LMFDB - Embedded newform 216.2.d.c.109.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [216,2,Mod(109,216)]

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, 0]))

N = Newforms(chi, 2, names="a")

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

chi := DirichletCharacter("216.109");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 216 = 2^{3} \cdot 3^{3} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	216.d (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:	$1.72476868366$
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:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{2}\cdot 3^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			109.1
Root			$-1.38255 - 0.297594i$ of defining polynomial
Character	$\chi$	$=$	216.109
Dual form			216.2.d.c.109.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.38255 - 0.297594i) q^{2} +(1.82288 + 0.822876i) q^{4} -3.36028i q^{5} -2.64575 q^{7} +(-2.27533 - 1.68014i) q^{8} +O(q^{10})$	\(q+(-1.38255 - 0.297594i) q^{2} +(1.82288 + 0.822876i) q^{4} -3.36028i q^{5} -2.64575 q^{7} +(-2.27533 - 1.68014i) q^{8} +(-1.00000 + 4.64575i) q^{10} +2.16991i q^{11} -4.64575i q^{13} +(3.65788 + 0.787360i) q^{14} +(2.64575 + 3.00000i) q^{16} -4.55066 q^{17} -6.29150i q^{19} +(2.76510 - 6.12538i) q^{20} +(0.645751 - 3.00000i) q^{22} -0.979531 q^{23} -6.29150 q^{25} +(-1.38255 + 6.42297i) q^{26} +(-4.82288 - 2.17712i) q^{28} -4.33981i q^{29} +2.00000 q^{31} +(-2.76510 - 4.93500i) q^{32} +(6.29150 + 1.35425i) q^{34} +8.89047i q^{35} +1.35425i q^{37} +(-1.87231 + 8.69830i) q^{38} +(-5.64575 + 7.64575i) q^{40} +11.0604 q^{41} +3.29150i q^{43} +(-1.78556 + 3.95547i) q^{44} +(1.35425 + 0.291503i) q^{46} +10.0808 q^{47} +(8.69830 + 1.87231i) q^{50} +(3.82288 - 8.46863i) q^{52} -4.33981i q^{53} +7.29150 q^{55} +(6.01996 + 4.44524i) q^{56} +(-1.29150 + 6.00000i) q^{58} +11.2712i q^{59} +1.93725i q^{61} +(-2.76510 - 0.595188i) q^{62} +(2.35425 + 7.64575i) q^{64} -15.6110 q^{65} +3.00000i q^{67} +(-8.29529 - 3.74463i) q^{68} +(2.64575 - 12.2915i) q^{70} +11.5830 q^{73} +(0.403016 - 1.87231i) q^{74} +(5.17712 - 11.4686i) q^{76} -5.74103i q^{77} -8.64575 q^{79} +(10.0808 - 8.89047i) q^{80} +(-15.2915 - 3.29150i) q^{82} -2.38075i q^{83} +15.2915i q^{85} +(0.979531 - 4.55066i) q^{86} +(3.64575 - 4.93725i) q^{88} +4.55066 q^{89} +12.2915i q^{91} +(-1.78556 - 0.806032i) q^{92} +(-13.9373 - 3.00000i) q^{94} -21.1412 q^{95} +2.29150 q^{97} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 4 q^{4}+O(q^{10}) $ 8 * q + 4 * q^4	$ 8 q + 4 q^{4} - 8 q^{10} - 16 q^{22} - 8 q^{25} - 28 q^{28} + 16 q^{31} + 8 q^{34} - 24 q^{40} + 32 q^{46} + 20 q^{52} + 16 q^{55} + 32 q^{58} + 40 q^{64} + 8 q^{73} + 52 q^{76} - 48 q^{79} - 80 q^{82} + 8 q^{88} - 48 q^{94} - 24 q^{97}+O(q^{100}) $ 8 * q + 4 * q^4 - 8 * q^10 - 16 * q^22 - 8 * q^25 - 28 * q^28 + 16 * q^31 + 8 * q^34 - 24 * q^40 + 32 * q^46 + 20 * q^52 + 16 * q^55 + 32 * q^58 + 40 * q^64 + 8 * q^73 + 52 * q^76 - 48 * q^79 - 80 * q^82 + 8 * q^88 - 48 * q^94 - 24 * 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 $

$2$	−1.38255	−	0.297594i	−0.977609	−	0.210431i
$2$	−1.38255	−	0.297594i	−0.977609	−	0.210431i
$3$		0			0
$3$		0			0
$4$	1.82288	+	0.822876i	0.911438	+	0.411438i
$5$		−	3.36028i		−	1.50276i	−0.659867	−	0.751382i	$-0.729388\pi$
$5$		−	3.36028i		−	1.50276i	0.659867	−	0.751382i	$-0.270612\pi$
$6$		0			0
$7$	−2.64575			−1.00000			−0.500000	−	0.866025i	$-0.666667\pi$
$7$	−2.64575			−1.00000			−0.500000	+	0.866025i	$0.666667\pi$
$8$	−2.27533	−	1.68014i	−0.804450	−	0.594020i
$9$		0			0
$10$	−1.00000	+	4.64575i	−0.316228	+	1.46912i
$11$			2.16991i			0.654252i	0.944981	+	0.327126i	$0.106080\pi$
$11$			2.16991i			0.654252i	−0.944981	+	0.327126i	$0.893920\pi$
$12$		0			0
$13$		−	4.64575i		−	1.28850i	−0.764815	−	0.644250i	$-0.777170\pi$
$13$		−	4.64575i		−	1.28850i	0.764815	−	0.644250i	$-0.222830\pi$
$14$	3.65788	+	0.787360i	0.977609	+	0.210431i
$15$		0			0
$16$	2.64575	+	3.00000i	0.661438	+	0.750000i
$17$	−4.55066			−1.10370			−0.551848	−	0.833944i	$-0.686077\pi$
$17$	−4.55066			−1.10370			−0.551848	+	0.833944i	$0.686077\pi$
$18$		0			0
$19$		−	6.29150i		−	1.44337i	−0.692222	−	0.721685i	$-0.743368\pi$
$19$		−	6.29150i		−	1.44337i	0.692222	−	0.721685i	$-0.256632\pi$
$20$	2.76510	−	6.12538i	0.618294	−	1.36968i
$21$		0			0
$22$	0.645751	−	3.00000i	0.137675	−	0.639602i
$23$	−0.979531			−0.204246			−0.102123	−	0.994772i	$-0.532564\pi$
$23$	−0.979531			−0.204246			−0.102123	+	0.994772i	$0.532564\pi$
$24$		0			0
$25$	−6.29150			−1.25830
$26$	−1.38255	+	6.42297i	−0.271140	+	1.25965i
$27$		0			0
$28$	−4.82288	−	2.17712i	−0.911438	−	0.411438i
$29$		−	4.33981i		−	0.805883i	−0.915226	−	0.402942i	$-0.867988\pi$
$29$		−	4.33981i		−	0.805883i	0.915226	−	0.402942i	$-0.132012\pi$
$30$		0			0
$31$	2.00000			0.359211			0.179605	−	0.983739i	$-0.442518\pi$
$31$	2.00000			0.359211			0.179605	+	0.983739i	$0.442518\pi$
$32$	−2.76510	−	4.93500i	−0.488804	−	0.872393i
$33$		0			0
$34$	6.29150	+	1.35425i	1.07898	+	0.232252i
$35$			8.89047i			1.50276i
$36$		0			0
$37$			1.35425i			0.222637i	0.993785	+	0.111319i	$0.0355074\pi$
$37$			1.35425i			0.222637i	−0.993785	+	0.111319i	$0.964493\pi$
$38$	−1.87231	+	8.69830i	−0.303729	+	1.41105i
$39$		0			0
$40$	−5.64575	+	7.64575i	−0.892672	+	1.20890i
$41$	11.0604			1.72734			0.863671	−	0.504057i	$-0.168160\pi$
$41$	11.0604			1.72734			0.863671	+	0.504057i	$0.168160\pi$
$42$		0			0
$43$			3.29150i			0.501949i	0.967994	+	0.250975i	$0.0807511\pi$
$43$			3.29150i			0.501949i	−0.967994	+	0.250975i	$0.919249\pi$
$44$	−1.78556	+	3.95547i	−0.269184	+	0.596310i
$45$		0			0
$46$	1.35425	+	0.291503i	0.199673	+	0.0429797i
$47$	10.0808			1.47044			0.735222	−	0.677827i	$-0.237078\pi$
$47$	10.0808			1.47044			0.735222	+	0.677827i	$0.237078\pi$
$48$		0			0
$49$		0			0
$50$	8.69830	+	1.87231i	1.23013	+	0.264785i
$51$		0			0
$52$	3.82288	−	8.46863i	0.530137	−	1.17439i
$53$		−	4.33981i		−	0.596119i	−0.954547	−	0.298060i	$-0.903661\pi$
$53$		−	4.33981i		−	0.596119i	0.954547	−	0.298060i	$-0.0963394\pi$
$54$		0			0
$55$	7.29150			0.983186
$56$	6.01996	+	4.44524i	0.804450	+	0.594020i
$57$		0			0
$58$	−1.29150	+	6.00000i	−0.169583	+	0.787839i
$59$			11.2712i			1.46739i	0.679480	+	0.733694i	$0.262206\pi$
$59$			11.2712i			1.46739i	−0.679480	+	0.733694i	$0.737794\pi$
$60$		0			0
$61$			1.93725i			0.248040i	0.992280	+	0.124020i	$0.0395787\pi$
$61$			1.93725i			0.248040i	−0.992280	+	0.124020i	$0.960421\pi$
$62$	−2.76510	−	0.595188i	−0.351167	−	0.0755889i
$63$		0			0
$64$	2.35425	+	7.64575i	0.294281	+	0.955719i
$65$	−15.6110			−1.93631
$66$		0			0
$67$			3.00000i			0.366508i	0.983066	+	0.183254i	$0.0586631\pi$
