LMFDB - Embedded newform 432.3.bc.a.65.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [432,3,Mod(65,432)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(432, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([0, 0, 13]))

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

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

chi := DirichletCharacter("432.65");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 432 = 2^{4} \cdot 3^{3} $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	432.bc (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:	$11.7711474204$
Analytic rank:	$0$
Dimension:	$30$
Relative dimension:	$5$ over $\Q(\zeta_{18})$
Twist minimal:	no (minimal twist has level 27)
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			65.4
Character	$\chi$	$=$	432.65
Dual form			432.3.bc.a.113.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(2.03568 - 2.20363i) q^{3} +(-2.35247 + 6.46335i) q^{5} +(-1.10811 + 6.28443i) q^{7} +(-0.712002 - 8.97179i) q^{9} +O(q^{10})$	\(q+(2.03568 - 2.20363i) q^{3} +(-2.35247 + 6.46335i) q^{5} +(-1.10811 + 6.28443i) q^{7} +(-0.712002 - 8.97179i) q^{9} +(-0.425636 - 1.16942i) q^{11} +(-4.09039 + 3.43225i) q^{13} +(9.45398 + 18.3413i) q^{15} +(-13.7418 + 7.93385i) q^{17} +(-6.78917 + 11.7592i) q^{19} +(11.5928 + 15.2350i) q^{21} +(-24.4347 + 4.30850i) q^{23} +(-17.0897 - 14.3399i) q^{25} +(-21.2200 - 16.6947i) q^{27} +(-19.9186 + 23.7381i) q^{29} +(2.75731 + 15.6375i) q^{31} +(-3.44344 - 1.44263i) q^{33} +(-38.0116 - 21.9460i) q^{35} +(26.0365 + 45.0965i) q^{37} +(-0.763322 + 16.0007i) q^{39} +(-0.694475 - 0.827643i) q^{41} +(45.3904 - 16.5207i) q^{43} +(59.6628 + 16.5039i) q^{45} +(56.7291 + 10.0029i) q^{47} +(7.77884 + 2.83127i) q^{49} +(-10.4907 + 46.4327i) q^{51} -13.8414i q^{53} +8.55969 q^{55} +(12.0924 + 38.8988i) q^{57} +(-20.6246 + 56.6655i) q^{59} +(17.5357 - 99.4497i) q^{61} +(57.1715 + 5.46725i) q^{63} +(-12.5613 - 34.5119i) q^{65} +(60.2302 - 50.5391i) q^{67} +(-40.2470 + 62.6160i) q^{69} +(-39.7545 + 22.9523i) q^{71} +(-34.4926 + 59.7430i) q^{73} +(-66.3891 + 8.46783i) q^{75} +(7.82081 - 1.37902i) q^{77} +(-30.2928 - 25.4187i) q^{79} +(-79.9861 + 12.7759i) q^{81} +(27.1277 - 32.3296i) q^{83} +(-18.9520 - 107.482i) q^{85} +(11.7621 + 92.2165i) q^{87} +(-61.8262 - 35.6954i) q^{89} +(-17.0371 - 29.5091i) q^{91} +(40.0723 + 25.7569i) q^{93} +(-60.0324 - 71.5439i) q^{95} +(-1.06372 + 0.387161i) q^{97} +(-10.1888 + 4.65135i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 30 q + 6 q^{3} - 15 q^{5} + 6 q^{7}+O(q^{10}) $ 30 * q + 6 * q^3 - 15 * q^5 + 6 * q^7	$ 30 q + 6 q^{3} - 15 q^{5} + 6 q^{7} + 6 q^{11} - 6 q^{13} + 9 q^{15} - 9 q^{17} + 3 q^{19} + 132 q^{21} - 120 q^{23} - 15 q^{25} + 90 q^{27} - 168 q^{29} - 39 q^{31} - 207 q^{33} + 252 q^{35} - 3 q^{37} - 15 q^{39} + 228 q^{41} + 96 q^{43} + 477 q^{45} - 399 q^{47} - 78 q^{49} - 36 q^{51} + 12 q^{55} - 192 q^{57} + 474 q^{59} + 138 q^{61} + 585 q^{63} - 411 q^{65} - 354 q^{67} + 99 q^{69} - 315 q^{71} - 66 q^{73} - 255 q^{75} + 201 q^{77} - 30 q^{79} + 36 q^{81} + 33 q^{83} - 261 q^{85} + 279 q^{87} + 72 q^{89} - 96 q^{91} + 591 q^{93} - 681 q^{95} - 582 q^{97} - 513 q^{99}+O(q^{100}) $ 30 * q + 6 * q^3 - 15 * q^5 + 6 * q^7 + 6 * q^11 - 6 * q^13 + 9 * q^15 - 9 * q^17 + 3 * q^19 + 132 * q^21 - 120 * q^23 - 15 * q^25 + 90 * q^27 - 168 * q^29 - 39 * q^31 - 207 * q^33 + 252 * q^35 - 3 * q^37 - 15 * q^39 + 228 * q^41 + 96 * q^43 + 477 * q^45 - 399 * q^47 - 78 * q^49 - 36 * q^51 + 12 * q^55 - 192 * q^57 + 474 * q^59 + 138 * q^61 + 585 * q^63 - 411 * q^65 - 354 * q^67 + 99 * q^69 - 315 * q^71 - 66 * q^73 - 255 * q^75 + 201 * q^77 - 30 * q^79 + 36 * q^81 + 33 * q^83 - 261 * q^85 + 279 * q^87 + 72 * q^89 - 96 * q^91 + 591 * q^93 - 681 * q^95 - 582 * q^97 - 513 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$271$	$325$	$353$
$\chi(n)$	$1$	$1$	$e\left(\frac{13}{18}\right)$

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			0
$2$		0			0
$3$	2.03568	−	2.20363i	0.678560	−	0.734545i
$3$	2.03568	−	2.20363i	0.678560	−	0.734545i
$4$		0			0
$5$	−2.35247	+	6.46335i	−0.470493	+	1.29267i	0.446863	+	0.894602i	$0.352541\pi$
$5$	−2.35247	+	6.46335i	−0.470493	+	1.29267i	−0.917356	+	0.398067i	$0.869681\pi$
$6$		0			0
$7$	−1.10811	+	6.28443i	−0.158302	+	0.897775i	0.797403	+	0.603448i	$0.206207\pi$
$7$	−1.10811	+	6.28443i	−0.158302	+	0.897775i	−0.955705	+	0.294328i	$0.904904\pi$
$8$		0			0
$9$	−0.712002	−	8.97179i	−0.0791113	−	0.996866i
$10$		0			0
$11$	−0.425636	−	1.16942i	−0.0386941	−	0.106311i	0.918841	−	0.394628i	$-0.129127\pi$
$11$	−0.425636	−	1.16942i	−0.0386941	−	0.106311i	−0.957535	+	0.288317i	$0.906904\pi$
$12$		0			0
$13$	−4.09039	+	3.43225i	−0.314646	+	0.264019i	−0.786409	−	0.617706i	$-0.788062\pi$
$13$	−4.09039	+	3.43225i	−0.314646	+	0.264019i	0.471763	+	0.881725i	$0.343618\pi$
$14$		0			0
$15$	9.45398	+	18.3413i	0.630265	+	1.22275i
$16$		0			0
$17$	−13.7418	+	7.93385i	−0.808343	+	0.466697i	−0.846380	−	0.532579i	$-0.821223\pi$
$17$	−13.7418	+	7.93385i	−0.808343	+	0.466697i	0.0380373	+	0.999276i	$0.487889\pi$
$18$		0			0
$19$	−6.78917	+	11.7592i	−0.357325	+	0.618905i	−0.987513	−	0.157538i	$-0.949644\pi$
$19$	−6.78917	+	11.7592i	−0.357325	+	0.618905i	0.630188	+	0.776442i	$0.282978\pi$
$20$		0			0
$21$	11.5928	+	15.2350i	0.552038	+	0.725475i
$22$		0			0
$23$	−24.4347	+	4.30850i	−1.06238	+	0.187326i	−0.677412	−	0.735604i	$-0.736899\pi$
$23$	−24.4347	+	4.30850i	−1.06238	+	0.187326i	−0.384968	+	0.922930i	$0.625787\pi$
$24$		0			0
$25$	−17.0897	−	14.3399i	−0.683587	−	0.573597i
$26$		0			0
$27$	−21.2200	−	16.6947i	−0.785924	−	0.618323i
$28$		0			0
$29$	−19.9186	+	23.7381i	−0.686849	+	0.818554i	−0.990971	−	0.134079i	$-0.957192\pi$
$29$	−19.9186	+	23.7381i	−0.686849	+	0.818554i	0.304122	+	0.952633i	$0.401637\pi$
$30$		0			0
$31$	2.75731	+	15.6375i	0.0889455	+	0.504435i	0.996435	+	0.0843610i	$0.0268849\pi$
$31$	2.75731	+	15.6375i	0.0889455	+	0.504435i	−0.907490	+	0.420074i	$0.862004\pi$
$32$		0			0
$33$	−3.44344	−	1.44263i	−0.104347	−	0.0437161i
$34$		0			0
$35$	−38.0116	−	21.9460i	−1.08605	−	0.627029i
$36$		0			0
$37$	26.0365	+	45.0965i	0.703688	+	1.21882i	0.967163	+	0.254158i	$0.0817982\pi$
$37$	26.0365	+	45.0965i	0.703688	+	1.21882i	−0.263474	+	0.964666i	$0.584868\pi$
$38$		0			0
$39$	−0.763322	+	16.0007i	−0.0195724	+	0.410274i
$40$		0			0
$41$	−0.694475	−	0.827643i	−0.0169384	−	0.0201864i	0.757509	−	0.652825i	$-0.226416\pi$
$41$	−0.694475	−	0.827643i	−0.0169384	−	0.0201864i	−0.774447	+	0.632639i	$0.781972\pi$
$42$		0			0
$43$	45.3904	−	16.5207i	1.05559	−	0.384203i	0.244820	−	0.969569i	$-0.421271\pi$
$43$	45.3904	−	16.5207i	1.05559	−	0.384203i	0.810770	+	0.585365i	$0.199049\pi$
$44$		0			0
$45$	59.6628	+	16.5039i	1.32584	+	0.366754i
$46$		0			0
$47$	56.7291	+	10.0029i	1.20700	+	0.212827i	0.740723	−	0.671811i	$-0.234483\pi$
$47$	56.7291	+	10.0029i	1.20700	+	0.212827i	0.466279	+	0.884638i	$0.345594\pi$
$48$		0			0
$49$	7.77884	+	2.83127i	0.158752	+	0.0577809i
$50$		0			0
$51$	−10.4907	+	46.4327i	−0.205700	+	0.910446i
$52$		0			0
$53$		−	13.8414i		−	0.261159i	−0.991438	−	0.130579i	$-0.958316\pi$
$53$		−	13.8414i		−	0.261159i	0.991438	−	0.130579i	$-0.0416837\pi$
$54$		0			0
