LMFDB - Embedded newform 405.3.n.a.179.14

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [405,3,Mod(44,405)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(405, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([5, 9]))

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

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

chi := DirichletCharacter("405.44");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 405 = 3^{4} \cdot 5 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	405.n (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:	$11.0354507066$
Analytic rank:	$0$
Dimension:	$204$
Relative dimension:	$34$ over $\Q(\zeta_{18})$
Twist minimal:	no (minimal twist has level 135)
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			179.14
Character	$\chi$	$=$	405.179
Dual form			405.3.n.a.224.14

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.721015 - 0.262428i) q^{2} +(-2.61318 - 2.19272i) q^{4} +(-2.96988 + 4.02242i) q^{5} +(3.17548 + 3.78438i) q^{7} +(2.84329 + 4.92472i) q^{8} +(3.19692 - 2.12084i) q^{10} +(-7.37526 + 1.30046i) q^{11} +(-6.15844 - 16.9202i) q^{13} +(-1.29644 - 3.56193i) q^{14} +(1.61177 + 9.14083i) q^{16} +(10.2979 - 17.8366i) q^{17} +(13.4766 + 23.3422i) q^{19} +(16.5809 - 3.99920i) q^{20} +(5.65895 + 0.997825i) q^{22} +(10.0889 + 8.46563i) q^{23} +(-7.35967 - 23.8922i) q^{25} +13.8158i q^{26} -16.8522i q^{28} +(13.1765 - 36.2022i) q^{29} +(-34.2162 - 28.7108i) q^{31} +(5.18655 - 29.4144i) q^{32} +(-12.1058 + 10.1580i) q^{34} +(-24.6531 + 1.53393i) q^{35} +(-39.3279 - 22.7060i) q^{37} +(-3.59121 - 20.3667i) q^{38} +(-28.2535 - 3.18892i) q^{40} +(-18.6544 - 51.2525i) q^{41} +(27.9365 - 4.92596i) q^{43} +(22.1245 + 12.7736i) q^{44} +(-5.05266 - 8.75146i) q^{46} +(21.0849 - 17.6923i) q^{47} +(4.27084 - 24.2211i) q^{49} +(-0.963538 + 19.1580i) q^{50} +(-21.0081 + 57.7193i) q^{52} +44.0339 q^{53} +(16.6726 - 33.5286i) q^{55} +(-9.60824 + 26.3984i) q^{56} +(-19.0009 + 22.6444i) q^{58} +(15.0907 + 2.66091i) q^{59} +(-44.3135 + 37.1834i) q^{61} +(17.1359 + 29.6802i) q^{62} +(7.10495 - 12.3061i) q^{64} +(86.3498 + 25.4790i) q^{65} +(-7.91614 - 21.7494i) q^{67} +(-66.0210 + 24.0297i) q^{68} +(18.1778 + 5.36368i) q^{70} +(-91.6966 - 52.9411i) q^{71} +(67.6524 - 39.0591i) q^{73} +(22.3973 + 26.6921i) q^{74} +(15.9661 - 90.5481i) q^{76} +(-28.3414 - 23.7813i) q^{77} +(64.5660 + 23.5001i) q^{79} +(-41.5550 - 20.6639i) q^{80} +41.8492i q^{82} +(71.0404 + 25.8566i) q^{83} +(41.1625 + 94.3950i) q^{85} +(-21.4353 - 3.77963i) q^{86} +(-27.3744 - 32.6235i) q^{88} +(-95.3491 + 55.0498i) q^{89} +(44.4765 - 77.0355i) q^{91} +(-7.80150 - 44.2445i) q^{92} +(-19.8455 + 7.22317i) q^{94} +(-133.916 - 15.1149i) q^{95} +(86.5584 - 15.2626i) q^{97} +(-9.43564 + 16.3430i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 204 q - 12 q^{4} - 3 q^{5} - 3 q^{10} - 6 q^{11} + 48 q^{14} + 12 q^{16} - 6 q^{19} - 63 q^{20} - 15 q^{25} - 96 q^{29} - 102 q^{31} + 12 q^{34} + 252 q^{35} + 117 q^{40} - 96 q^{41} + 666 q^{44} - 6 q^{46}+ \cdots + 543 q^{95}+O(q^{100}) $ 204 * q - 12 * q^4 - 3 * q^5 - 3 * q^10 - 6 * q^11 + 48 * q^14 + 12 * q^16 - 6 * q^19 - 63 * q^20 - 15 * q^25 - 96 * q^29 - 102 * q^31 + 12 * q^34 + 252 * q^35 + 117 * q^40 - 96 * q^41 + 666 * q^44 - 6 * q^46 + 60 * q^49 - 48 * q^50 - 12 * q^55 - 294 * q^56 - 510 * q^59 + 132 * q^61 - 486 * q^64 - 147 * q^65 - 141 * q^70 + 18 * q^71 + 954 * q^74 + 84 * q^76 - 48 * q^79 + 69 * q^85 + 1506 * q^86 - 792 * q^89 - 6 * q^91 + 492 * q^94 + 543 * q^95

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/405\mathbb{Z}\right)^\times$.

$n$	$82$	$326$
$\chi(n)$	$-1$	$e\left(\frac{11}{18}\right)$

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 $

$2$	−0.721015	−	0.262428i	−0.360507	−	0.131214i	0.155415	−	0.987849i	$-0.450328\pi$
$2$	−0.721015	−	0.262428i	−0.360507	−	0.131214i	−0.515922	+	0.856635i	$0.672551\pi$
$3$		0			0
$3$		0			0
$4$	−2.61318	−	2.19272i	−0.653296	−	0.548180i
$5$	−2.96988	+	4.02242i	−0.593975	+	0.804483i
$5$	−2.96988	+	4.02242i	−0.593975	+	0.804483i
$6$		0			0
$7$	3.17548	+	3.78438i	0.453639	+	0.540626i	0.943587	−	0.331126i	$-0.107428\pi$
$7$	3.17548	+	3.78438i	0.453639	+	0.540626i	−0.489947	+	0.871752i	$0.662984\pi$
$8$	2.84329	+	4.92472i	0.355411	+	0.615590i
$9$		0			0
$10$	3.19692	−	2.12084i	0.319692	−	0.212084i
$11$	−7.37526	+	1.30046i	−0.670479	+	0.118223i	−0.498517	−	0.866880i	$-0.666122\pi$
$11$	−7.37526	+	1.30046i	−0.670479	+	0.118223i	−0.171962	+	0.985104i	$0.555011\pi$
$12$		0			0
$13$	−6.15844	−	16.9202i	−0.473726	−	1.30155i	−0.914737	−	0.404050i	$-0.867602\pi$
$13$	−6.15844	−	16.9202i	−0.473726	−	1.30155i	0.441011	−	0.897502i	$-0.354620\pi$
$14$	−1.29644	−	3.56193i	−0.0926026	−	0.254424i
$15$		0			0
$16$	1.61177	+	9.14083i	0.100736	+	0.571302i
$17$	10.2979	−	17.8366i	0.605761	−	1.04921i	−0.386169	−	0.922428i	$-0.626202\pi$
$17$	10.2979	−	17.8366i	0.605761	−	1.04921i	0.991931	−	0.126781i	$-0.0404647\pi$
$18$		0			0
$19$	13.4766	+	23.3422i	0.709297	+	1.22854i	0.965118	+	0.261815i	$0.0843209\pi$
$19$	13.4766	+	23.3422i	0.709297	+	1.22854i	−0.255821	+	0.966724i	$0.582346\pi$
$20$	16.5809	−	3.99920i	0.829044	−	0.199960i
$21$		0			0
$22$	5.65895	+	0.997825i	0.257225	+	0.0453557i
$23$	10.0889	+	8.46563i	0.438650	+	0.368071i	0.835204	−	0.549940i	$-0.185350\pi$
$23$	10.0889	+	8.46563i	0.438650	+	0.368071i	−0.396554	+	0.918011i	$0.629794\pi$
$24$		0			0
$25$	−7.35967	−	23.8922i	−0.294387	−	0.955686i
$26$			13.8158i			0.531378i
$27$		0			0
$28$		−	16.8522i		−	0.601865i
$29$	13.1765	−	36.2022i	0.454363	−	1.24835i	−0.475262	−	0.879845i	$-0.657647\pi$
$29$	13.1765	−	36.2022i	0.454363	−	1.24835i	0.929625	−	0.368508i	$-0.120131\pi$
$30$		0			0
$31$	−34.2162	−	28.7108i	−1.10375	−	0.926156i	−0.106078	−	0.994358i	$-0.533829\pi$
$31$	−34.2162	−	28.7108i	−1.10375	−	0.926156i	−0.997672	+	0.0682022i	$0.978274\pi$
$32$	5.18655	−	29.4144i	0.162080	−	0.919199i
$33$		0			0
$34$	−12.1058	+	10.1580i	−0.356052	+	0.298763i
$35$	−24.6531	+	1.53393i	−0.704375	+	0.0438266i
$36$		0			0
$37$	−39.3279	−	22.7060i	−1.06292	−	0.613675i	−0.136678	−	0.990615i	$-0.543643\pi$
$37$	−39.3279	−	22.7060i	−1.06292	−	0.613675i	−0.926237	+	0.376941i	$0.876976\pi$
$38$	−3.59121	−	20.3667i	−0.0945054	−	0.535967i
$39$		0			0
$40$	−28.2535	−	3.18892i	−0.706337	−	0.0797229i
$41$	−18.6544	−	51.2525i	−0.454985	−	1.25006i	−0.929176	−	0.369638i	$-0.879482\pi$
$41$	−18.6544	−	51.2525i	−0.454985	−	1.25006i	0.474191	−	0.880422i	$-0.342741\pi$
$42$		0			0
$43$	27.9365	−	4.92596i	0.649686	−	0.114557i	0.160913	−	0.986969i	$-0.448556\pi$
$43$	27.9365	−	4.92596i	0.649686	−	0.114557i	0.488772	+	0.872411i	$0.337445\pi$
$44$	22.1245	+	12.7736i	0.502829	+	0.290308i
$45$		0			0
$46$	−5.05266	−	8.75146i	−0.109840	−	0.190249i
$47$	21.0849	−	17.6923i	0.448615	−	0.376433i	−0.390307	−	0.920685i	$-0.627631\pi$
$47$	21.0849	−	17.6923i	0.448615	−	0.376433i	0.838922	+	0.544252i	$0.183187\pi$
$48$		0			0
$49$	4.27084	−	24.2211i	0.0871600	−	0.494309i
$50$	−0.963538	+	19.1580i	−0.0192708	+	0.383160i
$51$		0			0
$52$	−21.0081	+	57.7193i	−0.404002	+	1.10999i
$53$	44.0339			0.830828			0.415414	−	0.909633i	$-0.363637\pi$
$53$	44.0339			0.830828			0.415414	+	0.909633i	$0.363637\pi$
$54$		0			0
$55$	16.6726	−	33.5286i	0.303139	−	0.609611i
$56$	−9.60824	+	26.3984i	−0.171576	+	0.471400i
$57$		0			0
$58$	−19.0009	+	22.6444i	−0.327602	+	0.390421i
$59$	15.0907	+	2.66091i	0.255775	+	0.0451001i	0.300065	−	0.953919i	$-0.402991\pi$
$59$	15.0907	+	2.66091i	0.255775	+	0.0451001i	−0.0442901	+	0.999019i	$0.514103\pi$
$60$		0			0
$61$	−44.3135	+	37.1834i	−0.726451	+	0.609564i	−0.929161	−	0.369674i	$-0.879469\pi$
$61$	−44.3135	+	37.1834i	−0.726451	+	0.609564i	0.202711	+	0.979239i	$0.435025\pi$
