LMFDB - Embedded newform 432.3.x.a.125.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [432,3,Mod(125,432)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(432, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([0, 9, 10]))

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

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

chi := DirichletCharacter("432.125");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 432 = 2^{4} \cdot 3^{3} $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	432.x (of order $12$, degree $4$, 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:	$11.7711474204$
Analytic rank:	$0$
Dimension:	$184$
Relative dimension:	$46$ over $\Q(\zeta_{12})$
Twist minimal:	no (minimal twist has level 144)
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			125.4
Character	$\chi$	$=$	432.125
Dual form			432.3.x.a.197.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.93717 - 0.497372i) q^{2} +(3.50524 + 1.92699i) q^{4} +(5.08604 - 1.36280i) q^{5} +(-9.00556 + 5.19936i) q^{7} +(-5.83182 - 5.47630i) q^{8} +O(q^{10})$	\(q+(-1.93717 - 0.497372i) q^{2} +(3.50524 + 1.92699i) q^{4} +(5.08604 - 1.36280i) q^{5} +(-9.00556 + 5.19936i) q^{7} +(-5.83182 - 5.47630i) q^{8} +(-10.5303 + 0.110321i) q^{10} +(0.522615 - 1.95043i) q^{11} +(17.4082 - 4.66453i) q^{13} +(20.0313 - 5.59293i) q^{14} +(8.57345 + 13.5091i) q^{16} -16.8015i q^{17} +(15.0950 + 15.0950i) q^{19} +(20.4539 + 5.02378i) q^{20} +(-1.98248 + 3.51837i) q^{22} +(-1.96438 + 3.40240i) q^{23} +(2.35994 - 1.36251i) q^{25} +(-36.0427 + 0.377601i) q^{26} +(-41.5858 + 0.871442i) q^{28} +(20.3777 + 5.46018i) q^{29} +(-14.4363 + 25.0043i) q^{31} +(-9.88917 - 30.4336i) q^{32} +(-8.35659 + 32.5473i) q^{34} +(-38.7169 + 38.7169i) q^{35} +(45.5055 - 45.5055i) q^{37} +(-21.7338 - 36.7495i) q^{38} +(-37.1240 - 19.9051i) q^{40} +(-21.3096 + 36.9093i) q^{41} +(62.7774 + 16.8212i) q^{43} +(5.59034 - 5.82965i) q^{44} +(5.49759 - 5.61400i) q^{46} +(34.8888 - 20.1431i) q^{47} +(29.5667 - 51.2110i) q^{49} +(-5.24928 + 1.46565i) q^{50} +(70.0086 + 17.1951i) q^{52} +(44.7349 + 44.7349i) q^{53} -10.6322i q^{55} +(80.9920 + 18.9955i) q^{56} +(-36.7593 - 20.7126i) q^{58} +(46.6277 - 12.4938i) q^{59} +(-11.8435 + 44.2007i) q^{61} +(40.4019 - 41.2574i) q^{62} +(4.02018 + 63.8736i) q^{64} +(82.1822 - 47.4479i) q^{65} +(89.1859 - 23.8973i) q^{67} +(32.3762 - 58.8933i) q^{68} +(94.2579 - 55.7445i) q^{70} +33.5395 q^{71} -22.2616i q^{73} +(-110.785 + 65.5187i) q^{74} +(23.8238 + 81.9997i) q^{76} +(5.43453 + 20.2819i) q^{77} +(-52.9631 - 91.7348i) q^{79} +(62.0151 + 57.0239i) q^{80} +(59.6379 - 60.9007i) q^{82} +(-43.5372 - 11.6657i) q^{83} +(-22.8971 - 85.4530i) q^{85} +(-113.244 - 63.8092i) q^{86} +(-13.7289 + 8.51253i) q^{88} -43.8448 q^{89} +(-132.518 + 132.518i) q^{91} +(-13.4420 + 8.14091i) q^{92} +(-77.6042 + 21.6678i) q^{94} +(97.3455 + 56.2024i) q^{95} +(56.4536 + 97.7805i) q^{97} +(-82.7466 + 84.4987i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 184 q + 6 q^{2} - 2 q^{4} + 6 q^{5}+O(q^{10}) $ 184 * q + 6 * q^2 - 2 * q^4 + 6 * q^5	$ 184 q + 6 q^{2} - 2 q^{4} + 6 q^{5} - 8 q^{10} + 6 q^{11} - 2 q^{13} + 6 q^{14} - 2 q^{16} - 8 q^{19} - 120 q^{20} - 2 q^{22} - 72 q^{28} + 6 q^{29} - 4 q^{31} + 6 q^{32} + 6 q^{34} - 8 q^{37} + 6 q^{38} - 2 q^{40} - 2 q^{43} - 160 q^{46} + 12 q^{47} + 472 q^{49} - 228 q^{50} - 2 q^{52} + 300 q^{56} - 92 q^{58} + 438 q^{59} - 2 q^{61} + 244 q^{64} + 12 q^{65} - 2 q^{67} + 144 q^{68} + 96 q^{70} - 246 q^{74} - 158 q^{76} + 6 q^{77} - 4 q^{79} - 388 q^{82} + 726 q^{83} + 48 q^{85} - 894 q^{86} + 22 q^{88} - 204 q^{91} + 348 q^{92} - 18 q^{94} + 12 q^{95} - 4 q^{97}+O(q^{100}) $ 184 * q + 6 * q^2 - 2 * q^4 + 6 * q^5 - 8 * q^10 + 6 * q^11 - 2 * q^13 + 6 * q^14 - 2 * q^16 - 8 * q^19 - 120 * q^20 - 2 * q^22 - 72 * q^28 + 6 * q^29 - 4 * q^31 + 6 * q^32 + 6 * q^34 - 8 * q^37 + 6 * q^38 - 2 * q^40 - 2 * q^43 - 160 * q^46 + 12 * q^47 + 472 * q^49 - 228 * q^50 - 2 * q^52 + 300 * q^56 - 92 * q^58 + 438 * q^59 - 2 * q^61 + 244 * q^64 + 12 * q^65 - 2 * q^67 + 144 * q^68 + 96 * q^70 - 246 * q^74 - 158 * q^76 + 6 * q^77 - 4 * q^79 - 388 * q^82 + 726 * q^83 + 48 * q^85 - 894 * q^86 + 22 * q^88 - 204 * q^91 + 348 * q^92 - 18 * q^94 + 12 * q^95 - 4 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/432\mathbb{Z}\right)^\times$.

$n$	$271$	$325$	$353$
$\chi(n)$	$1$	$e\left(\frac{3}{4}\right)$	$e\left(\frac{5}{6}\right)$

Coefficient data

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

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

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

$2$	−1.93717	−	0.497372i	−0.968584	−	0.248686i
$2$	−1.93717	−	0.497372i	−0.968584	−	0.248686i
$3$		0			0
$3$		0			0
$4$	3.50524	+	1.92699i	0.876311	+	0.481746i
$5$	5.08604	−	1.36280i	1.01721	−	0.272560i	0.288570	−	0.957459i	$-0.406820\pi$
$5$	5.08604	−	1.36280i	1.01721	−	0.272560i	0.728638	+	0.684899i	$0.240154\pi$
$6$		0			0
$7$	−9.00556	+	5.19936i	−1.28651	+	0.742766i	−0.978030	−	0.208466i	$-0.933153\pi$
$7$	−9.00556	+	5.19936i	−1.28651	+	0.742766i	−0.308478	+	0.951231i	$0.599820\pi$
$8$	−5.83182	−	5.47630i	−0.728977	−	0.684538i
$9$		0			0
$10$	−10.5303	+	0.110321i	−1.05303	+	0.0110321i
$11$	0.522615	−	1.95043i	0.0475105	−	0.177312i	−0.938093	−	0.346382i	$-0.887410\pi$
$11$	0.522615	−	1.95043i	0.0475105	−	0.177312i	0.985604	+	0.169071i	$0.0540767\pi$
$12$		0			0
$13$	17.4082	−	4.66453i	1.33910	−	0.358810i	0.482997	−	0.875622i	$-0.339548\pi$
$13$	17.4082	−	4.66453i	1.33910	−	0.358810i	0.856099	+	0.516812i	$0.172881\pi$
$14$	20.0313	−	5.59293i	1.43081	−	0.399495i
$15$		0			0
$16$	8.57345	+	13.5091i	0.535841	+	0.844319i
$17$		−	16.8015i		−	0.988323i	−0.869370	−	0.494161i	$-0.835475\pi$
$17$		−	16.8015i		−	0.988323i	0.869370	−	0.494161i	$-0.164525\pi$
$18$		0			0
$19$	15.0950	+	15.0950i	0.794476	+	0.794476i	0.982218	−	0.187743i	$-0.0601171\pi$
$19$	15.0950	+	15.0950i	0.794476	+	0.794476i	−0.187743	+	0.982218i	$0.560117\pi$
$20$	20.4539	+	5.02378i	1.02270	+	0.251189i
$21$		0			0
$22$	−1.98248	+	3.51837i	−0.0901128	+	0.159926i
$23$	−1.96438	+	3.40240i	−0.0854077	+	0.147930i	−0.905565	−	0.424208i	$-0.860553\pi$
$23$	−1.96438	+	3.40240i	−0.0854077	+	0.147930i	0.820157	+	0.572138i	$0.193886\pi$
$24$		0			0
$25$	2.35994	−	1.36251i	0.0943977	−	0.0545006i
$26$	−36.0427	+	0.377601i	−1.38626	+	0.0145231i
$27$		0			0
$28$	−41.5858	+	0.871442i	−1.48521	+	0.0311229i
$29$	20.3777	+	5.46018i	0.702679	+	0.188282i	0.592430	−	0.805622i	$-0.298169\pi$
$29$	20.3777	+	5.46018i	0.702679	+	0.188282i	0.110248	+	0.993904i	$0.464835\pi$
$30$		0			0
$31$	−14.4363	+	25.0043i	−0.465686	+	0.806592i	−0.999232	−	0.0391791i	$-0.987526\pi$
$31$	−14.4363	+	25.0043i	−0.465686	+	0.806592i	0.533546	+	0.845771i	$0.320859\pi$
$32$	−9.88917	−	30.4336i	−0.309037	−	0.951050i
$33$		0			0
$34$	−8.35659	+	32.5473i	−0.245782	+	0.957274i
$35$	−38.7169	+	38.7169i	−1.10620	+	1.10620i
$36$		0			0
$37$	45.5055	−	45.5055i	1.22988	−	1.22988i	0.265871	−	0.964009i	$-0.414341\pi$
$37$	45.5055	−	45.5055i	1.22988	−	1.22988i	0.964009	−	0.265871i	$-0.0856594\pi$
$38$	−21.7338	−	36.7495i	−0.571942	−	0.967091i
$39$		0			0
$40$	−37.1240	−	19.9051i	−0.928099	−	0.497628i
$41$	−21.3096	+	36.9093i	−0.519746	+	0.900226i	0.479991	+	0.877274i	$0.340640\pi$
$41$	−21.3096	+	36.9093i	−0.519746	+	0.900226i	−0.999737	+	0.0229527i	$0.992693\pi$
$42$		0			0
$43$	62.7774	+	16.8212i	1.45994	+	0.391190i	0.899469	−	0.436984i	$-0.143953\pi$
$43$	62.7774	+	16.8212i	1.45994	+	0.391190i	0.560471	+	0.828174i	$0.310620\pi$
$44$	5.59034	−	5.82965i	0.127053	−	0.132492i
$45$		0			0
$46$	5.49759	−	5.61400i	0.119513	−	0.122043i
$47$	34.8888	−	20.1431i	0.742316	−	0.428576i	−0.0805948	−	0.996747i	$-0.525682\pi$
$47$	34.8888	−	20.1431i	0.742316	−	0.428576i	0.822911	+	0.568171i	$0.192349\pi$
$48$		0			0
$49$	29.5667	−	51.2110i	0.603402	−	1.04512i
$50$	−5.24928	+	1.46565i	−0.104986	+	0.0293130i
$51$		0			0
