LMFDB - Embedded newform 162.3.f.a.35.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("162.17");

S:= CuspForms(chi, 3);

N := Newforms(S);

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

Newform invariants

comment: select newform

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

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

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

Embedding invariants

Embedding label			35.2
Character	$\chi$	$=$	162.35
Dual form			162.3.f.a.125.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.909039 + 1.08335i) q^{2} +(-0.347296 - 1.96962i) q^{4} +(-0.387127 + 1.06362i) q^{5} +(-0.332318 + 1.88467i) q^{7} +(2.44949 + 1.41421i) q^{8} +O(q^{10})$	\(q+(-0.909039 + 1.08335i) q^{2} +(-0.347296 - 1.96962i) q^{4} +(-0.387127 + 1.06362i) q^{5} +(-0.332318 + 1.88467i) q^{7} +(2.44949 + 1.41421i) q^{8} +(-0.800362 - 1.38627i) q^{10} +(6.05561 + 16.6376i) q^{11} +(-9.14397 + 7.67270i) q^{13} +(-1.73967 - 2.07326i) q^{14} +(-3.75877 + 1.36808i) q^{16} +(2.93931 - 1.69701i) q^{17} +(-10.2259 + 17.7118i) q^{19} +(2.22937 + 0.393099i) q^{20} +(-23.5292 - 8.56392i) q^{22} +(-0.678043 + 0.119557i) q^{23} +(18.1697 + 15.2462i) q^{25} -16.8809i q^{26} +3.82749 q^{28} +(-34.6788 + 41.3286i) q^{29} +(-7.33824 - 41.6172i) q^{31} +(1.93476 - 5.31570i) q^{32} +(-0.833488 + 4.72695i) q^{34} +(-1.87593 - 1.08307i) q^{35} +(8.24382 + 14.2787i) q^{37} +(-9.89233 - 27.1790i) q^{38} +(-2.45245 + 2.05785i) q^{40} +(-26.0070 - 30.9939i) q^{41} +(66.4698 - 24.1930i) q^{43} +(30.6667 - 17.7054i) q^{44} +(0.486845 - 0.843240i) q^{46} +(62.9822 + 11.1055i) q^{47} +(42.6034 + 15.5064i) q^{49} +(-33.0339 + 5.82477i) q^{50} +(18.2879 + 15.3454i) q^{52} -17.6375i q^{53} -20.0405 q^{55} +(-3.47934 + 4.14651i) q^{56} +(-13.2490 - 75.1385i) q^{58} +(19.1264 - 52.5494i) q^{59} +(11.5245 - 65.3586i) q^{61} +(51.7568 + 29.8818i) q^{62} +(4.00000 + 6.92820i) q^{64} +(-4.62098 - 12.6960i) q^{65} +(-17.2826 + 14.5018i) q^{67} +(-4.36327 - 5.19994i) q^{68} +(2.87864 - 1.04774i) q^{70} +(43.0775 - 24.8708i) q^{71} +(-45.2424 + 78.3622i) q^{73} +(-22.9628 - 4.04896i) q^{74} +(38.4369 + 13.9899i) q^{76} +(-33.3689 + 5.88383i) q^{77} +(-57.2341 - 48.0251i) q^{79} -4.52753i q^{80} +57.2187 q^{82} +(-8.15901 + 9.72353i) q^{83} +(0.667093 + 3.78327i) q^{85} +(-34.2141 + 94.0025i) q^{86} +(-8.69603 + 49.3177i) q^{88} +(-58.5070 - 33.7790i) q^{89} +(-11.4218 - 19.7832i) q^{91} +(0.470964 + 1.29396i) q^{92} +(-69.2844 + 58.1365i) q^{94} +(-14.8799 - 17.7332i) q^{95} +(-44.2956 + 16.1223i) q^{97} +(-55.5270 + 32.0585i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$5$	−0.387127	+	1.06362i	−0.0774254	+	0.212724i	−0.972366	−	0.233460i	$-0.924995\pi$
$5$	−0.387127	+	1.06362i	−0.0774254	+	0.212724i	0.894941	+	0.446184i	$0.147217\pi$
$6$		0			0
$7$	−0.332318	+	1.88467i	−0.0474741	+	0.269239i	−0.999300	−	0.0373988i	$-0.988093\pi$
$7$	−0.332318	+	1.88467i	−0.0474741	+	0.269239i	0.951826	+	0.306638i	$0.0992039\pi$
$8$	2.44949	+	1.41421i	0.306186	+	0.176777i
$9$		0			0
$10$	−0.800362	−	1.38627i	−0.0800362	−	0.138627i
$11$	6.05561	+	16.6376i	0.550510	+	1.51251i	0.833017	+	0.553248i	$0.186612\pi$
$11$	6.05561	+	16.6376i	0.550510	+	1.51251i	−0.282507	+	0.959265i	$0.591166\pi$
$12$		0			0
$13$	−9.14397	+	7.67270i	−0.703382	+	0.590208i	−0.922734	−	0.385438i	$-0.874050\pi$
$13$	−9.14397	+	7.67270i	−0.703382	+	0.590208i	0.219351	+	0.975646i	$0.429606\pi$
$14$	−1.73967	−	2.07326i	−0.124262	−	0.148090i
$15$		0			0
$16$	−3.75877	+	1.36808i	−0.234923	+	0.0855050i
$17$	2.93931	−	1.69701i	0.172900	−	0.0998241i	−0.411052	−	0.911612i	$-0.634839\pi$
$17$	2.93931	−	1.69701i	0.172900	−	0.0998241i	0.583953	+	0.811788i	$0.301505\pi$
$18$		0			0
$19$	−10.2259	+	17.7118i	−0.538206	+	0.932200i	0.460795	+	0.887507i	$0.347564\pi$
$19$	−10.2259	+	17.7118i	−0.538206	+	0.932200i	−0.999001	+	0.0446932i	$0.985769\pi$
$20$	2.22937	+	0.393099i	0.111469	+	0.0196549i
$21$		0			0
$22$	−23.5292	−	8.56392i	−1.06951	−	0.389269i
$23$	−0.678043	+	0.119557i	−0.0294801	+	0.00519814i	−0.188369	−	0.982098i	$-0.560320\pi$
$23$	−0.678043	+	0.119557i	−0.0294801	+	0.00519814i	0.158889	+	0.987297i	$0.449209\pi$
$24$		0			0
$25$	18.1697	+	15.2462i	0.726787	+	0.609847i
$26$		−	16.8809i		−	0.649266i
$27$		0			0
$28$	3.82749			0.136696
$29$	−34.6788	+	41.3286i	−1.19582	+	1.42512i	−0.316698	+	0.948527i	$0.602574\pi$
$29$	−34.6788	+	41.3286i	−1.19582	+	1.42512i	−0.879122	+	0.476596i	$0.841870\pi$
$30$		0			0
$31$	−7.33824	−	41.6172i	−0.236717	−	1.34249i	−0.838966	−	0.544183i	$-0.816840\pi$
$31$	−7.33824	−	41.6172i	−0.236717	−	1.34249i	0.602249	−	0.798308i	$-0.294271\pi$
$32$	1.93476	−	5.31570i	0.0604612	−	0.166116i
$33$		0			0
$34$	−0.833488	+	4.72695i	−0.0245144	+	0.139028i
$35$	−1.87593	−	1.08307i	−0.0535980	−	0.0309448i
$36$		0			0
$37$	8.24382	+	14.2787i	0.222806	+	0.385911i	0.955659	−	0.294476i	$-0.0951450\pi$
$37$	8.24382	+	14.2787i	0.222806	+	0.385911i	−0.732853	+	0.680387i	$0.761812\pi$
$38$	−9.89233	−	27.1790i	−0.260325	−	0.715236i
$39$		0			0
$40$	−2.45245	+	2.05785i	−0.0613113	+	0.0514463i
$41$	−26.0070	−	30.9939i	−0.634317	−	0.755950i	0.349144	−	0.937069i	$-0.386472\pi$
$41$	−26.0070	−	30.9939i	−0.634317	−	0.755950i	−0.983461	+	0.181119i	$0.942028\pi$
$42$		0			0
$43$	66.4698	−	24.1930i	1.54581	−	0.562628i	0.578379	−	0.815768i	$-0.303685\pi$
$43$	66.4698	−	24.1930i	1.54581	−	0.562628i	0.967430	+	0.253140i	$0.0814632\pi$
$44$	30.6667	−	17.7054i	0.696970	−	0.402396i
$45$		0			0
$46$	0.486845	−	0.843240i	0.0105836	−	0.0183313i
$47$	62.9822	+	11.1055i	1.34005	+	0.236286i	0.797286	−	0.603601i	$-0.206268\pi$
$47$	62.9822	+	11.1055i	1.34005	+	0.236286i	0.542760	+	0.839888i	$0.317379\pi$
$48$		0			0
$49$	42.6034	+	15.5064i	0.869457	+	0.316456i
$50$	−33.0339	+	5.82477i	−0.660678	+	0.116495i
$51$		0			0
$52$	18.2879	+	15.3454i	0.351691	+	0.295104i
$53$		−	17.6375i		−	0.332783i	−0.986060	−	0.166392i	$-0.946788\pi$
$53$		−	17.6375i		−	0.332783i	0.986060	−	0.166392i	$-0.0532116\pi$
$54$		0			0
$55$	−20.0405			−0.364372
$56$	−3.47934	+	4.14651i	−0.0621310	+	0.0740449i
$57$		0			0
$58$	−13.2490	−	75.1385i	−0.228430	−	1.29549i
$59$	19.1264	−	52.5494i	0.324177	−	0.890668i	−0.665377	−	0.746507i	$-0.731729\pi$
$59$	19.1264	−	52.5494i	0.324177	−	0.890668i	0.989554	−	0.144161i	$-0.0460484\pi$
$60$		0			0
$61$	11.5245	−	65.3586i	0.188926	−	1.07145i	−0.731881	−	0.681433i	$-0.761357\pi$
$61$	11.5245	−	65.3586i	0.188926	−	1.07145i	0.920807	−	0.390020i	$-0.127532\pi$
$62$	51.7568	+	29.8818i	0.834787	+	0.481965i
$63$		0			0
$64$	4.00000	+	6.92820i	0.0625000	+	0.108253i
$65$	−4.62098	−	12.6960i	−0.0710920	−	0.195324i
$66$		0			0
$67$	−17.2826	+	14.5018i	−0.257949	+	0.216445i	−0.762586	−	0.646887i	$-0.776071\pi$
$67$	−17.2826	+	14.5018i	−0.257949	+	0.216445i	0.504637	+	0.863331i	$0.331626\pi$
$68$	−4.36327	−	5.19994i	−0.0641657	−	0.0764697i
$69$		0			0
$70$	2.87864	−	1.04774i	0.0411234	−	0.0149677i
$71$	43.0775	−	24.8708i	0.606726	−	0.350293i	−0.164957	−	0.986301i	$-0.552749\pi$
$71$	43.0775	−	24.8708i	0.606726	−	0.350293i	0.771683	+	0.636007i	$0.219415\pi$
$72$		0			0
$73$	−45.2424	+	78.3622i	−0.619759	+	1.07345i	0.369770	+	0.929123i	$0.379436\pi$
$73$	−45.2424	+	78.3622i	−0.619759	+	1.07345i	−0.989529	+	0.144331i	$0.953897\pi$
$74$	−22.9628	−	4.04896i	−0.310308	−	0.0547157i
$75$		0			0
$76$	38.4369	+	13.9899i	0.505748	+	0.184077i
$77$	−33.3689	+	5.88383i	−0.433362	+	0.0764134i
$78$		0			0
$79$	−57.2341	−	48.0251i	−0.724482	−	0.607913i	0.204139	−	0.978942i	$-0.434561\pi$
