LMFDB - Embedded newform 162.3.f.a.35.6

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			35.6
Character	$\chi$	$=$	162.35
Dual form			162.3.f.a.125.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.909039 - 1.08335i) q^{2} +(-0.347296 - 1.96962i) q^{4} +(1.54033 - 4.23203i) q^{5} +(0.223815 - 1.26932i) q^{7} +(-2.44949 - 1.41421i) q^{8} +O(q^{10})$	\(q+(0.909039 - 1.08335i) q^{2} +(-0.347296 - 1.96962i) q^{4} +(1.54033 - 4.23203i) q^{5} +(0.223815 - 1.26932i) q^{7} +(-2.44949 - 1.41421i) q^{8} +(-3.18455 - 5.51580i) q^{10} +(-2.33433 - 6.41353i) q^{11} +(8.48521 - 7.11994i) q^{13} +(-1.17166 - 1.39633i) q^{14} +(-3.75877 + 1.36808i) q^{16} +(-24.1831 + 13.9621i) q^{17} +(14.5238 - 25.1559i) q^{19} +(-8.87042 - 1.56409i) q^{20} +(-9.07010 - 3.30125i) q^{22} +(29.2129 - 5.15103i) q^{23} +(3.61368 + 3.03223i) q^{25} -15.6648i q^{26} -2.57779 q^{28} +(-9.87390 + 11.7673i) q^{29} +(8.09047 + 45.8833i) q^{31} +(-1.93476 + 5.31570i) q^{32} +(-6.85753 + 38.8910i) q^{34} +(-5.02703 - 2.90236i) q^{35} +(-6.62043 - 11.4669i) q^{37} +(-14.0500 - 38.6020i) q^{38} +(-9.75802 + 8.18795i) q^{40} +(27.2051 + 32.4217i) q^{41} +(-48.0441 + 17.4866i) q^{43} +(-11.8215 + 6.82513i) q^{44} +(20.9753 - 36.3303i) q^{46} +(57.3481 + 10.1120i) q^{47} +(44.4839 + 16.1908i) q^{49} +(6.56995 - 1.15846i) q^{50} +(-16.9704 - 14.2399i) q^{52} +72.9927i q^{53} -30.7379 q^{55} +(-2.34332 + 2.79265i) q^{56} +(3.77230 + 21.3938i) q^{58} +(10.4251 - 28.6427i) q^{59} +(2.62991 - 14.9150i) q^{61} +(57.0623 + 32.9449i) q^{62} +(4.00000 + 6.92820i) q^{64} +(-17.0617 - 46.8767i) q^{65} +(86.2916 - 72.4073i) q^{67} +(35.8988 + 42.7825i) q^{68} +(-7.71404 + 2.80768i) q^{70} +(-7.53244 + 4.34886i) q^{71} +(-52.2695 + 90.5334i) q^{73} +(-18.4409 - 3.25163i) q^{74} +(-54.5914 - 19.8697i) q^{76} +(-8.66325 + 1.52756i) q^{77} +(-46.1874 - 38.7558i) q^{79} +18.0145i q^{80} +59.8545 q^{82} +(17.6633 - 21.0502i) q^{83} +(21.8381 + 123.850i) q^{85} +(-24.7298 + 67.9446i) q^{86} +(-3.35217 + 19.0111i) q^{88} +(-106.619 - 61.5564i) q^{89} +(-7.13834 - 12.3640i) q^{91} +(-20.2911 - 55.7493i) q^{92} +(63.0865 - 52.9358i) q^{94} +(-84.0890 - 100.213i) q^{95} +(40.5097 - 14.7443i) q^{97} +(57.9779 - 33.4735i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/162\mathbb{Z}\right)^\times$.

$n$	$83$
$\chi(n)$	$e\left(\frac{13}{18}\right)$

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 $

$2$	0.909039	−	1.08335i	0.454519	−	0.541675i
$2$	0.909039	−	1.08335i	0.454519	−	0.541675i
$3$		0			0
$3$		0			0
$4$	−0.347296	−	1.96962i	−0.0868241	−	0.492404i
$5$	1.54033	−	4.23203i	0.308066	−	0.846406i	−0.684967	−	0.728574i	$-0.740183\pi$
$5$	1.54033	−	4.23203i	0.308066	−	0.846406i	0.993034	−	0.117832i	$-0.0375943\pi$
$6$		0			0
$7$	0.223815	−	1.26932i	0.0319735	−	0.181331i	−0.964639	−	0.263576i	$-0.915098\pi$
$7$	0.223815	−	1.26932i	0.0319735	−	0.181331i	0.996612	+	0.0822453i	$0.0262091\pi$
$8$	−2.44949	−	1.41421i	−0.306186	−	0.176777i
$9$		0			0
$10$	−3.18455	−	5.51580i	−0.318455	−	0.551580i
$11$	−2.33433	−	6.41353i	−0.212212	−	0.583048i	0.787223	−	0.616669i	$-0.211518\pi$
$11$	−2.33433	−	6.41353i	−0.212212	−	0.583048i	−0.999435	+	0.0336211i	$0.989296\pi$
$12$		0			0
$13$	8.48521	−	7.11994i	0.652709	−	0.547688i	−0.255183	−	0.966893i	$-0.582136\pi$
$13$	8.48521	−	7.11994i	0.652709	−	0.547688i	0.907892	+	0.419205i	$0.137691\pi$
$14$	−1.17166	−	1.39633i	−0.0836898	−	0.0997377i
$15$		0			0
$16$	−3.75877	+	1.36808i	−0.234923	+	0.0855050i
$17$	−24.1831	+	13.9621i	−1.42254	+	0.821303i	−0.996515	−	0.0834096i	$-0.973419\pi$
$17$	−24.1831	+	13.9621i	−1.42254	+	0.821303i	−0.426023	+	0.904712i	$0.640086\pi$
$18$		0			0
$19$	14.5238	−	25.1559i	0.764408	−	1.32399i	−0.176151	−	0.984363i	$-0.556365\pi$
$19$	14.5238	−	25.1559i	0.764408	−	1.32399i	0.940559	−	0.339630i	$-0.110302\pi$
$20$	−8.87042	−	1.56409i	−0.443521	−	0.0782047i
$21$		0			0
$22$	−9.07010	−	3.30125i	−0.412277	−	0.150057i
$23$	29.2129	−	5.15103i	1.27013	−	0.223958i	0.502344	−	0.864668i	$-0.332471\pi$
$23$	29.2129	−	5.15103i	1.27013	−	0.223958i	0.767783	+	0.640710i	$0.221360\pi$
$24$		0			0
$25$	3.61368	+	3.03223i	0.144547	+	0.121289i
$26$		−	15.6648i		−	0.602491i
$27$		0			0
$28$	−2.57779			−0.0920641
$29$	−9.87390	+	11.7673i	−0.340479	+	0.405767i	−0.908929	−	0.416951i	$-0.863099\pi$
$29$	−9.87390	+	11.7673i	−0.340479	+	0.405767i	0.568450	+	0.822718i	$0.307543\pi$
$30$		0			0
$31$	8.09047	+	45.8833i	0.260983	+	1.48011i	0.780235	+	0.625487i	$0.215100\pi$
$31$	8.09047	+	45.8833i	0.260983	+	1.48011i	−0.519252	+	0.854621i	$0.673789\pi$
$32$	−1.93476	+	5.31570i	−0.0604612	+	0.166116i
$33$		0			0
$34$	−6.85753	+	38.8910i	−0.201692	+	1.14385i
$35$	−5.02703	−	2.90236i	−0.143629	−	0.0829245i
$36$		0			0
$37$	−6.62043	−	11.4669i	−0.178931	−	0.309917i	0.762584	−	0.646889i	$-0.223930\pi$
$37$	−6.62043	−	11.4669i	−0.178931	−	0.309917i	−0.941515	+	0.336972i	$0.890597\pi$
$38$	−14.0500	−	38.6020i	−0.369736	−	1.01584i
$39$		0			0
$40$	−9.75802	+	8.18795i	−0.243950	+	0.204699i
$41$	27.2051	+	32.4217i	0.663538	+	0.790774i	0.987889	−	0.155163i	$-0.0495903\pi$
$41$	27.2051	+	32.4217i	0.663538	+	0.790774i	−0.324351	+	0.945937i	$0.605146\pi$
$42$		0			0
$43$	−48.0441	+	17.4866i	−1.11730	+	0.406665i	−0.833668	−	0.552267i	$-0.813763\pi$
$43$	−48.0441	+	17.4866i	−1.11730	+	0.406665i	−0.283636	+	0.958932i	$0.591541\pi$
$44$	−11.8215	+	6.82513i	−0.268670	+	0.155117i
$45$		0			0
$46$	20.9753	−	36.3303i	0.455985	−	0.789790i
$47$	57.3481	+	10.1120i	1.22017	+	0.215149i	0.746399	−	0.665498i	$-0.231781\pi$
$47$	57.3481	+	10.1120i	1.22017	+	0.215149i	0.473772	+	0.880647i	$0.342892\pi$
$48$		0			0
$49$	44.4839	+	16.1908i	0.907834	+	0.330425i
$50$	6.56995	−	1.15846i	0.131399	−	0.0231692i
$51$		0			0
$52$	−16.9704	−	14.2399i	−0.326354	−	0.273844i
$53$			72.9927i			1.37722i	0.725131	+	0.688611i	$0.241779\pi$
$53$			72.9927i			1.37722i	−0.725131	+	0.688611i	$0.758221\pi$
$54$		0			0
$55$	−30.7379			−0.558870
$56$	−2.34332	+	2.79265i	−0.0418449	+	0.0498688i
$57$		0			0
$58$	3.77230	+	21.3938i	0.0650397	+	0.368858i
$59$	10.4251	−	28.6427i	0.176697	−	0.485470i	−0.819452	−	0.573148i	$-0.805722\pi$
$59$	10.4251	−	28.6427i	0.176697	−	0.485470i	0.996149	+	0.0876773i	$0.0279444\pi$
$60$		0			0
$61$	2.62991	−	14.9150i	0.0431133	−	0.244508i	−0.955633	−	0.294559i	$-0.904827\pi$
$61$	2.62991	−	14.9150i	0.0431133	−	0.244508i	0.998747	+	0.0500511i	$0.0159384\pi$
$62$	57.0623	+	32.9449i	0.920360	+	0.531370i
$63$		0			0
$64$	4.00000	+	6.92820i	0.0625000	+	0.108253i
$65$	−17.0617	−	46.8767i	−0.262488	−	0.721180i
$66$		0			0
$67$	86.2916	−	72.4073i	1.28793	−	1.08071i	0.295837	−	0.955239i	$-0.404402\pi$
$67$	86.2916	−	72.4073i	1.28793	−	1.08071i	0.992098	−	0.125467i	$-0.0400428\pi$
$68$	35.8988	+	42.7825i	0.527923	+	0.629154i
$69$		0			0
$70$	−7.71404	+	2.80768i	−0.110201	+	0.0401097i
$71$	−7.53244	+	4.34886i	−0.106091	+	0.0612515i	−0.552107	−	0.833774i	$-0.686176\pi$
$71$	−7.53244	+	4.34886i	−0.106091	+	0.0612515i	0.446016	+	0.895025i	$0.352843\pi$
$72$		0			0
$73$	−52.2695	+	90.5334i	−0.716020	+	1.24018i	0.246544	+	0.969132i	$0.420705\pi$
$73$	−52.2695	+	90.5334i	−0.716020	+	1.24018i	−0.962565	+	0.271052i	$0.912628\pi$
$74$	−18.4409	−	3.25163i	−0.249202	−	0.0439410i
$75$		0			0
$76$	−54.5914	−	19.8697i	−0.718308	−	0.261443i
$77$	−8.66325	+	1.52756i	−0.112510	+	0.0198385i
$78$		0			0
$79$	−46.1874	−	38.7558i	−0.584650	−	0.490580i	0.301820	−	0.953365i	$-0.402406\pi$
$79$	−46.1874	−	38.7558i	−0.584650	−	0.490580i	−0.886471	+	0.462785i	$0.846850\pi$