$55$	8.55969			0.155631
$56$		0			0
$57$	12.0924	+	38.8988i	0.212147	+	0.682435i
$58$		0			0
$59$	−20.6246	+	56.6655i	−0.349569	+	0.960432i	0.632938	+	0.774203i	$0.281849\pi$
$59$	−20.6246	+	56.6655i	−0.349569	+	0.960432i	−0.982506	+	0.186229i	$0.940373\pi$
$60$		0			0
$61$	17.5357	−	99.4497i	0.287470	−	1.63032i	−0.408857	−	0.912598i	$-0.634073\pi$
$61$	17.5357	−	99.4497i	0.287470	−	1.63032i	0.696327	−	0.717725i	$-0.254816\pi$
$62$		0			0
$63$	57.1715	+	5.46725i	0.907485	+	0.0867817i
$64$		0			0
$65$	−12.5613	−	34.5119i	−0.193251	−	0.530952i
$66$		0			0
$67$	60.2302	−	50.5391i	0.898958	−	0.754315i	−0.0710284	−	0.997474i	$-0.522628\pi$
$67$	60.2302	−	50.5391i	0.898958	−	0.754315i	0.969986	+	0.243159i	$0.0781837\pi$
$68$		0			0
$69$	−40.2470	+	62.6160i	−0.583290	+	0.907478i
$70$		0			0
$71$	−39.7545	+	22.9523i	−0.559922	+	0.323271i	−0.753114	−	0.657890i	$-0.771449\pi$
$71$	−39.7545	+	22.9523i	−0.559922	+	0.323271i	0.193192	+	0.981161i	$0.438116\pi$
$72$		0			0
$73$	−34.4926	+	59.7430i	−0.472502	+	0.818397i	−0.999505	−	0.0314663i	$-0.989982\pi$
$73$	−34.4926	+	59.7430i	−0.472502	+	0.818397i	0.527003	+	0.849863i	$0.323316\pi$
$74$		0			0
$75$	−66.3891	+	8.46783i	−0.885188	+	0.112904i
$76$		0			0
$77$	7.82081	−	1.37902i	0.101569	−	0.0179094i
$78$		0			0
$79$	−30.2928	−	25.4187i	−0.383453	−	0.321756i	0.430603	−	0.902541i	$-0.358301\pi$
$79$	−30.2928	−	25.4187i	−0.383453	−	0.321756i	−0.814056	+	0.580786i	$0.802745\pi$
$80$		0			0
$81$	−79.9861	+	12.7759i	−0.987483	+	0.157727i
$82$		0			0
$83$	27.1277	−	32.3296i	0.326840	−	0.389513i	−0.577454	−	0.816423i	$-0.695954\pi$
$83$	27.1277	−	32.3296i	0.326840	−	0.389513i	0.904294	+	0.426910i	$0.140398\pi$
$84$		0			0
$85$	−18.9520	−	107.482i	−0.222965	−	1.26450i
$86$		0			0
$87$	11.7621	+	92.2165i	0.135196	+	1.05996i
$88$		0			0
$89$	−61.8262	−	35.6954i	−0.694676	−	0.401072i	0.110685	−	0.993856i	$-0.464695\pi$
$89$	−61.8262	−	35.6954i	−0.694676	−	0.401072i	−0.805361	+	0.592784i	$0.798029\pi$
$90$		0			0
$91$	−17.0371	−	29.5091i	−0.187221	−	0.324276i
$92$		0			0
$93$	40.0723	+	25.7569i	0.430885	+	0.276955i
$94$		0			0
$95$	−60.0324	−	71.5439i	−0.631920	−	0.753093i
$96$		0			0
$97$	−1.06372	+	0.387161i	−0.0109662	+	0.00399135i	−0.347497	−	0.937681i	$-0.612968\pi$
$97$	−1.06372	+	0.387161i	−0.0109662	+	0.00399135i	0.336531	+	0.941672i	$0.390746\pi$
$98$		0			0
$99$	−10.1888	+	4.65135i	−0.102917	+	0.0469833i
$100$		0			0
$101$	11.1819	+	1.97167i	0.110712	+	0.0195215i	0.228730	−	0.973490i	$-0.426543\pi$
$101$	11.1819	+	1.97167i	0.110712	+	0.0195215i	−0.118018	+	0.993011i	$0.537654\pi$
$102$		0			0
$103$	−154.650	−	56.2881i	−1.50146	−	0.546486i	−0.545020	−	0.838423i	$-0.683478\pi$
$103$	−154.650	−	56.2881i	−1.50146	−	0.546486i	−0.956438	+	0.291937i	$0.905700\pi$
$104$		0			0
$105$	−125.741	+	39.0886i	−1.19753	+	0.372272i
$106$		0			0
$107$			107.863i			1.00807i	0.863685	+	0.504033i	$0.168151\pi$
$107$			107.863i			1.00807i	−0.863685	+	0.504033i	$0.831849\pi$
$108$		0			0
$109$	176.312			1.61754			0.808770	−	0.588125i	$-0.200134\pi$
$109$	176.312			1.61754			0.808770	+	0.588125i	$0.200134\pi$
$110$		0			0
$111$	152.378	+	34.4273i	1.37278	+	0.310155i
$112$		0			0
$113$	−42.8327	+	117.682i	−0.379050	+	1.04143i	0.592701	+	0.805423i	$0.298062\pi$
$113$	−42.8327	+	117.682i	−0.379050	+	1.04143i	−0.971751	+	0.236009i	$0.924161\pi$
$114$		0			0
$115$	29.6345	−	168.066i	0.257692	−	1.46144i
$116$		0			0
$117$	33.7058	+	34.2544i	0.288084	+	0.292773i
$118$		0			0
$119$	−34.6322	−	95.1511i	−0.291027	−	0.799589i
$120$		0			0
$121$	91.5050	−	76.7818i	0.756240	−	0.634560i
$122$		0			0
$123$	−3.23755	−	0.154449i	−0.0263216	−	0.00125569i
$124$		0			0
$125$	−16.0295	+	9.25462i	−0.128236	+	0.0740369i
$126$		0			0
$127$	0.644295	−	1.11595i	0.00507319	−	0.00878702i	−0.863478	−	0.504387i	$-0.831718\pi$
$127$	0.644295	−	1.11595i	0.00507319	−	0.00878702i	0.868551	+	0.495600i	$0.165052\pi$
$128$		0			0
$129$	55.9947	−	133.655i	0.434067	−	1.03608i
$130$		0			0
$131$	−90.5024	+	15.9580i	−0.690858	+	0.121817i	−0.508045	−	0.861331i	$-0.669632\pi$
$131$	−90.5024	+	15.9580i	−0.690858	+	0.121817i	−0.182814	+	0.983148i	$0.558520\pi$
$132$		0			0
$133$	−66.3766	−	55.6966i	−0.499072	−	0.418771i
$134$		0			0
$135$	157.823	−	97.8782i	1.16906	−	0.725024i
$136$		0			0
$137$	37.9669	−	45.2471i	0.277130	−	0.330271i	−0.609469	−	0.792810i	$-0.708617\pi$
$137$	37.9669	−	45.2471i	0.277130	−	0.330271i	0.886599	+	0.462539i	$0.153062\pi$
$138$		0			0
$139$	8.76836	+	49.7279i	0.0630817	+	0.357754i	0.999967	+	0.00811749i	$0.00258391\pi$
$139$	8.76836	+	49.7279i	0.0630817	+	0.357754i	−0.936885	+	0.349637i	$0.886305\pi$
$140$		0			0
$141$	137.525	−	104.647i	0.975355	−	0.742180i
$142$		0			0
$143$	5.75477	+	3.32252i	0.0402432	+	0.0232344i
$144$		0			0
$145$	−106.570	−	184.584i	−0.734963	−	1.27299i
$146$		0			0
$147$	22.0743	−	11.3782i	0.150165	−	0.0774024i
$148$		0			0
$149$	−46.7223	−	55.6815i	−0.313573	−	0.373701i	0.586121	−	0.810224i	$-0.300654\pi$
$149$	−46.7223	−	55.6815i	−0.313573	−	0.373701i	−0.899693	+	0.436522i	$0.856210\pi$
$150$		0			0
$151$	−3.18866	+	1.16058i	−0.0211170	+	0.00768595i	−0.352557	−	0.935790i	$-0.614688\pi$
$151$	−3.18866	+	1.16058i	−0.0211170	+	0.00768595i	0.331440	+	0.943476i	$0.392466\pi$
$152$		0			0
$153$	80.9650	+	117.640i	0.529183	+	0.768888i
$154$		0			0
$155$	−107.557	−	18.9652i	−0.693917	−	0.122356i
$156$		0			0
$157$	241.142	+	87.7685i	1.53594	+	0.559035i	0.965066	−	0.262005i	$-0.0843838\pi$
$157$	241.142	+	87.7685i	1.53594	+	0.559035i	0.570870	+	0.821040i	$0.306606\pi$
$158$		0			0
$159$	−30.5014	−	28.1767i	−0.191833	−	0.177212i
$160$		0			0
$161$		−	158.333i		−	0.983433i
$162$		0			0
$163$	265.211			1.62706			0.813530	−	0.581523i	$-0.197543\pi$
$163$	265.211			1.62706			0.813530	+	0.581523i	$0.197543\pi$
$164$		0			0
$165$	17.4248	−	18.8624i	0.105605	−	0.114318i
$166$		0			0
$167$	1.10732	−	3.04234i	0.00663066	−	0.0182176i	−0.936333	−	0.351113i	$-0.885803\pi$
$167$	1.10732	−	3.04234i	0.00663066	−	0.0182176i	0.942964	+	0.332895i	$0.108026\pi$
$168$		0			0
$169$	−24.3955	+	138.354i	−0.144352	+	0.818663i
$170$		0			0
$171$	110.335	+	52.5385i	0.645233	+	0.307242i
$172$		0			0
$173$	−65.8301	−	180.867i	−0.380521	−	1.04547i	−0.971138	−	0.238520i	$-0.923338\pi$
$173$	−65.8301	−	180.867i	−0.380521	−	1.04547i	0.590617	−	0.806952i	$-0.298884\pi$
$174$		0			0
$175$	109.056	−	91.5085i	0.623175	−	0.522906i
$176$		0			0
$177$	82.8850	+	160.802i	0.468277	+	0.908485i
$178$		0			0
$179$	191.363	−	110.484i	1.06907	−	0.617228i	0.141142	−	0.989989i	$-0.454922\pi$
$179$	191.363	−	110.484i	1.06907	−	0.617228i	0.927927	+	0.372762i	$0.121589\pi$
$180$		0			0
$181$	−72.7860	+	126.069i	−0.402133	+	0.696514i	−0.993983	−	0.109534i	$-0.965064\pi$
$181$	−72.7860	+	126.069i	−0.402133	+	0.696514i	0.591851	+	0.806048i	$0.298398\pi$
$182$		0			0
$183$	−183.454	−	241.090i	−1.00248	−	1.31743i
$184$		0			0
$185$	−352.724	+	62.1948i	−1.90662	+	0.336188i
$186$		0			0
$187$	15.1270	+	12.6931i	0.0808933	+	0.0678775i
$188$		0			0
$189$	128.431	−	114.856i	0.679528	−	0.607701i
$190$		0			0
$191$	−50.2313	+	59.8633i	−0.262991	+	0.313420i	−0.881339	−	0.472484i	$-0.843358\pi$
$191$	−50.2313	+	59.8633i	−0.262991	+	0.313420i	0.618349	+	0.785904i	$0.287802\pi$
