0.999783i	$0.493366\pi$
$674$	−4.46676e29	−	1.38262e29i	−0.889332	−	0.275280i
$675$		0			0
$676$	4.13089e29	+	2.82831e29i	0.797267	+	0.545866i
$677$	−9.69834e29			−1.84296			−0.921481	−	0.388424i	$-0.873020\pi$
$677$	−9.69834e29			−1.84296			−0.921481	+	0.388424i	$0.873020\pi$
$678$		0			0
$679$		−	1.08075e28i		−	0.0199110i
$680$	1.28739e30	−	1.02047e30i	2.33543	−	1.85121i
$681$		0			0
$682$	−2.68310e29	−	8.30515e28i	−0.471955	−	0.146087i
$683$		−	1.07877e29i		−	0.186858i	−0.995626	−	0.0934292i	$-0.970217\pi$
$683$		−	1.07877e29i		−	0.186858i	0.995626	−	0.0934292i	$-0.0297829\pi$
$684$		0			0
$685$		−	2.79503e28i		−	0.0469500i
$686$	−1.20980e29	+	3.90843e29i	−0.200129	+	0.646546i
$687$		0			0
$688$	4.20722e28	+	1.08450e29i	0.0675019	+	0.174001i
$689$		−	6.79397e28i		−	0.107355i
$690$		0			0
$691$	5.29139e29			0.811054			0.405527	−	0.914083i	$-0.367088\pi$
$691$	5.29139e29			0.811054			0.405527	+	0.914083i	$0.367088\pi$
$692$	1.00646e29	+	6.89095e28i	0.151944	+	0.104032i
$693$		0			0
$694$	1.93885e29	−	6.26372e29i	0.283968	−	0.917398i
$695$	9.14024e29			1.31861
$696$		0			0
$697$	−1.38091e30			−1.93295
$698$	−1.40381e29	+	4.53521e29i	−0.193565	+	0.625339i
$699$		0			0
$700$	−3.98642e29	+	5.82238e29i	−0.533401	+	0.779061i
$701$	−2.70843e29			−0.357008			−0.178504	−	0.983939i	$-0.557126\pi$
$701$	−2.70843e29			−0.357008			−0.178504	+	0.983939i	$0.557126\pi$
$702$		0			0
$703$		−	1.68759e30i		−	2.15892i
$704$	−1.10108e30	−	2.58154e29i	−1.38773	−	0.325362i
$705$		0			0
$706$	−2.40588e28	+	7.77252e28i	−0.0294323	+	0.0950852i
$707$			1.74962e29i			0.210882i
$708$		0			0
$709$		−	3.81867e28i		−	0.0446813i	−0.999750	−	0.0223407i	$-0.992888\pi$
$709$		−	3.81867e28i		−	0.0446813i	0.999750	−	0.0223407i	$-0.00711185\pi$
$710$	1.03546e30	+	3.20511e29i	1.19376	+	0.369513i
$711$		0			0
$712$	3.59389e29	−	2.84874e29i	0.402277	−	0.318869i
$713$			2.59776e29i			0.286522i
$714$		0			0
$715$	−4.64482e29			−0.497457
$716$	6.81488e29	−	9.95349e29i	0.719236	−	1.05048i
$717$		0			0
$718$	−4.50349e29	−	1.39399e29i	−0.461576	−	0.142874i
$719$	3.85193e29			0.389068			0.194534	−	0.980896i	$-0.437681\pi$
$719$	3.85193e29			0.389068			0.194534	+	0.980896i	$0.437681\pi$
$720$		0			0
$721$	4.43421e29			0.435006
$722$	1.72478e30	+	5.33881e29i	1.66760	+	0.516184i
$723$		0			0
$724$	8.24394e29	−	1.20407e30i	0.774247	−	1.13083i
$725$	−2.87522e30			−2.66147
$726$		0			0
$727$			1.17649e30i			1.05798i	0.848629	+	0.528988i	$0.177428\pi$
$727$			1.17649e30i			1.05798i	−0.848629	+	0.528988i	$0.822572\pi$
$728$	4.66387e28	+	5.88381e28i	0.0413396	+	0.0521530i
$729$		0			0
$730$	3.56824e30	+	1.10450e30i	3.07301	+	0.951208i
$731$			3.44972e29i			0.292854i
$732$		0			0
