LMFDB - Embedded newform 324.3.d.i.163.5

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			163.5
Root			$1.40960 + 1.41881i$ of defining polynomial
Character	$\chi$	$=$	324.163
Dual form			324.3.d.i.163.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.40960 - 1.41881i) q^{2} +(-0.0260491 - 3.99992i) q^{4} +8.06209 q^{5} -4.50627i q^{7} +(-5.71184 - 5.60133i) q^{8} +O(q^{10})$	\(q+(1.40960 - 1.41881i) q^{2} +(-0.0260491 - 3.99992i) q^{4} +8.06209 q^{5} -4.50627i q^{7} +(-5.71184 - 5.60133i) q^{8} +(11.3643 - 11.4386i) q^{10} +3.76250i q^{11} +7.05210 q^{13} +(-6.39354 - 6.35204i) q^{14} +(-15.9986 + 0.208388i) q^{16} +0.517890 q^{17} +16.4164i q^{19} +(-0.210010 - 32.2477i) q^{20} +(5.33828 + 5.30363i) q^{22} -31.9909i q^{23} +39.9973 q^{25} +(9.94065 - 10.0056i) q^{26} +(-18.0247 + 0.117384i) q^{28} -18.9679 q^{29} +15.1675i q^{31} +(-22.2560 + 22.9928i) q^{32} +(0.730018 - 0.734788i) q^{34} -36.3299i q^{35} +0.592061 q^{37} +(23.2918 + 23.1406i) q^{38} +(-46.0494 - 45.1584i) q^{40} -24.7532 q^{41} +32.1799i q^{43} +(15.0497 - 0.0980099i) q^{44} +(-45.3890 - 45.0944i) q^{46} -60.5850i q^{47} +28.6935 q^{49} +(56.3802 - 56.7486i) q^{50} +(-0.183701 - 28.2078i) q^{52} -0.664765 q^{53} +30.3336i q^{55} +(-25.2411 + 25.7391i) q^{56} +(-26.7372 + 26.9118i) q^{58} +35.3247i q^{59} -67.5500 q^{61} +(21.5199 + 21.3802i) q^{62} +(1.25029 + 63.9878i) q^{64} +56.8546 q^{65} +85.9897i q^{67} +(-0.0134906 - 2.07152i) q^{68} +(-51.5453 - 51.2107i) q^{70} +56.4434i q^{71} +131.921 q^{73} +(0.834571 - 0.840023i) q^{74} +(65.6644 - 0.427634i) q^{76} +16.9549 q^{77} +146.496i q^{79} +(-128.982 + 1.68005i) q^{80} +(-34.8921 + 35.1201i) q^{82} +100.578i q^{83} +4.17528 q^{85} +(45.6572 + 45.3608i) q^{86} +(21.0750 - 21.4908i) q^{88} -25.8362 q^{89} -31.7786i q^{91} +(-127.961 + 0.833334i) q^{92} +(-85.9587 - 85.4007i) q^{94} +132.351i q^{95} +96.5067 q^{97} +(40.4465 - 40.7107i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	1.40960	−	1.41881i	0.704801	−	0.709405i
$2$	1.40960	−	1.41881i	0.704801	−	0.709405i
$3$		0			0
$3$		0			0
$4$	−0.0260491	−	3.99992i	−0.00651228	−	0.999979i
$5$	8.06209			1.61242			0.806209	−	0.591631i	$-0.201516\pi$
$5$	8.06209			1.61242			0.806209	+	0.591631i	$0.201516\pi$
$6$		0			0
$7$		−	4.50627i		−	0.643753i	−0.946782	−	0.321876i	$-0.895686\pi$
$7$		−	4.50627i		−	0.643753i	0.946782	−	0.321876i	$-0.104314\pi$
$8$	−5.71184	−	5.60133i	−0.713980	−	0.700166i
$9$		0			0
$10$	11.3643	−	11.4386i	1.13643	−	1.14386i
$11$			3.76250i			0.342046i	0.985267	+	0.171023i	$0.0547072\pi$
$11$			3.76250i			0.342046i	−0.985267	+	0.171023i	$0.945293\pi$
$12$		0			0
$13$	7.05210			0.542469			0.271235	−	0.962513i	$-0.412568\pi$
$13$	7.05210			0.542469			0.271235	+	0.962513i	$0.412568\pi$
$14$	−6.39354	−	6.35204i	−0.456682	−	0.453717i
$15$		0			0
$16$	−15.9986	+	0.208388i	−0.999915	+	0.0130243i
$17$	0.517890			0.0304641			0.0152321	−	0.999884i	$-0.495151\pi$
$17$	0.517890			0.0304641			0.0152321	+	0.999884i	$0.495151\pi$
$18$		0			0
$19$			16.4164i			0.864023i	0.901868	+	0.432012i	$0.142196\pi$
$19$			16.4164i			0.864023i	−0.901868	+	0.432012i	$0.857804\pi$
$20$	−0.210010	−	32.2477i	−0.0105005	−	1.61238i
$21$		0			0
$22$	5.33828	+	5.30363i	0.242649	+	0.241074i
$23$		−	31.9909i		−	1.39091i	−0.718571	−	0.695454i	$-0.755203\pi$
$23$		−	31.9909i		−	1.39091i	0.718571	−	0.695454i	$-0.244797\pi$
$24$		0			0
$25$	39.9973			1.59989
$26$	9.94065	−	10.0056i	0.382333	−	0.384831i
$27$		0			0
$28$	−18.0247	+	0.117384i	−0.643739	+	0.00419230i
$29$	−18.9679			−0.654065			−0.327032	−	0.945013i	$-0.606049\pi$
$29$	−18.9679			−0.654065			−0.327032	+	0.945013i	$0.606049\pi$
$30$		0			0
$31$			15.1675i			0.489275i	0.969615	+	0.244638i	$0.0786690\pi$
$31$			15.1675i			0.489275i	−0.969615	+	0.244638i	$0.921331\pi$
$32$	−22.2560	+	22.9928i	−0.695501	+	0.718525i
$33$		0			0
$34$	0.730018	−	0.734788i	0.0214711	−	0.0216114i
$35$		−	36.3299i		−	1.03800i
$36$		0			0
$37$	0.592061			0.0160017			0.00800083	−	0.999968i	$-0.497453\pi$
$37$	0.592061			0.0160017			0.00800083	+	0.999968i	$0.497453\pi$
$38$	23.2918	+	23.1406i	0.612943	+	0.608964i
$39$		0			0
$40$	−46.0494	−	45.1584i	−1.15123	−	1.12896i
$41$	−24.7532			−0.603736			−0.301868	−	0.953350i	$-0.597610\pi$
$41$	−24.7532			−0.603736			−0.301868	+	0.953350i	$0.597610\pi$
$42$		0			0
$43$			32.1799i			0.748370i	0.927354	+	0.374185i	$0.122077\pi$
$43$			32.1799i			0.748370i	−0.927354	+	0.374185i	$0.877923\pi$
$44$	15.0497	−	0.0980099i	0.342039	−	0.00222750i
$45$		0			0
$46$	−45.3890	−	45.0944i	−0.986718	−	0.980313i
$47$		−	60.5850i		−	1.28904i	−0.764586	−	0.644521i	$-0.777057\pi$
$47$		−	60.5850i		−	1.28904i	0.764586	−	0.644521i	$-0.222943\pi$
$48$		0			0
$49$	28.6935			0.585583
$50$	56.3802	−	56.7486i	1.12760	−	1.13497i
$51$		0			0
$52$	−0.183701	−	28.2078i	−0.00353271	−	0.542458i
$53$	−0.664765			−0.0125427			−0.00627137	−	0.999980i	$-0.501996\pi$
$53$	−0.664765			−0.0125427			−0.00627137	+	0.999980i	$0.501996\pi$
$54$		0			0
$55$			30.3336i			0.551521i
$56$	−25.2411	+	25.7391i	−0.450734	+	0.459627i
$57$		0			0
$58$	−26.7372	+	26.9118i	−0.460985	+	0.463997i
$59$			35.3247i			0.598723i	0.954140	+	0.299362i	$0.0967737\pi$
$59$			35.3247i			0.598723i	−0.954140	+	0.299362i	$0.903226\pi$
$60$		0			0
$61$	−67.5500			−1.10738			−0.553688	−	0.832724i	$-0.686780\pi$
$61$	−67.5500			−1.10738			−0.553688	+	0.832724i	$0.686780\pi$
$62$	21.5199	+	21.3802i	0.347095	+	0.344842i
$63$		0			0
$64$	1.25029	+	63.9878i	0.0195357	+	0.999809i
$65$	56.8546			0.874687
$66$		0			0
$67$			85.9897i			1.28343i	0.766944	+	0.641714i	$0.221776\pi$
$67$			85.9897i			1.28343i	−0.766944	+	0.641714i	$0.778224\pi$
$68$	−0.0134906	−	2.07152i	−0.000198391	−	0.0304635i
$69$		0			0
$70$	−51.5453	−	51.2107i	−0.736362	−	0.731582i
$71$			56.4434i			0.794977i	0.917607	+	0.397489i	$0.130118\pi$
$71$			56.4434i			0.794977i	−0.917607	+	0.397489i	$0.869882\pi$
$72$		0			0
$73$	131.921			1.80713			0.903567	−	0.428447i	$-0.140939\pi$
$73$	131.921			1.80713			0.903567	+	0.428447i	$0.140939\pi$
$74$	0.834571	−	0.840023i	0.0112780	−	0.0113517i
$75$		0			0
$76$	65.6644	−	0.427634i	0.864005	−	0.00562676i
$77$	16.9549			0.220193
$78$		0			0
$79$			146.496i			1.85438i	0.374589	+	0.927191i	$0.377784\pi$
$79$			146.496i			1.85438i	−0.374589	+	0.927191i	$0.622216\pi$
$80$	−128.982	+	1.68005i	−1.61228	+	0.0210006i
$81$		0			0
$82$	−34.8921	+	35.1201i	−0.425513	+	0.428293i
$83$			100.578i			1.21178i	0.795548	+	0.605890i	$0.207183\pi$
$83$			100.578i			1.21178i	−0.795548	+	0.605890i	$0.792817\pi$
