LMFDB - Embedded newform 216.3.h.e.53.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [216,3,Mod(53,216)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(216, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 3, names="a")

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

chi := DirichletCharacter("216.53");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 216 = 2^{3} \cdot 3^{3} $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	216.h (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:	$5.88557371018$
Analytic rank:	$0$
Dimension:	$8$
Coefficient field:	8.0.629407744.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 2x^{6} + 2x^{4} - 8x^{2} + 16 $ x^8 - 2x^6 + 2x^4 - 8*x^2 + 16
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 2^{4}\cdot 3^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			53.8
Root			$1.38255 - 0.297594i$ of defining polynomial
Character	$\chi$	$=$	216.53
Dual form			216.3.h.e.53.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.68014 + 1.08495i) q^{2} +(1.64575 + 3.64575i) q^{4} -8.89047 q^{5} -3.35425 q^{7} +(-1.19038 + 7.91094i) q^{8} +O(q^{10})$	\(q+(1.68014 + 1.08495i) q^{2} +(1.64575 + 3.64575i) q^{4} -8.89047 q^{5} -3.35425 q^{7} +(-1.19038 + 7.91094i) q^{8} +(-14.9373 - 9.64575i) q^{10} -8.12179 q^{11} +22.5203i q^{13} +(-5.63561 - 3.63920i) q^{14} +(-10.5830 + 12.0000i) q^{16} -14.4207i q^{17} -13.7085i q^{19} +(-14.6315 - 32.4125i) q^{20} +(-13.6458 - 8.81176i) q^{22} +29.4739i q^{23} +54.0405 q^{25} +(-24.4334 + 37.8372i) q^{26} +(-5.52026 - 12.2288i) q^{28} -11.0604 q^{29} +41.8745 q^{31} +(-30.8004 + 8.67963i) q^{32} +(15.6458 - 24.2288i) q^{34} +29.8209 q^{35} -11.3542i q^{37} +(14.8731 - 23.0322i) q^{38} +(10.5830 - 70.3320i) q^{40} +4.33981i q^{41} +54.4575i q^{43} +(-13.3664 - 29.6100i) q^{44} +(-31.9778 + 49.5203i) q^{46} +12.3869i q^{47} -37.7490 q^{49} +(90.7957 + 58.6315i) q^{50} +(-82.1033 + 37.0627i) q^{52} -50.1187 q^{53} +72.2065 q^{55} +(3.99282 - 26.5353i) q^{56} +(-18.5830 - 12.0000i) q^{58} +49.5609 q^{59} -67.9373i q^{61} +(70.3551 + 45.4319i) q^{62} +(-61.1660 - 18.8340i) q^{64} -200.216i q^{65} +80.2470i q^{67} +(52.5742 - 23.7328i) q^{68} +(50.1033 + 32.3542i) q^{70} +81.9119i q^{71} +11.9150 q^{73} +(12.3188 - 19.0767i) q^{74} +(49.9778 - 22.5608i) q^{76} +27.2425 q^{77} -37.2288 q^{79} +(94.0879 - 106.686i) q^{80} +(-4.70850 + 7.29150i) q^{82} +58.3767 q^{83} +128.207i q^{85} +(-59.0839 + 91.4963i) q^{86} +(9.66798 - 64.2510i) q^{88} +92.5373i q^{89} -75.5385i q^{91} +(-107.454 + 48.5066i) q^{92} +(-13.4392 + 20.8118i) q^{94} +121.875i q^{95} -14.2915 q^{97} +(-63.4237 - 40.9559i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 8 q^{4} - 48 q^{7}+O(q^{10}) $ 8 * q - 8 * q^4 - 48 * q^7	$ 8 q - 8 q^{4} - 48 q^{7} - 56 q^{10} - 88 q^{22} + 136 q^{25} + 104 q^{28} + 208 q^{31} + 104 q^{34} + 104 q^{46} - 48 q^{49} - 424 q^{52} + 112 q^{55} - 64 q^{58} - 320 q^{64} + 168 q^{70} - 328 q^{73} + 40 q^{76} - 192 q^{79} - 80 q^{82} + 416 q^{88} - 552 q^{94} - 72 q^{97}+O(q^{100}) $ 8 * q - 8 * q^4 - 48 * q^7 - 56 * q^10 - 88 * q^22 + 136 * q^25 + 104 * q^28 + 208 * q^31 + 104 * q^34 + 104 * q^46 - 48 * q^49 - 424 * q^52 + 112 * q^55 - 64 * q^58 - 320 * q^64 + 168 * q^70 - 328 * q^73 + 40 * q^76 - 192 * q^79 - 80 * q^82 + 416 * q^88 - 552 * q^94 - 72 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/216\mathbb{Z}\right)^\times$.

$n$	$55$	$109$	$137$
$\chi(n)$	$1$	$-1$	$-1$

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 $

$2$	1.68014	+	1.08495i	0.840071	+	0.542477i
$2$	1.68014	+	1.08495i	0.840071	+	0.542477i
$3$		0			0
$3$		0			0
$4$	1.64575	+	3.64575i	0.411438	+	0.911438i
$5$	−8.89047			−1.77809			−0.889047	−	0.457815i	$-0.848632\pi$
$5$	−8.89047			−1.77809			−0.889047	+	0.457815i	$0.848632\pi$
$6$		0			0
$7$	−3.35425			−0.479178			−0.239589	−	0.970874i	$-0.577013\pi$
$7$	−3.35425			−0.479178			−0.239589	+	0.970874i	$0.577013\pi$
$8$	−1.19038	+	7.91094i	−0.148797	+	0.988868i
$9$		0			0
$10$	−14.9373	−	9.64575i	−1.49373	−	0.964575i
$11$	−8.12179			−0.738344			−0.369172	−	0.929361i	$-0.620359\pi$
$11$	−8.12179			−0.738344			−0.369172	+	0.929361i	$0.620359\pi$
$12$		0			0
$13$			22.5203i			1.73233i	0.499760	+	0.866164i	$0.333421\pi$
$13$			22.5203i			1.73233i	−0.499760	+	0.866164i	$0.666579\pi$
$14$	−5.63561	−	3.63920i	−0.402544	−	0.259943i
$15$		0			0
$16$	−10.5830	+	12.0000i	−0.661438	+	0.750000i
$17$		−	14.4207i		−	0.848274i	−0.905598	−	0.424137i	$-0.860577\pi$
$17$		−	14.4207i		−	0.848274i	0.905598	−	0.424137i	$-0.139423\pi$
$18$		0			0
$19$		−	13.7085i		−	0.721500i	−0.932663	−	0.360750i	$-0.882521\pi$
$19$		−	13.7085i		−	0.721500i	0.932663	−	0.360750i	$-0.117479\pi$
$20$	−14.6315	−	32.4125i	−0.731575	−	1.62062i
$21$		0			0
$22$	−13.6458	−	8.81176i	−0.620261	−	0.400535i
$23$			29.4739i			1.28147i	0.767761	+	0.640736i	$0.221371\pi$
$23$			29.4739i			1.28147i	−0.767761	+	0.640736i	$0.778629\pi$
$24$		0			0
$25$	54.0405			2.16162
$26$	−24.4334	+	37.8372i	−0.939748	+	1.45528i
$27$		0			0
$28$	−5.52026	−	12.2288i	−0.197152	−	0.436741i
$29$	−11.0604			−0.381392			−0.190696	−	0.981649i	$-0.561075\pi$
$29$	−11.0604			−0.381392			−0.190696	+	0.981649i	$0.561075\pi$
$30$		0			0
$31$	41.8745			1.35079			0.675395	−	0.737456i	$-0.263973\pi$
$31$	41.8745			1.35079			0.675395	+	0.737456i	$0.263973\pi$
$32$	−30.8004	+	8.67963i	−0.962512	+	0.271238i
$33$		0			0
$34$	15.6458	−	24.2288i	0.460169	−	0.712610i
$35$	29.8209			0.852025
$36$		0			0
$37$		−	11.3542i		−	0.306872i	−0.988159	−	0.153436i	$-0.950966\pi$
$37$		−	11.3542i		−	0.306872i	0.988159	−	0.153436i	$-0.0490338\pi$
$38$	14.8731	−	23.0322i	0.391397	−	0.606111i
$39$		0			0
$40$	10.5830	−	70.3320i	0.264575	−	1.75830i
$41$			4.33981i			0.105849i	0.998599	+	0.0529246i	$0.0168543\pi$
$41$			4.33981i			0.105849i	−0.998599	+	0.0529246i	$0.983146\pi$
$42$		0			0
$43$			54.4575i			1.26645i	0.773966	+	0.633227i	$0.218270\pi$
$43$			54.4575i			1.26645i	−0.773966	+	0.633227i	$0.781730\pi$
$44$	−13.3664	−	29.6100i	−0.303783	−	0.672955i
$45$		0			0
$46$	−31.9778	+	49.5203i	−0.695169	+	1.07653i
$47$			12.3869i			0.263551i	0.991280	+	0.131776i	$0.0420678\pi$
$47$			12.3869i			0.263551i	−0.991280	+	0.131776i	$0.957932\pi$
$48$		0			0
$49$	−37.7490			−0.770388
$50$	90.7957	+	58.6315i	1.81591	+	1.17263i
$51$		0			0
$52$	−82.1033	+	37.0627i	−1.57891	+	0.712745i
$53$	−50.1187			−0.945636			−0.472818	−	0.881160i	$-0.656763\pi$
$53$	−50.1187			−0.945636			−0.472818	+	0.881160i	$0.656763\pi$
$54$		0			0
$55$	72.2065			1.31285
$56$	3.99282	−	26.5353i	0.0713003	−	0.473844i
$57$		0			0
$58$	−18.5830	−	12.0000i	−0.320397	−	0.206897i
