LMFDB - Embedded newform 135.3.i.a.71.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [135,3,Mod(71,135)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(135, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([5, 0]))

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

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

chi := DirichletCharacter("135.71");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 135 = 3^{3} \cdot 5 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	135.i (of order $6$, degree $2$, 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:	$3.67848356886$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} + 48x^{14} + 912x^{12} + 8704x^{10} + 43602x^{8} + 109032x^{6} + 117844x^{4} + 36000x^{2} + 81 $ x^16 + 48x^14 + 912x^12 + 8704x^10 + 43602x^8 + 109032x^6 + 117844x^4 + 36000*x^2 + 81
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 3^{6} $
Twist minimal:	no (minimal twist has level 45)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			71.4
Root			$0.692902i$ of defining polynomial
Character	$\chi$	$=$	135.71
Dual form			135.3.i.a.116.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.600071 + 0.346451i) q^{2} +(-1.75994 + 3.04831i) q^{4} +(-1.93649 - 1.11803i) q^{5} +(-6.14112 - 10.6367i) q^{7} -5.21055i q^{8} +O(q^{10})$	\(q+(-0.600071 + 0.346451i) q^{2} +(-1.75994 + 3.04831i) q^{4} +(-1.93649 - 1.11803i) q^{5} +(-6.14112 - 10.6367i) q^{7} -5.21055i q^{8} +1.54938 q^{10} +(11.5582 - 6.67314i) q^{11} +(0.865680 - 1.49940i) q^{13} +(7.37022 + 4.25520i) q^{14} +(-5.23457 - 9.06655i) q^{16} -5.84583i q^{17} -16.8119 q^{19} +(6.81623 - 3.93535i) q^{20} +(-4.62383 + 8.00871i) q^{22} +(-28.8974 - 16.6839i) q^{23} +(2.50000 + 4.33013i) q^{25} +1.19966i q^{26} +43.2321 q^{28} +(-28.4290 + 16.4135i) q^{29} +(-0.0240073 + 0.0415819i) q^{31} +(24.3321 + 14.0481i) q^{32} +(2.02529 + 3.50791i) q^{34} +27.4639i q^{35} +29.7861 q^{37} +(10.0883 - 5.82451i) q^{38} +(-5.82557 + 10.0902i) q^{40} +(-8.34843 - 4.81997i) q^{41} +(-8.45424 - 14.6432i) q^{43} +46.9774i q^{44} +23.1206 q^{46} +(6.30332 - 3.63922i) q^{47} +(-50.9268 + 88.2078i) q^{49} +(-3.00035 - 1.73226i) q^{50} +(3.04710 + 5.27773i) q^{52} -29.6224i q^{53} -29.8432 q^{55} +(-55.4232 + 31.9986i) q^{56} +(11.3730 - 19.6985i) q^{58} +(79.7972 + 46.0709i) q^{59} +(10.0101 + 17.3380i) q^{61} -0.0332694i q^{62} +22.4086 q^{64} +(-3.35277 + 1.93572i) q^{65} +(17.4538 - 30.2308i) q^{67} +(17.8199 + 10.2883i) q^{68} +(-9.51491 - 16.4803i) q^{70} -83.7798i q^{71} -7.39110 q^{73} +(-17.8738 + 10.3194i) q^{74} +(29.5880 - 51.2480i) q^{76} +(-141.961 - 81.9612i) q^{77} +(-10.6039 - 18.3666i) q^{79} +23.4097i q^{80} +6.67953 q^{82} +(51.3619 - 29.6538i) q^{83} +(-6.53583 + 11.3204i) q^{85} +(10.1463 + 5.85796i) q^{86} +(-34.7707 - 60.2246i) q^{88} -46.7578i q^{89} -21.2650 q^{91} +(101.715 - 58.7254i) q^{92} +(-2.52163 + 4.36758i) q^{94} +(32.5561 + 18.7963i) q^{95} +(-11.5746 - 20.0478i) q^{97} -70.5746i q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 16 q^{4} + 2 q^{7}+O(q^{10}) $ 16 * q + 16 * q^4 + 2 * q^7	$ 16 q + 16 q^{4} + 2 q^{7} + 18 q^{11} - 10 q^{13} + 54 q^{14} - 32 q^{16} - 52 q^{19} - 24 q^{22} + 54 q^{23} + 40 q^{25} + 32 q^{28} + 54 q^{29} + 32 q^{31} - 216 q^{32} + 54 q^{34} + 44 q^{37} - 252 q^{38} - 30 q^{40} - 144 q^{41} - 124 q^{43} - 108 q^{46} + 216 q^{47} - 54 q^{49} + 62 q^{52} + 18 q^{56} + 90 q^{58} + 486 q^{59} + 62 q^{61} + 256 q^{64} + 90 q^{65} + 14 q^{67} + 288 q^{68} - 60 q^{70} - 268 q^{73} - 540 q^{74} - 106 q^{76} - 702 q^{77} - 40 q^{79} - 204 q^{82} - 522 q^{83} + 30 q^{85} - 54 q^{86} + 144 q^{88} + 136 q^{91} + 1332 q^{92} - 150 q^{94} - 180 q^{95} - 142 q^{97}+O(q^{100}) $ 16 * q + 16 * q^4 + 2 * q^7 + 18 * q^11 - 10 * q^13 + 54 * q^14 - 32 * q^16 - 52 * q^19 - 24 * q^22 + 54 * q^23 + 40 * q^25 + 32 * q^28 + 54 * q^29 + 32 * q^31 - 216 * q^32 + 54 * q^34 + 44 * q^37 - 252 * q^38 - 30 * q^40 - 144 * q^41 - 124 * q^43 - 108 * q^46 + 216 * q^47 - 54 * q^49 + 62 * q^52 + 18 * q^56 + 90 * q^58 + 486 * q^59 + 62 * q^61 + 256 * q^64 + 90 * q^65 + 14 * q^67 + 288 * q^68 - 60 * q^70 - 268 * q^73 - 540 * q^74 - 106 * q^76 - 702 * q^77 - 40 * q^79 - 204 * q^82 - 522 * q^83 + 30 * q^85 - 54 * q^86 + 144 * q^88 + 136 * q^91 + 1332 * q^92 - 150 * q^94 - 180 * q^95 - 142 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/135\mathbb{Z}\right)^\times$.

