LMFDB - Embedded newform 162.3.f.a.35.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("162.17");

S:= CuspForms(chi, 3);

N := Newforms(S);

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

Newform invariants

comment: select newform

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

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

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

Embedding invariants

Embedding label			35.3
Character	$\chi$	$=$	162.35
Dual form			162.3.f.a.125.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.909039 + 1.08335i) q^{2} +(-0.347296 - 1.96962i) q^{4} +(1.07911 - 2.96482i) q^{5} +(-0.250410 + 1.42015i) q^{7} +(2.44949 + 1.41421i) q^{8} +O(q^{10})$	\(q+(-0.909039 + 1.08335i) q^{2} +(-0.347296 - 1.96962i) q^{4} +(1.07911 - 2.96482i) q^{5} +(-0.250410 + 1.42015i) q^{7} +(2.44949 + 1.41421i) q^{8} +(2.23099 + 3.86419i) q^{10} +(-6.39485 - 17.5697i) q^{11} +(10.5936 - 8.88908i) q^{13} +(-1.31088 - 1.56225i) q^{14} +(-3.75877 + 1.36808i) q^{16} +(16.3520 - 9.44086i) q^{17} +(-1.14343 + 1.98047i) q^{19} +(-6.21434 - 1.09575i) q^{20} +(24.8473 + 9.04368i) q^{22} +(26.5788 - 4.68656i) q^{23} +(11.5254 + 9.67096i) q^{25} +19.5571i q^{26} +2.88411 q^{28} +(-17.2495 + 20.5571i) q^{29} +(-4.55767 - 25.8478i) q^{31} +(1.93476 - 5.31570i) q^{32} +(-4.63689 + 26.2971i) q^{34} +(3.94026 + 2.27491i) q^{35} +(-33.8611 - 58.6492i) q^{37} +(-1.10613 - 3.03906i) q^{38} +(6.83616 - 5.73622i) q^{40} +(13.0402 + 15.5407i) q^{41} +(-32.2609 + 11.7420i) q^{43} +(-32.3847 + 18.6973i) q^{44} +(-19.0840 + 33.0544i) q^{46} +(-46.4969 - 8.19866i) q^{47} +(44.0908 + 16.0478i) q^{49} +(-20.9541 + 3.69477i) q^{50} +(-21.1872 - 17.7782i) q^{52} +49.0655i q^{53} -58.9918 q^{55} +(-2.62176 + 3.12450i) q^{56} +(-6.59012 - 37.3744i) q^{58} +(13.0684 - 35.9050i) q^{59} +(-9.55898 + 54.2117i) q^{61} +(32.1454 + 18.5591i) q^{62} +(4.00000 + 6.92820i) q^{64} +(-14.9229 - 41.0004i) q^{65} +(-95.2638 + 79.9358i) q^{67} +(-24.2739 - 28.9285i) q^{68} +(-6.04638 + 2.20070i) q^{70} +(-10.4669 + 6.04307i) q^{71} +(37.3933 - 64.7671i) q^{73} +(94.3187 + 16.6309i) q^{74} +(4.29788 + 1.56430i) q^{76} +(26.5529 - 4.68199i) q^{77} +(74.8249 + 62.7855i) q^{79} +12.6204i q^{80} -28.6900 q^{82} +(-81.1294 + 96.6863i) q^{83} +(-10.3449 - 58.6687i) q^{85} +(16.6057 - 45.6238i) q^{86} +(9.18320 - 52.0805i) q^{88} +(-9.23832 - 5.33375i) q^{89} +(9.97104 + 17.2703i) q^{91} +(-18.4614 - 50.7224i) q^{92} +(51.1495 - 42.9196i) q^{94} +(4.63788 + 5.52721i) q^{95} +(145.826 - 53.0765i) q^{97} +(-57.4656 + 33.1778i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$5$	1.07911	−	2.96482i	0.215822	−	0.592965i	−0.783784	−	0.621033i	$-0.786713\pi$
$5$	1.07911	−	2.96482i	0.215822	−	0.592965i	0.999606	+	0.0280680i	$0.00893551\pi$
$6$		0			0
$7$	−0.250410	+	1.42015i	−0.0357728	+	0.202878i	−0.997456	−	0.0712856i	$-0.977290\pi$
$7$	−0.250410	+	1.42015i	−0.0357728	+	0.202878i	0.961683	+	0.274163i	$0.0884009\pi$
$8$	2.44949	+	1.41421i	0.306186	+	0.176777i
$9$		0			0
$10$	2.23099	+	3.86419i	0.223099	+	0.386419i
$11$	−6.39485	−	17.5697i	−0.581350	−	1.59725i	−0.785876	−	0.618385i	$-0.787787\pi$
$11$	−6.39485	−	17.5697i	−0.581350	−	1.59725i	0.204526	−	0.978861i	$-0.434435\pi$
$12$		0			0
$13$	10.5936	−	8.88908i	0.814891	−	0.683775i	−0.136879	−	0.990588i	$-0.543707\pi$
$13$	10.5936	−	8.88908i	0.814891	−	0.683775i	0.951770	+	0.306813i	$0.0992625\pi$
$14$	−1.31088	−	1.56225i	−0.0936345	−	0.111589i
$15$		0			0
$16$	−3.75877	+	1.36808i	−0.234923	+	0.0855050i
$17$	16.3520	−	9.44086i	0.961885	−	0.555345i	0.0651325	−	0.997877i	$-0.479253\pi$
$17$	16.3520	−	9.44086i	0.961885	−	0.555345i	0.896753	+	0.442532i	$0.145920\pi$
$18$		0			0
$19$	−1.14343	+	1.98047i	−0.0601804	+	0.104236i	−0.894546	−	0.446976i	$-0.852501\pi$
$19$	−1.14343	+	1.98047i	−0.0601804	+	0.104236i	0.834366	+	0.551212i	$0.185834\pi$
$20$	−6.21434	−	1.09575i	−0.310717	−	0.0547877i
$21$		0			0
$22$	24.8473	+	9.04368i	1.12942	+	0.411077i
$23$	26.5788	−	4.68656i	1.15560	−	0.203763i	0.437181	−	0.899374i	$-0.355977\pi$
$23$	26.5788	−	4.68656i	1.15560	−	0.203763i	0.718419	+	0.695610i	$0.244866\pi$
$24$		0			0
$25$	11.5254	+	9.67096i	0.461016	+	0.386838i
$26$			19.5571i			0.752196i
$27$		0			0
$28$	2.88411			0.103004
$29$	−17.2495	+	20.5571i	−0.594809	+	0.708865i	−0.976523	−	0.215415i	$-0.930890\pi$
$29$	−17.2495	+	20.5571i	−0.594809	+	0.708865i	0.381714	+	0.924281i	$0.375334\pi$
$30$		0			0
$31$	−4.55767	−	25.8478i	−0.147022	−	0.833801i	−0.965722	−	0.259580i	$-0.916416\pi$
$31$	−4.55767	−	25.8478i	−0.147022	−	0.833801i	0.818700	−	0.574221i	$-0.194695\pi$
$32$	1.93476	−	5.31570i	0.0604612	−	0.166116i
$33$		0			0
$34$	−4.63689	+	26.2971i	−0.136379	+	0.773444i
$35$	3.94026	+	2.27491i	0.112579	+	0.0649975i
$36$		0			0
$37$	−33.8611	−	58.6492i	−0.915166	−	1.58511i	−0.806659	−	0.591018i	$-0.798726\pi$
$37$	−33.8611	−	58.6492i	−0.915166	−	1.58511i	−0.108507	−	0.994096i	$-0.534607\pi$
$38$	−1.10613	−	3.03906i	−0.0291086	−	0.0799753i
$39$		0			0
$40$	6.83616	−	5.73622i	0.170904	−	0.143405i
$41$	13.0402	+	15.5407i	0.318053	+	0.379041i	0.901257	−	0.433285i	$-0.142646\pi$
$41$	13.0402	+	15.5407i	0.318053	+	0.379041i	−0.583204	+	0.812326i	$0.698201\pi$
$42$		0			0
$43$	−32.2609	+	11.7420i	−0.750254	+	0.273070i	−0.688713	−	0.725034i	$-0.741824\pi$
$43$	−32.2609	+	11.7420i	−0.750254	+	0.273070i	−0.0615413	+	0.998105i	$0.519602\pi$
$44$	−32.3847	+	18.6973i	−0.736015	+	0.424938i
$45$		0			0
$46$	−19.0840	+	33.0544i	−0.414869	+	0.718574i
$47$	−46.4969	−	8.19866i	−0.989296	−	0.174440i	−0.344494	−	0.938789i	$-0.611949\pi$
$47$	−46.4969	−	8.19866i	−0.989296	−	0.174440i	−0.644803	+	0.764349i	$0.723060\pi$
$48$		0			0
$49$	44.0908	+	16.0478i	0.899813	+	0.327505i
$50$	−20.9541	+	3.69477i	−0.419081	+	0.0738954i
$51$		0			0
$52$	−21.1872	−	17.7782i	−0.407446	−	0.341888i
$53$			49.0655i			0.925765i	0.886420	+	0.462882i	$0.153185\pi$
$53$			49.0655i			0.925765i	−0.886420	+	0.462882i	$0.846815\pi$
$54$		0			0
$55$	−58.9918			−1.07258
$56$	−2.62176	+	3.12450i	−0.0468172	+	0.0557946i
$57$		0			0
$58$	−6.59012	−	37.3744i	−0.113623	−	0.644386i
$59$	13.0684	−	35.9050i	0.221498	−	0.608560i	−0.778316	−	0.627873i	$-0.783926\pi$
$59$	13.0684	−	35.9050i	0.221498	−	0.608560i	0.999813	+	0.0193130i	$0.00614791\pi$
$60$		0			0
$61$	−9.55898	+	54.2117i	−0.156705	+	0.888716i	0.800506	+	0.599324i	$0.204564\pi$
$61$	−9.55898	+	54.2117i	−0.156705	+	0.888716i	−0.957211	+	0.289391i	$0.906547\pi$
$62$	32.1454	+	18.5591i	0.518474	+	0.299341i
$63$		0			0
$64$	4.00000	+	6.92820i	0.0625000	+	0.108253i
$65$	−14.9229	−	41.0004i	−0.229583	−	0.630775i
$66$		0			0
$67$	−95.2638	+	79.9358i	−1.42185	+	1.19307i	−0.471505	+	0.881863i	$0.656289\pi$
$67$	−95.2638	+	79.9358i	−1.42185	+	1.19307i	−0.950342	+	0.311208i	$0.899266\pi$
$68$	−24.2739	−	28.9285i	−0.356969	−	0.425419i
$69$		0			0
$70$	−6.04638	+	2.20070i	−0.0863768	+	0.0314386i
$71$	−10.4669	+	6.04307i	−0.147421	+	0.0851136i	−0.571896	−	0.820326i	$-0.693792\pi$
$71$	−10.4669	+	6.04307i	−0.147421	+	0.0851136i	0.424475	+	0.905440i	$0.360459\pi$
$72$		0			0
$73$	37.3933	−	64.7671i	0.512237	−	0.887220i	−0.487663	−	0.873032i	$-0.662150\pi$
$73$	37.3933	−	64.7671i	0.512237	−	0.887220i	0.999899	−	0.0141878i	$-0.00451627\pi$
$74$	94.3187	+	16.6309i	1.27458	+	0.224742i
$75$		0			0
$76$	4.29788	+	1.56430i	0.0565511	+	0.0205829i
$77$	26.5529	−	4.68199i	0.344842	−	0.0608050i
$78$		0			0
$79$	74.8249	+	62.7855i	0.947151	+	0.794754i	0.978815	−	0.204745i	$-0.0656364\pi$
