LMFDB - Embedded newform 432.3.bc.c.209.6

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

Embedding invariants

Embedding label			209.6
Character	$\chi$	$=$	432.209
Dual form			432.3.bc.c.401.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(2.93655 - 0.613727i) q^{3} +(-7.71206 + 1.35984i) q^{5} +(0.690206 + 0.579152i) q^{7} +(8.24668 - 3.60448i) q^{9} +(15.2420 + 2.68757i) q^{11} +(-0.854187 - 0.310899i) q^{13} +(-21.8123 + 8.72635i) q^{15} +(10.6672 - 6.15869i) q^{17} +(5.40619 - 9.36379i) q^{19} +(2.38227 + 1.27711i) q^{21} +(21.0966 + 25.1419i) q^{23} +(34.1344 - 12.4239i) q^{25} +(22.0046 - 15.6460i) q^{27} +(19.3495 + 53.1622i) q^{29} +(37.9518 - 31.8453i) q^{31} +(46.4083 - 1.46222i) q^{33} +(-6.11047 - 3.52788i) q^{35} +(-17.4417 - 30.2099i) q^{37} +(-2.69917 - 0.388733i) q^{39} +(-12.2490 + 33.6538i) q^{41} +(-7.20864 + 40.8822i) q^{43} +(-58.6974 + 39.0122i) q^{45} +(15.9152 - 18.9670i) q^{47} +(-8.36779 - 47.4561i) q^{49} +(27.5449 - 24.6320i) q^{51} -50.3340i q^{53} -121.202 q^{55} +(10.1287 - 30.8152i) q^{57} +(-65.7126 + 11.5869i) q^{59} +(-18.7893 - 15.7661i) q^{61} +(7.77945 + 2.28824i) q^{63} +(7.01032 + 1.23611i) q^{65} +(61.2882 + 22.3071i) q^{67} +(77.3814 + 60.8830i) q^{69} +(-24.4496 + 14.1160i) q^{71} +(-10.7760 + 18.6646i) q^{73} +(92.6126 - 57.4327i) q^{75} +(8.96360 + 10.6824i) q^{77} +(27.2240 - 9.90872i) q^{79} +(55.0154 - 59.4500i) q^{81} +(0.0509121 + 0.139880i) q^{83} +(-73.8910 + 62.0019i) q^{85} +(89.4477 + 144.238i) q^{87} +(-79.3008 - 45.7843i) q^{89} +(-0.409508 - 0.709288i) q^{91} +(91.9031 - 116.807i) q^{93} +(-28.9595 + 79.5657i) q^{95} +(-17.4501 + 98.9646i) q^{97} +(135.383 - 32.7759i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 36 q + 18 q^{5} - 12 q^{9} + 18 q^{11} + 18 q^{15} - 228 q^{21} + 180 q^{23} + 18 q^{25} - 54 q^{27} + 144 q^{29} + 90 q^{31} + 324 q^{33} - 486 q^{35} - 102 q^{39} - 90 q^{41} - 90 q^{43} - 378 q^{45}+ \cdots - 126 q^{99}+O(q^{100}) $ 36 * q + 18 * q^5 - 12 * q^9 + 18 * q^11 + 18 * q^15 - 228 * q^21 + 180 * q^23 + 18 * q^25 - 54 * q^27 + 144 * q^29 + 90 * q^31 + 324 * q^33 - 486 * q^35 - 102 * q^39 - 90 * q^41 - 90 * q^43 - 378 * q^45 + 378 * q^47 + 72 * q^49 + 54 * q^51 + 72 * q^57 - 252 * q^59 - 144 * q^61 - 318 * q^63 + 18 * q^65 + 594 * q^67 - 522 * q^69 + 648 * q^71 + 126 * q^73 + 438 * q^75 - 342 * q^77 + 72 * q^79 + 324 * q^81 - 594 * q^83 + 360 * q^85 - 1062 * q^87 + 648 * q^89 + 198 * q^91 + 462 * q^93 - 252 * q^95 + 702 * q^97 - 126 * q^99

Character values

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

$n$	$271$	$325$	$353$
$\chi(n)$	$1$	$1$	$e\left(\frac{7}{18}\right)$

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
$3$	2.93655	−	0.613727i	0.978851	−	0.204576i
$3$	2.93655	−	0.613727i	0.978851	−	0.204576i
$4$		0			0
$5$	−7.71206	+	1.35984i	−1.54241	+	0.271969i	−0.879197	−	0.476459i	$-0.841920\pi$
$5$	−7.71206	+	1.35984i	−1.54241	+	0.271969i	−0.663216	+	0.748428i	$0.730809\pi$
$6$		0			0
$7$	0.690206	+	0.579152i	0.0986009	+	0.0827360i	0.690756	−	0.723088i	$-0.257278\pi$
$7$	0.690206	+	0.579152i	0.0986009	+	0.0827360i	−0.592155	+	0.805824i	$0.701723\pi$
$8$		0			0
$9$	8.24668	−	3.60448i	0.916298	−	0.400498i
$10$		0			0
$11$	15.2420	+	2.68757i	1.38564	+	0.244325i	0.816228	−	0.577730i	$-0.196062\pi$
$11$	15.2420	+	2.68757i	1.38564	+	0.244325i	0.569408	+	0.822055i	$0.307173\pi$
$12$		0			0
$13$	−0.854187	−	0.310899i	−0.0657067	−	0.0239153i	0.308958	−	0.951076i	$-0.400020\pi$
$13$	−0.854187	−	0.310899i	−0.0657067	−	0.0239153i	−0.374664	+	0.927160i	$0.622242\pi$
$14$		0			0
$15$	−21.8123	+	8.72635i	−1.45415	+	0.581757i
$16$		0			0
$17$	10.6672	−	6.15869i	0.627480	−	0.362276i	−0.152295	−	0.988335i	$-0.548666\pi$
$17$	10.6672	−	6.15869i	0.627480	−	0.362276i	0.779776	+	0.626059i	$0.215333\pi$
$18$		0			0
$19$	5.40619	−	9.36379i	0.284536	−	0.492831i	−0.687960	−	0.725748i	$-0.741494\pi$
$19$	5.40619	−	9.36379i	0.284536	−	0.492831i	0.972497	+	0.232917i	$0.0748271\pi$
$20$		0			0
$21$	2.38227	+	1.27711i	0.113441	+	0.0608148i
$22$		0			0
$23$	21.0966	+	25.1419i	0.917241	+	1.09313i	0.995364	+	0.0961819i	$0.0306631\pi$
$23$	21.0966	+	25.1419i	0.917241	+	1.09313i	−0.0781224	+	0.996944i	$0.524892\pi$
$24$		0			0
$25$	34.1344	−	12.4239i	1.36538	−	0.496956i
$26$		0			0
$27$	22.0046	−	15.6460i	0.814987	−	0.579480i
$28$		0			0
$29$	19.3495	+	53.1622i	0.667222	+	1.83318i	0.540701	+	0.841215i	$0.318159\pi$
$29$	19.3495	+	53.1622i	0.667222	+	1.83318i	0.126521	+	0.991964i	$0.459619\pi$
$30$		0			0
$31$	37.9518	−	31.8453i	1.22425	−	1.02727i	0.225660	−	0.974206i	$-0.427546\pi$
$31$	37.9518	−	31.8453i	1.22425	−	1.02727i	0.998591	−	0.0530624i	$-0.0168982\pi$
$32$		0			0
$33$	46.4083	−	1.46222i	1.40631	−	0.0443096i
$34$		0			0
$35$	−6.11047	−	3.52788i	−0.174585	−	0.100797i
$36$		0			0
$37$	−17.4417	−	30.2099i	−0.471398	−	0.816485i	0.528067	−	0.849203i	$-0.322917\pi$
$37$	−17.4417	−	30.2099i	−0.471398	−	0.816485i	−0.999465	+	0.0327181i	$0.989584\pi$
$38$		0			0
$39$	−2.69917	−	0.388733i	−0.0692095	−	0.00996751i
$40$		0			0
$41$	−12.2490	+	33.6538i	−0.298756	+	0.820824i	0.695953	+	0.718087i	$0.254982\pi$
$41$	−12.2490	+	33.6538i	−0.298756	+	0.820824i	−0.994709	+	0.102737i	$0.967240\pi$
$42$		0			0
$43$	−7.20864	+	40.8822i	−0.167643	+	0.950750i	0.778655	+	0.627453i	$0.215902\pi$
$43$	−7.20864	+	40.8822i	−0.167643	+	0.950750i	−0.946298	+	0.323297i	$0.895209\pi$
$44$		0			0
$45$	−58.6974	+	39.0122i	−1.30439	+	0.866938i
$46$		0			0
$47$	15.9152	−	18.9670i	0.338622	−	0.403554i	−0.569682	−	0.821865i	$-0.692933\pi$
$47$	15.9152	−	18.9670i	0.338622	−	0.403554i	0.908304	+	0.418311i	$0.137378\pi$
$48$		0			0
$49$	−8.36779	−	47.4561i	−0.170771	−	0.968492i
$50$		0			0
$51$	27.5449	−	24.6320i	0.540097	−	0.482981i
$52$		0			0
$53$		−	50.3340i		−	0.949699i	−0.880067	−	0.474850i	$-0.842502\pi$
$53$		−	50.3340i		−	0.949699i	0.880067	−	0.474850i	$-0.157498\pi$
$54$		0			0
$55$	−121.202			−2.20367
$56$		0			0
$57$	10.1287	−	30.8152i	0.177697	−	0.540617i
$58$		0			0
$59$	−65.7126	+	11.5869i	−1.11377	+	0.196388i	−0.700105	−	0.714040i	$-0.746863\pi$
$59$	−65.7126	+	11.5869i	−1.11377	+	0.196388i	−0.413667	+	0.910428i	$0.635752\pi$
$60$		0			0
$61$	−18.7893	−	15.7661i	−0.308021	−	0.258460i	0.475653	−	0.879633i	$-0.342212\pi$
$61$	−18.7893	−	15.7661i	−0.308021	−	0.258460i	−0.783673	+	0.621173i	$0.786656\pi$
$62$		0			0
$63$	7.77945	+	2.28824i	0.123483	+	0.0363213i
$64$		0			0
$65$	7.01032	+	1.23611i	0.107851	+	0.0190170i
$66$		0			0
$67$	61.2882	+	22.3071i	0.914750	+	0.332942i	0.756148	−	0.654401i	$-0.227079\pi$
$67$	61.2882	+	22.3071i	0.914750	+	0.332942i	0.158602	+	0.987343i	$0.449301\pi$
$68$		0			0
$69$	77.3814	+	60.8830i	1.12147	+	0.882362i
$70$		0			0
$71$	−24.4496	+	14.1160i	−0.344361	+	0.198817i	−0.662199	−	0.749328i	$-0.730377\pi$
$71$	−24.4496	+	14.1160i	−0.344361	+	0.198817i	0.317838	+	0.948145i	$0.397043\pi$
$72$		0			0
