LMFDB - Embedded newform 162.3.f.a.71.2

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			71.2
Character	$\chi$	$=$	162.71
Dual form			162.3.f.a.89.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.39273 + 0.245576i) q^{2} +(1.87939 - 0.684040i) q^{4} +(-0.379008 + 0.451684i) q^{5} +(2.96297 + 1.07843i) q^{7} +(-2.44949 + 1.41421i) q^{8} +O(q^{10})$	\(q+(-1.39273 + 0.245576i) q^{2} +(1.87939 - 0.684040i) q^{4} +(-0.379008 + 0.451684i) q^{5} +(2.96297 + 1.07843i) q^{7} +(-2.44949 + 1.41421i) q^{8} +(0.416932 - 0.722148i) q^{10} +(6.03341 + 7.19034i) q^{11} +(2.11998 - 12.0230i) q^{13} +(-4.39145 - 0.774332i) q^{14} +(3.06418 - 2.57115i) q^{16} +(24.5140 + 14.1532i) q^{17} +(11.2011 + 19.4008i) q^{19} +(-0.403332 + 1.10814i) q^{20} +(-10.1687 - 8.53254i) q^{22} +(-3.44380 - 9.46175i) q^{23} +(4.28083 + 24.2778i) q^{25} +17.2654i q^{26} +6.30626 q^{28} +(23.6767 - 4.17484i) q^{29} +(42.7251 - 15.5506i) q^{31} +(-3.63616 + 4.33340i) q^{32} +(-37.6170 - 13.6915i) q^{34} +(-1.61010 + 0.929592i) q^{35} +(-15.7500 + 27.2799i) q^{37} +(-20.3644 - 24.2694i) q^{38} +(0.289598 - 1.64239i) q^{40} +(-69.7771 - 12.3036i) q^{41} +(-11.1607 + 9.36490i) q^{43} +(16.2576 + 9.38633i) q^{44} +(7.11985 + 12.3319i) q^{46} +(18.9216 - 51.9868i) q^{47} +(-29.9200 - 25.1059i) q^{49} +(-11.9241 - 32.7611i) q^{50} +(-4.23996 - 24.0460i) q^{52} -25.4089i q^{53} -5.53447 q^{55} +(-8.78291 + 1.54866i) q^{56} +(-31.9499 + 11.6288i) q^{58} +(-18.4282 + 21.9619i) q^{59} +(-106.265 - 38.6772i) q^{61} +(-55.6855 + 32.1501i) q^{62} +(4.00000 - 6.92820i) q^{64} +(4.62711 + 5.51438i) q^{65} +(8.68700 - 49.2664i) q^{67} +(55.7526 + 9.83069i) q^{68} +(2.01415 - 1.69007i) q^{70} +(7.59817 + 4.38680i) q^{71} +(-11.7358 - 20.3271i) q^{73} +(15.2363 - 41.8613i) q^{74} +(34.3221 + 28.7997i) q^{76} +(10.1225 + 27.8114i) q^{77} +(23.0535 + 130.743i) q^{79} +2.35853i q^{80} +100.202 q^{82} +(66.1377 - 11.6619i) q^{83} +(-15.6838 + 5.70842i) q^{85} +(13.2440 - 15.7835i) q^{86} +(-24.9475 - 9.08013i) q^{88} +(-62.9935 + 36.3693i) q^{89} +(19.2475 - 33.3376i) q^{91} +(-12.9444 - 15.4266i) q^{92} +(-13.5860 + 77.0502i) q^{94} +(-13.0083 - 2.29372i) q^{95} +(120.419 - 101.043i) q^{97} +(47.8358 + 27.6180i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/162\mathbb{Z}\right)^\times$.

$n$	$83$
$\chi(n)$	$e\left(\frac{17}{18}\right)$

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 $

$2$	−1.39273	+	0.245576i	−0.696364	+	0.122788i
$2$	−1.39273	+	0.245576i	−0.696364	+	0.122788i
$3$		0			0
$3$		0			0
$4$	1.87939	−	0.684040i	0.469846	−	0.171010i
$5$	−0.379008	+	0.451684i	−0.0758015	+	0.0903368i	−0.802612	−	0.596501i	$-0.796557\pi$
$5$	−0.379008	+	0.451684i	−0.0758015	+	0.0903368i	0.726811	+	0.686838i	$0.241002\pi$
$6$		0			0
$7$	2.96297	+	1.07843i	0.423282	+	0.154062i	0.544874	−	0.838518i	$-0.316578\pi$
$7$	2.96297	+	1.07843i	0.423282	+	0.154062i	−0.121592	+	0.992580i	$0.538800\pi$
$8$	−2.44949	+	1.41421i	−0.306186	+	0.176777i
$9$		0			0
$10$	0.416932	−	0.722148i	0.0416932	−	0.0722148i
$11$	6.03341	+	7.19034i	0.548492	+	0.653667i	0.967069	−	0.254514i	$-0.0819154\pi$
$11$	6.03341	+	7.19034i	0.548492	+	0.653667i	−0.418577	+	0.908181i	$0.637471\pi$
$12$		0			0
$13$	2.11998	−	12.0230i	0.163076	−	0.924847i	−0.787951	−	0.615738i	$-0.788858\pi$
$13$	2.11998	−	12.0230i	0.163076	−	0.924847i	0.951027	−	0.309109i	$-0.100031\pi$
$14$	−4.39145	−	0.774332i	−0.313675	−	0.0553094i
$15$		0			0
$16$	3.06418	−	2.57115i	0.191511	−	0.160697i
$17$	24.5140	+	14.1532i	1.44200	+	0.832539i	0.997983	−	0.0634789i	$-0.0202195\pi$
$17$	24.5140	+	14.1532i	1.44200	+	0.832539i	0.444017	+	0.896018i	$0.353553\pi$
$18$		0			0
$19$	11.2011	+	19.4008i	0.589530	+	1.02110i	0.994294	+	0.106675i	$0.0340205\pi$
$19$	11.2011	+	19.4008i	0.589530	+	1.02110i	−0.404764	+	0.914421i	$0.632646\pi$
$20$	−0.403332	+	1.10814i	−0.0201666	+	0.0554072i
$21$		0			0
$22$	−10.1687	−	8.53254i	−0.462213	−	0.387843i
$23$	−3.44380	−	9.46175i	−0.149730	−	0.411381i	0.842039	−	0.539416i	$-0.181355\pi$
$23$	−3.44380	−	9.46175i	−0.149730	−	0.411381i	−0.991770	+	0.128036i	$0.959133\pi$
$24$		0			0
$25$	4.28083	+	24.2778i	0.171233	+	0.971112i
$26$			17.2654i			0.664054i
$27$		0			0
$28$	6.30626			0.225224
$29$	23.6767	−	4.17484i	0.816437	−	0.143960i	0.250191	−	0.968196i	$-0.419506\pi$
$29$	23.6767	−	4.17484i	0.816437	−	0.143960i	0.566246	+	0.824237i	$0.308395\pi$
$30$		0			0
$31$	42.7251	−	15.5506i	1.37823	−	0.501634i	0.456587	−	0.889679i	$-0.349072\pi$
$31$	42.7251	−	15.5506i	1.37823	−	0.501634i	0.921640	+	0.388045i	$0.126849\pi$
$32$	−3.63616	+	4.33340i	−0.113630	+	0.135419i
$33$		0			0
$34$	−37.6170	−	13.6915i	−1.10638	−	0.402691i
$35$	−1.61010	+	0.929592i	−0.0460029	+	0.0265598i
$36$		0			0
$37$	−15.7500	+	27.2799i	−0.425677	+	0.737293i	−0.996483	−	0.0837909i	$-0.973297\pi$
$37$	−15.7500	+	27.2799i	−0.425677	+	0.737293i	0.570807	+	0.821084i	$0.306631\pi$
$38$	−20.3644	−	24.2694i	−0.535906	−	0.638668i
$39$		0			0
$40$	0.289598	−	1.64239i	0.00723995	−	0.0410598i
$41$	−69.7771	−	12.3036i	−1.70188	−	0.300087i	−0.763530	−	0.645773i	$-0.776535\pi$
$41$	−69.7771	−	12.3036i	−1.70188	−	0.300087i	−0.938351	+	0.345685i	$0.887646\pi$
$42$		0			0
$43$	−11.1607	+	9.36490i	−0.259550	+	0.217788i	−0.763272	−	0.646078i	$-0.776408\pi$
$43$	−11.1607	+	9.36490i	−0.259550	+	0.217788i	0.503722	+	0.863866i	$0.331964\pi$
$44$	16.2576	+	9.38633i	0.369491	+	0.213326i
$45$		0			0
$46$	7.11985	+	12.3319i	0.154779	+	0.268086i
$47$	18.9216	−	51.9868i	0.402588	−	1.10610i	−0.558414	−	0.829562i	$-0.688590\pi$
$47$	18.9216	−	51.9868i	0.402588	−	1.10610i	0.961002	−	0.276540i	$-0.0891878\pi$
$48$		0			0
$49$	−29.9200	−	25.1059i	−0.610612	−	0.512364i
$50$	−11.9241	−	32.7611i	−0.238482	−	0.655223i
$51$		0			0
$52$	−4.23996	−	24.0460i	−0.0815378	−	0.462424i
$53$		−	25.4089i		−	0.479412i	−0.970845	−	0.239706i	$-0.922949\pi$
$53$		−	25.4089i		−	0.479412i	0.970845	−	0.239706i	$-0.0770511\pi$
$54$		0			0
$55$	−5.53447			−0.100627
$56$	−8.78291	+	1.54866i	−0.156838	+	0.0276547i
$57$		0			0
$58$	−31.9499	+	11.6288i	−0.550861	+	0.200497i
$59$	−18.4282	+	21.9619i	−0.312343	+	0.372236i	−0.899263	−	0.437409i	$-0.855896\pi$
$59$	−18.4282	+	21.9619i	−0.312343	+	0.372236i	0.586919	+	0.809645i	$0.300341\pi$
$60$		0			0
$61$	−106.265	−	38.6772i	−1.74205	−	0.634053i	−0.742680	−	0.669646i	$-0.766446\pi$
$61$	−106.265	−	38.6772i	−1.74205	−	0.634053i	−0.999366	+	0.0355933i	$0.988668\pi$
$62$	−55.6855	+	32.1501i	−0.898154	+	0.518549i
$63$		0			0
$64$	4.00000	−	6.92820i	0.0625000	−	0.108253i
$65$	4.62711	+	5.51438i	0.0711863	+	0.0848365i
$66$		0			0
$67$	8.68700	−	49.2664i	0.129657	−	0.735320i	−0.848776	−	0.528753i	$-0.822660\pi$
$67$	8.68700	−	49.2664i	0.129657	−	0.735320i	0.978432	−	0.206567i	$-0.0662291\pi$
$68$	55.7526	+	9.83069i	0.819891	+	0.144569i
$69$		0			0
$70$	2.01415	−	1.69007i	0.0287735	−	0.0241439i
$71$	7.59817	+	4.38680i	0.107016	+	0.0617860i	0.552553	−	0.833478i	$-0.313654\pi$
$71$	7.59817	+	4.38680i	0.107016	+	0.0617860i	−0.445536	+	0.895264i	$0.646987\pi$
$72$		0			0
$73$	−11.7358	−	20.3271i	−0.160765	−	0.278453i	0.774378	−	0.632723i	$-0.218063\pi$
$73$	−11.7358	−	20.3271i	−0.160765	−	0.278453i	−0.935143	+	0.354270i	$0.884729\pi$
$74$	15.2363	−	41.8613i	0.205895	−	0.565693i
$75$		0			0
$76$	34.3221	+	28.7997i	0.451606	+	0.378943i
$77$	10.1225	+	27.8114i	0.131461	+	0.361187i
$78$		0			0
$79$	23.0535	+	130.743i	0.291816	+	1.65497i	0.679869	+	0.733334i	$0.262037\pi$
$79$	23.0535	+	130.743i	0.291816	+	1.65497i	−0.388053	+	0.921637i	$0.626852\pi$