$n$	$56$	$82$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$1$

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 $

$2$	−0.600071	+	0.346451i	−0.300035	+	0.173226i	−0.642459	−	0.766320i	$-0.722086\pi$
$2$	−0.600071	+	0.346451i	−0.300035	+	0.173226i	0.342423	+	0.939546i	$0.388752\pi$
$3$		0			0
$3$		0			0
$4$	−1.75994	+	3.04831i	−0.439986	+	0.762078i
$5$	−1.93649	−	1.11803i	−0.387298	−	0.223607i
$5$	−1.93649	−	1.11803i	−0.387298	−	0.223607i
$6$		0			0
$7$	−6.14112	−	10.6367i	−0.877303	−	1.51953i	−0.854289	−	0.519799i	$-0.826007\pi$
$7$	−6.14112	−	10.6367i	−0.877303	−	1.51953i	−0.0230145	−	0.999735i	$-0.507326\pi$
$8$		−	5.21055i		−	0.651318i
$9$		0			0
$10$	1.54938			0.154938
$11$	11.5582	−	6.67314i	1.05075	−	0.606649i	0.127889	−	0.991789i	$-0.459180\pi$
$11$	11.5582	−	6.67314i	1.05075	−	0.606649i	0.922858	+	0.385139i	$0.125847\pi$
$12$		0			0
$13$	0.865680	−	1.49940i	0.0665908	−	0.115339i	−0.830808	−	0.556560i	$-0.812121\pi$
$13$	0.865680	−	1.49940i	0.0665908	−	0.115339i	0.897399	+	0.441221i	$0.145454\pi$
$14$	7.37022	+	4.25520i	0.526444	+	0.303943i
$15$		0			0
$16$	−5.23457	−	9.06655i	−0.327161	−	0.566659i
$17$		−	5.84583i		−	0.343872i	−0.985108	−	0.171936i	$-0.944998\pi$
$17$		−	5.84583i		−	0.343872i	0.985108	−	0.171936i	$-0.0550023\pi$
$18$		0			0
$19$	−16.8119			−0.884838			−0.442419	−	0.896809i	$-0.645880\pi$
$19$	−16.8119			−0.884838			−0.442419	+	0.896809i	$0.645880\pi$
$20$	6.81623	−	3.93535i	0.340812	−	0.196768i
$21$		0			0
$22$	−4.62383	+	8.00871i	−0.210174	+	0.364032i
$23$	−28.8974	−	16.6839i	−1.25641	−	0.725387i	−0.284033	−	0.958815i	$-0.591672\pi$
$23$	−28.8974	−	16.6839i	−1.25641	−	0.725387i	−0.972374	+	0.233428i	$0.925006\pi$
$24$		0			0
$25$	2.50000	+	4.33013i	0.100000	+	0.173205i
$26$			1.19966i			0.0461409i
$27$		0			0
$28$	43.2321			1.54400
$29$	−28.4290	+	16.4135i	−0.980312	+	0.565983i	−0.902364	−	0.430974i	$-0.858170\pi$
$29$	−28.4290	+	16.4135i	−0.980312	+	0.565983i	−0.0779475	+	0.996957i	$0.524837\pi$
$30$		0			0
$31$	−0.0240073	+	0.0415819i	−0.000774429	+	0.00134135i	−0.866412	−	0.499329i	$-0.833580\pi$
$31$	−0.0240073	+	0.0415819i	−0.000774429	+	0.00134135i	0.865638	+	0.500671i	$0.166913\pi$
$32$	24.3321	+	14.0481i	0.760378	+	0.439004i
$33$		0			0
$34$	2.02529	+	3.50791i	0.0595674	+	0.103174i
$35$			27.4639i			0.784684i
$36$		0			0
$37$	29.7861			0.805030			0.402515	−	0.915413i	$-0.368136\pi$
$37$	29.7861			0.805030			0.402515	+	0.915413i	$0.368136\pi$
$38$	10.0883	−	5.82451i	0.265483	−	0.153276i
$39$		0			0
$40$	−5.82557	+	10.0902i	−0.145639	+	0.252254i
$41$	−8.34843	−	4.81997i	−0.203620	−	0.117560i	0.394723	−	0.918800i	$-0.370841\pi$
$41$	−8.34843	−	4.81997i	−0.203620	−	0.117560i	−0.598343	+	0.801240i	$0.704174\pi$
$42$		0			0
$43$	−8.45424	−	14.6432i	−0.196610	−	0.340539i	0.750817	−	0.660510i	$-0.229660\pi$
$43$	−8.45424	−	14.6432i	−0.196610	−	0.340539i	−0.947427	+	0.319971i	$0.896327\pi$
$44$			46.9774i			1.06767i
$45$		0			0
$46$	23.1206			0.502622
$47$	6.30332	−	3.63922i	0.134113	−	0.0774303i	−0.431442	−	0.902141i	$-0.641995\pi$
