LMFDB - Embedded newform 162.3.f.a.17.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [162,3,Mod(17,162)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(162, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([11]))

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

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

chi := DirichletCharacter("162.17");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 162 = 2 \cdot 3^{4} $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	162.f (of order $18$, degree $6$, not minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$4.41418028264$
Analytic rank:	$0$
Dimension:	$36$
Relative dimension:	$6$ over $\Q(\zeta_{18})$
Twist minimal:	no (minimal twist has level 54)
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			17.3
Character	$\chi$	$=$	162.17
Dual form			162.3.f.a.143.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.483690 + 1.32893i) q^{2} +(-1.53209 - 1.28558i) q^{4} +(2.99623 + 0.528316i) q^{5} +(6.30359 - 5.28934i) q^{7} +(2.44949 - 1.41421i) q^{8} +O(q^{10})$	\(q+(-0.483690 + 1.32893i) q^{2} +(-1.53209 - 1.28558i) q^{4} +(2.99623 + 0.528316i) q^{5} +(6.30359 - 5.28934i) q^{7} +(2.44949 - 1.41421i) q^{8} +(-2.15134 + 3.72623i) q^{10} +(-6.45500 + 1.13819i) q^{11} +(17.4093 - 6.33646i) q^{13} +(3.98016 + 10.9354i) q^{14} +(0.694593 + 3.93923i) q^{16} +(11.4293 + 6.59870i) q^{17} +(17.4160 + 30.1654i) q^{19} +(-3.91130 - 4.66131i) q^{20} +(1.60964 - 9.12874i) q^{22} +(-2.12998 + 2.53841i) q^{23} +(-14.7940 - 5.38459i) q^{25} +26.2005i q^{26} -16.4575 q^{28} +(9.72486 - 26.7188i) q^{29} +(-10.6385 - 8.92675i) q^{31} +(-5.57091 - 0.982302i) q^{32} +(-14.2974 + 11.9970i) q^{34} +(21.6815 - 12.5178i) q^{35} +(-3.33360 + 5.77397i) q^{37} +(-48.5116 + 8.55390i) q^{38} +(8.08639 - 2.94320i) q^{40} +(19.4863 + 53.5382i) q^{41} +(-5.68525 - 32.2426i) q^{43} +(11.3529 + 6.55457i) q^{44} +(-2.34311 - 4.05838i) q^{46} +(-34.5145 - 41.1328i) q^{47} +(3.24938 - 18.4281i) q^{49} +(14.3114 - 17.0557i) q^{50} +(-34.8186 - 12.6729i) q^{52} -98.5651i q^{53} -19.9420 q^{55} +(7.96033 - 21.8708i) q^{56} +(30.8035 + 25.8472i) q^{58} +(-101.204 - 17.8449i) q^{59} +(-5.50484 + 4.61911i) q^{61} +(17.0087 - 9.81998i) q^{62} +(4.00000 - 6.92820i) q^{64} +(55.5099 - 9.78789i) q^{65} +(-28.2566 + 10.2846i) q^{67} +(-9.02755 - 24.8030i) q^{68} +(6.14813 + 34.8678i) q^{70} +(-8.46959 - 4.88992i) q^{71} +(64.7978 + 112.233i) q^{73} +(-6.06075 - 7.22291i) q^{74} +(12.0970 - 68.6057i) q^{76} +(-34.6694 + 41.3174i) q^{77} +(-96.4782 - 35.1152i) q^{79} +12.1698i q^{80} -80.5737 q^{82} +(-37.0524 + 101.800i) q^{83} +(30.7586 + 25.8095i) q^{85} +(45.5980 + 8.04015i) q^{86} +(-14.2018 + 11.9167i) q^{88} +(20.1649 - 11.6422i) q^{89} +(76.2254 - 132.026i) q^{91} +(6.52663 - 1.15082i) q^{92} +(71.3568 - 25.9718i) q^{94} +(36.2455 + 99.5837i) q^{95} +(-8.89809 - 50.4636i) q^{97} +(22.9179 + 13.2317i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 36 q - 18 q^{5}+O(q^{10}) $ 36 * q - 18 * q^5	$ 36 q - 18 q^{5} + 18 q^{11} + 36 q^{14} + 72 q^{20} + 36 q^{22} + 180 q^{23} + 18 q^{25} - 144 q^{29} - 90 q^{31} - 72 q^{34} - 486 q^{35} - 180 q^{38} + 90 q^{41} + 90 q^{43} + 378 q^{47} + 72 q^{49} + 72 q^{56} - 252 q^{59} - 144 q^{61} + 144 q^{64} - 18 q^{65} - 594 q^{67} + 180 q^{68} - 360 q^{70} + 648 q^{71} + 126 q^{73} + 504 q^{74} - 72 q^{76} + 342 q^{77} - 72 q^{79} - 594 q^{83} + 360 q^{85} - 540 q^{86} + 144 q^{88} - 648 q^{89} - 198 q^{91} - 396 q^{92} + 504 q^{94} - 252 q^{95} + 702 q^{97} - 648 q^{98}+O(q^{100}) $ 36 * q - 18 * q^5 + 18 * q^11 + 36 * q^14 + 72 * q^20 + 36 * q^22 + 180 * q^23 + 18 * q^25 - 144 * q^29 - 90 * q^31 - 72 * q^34 - 486 * q^35 - 180 * q^38 + 90 * q^41 + 90 * q^43 + 378 * q^47 + 72 * q^49 + 72 * q^56 - 252 * q^59 - 144 * q^61 + 144 * q^64 - 18 * q^65 - 594 * q^67 + 180 * q^68 - 360 * q^70 + 648 * q^71 + 126 * q^73 + 504 * q^74 - 72 * q^76 + 342 * q^77 - 72 * q^79 - 594 * q^83 + 360 * q^85 - 540 * q^86 + 144 * q^88 - 648 * q^89 - 198 * q^91 - 396 * q^92 + 504 * q^94 - 252 * q^95 + 702 * q^97 - 648 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/162\mathbb{Z}\right)^\times$.

$n$	$83$
$\chi(n)$	$e\left(\frac{11}{18}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−0.483690	+	1.32893i	−0.241845	+	0.664463i
$2$	−0.483690	+	1.32893i	−0.241845	+	0.664463i
$3$		0			0
$3$		0			0
$4$	−1.53209	−	1.28558i	−0.383022	−	0.321394i
$5$	2.99623	+	0.528316i	0.599246	+	0.105663i	0.465039	−	0.885290i	$-0.346040\pi$
$5$	2.99623	+	0.528316i	0.599246	+	0.105663i	0.134207	+	0.990953i	$0.457151\pi$
$6$		0			0
$7$	6.30359	−	5.28934i	0.900513	−	0.755620i	−0.0697775	−	0.997563i	$-0.522229\pi$
$7$	6.30359	−	5.28934i	0.900513	−	0.755620i	0.970291	+	0.241942i	$0.0777845\pi$
$8$	2.44949	−	1.41421i	0.306186	−	0.176777i
$9$		0			0
$10$	−2.15134	+	3.72623i	−0.215134	+	0.372623i
$11$	−6.45500	+	1.13819i	−0.586818	+	0.103472i	−0.459171	−	0.888348i	$-0.651853\pi$
$11$	−6.45500	+	1.13819i	−0.586818	+	0.103472i	−0.127647	+	0.991820i	$0.540742\pi$
$12$		0			0
$13$	17.4093	−	6.33646i	1.33918	−	0.487420i	0.429623	−	0.903008i	$-0.358646\pi$
$13$	17.4093	−	6.33646i	1.33918	−	0.487420i	0.909553	+	0.415588i	$0.136424\pi$
$14$	3.98016	+	10.9354i	0.284297	+	0.781101i
$15$		0			0
$16$	0.694593	+	3.93923i	0.0434120	+	0.246202i
$17$	11.4293	+	6.59870i	0.672311	+	0.388159i	0.796952	−	0.604043i	$-0.206445\pi$
$17$	11.4293	+	6.59870i	0.672311	+	0.388159i	−0.124641	+	0.992202i	$0.539778\pi$
$18$		0			0
$19$	17.4160	+	30.1654i	0.916632	+	1.58765i	0.804494	+	0.593961i	$0.202437\pi$
$19$	17.4160	+	30.1654i	0.916632	+	1.58765i	0.112139	+	0.993693i	$0.464230\pi$
$20$	−3.91130	−	4.66131i	−0.195565	−	0.233065i
$21$		0			0
$22$	1.60964	−	9.12874i	0.0731656	−	0.414943i
$23$	−2.12998	+	2.53841i	−0.0926077	+	0.110366i	−0.810358	−	0.585935i	$-0.800727\pi$
$23$	−2.12998	+	2.53841i	−0.0926077	+	0.110366i	0.717750	+	0.696300i	$0.245172\pi$
$24$		0			0
$25$	−14.7940	−	5.38459i	−0.591762	−	0.215384i
$26$			26.2005i			1.00771i
$27$		0			0
$28$	−16.4575			−0.587768
$29$	9.72486	−	26.7188i	0.335340	−	0.921339i	−0.651357	−	0.758771i	$-0.725800\pi$
$29$	9.72486	−	26.7188i	0.335340	−	0.921339i	0.986697	−	0.162568i	$-0.0519777\pi$
$30$		0			0
$31$	−10.6385	−	8.92675i	−0.343177	−	0.287960i	0.454866	−	0.890560i	$-0.349687\pi$
$31$	−10.6385	−	8.92675i	−0.343177	−	0.287960i	−0.798043	+	0.602600i	$0.794131\pi$
$32$	−5.57091	−	0.982302i	−0.174091	−	0.0306970i
$33$		0			0
$34$	−14.2974	+	11.9970i	−0.420512	+	0.352851i
$35$	21.6815	−	12.5178i	0.619470	−	0.357651i
$36$		0			0
$37$	−3.33360	+	5.77397i	−0.0900973	+	0.156053i	−0.907552	−	0.419940i	$-0.862051\pi$
$37$	−3.33360	+	5.77397i	−0.0900973	+	0.156053i	0.817455	+	0.575993i	$0.195384\pi$
$38$	−48.5116	+	8.55390i	−1.27662	+	0.225103i
$39$		0			0
$40$	8.08639	−	2.94320i	0.202160	−	0.0735801i
$41$	19.4863	+	53.5382i	0.475276	+	1.30581i	0.913461	+	0.406926i	$0.133399\pi$
$41$	19.4863	+	53.5382i	0.475276	+	1.30581i	−0.438185	+	0.898885i	$0.644379\pi$
$42$		0			0
$43$	−5.68525	−	32.2426i	−0.132215	−	0.749829i	−0.976759	−	0.214342i	$-0.931239\pi$
$43$	−5.68525	−	32.2426i	−0.132215	−	0.749829i	0.844544	−	0.535487i	$-0.179872\pi$
$44$	11.3529	+	6.55457i	0.258019	+	0.148968i
$45$		0			0
$46$	−2.34311	−	4.05838i	−0.0509371	−	0.0882257i
$47$	−34.5145	−	41.1328i	−0.734352	−	0.875167i	0.261589	−	0.965179i	$-0.415754\pi$
$47$	−34.5145	−	41.1328i	−0.734352	−	0.875167i	−0.995941	+	0.0900128i	$0.971309\pi$
$48$		0			0
$49$	3.24938	−	18.4281i	0.0663138	−	0.376084i
$50$	14.3114	−	17.0557i	0.286229	−	0.341114i
$51$		0			0
$52$	−34.8186	−	12.6729i	−0.669588	−	0.243710i
$53$		−	98.5651i		−	1.85972i	−0.367914	−	0.929860i	$-0.619928\pi$
$53$		−	98.5651i		−	1.85972i	0.367914	−	0.929860i	$-0.380072\pi$
$54$		0			0
$55$	−19.9420			−0.362581
$56$	7.96033	−	21.8708i	0.142149	−	0.390550i
$57$		0			0