$52$	70.0086	+	17.1951i	1.34632	+	0.330676i
$53$	44.7349	+	44.7349i	0.844055	+	0.844055i	0.989383	−	0.145329i	$-0.0464240\pi$
$53$	44.7349	+	44.7349i	0.844055	+	0.844055i	−0.145329	+	0.989383i	$0.546424\pi$
$54$		0			0
$55$		−	10.6322i		−	0.193312i
$56$	80.9920	+	18.9955i	1.44629	+	0.339204i
$57$		0			0
$58$	−36.7593	−	20.7126i	−0.633780	−	0.357113i
$59$	46.6277	−	12.4938i	0.790300	−	0.211760i	0.158979	−	0.987282i	$-0.449180\pi$
$59$	46.6277	−	12.4938i	0.790300	−	0.211760i	0.631321	+	0.775522i	$0.282513\pi$
$60$		0			0
$61$	−11.8435	+	44.2007i	−0.194156	+	0.724601i	0.798327	+	0.602224i	$0.205718\pi$
$61$	−11.8435	+	44.2007i	−0.194156	+	0.724601i	−0.992484	+	0.122377i	$0.960948\pi$
$62$	40.4019	−	41.2574i	0.651644	−	0.665443i
$63$		0			0
$64$	4.02018	+	63.8736i	0.0628153	+	0.998025i
$65$	82.1822	−	47.4479i	1.26434	−	0.729968i
$66$		0			0
$67$	89.1859	−	23.8973i	1.33113	−	0.356676i	0.477996	−	0.878362i	$-0.341363\pi$
$67$	89.1859	−	23.8973i	1.33113	−	0.356676i	0.853138	+	0.521686i	$0.174697\pi$
$68$	32.3762	−	58.8933i	0.476121	−	0.866078i
$69$		0			0
$70$	94.2579	−	55.7445i	1.34654	−	0.796350i
$71$	33.5395			0.472387			0.236194	−	0.971706i	$-0.424100\pi$
$71$	33.5395			0.472387			0.236194	+	0.971706i	$0.424100\pi$
$72$		0			0
$73$		−	22.2616i		−	0.304953i	−0.988307	−	0.152476i	$-0.951275\pi$
$73$		−	22.2616i		−	0.304953i	0.988307	−	0.152476i	$-0.0487248\pi$
$74$	−110.785	+	65.5187i	−1.49710	+	0.885388i
$75$		0			0
$76$	23.8238	+	81.9997i	0.313472	+	1.07894i
$77$	5.43453	+	20.2819i	0.0705783	+	0.263402i
$78$		0			0
$79$	−52.9631	−	91.7348i	−0.670419	−	1.16120i	−0.977785	−	0.209609i	$-0.932781\pi$
$79$	−52.9631	−	91.7348i	−0.670419	−	1.16120i	0.307366	−	0.951591i	$-0.400552\pi$
$80$	62.0151	+	57.0239i	0.775189	+	0.712799i
$81$		0			0
$82$	59.6379	−	60.9007i	0.727291	−	0.742692i
$83$	−43.5372	−	11.6657i	−0.524544	−	0.140551i	−0.0131763	−	0.999913i	$-0.504194\pi$
$83$	−43.5372	−	11.6657i	−0.524544	−	0.140551i	−0.511368	+	0.859362i	$0.670861\pi$
$84$		0			0
$85$	−22.8971	−	85.4530i	−0.269377	−	1.00533i
$86$	−113.244	−	63.8092i	−1.31679	−	0.741967i
$87$		0			0
$88$	−13.7289	+	8.51253i	−0.156011	+	0.0967333i
$89$	−43.8448			−0.492638			−0.246319	−	0.969189i	$-0.579221\pi$
$89$	−43.8448			−0.492638			−0.246319	+	0.969189i	$0.579221\pi$
$90$		0			0
$91$	−132.518	+	132.518i	−1.45625	+	1.45625i
$92$	−13.4420	+	8.14091i	−0.146109	+	0.0884882i
$93$		0			0
$94$	−77.6042	+	21.6678i	−0.825576	+	0.230509i
$95$	97.3455	+	56.2024i	1.02469	+	0.591605i
$96$		0			0
$97$	56.4536	+	97.7805i	0.581996	+	1.00805i	0.995243	+	0.0974273i	$0.0310614\pi$
$97$	56.4536	+	97.7805i	0.581996	+	1.00805i	−0.413247	+	0.910619i	$0.635605\pi$
$98$	−82.7466	+	84.4987i	−0.844353	+	0.862232i
$99$		0			0
$100$	10.8977	−	0.228365i	0.108977	−	0.00228365i
$101$	44.1122	−	164.629i	0.436755	−	1.62999i	−0.300077	−	0.953915i	$-0.597012\pi$
$101$	44.1122	−	164.629i	0.436755	−	1.62999i	0.736831	−	0.676076i	$-0.236321\pi$
$102$		0			0
$103$	22.6260	+	13.0631i	0.219670	+	0.126827i	0.605798	−	0.795619i	$-0.292854\pi$
$103$	22.6260	+	13.0631i	0.219670	+	0.126827i	−0.386127	+	0.922445i	$0.626187\pi$
$104$	−127.066	−	68.1302i	−1.22179	−	0.655098i
$105$		0			0
$106$	−64.4092	−	108.909i	−0.607634	−	1.02744i
$107$	43.0411	+	43.0411i	0.402253	+	0.402253i	0.879026	−	0.476773i	$-0.158194\pi$
$107$	43.0411	+	43.0411i	0.402253	+	0.402253i	−0.476773	+	0.879026i	$0.658194\pi$
$108$		0			0
$109$	−15.3831	−	15.3831i	−0.141130	−	0.141130i	0.633012	−	0.774142i	$-0.281818\pi$
$109$	−15.3831	−	15.3831i	−0.141130	−	0.141130i	−0.774142	+	0.633012i	$0.781818\pi$
$110$	−5.28814	+	20.5963i	−0.0480740	+	0.187239i
$111$		0			0
$112$	−147.447	−	77.0805i	−1.31649	−	0.688219i
$113$	−102.531	−	59.1964i	−0.907356	−	0.523862i	−0.0277765	−	0.999614i	$-0.508843\pi$
$113$	−102.531	−	59.1964i	−0.907356	−	0.523862i	−0.879579	+	0.475752i	$0.842176\pi$
$114$		0			0
$115$	−5.35411	+	19.9818i	−0.0465575	+	0.173755i
$116$	60.9070	+	58.4068i	0.525060	+	0.503507i
$117$		0			0
$118$	−96.5397	+	1.01140i	−0.818133	+	0.00857117i
$119$	87.3570	+	151.307i	0.734092	+	1.27149i
$120$		0			0
$121$	101.258	+	58.4614i	0.836843	+	0.483152i
$122$	44.9271	−	79.7335i	0.368255	−	0.653553i
$123$		0			0
$124$	−98.7856	+	59.8278i	−0.796658	+	0.482482i
$125$	−82.9351	+	82.9351i	−0.663480	+	0.663480i
$126$		0			0
$127$	−17.1308			−0.134888			−0.0674441	−	0.997723i	$-0.521484\pi$
$127$	−17.1308			−0.134888			−0.0674441	+	0.997723i	$0.521484\pi$
$128$	23.9812	−	125.733i	0.187353	−	0.982293i
$129$		0			0
$130$	−182.800	+	51.0395i	−1.40615	+	0.392612i
$131$	−17.4766	−	65.2234i	−0.133409	−	0.497888i	0.866591	−	0.499020i	$-0.166307\pi$
$131$	−17.4766	−	65.2234i	−0.133409	−	0.497888i	−0.999999	+	0.00113138i	$0.999640\pi$
$132$		0			0
$133$	−214.424	−	57.4547i	−1.61221	−	0.431990i
$134$	−184.654	+	1.93453i	−1.37801	+	0.0144368i
$135$		0			0
$136$	−92.0101	+	97.9832i	−0.676545	+	0.720465i
$137$	83.2386	+	144.174i	0.607581	+	1.05236i	0.991638	+	0.129052i	$0.0411934\pi$
$137$	83.2386	+	144.174i	0.607581	+	1.05236i	−0.384057	+	0.923310i	$0.625473\pi$
$138$		0			0
$139$	−2.18000	−	8.13587i	−0.0156835	−	0.0585314i	0.957641	−	0.287966i	$-0.0929790\pi$
$139$	−2.18000	−	8.13587i	−0.0156835	−	0.0585314i	−0.973324	+	0.229434i	$0.926312\pi$
$140$	−210.319	+	61.1053i	−1.50228	+	0.436466i
$141$		0			0
$142$	−64.9716	−	16.6816i	−0.457547	−	0.117476i
$143$		−	36.3913i		−	0.254484i
$144$		0			0
$145$	111.083			0.766088
$146$	−11.0723	+	43.1244i	−0.0758375	+	0.295372i
$147$		0			0
$148$	247.196	−	71.8194i	1.67025	−	0.485266i
$149$	−140.753	+	37.7147i	−0.944652	+	0.253119i	−0.698091	−	0.716009i	$-0.745967\pi$
$149$	−140.753	+	37.7147i	−0.944652	+	0.253119i	−0.246560	+	0.969127i	$0.579300\pi$
$150$		0			0
$151$	−114.744	+	66.2472i	−0.759891	+	0.438723i	−0.829257	−	0.558868i	$-0.811236\pi$
$151$	−114.744	+	66.2472i	−0.759891	+	0.438723i	0.0693655	+	0.997591i	$0.477903\pi$
$152$	−5.36647	−	170.696i	−0.0353057	−	1.12300i
$153$		0			0
$154$	−0.439934	−	41.9925i	−0.00285672	−	0.272679i
$155$	−39.3475	+	146.847i	−0.253855	+	0.947399i
$156$		0			0
$157$	252.032	−	67.5317i	1.60530	−	0.430138i	0.658661	−	0.752439i	$-0.271123\pi$
$157$	252.032	−	67.5317i	1.60530	−	0.430138i	0.946637	+	0.322301i	$0.104456\pi$
$158$	56.9722	+	204.048i	0.360583	+	1.29144i
$159$		0			0
$160$	−91.7717	−	141.310i	−0.573573	−	0.883185i
$161$		−	40.8540i		−	0.253752i
$162$		0			0
$163$	−109.803	−	109.803i	−0.673637	−	0.673637i	0.284916	−	0.958553i	$-0.408034\pi$
$163$	−109.803	−	109.803i	−0.673637	−	0.673637i	−0.958553	+	0.284916i	$0.908034\pi$
$164$	−145.819	+	88.3127i	−0.889140	+	0.538492i
$165$		0			0
$166$	78.5366	+	44.2527i	0.473112	+	0.266582i
$167$	−41.1115	+	71.2072i	−0.246177	+	0.426391i	−0.962462	−	0.271417i	$-0.912508\pi$
$167$	−41.1115	+	71.2072i	−0.246177	+	0.426391i	0.716285	+	0.697808i	$0.245841\pi$
$168$		0			0
$169$	134.931	−	77.9025i	0.798408	−	0.460961i
$170$	1.85356	+	176.925i	0.0109033	+	1.04074i
$171$		0			0
$172$	187.636	+	179.933i	1.09091	+	1.04612i
$173$	−10.1145	−	2.71016i	−0.0584651	−	0.0156657i	0.229468	−	0.973316i	$-0.426301\pi$
$173$	−10.1145	−	2.71016i	−0.0584651	−	0.0156657i	−0.287933	+	0.957651i	$0.592968\pi$
$174$		0			0
$175$	−14.1684	+	24.5404i	−0.0809623	+	0.140231i
$176$	30.8291	−	9.66183i	0.175166	−	0.0548967i
$177$		0			0
$178$	84.9347	+	21.8072i	0.477161	+	0.122512i
$179$	−206.509	+	206.509i	−1.15368	+	1.15368i	−0.167870	+	0.985809i	$0.553689\pi$
$179$	−206.509	+	206.509i	−1.15368	+	1.15368i	−0.985809	+	0.167870i	$0.946311\pi$
$180$		0			0
$181$	14.5527	−	14.5527i	0.0804016	−	0.0804016i	−0.665762	−	0.746164i	$-0.731894\pi$
$181$	14.5527	−	14.5527i	0.0804016	−	0.0804016i	0.746164	+	0.665762i	$0.231894\pi$
$182$	322.621	−	190.800i	1.77264	−	1.04835i
$183$		0			0
$184$	30.0885	−	9.08465i	0.163524	−	0.0493731i
$185$	169.428	−	293.458i	0.915827	−	1.58626i
$186$		0			0
$187$	−32.7701	−	8.78071i	−0.175241	−	0.0469557i
$188$	161.109	−	3.37609i	0.856964	−	0.0179579i