$47$	6.30332	−	3.63922i	0.134113	−	0.0774303i	0.565555	+	0.824710i	$0.308662\pi$
$48$		0			0
$49$	−50.9268	+	88.2078i	−1.03932	+	1.80016i
$50$	−3.00035	−	1.73226i	−0.0600071	−	0.0346451i
$51$		0			0
$52$	3.04710	+	5.27773i	0.0585980	+	0.101495i
$53$		−	29.6224i		−	0.558913i	−0.960158	−	0.279457i	$-0.909846\pi$
$53$		−	29.6224i		−	0.558913i	0.960158	−	0.279457i	$-0.0901543\pi$
$54$		0			0
$55$	−29.8432			−0.542604
$56$	−55.4232	+	31.9986i	−0.989700	+	0.571404i
$57$		0			0
$58$	11.3730	−	19.6985i	0.196086	−	0.339630i
$59$	79.7972	+	46.0709i	1.35249	+	0.780863i	0.988598	−	0.150576i	$-0.0481129\pi$
$59$	79.7972	+	46.0709i	1.35249	+	0.780863i	0.363896	+	0.931439i	$0.381446\pi$
$60$		0			0
$61$	10.0101	+	17.3380i	0.164100	+	0.284229i	0.936335	−	0.351108i	$-0.114195\pi$
$61$	10.0101	+	17.3380i	0.164100	+	0.284229i	−0.772236	+	0.635336i	$0.780862\pi$
$62$		−	0.0332694i		−	0.000536604i
$63$		0			0
$64$	22.4086			0.350135
$65$	−3.35277	+	1.93572i	−0.0515810	+	0.0297803i
$66$		0			0
$67$	17.4538	−	30.2308i	0.260504	−	0.451207i	−0.705872	−	0.708340i	$-0.749445\pi$
$67$	17.4538	−	30.2308i	0.260504	−	0.451207i	0.966376	+	0.257133i	$0.0827779\pi$
$68$	17.8199	+	10.2883i	0.262057	+	0.151299i
$69$		0			0
$70$	−9.51491	−	16.4803i	−0.135927	−	0.235433i
$71$		−	83.7798i		−	1.18000i	−0.807404	−	0.589998i	$-0.799128\pi$
$71$		−	83.7798i		−	1.18000i	0.807404	−	0.589998i	$-0.200872\pi$
$72$		0			0
$73$	−7.39110			−0.101248			−0.0506240	−	0.998718i	$-0.516121\pi$
$73$	−7.39110			−0.101248			−0.0506240	+	0.998718i	$0.516121\pi$
$74$	−17.8738	+	10.3194i	−0.241538	+	0.139452i
$75$		0			0
$76$	29.5880	−	51.2480i	0.389316	−	0.674315i
$77$	−141.961	−	81.9612i	−1.84365	−	1.06443i
$78$		0			0
$79$	−10.6039	−	18.3666i	−0.134227	−	0.232488i	0.791075	−	0.611719i	$-0.209522\pi$
$79$	−10.6039	−	18.3666i	−0.134227	−	0.232488i	−0.925302	+	0.379231i	$0.876188\pi$
$80$			23.4097i			0.292622i
$81$		0			0
$82$	6.67953			0.0814577
$83$	51.3619	−	29.6538i	0.618818	−	0.357275i	−0.157591	−	0.987505i	$-0.550373\pi$
$83$	51.3619	−	29.6538i	0.618818	−	0.357275i	0.776409	+	0.630230i	$0.217039\pi$
$84$		0			0
$85$	−6.53583	+	11.3204i	−0.0768921	+	0.133181i
$86$	10.1463	+	5.85796i	0.117980	+	0.0681158i
$87$		0			0
$88$	−34.7707	−	60.2246i	−0.395122	−	0.684371i
$89$		−	46.7578i		−	0.525369i	−0.964882	−	0.262684i	$-0.915392\pi$
$89$		−	46.7578i		−	0.525369i	0.964882	−	0.262684i	$-0.0846078\pi$
$90$		0			0
$91$	−21.2650			−0.233681
$92$	101.715	−	58.7254i	1.10560	−	0.638320i
$93$		0			0
$94$	−2.52163	+	4.36758i	−0.0268258	+	0.0464637i
$95$	32.5561	+	18.7963i	0.342696	+	0.197856i
$96$		0			0
$97$	−11.5746	−	20.0478i	−0.119326	−	0.206678i	0.800175	−	0.599767i	$-0.204740\pi$
$97$	−11.5746	−	20.0478i	−0.119326	−	0.206678i	−0.919501	+	0.393088i	$0.871407\pi$
$98$		−	70.5746i		−	0.720148i
$99$		0			0
$100$	−17.5994			−0.175994
$101$	27.8068	−	16.0542i	0.275315	−	0.158953i	−0.355986	−	0.934491i	$-0.615855\pi$
$101$	27.8068	−	16.0542i	0.275315	−	0.158953i	0.631300	+	0.775538i	$0.282522\pi$
$102$		0			0
$103$	67.3143	−	116.592i	0.653537	−	1.13196i	−0.328721	−	0.944427i	$-0.606618\pi$