$62$	17.1359	+	29.6802i	0.276385	+	0.478713i
$63$		0			0
$64$	7.10495	−	12.3061i	0.111015	−	0.192283i
$65$	86.3498	+	25.4790i	1.32846	+	0.391985i
$66$		0			0
$67$	−7.91614	−	21.7494i	−0.118151	−	0.324618i	0.866493	−	0.499189i	$-0.166369\pi$
$67$	−7.91614	−	21.7494i	−0.118151	−	0.324618i	−0.984645	+	0.174571i	$0.944146\pi$
$68$	−66.0210	+	24.0297i	−0.970897	+	0.353378i
$69$		0			0
$70$	18.1778	+	5.36368i	0.259683	+	0.0766240i
$71$	−91.6966	−	52.9411i	−1.29150	−	0.745649i	−0.312582	−	0.949891i	$-0.601194\pi$
$71$	−91.6966	−	52.9411i	−1.29150	−	0.745649i	−0.978920	+	0.204242i	$0.934527\pi$
$72$		0			0
$73$	67.6524	−	39.0591i	0.926745	−	0.535056i	0.0409643	−	0.999161i	$-0.486957\pi$
$73$	67.6524	−	39.0591i	0.926745	−	0.535056i	0.885781	+	0.464104i	$0.153624\pi$
$74$	22.3973	+	26.6921i	0.302666	+	0.360703i
$75$		0			0
$76$	15.9661	−	90.5481i	0.210080	−	1.19142i
$77$	−28.3414	−	23.7813i	−0.368070	−	0.308848i
$78$		0			0
$79$	64.5660	+	23.5001i	0.817291	+	0.297470i	0.716632	−	0.697451i	$-0.245683\pi$
$79$	64.5660	+	23.5001i	0.817291	+	0.297470i	0.100659	+	0.994921i	$0.467905\pi$
$80$	−41.5550	−	20.6639i	−0.519437	−	0.258299i
$81$		0			0
$82$			41.8492i			0.510356i
$83$	71.0404	+	25.8566i	0.855908	+	0.311525i	0.732447	−	0.680824i	$-0.238378\pi$
$83$	71.0404	+	25.8566i	0.855908	+	0.311525i	0.123461	+	0.992349i	$0.460601\pi$
$84$		0			0
$85$	41.1625	+	94.3950i	0.484264	+	1.11053i
$86$	−21.4353	−	3.77963i	−0.249248	−	0.0439491i
$87$		0			0
$88$	−27.3744	−	32.6235i	−0.311073	−	0.370722i
$89$	−95.3491	+	55.0498i	−1.07134	+	0.618538i	−0.928547	−	0.371215i	$-0.878941\pi$
$89$	−95.3491	+	55.0498i	−1.07134	+	0.618538i	−0.142792	+	0.989753i	$0.545608\pi$
$90$		0			0
$91$	44.4765	−	77.0355i	0.488752	−	0.846544i
$92$	−7.80150	−	44.2445i	−0.0847989	−	0.480919i
$93$		0			0
$94$	−19.8455	+	7.22317i	−0.211122	+	0.0768422i
$95$	−133.916	−	15.1149i	−1.40964	−	0.159104i
$96$		0			0
$97$	86.5584	−	15.2626i	0.892355	−	0.157346i	0.291373	−	0.956609i	$-0.405888\pi$
$97$	86.5584	−	15.2626i	0.892355	−	0.157346i	0.600981	+	0.799263i	$0.294777\pi$
$98$	−9.43564	+	16.3430i	−0.0962820	+	0.166765i
$99$		0			0
$100$	−33.1567	+	78.5723i	−0.331567	+	0.785723i
$101$	55.4210	+	66.0482i	0.548723	+	0.653942i	0.967120	−	0.254322i	$-0.0818524\pi$
$101$	55.4210	+	66.0482i	0.548723	+	0.653942i	−0.418397	+	0.908264i	$0.637408\pi$
$102$		0			0
$103$	64.4706	+	11.3679i	0.625928	+	0.110368i	0.477611	−	0.878572i	$-0.341503\pi$
$103$	64.4706	+	11.3679i	0.625928	+	0.110368i	0.148318	+	0.988940i	$0.452614\pi$
$104$	65.8169	−	78.4375i	0.632854	−	0.754207i
$105$		0			0
$106$	−31.7491	−	11.5557i	−0.299519	−	0.109016i
$107$	17.0726			0.159557			0.0797785	−	0.996813i	$-0.474579\pi$
$107$	17.0726			0.159557			0.0797785	+	0.996813i	$0.474579\pi$
$108$		0			0
$109$	72.2226			0.662592			0.331296	−	0.943527i	$-0.392514\pi$
$109$	72.2226			0.662592			0.331296	+	0.943527i	$0.392514\pi$
$110$	−20.8200	+	19.7992i	−0.189273	+	0.179993i
$111$		0			0
$112$	−29.4743	+	35.1261i	−0.263163	+	0.313625i
$113$	3.89736	−	22.1030i	0.0344899	−	0.195602i	−0.962694	−	0.270591i	$-0.912781\pi$
$113$	3.89736	−	22.1030i	0.0344899	−	0.195602i	0.997184	+	0.0749887i	$0.0238921\pi$
$114$		0			0
$115$	−64.0152	+	15.4401i	−0.556654	+	0.134261i
$116$	−113.814	+	65.7106i	−0.981156	+	0.566471i
$117$		0			0
$118$	−10.1824	−	5.87878i	−0.0862911	−	0.0498202i
$119$	100.201	−	17.6682i	0.842027	−	0.148472i
$120$		0			0
$121$	−60.9995	+	22.2020i	−0.504128	+	0.183488i
$122$	41.7086	−	15.1807i	0.341874	−	0.124432i
$123$		0			0
$124$	26.4585	+	150.053i	0.213375	+	1.21011i
$125$	117.962	+	41.3531i	0.943692	+	0.330825i
$126$		0			0
$127$	−47.3382	+	27.3308i	−0.372742	+	0.215203i	−0.674656	−	0.738133i	$-0.735708\pi$
$127$	−47.3382	+	27.3308i	−0.372742	+	0.215203i	0.301914	+	0.953335i	$0.402375\pi$
$128$	−99.8735	+	83.8039i	−0.780262	+	0.654718i
$129$		0			0
$130$	−55.5730	−	41.0313i	−0.427485	−	0.315625i
$131$	−26.7119	+	31.8340i	−0.203908	+	0.243008i	−0.858301	−	0.513147i	$-0.828480\pi$
$131$	−26.7119	+	31.8340i	−0.203908	+	0.243008i	0.654393	+	0.756154i	$0.272924\pi$
$132$		0			0
$133$	−45.5412	+	125.124i	−0.342415	+	0.940778i
$134$			17.7591i			0.132530i
$135$		0			0
$136$	117.120			0.861177
$137$	−134.025	−	48.7812i	−0.978286	−	0.356067i	−0.197112	−	0.980381i	$-0.563156\pi$
$137$	−134.025	−	48.7812i	−0.978286	−	0.356067i	−0.781173	+	0.624314i	$0.785379\pi$
$138$		0			0
$139$	−143.525	−	120.432i	−1.03256	−	0.866418i	−0.0414040	−	0.999142i	$-0.513183\pi$
$139$	−143.525	−	120.432i	−1.03256	−	0.866418i	−0.991153	+	0.132724i	$0.957628\pi$
$140$	67.7867	+	50.0490i	0.484191	+	0.357493i
$141$		0			0
$142$	52.2214	+	62.2350i	0.367756	+	0.438275i
$143$	67.4241	+	116.782i	0.471497	+	0.816657i
$144$		0			0
$145$	106.488	+	160.518i	0.734398	+	1.10702i
$146$	−59.0285	+	10.4083i	−0.404305	+	0.0712899i
$147$		0			0
$148$	52.9831	+	145.570i	0.357994	+	0.983581i
$149$	−7.98047	−	21.9262i	−0.0535602	−	0.147155i	0.910028	−	0.414548i	$-0.136060\pi$
$149$	−7.98047	−	21.9262i	−0.0535602	−	0.147155i	−0.963588	+	0.267392i	$0.913838\pi$
$150$		0			0
$151$	−40.1381	−	227.635i	−0.265815	−	1.50751i	−0.766703	−	0.642002i	$-0.778104\pi$
$151$	−40.1381	−	227.635i	−0.265815	−	1.50751i	0.500888	−	0.865512i	$-0.333007\pi$
$152$	−76.6360	+	132.737i	−0.504184	+	0.873272i
$153$		0			0
$154$	14.1937	+	24.5842i	0.0921669	+	0.159638i
$155$	217.105	−	52.3643i	1.40068	−	0.337834i
$156$		0			0
$157$	8.04210	+	1.41804i	0.0512236	+	0.00903209i	0.199201	−	0.979959i	$-0.436165\pi$
$157$	8.04210	+	1.41804i	0.0512236	+	0.00903209i	−0.147978	+	0.988991i	$0.547276\pi$
$158$	−40.3860	−	33.8878i	−0.255607	−	0.214480i
$159$		0			0
$160$	102.913	+	108.220i	0.643209	+	0.676372i
$161$			65.0629i			0.404117i
$162$		0			0
$163$		−	43.1204i		−	0.264542i	−0.991214	−	0.132271i	$-0.957773\pi$
$163$		−	43.1204i		−	0.264542i	0.991214	−	0.132271i	$-0.0422269\pi$
$164$	−63.6351	+	174.836i	−0.388019	+	1.06607i
$165$		0			0
$166$	−44.4356	−	37.2859i	−0.267685	−	0.224614i
$167$	−27.8841	+	158.139i	−0.166971	+	0.946937i	0.780039	+	0.625731i	$0.215199\pi$
$167$	−27.8841	+	158.139i	−0.166971	+	0.946937i	−0.947009	+	0.321206i	$0.895912\pi$
$168$		0			0
$169$	−118.904	+	99.7725i	−0.703575	+	0.590370i
$170$	−4.90686	−	78.8623i	−0.0288639	−	0.463896i
$171$		0			0
$172$	−83.8044	−	48.3845i	−0.487235	−	0.281305i
$173$	−19.1710	−	108.724i	−0.110815	−	0.628462i	−0.988738	−	0.149660i	$-0.952182\pi$
$173$	−19.1710	−	108.724i	−0.110815	−	0.628462i	0.877923	−	0.478802i	$-0.158929\pi$
$174$		0			0
$175$	67.0467	−	103.721i	0.383124	−	0.592690i
$176$	−23.7745	−	65.3200i	−0.135083	−	0.371136i
$177$		0			0
$178$	83.1947	−	14.6695i	0.467386	−	0.0824128i
$179$	173.652	+	100.258i	0.970122	+	0.560100i	0.899273	−	0.437387i	$-0.144096\pi$
$179$	173.652	+	100.258i	0.970122	+	0.560100i	0.0708485	+	0.997487i	$0.477429\pi$
$180$		0			0
$181$	−45.7267	−	79.2010i	−0.252634	−	0.437575i	0.711616	−	0.702568i	$-0.247963\pi$
$181$	−45.7267	−	79.2010i	−0.252634	−	0.437575i	−0.964250	+	0.264994i	$0.914630\pi$
$182$	−52.2844	+	43.8718i	−0.287277	+	0.241054i
$183$		0			0
$184$	−13.0051	+	73.7555i	−0.0706798	+	0.400845i
$185$	208.132	−	90.7592i	1.12504	−	0.490590i
$186$		0			0
$187$	−52.7543	+	144.941i	−0.282109	+	0.775088i
$188$	−93.8932			−0.499432
$189$		0			0
$190$	92.5890	+	46.0414i	0.487310	+	0.242323i
$191$	74.8263	−	205.584i	0.391761	−	1.07635i	−0.574436	−	0.818549i	$-0.694779\pi$
$191$	74.8263	−	205.584i	0.391761	−	1.07635i	0.966197	−	0.257804i	$-0.0829990\pi$
$192$		0			0
$193$	−124.937	+	148.894i	−0.647341	+	0.771471i	−0.985510	−	0.169614i	$-0.945748\pi$
$193$	−124.937	+	148.894i	−0.647341	+	0.771471i	0.338170	+	0.941085i	$0.390192\pi$
$194$	−66.4152	−	11.7108i	−0.342346	−	0.0603649i
$195$		0			0