$80$			18.0145i			0.225181i
$81$		0			0
$82$	59.8545			0.729933
$83$	17.6633	−	21.0502i	0.212810	−	0.253617i	−0.649071	−	0.760728i	$-0.724842\pi$
$83$	17.6633	−	21.0502i	0.212810	−	0.253617i	0.861881	+	0.507111i	$0.169286\pi$
$84$		0			0
$85$	21.8381	+	123.850i	0.256919	+	1.45706i
$86$	−24.7298	+	67.9446i	−0.287556	+	0.790053i
$87$		0			0
$88$	−3.35217	+	19.0111i	−0.0380929	+	0.216035i
$89$	−106.619	−	61.5564i	−1.19796	−	0.691645i	−0.237863	−	0.971299i	$-0.576447\pi$
$89$	−106.619	−	61.5564i	−1.19796	−	0.691645i	−0.960101	+	0.279654i	$0.909780\pi$
$90$		0			0
$91$	−7.13834	−	12.3640i	−0.0784433	−	0.135868i
$92$	−20.2911	−	55.7493i	−0.220555	−	0.605971i
$93$		0			0
$94$	63.0865	−	52.9358i	0.671133	−	0.563147i
$95$	−84.0890	−	100.213i	−0.885147	−	1.05488i
$96$		0			0
$97$	40.5097	−	14.7443i	0.417626	−	0.152003i	−0.124656	−	0.992200i	$-0.539783\pi$
$97$	40.5097	−	14.7443i	0.417626	−	0.152003i	0.542282	+	0.840197i	$0.317560\pi$
$98$	57.9779	−	33.4735i	0.591611	−	0.341567i
$99$		0			0
$100$	4.71732	−	8.17064i	0.0471732	−	0.0817064i
$101$	−35.2224	−	6.21065i	−0.348736	−	0.0614916i	−0.00346349	−	0.999994i	$-0.501102\pi$
$101$	−35.2224	−	6.21065i	−0.348736	−	0.0614916i	−0.345273	+	0.938502i	$0.612214\pi$
$102$		0			0
$103$	−149.691	−	54.4832i	−1.45331	−	0.528963i	−0.509799	−	0.860294i	$-0.670280\pi$
$103$	−149.691	−	54.4832i	−1.45331	−	0.528963i	−0.943515	+	0.331331i	$0.892502\pi$
$104$	−30.8536	+	5.44031i	−0.296669	+	0.0523107i
$105$		0			0
$106$	79.0767	+	66.3532i	0.746007	+	0.625974i
$107$			0.912530i			0.00852832i	0.999991	+	0.00426416i	$0.00135733\pi$
$107$			0.912530i			0.00852832i	−0.999991	+	0.00426416i	$0.998643\pi$
$108$		0			0
$109$	−58.9907			−0.541199			−0.270600	−	0.962692i	$-0.587222\pi$
$109$	−58.9907			−0.541199			−0.270600	+	0.962692i	$0.587222\pi$
$110$	−27.9419	+	33.2999i	−0.254017	+	0.302726i
$111$		0			0
$112$	0.895259	+	5.07726i	0.00799338	+	0.0453327i
$113$	8.75370	−	24.0506i	0.0774664	−	0.212837i	−0.894914	−	0.446238i	$-0.852763\pi$
$113$	8.75370	−	24.0506i	0.0774664	−	0.212837i	0.972381	+	0.233401i	$0.0749855\pi$
$114$		0			0
$115$	23.1983	−	131.564i	0.201725	−	1.14404i
$116$	26.6061	+	15.3611i	0.229363	+	0.132423i
$117$		0			0
$118$	−21.5533	−	37.3314i	−0.182655	−	0.316368i
$119$	12.3098	+	33.8210i	0.103444	+	0.284210i
$120$		0			0
$121$	57.0072	−	47.8347i	0.471134	−	0.395328i
$122$	−13.7675	−	16.4074i	−0.112848	−	0.134487i
$123$		0			0
$124$	87.5628	−	31.8702i	0.706151	−	0.257018i
$125$	115.905	−	66.9179i	0.927242	−	0.535343i
$126$		0			0
$127$	23.0881	−	39.9898i	0.181796	−	0.314880i	−0.760696	−	0.649108i	$-0.775142\pi$
$127$	23.0881	−	39.9898i	0.181796	−	0.314880i	0.942492	+	0.334228i	$0.108476\pi$
$128$	11.1418	+	1.96460i	0.0870455	+	0.0153485i
$129$		0			0
$130$	−66.2937	−	24.1289i	−0.509952	−	0.185607i
$131$	−28.0845	+	4.95206i	−0.214385	+	0.0378019i	−0.279809	−	0.960056i	$-0.590271\pi$
$131$	−28.0845	+	4.95206i	−0.214385	+	0.0378019i	0.0654237	+	0.997858i	$0.479160\pi$
$132$		0			0
$133$	−28.6801	−	24.0655i	−0.215640	−	0.180943i
$134$		−	159.305i		−	1.18884i
$135$		0			0
$136$	78.9818			0.580749
$137$	−98.9043	+	117.870i	−0.721929	+	0.860361i	−0.994817	−	0.101684i	$-0.967577\pi$
$137$	−98.9043	+	117.870i	−0.721929	+	0.860361i	0.272888	+	0.962046i	$0.412021\pi$
$138$		0			0
$139$	−4.50882	−	25.5708i	−0.0324376	−	0.183963i	0.964284	−	0.264870i	$-0.0853292\pi$
$139$	−4.50882	−	25.5708i	−0.0324376	−	0.183963i	−0.996722	+	0.0809078i	$0.974218\pi$
$140$	−3.97066	+	10.9093i	−0.0283619	+	0.0779236i
$141$		0			0
$142$	−2.13595	+	12.1136i	−0.0150419	+	0.0853067i
$143$	−65.4712	−	37.7998i	−0.457841	−	0.264335i
$144$		0			0
$145$	34.5903	+	59.9121i	0.238553	+	0.413187i
$146$	50.5644	+	138.925i	0.346332	+	0.951538i
$147$		0			0
$148$	−20.2862	+	17.0221i	−0.137069	+	0.115014i
$149$	−34.3423	−	40.9276i	−0.230485	−	0.274682i	0.638390	−	0.769713i	$-0.279601\pi$
$149$	−34.3423	−	40.9276i	−0.230485	−	0.274682i	−0.868875	+	0.495032i	$0.835156\pi$
$150$		0			0
$151$	81.4813	−	29.6568i	0.539611	−	0.196403i	−0.0578134	−	0.998327i	$-0.518413\pi$
$151$	81.4813	−	29.6568i	0.539611	−	0.196403i	0.597425	+	0.801925i	$0.296191\pi$
$152$	−71.1516	+	41.0794i	−0.468102	+	0.270259i
$153$		0			0
$154$	−6.22034	+	10.7740i	−0.0403918	+	0.0699607i
$155$	206.642	+	36.4365i	1.33317	+	0.235074i
$156$		0			0
$157$	−197.751	−	71.9753i	−1.25956	−	0.458442i	−0.375937	−	0.926645i	$-0.622679\pi$
$157$	−197.751	−	71.9753i	−1.25956	−	0.458442i	−0.883621	+	0.468204i	$0.844901\pi$
$158$	−83.9722	+	14.8066i	−0.531470	+	0.0937125i
$159$		0			0
$160$	19.5160	+	16.3759i	0.121975	+	0.102349i
$161$		−	38.2333i		−	0.237474i
$162$		0			0
$163$	95.6406			0.586752			0.293376	−	0.955997i	$-0.405221\pi$
$163$	95.6406			0.586752			0.293376	+	0.955997i	$0.405221\pi$
$164$	54.4101	−	64.8434i	0.331769	−	0.395387i
$165$		0			0
$166$	−6.74821	−	38.2710i	−0.0406519	−	0.230548i
$167$	33.2406	−	91.3278i	0.199045	−	0.546873i	−0.799507	−	0.600657i	$-0.794906\pi$
$167$	33.2406	−	91.3278i	0.199045	−	0.546873i	0.998553	+	0.0537837i	$0.0171282\pi$
$168$		0			0
$169$	−8.04123	+	45.6041i	−0.0475813	+	0.269847i
$170$	154.025	+	88.9262i	0.906028	+	0.523095i
$171$		0			0
$172$	51.1274	+	88.5553i	0.297252	+	0.514856i
$173$	94.9645	+	260.913i	0.548928	+	1.50817i	0.835160	+	0.550007i	$0.185375\pi$
$173$	94.9645	+	260.913i	0.548928	+	1.50817i	−0.286232	+	0.958160i	$0.592403\pi$
$174$		0			0
$175$	4.65766	−	3.90824i	0.0266152	−	0.0223328i
$176$	17.5484	+	20.9134i	0.0997071	+	0.118826i
$177$		0			0
$178$	−163.608	+	59.5483i	−0.919144	+	0.334541i
$179$	66.4554	−	38.3680i	0.371259	−	0.214347i	−0.302749	−	0.953070i	$-0.597904\pi$
$179$	66.4554	−	38.3680i	0.371259	−	0.214347i	0.674008	+	0.738724i	$0.264571\pi$
$180$		0			0
$181$	−142.550	+	246.903i	−0.787567	+	1.36411i	0.139887	+	0.990167i	$0.455326\pi$
$181$	−142.550	+	246.903i	−0.787567	+	1.36411i	−0.927454	+	0.373938i	$0.878007\pi$
$182$	−19.8835	−	3.50600i	−0.109250	−	0.0192638i
$183$		0			0
$184$	−78.8414	−	28.6959i	−0.428486	−	0.155956i
$185$	−58.7260	+	10.3550i	−0.317438	+	0.0559729i
$186$		0			0
$187$	145.998	+	122.507i	0.780739	+	0.655118i
$188$		−	116.466i		−	0.619497i
$189$		0			0
$190$	−185.006			−0.973717
$191$	40.8397	−	48.6709i	0.213821	−	0.254821i	−0.648464	−	0.761245i	$-0.724588\pi$
$191$	40.8397	−	48.6709i	0.213821	−	0.254821i	0.862285	+	0.506424i	$0.169033\pi$
$192$		0			0
$193$	46.9353	+	266.184i	0.243188	+	1.37919i	0.824663	+	0.565625i	$0.191365\pi$
$193$	46.9353	+	266.184i	0.243188	+	1.37919i	−0.581475	+	0.813565i	$0.697524\pi$
$194$	20.8516	−	57.2894i	0.107483	−	0.295306i
$195$		0			0
$196$	16.4406	−	93.2391i	0.0838805	−	0.475710i
$197$	46.6888	+	26.9558i	0.236999	+	0.136831i	0.613797	−	0.789464i	$-0.289641\pi$
$197$	46.6888	+	26.9558i	0.236999	+	0.136831i	−0.376798	+	0.926296i	$0.622975\pi$
$198$		0			0
$199$	67.4909	+	116.898i	0.339150	+	0.587425i	0.984273	−	0.176654i	$-0.0565272\pi$
$199$	67.4909	+	116.898i	0.339150	+	0.587425i	−0.645123	+	0.764079i	$0.723194\pi$
$200$	−4.56344	−	12.5379i	−0.0228172	−	0.0626897i
$201$		0			0
$202$	−38.7468	+	32.5124i	−0.191816	+	0.160953i
$203$	12.7264	+	15.1668i	0.0626918	+	0.0747132i
$204$		0			0
$205$	179.114	−	65.1923i	0.873729	−	0.318011i
$206$	−195.100	+	112.641i	−0.947086	+	0.546800i
$207$		0			0
$208$	−22.1533	+	38.3707i	−0.106506	+	0.184474i
$209$	−195.241	−	34.4263i	−0.934168	−	0.164719i
$210$		0			0
$211$	−188.073	−	68.4530i	−0.891341	−	0.324422i	−0.144564	−	0.989496i	$-0.546178\pi$