$103$	67.3143	−	116.592i	0.653537	−	1.13196i	0.982258	−	0.187533i	$-0.0600490\pi$
$104$	−7.81270	−	4.51067i	−0.0751222	−	0.0433718i
$105$		0			0
$106$	10.2627	+	17.7755i	0.0968180	+	0.167694i
$107$			181.601i			1.69720i	0.529034	+	0.848601i	$0.322554\pi$
$107$			181.601i			1.69720i	−0.529034	+	0.848601i	$0.677446\pi$
$108$		0			0
$109$	−153.622			−1.40938			−0.704690	−	0.709515i	$-0.748914\pi$
$109$	−153.622			−1.40938			−0.704690	+	0.709515i	$0.748914\pi$
$110$	17.9080	−	10.3392i	0.162800	−	0.0939928i
$111$		0			0
$112$	−64.2923	+	111.358i	−0.574039	+	0.994264i
$113$	8.28290	+	4.78214i	0.0733000	+	0.0423198i	0.536202	−	0.844090i	$-0.319859\pi$
$113$	8.28290	+	4.78214i	0.0733000	+	0.0423198i	−0.462902	+	0.886409i	$0.653192\pi$
$114$		0			0
$115$	37.3063	+	64.6164i	0.324403	+	0.561882i
$116$		−	115.547i		−	0.996099i
$117$		0			0
$118$	−63.8453			−0.541062
$119$	−62.1805	+	35.8999i	−0.522525	+	0.301680i
$120$		0			0
$121$	28.5616	−	49.4702i	0.236046	−	0.408844i
$122$	−12.0135	−	6.93600i	−0.0984713	−	0.0568525i
$123$		0			0
$124$	−0.0845030	−	0.146364i	−0.000681476	−	0.00118035i
$125$		−	11.1803i		−	0.0894427i
$126$		0			0
$127$	−85.6937			−0.674754			−0.337377	−	0.941370i	$-0.609540\pi$
$127$	−85.6937			−0.674754			−0.337377	+	0.941370i	$0.609540\pi$
$128$	−110.775	+	63.9560i	−0.865431	+	0.499657i
$129$		0			0
$130$	1.34126	−	2.32314i	0.0103174	−	0.0178703i
$131$	78.9075	+	45.5573i	0.602347	+	0.347765i	0.769964	−	0.638087i	$-0.220274\pi$
$131$	78.9075	+	45.5573i	0.602347	+	0.347765i	−0.167617	+	0.985852i	$0.553607\pi$
$132$		0			0
$133$	103.244	+	178.824i	0.776271	+	1.34454i
$134$			24.1875i			0.180504i
$135$		0			0
$136$	−30.4599			−0.223970
$137$	28.9260	−	16.7004i	0.211139	−	0.121901i	−0.390702	−	0.920517i	$-0.627768\pi$
$137$	28.9260	−	16.7004i	0.211139	−	0.121901i	0.601841	+	0.798616i	$0.294434\pi$
$138$		0			0
$139$	124.523	−	215.680i	0.895846	−	1.55165i	0.0630929	−	0.998008i	$-0.479904\pi$
$139$	124.523	−	215.680i	0.895846	−	1.55165i	0.832754	−	0.553644i	$-0.186763\pi$
$140$	−83.7186	−	48.3350i	−0.597990	−	0.345250i
$141$		0			0
$142$	29.0256	+	50.2738i	0.204406	+	0.354041i
$143$		−	23.1072i		−	0.161589i
$144$		0			0
$145$	73.4035			0.506231
$146$	4.43519	−	2.56066i	0.0303780	−	0.0175387i
$147$		0			0
$148$	−52.4219	+	90.7974i	−0.354202	+	0.613496i
$149$	102.542	+	59.2028i	0.688203	+	0.397334i	0.802938	−	0.596062i	$-0.203269\pi$
$149$	102.542	+	59.2028i	0.688203	+	0.397334i	−0.114736	+	0.993396i	$0.536602\pi$
$150$		0			0
$151$	80.7781	+	139.912i	0.534954	+	0.926568i	0.999166	+	0.0408436i	$0.0130045\pi$
$151$	80.7781	+	139.912i	0.534954	+	0.926568i	−0.464211	+	0.885725i	$0.653662\pi$
$152$			87.5993i			0.576311i
$153$		0			0
$154$	113.582			0.737546
$155$	0.0929799	−	0.0536820i	0.000599870	−	0.000346335i
$156$		0			0
$157$	74.3645	−	128.803i	0.473659	−	0.820402i	−0.525886	−	0.850555i	$-0.676266\pi$
$157$	74.3645	−	128.803i	0.473659	−	0.820402i	0.999545	+	0.0301530i	$0.00959944\pi$
$158$	12.7262	+	7.34749i	0.0805457	+	0.0465031i
$159$		0			0
$160$	−31.4126	−	54.4082i	−0.196329	−	0.340051i
$161$			409.831i			2.54554i