$80$			2.35853i			0.0294816i
$81$		0			0
$82$	100.202			1.22198
$83$	66.1377	−	11.6619i	0.796839	−	0.140504i	0.239617	−	0.970868i	$-0.422978\pi$
$83$	66.1377	−	11.6619i	0.796839	−	0.140504i	0.557223	+	0.830363i	$0.311867\pi$
$84$		0			0
$85$	−15.6838	+	5.70842i	−0.184515	+	0.0671579i
$86$	13.2440	−	15.7835i	0.154000	−	0.183530i
$87$		0			0
$88$	−24.9475	−	9.08013i	−0.283494	−	0.103183i
$89$	−62.9935	+	36.3693i	−0.707792	+	0.408644i	−0.810243	−	0.586094i	$-0.800665\pi$
$89$	−62.9935	+	36.3693i	−0.707792	+	0.408644i	0.102451	+	0.994738i	$0.467332\pi$
$90$		0			0
$91$	19.2475	−	33.3376i	0.211511	−	0.366347i
$92$	−12.9444	−	15.4266i	−0.140700	−	0.167680i
$93$		0			0
$94$	−13.5860	+	77.0502i	−0.144532	+	0.819683i
$95$	−13.0083	−	2.29372i	−0.136930	−	0.0241444i
$96$		0			0
$97$	120.419	−	101.043i	1.24143	−	1.04168i	0.244021	−	0.969770i	$-0.421534\pi$
$97$	120.419	−	101.043i	1.24143	−	1.04168i	0.997411	−	0.0719147i	$-0.0229109\pi$
$98$	47.8358	+	27.6180i	0.488120	+	0.281816i
$99$		0			0
$100$	24.6523	+	42.6991i	0.246523	+	0.426991i
$101$	−42.9450	+	117.991i	−0.425198	+	1.16822i	0.523496	+	0.852028i	$0.324628\pi$
$101$	−42.9450	+	117.991i	−0.425198	+	1.16822i	−0.948694	+	0.316195i	$0.897595\pi$
$102$		0			0
$103$	72.1665	+	60.5548i	0.700645	+	0.587911i	0.921957	−	0.387292i	$-0.126589\pi$
$103$	72.1665	+	60.5548i	0.700645	+	0.587911i	−0.221312	+	0.975203i	$0.571034\pi$
$104$	11.8102	+	32.4484i	0.113560	+	0.312003i
$105$		0			0
$106$	6.23979	+	35.3876i	0.0588660	+	0.333846i
$107$		−	107.896i		−	1.00838i	−0.863594	−	0.504188i	$-0.831792\pi$
$107$		−	107.896i		−	1.00838i	0.863594	−	0.504188i	$-0.168208\pi$
$108$		0			0
$109$	−42.9667			−0.394190			−0.197095	−	0.980384i	$-0.563151\pi$
$109$	−42.9667			−0.394190			−0.197095	+	0.980384i	$0.563151\pi$
$110$	7.70802	−	1.35913i	0.0700729	−	0.0123557i
$111$		0			0
$112$	11.8519	−	4.31374i	0.105820	−	0.0385155i
$113$	−6.89768	+	8.22034i	−0.0610414	+	0.0727463i	−0.795701	−	0.605689i	$-0.792897\pi$
$113$	−6.89768	+	8.22034i	−0.0610414	+	0.0727463i	0.734660	+	0.678436i	$0.237342\pi$
$114$		0			0
$115$	5.57895	+	2.03057i	0.0485126	+	0.0176571i
$116$	41.6418	−	24.0419i	0.358981	−	0.207258i
$117$		0			0
$118$	20.2722	−	35.1125i	0.171799	−	0.297564i
$119$	57.3711	+	68.3722i	0.482110	+	0.574556i
$120$		0			0
$121$	5.71249	−	32.3971i	0.0472106	−	0.267745i
$122$	157.496	+	27.7708i	1.29095	+	0.227630i
$123$		0			0
$124$	69.6596	−	58.4513i	0.561771	−	0.471382i
$125$	−25.3543	−	14.6383i	−0.202834	−	0.117106i
$126$		0			0
$127$	−49.1507	−	85.1315i	−0.387013	−	0.670327i	0.605033	−	0.796200i	$-0.293160\pi$
$127$	−49.1507	−	85.1315i	−0.387013	−	0.670327i	−0.992046	+	0.125874i	$0.959827\pi$
$128$	−3.86952	+	10.6314i	−0.0302306	+	0.0830579i
$129$		0			0
$130$	−7.79850	−	6.54372i	−0.0599885	−	0.0503363i
$131$	46.8665	+	128.765i	0.357760	+	0.982937i	0.979805	+	0.199956i	$0.0640799\pi$
$131$	46.8665	+	128.765i	0.357760	+	0.982937i	−0.622045	+	0.782981i	$0.713698\pi$
$132$		0			0
$133$	12.2660	+	69.5638i	0.0922253	+	0.523036i
$134$			70.7481i			0.527971i
$135$		0			0
$136$	−80.0624			−0.588694
$137$	−197.146	+	34.7622i	−1.43902	+	0.253739i	−0.838078	−	0.545550i	$-0.816321\pi$
$137$	−197.146	+	34.7622i	−1.43902	+	0.253739i	−0.600947	+	0.799289i	$0.705210\pi$
$138$		0			0
$139$	−6.69802	+	2.43788i	−0.0481872	+	0.0175387i	−0.366001	−	0.930614i	$-0.619273\pi$
$139$	−6.69802	+	2.43788i	−0.0481872	+	0.0175387i	0.317814	+	0.948153i	$0.397051\pi$
$140$	−2.39012	+	2.84844i	−0.0170723	+	0.0203460i
$141$		0			0
$142$	−11.6595	−	4.24370i	−0.0821090	−	0.0298852i
$143$	99.2403	−	57.2964i	0.693988	−	0.400674i
$144$		0			0
$145$	−7.08794	+	12.2767i	−0.0488823	+	0.0846666i
$146$	21.3367	+	25.4281i	0.146142	+	0.174165i
$147$		0			0
$148$	−10.9399	+	62.0430i	−0.0739180	+	0.419210i
$149$	−92.3284	−	16.2800i	−0.619654	−	0.109262i	−0.144996	−	0.989432i	$-0.546317\pi$
$149$	−92.3284	−	16.2800i	−0.619654	−	0.109262i	−0.474658	+	0.880171i	$0.657428\pi$
$150$		0			0
$151$	154.567	−	129.697i	1.02362	−	0.858921i	0.0335439	−	0.999437i	$-0.489321\pi$
$151$	154.567	−	129.697i	1.02362	−	0.858921i	0.990078	+	0.140516i	$0.0448762\pi$
$152$	−54.8738	−	31.6814i	−0.361012	−	0.208430i
$153$		0			0
$154$	−20.9277	−	36.2479i	−0.135894	−	0.235376i
$155$	−9.16915	+	25.1920i	−0.0591558	+	0.162529i
$156$		0			0
$157$	−56.2262	−	47.1794i	−0.358128	−	0.300505i	0.445916	−	0.895075i	$-0.352878\pi$
$157$	−56.2262	−	47.1794i	−0.358128	−	0.300505i	−0.804044	+	0.594569i	$0.797323\pi$
$158$	−64.2144	−	176.428i	−0.406420	−	1.11663i
$159$		0			0
$160$	−0.579196	−	3.28479i	−0.00361998	−	0.0205299i
$161$		−	31.7488i		−	0.197198i
$162$		0			0
$163$	−217.128			−1.33208			−0.666038	−	0.745918i	$-0.732011\pi$
$163$	−217.128			−1.33208			−0.666038	+	0.745918i	$0.732011\pi$
$164$	−139.554	+	24.6072i	−0.850940	+	0.150044i
$165$		0			0
$166$	−89.2480	+	32.4836i	−0.537638	+	0.195684i
$167$	138.533	−	165.098i	0.829541	−	0.988609i	−0.170454	−	0.985366i	$-0.554523\pi$
$167$	138.533	−	165.098i	0.829541	−	0.988609i	0.999995	−	0.00324290i	$-0.00103225\pi$
$168$		0			0
$169$	18.7495	+	6.82427i	0.110944	+	0.0403803i
$170$	20.4414	−	11.8018i	0.120243	−	0.0694225i
$171$		0			0
$172$	−14.5692	+	25.2346i	−0.0847046	+	0.146713i
$173$	−40.5261	−	48.2971i	−0.234255	−	0.279174i	0.636092	−	0.771613i	$-0.280550\pi$
$173$	−40.5261	−	48.2971i	−0.234255	−	0.279174i	−0.870347	+	0.492439i	$0.836105\pi$
$174$		0			0
$175$	−13.4980	+	76.5511i	−0.0771316	+	0.437435i
$176$	36.9749	+	6.51967i	0.210085	+	0.0370436i
$177$		0			0
$178$	78.8015	−	66.1223i	0.442705	−	0.371473i
$179$	−172.225	−	99.4340i	−0.962150	−	0.555497i	−0.0653157	−	0.997865i	$-0.520805\pi$
$179$	−172.225	−	99.4340i	−0.962150	−	0.555497i	−0.896834	+	0.442367i	$0.854139\pi$
$180$		0			0
$181$	−35.6490	−	61.7458i	−0.196956	−	0.341137i	0.750584	−	0.660775i	$-0.229772\pi$
$181$	−35.6490	−	61.7458i	−0.196956	−	0.341137i	−0.947540	+	0.319638i	$0.896439\pi$
$182$	−18.6196	+	51.1569i	−0.102306	+	0.281082i
$183$		0			0
$184$	21.8165	+	18.3062i	0.118568	+	0.0994902i
$185$	−6.35249	−	17.4533i	−0.0343378	−	0.0943422i
$186$		0			0
$187$	46.1370	+	261.656i	0.246722	+	1.39923i
$188$		−	110.646i		−	0.588545i
$189$		0			0
$190$	18.6804			0.0983177
$191$	98.1741	−	17.3107i	0.514000	−	0.0906322i	0.0893693	−	0.995999i	$-0.471515\pi$
$191$	98.1741	−	17.3107i	0.514000	−	0.0906322i	0.424631	+	0.905366i	$0.360404\pi$
$192$		0			0
$193$	−178.750	+	65.0595i	−0.926164	+	0.337096i	−0.760688	−	0.649118i	$-0.775138\pi$
$193$	−178.750	+	65.0595i	−0.926164	+	0.337096i	−0.165476	+	0.986214i	$0.552916\pi$
$194$	−142.897	+	170.298i	−0.736582	+	0.877825i
$195$		0			0
$196$	−73.4046	−	26.7171i	−0.374513	−	0.136312i
$197$	159.929	−	92.3348i	0.811820	−	0.468705i	−0.0357675	−	0.999360i	$-0.511388\pi$
$197$	159.929	−	92.3348i	0.811820	−	0.468705i	0.847588	+	0.530656i	$0.178054\pi$
$198$		0			0
$199$	−31.0944	+	53.8571i	−0.156253	+	0.270639i	−0.933515	−	0.358539i	$-0.883275\pi$
$199$	−31.0944	+	53.8571i	−0.156253	+	0.270639i	0.777261	+	0.629178i	$0.216608\pi$
$200$	−44.8199	−	53.4142i	−0.224099	−	0.267071i
$201$		0			0
$202$	30.8352	−	174.875i	0.152649	−	0.865718i
$203$	74.6556	+	13.1638i	0.367762	+	0.0648463i
$204$		0			0
$205$	32.0034	−	26.8540i	0.156114	−	0.130995i
$206$	−115.379	−	66.6141i	−0.560093	−	0.323370i
$207$		0			0
$208$	−24.4170	−	42.2914i	−0.117389	−	0.203324i
$209$	−71.9179	+	197.593i	−0.344105	+	0.945420i
$210$		0			0
$211$	5.60018	+	4.69911i	0.0265411	+	0.0222706i	0.655962	−	0.754794i	$-0.272263\pi$
