LMFDB - Embedded newform 324.3.d.g.163.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [324,3,Mod(163,324)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(324, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("324.163");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 324 = 2^{2} \cdot 3^{4} $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	324.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:	$8.82836056527$
Analytic rank:	$0$
Dimension:	$8$
Coefficient field:	8.0.1919698923024.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 3x^{7} + 2x^{6} + 12x^{5} - 36x^{4} + 48x^{3} + 32x^{2} - 192x + 256 $ x^8 - 3x^7 + 2x^6 + 12x^5 - 36x^4 + 48x^3 + 32x^2 - 192*x + 256
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{4} $
Twist minimal:	no (minimal twist has level 36)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			163.8
Root			$-1.97436 - 0.319229i$ of defining polynomial
Character	$\chi$	$=$	324.163
Dual form			324.3.d.g.163.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.97436 + 0.319229i) q^{2} +(3.79619 + 1.26055i) q^{4} +2.71218 q^{5} -11.5967i q^{7} +(7.09263 + 3.70062i) q^{8} +O(q^{10})$	\(q+(1.97436 + 0.319229i) q^{2} +(3.79619 + 1.26055i) q^{4} +2.71218 q^{5} -11.5967i q^{7} +(7.09263 + 3.70062i) q^{8} +(5.35481 + 0.865806i) q^{10} -9.87064i q^{11} -0.592371 q^{13} +(3.70202 - 22.8961i) q^{14} +(12.8220 + 9.57053i) q^{16} +8.87968 q^{17} +14.0989i q^{19} +(10.2959 + 3.41882i) q^{20} +(3.15100 - 19.4882i) q^{22} +21.1026i q^{23} -17.6441 q^{25} +(-1.16955 - 0.189102i) q^{26} +(14.6182 - 44.0234i) q^{28} +20.3528 q^{29} +16.5534i q^{31} +(22.2601 + 22.9888i) q^{32} +(17.5317 + 2.83465i) q^{34} -31.4524i q^{35} -40.6557 q^{37} +(-4.50077 + 27.8363i) q^{38} +(19.2365 + 10.0367i) q^{40} +42.4355 q^{41} +37.2258i q^{43} +(12.4424 - 37.4708i) q^{44} +(-6.73658 + 41.6642i) q^{46} +1.81442i q^{47} -85.4845 q^{49} +(-34.8358 - 5.63251i) q^{50} +(-2.24875 - 0.746711i) q^{52} +21.1005 q^{53} -26.7709i q^{55} +(42.9152 - 82.2514i) q^{56} +(40.1836 + 6.49719i) q^{58} -88.5516i q^{59} -72.9851 q^{61} +(-5.28433 + 32.6823i) q^{62} +(36.6108 + 52.4943i) q^{64} -1.60661 q^{65} -44.2378i q^{67} +(33.7089 + 11.1932i) q^{68} +(10.0405 - 62.0984i) q^{70} +111.798i q^{71} -76.2003 q^{73} +(-80.2690 - 12.9785i) q^{74} +(-17.7723 + 53.5220i) q^{76} -114.467 q^{77} +9.58903i q^{79} +(34.7757 + 25.9570i) q^{80} +(83.7828 + 13.5466i) q^{82} +85.0141i q^{83} +24.0833 q^{85} +(-11.8836 + 73.4971i) q^{86} +(36.5275 - 70.0088i) q^{88} -64.7845 q^{89} +6.86958i q^{91} +(-26.6008 + 80.1095i) q^{92} +(-0.579216 + 3.58232i) q^{94} +38.2387i q^{95} +7.18278 q^{97} +(-168.777 - 27.2892i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 3 q^{2} + 5 q^{4} + 6 q^{5} + 27 q^{8}+O(q^{10}) $ 8 * q - 3 * q^2 + 5 * q^4 + 6 * q^5 + 27 * q^8	$ 8 q - 3 q^{2} + 5 q^{4} + 6 q^{5} + 27 q^{8} + 10 q^{10} + 46 q^{13} - 12 q^{14} + 17 q^{16} - 6 q^{17} + 36 q^{20} - 33 q^{22} + 30 q^{25} - 36 q^{26} + 6 q^{28} + 42 q^{29} + 87 q^{32} - 11 q^{34} + 28 q^{37} - 99 q^{38} - 68 q^{40} + 84 q^{41} + 111 q^{44} - 132 q^{46} - 58 q^{49} - 219 q^{50} - 110 q^{52} + 36 q^{53} + 270 q^{56} + 16 q^{58} + 34 q^{61} - 258 q^{62} - 127 q^{64} - 30 q^{65} + 375 q^{68} - 150 q^{70} + 58 q^{73} - 372 q^{74} + 15 q^{76} - 330 q^{77} + 360 q^{80} + 127 q^{82} + 140 q^{85} - 273 q^{86} - 75 q^{88} + 192 q^{89} + 258 q^{92} - 36 q^{94} + 148 q^{97} - 585 q^{98}+O(q^{100}) $ 8 * q - 3 * q^2 + 5 * q^4 + 6 * q^5 + 27 * q^8 + 10 * q^10 + 46 * q^13 - 12 * q^14 + 17 * q^16 - 6 * q^17 + 36 * q^20 - 33 * q^22 + 30 * q^25 - 36 * q^26 + 6 * q^28 + 42 * q^29 + 87 * q^32 - 11 * q^34 + 28 * q^37 - 99 * q^38 - 68 * q^40 + 84 * q^41 + 111 * q^44 - 132 * q^46 - 58 * q^49 - 219 * q^50 - 110 * q^52 + 36 * q^53 + 270 * q^56 + 16 * q^58 + 34 * q^61 - 258 * q^62 - 127 * q^64 - 30 * q^65 + 375 * q^68 - 150 * q^70 + 58 * q^73 - 372 * q^74 + 15 * q^76 - 330 * q^77 + 360 * q^80 + 127 * q^82 + 140 * q^85 - 273 * q^86 - 75 * q^88 + 192 * q^89 + 258 * q^92 - 36 * q^94 + 148 * q^97 - 585 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/324\mathbb{Z}\right)^\times$.

$n$	$163$	$245$
$\chi(n)$	$-1$	$1$

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 $

$2$	1.97436	+	0.319229i	0.987179	+	0.159615i
$2$	1.97436	+	0.319229i	0.987179	+	0.159615i
$3$		0			0
$3$		0			0
$4$	3.79619	+	1.26055i	0.949046	+	0.315136i
$5$	2.71218			0.542435			0.271218	−	0.962518i	$-0.412574\pi$
$5$	2.71218			0.542435			0.271218	+	0.962518i	$0.412574\pi$
$6$		0			0
$7$		−	11.5967i		−	1.65668i	−0.560227	−	0.828339i	$-0.689286\pi$
$7$		−	11.5967i		−	1.65668i	0.560227	−	0.828339i	$-0.310714\pi$
$8$	7.09263	+	3.70062i	0.886579	+	0.462578i
$9$		0			0
$10$	5.35481	+	0.865806i	0.535481	+	0.0865806i
$11$		−	9.87064i		−	0.897331i	−0.893700	−	0.448665i	$-0.851899\pi$
$11$		−	9.87064i		−	0.897331i	0.893700	−	0.448665i	$-0.148101\pi$
$12$		0			0
$13$	−0.592371			−0.0455670			−0.0227835	−	0.999740i	$-0.507253\pi$
$13$	−0.592371			−0.0455670			−0.0227835	+	0.999740i	$0.507253\pi$
$14$	3.70202	−	22.8961i	0.264430	−	1.63544i
$15$		0			0
$16$	12.8220	+	9.57053i	0.801378	+	0.598158i
$17$	8.87968			0.522334			0.261167	−	0.965294i	$-0.415893\pi$
$17$	8.87968			0.522334			0.261167	+	0.965294i	$0.415893\pi$
$18$		0			0
$19$			14.0989i			0.742046i	0.928624	+	0.371023i	$0.120993\pi$
$19$			14.0989i			0.742046i	−0.928624	+	0.371023i	$0.879007\pi$
$20$	10.2959	+	3.41882i	0.514796	+	0.170941i
$21$		0			0
$22$	3.15100	−	19.4882i	0.143227	−	0.885826i
$23$			21.1026i			0.917506i	0.888564	+	0.458753i	$0.151704\pi$
$23$			21.1026i			0.917506i	−0.888564	+	0.458753i	$0.848296\pi$
$24$		0			0
$25$	−17.6441			−0.705764
$26$	−1.16955	−	0.189102i	−0.0449828	−	0.00727316i
$27$		0			0
$28$	14.6182	−	44.0234i	0.522080	−	1.57226i
$29$	20.3528			0.701819			0.350910	−	0.936409i	$-0.385872\pi$
$29$	20.3528			0.701819			0.350910	+	0.936409i	$0.385872\pi$
$30$		0			0
$31$			16.5534i			0.533980i	0.963699	+	0.266990i	$0.0860291\pi$
$31$			16.5534i			0.533980i	−0.963699	+	0.266990i	$0.913971\pi$
$32$	22.2601	+	22.9888i	0.695629	+	0.718401i
$33$		0			0
$34$	17.5317	+	2.83465i	0.515637	+	0.0833721i
$35$		−	31.4524i		−	0.898641i
$36$		0			0
$37$	−40.6557			−1.09880			−0.549401	−	0.835559i	$-0.685144\pi$
$37$	−40.6557			−1.09880			−0.549401	+	0.835559i	$0.685144\pi$
$38$	−4.50077	+	27.8363i	−0.118441	+	0.732533i
$39$		0			0
$40$	19.2365	+	10.0367i	0.480912	+	0.250919i
$41$	42.4355			1.03501			0.517506	−	0.855680i	$-0.326861\pi$
$41$	42.4355			1.03501			0.517506	+	0.855680i	$0.326861\pi$
$42$		0			0
$43$			37.2258i			0.865716i	0.901462	+	0.432858i	$0.142495\pi$
$43$			37.2258i			0.865716i	−0.901462	+	0.432858i	$0.857505\pi$
$44$	12.4424	−	37.4708i	0.282782	−	0.851609i
$45$		0			0
$46$	−6.73658	+	41.6642i	−0.146447	+	0.905743i
$47$			1.81442i			0.0386047i	0.999814	+	0.0193024i	$0.00614451\pi$
$47$			1.81442i			0.0386047i	−0.999814	+	0.0193024i	$0.993855\pi$
$48$		0			0