$79$	74.8249	+	62.7855i	0.947151	+	0.794754i	−0.0316647	+	0.999499i	$0.510081\pi$
$80$			12.6204i			0.157755i
$81$		0			0
$82$	−28.6900			−0.349879
$83$	−81.1294	+	96.6863i	−0.977463	+	1.16490i	0.00884154	+	0.999961i	$0.497186\pi$
$83$	−81.1294	+	96.6863i	−0.977463	+	1.16490i	−0.986305	+	0.164934i	$0.947259\pi$
$84$		0			0
$85$	−10.3449	−	58.6687i	−0.121704	−	0.690220i
$86$	16.6057	−	45.6238i	0.193090	−	0.530510i
$87$		0			0
$88$	9.18320	−	52.0805i	0.104355	−	0.591824i
$89$	−9.23832	−	5.33375i	−0.103801	−	0.0599298i	0.447201	−	0.894434i	$-0.352421\pi$
$89$	−9.23832	−	5.33375i	−0.103801	−	0.0599298i	−0.551002	+	0.834504i	$0.685754\pi$
$90$		0			0
$91$	9.97104	+	17.2703i	0.109572	+	0.189784i
$92$	−18.4614	−	50.7224i	−0.200668	−	0.551330i
$93$		0			0
$94$	51.1495	−	42.9196i	0.544144	−	0.456591i
$95$	4.63788	+	5.52721i	0.0488198	+	0.0581811i
$96$		0			0
$97$	145.826	−	53.0765i	1.50337	−	0.547180i	0.546436	−	0.837501i	$-0.315984\pi$
$97$	145.826	−	53.0765i	1.50337	−	0.547180i	0.956929	+	0.290320i	$0.0937619\pi$
$98$	−57.4656	+	33.1778i	−0.586384	+	0.338549i
$99$		0			0
$100$	15.0453	−	26.0593i	0.150453	−	0.260593i
$101$	98.5993	+	17.3857i	0.976231	+	0.172136i	0.638933	−	0.769262i	$-0.279376\pi$
$101$	98.5993	+	17.3857i	0.976231	+	0.172136i	0.337298	+	0.941398i	$0.390487\pi$
$102$		0			0
$103$	121.218	+	44.1198i	1.17687	+	0.428347i	0.855097	−	0.518468i	$-0.173498\pi$
$103$	121.218	+	44.1198i	1.17687	+	0.428347i	0.321777	+	0.946815i	$0.395720\pi$
$104$	38.5199	−	6.79210i	0.370384	−	0.0653087i
$105$		0			0
$106$	−53.1552	−	44.6025i	−0.501464	−	0.420778i
$107$		−	106.516i		−	0.995473i	−0.867328	−	0.497736i	$-0.834165\pi$
$107$		−	106.516i		−	0.995473i	0.867328	−	0.497736i	$-0.165835\pi$
$108$		0			0
$109$	102.881			0.943865			0.471933	−	0.881635i	$-0.343557\pi$
$109$	102.881			0.943865			0.471933	+	0.881635i	$0.343557\pi$
$110$	53.6259	−	63.9088i	0.487508	−	0.580989i
$111$		0			0
$112$	−1.00164	−	5.68058i	−0.00894321	−	0.0507195i
$113$	−30.8936	+	84.8796i	−0.273395	+	0.751147i	0.724678	+	0.689088i	$0.241989\pi$
$113$	−30.8936	+	84.8796i	−0.273395	+	0.751147i	−0.998073	+	0.0620584i	$0.980233\pi$
$114$		0			0
$115$	14.7866	−	83.8588i	0.128579	−	0.729207i
$116$	46.4802	+	26.8354i	0.400692	+	0.231340i
$117$		0			0
$118$	27.0181	+	46.7967i	0.228967	+	0.396582i
$119$	9.31268	+	25.5864i	0.0782578	+	0.215011i
$120$		0			0
$121$	−175.109	+	146.934i	−1.44718	+	1.21433i
$122$	−50.0408	−	59.6362i	−0.410170	−	0.488822i
$123$		0			0
$124$	−49.3274	+	17.9537i	−0.397802	+	0.144788i
$125$	109.420	−	63.1735i	0.875358	−	0.505388i
$126$		0			0
$127$	−20.3684	+	35.2791i	−0.160381	+	0.277788i	−0.935005	−	0.354634i	$-0.884606\pi$
$127$	−20.3684	+	35.2791i	−0.160381	+	0.277788i	0.774624	+	0.632422i	$0.217939\pi$
$128$	−11.1418	−	1.96460i	−0.0870455	−	0.0153485i
$129$		0			0
$130$	57.9833	+	21.1042i	0.446026	+	0.162340i
$131$	−48.6358	+	8.57581i	−0.371266	+	0.0654642i	−0.356168	−	0.934422i	$-0.615917\pi$
$131$	−48.6358	+	8.57581i	−0.371266	+	0.0654642i	−0.0150977	+	0.999886i	$0.504806\pi$
$132$		0			0
$133$	−2.52624	−	2.11976i	−0.0189943	−	0.0159381i
$134$		−	175.869i		−	1.31245i
$135$		0			0
$136$	53.4056			0.392688
$137$	86.7066	−	103.333i	0.632895	−	0.754255i	−0.350335	−	0.936624i	$-0.613932\pi$
$137$	86.7066	−	103.333i	0.632895	−	0.754255i	0.983230	+	0.182369i	$0.0583767\pi$
$138$		0			0
$139$	−13.8192	−	78.3726i	−0.0994187	−	0.563832i	−0.993303	−	0.115535i	$-0.963142\pi$
$139$	−13.8192	−	78.3726i	−0.0994187	−	0.563832i	0.893885	−	0.448297i	$-0.147969\pi$
$140$	3.11226	−	8.55087i	0.0222304	−	0.0610776i
$141$		0			0
$142$	2.96806	−	16.8327i	0.0209018	−	0.118540i
$143$	−223.923	−	129.282i	−1.56589	−	0.904069i
$144$		0			0
$145$	42.3342	+	73.3249i	0.291960	+	0.505689i
$146$	36.1735	+	99.3858i	0.247764	+	0.680725i
$147$		0			0
$148$	−103.757	+	87.0621i	−0.701058	+	0.588257i
$149$	80.7384	+	96.2203i	0.541869	+	0.645774i	0.965606	−	0.260011i	$-0.0837263\pi$
$149$	80.7384	+	96.2203i	0.541869	+	0.645774i	−0.423737	+	0.905785i	$0.639282\pi$
$150$		0			0
$151$	−106.373	+	38.7167i	−0.704459	+	0.256402i	−0.669314	−	0.742980i	$-0.733412\pi$
$151$	−106.373	+	38.7167i	−0.704459	+	0.256402i	−0.0351455	+	0.999382i	$0.511189\pi$
$152$	−5.60163	+	3.23410i	−0.0368528	+	0.0212770i
$153$		0			0
$154$	−19.0654	+	33.0222i	−0.123801	+	0.214430i
$155$	−81.5525	−	14.3799i	−0.526145	−	0.0927736i
$156$		0			0
$157$	−48.5338	−	17.6648i	−0.309132	−	0.112515i	0.182796	−	0.983151i	$-0.441485\pi$
$157$	−48.5338	−	17.6648i	−0.309132	−	0.112515i	−0.491928	+	0.870636i	$0.663708\pi$
$158$	−136.038	+	23.9871i	−0.860997	+	0.151817i
$159$		0			0
$160$	−13.6723	−	11.4724i	−0.0854520	−	0.0717027i
$161$			38.9193i			0.241735i
$162$		0			0
$163$	1.04117			0.00638756			0.00319378	−	0.999995i	$-0.498983\pi$
$163$	1.04117			0.00638756			0.00319378	+	0.999995i	$0.498983\pi$
$164$	26.0804	−	31.0814i	0.159027	−	0.189521i
$165$		0			0
$166$	−30.9953	−	175.783i	−0.186719	−	1.05894i
$167$	−79.8469	+	219.378i	−0.478125	+	1.31364i	0.432957	+	0.901414i	$0.357470\pi$
$167$	−79.8469	+	219.378i	−0.478125	+	1.31364i	−0.911083	+	0.412224i	$0.864752\pi$
$168$		0			0
$169$	3.86190	−	21.9019i	0.0228515	−	0.129597i
$170$	72.9626	+	42.1250i	0.429192	+	0.247794i
$171$		0			0
$172$	34.3313	+	59.4636i	0.199601	+	0.345719i
$173$	39.2036	+	107.711i	0.226611	+	0.622607i	0.999935	−	0.0114031i	$-0.00362981\pi$
$173$	39.2036	+	107.711i	0.226611	+	0.622607i	−0.773324	+	0.634011i	$0.781408\pi$
$174$		0			0
$175$	−16.6202	+	13.9460i	−0.0949728	+	0.0796916i
$176$	48.0735	+	57.2918i	0.273145	+	0.325522i
$177$		0			0
$178$	14.1763	−	5.15976i	0.0796422	−	0.0289874i
$179$	156.103	−	90.1263i	0.872086	−	0.503499i	0.00404482	−	0.999992i	$-0.498712\pi$
$179$	156.103	−	90.1263i	0.872086	−	0.503499i	0.868041	+	0.496493i	$0.165379\pi$
$180$		0			0
$181$	17.6283	−	30.5332i	0.0973941	−	0.168691i	−0.813211	−	0.581969i	$-0.802283\pi$
$181$	17.6283	−	30.5332i	0.0973941	−	0.168691i	0.910605	+	0.413277i	$0.135616\pi$
$182$	−27.7739	−	4.89729i	−0.152604	−	0.0269082i
$183$		0			0
$184$	71.7323	+	26.1084i	0.389849	+	0.141894i
$185$	−210.424	+	37.1035i	−1.13743	+	0.200559i
$186$		0			0
$187$	−270.442	−	226.928i	−1.44621	−	1.21352i
$188$			94.4284i			0.502279i
$189$		0			0
$190$	−10.2039			−0.0537048
$191$	13.7198	−	16.3506i	0.0718313	−	0.0856053i	−0.728932	−	0.684586i	$-0.759983\pi$
$191$	13.7198	−	16.3506i	0.0718313	−	0.0856053i	0.800763	+	0.598981i	$0.204427\pi$
$192$		0			0
$193$	−22.8734	−	129.722i	−0.118515	−	0.672133i	−0.984950	−	0.172842i	$-0.944705\pi$
$193$	−22.8734	−	129.722i	−0.118515	−	0.672133i	0.866434	−	0.499291i	$-0.166406\pi$
$194$	−75.0615	+	206.230i	−0.386915	+	1.06304i
$195$		0			0
$196$	16.2953	−	92.4153i	0.0831394	−	0.471507i
$197$	26.6300	+	15.3748i	0.135177	+	0.0780447i	0.566064	−	0.824362i	$-0.308466\pi$
$197$	26.6300	+	15.3748i	0.135177	+	0.0780447i	−0.430886	+	0.902406i	$0.641799\pi$
$198$		0			0
$199$	122.692	+	212.509i	0.616545	+	1.06789i	0.990111	+	0.140283i	$0.0448013\pi$
$199$	122.692	+	212.509i	0.616545	+	1.06789i	−0.373567	+	0.927603i	$0.621865\pi$
$200$	14.5545	+	39.9883i	0.0727727	+	0.199941i
$201$		0			0
$202$	−108.465	+	91.0133i	−0.536958	+	0.450561i
$203$	−24.8746	−	29.6444i	−0.122535	−	0.146032i
$204$		0			0
$205$	60.1472	−	21.8918i	0.293401	−	0.106789i
$206$	−157.989	+	91.2150i	−0.766937	+	0.442791i
$207$		0			0
$208$	−27.6579	+	47.9049i	−0.132971	+	0.230312i
$209$	42.1084	+	7.42485i	0.201476	+	0.0355256i
$210$		0			0