$211$	5.60018	+	4.69911i	0.0265411	+	0.0222706i	−0.629421	+	0.777065i	$0.716708\pi$
$212$	−17.3807	−	47.7530i	−0.0819843	−	0.225250i
$213$		0			0
$214$	26.4967	+	150.270i	0.123816	+	0.702197i
$215$		−	8.59045i		−	0.0399556i
$216$		0			0
$217$	143.364			0.660661
$218$	59.8410	−	10.5516i	0.274500	−	0.0484017i
$219$		0			0
$220$	−10.4014	+	3.78580i	−0.0472791	+	0.0172082i
$221$	222.133	−	264.728i	1.00513	−	1.19786i
$222$		0			0
$223$	−80.8775	−	29.4370i	−0.362679	−	0.132004i	0.154252	−	0.988032i	$-0.450703\pi$
$223$	−80.8775	−	29.4370i	−0.362679	−	0.132004i	−0.516931	+	0.856027i	$0.672926\pi$
$224$	−15.4471	+	8.91840i	−0.0689604	+	0.0398143i
$225$		0			0
$226$	7.58788	−	13.1426i	0.0335747	−	0.0581531i
$227$	−42.0709	−	50.1382i	−0.185335	−	0.220873i	0.665375	−	0.746509i	$-0.268272\pi$
$227$	−42.0709	−	50.1382i	−0.185335	−	0.220873i	−0.850709	+	0.525636i	$0.823827\pi$
$228$		0			0
$229$	−57.3799	+	325.418i	−0.250567	+	1.42104i	0.556632	+	0.830759i	$0.312093\pi$
$229$	−57.3799	+	325.418i	−0.250567	+	1.42104i	−0.807199	+	0.590279i	$0.799018\pi$
$230$	−8.26862	−	1.45798i	−0.0359505	−	0.00633904i
$231$		0			0
$232$	−52.0917	+	43.7101i	−0.224533	+	0.188406i
$233$	123.820	+	71.4877i	0.531418	+	0.306814i	0.741594	−	0.670849i	$-0.234070\pi$
$233$	123.820	+	71.4877i	0.531418	+	0.306814i	−0.210176	+	0.977664i	$0.567404\pi$
$234$		0			0
$235$	16.3101	+	28.2500i	0.0694049	+	0.120213i
$236$	−19.6109	+	53.8806i	−0.0830971	+	0.228308i
$237$		0			0
$238$	−96.6929	−	81.1350i	−0.406273	−	0.340903i
$239$	103.746	+	285.040i	0.434084	+	1.19264i	0.943284	+	0.331988i	$0.107719\pi$
$239$	103.746	+	285.040i	0.434084	+	1.19264i	−0.509200	+	0.860649i	$0.670058\pi$
$240$		0			0
$241$	−54.3108	−	308.012i	−0.225356	−	1.27806i	−0.862003	−	0.506903i	$-0.830790\pi$
$241$	−54.3108	−	308.012i	−0.225356	−	1.27806i	0.636647	−	0.771155i	$-0.280321\pi$
$242$			46.5232i			0.192245i
$243$		0			0
$244$	−226.169			−0.926924
$245$	22.6798	−	3.99906i	0.0925707	−	0.0163227i
$246$		0			0
$247$	257.003	−	93.5413i	1.04050	−	0.378710i
$248$	−82.6626	+	98.5135i	−0.333317	+	0.397232i
$249$		0			0
$250$	38.9064	+	14.1608i	0.155626	+	0.0566431i
$251$	−116.446	+	67.2298i	−0.463926	+	0.267848i	−0.713694	−	0.700458i	$-0.752979\pi$
$251$	−116.446	+	67.2298i	−0.463926	+	0.267848i	0.249767	+	0.968306i	$0.419646\pi$
$252$		0			0
$253$	47.2554	−	81.8488i	0.186780	−	0.323513i
$254$	89.3598	+	106.495i	0.351810	+	0.419271i
$255$		0			0
$256$	2.77837	−	15.7569i	0.0108530	−	0.0615505i
$257$	−46.8542	−	8.26166i	−0.182312	−	0.0321465i	0.0817466	−	0.996653i	$-0.473950\pi$
$257$	−46.8542	−	8.26166i	−0.182312	−	0.0321465i	−0.264059	+	0.964507i	$0.585061\pi$
$258$		0			0
$259$	−76.0865	+	63.8441i	−0.293770	+	0.246502i
$260$	12.4682	+	7.19851i	0.0479545	+	0.0276866i
$261$		0			0
$262$	−96.8939	−	167.825i	−0.369824	−	0.640554i
$263$	162.251	−	445.781i	0.616924	−	1.69498i	−0.0974685	−	0.995239i	$-0.531075\pi$
$263$	162.251	−	445.781i	0.616924	−	1.69498i	0.714392	−	0.699745i	$-0.246703\pi$
$264$		0			0
$265$	11.4768	+	9.63015i	0.0433085	+	0.0363402i
$266$	−34.1663	−	93.8712i	−0.128445	−	0.352899i
$267$		0			0
$268$	−17.3740	−	98.5329i	−0.0648284	−	0.367660i
$269$			455.081i			1.69175i	0.533380	+	0.845876i	$0.320922\pi$
$269$			455.081i			1.69175i	−0.533380	+	0.845876i	$0.679078\pi$
$270$		0			0
$271$	440.939			1.62708			0.813541	−	0.581508i	$-0.197537\pi$
$271$	440.939			1.62708			0.813541	+	0.581508i	$0.197537\pi$
$272$	111.505	−	19.6614i	0.409946	−	0.0722845i
$273$		0			0
$274$	266.035	−	96.8287i	0.970929	−	0.353389i
$275$	−148.738	+	177.259i	−0.540864	+	0.644577i
$276$		0			0
$277$	−70.8393	−	25.7834i	−0.255738	−	0.0930808i	0.210970	−	0.977493i	$-0.432338\pi$
$277$	−70.8393	−	25.7834i	−0.255738	−	0.0930808i	−0.466708	+	0.884412i	$0.654560\pi$
$278$	8.72984	−	5.04017i	0.0314023	−	0.0181301i
$279$		0			0
$280$	2.62928	−	4.55405i	0.00939030	−	0.0162645i
$281$	−4.98848	−	5.94504i	−0.0177526	−	0.0211567i	0.757095	−	0.653305i	$-0.226618\pi$
$281$	−4.98848	−	5.94504i	−0.0177526	−	0.0211567i	−0.774848	+	0.632148i	$0.782173\pi$
$282$		0			0
$283$	28.3852	−	160.981i	0.100301	−	0.568836i	−0.892692	−	0.450667i	$-0.851186\pi$
$283$	28.3852	−	160.981i	0.100301	−	0.568836i	0.992993	−	0.118169i	$-0.0377026\pi$
$284$	17.2806	+	3.04704i	0.0608473	+	0.0107290i
$285$		0			0
$286$	−124.144	+	104.169i	−0.434071	+	0.364229i
$287$	−193.479	−	111.705i	−0.674143	−	0.389217i
$288$		0			0
$289$	256.124	+	443.620i	0.886244	+	1.53502i
$290$	6.85672	−	18.8387i	0.0236439	−	0.0649610i
$291$		0			0
$292$	−35.9607	−	30.1746i	−0.123153	−	0.103338i
$293$	−18.4986	−	50.8246i	−0.0631353	−	0.173463i	0.904114	−	0.427292i	$-0.140532\pi$
$293$	−18.4986	−	50.8246i	−0.0631353	−	0.173463i	−0.967249	+	0.253829i	$0.918310\pi$
$294$		0			0
$295$	−2.93540	−	16.6475i	−0.00995051	−	0.0564321i
$296$		−	89.0956i		−	0.300999i
$297$		0			0
$298$	132.586			0.444921
$299$	−121.060	+	21.3461i	−0.404882	+	0.0713915i
$300$		0			0
$301$	−43.1681	+	15.7119i	−0.143416	+	0.0521991i
$302$	−183.419	+	218.591i	−0.607349	+	0.723810i
$303$		0			0
$304$	84.2046	+	30.6480i	0.276989	+	0.100816i
$305$	57.7451	−	33.3391i	0.189328	−	0.109309i
$306$		0			0
$307$	73.1993	−	126.785i	0.238434	−	0.412980i	−0.721831	−	0.692069i	$-0.756699\pi$
$307$	73.1993	−	126.785i	0.238434	−	0.412980i	0.960265	+	0.279089i	$0.0900325\pi$
$308$	38.0483	+	45.3442i	0.123533	+	0.147221i
$309$		0			0
$310$	6.58359	−	37.3374i	0.0212374	−	0.120443i
$311$	−272.335	−	48.0200i	−0.875676	−	0.154405i	−0.282295	−	0.959328i	$-0.591096\pi$
$311$	−272.335	−	48.0200i	−0.875676	−	0.154405i	−0.593380	+	0.804922i	$0.702207\pi$
$312$		0			0
$313$	−22.9780	+	19.2809i	−0.0734123	+	0.0616002i	−0.678755	−	0.734364i	$-0.737480\pi$
$313$	−22.9780	+	19.2809i	−0.0734123	+	0.0616002i	0.605343	+	0.795965i	$0.293036\pi$
$314$	89.8939	+	51.9003i	0.286286	+	0.165287i
$315$		0			0
$316$	132.760	+	229.946i	0.420125	+	0.727678i
$317$	91.5339	−	251.487i	0.288750	−	0.793335i	−0.707492	−	0.706722i	$-0.750173\pi$
$317$	91.5339	−	251.487i	0.288750	−	0.793335i	0.996242	−	0.0866133i	$-0.0276045\pi$
$318$		0			0
$319$	172.870	+	145.055i	0.541911	+	0.454717i
$320$	1.61333	+	4.43258i	0.00504164	+	0.0138518i
$321$		0			0
$322$	7.79674	+	44.2175i	0.0242135	+	0.137321i
$323$			634.123i			1.96323i
$324$		0			0
$325$	300.968			0.926055
$326$	302.401	−	53.3214i	0.927610	−	0.163563i
$327$		0			0
$328$	188.318	−	68.5422i	0.574141	−	0.208970i
$329$	112.129	−	133.630i	0.340817	−	0.406169i
$330$		0			0
$331$	−358.351	−	130.429i	−1.08263	−	0.394045i	−0.261744	−	0.965137i	$-0.584298\pi$
$331$	−358.351	−	130.429i	−1.08263	−	0.394045i	−0.820886	+	0.571092i	$0.806520\pi$
$332$	116.321	−	67.1580i	0.350364	−	0.202283i
$333$		0			0
$334$	−152.395	+	263.957i	−0.456274	+	0.790289i
$335$	18.9604	+	22.5961i	0.0565982	+	0.0674511i
$336$		0			0
$337$	20.7953	−	117.936i	0.0617071	−	0.349958i	−0.938285	−	0.345864i	$-0.887586\pi$
$337$	20.7953	−	117.936i	0.0617071	−	0.349958i	0.999992	−	0.00409401i	$-0.00130317\pi$
$338$	−27.7889	−	4.89993i	−0.0822156	−	0.0144968i
$339$		0			0
$340$	−25.5710	+	21.4566i	−0.0752089	+	0.0631078i
$341$	369.592	+	213.384i	1.08385	+	0.625760i
$342$		0			0
$343$	−138.829	−	240.459i	−0.404749	−	0.701045i
$344$	14.0939	−	38.7228i	0.0409707	−	0.112566i
$345$		0			0
$346$	68.3024	+	57.3125i	0.197406	+	0.165643i
$347$	85.0851	+	233.769i	0.245202	+	0.673687i	0.999846	+	0.0175526i	$0.00558746\pi$
$347$	85.0851	+	233.769i	0.245202	+	0.673687i	−0.754644	+	0.656135i	$0.772190\pi$