$211$	−188.073	−	68.4530i	−0.891341	−	0.324422i	−0.746778	+	0.665074i	$0.768400\pi$
$212$	143.768	−	25.3501i	0.678149	−	0.119576i
$213$		0			0
$214$	0.988590	+	0.829525i	0.00461958	+	0.00387629i
$215$			230.259i			1.07097i
$216$		0			0
$217$	60.0512			0.276734
$218$	−53.6248	+	63.9076i	−0.245986	+	0.293154i
$219$		0			0
$220$	10.6751	+	60.5418i	0.0485234	+	0.275190i
$221$	−105.790	+	290.654i	−0.478686	+	1.31518i
$222$		0			0
$223$	−63.4683	+	359.947i	−0.284611	+	1.61411i	0.422059	+	0.906568i	$0.361307\pi$
$223$	−63.4683	+	359.947i	−0.284611	+	1.61411i	−0.706671	+	0.707543i	$0.749804\pi$
$224$	6.31428	+	3.64555i	0.0281888	+	0.0162748i
$225$		0			0
$226$	−18.0978	−	31.3463i	−0.0800787	−	0.138700i
$227$	57.2400	+	157.266i	0.252158	+	0.692800i	0.999595	+	0.0284662i	$0.00906230\pi$
$227$	57.2400	+	157.266i	0.252158	+	0.692800i	−0.747436	+	0.664334i	$0.768715\pi$
$228$		0			0
$229$	124.355	−	104.346i	0.543036	−	0.455661i	−0.329539	−	0.944142i	$-0.606893\pi$
$229$	124.355	−	104.346i	0.543036	−	0.455661i	0.872575	+	0.488481i	$0.162449\pi$
$230$	−121.442	−	144.729i	−0.528009	−	0.629256i
$231$		0			0
$232$	40.8274	−	14.8600i	0.175980	−	0.0640516i
$233$	159.193	−	91.9104i	0.683234	−	0.394465i	−0.117839	−	0.993033i	$-0.537597\pi$
$233$	159.193	−	91.9104i	0.683234	−	0.394465i	0.801072	+	0.598568i	$0.204263\pi$
$234$		0			0
$235$	131.129	−	227.123i	0.557997	−	0.966480i
$236$	−60.0358	−	10.5859i	−0.254389	−	0.0448556i
$237$		0			0
$238$	47.8301	+	17.4087i	0.200967	+	0.0731459i
$239$	42.5536	−	7.50334i	0.178048	−	0.0313947i	−0.0839130	−	0.996473i	$-0.526742\pi$
$239$	42.5536	−	7.50334i	0.178048	−	0.0313947i	0.261961	+	0.965078i	$0.415631\pi$
$240$		0			0
$241$	−49.8948	−	41.8667i	−0.207032	−	0.173721i	0.533376	−	0.845879i	$-0.320923\pi$
$241$	−49.8948	−	41.8667i	−0.207032	−	0.173721i	−0.740408	+	0.672158i	$0.765368\pi$
$242$		−	105.242i		−	0.434886i
$243$		0			0
$244$	−30.2901			−0.124140
$245$	137.040	−	163.318i	0.559346	−	0.666603i
$246$		0			0
$247$	−55.8712	−	316.861i	−0.226199	−	1.28284i
$248$	45.0713	−	123.832i	0.181739	−	0.499324i
$249$		0			0
$250$	32.8668	−	186.397i	0.131467	−	0.745588i
$251$	14.3446	+	8.28183i	0.0571496	+	0.0329953i	0.528303	−	0.849056i	$-0.322829\pi$
$251$	14.3446	+	8.28183i	0.0571496	+	0.0329953i	−0.471153	+	0.882052i	$0.656162\pi$
$252$		0			0
$253$	−101.229	−	175.334i	−0.400114	−	0.693019i
$254$	−22.3350	−	61.3648i	−0.0879329	−	0.241594i
$255$		0			0
$256$	12.2567	−	10.2846i	0.0478778	−	0.0401742i
$257$	260.890	+	310.917i	1.01514	+	1.20979i	0.977594	+	0.210499i	$0.0675090\pi$
$257$	260.890	+	310.917i	1.01514	+	1.20979i	0.0375440	+	0.999295i	$0.488047\pi$
$258$		0			0
$259$	−16.0369	+	5.83696i	−0.0619186	+	0.0225365i
$260$	−86.4037	+	49.8852i	−0.332322	+	0.191866i
$261$		0			0
$262$	−20.1651	+	34.9270i	−0.0769660	+	0.133309i
$263$	−304.273	−	53.6515i	−1.15693	−	0.203998i	−0.437931	−	0.899008i	$-0.644289\pi$
$263$	−304.273	−	53.6515i	−1.15693	−	0.203998i	−0.719000	+	0.695010i	$0.755400\pi$
$264$		0			0
$265$	308.907	+	112.433i	1.16569	+	0.424276i
$266$	−52.1427	+	9.19417i	−0.196025	+	0.0345645i
$267$		0			0
$268$	−172.583	−	144.815i	−0.643967	−	0.540353i
$269$		−	243.504i		−	0.905221i	−0.891708	−	0.452611i	$-0.850493\pi$
$269$		−	243.504i		−	0.905221i	0.891708	−	0.452611i	$-0.149507\pi$
$270$		0			0
$271$	−138.215			−0.510018			−0.255009	−	0.966939i	$-0.582078\pi$
$271$	−138.215			−0.510018			−0.255009	+	0.966939i	$0.582078\pi$
$272$	71.7976	−	85.5650i	0.263962	−	0.314577i
$273$		0			0
$274$	37.7862	+	214.296i	0.137906	+	0.782102i
$275$	11.0118	−	30.2547i	0.0400429	−	0.110017i
$276$		0			0
$277$	72.4801	−	411.055i	0.261661	−	1.48395i	−0.516716	−	0.856157i	$-0.672846\pi$
$277$	72.4801	−	411.055i	0.261661	−	1.48395i	0.778377	−	0.627797i	$-0.216043\pi$
$278$	−31.8008	−	18.3602i	−0.114392	−	0.0660440i
$279$		0			0
$280$	8.20911	+	14.2186i	0.0293182	+	0.0507807i
$281$	−133.507	−	366.807i	−0.475114	−	1.30536i	−0.913596	−	0.406624i	$-0.866706\pi$
$281$	−133.507	−	366.807i	−0.475114	−	1.30536i	0.438482	−	0.898740i	$-0.355516\pi$
$282$		0			0
$283$	−10.0486	+	8.43181i	−0.0355076	+	0.0297944i	−0.660369	−	0.750941i	$-0.729600\pi$
$283$	−10.0486	+	8.43181i	−0.0355076	+	0.0297944i	0.624861	+	0.780736i	$0.285156\pi$
$284$	11.1816	+	13.3257i	0.0393717	+	0.0469214i
$285$		0			0
$286$	−100.466	+	36.5668i	−0.351281	+	0.127856i
$287$	47.2423	−	27.2754i	0.164607	−	0.0950361i
$288$		0			0
$289$	245.383	−	425.016i	0.849077	−	1.47064i
$290$	96.3497	+	16.9890i	0.332240	+	0.0585829i
$291$		0			0
$292$	196.469	+	71.5089i	0.672839	+	0.244893i
$293$	−162.152	+	28.5919i	−0.553421	+	0.0975831i	−0.443363	−	0.896342i	$-0.646215\pi$
$293$	−162.152	+	28.5919i	−0.553421	+	0.0975831i	−0.110058	+	0.993925i	$0.535104\pi$
$294$		0			0
$295$	−105.159	−	88.2387i	−0.356470	−	0.299114i
$296$			37.4508i			0.126523i
$297$		0			0
$298$	−75.5574			−0.253548
$299$	211.203	−	251.702i	0.706364	−	0.841812i
$300$		0			0
$301$	11.4431	+	64.8969i	0.0380168	+	0.215604i
$302$	41.9410	−	115.232i	0.138878	−	0.381563i
$303$		0			0
$304$	−20.1762	+	114.425i	−0.0663690	+	0.376397i
$305$	−59.0696	−	34.1039i	−0.193671	−	0.111816i
$306$		0			0
$307$	97.0102	+	168.027i	0.315994	+	0.547318i	0.979648	−	0.200722i	$-0.0643287\pi$
$307$	97.0102	+	168.027i	0.315994	+	0.547318i	−0.663654	+	0.748039i	$0.730995\pi$
$308$	6.01743	+	16.5328i	0.0195371	+	0.0536778i
$309$		0			0
$310$	227.319	−	190.743i	0.733286	−	0.615300i
$311$	−236.947	−	282.383i	−0.761888	−	0.907983i	0.236077	−	0.971734i	$-0.424138\pi$
$311$	−236.947	−	282.383i	−0.761888	−	0.907983i	−0.997966	+	0.0637510i	$0.979694\pi$
$312$		0			0
$313$	−408.961	+	148.850i	−1.30658	+	0.475558i	−0.899136	−	0.437670i	$-0.855804\pi$
$313$	−408.961	+	148.850i	−1.30658	+	0.475558i	−0.407449	+	0.913228i	$0.633581\pi$
$314$	−257.737	+	148.805i	−0.820820	+	0.473901i
$315$		0			0
$316$	−60.2933	+	104.431i	−0.190802	+	0.330478i
$317$	−240.306	−	42.3725i	−0.758064	−	0.133667i	−0.218761	−	0.975779i	$-0.570201\pi$
$317$	−240.306	−	42.3725i	−0.758064	−	0.133667i	−0.539304	+	0.842111i	$0.681312\pi$
$318$		0			0
$319$	98.5185	+	35.8578i	0.308836	+	0.112407i
$320$	35.4817	−	6.25638i	0.110880	−	0.0195512i
$321$		0			0
$322$	−41.4201	−	34.7556i	−0.128634	−	0.107937i
$323$			811.131i			2.51124i
$324$		0			0
$325$	52.2522			0.160776
$326$	86.9410	−	103.612i	0.266690	−	0.317829i
$327$		0			0
$328$	−20.7873	−	117.890i	−0.0633758	−	0.359422i
$329$	25.6707	−	70.5296i	0.0780264	−	0.214376i
$330$		0			0
$331$	−73.7627	+	418.329i	−0.222848	+	1.26383i	0.643908	+	0.765103i	$0.277312\pi$
$331$	−73.7627	+	418.329i	−0.222848	+	1.26383i	−0.866757	+	0.498732i	$0.833799\pi$
$332$	−47.5953	−	27.4791i	−0.143359	−	0.0827685i
$333$		0			0
$334$	−68.7230	−	119.032i	−0.205757	−	0.356382i
$335$	−173.512	−	476.720i	−0.517946	−	1.42304i
$336$		0			0
$337$	−115.028	+	96.5199i	−0.341329	+	0.286409i	−0.797297	−	0.603587i	$-0.793738\pi$
$337$	−115.028	+	96.5199i	−0.341329	+	0.286409i	0.455968	+	0.889996i	$0.349293\pi$
$338$	42.0954	+	50.1674i	0.124543	+	0.148424i
$339$		0			0
$340$	236.353	−	86.0254i	0.695155	−	0.253016i
$341$	275.388	−	158.995i	0.807590	−	0.466262i
$342$		0			0
$343$	62.0854	−	107.535i	0.181007	−	0.313513i
$344$	142.413	+	25.1113i	0.413992	+	0.0729980i
$345$		0			0
$346$	368.987	+	134.300i	1.06644	+	0.388151i
$347$	230.409	−	40.6273i	0.664003	−	0.117082i	0.168518	−	0.985698i	$-0.446102\pi$
$347$	230.409	−	40.6273i	0.664003	−	0.117082i	0.495484	+	0.868617i	$0.334991\pi$
$348$		0			0