$162$		0			0
$163$	88.1083			0.540542			0.270271	−	0.962784i	$-0.412887\pi$
$163$	88.1083			0.540542			0.270271	+	0.962784i	$0.412887\pi$
$164$	29.3855	−	16.9657i	0.179180	−	0.103450i
$165$		0			0
$166$	−20.5472	+	35.5888i	−0.123778	+	0.214390i
$167$	−124.148	−	71.6766i	−0.743399	−	0.429201i	0.0799051	−	0.996802i	$-0.474538\pi$
$167$	−124.148	−	71.6766i	−0.743399	−	0.429201i	−0.823304	+	0.567601i	$0.807872\pi$
$168$		0			0
$169$	83.0012	+	143.762i	0.491131	+	0.850664i
$170$		−	9.05738i		−	0.0532787i
$171$		0			0
$172$	59.5159			0.346023
$173$	−210.230	+	121.376i	−1.21520	+	0.701597i	−0.963888	−	0.266309i	$-0.914196\pi$
$173$	−210.230	+	121.376i	−1.21520	+	0.701597i	−0.251314	+	0.967906i	$0.580863\pi$
$174$		0			0
$175$	30.7056	−	53.1837i	0.175461	−	0.303907i
$176$	−121.005	−	69.8621i	−0.687527	−	0.396944i
$177$		0			0
$178$	16.1993	+	28.0580i	0.0910073	+	0.157629i
$179$		−	341.991i		−	1.91056i	−0.295698	−	0.955282i	$-0.595552\pi$
$179$		−	341.991i		−	1.91056i	0.295698	−	0.955282i	$-0.404448\pi$
$180$		0			0
$181$	−179.761			−0.993154			−0.496577	−	0.867993i	$-0.665410\pi$
$181$	−179.761			−0.993154			−0.496577	+	0.867993i	$0.665410\pi$
$182$	12.7605	−	7.36728i	0.0701127	−	0.0404796i
$183$		0			0
$184$	−86.9322	+	150.571i	−0.472458	+	0.818321i
$185$	−57.6806	−	33.3019i	−0.311787	−	0.180010i
$186$		0			0
$187$	−39.0100	−	67.5673i	−0.208610	−	0.361323i
$188$			25.6193i			0.136273i
$189$		0			0
$190$	−26.0480			−0.137095
$191$	194.687	−	112.403i	1.01931	−	0.588496i	0.105403	−	0.994430i	$-0.466387\pi$
$191$	194.687	−	112.403i	1.01931	−	0.588496i	0.913903	+	0.405933i	$0.133054\pi$
$192$		0			0
$193$	−135.578	+	234.828i	−0.702476	+	1.21672i	0.265118	+	0.964216i	$0.414589\pi$
$193$	−135.578	+	234.828i	−0.702476	+	1.21672i	−0.967595	+	0.252509i	$0.918744\pi$
$194$	13.8912	+	8.02007i	0.0716040	+	0.0413406i
$195$		0			0
$196$	−179.257	−	310.481i	−0.914574	−	1.58409i
$197$		−	11.6900i		−	0.0593399i	−0.999560	−	0.0296699i	$-0.990554\pi$
$197$		−	11.6900i		−	0.0593399i	0.999560	−	0.0296699i	$-0.00944562\pi$
$198$		0			0
$199$	230.832			1.15996			0.579979	−	0.814632i	$-0.303061\pi$
$199$	230.832			1.15996			0.579979	+	0.814632i	$0.303061\pi$
$200$	22.5623	−	13.0264i	0.112812	−	0.0651318i
$201$		0			0
$202$	−11.1240	+	19.2674i	−0.0550694	+	0.0953830i
$203$	349.172	+	201.595i	1.72006	+	0.993078i
$204$		0			0
$205$	10.7778	+	18.6676i	0.0525745	+	0.0910617i
$206$			93.2845i			0.452837i
$207$		0			0
$208$	−18.1259			−0.0871436
$209$	−194.316	+	112.188i	−0.929741	+	0.536786i
$210$		0			0
$211$	−97.7462	+	169.301i	−0.463252	+	0.802376i	−0.999121	−	0.0419252i	$-0.986651\pi$
$211$	−97.7462	+	169.301i	−0.463252	+	0.802376i	0.535869	+	0.844301i	$0.319984\pi$
$212$	90.2983	+	52.1337i	0.425935	+	0.245914i
$213$		0			0
$214$	−62.9157	−	108.973i	−0.293999	−	0.509221i
$215$			37.8085i			0.175854i
$216$		0			0
$217$	0.589727			0.00271764
$218$	92.1844	−	53.2227i	0.422864	−	0.244141i
$219$		0			0
$220$	52.5223	−	90.9713i	0.238738	−	0.413506i
$221$	−8.76525	−	5.06062i	−0.0396617	−	0.0228987i
$222$		0			0