$348$		0			0
$349$	−55.5583	−	315.087i	−0.159193	−	0.902827i	−0.954852	−	0.297082i	$-0.903986\pi$
$349$	−55.5583	−	315.087i	−0.159193	−	0.902827i	0.795659	−	0.605745i	$-0.207125\pi$
$350$		−	109.930i		−	0.314085i
$351$		0			0
$352$	−53.0971			−0.150844
$353$	326.236	−	57.5243i	0.924182	−	0.162958i	0.308746	−	0.951145i	$-0.400091\pi$
$353$	326.236	−	57.5243i	0.924182	−	0.162958i	0.615437	+	0.788186i	$0.288980\pi$
$354$		0			0
$355$	−4.86121	+	1.76934i	−0.0136936	+	0.00498405i
$356$	−93.5110	+	111.442i	−0.262671	+	0.313040i
$357$		0			0
$358$	264.281	+	96.1904i	0.738215	+	0.268688i
$359$	−277.930	+	160.463i	−0.774178	+	0.446972i	−0.834363	−	0.551216i	$-0.814164\pi$
$359$	−277.930	+	160.463i	−0.774178	+	0.446972i	0.0601853	+	0.998187i	$0.480831\pi$
$360$		0			0
$361$	−70.4283	+	121.985i	−0.195092	+	0.337910i
$362$	64.8126	+	77.2407i	0.179040	+	0.213372i
$363$		0			0
$364$	13.3692	−	75.8202i	0.0367284	−	0.208297i
$365$	13.6294	+	2.40323i	0.0373408	+	0.00658419i
$366$		0			0
$367$	−558.217	+	468.400i	−1.52103	+	1.27629i	−0.683410	+	0.730035i	$0.739504\pi$
$367$	−558.217	+	468.400i	−1.52103	+	1.27629i	−0.837617	+	0.546258i	$0.816052\pi$
$368$	−34.8800	−	20.1380i	−0.0947826	−	0.0547228i
$369$		0			0
$370$	13.1334	+	22.7477i	0.0354957	+	0.0614803i
$371$	27.4018	−	75.2857i	0.0738592	−	0.202927i
$372$		0			0
$373$	−262.562	−	220.316i	−0.703920	−	0.590659i	0.218966	−	0.975733i	$-0.429732\pi$
$373$	−262.562	−	220.316i	−0.703920	−	0.590659i	−0.922886	+	0.385073i	$0.874176\pi$
$374$	−128.513	−	353.086i	−0.343617	−	0.944079i
$375$		0			0
$376$	27.1721	+	154.100i	0.0722661	+	0.409841i
$377$		−	293.516i		−	0.778556i
$378$		0			0
$379$	−607.166			−1.60202			−0.801011	−	0.598650i	$-0.795704\pi$
$379$	−607.166			−1.60202			−0.801011	+	0.598650i	$0.795704\pi$
$380$	−26.0167	+	4.58744i	−0.0684649	+	0.0120722i
$381$		0			0
$382$	−132.479	+	48.2183i	−0.346803	+	0.126226i
$383$	97.3839	−	116.058i	0.254266	−	0.303023i	−0.623779	−	0.781601i	$-0.714403\pi$
$383$	97.3839	−	116.058i	0.254266	−	0.303023i	0.878045	+	0.478578i	$0.158848\pi$
$384$		0			0
$385$	−16.3985	−	5.96856i	−0.0425935	−	0.0155028i
$386$	232.973	−	134.507i	0.603556	−	0.348463i
$387$		0			0
$388$	157.196	−	272.271i	0.405143	−	0.701729i
$389$	−389.211	−	463.844i	−1.00054	−	1.19240i	−0.981280	−	0.192587i	$-0.938312\pi$
$389$	−389.211	−	463.844i	−1.00054	−	1.19240i	−0.0192633	−	0.999814i	$-0.506132\pi$
$390$		0			0
$391$	49.4925	−	280.686i	0.126579	−	0.717867i
$392$	108.794	+	19.1833i	0.277535	+	0.0489369i
$393$		0			0
$394$	−200.062	+	167.872i	−0.507771	+	0.426071i
$395$	−67.7918	−	39.1396i	−0.171625	−	0.0990876i
$396$		0			0
$397$	301.433	+	522.097i	0.759277	+	1.31511i	0.943220	+	0.332170i	$0.107781\pi$
$397$	301.433	+	522.097i	0.759277	+	1.31511i	−0.183942	+	0.982937i	$0.558886\pi$
$398$	30.0801	−	82.6444i	0.0755782	−	0.207649i
$399$		0			0
$400$	75.5391	+	63.3849i	0.188848	+	0.158462i
$401$	−151.840	−	417.177i	−0.378653	−	1.04034i	−0.971915	−	0.235332i	$-0.924382\pi$
$401$	−151.840	−	417.177i	−0.378653	−	1.04034i	0.593262	−	0.805010i	$-0.297840\pi$
$402$		0			0
$403$	−96.3893	−	546.651i	−0.239179	−	1.35645i
$404$			251.126i			0.621599i
$405$		0			0
$406$	−107.208			−0.264058
$407$	−291.178	+	51.3425i	−0.715425	+	0.126149i
$408$		0			0
$409$	−388.673	+	141.465i	−0.950300	+	0.345881i	−0.770225	−	0.637772i	$-0.779856\pi$
$409$	−388.673	+	141.465i	−0.950300	+	0.345881i	−0.180075	+	0.983653i	$0.557634\pi$
$410$	−37.9773	+	45.2596i	−0.0926276	+	0.110389i
$411$		0			0
$412$	177.051	+	64.4411i	0.429734	+	0.156410i
$413$	−78.2869	+	45.1989i	−0.189557	+	0.109441i
$414$		0			0
$415$	−19.7992	+	34.2932i	−0.0477090	+	0.0826343i
$416$	44.3920	+	52.9043i	0.106711	+	0.127174i
$417$		0			0
$418$	51.6381	−	292.854i	0.123536	−	0.700609i
$419$	−606.886	−	107.010i	−1.44842	−	0.255395i	−0.606534	−	0.795057i	$-0.707441\pi$
$419$	−606.886	−	107.010i	−1.44842	−	0.255395i	−0.841881	+	0.539662i	$0.818552\pi$
$420$		0			0
$421$	2.88941	−	2.42451i	0.00686322	−	0.00575892i	−0.639350	−	0.768916i	$-0.720796\pi$
$421$	2.88941	−	2.42451i	0.00686322	−	0.00575892i	0.646213	+	0.763157i	$0.276352\pi$
$422$	−8.95351	−	5.16931i	−0.0212169	−	0.0122496i
$423$		0			0
$424$	35.9335	+	62.2387i	0.0847489	+	0.146789i
$425$	−238.668	+	655.734i	−0.561571	+	1.54290i
$426$		0			0
$427$	−273.149	−	229.199i	−0.639693	−	0.536766i
$428$	−73.8054	−	202.779i	−0.172442	−	0.473782i
$429$		0			0
$430$	2.10961	+	11.9642i	0.00490606	+	0.0278237i
$431$		−	658.872i		−	1.52871i	−0.644798	−	0.764353i	$-0.723059\pi$
$431$		−	658.872i		−	1.52871i	0.644798	−	0.764353i	$-0.276941\pi$
$432$		0			0
$433$	170.484			0.393728			0.196864	−	0.980431i	$-0.436924\pi$
$433$	170.484			0.393728			0.196864	+	0.980431i	$0.436924\pi$
$434$	−199.666	+	35.2066i	−0.460061	+	0.0811212i
$435$		0			0
$436$	−80.7510	+	29.3910i	−0.185209	+	0.0674105i
$437$	144.992	−	172.794i	0.331789	−	0.395410i
$438$		0			0
$439$	805.882	+	293.317i	1.83572	+	0.668148i	0.991157	+	0.132697i	$0.0423636\pi$
$439$	805.882	+	293.317i	1.83572	+	0.668148i	0.844566	+	0.535452i	$0.179859\pi$
$440$	13.5566	−	7.82692i	0.0308105	−	0.0177885i
$441$		0			0
$442$	−244.360	+	423.244i	−0.552851	+	0.957566i
$443$	160.598	+	191.394i	0.362524	+	0.432040i	0.916218	−	0.400681i	$-0.131226\pi$
$443$	160.598	+	191.394i	0.362524	+	0.432040i	−0.553693	+	0.832721i	$0.686782\pi$
$444$		0			0
$445$	7.44759	−	42.2374i	0.0167362	−	0.0949155i
$446$	119.869	+	21.1362i	0.268765	+	0.0473906i
$447$		0			0
$448$	19.3235	−	16.2143i	0.0431328	−	0.0361927i
$449$	208.642	+	120.460i	0.464682	+	0.268284i	0.714011	−	0.700135i	$-0.246877\pi$
$449$	208.642	+	120.460i	0.464682	+	0.268284i	−0.249329	+	0.968419i	$0.580210\pi$
$450$		0			0
$451$	−332.527	−	575.954i	−0.737311	−	1.27706i
$452$	−7.34036	+	20.1675i	−0.0162397	+	0.0446183i
$453$		0			0
$454$	70.9061	+	59.4973i	0.156181	+	0.131051i
$455$	7.76311	+	21.3290i	0.0170618	+	0.0468769i
$456$		0			0
$457$	−33.0420	−	187.391i	−0.0723020	−	0.410045i	−0.999381	−	0.0351791i	$-0.988800\pi$
$457$	−33.0420	−	187.391i	−0.0723020	−	0.410045i	0.927079	−	0.374866i	$-0.122311\pi$
$458$		−	467.310i		−	1.02033i
$459$		0			0
$460$	11.8740			0.0258130
$461$	−282.999	+	49.9003i	−0.613880	+	0.108244i	−0.471938	−	0.881632i	$-0.656446\pi$
$461$	−282.999	+	49.9003i	−0.613880	+	0.108244i	−0.141941	+	0.989875i	$0.545334\pi$
$462$		0			0
$463$	15.8899	−	5.78346i	0.0343195	−	0.0124913i	−0.324803	−	0.945782i	$-0.605298\pi$
$463$	15.8899	−	5.78346i	0.0343195	−	0.0124913i	0.359123	+	0.933290i	$0.383076\pi$
$464$	61.8154	−	73.6687i	0.133223	−	0.158769i
$465$		0			0
$466$	−190.004	−	69.1557i	−0.407734	−	0.148403i
$467$	−590.760	+	341.075i	−1.26501	+	0.730354i	−0.974040	−	0.226378i	$-0.927312\pi$
$467$	−590.760	+	341.075i	−1.26501	+	0.730354i	−0.290971	+	0.956732i	$0.593978\pi$
$468$		0			0
$469$	78.8699	−	136.607i	0.168166	−	0.291272i
$470$	−29.6531	−	35.3392i	−0.0630917	−	0.0751898i
$471$		0			0
$472$	14.0809	−	79.8570i	0.0298325	−	0.169189i
$473$	−134.674	−	23.7466i	−0.284722	−	0.0502042i
$474$		0			0
$475$	−423.060	+	354.989i	−0.890652	+	0.747346i
$476$	154.592	+	89.2536i	0.324772	+	0.187507i
$477$		0			0
$478$	−214.489	−	371.506i	−0.448722	−	0.777209i
$479$	191.036	−	524.867i	0.398822	−	1.09576i	−0.564037	−	0.825750i	$-0.690752\pi$
$479$	191.036	−	524.867i	0.398822	−	1.09576i	0.962859	−	0.270005i	$-0.0870255\pi$
$480$		0			0
$481$	294.596	+	247.196i	0.612466	+	0.513920i
$482$	151.280	+	415.640i	0.313860	+	0.862323i