$59$	49.5609			0.840015			0.420007	−	0.907521i	$-0.362027\pi$
$59$	49.5609			0.840015			0.420007	+	0.907521i	$0.362027\pi$
$60$		0			0
$61$		−	67.9373i		−	1.11373i	−0.830605	−	0.556863i	$-0.812005\pi$
$61$		−	67.9373i		−	1.11373i	0.830605	−	0.556863i	$-0.187995\pi$
$62$	70.3551	+	45.4319i	1.13476	+	0.732773i
$63$		0			0
$64$	−61.1660	−	18.8340i	−0.955719	−	0.294281i
$65$		−	200.216i		−	3.08024i
$66$		0			0
$67$			80.2470i			1.19772i	0.800855	+	0.598859i	$0.204379\pi$
$67$			80.2470i			1.19772i	−0.800855	+	0.598859i	$0.795621\pi$
$68$	52.5742	−	23.7328i	0.773149	−	0.349012i
$69$		0			0
$70$	50.1033	+	32.3542i	0.715761	+	0.462204i
$71$			81.9119i			1.15369i	0.816854	+	0.576844i	$0.195716\pi$
$71$			81.9119i			1.15369i	−0.816854	+	0.576844i	$0.804284\pi$
$72$		0			0
$73$	11.9150			0.163220			0.0816098	−	0.996664i	$-0.473994\pi$
$73$	11.9150			0.163220			0.0816098	+	0.996664i	$0.473994\pi$
$74$	12.3188	−	19.0767i	0.166471	−	0.257794i
$75$		0			0
$76$	49.9778	−	22.5608i	0.657602	−	0.296852i
$77$	27.2425			0.353799
$78$		0			0
$79$	−37.2288			−0.471250			−0.235625	−	0.971844i	$-0.575714\pi$
$79$	−37.2288			−0.471250			−0.235625	+	0.971844i	$0.575714\pi$
$80$	94.0879	−	106.686i	1.17610	−	1.33357i
$81$		0			0
$82$	−4.70850	+	7.29150i	−0.0574207	+	0.0889208i
$83$	58.3767			0.703333			0.351667	−	0.936125i	$-0.385615\pi$
$83$	58.3767			0.703333			0.351667	+	0.936125i	$0.385615\pi$
$84$		0			0
$85$			128.207i			1.50831i
$86$	−59.0839	+	91.4963i	−0.687022	+	1.06391i
$87$		0			0
$88$	9.66798	−	64.2510i	0.109863	−	0.730125i
$89$			92.5373i			1.03975i	0.854244	+	0.519873i	$0.174021\pi$
$89$			92.5373i			1.03975i	−0.854244	+	0.519873i	$0.825979\pi$
$90$		0			0
$91$		−	75.5385i		−	0.830094i
$92$	−107.454	+	48.5066i	−1.16798	+	0.527246i
$93$		0			0
$94$	−13.4392	+	20.8118i	−0.142970	+	0.221402i
$95$			121.875i			1.28290i
$96$		0			0
$97$	−14.2915			−0.147335			−0.0736675	−	0.997283i	$-0.523470\pi$
$97$	−14.2915			−0.147335			−0.0736675	+	0.997283i	$0.523470\pi$
$98$	−63.4237	−	40.9559i	−0.647181	−	0.417918i
$99$		0			0
$100$	88.9373	+	197.018i	0.889373	+	1.97018i
$101$	46.3500			0.458911			0.229455	−	0.973319i	$-0.426306\pi$
$101$	46.3500			0.458911			0.229455	+	0.973319i	$0.426306\pi$
$102$		0			0
$103$	−163.391			−1.58632			−0.793159	−	0.609014i	$-0.791565\pi$
$103$	−163.391			−1.58632			−0.793159	+	0.609014i	$0.791565\pi$
$104$	−178.156	−	26.8076i	−1.71304	−	0.257765i
$105$		0			0
$106$	−84.2065	−	54.3765i	−0.794401	−	0.512986i
$107$	192.230			1.79654			0.898272	−	0.439441i	$-0.144823\pi$
$107$	192.230			1.79654			0.898272	+	0.439441i	$0.144823\pi$
$108$		0			0
$109$		−	63.9555i		−	0.586748i	−0.955998	−	0.293374i	$-0.905222\pi$
$109$		−	63.9555i		−	0.586748i	0.955998	−	0.293374i	$-0.0947781\pi$
$110$	121.317	+	78.3407i	1.10288	+	0.712188i
$111$		0			0
$112$	35.4980	−	40.2510i	0.316947	−	0.359384i
$113$		−	174.721i		−	1.54621i	−0.634279	−	0.773104i	$-0.718703\pi$
$113$		−	174.721i		−	1.54621i	0.634279	−	0.773104i	$-0.281297\pi$
$114$		0			0
$115$		−	262.037i		−	2.27858i
$116$	−18.2026	−	40.3234i	−0.156919	−	0.347615i
$117$		0			0
$118$	83.2693	+	53.7712i	0.705672	+	0.455689i
$119$			48.3705i			0.406475i
$120$		0			0
$121$	−55.0366			−0.454848
$122$	73.7088	−	114.144i	0.604170	−	0.935608i
$123$		0			0
$124$	68.9150	+	152.664i	0.555766	+	1.23116i
$125$	−258.184			−2.06547
$126$		0			0
$127$	−85.4170			−0.672575			−0.336287	−	0.941759i	$-0.609171\pi$
$127$	−85.4170			−0.672575			−0.336287	+	0.941759i	$0.609171\pi$
$128$	−82.3336	−	98.0061i	−0.643231	−	0.765672i
$129$		0			0
$130$	217.225	−	336.391i	1.67096	−	2.58762i
$131$	−154.995			−1.18317			−0.591583	−	0.806244i	$-0.701497\pi$
$131$	−154.995			−1.18317			−0.591583	+	0.806244i	$0.701497\pi$
$132$		0			0
$133$			45.9817i			0.345727i
$134$	−87.0643	+	134.826i	−0.649734	+	1.00617i
$135$		0			0
$136$	114.081	+	17.1660i	0.838831	+	0.126221i
$137$			139.458i			1.01794i	0.860783	+	0.508972i	$0.169974\pi$
$137$			139.458i			1.01794i	−0.860783	+	0.508972i	$0.830026\pi$
$138$		0			0
$139$			54.7935i			0.394198i	0.980384	+	0.197099i	$0.0631520\pi$
$139$			54.7935i			0.394198i	−0.980384	+	0.197099i	$0.936848\pi$
$140$	49.0777	+	108.719i	0.350555	+	0.776567i
$141$		0			0
$142$	−88.8706	+	137.624i	−0.625849	+	0.969180i
$143$		−	182.905i		−	1.27905i
$144$		0			0
$145$	98.3320			0.678152
$146$	20.0189	+	12.9273i	0.137116	+	0.0885428i
$147$		0			0
$148$	41.3948	−	18.6863i	0.279694	−	0.126259i
$149$	−48.0367			−0.322394			−0.161197	−	0.986922i	$-0.551535\pi$
$149$	−48.0367			−0.322394			−0.161197	+	0.986922i	$0.551535\pi$
$150$		0			0
$151$	92.7268			0.614085			0.307042	−	0.951696i	$-0.400661\pi$
$151$	92.7268			0.614085			0.307042	+	0.951696i	$0.400661\pi$
$152$	108.447	+	16.3183i	0.713468	+	0.107357i
$153$		0			0
$154$	45.7712	+	29.5568i	0.297216	+	0.191928i
$155$	−372.284			−2.40183
$156$		0			0
$157$		−	75.7935i		−	0.482761i	−0.970431	−	0.241380i	$-0.922400\pi$
$157$		−	75.7935i		−	0.482761i	0.970431	−	0.241380i	$-0.0776002\pi$
$158$	−62.5496	−	40.3915i	−0.395883	−	0.255642i
$159$		0			0
$160$	273.830	−	77.1660i	1.71144	−	0.482288i
$161$		−	98.8627i		−	0.614054i
$162$		0			0
$163$		−	4.29150i		−	0.0263282i	−0.999913	−	0.0131641i	$-0.995810\pi$
$163$		−	4.29150i		−	0.0263282i	0.999913	−	0.0131641i	$-0.00419039\pi$
$164$	−15.8219	+	7.14226i	−0.0964749	+	0.0435503i
$165$		0			0
$166$	98.0810	+	63.3360i	0.590850	+	0.381542i
$167$		−	18.9846i		−	0.113680i	−0.998383	−	0.0568400i	$-0.981898\pi$
$167$		−	18.9846i		−	0.113680i	0.998383	−	0.0568400i	$-0.0181025\pi$
$168$		0			0
$169$	−338.162			−2.00096
$170$	−139.098	+	215.405i	−0.818224	+	1.26709i
$171$		0			0
$172$	−198.539	+	89.6235i	−1.15429	+	0.521067i
$173$	108.645			0.628004			0.314002	−	0.949422i	$-0.398330\pi$
$173$	108.645			0.628004			0.314002	+	0.949422i	$0.398330\pi$
$174$		0			0
$175$	−181.265			−1.03580
$176$	85.9529	−	97.4614i	0.488369	−	0.553758i
$177$		0			0
$178$	−100.399	+	155.476i	−0.564038	+	0.873460i
$179$	102.495			0.572599			0.286300	−	0.958140i	$-0.407575\pi$
$179$	102.495			0.572599			0.286300	+	0.958140i	$0.407575\pi$
$180$		0			0
$181$		−	149.516i		−	0.826057i	−0.910718	−	0.413029i	$-0.864471\pi$
$181$		−	149.516i		−	0.826057i	0.910718	−	0.413029i	$-0.135529\pi$
$182$	81.9558	−	126.915i	0.450307	−	0.697338i
$183$		0			0
$184$	−233.166	−	35.0850i	−1.26721	−	0.190679i
$185$			100.945i			0.545647i
$186$		0			0
$187$			117.122i			0.626318i
$188$	−45.1596	+	20.3858i	−0.240211	+	0.108435i
$189$		0			0
$190$	−132.229	+	204.767i	−0.695941	+	1.07772i
$191$			343.654i			1.79923i	0.436680	+	0.899617i	$0.356154\pi$
$191$			343.654i			1.79923i	−0.436680	+	0.899617i	$0.643846\pi$
$192$		0			0