$733$			2.09025e29i			0.172427i	0.996277	+	0.0862136i	$0.0274768\pi$
$733$			2.09025e29i			0.172427i	−0.996277	+	0.0862136i	$0.972523\pi$
$734$	−2.93278e29	+	9.47478e29i	−0.238491	+	0.770478i
$735$		0			0
$736$	7.30406e28	+	1.04345e30i	0.0577228	+	0.824618i
$737$		−	3.01645e30i		−	2.35010i
$738$		0			0
$739$	2.16141e29			0.163670			0.0818352	−	0.996646i	$-0.473922\pi$
$739$	2.16141e29			0.163670			0.0818352	+	0.996646i	$0.473922\pi$
$740$	−1.87253e30	+	2.73493e30i	−1.39796	+	2.04180i
$741$		0			0
$742$	−8.62078e28	+	2.78506e29i	−0.0625612	+	0.202113i
$743$	−1.11801e30			−0.799953			−0.399977	−	0.916525i	$-0.630982\pi$
$743$	−1.11801e30			−0.799953			−0.399977	+	0.916525i	$0.630982\pi$
$744$		0			0
$745$	−4.26219e30			−2.96477
$746$	−5.71351e29	+	1.84583e30i	−0.391873	+	1.26600i
$747$		0			0
$748$	−2.76740e30	−	1.89476e30i	−1.84546	−	1.26353i
$749$	−5.80880e29			−0.381969
$750$		0			0
$751$			9.71110e29i			0.620939i	0.950583	+	0.310470i	$0.100486\pi$
$751$			9.71110e29i			0.620939i	−0.950583	+	0.310470i	$0.899514\pi$
$752$	5.72869e29	+	1.47669e30i	0.361217	+	0.931114i
$753$		0			0
$754$	−9.04613e28	+	2.92248e29i	−0.0554707	+	0.179206i
$755$		−	1.27534e30i		−	0.771225i
$756$		0			0
$757$		−	8.71480e29i		−	0.512567i	−0.966602	−	0.256284i	$-0.917502\pi$
$757$		−	8.71480e29i		−	0.512567i	0.966602	−	0.256284i	$-0.0824981\pi$
$758$	6.91457e29	+	2.14031e29i	0.401087	+	0.124151i
$759$		0			0
$760$	−3.46468e30	−	4.37095e30i	−1.95488	−	2.46623i
$761$		−	5.58699e27i		−	0.00310913i	−0.999999	−	0.00155457i	$-0.999505\pi$
$761$		−	5.58699e27i		−	0.00310913i	0.999999	−	0.00155457i	$-0.000494834\pi$
$762$		0			0
$763$	6.06254e28			0.0328206
$764$	−2.29648e30	−	1.57233e30i	−1.22626	−	0.839584i
$765$		0			0
$766$	−3.49986e30	−	1.08333e30i	−1.81823	−	0.562807i
$767$	3.62345e29			0.185683
$768$		0			0
$769$	−8.80205e29			−0.438892			−0.219446	−	0.975625i	$-0.570425\pi$
$769$	−8.80205e29			−0.438892			−0.219446	+	0.975625i	$0.570425\pi$
$770$	1.90406e30	+	5.89376e29i	0.936545	+	0.289894i
$771$		0			0
$772$	4.16731e28	+	2.85324e28i	0.0199468	+	0.0136570i
$773$	3.12368e30			1.47496			0.737482	−	0.675366i	$-0.236014\pi$
$773$	3.12368e30			1.47496			0.737482	+	0.675366i	$0.236014\pi$
$774$		0			0
$775$			1.96638e30i			0.903647i
$776$	−7.53297e28	−	9.50339e28i	−0.0341522	−	0.0430855i
$777$		0			0
$778$	−8.07801e29	−	2.50043e29i	−0.356466	−	0.110339i
$779$			4.68846e30i			2.04121i
$780$		0			0
$781$		−	2.21294e30i		−	0.937850i
$782$	−9.17247e29	+	2.96330e30i	−0.383544	+	1.23909i
$783$		0			0
$784$	7.71939e29	+	1.98984e30i	0.314242	+	0.810026i
$785$		−	3.86758e30i		−	1.55349i
$786$		0			0
$787$	−1.57921e30			−0.617596			−0.308798	−	0.951128i	$-0.599927\pi$
$787$	−1.57921e30			−0.617596			−0.308798	+	0.951128i	$0.599927\pi$