$483$		0			0
$484$	−11.4250	−	64.7942i	−0.0236053	−	0.133872i
$485$			92.6875i			0.191108i
$486$		0			0
$487$	−115.842			−0.237869			−0.118935	−	0.992902i	$-0.537948\pi$
$487$	−115.842			−0.237869			−0.118935	+	0.992902i	$0.537948\pi$
$488$	314.992	−	55.5417i	0.645476	−	0.113815i
$489$		0			0
$490$	−30.6047	+	11.1392i	−0.0624587	+	0.0227331i
$491$	−79.5701	+	94.8280i	−0.162057	+	0.193132i	−0.840962	−	0.541094i	$-0.818010\pi$
$491$	−79.5701	+	94.8280i	−0.162057	+	0.193132i	0.678905	+	0.734226i	$0.262455\pi$
$492$		0			0
$493$	639.497	+	232.758i	1.29715	+	0.472126i
$494$	−334.963	+	193.391i	−0.678063	+	0.391480i
$495$		0			0
$496$	90.9341	−	157.502i	0.183335	−	0.317545i
$497$	17.7823	+	21.1921i	0.0357793	+	0.0426401i
$498$		0			0
$499$	−65.4282	+	371.062i	−0.131119	+	0.743610i	0.846366	+	0.532602i	$0.178786\pi$
$499$	−65.4282	+	371.062i	−0.131119	+	0.743610i	−0.977484	+	0.211008i	$0.932325\pi$
$500$	−57.6636	−	10.1676i	−0.115327	−	0.0203353i
$501$		0			0
$502$	145.667	−	122.229i	0.290173	−	0.243484i
$503$	363.520	+	209.878i	0.722704	+	0.417253i	0.815747	−	0.578409i	$-0.196326\pi$
$503$	363.520	+	209.878i	0.722704	+	0.417253i	−0.0930432	+	0.995662i	$0.529659\pi$
$504$		0			0
$505$	−37.0179	−	64.1169i	−0.0733028	−	0.126964i
$506$	−45.7139	+	125.598i	−0.0903436	+	0.248217i
$507$		0			0
$508$	−150.606	−	126.374i	−0.296469	−	0.248767i
$509$	41.8155	+	114.887i	0.0821523	+	0.225712i	0.973967	−	0.226689i	$-0.0727900\pi$
$509$	41.8155	+	114.887i	0.0821523	+	0.225712i	−0.891815	+	0.452400i	$0.850568\pi$
$510$		0			0
$511$	−12.8516	−	72.8849i	−0.0251498	−	0.142632i
$512$			22.6274i			0.0441942i
$513$		0			0
$514$	67.2841			0.130903
$515$	−54.7033	+	9.64566i	−0.106220	+	0.0187294i
$516$		0			0
$517$	487.965	−	177.605i	0.943840	−	0.343530i
$518$	90.2892	−	107.602i	0.174303	−	0.207727i
$519$		0			0
$520$	−19.1326	−	6.96368i	−0.0367934	−	0.0133917i
$521$	891.453	−	514.680i	1.71104	−	0.987870i	0.777880	−	0.628412i	$-0.216295\pi$
$521$	891.453	−	514.680i	1.71104	−	0.987870i	0.933161	−	0.359458i	$-0.117038\pi$
$522$		0			0
$523$	−131.269	+	227.364i	−0.250992	+	0.434731i	−0.963799	−	0.266629i	$-0.914090\pi$
$523$	−131.269	+	227.364i	−0.250992	+	0.434731i	0.712807	+	0.701360i	$0.247423\pi$
$524$	176.161	+	209.940i	0.336184	+	0.400649i
$525$		0			0
$526$	−116.499	+	660.697i	−0.221480	+	1.25608i
$527$	1267.45	+	223.486i	2.40503	+	0.424072i
$528$		0			0
$529$	327.572	−	274.866i	0.619230	−	0.519595i
$530$	−18.3489	−	10.5938i	−0.0346207	−	0.0199882i
$531$		0			0
$532$	70.6369	+	122.347i	0.132776	+	0.229975i
$533$	−295.852	+	812.848i	−0.555070	+	1.52504i
$534$		0			0
$535$	48.7350	+	40.8935i	0.0910934	+	0.0764364i
$536$	48.3945	+	132.963i	0.0902883	+	0.248065i
$537$		0			0
$538$	−111.757	−	633.804i	−0.207726	−	1.17808i
$539$		−	366.609i		−	0.680165i
$540$		0			0
$541$	14.7044			0.0271800			0.0135900	−	0.999908i	$-0.495674\pi$
$541$	14.7044			0.0271800			0.0135900	+	0.999908i	$0.495674\pi$
$542$	−614.109	+	108.284i	−1.13304	+	0.199786i
$543$		0			0
$544$	−150.468	+	54.7659i	−0.276596	+	0.100673i
$545$	16.2847	−	19.4074i	0.0298802	−	0.0356098i
$546$		0			0
$547$	353.812	+	128.777i	0.646823	+	0.235424i	0.644537	−	0.764573i	$-0.277050\pi$
$547$	353.812	+	128.777i	0.646823	+	0.235424i	0.00228579	+	0.999997i	$0.499272\pi$
$548$	−346.735	+	200.188i	−0.632729	+	0.365306i
$549$		0			0
$550$	163.621	−	283.400i	0.297492	−	0.515272i
$551$	346.200	+	412.585i	0.628311	+	0.748792i
$552$		0			0
$553$	−72.6906	+	412.249i	−0.131448	+	0.745477i
$554$	104.992	+	18.5129i	0.189516	+	0.0334167i
$555$		0			0
$556$	−10.9205	+	9.16343i	−0.0196413	+	0.0164810i
$557$	−339.531	−	196.028i	−0.609571	−	0.351936i	0.163226	−	0.986589i	$-0.447810\pi$
$557$	−339.531	−	196.028i	−0.609571	−	0.351936i	−0.772798	+	0.634653i	$0.781143\pi$
$558$		0			0
$559$	88.9339	+	154.038i	0.159095	+	0.275560i
$560$	−2.54351	+	6.98825i	−0.00454199	+	0.0124790i
$561$		0			0
$562$	8.40755	+	7.05477i	0.0149601	+	0.0125530i
$563$	282.488	+	776.129i	0.501754	+	1.37856i	0.889560	+	0.456818i	$0.151011\pi$
$563$	282.488	+	776.129i	0.501754	+	1.37856i	−0.387806	+	0.921741i	$0.626767\pi$
$564$		0			0
$565$	−1.09872	−	6.23114i	−0.00194463	−	0.0110286i
$566$			231.173i			0.408433i
$567$		0			0
$568$	−24.8155			−0.0436893
$569$	820.292	−	144.640i	1.44164	−	0.254200i	0.602501	−	0.798118i	$-0.294171\pi$
$569$	820.292	−	144.640i	1.44164	−	0.254200i	0.839138	+	0.543919i	$0.183060\pi$
$570$		0			0
$571$	−171.024	+	62.2478i	−0.299517	+	0.109015i	−0.487407	−	0.873175i	$-0.662057\pi$
$571$	−171.024	+	62.2478i	−0.299517	+	0.109015i	0.187890	+	0.982190i	$0.439835\pi$
$572$	147.318	−	175.566i	0.257548	−	0.306934i
$573$		0			0
$574$	296.896	+	108.061i	0.517240	+	0.188260i
$575$	214.968	−	124.112i	0.373858	−	0.215847i
$576$		0			0
$577$	−25.3860	+	43.9699i	−0.0439966	+	0.0762043i	−0.887185	−	0.461414i	$-0.847342\pi$
$577$	−25.3860	+	43.9699i	−0.0439966	+	0.0762043i	0.843189	+	0.537618i	$0.180676\pi$
$578$	−465.654	−	554.945i	−0.805630	−	0.960112i
$579$		0			0
$580$	−4.92323	+	27.9210i	−0.00848832	+	0.0481397i
$581$	208.541	+	36.7713i	0.358934	+	0.0632898i
$582$		0			0
$583$	182.698	−	153.302i	0.313376	−	0.262954i
$584$	57.4936	+	33.1940i	0.0984480	+	0.0568390i
$585$		0			0
$586$	38.2449	+	66.2421i	0.0652643	+	0.113041i
$587$	−29.4058	+	80.7919i	−0.0500951	+	0.137635i	−0.962217	−	0.272284i	$-0.912221\pi$
$587$	−29.4058	+	80.7919i	−0.0500951	+	0.137635i	0.912122	+	0.409919i	$0.134443\pi$
$588$		0			0
$589$	780.262	+	654.718i	1.32472	+	1.11158i
$590$	8.17643	+	22.4646i	0.0138584	+	0.0380755i
$591$		0			0
$592$	21.8797	+	124.086i	0.0369590	+	0.209605i
$593$		−	333.051i		−	0.561638i	−0.959761	−	0.280819i	$-0.909394\pi$
$593$		−	333.051i		−	0.561638i	0.959761	−	0.280819i	$-0.0906060\pi$
$594$		0			0
$595$	−52.6267			−0.0884482
$596$	−184.657	+	32.5600i	−0.309827	+	0.0546308i
$597$		0			0
$598$	163.361	−	59.4586i	0.273179	−	0.0994290i
$599$	−376.276	+	448.428i	−0.628173	+	0.748628i	−0.982453	−	0.186512i	$-0.940282\pi$
$599$	−376.276	+	448.428i	−0.628173	+	0.748628i	0.354279	+	0.935140i	$0.384726\pi$
$600$		0			0
$601$	684.489	+	249.134i	1.13892	+	0.414532i	0.841522	−	0.540223i	$-0.181660\pi$
$601$	684.489	+	249.134i	1.13892	+	0.414532i	0.297395	+	0.954755i	$0.403882\pi$
$602$	56.2630	−	32.4835i	0.0934602	−	0.0539593i
$603$		0			0
$604$	201.773	−	349.481i	0.334061	−	0.578611i
$605$	12.4682	+	14.8590i	0.0206086	+	0.0245603i
$606$		0			0
$607$	50.2841	−	285.175i	0.0828404	−	0.469811i	−0.914961	−	0.403541i	$-0.867779\pi$
$607$	50.2841	−	285.175i	0.0828404	−	0.469811i	0.997802	−	0.0662697i	$-0.0211098\pi$
$608$	−124.800	−	22.0057i	−0.205264	−	0.0361936i
$609$		0			0
$610$	−72.2359	+	60.6131i	−0.118420	+	0.0993658i
$611$	−584.925	−	337.706i	−0.957323	−	0.552711i
$612$		0			0
$613$	−431.468	−	747.325i	−0.703864	−	1.21913i	−0.967100	−	0.254396i	$-0.918123\pi$
$613$	−431.468	−	747.325i	−0.703864	−	1.21913i	0.263236	−	0.964731i	$-0.415210\pi$
$614$	−70.8115	+	194.553i	−0.115328	+	0.316862i
$615$		0			0
$616$	−64.1263	−	53.8084i	−0.104101	−	0.0873513i
$617$	37.3588	+	102.642i	0.0605491	+	0.166357i	0.966279	−	0.257499i	$-0.0828984\pi$
$617$	37.3588	+	102.642i	0.0605491	+	0.166357i	−0.905729	+	0.423856i	$0.860676\pi$
$618$		0			0
$619$	16.5748	+	94.0001i	0.0267767	+	0.151858i	0.995265	−	0.0972023i	$-0.0309894\pi$
$619$	16.5748	+	94.0001i	0.0267767	+	0.151858i	−0.968488	+	0.249060i	$0.919878\pi$
$620$			53.6176i			0.0864800i
$621$		0			0
$622$	391.081			0.628748
$623$	−225.870	+	39.8270i	−0.362552	+	0.0639277i