$58$	30.8035	+	25.8472i	0.531096	+	0.445642i
$59$	−101.204	−	17.8449i	−1.71532	−	0.302457i	−0.772314	−	0.635241i	$-0.780901\pi$
$59$	−101.204	−	17.8449i	−1.71532	−	0.302457i	−0.943003	+	0.332785i	$0.892012\pi$
$60$		0			0
$61$	−5.50484	+	4.61911i	−0.0902432	+	0.0757230i	−0.686793	−	0.726853i	$-0.740982\pi$
$61$	−5.50484	+	4.61911i	−0.0902432	+	0.0757230i	0.596550	+	0.802576i	$0.296538\pi$
$62$	17.0087	−	9.81998i	0.274334	−	0.158387i
$63$		0			0
$64$	4.00000	−	6.92820i	0.0625000	−	0.108253i
$65$	55.5099	−	9.78789i	0.853998	−	0.150583i
$66$		0			0
$67$	−28.2566	+	10.2846i	−0.421740	+	0.153501i	−0.544167	−	0.838977i	$-0.683154\pi$
$67$	−28.2566	+	10.2846i	−0.421740	+	0.153501i	0.122427	+	0.992477i	$0.460932\pi$
$68$	−9.02755	−	24.8030i	−0.132758	−	0.364750i
$69$		0			0
$70$	6.14813	+	34.8678i	0.0878304	+	0.498111i
$71$	−8.46959	−	4.88992i	−0.119290	−	0.0688721i	0.439168	−	0.898405i	$-0.355273\pi$
$71$	−8.46959	−	4.88992i	−0.119290	−	0.0688721i	−0.558458	+	0.829533i	$0.688607\pi$
$72$		0			0
$73$	64.7978	+	112.233i	0.887642	+	1.53744i	0.842656	+	0.538453i	$0.180991\pi$
$73$	64.7978	+	112.233i	0.887642	+	1.53744i	0.0449857	+	0.998988i	$0.485676\pi$
$74$	−6.06075	−	7.22291i	−0.0819020	−	0.0976070i
$75$		0			0
$76$	12.0970	−	68.6057i	0.159172	−	0.902707i
$77$	−34.6694	+	41.3174i	−0.450252	+	0.536589i
$78$		0			0
$79$	−96.4782	−	35.1152i	−1.22124	−	0.444496i	−0.350653	−	0.936505i	$-0.614040\pi$
$79$	−96.4782	−	35.1152i	−1.22124	−	0.444496i	−0.870590	+	0.492009i	$0.836263\pi$
$80$			12.1698i			0.152123i
$81$		0			0
$82$	−80.5737			−0.982606
$83$	−37.0524	+	101.800i	−0.446414	+	1.22651i	0.488790	+	0.872402i	$0.337439\pi$
$83$	−37.0524	+	101.800i	−0.446414	+	1.22651i	−0.935204	+	0.354110i	$0.884784\pi$
$84$		0			0
$85$	30.7586	+	25.8095i	0.361865	+	0.303641i
$86$	45.5980	+	8.04015i	0.530209	+	0.0934902i
$87$		0			0
$88$	−14.2018	+	11.9167i	−0.161384	+	0.135417i
$89$	20.1649	−	11.6422i	0.226572	−	0.130811i	−0.382418	−	0.923990i	$-0.624908\pi$
$89$	20.1649	−	11.6422i	0.226572	−	0.130811i	0.608989	+	0.793178i	$0.291575\pi$
$90$		0			0
$91$	76.2254	−	132.026i	0.837641	−	1.45084i
$92$	6.52663	−	1.15082i	0.0709416	−	0.0125089i
$93$		0			0
$94$	71.3568	−	25.9718i	0.759115	−	0.276295i
$95$	36.2455	+	99.5837i	0.381532	+	1.04825i
$96$		0			0
$97$	−8.89809	−	50.4636i	−0.0917329	−	0.520243i	−0.995700	−	0.0926404i	$-0.970469\pi$
$97$	−8.89809	−	50.4636i	−0.0917329	−	0.520243i	0.903967	−	0.427603i	$-0.140642\pi$
$98$	22.9179	+	13.2317i	0.233856	+	0.135017i
$99$		0			0
$100$	15.7435	+	27.2685i	0.157435	+	0.272685i
$101$	69.9824	+	83.4017i	0.692895	+	0.825760i	0.991703	−	0.128554i	$-0.0410334\pi$
$101$	69.9824	+	83.4017i	0.692895	+	0.825760i	−0.298808	+	0.954313i	$0.596589\pi$
$102$		0			0
$103$	−19.5497	+	110.872i	−0.189803	+	1.07643i	0.729824	+	0.683635i	$0.239602\pi$
$103$	−19.5497	+	110.872i	−0.189803	+	1.07643i	−0.919627	+	0.392792i	$0.871509\pi$
$104$	33.6828	−	40.1416i	0.323873	−	0.385977i
$105$		0			0
$106$	130.986	+	47.6749i	1.23571	+	0.449763i
$107$			125.974i			1.17733i	0.808378	+	0.588664i	$0.200346\pi$
$107$			125.974i			1.17733i	−0.808378	+	0.588664i	$0.799654\pi$
$108$		0			0
$109$	−71.2685			−0.653839			−0.326920	−	0.945052i	$-0.606011\pi$
$109$	−71.2685			−0.653839			−0.326920	+	0.945052i	$0.606011\pi$
$110$	9.64572	−	26.5014i	0.0876884	−	0.240922i
$111$		0			0
$112$	25.2144	+	21.1574i	0.225128	+	0.188905i
$113$	40.2664	+	7.10006i	0.356340	+	0.0628324i	0.348953	−	0.937140i	$-0.386537\pi$
$113$	40.2664	+	7.10006i	0.356340	+	0.0628324i	0.00738746	+	0.999973i	$0.497648\pi$
$114$		0			0
$115$	−7.72298	+	6.48035i	−0.0671564	+	0.0563509i
$116$	−49.2484	+	28.4336i	−0.424555	+	0.245117i
$117$		0			0
$118$	72.6658	−	125.861i	0.615811	−	1.06662i
$119$	106.948	−	18.8579i	0.898725	−	0.158470i
$120$		0			0
$121$	−73.3313	+	26.6904i	−0.606044	+	0.220582i
$122$	−3.47582	−	9.54973i	−0.0284903	−	0.0782765i
$123$		0			0
$124$	4.82310	+	27.3531i	0.0388959	+	0.220590i
$125$	−107.353	−	61.9800i	−0.858821	−	0.495840i
$126$		0			0
$127$	6.05212	+	10.4826i	0.0476545	+	0.0825399i	0.888869	−	0.458162i	$-0.151492\pi$
$127$	6.05212	+	10.4826i	0.0476545	+	0.0825399i	−0.841214	+	0.540702i	$0.818159\pi$
$128$	7.27231	+	8.66680i	0.0568149	+	0.0677094i
$129$		0			0
$130$	−13.8422	+	78.5029i	−0.106478	+	0.603868i
$131$	47.7541	−	56.9111i	0.364535	−	0.434436i	−0.552335	−	0.833622i	$-0.686263\pi$
$131$	47.7541	−	56.9111i	0.364535	−	0.434436i	0.916870	+	0.399187i	$0.130707\pi$
$132$		0			0
$133$	269.339	+	98.0313i	2.02510	+	0.737077i
$134$		−	42.5255i		−	0.317354i
$135$		0			0
$136$	37.3279			0.274470
$137$	−14.1317	+	38.8266i	−0.103151	+	0.283406i	−0.980523	−	0.196406i	$-0.937073\pi$
$137$	−14.1317	+	38.8266i	−0.103151	+	0.283406i	0.877371	+	0.479812i	$0.159295\pi$
$138$		0			0
$139$	−108.810	−	91.3026i	−0.782807	−	0.656853i	0.161147	−	0.986930i	$-0.448481\pi$
$139$	−108.810	−	91.3026i	−0.782807	−	0.656853i	−0.943954	+	0.330077i	$0.892925\pi$
$140$	−49.3105	−	8.69477i	−0.352218	−	0.0621055i
$141$		0			0
$142$	10.5950	−	8.89025i	0.0746126	−	0.0626074i
$143$	−105.165	+	60.7169i	−0.735418	+	0.424594i
$144$		0			0
$145$	43.2539	−	74.9180i	0.298303	−	0.516676i
$146$	−180.492	+	31.8255i	−1.23624	+	0.217983i
$147$		0			0
$148$	12.5302	−	4.56063i	0.0846638	−	0.0308151i
$149$	−79.8207	−	219.306i	−0.535709	−	1.47185i	−0.852181	−	0.523247i	$-0.824720\pi$
$149$	−79.8207	−	219.306i	−0.535709	−	1.47185i	0.316471	−	0.948602i	$-0.397502\pi$
$150$		0			0
$151$	1.35424	+	7.68028i	0.00896848	+	0.0508628i	0.988964	−	0.148159i	$-0.0473347\pi$
$151$	1.35424	+	7.68028i	0.00896848	+	0.0508628i	−0.979995	+	0.199022i	$0.936224\pi$
$152$	85.3207	+	49.2599i	0.561320	+	0.324078i
$153$		0			0
$154$	−38.1385	−	66.0578i	−0.247653	−	0.428947i
$155$	−27.1592	−	32.3671i	−0.175221	−	0.208820i
$156$		0			0
$157$	−4.42811	+	25.1131i	−0.0282045	+	0.159956i	−0.995657	−	0.0930967i	$-0.970323\pi$
$157$	−4.42811	+	25.1131i	−0.0282045	+	0.159956i	0.967453	+	0.253053i	$0.0814345\pi$
$158$	93.3310	−	111.228i	0.590703	−	0.703972i
$159$		0			0
$160$	−16.1728	−	5.88641i	−0.101080	−	0.0367900i
$161$			27.2673i			0.169362i
$162$		0			0
$163$	−211.039			−1.29472			−0.647358	−	0.762186i	$-0.724126\pi$
$163$	−211.039			−1.29472			−0.647358	+	0.762186i	$0.724126\pi$
$164$	38.9726	−	107.076i	0.237638	−	0.652905i
$165$		0			0
$166$	−117.363	−	98.4797i	−0.707009	−	0.593251i
$167$	11.3278	+	1.99740i	0.0678311	+	0.0119605i	0.207461	−	0.978243i	$-0.433480\pi$
$167$	11.3278	+	1.99740i	0.0678311	+	0.0119605i	−0.139630	+	0.990204i	$0.544591\pi$
$168$		0			0
$169$	133.471	−	111.996i	0.789771	−	0.662696i
$170$	−49.1765	+	28.3921i	−0.289274	+	0.167012i
$171$		0			0
$172$	−32.7400	+	56.7074i	−0.190349	+	0.329694i
$173$	227.512	−	40.1166i	1.31510	−	0.231888i	0.528281	−	0.849070i	$-0.322837\pi$
$173$	227.512	−	40.1166i	1.31510	−	0.231888i	0.786820	+	0.617182i	$0.211726\pi$
$174$		0			0
$175$	−121.737	+	44.3085i	−0.695637	+	0.253191i
$176$	−8.96719	−	24.6371i	−0.0509499	−	0.139984i
$177$		0			0
$178$	5.71808	+	32.4288i	0.0321240	+	0.182185i
$179$	−71.6862	−	41.3880i	−0.400481	−	0.231218i	0.286210	−	0.958167i	$-0.407604\pi$
$179$	−71.6862	−	41.3880i	−0.400481	−	0.231218i	−0.686692	+	0.726949i	$0.740938\pi$
$180$		0			0
$181$	83.1040	+	143.940i	0.459138	+	0.795250i	0.998916	−	0.0465572i	$-0.0148250\pi$
$181$	83.1040	+	143.940i	0.459138	+	0.795250i	−0.539778	+	0.841808i	$0.681492\pi$
$182$	138.584	+	165.158i	0.761449	+	0.907459i
$183$		0			0
$184$	−1.62751	+	9.23005i	−0.00884514	+	0.0501633i
$185$	−13.0387	+	15.5389i	−0.0704795	+	0.0839942i
$186$		0			0
$187$	−81.2866	−	29.5859i	−0.434687	−	0.158213i
$188$			107.390i			0.571224i
$189$		0			0
$190$	−149.871			−0.788794
$191$	−42.8208	+	117.649i	−0.224192	+	0.615964i	−0.999885	−	0.0151469i	$-0.995178\pi$
$191$	−42.8208	+	117.649i	−0.224192	+	0.615964i	0.775693	+	0.631111i	$0.217401\pi$