$196$	−64.2707	+	53.9295i	−0.327912	+	0.275151i
$197$	55.9942	+	96.9847i	0.284234	+	0.492308i	0.972423	−	0.233223i	$-0.0749273\pi$
$197$	55.9942	+	96.9847i	0.284234	+	0.492308i	−0.688189	+	0.725532i	$0.741594\pi$
$198$		0			0
$199$	11.4037	−	19.7519i	0.0573053	−	0.0992556i	−0.835950	−	0.548806i	$-0.815083\pi$
$199$	11.4037	−	19.7519i	0.0573053	−	0.0992556i	0.893255	+	0.449551i	$0.148416\pi$
$200$	96.7365	−	104.177i	0.483683	−	0.520883i
$201$		0			0
$202$	−22.6265	−	62.1657i	−0.112012	−	0.307751i
$203$	178.845	−	65.0942i	0.881009	−	0.320661i
$204$		0			0
$205$	261.560	+	77.1778i	1.27590	+	0.376477i
$206$	−43.5010	−	25.1153i	−0.211170	−	0.121919i
$207$		0			0
$208$	144.738	−	83.5647i	0.695857	−	0.401753i
$209$	−129.749	−	154.629i	−0.620811	−	0.739853i
$210$		0			0
$211$	22.0191	−	124.877i	0.104356	−	0.591833i	−0.887119	−	0.461540i	$-0.847297\pi$
$211$	22.0191	−	124.877i	0.104356	−	0.591833i	0.991476	−	0.130293i	$-0.0415918\pi$
$212$	−115.069	−	96.5540i	−0.542777	−	0.455444i
$213$		0			0
$214$	−12.3096	−	4.48033i	−0.0575215	−	0.0209361i
$215$	−63.1537	+	127.002i	−0.293738	+	0.590705i
$216$		0			0
$217$		−	220.658i		−	1.01686i
$218$	−52.0735	−	18.9532i	−0.238869	−	0.0869413i
$219$		0			0
$220$	−117.088	+	51.0579i	−0.532216	+	0.232081i
$221$	−365.217	−	64.3976i	−1.65256	−	0.291392i
$222$		0			0
$223$	−265.212	−	316.068i	−1.18929	−	1.41734i	−0.885521	−	0.464600i	$-0.846198\pi$
$223$	−265.212	−	316.068i	−1.18929	−	1.41734i	−0.303773	−	0.952744i	$-0.598246\pi$
$224$	127.785	−	73.7767i	0.570469	−	0.329360i
$225$		0			0
$226$	−8.61051	+	14.9138i	−0.0380996	+	0.0659904i
$227$	18.5556	+	105.234i	0.0817428	+	0.463586i	0.998012	+	0.0630234i	$0.0200743\pi$
$227$	18.5556	+	105.234i	0.0817428	+	0.463586i	−0.916269	+	0.400563i	$0.868815\pi$
$228$		0			0
$229$	130.547	−	47.5153i	0.570076	−	0.207491i	−0.0408682	−	0.999165i	$-0.513012\pi$
$229$	130.547	−	47.5153i	0.570076	−	0.207491i	0.610944	+	0.791674i	$0.290790\pi$
$230$	50.2078	+	5.66686i	0.218295	+	0.0246385i
$231$		0			0
$232$	215.750	−	38.0426i	0.929959	−	0.163977i
$233$	53.0900	−	91.9546i	0.227854	−	0.394655i	−0.729318	−	0.684175i	$-0.760162\pi$
$233$	53.0900	−	91.9546i	0.227854	−	0.394655i	0.957172	+	0.289520i	$0.0934957\pi$
$234$		0			0
$235$	8.54639	+	137.356i	0.0363676	+	0.584495i
$236$	−33.6003	−	40.0433i	−0.142374	−	0.169675i
$237$		0			0
$238$	−76.8832	−	13.5566i	−0.323039	−	0.0569604i
$239$	−162.764	+	193.975i	−0.681023	+	0.811611i	−0.990239	−	0.139381i	$-0.955489\pi$
$239$	−162.764	+	193.975i	−0.681023	+	0.811611i	0.309216	+	0.950992i	$0.399933\pi$
$240$		0			0
$241$	3.56022	+	1.29581i	0.0147727	+	0.00537682i	0.349396	−	0.936975i	$-0.386387\pi$
$241$	3.56022	+	1.29581i	0.0147727	+	0.00537682i	−0.334623	+	0.942352i	$0.608609\pi$
$242$	49.8079			0.205818
$243$		0			0
$244$	197.332			0.808739
$245$	84.7436	+	89.1129i	0.345892	+	0.363726i
$246$		0			0
$247$	311.960	−	371.779i	1.26299	−	1.50518i
$248$	44.1062	−	250.138i	0.177847	−	1.00862i
$249$		0			0
$250$	−74.1998	−	60.7726i	−0.296799	−	0.243090i
$251$	−155.039	+	89.5116i	−0.617684	+	0.356620i	−0.775967	−	0.630774i	$-0.782738\pi$
$251$	−155.039	+	89.5116i	−0.617684	+	0.356620i	0.158283	+	0.987394i	$0.449404\pi$
$252$		0			0
$253$	−85.4179	−	49.3160i	−0.337620	−	0.194925i
$254$	41.3039	−	7.28299i	0.162614	−	0.0286732i
$255$		0			0
$256$	40.5910	−	14.7739i	0.158558	−	0.0577106i
$257$	151.112	−	55.0003i	0.587985	−	0.214009i	−0.0308578	−	0.999524i	$-0.509824\pi$
$257$	151.112	−	55.0003i	0.587985	−	0.214009i	0.618843	+	0.785515i	$0.287602\pi$
$258$		0			0
$259$	−38.9566	−	220.934i	−0.150412	−	0.853027i
$260$	−169.779	−	255.922i	−0.652998	−	0.984317i
$261$		0			0
$262$	27.6138	−	15.9428i	0.105396	−	0.0608505i
$263$	−131.661	+	110.477i	−0.500613	+	0.420064i	−0.857811	−	0.513965i	$-0.828176\pi$
$263$	−131.661	+	110.477i	−0.500613	+	0.420064i	0.357199	+	0.934028i	$0.383732\pi$
$264$		0			0
$265$	−130.775	+	177.123i	−0.493491	+	0.668387i
$266$	65.6718	−	78.2646i	0.246886	−	0.294228i
$267$		0			0
$268$	−27.0041	+	74.1931i	−0.100761	+	0.276840i
$269$		−	352.895i		−	1.31188i	−0.754814	−	0.655939i	$-0.772273\pi$
$269$		−	352.895i		−	1.31188i	0.754814	−	0.655939i	$-0.227727\pi$
$270$		0			0
$271$	−477.336			−1.76139			−0.880693	−	0.473687i	$-0.842923\pi$
$271$	−477.336			−1.76139			−0.880693	+	0.473687i	$0.842923\pi$
$272$	179.639	+	65.3832i	0.660437	+	0.240379i
$273$		0			0
$274$	83.8325	+	70.3438i	0.305958	+	0.256729i
$275$	85.3503	+	166.640i	0.310365	+	0.605964i
$276$		0			0
$277$	−293.699	−	350.017i	−1.06028	−	1.26360i	−0.963333	−	0.268309i	$-0.913535\pi$
$277$	−293.699	−	350.017i	−1.06028	−	1.26360i	−0.0969521	−	0.995289i	$-0.530909\pi$
$278$	71.8792	+	124.498i	0.258558	+	0.447836i
$279$		0			0
$280$	−77.6502	−	117.048i	−0.277322	−	0.418030i
$281$	−409.029	+	72.1229i	−1.45562	+	0.256665i	−0.844791	−	0.535097i	$-0.820275\pi$
$281$	−409.029	+	72.1229i	−1.45562	+	0.256665i	−0.610830	+	0.791762i	$0.709164\pi$
$282$		0			0
$283$	71.4696	+	196.361i	0.252543	+	0.693856i	0.999577	+	0.0290706i	$0.00925476\pi$
$283$	71.4696	+	196.361i	0.252543	+	0.693856i	−0.747034	+	0.664785i	$0.768523\pi$
$284$	123.535	+	339.410i	0.434983	+	1.19511i
$285$		0			0
$286$	−17.9669	−	101.895i	−0.0628214	−	0.356278i
$287$	134.723	−	233.346i	0.469416	−	0.813053i
$288$		0			0
$289$	−67.5952	−	117.078i	−0.233893	−	0.405115i
$290$	−34.6549	−	143.681i	−0.119500	−	0.495451i
$291$		0			0
$292$	−262.434	−	46.2742i	−0.898746	−	0.158473i
$293$	−115.593	−	96.9943i	−0.394516	−	0.331038i	0.423853	−	0.905731i	$-0.360677\pi$
$293$	−115.593	−	96.9943i	−0.394516	−	0.331038i	−0.818369	+	0.574692i	$0.805122\pi$
$294$		0			0
$295$	−55.5209	+	52.7987i	−0.188207	+	0.178979i
$296$		−	258.238i		−	0.872427i
$297$		0			0
$298$			17.9034i			0.0600784i
$299$	81.1078	−	222.842i	0.271263	−	0.745290i
$300$		0			0
$301$	107.353	+	90.0802i	0.356656	+	0.299270i
$302$	−30.7975	+	174.661i	−0.101978	+	0.578348i
$303$		0			0
$304$	−191.646	+	160.810i	−0.630415	+	0.528981i
$305$	−17.9617	−	288.677i	−0.0588907	−	0.946483i
$306$		0			0
$307$	302.653	+	174.737i	0.985842	+	0.569176i	0.904029	−	0.427472i	$-0.140596\pi$
$307$	302.653	+	174.737i	0.985842	+	0.569176i	0.0818129	+	0.996648i	$0.473929\pi$
$308$	21.9156	+	124.290i	0.0711546	+	0.403538i
$309$		0			0
$310$	−170.278	−	19.2189i	−0.549283	−	0.0619965i
$311$	7.30453	+	20.0690i	0.0234872	+	0.0645306i	0.950882	−	0.309553i	$-0.100179\pi$
$311$	7.30453	+	20.0690i	0.0234872	+	0.0645306i	−0.927395	+	0.374084i	$0.877957\pi$
$312$		0			0
$313$	−383.992	+	67.7082i	−1.22681	+	0.216320i	−0.749256	−	0.662281i	$-0.769589\pi$
$313$	−383.992	+	67.7082i	−1.22681	+	0.216320i	−0.477557	+	0.878601i	$0.658477\pi$
$314$	−5.42634	−	3.13290i	−0.0172813	−	0.00997738i
$315$		0			0
$316$	−117.194	−	202.985i	−0.370866	−	0.642359i
$317$	209.280	−	175.607i	0.660190	−	0.553965i	−0.249954	−	0.968258i	$-0.580415\pi$
$317$	209.280	−	175.607i	0.660190	−	0.553965i	0.910144	+	0.414293i	$0.135971\pi$
$318$		0			0
$319$	−50.1009	+	284.136i	−0.157056	+	0.890710i
$320$	28.3996	+	65.1268i	0.0887487	+	0.203521i
$321$		0			0
$322$	17.0743	−	46.9113i	0.0530258	−	0.145687i
$323$	555.127			1.71866
$324$		0			0
$325$	−358.935	+	271.665i	−1.10442	+	0.835893i
$326$	−11.3160	+	31.0904i	−0.0347116	+	0.0953693i
$327$		0			0
$328$	199.364	−	237.593i	0.607818	−	0.724369i
$329$	133.909	+	23.6118i	0.407019	+	0.0717684i
$330$		0			0
$331$	231.258	−	194.049i	0.698665	−	0.586249i	−0.222729	−	0.974880i	$-0.571496\pi$
$331$	231.258	−	194.049i	0.698665	−	0.586249i	0.921393	+	0.388631i	$0.127052\pi$
$332$	−128.945	−	223.340i	−0.388389	−	0.672710i
$333$		0			0
$334$	61.6048	−	106.703i	0.184445	−	0.319469i
$335$	110.995	+	32.7510i	0.331329	+	0.0977643i
$336$		0			0
$337$	52.9227	+	145.404i	0.157041	+	0.431466i	0.993114	−	0.117152i	$-0.0373764\pi$