$624$		0			0
$625$	−562.919	+	204.886i	−0.900671	+	0.327817i
$626$	27.2673	−	32.4959i	0.0435579	−	0.0519103i
$627$		0			0
$628$	−137.943	−	50.2072i	−0.219655	−	0.0799478i
$629$	−772.193	+	445.826i	−1.22765	+	0.708785i
$630$		0			0
$631$	264.888	−	458.800i	0.419791	−	0.727100i	−0.576127	−	0.817360i	$-0.695437\pi$
$631$	264.888	−	458.800i	0.419791	−	0.727100i	0.995918	+	0.0902603i	$0.0287699\pi$
$632$	−241.367	−	287.650i	−0.381910	−	0.455143i
$633$		0			0
$634$	−65.7227	+	372.732i	−0.103664	+	0.587905i
$635$	57.0810	+	10.0649i	0.0898914	+	0.0158503i
$636$		0			0
$637$	−365.278	+	306.504i	−0.573435	+	0.481169i
$638$	−276.382	−	159.569i	−0.433201	−	0.250109i
$639$		0			0
$640$	−3.33546	−	5.77718i	−0.00521165	−	0.00902685i
$641$	90.7979	−	249.465i	0.141650	−	0.389181i	−0.848499	−	0.529197i	$-0.822493\pi$
$641$	90.7979	−	249.465i	0.141650	−	0.389181i	0.990149	+	0.140016i	$0.0447154\pi$
$642$		0			0
$643$	111.106	+	93.2293i	0.172794	+	0.144991i	0.725083	−	0.688661i	$-0.241801\pi$
$643$	111.106	+	93.2293i	0.172794	+	0.144991i	−0.552290	+	0.833652i	$0.686246\pi$
$644$	−21.7175	−	59.6683i	−0.0337228	−	0.0926526i
$645$		0			0
$646$	−155.725	−	883.161i	−0.241061	−	1.36712i
$647$		−	578.671i		−	0.894391i	−0.894436	−	0.447196i	$-0.852423\pi$
$647$		−	578.671i		−	0.894391i	0.894436	−	0.447196i	$-0.147577\pi$
$648$		0			0
$649$	−269.099			−0.414636
$650$	−419.166	+	73.9103i	−0.644871	+	0.113708i
$651$		0			0
$652$	−408.068	+	148.525i	−0.625871	+	0.227798i
$653$	417.061	−	497.034i	0.638684	−	0.761154i	−0.345477	−	0.938427i	$-0.612283\pi$
$653$	417.061	−	497.034i	0.638684	−	0.761154i	0.984162	+	0.177273i	$0.0567275\pi$
$654$		0			0
$655$	−75.9237	−	27.6340i	−0.115914	−	0.0421893i
$656$	−245.444	+	141.707i	−0.374152	+	0.216017i
$657$		0			0
$658$	−123.349	+	213.646i	−0.187460	+	0.324690i
$659$	346.075	+	412.436i	0.525151	+	0.625851i	0.961791	−	0.273785i	$-0.0882758\pi$
$659$	346.075	+	412.436i	0.525151	+	0.625851i	−0.436639	+	0.899637i	$0.643831\pi$
$660$		0			0
$661$	−66.4965	+	377.120i	−0.100600	+	0.570530i	0.892287	+	0.451468i	$0.149100\pi$
$661$	−66.4965	+	377.120i	−0.100600	+	0.570530i	−0.992887	+	0.119061i	$0.962011\pi$
$662$	531.115	+	93.6500i	0.802289	+	0.141465i
$663$		0			0
$664$	−145.511	+	122.098i	−0.219143	+	0.183883i
$665$	−36.0697	−	20.8249i	−0.0542402	−	0.0313156i
$666$		0			0
$667$	−121.039	−	209.646i	−0.181468	−	0.314311i
$668$	147.424	−	405.044i	0.220695	−	0.606354i
$669$		0			0
$670$	−31.9558	−	26.8141i	−0.0476952	−	0.0400210i
$671$	−363.037	−	997.436i	−0.541039	−	1.48649i
$672$		0			0
$673$	28.0045	+	158.821i	0.0416114	+	0.235990i	0.998519	−	0.0544023i	$-0.0173253\pi$
$673$	28.0045	+	158.821i	0.0416114	+	0.235990i	−0.956908	+	0.290392i	$0.906214\pi$
$674$			169.360i			0.251275i
$675$		0			0
$676$	39.9056			0.0590320
$677$	−126.078	+	22.2310i	−0.186231	+	0.0328375i	−0.265986	−	0.963977i	$-0.585697\pi$
$677$	−126.078	+	22.2310i	−0.186231	+	0.0328375i	0.0797548	+	0.996815i	$0.474586\pi$
$678$		0			0
$679$	465.766	−	169.525i	0.685959	−	0.249669i
$680$	30.3443	−	36.1629i	0.0446239	−	0.0531807i
$681$		0			0
$682$	−567.144	−	206.423i	−0.831589	−	0.302674i
$683$	410.786	−	237.168i	0.601444	−	0.347244i	−0.168165	−	0.985759i	$-0.553784\pi$
$683$	410.786	−	237.168i	0.601444	−	0.347244i	0.769609	+	0.638515i	$0.220451\pi$
$684$		0			0
$685$	59.0185	−	102.223i	0.0861583	−	0.149231i
$686$	252.402	+	300.800i	0.367932	+	0.438485i
$687$		0			0
$688$	−10.1197	+	57.3914i	−0.0147088	+	0.0834178i
$689$	−305.491	−	53.8663i	−0.443383	−	0.0781804i
$690$		0			0
$691$	−218.877	+	183.660i	−0.316754	+	0.265788i	−0.787277	−	0.616600i	$-0.788510\pi$
$691$	−218.877	+	183.660i	−0.316754	+	0.265788i	0.470523	+	0.882388i	$0.344065\pi$
$692$	−109.201	−	63.0474i	−0.157805	−	0.0911089i
$693$		0			0
$694$	−175.909	−	304.683i	−0.253471	−	0.439024i
$695$	1.43745	−	3.94936i	0.00206827	−	0.00568253i
$696$		0			0
$697$	−1536.38	−	1289.18i	−2.20428	−	1.84961i
$698$	154.755	+	425.186i	0.221712	+	0.609149i
$699$		0			0
$700$	26.9960	+	153.102i	0.0385658	+	0.218717i
$701$		−	320.086i		−	0.456613i	−0.973589	−	0.228307i	$-0.926681\pi$
$701$		−	320.086i		−	0.456613i	0.973589	−	0.228307i	$-0.0733189\pi$
$702$		0			0
$703$	−705.669			−1.00380
$704$	73.9498	−	13.0393i	0.105042	−	0.0185218i
$705$		0			0
$706$	−440.232	+	160.231i	−0.623558	+	0.226957i
$707$	−254.490	+	303.289i	−0.359958	+	0.428981i
$708$		0			0
$709$	−796.794	−	290.009i	−1.12383	−	0.409040i	−0.287780	−	0.957697i	$-0.592917\pi$
$709$	−796.794	−	290.009i	−1.12383	−	0.409040i	−0.836048	+	0.548657i	$0.815139\pi$
$710$	6.33584	−	3.65800i	0.00892372	−	0.00515211i
$711$		0			0
$712$	102.868	−	178.173i	0.144478	−	0.250242i
$713$	−294.273	−	350.701i	−0.412725	−	0.491866i
$714$		0			0
$715$	−11.7330	+	66.5410i	−0.0164098	+	0.0930644i
$716$	−391.694	−	69.0662i	−0.547058	−	0.0964611i
$717$		0			0
$718$	347.675	−	291.734i	0.484227	−	0.406315i
$719$	−143.869	−	83.0628i	−0.200096	−	0.115525i	0.396604	−	0.917990i	$-0.370189\pi$
$719$	−143.869	−	83.0628i	−0.200096	−	0.115525i	−0.596700	+	0.802464i	$0.703522\pi$
$720$		0			0
$721$	148.523	+	257.249i	0.205996	+	0.356795i
$722$	68.1308	−	187.188i	0.0943640	−	0.259263i
$723$		0			0
$724$	−109.235	−	91.6589i	−0.150877	−	0.126601i
$725$	202.712	+	556.946i	0.279602	+	0.768201i
$726$		0			0
$727$	136.863	+	776.190i	0.188258	+	1.06766i	0.921698	+	0.387908i	$0.126802\pi$
$727$	136.863	+	776.190i	0.188258	+	1.06766i	−0.733440	+	0.679754i	$0.762087\pi$
$728$			108.880i			0.149561i
$729$		0			0
$730$	−19.5722			−0.0268112
$731$	−406.135	+	71.6126i	−0.555589	+	0.0979653i
$732$		0			0
$733$	650.225	−	236.663i	0.887074	−	0.322869i	0.142013	−	0.989865i	$-0.454643\pi$
$733$	650.225	−	236.663i	0.887074	−	0.322869i	0.745061	+	0.666996i	$0.232420\pi$
$734$	662.417	−	789.438i	0.902475	−	1.07553i
$735$		0			0
$736$	53.5238	+	19.4811i	0.0727225	+	0.0264688i
$737$	406.655	−	234.782i	0.551770	−	0.318565i
$738$		0			0
$739$	−117.695	+	203.854i	−0.159262	+	0.275851i	−0.934603	−	0.355693i	$-0.884245\pi$
$739$	−117.695	+	203.854i	−0.159262	+	0.275851i	0.775340	+	0.631543i	$0.217578\pi$
$740$	−23.8775	−	28.4561i	−0.0322669	−	0.0384542i
$741$		0			0
$742$	−19.6749	+	111.582i	−0.0265160	+	0.150380i
$743$	−600.536	−	105.891i	−0.808259	−	0.142518i	−0.245776	−	0.969327i	$-0.579043\pi$
$743$	−600.536	−	105.891i	−0.808259	−	0.142518i	−0.562483	+	0.826809i	$0.690154\pi$
$744$		0			0
$745$	42.3466	−	35.5330i	0.0568411	−	0.0476953i
$746$	419.782	+	242.361i	0.562711	+	0.324881i
$747$		0			0
$748$	265.692	+	460.193i	0.355204	+	0.615231i
$749$	116.359	−	319.694i	0.155352	−	0.426827i
$750$		0			0
$751$	163.414	+	137.121i	0.217596	+	0.182585i	0.745070	−	0.666987i	$-0.232416\pi$
$751$	163.414	+	137.121i	0.217596	+	0.182585i	−0.527474	+	0.849571i	$0.676861\pi$
$752$	−75.6866	−	207.947i	−0.100647	−	0.276526i
$753$		0			0
$754$	72.0803	+	408.787i	0.0955972	+	0.542158i
$755$			118.972i			0.157578i
$756$		0			0
$757$	−212.260			−0.280397			−0.140198	−	0.990123i	$-0.544774\pi$
$757$	−212.260			−0.280397			−0.140198	+	0.990123i	$0.544774\pi$
$758$	845.618	−	149.105i	1.11559	−	0.196709i
$759$		0			0
$760$	35.1076	−	12.7781i	0.0461942	−	0.0168133i
$761$	−934.612	+	1113.83i	−1.22814	+	1.46364i	−0.387649	+	0.921807i	$0.626713\pi$
$761$	−934.612	+	1113.83i	−1.22814	+	1.46364i	−0.840488	+	0.541830i	$0.817732\pi$
$762$		0			0
$763$	−127.309	−	46.3368i	−0.166853	−	0.0607297i
$764$	172.666	−	99.6886i	0.226002	−	0.130482i
$765$		0			0