$211$	−43.4786	−	15.8249i	−0.206059	−	0.0749995i	0.236928	−	0.971527i	$-0.423859\pi$
$211$	−43.4786	−	15.8249i	−0.206059	−	0.0749995i	−0.442988	+	0.896528i	$0.646082\pi$
$212$	96.6402	−	17.0403i	0.455850	−	0.0803787i
$213$		0			0
$214$	115.394	+	96.8268i	0.539223	+	0.452462i
$215$			108.319i			0.503809i
$216$		0			0
$217$	37.8490			0.174419
$218$	−93.5231	+	111.457i	−0.429005	+	0.511269i
$219$		0			0
$220$	20.4876	+	116.191i	0.0931257	+	0.528142i
$221$	89.3063	−	245.367i	0.404101	−	1.11026i
$222$		0			0
$223$	9.89164	−	56.0983i	0.0443571	−	0.251562i	−0.954564	−	0.298007i	$-0.903678\pi$
$223$	9.89164	−	56.0983i	0.0443571	−	0.251562i	0.998921	+	0.0464451i	$0.0147893\pi$
$224$	7.06459	+	4.07874i	0.0315383	+	0.0182087i
$225$		0			0
$226$	−63.8708	−	110.627i	−0.282614	−	0.489502i
$227$	29.6402	+	81.4359i	0.130574	+	0.358748i	0.987701	−	0.156357i	$-0.0499750\pi$
$227$	29.6402	+	81.4359i	0.130574	+	0.358748i	−0.857127	+	0.515105i	$0.827753\pi$
$228$		0			0
$229$	−99.4359	+	83.4366i	−0.434218	+	0.364352i	−0.833540	−	0.552458i	$-0.813690\pi$
$229$	−99.4359	+	83.4366i	−0.434218	+	0.364352i	0.399322	+	0.916811i	$0.369245\pi$
$230$	77.4069	+	92.2499i	0.336552	+	0.401087i
$231$		0			0
$232$	−71.3245	+	25.9600i	−0.307433	+	0.111897i
$233$	98.9330	−	57.1190i	0.424605	−	0.245146i	−0.272441	−	0.962173i	$-0.587831\pi$
$233$	98.9330	−	57.1190i	0.424605	−	0.245146i	0.697046	+	0.717027i	$0.254497\pi$
$234$		0			0
$235$	−74.4828	+	129.008i	−0.316948	+	0.548970i
$236$	−75.2577	−	13.2700i	−0.318889	−	0.0562287i
$237$		0			0
$238$	−36.1846	−	13.1701i	−0.152036	−	0.0553366i
$239$	300.307	−	52.9523i	1.25652	−	0.221558i	0.494535	−	0.869158i	$-0.335338\pi$
$239$	300.307	−	52.9523i	1.25652	−	0.221558i	0.761980	+	0.647600i	$0.224227\pi$
$240$		0			0
$241$	103.761	+	87.0654i	0.430542	+	0.361267i	0.832156	−	0.554542i	$-0.187106\pi$
$241$	103.761	+	87.0654i	0.430542	+	0.361267i	−0.401614	+	0.915809i	$0.631551\pi$
$242$		−	323.273i		−	1.33584i
$243$		0			0
$244$	110.096			0.451213
$245$	95.1575	−	113.404i	0.388398	−	0.462875i
$246$		0			0
$247$	5.49159	+	31.1443i	0.0222332	+	0.126090i
$248$	25.3904	−	69.7595i	0.102381	−	0.281288i
$249$		0			0
$250$	−31.0278	+	175.967i	−0.124111	+	0.703869i
$251$	−218.202	−	125.979i	−0.869331	−	0.501909i	−0.00220530	−	0.999998i	$-0.500702\pi$
$251$	−218.202	−	125.979i	−0.869331	−	0.501909i	−0.867126	+	0.498089i	$0.834035\pi$
$252$		0			0
$253$	−252.309	−	437.012i	−0.997268	−	1.72732i
$254$	−19.7040	−	54.1362i	−0.0775746	−	0.213135i
$255$		0			0
$256$	12.2567	−	10.2846i	0.0478778	−	0.0401742i
$257$	−208.414	−	248.378i	−0.810948	−	0.966450i	0.188931	−	0.981990i	$-0.439498\pi$
$257$	−208.414	−	248.378i	−0.810948	−	0.966450i	−0.999879	+	0.0155401i	$0.995053\pi$
$258$		0			0
$259$	91.7695	−	33.4014i	0.354323	−	0.128963i
$260$	−75.5724	+	43.6317i	−0.290663	+	0.167814i
$261$		0			0
$262$	34.9213	−	60.4854i	0.133287	−	0.230860i
$263$	26.0438	+	4.59223i	0.0990259	+	0.0174609i	0.222942	−	0.974832i	$-0.428434\pi$
$263$	26.0438	+	4.59223i	0.0990259	+	0.0174609i	−0.123916	+	0.992293i	$0.539545\pi$
$264$		0			0
$265$	145.471	+	52.9470i	0.548946	+	0.199800i
$266$	4.59289	−	0.809851i	0.0172665	−	0.00304455i
$267$		0			0
$268$	190.528	+	159.872i	0.710924	+	0.596536i
$269$			499.973i			1.85864i	0.369280	+	0.929318i	$0.379604\pi$
$269$			499.973i			1.85864i	−0.369280	+	0.929318i	$0.620396\pi$
$270$		0			0
$271$	−101.367			−0.374047			−0.187024	−	0.982355i	$-0.559884\pi$
$271$	−101.367			−0.374047			−0.187024	+	0.982355i	$0.559884\pi$
$272$	−48.5477	+	57.8569i	−0.178484	+	0.212709i
$273$		0			0
$274$	33.1261	+	187.867i	0.120898	+	0.685647i
$275$	96.2127	−	264.342i	0.349864	−	0.961244i
$276$		0			0
$277$	−9.93895	+	56.3666i	−0.0358807	+	0.203489i	−0.997478	−	0.0709742i	$-0.977389\pi$
$277$	−9.93895	+	56.3666i	−0.0358807	+	0.203489i	0.961597	+	0.274464i	$0.0885003\pi$
$278$	97.4672	+	56.2727i	0.350601	+	0.202420i
$279$		0			0
$280$	6.43442	+	11.1447i	0.0229801	+	0.0398027i
$281$	−41.8819	−	115.069i	−0.149046	−	0.409500i	0.842592	−	0.538552i	$-0.181029\pi$
$281$	−41.8819	−	115.069i	−0.149046	−	0.409500i	−0.991638	+	0.129053i	$0.958806\pi$
$282$		0			0
$283$	360.147	−	302.199i	1.27260	−	1.06784i	0.278384	−	0.960470i	$-0.410201\pi$
$283$	360.147	−	302.199i	1.27260	−	1.06784i	0.994219	−	0.107371i	$-0.0342432\pi$
$284$	15.5376	+	18.5170i	0.0547100	+	0.0652008i
$285$		0			0
$286$	343.612	−	125.065i	1.20144	−	0.437289i
$287$	−25.3354	+	14.6274i	−0.0882767	+	0.0509666i
$288$		0			0
$289$	33.7597	−	58.4734i	0.116815	−	0.202330i
$290$	−117.920	−	20.7925i	−0.406621	−	0.0716982i
$291$		0			0
$292$	−140.553	−	51.1570i	−0.481345	−	0.175195i
$293$	−201.841	+	35.5901i	−0.688879	+	0.121468i	−0.507120	−	0.861875i	$-0.669290\pi$
$293$	−201.841	+	35.5901i	−0.688879	+	0.121468i	−0.181758	+	0.983343i	$0.558179\pi$
$294$		0			0
$295$	−92.3500	−	77.4908i	−0.313051	−	0.262681i
$296$		−	191.547i		−	0.647120i
$297$		0			0
$298$	−177.635			−0.596090
$299$	239.906	−	285.908i	0.802360	−	0.956215i
$300$		0			0
$301$	−8.59691	−	48.7555i	−0.0285612	−	0.161978i
$302$	54.7537	−	150.435i	0.181304	−	0.498128i
$303$		0			0
$304$	1.58843	−	9.00845i	0.00522511	−	0.0296331i
$305$	150.413	+	86.8409i	0.493157	+	0.284724i
$306$		0			0
$307$	−28.8883	−	50.0359i	−0.0940986	−	0.162984i	0.815133	−	0.579273i	$-0.196664\pi$
$307$	−28.8883	−	50.0359i	−0.0940986	−	0.162984i	−0.909232	+	0.416290i	$0.863330\pi$
$308$	−18.4434	−	50.6729i	−0.0598813	−	0.164522i
$309$		0			0
$310$	89.7129	−	75.2780i	0.289396	−	0.242832i
$311$	11.1131	+	13.2441i	0.0357336	+	0.0425856i	0.783615	−	0.621246i	$-0.213373\pi$
$311$	11.1131	+	13.2441i	0.0357336	+	0.0425856i	−0.747882	+	0.663832i	$0.768929\pi$
$312$		0			0
$313$	−327.046	+	119.035i	−1.04488	+	0.380304i	−0.806727	−	0.590925i	$-0.798763\pi$
$313$	−327.046	+	119.035i	−1.04488	+	0.380304i	−0.238149	+	0.971229i	$0.576541\pi$
$314$	63.2563	−	36.5210i	0.201453	−	0.116309i
$315$		0			0
$316$	97.6770	−	169.181i	0.309104	−	0.535384i
$317$	−255.079	−	44.9772i	−0.804664	−	0.141884i	−0.243836	−	0.969816i	$-0.578406\pi$
$317$	−255.079	−	44.9772i	−0.804664	−	0.141884i	−0.560828	+	0.827932i	$0.689517\pi$
$318$		0			0
$319$	471.490	+	171.608i	1.47802	+	0.537957i
$320$	24.8573	−	4.38302i	0.0776792	−	0.0136969i
$321$		0			0
$322$	−42.1633	−	35.3792i	−0.130942	−	0.109873i
$323$			43.1798i			0.133683i
$324$		0			0
$325$	208.061			0.640188
$326$	−0.946467	+	1.12796i	−0.00290327	+	0.00345998i
$327$		0			0
$328$	9.96395	+	56.5084i	0.0303779	+	0.172282i
$329$	23.2866	−	63.9794i	0.0707799	−	0.194466i
$330$		0			0
$331$	−57.9326	+	328.552i	−0.175023	+	0.992605i	0.763094	+	0.646287i	$0.223679\pi$
$331$	−57.9326	+	328.552i	−0.175023	+	0.992605i	−0.938117	+	0.346318i	$0.887432\pi$
$332$	218.611	+	126.215i	0.658466	+	0.380166i
$333$		0			0
$334$	−165.079	−	285.925i	−0.494248	−	0.856063i
$335$	134.196	+	368.700i	0.400584	+	1.10060i
$336$		0			0
$337$	192.673	−	161.672i	0.571731	−	0.479739i	−0.310489	−	0.950577i	$-0.600493\pi$
$337$	192.673	−	161.672i	0.571731	−	0.479739i	0.882220	+	0.470838i	$0.156048\pi$
$338$	20.2168	+	24.0935i	0.0598131	+	0.0712825i
$339$		0			0
$340$	−111.962	+	40.7508i	−0.329300	+	0.119855i
$341$	−424.993	+	245.370i	−1.24631	+	0.719560i
$342$		0			0
$343$	−69.1612	+	119.791i	−0.201636	+	0.349244i
$344$	−95.6285	−	16.8619i	−0.277990	−	0.0490171i
$345$		0			0
$346$	−152.326	−	55.4423i	−0.440250	−	0.160238i
$347$	532.939	−	93.9715i	1.53585	−	0.270811i	0.659208	−	0.751961i	$-0.270892\pi$