$337$	52.9227	+	145.404i	0.157041	+	0.431466i	−0.836073	+	0.548618i	$0.815154\pi$
$338$	111.915	−	40.7336i	0.331109	−	0.120514i
$339$		0			0
$340$	99.4169	−	336.929i	0.292403	−	0.990968i
$341$	289.691	+	167.253i	0.849534	+	0.490478i
$342$		0			0
$343$	314.861	−	181.785i	0.917962	−	0.529986i
$344$	103.690	+	123.573i	0.301426	+	0.359225i
$345$		0			0
$346$	−14.7096	+	83.4225i	−0.0425134	+	0.241106i
$347$	164.299	+	137.863i	0.473483	+	0.397300i	0.848063	−	0.529895i	$-0.177769\pi$
$347$	164.299	+	137.863i	0.473483	+	0.397300i	−0.374580	+	0.927195i	$0.622213\pi$
$348$		0			0
$349$	370.917	+	135.003i	1.06280	+	0.386827i	0.813479	−	0.581594i	$-0.197571\pi$
$349$	370.917	+	135.003i	1.06280	+	0.386827i	0.249320	+	0.968421i	$0.419793\pi$
$350$	−75.5608	+	57.1893i	−0.215888	+	0.163398i
$351$		0			0
$352$			223.684i			0.635465i
$353$	−628.739	−	228.842i	−1.78113	−	0.648278i	−0.999705	−	0.0242794i	$-0.992271\pi$
$353$	−628.739	−	228.842i	−1.78113	−	0.648278i	−0.781425	−	0.623999i	$-0.785507\pi$
$354$		0			0
$355$	485.279	−	211.614i	1.36698	−	0.596095i
$356$	369.874	+	65.2187i	1.03897	+	0.183199i
$357$		0			0
$358$	−98.8950	−	117.858i	−0.276243	−	0.329214i
$359$	212.551	−	122.716i	0.592064	−	0.341828i	−0.173849	−	0.984772i	$-0.555620\pi$
$359$	212.551	−	122.716i	0.592064	−	0.341828i	0.765913	+	0.642944i	$0.222287\pi$
$360$		0			0
$361$	−182.740	+	316.515i	−0.506205	+	0.876773i
$362$	12.1851	+	69.1050i	0.0336604	+	0.190898i
$363$		0			0
$364$	−285.143	+	103.783i	−0.783359	+	0.285119i
$365$	−43.8071	+	388.127i	−0.120020	+	1.06336i
$366$		0			0
$367$	458.235	−	80.7991i	1.24860	−	0.220161i	0.490000	−	0.871723i	$-0.336997\pi$
$367$	458.235	−	80.7991i	1.24860	−	0.220161i	0.758596	+	0.651561i	$0.225886\pi$
$368$	−61.1218	+	105.866i	−0.166092	+	0.287679i
$369$		0			0
$370$	−173.884	+	10.8191i	−0.469956	+	0.0292409i
$371$	139.828	+	166.641i	0.376896	+	0.449167i
$372$		0			0
$373$	516.884	+	91.1405i	1.38575	+	0.244345i	0.816274	−	0.577665i	$-0.196036\pi$
$373$	516.884	+	91.1405i	1.38575	+	0.244345i	0.569473	+	0.822010i	$0.307147\pi$
$374$	76.0733	−	90.6606i	0.203405	−	0.242408i
$375$		0			0
$376$	147.080	+	53.5328i	0.391171	+	0.142375i
$377$	−693.694			−1.84004
$378$		0			0
$379$	−368.487			−0.972262			−0.486131	−	0.873886i	$-0.661592\pi$
$379$	−368.487			−0.972262			−0.486131	+	0.873886i	$0.661592\pi$
$380$	316.805	+	333.139i	0.833697	+	0.876681i
$381$		0			0
$382$	−107.902	+	128.592i	−0.282465	+	0.336629i
$383$	102.899	−	583.571i	0.268667	−	1.52368i	−0.489720	−	0.871880i	$-0.662901\pi$
$383$	102.899	−	583.571i	0.268667	−	1.52368i	0.758387	−	0.651805i	$-0.225988\pi$
$384$		0			0
$385$	179.829	−	43.3735i	0.467087	−	0.112659i
$386$	129.155	−	74.5677i	0.334599	−	0.193181i
$387$		0			0
$388$	−259.660	−	149.915i	−0.669226	−	0.386378i
$389$	−319.283	+	56.2982i	−0.820778	+	0.144725i	−0.568241	−	0.822862i	$-0.692376\pi$
$389$	−319.283	+	56.2982i	−0.820778	+	0.144725i	−0.252537	+	0.967587i	$0.581265\pi$
$390$		0			0
$391$	254.893	−	92.7735i	0.651901	−	0.237272i
$392$	131.426	−	47.8350i	0.335269	−	0.122028i
$393$		0			0
$394$	−14.9211	−	84.6218i	−0.0378708	−	0.214776i
$395$	−286.280	+	189.919i	−0.724760	+	0.480808i
$396$		0			0
$397$	−652.770	+	376.877i	−1.64426	+	0.949313i	−0.664962	+	0.746877i	$0.731552\pi$
$397$	−652.770	+	376.877i	−1.64426	+	0.949313i	−0.979296	+	0.202436i	$0.935114\pi$
$398$	−13.4057	+	11.2487i	−0.0336827	+	0.0282631i
$399$		0			0
$400$	206.532	−	105.782i	0.516330	−	0.264456i
$401$	−197.570	+	235.455i	−0.492693	+	0.587168i	−0.953900	−	0.300124i	$-0.902972\pi$
$401$	−197.570	+	235.455i	−0.492693	+	0.587168i	0.461207	+	0.887292i	$0.347416\pi$
$402$		0			0
$403$	−275.073	+	755.758i	−0.682564	+	1.87533i
$404$		−	294.119i		−	0.728017i
$405$		0			0
$406$	−146.032			−0.359685
$407$	319.582	+	116.318i	0.785213	+	0.285794i
$408$		0			0
$409$	379.249	+	318.228i	0.927260	+	0.778064i	0.975324	−	0.220781i	$-0.0708605\pi$
$409$	379.249	+	318.228i	0.927260	+	0.778064i	−0.0480632	+	0.998844i	$0.515305\pi$
$410$	−168.335	−	124.287i	−0.410573	−	0.303139i
$411$		0			0
$412$	−143.547	−	171.073i	−0.348415	−	0.415225i
$413$	37.8504	+	65.5588i	0.0916475	+	0.158738i
$414$		0			0
$415$	−314.987	+	208.963i	−0.759005	+	0.503526i
$416$	−529.637	+	93.3893i	−1.27317	+	0.224494i
$417$		0			0
$418$	52.9722	+	145.540i	0.126728	+	0.348182i
$419$	−94.5066	−	259.655i	−0.225553	−	0.619701i	0.774362	−	0.632743i	$-0.218071\pi$
$419$	−94.5066	−	259.655i	−0.225553	−	0.619701i	−0.999915	+	0.0130416i	$0.995849\pi$
$420$		0			0
$421$	−74.2093	−	420.862i	−0.176269	−	0.999672i	−0.936669	−	0.350217i	$-0.886108\pi$
$421$	−74.2093	−	420.862i	−0.176269	−	0.999672i	0.760400	−	0.649455i	$-0.225003\pi$
$422$	−48.6473	+	84.2595i	−0.115278	+	0.199667i
$423$		0			0
$424$	125.201	+	216.854i	0.295285	+	0.511449i
$425$	−501.943	−	114.769i	−1.18104	−	0.270044i
$426$		0			0
$427$	−281.433	−	49.6242i	−0.659093	−	0.116216i
$428$	−44.6139	−	37.4355i	−0.104238	−	0.0874661i
$429$		0			0
$430$	78.8635	−	74.9968i	0.183403	−	0.174411i
$431$			243.191i			0.564247i	0.959378	+	0.282124i	$0.0910389\pi$
$431$			243.191i			0.564247i	−0.959378	+	0.282124i	$0.908961\pi$
$432$		0			0
$433$		−	279.518i		−	0.645539i	−0.946478	−	0.322769i	$-0.895386\pi$
$433$		−	279.518i		−	0.645539i	0.946478	−	0.322769i	$-0.104614\pi$
$434$	−57.9068	+	159.098i	−0.133426	+	0.366584i
$435$		0			0
$436$	−188.731	−	158.364i	−0.432869	−	0.363220i
$437$	−61.6416	+	349.587i	−0.141056	+	0.799970i
$438$		0			0
$439$	420.534	−	352.870i	0.957937	−	0.803805i	−0.0226791	−	0.999743i	$-0.507220\pi$
$439$	420.534	−	352.870i	0.957937	−	0.803805i	0.980616	+	0.195938i	$0.0627752\pi$
$440$	212.524	−	13.2234i	0.483009	−	0.0300531i
$441$		0			0
$442$	246.427	+	142.275i	0.557527	+	0.321888i
$443$	117.125	+	664.248i	0.264390	+	1.49943i	0.770766	+	0.637119i	$0.219874\pi$
$443$	117.125	+	664.248i	0.264390	+	1.49943i	−0.506376	+	0.862313i	$0.669015\pi$
$444$		0			0
$445$	61.7417	−	547.025i	0.138745	−	1.22927i
$446$	108.277	+	297.489i	0.242774	+	0.667015i
$447$		0			0
$448$	69.1328	−	12.1900i	0.154314	−	0.0272098i
$449$	277.596	+	160.270i	0.618255	+	0.356950i	0.776189	−	0.630500i	$-0.217150\pi$
$449$	277.596	+	160.270i	0.618255	+	0.356950i	−0.157934	+	0.987450i	$0.550483\pi$
$450$		0			0
$451$	204.233	+	353.741i	0.452844	+	0.784349i
$452$	−58.6503	+	49.2135i	−0.129757	+	0.108879i
$453$		0			0
$454$	14.2375	−	80.7448i	0.0313601	−	0.177852i
$455$	177.779	+	407.689i	0.390724	+	0.896019i
$456$		0			0
$457$	−187.236	+	514.427i	−0.409707	+	1.12566i	0.547638	+	0.836715i	$0.315527\pi$
$457$	−187.236	+	514.427i	−0.409707	+	1.12566i	−0.957345	+	0.288946i	$0.906695\pi$
$458$	−106.596			−0.232742
$459$		0			0
$460$	201.139	+	100.020i	0.437259	+	0.217434i
$461$	147.291	−	404.678i	0.319503	−	0.877826i	−0.671138	−	0.741332i	$-0.734194\pi$
$461$	147.291	−	404.678i	0.319503	−	0.877826i	0.990641	−	0.136494i	$-0.0435835\pi$
$462$		0			0
$463$	−198.499	+	236.562i	−0.428724	+	0.510933i	−0.936554	−	0.350524i	$-0.886003\pi$
$463$	−198.499	+	236.562i	−0.428724	+	0.510933i	0.507830	+	0.861457i	$0.330448\pi$
$464$	352.156	+	62.0946i	0.758957	+	0.133825i
$465$		0			0
$466$	−62.4101	+	52.3683i	−0.133927	+	0.112378i
$467$	−372.274	−	644.797i	−0.797161	−	1.38072i	−0.921458	−	0.388478i	$-0.873001\pi$
$467$	−372.274	−	644.797i	−0.797161	−	1.38072i	0.124298	−	0.992245i	$-0.460332\pi$
$468$		0			0
$469$	57.1706	−	99.0224i	0.121899	−	0.211135i
$470$	29.8841	−	101.279i	0.0635831	−	0.215487i
$471$		0			0
$472$	29.8031	+	81.8834i	0.0631422	+	0.173482i
$473$	−199.633	+	72.6605i	−0.422057	+	0.153616i
$474$		0			0
$475$	458.513	−	493.777i	0.965290	−	1.03953i
$476$	−300.586	−	173.543i	−0.631483	−	0.364587i
$477$		0			0
$478$	168.260	−	97.1449i	0.352008	−	0.203232i