$73$	−10.7760	+	18.6646i	−0.147617	+	0.255680i	−0.930346	−	0.366682i	$-0.880494\pi$
$73$	−10.7760	+	18.6646i	−0.147617	+	0.255680i	0.782729	+	0.622362i	$0.213827\pi$
$74$		0			0
$75$	92.6126	−	57.4327i	1.23483	−	0.765769i
$76$		0			0
$77$	8.96360	+	10.6824i	0.116410	+	0.138732i
$78$		0			0
$79$	27.2240	−	9.90872i	0.344608	−	0.125427i	−0.163918	−	0.986474i	$-0.552413\pi$
$79$	27.2240	−	9.90872i	0.344608	−	0.125427i	0.508525	+	0.861047i	$0.330191\pi$
$80$		0			0
$81$	55.0154	−	59.4500i	0.679203	−	0.733951i
$82$		0			0
$83$	0.0509121	+	0.139880i	0.000613399	+	0.00168530i	0.939999	−	0.341177i	$-0.110826\pi$
$83$	0.0509121	+	0.139880i	0.000613399	+	0.00168530i	−0.939386	+	0.342863i	$0.888603\pi$
$84$		0			0
$85$	−73.8910	+	62.0019i	−0.869306	+	0.729434i
$86$		0			0
$87$	89.4477	+	144.238i	1.02813	+	1.65791i
$88$		0			0
$89$	−79.3008	−	45.7843i	−0.891020	−	0.514431i	−0.0167439	−	0.999860i	$-0.505330\pi$
$89$	−79.3008	−	45.7843i	−0.891020	−	0.514431i	−0.874276	+	0.485429i	$0.838663\pi$
$90$		0			0
$91$	−0.409508	−	0.709288i	−0.00450008	−	0.00779437i
$92$		0			0
$93$	91.9031	−	116.807i	0.988205	−	1.25599i
$94$		0			0
$95$	−28.9595	+	79.5657i	−0.304837	+	0.837534i
$96$		0			0
$97$	−17.4501	+	98.9646i	−0.179898	+	1.02025i	0.752439	+	0.658662i	$0.228877\pi$
$97$	−17.4501	+	98.9646i	−0.179898	+	1.02025i	−0.932337	+	0.361591i	$0.882234\pi$
$98$		0			0
$99$	135.383	−	32.7759i	1.36751	−	0.331070i
$100$		0			0
$101$	−67.8785	+	80.8944i	−0.672064	+	0.800935i	−0.989063	−	0.147491i	$-0.952880\pi$
$101$	−67.8785	+	80.8944i	−0.672064	+	0.800935i	0.316999	+	0.948426i	$0.397325\pi$
$102$		0			0
$103$	−15.1042	−	85.6604i	−0.146643	−	0.831654i	−0.966033	−	0.258418i	$-0.916799\pi$
$103$	−15.1042	−	85.6604i	−0.146643	−	0.831654i	0.819390	−	0.573236i	$-0.194312\pi$
$104$		0			0
$105$	−20.1089	−	6.60965i	−0.191513	−	0.0629490i
$106$		0			0
$107$			24.5062i			0.229030i	0.993422	+	0.114515i	$0.0365313\pi$
$107$			24.5062i			0.229030i	−0.993422	+	0.114515i	$0.963469\pi$
$108$		0			0
$109$	−33.5716			−0.307996			−0.153998	−	0.988071i	$-0.549215\pi$
$109$	−33.5716			−0.307996			−0.153998	+	0.988071i	$0.549215\pi$
$110$		0			0
$111$	−69.7591	−	78.0086i	−0.628461	−	0.702780i
$112$		0			0
$113$	120.158	−	21.1870i	1.06334	−	0.187496i	0.385503	−	0.922707i	$-0.374028\pi$
$113$	120.158	−	21.1870i	1.06334	−	0.187496i	0.677839	+	0.735211i	$0.262917\pi$
$114$		0			0
$115$	−196.887	−	165.208i	−1.71206	−	1.43659i
$116$		0			0
$117$	−8.16484	+	0.515020i	−0.0697849	+	0.00440188i
$118$		0			0
$119$	10.9294	+	1.92714i	0.0918433	+	0.0161945i
$120$		0			0
$121$	111.392	+	40.5435i	0.920598	+	0.335070i
$122$		0			0
$123$	−15.3155	+	106.344i	−0.124517	+	0.864583i
$124$		0			0
$125$	−76.8053	+	44.3435i	−0.614442	+	0.354748i
$126$		0			0
$127$	52.2314	−	90.4674i	0.411271	−	0.712342i	−0.583758	−	0.811927i	$-0.698418\pi$
$127$	52.2314	−	90.4674i	0.411271	−	0.712342i	0.995029	+	0.0995859i	$0.0317518\pi$
$128$		0			0
$129$	3.92197	+	124.477i	0.0304029	+	0.964938i
$130$		0			0
$131$	0.587532	+	0.700193i	0.00448497	+	0.00534498i	0.768282	−	0.640111i	$-0.221112\pi$
$131$	0.587532	+	0.700193i	0.00448497	+	0.00534498i	−0.763797	+	0.645456i	$0.776667\pi$
$132$		0			0
$133$	9.15444	−	3.33194i	0.0688304	−	0.0250522i
$134$		0			0
$135$	−148.425	+	150.585i	−1.09944	+	1.11545i
$136$		0			0
$137$	4.80632	+	13.2053i	0.0350826	+	0.0963887i	0.955997	−	0.293376i	$-0.0947787\pi$
$137$	4.80632	+	13.2053i	0.0350826	+	0.0963887i	−0.920915	+	0.389764i	$0.872556\pi$
$138$		0			0
$139$	−142.580	+	119.639i	−1.02576	+	0.860714i	−0.990340	−	0.138659i	$-0.955721\pi$
$139$	−142.580	+	119.639i	−1.02576	+	0.860714i	−0.0354184	+	0.999373i	$0.511276\pi$
$140$		0			0
$141$	35.0953	−	65.4653i	0.248903	−	0.464293i
$142$		0			0
$143$	−12.1839	−	7.03440i	−0.0852024	−	0.0491916i
$144$		0			0
$145$	−221.516	−	383.678i	−1.52770	−	2.64605i
$146$		0			0
$147$	−53.6975	−	134.222i	−0.365289	−	0.913074i
$148$		0			0
$149$	−43.3633	+	119.140i	−0.291029	+	0.799595i	0.704888	+	0.709319i	$0.250997\pi$
$149$	−43.3633	+	119.140i	−0.291029	+	0.799595i	−0.995917	+	0.0902764i	$0.971225\pi$
$150$		0			0
$151$	23.8651	−	135.346i	0.158047	−	0.896331i	−0.797899	−	0.602791i	$-0.794055\pi$
$151$	23.8651	−	135.346i	0.158047	−	0.896331i	0.955947	−	0.293540i	$-0.0948334\pi$
$152$		0			0
$153$	65.7698	−	89.2383i	0.429868	−	0.583257i
$154$		0			0
$155$	−249.382	+	297.202i	−1.60891	+	1.91743i
$156$		0			0
$157$	4.03656	+	22.8925i	0.0257106	+	0.145812i	0.994961	−	0.100266i	$-0.0319693\pi$
$157$	4.03656	+	22.8925i	0.0257106	+	0.145812i	−0.969250	+	0.246078i	$0.920858\pi$
$158$		0			0
$159$	−30.8914	−	147.809i	−0.194285	−	0.929614i
$160$		0			0
$161$			29.5712i			0.183672i
$162$		0			0
$163$	−157.977			−0.969187			−0.484593	−	0.874740i	$-0.661032\pi$
$163$	−157.977			−0.969187			−0.484593	+	0.874740i	$0.661032\pi$
$164$		0			0
$165$	−355.916	+	74.3848i	−2.15706	+	0.450817i
$166$		0			0
$167$	93.0755	−	16.4117i	0.557338	−	0.0982737i	0.112118	−	0.993695i	$-0.464237\pi$
$167$	93.0755	−	16.4117i	0.557338	−	0.0982737i	0.445220	+	0.895421i	$0.353125\pi$
$168$		0			0
$169$	−128.829	−	108.100i	−0.762299	−	0.639645i
$170$		0			0
$171$	10.8315	−	96.7067i	0.0633420	−	0.565536i
$172$		0			0
$173$	−286.053	−	50.4388i	−1.65348	−	0.291554i	−0.732388	−	0.680888i	$-0.761594\pi$
$173$	−286.053	−	50.4388i	−1.65348	−	0.291554i	−0.921097	+	0.389334i	$0.872705\pi$
$174$		0			0
$175$	30.7551	+	11.1939i	0.175743	+	0.0639654i
$176$		0			0
$177$	−185.857	+	74.3551i	−1.05004	+	0.420085i
$178$		0			0
$179$	−9.64834	+	5.57047i	−0.0539013	+	0.0311200i	−0.526709	−	0.850046i	$-0.676574\pi$
$179$	−9.64834	+	5.57047i	−0.0539013	+	0.0311200i	0.472807	+	0.881166i	$0.343241\pi$
$180$		0			0
$181$	−95.2763	+	165.023i	−0.526389	+	0.911732i	0.473139	+	0.880988i	$0.343121\pi$
$181$	−95.2763	+	165.023i	−0.526389	+	0.911732i	−0.999527	+	0.0307438i	$0.990212\pi$
$182$		0			0
$183$	−64.8517	−	34.7664i	−0.354381	−	0.189980i
$184$		0			0
$185$	175.592	+	209.263i	0.949148	+	1.13115i
$186$		0			0
$187$	179.141	−	65.2019i	0.957972	−	0.348673i
$188$		0			0
$189$	24.2491	+	1.94509i	0.128302	+	0.0102915i
$190$		0			0
$191$	−5.86380	−	16.1107i	−0.0307005	−	0.0843490i	0.923395	−	0.383850i	$-0.125402\pi$
$191$	−5.86380	−	16.1107i	−0.0307005	−	0.0843490i	−0.954096	+	0.299501i	$0.903180\pi$
$192$		0			0
$193$	118.098	−	99.0962i	0.611908	−	0.513452i	−0.283340	−	0.959019i	$-0.591443\pi$
$193$	118.098	−	99.0962i	0.611908	−	0.513452i	0.895248	+	0.445568i	$0.146998\pi$
$194$		0			0
$195$	21.3448	−	0.672524i	0.109460	−	0.00344884i
$196$		0			0
$197$	107.213	+	61.8996i	0.544230	+	0.314211i	0.746792	−	0.665058i	$-0.231593\pi$
$197$	107.213	+	61.8996i	0.544230	+	0.314211i	−0.202561	+	0.979270i	$0.564927\pi$
$198$		0			0
$199$	117.239	+	203.063i	0.589139	+	1.02042i	0.994345	+	0.106193i	$0.0338663\pi$
$199$	117.239	+	203.063i	0.589139	+	1.02042i	−0.405207	+	0.914225i	$0.632800\pi$
$200$		0			0