$192$		0			0
$193$	−70.6839	−	59.3108i	−0.366238	−	0.307310i	0.441033	−	0.897491i	$-0.354612\pi$
$193$	−70.6839	−	59.3108i	−0.366238	−	0.307310i	−0.807271	+	0.590181i	$0.799056\pi$
$194$	71.3663	+	12.5838i	0.367867	+	0.0648650i
$195$		0			0
$196$	−28.6691	+	24.0562i	−0.146271	+	0.122736i
$197$	−34.0836	+	19.6782i	−0.173013	+	0.0998893i	−0.584006	−	0.811749i	$-0.698516\pi$
$197$	−34.0836	+	19.6782i	−0.173013	+	0.0998893i	0.410993	+	0.911639i	$0.365182\pi$
$198$		0			0
$199$	95.3069	−	165.076i	0.478929	−	0.829530i	−0.520779	−	0.853692i	$-0.674358\pi$
$199$	95.3069	−	165.076i	0.478929	−	0.829530i	0.999708	+	0.0241618i	$0.00769168\pi$
$200$	−43.8528	+	7.73243i	−0.219264	+	0.0386622i
$201$		0			0
$202$	−144.684	+	52.6608i	−0.716260	+	0.260697i
$203$	−80.0235	−	219.863i	−0.394204	−	1.08307i
$204$		0			0
$205$	30.1004	+	170.708i	0.146831	+	0.832721i
$206$	−137.885	−	79.6077i	−0.669343	−	0.386445i
$207$		0			0
$208$	37.0532	+	64.1780i	0.178140	+	0.308548i
$209$	−146.754	−	174.895i	−0.702174	−	0.836818i
$210$		0			0
$211$	13.2835	−	75.3347i	0.0629551	−	0.357036i	−0.937015	−	0.349289i	$-0.886423\pi$
$211$	13.2835	−	75.3347i	0.0629551	−	0.357036i	0.999970	−	0.00774680i	$-0.00246591\pi$
$212$	−126.713	+	151.011i	−0.597702	+	0.712314i
$213$		0			0
$214$	−167.410	−	60.9324i	−0.782291	−	0.284731i
$215$		−	99.6100i		−	0.463302i
$216$		0			0
$217$	−114.277			−0.526623
$218$	34.4718	−	94.7105i	0.158128	−	0.434452i
$219$		0			0
$220$	30.5529	+	25.6369i	0.138877	+	0.116531i
$221$	240.788	+	42.4575i	1.08954	+	0.192115i
$222$		0			0
$223$	−38.1027	+	31.9720i	−0.170864	+	0.143372i	−0.724210	−	0.689580i	$-0.757795\pi$
$223$	−38.1027	+	31.9720i	−0.170864	+	0.143372i	0.553346	+	0.832952i	$0.313351\pi$
$224$	−40.3125	+	23.2744i	−0.179967	+	0.103904i
$225$		0			0
$226$	−28.9119	+	50.0769i	−0.127929	+	0.221579i
$227$	−298.583	+	52.6482i	−1.31534	+	0.231930i	−0.786922	−	0.617052i	$-0.788327\pi$
$227$	−298.583	+	52.6482i	−1.31534	+	0.231930i	−0.528420	+	0.848983i	$0.677216\pi$
$228$		0			0
$229$	−18.3111	+	6.66470i	−0.0799611	+	0.0291035i	−0.381691	−	0.924290i	$-0.624658\pi$
$229$	−18.3111	+	6.66470i	−0.0799611	+	0.0291035i	0.301730	+	0.953393i	$0.402436\pi$
$230$	−4.87638	−	13.3978i	−0.0212017	−	0.0582511i
$231$		0			0
$232$	−13.9652	−	79.2005i	−0.0601948	−	0.341382i
$233$	89.3347	+	51.5774i	0.383411	+	0.221362i	0.679301	−	0.733860i	$-0.262283\pi$
$233$	89.3347	+	51.5774i	0.383411	+	0.221362i	−0.295890	+	0.955222i	$0.595616\pi$
$234$		0			0
$235$	−81.6824	−	141.478i	−0.347585	−	0.602034i
$236$	132.112	+	157.445i	0.559797	+	0.667140i
$237$		0			0
$238$	−26.6691	+	151.248i	−0.112055	+	0.635495i
$239$	135.523	−	161.510i	0.567041	−	0.675773i	−0.403980	−	0.914768i	$-0.632374\pi$
$239$	135.523	−	161.510i	0.567041	−	0.675773i	0.971021	+	0.238995i	$0.0768179\pi$
$240$		0			0
$241$	58.1501	+	21.1649i	0.241287	+	0.0878211i	0.459833	−	0.888005i	$-0.347909\pi$
$241$	58.1501	+	21.1649i	0.241287	+	0.0878211i	−0.218546	+	0.975827i	$0.570132\pi$
$242$		−	110.362i		−	0.456040i
$243$		0			0
$244$	14.3721			0.0589021
$245$	19.4718	−	53.4982i	0.0794766	−	0.218360i
$246$		0			0
$247$	494.343	+	414.803i	2.00139	+	1.67936i
$248$	−38.6832	−	6.82089i	−0.155981	−	0.0275036i
$249$		0			0
$250$	134.292	−	112.685i	0.537169	−	0.450738i
$251$	99.2490	−	57.3014i	0.395414	−	0.228293i	−0.289089	−	0.957302i	$-0.593352\pi$
$251$	99.2490	−	57.3014i	0.395414	−	0.228293i	0.684503	+	0.729010i	$0.260019\pi$
$252$		0			0
$253$	10.8598	−	18.8097i	0.0429241	−	0.0743468i
$254$	−16.8579	+	2.97250i	−0.0663697	+	0.0117028i
$255$		0			0
$256$	−15.0351	+	5.47232i	−0.0587308	+	0.0213763i
$257$	60.5933	+	166.479i	0.235772	+	0.647777i	0.999996	+	0.00282659i	$0.000899733\pi$
$257$	60.5933	+	166.479i	0.235772	+	0.647777i	−0.764224	+	0.644950i	$0.776878\pi$
$258$		0			0
$259$	9.52682	+	54.0293i	0.0367831	+	0.208607i
$260$	−97.6292	−	56.3662i	−0.375497	−	0.216793i
$261$		0			0
$262$	52.5325	+	90.9889i	0.200506	+	0.347286i
$263$	−44.5945	−	53.1457i	−0.169561	−	0.202075i	0.674572	−	0.738209i	$-0.264328\pi$
$263$	−44.5945	−	53.1457i	−0.169561	−	0.202075i	−0.844133	+	0.536135i	$0.819884\pi$
$264$		0			0
$265$	52.0735	−	295.324i	0.196504	−	1.11443i
$266$	−260.553	+	310.515i	−0.979521	+	1.16735i
$267$		0			0
$268$	56.5132	+	20.5691i	0.210870	+	0.0767504i
$269$		−	117.199i		−	0.435684i	−0.975984	−	0.217842i	$-0.930098\pi$
$269$		−	117.199i		−	0.435684i	0.975984	−	0.217842i	$-0.0699018\pi$
$270$		0			0
$271$	401.626			1.48201			0.741007	−	0.671497i	$-0.234349\pi$
$271$	401.626			1.48201			0.741007	+	0.671497i	$0.234349\pi$
$272$	−18.0551	+	49.6060i	−0.0663791	+	0.182375i
$273$		0			0
$274$	−44.7624	−	37.5601i	−0.163366	−	0.137081i
$275$	101.624	+	17.9191i	0.369542	+	0.0651603i
$276$		0			0
$277$	−165.256	+	138.666i	−0.596592	+	0.500600i	−0.890348	−	0.455280i	$-0.849539\pi$
$277$	−165.256	+	138.666i	−0.596592	+	0.500600i	0.293756	+	0.955880i	$0.405095\pi$
$278$	173.965	−	100.439i	0.625773	−	0.361290i
$279$		0			0
$280$	35.4057	−	61.3244i	0.126449	−	0.219016i
$281$	313.847	−	55.3398i	1.11689	−	0.196939i	0.415418	−	0.909631i	$-0.363635\pi$
$281$	313.847	−	55.3398i	1.11689	−	0.196939i	0.701477	+	0.712692i	$0.252524\pi$
$282$		0			0
$283$	408.351	−	148.628i	1.44294	−	0.525186i	0.502328	−	0.864677i	$-0.332477\pi$
$283$	408.351	−	148.628i	1.44294	−	0.525186i	0.940609	+	0.339491i	$0.110255\pi$
$284$	6.68980	+	18.3801i	0.0235556	+	0.0647186i
$285$		0			0
$286$	−29.8212	−	169.124i	−0.104270	−	0.591344i
$287$	406.016	+	234.413i	1.41469	+	0.816771i
$288$		0			0
$289$	−57.4143	−	99.4445i	−0.198665	−	0.344099i
$290$	78.6390	+	93.7183i	0.271169	+	0.323167i
$291$		0			0
$292$	45.0081	−	255.254i	0.154137	−	0.874156i
$293$	−341.948	+	407.518i	−1.16706	+	1.39085i	−0.262267	+	0.964995i	$0.584470\pi$
$293$	−341.948	+	407.518i	−1.16706	+	1.39085i	−0.904793	+	0.425852i	$0.859974\pi$
$294$		0			0
$295$	−293.802	−	106.935i	−0.995938	−	0.362492i
$296$			18.8577i			0.0637084i
$297$		0			0
$298$	330.049			1.10755
$299$	−20.9969	+	57.6884i	−0.0702236	+	0.192938i
$300$		0			0
$301$	−206.380	−	173.173i	−0.685647	−	0.575326i
$302$	−10.8616	−	1.91519i	−0.0359654	−	0.00634167i
$303$		0			0
$304$	−106.732	+	89.5584i	−0.351091	+	0.294600i
$305$	−18.9341	+	10.9316i	−0.0620790	+	0.0358413i
$306$		0			0
$307$	−58.8902	+	102.001i	−0.191825	+	0.332250i	−0.945855	−	0.324590i	$-0.894774\pi$
$307$	−58.8902	+	102.001i	−0.191825	+	0.332250i	0.754030	+	0.656840i	$0.228107\pi$
$308$	106.233	−	18.7318i	0.344913	−	0.0608174i
$309$		0			0
$310$	56.1501	−	20.4370i	0.181129	−	0.0659256i
$311$	−5.42440	−	14.9034i	−0.0174418	−	0.0479210i	0.930666	−	0.365869i	$-0.119228\pi$
$311$	−5.42440	−	14.9034i	−0.0174418	−	0.0479210i	−0.948108	+	0.317948i	$0.897006\pi$
$312$		0			0
$313$	−15.1085	−	85.6847i	−0.0482700	−	0.273753i	0.951114	−	0.308839i	$-0.0999405\pi$
$313$	−15.1085	−	85.6847i	−0.0482700	−	0.273753i	−0.999384	+	0.0350863i	$0.988829\pi$
$314$	−31.2316	−	18.0316i	−0.0994636	−	0.0574254i
$315$		0			0
$316$	102.670	+	177.830i	0.324905	+	0.562752i
$317$	−120.434	−	143.528i	−0.379918	−	0.452769i	0.541870	−	0.840462i	$-0.317716\pi$
$317$	−120.434	−	143.528i	−0.379918	−	0.452769i	−0.921788	+	0.387693i	$0.873272\pi$
$318$		0			0
$319$	−32.3628	+	183.539i	−0.101451	+	0.575357i
$320$	15.6452	−	18.6452i	0.0488913	−	0.0582663i
$321$		0			0
$322$	−36.2362	−	13.1889i	−0.112535	−	0.0409593i
$323$			459.692i			1.42320i
$324$		0			0
$325$	−291.673			−0.897456
$326$	102.077	−	280.455i	0.313120	−	0.860291i
$327$		0			0
$328$	123.446	+	103.584i	0.376360	+	0.315803i
$329$	−435.131	−	76.7254i	−1.32259	−	0.233208i
$330$		0			0
$331$	−14.7758	+	12.3984i	−0.0446400	+	0.0374574i	−0.664835	−	0.746990i	$-0.731498\pi$
$331$	−14.7758	+	12.3984i	−0.0446400	+	0.0374574i	0.620195	+	0.784448i	$0.287054\pi$
$332$	187.640	−	108.334i	0.565180	−	0.326307i
$333$		0			0
$334$	−8.13353	+	14.0877i	−0.0243519	+	0.0421787i