$349$	−11.6765	−	9.79778i	−0.0334571	−	0.0280739i	0.625906	−	0.779899i	$-0.284729\pi$
$349$	−11.6765	−	9.79778i	−0.0334571	−	0.0280739i	−0.659363	+	0.751825i	$0.729174\pi$
$350$		−	8.59862i		−	0.0245675i
$351$		0			0
$352$	38.6088			0.109684
$353$	−152.164	+	181.341i	−0.431058	+	0.513715i	−0.937227	−	0.348719i	$-0.886617\pi$
$353$	−152.164	+	181.341i	−0.431058	+	0.513715i	0.506169	+	0.862434i	$0.331061\pi$
$354$		0			0
$355$	6.80202	+	38.5762i	0.0191606	+	0.108665i
$356$	−84.2141	+	231.376i	−0.236556	+	0.649933i
$357$		0			0
$358$	18.8445	−	106.873i	0.0526383	−	0.298527i
$359$	−486.522	−	280.894i	−1.35521	−	0.782433i	−0.366240	−	0.930520i	$-0.619355\pi$
$359$	−486.522	−	280.894i	−1.35521	−	0.782433i	−0.988974	+	0.148087i	$0.952688\pi$
$360$		0			0
$361$	−241.379	−	418.080i	−0.668639	−	1.15812i
$362$	137.899	+	378.876i	0.380938	+	1.04662i
$363$		0			0
$364$	−21.8731	+	18.3537i	−0.0600910	+	0.0504224i
$365$	302.627	+	360.657i	0.829116	+	0.988102i
$366$		0			0
$367$	−538.579	+	196.027i	−1.46752	+	0.534133i	−0.947426	−	0.319976i	$-0.896325\pi$
$367$	−538.579	+	196.027i	−1.46752	+	0.534133i	−0.520093	+	0.854109i	$0.674103\pi$
$368$	−102.758	+	59.3272i	−0.279233	+	0.161215i
$369$		0			0
$370$	−42.1662	+	73.0340i	−0.113963	+	0.197389i
$371$	92.6508	+	16.3368i	0.249733	+	0.0440346i
$372$		0			0
$373$	355.729	+	129.475i	0.953696	+	0.347117i	0.771560	−	0.636156i	$-0.219477\pi$
$373$	355.729	+	129.475i	0.953696	+	0.347117i	0.182136	+	0.983273i	$0.441699\pi$
$374$	265.436	−	46.8035i	0.709722	−	0.125143i
$375$		0			0
$376$	−126.173	−	105.872i	−0.335566	−	0.281574i
$377$			170.149i			0.451324i
$378$		0			0
$379$	424.202			1.11927			0.559633	−	0.828741i	$-0.310942\pi$
$379$	424.202			1.11927			0.559633	+	0.828741i	$0.310942\pi$
$380$	−168.178	+	200.427i	−0.442573	+	0.527438i
$381$		0			0
$382$	−15.6027	−	88.4875i	−0.0408448	−	0.231643i
$383$	−176.276	+	484.314i	−0.460250	+	1.26453i	0.465047	+	0.885286i	$0.346037\pi$
$383$	−176.276	+	484.314i	−0.460250	+	1.26453i	−0.925298	+	0.379241i	$0.876185\pi$
$384$		0			0
$385$	−6.87959	+	39.0161i	−0.0178691	+	0.101340i
$386$	331.036	+	191.124i	0.857606	+	0.495139i
$387$		0			0
$388$	−43.1095	−	74.6679i	−0.111107	−	0.192443i
$389$	−99.9515	−	274.614i	−0.256945	−	0.705950i	−0.999352	−	0.0360005i	$-0.988538\pi$
$389$	−99.9515	−	274.614i	−0.256945	−	0.705950i	0.742407	−	0.669949i	$-0.233684\pi$
$390$		0			0
$391$	−634.541	+	532.443i	−1.62287	+	1.36175i
$392$	−86.0655	−	102.569i	−0.219555	−	0.261655i
$393$		0			0
$394$	71.6445	−	26.0765i	0.181839	−	0.0661839i
$395$	−235.160	+	135.769i	−0.595341	+	0.343720i
$396$		0			0
$397$	−250.807	+	434.410i	−0.631755	+	1.09423i	0.355438	+	0.934700i	$0.384332\pi$
$397$	−250.807	+	434.410i	−0.631755	+	1.09423i	−0.987193	+	0.159532i	$0.949002\pi$
$398$	187.993	+	33.1482i	0.472344	+	0.0832870i
$399$		0			0
$400$	−17.7313	−	6.45367i	−0.0443283	−	0.0161342i
$401$	422.750	−	74.5422i	1.05424	−	0.185891i	0.380440	−	0.924806i	$-0.375773\pi$
$401$	422.750	−	74.5422i	1.05424	−	0.185891i	0.673799	+	0.738915i	$0.264661\pi$
$402$		0			0
$403$	395.336	+	331.726i	0.980983	+	0.823142i
$404$			71.5314i			0.177058i
$405$		0			0
$406$	27.9998			0.0689649
$407$	−58.0892	+	69.2280i	−0.142725	+	0.170093i
$408$		0			0
$409$	−99.2273	−	562.746i	−0.242609	−	1.37591i	−0.825979	−	0.563700i	$-0.809377\pi$
$409$	−99.2273	−	562.746i	−0.242609	−	1.37591i	0.583370	−	0.812207i	$-0.301734\pi$
$410$	92.1959	−	253.306i	0.224868	−	0.617820i
$411$		0			0
$412$	−55.3237	+	313.756i	−0.134281	+	0.761544i
$413$	−34.0234	−	19.6434i	−0.0823811	−	0.0475628i
$414$		0			0
$415$	−61.8780	−	107.176i	−0.149104	−	0.258255i
$416$	21.4307	+	58.8802i	0.0515160	+	0.141539i
$417$		0			0
$418$	−214.778	+	180.220i	−0.513822	+	0.431148i
$419$	−8.84006	−	10.5352i	−0.0210980	−	0.0251436i	0.755392	−	0.655273i	$-0.227446\pi$
$419$	−8.84006	−	10.5352i	−0.0210980	−	0.0251436i	−0.776490	+	0.630129i	$0.783002\pi$
$420$		0			0
$421$	272.056	−	99.0204i	0.646215	−	0.235203i	0.00194130	−	0.999998i	$-0.499382\pi$
$421$	272.056	−	99.0204i	0.646215	−	0.235203i	0.644274	+	0.764795i	$0.277160\pi$
$422$	−245.124	+	141.523i	−0.580863	+	0.335362i
$423$		0			0
$424$	103.227	−	178.795i	0.243461	−	0.421686i
$425$	−129.727	−	22.8743i	−0.305239	−	0.0538219i
$426$		0			0
$427$	−18.3432	−	6.67638i	−0.0429583	−	0.0156356i
$428$	1.79733	−	0.316918i	0.00419938	−	0.000740464i
$429$		0			0
$430$	249.451	+	209.314i	0.580119	+	0.486778i
$431$		−	373.898i		−	0.867514i	−0.901030	−	0.433757i	$-0.857188\pi$
$431$		−	373.898i		−	0.867514i	0.901030	−	0.433757i	$-0.142812\pi$
$432$		0			0
$433$	−280.461			−0.647716			−0.323858	−	0.946106i	$-0.604980\pi$
$433$	−280.461			−0.647716			−0.323858	+	0.946106i	$0.604980\pi$
$434$	54.5889	−	65.0565i	0.125781	−	0.149900i
$435$		0			0
$436$	20.4873	+	116.189i	0.0469891	+	0.266489i
$437$	294.703	−	809.689i	0.674377	−	1.85284i
$438$		0			0
$439$	−62.0317	+	351.799i	−0.141302	+	0.801365i	0.828960	+	0.559308i	$0.188933\pi$
$439$	−62.0317	+	351.799i	−0.141302	+	0.801365i	−0.970262	+	0.242057i	$0.922178\pi$
$440$	75.2921	+	43.4699i	0.171118	+	0.0987953i
$441$		0			0
$442$	218.714	+	378.823i	0.494827	+	0.857066i
$443$	163.660	+	449.653i	0.369436	+	1.01502i	0.975577	+	0.219660i	$0.0704948\pi$
$443$	163.660	+	449.653i	0.369436	+	1.01502i	−0.606140	+	0.795358i	$0.707283\pi$
$444$		0			0
$445$	−424.737	+	356.396i	−0.954464	+	0.800890i
$446$	332.253	+	395.964i	0.744962	+	0.887812i
$447$		0			0
$448$	9.68934	−	3.52663i	0.0216280	−	0.00787194i
$449$	489.279	−	282.485i	1.08971	−	0.629143i	0.156209	−	0.987724i	$-0.450073\pi$
$449$	489.279	−	282.485i	1.08971	−	0.629143i	0.933499	+	0.358581i	$0.116739\pi$
$450$		0			0
$451$	144.432	−	250.163i	0.320248	−	0.554686i
$452$	−50.4106	−	8.88874i	−0.111528	−	0.0196654i
$453$		0			0
$454$	222.407	+	80.9496i	0.489883	+	0.178303i
$455$	−63.3201	+	11.1650i	−0.139165	+	0.0245385i
$456$		0			0
$457$	−81.2867	−	68.2076i	−0.177870	−	0.149251i	0.549506	−	0.835490i	$-0.314816\pi$
$457$	−81.2867	−	68.2076i	−0.177870	−	0.149251i	−0.727376	+	0.686239i	$0.759260\pi$
$458$		−	229.575i		−	0.501256i
$459$		0			0
$460$	−267.188			−0.580843
$461$	−81.6939	+	97.3590i	−0.177210	+	0.211191i	−0.847337	−	0.531056i	$-0.821795\pi$
$461$	−81.6939	+	97.3590i	−0.177210	+	0.211191i	0.670127	+	0.742247i	$0.266240\pi$
$462$		0			0
$463$	−43.2955	−	245.541i	−0.0935109	−	0.530327i	−0.995193	−	0.0979280i	$-0.968778\pi$
$463$	−43.2955	−	245.541i	−0.0935109	−	0.530327i	0.901683	−	0.432398i	$-0.142333\pi$
$464$	21.0152	−	57.7387i	0.0452913	−	0.124437i
$465$		0			0
$466$	45.1419	−	256.012i	0.0968710	−	0.549383i
$467$	338.170	+	195.242i	0.724132	+	0.418078i	0.816272	−	0.577668i	$-0.196037\pi$
$467$	338.170	+	195.242i	0.724132	+	0.418078i	−0.0921395	+	0.995746i	$0.529371\pi$
$468$		0			0
$469$	−72.5944	−	125.737i	−0.154785	−	0.268096i
$470$	−126.852	−	348.523i	−0.269898	−	0.741537i
$471$		0			0
$472$	−66.0432	+	55.4168i	−0.139922	+	0.117408i
$473$	224.302	+	267.312i	0.474211	+	0.565142i
$474$		0			0
$475$	128.763	−	46.8658i	0.271079	−	0.0986648i
$476$	62.3392	−	35.9915i	0.130965	−	0.0756125i
$477$		0			0
$478$	30.5541	−	52.9212i	0.0639207	−	0.110714i
$479$	772.342	+	136.185i	1.61240	+	0.284310i	0.905930	−	0.423428i	$-0.139173\pi$
$479$	772.342	+	136.185i	1.61240	+	0.284310i	0.706475	+	0.707738i	$0.250284\pi$
$480$		0			0
$481$	−137.820	−	50.1622i	−0.286527	−	0.104287i
$482$	−90.7127	+	15.9951i	−0.188201	+	0.0331848i
$483$		0			0
$484$	−114.014	−	95.6694i	−0.235567	−	0.197664i