$193$	−42.4615			−0.220008			−0.110004	−	0.993931i	$-0.535086\pi$
$193$	−42.4615			−0.220008			−0.110004	+	0.993931i	$0.535086\pi$
$194$	−24.0117	−	15.5056i	−0.123772	−	0.0799259i
$195$		0			0
$196$	−62.1255	−	137.624i	−0.316967	−	0.702161i
$197$	−33.3920			−0.169502			−0.0847512	−	0.996402i	$-0.527010\pi$
$197$	−33.3920			−0.169502			−0.0847512	+	0.996402i	$0.527010\pi$
$198$		0			0
$199$	−114.476			−0.575255			−0.287628	−	0.957742i	$-0.592867\pi$
$199$	−114.476			−0.575255			−0.287628	+	0.957742i	$0.592867\pi$
$200$	−64.3285	+	427.511i	−0.321643	+	2.13756i
$201$		0			0
$202$	77.8745	+	50.2876i	0.385517	+	0.248948i
$203$	37.0993			0.182755
$204$		0			0
$205$		−	38.5830i		−	0.188210i
$206$	−274.520	−	177.271i	−1.33262	−	0.860541i
$207$		0			0
$208$	−270.243	−	238.332i	−1.29925	−	1.14583i
$209$			111.337i			0.532715i
$210$		0			0
$211$			316.454i			1.49978i	0.661563	+	0.749890i	$0.269894\pi$
$211$			316.454i			1.49978i	−0.661563	+	0.749890i	$0.730106\pi$
$212$	−82.4829	−	182.720i	−0.389070	−	0.861888i
$213$		0			0
$214$	322.974	+	208.561i	1.50922	+	0.974583i
$215$		−	484.153i		−	2.25187i
$216$		0			0
$217$	−140.458			−0.647270
$218$	69.3888	−	107.454i	0.318297	−	0.492910i
$219$		0			0
$220$	118.834	+	263.247i	0.540154	+	1.19658i
$221$	324.757			1.46949
$222$		0			0
$223$	336.871			1.51063			0.755315	−	0.655362i	$-0.227484\pi$
$223$	336.871			1.51063			0.755315	+	0.655362i	$0.227484\pi$
$224$	103.312	−	29.1136i	0.461215	−	0.129972i
$225$		0			0
$226$	189.565	−	293.557i	0.838782	−	1.29892i
$227$	229.070			1.00912			0.504560	−	0.863377i	$-0.331655\pi$
$227$	229.070			1.00912			0.504560	+	0.863377i	$0.331655\pi$
$228$		0			0
$229$			121.668i			0.531301i	0.964069	+	0.265651i	$0.0855868\pi$
$229$			121.668i			0.531301i	−0.964069	+	0.265651i	$0.914413\pi$
$230$	284.298	−	440.259i	1.23608	−	1.91417i
$231$		0			0
$232$	13.1660	−	87.4980i	0.0567500	−	0.377147i
$233$			369.332i			1.58512i	0.609796	+	0.792559i	$0.291252\pi$
$233$			369.332i			1.58512i	−0.609796	+	0.792559i	$0.708748\pi$
$234$		0			0
$235$		−	110.125i		−	0.468619i
$236$	81.5649	+	180.687i	0.345614	+	0.765621i
$237$		0			0
$238$	−52.4797	+	81.2693i	−0.220503	+	0.341468i
$239$		−	334.342i		−	1.39892i	−0.714672	−	0.699459i	$-0.753424\pi$
$239$		−	334.342i		−	1.39892i	0.714672	−	0.699459i	$-0.246576\pi$
$240$		0			0
$241$	240.373			0.997396			0.498698	−	0.866776i	$-0.333812\pi$
$241$	240.373			0.997396			0.498698	+	0.866776i	$0.333812\pi$
$242$	−92.4692	−	59.7121i	−0.382104	−	0.246744i
$243$		0			0
$244$	247.682	−	111.808i	1.01509	−	0.458229i
$245$	335.607			1.36982
$246$		0			0
$247$	308.719			1.24987
$248$	−49.8464	+	331.267i	−0.200994	+	1.33575i
$249$		0			0
$250$	−433.786	−	280.118i	−1.73514	−	1.12047i
$251$	253.572			1.01025			0.505123	−	0.863047i	$-0.331447\pi$
$251$	253.572			1.01025			0.505123	+	0.863047i	$0.331447\pi$
$252$		0			0
$253$		−	239.380i		−	0.946168i
$254$	−143.513	−	92.6735i	−0.565010	−	0.364856i
$255$		0			0
$256$	−32.0000	−	253.992i	−0.125000	−	0.992157i
$257$		−	18.0797i		−	0.0703491i	−0.999381	−	0.0351745i	$-0.988801\pi$
$257$		−	18.0797i		−	0.0703491i	0.999381	−	0.0351745i	$-0.0111987\pi$
$258$		0			0
$259$			38.0850i			0.147046i
$260$	729.937	−	329.505i	2.80745	−	1.26733i
$261$		0			0
$262$	−260.413	−	168.162i	−0.993943	−	0.641840i
$263$			38.3379i			0.145771i	0.997340	+	0.0728857i	$0.0232208\pi$
$263$			38.3379i			0.145771i	−0.997340	+	0.0728857i	$0.976779\pi$
$264$		0			0
$265$	445.579			1.68143
$266$	−49.8880	+	77.2558i	−0.187549	+	0.290435i
$267$		0			0
$268$	−292.561	+	132.067i	−1.09164	+	0.492786i
$269$	−58.3416			−0.216883			−0.108442	−	0.994103i	$-0.534586\pi$
$269$	−58.3416			−0.216883			−0.108442	+	0.994103i	$0.534586\pi$
$270$		0			0
$271$	218.350			0.805721			0.402860	−	0.915261i	$-0.368016\pi$
$271$	218.350			0.805721			0.402860	+	0.915261i	$0.368016\pi$
$272$	173.048	+	152.614i	0.636206	+	0.561081i
$273$		0			0
$274$	−151.306	+	234.310i	−0.552211	+	0.855145i
$275$	−438.906			−1.59602
$276$		0			0
$277$			369.284i			1.33315i	0.745436	+	0.666577i	$0.232241\pi$
$277$			369.284i			1.33315i	−0.745436	+	0.666577i	$0.767759\pi$
$278$	−59.4484	+	92.0608i	−0.213843	+	0.331154i
$279$		0			0
$280$	−35.4980	+	235.911i	−0.126779	+	0.842540i
$281$		−	206.229i		−	0.733911i	−0.930238	−	0.366956i	$-0.880400\pi$
$281$		−	206.229i		−	0.733911i	0.930238	−	0.366956i	$-0.119600\pi$
$282$		0			0
$283$		−	345.793i		−	1.22189i	−0.791675	−	0.610943i	$-0.790791\pi$
$283$		−	345.793i		−	1.22189i	0.791675	−	0.610943i	$-0.209209\pi$
$284$	−298.630	+	134.807i	−1.05152	+	0.474671i
$285$		0			0
$286$	198.443	−	307.306i	0.693857	−	1.07450i
$287$		−	14.5568i		−	0.0507206i
$288$		0			0
$289$	81.0445			0.280431
$290$	165.212	+	106.686i	0.569696	+	0.367882i
$291$		0			0
$292$	19.6092	+	43.4392i	0.0671547	+	0.148764i
$293$	63.8936			0.218067			0.109033	−	0.994038i	$-0.465224\pi$
$293$	63.8936			0.218067			0.109033	+	0.994038i	$0.465224\pi$
$294$		0			0
$295$	−440.620			−1.49363
$296$	89.8228	+	13.5158i	0.303455	+	0.0456616i
$297$		0			0
$298$	−80.7085	−	52.1176i	−0.270834	−	0.174891i
$299$	−663.759			−2.21993
$300$		0			0
$301$		−	182.664i		−	0.606857i
$302$	155.794	+	100.604i	0.515875	+	0.333127i
$303$		0			0
$304$	164.502	+	145.077i	0.541125	+	0.477227i
$305$			603.994i			1.98031i
$306$		0			0
$307$			199.373i			0.649422i	0.945813	+	0.324711i	$0.105267\pi$
$307$			199.373i			0.649422i	−0.945813	+	0.324711i	$0.894733\pi$
$308$	44.8344	+	99.3194i	0.145566	+	0.322465i
$309$		0			0
$310$	−625.490	−	403.911i	−2.01771	−	1.30294i
$311$		−	212.467i		−	0.683172i	−0.939851	−	0.341586i	$-0.889036\pi$
$311$		−	212.467i		−	0.683172i	0.939851	−	0.341586i	$-0.110964\pi$
$312$		0			0
$313$	571.612			1.82624			0.913118	−	0.407696i	$-0.133668\pi$
$313$	571.612			1.82624			0.913118	+	0.407696i	$0.133668\pi$
$314$	82.2324	−	127.344i	0.261887	−	0.405553i
$315$		0			0
$316$	−61.2693	−	135.727i	−0.193890	−	0.429515i
$317$	410.077			1.29362			0.646810	−	0.762651i	$-0.276103\pi$
$317$	410.077			1.29362			0.646810	+	0.762651i	$0.276103\pi$
$318$		0			0
$319$	89.8301			0.281599
$320$	543.795	+	167.443i	1.69936	+	0.523260i
$321$		0			0
$322$	107.261	−	166.103i	0.333110	−	0.515849i
$323$	−197.686			−0.612030
$324$		0			0
$325$			1217.01i			3.74464i
$326$	4.65608	−	7.21033i	0.0142825	−	0.0221176i
$327$		0			0
$328$	−34.3320	−	5.16601i	−0.104671	−	0.0157500i
$329$		−	41.5488i		−	0.126288i
$330$		0			0
$331$			14.7046i			0.0444247i	0.999753	+	0.0222123i	$0.00707098\pi$
$331$			14.7046i			0.0444247i	−0.999753	+	0.0222123i	$0.992929\pi$
$332$	96.0734	+	212.827i	0.289378	+	0.641044i
$333$		0			0
$334$	20.5974	−	31.8967i	0.0616687	−	0.0954992i
$335$		−	713.434i		−	2.12965i