$335$	−90.0967	+	15.8865i	−0.268946	+	0.0474223i
$336$		0			0
$337$	389.139	−	141.635i	1.15472	−	0.420282i	0.307509	−	0.951545i	$-0.400505\pi$
$337$	389.139	−	141.635i	1.15472	−	0.420282i	0.847207	+	0.531263i	$0.178282\pi$
$338$	84.2753	+	231.544i	0.249335	+	0.685043i
$339$		0			0
$340$	−13.9448	−	79.0849i	−0.0410141	−	0.232603i
$341$	78.8317	+	45.5135i	0.231178	+	0.133471i
$342$		0			0
$343$	124.615	+	215.839i	0.363308	+	0.629268i
$344$	−59.5239	−	70.9379i	−0.173035	−	0.206215i
$345$		0			0
$346$	−56.7334	+	321.751i	−0.163969	+	0.929917i
$347$	72.6578	−	86.5902i	0.209389	−	0.249540i	−0.651121	−	0.758974i	$-0.725701\pi$
$347$	72.6578	−	86.5902i	0.209389	−	0.249540i	0.860509	+	0.509434i	$0.170145\pi$
$348$		0			0
$349$	−24.8178	−	9.03294i	−0.0711112	−	0.0258824i	0.306220	−	0.951961i	$-0.400936\pi$
$349$	−24.8178	−	9.03294i	−0.0711112	−	0.0258824i	−0.377331	+	0.926079i	$0.623158\pi$
$350$		−	183.210i		−	0.523458i
$351$		0			0
$352$	37.0783			0.105336
$353$	−207.210	+	569.305i	−0.586998	+	1.61276i	0.188964	+	0.981984i	$0.439487\pi$
$353$	−207.210	+	569.305i	−0.586998	+	1.61276i	−0.775962	+	0.630779i	$0.782735\pi$
$354$		0			0
$355$	−22.7934	−	19.1259i	−0.0642068	−	0.0538759i
$356$	−45.8613	−	8.08659i	−0.128824	−	0.0227151i
$357$		0			0
$358$	89.6755	−	75.2466i	0.250490	−	0.210186i
$359$	387.446	−	223.692i	1.07924	−	0.623097i	0.148546	−	0.988906i	$-0.452541\pi$
$359$	387.446	−	223.692i	1.07924	−	0.623097i	0.930690	+	0.365808i	$0.119207\pi$
$360$		0			0
$361$	−426.135	+	738.088i	−1.18043	+	2.04456i
$362$	−231.483	+	40.8166i	−0.639455	+	0.112753i
$363$		0			0
$364$	−286.514	+	104.282i	−0.787125	+	0.286490i
$365$	134.855	+	370.510i	0.369465	+	1.01510i
$366$		0			0
$367$	25.2806	+	143.373i	0.0688844	+	0.390663i	0.999684	+	0.0251331i	$0.00800095\pi$
$367$	25.2806	+	143.373i	0.0688844	+	0.390663i	−0.930800	+	0.365529i	$0.880888\pi$
$368$	−11.4788	−	6.62731i	−0.0311925	−	0.0180090i
$369$		0			0
$370$	−14.3434	−	24.8435i	−0.0387660	−	0.0671446i
$371$	−521.345	−	621.314i	−1.40524	−	1.67470i
$372$		0			0
$373$	37.2253	−	211.115i	0.0997998	−	0.565993i	−0.893371	−	0.449320i	$-0.851666\pi$
$373$	37.2253	−	211.115i	0.0997998	−	0.565993i	0.993170	−	0.116672i	$-0.0372227\pi$
$374$	78.6349	−	93.7134i	0.210254	−	0.250571i
$375$		0			0
$376$	−142.714	−	51.9435i	−0.379558	−	0.138148i
$377$		−	526.777i		−	1.39729i
$378$		0			0
$379$	253.546			0.668988			0.334494	−	0.942398i	$-0.391435\pi$
$379$	253.546			0.668988			0.334494	+	0.942398i	$0.391435\pi$
$380$	72.4910	−	199.167i	0.190766	−	0.524125i
$381$		0			0
$382$	−135.635	−	113.811i	−0.355065	−	0.297935i
$383$	552.793	+	97.4722i	1.44332	+	0.254497i	0.839820	−	0.542864i	$-0.182660\pi$
$383$	552.793	+	97.4722i	1.44332	+	0.254497i	0.603502	+	0.797361i	$0.293771\pi$
$384$		0			0
$385$	−125.706	+	105.480i	−0.326509	+	0.273974i
$386$	113.009	−	65.2456i	0.292769	−	0.169030i
$387$		0			0
$388$	−51.2421	+	88.7539i	−0.132067	+	0.228747i
$389$	37.4969	−	6.61172i	0.0963931	−	0.0169967i	−0.125244	−	0.992126i	$-0.539971\pi$
$389$	37.4969	−	6.61172i	0.0963931	−	0.0169967i	0.221637	+	0.975129i	$0.428860\pi$
$390$		0			0
$391$	−41.0943	+	14.9571i	−0.105101	+	0.0382535i
$392$	−18.1020	−	49.7348i	−0.0461786	−	0.126875i
$393$		0			0
$394$	−9.66497	−	54.8128i	−0.0245304	−	0.139119i
$395$	−270.519	−	156.184i	−0.684858	−	0.395403i
$396$		0			0
$397$	−382.127	−	661.864i	−0.962538	−	1.66716i	−0.716090	−	0.698008i	$-0.754070\pi$
$397$	−382.127	−	661.864i	−0.962538	−	1.66716i	−0.246448	−	0.969156i	$-0.579263\pi$
$398$	173.275	+	206.502i	0.435365	+	0.518848i
$399$		0			0
$400$	10.9353	−	62.0172i	0.0273383	−	0.155043i
$401$	−10.0249	+	11.9472i	−0.0249998	+	0.0297936i	−0.778399	−	0.627769i	$-0.783968\pi$
$401$	−10.0249	+	11.9472i	−0.0249998	+	0.0297936i	0.753400	+	0.657563i	$0.228413\pi$
$402$		0			0
$403$	−241.773	−	87.9980i	−0.599932	−	0.218357i
$404$		−	217.746i		−	0.538976i
$405$		0			0
$406$	330.888			0.814995
$407$	14.9465	−	41.0652i	0.0367236	−	0.100897i
$408$		0			0
$409$	−346.354	−	290.625i	−0.846830	−	0.710575i	0.112259	−	0.993679i	$-0.464191\pi$
$409$	−346.354	−	290.625i	−0.846830	−	0.710575i	−0.959089	+	0.283104i	$0.908636\pi$
$410$	−241.417	−	42.5684i	−0.588823	−	0.103825i
$411$		0			0
$412$	172.486	−	144.733i	0.418656	−	0.351294i
$413$	−732.335	+	422.814i	−1.77321	+	1.02376i
$414$		0			0
$415$	−164.800	+	285.442i	−0.397109	+	0.687813i
$416$	−103.210	+	18.1987i	−0.248101	+	0.0437469i
$417$		0			0
$418$	303.406	−	110.431i	0.725852	−	0.264188i
$419$	−130.522	−	358.605i	−0.311507	−	0.855859i	−0.992353	−	0.123432i	$-0.960610\pi$
$419$	−130.522	−	358.605i	−0.311507	−	0.855859i	0.680846	−	0.732427i	$-0.261612\pi$
$420$		0			0
$421$	−18.0874	−	102.579i	−0.0429629	−	0.243655i	0.955762	−	0.294142i	$-0.0950338\pi$
$421$	−18.0874	−	102.579i	−0.0429629	−	0.243655i	−0.998725	+	0.0504869i	$0.983923\pi$
$422$	93.6891	+	54.0914i	0.222012	+	0.128179i
$423$		0			0
$424$	−139.392	−	241.434i	−0.328755	−	0.569420i
$425$	−133.554	−	159.163i	−0.314245	−	0.374502i
$426$		0			0
$427$	−10.2682	+	58.2339i	−0.0240473	+	0.136379i
$428$	161.949	−	193.004i	0.378386	−	0.450943i
$429$		0			0
$430$	132.374	+	48.1803i	0.307847	+	0.112047i
$431$			754.466i			1.75050i	0.483669	+	0.875251i	$0.339304\pi$
$431$			754.466i			1.75050i	−0.483669	+	0.875251i	$0.660696\pi$
$432$		0			0
$433$	−22.8890			−0.0528615			−0.0264308	−	0.999651i	$-0.508414\pi$
$433$	−22.8890			−0.0528615			−0.0264308	+	0.999651i	$0.508414\pi$
$434$	55.2747	−	151.866i	0.127361	−	0.349922i
$435$		0			0
$436$	109.190	+	91.6210i	0.250435	+	0.210140i
$437$	−113.668	−	20.0427i	−0.260110	−	0.0458643i
$438$		0			0
$439$	−345.329	+	289.765i	−0.786625	+	0.660057i	−0.944908	−	0.327337i	$-0.893849\pi$
$439$	−345.329	+	289.765i	−0.786625	+	0.660057i	0.158282	+	0.987394i	$0.449404\pi$
$440$	−48.8477	+	28.2022i	−0.111017	+	0.0640959i
$441$		0			0
$442$	−172.890	+	299.453i	−0.391153	+	0.677497i
$443$	−382.296	+	67.4092i	−0.862972	+	0.152165i	−0.587579	−	0.809167i	$-0.699919\pi$
$443$	−382.296	+	67.4092i	−0.862972	+	0.152165i	−0.275393	+	0.961332i	$0.588808\pi$
$444$		0			0
$445$	66.5694	−	24.2293i	0.149594	−	0.0544478i
$446$	−24.0585	−	66.1002i	−0.0539428	−	0.148207i
$447$		0			0
$448$	−11.4313	−	64.8299i	−0.0255162	−	0.144710i
$449$	93.1858	+	53.8008i	0.207541	+	0.119824i	0.600168	−	0.799874i	$-0.295100\pi$
$449$	93.1858	+	53.8008i	0.207541	+	0.119824i	−0.392627	+	0.919698i	$0.628434\pi$
$450$		0			0
$451$	−186.721	−	323.410i	−0.414015	−	0.717095i
$452$	−52.5641	−	62.6435i	−0.116292	−	0.138592i
$453$		0			0
$454$	74.4558	−	422.260i	0.164000	−	0.930088i
$455$	298.140	−	355.310i	0.655253	−	0.780901i
$456$		0			0
$457$	170.310	+	61.9876i	0.372669	+	0.135640i	0.521563	−	0.853213i	$-0.325349\pi$
$457$	170.310	+	61.9876i	0.372669	+	0.135640i	−0.148894	+	0.988853i	$0.547571\pi$
$458$		−	27.5577i		−	0.0601697i
$459$		0			0
$460$	20.1633			0.0438332
$461$	200.952	−	552.110i	0.435904	−	1.19764i	−0.506230	−	0.862399i	$-0.668961\pi$
$461$	200.952	−	552.110i	0.435904	−	1.19764i	0.942134	−	0.335237i	$-0.108817\pi$
$462$		0			0
$463$	−37.7513	−	31.6771i	−0.0815363	−	0.0684170i	0.601109	−	0.799167i	$-0.294726\pi$
$463$	−37.7513	−	31.6771i	−0.0815363	−	0.0684170i	−0.682645	+	0.730750i	$0.739170\pi$
$464$	112.006	+	19.7498i	0.241393	+	0.0425642i
$465$		0			0
$466$	−111.753	+	93.7718i	−0.239813	+	0.201227i
$467$	614.382	−	354.714i	1.31559	−	0.759558i	0.332577	−	0.943076i	$-0.392082\pi$
$467$	614.382	−	354.714i	1.31559	−	0.759558i	0.983016	+	0.183518i	$0.0587484\pi$
$468$		0			0
$469$	−123.719	+	214.288i	−0.263794	+	0.456905i
$470$	227.523	−	40.1184i	0.484091	−	0.0853583i
$471$		0			0
$472$	−273.134	+	99.4126i	−0.578674	+	0.210620i
$473$	73.3965	+	201.655i	0.155172	+	0.426332i
$474$		0			0
$475$	−95.2248	−	540.047i	−0.200473	−	1.13694i
$476$	−188.098	−	108.598i	−0.395163	−	0.228147i
$477$		0			0