$84$		0			0
$85$	4.17528			0.0491209
$86$	45.6572	+	45.3608i	0.530898	+	0.527451i
$87$		0			0
$88$	21.0750	−	21.4908i	0.239489	−	0.244214i
$89$	−25.8362			−0.290295			−0.145147	−	0.989410i	$-0.546366\pi$
$89$	−25.8362			−0.290295			−0.145147	+	0.989410i	$0.546366\pi$
$90$		0			0
$91$		−	31.7786i		−	0.349216i
$92$	−127.961	+	0.833334i	−1.39088	+	0.00905798i
$93$		0			0
$94$	−85.9587	−	85.4007i	−0.914454	−	0.908518i
$95$			132.351i			1.39317i
$96$		0			0
$97$	96.5067			0.994915			0.497457	−	0.867488i	$-0.334267\pi$
$97$	96.5067			0.994915			0.497457	+	0.867488i	$0.334267\pi$
$98$	40.4465	−	40.7107i	0.412719	−	0.415415i
$99$		0			0
$100$	−1.04189	−	159.986i	−0.0104189	−	1.59986i
$101$	43.3201			0.428911			0.214456	−	0.976734i	$-0.431202\pi$
$101$	43.3201			0.428911			0.214456	+	0.976734i	$0.431202\pi$
$102$		0			0
$103$		−	144.845i		−	1.40626i	−0.711062	−	0.703129i	$-0.751786\pi$
$103$		−	144.845i		−	1.40626i	0.711062	−	0.703129i	$-0.248214\pi$
$104$	−40.2805	−	39.5011i	−0.387312	−	0.379818i
$105$		0			0
$106$	−0.937054	+	0.943177i	−0.00884013	+	0.00889789i
$107$			54.9861i			0.513889i	0.966426	+	0.256944i	$0.0827158\pi$
$107$			54.9861i			0.513889i	−0.966426	+	0.256944i	$0.917284\pi$
$108$		0			0
$109$	−63.9235			−0.586454			−0.293227	−	0.956043i	$-0.594729\pi$
$109$	−63.9235			−0.586454			−0.293227	+	0.956043i	$0.594729\pi$
$110$	43.0377	+	42.7583i	0.391252	+	0.388712i
$111$		0			0
$112$	0.939054	+	72.0942i	0.00838442	+	0.643698i
$113$	−35.6479			−0.315468			−0.157734	−	0.987482i	$-0.550419\pi$
$113$	−35.6479			−0.315468			−0.157734	+	0.987482i	$0.550419\pi$
$114$		0			0
$115$		−	257.913i		−	2.24273i
$116$	0.494097	+	75.8699i	0.00425945	+	0.654051i
$117$		0			0
$118$	50.1190	+	49.7937i	0.424738	+	0.421981i
$119$		−	2.33375i		−	0.0196114i
$120$		0			0
$121$	106.844			0.883005
$122$	−95.2185	+	95.8406i	−0.780479	+	0.785579i
$123$		0			0
$124$	60.6689	−	0.395101i	0.489265	−	0.00318630i
$125$	120.909			0.967276
$126$		0			0
$127$		−	9.81219i		−	0.0772613i	−0.999254	−	0.0386307i	$-0.987700\pi$
$127$		−	9.81219i		−	0.0772613i	0.999254	−	0.0386307i	$-0.0122996\pi$
$128$	92.5490	+	88.4233i	0.723039	+	0.690807i
$129$		0			0
$130$	80.1424	−	80.6660i	0.616480	−	0.620508i
$131$		−	117.273i		−	0.895214i	−0.894230	−	0.447607i	$-0.852276\pi$
$131$		−	117.273i		−	0.895214i	0.894230	−	0.447607i	$-0.147724\pi$
$132$		0			0
$133$	73.9769			0.556217
$134$	122.003	+	121.211i	0.910471	+	0.904561i
$135$		0			0
$136$	−2.95811	−	2.90087i	−0.0217508	−	0.0213299i
$137$	−251.212			−1.83366			−0.916831	−	0.399274i	$-0.869262\pi$
$137$	−251.212			−1.83366			−0.916831	+	0.399274i	$0.869262\pi$
$138$		0			0
$139$			153.660i			1.10546i	0.833359	+	0.552732i	$0.186415\pi$
$139$			153.660i			1.10546i	−0.833359	+	0.552732i	$0.813585\pi$
$140$	−145.317	+	0.946363i	−1.03798	+	0.00675973i
$141$		0			0
$142$	80.0825	+	79.5627i	0.563961	+	0.560300i
$143$			26.5335i			0.185549i
$144$		0			0
$145$	−152.921			−1.05463
$146$	185.956	−	187.171i	1.27367	−	1.28199i
$147$		0			0
$148$	−0.0154227	−	2.36820i	−0.000104207	−	0.0160013i
$149$	91.7286			0.615629			0.307814	−	0.951446i	$-0.400402\pi$
$149$	91.7286			0.615629			0.307814	+	0.951446i	$0.400402\pi$
$150$		0			0
$151$			41.5941i			0.275457i	0.990470	+	0.137729i	$0.0439802\pi$
$151$			41.5941i			0.275457i	−0.990470	+	0.137729i	$0.956020\pi$
$152$	91.9538	−	93.7681i	0.604959	−	0.616895i
$153$		0			0
$154$	23.8996	−	24.0557i	0.155192	−	0.156206i
$155$			122.282i			0.788916i
$156$		0			0
$157$	−225.819			−1.43833			−0.719167	−	0.694837i	$-0.755477\pi$
$157$	−225.819			−1.43833			−0.719167	+	0.694837i	$0.755477\pi$
$158$	207.850	+	206.501i	1.31551	+	1.30697i
$159$		0			0
$160$	−179.430	+	185.370i	−1.12144	+	1.15856i
$161$	−144.160			−0.895401
$162$		0			0
$163$			125.175i			0.767945i	0.923344	+	0.383973i	$0.125444\pi$
$163$			125.175i			0.767945i	−0.923344	+	0.383973i	$0.874556\pi$
$164$	0.644798	+	99.0106i	0.00393170	+	0.603723i
$165$		0			0
$166$	142.701	+	141.775i	0.859644	+	0.854064i
$167$		−	178.255i		−	1.06739i	−0.845676	−	0.533697i	$-0.820802\pi$
$167$		−	178.255i		−	1.06739i	0.845676	−	0.533697i	$-0.179198\pi$
$168$		0			0
$169$	−119.268			−0.705727
$170$	5.88547	−	5.92393i	0.0346204	−	0.0348466i
$171$		0			0
$172$	128.717	−	0.838258i	0.748354	−	0.00487359i
$173$	151.181			0.873878			0.436939	−	0.899491i	$-0.356063\pi$
$173$	151.181			0.873878			0.436939	+	0.899491i	$0.356063\pi$
$174$		0			0
$175$		−	180.239i		−	1.02993i
$176$	−0.784062	−	60.1950i	−0.00445490	−	0.342017i
$177$		0			0
$178$	−36.4188	+	36.6567i	−0.204600	+	0.205937i
$179$		−	276.827i		−	1.54652i	−0.634088	−	0.773261i	$-0.718624\pi$
$179$		−	276.827i		−	1.54652i	0.634088	−	0.773261i	$-0.281376\pi$
$180$		0			0
$181$	−104.729			−0.578612			−0.289306	−	0.957237i	$-0.593425\pi$
$181$	−104.729			−0.578612			−0.289306	+	0.957237i	$0.593425\pi$
$182$	−45.0879	−	44.7952i	−0.247736	−	0.246128i
$183$		0			0
$184$	−179.191	+	182.727i	−0.973866	+	0.993081i
$185$	4.77325			0.0258014
$186$		0			0
$187$			1.94856i			0.0104201i
$188$	−242.335	+	1.57819i	−1.28902	+	0.00839461i
$189$		0			0
$190$	187.781	+	186.562i	0.988320	+	0.981904i
$191$		−	222.825i		−	1.16662i	−0.812248	−	0.583312i	$-0.801757\pi$
$191$		−	222.825i		−	1.16662i	0.812248	−	0.583312i	$-0.198243\pi$
$192$		0			0
$193$	−113.358			−0.587347			−0.293674	−	0.955906i	$-0.594878\pi$
$193$	−113.358			−0.587347			−0.293674	+	0.955906i	$0.594878\pi$
$194$	136.036	−	136.925i	0.701216	−	0.705798i
$195$		0			0
$196$	−0.747441	−	114.772i	−0.00381348	−	0.585570i
$197$	−120.998			−0.614201			−0.307100	−	0.951677i	$-0.599359\pi$
$197$	−120.998			−0.614201			−0.307100	+	0.951677i	$0.599359\pi$
$198$		0			0
$199$		−	82.2364i		−	0.413248i	−0.978420	−	0.206624i	$-0.933752\pi$
$199$		−	82.2364i		−	0.413248i	0.978420	−	0.206624i	$-0.0662477\pi$
$200$	−228.458	−	224.038i	−1.14229	−	1.12019i
$201$		0			0
$202$	61.0640	−	61.4630i	0.302297	−	0.304272i
$203$			85.4744i			0.421056i
$204$		0			0
$205$	−199.562			−0.973474
$206$	−205.507	−	204.173i	−0.997607	−	0.991132i
$207$		0			0
$208$	−112.824	+	1.46958i	−0.542423	+	0.00706527i
$209$	−61.7669			−0.295535
$210$		0			0
$211$		−	108.059i		−	0.512128i	−0.966660	−	0.256064i	$-0.917574\pi$
$211$		−	108.059i		−	0.512128i	0.966660	−	0.256064i	$-0.0824259\pi$
$212$	0.0173166	+	2.65901i	8.16818e−5	+	0.0125425i
$213$		0			0
$214$	78.0149	+	77.5085i	0.364556	+	0.362189i
$215$			259.437i			1.20668i
$216$		0			0
$217$	68.3490			0.314972
$218$	−90.1066	+	90.6954i	−0.413333	+	0.416034i