$189$		0			0
$190$	−160.621	−	157.290i	−0.845374	−	0.827845i
$191$	−226.823	+	130.957i	−1.18756	+	0.685636i	−0.957751	−	0.287600i	$-0.907143\pi$
$191$	−226.823	+	130.957i	−1.18756	+	0.685636i	−0.229806	+	0.973236i	$0.573809\pi$
$192$		0			0
$193$	−88.6506	+	153.547i	−0.459330	+	0.795582i	−0.998926	−	0.0463419i	$-0.985244\pi$
$193$	−88.6506	+	153.547i	−0.459330	+	0.795582i	0.539596	+	0.841924i	$0.318577\pi$
$194$	−60.7269	−	217.496i	−0.313025	−	1.12111i
$195$		0			0
$196$	202.321	−	122.532i	1.03225	−	0.625166i
$197$	−270.761	−	270.761i	−1.37442	−	1.37442i	−0.853772	−	0.520648i	$-0.825690\pi$
$197$	−270.761	−	270.761i	−1.37442	−	1.37442i	−0.520648	−	0.853772i	$-0.674310\pi$
$198$		0			0
$199$		−	180.875i		−	0.908918i	−0.890768	−	0.454459i	$-0.849833\pi$
$199$		−	180.875i		−	0.908918i	0.890768	−	0.454459i	$-0.150167\pi$
$200$	−21.2243	−	4.97784i	−0.106121	−	0.0248892i
$201$		0			0
$202$	−167.335	+	296.974i	−0.828390	+	1.47017i
$203$	−211.902	+	56.7789i	−1.04385	+	0.279699i
$204$		0			0
$205$	−58.0814	+	216.763i	−0.283324	+	1.05738i
$206$	−37.3332	−	36.5591i	−0.181229	−	0.177471i
$207$		0			0
$208$	212.262	+	195.179i	1.02049	+	0.938359i
$209$	37.3307	−	21.5529i	0.178616	−	0.103124i
$210$		0			0
$211$	−342.062	+	91.6551i	−1.62114	+	0.434384i	−0.951338	−	0.308151i	$-0.900290\pi$
$211$	−342.062	+	91.6551i	−1.62114	+	0.434384i	−0.669807	+	0.742535i	$0.733623\pi$
$212$	70.6032	+	243.010i	0.333034	+	1.14627i
$213$		0			0
$214$	−61.9704	−	104.785i	−0.289581	−	0.489651i
$215$	342.212			1.59169
$216$		0			0
$217$		−	300.237i		−	1.38358i
$218$	22.1486	+	37.4508i	0.101599	+	0.171793i
$219$		0			0
$220$	20.4880	−	37.2683i	0.0931274	−	0.169401i
$221$	−78.3710	−	292.484i	−0.354620	−	1.32346i
$222$		0			0
$223$	−127.935	−	221.589i	−0.573698	−	0.993675i	−0.996182	−	0.0873039i	$-0.972175\pi$
$223$	−127.935	−	221.589i	−0.573698	−	0.993675i	0.422483	−	0.906371i	$-0.361158\pi$
$224$	247.293	+	222.654i	1.10399	+	0.993992i
$225$		0			0
$226$	169.178	+	165.670i	0.748574	+	0.733051i
$227$	−223.342	−	59.8442i	−0.983884	−	0.263631i	−0.269205	−	0.963083i	$-0.586761\pi$
$227$	−223.342	−	59.8442i	−0.983884	−	0.263631i	−0.714680	+	0.699452i	$0.753428\pi$
$228$		0			0
$229$	−54.8188	−	204.587i	−0.239384	−	0.893391i	−0.976124	−	0.217215i	$-0.930303\pi$
$229$	−54.8188	−	204.587i	−0.239384	−	0.893391i	0.736740	−	0.676176i	$-0.236364\pi$
$230$	20.3102	−	36.0451i	0.0883052	−	0.156718i
$231$		0			0
$232$	−88.9373	−	143.437i	−0.383350	−	0.618264i
$233$	−112.179			−0.481455			−0.240728	−	0.970593i	$-0.577386\pi$
$233$	−112.179			−0.481455			−0.240728	+	0.970593i	$0.577386\pi$
$234$		0			0
$235$	149.995	−	149.995i	0.638277	−	0.638277i
$236$	187.517	+	46.0569i	0.794563	+	0.195156i
$237$		0			0
$238$	−93.9695	−	336.556i	−0.394830	−	1.41410i
$239$	112.206	+	64.7823i	0.469482	+	0.271056i	0.716023	−	0.698077i	$-0.245961\pi$
$239$	112.206	+	64.7823i	0.469482	+	0.271056i	−0.246541	+	0.969132i	$0.579294\pi$
$240$		0			0
$241$	13.6028	+	23.5607i	0.0564431	+	0.0977624i	0.892866	−	0.450322i	$-0.148691\pi$
$241$	13.6028	+	23.5607i	0.0564431	+	0.0977624i	−0.836423	+	0.548084i	$0.815357\pi$
$242$	−167.077	−	163.612i	−0.690400	−	0.676084i
$243$		0			0
$244$	−126.688	+	132.112i	−0.519215	+	0.541442i
$245$	80.5870	−	300.755i	0.328927	−	1.22757i
$246$		0			0
$247$	333.189	+	192.367i	1.34894	+	0.778813i
$248$	221.121	−	66.7634i	0.891617	−	0.269207i
$249$		0			0
$250$	201.909	−	119.410i	0.807635	−	0.477638i
$251$	248.094	+	248.094i	0.988422	+	0.988422i	0.999934	−	0.0115117i	$-0.00366435\pi$
$251$	248.094	+	248.094i	0.988422	+	0.988422i	−0.0115117	+	0.999934i	$0.503664\pi$
$252$		0			0
$253$	5.60952	+	5.60952i	0.0221720	+	0.0221720i
$254$	33.1853	+	8.52038i	0.130651	+	0.0335448i
$255$		0			0
$256$	−108.992	+	231.639i	−0.425749	+	0.904841i
$257$	123.347	+	71.2145i	0.479950	+	0.277099i	0.720396	−	0.693563i	$-0.243960\pi$
$257$	123.347	+	71.2145i	0.479950	+	0.277099i	−0.240446	+	0.970663i	$0.577294\pi$
$258$		0			0
$259$	−173.203	+	646.402i	−0.668737	+	2.49576i
$260$	379.500	−	7.95254i	1.45962	−	0.0305867i
$261$		0			0
$262$	1.41476	+	135.041i	0.00539983	+	0.515424i
$263$	−161.666	−	280.013i	−0.614699	−	1.06469i	−0.990437	−	0.137964i	$-0.955944\pi$
$263$	−161.666	−	280.013i	−0.614699	−	1.06469i	0.375738	−	0.926726i	$-0.377389\pi$
$264$		0			0
$265$	288.488	+	166.559i	1.08863	+	0.628524i
$266$	386.799	+	217.948i	1.45413	+	0.819352i
$267$		0			0
$268$	358.668	+	88.0942i	1.33831	+	0.328710i
$269$	100.367	−	100.367i	0.373110	−	0.373110i	−0.495498	−	0.868609i	$-0.665015\pi$
$269$	100.367	−	100.367i	0.373110	−	0.373110i	0.868609	+	0.495498i	$0.165015\pi$
$270$		0			0
$271$	−106.293			−0.392224			−0.196112	−	0.980581i	$-0.562832\pi$
$271$	−106.293			−0.392224			−0.196112	+	0.980581i	$0.562832\pi$
$272$	226.973	−	144.047i	0.834460	−	0.529584i
$273$		0			0
$274$	−89.5394	−	320.689i	−0.326786	−	1.17040i
$275$	−1.42414	−	5.31497i	−0.00517869	−	0.0193272i
$276$		0			0
$277$	−60.0784	−	16.0980i	−0.216890	−	0.0581154i	0.148738	−	0.988877i	$-0.452479\pi$
$277$	−60.0784	−	16.0980i	−0.216890	−	0.0581154i	−0.365627	+	0.930761i	$0.619146\pi$
$278$	0.176475	+	16.8448i	0.000634801	+	0.0605929i
$279$		0			0
$280$	437.816	−	13.7644i	1.56363	−	0.0491584i
$281$	216.210	+	374.487i	0.769431	+	1.33269i	0.937872	+	0.346982i	$0.112794\pi$
$281$	216.210	+	374.487i	0.769431	+	1.33269i	−0.168440	+	0.985712i	$0.553873\pi$
$282$		0			0
$283$	86.9601	+	324.540i	0.307280	+	1.14678i	0.930965	+	0.365108i	$0.118968\pi$
$283$	86.9601	+	324.540i	0.307280	+	1.14678i	−0.623686	+	0.781675i	$0.714366\pi$
$284$	117.564	+	64.6301i	0.413958	+	0.227571i
$285$		0			0
$286$	−18.1000	+	70.4960i	−0.0632867	+	0.246490i
$287$		−	443.185i		−	1.54420i
$288$		0			0
$289$	6.70996			0.0232179
$290$	−215.186	−	55.2495i	−0.742021	−	0.190515i
$291$		0			0
$292$	42.8977	−	78.0322i	0.146910	−	0.267233i
$293$	98.9358	−	26.5098i	0.337665	−	0.0904770i	−0.0860024	−	0.996295i	$-0.527409\pi$
$293$	98.9358	−	26.5098i	0.337665	−	0.0904770i	0.423667	+	0.905818i	$0.360743\pi$
$294$		0			0
$295$	220.124	−	127.088i	0.746182	−	0.430808i
$296$	−514.582	+	16.1778i	−1.73845	+	0.0546547i
$297$		0			0
$298$	291.421	−	3.05307i	0.977922	−	0.0102452i
$299$	−18.3258	+	68.3927i	−0.0612902	+	0.228738i
$300$		0			0
$301$	−652.805	+	174.919i	−2.16879	+	0.581125i
$302$	255.227	−	71.2618i	0.845123	−	0.235966i
$303$		0			0
$304$	−74.5039	+	333.337i	−0.245078	+	1.09650i
$305$			240.947i			0.789989i
$306$		0			0
$307$	−162.681	−	162.681i	−0.529907	−	0.529907i	0.390638	−	0.920545i	$-0.372255\pi$
$307$	−162.681	−	162.681i	−0.529907	−	0.529907i	−0.920545	+	0.390638i	$0.872255\pi$
$308$	−20.0337	+	81.5654i	−0.0650444	+	0.264823i
$309$		0			0
$310$	149.260	−	264.897i	0.481485	−	0.854506i
$311$	90.2216	−	156.268i	0.290102	−	0.502471i	−0.683732	−	0.729733i	$-0.739644\pi$
$311$	90.2216	−	156.268i	0.290102	−	0.502471i	0.973834	+	0.227263i	$0.0729776\pi$
$312$		0			0
$313$	−20.0591	+	11.5811i	−0.0640865	+	0.0370003i	−0.531701	−	0.846932i	$-0.678447\pi$
$313$	−20.0591	+	11.5811i	−0.0640865	+	0.0370003i	0.467614	+	0.883933i	$0.345114\pi$
$314$	−521.817	+	5.46681i	−1.66184	+	0.0174102i
$315$		0			0
$316$	−8.87691	−	423.612i	−0.0280915	−	1.34054i
$317$	4.64388	+	1.24432i	0.0146494	+	0.00392531i	0.266136	−	0.963935i	$-0.414253\pi$
$317$	4.64388	+	1.24432i	0.0146494	+	0.00392531i	−0.251487	+	0.967861i	$0.580920\pi$
$318$		0			0
$319$	21.2994	−	36.8916i	0.0667692	−	0.115648i
$320$	107.494	+	319.385i	0.335918	+	0.998078i
$321$		0			0
$322$	−20.3196	+	79.1411i	−0.0631045	+	0.245780i
$323$	253.619	−	253.619i	0.785198	−	0.785198i
$324$		0			0
$325$	34.7270	−	34.7270i	0.106852	−	0.106852i
$326$	158.094	+	267.319i	0.484950	+	0.819998i
$327$		0			0
$328$	326.400	−	98.5504i	0.995122	−	0.300459i
$329$	−209.462	+	362.799i	−0.636664	+	1.10273i
$330$		0			0
$331$	228.200	+	61.1461i	0.689427	+	0.184731i	0.586490	−	0.809956i	$-0.300509\pi$