$478$	149.084	+	258.220i	0.311890	+	0.540210i
$479$	271.827	+	323.951i	0.567489	+	0.676308i	0.971114	−	0.238617i	$-0.0766941\pi$
$479$	271.827	+	323.951i	0.567489	+	0.676308i	−0.403624	+	0.914925i	$0.632250\pi$
$480$		0			0
$481$	−21.4491	+	121.644i	−0.0445927	+	0.252898i
$482$	−56.2531	+	67.0399i	−0.116708	+	0.139087i
$483$		0			0
$484$	146.663	+	53.3808i	0.303022	+	0.110291i
$485$		−	155.902i		−	0.321446i
$486$		0			0
$487$	444.129			0.911969			0.455985	−	0.889988i	$-0.349287\pi$
$487$	444.129			0.911969			0.455985	+	0.889988i	$0.349287\pi$
$488$	−6.95164	+	19.0995i	−0.0142452	+	0.0391382i
$489$		0			0
$490$	61.6769	+	51.7530i	0.125871	+	0.105618i
$491$	−399.029	−	70.3596i	−0.812686	−	0.143298i	−0.248166	−	0.968718i	$-0.579828\pi$
$491$	−399.029	−	70.3596i	−0.812686	−	0.143298i	−0.564520	+	0.825419i	$0.690939\pi$
$492$		0			0
$493$	287.458	−	241.206i	0.583079	−	0.489261i
$494$	−790.351	+	456.309i	−1.59990	+	0.923703i
$495$		0			0
$496$	27.7751	−	48.1079i	0.0559982	−	0.0969917i
$497$	−79.2533	+	13.9745i	−0.159463	+	0.0281177i
$498$		0			0
$499$	−545.267	+	198.461i	−1.09272	+	0.397718i	−0.824628	−	0.565676i	$-0.808615\pi$
$499$	−545.267	+	198.461i	−1.09272	+	0.397718i	−0.268092	+	0.963393i	$0.586393\pi$
$500$	84.7937	+	232.969i	0.169587	+	0.465938i
$501$		0			0
$502$	28.1437	+	159.611i	0.0560631	+	0.317949i
$503$	284.955	+	164.519i	0.566510	+	0.327075i	0.755754	−	0.654855i	$-0.227270\pi$
$503$	284.955	+	164.519i	0.566510	+	0.327075i	−0.189244	+	0.981930i	$0.560604\pi$
$504$		0			0
$505$	165.621	+	286.864i	0.327962	+	0.568047i
$506$	19.7440	+	23.5299i	0.0390197	+	0.0465019i
$507$		0			0
$508$	4.20376	−	23.8407i	0.00827511	−	0.0469305i
$509$	346.327	−	412.736i	0.680406	−	0.810876i	−0.309754	−	0.950817i	$-0.600247\pi$
$509$	346.327	−	412.736i	0.680406	−	0.810876i	0.990160	+	0.139941i	$0.0446911\pi$
$510$		0			0
$511$	1002.10	+	364.734i	1.96105	+	0.713765i
$512$		−	22.6274i		−	0.0441942i
$513$		0			0
$514$	−250.546			−0.487444
$515$	−117.151	+	321.869i	−0.227477	+	0.624989i
$516$		0			0
$517$	269.608	+	226.228i	0.521486	+	0.437579i
$518$	−76.4089	−	13.4730i	−0.147508	−	0.0260096i
$519$		0			0
$520$	122.129	−	102.478i	0.234863	−	0.197073i
$521$	−258.670	+	149.343i	−0.496488	+	0.286647i	−0.727262	−	0.686360i	$-0.759207\pi$
$521$	−258.670	+	149.343i	−0.496488	+	0.286647i	0.230774	+	0.973007i	$0.425874\pi$
$522$		0			0
$523$	416.746	−	721.825i	0.796837	−	1.38016i	−0.124829	−	0.992178i	$-0.539838\pi$
$523$	416.746	−	721.825i	0.796837	−	1.38016i	0.921666	−	0.387984i	$-0.126828\pi$
$524$	−146.327	+	25.8014i	−0.279250	+	0.0492393i
$525$		0			0
$526$	92.1966	−	33.5568i	0.175279	−	0.0637962i
$527$	−62.6853	−	172.226i	−0.118947	−	0.326805i
$528$		0			0
$529$	89.9532	+	510.150i	0.170044	+	0.964366i
$530$	367.276	+	212.047i	0.692974	+	0.400089i
$531$		0			0
$532$	−286.624	−	496.448i	−0.538767	−	0.933172i
$533$	678.486	+	808.588i	1.27296	+	1.51705i
$534$		0			0
$535$	−66.5542	+	377.448i	−0.124400	+	0.705509i
$536$	−54.6697	+	65.1528i	−0.101996	+	0.121554i
$537$		0			0
$538$	155.749	+	56.6880i	0.289496	+	0.105368i
$539$			122.652i			0.227555i
$540$		0			0
$541$	639.685			1.18241			0.591206	−	0.806521i	$-0.298652\pi$
$541$	639.685			1.18241			0.591206	+	0.806521i	$0.298652\pi$
$542$	−194.262	+	533.731i	−0.358417	+	0.984743i
$543$		0			0
$544$	−57.1896	−	47.9878i	−0.105128	−	0.0882129i
$545$	−213.537	−	37.6523i	−0.391811	−	0.0690868i
$546$		0			0
$547$	310.339	−	260.405i	0.567347	−	0.476060i	−0.313418	−	0.949615i	$-0.601474\pi$
$547$	310.339	−	260.405i	0.567347	−	0.476060i	0.880764	+	0.473555i	$0.157030\pi$
$548$	71.5656	−	41.3184i	0.130594	−	0.0753986i
$549$		0			0
$550$	−72.9677	+	126.384i	−0.132669	+	0.229789i
$551$	975.353	−	171.981i	1.77015	−	0.312125i
$552$		0			0
$553$	−793.896	+	288.954i	−1.43562	+	0.522522i
$554$	−104.345	−	286.685i	−0.188348	−	0.517481i
$555$		0			0
$556$	49.3305	+	279.767i	0.0887240	+	0.503179i
$557$	−810.145	−	467.737i	−1.45448	−	0.839744i	−0.455748	−	0.890109i	$-0.650628\pi$
$557$	−810.145	−	467.737i	−1.45448	−	0.839744i	−0.998731	+	0.0503648i	$0.983962\pi$
$558$		0			0
$559$	−303.280	−	525.297i	−0.542541	−	0.939709i
$560$	64.3703	+	76.7135i	0.114947	+	0.136988i
$561$		0			0
$562$	−78.2623	+	443.847i	−0.139257	+	0.789764i
$563$	−82.3153	+	98.0996i	−0.146208	+	0.174244i	−0.834178	−	0.551495i	$-0.814058\pi$
$563$	−82.3153	+	98.0996i	−0.146208	+	0.174244i	0.687970	+	0.725739i	$0.258502\pi$
$564$		0			0
$565$	116.896	+	42.5468i	0.206896	+	0.0753041i
$566$			614.558i			1.08579i
$567$		0			0
$568$	−27.6616			−0.0486999
$569$	10.7972	−	29.6651i	0.0189758	−	0.0521355i	−0.929843	−	0.367956i	$-0.880058\pi$
$569$	10.7972	−	29.6651i	0.0189758	−	0.0521355i	0.948819	+	0.315821i	$0.102280\pi$
$570$		0			0
$571$	323.739	+	271.649i	0.566968	+	0.475743i	0.880638	−	0.473789i	$-0.157114\pi$
$571$	323.739	+	271.649i	0.566968	+	0.475743i	−0.313670	+	0.949532i	$0.601559\pi$
$572$	239.178	+	42.1735i	0.418143	+	0.0737300i
$573$		0			0
$574$	−507.904	+	426.182i	−0.884849	+	0.742477i
$575$	45.1793	−	26.0843i	0.0785726	−	0.0453639i
$576$		0			0
$577$	42.1505	−	73.0068i	0.0730511	−	0.126528i	−0.827186	−	0.561928i	$-0.810060\pi$
$577$	42.1505	−	73.0068i	0.0730511	−	0.126528i	0.900237	+	0.435400i	$0.143393\pi$
$578$	159.925	−	28.1991i	0.276687	−	0.0487874i
$579$		0			0
$580$	−162.582	+	59.1748i	−0.280313	+	0.102026i
$581$	304.895	+	837.691i	0.524776	+	1.44181i
$582$		0			0
$583$	112.186	+	636.238i	0.192429	+	1.09132i
$584$	317.443	+	183.276i	0.543567	+	0.313829i
$585$		0			0
$586$	−376.165	−	651.537i	−0.641919	−	1.11184i
$587$	474.170	+	565.094i	0.807786	+	0.962682i	0.999825	−	0.0187054i	$-0.00595445\pi$
$587$	474.170	+	565.094i	0.807786	+	0.962682i	−0.192039	+	0.981387i	$0.561510\pi$
$588$		0			0
$589$	83.9991	−	476.383i	0.142613	−	0.808799i
$590$	284.218	−	338.717i	0.481725	−	0.574097i
$591$		0			0
$592$	−25.0605	−	9.12127i	−0.0423319	−	0.0154075i
$593$		−	361.460i		−	0.609545i	−0.952425	−	0.304773i	$-0.901420\pi$
$593$		−	361.460i		−	0.609545i	0.952425	−	0.304773i	$-0.0985804\pi$
$594$		0			0
$595$	330.405			0.555302
$596$	−159.641	+	438.611i	−0.267855	+	0.735925i
$597$		0			0
$598$	−66.5077	−	55.8066i	−0.111217	−	0.0933220i
$599$	−201.974	−	35.6135i	−0.337185	−	0.0594549i	0.00249203	−	0.999997i	$-0.499207\pi$
$599$	−201.974	−	35.6135i	−0.337185	−	0.0594549i	−0.339677	+	0.940542i	$0.610318\pi$
$600$		0			0
$601$	726.408	−	609.528i	1.20866	−	1.01419i	0.209326	−	0.977846i	$-0.432873\pi$
$601$	726.408	−	609.528i	1.20866	−	1.01419i	0.999339	−	0.0363443i	$-0.0115713\pi$
$602$	329.958	−	190.501i	0.548103	−	0.316448i
$603$		0			0
$604$	7.79876	−	13.5079i	0.0129119	−	0.0223640i
$605$	−233.818	+	41.2285i	−0.386477	+	0.0681463i
$606$		0			0
$607$	382.467	−	139.207i	0.630094	−	0.229335i	−0.00717822	−	0.999974i	$-0.502285\pi$
$607$	382.467	−	139.207i	0.630094	−	0.229335i	0.637272	+	0.770639i	$0.280063\pi$
$608$	−67.3916	−	185.157i	−0.110841	−	0.304534i
$609$		0			0
$610$	−5.36907	−	30.4495i	−0.00880176	−	0.0499173i
$611$	−861.511	−	497.393i	−1.41000	−	0.814064i
$612$		0			0
$613$	−325.258	−	563.364i	−0.530601	−	0.919028i	−0.999362	−	0.0357032i	$-0.988633\pi$
$613$	−325.258	−	563.364i	−0.530601	−	0.919028i	0.468761	−	0.883325i	$-0.344700\pi$
$614$	−107.067	−	127.597i	−0.174376	−	0.207813i
$615$		0			0
$616$	−26.4907	+	150.236i	−0.0430044	+	0.243890i
$617$	72.2760	−	86.1351i	0.117141	−	0.139603i	−0.704287	−	0.709915i	$-0.748733\pi$
$617$	72.2760	−	86.1351i	0.117141	−	0.139603i	0.821428	+	0.570312i	$0.193178\pi$
$618$		0			0
$619$	−595.574	−	216.771i	−0.962155	−	0.350196i	−0.187277	−	0.982307i	$-0.559966\pi$
$619$	−595.574	−	216.771i	−0.962155	−	0.350196i	−0.774878	+	0.632111i	$0.782188\pi$
$620$			84.5044i			0.136297i
$621$		0			0
$622$	22.4293			0.0360599
$623$	65.5316	−	180.047i	0.105187	−	0.288999i
$624$		0			0
$625$	12.5974	+	10.5704i	0.0201558	+	0.0169127i