$219$		0			0
$220$	121.332	−	0.790164i	0.551509	−	0.00359166i
$221$	3.65221			0.0165258
$222$		0			0
$223$		−	163.274i		−	0.732172i	−0.930581	−	0.366086i	$-0.880698\pi$
$223$		−	163.274i		−	0.732172i	0.930581	−	0.366086i	$-0.119302\pi$
$224$	103.612	+	100.292i	0.462552	+	0.447731i
$225$		0			0
$226$	−50.2493	+	50.5776i	−0.222342	+	0.223795i
$227$			11.0473i			0.0486664i	0.999704	+	0.0243332i	$0.00774626\pi$
$227$			11.0473i			0.0486664i	−0.999704	+	0.0243332i	$0.992254\pi$
$228$		0			0
$229$	32.3450			0.141244			0.0706222	−	0.997503i	$-0.477502\pi$
$229$	32.3450			0.141244			0.0706222	+	0.997503i	$0.477502\pi$
$230$	−365.930	−	363.555i	−1.59100	−	1.58067i
$231$		0			0
$232$	108.342	+	106.245i	0.466990	+	0.457954i
$233$	181.049			0.777036			0.388518	−	0.921441i	$-0.372987\pi$
$233$	181.049			0.777036			0.388518	+	0.921441i	$0.372987\pi$
$234$		0			0
$235$		−	488.442i		−	2.07848i
$236$	141.296	−	0.920177i	0.598711	−	0.00389905i
$237$		0			0
$238$	−3.31115	−	3.28966i	−0.0139124	−	0.0138221i
$239$			45.7760i			0.191532i	0.995404	+	0.0957658i	$0.0305300\pi$
$239$			45.7760i			0.191532i	−0.995404	+	0.0957658i	$0.969470\pi$
$240$		0			0
$241$	−338.432			−1.40428			−0.702140	−	0.712039i	$-0.747772\pi$
$241$	−338.432			−1.40428			−0.702140	+	0.712039i	$0.747772\pi$
$242$	150.607	−	151.591i	0.622342	−	0.626408i
$243$		0			0
$244$	1.75962	+	270.194i	0.00721154	+	1.10735i
$245$	231.330			0.944204
$246$		0			0
$247$			115.770i			0.468706i
$248$	84.9583	−	86.6346i	0.342574	−	0.349333i
$249$		0			0
$250$	170.434	−	171.548i	0.681736	−	0.686191i
$251$		−	282.587i		−	1.12585i	−0.826510	−	0.562923i	$-0.809677\pi$
$251$		−	282.587i		−	1.12585i	0.826510	−	0.562923i	$-0.190323\pi$
$252$		0			0
$253$	120.366			0.475754
$254$	−13.9216	−	13.8313i	−0.0548096	−	0.0544538i
$255$		0			0
$256$	255.913	−	6.66787i	0.999661	−	0.0260464i
$257$	−77.7793			−0.302643			−0.151322	−	0.988485i	$-0.548353\pi$
$257$	−77.7793			−0.302643			−0.151322	+	0.988485i	$0.548353\pi$
$258$		0			0
$259$		−	2.66799i		−	0.0103011i
$260$	−1.48101	−	227.414i	−0.00569620	−	0.874668i
$261$		0			0
$262$	−166.388	−	165.308i	−0.635070	−	0.630947i
$263$		−	225.399i		−	0.857031i	−0.903534	−	0.428516i	$-0.859037\pi$
$263$		−	225.399i		−	0.857031i	0.903534	−	0.428516i	$-0.140963\pi$
$264$		0			0
$265$	−5.35940			−0.0202241
$266$	104.278	−	104.959i	0.392022	−	0.394583i
$267$		0			0
$268$	343.951	−	2.23995i	1.28340	−	0.00835804i
$269$	425.808			1.58293			0.791465	−	0.611214i	$-0.209319\pi$
$269$	425.808			1.58293			0.791465	+	0.611214i	$0.209319\pi$
$270$		0			0
$271$			56.3665i			0.207995i	0.994578	+	0.103997i	$0.0331633\pi$
$271$			56.3665i			0.207995i	−0.994578	+	0.103997i	$0.966837\pi$
$272$	−8.28554	+	0.107922i	−0.0304615	+	0.000396773i
$273$		0			0
$274$	−354.108	+	356.422i	−1.29237	+	1.30081i
$275$			150.490i			0.547236i
$276$		0			0
$277$	419.282			1.51366			0.756828	−	0.653615i	$-0.226748\pi$
$277$	419.282			1.51366			0.756828	+	0.653615i	$0.226748\pi$
$278$	218.014	+	216.599i	0.784223	+	0.779132i
$279$		0			0
$280$	−203.496	+	207.511i	−0.726771	+	0.741110i
$281$	147.928			0.526433			0.263216	−	0.964737i	$-0.415217\pi$
$281$	147.928			0.526433			0.263216	+	0.964737i	$0.415217\pi$
$282$		0			0
$283$		−	265.410i		−	0.937845i	−0.883239	−	0.468923i	$-0.844642\pi$
$283$		−	265.410i		−	0.937845i	0.883239	−	0.468923i	$-0.155358\pi$
$284$	225.769	−	1.47030i	0.794960	−	0.00517711i
$285$		0			0
$286$	37.6461	+	37.4017i	0.131630	+	0.130775i
$287$			111.544i			0.388656i
$288$		0			0
$289$	−288.732			−0.999072
$290$	−215.557	+	216.966i	−0.743301	+	0.748158i
$291$		0			0
$292$	−3.43642	−	527.672i	−0.0117686	−	1.80710i
$293$	−249.688			−0.852176			−0.426088	−	0.904682i	$-0.640109\pi$
$293$	−249.688			−0.852176			−0.426088	+	0.904682i	$0.640109\pi$
$294$		0			0
$295$			284.791i			0.965392i
$296$	−3.38176	−	3.31633i	−0.0114249	−	0.0112038i
$297$		0			0
$298$	129.301	−	130.146i	0.433895	−	0.436730i
$299$		−	225.603i		−	0.754525i
$300$		0			0
$301$	145.011			0.481765
$302$	59.0141	+	58.6310i	0.195411	+	0.194142i
$303$		0			0
$304$	−3.42100	−	262.641i	−0.0112533	−	0.863950i
$305$	−544.594			−1.78555
$306$		0			0
$307$			259.968i			0.846801i	0.905943	+	0.423401i	$0.139164\pi$
$307$			259.968i			0.846801i	−0.905943	+	0.423401i	$0.860836\pi$
$308$	−0.441659	−	67.8180i	−0.00143396	−	0.220188i
$309$		0			0
$310$	173.495	+	172.369i	0.559662	+	0.556029i
$311$			19.1633i			0.0616182i	0.999525	+	0.0308091i	$0.00980840\pi$
$311$			19.1633i			0.0616182i	−0.999525	+	0.0308091i	$0.990192\pi$
$312$		0			0
$313$	43.8715			0.140165			0.0700823	−	0.997541i	$-0.477674\pi$
$313$	43.8715			0.140165			0.0700823	+	0.997541i	$0.477674\pi$
$314$	−318.314	+	320.394i	−1.01374	+	1.02036i
$315$		0			0
$316$	585.972	−	3.81610i	1.85434	−	0.0120763i
$317$	−137.938			−0.435135			−0.217568	−	0.976045i	$-0.569812\pi$
$317$	−137.938			−0.435135			−0.217568	+	0.976045i	$0.569812\pi$
$318$		0			0
$319$		−	71.3667i		−	0.223720i
$320$	10.0799	+	515.875i	0.0314998	+	1.61211i
$321$		0			0
$322$	−203.207	+	204.535i	−0.631079	+	0.635202i
$323$			8.50191i			0.0263217i
$324$		0			0
$325$	282.065			0.867892
$326$	177.600	+	176.447i	0.544785	+	0.541248i
$327$		0			0
$328$	141.386	+	138.651i	0.431055	+	0.422715i
$329$	−273.012			−0.829825
$330$		0			0
$331$		−	59.7546i		−	0.180528i	−0.995918	−	0.0902638i	$-0.971229\pi$
$331$		−	59.7546i		−	0.180528i	0.995918	−	0.0902638i	$-0.0287710\pi$
$332$	402.303	−	2.61996i	1.21176	−	0.00789145i
$333$		0			0
$334$	−252.910	−	251.268i	−0.757215	−	0.752300i
$335$			693.256i			2.06942i
$336$		0			0
$337$	−448.711			−1.33149			−0.665743	−	0.746181i	$-0.731885\pi$
$337$	−448.711			−1.33149			−0.665743	+	0.746181i	$0.731885\pi$
$338$	−168.120	+	169.219i	−0.497397	+	0.500647i
$339$		0			0
$340$	−0.108762	−	16.7007i	−0.000319889	−	0.0491198i
$341$	−57.0679			−0.167355
$342$		0			0
$343$		−	350.108i		−	1.02072i
$344$	180.250	−	183.807i	0.523983	−	0.534321i
$345$		0			0
$346$	213.105	−	214.497i	0.615909	−	0.619934i
$347$		−	577.860i		−	1.66530i	−0.553798	−	0.832651i	$-0.686822\pi$
$347$		−	577.860i		−	1.66530i	0.553798	−	0.832651i	$-0.313178\pi$
$348$		0			0
$349$	−132.262			−0.378975			−0.189487	−	0.981883i	$-0.560683\pi$
$349$	−132.262			−0.378975			−0.189487	+	0.981883i	$0.560683\pi$
$350$	−255.724	−	254.064i	−0.730641	−	0.725898i
$351$		0			0
$352$	−86.5105	−	83.7384i	−0.245768	−	0.237893i
$353$	−541.125			−1.53293			−0.766465	−	0.642286i	$-0.777986\pi$
$353$	−541.125			−1.53293			−0.766465	+	0.642286i	$0.777986\pi$