$336$		0			0
$337$	−286.793			−0.851019			−0.425510	−	0.904954i	$-0.639905\pi$
$337$	−286.793			−0.851019			−0.425510	+	0.904954i	$0.639905\pi$
$338$	−568.160	−	366.890i	−1.68095	−	1.08547i
$339$		0			0
$340$	−467.409	+	210.996i	−1.37473	+	0.620577i
$341$	−340.096			−0.997348
$342$		0			0
$343$	290.978			0.848332
$344$	−430.810	−	64.8249i	−1.25236	−	0.188445i
$345$		0			0
$346$	182.539	+	117.875i	0.527568	+	0.340678i
$347$	381.957			1.10074			0.550370	−	0.834921i	$-0.314487\pi$
$347$	381.957			1.10074			0.550370	+	0.834921i	$0.314487\pi$
$348$		0			0
$349$		−	483.605i		−	1.38569i	−0.721087	−	0.692844i	$-0.756357\pi$
$349$		−	483.605i		−	1.38569i	0.721087	−	0.692844i	$-0.243643\pi$
$350$	−304.551	−	196.664i	−0.870147	−	0.561899i
$351$		0			0
$352$	250.154	−	70.4941i	0.710665	−	0.200267i
$353$			429.273i			1.21607i	0.793910	+	0.608035i	$0.208042\pi$
$353$			429.273i			1.21607i	−0.793910	+	0.608035i	$0.791958\pi$
$354$		0			0
$355$		−	728.235i		−	2.05137i
$356$	−337.368	+	152.293i	−0.947663	+	0.427791i
$357$		0			0
$358$	172.207	+	111.203i	0.481024	+	0.310622i
$359$			159.300i			0.443731i	0.975077	+	0.221866i	$0.0712146\pi$
$359$			159.300i			0.443731i	−0.975077	+	0.221866i	$0.928785\pi$
$360$		0			0
$361$	173.077			0.479438
$362$	162.218	−	251.209i	0.448117	−	0.693946i
$363$		0			0
$364$	275.395	−	124.318i	0.756579	−	0.341532i
$365$	−105.930			−0.290220
$366$		0			0
$367$	−293.265			−0.799088			−0.399544	−	0.916714i	$-0.630832\pi$
$367$	−293.265			−0.799088			−0.399544	+	0.916714i	$0.630832\pi$
$368$	−353.686	−	311.922i	−0.961104	−	0.847614i
$369$		0			0
$370$	−109.520	+	169.601i	−0.296001	+	0.458382i
$371$	168.111			0.453128
$372$		0			0
$373$			99.2288i			0.266029i	0.991114	+	0.133014i	$0.0424657\pi$
$373$			99.2288i			0.266029i	−0.991114	+	0.133014i	$0.957534\pi$
$374$	−127.071	+	196.781i	−0.339763	+	0.526152i
$375$		0			0
$376$	−97.9921	−	14.7451i	−0.260617	−	0.0392156i
$377$		−	249.083i		−	0.660697i
$378$		0			0
$379$			399.405i			1.05384i	0.849915	+	0.526920i	$0.176653\pi$
$379$			399.405i			1.05384i	−0.849915	+	0.526920i	$0.823347\pi$
$380$	−444.326	+	200.576i	−1.16928	+	0.527832i
$381$		0			0
$382$	−372.848	+	577.387i	−0.976043	+	1.51148i
$383$			543.918i			1.42015i	0.704126	+	0.710075i	$0.251339\pi$
$383$			543.918i			1.42015i	−0.704126	+	0.710075i	$0.748661\pi$
$384$		0			0
$385$	−242.199			−0.629087
$386$	−71.3412	−	46.0687i	−0.184822	−	0.119349i
$387$		0			0
$388$	−23.5203	−	52.1033i	−0.0606192	−	0.134287i
$389$	−111.957			−0.287807			−0.143903	−	0.989592i	$-0.545965\pi$
$389$	−111.957			−0.287807			−0.143903	+	0.989592i	$0.545965\pi$
$390$		0			0
$391$	425.033			1.08704
$392$	44.9355	−	298.630i	0.114631	−	0.761812i
$393$		0			0
$394$	−56.1033	−	36.2288i	−0.142394	−	0.0919512i
$395$	330.981			0.837927
$396$		0			0
$397$		−	351.956i		−	0.886538i	−0.896389	−	0.443269i	$-0.853819\pi$
$397$		−	351.956i		−	0.886538i	0.896389	−	0.443269i	$-0.146181\pi$
$398$	−192.336	−	124.201i	−0.483255	−	0.312063i
$399$		0			0
$400$	−571.911	+	648.486i	−1.42978	+	1.62122i
$401$			460.372i			1.14806i	0.818834	+	0.574030i	$0.194621\pi$
$401$			460.372i			1.14806i	−0.818834	+	0.574030i	$0.805379\pi$
$402$		0			0
$403$			943.025i			2.34001i
$404$	76.2805	+	168.980i	0.188813	+	0.418268i
$405$		0			0
$406$	62.3320	+	40.2510i	0.153527	+	0.0991404i
$407$			92.2168i			0.226577i
$408$		0			0
$409$	−300.542			−0.734823			−0.367411	−	0.930059i	$-0.619756\pi$
$409$	−300.542			−0.734823			−0.367411	+	0.930059i	$0.619756\pi$
$410$	41.8608	−	64.8249i	0.102099	−	0.158110i
$411$		0			0
$412$	−268.901	−	595.682i	−0.652672	−	1.44583i
$413$	−166.239			−0.402517
$414$		0			0
$415$	−518.996			−1.25059
$416$	−195.467	−	693.633i	−0.469874	−	1.66739i
$417$		0			0
$418$	−120.796	+	187.063i	−0.288986	+	0.447519i
$419$	−595.341			−1.42086			−0.710431	−	0.703767i	$-0.751500\pi$
$419$	−595.341			−1.42086			−0.710431	+	0.703767i	$0.751500\pi$
$420$		0			0
$421$		−	233.759i		−	0.555248i	−0.960690	−	0.277624i	$-0.910453\pi$
$421$		−	233.759i		−	0.555248i	0.960690	−	0.277624i	$-0.0895469\pi$
$422$	−343.337	+	531.687i	−0.813596	+	1.25992i
$423$		0			0
$424$	59.6601	−	396.486i	0.140708	−	0.935109i
$425$		−	779.300i		−	1.83365i
$426$		0			0
$427$			227.878i			0.533673i
$428$	316.363	+	700.823i	0.739166	+	1.63744i
$429$		0			0
$430$	525.284	−	813.446i	1.22159	−	1.89173i
$431$		−	361.013i		−	0.837617i	−0.908075	−	0.418809i	$-0.862448\pi$
$431$		−	361.013i		−	0.837617i	0.908075	−	0.418809i	$-0.137552\pi$
$432$		0			0
$433$	−527.859			−1.21907			−0.609537	−	0.792758i	$-0.708644\pi$
$433$	−527.859			−1.21907			−0.609537	+	0.792758i	$0.708644\pi$
$434$	−235.989	−	152.390i	−0.543752	−	0.351129i
$435$		0			0
$436$	233.166	−	105.255i	0.534784	−	0.241410i
$437$	404.042			0.924582
$438$		0			0
$439$	−174.450			−0.397380			−0.198690	−	0.980062i	$-0.563669\pi$
$439$	−174.450			−0.397380			−0.198690	+	0.980062i	$0.563669\pi$
$440$	−85.9529	+	571.222i	−0.195348	+	1.29823i
$441$		0			0
$442$	545.638	+	352.346i	1.23447	+	0.797164i
$443$	−693.211			−1.56481			−0.782405	−	0.622770i	$-0.786007\pi$
$443$	−693.211			−1.56481			−0.782405	+	0.622770i	$0.786007\pi$
$444$		0			0
$445$		−	822.701i		−	1.84877i
$446$	565.990	+	365.489i	1.26904	+	0.819482i
$447$		0			0
$448$	205.166	+	63.1739i	0.457960	+	0.141013i
$449$			125.991i			0.280603i	0.990109	+	0.140302i	$0.0448072\pi$
$449$			125.991i			0.280603i	−0.990109	+	0.140302i	$0.955193\pi$
$450$		0			0
$451$		−	35.2470i		−	0.0781531i
$452$	636.991	−	287.548i	1.40927	−	0.636168i
$453$		0			0
$454$	384.871	+	248.531i	0.847733	+	0.547424i
$455$			671.573i			1.47599i
$456$		0			0
$457$	−181.365			−0.396859			−0.198430	−	0.980115i	$-0.563584\pi$
$457$	−181.365			−0.396859			−0.198430	+	0.980115i	$0.563584\pi$
$458$	−132.004	+	204.419i	−0.288219	+	0.446331i
$459$		0			0
$460$	955.320	−	431.247i	2.07678	−	0.937494i
$461$	−724.046			−1.57060			−0.785300	−	0.619116i	$-0.787491\pi$
$461$	−724.046			−1.57060			−0.785300	+	0.619116i	$0.787491\pi$
$462$		0			0
$463$	614.755			1.32777			0.663883	−	0.747837i	$-0.268907\pi$
$463$	614.755			1.32777			0.663883	+	0.747837i	$0.268907\pi$
$464$	117.052	−	132.725i	0.252267	−	0.286044i
$465$		0			0
$466$	−400.708	+	620.531i	−0.859889	+	1.33161i
$467$	38.7993			0.0830819			0.0415410	−	0.999137i	$-0.486773\pi$
$467$	38.7993			0.0830819			0.0415410	+	0.999137i	$0.486773\pi$
$468$		0			0
$469$		−	269.169i		−	0.573920i
$470$	119.481	−	185.026i	0.254215	−	0.393673i
$471$		0			0
$472$	−58.9961	+	392.073i	−0.124992	+	0.830663i
$473$		−	442.292i		−	0.935079i
$474$		0			0
$475$		−	740.814i		−	1.55961i
$476$	−176.347	+	79.6058i	−0.370476	+	0.167239i
$477$		0			0