$331$	228.200	+	61.1461i	0.689427	+	0.184731i	0.102937	+	0.994688i	$0.467176\pi$
$332$	−130.129	−	124.787i	−0.391953	−	0.375864i
$333$		0			0
$334$	115.056	−	117.493i	0.344480	−	0.351774i
$335$	421.036	−	243.085i	1.25682	−	0.725628i
$336$		0			0
$337$	−36.1293	+	62.5777i	−0.107209	+	0.185691i	−0.914638	−	0.404273i	$-0.867525\pi$
$337$	−36.1293	+	62.5777i	−0.107209	+	0.185691i	0.807430	+	0.589964i	$0.200858\pi$
$338$	−300.131	+	83.7993i	−0.887960	+	0.247927i
$339$		0			0
$340$	84.4070	−	343.656i	0.248256	−	1.01075i
$341$	41.2245	+	41.2245i	0.120893	+	0.120893i
$342$		0			0
$343$			105.374i			0.307214i
$344$	−273.989	−	441.886i	−0.796479	−	1.28455i
$345$		0			0
$346$	18.2455	+	10.2807i	0.0527325	+	0.0297130i
$347$	151.528	−	40.6017i	0.436679	−	0.117008i	−0.0337807	−	0.999429i	$-0.510755\pi$
$347$	151.528	−	40.6017i	0.436679	−	0.117008i	0.470460	+	0.882421i	$0.344088\pi$
$348$		0			0
$349$	41.3432	−	154.295i	0.118462	−	0.442105i	−0.881061	−	0.473003i	$-0.843170\pi$
$349$	41.3432	−	154.295i	0.118462	−	0.442105i	0.999523	+	0.0308977i	$0.00983661\pi$
$350$	39.6523	−	40.4919i	0.113292	−	0.115691i
$351$		0			0
$352$	−64.5267	+	3.38304i	−0.183315	+	0.00961091i
$353$	−298.952	+	172.600i	−0.846891	+	0.488953i	−0.859601	−	0.510967i	$-0.829288\pi$
$353$	−298.952	+	172.600i	−0.846891	+	0.488953i	0.0127098	+	0.999919i	$0.495954\pi$
$354$		0			0
$355$	170.583	−	45.7076i	0.480516	−	0.128754i
$356$	−153.687	−	84.4883i	−0.431704	−	0.237327i
$357$		0			0
$358$	502.754	−	297.330i	1.40434	−	0.830532i
$359$	−111.390			−0.310279			−0.155140	−	0.987893i	$-0.549583\pi$
$359$	−111.390			−0.310279			−0.155140	+	0.987893i	$0.549583\pi$
$360$		0			0
$361$			94.7202i			0.262383i
$362$	−35.4291	+	20.9529i	−0.0978705	+	0.0578810i
$363$		0			0
$364$	−719.870	+	209.148i	−1.97767	+	0.574583i
$365$	−30.3381	−	113.223i	−0.0831180	−	0.310200i
$366$		0			0
$367$	−172.640	−	299.022i	−0.470409	−	0.814773i	0.529018	−	0.848611i	$-0.322560\pi$
$367$	−172.640	−	299.022i	−0.470409	−	0.814773i	−0.999427	+	0.0338379i	$0.989227\pi$
$368$	−62.8049	+	2.63335i	−0.170665	+	0.00715583i
$369$		0			0
$370$	−474.168	+	484.209i	−1.28154	+	1.30867i
$371$	−635.456	−	170.270i	−1.71282	−	0.458948i
$372$		0			0
$373$	13.4560	+	50.2187i	0.0360752	+	0.134634i	0.981615	−	0.190873i	$-0.0611317\pi$
$373$	13.4560	+	50.2187i	0.0360752	+	0.134634i	−0.945540	+	0.325507i	$0.894465\pi$
$374$	59.1139	+	33.3086i	0.158058	+	0.0890605i
$375$		0			0
$376$	−313.775	−	73.5912i	−0.834508	−	0.195721i
$377$	380.209			1.00851
$378$		0			0
$379$	−164.123	+	164.123i	−0.433043	+	0.433043i	−0.889662	−	0.456619i	$-0.849060\pi$
$379$	−164.123	+	164.123i	−0.433043	+	0.433043i	0.456619	+	0.889662i	$0.349060\pi$
$380$	232.918	+	384.586i	0.612943	+	1.01207i
$381$		0			0
$382$	504.529	−	140.869i	1.32076	−	0.368768i
$383$	153.802	+	88.7974i	0.401571	+	0.231847i	0.687162	−	0.726505i	$-0.258856\pi$
$383$	153.802	+	88.7974i	0.401571	+	0.231847i	−0.285591	+	0.958352i	$0.592190\pi$
$384$		0			0
$385$	55.2805	+	95.7486i	0.143586	+	0.248698i
$386$	248.101	−	253.355i	0.642749	−	0.656359i
$387$		0			0
$388$	9.46193	+	451.530i	0.0243864	+	1.16374i
$389$	121.737	−	454.328i	0.312948	−	1.16794i	−0.612936	−	0.790132i	$-0.710012\pi$
$389$	121.737	−	454.328i	0.312948	−	1.16794i	0.925885	−	0.377806i	$-0.123321\pi$
$390$		0			0
$391$	57.1654	+	33.0045i	0.146203	+	0.0844104i
$392$	−452.875	+	136.737i	−1.15529	+	0.348819i
$393$		0			0
$394$	389.840	+	659.178i	0.989442	+	1.67304i
$395$	−394.389	−	394.389i	−0.998453	−	0.998453i
$396$		0			0
$397$	−2.22565	−	2.22565i	−0.00560617	−	0.00560617i	0.704298	−	0.709904i	$-0.251262\pi$
$397$	−2.22565	−	2.22565i	−0.00560617	−	0.00560617i	−0.709904	+	0.704298i	$0.751262\pi$
$398$	−89.9620	+	350.385i	−0.226035	+	0.880364i
$399$		0			0
$400$	38.6392	+	20.1993i	0.0965980	+	0.0504982i
$401$	−541.410	−	312.583i	−1.35015	−	0.779509i	−0.361878	−	0.932225i	$-0.617864\pi$
$401$	−541.410	−	312.583i	−1.35015	−	0.779509i	−0.988270	+	0.152717i	$0.951198\pi$
$402$		0			0
$403$	−134.677	+	502.620i	−0.334185	+	1.24720i
$404$	471.862	−	492.061i	1.16798	−	1.21797i
$405$		0			0
$406$	438.730	−	4.59635i	1.08061	−	0.0113211i
$407$	−64.9733	−	112.537i	−0.159640	−	0.276504i
$408$		0			0
$409$	−67.3594	−	38.8900i	−0.164693	−	0.0950855i	0.415388	−	0.909644i	$-0.363646\pi$
$409$	−67.3594	−	38.8900i	−0.164693	−	0.0950855i	−0.580081	+	0.814559i	$0.696979\pi$
$410$	220.325	−	391.018i	0.537378	−	0.953702i
$411$		0			0
$412$	54.1372	+	89.3896i	0.131401	+	0.216965i
$413$	−354.948	+	354.948i	−0.859439	+	0.859439i
$414$		0			0
$415$	−237.330			−0.571879
$416$	−314.112	−	483.667i	−0.755076	−	1.16266i
$417$		0			0
$418$	−83.0355	+	23.1843i	−0.198650	+	0.0554649i
$419$	137.983	+	514.960i	0.329316	+	1.22902i	0.909902	+	0.414824i	$0.136157\pi$
$419$	137.983	+	514.960i	0.329316	+	1.22902i	−0.580586	+	0.814199i	$0.697177\pi$
$420$		0			0
$421$	286.986	+	76.8978i	0.681678	+	0.182655i	0.583010	−	0.812465i	$-0.301875\pi$
$421$	286.986	+	76.8978i	0.681678	+	0.182655i	0.0986685	+	0.995120i	$0.468542\pi$
$422$	708.218	−	7.41964i	1.67824	−	0.0175821i
$423$		0			0
$424$	−15.9038	−	505.868i	−0.0375090	−	1.19308i
$425$	−22.8923	−	39.6506i	−0.0538641	−	0.0932954i
$426$		0			0
$427$	−123.158	−	459.630i	−0.288425	−	1.07642i
$428$	67.9299	+	233.809i	0.158715	+	0.546283i
$429$		0			0
$430$	−662.923	−	170.207i	−1.54168	−	0.395830i
$431$		−	583.533i		−	1.35391i	−0.736026	−	0.676953i	$-0.763300\pi$
$431$		−	583.533i		−	1.35391i	0.736026	−	0.676953i	$-0.236700\pi$
$432$		0			0
$433$	−458.657			−1.05925			−0.529627	−	0.848231i	$-0.677668\pi$
$433$	−458.657			−1.05925			−0.529627	+	0.848231i	$0.677668\pi$
$434$	−149.330	+	581.610i	−0.344077	+	1.34012i
$435$		0			0
$436$	−24.2785	−	83.5646i	−0.0556847	−	0.191662i
$437$	−81.0117	+	21.7070i	−0.185381	+	0.0496728i
$438$		0			0
$439$	−118.122	+	68.1979i	−0.269071	+	0.155348i	−0.628465	−	0.777838i	$-0.716317\pi$
$439$	−118.122	+	68.1979i	−0.269071	+	0.155348i	0.359394	+	0.933186i	$0.382983\pi$
$440$	−58.2250	+	62.0049i	−0.132330	+	0.140920i
$441$		0			0
$442$	6.34426	+	605.571i	0.0143535	+	1.37007i
$443$	15.1614	−	56.5830i	0.0342243	−	0.127727i	−0.946700	−	0.322116i	$-0.895606\pi$
$443$	15.1614	−	56.5830i	0.0342243	−	0.127727i	0.980924	+	0.194389i	$0.0622725\pi$
$444$		0			0
$445$	−222.996	+	59.7517i	−0.501115	+	0.134273i
$446$	137.619	+	492.887i	0.308562	+	1.10513i
$447$		0			0
$448$	−368.306	−	554.315i	−0.822111	−	1.23731i
$449$			515.725i			1.14861i	0.818642	+	0.574304i	$0.194727\pi$
$449$			515.725i			1.14861i	−0.818642	+	0.574304i	$0.805273\pi$
$450$		0			0
$451$	60.8521	+	60.8521i	0.134927	+	0.134927i
$452$	−245.326	−	405.074i	−0.542757	−	0.896182i
$453$		0			0
$454$	402.886	+	227.012i	0.887414	+	0.500027i
$455$	−493.398	+	854.590i	−1.08439	+	1.87822i
$456$		0			0
$457$	−340.028	+	196.315i	−0.744043	+	0.429573i	−0.823537	−	0.567262i	$-0.808003\pi$
$457$	−340.028	+	196.315i	−0.744043	+	0.429573i	0.0794947	+	0.996835i	$0.474669\pi$
$458$	4.43768	+	423.584i	0.00968925	+	0.924856i
$459$		0			0
$460$	−57.2721	+	59.7238i	−0.124505	+	0.129834i
$461$	7.54381	+	2.02136i	0.0163640	+	0.00438472i	0.266992	−	0.963699i	$-0.413970\pi$
$461$	7.54381	+	2.02136i	0.0163640	+	0.00438472i	−0.250628	+	0.968084i	$0.580637\pi$
$462$		0			0
$463$	322.500	−	558.586i	0.696544	−	1.20645i	−0.273114	−	0.961982i	$-0.588054\pi$
$463$	322.500	−	558.586i	0.696544	−	1.20645i	0.969657	−	0.244468i	$-0.0786132\pi$
$464$	100.945	+	322.097i	0.217554	+	0.694174i
$465$		0			0
$466$	217.310	+	55.7947i	0.466330	+	0.119731i
$467$	267.025	−	267.025i	0.571788	−	0.571788i	−0.360840	−	0.932628i	$-0.617510\pi$
$467$	267.025	−	267.025i	0.571788	−	0.571788i	0.932628	+	0.360840i	$0.117510\pi$
$468$		0			0
$469$	−678.918	+	678.918i	−1.44759	+	1.44759i
$470$	−365.169	+	215.962i	−0.776955	+	0.459494i
$471$		0			0
$472$	−340.344	−	182.486i	−0.721068	−	0.386622i
$473$	65.6169	−	113.652i	0.138725	−	0.240279i
$474$		0			0
$475$	56.1906	+	15.0562i	0.118296	+	0.0316973i