$201$	193.667	+	27.8917i	0.963515	+	0.138765i
$202$		0			0
$203$	−17.4339	+	47.8991i	−0.0858811	+	0.235956i
$204$		0			0
$205$	48.7010	−	276.197i	0.237566	−	1.34730i
$206$		0			0
$207$	264.600	+	131.295i	1.27826	+	0.634275i
$208$		0			0
$209$	107.567	−	128.193i	0.514674	−	0.613365i
$210$		0			0
$211$	9.24958	+	52.4570i	0.0438369	+	0.248611i	0.998850	−	0.0479537i	$-0.0152700\pi$
$211$	9.24958	+	52.4570i	0.0438369	+	0.248611i	−0.955013	+	0.296565i	$0.904159\pi$
$212$		0			0
$213$	−63.1342	+	56.4577i	−0.296405	+	0.265060i
$214$		0			0
$215$		−	325.089i		−	1.51204i
$216$		0			0
$217$	44.6378			0.205704
$218$		0			0
$219$	−20.1894	+	61.4233i	−0.0921891	+	0.280472i
$220$		0			0
$221$	−11.0265	+	1.94427i	−0.0498936	+	0.00879759i
$222$		0			0
$223$	45.9011	+	38.5156i	0.205835	+	0.172716i	0.739878	−	0.672742i	$-0.234883\pi$
$223$	45.9011	+	38.5156i	0.205835	+	0.172716i	−0.534043	+	0.845457i	$0.679328\pi$
$224$		0			0
$225$	236.714	−	225.493i	1.05206	−	1.00219i
$226$		0			0
$227$	62.7048	+	11.0565i	0.276232	+	0.0487072i	0.310048	−	0.950721i	$-0.399655\pi$
$227$	62.7048	+	11.0565i	0.276232	+	0.0487072i	−0.0338157	+	0.999428i	$0.510766\pi$
$228$		0			0
$229$	−201.212	−	73.2350i	−0.878653	−	0.319804i	−0.136987	−	0.990573i	$-0.543742\pi$
$229$	−201.212	−	73.2350i	−0.878653	−	0.319804i	−0.741666	+	0.670769i	$0.765964\pi$
$230$		0			0
$231$	32.8782	+	25.8682i	0.142330	+	0.111984i
$232$		0			0
$233$	−186.691	+	107.786i	−0.801248	+	0.462601i	−0.843907	−	0.536489i	$-0.819750\pi$
$233$	−186.691	+	107.786i	−0.801248	+	0.462601i	0.0426593	+	0.999090i	$0.486417\pi$
$234$		0			0
$235$	−96.9470	+	167.917i	−0.412541	+	0.714541i
$236$		0			0
$237$	73.8634	−	45.8056i	0.311660	−	0.193272i
$238$		0			0
$239$	−26.8944	−	32.0515i	−0.112529	−	0.134107i	0.706840	−	0.707374i	$-0.250120\pi$
$239$	−26.8944	−	32.0515i	−0.112529	−	0.134107i	−0.819369	+	0.573267i	$0.805676\pi$
$240$		0			0
$241$	421.281	−	153.334i	1.74805	−	0.636240i	0.748418	−	0.663227i	$-0.230814\pi$
$241$	421.281	−	153.334i	1.74805	−	0.636240i	0.999636	+	0.0269874i	$0.00859139\pi$
$242$		0			0
$243$	125.070	−	208.342i	0.514690	−	0.857376i
$244$		0			0
$245$	129.066	+	354.606i	0.526800	+	1.44737i
$246$		0			0
$247$	−7.52908	+	6.31765i	−0.0304821	+	0.0255775i
$248$		0			0
$249$	0.235354	+	0.379518i	0.000945197	+	0.00152417i
$250$		0			0
$251$	222.273	+	128.329i	0.885549	+	0.511272i	0.872484	−	0.488643i	$-0.162508\pi$
$251$	222.273	+	128.329i	0.885549	+	0.511272i	0.0130650	+	0.999915i	$0.495841\pi$
$252$		0			0
$253$	253.983	+	439.911i	1.00388	+	1.73878i
$254$		0			0
$255$	−178.932	+	227.421i	−0.701696	+	0.891846i
$256$		0			0
$257$	134.312	−	369.019i	0.522614	−	1.43587i	−0.344986	−	0.938608i	$-0.612116\pi$
$257$	134.312	−	369.019i	0.522614	−	1.43587i	0.867600	−	0.497262i	$-0.165661\pi$
$258$		0			0
$259$	5.45776	−	30.9525i	0.0210724	−	0.119508i
$260$		0			0
$261$	351.191	+	368.667i	1.34556	+	1.41252i
$262$		0			0
$263$	−78.9273	+	94.0619i	−0.300104	+	0.357650i	−0.894932	−	0.446203i	$-0.852776\pi$
$263$	−78.9273	+	94.0619i	−0.300104	+	0.357650i	0.594828	+	0.803853i	$0.297220\pi$
$264$		0			0
$265$	68.4465	+	388.179i	0.258289	+	1.46483i
$266$		0			0
$267$	−260.970	−	85.7790i	−0.977415	−	0.321270i
$268$		0			0
$269$		−	392.295i		−	1.45835i	−0.684329	−	0.729173i	$-0.739905\pi$
$269$		−	392.295i		−	1.45835i	0.684329	−	0.729173i	$-0.260095\pi$
$270$		0			0
$271$	43.9569			0.162203			0.0811013	−	0.996706i	$-0.474156\pi$
$271$	43.9569			0.162203			0.0811013	+	0.996706i	$0.474156\pi$
$272$		0			0
$273$	−1.63785	−	1.83154i	−0.00599945	−	0.00670892i
$274$		0			0
$275$	553.666	−	97.6263i	2.01333	−	0.355005i
$276$		0			0
$277$	−253.346	−	212.582i	−0.914606	−	0.767446i	0.0583836	−	0.998294i	$-0.481405\pi$
$277$	−253.346	−	212.582i	−0.914606	−	0.767446i	−0.972990	+	0.230849i	$0.925850\pi$
$278$		0			0
$279$	198.190	−	399.415i	0.710359	−	1.43159i
$280$		0			0
$281$	−252.252	−	44.4788i	−0.897692	−	0.158287i	−0.294282	−	0.955719i	$-0.595081\pi$
$281$	−252.252	−	44.4788i	−0.897692	−	0.158287i	−0.603410	+	0.797431i	$0.706192\pi$
$282$		0			0
$283$	−146.361	−	53.2711i	−0.517177	−	0.188237i	0.0702267	−	0.997531i	$-0.477628\pi$
$283$	−146.361	−	53.2711i	−0.517177	−	0.188237i	−0.587404	+	0.809294i	$0.699850\pi$
$284$		0			0
$285$	−36.2096	+	251.422i	−0.127051	+	0.882183i
$286$		0			0
$287$	−27.9450	+	16.1340i	−0.0973693	+	0.0562162i
$288$		0			0
$289$	−68.6411	+	118.890i	−0.237512	+	0.411383i
$290$		0			0
$291$	9.49400	+	301.324i	0.0326254	+	1.03548i
$292$		0			0
$293$	−131.430	−	156.632i	−0.448566	−	0.534580i	0.493617	−	0.869679i	$-0.335674\pi$
$293$	−131.430	−	156.632i	−0.448566	−	0.534580i	−0.942183	+	0.335100i	$0.891230\pi$
$294$		0			0
$295$	491.023	−	178.718i	1.66448	−	0.605823i
$296$		0			0
$297$	377.444	−	179.336i	1.27086	−	0.603826i
$298$		0			0
$299$	−10.2038	−	28.0348i	−0.0341265	−	0.0937618i
$300$		0			0
$301$	−28.6525	+	24.0423i	−0.0951909	+	0.0798747i
$302$		0			0
$303$	−149.682	+	279.209i	−0.493999	+	0.921483i
$304$		0			0
$305$	166.343	+	96.0384i	0.545388	+	0.314880i
$306$		0			0
$307$	−284.956	−	493.559i	−0.928196	−	1.60768i	−0.786339	−	0.617796i	$-0.788026\pi$
$307$	−284.956	−	493.559i	−0.928196	−	1.60768i	−0.141857	−	0.989887i	$-0.545307\pi$
$308$		0			0
$309$	−96.9264	−	242.276i	−0.313678	−	0.784066i
$310$		0			0
$311$	152.905	−	420.102i	0.491654	−	1.35081i	−0.407511	−	0.913200i	$-0.633603\pi$
$311$	152.905	−	420.102i	0.491654	−	1.35081i	0.899165	−	0.437609i	$-0.144175\pi$
$312$		0			0
$313$	−50.5690	+	286.791i	−0.161562	+	0.916265i	0.790976	+	0.611847i	$0.209573\pi$
$313$	−50.5690	+	286.791i	−0.161562	+	0.916265i	−0.952538	+	0.304418i	$0.901538\pi$
$314$		0			0
$315$	−63.1073	−	7.06823i	−0.200340	−	0.0224388i
$316$		0			0
$317$	−216.870	+	258.455i	−0.684131	+	0.815316i	−0.990633	−	0.136554i	$-0.956397\pi$
$317$	−216.870	+	258.455i	−0.684131	+	0.815316i	0.306501	+	0.951870i	$0.400842\pi$
$318$		0			0
$319$	152.047	+	862.300i	0.476636	+	2.70314i
$320$		0			0
$321$	15.0401	+	71.9636i	0.0468539	+	0.224186i
$322$		0			0
$323$		−	133.180i		−	0.412322i
$324$		0			0
$325$	−33.0197			−0.101599
$326$		0			0
$327$	−98.5848	+	20.6038i	−0.301482	+	0.0630085i
$328$		0			0
$329$	21.9696	−	3.87383i	0.0667768	−	0.0117746i
$330$		0			0
$331$	−116.755	−	97.9694i	−0.352735	−	0.295980i	0.449152	−	0.893455i	$-0.351726\pi$
$331$	−116.755	−	97.9694i	−0.352735	−	0.295980i	−0.801887	+	0.597475i	$0.796171\pi$
$332$		0			0
$333$	−252.727	−	186.263i	−0.758941	−	0.559349i
$334$		0			0
$335$	−502.993	−	88.6912i	−1.50147	−	0.264750i
$336$		0			0
$337$	219.421	+	79.8628i	0.651102	+	0.236982i	0.646390	−	0.763007i	$-0.276278\pi$
$337$	219.421	+	79.8628i	0.651102	+	0.236982i	0.00471178	+	0.999989i	$0.498500\pi$
$338$		0			0
$339$	339.846	−	135.961i	1.00250	−	0.401064i
$340$		0			0
$341$	664.047	−	383.388i	1.94735	−	1.12430i
$342$		0			0
$343$	43.7833	−	75.8349i	0.127648	−	0.221093i
$344$		0			0