$478$	362.745	−	561.741i	0.758881	−	1.17519i
$479$			444.919i			0.928849i	0.885613	+	0.464425i	$0.153739\pi$
$479$			444.919i			0.928849i	−0.885613	+	0.464425i	$0.846261\pi$
$480$		0			0
$481$	255.701			0.531602
$482$	403.860	+	260.793i	0.837884	+	0.541064i
$483$		0			0
$484$	−90.5765	−	200.650i	−0.187142	−	0.414565i
$485$	127.058			0.261976
$486$		0			0
$487$	330.196			0.678021			0.339010	−	0.940783i	$-0.389908\pi$
$487$	330.196			0.678021			0.339010	+	0.940783i	$0.389908\pi$
$488$	537.448	+	80.8709i	1.10133	+	0.165719i
$489$		0			0
$490$	563.867	+	364.118i	1.15075	+	0.743097i
$491$	291.053			0.592776			0.296388	−	0.955068i	$-0.404218\pi$
$491$	291.053			0.592776			0.296388	+	0.955068i	$0.404218\pi$
$492$		0			0
$493$			159.498i			0.323525i
$494$	518.691	+	334.946i	1.04998	+	0.678028i
$495$		0			0
$496$	−443.158	+	502.494i	−0.893464	+	1.01309i
$497$		−	274.753i		−	0.552822i
$498$		0			0
$499$		−	556.980i		−	1.11619i	−0.829776	−	0.558097i	$-0.811532\pi$
$499$		−	556.980i		−	1.11619i	0.829776	−	0.558097i	$-0.188468\pi$
$500$	−424.907	−	941.275i	−0.849813	−	1.88255i
$501$		0			0
$502$	426.037	+	275.114i	0.848678	+	0.548035i
$503$		−	313.547i		−	0.623355i	−0.950188	−	0.311677i	$-0.899109\pi$
$503$		−	313.547i		−	0.623355i	0.950188	−	0.311677i	$-0.100891\pi$
$504$		0			0
$505$	−412.073			−0.815986
$506$	259.717	−	402.193i	0.513274	−	0.794848i
$507$		0			0
$508$	−140.575	−	311.409i	−0.276723	−	0.613010i
$509$	−379.216			−0.745021			−0.372510	−	0.928028i	$-0.621503\pi$
$509$	−379.216			−0.745021			−0.372510	+	0.928028i	$0.621503\pi$
$510$		0			0
$511$	−39.9660			−0.0782113
$512$	221.805	−	461.461i	0.433213	−	0.901291i
$513$		0			0
$514$	19.6156	−	30.3765i	0.0381627	−	0.0590982i
$515$	1452.62			2.82062
$516$		0			0
$517$		−	100.604i		−	0.194592i
$518$	−41.3204	+	63.9881i	−0.0797692	+	0.123529i
$519$		0			0
$520$	1583.90	+	238.332i	3.04595	+	0.458331i
$521$		−	753.085i		−	1.44546i	−0.691130	−	0.722731i	$-0.742887\pi$
$521$		−	753.085i		−	1.44546i	0.691130	−	0.722731i	$-0.257113\pi$
$522$		0			0
$523$			239.125i			0.457219i	0.973518	+	0.228609i	$0.0734179\pi$
$523$			239.125i			0.457219i	−0.973518	+	0.228609i	$0.926582\pi$
$524$	−255.083	−	565.072i	−0.486799	−	1.07838i
$525$		0			0
$526$	−41.5948	+	64.4131i	−0.0790776	+	0.122458i
$527$		−	603.858i		−	1.14584i
$528$		0			0
$529$	−339.708			−0.642171
$530$	748.636	+	483.433i	1.41252	+	0.912137i
$531$		0			0
$532$	−167.638	+	75.6745i	−0.315109	+	0.142245i
$533$	−97.7337			−0.183365
$534$		0			0
$535$	−1709.02			−3.19442
$536$	−634.830	−	95.5242i	−1.18438	−	0.178217i
$537$		0			0
$538$	−98.0222	−	63.2980i	−0.182197	−	0.117654i
$539$	306.589			0.568812
$540$		0			0
$541$			120.379i			0.222512i	0.993792	+	0.111256i	$0.0354874\pi$
$541$			120.379i			0.222512i	−0.993792	+	0.111256i	$0.964513\pi$
$542$	366.859	+	236.900i	0.676862	+	0.437085i
$543$		0			0
$544$	125.166	+	444.162i	0.230085	+	0.816474i
$545$			568.595i			1.04329i
$546$		0			0
$547$		−	188.838i		−	0.345225i	−0.984990	−	0.172612i	$-0.944779\pi$
$547$		−	188.838i		−	0.345225i	0.984990	−	0.172612i	$-0.0552208\pi$
$548$	−508.431	+	229.514i	−0.927793	+	0.418821i
$549$		0			0
$550$	−737.423	−	476.192i	−1.34077	−	0.865804i
$551$			151.621i			0.275175i
$552$		0			0
$553$	124.875			0.225813
$554$	−400.656	+	620.449i	−0.723205	+	1.11994i
$555$		0			0
$556$	−199.763	+	90.1764i	−0.359287	+	0.162188i
$557$	853.626			1.53254			0.766271	−	0.642517i	$-0.222110\pi$
$557$	853.626			1.53254			0.766271	+	0.642517i	$0.222110\pi$
$558$		0			0
$559$	−1226.40			−2.19391
$560$	−315.594	+	357.850i	−0.563561	+	0.639018i
$561$		0			0
$562$	223.749	−	346.494i	0.398130	−	0.616538i
$563$	512.327			0.909994			0.454997	−	0.890493i	$-0.349640\pi$
$563$	512.327			0.909994			0.454997	+	0.890493i	$0.349640\pi$
$564$		0			0
$565$			1553.36i			2.74930i
$566$	375.170	−	580.982i	0.662844	−	1.02647i
$567$		0			0
$568$	−648.000	−	97.5059i	−1.14085	−	0.171665i
$569$			31.5076i			0.0553737i	0.999617	+	0.0276868i	$0.00881412\pi$
$569$			31.5076i			0.0553737i	−0.999617	+	0.0276868i	$0.991186\pi$
$570$		0			0
$571$		−	186.712i		−	0.326992i	−0.986544	−	0.163496i	$-0.947723\pi$
$571$		−	186.712i		−	0.326992i	0.986544	−	0.163496i	$-0.0522771\pi$
$572$	666.825	−	301.016i	1.16578	−	0.526251i
$573$		0			0
$574$	15.7935	−	24.4575i	0.0275148	−	0.0426089i
$575$			1592.78i			2.77006i
$576$		0			0
$577$	563.405			0.976439			0.488219	−	0.872721i	$-0.337647\pi$
$577$	563.405			0.976439			0.488219	+	0.872721i	$0.337647\pi$
$578$	136.166	+	87.9295i	0.235582	+	0.152127i
$579$		0			0
$580$	161.830	+	358.494i	0.279017	+	0.618093i
$581$	−195.810			−0.337022
$582$		0			0
$583$	407.053			0.698205
$584$	−14.1834	+	94.2591i	−0.0242866	+	0.161403i
$585$		0			0
$586$	107.350	+	69.3216i	0.183192	+	0.118296i
$587$	191.958			0.327015			0.163508	−	0.986542i	$-0.447719\pi$
$587$	191.958			0.327015			0.163508	+	0.986542i	$0.447719\pi$
$588$		0			0
$589$		−	574.037i		−	0.974595i
$590$	−740.303	−	478.052i	−1.25475	−	0.810257i
$591$		0			0
$592$	136.251	+	120.162i	0.230154	+	0.202976i
$593$		−	151.621i		−	0.255685i	−0.991794	−	0.127842i	$-0.959195\pi$
$593$		−	151.621i		−	0.255685i	0.991794	−	0.127842i	$-0.0408052\pi$
$594$		0			0
$595$		−	430.037i		−	0.722751i
$596$	−79.0565	−	175.130i	−0.132645	−	0.293842i
$597$		0			0
$598$	−1115.21	−	720.148i	−1.86490	−	1.20426i
$599$			260.292i			0.434545i	0.976111	+	0.217272i	$0.0697160\pi$
$599$			260.292i			0.434545i	−0.976111	+	0.217272i	$0.930284\pi$
$600$		0			0
$601$	−772.863			−1.28596			−0.642981	−	0.765882i	$-0.722302\pi$
$601$	−772.863			−1.28596			−0.642981	+	0.765882i	$0.722302\pi$
$602$	198.182	−	306.901i	0.329206	−	0.509803i
$603$		0			0
$604$	152.605	+	338.059i	0.252658	+	0.559700i
$605$	489.301			0.808762
$606$		0			0
$607$	60.8967			0.100324			0.0501621	−	0.998741i	$-0.484026\pi$
$607$	60.8967			0.100324			0.0501621	+	0.998741i	$0.484026\pi$
$608$	118.985	+	422.227i	0.195698	+	0.694452i
$609$		0			0
$610$	−655.306	+	1014.80i	−1.07427	+	1.66360i
$611$	−278.956			−0.456557
$612$		0			0
$613$			590.586i			0.963435i	0.876327	+	0.481717i	$0.159987\pi$
$613$			590.586i			0.963435i	−0.876327	+	0.481717i	$0.840013\pi$
$614$	−216.310	+	334.974i	−0.352296	+	0.545560i
$615$		0			0
$616$	−32.4288	+	215.514i	−0.0526442	+	0.349860i
$617$		−	769.707i		−	1.24750i	−0.781624	−	0.623750i	$-0.785608\pi$
$617$		−	769.707i		−	1.24750i	0.781624	−	0.623750i	$-0.214392\pi$
$618$		0			0
$619$		−	160.482i		−	0.259261i	−0.991562	−	0.129630i	$-0.958621\pi$
$619$		−	160.482i		−	0.259261i	0.991562	−	0.129630i	$-0.0413790\pi$
$620$	−612.687	−	1357.26i	−0.988205	−	2.18912i
$621$		0			0
$622$	230.516	−	356.974i	0.370605	−	0.573913i
$623$		−	310.393i		−	0.498223i
