LMFDB - Embedded newform 64.14.e.a.17.11

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [64,14,Mod(17,64)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(64, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([0, 3]))

N = Newforms(chi, 14, names="a")

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

chi := DirichletCharacter("64.17");

S:= CuspForms(chi, 14);

N := Newforms(S);

Level:	$ N $	$=$	$ 64 = 2^{6} $
Weight:	$ k $	$=$	$ 14 $
Character orbit:	$[\chi]$	$=$	64.e (of order $4$, degree $2$, not 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:	$68.6277945292$
Analytic rank:	$0$
Dimension:	$50$
Relative dimension:	$25$ over $\Q(i)$
Twist minimal:	no (minimal twist has level 16)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			17.11
Character	$\chi$	$=$	64.17
Dual form			64.14.e.a.49.11

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-293.446 - 293.446i) q^{3} +(22716.6 - 22716.6i) q^{5} -343566. i q^{7} -1.42210e6i q^{9} +O(q^{10})$	\(q+(-293.446 - 293.446i) q^{3} +(22716.6 - 22716.6i) q^{5} -343566. i q^{7} -1.42210e6i q^{9} +(7.55337e6 - 7.55337e6i) q^{11} +(-6.02369e6 - 6.02369e6i) q^{13} -1.33322e7 q^{15} +1.22712e8 q^{17} +(-1.66266e8 - 1.66266e8i) q^{19} +(-1.00818e8 + 1.00818e8i) q^{21} -7.77189e8i q^{23} +1.88614e8i q^{25} +(-8.85157e8 + 8.85157e8i) q^{27} +(3.04458e9 + 3.04458e9i) q^{29} +6.68256e9 q^{31} -4.43301e9 q^{33} +(-7.80465e9 - 7.80465e9i) q^{35} +(7.06457e9 - 7.06457e9i) q^{37} +3.53525e9i q^{39} +4.77022e10i q^{41} +(3.20320e10 - 3.20320e10i) q^{43} +(-3.23053e10 - 3.23053e10i) q^{45} -4.56238e10 q^{47} -2.11484e10 q^{49} +(-3.60092e10 - 3.60092e10i) q^{51} +(-5.36351e10 + 5.36351e10i) q^{53} -3.43174e11i q^{55} +9.75800e10i q^{57} +(-3.79276e10 + 3.79276e10i) q^{59} +(2.48611e11 + 2.48611e11i) q^{61} -4.88586e11 q^{63} -2.73676e11 q^{65} +(-6.55193e10 - 6.55193e10i) q^{67} +(-2.28063e11 + 2.28063e11i) q^{69} +4.07717e11i q^{71} -1.83359e12i q^{73} +(5.53481e10 - 5.53481e10i) q^{75} +(-2.59508e12 - 2.59508e12i) q^{77} -8.45785e11 q^{79} -1.74780e12 q^{81} +(2.16418e11 + 2.16418e11i) q^{83} +(2.78760e12 - 2.78760e12i) q^{85} -1.78684e12i q^{87} -2.96051e12i q^{89} +(-2.06953e12 + 2.06953e12i) q^{91} +(-1.96097e12 - 1.96097e12i) q^{93} -7.55399e12 q^{95} -6.69684e12 q^{97} +(-1.07417e13 - 1.07417e13i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 50 q + 2 q^{3} - 2 q^{5}+O(q^{10}) $ 50 * q + 2 * q^3 - 2 * q^5	$ 50 q + 2 q^{3} - 2 q^{5} + 4723998 q^{11} - 2 q^{13} - 91124996 q^{15} - 4 q^{17} - 422008902 q^{19} + 3188644 q^{21} + 2068699784 q^{27} - 3661663834 q^{29} + 10650044176 q^{31} - 4 q^{33} - 7767977276 q^{35} + 21527986470 q^{37} + 18577860182 q^{43} + 2438217602 q^{45} - 215584306576 q^{47} - 525968913642 q^{49} + 551664571452 q^{51} + 223019793366 q^{53} - 1167423209882 q^{59} + 81543039150 q^{61} + 862914002556 q^{63} - 27850095516 q^{65} - 1390089097910 q^{67} - 168685276844 q^{69} + 1675683188954 q^{75} - 2147852144860 q^{77} - 8517123343488 q^{79} - 9602604240358 q^{81} - 2192965629438 q^{83} + 2809965843748 q^{85} - 3291182399236 q^{91} + 3412032366928 q^{93} - 7322122332660 q^{95} - 4 q^{97} - 19363874529854 q^{99}+O(q^{100}) $ 50 * q + 2 * q^3 - 2 * q^5 + 4723998 * q^11 - 2 * q^13 - 91124996 * q^15 - 4 * q^17 - 422008902 * q^19 + 3188644 * q^21 + 2068699784 * q^27 - 3661663834 * q^29 + 10650044176 * q^31 - 4 * q^33 - 7767977276 * q^35 + 21527986470 * q^37 + 18577860182 * q^43 + 2438217602 * q^45 - 215584306576 * q^47 - 525968913642 * q^49 + 551664571452 * q^51 + 223019793366 * q^53 - 1167423209882 * q^59 + 81543039150 * q^61 + 862914002556 * q^63 - 27850095516 * q^65 - 1390089097910 * q^67 - 168685276844 * q^69 + 1675683188954 * q^75 - 2147852144860 * q^77 - 8517123343488 * q^79 - 9602604240358 * q^81 - 2192965629438 * q^83 + 2809965843748 * q^85 - 3291182399236 * q^91 + 3412032366928 * q^93 - 7322122332660 * q^95 - 4 * q^97 - 19363874529854 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/64\mathbb{Z}\right)^\times$.