$345$	−679.561	−	364.307i	−1.96974	−	1.05596i
$346$		0			0
$347$	409.259	+	487.736i	1.17942	+	1.40558i	0.894523	+	0.447022i	$0.147516\pi$
$347$	409.259	+	487.736i	1.17942	+	1.40558i	0.284899	+	0.958558i	$0.408040\pi$
$348$		0			0
$349$	268.471	−	97.7153i	0.769257	−	0.279987i	0.0725714	−	0.997363i	$-0.476879\pi$
$349$	268.471	−	97.7153i	0.769257	−	0.279987i	0.696686	+	0.717377i	$0.254657\pi$
$350$		0			0
$351$	−23.6604	+	6.52336i	−0.0674085	+	0.0185851i
$352$		0			0
$353$	−112.137	−	308.094i	−0.317669	−	0.872788i	−0.991050	−	0.133492i	$-0.957381\pi$
$353$	−112.137	−	308.094i	−0.317669	−	0.872788i	0.673381	−	0.739296i	$-0.264841\pi$
$354$		0			0
$355$	169.361	−	142.111i	0.477074	−	0.400313i
$356$		0			0
$357$	33.2774	−	1.04849i	0.0932139	−	0.00293695i
$358$		0			0
$359$	−484.455	−	279.700i	−1.34946	−	0.779109i	−0.361284	−	0.932456i	$-0.617661\pi$
$359$	−484.455	−	279.700i	−1.34946	−	0.779109i	−0.988172	+	0.153347i	$0.950995\pi$
$360$		0			0
$361$	122.046	+	211.390i	0.338078	+	0.585569i
$362$		0			0
$363$	351.992	+	50.6936i	0.969675	+	0.139652i
$364$		0			0
$365$	57.7245	−	158.597i	0.158149	−	0.434511i
$366$		0			0
$367$	−83.2991	+	472.413i	−0.226973	+	1.28723i	0.631904	+	0.775047i	$0.282274\pi$
$367$	−83.2991	+	472.413i	−0.226973	+	1.28723i	−0.858877	+	0.512182i	$0.828837\pi$
$368$		0			0
$369$	20.2911	+	321.683i	0.0549894	+	0.871770i
$370$		0			0
$371$	29.1510	−	34.7409i	0.0785743	−	0.0936411i
$372$		0			0
$373$	59.7262	+	338.724i	0.160124	+	0.908107i	0.953951	+	0.299964i	$0.0969745\pi$
$373$	59.7262	+	338.724i	0.160124	+	0.908107i	−0.793827	+	0.608144i	$0.791914\pi$
$374$		0			0
$375$	−198.328	+	177.355i	−0.528874	+	0.472946i
$376$		0			0
$377$		−	51.4262i		−	0.136409i
$378$		0			0
$379$	104.156			0.274817			0.137408	−	0.990514i	$-0.456123\pi$
$379$	104.156			0.274817			0.137408	+	0.990514i	$0.456123\pi$
$380$		0			0
$381$	97.8579	−	297.718i	0.256845	−	0.781412i
$382$		0			0
$383$	63.8855	−	11.2647i	0.166803	−	0.0294118i	−0.0896229	−	0.995976i	$-0.528566\pi$
$383$	63.8855	−	11.2647i	0.166803	−	0.0294118i	0.256426	+	0.966564i	$0.417455\pi$
$384$		0			0
$385$	−83.6542	−	70.1942i	−0.217284	−	0.182323i
$386$		0			0
$387$	87.9119	+	363.126i	0.227163	+	0.938310i
$388$		0			0
$389$	232.365	+	40.9722i	0.597339	+	0.105327i	0.464139	−	0.885762i	$-0.346364\pi$
$389$	232.365	+	40.9722i	0.597339	+	0.105327i	0.133200	+	0.991089i	$0.457475\pi$
$390$		0			0
$391$	379.882	+	138.266i	0.971564	+	0.353620i
$392$		0			0
$393$	2.15504	+	1.69557i	0.00548357	+	0.00431443i
$394$		0			0
$395$	−196.479	+	113.437i	−0.497415	+	0.287183i
$396$		0			0
$397$	−2.59349	+	4.49206i	−0.00653272	+	0.0113150i	−0.869273	−	0.494332i	$-0.835413\pi$
$397$	−2.59349	+	4.49206i	−0.00653272	+	0.0113150i	0.862741	+	0.505647i	$0.168746\pi$
$398$		0			0
$399$	24.8376	−	15.4027i	0.0622496	−	0.0386034i
$400$		0			0
$401$	103.381	+	123.205i	0.257808	+	0.307244i	0.879387	−	0.476108i	$-0.157953\pi$
$401$	103.381	+	123.205i	0.257808	+	0.307244i	−0.621579	+	0.783352i	$0.713508\pi$
$402$		0			0
$403$	−42.3186	+	15.4027i	−0.105009	+	0.0382201i
$404$		0			0
$405$	−343.440	+	533.295i	−0.847999	+	1.31678i
$406$		0			0
$407$	−184.655	−	507.335i	−0.453698	−	1.24652i
$408$		0			0
$409$	−132.217	+	110.943i	−0.323269	+	0.271255i	−0.789950	−	0.613171i	$-0.789894\pi$
$409$	−132.217	+	110.943i	−0.323269	+	0.271255i	0.466682	+	0.884425i	$0.345449\pi$
$410$		0			0
$411$	22.2184	+	35.8282i	0.0540594	+	0.0871731i
$412$		0			0
$413$	−52.0658	−	30.0602i	−0.126067	−	0.0727850i
$414$		0			0
$415$	−0.582852	−	1.00953i	−0.00140446	−	0.00243260i
$416$		0			0
$417$	−345.269	+	438.832i	−0.827984	+	1.05236i
$418$		0			0
$419$	−97.9330	+	269.069i	−0.233730	+	0.642169i	−1.00000		0.000350278i	$-0.999889\pi$
$419$	−97.9330	+	269.069i	−0.233730	+	0.642169i	0.766270	+	0.642519i	$0.222111\pi$
$420$		0			0
$421$	117.029	−	663.704i	0.277979	−	1.57649i	−0.451360	−	0.892342i	$-0.649061\pi$
$421$	117.029	−	663.704i	0.277979	−	1.57649i	0.729339	−	0.684153i	$-0.239828\pi$
$422$		0			0
$423$	62.8815	−	213.781i	0.148656	−	0.505393i
$424$		0			0
$425$	287.602	−	342.751i	0.676711	−	0.806473i
$426$		0			0
$427$	−3.83752	−	21.7637i	−0.00898717	−	0.0509688i
$428$		0			0
$429$	−40.0960	−	13.1793i	−0.0934639	−	0.0307209i
$430$		0			0
$431$		−	539.138i		−	1.25090i	−0.780264	−	0.625450i	$-0.784915\pi$
$431$		−	539.138i		−	1.25090i	0.780264	−	0.625450i	$-0.215085\pi$
$432$		0			0
$433$	−802.991			−1.85448			−0.927241	−	0.374466i	$-0.877826\pi$
$433$	−802.991			−1.85448			−0.927241	+	0.374466i	$0.877826\pi$
$434$		0			0
$435$	−885.968	−	990.739i	−2.03671	−	2.27756i
$436$		0			0
$437$	349.475	−	61.6219i	0.799715	−	0.141011i
$438$		0			0
$439$	59.9232	+	50.2816i	0.136499	+	0.114537i	0.708481	−	0.705730i	$-0.249381\pi$
$439$	59.9232	+	50.2816i	0.136499	+	0.114537i	−0.571982	+	0.820266i	$0.693825\pi$
$440$		0			0
$441$	−240.061	−	361.194i	−0.544356	−	0.819033i
$442$		0			0
$443$	537.994	+	94.8628i	1.21443	+	0.214137i	0.743928	−	0.668260i	$-0.232961\pi$
$443$	537.994	+	94.8628i	1.21443	+	0.214137i	0.470505	+	0.882397i	$0.344072\pi$
$444$		0			0
$445$	673.832	+	245.255i	1.51423	+	0.551134i
$446$		0			0
$447$	−54.2194	+	376.473i	−0.121296	+	0.842222i
$448$		0			0
$449$	−592.342	+	341.989i	−1.31925	+	0.761667i	−0.983607	−	0.180323i	$-0.942286\pi$
$449$	−592.342	+	341.989i	−1.31925	+	0.761667i	−0.335639	+	0.941991i	$0.608952\pi$
$450$		0			0
$451$	−277.146	+	480.031i	−0.614514	+	1.06437i
$452$		0			0
$453$	−12.9842	−	412.097i	−0.0286627	−	0.909707i
$454$		0			0
$455$	4.12267	+	4.91321i	0.00906081	+	0.0107983i
$456$		0			0
$457$	−80.6475	+	29.3533i	−0.176472	+	0.0642304i	−0.428745	−	0.903426i	$-0.641044\pi$
$457$	−80.6475	+	29.3533i	−0.176472	+	0.0642304i	0.252273	+	0.967656i	$0.418822\pi$
$458$		0			0
$459$	138.368	−	302.418i	0.301456	−	0.658862i
$460$		0			0
$461$	1.94941	+	5.35597i	0.00422866	+	0.0116181i	0.941789	−	0.336205i	$-0.109143\pi$
$461$	1.94941	+	5.35597i	0.00422866	+	0.0116181i	−0.937560	+	0.347823i	$0.886921\pi$
$462$		0			0
$463$	247.066	−	207.313i	0.533620	−	0.447760i	−0.335729	−	0.941959i	$-0.608983\pi$
$463$	247.066	−	207.313i	0.533620	−	0.447760i	0.869349	+	0.494198i	$0.164538\pi$
$464$		0			0
$465$	−549.922	+	1025.80i	−1.18263	+	2.20602i
$466$		0			0
$467$	−32.7859	−	18.9290i	−0.0702054	−	0.0405331i	0.464486	−	0.885580i	$-0.346239\pi$
$467$	−32.7859	−	18.9290i	−0.0702054	−	0.0405331i	−0.534692	+	0.845047i	$0.679572\pi$
$468$		0			0
$469$	29.3823	+	50.8917i	0.0626489	+	0.108511i
$470$		0			0
$471$	25.9033	+	64.7476i	0.0549964	+	0.137468i
$472$		0			0
$473$	−219.748	+	603.753i	−0.464584	+	1.27643i
$474$		0			0
$475$	68.2021	−	386.793i	0.143583	−	0.814302i
$476$		0			0
$477$	−181.428	−	415.089i	−0.380353	−	0.870207i
$478$		0			0
$479$	−461.346	+	549.811i	−0.963145	+	1.14783i	0.0258182	+	0.999667i	$0.491781\pi$
$479$	−461.346	+	549.811i	−0.963145	+	1.14783i	−0.988963	+	0.148164i	$0.952664\pi$
$480$		0			0