$79$	−57.2341	−	48.0251i	−0.724482	−	0.607913i	−0.928621	+	0.371029i	$0.879005\pi$
$80$		−	4.52753i		−	0.0565942i
$81$		0			0
$82$	57.2187			0.697789
$83$	−8.15901	+	9.72353i	−0.0983014	+	0.117151i	−0.812952	−	0.582330i	$-0.802141\pi$
$83$	−8.15901	+	9.72353i	−0.0983014	+	0.117151i	0.714651	+	0.699481i	$0.246586\pi$
$84$		0			0
$85$	0.667093	+	3.78327i	0.00784815	+	0.0445091i
$86$	−34.2141	+	94.0025i	−0.397838	+	1.09305i
$87$		0			0
$88$	−8.69603	+	49.3177i	−0.0988186	+	0.560428i
$89$	−58.5070	−	33.7790i	−0.657382	−	0.379540i	0.133897	−	0.990995i	$-0.457251\pi$
$89$	−58.5070	−	33.7790i	−0.657382	−	0.379540i	−0.791279	+	0.611455i	$0.790584\pi$
$90$		0			0
$91$	−11.4218	−	19.7832i	−0.125514	−	0.217397i
$92$	0.470964	+	1.29396i	0.00511917	+	0.0140648i
$93$		0			0
$94$	−69.2844	+	58.1365i	−0.737068	+	0.618473i
$95$	−14.8799	−	17.7332i	−0.156631	−	0.186665i
$96$		0			0
$97$	−44.2956	+	16.1223i	−0.456655	+	0.166209i	−0.560098	−	0.828427i	$-0.689236\pi$
$97$	−44.2956	+	16.1223i	−0.456655	+	0.166209i	0.103442	+	0.994635i	$0.467014\pi$
$98$	−55.5270	+	32.0585i	−0.566602	+	0.327128i
$99$		0			0
$100$	23.7188	−	41.0822i	0.237188	−	0.410822i
$101$	9.94227	+	1.75309i	0.0984383	+	0.0173573i	0.222650	−	0.974898i	$-0.428529\pi$
$101$	9.94227	+	1.75309i	0.0984383	+	0.0173573i	−0.124212	+	0.992256i	$0.539640\pi$
$102$		0			0
$103$	121.488	+	44.2181i	1.17950	+	0.429301i	0.856024	−	0.516936i	$-0.172928\pi$
$103$	121.488	+	44.2181i	1.17950	+	0.429301i	0.323472	+	0.946238i	$0.395150\pi$
$104$	−33.2489	+	5.86268i	−0.319701	+	0.0563719i
$105$		0			0
$106$	19.1076	+	16.0332i	0.180260	+	0.151257i
$107$			135.970i			1.27075i	0.772204	+	0.635375i	$0.219154\pi$
$107$			135.970i			1.27075i	−0.772204	+	0.635375i	$0.780846\pi$
$108$		0			0
$109$	−182.307			−1.67254			−0.836269	−	0.548320i	$-0.815268\pi$
$109$	−182.307			−1.67254			−0.836269	+	0.548320i	$0.815268\pi$
$110$	18.2176	−	21.7108i	0.165614	−	0.197371i
$111$		0			0
$112$	−1.32927	−	7.53869i	−0.0118685	−	0.0673097i
$113$	−5.48933	+	15.0818i	−0.0485781	+	0.133467i	−0.961609	−	0.274423i	$-0.911513\pi$
$113$	−5.48933	+	15.0818i	−0.0485781	+	0.133467i	0.913031	+	0.407890i	$0.133735\pi$
$114$		0			0
$115$	0.135325	−	0.767465i	0.00117674	−	0.00667361i
$116$	93.4452	+	53.9506i	0.805562	+	0.465091i
$117$		0			0
$118$	39.5428	+	68.4901i	0.335108	+	0.580425i
$119$	2.22152	+	6.10358i	0.0186682	+	0.0512905i
$120$		0			0
$121$	−147.449	+	123.725i	−1.21859	+	1.02252i
$122$	60.3301	+	71.8986i	0.494509	+	0.589333i
$123$		0			0
$124$	−79.4214	+	28.9070i	−0.640495	+	0.233121i
$125$	−47.7561	+	27.5720i	−0.382049	+	0.220576i
$126$		0			0
$127$	81.7231	−	141.549i	0.643489	−	1.11456i	−0.341160	−	0.940005i	$-0.610820\pi$
$127$	81.7231	−	141.549i	0.643489	−	1.11456i	0.984648	−	0.174550i	$-0.0558470\pi$
$128$	−11.1418	−	1.96460i	−0.0870455	−	0.0153485i
$129$		0			0
$130$	17.9549	+	6.53505i	0.138115	+	0.0502696i
$131$	194.629	−	34.3184i	1.48572	−	0.261972i	0.628858	−	0.777520i	$-0.283523\pi$
$131$	194.629	−	34.3184i	1.48572	−	0.261972i	0.856861	+	0.515548i	$0.172412\pi$
$132$		0			0
$133$	−29.9827	−	25.1584i	−0.225434	−	0.189161i
$134$		−	31.9058i		−	0.238103i
$135$		0			0
$136$	9.59974			0.0705863
$137$	19.4564	−	23.1872i	0.142017	−	0.169250i	−0.690347	−	0.723478i	$-0.742542\pi$
$137$	19.4564	−	23.1872i	0.142017	−	0.169250i	0.832364	+	0.554229i	$0.186987\pi$
$138$		0			0
$139$	−26.6334	−	151.046i	−0.191607	−	1.08666i	−0.917168	−	0.398500i	$-0.869531\pi$
$139$	−26.6334	−	151.046i	−0.191607	−	1.08666i	0.725561	−	0.688158i	$-0.241580\pi$
$140$	−1.48172	+	4.07100i	−0.0105837	+	0.0290786i
$141$		0			0
$142$	−12.2153	+	69.2766i	−0.0860235	+	0.487863i
$143$	−183.028	−	105.671i	−1.27992	−	0.738960i
$144$		0			0
$145$	−30.5329	−	52.8845i	−0.210572	−	0.364721i
$146$	−43.7666	−	120.248i	−0.299771	−	0.823614i
$147$		0			0
$148$	25.2605	−	21.1961i	0.170679	−	0.143217i
$149$	130.956	+	156.067i	0.878898	+	1.04743i	0.998508	+	0.0546085i	$0.0173911\pi$
$149$	130.956	+	156.067i	0.878898	+	1.04743i	−0.119610	+	0.992821i	$0.538164\pi$
$150$		0			0
$151$	−124.926	+	45.4693i	−0.827324	+	0.301121i	−0.720760	−	0.693184i	$-0.756207\pi$
$151$	−124.926	+	45.4693i	−0.827324	+	0.301121i	−0.106564	+	0.994306i	$0.533985\pi$
$152$	−50.0965	+	28.9232i	−0.329582	+	0.190285i
$153$		0			0
$154$	23.9594	−	41.4988i	0.155580	−	0.269473i
$155$	47.1059	+	8.30603i	0.303909	+	0.0535873i
$156$		0			0
$157$	238.313	+	86.7387i	1.51791	+	0.552476i	0.960626	−	0.277844i	$-0.0896197\pi$
$157$	238.313	+	86.7387i	1.51791	+	0.552476i	0.557288	+	0.830319i	$0.311842\pi$
$158$	104.056	−	18.3479i	0.658583	−	0.116126i
$159$		0			0
$160$	4.90490	+	4.11570i	0.0306557	+	0.0257231i
$161$		−	1.31762i		−	0.00818397i
$162$		0			0
$163$	261.536			1.60451			0.802257	−	0.596979i	$-0.203632\pi$
$163$	261.536			1.60451			0.802257	+	0.596979i	$0.203632\pi$
$164$	−52.0140	+	61.9879i	−0.317159	+	0.377975i
$165$		0			0
$166$	−3.11713	−	17.6781i	−0.0187779	−	0.106495i
$167$	26.5485	−	72.9413i	0.158973	−	0.436774i	−0.834477	−	0.551043i	$-0.814230\pi$
$167$	26.5485	−	72.9413i	0.158973	−	0.436774i	0.993450	+	0.114268i	$0.0364523\pi$
$168$		0			0
$169$	−4.60471	+	26.1146i	−0.0272468	+	0.154524i
$170$	−4.70502	−	2.71644i	−0.0276766	−	0.0159791i
$171$		0			0
$172$	−70.7357	−	122.518i	−0.411254	−	0.712313i
$173$	−36.6545	−	100.707i	−0.211876	−	0.582123i	0.787542	−	0.616262i	$-0.211354\pi$
$173$	−36.6545	−	100.707i	−0.211876	−	0.582123i	−0.999417	+	0.0341382i	$0.989131\pi$
$174$		0			0
$175$	−34.7722	+	29.1773i	−0.198698	+	0.166727i
$176$	−45.5233	−	54.2525i	−0.258655	−	0.308253i
$177$		0			0
$178$	89.7797	−	32.6771i	0.504380	−	0.183579i
$179$	−102.022	+	58.9024i	−0.569955	+	0.329064i	−0.757131	−	0.653263i	$-0.773400\pi$
$179$	−102.022	+	58.9024i	−0.569955	+	0.329064i	0.187176	+	0.982326i	$0.440066\pi$
$180$		0			0
$181$	59.7681	−	103.521i	0.330210	−	0.571941i	−0.652343	−	0.757924i	$-0.726214\pi$
$181$	59.7681	−	103.521i	0.330210	−	0.571941i	0.982553	+	0.185983i	$0.0595470\pi$
$182$	31.8150	+	5.60984i	0.174808	+	0.0308233i
$183$		0			0
$184$	−1.82994	−	0.666043i	−0.00994532	−	0.00361980i
$185$	−18.3786	+	3.24064i	−0.0993436	+	0.0175170i
$186$		0			0
$187$	46.0335	+	38.6267i	0.246169	+	0.206560i
$188$		−	127.908i		−	0.680359i
$189$		0			0
$190$	32.7377			0.172304
$191$	146.062	−	174.070i	0.764722	−	0.911361i	−0.233414	−	0.972377i	$-0.574990\pi$
$191$	146.062	−	174.070i	0.764722	−	0.911361i	0.998137	+	0.0610168i	$0.0194343\pi$
$192$		0			0
$193$	12.7566	+	72.3465i	0.0660966	+	0.374853i	0.999856	+	0.0169519i	$0.00539623\pi$
$193$	12.7566	+	72.3465i	0.0660966	+	0.374853i	−0.933760	+	0.357901i	$0.883493\pi$
$194$	22.8003	−	62.6434i	0.117527	−	0.322904i
$195$		0			0
$196$	15.7456	−	89.2976i	0.0803346	−	0.455600i
$197$	−80.0547	−	46.2196i	−0.406369	−	0.234617i	0.282859	−	0.959161i	$-0.408717\pi$
$197$	−80.0547	−	46.2196i	−0.406369	−	0.234617i	−0.689228	+	0.724544i	$0.742050\pi$
$198$		0			0
$199$	1.97251	+	3.41650i	0.00991214	+	0.0171683i	0.870939	−	0.491391i	$-0.163511\pi$
$199$	1.97251	+	3.41650i	0.00991214	+	0.0171683i	−0.861027	+	0.508560i	$0.830178\pi$
$200$	22.9451	+	63.0412i	0.114726	+	0.315206i
$201$		0			0
$202$	−10.9371	+	9.17733i	−0.0541441	+	0.0454323i
$203$	−66.3664	−	79.0923i	−0.326928	−	0.389617i
$204$		0			0
$205$	43.0339	−	15.6630i	0.209921	−	0.0764051i
$206$	−158.341	+	91.4183i	−0.768646	+	0.443778i
$207$		0			0
$208$	23.8732	−	41.3496i	0.114775	−	0.198796i
$209$	−356.607	−	62.8794i	−1.70625	−	0.300858i
$210$		0			0