$624$		0			0
$625$	944.365			1.51098
$626$	960.389	+	620.172i	1.53417	+	0.990690i
$627$		0			0
$628$	276.324	−	124.737i	0.440007	−	0.198626i
$629$	−163.736			−0.260311
$630$		0			0
$631$	169.893			0.269244			0.134622	−	0.990897i	$-0.457018\pi$
$631$	169.893			0.269244			0.134622	+	0.990897i	$0.457018\pi$
$632$	44.3162	−	294.515i	0.0701206	−	0.466004i
$633$		0			0
$634$	688.988	+	444.915i	1.08673	+	0.701759i
$635$	759.398			1.19590
$636$		0			0
$637$		−	850.118i		−	1.33456i
$638$	150.927	+	97.4614i	0.236563	+	0.152761i
$639$		0			0
$640$	731.984	+	871.320i	1.14373	+	1.36144i
$641$		−	440.755i		−	0.687605i	−0.939042	−	0.343803i	$-0.888285\pi$
$641$		−	440.755i		−	0.687605i	0.939042	−	0.343803i	$-0.111715\pi$
$642$		0			0
$643$			644.936i			1.00301i	0.865155	+	0.501505i	$0.167220\pi$
$643$			644.936i			1.00301i	−0.865155	+	0.501505i	$0.832780\pi$
$644$	360.429	−	162.703i	0.559672	−	0.252645i
$645$		0			0
$646$	−332.140	−	214.480i	−0.514148	−	0.332012i
$647$			1100.41i			1.70078i	0.526150	+	0.850392i	$0.323635\pi$
$647$			1100.41i			1.70078i	−0.526150	+	0.850392i	$0.676365\pi$
$648$		0			0
$649$	−402.523			−0.620220
$650$	−1320.40	+	2044.74i	−2.03138	+	3.14576i
$651$		0			0
$652$	15.6458	−	7.06275i	0.0239966	−	0.0108324i
$653$	−626.032			−0.958701			−0.479351	−	0.877623i	$-0.659128\pi$
$653$	−626.032			−0.958701			−0.479351	+	0.877623i	$0.659128\pi$
$654$		0			0
$655$	1377.98			2.10378
$656$	−52.0778	−	45.9283i	−0.0793868	−	0.0700126i
$657$		0			0
$658$	45.0785	−	69.8078i	0.0685084	−	0.106091i
$659$	−264.835			−0.401873			−0.200937	−	0.979604i	$-0.564399\pi$
$659$	−264.835			−0.401873			−0.200937	+	0.979604i	$0.564399\pi$
$660$		0			0
$661$			1311.50i			1.98412i	0.125782	+	0.992058i	$0.459856\pi$
$661$			1311.50i			1.98412i	−0.125782	+	0.992058i	$0.540144\pi$
$662$	−15.9538	+	24.7057i	−0.0240993	+	0.0373199i
$663$		0			0
$664$	−69.4902	+	461.814i	−0.104654	+	0.695503i
$665$		−	408.799i		−	0.614736i
$666$		0			0
$667$		−	325.992i		−	0.488744i
$668$	69.2130	−	31.2439i	0.103612	−	0.0467722i
$669$		0			0
$670$	774.043	−	1198.67i	1.15529	−	1.78906i
$671$			551.772i			0.822313i
$672$		0			0
$673$	185.620			0.275809			0.137905	−	0.990446i	$-0.455963\pi$
$673$	185.620			0.275809			0.137905	+	0.990446i	$0.455963\pi$
$674$	−481.854	−	311.158i	−0.714916	−	0.461658i
$675$		0			0
$676$	−556.531	−	1232.85i	−0.823270	−	1.82375i
$677$	−870.607			−1.28598			−0.642989	−	0.765875i	$-0.722306\pi$
$677$	−870.607			−1.28598			−0.642989	+	0.765875i	$0.722306\pi$
$678$		0			0
$679$	47.9373			0.0705998
$680$	−1014.23	−	152.614i	−1.49152	−	0.224432i
$681$		0			0
$682$	−571.409	−	368.988i	−0.837843	−	0.541038i
$683$	−1282.78			−1.87816			−0.939081	−	0.343696i	$-0.888321\pi$
$683$	−1282.78			−1.87816			−0.939081	+	0.343696i	$0.888321\pi$
$684$		0			0
$685$		−	1239.85i		−	1.81000i
$686$	488.884	+	315.697i	0.712659	+	0.460200i
$687$		0			0
$688$	−653.490	−	576.324i	−0.949840	−	0.837680i
$689$		−	1128.69i		−	1.63815i
$690$		0			0
$691$		−	247.963i		−	0.358847i	−0.983772	−	0.179424i	$-0.942577\pi$
$691$		−	247.963i		−	0.358847i	0.983772	−	0.179424i	$-0.0574233\pi$
$692$	178.802	+	396.092i	0.258385	+	0.572387i
$693$		0			0
$694$	641.741	+	414.405i	0.924699	+	0.597126i
$695$		−	487.140i		−	0.700921i
$696$		0			0
$697$	62.5830			0.0897891
$698$	524.689	−	812.525i	0.751704	−	1.16408i
$699$		0			0
$700$	−298.318	−	660.848i	−0.426168	−	0.944069i
$701$	−940.493			−1.34164			−0.670822	−	0.741618i	$-0.734059\pi$
$701$	−940.493			−1.34164			−0.670822	+	0.741618i	$0.734059\pi$
$702$		0			0
$703$	−155.650			−0.221408
$704$	496.777	+	152.966i	0.705650	+	0.217281i
$705$		0			0
$706$	−465.741	+	721.239i	−0.659690	+	1.02159i
$707$	−155.469			−0.219900
$708$		0			0
$709$			189.119i			0.266740i	0.991066	+	0.133370i	$0.0425799\pi$
$709$			189.119i			0.266740i	−0.991066	+	0.133370i	$0.957420\pi$
$710$	790.101	−	1223.54i	1.11282	−	1.72329i
$711$		0			0
$712$	−732.057	−	110.154i	−1.02817	−	0.154711i
$713$			1234.20i			1.73100i
$714$		0			0
$715$			1626.11i			2.27428i
$716$	168.682	+	373.672i	0.235589	+	0.521889i
$717$		0			0
$718$	−172.833	+	267.646i	−0.240714	+	0.372766i
$719$		−	572.214i		−	0.795848i	−0.917418	−	0.397924i	$-0.869731\pi$
$719$		−	572.214i		−	0.795848i	0.917418	−	0.397924i	$-0.130269\pi$
$720$		0			0
$721$	548.053			0.760130
$722$	290.794	+	187.781i	0.402762	+	0.260084i
$723$		0			0
$724$	545.099	−	246.067i	0.752900	−	0.339871i
$725$	−597.709			−0.824426
$726$		0			0
$727$	−323.940			−0.445584			−0.222792	−	0.974866i	$-0.571517\pi$
$727$	−323.940			−0.445584			−0.222792	+	0.974866i	$0.571517\pi$
$728$	597.581	+	89.9193i	0.820853	+	0.123515i
$729$		0			0
$730$	−177.978	−	114.929i	−0.243805	−	0.157438i
$731$	785.313			1.07430
$732$		0			0
$733$		−	705.550i		−	0.962552i	−0.876569	−	0.481276i	$-0.840174\pi$
$733$		−	705.550i		−	0.962552i	0.876569	−	0.481276i	$-0.159826\pi$
$734$	−492.727	−	318.179i	−0.671291	−	0.433487i
$735$		0			0
$736$	−255.822	−	907.806i	−0.347584	−	1.23343i
$737$		−	651.749i		−	0.884328i
$738$		0			0
$739$			64.1987i			0.0868723i	0.999056	+	0.0434362i	$0.0138305\pi$
$739$			64.1987i			0.0868723i	−0.999056	+	0.0434362i	$0.986169\pi$
$740$	−368.019	+	166.130i	−0.497323	+	0.224500i
$741$		0			0
$742$	282.450	+	182.392i	0.380660	+	0.245812i
$743$		−	1254.73i		−	1.68873i	−0.535769	−	0.844364i	$-0.679978\pi$
$743$		−	1254.73i		−	1.68873i	0.535769	−	0.844364i	$-0.320022\pi$
$744$		0			0
$745$	427.069			0.573247
$746$	−107.659	+	166.718i	−0.144314	+	0.223483i
$747$		0			0
$748$	−426.996	+	192.753i	−0.570850	+	0.257691i
$749$	−644.788			−0.860865
$750$		0			0
$751$	604.071			0.804355			0.402178	−	0.915562i	$-0.368253\pi$
$751$	604.071			0.804355			0.402178	+	0.915562i	$0.368253\pi$
$752$	−148.643	−	131.091i	−0.197663	−	0.174323i
$753$		0			0
$754$	270.243	−	418.494i	0.358413	−	0.555032i
$755$	−824.385			−1.09190
$756$		0			0
$757$		−	42.0549i		−	0.0555547i	−0.999614	−	0.0277773i	$-0.991157\pi$
$757$		−	42.0549i		−	0.0555547i	0.999614	−	0.0277773i	$-0.00884293\pi$
$758$	−433.336	+	671.057i	−0.571684	+	0.885300i
$759$		0			0
$760$	−964.146	−	145.077i	−1.26861	−	0.190891i
$761$			645.038i			0.847619i	0.905751	+	0.423810i	$0.139307\pi$
$761$			645.038i			0.847619i	−0.905751	+	0.423810i	$0.860693\pi$
$762$		0			0
$763$			214.523i			0.281157i
$764$	−1252.88	+	565.569i	−1.63989	+	0.740273i
$765$		0			0
$766$	−590.125	+	913.859i	−0.770399	+	1.19303i
$767$			1116.12i			1.45518i
$768$		0			0
$769$	−940.393			−1.22288			−0.611439	−	0.791291i	$-0.709409\pi$
$769$	−940.393			−1.22288			−0.611439	+	0.791291i	$0.709409\pi$
$770$	−406.928	−	262.774i	−0.528478	−	0.341265i
$771$		0			0
$772$	−69.8810	−	154.804i	−0.0905194	−	0.200523i