$354$		0			0
$355$			455.052i			1.28184i
$356$	0.673011	+	103.343i	0.00189048	+	0.290289i
$357$		0			0
$358$	−392.766	−	390.216i	−1.09711	−	1.08999i
$359$		−	292.754i		−	0.815470i	−0.913100	−	0.407735i	$-0.866319\pi$
$359$		−	292.754i		−	0.815470i	0.913100	−	0.407735i	$-0.133681\pi$
$360$		0			0
$361$	91.5006			0.253464
$362$	−147.626	+	148.590i	−0.407806	+	0.410471i
$363$		0			0
$364$	−127.112	+	0.827806i	−0.349209	+	0.00227419i
$365$	1063.56			2.91386
$366$		0			0
$367$		−	437.482i		−	1.19205i	−0.802966	−	0.596024i	$-0.796746\pi$
$367$		−	437.482i		−	1.19205i	0.802966	−	0.596024i	$-0.203254\pi$
$368$	6.66653	+	511.811i	0.0181156	+	1.39079i
$369$		0			0
$370$	6.72838	−	6.77234i	0.0181848	−	0.0183036i
$371$			2.99561i			0.00807443i
$372$		0			0
$373$	705.957			1.89265			0.946323	−	0.323222i	$-0.104766\pi$
$373$	705.957			1.89265			0.946323	+	0.323222i	$0.104766\pi$
$374$	2.76464	+	2.74670i	0.00739209	+	0.00734411i
$375$		0			0
$376$	−339.356	+	346.052i	−0.902544	+	0.920351i
$377$	−133.763			−0.354810
$378$		0			0
$379$			541.432i			1.42858i	0.699850	+	0.714290i	$0.253250\pi$
$379$			541.432i			1.42858i	−0.699850	+	0.714290i	$0.746750\pi$
$380$	529.392	−	3.44762i	1.39314	−	0.00907269i
$381$		0			0
$382$	−316.147	−	314.095i	−0.827609	−	0.822237i
$383$			360.198i			0.940466i	0.882542	+	0.470233i	$0.155830\pi$
$383$			360.198i			0.940466i	−0.882542	+	0.470233i	$0.844170\pi$
$384$		0			0
$385$	136.692			0.355043
$386$	−159.790	+	160.834i	−0.413963	+	0.416667i
$387$		0			0
$388$	−2.51391	−	386.019i	−0.00647916	−	0.994893i
$389$	87.8113			0.225736			0.112868	−	0.993610i	$-0.463996\pi$
$389$	87.8113			0.225736			0.112868	+	0.993610i	$0.463996\pi$
$390$		0			0
$391$		−	16.5678i		−	0.0423728i
$392$	−163.893	−	160.722i	−0.418094	−	0.410005i
$393$		0			0
$394$	−170.558	+	171.673i	−0.432889	+	0.435717i
$395$			1181.07i			2.99004i
$396$		0			0
$397$	−48.4128			−0.121947			−0.0609733	−	0.998139i	$-0.519420\pi$
$397$	−48.4128			−0.121947			−0.0609733	+	0.998139i	$0.519420\pi$
$398$	−116.678	−	115.920i	−0.293160	−	0.291257i
$399$		0			0
$400$	−639.902	+	8.33497i	−1.59976	+	0.0208374i
$401$	−435.718			−1.08658			−0.543290	−	0.839545i	$-0.682821\pi$
$401$	−435.718			−1.08658			−0.543290	+	0.839545i	$0.682821\pi$
$402$		0			0
$403$			106.963i			0.265417i
$404$	−1.12845	−	173.277i	−0.00279319	−	0.428902i
$405$		0			0
$406$	121.272	+	120.485i	0.298699	+	0.296761i
$407$			2.22763i			0.00547330i
$408$		0			0
$409$	54.2289			0.132589			0.0662945	−	0.997800i	$-0.478882\pi$
$409$	54.2289			0.132589			0.0662945	+	0.997800i	$0.478882\pi$
$410$	−281.303	+	283.141i	−0.686105	+	0.690588i
$411$		0			0
$412$	−579.366	+	3.77307i	−1.40623	+	0.00915794i
$413$	159.182			0.385430
$414$		0			0
$415$			810.867i			1.95390i
$416$	−156.952	+	162.147i	−0.377288	+	0.389778i
$417$		0			0
$418$	−87.0667	+	87.6356i	−0.208294	+	0.209654i
$419$			637.429i			1.52131i	0.649157	+	0.760655i	$0.275122\pi$
$419$			637.429i			1.52131i	−0.649157	+	0.760655i	$0.724878\pi$
$420$		0			0
$421$	191.551			0.454991			0.227496	−	0.973779i	$-0.426946\pi$
$421$	191.551			0.454991			0.227496	+	0.973779i	$0.426946\pi$
$422$	−153.315	−	152.320i	−0.363307	−	0.360948i
$423$		0			0
$424$	3.79704	+	3.72357i	0.00895527	+	0.00878200i
$425$	20.7142			0.0487393
$426$		0			0
$427$			304.398i			0.712876i
$428$	219.940	−	1.43234i	0.513878	−	0.00334659i
$429$		0			0
$430$	368.092	+	365.703i	0.856029	+	0.850472i
$431$		−	481.190i		−	1.11645i	−0.829689	−	0.558225i	$-0.811482\pi$
$431$		−	481.190i		−	1.11645i	0.829689	−	0.558225i	$-0.188518\pi$
$432$		0			0
$433$	−360.347			−0.832209			−0.416105	−	0.909317i	$-0.636605\pi$
$433$	−360.347			−0.832209			−0.416105	+	0.909317i	$0.636605\pi$
$434$	96.3448	−	96.9743i	0.221993	−	0.223443i
$435$		0			0
$436$	1.66515	+	255.689i	0.00381915	+	0.586442i
$437$	525.176			1.20178
$438$		0			0
$439$			563.803i			1.28429i	0.766584	+	0.642144i	$0.221955\pi$
$439$			563.803i			1.28429i	−0.766584	+	0.642144i	$0.778045\pi$
$440$	169.909	−	173.261i	0.386156	−	0.393775i
$441$		0			0
$442$	5.14816	−	5.18180i	0.0116474	−	0.0117235i
$443$			658.083i			1.48551i	0.669561	+	0.742757i	$0.266482\pi$
$443$			658.083i			1.48551i	−0.669561	+	0.742757i	$0.733518\pi$
$444$		0			0
$445$	−208.294			−0.468076
$446$	−231.655	−	230.152i	−0.519407	−	0.516035i
$447$		0			0
$448$	288.346	−	5.63413i	0.643630	−	0.0125762i
$449$	227.569			0.506836			0.253418	−	0.967357i	$-0.418445\pi$
$449$	227.569			0.506836			0.253418	+	0.967357i	$0.418445\pi$
$450$		0			0
$451$		−	93.1339i		−	0.206505i
$452$	0.928596	+	142.588i	0.00205441	+	0.315461i
$453$		0			0
$454$	15.6740	+	15.5723i	0.0345242	+	0.0343001i
$455$		−	256.202i		−	0.563082i
$456$		0			0
$457$	717.757			1.57058			0.785292	−	0.619125i	$-0.212513\pi$
$457$	717.757			1.57058			0.785292	+	0.619125i	$0.212513\pi$
$458$	45.5935	−	45.8914i	0.0995492	−	0.100200i
$459$		0			0
$460$	−1031.63	+	6.71842i	−2.24268	+	0.0146053i
$461$	401.746			0.871466			0.435733	−	0.900076i	$-0.356489\pi$
$461$	401.746			0.871466			0.435733	+	0.900076i	$0.356489\pi$
$462$		0			0
$463$			458.132i			0.989486i	0.869039	+	0.494743i	$0.164738\pi$
$463$			458.132i			0.989486i	−0.869039	+	0.494743i	$0.835262\pi$
$464$	303.460	−	3.95269i	0.654009	−	0.00851873i
$465$		0			0
$466$	255.207	−	256.875i	0.547656	−	0.551234i
$467$		−	204.395i		−	0.437677i	−0.975761	−	0.218838i	$-0.929773\pi$
$467$		−	204.395i		−	0.437677i	0.975761	−	0.218838i	$-0.0702267\pi$
$468$		0			0
$469$	387.493			0.826210
$470$	−693.007	−	688.508i	−1.47448	−	1.46491i
$471$		0			0
$472$	197.865	−	201.769i	0.419206	−	0.427477i
$473$	−121.077			−0.255977
$474$		0			0
$475$			656.613i			1.38234i
$476$	−9.33481	+	0.0607922i	−0.0196109	+	0.000127715i
$477$		0			0
$478$	64.9475	+	64.5259i	0.135874	+	0.134992i
$479$			90.5918i			0.189127i	0.995519	+	0.0945634i	$0.0301455\pi$
$479$			90.5918i			0.189127i	−0.995519	+	0.0945634i	$0.969854\pi$
$480$		0			0
$481$	4.17528			0.00868041
$482$	−477.054	+	480.170i	−0.989738	+	0.996204i
$483$		0			0
$484$	−2.78318	−	427.365i	−0.00575037	−	0.882986i
$485$	778.046			1.60422
$486$		0			0
$487$		−	301.289i		−	0.618663i	−0.950954	−	0.309332i	$-0.899895\pi$
$487$		−	301.289i		−	0.618663i	0.950954	−	0.309332i	$-0.100105\pi$
$488$	385.835	+	378.369i	0.790645	+	0.775347i
$489$		0			0
$490$	326.083	−	328.213i	0.665475	−	0.669823i
$491$		−	449.821i		−	0.916133i	−0.888918	−	0.458066i	$-0.848542\pi$
$491$		−	449.821i		−	0.916133i	0.888918	−	0.458066i	$-0.151458\pi$
$492$		0			0
$493$	−9.82328			−0.0199255