$788$	1.57106e30	+	1.07566e30i	0.606272	+	0.415097i
$789$		0			0
$790$	2.07870e30	−	6.71552e30i	0.781100	−	2.52345i
$791$	−6.23073e29			−0.231039
$792$		0			0
$793$	4.30126e29			0.155320
$794$	4.51670e29	−	1.45918e30i	0.160955	−	0.519990i
$795$		0			0
$796$	2.75271e30	−	4.02048e30i	0.955374	−	1.39537i
$797$	−2.55126e30			−0.873862			−0.436931	−	0.899495i	$-0.643935\pi$
$797$	−2.55126e30			−0.873862			−0.436931	+	0.899495i	$0.643935\pi$
$798$		0			0
$799$			4.69726e30i			1.56713i
$800$	5.52882e29	+	7.89838e30i	0.182049	+	2.60072i
$801$		0			0
$802$	2.06747e29	−	6.67927e29i	0.0663146	−	0.214239i
$803$		−	7.62592e30i		−	2.41423i
$804$		0			0
$805$		−	1.84350e30i		−	0.568574i
$806$	1.99870e29	+	6.18669e28i	0.0608457	+	0.0188339i
$807$		0			0
$808$	1.21950e30	+	1.53849e30i	0.361713	+	0.456327i
$809$			5.27500e30i			1.54441i	0.635372	+	0.772206i	$0.280847\pi$
$809$			5.27500e30i			1.54441i	−0.635372	+	0.772206i	$0.719153\pi$
$810$		0			0
$811$	−2.74255e30			−0.782412			−0.391206	−	0.920303i	$-0.627942\pi$
$811$	−2.74255e30			−0.782412			−0.391206	+	0.920303i	$0.627942\pi$
$812$	7.41659e29	−	1.08323e30i	0.208865	−	0.305059i
$813$		0			0
$814$	6.46436e30	+	2.00095e30i	1.77406	+	0.549137i
$815$	1.22963e30			0.333133
$816$		0			0
$817$	1.17125e30			0.309256
$818$	5.08996e30	+	1.57553e30i	1.32680	+	0.410692i
$819$		0			0
$820$	5.20225e30	−	7.59817e30i	1.32174	−	1.93047i
$821$	−2.49651e30			−0.626225			−0.313113	−	0.949716i	$-0.601372\pi$
$821$	−2.49651e30			−0.626225			−0.313113	+	0.949716i	$0.601372\pi$
$822$		0			0
$823$			1.84477e30i			0.451071i	0.974235	+	0.225536i	$0.0724132\pi$
$823$			1.84477e30i			0.451071i	−0.974235	+	0.225536i	$0.927587\pi$
$824$	3.89914e30	−	3.09069e30i	0.941310	−	0.746139i
$825$		0			0
$826$	−1.48537e30	−	4.59775e29i	−0.349578	−	0.108207i
$827$		−	4.67681e30i		−	1.08678i	−0.839480	−	0.543391i	$-0.817140\pi$
$827$		−	4.67681e30i		−	1.08678i	0.839480	−	0.543391i	$-0.182860\pi$
$828$		0			0
$829$		−	2.02108e30i		−	0.457889i	−0.973439	−	0.228945i	$-0.926472\pi$
$829$		−	2.02108e30i		−	0.457889i	0.973439	−	0.228945i	$-0.0735275\pi$
$830$	4.81446e29	−	1.55538e30i	0.107703	−	0.347950i
$831$		0			0
$832$	8.20216e29	+	1.92305e29i	0.178910	+	0.0419465i
$833$			6.32954e30i			1.36333i
$834$		0			0
$835$	−1.08871e30			−0.228667
$836$	−6.43308e30	+	9.39586e30i	−1.33430	+	1.94881i
$837$		0			0
$838$	−1.17239e30	+	3.78756e30i	−0.237142	+	0.766121i
$839$	3.05059e30			0.609373			0.304686	−	0.952453i	$-0.401448\pi$
$839$	3.05059e30			0.609373			0.304686	+	0.952453i	$0.401448\pi$
$840$		0			0
$841$	2.16399e29			0.0421596
$842$	2.96824e30	−	9.58933e30i	0.571113	−	1.84506i
$843$		0			0
$844$	−3.78123e30	−	2.58890e30i	−0.709639	−	0.485870i