$485$		−	194.149i		−	0.400308i
$486$		0			0
$487$	386.211			0.793041			0.396521	−	0.918026i	$-0.370218\pi$
$487$	386.211			0.793041			0.396521	+	0.918026i	$0.370218\pi$
$488$	−27.5349	+	32.8148i	−0.0564240	+	0.0672435i
$489$		0			0
$490$	−52.3558	−	296.924i	−0.106849	−	0.605968i
$491$	−115.980	+	318.653i	−0.236212	+	0.648987i	0.763782	+	0.645474i	$0.223340\pi$
$491$	−115.980	+	318.653i	−0.236212	+	0.648987i	−0.999994	+	0.00351250i	$0.998882\pi$
$492$		0			0
$493$	74.4858	−	422.430i	0.151087	−	0.856856i
$494$	−394.061	−	227.511i	−0.797694	−	0.460549i
$495$		0			0
$496$	−93.1823	−	161.397i	−0.187868	−	0.325396i
$497$	3.83420	+	10.5344i	0.00771469	+	0.0211959i
$498$		0			0
$499$	558.687	−	468.794i	1.11961	−	0.939467i	0.121028	−	0.992649i	$-0.461381\pi$
$499$	558.687	−	468.794i	1.11961	−	0.939467i	0.998585	+	0.0531821i	$0.0169364\pi$
$500$	−172.056	−	205.048i	−0.344112	−	0.410097i
$501$		0			0
$502$	22.0119	−	8.01167i	0.0438484	−	0.0159595i
$503$	−544.974	+	314.641i	−1.08345	+	0.625529i	−0.931824	−	0.362909i	$-0.881783\pi$
$503$	−544.974	+	314.641i	−1.08345	+	0.625529i	−0.151624	+	0.988438i	$0.548450\pi$
$504$		0			0
$505$	−80.5378	+	139.496i	−0.159481	+	0.276229i
$506$	−281.969	−	49.7187i	−0.557251	−	0.0982584i
$507$		0			0
$508$	−86.7829	−	31.5864i	−0.170832	−	0.0621779i
$509$	−931.922	+	164.323i	−1.83089	+	0.322835i	−0.979460	−	0.201637i	$-0.935374\pi$
$509$	−931.922	+	164.323i	−1.83089	+	0.322835i	−0.851428	+	0.524472i	$0.824263\pi$
$510$		0			0
$511$	103.217	+	86.6092i	0.201990	+	0.169490i
$512$		−	22.6274i		−	0.0441942i
$513$		0			0
$514$	573.992			1.11672
$515$	−461.149	+	549.576i	−0.895434	+	1.06714i
$516$		0			0
$517$	−69.0158	−	391.408i	−0.133493	−	0.757076i
$518$	−8.25470	+	22.6796i	−0.0159357	+	0.0437830i
$519$		0			0
$520$	−24.5012	+	138.953i	−0.0471176	+	0.267217i
$521$	−0.653449	−	0.377269i	−0.00125422	−	0.000724125i	0.499373	−	0.866387i	$-0.333564\pi$
$521$	−0.653449	−	0.377269i	−0.00125422	−	0.000724125i	−0.500627	+	0.865663i	$0.666897\pi$
$522$		0			0
$523$	209.797	+	363.379i	0.401141	+	0.694797i	0.993864	−	0.110610i	$-0.0352804\pi$
$523$	209.797	+	363.379i	0.401141	+	0.694797i	−0.592723	+	0.805407i	$0.701947\pi$
$524$	19.5073	+	53.5958i	0.0372277	+	0.102282i
$525$		0			0
$526$	−334.719	+	280.863i	−0.636349	+	0.533960i
$527$	−836.283	−	996.643i	−1.58687	−	1.89116i
$528$		0			0
$529$	329.765	−	120.025i	0.623374	−	0.226890i
$530$	402.613	−	232.449i	0.759647	−	0.438583i
$531$		0			0
$532$	−37.4392	+	64.8467i	−0.0703745	+	0.121892i
$533$	461.681	+	81.4069i	0.866194	+	0.152733i
$534$		0			0
$535$	3.86185	+	1.40560i	0.00721842	+	0.00262729i
$536$	−313.770	+	55.3261i	−0.585391	+	0.103220i
$537$		0			0
$538$	−263.801	−	221.355i	−0.490336	−	0.411441i
$539$		−	323.093i		−	0.599431i
$540$		0			0
$541$	−641.079			−1.18499			−0.592494	−	0.805575i	$-0.701857\pi$
$541$	−641.079			−1.18499			−0.592494	+	0.805575i	$0.701857\pi$
$542$	−125.643	+	149.735i	−0.231813	+	0.276264i
$543$		0			0
$544$	−27.4301	−	155.564i	−0.0504230	−	0.285963i
$545$	−90.8653	+	249.650i	−0.166725	+	0.458074i
$546$		0			0
$547$	116.883	−	662.876i	0.213680	−	1.21184i	−0.669503	−	0.742809i	$-0.733493\pi$
$547$	116.883	−	662.876i	0.213680	−	1.21184i	0.883183	−	0.469029i	$-0.155396\pi$
$548$	266.507	+	153.868i	0.486326	+	0.280781i
$549$		0			0
$550$	−22.7662	−	39.4323i	−0.0413932	−	0.0716951i
$551$	152.609	+	419.291i	0.276968	+	0.760964i
$552$		0			0
$553$	−59.5308	+	49.9523i	−0.107651	+	0.0903296i
$554$	−379.429	−	452.186i	−0.684891	−	0.816221i
$555$		0			0
$556$	−48.7988	+	17.7613i	−0.0877676	+	0.0319448i
$557$	−144.605	+	83.4878i	−0.259614	+	0.149888i	−0.624159	−	0.781298i	$-0.714558\pi$
$557$	−144.605	+	83.4878i	−0.259614	+	0.149888i	0.364544	+	0.931186i	$0.381225\pi$
$558$		0			0
$559$	−283.161	+	490.448i	−0.506548	+	0.877367i
$560$	22.8661	+	4.03191i	0.0408324	+	0.00719985i
$561$		0			0
$562$	−518.744	−	188.807i	−0.923032	−	0.335956i
$563$	−46.6771	+	8.23043i	−0.0829078	+	0.0146189i	−0.214948	−	0.976625i	$-0.568958\pi$
$563$	−46.6771	+	8.23043i	−0.0829078	+	0.0146189i	0.132040	+	0.991244i	$0.457847\pi$
$564$		0			0
$565$	−88.2992	−	74.0918i	−0.156282	−	0.131136i
$566$			18.5510i			0.0327757i
$567$		0			0
$568$	24.6008			0.0433113
$569$	191.073	−	227.712i	0.335805	−	0.400196i	−0.571547	−	0.820570i	$-0.693656\pi$
$569$	191.073	−	227.712i	0.335805	−	0.400196i	0.907351	+	0.420373i	$0.138101\pi$
$570$		0			0
$571$	−19.1038	−	108.343i	−0.0334568	−	0.189743i	0.963499	−	0.267712i	$-0.0862676\pi$
$571$	−19.1038	−	108.343i	−0.0334568	−	0.189743i	−0.996956	+	0.0779691i	$0.975156\pi$
$572$	−51.7132	+	142.081i	−0.0904077	+	0.248393i
$573$		0			0
$574$	13.3963	−	75.9743i	0.0233385	−	0.132359i
$575$	121.185	+	69.9663i	0.210757	+	0.121681i
$576$		0			0
$577$	508.094	+	880.045i	0.880580	+	1.52521i	0.850698	+	0.525655i	$0.176180\pi$
$577$	508.094	+	880.045i	0.880580	+	1.52521i	0.0298820	+	0.999553i	$0.490487\pi$
$578$	−237.379	−	652.192i	−0.410689	−	1.12836i
$579$		0			0
$580$	105.991	−	88.9367i	0.182743	−	0.153339i
$581$	−22.7661	−	27.1316i	−0.0391844	−	0.0466981i
$582$		0			0
$583$	468.141	−	170.389i	0.802986	−	0.292263i
$584$	256.067	−	147.840i	0.438471	−	0.253151i
$585$		0			0
$586$	−116.428	+	201.659i	−0.198682	+	0.344128i
$587$	−135.199	−	23.8393i	−0.230323	−	0.0406121i	0.0572954	−	0.998357i	$-0.481752\pi$
$587$	−135.199	−	23.8393i	−0.230323	−	0.0406121i	−0.287618	+	0.957745i	$0.592863\pi$
$588$		0			0
$589$	1271.74	+	462.875i	2.15915	+	0.785866i
$590$	−191.187	+	33.7114i	−0.324045	+	0.0571380i
$591$		0			0
$592$	40.5724	+	34.0443i	0.0685344	+	0.0575072i
$593$		−	697.717i		−	1.17659i	−0.808647	−	0.588295i	$-0.799800\pi$
$593$		−	697.717i		−	1.17659i	0.808647	−	0.588295i	$-0.200200\pi$
$594$		0			0
$595$	162.093			0.272425
$596$	−68.6847	+	81.8552i	−0.115243	+	0.137341i
$597$		0			0
$598$	−80.6896	−	457.614i	−0.134932	−	0.765240i
$599$	16.5865	−	45.5711i	0.0276903	−	0.0760786i	−0.925077	−	0.379779i	$-0.876000\pi$
$599$	16.5865	−	45.5711i	0.0276903	−	0.0760786i	0.952768	+	0.303701i	$0.0982222\pi$
$600$		0			0
$601$	75.1561	−	426.231i	0.125052	−	0.709204i	−0.856225	−	0.516602i	$-0.827197\pi$
$601$	75.1561	−	426.231i	0.125052	−	0.709204i	0.981277	−	0.192601i	$-0.0616924\pi$
$602$	80.7082	+	46.5969i	0.134067	+	0.0774035i
$603$		0			0
$604$	−86.7106	−	150.187i	−0.143561	−	0.248654i
$605$	−114.628	−	314.937i	−0.189467	−	0.520557i
$606$		0			0
$607$	−466.444	+	391.393i	−0.768441	+	0.644799i	−0.940309	−	0.340321i	$-0.889464\pi$
$607$	−466.444	+	391.393i	−0.768441	+	0.644799i	0.171868	+	0.985120i	$0.445020\pi$
$608$	105.621	+	125.874i	0.173719	+	0.207030i
$609$		0			0
$610$	−90.6431	+	32.9914i	−0.148595	+	0.0540842i
$611$	558.608	−	322.512i	0.914251	−	0.527843i
$612$		0			0
$613$	55.1131	−	95.4586i	0.0899071	−	0.155724i	−0.817565	−	0.575837i	$-0.804676\pi$
$613$	55.1131	−	95.4586i	0.0899071	−	0.155724i	0.907472	+	0.420113i	$0.138010\pi$
$614$	270.218	+	47.6467i	0.440094	+	0.0776004i
$615$		0			0
$616$	23.3808	+	8.50993i	0.0379559	+	0.0138148i
$617$	410.150	−	72.3205i	0.664749	−	0.117213i	0.168915	−	0.985631i	$-0.445974\pi$
$617$	410.150	−	72.3205i	0.664749	−	0.117213i	0.495834	+	0.868417i	$0.334863\pi$
$618$		0			0
$619$	−387.982	−	325.555i	−0.626788	−	0.525938i	0.273141	−	0.961974i	$-0.411937\pi$
$619$	−387.982	−	325.555i	−0.626788	−	0.525938i	−0.899929	+	0.436036i	$0.856382\pi$
$620$		−	419.659i		−	0.676869i
$621$		0			0
$622$	−521.314			−0.838125
$623$	−101.997	+	121.556i	−0.163720	+	0.195113i
$624$		0			0