$481$	5.50626	+	31.2275i	0.0114475	+	0.0649221i
$482$		0			0
$483$	18.1486	+	86.8373i	0.0375748	+	0.179787i
$484$		0			0
$485$		−	786.950i		−	1.62258i
$486$		0			0
$487$	−52.1558			−0.107096			−0.0535480	−	0.998565i	$-0.517053\pi$
$487$	−52.1558			−0.107096			−0.0535480	+	0.998565i	$0.517053\pi$
$488$		0			0
$489$	−463.909	+	96.9550i	−0.948689	+	0.198272i
$490$		0			0
$491$	−77.8114	+	13.7202i	−0.158475	+	0.0279435i	−0.252323	−	0.967643i	$-0.581194\pi$
$491$	−77.8114	+	13.7202i	−0.158475	+	0.0279435i	0.0938475	+	0.995587i	$0.470083\pi$
$492$		0			0
$493$	533.813	+	447.922i	1.08279	+	0.908565i
$494$		0			0
$495$	−999.513	+	436.870i	−2.01922	+	0.882565i
$496$		0			0
$497$	−25.0506	−	4.41709i	−0.0504036	−	0.00888751i
$498$		0			0
$499$	−27.9915	−	10.1881i	−0.0560952	−	0.0204170i	0.313820	−	0.949482i	$-0.398391\pi$
$499$	−27.9915	−	10.1881i	−0.0560952	−	0.0204170i	−0.369915	+	0.929065i	$0.620613\pi$
$500$		0			0
$501$	263.249	−	105.317i	0.525446	−	0.210213i
$502$		0			0
$503$	146.080	−	84.3394i	0.290418	−	0.167673i	−0.347713	−	0.937601i	$-0.613041\pi$
$503$	146.080	−	84.3394i	0.290418	−	0.167673i	0.638130	+	0.769928i	$0.279708\pi$
$504$		0			0
$505$	413.479	−	716.167i	0.818771	−	1.41815i
$506$		0			0
$507$	−444.656	−	238.376i	−0.877033	−	0.470169i
$508$		0			0
$509$	223.993	+	266.945i	0.440066	+	0.524450i	0.939798	−	0.341730i	$-0.111013\pi$
$509$	223.993	+	266.945i	0.440066	+	0.524450i	−0.499733	+	0.866180i	$0.666568\pi$
$510$		0			0
$511$	−18.2474	+	6.64149i	−0.0357091	+	0.0129971i
$512$		0			0
$513$	−27.5443	−	290.632i	−0.0536925	−	0.566534i
$514$		0			0
$515$	232.970	+	640.079i	0.452368	+	1.24287i
$516$		0			0
$517$	293.555	−	246.322i	0.567805	−	0.476445i
$518$		0			0
$519$	−870.965	+	27.4420i	−1.67816	+	0.0528748i
$520$		0			0
$521$	−95.9710	−	55.4089i	−0.184205	−	0.106351i	0.405062	−	0.914289i	$-0.367250\pi$
$521$	−95.9710	−	55.4089i	−0.184205	−	0.106351i	−0.589267	+	0.807938i	$0.700583\pi$
$522$		0			0
$523$	−280.197	−	485.316i	−0.535750	−	0.927946i	−0.999127	−	0.0417848i	$-0.986696\pi$
$523$	−280.197	−	485.316i	−0.535750	−	0.927946i	0.463377	−	0.886161i	$-0.346638\pi$
$524$		0			0
$525$	97.1840	+	13.9964i	0.185112	+	0.0266597i
$526$		0			0
$527$	208.712	−	573.433i	0.396039	−	1.08811i
$528$		0			0
$529$	−95.1903	+	539.851i	−0.179944	+	1.02051i
$530$		0			0
$531$	−500.146	+	332.413i	−0.941894	+	0.626013i
$532$		0			0
$533$	20.9258	−	24.9384i	0.0392605	−	0.0467888i
$534$		0			0
$535$	−33.3246	−	188.993i	−0.0622889	−	0.353258i
$536$		0			0
$537$	−24.9141	+	22.2794i	−0.0463950	+	0.0414887i
$538$		0			0
$539$		−	745.814i		−	1.38370i
$540$		0			0
$541$	−313.055			−0.578660			−0.289330	−	0.957229i	$-0.593433\pi$
$541$	−313.055			−0.578660			−0.289330	+	0.957229i	$0.593433\pi$
$542$		0			0
$543$	−178.505	+	543.074i	−0.328738	+	1.00014i
$544$		0			0
$545$	258.906	−	45.6522i	0.475057	−	0.0837654i
$546$		0			0
$547$	564.255	+	473.466i	1.03155	+	0.865569i	0.991034	−	0.133610i	$-0.0426569\pi$
$547$	564.255	+	473.466i	1.03155	+	0.865569i	0.0405113	+	0.999179i	$0.487101\pi$
$548$		0			0
$549$	−211.778	−	62.2921i	−0.385751	−	0.113465i
$550$		0			0
$551$	602.406	+	106.220i	1.09330	+	0.192778i
$552$		0			0
$553$	24.5288	+	8.92776i	0.0443559	+	0.0161442i
$554$		0			0
$555$	644.066	+	506.746i	1.16048	+	0.913055i
$556$		0			0
$557$	−552.604	+	319.046i	−0.992108	+	0.572794i	−0.905904	−	0.423483i	$-0.860807\pi$
$557$	−552.604	+	319.046i	−0.992108	+	0.572794i	−0.0862045	+	0.996277i	$0.527474\pi$
$558$		0			0
$559$	18.8678	−	32.6799i	0.0337527	−	0.0584614i
$560$		0			0
$561$	486.040	−	301.412i	0.866381	−	0.537277i
$562$		0			0
$563$	−224.179	−	267.166i	−0.398187	−	0.474541i	0.529279	−	0.848448i	$-0.322462\pi$
$563$	−224.179	−	267.166i	−0.398187	−	0.474541i	−0.927466	+	0.373907i	$0.878018\pi$
$564$		0			0
$565$	−897.852	+	326.791i	−1.58912	+	0.578392i
$566$		0			0
$567$	72.4026	−	9.17048i	0.127694	−	0.0161737i
$568$		0			0
$569$	187.157	+	514.209i	0.328922	+	0.903707i	0.988385	+	0.151970i	$0.0485616\pi$
$569$	187.157	+	514.209i	0.328922	+	0.903707i	−0.659463	+	0.751737i	$0.729216\pi$
$570$		0			0
$571$	−534.384	+	448.402i	−0.935874	+	0.785292i	−0.976863	−	0.213868i	$-0.931394\pi$
$571$	−534.384	+	448.402i	−0.935874	+	0.785292i	0.0409882	+	0.999160i	$0.486949\pi$
$572$		0			0
$573$	−27.1069	−	43.7110i	−0.0473070	−	0.0762845i
$574$		0			0
$575$	1032.48	+	596.102i	1.79562	+	1.03670i
$576$		0			0
$577$	−193.884	−	335.816i	−0.336020	−	0.582004i	0.647660	−	0.761929i	$-0.275748\pi$
$577$	−193.884	−	335.816i	−0.336020	−	0.582004i	−0.983680	+	0.179925i	$0.942414\pi$
$578$		0			0
$579$	285.984	−	363.481i	0.493927	−	0.627774i
$580$		0			0
$581$	−0.0458718	+	0.126032i	−7.89532e−5	+	0.000216922i
$582$		0			0
$583$	135.276	−	767.191i	0.232035	−	1.31594i
$584$		0			0
$585$	62.2674	−	15.0748i	0.106440	−	0.0257688i
$586$		0			0
$587$	229.618	−	273.648i	0.391173	−	0.466181i	−0.534135	−	0.845399i	$-0.679363\pi$
$587$	229.618	−	273.648i	0.391173	−	0.466181i	0.925307	+	0.379218i	$0.123807\pi$
$588$		0			0
$589$	−93.0185	−	527.534i	−0.157926	−	0.895644i
$590$		0			0
$591$	352.827	+	115.972i	0.597000	+	0.196230i
$592$		0			0
$593$		−	828.411i		−	1.39698i	−0.715618	−	0.698492i	$-0.753855\pi$
$593$		−	828.411i		−	1.39698i	0.715618	−	0.698492i	$-0.246145\pi$
$594$		0			0
$595$	−86.9085			−0.146065
$596$		0			0
$597$	468.903	+	524.353i	0.785432	+	0.878314i
$598$		0			0
$599$	−863.376	+	152.237i	−1.44136	+	0.254151i	−0.839026	−	0.544091i	$-0.816875\pi$
$599$	−863.376	+	152.237i	−1.44136	+	0.254151i	−0.602337	+	0.798242i	$0.705763\pi$
$600$		0			0
$601$	627.682	+	526.688i	1.04440	+	0.876353i	0.992493	−	0.122299i	$-0.0390267\pi$
$601$	627.682	+	526.688i	1.04440	+	0.876353i	0.0519035	+	0.998652i	$0.483471\pi$
$602$		0			0
$603$	585.830	−	36.9529i	0.971525	−	0.0612817i
$604$		0			0
$605$	−914.197	−	161.198i	−1.51107	−	0.266442i
$606$		0			0
$607$	544.372	+	198.135i	0.896823	+	0.326417i	0.748979	−	0.662594i	$-0.230544\pi$
$607$	544.372	+	198.135i	0.896823	+	0.326417i	0.147844	+	0.989011i	$0.452767\pi$
$608$		0			0
$609$	−21.7985	+	151.358i	−0.0357938	+	0.248535i
$610$		0			0
$611$	−19.4914	+	11.2534i	−0.0319008	+	0.0184180i
$612$		0			0
$613$	−163.781	+	283.677i	−0.267179	+	0.462768i	−0.968132	−	0.250439i	$-0.919425\pi$
$613$	−163.781	+	283.677i	−0.267179	+	0.462768i	0.700953	+	0.713207i	$0.252758\pi$
$614$		0			0
$615$	−26.4965	−	840.956i	−0.0430837	−	1.36741i
$616$		0			0
$617$	−685.484	−	816.928i	−1.11099	−	1.32403i	−0.940931	−	0.338599i	$-0.890047\pi$
$617$	−685.484	−	816.928i	−1.11099	−	1.32403i	−0.170064	−	0.985433i	$-0.554397\pi$
$618$		0			0
$619$	−835.904	+	304.244i	−1.35041	+	0.491509i	−0.913076	−	0.407789i	$-0.866300\pi$
$619$	−835.904	+	304.244i	−1.35041	+	0.491509i	−0.437335	+	0.899299i	$0.644078\pi$
$620$		0			0
$621$	857.591	+	223.162i	1.38098	+	0.359360i
$622$		0			0
$623$	−28.2178	−	77.5278i	−0.0452934	−	0.124443i
$624$		0			0