$n$	$5$	$63$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$1$

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 $

$2$		0			0
$2$		0			0
$3$	−293.446	−	293.446i	−0.232402	−	0.232402i	0.581293	−	0.813695i	$-0.302547\pi$
$3$	−293.446	−	293.446i	−0.232402	−	0.232402i	−0.813695	+	0.581293i	$0.802547\pi$
$4$		0			0
$5$	22716.6	−	22716.6i	0.650187	−	0.650187i	−0.302851	−	0.953038i	$-0.597938\pi$
$5$	22716.6	−	22716.6i	0.650187	−	0.650187i	0.953038	+	0.302851i	$0.0979384\pi$
$6$		0			0
$7$		−	343566.i		−	1.10375i	−0.833925	−	0.551877i	$-0.813912\pi$
$7$		−	343566.i		−	1.10375i	0.833925	−	0.551877i	$-0.186088\pi$
$8$		0			0
$9$		−	1.42210e6i		−	0.891979i
$10$		0			0
$11$	7.55337e6	−	7.55337e6i	1.28555	−	1.28555i	0.348085	−	0.937463i	$-0.386832\pi$
$11$	7.55337e6	−	7.55337e6i	1.28555	−	1.28555i	0.937463	−	0.348085i	$-0.113168\pi$
$12$		0			0
$13$	−6.02369e6	−	6.02369e6i	−0.346123	−	0.346123i	0.512540	−	0.858663i	$-0.328705\pi$
$13$	−6.02369e6	−	6.02369e6i	−0.346123	−	0.346123i	−0.858663	+	0.512540i	$0.828705\pi$
$14$		0			0
$15$	−1.33322e7			−0.302209
$16$		0			0
$17$	1.22712e8			1.23302			0.616508	−	0.787349i	$-0.288547\pi$
$17$	1.22712e8			1.23302			0.616508	+	0.787349i	$0.288547\pi$
$18$		0			0
$19$	−1.66266e8	−	1.66266e8i	−0.810783	−	0.810783i	0.173968	−	0.984751i	$-0.444341\pi$
$19$	−1.66266e8	−	1.66266e8i	−0.810783	−	0.810783i	−0.984751	+	0.173968i	$0.944341\pi$
$20$		0			0
$21$	−1.00818e8	+	1.00818e8i	−0.256514	+	0.256514i
$22$		0			0
$23$		−	7.77189e8i		−	1.09470i	−0.836904	−	0.547350i	$-0.815637\pi$
$23$		−	7.77189e8i		−	1.09470i	0.836904	−	0.547350i	$-0.184363\pi$
$24$		0			0
$25$			1.88614e8i			0.154513i
$26$		0			0
$27$	−8.85157e8	+	8.85157e8i	−0.439699	+	0.439699i
$28$		0			0
$29$	3.04458e9	+	3.04458e9i	0.950476	+	0.950476i	0.998830	−	0.0483544i	$-0.0153977\pi$
$29$	3.04458e9	+	3.04458e9i	0.950476	+	0.950476i	−0.0483544	+	0.998830i	$0.515398\pi$
$30$		0			0
$31$	6.68256e9			1.35236			0.676180	−	0.736737i	$-0.263634\pi$
$31$	6.68256e9			1.35236			0.676180	+	0.736737i	$0.263634\pi$
$32$		0			0
$33$	−4.43301e9			−0.597527
$34$		0			0
$35$	−7.80465e9	−	7.80465e9i	−0.717647	−	0.717647i
$36$		0			0
$37$	7.06457e9	−	7.06457e9i	0.452663	−	0.452663i	−0.443575	−	0.896237i	$-0.646290\pi$
$37$	7.06457e9	−	7.06457e9i	0.452663	−	0.452663i	0.896237	+	0.443575i	$0.146290\pi$
$38$		0			0
$39$			3.53525e9i			0.160879i
$40$		0			0
$41$			4.77022e10i			1.56835i	0.620538	+	0.784176i	$0.286914\pi$
$41$			4.77022e10i			1.56835i	−0.620538	+	0.784176i	$0.713086\pi$
$42$		0			0
$43$	3.20320e10	−	3.20320e10i	0.772749	−	0.772749i	−0.205837	−	0.978586i	$-0.565992\pi$
$43$	3.20320e10	−	3.20320e10i	0.772749	−	0.772749i	0.978586	+	0.205837i	$0.0659916\pi$
$44$		0			0
$45$	−3.23053e10	−	3.23053e10i	−0.579953	−	0.579953i
$46$		0			0
$47$	−4.56238e10			−0.617384			−0.308692	−	0.951162i	$-0.599891\pi$
$47$	−4.56238e10			−0.617384			−0.308692	+	0.951162i	$0.599891\pi$
$48$		0			0
$49$	−2.11484e10			−0.218274
$50$		0			0
$51$	−3.60092e10	−	3.60092e10i	−0.286555	−	0.286555i
$52$		0			0
$53$	−5.36351e10	+	5.36351e10i	−0.332396	+	0.332396i	−0.853496	−	0.521100i	$-0.825522\pi$
$53$	−5.36351e10	+	5.36351e10i	−0.332396	+	0.332396i	0.521100	+	0.853496i	$0.325522\pi$
$54$		0			0
$55$		−	3.43174e11i		−	1.67169i
$56$		0			0
$57$			9.75800e10i			0.376855i
$58$		0			0
$59$	−3.79276e10	+	3.79276e10i	−0.117062	+	0.117062i	−0.763211	−	0.646149i	$-0.776378\pi$
$59$	−3.79276e10	+	3.79276e10i	−0.117062	+	0.117062i	0.646149	+	0.763211i	$0.276378\pi$
$60$		0			0
$61$	2.48611e11	+	2.48611e11i	0.617840	+	0.617840i	0.944977	−	0.327137i	$-0.106084\pi$
$61$	2.48611e11	+	2.48611e11i	0.617840	+	0.617840i	−0.327137	+	0.944977i	$0.606084\pi$
$62$		0			0
$63$	−4.88586e11			−0.984526
$64$		0			0
$65$	−2.73676e11			−0.450090
$66$		0			0
$67$	−6.55193e10	−	6.55193e10i	−0.0884878	−	0.0884878i	0.661477	−	0.749965i	$-0.269930\pi$
$67$	−6.55193e10	−	6.55193e10i	−0.0884878	−	0.0884878i	−0.749965	+	0.661477i	$0.769930\pi$
$68$		0			0
$69$	−2.28063e11	+	2.28063e11i	−0.254410	+	0.254410i
$70$		0			0
$71$			4.07717e11i			0.377728i	0.982003	+	0.188864i	$0.0604806\pi$
$71$			4.07717e11i			0.377728i	−0.982003	+	0.188864i	$0.939519\pi$
$72$		0			0
$73$		−	1.83359e12i		−	1.41809i	−0.705163	−	0.709046i	$-0.749126\pi$
$73$		−	1.83359e12i		−	1.41809i	0.705163	−	0.709046i	$-0.250874\pi$
$74$		0			0
$75$	5.53481e10	−	5.53481e10i	0.0359091	−	0.0359091i
$76$		0			0
$77$	−2.59508e12	−	2.59508e12i	−1.41893	−	1.41893i
$78$		0			0
$79$	−8.45785e11			−0.391457			−0.195728	−	0.980658i	$-0.562707\pi$
$79$	−8.45785e11			−0.391457			−0.195728	+	0.980658i	$0.562707\pi$
$80$		0			0
$81$	−1.74780e12			−0.687605
$82$		0			0
$83$	2.16418e11	+	2.16418e11i	0.0726583	+	0.0726583i	0.742502	−	0.669844i	$-0.233639\pi$
$83$	2.16418e11	+	2.16418e11i	0.0726583	+	0.0726583i	−0.669844	+	0.742502i	$0.733639\pi$
$84$		0			0
$85$	2.78760e12	−	2.78760e12i	0.801691	−	0.801691i
$86$		0			0
$87$		−	1.78684e12i		−	0.441785i
$88$		0			0
$89$		−	2.96051e12i		−	0.631440i	−0.948852	−	0.315720i	$-0.897754\pi$
$89$		−	2.96051e12i		−	0.631440i	0.948852	−	0.315720i	$-0.102246\pi$
$90$		0			0
$91$	−2.06953e12	+	2.06953e12i	−0.382035	+	0.382035i
$92$		0			0
$93$	−1.96097e12	−	1.96097e12i	−0.314291	−	0.314291i
$94$		0			0
$95$	−7.55399e12			−1.05432
$96$		0			0
$97$	−6.69684e12			−0.816307			−0.408154	−	0.912913i	$-0.633827\pi$
$97$	−6.69684e12			−0.816307			−0.408154	+	0.912913i	$0.633827\pi$
$98$		0			0
$99$	−1.07417e13	−	1.07417e13i	−1.14668	−	1.14668i
$100$		0			0
$101$	−7.31992e12	+	7.31992e12i	−0.686147	+	0.686147i	−0.961378	−	0.275231i	$-0.911246\pi$
$101$	−7.31992e12	+	7.31992e12i	−0.686147	+	0.686147i	0.275231	+	0.961378i	$0.411246\pi$
$102$		0			0
$103$			2.97460e12i			0.245463i	0.992440	+	0.122732i	$0.0391654\pi$
$103$			2.97460e12i			0.245463i	−0.992440	+	0.122732i	$0.960835\pi$
$104$		0			0
$105$			4.58048e12i			0.333565i
$106$		0			0
$107$	5.12568e12	−	5.12568e12i	0.330185	−	0.330185i	−0.522472	−	0.852657i	$-0.674990\pi$
$107$	5.12568e12	−	5.12568e12i	0.330185	−	0.330185i	0.852657	+	0.522472i	$0.174990\pi$
$108$		0			0
$109$	−3.50459e12	−	3.50459e12i	−0.200154	−	0.200154i	0.599912	−	0.800066i	$-0.295202\pi$
$109$	−3.50459e12	−	3.50459e12i	−0.200154	−	0.200154i	−0.800066	+	0.599912i	$0.795202\pi$
$110$		0			0
$111$	−4.14614e12			−0.210399
$112$		0			0
$113$	−7.44539e12			−0.336417			−0.168208	−	0.985751i	$-0.553798\pi$
$113$	−7.44539e12			−0.336417			−0.168208	+	0.985751i	$0.553798\pi$
$114$		0			0
$115$	−1.76551e13	−	1.76551e13i	−0.711761	−	0.711761i
$116$		0			0
$117$	−8.56631e12	+	8.56631e12i	−0.308735	+	0.308735i
$118$		0			0
$119$		−	4.21596e13i		−	1.36095i
$120$		0			0
$121$		−	7.95841e13i		−	2.30527i
$122$		0			0
$123$	1.39980e13	−	1.39980e13i	0.364488	−	0.364488i
$124$		0			0
$125$	3.20149e13	+	3.20149e13i	0.750650	+	0.750650i
$126$		0			0
$127$	−3.24526e13			−0.686317			−0.343159	−	0.939277i	$-0.611497\pi$
$127$	−3.24526e13			−0.686317			−0.343159	+	0.939277i	$0.611497\pi$
$128$		0			0
$129$	−1.87993e13			−0.359177
$130$		0			0
$131$	7.12234e13	+	7.12234e13i	1.23129	+	1.23129i	0.963470	+	0.267816i	$0.0863020\pi$
$131$	7.12234e13	+	7.12234e13i	1.23129	+	1.23129i	0.267816	+	0.963470i	$0.413698\pi$
$132$		0			0
$133$	−5.71233e13	+	5.71233e13i	−0.894906	+	0.894906i
$134$		0			0
$135$			4.02155e13i			0.571774i
$136$		0			0
$137$			1.01011e14i			1.30523i	0.757691	+	0.652613i	$0.226327\pi$
$137$			1.01011e14i			1.30523i	−0.757691	+	0.652613i	$0.773673\pi$
$138$		0			0
$139$	3.19946e13	−	3.19946e13i	0.376254	−	0.376254i	−0.493495	−	0.869749i	$-0.664281\pi$
$139$	3.19946e13	−	3.19946e13i	0.376254	−	0.376254i	0.869749	+	0.493495i	$0.164281\pi$
$140$		0			0
$141$	1.33881e13	+	1.33881e13i	0.143481	+	0.143481i
$142$		0			0
$143$	−9.09984e13			−0.889917
$144$		0			0
$145$	1.38325e14			1.23597
$146$		0			0
$147$	6.20589e12	+	6.20589e12i	0.0507273	+	0.0507273i
$148$		0			0