$494$	164.256	+	163.190i	0.332502	+	0.330344i
$495$		0			0
$496$	−3.16074	−	242.660i	−0.00637246	−	0.489234i
$497$	254.349			0.511769
$498$		0			0
$499$		−	638.123i		−	1.27880i	−0.768873	−	0.639401i	$-0.779182\pi$
$499$		−	638.123i		−	1.27880i	0.768873	−	0.639401i	$-0.220818\pi$
$500$	−3.14958	−	483.628i	−0.00629917	−	0.967255i
$501$		0			0
$502$	−400.938	−	398.335i	−0.798681	−	0.793497i
$503$			182.179i			0.362185i	0.983466	+	0.181093i	$0.0579634\pi$
$503$			182.179i			0.362185i	−0.983466	+	0.181093i	$0.942037\pi$
$504$		0			0
$505$	349.250			0.691585
$506$	169.668	−	170.776i	0.335312	−	0.337503i
$507$		0			0
$508$	−39.2479	+	0.255599i	−0.0772597	+	0.000503147i
$509$	−942.246			−1.85117			−0.925585	−	0.378539i	$-0.876426\pi$
$509$	−942.246			−1.85117			−0.925585	+	0.378539i	$0.876426\pi$
$510$		0			0
$511$		−	594.470i		−	1.16335i
$512$	351.275	−	372.491i	0.686084	−	0.727522i
$513$		0			0
$514$	−109.638	+	110.354i	−0.213303	+	0.214697i
$515$		−	1167.75i		−	2.26748i
$516$		0			0
$517$	227.951			0.440912
$518$	−3.78537	−	3.76080i	−0.00730767	−	0.00726023i
$519$		0			0
$520$	−324.745	−	318.461i	−0.624509	−	0.612426i
$521$	−634.330			−1.21752			−0.608762	−	0.793353i	$-0.708334\pi$
$521$	−634.330			−1.21752			−0.608762	+	0.793353i	$0.708334\pi$
$522$		0			0
$523$		−	534.777i		−	1.02252i	−0.859426	−	0.511259i	$-0.829179\pi$
$523$		−	534.777i		−	1.02252i	0.859426	−	0.511259i	$-0.170821\pi$
$524$	−469.082	+	3.05486i	−0.895195	+	0.00582988i
$525$		0			0
$526$	−319.799	−	317.723i	−0.607983	−	0.604036i
$527$			7.85511i			0.0149053i
$528$		0			0
$529$	−494.417			−0.934626
$530$	−7.55461	+	7.60397i	−0.0142540	+	0.0143471i
$531$		0			0
$532$	−1.92703	−	295.901i	−0.00362224	−	0.556205i
$533$	−174.562			−0.327508
$534$		0			0
$535$			443.303i			0.828604i
$536$	481.656	−	491.159i	0.898612	−	0.916342i
$537$		0			0
$538$	600.220	−	604.142i	1.11565	−	1.12294i
$539$			107.960i			0.200296i
$540$		0			0
$541$	−61.0097			−0.112772			−0.0563860	−	0.998409i	$-0.517958\pi$
$541$	−61.0097			−0.112772			−0.0563860	+	0.998409i	$0.517958\pi$
$542$	79.9734	+	79.4543i	0.147552	+	0.146595i
$543$		0			0
$544$	−11.5262	+	11.9077i	−0.0211878	+	0.0218892i
$545$	−515.357			−0.945609
$546$		0			0
$547$			120.585i			0.220448i	0.993907	+	0.110224i	$0.0351568\pi$
$547$			120.585i			0.220448i	−0.993907	+	0.110224i	$0.964843\pi$
$548$	6.54385	+	1004.83i	0.0119413	+	1.83362i
$549$		0			0
$550$	213.517	+	212.131i	0.388212	+	0.385692i
$551$		−	311.385i		−	0.565127i
$552$		0			0
$553$	660.151			1.19376
$554$	591.021	−	594.883i	1.06683	−	1.07380i
$555$		0			0
$556$	614.625	−	4.00270i	1.10544	−	0.00719909i
$557$	−527.461			−0.946968			−0.473484	−	0.880802i	$-0.657004\pi$
$557$	−527.461			−0.946968			−0.473484	+	0.880802i	$0.657004\pi$
$558$		0			0
$559$			226.936i			0.405967i
$560$	7.57074	+	581.230i	0.0135192	+	1.03791i
$561$		0			0
$562$	208.519	−	209.881i	0.371030	−	0.373454i
$563$			687.599i			1.22131i	0.791896	+	0.610656i	$0.209094\pi$
$563$			687.599i			1.22131i	−0.791896	+	0.610656i	$0.790906\pi$
$564$		0			0
$565$	−287.396			−0.508666
$566$	−376.567	−	374.123i	−0.665313	−	0.660994i
$567$		0			0
$568$	316.158	−	322.396i	0.556616	−	0.567598i
$569$	−587.354			−1.03226			−0.516128	−	0.856511i	$-0.672627\pi$
$569$	−587.354			−1.03226			−0.516128	+	0.856511i	$0.672627\pi$
$570$		0			0
$571$		−	857.071i		−	1.50100i	−0.660871	−	0.750500i	$-0.729813\pi$
$571$		−	857.071i		−	1.50100i	0.660871	−	0.750500i	$-0.270187\pi$
$572$	106.132	−	0.691175i	0.185545	−	0.00120835i
$573$		0			0
$574$	158.260	+	157.233i	0.275715	+	0.273925i
$575$		−	1279.55i		−	2.22530i
$576$		0			0
$577$	871.732			1.51080			0.755401	−	0.655263i	$-0.227442\pi$
$577$	871.732			1.51080			0.755401	+	0.655263i	$0.227442\pi$
$578$	−406.997	+	409.656i	−0.704146	+	0.708747i
$579$		0			0
$580$	3.98345	+	611.670i	0.00686802	+	1.05460i
$581$	453.231			0.780087
$582$		0			0
$583$		−	2.50118i		−	0.00429019i
$584$	−753.511	−	738.931i	−1.29026	−	1.26529i
$585$		0			0
$586$	−351.960	+	354.259i	−0.600614	+	0.604538i
$587$		−	808.373i		−	1.37713i	−0.725177	−	0.688563i	$-0.758242\pi$
$587$		−	808.373i		−	1.37713i	0.725177	−	0.688563i	$-0.241758\pi$
$588$		0			0
$589$	−248.997			−0.422745
$590$	404.064	+	401.441i	0.684855	+	0.680409i
$591$		0			0
$592$	−9.47218	+	0.123379i	−0.0160003	+	0.000208410i
$593$	−445.123			−0.750628			−0.375314	−	0.926898i	$-0.622465\pi$
$593$	−445.123			−0.750628			−0.375314	+	0.926898i	$0.622465\pi$
$594$		0			0
$595$		−	18.8149i		−	0.0316217i
$596$	−2.38945	−	366.907i	−0.00400914	−	0.615615i
$597$		0			0
$598$	−320.088	−	318.010i	−0.535264	−	0.531789i
$599$		−	790.891i		−	1.32035i	−0.751111	−	0.660176i	$-0.770482\pi$
$599$		−	790.891i		−	1.32035i	0.751111	−	0.660176i	$-0.229518\pi$
$600$		0			0
$601$	−387.065			−0.644035			−0.322017	−	0.946734i	$-0.604361\pi$
$601$	−387.065			−0.644035			−0.322017	+	0.946734i	$0.604361\pi$
$602$	204.408	−	205.744i	0.339548	−	0.341767i
$603$		0			0
$604$	166.373	−	1.08349i	0.275451	−	0.00179385i
$605$	861.382			1.42377
$606$		0			0
$607$			1042.13i			1.71686i	0.512934	+	0.858428i	$0.328558\pi$
$607$			1042.13i			1.71686i	−0.512934	+	0.858428i	$0.671442\pi$
$608$	−377.460	−	365.365i	−0.620822	−	0.600929i
$609$		0			0
$610$	−767.660	+	772.676i	−1.25846	+	1.26668i
$611$		−	427.251i		−	0.699266i
$612$		0			0
$613$	256.336			0.418166			0.209083	−	0.977898i	$-0.432952\pi$
$613$	256.336			0.418166			0.209083	+	0.977898i	$0.432952\pi$
$614$	368.845	+	366.451i	0.600726	+	0.596826i
$615$		0			0
$616$	−96.8434	−	94.9697i	−0.157213	−	0.154172i
$617$	507.039			0.821780			0.410890	−	0.911685i	$-0.365218\pi$
$617$	507.039			0.821780			0.410890	+	0.911685i	$0.365218\pi$
$618$		0			0
$619$			765.321i			1.23638i	0.786028	+	0.618191i	$0.212134\pi$
$619$			765.321i			1.23638i	−0.786028	+	0.618191i	$0.787866\pi$
$620$	489.118	−	3.18534i	0.788900	−	0.00513764i
$621$		0			0
$622$	27.1891	+	27.0126i	0.0437123	+	0.0434286i
$623$			116.425i			0.186878i
$624$		0			0
$625$	−25.1493			−0.0402388
$626$	61.8414	−	62.2454i	0.0987881	−	0.0994336i
$627$		0			0
$628$	5.88237	+	903.255i	0.00936684	+	1.43830i
$629$	0.306623			0.000487477
$630$		0			0
$631$		−	719.756i		−	1.14066i	−0.821416	−	0.570330i	$-0.806815\pi$
$631$		−	719.756i		−	1.14066i	0.821416	−	0.570330i	$-0.193185\pi$
$632$	820.573	−	836.763i	1.29837	−	1.32399i
$633$		0			0
$634$	−194.437	+	195.708i	−0.306684	+	0.308687i
$635$		−	79.1067i		−	0.124578i
$636$		0			0
$637$	202.350			0.317660
$638$	−101.256	−	100.599i	−0.158708	−	0.157678i
$639$		0			0