$223$	−152.251	−	263.707i	−0.682741	−	1.18254i	−0.974141	−	0.225941i	$-0.927454\pi$
$223$	−152.251	−	263.707i	−0.682741	−	1.18254i	0.291400	−	0.956601i	$-0.405879\pi$
$224$		−	345.085i		−	1.54056i
$225$		0			0
$226$	−6.62710			−0.0293235
$227$	321.657	−	185.709i	1.41699	−	0.818100i	0.420957	−	0.907080i	$-0.361694\pi$
$227$	321.657	−	185.709i	1.41699	−	0.818100i	0.996033	+	0.0889806i	$0.0283609\pi$
$228$		0			0
$229$	189.778	−	328.706i	0.828726	−	1.43540i	−0.0703123	−	0.997525i	$-0.522400\pi$
$229$	189.778	−	328.706i	0.828726	−	1.43540i	0.899038	−	0.437870i	$-0.144267\pi$
$230$	−44.7729	−	25.8496i	−0.194665	−	0.112390i
$231$		0			0
$232$	85.5234	+	148.131i	0.368635	+	0.638495i
$233$			39.8225i			0.170912i	0.996342	+	0.0854561i	$0.0272347\pi$
$233$			39.8225i			0.170912i	−0.996342	+	0.0854561i	$0.972765\pi$
$234$		0			0
$235$	−16.2751			−0.0692558
$236$	−280.877	+	162.164i	−1.19016	+	0.687138i
$237$		0			0
$238$	24.8751	−	43.0850i	0.104517	−	0.181029i
$239$	−249.563	−	144.085i	−1.04420	−	0.602867i	−0.123178	−	0.992385i	$-0.539309\pi$
$239$	−249.563	−	144.085i	−1.04420	−	0.602867i	−0.921019	+	0.389517i	$0.872642\pi$
$240$		0			0
$241$	98.7566	+	171.051i	0.409778	+	0.709757i	0.994865	−	0.101214i	$-0.0322728\pi$
$241$	98.7566	+	171.051i	0.409778	+	0.709757i	−0.585086	+	0.810971i	$0.698939\pi$
$242$			39.5808i			0.163557i
$243$		0			0
$244$	−70.4686			−0.288806
$245$	197.239	−	113.876i	0.805055	−	0.464799i
$246$		0			0
$247$	−14.5537	+	25.2078i	−0.0589221	+	0.102056i
$248$	0.216664	+	0.125091i	0.000873646	+	0.000504400i
$249$		0			0
$250$	3.87344	+	6.70900i	0.0154938	+	0.0268360i
$251$		−	271.187i		−	1.08043i	−0.841528	−	0.540213i	$-0.818343\pi$
$251$		−	271.187i		−	1.08043i	0.841528	−	0.540213i	$-0.181657\pi$
$252$		0			0
$253$	−445.336			−1.76022
$254$	51.4223	−	29.6887i	0.202450	−	0.116885i
$255$		0			0
$256$	−0.501974	+	0.869445i	−0.00196084	+	0.00339627i
$257$	−51.9789	−	30.0100i	−0.202252	−	0.116771i	0.395453	−	0.918486i	$-0.370588\pi$
$257$	−51.9789	−	30.0100i	−0.202252	−	0.116771i	−0.597706	+	0.801716i	$0.703921\pi$
$258$		0			0
$259$	−182.920	−	316.827i	−0.706256	−	1.22327i
$260$		−	13.6270i		−	0.0524117i
$261$		0			0
$262$	−63.1334			−0.240967
$263$	−231.720	+	133.784i	−0.881067	+	0.508684i	−0.871010	−	0.491265i	$-0.836535\pi$
$263$	−231.720	+	133.784i	−0.881067	+	0.508684i	−0.0100566	+	0.999949i	$0.503201\pi$
$264$		0			0
$265$	−33.1188	+	57.3635i	−0.124977	+	0.216466i
$266$	−123.907	−	71.5380i	−0.465818	−	0.268940i
$267$		0			0
$268$	61.4353	+	106.409i	0.229236	+	0.397049i
$269$		−	113.033i		−	0.420199i	−0.977680	−	0.210099i	$-0.932621\pi$
$269$		−	113.033i		−	0.420199i	0.977680	−	0.210099i	$-0.0673788\pi$
$270$		0			0
$271$	431.200			1.59114			0.795572	−	0.605860i	$-0.207171\pi$
$271$	431.200			1.59114			0.795572	+	0.605860i	$0.207171\pi$
$272$	−53.0015	+	30.6004i	−0.194858	+	0.112502i
$273$		0			0
$274$	−11.5718	+	20.0429i	−0.0422327	+	0.0731492i
$275$	57.7911	+	33.3657i	0.210149	+	0.121330i
$276$		0			0
$277$	−73.7127	−	127.674i	−0.266111	−	0.460917i	0.701743	−	0.712430i	$-0.252405\pi$
