LMFDB - Embedded newform 72.22.f.a.35.1

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			35.1
Character	$\chi$	$=$	72.35
Dual form			72.22.f.a.35.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1443.33 - 118.056i) q^{2} +(2.06928e6 + 340787. i) q^{4} -2.14944e6 q^{5} +2.68546e8i q^{7} +(-2.94643e9 - 7.36160e8i) q^{8} +O(q^{10})$	\(q+(-1443.33 - 118.056i) q^{2} +(2.06928e6 + 340787. i) q^{4} -2.14944e6 q^{5} +2.68546e8i q^{7} +(-2.94643e9 - 7.36160e8i) q^{8} +(3.10237e9 + 2.53754e8i) q^{10} +1.38410e11i q^{11} +5.50274e11i q^{13} +(3.17034e10 - 3.87602e11i) q^{14} +(4.16577e12 + 1.41037e12i) q^{16} -1.14752e13i q^{17} +1.05813e13 q^{19} +(-4.44780e12 - 7.32503e11i) q^{20} +(1.63400e13 - 1.99771e14i) q^{22} +3.08144e14 q^{23} -4.72217e14 q^{25} +(6.49629e13 - 7.94230e14i) q^{26} +(-9.15172e13 + 5.55697e14i) q^{28} -7.39318e14 q^{29} +3.37254e14i q^{31} +(-5.84611e15 - 2.52742e15i) q^{32} +(-1.35471e15 + 1.65625e16i) q^{34} -5.77225e14i q^{35} -1.83826e16i q^{37} +(-1.52723e16 - 1.24918e15i) q^{38} +(6.33318e15 + 1.58233e15i) q^{40} -1.58363e17i q^{41} +2.11471e17 q^{43} +(-4.71682e16 + 2.86408e17i) q^{44} +(-4.44754e17 - 3.63781e16i) q^{46} +6.25398e17 q^{47} +4.86429e17 q^{49} +(6.81567e17 + 5.57478e16i) q^{50} +(-1.87527e17 + 1.13867e18i) q^{52} -1.17467e18 q^{53} -2.97504e17i q^{55} +(1.97693e17 - 7.91253e17i) q^{56} +(1.06708e18 + 8.72805e16i) q^{58} -5.10779e17i q^{59} +8.82423e18i q^{61} +(3.98147e16 - 4.86771e17i) q^{62} +(8.13951e18 + 4.33808e18i) q^{64} -1.18278e18i q^{65} -1.98219e19 q^{67} +(3.91059e18 - 2.37453e19i) q^{68} +(-6.81446e16 + 8.33129e17i) q^{70} +4.98690e19 q^{71} +2.92144e19 q^{73} +(-2.17017e18 + 2.65323e19i) q^{74} +(2.18956e19 + 3.60597e18i) q^{76} -3.71694e19 q^{77} -6.58629e19i q^{79} +(-8.95410e18 - 3.03151e18i) q^{80} +(-1.86957e19 + 2.28571e20i) q^{82} +5.73700e19i q^{83} +2.46652e19i q^{85} +(-3.05223e20 - 2.49653e19i) q^{86} +(1.01892e20 - 4.07814e20i) q^{88} -2.99565e20i q^{89} -1.47774e20 q^{91} +(6.37635e20 + 1.05011e20i) q^{92} +(-9.02659e20 - 7.38317e19i) q^{94} -2.27439e19 q^{95} -2.11276e20 q^{97} +(-7.02079e20 - 5.74256e19i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−1443.33	−	118.056i	−0.996672	−	0.0815213i
$2$	−1443.33	−	118.056i	−0.996672	−	0.0815213i
$3$		0			0
$3$		0			0
$4$	2.06928e6	+	340787.i	0.986709	+	0.162500i
$5$	−2.14944e6			−0.0984331			−0.0492166	−	0.998788i	$-0.515672\pi$
$5$	−2.14944e6			−0.0984331			−0.0492166	+	0.998788i	$0.515672\pi$
$6$		0			0
$7$			2.68546e8i			0.359327i	0.983728	+	0.179663i	$0.0575009\pi$
$7$			2.68546e8i			0.359327i	−0.983728	+	0.179663i	$0.942499\pi$
$8$	−2.94643e9	−	7.36160e8i	−0.970177	−	0.242397i
$9$		0			0
$10$	3.10237e9	+	2.53754e8i	0.0981055	+	0.00802440i
$11$			1.38410e11i			1.60895i	0.593986	+	0.804475i	$0.297553\pi$
$11$			1.38410e11i			1.60895i	−0.593986	+	0.804475i	$0.702447\pi$
$12$		0			0
$13$			5.50274e11i			1.10707i	0.832827	+	0.553534i	$0.186721\pi$
$13$			5.50274e11i			1.10707i	−0.832827	+	0.553534i	$0.813279\pi$
$14$	3.17034e10	−	3.87602e11i	0.0292928	−	0.358131i
$15$		0			0
$16$	4.16577e12	+	1.41037e12i	0.947187	+	0.320680i
$17$		−	1.14752e13i		−	1.38053i	−0.723558	−	0.690264i	$-0.757494\pi$
$17$		−	1.14752e13i		−	1.38053i	0.723558	−	0.690264i	$-0.242506\pi$
$18$		0			0
$19$	1.05813e13			0.395936			0.197968	−	0.980208i	$-0.436566\pi$
$19$	1.05813e13			0.395936			0.197968	+	0.980208i	$0.436566\pi$
$20$	−4.44780e12	−	7.32503e11i	−0.0971248	−	0.0159954i
$21$		0			0
$22$	1.63400e13	−	1.99771e14i	0.131164	−	1.60360i
$23$	3.08144e14			1.55100			0.775499	−	0.631349i	$-0.217499\pi$
$23$	3.08144e14			1.55100			0.775499	+	0.631349i	$0.217499\pi$
$24$		0			0
$25$	−4.72217e14			−0.990311
$26$	6.49629e13	−	7.94230e14i	0.0902496	−	1.10338i
$27$		0			0
$28$	−9.15172e13	+	5.55697e14i	−0.0583906	+	0.354551i
$29$	−7.39318e14			−0.326326			−0.163163	−	0.986599i	$-0.552170\pi$
$29$	−7.39318e14			−0.326326			−0.163163	+	0.986599i	$0.552170\pi$
$30$		0			0
$31$			3.37254e14i			0.0739026i	0.999317	+	0.0369513i	$0.0117646\pi$
$31$			3.37254e14i			0.0739026i	−0.999317	+	0.0369513i	$0.988235\pi$
$32$	−5.84611e15	−	2.52742e15i	−0.917893	−	0.396829i
$33$		0			0
$34$	−1.35471e15	+	1.65625e16i	−0.112542	+	1.37593i
$35$		−	5.77225e14i		−	0.0353697i
$36$		0			0
$37$		−	1.83826e16i		−	0.628478i	−0.949344	−	0.314239i	$-0.898251\pi$
$37$		−	1.83826e16i		−	0.628478i	0.949344	−	0.314239i	$-0.101749\pi$
$38$	−1.52723e16	−	1.24918e15i	−0.394619	−	0.0322773i
$39$		0			0
$40$	6.33318e15	+	1.58233e15i	0.0954975	+	0.0238599i
$41$		−	1.58363e17i		−	1.84257i	−0.388886	−	0.921286i	$-0.627140\pi$
$41$		−	1.58363e17i		−	1.84257i	0.388886	−	0.921286i	$-0.372860\pi$
$42$		0			0
$43$	2.11471e17			1.49221			0.746107	−	0.665826i	$-0.231921\pi$
$43$	2.11471e17			1.49221			0.746107	+	0.665826i	$0.231921\pi$
$44$	−4.71682e16	+	2.86408e17i	−0.261455	+	1.58757i
$45$		0			0
$46$	−4.44754e17	−	3.63781e16i	−1.54583	−	0.126439i
$47$	6.25398e17			1.73432			0.867160	−	0.498030i	$-0.165943\pi$
$47$	6.25398e17			1.73432			0.867160	+	0.498030i	$0.165943\pi$
$48$		0			0
$49$	4.86429e17			0.870884
$50$	6.81567e17	+	5.57478e16i	0.987015	+	0.0807315i
$51$		0			0
$52$	−1.87527e17	+	1.13867e18i	−0.179899	+	1.09235i
$53$	−1.17467e18			−0.922616			−0.461308	−	0.887240i	$-0.652620\pi$
$53$	−1.17467e18			−0.922616			−0.461308	+	0.887240i	$0.652620\pi$
$54$		0			0
$55$		−	2.97504e17i		−	0.158374i
$56$	1.97693e17	−	7.91253e17i	0.0870998	−	0.348611i
$57$		0			0
$58$	1.06708e18	+	8.72805e16i	0.325240	+	0.0266026i
$59$		−	5.10779e17i		−	0.130103i	−0.997882	−	0.0650515i	$-0.979279\pi$
$59$		−	5.10779e17i		−	0.130103i	0.997882	−	0.0650515i	$-0.0207212\pi$
$60$		0			0
$61$			8.82423e18i			1.58385i	0.610620	+	0.791924i	$0.290920\pi$
$61$			8.82423e18i			1.58385i	−0.610620	+	0.791924i	$0.709080\pi$
$62$	3.98147e16	−	4.86771e17i	0.00602464	−	0.0736566i
$63$		0			0
$64$	8.13951e18	+	4.33808e18i	0.882487	+	0.470336i
$65$		−	1.18278e18i		−	0.108972i
$66$		0			0
$67$	−1.98219e19			−1.32850			−0.664248	−	0.747512i	$-0.731248\pi$
$67$	−1.98219e19			−1.32850			−0.664248	+	0.747512i	$0.731248\pi$
$68$	3.91059e18	−	2.37453e19i	0.224336	−	1.36218i
$69$		0			0
$70$	−6.81446e16	+	8.33129e17i	−0.00288338	+	0.0352519i
$71$	4.98690e19			1.81810			0.909050	−	0.416686i	$-0.136809\pi$
$71$	4.98690e19			1.81810			0.909050	+	0.416686i	$0.136809\pi$
$72$		0			0
$73$	2.92144e19			0.795622			0.397811	−	0.917467i	$-0.369770\pi$
$73$	2.92144e19			0.795622			0.397811	+	0.917467i	$0.369770\pi$
$74$	−2.17017e18	+	2.65323e19i	−0.0512344	+	0.626386i
$75$		0			0
$76$	2.18956e19	+	3.60597e18i	0.390674	+	0.0643397i
$77$	−3.71694e19			−0.578139
$78$		0			0
$79$		−	6.58629e19i		−	0.782630i	−0.920257	−	0.391315i	$-0.872020\pi$
$79$		−	6.58629e19i		−	0.782630i	0.920257	−	0.391315i	$-0.127980\pi$
$80$	−8.95410e18	−	3.03151e18i	−0.0932346	−	0.0315656i
$81$		0			0