$192$		0			0
$193$	−38.8821	−	220.511i	−0.201462	−	1.14255i	−0.902911	−	0.429827i	$-0.858575\pi$
$193$	−38.8821	−	220.511i	−0.201462	−	1.14255i	0.701450	−	0.712719i	$-0.252537\pi$
$194$		0			0
$195$	−101.622	−	42.5747i	−0.521140	−	0.218332i
$196$		0			0
$197$	299.369	+	172.841i	1.51964	+	0.877364i	0.999732	+	0.0231411i	$0.00736671\pi$
$197$	299.369	+	172.841i	1.51964	+	0.877364i	0.519907	+	0.854223i	$0.325967\pi$
$198$		0			0
$199$	−78.7794	−	136.450i	−0.395876	−	0.685678i	0.597336	−	0.801991i	$-0.296226\pi$
$199$	−78.7794	−	136.450i	−0.395876	−	0.685678i	−0.993213	+	0.116313i	$0.962892\pi$
$200$		0			0
$201$	11.2398	−	235.607i	0.0559192	−	1.17217i
$202$		0			0
$203$	−127.108	−	151.482i	−0.626148	−	0.746214i
$204$		0			0
$205$	6.98308	−	2.54163i	0.0340638	−	0.0123982i
$206$		0			0
$207$	56.0526	+	216.156i	0.270785	+	1.04423i
$208$		0			0
$209$	16.6412	+	2.93429i	0.0796229	+	0.0140397i
$210$		0			0
$211$	349.874	+	127.344i	1.65817	+	0.603524i	0.990073	−	0.140552i	$-0.0448877\pi$
$211$	349.874	+	127.344i	1.65817	+	0.603524i	0.668095	+	0.744076i	$0.267110\pi$
$212$		0			0
$213$	−30.3491	+	134.328i	−0.142484	+	0.630647i
$214$		0			0
$215$			332.238i			1.54529i
$216$		0			0
$217$	−101.328			−0.466950
$218$		0			0
$219$	61.4356	+	197.627i	0.280528	+	0.902406i
$220$		0			0
$221$	28.9786	−	79.6179i	0.131125	−	0.360262i
$222$		0			0
$223$	−16.2189	+	91.9821i	−0.0727306	+	0.412476i	0.926605	+	0.376036i	$0.122713\pi$
$223$	−16.2189	+	91.9821i	−0.0727306	+	0.412476i	−0.999336	+	0.0364403i	$0.988398\pi$
$224$		0			0
$225$	−116.487	+	163.535i	−0.517720	+	0.726822i
$226$		0			0
$227$	−124.898	−	343.154i	−0.550211	−	1.51169i	−0.833423	−	0.552636i	$-0.813622\pi$
$227$	−124.898	−	343.154i	−0.550211	−	1.51169i	0.283211	−	0.959058i	$-0.408600\pi$
$228$		0			0
$229$	−81.6070	+	68.4764i	−0.356362	+	0.299023i	−0.803339	−	0.595522i	$-0.796945\pi$
$229$	−81.6070	+	68.4764i	−0.356362	+	0.299023i	0.446977	+	0.894546i	$0.352501\pi$
$230$		0			0
$231$	12.8818	−	20.0415i	0.0557655	−	0.0867595i
$232$		0			0
$233$	−206.035	+	118.954i	−0.884270	+	0.510533i	−0.872064	−	0.489392i	$-0.837219\pi$
$233$	−206.035	+	118.954i	−0.884270	+	0.510533i	−0.0122058	+	0.999926i	$0.503885\pi$
$234$		0			0
$235$	−198.105	+	343.128i	−0.843001	+	1.46012i
$236$		0			0
$237$	−117.680	+	15.0099i	−0.496540	+	0.0633329i
$238$		0			0
$239$	−84.6278	+	14.9222i	−0.354091	+	0.0624358i	−0.347865	−	0.937545i	$-0.613093\pi$
$239$	−84.6278	+	14.9222i	−0.354091	+	0.0624358i	−0.00622654	+	0.999981i	$0.501982\pi$
$240$		0			0
$241$	−22.4930	−	18.8739i	−0.0933319	−	0.0783148i	0.594928	−	0.803779i	$-0.297181\pi$
$241$	−22.4930	−	18.8739i	−0.0933319	−	0.0783148i	−0.688260	+	0.725464i	$0.741625\pi$
$242$		0			0
$243$	−134.673	+	202.268i	−0.554210	+	0.832377i
$244$		0			0
$245$	−36.5989	+	43.6169i	−0.149383	+	0.178028i
$246$		0			0
$247$	−12.5901	−	71.4018i	−0.0509719	−	0.289076i
$248$		0			0
$249$	−16.0191	−	125.592i	−0.0643338	−	0.504387i
$250$		0			0
$251$	108.333	+	62.5458i	0.431604	+	0.249186i	0.700030	−	0.714114i	$-0.253170\pi$
$251$	108.333	+	62.5458i	0.431604	+	0.249186i	−0.268426	+	0.963300i	$0.586503\pi$
$252$		0			0
$253$	15.4388	+	26.7407i	0.0610228	+	0.105695i
$254$		0			0
$255$	−275.432	−	177.036i	−1.08013	−	0.694261i
$256$		0			0
$257$	−150.115	−	178.900i	−0.584104	−	0.696108i	0.390357	−	0.920663i	$-0.372352\pi$
$257$	−150.115	−	178.900i	−0.584104	−	0.696108i	−0.974461	+	0.224555i	$0.927907\pi$
$258$		0			0
$259$	−312.257	+	113.652i	−1.20563	+	0.438812i
$260$		0			0
$261$	227.155	+	161.804i	0.870326	+	0.619939i
$262$		0			0
$263$	121.603	+	21.4418i	0.462368	+	0.0815279i	0.399980	−	0.916524i	$-0.369017\pi$
$263$	121.603	+	21.4418i	0.462368	+	0.0815279i	0.0623882	+	0.998052i	$0.480128\pi$
$264$		0			0
$265$	89.4618	+	32.5614i	0.337592	+	0.122873i
$266$		0			0
$267$	−204.518	+	63.5779i	−0.765985	+	0.238119i
$268$		0			0
$269$			509.553i			1.89425i	0.320867	+	0.947124i	$0.396026\pi$
$269$			509.553i			1.89425i	−0.320867	+	0.947124i	$0.603974\pi$
$270$		0			0
$271$	−49.6722			−0.183292			−0.0916461	−	0.995792i	$-0.529213\pi$
$271$	−49.6722			−0.183292			−0.0916461	+	0.995792i	$0.529213\pi$
$272$		0			0
$273$	−99.7093	−	22.5276i	−0.365236	−	0.0825188i
$274$		0			0
$275$	−9.49550	+	26.0887i	−0.0345291	+	0.0948679i
$276$		0			0
$277$	19.8143	−	112.372i	0.0715316	−	0.405676i	−0.927927	−	0.372763i	$-0.878410\pi$
$277$	19.8143	−	112.372i	0.0715316	−	0.405676i	0.999458	−	0.0329130i	$-0.0104784\pi$
$278$		0			0
$279$	138.333	−	35.8720i	0.495818	−	0.128573i
$280$		0			0
$281$	−8.86037	−	24.3437i	−0.0315316	−	0.0866323i	0.922928	−	0.384973i	$-0.125789\pi$
$281$	−8.86037	−	24.3437i	−0.0315316	−	0.0866323i	−0.954460	+	0.298340i	$0.903567\pi$
$282$		0			0
$283$	120.665	−	101.250i	0.426380	−	0.357775i	−0.404204	−	0.914669i	$-0.632451\pi$
$283$	120.665	−	101.250i	0.426380	−	0.357775i	0.830584	+	0.556894i	$0.188007\pi$
$284$		0			0
$285$	−279.863	−	13.3510i	−0.981977	−	0.0468458i
$286$		0			0
$287$	5.97082	−	3.44725i	0.0208042	−	0.0120113i
$288$		0			0
$289$	−18.6082	+	32.2303i	−0.0643881	+	0.111523i
$290$		0			0
$291$	−1.31223	+	3.13218i	−0.00450937	+	0.0107635i
$292$		0			0
$293$	413.555	−	72.9209i	1.41145	−	0.248877i	0.584611	−	0.811314i	$-0.301247\pi$
$293$	413.555	−	72.9209i	1.41145	−	0.248877i	0.826840	+	0.562437i	$0.190136\pi$
$294$		0			0
$295$	−317.730	−	266.607i	−1.07705	−	0.903754i
$296$		0			0
$297$	−10.4912	+	31.9210i	−0.0353241	+	0.107478i
$298$		0			0
$299$	85.1599	−	101.490i	0.284816	−	0.339430i
$300$		0			0
$301$	53.5257	+	303.559i	0.177826	+	1.00850i
$302$		0			0
$303$	27.1076	−	20.6271i	0.0894642	−	0.0680763i
$304$		0			0
$305$	601.526	+	347.291i	1.97222	+	1.13866i
$306$		0			0
$307$	101.037	+	175.001i	0.329110	+	0.570035i	0.982336	−	0.187128i	$-0.0599180\pi$
$307$	101.037	+	175.001i	0.329110	+	0.570035i	−0.653225	+	0.757163i	$0.726585\pi$
$308$		0			0
$309$	−438.857	+	226.208i	−1.42025	+	0.732064i
$310$		0			0
$311$	170.488	+	203.179i	0.548192	+	0.653310i	0.967003	−	0.254763i	$-0.0819976\pi$
$311$	170.488	+	203.179i	0.548192	+	0.653310i	−0.418811	+	0.908073i	$0.637553\pi$
$312$		0			0
$313$	−259.112	+	94.3092i	−0.827835	+	0.301307i	−0.720970	−	0.692966i	$-0.756304\pi$
$313$	−259.112	+	94.3092i	−0.827835	+	0.301307i	−0.106865	+	0.994274i	$0.534081\pi$
$314$		0			0
$315$	−169.831	+	356.658i	−0.539146	+	1.13225i
$316$		0			0
$317$	34.4742	+	6.07873i	0.108751	+	0.0191758i	0.227759	−	0.973718i	$-0.426860\pi$
$317$	34.4742	+	6.07873i	0.108751	+	0.0191758i	−0.119008	+	0.992893i	$0.537971\pi$
$318$		0			0
$319$	36.2379	+	13.1895i	0.113599	+	0.0413465i
$320$		0			0
$321$	237.690	+	219.575i	0.740469	+	0.684033i
$322$		0			0
$323$		−	215.457i		−	0.667049i
$324$		0			0
$325$	119.122			0.366528
$326$		0			0
$327$	358.915	−	388.527i	1.09760	−	1.18816i
$328$		0			0
$329$	−125.725	+	345.425i	−0.382142	+	1.04993i
$330$		0			0
$331$	−36.6162	+	207.661i	−0.110623	+	0.627373i	0.878202	+	0.478290i	$0.158743\pi$
$331$	−36.6162	+	207.661i	−0.110623	+	0.627373i	−0.988825	+	0.149083i	$0.952368\pi$
$332$		0			0
$333$	386.058	−	265.703i	1.15933	−	0.797906i
$334$		0			0
$335$	184.963	+	508.180i	0.552127	+	1.51696i
$336$		0			0