$773$	881.308			1.14011			0.570057	−	0.821605i	$-0.306921\pi$
$773$	881.308			1.14011			0.570057	+	0.821605i	$0.306921\pi$
$774$		0			0
$775$	2262.92			2.91990
$776$	17.0123	−	113.059i	0.0219230	−	0.145695i
$777$		0			0
$778$	−188.103	−	121.468i	−0.241778	−	0.156128i
$779$	59.4923			0.0763701
$780$		0			0
$781$		−	665.271i		−	0.851819i
$782$	714.115	+	461.141i	0.913191	+	0.589694i
$783$		0			0
$784$	399.498	−	452.988i	0.509564	−	0.577791i
$785$			673.840i			0.858395i
$786$		0			0
$787$		−	291.376i		−	0.370237i	−0.982716	−	0.185118i	$-0.940733\pi$
$787$		−	291.376i		−	0.370237i	0.982716	−	0.185118i	$-0.0592669\pi$
$788$	−54.9549	−	121.739i	−0.0697397	−	0.154491i
$789$		0			0
$790$	556.095	+	359.099i	0.703918	+	0.454556i
$791$			586.059i			0.740909i
$792$		0			0
$793$	1529.96			1.92934
$794$	381.855	−	591.335i	0.480926	−	0.744755i
$795$		0			0
$796$	−188.399	−	417.350i	−0.236682	−	0.524309i
$797$	184.328			0.231277			0.115638	−	0.993291i	$-0.463109\pi$
$797$	184.328			0.231277			0.115638	+	0.993291i	$0.463109\pi$
$798$		0			0
$799$	178.627			0.223564
$800$	−1664.47	+	469.052i	−2.08059	+	0.586315i
$801$		0			0
$802$	−499.482	+	773.490i	−0.622796	+	0.964452i
$803$	−96.7713			−0.120512
$804$		0			0
$805$			878.936i			1.09185i
$806$	−1023.14	+	1584.42i	−1.26940	+	1.96578i
$807$		0			0
$808$	−55.1739	+	366.672i	−0.0682845	+	0.453802i
$809$			52.8947i			0.0653828i	0.999465	+	0.0326914i	$0.0104079\pi$
$809$			52.8947i			0.0653828i	−0.999465	+	0.0326914i	$0.989592\pi$
$810$		0			0
$811$			1134.19i			1.39851i	0.714873	+	0.699254i	$0.246485\pi$
$811$			1134.19i			1.39851i	−0.714873	+	0.699254i	$0.753515\pi$
$812$	61.0562	+	135.255i	0.0751923	+	0.166570i
$813$		0			0
$814$	−100.051	+	154.937i	−0.122913	+	0.190341i
$815$			38.1535i			0.0468141i
$816$		0			0
$817$	746.531			0.913746
$818$	−504.954	−	326.075i	−0.617303	−	0.398624i
$819$		0			0
$820$	140.664	−	63.4980i	0.171542	−	0.0774366i
$821$	−402.083			−0.489748			−0.244874	−	0.969555i	$-0.578747\pi$
$821$	−402.083			−0.489748			−0.244874	+	0.969555i	$0.578747\pi$
$822$		0			0
$823$	678.172			0.824025			0.412012	−	0.911178i	$-0.364826\pi$
$823$	678.172			0.824025			0.412012	+	0.911178i	$0.364826\pi$
$824$	194.497	−	1292.58i	0.236039	−	1.56866i
$825$		0			0
$826$	−279.306	−	180.362i	−0.338143	−	0.218356i
$827$	−27.8353			−0.0336582			−0.0168291	−	0.999858i	$-0.505357\pi$
$827$	−27.8353			−0.0336582			−0.0168291	+	0.999858i	$0.505357\pi$
$828$		0			0
$829$			77.8641i			0.0939253i	0.998897	+	0.0469627i	$0.0149542\pi$
$829$			77.8641i			0.0939253i	−0.998897	+	0.0469627i	$0.985046\pi$
$830$	−871.987	−	563.087i	−1.05059	−	0.678418i
$831$		0			0
$832$	424.146	−	1377.47i	0.509791	−	1.65562i
$833$			544.366i			0.653500i
$834$		0			0
$835$			168.782i			0.202134i
$836$	−405.909	+	183.234i	−0.485537	+	0.219179i
$837$		0			0
$838$	−1000.26	−	645.918i	−1.19362	−	0.770785i
$839$			337.496i			0.402259i	0.979565	+	0.201130i	$0.0644613\pi$
$839$			337.496i			0.402259i	−0.979565	+	0.201130i	$0.935539\pi$
$840$		0			0
$841$	−718.668			−0.854540
$842$	253.618	−	392.749i	0.301209	−	0.466448i
$843$		0			0
$844$	−1153.71	+	520.804i	−1.36696	+	0.617066i
$845$	3006.42			3.55789
$846$		0			0
$847$	184.606			0.217953
$848$	530.407	−	601.425i	0.625479	−	0.709227i
$849$		0			0
$850$	845.505	−	1309.33i	0.994711	−	1.54039i
$851$	334.654			0.393247
$852$		0			0
$853$		−	334.306i		−	0.391918i	−0.980612	−	0.195959i	$-0.937218\pi$
$853$		−	334.306i		−	0.391918i	0.980612	−	0.195959i	$-0.0627819\pi$
$854$	−247.238	+	382.868i	−0.289505	+	0.448323i
$855$		0			0
$856$	−228.826	+	1520.72i	−0.267320	+	1.77654i
$857$			1027.35i			1.19878i	0.800459	+	0.599388i	$0.204589\pi$
$857$			1027.35i			1.19878i	−0.800459	+	0.599388i	$0.795411\pi$
$858$		0			0
$859$		−	703.413i		−	0.818874i	−0.912338	−	0.409437i	$-0.865725\pi$
$859$		−	703.413i		−	0.818874i	0.912338	−	0.409437i	$-0.134275\pi$
$860$	1765.10	−	796.796i	2.05244	−	0.926506i
$861$		0			0
$862$	391.682	−	606.553i	0.454388	−	0.703658i
$863$		−	1021.74i		−	1.18394i	−0.805961	−	0.591968i	$-0.798351\pi$
$863$		−	1021.74i		−	1.18394i	0.805961	−	0.591968i	$-0.201649\pi$
$864$		0			0
$865$	−965.903			−1.11665
$866$	−886.877	−	572.702i	−1.02411	−	0.661319i
$867$		0			0
$868$	−231.158	−	512.073i	−0.266311	−	0.589946i
$869$	302.364			0.347945
$870$		0			0
$871$	−1807.18			−2.07484
$872$	505.949	+	76.1311i	0.580216	+	0.0873064i
$873$		0			0
$874$	678.848	+	438.367i	0.776714	+	0.501564i
$875$	866.013			0.989729
$876$		0			0
$877$			1459.57i			1.66427i	0.554572	+	0.832136i	$0.312882\pi$
$877$			1459.57i			1.66427i	−0.554572	+	0.832136i	$0.687118\pi$
$878$	−293.100	−	189.270i	−0.333827	−	0.215569i
$879$		0			0
$880$	−764.162	+	866.478i	−0.868366	+	0.984634i
$881$		−	1678.35i		−	1.90505i	−0.304467	−	0.952523i	$-0.598478\pi$
$881$		−	1678.35i		−	1.90505i	0.304467	−	0.952523i	$-0.401522\pi$
$882$		0			0
$883$			35.3399i			0.0400225i	0.999800	+	0.0200113i	$0.00637021\pi$
$883$			35.3399i			0.0400225i	−0.999800	+	0.0200113i	$0.993630\pi$
$884$	534.469	+	1183.98i	0.604603	+	1.33935i
$885$		0			0
$886$	−1164.69	−	752.102i	−1.31455	−	0.848873i
$887$		−	1185.75i		−	1.33680i	−0.743800	−	0.668402i	$-0.766979\pi$
$887$		−	1185.75i		−	1.33680i	0.743800	−	0.668402i	$-0.233021\pi$
$888$		0			0
$889$	286.510			0.322283
$890$	892.592	−	1382.25i	1.00291	−	1.55309i
$891$		0			0
$892$	554.405	+	1228.15i	0.621530	+	1.37685i
$893$	169.806			0.190152
$894$		0			0
$895$	−911.231			−1.01814
$896$	276.167	+	328.737i	0.308222	+	0.366894i
$897$		0			0
$898$	−136.694	+	211.682i	−0.152221	+	0.235726i
$899$	−463.148			−0.515181
$900$		0			0
$901$			722.745i			0.802159i
$902$	38.2414	−	59.2200i	0.0423962	−	0.0656541i
$903$		0			0
$904$	1382.21	+	207.984i	1.52900	+	0.230071i
$905$			1329.27i			1.46881i
$906$		0			0
$907$			663.539i			0.731575i	0.930698	+	0.365788i	$0.119200\pi$
$907$			663.539i			0.731575i	−0.930698	+	0.365788i	$0.880800\pi$
$908$	376.993	+	835.133i	0.415190	+	0.919750i
$909$		0			0
$910$	−728.626	+	1128.34i	−0.800688	+	1.23993i
$911$		−	271.326i		−	0.297834i	−0.988850	−	0.148917i	$-0.952421\pi$
$911$		−	271.326i		−	0.297834i	0.988850	−	0.148917i	$-0.0475786\pi$
$912$		0			0
$913$	−474.123			−0.519302
$914$	−304.718	−	196.772i	−0.333390	−	0.215287i
$915$		0			0
$916$	−443.571	+	200.235i	−0.484248	+	0.218597i
$917$	519.891			0.566947
$918$		0			0
$919$	−611.673			−0.665585			−0.332793	−	0.943000i	$-0.607991\pi$
$919$	−611.673			−0.665585			−0.332793	+	0.943000i	$0.607991\pi$
$920$	2072.96	+	311.922i	2.25321	+	0.339046i
$921$		0			0
$922$	−1216.50	−	785.557i	−1.31941	−	0.852014i
$923$	−1844.68			−1.99857
$924$		0			0
$925$		−	613.589i		−	0.663340i