$625$	−84.1870	−	477.448i	−0.134699	−	0.763918i
$626$	−210.505	+	578.358i	−0.336270	+	0.923895i
$627$		0			0
$628$	−73.0857	+	414.489i	−0.116378	+	0.660015i
$629$	320.206	+	184.871i	0.509071	+	0.293913i
$630$		0			0
$631$	−146.314	−	253.423i	−0.231876	−	0.401621i	0.726484	−	0.687183i	$-0.241153\pi$
$631$	−146.314	−	253.423i	−0.231876	−	0.401621i	−0.958360	+	0.285562i	$0.907820\pi$
$632$	58.3265	+	160.251i	0.0922888	+	0.253561i
$633$		0			0
$634$	−264.352	+	221.818i	−0.416959	+	0.349870i
$635$	−133.674	−	159.307i	−0.210511	−	0.250877i
$636$		0			0
$637$	492.733	−	179.340i	0.773521	−	0.281538i
$638$	128.404	−	74.1340i	0.201260	−	0.116197i
$639$		0			0
$640$	25.4764	−	44.1264i	0.0398068	−	0.0689475i
$641$	180.102	+	31.7568i	0.280970	+	0.0495426i	0.312357	−	0.949965i	$-0.398881\pi$
$641$	180.102	+	31.7568i	0.280970	+	0.0495426i	−0.0313871	+	0.999507i	$0.509992\pi$
$642$		0			0
$643$	318.883	+	116.064i	0.495930	+	0.180504i	0.577863	−	0.816134i	$-0.303887\pi$
$643$	318.883	+	116.064i	0.495930	+	0.180504i	−0.0819323	+	0.996638i	$0.526109\pi$
$644$	−75.3049	+	13.2783i	−0.116933	+	0.0206185i
$645$		0			0
$646$	878.739	+	737.350i	1.36028	+	1.14141i
$647$			489.141i			0.756014i	0.925803	+	0.378007i	$0.123390\pi$
$647$			489.141i			0.756014i	−0.925803	+	0.378007i	$0.876610\pi$
$648$		0			0
$649$	−208.037			−0.320550
$650$	47.4992	−	56.6074i	0.0730758	−	0.0870883i
$651$		0			0
$652$	−33.2156	−	188.375i	−0.0509442	−	0.288919i
$653$	122.478	−	336.505i	0.187562	−	0.515321i	−0.809897	−	0.586572i	$-0.800477\pi$
$653$	122.478	−	336.505i	0.187562	−	0.515321i	0.997458	+	0.0712511i	$0.0226992\pi$
$654$		0			0
$655$	−22.3022	+	126.482i	−0.0340492	+	0.193103i
$656$	−146.613	−	84.6471i	−0.223496	−	0.129035i
$657$		0			0
$658$	−53.0726	−	91.9245i	−0.0806575	−	0.139703i
$659$	63.2203	+	173.696i	0.0959337	+	0.263576i	0.978372	−	0.206852i	$-0.0663219\pi$
$659$	63.2203	+	173.696i	0.0959337	+	0.263576i	−0.882439	+	0.470428i	$0.844100\pi$
$660$		0			0
$661$	50.5328	−	42.4021i	0.0764490	−	0.0641483i	−0.603762	−	0.797164i	$-0.706332\pi$
$661$	50.5328	−	42.4021i	0.0764490	−	0.0641483i	0.680211	+	0.733016i	$0.261888\pi$
$662$	386.144	+	460.188i	0.583299	+	0.695148i
$663$		0			0
$664$	−73.0355	+	26.5828i	−0.109993	+	0.0400343i
$665$	−146.023	+	84.3062i	−0.219583	+	0.126776i
$666$		0			0
$667$	−227.832	+	394.617i	−0.341577	+	0.591629i
$668$	−191.425	−	33.7534i	−0.286564	−	0.0505290i
$669$		0			0
$670$	−674.183	−	245.383i	−1.00624	−	0.366243i
$671$	−101.797	+	17.9495i	−0.151709	+	0.0267504i
$672$		0			0
$673$	−79.3186	−	66.5562i	−0.117858	−	0.0988948i	0.581954	−	0.813222i	$-0.302288\pi$
$673$	−79.3186	−	66.5562i	−0.117858	−	0.0988948i	−0.699812	+	0.714327i	$0.746733\pi$
$674$			212.356i			0.315068i
$675$		0			0
$676$	92.6152			0.137005
$677$	−253.554	+	302.174i	−0.374526	+	0.446343i	−0.920079	−	0.391734i	$-0.871875\pi$
$677$	−253.554	+	302.174i	−0.374526	+	0.446343i	0.545553	+	0.838077i	$0.316320\pi$
$678$		0			0
$679$	−9.64855	−	54.7196i	−0.0142099	−	0.0805886i
$680$	121.658	−	334.253i	0.178909	−	0.491549i
$681$		0			0
$682$	78.0908	−	442.875i	0.114503	−	0.649377i
$683$	152.220	+	87.8842i	0.222870	+	0.128674i	0.607278	−	0.794489i	$-0.292261\pi$
$683$	152.220	+	87.8842i	0.222870	+	0.128674i	−0.384409	+	0.923163i	$0.625595\pi$
$684$		0			0
$685$	346.482	+	600.124i	0.505813	+	0.876093i
$686$	−60.0601	−	165.014i	−0.0875512	−	0.240545i
$687$		0			0
$688$	156.664	−	131.456i	0.227709	−	0.191070i
$689$	519.704	+	619.359i	0.754287	+	0.898924i
$690$		0			0
$691$	100.843	−	36.7038i	0.145938	−	0.0531170i	−0.268019	−	0.963414i	$-0.586369\pi$
$691$	100.843	−	36.7038i	0.145938	−	0.0531170i	0.413956	+	0.910297i	$0.364147\pi$
$692$	480.917	−	277.658i	0.694967	−	0.401240i
$693$		0			0
$694$	165.437	−	286.545i	0.238382	−	0.412890i
$695$	−115.161	−	20.3061i	−0.165700	−	0.0292174i
$696$		0			0
$697$	−1110.58	−	404.218i	−1.59337	−	0.579940i
$698$	−21.2289	+	3.74322i	−0.0304138	+	0.00536278i
$699$		0			0
$700$	−9.31532	−	7.81648i	−0.0133076	−	0.0111664i
$701$			1348.09i			1.92309i	0.274639	+	0.961547i	$0.411442\pi$
$701$			1348.09i			1.92309i	−0.274639	+	0.961547i	$0.588558\pi$
$702$		0			0
$703$	−384.614			−0.547104
$704$	35.0969	−	41.8268i	0.0498535	−	0.0594131i
$705$		0			0
$706$	58.1338	+	329.693i	0.0823424	+	0.466987i
$707$	−15.7666	+	43.3183i	−0.0223007	+	0.0612705i
$708$		0			0
$709$	−37.4182	+	212.209i	−0.0527761	+	0.299308i	−0.999758	−	0.0219775i	$-0.993004\pi$
$709$	−37.4182	+	212.209i	−0.0527761	+	0.299308i	0.946982	+	0.321285i	$0.104115\pi$
$710$	47.9748	+	27.6983i	0.0675702	+	0.0390117i
$711$		0			0
$712$	174.108	+	301.563i	0.244533	+	0.423544i
$713$	472.693	+	1298.71i	0.662963	+	1.82148i
$714$		0			0
$715$	−260.817	+	218.852i	−0.364780	+	0.306086i
$716$	−98.6500	−	117.566i	−0.137779	−	0.164199i
$717$		0			0
$718$	−746.574	+	271.731i	−1.03980	+	0.378455i
$719$	−255.819	+	147.697i	−0.355799	+	0.205421i	−0.667236	−	0.744846i	$-0.732523\pi$
$719$	−255.819	+	147.697i	−0.355799	+	0.205421i	0.311438	+	0.950267i	$0.399190\pi$
$720$		0			0
$721$	−102.659	+	177.811i	−0.142385	+	0.246618i
$722$	−672.350	−	118.553i	−0.931233	−	0.164201i
$723$		0			0
$724$	535.811	+	195.019i	0.740070	+	0.269364i
$725$	−71.3621	+	12.5831i	−0.0984305	+	0.0173560i
$726$		0			0
$727$	−240.490	−	201.795i	−0.330798	−	0.277573i	0.462227	−	0.886762i	$-0.347051\pi$
$727$	−240.490	−	201.795i	−0.330798	−	0.277573i	−0.793025	+	0.609189i	$0.791495\pi$
$728$			40.3805i			0.0554678i
$729$		0			0
$730$	665.819			0.912080
$731$	917.706	−	1093.68i	1.25541	−	1.49614i
$732$		0			0
$733$	248.957	+	1411.91i	0.339642	+	1.92620i	0.375446	+	0.926844i	$0.377489\pi$
$733$	248.957	+	1411.91i	0.339642	+	1.92620i	−0.0358047	+	0.999359i	$0.511399\pi$
$734$	−277.224	+	761.666i	−0.377689	+	1.03769i
$735$		0			0
$736$	−29.1386	+	165.253i	−0.0395905	+	0.224529i
$737$	−665.819	−	384.411i	−0.903418	−	0.521589i
$738$		0			0
$739$	−459.948	−	796.653i	−0.622392	−	1.07801i	−0.989039	−	0.147654i	$-0.952828\pi$
$739$	−459.948	−	796.653i	−0.622392	−	1.07801i	0.366647	−	0.930360i	$-0.380506\pi$
$740$	40.7907	+	112.071i	0.0551225	+	0.151448i
$741$		0			0
$742$	101.922	−	85.5225i	0.137361	−	0.115259i
$743$	303.777	+	362.028i	0.408852	+	0.487251i	0.930698	−	0.365789i	$-0.119201\pi$
$743$	303.777	+	362.028i	0.408852	+	0.487251i	−0.521846	+	0.853040i	$0.674756\pi$
$744$		0			0
$745$	−226.105	+	82.2956i	−0.303497	+	0.110464i
$746$	463.638	−	267.681i	0.621498	−	0.358822i
$747$		0			0
$748$	190.587	−	330.106i	0.254795	−	0.441319i
$749$	1.15829	+	0.204238i	0.00154645	+	0.000272680i
$750$		0			0
$751$	606.653	+	220.804i	0.807794	+	0.294013i	0.712712	−	0.701457i	$-0.247467\pi$
$751$	606.653	+	220.804i	0.807794	+	0.294013i	0.0950817	+	0.995469i	$0.469689\pi$
$752$	−229.392	+	40.4481i	−0.305043	+	0.0537873i
$753$		0			0
$754$	184.331	+	154.672i	0.244471	+	0.205136i
$755$		−	390.513i		−	0.517235i
$756$		0			0
$757$	−482.464			−0.637337			−0.318668	−	0.947866i	$-0.603236\pi$
$757$	−482.464			−0.637337			−0.318668	+	0.947866i	$0.603236\pi$
$758$	385.616	−	459.559i	0.508728	−	0.606278i
$759$		0			0
$760$	64.2520	+	364.391i	0.0845421	+	0.479462i
$761$	235.486	−	646.992i	0.309443	−	0.850186i	−0.683323	−	0.730116i	$-0.739466\pi$
$761$	235.486	−	646.992i	0.309443	−	0.850186i	0.992765	−	0.120070i	$-0.0383119\pi$
$762$		0			0
$763$	−13.2030	+	74.8778i	−0.0173040	+	0.0981361i
$764$	−110.046	−	63.5353i	−0.144040	−	0.0831614i
$765$		0			0
$766$	364.440	+	631.229i	0.475770	+	0.824058i