$476$	14.6415	+	698.703i	0.0307595	+	1.46786i
$477$		0			0
$478$	−185.142	−	181.303i	−0.387326	−	0.379294i
$479$	−415.988	+	240.171i	−0.868451	+	0.501401i	−0.866833	−	0.498598i	$-0.833848\pi$
$479$	−415.988	+	240.171i	−0.868451	+	0.501401i	−0.00161815	+	0.999999i	$0.500515\pi$
$480$		0			0
$481$	579.910	−	1004.43i	1.20563	−	2.08822i
$482$	−14.6325	−	52.4068i	−0.0303578	−	0.108728i
$483$		0			0
$484$	242.280	+	400.044i	0.500578	+	0.826537i
$485$	420.381	+	420.381i	0.866764	+	0.866764i
$486$		0			0
$487$		−	525.267i		−	1.07858i	−0.842121	−	0.539288i	$-0.818693\pi$
$487$		−	525.267i		−	1.07858i	0.842121	−	0.539288i	$-0.181307\pi$
$488$	311.126	−	192.911i	0.637552	−	0.395310i
$489$		0			0
$490$	−305.698	+	542.531i	−0.623873	+	1.10721i
$491$	532.204	−	142.604i	1.08392	−	0.290435i	0.327718	−	0.944776i	$-0.393720\pi$
$491$	532.204	−	142.604i	1.08392	−	0.290435i	0.756200	+	0.654341i	$0.227054\pi$
$492$		0			0
$493$	91.7392	−	342.375i	0.186084	−	0.694473i
$494$	−549.766	−	538.366i	−1.11289	−	1.08981i
$495$		0			0
$496$	−461.555	+	19.3525i	−0.930554	+	0.0390172i
$497$	−302.042	+	174.384i	−0.607730	+	0.350873i
$498$		0			0
$499$	96.8737	−	25.9572i	0.194136	−	0.0520185i	−0.160441	−	0.987045i	$-0.551292\pi$
$499$	96.8737	−	25.9572i	0.194136	−	0.0520185i	0.354577	+	0.935027i	$0.384625\pi$
$500$	−450.522	+	130.893i	−0.901044	+	0.261786i
$501$		0			0
$502$	−357.205	−	603.995i	−0.711563	−	1.20318i
$503$	−560.262			−1.11384			−0.556920	−	0.830566i	$-0.688017\pi$
$503$	−560.262			−1.11384			−0.556920	+	0.830566i	$0.688017\pi$
$504$		0			0
$505$		−	897.427i		−	1.77708i
$506$	−8.07657	−	13.6566i	−0.0159616	−	0.0269893i
$507$		0			0
$508$	−60.0477	−	33.0108i	−0.118204	−	0.0649819i
$509$	76.8337	+	286.747i	0.150950	+	0.563354i	0.999418	+	0.0341072i	$0.0108588\pi$
$509$	76.8337	+	286.747i	0.150950	+	0.563354i	−0.848468	+	0.529247i	$0.822475\pi$
$510$		0			0
$511$	115.746	+	200.478i	0.226509	+	0.392324i
$512$	326.346	−	394.515i	0.637395	−	0.770537i
$513$		0			0
$514$	−203.524	−	199.304i	−0.395961	−	0.387751i
$515$	132.879	+	35.6049i	0.258018	+	0.0691358i
$516$		0			0
$517$	−21.0542	−	78.5752i	−0.0407237	−	0.151983i
$518$	657.026	−	1166.04i	1.26839	−	2.25105i
$519$		0			0
$520$	−739.111	−	173.347i	−1.42137	−	0.333360i
$521$	897.111			1.72190			0.860951	−	0.508688i	$-0.169869\pi$
$521$	897.111			1.72190			0.860951	+	0.508688i	$0.169869\pi$
$522$		0			0
$523$	149.913	−	149.913i	0.286641	−	0.286641i	−0.549109	−	0.835751i	$-0.685033\pi$
$523$	149.913	−	149.913i	0.286641	−	0.286641i	0.835751	+	0.549109i	$0.185033\pi$
$524$	64.4250	−	262.301i	0.122948	−	0.500574i
$525$		0			0
$526$	173.903	+	622.841i	0.330614	+	1.18411i
$527$	420.110	+	242.551i	0.797173	+	0.460248i
$528$		0			0
$529$	256.782	+	444.760i	0.485411	+	0.840757i
$530$	−476.009	−	466.138i	−0.898129	−	0.879506i
$531$		0			0
$532$	−640.893	−	614.584i	−1.20469	−	1.15523i
$533$	−198.798	+	741.925i	−0.372980	+	1.39198i
$534$		0			0
$535$	277.565	+	160.252i	0.518813	+	0.299537i
$536$	−650.985	−	349.045i	−1.21452	−	0.651203i
$537$		0			0
$538$	−244.347	+	144.508i	−0.454176	+	0.268602i
$539$	−84.4313	−	84.4313i	−0.156644	−	0.156644i
$540$		0			0
$541$	621.036	+	621.036i	1.14794	+	1.14794i	0.986957	+	0.160983i	$0.0514663\pi$
$541$	621.036	+	621.036i	1.14794	+	1.14794i	0.160983	+	0.986957i	$0.448534\pi$
$542$	205.907	+	52.8671i	0.379902	+	0.0975407i
$543$		0			0
$544$	−511.330	+	166.153i	−0.939945	+	0.305428i
$545$	−99.2033	−	57.2750i	−0.182024	−	0.105092i
$546$		0			0
$547$	201.133	−	750.638i	0.367702	−	1.37228i	−0.496019	−	0.868311i	$-0.665205\pi$
$547$	201.133	−	750.638i	0.367702	−	1.37228i	0.863721	−	0.503970i	$-0.168128\pi$
$548$	13.9513	+	665.763i	0.0254585	+	1.21490i
$549$		0			0
$550$	0.115287	+	11.0043i	0.000209612	+	0.0200078i
$551$	225.180	+	390.023i	0.408675	+	0.707846i
$552$		0			0
$553$	953.925	+	550.749i	1.72500	+	0.995929i
$554$	108.375	+	61.0658i	0.195623	+	0.110227i
$555$		0			0
$556$	8.03628	−	32.7190i	0.0144537	−	0.0588472i
$557$	−115.843	+	115.843i	−0.207977	+	0.207977i	−0.803407	−	0.595430i	$-0.796982\pi$
$557$	−115.843	+	115.843i	−0.207977	+	0.207977i	0.595430	+	0.803407i	$0.296982\pi$
$558$		0			0
$559$	1171.31			2.09536
$560$	−854.969	−	191.093i	−1.52673	−	0.341238i
$561$		0			0
$562$	−232.576	−	832.981i	−0.413837	−	1.48217i
$563$	−182.665	−	681.715i	−0.324450	−	1.21086i	−0.914864	−	0.403762i	$-0.867702\pi$
$563$	−182.665	−	681.715i	−0.324450	−	1.21086i	0.590414	−	0.807100i	$-0.298964\pi$
$564$		0			0
$565$	−602.151	−	161.346i	−1.06575	−	0.285568i
$566$	−7.03957	−	671.939i	−0.0124374	−	1.18717i
$567$		0			0
$568$	−195.596	−	183.672i	−0.344359	−	0.323367i
$569$	155.098	+	268.638i	0.272580	+	0.472123i	0.969522	−	0.245005i	$-0.0787897\pi$
$569$	155.098	+	268.638i	0.272580	+	0.472123i	−0.696942	+	0.717128i	$0.745456\pi$
$570$		0			0
$571$	−147.368	−	549.986i	−0.258088	−	0.963198i	−0.966346	−	0.257245i	$-0.917185\pi$
$571$	−147.368	−	549.986i	−0.258088	−	0.963198i	0.708258	−	0.705954i	$-0.249481\pi$
$572$	70.1254	−	127.560i	0.122597	−	0.223007i
$573$		0			0
$574$	−220.428	+	858.524i	−0.384020	+	1.49569i
$575$			10.7060i			0.0186191i
$576$		0			0
$577$	−241.559			−0.418647			−0.209323	−	0.977846i	$-0.567126\pi$
$577$	−241.559			−0.418647			−0.209323	+	0.977846i	$0.567126\pi$
$578$	−12.9983	−	3.33735i	−0.0224885	−	0.00577396i
$579$		0			0
$580$	389.372	+	214.055i	0.671331	+	0.369060i
$581$	452.731	−	121.309i	0.779227	−	0.208793i
$582$		0			0
$583$	110.631	−	63.8730i	0.189762	−	0.109559i
$584$	−121.911	+	129.825i	−0.208752	+	0.222304i
$585$		0			0
$586$	−204.840	+	2.14601i	−0.349557	+	0.00366213i
$587$	−233.105	+	869.961i	−0.397113	+	1.48205i	0.421038	+	0.907043i	$0.361666\pi$
$587$	−233.105	+	869.961i	−0.397113	+	1.48205i	−0.818151	+	0.575004i	$0.805001\pi$
$588$		0			0
$589$	−595.357	+	159.526i	−1.01079	+	0.270841i
$590$	−489.627	+	136.708i	−0.829876	+	0.231709i
$591$		0			0
$592$	1004.88	+	224.600i	1.69743	+	0.379391i
$593$			695.287i			1.17249i	0.810134	+	0.586245i	$0.199394\pi$
$593$			695.287i			1.17249i	−0.810134	+	0.586245i	$0.800606\pi$
$594$		0			0
$595$	650.502	+	650.502i	1.09328	+	1.09328i
$596$	−566.049	−	139.030i	−0.949747	−	0.233272i
$597$		0			0
$598$	69.5167	−	123.374i	0.116249	−	0.206310i
$599$	401.581	−	695.558i	0.670419	−	1.16120i	−0.307367	−	0.951591i	$-0.599448\pi$
$599$	401.581	−	695.558i	0.670419	−	1.16120i	0.977785	−	0.209608i	$-0.0672188\pi$
$600$		0			0
$601$	−76.1382	+	43.9584i	−0.126686	+	0.0731421i	−0.562004	−	0.827135i	$-0.689969\pi$
$601$	−76.1382	+	43.9584i	−0.126686	+	0.0731421i	0.435318	+	0.900277i	$0.356636\pi$
$602$	1351.59	−	14.1600i	2.24517	−	0.0235215i
$603$		0			0
$604$	−529.862	+	11.1034i	−0.877254	+	0.0183831i
$605$	594.674	+	159.342i	0.982932	+	0.263376i
$606$		0			0
$607$	−5.20392	+	9.01345i	−0.00857318	+	0.0148492i	−0.870280	−	0.492557i	$-0.836062\pi$
$607$	−5.20392	+	9.01345i	−0.00857318	+	0.0148492i	0.861707	+	0.507406i	$0.169396\pi$
$608$	310.119	−	608.674i	0.510064	−	1.00111i
$609$		0			0
$610$	119.840	−	466.754i	0.196459	−	0.765171i
$611$	513.396	−	513.396i	0.840255	−	0.840255i
$612$		0			0
$613$	−270.989	+	270.989i	−0.442071	+	0.442071i	−0.892707	−	0.450637i	$-0.851197\pi$
$613$	−270.989	+	270.989i	−0.442071	+	0.442071i	0.450637	+	0.892707i	$0.351197\pi$
$614$	234.228	+	396.054i	0.381479	+	0.645040i
$615$		0			0
$616$	79.3769	−	148.042i	0.128859	−	0.240327i
$617$	−321.929	+	557.597i	−0.521765	+	0.903723i	0.477915	+	0.878406i	$0.341393\pi$
$617$	−321.929	+	557.597i	−0.521765	+	0.903723i	−0.999679	+	0.0253169i	$0.991941\pi$
$618$		0			0
$619$	603.787	+	161.784i	0.975423	+	0.261364i	0.711116	−	0.703075i	$-0.248190\pi$
$619$	603.787	+	161.784i	0.975423	+	0.261364i	0.264307	+	0.964439i	$0.414857\pi$
$620$	−420.894	+	438.912i	−0.678862	+	0.707922i
$621$		0			0
$622$	−252.498	+	257.845i	−0.405945	+	0.414541i
$623$	394.847	−	227.965i	0.633783	−	0.365915i
$624$		0			0
$625$	−342.850	+	593.834i	−0.548560	+	0.950134i