$82$	−1.86957e19	+	2.28571e20i	−0.150209	+	1.83644i
$83$			5.73700e19i			0.405849i	0.979194	+	0.202925i	$0.0650447\pi$
$83$			5.73700e19i			0.405849i	−0.979194	+	0.202925i	$0.934955\pi$
$84$		0			0
$85$			2.46652e19i			0.135890i
$86$	−3.05223e20	−	2.49653e19i	−1.48725	−	0.121647i
$87$		0			0
$88$	1.01892e20	−	4.07814e20i	0.390005	−	1.56097i
$89$		−	2.99565e20i		−	1.01835i	−0.860663	−	0.509174i	$-0.829951\pi$
$89$		−	2.99565e20i		−	1.01835i	0.860663	−	0.509174i	$-0.170049\pi$
$90$		0			0
$91$	−1.47774e20			−0.397799
$92$	6.37635e20	+	1.05011e20i	1.53038	+	0.252037i
$93$		0			0
$94$	−9.02659e20	−	7.38317e19i	−1.72855	−	0.141384i
$95$	−2.27439e19			−0.0389732
$96$		0			0
$97$	−2.11276e20			−0.290902			−0.145451	−	0.989365i	$-0.546463\pi$
$97$	−2.11276e20			−0.290902			−0.145451	+	0.989365i	$0.546463\pi$
$98$	−7.02079e20	−	5.74256e19i	−0.867985	−	0.0709956i
$99$		0			0
$100$	−9.77148e20	−	1.60926e20i	−0.977148	−	0.160926i
$101$	−1.79627e21			−1.61807			−0.809036	−	0.587760i	$-0.800010\pi$
$101$	−1.79627e21			−1.61807			−0.809036	+	0.587760i	$0.800010\pi$
$102$		0			0
$103$		−	1.00878e21i		−	0.739617i	−0.929108	−	0.369808i	$-0.879423\pi$
$103$		−	1.00878e21i		−	0.739617i	0.929108	−	0.369808i	$-0.120577\pi$
$104$	4.05090e20	−	1.62134e21i	0.268350	−	1.07405i
$105$		0			0
$106$	1.69545e21	+	1.38677e20i	0.919545	+	0.0752129i
$107$		−	2.53002e21i		−	1.24335i	−0.783274	−	0.621677i	$-0.786452\pi$
$107$		−	2.53002e21i		−	1.24335i	0.783274	−	0.621677i	$-0.213548\pi$
$108$		0			0
$109$			1.82636e21i			0.738938i	0.929243	+	0.369469i	$0.120460\pi$
$109$			1.82636e21i			0.738938i	−0.929243	+	0.369469i	$0.879540\pi$
$110$	−3.51219e19	+	4.29397e20i	−0.0129109	+	0.157847i
$111$		0			0
$112$	−3.78749e20	+	1.11870e21i	−0.115229	+	0.340350i
$113$			1.62079e21i			0.449163i	0.974455	+	0.224582i	$0.0721015\pi$
$113$			1.62079e21i			0.449163i	−0.974455	+	0.224582i	$0.927898\pi$
$114$		0			0
$115$	−6.62338e20			−0.152669
$116$	−1.52985e21	−	2.51950e20i	−0.321989	−	0.0530280i
$117$		0			0
$118$	−6.03003e19	+	7.37225e20i	−0.0106062	+	0.129670i
$119$	3.08161e21			0.496061
$120$		0			0
$121$	−1.17569e22			−1.58872
$122$	1.04175e21	−	1.27363e22i	0.129117	−	1.57858i
$123$		0			0
$124$	−1.14932e20	+	6.97873e20i	−0.0120092	+	0.0729203i
$125$	2.03994e21			0.195912
$126$		0			0
$127$			1.04227e22i			0.847312i	0.905823	+	0.423656i	$0.139253\pi$
$127$			1.04227e22i			0.847312i	−0.905823	+	0.423656i	$0.860747\pi$
$128$	−1.12359e22	−	7.22222e21i	−0.841208	−	0.540712i
$129$		0			0
$130$	−1.39634e20	+	1.70715e21i	−0.00888355	+	0.108609i
$131$		−	1.76627e22i		−	1.03683i	−0.855128	−	0.518417i	$-0.826521\pi$
$131$		−	1.76627e22i		−	1.03683i	0.855128	−	0.518417i	$-0.173479\pi$
$132$		0			0
$133$			2.84156e21i			0.142271i
$134$	2.86097e22	+	2.34009e21i	1.32407	+	0.108301i
$135$		0			0
$136$	−8.44755e21	+	3.38107e22i	−0.334636	+	1.33936i
$137$		−	3.78672e22i		−	1.38898i	−0.719501	−	0.694492i	$-0.755629\pi$
$137$		−	3.78672e22i		−	1.38898i	0.719501	−	0.694492i	$-0.244371\pi$
$138$		0			0
$139$	1.81167e22			0.570722			0.285361	−	0.958420i	$-0.407887\pi$
$139$	1.81167e22			0.570722			0.285361	+	0.958420i	$0.407887\pi$
$140$	1.96711e20	−	1.19444e21i	0.00574757	−	0.0348996i
$141$		0			0
$142$	−7.19776e22	−	5.88731e21i	−1.81205	−	0.148214i
$143$	−7.61632e22			−1.78122
$144$		0			0
$145$	1.58912e21			0.0321213
$146$	−4.21662e22	−	3.44892e21i	−0.792974	−	0.0648602i
$147$		0			0
$148$	6.26457e21	−	3.80388e22i	0.102128	−	0.620124i
$149$	9.26618e22			1.40749			0.703745	−	0.710453i	$-0.251510\pi$
$149$	9.26618e22			1.40749			0.703745	+	0.710453i	$0.251510\pi$
$150$		0			0
$151$			4.73770e22i			0.625618i	0.949816	+	0.312809i	$0.101270\pi$
$151$			4.73770e22i			0.625618i	−0.949816	+	0.312809i	$0.898730\pi$
$152$	−3.11770e22	−	7.78951e21i	−0.384128	−	0.0959738i
$153$		0			0
$154$	5.36478e22	+	4.38805e21i	0.576215	+	0.0471307i
$155$		−	7.24909e20i		−	0.00727446i
$156$		0			0
$157$		−	1.10800e23i		−	0.971838i	−0.874004	−	0.485919i	$-0.838485\pi$
$157$		−	1.10800e23i		−	0.971838i	0.874004	−	0.485919i	$-0.161515\pi$
$158$	−7.77548e21	+	9.50622e22i	−0.0638011	+	0.780025i
$159$		0			0
$160$	1.25659e22	+	5.43256e21i	0.0903510	+	0.0390611i
$161$			8.27509e22i			0.557315i
$162$		0			0
$163$	−1.95808e23			−1.15840			−0.579202	−	0.815184i	$-0.696636\pi$
$163$	−1.95808e23			−1.15840			−0.579202	+	0.815184i	$0.696636\pi$
$164$	5.39682e22	−	3.27698e23i	0.299418	−	1.81808i
$165$		0			0
$166$	6.77285e21	−	8.28041e22i	0.0330854	−	0.404499i
$167$	2.40871e23			1.10474			0.552372	−	0.833598i	$-0.313723\pi$
$167$	2.40871e23			1.10474			0.552372	+	0.833598i	$0.313723\pi$
$168$		0			0
$169$	−5.57375e22			−0.225599
$170$	2.91187e21	−	3.56002e22i	0.0110779	−	0.135437i
$171$		0			0
$172$	4.37591e23	+	7.20665e22i	1.47238	+	0.242485i
$173$	−3.82081e23			−1.20968			−0.604841	−	0.796346i	$-0.706763\pi$
$173$	−3.82081e23			−1.20968			−0.604841	+	0.796346i	$0.706763\pi$
$174$		0			0
$175$		−	1.26812e23i		−	0.355845i
$176$	−1.95208e23	+	5.76583e23i	−0.515959	+	1.52398i
$177$		0			0
$178$	−3.53653e22	+	4.32373e23i	−0.0830171	+	1.01496i
$179$			2.45839e23i			0.544118i	0.962281	+	0.272059i	$0.0877046\pi$
$179$			2.45839e23i			0.544118i	−0.962281	+	0.272059i	$0.912295\pi$
$180$		0			0
$181$			9.87717e23i			1.94539i	0.232081	+	0.972696i	$0.425446\pi$
$181$			9.87717e23i			1.94539i	−0.232081	+	0.972696i	$0.574554\pi$
$182$	2.13288e23	+	1.74456e22i	0.396475	+	0.0324291i
$183$		0			0
$184$	−9.07923e23	−	2.26843e23i	−1.50474	−	0.375957i
$185$			3.95125e22i			0.0618630i
$186$		0			0
$187$	1.58827e24			2.22120
$188$	1.29412e24	+	2.13128e23i	1.71127	+	0.281827i
$189$		0			0
$190$	3.28270e22	+	2.68504e21i	0.0388435	+	0.00317715i
$191$	1.08437e24			1.21430			0.607150	−	0.794587i	$-0.292313\pi$
$191$	1.08437e24			1.21430			0.607150	+	0.794587i	$0.292313\pi$
$192$		0			0
$193$	7.80642e23			0.783611			0.391805	−	0.920048i	$-0.371851\pi$
$193$	7.80642e23			0.783611			0.391805	+	0.920048i	$0.371851\pi$
$194$	3.04942e23	+	2.49423e22i	0.289934	+	0.0237148i
$195$		0			0
$196$	1.00656e24	+	1.65769e23i	0.859309	+	0.141519i
$197$	6.60285e23			0.534362			0.267181	−	0.963646i	$-0.413908\pi$
$197$	6.60285e23			0.534362			0.267181	+	0.963646i	$0.413908\pi$
$198$		0			0
$199$			9.95218e22i			0.0724371i	0.999344	+	0.0362185i	$0.0115312\pi$
$199$			9.95218e22i			0.0724371i	−0.999344	+	0.0362185i	$0.988469\pi$
$200$	1.39135e24	+	3.47627e23i	0.960777	+	0.240048i
$201$		0			0
$202$	2.59262e24	+	2.12060e23i	1.61269	+	0.131907i
$203$		−	1.98541e23i		−	0.117258i
$204$		0			0
$205$			3.40393e23i			0.181370i
$206$	−1.19092e23	+	1.45601e24i	−0.0602945	+	0.737155i
$207$		0			0
$208$	−7.76089e23	+	2.29232e24i	−0.355015	+	1.04860i
$209$			1.46455e24i			0.637042i
$210$		0			0
$211$	−1.78924e24			−0.704212			−0.352106	−	0.935960i	$-0.614534\pi$
$211$	−1.78924e24			−0.704212			−0.352106	+	0.935960i	$0.614534\pi$