$640$	746.138	+	712.877i	1.16584	+	1.11387i
$641$	−703.033			−1.09678			−0.548388	−	0.836224i	$-0.684758\pi$
$641$	−703.033			−1.09678			−0.548388	+	0.836224i	$0.684758\pi$
$642$		0			0
$643$		−	585.692i		−	0.910875i	−0.890268	−	0.455437i	$-0.849483\pi$
$643$		−	585.692i		−	0.910875i	0.890268	−	0.455437i	$-0.150517\pi$
$644$	3.75523	+	576.626i	0.00583110	+	0.895382i
$645$		0			0
$646$	12.0626	+	11.9843i	0.0186728	+	0.0185515i
$647$			791.553i			1.22342i	0.791082	+	0.611710i	$0.209518\pi$
$647$			791.553i			1.22342i	−0.791082	+	0.611710i	$0.790482\pi$
$648$		0			0
$649$	−132.909			−0.204791
$650$	397.599	−	400.197i	0.611691	−	0.615687i
$651$		0			0
$652$	500.690	−	3.26070i	0.767929	−	0.00500107i
$653$	392.769			0.601484			0.300742	−	0.953705i	$-0.402766\pi$
$653$	392.769			0.601484			0.300742	+	0.953705i	$0.402766\pi$
$654$		0			0
$655$		−	945.466i		−	1.44346i
$656$	396.017	−	5.15827i	0.603685	−	0.00786322i
$657$		0			0
$658$	−384.838	+	387.353i	−0.584861	+	0.588682i
$659$			430.192i			0.652795i	0.945233	+	0.326398i	$0.105835\pi$
$659$			430.192i			0.652795i	−0.945233	+	0.326398i	$0.894165\pi$
$660$		0			0
$661$	−907.729			−1.37327			−0.686633	−	0.727004i	$-0.740912\pi$
$661$	−907.729			−1.37327			−0.686633	+	0.727004i	$0.740912\pi$
$662$	−84.7805	−	84.2302i	−0.128067	−	0.127236i
$663$		0			0
$664$	563.369	−	574.485i	0.848447	−	0.865188i
$665$	596.408			0.896854
$666$		0			0
$667$			606.799i			0.909744i
$668$	−713.004	+	4.64338i	−1.06737	+	0.00695117i
$669$		0			0
$670$	983.600	+	977.215i	1.46806	+	1.45853i
$671$		−	254.157i		−	0.378773i
$672$		0			0
$673$	69.7055			0.103574			0.0517872	−	0.998658i	$-0.483508\pi$
$673$	69.7055			0.103574			0.0517872	+	0.998658i	$0.483508\pi$
$674$	−632.504	+	636.636i	−0.938433	+	0.944564i
$675$		0			0
$676$	3.10682	+	477.062i	0.00459589	+	0.705712i
$677$	289.004			0.426889			0.213444	−	0.976955i	$-0.431532\pi$
$677$	289.004			0.426889			0.213444	+	0.976955i	$0.431532\pi$
$678$		0			0
$679$		−	434.885i		−	0.640479i
$680$	−23.8485	−	23.3871i	−0.0350713	−	0.0343928i
$681$		0			0
$682$	−80.4430	+	80.9686i	−0.117952	+	0.118722i
$683$			522.729i			0.765343i	0.923884	+	0.382672i	$0.124996\pi$
$683$			522.729i			0.765343i	−0.923884	+	0.382672i	$0.875004\pi$
$684$		0			0
$685$	−2025.29			−2.95663
$686$	−496.737	−	493.513i	−0.724106	−	0.719406i
$687$		0			0
$688$	−6.70592	−	514.835i	−0.00974698	−	0.748306i
$689$	−4.68799			−0.00680405
$690$		0			0
$691$		−	561.088i		−	0.811994i	−0.913874	−	0.405997i	$-0.866924\pi$
$691$		−	561.088i		−	0.811994i	0.913874	−	0.405997i	$-0.133076\pi$
$692$	−3.93813	−	604.711i	−0.00569093	−	0.873859i
$693$		0			0
$694$	−819.874	−	814.552i	−1.18137	−	1.17371i
$695$			1238.82i			1.78247i
$696$		0			0
$697$	−12.8194			−0.0183923
$698$	−186.437	+	187.655i	−0.267102	+	0.268847i
$699$		0			0
$700$	−720.939	+	4.69505i	−1.02991	+	0.00670722i
$701$	1203.11			1.71627			0.858137	−	0.513421i	$-0.171622\pi$
$701$	1203.11			1.71627			0.858137	+	0.513421i	$0.171622\pi$
$702$		0			0
$703$			9.71954i			0.0138258i
$704$	−240.754	+	4.70421i	−0.341981	+	0.00668211i
$705$		0			0
$706$	−762.770	+	767.753i	−1.08041	+	1.08747i
$707$		−	195.212i		−	0.276113i
$708$		0			0
$709$	−178.545			−0.251826			−0.125913	−	0.992041i	$-0.540186\pi$
$709$	−178.545			−0.251826			−0.125913	+	0.992041i	$0.540186\pi$
$710$	645.632	+	641.441i	0.909341	+	0.903439i
$711$		0			0
$712$	147.572	+	144.717i	0.207265	+	0.203254i
$713$	485.223			0.680537
$714$		0			0
$715$			213.916i			0.299183i
$716$	−1107.29	+	7.21111i	−1.54649	+	0.0100714i
$717$		0			0
$718$	−415.362	−	412.666i	−0.578499	−	0.574744i
$719$		−	53.0278i		−	0.0737521i	−0.999320	−	0.0368760i	$-0.988259\pi$
$719$		−	53.0278i		−	0.0737521i	0.999320	−	0.0368760i	$-0.0117407\pi$
$720$		0			0
$721$	−652.709			−0.905282
$722$	128.979	−	129.822i	0.178642	−	0.179809i
$723$		0			0
$724$	2.72809	+	418.906i	0.00376808	+	0.578600i
$725$	−758.664			−1.04643
$726$		0			0
$727$		−	504.554i		−	0.694022i	−0.937861	−	0.347011i	$-0.887197\pi$
$727$		−	504.554i		−	0.694022i	0.937861	−	0.347011i	$-0.112803\pi$
$728$	−178.003	+	181.515i	−0.244509	+	0.249333i
$729$		0			0
$730$	1499.19	−	1508.99i	2.05369	−	2.06710i
$731$			16.6657i			0.0227984i
$732$		0			0
$733$	−821.928			−1.12132			−0.560660	−	0.828046i	$-0.689453\pi$
$733$	−821.928			−1.12132			−0.560660	+	0.828046i	$0.689453\pi$
$734$	−620.704	−	616.675i	−0.845646	−	0.840156i
$735$		0			0
$736$	735.560	+	711.991i	0.999402	+	0.967378i
$737$	−323.536			−0.438991
$738$		0			0
$739$			190.298i			0.257507i	0.991677	+	0.128754i	$0.0410977\pi$
$739$			190.298i			0.257507i	−0.991677	+	0.128754i	$0.958902\pi$
$740$	−0.124339	−	19.0926i	−0.000168026	−	0.0258008i
$741$		0			0
$742$	4.25021	+	4.22262i	0.00572804	+	0.00569086i
$743$			766.869i			1.03213i	0.856551	+	0.516063i	$0.172603\pi$
$743$			766.869i			1.03213i	−0.856551	+	0.516063i	$0.827397\pi$
$744$		0			0
$745$	739.525			0.992650
$746$	995.118	−	1001.62i	1.33394	−	1.34265i
$747$		0			0
$748$	7.79409	−	0.0507583i	0.0104199	−	6.78587e-5i
$749$	247.782			0.330817
$750$		0			0
$751$		−	599.984i		−	0.798913i	−0.916752	−	0.399456i	$-0.869199\pi$
$751$		−	599.984i		−	0.798913i	0.916752	−	0.399456i	$-0.130801\pi$
$752$	12.6252	+	969.278i	0.0167889	+	1.28893i
$753$		0			0
$754$	−188.553	+	189.785i	−0.250070	+	0.251704i
$755$			335.335i			0.444152i
$756$		0			0
$757$	−343.082			−0.453213			−0.226606	−	0.973986i	$-0.572763\pi$
$757$	−343.082			−0.453213			−0.226606	+	0.973986i	$0.572763\pi$
$758$	768.189	+	763.203i	1.01344	+	1.00686i
$759$		0			0
$760$	741.340	−	755.967i	0.975447	−	0.994693i
$761$	298.730			0.392550			0.196275	−	0.980549i	$-0.437116\pi$
$761$	298.730			0.392550			0.196275	+	0.980549i	$0.437116\pi$
$762$		0			0
$763$			288.056i			0.377531i
$764$	−891.282	+	5.80440i	−1.16660	+	0.00759738i
$765$		0			0
$766$	511.053	+	507.736i	0.667171	+	0.662841i
$767$			249.113i			0.324789i
$768$		0			0
$769$	932.482			1.21259			0.606295	−	0.795240i	$-0.292655\pi$
$769$	932.482			1.21259			0.606295	+	0.795240i	$0.292655\pi$
$770$	192.681	−	193.939i	0.250234	−	0.251869i
$771$		0			0
$772$	2.95287	+	453.422i	0.00382497	+	0.587335i
$773$	−173.239			−0.224113			−0.112056	−	0.993702i	$-0.535744\pi$
$773$	−173.239			−0.224113			−0.112056	+	0.993702i	$0.535744\pi$
$774$		0			0
$775$			606.660i			0.782787i
$776$	−551.231	−	540.566i	−0.710349	−	0.696605i
$777$		0			0
$778$	123.779	−	124.588i	0.159099	−	0.160138i
$779$		−	406.359i		−	0.521642i
$780$		0			0
$781$	−212.368			−0.271919
$782$	−23.5065	−	23.3539i	−0.0300595	−	0.0298644i