$479$	−419.779	−	500.273i	−0.876365	−	1.04441i	−0.998651	−	0.0519167i	$-0.983467\pi$
$479$	−419.779	−	500.273i	−0.876365	−	1.04441i	0.122286	−	0.992495i	$-0.460977\pi$
$480$		0			0
$481$	−141.990	+	805.268i	−0.295198	+	1.67415i
$482$	−2.22691	−	1.86860i	−0.00462015	−	0.00387677i
$483$		0			0
$484$	208.086	+	75.7370i	0.429929	+	0.156481i
$485$	−195.675	+	393.502i	−0.403454	+	0.811344i
$486$		0			0
$487$			645.774i			1.32603i	0.748608	+	0.663013i	$0.230722\pi$
$487$			645.774i			1.32603i	−0.748608	+	0.663013i	$0.769278\pi$
$488$	−309.114	−	112.508i	−0.633430	−	0.230550i
$489$		0			0
$490$	−37.7157	−	86.4908i	−0.0769708	−	0.176512i
$491$	293.377	+	51.7303i	0.597509	+	0.105357i	0.464219	−	0.885720i	$-0.346335\pi$
$491$	293.377	+	51.7303i	0.597509	+	0.105357i	0.133289	+	0.991077i	$0.457446\pi$
$492$		0			0
$493$	−510.032	−	607.832i	−1.03455	−	1.23293i
$494$	−322.492	+	186.191i	−0.652819	+	0.376905i
$495$		0			0
$496$	207.292	−	359.040i	0.417927	−	0.723871i
$497$	−90.8310	−	515.128i	−0.182759	−	1.03648i
$498$		0			0
$499$	24.0172	−	8.74156i	0.0481307	−	0.0175182i	−0.317843	−	0.948143i	$-0.602958\pi$
$499$	24.0172	−	8.74156i	0.0481307	−	0.0175182i	0.365973	+	0.930625i	$0.380736\pi$
$500$	−217.579	−	366.720i	−0.435159	−	0.733440i
$501$		0			0
$502$	135.275	−	23.8527i	0.269473	−	0.0475154i
$503$	−186.800	+	323.547i	−0.371372	+	0.643234i	−0.989777	−	0.142625i	$-0.954446\pi$
$503$	−186.800	+	323.547i	−0.371372	+	0.643234i	0.618405	+	0.785859i	$0.287779\pi$
$504$		0			0
$505$	−430.267	+	26.7714i	−0.852013	+	0.0530127i
$506$	48.6456	+	57.9736i	0.0961376	+	0.114572i
$507$		0			0
$508$	183.632	+	32.3793i	0.361481	+	0.0637388i
$509$	−472.660	+	563.294i	−0.928605	+	1.10667i	0.0654568	+	0.997855i	$0.479150\pi$
$509$	−472.660	+	563.294i	−0.928605	+	1.10667i	−0.994062	+	0.108813i	$0.965295\pi$
$510$		0			0
$511$	362.643	+	131.991i	0.709674	+	0.258300i
$512$	488.359			0.953826
$513$		0			0
$514$	−123.388			−0.240054
$515$	−237.196	+	225.566i	−0.460575	+	0.437993i
$516$		0			0
$517$	−132.499	+	157.906i	−0.256284	+	0.305427i
$518$	−29.8909	+	169.520i	−0.0577045	+	0.327259i
$519$		0			0
$520$	120.040	+	497.692i	0.230847	+	0.957101i
$521$	817.489	−	471.978i	1.56908	−	0.905907i	0.572800	−	0.819695i	$-0.305857\pi$
$521$	817.489	−	471.978i	1.56908	−	0.905907i	0.996277	−	0.0862122i	$-0.0274763\pi$
$522$		0			0
$523$	433.608	+	250.343i	0.829077	+	0.478668i	0.853537	−	0.521033i	$-0.174453\pi$
$523$	433.608	+	250.343i	0.829077	+	0.478668i	−0.0244592	+	0.999701i	$0.507786\pi$
$524$	139.606	−	24.6163i	0.266424	−	0.0469777i
$525$		0			0
$526$	123.922	−	45.1038i	0.235593	−	0.0857487i
$527$	−864.459	+	314.637i	−1.64034	+	0.597035i
$528$		0			0
$529$	−61.7400	−	350.145i	−0.116711	−	0.661899i
$530$	140.773	−	93.3889i	0.265609	−	0.176205i
$531$		0			0
$532$	393.369	−	227.112i	0.739415	−	0.426901i
$533$	−752.319	+	631.270i	−1.41148	+	1.18437i
$534$		0			0
$535$	−50.7035	+	68.6731i	−0.0947729	+	0.128361i
$536$	84.6019	−	100.825i	0.157839	−	0.188106i
$537$		0			0
$538$	−92.6095	+	254.443i	−0.172137	+	0.472942i
$539$			184.191i			0.341728i
$540$		0			0
$541$	788.754			1.45796			0.728978	−	0.684538i	$-0.239996\pi$
$541$	788.754			1.45796			0.728978	+	0.684538i	$0.239996\pi$
$542$	344.166	+	125.266i	0.634993	+	0.231118i
$543$		0			0
$544$	−471.240	−	395.418i	−0.866251	−	0.726871i
$545$	−214.492	+	290.509i	−0.393564	+	0.533045i
$546$		0			0
$547$	161.404	+	192.354i	0.295071	+	0.351652i	0.893129	−	0.449801i	$-0.148505\pi$
$547$	161.404	+	192.354i	0.295071	+	0.351652i	−0.598058	+	0.801453i	$0.704061\pi$
$548$	243.269	+	421.354i	0.443921	+	0.768894i
$549$		0			0
$550$	−17.8078	−	142.548i	−0.0323778	−	0.259178i
$551$	1022.62	−	180.315i	1.85593	−	0.327250i
$552$		0			0
$553$	116.094	+	318.967i	0.209936	+	0.576793i
$554$	119.907	+	329.442i	0.216439	+	0.594660i
$555$		0			0
$556$	110.984	+	629.423i	0.199612	+	1.13206i
$557$	250.586	−	434.027i	0.449884	−	0.779223i	−0.548494	−	0.836155i	$-0.684798\pi$
$557$	250.586	−	434.027i	0.449884	−	0.779223i	0.998378	+	0.0569320i	$0.0181318\pi$
$558$		0			0
$559$	−255.393	−	442.354i	−0.456875	−	0.791331i
$560$	−53.7567	−	222.878i	−0.0959941	−	0.397996i
$561$		0			0
$562$	313.843	+	55.3390i	0.558440	+	0.0984680i
$563$	−73.5000	−	61.6738i	−0.130551	−	0.109545i	0.575174	−	0.818031i	$-0.304934\pi$
$563$	−73.5000	−	61.6738i	−0.130551	−	0.109545i	−0.705725	+	0.708486i	$0.749379\pi$
$564$		0			0
$565$	77.3329	+	81.3201i	0.136872	+	0.143929i
$566$		−	160.335i		−	0.283277i
$567$		0			0
$568$		−	602.107i		−	1.06005i
$569$	−65.3089	+	179.435i	−0.114778	+	0.315351i	−0.983759	−	0.179496i	$-0.942553\pi$
$569$	−65.3089	+	179.435i	−0.114778	+	0.315351i	0.868980	+	0.494846i	$0.164776\pi$
$570$		0			0
$571$	490.869	+	411.888i	0.859666	+	0.721345i	0.961896	−	0.273415i	$-0.0881534\pi$
$571$	490.869	+	411.888i	0.859666	+	0.721345i	−0.102230	+	0.994761i	$0.532598\pi$
$572$	79.8788	−	453.015i	0.139648	−	0.791984i
$573$		0			0
$574$	−158.373	+	132.891i	−0.275912	+	0.231518i
$575$	128.011	−	303.351i	0.222628	−	0.527567i
$576$		0			0
$577$	−101.569	−	58.6408i	−0.176029	−	0.101630i	0.409397	−	0.912357i	$-0.365739\pi$
$577$	−101.569	−	58.6408i	−0.176029	−	0.101630i	−0.585426	+	0.810726i	$0.699073\pi$
$578$	18.0125	+	102.154i	0.0311635	+	0.176737i
$579$		0			0
$580$	73.6984	−	652.960i	0.127066	−	1.12579i
$581$	127.736	+	350.951i	0.219855	+	0.604046i
$582$		0			0
$583$	−324.761	+	57.2642i	−0.557052	+	0.0982233i
$584$	384.710	+	222.113i	0.658751	+	0.380330i
$585$		0			0
$586$	57.8904	+	100.269i	0.0987891	+	0.171108i
$587$	177.386	−	148.845i	0.302191	−	0.253569i	−0.479064	−	0.877780i	$-0.659024\pi$
$587$	177.386	−	148.845i	0.302191	−	0.253569i	0.781256	+	0.624211i	$0.214580\pi$
$588$		0			0
$589$	209.055	−	1185.61i	0.354932	−	2.01292i
$590$	53.8872	−	23.4984i	0.0913343	−	0.0398278i
$591$		0			0
$592$	144.164	−	396.086i	0.243520	−	0.669065i
$593$	557.117			0.939489			0.469745	−	0.882802i	$-0.344346\pi$
$593$	557.117			0.939489			0.469745	+	0.882802i	$0.344346\pi$
$594$		0			0
$595$	−226.517	+	455.523i	−0.380700	+	0.765586i
$596$	−27.2235	+	74.7960i	−0.0456771	+	0.125497i
$597$		0			0
$598$	−116.960	+	139.387i	−0.195585	+	0.233089i
$599$	−459.818	−	81.0783i	−0.767642	−	0.135356i	−0.223904	−	0.974611i	$-0.571880\pi$
$599$	−459.818	−	81.0783i	−0.767642	−	0.135356i	−0.543738	+	0.839255i	$0.682991\pi$
$600$		0			0
$601$	−568.779	+	477.262i	−0.946387	+	0.794113i	−0.978685	−	0.205365i	$-0.934162\pi$
$601$	−568.779	+	477.262i	−0.946387	+	0.794113i	0.0322984	+	0.999478i	$0.489717\pi$
$602$	−53.7638	−	93.1216i	−0.0893086	−	0.154687i
$603$		0			0
$604$	−394.251	+	682.863i	−0.652734	+	1.13057i
$605$	91.8552	−	311.302i	0.151827	−	0.514550i
$606$		0			0
$607$	−61.7933	−	169.776i	−0.101801	−	0.279696i	0.878327	−	0.478060i	$-0.158660\pi$
$607$	−61.7933	−	169.776i	−0.101801	−	0.279696i	−0.980129	+	0.198363i	$0.936437\pi$
$608$	756.495	−	275.342i	1.24423	−	0.452864i
$609$		0			0
$610$	−62.8064	+	212.854i	−0.102961	+	0.348941i
$611$	−429.208	−	247.803i	−0.702467	−	0.405570i
$612$		0			0
$613$	−259.241	+	149.673i	−0.422905	+	0.244164i	−0.696319	−	0.717732i	$-0.745180\pi$
$613$	−259.241	+	149.673i	−0.422905	+	0.244164i	0.273414	+	0.961896i	$0.411847\pi$
$614$	−172.362	−	205.413i	−0.280719	−	0.334548i
$615$		0			0
$616$	36.5333	−	207.190i	0.0593072	−	0.336348i
$617$	422.548	+	354.560i	0.684842	+	0.574651i	0.917417	−	0.397928i	$-0.130271\pi$
$617$	422.548	+	354.560i	0.684842	+	0.574651i	−0.232575	+	0.972579i	$0.574715\pi$
$618$		0			0
$619$	−872.582	−	317.594i	−1.40966	−	0.513076i	−0.478633	−	0.878015i	$-0.658867\pi$
$619$	−872.582	−	317.594i	−1.40966	−	0.513076i	−0.931031	+	0.364940i	$0.881090\pi$
$620$	−682.155	−	339.213i	−1.10025	−	0.547118i
$621$		0			0