$149$	1.44351e14	−	1.44351e14i	1.08071	−	1.08071i	0.0842647	−	0.996443i	$-0.473146\pi$
$149$	1.44351e14	−	1.44351e14i	1.08071	−	1.08071i	0.996443	−	0.0842647i	$-0.0268541\pi$
$150$		0			0
$151$			1.60244e14i			1.10010i	0.835132	+	0.550050i	$0.185391\pi$
$151$			1.60244e14i			1.10010i	−0.835132	+	0.550050i	$0.814609\pi$
$152$		0			0
$153$		−	1.74509e14i		−	1.09982i
$154$		0			0
$155$	1.51805e14	−	1.51805e14i	0.879287	−	0.879287i
$156$		0			0
$157$	1.47780e14	+	1.47780e14i	0.787529	+	0.787529i	0.981089	−	0.193560i	$-0.0620033\pi$
$157$	1.47780e14	+	1.47780e14i	0.787529	+	0.787529i	−0.193560	+	0.981089i	$0.562003\pi$
$158$		0			0
$159$	3.14780e13			0.154499
$160$		0			0
$161$	−2.67015e14			−1.20828
$162$		0			0
$163$	2.03576e14	+	2.03576e14i	0.850174	+	0.850174i	0.990154	−	0.139980i	$-0.0447039\pi$
$163$	2.03576e14	+	2.03576e14i	0.850174	+	0.850174i	−0.139980	+	0.990154i	$0.544704\pi$
$164$		0			0
$165$	−1.00703e14	+	1.00703e14i	−0.388505	+	0.388505i
$166$		0			0
$167$			2.34851e14i			0.837789i	0.908035	+	0.418895i	$0.137582\pi$
$167$			2.34851e14i			0.837789i	−0.908035	+	0.418895i	$0.862418\pi$
$168$		0			0
$169$		−	2.30305e14i		−	0.760397i
$170$		0			0
$171$	−2.36447e14	+	2.36447e14i	−0.723202	+	0.723202i
$172$		0			0
$173$	3.61694e14	+	3.61694e14i	1.02575	+	1.02575i	0.999660	+	0.0260912i	$0.00830603\pi$
$173$	3.61694e14	+	3.61694e14i	1.02575	+	1.02575i	0.0260912	+	0.999660i	$0.491694\pi$
$174$		0			0
$175$	6.48014e13			0.170544
$176$		0			0
$177$	2.22594e13			0.0544110
$178$		0			0
$179$	4.19323e14	+	4.19323e14i	0.952804	+	0.952804i	0.998935	−	0.0461313i	$-0.0146893\pi$
$179$	4.19323e14	+	4.19323e14i	0.952804	+	0.952804i	−0.0461313	+	0.998935i	$0.514689\pi$
$180$		0			0
$181$	−1.58212e14	+	1.58212e14i	−0.334447	+	0.334447i	−0.854273	−	0.519825i	$-0.825997\pi$
$181$	−1.58212e14	+	1.58212e14i	−0.334447	+	0.334447i	0.519825	+	0.854273i	$0.325997\pi$
$182$		0			0
$183$		−	1.45907e14i		−	0.287174i
$184$		0			0
$185$		−	3.20966e14i		−	0.588631i
$186$		0			0
$187$	9.26888e14	−	9.26888e14i	1.58510	−	1.58510i
$188$		0			0
$189$	3.04109e14	+	3.04109e14i	0.485320	+	0.485320i
$190$		0			0
$191$	−1.18737e15			−1.76958			−0.884788	−	0.465994i	$-0.845697\pi$
$191$	−1.18737e15			−1.76958			−0.884788	+	0.465994i	$0.845697\pi$
$192$		0			0
$193$	1.25166e15			1.74326			0.871632	−	0.490160i	$-0.163062\pi$
$193$	1.25166e15			1.74326			0.871632	+	0.490160i	$0.163062\pi$
$194$		0			0
$195$	8.03090e13	+	8.03090e13i	0.104602	+	0.104602i
$196$		0			0
$197$	−8.34124e14	+	8.34124e14i	−1.01672	+	1.01672i	−0.0168587	+	0.999858i	$0.505367\pi$
$197$	−8.34124e14	+	8.34124e14i	−1.01672	+	1.01672i	−0.999858	+	0.0168587i	$0.994633\pi$
$198$		0			0
$199$			4.02808e14i			0.459783i	0.973216	+	0.229892i	$0.0738371\pi$
$199$			4.02808e14i			0.459783i	−0.973216	+	0.229892i	$0.926163\pi$
$200$		0			0
$201$			3.84527e13i			0.0411294i
$202$		0			0
$203$	1.04601e15	−	1.04601e15i	1.04909	−	1.04909i
$204$		0			0
$205$	1.08363e15	+	1.08363e15i	1.01972	+	1.01972i
$206$		0			0
$207$	−1.10524e15			−0.976450
$208$		0			0
$209$	−2.51174e15			−2.08460
$210$		0			0
$211$	−3.89582e14	−	3.89582e14i	−0.303923	−	0.303923i	0.538624	−	0.842546i	$-0.318944\pi$
$211$	−3.89582e14	−	3.89582e14i	−0.303923	−	0.303923i	−0.842546	+	0.538624i	$0.818944\pi$
$212$		0			0
$213$	1.19643e14	−	1.19643e14i	0.0877847	−	0.0877847i
$214$		0			0
$215$		−	1.45532e15i		−	1.00486i
$216$		0			0
$217$		−	2.29590e15i		−	1.49267i
$218$		0			0
$219$	−5.38060e14	+	5.38060e14i	−0.329567	+	0.329567i
$220$		0			0
$221$	−7.39178e14	−	7.39178e14i	−0.426776	−	0.426776i
$222$		0			0
$223$	−2.65268e14			−0.144445			−0.0722226	−	0.997389i	$-0.523009\pi$
$223$	−2.65268e14			−0.144445			−0.0722226	+	0.997389i	$0.523009\pi$
$224$		0			0
$225$	2.68229e14			0.137822
$226$		0			0
$227$	−1.16656e15	−	1.16656e15i	−0.565899	−	0.565899i	0.365078	−	0.930977i	$-0.381042\pi$
$227$	−1.16656e15	−	1.16656e15i	−0.565899	−	0.565899i	−0.930977	+	0.365078i	$0.881042\pi$
$228$		0			0
$229$	−5.57443e14	+	5.57443e14i	−0.255429	+	0.255429i	−0.823192	−	0.567763i	$-0.807809\pi$
$229$	−5.57443e14	+	5.57443e14i	−0.255429	+	0.255429i	0.567763	+	0.823192i	$0.307809\pi$
$230$		0			0
$231$			1.52303e15i			0.659523i
$232$		0			0
$233$		−	3.13653e15i		−	1.28421i	−0.766617	−	0.642105i	$-0.778061\pi$
$233$		−	3.13653e15i		−	1.28421i	0.766617	−	0.642105i	$-0.221939\pi$
$234$		0			0
$235$	−1.03642e15	+	1.03642e15i	−0.401415	+	0.401415i
$236$		0			0
$237$	2.48192e14	+	2.48192e14i	0.0909752	+	0.0909752i
$238$		0			0
$239$	−1.62464e15			−0.563861			−0.281930	−	0.959435i	$-0.590975\pi$
$239$	−1.62464e15			−0.563861			−0.281930	+	0.959435i	$0.590975\pi$
$240$		0			0
$241$	−3.02627e15			−0.994938			−0.497469	−	0.867482i	$-0.665737\pi$
$241$	−3.02627e15			−0.994938			−0.497469	+	0.867482i	$0.665737\pi$
$242$		0			0
$243$	1.92411e15	+	1.92411e15i	0.599500	+	0.599500i
$244$		0			0
$245$	−4.80419e14	+	4.80419e14i	−0.141919	+	0.141919i
$246$		0			0
$247$			2.00307e15i			0.561262i
$248$		0			0
$249$		−	1.27014e14i		−	0.0337718i
$250$		0			0
$251$	1.92499e15	−	1.92499e15i	0.485902	−	0.485902i	−0.421108	−	0.907010i	$-0.638359\pi$
$251$	1.92499e15	−	1.92499e15i	0.485902	−	0.485902i	0.907010	+	0.421108i	$0.138359\pi$
$252$		0			0
$253$	−5.87039e15	−	5.87039e15i	−1.40729	−	1.40729i
$254$		0			0
$255$	−1.63602e15			−0.372629
$256$		0			0
$257$	1.85161e14			0.0400852			0.0200426	−	0.999799i	$-0.493620\pi$
$257$	1.85161e14			0.0400852			0.0200426	+	0.999799i	$0.493620\pi$
$258$		0			0
$259$	−2.42714e15	−	2.42714e15i	−0.499628	−	0.499628i
$260$		0			0
$261$	4.32971e15	−	4.32971e15i	0.847804	−	0.847804i
$262$		0			0
$263$		−	1.67127e15i		−	0.311410i	−0.987804	−	0.155705i	$-0.950235\pi$
$263$		−	1.67127e15i		−	0.311410i	0.987804	−	0.155705i	$-0.0497650\pi$
$264$		0			0
$265$			2.43681e15i			0.432239i
$266$		0			0
$267$	−8.68749e14	+	8.68749e14i	−0.146748	+	0.146748i
$268$		0			0
$269$	6.13567e15	+	6.13567e15i	0.987353	+	0.987353i	0.999921	−	0.0125680i	$-0.00400063\pi$
$269$	6.13567e15	+	6.13567e15i	0.987353	+	0.987353i	−0.0125680	+	0.999921i	$0.504001\pi$
$270$		0			0
$271$	−6.73622e15			−1.03304			−0.516519	−	0.856276i	$-0.672772\pi$
$271$	−6.73622e15			−1.03304			−0.516519	+	0.856276i	$0.672772\pi$
$272$		0			0
$273$	1.21459e15			0.177571
$274$		0			0
$275$	1.42467e15	+	1.42467e15i	0.198634	+	0.198634i
$276$		0			0
$277$	−2.78922e15	+	2.78922e15i	−0.370992	+	0.370992i	−0.867839	−	0.496846i	$-0.834491\pi$
$277$	−2.78922e15	+	2.78922e15i	−0.370992	+	0.370992i	0.496846	+	0.867839i	$0.334491\pi$
$278$		0			0
$279$		−	9.50329e15i		−	1.20628i
$280$		0			0
$281$			1.62414e15i			0.196804i	0.995147	+	0.0984019i	$0.0313731\pi$
$281$			1.62414e15i			0.196804i	−0.995147	+	0.0984019i	$0.968627\pi$
$282$		0			0
$283$	1.76200e15	−	1.76200e15i	0.203889	−	0.203889i	−0.597775	−	0.801664i	$-0.703948\pi$
$283$	1.76200e15	−	1.76200e15i	0.203889	−	0.203889i	0.801664	+	0.597775i	$0.203948\pi$
$284$		0			0
$285$	2.21669e15	+	2.21669e15i	0.245026	+	0.245026i
$286$		0			0
$287$	1.63888e16			1.73108
$288$		0			0
$289$	5.15362e15			0.520327
$290$		0			0
$291$	1.96516e15	+	1.96516e15i	0.189711	+	0.189711i
$292$		0			0
$293$	−1.62937e15	+	1.62937e15i	−0.150446	+	0.150446i	−0.778317	−	0.627871i	$-0.783926\pi$
$293$	−1.62937e15	+	1.62937e15i	−0.150446	+	0.150446i	0.627871	+	0.778317i	$0.283926\pi$
$294$		0			0
$295$			1.72317e15i			0.152225i
$296$		0			0
$297$			1.33718e16i			1.13051i
$298$		0			0
$299$	−4.68155e15	+	4.68155e15i	−0.378902	+	0.378902i
$300$		0			0
$301$	−1.10051e16	−	1.10051e16i	−0.852926	−	0.852926i
$302$		0			0
$303$	4.29599e15			0.318924
$304$		0			0
$305$	1.12952e16			0.803423
$306$		0			0
$307$	4.08343e15	+	4.08343e15i	0.278372	+	0.278372i	0.832459	−	0.554087i	$-0.186932\pi$
$307$	4.08343e15	+	4.08343e15i	0.278372	+	0.278372i	−0.554087	+	0.832459i	$0.686932\pi$
$308$		0			0
$309$	8.72882e14	−	8.72882e14i	0.0570460	−	0.0570460i
$310$		0			0