$49$	−85.4845			−1.74458
$50$	−34.8358	−	5.63251i	−0.696716	−	0.112650i
$51$		0			0
$52$	−2.24875	−	0.746711i	−0.0432452	−	0.0143598i
$53$	21.1005			0.398122			0.199061	−	0.979987i	$-0.436211\pi$
$53$	21.1005			0.398122			0.199061	+	0.979987i	$0.436211\pi$
$54$		0			0
$55$		−	26.7709i		−	0.486744i
$56$	42.9152	−	82.2514i	0.766343	−	1.46878i
$57$		0			0
$58$	40.1836	+	6.49719i	0.692822	+	0.112021i
$59$		−	88.5516i		−	1.50087i	−0.660942	−	0.750437i	$-0.729843\pi$
$59$		−	88.5516i		−	1.50087i	0.660942	−	0.750437i	$-0.270157\pi$
$60$		0			0
$61$	−72.9851			−1.19648			−0.598238	−	0.801318i	$-0.704132\pi$
$61$	−72.9851			−1.19648			−0.598238	+	0.801318i	$0.704132\pi$
$62$	−5.28433	+	32.6823i	−0.0852311	+	0.527134i
$63$		0			0
$64$	36.6108	+	52.4943i	0.572043	+	0.820223i
$65$	−1.60661			−0.0247171
$66$		0			0
$67$		−	44.2378i		−	0.660265i	−0.943935	−	0.330133i	$-0.892906\pi$
$67$		−	44.2378i		−	0.660265i	0.943935	−	0.330133i	$-0.107094\pi$
$68$	33.7089	+	11.1932i	0.495719	+	0.164606i
$69$		0			0
$70$	10.0405	−	62.0984i	0.143436	−	0.887120i
$71$			111.798i			1.57462i	0.616557	+	0.787310i	$0.288527\pi$
$71$			111.798i			1.57462i	−0.616557	+	0.787310i	$0.711473\pi$
$72$		0			0
$73$	−76.2003			−1.04384			−0.521920	−	0.852995i	$-0.674784\pi$
$73$	−76.2003			−1.04384			−0.521920	+	0.852995i	$0.674784\pi$
$74$	−80.2690	−	12.9785i	−1.08472	−	0.175385i
$75$		0			0
$76$	−17.7723	+	53.5220i	−0.233846	+	0.704236i
$77$	−114.467			−1.48659
$78$		0			0
$79$			9.58903i			0.121380i	0.998157	+	0.0606901i	$0.0193301\pi$
$79$			9.58903i			0.121380i	−0.998157	+	0.0606901i	$0.980670\pi$
$80$	34.7757	+	25.9570i	0.434696	+	0.324462i
$81$		0			0
$82$	83.7828	+	13.5466i	1.02174	+	0.165203i
$83$			85.0141i			1.02427i	0.858906	+	0.512133i	$0.171145\pi$
$83$			85.0141i			1.02427i	−0.858906	+	0.512133i	$0.828855\pi$
$84$		0			0
$85$	24.0833			0.283332
$86$	−11.8836	+	73.4971i	−0.138181	+	0.854617i
$87$		0			0
$88$	36.5275	−	70.0088i	0.415085	−	0.795554i
$89$	−64.7845			−0.727916			−0.363958	−	0.931415i	$-0.618575\pi$
$89$	−64.7845			−0.727916			−0.363958	+	0.931415i	$0.618575\pi$
$90$		0			0
$91$			6.86958i			0.0754898i
$92$	−26.6008	+	80.1095i	−0.289140	+	0.870756i
$93$		0			0
$94$	−0.579216	+	3.58232i	−0.00616188	+	0.0381098i
$95$			38.2387i			0.402512i
$96$		0			0
$97$	7.18278			0.0740492			0.0370246	−	0.999314i	$-0.488212\pi$
$97$	7.18278			0.0740492			0.0370246	+	0.999314i	$0.488212\pi$
$98$	−168.777	−	27.2892i	−1.72222	−	0.278461i
$99$		0			0
$100$	−66.9803	−	22.2412i	−0.669803	−	0.222412i
$101$	−111.007			−1.09908			−0.549542	−	0.835466i	$-0.685198\pi$
$101$	−111.007			−1.09908			−0.549542	+	0.835466i	$0.685198\pi$
$102$		0			0
$103$			91.9295i			0.892520i	0.894903	+	0.446260i	$0.147244\pi$
$103$			91.9295i			0.892520i	−0.894903	+	0.446260i	$0.852756\pi$
$104$	−4.20147	−	2.19214i	−0.0403987	−	0.0210783i
$105$		0			0
$106$	41.6599	+	6.73588i	0.393018	+	0.0635460i
$107$		−	107.741i		−	1.00693i	−0.864016	−	0.503465i	$-0.832058\pi$
$107$		−	107.741i		−	1.00693i	0.864016	−	0.503465i	$-0.167942\pi$
$108$		0			0
$109$	86.5562			0.794093			0.397047	−	0.917798i	$-0.370035\pi$
$109$	86.5562			0.794093			0.397047	+	0.917798i	$0.370035\pi$
$110$	8.54606	−	52.8554i	0.0776915	−	0.480504i
$111$		0			0
$112$	110.987	−	148.694i	0.990956	−	1.32763i
$113$	−4.70397			−0.0416280			−0.0208140	−	0.999783i	$-0.506626\pi$
$113$	−4.70397			−0.0416280			−0.0208140	+	0.999783i	$0.506626\pi$
$114$		0			0
$115$			57.2341i			0.497688i
$116$	77.2628	+	25.6556i	0.666059	+	0.221169i
$117$		0			0
$118$	28.2682	−	174.833i	0.239561	−	1.48163i
$119$		−	102.975i		−	0.865339i
$120$		0			0
$121$	23.5705			0.194797
$122$	−144.099	−	23.2990i	−1.18114	−	0.190975i
$123$		0			0
$124$	−20.8663	+	62.8398i	−0.168277	+	0.506772i
$125$	−115.658			−0.925267
$126$		0			0
$127$			8.37118i			0.0659148i	0.999457	+	0.0329574i	$0.0104926\pi$
$127$			8.37118i			0.0659148i	−0.999457	+	0.0329574i	$0.989507\pi$
$128$	55.5251	+	115.330i	0.433790	+	0.901014i
$129$		0			0
$130$	−3.17203	−	0.512878i	−0.0244003	−	0.00394522i
$131$			132.868i			1.01426i	0.861870	+	0.507129i	$0.169293\pi$
$131$			132.868i			1.01426i	−0.861870	+	0.507129i	$0.830707\pi$
$132$		0			0
$133$	163.501			1.22933
$134$	14.1220	−	87.3413i	0.105388	−	0.651800i
$135$		0			0
$136$	62.9803	+	32.8603i	0.463090	+	0.241620i
$137$	45.1159			0.329313			0.164656	−	0.986351i	$-0.447348\pi$
$137$	45.1159			0.329313			0.164656	+	0.986351i	$0.447348\pi$
$138$		0			0
$139$		−	150.970i		−	1.08611i	−0.839696	−	0.543056i	$-0.817267\pi$
$139$		−	150.970i		−	1.08611i	0.839696	−	0.543056i	$-0.182733\pi$
$140$	39.6472	−	119.399i	0.283195	−	0.852852i
$141$		0			0
$142$	−35.6892	+	220.729i	−0.251332	+	1.55443i
$143$			5.84708i			0.0408887i
$144$		0			0
$145$	55.2003			0.380692
$146$	−150.447	−	24.3254i	−1.03046	−	0.166612i
$147$		0			0
$148$	−154.337	−	51.2484i	−1.04281	−	0.346273i
$149$	142.783			0.958274			0.479137	−	0.877740i	$-0.340950\pi$
$149$	142.783			0.958274			0.479137	+	0.877740i	$0.340950\pi$
$150$		0			0
$151$		−	254.065i		−	1.68255i	−0.540606	−	0.841276i	$-0.681805\pi$
$151$		−	254.065i		−	1.68255i	0.540606	−	0.841276i	$-0.318195\pi$
$152$	−52.1746	+	99.9981i	−0.343254	+	0.657882i
$153$		0			0
$154$	−226.000	−	36.5413i	−1.46753	−	0.237281i
$155$			44.8957i			0.289650i
$156$		0			0
$157$	−5.30722			−0.0338039			−0.0169020	−	0.999857i	$-0.505380\pi$
$157$	−5.30722			−0.0338039			−0.0169020	+	0.999857i	$0.505380\pi$
$158$	−3.06110	+	18.9322i	−0.0193740	+	0.119824i
$159$		0			0
$160$	60.3734	+	62.3498i	0.377334	+	0.389686i
$161$	244.722			1.52001
$162$		0			0
$163$			59.5534i			0.365359i	0.983173	+	0.182679i	$0.0584770\pi$
$163$			59.5534i			0.365359i	−0.983173	+	0.182679i	$0.941523\pi$
$164$	161.093	+	53.4918i	0.982273	+	0.326170i
$165$		0			0
$166$	−27.1390	+	167.848i	−0.163488	+	1.01113i
$167$			99.0080i			0.592862i	0.955054	+	0.296431i	$0.0957965\pi$
$167$			99.0080i			0.592862i	−0.955054	+	0.296431i	$0.904203\pi$
$168$		0			0
$169$	−168.649			−0.997924
$170$	47.5490	+	7.68808i	0.279700	+	0.0452240i
$171$		0			0
$172$	−46.9248	+	141.316i	−0.272819	+	0.821605i
$173$	38.5929			0.223081			0.111540	−	0.993760i	$-0.464422\pi$
$173$	38.5929			0.223081			0.111540	+	0.993760i	$0.464422\pi$
$174$		0			0
$175$			204.614i			1.16922i
$176$	94.4673	−	126.562i	0.536746	−	0.719101i
$177$		0			0
$178$	−127.908	−	20.6811i	−0.718584	−	0.116186i
$179$		−	36.4264i		−	0.203499i	−0.994810	−	0.101750i	$-0.967556\pi$
$179$		−	36.4264i		−	0.203499i	0.994810	−	0.101750i	$-0.0324441\pi$
$180$		0			0
$181$	−18.5921			−0.102719			−0.0513594	−	0.998680i	$-0.516355\pi$
$181$	−18.5921			−0.102719			−0.0513594	+	0.998680i	$0.516355\pi$
$182$	−2.19297	+	13.5630i	−0.0120493	+	0.0745220i
$183$		0			0
$184$	−78.0929	+	149.673i	−0.424418	+	0.813441i
$185$	−110.265			−0.596030
$186$		0			0
$187$		−	87.6481i		−	0.468706i
$188$	−2.28716	+	6.88788i	−0.0121658	+	0.0366377i
$189$		0			0
$190$	−12.2069	+	75.4968i	−0.0642468	+	0.397352i