$67$			3.00000i			0.366508i	−0.983066	+	0.183254i	$0.941337\pi$
$68$	−8.29529	−	3.74463i	−1.00595	−	0.454103i
$69$		0			0
$70$	2.64575	−	12.2915i	0.316228	−	1.46912i
$71$		0			0			−	1.00000i	$-0.5\pi$
$71$		0			0				1.00000i	$0.5\pi$
$72$		0			0
$73$	11.5830			1.35569			0.677844	−	0.735206i	$-0.262914\pi$
$73$	11.5830			1.35569			0.677844	+	0.735206i	$0.262914\pi$
$74$	0.403016	−	1.87231i	0.0468497	−	0.217652i
$75$		0			0
$76$	5.17712	−	11.4686i	0.593857	−	1.31554i
$77$		−	5.74103i		−	0.654252i
$78$		0			0
$79$	−8.64575			−0.972723			−0.486362	−	0.873758i	$-0.661676\pi$
$79$	−8.64575			−0.972723			−0.486362	+	0.873758i	$0.661676\pi$
$80$	10.0808	−	8.89047i	1.12707	−	0.993985i
$81$		0			0
$82$	−15.2915	−	3.29150i	−1.68866	−	0.363486i
$83$		−	2.38075i		−	0.261321i	−0.991427	−	0.130661i	$-0.958290\pi$
$83$		−	2.38075i		−	0.261321i	0.991427	−	0.130661i	$-0.0417099\pi$
$84$		0			0
$85$			15.2915i			1.65860i
$86$	0.979531	−	4.55066i	0.105626	−	0.490710i
$87$		0			0
$88$	3.64575	−	4.93725i	0.388638	−	0.526313i
$89$	4.55066			0.482369			0.241184	−	0.970479i	$-0.422464\pi$
$89$	4.55066			0.482369			0.241184	+	0.970479i	$0.422464\pi$
$90$		0			0
$91$			12.2915i			1.28850i
$92$	−1.78556	−	0.806032i	−0.186158	−	0.0840347i
$93$		0			0
$94$	−13.9373	−	3.00000i	−1.43752	−	0.309426i
$95$	−21.1412			−2.16904
$96$		0			0
$97$	2.29150			0.232667			0.116333	−	0.993210i	$-0.462886\pi$
$97$	2.29150			0.232667			0.116333	+	0.993210i	$0.462886\pi$
$98$		0			0
$99$		0			0
$100$	−11.4686	−	5.17712i	−1.14686	−	0.517712i
$101$			6.72057i			0.668721i	0.942445	+	0.334361i	$0.108520\pi$
$101$			6.72057i			0.668721i	−0.942445	+	0.334361i	$0.891480\pi$
$102$		0			0
$103$	−5.35425			−0.527570			−0.263785	−	0.964582i	$-0.584971\pi$
$103$	−5.35425			−0.527570			−0.263785	+	0.964582i	$0.584971\pi$
$104$	−7.80552	+	10.5706i	−0.765394	+	1.03653i
$105$		0			0
$106$	−1.29150	+	6.00000i	−0.125442	+	0.582772i
$107$		−	17.9918i		−	1.73933i	−0.493640	−	0.869666i	$-0.664334\pi$
$107$		−	17.9918i		−	1.73933i	0.493640	−	0.869666i	$-0.335666\pi$
$108$		0			0
$109$		−	15.2915i		−	1.46466i	−0.680950	−	0.732330i	$-0.738433\pi$
$109$		−	15.2915i		−	1.46466i	0.680950	−	0.732330i	$-0.261567\pi$
$110$	−10.0808	−	2.16991i	−0.961171	−	0.206893i
$111$		0			0
$112$	−7.00000	−	7.93725i	−0.661438	−	0.750000i
$113$	6.50972			0.612383			0.306192	−	0.951970i	$-0.400945\pi$
$113$	6.50972			0.612383			0.306192	+	0.951970i	$0.400945\pi$
$114$		0			0
$115$			3.29150i			0.306934i
$116$	3.57113	−	7.91094i	0.331571	−	0.734513i
$117$		0			0
$118$	3.35425	−	15.5830i	0.308784	−	1.43453i
$119$	12.0399			1.10370
$120$		0			0
$121$	6.29150			0.571955
$122$	0.576515	−	2.67835i	0.0521952	−	0.242486i
$123$		0			0
$124$	3.64575	+	1.64575i	0.327398	+	0.147793i
$125$			4.33981i			0.388165i
$126$		0			0
$127$	5.29150			0.469545			0.234772	−	0.972050i	$-0.424565\pi$
$127$	5.29150			0.469545			0.234772	+	0.972050i	$0.424565\pi$
$128$	−0.979531	−	11.2712i	−0.0865792	−	0.996245i
$129$		0			0
$130$	21.5830	+	4.64575i	1.89295	+	0.407459i
$131$		−	15.4002i		−	1.34552i	−0.739860	−	0.672761i	$-0.765108\pi$
$131$		−	15.4002i		−	1.34552i	0.739860	−	0.672761i	$-0.234892\pi$
$132$		0			0
$133$			16.6458i			1.44337i
$134$	0.892782	−	4.14764i	0.0771246	−	0.358302i
$135$		0			0
$136$	10.3542	+	7.64575i	0.887870	+	0.655618i
$137$	−6.50972			−0.556163			−0.278082	−	0.960557i	$-0.589699\pi$
$137$	−6.50972			−0.556163			−0.278082	+	0.960557i	$0.589699\pi$
$138$		0			0
$139$		−	12.2915i		−	1.04255i	−0.853388	−	0.521276i	$-0.825456\pi$
$139$		−	12.2915i		−	1.04255i	0.853388	−	0.521276i	$-0.174544\pi$
$140$	−7.31575	+	16.2062i	−0.618294	+	1.36968i
$141$		0			0
$142$		0			0
$143$	10.0808			0.843003
$144$		0			0
$145$	−14.5830			−1.21105
$146$	−16.0141	−	3.44703i	−1.32533	−	0.285278i
$147$		0			0
$148$	−1.11438	+	2.46863i	−0.0916013	+	0.202920i
$149$			8.67963i			0.711063i	0.934664	+	0.355531i	$0.115700\pi$
$149$			8.67963i			0.711063i	−0.934664	+	0.355531i	$0.884300\pi$
$150$		0			0
$151$	12.6458			1.02910			0.514548	−	0.857461i	$-0.327960\pi$
$151$	12.6458			1.02910			0.514548	+	0.857461i	$0.327960\pi$
$152$	−10.5706	+	14.3152i	−0.857390	+	1.16112i
$153$		0			0
$154$	−1.70850	+	7.93725i	−0.137675	+	0.639602i
$155$		−	6.72057i		−	0.539809i
$156$		0			0
$157$		−	8.70850i		−	0.695014i	−0.937677	−	0.347507i	$-0.887028\pi$
$157$		−	8.70850i		−	0.695014i	0.937677	−	0.347507i	$-0.112972\pi$
$158$	11.9532	+	2.57292i	0.950943	+	0.204691i
$159$		0			0
$160$	−16.5830	+	9.29150i	−1.31100	+	0.734558i
$161$	2.59160			0.204246
$162$		0			0
$163$			6.29150i			0.492789i	0.969170	+	0.246394i	$0.0792458\pi$
$163$			6.29150i			0.492789i	−0.969170	+	0.246394i	$0.920754\pi$
$164$	20.1617	+	9.10132i	1.57436	+	0.710694i
$165$		0			0
$166$	−0.708497	+	3.29150i	−0.0549901	+	0.255470i
$167$	−19.1822			−1.48436			−0.742180	−	0.670200i	$-0.766208\pi$
$167$	−19.1822			−1.48436			−0.742180	+	0.670200i	$0.766208\pi$
$168$		0			0
$169$	−8.58301			−0.660231
$170$	4.55066	−	21.1412i	0.349020	−	1.62146i
$171$		0			0
$172$	−2.70850	+	6.00000i	−0.206521	+	0.457496i
$173$			15.8219i			1.20292i	0.798905	+	0.601458i	$0.205413\pi$
$173$			15.8219i			1.20292i	−0.798905	+	0.601458i	$0.794587\pi$
$174$		0			0
$175$	16.6458			1.25830
$176$	−6.50972	+	5.74103i	−0.490689	+	0.432747i
$177$		0			0
$178$	−6.29150	−	1.35425i	−0.471568	−	0.101505i
$179$			4.76150i			0.355891i	0.984040	+	0.177946i	$0.0569452\pi$
$179$			4.76150i			0.355891i	−0.984040	+	0.177946i	$0.943055\pi$
$180$		0			0
$181$			16.6458i			1.23727i	0.785679	+	0.618634i	$0.212314\pi$
$181$			16.6458i			1.23727i	−0.785679	+	0.618634i	$0.787686\pi$
$182$	3.65788	−	16.9936i	0.271140	−	1.25965i
$183$		0			0
$184$	2.22876	+	1.64575i	0.164306	+	0.121326i
$185$	4.55066			0.334571
$186$		0			0
$187$		−	9.87451i		−	0.722096i
$188$	18.3761	+	8.29529i	1.34022	+	0.604996i
$189$		0			0
$190$	29.2288	+	6.29150i	2.12048	+	0.456434i
$191$	−8.12179			−0.587672			−0.293836	−	0.955856i	$-0.594932\pi$
$191$	−8.12179			−0.587672			−0.293836	+	0.955856i	$0.594932\pi$
$192$		0			0
$193$	−4.29150			−0.308909			−0.154455	−	0.988000i	$-0.549362\pi$
$193$	−4.29150			−0.308909			−0.154455	+	0.988000i	$0.549362\pi$
$194$	−3.16811	−	0.681937i	−0.227457	−	0.0489602i
$195$		0			0
$196$		0			0
$197$			7.70010i			0.548609i	0.961643	+	0.274305i	$0.0884477\pi$
$197$			7.70010i			0.548609i	−0.961643	+	0.274305i	$0.911552\pi$
$198$		0			0
$199$	−18.5203			−1.31287			−0.656433	−	0.754384i	$-0.727936\pi$
$199$	−18.5203			−1.31287			−0.656433	+	0.754384i	$0.727936\pi$
$200$	14.3152	+	10.5706i	1.01224	+	0.747455i
$201$		0			0
$202$	2.00000	−	9.29150i	0.140720	−	0.653748i
$203$			11.4821i			0.805883i
$204$		0			0
$205$		−	37.1660i		−	2.59579i