$211$	57.0834	+	20.7767i	0.270538	+	0.0984676i	0.473727	−	0.880672i	$-0.342908\pi$
$211$	57.0834	+	20.7767i	0.270538	+	0.0984676i	−0.203189	+	0.979139i	$0.565131\pi$
$212$	−34.7391	+	6.12545i	−0.163864	+	0.0288936i
$213$		0			0
$214$	−147.303	−	123.602i	−0.688334	−	0.577581i
$215$			80.0645i			0.372393i
$216$		0			0
$217$	80.8735			0.372689
$218$	165.724	−	197.502i	0.760201	−	0.905972i
$219$		0			0
$220$	6.95998	+	39.4720i	0.0316363	+	0.179418i
$221$	−13.8563	+	38.0698i	−0.0626981	+	0.172262i
$222$		0			0
$223$	−28.2197	+	160.042i	−0.126546	+	0.717678i	0.853832	+	0.520549i	$0.174273\pi$
$223$	−28.2197	+	160.042i	−0.126546	+	0.717678i	−0.980378	+	0.197129i	$0.936838\pi$
$224$	9.37540	+	5.41289i	0.0418545	+	0.0241647i
$225$		0			0
$226$	−11.3489	−	19.6568i	−0.0502162	−	0.0869771i
$227$	89.6325	+	246.263i	0.394857	+	1.08486i	0.964756	+	0.263146i	$0.0847601\pi$
$227$	89.6325	+	246.263i	0.394857	+	1.08486i	−0.569899	+	0.821715i	$0.693018\pi$
$228$		0			0
$229$	−93.1242	+	78.1405i	−0.406656	+	0.341225i	−0.823060	−	0.567955i	$-0.807735\pi$
$229$	−93.1242	+	78.1405i	−0.406656	+	0.341225i	0.416404	+	0.909180i	$0.363290\pi$
$230$	0.708418	+	0.844260i	0.00308008	+	0.00367070i
$231$		0			0
$232$	−143.393	+	52.1907i	−0.618072	+	0.224960i
$233$	362.949	−	209.549i	1.55772	−	0.899352i	0.560248	−	0.828325i	$-0.310706\pi$
$233$	362.949	−	209.549i	1.55772	−	0.899352i	0.997474	−	0.0710267i	$-0.0226275\pi$
$234$		0			0
$235$	−36.1941	+	62.6900i	−0.154017	+	0.266766i
$236$	−110.145	−	19.4215i	−0.466715	−	0.0822944i
$237$		0			0
$238$	−8.63176	−	3.14170i	−0.0362679	−	0.0132004i
$239$	−102.988	+	18.1595i	−0.430912	+	0.0759813i	−0.384897	−	0.922959i	$-0.625763\pi$
$239$	−102.988	+	18.1595i	−0.430912	+	0.0759813i	−0.0460143	+	0.998941i	$0.514652\pi$
$240$		0			0
$241$	36.2898	+	30.4507i	0.150580	+	0.126352i	0.714966	−	0.699160i	$-0.246442\pi$
$241$	36.2898	+	30.4507i	0.150580	+	0.126352i	−0.564385	+	0.825511i	$0.690887\pi$
$242$		−	272.210i		−	1.12483i
$243$		0			0
$244$	−132.734			−0.543991
$245$	−32.9858	+	39.3110i	−0.134636	+	0.160453i
$246$		0			0
$247$	−42.3919	−	240.417i	−0.171627	−	0.973346i
$248$	40.8807	−	112.319i	0.164842	−	0.452899i
$249$		0			0
$250$	13.5420	−	76.8007i	0.0541681	−	0.307203i
$251$	147.898	+	85.3890i	0.589235	+	0.340195i	0.764795	−	0.644274i	$-0.222840\pi$
$251$	147.898	+	85.3890i	0.589235	+	0.340195i	−0.175560	+	0.984469i	$0.556174\pi$
$252$		0			0
$253$	−6.09511	−	10.5570i	−0.0240914	−	0.0417274i
$254$	79.0572	+	217.208i	0.311249	+	0.855149i
$255$		0			0
$256$	12.2567	−	10.2846i	0.0478778	−	0.0401742i
$257$	135.000	+	160.886i	0.525291	+	0.626017i	0.961823	−	0.273671i	$-0.0882381\pi$
$257$	135.000	+	160.886i	0.525291	+	0.626017i	−0.436533	+	0.899688i	$0.643794\pi$
$258$		0			0
$259$	−29.6503	+	10.7918i	−0.114480	+	0.0416672i
$260$	−23.4015	+	13.5108i	−0.0900056	+	0.0519648i
$261$		0			0
$262$	−139.747	+	242.048i	−0.533384	+	0.923848i
$263$	87.0793	+	15.3544i	0.331100	+	0.0583818i	0.336727	−	0.941602i	$-0.390680\pi$
$263$	87.0793	+	15.3544i	0.331100	+	0.0583818i	−0.00562710	+	0.999984i	$0.501791\pi$
$264$		0			0
$265$	18.7597	+	6.82796i	0.0707912	+	0.0257659i
$266$	54.5108	−	9.61173i	0.204928	−	0.0361343i
$267$		0			0
$268$	34.5651	+	29.0036i	0.128974	+	0.108222i
$269$			417.890i			1.55350i	0.629812	+	0.776748i	$0.283132\pi$
$269$			417.890i			1.55350i	−0.629812	+	0.776748i	$0.716868\pi$
$270$		0			0
$271$	29.3344			0.108245			0.0541226	−	0.998534i	$-0.482764\pi$
$271$	29.3344			0.108245			0.0541226	+	0.998534i	$0.482764\pi$
$272$	−8.72653	+	10.3999i	−0.0320828	+	0.0382348i
$273$		0			0
$274$	7.43326	+	42.1561i	0.0271287	+	0.153854i
$275$	−143.632	+	394.626i	−0.522298	+	1.43500i
$276$		0			0
$277$	32.7591	−	185.786i	0.118264	−	0.670707i	−0.866819	−	0.498624i	$-0.833839\pi$
$277$	32.7591	−	185.786i	0.118264	−	0.670707i	0.985082	−	0.172083i	$-0.0550499\pi$
$278$	187.846	+	108.453i	0.675705	+	0.390119i
$279$		0			0
$280$	−3.06338	−	5.30593i	−0.0109406	−	0.0189497i
$281$	−16.2664	−	44.6916i	−0.0578876	−	0.159045i	0.907378	−	0.420316i	$-0.138081\pi$
$281$	−16.2664	−	44.6916i	−0.0578876	−	0.159045i	−0.965266	+	0.261271i	$0.915858\pi$
$282$		0			0
$283$	58.5606	−	49.1382i	0.206928	−	0.173633i	−0.533434	−	0.845842i	$-0.679099\pi$
$283$	58.5606	−	49.1382i	0.206928	−	0.173633i	0.740362	+	0.672209i	$0.234654\pi$
$284$	−63.9466	−	76.2086i	−0.225164	−	0.268340i
$285$		0			0
$286$	280.859	−	102.224i	0.982023	−	0.357427i
$287$	67.0560	−	38.7148i	0.233645	−	0.134895i
$288$		0			0
$289$	−138.740	+	240.305i	−0.480070	+	0.831506i
$290$	85.0480	+	14.9963i	0.293269	+	0.0517113i
$291$		0			0
$292$	170.056	+	61.8953i	0.582383	+	0.211970i
$293$	−321.453	+	56.6808i	−1.09711	+	0.193450i	−0.692770	−	0.721159i	$-0.743610\pi$
$293$	−321.453	+	56.6808i	−1.09711	+	0.193450i	−0.404339	+	0.914609i	$0.632499\pi$
$294$		0			0
$295$	48.4884	+	40.6866i	0.164367	+	0.137921i
$296$			46.6341i			0.157548i
$297$		0			0
$298$	−288.119			−0.966843
$299$	5.28268	−	6.29565i	0.0176678	−	0.0210557i
$300$		0			0
$301$	23.5068	+	133.314i	0.0780956	+	0.442902i
$302$	64.3034	−	176.672i	0.212925	−	0.585007i
$303$		0			0
$304$	14.2057	−	80.5645i	0.0467292	−	0.265015i
$305$	65.0554	+	37.5598i	0.213296	+	0.123147i
$306$		0			0
$307$	135.270	+	234.294i	0.440618	+	0.763172i	0.997735	−	0.0672612i	$-0.0214261\pi$
$307$	135.270	+	234.294i	0.440618	+	0.763172i	−0.557118	+	0.830434i	$0.688093\pi$
$308$	23.1778	+	63.6804i	0.0752525	+	0.206755i
$309$		0			0
$310$	−51.8194	+	43.4816i	−0.167159	+	0.140263i
$311$	−271.552	−	323.624i	−0.873159	−	1.04059i	−0.998822	−	0.0485173i	$-0.984550\pi$
$311$	−271.552	−	323.624i	−0.873159	−	1.04059i	0.125663	−	0.992073i	$-0.459894\pi$
$312$		0			0
$313$	314.648	−	114.523i	1.00527	−	0.365887i	0.213653	−	0.976910i	$-0.431464\pi$
$313$	314.648	−	114.523i	1.00527	−	0.365887i	0.791613	+	0.611023i	$0.209242\pi$
$314$	−310.604	+	179.327i	−0.989184	+	0.571106i
$315$		0			0
$316$	−74.7138	+	129.408i	−0.236436	+	0.409519i
$317$	−61.1385	−	10.7804i	−0.192866	−	0.0340075i	0.0763807	−	0.997079i	$-0.475664\pi$
$317$	−61.1385	−	10.7804i	−0.192866	−	0.0340075i	−0.269247	+	0.963071i	$0.586775\pi$
$318$		0			0
$319$	−897.611	−	326.704i	−2.81383	−	1.02415i
$320$	−8.91750	+	1.57240i	−0.0278672	+	0.00491374i
$321$		0			0
$322$	1.42744	+	1.19777i	0.00443305	+	0.00371977i
$323$			69.4139i			0.214904i
$324$		0			0
$325$	−283.122			−0.871146
$326$	−237.746	+	283.335i	−0.729283	+	0.869125i
$327$		0			0
$328$	−19.8718	−	112.699i	−0.0605849	−	0.343594i
$329$	−41.8603	+	115.010i	−0.127235	+	0.349575i
$330$		0			0
$331$	−47.4950	+	269.357i	−0.143489	+	0.813768i	0.825078	+	0.565018i	$0.191131\pi$
$331$	−47.4950	+	269.357i	−0.143489	+	0.813768i	−0.968568	+	0.248750i	$0.919980\pi$
$332$	21.9852	+	12.6932i	0.0662205	+	0.0382324i
$333$		0			0
$334$	54.8874	+	95.0678i	0.164334	+	0.284634i
$335$	−8.73389	−	23.9962i	−0.0260713	−	0.0716303i
$336$		0			0
$337$	420.078	−	352.488i	1.24652	−	1.04596i	0.249538	−	0.968365i	$-0.419721\pi$
$337$	420.078	−	352.488i	1.24652	−	1.04596i	0.996985	−	0.0775926i	$-0.0247233\pi$
$338$	−24.1054	−	28.7277i	−0.0713178	−	0.0849932i
$339$		0			0
$340$	7.21991	−	2.62783i	0.0212350	−	0.00772892i
$341$	647.975	−	374.109i	1.90022	−	1.09709i
$342$		0			0
$343$	−90.2691	+	156.351i	−0.263175	+	0.455833i
$344$	197.031	+	34.7419i	0.572765	+	0.100994i
$345$		0			0
$346$	142.422	+	51.8373i	0.411623	+	0.149819i
$347$	−12.6788	+	2.23561i	−0.0365382	+	0.00644267i	−0.191887	−	0.981417i	$-0.561461\pi$