$191$		−	282.870i		−	1.48099i	−0.672059	−	0.740497i	$-0.734590\pi$
$191$		−	282.870i		−	1.48099i	0.672059	−	0.740497i	$-0.265410\pi$
$192$		0			0
$193$	303.085			1.57039			0.785193	−	0.619251i	$-0.212564\pi$
$193$	303.085			1.57039			0.785193	+	0.619251i	$0.212564\pi$
$194$	14.1814	+	2.29295i	0.0730999	+	0.0118193i
$195$		0			0
$196$	−324.515	−	107.757i	−1.65569	−	0.549782i
$197$	−139.184			−0.706520			−0.353260	−	0.935525i	$-0.614927\pi$
$197$	−139.184			−0.706520			−0.353260	+	0.935525i	$0.614927\pi$
$198$		0			0
$199$			11.2337i			0.0564505i	0.999602	+	0.0282253i	$0.00898558\pi$
$199$			11.2337i			0.0564505i	−0.999602	+	0.0282253i	$0.991014\pi$
$200$	−125.143	−	65.2942i	−0.625715	−	0.326471i
$201$		0			0
$202$	−219.169	−	35.4368i	−1.08499	−	0.175430i
$203$		−	236.026i		−	1.16269i
$204$		0			0
$205$	115.092			0.561427
$206$	−29.3466	+	181.502i	−0.142459	+	0.881077i
$207$		0			0
$208$	−7.59541	−	5.66930i	−0.0365164	−	0.0272563i
$209$	139.165			0.665861
$210$		0			0
$211$		−	129.346i		−	0.613012i	−0.951869	−	0.306506i	$-0.900840\pi$
$211$		−	129.346i		−	0.613012i	0.951869	−	0.306506i	$-0.0991599\pi$
$212$	80.1012	+	26.5981i	0.377836	+	0.125463i
$213$		0			0
$214$	34.3942	−	212.720i	0.160721	−	0.994020i
$215$			100.963i			0.469595i
$216$		0			0
$217$	191.966			0.884634
$218$	170.893	+	27.6313i	0.783913	+	0.126749i
$219$		0			0
$220$	33.7460	−	101.627i	0.153391	−	0.461943i
$221$	−5.26006			−0.0238012
$222$		0			0
$223$			241.574i			1.08329i	0.840606	+	0.541647i	$0.182199\pi$
$223$			241.574i			1.08329i	−0.840606	+	0.541647i	$0.817801\pi$
$224$	266.596	−	258.145i	1.19016	−	1.15243i
$225$		0			0
$226$	−9.28732	−	1.50164i	−0.0410943	−	0.00664444i
$227$			381.871i			1.68225i	0.540840	+	0.841126i	$0.318107\pi$
$227$			381.871i			1.68225i	−0.540840	+	0.841126i	$0.681893\pi$
$228$		0			0
$229$	−149.328			−0.652089			−0.326044	−	0.945354i	$-0.605716\pi$
$229$	−149.328			−0.652089			−0.326044	+	0.945354i	$0.605716\pi$
$230$	−18.2708	+	113.001i	−0.0794382	+	0.491307i
$231$		0			0
$232$	144.355	+	75.3179i	0.622218	+	0.324646i
$233$	218.934			0.939631			0.469816	−	0.882765i	$-0.344320\pi$
$233$	218.934			0.939631			0.469816	+	0.882765i	$0.344320\pi$
$234$		0			0
$235$			4.92103i			0.0209406i
$236$	111.623	−	336.158i	0.472980	−	1.42440i
$237$		0			0
$238$	32.8727	−	203.310i	0.138121	−	0.854245i
$239$		−	252.018i		−	1.05447i	−0.849720	−	0.527235i	$-0.823229\pi$
$239$		−	252.018i		−	1.05447i	0.849720	−	0.527235i	$-0.176771\pi$
$240$		0			0
$241$	452.027			1.87563			0.937816	−	0.347133i	$-0.112845\pi$
$241$	452.027			1.87563			0.937816	+	0.347133i	$0.112845\pi$
$242$	46.5366	+	7.52439i	0.192300	+	0.0310925i
$243$		0			0
$244$	−277.065	−	92.0011i	−1.13551	−	0.377053i
$245$	−231.849			−0.946323
$246$		0			0
$247$		−	8.35177i		−	0.0338128i
$248$	−61.2579	+	117.407i	−0.247008	+	0.473416i
$249$		0			0
$250$	−228.351	−	36.9215i	−0.913404	−	0.147686i
$251$			139.429i			0.555492i	0.960655	+	0.277746i	$0.0895874\pi$
$251$			139.429i			0.555492i	−0.960655	+	0.277746i	$0.910413\pi$
$252$		0			0
$253$	208.297			0.823306
$254$	−2.67232	+	16.5277i	−0.0105210	+	0.0650697i
$255$		0			0
$256$	72.8098	+	245.428i	0.284413	+	0.958702i
$257$	470.615			1.83119			0.915594	−	0.402104i	$-0.131721\pi$
$257$	470.615			1.83119			0.915594	+	0.402104i	$0.131721\pi$
$258$		0			0
$259$			471.474i			1.82036i
$260$	−6.09901	−	2.02521i	−0.0234577	−	0.00778928i
$261$		0			0
$262$	−42.4152	+	262.328i	−0.161890	+	1.00125i
$263$			25.6376i			0.0974814i	0.998811	+	0.0487407i	$0.0155208\pi$
$263$			25.6376i			0.0974814i	−0.998811	+	0.0487407i	$0.984479\pi$
$264$		0			0
$265$	57.2282			0.215955
$266$	322.810	+	52.1943i	1.21357	+	0.196219i
$267$		0			0
$268$	55.7638	−	167.935i	0.208074	−	0.626622i
$269$	−8.15075			−0.0303002			−0.0151501	−	0.999885i	$-0.504823\pi$
$269$	−8.15075			−0.0303002			−0.0151501	+	0.999885i	$0.504823\pi$
$270$		0			0
$271$		−	401.979i		−	1.48332i	−0.670777	−	0.741659i	$-0.734039\pi$
$271$		−	401.979i		−	1.48332i	0.670777	−	0.741659i	$-0.265961\pi$
$272$	113.856	+	84.9832i	0.418587	+	0.312438i
$273$		0			0
$274$	89.0749	+	14.4023i	0.325091	+	0.0525632i
$275$			174.158i			0.633304i
$276$		0			0
$277$	−112.404			−0.405791			−0.202896	−	0.979200i	$-0.565035\pi$
$277$	−112.404			−0.405791			−0.202896	+	0.979200i	$0.565035\pi$
$278$	48.1939	−	298.068i	0.173359	−	1.07219i
$279$		0			0
$280$	116.394	−	223.080i	0.415691	−	0.796716i
$281$	537.734			1.91365			0.956823	−	0.290673i	$-0.0938791\pi$
$281$	537.734			1.91365			0.956823	+	0.290673i	$0.0938791\pi$
$282$		0			0
$283$		−	141.223i		−	0.499021i	−0.968372	−	0.249510i	$-0.919730\pi$
$283$		−	141.223i		−	0.499021i	0.968372	−	0.249510i	$-0.0802696\pi$
$284$	−140.927	+	424.406i	−0.496220	+	1.49439i
$285$		0			0
$286$	−1.86656	+	11.5442i	−0.00652643	+	0.0403644i
$287$		−	492.113i		−	1.71468i
$288$		0			0
$289$	−210.151			−0.727167
$290$	108.985	+	17.6215i	0.375811	+	0.0607639i
$291$		0			0
$292$	−289.270	−	96.0540i	−0.990652	−	0.328952i
$293$	−460.581			−1.57195			−0.785975	−	0.618259i	$-0.787838\pi$
$293$	−460.581			−1.57195			−0.785975	+	0.618259i	$0.787838\pi$
$294$		0			0
$295$		−	240.168i		−	0.814127i
$296$	−288.356	−	150.451i	−0.974175	−	0.508282i
$297$		0			0
$298$	281.904	+	45.5804i	0.945988	+	0.152954i
$299$		−	12.5006i		−	0.0418080i
$300$		0			0
$301$	431.698			1.43421
$302$	81.1051	−	501.616i	0.268560	−	1.66098i
$303$		0			0
$304$	−134.934	+	180.777i	−0.443861	+	0.594660i
$305$	−197.948			−0.649011
$306$		0			0
$307$		−	210.322i		−	0.685089i	−0.939502	−	0.342545i	$-0.888711\pi$
$307$		−	210.322i		−	0.685089i	0.939502	−	0.342545i	$-0.111289\pi$
$308$	−434.539	−	144.291i	−1.41084	−	0.468478i
$309$		0			0
$310$	−14.3320	+	88.6403i	−0.0462324	+	0.285936i
$311$		−	128.164i		−	0.412104i	−0.978541	−	0.206052i	$-0.933938\pi$
$311$		−	128.164i		−	0.412104i	0.978541	−	0.206052i	$-0.0660616\pi$
$312$		0			0
$313$	7.24281			0.0231400			0.0115700	−	0.999933i	$-0.496317\pi$
$313$	7.24281			0.0231400			0.0115700	+	0.999933i	$0.496317\pi$
$314$	−10.4784	−	1.69422i	−0.0333705	−	0.00539560i
$315$		0			0
$316$	−12.0874	+	36.4017i	−0.0382513	+	0.115195i
$317$	−240.291			−0.758015			−0.379007	−	0.925394i	$-0.623734\pi$
$317$	−240.291			−0.758015			−0.379007	+	0.925394i	$0.623734\pi$
$318$		0			0
$319$		−	200.895i		−	0.629764i
$320$	99.2949	+	142.374i	0.310297	+	0.444918i
$321$		0			0
$322$	483.169	+	78.1224i	1.50052	+	0.242616i
$323$			125.194i			0.387596i
$324$		0			0
$325$	10.4518			0.0321595
$326$	−19.0112	+	117.580i	−0.0583166	+	0.360674i
$327$		0			0
$328$	300.979	+	157.038i	0.917619	+	0.478773i
$329$	21.0414			0.0639556
$330$		0			0
$331$		−	427.684i		−	1.29210i	−0.763297	−	0.646048i	$-0.776421\pi$
$331$		−	427.684i		−	1.29210i	0.763297	−	0.646048i	$-0.223579\pi$
$332$	−107.164	+	322.729i	−0.322784	+	0.972076i
$333$		0			0
$334$	−31.6062	+	195.477i	−0.0946295	+	0.585261i
$335$		−	119.981i		−	0.358151i
$336$		0			0
$337$	−304.883			−0.904698			−0.452349	−	0.891841i	$-0.649414\pi$