$212$	−2.43073e24	−	4.00314e23i	−0.910353	−	0.149925i
$213$		0			0
$214$	−2.98683e23	+	3.65167e24i	−0.101360	+	1.23922i
$215$	−4.54544e23			−0.146883
$216$		0			0
$217$	−9.05684e22			−0.0265552
$218$	2.15612e23	−	2.63605e24i	0.0602392	−	0.736478i
$219$		0			0
$220$	1.01385e23	−	6.15618e23i	0.0257358	−	0.156269i
$221$	6.31449e24			1.52834
$222$		0			0
$223$			7.66575e24i			1.68793i	0.536400	+	0.843964i	$0.319784\pi$
$223$			7.66575e24i			1.68793i	−0.536400	+	0.843964i	$0.680216\pi$
$224$	6.78730e23	−	1.56995e24i	0.142591	−	0.329824i
$225$		0			0
$226$	1.91344e23	−	2.33935e24i	0.0366164	−	0.447668i
$227$			3.63328e24i			0.663785i	0.943317	+	0.331892i	$0.107687\pi$
$227$			3.63328e24i			0.663785i	−0.943317	+	0.331892i	$0.892313\pi$
$228$		0			0
$229$		−	3.71331e24i		−	0.618712i	−0.950946	−	0.309356i	$-0.899887\pi$
$229$		−	3.71331e24i		−	0.618712i	0.950946	−	0.309356i	$-0.100113\pi$
$230$	9.55975e23	+	7.81926e22i	0.152161	+	0.0124458i
$231$		0			0
$232$	2.17835e24	+	5.44256e23i	0.316594	+	0.0791005i
$233$		−	8.67117e24i		−	1.20459i	−0.798272	−	0.602297i	$-0.794252\pi$
$233$		−	8.67117e24i		−	1.20459i	0.798272	−	0.602297i	$-0.205748\pi$
$234$		0			0
$235$	−1.34426e24			−0.170714
$236$	1.74067e23	−	1.05694e24i	0.0211417	−	0.128374i
$237$		0			0
$238$	−4.44780e24	−	3.63801e23i	−0.494410	−	0.0404395i
$239$	−9.36551e23			−0.0996215			−0.0498108	−	0.998759i	$-0.515862\pi$
$239$	−9.36551e23			−0.0996215			−0.0498108	+	0.998759i	$0.515862\pi$
$240$		0			0
$241$	4.99621e24			0.486924			0.243462	−	0.969910i	$-0.421717\pi$
$241$	4.99621e24			0.486924			0.243462	+	0.969910i	$0.421717\pi$
$242$	1.69692e25	+	1.38797e24i	1.58343	+	0.129515i
$243$		0			0
$244$	−3.00719e24	+	1.82598e25i	−0.257375	+	1.56280i
$245$	−1.04555e24			−0.0857238
$246$		0			0
$247$			5.82261e24i			0.438328i
$248$	2.48273e23	−	9.93696e23i	0.0179138	−	0.0716986i
$249$		0			0
$250$	−2.94432e24	−	2.40826e23i	−0.195260	−	0.0159710i
$251$		−	7.15897e24i		−	0.455278i	−0.973746	−	0.227639i	$-0.926899\pi$
$251$		−	7.15897e24i		−	0.455278i	0.973746	−	0.227639i	$-0.0731006\pi$
$252$		0			0
$253$			4.26500e25i			2.49548i
$254$	1.23046e24	−	1.50435e25i	0.0690740	−	0.844491i
$255$		0			0
$256$	1.53645e25	+	1.17505e25i	0.794328	+	0.607489i
$257$		−	1.68026e25i		−	0.833833i	−0.908945	−	0.416916i	$-0.863111\pi$
$257$		−	1.68026e25i		−	0.833833i	0.908945	−	0.416916i	$-0.136889\pi$
$258$		0			0
$259$	4.93659e24			0.225829
$260$	4.03078e23	−	2.44751e24i	0.0177080	−	0.107524i
$261$		0			0
$262$	−2.08518e24	+	2.54933e25i	−0.0845242	+	1.03338i
$263$	3.23185e25			1.25868			0.629341	−	0.777129i	$-0.283325\pi$
$263$	3.23185e25			1.25868			0.629341	+	0.777129i	$0.283325\pi$
$264$		0			0
$265$	2.52490e24			0.0908159
$266$	3.35462e23	−	4.10133e24i	0.0115981	−	0.141797i
$267$		0			0
$268$	−4.10170e25	−	6.75505e24i	−1.31084	−	0.215881i
$269$	1.97262e25			0.606238			0.303119	−	0.952953i	$-0.401972\pi$
$269$	1.97262e25			0.606238			0.303119	+	0.952953i	$0.401972\pi$
$270$		0			0
$271$			3.71618e25i			1.05662i	0.849051	+	0.528311i	$0.177174\pi$
$271$			3.71618e25i			1.05662i	−0.849051	+	0.528311i	$0.822826\pi$
$272$	1.61842e25	−	4.78029e25i	0.442708	−	1.30762i
$273$		0			0
$274$	−4.47043e24	+	5.46550e25i	−0.113232	+	1.38436i
$275$		−	6.53593e25i		−	1.59336i
$276$		0			0
$277$			1.00635e25i			0.227358i	0.993518	+	0.113679i	$0.0362635\pi$
$277$			1.00635e25i			0.227358i	−0.993518	+	0.113679i	$0.963736\pi$
$278$	−2.61485e25	−	2.13878e24i	−0.568822	−	0.0465260i
$279$		0			0
$280$	−4.24930e23	+	1.70075e24i	−0.00857350	+	0.0343148i
$281$			6.50611e25i			1.26446i	0.774781	+	0.632230i	$0.217860\pi$
$281$			6.50611e25i			1.26446i	−0.774781	+	0.632230i	$0.782140\pi$
$282$		0			0
$283$	1.72762e25			0.311667			0.155833	−	0.987783i	$-0.450194\pi$
$283$	1.72762e25			0.311667			0.155833	+	0.987783i	$0.450194\pi$
$284$	1.03193e26	+	1.69947e25i	1.79394	+	0.295441i
$285$		0			0
$286$	1.09929e26	+	8.99149e24i	1.77529	+	0.145207i
$287$	4.25279e25			0.662086
$288$		0			0
$289$	−6.25874e25			−0.905857
$290$	−2.29364e24	−	1.87605e23i	−0.0320144	−	0.00261857i
$291$		0			0
$292$	6.04527e25	+	9.95590e24i	0.785047	+	0.129289i
$293$	−2.41738e25			−0.302855			−0.151427	−	0.988468i	$-0.548387\pi$
$293$	−2.41738e25			−0.302855			−0.151427	+	0.988468i	$0.548387\pi$
$294$		0			0
$295$			1.09789e24i			0.0128064i
$296$	−1.35326e25	+	5.41632e25i	−0.152341	+	0.609735i
$297$		0			0
$298$	−1.33742e26	−	1.09392e25i	−1.40280	−	0.114740i
$299$			1.69564e26i			1.71706i
$300$		0			0
$301$			5.67896e25i			0.536193i
$302$	5.59311e24	−	6.83808e25i	0.0510012	−	0.623536i
$303$		0			0
$304$	4.40792e25	+	1.49235e25i	0.375026	+	0.126969i
$305$		−	1.89672e25i		−	0.155903i
$306$		0			0
$307$	1.15414e26			0.885737			0.442869	−	0.896586i	$-0.353961\pi$
$307$	1.15414e26			0.885737			0.442869	+	0.896586i	$0.353961\pi$
$308$	−7.69137e25	−	1.26668e25i	−0.570455	−	0.0939477i
$309$		0			0
$310$	−8.55795e22	+	1.04629e24i	−0.000593024	+	0.00725025i
$311$	−4.72558e25			−0.316571			−0.158286	−	0.987393i	$-0.550597\pi$
$311$	−4.72558e25			−0.316571			−0.158286	+	0.987393i	$0.550597\pi$
$312$		0			0
$313$	2.01420e26			1.26150			0.630750	−	0.775986i	$-0.282747\pi$
$313$	2.01420e26			1.26150			0.630750	+	0.775986i	$0.282747\pi$
$314$	−1.30806e25	+	1.59922e26i	−0.0792255	+	0.968603i
$315$		0			0
$316$	2.24452e25	−	1.36289e26i	0.127177	−	0.772228i
$317$	1.74834e26			0.958304			0.479152	−	0.877732i	$-0.340944\pi$
$317$	1.74834e26			0.958304			0.479152	+	0.877732i	$0.340944\pi$
$318$		0			0
$319$		−	1.02329e26i		−	0.525043i
$320$	−1.74954e25	−	9.32447e24i	−0.0868660	−	0.0462966i
$321$		0			0
$322$	9.76920e24	−	1.19437e26i	0.0454331	−	0.555460i
$323$		−	1.21422e26i		−	0.546601i
$324$		0			0
$325$		−	2.59849e26i		−	1.09634i
$326$	2.82616e26	+	2.31162e25i	1.15455	+	0.0944346i
$327$		0			0
$328$	−1.16581e26	+	4.66607e26i	−0.446634	+	1.78762i
$329$			1.67948e26i			0.623188i
$330$		0			0
$331$	−9.78837e25			−0.340813			−0.170407	−	0.985374i	$-0.554508\pi$
$331$	−9.78837e25			−0.340813			−0.170407	+	0.985374i	$0.554508\pi$
$332$	−1.95510e25	+	1.18714e26i	−0.0659505	+	0.400455i
$333$		0			0
$334$	−3.47658e26	−	2.84362e25i	−1.10107	−	0.0900602i
$335$	4.26061e25			0.130768
$336$		0			0
$337$	2.99180e26			0.862619			0.431309	−	0.902204i	$-0.358052\pi$
$337$	2.99180e26			0.862619			0.431309	+	0.902204i	$0.358052\pi$
$338$	8.04478e25	+	6.58012e24i	0.224848	+	0.0183911i
$339$		0			0
$340$	−8.40559e24	+	5.10392e25i	−0.0220821	+	0.134083i
$341$	−4.66792e25			−0.118906
$342$		0			0
$343$			2.80624e26i			0.672259i
$344$	−6.23083e26	−	1.55676e26i	−1.44771	−	0.361708i
$345$		0			0
$346$	5.51470e26	+	4.51067e25i	1.20566	+	0.0986149i
$347$			7.05424e26i			1.49620i	0.663584	+	0.748102i	$0.269035\pi$
$347$			7.05424e26i			1.49620i	−0.663584	+	0.748102i	$0.730965\pi$
$348$		0			0
$349$			1.64936e26i			0.329343i	0.986348	+	0.164671i	$0.0526564\pi$