$347$	−12.6788	+	2.23561i	−0.0365382	+	0.00644267i	0.155349	+	0.987860i	$0.450350\pi$
$348$		0			0
$349$	8.25639	+	6.92793i	0.0236573	+	0.0198508i	0.654540	−	0.756028i	$-0.272863\pi$
$349$	8.25639	+	6.92793i	0.0236573	+	0.0198508i	−0.630882	+	0.775879i	$0.717307\pi$
$350$		−	64.1937i		−	0.183411i
$351$		0			0
$352$	100.157			0.284537
$353$	−33.8253	+	40.3115i	−0.0958225	+	0.114197i	−0.811825	−	0.583901i	$-0.801526\pi$
$353$	−33.8253	+	40.3115i	−0.0958225	+	0.114197i	0.716002	+	0.698098i	$0.245970\pi$
$354$		0			0
$355$	9.77669	+	55.4464i	0.0275400	+	0.156187i
$356$	−46.2125	+	126.968i	−0.129810	+	0.356651i
$357$		0			0
$358$	28.9300	−	164.070i	0.0808100	−	0.458297i
$359$	−85.6783	−	49.4664i	−0.238658	−	0.137789i	0.375902	−	0.926660i	$-0.377333\pi$
$359$	−85.6783	−	49.4664i	−0.238658	−	0.137789i	−0.614560	+	0.788870i	$0.710666\pi$
$360$		0			0
$361$	−28.6385	−	49.6034i	−0.0793311	−	0.137405i
$362$	57.8184	+	158.855i	0.159719	+	0.438825i
$363$		0			0
$364$	−34.9985	+	29.3672i	−0.0961496	+	0.0806791i
$365$	−65.8332	−	78.4569i	−0.180365	−	0.214951i
$366$		0			0
$367$	−478.024	+	173.987i	−1.30252	+	0.474078i	−0.897816	−	0.440370i	$-0.854847\pi$
$367$	−478.024	+	173.987i	−1.30252	+	0.474078i	−0.404702	+	0.914448i	$0.632625\pi$
$368$	2.38504	−	1.37701i	0.00648110	−	0.00374186i
$369$		0			0
$370$	13.1961	−	22.8563i	0.0356651	−	0.0617738i
$371$	33.2409	+	5.86127i	0.0895982	+	0.0157986i
$372$		0			0
$373$	−412.649	−	150.192i	−1.10630	−	0.402660i	−0.276664	−	0.960967i	$-0.589229\pi$
$373$	−412.649	−	150.192i	−1.10630	−	0.402660i	−0.829634	+	0.558307i	$0.811451\pi$
$374$	−83.6925	+	14.7573i	−0.223777	+	0.0394579i
$375$		0			0
$376$	138.569	+	116.273i	0.368534	+	0.309237i
$377$		−	643.987i		−	1.70819i
$378$		0			0
$379$	216.141			0.570293			0.285147	−	0.958484i	$-0.407958\pi$
$379$	216.141			0.570293			0.285147	+	0.958484i	$0.407958\pi$
$380$	−29.7599	+	35.4664i	−0.0783155	+	0.0933327i
$381$		0			0
$382$	55.8027	+	316.473i	0.146080	+	0.828462i
$383$	224.513	−	616.845i	0.586197	−	1.61056i	−0.191200	−	0.981551i	$-0.561238\pi$
$383$	224.513	−	616.845i	0.586197	−	1.61056i	0.777397	−	0.629011i	$-0.216540\pi$
$384$		0			0
$385$	6.65981	−	37.7697i	0.0172982	−	0.0981031i
$386$	−89.9729	−	51.9459i	−0.233091	−	0.134575i
$387$		0			0
$388$	47.1384	+	81.6460i	0.121491	+	0.210428i
$389$	−80.9652	−	222.450i	−0.208137	−	0.571851i	0.791068	−	0.611729i	$-0.209526\pi$
$389$	−80.9652	−	222.450i	−0.208137	−	0.571851i	−0.999205	+	0.0398773i	$0.987303\pi$
$390$		0			0
$391$	−1.79009	+	1.50206i	−0.00457822	+	0.00384159i
$392$	82.4272	+	98.2330i	0.210274	+	0.250594i
$393$		0			0
$394$	122.845	−	44.7119i	0.311789	−	0.113482i
$395$	73.2374	−	42.2836i	0.185411	−	0.107047i
$396$		0			0
$397$	150.540	−	260.743i	0.379194	−	0.656783i	−0.611751	−	0.791050i	$-0.709535\pi$
$397$	150.540	−	260.743i	0.379194	−	0.656783i	0.990945	+	0.134267i	$0.0428680\pi$
$398$	−5.49436	−	0.968803i	−0.0138049	−	0.00243418i
$399$		0			0
$400$	−89.1537	−	32.4493i	−0.222884	−	0.0811232i
$401$	−34.8014	+	6.13642i	−0.0867864	+	0.0153028i	−0.216873	−	0.976200i	$-0.569586\pi$
$401$	−34.8014	+	6.13642i	−0.0867864	+	0.0153028i	0.130086	+	0.991503i	$0.458475\pi$
$402$		0			0
$403$	386.417	+	324.243i	0.958852	+	0.804572i
$404$		−	20.1913i		−	0.0499784i
$405$		0			0
$406$	146.014			0.359641
$407$	−187.643	+	223.624i	−0.461039	+	0.549445i
$408$		0			0
$409$	−46.1552	−	261.759i	−0.112849	−	0.639998i	−0.987793	−	0.155773i	$-0.950213\pi$
$409$	−46.1552	−	261.759i	−0.112849	−	0.639998i	0.874944	−	0.484224i	$-0.160898\pi$
$410$	−22.1509	+	60.8591i	−0.0540266	+	0.148437i
$411$		0			0
$412$	44.9002	−	254.642i	0.108981	−	0.618062i
$413$	92.6823	+	53.5102i	0.224412	+	0.129565i
$414$		0			0
$415$	−7.18359	−	12.4423i	−0.0173099	−	0.0299816i
$416$	23.0944	+	63.4515i	0.0555155	+	0.152528i
$417$		0			0
$418$	392.290	−	329.170i	0.938492	−	0.787488i
$419$	−297.132	−	354.108i	−0.709145	−	0.845127i	0.284383	−	0.958711i	$-0.408211\pi$
$419$	−297.132	−	354.108i	−0.709145	−	0.845127i	−0.993528	+	0.113584i	$0.963767\pi$
$420$		0			0
$421$	744.427	−	270.949i	1.76824	−	0.643585i	0.768242	−	0.640159i	$-0.221132\pi$
$421$	744.427	−	270.949i	1.76824	−	0.643585i	0.999994	−	0.00342601i	$-0.00109054\pi$
$422$	−74.3995	+	42.9546i	−0.176302	+	0.101788i
$423$		0			0
$424$	24.9432	−	43.2029i	0.0588283	−	0.101894i
$425$	79.2792	+	13.9791i	0.186539	+	0.0328919i
$426$		0			0
$427$	119.350	+	43.4397i	0.279508	+	0.101732i
$428$	267.809	−	47.2220i	0.625722	−	0.110332i
$429$		0			0
$430$	−86.7379	−	72.7818i	−0.201716	−	0.169260i
$431$			213.975i			0.496462i	0.968701	+	0.248231i	$0.0798492\pi$
$431$			213.975i			0.496462i	−0.968701	+	0.248231i	$0.920151\pi$
$432$		0			0
$433$	122.246			0.282323			0.141162	−	0.989987i	$-0.454916\pi$
$433$	122.246			0.282323			0.141162	+	0.989987i	$0.454916\pi$
$434$	−73.5171	+	87.6143i	−0.169394	+	0.201876i
$435$		0			0
$436$	63.3144	+	359.074i	0.145217	+	0.823564i
$437$	4.81603	−	13.2319i	0.0110207	−	0.0302790i
$438$		0			0
$439$	23.1853	−	131.490i	0.0528139	−	0.299522i	−0.946947	−	0.321390i	$-0.895850\pi$
$439$	23.1853	−	131.490i	0.0528139	−	0.299522i	0.999761	+	0.0218673i	$0.00696114\pi$
$440$	−49.0889	−	28.3415i	−0.111566	−	0.0644125i
$441$		0			0
$442$	−28.6471	−	49.6182i	−0.0648124	−	0.112258i
$443$	48.3138	+	132.741i	0.109060	+	0.299641i	0.982203	−	0.187825i	$-0.0601437\pi$
$443$	48.3138	+	132.741i	0.109060	+	0.299641i	−0.873142	+	0.487466i	$0.837921\pi$
$444$		0			0
$445$	58.5778	−	49.1526i	0.131635	−	0.110455i
$446$	−147.729	−	176.056i	−0.331231	−	0.394745i
$447$		0			0
$448$	−14.3867	+	5.23632i	−0.0321131	+	0.0116882i
$449$	14.1480	−	8.16837i	0.0315101	−	0.0181924i	−0.484162	−	0.874978i	$-0.660876\pi$
$449$	14.1480	−	8.16837i	0.0315101	−	0.0181924i	0.515672	+	0.856786i	$0.327542\pi$
$450$		0			0
$451$	358.178	−	620.382i	0.794186	−	1.37557i
$452$	31.6118	+	5.57401i	0.0699376	+	0.0123319i
$453$		0			0
$454$	−348.269	−	126.760i	−0.767112	−	0.279206i
$455$	25.4635	−	4.48990i	0.0559637	−	0.00986792i
$456$		0			0
$457$	−413.177	−	346.697i	−0.904107	−	0.758636i	0.0668816	−	0.997761i	$-0.478695\pi$
$457$	−413.177	−	346.697i	−0.904107	−	0.758636i	−0.970989	+	0.239125i	$0.923139\pi$
$458$		−	171.919i		−	0.375369i
$459$		0			0
$460$	−1.55861			−0.00338828
$461$	232.751	−	277.382i	0.504882	−	0.601696i	−0.452055	−	0.891990i	$-0.649309\pi$
$461$	232.751	−	277.382i	0.504882	−	0.601696i	0.956937	+	0.290295i	$0.0937533\pi$
$462$		0			0
$463$	33.1055	+	187.751i	0.0715022	+	0.405509i	0.999461	+	0.0328264i	$0.0104508\pi$
$463$	33.1055	+	187.751i	0.0715022	+	0.405509i	−0.927959	+	0.372683i	$0.878438\pi$
$464$	73.8088	−	202.788i	0.159071	−	0.437043i
$465$		0			0
$466$	−102.920	+	583.689i	−0.220859	+	1.25255i
$467$	−617.016	−	356.234i	−1.32123	−	0.762814i	−0.337308	−	0.941394i	$-0.609516\pi$
$467$	−617.016	−	356.234i	−1.32123	−	0.762814i	−0.983925	+	0.178580i	$0.942850\pi$
$468$		0			0
$469$	−21.5878	−	37.3912i	−0.0460294	−	0.0797253i
$470$	−35.0134	−	96.1986i	−0.0744966	−	0.204678i
$471$		0			0
$472$	121.166	−	101.670i	0.256708	−	0.215403i
$473$	805.030	+	959.397i	1.70197	+	2.02832i
$474$		0			0
$475$	−455.839	+	165.912i	−0.959661	+	0.349288i
$476$	11.2502	−	6.49529i	0.0236348	−	0.0136456i
$477$		0			0
$478$	73.9468	−	128.080i	0.154700	−	0.267949i
$479$	−224.974	−	39.6689i	−0.469674	−	0.0828162i	−0.0661981	−	0.997807i	$-0.521087\pi$
$479$	−224.974	−	39.6689i	−0.469674	−	0.0828162i	−0.403476	+	0.914990i	$0.632198\pi$
$480$		0			0
$481$	−184.938	−	67.3118i	−0.384486	−	0.139941i