$337$	−304.883			−0.904698			−0.452349	+	0.891841i	$0.649414\pi$
$338$	−332.974	−	53.8377i	−0.985130	−	0.159283i
$339$		0			0
$340$	91.4245	+	30.3581i	0.268896	+	0.0892884i
$341$	163.393			0.479157
$342$		0			0
$343$			423.102i			1.23353i
$344$	−137.759	+	264.029i	−0.400461	+	0.767525i
$345$		0			0
$346$	76.1963	+	12.3200i	0.220221	+	0.0356069i
$347$			169.055i			0.487191i	0.969877	+	0.243595i	$0.0783269\pi$
$347$			169.055i			0.487191i	−0.969877	+	0.243595i	$0.921673\pi$
$348$		0			0
$349$	−214.596			−0.614888			−0.307444	−	0.951566i	$-0.599474\pi$
$349$	−214.596			−0.614888			−0.307444	+	0.951566i	$0.599474\pi$
$350$	−65.3188	+	403.982i	−0.186625	+	1.15423i
$351$		0			0
$352$	226.915	−	219.722i	0.644644	−	0.624209i
$353$	−551.791			−1.56315			−0.781574	−	0.623813i	$-0.785583\pi$
$353$	−551.791			−1.56315			−0.781574	+	0.623813i	$0.785583\pi$
$354$		0			0
$355$			303.216i			0.854130i
$356$	−245.934	−	81.6639i	−0.690826	−	0.229393i
$357$		0			0
$358$	11.6284	−	71.9188i	0.0324815	−	0.200890i
$359$			554.828i			1.54548i	0.634721	+	0.772741i	$0.281115\pi$
$359$			554.828i			1.54548i	−0.634721	+	0.772741i	$0.718885\pi$
$360$		0			0
$361$	162.222			0.449367
$362$	−36.7075	−	5.93514i	−0.101402	−	0.0163954i
$363$		0			0
$364$	−8.65942	+	26.0782i	−0.0237896	+	0.0716434i
$365$	−206.669			−0.566216
$366$		0			0
$367$		−	168.173i		−	0.458237i	−0.973399	−	0.229118i	$-0.926416\pi$
$367$		−	168.173i		−	0.458237i	0.973399	−	0.229118i	$-0.0735843\pi$
$368$	−201.963	+	270.579i	−0.548814	+	0.735269i
$369$		0			0
$370$	−217.704	−	35.2000i	−0.588388	−	0.0951350i
$371$		−	244.697i		−	0.659560i
$372$		0			0
$373$	−343.397			−0.920637			−0.460318	−	0.887754i	$-0.652265\pi$
$373$	−343.397			−0.920637			−0.460318	+	0.887754i	$0.652265\pi$
$374$	27.9798	−	173.049i	0.0748124	−	0.462697i
$375$		0			0
$376$	−6.71449	+	12.8690i	−0.0178577	+	0.0342261i
$377$	−12.0564			−0.0319798
$378$		0			0
$379$			602.392i			1.58943i	0.606986	+	0.794713i	$0.292379\pi$
$379$			602.392i			1.58943i	−0.606986	+	0.794713i	$0.707621\pi$
$380$	−48.2016	+	145.161i	−0.126846	+	0.382003i
$381$		0			0
$382$	90.3004	−	558.487i	0.236388	−	1.46201i
$383$			364.610i			0.951984i	0.879450	+	0.475992i	$0.157911\pi$
$383$			364.610i			0.951984i	−0.879450	+	0.475992i	$0.842089\pi$
$384$		0			0
$385$	−310.456			−0.806378
$386$	598.398	+	96.7534i	1.55025	+	0.250657i
$387$		0			0
$388$	27.2672	+	9.05422i	0.0702762	+	0.0233356i
$389$	214.651			0.551802			0.275901	−	0.961186i	$-0.411024\pi$
$389$	214.651			0.551802			0.275901	+	0.961186i	$0.411024\pi$
$390$		0			0
$391$			187.385i			0.479244i
$392$	−606.310	−	316.346i	−1.54671	−	0.807005i
$393$		0			0
$394$	−274.800	−	44.4317i	−0.697462	−	0.112771i
$395$			26.0071i			0.0658409i
$396$		0			0
$397$	−684.628			−1.72450			−0.862251	−	0.506480i	$-0.830946\pi$
$397$	−684.628			−1.72450			−0.862251	+	0.506480i	$0.830946\pi$
$398$	−3.58611	+	22.1793i	−0.00901033	+	0.0557268i
$399$		0			0
$400$	−226.233	−	168.863i	−0.565584	−	0.422158i
$401$	190.384			0.474772			0.237386	−	0.971415i	$-0.423709\pi$
$401$	190.384			0.474772			0.237386	+	0.971415i	$0.423709\pi$
$402$		0			0
$403$		−	9.80575i		−	0.0243319i
$404$	−421.405	−	139.930i	−1.04308	−	0.346361i
$405$		0			0
$406$	75.3463	−	466.000i	0.185582	−	1.14778i
$407$			401.298i			0.985990i
$408$		0			0
$409$	−377.956			−0.924099			−0.462049	−	0.886854i	$-0.652886\pi$
$409$	−377.956			−0.924099			−0.462049	+	0.886854i	$0.652886\pi$
$410$	227.234	+	36.7409i	0.554229	+	0.0896119i
$411$		0			0
$412$	−115.881	+	348.982i	−0.281266	+	0.847043i
$413$	−1026.91			−2.48647
$414$		0			0
$415$			230.573i			0.555598i
$416$	−13.1863	−	13.6179i	−0.0316977	−	0.0327354i
$417$		0			0
$418$	274.762	+	44.4255i	0.657324	+	0.106281i
$419$			308.681i			0.736709i	0.929685	+	0.368355i	$0.120079\pi$
$419$			308.681i			0.736709i	−0.929685	+	0.368355i	$0.879921\pi$
$420$		0			0
$421$	−353.669			−0.840069			−0.420034	−	0.907508i	$-0.637982\pi$
$421$	−353.669			−0.840069			−0.420034	+	0.907508i	$0.637982\pi$
$422$	41.2909	−	255.374i	0.0978457	−	0.605153i
$423$		0			0
$424$	149.658	+	78.0848i	0.352966	+	0.184162i
$425$	−156.674			−0.368644
$426$		0			0
$427$			846.390i			1.98218i
$428$	135.813	−	409.007i	0.317320	−	0.955623i
$429$		0			0
$430$	−32.2303	+	199.337i	−0.0749542	+	0.463575i
$431$		−	472.777i		−	1.09693i	−0.836174	−	0.548465i	$-0.815213\pi$
$431$		−	472.777i		−	1.09693i	0.836174	−	0.548465i	$-0.184787\pi$
$432$		0			0
$433$	61.4188			0.141845			0.0709224	−	0.997482i	$-0.477406\pi$
$433$	61.4188			0.141845			0.0709224	+	0.997482i	$0.477406\pi$
$434$	379.009	+	61.2810i	0.873292	+	0.141200i
$435$		0			0
$436$	328.583	+	109.108i	0.753632	+	0.250248i
$437$	−297.524			−0.680832
$438$		0			0
$439$			409.165i			0.932038i	0.884775	+	0.466019i	$0.154312\pi$
$439$			409.165i			0.932038i	−0.884775	+	0.466019i	$0.845688\pi$
$440$	99.0691	−	189.876i	0.225157	−	0.431537i
$441$		0			0
$442$	−10.3853	−	1.67917i	−0.0234960	−	0.00379902i
$443$		−	772.271i		−	1.74328i	−0.490151	−	0.871638i	$-0.663058\pi$
$443$		−	772.271i		−	1.74328i	0.490151	−	0.871638i	$-0.336942\pi$
$444$		0			0
$445$	−175.707			−0.394848
$446$	−77.1176	+	476.954i	−0.172909	+	1.06940i
$447$		0			0
$448$	608.763	−	424.566i	1.35885	−	0.947692i
$449$	789.037			1.75732			0.878660	−	0.477448i	$-0.158438\pi$
$449$	789.037			1.75732			0.878660	+	0.477448i	$0.158438\pi$
$450$		0			0
$451$		−	418.865i		−	0.928747i
$452$	−17.8571	−	5.92957i	−0.0395069	−	0.0131185i
$453$		0			0
$454$	−121.904	+	753.950i	−0.268512	+	1.66068i
$455$			18.6315i			0.0409484i
$456$		0			0
$457$	−276.331			−0.604662			−0.302331	−	0.953203i	$-0.597765\pi$
$457$	−276.331			−0.604662			−0.302331	+	0.953203i	$0.597765\pi$
$458$	−294.828	−	47.6700i	−0.643728	−	0.104083i
$459$		0			0
$460$	−72.1462	+	217.271i	−0.156840	+	0.472329i
$461$	−588.083			−1.27567			−0.637834	−	0.770174i	$-0.720169\pi$
$461$	−588.083			−1.27567			−0.637834	+	0.770174i	$0.720169\pi$
$462$		0			0
$463$		−	782.061i		−	1.68912i	−0.535464	−	0.844558i	$-0.679863\pi$
$463$		−	782.061i		−	1.68912i	0.535464	−	0.844558i	$-0.320137\pi$
$464$	260.964	+	194.787i	0.562422	+	0.419799i
$465$		0			0
$466$	432.254	+	69.8901i	0.927585	+	0.149979i
$467$		−	663.203i		−	1.42014i	−0.704133	−	0.710068i	$-0.748664\pi$
$467$		−	663.203i		−	1.42014i	0.704133	−	0.710068i	$-0.251336\pi$
$468$		0			0
$469$	−513.014			−1.09385
$470$	−1.57094	+	9.71589i	−0.00334242	+	0.0206721i
$471$		0			0
$472$	327.696	−	628.063i	0.694271	−	1.33064i
$473$	367.442			0.776834
$474$		0			0
$475$		−	248.762i		−	0.523709i
$476$	129.805	−	390.914i	0.272700	−	0.821247i
$477$		0			0
$478$	80.4516	−	497.574i	0.168309	−	1.04095i
$479$			648.962i			1.35483i	0.735602	+	0.677414i	$0.236899\pi$
$479$			648.962i			1.35483i	−0.735602	+	0.677414i	$0.763101\pi$
$480$		0			0
$481$	24.0833			0.0500691
$482$	892.464	+	144.300i	1.85159	+	0.299378i
$483$		0			0
$484$	89.4779	+	29.7117i	0.184872	+	0.0613878i