$767$	−115.475	−	317.266i	−0.150555	−	0.413645i
$768$		0			0
$769$	750.225	−	629.514i	0.975586	−	0.818614i	−0.00783195	−	0.999969i	$-0.502493\pi$
$769$	750.225	−	629.514i	0.975586	−	0.818614i	0.983418	+	0.181356i	$0.0580486\pi$
$770$	36.0143	+	42.9201i	0.0467718	+	0.0557404i
$771$		0			0
$772$	507.979	−	184.889i	0.658004	−	0.239494i
$773$	−720.911	+	416.218i	−0.932615	+	0.538445i	−0.887638	−	0.460543i	$-0.847655\pi$
$773$	−720.911	+	416.218i	−0.932615	+	0.538445i	−0.0449772	+	0.998988i	$0.514322\pi$
$774$		0			0
$775$	−109.893	+	190.340i	−0.141797	+	0.245600i
$776$	−120.080	−	21.1733i	−0.154742	−	0.0272852i
$777$		0			0
$778$	−388.363	−	141.353i	−0.499182	−	0.181687i
$779$	1210.72	−	213.482i	1.55419	−	0.274046i
$780$		0			0
$781$	45.4747	+	38.1578i	0.0582263	+	0.0488577i
$782$			1171.44i			1.49801i
$783$		0			0
$784$	−189.355			−0.241524
$785$	−609.203	+	726.020i	−0.776055	+	0.924866i
$786$		0			0
$787$	51.5872	+	292.565i	0.0655491	+	0.371748i	0.999882	+	0.0153466i	$0.00488517\pi$
$787$	51.5872	+	292.565i	0.0655491	+	0.371748i	−0.934333	+	0.356401i	$0.884004\pi$
$788$	36.8777	−	101.321i	0.0467991	−	0.128579i
$789$		0			0
$790$	−66.6833	+	378.180i	−0.0844093	+	0.478709i
$791$	−28.5686	−	16.4941i	−0.0361171	−	0.0208522i
$792$		0			0
$793$	−83.8783	−	145.282i	−0.105773	−	0.183205i
$794$	242.625	+	666.607i	0.305573	+	0.839556i
$795$		0			0
$796$	206.804	−	173.529i	0.259804	−	0.218001i
$797$	−751.220	−	895.270i	−0.942560	−	1.12330i	−0.992215	−	0.124533i	$-0.960257\pi$
$797$	−751.220	−	895.270i	−0.942560	−	1.12330i	0.0496555	−	0.998766i	$-0.484188\pi$
$798$		0			0
$799$	−1528.04	+	556.162i	−1.91244	+	0.696073i
$800$	−23.1101	+	13.3426i	−0.0288876	+	0.0166782i
$801$		0			0
$802$	303.541	−	525.748i	0.378480	−	0.655546i
$803$	702.653	+	123.897i	0.875035	+	0.154292i
$804$		0			0
$805$	−161.804	−	58.8920i	−0.200999	−	0.0731578i
$806$	718.752	−	126.735i	0.891751	−	0.157240i
$807$		0			0
$808$	77.4936	+	65.0249i	0.0959079	+	0.0804763i
$809$		−	947.214i		−	1.17085i	−0.810728	−	0.585423i	$-0.800929\pi$
$809$		−	947.214i		−	1.17085i	0.810728	−	0.585423i	$-0.199071\pi$
$810$		0			0
$811$	209.571			0.258411			0.129205	−	0.991618i	$-0.458757\pi$
$811$	209.571			0.258411			0.129205	+	0.991618i	$0.458757\pi$
$812$	25.4529	−	30.3336i	0.0313459	−	0.0373566i
$813$		0			0
$814$	22.1928	+	125.862i	0.0272639	+	0.154621i
$815$	147.318	−	404.754i	0.180759	−	0.496630i
$816$		0			0
$817$	−257.889	+	1462.56i	−0.315654	+	1.79016i
$818$	−699.852	−	404.060i	−0.855565	−	0.493961i
$819$		0			0
$820$	−190.610	−	330.145i	−0.232451	−	0.402616i
$821$	−318.898	−	876.165i	−0.388426	−	1.06719i	−0.967710	−	0.252066i	$-0.918890\pi$
$821$	−318.898	−	876.165i	−0.388426	−	1.06719i	0.579284	−	0.815126i	$-0.303332\pi$
$822$		0			0
$823$	457.598	−	383.970i	0.556012	−	0.466549i	−0.320959	−	0.947093i	$-0.604005\pi$
$823$	457.598	−	383.970i	0.556012	−	0.466549i	0.876971	+	0.480544i	$0.159561\pi$
$824$	289.616	+	345.151i	0.351476	+	0.418873i
$825$		0			0
$826$	−52.2093	+	19.0026i	−0.0632074	+	0.0230056i
$827$	−897.728	+	518.303i	−1.08552	+	0.626727i	−0.932381	−	0.361477i	$-0.882273\pi$
$827$	−897.728	+	518.303i	−1.08552	+	0.626727i	−0.153142	+	0.988204i	$0.548939\pi$
$828$		0			0
$829$	561.238	−	972.093i	0.677006	−	1.17261i	−0.298872	−	0.954293i	$-0.596610\pi$
$829$	561.238	−	972.093i	0.677006	−	1.17261i	0.975878	−	0.218316i	$-0.0700563\pi$
$830$	−172.358	−	30.3914i	−0.207661	−	0.0366162i
$831$		0			0
$832$	83.2692	+	30.3075i	0.100083	+	0.0364273i
$833$	−1301.82	+	229.546i	−1.56281	+	0.275565i
$834$		0			0
$835$	−335.300	−	281.350i	−0.401557	−	0.336946i
$836$			396.506i			0.474290i
$837$		0			0
$838$	−19.4492			−0.0232091
$839$	241.391	−	287.679i	0.287713	−	0.342883i	−0.602757	−	0.797925i	$-0.705931\pi$
$839$	241.391	−	287.679i	0.287713	−	0.342883i	0.890470	+	0.455042i	$0.150376\pi$
$840$		0			0
$841$	105.064	+	595.846i	0.124927	+	0.708497i
$842$	140.036	−	384.746i	0.166314	−	0.456943i
$843$		0			0
$844$	−69.5090	+	394.205i	−0.0823566	+	0.467068i
$845$	180.612	+	104.276i	0.213742	+	0.123404i
$846$		0			0
$847$	−47.9583	−	83.0662i	−0.0566214	−	0.0980711i
$848$	−99.8599	−	274.363i	−0.117759	−	0.323541i
$849$		0			0
$850$	−142.707	+	119.746i	−0.167891	+	0.140877i
$851$	−252.469	−	300.881i	−0.296673	−	0.353561i
$852$		0			0
$853$	−321.687	+	117.085i	−0.377125	+	0.137262i	−0.523626	−	0.851948i	$-0.675421\pi$
$853$	−321.687	+	117.085i	−0.377125	+	0.137262i	0.146501	+	0.989210i	$0.453199\pi$
$854$	−23.9075	+	13.8030i	−0.0279948	+	0.0161628i
$855$		0			0
$856$	1.29051	−	2.23523i	0.00150761	−	0.00261125i
$857$	−1607.59	−	283.462i	−1.87584	−	0.330761i	−0.884976	−	0.465637i	$-0.845825\pi$
$857$	−1607.59	−	283.462i	−1.87584	−	0.330761i	−0.990862	+	0.134876i	$0.956936\pi$
$858$		0			0
$859$	−746.647	−	271.757i	−0.869205	−	0.316365i	−0.131360	−	0.991335i	$-0.541934\pi$
$859$	−746.647	−	271.757i	−0.869205	−	0.316365i	−0.737845	+	0.674970i	$0.764157\pi$
$860$	453.522	−	79.9681i	0.527351	−	0.0929862i
$861$		0			0
$862$	−405.063	−	339.888i	−0.469911	−	0.394302i
$863$		−	1059.53i		−	1.22772i	−0.789414	−	0.613862i	$-0.789615\pi$
$863$		−	1059.53i		−	1.22772i	0.789414	−	0.613862i	$-0.210385\pi$
$864$		0			0
$865$	1250.47			1.44563
$866$	−254.950	+	303.838i	−0.294400	+	0.350852i
$867$		0			0
$868$	−20.8556	−	118.278i	−0.0240272	−	0.136265i
$869$	−140.745	+	386.693i	−0.161962	+	0.444986i
$870$		0			0
$871$	216.667	−	1228.78i	0.248757	−	1.41077i
$872$	144.497	+	83.4254i	0.165708	+	0.0956714i
$873$		0			0
$874$	−609.281	−	1055.31i	−0.697118	−	1.20744i
$875$	−58.9987	−	162.098i	−0.0674271	−	0.185254i
$876$		0			0
$877$	−8.15596	+	6.84366i	−0.00929984	+	0.00780349i	−0.647426	−	0.762129i	$-0.724154\pi$
$877$	−8.15596	+	6.84366i	−0.00929984	+	0.00780349i	0.638126	+	0.769932i	$0.279710\pi$
$878$	324.733	+	387.001i	0.369855	+	0.440776i
$879$		0			0
$880$	115.537	−	42.0519i	0.131292	−	0.0477862i
$881$	−864.640	+	499.200i	−0.981430	+	0.566629i	−0.902702	−	0.430267i	$-0.858419\pi$
$881$	−864.640	+	499.200i	−0.981430	+	0.566629i	−0.0787284	+	0.996896i	$0.525086\pi$
$882$		0			0
$883$	234.685	−	406.487i	0.265782	−	0.460348i	−0.701986	−	0.712190i	$-0.747703\pi$
$883$	234.685	−	406.487i	0.265782	−	0.460348i	0.967768	+	0.251843i	$0.0810366\pi$
$884$	609.218	+	107.422i	0.689160	+	0.121518i
$885$		0			0
$886$	635.905	+	231.451i	0.717726	+	0.261231i
$887$	1736.47	−	306.186i	1.95769	−	0.345193i	0.959761	−	0.280818i	$-0.0906056\pi$
$887$	1736.47	−	306.186i	1.95769	−	0.345193i	0.997926	−	0.0643754i	$-0.0205055\pi$
$888$		0			0
$889$	−45.5922	−	38.2564i	−0.0512848	−	0.0430331i
$890$			784.117i			0.881030i
$891$		0			0
$892$	730.999			0.819505
$893$	1087.29	−	1295.78i	1.21757	−	1.45104i
$894$		0			0
$895$	−60.0112	−	340.341i	−0.0670516	−	0.380269i
$896$	4.98741	−	13.7028i	0.00556630	−	0.0152933i
$897$		0			0
$898$	138.743	−	786.851i	0.154502	−	0.876226i
$899$	−619.805	−	357.845i	−0.689439	−	0.398048i
$900$		0			0
$901$	−1019.14	−	1765.19i	−1.13112	−	1.95915i
$902$	−139.720	−	383.879i	−0.154901	−	0.425586i
$903$		0			0
$904$	−55.4548	+	46.5321i	−0.0613438	+	0.0514736i
$905$	825.327	+	983.586i	0.911963	+	1.08684i
$906$		0			0
$907$	1393.67	−	507.255i	1.53657	−	0.559267i	0.571354	−	0.820704i	$-0.306418\pi$
$907$	1393.67	−	507.255i	1.53657	−	0.559267i	0.965221	+	0.261437i	$0.0841962\pi$
$908$	289.873	−	167.358i	0.319244	−	0.184316i
$909$		0			0
$910$	−45.4647	+	78.7473i	−0.0499613	+	0.0865354i
$911$	−1475.18	−	260.115i	−1.61930	−	0.285527i	−0.710796	−	0.703398i	$-0.751665\pi$