$626$	121.176	+	21.3667i	0.193573	+	0.0341321i
$627$		0			0
$628$	39.0690	−	32.7828i	0.0622118	−	0.0522019i
$629$	−76.2013	+	43.9949i	−0.121147	+	0.0699441i
$630$		0			0
$631$	−320.988	+	555.967i	−0.508697	+	0.881089i	0.491252	+	0.871017i	$0.336539\pi$
$631$	−320.988	+	555.967i	−0.508697	+	0.881089i	−0.999949	+	0.0100717i	$0.996794\pi$
$632$	−285.983	+	50.4265i	−0.452504	+	0.0797887i
$633$		0			0
$634$	248.991	−	90.6251i	0.392730	−	0.142942i
$635$	12.5954	+	34.6056i	0.0198353	+	0.0544970i
$636$		0			0
$637$	−60.1998	−	341.410i	−0.0945052	−	0.535966i
$638$	−228.256	−	131.784i	−0.357768	−	0.206557i
$639$		0			0
$640$	17.2107	+	29.8098i	0.0268917	+	0.0465778i
$641$	−114.585	−	136.557i	−0.178759	−	0.213037i	0.669223	−	0.743062i	$-0.266627\pi$
$641$	−114.585	−	136.557i	−0.178759	−	0.213037i	−0.847982	+	0.530025i	$0.822183\pi$
$642$		0			0
$643$	−98.7806	+	560.213i	−0.153625	+	0.871248i	0.806408	+	0.591360i	$0.201409\pi$
$643$	−98.7806	+	560.213i	−0.153625	+	0.871248i	−0.960032	+	0.279889i	$0.909702\pi$
$644$	35.0541	−	41.7759i	0.0544319	−	0.0648694i
$645$		0			0
$646$	−610.897	−	222.348i	−0.945661	−	0.344192i
$647$		−	331.991i		−	0.513124i	−0.966528	−	0.256562i	$-0.917410\pi$
$647$		−	331.991i		−	0.513124i	0.966528	−	0.256562i	$-0.0825898\pi$
$648$		0			0
$649$	673.580			1.03787
$650$	141.079	−	387.612i	0.217045	−	0.596326i
$651$		0			0
$652$	323.330	+	271.306i	0.495905	+	0.416114i
$653$	−867.467	−	152.958i	−1.32843	−	0.234239i	−0.536011	−	0.844211i	$-0.680070\pi$
$653$	−867.467	−	152.958i	−1.32843	−	0.234239i	−0.792423	+	0.609972i	$0.791181\pi$
$654$		0			0
$655$	173.149	−	145.289i	0.264350	−	0.221816i
$656$	−197.364	+	113.948i	−0.300860	+	0.173702i
$657$		0			0
$658$	312.431	−	541.146i	0.474819	−	0.822410i
$659$	956.120	−	168.590i	1.45087	−	0.255827i	0.607994	−	0.793942i	$-0.291975\pi$
$659$	956.120	−	168.590i	1.45087	−	0.255827i	0.842871	+	0.538115i	$0.180863\pi$
$660$		0			0
$661$	207.696	−	75.5952i	0.314215	−	0.114365i	−0.180099	−	0.983649i	$-0.557642\pi$
$661$	207.696	−	75.5952i	0.314215	−	0.114365i	0.494313	+	0.869284i	$0.335419\pi$
$662$	−9.32965	−	25.6330i	−0.0140931	−	0.0387205i
$663$		0			0
$664$	53.2083	+	301.759i	0.0801330	+	0.454457i
$665$	755.209	+	436.020i	1.13565	+	0.655669i
$666$		0			0
$667$	47.1096	+	81.5962i	0.0706291	+	0.122333i
$668$	−14.7874	−	17.6229i	−0.0221368	−	0.0263816i
$669$		0			0
$670$	22.4669	−	127.416i	0.0335327	−	0.190173i
$671$	30.2763	−	36.0819i	0.0451211	−	0.0537733i
$672$		0			0
$673$	−484.870	−	176.478i	−0.720461	−	0.262226i	−0.0443393	−	0.999017i	$-0.514118\pi$
$673$	−484.870	−	176.478i	−0.720461	−	0.262226i	−0.676121	+	0.736790i	$0.736340\pi$
$674$			585.645i			0.868909i
$675$		0			0
$676$	−348.469			−0.515486
$677$	11.8258	−	32.4910i	0.0174679	−	0.0479927i	−0.930652	−	0.365905i	$-0.880760\pi$
$677$	11.8258	−	32.4910i	0.0174679	−	0.0479927i	0.948120	+	0.317912i	$0.102982\pi$
$678$		0			0
$679$	−323.009	−	271.037i	−0.475713	−	0.399171i
$680$	111.843	+	19.7209i	0.164475	+	0.0290014i
$681$		0			0
$682$	−98.6142	+	82.7471i	−0.144596	+	0.121330i
$683$	−502.287	+	289.996i	−0.735413	+	0.424591i	−0.820399	−	0.571791i	$-0.806249\pi$
$683$	−502.287	+	289.996i	−0.735413	+	0.424591i	0.0849858	+	0.996382i	$0.472915\pi$
$684$		0			0
$685$	−62.8547	+	108.868i	−0.0917587	+	0.158931i
$686$	−347.109	+	61.2046i	−0.505989	+	0.0892195i
$687$		0			0
$688$	123.062	−	44.7910i	0.178870	−	0.0651032i
$689$	−624.554	−	1715.95i	−0.906465	−	2.49049i
$690$		0			0
$691$	−67.3628	−	382.033i	−0.0974859	−	0.552870i	−0.993957	−	0.109768i	$-0.964989\pi$
$691$	−67.3628	−	382.033i	−0.0974859	−	0.552870i	0.896471	−	0.443102i	$-0.146122\pi$
$692$	−400.142	−	231.022i	−0.578240	−	0.333847i
$693$		0			0
$694$	79.9282	+	138.440i	0.115170	+	0.199481i
$695$	−277.784	−	331.050i	−0.399689	−	0.476331i
$696$		0			0
$697$	−130.568	+	740.488i	−0.187329	+	1.06239i
$698$	24.0082	−	28.6119i	0.0343957	−	0.0409912i
$699$		0			0
$700$	243.473	+	88.6170i	0.347819	+	0.126596i
$701$		−	1037.76i		−	1.48040i	−0.672387	−	0.740200i	$-0.734731\pi$
$701$		−	1037.76i		−	1.48040i	0.672387	−	0.740200i	$-0.265269\pi$
$702$		0			0
$703$	−232.232			−0.330344
$704$	−17.9344	+	49.2743i	−0.0254750	+	0.0699919i
$705$		0			0
$706$	−656.339	−	550.734i	−0.929659	−	0.780077i
$707$	882.280	+	155.570i	1.24792	+	0.220042i
$708$		0			0
$709$	−818.303	+	686.637i	−1.15416	+	0.968459i	−0.999809	−	0.0195564i	$-0.993775\pi$
$709$	−818.303	+	686.637i	−1.15416	+	0.968459i	−0.154356	+	0.988015i	$0.549330\pi$
$710$	36.4419	−	21.0397i	0.0513266	−	0.0296334i
$711$		0			0
$712$	32.9291	−	57.0349i	0.0462488	−	0.0801052i
$713$	45.3195	−	7.99104i	0.0635616	−	0.0112076i
$714$		0			0
$715$	−347.176	+	126.362i	−0.485560	+	0.176730i
$716$	56.6221	+	155.568i	0.0790812	+	0.217274i
$717$		0			0
$718$	109.867	+	623.084i	0.153017	+	0.867805i
$719$	−642.439	−	370.913i	−0.893518	−	0.515873i	−0.0184263	−	0.999830i	$-0.505866\pi$
$719$	−642.439	−	370.913i	−0.893518	−	0.515873i	−0.875092	+	0.483957i	$0.839199\pi$
$720$		0			0
$721$	463.206	+	802.296i	0.642449	+	1.11276i
$722$	−774.747	−	923.307i	−1.07306	−	1.27882i
$723$		0			0
$724$	57.7234	−	327.366i	0.0797285	−	0.452163i
$725$	−287.740	+	342.915i	−0.396883	+	0.472986i
$726$		0			0
$727$	−148.771	−	54.1481i	−0.204637	−	0.0744816i	0.237668	−	0.971346i	$-0.423617\pi$
$727$	−148.771	−	54.1481i	−0.204637	−	0.0744816i	−0.442305	+	0.896865i	$0.645839\pi$
$728$		−	431.196i		−	0.592302i
$729$		0			0
$730$	−557.608			−0.763847
$731$	147.781	−	406.026i	0.202163	−	0.555438i
$732$		0			0
$733$	−419.711	−	352.179i	−0.572594	−	0.480463i	0.309912	−	0.950765i	$-0.399700\pi$
$733$	−419.711	−	352.179i	−0.572594	−	0.480463i	−0.882505	+	0.470302i	$0.844145\pi$
$734$	−202.760	−	35.7521i	−0.276240	−	0.0487086i
$735$		0			0
$736$	14.3594	−	12.0490i	0.0195101	−	0.0163709i
$737$	170.690	−	98.5482i	0.231602	−	0.133715i
$738$		0			0
$739$	264.592	−	458.286i	0.358040	−	0.620143i	−0.629593	−	0.776925i	$-0.716778\pi$
$739$	264.592	−	458.286i	0.358040	−	0.620143i	0.987633	+	0.156781i	$0.0501118\pi$
$740$	39.9529	−	7.04478i	0.0539904	−	0.00951997i
$741$		0			0
$742$	1077.85	−	392.305i	1.45263	−	0.528713i
$743$	75.5254	+	207.504i	0.101649	+	0.279279i	0.980084	−	0.198583i	$-0.0636340\pi$
$743$	75.5254	+	207.504i	0.101649	+	0.279279i	−0.878435	+	0.477862i	$0.841412\pi$
$744$		0			0
$745$	−123.298	−	699.260i	−0.165501	−	0.938605i
$746$	262.551	+	151.584i	0.351945	+	0.203196i
$747$		0			0
$748$	86.5033	+	149.828i	0.115646	+	0.200305i
$749$	666.320	+	794.090i	0.889613	+	1.06020i
$750$		0			0
$751$	62.2580	−	353.083i	0.0829001	−	0.470150i	−0.914890	−	0.403703i	$-0.867723\pi$
$751$	62.2580	−	353.083i	0.0829001	−	0.470150i	0.997790	−	0.0664464i	$-0.0211661\pi$
$752$	138.058	−	164.531i	0.183588	−	0.218792i
$753$		0			0
$754$	700.048	+	254.797i	0.928446	+	0.337927i
$755$			23.7274i			0.0314270i
$756$		0			0
$757$	−1279.40			−1.69009			−0.845044	−	0.534697i	$-0.820426\pi$
$757$	−1279.40			−1.69009			−0.845044	+	0.534697i	$0.820426\pi$
$758$	−122.638	+	336.944i	−0.161791	+	0.444518i
$759$		0			0
$760$	229.616	+	192.670i	0.302126	+	0.253514i
$761$	1032.55	+	182.067i	1.35684	+	0.239247i	0.804292	−	0.594234i	$-0.202545\pi$
$761$	1032.55	+	182.067i	1.35684	+	0.239247i	0.552547	+	0.833482i	$0.313656\pi$
$762$		0			0
$763$	−449.247	+	376.963i	−0.588791	+	0.494054i
$764$	216.852	−	125.200i	0.283838	−	0.163874i
$765$		0			0
$766$	−396.913	+	687.474i	−0.518164	+	0.897486i
$767$	−1874.96	+	330.606i	−2.44453	+	0.431037i
$768$		0			0
$769$	−838.041	+	305.022i	−1.08978	+	0.396648i	−0.823540	−	0.567259i	$-0.808004\pi$
$769$	−838.041	+	305.022i	−1.08978	+	0.396648i	−0.266241	+	0.963906i	$0.585782\pi$
$770$	−79.3723	−	218.074i	−0.103081	−	0.283212i
$771$		0			0
$772$	32.0455	+	181.739i	0.0415097	+	0.235413i
$773$	1112.34	+	642.211i	1.43899	+	0.830803i	0.997780	−	0.0665994i	$-0.0212149\pi$