$766$	−107.128	+	185.552i	−0.139854	+	0.242235i
$767$	224.981	+	268.122i	0.293326	+	0.349572i
$768$		0			0
$769$	150.826	−	855.378i	0.196133	−	1.11233i	−0.714663	−	0.699469i	$-0.753420\pi$
$769$	150.826	−	855.378i	0.196133	−	1.11233i	0.910796	−	0.412856i	$-0.135469\pi$
$770$	24.3044	+	4.28552i	0.0315641	+	0.00556561i
$771$		0			0
$772$	−291.436	+	244.544i	−0.377508	+	0.316767i
$773$	14.6924	+	8.48268i	0.0190070	+	0.0109737i	0.509473	−	0.860486i	$-0.329840\pi$
$773$	14.6924	+	8.48268i	0.0190070	+	0.0109737i	−0.490466	+	0.871460i	$0.663174\pi$
$774$		0			0
$775$	560.435	+	970.701i	0.723141	+	1.25252i
$776$	−152.068	+	417.803i	−0.195964	+	0.538406i
$777$		0			0
$778$	655.974	+	550.428i	0.843155	+	0.707491i
$779$	−542.879	−	1491.55i	−0.696892	−	1.91469i
$780$		0			0
$781$	14.3003	+	81.1008i	0.0183102	+	0.103842i
$782$			403.074i			0.515440i
$783$		0			0
$784$	−156.231			−0.199274
$785$	42.6203	−	7.51511i	0.0542934	−	0.00957339i
$786$		0			0
$787$	382.780	−	139.321i	0.486379	−	0.177027i	−0.0871788	−	0.996193i	$-0.527785\pi$
$787$	382.780	−	139.321i	0.486379	−	0.177027i	0.573557	+	0.819165i	$0.305563\pi$
$788$	237.407	−	282.930i	0.301277	−	0.359048i
$789$		0			0
$790$	104.027	+	37.8628i	0.131680	+	0.0479276i
$791$	−29.3027	+	16.9179i	−0.0370452	+	0.0213880i
$792$		0			0
$793$	−690.296	+	1195.63i	−0.870487	+	1.50773i
$794$	−548.029	−	653.115i	−0.690213	−	0.822563i
$795$		0			0
$796$	−21.5980	+	122.488i	−0.0271331	+	0.153880i
$797$	−114.221	−	20.1403i	−0.143314	−	0.0252702i	0.101531	−	0.994832i	$-0.467626\pi$
$797$	−114.221	−	20.1403i	−0.143314	−	0.0252702i	−0.244845	+	0.969562i	$0.578737\pi$
$798$		0			0
$799$	1199.62	−	1006.60i	1.50141	−	1.25983i
$800$	−120.771	−	69.7273i	−0.150964	−	0.0871592i
$801$		0			0
$802$	313.920	+	543.726i	0.391422	+	0.677963i
$803$	75.3514	−	207.026i	0.0938374	−	0.257816i
$804$		0			0
$805$	14.3404	+	12.0331i	0.0178142	+	0.0149479i
$806$	268.488	+	737.666i	0.333112	+	0.915218i
$807$		0			0
$808$	−61.6704	−	349.750i	−0.0763247	−	0.432859i
$809$			1246.51i			1.54080i	0.637560	+	0.770401i	$0.279944\pi$
$809$			1246.51i			1.54080i	−0.637560	+	0.770401i	$0.720056\pi$
$810$		0			0
$811$	593.707			0.732067			0.366034	−	0.930602i	$-0.380715\pi$
$811$	593.707			0.732067			0.366034	+	0.930602i	$0.380715\pi$
$812$	149.311	−	26.3276i	0.183881	−	0.0324232i
$813$		0			0
$814$	392.923	−	143.012i	0.482707	−	0.175691i
$815$	82.2933	−	98.0734i	0.100973	−	0.120335i
$816$		0			0
$817$	−306.698	−	111.629i	−0.375396	−	0.136633i
$818$	506.575	−	292.471i	0.619285	−	0.357544i
$819$		0			0
$820$	41.7774	−	72.3607i	0.0509481	−	0.0882447i
$821$	−291.743	−	347.685i	−0.355350	−	0.423490i	0.558523	−	0.829489i	$-0.311368\pi$
$821$	−291.743	−	347.685i	−0.355350	−	0.423490i	−0.913874	+	0.405999i	$0.866924\pi$
$822$		0			0
$823$	25.9808	−	147.345i	0.0315685	−	0.179034i	−0.964947	−	0.262446i	$-0.915471\pi$
$823$	25.9808	−	147.345i	0.0315685	−	0.179034i	0.996515	+	0.0834125i	$0.0265819\pi$
$824$	−262.408	−	46.2697i	−0.318457	−	0.0561525i
$825$		0			0
$826$	97.9326	−	82.1752i	0.118562	−	0.0994857i
$827$	858.941	+	495.910i	1.03862	+	0.599649i	0.919443	−	0.393223i	$-0.128640\pi$
$827$	858.941	+	495.910i	1.03862	+	0.599649i	0.119180	+	0.992873i	$0.461973\pi$
$828$		0			0
$829$	−554.523	−	960.463i	−0.668906	−	1.15858i	−0.978210	−	0.207617i	$-0.933429\pi$
$829$	−554.523	−	960.463i	−0.668906	−	1.15858i	0.309304	−	0.950963i	$-0.399904\pi$
$830$	19.1533	−	52.6234i	0.0230763	−	0.0634017i
$831$		0			0
$832$	−74.8180	−	62.7797i	−0.0899254	−	0.0754564i
$833$	−378.131	−	1038.91i	−0.453939	−	1.24719i
$834$		0			0
$835$	22.0667	+	125.147i	0.0264272	+	0.149876i
$836$			420.548i			0.503048i
$837$		0			0
$838$	871.507			1.03998
$839$	717.074	−	126.440i	0.854677	−	0.150703i	0.270891	−	0.962610i	$-0.412682\pi$
$839$	717.074	−	126.440i	0.854677	−	0.150703i	0.583786	+	0.811907i	$0.301571\pi$
$840$		0			0
$841$	−247.126	+	89.9465i	−0.293848	+	0.106952i
$842$	−3.42877	+	4.08625i	−0.00407217	+	0.00485303i
$843$		0			0
$844$	13.7393	+	5.00069i	0.0162788	+	0.00592498i
$845$	−10.1886	+	5.88240i	−0.0120575	+	0.00696142i
$846$		0			0
$847$	51.8641	−	89.8313i	0.0612327	−	0.106058i
$848$	−65.3300	−	77.8572i	−0.0770401	−	0.0918128i
$849$		0			0
$850$	171.367	−	971.870i	0.201608	−	1.14338i
$851$	312.355	+	55.0767i	0.367045	+	0.0647199i
$852$		0			0
$853$	−1035.22	+	868.650i	−1.21362	+	1.01835i	−0.214485	+	0.976727i	$0.568807\pi$
$853$	−1035.22	+	868.650i	−1.21362	+	1.01835i	−0.999134	+	0.0416200i	$0.986748\pi$
$854$	436.708	+	252.134i	0.511368	+	0.295238i
$855$		0			0
$856$	152.588	+	264.291i	0.178257	+	0.308751i
$857$	−469.442	+	1289.78i	−0.547774	+	1.50500i	0.288936	+	0.957348i	$0.406699\pi$
$857$	−469.442	+	1289.78i	−0.547774	+	1.50500i	−0.836709	+	0.547647i	$0.815524\pi$
$858$		0			0
$859$	−49.4325	−	41.4788i	−0.0575466	−	0.0482873i	0.613561	−	0.789648i	$-0.289737\pi$
$859$	−49.4325	−	41.4788i	−0.0575466	−	0.0482873i	−0.671107	+	0.741360i	$0.734181\pi$
$860$	−5.87622	−	16.1448i	−0.00683281	−	0.0187730i
$861$		0			0
$862$	161.803	+	917.630i	0.187706	+	1.06454i
$863$			998.597i			1.15712i	0.815639	+	0.578561i	$0.196386\pi$
$863$			998.597i			1.15712i	−0.815639	+	0.578561i	$0.803614\pi$
$864$		0			0
$865$	37.1747			0.0429765
$866$	−237.438	+	41.8667i	−0.274178	+	0.0483449i
$867$		0			0
$868$	269.435	−	98.0664i	0.310409	−	0.112980i
$869$	−800.994	+	954.587i	−0.921742	+	1.09849i
$870$		0			0
$871$	−573.915	−	208.888i	−0.658915	−	0.239825i
$872$	105.247	−	60.7641i	0.120696	−	0.0696836i
$873$		0			0
$874$	−159.500	+	276.262i	−0.182494	+	0.316089i
$875$	−59.3375	−	70.7157i	−0.0678143	−	0.0808180i
$876$		0			0
$877$	263.675	−	1495.37i	0.300656	−	1.70510i	−0.342625	−	0.939472i	$-0.611316\pi$
$877$	263.675	−	1495.37i	0.300656	−	1.70510i	0.643281	−	0.765630i	$-0.277573\pi$
$878$	−1194.41	−	210.606i	−1.36037	−	0.239870i
$879$		0			0
$880$	−16.9586	+	14.2300i	−0.0192711	+	0.0161704i
$881$	−462.122	−	266.806i	−0.524543	−	0.302845i	0.214249	−	0.976779i	$-0.431270\pi$
$881$	−462.122	−	266.806i	−0.524543	−	0.302845i	−0.738791	+	0.673934i	$0.764603\pi$
$882$		0			0
$883$	268.778	+	465.537i	0.304392	+	0.527222i	0.977126	−	0.212662i	$-0.0682134\pi$
$883$	268.778	+	465.537i	0.304392	+	0.527222i	−0.672734	+	0.739885i	$0.734880\pi$
$884$	236.389	−	649.473i	0.267408	−	0.734698i
$885$		0			0
$886$	−270.671	−	227.120i	−0.305498	−	0.256343i
$887$	335.258	+	921.113i	0.377968	+	1.03846i	0.972197	+	0.234163i	$0.0752350\pi$
$887$	335.258	+	921.113i	0.377968	+	1.03846i	−0.594229	+	0.804296i	$0.702543\pi$
$888$		0			0
$889$	−53.8235	−	305.248i	−0.0605439	−	0.343361i
$890$			60.6542i			0.0681508i
$891$		0			0
$892$	−172.136			−0.192978
$893$	1220.53	−	215.212i	1.36678	−	0.240999i
$894$		0			0
$895$	110.187	−	40.1049i	0.123114	−	0.0448099i
$896$	−22.9305	+	27.3276i	−0.0255921	+	0.0304995i
$897$		0			0
$898$	−320.164	−	116.530i	−0.356530	−	0.129766i
$899$	946.666	−	546.558i	1.05302	−	0.607962i
$900$		0			0
$901$	359.616	−	622.873i	0.399130	−	0.691313i
$902$	604.560	+	720.487i	0.670244	+	0.798766i
$903$		0			0
$904$	5.27049	−	29.8904i	0.00583019	−	0.0330646i
$905$	41.4008	+	7.30008i	0.0457468	+	0.00806639i
$906$		0			0
$907$	261.282	−	219.241i	0.288072	−	0.241721i	−0.487287	−	0.873242i	$-0.662013\pi$
$907$	261.282	−	219.241i	0.288072	−	0.241721i	0.775359	+	0.631521i	$0.217569\pi$
$908$	−113.364	−	65.4508i	−0.124850	−	0.0720823i
$909$		0			0
$910$	−16.0498	−	27.7990i	−0.0176371	−	0.0305484i
$911$	468.039	−	1285.93i	0.513764	−	1.41156i	−0.363520	−	0.931586i	$-0.618425\pi$