$337$	118.176	−	99.1618i	0.350672	−	0.294249i	−0.450388	−	0.892833i	$-0.648714\pi$
$337$	118.176	−	99.1618i	0.350672	−	0.294249i	0.801060	+	0.598584i	$0.204270\pi$
$338$		0			0
$339$	172.134	+	333.950i	0.507769	+	0.985104i
$340$		0			0
$341$	17.1133	−	9.88034i	0.0501855	−	0.0289746i
$342$		0			0
$343$	−182.756	+	316.543i	−0.532817	+	0.922867i
$344$		0			0
$345$	−310.029	−	407.432i	−0.898635	−	1.18096i
$346$		0			0
$347$	288.832	−	50.9288i	0.832368	−	0.146769i	0.258804	−	0.965930i	$-0.416672\pi$
$347$	288.832	−	50.9288i	0.832368	−	0.146769i	0.573564	+	0.819161i	$0.305560\pi$
$348$		0			0
$349$	−313.333	−	262.918i	−0.897803	−	0.753346i	0.0719569	−	0.997408i	$-0.477076\pi$
$349$	−313.333	−	262.918i	−0.897803	−	0.753346i	−0.969760	+	0.244062i	$0.921520\pi$
$350$		0			0
$351$	144.098	−	4.54415i	0.410537	−	0.0129463i
$352$		0			0
$353$	321.434	−	383.070i	0.910577	−	1.08518i	−0.0854686	−	0.996341i	$-0.527239\pi$
$353$	321.434	−	383.070i	0.910577	−	1.08518i	0.996046	−	0.0888426i	$-0.0283168\pi$
$354$		0			0
$355$	−54.8274	−	310.941i	−0.154443	−	0.875892i
$356$		0			0
$357$	−280.178	−	117.381i	−0.784813	−	0.328798i
$358$		0			0
$359$	216.295	+	124.878i	0.602492	+	0.347849i	0.770021	−	0.638018i	$-0.220246\pi$
$359$	216.295	+	124.878i	0.602492	+	0.347849i	−0.167529	+	0.985867i	$0.553579\pi$
$360$		0			0
$361$	88.3143	+	152.965i	0.244638	+	0.423725i
$362$		0			0
$363$	17.0761	−	357.947i	0.0470415	−	0.986079i
$364$		0			0
$365$	−304.997	−	363.481i	−0.835608	−	0.995839i
$366$		0			0
$367$	−300.825	+	109.491i	−0.819686	+	0.298341i	−0.717619	−	0.696436i	$-0.754768\pi$
$367$	−300.825	+	109.491i	−0.819686	+	0.298341i	−0.102068	+	0.994777i	$0.532546\pi$
$368$		0			0
$369$	−6.93097	+	6.81997i	−0.0187831	+	0.0184823i
$370$		0			0
$371$	86.9853	+	15.3379i	0.234462	+	0.0413419i
$372$		0			0
$373$	−185.784	−	67.6197i	−0.498079	−	0.181286i	0.0807505	−	0.996734i	$-0.474268\pi$
$373$	−185.784	−	67.6197i	−0.498079	−	0.181286i	−0.578830	+	0.815448i	$0.696491\pi$
$374$		0			0
$375$	−12.2371	+	54.1625i	−0.0326323	+	0.144433i
$376$		0			0
$377$		−	165.464i		−	0.438896i
$378$		0			0
$379$	−364.905			−0.962811			−0.481405	−	0.876498i	$-0.659873\pi$
$379$	−364.905			−0.962811			−0.481405	+	0.876498i	$0.659873\pi$
$380$		0			0
$381$	−1.14757	−	3.69151i	−0.00301199	−	0.00968901i
$382$		0			0
$383$	−221.375	+	608.221i	−0.578001	+	1.58805i	0.213543	+	0.976934i	$0.431500\pi$
$383$	−221.375	+	608.221i	−0.578001	+	1.58805i	−0.791544	+	0.611112i	$0.790723\pi$
$384$		0			0
$385$	−9.48511	+	53.7927i	−0.0246367	+	0.139721i
$386$		0			0
$387$	−180.539	−	395.470i	−0.466508	−	1.02189i
$388$		0			0
$389$	19.3516	+	53.1682i	0.0497471	+	0.136679i	0.962078	−	0.272775i	$-0.0879414\pi$
$389$	19.3516	+	53.1682i	0.0497471	+	0.136679i	−0.912331	+	0.409454i	$0.865719\pi$
$390$		0			0
$391$	301.595	−	253.068i	0.771343	−	0.647233i
$392$		0			0
$393$	−149.069	+	231.920i	−0.379309	+	0.590126i
$394$		0			0
$395$	235.553	−	135.996i	0.596336	−	0.344295i
$396$		0			0
$397$	−327.487	+	567.224i	−0.824905	+	1.42878i	0.0770876	+	0.997024i	$0.475438\pi$
$397$	−327.487	+	567.224i	−0.824905	+	1.42878i	−0.901992	+	0.431752i	$0.857895\pi$
$398$		0			0
$399$	−257.856	+	32.8892i	−0.646257	+	0.0824291i
$400$		0			0
$401$	124.761	−	21.9988i	0.311125	−	0.0548598i	−0.0159053	−	0.999874i	$-0.505063\pi$
$401$	124.761	−	21.9988i	0.311125	−	0.0548598i	0.327031	+	0.945014i	$0.393952\pi$
$402$		0			0
$403$	−64.9502	−	54.4997i	−0.161167	−	0.135235i
$404$		0			0
$405$	105.590	−	547.033i	0.260716	−	1.35070i
$406$		0			0
$407$	41.6549	−	49.6424i	0.102346	−	0.121971i
$408$		0			0
$409$	94.5803	+	536.391i	0.231248	+	1.31147i	0.850374	+	0.526179i	$0.176376\pi$
$409$	94.5803	+	536.391i	0.231248	+	1.31147i	−0.619126	+	0.785291i	$0.712513\pi$
$410$		0			0
$411$	−22.4197	−	175.774i	−0.0545491	−	0.427673i
$412$		0			0
$413$	−333.256	−	192.405i	−0.806915	−	0.465873i
$414$		0			0
$415$	145.140	+	251.390i	0.349736	+	0.605760i
$416$		0			0
$417$	127.432	+	81.9078i	0.305591	+	0.196422i
$418$		0			0
$419$	−429.462	−	511.813i	−1.02497	−	1.22151i	−0.974872	−	0.222765i	$-0.928492\pi$
$419$	−429.462	−	511.813i	−1.02497	−	1.22151i	−0.0500962	−	0.998744i	$-0.515953\pi$
$420$		0			0
$421$	−213.714	+	77.7856i	−0.507635	+	0.184764i	−0.583125	−	0.812383i	$-0.698170\pi$
$421$	−213.714	+	77.7856i	−0.507635	+	0.184764i	0.0754901	+	0.997147i	$0.475948\pi$
$422$		0			0
$423$	49.3524	−	516.084i	0.116672	−	1.22006i
$424$		0			0
$425$	348.614	+	61.4701i	0.820269	+	0.144635i
$426$		0			0
$427$	605.553	+	220.403i	1.41816	+	0.516167i
$428$		0			0
$429$	19.0365	−	5.91782i	0.0443741	−	0.0137944i
$430$		0			0
$431$			429.608i			0.996769i	0.866956	+	0.498385i	$0.166073\pi$
$431$			429.608i			0.996769i	−0.866956	+	0.498385i	$0.833927\pi$
$432$		0			0
$433$	−11.9987			−0.0277106			−0.0138553	−	0.999904i	$-0.504410\pi$
$433$	−11.9987			−0.0277106			−0.0138553	+	0.999904i	$0.504410\pi$
$434$		0			0
$435$	−623.697	−	140.914i	−1.43379	−	0.323940i
$436$		0			0
$437$	115.227	−	316.584i	0.263678	−	0.724448i
$438$		0			0
$439$	13.0874	−	74.2226i	0.0298119	−	0.169072i	−0.966267	−	0.257543i	$-0.917087\pi$
$439$	13.0874	−	74.2226i	0.0298119	−	0.169072i	0.996079	+	0.0884713i	$0.0281982\pi$
$440$		0			0
$441$	19.8630	−	71.8060i	0.0450408	−	0.162825i
$442$		0			0
$443$	−84.8156	−	233.029i	−0.191457	−	0.526024i	0.806406	−	0.591362i	$-0.201410\pi$
$443$	−84.8156	−	233.029i	−0.191457	−	0.526024i	−0.997863	+	0.0653379i	$0.979187\pi$
$444$		0			0
$445$	376.156	−	315.632i	0.845294	−	0.709286i
$446$		0			0
$447$	−217.813	−	10.3909i	−0.487278	−	0.0232459i
$448$		0			0
$449$	178.012	−	102.775i	0.396462	−	0.228898i	−0.288494	−	0.957482i	$-0.593155\pi$
$449$	178.012	−	102.775i	0.396462	−	0.228898i	0.684956	+	0.728584i	$0.259821\pi$
$450$		0			0
$451$	−0.672273	+	1.16441i	−0.00149063	+	0.00258184i
$452$		0			0
$453$	−3.93361	+	9.38921i	−0.00868347	+	0.0207267i
$454$		0			0
$455$	230.807	−	40.6975i	0.507268	−	0.0894450i
$456$		0			0
$457$	489.550	+	410.781i	1.07122	+	0.898864i	0.995163	−	0.0982390i	$-0.0313210\pi$
$457$	489.550	+	410.781i	1.07122	+	0.898864i	0.0760617	+	0.997103i	$0.475765\pi$
$458$		0			0
$459$	424.054	+	61.0601i	0.923865	+	0.133029i
$460$		0			0
$461$	91.0478	−	108.507i	0.197501	−	0.235372i	−0.658200	−	0.752843i	$-0.728682\pi$
$461$	91.0478	−	108.507i	0.197501	−	0.235372i	0.855701	+	0.517471i	$0.173126\pi$
$462$		0			0
$463$	48.9254	+	277.470i	0.105670	+	0.599287i	0.990950	+	0.134229i	$0.0428556\pi$
$463$	48.9254	+	277.470i	0.105670	+	0.599287i	−0.885280	+	0.465059i	$0.846033\pi$
$464$		0			0
$465$	−260.744	+	198.409i	−0.560740	+	0.426687i
$466$		0			0
$467$	−462.423	−	266.980i	−0.990199	−	0.571692i	−0.0848656	−	0.996392i	$-0.527046\pi$
$467$	−462.423	−	266.980i	−0.990199	−	0.571692i	−0.905334	+	0.424700i	$0.860379\pi$
$468$		0			0
$469$	250.868	+	434.515i	0.534899	+	0.926472i
$470$		0			0
$471$	684.298	−	352.720i	1.45286	−	0.748875i
$472$		0			0
$473$	−38.6395	−	46.0488i	−0.0816903	−	0.0973547i
$474$		0			0
$475$	284.651	−	103.604i	0.599265	−	0.218114i
$476$		0			0
$477$	−124.182	+	9.85510i	−0.260340	+	0.0206606i
$478$		0			0
$479$	167.090	+	29.4625i	0.348831	+	0.0615084i	0.345319	−	0.938485i	$-0.387771\pi$
$479$	167.090	+	29.4625i	0.348831	+	0.0615084i	0.00351250	+	0.999994i	$0.498882\pi$