$311$			1.44598e16i			0.906189i	0.891462	+	0.453095i	$0.149680\pi$
$311$			1.44598e16i			0.906189i	−0.891462	+	0.453095i	$0.850320\pi$
$312$		0			0
$313$			1.63276e16i			0.981488i	0.871304	+	0.490744i	$0.163275\pi$
$313$			1.63276e16i			0.981488i	−0.871304	+	0.490744i	$0.836725\pi$
$314$		0			0
$315$	−1.10990e16	+	1.10990e16i	−0.640126	+	0.640126i
$316$		0			0
$317$	1.29843e16	+	1.29843e16i	0.718674	+	0.718674i	0.968334	−	0.249659i	$-0.0803186\pi$
$317$	1.29843e16	+	1.29843e16i	0.718674	+	0.718674i	−0.249659	+	0.968334i	$0.580319\pi$
$318$		0			0
$319$	4.59937e16			2.44376
$320$		0			0
$321$	−3.00822e15			−0.153471
$322$		0			0
$323$	−2.04028e16	−	2.04028e16i	−0.999708	−	0.999708i
$324$		0			0
$325$	1.13616e15	−	1.13616e15i	0.0534806	−	0.0534806i
$326$		0			0
$327$			2.05681e15i			0.0930323i
$328$		0			0
$329$			1.56748e16i			0.681440i
$330$		0			0
$331$	−1.22652e16	+	1.22652e16i	−0.512615	+	0.512615i	−0.915327	−	0.402712i	$-0.868068\pi$
$331$	−1.22652e16	+	1.22652e16i	−0.512615	+	0.512615i	0.402712	+	0.915327i	$0.368068\pi$
$332$		0			0
$333$	−1.00465e16	−	1.00465e16i	−0.403766	−	0.403766i
$334$		0			0
$335$	−2.97675e15			−0.115067
$336$		0			0
$337$	1.50059e16			0.558044			0.279022	−	0.960285i	$-0.409990\pi$
$337$	1.50059e16			0.558044			0.279022	+	0.960285i	$0.409990\pi$
$338$		0			0
$339$	2.18482e15	+	2.18482e15i	0.0781838	+	0.0781838i
$340$		0			0
$341$	5.04759e16	−	5.04759e16i	1.73852	−	1.73852i
$342$		0			0
$343$		−	2.60219e16i		−	0.862834i
$344$		0			0
$345$			1.03616e16i			0.330829i
$346$		0			0
$347$	1.33756e15	−	1.33756e15i	0.0411313	−	0.0411313i	−0.686242	−	0.727373i	$-0.740741\pi$
$347$	1.33756e15	−	1.33756e15i	0.0411313	−	0.0411313i	0.727373	+	0.686242i	$0.240741\pi$
$348$		0			0
$349$	−1.97272e16	−	1.97272e16i	−0.584386	−	0.584386i	0.351719	−	0.936106i	$-0.385597\pi$
$349$	−1.97272e16	−	1.97272e16i	−0.584386	−	0.584386i	−0.936106	+	0.351719i	$0.885597\pi$
$350$		0			0
$351$	1.06638e16			0.304380
$352$		0			0
$353$	−8.42547e15			−0.231771			−0.115885	−	0.993263i	$-0.536970\pi$
$353$	−8.42547e15			−0.231771			−0.115885	+	0.993263i	$0.536970\pi$
$354$		0			0
$355$	9.26194e15	+	9.26194e15i	0.245594	+	0.245594i
$356$		0			0
$357$	−1.23715e16	+	1.23715e16i	−0.316286	+	0.316286i
$358$		0			0
$359$			5.08084e16i			1.25263i	0.779571	+	0.626313i	$0.215437\pi$
$359$			5.08084e16i			1.25263i	−0.779571	+	0.626313i	$0.784563\pi$
$360$		0			0
$361$			1.32357e16i			0.314739i
$362$		0			0
$363$	−2.33536e16	+	2.33536e16i	−0.535748	+	0.535748i
$364$		0			0
$365$	−4.16530e16	−	4.16530e16i	−0.922025	−	0.922025i
$366$		0			0
$367$	3.52963e16			0.754049			0.377024	−	0.926203i	$-0.376947\pi$
$367$	3.52963e16			0.754049			0.377024	+	0.926203i	$0.376947\pi$
$368$		0			0
$369$	6.78374e16			1.39894
$370$		0			0
$371$	1.84272e16	+	1.84272e16i	0.366884	+	0.366884i
$372$		0			0
$373$	−5.91192e16	+	5.91192e16i	−1.13664	+	1.13664i	−0.147587	+	0.989049i	$0.547151\pi$
$373$	−5.91192e16	+	5.91192e16i	−1.13664	+	1.13664i	−0.989049	+	0.147587i	$0.952849\pi$
$374$		0			0
$375$		−	1.87893e16i		−	0.348905i
$376$		0			0
$377$		−	3.66793e16i		−	0.657964i
$378$		0			0
$379$	1.43227e15	−	1.43227e15i	0.0248238	−	0.0248238i	−0.694586	−	0.719410i	$-0.744412\pi$
$379$	1.43227e15	−	1.43227e15i	0.0248238	−	0.0248238i	0.719410	+	0.694586i	$0.244412\pi$
$380$		0			0
$381$	9.52307e15	+	9.52307e15i	0.159501	+	0.159501i
$382$		0			0
$383$	−1.07408e17			−1.73878			−0.869388	−	0.494131i	$-0.835486\pi$
$383$	−1.07408e17			−1.73878			−0.869388	+	0.494131i	$0.835486\pi$
$384$		0			0
$385$	−1.17903e17			−1.84514
$386$		0			0
$387$	−4.55527e16	−	4.55527e16i	−0.689276	−	0.689276i
$388$		0			0
$389$	5.13035e16	−	5.13035e16i	0.750715	−	0.750715i	−0.223898	−	0.974613i	$-0.571878\pi$
$389$	5.13035e16	−	5.13035e16i	0.750715	−	0.750715i	0.974613	+	0.223898i	$0.0718782\pi$
$390$		0			0
$391$		−	9.53702e16i		−	1.34978i
$392$		0			0
$393$		−	4.18004e16i		−	0.572306i
$394$		0			0
$395$	−1.92134e16	+	1.92134e16i	−0.254520	+	0.254520i
$396$		0			0
$397$	−6.27438e15	−	6.27438e15i	−0.0804327	−	0.0804327i	0.665746	−	0.746179i	$-0.268113\pi$
$397$	−6.27438e15	−	6.27438e15i	−0.0804327	−	0.0804327i	−0.746179	+	0.665746i	$0.768113\pi$
$398$		0			0
$399$	3.35251e16			0.415955
$400$		0			0
$401$	−3.64995e16			−0.438378			−0.219189	−	0.975682i	$-0.570341\pi$
$401$	−3.64995e16			−0.438378			−0.219189	+	0.975682i	$0.570341\pi$
$402$		0			0
$403$	−4.02537e16	−	4.02537e16i	−0.468083	−	0.468083i
$404$		0			0
$405$	−3.97041e16	+	3.97041e16i	−0.447072	+	0.447072i
$406$		0			0
$407$		−	1.06723e17i		−	1.16384i
$408$		0			0
$409$			6.13593e16i			0.648155i	0.946030	+	0.324078i	$0.105054\pi$
$409$			6.13593e16i			0.648155i	−0.946030	+	0.324078i	$0.894946\pi$
$410$		0			0
$411$	2.96413e16	−	2.96413e16i	0.303337	−	0.303337i
$412$		0			0
$413$	1.30306e16	+	1.30306e16i	0.129208	+	0.129208i
$414$		0			0
$415$	9.83255e15			0.0944830
$416$		0			0
$417$	−1.87774e16			−0.174884
$418$		0			0
$419$	−7.29324e16	−	7.29324e16i	−0.658460	−	0.658460i	0.296556	−	0.955016i	$-0.404162\pi$
$419$	−7.29324e16	−	7.29324e16i	−0.658460	−	0.658460i	−0.955016	+	0.296556i	$0.904162\pi$
$420$		0			0
$421$	6.76005e16	−	6.76005e16i	0.591720	−	0.591720i	−0.346376	−	0.938096i	$-0.612588\pi$
$421$	6.76005e16	−	6.76005e16i	0.591720	−	0.591720i	0.938096	+	0.346376i	$0.112588\pi$
$422$		0			0
$423$			6.48817e16i			0.550693i
$424$		0			0
$425$			2.31452e16i			0.190517i
$426$		0			0
$427$	8.54141e16	−	8.54141e16i	0.681943	−	0.681943i
$428$		0			0
$429$	2.67031e16	+	2.67031e16i	0.206818	+	0.206818i
$430$		0			0
$431$	−2.26962e17			−1.70549			−0.852747	−	0.522325i	$-0.825065\pi$
$431$	−2.26962e17			−1.70549			−0.852747	+	0.522325i	$0.825065\pi$
$432$		0			0
$433$	−4.96252e16			−0.361852			−0.180926	−	0.983497i	$-0.557909\pi$
$433$	−4.96252e16			−0.361852			−0.180926	+	0.983497i	$0.557909\pi$
$434$		0			0
$435$	−4.05909e16	−	4.05909e16i	−0.287243	−	0.287243i
$436$		0			0
$437$	−1.29220e17	+	1.29220e17i	−0.887565	+	0.887565i
$438$		0			0
$439$			1.97392e17i			1.31617i	0.752945	+	0.658083i	$0.228633\pi$
$439$			1.97392e17i			1.31617i	−0.752945	+	0.658083i	$0.771367\pi$
$440$		0			0
$441$			3.00751e16i			0.194696i
$442$		0			0
$443$	8.93580e16	−	8.93580e16i	0.561706	−	0.561706i	−0.368086	−	0.929792i	$-0.619987\pi$
$443$	8.93580e16	−	8.93580e16i	0.561706	−	0.561706i	0.929792	+	0.368086i	$0.119987\pi$
$444$		0			0
$445$	−6.72528e16	−	6.72528e16i	−0.410554	−	0.410554i
$446$		0			0
$447$	−8.47182e16			−0.502317
$448$		0			0
$449$	2.06083e17			1.18698			0.593488	−	0.804843i	$-0.297750\pi$
$449$	2.06083e17			1.18698			0.593488	+	0.804843i	$0.297750\pi$
$450$		0			0
$451$	3.60313e17	+	3.60313e17i	2.01619	+	2.01619i
$452$		0			0
$453$	4.70229e16	−	4.70229e16i	0.255665	−	0.255665i
$454$		0			0
$455$			9.40256e16i			0.496789i
$456$		0			0
$457$		−	3.10607e17i		−	1.59498i	−0.603330	−	0.797492i	$-0.706160\pi$
$457$		−	3.10607e17i		−	1.59498i	0.603330	−	0.797492i	$-0.293840\pi$
$458$		0			0
$459$	−1.08619e17	+	1.08619e17i	−0.542156	+	0.542156i
$460$		0			0
$461$	2.29251e17	+	2.29251e17i	1.11238	+	1.11238i	0.992827	+	0.119556i	$0.0381471\pi$
$461$	2.29251e17	+	2.29251e17i	1.11238	+	1.11238i	0.119556	+	0.992827i	$0.461853\pi$
$462$		0			0
$463$	2.38087e17			1.12320			0.561602	−	0.827408i	$-0.310185\pi$
$463$	2.38087e17			1.12320			0.561602	+	0.827408i	$0.310185\pi$
$464$		0			0
$465$	−8.90931e16			−0.408696
$466$		0			0
$467$	3.46725e15	+	3.46725e15i	0.0154677	+	0.0154677i	0.714798	−	0.699331i	$-0.246518\pi$
$467$	3.46725e15	+	3.46725e15i	0.0154677	+	0.0154677i	−0.699331	+	0.714798i	$0.746518\pi$
$468$		0			0
$469$	−2.25102e16	+	2.25102e16i	−0.0976688	+	0.0976688i
$470$		0			0
$471$		−	8.67305e16i		−	0.366046i
$472$		0			0
$473$		−	4.83899e17i		−	1.98681i
$474$		0			0
$475$	3.13601e16	−	3.13601e16i	0.125276	−	0.125276i
$476$		0			0
$477$	7.62746e16	+	7.62746e16i	0.296490	+	0.296490i
$478$		0			0