$622$		−	16.3870i		−	0.0263456i
$623$	−511.109	−	186.028i	−0.820399	−	0.298601i
$624$		0			0
$625$	−516.671	+	351.677i	−0.826673	+	0.562683i
$626$	294.632	+	51.9516i	0.470659	+	0.0829899i
$627$		0			0
$628$	−17.9061	−	21.3397i	−0.0285129	−	0.0339804i
$629$	−809.992	+	467.649i	−1.28775	+	0.743481i
$630$		0			0
$631$	−144.104	+	249.596i	−0.228374	+	0.395556i	−0.957326	−	0.289009i	$-0.906674\pi$
$631$	−144.104	+	249.596i	−0.228374	+	0.395556i	0.728952	+	0.684565i	$0.240008\pi$
$632$	67.8483	+	384.787i	0.107355	+	0.608840i
$633$		0			0
$634$	−196.978	+	71.6942i	−0.310691	+	0.113082i
$635$	30.6531	−	271.583i	0.0482726	−	0.427690i
$636$		0			0
$637$	−436.127	+	76.9010i	−0.684659	+	0.120724i
$638$	110.689	−	191.719i	0.173493	−	0.300499i
$639$		0			0
$640$	−40.4819	−	650.620i	−0.0632530	−	1.01659i
$641$	589.951	+	703.077i	0.920361	+	1.09684i	0.995024	+	0.0996345i	$0.0317673\pi$
$641$	589.951	+	703.077i	0.920361	+	1.09684i	−0.0746633	+	0.997209i	$0.523788\pi$
$642$		0			0
$643$	814.024	+	143.534i	1.26598	+	0.223226i	0.766016	−	0.642822i	$-0.222236\pi$
$643$	814.024	+	143.534i	1.26598	+	0.223226i	0.499962	+	0.866048i	$0.333347\pi$
$644$	142.665	−	170.021i	0.221529	−	0.264008i
$645$		0			0
$646$	−400.255	−	145.681i	−0.619589	−	0.225512i
$647$	−166.913			−0.257979			−0.128990	−	0.991646i	$-0.541173\pi$
$647$	−166.913			−0.257979			−0.128990	+	0.991646i	$0.541173\pi$
$648$		0			0
$649$	−114.759			−0.176824
$650$	330.090	−	101.680i	0.507831	−	0.156431i
$651$		0			0
$652$	−94.5510	+	112.681i	−0.145017	+	0.172824i
$653$	206.391	−	1170.50i	0.316067	−	1.79250i	−0.250109	−	0.968218i	$-0.580466\pi$
$653$	206.391	−	1170.50i	0.316067	−	1.79250i	0.566175	−	0.824285i	$-0.308423\pi$
$654$		0			0
$655$	−48.7186	−	201.989i	−0.0743795	−	0.308381i
$656$	438.423	−	253.124i	0.668328	−	0.385859i
$657$		0			0
$658$	−90.3541	−	52.1660i	−0.137316	−	0.0792796i
$659$	−190.385	+	33.5700i	−0.288900	+	0.0509408i	−0.316220	−	0.948686i	$-0.602414\pi$
$659$	−190.385	+	33.5700i	−0.288900	+	0.0509408i	0.0273202	+	0.999627i	$0.491303\pi$
$660$		0			0
$661$	−714.570	+	260.082i	−1.08104	+	0.393468i	−0.820296	−	0.571940i	$-0.806191\pi$
$661$	−714.570	+	260.082i	−1.08104	+	0.393468i	−0.260747	+	0.965407i	$0.583969\pi$
$662$	−217.664	+	79.2233i	−0.328798	+	0.119673i
$663$		0			0
$664$	74.6518	+	423.371i	0.112427	+	0.637608i
$665$	−368.047	−	554.787i	−0.553454	−	0.834267i
$666$		0			0
$667$	439.412	−	253.695i	0.658789	−	0.380352i
$668$	419.620	−	352.103i	0.628174	−	0.527100i
$669$		0			0
$670$	−71.4343	−	52.7422i	−0.106618	−	0.0787197i
$671$	278.468	−	331.865i	0.415005	−	0.494583i
$672$		0			0
$673$	259.131	−	711.958i	0.385039	−	1.05789i	−0.584166	−	0.811634i	$-0.698578\pi$
$673$	259.131	−	711.958i	0.385039	−	1.05789i	0.969206	−	0.246253i	$-0.0791993\pi$
$674$		−	118.727i		−	0.176153i
$675$		0			0
$676$	529.492			0.783272
$677$	185.869	+	67.6509i	0.274549	+	0.0999275i	0.475625	−	0.879648i	$-0.342222\pi$
$677$	185.869	+	67.6509i	0.274549	+	0.0999275i	−0.201077	+	0.979575i	$0.564444\pi$
$678$		0			0
$679$	332.624	+	279.104i	0.489873	+	0.411052i
$680$	−347.832	+	471.106i	−0.511518	+	0.692802i
$681$		0			0
$682$	−164.979	−	196.615i	−0.241905	−	0.288292i
$683$	521.767	+	903.727i	0.763934	+	1.32317i	0.940808	+	0.338939i	$0.110068\pi$
$683$	521.767	+	903.727i	0.763934	+	1.32317i	−0.176874	+	0.984233i	$0.556599\pi$
$684$		0			0
$685$	594.256	−	394.231i	0.867527	−	0.575520i
$686$	−274.725	+	48.4414i	−0.400474	+	0.0706143i
$687$		0			0
$688$	90.0546	+	247.423i	0.130893	+	0.359627i
$689$	−271.180	−	745.061i	−0.393585	−	1.08137i
$690$		0			0
$691$	120.650	+	684.241i	0.174602	+	0.990219i	0.938602	+	0.345002i	$0.112122\pi$
$691$	120.650	+	684.241i	0.174602	+	0.990219i	−0.764000	+	0.645217i	$0.776767\pi$
$692$	−188.304	+	326.152i	−0.272116	+	0.471318i
$693$		0			0
$694$	−82.2826	−	142.518i	−0.118563	−	0.205357i
$695$	910.681	−	219.651i	1.31033	−	0.316044i
$696$		0			0
$697$	−1106.27	−	195.065i	−1.58719	−	0.279864i
$698$	−232.008	−	194.678i	−0.332390	−	0.278908i
$699$		0			0
$700$	−402.636	+	124.027i	−0.575194	+	0.177181i
$701$			1192.44i			1.70105i	0.525936	+	0.850524i	$0.323715\pi$
$701$			1192.44i			1.70105i	−0.525936	+	0.850524i	$0.676285\pi$
$702$		0			0
$703$		−	1224.00i		−	1.74111i
$704$	−36.3973	+	100.001i	−0.0517007	+	0.142046i
$705$		0			0
$706$	393.275	+	329.997i	0.557047	+	0.467418i
$707$	−73.9636	+	419.469i	−0.104616	+	0.593308i
$708$		0			0
$709$	−128.669	+	107.966i	−0.181479	+	0.152279i	−0.729002	−	0.684512i	$-0.760015\pi$
$709$	−128.669	+	107.966i	−0.181479	+	0.152279i	0.547523	+	0.836791i	$0.315571\pi$
$710$	−405.426	+	25.2259i	−0.571023	+	0.0355294i
$711$		0			0
$712$	−542.210	−	313.045i	−0.761531	−	0.439670i
$713$	−102.150	−	579.324i	−0.143269	−	0.812516i
$714$		0			0
$715$	−669.987	−	75.6201i	−0.937044	−	0.105762i
$716$	−233.946	−	642.763i	−0.326741	−	0.897713i
$717$		0			0
$718$	−185.457	+	32.7010i	−0.258296	+	0.0455446i
$719$	−35.4071	−	20.4423i	−0.0492449	−	0.0284315i	0.475175	−	0.879891i	$-0.342385\pi$
$719$	−35.4071	−	20.4423i	−0.0492449	−	0.0284315i	−0.524420	+	0.851460i	$0.675718\pi$
$720$		0			0
$721$	161.704	+	280.080i	0.224278	+	0.388461i
$722$	214.821	−	180.256i	0.297535	−	0.249662i
$723$		0			0
$724$	−54.1734	+	307.233i	−0.0748252	+	0.424355i
$725$	−961.924	−	48.3794i	−1.32679	−	0.0667302i
$726$		0			0
$727$	315.233	−	866.096i	0.433608	−	1.19133i	−0.509974	−	0.860190i	$-0.670345\pi$
$727$	315.233	−	866.096i	0.433608	−	1.19133i	0.943582	−	0.331139i	$-0.107433\pi$
$728$	505.837			0.694832
$729$		0			0
$730$	133.441	−	268.349i	0.182796	−	0.367601i
$731$	199.826	−	549.018i	0.273360	−	0.751051i
$732$		0			0
$733$	−238.564	+	284.310i	−0.325463	+	0.387871i	−0.903820	−	0.427912i	$-0.859249\pi$
$733$	−238.564	+	284.310i	−0.325463	+	0.387871i	0.578358	+	0.815783i	$0.303694\pi$
$734$	−351.598	−	61.9962i	−0.479016	−	0.0844635i
$735$		0			0
$736$	301.338	−	252.853i	0.409427	−	0.343550i
$737$	86.6678	+	150.113i	0.117595	+	0.203681i
$738$		0			0
$739$	254.858	−	441.428i	0.344869	−	0.597331i	−0.640461	−	0.767991i	$-0.721257\pi$
$739$	254.858	−	441.428i	0.344869	−	0.597331i	0.985330	+	0.170660i	$0.0545899\pi$
$740$	−742.896	−	219.205i	−1.00391	−	0.296222i
$741$		0			0
$742$	−57.0871	−	156.846i	−0.0769368	−	0.211382i
$743$	585.060	−	212.945i	0.787430	−	0.286601i	0.0831627	−	0.996536i	$-0.473498\pi$
$743$	585.060	−	212.945i	0.787430	−	0.286601i	0.704267	+	0.709935i	$0.251276\pi$
$744$		0			0
$745$	111.897	+	33.0172i	0.150198	+	0.0443184i
$746$	−348.763	−	201.358i	−0.467510	−	0.269917i
$747$		0			0
$748$	455.673	−	263.083i	0.609188	−	0.351715i
$749$	54.2136	+	64.6093i	0.0723814	+	0.0862607i
$750$		0			0
$751$	68.2732	−	387.196i	0.0909097	−	0.515575i	−0.905015	−	0.425381i	$-0.860140\pi$
$751$	68.2732	−	387.196i	0.0909097	−	0.515575i	0.995924	−	0.0901939i	$-0.0287487\pi$
$752$	195.707	+	164.218i	0.260248	+	0.218374i
$753$		0			0
$754$	500.164	+	182.045i	0.663347	+	0.241439i
$755$	1034.85	+	514.594i	1.37066	+	0.681582i
$756$		0			0
$757$		−	480.153i		−	0.634283i	−0.948378	−	0.317142i	$-0.897277\pi$
$757$		−	480.153i		−	0.634283i	0.948378	−	0.317142i	$-0.102723\pi$
$758$	265.685	+	96.7013i	0.350508	+	0.127574i
$759$		0			0
$760$	−306.326	−	702.475i	−0.403060	−	0.924310i
$761$	13.3027	+	2.34562i	0.0174805	+	0.00308229i	0.182382	−	0.983228i	$-0.441619\pi$
$761$	13.3027	+	2.34562i	0.0174805	+	0.00308229i	−0.164901	+	0.986310i	$0.552730\pi$
$762$		0			0
$763$	229.341	+	273.318i	0.300578	+	0.358215i
$764$	−646.322	+	373.154i	−0.845972	+	0.488422i
$765$		0			0
$766$	−227.337	+	393.760i	−0.296785	+	0.514047i
$767$	−47.9125	−	271.725i	−0.0624673	−	0.354270i
$768$		0			0
$769$	−54.1363	+	19.7040i	−0.0703983	+	0.0256229i	−0.376979	−	0.926222i	$-0.623037\pi$