$482$	−65.9777	+	11.6336i	−0.136883	+	0.0241362i
$483$		0			0
$484$	294.899	+	247.450i	0.609295	+	0.511259i
$485$		−	53.3551i		−	0.110011i
$486$		0			0
$487$	115.510			0.237188			0.118594	−	0.992943i	$-0.462161\pi$
$487$	115.510			0.237188			0.118594	+	0.992943i	$0.462161\pi$
$488$	120.660	−	143.797i	0.247254	−	0.294666i
$489$		0			0
$490$	−12.6022	−	71.4704i	−0.0257187	−	0.145858i
$491$	−150.903	+	414.604i	−0.307339	+	0.844406i	0.685834	+	0.727758i	$0.259437\pi$
$491$	−150.903	+	414.604i	−0.307339	+	0.844406i	−0.993173	+	0.116649i	$0.962785\pi$
$492$		0			0
$493$	−31.7966	+	180.328i	−0.0644962	+	0.365776i
$494$	298.991	+	172.623i	0.605245	+	0.349439i
$495$		0			0
$496$	84.5185	+	146.390i	0.170400	+	0.295142i
$497$	32.5579	+	89.4520i	0.0655088	+	0.179984i
$498$		0			0
$499$	216.247	−	181.453i	0.433361	−	0.363633i	−0.399857	−	0.916577i	$-0.630940\pi$
$499$	216.247	−	181.453i	0.433361	−	0.363633i	0.833218	+	0.552945i	$0.186496\pi$
$500$	70.8918	+	84.4856i	0.141784	+	0.168971i
$501$		0			0
$502$	−226.951	+	82.6035i	−0.452094	+	0.164549i
$503$	−595.298	+	343.696i	−1.18350	+	0.683291i	−0.956821	−	0.290679i	$-0.906119\pi$
$503$	−595.298	+	343.696i	−1.18350	+	0.683291i	−0.226675	+	0.973971i	$0.572785\pi$
$504$		0			0
$505$	−5.71354	+	9.89615i	−0.0113139	+	0.0195963i
$506$	16.9777	+	2.99362i	0.0335527	+	0.00591625i
$507$		0			0
$508$	−307.178	−	111.804i	−0.604682	−	0.220086i
$509$	440.490	−	77.6702i	0.865402	−	0.152594i	0.276712	−	0.960953i	$-0.410755\pi$
$509$	440.490	−	77.6702i	0.865402	−	0.152594i	0.588690	+	0.808359i	$0.299644\pi$
$510$		0			0
$511$	−132.652	−	111.308i	−0.259593	−	0.217824i
$512$			22.6274i			0.0441942i
$513$		0			0
$514$	−297.016			−0.577853
$515$	−94.0626	+	112.099i	−0.182646	+	0.217669i
$516$		0			0
$517$	196.627	+	1115.13i	0.380322	+	2.15692i
$518$	15.2619	−	41.9318i	0.0294632	−	0.0809494i
$519$		0			0
$520$	6.63587	−	37.6339i	0.0127613	−	0.0723728i
$521$	265.555	+	153.318i	0.509703	+	0.294277i	0.732712	−	0.680539i	$-0.238254\pi$
$521$	265.555	+	153.318i	0.509703	+	0.294277i	−0.223008	+	0.974817i	$0.571588\pi$
$522$		0			0
$523$	185.369	+	321.068i	0.354434	+	0.613897i	0.987021	−	0.160592i	$-0.0513403\pi$
$523$	185.369	+	321.068i	0.354434	+	0.613897i	−0.632587	+	0.774489i	$0.718007\pi$
$524$	−135.188	−	371.426i	−0.257992	−	0.708828i
$525$		0			0
$526$	−95.7927	+	80.3796i	−0.182115	+	0.152813i
$527$	−92.1942	−	109.873i	−0.174942	−	0.208487i
$528$		0			0
$529$	−496.652	+	180.767i	−0.938851	+	0.341714i
$530$	−24.4503	+	14.1164i	−0.0461327	+	0.0266347i
$531$		0			0
$532$	−39.1396	+	67.7918i	−0.0735707	+	0.127428i
$533$	475.615	+	83.8637i	0.892335	+	0.157343i
$534$		0			0
$535$	−144.621	−	52.6377i	−0.270320	−	0.0983883i
$536$	−62.8421	+	11.0808i	−0.117243	+	0.0206731i
$537$		0			0
$538$	−452.722	−	379.879i	−0.841490	−	0.706094i
$539$			802.720i			1.48928i
$540$		0			0
$541$	−656.732			−1.21392			−0.606961	−	0.794732i	$-0.707612\pi$
$541$	−656.732			−1.21392			−0.606961	+	0.794732i	$0.707612\pi$
$542$	−26.6662	+	31.7795i	−0.0491995	+	0.0586337i
$543$		0			0
$544$	−3.33395	−	18.9078i	−0.00612859	−	0.0347570i
$545$	70.5758	−	193.905i	0.129497	−	0.355790i
$546$		0			0
$547$	−73.1807	+	415.029i	−0.133786	+	0.758736i	0.841912	+	0.539615i	$0.181430\pi$
$547$	−73.1807	+	415.029i	−0.133786	+	0.758736i	−0.975698	+	0.219121i	$0.929681\pi$
$548$	−52.4270	−	30.2687i	−0.0956696	−	0.0552349i
$549$		0			0
$550$	−296.951	−	514.334i	−0.539910	−	0.935152i
$551$	−377.381	−	1036.85i	−0.684902	−	1.88175i
$552$		0			0
$553$	109.532	−	91.9078i	0.198068	−	0.166199i
$554$	171.492	+	204.376i	0.309552	+	0.368910i
$555$		0			0
$556$	−288.252	+	104.915i	−0.518439	+	0.188696i
$557$	−412.640	+	238.238i	−0.740825	+	0.427715i	−0.822369	−	0.568954i	$-0.807348\pi$
$557$	−412.640	+	238.238i	−0.740825	+	0.427715i	0.0815442	+	0.996670i	$0.474015\pi$
$558$		0			0
$559$	−422.172	+	731.223i	−0.755227	+	1.30809i
$560$	8.53291	+	1.50458i	0.0152373	+	0.00268675i
$561$		0			0
$562$	63.2035	+	23.0042i	0.112462	+	0.0409327i
$563$	206.039	−	36.3303i	0.365967	−	0.0645298i	0.0123591	−	0.999924i	$-0.496066\pi$
$563$	206.039	−	36.3303i	0.365967	−	0.0645298i	0.353608	+	0.935394i	$0.384955\pi$
$564$		0			0
$565$	−13.9163	−	11.6771i	−0.0246306	−	0.0206675i
$566$			108.110i			0.191007i
$567$		0			0
$568$	140.691			0.247695
$569$	−569.179	+	678.321i	−1.00031	+	1.19213i	−0.0189794	+	0.999820i	$0.506042\pi$
$569$	−569.179	+	678.321i	−1.00031	+	1.19213i	−0.981335	+	0.192308i	$0.938403\pi$
$570$		0			0
$571$	127.475	+	722.948i	0.223249	+	1.26611i	0.866004	+	0.500037i	$0.166680\pi$
$571$	127.475	+	722.948i	0.223249	+	1.26611i	−0.642755	+	0.766072i	$0.722209\pi$
$572$	−144.567	+	397.194i	−0.252739	+	0.694395i
$573$		0			0
$574$	−19.0148	+	107.838i	−0.0331269	+	0.187872i
$575$	−14.1426	−	8.16524i	−0.0245959	−	0.0142004i
$576$		0			0
$577$	−349.289	−	604.986i	−0.605353	−	1.04850i	−0.991996	−	0.126273i	$-0.959699\pi$
$577$	−349.289	−	604.986i	−0.605353	−	1.04850i	0.386642	−	0.922230i	$-0.373635\pi$
$578$	−134.214	−	368.751i	−0.232205	−	0.637978i
$579$		0			0
$580$	−93.5582	+	78.5047i	−0.161307	+	0.135353i
$581$	−15.6143	−	18.6084i	−0.0268748	−	0.0320282i
$582$		0			0
$583$	293.447	−	106.806i	0.503339	−	0.183200i
$584$	−221.642	+	127.965i	−0.379523	+	0.219118i
$585$		0			0
$586$	230.808	−	399.771i	0.393870	−	0.682204i
$587$	1118.40	+	197.205i	1.90529	+	0.335953i	0.996660	−	0.0816570i	$-0.0260212\pi$
$587$	1118.40	+	197.205i	1.90529	+	0.335953i	0.908626	+	0.417610i	$0.137132\pi$
$588$		0			0
$589$	812.156	+	295.601i	1.37887	+	0.501869i
$590$	−88.1557	+	15.5442i	−0.149416	+	0.0263461i
$591$		0			0
$592$	−50.5211	−	42.3922i	−0.0853396	−	0.0716085i
$593$			463.710i			0.781973i	0.920396	+	0.390987i	$0.127866\pi$
$593$			463.710i			0.781973i	−0.920396	+	0.390987i	$0.872134\pi$
$594$		0			0
$595$	−7.35191			−0.0123561
$596$	261.911	−	312.134i	0.439449	−	0.523715i
$597$		0			0
$598$	2.01823	+	11.4460i	0.00337497	+	0.0191404i
$599$	−192.617	+	529.210i	−0.321564	+	0.883489i	0.668606	+	0.743617i	$0.266891\pi$
$599$	−192.617	+	529.210i	−0.321564	+	0.883489i	−0.990170	+	0.139872i	$0.955331\pi$
$600$		0			0
$601$	122.144	−	692.715i	0.203235	−	1.15260i	−0.696958	−	0.717112i	$-0.745463\pi$
$601$	122.144	−	692.715i	0.203235	−	1.15260i	0.900193	−	0.435492i	$-0.143425\pi$
$602$	−165.794	−	95.7211i	−0.275405	−	0.159005i
$603$		0			0
$604$	132.943	+	230.265i	0.220105	+	0.381233i
$605$	−74.5148	−	204.728i	−0.123165	−	0.338393i
$606$		0			0
$607$	313.569	−	263.116i	0.516589	−	0.433470i	−0.346852	−	0.937920i	$-0.612749\pi$
$607$	313.569	−	263.116i	0.516589	−	0.433470i	0.863441	+	0.504450i	$0.168305\pi$
$608$	74.3660	+	88.6260i	0.122313	+	0.145766i
$609$		0			0
$610$	−99.8283	+	36.3345i	−0.163653	+	0.0595648i
$611$	−661.116	+	381.696i	−1.08202	+	0.624706i
$612$		0			0
$613$	55.6369	−	96.3660i	0.0907617	−	0.157204i	−0.817070	−	0.576538i	$-0.804403\pi$
$613$	55.6369	−	96.3660i	0.0907617	−	0.157204i	0.907832	+	0.419334i	$0.137737\pi$
$614$	−376.788	−	66.4379i	−0.613661	−	0.108205i
$615$		0			0
$616$	−90.0577	−	32.7783i	−0.146198	−	0.0532116i
$617$	−438.710	+	77.3564i	−0.711037	+	0.125375i	−0.517457	−	0.855709i	$-0.673121\pi$
$617$	−438.710	+	77.3564i	−0.711037	+	0.125375i	−0.193581	+	0.981084i	$0.562010\pi$
$618$		0			0
$619$	−308.760	−	259.080i	−0.498804	−	0.418546i	0.358365	−	0.933582i	$-0.383334\pi$
$619$	−308.760	−	259.080i	−0.498804	−	0.418546i	−0.857169	+	0.515035i	$0.827779\pi$
$620$		−	95.6651i		−	0.154299i
$621$		0			0
$622$	597.449			0.960530
$623$	83.1054	−	99.0411i	0.133395	−	0.158975i