$783$		0			0
$784$	−459.058	+	5.97940i	−0.585533	+	0.00762679i
$785$	−1820.57			−2.31920
$786$		0			0
$787$			49.8711i			0.0633686i	0.999498	+	0.0316843i	$0.0100871\pi$
$787$			49.8711i			0.0633686i	−0.999498	+	0.0316843i	$0.989913\pi$
$788$	3.15188	+	483.980i	0.00399984	+	0.614188i
$789$		0			0
$790$	1675.71	+	1664.83i	2.12115	+	2.10738i
$791$			160.639i			0.203083i
$792$		0			0
$793$	−476.369			−0.600717
$794$	−68.2428	+	68.6886i	−0.0859481	+	0.0865096i
$795$		0			0
$796$	−328.938	+	2.14218i	−0.413239	+	0.00269119i
$797$	1027.51			1.28922			0.644608	−	0.764513i	$-0.277020\pi$
$797$	1027.51			1.28922			0.644608	+	0.764513i	$0.277020\pi$
$798$		0			0
$799$		−	31.3764i		−	0.0392696i
$800$	−890.181	+	919.649i	−1.11273	+	1.14956i
$801$		0			0
$802$	−614.189	+	618.202i	−0.765822	+	0.770825i
$803$			496.352i			0.618123i
$804$		0			0
$805$	−1162.23			−1.44376
$806$	151.760	+	150.775i	0.188288	+	0.187066i
$807$		0			0
$808$	−247.437	−	242.650i	−0.306234	−	0.300309i
$809$	−637.363			−0.787841			−0.393920	−	0.919145i	$-0.628881\pi$
$809$	−637.363			−0.787841			−0.393920	+	0.919145i	$0.628881\pi$
$810$		0			0
$811$		−	1486.54i		−	1.83298i	−0.400061	−	0.916489i	$-0.631011\pi$
$811$		−	1486.54i		−	1.83298i	0.400061	−	0.916489i	$-0.368989\pi$
$812$	341.890	−	2.22653i	0.421047	−	0.00274203i
$813$		0			0
$814$	3.16059	+	3.14007i	0.00388279	+	0.00385759i
$815$			1009.17i			1.23825i
$816$		0			0
$817$	−528.279			−0.646609
$818$	76.4412	−	76.9406i	0.0934488	−	0.0940594i
$819$		0			0
$820$	5.19842	+	798.232i	0.00633954	+	0.973454i
$821$	−1035.73			−1.26155			−0.630773	−	0.775967i	$-0.717262\pi$
$821$	−1035.73			−1.26155			−0.630773	+	0.775967i	$0.717262\pi$
$822$		0			0
$823$			321.272i			0.390367i	0.980767	+	0.195184i	$0.0625303\pi$
$823$			321.272i			0.390367i	−0.980767	+	0.195184i	$0.937470\pi$
$824$	−811.322	+	827.330i	−0.984614	+	1.00404i
$825$		0			0
$826$	224.384	−	225.850i	0.271651	−	0.273426i
$827$			119.865i			0.144939i	0.997371	+	0.0724695i	$0.0230880\pi$
$827$			119.865i			0.144939i	−0.997371	+	0.0724695i	$0.976912\pi$
$828$		0			0
$829$	810.947			0.978223			0.489112	−	0.872221i	$-0.337321\pi$
$829$	810.947			0.978223			0.489112	+	0.872221i	$0.337321\pi$
$830$	1150.47	+	1143.00i	1.38611	+	1.37711i
$831$		0			0
$832$	8.81714	+	451.248i	0.0105975	+	0.542366i
$833$	14.8601			0.0178393
$834$		0			0
$835$		−	1437.11i		−	1.72109i
$836$	1.60897	+	247.062i	0.00192461	+	0.295529i
$837$		0			0
$838$	904.391	+	898.520i	1.07923	+	1.07222i
$839$		−	59.2928i		−	0.0706708i	−0.999376	−	0.0353354i	$-0.988750\pi$
$839$		−	59.2928i		−	0.0706708i	0.999376	−	0.0353354i	$-0.0112499\pi$
$840$		0			0
$841$	−481.219			−0.572199
$842$	270.011	−	271.775i	0.320678	−	0.322773i
$843$		0			0
$844$	−432.227	+	2.81484i	−0.512118	+	0.00333512i
$845$	−961.549			−1.13793
$846$		0			0
$847$		−	481.466i		−	0.568437i
$848$	10.6353	−	0.138529i	0.0125417	−	0.000163360i
$849$		0			0
$850$	29.1988	−	29.3895i	0.0343515	−	0.0345759i
$851$		−	18.9406i		−	0.0222568i
$852$		0			0
$853$	−1095.46			−1.28424			−0.642121	−	0.766604i	$-0.721945\pi$
$853$	−1095.46			−1.28424			−0.642121	+	0.766604i	$0.721945\pi$
$854$	431.884	+	429.080i	0.505718	+	0.502436i
$855$		0			0
$856$	307.995	−	314.072i	0.359807	−	0.366907i
$857$	1384.32			1.61532			0.807658	−	0.589652i	$-0.200735\pi$
$857$	1384.32			1.61532			0.807658	+	0.589652i	$0.200735\pi$
$858$		0			0
$859$			479.182i			0.557837i	0.960315	+	0.278918i	$0.0899759\pi$
$859$			479.182i			0.557837i	−0.960315	+	0.278918i	$0.910024\pi$
$860$	1037.73	−	6.75811i	1.20666	−	0.00785827i
$861$		0			0
$862$	−682.718	−	678.286i	−0.792016	−	0.786875i
$863$			4.93230i			0.00571530i	0.999996	+	0.00285765i	$0.000909619\pi$
$863$			4.93230i			0.00571530i	−0.999996	+	0.00285765i	$0.999090\pi$
$864$		0			0
$865$	1218.83			1.40906
$866$	−507.945	+	511.264i	−0.586542	+	0.590374i
$867$		0			0
$868$	−1.78043	−	273.390i	−0.00205119	−	0.314966i
$869$	−551.192			−0.634284
$870$		0			0
$871$			606.408i			0.696220i
$872$	365.121	+	358.056i	0.418717	+	0.410615i
$873$		0			0
$874$	740.289	−	745.126i	0.847013	−	0.852547i
$875$		−	544.850i		−	0.622686i
$876$		0			0
$877$	1678.99			1.91447			0.957234	−	0.289316i	$-0.0934278\pi$
$877$	1678.99			1.91447			0.957234	+	0.289316i	$0.0934278\pi$
$878$	799.929	+	794.737i	0.911081	+	0.905167i
$879$		0			0
$880$	−6.32118	−	485.297i	−0.00718316	−	0.551474i
$881$	830.879			0.943109			0.471555	−	0.881837i	$-0.343693\pi$
$881$	830.879			0.943109			0.471555	+	0.881837i	$0.343693\pi$
$882$		0			0
$883$			1228.46i			1.39123i	0.718414	+	0.695615i	$0.244868\pi$
$883$			1228.46i			1.39123i	−0.718414	+	0.695615i	$0.755132\pi$
$884$	−0.0951369	−	14.6085i	−0.000107621	−	0.0165255i
$885$		0			0
$886$	933.696	+	927.635i	1.05383	+	1.04699i
$887$		−	762.194i		−	0.859294i	−0.902997	−	0.429647i	$-0.858638\pi$
$887$		−	762.194i		−	0.859294i	0.902997	−	0.429647i	$-0.141362\pi$
$888$		0			0
$889$	−44.2164			−0.0497372
$890$	−293.612	+	295.530i	−0.329901	+	0.332056i
$891$		0			0
$892$	−653.083	+	4.25315i	−0.732156	+	0.00476810i
$893$	994.590			1.11376
$894$		0			0
$895$		−	2231.81i		−	2.49364i
$896$	398.459	−	417.051i	0.444709	−	0.465458i
$897$		0			0
$898$	320.782	−	322.878i	0.357218	−	0.359552i
$899$		−	287.696i		−	0.320018i
$900$		0			0
$901$	−0.344275			−0.000382104
$902$	−132.139	−	131.282i	−0.146496	−	0.145545i
$903$		0			0
$904$	203.615	+	199.675i	0.225238	+	0.220880i
$905$	−844.333			−0.932965
$906$		0			0
$907$			374.211i			0.412581i	0.978491	+	0.206291i	$0.0661392\pi$
$907$			374.211i			0.412581i	−0.978491	+	0.206291i	$0.933861\pi$
$908$	44.1882	−	0.287772i	0.0486654	−	0.000316929i
$909$		0			0
$910$	−363.503	−	361.143i	−0.399453	−	0.396861i
$911$		−	1461.28i		−	1.60404i	−0.597300	−	0.802018i	$-0.703760\pi$
$911$		−	1461.28i		−	1.60404i	0.597300	−	0.802018i	$-0.296240\pi$
$912$		0			0
$913$	−378.424			−0.414485
$914$	1011.75	−	1018.36i	1.10695	−	1.11418i
$915$		0			0
$916$	−0.842558	−	129.377i	−0.000919823	−	0.141241i
$917$	−528.464			−0.576296
$918$		0			0
$919$		−	1112.72i		−	1.21080i	−0.795923	−	0.605398i	$-0.793014\pi$
$919$		−	1112.72i		−	1.21080i	0.795923	−	0.605398i	$-0.206986\pi$
$920$	−1444.66	+	1473.16i	−1.57028	+	1.60126i
$921$		0			0
$922$	566.302	−	570.002i	0.614210	−	0.618223i
$923$			398.044i			0.431251i
$924$		0			0
$925$	23.6809			0.0256009
$926$	650.003	+	645.784i	0.701947	+	0.697390i
$927$		0			0
$928$	422.150	−	436.125i	0.454903	−	0.469962i
$929$	1016.41			1.09409			0.547044	−	0.837104i	$-0.315753\pi$