$206$	7.40250	+	1.59339i	0.515757	+	0.111017i
$207$		0			0
$208$	13.9373	−	12.2915i	0.966375	−	0.852262i
$209$	13.6520			0.944327
$210$		0			0
$211$			0.291503i			0.0200679i	0.999950	+	0.0100339i	$0.00319395\pi$
$211$			0.291503i			0.0200679i	−0.999950	+	0.0100339i	$0.996806\pi$
$212$	3.57113	−	7.91094i	0.245266	−	0.543326i
$213$		0			0
$214$	−5.35425	+	24.8745i	−0.366009	+	1.70039i
$215$	11.0604			0.754312
$216$		0			0
$217$	−5.29150			−0.359211
$218$	−4.55066	+	21.1412i	−0.308210	+	1.43186i
$219$		0			0
$220$	13.2915	+	6.00000i	0.896113	+	0.404520i
$221$			21.1412i			1.42211i
$222$		0			0
$223$	−10.0000			−0.669650			−0.334825	−	0.942280i	$-0.608677\pi$
$223$	−10.0000			−0.669650			−0.334825	+	0.942280i	$0.608677\pi$
$224$	7.31575	+	13.0568i	0.488804	+	0.872393i
$225$		0			0
$226$	−9.00000	−	1.93725i	−0.598671	−	0.128864i
$227$		−	13.4411i		−	0.892119i	−0.895003	−	0.446060i	$-0.852827\pi$
$227$		−	13.4411i		−	0.892119i	0.895003	−	0.446060i	$-0.147173\pi$
$228$		0			0
$229$		−	13.1660i		−	0.870034i	−0.900422	−	0.435017i	$-0.856742\pi$
$229$		−	13.1660i		−	0.870034i	0.900422	−	0.435017i	$-0.143258\pi$
$230$	0.979531	−	4.55066i	0.0645884	−	0.300062i
$231$		0			0
$232$	−7.29150	+	9.87451i	−0.478711	+	0.648293i
$233$	−9.10132			−0.596247			−0.298124	−	0.954527i	$-0.596361\pi$
$233$	−9.10132			−0.596247			−0.298124	+	0.954527i	$0.596361\pi$
$234$		0			0
$235$		−	33.8745i		−	2.20973i
$236$	−9.27482	+	20.5460i	−0.603739	+	1.33743i
$237$		0			0
$238$	−16.6458	−	3.58301i	−1.07898	−	0.232252i
$239$	20.1617			1.30415			0.652076	−	0.758154i	$-0.273898\pi$
$239$	20.1617			1.30415			0.652076	+	0.758154i	$0.273898\pi$
$240$		0			0
$241$	26.8745			1.73114			0.865570	−	0.500789i	$-0.166957\pi$
$241$	26.8745			1.73114			0.865570	+	0.500789i	$0.166957\pi$
$242$	−8.69830	−	1.87231i	−0.559148	−	0.120357i
$243$		0			0
$244$	−1.59412	+	3.53137i	−0.102053	+	0.226073i
$245$		0			0
$246$		0			0
$247$	−29.2288			−1.85978
$248$	−4.55066	−	3.36028i	−0.288967	−	0.213378i
$249$		0			0
$250$	1.29150	−	6.00000i	0.0816818	−	0.379473i
$251$		−	24.5015i		−	1.54652i	−0.634088	−	0.773261i	$-0.718624\pi$
$251$		−	24.5015i		−	1.54652i	0.634088	−	0.773261i	$-0.281376\pi$
$252$		0			0
$253$		−	2.12549i		−	0.133629i
$254$	−7.31575	−	1.57472i	−0.459031	−	0.0988067i
$255$		0			0
$256$	−2.00000	+	15.8745i	−0.125000	+	0.992157i
$257$	20.1617			1.25765			0.628826	−	0.777546i	$-0.283536\pi$
$257$	20.1617			1.25765			0.628826	+	0.777546i	$0.283536\pi$
$258$		0			0
$259$		−	3.58301i		−	0.222637i
$260$	−28.4570	−	12.8459i	−1.76483	−	0.796672i
$261$		0			0
$262$	−4.58301	+	21.2915i	−0.283139	+	1.31539i
$263$	−1.95906			−0.120801			−0.0604005	−	0.998174i	$-0.519238\pi$
$263$	−1.95906			−0.120801			−0.0604005	+	0.998174i	$0.519238\pi$
$264$		0			0
$265$	−14.5830			−0.895827
$266$	4.95368	−	23.0135i	0.303729	−	1.41105i
$267$		0			0
$268$	−2.46863	+	5.46863i	−0.150795	+	0.334050i
$269$			5.74103i			0.350037i	0.984565	+	0.175019i	$0.0559985\pi$
$269$			5.74103i			0.350037i	−0.984565	+	0.175019i	$0.944001\pi$
$270$		0			0
$271$	−21.2288			−1.28956			−0.644778	−	0.764370i	$-0.723050\pi$
$271$	−21.2288			−1.28956			−0.644778	+	0.764370i	$0.723050\pi$
$272$	−12.0399	−	13.6520i	−0.730027	−	0.827773i
$273$		0			0
$274$	9.00000	+	1.93725i	0.543710	+	0.117034i
$275$		−	13.6520i		−	0.823245i
$276$		0			0
$277$			8.70850i			0.523243i	0.965171	+	0.261621i	$0.0842572\pi$
$277$			8.70850i			0.523243i	−0.965171	+	0.261621i	$0.915743\pi$
$278$	−3.65788	+	16.9936i	−0.219385	+	1.01921i
$279$		0			0
$280$	14.9373	−	20.2288i	0.892672	−	1.20890i
$281$	−20.1617			−1.20275			−0.601373	−	0.798968i	$-0.705379\pi$
$281$	−20.1617			−1.20275			−0.601373	+	0.798968i	$0.705379\pi$
$282$		0			0
$283$			27.2915i			1.62231i	0.584830	+	0.811156i	$0.301161\pi$
$283$			27.2915i			1.62231i	−0.584830	+	0.811156i	$0.698839\pi$
$284$		0			0
$285$		0			0
$286$	−13.9373	−	3.00000i	−0.824127	−	0.177394i
$287$	−29.2630			−1.72734
$288$		0			0
$289$	3.70850			0.218147
$290$	20.1617	+	4.33981i	1.18394	+	0.254843i
$291$		0			0
$292$	21.1144	+	9.53137i	1.23563	+	0.557781i
$293$		−	14.4207i		−	0.842464i	−0.906953	−	0.421232i	$-0.861598\pi$
$293$		−	14.4207i		−	0.842464i	0.906953	−	0.421232i	$-0.138402\pi$
$294$		0			0
$295$	37.8745			2.20514
$296$	2.27533	−	3.08136i	0.132251	−	0.179101i
$297$		0			0
$298$	2.58301	−	12.0000i	0.149629	−	0.695141i
$299$			4.55066i			0.263171i
$300$		0			0
$301$		−	8.70850i		−	0.501949i
$302$	−17.4834	−	3.76330i	−1.00605	−	0.216554i
$303$		0			0
$304$	18.8745	−	16.6458i	1.08253	−	0.954699i
$305$	6.50972			0.372746
$306$		0			0
$307$			9.87451i			0.563568i	0.959478	+	0.281784i	$0.0909261\pi$
$307$			9.87451i			0.563568i	−0.959478	+	0.281784i	$0.909074\pi$
$308$	4.72416	−	10.4652i	0.269184	−	0.596310i
$309$		0			0
$310$	−2.00000	+	9.29150i	−0.113592	+	0.527722i
$311$	−0.979531			−0.0555441			−0.0277721	−	0.999614i	$-0.508841\pi$
$311$	−0.979531			−0.0555441			−0.0277721	+	0.999614i	$0.508841\pi$
$312$		0			0
$313$	14.8745			0.840757			0.420378	−	0.907349i	$-0.361897\pi$
$313$	14.8745			0.840757			0.420378	+	0.907349i	$0.361897\pi$
$314$	−2.59160	+	12.0399i	−0.146252	+	0.679452i
$315$		0			0
$316$	−15.7601	−	7.11438i	−0.886577	−	0.400215i
$317$		−	20.5834i		−	1.15608i	−0.816009	−	0.578039i	$-0.803818\pi$
$317$		−	20.5834i		−	1.15608i	0.816009	−	0.578039i	$-0.196182\pi$
$318$		0			0
$319$	9.41699			0.527250
$320$	25.6919	−	7.91094i	1.43622	−	0.442235i
$321$		0			0
$322$	−3.58301	−	0.771243i	−0.199673	−	0.0429797i
$323$			28.6305i			1.59304i
$324$		0			0
$325$			29.2288i			1.62132i
$326$	1.87231	−	8.69830i	0.103698	−	0.481754i
$327$		0			0
$328$	−25.1660	−	18.5830i	−1.38956	−	1.02607i
$329$	−26.6714			−1.47044
$330$		0			0
$331$		−	5.70850i		−	0.313767i	−0.987617	−	0.156884i	$-0.949855\pi$
$331$		−	5.70850i		−	0.313767i	0.987617	−	0.156884i	$-0.0501448\pi$
$332$	1.95906	−	4.33981i	0.107518	−	0.238178i
$333$		0			0
$334$	26.5203	+	5.70850i	1.45112	+	0.312355i
$335$	10.0808			0.550776
$336$		0			0
$337$	2.29150			0.124826			0.0624131	−	0.998050i	$-0.480120\pi$
$337$	2.29150			0.124826			0.0624131	+	0.998050i	$0.480120\pi$
$338$	11.8664	+	2.55425i	0.645448	+	0.138933i
$339$		0			0
$340$	−12.5830	+	27.8745i	−0.682409	+	1.51171i
$341$			4.33981i			0.235014i
$342$		0			0
$343$	18.5203			1.00000
$344$	5.53019	−	7.48925i	0.298168	−	0.403793i
$345$		0			0
$346$	4.70850	−	21.8745i	0.253130	−	1.17598i
$347$		−	0.421689i		−	0.0226375i	−0.999936	−	0.0113187i	$-0.996397\pi$
$347$		−	0.421689i		−	0.0226375i	0.999936	−	0.0113187i	$-0.00360294\pi$
$348$		0			0
$349$		−	10.6458i		−	0.569854i	−0.958549	−	0.284927i	$-0.908031\pi$
$349$		−	10.6458i		−	0.569854i	0.958549	−	0.284927i	$-0.0919694\pi$