$349$			1.64936e26i			0.329343i	−0.986348	+	0.164671i	$0.947344\pi$
$350$	−1.49709e25	+	1.83032e26i	−0.0290090	+	0.354661i
$351$		0			0
$352$	3.49820e26	−	8.09157e26i	0.638478	−	1.47684i
$353$			3.12318e26i			0.553302i	0.960970	+	0.276651i	$0.0892246\pi$
$353$			3.12318e26i			0.553302i	−0.960970	+	0.276651i	$0.910775\pi$
$354$		0			0
$355$	−1.07191e26			−0.178961
$356$	1.02088e26	−	6.19884e26i	0.165482	−	1.00481i
$357$		0			0
$358$	2.90226e25	−	3.54827e26i	0.0443573	−	0.542307i
$359$	−5.50617e26			−0.817256			−0.408628	−	0.912701i	$-0.633993\pi$
$359$	−5.50617e26			−0.817256			−0.408628	+	0.912701i	$0.633993\pi$
$360$		0			0
$361$	−6.02246e26			−0.843234
$362$	1.16605e26	−	1.42561e27i	0.158591	−	1.93892i
$363$		0			0
$364$	−3.05786e26	−	5.03596e25i	−0.392512	−	0.0646424i
$365$	−6.27947e25			−0.0783156
$366$		0			0
$367$		−	3.48708e26i		−	0.410647i	−0.978694	−	0.205323i	$-0.934175\pi$
$367$		−	3.48708e26i		−	0.410647i	0.978694	−	0.205323i	$-0.0658246\pi$
$368$	1.28366e27	+	4.34596e26i	1.46909	+	0.497374i
$369$		0			0
$370$	4.66467e24	−	5.70297e25i	0.00504316	−	0.0616571i
$371$		−	3.15454e26i		−	0.331521i
$372$		0			0
$373$		−	1.09781e27i		−	1.09040i	−0.838307	−	0.545199i	$-0.816454\pi$
$373$		−	1.09781e27i		−	1.09040i	0.838307	−	0.545199i	$-0.183546\pi$
$374$	−2.29241e27	−	1.87504e26i	−2.21381	−	0.181075i
$375$		0			0
$376$	−1.84269e27	−	4.60393e26i	−1.68260	−	0.420394i
$377$		−	4.06828e26i		−	0.361265i
$378$		0			0
$379$	7.37440e26			0.619462			0.309731	−	0.950824i	$-0.399761\pi$
$379$	7.37440e26			0.619462			0.309731	+	0.950824i	$0.399761\pi$
$380$	−4.70634e25	−	7.75082e24i	−0.0384552	−	0.00633315i
$381$		0			0
$382$	−1.56510e27	−	1.28016e26i	−1.21026	−	0.0989914i
$383$	−3.67081e26			−0.276169			−0.138085	−	0.990420i	$-0.544095\pi$
$383$	−3.67081e26			−0.276169			−0.138085	+	0.990420i	$0.544095\pi$
$384$		0			0
$385$	7.98935e25			0.0569081
$386$	−1.12673e27	−	9.21592e25i	−0.781003	−	0.0638810i
$387$		0			0
$388$	−4.37189e26	−	7.20002e25i	−0.287036	−	0.0472716i
$389$	−2.61039e27			−1.66815			−0.834074	−	0.551652i	$-0.813998\pi$
$389$	−2.61039e27			−1.66815			−0.834074	+	0.551652i	$0.813998\pi$
$390$		0			0
$391$		−	3.53600e27i		−	2.14119i
$392$	−1.43323e27	−	3.58089e26i	−0.844912	−	0.211100i
$393$		0			0
$394$	−9.53012e26	−	7.79502e25i	−0.532584	−	0.0435619i
$395$			1.41569e26i			0.0770367i
$396$		0			0
$397$			2.25300e26i			0.116268i	0.998309	+	0.0581340i	$0.0185151\pi$
$397$			2.25300e26i			0.116268i	−0.998309	+	0.0581340i	$0.981485\pi$
$398$	1.17491e25	−	1.43643e26i	0.00590517	−	0.0721960i
$399$		0			0
$400$	−1.96715e27	−	6.65999e26i	−0.938010	−	0.317573i
$401$			1.39358e27i			0.647315i	0.946174	+	0.323657i	$0.104913\pi$
$401$			1.39358e27i			0.647315i	−0.946174	+	0.323657i	$0.895087\pi$
$402$		0			0
$403$	−1.85582e26			−0.0818152
$404$	−3.71699e27	−	6.12147e26i	−1.59656	−	0.262937i
$405$		0			0
$406$	−2.34389e25	+	2.86561e26i	−0.00955902	+	0.116868i
$407$	2.54433e27			1.01119
$408$		0			0
$409$	1.49403e27			0.563980			0.281990	−	0.959417i	$-0.409005\pi$
$409$	1.49403e27			0.563980			0.281990	+	0.959417i	$0.409005\pi$
$410$	4.01853e25	−	4.91302e26i	0.0147855	−	0.180766i
$411$		0			0
$412$	3.43780e26	−	2.08745e27i	0.120188	−	0.729786i
$413$	1.37168e26			0.0467495
$414$		0			0
$415$		−	1.23314e26i		−	0.0399490i
$416$	1.39078e27	−	3.21696e27i	0.439317	−	1.01617i
$417$		0			0
$418$	1.72898e26	−	2.11384e27i	0.0519325	−	0.634922i
$419$			3.82004e27i			1.11897i	0.828839	+	0.559487i	$0.189002\pi$
$419$			3.82004e27i			1.11897i	−0.828839	+	0.559487i	$0.810998\pi$
$420$		0			0
$421$		−	2.81115e27i		−	0.783289i	−0.920117	−	0.391644i	$-0.871906\pi$
$421$		−	2.81115e27i		−	0.783289i	0.920117	−	0.391644i	$-0.128094\pi$
$422$	2.58248e27	+	2.11230e26i	0.701868	+	0.0574083i
$423$		0			0
$424$	3.46109e27	+	8.64748e26i	0.895101	+	0.223639i
$425$			5.41877e27i			1.36715i
$426$		0			0
$427$	−2.36971e27			−0.569119
$428$	8.62199e26	−	5.23532e27i	0.202045	−	1.22683i
$429$		0			0
$430$	6.56059e26	+	5.36615e25i	0.146394	+	0.0119741i
$431$	−6.00753e27			−1.30823			−0.654116	−	0.756395i	$-0.726959\pi$
$431$	−6.00753e27			−1.30823			−0.654116	+	0.756395i	$0.726959\pi$
$432$		0			0
$433$	1.45812e27			0.302461			0.151231	−	0.988498i	$-0.451676\pi$
$433$	1.45812e27			0.302461			0.151231	+	0.988498i	$0.451676\pi$
$434$	1.30720e26	+	1.06921e25i	0.0264668	+	0.00216481i
$435$		0			0
$436$	−6.22400e26	+	3.77924e27i	−0.120077	+	0.729116i
$437$	3.26055e27			0.614096
$438$		0			0
$439$			4.43022e27i			0.795331i	0.917531	+	0.397665i	$0.130179\pi$
$439$			4.43022e27i			0.795331i	−0.917531	+	0.397665i	$0.869821\pi$
$440$	−2.19010e26	+	8.76573e26i	−0.0383894	+	0.153651i
$441$		0			0
$442$	−9.11392e27	−	7.45460e26i	−1.52325	−	0.124592i
$443$			1.00665e28i			1.64301i	0.570200	+	0.821506i	$0.306866\pi$
$443$			1.00665e28i			1.64301i	−0.570200	+	0.821506i	$0.693134\pi$
$444$		0			0
$445$			6.43899e26i			0.100239i
$446$	9.04985e26	−	1.10642e28i	0.137602	−	1.68231i
$447$		0			0
$448$	−1.16498e27	+	2.18584e27i	−0.169004	+	0.317102i
$449$		−	1.35340e27i		−	0.191796i	−0.995391	−	0.0958978i	$-0.969428\pi$
$449$		−	1.35340e27i		−	0.191796i	0.995391	−	0.0958978i	$-0.0305722\pi$
$450$		0			0
$451$	2.19190e28			2.96461
$452$	−5.52346e26	+	3.35387e27i	−0.0729890	+	0.443193i
$453$		0			0
$454$	4.28929e26	−	5.24404e27i	0.0541126	−	0.661575i
$455$	3.17632e26			0.0391566
$456$		0			0
$457$	8.49017e27			0.999531			0.499766	−	0.866161i	$-0.333419\pi$
$457$	8.49017e27			0.999531			0.499766	+	0.866161i	$0.333419\pi$
$458$	−4.38376e26	+	5.35955e27i	−0.0504382	+	0.616652i
$459$		0			0
$460$	−1.37056e27	−	2.25716e26i	−0.150640	−	0.0248088i
$461$	1.27978e28			1.37492			0.687458	−	0.726224i	$-0.258727\pi$
$461$	1.27978e28			1.37492			0.687458	+	0.726224i	$0.258727\pi$
$462$		0			0
$463$			1.04347e27i			0.107122i	0.998565	+	0.0535609i	$0.0170571\pi$
$463$			1.04347e27i			0.107122i	−0.998565	+	0.0535609i	$0.982943\pi$
$464$	−3.07983e27	−	1.04271e27i	−0.309092	−	0.104646i
$465$		0			0
$466$	−1.02368e27	+	1.25154e28i	−0.0982001	+	1.20058i
$467$			1.66252e27i			0.155933i	0.996956	+	0.0779666i	$0.0248427\pi$
$467$			1.66252e27i			0.155933i	−0.996956	+	0.0779666i	$0.975157\pi$
$468$		0			0
$469$		−	5.32310e27i		−	0.477364i
$470$	1.94022e27	+	1.58697e26i	0.170146	+	0.0139169i
$471$		0			0
$472$	−3.76015e26	+	1.50497e27i	−0.0315366	+	0.126223i
$473$			2.92695e28i			2.40090i
$474$		0			0
$475$	−4.99666e27			−0.392100
$476$	6.37671e27	+	1.05017e27i	0.489467	+	0.0806099i
$477$		0			0
$478$	1.35176e27	+	1.10565e26i	0.0992900	+	0.00812128i
$479$	8.99237e27			0.646177			0.323088	−	0.946369i	$-0.395279\pi$
$479$	8.99237e27			0.646177			0.323088	+	0.946369i	$0.395279\pi$
$480$		0			0
$481$	1.01155e28			0.695767
$482$	−7.21120e27	−	5.89830e26i	−0.485304	−	0.0396947i
$483$		0			0
$484$	−2.43284e28	−	4.00662e27i	−1.56761	−	0.258167i
$485$	4.54126e26			0.0286344
$486$		0			0