$625$	−163.639	+	137.309i	−0.261822	+	0.219695i
$626$		0			0
$627$	237.200	−	442.463i	0.378310	−	0.705682i
$628$		0			0
$629$	−372.107	−	214.836i	−0.591585	−	0.341552i
$630$		0			0
$631$	477.341	+	826.778i	0.756483	+	1.31027i	0.944634	+	0.328126i	$0.106417\pi$
$631$	477.341	+	826.778i	0.756483	+	1.31027i	−0.188151	+	0.982140i	$0.560250\pi$
$632$		0			0
$633$	59.3561	+	148.366i	0.0937695	+	0.234385i
$634$		0			0
$635$	−279.790	+	768.717i	−0.440614	+	1.21058i
$636$		0			0
$637$	−7.60638	+	43.1379i	−0.0119409	+	0.0677205i
$638$		0			0
$639$	−150.747	+	204.538i	−0.235911	+	0.320091i
$640$		0			0
$641$	−456.345	+	543.850i	−0.711926	+	0.848440i	−0.993820	−	0.111005i	$-0.964593\pi$
$641$	−456.345	+	543.850i	−0.711926	+	0.848440i	0.281894	+	0.959446i	$0.409037\pi$
$642$		0			0
$643$	−8.61807	−	48.8755i	−0.0134029	−	0.0760116i	0.977373	−	0.211525i	$-0.0678429\pi$
$643$	−8.61807	−	48.8755i	−0.0134029	−	0.0760116i	−0.990776	+	0.135513i	$0.956732\pi$
$644$		0			0
$645$	−199.516	−	954.641i	−0.309327	−	1.48006i
$646$		0			0
$647$		−	918.622i		−	1.41982i	−0.704294	−	0.709909i	$-0.748736\pi$
$647$		−	918.622i		−	1.41982i	0.704294	−	0.709909i	$-0.251264\pi$
$648$		0			0
$649$	−1032.73			−1.59126
$650$		0			0
$651$	131.081	−	27.3954i	0.201354	−	0.0420821i
$652$		0			0
$653$	342.395	−	60.3734i	0.524341	−	0.0924555i	0.0947886	−	0.995497i	$-0.469782\pi$
$653$	342.395	−	60.3734i	0.524341	−	0.0924555i	0.429552	+	0.903042i	$0.358671\pi$
$654$		0			0
$655$	−5.48323	−	4.60098i	−0.00837135	−	0.00702440i
$656$		0			0
$657$	−21.5902	+	192.763i	−0.0328617	+	0.293399i
$658$		0			0
$659$	−1263.48	−	222.786i	−1.91728	−	0.338068i	−0.918873	−	0.394554i	$-0.870899\pi$
$659$	−1263.48	−	222.786i	−1.91728	−	0.338068i	−0.998403	+	0.0564864i	$0.982010\pi$
$660$		0			0
$661$	−126.358	−	45.9904i	−0.191161	−	0.0695770i	0.244666	−	0.969608i	$-0.421322\pi$
$661$	−126.358	−	45.9904i	−0.191161	−	0.0695770i	−0.435827	+	0.900030i	$0.643544\pi$
$662$		0			0
$663$	−31.1866	+	12.4767i	−0.0470386	+	0.0188185i
$664$		0			0
$665$	−66.0687	+	38.1448i	−0.0993514	+	0.0573605i
$666$		0			0
$667$	−928.391	+	1608.02i	−1.39189	+	2.41083i
$668$		0			0
$669$	158.429	+	84.9324i	0.236815	+	0.126954i
$670$		0			0
$671$	−244.013	−	290.804i	−0.363656	−	0.433389i
$672$		0			0
$673$	522.659	−	190.232i	0.776610	−	0.282663i	0.0768517	−	0.997043i	$-0.475513\pi$
$673$	522.659	−	190.232i	0.776610	−	0.282663i	0.699758	+	0.714380i	$0.253291\pi$
$674$		0			0
$675$	556.731	−	807.449i	0.824787	−	1.19622i
$676$		0			0
$677$	−116.809	−	320.931i	−0.172540	−	0.474049i	0.823039	−	0.567985i	$-0.192277\pi$
$677$	−116.809	−	320.931i	−0.172540	−	0.474049i	−0.995578	+	0.0939369i	$0.970055\pi$
$678$		0			0
$679$	−69.3597	+	58.1997i	−0.102150	+	0.0857138i
$680$		0			0
$681$	190.922	−	6.01548i	0.280355	−	0.00883331i
$682$		0			0
$683$	−181.638	−	104.869i	−0.265942	−	0.153542i	0.361100	−	0.932527i	$-0.382401\pi$
$683$	−181.638	−	104.869i	−0.265942	−	0.153542i	−0.627042	+	0.778985i	$0.715735\pi$
$684$		0			0
$685$	−55.0237	−	95.3039i	−0.0803266	−	0.139130i
$686$		0			0
$687$	−635.815	−	91.5695i	−0.925494	−	0.133289i
$688$		0			0
$689$	−15.6488	+	42.9947i	−0.0227123	+	0.0624016i
$690$		0			0
$691$	50.5894	−	286.907i	0.0732119	−	0.415205i	−0.926071	−	0.377349i	$-0.876836\pi$
$691$	50.5894	−	286.907i	0.0732119	−	0.415205i	0.999283	−	0.0378567i	$-0.0120531\pi$
$692$		0			0
$693$	112.424	+	55.7852i	0.162229	+	0.0804981i
$694$		0			0
$695$	936.899	−	1116.55i	1.34806	−	1.60655i
$696$		0			0
$697$	76.6014	+	434.428i	0.109902	+	0.623283i
$698$		0			0
$699$	−482.076	+	431.096i	−0.689665	+	0.616733i
$700$		0			0
$701$		−	445.528i		−	0.635560i	−0.948164	−	0.317780i	$-0.897063\pi$
$701$		−	445.528i		−	0.635560i	0.948164	−	0.317780i	$-0.102937\pi$
$702$		0			0
$703$	−377.173			−0.536519
$704$		0			0
$705$	−181.635	+	552.597i	−0.257638	+	0.783825i
$706$		0			0
$707$	−93.7003	+	16.5219i	−0.132532	+	0.0233690i
$708$		0			0
$709$	−112.307	−	94.2371i	−0.158402	−	0.132915i	0.560142	−	0.828397i	$-0.310747\pi$
$709$	−112.307	−	94.2371i	−0.158402	−	0.132915i	−0.718544	+	0.695481i	$0.755191\pi$
$710$		0			0
$711$	188.792	−	179.842i	0.265530	−	0.252943i
$712$		0			0
$713$	1601.30	+	282.353i	2.24587	+	0.396007i
$714$		0			0
$715$	103.529	+	37.6815i	0.144796	+	0.0527014i
$716$		0			0
$717$	−98.6477	−	77.6151i	−0.137584	−	0.108250i
$718$		0			0
$719$	−442.793	+	255.647i	−0.615845	+	0.355559i	−0.775250	−	0.631655i	$-0.782376\pi$
$719$	−442.793	+	255.647i	−0.615845	+	0.355559i	0.159404	+	0.987213i	$0.449043\pi$
$720$		0			0
$721$	39.1853	−	67.8710i	0.0543486	−	0.0941345i
$722$		0			0
$723$	1143.01	−	708.824i	1.58092	−	0.980393i
$724$		0			0
$725$	1320.96	+	1574.26i	1.82202	+	2.17140i
$726$		0			0
$727$	233.836	−	85.1092i	0.321644	−	0.117069i	−0.176152	−	0.984363i	$-0.556365\pi$
$727$	233.836	−	85.1092i	0.321644	−	0.117069i	0.497796	+	0.867294i	$0.334143\pi$
$728$		0			0
$729$	239.408	−	688.567i	0.328406	−	0.944537i
$730$		0			0
$731$	174.885	+	480.493i	0.239241	+	0.657310i
$732$		0			0
$733$	645.868	−	541.947i	0.881129	−	0.739355i	−0.0852818	−	0.996357i	$-0.527179\pi$
$733$	645.868	−	541.947i	0.881129	−	0.739355i	0.966411	+	0.257002i	$0.0827346\pi$
$734$		0			0
$735$	596.640	+	962.107i	0.811755	+	1.30899i
$736$		0			0
$737$	874.202	+	504.721i	1.18616	+	0.684832i
$738$		0			0
$739$	−339.638	−	588.271i	−0.459592	−	0.796036i	0.539347	−	0.842083i	$-0.318671\pi$
$739$	−339.638	−	588.271i	−0.459592	−	0.796036i	−0.998939	+	0.0460469i	$0.985338\pi$
$740$		0			0
$741$	−18.2322	+	23.1729i	−0.0246049	+	0.0312725i
$742$		0			0
$743$	−215.273	+	591.458i	−0.289735	+	0.796040i	0.706368	+	0.707845i	$0.250332\pi$
$743$	−215.273	+	591.458i	−0.289735	+	0.796040i	−0.996103	+	0.0881957i	$0.971890\pi$
$744$		0			0
$745$	172.409	−	977.780i	0.231421	−	1.31246i
$746$		0			0
$747$	0.924050	+	0.970033i	0.00123701	+	0.00129857i
$748$		0			0
$749$	−14.1928	+	16.9143i	−0.0189490	+	0.0225825i
$750$		0			0
$751$	−123.896	−	702.649i	−0.164975	−	0.935618i	−0.949090	−	0.315004i	$-0.897994\pi$
$751$	−123.896	−	702.649i	−0.164975	−	0.935618i	0.784116	−	0.620615i	$-0.213117\pi$
$752$		0			0
$753$	731.475	+	240.431i	0.971414	+	0.319297i
$754$		0			0
$755$			1076.25i			1.42550i
$756$		0			0
$757$	1327.86			1.75411			0.877055	−	0.480390i	$-0.159505\pi$
$757$	1327.86			1.75411			0.877055	+	0.480390i	$0.159505\pi$
$758$		0			0
$759$	1015.82	+	1135.95i	1.33836	+	1.49663i
$760$		0			0
$761$	−928.015	+	163.634i	−1.21947	+	0.215025i	−0.746096	−	0.665838i	$-0.768074\pi$
$761$	−928.015	+	163.634i	−1.21947	+	0.215025i	−0.473371	+	0.880863i	$0.656963\pi$
$762$		0			0
$763$	−23.1713	−	19.4430i	−0.0303687	−	0.0254824i
$764$		0			0
$765$	−385.870	+	777.648i	−0.504406	+	1.01653i
$766$		0			0
$767$	59.7332	+	10.5326i	0.0778790	+	0.0137322i
$768$		0			0
$769$	−999.812	−	363.902i	−1.30015	−	0.473214i	−0.403102	−	0.915155i	$-0.632068\pi$
$769$	−999.812	−	363.902i	−1.30015	−	0.473214i	−0.897044	+	0.441941i	$0.854290\pi$