$350$	−23.0135	−	4.95368i	−1.23013	−	0.264785i
$351$		0			0
$352$	10.7085	−	6.00000i	0.570765	−	0.319801i
$353$	13.0194			0.692955			0.346478	−	0.938058i	$-0.387378\pi$
$353$	13.0194			0.692955			0.346478	+	0.938058i	$0.387378\pi$
$354$		0			0
$355$		0			0
$356$	8.29529	+	3.74463i	0.439649	+	0.198465i
$357$		0			0
$358$	1.41699	−	6.58301i	0.0748905	−	0.347923i
$359$	−21.1412			−1.11579			−0.557896	−	0.829911i	$-0.688391\pi$
$359$	−21.1412			−1.11579			−0.557896	+	0.829911i	$0.688391\pi$
$360$		0			0
$361$	−20.5830			−1.08332
$362$	4.95368	−	23.0135i	0.260359	−	1.20956i
$363$		0			0
$364$	−10.1144	+	22.4059i	−0.530137	+	1.17439i
$365$		−	38.9222i		−	2.03728i
$366$		0			0
$367$	4.52026			0.235956			0.117978	−	0.993016i	$-0.462359\pi$
$367$	4.52026			0.235956			0.117978	+	0.993016i	$0.462359\pi$
$368$	−2.59160	−	2.93859i	−0.135096	−	0.153185i
$369$		0			0
$370$	−6.29150	−	1.35425i	−0.327080	−	0.0704040i
$371$			11.4821i			0.596119i
$372$		0			0
$373$			38.5203i			1.99450i	0.0740880	+	0.997252i	$0.476395\pi$
$373$			38.5203i			1.99450i	−0.0740880	+	0.997252i	$0.523605\pi$
$374$	−2.93859	+	13.6520i	−0.151951	+	0.705927i
$375$		0			0
$376$	−22.9373	−	16.9373i	−1.18290	−	0.873472i
$377$	−20.1617			−1.03838
$378$		0			0
$379$			21.5830i			1.10864i	0.832302	+	0.554322i	$0.187022\pi$
$379$			21.5830i			1.10864i	−0.832302	+	0.554322i	$0.812978\pi$
$380$	−38.5378	−	17.3966i	−1.97695	−	0.892427i
$381$		0			0
$382$	11.2288	+	2.41699i	0.574513	+	0.123664i
$383$	20.1617			1.03021			0.515107	−	0.857126i	$-0.327752\pi$
$383$	20.1617			1.03021			0.515107	+	0.857126i	$0.327752\pi$
$384$		0			0
$385$	−19.2915			−0.983186
$386$	5.93321	+	1.27713i	0.301992	+	0.0650040i
$387$		0			0
$388$	4.17712	+	1.88562i	0.212061	+	0.0957279i
$389$		−	5.31935i		−	0.269702i	−0.990866	−	0.134851i	$-0.956944\pi$
$389$		−	5.31935i		−	0.269702i	0.990866	−	0.134851i	$-0.0430555\pi$
$390$		0			0
$391$	4.45751			0.225426
$392$		0			0
$393$		0			0
$394$	2.29150	−	10.6458i	0.115444	−	0.536325i
$395$			29.0522i			1.46177i
$396$		0			0
$397$		−	15.2915i		−	0.767459i	−0.923446	−	0.383729i	$-0.874640\pi$
$397$		−	15.2915i		−	0.767459i	0.923446	−	0.383729i	$-0.125360\pi$
$398$	25.6051	+	5.51152i	1.28347	+	0.276267i
$399$		0			0
$400$	−16.6458	−	18.8745i	−0.832288	−	0.943725i
$401$	−13.0194			−0.650160			−0.325080	−	0.945687i	$-0.605391\pi$
$401$	−13.0194			−0.650160			−0.325080	+	0.945687i	$0.605391\pi$
$402$		0			0
$403$		−	9.29150i		−	0.462843i
$404$	−5.53019	+	12.2508i	−0.275137	+	0.609498i
$405$		0			0
$406$	3.41699	−	15.8745i	0.169583	−	0.787839i
$407$	−2.93859			−0.145661
$408$		0			0
$409$	8.29150			0.409988			0.204994	−	0.978763i	$-0.434282\pi$
$409$	8.29150			0.409988			0.204994	+	0.978763i	$0.434282\pi$
$410$	−11.0604	+	51.3838i	−0.546233	+	2.53766i
$411$		0			0
$412$	−9.76013	−	4.40588i	−0.480847	−	0.217062i
$413$		−	29.8209i		−	1.46739i
$414$		0			0
$415$	−8.00000			−0.392705
$416$	−22.9268	+	12.8459i	−1.12408	+	0.629824i
$417$		0			0
$418$	−18.8745	−	4.06275i	−0.923182	−	0.198715i
$419$			2.16991i			0.106007i	0.998594	+	0.0530035i	$0.0168794\pi$
$419$			2.16991i			0.106007i	−0.998594	+	0.0530035i	$0.983121\pi$
$420$		0			0
$421$			22.6458i			1.10369i	0.833948	+	0.551843i	$0.186075\pi$
$421$			22.6458i			1.10369i	−0.833948	+	0.551843i	$0.813925\pi$
$422$	0.0867494	−	0.403016i	0.00422290	−	0.0196185i
$423$		0			0
$424$	−7.29150	+	9.87451i	−0.354107	+	0.479548i
$425$	28.6305			1.38878
$426$		0			0
$427$		−	5.12549i		−	0.248040i
$428$	14.8050	−	32.7968i	0.715627	−	1.58529i
$429$		0			0
$430$	−15.2915	−	3.29150i	−0.737422	−	0.158730i
$431$	30.2425			1.45673			0.728366	−	0.685188i	$-0.240280\pi$
$431$	30.2425			1.45673			0.728366	+	0.685188i	$0.240280\pi$
$432$		0			0
$433$	−0.125492			−0.00603077			−0.00301538	−	0.999995i	$-0.500960\pi$
$433$	−0.125492			−0.00603077			−0.00301538	+	0.999995i	$0.500960\pi$
$434$	7.31575	+	1.57472i	0.351167	+	0.0755889i
$435$		0			0
$436$	12.5830	−	27.8745i	0.602617	−	1.33495i
$437$			6.16272i			0.294803i
$438$		0			0
$439$	−11.1660			−0.532925			−0.266462	−	0.963845i	$-0.585855\pi$
$439$	−11.1660			−0.532925			−0.266462	+	0.963845i	$0.585855\pi$
$440$	−16.5906	−	12.2508i	−0.790924	−	0.584032i
$441$		0			0
$442$	6.29150	−	29.2288i	0.299256	−	1.39027i
$443$			28.8413i			1.37029i	0.728405	+	0.685146i	$0.240262\pi$
$443$			28.8413i			1.37029i	−0.728405	+	0.685146i	$0.759738\pi$
$444$		0			0
$445$		−	15.2915i		−	0.724887i
$446$	13.8255	+	2.97594i	0.654655	+	0.140915i
$447$		0			0
$448$	−6.22876	−	20.2288i	−0.294281	−	0.955719i
$449$	19.5292			0.921638			0.460819	−	0.887494i	$-0.347556\pi$
$449$	19.5292			0.921638			0.460819	+	0.887494i	$0.347556\pi$
$450$		0			0
$451$			24.0000i			1.13012i
$452$	11.8664	+	5.35669i	0.558149	+	0.251958i
$453$		0			0
$454$	−4.00000	+	18.5830i	−0.187729	+	0.872144i
$455$	41.3029			1.93631
$456$		0			0
$457$	23.8745			1.11680			0.558401	−	0.829571i	$-0.311415\pi$
$457$	23.8745			1.11680			0.558401	+	0.829571i	$0.311415\pi$
$458$	−3.91813	+	18.2026i	−0.183082	+	0.850553i
$459$		0			0
$460$	−2.70850	+	6.00000i	−0.126284	+	0.279751i
$461$			18.7605i			0.873763i	0.899519	+	0.436881i	$0.143917\pi$
$461$			18.7605i			0.873763i	−0.899519	+	0.436881i	$0.856083\pi$
$462$		0			0
$463$	31.2288			1.45132			0.725662	−	0.688052i	$-0.241534\pi$
$463$	31.2288			1.45132			0.725662	+	0.688052i	$0.241534\pi$
$464$	13.0194	−	11.4821i	0.604412	−	0.533042i
$465$		0			0
$466$	12.5830	+	2.70850i	0.582896	+	0.125469i
$467$			0.210845i			0.00975672i	0.999988	+	0.00487836i	$0.00155284\pi$
$467$			0.210845i			0.00975672i	−0.999988	+	0.00487836i	$0.998447\pi$
$468$		0			0
$469$		−	7.93725i		−	0.366508i
$470$	−10.0808	+	46.8331i	−0.464995	+	2.16025i
$471$		0			0
$472$	18.9373	−	25.6458i	0.871658	−	1.18044i
$473$	−7.14226			−0.328401
$474$		0			0
$475$			39.5830i			1.81619i
$476$	21.9473	+	9.90735i	1.00595	+	0.454103i
$477$		0			0
$478$	−27.8745	−	6.00000i	−1.27495	−	0.274434i
$479$	−35.1402			−1.60560			−0.802798	−	0.596250i	$-0.796657\pi$
$479$	−35.1402			−1.60560			−0.802798	+	0.596250i	$0.796657\pi$
$480$		0			0
$481$	6.29150			0.286868
$482$	−37.1553	−	7.99769i	−1.69238	−	0.364285i
$483$		0			0
$484$	11.4686	+	5.17712i	0.521301	+	0.235324i
$485$		−	7.70010i		−	0.349643i
$486$		0			0
$487$	6.06275			0.274729			0.137365	−	0.990521i	$-0.456137\pi$
$487$	6.06275			0.274729			0.137365	+	0.990521i	$0.456137\pi$
$488$	3.25486	−	4.40789i	0.147341	−	0.199536i
$489$		0			0
$490$		0			0
$491$			4.12897i			0.186338i	0.995650	+	0.0931689i	$0.0296997\pi$
$491$			4.12897i			0.186338i	−0.995650	+	0.0931689i	$0.970300\pi$
$492$		0			0
$493$			19.7490i			0.889451i
$494$	40.4101	+	8.69830i	1.81814	+	0.391355i
$495$		0			0
$496$	5.29150	+	6.00000i	0.237595	+	0.269408i