$277$	−73.7127	−	127.674i	−0.266111	−	0.460917i	−0.967854	+	0.251513i	$0.919072\pi$
$278$			172.564i			0.620734i
$279$		0			0
$280$	143.102			0.511079
$281$	51.5187	−	29.7444i	0.183341	−	0.105852i	−0.405521	−	0.914086i	$-0.632910\pi$
$281$	51.5187	−	29.7444i	0.183341	−	0.105852i	0.588861	+	0.808234i	$0.299576\pi$
$282$		0			0
$283$	−90.6633	+	157.033i	−0.320365	+	0.554888i	−0.980563	−	0.196203i	$-0.937139\pi$
$283$	−90.6633	+	157.033i	−0.320365	+	0.554888i	0.660198	+	0.751091i	$0.270472\pi$
$284$	255.387	+	147.448i	0.899249	+	0.519182i
$285$		0			0
$286$	8.00552	+	13.8660i	0.0279913	+	0.0484824i
$287$			118.400i			0.412544i
$288$		0			0
$289$	254.826			0.881752
$290$	−44.0473	+	25.4307i	−0.151887	+	0.0876921i
$291$		0			0
$292$	13.0079	−	22.5304i	0.0445477	−	0.0771589i
$293$	−29.9303	−	17.2803i	−0.102151	−	0.0589771i	0.448054	−	0.894006i	$-0.352117\pi$
$293$	−29.9303	−	17.2803i	−0.102151	−	0.0589771i	−0.550205	+	0.835029i	$0.685451\pi$
$294$		0			0
$295$	−103.018	−	178.432i	−0.349213	−	0.604854i
$296$		−	155.202i		−	0.524331i
$297$		0			0
$298$	−82.0434			−0.275314
$299$	−50.0317	+	28.8858i	−0.167330	+	0.0966082i
$300$		0			0
$301$	−103.837	+	179.851i	−0.344974	+	0.597512i
$302$	−96.9452	−	55.9713i	−0.321011	−	0.185336i
$303$		0			0
$304$	88.0032	+	152.426i	0.289484	+	0.501402i
$305$		−	44.7664i		−	0.146775i
$306$		0			0
$307$	42.5201			0.138502			0.0692509	−	0.997599i	$-0.477939\pi$
$307$	42.5201			0.138502			0.0692509	+	0.997599i	$0.477939\pi$
$308$	499.686	−	288.494i	1.62236	−	0.936669i
$309$		0			0
$310$	−0.0371964	+	0.0644260i	−0.000119988	+	0.000207826i
$311$	462.711	+	267.146i	1.48782	+	0.858991i	0.999903	−	0.0139020i	$-0.00442529\pi$
$311$	462.711	+	267.146i	1.48782	+	0.858991i	0.487912	+	0.872893i	$0.337759\pi$
$312$		0			0
$313$	−36.1934	−	62.6888i	−0.115634	−	0.200284i	0.802399	−	0.596788i	$-0.203557\pi$
$313$	−36.1934	−	62.6888i	−0.115634	−	0.200284i	−0.918033	+	0.396504i	$0.870223\pi$
$314$			103.055i			0.328200i
$315$		0			0
$316$	74.6493			0.236232
$317$	−266.939	+	154.118i	−0.842080	+	0.486175i	−0.857971	−	0.513698i	$-0.828275\pi$
$317$	−266.939	+	154.118i	−0.842080	+	0.486175i	0.0158904	+	0.999874i	$0.494942\pi$
$318$		0			0
$319$	−219.059	+	379.422i	−0.686707	+	1.18941i
$320$	−43.3941	−	25.0536i	−0.135607	−	0.0782925i
$321$		0			0
$322$	−141.987	−	245.928i	−0.440952	−	0.763751i
$323$			98.2796i			0.304271i
$324$		0			0
$325$	8.65680			0.0266363
$326$	−52.8712	+	30.5252i	−0.162182	+	0.0936356i
$327$		0			0
$328$	−25.1146	+	43.4998i	−0.0765691	+	0.132621i
$329$	−77.4189	−	44.6978i	−0.235316	−	0.135860i
$330$		0			0
$331$	−31.0713	−	53.8170i	−0.0938709	−	0.162589i	0.815266	−	0.579087i	$-0.196591\pi$
$331$	−31.0713	−	53.8170i	−0.0938709	−	0.162589i	−0.909137	+	0.416498i	$0.863257\pi$
$332$			208.756i			0.628783i
$333$		0			0
$334$	99.3298			0.297395
$335$	−67.5982	+	39.0279i	−0.201786	+	0.116501i
$336$		0			0
$337$	−59.4302	+	102.936i	−0.176351	+	0.305448i	−0.940628	−	0.339440i	$-0.889763\pi$
$337$	−59.4302	+	102.936i	−0.176351	+	0.305448i	0.764277	+	0.644888i	$0.223096\pi$
$338$	−99.6132	−	57.5117i	−0.294714	−	0.170153i