$770$		0			0
$771$	167.937	−	1166.07i	0.217817	−	1.51242i
$772$		0			0
$773$	250.289	−	144.504i	0.323789	−	0.186939i	−0.329291	−	0.944228i	$-0.606810\pi$
$773$	250.289	−	144.504i	0.323789	−	0.186939i	0.653080	+	0.757289i	$0.273477\pi$
$774$		0			0
$775$	899.818	−	1558.53i	1.16106	−	2.01101i
$776$		0			0
$777$	−2.96938	−	94.2431i	−0.00382159	−	0.121291i
$778$		0			0
$779$	248.907	+	296.636i	0.319521	+	0.380790i
$780$		0			0
$781$	−410.598	+	149.446i	−0.525734	+	0.191352i
$782$		0			0
$783$	1257.55	+	867.074i	1.60607	+	1.10737i
$784$		0			0
$785$	−62.2604	−	171.059i	−0.0793126	−	0.217910i
$786$		0			0
$787$	513.070	−	430.517i	0.651931	−	0.547035i	−0.255725	−	0.966750i	$-0.582314\pi$
$787$	513.070	−	430.517i	0.651931	−	0.547035i	0.907656	+	0.419714i	$0.137870\pi$
$788$		0			0
$789$	−174.046	+	324.657i	−0.220590	+	0.411480i
$790$		0			0
$791$	95.2040	+	54.9661i	0.120359	+	0.0694893i
$792$		0			0
$793$	11.1479	+	19.3087i	0.0140579	+	0.0243490i
$794$		0			0
$795$	439.233	+	1097.90i	0.552494	+	1.38101i
$796$		0			0
$797$	96.3773	−	264.795i	0.120925	−	0.332239i	−0.864430	−	0.502753i	$-0.832321\pi$
$797$	96.3773	−	264.795i	0.120925	−	0.332239i	0.985355	+	0.170514i	$0.0545428\pi$
$798$		0			0
$799$	52.9583	−	300.342i	0.0662807	−	0.375897i
$800$		0			0
$801$	−818.997	−	91.7304i	−1.02247	−	0.114520i
$802$		0			0
$803$	−214.411	+	255.525i	−0.267012	+	0.318213i
$804$		0			0
$805$	−40.2122	−	228.055i	−0.0499531	−	0.283298i
$806$		0			0
$807$	−240.762	−	1152.00i	−0.298342	−	1.42750i
$808$		0			0
$809$			747.542i			0.924032i	0.886872	+	0.462016i	$0.152874\pi$
$809$			747.542i			0.924032i	−0.886872	+	0.462016i	$0.847126\pi$
$810$		0			0
$811$	1416.36			1.74644			0.873218	−	0.487330i	$-0.162029\pi$
$811$	1416.36			1.74644			0.873218	+	0.487330i	$0.162029\pi$
$812$		0			0
$813$	129.082	−	26.9775i	0.158772	−	0.0331827i
$814$		0			0
$815$	1218.33	−	214.825i	1.49489	−	0.263589i
$816$		0			0
$817$	343.841	+	288.517i	0.420859	+	0.353142i
$818$		0			0
$819$	−5.93369	−	4.37321i	−0.00724505	−	0.00533969i
$820$		0			0
$821$	91.5752	+	16.1472i	0.111541	+	0.0196677i	0.229140	−	0.973393i	$-0.426409\pi$
$821$	91.5752	+	16.1472i	0.111541	+	0.0196677i	−0.117599	+	0.993061i	$0.537520\pi$
$822$		0			0
$823$	−35.2640	−	12.8350i	−0.0428481	−	0.0155954i	0.320507	−	0.947246i	$-0.396147\pi$
$823$	−35.2640	−	12.8350i	−0.0428481	−	0.0155954i	−0.363355	+	0.931651i	$0.618369\pi$
$824$		0			0
$825$	1565.95	−	626.485i	1.89813	−	0.759375i
$826$		0			0
$827$	−1138.29	+	657.194i	−1.37641	+	0.794673i	−0.991726	−	0.128374i	$-0.959024\pi$
$827$	−1138.29	+	657.194i	−1.37641	+	0.794673i	−0.384688	+	0.923047i	$0.625691\pi$
$828$		0			0
$829$	−27.7172	+	48.0077i	−0.0334346	+	0.0579103i	−0.882258	−	0.470765i	$-0.843978\pi$
$829$	−27.7172	+	48.0077i	−0.0334346	+	0.0579103i	0.848824	+	0.528676i	$0.177311\pi$
$830$		0			0
$831$	−874.431	−	468.774i	−1.05226	−	0.564109i
$832$		0			0
$833$	−381.528	−	454.688i	−0.458017	−	0.545843i
$834$		0			0
$835$	−695.486	+	253.136i	−0.832918	+	0.303157i
$836$		0			0
$837$	336.865	−	1294.54i	0.402467	−	1.54664i
$838$		0			0
$839$	192.782	+	529.664i	0.229776	+	0.631305i	0.999979	−	0.00649448i	$-0.00206727\pi$
$839$	192.782	+	529.664i	0.229776	+	0.631305i	−0.770203	+	0.637799i	$0.779845\pi$
$840$		0			0
$841$	−1807.57	+	1516.73i	−2.14931	+	1.80349i
$842$		0			0
$843$	−768.048	+	24.1993i	−0.911089	+	0.0287062i
$844$		0			0
$845$	1140.53	+	658.487i	1.34974	+	0.779274i
$846$		0			0
$847$	53.4028	+	92.4964i	0.0630494	+	0.109205i
$848$		0			0
$849$	−462.491	−	66.6076i	−0.544748	−	0.0784542i
$850$		0			0
$851$	391.575	−	1075.84i	0.460135	−	1.26421i
$852$		0			0
$853$	82.4484	−	467.588i	0.0966570	−	0.548169i	−0.897570	−	0.440872i	$-0.854669\pi$
$853$	82.4484	−	467.588i	0.0966570	−	0.548169i	0.994227	−	0.107297i	$-0.0342196\pi$
$854$		0			0
$855$	47.9730	+	760.537i	0.0561088	+	0.889517i
$856$		0			0
$857$	−478.426	+	570.166i	−0.558257	+	0.665305i	−0.969177	−	0.246367i	$-0.920763\pi$
$857$	−478.426	+	570.166i	−0.558257	+	0.665305i	0.410920	+	0.911672i	$0.365208\pi$
$858$		0			0
$859$	−72.5615	−	411.517i	−0.0844721	−	0.479065i	−0.997469	−	0.0710990i	$-0.977349\pi$
$859$	−72.5615	−	411.517i	−0.0844721	−	0.479065i	0.912997	−	0.407966i	$-0.133762\pi$
$860$		0			0
$861$	−72.1600	+	64.5290i	−0.0838095	+	0.0749466i
$862$		0			0
$863$			816.761i			0.946420i	0.880950	+	0.473210i	$0.156905\pi$
$863$			816.761i			0.946420i	−0.880950	+	0.473210i	$0.843095\pi$
$864$		0			0
$865$	2274.65			2.62965
$866$		0			0
$867$	−128.602	+	391.253i	−0.148330	+	0.451272i
$868$		0			0
$869$	441.578	−	77.8621i	0.508145	−	0.0895997i
$870$		0			0
$871$	−45.4164	−	38.1089i	−0.0521428	−	0.0437530i
$872$		0			0
$873$	212.810	+	879.028i	0.243769	+	1.00690i
$874$		0			0
$875$	−78.6931	−	13.8757i	−0.0899350	−	0.0158580i
$876$		0			0
$877$	518.635	+	188.768i	0.591374	+	0.215242i	0.620333	−	0.784338i	$-0.286997\pi$
$877$	518.635	+	188.768i	0.591374	+	0.215242i	−0.0289599	+	0.999581i	$0.509220\pi$
$878$		0			0
$879$	−482.080	−	379.296i	−0.548441	−	0.431508i
$880$		0			0
$881$	−1220.85	+	704.859i	−1.38576	+	0.800067i	−0.992834	−	0.119504i	$-0.961870\pi$
$881$	−1220.85	+	704.859i	−1.38576	+	0.800067i	−0.392923	+	0.919571i	$0.628536\pi$
$882$		0			0
$883$	804.703	−	1393.79i	0.911328	−	1.57847i	0.0991386	−	0.995074i	$-0.468391\pi$
$883$	804.703	−	1393.79i	0.911328	−	1.57847i	0.812190	−	0.583393i	$-0.198275\pi$
$884$		0			0
$885$	1332.23	−	826.168i	1.50535	−	0.933523i
$886$		0			0
$887$	761.451	+	907.462i	0.858457	+	1.02307i	0.999453	+	0.0330591i	$0.0105250\pi$
$887$	761.451	+	907.462i	0.858457	+	1.02307i	−0.140996	+	0.990010i	$0.545031\pi$
$888$		0			0
$889$	88.4447	−	32.1913i	0.0994879	−	0.0362106i
$890$		0			0
$891$	998.321	−	758.278i	1.12045	−	0.851042i
$892$		0			0
$893$	−91.5626	−	251.566i	−0.102534	−	0.281709i
$894$		0			0
$895$	66.8336	−	56.0801i	0.0746745	−	0.0626593i
$896$		0			0
$897$	−47.1697	−	76.0632i	−0.0525861	−	0.0847973i
$898$		0			0
$899$	2427.31	+	1401.41i	2.70001	+	1.55885i
$900$		0			0
$901$	−309.992	−	536.922i	−0.344053	−	0.595917i
$902$		0			0
$903$	−69.3841	+	88.1862i	−0.0768373	+	0.0976591i
$904$		0			0
$905$	510.371	−	1402.23i	0.563946	−	1.54943i
$906$		0			0
$907$	−69.1106	+	391.946i	−0.0761969	+	0.432134i	0.922714	+	0.385484i	$0.125966\pi$
$907$	−69.1106	+	391.946i	−0.0761969	+	0.432134i	−0.998911	+	0.0466499i	$0.985145\pi$
$908$		0			0
$909$	−268.190	+	911.777i	−0.295038	+	1.00305i
$910$		0			0
$911$	−521.570	+	621.583i	−0.572524	+	0.682308i	−0.972147	−	0.234372i	$-0.924697\pi$
$911$	−521.570	+	621.583i	−0.572524	+	0.682308i	0.399623	+	0.916680i	$0.369141\pi$
$912$		0			0
$913$	0.400064	+	2.26888i	0.000438186	+	0.00248508i
$914$		0			0
$915$	547.417	+	179.932i	0.598270	+	0.196647i
$916$		0			0
$917$			0.823547i			0.000898089i
$918$		0			0
$919$	−1571.44			−1.70994			−0.854972	−	0.518674i	$-0.826426\pi$