$497$		0			0
$498$		0			0
$499$		−	43.7490i		−	1.95847i	−0.202717	−	0.979237i	$-0.564977\pi$
$499$		−	43.7490i		−	1.95847i	0.202717	−	0.979237i	$-0.435023\pi$
$500$	−3.57113	+	7.91094i	−0.159706	+	0.353788i
$501$		0			0
$502$	−7.29150	+	33.8745i	−0.325436	+	1.51189i
$503$	−2.93859			−0.131025			−0.0655127	−	0.997852i	$-0.520868\pi$
$503$	−2.93859			−0.131025			−0.0655127	+	0.997852i	$0.520868\pi$
$504$		0			0
$505$	22.5830			1.00493
$506$	−0.632534	+	2.93859i	−0.0281196	+	0.130636i
$507$		0			0
$508$	9.64575	+	4.35425i	0.427961	+	0.193189i
$509$			33.0450i			1.46469i	0.680932	+	0.732347i	$0.261575\pi$
$509$			33.0450i			1.46469i	−0.680932	+	0.732347i	$0.738425\pi$
$510$		0			0
$511$	−30.6458			−1.35569
$512$	7.48925	−	21.3521i	0.330981	−	0.943637i
$513$		0			0
$514$	−27.8745	−	6.00000i	−1.22949	−	0.264649i
$515$			17.9918i			0.792813i
$516$		0			0
$517$			21.8745i			0.962040i
$518$	−1.06628	+	4.95368i	−0.0468497	+	0.217652i
$519$		0			0
$520$	35.5203	+	26.2288i	1.55767	+	1.15021i
$521$	13.6520			0.598104			0.299052	−	0.954237i	$-0.403330\pi$
$521$	13.6520			0.598104			0.299052	+	0.954237i	$0.403330\pi$
$522$		0			0
$523$			0.874508i			0.0382396i	0.999817	+	0.0191198i	$0.00608639\pi$
$523$			0.874508i			0.0382396i	−0.999817	+	0.0191198i	$0.993914\pi$
$524$	12.6724	−	28.0726i	0.553598	−	1.22636i
$525$		0			0
$526$	2.70850	+	0.583005i	0.118096	+	0.0254202i
$527$	−9.10132			−0.396460
$528$		0			0
$529$	−22.0405			−0.958283
$530$	20.1617	+	4.33981i	0.875768	+	0.188509i
$531$		0			0
$532$	−13.6974	+	30.3431i	−0.593857	+	1.31554i
$533$		−	51.3838i		−	2.22568i
$534$		0			0
$535$	−60.4575			−2.61381
$536$	5.04042	−	6.82599i	0.217713	−	0.294838i
$537$		0			0
$538$	1.70850	−	7.93725i	0.0736586	−	0.342199i
$539$		0			0
$540$		0			0
$541$		−	26.5203i		−	1.14019i	−0.821577	−	0.570097i	$-0.806905\pi$
$541$		−	26.5203i		−	1.14019i	0.821577	−	0.570097i	$-0.193095\pi$
$542$	29.3498	+	6.31755i	1.26068	+	0.271362i
$543$		0			0
$544$	12.5830	+	22.4575i	0.539492	+	0.962858i
$545$	−51.3838			−2.20104
$546$		0			0
$547$			9.58301i			0.409740i	0.978789	+	0.204870i	$0.0656771\pi$
$547$			9.58301i			0.409740i	−0.978789	+	0.204870i	$0.934323\pi$
$548$	−11.8664	−	5.35669i	−0.506908	−	0.228827i
$549$		0			0
$550$	−4.06275	+	18.8745i	−0.173236	+	0.804812i
$551$	−27.3040			−1.16319
$552$		0			0
$553$	22.8745			0.972723
$554$	2.59160	−	12.0399i	0.110106	−	0.511527i
$555$		0			0
$556$	10.1144	−	22.4059i	0.428945	−	0.950221i
$557$		−	1.40122i		−	0.0593716i	−0.999559	−	0.0296858i	$-0.990549\pi$
$557$		−	1.40122i		−	0.0593716i	0.999559	−	0.0296858i	$-0.00945067\pi$
$558$		0			0
$559$	15.2915			0.646762
$560$	−26.6714	+	23.5220i	−1.12707	+	0.993985i
$561$		0			0
$562$	27.8745	+	6.00000i	1.17582	+	0.253095i
$563$			41.8608i			1.76422i	0.471042	+	0.882111i	$0.343878\pi$
$563$			41.8608i			1.76422i	−0.471042	+	0.882111i	$0.656122\pi$
$564$		0			0
$565$		−	21.8745i		−	0.920267i
$566$	8.12179	−	37.7318i	0.341384	−	1.58599i
$567$		0			0
$568$		0			0
$569$	26.6714			1.11812			0.559062	−	0.829126i	$-0.311161\pi$
$569$	26.6714			1.11812			0.559062	+	0.829126i	$0.311161\pi$
$570$		0			0
$571$			5.70850i			0.238893i	0.992841	+	0.119447i	$0.0381120\pi$
$571$			5.70850i			0.238893i	−0.992841	+	0.119447i	$0.961888\pi$
$572$	18.3761	+	8.29529i	0.768345	+	0.346843i
$573$		0			0
$574$	40.4575	+	8.70850i	1.68866	+	0.363486i
$575$	6.16272			0.257003
$576$		0			0
$577$	23.5830			0.981773			0.490887	−	0.871223i	$-0.336673\pi$
$577$	23.5830			0.981773			0.490887	+	0.871223i	$0.336673\pi$
$578$	−5.12717	−	1.10363i	−0.213262	−	0.0459048i
$579$		0			0
$580$	−26.5830	−	12.0000i	−1.10380	−	0.498273i
$581$			6.29888i			0.261321i
$582$		0			0
$583$	9.41699			0.390012
$584$	−26.3552	−	19.4611i	−1.09058	−	0.805306i
$585$		0			0
$586$	−4.29150	+	19.9373i	−0.177280	+	0.823600i
$587$		−	21.9099i		−	0.904319i	−0.891937	−	0.452160i	$-0.850654\pi$
$587$		−	21.9099i		−	0.904319i	0.891937	−	0.452160i	$-0.149346\pi$
$588$		0			0
$589$		−	12.5830i		−	0.518474i
$590$	−52.3633	−	11.2712i	−2.15576	−	0.464029i
$591$		0			0
$592$	−4.06275	+	3.58301i	−0.166978	+	0.147261i
$593$	−33.1811			−1.36259			−0.681293	−	0.732011i	$-0.738582\pi$
$593$	−33.1811			−1.36259			−0.681293	+	0.732011i	$0.738582\pi$
$594$		0			0
$595$		−	40.4575i		−	1.65860i
$596$	−7.14226	+	15.8219i	−0.292558	+	0.648090i
$597$		0			0
$598$	1.35425	−	6.29150i	0.0553793	−	0.257279i
$599$	35.1402			1.43579			0.717895	−	0.696151i	$-0.245106\pi$
$599$	35.1402			1.43579			0.717895	+	0.696151i	$0.245106\pi$
$600$		0			0
$601$	−31.8745			−1.30019			−0.650094	−	0.759854i	$-0.725271\pi$
$601$	−31.8745			−1.30019			−0.650094	+	0.759854i	$0.725271\pi$
$602$	−2.59160	+	12.0399i	−0.105626	+	0.490710i
$603$		0			0
$604$	23.0516	+	10.4059i	0.937958	+	0.423409i
$605$		−	21.1412i		−	0.859513i
$606$		0			0
$607$	33.3542			1.35381			0.676904	−	0.736072i	$-0.263321\pi$
$607$	33.3542			1.35381			0.676904	+	0.736072i	$0.263321\pi$
$608$	−31.0486	+	17.3966i	−1.25919	+	0.705525i
$609$		0			0
$610$	−9.00000	−	1.93725i	−0.364399	−	0.0784371i
$611$		−	46.8331i		−	1.89467i
$612$		0			0
$613$		−	21.1033i		−	0.852353i	−0.904640	−	0.426176i	$-0.859860\pi$
$613$		−	21.1033i		−	0.852353i	0.904640	−	0.426176i	$-0.140140\pi$
$614$	2.93859	−	13.6520i	0.118592	−	0.550949i
$615$		0			0
$616$	−9.64575	+	13.0627i	−0.388638	+	0.526313i
$617$	−17.5701			−0.707346			−0.353673	−	0.935369i	$-0.615067\pi$
$617$	−17.5701			−0.707346			−0.353673	+	0.935369i	$0.615067\pi$
$618$		0			0
$619$		−	39.0000i		−	1.56754i	−0.621050	−	0.783771i	$-0.713294\pi$
$619$		−	39.0000i		−	1.56754i	0.621050	−	0.783771i	$-0.286706\pi$
$620$	5.53019	−	12.2508i	0.222098	−	0.492002i
$621$		0			0
$622$	1.35425	+	0.291503i	0.0543004	+	0.0116882i
$623$	−12.0399			−0.482369
$624$		0			0
$625$	−16.8745			−0.674980
$626$	−20.5647	−	4.42656i	−0.821931	−	0.176921i
$627$		0			0
$628$	7.16601	−	15.8745i	0.285955	−	0.633462i
$629$		−	6.16272i		−	0.245724i
$630$		0			0
$631$	19.2288			0.765485			0.382742	−	0.923855i	$-0.374980\pi$
$631$	19.2288			0.765485			0.382742	+	0.923855i	$0.374980\pi$
$632$	19.6719	+	14.5261i	0.782507	+	0.577817i
$633$		0			0
$634$	−6.12549	+	28.4575i	−0.243274	+	1.13019i
$635$		−	17.7809i		−	0.705615i
$636$		0			0
$637$		0			0
$638$	−13.0194	−	2.80244i	−0.515445	−	0.110950i
$639$		0			0
$640$	−37.8745	+	3.29150i	−1.49712	+	0.130108i
$641$	22.1208			0.873718			0.436859	−	0.899530i	$-0.356091\pi$
$641$	22.1208			0.873718			0.436859	+	0.899530i	$0.356091\pi$
$642$		0			0
$643$			27.2915i			1.07627i	0.842858	+	0.538136i	$0.180871\pi$
$643$			27.2915i			1.07627i	−0.842858	+	0.538136i	$0.819129\pi$
$644$	4.72416	+	2.13256i	0.186158	+	0.0840347i
$645$		0			0