$911$	−1475.18	−	260.115i	−1.61930	−	0.285527i	−0.908506	+	0.417871i	$0.862776\pi$
$912$		0			0
$913$	−176.238	−	64.1455i	−0.193032	−	0.0702579i
$914$	−147.786	+	26.0586i	−0.161691	+	0.0285105i
$915$		0			0
$916$	−248.710	−	208.693i	−0.271518	−	0.227830i
$917$			36.7564i			0.0400834i
$918$		0			0
$919$	−610.689			−0.664515			−0.332257	−	0.943189i	$-0.607810\pi$
$919$	−610.689			−0.664515			−0.332257	+	0.943189i	$0.607810\pi$
$920$	−242.884	+	289.458i	−0.264004	+	0.314628i
$921$		0			0
$922$	31.2110	+	177.006i	0.0338514	+	0.191981i
$923$	−32.9508	+	90.5315i	−0.0356996	+	0.0980840i
$924$		0			0
$925$	10.8463	−	61.5125i	0.0117257	−	0.0665000i
$926$	−305.364	−	176.302i	−0.329767	−	0.190391i
$927$		0			0
$928$	−43.4476	−	75.2535i	−0.0468186	−	0.0810921i
$929$	309.237	+	849.622i	0.332871	+	0.914556i	0.987361	+	0.158485i	$0.0506610\pi$
$929$	309.237	+	849.622i	0.332871	+	0.914556i	−0.654490	+	0.756070i	$0.727117\pi$
$930$		0			0
$931$	1053.37	−	883.879i	1.13144	−	0.949387i
$932$	−236.315	−	281.630i	−0.253557	−	0.302178i
$933$		0			0
$934$	518.925	−	188.873i	0.555595	−	0.202220i
$935$	743.338	−	429.167i	0.795014	−	0.459002i
$936$		0			0
$937$	259.623	−	449.680i	0.277079	−	0.479915i	−0.693579	−	0.720381i	$-0.743967\pi$
$937$	259.623	−	449.680i	0.277079	−	0.479915i	0.970658	+	0.240466i	$0.0773003\pi$
$938$	−202.208	−	35.6548i	−0.215574	−	0.0380115i
$939$		0			0
$940$	−492.885	−	179.396i	−0.524346	−	0.190846i
$941$	−808.796	+	142.613i	−0.859507	+	0.151554i	−0.585995	−	0.810314i	$-0.699296\pi$
$941$	−808.796	+	142.613i	−0.859507	+	0.151554i	−0.273512	+	0.961869i	$0.588185\pi$
$942$		0			0
$943$	961.744	+	806.999i	1.01988	+	0.855779i
$944$			121.924i			0.129157i
$945$		0			0
$946$	493.492			0.521662
$947$	−74.7672	+	89.1040i	−0.0789516	+	0.0940909i	−0.804074	−	0.594529i	$-0.797339\pi$
$947$	−74.7672	+	89.1040i	−0.0789516	+	0.0940909i	0.725123	+	0.688620i	$0.241783\pi$
$948$		0			0
$949$	201.075	+	1140.35i	0.211881	+	1.20163i
$950$	66.2782	−	182.098i	0.0697665	−	0.191682i
$951$		0			0
$952$	17.6773	−	100.253i	0.0185686	−	0.105308i
$953$	686.346	+	396.262i	0.720195	+	0.415805i	0.814824	−	0.579708i	$-0.196833\pi$
$953$	686.346	+	396.262i	0.720195	+	0.415805i	−0.0946295	+	0.995513i	$0.530167\pi$
$954$		0			0
$955$	−143.070	−	247.804i	−0.149811	−	0.259481i
$956$	−29.5574	−	81.2083i	−0.0309178	−	0.0849459i
$957$		0			0
$958$	849.624	−	712.920i	0.886873	−	0.744175i
$959$	127.477	+	151.922i	0.132927	+	0.158417i
$960$		0			0
$961$	−1136.78	+	413.754i	−1.18291	+	0.430546i
$962$	−179.627	+	103.708i	−0.186722	+	0.107804i
$963$		0			0
$964$	−65.1331	+	112.814i	−0.0675654	+	0.117027i
$965$	1198.79	+	211.379i	1.24227	+	0.219046i
$966$		0			0
$967$	−609.471	−	221.829i	−0.630270	−	0.229399i	0.00707887	−	0.999975i	$-0.497747\pi$
$967$	−609.471	−	221.829i	−0.630270	−	0.229399i	−0.637349	+	0.770575i	$0.719969\pi$
$968$	−207.287	+	36.5503i	−0.214139	+	0.0377586i
$969$		0			0
$970$	−210.332	−	176.489i	−0.216837	−	0.181948i
$971$		−	144.756i		−	0.149079i	−0.997218	−	0.0745395i	$-0.976251\pi$
$971$		−	144.756i		−	0.149079i	0.997218	−	0.0745395i	$-0.0237487\pi$
$972$		0			0
$973$	−33.4666			−0.0343953
$974$	351.081	−	418.402i	0.360453	−	0.429571i
$975$		0			0
$976$	10.5196	+	59.6599i	0.0107783	+	0.0611269i
$977$	307.745	−	845.523i	0.314990	−	0.865427i	−0.676640	−	0.736314i	$-0.736565\pi$
$977$	307.745	−	845.523i	0.314990	−	0.865427i	0.991630	−	0.129113i	$-0.0412131\pi$
$978$		0			0
$979$	−145.910	+	827.495i	−0.149040	+	0.845245i
$980$	−369.267	−	213.196i	−0.376803	−	0.217547i
$981$		0			0
$982$	239.782	+	415.315i	0.244177	+	0.422927i
$983$	−589.102	−	1618.54i	−0.599290	−	1.64654i	−0.752693	−	0.658372i	$-0.771245\pi$
$983$	−589.102	−	1618.54i	−0.599290	−	1.64654i	0.153402	−	0.988164i	$-0.450977\pi$
$984$		0			0
$985$	185.994	−	156.067i	0.188826	−	0.158444i
$986$	−389.929	−	464.700i	−0.395466	−	0.471298i
$987$		0			0
$988$	−604.691	+	220.089i	−0.612035	+	0.222763i
$989$	−1313.43	+	758.311i	−1.32804	+	0.766746i
$990$		0			0
$991$	−75.6965	+	131.110i	−0.0763839	+	0.132301i	−0.901687	−	0.432389i	$-0.857671\pi$
$991$	−75.6965	+	131.110i	−0.0763839	+	0.132301i	0.825303	+	0.564690i	$0.191004\pi$
$992$	−259.555	−	45.7666i	−0.261649	−	0.0461357i
$993$		0			0
$994$	14.8979	+	5.42238i	0.0149878	+	0.00545511i
$995$	598.672	−	105.562i	0.601681	−	0.106093i
$996$		0			0
$997$	−253.078	−	212.357i	−0.253839	−	0.212996i	0.506984	−	0.861955i	$-0.330760\pi$
$997$	−253.078	−	212.357i	−0.253839	−	0.212996i	−0.760823	+	0.648959i	$0.775205\pi$
$998$		−	1031.41i		−	1.03347i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	162.3.f.a.35.6		36
3.2	odd	2		54.3.f.a.11.2	yes	36
12.11	even	2		432.3.bc.c.65.4		36
27.5	odd	18	inner	162.3.f.a.125.6		36
27.7	even	9		1458.3.b.c.1457.14		36
27.20	odd	18		1458.3.b.c.1457.23		36
27.22	even	9		54.3.f.a.5.2	✓	36
108.103	odd	18		432.3.bc.c.113.4		36

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
54.3.f.a.5.2	✓	36	27.22	even	9
54.3.f.a.11.2	yes	36	3.2	odd	2
162.3.f.a.35.6		36	1.1	even	1	trivial
162.3.f.a.125.6		36	27.5	odd	18	inner
432.3.bc.c.65.4		36	12.11	even	2
432.3.bc.c.113.4		36	108.103	odd	18
1458.3.b.c.1457.14		36	27.7	even	9
1458.3.b.c.1457.23		36	27.20	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)

\(f(q)\)	\(=\)	\(q+(0.909039 - 1.08335i) q^{2} +(-0.347296 - 1.96962i) q^{4} +(1.54033 - 4.23203i) q^{5} +(0.223815 - 1.26932i) q^{7} +(-2.44949 - 1.41421i) q^{8} +O(q^{10})\)	\(q+(0.909039 - 1.08335i) q^{2} +(-0.347296 - 1.96962i) q^{4} +(1.54033 - 4.23203i) q^{5} +(0.223815 - 1.26932i) q^{7} +(-2.44949 - 1.41421i) q^{8} +(-3.18455 - 5.51580i) q^{10} +(-2.33433 - 6.41353i) q^{11} +(8.48521 - 7.11994i) q^{13} +(-1.17166 - 1.39633i) q^{14} +(-3.75877 + 1.36808i) q^{16} +(-24.1831 + 13.9621i) q^{17} +(14.5238 - 25.1559i) q^{19} +(-8.87042 - 1.56409i) q^{20} +(-9.07010 - 3.30125i) q^{22} +(29.2129 - 5.15103i) q^{23} +(3.61368 + 3.03223i) q^{25} -15.6648i q^{26} -2.57779 q^{28} +(-9.87390 + 11.7673i) q^{29} +(8.09047 + 45.8833i) q^{31} +(-1.93476 + 5.31570i) q^{32} +(-6.85753 + 38.8910i) q^{34} +(-5.02703 - 2.90236i) q^{35} +(-6.62043 - 11.4669i) q^{37} +(-14.0500 - 38.6020i) q^{38} +(-9.75802 + 8.18795i) q^{40} +(27.2051 + 32.4217i) q^{41} +(-48.0441 + 17.4866i) q^{43} +(-11.8215 + 6.82513i) q^{44} +(20.9753 - 36.3303i) q^{46} +(57.3481 + 10.1120i) q^{47} +(44.4839 + 16.1908i) q^{49} +(6.56995 - 1.15846i) q^{50} +(-16.9704 - 14.2399i) q^{52} +72.9927i q^{53} -30.7379 q^{55} +(-2.34332 + 2.79265i) q^{56} +(3.77230 + 21.3938i) q^{58} +(10.4251 - 28.6427i) q^{59} +(2.62991 - 14.9150i) q^{61} +(57.0623 + 32.9449i) q^{62} +(4.00000 + 6.92820i) q^{64} +(-17.0617 - 46.8767i) q^{65} +(86.2916 - 72.4073i) q^{67} +(35.8988 + 42.7825i) q^{68} +(-7.71404 + 2.80768i) q^{70} +(-7.53244 + 4.34886i) q^{71} +(-52.2695 + 90.5334i) q^{73} +(-18.4409 - 3.25163i) q^{74} +(-54.5914 - 19.8697i) q^{76} +(-8.66325 + 1.52756i) q^{77} +(-46.1874 - 38.7558i) q^{79} +18.0145i q^{80} +59.8545 q^{82} +(17.6633 - 21.0502i) q^{83} +(21.8381 + 123.850i) q^{85} +(-24.7298 + 67.9446i) q^{86} +(-3.35217 + 19.0111i) q^{88} +(-106.619 - 61.5564i) q^{89} +(-7.13834 - 12.3640i) q^{91} +(-20.2911 - 55.7493i) q^{92} +(63.0865 - 52.9358i) q^{94} +(-84.0890 - 100.213i) q^{95} +(40.5097 - 14.7443i) q^{97} +(57.9779 - 33.4735i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 36 q - 18 q^{5}+O(q^{10}) \) 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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