$485$	19.4810			0.0401669
$486$		0			0
$487$		−	282.104i		−	0.579269i	−0.957137	−	0.289635i	$-0.906466\pi$
$487$		−	282.104i		−	0.579269i	0.957137	−	0.289635i	$-0.0935338\pi$
$488$	−517.656	−	270.090i	−1.06077	−	0.553464i
$489$		0			0
$490$	−457.754	−	74.0130i	−0.934191	−	0.151047i
$491$		−	753.942i		−	1.53552i	−0.640735	−	0.767762i	$-0.721370\pi$
$491$		−	753.942i		−	1.53552i	0.640735	−	0.767762i	$-0.278630\pi$
$492$		0			0
$493$	180.726			0.366584
$494$	2.66613	−	16.4894i	0.00539702	−	0.0333793i
$495$		0			0
$496$	−158.425	+	212.248i	−0.319405	+	0.427920i
$497$	1296.49			2.60864
$498$		0			0
$499$		−	515.192i		−	1.03245i	−0.856454	−	0.516224i	$-0.827337\pi$
$499$		−	515.192i		−	1.03245i	0.856454	−	0.516224i	$-0.172663\pi$
$500$	−439.061	−	145.793i	−0.878121	−	0.291585i
$501$		0			0
$502$	−44.5096	+	275.282i	−0.0886646	+	0.548370i
$503$			523.660i			1.04107i	0.853839	+	0.520537i	$0.174268\pi$
$503$			523.660i			1.04107i	−0.853839	+	0.520537i	$0.825732\pi$
$504$		0			0
$505$	−301.072			−0.596182
$506$	411.252	+	66.4943i	0.812751	+	0.131412i
$507$		0			0
$508$	−10.5523	+	31.7785i	−0.0207722	+	0.0625562i
$509$	−535.371			−1.05181			−0.525905	−	0.850544i	$-0.676273\pi$
$509$	−535.371			−1.05181			−0.525905	+	0.850544i	$0.676273\pi$
$510$		0			0
$511$			883.675i			1.72931i
$512$	65.4050	+	507.805i	0.127744	+	0.991807i
$513$		0			0
$514$	929.163	+	150.234i	1.80771	+	0.292284i
$515$			249.329i			0.484134i
$516$		0			0
$517$	17.9095			0.0346412
$518$	−150.508	+	930.859i	−0.290556	+	1.79702i
$519$		0			0
$520$	−11.3951	−	5.94548i	−0.0219137	−	0.0114336i
$521$	−177.268			−0.340246			−0.170123	−	0.985423i	$-0.554416\pi$
$521$	−177.268			−0.340246			−0.170123	+	0.985423i	$0.554416\pi$
$522$		0			0
$523$		−	444.206i		−	0.849343i	−0.905347	−	0.424672i	$-0.860390\pi$
$523$		−	444.206i		−	0.849343i	0.905347	−	0.424672i	$-0.139610\pi$
$524$	−167.486	+	504.390i	−0.319629	+	0.962577i
$525$		0			0
$526$	−8.18427	+	50.6178i	−0.0155595	+	0.0962316i
$527$			146.989i			0.278916i
$528$		0			0
$529$	83.6788			0.158183
$530$	112.989	+	18.2689i	0.213187	+	0.0344696i
$531$		0			0
$532$	620.681	+	206.101i	1.16669	+	0.387407i
$533$	−25.1375			−0.0471623
$534$		0			0
$535$		−	292.214i		−	0.546194i
$536$	163.707	−	313.762i	0.305424	−	0.585377i
$537$		0			0
$538$	−16.0925	−	2.60196i	−0.0299117	−	0.00483635i
$539$			843.787i			1.56547i
$540$		0			0
$541$	571.163			1.05575			0.527877	−	0.849321i	$-0.322988\pi$
$541$	571.163			1.05575			0.527877	+	0.849321i	$0.322988\pi$
$542$	128.323	−	793.651i	0.236759	−	1.46430i
$543$		0			0
$544$	197.663	+	204.133i	0.363351	+	0.375245i
$545$	234.756			0.430744
$546$		0			0
$547$		−	161.514i		−	0.295272i	−0.989042	−	0.147636i	$-0.952834\pi$
$547$		−	161.514i		−	0.295272i	0.989042	−	0.147636i	$-0.0471664\pi$
$548$	171.268	+	56.8706i	0.312533	+	0.103779i
$549$		0			0
$550$	−55.5965	+	343.851i	−0.101085	+	0.625184i
$551$			286.951i			0.520782i
$552$		0			0
$553$	111.202			0.201088
$554$	−221.926	−	35.8827i	−0.400589	−	0.0647702i
$555$		0			0
$556$	190.304	−	573.109i	0.342274	−	1.03077i
$557$	568.917			1.02139			0.510697	−	0.859761i	$-0.329387\pi$
$557$	568.917			1.02139			0.510697	+	0.859761i	$0.329387\pi$
$558$		0			0
$559$		−	22.0515i		−	0.0394481i
$560$	301.017	−	403.285i	0.537530	−	0.720151i
$561$		0			0
$562$	1061.68	+	171.660i	1.88911	+	0.305446i
$563$		−	289.283i		−	0.513825i	−0.966435	−	0.256912i	$-0.917295\pi$
$563$		−	289.283i		−	0.513825i	0.966435	−	0.256912i	$-0.0827051\pi$
$564$		0			0
$565$	−12.7580			−0.0225805
$566$	45.0824	−	278.824i	0.0796510	−	0.492623i
$567$		0			0
$568$	−413.723	+	792.942i	−0.728385	+	1.39603i
$569$	−446.234			−0.784243			−0.392121	−	0.919913i	$-0.628259\pi$
$569$	−446.234			−0.784243			−0.392121	+	0.919913i	$0.628259\pi$
$570$		0			0
$571$			429.994i			0.753054i	0.926406	+	0.376527i	$0.122882\pi$
$571$			429.994i			0.753054i	−0.926406	+	0.376527i	$0.877118\pi$
$572$	−7.37051	+	22.1966i	−0.0128855	+	0.0388052i
$573$		0			0
$574$	157.097	−	971.608i	0.273688	−	1.69270i
$575$		−	372.337i		−	0.647542i
$576$		0			0
$577$	50.9694			0.0883353			0.0441676	−	0.999024i	$-0.485936\pi$
$577$	50.9694			0.0883353			0.0441676	+	0.999024i	$0.485936\pi$
$578$	−414.914	−	67.0864i	−0.717845	−	0.116067i
$579$		0			0
$580$	209.551	+	69.5825i	0.361294	+	0.119970i
$581$	985.887			1.69688
$582$		0			0
$583$		−	208.275i		−	0.357247i
$584$	−540.460	−	281.989i	−0.925446	−	0.482857i
$585$		0			0
$586$	−909.353	−	147.031i	−1.55180	−	0.250906i
$587$		−	743.363i		−	1.26638i	−0.773998	−	0.633188i	$-0.781746\pi$
$587$		−	743.363i		−	1.26638i	0.773998	−	0.633188i	$-0.218254\pi$
$588$		0			0
$589$	−233.384			−0.396238
$590$	76.6685	−	474.177i	0.129947	−	0.803690i
$591$		0			0
$592$	−521.289	−	389.097i	−0.880556	−	0.657258i
$593$	382.547			0.645104			0.322552	−	0.946552i	$-0.395459\pi$
$593$	382.547			0.645104			0.322552	+	0.946552i	$0.395459\pi$
$594$		0			0
$595$		−	279.287i		−	0.469391i
$596$	542.030	+	179.984i	0.909446	+	0.301987i
$597$		0			0
$598$	3.99055	−	24.6806i	0.00667316	−	0.0412720i
$599$		−	988.710i		−	1.65060i	−0.564694	−	0.825301i	$-0.691006\pi$
$599$		−	988.710i		−	1.65060i	0.564694	−	0.825301i	$-0.308994\pi$
$600$		0			0
$601$	526.560			0.876140			0.438070	−	0.898941i	$-0.355662\pi$
$601$	526.560			0.876140			0.438070	+	0.898941i	$0.355662\pi$
$602$	852.327	+	137.811i	1.41583	+	0.228921i
$603$		0			0
$604$	320.261	−	964.479i	0.530233	−	1.59682i
$605$	63.9273			0.105665
$606$		0			0
$607$			516.880i			0.851531i	0.904833	+	0.425766i	$0.139995\pi$
$607$			516.880i			0.851531i	−0.904833	+	0.425766i	$0.860005\pi$
$608$	−324.117	+	313.843i	−0.533087	+	0.516189i
$609$		0			0
$610$	−390.821	−	63.1909i	−0.640691	−	0.103592i
$611$		−	1.07481i		−	0.00175910i
$612$		0			0
$613$	762.957			1.24463			0.622314	−	0.782768i	$-0.286193\pi$
$613$	762.957			1.24463			0.622314	+	0.782768i	$0.286193\pi$
$614$	67.1411	−	415.252i	0.109350	−	0.676306i
$615$		0			0
$616$	−811.874	−	423.600i	−1.31798	−	0.687663i
$617$	121.834			0.197461			0.0987307	−	0.995114i	$-0.468522\pi$
$617$	121.834			0.197461			0.0987307	+	0.995114i	$0.468522\pi$
$618$		0			0
$619$		−	306.775i		−	0.495598i	−0.968811	−	0.247799i	$-0.920293\pi$
$619$		−	306.775i		−	0.495598i	0.968811	−	0.247799i	$-0.0797072\pi$
$620$	−56.5931	+	170.433i	−0.0912793	+	0.274891i
$621$		0			0
$622$	40.9138	−	253.042i	0.0657778	−	0.406820i
$623$			751.290i			1.20592i
$624$		0			0
$625$	127.416			0.203866
$626$	14.2999	+	2.31212i	0.0228433	+	0.00369348i
$627$		0			0
$628$	−20.1472	−	6.68999i	−0.0320815	−	0.0106529i
$629$	−361.010			−0.573942
$630$		0			0
$631$			1071.11i			1.69749i	0.528805	+	0.848744i	$0.322640\pi$
$631$			1071.11i			1.69749i	−0.528805	+	0.848744i	$0.677360\pi$
$632$	−35.4854	+	68.0114i	−0.0561478	+	0.107613i
$633$		0			0
$634$	−474.420	−	76.7078i	−0.748296	−	0.120990i
$635$			22.7041i			0.0357545i
$636$		0			0
$637$	50.6386			0.0794954
$638$	64.1315	−	396.638i	0.100520	−	0.621690i
$639$		0			0