$487$		−	7.48673e27i		−	0.452104i	−0.974115	−	0.226052i	$-0.927418\pi$
$487$		−	7.48673e27i		−	0.452104i	0.974115	−	0.226052i	$-0.0725819\pi$
$488$	6.49604e27	−	2.60000e28i	0.383920	−	1.53661i
$489$		0			0
$490$	1.50908e27	+	1.23433e26i	0.0854385	+	0.00698832i
$491$			1.74661e28i			0.967922i	0.875090	+	0.483961i	$0.160802\pi$
$491$			1.74661e28i			0.967922i	−0.875090	+	0.483961i	$0.839198\pi$
$492$		0			0
$493$			8.48379e27i			0.450503i
$494$	6.87391e26	−	8.40397e27i	0.0357331	−	0.436869i
$495$		0			0
$496$	−4.75652e26	+	1.40493e27i	−0.0236991	+	0.0699996i
$497$			1.33921e28i			0.653293i
$498$		0			0
$499$	3.03858e28			1.42107			0.710533	−	0.703663i	$-0.248454\pi$
$499$	3.03858e28			1.42107			0.710533	+	0.703663i	$0.248454\pi$
$500$	4.22120e27	+	6.95185e26i	0.193309	+	0.0318358i
$501$		0			0
$502$	−8.45156e26	+	1.03328e28i	−0.0371149	+	0.453763i
$503$	3.68322e28			1.58403			0.792015	−	0.610501i	$-0.209032\pi$
$503$	3.68322e28			1.58403			0.792015	+	0.610501i	$0.209032\pi$
$504$		0			0
$505$	3.86099e27			0.159272
$506$	5.03507e27	−	6.15582e28i	0.203435	−	2.48717i
$507$		0			0
$508$	−3.55194e27	+	2.15676e28i	−0.137688	+	0.836050i
$509$	−3.74929e28			−1.42368			−0.711840	−	0.702342i	$-0.752138\pi$
$509$	−3.74929e28			−1.42368			−0.711840	+	0.702342i	$0.752138\pi$
$510$		0			0
$511$			7.84542e27i			0.285889i
$512$	−2.07890e28	−	1.87738e28i	−0.742161	−	0.670222i
$513$		0			0
$514$	−1.98364e27	+	2.42518e28i	−0.0679752	+	0.831058i
$515$			2.16832e27i			0.0728028i
$516$		0			0
$517$			8.65611e28i			2.79044i
$518$	−7.12515e27	−	5.82792e26i	−0.225077	−	0.0184099i
$519$		0			0
$520$	−8.70718e26	+	3.48499e27i	−0.0264145	+	0.105722i
$521$		−	9.22865e27i		−	0.274373i	−0.990545	−	0.137187i	$-0.956194\pi$
$521$		−	9.22865e27i		−	0.274373i	0.990545	−	0.137187i	$-0.0438060\pi$
$522$		0			0
$523$	−3.80552e28			−1.08679			−0.543395	−	0.839477i	$-0.682862\pi$
$523$	−3.80552e28			−1.08679			−0.543395	+	0.839477i	$0.682862\pi$
$524$	6.01924e27	−	3.65491e28i	0.168486	−	1.02305i
$525$		0			0
$526$	−4.66464e28	−	3.81538e27i	−1.25449	−	0.102609i
$527$	3.87005e27			0.102025
$528$		0			0
$529$	5.54810e28			1.40559
$530$	−3.64427e27	−	2.98078e26i	−0.0905136	−	0.00740344i
$531$		0			0
$532$	−9.68369e26	+	5.87999e27i	−0.0231190	+	0.140380i
$533$	8.71434e28			2.03985
$534$		0			0
$535$			5.43814e27i			0.122387i
$536$	5.84038e28	+	1.45921e28i	1.28888	+	0.322023i
$537$		0			0
$538$	−2.84714e28	−	2.32878e27i	−0.604221	−	0.0494214i
$539$			6.73264e28i			1.40121i
$540$		0			0
$541$		−	8.54488e28i		−	1.71055i	−0.518177	−	0.855273i	$-0.673389\pi$
$541$		−	8.54488e28i		−	1.71055i	0.518177	−	0.855273i	$-0.326611\pi$
$542$	4.38716e27	−	5.36369e28i	0.0861372	−	1.05310i
$543$		0			0
$544$	−2.90026e28	+	6.70850e28i	−0.547833	+	1.26718i
$545$		−	3.92566e27i		−	0.0727359i
$546$		0			0
$547$	6.54490e28			1.16691			0.583453	−	0.812147i	$-0.301701\pi$
$547$	6.54490e28			1.16691			0.583453	+	0.812147i	$0.301701\pi$
$548$	1.29047e28	−	7.83577e28i	0.225710	−	1.37052i
$549$		0			0
$550$	−7.71603e27	+	9.43354e28i	−0.129893	+	1.58806i
$551$	−7.82293e27			−0.129204
$552$		0			0
$553$	1.76872e28			0.281220
$554$	1.18805e27	−	1.45250e28i	0.0185345	−	0.226601i
$555$		0			0
$556$	3.74886e28	+	6.17395e27i	0.563136	+	0.0927423i
$557$	2.43076e28			0.358312			0.179156	−	0.983821i	$-0.442663\pi$
$557$	2.43076e28			0.358312			0.179156	+	0.983821i	$0.442663\pi$
$558$		0			0
$559$			1.16367e29i			1.65198i
$560$	8.14100e26	−	2.40459e27i	0.0113424	−	0.0335017i
$561$		0			0
$562$	7.68082e27	−	9.39049e28i	0.103080	−	1.26025i
$563$			1.33175e28i			0.175422i	0.996146	+	0.0877111i	$0.0279552\pi$
$563$			1.33175e28i			0.175422i	−0.996146	+	0.0877111i	$0.972045\pi$
$564$		0			0
$565$		−	3.48381e27i		−	0.0442125i
$566$	−2.49353e28	−	2.03955e27i	−0.310630	−	0.0254075i
$567$		0			0
$568$	−1.46935e29	−	3.67115e28i	−1.76388	−	0.440702i
$569$			1.02329e29i			1.20593i	0.797768	+	0.602964i	$0.206014\pi$
$569$			1.02329e29i			1.20593i	−0.797768	+	0.602964i	$0.793986\pi$
$570$		0			0
$571$	5.10541e28			0.579898			0.289949	−	0.957042i	$-0.406362\pi$
$571$	5.10541e28			0.579898			0.289949	+	0.957042i	$0.406362\pi$
$572$	−1.57603e29	−	2.59555e28i	−1.75754	−	0.289448i
$573$		0			0
$574$	−6.13820e28	−	5.02066e27i	−0.659882	−	0.0539741i
$575$	−1.45511e29			−1.53597
$576$		0			0
$577$	9.99202e28			1.01697			0.508484	−	0.861072i	$-0.330206\pi$
$577$	9.99202e28			1.01697			0.508484	+	0.861072i	$0.330206\pi$
$578$	9.03346e28	+	7.38879e27i	0.902842	+	0.0738467i
$579$		0			0
$580$	3.28834e27	+	5.41553e26i	0.0316944	+	0.00521971i
$581$	−1.54065e28			−0.145833
$582$		0			0
$583$		−	1.62586e29i		−	1.48444i
$584$	−8.60782e28	−	2.15065e28i	−0.771895	−	0.192856i
$585$		0			0
$586$	3.48908e28	+	2.85385e27i	0.301847	+	0.0246891i
$587$		−	5.08606e27i		−	0.0432197i	−0.999766	−	0.0216098i	$-0.993121\pi$
$587$		−	5.08606e27i		−	0.0432197i	0.999766	−	0.0216098i	$-0.00687916\pi$
$588$		0			0
$589$			3.56858e27i			0.0292607i
$590$	1.29612e26	−	1.58462e27i	0.00104400	−	0.0127638i
$591$		0			0
$592$	2.59263e28	−	7.65780e28i	0.201540	−	0.595286i
$593$			1.46496e29i			1.11880i	0.828898	+	0.559400i	$0.188968\pi$
$593$			1.46496e29i			1.11880i	−0.828898	+	0.559400i	$0.811032\pi$
$594$		0			0
$595$	−6.62376e27			−0.0488288
$596$	1.91743e29	+	3.15780e28i	1.38878	+	0.228717i
$597$		0			0
$598$	2.00179e28	−	2.44737e29i	0.139977	−	1.71134i
$599$	8.86133e28			0.608859			0.304430	−	0.952535i	$-0.401534\pi$
$599$	8.86133e28			0.608859			0.304430	+	0.952535i	$0.401534\pi$
$600$		0			0
$601$	−2.50826e29			−1.66414			−0.832070	−	0.554670i	$-0.812845\pi$
$601$	−2.50826e29			−1.66414			−0.832070	+	0.554670i	$0.812845\pi$
$602$	6.70433e27	−	8.19665e28i	0.0437112	−	0.534408i
$603$		0			0
$604$	−1.61455e28	+	9.80361e28i	−0.101663	+	0.617303i
$605$	2.52709e28			0.156383
$606$		0			0
$607$		−	2.02859e29i		−	1.21259i	−0.795240	−	0.606295i	$-0.792655\pi$
$607$		−	2.02859e29i		−	1.21259i	0.795240	−	0.606295i	$-0.207345\pi$
$608$	−6.18593e28	−	2.67434e28i	−0.363427	−	0.157119i
$609$		0			0
$610$	−2.23918e27	+	2.73760e28i	−0.0127094	+	0.155384i
$611$			3.44141e29i			1.92001i
$612$		0			0
$613$		−	1.19775e29i		−	0.645699i	−0.946450	−	0.322849i	$-0.895359\pi$
$613$		−	1.19775e29i		−	0.645699i	0.946450	−	0.322849i	$-0.104641\pi$
$614$	−1.66581e29	−	1.36252e28i	−0.882789	−	0.0722065i
$615$		0			0
$616$	1.09517e29	+	2.73626e28i	0.560898	+	0.140139i
$617$			2.02124e29i			1.01771i	0.860853	+	0.508854i	$0.169931\pi$
$617$			2.02124e29i			1.01771i	−0.860853	+	0.508854i	$0.830069\pi$
$618$		0			0
$619$	2.98741e29			1.45393			0.726964	−	0.686676i	$-0.240931\pi$
$619$	2.98741e29			1.45393			0.726964	+	0.686676i	$0.240931\pi$
$620$	2.47040e26	−	1.50004e27i	0.00118210	−	0.00717777i
$621$		0			0
$622$	6.82060e28	+	5.57881e27i	0.315517	+	0.0258073i
$623$	8.04472e28			0.365920
$624$		0			0
$625$	2.20786e29			0.971027