$926$	1032.88	+	666.981i	1.11542	+	0.720282i
$927$		0			0
$928$	340.664	−	96.0000i	0.367095	−	0.103448i
$929$		−	45.0320i		−	0.0484736i	−0.999706	−	0.0242368i	$-0.992284\pi$
$929$		−	45.0320i		−	0.0484736i	0.999706	−	0.0242368i	$-0.00771557\pi$
$930$		0			0
$931$			517.482i			0.555835i
$932$	−1346.49	+	607.829i	−1.44474	+	0.652177i
$933$		0			0
$934$	65.1882	+	42.0954i	0.0697947	+	0.0450700i
$935$		−	1041.27i		−	1.11365i
$936$		0			0
$937$	510.859			0.545207			0.272603	−	0.962126i	$-0.412115\pi$
$937$	510.859			0.545207			0.272603	+	0.962126i	$0.412115\pi$
$938$	292.035	−	452.241i	0.311338	−	0.482134i
$939$		0			0
$940$	401.490	−	181.239i	0.427117	−	0.192808i
$941$	−386.278			−0.410498			−0.205249	−	0.978710i	$-0.565800\pi$
$941$	−386.278			−0.410498			−0.205249	+	0.978710i	$0.565800\pi$
$942$		0			0
$943$	−127.911			−0.135643
$944$	−524.503	+	594.730i	−0.555618	+	0.630011i
$945$		0			0
$946$	479.867	−	743.114i	0.507259	−	0.785532i
$947$	229.206			0.242034			0.121017	−	0.992650i	$-0.461384\pi$
$947$	229.206			0.242034			0.121017	+	0.992650i	$0.461384\pi$
$948$		0			0
$949$			268.329i			0.282750i
$950$	803.749	−	1244.67i	0.846052	−	1.31018i
$951$		0			0
$952$	−382.656	−	57.5791i	−0.401950	−	0.0604822i
$953$			1016.98i			1.06714i	0.845757	+	0.533568i	$0.179149\pi$
$953$			1016.98i			1.06714i	−0.845757	+	0.533568i	$0.820851\pi$
$954$		0			0
$955$		−	3055.24i		−	3.19921i
$956$	1218.93	−	550.243i	1.27503	−	0.575568i
$957$		0			0
$958$	−482.716	+	747.527i	−0.503879	+	0.780299i
$959$		−	467.778i		−	0.487777i
$960$		0			0
$961$	792.474			0.824635
$962$	429.613	+	277.423i	0.446583	+	0.288382i
$963$		0			0
$964$	395.593	+	876.339i	0.410367	+	0.909065i
$965$	377.502			0.391194
$966$		0			0
$967$	211.702			0.218927			0.109463	−	0.993991i	$-0.465087\pi$
$967$	211.702			0.218927			0.109463	+	0.993991i	$0.465087\pi$
$968$	65.5142	−	435.391i	0.0676800	−	0.449784i
$969$		0			0
$970$	213.476	+	137.852i	0.220078	+	0.142116i
$971$	−188.312			−0.193936			−0.0969681	−	0.995287i	$-0.530914\pi$
$971$	−188.312			−0.193936			−0.0969681	+	0.995287i	$0.530914\pi$
$972$		0			0
$973$		−	183.791i		−	0.188891i
$974$	554.776	+	358.247i	0.569585	+	0.367811i
$975$		0			0
$976$	815.247	+	718.980i	0.835294	+	0.736660i
$977$		−	932.595i		−	0.954550i	−0.878754	−	0.477275i	$-0.841625\pi$
$977$		−	932.595i		−	0.954550i	0.878754	−	0.477275i	$-0.158375\pi$
$978$		0			0
$979$		−	751.568i		−	0.767690i
$980$	552.325	+	1223.54i	0.563597	+	1.24851i
$981$		0			0
$982$	489.010	+	315.779i	0.497974	+	0.321567i
$983$		−	1251.38i		−	1.27302i	−0.771269	−	0.636510i	$-0.780377\pi$
$983$		−	1251.38i		−	1.27302i	0.771269	−	0.636510i	$-0.219623\pi$
$984$		0			0
$985$	296.871			0.301391
$986$	−173.048	+	267.979i	−0.175505	+	0.271784i
$987$		0			0
$988$	508.075	+	1125.51i	0.514246	+	1.13918i
$989$	−1605.07			−1.62293
$990$		0			0
$991$	−468.204			−0.472456			−0.236228	−	0.971698i	$-0.575911\pi$
$991$	−468.204			−0.472456			−0.236228	+	0.971698i	$0.575911\pi$
$992$	−1289.75	+	363.455i	−1.30015	+	0.366386i
$993$		0			0
$994$	298.094	−	461.624i	0.299893	−	0.464410i
$995$	1017.74			1.02286
$996$		0			0
$997$			225.875i			0.226554i	0.993563	+	0.113277i	$0.0361348\pi$
$997$			225.875i			0.226554i	−0.993563	+	0.113277i	$0.963865\pi$
$998$	604.298	−	935.806i	0.605509	−	0.937681i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	216.3.h.e.53.8	yes	8
3.2	odd	2	inner	216.3.h.e.53.1	✓	8
4.3	odd	2		864.3.h.f.593.2		8
8.3	odd	2		864.3.h.f.593.7		8
8.5	even	2	inner	216.3.h.e.53.2	yes	8
12.11	even	2		864.3.h.f.593.8		8
24.5	odd	2	inner	216.3.h.e.53.7	yes	8
24.11	even	2		864.3.h.f.593.1		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
216.3.h.e.53.1	✓	8	3.2	odd	2	inner
216.3.h.e.53.2	yes	8	8.5	even	2	inner
216.3.h.e.53.7	yes	8	24.5	odd	2	inner
216.3.h.e.53.8	yes	8	1.1	even	1	trivial
864.3.h.f.593.1		8	24.11	even	2
864.3.h.f.593.2		8	4.3	odd	2
864.3.h.f.593.7		8	8.3	odd	2
864.3.h.f.593.8		8	12.11	even	2

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:	\( N \)	\(=\)	\( 216 = 2^{3} \cdot 3^{3} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	216.h (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(1.68014 + 1.08495i) q^{2} +(1.64575 + 3.64575i) q^{4} -8.89047 q^{5} -3.35425 q^{7} +(-1.19038 + 7.91094i) q^{8} +O(q^{10})\)	\(q+(1.68014 + 1.08495i) q^{2} +(1.64575 + 3.64575i) q^{4} -8.89047 q^{5} -3.35425 q^{7} +(-1.19038 + 7.91094i) q^{8} +(-14.9373 - 9.64575i) q^{10} -8.12179 q^{11} +22.5203i q^{13} +(-5.63561 - 3.63920i) q^{14} +(-10.5830 + 12.0000i) q^{16} -14.4207i q^{17} -13.7085i q^{19} +(-14.6315 - 32.4125i) q^{20} +(-13.6458 - 8.81176i) q^{22} +29.4739i q^{23} +54.0405 q^{25} +(-24.4334 + 37.8372i) q^{26} +(-5.52026 - 12.2288i) q^{28} -11.0604 q^{29} +41.8745 q^{31} +(-30.8004 + 8.67963i) q^{32} +(15.6458 - 24.2288i) q^{34} +29.8209 q^{35} -11.3542i q^{37} +(14.8731 - 23.0322i) q^{38} +(10.5830 - 70.3320i) q^{40} +4.33981i q^{41} +54.4575i q^{43} +(-13.3664 - 29.6100i) q^{44} +(-31.9778 + 49.5203i) q^{46} +12.3869i q^{47} -37.7490 q^{49} +(90.7957 + 58.6315i) q^{50} +(-82.1033 + 37.0627i) q^{52} -50.1187 q^{53} +72.2065 q^{55} +(3.99282 - 26.5353i) q^{56} +(-18.5830 - 12.0000i) q^{58} +49.5609 q^{59} -67.9373i q^{61} +(70.3551 + 45.4319i) q^{62} +(-61.1660 - 18.8340i) q^{64} -200.216i q^{65} +80.2470i q^{67} +(52.5742 - 23.7328i) q^{68} +(50.1033 + 32.3542i) q^{70} +81.9119i q^{71} +11.9150 q^{73} +(12.3188 - 19.0767i) q^{74} +(49.9778 - 22.5608i) q^{76} +27.2425 q^{77} -37.2288 q^{79} +(94.0879 - 106.686i) q^{80} +(-4.70850 + 7.29150i) q^{82} +58.3767 q^{83} +128.207i q^{85} +(-59.0839 + 91.4963i) q^{86} +(9.66798 - 64.2510i) q^{88} +92.5373i q^{89} -75.5385i q^{91} +(-107.454 + 48.5066i) q^{92} +(-13.4392 + 20.8118i) q^{94} +121.875i q^{95} -14.2915 q^{97} +(-63.4237 - 40.9559i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 8 q^{4} - 48 q^{7}+O(q^{10}) \) 8 * q - 8 * q^4 - 48 * q^7	\( 8 q - 8 q^{4} - 48 q^{7} - 56 q^{10} - 88 q^{22} + 136 q^{25} + 104 q^{28} + 208 q^{31} + 104 q^{34} + 104 q^{46} - 48 q^{49} - 424 q^{52} + 112 q^{55} - 64 q^{58} - 320 q^{64} + 168 q^{70} - 328 q^{73} + 40 q^{76} - 192 q^{79} - 80 q^{82} + 416 q^{88} - 552 q^{94} - 72 q^{97}+O(q^{100}) \) 8 * q - 8 * q^4 - 48 * q^7 - 56 * q^10 - 88 * q^22 + 136 * q^25 + 104 * q^28 + 208 * q^31 + 104 * q^34 + 104 * q^46 - 48 * q^49 - 424 * q^52 + 112 * q^55 - 64 * q^58 - 320 * q^64 + 168 * q^70 - 328 * q^73 + 40 * q^76 - 192 * q^79 - 80 * q^82 + 416 * q^88 - 552 * q^94 - 72 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

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Database

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