$773$	1112.34	+	642.211i	1.43899	+	0.830803i	0.441213	+	0.897402i	$0.354548\pi$
$774$		0			0
$775$	109.319	+	189.347i	0.141057	+	0.244318i
$776$	−93.1621	−	111.026i	−0.120054	−	0.143075i
$777$		0			0
$778$	−9.35038	+	53.0286i	−0.0120185	+	0.0681602i
$779$	−1275.63	+	1520.24i	−1.63752	+	1.95152i
$780$		0			0
$781$	60.2368	+	21.9244i	0.0771278	+	0.0280722i
$782$		−	61.8459i		−	0.0790868i
$783$		0			0
$784$	74.8496			0.0954715
$785$	−26.5353	+	72.9051i	−0.0338029	+	0.0928727i
$786$		0			0
$787$	−9.06386	−	7.60548i	−0.0115170	−	0.00966389i	0.637011	−	0.770855i	$-0.280171\pi$
$787$	−9.06386	−	7.60548i	−0.0115170	−	0.00966389i	−0.648528	+	0.761191i	$0.724615\pi$
$788$	77.5170	+	13.6683i	0.0983718	+	0.0173456i
$789$		0			0
$790$	338.404	−	283.955i	0.428360	−	0.359437i
$791$	291.378	−	168.227i	0.368366	−	0.212676i
$792$		0			0
$793$	−66.5665	+	115.297i	−0.0839426	+	0.145393i
$794$	1064.40	−	187.682i	1.34055	−	0.236376i
$795$		0			0
$796$	−358.237	+	130.388i	−0.450046	+	0.163803i
$797$	356.953	+	980.720i	0.447871	+	1.23051i	0.934203	+	0.356741i	$0.116112\pi$
$797$	356.953	+	980.720i	0.447871	+	1.23051i	−0.486332	+	0.873774i	$0.661666\pi$
$798$		0			0
$799$	−123.053	−	697.870i	−0.154009	−	0.873429i
$800$	77.1270	+	44.5293i	0.0964088	+	0.0556616i
$801$		0			0
$802$	−11.0280	−	19.1011i	−0.0137507	−	0.0238169i
$803$	−546.012	−	650.712i	−0.679966	−	0.810351i
$804$		0			0
$805$	−14.4057	+	81.6990i	−0.0178953	+	0.101489i
$806$	233.886	−	278.734i	0.290181	−	0.345824i
$807$		0			0
$808$	289.369	+	105.322i	0.358130	+	0.130349i
$809$			924.372i			1.14261i	0.820738	+	0.571305i	$0.193563\pi$
$809$			924.372i			1.14261i	−0.820738	+	0.571305i	$0.806437\pi$
$810$		0			0
$811$	−605.678			−0.746828			−0.373414	−	0.927665i	$-0.621813\pi$
$811$	−605.678			−0.746828			−0.373414	+	0.927665i	$0.621813\pi$
$812$	−160.047	+	439.726i	−0.197102	+	0.541534i
$813$		0			0
$814$	47.3431	+	39.7256i	0.0581611	+	0.0488030i
$815$	−632.320	−	111.495i	−0.775853	−	0.136804i
$816$		0			0
$817$	873.599	−	733.036i	1.06928	−	0.897229i
$818$	553.747	−	319.706i	0.676952	−	0.390839i
$819$		0			0
$820$	173.341	−	300.236i	0.211392	−	0.366141i
$821$	325.347	−	57.3675i	0.396282	−	0.0698752i	0.0280437	−	0.999607i	$-0.491072\pi$
$821$	325.347	−	57.3675i	0.396282	−	0.0698752i	0.368238	+	0.929732i	$0.379961\pi$
$822$		0			0
$823$	59.1086	−	21.5138i	0.0718209	−	0.0261407i	−0.305860	−	0.952077i	$-0.598944\pi$
$823$	59.1086	−	21.5138i	0.0718209	−	0.0261407i	0.377681	+	0.925936i	$0.376722\pi$
$824$	108.910	+	299.227i	0.132172	+	0.363140i
$825$		0			0
$826$	−207.665	−	1177.73i	−0.251411	−	1.42582i
$827$	248.798	+	143.644i	0.300844	+	0.173692i	0.642822	−	0.766016i	$-0.277763\pi$
$827$	248.798	+	143.644i	0.300844	+	0.173692i	−0.341978	+	0.939708i	$0.611097\pi$
$828$		0			0
$829$	575.280	+	996.414i	0.693945	+	1.20195i	0.970535	+	0.240960i	$0.0774621\pi$
$829$	575.280	+	996.414i	0.693945	+	1.20195i	−0.276590	+	0.960988i	$0.589205\pi$
$830$	−299.620	−	357.073i	−0.360987	−	0.430208i
$831$		0			0
$832$	25.7369	−	145.961i	0.0309337	−	0.175434i
$833$	158.740	−	189.179i	0.190564	−	0.227105i
$834$		0			0
$835$	32.8854	+	11.9693i	0.0393837	+	0.0143345i
$836$			456.618i			0.546194i
$837$		0			0
$838$	539.692			0.644023
$839$	−154.375	+	424.141i	−0.183999	+	0.505532i	−0.997058	−	0.0766485i	$-0.975578\pi$
$839$	−154.375	+	424.141i	−0.183999	+	0.505532i	0.813060	+	0.582180i	$0.197800\pi$
$840$		0			0
$841$	24.9200	+	20.9104i	0.0296314	+	0.0248637i
$842$	145.068	+	25.5794i	0.172290	+	0.0303794i
$843$		0			0
$844$	−117.200	+	98.3424i	−0.138862	+	0.116519i
$845$	459.080	−	265.050i	0.543289	−	0.313668i
$846$		0			0
$847$	−321.076	+	556.120i	−0.379074	+	0.656576i
$848$	388.271	−	68.4626i	0.457867	−	0.0807342i
$849$		0			0
$850$	276.115	−	100.498i	0.324841	−	0.118233i
$851$	−7.55619	−	20.7605i	−0.00887919	−	0.0243954i
$852$		0			0
$853$	242.826	+	1377.14i	0.284673	+	1.61446i	0.706450	+	0.707763i	$0.250296\pi$
$853$	242.826	+	1377.14i	0.284673	+	1.61446i	−0.421776	+	0.906700i	$0.638593\pi$
$854$	−72.4219	−	41.8128i	−0.0848032	−	0.0489612i
$855$		0			0
$856$	178.154	+	308.572i	0.208124	+	0.360482i
$857$	−523.122	−	623.433i	−0.610411	−	0.727459i	0.368979	−	0.929438i	$-0.379707\pi$
$857$	−523.122	−	623.433i	−0.610411	−	0.727459i	−0.979390	+	0.201978i	$0.935263\pi$
$858$		0			0
$859$	284.770	−	1615.01i	0.331514	−	1.88011i	−0.127747	−	0.991807i	$-0.540775\pi$
$859$	284.770	−	1615.01i	0.331514	−	1.88011i	0.459261	−	0.888301i	$-0.348114\pi$
$860$	−128.056	+	152.611i	−0.148902	+	0.177455i
$861$		0			0
$862$	−1002.63	−	364.927i	−1.16314	−	0.423350i
$863$			431.616i			0.500134i	0.968229	+	0.250067i	$0.0804527\pi$
$863$			431.616i			0.500134i	−0.968229	+	0.250067i	$0.919547\pi$
$864$		0			0
$865$	702.874			0.812571
$866$	11.0712	−	30.4178i	0.0127843	−	0.0351245i
$867$		0			0
$868$	175.083	+	146.912i	0.201708	+	0.169254i
$869$	662.734	+	116.858i	0.762640	+	0.134474i
$870$		0			0
$871$	−426.760	+	358.094i	−0.489965	+	0.411130i
$872$	−174.571	+	100.789i	−0.200197	+	0.115584i
$873$		0			0
$874$	81.6152	−	141.362i	0.0933813	−	0.161741i
$875$	−1004.54	+	177.128i	−1.14805	+	0.202432i
$876$		0			0
$877$	1231.89	−	448.372i	1.40467	−	0.511257i	0.475107	−	0.879928i	$-0.342409\pi$
$877$	1231.89	−	448.372i	1.40467	−	0.511257i	0.929560	+	0.368671i	$0.120187\pi$
$878$	−218.045	−	599.072i	−0.248342	−	0.682315i
$879$		0			0
$880$	−13.8516	−	78.5560i	−0.0157404	−	0.0892682i
$881$	577.964	+	333.687i	0.656031	+	0.378760i	0.790763	−	0.612122i	$-0.209684\pi$
$881$	577.964	+	333.687i	0.656031	+	0.378760i	−0.134732	+	0.990882i	$0.543017\pi$
$882$		0			0
$883$	628.528	+	1088.64i	0.711809	+	1.23289i	0.964177	+	0.265259i	$0.0854574\pi$
$883$	628.528	+	1088.64i	0.711809	+	1.23289i	−0.252368	+	0.967631i	$0.581209\pi$
$884$	−314.327	−	374.600i	−0.355573	−	0.423756i
$885$		0			0
$886$	95.3310	−	540.649i	0.107597	−	0.610213i
$887$	−139.550	+	166.309i	−0.157328	+	0.187496i	−0.838950	−	0.544208i	$-0.816830\pi$
$887$	−139.550	+	166.309i	−0.157328	+	0.187496i	0.681622	+	0.731704i	$0.261275\pi$
$888$		0			0
$889$	93.5960	+	34.0661i	0.105282	+	0.0383196i
$890$			100.185i			0.112568i
$891$		0			0
$892$	99.4791			0.111524
$893$	639.683	−	1757.52i	0.716331	−	1.96810i
$894$		0			0
$895$	−192.922	−	161.881i	−0.215556	−	0.180873i
$896$	91.6834	+	16.1663i	0.102325	+	0.0180427i
$897$		0			0
$898$	−116.570	+	97.8141i	−0.129811	+	0.108924i
$899$	−341.970	+	197.437i	−0.380389	+	0.219618i
$900$		0			0
$901$	650.402	−	1126.53i	0.721866	−	1.25031i
$902$	520.103	−	91.7081i	0.576611	−	0.101672i
$903$		0			0
$904$	108.673	−	39.5538i	0.120214	−	0.0437542i
$905$	172.953	+	475.183i	0.191108	+	0.525065i
$906$		0			0
$907$	−31.7788	−	180.226i	−0.0350372	−	0.198706i	0.962265	−	0.272115i	$-0.0877232\pi$
$907$	−31.7788	−	180.226i	−0.0350372	−	0.198706i	−0.997302	+	0.0734092i	$0.976612\pi$
$908$	525.139	+	303.189i	0.578346	+	0.333908i
$909$		0			0
$910$	327.973	+	568.066i	0.360410	+	0.624248i
$911$	921.784	+	1098.54i	1.01184	+	1.20586i	0.978464	+	0.206418i	$0.0661807\pi$
$911$	921.784	+	1098.54i	1.01184	+	1.20586i	0.0333736	+	0.999443i	$0.489375\pi$
$912$		0			0
$913$	123.304	−	699.294i	0.135054	−	0.765930i
$914$	−164.754	+	196.346i	−0.180256	+	0.214821i
$915$		0			0
$916$	36.6222	+	13.3294i	0.0399806	+	0.0145517i
$917$		−	611.332i		−	0.666665i
$918$		0			0
$919$	−121.386			−0.132085			−0.0660425	−	0.997817i	$-0.521037\pi$
$919$	−121.386			−0.132085			−0.0660425	+	0.997817i	$0.521037\pi$
$920$	−9.75277	+	26.7955i	−0.0106008	+	0.0291255i
$921$		0			0
$922$	636.515	+	534.100i	0.690364	+	0.579284i
$923$	−178.434	−	31.4628i	−0.193320	−	0.0340875i
$924$		0			0
$925$	80.4079	−	67.4702i	0.0869274	−	0.0729408i
$926$	60.3564	−	34.8468i	0.0651797	−	0.0376315i
$927$		0			0
$928$	−80.4223	+	139.296i	−0.0866620	+	0.150103i
$929$	−1078.57	+	190.181i	−1.16100	+	0.204716i	−0.720774	−	0.693170i	$-0.756214\pi$