$929$	1016.41			1.09409			0.547044	+	0.837104i	$0.315753\pi$
$930$		0			0
$931$			471.046i			0.505957i
$932$	−4.71618	−	724.182i	−0.00506028	−	0.777020i
$933$		0			0
$934$	−289.998	−	288.115i	−0.310490	−	0.308475i
$935$			15.7095i			0.0168016i
$936$		0			0
$937$	170.282			0.181731			0.0908654	−	0.995863i	$-0.471037\pi$
$937$	170.282			0.181731			0.0908654	+	0.995863i	$0.471037\pi$
$938$	546.210	−	549.779i	0.582313	−	0.586118i
$939$		0			0
$940$	−1953.73	+	12.7235i	−2.07843	+	0.0135356i
$941$	301.858			0.320785			0.160392	−	0.987053i	$-0.448724\pi$
$941$	301.858			0.320785			0.160392	+	0.987053i	$0.448724\pi$
$942$		0			0
$943$			791.876i			0.839741i
$944$	−7.36126	−	565.147i	−0.00779794	−	0.598673i
$945$		0			0
$946$	−170.670	+	171.785i	−0.180413	+	0.181591i
$947$			843.111i			0.890296i	0.895457	+	0.445148i	$0.146849\pi$
$947$			843.111i			0.890296i	−0.895457	+	0.445148i	$0.853151\pi$
$948$		0			0
$949$	930.318			0.980314
$950$	931.610	+	925.562i	0.980642	+	0.974276i
$951$		0			0
$952$	−13.0721	+	13.3300i	−0.0137312	+	0.0140021i
$953$	306.171			0.321270			0.160635	−	0.987014i	$-0.448646\pi$
$953$	306.171			0.321270			0.160635	+	0.987014i	$0.448646\pi$
$954$		0			0
$955$		−	1796.44i		−	1.88109i
$956$	183.100	−	1.19243i	0.191527	−	0.00124731i
$957$		0			0
$958$	128.533	+	127.698i	0.134168	+	0.133297i
$959$			1132.03i			1.18043i
$960$		0			0
$961$	730.946			0.760610
$962$	5.88547	−	5.92393i	0.00611796	−	0.00615793i
$963$		0			0
$964$	8.81584	+	1353.70i	0.00914507	+	1.40425i
$965$	−913.902			−0.947049
$966$		0			0
$967$			119.883i			0.123975i	0.998077	+	0.0619873i	$0.0197438\pi$
$967$			119.883i			0.123975i	−0.998077	+	0.0619873i	$0.980256\pi$
$968$	−610.274	−	598.466i	−0.630448	−	0.618250i
$969$		0			0
$970$	1096.73	−	1103.90i	1.13065	−	1.13804i
$971$		−	62.7602i		−	0.0646346i	−0.999478	−	0.0323173i	$-0.989711\pi$
$971$		−	62.7602i		−	0.0646346i	0.999478	−	0.0323173i	$-0.0102887\pi$
$972$		0			0
$973$	692.431			0.711646
$974$	−427.472	−	424.697i	−0.438883	−	0.436034i
$975$		0			0
$976$	1080.71	−	14.0766i	1.10728	−	0.0144228i
$977$	−1236.23			−1.26533			−0.632666	−	0.774425i	$-0.718039\pi$
$977$	−1236.23			−1.26533			−0.632666	+	0.774425i	$0.718039\pi$
$978$		0			0
$979$		−	97.2089i		−	0.0992941i
$980$	−6.02594	−	925.300i	−0.00614892	−	0.944184i
$981$		0			0
$982$	−638.211	−	634.068i	−0.649909	−	0.645691i
$983$			566.517i			0.576314i	0.957583	+	0.288157i	$0.0930425\pi$
$983$			566.517i			0.576314i	−0.957583	+	0.288157i	$0.906957\pi$
$984$		0			0
$985$	−975.493			−0.990348
$986$	−13.8469	+	13.9374i	−0.0140435	+	0.0141353i
$987$		0			0
$988$	463.072	−	3.01571i	0.468696	−	0.00305234i
$989$	1029.46			1.04091
$990$		0			0
$991$			457.774i			0.461931i	0.972962	+	0.230966i	$0.0741885\pi$
$991$			457.774i			0.461931i	−0.972962	+	0.230966i	$0.925812\pi$
$992$	−348.744	−	337.569i	−0.351556	−	0.340292i
$993$		0			0
$994$	358.531	−	360.873i	0.360695	−	0.363052i
$995$		−	662.997i		−	0.666329i
$996$		0			0
$997$	−38.7595			−0.0388761			−0.0194381	−	0.999811i	$-0.506188\pi$
$997$	−38.7595			−0.0388761			−0.0194381	+	0.999811i	$0.506188\pi$
$998$	−905.375	−	899.498i	−0.907190	−	0.901301i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	324.3.d.i.163.5		8
3.2	odd	2		324.3.d.g.163.4		8
4.3	odd	2	inner	324.3.d.i.163.6		8
9.2	odd	6		108.3.f.c.91.8		16
9.4	even	3		36.3.f.c.7.5	yes	16
9.5	odd	6		108.3.f.c.19.4		16
9.7	even	3		36.3.f.c.31.1	yes	16
12.11	even	2		324.3.d.g.163.3		8
36.7	odd	6		36.3.f.c.31.5	yes	16
36.11	even	6		108.3.f.c.91.4		16
36.23	even	6		108.3.f.c.19.8		16
36.31	odd	6		36.3.f.c.7.1	✓	16
72.5	odd	6		1728.3.o.g.127.2		16
72.11	even	6		1728.3.o.g.1279.2		16
72.13	even	6		576.3.o.g.511.1		16
72.29	odd	6		1728.3.o.g.1279.1		16
72.43	odd	6		576.3.o.g.319.1		16
72.59	even	6		1728.3.o.g.127.1		16
72.61	even	6		576.3.o.g.319.8		16
72.67	odd	6		576.3.o.g.511.8		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
36.3.f.c.7.1	✓	16	36.31	odd	6
36.3.f.c.7.5	yes	16	9.4	even	3
36.3.f.c.31.1	yes	16	9.7	even	3
36.3.f.c.31.5	yes	16	36.7	odd	6
108.3.f.c.19.4		16	9.5	odd	6
108.3.f.c.19.8		16	36.23	even	6
108.3.f.c.91.4		16	36.11	even	6
108.3.f.c.91.8		16	9.2	odd	6
324.3.d.g.163.3		8	12.11	even	2
324.3.d.g.163.4		8	3.2	odd	2
324.3.d.i.163.5		8	1.1	even	1	trivial
324.3.d.i.163.6		8	4.3	odd	2	inner
576.3.o.g.319.1		16	72.43	odd	6
576.3.o.g.319.8		16	72.61	even	6
576.3.o.g.511.1		16	72.13	even	6
576.3.o.g.511.8		16	72.67	odd	6
1728.3.o.g.127.1		16	72.59	even	6
1728.3.o.g.127.2		16	72.5	odd	6
1728.3.o.g.1279.1		16	72.29	odd	6
1728.3.o.g.1279.2		16	72.11	even	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)

\(f(q)\)	\(=\)	\(q+(1.40960 - 1.41881i) q^{2} +(-0.0260491 - 3.99992i) q^{4} +8.06209 q^{5} -4.50627i q^{7} +(-5.71184 - 5.60133i) q^{8} +O(q^{10})\)	\(q+(1.40960 - 1.41881i) q^{2} +(-0.0260491 - 3.99992i) q^{4} +8.06209 q^{5} -4.50627i q^{7} +(-5.71184 - 5.60133i) q^{8} +(11.3643 - 11.4386i) q^{10} +3.76250i q^{11} +7.05210 q^{13} +(-6.39354 - 6.35204i) q^{14} +(-15.9986 + 0.208388i) q^{16} +0.517890 q^{17} +16.4164i q^{19} +(-0.210010 - 32.2477i) q^{20} +(5.33828 + 5.30363i) q^{22} -31.9909i q^{23} +39.9973 q^{25} +(9.94065 - 10.0056i) q^{26} +(-18.0247 + 0.117384i) q^{28} -18.9679 q^{29} +15.1675i q^{31} +(-22.2560 + 22.9928i) q^{32} +(0.730018 - 0.734788i) q^{34} -36.3299i q^{35} +0.592061 q^{37} +(23.2918 + 23.1406i) q^{38} +(-46.0494 - 45.1584i) q^{40} -24.7532 q^{41} +32.1799i q^{43} +(15.0497 - 0.0980099i) q^{44} +(-45.3890 - 45.0944i) q^{46} -60.5850i q^{47} +28.6935 q^{49} +(56.3802 - 56.7486i) q^{50} +(-0.183701 - 28.2078i) q^{52} -0.664765 q^{53} +30.3336i q^{55} +(-25.2411 + 25.7391i) q^{56} +(-26.7372 + 26.9118i) q^{58} +35.3247i q^{59} -67.5500 q^{61} +(21.5199 + 21.3802i) q^{62} +(1.25029 + 63.9878i) q^{64} +56.8546 q^{65} +85.9897i q^{67} +(-0.0134906 - 2.07152i) q^{68} +(-51.5453 - 51.2107i) q^{70} +56.4434i q^{71} +131.921 q^{73} +(0.834571 - 0.840023i) q^{74} +(65.6644 - 0.427634i) q^{76} +16.9549 q^{77} +146.496i q^{79} +(-128.982 + 1.68005i) q^{80} +(-34.8921 + 35.1201i) q^{82} +100.578i q^{83} +4.17528 q^{85} +(45.6572 + 45.3608i) q^{86} +(21.0750 - 21.4908i) q^{88} -25.8362 q^{89} -31.7786i q^{91} +(-127.961 + 0.833334i) q^{92} +(-85.9587 - 85.4007i) q^{94} +132.351i q^{95} +96.5067 q^{97} +(40.4465 - 40.7107i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 3 q^{2} + 5 q^{4} - 6 q^{5} - 27 q^{8}+O(q^{10}) \) 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

L-functions

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