$626$	44.6179	−	12.4577i	0.0712746	−	0.0199005i
$627$		0			0
$628$	1013.57	+	248.947i	1.61396	+	0.396412i
$629$	−764.561	−	764.561i	−1.21552	−	1.21552i
$630$		0			0
$631$			412.171i			0.653203i	0.945162	+	0.326602i	$0.105904\pi$
$631$			412.171i			0.653203i	−0.945162	+	0.326602i	$0.894096\pi$
$632$	−193.497	+	825.023i	−0.306165	+	1.30542i
$633$		0			0
$634$	−8.37708	−	4.72020i	−0.0132131	−	0.00744510i
$635$	−87.1280	+	23.3459i	−0.137209	+	0.0367652i
$636$		0			0
$637$	275.829	−	1029.41i	0.433013	−	1.61603i
$638$	−59.6093	+	60.8715i	−0.0934315	+	0.0954099i
$639$		0			0
$640$	−49.3804	−	672.167i	−0.0771569	−	1.05026i
$641$	860.615	−	496.877i	1.34261	−	0.775158i	0.355423	−	0.934705i	$-0.384337\pi$
$641$	860.615	−	496.877i	1.34261	−	0.775158i	0.987190	+	0.159547i	$0.0510034\pi$
$642$		0			0
$643$	−222.010	+	59.4873i	−0.345272	+	0.0925152i	−0.427288	−	0.904116i	$-0.640531\pi$
$643$	−222.010	+	59.4873i	−0.345272	+	0.0925152i	0.0820160	+	0.996631i	$0.473864\pi$
$644$	78.7251	−	143.203i	0.122244	−	0.222365i
$645$		0			0
$646$	−617.446	+	365.160i	−0.955798	+	0.565263i
$647$	127.829			0.197572			0.0987862	−	0.995109i	$-0.468504\pi$
$647$	127.829			0.197572			0.0987862	+	0.995109i	$0.468504\pi$
$648$		0			0
$649$		−	97.4733i		−	0.150190i
$650$	−84.5443	+	49.9998i	−0.130068	+	0.0769228i
$651$		0			0
$652$	−173.297	−	596.474i	−0.265793	−	0.914837i
$653$	−48.3253	−	180.352i	−0.0740051	−	0.276191i	0.919001	−	0.394256i	$-0.128998\pi$
$653$	−48.3253	−	180.352i	−0.0740051	−	0.276191i	−0.993006	+	0.118065i	$0.962331\pi$
$654$		0			0
$655$	−177.773	−	307.912i	−0.271409	−	0.470094i
$656$	−681.308	+	28.5666i	−1.03858	+	0.0435466i
$657$		0			0
$658$	586.210	−	598.623i	0.890897	−	0.909761i
$659$	−254.305	−	68.1407i	−0.385895	−	0.103400i	0.0606554	−	0.998159i	$-0.480681\pi$
$659$	−254.305	−	68.1407i	−0.385895	−	0.103400i	−0.446550	+	0.894759i	$0.647348\pi$
$660$		0			0
$661$	−15.3918	−	57.4428i	−0.0232856	−	0.0869029i	0.953305	−	0.302008i	$-0.0976571\pi$
$661$	−15.3918	−	57.4428i	−0.0232856	−	0.0869029i	−0.976591	+	0.215106i	$0.930990\pi$
$662$	−411.650	−	231.951i	−0.621828	−	0.350379i
$663$		0			0
$664$	190.016	+	306.455i	0.286168	+	0.461529i
$665$	−1168.87			−1.75769
$666$		0			0
$667$	−58.6072	+	58.6072i	−0.0878668	+	0.0878668i
$668$	−281.321	+	170.377i	−0.421139	+	0.255056i
$669$		0			0
$670$	−936.521	+	261.486i	−1.39779	+	0.390277i
$671$	80.0205	+	46.1999i	0.119256	+	0.0688523i
$672$		0			0
$673$	−543.120	−	940.711i	−0.807013	−	1.39779i	−0.914924	−	0.403627i	$-0.867749\pi$
$673$	−543.120	−	940.711i	−0.807013	−	1.39779i	0.107911	−	0.994161i	$-0.465584\pi$
$674$	101.113	−	103.254i	0.150019	−	0.153196i
$675$		0			0
$676$	623.083	−	13.0569i	0.921720	−	0.0193149i
$677$	149.940	−	559.583i	0.221477	−	0.826562i	−0.762309	−	0.647213i	$-0.775934\pi$
$677$	149.940	−	559.583i	0.221477	−	0.826562i	0.983786	−	0.179349i	$-0.0573990\pi$
$678$		0			0
$679$	−1016.79	−	587.045i	−1.49748	−	0.864573i
$680$	−334.435	+	623.738i	−0.491817	+	0.917262i
$681$		0			0
$682$	−59.3549	−	100.363i	−0.0870307	−	0.147159i
$683$	−750.817	−	750.817i	−1.09929	−	1.09929i	−0.994493	−	0.104800i	$-0.966580\pi$
$683$	−750.817	−	750.817i	−1.09929	−	1.09929i	−0.104800	−	0.994493i	$-0.533420\pi$
$684$		0			0
$685$	619.835	+	619.835i	0.904868	+	0.904868i
$686$	52.4102	−	204.128i	0.0763998	−	0.297563i
$687$		0			0
$688$	310.981	+	992.282i	0.452007	+	1.44227i
$689$	987.423	+	570.089i	1.43313	+	0.827415i
$690$		0			0
$691$	159.169	−	594.026i	0.230346	−	0.859661i	−0.749847	−	0.661612i	$-0.769873\pi$
$691$	159.169	−	594.026i	0.230346	−	0.859661i	0.980192	−	0.198049i	$-0.0634606\pi$
$692$	−30.2312	−	28.9902i	−0.0436867	−	0.0418933i
$693$		0			0
$694$	−313.729	+	3.28678i	−0.452059	+	0.00473599i
$695$	−22.1751	−	38.4085i	−0.0319067	−	0.0552640i
$696$		0			0
$697$	620.131	+	358.033i	0.889714	+	0.513677i
$698$	−156.831	+	278.332i	−0.224686	+	0.398757i
$699$		0			0
$700$	−96.9527	+	58.7177i	−0.138504	+	0.0838825i
$701$	−601.864	+	601.864i	−0.858579	+	0.858579i	−0.991171	−	0.132592i	$-0.957670\pi$
$701$	−601.864	+	601.864i	−0.858579	+	0.858579i	0.132592	+	0.991171i	$0.457670\pi$
$702$		0			0
$703$	1373.82			1.95422
$704$	126.682	+	25.5403i	0.179946	+	0.0362788i
$705$		0			0
$706$	664.968	−	185.665i	0.941881	−	0.262982i
$707$	458.711	+	1711.93i	0.648813	+	2.42140i
$708$		0			0
$709$	581.464	+	155.803i	0.820119	+	0.219750i	0.644398	−	0.764690i	$-0.277108\pi$
$709$	581.464	+	155.803i	0.820119	+	0.219750i	0.175720	+	0.984440i	$0.443775\pi$
$710$	−353.182	+	3.70011i	−0.497439	+	0.00521142i
$711$		0			0
$712$	255.695	+	240.107i	0.359122	+	0.337229i
$713$	−56.7165	−	98.2359i	−0.0795463	−	0.137778i
$714$		0			0
$715$	−49.5940	−	185.087i	−0.0693623	−	0.258864i
$716$	−1121.80	+	325.924i	−1.56676	+	0.455201i
$717$		0			0
$718$	215.782	+	55.4024i	0.300532	+	0.0771621i
$719$			365.220i			0.507955i	0.967210	+	0.253978i	$0.0817389\pi$
$719$			365.220i			0.507955i	−0.967210	+	0.253978i	$0.918261\pi$
$720$		0			0
$721$	−271.680			−0.376810
$722$	47.1111	−	183.489i	0.0652509	−	0.254140i
$723$		0			0
$724$	79.0535	−	22.9679i	0.109190	−	0.0317236i
$725$	55.5297	−	14.8791i	0.0765927	−	0.0205230i
$726$		0			0
$727$	−725.181	+	418.684i	−0.997499	+	0.575906i	−0.907507	−	0.420036i	$-0.862017\pi$
$727$	−725.181	+	418.684i	−0.997499	+	0.575906i	−0.0899914	+	0.995943i	$0.528684\pi$
$728$	1498.53	−	47.1119i	2.05843	−	0.0647142i
$729$		0			0
$730$	2.45592	+	234.422i	0.00336427	+	0.321126i
$731$	282.621	−	1054.75i	0.386622	−	1.44289i
$732$		0			0
$733$	−195.015	+	52.2542i	−0.266051	+	0.0712881i	−0.389378	−	0.921078i	$-0.627310\pi$
$733$	−195.015	+	52.2542i	−0.266051	+	0.0712881i	0.123327	+	0.992366i	$0.460643\pi$
$734$	185.708	+	665.121i	0.253008	+	0.906160i
$735$		0			0
$736$	122.973	+	26.1361i	0.167083	+	0.0355111i
$737$		−	186.440i		−	0.252971i
$738$		0			0
$739$	−369.474	−	369.474i	−0.499965	−	0.499965i	0.411462	−	0.911427i	$-0.365018\pi$
$739$	−369.474	−	369.474i	−0.499965	−	0.499965i	−0.911427	+	0.411462i	$0.865018\pi$
$740$	1159.38	−	702.156i	1.56672	−	0.948859i
$741$		0			0
$742$	1146.30	+	645.899i	1.54487	+	0.870484i
$743$	69.4193	−	120.238i	0.0934311	−	0.161827i	−0.815522	−	0.578727i	$-0.803550\pi$
$743$	69.4193	−	120.238i	0.0934311	−	0.161827i	0.908953	+	0.416899i	$0.136883\pi$
$744$		0			0
$745$	−664.478	+	383.637i	−0.891917	+	0.514949i
$746$	−1.08929	−	103.975i	−0.00146017	−	0.139376i
$747$		0			0
$748$	−97.9467	−	93.9260i	−0.130945	−	0.125570i
$749$	−611.395	−	163.823i	−0.816282	−	0.218722i
$750$		0			0
$751$	−578.162	+	1001.41i	−0.769856	+	1.33343i	0.167784	+	0.985824i	$0.446339\pi$
$751$	−578.162	+	1001.41i	−0.769856	+	1.33343i	−0.937641	+	0.347606i	$0.886995\pi$
$752$	571.233	+	298.621i	0.759618	+	0.397103i
$753$		0			0
$754$	−736.528	−	189.105i	−0.976828	−	0.250803i
$755$	−493.309	+	493.309i	−0.653389	+	0.653389i
$756$		0			0
$757$	191.468	−	191.468i	0.252930	−	0.252930i	−0.569241	−	0.822171i	$-0.692763\pi$
$757$	191.468	−	191.468i	0.252930	−	0.252930i	0.822171	+	0.569241i	$0.192763\pi$
$758$	399.564	−	236.304i	0.527130	−	0.311747i
$759$		0			0
$760$	−259.919	−	860.856i	−0.341999	−	1.13270i
$761$	606.853	−	1051.10i	0.797442	−	1.38121i	−0.123835	−	0.992303i	$-0.539519\pi$
$761$	606.853	−	1051.10i	0.797442	−	1.38121i	0.921277	−	0.388907i	$-0.127147\pi$
$762$		0			0
$763$	218.516	+	58.5512i	0.286390	+	0.0767381i
$764$	−1047.42	+	21.9490i	−1.37097	+	0.0287291i
$765$		0			0
$766$	−253.774	−	248.512i	−0.331298	−	0.324428i
$767$	753.428	−	434.992i	0.982305	−	0.567134i
$768$		0			0
$769$	−572.412	+	991.446i	−0.744358	+	1.28927i	0.206136	+	0.978523i	$0.433911\pi$
$769$	−572.412	+	991.446i	−0.744358	+	1.28927i	−0.950494	+	0.310743i	$0.899422\pi$
$770$	−59.4649	−	212.976i	−0.0772272	−	0.276592i
$771$		0			0
$772$	−606.625	+	367.392i	−0.785784	+	0.475897i
$773$	980.007	+	980.007i	1.26780	+	1.26780i	0.947224	+	0.320573i	$0.103876\pi$
$773$	980.007	+	980.007i	1.26780	+	1.26780i	0.320573	+	0.947224i	$0.396124\pi$