$480$		0			0
$481$	−261.282	−	95.0988i	−0.543205	−	0.197711i
$482$		0			0
$483$	−348.907	−	322.315i	−0.722375	−	0.667319i
$484$		0			0
$485$		−	7.78596i		−	0.0160535i
$486$		0			0
$487$	−20.8058			−0.0427223			−0.0213612	−	0.999772i	$-0.506800\pi$
$487$	−20.8058			−0.0427223			−0.0213612	+	0.999772i	$0.506800\pi$
$488$		0			0
$489$	539.885	−	584.428i	1.10406	−	1.19515i
$490$		0			0
$491$	−51.6877	+	142.011i	−0.105270	+	0.289228i	−0.981133	−	0.193332i	$-0.938071\pi$
$491$	−51.6877	+	142.011i	−0.105270	+	0.289228i	0.875863	+	0.482560i	$0.160293\pi$
$492$		0			0
$493$	85.3838	−	484.236i	0.173192	−	0.982222i
$494$		0			0
$495$	−6.09451	−	76.7958i	−0.0123122	−	0.155143i
$496$		0			0
$497$	−100.189	−	275.268i	−0.201588	−	0.553859i
$498$		0			0
$499$	−626.300	+	525.528i	−1.25511	+	1.05316i	−0.258925	+	0.965897i	$0.583368\pi$
$499$	−626.300	+	525.528i	−1.25511	+	1.05316i	−0.996185	+	0.0872648i	$0.972187\pi$
$500$		0			0
$501$	−4.45004	−	8.63335i	−0.00888232	−	0.0172322i
$502$		0			0
$503$	201.176	−	116.149i	0.399953	−	0.230913i	−0.286511	−	0.958077i	$-0.592495\pi$
$503$	201.176	−	116.149i	0.399953	−	0.230913i	0.686464	+	0.727164i	$0.259162\pi$
$504$		0			0
$505$	−39.0487	+	67.6343i	−0.0773241	+	0.133929i
$506$		0			0
$507$	255.220	+	335.404i	0.503392	+	0.661545i
$508$		0			0
$509$	−318.833	+	56.2189i	−0.626392	+	0.110450i	−0.477828	−	0.878453i	$-0.658576\pi$
$509$	−318.833	+	56.2189i	−0.626392	+	0.110450i	−0.148563	+	0.988903i	$0.547465\pi$
$510$		0			0
$511$	−337.229	−	282.968i	−0.659939	−	0.553754i
$512$		0			0
$513$	340.382	−	136.186i	0.663513	−	0.265470i
$514$		0			0
$515$	727.619	−	867.142i	1.41285	−	1.68377i
$516$		0			0
$517$	−12.4483	−	70.5979i	−0.0240780	−	0.136553i
$518$		0			0
$519$	−532.573	−	223.121i	−1.02615	−	0.429906i
$520$		0			0
$521$	480.156	+	277.218i	0.921604	+	0.532088i	0.884146	−	0.467210i	$-0.154741\pi$
$521$	480.156	+	277.218i	0.921604	+	0.532088i	0.0374577	+	0.999298i	$0.488074\pi$
$522$		0			0
$523$	472.881	+	819.053i	0.904170	+	1.56607i	0.822028	+	0.569447i	$0.192843\pi$
$523$	472.881	+	819.053i	0.904170	+	1.56607i	0.0821414	+	0.996621i	$0.473824\pi$
$524$		0			0
$525$	20.3512	−	426.601i	0.0387643	−	0.812573i
$526$		0			0
$527$	−161.956	−	193.012i	−0.307317	−	0.366246i
$528$		0			0
$529$	81.3960	−	29.6257i	0.153868	−	0.0560033i
$530$		0			0
$531$	523.076	+	144.693i	0.985077	+	0.272492i
$532$		0			0
$533$	5.68135	+	1.00178i	0.0106592	+	0.00187950i
$534$		0			0
$535$	−697.156	−	253.744i	−1.30310	−	0.474288i
$536$		0			0
$537$	146.089	−	646.605i	0.272047	−	1.20411i
$538$		0			0
$539$		−	10.3019i		−	0.0191129i
$540$		0			0
$541$	−390.158			−0.721179			−0.360590	−	0.932725i	$-0.617425\pi$
$541$	−390.158			−0.721179			−0.360590	+	0.932725i	$0.617425\pi$
$542$		0			0
$543$	129.641	+	417.030i	0.238749	+	0.768011i
$544$		0			0
$545$	−414.768	+	1139.57i	−0.761042	+	2.09095i
$546$		0			0
$547$	80.6120	−	457.174i	0.147371	−	0.835784i	−0.818061	−	0.575131i	$-0.804951\pi$
$547$	80.6120	−	457.174i	0.147371	−	0.835784i	0.965433	−	0.260653i	$-0.0839378\pi$
$548$		0			0
$549$	−904.727	−	86.5180i	−1.64796	−	0.157592i
$550$		0			0
$551$	−143.910	−	395.388i	−0.261179	−	0.717583i
$552$		0			0
$553$	193.310	−	162.206i	0.349566	−	0.293320i
$554$		0			0
$555$	−580.980	+	903.884i	−1.04681	+	1.62862i
$556$		0			0
$557$	−203.531	+	117.509i	−0.365406	+	0.210967i	−0.671450	−	0.741050i	$-0.734328\pi$
$557$	−203.531	+	117.509i	−0.365406	+	0.210967i	0.306043	+	0.952018i	$0.400995\pi$
$558$		0			0
$559$	−128.961	+	223.367i	−0.230700	+	0.399584i
$560$		0			0
$561$	58.7648	−	7.49536i	0.104750	−	0.0133607i
$562$		0			0
$563$	82.3270	−	14.5165i	0.146229	−	0.0257842i	−0.100054	−	0.994982i	$-0.531902\pi$
$563$	82.3270	−	14.5165i	0.146229	−	0.0257842i	0.246284	+	0.969198i	$0.420791\pi$
$564$		0			0
$565$	−659.856	−	553.685i	−1.16789	−	0.979973i
$566$		0			0
$567$	8.34476	−	516.824i	0.0147174	−	0.911506i
$568$		0			0
$569$	592.627	−	706.266i	1.04152	−	1.24124i	0.0717022	−	0.997426i	$-0.477157\pi$
$569$	592.627	−	706.266i	1.04152	−	1.24124i	0.969822	−	0.243814i	$-0.0783987\pi$
$570$		0			0
$571$	−69.2165	−	392.546i	−0.121220	−	0.687471i	−0.983482	−	0.181008i	$-0.942064\pi$
$571$	−69.2165	−	392.546i	−0.121220	−	0.687471i	0.862262	−	0.506463i	$-0.169047\pi$
$572$		0			0
$573$	29.6619	+	232.554i	0.0517660	+	0.405853i
$574$		0			0
$575$	479.365	+	276.762i	0.833679	+	0.481325i
$576$		0			0
$577$	8.33213	+	14.4317i	0.0144404	+	0.0250116i	0.873155	−	0.487442i	$-0.162070\pi$
$577$	8.33213	+	14.4317i	0.0144404	+	0.0250116i	−0.858715	+	0.512454i	$0.828737\pi$
$578$		0			0
$579$	−565.078	−	363.209i	−0.975955	−	0.627304i
$580$		0			0
$581$	173.112	+	206.307i	0.297956	+	0.355090i
$582$		0			0
$583$	−16.1865	+	5.89139i	−0.0277641	+	0.0101053i
$584$		0			0
$585$	−300.690	+	137.270i	−0.514000	+	0.234649i
$586$		0			0
$587$	−183.618	−	32.3769i	−0.312808	−	0.0551565i	0.0150403	−	0.999887i	$-0.495212\pi$
$587$	−183.618	−	32.3769i	−0.312808	−	0.0551565i	−0.327848	+	0.944730i	$0.606323\pi$
$588$		0			0
$589$	−202.604	−	73.7419i	−0.343980	−	0.125198i
$590$		0			0
$591$	990.297	−	307.851i	1.67563	−	0.520898i
$592$		0			0
$593$		−	373.725i		−	0.630228i	−0.949054	−	0.315114i	$-0.897957\pi$
$593$		−	373.725i		−	0.630228i	0.949054	−	0.315114i	$-0.102043\pi$
$594$		0			0
$595$	696.466			1.17053
$596$		0			0
$597$	−461.055	−	104.168i	−0.772287	−	0.174485i
$598$		0			0
$599$	−5.06227	+	13.9085i	−0.00845120	+	0.0232195i	−0.943846	−	0.330384i	$-0.892822\pi$
$599$	−5.06227	+	13.9085i	−0.00845120	+	0.0232195i	0.935395	+	0.353604i	$0.115044\pi$
$600$		0			0
$601$	−33.7445	+	191.375i	−0.0561473	+	0.318427i	−0.999926	−	0.0121504i	$-0.996132\pi$
$601$	−33.7445	+	191.375i	−0.0561473	+	0.318427i	0.943779	+	0.330577i	$0.107243\pi$
$602$		0			0
$603$	−496.311	−	504.389i	−0.823069	−	0.836466i
$604$		0			0
$605$	281.005	+	772.055i	0.464471	+	1.27612i
$606$		0			0
$607$	−444.453	+	372.941i	−0.732213	+	0.614400i	−0.930734	−	0.365697i	$-0.880831\pi$
$607$	−444.453	+	372.941i	−0.732213	+	0.614400i	0.198521	+	0.980097i	$0.436386\pi$
$608$		0			0
$609$	−592.561	−	28.2685i	−0.973007	−	0.0464179i
$610$		0			0
$611$	−266.377	+	153.793i	−0.435968	+	0.251706i
$612$		0			0
$613$	80.1803	−	138.876i	0.130800	−	0.226552i	−0.793185	−	0.608980i	$-0.791579\pi$
$613$	80.1803	−	138.876i	0.130800	−	0.226552i	0.923985	+	0.382428i	$0.124912\pi$
$614$		0			0
$615$	8.61449	−	20.5621i	0.0140073	−	0.0334343i
$616$		0			0
$617$	409.534	−	72.2118i	0.663750	−	0.117037i	0.168384	−	0.985721i	$-0.446145\pi$
$617$	409.534	−	72.2118i	0.663750	−	0.117037i	0.495366	+	0.868685i	$0.335034\pi$
$618$		0			0
$619$	502.301	+	421.481i	0.811472	+	0.680906i	0.950959	−	0.309318i	$-0.100101\pi$
$619$	502.301	+	421.481i	0.811472	+	0.680906i	−0.139486	+	0.990224i	$0.544545\pi$
$620$		0			0
$621$	590.433	+	316.505i	0.950778	+	0.509670i
$622$		0			0
$623$	292.835	−	348.988i	0.470041	−	0.560173i
$624$		0			0
$625$	−118.955	−	674.627i	−0.190328	−	1.07940i
$626$		0			0
$627$	40.3423	−	30.6978i	0.0643417	−	0.0489598i
$628$		0			0
$629$	−715.577	−	413.139i	−1.13764	−	0.656818i
$630$		0			0
$631$	−321.500	−	556.855i	−0.509509	−	0.882496i	−0.999939	−	0.0110155i	$-0.996494\pi$