$626$	−2.90717e29	−	2.37788e28i	−1.25730	−	0.102839i
$627$		0			0
$628$	3.77593e28	−	2.29276e29i	0.157924	−	0.958921i
$629$	−2.10944e29			−0.867631
$630$		0			0
$631$		−	2.40188e29i		−	0.955528i	−0.878488	−	0.477764i	$-0.841447\pi$
$631$		−	2.40188e29i		−	0.955528i	0.878488	−	0.477764i	$-0.158553\pi$
$632$	−4.84856e28	+	1.94060e29i	−0.189707	+	0.759290i
$633$		0			0
$634$	−2.52344e29	−	2.06401e28i	−0.955115	−	0.0781223i
$635$		−	2.24031e28i		−	0.0834035i
$636$		0			0
$637$			2.67669e29i			0.964128i
$638$	−1.20805e28	+	1.47694e29i	−0.0428022	+	0.523295i
$639$		0			0
$640$	2.41509e28	+	1.55238e28i	0.0828027	+	0.0532240i
$641$		−	2.96425e29i		−	0.999782i	−0.866088	−	0.499891i	$-0.833373\pi$
$641$		−	2.96425e29i		−	0.999782i	0.866088	−	0.499891i	$-0.166627\pi$
$642$		0			0
$643$	−2.15607e29			−0.703797			−0.351898	−	0.936038i	$-0.614464\pi$
$643$	−2.15607e29			−0.703797			−0.351898	+	0.936038i	$0.614464\pi$
$644$	−2.82004e28	+	1.71235e29i	−0.0905637	+	0.549908i
$645$		0			0
$646$	−1.43345e28	+	1.75252e29i	−0.0445597	+	0.544782i
$647$	1.90384e29			0.582286			0.291143	−	0.956680i	$-0.405964\pi$
$647$	1.90384e29			0.582286			0.291143	+	0.956680i	$0.405964\pi$
$648$		0			0
$649$	7.06967e28			0.209329
$650$	−3.06766e28	+	3.75049e29i	−0.0893752	+	1.09269i
$651$		0			0
$652$	−4.05181e29	−	6.67288e28i	−1.14301	−	0.188241i
$653$	−3.76760e27			−0.0104587			−0.00522933	−	0.999986i	$-0.501665\pi$
$653$	−3.76760e27			−0.0104587			−0.00522933	+	0.999986i	$0.501665\pi$
$654$		0			0
$655$			3.79651e28i			0.102059i
$656$	2.23351e29	−	6.59706e29i	0.590877	−	1.74526i
$657$		0			0
$658$	1.98272e28	−	2.42406e29i	0.0508031	−	0.621114i
$659$		−	5.72298e29i		−	1.44320i	−0.692312	−	0.721598i	$-0.743408\pi$
$659$		−	5.72298e29i		−	1.44320i	0.692312	−	0.721598i	$-0.256592\pi$
$660$		0			0
$661$		−	3.93410e29i		−	0.961015i	−0.876991	−	0.480507i	$-0.840453\pi$
$661$		−	3.93410e29i		−	0.961015i	0.876991	−	0.480507i	$-0.159547\pi$
$662$	1.41279e29	+	1.15557e28i	0.339679	+	0.0277836i
$663$		0			0
$664$	4.22335e28	−	1.69037e29i	0.0983767	−	0.393746i
$665$		−	6.10778e27i		−	0.0140041i
$666$		0			0
$667$	−2.27816e29			−0.506131
$668$	4.98429e29	+	8.20858e28i	1.09006	+	0.179521i
$669$		0			0
$670$	−6.14949e28	−	5.02989e27i	−0.130333	−	0.0106604i
$671$	−1.22136e30			−2.54833
$672$		0			0
$673$	3.90178e29			0.789050			0.394525	−	0.918885i	$-0.370909\pi$
$673$	3.90178e29			0.789050			0.394525	+	0.918885i	$0.370909\pi$
$674$	−4.31817e29	−	3.53199e28i	−0.859748	−	0.0703218i
$675$		0			0
$676$	−1.15336e29	−	1.89946e28i	−0.222600	−	0.0366598i
$677$	−6.71548e28			−0.127613			−0.0638067	−	0.997962i	$-0.520324\pi$
$677$	−6.71548e28			−0.127613			−0.0638067	+	0.997962i	$0.520324\pi$
$678$		0			0
$679$		−	5.67374e28i		−	0.104529i
$680$	1.81575e28	−	7.26743e28i	0.0329392	−	0.131837i
$681$		0			0
$682$	6.73737e28	+	5.51074e27i	0.118510	+	0.00969335i
$683$			5.76744e29i			0.999000i	0.866314	+	0.499500i	$0.166483\pi$
$683$			5.76744e29i			0.999000i	−0.866314	+	0.499500i	$0.833517\pi$
$684$		0			0
$685$			8.13934e28i			0.136722i
$686$	3.31292e28	−	4.05034e29i	0.0548035	−	0.670022i
$687$		0			0
$688$	8.80939e29	+	2.98251e29i	1.41341	+	0.478524i
$689$		−	6.46393e29i		−	1.02140i
$690$		0			0
$691$	−1.04807e30			−1.60646			−0.803232	−	0.595667i	$-0.796888\pi$
$691$	−1.04807e30			−1.60646			−0.803232	+	0.595667i	$0.796888\pi$
$692$	−7.90631e29	−	1.30208e29i	−1.19360	−	0.196573i
$693$		0			0
$694$	8.32792e28	−	1.01816e30i	0.121973	−	1.49122i
$695$	−3.89409e28			−0.0561779
$696$		0			0
$697$	−1.81725e30			−2.54372
$698$	1.94716e28	−	2.38058e29i	0.0268485	−	0.328247i
$699$		0			0
$700$	4.32160e28	−	2.62410e29i	0.0578249	−	0.351116i
$701$	5.52002e29			0.727615			0.363807	−	0.931474i	$-0.381477\pi$
$701$	5.52002e29			0.727615			0.363807	+	0.931474i	$0.381477\pi$
$702$		0			0
$703$		−	1.94512e29i		−	0.248837i
$704$	−6.00432e29	+	1.12659e30i	−0.756747	+	1.41988i
$705$		0			0
$706$	3.68708e28	−	4.50779e29i	0.0451059	−	0.551461i
$707$		−	4.82382e29i		−	0.581417i
$708$		0			0
$709$			9.98932e29i			1.16883i	0.811456	+	0.584414i	$0.198676\pi$
$709$			9.98932e29i			1.16883i	−0.811456	+	0.584414i	$0.801324\pi$
$710$	1.54712e29	+	1.26544e28i	0.178366	+	0.0145892i
$711$		0			0
$712$	−2.20528e29	+	8.82648e29i	−0.246845	+	0.987978i
$713$			1.03923e29i			0.114623i
$714$		0			0
$715$	1.63709e29			0.175331
$716$	−8.37787e28	+	5.08708e29i	−0.0884192	+	0.536886i
$717$		0			0
$718$	7.94725e29	+	6.50034e28i	0.814536	+	0.0666238i
$719$	−2.92611e29			−0.295554			−0.147777	−	0.989021i	$-0.547212\pi$
$719$	−2.92611e29			−0.295554			−0.147777	+	0.989021i	$0.547212\pi$
$720$		0			0
$721$	2.70905e29			0.265764
$722$	8.69243e29	+	7.10985e28i	0.840428	+	0.0687416i
$723$		0			0
$724$	−3.36601e29	+	2.04386e30i	−0.316126	+	1.91954i
$725$	3.49118e29			0.323164
$726$		0			0
$727$		−	1.27358e30i		−	1.14529i	−0.819803	−	0.572645i	$-0.805917\pi$
$727$		−	1.27358e30i		−	1.14529i	0.819803	−	0.572645i	$-0.194083\pi$
$728$	4.35406e29	+	1.08785e29i	0.385936	+	0.0964253i
$729$		0			0
$730$	9.06338e28	+	7.41327e27i	0.0780549	+	0.00638439i
$731$		−	2.42666e30i		−	2.06004i
$732$		0			0
$733$		−	3.50891e28i		−	0.0289454i	−0.999895	−	0.0144727i	$-0.995393\pi$
$733$		−	3.50891e28i		−	0.0289454i	0.999895	−	0.0144727i	$-0.00460697\pi$
$734$	−4.11669e28	+	5.03303e29i	−0.0334765	+	0.409280i
$735$		0			0
$736$	−1.80144e30	−	7.78810e29i	−1.42365	−	0.615481i
$737$		−	2.74354e30i		−	2.13748i
$738$		0			0
$739$	5.61183e29			0.424950			0.212475	−	0.977167i	$-0.431848\pi$
$739$	5.61183e29			0.424950			0.212475	+	0.977167i	$0.431848\pi$
$740$	−1.34653e28	+	8.17623e28i	−0.0100527	+	0.0610408i
$741$		0			0
$742$	−3.72411e28	+	4.55306e29i	−0.0270260	+	0.330417i
$743$	4.81542e29			0.344550			0.172275	−	0.985049i	$-0.444888\pi$
$743$	4.81542e29			0.344550			0.172275	+	0.985049i	$0.444888\pi$
$744$		0			0
$745$	−1.99171e29			−0.138544
$746$	−1.29603e29	+	1.58451e30i	−0.0888906	+	1.08677i
$747$		0			0
$748$	3.28658e30	+	5.41263e29i	2.19168	+	0.360945i
$749$	6.79428e29			0.446770
$750$		0			0
$751$			2.84564e30i			1.81954i	0.415114	+	0.909769i	$0.363742\pi$
$751$			2.84564e30i			1.81954i	−0.415114	+	0.909769i	$0.636258\pi$
$752$	2.60527e30	+	8.82041e29i	1.64273	+	0.556162i
$753$		0			0
$754$	−4.80282e28	+	5.87188e29i	−0.0294508	+	0.360063i
$755$		−	1.01834e29i		−	0.0615815i
$756$		0			0
$757$			1.34966e30i			0.793814i	0.917859	+	0.396907i	$0.129916\pi$
$757$			1.34966e30i			0.793814i	−0.917859	+	0.396907i	$0.870084\pi$
$758$	−1.06437e30	−	8.70588e28i	−0.617400	−	0.0504994i
$759$		0			0
$760$	6.70132e28	+	1.67431e28i	0.0378110	+	0.00944700i
$761$			1.38344e30i			0.769880i	0.922942	+	0.384940i	$0.125778\pi$
$761$			1.38344e30i			0.769880i	−0.922942	+	0.384940i	$0.874222\pi$
$762$		0			0
$763$	−4.90462e29			−0.265520
$764$	2.24386e30	+	3.69538e29i	1.19816	+	0.197324i
$765$		0			0
$766$	5.29821e29	+	4.33360e28i	0.275250	+	0.0225137i