$347$	532.939	−	93.9715i	1.53585	−	0.270811i	0.876638	+	0.481150i	$0.159781\pi$
$348$		0			0
$349$	473.306	+	397.151i	1.35618	+	1.13797i	0.977142	+	0.212586i	$0.0681886\pi$
$349$	473.306	+	397.151i	1.35618	+	1.13797i	0.379036	+	0.925382i	$0.376256\pi$
$350$		−	30.6830i		−	0.0876658i
$351$		0			0
$352$	−105.768			−0.300477
$353$	84.7293	−	100.976i	0.240026	−	0.286052i	−0.632561	−	0.774511i	$-0.717996\pi$
$353$	84.7293	−	100.976i	0.240026	−	0.286052i	0.872587	+	0.488458i	$0.162441\pi$
$354$		0			0
$355$	6.62172	+	37.5537i	0.0186527	+	0.105785i
$356$	−7.29700	+	20.0483i	−0.0204972	+	0.0563156i
$357$		0			0
$358$	−44.2656	+	251.043i	−0.123647	+	0.701237i
$359$	114.766	+	66.2604i	0.319683	+	0.184569i	0.651251	−	0.758862i	$-0.274244\pi$
$359$	114.766	+	66.2604i	0.319683	+	0.184569i	−0.331568	+	0.943431i	$0.607578\pi$
$360$		0			0
$361$	177.885	+	308.106i	0.492757	+	0.853480i
$362$	17.0533	+	46.8535i	0.0471085	+	0.129429i
$363$		0			0
$364$	30.5530	−	25.6370i	0.0839369	−	0.0704314i
$365$	−151.672	−	180.755i	−0.415539	−	0.495220i
$366$		0			0
$367$	−74.9103	+	27.2651i	−0.204115	+	0.0742919i	−0.442055	−	0.896988i	$-0.645750\pi$
$367$	−74.9103	+	27.2651i	−0.204115	+	0.0742919i	0.237939	+	0.971280i	$0.423528\pi$
$368$	−93.4920	+	53.9776i	−0.254054	+	0.146678i
$369$		0			0
$370$	151.088	−	261.692i	0.408346	−	0.707275i
$371$	−69.6802	−	12.2865i	−0.187817	−	0.0331172i
$372$		0			0
$373$	−526.327	−	191.567i	−1.41106	−	0.513586i	−0.479623	−	0.877475i	$-0.659226\pi$
$373$	−526.327	−	191.567i	−1.41106	−	0.513586i	−0.931442	+	0.363889i	$0.881449\pi$
$374$	491.685	−	86.6973i	1.31466	−	0.231811i
$375$		0			0
$376$	−102.299	−	85.8391i	−0.272072	−	0.228296i
$377$			371.105i			0.984364i
$378$		0			0
$379$	−485.129			−1.28002			−0.640012	−	0.768365i	$-0.721071\pi$
$379$	−485.129			−1.28002			−0.640012	+	0.768365i	$0.721071\pi$
$380$	9.27576	−	11.0544i	0.0244099	−	0.0290906i
$381$		0			0
$382$	5.24161	+	29.7267i	0.0137215	+	0.0778185i
$383$	−60.5772	+	166.434i	−0.158165	+	0.434555i	−0.993310	−	0.115474i	$-0.963161\pi$
$383$	−60.5772	+	166.434i	−0.158165	+	0.434555i	0.835145	+	0.550029i	$0.185383\pi$
$384$		0			0
$385$	14.7721	−	83.7770i	0.0383692	−	0.217602i
$386$	161.327	+	93.1422i	0.417945	+	0.241301i
$387$		0			0
$388$	−155.185	−	268.789i	−0.399962	−	0.692755i
$389$	−200.042	−	549.610i	−0.514246	−	1.41288i	−0.876773	−	0.480905i	$-0.840308\pi$
$389$	−200.042	−	549.610i	−0.514246	−	1.41288i	0.362527	−	0.931973i	$-0.381914\pi$
$390$		0			0
$391$	390.373	−	327.562i	0.998396	−	0.837753i
$392$	85.3051	+	101.663i	0.217615	+	0.259343i
$393$		0			0
$394$	−40.8640	+	14.8733i	−0.103716	+	0.0377494i
$395$	266.892	−	154.090i	0.675677	−	0.390102i
$396$		0			0
$397$	−167.855	+	290.734i	−0.422810	+	0.732328i	−0.996213	−	0.0869453i	$-0.972289\pi$
$397$	−167.855	+	290.734i	−0.422810	+	0.732328i	0.573403	+	0.819273i	$0.305623\pi$
$398$	−341.754	−	60.2605i	−0.858679	−	0.151408i
$399$		0			0
$400$	−56.5520	−	20.5832i	−0.141380	−	0.0514581i
$401$	−656.528	+	115.764i	−1.63723	+	0.288687i	−0.915146	−	0.403123i	$-0.867925\pi$
$401$	−656.528	+	115.764i	−1.63723	+	0.288687i	−0.722080	+	0.691810i	$0.756814\pi$
$402$		0			0
$403$	−278.045	−	233.308i	−0.689939	−	0.578928i
$404$		−	200.241i		−	0.495645i
$405$		0			0
$406$	54.7273			0.134796
$407$	−813.912	+	969.983i	−1.99978	+	2.38325i
$408$		0			0
$409$	83.1381	+	471.500i	0.203272	+	1.15281i	0.900136	+	0.435608i	$0.143467\pi$
$409$	83.1381	+	471.500i	0.203272	+	1.15281i	−0.696865	+	0.717203i	$0.745422\pi$
$410$	−30.9597	+	85.0610i	−0.0755114	+	0.207466i
$411$		0			0
$412$	44.8004	−	254.076i	0.108739	−	0.616688i
$413$	47.7179	+	27.5500i	0.115540	+	0.0667069i
$414$		0			0
$415$	199.110	+	344.869i	0.479784	+	0.831011i
$416$	−26.7557	−	73.5106i	−0.0643165	−	0.176708i
$417$		0			0
$418$	−46.3219	+	38.8687i	−0.110818	+	0.0929873i
$419$	111.219	+	132.545i	0.265438	+	0.316337i	0.882257	−	0.470769i	$-0.156023\pi$
$419$	111.219	+	132.545i	0.265438	+	0.316337i	−0.616819	+	0.787105i	$0.711579\pi$
$420$		0			0
$421$	−252.806	+	92.0139i	−0.600490	+	0.218560i	−0.624337	−	0.781155i	$-0.714631\pi$
$421$	−252.806	+	92.0139i	−0.600490	+	0.218560i	0.0238471	+	0.999716i	$0.492409\pi$
$422$	56.6676	−	32.7171i	0.134283	−	0.0775286i
$423$		0			0
$424$	−69.3891	+	120.185i	−0.163654	+	0.283456i
$425$	279.766	+	49.3303i	0.658273	+	0.116071i
$426$		0			0
$427$	−74.5948	−	27.1503i	−0.174695	−	0.0635838i
$428$	−209.795	+	36.9925i	−0.490175	+	0.0864310i
$429$		0			0
$430$	−117.347	−	98.4661i	−0.272901	−	0.228991i
$431$			457.490i			1.06146i	0.847540	+	0.530731i	$0.178082\pi$
$431$			457.490i			1.06146i	−0.847540	+	0.530731i	$0.821918\pi$
$432$		0			0
$433$	−541.733			−1.25112			−0.625558	−	0.780178i	$-0.715129\pi$
$433$	−541.733			−1.25112			−0.625558	+	0.780178i	$0.715129\pi$
$434$	−34.4062	+	41.0037i	−0.0792769	+	0.0944785i
$435$		0			0
$436$	−35.7303	−	202.637i	−0.0819503	−	0.464763i
$437$	−21.1093	+	57.9974i	−0.0483051	+	0.132717i
$438$		0			0
$439$	48.5394	−	275.280i	0.110568	−	0.627062i	−0.878281	−	0.478144i	$-0.841310\pi$
$439$	48.5394	−	275.280i	0.110568	−	0.627062i	0.988849	−	0.148918i	$-0.0475792\pi$
$440$	−144.500	−	83.4270i	−0.328409	−	0.189607i
$441$		0			0
$442$	184.636	+	319.798i	0.417728	+	0.723526i
$443$	−80.1232	−	220.137i	−0.180865	−	0.496923i	0.815818	−	0.578309i	$-0.196287\pi$
$443$	−80.1232	−	220.137i	−0.180865	−	0.496923i	−0.996683	+	0.0813867i	$0.974065\pi$
$444$		0			0
$445$	−25.7828	+	21.6343i	−0.0579388	+	0.0486165i
$446$	51.7822	+	61.7116i	0.116104	+	0.138367i
$447$		0			0
$448$	−10.8407	+	3.94569i	−0.0241980	+	0.00880734i
$449$	26.8989	−	15.5301i	0.0599085	−	0.0345882i	−0.469747	−	0.882801i	$-0.655655\pi$
$449$	26.8989	−	15.5301i	0.0599085	−	0.0345882i	0.529655	+	0.848213i	$0.322321\pi$
$450$		0			0
$451$	189.655	−	328.493i	0.420522	−	0.728365i
$452$	177.909	+	31.3702i	0.393605	+	0.0694031i
$453$		0			0
$454$	−115.168	−	41.9176i	−0.253673	−	0.0923296i
$455$	61.9634	−	10.9258i	0.136183	−	0.0240128i
$456$		0			0
$457$	−299.624	−	251.414i	−0.655632	−	0.550140i	0.253142	−	0.967429i	$-0.418536\pi$
$457$	−299.624	−	251.414i	−0.655632	−	0.550140i	−0.908774	+	0.417289i	$0.862980\pi$
$458$		−	183.571i		−	0.400810i
$459$		0			0
$460$	−170.305			−0.370228
$461$	29.1528	−	34.7429i	0.0632381	−	0.0753642i	−0.733498	−	0.679692i	$-0.762114\pi$
$461$	29.1528	−	34.7429i	0.0632381	−	0.0753642i	0.796736	+	0.604327i	$0.206558\pi$
$462$		0			0
$463$	37.4481	+	212.379i	0.0808815	+	0.458702i	0.998170	+	0.0604774i	$0.0192623\pi$
$463$	37.4481	+	212.379i	0.0808815	+	0.458702i	−0.917288	+	0.398224i	$0.869627\pi$
$464$	36.7130	−	100.868i	0.0791228	−	0.217388i
$465$		0			0
$466$	−28.0541	+	159.102i	−0.0602018	+	0.341422i
$467$	−336.385	−	194.212i	−0.720312	−	0.415872i	0.0945558	−	0.995520i	$-0.469857\pi$
$467$	−336.385	−	194.212i	−0.720312	−	0.415872i	−0.814867	+	0.579648i	$0.803190\pi$
$468$		0			0
$469$	−89.6654	−	155.305i	−0.191184	−	0.331141i
$470$	−72.0531	−	197.964i	−0.153304	−	0.421201i
$471$		0			0
$472$	82.7882	−	69.4676i	0.175399	−	0.147177i
$473$	412.607	+	491.726i	0.872320	+	1.03959i
$474$		0			0
$475$	−32.3315	+	11.7677i	−0.0680664	+	0.0247742i
$476$	47.1610	−	27.2284i	0.0990778	−	0.0572026i
$477$		0			0
$478$	−215.625	+	373.474i	−0.451099	+	0.781326i
$479$	301.385	+	53.1423i	0.629196	+	0.110944i	0.479147	−	0.877734i	$-0.340946\pi$
$479$	301.385	+	53.1423i	0.629196	+	0.110944i	0.150048	+	0.988679i	$0.452057\pi$
$480$		0			0
$481$	−880.048	−	320.311i	−1.82962	−	0.665928i
$482$	−188.645	+	33.2632i	−0.391379	+	0.0690107i