$631$	−321.500	−	556.855i	−0.509509	−	0.882496i	0.490430	−	0.871481i	$-0.336840\pi$
$632$		0			0
$633$	992.850	−	511.762i	1.56848	−	0.808471i
$634$		0			0
$635$	5.69710	+	6.78954i	0.00897182	+	0.0106922i
$636$		0			0
$637$	−41.5361	+	15.1179i	−0.0652058	+	0.0237330i
$638$		0			0
$639$	234.228	+	340.327i	0.366554	+	0.532593i
$640$		0			0
$641$	−115.857	−	20.4287i	−0.180744	−	0.0318700i	0.0825436	−	0.996587i	$-0.473696\pi$
$641$	−115.857	−	20.4287i	−0.180744	−	0.0318700i	−0.263287	+	0.964717i	$0.584807\pi$
$642$		0			0
$643$	407.907	+	148.466i	0.634382	+	0.230896i	0.639137	−	0.769093i	$-0.279292\pi$
$643$	407.907	+	148.466i	0.634382	+	0.230896i	−0.00475561	+	0.999989i	$0.501514\pi$
$644$		0			0
$645$	732.131	+	676.331i	1.13509	+	1.04858i
$646$		0			0
$647$			202.797i			0.313443i	0.987643	+	0.156721i	$0.0500924\pi$
$647$			202.797i			0.313443i	−0.987643	+	0.156721i	$0.949908\pi$
$648$		0			0
$649$	75.0446			0.115631
$650$		0			0
$651$	−206.272	+	223.290i	−0.316854	+	0.342995i
$652$		0			0
$653$	−306.142	+	841.119i	−0.468824	+	1.28808i	0.449862	+	0.893098i	$0.351473\pi$
$653$	−306.142	+	841.119i	−0.468824	+	1.28808i	−0.918687	+	0.394987i	$0.870749\pi$
$654$		0			0
$655$	109.762	−	622.490i	0.167575	−	0.950366i
$656$		0			0
$657$	560.561	+	266.924i	0.853212	+	0.406276i
$658$		0			0
$659$	287.917	+	791.045i	0.436899	+	1.20037i	0.941498	+	0.337017i	$0.109418\pi$
$659$	287.917	+	791.045i	0.436899	+	1.20037i	−0.504599	+	0.863354i	$0.668360\pi$
$660$		0			0
$661$	173.104	−	145.252i	0.261882	−	0.219745i	−0.502386	−	0.864643i	$-0.667545\pi$
$661$	173.104	−	145.252i	0.261882	−	0.219745i	0.764269	+	0.644898i	$0.223100\pi$
$662$		0			0
$663$	−116.458	−	225.935i	−0.175652	−	0.340776i
$664$		0			0
$665$	516.135	−	297.991i	0.776143	−	0.448106i
$666$		0			0
$667$	384.430	−	665.853i	0.576357	−	0.998280i
$668$		0			0
$669$	169.678	+	222.987i	0.253630	+	0.333314i
$670$		0			0
$671$	−123.763	+	21.8227i	−0.184445	+	0.0325227i
$672$		0			0
$673$	−84.6901	−	71.0634i	−0.125840	−	0.105592i	0.577696	−	0.816252i	$-0.303952\pi$
$673$	−84.6901	−	71.0634i	−0.125840	−	0.105592i	−0.703536	+	0.710660i	$0.748396\pi$
$674$		0			0
$675$	123.241	+	589.600i	0.182579	+	0.873482i
$676$		0			0
$677$	1.83780	−	2.19020i	0.00271462	−	0.00323516i	−0.764685	−	0.644404i	$-0.777106\pi$
$677$	1.83780	−	2.19020i	0.00271462	−	0.00323516i	0.767400	+	0.641169i	$0.221550\pi$
$678$		0			0
$679$	−1.25437	−	7.11387i	−0.00184737	−	0.0104770i
$680$		0			0
$681$	−1010.44	−	423.324i	−1.48376	−	0.621621i
$682$		0			0
$683$	843.279	+	486.868i	1.23467	+	0.712837i	0.968000	−	0.250951i	$-0.0807434\pi$
$683$	843.279	+	486.868i	1.23467	+	0.712837i	0.266670	+	0.963788i	$0.414077\pi$
$684$		0			0
$685$	203.132	+	351.835i	0.296543	+	0.513628i
$686$		0			0
$687$	−15.2290	+	319.228i	−0.0221673	+	0.464669i
$688$		0			0
$689$	47.5071	+	56.6168i	0.0689508	+	0.0821724i
$690$		0			0
$691$	614.590	−	223.693i	0.889421	−	0.323723i	0.143416	−	0.989663i	$-0.454191\pi$
$691$	614.590	−	223.693i	0.889421	−	0.323723i	0.746006	+	0.665940i	$0.231969\pi$
$692$		0			0
$693$	−17.9407	−	69.1848i	−0.0258885	−	0.0998338i
$694$		0			0
$695$	−342.036	−	60.3101i	−0.492138	−	0.0867772i
$696$		0			0
$697$	16.1097	+	5.86347i	0.0231130	+	0.00841244i
$698$		0			0
$699$	−157.290	+	696.178i	−0.225021	+	0.995963i
$700$		0			0
$701$			41.7083i			0.0594983i	0.999557	+	0.0297492i	$0.00947085\pi$
$701$			41.7083i			0.0594983i	−0.999557	+	0.0297492i	$0.990529\pi$
$702$		0			0
$703$	−707.064			−1.00578
$704$		0			0
$705$	352.850	+	1135.05i	0.500497	+	1.61000i
$706$		0			0
$707$	−24.7817	+	68.0870i	−0.0350518	+	0.0963042i
$708$		0			0
$709$	−86.0416	+	487.966i	−0.121356	+	0.688246i	0.862049	+	0.506825i	$0.169181\pi$
$709$	−86.0416	+	487.966i	−0.121356	+	0.688246i	−0.983406	+	0.181421i	$0.941930\pi$
$710$		0			0
$711$	−206.483	+	289.879i	−0.290412	+	0.407706i
$712$		0			0
$713$	−134.748	−	370.218i	−0.188988	−	0.519240i
$714$		0			0
$715$	−35.0125	+	29.3790i	−0.0489685	+	0.0410895i
$716$		0			0
$717$	−139.392	+	216.865i	−0.194410	+	0.302462i
$718$		0			0
$719$	−124.160	+	71.6839i	−0.172684	+	0.0996994i	−0.583851	−	0.811861i	$-0.698455\pi$
$719$	−124.160	+	71.6839i	−0.172684	+	0.0996994i	0.411167	+	0.911560i	$0.365121\pi$
$720$		0			0
$721$	525.108	−	909.514i	0.728305	−	1.26146i
$722$		0			0
$723$	−87.3796	+	11.1451i	−0.120857	+	0.0154151i
$724$		0			0
$725$	680.805	−	120.044i	0.939041	−	0.165578i
$726$		0			0
$727$	252.723	+	212.060i	0.347624	+	0.291692i	0.799835	−	0.600220i	$-0.204920\pi$
$727$	252.723	+	212.060i	0.347624	+	0.291692i	−0.452211	+	0.891911i	$0.649365\pi$
$728$		0			0
$729$	171.573	+	708.522i	0.235353	+	0.971910i
$730$		0			0
$731$	−492.673	+	587.145i	−0.673972	+	0.803208i
$732$		0			0
$733$	32.0098	+	181.537i	0.0436696	+	0.247663i	0.998826	−	0.0484385i	$-0.0154245\pi$
$733$	32.0098	+	181.537i	0.0436696	+	0.247663i	−0.955157	+	0.296101i	$0.904313\pi$
$734$		0			0
$735$	21.6119	+	169.441i	0.0294040	+	0.230532i
$736$		0			0
$737$	−84.7378	−	48.9234i	−0.114977	−	0.0663818i
$738$		0			0
$739$	−225.818	−	391.128i	−0.305572	−	0.529267i	0.671816	−	0.740718i	$-0.265514\pi$
$739$	−225.818	−	391.128i	−0.305572	−	0.529267i	−0.977389	+	0.211451i	$0.932181\pi$
$740$		0			0
$741$	−182.973	−	117.607i	−0.246927	−	0.158715i
$742$		0			0
$743$	−384.245	−	457.925i	−0.517153	−	0.616319i	0.442752	−	0.896644i	$-0.354002\pi$
$743$	−384.245	−	457.925i	−0.517153	−	0.616319i	−0.959905	+	0.280325i	$0.909558\pi$
$744$		0			0
$745$	469.802	−	170.994i	0.630606	−	0.229522i
$746$		0			0
$747$	−309.369	−	220.366i	−0.414149	−	0.295001i
$748$		0			0
$749$	−677.857	−	119.524i	−0.905016	−	0.159579i
$750$		0			0
$751$	−585.524	−	213.113i	−0.779659	−	0.283773i	−0.0786285	−	0.996904i	$-0.525054\pi$
$751$	−585.524	−	213.113i	−0.779659	−	0.283773i	−0.701030	+	0.713131i	$0.747276\pi$
$752$		0			0
$753$	358.358	−	111.402i	0.475908	−	0.147944i
$754$		0			0
$755$		−	23.3397i		−	0.0309135i
$756$		0			0
$757$	−1029.21			−1.35960			−0.679798	−	0.733399i	$-0.737933\pi$
$757$	−1029.21			−1.35960			−0.679798	+	0.733399i	$0.737933\pi$
$758$		0			0
$759$	90.3552	+	20.4142i	0.119045	+	0.0268962i
$760$		0			0
$761$	213.042	−	585.329i	0.279951	−	0.769158i	−0.717417	−	0.696644i	$-0.754676\pi$
$761$	213.042	−	585.329i	0.279951	−	0.769158i	0.997367	−	0.0725138i	$-0.0231021\pi$
$762$		0			0
$763$	−195.374	+	1108.02i	−0.256060	+	1.45219i
$764$		0			0
$765$	−950.815	+	246.561i	−1.24290	+	0.322302i
$766$		0			0
$767$	−110.128	−	302.573i	−0.143582	−	0.394489i
$768$		0			0
$769$	−803.159	+	673.931i	−1.04442	+	0.876373i	−0.992496	−	0.122278i	$-0.960980\pi$
$769$	−803.159	+	673.931i	−1.04442	+	0.876373i	−0.0519247	+	0.998651i	$0.516536\pi$
$770$		0			0
$771$	−699.815	−	33.3851i	−0.907672	−	0.0433010i
$772$		0			0
$773$	719.632	−	415.480i	0.930960	−	0.537490i	0.0438447	−	0.999038i	$-0.486039\pi$
$773$	719.632	−	415.480i	0.930960	−	0.537490i	0.887115	+	0.461549i	$0.152706\pi$
$774$		0			0
$775$	177.119	−	306.779i	0.228541	−	0.395844i
$776$		0			0
$777$	−385.208	+	919.460i	−0.495763	+	1.18335i
$778$		0			0
$779$	14.4473	−	2.54745i	0.0185460	−	0.00327016i
$780$		0			0
$781$	43.7619	+	36.7206i	0.0560331	+	0.0470174i
$782$		0			0
$783$	818.972	−	171.185i	1.04594	−	0.218627i
$784$		0			0