$479$	1.57553e17			0.595998			0.297999	−	0.954566i	$-0.403681\pi$
$479$	1.57553e17			0.595998			0.297999	+	0.954566i	$0.403681\pi$
$480$		0			0
$481$	−8.51096e16			−0.313354
$482$		0			0
$483$	7.83545e16	+	7.83545e16i	0.280807	+	0.280807i
$484$		0			0
$485$	−1.52129e17	+	1.52129e17i	−0.530753	+	0.530753i
$486$		0			0
$487$			2.59604e16i			0.0881807i	0.999028	+	0.0440904i	$0.0140389\pi$
$487$			2.59604e16i			0.0881807i	−0.999028	+	0.0440904i	$0.985961\pi$
$488$		0			0
$489$		−	1.19477e17i		−	0.395164i
$490$		0			0
$491$	2.48030e17	−	2.48030e17i	0.798866	−	0.798866i	−0.184051	−	0.982917i	$-0.558921\pi$
$491$	2.48030e17	−	2.48030e17i	0.798866	−	0.798866i	0.982917	+	0.184051i	$0.0589211\pi$
$492$		0			0
$493$	3.73607e17	+	3.73607e17i	1.17195	+	1.17195i
$494$		0			0
$495$	−4.88028e17			−1.49112
$496$		0			0
$497$	1.40077e17			0.416919
$498$		0			0
$499$	1.10110e17	+	1.10110e17i	0.319281	+	0.319281i	0.848491	−	0.529210i	$-0.177512\pi$
$499$	1.10110e17	+	1.10110e17i	0.319281	+	0.319281i	−0.529210	+	0.848491i	$0.677512\pi$
$500$		0			0
$501$	6.89159e16	−	6.89159e16i	0.194704	−	0.194704i
$502$		0			0
$503$			5.73331e17i			1.57839i	0.614144	+	0.789194i	$0.289501\pi$
$503$			5.73331e17i			1.57839i	−0.614144	+	0.789194i	$0.710499\pi$
$504$		0			0
$505$			3.32567e17i			0.892248i
$506$		0			0
$507$	−6.75821e16	+	6.75821e16i	−0.176718	+	0.176718i
$508$		0			0
$509$	8.76378e16	+	8.76378e16i	0.223371	+	0.223371i	0.809916	−	0.586546i	$-0.199513\pi$
$509$	8.76378e16	+	8.76378e16i	0.223371	+	0.223371i	−0.586546	+	0.809916i	$0.699513\pi$
$510$		0			0
$511$	−6.29959e17			−1.56522
$512$		0			0
$513$	2.94343e17			0.713002
$514$		0			0
$515$	6.75727e16	+	6.75727e16i	0.159597	+	0.159597i
$516$		0			0
$517$	−3.44613e17	+	3.44613e17i	−0.793676	+	0.793676i
$518$		0			0
$519$		−	2.12275e17i		−	0.476773i
$520$		0			0
$521$			7.15300e17i			1.56691i	0.621450	+	0.783454i	$0.286544\pi$
$521$			7.15300e17i			1.56691i	−0.621450	+	0.783454i	$0.713456\pi$
$522$		0			0
$523$	4.93119e17	−	4.93119e17i	1.05364	−	1.05364i	0.0551579	−	0.998478i	$-0.482434\pi$
$523$	4.93119e17	−	4.93119e17i	1.05364	−	1.05364i	0.998478	−	0.0551579i	$-0.0175662\pi$
$524$		0			0
$525$	−1.90157e16	−	1.90157e16i	−0.0396348	−	0.0396348i
$526$		0			0
$527$	8.20030e17			1.66748
$528$		0			0
$529$	−9.99856e16			−0.198370
$530$		0			0
$531$	5.39369e16	+	5.39369e16i	0.104417	+	0.104417i
$532$		0			0
$533$	2.87344e17	−	2.87344e17i	0.542844	−	0.542844i
$534$		0			0
$535$		−	2.32876e17i		−	0.429364i
$536$		0			0
$537$		−	2.46097e17i		−	0.442867i
$538$		0			0
$539$	−1.59741e17	+	1.59741e17i	−0.280602	+	0.280602i
$540$		0			0
$541$	−3.09275e17	−	3.09275e17i	−0.530350	−	0.530350i	0.390327	−	0.920676i	$-0.372362\pi$
$541$	−3.09275e17	−	3.09275e17i	−0.530350	−	0.530350i	−0.920676	+	0.390327i	$0.872362\pi$
$542$		0			0
$543$	9.28530e16			0.155452
$544$		0			0
$545$	−1.59225e17			−0.260275
$546$		0			0
$547$	−2.63168e17	−	2.63168e17i	−0.420064	−	0.420064i	0.465162	−	0.885226i	$-0.345996\pi$
$547$	−2.63168e17	−	2.63168e17i	−0.420064	−	0.420064i	−0.885226	+	0.465162i	$0.845996\pi$
$548$		0			0
$549$	3.53550e17	−	3.53550e17i	0.551100	−	0.551100i
$550$		0			0
$551$		−	1.01242e18i		−	1.54126i
$552$		0			0
$553$			2.90583e17i			0.432072i
$554$		0			0
$555$	−9.41861e16	+	9.41861e16i	−0.136799	+	0.136799i
$556$		0			0
$557$	−1.23321e17	−	1.23321e17i	−0.174977	−	0.174977i	0.614185	−	0.789162i	$-0.289485\pi$
$557$	−1.23321e17	−	1.23321e17i	−0.174977	−	0.174977i	−0.789162	+	0.614185i	$0.789485\pi$
$558$		0			0
$559$	−3.85902e17			−0.534933
$560$		0			0
$561$	−5.43982e17			−0.736760
$562$		0			0
$563$	−1.40428e17	−	1.40428e17i	−0.185844	−	0.185844i	0.608053	−	0.793897i	$-0.291951\pi$
$563$	−1.40428e17	−	1.40428e17i	−0.185844	−	0.185844i	−0.793897	+	0.608053i	$0.791951\pi$
$564$		0			0
$565$	−1.69134e17	+	1.69134e17i	−0.218734	+	0.218734i
$566$		0			0
$567$			6.00484e17i			0.758947i
$568$		0			0
$569$		−	8.38708e17i		−	1.03605i	−0.855365	−	0.518026i	$-0.826667\pi$
$569$		−	8.38708e17i		−	1.03605i	0.855365	−	0.518026i	$-0.173333\pi$
$570$		0			0
$571$	−7.38761e17	+	7.38761e17i	−0.892009	+	0.892009i	−0.994712	−	0.102703i	$-0.967251\pi$
$571$	−7.38761e17	+	7.38761e17i	−0.892009	+	0.892009i	0.102703	+	0.994712i	$0.467251\pi$
$572$		0			0
$573$	3.48428e17	+	3.48428e17i	0.411252	+	0.411252i
$574$		0			0
$575$	1.46589e17			0.169145
$576$		0			0
$577$	−8.72486e17			−0.984274			−0.492137	−	0.870518i	$-0.663784\pi$
$577$	−8.72486e17			−0.984274			−0.492137	+	0.870518i	$0.663784\pi$
$578$		0			0
$579$	−3.67294e17	−	3.67294e17i	−0.405138	−	0.405138i
$580$		0			0
$581$	7.43537e16	−	7.43537e16i	0.0801969	−	0.0801969i
$582$		0			0
$583$			8.10251e17i			0.854622i
$584$		0			0
$585$			3.89195e17i			0.401471i
$586$		0			0
$587$	1.22125e17	−	1.22125e17i	0.123213	−	0.123213i	−0.642811	−	0.766025i	$-0.722232\pi$
$587$	1.22125e17	−	1.22125e17i	0.123213	−	0.123213i	0.766025	+	0.642811i	$0.222232\pi$
$588$		0			0
$589$	−1.11108e18	−	1.11108e18i	−1.09647	−	1.09647i
$590$		0			0
$591$	4.89540e17			0.472573
$592$		0			0
$593$	1.52585e18			1.44097			0.720485	−	0.693470i	$-0.243919\pi$
$593$	1.52585e18			1.44097			0.720485	+	0.693470i	$0.243919\pi$
$594$		0			0
$595$	−9.57723e17	−	9.57723e17i	−0.884870	−	0.884870i
$596$		0			0
$597$	1.18202e17	−	1.18202e17i	0.106854	−	0.106854i
$598$		0			0
$599$		−	1.44273e18i		−	1.27618i	−0.769962	−	0.638089i	$-0.779725\pi$
$599$		−	1.44273e18i		−	1.27618i	0.769962	−	0.638089i	$-0.220275\pi$
$600$		0			0
$601$		−	6.73438e17i		−	0.582926i	−0.956582	−	0.291463i	$-0.905858\pi$
$601$		−	6.73438e17i		−	0.582926i	0.956582	−	0.291463i	$-0.0941420\pi$
$602$		0			0
$603$	−9.31752e16	+	9.31752e16i	−0.0789292	+	0.0789292i
$604$		0			0
$605$	−1.80788e18	−	1.80788e18i	−1.49886	−	1.49886i
$606$		0			0
$607$	1.84024e17			0.149331			0.0746653	−	0.997209i	$-0.476211\pi$
$607$	1.84024e17			0.149331			0.0746653	+	0.997209i	$0.476211\pi$
$608$		0			0
$609$	−6.13897e17			−0.487622
$610$		0			0
$611$	2.74824e17	+	2.74824e17i	0.213691	+	0.213691i
$612$		0			0
$613$	−3.95118e17	+	3.95118e17i	−0.300770	+	0.300770i	−0.841315	−	0.540545i	$-0.818218\pi$
$613$	−3.95118e17	+	3.95118e17i	−0.300770	+	0.300770i	0.540545	+	0.841315i	$0.318218\pi$
$614$		0			0
$615$		−	6.35975e17i		−	0.473971i
$616$		0			0
$617$			1.19315e18i			0.870645i	0.900275	+	0.435322i	$0.143366\pi$
$617$			1.19315e18i			0.870645i	−0.900275	+	0.435322i	$0.856634\pi$
$618$		0			0
$619$	−1.32374e18	+	1.32374e18i	−0.945830	+	0.945830i	−0.998606	−	0.0527764i	$-0.983193\pi$
$619$	−1.32374e18	+	1.32374e18i	−0.945830	+	0.945830i	0.0527764	+	0.998606i	$0.483193\pi$
$620$		0			0
$621$	6.87934e17	+	6.87934e17i	0.481339	+	0.481339i
$622$		0			0
$623$	−1.01713e18			−0.696954
$624$		0			0
$625$	1.22430e18			0.821613
$626$		0			0
$627$	7.37058e17	+	7.37058e17i	0.484465	+	0.484465i
$628$		0			0
$629$	8.66907e17	−	8.66907e17i	0.558140	−	0.558140i
$630$		0			0
$631$			1.80315e18i			1.13721i	0.822610	+	0.568607i	$0.192517\pi$
$631$			1.80315e18i			1.13721i	−0.822610	+	0.568607i	$0.807483\pi$
$632$		0			0
$633$			2.28642e17i			0.141264i
$634$		0			0
$635$	−7.37213e17	+	7.37213e17i	−0.446235	+	0.446235i
$636$		0			0
$637$	1.27391e17	+	1.27391e17i	0.0755498	+	0.0755498i
$638$		0			0
$639$	5.79815e17			0.336925
$640$		0			0
$641$	−3.35393e17			−0.190975			−0.0954875	−	0.995431i	$-0.530441\pi$
$641$	−3.35393e17			−0.190975			−0.0954875	+	0.995431i	$0.530441\pi$
$642$		0			0
$643$	−7.36641e17	−	7.36641e17i	−0.411041	−	0.411041i	0.471060	−	0.882101i	$-0.343871\pi$
$643$	−7.36641e17	−	7.36641e17i	−0.411041	−	0.411041i	−0.882101	+	0.471060i	$0.843871\pi$
$644$		0			0
$645$	−4.27056e17	+	4.27056e17i	−0.233532	+	0.233532i
$646$		0			0
$647$		−	2.19579e18i		−	1.17683i	−0.808560	−	0.588413i	$-0.799753\pi$
$647$		−	2.19579e18i		−	1.17683i	0.808560	−	0.588413i	$-0.200247\pi$
$648$		0			0
$649$			5.72962e17i			0.300978i
$650$		0			0
$651$	−6.73722e17	+	6.73722e17i	−0.346900	+	0.346900i