$774$		0			0
$775$			78.6784i			0.101521i
$776$	206.249	−	879.395i	0.265784	−	1.13324i
$777$		0			0
$778$	−461.795	+	819.562i	−0.593566	+	1.05342i
$779$	−878.816	+	235.478i	−1.12813	+	0.302282i
$780$		0			0
$781$	17.5282	−	65.4163i	0.0224433	−	0.0837597i
$782$	−94.3235	−	92.3677i	−0.120618	−	0.118117i
$783$		0			0
$784$	945.304	−	39.6356i	1.20574	−	0.0505557i
$785$	1189.81	−	686.938i	1.51568	−	0.875081i
$786$		0			0
$787$	163.984	−	43.9393i	0.208366	−	0.0558314i	−0.153126	−	0.988207i	$-0.548934\pi$
$787$	163.984	−	43.9393i	0.208366	−	0.0558314i	0.361492	+	0.932375i	$0.382267\pi$
$788$	−427.330	−	1470.83i	−0.542297	−	1.86654i
$789$		0			0
$790$	567.840	+	960.155i	0.718784	+	1.21539i
$791$	1231.13			1.55643
$792$		0			0
$793$			824.701i			1.03998i
$794$	3.20448	+	5.41844i	0.00403587	+	0.00682423i
$795$		0			0
$796$	348.543	−	634.010i	0.437868	−	0.796495i
$797$	−195.256	−	728.705i	−0.244989	−	0.914310i	−0.973389	−	0.229158i	$-0.926403\pi$
$797$	−195.256	−	728.705i	−0.244989	−	0.914310i	0.728401	−	0.685152i	$-0.240264\pi$
$798$		0			0
$799$	−338.434	−	586.185i	−0.423572	−	0.733648i
$800$	−64.8041	−	58.3474i	−0.0810051	−	0.0729343i
$801$		0			0
$802$	893.332	+	874.808i	1.11388	+	1.09078i
$803$	−43.4195	−	11.6342i	−0.0540716	−	0.0144885i
$804$		0			0
$805$	−55.6759	−	207.785i	−0.0691626	−	0.258118i
$806$	510.880	−	906.676i	0.633847	−	1.12491i
$807$		0			0
$808$	−1158.81	+	718.515i	−1.43418	+	0.889251i
$809$	−69.5741			−0.0860001			−0.0430001	−	0.999075i	$-0.513692\pi$
$809$	−69.5741			−0.0860001			−0.0430001	+	0.999075i	$0.513692\pi$
$810$		0			0
$811$	−180.068	+	180.068i	−0.222032	+	0.222032i	−0.809354	−	0.587322i	$-0.800182\pi$
$811$	−180.068	+	180.068i	−0.222032	+	0.222032i	0.587322	+	0.809354i	$0.300182\pi$
$812$	−852.179	−	209.308i	−1.04948	−	0.257768i
$813$		0			0
$814$	69.8915	+	250.319i	0.0858618	+	0.307517i
$815$	−708.101	−	408.822i	−0.868835	−	0.501622i
$816$		0			0
$817$	693.712	+	1201.54i	0.849096	+	1.47068i
$818$	111.144	+	108.839i	0.135873	+	0.133055i
$819$		0			0
$820$	−621.288	+	647.884i	−0.757669	+	0.790103i
$821$	−395.351	+	1475.47i	−0.481548	+	1.79716i	0.113576	+	0.993529i	$0.463769\pi$
$821$	−395.351	+	1475.47i	−0.481548	+	1.79716i	−0.595125	+	0.803633i	$0.702897\pi$
$822$		0			0
$823$	140.453	+	81.0905i	0.170660	+	0.0985304i	0.582897	−	0.812546i	$-0.301919\pi$
$823$	140.453	+	81.0905i	0.170660	+	0.0985304i	−0.412237	+	0.911077i	$0.635252\pi$
$824$	−60.4131	−	200.089i	−0.0733169	−	0.242826i
$825$		0			0
$826$	864.136	−	511.053i	1.04617	−	0.618708i
$827$	575.338	+	575.338i	0.695692	+	0.695692i	0.963478	−	0.267786i	$-0.0862920\pi$
$827$	575.338	+	575.338i	0.695692	+	0.695692i	−0.267786	+	0.963478i	$0.586292\pi$
$828$		0			0
$829$	−436.643	−	436.643i	−0.526711	−	0.526711i	0.392879	−	0.919590i	$-0.371479\pi$
$829$	−436.643	−	436.643i	−0.526711	−	0.526711i	−0.919590	+	0.392879i	$0.871479\pi$
$830$	459.748	+	118.041i	0.553913	+	0.142218i
$831$		0			0
$832$	367.924	+	1093.18i	0.442217	+	1.31391i
$833$	−860.421	−	496.765i	−1.03292	−	0.596356i
$834$		0			0
$835$	−112.054	+	418.190i	−0.134196	+	0.500826i
$836$	172.385	−	3.61238i	0.206202	−	0.00432103i
$837$		0			0
$838$	−11.1700	−	1066.19i	−0.0133293	−	1.27231i
$839$	−2.35593	−	4.08058i	−0.00280802	−	0.00486363i	0.864618	−	0.502430i	$-0.167560\pi$
$839$	−2.35593	−	4.08058i	−0.00280802	−	0.00486363i	−0.867426	+	0.497566i	$0.834227\pi$
$840$		0			0
$841$	−342.891	−	197.968i	−0.407718	−	0.235396i
$842$	−517.694	−	291.703i	−0.614839	−	0.346441i
$843$		0			0
$844$	−1375.63	−	337.874i	−1.62989	−	0.400325i
$845$	580.099	−	580.099i	0.686508	−	0.686508i
$846$		0			0
$847$	−1215.85			−1.43547
$848$	−220.796	+	987.861i	−0.260373	+	1.16493i
$849$		0			0
$850$	24.6251	+	88.1958i	0.0289707	+	0.103760i
$851$	65.4380	+	244.218i	0.0768955	+	0.286978i
$852$		0			0
$853$	255.888	+	68.5651i	0.299986	+	0.0803811i	0.405673	−	0.914018i	$-0.367037\pi$
$853$	255.888	+	68.5651i	0.299986	+	0.0803811i	−0.105686	+	0.994400i	$0.533704\pi$
$854$	9.96981	+	951.636i	0.0116743	+	1.11433i
$855$		0			0
$856$	−15.3016	−	486.714i	−0.0178758	−	0.568591i
$857$	−778.832	−	1348.98i	−0.908789	−	1.57407i	−0.815749	−	0.578407i	$-0.803675\pi$
$857$	−778.832	−	1348.98i	−0.908789	−	1.57407i	−0.0930404	−	0.995662i	$-0.529659\pi$
$858$		0			0
$859$	−256.728	−	958.120i	−0.298868	−	1.11539i	−0.938097	−	0.346374i	$-0.887413\pi$
$859$	−256.728	−	958.120i	−0.298868	−	1.11539i	0.639229	−	0.769017i	$-0.279254\pi$
$860$	1199.54	+	659.439i	1.39481	+	0.766789i
$861$		0			0
$862$	−290.233	+	1130.40i	−0.336697	+	1.31137i
$863$		−	423.375i		−	0.490585i	−0.969449	−	0.245292i	$-0.921116\pi$
$863$		−	423.375i		−	0.490585i	0.969449	−	0.245292i	$-0.0788840\pi$
$864$		0			0
$865$	−55.1360			−0.0637410
$866$	888.495	+	228.123i	1.02598	+	0.263421i
$867$		0			0
$868$	578.553	−	1052.40i	0.666536	−	1.21245i
$869$	−206.601	+	55.3587i	−0.237746	+	0.0637039i
$870$		0			0
$871$	1441.10	−	832.020i	1.65454	−	0.955247i
$872$	5.46889	+	173.954i	0.00627166	+	0.199489i
$873$		0			0
$874$	167.730	−	1.75722i	0.191910	−	0.00201055i
$875$	315.667	−	1178.09i	0.360762	−	1.34638i
$876$		0			0
$877$	1091.81	−	292.549i	1.24493	−	0.333579i	0.424557	−	0.905401i	$-0.360430\pi$
$877$	1091.81	−	292.549i	1.24493	−	0.333579i	0.820378	+	0.571822i	$0.193763\pi$
$878$	262.742	−	73.3601i	0.299251	−	0.0835537i
$879$		0			0
$880$	143.631	−	91.1544i	0.163217	−	0.103585i
$881$		−	728.130i		−	0.826482i	−0.910622	−	0.413241i	$-0.864397\pi$
$881$		−	728.130i		−	0.826482i	0.910622	−	0.413241i	$-0.135603\pi$
$882$		0			0
$883$	535.917	+	535.917i	0.606928	+	0.606928i	0.942142	−	0.335214i	$-0.108809\pi$
$883$	535.917	+	535.917i	0.606928	+	0.606928i	−0.335214	+	0.942142i	$0.608809\pi$
$884$	288.904	−	1176.25i	0.326815	−	1.33060i
$885$		0			0
$886$	−57.5129	+	102.070i	−0.0649129	+	0.115203i
$887$	−230.697	+	399.579i	−0.260087	+	0.450484i	−0.966265	−	0.257551i	$-0.917085\pi$
$887$	−230.697	+	399.579i	−0.260087	+	0.450484i	0.706178	+	0.708035i	$0.250418\pi$
$888$		0			0
$889$	154.272	−	89.0693i	0.173535	−	0.100190i
$890$	461.700	−	4.83700i	0.518764	−	0.00543483i
$891$		0			0
$892$	−21.4426	−	1023.25i	−0.0240387	−	1.14714i
$893$	830.709	+	222.588i	0.930245	+	0.249258i
$894$		0			0
$895$	−768.881	+	1331.74i	−0.859085	+	1.48798i
$896$	437.770	+	1256.99i	0.488582	+	1.40289i
$897$		0			0
$898$	256.507	−	999.046i	0.285643	−	1.11252i
$899$	−430.706	+	430.706i	−0.479094	+	0.479094i
$900$		0			0
$901$	751.613	−	751.613i	0.834199	−	0.834199i
$902$	−87.6147	−	148.147i	−0.0971338	−	0.164243i
$903$		0			0
$904$	273.766	+	906.715i	0.302838	+	1.00300i
$905$	54.1832	−	93.8480i	0.0598709	−	0.103699i
$906$		0			0
$907$	1013.97	+	271.691i	1.11793	+	0.299549i	0.770047	−	0.637987i	$-0.220233\pi$
$907$	1013.97	+	271.691i	1.11793	+	0.299549i	0.347887	+	0.937537i	$0.386899\pi$
$908$	−667.548	−	640.145i	−0.735185	−	0.705005i
$909$		0			0
$910$	1380.84	−	1410.08i	1.51741	−	1.54954i
$911$	−916.609	+	529.204i	−1.00616	+	0.580905i	−0.910064	−	0.414467i	$-0.863968\pi$
$911$	−916.609	+	529.204i	−1.00616	+	0.580905i	−0.0960927	+	0.995372i	$0.530635\pi$
$912$		0			0
$913$	−45.5064	+	78.8193i	−0.0498427	+	0.0863300i
$914$	756.332	−	211.175i	0.827497	−	0.231045i
$915$		0			0
$916$	202.082	−	822.761i	0.220614	−	0.898211i
$917$	496.506	+	496.506i	0.541446	+	0.541446i
$918$		0			0
$919$		−	880.215i		−	0.957796i	−0.877871	−	0.478898i	$-0.841036\pi$
$919$		−	880.215i		−	0.957796i	0.877871	−	0.478898i	$-0.158964\pi$
$920$	140.651	−	87.2095i	0.152881	−	0.0947929i
$921$		0			0
$922$	−13.6083	−	7.66778i	−0.0147595	−	0.00831647i
$923$	583.864	−	156.446i	0.632572	−	0.169497i
$924$		0			0
$925$	45.3886	−	169.392i	0.0490687	−	0.183127i
$926$	−902.561	+	921.673i	−0.974688	+	0.995327i
$927$		0			0
$928$	−35.3454	−	674.163i	−0.0380877	−	0.726469i
$929$	−1220.81	+	704.834i	−1.31411	+	0.758702i	−0.982774	−	0.184810i	$-0.940833\pi$
$929$	−1220.81	+	704.834i	−1.31411	+	0.758702i	−0.331337	+	0.943513i	$0.607500\pi$