$785$	−1134.56	+	1352.11i	−1.44530	+	1.72244i
$786$		0			0
$787$	−32.2419	−	182.853i	−0.0409682	−	0.232342i	0.957448	−	0.288607i	$-0.0931920\pi$
$787$	−32.2419	−	182.853i	−0.0409682	−	0.232342i	−0.998416	+	0.0562647i	$0.982081\pi$
$788$		0			0
$789$	294.794	−	224.319i	0.373630	−	0.284308i
$790$		0			0
$791$	−692.099	−	399.584i	−0.874967	−	0.505162i
$792$		0			0
$793$	269.608	+	466.975i	0.339985	+	0.588872i
$794$		0			0
$795$	253.869	−	130.856i	0.319332	−	0.164599i
$796$		0			0
$797$	−949.323	−	1131.36i	−1.19112	−	1.41952i	−0.883768	−	0.467926i	$-0.845001\pi$
$797$	−949.323	−	1131.36i	−1.19112	−	1.41952i	−0.307352	−	0.951596i	$-0.599443\pi$
$798$		0			0
$799$	−858.922	+	312.622i	−1.07500	+	0.391267i
$800$		0			0
$801$	−276.231	+	580.107i	−0.344858	+	0.724228i
$802$		0			0
$803$	84.5462	+	14.9078i	0.105288	+	0.0185651i
$804$		0			0
$805$	1023.36	+	372.472i	1.27125	+	0.462698i
$806$		0			0
$807$	1122.87	+	1037.29i	1.39141	+	1.28536i
$808$		0			0
$809$			1487.78i			1.83903i	0.393055	+	0.919515i	$0.371418\pi$
$809$			1487.78i			1.83903i	−0.393055	+	0.919515i	$0.628582\pi$
$810$		0			0
$811$	−391.709			−0.482995			−0.241497	−	0.970401i	$-0.577639\pi$
$811$	−391.709			−0.482995			−0.241497	+	0.970401i	$0.577639\pi$
$812$		0			0
$813$	−101.117	+	109.459i	−0.124375	+	0.134636i
$814$		0			0
$815$	−623.900	+	1714.15i	−0.765521	+	2.10325i
$816$		0			0
$817$	−113.892	+	645.916i	−0.139403	+	0.790595i
$818$		0			0
$819$	−252.619	+	173.864i	−0.308448	+	0.212288i
$820$		0			0
$821$	1.02976	+	2.82925i	0.00125428	+	0.00344610i	0.940318	−	0.340297i	$-0.110527\pi$
$821$	1.02976	+	2.82925i	0.00125428	+	0.00344610i	−0.939064	+	0.343743i	$0.888305\pi$
$822$		0			0
$823$	1037.37	−	870.460i	1.26048	−	1.05767i	0.264847	−	0.964290i	$-0.414678\pi$
$823$	1037.37	−	870.460i	1.26048	−	1.05767i	0.995631	−	0.0933764i	$-0.0297660\pi$
$824$		0			0
$825$	38.1600	+	74.0328i	0.0462546	+	0.0897367i
$826$		0			0
$827$	−1186.03	+	684.755i	−1.43414	+	0.827999i	−0.997433	−	0.0716069i	$-0.977187\pi$
$827$	−1186.03	+	684.755i	−1.43414	+	0.827999i	−0.436703	+	0.899606i	$0.643854\pi$
$828$		0			0
$829$	−39.8034	+	68.9416i	−0.0480138	+	0.0831623i	−0.889033	−	0.457842i	$-0.848622\pi$
$829$	−39.8034	+	68.9416i	−0.0480138	+	0.0831623i	0.841020	+	0.541005i	$0.181956\pi$
$830$		0			0
$831$	−207.292	−	272.417i	−0.249449	−	0.327819i
$832$		0			0
$833$	−129.358	+	22.8094i	−0.155292	+	0.0273822i
$834$		0			0
$835$	17.0587	+	14.3140i	0.0204296	+	0.0171425i
$836$		0			0
$837$	202.554	−	377.859i	0.241999	−	0.451445i
$838$		0			0
$839$	−646.328	+	770.264i	−0.770355	+	0.918074i	−0.998455	−	0.0555640i	$-0.982304\pi$
$839$	−646.328	+	770.264i	−0.770355	+	0.918074i	0.228100	+	0.973638i	$0.426749\pi$
$840$		0			0
$841$	−20.7070	−	117.435i	−0.0246219	−	0.139638i
$842$		0			0
$843$	−71.6814	−	30.0309i	−0.0850313	−	0.0356239i
$844$		0			0
$845$	−836.841	−	483.150i	−0.990344	−	0.571775i
$846$		0			0
$847$	381.132	+	660.139i	0.449978	+	0.779385i
$848$		0			0
$849$	22.5178	−	472.016i	0.0265227	−	0.555967i
$850$		0			0
$851$	−830.493	−	989.743i	−0.975902	−	1.16304i
$852$		0			0
$853$	−331.253	+	120.566i	−0.388339	+	0.141344i	−0.528808	−	0.848741i	$-0.677361\pi$
$853$	−331.253	+	120.566i	−0.388339	+	0.141344i	0.140470	+	0.990085i	$0.455139\pi$
$854$		0			0
$855$	−599.134	+	589.538i	−0.700741	+	0.689518i
$856$		0			0
$857$	−1186.99	−	209.299i	−1.38506	−	0.244223i	−0.569068	−	0.822290i	$-0.692696\pi$
$857$	−1186.99	−	209.299i	−1.38506	−	0.244223i	−0.815989	+	0.578067i	$0.803807\pi$
$858$		0			0
$859$	594.390	+	216.340i	0.691956	+	0.251851i	0.663973	−	0.747757i	$-0.268869\pi$
$859$	594.390	+	216.340i	0.691956	+	0.251851i	0.0279836	+	0.999608i	$0.491091\pi$
$860$		0			0
$861$	4.55820	−	20.1750i	0.00529408	−	0.0234321i
$862$		0			0
$863$		−	1076.50i		−	1.24739i	−0.781668	−	0.623695i	$-0.785631\pi$
$863$		−	1076.50i		−	1.24739i	0.781668	−	0.623695i	$-0.214369\pi$
$864$		0			0
$865$	1323.87			1.53048
$866$		0			0
$867$	33.1434	+	106.616i	0.0382277	+	0.122971i
$868$		0			0
$869$	−16.8315	+	46.2443i	−0.0193689	+	0.0532155i
$870$		0			0
$871$	−72.9024	+	413.450i	−0.0836996	+	0.474684i
$872$		0			0
$873$	4.23090	+	9.26779i	0.00484639	+	0.0106160i
$874$		0			0
$875$	−40.3975	−	110.991i	−0.0461686	−	0.126847i
$876$		0			0
$877$	981.482	−	823.562i	1.11914	−	0.939067i	0.120576	−	0.992704i	$-0.461526\pi$
$877$	981.482	−	823.562i	1.11914	−	0.939067i	0.998560	+	0.0536374i	$0.0170815\pi$
$878$		0			0
$879$	681.175	−	1059.77i	0.774943	−	1.20565i
$880$		0			0
$881$	−787.917	+	454.904i	−0.894344	+	0.516350i	−0.875361	−	0.483470i	$-0.839376\pi$
$881$	−787.917	+	454.904i	−0.894344	+	0.516350i	−0.0189831	+	0.999820i	$0.506043\pi$
$882$		0			0
$883$	817.068	−	1415.20i	0.925332	−	1.60272i	0.134305	−	0.990940i	$-0.457120\pi$
$883$	817.068	−	1415.20i	0.925332	−	1.60272i	0.791027	−	0.611782i	$-0.209547\pi$
$884$		0			0
$885$	−1234.30	+	157.433i	−1.39469	+	0.177891i
$886$		0			0
$887$	585.651	−	103.266i	0.660260	−	0.116422i	0.166529	−	0.986037i	$-0.446744\pi$
$887$	585.651	−	103.266i	0.660260	−	0.116422i	0.493731	+	0.869615i	$0.335633\pi$
$888$		0			0
$889$	6.29916	+	5.28563i	0.00708567	+	0.00594559i
$890$		0			0
$891$	48.9853	+	88.0998i	0.0549779	+	0.0988775i
$892$		0			0
$893$	−502.769	+	599.177i	−0.563011	+	0.670971i
$894$		0			0
$895$	263.919	+	1496.76i	0.294881	+	1.67236i
$896$		0			0
$897$	−50.2875	−	394.262i	−0.0560618	−	0.439534i
$898$		0			0
$899$	−426.126	−	246.024i	−0.474000	−	0.273664i
$900$		0			0
$901$	109.816	+	190.206i	0.121882	+	0.211106i
$902$		0			0
$903$	777.895	+	499.999i	0.861456	+	0.553709i
$904$		0			0
$905$	−643.602	−	767.014i	−0.711162	−	0.847530i
$906$		0			0
$907$	276.952	−	100.802i	0.305349	−	0.111138i	−0.184801	−	0.982776i	$-0.559164\pi$
$907$	276.952	−	100.802i	0.305349	−	0.111138i	0.490150	+	0.871638i	$0.336942\pi$
$908$		0			0
$909$	9.72789	−	101.726i	0.0107018	−	0.111909i
$910$		0			0
$911$	820.799	+	144.729i	0.900986	+	0.158868i	0.604908	−	0.796295i	$-0.293210\pi$
$911$	820.799	+	144.729i	0.900986	+	0.158868i	0.296078	+	0.955164i	$0.404321\pi$
$912$		0			0
$913$	−49.3535	−	17.9632i	−0.0540565	−	0.0196749i
$914$		0			0
$915$	1989.82	−	618.569i	2.17466	−	0.676031i
$916$		0			0
$917$		−	586.439i		−	0.639519i
$918$		0			0
$919$	−1687.49			−1.83623			−0.918114	−	0.396315i	$-0.870289\pi$
$919$	−1687.49			−1.83623			−0.918114	+	0.396315i	$0.870289\pi$
$920$		0			0
$921$	591.316	+	133.598i	0.642037	+	0.145057i
$922$		0			0
$923$	83.8336	−	230.331i	0.0908273	−	0.249546i
$924$		0			0
$925$	201.726	−	1144.05i	0.218082	−	1.23681i
$926$		0			0
$927$	−394.894	+	1427.57i	−0.425991	+	1.53999i
$928$		0			0
$929$	−354.196	−	973.147i	−0.381266	−	1.04752i	−0.970824	−	0.239794i	$-0.922920\pi$
$929$	−354.196	−	973.147i	−0.381266	−	1.04752i	0.589557	−	0.807726i	$-0.299302\pi$
$930$		0			0
$931$	−86.1053	+	72.2509i	−0.0924869	+	0.0776057i
$932$		0			0
$933$	794.791	+	37.9160i	0.851867	+	0.0406388i
$934$		0			0
$935$	−117.626	+	67.9113i	−0.125803	+	0.0726324i
$936$		0			0
$937$	687.817	−	1191.33i	0.734063	−	1.27143i	−0.221071	−	0.975258i	$-0.570955\pi$
$937$	687.817	−	1191.33i	0.734063	−	1.27143i	0.955133	−	0.296176i	$-0.0957115\pi$
$938$		0			0
$939$	−319.647	+	762.972i	−0.340413	+	0.812537i
$940$		0			0