$646$	8.52026	−	39.5830i	0.335225	−	1.55737i
$647$	33.1811			1.30449			0.652243	−	0.758010i	$-0.273828\pi$
$647$	33.1811			1.30449			0.652243	+	0.758010i	$0.273828\pi$
$648$		0			0
$649$	−24.4575			−0.960041
$650$	8.69830	−	40.4101i	0.341175	−	1.58502i
$651$		0			0
$652$	−5.17712	+	11.4686i	−0.202752	+	0.449146i
$653$		−	24.5015i		−	0.958818i	−0.877592	−	0.479409i	$-0.840851\pi$
$653$		−	24.5015i		−	0.958818i	0.877592	−	0.479409i	$-0.159149\pi$
$654$		0			0
$655$	−51.7490			−2.02200
$656$	29.2630	+	33.1811i	1.14253	+	1.29551i
$657$		0			0
$658$	36.8745	+	7.93725i	1.43752	+	0.309426i
$659$		−	11.4821i		−	0.447278i	−0.974672	−	0.223639i	$-0.928206\pi$
$659$		−	11.4821i		−	0.447278i	0.974672	−	0.223639i	$-0.0717937\pi$
$660$		0			0
$661$		−	14.5203i		−	0.564773i	−0.959301	−	0.282386i	$-0.908874\pi$
$661$		−	14.5203i		−	0.564773i	0.959301	−	0.282386i	$-0.0911260\pi$
$662$	−1.69881	+	7.89227i	−0.0660263	+	0.306742i
$663$		0			0
$664$	−4.00000	+	5.41699i	−0.155230	+	0.210220i
$665$	55.9344			2.16904
$666$		0			0
$667$			4.25098i			0.164599i
$668$	−34.9667	−	15.7845i	−1.35290	−	0.610722i
$669$		0			0
$670$	−13.9373	−	3.00000i	−0.538443	−	0.115900i
$671$	−4.20366			−0.162281
$672$		0			0
$673$	−40.8745			−1.57560			−0.787798	−	0.615933i	$-0.788779\pi$
$673$	−40.8745			−1.57560			−0.787798	+	0.615933i	$0.788779\pi$
$674$	−3.16811	−	0.681937i	−0.122031	−	0.0262672i
$675$		0			0
$676$	−15.6458	−	7.06275i	−0.601760	−	0.271644i
$677$			31.7799i			1.22140i	0.791861	+	0.610701i	$0.209112\pi$
$677$			31.7799i			1.22140i	−0.791861	+	0.610701i	$0.790888\pi$
$678$		0			0
$679$	−6.06275			−0.232667
$680$	25.6919	−	34.7932i	0.985239	−	1.33426i
$681$		0			0
$682$	1.29150	−	6.00000i	0.0494542	−	0.229752i
$683$			17.7809i			0.680369i	0.940359	+	0.340185i	$0.110490\pi$
$683$			17.7809i			0.680369i	−0.940359	+	0.340185i	$0.889510\pi$
$684$		0			0
$685$			21.8745i			0.835782i
$686$	−25.6051	−	5.51152i	−0.977609	−	0.210431i
$687$		0			0
$688$	−9.87451	+	8.70850i	−0.376462	+	0.332008i
$689$	−20.1617			−0.768100
$690$		0			0
$691$		−	27.2915i		−	1.03822i	−0.854708	−	0.519109i	$-0.826264\pi$
$691$		−	27.2915i		−	1.03822i	0.854708	−	0.519109i	$-0.173736\pi$
$692$	−13.0194	+	28.8413i	−0.494925	+	1.09638i
$693$		0			0
$694$	−0.125492	+	0.583005i	−0.00476362	+	0.0221306i
$695$	−41.3029			−1.56671
$696$		0			0
$697$	−50.3320			−1.90646
$698$	−3.16811	+	14.7183i	−0.119915	+	0.557094i
$699$		0			0
$700$	30.3431	+	13.6974i	1.14686	+	0.517712i
$701$			16.8014i			0.634581i	0.948328	+	0.317290i	$0.102773\pi$
$701$			16.8014i			0.634581i	−0.948328	+	0.317290i	$0.897227\pi$
$702$		0			0
$703$	8.52026			0.321348
$704$	−16.5906	+	5.10850i	−0.625281	+	0.192534i
$705$		0			0
$706$	−18.0000	−	3.87451i	−0.677439	−	0.145819i
$707$		−	17.7809i		−	0.668721i
$708$		0			0
$709$		−	3.47974i		−	0.130684i	−0.997863	−	0.0653422i	$-0.979186\pi$
$709$		−	3.47974i		−	0.130684i	0.997863	−	0.0653422i	$-0.0208139\pi$
$710$		0			0
$711$		0			0
$712$	−10.3542	−	7.64575i	−0.388042	−	0.286537i
$713$	−1.95906			−0.0733675
$714$		0			0
$715$		−	33.8745i		−	1.26683i
$716$	−3.91813	+	8.67963i	−0.146427	+	0.324373i
$717$		0			0
$718$	29.2288	+	6.29150i	1.09081	+	0.234797i
$719$	−51.3838			−1.91629			−0.958146	−	0.286281i	$-0.907581\pi$
$719$	−51.3838			−1.91629			−0.958146	+	0.286281i	$0.907581\pi$
$720$		0			0
$721$	14.1660			0.527570
$722$	28.4570	+	6.12538i	1.05906	+	0.227963i
$723$		0			0
$724$	−13.6974	+	30.3431i	−0.509059	+	1.12769i
$725$			27.3040i			1.01404i
$726$		0			0
$727$	44.5830			1.65349			0.826746	−	0.562575i	$-0.190189\pi$
$727$	44.5830			1.65349			0.826746	+	0.562575i	$0.190189\pi$
$728$	20.6515	−	27.9672i	0.765394	−	1.03653i
$729$		0			0
$730$	−11.5830	+	53.8118i	−0.428706	+	1.99166i
$731$		−	14.9785i		−	0.554000i
$732$		0			0
$733$		−	28.4575i		−	1.05110i	−0.850762	−	0.525551i	$-0.823859\pi$
$733$		−	28.4575i		−	1.05110i	0.850762	−	0.525551i	$-0.176141\pi$
$734$	−6.24947	−	1.34520i	−0.230672	−	0.0496523i
$735$		0			0
$736$	2.70850	+	4.83399i	0.0998365	+	0.178183i
$737$	−6.50972			−0.239789
$738$		0			0
$739$		−	40.4575i		−	1.48825i	−0.668038	−	0.744127i	$-0.732866\pi$
$739$		−	40.4575i		−	1.48825i	0.668038	−	0.744127i	$-0.267134\pi$
$740$	8.29529	+	3.74463i	0.304941	+	0.137655i
$741$		0			0
$742$	3.41699	−	15.8745i	0.125442	−	0.582772i
$743$	−25.0594			−0.919339			−0.459669	−	0.888090i	$-0.652032\pi$
$743$	−25.0594			−0.919339			−0.459669	+	0.888090i	$0.652032\pi$
$744$		0			0
$745$	29.1660			1.06856
$746$	11.4634	−	53.2561i	0.419705	−	1.94984i
$747$		0			0
$748$	8.12549	−	18.0000i	0.297097	−	0.658145i
$749$			47.6018i			1.73933i
$750$		0			0
$751$	24.0627			0.878062			0.439031	−	0.898472i	$-0.355322\pi$
$751$	24.0627			0.878062			0.439031	+	0.898472i	$0.355322\pi$
$752$	26.6714	+	30.2425i	0.972607	+	1.10283i
$753$		0			0
$754$	27.8745	+	6.00000i	1.01513	+	0.218507i
$755$		−	42.4933i		−	1.54649i
$756$		0			0
$757$			13.9373i			0.506558i	0.967393	+	0.253279i	$0.0815091\pi$
$757$			13.9373i			0.506558i	−0.967393	+	0.253279i	$0.918491\pi$
$758$	6.42297	−	29.8395i	0.233293	−	1.08382i
$759$		0			0
$760$	48.1033	+	35.5203i	1.74489	+	1.28846i
$761$	9.73385			0.352852			0.176426	−	0.984314i	$-0.443546\pi$
$761$	9.73385			0.352852			0.176426	+	0.984314i	$0.443546\pi$
$762$		0			0
$763$			40.4575i			1.46466i
$764$	−14.8050	−	6.68322i	−0.535626	−	0.241790i
$765$		0			0
$766$	−27.8745	−	6.00000i	−1.00715	−	0.216789i
$767$	52.3633			1.89073
$768$		0			0
$769$	36.1660			1.30418			0.652090	−	0.758142i	$-0.273892\pi$
$769$	36.1660			1.30418			0.652090	+	0.758142i	$0.273892\pi$
$770$	26.6714	+	5.74103i	0.961171	+	0.206893i
$771$		0			0
$772$	−7.82288	−	3.53137i	−0.281551	−	0.127097i
$773$		−	6.29888i		−	0.226555i	−0.993563	−	0.113277i	$-0.963865\pi$
$773$		−	6.29888i		−	0.226555i	0.993563	−	0.113277i	$-0.0361349\pi$
$774$		0			0
$775$	−12.5830			−0.451995
$776$	−5.21392	−	3.85005i	−0.187169	−	0.138209i
$777$		0			0
$778$	−1.58301	+	7.35425i	−0.0567535	+	0.263663i
$779$		−	69.5864i		−	2.49319i
$780$		0			0
$781$		0			0
$782$	−6.16272	−	1.32653i	−0.220379	−	0.0474366i
$783$		0			0
$784$		0			0
$785$	−29.2630			−1.04444
$786$		0			0
$787$			50.6235i			1.80453i	0.431178	+	0.902267i	$0.358098\pi$
$787$			50.6235i			1.80453i	−0.431178	+	0.902267i	$0.641902\pi$
$788$	−6.33622	+	14.0363i	−0.225719	+	0.500023i
$789$		0			0
$790$	8.64575	−	40.1660i	0.307602	−	1.42904i
$791$	−17.2231			−0.612383
$792$		0			0
$793$	9.00000			0.319599
$794$	−4.55066	+	21.1412i	−0.161497	+	0.750274i
$795$		0			0
$796$	−33.7601	−	15.2399i	−1.19660	−	0.540163i
$797$			50.9621i			1.80517i	0.430512	+	0.902585i	$0.358333\pi$
$797$			50.9621i			1.80517i	−0.430512	+	0.902585i	$0.641667\pi$
$798$		0			0
$799$	−45.8745			−1.62292