$483$		0			0
$484$	350.218	+	293.868i	0.723591	+	0.607165i
$485$		−	489.625i		−	1.00954i
$486$		0			0
$487$	947.316			1.94521			0.972604	−	0.232469i	$-0.0746805\pi$
$487$	947.316			1.94521			0.972604	+	0.232469i	$0.0746805\pi$
$488$	−100.082	+	119.272i	−0.205085	+	0.244411i
$489$		0			0
$490$	36.3547	+	206.178i	0.0741933	+	0.420771i
$491$	−49.4422	+	135.841i	−0.100697	+	0.276663i	−0.979804	−	0.199963i	$-0.935918\pi$
$491$	−49.4422	+	135.841i	−0.100697	+	0.276663i	0.879107	+	0.476625i	$0.158140\pi$
$492$		0			0
$493$	−87.9872	+	499.000i	−0.178473	+	1.01217i
$494$	−38.7323	−	22.3621i	−0.0784055	−	0.0452674i
$495$		0			0
$496$	52.4932	+	90.9208i	0.105833	+	0.183308i
$497$	−5.96102	−	16.3778i	−0.0119940	−	0.0329532i
$498$		0			0
$499$	636.655	−	534.217i	1.27586	−	1.07058i	0.282062	−	0.959396i	$-0.408982\pi$
$499$	636.655	−	534.217i	1.27586	−	1.07058i	0.993800	−	0.111179i	$-0.0354628\pi$
$500$	−162.429	−	193.575i	−0.324857	−	0.387150i
$501$		0			0
$502$	334.834	−	121.870i	0.666999	−	0.242768i
$503$	252.425	−	145.738i	0.501840	−	0.289737i	−0.227633	−	0.973747i	$-0.573099\pi$
$503$	252.425	−	145.738i	0.501840	−	0.289737i	0.729473	+	0.684010i	$0.239765\pi$
$504$		0			0
$505$	157.945	−	273.569i	0.312762	−	0.541720i
$506$	702.796	+	123.922i	1.38892	+	0.244905i
$507$		0			0
$508$	76.5601	+	27.8656i	0.150709	+	0.0548536i
$509$	−50.9622	+	8.98602i	−0.100122	+	0.0176543i	−0.223485	−	0.974707i	$-0.571743\pi$
$509$	−50.9622	+	8.98602i	−0.100122	+	0.0176543i	0.123363	+	0.992362i	$0.460632\pi$
$510$		0			0
$511$	82.6150	+	69.3222i	0.161673	+	0.135660i
$512$			22.6274i			0.0441942i
$513$		0			0
$514$	458.536			0.892094
$515$	261.615	−	311.780i	0.507990	−	0.605399i
$516$		0			0
$517$	153.293	+	869.366i	0.296504	+	1.68156i
$518$	−47.2367	+	129.782i	−0.0911905	+	0.250544i
$519$		0			0
$520$	21.4298	−	121.534i	0.0412111	−	0.233720i
$521$	−230.062	−	132.827i	−0.441578	−	0.254945i	0.262689	−	0.964881i	$-0.415391\pi$
$521$	−230.062	−	132.827i	−0.441578	−	0.254945i	−0.704267	+	0.709935i	$0.748724\pi$
$522$		0			0
$523$	−9.24084	−	16.0056i	−0.0176689	−	0.0306035i	0.857056	−	0.515224i	$-0.172291\pi$
$523$	−9.24084	−	16.0056i	−0.0176689	−	0.0306035i	−0.874725	+	0.484620i	$0.838958\pi$
$524$	33.7821	+	92.8156i	0.0644697	+	0.177129i
$525$		0			0
$526$	−28.6498	+	24.0401i	−0.0544673	+	0.0457035i
$527$	−318.553	−	379.637i	−0.604465	−	0.720373i
$528$		0			0
$529$	187.371	−	68.1976i	0.354199	−	0.128918i
$530$	−189.599	+	109.465i	−0.357733	+	0.206537i
$531$		0			0
$532$	−3.29777	+	5.71190i	−0.00619881	+	0.0107367i
$533$	276.285	+	48.7165i	0.518358	+	0.0914005i
$534$		0			0
$535$	−315.800	−	114.942i	−0.590280	−	0.214845i
$536$	−346.394	+	61.0786i	−0.646257	+	0.113953i
$537$		0			0
$538$	−541.646	−	454.495i	−1.00678	−	0.844786i
$539$		−	877.286i		−	1.62762i
$540$		0			0
$541$	469.047			0.867000			0.433500	−	0.901154i	$-0.357278\pi$
$541$	469.047			0.867000			0.433500	+	0.901154i	$0.357278\pi$
$542$	92.1464	−	109.816i	0.170012	−	0.202612i
$543$		0			0
$544$	−18.5476	−	105.188i	−0.0340948	−	0.193361i
$545$	111.020	−	305.025i	0.203707	−	0.559679i
$546$		0			0
$547$	172.475	−	978.152i	0.315310	−	1.78821i	−0.255166	−	0.966897i	$-0.582130\pi$
$547$	172.475	−	978.152i	0.315310	−	1.78821i	0.570476	−	0.821314i	$-0.306759\pi$
$548$	−233.639	−	134.892i	−0.426349	−	0.246152i
$549$		0			0
$550$	198.914	+	344.529i	0.361662	+	0.626417i
$551$	−20.9893	−	57.6677i	−0.0380931	−	0.104660i
$552$		0			0
$553$	−107.901	+	90.5401i	−0.195120	+	0.163725i
$554$	−52.0299	−	62.0068i	−0.0939167	−	0.111926i
$555$		0			0
$556$	−149.564	+	54.4370i	−0.269001	+	0.0979083i
$557$	743.009	−	428.977i	1.33395	−	0.770155i	0.348046	−	0.937477i	$-0.386845\pi$
$557$	743.009	−	428.977i	1.33395	−	0.770155i	0.985902	+	0.167322i	$0.0535119\pi$
$558$		0			0
$559$	−237.383	+	411.160i	−0.424657	+	0.735527i
$560$	−17.9228	−	3.16027i	−0.0320050	−	0.00564335i
$561$		0			0
$562$	162.733	+	59.2299i	0.289560	+	0.105391i
$563$	367.498	−	64.7999i	0.652750	−	0.115097i	0.162540	−	0.986702i	$-0.448031\pi$
$563$	367.498	−	64.7999i	0.652750	−	0.115097i	0.490210	+	0.871604i	$0.336920\pi$
$564$		0			0
$565$	218.315	+	183.188i	0.386399	+	0.324227i
$566$			664.876i			1.17469i
$567$		0			0
$568$	−34.1848			−0.0601844
$569$	392.267	−	467.485i	0.689396	−	0.821591i	−0.301886	−	0.953344i	$-0.597616\pi$
$569$	392.267	−	467.485i	0.689396	−	0.821591i	0.991283	+	0.131753i	$0.0420607\pi$
$570$		0			0
$571$	−18.1196	−	102.761i	−0.0317331	−	0.179967i	0.964822	−	0.262905i	$-0.0846807\pi$
$571$	−18.1196	−	102.761i	−0.0317331	−	0.179967i	−0.996555	+	0.0829382i	$0.973570\pi$
$572$	−176.868	+	485.941i	−0.309210	+	0.849547i
$573$		0			0
$574$	7.18427	−	40.7440i	0.0125162	−	0.0709826i
$575$	351.655	+	203.028i	0.611574	+	0.353092i
$576$		0			0
$577$	−53.6060	−	92.8483i	−0.0929046	−	0.160916i	0.815828	−	0.578295i	$-0.196282\pi$
$577$	−53.6060	−	92.8483i	−0.0929046	−	0.160916i	−0.908732	+	0.417380i	$0.862949\pi$
$578$	32.6584	+	89.7282i	0.0565024	+	0.155239i
$579$		0			0
$580$	129.719	−	108.848i	0.223654	−	0.187668i
$581$	−116.993	−	139.427i	−0.201365	−	0.239977i
$582$		0			0
$583$	862.067	−	313.767i	1.47867	−	0.538193i
$584$	183.189	−	105.764i	0.313680	−	0.181103i
$585$		0			0
$586$	144.925	−	251.018i	0.247313	−	0.428358i
$587$	272.582	+	48.0636i	0.464365	+	0.0818801i	0.400936	−	0.916106i	$-0.368685\pi$
$587$	272.582	+	48.0636i	0.464365	+	0.0818801i	0.0634293	+	0.997986i	$0.479796\pi$
$588$		0			0
$589$	56.4023	+	20.5288i	0.0957595	+	0.0348536i
$590$	167.899	−	29.6052i	0.284575	−	0.0501783i
$591$		0			0
$592$	207.513	+	174.124i	0.350529	+	0.294129i
$593$		−	44.7982i		−	0.0755451i	−0.999286	−	0.0377725i	$-0.987974\pi$
$593$		−	44.7982i		−	0.0755451i	0.999286	−	0.0377725i	$-0.0120262\pi$
$594$		0			0
$595$	85.9085			0.144384
$596$	161.477	−	192.441i	0.270934	−	0.322887i
$597$		0			0
$598$	91.6554	+	519.804i	0.153270	+	0.869237i
$599$	−318.570	+	875.264i	−0.531836	+	1.46121i	0.325047	+	0.945698i	$0.394620\pi$
$599$	−318.570	+	875.264i	−0.531836	+	1.46121i	−0.856883	+	0.515511i	$0.827602\pi$
$600$		0			0
$601$	59.0610	−	334.951i	0.0982712	−	0.557323i	−0.895425	−	0.445213i	$-0.853128\pi$
$601$	59.0610	−	334.951i	0.0982712	−	0.557323i	0.993696	−	0.112110i	$-0.0357610\pi$
$602$	60.6342	+	35.0072i	0.100721	+	0.0581515i
$603$		0			0
$604$	113.200	+	196.068i	0.187417	+	0.324616i
$605$	246.672	+	677.725i	0.407722	+	1.12021i
$606$		0			0
$607$	−857.856	+	719.827i	−1.41327	+	1.18588i	−0.458441	+	0.888725i	$0.651592\pi$
$607$	−857.856	+	719.827i	−1.41327	+	1.18588i	−0.954830	+	0.297151i	$0.903963\pi$
$608$	8.31536	+	9.90986i	0.0136766	+	0.0162991i
$609$		0			0
$610$	−230.810	+	84.0081i	−0.378378	+	0.137718i
$611$	−565.448	+	326.461i	−0.925446	+	0.534307i
$612$		0			0
$613$	503.975	−	872.910i	0.822144	−	1.42400i	−0.0819377	−	0.996637i	$-0.526111\pi$
$613$	503.975	−	872.910i	0.822144	−	1.42400i	0.904082	−	0.427359i	$-0.140556\pi$
$614$	80.4670	+	14.1885i	0.131054	+	0.0231083i
$615$		0			0
$616$	71.6623	+	26.0829i	0.116335	+	0.0423424i
$617$	−811.213	+	143.039i	−1.31477	+	0.231830i	−0.786681	−	0.617359i	$-0.788202\pi$
$617$	−811.213	+	143.039i	−1.31477	+	0.231830i	−0.528089	+	0.849189i	$0.677091\pi$
$618$		0			0
$619$	101.667	+	85.3084i	0.164243	+	0.137817i	0.721205	−	0.692722i	$-0.243589\pi$
$619$	101.667	+	85.3084i	0.164243	+	0.137817i	−0.556962	+	0.830538i	$0.688033\pi$
$620$			165.621i			0.267131i
$621$		0			0
$622$	−24.4503			−0.0393092
$623$	9.88807	−	11.7841i	0.0158717	−	0.0189151i