$624$		0			0
$625$	92.1298	+	522.494i	0.147408	+	0.835991i
$626$	−161.959	+	444.980i	−0.258721	+	0.710831i
$627$		0			0
$628$	88.0768	−	499.508i	0.140250	−	0.795395i
$629$	48.4622	+	27.9797i	0.0770465	+	0.0444828i
$630$		0			0
$631$	−157.151	−	272.194i	−0.249052	−	0.431370i	0.714211	−	0.699930i	$-0.246786\pi$
$631$	−157.151	−	272.194i	−0.249052	−	0.431370i	−0.963263	+	0.268560i	$0.913452\pi$
$632$	−72.2766	−	198.578i	−0.114362	−	0.314206i
$633$		0			0
$634$	67.2562	−	56.4346i	0.106082	−	0.0890136i
$635$	118.917	+	141.720i	0.187271	+	0.223181i
$636$		0			0
$637$	−508.540	+	185.093i	−0.798336	+	0.290570i
$638$	1169.90	−	675.441i	1.83370	−	1.05868i
$639$		0			0
$640$	6.40290	−	11.0901i	0.0100045	−	0.0173284i
$641$	−831.894	−	146.685i	−1.29781	−	0.228838i	−0.518282	−	0.855210i	$-0.673428\pi$
$641$	−831.894	−	146.685i	−1.29781	−	0.228838i	−0.779525	+	0.626371i	$0.784539\pi$
$642$		0			0
$643$	305.658	+	111.250i	0.475363	+	0.173018i	0.568580	−	0.822628i	$-0.307493\pi$
$643$	305.658	+	111.250i	0.475363	+	0.173018i	−0.0932174	+	0.995646i	$0.529715\pi$
$644$	−2.59520	+	0.457604i	−0.00402982	+	0.000710566i
$645$		0			0
$646$	−75.1995	−	63.0999i	−0.116408	−	0.0976779i
$647$		−	1029.91i		−	1.59182i	−0.605412	−	0.795912i	$-0.706992\pi$
$647$		−	1029.91i		−	1.59182i	0.605412	−	0.795912i	$-0.293008\pi$
$648$		0			0
$649$	990.121			1.52561
$650$	257.369	−	306.721i	0.395953	−	0.471878i
$651$		0			0
$652$	−90.8304	−	515.125i	−0.139310	−	0.790069i
$653$	247.063	−	678.801i	0.378351	−	1.03951i	−0.593688	−	0.804695i	$-0.702329\pi$
$653$	247.063	−	678.801i	0.378351	−	1.03951i	0.972040	−	0.234817i	$-0.0754490\pi$
$654$		0			0
$655$	−38.8444	+	220.297i	−0.0593044	+	0.336332i
$656$	140.157	+	80.9194i	0.213653	+	0.123353i
$657$		0			0
$658$	−86.5437	−	149.898i	−0.131525	−	0.227809i
$659$	325.530	+	894.386i	0.493975	+	1.35719i	0.897014	+	0.442003i	$0.145732\pi$
$659$	325.530	+	894.386i	0.493975	+	1.35719i	−0.403038	+	0.915183i	$0.632046\pi$
$660$		0			0
$661$	149.297	−	125.275i	0.225866	−	0.189524i	−0.522831	−	0.852436i	$-0.675124\pi$
$661$	149.297	−	125.275i	0.225866	−	0.189524i	0.748697	+	0.662912i	$0.230680\pi$
$662$	−248.634	−	296.310i	−0.375579	−	0.447598i
$663$		0			0
$664$	−33.7366	+	12.2791i	−0.0508081	+	0.0184926i
$665$	38.3662	−	22.1507i	0.0576935	−	0.0333094i
$666$		0			0
$667$	18.5726	−	32.1686i	0.0278449	−	0.0482288i
$668$	−152.887	−	26.9580i	−0.228872	−	0.0403563i
$669$		0			0
$670$	33.9357	+	12.3516i	0.0506503	+	0.0184352i
$671$	1157.20	−	204.046i	1.72459	−	0.304092i
$672$		0			0
$673$	268.446	+	225.253i	0.398880	+	0.334700i	0.820060	−	0.572277i	$-0.193940\pi$
$673$	268.446	+	225.253i	0.398880	+	0.334700i	−0.421181	+	0.906977i	$0.638384\pi$
$674$			775.517i			1.15062i
$675$		0			0
$676$	53.0349			0.0784541
$677$	722.303	−	860.807i	1.06692	−	1.27150i	0.106089	−	0.994357i	$-0.466167\pi$
$677$	722.303	−	860.807i	1.06692	−	1.27150i	0.960828	−	0.277145i	$-0.0893883\pi$
$678$		0			0
$679$	−15.6649	−	88.8403i	−0.0230706	−	0.130840i
$680$	−3.71632	+	10.2105i	−0.00546517	+	0.0150154i
$681$		0			0
$682$	−183.744	+	1042.06i	−0.269419	+	1.52795i
$683$	132.500	+	76.4992i	0.193998	+	0.112005i	0.593853	−	0.804574i	$-0.297606\pi$
$683$	132.500	+	76.4992i	0.193998	+	0.112005i	−0.399855	+	0.916578i	$0.630940\pi$
$684$		0			0
$685$	17.1303	+	29.6706i	0.0250078	+	0.0433147i
$686$	−87.3244	−	239.922i	−0.127295	−	0.349740i
$687$		0			0
$688$	−216.747	+	181.872i	−0.315039	+	0.264349i
$689$	135.327	+	161.277i	0.196411	+	0.234074i
$690$		0			0
$691$	889.111	−	323.610i	1.28670	−	0.468321i	0.394059	−	0.919085i	$-0.371071\pi$
$691$	889.111	−	323.610i	1.28670	−	0.468321i	0.892643	+	0.450764i	$0.148848\pi$
$692$	−185.625	+	107.171i	−0.268244	+	0.154871i
$693$		0			0
$694$	9.10354	−	15.7678i	0.0131175	−	0.0227202i
$695$	170.966	+	30.1459i	0.245994	+	0.0433754i
$696$		0			0
$697$	−129.040	−	46.9666i	−0.185136	−	0.0673839i
$698$	−15.0108	+	2.64680i	−0.0215054	+	0.00379198i
$699$		0			0
$700$	69.5443	+	58.3546i	0.0993490	+	0.0833637i
$701$		−	250.910i		−	0.357932i	−0.983855	−	0.178966i	$-0.942725\pi$
$701$		−	250.910i		−	0.357932i	0.983855	−	0.178966i	$-0.0572752\pi$
$702$		0			0
$703$	−337.202			−0.479662
$704$	−91.0465	+	108.505i	−0.129327	+	0.154126i
$705$		0			0
$706$	−12.9229	−	73.2894i	−0.0183044	−	0.103809i
$707$	−6.60800	+	18.1553i	−0.00934653	+	0.0256794i
$708$		0			0
$709$	228.169	−	1294.01i	0.321818	−	1.82512i	−0.209333	−	0.977844i	$-0.567129\pi$
$709$	228.169	−	1294.01i	0.321818	−	1.82512i	0.531151	−	0.847277i	$-0.321760\pi$
$710$	−68.9553	−	39.8113i	−0.0971201	−	0.0560723i
$711$		0			0
$712$	−95.5416	−	165.483i	−0.134188	−	0.232420i
$713$	9.95128	+	27.3409i	0.0139569	+	0.0383463i
$714$		0			0
$715$	183.249	−	153.764i	0.256293	−	0.215055i
$716$	151.447	+	180.487i	0.211518	+	0.252078i
$717$		0			0
$718$	131.474	−	47.8528i	0.183112	−	0.0666473i
$719$	503.280	−	290.569i	0.699972	−	0.404129i	−0.107365	−	0.994220i	$-0.534241\pi$
$719$	503.280	−	290.569i	0.699972	−	0.404129i	0.807337	+	0.590091i	$0.200908\pi$
$720$		0			0
$721$	−123.709	+	214.271i	−0.171580	+	0.297185i
$722$	79.7714	+	14.0658i	0.110487	+	0.0194818i
$723$		0			0
$724$	−224.654	−	81.7675i	−0.310296	−	0.112939i
$725$	−1260.20	+	222.208i	−1.73821	+	0.306494i
$726$		0			0
$727$	−516.182	−	433.128i	−0.710016	−	0.595774i	0.214588	−	0.976705i	$-0.431159\pi$
$727$	−516.182	−	433.128i	−0.710016	−	0.595774i	−0.924604	+	0.380931i	$0.875604\pi$
$728$		−	64.6115i		−	0.0887521i
$729$		0			0
$730$	144.841			0.198413
$731$	154.319	−	183.911i	0.211107	−	0.251588i
$732$		0			0
$733$	43.1418	+	244.669i	0.0588565	+	0.333792i	0.999991	−	0.00424043i	$-0.00134977\pi$
$733$	43.1418	+	244.669i	0.0588565	+	0.333792i	−0.941134	+	0.338032i	$0.890239\pi$
$734$	246.054	−	676.029i	0.335224	−	0.921020i
$735$		0			0
$736$	−0.676318	+	3.83559i	−0.000918910	+	0.00521140i
$737$	−345.932	−	199.724i	−0.469379	−	0.270996i
$738$		0			0
$739$	−21.7967	−	37.7530i	−0.0294949	−	0.0510866i	0.850901	−	0.525326i	$-0.176057\pi$
$739$	−21.7967	−	37.7530i	−0.0294949	−	0.0510866i	−0.880396	+	0.474239i	$0.842723\pi$
$740$	12.7656	+	35.0732i	0.0172508	+	0.0473963i
$741$		0			0
$742$	−36.5671	+	30.6834i	−0.0492818	+	0.0413524i
$743$	−805.304	−	959.724i	−1.08385	−	1.29169i	−0.953886	−	0.300169i	$-0.902957\pi$
$743$	−805.304	−	959.724i	−1.08385	−	1.29169i	−0.129968	−	0.991518i	$-0.541488\pi$
$744$		0			0
$745$	−216.693	+	78.8697i	−0.290863	+	0.105865i
$746$	537.825	−	310.513i	0.720945	−	0.416238i
$747$		0			0
$748$	60.0925	−	104.083i	0.0803376	−	0.139149i
$749$	−256.259	−	45.1854i	−0.342135	−	0.0603277i
$750$		0			0
$751$	−81.7809	−	29.7658i	−0.108896	−	0.0396349i	0.286998	−	0.957931i	$-0.407343\pi$
$751$	−81.7809	−	29.7658i	−0.108896	−	0.0396349i	−0.395894	+	0.918296i	$0.629565\pi$
$752$	−251.929	+	44.4218i	−0.335012	+	0.0590716i
$753$		0			0
$754$	697.664	+	585.409i	0.925283	+	0.776405i
$755$		−	150.476i		−	0.199307i
$756$		0			0
$757$	−849.639			−1.12238			−0.561188	−	0.827688i	$-0.689656\pi$
$757$	−849.639			−1.12238			−0.561188	+	0.827688i	$0.689656\pi$
$758$	−196.481	+	234.157i	−0.259209	+	0.308914i
$759$		0			0
$760$	−11.3697	−	64.4807i	−0.0149601	−	0.0848431i
$761$	218.959	−	601.584i	0.287725	−	0.790518i	−0.708659	−	0.705551i	$-0.750700\pi$
$761$	218.959	−	601.584i	0.287725	−	0.790518i	0.996384	−	0.0849663i	$-0.0270783\pi$
$762$		0			0
$763$	60.5838	−	343.588i	0.0794021	−	0.450312i
$764$	−393.578	−	227.232i	−0.515154	−	0.297424i
$765$		0			0
$766$	464.168	+	803.963i	0.605964	+	1.04956i