$800$	17.3966	+	31.0486i	0.615063	+	1.09773i
$801$		0			0
$802$	18.0000	+	3.87451i	0.635602	+	0.136814i
$803$			25.1340i			0.886961i
$804$		0			0
$805$		−	8.70850i		−	0.306934i
$806$	−2.76510	+	12.8459i	−0.0973963	+	0.452479i
$807$		0			0
$808$	11.2915	−	15.2915i	0.397234	−	0.537953i
$809$		0			0			−	1.00000i	$-0.5\pi$
$809$		0			0				1.00000i	$0.5\pi$
$810$		0			0
$811$		−	20.7085i		−	0.727174i	−0.931560	−	0.363587i	$-0.881552\pi$
$811$		−	20.7085i		−	0.727174i	0.931560	−	0.363587i	$-0.118448\pi$
$812$	−9.44832	+	20.9304i	−0.331571	+	0.734513i
$813$		0			0
$814$	4.06275	+	0.874508i	0.142399	+	0.0306515i
$815$	21.1412			0.740545
$816$		0			0
$817$	20.7085			0.724499
$818$	−11.4634	−	2.46750i	−0.400808	−	0.0862742i
$819$		0			0
$820$	30.5830	−	67.7490i	1.06800	−	2.36590i
$821$			49.9826i			1.74440i	0.489146	+	0.872202i	$0.337308\pi$
$821$			49.9826i			1.74440i	−0.489146	+	0.872202i	$0.662692\pi$
$822$		0			0
$823$	−20.0627			−0.699343			−0.349672	−	0.936872i	$-0.613707\pi$
$823$	−20.0627			−0.699343			−0.349672	+	0.936872i	$0.613707\pi$
$824$	12.1827	+	8.99590i	0.424404	+	0.313387i
$825$		0			0
$826$	−8.87451	+	41.2288i	−0.308784	+	1.43453i
$827$			49.6356i			1.72600i	0.505206	+	0.862999i	$0.331417\pi$
$827$			49.6356i			1.72600i	−0.505206	+	0.862999i	$0.668583\pi$
$828$		0			0
$829$			6.77124i			0.235175i	0.993063	+	0.117588i	$0.0375161\pi$
$829$			6.77124i			0.235175i	−0.993063	+	0.117588i	$0.962484\pi$
$830$	11.0604	+	2.38075i	0.383911	+	0.0826371i
$831$		0			0
$832$	35.5203	−	10.9373i	1.23144	−	0.379181i
$833$		0			0
$834$		0			0
$835$			64.4575i			2.23064i
$836$	24.8859	+	11.2339i	0.860695	+	0.388532i
$837$		0			0
$838$	0.645751	−	3.00000i	0.0223071	−	0.103633i
$839$	31.2221			1.07791			0.538953	−	0.842336i	$-0.318820\pi$
$839$	31.2221			1.07791			0.538953	+	0.842336i	$0.318820\pi$
$840$		0			0
$841$	10.1660			0.350552
$842$	6.73924	−	31.3088i	0.232250	−	1.07897i
$843$		0			0
$844$	−0.239870	+	0.531373i	−0.00825668	+	0.0182906i
$845$			28.8413i			0.992172i
$846$		0			0
$847$	−16.6458			−0.571955
$848$	13.0194	−	11.4821i	0.447090	−	0.394296i
$849$		0			0
$850$	−39.5830	−	8.52026i	−1.35769	−	0.292242i
$851$		−	1.32653i		−	0.0454728i
$852$		0			0
$853$			29.8118i			1.02074i	0.859956	+	0.510368i	$0.170491\pi$
$853$			29.8118i			1.02074i	−0.859956	+	0.510368i	$0.829509\pi$
$854$	−1.52532	+	7.08624i	−0.0521952	+	0.242486i
$855$		0			0
$856$	−30.2288	+	40.9373i	−1.03320	+	1.39921i
$857$	40.3234			1.37742			0.688711	−	0.725036i	$-0.258177\pi$
$857$	40.3234			1.37742			0.688711	+	0.725036i	$0.258177\pi$
$858$		0			0
$859$			26.4170i			0.901336i	0.892692	+	0.450668i	$0.148814\pi$
$859$			26.4170i			0.901336i	−0.892692	+	0.450668i	$0.851186\pi$
$860$	20.1617	+	9.10132i	0.687508	+	0.310352i
$861$		0			0
$862$	−41.8118	−	9.00000i	−1.42411	−	0.306541i
$863$	36.1197			1.22953			0.614765	−	0.788710i	$-0.289251\pi$
$863$	36.1197			1.22953			0.614765	+	0.788710i	$0.289251\pi$
$864$		0			0
$865$	53.1660			1.80770
$866$	0.173499	+	0.0373457i	0.00589573	+	0.00126906i
$867$		0			0
$868$	−9.64575	−	4.35425i	−0.327398	−	0.147793i
$869$		−	18.7605i		−	0.636406i
$870$		0			0
$871$	13.9373			0.472246
$872$	−25.6919	+	34.7932i	−0.870037	+	1.17825i
$873$		0			0
$874$	1.83399	−	8.52026i	0.0620356	−	0.288202i
$875$		−	11.4821i		−	0.388165i
$876$		0			0
$877$			48.3948i			1.63418i	0.576514	+	0.817088i	$0.304413\pi$
$877$			48.3948i			1.63418i	−0.576514	+	0.817088i	$0.695587\pi$
$878$	15.4375	+	3.32294i	0.520992	+	0.112144i
$879$		0			0
$880$	19.2915	+	21.8745i	0.650316	+	0.737390i
$881$	31.8546			1.07321			0.536605	−	0.843834i	$-0.319707\pi$
$881$	31.8546			1.07321			0.536605	+	0.843834i	$0.319707\pi$
$882$		0			0
$883$			16.1660i			0.544030i	0.962293	+	0.272015i	$0.0876900\pi$
$883$			16.1660i			0.544030i	−0.962293	+	0.272015i	$0.912310\pi$
$884$	−17.3966	+	38.5378i	−0.585111	+	1.29617i
$885$		0			0
$886$	8.58301	−	39.8745i	0.288352	−	1.33961i
$887$	−7.14226			−0.239813			−0.119907	−	0.992785i	$-0.538260\pi$
$887$	−7.14226			−0.239813			−0.119907	+	0.992785i	$0.538260\pi$
$888$		0			0
$889$	−14.0000			−0.469545
$890$	−4.55066	+	21.1412i	−0.152538	+	0.708656i
$891$		0			0
$892$	−18.2288	−	8.22876i	−0.610344	−	0.275519i
$893$		−	63.4237i		−	2.12239i
$894$		0			0
$895$	16.0000			0.534821
$896$	2.59160	+	29.8209i	0.0865792	+	0.996245i
$897$		0			0
$898$	−27.0000	−	5.81176i	−0.901002	−	0.193941i
$899$		−	8.67963i		−	0.289482i
$900$		0			0
$901$			19.7490i			0.657935i
$902$	7.14226	−	33.1811i	0.237811	−	1.10481i
$903$		0			0
$904$	−14.8118	−	10.9373i	−0.492632	−	0.363768i
$905$	55.9344			1.85932
$906$		0			0
$907$		−	56.0405i		−	1.86079i	−0.366552	−	0.930397i	$-0.619462\pi$
$907$		−	56.0405i		−	1.86079i	0.366552	−	0.930397i	$-0.380538\pi$
$908$	11.0604	−	24.5015i	0.367052	−	0.813111i
$909$		0			0
$910$	−57.1033	−	12.2915i	−1.89295	−	0.407459i
$911$	−47.4657			−1.57261			−0.786304	−	0.617840i	$-0.788008\pi$
$911$	−47.4657			−1.57261			−0.786304	+	0.617840i	$0.788008\pi$
$912$		0			0
$913$	5.16601			0.170970
$914$	−33.0076	−	7.10491i	−1.09180	−	0.235010i
$915$		0			0
$916$	10.8340	−	24.0000i	0.357965	−	0.792982i
$917$			40.7451i			1.34552i
$918$		0			0
$919$	20.5830			0.678971			0.339485	−	0.940611i	$-0.389747\pi$
$919$	20.5830			0.678971			0.339485	+	0.940611i	$0.389747\pi$
$920$	5.53019	−	7.48925i	0.182325	−	0.246913i
$921$		0			0
$922$	5.58301	−	25.9373i	0.183866	−	0.854198i
$923$		0			0
$924$		0			0
$925$		−	8.52026i		−	0.280144i
$926$	−43.1752	−	9.29349i	−1.41883	−	0.305403i
$927$		0			0
$928$	−21.4170	+	12.0000i	−0.703047	+	0.393919i
$929$	−16.9376			−0.555704			−0.277852	−	0.960624i	$-0.589622\pi$
$929$	−16.9376			−0.555704			−0.277852	+	0.960624i	$0.589622\pi$
$930$		0			0
$931$		0			0
$932$	−16.5906	−	7.48925i	−0.543442	−	0.245319i
$933$		0			0
$934$	0.0627461	−	0.291503i	0.00205311	−	0.00953826i
$935$	−33.1811			−1.08514
$936$		0			0
$937$	−9.12549			−0.298117			−0.149058	−	0.988828i	$-0.547624\pi$
$937$	−9.12549			−0.298117			−0.149058	+	0.988828i	$0.547624\pi$
$938$	−2.36208	+	10.9736i	−0.0771246	+	0.358302i
$939$		0			0
$940$	27.8745	−	61.7490i	0.909166	−	2.01403i
$941$		−	21.5629i		−	0.702931i	−0.936201	−	0.351466i	$-0.885683\pi$
$941$		−	21.5629i		−	0.702931i	0.936201	−	0.351466i	$-0.114317\pi$
$942$		0			0
$943$	−10.8340			−0.352803
$944$	−33.8137	+	29.8209i	−1.10054	+	0.970586i
$945$		0			0
$946$	9.87451	+	2.12549i	0.321048	+	0.0691057i
$947$		−	31.0112i		−	1.00773i	−0.863782	−	0.503865i	$-0.831911\pi$
$947$		−	31.0112i		−	1.00773i	0.863782	−	0.503865i	$-0.168089\pi$
$948$		0			0
$949$		−	53.8118i		−	1.74680i
$950$	11.7797	−	54.7254i	0.382183	−	1.77553i
$951$		0			0
$952$	−27.3948	−	20.2288i	−0.887870	−	0.655618i