$624$		0			0
$625$	−3.90782	−	22.1623i	−0.00625251	−	0.0354598i
$626$	168.341	−	462.513i	0.268915	−	0.738839i
$627$		0			0
$628$	−17.9374	+	101.728i	−0.0285627	+	0.161987i
$629$	−1107.40	−	639.356i	−1.76057	−	1.01646i
$630$		0			0
$631$	−52.2617	−	90.5198i	−0.0828235	−	0.143455i	0.821638	−	0.570009i	$-0.193060\pi$
$631$	−52.2617	−	90.5198i	−0.0828235	−	0.143455i	−0.904462	+	0.426555i	$0.859727\pi$
$632$	94.4907	+	259.611i	0.149511	+	0.410777i
$633$		0			0
$634$	280.602	−	235.453i	0.442591	−	0.371378i
$635$	82.6166	+	98.4587i	0.130105	+	0.155053i
$636$		0			0
$637$	609.730	−	221.923i	0.957190	−	0.348389i
$638$	−614.514	+	354.790i	−0.963189	+	0.556097i
$639$		0			0
$640$	−17.8479	+	30.9135i	−0.0278874	+	0.0483024i
$641$	−144.994	−	25.5664i	−0.226200	−	0.0398852i	0.0593990	−	0.998234i	$-0.481082\pi$
$641$	−144.994	−	25.5664i	−0.226200	−	0.0398852i	−0.285599	+	0.958349i	$0.592193\pi$
$642$		0			0
$643$	−986.208	−	358.950i	−1.53376	−	0.558243i	−0.569221	−	0.822184i	$-0.692755\pi$
$643$	−986.208	−	358.950i	−1.53376	−	0.558243i	−0.964539	+	0.263941i	$0.914977\pi$
$644$	76.6561	−	13.5165i	0.119031	−	0.0209884i
$645$		0			0
$646$	−46.7788	−	39.2521i	−0.0724130	−	0.0607617i
$647$		−	828.962i		−	1.28124i	−0.767858	−	0.640620i	$-0.778677\pi$
$647$		−	828.962i		−	1.28124i	0.767858	−	0.640620i	$-0.221323\pi$
$648$		0			0
$649$	−714.411			−1.10079
$650$	−189.136	+	225.403i	−0.290978	+	0.346774i
$651$		0			0
$652$	−0.361596	−	2.05071i	−0.000554594	−	0.00314526i
$653$	244.816	−	672.626i	0.374910	−	1.03006i	−0.598528	−	0.801102i	$-0.704247\pi$
$653$	244.816	−	672.626i	0.374910	−	1.03006i	0.973437	−	0.228953i	$-0.0735304\pi$
$654$		0			0
$655$	−27.0575	+	153.451i	−0.0413092	+	0.234276i
$656$	−70.2760	−	40.5739i	−0.107128	−	0.0618504i
$657$		0			0
$658$	48.1437	+	83.3873i	0.0731666	+	0.126728i
$659$	77.5795	+	213.148i	0.117723	+	0.323442i	0.984534	−	0.175196i	$-0.0560560\pi$
$659$	77.5795	+	213.148i	0.117723	+	0.323442i	−0.866810	+	0.498638i	$0.833834\pi$
$660$		0			0
$661$	−494.893	+	415.264i	−0.748703	+	0.628237i	−0.935160	−	0.354227i	$-0.884744\pi$
$661$	−494.893	+	415.264i	−0.748703	+	0.628237i	0.186456	+	0.982463i	$0.440300\pi$
$662$	−303.274	−	361.428i	−0.458118	−	0.545964i
$663$		0			0
$664$	−335.461	+	122.098i	−0.505212	+	0.183882i
$665$	−9.01081	+	5.20239i	−0.0135501	+	0.00782315i
$666$		0			0
$667$	−362.128	+	627.223i	−0.542920	+	0.940365i
$668$	459.820	+	81.0787i	0.688353	+	0.121375i
$669$		0			0
$670$	−521.420	−	189.781i	−0.778239	−	0.283256i
$671$	1013.61	−	178.727i	1.51060	−	0.266359i
$672$		0			0
$673$	−322.666	−	270.749i	−0.479444	−	0.402301i	0.370781	−	0.928720i	$-0.379090\pi$
$673$	−322.666	−	270.749i	−0.479444	−	0.402301i	−0.850225	+	0.526419i	$0.823534\pi$
$674$			355.699i			0.527743i
$675$		0			0
$676$	−44.4796			−0.0657982
$677$	−568.791	+	677.859i	−0.840164	+	1.00127i	0.159736	+	0.987160i	$0.448936\pi$
$677$	−568.791	+	677.859i	−0.840164	+	1.00127i	−0.999900	+	0.0141088i	$0.995509\pi$
$678$		0			0
$679$	38.8599	+	220.386i	0.0572311	+	0.324574i
$680$	57.6304	−	158.338i	0.0847505	−	0.232850i
$681$		0			0
$682$	120.514	−	683.467i	0.176706	−	1.00215i
$683$	179.989	+	103.917i	0.263527	+	0.152148i	0.625943	−	0.779869i	$-0.284714\pi$
$683$	179.989	+	103.917i	0.263527	+	0.152148i	−0.362415	+	0.932017i	$0.618048\pi$
$684$		0			0
$685$	−212.798	−	368.577i	−0.310654	−	0.538069i
$686$	−66.9051	−	183.820i	−0.0975293	−	0.267960i
$687$		0			0
$688$	105.197	−	88.2711i	0.152903	−	0.128301i
$689$	436.147	+	519.780i	0.633015	+	0.754398i
$690$		0			0
$691$	−688.491	+	250.590i	−0.996370	+	0.362649i	−0.788184	−	0.615440i	$-0.788978\pi$
$691$	−688.491	+	250.590i	−0.996370	+	0.362649i	−0.208186	+	0.978089i	$0.566756\pi$
$692$	198.534	−	114.624i	0.286899	−	0.165641i
$693$		0			0
$694$	−382.658	+	662.783i	−0.551380	+	0.955019i
$695$	−247.273	−	43.6010i	−0.355789	−	0.0627352i
$696$		0			0
$697$	359.951	+	131.012i	0.516429	+	0.187965i
$698$	−860.507	+	151.731i	−1.23282	+	0.217379i
$699$		0			0
$700$	33.2405	+	27.8921i	0.0474864	+	0.0398458i
$701$		−	176.592i		−	0.251915i	−0.992036	−	0.125957i	$-0.959800\pi$
$701$		−	176.592i		−	0.251915i	0.992036	−	0.125957i	$-0.0402002\pi$
$702$		0			0
$703$	154.871			0.220300
$704$	96.1471	−	114.584i	0.136573	−	0.162761i
$705$		0			0
$706$	32.3707	+	183.583i	0.0458508	+	0.260033i
$707$	−49.3805	+	135.672i	−0.0698451	+	0.191898i
$708$		0			0
$709$	−158.919	+	901.273i	−0.224145	+	1.27119i	0.640168	+	0.768235i	$0.278865\pi$
$709$	−158.919	+	901.273i	−0.224145	+	1.27119i	−0.864313	+	0.502954i	$0.832247\pi$
$710$	−46.7032	−	26.9641i	−0.0657791	−	0.0379776i
$711$		0			0
$712$	−15.0861	−	26.1299i	−0.0211884	−	0.0366993i
$713$	−242.275	−	665.644i	−0.339796	−	0.933583i
$714$		0			0
$715$	−624.935	+	524.383i	−0.874035	+	0.733403i
$716$	−231.728	−	276.163i	−0.323643	−	0.385702i
$717$		0			0
$718$	−176.110	+	64.0989i	−0.245279	+	0.0892742i
$719$	−555.297	+	320.601i	−0.772319	+	0.445898i	−0.833701	−	0.552216i	$-0.813782\pi$
$719$	−555.297	+	320.601i	−0.772319	+	0.445898i	0.0613824	+	0.998114i	$0.480449\pi$
$720$		0			0
$721$	−93.0107	+	161.099i	−0.129002	+	0.223439i
$722$	−495.491	−	87.3685i	−0.686276	−	0.121009i
$723$		0			0
$724$	−66.2608	−	24.1170i	−0.0915205	−	0.0333107i
$725$	−397.614	+	70.1100i	−0.548433	+	0.0967035i
$726$		0			0
$727$	140.649	+	118.019i	0.193465	+	0.162337i	0.734375	−	0.678744i	$-0.237475\pi$
$727$	140.649	+	118.019i	0.193465	+	0.162337i	−0.540910	+	0.841081i	$0.681920\pi$
$728$			56.4047i			0.0774790i
$729$		0			0
$730$	333.697			0.457119
$731$	−416.677	+	496.577i	−0.570010	+	0.679312i
$732$		0			0
$733$	−224.357	−	1272.39i	−0.306081	−	1.73587i	−0.618373	−	0.785885i	$-0.712208\pi$
$733$	−224.357	−	1272.39i	−0.306081	−	1.73587i	0.312292	−	0.949986i	$-0.398903\pi$
$734$	38.5587	−	105.939i	0.0525323	−	0.144331i
$735$		0			0
$736$	26.5112	−	150.352i	0.0360206	−	0.204283i
$737$	2013.65	+	1162.58i	2.73222	+	1.57745i
$738$		0			0
$739$	−372.906	−	645.892i	−0.504609	−	0.874008i	−0.999986	−	0.00533011i	$-0.998303\pi$
$739$	−372.906	−	645.892i	−0.504609	−	0.874008i	0.495377	−	0.868678i	$-0.335030\pi$
$740$	146.159	+	401.569i	0.197513	+	0.542661i
$741$		0			0
$742$	76.6526	−	64.3191i	0.103305	−	0.0866835i
$743$	20.0884	+	23.9404i	0.0270368	+	0.0322212i	0.779393	−	0.626535i	$-0.215527\pi$
$743$	20.0884	+	23.9404i	0.0270368	+	0.0322212i	−0.752357	+	0.658756i	$0.771083\pi$
$744$		0			0
$745$	372.402	−	135.543i	0.499868	−	0.181937i
$746$	685.987	−	396.055i	0.919553	−	0.530904i
$747$		0			0
$748$	−353.037	+	611.478i	−0.471975	+	0.817484i
$749$	151.268	+	26.6726i	0.201959	+	0.0356109i
$750$		0			0
$751$	871.195	+	317.089i	1.16005	+	0.422222i	0.849114	−	0.528210i	$-0.177136\pi$
$751$	871.195	+	317.089i	1.16005	+	0.422222i	0.310932	+	0.950432i	$0.399359\pi$
$752$	185.988	−	32.7946i	0.247324	−	0.0436099i
$753$		0			0
$754$	−402.037	−	337.349i	−0.533205	−	0.447412i
$755$			357.158i			0.473057i
$756$		0			0
$757$	358.777			0.473946			0.236973	−	0.971516i	$-0.423845\pi$
$757$	358.777			0.473946			0.236973	+	0.971516i	$0.423845\pi$
$758$	441.001	−	525.565i	0.581796	−	0.693357i
$759$		0			0
$760$	3.54378	+	20.0978i	0.00466287	+	0.0264445i
$761$	−402.928	+	1107.03i	−0.529471	+	1.45471i	0.330224	+	0.943903i	$0.392876\pi$
$761$	−402.928	+	1107.03i	−0.529471	+	1.45471i	−0.859695	+	0.510807i	$0.829347\pi$
$762$		0			0
$763$	−25.7625	+	146.106i	−0.0337647	+	0.191489i
$764$	−36.9692	−	21.3442i	−0.0483891	−	0.0279374i
$765$		0			0