$652$		0			0
$653$	−1.90578e18	−	1.90578e18i	−0.961915	−	0.961915i	0.0373856	−	0.999301i	$-0.488097\pi$
$653$	−1.90578e18	−	1.90578e18i	−0.961915	−	0.961915i	−0.999301	+	0.0373856i	$0.988097\pi$
$654$		0			0
$655$	3.23591e18			1.60113
$656$		0			0
$657$	−2.60756e18			−1.26491
$658$		0			0
$659$	−1.14118e18	−	1.14118e18i	−0.542751	−	0.542751i	0.381584	−	0.924334i	$-0.375379\pi$
$659$	−1.14118e18	−	1.14118e18i	−0.542751	−	0.542751i	−0.924334	+	0.381584i	$0.875379\pi$
$660$		0			0
$661$	6.30774e17	−	6.30774e17i	0.294147	−	0.294147i	−0.544569	−	0.838716i	$-0.683307\pi$
$661$	6.30774e17	−	6.30774e17i	0.294147	−	0.294147i	0.838716	+	0.544569i	$0.183307\pi$
$662$		0			0
$663$			4.33817e17i			0.198367i
$664$		0			0
$665$			2.59529e18i			1.16371i
$666$		0			0
$667$	2.36622e18	−	2.36622e18i	1.04049	−	1.04049i
$668$		0			0
$669$	7.78416e16	+	7.78416e16i	0.0335693	+	0.0335693i
$670$		0			0
$671$	3.75570e18			1.58852
$672$		0			0
$673$	3.99345e18			1.65672			0.828362	−	0.560194i	$-0.189273\pi$
$673$	3.99345e18			1.65672			0.828362	+	0.560194i	$0.189273\pi$
$674$		0			0
$675$	−1.66953e17	−	1.66953e17i	−0.0679392	−	0.0679392i
$676$		0			0
$677$	3.03762e18	−	3.03762e18i	1.21257	−	1.21257i	0.242390	−	0.970179i	$-0.422069\pi$
$677$	3.03762e18	−	3.03762e18i	1.21257	−	1.21257i	0.970179	−	0.242390i	$-0.0779314\pi$
$678$		0			0
$679$			2.30080e18i			0.901003i
$680$		0			0
$681$			6.84643e17i			0.263032i
$682$		0			0
$683$	−1.35309e17	+	1.35309e17i	−0.0510025	+	0.0510025i	−0.732148	−	0.681146i	$-0.761482\pi$
$683$	−1.35309e17	+	1.35309e17i	−0.0510025	+	0.0510025i	0.681146	+	0.732148i	$0.261482\pi$
$684$		0			0
$685$	2.29463e18	+	2.29463e18i	0.848642	+	0.848642i
$686$		0			0
$687$	3.27158e17			0.118724
$688$		0			0
$689$	6.46163e17			0.230100
$690$		0			0
$691$	−6.46190e16	−	6.46190e16i	−0.0225815	−	0.0225815i	0.695726	−	0.718307i	$-0.255083\pi$
$691$	−6.46190e16	−	6.46190e16i	−0.0225815	−	0.0225815i	−0.718307	+	0.695726i	$0.755083\pi$
$692$		0			0
$693$	−3.69047e18	+	3.69047e18i	−1.26565	+	1.26565i
$694$		0			0
$695$		−	1.45362e18i		−	0.489271i
$696$		0			0
$697$			5.85363e18i			1.93380i
$698$		0			0
$699$	−9.20401e17	+	9.20401e17i	−0.298453	+	0.298453i
$700$		0			0
$701$	3.38005e18	+	3.38005e18i	1.07586	+	1.07586i	0.996876	+	0.0789849i	$0.0251679\pi$
$701$	3.38005e18	+	3.38005e18i	1.07586	+	1.07586i	0.0789849	+	0.996876i	$0.474832\pi$
$702$		0			0
$703$	−2.34919e18			−0.734023
$704$		0			0
$705$	6.08264e17			0.186579
$706$		0			0
$707$	2.51487e18	+	2.51487e18i	0.757338	+	0.757338i
$708$		0			0
$709$	5.90987e17	−	5.90987e17i	0.174734	−	0.174734i	−0.614322	−	0.789056i	$-0.710570\pi$
$709$	5.90987e17	−	5.90987e17i	0.174734	−	0.174734i	0.789056	+	0.614322i	$0.210570\pi$
$710$		0			0
$711$			1.20279e18i			0.349171i
$712$		0			0
$713$		−	5.19361e18i		−	1.48043i
$714$		0			0
$715$	−2.06717e18	+	2.06717e18i	−0.578612	+	0.578612i
$716$		0			0
$717$	4.76744e17	+	4.76744e17i	0.131042	+	0.131042i
$718$		0			0
$719$	−1.37017e18			−0.369858			−0.184929	−	0.982752i	$-0.559206\pi$
$719$	−1.37017e18			−0.369858			−0.184929	+	0.982752i	$0.559206\pi$
$720$		0			0
$721$	1.02197e18			0.270931
$722$		0			0
$723$	8.88044e17	+	8.88044e17i	0.231225	+	0.231225i
$724$		0			0
$725$	−5.74253e17	+	5.74253e17i	−0.146861	+	0.146861i
$726$		0			0
$727$		−	5.82502e18i		−	1.46327i	−0.681698	−	0.731634i	$-0.738758\pi$
$727$		−	5.82502e18i		−	1.46327i	0.681698	−	0.731634i	$-0.261242\pi$
$728$		0			0
$729$			1.65731e18i			0.408955i
$730$		0			0
$731$	3.93070e18	−	3.93070e18i	0.952812	−	0.952812i
$732$		0			0
$733$	−5.44176e17	−	5.44176e17i	−0.129588	−	0.129588i	0.639338	−	0.768926i	$-0.279208\pi$
$733$	−5.44176e17	−	5.44176e17i	−0.129588	−	0.129588i	−0.768926	+	0.639338i	$0.779208\pi$
$734$		0			0
$735$	2.81954e17			0.0659645
$736$		0			0
$737$	−9.89783e17			−0.227511
$738$		0			0
$739$	2.71486e18	+	2.71486e18i	0.613139	+	0.613139i	0.943763	−	0.330624i	$-0.107259\pi$
$739$	2.71486e18	+	2.71486e18i	0.613139	+	0.613139i	−0.330624	+	0.943763i	$0.607259\pi$
$740$		0			0
$741$	5.87792e17	−	5.87792e17i	0.130438	−	0.130438i
$742$		0			0
$743$			6.65477e18i			1.45113i	0.688155	+	0.725564i	$0.258421\pi$
$743$			6.65477e18i			1.45113i	−0.688155	+	0.725564i	$0.741579\pi$
$744$		0			0
$745$		−	6.55832e18i		−	1.40533i
$746$		0			0
$747$	3.07768e17	−	3.07768e17i	0.0648096	−	0.0648096i
$748$		0			0
$749$	−1.76101e18	−	1.76101e18i	−0.364443	−	0.364443i
$750$		0			0
$751$	−7.13203e18			−1.45062			−0.725310	−	0.688422i	$-0.758304\pi$
$751$	−7.13203e18			−1.45062			−0.725310	+	0.688422i	$0.758304\pi$
$752$		0			0
$753$	−1.12976e18			−0.225849
$754$		0			0
$755$	3.64020e18	+	3.64020e18i	0.715271	+	0.715271i
$756$		0			0
$757$	−9.17647e17	+	9.17647e17i	−0.177236	+	0.177236i	−0.790150	−	0.612914i	$-0.789997\pi$
$757$	−9.17647e17	+	9.17647e17i	−0.177236	+	0.177236i	0.612914	+	0.790150i	$0.289997\pi$
$758$		0			0
$759$			3.44528e18i			0.654113i
$760$		0			0
$761$		−	8.12111e18i		−	1.51571i	−0.652425	−	0.757853i	$-0.726248\pi$
$761$		−	8.12111e18i		−	1.51571i	0.652425	−	0.757853i	$-0.273752\pi$
$762$		0			0
$763$	−1.20406e18	+	1.20406e18i	−0.220921	+	0.220921i
$764$		0			0
$765$	−3.96425e18	−	3.96425e18i	−0.715091	−	0.715091i
$766$		0			0
$767$	4.56928e17			0.0810360
$768$		0			0
$769$	−6.18427e18			−1.07837			−0.539185	−	0.842188i	$-0.681267\pi$
$769$	−6.18427e18			−1.07837			−0.539185	+	0.842188i	$0.681267\pi$
$770$		0			0
$771$	−5.43347e16	−	5.43347e16i	−0.00931588	−	0.00931588i
$772$		0			0
$773$	1.23575e18	−	1.23575e18i	0.208335	−	0.208335i	−0.595224	−	0.803560i	$-0.702937\pi$
$773$	1.23575e18	−	1.23575e18i	0.208335	−	0.208335i	0.803560	+	0.595224i	$0.202937\pi$
$774$		0			0
$775$			1.26043e18i			0.208957i
$776$		0			0
$777$			1.42447e18i			0.232229i
$778$		0			0
$779$	7.93125e18	−	7.93125e18i	1.27159	−	1.27159i
$780$		0			0
$781$	3.07964e18	+	3.07964e18i	0.485588	+	0.485588i
$782$		0			0
$783$	−5.38987e18			−0.835847
$784$		0			0
$785$	6.71410e18			1.02408
$786$		0			0
$787$	−2.12607e18	−	2.12607e18i	−0.318963	−	0.318963i	0.529406	−	0.848369i	$-0.322415\pi$
$787$	−2.12607e18	−	2.12607e18i	−0.318963	−	0.318963i	−0.848369	+	0.529406i	$0.822415\pi$
$788$		0			0
$789$	−4.90425e17	+	4.90425e17i	−0.0723723	+	0.0723723i
$790$		0			0
$791$			2.55798e18i			0.371321i
$792$		0			0
$793$		−	2.99511e18i		−	0.427698i
$794$		0			0
$795$	7.15072e17	−	7.15072e17i	0.100453	−	0.100453i
$796$		0			0
$797$	5.34706e18	+	5.34706e18i	0.738986	+	0.738986i	0.972382	−	0.233396i	$-0.0749837\pi$
$797$	5.34706e18	+	5.34706e18i	0.738986	+	0.738986i	−0.233396	+	0.972382i	$0.574984\pi$
$798$		0			0
$799$	−5.59858e18			−0.761244
$800$		0			0
$801$	−4.21015e18			−0.563231
$802$		0			0
$803$	−1.38498e19	−	1.38498e19i	−1.82302	−	1.82302i
$804$		0			0
$805$	−6.06568e18	+	6.06568e18i	−0.785609	+	0.785609i
$806$		0			0
$807$		−	3.60097e18i		−	0.458925i
$808$		0			0
$809$		−	6.83209e18i		−	0.856817i	−0.903585	−	0.428408i	$-0.859074\pi$
$809$		−	6.83209e18i		−	0.856817i	0.903585	−	0.428408i	$-0.140926\pi$
$810$		0			0
$811$	−9.68349e18	+	9.68349e18i	−1.19508	+	1.19508i	−0.219456	+	0.975622i	$0.570428\pi$
$811$	−9.68349e18	+	9.68349e18i	−1.19508	+	1.19508i	−0.975622	+	0.219456i	$0.929572\pi$
$812$		0			0
$813$	1.97671e18	+	1.97671e18i	0.240080	+	0.240080i
$814$		0			0
$815$	9.24913e18			1.10554
$816$		0			0
$817$	−1.06516e19			−1.25306
$818$		0			0
$819$	2.94309e18	+	2.94309e18i	0.340767	+	0.340767i
$820$		0			0
$821$	−1.28643e18	+	1.28643e18i	−0.146608	+	0.146608i	−0.776601	−	0.629993i	$-0.783058\pi$
$821$	−1.28643e18	+	1.28643e18i	−0.146608	+	0.146608i	0.629993	+	0.776601i	$0.283058\pi$
$822$		0			0
$823$		−	8.52257e18i		−	0.956031i	−0.878351	−	0.478015i	$-0.841356\pi$
$823$		−	8.52257e18i		−	0.956031i	0.878351	−	0.478015i	$-0.158644\pi$
$824$		0			0
$825$		−	8.36129e17i		−	0.0923257i
$826$		0			0
$827$	6.35558e18	−	6.35558e18i	0.690827	−	0.690827i	−0.271587	−	0.962414i	$-0.587548\pi$