$929$	−1078.57	+	190.181i	−1.16100	+	0.204716i	−0.440228	+	0.897886i	$0.645103\pi$
$930$		0			0
$931$	612.483	−	222.926i	0.657877	−	0.239448i
$932$	−70.5621	−	193.868i	−0.0757104	−	0.208013i
$933$		0			0
$934$	174.218	+	988.040i	0.186529	+	1.05786i
$935$	−227.922	−	131.591i	−0.243767	−	0.140739i
$936$		0			0
$937$	260.320	+	450.887i	0.277823	+	0.481203i	0.970843	−	0.239715i	$-0.0770539\pi$
$937$	260.320	+	450.887i	0.277823	+	0.481203i	−0.693021	+	0.720918i	$0.743721\pi$
$938$	−224.932	−	268.063i	−0.239799	−	0.285782i
$939$		0			0
$940$	−56.7360	+	321.766i	−0.0603574	+	0.342304i
$941$	−588.900	+	701.824i	−0.625824	+	0.745828i	−0.982060	−	0.188568i	$-0.939615\pi$
$941$	−588.900	+	701.824i	−0.625824	+	0.745828i	0.356236	+	0.934396i	$0.384060\pi$
$942$		0			0
$943$	−177.407	−	64.5710i	−0.188131	−	0.0684740i
$944$		−	411.060i		−	0.435444i
$945$		0			0
$946$	−303.486			−0.320810
$947$	275.472	−	756.854i	0.290890	−	0.799213i	−0.705047	−	0.709160i	$-0.749074\pi$
$947$	275.472	−	756.854i	0.290890	−	0.799213i	0.995937	−	0.0900525i	$-0.0287035\pi$
$948$		0			0
$949$	1839.25	+	1543.31i	1.93809	+	1.62625i
$950$	763.741	+	134.668i	0.803938	+	0.141756i
$951$		0			0
$952$	235.300	−	197.440i	0.247164	−	0.207395i
$953$	−829.337	+	478.818i	−0.870238	+	0.502432i	−0.867427	−	0.497564i	$-0.834228\pi$
$953$	−829.337	+	478.818i	−0.870238	+	0.502432i	−0.00281092	+	0.999996i	$0.500895\pi$
$954$		0			0
$955$	−190.457	+	329.881i	−0.199431	+	0.345425i
$956$	−415.266	+	73.2226i	−0.434378	+	0.0765926i
$957$		0			0
$958$	−561.987	+	204.547i	−0.586626	+	0.213514i
$959$	116.287	+	319.495i	0.121258	+	0.333154i
$960$		0			0
$961$	−133.385	−	756.466i	−0.138799	−	0.787166i
$962$	−151.281	−	87.3421i	−0.157257	−	0.0907923i
$963$		0			0
$964$	−61.8820	−	107.183i	−0.0641929	−	0.111185i
$965$	−180.450	−	215.052i	−0.186995	−	0.222852i
$966$		0			0
$967$	−84.1560	+	477.272i	−0.0870279	+	0.493560i	0.909873	+	0.414888i	$0.136179\pi$
$967$	−84.1560	+	477.272i	−0.0870279	+	0.493560i	−0.996901	+	0.0786721i	$0.974932\pi$
$968$	−141.878	+	169.084i	−0.146569	+	0.174674i
$969$		0			0
$970$	207.182	+	75.4079i	0.213589	+	0.0777401i
$971$			344.432i			0.354719i	0.984146	+	0.177359i	$0.0567555\pi$
$971$			344.432i			0.354719i	−0.984146	+	0.177359i	$0.943245\pi$
$972$		0			0
$973$	−1168.83			−1.20126
$974$	−214.821	+	590.215i	−0.220555	+	0.605970i
$975$		0			0
$976$	−22.0193	−	18.4764i	−0.0225608	−	0.0189308i
$977$	514.987	+	90.8061i	0.527110	+	0.0929438i	0.430869	−	0.902414i	$-0.358207\pi$
$977$	514.987	+	90.8061i	0.527110	+	0.0929438i	0.0962409	+	0.995358i	$0.469318\pi$
$978$		0			0
$979$	−116.913	+	98.1018i	−0.119421	+	0.100206i
$980$	−98.6084	+	56.9316i	−0.100621	+	0.0580935i
$981$		0			0
$982$	286.509	−	496.248i	0.291760	−	0.505344i
$983$	152.607	−	26.9087i	0.155246	−	0.0273741i	−0.0954849	−	0.995431i	$-0.530440\pi$
$983$	152.607	−	26.9087i	0.155246	−	0.0273741i	0.250731	+	0.968057i	$0.419329\pi$
$984$		0			0
$985$	−112.519	+	40.9535i	−0.114232	+	0.0415771i
$986$	181.504	+	498.679i	0.184081	+	0.505759i
$987$		0			0
$988$	−224.117	−	1271.03i	−0.226839	−	1.28647i
$989$	93.9544	+	54.2446i	0.0949994	+	0.0548479i
$990$		0			0
$991$	57.0350	+	98.7876i	0.0575530	+	0.0996847i	0.893366	−	0.449329i	$-0.148337\pi$
$991$	57.0350	+	98.7876i	0.0575530	+	0.0996847i	−0.835813	+	0.549014i	$0.815004\pi$
$992$	50.4973	+	60.1804i	0.0509045	+	0.0606657i
$993$		0			0
$994$	19.7629	−	112.081i	0.0198822	−	0.112758i
$995$	372.774	−	444.255i	0.374647	−	0.446487i
$996$		0			0
$997$	−1170.61	−	426.068i	−1.17413	−	0.427350i	−0.320008	−	0.947415i	$-0.603686\pi$
$997$	−1170.61	−	426.068i	−1.17413	−	0.427350i	−0.854127	+	0.520065i	$0.825908\pi$
$998$		−	820.613i		−	0.822258i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	162.3.f.a.17.3		36
3.2	odd	2		54.3.f.a.23.4	✓	36
12.11	even	2		432.3.bc.c.401.5		36
27.7	even	9		54.3.f.a.47.4	yes	36
27.13	even	9		1458.3.b.c.1457.12		36
27.14	odd	18		1458.3.b.c.1457.25		36
27.20	odd	18	inner	162.3.f.a.143.3		36
108.7	odd	18		432.3.bc.c.209.5		36

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
54.3.f.a.23.4	✓	36	3.2	odd	2
54.3.f.a.47.4	yes	36	27.7	even	9
162.3.f.a.17.3		36	1.1	even	1	trivial
162.3.f.a.143.3		36	27.20	odd	18	inner
432.3.bc.c.209.5		36	108.7	odd	18
432.3.bc.c.401.5		36	12.11	even	2
1458.3.b.c.1457.12		36	27.13	even	9
1458.3.b.c.1457.25		36	27.14	odd	18

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:	\( N \)	\(=\)	\( 162 = 2 \cdot 3^{4} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	162.f (of order \(18\), degree \(6\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.483690 + 1.32893i) q^{2} +(-1.53209 - 1.28558i) q^{4} +(2.99623 + 0.528316i) q^{5} +(6.30359 - 5.28934i) q^{7} +(2.44949 - 1.41421i) q^{8} +O(q^{10})\)	\(q+(-0.483690 + 1.32893i) q^{2} +(-1.53209 - 1.28558i) q^{4} +(2.99623 + 0.528316i) q^{5} +(6.30359 - 5.28934i) q^{7} +(2.44949 - 1.41421i) q^{8} +(-2.15134 + 3.72623i) q^{10} +(-6.45500 + 1.13819i) q^{11} +(17.4093 - 6.33646i) q^{13} +(3.98016 + 10.9354i) q^{14} +(0.694593 + 3.93923i) q^{16} +(11.4293 + 6.59870i) q^{17} +(17.4160 + 30.1654i) q^{19} +(-3.91130 - 4.66131i) q^{20} +(1.60964 - 9.12874i) q^{22} +(-2.12998 + 2.53841i) q^{23} +(-14.7940 - 5.38459i) q^{25} +26.2005i q^{26} -16.4575 q^{28} +(9.72486 - 26.7188i) q^{29} +(-10.6385 - 8.92675i) q^{31} +(-5.57091 - 0.982302i) q^{32} +(-14.2974 + 11.9970i) q^{34} +(21.6815 - 12.5178i) q^{35} +(-3.33360 + 5.77397i) q^{37} +(-48.5116 + 8.55390i) q^{38} +(8.08639 - 2.94320i) q^{40} +(19.4863 + 53.5382i) q^{41} +(-5.68525 - 32.2426i) q^{43} +(11.3529 + 6.55457i) q^{44} +(-2.34311 - 4.05838i) q^{46} +(-34.5145 - 41.1328i) q^{47} +(3.24938 - 18.4281i) q^{49} +(14.3114 - 17.0557i) q^{50} +(-34.8186 - 12.6729i) q^{52} -98.5651i q^{53} -19.9420 q^{55} +(7.96033 - 21.8708i) q^{56} +(30.8035 + 25.8472i) q^{58} +(-101.204 - 17.8449i) q^{59} +(-5.50484 + 4.61911i) q^{61} +(17.0087 - 9.81998i) q^{62} +(4.00000 - 6.92820i) q^{64} +(55.5099 - 9.78789i) q^{65} +(-28.2566 + 10.2846i) q^{67} +(-9.02755 - 24.8030i) q^{68} +(6.14813 + 34.8678i) q^{70} +(-8.46959 - 4.88992i) q^{71} +(64.7978 + 112.233i) q^{73} +(-6.06075 - 7.22291i) q^{74} +(12.0970 - 68.6057i) q^{76} +(-34.6694 + 41.3174i) q^{77} +(-96.4782 - 35.1152i) q^{79} +12.1698i q^{80} -80.5737 q^{82} +(-37.0524 + 101.800i) q^{83} +(30.7586 + 25.8095i) q^{85} +(45.5980 + 8.04015i) q^{86} +(-14.2018 + 11.9167i) q^{88} +(20.1649 - 11.6422i) q^{89} +(76.2254 - 132.026i) q^{91} +(6.52663 - 1.15082i) q^{92} +(71.3568 - 25.9718i) q^{94} +(36.2455 + 99.5837i) q^{95} +(-8.89809 - 50.4636i) q^{97} +(22.9179 + 13.2317i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 36 q - 18 q^{5}+O(q^{10}) \) 36 * q - 18 * q^5	\( 36 q - 18 q^{5} + 18 q^{11} + 36 q^{14} + 72 q^{20} + 36 q^{22} + 180 q^{23} + 18 q^{25} - 144 q^{29} - 90 q^{31} - 72 q^{34} - 486 q^{35} - 180 q^{38} + 90 q^{41} + 90 q^{43} + 378 q^{47} + 72 q^{49} + 72 q^{56} - 252 q^{59} - 144 q^{61} + 144 q^{64} - 18 q^{65} - 594 q^{67} + 180 q^{68} - 360 q^{70} + 648 q^{71} + 126 q^{73} + 504 q^{74} - 72 q^{76} + 342 q^{77} - 72 q^{79} - 594 q^{83} + 360 q^{85} - 540 q^{86} + 144 q^{88} - 648 q^{89} - 198 q^{91} - 396 q^{92} + 504 q^{94} - 252 q^{95} + 702 q^{97} - 648 q^{98}+O(q^{100}) \) 36 * q - 18 * q^5 + 18 * q^11 + 36 * q^14 + 72 * q^20 + 36 * q^22 + 180 * q^23 + 18 * q^25 - 144 * q^29 - 90 * q^31 - 72 * q^34 - 486 * q^35 - 180 * q^38 + 90 * q^41 + 90 * q^43 + 378 * q^47 + 72 * q^49 + 72 * q^56 - 252 * q^59 - 144 * q^61 + 144 * q^64 - 18 * q^65 - 594 * q^67 + 180 * q^68 - 360 * q^70 + 648 * q^71 + 126 * q^73 + 504 * q^74 - 72 * q^76 + 342 * q^77 - 72 * q^79 - 594 * q^83 + 360 * q^85 - 540 * q^86 + 144 * q^88 - 648 * q^89 - 198 * q^91 - 396 * q^92 + 504 * q^94 - 252 * q^95 + 702 * q^97 - 648 * q^98

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