$766$	−125.240	−	216.922i	−0.163498	−	0.283188i
$767$	−180.722	−	496.529i	−0.235622	−	0.647365i
$768$		0			0
$769$	830.766	−	697.096i	1.08032	−	0.906497i	0.0843731	−	0.996434i	$-0.473111\pi$
$769$	830.766	−	697.096i	1.08032	−	0.906497i	0.995947	+	0.0899377i	$0.0286668\pi$
$770$	77.3314	+	92.1599i	0.100430	+	0.119688i
$771$		0			0
$772$	−247.558	+	90.1038i	−0.320671	+	0.116715i
$773$	−941.215	+	543.410i	−1.21761	+	0.702989i	−0.964407	−	0.264423i	$-0.914818\pi$
$773$	−941.215	+	543.410i	−1.21761	+	0.702989i	−0.253206	+	0.967412i	$0.581485\pi$
$774$		0			0
$775$	197.444	−	341.984i	0.254767	−	0.441269i
$776$	432.262	+	76.2194i	0.557039	+	0.0982209i
$777$		0			0
$778$	777.265	+	282.901i	0.999056	+	0.363627i
$779$	−45.6885	+	8.05611i	−0.0586501	+	0.0103416i
$780$		0			0
$781$	173.109	+	145.256i	0.221651	+	0.185987i
$782$			720.677i			0.921581i
$783$		0			0
$784$	−187.682			−0.239390
$785$	−104.746	+	124.832i	−0.133435	+	0.159021i
$786$		0			0
$787$	113.607	+	644.299i	0.144355	+	0.818677i	0.967883	+	0.251402i	$0.0808915\pi$
$787$	113.607	+	644.299i	0.144355	+	0.818677i	−0.823528	+	0.567276i	$0.807997\pi$
$788$	21.0340	−	57.7904i	0.0266929	−	0.0733381i
$789$		0			0
$790$	−75.6817	+	429.212i	−0.0957996	+	0.543306i
$791$	−112.805	−	65.1281i	−0.142611	−	0.0823364i
$792$		0			0
$793$	380.628	+	659.267i	0.479985	+	0.831358i
$794$	−162.380	−	446.135i	−0.204509	−	0.561883i
$795$		0			0
$796$	375.951	−	315.461i	0.472301	−	0.396307i
$797$	810.061	+	965.393i	1.01639	+	1.21128i	0.977259	+	0.212049i	$0.0680138\pi$
$797$	810.061	+	965.393i	1.01639	+	1.21128i	0.0391286	+	0.999234i	$0.487542\pi$
$798$		0			0
$799$	−837.722	+	304.906i	−1.04846	+	0.381610i
$800$	73.7068	−	42.5546i	0.0921335	−	0.0531933i
$801$		0			0
$802$	471.397	−	816.483i	0.587776	−	1.01806i
$803$	−1377.06	−	242.813i	−1.71490	−	0.302383i
$804$		0			0
$805$	115.389	+	41.9981i	0.143340	+	0.0521716i
$806$	505.508	−	89.1347i	0.627181	−	0.110589i
$807$		0			0
$808$	216.931	+	182.027i	0.268479	+	0.225280i
$809$		−	65.7562i		−	0.0812808i	−0.999174	−	0.0406404i	$-0.987060\pi$
$809$		−	65.7562i		−	0.0812808i	0.999174	−	0.0406404i	$-0.0129398\pi$
$810$		0			0
$811$	−592.061			−0.730039			−0.365019	−	0.931000i	$-0.618938\pi$
$811$	−592.061			−0.730039			−0.365019	+	0.931000i	$0.618938\pi$
$812$	−49.7493	+	59.2889i	−0.0612676	+	0.0730158i
$813$		0			0
$814$	−310.953	−	1763.50i	−0.382007	−	2.16647i
$815$	1.12354	−	3.08690i	0.00137857	−	0.00378760i
$816$		0			0
$817$	13.6333	−	77.3181i	0.0166870	−	0.0946366i
$818$	−586.375	−	338.544i	−0.716840	−	0.413868i
$819$		0			0
$820$	−64.0073	−	110.864i	−0.0780577	−	0.135200i
$821$	377.182	+	1036.30i	0.459418	+	1.26224i	0.925920	+	0.377721i	$0.123292\pi$
$821$	377.182	+	1036.30i	0.459418	+	1.26224i	−0.466501	+	0.884521i	$0.654486\pi$
$822$		0			0
$823$	693.326	−	581.770i	0.842438	−	0.706889i	−0.115673	−	0.993287i	$-0.536902\pi$
$823$	693.326	−	581.770i	0.842438	−	0.706889i	0.958111	+	0.286398i	$0.0924580\pi$
$824$	234.528	+	279.499i	0.284621	+	0.339198i
$825$		0			0
$826$	−73.2237	+	26.6512i	−0.0886486	+	0.0322654i
$827$	765.593	−	442.016i	0.925748	−	0.534481i	0.0402835	−	0.999188i	$-0.487174\pi$
$827$	765.593	−	442.016i	0.925748	−	0.534481i	0.885464	+	0.464708i	$0.153841\pi$
$828$		0			0
$829$	123.007	−	213.054i	0.148380	−	0.257001i	−0.782249	−	0.622966i	$-0.785928\pi$
$829$	123.007	−	213.054i	0.148380	−	0.257001i	0.930629	+	0.365965i	$0.119261\pi$
$830$	−554.614	−	97.7934i	−0.668209	−	0.117823i
$831$		0			0
$832$	103.960	+	37.8382i	0.124952	+	0.0454786i
$833$	872.480	−	153.842i	1.04739	−	0.184684i
$834$		0			0
$835$	564.253	+	473.464i	0.675752	+	0.567023i
$836$		−	85.5160i		−	0.102292i
$837$		0			0
$838$	−244.695			−0.291998
$839$	661.747	−	788.639i	0.788732	−	0.939975i	−0.210560	−	0.977581i	$-0.567529\pi$
$839$	661.747	−	788.639i	0.788732	−	0.939975i	0.999293	+	0.0376062i	$0.0119732\pi$
$840$		0			0
$841$	20.9875	+	119.026i	0.0249554	+	0.141529i
$842$	130.127	−	357.522i	0.154546	−	0.424610i
$843$		0			0
$844$	−16.0690	+	91.1320i	−0.0190391	+	0.107976i
$845$	−60.7679	−	35.0844i	−0.0719147	−	0.0415200i
$846$		0			0
$847$	−164.818	−	285.474i	−0.194591	−	0.337041i
$848$	−67.1256	−	184.426i	−0.0791575	−	0.217484i
$849$		0			0
$850$	−307.760	+	258.242i	−0.362071	+	0.303814i
$851$	−1174.85	−	1400.13i	−1.38055	−	1.64528i
$852$		0			0
$853$	106.671	−	38.8249i	0.125054	−	0.0455158i	−0.278735	−	0.960368i	$-0.589915\pi$
$853$	106.671	−	38.8249i	0.125054	−	0.0455158i	0.403789	+	0.914852i	$0.367693\pi$
$854$	97.2228	−	56.1316i	0.113844	−	0.0657279i
$855$		0			0
$856$	150.636	−	260.909i	0.175976	−	0.304800i
$857$	−1415.76	−	249.637i	−1.65200	−	0.291292i	−0.731442	−	0.681904i	$-0.761152\pi$
$857$	−1415.76	−	249.637i	−1.65200	−	0.291292i	−0.920555	+	0.390612i	$0.872263\pi$
$858$		0			0
$859$	410.122	+	149.272i	0.477441	+	0.173774i	0.569520	−	0.821977i	$-0.307129\pi$
$859$	410.122	+	149.272i	0.477441	+	0.173774i	−0.0920793	+	0.995752i	$0.529351\pi$
$860$	213.347	−	37.6187i	0.248077	−	0.0437427i
$861$		0			0
$862$	−495.622	−	415.876i	−0.574967	−	0.482455i
$863$		−	384.435i		−	0.445463i	−0.974880	−	0.222732i	$-0.928503\pi$
$863$		−	384.435i		−	0.445463i	0.974880	−	0.222732i	$-0.0714974\pi$
$864$		0			0
$865$	361.649			0.418092
$866$	492.457	−	586.887i	0.568656	−	0.677698i
$867$		0			0
$868$	−13.1448	−	74.5479i	−0.0151438	−	0.0858847i
$869$	624.630	−	1716.16i	0.718791	−	1.97486i
$870$		0			0
$871$	−298.630	+	1693.61i	−0.342858	+	1.94445i
$872$	252.007	+	145.496i	0.288999	+	0.166853i
$873$		0			0
$874$	−43.6423	−	75.5907i	−0.0499340	−	0.0864882i
$875$	62.3158	+	171.211i	0.0712181	+	0.195670i
$876$		0			0
$877$	−350.883	+	294.425i	−0.400094	+	0.335719i	−0.820530	−	0.571603i	$-0.806322\pi$
$877$	−350.883	+	294.425i	−0.400094	+	0.335719i	0.420436	+	0.907322i	$0.361877\pi$
$878$	254.101	+	302.826i	0.289409	+	0.344904i
$879$		0			0
$880$	221.737	−	80.7056i	0.251974	−	0.0917109i
$881$	437.756	−	252.738i	0.496885	−	0.286877i	−0.230541	−	0.973063i	$-0.574050\pi$
$881$	437.756	−	252.738i	0.496885	−	0.286877i	0.727426	+	0.686186i	$0.240716\pi$
$882$		0			0
$883$	202.337	−	350.457i	0.229147	−	0.396894i	−0.728409	−	0.685143i	$-0.759740\pi$
$883$	202.337	−	350.457i	0.229147	−	0.396894i	0.957555	+	0.288249i	$0.0930731\pi$
$884$	−514.295	−	90.6840i	−0.581781	−	0.102584i
$885$		0			0
$886$	311.320	+	113.311i	0.351377	+	0.127891i
$887$	−810.695	+	142.947i	−0.913974	+	0.161158i	−0.610807	−	0.791779i	$-0.709155\pi$
$887$	−810.695	+	142.947i	−0.913974	+	0.161158i	−0.303166	+	0.952938i	$0.598044\pi$
$888$		0			0
$889$	−45.0010	−	37.7603i	−0.0506198	−	0.0424750i
$890$		−	47.5982i		−	0.0534812i
$891$		0			0
$892$	−113.927			−0.127721
$893$	69.4031	−	82.7114i	0.0777191	−	0.0926220i
$894$		0			0
$895$	−98.7563	−	560.075i	−0.110342	−	0.625782i
$896$	5.58005	−	15.3311i	0.00622773	−	0.0171106i
$897$		0			0
$898$	−7.62763	+	43.2585i	−0.00849402	+	0.0481720i
$899$	609.974	+	352.168i	0.678502	+	0.391734i
$900$		0			0
$901$	463.221	+	802.322i	0.514118	+	0.890479i
$902$	183.469	+	504.076i	0.203402	+	0.558842i
$903$		0			0
$904$	−195.711	+	164.221i	−0.216495	+	0.181661i
$905$	−71.5026	−	85.2135i	−0.0790084	−	0.0941585i
$906$		0			0
$907$	−296.660	+	107.975i	−0.327078	+	0.119047i	−0.500340	−	0.865829i	$-0.666792\pi$
$907$	−296.660	+	107.975i	−0.327078	+	0.119047i	0.173262	+	0.984876i	$0.444569\pi$
$908$	150.103	−	86.6622i	0.165312	−	0.0954430i
$909$		0			0
$910$	−44.4906	+	77.0600i	−0.0488908	+	0.0846814i
$911$	−409.179	−	72.1493i	−0.449154	−	0.0791980i	−0.0555042	−	0.998458i	$-0.517677\pi$