$767$	2.81069e29			0.144033
$768$		0			0
$769$	2.23078e30			1.11232			0.556161	−	0.831074i	$-0.312274\pi$
$769$	2.23078e30			1.11232			0.556161	+	0.831074i	$0.312274\pi$
$770$	−1.15313e29	−	9.43187e27i	−0.0567186	−	0.00463922i
$771$		0			0
$772$	1.61537e30	+	2.66033e29i	0.773196	+	0.127337i
$773$	9.81452e29			0.463430			0.231715	−	0.972784i	$-0.425566\pi$
$773$	9.81452e29			0.463430			0.231715	+	0.972784i	$0.425566\pi$
$774$		0			0
$775$		−	1.59257e29i		−	0.0731865i
$776$	6.22510e29	+	1.55533e29i	0.282227	+	0.0705139i
$777$		0			0
$778$	3.76767e30	+	3.08171e29i	1.66260	+	0.135990i
$779$		−	1.67569e30i		−	0.729541i
$780$		0			0
$781$			6.90234e30i			2.92523i
$782$	−4.17444e29	+	5.10363e30i	−0.174553	+	2.13407i
$783$		0			0
$784$	2.02635e30	+	6.86043e29i	0.824891	+	0.279275i
$785$			2.38159e29i			0.0956610i
$786$		0			0
$787$	−3.24592e30			−1.26941			−0.634706	−	0.772753i	$-0.718879\pi$
$787$	−3.24592e30			−1.26941			−0.634706	+	0.772753i	$0.718879\pi$
$788$	1.36631e30	+	2.25017e29i	0.527260	+	0.0868339i
$789$		0			0
$790$	1.67130e28	−	2.04331e29i	0.00628014	−	0.0767803i
$791$	−4.35258e29			−0.161396
$792$		0			0
$793$	−4.85575e30			−1.75343
$794$	2.65979e28	−	3.25183e29i	0.00947833	−	0.115881i
$795$		0			0
$796$	−3.39158e28	+	2.05938e29i	−0.0117710	+	0.0714743i
$797$	2.66837e30			0.913973			0.456986	−	0.889474i	$-0.348929\pi$
$797$	2.66837e30			0.913973			0.456986	+	0.889474i	$0.348929\pi$
$798$		0			0
$799$		−	7.17655e30i		−	2.39428i
$800$	2.76063e30	+	1.19349e30i	0.908999	+	0.392984i
$801$		0			0
$802$	1.64520e29	−	2.01140e30i	0.0527700	−	0.645160i
$803$			4.04355e30i			1.28012i
$804$		0			0
$805$		−	1.77868e29i		−	0.0548583i
$806$	2.67858e29	+	2.19090e28i	0.0815429	+	0.00666968i
$807$		0			0
$808$	5.29259e30	+	1.32234e30i	1.56982	+	0.392216i
$809$		−	4.96815e30i		−	1.45457i	−0.686334	−	0.727286i	$-0.740781\pi$
$809$		−	4.96815e30i		−	1.45457i	0.686334	−	0.727286i	$-0.259219\pi$
$810$		0			0
$811$	1.25320e30			0.357521			0.178761	−	0.983893i	$-0.442791\pi$
$811$	1.25320e30			0.357521			0.178761	+	0.983893i	$0.442791\pi$
$812$	6.76603e28	−	4.10837e29i	0.0190544	−	0.115699i
$813$		0			0
$814$	−3.67232e30	−	3.00373e29i	−1.00782	−	0.0824336i
$815$	4.20878e29			0.114025
$816$		0			0
$817$	2.23763e30			0.590822
$818$	−2.15638e30	−	1.76378e29i	−0.562103	−	0.0459764i
$819$		0			0
$820$	−1.16002e29	+	7.04369e29i	−0.0294726	+	0.178959i
$821$	−9.53926e29			−0.239283			−0.119641	−	0.992817i	$-0.538174\pi$
$821$	−9.53926e29			−0.239283			−0.119641	+	0.992817i	$0.538174\pi$
$822$		0			0
$823$			3.17566e30i			0.776489i	0.921556	+	0.388245i	$0.126918\pi$
$823$			3.17566e30i			0.776489i	−0.921556	+	0.388245i	$0.873082\pi$
$824$	−7.42625e29	+	2.97231e30i	−0.179281	+	0.717559i
$825$		0			0
$826$	−1.97979e29	−	1.61934e28i	−0.0465939	−	0.00381108i
$827$		−	6.26257e30i		−	1.45527i	−0.685963	−	0.727636i	$-0.740619\pi$
$827$		−	6.26257e30i		−	1.45527i	0.685963	−	0.727636i	$-0.259381\pi$
$828$		0			0
$829$		−	6.71383e29i		−	0.152107i	−0.997104	−	0.0760533i	$-0.975768\pi$
$829$		−	6.71383e29i		−	0.152107i	0.997104	−	0.0760533i	$-0.0242319\pi$
$830$	−1.45579e28	+	1.77983e29i	−0.00325670	+	0.0398161i
$831$		0			0
$832$	−2.38714e30	+	4.47896e30i	−0.520694	+	0.976973i
$833$		−	5.58185e30i		−	1.20228i
$834$		0			0
$835$	−5.17739e29			−0.108743
$836$	−4.99100e29	+	3.03056e30i	−0.103519	+	0.628575i
$837$		0			0
$838$	4.50976e29	−	5.51359e30i	0.0912203	−	1.11525i
$839$	−7.92009e30			−1.58208			−0.791042	−	0.611762i	$-0.790461\pi$
$839$	−7.92009e30			−1.58208			−0.791042	+	0.611762i	$0.790461\pi$
$840$		0			0
$841$	−4.58625e30			−0.893511
$842$	−3.31872e29	+	4.05743e30i	−0.0638548	+	0.780682i
$843$		0			0
$844$	−3.70244e30	−	6.09751e29i	−0.694852	−	0.114434i
$845$	1.19805e29			0.0222064
$846$		0			0
$847$		−	3.15728e30i		−	0.570871i
$848$	−4.89343e30	−	1.65672e30i	−0.873890	−	0.295865i
$849$		0			0
$850$	6.39715e29	−	7.82109e30i	0.111452	−	1.36260i
$851$		−	5.66450e30i		−	0.974767i
$852$		0			0
$853$			9.52144e30i			1.59859i	0.600938	+	0.799296i	$0.294794\pi$
$853$			9.52144e30i			1.59859i	−0.600938	+	0.799296i	$0.705206\pi$
$854$	3.42029e30	+	2.79758e29i	0.567225	+	0.0463954i
$855$		0			0
$856$	−1.86250e30	+	7.45453e30i	−0.301385	+	1.20627i
$857$			8.34978e30i			1.33468i	0.744754	+	0.667339i	$0.232567\pi$
$857$			8.34978e30i			1.33468i	−0.744754	+	0.667339i	$0.767433\pi$
$858$		0			0
$859$	−3.46393e30			−0.540308			−0.270154	−	0.962817i	$-0.587075\pi$
$859$	−3.46393e30			−0.540308			−0.270154	+	0.962817i	$0.587075\pi$
$860$	−9.40578e29	−	1.54903e29i	−0.144931	−	0.0238685i
$861$		0			0
$862$	8.67087e30	+	7.09222e29i	1.30388	+	0.106649i
$863$	−5.50275e30			−0.817460			−0.408730	−	0.912655i	$-0.634028\pi$
$863$	−5.50275e30			−0.817460			−0.408730	+	0.912655i	$0.634028\pi$
$864$		0			0
$865$	8.21261e29			0.119073
$866$	−2.10455e30	−	1.72139e29i	−0.301455	−	0.0246571i
$867$		0			0
$868$	−1.87411e29	−	3.08646e28i	−0.0262022	−	0.00431522i
$869$	9.11605e30			1.25921
$870$		0			0
$871$		−	1.09075e31i		−	1.47073i
$872$	1.34449e30	−	5.38123e30i	0.179116	−	0.716900i
$873$		0			0
$874$	−4.70607e30	−	3.84926e29i	−0.612052	−	0.0500619i
$875$			5.47818e29i			0.0703966i
$876$		0			0
$877$		−	8.33046e30i		−	1.04514i	−0.852597	−	0.522569i	$-0.824974\pi$
$877$		−	8.33046e30i		−	1.04514i	0.852597	−	0.522569i	$-0.175026\pi$
$878$	5.23012e29	−	6.39429e30i	0.0648364	−	0.792683i
$879$		0			0
$880$	4.19589e29	−	1.23933e30i	0.0507874	−	0.150010i
$881$		−	9.27206e30i		−	1.10899i	−0.832186	−	0.554497i	$-0.812911\pi$
$881$		−	9.27206e30i		−	1.10899i	0.832186	−	0.554497i	$-0.187089\pi$
$882$		0			0
$883$	4.07358e28			0.00475761			0.00237880	−	0.999997i	$-0.499243\pi$
$883$	4.07358e28			0.00475761			0.00237880	+	0.999997i	$0.499243\pi$
$884$	1.30664e31	+	2.15190e30i	1.50802	+	0.248355i
$885$		0			0
$886$	1.18841e30	−	1.45294e31i	0.133941	−	1.63754i
$887$	−1.04464e31			−1.16350			−0.581750	−	0.813367i	$-0.697632\pi$
$887$	−1.04464e31			−1.16350			−0.581750	+	0.813367i	$0.697632\pi$
$888$		0			0
$889$	−2.79899e30			−0.304462
$890$	7.60158e28	−	9.29362e29i	0.00817163	−	0.0999056i
$891$		0			0
$892$	−2.61239e30	+	1.58626e31i	−0.274288	+	1.66549i
$893$	6.61751e30			0.686680
$894$		0			0
$895$		−	5.28416e29i		−	0.0535592i
$896$	1.93950e30	−	3.01736e30i	0.194292	−	0.302269i
$897$		0			0
$898$	−1.59776e29	+	1.95341e30i	−0.0156354	+	0.191157i
$899$		−	2.49338e29i		−	0.0241164i
$900$		0			0
$901$			1.34796e31i			1.27370i
$902$	−3.16365e31	−	2.58766e30i	−2.95474	−	0.241679i
$903$		0			0
$904$	1.19316e30	−	4.77555e30i	0.108876	−	0.435768i
$905$		−	2.12304e30i		−	0.191491i
$906$		0			0
$907$	−1.06013e31			−0.934293			−0.467146	−	0.884180i	$-0.654718\pi$
$907$	−1.06013e31			−0.934293			−0.467146	+	0.884180i	$0.654718\pi$
$908$	−1.23818e30	+	7.51826e30i	−0.107865	+	0.654962i
$909$		0			0
$910$	−4.58450e29	−	3.74983e28i	−0.0390263	−	0.00319210i