$640$	150.594	+	312.795i	0.235303	+	0.488742i
$641$	1054.52			1.64511			0.822557	−	0.568682i	$-0.192546\pi$
$641$	1054.52			1.64511			0.822557	+	0.568682i	$0.192546\pi$
$642$		0			0
$643$		−	48.5759i		−	0.0755458i	−0.999286	−	0.0377729i	$-0.987974\pi$
$643$		−	48.5759i		−	0.0755458i	0.999286	−	0.0377729i	$-0.0120263\pi$
$644$	929.010	+	308.483i	1.44256	+	0.479011i
$645$		0			0
$646$	−39.9654	+	247.177i	−0.0618660	+	0.382627i
$647$		−	539.373i		−	0.833653i	−0.908986	−	0.416826i	$-0.863142\pi$
$647$		−	539.373i		−	0.833653i	0.908986	−	0.416826i	$-0.136858\pi$
$648$		0			0
$649$	−874.061			−1.34678
$650$	20.6357	+	3.33654i	0.0317472	+	0.00513313i
$651$		0			0
$652$	−75.0699	+	226.076i	−0.115138	+	0.346742i
$653$	−552.915			−0.846730			−0.423365	−	0.905959i	$-0.639151\pi$
$653$	−552.915			−0.846730			−0.423365	+	0.905959i	$0.639151\pi$
$654$		0			0
$655$			360.361i			0.550169i
$656$	544.109	+	406.130i	0.829435	+	0.619100i
$657$		0			0
$658$	41.5433	+	6.71703i	0.0631357	+	0.0102082i
$659$		−	847.738i		−	1.28640i	−0.765698	−	0.643200i	$-0.777606\pi$
$659$		−	847.738i		−	1.28640i	0.765698	−	0.643200i	$-0.222394\pi$
$660$		0			0
$661$	718.893			1.08758			0.543792	−	0.839220i	$-0.316988\pi$
$661$	718.893			1.08758			0.543792	+	0.839220i	$0.316988\pi$
$662$	136.529	−	844.401i	0.206237	−	1.27553i
$663$		0			0
$664$	−314.605	+	602.973i	−0.473803	+	0.908093i
$665$	443.444			0.666833
$666$		0			0
$667$			429.497i			0.643923i
$668$	−124.804	+	375.853i	−0.186833	+	0.562654i
$669$		0			0
$670$	38.3013	−	236.885i	0.0571662	−	0.353560i
$671$			720.409i			1.07364i
$672$		0			0
$673$	−576.975			−0.857318			−0.428659	−	0.903466i	$-0.641014\pi$
$673$	−576.975			−0.857318			−0.428659	+	0.903466i	$0.641014\pi$
$674$	−601.949	−	97.3277i	−0.893100	−	0.144403i
$675$		0			0
$676$	−640.223	−	212.590i	−0.947076	−	0.314482i
$677$	−202.042			−0.298437			−0.149219	−	0.988804i	$-0.547676\pi$
$677$	−202.042			−0.298437			−0.149219	+	0.988804i	$0.547676\pi$
$678$		0			0
$679$		−	83.2968i		−	0.122676i
$680$	170.814	+	89.1231i	0.251196	+	0.131063i
$681$		0			0
$682$	322.596	+	52.1597i	0.473014	+	0.0764805i
$683$			568.249i			0.831990i	0.909367	+	0.415995i	$0.136567\pi$
$683$			568.249i			0.831990i	−0.909367	+	0.415995i	$0.863433\pi$
$684$		0			0
$685$	122.362			0.178631
$686$	−135.067	+	835.355i	−0.196890	+	1.21772i
$687$		0			0
$688$	−356.271	+	477.311i	−0.517835	+	0.693766i
$689$	−12.4993			−0.0181412
$690$		0			0
$691$			405.734i			0.587170i	0.955933	+	0.293585i	$0.0948483\pi$
$691$			405.734i			0.587170i	−0.955933	+	0.293585i	$0.905152\pi$
$692$	146.506	+	48.6482i	0.211714	+	0.0703008i
$693$		0			0
$694$	−53.9673	+	333.775i	−0.0777627	+	0.480945i
$695$		−	409.456i		−	0.589146i
$696$		0			0
$697$	376.813			0.540621
$698$	−423.689	−	68.5053i	−0.607005	−	0.0981451i
$699$		0			0
$700$	−257.925	+	776.753i	−0.368465	+	1.10965i
$701$	−83.5164			−0.119139			−0.0595695	−	0.998224i	$-0.518973\pi$
$701$	−83.5164			−0.119139			−0.0595695	+	0.998224i	$0.518973\pi$
$702$		0			0
$703$		−	573.200i		−	0.815363i
$704$	518.152	−	361.372i	0.736012	−	0.513312i
$705$		0			0
$706$	−1089.43	−	176.148i	−1.54311	−	0.249501i
$707$			1287.33i			1.82083i
$708$		0			0
$709$	347.815			0.490572			0.245286	−	0.969451i	$-0.421118\pi$
$709$	347.815			0.490572			0.245286	+	0.969451i	$0.421118\pi$
$710$	−96.7955	+	598.657i	−0.136332	+	0.843180i
$711$		0			0
$712$	−459.493	−	239.743i	−0.645355	−	0.336718i
$713$	−349.320			−0.489930
$714$		0			0
$715$			15.8583i			0.0221795i
$716$	45.9172	−	138.281i	0.0641301	−	0.193130i
$717$		0			0
$718$	−177.117	+	1095.43i	−0.246682	+	1.52567i
$719$		−	536.277i		−	0.745865i	−0.927858	−	0.372933i	$-0.878352\pi$
$719$		−	536.277i		−	0.745865i	0.927858	−	0.372933i	$-0.121648\pi$
$720$		0			0
$721$	1066.08			1.47862
$722$	320.284	+	51.7859i	0.443606	+	0.0717256i
$723$		0			0
$724$	−70.5791	−	23.4362i	−0.0974849	−	0.0323704i
$725$	−359.106			−0.495319
$726$		0			0
$727$		−	941.145i		−	1.29456i	−0.762252	−	0.647280i	$-0.775906\pi$
$727$		−	941.145i		−	1.29456i	0.762252	−	0.647280i	$-0.224094\pi$
$728$	−25.4217	+	48.7233i	−0.0349199	+	0.0669277i
$729$		0			0
$730$	−408.038	−	65.9747i	−0.558956	−	0.0903763i
$731$			330.553i			0.452193i
$732$		0			0
$733$	−622.126			−0.848740			−0.424370	−	0.905489i	$-0.639504\pi$
$733$	−622.126			−0.848740			−0.424370	+	0.905489i	$0.639504\pi$
$734$	53.6857	−	332.033i	0.0731412	−	0.452362i
$735$		0			0
$736$	−485.125	+	469.747i	−0.659137	+	0.638244i
$737$	−436.655			−0.592477
$738$		0			0
$739$		−	444.439i		−	0.601406i	−0.953718	−	0.300703i	$-0.902779\pi$
$739$		−	444.439i		−	0.601406i	0.953718	−	0.300703i	$-0.0972213\pi$
$740$	−418.588	−	138.995i	−0.565660	−	0.187831i
$741$		0			0
$742$	78.1143	−	483.119i	0.105275	−	0.651104i
$743$			76.4724i			0.102924i	0.998675	+	0.0514619i	$0.0163881\pi$
$743$			76.4724i			0.102924i	−0.998675	+	0.0514619i	$0.983612\pi$
$744$		0			0
$745$	387.252			0.519801
$746$	−677.990	−	109.622i	−0.908833	−	0.146947i
$747$		0			0
$748$	110.484	−	332.728i	0.147706	−	0.444824i
$749$	−1249.45			−1.66816
$750$		0			0
$751$		−	1095.84i		−	1.45917i	−0.683888	−	0.729587i	$-0.739712\pi$
$751$		−	1095.84i		−	1.45917i	0.683888	−	0.729587i	$-0.260288\pi$
$752$	−17.3650	+	23.2646i	−0.0230917	+	0.0309370i
$753$		0			0
$754$	−23.8036	−	3.84875i	−0.0315698	−	0.00510444i
$755$		−	689.070i		−	0.912676i
$756$		0			0
$757$	−346.346			−0.457525			−0.228762	−	0.973482i	$-0.573468\pi$
$757$	−346.346			−0.457525			−0.228762	+	0.973482i	$0.573468\pi$
$758$	−192.301	+	1189.34i	−0.253696	+	1.56905i
$759$		0			0
$760$	−141.507	+	271.213i	−0.186193	+	0.356859i
$761$	−213.130			−0.280065			−0.140033	−	0.990147i	$-0.544721\pi$
$761$	−213.130			−0.280065			−0.140033	+	0.990147i	$0.544721\pi$
$762$		0			0
$763$		−	1003.77i		−	1.31556i
$764$	356.571	−	1073.83i	0.466715	−	1.40553i
$765$		0			0
$766$	−116.394	+	719.871i	−0.151951	+	0.939779i
$767$			52.4554i			0.0683903i
$768$		0			0
$769$	541.572			0.704254			0.352127	−	0.935952i	$-0.385458\pi$
$769$	541.572			0.704254			0.352127	+	0.935952i	$0.385458\pi$
$770$	−612.951	−	99.1065i	−0.796040	−	0.128710i
$771$		0			0
$772$	1150.56	+	382.052i	1.49037	+	0.494886i
$773$	−1255.73			−1.62449			−0.812245	−	0.583317i	$-0.801755\pi$
$773$	−1255.73			−1.62449			−0.812245	+	0.583317i	$0.801755\pi$
$774$		0			0
$775$		−	292.070i		−	0.376864i
$776$	50.9448	+	26.5808i	0.0656505	+	0.0342535i
$777$		0			0
$778$	423.798	+	68.5229i	0.544728	+	0.0880757i
$779$			598.292i			0.768026i
$780$		0			0
$781$	1103.52			1.41296
$782$	−59.8186	+	369.964i	−0.0764944	+	0.473100i
$783$		0			0
$784$	−1096.09	−	818.133i	−1.39807	−	1.04354i
$785$	−14.3941			−0.0183364
$786$		0			0
$787$			992.405i			1.26100i	0.776190	+	0.630499i	$0.217150\pi$
$787$			992.405i			1.26100i	−0.776190	+	0.630499i	$0.782850\pi$
$788$	−528.370	−	175.448i	−0.670520	−	0.222650i
$789$		0			0
$790$	−8.30224	+	51.3474i	−0.0105092	+	0.0649967i
$791$			54.5507i			0.0689643i
$792$		0			0