$767$	228.305	+	627.262i	0.297659	+	0.817812i
$768$		0			0
$769$	−129.861	+	108.966i	−0.168869	+	0.141698i	−0.723306	−	0.690528i	$-0.757378\pi$
$769$	−129.861	+	108.966i	−0.168869	+	0.141698i	0.554436	+	0.832226i	$0.312934\pi$
$770$	34.8638	+	41.5490i	0.0452776	+	0.0539598i
$771$		0			0
$772$	138.065	−	50.2514i	0.178840	−	0.0650925i
$773$	−1141.45	+	659.019i	−1.47666	+	0.852547i	−0.999653	−	0.0263542i	$-0.991610\pi$
$773$	−1141.45	+	659.019i	−1.47666	+	0.852547i	−0.477003	+	0.878902i	$0.658277\pi$
$774$		0			0
$775$	501.170	−	868.052i	0.646671	−	1.12007i
$776$	−131.302	−	23.1521i	−0.169203	−	0.0298351i
$777$		0			0
$778$	314.592	+	114.502i	0.404360	+	0.147175i
$779$	814.904	−	143.690i	1.04609	−	0.184454i
$780$		0			0
$781$	674.652	+	566.101i	0.863832	+	0.724841i
$782$		−	3.30472i		−	0.00422599i
$783$		0			0
$784$	−181.350			−0.231314
$785$	−184.514	+	219.896i	−0.235050	+	0.280122i
$786$		0			0
$787$	−199.680	−	1132.44i	−0.253723	−	1.43893i	−0.799331	−	0.600891i	$-0.794812\pi$
$787$	−199.680	−	1132.44i	−0.253723	−	1.43893i	0.545608	−	0.838040i	$-0.316299\pi$
$788$	−63.2321	+	173.729i	−0.0802438	+	0.220468i
$789$		0			0
$790$	−20.7677	+	117.779i	−0.0262882	+	0.149088i
$791$	−26.6001	−	15.3575i	−0.0336284	−	0.0194154i
$792$		0			0
$793$	396.098	+	686.061i	0.499492	+	0.865146i
$794$	145.629	+	400.113i	0.183412	+	0.503921i
$795$		0			0
$796$	6.04414	−	5.07163i	0.00759314	−	0.00637140i
$797$	−97.8409	−	116.602i	−0.122762	−	0.146301i	0.701163	−	0.713001i	$-0.252664\pi$
$797$	−97.8409	−	116.602i	−0.122762	−	0.146301i	−0.823925	+	0.566699i	$0.808220\pi$
$798$		0			0
$799$	203.970	−	74.2390i	0.255282	−	0.0929149i
$800$	116.198	−	67.0870i	0.145248	−	0.0838588i
$801$		0			0
$802$	24.9879	−	43.2803i	0.0311570	−	0.0539655i
$803$	−1577.73	−	278.197i	−1.96480	−	0.346447i
$804$		0			0
$805$	1.40145	+	0.510086i	0.00174093	+	0.000633647i
$806$	−702.537	+	123.876i	−0.871634	+	0.153693i
$807$		0			0
$808$	21.8742	+	18.3547i	0.0270721	+	0.0227162i
$809$		−	1046.40i		−	1.29345i	−0.762725	−	0.646723i	$-0.776139\pi$
$809$		−	1046.40i		−	1.29345i	0.762725	−	0.646723i	$-0.223861\pi$
$810$		0			0
$811$	−360.583			−0.444615			−0.222308	−	0.974977i	$-0.571359\pi$
$811$	−360.583			−0.444615			−0.222308	+	0.974977i	$0.571359\pi$
$812$	−132.733	+	158.185i	−0.163464	+	0.194809i
$813$		0			0
$814$	−71.6885	−	406.566i	−0.0880695	−	0.499467i
$815$	−101.248	+	278.175i	−0.124230	+	0.341319i
$816$		0			0
$817$	−251.212	+	1424.70i	−0.307481	+	1.74381i
$818$	325.534	+	187.947i	0.397963	+	0.229764i
$819$		0			0
$820$	−45.7957	−	79.3204i	−0.0558484	−	0.0967322i
$821$	519.549	+	1427.45i	0.632824	+	1.73867i	0.673173	+	0.739485i	$0.264931\pi$
$821$	519.549	+	1427.45i	0.632824	+	1.73867i	−0.0403490	+	0.999186i	$0.512847\pi$
$822$		0			0
$823$	−647.973	+	543.714i	−0.787331	+	0.660649i	−0.945083	−	0.326830i	$-0.894020\pi$
$823$	−647.973	+	543.714i	−0.787331	+	0.660649i	0.157753	+	0.987479i	$0.449575\pi$
$824$	235.050	+	280.122i	0.285255	+	0.339954i
$825$		0			0
$826$	−142.222	+	51.7646i	−0.172182	+	0.0626690i
$827$	939.412	−	542.370i	1.13593	−	0.655828i	0.190508	−	0.981686i	$-0.438986\pi$
$827$	939.412	−	542.370i	1.13593	−	0.655828i	0.945419	+	0.325858i	$0.105653\pi$
$828$		0			0
$829$	−765.727	+	1326.28i	−0.923675	+	1.59985i	−0.129997	+	0.991514i	$0.541497\pi$
$829$	−765.727	+	1326.28i	−0.923675	+	1.59985i	−0.793678	+	0.608338i	$0.791836\pi$
$830$	20.0096	+	3.52823i	0.0241079	+	0.00425088i
$831$		0			0
$832$	−89.7339	−	32.6605i	−0.107853	−	0.0392554i
$833$	151.539	−	26.7204i	0.181919	−	0.0320773i
$834$		0			0
$835$	67.3044	+	56.4751i	0.0806041	+	0.0676348i
$836$			724.216i			0.866287i
$837$		0			0
$838$	653.728			0.780105
$839$	−83.5716	+	99.5967i	−0.0996085	+	0.118709i	−0.813546	−	0.581501i	$-0.802466\pi$
$839$	−83.5716	+	99.5967i	−0.0996085	+	0.118709i	0.713937	+	0.700210i	$0.246910\pi$
$840$		0			0
$841$	−359.394	−	2038.22i	−0.427341	−	2.42357i
$842$	−383.180	+	1052.78i	−0.455084	+	1.25033i
$843$		0			0
$844$	21.0972	−	119.648i	0.0249967	−	0.141763i
$845$	−25.9935	−	15.0073i	−0.0307615	−	0.0177602i
$846$		0			0
$847$	−184.180	−	319.010i	−0.217450	−	0.376635i
$848$	24.1295	+	66.2954i	0.0284547	+	0.0781785i
$849$		0			0
$850$	−87.2121	+	73.1796i	−0.102602	+	0.0860937i
$851$	−7.29679	−	8.69597i	−0.00857437	−	0.0102185i
$852$		0			0
$853$	440.159	−	160.205i	0.516012	−	0.187813i	−0.0708696	−	0.997486i	$-0.522577\pi$
$853$	440.159	−	160.205i	0.516012	−	0.187813i	0.586882	+	0.809672i	$0.300355\pi$
$854$	−155.554	+	89.8091i	−0.182148	+	0.105163i
$855$		0			0
$856$	−192.291	+	333.058i	−0.224639	+	0.389086i
$857$	871.104	+	153.599i	1.01646	+	0.179229i	0.656967	−	0.753920i	$-0.271839\pi$
$857$	871.104	+	153.599i	1.01646	+	0.179229i	0.359491	+	0.933149i	$0.382950\pi$
$858$		0			0
$859$	−405.595	−	147.624i	−0.472171	−	0.171856i	0.0949648	−	0.995481i	$-0.469726\pi$
$859$	−405.595	−	147.624i	−0.472171	−	0.171856i	−0.567135	+	0.823625i	$0.691948\pi$
$860$	157.696	−	27.8061i	0.183368	−	0.0323327i
$861$		0			0
$862$	−231.810	−	194.512i	−0.268921	−	0.225652i
$863$		−	279.578i		−	0.323961i	−0.986794	−	0.161980i	$-0.948212\pi$
$863$		−	279.578i		−	0.323961i	0.986794	−	0.161980i	$-0.0517881\pi$
$864$		0			0
$865$	121.305			0.140236
$866$	−111.126	+	132.435i	−0.128321	+	0.152927i
$867$		0			0
$868$	−28.0871	−	159.290i	−0.0323584	−	0.183513i
$869$	452.437	−	1243.06i	0.520641	−	1.43045i
$870$		0			0
$871$	46.7633	−	265.208i	0.0536892	−	0.304487i
$872$	−446.558	−	257.820i	−0.512108	−	0.295666i
$873$		0			0
$874$	9.95687	+	17.2458i	0.0113923	+	0.0197320i
$875$	−36.0940	−	99.1673i	−0.0412502	−	0.113334i
$876$		0			0
$877$	−1227.88	+	1030.31i	−1.40009	+	1.17482i	−0.439033	+	0.898471i	$0.644679\pi$
$877$	−1227.88	+	1030.31i	−1.40009	+	1.17482i	−0.961058	+	0.276346i	$0.910877\pi$
$878$	121.374	+	144.648i	0.138239	+	0.164747i
$879$		0			0
$880$	75.3275	−	27.4170i	0.0855994	−	0.0311556i
$881$	−37.7796	+	21.8121i	−0.0428827	+	0.0247583i	−0.521288	−	0.853381i	$-0.674548\pi$
$881$	−37.7796	+	21.8121i	−0.0428827	+	0.0247583i	0.478405	+	0.878139i	$0.341215\pi$
$882$		0			0
$883$	−460.205	+	797.099i	−0.521184	+	0.902717i	0.478513	+	0.878081i	$0.341176\pi$
$883$	−460.205	+	797.099i	−0.521184	+	0.902717i	−0.999696	+	0.0246363i	$0.992157\pi$
$884$	79.7952	+	14.0700i	0.0902660	+	0.0159163i
$885$		0			0
$886$	−187.724	−	68.3260i	−0.211878	−	0.0771174i
$887$	233.205	−	41.1203i	0.262914	−	0.0463588i	−0.0406372	−	0.999174i	$-0.512939\pi$
$887$	233.205	−	41.1203i	0.262914	−	0.0463588i	0.303551	+	0.952815i	$0.401828\pi$
$888$		0			0
$889$	239.614	+	201.060i	0.269533	+	0.226165i
$890$			108.142i			0.121508i
$891$		0			0
$892$	325.022			0.364374
$893$	−840.748	+	1001.96i	−0.941487	+	1.12202i
$894$		0			0
$895$	−23.1545	−	131.316i	−0.0258709	−	0.146721i
$896$	7.40527	−	20.3458i	0.00826481	−	0.0227074i
$897$		0			0
$898$	−4.01190	+	22.7526i	−0.00446760	+	0.0253370i
$899$	1974.46	+	1139.96i	2.19629	+	1.26803i
$900$		0			0
$901$	−29.9310	−	51.8421i	−0.0332198	−	0.0575384i
$902$	346.494	+	951.984i	0.384140	+	1.05541i
$903$		0			0
$904$	−34.7750	+	29.1797i	−0.0384679	+	0.0322784i
$905$	86.9698	+	103.647i	0.0960992	+	0.114527i
$906$		0			0
$907$	302.489	−	110.097i	0.333505	−	0.121386i	−0.169839	−	0.985472i	$-0.554325\pi$
$907$	302.489	−	110.097i	0.333505	−	0.121386i	0.503345	+	0.864086i	$0.332103\pi$
$908$	453.915	−	262.068i	0.499907	−	0.288621i
$909$		0			0
$910$	−18.2832	+	31.6674i	−0.0200914	+	0.0347993i
$911$	1105.64	+	194.955i	1.21366	+	0.214001i	0.743595	−	0.668631i	$-0.233119\pi$