$911$	−409.179	−	72.1493i	−0.449154	−	0.0791980i	−0.393650	+	0.919260i	$0.628788\pi$
$912$		0			0
$913$	2217.56	+	807.126i	2.42887	+	0.884037i
$914$	544.739	−	96.0522i	0.595995	−	0.105090i
$915$		0			0
$916$	198.872	+	166.873i	0.217109	+	0.182176i
$917$		−	71.2174i		−	0.0776635i
$918$		0			0
$919$	−1455.83			−1.58415			−0.792075	−	0.610424i	$-0.790999\pi$
$919$	−1455.83			−1.58415			−0.792075	+	0.610424i	$0.790999\pi$
$920$	154.814	−	184.500i	0.168276	−	0.200543i
$921$		0			0
$922$	11.1377	+	63.1653i	0.0120800	+	0.0685090i
$923$	−57.1648	+	157.059i	−0.0619336	+	0.170161i
$924$		0			0
$925$	176.931	−	1003.42i	0.191277	−	1.08478i
$926$	−264.123	−	152.491i	−0.285230	−	0.164677i
$927$		0			0
$928$	75.9019	+	131.466i	0.0817909	+	0.141666i
$929$	−275.058	−	755.714i	−0.296079	−	0.813471i	−0.995146	−	0.0984140i	$-0.968623\pi$
$929$	−275.058	−	755.714i	−0.296079	−	0.813471i	0.699066	−	0.715057i	$-0.253599\pi$
$930$		0			0
$931$	−82.1968	+	68.9713i	−0.0882888	+	0.0740831i
$932$	−146.861	−	175.023i	−0.157577	−	0.187793i
$933$		0			0
$934$	516.187	−	187.877i	0.552663	−	0.201153i
$935$	−964.637	+	556.934i	−1.03170	+	0.595651i
$936$		0			0
$937$	−404.494	+	700.604i	−0.431690	+	0.747710i	−0.997019	−	0.0771562i	$-0.975416\pi$
$937$	−404.494	+	700.604i	−0.431690	+	0.747710i	0.565329	+	0.824866i	$0.308749\pi$
$938$	249.759	+	44.0393i	0.266268	+	0.0469502i
$939$		0			0
$940$	279.964	+	101.898i	0.297834	+	0.108403i
$941$	1212.64	−	213.821i	1.28867	−	0.227227i	0.513012	−	0.858382i	$-0.328530\pi$
$941$	1212.64	−	213.821i	1.28867	−	0.227227i	0.775657	+	0.631155i	$0.217419\pi$
$942$		0			0
$943$	419.425	+	351.939i	0.444777	+	0.373212i
$944$			152.837i			0.161904i
$945$		0			0
$946$	−907.788			−0.959607
$947$	304.967	−	363.445i	0.322034	−	0.383786i	−0.580604	−	0.814186i	$-0.697183\pi$
$947$	304.967	−	363.445i	0.322034	−	0.383786i	0.902638	+	0.430401i	$0.141628\pi$
$948$		0			0
$949$	−179.590	−	1018.51i	−0.189242	−	1.07324i
$950$	16.6421	−	45.7237i	0.0175180	−	0.0481302i
$951$		0			0
$952$	−13.3733	+	75.8437i	−0.0140476	+	0.0796677i
$953$	270.697	+	156.287i	0.284047	+	0.163995i	0.635254	−	0.772303i	$-0.280895\pi$
$953$	270.697	+	156.287i	0.284047	+	0.163995i	−0.351207	+	0.936298i	$0.614229\pi$
$954$		0			0
$955$	−33.6715	−	58.3208i	−0.0352582	−	0.0610689i
$956$	−208.591	−	573.100i	−0.218192	−	0.599477i
$957$		0			0
$958$	−331.542	+	278.197i	−0.346077	+	0.290393i
$959$	125.036	+	149.012i	0.130381	+	0.155382i
$960$		0			0
$961$	255.707	−	93.0696i	0.266084	−	0.0968466i
$962$	1147.01	−	662.225i	1.19232	−	0.688384i
$963$		0			0
$964$	135.450	−	234.606i	0.140508	−	0.243367i
$965$	−409.285	−	72.1680i	−0.424130	−	0.0747855i
$966$		0			0
$967$	179.037	+	65.1640i	0.185146	+	0.0673878i	0.432930	−	0.901428i	$-0.357480\pi$
$967$	179.037	+	65.1640i	0.185146	+	0.0673878i	−0.247783	+	0.968816i	$0.579702\pi$
$968$	−636.724	+	112.272i	−0.657773	+	0.115983i
$969$		0			0
$970$	530.436	+	445.088i	0.546841	+	0.458854i
$971$			415.384i			0.427790i	0.976857	+	0.213895i	$0.0686151\pi$
$971$			415.384i			0.427790i	−0.976857	+	0.213895i	$0.931385\pi$
$972$		0			0
$973$	114.761			0.117945
$974$	−861.147	+	1026.28i	−0.884135	+	1.05367i
$975$		0			0
$976$	−38.2359	−	216.847i	−0.0391761	−	0.222179i
$977$	418.862	−	1150.81i	0.428722	−	1.17790i	−0.517867	−	0.855461i	$-0.673274\pi$
$977$	418.862	−	1150.81i	0.428722	−	1.17790i	0.946589	−	0.322443i	$-0.104504\pi$
$978$		0			0
$979$	−34.6347	+	196.423i	−0.0353776	+	0.200637i
$980$	−256.411	−	148.039i	−0.261644	−	0.151060i
$981$		0			0
$982$	−102.219	−	177.048i	−0.104093	−	0.180294i
$983$	107.429	+	295.159i	0.109287	+	0.300263i	0.982265	−	0.187495i	$-0.0600369\pi$
$983$	107.429	+	295.159i	0.109287	+	0.300263i	−0.872979	+	0.487758i	$0.837815\pi$
$984$		0			0
$985$	74.3202	−	62.3621i	0.0754520	−	0.0633118i
$986$	−460.608	−	548.932i	−0.467148	−	0.556726i
$987$		0			0
$988$	59.4352	−	21.6326i	0.0601571	−	0.0218954i
$989$	−802.427	+	463.281i	−0.811352	+	0.468434i
$990$		0			0
$991$	174.247	−	301.804i	0.175829	−	0.304545i	−0.764619	−	0.644483i	$-0.777073\pi$
$991$	174.247	−	301.804i	0.175829	−	0.304545i	0.940448	+	0.339938i	$0.110406\pi$
$992$	−146.217	−	25.7821i	−0.147397	−	0.0259900i
$993$		0			0
$994$	23.1617	+	8.43015i	0.0233015	+	0.00848104i
$995$	762.452	−	134.441i	0.766283	−	0.135116i
$996$		0			0
$997$	−461.810	−	387.504i	−0.463199	−	0.388670i	0.381107	−	0.924531i	$-0.375543\pi$
$997$	−461.810	−	387.504i	−0.463199	−	0.388670i	−0.844307	+	0.535860i	$0.819987\pi$
$998$			1175.34i			1.17770i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	162.3.f.a.35.3		36
3.2	odd	2		54.3.f.a.11.5	yes	36
12.11	even	2		432.3.bc.c.65.3		36
27.5	odd	18	inner	162.3.f.a.125.3		36
27.7	even	9		1458.3.b.c.1457.32		36
27.20	odd	18		1458.3.b.c.1457.5		36
27.22	even	9		54.3.f.a.5.5	✓	36
108.103	odd	18		432.3.bc.c.113.3		36

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
54.3.f.a.5.5	✓	36	27.22	even	9
54.3.f.a.11.5	yes	36	3.2	odd	2
162.3.f.a.35.3		36	1.1	even	1	trivial
162.3.f.a.125.3		36	27.5	odd	18	inner
432.3.bc.c.65.3		36	12.11	even	2
432.3.bc.c.113.3		36	108.103	odd	18
1458.3.b.c.1457.5		36	27.20	odd	18
1458.3.b.c.1457.32		36	27.7	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)

\(f(q)\)	\(=\)	\(q+(-0.909039 + 1.08335i) q^{2} +(-0.347296 - 1.96962i) q^{4} +(1.07911 - 2.96482i) q^{5} +(-0.250410 + 1.42015i) q^{7} +(2.44949 + 1.41421i) q^{8} +O(q^{10})\)	\(q+(-0.909039 + 1.08335i) q^{2} +(-0.347296 - 1.96962i) q^{4} +(1.07911 - 2.96482i) q^{5} +(-0.250410 + 1.42015i) q^{7} +(2.44949 + 1.41421i) q^{8} +(2.23099 + 3.86419i) q^{10} +(-6.39485 - 17.5697i) q^{11} +(10.5936 - 8.88908i) q^{13} +(-1.31088 - 1.56225i) q^{14} +(-3.75877 + 1.36808i) q^{16} +(16.3520 - 9.44086i) q^{17} +(-1.14343 + 1.98047i) q^{19} +(-6.21434 - 1.09575i) q^{20} +(24.8473 + 9.04368i) q^{22} +(26.5788 - 4.68656i) q^{23} +(11.5254 + 9.67096i) q^{25} +19.5571i q^{26} +2.88411 q^{28} +(-17.2495 + 20.5571i) q^{29} +(-4.55767 - 25.8478i) q^{31} +(1.93476 - 5.31570i) q^{32} +(-4.63689 + 26.2971i) q^{34} +(3.94026 + 2.27491i) q^{35} +(-33.8611 - 58.6492i) q^{37} +(-1.10613 - 3.03906i) q^{38} +(6.83616 - 5.73622i) q^{40} +(13.0402 + 15.5407i) q^{41} +(-32.2609 + 11.7420i) q^{43} +(-32.3847 + 18.6973i) q^{44} +(-19.0840 + 33.0544i) q^{46} +(-46.4969 - 8.19866i) q^{47} +(44.0908 + 16.0478i) q^{49} +(-20.9541 + 3.69477i) q^{50} +(-21.1872 - 17.7782i) q^{52} +49.0655i q^{53} -58.9918 q^{55} +(-2.62176 + 3.12450i) q^{56} +(-6.59012 - 37.3744i) q^{58} +(13.0684 - 35.9050i) q^{59} +(-9.55898 + 54.2117i) q^{61} +(32.1454 + 18.5591i) q^{62} +(4.00000 + 6.92820i) q^{64} +(-14.9229 - 41.0004i) q^{65} +(-95.2638 + 79.9358i) q^{67} +(-24.2739 - 28.9285i) q^{68} +(-6.04638 + 2.20070i) q^{70} +(-10.4669 + 6.04307i) q^{71} +(37.3933 - 64.7671i) q^{73} +(94.3187 + 16.6309i) q^{74} +(4.29788 + 1.56430i) q^{76} +(26.5529 - 4.68199i) q^{77} +(74.8249 + 62.7855i) q^{79} +12.6204i q^{80} -28.6900 q^{82} +(-81.1294 + 96.6863i) q^{83} +(-10.3449 - 58.6687i) q^{85} +(16.6057 - 45.6238i) q^{86} +(9.18320 - 52.0805i) q^{88} +(-9.23832 - 5.33375i) q^{89} +(9.97104 + 17.2703i) q^{91} +(-18.4614 - 50.7224i) q^{92} +(51.1495 - 42.9196i) q^{94} +(4.63788 + 5.52721i) q^{95} +(145.826 - 53.0765i) q^{97} +(-57.4656 + 33.1778i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 36 q - 18 q^{5}+O(q^{10}) \) 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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