$919$	−1571.44			−1.70994			−0.854972	+	0.518674i	$0.826426\pi$
$920$		0			0
$921$	−1139.70	−	1274.48i	−1.23746	−	1.38380i
$922$		0			0
$923$	25.2732	−	4.45635i	0.0273816	−	0.00482811i
$924$		0			0
$925$	−970.688	−	814.504i	−1.04939	−	0.880545i
$926$		0			0
$927$	−433.321	−	651.971i	−0.467444	−	0.703312i
$928$		0			0
$929$	−509.792	−	89.8902i	−0.548754	−	0.0967601i	−0.107605	−	0.994194i	$-0.534318\pi$
$929$	−509.792	−	89.8902i	−0.548754	−	0.0967601i	−0.441149	+	0.897434i	$0.645429\pi$
$930$		0			0
$931$	−489.607	−	178.202i	−0.525894	−	0.191410i
$932$		0			0
$933$	191.184	−	1327.49i	0.204914	−	1.42282i
$934$		0			0
$935$	−1292.88	+	746.445i	−1.38276	+	0.798336i
$936$		0			0
$937$	−171.737	+	297.457i	−0.183284	+	0.317457i	−0.942997	−	0.332801i	$-0.892006\pi$
$937$	−171.737	+	297.457i	−0.183284	+	0.317457i	0.759713	+	0.650259i	$0.225339\pi$
$938$		0			0
$939$	27.5128	+	873.212i	0.0293001	+	0.929938i
$940$		0			0
$941$	−538.505	−	641.766i	−0.572269	−	0.682004i	0.399826	−	0.916591i	$-0.369071\pi$
$941$	−538.505	−	641.766i	−0.572269	−	0.682004i	−0.972095	+	0.234587i	$0.924626\pi$
$942$		0			0
$943$	−1104.53	+	402.017i	−1.17130	+	0.426317i
$944$		0			0
$945$	−189.656	+	17.9744i	−0.200694	+	0.0190205i
$946$		0			0
$947$	−493.939	−	1357.09i	−0.521583	−	1.43304i	−0.868757	−	0.495238i	$-0.835081\pi$
$947$	−493.939	−	1357.09i	−0.521583	−	1.43304i	0.347174	−	0.937801i	$-0.387141\pi$
$948$		0			0
$949$	15.0076	−	12.5928i	0.0158141	−	0.0132696i
$950$		0			0
$951$	−478.228	+	892.066i	−0.502869	+	0.938029i
$952$		0			0
$953$	1132.07	+	653.600i	1.18790	+	0.685835i	0.957829	−	0.287339i	$-0.0927707\pi$
$953$	1132.07	+	653.600i	1.18790	+	0.685835i	0.230072	+	0.973174i	$0.426104\pi$
$954$		0			0
$955$	67.1300	+	116.273i	0.0702932	+	0.121751i
$956$		0			0
$957$	975.710	+	2438.87i	1.01955	+	2.54846i
$958$		0			0
$959$	−4.33049	+	11.8979i	−0.00451564	+	0.0124066i
$960$		0			0
$961$	259.337	−	1470.77i	0.269862	−	1.53046i
$962$		0			0
$963$	88.3320	+	202.094i	0.0917259	+	0.209859i
$964$		0			0
$965$	−776.025	+	924.831i	−0.804171	+	0.958374i
$966$		0			0
$967$	−117.727	−	667.665i	−0.121745	−	0.690450i	−0.983188	−	0.182596i	$-0.941550\pi$
$967$	−117.727	−	667.665i	−0.121745	−	0.690450i	0.861443	−	0.507854i	$-0.169561\pi$
$968$		0			0
$969$	−81.7362	−	391.090i	−0.0843511	−	0.403602i
$970$		0			0
$971$		−	172.492i		−	0.177644i	−0.996048	−	0.0888219i	$-0.971690\pi$
$971$		−	172.492i		−	0.177644i	0.996048	−	0.0888219i	$-0.0283102\pi$
$972$		0			0
$973$	−167.699			−0.172353
$974$		0			0
$975$	−96.9642	+	20.2651i	−0.0994505	+	0.0207847i
$976$		0			0
$977$	−1622.94	+	286.168i	−1.66115	+	0.292905i	−0.923876	−	0.382692i	$-0.874997\pi$
$977$	−1622.94	+	286.168i	−1.66115	+	0.292905i	−0.737271	+	0.675597i	$0.763886\pi$
$978$		0			0
$979$	−1085.65	−	910.971i	−1.10894	−	0.930511i
$980$		0			0
$981$	−276.854	+	121.008i	−0.282216	+	0.123352i
$982$		0			0
$983$	−764.198	−	134.749i	−0.777414	−	0.137079i	−0.229157	−	0.973389i	$-0.573597\pi$
$983$	−764.198	−	134.749i	−0.777414	−	0.137079i	−0.548256	+	0.836310i	$0.684708\pi$
$984$		0			0
$985$	−911.010	−	331.580i	−0.924883	−	0.336630i
$986$		0			0
$987$	62.1374	−	24.8590i	0.0629558	−	0.0251865i
$988$		0			0
$989$	−1179.93	+	681.235i	−1.19306	+	0.688812i
$990$		0			0
$991$	191.688	−	332.014i	0.193429	−	0.335029i	−0.752955	−	0.658072i	$-0.771372\pi$
$991$	191.688	−	332.014i	0.193429	−	0.335029i	0.946384	+	0.323043i	$0.104706\pi$
$992$		0			0
$993$	−402.985	−	216.036i	−0.405826	−	0.217559i
$994$		0			0
$995$	−1180.29	−	1406.61i	−1.18622	−	1.41368i
$996$		0			0
$997$	−1455.50	+	529.759i	−1.45988	+	0.531353i	−0.945333	−	0.326108i	$-0.894263\pi$
$997$	−1455.50	+	529.759i	−1.45988	+	0.531353i	−0.514549	+	0.857461i	$0.672041\pi$
$998$		0			0
$999$	−856.462	−	391.866i	−0.857319	−	0.392259i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	432.3.bc.c.209.6		36
4.3	odd	2		54.3.f.a.47.1	yes	36
12.11	even	2		162.3.f.a.143.6		36
27.23	odd	18	inner	432.3.bc.c.401.6		36
108.23	even	18		54.3.f.a.23.1	✓	36
108.31	odd	18		162.3.f.a.17.6		36
108.79	odd	18		1458.3.b.c.1457.34		36
108.83	even	18		1458.3.b.c.1457.3		36

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
54.3.f.a.23.1	✓	36	108.23	even	18
54.3.f.a.47.1	yes	36	4.3	odd	2
162.3.f.a.17.6		36	108.31	odd	18
162.3.f.a.143.6		36	12.11	even	2
432.3.bc.c.209.6		36	1.1	even	1	trivial
432.3.bc.c.401.6		36	27.23	odd	18	inner
1458.3.b.c.1457.3		36	108.83	even	18
1458.3.b.c.1457.34		36	108.79	odd	18

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(2.93655 - 0.613727i) q^{3} +(-7.71206 + 1.35984i) q^{5} +(0.690206 + 0.579152i) q^{7} +(8.24668 - 3.60448i) q^{9} +(15.2420 + 2.68757i) q^{11} +(-0.854187 - 0.310899i) q^{13} +(-21.8123 + 8.72635i) q^{15} +(10.6672 - 6.15869i) q^{17} +(5.40619 - 9.36379i) q^{19} +(2.38227 + 1.27711i) q^{21} +(21.0966 + 25.1419i) q^{23} +(34.1344 - 12.4239i) q^{25} +(22.0046 - 15.6460i) q^{27} +(19.3495 + 53.1622i) q^{29} +(37.9518 - 31.8453i) q^{31} +(46.4083 - 1.46222i) q^{33} +(-6.11047 - 3.52788i) q^{35} +(-17.4417 - 30.2099i) q^{37} +(-2.69917 - 0.388733i) q^{39} +(-12.2490 + 33.6538i) q^{41} +(-7.20864 + 40.8822i) q^{43} +(-58.6974 + 39.0122i) q^{45} +(15.9152 - 18.9670i) q^{47} +(-8.36779 - 47.4561i) q^{49} +(27.5449 - 24.6320i) q^{51} -50.3340i q^{53} -121.202 q^{55} +(10.1287 - 30.8152i) q^{57} +(-65.7126 + 11.5869i) q^{59} +(-18.7893 - 15.7661i) q^{61} +(7.77945 + 2.28824i) q^{63} +(7.01032 + 1.23611i) q^{65} +(61.2882 + 22.3071i) q^{67} +(77.3814 + 60.8830i) q^{69} +(-24.4496 + 14.1160i) q^{71} +(-10.7760 + 18.6646i) q^{73} +(92.6126 - 57.4327i) q^{75} +(8.96360 + 10.6824i) q^{77} +(27.2240 - 9.90872i) q^{79} +(55.0154 - 59.4500i) q^{81} +(0.0509121 + 0.139880i) q^{83} +(-73.8910 + 62.0019i) q^{85} +(89.4477 + 144.238i) q^{87} +(-79.3008 - 45.7843i) q^{89} +(-0.409508 - 0.709288i) q^{91} +(91.9031 - 116.807i) q^{93} +(-28.9595 + 79.5657i) q^{95} +(-17.4501 + 98.9646i) q^{97} +(135.383 - 32.7759i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 36 q + 18 q^{5} - 12 q^{9} + 18 q^{11} + 18 q^{15} - 228 q^{21} + 180 q^{23} + 18 q^{25} - 54 q^{27} + 144 q^{29} + 90 q^{31} + 324 q^{33} - 486 q^{35} - 102 q^{39} - 90 q^{41} - 90 q^{43} - 378 q^{45}+ \cdots - 126 q^{99}+O(q^{100}) \) 36 * q + 18 * q^5 - 12 * q^9 + 18 * q^11 + 18 * q^15 - 228 * q^21 + 180 * q^23 + 18 * q^25 - 54 * q^27 + 144 * q^29 + 90 * q^31 + 324 * q^33 - 486 * q^35 - 102 * q^39 - 90 * q^41 - 90 * q^43 - 378 * q^45 + 378 * q^47 + 72 * q^49 + 54 * q^51 + 72 * q^57 - 252 * q^59 - 144 * q^61 - 318 * q^63 + 18 * q^65 + 594 * q^67 - 522 * q^69 + 648 * q^71 + 126 * q^73 + 438 * q^75 - 342 * q^77 + 72 * q^79 + 324 * q^81 - 594 * q^83 + 360 * q^85 - 1062 * q^87 + 648 * q^89 + 198 * q^91 + 462 * q^93 - 252 * q^95 + 702 * q^97 - 126 * q^99

Introduction

L-functions

Modular forms

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Database

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