$845$	−9.90045e30			−1.83510
$846$		0			0
$847$		−	2.06634e30i		−	0.373617i
$848$	1.18317e30	+	3.04987e30i	0.211296	+	0.544660i
$849$		0			0
$850$	−6.94311e30	+	2.24307e31i	−1.20964	+	3.90791i
$851$		−	6.25876e30i		−	1.07703i
$852$		0			0
$853$		−	8.19544e30i		−	1.37597i	−0.725727	−	0.687983i	$-0.758496\pi$
$853$		−	8.19544e30i		−	1.37597i	0.725727	−	0.687983i	$-0.241504\pi$
$854$	−1.76322e30	−	5.45781e29i	−0.292415	−	0.0905130i
$855$		0			0
$856$	−5.10786e30	+	4.04880e30i	−0.826541	+	0.655167i
$857$			2.15319e29i			0.0344179i	0.999852	+	0.0172089i	$0.00547804\pi$
$857$			2.15319e29i			0.0344179i	−0.999852	+	0.0172089i	$0.994522\pi$
$858$		0			0
$859$	−2.37529e30			−0.370500			−0.185250	−	0.982691i	$-0.559310\pi$
$859$	−2.37529e30			−0.370500			−0.185250	+	0.982691i	$0.559310\pi$
$860$	−1.89814e30	−	1.29960e30i	−0.292478	−	0.200252i
$861$		0			0
$862$	2.25773e30	+	6.98850e29i	0.339505	+	0.105089i
$863$	9.44602e29			0.140325			0.0701626	−	0.997536i	$-0.477648\pi$
$863$	9.44602e29			0.140325			0.0701626	+	0.997536i	$0.477648\pi$
$864$		0			0
$865$	−2.41217e30			−0.349734
$866$	2.02083e30	+	6.25520e29i	0.289463	+	0.0895991i
$867$		0			0
$868$	−7.40829e29	−	5.07225e29i	−0.103576	−	0.0709158i
$869$	−1.43522e31			−1.98249
$870$		0			0
$871$			2.24702e30i			0.302982i
$872$	5.33098e29	−	4.22566e29i	0.0710206	−	0.0562952i
$873$		0			0
$874$	1.00610e31	+	3.11423e30i	1.30849	+	0.405024i
$875$		−	8.60191e30i		−	1.10538i
$876$		0			0
$877$			2.69320e30i			0.337888i	0.985626	+	0.168944i	$0.0540357\pi$
$877$			2.69320e30i			0.337888i	−0.985626	+	0.168944i	$0.945964\pi$
$878$	3.79931e30	−	1.22742e31i	0.470991	−	1.52160i
$879$		0			0
$880$	2.08510e31	−	8.08897e30i	2.52383	−	0.979095i
$881$		−	1.07042e31i		−	1.28029i	−0.768253	−	0.640146i	$-0.778874\pi$
$881$		−	1.07042e31i		−	1.28029i	0.768253	−	0.640146i	$-0.221126\pi$
$882$		0			0
$883$	−1.08446e31			−1.26656			−0.633280	−	0.773923i	$-0.718292\pi$
$883$	−1.08446e31			−1.26656			−0.633280	+	0.773923i	$0.718292\pi$
$884$	2.06150e30	+	1.41145e30i	0.237922	+	0.162898i
$885$		0			0
$886$	−4.05058e30	+	1.30860e31i	−0.456524	+	1.47487i
$887$	−1.33132e31			−1.48280			−0.741400	−	0.671063i	$-0.765838\pi$
$887$	−1.33132e31			−1.48280			−0.741400	+	0.671063i	$0.765838\pi$
$888$		0			0
$889$	−3.06291e30			−0.333170
$890$	−2.68170e30	+	8.66360e30i	−0.288280	+	0.931330i
$891$		0			0
$892$	9.43391e29	−	1.37787e30i	0.0990514	−	0.144670i
$893$	1.59481e31			1.65489
$894$		0			0
$895$			2.38554e31i			2.41793i
$896$	−3.11832e30	−	1.82908e30i	−0.312382	−	0.183231i
$897$		0			0
$898$	2.02433e30	−	6.53990e30i	0.198098	−	0.639985i
$899$		−	3.65837e30i		−	0.353844i
$900$		0			0
$901$			9.70145e30i			0.916698i
$902$	−1.79592e31	−	5.55903e30i	−1.67733	−	0.519195i