$930$		0			0
$931$	1219.34	−	326.722i	1.30971	−	0.350936i
$932$	−393.215	−	216.168i	−0.421905	−	0.231939i
$933$		0			0
$934$	−650.083	+	384.462i	−0.696020	+	0.411629i
$935$	−178.636			−0.191055
$936$		0			0
$937$		−	121.127i		−	0.129271i	−0.997909	−	0.0646356i	$-0.979412\pi$
$937$		−	121.127i		−	0.129271i	0.997909	−	0.0646356i	$-0.0205885\pi$
$938$	1652.85	−	977.504i	1.76210	−	1.04212i
$939$		0			0
$940$	814.807	−	236.731i	0.866816	−	0.251841i
$941$	90.1803	+	336.558i	0.0958346	+	0.357660i	0.997145	−	0.0755149i	$-0.0240601\pi$
$941$	90.1803	+	336.558i	0.0958346	+	0.357660i	−0.901310	+	0.433174i	$0.857393\pi$
$942$		0			0
$943$	−83.7201	−	145.007i	−0.0887806	−	0.153773i
$944$	568.541	+	522.783i	0.602268	+	0.553795i
$945$		0			0
$946$	−183.638	+	187.527i	−0.194121	+	0.198231i
$947$	1225.91	+	328.480i	1.29451	+	0.346864i	0.839373	−	0.543555i	$-0.182922\pi$
$947$	1225.91	+	328.480i	1.29451	+	0.346864i	0.455141	+	0.890419i	$0.349589\pi$
$948$		0			0
$949$	−103.840	−	387.535i	−0.109420	−	0.408361i
$950$	−101.362	−	57.1141i	−0.106697	−	0.0601201i
$951$		0			0
$952$	319.152	−	1360.79i	0.335244	−	1.42940i
$953$	−771.315			−0.809355			−0.404678	−	0.914459i	$-0.632616\pi$
$953$	−771.315			−0.809355			−0.404678	+	0.914459i	$0.632616\pi$
$954$		0			0
$955$	−975.165	+	975.165i	−1.02112	+	1.02112i
$956$	268.476	+	443.298i	0.280832	+	0.463701i
$957$		0			0
$958$	925.294	−	258.351i	0.965860	−	0.269677i
$959$	−1499.22	−	865.575i	−1.56332	−	0.902581i
$960$		0			0
$961$	63.6884	+	110.312i	0.0662731	+	0.114788i
$962$	−1622.96	+	1657.33i	−1.68707	+	1.72279i
$963$		0			0
$964$	2.27990	+	108.798i	0.00236505	+	0.112861i
$965$	−241.626	+	901.761i	−0.250390	+	0.934467i
$966$		0			0
$967$	−243.033	−	140.315i	−0.251327	−	0.145103i	0.369045	−	0.929412i	$-0.379685\pi$
$967$	−243.033	−	140.315i	−0.251327	−	0.145103i	−0.620372	+	0.784308i	$0.713018\pi$
$968$	−270.366	−	895.456i	−0.279304	−	0.925058i
$969$		0			0
$970$	−605.263	−	1023.43i	−0.623982	−	1.05509i
$971$	703.757	+	703.757i	0.724775	+	0.724775i	0.969574	−	0.244799i	$-0.0787219\pi$
$971$	703.757	+	703.757i	0.724775	+	0.724775i	−0.244799	+	0.969574i	$0.578722\pi$
$972$		0			0
$973$	61.9334	+	61.9334i	0.0636520	+	0.0636520i
$974$	−261.253	+	1017.53i	−0.268227	+	1.04469i
$975$		0			0
$976$	−698.651	+	218.957i	−0.715831	+	0.224341i
$977$	−1272.36	−	734.600i	−1.30232	−	0.751894i	−0.321517	−	0.946904i	$-0.604193\pi$
$977$	−1272.36	−	734.600i	−1.30232	−	0.751894i	−0.980801	+	0.195010i	$0.937526\pi$
$978$		0			0
$979$	−22.9140	+	85.5160i	−0.0234055	+	0.0873504i
$980$	862.027	−	898.929i	0.879620	−	0.917274i
$981$		0			0
$982$	−1101.90	+	11.5440i	−1.12209	+	0.0117556i
$983$	−337.940	−	585.330i	−0.343785	−	0.595453i	0.641348	−	0.767251i	$-0.278376\pi$
$983$	−337.940	−	585.330i	−0.343785	−	0.595453i	−0.985132	+	0.171798i	$0.945042\pi$
$984$		0			0
$985$	−1746.09	−	1008.11i	−1.77268	−	1.02346i
$986$	−348.002	+	617.610i	−0.352943	+	0.626379i
$987$		0			0
$988$	797.221	+	1316.34i	0.806904	+	1.33233i
$989$	−180.551	+	180.551i	−0.182559	+	0.182559i
$990$		0			0
$991$	1448.45			1.46161			0.730804	−	0.682587i	$-0.239145\pi$
$991$	1448.45			1.46161			0.730804	+	0.682587i	$0.239145\pi$
$992$	903.735	+	192.075i	0.911023	+	0.193624i
$993$		0			0
$994$	671.839	−	187.584i	0.675895	−	0.188716i
$995$	−246.496	−	919.936i	−0.247735	−	0.924559i
$996$		0			0
$997$	735.194	+	196.995i	0.737406	+	0.197587i	0.607925	−	0.793995i	$-0.292002\pi$
$997$	735.194	+	196.995i	0.737406	+	0.197587i	0.129481	+	0.991582i	$0.458669\pi$
$998$	−200.571	+	2.10128i	−0.200973	+	0.00210549i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	432.3.x.a.125.4		184
3.2	odd	2		144.3.w.a.77.43	yes	184
9.2	odd	6	inner	432.3.x.a.413.19		184
9.7	even	3		144.3.w.a.29.28	yes	184
16.5	even	4	inner	432.3.x.a.341.19		184
48.5	odd	4		144.3.w.a.5.28	✓	184
144.101	odd	12	inner	432.3.x.a.197.4		184
144.133	even	12		144.3.w.a.101.43	yes	184

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
144.3.w.a.5.28	✓	184	48.5	odd	4
144.3.w.a.29.28	yes	184	9.7	even	3
144.3.w.a.77.43	yes	184	3.2	odd	2
144.3.w.a.101.43	yes	184	144.133	even	12
432.3.x.a.125.4		184	1.1	even	1	trivial
432.3.x.a.197.4		184	144.101	odd	12	inner
432.3.x.a.341.19		184	16.5	even	4	inner
432.3.x.a.413.19		184	9.2	odd	6	inner

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:	\( N \)	\(=\)	\( 432 = 2^{4} \cdot 3^{3} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	432.x (of order \(12\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.93717 - 0.497372i) q^{2} +(3.50524 + 1.92699i) q^{4} +(5.08604 - 1.36280i) q^{5} +(-9.00556 + 5.19936i) q^{7} +(-5.83182 - 5.47630i) q^{8} +O(q^{10})\)	\(q+(-1.93717 - 0.497372i) q^{2} +(3.50524 + 1.92699i) q^{4} +(5.08604 - 1.36280i) q^{5} +(-9.00556 + 5.19936i) q^{7} +(-5.83182 - 5.47630i) q^{8} +(-10.5303 + 0.110321i) q^{10} +(0.522615 - 1.95043i) q^{11} +(17.4082 - 4.66453i) q^{13} +(20.0313 - 5.59293i) q^{14} +(8.57345 + 13.5091i) q^{16} -16.8015i q^{17} +(15.0950 + 15.0950i) q^{19} +(20.4539 + 5.02378i) q^{20} +(-1.98248 + 3.51837i) q^{22} +(-1.96438 + 3.40240i) q^{23} +(2.35994 - 1.36251i) q^{25} +(-36.0427 + 0.377601i) q^{26} +(-41.5858 + 0.871442i) q^{28} +(20.3777 + 5.46018i) q^{29} +(-14.4363 + 25.0043i) q^{31} +(-9.88917 - 30.4336i) q^{32} +(-8.35659 + 32.5473i) q^{34} +(-38.7169 + 38.7169i) q^{35} +(45.5055 - 45.5055i) q^{37} +(-21.7338 - 36.7495i) q^{38} +(-37.1240 - 19.9051i) q^{40} +(-21.3096 + 36.9093i) q^{41} +(62.7774 + 16.8212i) q^{43} +(5.59034 - 5.82965i) q^{44} +(5.49759 - 5.61400i) q^{46} +(34.8888 - 20.1431i) q^{47} +(29.5667 - 51.2110i) q^{49} +(-5.24928 + 1.46565i) q^{50} +(70.0086 + 17.1951i) q^{52} +(44.7349 + 44.7349i) q^{53} -10.6322i q^{55} +(80.9920 + 18.9955i) q^{56} +(-36.7593 - 20.7126i) q^{58} +(46.6277 - 12.4938i) q^{59} +(-11.8435 + 44.2007i) q^{61} +(40.4019 - 41.2574i) q^{62} +(4.02018 + 63.8736i) q^{64} +(82.1822 - 47.4479i) q^{65} +(89.1859 - 23.8973i) q^{67} +(32.3762 - 58.8933i) q^{68} +(94.2579 - 55.7445i) q^{70} +33.5395 q^{71} -22.2616i q^{73} +(-110.785 + 65.5187i) q^{74} +(23.8238 + 81.9997i) q^{76} +(5.43453 + 20.2819i) q^{77} +(-52.9631 - 91.7348i) q^{79} +(62.0151 + 57.0239i) q^{80} +(59.6379 - 60.9007i) q^{82} +(-43.5372 - 11.6657i) q^{83} +(-22.8971 - 85.4530i) q^{85} +(-113.244 - 63.8092i) q^{86} +(-13.7289 + 8.51253i) q^{88} -43.8448 q^{89} +(-132.518 + 132.518i) q^{91} +(-13.4420 + 8.14091i) q^{92} +(-77.6042 + 21.6678i) q^{94} +(97.3455 + 56.2024i) q^{95} +(56.4536 + 97.7805i) q^{97} +(-82.7466 + 84.4987i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 184 q + 6 q^{2} - 2 q^{4} + 6 q^{5}+O(q^{10}) \) 184 * q + 6 * q^2 - 2 * q^4 + 6 * q^5	\( 184 q + 6 q^{2} - 2 q^{4} + 6 q^{5} - 8 q^{10} + 6 q^{11} - 2 q^{13} + 6 q^{14} - 2 q^{16} - 8 q^{19} - 120 q^{20} - 2 q^{22} - 72 q^{28} + 6 q^{29} - 4 q^{31} + 6 q^{32} + 6 q^{34} - 8 q^{37} + 6 q^{38} - 2 q^{40} - 2 q^{43} - 160 q^{46} + 12 q^{47} + 472 q^{49} - 228 q^{50} - 2 q^{52} + 300 q^{56} - 92 q^{58} + 438 q^{59} - 2 q^{61} + 244 q^{64} + 12 q^{65} - 2 q^{67} + 144 q^{68} + 96 q^{70} - 246 q^{74} - 158 q^{76} + 6 q^{77} - 4 q^{79} - 388 q^{82} + 726 q^{83} + 48 q^{85} - 894 q^{86} + 22 q^{88} - 204 q^{91} + 348 q^{92} - 18 q^{94} + 12 q^{95} - 4 q^{97}+O(q^{100}) \) 184 * q + 6 * q^2 - 2 * q^4 + 6 * q^5 - 8 * q^10 + 6 * q^11 - 2 * q^13 + 6 * q^14 - 2 * q^16 - 8 * q^19 - 120 * q^20 - 2 * q^22 - 72 * q^28 + 6 * q^29 - 4 * q^31 + 6 * q^32 + 6 * q^34 - 8 * q^37 + 6 * q^38 - 2 * q^40 - 2 * q^43 - 160 * q^46 + 12 * q^47 + 472 * q^49 - 228 * q^50 - 2 * q^52 + 300 * q^56 - 92 * q^58 + 438 * q^59 - 2 * q^61 + 244 * q^64 + 12 * q^65 - 2 * q^67 + 144 * q^68 + 96 * q^70 - 246 * q^74 - 158 * q^76 + 6 * q^77 - 4 * q^79 - 388 * q^82 + 726 * q^83 + 48 * q^85 - 894 * q^86 + 22 * q^88 - 204 * q^91 + 348 * q^92 - 18 * q^94 + 12 * q^95 - 4 * q^97

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