$827$	6.35558e18	−	6.35558e18i	0.690827	−	0.690827i	0.962414	+	0.271587i	$0.0875484\pi$
$828$		0			0
$829$	6.37296e18	+	6.37296e18i	0.681925	+	0.681925i	0.960434	−	0.278509i	$-0.0898402\pi$
$829$	6.37296e18	+	6.37296e18i	0.681925	+	0.681925i	−0.278509	+	0.960434i	$0.589840\pi$
$830$		0			0
$831$	1.63697e18			0.172438
$832$		0			0
$833$	−2.59515e18			−0.269135
$834$		0			0
$835$	5.33501e18	+	5.33501e18i	0.544720	+	0.544720i
$836$		0			0
$837$	−5.91512e18	+	5.91512e18i	−0.594631	+	0.594631i
$838$		0			0
$839$		−	1.31992e19i		−	1.30646i	−0.757161	−	0.653229i	$-0.773414\pi$
$839$		−	1.31992e19i		−	1.30646i	0.757161	−	0.653229i	$-0.226586\pi$
$840$		0			0
$841$			8.27837e18i			0.806809i
$842$		0			0
$843$	4.76598e17	−	4.76598e17i	0.0457375	−	0.0457375i
$844$		0			0
$845$	−5.23176e18	−	5.23176e18i	−0.494401	−	0.494401i
$846$		0			0
$847$	−2.73423e19			−2.54445
$848$		0			0
$849$	−1.03410e18			−0.0947682
$850$		0			0
$851$	−5.49050e18	−	5.49050e18i	−0.495530	−	0.495530i
$852$		0			0
$853$	9.24592e18	−	9.24592e18i	0.821829	−	0.821829i	−0.164542	−	0.986370i	$-0.552614\pi$
$853$	9.24592e18	−	9.24592e18i	0.821829	−	0.821829i	0.986370	+	0.164542i	$0.0526145\pi$
$854$		0			0
$855$			1.07426e19i			0.940433i
$856$		0			0
$857$		−	2.02618e19i		−	1.74704i	−0.486789	−	0.873519i	$-0.661832\pi$
$857$		−	2.02618e19i		−	1.74704i	0.486789	−	0.873519i	$-0.338168\pi$
$858$		0			0
$859$	1.17878e19	−	1.17878e19i	1.00110	−	1.00110i	0.00109764	−	0.999999i	$-0.499651\pi$
$859$	1.17878e19	−	1.17878e19i	1.00110	−	1.00110i	0.999999	−	0.00109764i	$-0.000349391\pi$
$860$		0			0
$861$	−4.80923e18	−	4.80923e18i	−0.402305	−	0.402305i
$862$		0			0
$863$	−2.92327e18			−0.240879			−0.120440	−	0.992721i	$-0.538430\pi$
$863$	−2.92327e18			−0.240879			−0.120440	+	0.992721i	$0.538430\pi$
$864$		0			0
$865$	1.64329e19			1.33386
$866$		0			0
$867$	−1.51231e18	−	1.51231e18i	−0.120925	−	0.120925i
$868$		0			0
$869$	−6.38852e18	+	6.38852e18i	−0.503236	+	0.503236i
$870$		0			0
$871$			7.89337e17i			0.0612554i
$872$		0			0
$873$			9.52359e18i			0.728129i
$874$		0			0
$875$	1.09992e19	−	1.09992e19i	0.828533	−	0.828533i
$876$		0			0
$877$	−1.07318e19	−	1.07318e19i	−0.796480	−	0.796480i	0.186059	−	0.982539i	$-0.440429\pi$
$877$	−1.07318e19	−	1.07318e19i	−0.796480	−	0.796480i	−0.982539	+	0.186059i	$0.940429\pi$
$878$		0			0
$879$	9.56261e17			0.0699276
$880$		0			0
$881$	−9.41168e18			−0.678147			−0.339074	−	0.940760i	$-0.610114\pi$
$881$	−9.41168e18			−0.678147			−0.339074	+	0.940760i	$0.610114\pi$
$882$		0			0
$883$	5.88134e18	+	5.88134e18i	0.417572	+	0.417572i	0.884366	−	0.466794i	$-0.154591\pi$
$883$	5.88134e18	+	5.88134e18i	0.417572	+	0.417572i	−0.466794	+	0.884366i	$0.654591\pi$
$884$		0			0
$885$	5.05657e17	−	5.05657e17i	0.0353773	−	0.0353773i
$886$		0			0
$887$			7.39885e18i			0.510106i	0.966927	+	0.255053i	$0.0820929\pi$
$887$			7.39885e18i			0.510106i	−0.966927	+	0.255053i	$0.917907\pi$
$888$		0			0
$889$			1.11496e19i			0.757526i
$890$		0			0
$891$	−1.32018e19	+	1.32018e19i	−0.883949	+	0.883949i
$892$		0			0
$893$	7.58568e18	+	7.58568e18i	0.500564	+	0.500564i
$894$		0			0
$895$	1.90512e19			1.23900
$896$		0			0
$897$	2.74756e18			0.176115
$898$		0			0
$899$	2.03456e19	+	2.03456e19i	1.28538	+	1.28538i
$900$		0			0
$901$	−6.58166e18	+	6.58166e18i	−0.409849	+	0.409849i
$902$		0			0
$903$			6.45879e18i			0.396443i
$904$		0			0
$905$			7.18807e18i			0.434907i
$906$		0			0
$907$	−2.19568e19	+	2.19568e19i	−1.30955	+	1.30955i	−0.387806	+	0.921741i	$0.626767\pi$
$907$	−2.19568e19	+	2.19568e19i	−1.30955	+	1.30955i	−0.921741	+	0.387806i	$0.873233\pi$
$908$		0			0
$909$	1.04097e19	+	1.04097e19i	0.612029	+	0.612029i
$910$		0			0
$911$	−5.49355e17			−0.0318408			−0.0159204	−	0.999873i	$-0.505068\pi$
$911$	−5.49355e17			−0.0318408			−0.0159204	+	0.999873i	$0.505068\pi$
$912$		0			0
$913$	3.26936e18			0.186811
$914$		0			0
$915$	−3.31452e18	−	3.31452e18i	−0.186717	−	0.186717i
$916$		0			0
$917$	2.44699e19	−	2.44699e19i	1.35904	−	1.35904i
$918$		0			0
$919$			2.47176e19i			1.35349i	0.736216	+	0.676747i	$0.236611\pi$
$919$			2.47176e19i			1.35349i	−0.736216	+	0.676747i	$0.763389\pi$
$920$		0			0
$921$		−	2.39653e18i		−	0.129388i
$922$		0			0
$923$	2.45596e18	−	2.45596e18i	0.130741	−	0.130741i
$924$		0			0
$925$	1.33248e18	+	1.33248e18i	0.0699422	+	0.0699422i
$926$		0			0
$927$	4.23018e18			0.218948
$928$		0			0
$929$	7.46663e17			0.0381086			0.0190543	−	0.999818i	$-0.493934\pi$
$929$	7.46663e17			0.0381086			0.0190543	+	0.999818i	$0.493934\pi$
$930$		0			0
$931$	3.51625e18	+	3.51625e18i	0.176973	+	0.176973i
$932$		0			0
$933$	4.24316e18	−	4.24316e18i	0.210600	−	0.210600i
$934$		0			0
$935$		−	4.21115e19i		−	2.06122i
$936$		0			0
$937$		−	1.22679e19i		−	0.592195i	−0.955158	−	0.296097i	$-0.904315\pi$
$937$		−	1.22679e19i		−	0.592195i	0.955158	−	0.296097i	$-0.0956853\pi$
$938$		0			0
$939$	4.79127e18	−	4.79127e18i	0.228100	−	0.228100i
$940$		0			0
$941$	6.08999e18	+	6.08999e18i	0.285946	+	0.285946i	0.835475	−	0.549529i	$-0.185193\pi$
$941$	6.08999e18	+	6.08999e18i	0.285946	+	0.285946i	−0.549529	+	0.835475i	$0.685193\pi$
$942$		0			0
$943$	3.70736e19			1.71688
$944$		0			0
$945$	1.38167e19			0.631098
$946$		0			0
$947$	−4.69729e18	−	4.69729e18i	−0.211627	−	0.211627i	0.593331	−	0.804959i	$-0.297813\pi$
$947$	−4.69729e18	−	4.69729e18i	−0.211627	−	0.211627i	−0.804959	+	0.593331i	$0.797813\pi$
$948$		0			0
$949$	−1.10450e19	+	1.10450e19i	−0.490835	+	0.490835i
$950$		0			0
$951$		−	7.62035e18i		−	0.334042i
$952$		0			0
$953$			3.04396e19i			1.31624i	0.752913	+	0.658120i	$0.228648\pi$
$953$			3.04396e19i			1.31624i	−0.752913	+	0.658120i	$0.771352\pi$
$954$		0			0
$955$	−2.69730e19	+	2.69730e19i	−1.15056	+	1.15056i
$956$		0			0
$957$	−1.34967e19	−	1.34967e19i	−0.567935	−	0.567935i
$958$		0			0
$959$	3.47040e19			1.44065
$960$		0			0
$961$	2.02391e19			0.828876
$962$		0			0
$963$	−7.28925e18	−	7.28925e18i	−0.294518	−	0.294518i
$964$		0			0
$965$	2.84334e19	−	2.84334e19i	1.13345	−	1.13345i
$966$		0			0
$967$			2.28887e19i			0.900220i	0.892973	+	0.450110i	$0.148615\pi$
$967$			2.28887e19i			0.900220i	−0.892973	+	0.450110i	$0.851385\pi$
$968$		0			0
$969$			1.19742e19i			0.464668i
$970$		0			0
$971$	9.18725e18	−	9.18725e18i	0.351771	−	0.351771i	−0.508997	−	0.860768i	$-0.669984\pi$
$971$	9.18725e18	−	9.18725e18i	0.351771	−	0.351771i	0.860768	+	0.508997i	$0.169984\pi$
$972$		0			0
$973$	−1.09923e19	−	1.09923e19i	−0.415292	−	0.415292i
$974$		0			0
$975$	−6.66800e17			−0.0248580
$976$		0			0
$977$	1.47368e19			0.542111			0.271056	−	0.962564i	$-0.412627\pi$
$977$	1.47368e19			0.542111			0.271056	+	0.962564i	$0.412627\pi$
$978$		0			0
$979$	−2.23618e19	−	2.23618e19i	−0.811746	−	0.811746i
$980$		0			0
$981$	−4.98388e18	+	4.98388e18i	−0.178533	+	0.178533i
$982$		0			0
$983$			2.23773e19i			0.791062i	0.918453	+	0.395531i	$0.129439\pi$
$983$			2.23773e19i			0.791062i	−0.918453	+	0.395531i	$0.870561\pi$
$984$		0			0
$985$			3.78969e19i			1.32211i
$986$		0			0
$987$	4.59969e18	−	4.59969e18i	0.158368	−	0.158368i
$988$		0			0
$989$	−2.48949e19	−	2.48949e19i	−0.845929	−	0.845929i
$990$		0			0
$991$	−7.75730e18			−0.260155			−0.130077	−	0.991504i	$-0.541523\pi$
$991$	−7.75730e18			−0.260155			−0.130077	+	0.991504i	$0.541523\pi$
$992$		0			0
$993$	7.19831e18			0.238265
$994$		0			0
$995$	9.15043e18	+	9.15043e18i	0.298945	+	0.298945i
$996$		0			0
$997$	−1.53061e19	+	1.53061e19i	−0.493568	+	0.493568i	−0.909428	−	0.415861i	$-0.863480\pi$
$997$	−1.53061e19	+	1.53061e19i	−0.493568	+	0.493568i	0.415861	+	0.909428i	$0.363480\pi$
$998$		0			0
$999$			1.25065e19i			0.398071i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	64.14.e.a.17.11		50
4.3	odd	2		16.14.e.a.13.6	yes	50
8.3	odd	2		128.14.e.b.33.11		50
8.5	even	2		128.14.e.a.33.15		50
16.3	odd	4		128.14.e.b.97.11		50
16.5	even	4	inner	64.14.e.a.49.11		50
16.11	odd	4		16.14.e.a.5.6	✓	50
16.13	even	4		128.14.e.a.97.15		50