$769$	−54.1363	+	19.7040i	−0.0703983	+	0.0256229i	0.306581	+	0.951845i	$0.400815\pi$
$770$	−141.041	−	15.9191i	−0.183171	−	0.0206741i
$771$		0			0
$772$	652.966	−	115.135i	0.845810	−	0.149139i
$773$	−163.063	+	282.433i	−0.210948	+	0.365372i	−0.952011	−	0.306062i	$-0.900988\pi$
$773$	−163.063	+	282.433i	−0.210948	+	0.365372i	0.741064	+	0.671435i	$0.234322\pi$
$774$		0			0
$775$	−434.143	+	1028.80i	−0.560185	+	1.32749i
$776$	321.274	+	382.880i	0.414013	+	0.493402i
$777$		0			0
$778$	244.982	+	43.1969i	0.314887	+	0.0555230i
$779$	944.949	−	1126.15i	1.21303	−	1.44563i
$780$		0			0
$781$	745.135	+	271.207i	0.954078	+	0.347256i
$782$	−208.128			−0.266148
$783$		0			0
$784$	228.285			0.291180
$785$	−29.5880	+	28.1373i	−0.0376917	+	0.0358437i
$786$		0			0
$787$	745.755	−	888.757i	0.947593	−	1.12930i	−0.0438871	−	0.999036i	$-0.513974\pi$
$787$	745.755	−	888.757i	0.947593	−	1.12930i	0.991480	−	0.130260i	$-0.0415814\pi$
$788$	66.3375	−	376.219i	0.0841846	−	0.477435i
$789$		0			0
$790$	256.252	−	61.8064i	0.324370	−	0.0782360i
$791$	96.0224	−	55.4385i	0.121394	−	0.0700866i
$792$		0			0
$793$	902.052	+	520.800i	1.13752	+	0.656746i
$794$	569.560	−	100.429i	0.717330	−	0.126485i
$795$		0			0
$796$	−73.1104	+	26.6100i	−0.0918473	+	0.0334297i
$797$	438.957	−	159.767i	0.550762	−	0.200461i	−0.0516233	−	0.998667i	$-0.516440\pi$
$797$	438.957	−	159.767i	0.550762	−	0.200461i	0.602385	+	0.798206i	$0.294217\pi$
$798$		0			0
$799$	−98.4393	−	558.277i	−0.123203	−	0.698720i
$800$	−740.944	+	92.5623i	−0.926180	+	0.115703i
$801$		0			0
$802$	204.241	−	117.918i	0.254664	−	0.147030i
$803$	−448.159	+	376.050i	−0.558106	+	0.468307i
$804$		0			0
$805$	−261.710	−	193.229i	−0.325105	−	0.240036i
$806$	396.664	−	472.726i	0.492139	−	0.586508i
$807$		0			0
$808$	−167.691	+	460.727i	−0.207538	+	0.570206i
$809$		−	1348.17i		−	1.66646i	−0.552923	−	0.833232i	$-0.686488\pi$
$809$		−	1348.17i		−	1.66646i	0.552923	−	0.833232i	$-0.313512\pi$
$810$		0			0
$811$	−802.634			−0.989685			−0.494842	−	0.868983i	$-0.664774\pi$
$811$	−802.634			−0.989685			−0.494842	+	0.868983i	$0.664774\pi$
$812$	−610.088	−	222.054i	−0.751340	−	0.273465i
$813$		0			0
$814$	−199.898	−	167.734i	−0.245575	−	0.206062i
$815$	173.448	+	128.062i	0.212820	+	0.157131i
$816$		0			0
$817$	491.473	+	585.715i	0.601558	+	0.716909i
$818$	−189.932	−	328.973i	−0.232191	−	0.402167i
$819$		0			0
$820$	−514.275	−	775.208i	−0.627164	−	0.945376i
$821$	−151.564	+	26.7248i	−0.184609	+	0.0325515i	−0.265188	−	0.964197i	$-0.585434\pi$
$821$	−151.564	+	26.7248i	−0.184609	+	0.0325515i	0.0805793	+	0.996748i	$0.474323\pi$
$822$		0			0
$823$	−22.3175	−	61.3168i	−0.0271172	−	0.0745040i	0.925395	−	0.379003i	$-0.123733\pi$
$823$	−22.3175	−	61.3168i	−0.0271172	−	0.0745040i	−0.952513	+	0.304499i	$0.901511\pi$
$824$	127.325	+	349.822i	0.154520	+	0.424541i
$825$		0			0
$826$	−10.0862	−	57.2019i	−0.0122109	−	0.0692517i
$827$	−535.860	+	928.136i	−0.647956	+	1.12229i	0.335654	+	0.941985i	$0.391043\pi$
$827$	−535.860	+	928.136i	−0.647956	+	1.12229i	−0.983610	+	0.180307i	$0.942291\pi$
$828$		0			0
$829$	377.159	+	653.259i	0.454957	+	0.788009i	0.998686	−	0.0512524i	$-0.0163213\pi$
$829$	377.159	+	653.259i	0.454957	+	0.788009i	−0.543729	+	0.839261i	$0.682988\pi$
$830$	281.948	−	68.0041i	0.339696	−	0.0819326i
$831$		0			0
$832$	−251.977	−	44.4304i	−0.302857	−	0.0534019i
$833$	−388.041	−	325.605i	−0.465835	−	0.390882i
$834$		0			0
$835$	−553.287	−	581.813i	−0.662619	−	0.696783i
$836$			688.579i			0.823660i
$837$		0			0
$838$			212.016i			0.253002i
$839$	−88.8598	+	244.140i	−0.105912	+	0.290990i	−0.981316	−	0.192401i	$-0.938373\pi$
$839$	−88.8598	+	244.140i	−0.105912	+	0.290990i	0.875405	+	0.483390i	$0.160595\pi$
$840$		0			0
$841$	−492.736	−	413.455i	−0.585893	−	0.491623i
$842$	−56.9399	+	322.922i	−0.0676246	+	0.383518i
$843$		0			0
$844$	−331.360	+	278.044i	−0.392607	+	0.329436i
$845$	−48.1957	−	774.594i	−0.0570363	−	0.916680i
$846$		0			0
$847$	−277.723	−	160.344i	−0.327890	−	0.189308i
$848$	70.9727	+	402.506i	0.0836942	+	0.474653i
$849$		0			0
$850$	331.790	+	214.474i	0.390341	+	0.252322i
$851$	−204.557	−	562.015i	−0.240372	−	0.660417i
$852$		0			0
$853$	−287.962	+	50.7754i	−0.337587	+	0.0595257i	−0.339872	−	0.940472i	$-0.610384\pi$
$853$	−287.962	+	50.7754i	−0.337587	+	0.0595257i	0.00228492	+	0.999997i	$0.499273\pi$
$854$	189.894	+	109.636i	0.222359	+	0.128379i
$855$		0			0
$856$	48.5423	+	84.0778i	0.0567083	+	0.0982217i
$857$	554.776	−	465.512i	0.647346	−	0.543188i	−0.258918	−	0.965899i	$-0.583366\pi$
$857$	554.776	−	465.512i	0.647346	−	0.543188i	0.906264	+	0.422711i	$0.138922\pi$
$858$		0			0
$859$	−57.6146	+	326.749i	−0.0670717	+	0.380383i	0.932732	+	0.360570i	$0.117418\pi$
$859$	−57.6146	+	326.749i	−0.0670717	+	0.380383i	−0.999804	+	0.0198122i	$0.993693\pi$
$860$	443.512	−	193.400i	0.515711	−	0.224884i
$861$		0			0
$862$	63.8200	−	175.344i	0.0740371	−	0.203415i
$863$	238.506			0.276369			0.138184	−	0.990407i	$-0.455873\pi$
$863$	238.506			0.276369			0.138184	+	0.990407i	$0.455873\pi$
$864$		0			0
$865$	494.268	+	245.783i	0.571408	+	0.284142i
$866$	−73.3533	+	201.537i	−0.0847036	+	0.232721i
$867$		0			0
$868$	−483.841	+	576.620i	−0.557421	+	0.664308i
$869$	−506.752	−	89.3541i	−0.583144	−	0.102824i
$870$		0			0
$871$	−319.253	+	267.885i	−0.366536	+	0.307560i
$872$	205.350	+	355.676i	0.235493	+	0.407885i
$873$		0			0
$874$	136.186	−	235.881i	0.155819	−	0.269886i
$875$	218.088	+	577.728i	0.249243	+	0.660260i
$876$		0			0
$877$	−31.9931	−	87.9005i	−0.0364802	−	0.100229i	0.920115	−	0.391648i	$-0.128095\pi$
$877$	−31.9931	−	87.9005i	−0.0364802	−	0.100229i	−0.956595	+	0.291419i	$0.905873\pi$
$878$	−395.814	+	144.065i	−0.450814	+	0.164083i
$879$		0			0
$880$	333.352	+	98.3612i	0.378809	+	0.111774i
$881$	1228.28	+	709.150i	1.39419	+	0.804937i	0.993776	−	0.111396i	$-0.0355322\pi$
$881$	1228.28	+	709.150i	1.39419	+	0.804937i	0.400416	+	0.916333i	$0.368865\pi$
$882$		0			0
$883$	47.9457	−	27.6814i	0.0542986	−	0.0313493i	−0.472605	−	0.881274i	$-0.656686\pi$
$883$	47.9457	−	27.6814i	0.0542986	−	0.0313493i	0.526904	+	0.849925i	$0.323353\pi$
$884$	813.173	+	969.102i	0.919879	+	1.09627i
$885$		0			0
$886$	89.8685	−	509.669i	0.101432	−	0.575248i
$887$	−500.234	−	419.746i	−0.563962	−	0.473220i	0.315674	−	0.948868i	$-0.397769\pi$
$887$	−500.234	−	419.746i	−0.563962	−	0.473220i	−0.879636	+	0.475647i	$0.842214\pi$
$888$		0			0
$889$	−253.752	−	92.3580i	−0.285435	−	0.103890i
$890$	−188.071	+	378.210i	−0.211316	+	0.424955i
$891$		0			0
$892$			1407.48i			1.57789i
$893$	697.133	+	253.736i	0.780664	+	0.284138i
$894$		0			0
$895$	−919.004	+	400.746i	−1.02682	+	0.447761i
$896$	−634.292	−	111.843i	−0.707915	−	0.124825i
$897$		0			0
$898$	−158.092	−	188.406i	−0.176049	−	0.209807i
$899$	−1490.25	+	860.394i	−1.65767	+	0.957057i
$900$		0			0
$901$	453.458	−	785.413i	0.503283	−	0.871712i
$902$	−54.4231	−	308.649i	−0.0603361	−	0.342183i
$903$		0			0
$904$	119.933	−	43.6519i	0.132669	−	0.0482875i
$905$	454.382	+	51.2853i	0.502080	+	0.0566688i
$906$		0			0
$907$	−105.493	+	18.6012i	−0.116309	+	0.0205085i	−0.231500	−	0.972835i	$-0.574363\pi$
$907$	−105.493	+	18.6012i	−0.116309	+	0.0205085i	0.115190	+	0.993343i	$0.463252\pi$
$908$	182.260	−	315.683i	0.200727	−	0.347669i
$909$		0			0
$910$	−21.1925	−	340.604i	−0.0232885	−	0.374290i
$911$	−427.389	−	509.342i	−0.469142	−	0.559102i	0.478644	−	0.878009i	$-0.341129\pi$
$911$	−427.389	−	509.342i	−0.469142	−	0.559102i	−0.947786	+	0.318907i	$0.896684\pi$
$912$		0			0
$913$	−557.567	−	98.3141i	−0.610698	−	0.107682i
$914$	270.000	−	321.774i	0.295405	−	0.352050i
$915$		0			0
$916$	−445.332	−	162.088i	−0.486170	−	0.176952i
$917$	−205.295			−0.223877
$918$		0			0
$919$	836.732			0.910481			0.455241	−	0.890368i	$-0.349553\pi$