$793$	43.2342			0.0545198
$794$	−1351.70	−	218.553i	−1.70239	−	0.275256i
$795$		0			0
$796$	−14.1605	+	42.6451i	−0.0177896	+	0.0535742i
$797$	638.524			0.801159			0.400580	−	0.916262i	$-0.368809\pi$
$797$	638.524			0.801159			0.400580	+	0.916262i	$0.368809\pi$
$798$		0			0
$799$			16.1115i			0.0201646i
$800$	−392.760	−	405.617i	−0.490950	−	0.507022i
$801$		0			0
$802$	375.885	+	60.7760i	0.468685	+	0.0757805i
$803$			752.146i			0.936669i
$804$		0			0
$805$	663.729			0.824508
$806$	3.13028	−	19.3601i	0.00388372	−	0.0240199i
$807$		0			0
$808$	−787.335	−	410.797i	−0.974424	−	0.508412i
$809$	174.260			0.215401			0.107701	−	0.994183i	$-0.465651\pi$
$809$	174.260			0.215401			0.107701	+	0.994183i	$0.465651\pi$
$810$		0			0
$811$			1182.19i			1.45770i	0.684675	+	0.728849i	$0.259944\pi$
$811$			1182.19i			1.45770i	−0.684675	+	0.728849i	$0.740056\pi$
$812$	297.521	−	895.998i	0.366406	−	1.10345i
$813$		0			0
$814$	−128.106	+	792.306i	−0.157378	+	0.973349i
$815$			161.519i			0.198183i
$816$		0			0
$817$	−524.842			−0.642402
$818$	−746.222	−	120.655i	−0.912251	−	0.147500i
$819$		0			0
$820$	436.912	+	145.079i	0.532820	+	0.176926i
$821$	587.909			0.716089			0.358045	−	0.933705i	$-0.383444\pi$
$821$	587.909			0.716089			0.358045	+	0.933705i	$0.383444\pi$
$822$		0			0
$823$			113.247i			0.137603i	0.997630	+	0.0688015i	$0.0219175\pi$
$823$			113.247i			0.137603i	−0.997630	+	0.0688015i	$0.978082\pi$
$824$	−340.197	+	652.022i	−0.412860	+	0.791289i
$825$		0			0
$826$	−2027.49	−	327.820i	−2.45459	−	0.396876i
$827$			800.560i			0.968030i	0.875060	+	0.484015i	$0.160822\pi$
$827$			800.560i			0.968030i	−0.875060	+	0.484015i	$0.839178\pi$
$828$		0			0
$829$	1162.87			1.40274			0.701369	−	0.712798i	$-0.252573\pi$
$829$	1162.87			1.40274			0.701369	+	0.712798i	$0.252573\pi$
$830$	−73.6057	+	455.234i	−0.0886816	+	0.548475i
$831$		0			0
$832$	−21.6872	−	31.0961i	−0.0260663	−	0.0373751i
$833$	−759.075			−0.911255
$834$		0			0
$835$			268.527i			0.321589i
$836$	528.296	+	175.424i	0.631933	+	0.209837i
$837$		0			0
$838$	−98.5400	+	609.447i	−0.117590	+	0.727264i
$839$		−	1565.68i		−	1.86613i	−0.359707	−	0.933065i	$-0.617123\pi$
$839$		−	1565.68i		−	1.86613i	0.359707	−	0.933065i	$-0.382877\pi$
$840$		0			0
$841$	−426.765			−0.507450
$842$	−698.269	−	112.901i	−0.829298	−	0.134087i
$843$		0			0
$844$	163.046	−	491.020i	0.193182	−	0.581777i
$845$	−457.406			−0.541309
$846$		0			0
$847$		−	273.341i		−	0.322717i
$848$	270.551	+	201.943i	0.319046	+	0.238140i
$849$		0			0
$850$	−309.330	−	50.0149i	−0.363918	−	0.0588410i
$851$		−	857.943i		−	1.00816i
$852$		0			0
$853$	137.618			0.161334			0.0806668	−	0.996741i	$-0.474295\pi$
$853$	137.618			0.161334			0.0806668	+	0.996741i	$0.474295\pi$
$854$	−270.192	+	1671.08i	−0.316384	+	1.95676i
$855$		0			0
$856$	398.711	−	764.170i	0.465783	−	0.892722i
$857$	−768.979			−0.897291			−0.448646	−	0.893710i	$-0.648093\pi$
$857$	−768.979			−0.897291			−0.448646	+	0.893710i	$0.648093\pi$
$858$		0			0
$859$			205.945i			0.239749i	0.992789	+	0.119875i	$0.0382493\pi$
$859$			205.945i			0.239749i	−0.992789	+	0.119875i	$0.961751\pi$
$860$	−127.268	+	383.274i	−0.147987	+	0.445668i
$861$		0			0
$862$	150.924	−	933.430i	0.175086	−	1.08287i
$863$			772.757i			0.895431i	0.894176	+	0.447716i	$0.147762\pi$
$863$			772.757i			0.895431i	−0.894176	+	0.447716i	$0.852238\pi$
$864$		0			0
$865$	104.671			0.121007
$866$	121.263	+	19.6067i	0.140026	+	0.0226405i
$867$		0			0
$868$	728.737	+	241.981i	0.839558	+	0.278780i
$869$	94.6498			0.108918
$870$		0			0
$871$			26.2052i			0.0300863i
$872$	613.911	+	320.312i	0.704026	+	0.367330i
$873$		0			0
$874$	−587.418	−	94.9782i	−0.672103	−	0.108671i
$875$			1341.26i			1.53287i
$876$		0			0
$877$	400.193			0.456320			0.228160	−	0.973624i	$-0.426729\pi$
$877$	400.193			0.456320			0.228160	+	0.973624i	$0.426729\pi$
$878$	−130.617	+	807.838i	−0.148767	+	0.920089i
$879$		0			0
$880$	256.212	−	343.258i	0.291150	−	0.390066i
$881$	728.323			0.826700			0.413350	−	0.910572i	$-0.364359\pi$
$881$	728.323			0.826700			0.413350	+	0.910572i	$0.364359\pi$
$882$		0			0
$883$		−	383.413i		−	0.434216i	−0.976148	−	0.217108i	$-0.930338\pi$
$883$		−	383.413i		−	0.434216i	0.976148	−	0.217108i	$-0.0696625\pi$
$884$	−19.9682	−	6.63055i	−0.0225884	−	0.00750062i
$885$		0			0
$886$	246.531	−	1524.74i	0.278252	−	1.72093i
$887$		−	1450.20i		−	1.63495i	−0.575968	−	0.817473i	$-0.695375\pi$
$887$		−	1450.20i		−	1.63495i	0.575968	−	0.817473i	$-0.304625\pi$
$888$		0			0
$889$	97.0784			0.109200
$890$	−346.909	−	56.0909i	−0.389785	−	0.0630234i
$891$		0			0
$892$	−304.516	+	917.061i	−0.341385	+	1.02810i
$893$	−25.5813			−0.0286465
$894$		0			0
$895$		−	98.7949i		−	0.110385i
$896$	1337.45	−	643.910i	1.49269	−	0.718650i
$897$		0			0
$898$	1557.84	+	251.884i	1.73479	+	0.280494i
$899$			336.907i			0.374758i
$900$		0			0
$901$	187.365			0.207952
$902$	133.714	−	826.990i	0.148242	−	0.916840i
$903$		0			0
$904$	−33.3635	−	17.4076i	−0.0369065	−	0.0192562i
$905$	−50.4251			−0.0557183
$906$		0			0
$907$			615.790i			0.678931i	0.940619	+	0.339465i	$0.110246\pi$
$907$			615.790i			0.678931i	−0.940619	+	0.339465i	$0.889754\pi$
$908$	−481.366	+	1449.65i	−0.530139	+	1.59653i
$909$		0			0
$910$	−5.94772	+	36.7853i	−0.00653596	+	0.0404234i
$911$			262.153i			0.287764i	0.989595	+	0.143882i	$0.0459586\pi$
$911$			262.153i			0.287764i	−0.989595	+	0.143882i	$0.954041\pi$
$912$		0			0
$913$	839.143			0.919106
$914$	−545.576	−	88.2128i	−0.596910	−	0.0965129i
$915$		0			0
$916$	−566.878	−	188.235i	−0.618862	−	0.205497i
$917$	1540.83			1.68030
$918$		0			0
$919$			566.458i			0.616385i	0.951324	+	0.308193i	$0.0997241\pi$
$919$			566.458i			0.616385i	−0.951324	+	0.308193i	$0.900276\pi$
$920$	−211.802	+	405.940i	−0.230219	+	0.441239i
$921$		0			0
$922$	−1161.09	−	187.733i	−1.25931	−	0.203615i
$923$		−	66.2259i		−	0.0717507i
$924$		0			0
$925$	717.333			0.775495
$926$	249.657	−	1544.07i	0.269608	−	1.66746i
$927$		0			0
$928$	453.055	+	467.886i	0.488206	+	0.504188i
$929$	597.491			0.643155			0.321577	−	0.946883i	$-0.395787\pi$
$929$	597.491			0.643155			0.321577	+	0.946883i	$0.395787\pi$
$930$		0			0
$931$		−	1205.24i		−	1.29456i
$932$	831.114	+	275.976i	0.891754	+	0.296112i
$933$		0			0
$934$	211.714	−	1309.40i	0.226674	−	1.40193i
$935$		−	237.717i		−	0.254243i
$936$		0			0
$937$	457.785			0.488564			0.244282	−	0.969704i	$-0.421448\pi$
$937$	457.785			0.488564			0.244282	+	0.969704i	$0.421448\pi$
$938$	−1012.87	−	163.769i	−1.07982	−	0.174594i
$939$		0			0
$940$	−6.20319	+	18.6812i	−0.00659914	+	0.0198736i
$941$	−1355.72			−1.44072			−0.720360	−	0.693601i	$-0.756023\pi$
$941$	−1355.72			−1.44072			−0.720360	+	0.693601i	$0.756023\pi$
$942$		0			0
$943$			895.500i			0.949629i
$944$	847.486	−	1135.41i	0.897760	−	1.20277i
$945$		0			0
$946$	725.463	+	117.298i	0.766874	+	0.123994i
$947$		−	655.783i		−	0.692484i	−0.938145	−	0.346242i	$-0.887458\pi$
$947$		−	655.783i		−	0.692484i	0.938145	−	0.346242i	$-0.112542\pi$