$911$	1105.64	+	194.955i	1.21366	+	0.214001i	0.470065	+	0.882632i	$0.344230\pi$
$912$		0			0
$913$	−211.184	−	76.8648i	−0.231308	−	0.0841893i
$914$	751.188	−	132.455i	0.821869	−	0.144918i
$915$		0			0
$916$	186.248	+	156.281i	0.203328	+	0.170612i
$917$			378.217i			0.412450i
$918$		0			0
$919$	−486.580			−0.529467			−0.264734	−	0.964322i	$-0.585284\pi$
$919$	−486.580			−0.529467			−0.264734	+	0.964322i	$0.585284\pi$
$920$	1.41684	−	1.68852i	0.00154004	−	0.00183535i
$921$		0			0
$922$	88.9219	+	504.301i	0.0964446	+	0.546965i
$923$	−203.073	+	557.939i	−0.220014	+	0.604484i
$924$		0			0
$925$	−67.9082	+	385.127i	−0.0734143	+	0.416353i
$926$	−233.494	−	134.808i	−0.252153	−	0.145581i
$927$		0			0
$928$	152.595	+	264.303i	0.164435	+	0.284809i
$929$	−264.986	−	728.043i	−0.285238	−	0.783684i	−0.996716	−	0.0809762i	$-0.974196\pi$
$929$	−264.986	−	728.043i	−0.285238	−	0.783684i	0.711478	−	0.702708i	$-0.248026\pi$
$930$		0			0
$931$	−710.304	+	596.016i	−0.762947	+	0.640189i
$932$	−538.782	−	642.095i	−0.578092	−	0.688943i
$933$		0			0
$934$	946.818	−	344.614i	1.01372	−	0.368965i
$935$	−58.9050	+	34.0088i	−0.0630000	+	0.0363731i
$936$		0			0
$937$	310.767	−	538.264i	0.331661	−	0.574454i	−0.651176	−	0.758926i	$-0.725724\pi$
$937$	310.767	−	538.264i	0.331661	−	0.574454i	0.982838	+	0.184472i	$0.0590575\pi$
$938$	60.1319	+	10.6029i	0.0641065	+	0.0113037i
$939$		0			0
$940$	136.045	+	49.5165i	0.144729	+	0.0526771i
$941$	−1840.64	+	324.554i	−1.95604	+	0.344903i	−0.957669	+	0.287870i	$0.907053\pi$
$941$	−1840.64	+	324.554i	−1.95604	+	0.344903i	−0.998372	+	0.0570327i	$0.981836\pi$
$942$		0			0
$943$	21.3394	+	17.9059i	0.0226293	+	0.0189882i
$944$			223.688i			0.236957i
$945$		0			0
$946$	−1771.17			−1.87227
$947$	339.780	−	404.935i	0.358797	−	0.427597i	−0.556206	−	0.831044i	$-0.687744\pi$
$947$	339.780	−	404.935i	0.358797	−	0.427597i	0.915003	+	0.403447i	$0.132188\pi$
$948$		0			0
$949$	−187.554	−	1063.67i	−0.197634	−	1.12084i
$950$	234.635	−	644.653i	0.246984	−	0.678583i
$951$		0			0
$952$	−3.19017	+	18.0923i	−0.00335102	+	0.0190046i
$953$	−226.233	−	130.616i	−0.237391	−	0.137058i	0.376586	−	0.926382i	$-0.377098\pi$
$953$	−226.233	−	130.616i	−0.237391	−	0.137058i	−0.613977	+	0.789324i	$0.710431\pi$
$954$		0			0
$955$	128.600	+	222.742i	0.134660	+	0.233238i
$956$	71.5346	+	196.540i	0.0748270	+	0.205585i
$957$		0			0
$958$	247.485	−	207.665i	0.258335	−	0.216769i
$959$	37.2345	+	44.3744i	0.0388264	+	0.0462715i
$960$		0			0
$961$	−775.100	+	282.113i	−0.806556	+	0.293562i
$962$	241.038	−	139.163i	0.250559	−	0.144660i
$963$		0			0
$964$	47.3730	−	82.0524i	0.0491421	−	0.0851166i
$965$	−81.8878	−	14.4390i	−0.0848579	−	0.0149627i
$966$		0			0
$967$	1645.56	+	598.934i	1.70172	+	0.619374i	0.996019	−	0.0891408i	$-0.0284121\pi$
$967$	1645.56	+	598.934i	1.70172	+	0.619374i	0.705696	+	0.708515i	$0.250634\pi$
$968$	−536.149	+	94.5375i	−0.553873	+	0.0976628i
$969$		0			0
$970$	57.8023	+	48.5019i	0.0595900	+	0.0500019i
$971$		−	718.037i		−	0.739482i	−0.929135	−	0.369741i	$-0.879446\pi$
$971$		−	718.037i		−	0.739482i	0.929135	−	0.369741i	$-0.120554\pi$
$972$		0			0
$973$	293.522			0.301667
$974$	−105.004	+	125.138i	−0.107807	+	0.128479i
$975$		0			0
$976$	46.0979	+	261.434i	0.0472315	+	0.267863i
$977$	−359.573	+	987.919i	−0.368038	+	1.01118i	0.608069	+	0.793884i	$0.291944\pi$
$977$	−359.573	+	987.919i	−0.368038	+	1.01118i	−0.976107	+	0.217291i	$0.930278\pi$
$978$		0			0
$979$	207.708	−	1177.97i	0.212164	−	1.20324i
$980$	88.8834	+	51.3168i	0.0906973	+	0.0523641i
$981$		0			0
$982$	−311.984	−	540.372i	−0.317703	−	0.550277i
$983$	280.070	+	769.486i	0.284913	+	0.782793i	0.996758	+	0.0804562i	$0.0256377\pi$
$983$	280.070	+	769.486i	0.284913	+	0.782793i	−0.711845	+	0.702337i	$0.752140\pi$
$984$		0			0
$985$	80.1515	−	67.2551i	0.0813721	−	0.0682793i
$986$	−166.454	−	198.372i	−0.168817	−	0.201188i
$987$		0			0
$988$	−458.806	+	166.992i	−0.464378	+	0.169020i
$989$	−42.1769	+	24.3509i	−0.0426460	+	0.0246217i
$990$		0			0
$991$	433.521	−	750.880i	0.437458	−	0.757699i	−0.560035	−	0.828469i	$-0.689212\pi$
$991$	433.521	−	750.880i	0.437458	−	0.757699i	0.997493	+	0.0707698i	$0.0225456\pi$
$992$	−235.423	−	41.5114i	−0.237321	−	0.0418461i
$993$		0			0
$994$	−126.504	−	46.0438i	−0.127268	−	0.0463217i
$995$	−4.39747	+	0.775393i	−0.00441957	+	0.000779290i
$996$		0			0
$997$	−502.010	−	421.237i	−0.503521	−	0.422504i	0.355321	−	0.934744i	$-0.384371\pi$
$997$	−502.010	−	421.237i	−0.503521	−	0.422504i	−0.858842	+	0.512240i	$0.828816\pi$
$998$			399.219i			0.400019i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	162.3.f.a.35.2		36
3.2	odd	2		54.3.f.a.11.6	yes	36
12.11	even	2		432.3.bc.c.65.2		36
27.5	odd	18	inner	162.3.f.a.125.2		36
27.7	even	9		1458.3.b.c.1457.26		36
27.20	odd	18		1458.3.b.c.1457.11		36
27.22	even	9		54.3.f.a.5.6	✓	36
108.103	odd	18		432.3.bc.c.113.2		36

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
54.3.f.a.5.6	✓	36	27.22	even	9
54.3.f.a.11.6	yes	36	3.2	odd	2
162.3.f.a.35.2		36	1.1	even	1	trivial
162.3.f.a.125.2		36	27.5	odd	18	inner
432.3.bc.c.65.2		36	12.11	even	2
432.3.bc.c.113.2		36	108.103	odd	18
1458.3.b.c.1457.11		36	27.20	odd	18
1458.3.b.c.1457.26		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)

\(f(q)\)	\(=\)	\(q+(-0.909039 + 1.08335i) q^{2} +(-0.347296 - 1.96962i) q^{4} +(-0.387127 + 1.06362i) q^{5} +(-0.332318 + 1.88467i) q^{7} +(2.44949 + 1.41421i) q^{8} +O(q^{10})\)	\(q+(-0.909039 + 1.08335i) q^{2} +(-0.347296 - 1.96962i) q^{4} +(-0.387127 + 1.06362i) q^{5} +(-0.332318 + 1.88467i) q^{7} +(2.44949 + 1.41421i) q^{8} +(-0.800362 - 1.38627i) q^{10} +(6.05561 + 16.6376i) q^{11} +(-9.14397 + 7.67270i) q^{13} +(-1.73967 - 2.07326i) q^{14} +(-3.75877 + 1.36808i) q^{16} +(2.93931 - 1.69701i) q^{17} +(-10.2259 + 17.7118i) q^{19} +(2.22937 + 0.393099i) q^{20} +(-23.5292 - 8.56392i) q^{22} +(-0.678043 + 0.119557i) q^{23} +(18.1697 + 15.2462i) q^{25} -16.8809i q^{26} +3.82749 q^{28} +(-34.6788 + 41.3286i) q^{29} +(-7.33824 - 41.6172i) q^{31} +(1.93476 - 5.31570i) q^{32} +(-0.833488 + 4.72695i) q^{34} +(-1.87593 - 1.08307i) q^{35} +(8.24382 + 14.2787i) q^{37} +(-9.89233 - 27.1790i) q^{38} +(-2.45245 + 2.05785i) q^{40} +(-26.0070 - 30.9939i) q^{41} +(66.4698 - 24.1930i) q^{43} +(30.6667 - 17.7054i) q^{44} +(0.486845 - 0.843240i) q^{46} +(62.9822 + 11.1055i) q^{47} +(42.6034 + 15.5064i) q^{49} +(-33.0339 + 5.82477i) q^{50} +(18.2879 + 15.3454i) q^{52} -17.6375i q^{53} -20.0405 q^{55} +(-3.47934 + 4.14651i) q^{56} +(-13.2490 - 75.1385i) q^{58} +(19.1264 - 52.5494i) q^{59} +(11.5245 - 65.3586i) q^{61} +(51.7568 + 29.8818i) q^{62} +(4.00000 + 6.92820i) q^{64} +(-4.62098 - 12.6960i) q^{65} +(-17.2826 + 14.5018i) q^{67} +(-4.36327 - 5.19994i) q^{68} +(2.87864 - 1.04774i) q^{70} +(43.0775 - 24.8708i) q^{71} +(-45.2424 + 78.3622i) q^{73} +(-22.9628 - 4.04896i) q^{74} +(38.4369 + 13.9899i) q^{76} +(-33.3689 + 5.88383i) q^{77} +(-57.2341 - 48.0251i) q^{79} -4.52753i q^{80} +57.2187 q^{82} +(-8.15901 + 9.72353i) q^{83} +(0.667093 + 3.78327i) q^{85} +(-34.2141 + 94.0025i) q^{86} +(-8.69603 + 49.3177i) q^{88} +(-58.5070 - 33.7790i) q^{89} +(-11.4218 - 19.7832i) q^{91} +(0.470964 + 1.29396i) q^{92} +(-69.2844 + 58.1365i) q^{94} +(-14.8799 - 17.7332i) q^{95} +(-44.2956 + 16.1223i) q^{97} +(-55.5270 + 32.0585i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 36 q - 18 q^{5}+O(q^{10}) \) 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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