$903$		0			0
$904$	−5.47887e30	+	4.34289e30i	−0.499945	+	0.396287i
$905$			2.88578e31i			2.60287i
$906$		0			0
$907$	2.08414e31			1.83675			0.918377	−	0.395708i	$-0.129501\pi$
$907$	2.08414e31			1.83675			0.918377	+	0.395708i	$0.129501\pi$
$908$	5.07351e30	−	7.41014e30i	0.441985	−	0.645543i
$909$		0			0
$910$	−1.41838e30	−	4.39039e29i	−0.120742	−	0.0373739i
$911$	7.18004e30			0.604204			0.302102	−	0.953276i	$-0.402312\pi$
$911$	7.18004e30			0.604204			0.302102	+	0.953276i	$0.402312\pi$
$912$		0			0
$913$	−3.32410e30			−0.273357
$914$	1.35205e31	+	4.18508e30i	1.09915	+	0.340227i
$915$		0			0
$916$	−2.02965e30	+	2.96442e30i	−0.161257	+	0.235525i
$917$	6.54668e30			0.514213
$918$		0			0
$919$			2.09169e31i			1.60578i	0.596129	+	0.802889i	$0.296705\pi$
$919$			2.09169e31i			1.60578i	−0.596129	+	0.802889i	$0.703295\pi$
$920$	−1.28494e31	−	1.62105e31i	−0.975239	−	1.23034i
$921$		0			0
$922$	4.87249e30	+	1.50821e30i	0.361473	+	0.111889i
$923$			1.64847e30i			0.120910i
$924$		0			0
$925$		−	4.73757e31i		−	3.39678i
$926$	2.84469e30	−	9.19016e30i	0.201660	−	0.651490i
$927$		0			0
$928$	−1.02862e30	−	1.46947e31i	−0.0712853	−	1.01837i
$929$		−	1.41504e31i		−	0.969624i	−0.874618	−	0.484812i	$-0.838888\pi$
$929$		−	1.41504e31i		−	0.969624i	0.874618	−	0.484812i	$-0.161112\pi$
$930$		0			0
$931$	2.14900e31			1.43968
$932$	−1.12579e31	+	1.64427e31i	−0.745743	+	1.08920i
$933$		0			0
$934$	3.00328e28	−	9.70251e28i	0.00194515	−	0.00628409i
$935$	6.63258e31			4.24776
$936$		0			0
$937$	1.74303e31			1.09154			0.545768	−	0.837936i	$-0.316238\pi$
$937$	1.74303e31			1.09154			0.545768	+	0.837936i	$0.316238\pi$
$938$	2.85121e30	−	9.21125e30i	0.176563	−	0.570412i
$939$		0			0
$940$	−2.58457e31	−	1.76958e31i	−1.56511	−	1.07159i
$941$	−1.54614e31			−0.925886			−0.462943	−	0.886388i	$-0.653207\pi$
$941$	−1.54614e31			−0.925886			−0.462943	+	0.886388i	$0.653207\pi$
$942$		0			0
$943$			1.73880e31i			1.01830i
$944$	−1.62660e31	+	6.31024e30i	−0.942052	+	0.365460i
$945$		0			0
$946$	−1.38873e30	+	4.48649e30i	−0.0786613	+	0.254126i
$947$			3.02895e31i			1.69675i	0.529397	+	0.848374i	$0.322418\pi$
$947$			3.02895e31i			1.69675i	−0.529397	+	0.848374i	$0.677582\pi$
$948$		0			0
$949$			5.68072e30i			0.311249i
$950$	7.61567e31	+	2.35732e31i	4.12677	+	1.27738i
$951$		0			0
$952$	−6.65977e30	−	8.40179e30i	−0.352997	−	0.445332i
$953$		−	2.88987e31i		−	1.51497i	−0.652855	−	0.757483i	$-0.726429\pi$
$953$		−	2.88987e31i		−	1.51497i	0.652855	−	0.757483i	$-0.273571\pi$
$954$		0			0
$955$	5.50393e31			2.82252
$956$	−5.78280e30	−	3.95932e30i	−0.293312	−	0.200823i
$957$		0			0
$958$	2.49489e31	+	7.72259e30i	1.23798	+	0.383200i
$959$	−1.82410e29			−0.00895266
$960$		0			0
$961$	1.83235e31			0.879860