$953$	−40.9559			−1.32669			−0.663346	−	0.748312i	$-0.730864\pi$
$953$	−40.9559			−1.32669			−0.663346	+	0.748312i	$0.730864\pi$
$954$		0			0
$955$			27.2915i			0.883132i
$956$	36.7523	+	16.5906i	1.18865	+	0.536577i
$957$		0			0
$958$	48.5830	+	10.4575i	1.56965	+	0.337867i
$959$	17.2231			0.556163
$960$		0			0
$961$	−27.0000			−0.870968
$962$	−8.69830	−	1.87231i	−0.280445	−	0.0603658i
$963$		0			0
$964$	48.9889	+	22.1144i	1.57783	+	0.712256i
$965$			14.4207i			0.464218i
$966$		0			0
$967$	−38.0627			−1.22402			−0.612008	−	0.790852i	$-0.709638\pi$
$967$	−38.0627			−1.22402			−0.612008	+	0.790852i	$0.709638\pi$
$968$	−14.3152	−	10.5706i	−0.460109	−	0.339752i
$969$		0			0
$970$	−2.29150	+	10.6458i	−0.0735757	+	0.341814i
$971$		−	17.9918i		−	0.577384i	−0.957422	−	0.288692i	$-0.906780\pi$
$971$		−	17.9918i		−	0.577384i	0.957422	−	0.288692i	$-0.0932204\pi$
$972$		0			0
$973$			32.5203i			1.04255i
$974$	−8.38203	−	1.80424i	−0.268578	−	0.0578115i
$975$		0			0
$976$	−5.81176	+	5.12549i	−0.186030	+	0.164063i
$977$	29.2630			0.936207			0.468103	−	0.883674i	$-0.344937\pi$
$977$	29.2630			0.936207			0.468103	+	0.883674i	$0.344937\pi$
$978$		0			0
$979$			9.87451i			0.315591i
$980$		0			0
$981$		0			0
$982$	1.22876	−	5.70850i	0.0392112	−	0.182165i
$983$	28.2835			0.902103			0.451052	−	0.892498i	$-0.351049\pi$
$983$	28.2835			0.902103			0.451052	+	0.892498i	$0.351049\pi$
$984$		0			0
$985$	25.8745			0.824430
$986$	5.87719	−	27.3040i	0.187168	−	0.869535i
$987$		0			0
$988$	−53.2804	−	24.0516i	−1.69507	−	0.765184i
$989$		−	3.22413i		−	0.102521i
$990$		0			0
$991$	21.9373			0.696860			0.348430	−	0.937335i	$-0.386715\pi$
$991$	21.9373			0.696860			0.348430	+	0.937335i	$0.386715\pi$
$992$	−5.53019	−	9.87000i	−0.175584	−	0.313373i
$993$		0			0
$994$		0			0
$995$			62.2333i			1.97293i
$996$		0			0
$997$		−	21.8745i		−	0.692773i	−0.938092	−	0.346386i	$-0.887409\pi$
$997$		−	21.8745i		−	0.692773i	0.938092	−	0.346386i	$-0.112591\pi$
$998$	−13.0194	+	60.4851i	−0.412123	+	1.91462i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	216.2.d.c.109.1	✓	8
3.2	odd	2	inner	216.2.d.c.109.8	yes	8
4.3	odd	2		864.2.d.c.433.1		8
8.3	odd	2		864.2.d.c.433.8		8
8.5	even	2	inner	216.2.d.c.109.2	yes	8
9.2	odd	6		648.2.n.q.109.4		16
9.4	even	3		648.2.n.q.541.7		16
9.5	odd	6		648.2.n.q.541.2		16
9.7	even	3		648.2.n.q.109.5		16
12.11	even	2		864.2.d.c.433.7		8
16.3	odd	4		6912.2.a.ci.1.1		4
16.5	even	4		6912.2.a.cc.1.4		4
16.11	odd	4		6912.2.a.cd.1.4		4
16.13	even	4		6912.2.a.cj.1.1		4
24.5	odd	2	inner	216.2.d.c.109.7	yes	8
24.11	even	2		864.2.d.c.433.2		8
36.7	odd	6		2592.2.r.q.433.8		16
36.11	even	6		2592.2.r.q.433.2		16
36.23	even	6		2592.2.r.q.2161.7		16
36.31	odd	6		2592.2.r.q.2161.1		16
48.5	odd	4		6912.2.a.cc.1.1		4
48.11	even	4		6912.2.a.cd.1.1		4
48.29	odd	4		6912.2.a.cj.1.4		4
48.35	even	4		6912.2.a.ci.1.4		4
72.5	odd	6		648.2.n.q.541.4		16
72.11	even	6		2592.2.r.q.433.7		16
72.13	even	6		648.2.n.q.541.5		16
72.29	odd	6		648.2.n.q.109.2		16
72.43	odd	6		2592.2.r.q.433.1		16
72.59	even	6		2592.2.r.q.2161.2		16
72.61	even	6		648.2.n.q.109.7		16
72.67	odd	6		2592.2.r.q.2161.8		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
216.2.d.c.109.1	✓	8	1.1	even	1	trivial
216.2.d.c.109.2	yes	8	8.5	even	2	inner
216.2.d.c.109.7	yes	8	24.5	odd	2	inner
216.2.d.c.109.8	yes	8	3.2	odd	2	inner
648.2.n.q.109.2		16	72.29	odd	6
648.2.n.q.109.4		16	9.2	odd	6
648.2.n.q.109.5		16	9.7	even	3
648.2.n.q.109.7		16	72.61	even	6
648.2.n.q.541.2		16	9.5	odd	6
648.2.n.q.541.4		16	72.5	odd	6
648.2.n.q.541.5		16	72.13	even	6
648.2.n.q.541.7		16	9.4	even	3
864.2.d.c.433.1		8	4.3	odd	2
864.2.d.c.433.2		8	24.11	even	2
864.2.d.c.433.7		8	12.11	even	2
864.2.d.c.433.8		8	8.3	odd	2
2592.2.r.q.433.1		16	72.43	odd	6
2592.2.r.q.433.2		16	36.11	even	6
2592.2.r.q.433.7		16	72.11	even	6
2592.2.r.q.433.8		16	36.7	odd	6
2592.2.r.q.2161.1		16	36.31	odd	6
2592.2.r.q.2161.2		16	72.59	even	6
2592.2.r.q.2161.7		16	36.23	even	6
2592.2.r.q.2161.8		16	72.67	odd	6
6912.2.a.cc.1.1		4	48.5	odd	4
6912.2.a.cc.1.4		4	16.5	even	4
6912.2.a.cd.1.1		4	48.11	even	4
6912.2.a.cd.1.4		4	16.11	odd	4
6912.2.a.ci.1.1		4	16.3	odd	4
6912.2.a.ci.1.4		4	48.35	even	4
6912.2.a.cj.1.1		4	16.13	even	4
6912.2.a.cj.1.4		4	48.29	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:	\( N \)	\(=\)	\( 216 = 2^{3} \cdot 3^{3} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	216.d (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.38255 - 0.297594i) q^{2} +(1.82288 + 0.822876i) q^{4} -3.36028i q^{5} -2.64575 q^{7} +(-2.27533 - 1.68014i) q^{8} +O(q^{10})\)	\(q+(-1.38255 - 0.297594i) q^{2} +(1.82288 + 0.822876i) q^{4} -3.36028i q^{5} -2.64575 q^{7} +(-2.27533 - 1.68014i) q^{8} +(-1.00000 + 4.64575i) q^{10} +2.16991i q^{11} -4.64575i q^{13} +(3.65788 + 0.787360i) q^{14} +(2.64575 + 3.00000i) q^{16} -4.55066 q^{17} -6.29150i q^{19} +(2.76510 - 6.12538i) q^{20} +(0.645751 - 3.00000i) q^{22} -0.979531 q^{23} -6.29150 q^{25} +(-1.38255 + 6.42297i) q^{26} +(-4.82288 - 2.17712i) q^{28} -4.33981i q^{29} +2.00000 q^{31} +(-2.76510 - 4.93500i) q^{32} +(6.29150 + 1.35425i) q^{34} +8.89047i q^{35} +1.35425i q^{37} +(-1.87231 + 8.69830i) q^{38} +(-5.64575 + 7.64575i) q^{40} +11.0604 q^{41} +3.29150i q^{43} +(-1.78556 + 3.95547i) q^{44} +(1.35425 + 0.291503i) q^{46} +10.0808 q^{47} +(8.69830 + 1.87231i) q^{50} +(3.82288 - 8.46863i) q^{52} -4.33981i q^{53} +7.29150 q^{55} +(6.01996 + 4.44524i) q^{56} +(-1.29150 + 6.00000i) q^{58} +11.2712i q^{59} +1.93725i q^{61} +(-2.76510 - 0.595188i) q^{62} +(2.35425 + 7.64575i) q^{64} -15.6110 q^{65} +3.00000i q^{67} +(-8.29529 - 3.74463i) q^{68} +(2.64575 - 12.2915i) q^{70} +11.5830 q^{73} +(0.403016 - 1.87231i) q^{74} +(5.17712 - 11.4686i) q^{76} -5.74103i q^{77} -8.64575 q^{79} +(10.0808 - 8.89047i) q^{80} +(-15.2915 - 3.29150i) q^{82} -2.38075i q^{83} +15.2915i q^{85} +(0.979531 - 4.55066i) q^{86} +(3.64575 - 4.93725i) q^{88} +4.55066 q^{89} +12.2915i q^{91} +(-1.78556 - 0.806032i) q^{92} +(-13.9373 - 3.00000i) q^{94} -21.1412 q^{95} +2.29150 q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 4 q^{4}+O(q^{10}) \) 8 * q + 4 * q^4	\( 8 q + 4 q^{4} - 8 q^{10} - 16 q^{22} - 8 q^{25} - 28 q^{28} + 16 q^{31} + 8 q^{34} - 24 q^{40} + 32 q^{46} + 20 q^{52} + 16 q^{55} + 32 q^{58} + 40 q^{64} + 8 q^{73} + 52 q^{76} - 48 q^{79} - 80 q^{82} + 8 q^{88} - 48 q^{94} - 24 q^{97}+O(q^{100}) \) 8 * q + 4 * q^4 - 8 * q^10 - 16 * q^22 - 8 * q^25 - 28 * q^28 + 16 * q^31 + 8 * q^34 - 24 * q^40 + 32 * q^46 + 20 * q^52 + 16 * q^55 + 32 * q^58 + 40 * q^64 + 8 * q^73 + 52 * q^76 - 48 * q^79 - 80 * q^82 + 8 * q^88 - 48 * q^94 - 24 * q^97

Introduction

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