$919$	836.732			0.910481			0.455241	+	0.890368i	$0.349553\pi$
$920$	−258.052	−	271.356i	−0.280491	−	0.294953i
$921$		0			0
$922$	−212.398	+	253.125i	−0.230366	+	0.274540i
$923$	−331.064	+	1877.56i	−0.358683	+	2.03419i
$924$		0			0
$925$	−253.054	+	1106.74i	−0.273572	+	1.19647i
$926$	205.201	−	118.473i	0.221600	−	0.127941i
$927$		0			0
$928$	−996.525	−	575.344i	−1.07384	−	0.619983i
$929$	973.810	−	171.709i	1.04823	−	0.184832i	0.377104	−	0.926171i	$-0.376920\pi$
$929$	973.810	−	171.709i	1.04823	−	0.184832i	0.671131	+	0.741339i	$0.265809\pi$
$930$		0			0
$931$	622.932	−	226.729i	0.669100	−	0.243533i
$932$	−340.365	+	123.883i	−0.365198	+	0.132921i
$933$		0			0
$934$	99.2022	+	562.603i	0.106212	+	0.602359i
$935$	−426.341	−	642.658i	−0.455979	−	0.687335i
$936$		0			0
$937$	−469.038	+	270.799i	−0.500575	+	0.289007i	−0.728951	−	0.684566i	$-0.759992\pi$
$937$	−469.038	+	270.799i	−0.500575	+	0.289007i	0.228376	+	0.973573i	$0.426658\pi$
$938$	−67.2071	+	56.3934i	−0.0716493	+	0.0601209i
$939$		0			0
$940$	278.851	−	377.677i	0.296650	−	0.401784i
$941$	−166.260	+	198.142i	−0.176685	+	0.210565i	−0.847118	−	0.531406i	$-0.821664\pi$
$941$	−166.260	+	198.142i	−0.176685	+	0.210565i	0.670433	+	0.741970i	$0.266109\pi$
$942$		0			0
$943$	245.682	−	675.004i	0.260532	−	0.715805i
$944$			142.231i			0.150668i
$945$		0			0
$946$	163.006			0.172311
$947$	−366.881	−	133.534i	−0.387414	−	0.141007i	0.140967	−	0.990014i	$-0.454979\pi$
$947$	−366.881	−	133.534i	−0.387414	−	0.141007i	−0.528382	+	0.849007i	$0.677201\pi$
$948$		0			0
$949$	−1077.52	−	904.146i	−1.13543	−	0.952736i
$950$	−460.175	+	235.694i	−0.484395	+	0.248099i
$951$		0			0
$952$	371.912	+	443.227i	0.390664	+	0.465575i
$953$	232.132	+	402.064i	0.243580	+	0.421893i	0.961732	−	0.273994i	$-0.0883447\pi$
$953$	232.132	+	402.064i	0.243580	+	0.421893i	−0.718151	+	0.695887i	$0.755011\pi$
$954$		0			0
$955$	604.718	+	911.540i	0.633212	+	0.954492i
$956$	850.667	−	149.995i	0.889819	−	0.156899i
$957$		0			0
$958$	171.381	+	470.866i	0.178895	+	0.491509i
$959$	−240.987	−	662.106i	−0.251290	−	0.690413i
$960$		0			0
$961$	179.563	+	1018.35i	0.186850	+	1.05968i
$962$	313.702	−	543.347i	0.326093	−	0.564810i
$963$		0			0
$964$	−6.46215	−	11.1928i	−0.00670348	−	0.0116108i
$965$	−227.866	−	944.744i	−0.236131	−	0.979009i
$966$		0			0
$967$	641.635	+	113.138i	0.663532	+	0.116999i	0.495264	−	0.868743i	$-0.335071\pi$
$967$	641.635	+	113.138i	0.663532	+	0.116999i	0.168268	+	0.985741i	$0.446183\pi$
$968$	−282.778	−	237.279i	−0.292126	−	0.245123i
$969$		0			0
$970$	244.351	−	232.370i	0.251908	−	0.239557i
$971$			40.3111i			0.0415150i	0.999785	+	0.0207575i	$0.00660779\pi$
$971$			40.3111i			0.0415150i	−0.999785	+	0.0207575i	$0.993392\pi$
$972$		0			0
$973$		−	925.585i		−	0.951269i
$974$	169.469	−	465.613i	0.173993	−	0.478042i
$975$		0			0
$976$	−411.311	−	345.131i	−0.421425	−	0.353617i
$977$	86.1735	−	488.714i	0.0882021	−	0.500219i	−0.908417	−	0.418064i	$-0.862709\pi$
$977$	86.1735	−	488.714i	0.0882021	−	0.500219i	0.996620	−	0.0821549i	$-0.0261802\pi$
$978$		0			0
$979$	631.635	−	530.005i	0.645184	−	0.541374i
$980$	−26.0510	−	418.688i	−0.0265826	−	0.427232i
$981$		0			0
$982$	−197.954	−	114.289i	−0.201582	−	0.116383i
$983$	−330.085	−	1872.00i	−0.335793	−	1.90438i	−0.419258	−	0.907867i	$-0.637710\pi$
$983$	−330.085	−	1872.00i	−0.335793	−	1.90438i	0.0834645	−	0.996511i	$-0.473401\pi$
$984$		0			0
$985$	−556.409	−	62.8008i	−0.564882	−	0.0637572i
$986$	208.228	+	572.102i	0.211185	+	0.580226i
$987$		0			0
$988$	−1630.42	+	287.486i	−1.65022	+	0.290978i
$989$	323.551	+	186.802i	0.327150	+	0.188880i
$990$		0			0
$991$	200.715	+	347.649i	0.202538	+	0.350806i	0.949345	−	0.314234i	$-0.101748\pi$
$991$	200.715	+	347.649i	0.202538	+	0.350806i	−0.746808	+	0.665040i	$0.768414\pi$
$992$	−1021.98	+	857.539i	−1.03022	+	0.864455i
$993$		0			0
$994$	−69.6935	+	395.252i	−0.0701142	+	0.397638i
$995$	45.5825	+	104.531i	0.0458116	+	0.105057i
$996$		0			0
$997$	−463.244	+	1272.75i	−0.464638	+	1.27658i	0.457323	+	0.889300i	$0.348808\pi$
$997$	−463.244	+	1272.75i	−0.464638	+	1.27658i	−0.921961	+	0.387282i	$0.873414\pi$
$998$	−19.6108			−0.0196501
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	405.3.n.a.179.14		204
3.2	odd	2		135.3.n.a.104.21	yes	204
5.4	even	2	inner	405.3.n.a.179.21		204
15.14	odd	2		135.3.n.a.104.14	yes	204
27.7	even	9		135.3.n.a.74.14	✓	204
27.20	odd	18	inner	405.3.n.a.224.21		204
135.34	even	18		135.3.n.a.74.21	yes	204
135.74	odd	18	inner	405.3.n.a.224.14		204

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
135.3.n.a.74.14	✓	204	27.7	even	9
135.3.n.a.74.21	yes	204	135.34	even	18
135.3.n.a.104.14	yes	204	15.14	odd	2
135.3.n.a.104.21	yes	204	3.2	odd	2
405.3.n.a.179.14		204	1.1	even	1	trivial
405.3.n.a.179.21		204	5.4	even	2	inner
405.3.n.a.224.14		204	135.74	odd	18	inner
405.3.n.a.224.21		204	27.20	odd	18	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 405 = 3^{4} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	405.n (of order \(18\), degree \(6\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.721015 - 0.262428i) q^{2} +(-2.61318 - 2.19272i) q^{4} +(-2.96988 + 4.02242i) q^{5} +(3.17548 + 3.78438i) q^{7} +(2.84329 + 4.92472i) q^{8} +(3.19692 - 2.12084i) q^{10} +(-7.37526 + 1.30046i) q^{11} +(-6.15844 - 16.9202i) q^{13} +(-1.29644 - 3.56193i) q^{14} +(1.61177 + 9.14083i) q^{16} +(10.2979 - 17.8366i) q^{17} +(13.4766 + 23.3422i) q^{19} +(16.5809 - 3.99920i) q^{20} +(5.65895 + 0.997825i) q^{22} +(10.0889 + 8.46563i) q^{23} +(-7.35967 - 23.8922i) q^{25} +13.8158i q^{26} -16.8522i q^{28} +(13.1765 - 36.2022i) q^{29} +(-34.2162 - 28.7108i) q^{31} +(5.18655 - 29.4144i) q^{32} +(-12.1058 + 10.1580i) q^{34} +(-24.6531 + 1.53393i) q^{35} +(-39.3279 - 22.7060i) q^{37} +(-3.59121 - 20.3667i) q^{38} +(-28.2535 - 3.18892i) q^{40} +(-18.6544 - 51.2525i) q^{41} +(27.9365 - 4.92596i) q^{43} +(22.1245 + 12.7736i) q^{44} +(-5.05266 - 8.75146i) q^{46} +(21.0849 - 17.6923i) q^{47} +(4.27084 - 24.2211i) q^{49} +(-0.963538 + 19.1580i) q^{50} +(-21.0081 + 57.7193i) q^{52} +44.0339 q^{53} +(16.6726 - 33.5286i) q^{55} +(-9.60824 + 26.3984i) q^{56} +(-19.0009 + 22.6444i) q^{58} +(15.0907 + 2.66091i) q^{59} +(-44.3135 + 37.1834i) q^{61} +(17.1359 + 29.6802i) q^{62} +(7.10495 - 12.3061i) q^{64} +(86.3498 + 25.4790i) q^{65} +(-7.91614 - 21.7494i) q^{67} +(-66.0210 + 24.0297i) q^{68} +(18.1778 + 5.36368i) q^{70} +(-91.6966 - 52.9411i) q^{71} +(67.6524 - 39.0591i) q^{73} +(22.3973 + 26.6921i) q^{74} +(15.9661 - 90.5481i) q^{76} +(-28.3414 - 23.7813i) q^{77} +(64.5660 + 23.5001i) q^{79} +(-41.5550 - 20.6639i) q^{80} +41.8492i q^{82} +(71.0404 + 25.8566i) q^{83} +(41.1625 + 94.3950i) q^{85} +(-21.4353 - 3.77963i) q^{86} +(-27.3744 - 32.6235i) q^{88} +(-95.3491 + 55.0498i) q^{89} +(44.4765 - 77.0355i) q^{91} +(-7.80150 - 44.2445i) q^{92} +(-19.8455 + 7.22317i) q^{94} +(-133.916 - 15.1149i) q^{95} +(86.5584 - 15.2626i) q^{97} +(-9.43564 + 16.3430i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 204 q - 12 q^{4} - 3 q^{5} - 3 q^{10} - 6 q^{11} + 48 q^{14} + 12 q^{16} - 6 q^{19} - 63 q^{20} - 15 q^{25} - 96 q^{29} - 102 q^{31} + 12 q^{34} + 252 q^{35} + 117 q^{40} - 96 q^{41} + 666 q^{44} - 6 q^{46}+ \cdots + 543 q^{95}+O(q^{100}) \) 204 * q - 12 * q^4 - 3 * q^5 - 3 * q^10 - 6 * q^11 + 48 * q^14 + 12 * q^16 - 6 * q^19 - 63 * q^20 - 15 * q^25 - 96 * q^29 - 102 * q^31 + 12 * q^34 + 252 * q^35 + 117 * q^40 - 96 * q^41 + 666 * q^44 - 6 * q^46 + 60 * q^49 - 48 * q^50 - 12 * q^55 - 294 * q^56 - 510 * q^59 + 132 * q^61 - 486 * q^64 - 147 * q^65 - 141 * q^70 + 18 * q^71 + 954 * q^74 + 84 * q^76 - 48 * q^79 + 69 * q^85 + 1506 * q^86 - 792 * q^89 - 6 * q^91 + 492 * q^94 + 543 * q^95

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