$911$	468.039	−	1285.93i	0.513764	−	1.41156i	0.877285	−	0.479970i	$-0.159352\pi$
$912$		0			0
$913$	482.889	+	405.192i	0.528903	+	0.443803i
$914$	92.0371	+	252.870i	0.100697	+	0.276663i
$915$		0			0
$916$	114.760	+	650.835i	0.125284	+	0.710519i
$917$			432.069i			0.471177i
$918$		0			0
$919$	558.729			0.607975			0.303987	−	0.952676i	$-0.401682\pi$
$919$	558.729			0.607975			0.303987	+	0.952676i	$0.401682\pi$
$920$	−16.5372	+	2.91596i	−0.0179753	+	0.00316952i
$921$		0			0
$922$	381.886	−	138.995i	0.414193	−	0.150754i
$923$	68.8506	−	82.0529i	0.0745944	−	0.0888981i
$924$		0			0
$925$	−729.719	−	265.596i	−0.788885	−	0.287131i
$926$	−20.7101	+	11.9570i	−0.0223651	+	0.0129125i
$927$		0			0
$928$	−68.0008	+	117.781i	−0.0732768	+	0.126919i
$929$	667.609	+	795.625i	0.718632	+	0.856432i	0.994497	−	0.104764i	$-0.0334088\pi$
$929$	667.609	+	795.625i	0.718632	+	0.856432i	−0.275865	+	0.961196i	$0.588964\pi$
$930$		0			0
$931$	151.938	−	861.685i	0.163199	−	0.925548i
$932$	281.607	+	49.6549i	0.302153	+	0.0532778i
$933$		0			0
$934$	739.008	−	620.102i	0.791230	−	0.663920i
$935$	−135.672	−	78.3303i	−0.145104	−	0.0837757i
$936$		0			0
$937$	323.576	+	560.450i	0.345332	+	0.598132i	0.985414	−	0.170174i	$-0.0544330\pi$
$937$	323.576	+	560.450i	0.345332	+	0.598132i	−0.640082	+	0.768306i	$0.721100\pi$
$938$	−76.2971	+	209.625i	−0.0813402	+	0.223480i
$939$		0			0
$940$	49.9772	+	41.9358i	0.0531672	+	0.0446126i
$941$	−228.423	−	627.587i	−0.242745	−	0.666936i	−0.999906	−	0.0137078i	$-0.995637\pi$
$941$	−228.423	−	627.587i	−0.242745	−	0.666936i	0.757161	−	0.653228i	$-0.226586\pi$
$942$		0			0
$943$	123.885	+	702.585i	0.131373	+	0.745053i
$944$			114.677i			0.121480i
$945$		0			0
$946$	193.395			0.204435
$947$	−1716.52	+	302.668i	−1.81258	+	0.319607i	−0.974237	−	0.225529i	$-0.927589\pi$
$947$	−1716.52	+	302.668i	−1.81258	+	0.319607i	−0.838347	+	0.545136i	$0.816478\pi$
$948$		0			0
$949$	−269.272	+	98.0071i	−0.283743	+	0.103274i
$950$	502.031	−	598.297i	0.528453	−	0.629786i
$951$		0			0
$952$	−237.223	−	86.3420i	−0.249184	−	0.0906954i
$953$	−671.945	+	387.948i	−0.705084	+	0.407080i	−0.809238	−	0.587481i	$-0.800120\pi$
$953$	−671.945	+	387.948i	−0.705084	+	0.407080i	0.104154	+	0.994561i	$0.466786\pi$
$954$		0			0
$955$	−29.3898	+	50.9045i	−0.0307746	+	0.0533032i
$956$	389.958	+	464.734i	0.407906	+	0.486123i
$957$		0			0
$958$	−137.167	+	777.911i	−0.143180	+	0.812015i
$959$	−621.628	−	109.610i	−0.648205	−	0.114296i
$960$		0			0
$961$	847.439	−	711.086i	0.881830	−	0.739943i
$962$	−470.998	−	271.931i	−0.489603	−	0.282672i
$963$		0			0
$964$	−312.764	−	541.722i	−0.324444	−	0.561953i
$965$	38.3611	−	105.396i	0.0397525	−	0.109219i
$966$		0			0
$967$	−149.339	−	125.310i	−0.154435	−	0.129586i	0.562296	−	0.826936i	$-0.309918\pi$
$967$	−149.339	−	125.310i	−0.154435	−	0.129586i	−0.716731	+	0.697350i	$0.754363\pi$
$968$	31.8238	+	87.4351i	0.0328758	+	0.0903255i
$969$		0			0
$970$	−22.7618	−	129.088i	−0.0234658	−	0.133081i
$971$			1753.94i			1.80633i	0.429299	+	0.903163i	$0.358761\pi$
$971$			1753.94i			1.80633i	−0.429299	+	0.903163i	$0.641239\pi$
$972$		0			0
$973$	−22.4751			−0.0230988
$974$	161.337	−	28.4481i	0.165644	−	0.0292075i
$975$		0			0
$976$	−425.059	+	154.709i	−0.435512	+	0.158513i
$977$	−88.8872	+	105.932i	−0.0909797	+	0.108425i	−0.809614	−	0.586963i	$-0.800323\pi$
$977$	−88.8872	+	105.932i	−0.0909797	+	0.108425i	0.718634	+	0.695389i	$0.244768\pi$
$978$		0			0
$979$	−641.574	−	233.514i	−0.655336	−	0.238523i
$980$	39.8886	−	23.0297i	0.0407026	−	0.0234997i
$981$		0			0
$982$	87.5321	−	151.610i	0.0891366	−	0.154389i
$983$	123.405	+	147.069i	0.125540	+	0.149612i	0.825153	−	0.564909i	$-0.191089\pi$
$983$	123.405	+	147.069i	0.125540	+	0.149612i	−0.699613	+	0.714522i	$0.746644\pi$
$984$		0			0
$985$	−18.9080	+	107.233i	−0.0191960	+	0.108866i
$986$	−947.806	−	167.124i	−0.961264	−	0.169497i
$987$		0			0
$988$	419.021	−	351.600i	0.424110	−	0.355871i
$989$	127.043	+	73.3485i	0.128456	+	0.0741644i
$990$		0			0
$991$	193.368	+	334.923i	0.195124	+	0.337964i	0.946941	−	0.321407i	$-0.104156\pi$
$991$	193.368	+	334.923i	0.195124	+	0.337964i	−0.751817	+	0.659372i	$0.770822\pi$
$992$	−87.9677	+	241.689i	−0.0886772	+	0.243639i
$993$		0			0
$994$	−29.9702	−	25.1480i	−0.0301511	−	0.0252998i
$995$	−12.5414	−	34.4571i	−0.0126044	−	0.0346303i
$996$		0			0
$997$	212.742	+	1206.52i	0.213382	+	1.21015i	0.883692	+	0.468069i	$0.155050\pi$
$997$	212.742	+	1206.52i	0.213382	+	1.21015i	−0.670310	+	0.742081i	$0.733839\pi$
$998$		−	532.856i		−	0.533923i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	162.3.f.a.71.2		36
3.2	odd	2		54.3.f.a.41.5	yes	36
12.11	even	2		432.3.bc.c.257.3		36
27.2	odd	18	inner	162.3.f.a.89.2		36
27.5	odd	18		1458.3.b.c.1457.10		36
27.22	even	9		1458.3.b.c.1457.27		36
27.25	even	9		54.3.f.a.29.5	✓	36
108.79	odd	18		432.3.bc.c.353.3		36

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
54.3.f.a.29.5	✓	36	27.25	even	9
54.3.f.a.41.5	yes	36	3.2	odd	2
162.3.f.a.71.2		36	1.1	even	1	trivial
162.3.f.a.89.2		36	27.2	odd	18	inner
432.3.bc.c.257.3		36	12.11	even	2
432.3.bc.c.353.3		36	108.79	odd	18
1458.3.b.c.1457.10		36	27.5	odd	18
1458.3.b.c.1457.27		36	27.22	even	9

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)

\(f(q)\)	\(=\)	\(q+(-1.39273 + 0.245576i) q^{2} +(1.87939 - 0.684040i) q^{4} +(-0.379008 + 0.451684i) q^{5} +(2.96297 + 1.07843i) q^{7} +(-2.44949 + 1.41421i) q^{8} +O(q^{10})\)	\(q+(-1.39273 + 0.245576i) q^{2} +(1.87939 - 0.684040i) q^{4} +(-0.379008 + 0.451684i) q^{5} +(2.96297 + 1.07843i) q^{7} +(-2.44949 + 1.41421i) q^{8} +(0.416932 - 0.722148i) q^{10} +(6.03341 + 7.19034i) q^{11} +(2.11998 - 12.0230i) q^{13} +(-4.39145 - 0.774332i) q^{14} +(3.06418 - 2.57115i) q^{16} +(24.5140 + 14.1532i) q^{17} +(11.2011 + 19.4008i) q^{19} +(-0.403332 + 1.10814i) q^{20} +(-10.1687 - 8.53254i) q^{22} +(-3.44380 - 9.46175i) q^{23} +(4.28083 + 24.2778i) q^{25} +17.2654i q^{26} +6.30626 q^{28} +(23.6767 - 4.17484i) q^{29} +(42.7251 - 15.5506i) q^{31} +(-3.63616 + 4.33340i) q^{32} +(-37.6170 - 13.6915i) q^{34} +(-1.61010 + 0.929592i) q^{35} +(-15.7500 + 27.2799i) q^{37} +(-20.3644 - 24.2694i) q^{38} +(0.289598 - 1.64239i) q^{40} +(-69.7771 - 12.3036i) q^{41} +(-11.1607 + 9.36490i) q^{43} +(16.2576 + 9.38633i) q^{44} +(7.11985 + 12.3319i) q^{46} +(18.9216 - 51.9868i) q^{47} +(-29.9200 - 25.1059i) q^{49} +(-11.9241 - 32.7611i) q^{50} +(-4.23996 - 24.0460i) q^{52} -25.4089i q^{53} -5.53447 q^{55} +(-8.78291 + 1.54866i) q^{56} +(-31.9499 + 11.6288i) q^{58} +(-18.4282 + 21.9619i) q^{59} +(-106.265 - 38.6772i) q^{61} +(-55.6855 + 32.1501i) q^{62} +(4.00000 - 6.92820i) q^{64} +(4.62711 + 5.51438i) q^{65} +(8.68700 - 49.2664i) q^{67} +(55.7526 + 9.83069i) q^{68} +(2.01415 - 1.69007i) q^{70} +(7.59817 + 4.38680i) q^{71} +(-11.7358 - 20.3271i) q^{73} +(15.2363 - 41.8613i) q^{74} +(34.3221 + 28.7997i) q^{76} +(10.1225 + 27.8114i) q^{77} +(23.0535 + 130.743i) q^{79} +2.35853i q^{80} +100.202 q^{82} +(66.1377 - 11.6619i) q^{83} +(-15.6838 + 5.70842i) q^{85} +(13.2440 - 15.7835i) q^{86} +(-24.9475 - 9.08013i) q^{88} +(-62.9935 + 36.3693i) q^{89} +(19.2475 - 33.3376i) q^{91} +(-12.9444 - 15.4266i) q^{92} +(-13.5860 + 77.0502i) q^{94} +(-13.0083 - 2.29372i) q^{95} +(120.419 - 101.043i) q^{97} +(47.8358 + 27.6180i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 36 q - 18 q^{5}+O(q^{10}) \) 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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