$948$		0			0
$949$	45.1388			0.0475646
$950$	79.4121	−	491.145i	0.0835917	−	0.516995i
$951$		0			0
$952$	381.073	−	730.366i	0.400287	−	0.767191i
$953$	−554.778			−0.582139			−0.291069	−	0.956702i	$-0.594011\pi$
$953$	−554.778			−0.582139			−0.291069	+	0.956702i	$0.594011\pi$
$954$		0			0
$955$		−	767.193i		−	0.803344i
$956$	317.680	−	956.708i	0.332302	−	1.00074i
$957$		0			0
$958$	−207.168	+	1281.28i	−0.216250	+	1.33746i
$959$		−	523.197i		−	0.545566i
$960$		0			0
$961$	686.985			0.714865
$962$	47.5490	+	7.68808i	0.0494272	+	0.00799177i
$963$		0			0
$964$	1715.98	+	569.801i	1.78006	+	0.591080i
$965$	822.019			0.851833
$966$		0			0
$967$			579.659i			0.599441i	0.954027	+	0.299720i	$0.0968934\pi$
$967$			579.659i			0.599441i	−0.954027	+	0.299720i	$0.903107\pi$
$968$	167.177	+	87.2255i	0.172703	+	0.0901090i
$969$		0			0
$970$	38.4624	+	6.21889i	0.0396520	+	0.00641123i
$971$		−	260.660i		−	0.268445i	−0.990951	−	0.134223i	$-0.957146\pi$
$971$		−	260.660i		−	0.268445i	0.990951	−	0.134223i	$-0.0428537\pi$
$972$		0			0
$973$	−1750.76			−1.79934
$974$	90.0559	−	556.975i	0.0924598	−	0.571843i
$975$		0			0
$976$	−935.818	−	698.506i	−0.958830	−	0.715682i
$977$	1277.91			1.30799			0.653995	−	0.756499i	$-0.273092\pi$
$977$	1277.91			1.30799			0.653995	+	0.756499i	$0.273092\pi$
$978$		0			0
$979$			639.465i			0.653182i
$980$	−880.143	−	292.257i	−0.898105	−	0.298221i
$981$		0			0
$982$	240.680	−	1488.55i	0.245092	−	1.51584i
$983$			436.852i			0.444407i	0.975000	+	0.222204i	$0.0713250\pi$
$983$			436.852i			0.444407i	−0.975000	+	0.222204i	$0.928675\pi$
$984$		0			0
$985$	−377.493			−0.383241
$986$	356.818	+	57.6930i	0.361884	+	0.0585122i
$987$		0			0
$988$	10.5278	−	31.7049i	0.0106557	−	0.0320899i
$989$	−785.562			−0.794300
$990$		0			0
$991$		−	1344.50i		−	1.35671i	−0.734734	−	0.678356i	$-0.762693\pi$
$991$		−	1344.50i		−	1.35671i	0.734734	−	0.678356i	$-0.237307\pi$
$992$	−380.543	+	368.481i	−0.383612	+	0.371452i
$993$		0			0
$994$	2559.74	+	413.879i	2.57520	+	0.416377i
$995$			30.4677i			0.0306208i
$996$		0			0
$997$	−1884.79			−1.89047			−0.945233	−	0.326396i	$-0.894166\pi$
$997$	−1884.79			−1.89047			−0.945233	+	0.326396i	$0.894166\pi$
$998$	164.464	−	1017.17i	0.164794	−	1.01921i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	324.3.d.g.163.8		8
3.2	odd	2		324.3.d.i.163.1		8
4.3	odd	2	inner	324.3.d.g.163.7		8
9.2	odd	6		36.3.f.c.31.6	yes	16
9.4	even	3		108.3.f.c.19.2		16
9.5	odd	6		36.3.f.c.7.7	yes	16
9.7	even	3		108.3.f.c.91.3		16
12.11	even	2		324.3.d.i.163.2		8
36.7	odd	6		108.3.f.c.91.2		16
36.11	even	6		36.3.f.c.31.7	yes	16
36.23	even	6		36.3.f.c.7.6	✓	16
36.31	odd	6		108.3.f.c.19.3		16
72.5	odd	6		576.3.o.g.511.6		16
72.11	even	6		576.3.o.g.319.6		16
72.13	even	6		1728.3.o.g.127.6		16
72.29	odd	6		576.3.o.g.319.3		16
72.43	odd	6		1728.3.o.g.1279.6		16
72.59	even	6		576.3.o.g.511.3		16
72.61	even	6		1728.3.o.g.1279.5		16
72.67	odd	6		1728.3.o.g.127.5		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
36.3.f.c.7.6	✓	16	36.23	even	6
36.3.f.c.7.7	yes	16	9.5	odd	6
36.3.f.c.31.6	yes	16	9.2	odd	6
36.3.f.c.31.7	yes	16	36.11	even	6
108.3.f.c.19.2		16	9.4	even	3
108.3.f.c.19.3		16	36.31	odd	6
108.3.f.c.91.2		16	36.7	odd	6
108.3.f.c.91.3		16	9.7	even	3
324.3.d.g.163.7		8	4.3	odd	2	inner
324.3.d.g.163.8		8	1.1	even	1	trivial
324.3.d.i.163.1		8	3.2	odd	2
324.3.d.i.163.2		8	12.11	even	2
576.3.o.g.319.3		16	72.29	odd	6
576.3.o.g.319.6		16	72.11	even	6
576.3.o.g.511.3		16	72.59	even	6
576.3.o.g.511.6		16	72.5	odd	6
1728.3.o.g.127.5		16	72.67	odd	6
1728.3.o.g.127.6		16	72.13	even	6
1728.3.o.g.1279.5		16	72.61	even	6
1728.3.o.g.1279.6		16	72.43	odd	6

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:	\( N \)	\(=\)	\( 324 = 2^{2} \cdot 3^{4} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	324.d (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(1.97436 + 0.319229i) q^{2} +(3.79619 + 1.26055i) q^{4} +2.71218 q^{5} -11.5967i q^{7} +(7.09263 + 3.70062i) q^{8} +O(q^{10})\)	\(q+(1.97436 + 0.319229i) q^{2} +(3.79619 + 1.26055i) q^{4} +2.71218 q^{5} -11.5967i q^{7} +(7.09263 + 3.70062i) q^{8} +(5.35481 + 0.865806i) q^{10} -9.87064i q^{11} -0.592371 q^{13} +(3.70202 - 22.8961i) q^{14} +(12.8220 + 9.57053i) q^{16} +8.87968 q^{17} +14.0989i q^{19} +(10.2959 + 3.41882i) q^{20} +(3.15100 - 19.4882i) q^{22} +21.1026i q^{23} -17.6441 q^{25} +(-1.16955 - 0.189102i) q^{26} +(14.6182 - 44.0234i) q^{28} +20.3528 q^{29} +16.5534i q^{31} +(22.2601 + 22.9888i) q^{32} +(17.5317 + 2.83465i) q^{34} -31.4524i q^{35} -40.6557 q^{37} +(-4.50077 + 27.8363i) q^{38} +(19.2365 + 10.0367i) q^{40} +42.4355 q^{41} +37.2258i q^{43} +(12.4424 - 37.4708i) q^{44} +(-6.73658 + 41.6642i) q^{46} +1.81442i q^{47} -85.4845 q^{49} +(-34.8358 - 5.63251i) q^{50} +(-2.24875 - 0.746711i) q^{52} +21.1005 q^{53} -26.7709i q^{55} +(42.9152 - 82.2514i) q^{56} +(40.1836 + 6.49719i) q^{58} -88.5516i q^{59} -72.9851 q^{61} +(-5.28433 + 32.6823i) q^{62} +(36.6108 + 52.4943i) q^{64} -1.60661 q^{65} -44.2378i q^{67} +(33.7089 + 11.1932i) q^{68} +(10.0405 - 62.0984i) q^{70} +111.798i q^{71} -76.2003 q^{73} +(-80.2690 - 12.9785i) q^{74} +(-17.7723 + 53.5220i) q^{76} -114.467 q^{77} +9.58903i q^{79} +(34.7757 + 25.9570i) q^{80} +(83.7828 + 13.5466i) q^{82} +85.0141i q^{83} +24.0833 q^{85} +(-11.8836 + 73.4971i) q^{86} +(36.5275 - 70.0088i) q^{88} -64.7845 q^{89} +6.86958i q^{91} +(-26.6008 + 80.1095i) q^{92} +(-0.579216 + 3.58232i) q^{94} +38.2387i q^{95} +7.18278 q^{97} +(-168.777 - 27.2892i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 3 q^{2} + 5 q^{4} + 6 q^{5} + 27 q^{8}+O(q^{10}) \) 8 * q - 3 * q^2 + 5 * q^4 + 6 * q^5 + 27 * q^8	\( 8 q - 3 q^{2} + 5 q^{4} + 6 q^{5} + 27 q^{8} + 10 q^{10} + 46 q^{13} - 12 q^{14} + 17 q^{16} - 6 q^{17} + 36 q^{20} - 33 q^{22} + 30 q^{25} - 36 q^{26} + 6 q^{28} + 42 q^{29} + 87 q^{32} - 11 q^{34} + 28 q^{37} - 99 q^{38} - 68 q^{40} + 84 q^{41} + 111 q^{44} - 132 q^{46} - 58 q^{49} - 219 q^{50} - 110 q^{52} + 36 q^{53} + 270 q^{56} + 16 q^{58} + 34 q^{61} - 258 q^{62} - 127 q^{64} - 30 q^{65} + 375 q^{68} - 150 q^{70} + 58 q^{73} - 372 q^{74} + 15 q^{76} - 330 q^{77} + 360 q^{80} + 127 q^{82} + 140 q^{85} - 273 q^{86} - 75 q^{88} + 192 q^{89} + 258 q^{92} - 36 q^{94} + 148 q^{97} - 585 q^{98}+O(q^{100}) \) 8 * q - 3 * q^2 + 5 * q^4 + 6 * q^5 + 27 * q^8 + 10 * q^10 + 46 * q^13 - 12 * q^14 + 17 * q^16 - 6 * q^17 + 36 * q^20 - 33 * q^22 + 30 * q^25 - 36 * q^26 + 6 * q^28 + 42 * q^29 + 87 * q^32 - 11 * q^34 + 28 * q^37 - 99 * q^38 - 68 * q^40 + 84 * q^41 + 111 * q^44 - 132 * q^46 - 58 * q^49 - 219 * q^50 - 110 * q^52 + 36 * q^53 + 270 * q^56 + 16 * q^58 + 34 * q^61 - 258 * q^62 - 127 * q^64 - 30 * q^65 + 375 * q^68 - 150 * q^70 + 58 * q^73 - 372 * q^74 + 15 * q^76 - 330 * q^77 + 360 * q^80 + 127 * q^82 + 140 * q^85 - 273 * q^86 - 75 * q^88 + 192 * q^89 + 258 * q^92 - 36 * q^94 + 148 * q^97 - 585 * q^98

Introduction

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