$941$	1678.41	−	295.949i	1.78365	−	0.314505i	0.818166	−	0.574983i	$-0.194991\pi$
$941$	1678.41	−	295.949i	1.78365	−	0.314505i	0.965480	+	0.260478i	$0.0838800\pi$
$942$		0			0
$943$	20.5352	+	17.2311i	0.0217765	+	0.0182726i
$944$		0			0
$945$	440.222	+	1100.29i	0.465844	+	1.16433i
$946$		0			0
$947$	14.5188	−	17.3028i	0.0153314	−	0.0182712i	−0.758324	−	0.651878i	$-0.773982\pi$
$947$	14.5188	−	17.3028i	0.0153314	−	0.0182712i	0.773656	+	0.633606i	$0.218426\pi$
$948$		0			0
$949$	−63.9643	−	362.760i	−0.0674018	−	0.382255i
$950$		0			0
$951$	83.5737	−	63.5941i	0.0878798	−	0.0668707i
$952$		0			0
$953$	877.360	+	506.544i	0.920630	+	0.531526i	0.883836	−	0.467797i	$-0.154952\pi$
$953$	877.360	+	506.544i	0.920630	+	0.531526i	0.0367941	+	0.999323i	$0.488285\pi$
$954$		0			0
$955$	−268.750	−	465.489i	−0.281414	−	0.487423i
$956$		0			0
$957$	102.834	−	53.0055i	0.107454	−	0.0553871i
$958$		0			0
$959$	242.281	+	288.739i	0.252639	+	0.301083i
$960$		0			0
$961$	666.116	−	242.446i	0.693149	−	0.252286i
$962$		0			0
$963$	967.724	−	76.7986i	1.00491	−	0.0797493i
$964$		0			0
$965$	1516.71	+	267.437i	1.57172	+	0.277137i
$966$		0			0
$967$	92.8853	+	33.8075i	0.0960551	+	0.0349612i	0.389601	−	0.920984i	$-0.372613\pi$
$967$	92.8853	+	33.8075i	0.0960551	+	0.0349612i	−0.293546	+	0.955945i	$0.594835\pi$
$968$		0			0
$969$	−474.788	−	438.602i	−0.489977	−	0.452633i
$970$		0			0
$971$		−	415.261i		−	0.427664i	−0.976871	−	0.213832i	$-0.931406\pi$
$971$		−	415.261i		−	0.427664i	0.976871	−	0.213832i	$-0.0685944\pi$
$972$		0			0
$973$	−322.227			−0.331169
$974$		0			0
$975$	242.494	−	262.501i	0.248712	−	0.269231i
$976$		0			0
$977$	−107.877	+	296.389i	−0.110416	+	0.303366i	−0.982578	−	0.185852i	$-0.940496\pi$
$977$	−107.877	+	296.389i	−0.110416	+	0.303366i	0.872161	+	0.489218i	$0.162718\pi$
$978$		0			0
$979$	−15.4276	+	87.4943i	−0.0157585	+	0.0893711i
$980$		0			0
$981$	−125.534	−	1581.83i	−0.127966	−	1.61247i
$982$		0			0
$983$	−219.236	−	602.345i	−0.223027	−	0.612762i	0.776829	−	0.629711i	$-0.216827\pi$
$983$	−219.236	−	602.345i	−0.223027	−	0.612762i	−0.999856	+	0.0169496i	$0.994605\pi$
$984$		0			0
$985$	−1821.39	+	1528.32i	−1.84912	+	1.55160i
$986$		0			0
$987$	505.256	+	980.227i	0.511911	+	0.993138i
$988$		0			0
$989$	−1037.92	+	599.245i	−1.04947	+	0.605910i
$990$		0			0
$991$	464.001	−	803.674i	0.468215	−	0.810973i	−0.531125	−	0.847294i	$-0.678231\pi$
$991$	464.001	−	803.674i	0.468215	−	0.810973i	0.999340	+	0.0363209i	$0.0115638\pi$
$992$		0			0
$993$	383.069	+	503.419i	0.385769	+	0.506968i
$994$		0			0
$995$	1067.25	−	188.185i	1.07261	−	0.189131i
$996$		0			0
$997$	872.811	+	732.376i	0.875438	+	0.734579i	0.965236	−	0.261381i	$-0.0841778\pi$
$997$	872.811	+	732.376i	0.875438	+	0.734579i	−0.0897982	+	0.995960i	$0.528622\pi$
$998$		0			0
$999$	200.381	−	1391.62i	0.200581	−	1.39301i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	432.3.bc.a.65.4		30
4.3	odd	2		27.3.f.a.11.5	yes	30
12.11	even	2		81.3.f.a.35.1		30
27.5	odd	18	inner	432.3.bc.a.113.4		30
36.7	odd	6		243.3.f.c.26.1		30
36.11	even	6		243.3.f.b.26.5		30
36.23	even	6		243.3.f.a.188.1		30
36.31	odd	6		243.3.f.d.188.5		30
108.7	odd	18		729.3.b.a.728.4		30
108.23	even	18		243.3.f.c.215.1		30
108.31	odd	18		243.3.f.b.215.5		30
108.47	even	18		729.3.b.a.728.27		30
108.59	even	18		27.3.f.a.5.5	✓	30
108.67	odd	18		243.3.f.a.53.1		30
108.95	even	18		243.3.f.d.53.5		30
108.103	odd	18		81.3.f.a.44.1		30

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
27.3.f.a.5.5	✓	30	108.59	even	18
27.3.f.a.11.5	yes	30	4.3	odd	2
81.3.f.a.35.1		30	12.11	even	2
81.3.f.a.44.1		30	108.103	odd	18
243.3.f.a.53.1		30	108.67	odd	18
243.3.f.a.188.1		30	36.23	even	6
243.3.f.b.26.5		30	36.11	even	6
243.3.f.b.215.5		30	108.31	odd	18
243.3.f.c.26.1		30	36.7	odd	6
243.3.f.c.215.1		30	108.23	even	18
243.3.f.d.53.5		30	108.95	even	18
243.3.f.d.188.5		30	36.31	odd	6
432.3.bc.a.65.4		30	1.1	even	1	trivial
432.3.bc.a.113.4		30	27.5	odd	18	inner
729.3.b.a.728.4		30	108.7	odd	18
729.3.b.a.728.27		30	108.47	even	18

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 432 = 2^{4} \cdot 3^{3} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	432.bc (of order \(18\), degree \(6\), not minimal)

\(f(q)\)	\(=\)	\(q+(2.03568 - 2.20363i) q^{3} +(-2.35247 + 6.46335i) q^{5} +(-1.10811 + 6.28443i) q^{7} +(-0.712002 - 8.97179i) q^{9} +O(q^{10})\)	\(q+(2.03568 - 2.20363i) q^{3} +(-2.35247 + 6.46335i) q^{5} +(-1.10811 + 6.28443i) q^{7} +(-0.712002 - 8.97179i) q^{9} +(-0.425636 - 1.16942i) q^{11} +(-4.09039 + 3.43225i) q^{13} +(9.45398 + 18.3413i) q^{15} +(-13.7418 + 7.93385i) q^{17} +(-6.78917 + 11.7592i) q^{19} +(11.5928 + 15.2350i) q^{21} +(-24.4347 + 4.30850i) q^{23} +(-17.0897 - 14.3399i) q^{25} +(-21.2200 - 16.6947i) q^{27} +(-19.9186 + 23.7381i) q^{29} +(2.75731 + 15.6375i) q^{31} +(-3.44344 - 1.44263i) q^{33} +(-38.0116 - 21.9460i) q^{35} +(26.0365 + 45.0965i) q^{37} +(-0.763322 + 16.0007i) q^{39} +(-0.694475 - 0.827643i) q^{41} +(45.3904 - 16.5207i) q^{43} +(59.6628 + 16.5039i) q^{45} +(56.7291 + 10.0029i) q^{47} +(7.77884 + 2.83127i) q^{49} +(-10.4907 + 46.4327i) q^{51} -13.8414i q^{53} +8.55969 q^{55} +(12.0924 + 38.8988i) q^{57} +(-20.6246 + 56.6655i) q^{59} +(17.5357 - 99.4497i) q^{61} +(57.1715 + 5.46725i) q^{63} +(-12.5613 - 34.5119i) q^{65} +(60.2302 - 50.5391i) q^{67} +(-40.2470 + 62.6160i) q^{69} +(-39.7545 + 22.9523i) q^{71} +(-34.4926 + 59.7430i) q^{73} +(-66.3891 + 8.46783i) q^{75} +(7.82081 - 1.37902i) q^{77} +(-30.2928 - 25.4187i) q^{79} +(-79.9861 + 12.7759i) q^{81} +(27.1277 - 32.3296i) q^{83} +(-18.9520 - 107.482i) q^{85} +(11.7621 + 92.2165i) q^{87} +(-61.8262 - 35.6954i) q^{89} +(-17.0371 - 29.5091i) q^{91} +(40.0723 + 25.7569i) q^{93} +(-60.0324 - 71.5439i) q^{95} +(-1.06372 + 0.387161i) q^{97} +(-10.1888 + 4.65135i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 30 q + 6 q^{3} - 15 q^{5} + 6 q^{7}+O(q^{10}) \) 30 * q + 6 * q^3 - 15 * q^5 + 6 * q^7	\( 30 q + 6 q^{3} - 15 q^{5} + 6 q^{7} + 6 q^{11} - 6 q^{13} + 9 q^{15} - 9 q^{17} + 3 q^{19} + 132 q^{21} - 120 q^{23} - 15 q^{25} + 90 q^{27} - 168 q^{29} - 39 q^{31} - 207 q^{33} + 252 q^{35} - 3 q^{37} - 15 q^{39} + 228 q^{41} + 96 q^{43} + 477 q^{45} - 399 q^{47} - 78 q^{49} - 36 q^{51} + 12 q^{55} - 192 q^{57} + 474 q^{59} + 138 q^{61} + 585 q^{63} - 411 q^{65} - 354 q^{67} + 99 q^{69} - 315 q^{71} - 66 q^{73} - 255 q^{75} + 201 q^{77} - 30 q^{79} + 36 q^{81} + 33 q^{83} - 261 q^{85} + 279 q^{87} + 72 q^{89} - 96 q^{91} + 591 q^{93} - 681 q^{95} - 582 q^{97} - 513 q^{99}+O(q^{100}) \) 30 * q + 6 * q^3 - 15 * q^5 + 6 * q^7 + 6 * q^11 - 6 * q^13 + 9 * q^15 - 9 * q^17 + 3 * q^19 + 132 * q^21 - 120 * q^23 - 15 * q^25 + 90 * q^27 - 168 * q^29 - 39 * q^31 - 207 * q^33 + 252 * q^35 - 3 * q^37 - 15 * q^39 + 228 * q^41 + 96 * q^43 + 477 * q^45 - 399 * q^47 - 78 * q^49 - 36 * q^51 + 12 * q^55 - 192 * q^57 + 474 * q^59 + 138 * q^61 + 585 * q^63 - 411 * q^65 - 354 * q^67 + 99 * q^69 - 315 * q^71 - 66 * q^73 - 255 * q^75 + 201 * q^77 - 30 * q^79 + 36 * q^81 + 33 * q^83 - 261 * q^85 + 279 * q^87 + 72 * q^89 - 96 * q^91 + 591 * q^93 - 681 * q^95 - 582 * q^97 - 513 * q^99

Introduction

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