$962$	−4.81545e30	−	1.49055e30i	−0.228717	−	0.0707961i
$963$		0			0
$964$	1.17367e31	+	8.03580e30i	0.545428	+	0.373440i
$965$	−9.98773e29			−0.0459124
$966$		0			0
$967$			1.05511e31i			0.474590i	0.971438	+	0.237295i	$0.0762609\pi$
$967$			1.05511e31i			0.474590i	−0.971438	+	0.237295i	$0.923739\pi$
$968$	−1.44026e31	−	1.81700e31i	−0.640842	−	0.808469i
$969$		0			0
$970$	2.29093e30	+	7.09126e29i	0.0997492	+	0.0308759i
$971$		−	2.73385e31i		−	1.17753i	−0.808304	−	0.588765i	$-0.799614\pi$
$971$		−	2.73385e31i		−	1.17753i	0.808304	−	0.588765i	$-0.200386\pi$
$972$		0			0
$973$		−	5.96511e30i		−	0.251440i
$974$	−7.04940e30	+	2.27741e31i	−0.293956	+	0.949668i
$975$		0			0
$976$	−1.93087e31	+	7.49065e30i	−0.788008	+	0.305701i
$977$			4.04409e28i			0.00163278i	1.00000		0.000816390i	$0.000259865\pi$
$977$			4.04409e28i			0.00163278i	−1.00000		0.000816390i	$0.999740\pi$
$978$		0			0
$979$	1.85155e31			0.731674
$980$	−3.48270e31	−	2.38451e31i	−1.36158	−	0.932233i
$981$		0			0
$982$	−1.32985e31	+	4.29628e31i	−0.508900	+	1.64408i
$983$	3.08040e31			1.16626			0.583130	−	0.812378i	$-0.301828\pi$
$983$	3.08040e31			1.16626			0.583130	+	0.812378i	$0.301828\pi$
$984$		0			0
$985$	−3.76533e31			−1.39548
$986$	1.29174e31	−	4.17316e31i	0.473662	−	1.53023i
$987$		0			0
$988$	4.79215e30	−	6.99919e30i	0.172021	−	0.251246i
$989$	4.34379e30			0.154279
$990$		0			0
$991$		−	4.21458e31i		−	1.46548i	−0.680507	−	0.732741i	$-0.738241\pi$
$991$		−	4.21458e31i		−	1.46548i	0.680507	−	0.732741i	$-0.261759\pi$
$992$	−1.00498e31	+	7.03476e29i	−0.345766	+	0.0242034i
$993$		0			0
$994$	2.09172e30	−	6.75759e30i	0.0704606	−	0.227633i
$995$			9.63582e31i			3.21179i
$996$		0			0
$997$		−	3.53074e31i		−	1.15230i	−0.817343	−	0.576151i	$-0.804554\pi$
$997$		−	3.53074e31i		−	1.15230i	0.817343	−	0.576151i	$-0.195446\pi$
$998$	−3.26094e31	−	1.00938e31i	−1.05311	−	0.325974i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	72.22.f.a.35.78	yes	84
3.2	odd	2	inner	72.22.f.a.35.7	✓	84
8.3	odd	2	inner	72.22.f.a.35.8	yes	84
24.11	even	2	inner	72.22.f.a.35.77	yes	84

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
72.22.f.a.35.7	✓	84	3.2	odd	2	inner
72.22.f.a.35.8	yes	84	8.3	odd	2	inner
72.22.f.a.35.77	yes	84	24.11	even	2	inner
72.22.f.a.35.78	yes	84	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:	\( k \)	\(=\)	\( 22 \)