$911$	−8.91151e30			−0.749908			−0.374954	−	0.927043i	$-0.622342\pi$
$911$	−8.91151e30			−0.749908			−0.374954	+	0.927043i	$0.622342\pi$
$912$		0			0
$913$	−7.94055e30			−0.652992
$914$	−1.22542e31	−	1.00231e30i	−0.996204	−	0.0814831i
$915$		0			0
$916$	1.26545e30	−	7.68387e30i	0.100541	−	0.610488i
$917$	4.74327e30			0.372563
$918$		0			0
$919$		−	2.07064e31i		−	1.58961i	−0.606862	−	0.794807i	$-0.707572\pi$
$919$		−	2.07064e31i		−	1.58961i	0.606862	−	0.794807i	$-0.292428\pi$
$920$	1.95153e30	+	4.87586e29i	0.148116	+	0.0370066i
$921$		0			0
$922$	−1.84715e31	−	1.51085e30i	−1.37034	−	0.112085i
$923$			2.74416e31i			2.01276i
$924$		0			0
$925$			8.68060e30i			0.622388i
$926$	1.23187e29	−	1.50607e30i	0.00873272	−	0.106765i
$927$		0			0
$928$	4.32213e30	+	1.86857e30i	0.299532	+	0.129496i
$929$		−	3.09174e30i		−	0.211855i	−0.994374	−	0.105927i	$-0.966219\pi$
$929$		−	3.09174e30i		−	0.211855i	0.994374	−	0.105927i	$-0.0337811\pi$
$930$		0			0
$931$	5.14704e30			0.344815
$932$	2.95502e30	−	1.79431e31i	0.195746	−	1.18858i
$933$		0			0
$934$	1.96269e29	−	2.39957e30i	0.0127119	−	0.155414i
$935$	−3.41390e30			−0.218640
$936$		0			0
$937$	2.78477e31			1.74391			0.871954	−	0.489587i	$-0.162853\pi$
$937$	2.78477e31			1.74391			0.871954	+	0.489587i	$0.162853\pi$
$938$	−6.28422e29	+	7.68302e30i	−0.0389154	+	0.475775i
$939$		0			0
$940$	−2.78165e30	−	4.58106e29i	−0.168445	−	0.0277411i
$941$	−2.09581e31			−1.25505			−0.627526	−	0.778596i	$-0.715932\pi$
$941$	−2.09581e31			−1.25505			−0.627526	+	0.778596i	$0.715932\pi$
$942$		0			0
$943$		−	4.87987e31i		−	2.85782i
$944$	7.20386e29	−	2.12779e30i	0.0417214	−	0.123232i
$945$		0			0
$946$	3.45543e30	−	4.22457e31i	0.195725	−	2.39291i
$947$		−	7.31568e30i		−	0.409807i	−0.978782	−	0.204904i	$-0.934312\pi$
$947$		−	7.31568e30i		−	0.409807i	0.978782	−	0.204904i	$-0.0656881\pi$
$948$		0			0
$949$			1.60759e31i			0.880808i
$950$	7.21185e30	+	5.89883e29i	0.390795	+	0.0319645i
$951$		0			0
$952$	−9.07975e30	−	2.26856e30i	−0.481267	−	0.120244i
$953$			3.20223e31i			1.67871i	0.543580	+	0.839357i	$0.317068\pi$
$953$			3.20223e31i			1.67871i	−0.543580	+	0.839357i	$0.682932\pi$
$954$		0			0
$955$	−2.33079e30			−0.119527
$956$	−1.93798e30	−	3.19164e29i	−0.0982974	−	0.0161885i
$957$		0			0
$958$	−1.29790e31	−	1.06160e30i	−0.644026	−	0.0526772i
$959$	1.01691e31			0.499099
$960$		0			0
$961$	2.07118e31			0.994538
$962$	−1.46001e31	−	1.19419e30i	−0.693452	−	0.0567199i
$963$		0			0
$964$	1.03385e31	+	1.70264e30i	0.480452	+	0.0791252i
$965$	−1.67795e30			−0.0771332
$966$		0			0
$967$		−	7.18490e30i		−	0.323179i	−0.986858	−	0.161589i	$-0.948338\pi$
$967$		−	7.18490e30i		−	0.323179i	0.986858	−	0.161589i	$-0.0516620\pi$
$968$	3.46410e31	+	8.65499e30i	1.54134	+	0.385101i
$969$		0			0
$970$	−6.55456e29	−	5.36121e28i	−0.0285391	−	0.00233432i
$971$			2.50153e31i			1.07747i	0.842476	+	0.538734i	$0.181097\pi$
$971$			2.50153e31i			1.07747i	−0.842476	+	0.538734i	$0.818903\pi$
$972$		0			0
$973$			4.86518e30i			0.205076i
$974$	−8.83850e29	+	1.08059e31i	−0.0368561	+	0.450599i
$975$		0			0
$976$	−1.24454e31	+	3.67598e31i	−0.507909	+	1.50020i
$977$			3.65570e31i			1.47597i	0.674818	+	0.737985i	$0.264222\pi$
$977$			3.65570e31i			1.47597i	−0.674818	+	0.737985i	$0.735778\pi$
$978$		0			0
$979$	4.14627e31			1.63847
$980$	−2.16354e30	−	3.56311e29i	−0.0845844	−	0.0139301i
$981$		0			0
$982$	2.06197e30	−	2.52094e31i	0.0789063	−	0.964701i
$983$	−3.77934e31			−1.43088			−0.715442	−	0.698672i	$-0.753775\pi$
$983$	−3.77934e31			−1.43088			−0.715442	+	0.698672i	$0.753775\pi$
$984$		0			0
$985$	−1.41925e30			−0.0525989
$986$	1.00156e30	−	1.22449e31i	0.0367256	−	0.449003i
$987$		0			0
$988$	−1.98427e30	+	1.20486e31i	−0.0712284	+	0.432502i
$989$	6.51633e31			2.31442
$990$		0			0
$991$		−	1.81645e31i		−	0.631613i	−0.948824	−	0.315806i	$-0.897725\pi$
$991$		−	1.81645e31i		−	0.631613i	0.948824	−	0.315806i	$-0.102275\pi$
$992$	8.52385e29	−	1.97162e30i	0.0293267	−	0.0678346i
$993$		0			0
$994$	1.58102e30	−	1.93293e31i	0.0532573	−	0.651118i
$995$		−	2.13917e29i		−	0.00713021i
$996$		0			0
$997$			2.71498e31i			0.886068i	0.896505	+	0.443034i	$0.146098\pi$
$997$			2.71498e31i			0.886068i	−0.896505	+	0.443034i	$0.853902\pi$
$998$	−4.38568e31	−	3.58721e30i	−1.41634	−	0.115847i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	72.22.f.a.35.1	✓	84
3.2	odd	2	inner	72.22.f.a.35.84	yes	84
8.3	odd	2	inner	72.22.f.a.35.83	yes	84
24.11	even	2	inner	72.22.f.a.35.2	yes	84

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
72.22.f.a.35.1	✓	84	1.1	even	1	trivial
72.22.f.a.35.2	yes	84	24.11	even	2	inner
72.22.f.a.35.83	yes	84	8.3	odd	2	inner
72.22.f.a.35.84	yes	84	3.2	odd	2	inner

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)

\(f(q)\)	\(=\)	\(q+(-1443.33 - 118.056i) q^{2} +(2.06928e6 + 340787. i) q^{4} -2.14944e6 q^{5} +2.68546e8i q^{7} +(-2.94643e9 - 7.36160e8i) q^{8} +O(q^{10})\)	\(q+(-1443.33 - 118.056i) q^{2} +(2.06928e6 + 340787. i) q^{4} -2.14944e6 q^{5} +2.68546e8i q^{7} +(-2.94643e9 - 7.36160e8i) q^{8} +(3.10237e9 + 2.53754e8i) q^{10} +1.38410e11i q^{11} +5.50274e11i q^{13} +(3.17034e10 - 3.87602e11i) q^{14} +(4.16577e12 + 1.41037e12i) q^{16} -1.14752e13i q^{17} +1.05813e13 q^{19} +(-4.44780e12 - 7.32503e11i) q^{20} +(1.63400e13 - 1.99771e14i) q^{22} +3.08144e14 q^{23} -4.72217e14 q^{25} +(6.49629e13 - 7.94230e14i) q^{26} +(-9.15172e13 + 5.55697e14i) q^{28} -7.39318e14 q^{29} +3.37254e14i q^{31} +(-5.84611e15 - 2.52742e15i) q^{32} +(-1.35471e15 + 1.65625e16i) q^{34} -5.77225e14i q^{35} -1.83826e16i q^{37} +(-1.52723e16 - 1.24918e15i) q^{38} +(6.33318e15 + 1.58233e15i) q^{40} -1.58363e17i q^{41} +2.11471e17 q^{43} +(-4.71682e16 + 2.86408e17i) q^{44} +(-4.44754e17 - 3.63781e16i) q^{46} +6.25398e17 q^{47} +4.86429e17 q^{49} +(6.81567e17 + 5.57478e16i) q^{50} +(-1.87527e17 + 1.13867e18i) q^{52} -1.17467e18 q^{53} -2.97504e17i q^{55} +(1.97693e17 - 7.91253e17i) q^{56} +(1.06708e18 + 8.72805e16i) q^{58} -5.10779e17i q^{59} +8.82423e18i q^{61} +(3.98147e16 - 4.86771e17i) q^{62} +(8.13951e18 + 4.33808e18i) q^{64} -1.18278e18i q^{65} -1.98219e19 q^{67} +(3.91059e18 - 2.37453e19i) q^{68} +(-6.81446e16 + 8.33129e17i) q^{70} +4.98690e19 q^{71} +2.92144e19 q^{73} +(-2.17017e18 + 2.65323e19i) q^{74} +(2.18956e19 + 3.60597e18i) q^{76} -3.71694e19 q^{77} -6.58629e19i q^{79} +(-8.95410e18 - 3.03151e18i) q^{80} +(-1.86957e19 + 2.28571e20i) q^{82} +5.73700e19i q^{83} +2.46652e19i q^{85} +(-3.05223e20 - 2.49653e19i) q^{86} +(1.01892e20 - 4.07814e20i) q^{88} -2.99565e20i q^{89} -1.47774e20 q^{91} +(6.37635e20 + 1.05011e20i) q^{92} +(-9.02659e20 - 7.38317e19i) q^{94} -2.27439e19 q^{95} -2.11276e20 q^{97} +(-7.02079e20 - 5.74256e19i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 84 q + 2424084 q^{4}+O(q^{10}) \) 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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