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
16.14.e.a.5.6	✓	50	16.11	odd	4
16.14.e.a.13.6	yes	50	4.3	odd	2
64.14.e.a.17.11		50	1.1	even	1	trivial
64.14.e.a.49.11		50	16.5	even	4	inner
128.14.e.a.33.15		50	8.5	even	2
128.14.e.a.97.15		50	16.13	even	4
128.14.e.b.33.11		50	8.3	odd	2
128.14.e.b.97.11		50	16.3	odd	4

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:	\( N \)	\(=\)	\( 64 = 2^{6} \)
Weight:	\( k \)	\(=\)	\( 14 \)
Character orbit:	\([\chi]\)	\(=\)	64.e (of order \(4\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-293.446 - 293.446i) q^{3} +(22716.6 - 22716.6i) q^{5} -343566. i q^{7} -1.42210e6i q^{9} +O(q^{10})\)	\(q+(-293.446 - 293.446i) q^{3} +(22716.6 - 22716.6i) q^{5} -343566. i q^{7} -1.42210e6i q^{9} +(7.55337e6 - 7.55337e6i) q^{11} +(-6.02369e6 - 6.02369e6i) q^{13} -1.33322e7 q^{15} +1.22712e8 q^{17} +(-1.66266e8 - 1.66266e8i) q^{19} +(-1.00818e8 + 1.00818e8i) q^{21} -7.77189e8i q^{23} +1.88614e8i q^{25} +(-8.85157e8 + 8.85157e8i) q^{27} +(3.04458e9 + 3.04458e9i) q^{29} +6.68256e9 q^{31} -4.43301e9 q^{33} +(-7.80465e9 - 7.80465e9i) q^{35} +(7.06457e9 - 7.06457e9i) q^{37} +3.53525e9i q^{39} +4.77022e10i q^{41} +(3.20320e10 - 3.20320e10i) q^{43} +(-3.23053e10 - 3.23053e10i) q^{45} -4.56238e10 q^{47} -2.11484e10 q^{49} +(-3.60092e10 - 3.60092e10i) q^{51} +(-5.36351e10 + 5.36351e10i) q^{53} -3.43174e11i q^{55} +9.75800e10i q^{57} +(-3.79276e10 + 3.79276e10i) q^{59} +(2.48611e11 + 2.48611e11i) q^{61} -4.88586e11 q^{63} -2.73676e11 q^{65} +(-6.55193e10 - 6.55193e10i) q^{67} +(-2.28063e11 + 2.28063e11i) q^{69} +4.07717e11i q^{71} -1.83359e12i q^{73} +(5.53481e10 - 5.53481e10i) q^{75} +(-2.59508e12 - 2.59508e12i) q^{77} -8.45785e11 q^{79} -1.74780e12 q^{81} +(2.16418e11 + 2.16418e11i) q^{83} +(2.78760e12 - 2.78760e12i) q^{85} -1.78684e12i q^{87} -2.96051e12i q^{89} +(-2.06953e12 + 2.06953e12i) q^{91} +(-1.96097e12 - 1.96097e12i) q^{93} -7.55399e12 q^{95} -6.69684e12 q^{97} +(-1.07417e13 - 1.07417e13i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 50 q + 2 q^{3} - 2 q^{5}+O(q^{10}) \) 50 * q + 2 * q^3 - 2 * q^5	\( 50 q + 2 q^{3} - 2 q^{5} + 4723998 q^{11} - 2 q^{13} - 91124996 q^{15} - 4 q^{17} - 422008902 q^{19} + 3188644 q^{21} + 2068699784 q^{27} - 3661663834 q^{29} + 10650044176 q^{31} - 4 q^{33} - 7767977276 q^{35} + 21527986470 q^{37} + 18577860182 q^{43} + 2438217602 q^{45} - 215584306576 q^{47} - 525968913642 q^{49} + 551664571452 q^{51} + 223019793366 q^{53} - 1167423209882 q^{59} + 81543039150 q^{61} + 862914002556 q^{63} - 27850095516 q^{65} - 1390089097910 q^{67} - 168685276844 q^{69} + 1675683188954 q^{75} - 2147852144860 q^{77} - 8517123343488 q^{79} - 9602604240358 q^{81} - 2192965629438 q^{83} + 2809965843748 q^{85} - 3291182399236 q^{91} + 3412032366928 q^{93} - 7322122332660 q^{95} - 4 q^{97} - 19363874529854 q^{99}+O(q^{100}) \) 50 * q + 2 * q^3 - 2 * q^5 + 4723998 * q^11 - 2 * q^13 - 91124996 * q^15 - 4 * q^17 - 422008902 * q^19 + 3188644 * q^21 + 2068699784 * q^27 - 3661663834 * q^29 + 10650044176 * q^31 - 4 * q^33 - 7767977276 * q^35 + 21527986470 * q^37 + 18577860182 * q^43 + 2438217602 * q^45 - 215584306576 * q^47 - 525968913642 * q^49 + 551664571452 * q^51 + 223019793366 * q^53 - 1167423209882 * q^59 + 81543039150 * q^61 + 862914002556 * q^63 - 27850095516 * q^65 - 1390089097910 * q^67 - 168685276844 * q^69 + 1675683188954 * q^75 - 2147852144860 * q^77 - 8517123343488 * q^79 - 9602604240358 * q^81 - 2192965629438 * q^83 + 2809965843748 * q^85 - 3291182399236 * q^91 + 3412032366928 * q^93 - 7322122332660 * q^95 - 4 * q^97 - 19363874529854 * q^99

Introduction

L-functions

Modular forms

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Database

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