Character orbit:	\([\chi]\)	\(=\)	72.f (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(1383.40 + 428.211i) q^{2} +(1.73042e6 + 1.18477e6i) q^{4} -4.14728e7 q^{5} +2.70660e8i q^{7} +(1.88653e9 + 2.38000e9i) q^{8} +O(q^{10})\)	\(q+(1383.40 + 428.211i) q^{2} +(1.73042e6 + 1.18477e6i) q^{4} -4.14728e7 q^{5} +2.70660e8i q^{7} +(1.88653e9 + 2.38000e9i) q^{8} +(-5.73733e10 - 1.77591e10i) q^{10} +1.22616e11i q^{11} -9.13395e10i q^{13} +(-1.15899e11 + 3.74430e11i) q^{14} +(1.59068e12 + 4.10031e12i) q^{16} +1.30428e13i q^{17} +4.42830e13 q^{19} +(-7.17654e13 - 4.91358e13i) q^{20} +(-5.25056e13 + 1.69627e14i) q^{22} +1.64232e14 q^{23} +1.24315e15 q^{25} +(3.91126e13 - 1.26359e14i) q^{26} +(-3.20670e14 + 4.68356e14i) q^{28} -2.31284e15 q^{29} +1.58177e15i q^{31} +(4.44741e14 + 6.35350e15i) q^{32} +(-5.58508e15 + 1.80434e16i) q^{34} -1.12250e16i q^{35} -3.81093e16i q^{37} +(6.12609e16 + 1.89625e16i) q^{38} +(-7.82396e16 - 9.87050e16i) q^{40} +1.05875e17i q^{41} +2.64492e16 q^{43} +(-1.45272e17 + 2.12178e17i) q^{44} +(2.27197e17 + 7.03258e16i) q^{46} +3.60142e17 q^{47} +4.85289e17 q^{49} +(1.71977e18 + 5.32332e17i) q^{50} +(1.08216e17 - 1.58056e17i) q^{52} +7.43815e17 q^{53} -5.08523e18i q^{55} +(-6.44169e17 + 5.10608e17i) q^{56} +(-3.19958e18 - 9.90385e17i) q^{58} +3.96701e18i q^{59} +4.70909e18i q^{61} +(-6.77329e17 + 2.18821e18i) q^{62} +(-2.10539e18 + 8.97986e18i) q^{64} +3.78810e18i q^{65} -2.46007e19 q^{67} +(-1.54528e19 + 2.25696e19i) q^{68} +(4.80667e18 - 1.55286e19i) q^{70} -1.80477e19 q^{71} -6.21935e19 q^{73} +(1.63188e19 - 5.27203e19i) q^{74} +(7.66282e19 + 5.24652e19i) q^{76} -3.31872e19 q^{77} +1.17050e20i q^{79} +(-6.59698e19 - 1.70051e20i) q^{80} +(-4.53369e19 + 1.46467e20i) q^{82} +2.71098e19i q^{83} -5.40922e20i q^{85} +(3.65897e19 + 1.13258e19i) q^{86} +(-2.91826e20 + 2.31319e20i) q^{88} -1.51004e20i q^{89} +2.47219e19 q^{91} +(2.84190e20 + 1.94577e20i) q^{92} +(4.98219e20 + 1.54217e20i) q^{94} -1.83654e21 q^{95} -3.99303e19 q^{97} +(6.71348e20 + 2.07806e20i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 84 q + 2424084 q^{4}+O(q^{10}) \) 84 * q + 2424084 * q^4	\( 84 q + 2424084 q^{4} + 17057181612 q^{10} - 4099708064904 q^{16} + 92015527242864 q^{19} - 236011369239528 q^{22} + 80\!\cdots\!00 q^{25}+ \cdots - 16\!\cdots\!12 q^{97}+O(q^{100}) \) 84 * q + 2424084 * q^4 + 17057181612 * q^10 - 4099708064904 * q^16 + 92015527242864 * q^19 - 236011369239528 * q^22 + 8010864257812500 * q^25 - 3042238700022024 * q^28 + 74414158327329924 * q^34 + 75018327243317184 * q^40 + 707788847336454432 * q^43 - 162639476543943288 * q^46 - 5423745715136249124 * q^49 - 70566629446202808 * q^52 - 14491558288019904108 * q^58 - 28749968749508108064 * q^64 - 13653811098426494352 * q^67 + 140256684870035374392 * q^70 - 71781309378863778384 * q^73 + 376055720386305092400 * q^76 - 368362114062816367548 * q^82 - 592572120184082106720 * q^88 - 522206955652189957200 * q^91 - 528772551789914644488 * q^94 - 1686050813935078492512 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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