$339$		0			0
$340$	−23.0054	−	39.8465i	−0.0676629	−	0.117196i
$341$			0.640817i			0.00187923i
$342$		0			0
$343$	649.161			1.89260
$344$	−76.2989	+	44.0512i	−0.221799	+	0.128056i
$345$		0			0
$346$	84.1019	−	145.669i	0.243069	−	0.421008i
$347$	−525.488	−	303.391i	−1.51437	−	0.874324i	−0.999858	−	0.0168433i	$-0.994638\pi$
$347$	−525.488	−	303.391i	−1.51437	−	0.874324i	−0.514516	−	0.857481i	$-0.672028\pi$
$348$		0			0
$349$	155.581	+	269.475i	0.445792	+	0.772135i	0.998107	−	0.0615009i	$-0.0195887\pi$
$349$	155.581	+	269.475i	0.445792	+	0.772135i	−0.552315	+	0.833636i	$0.686255\pi$
$350$			42.5520i			0.121577i
$351$		0			0
$352$	374.981			1.06529
$353$	−183.381	+	105.875i	−0.519493	+	0.299930i	−0.736727	−	0.676190i	$-0.763630\pi$
$353$	−183.381	+	105.875i	−0.519493	+	0.299930i	0.217234	+	0.976120i	$0.430297\pi$
$354$		0			0
$355$	−93.6686	+	162.239i	−0.263855	+	0.457011i
$356$	142.532	+	82.2911i	0.400372	+	0.231155i
$357$		0			0
$358$	118.483	+	205.219i	0.330958	+	0.573237i
$359$			537.972i			1.49853i	0.662271	+	0.749264i	$0.269593\pi$
$359$			537.972i			1.49853i	−0.662271	+	0.749264i	$0.730407\pi$
$360$		0			0
$361$	−78.3594			−0.217062
$362$	107.869	−	62.2783i	0.297981	−	0.172040i
$363$		0			0
$364$	37.4252	−	64.8223i	0.102816	−	0.178083i
$365$	14.3128	+	8.26351i	0.0392132	+	0.0226397i
$366$		0			0
$367$	113.608	+	196.775i	0.309559	+	0.536171i	0.978266	−	0.207354i	$-0.0664853\pi$
$367$	113.608	+	196.775i	0.309559	+	0.536171i	−0.668707	+	0.743526i	$0.733152\pi$
$368$			349.332i			0.949273i
$369$		0			0
$370$	46.1499			0.124730
$371$	−315.086	+	181.915i	−0.849287	+	0.490336i
$372$		0			0
$373$	198.790	−	344.315i	0.532950	−	0.923096i	−0.466310	−	0.884621i	$-0.654417\pi$
$373$	198.790	−	344.315i	0.532950	−	0.923096i	0.999260	−	0.0384743i	$-0.0122498\pi$
$374$	46.8176	+	27.0301i	0.125181	+	0.0722731i
$375$		0			0
$376$	−18.9623	−	32.8437i	−0.0504318	−	0.0873504i
$377$			56.8354i			0.150757i
$378$		0			0
$379$	−583.745			−1.54022			−0.770112	−	0.637908i	$-0.779800\pi$
$379$	−583.745			−1.54022			−0.770112	+	0.637908i	$0.779800\pi$
$380$	−114.594	+	66.1608i	−0.301563	+	0.174107i
$381$		0			0
$382$	−77.8841	+	134.899i	−0.203885	+	0.353139i
$383$	−179.618	−	103.702i	−0.468976	−	0.270763i	0.246835	−	0.969058i	$-0.420609\pi$
$383$	−179.618	−	103.702i	−0.468976	−	0.270763i	−0.715811	+	0.698294i	$0.753943\pi$
$384$		0			0
$385$	183.271	+	317.434i	0.476028	+	0.824504i
$386$		−	187.884i		−	0.486747i
$387$		0			0
$388$	81.4826			0.210007
$389$	310.718	−	179.393i	0.798762	−	0.461165i	−0.0442761	−	0.999019i	$-0.514098\pi$
$389$	310.718	−	179.393i	0.798762	−	0.461165i	0.843038	+	0.537854i	$0.180765\pi$
$390$		0			0
$391$	−97.5312	+	168.929i	−0.249440	+	0.432043i
$392$	459.611	+	265.356i	1.17248	+	0.676929i
$393$		0			0
$394$	4.05000	+	7.01480i	0.0102792	+	0.0178041i
$395$			47.4222i			0.120056i
$396$		0			0
$397$	−667.571			−1.68154			−0.840770	−	0.541392i	$-0.817897\pi$
$397$	−667.571			−1.68154			−0.840770	+	0.541392i	$0.817897\pi$
$398$	−138.515	+	79.9718i	−0.348028	+	0.200934i
$399$		0			0
$400$	26.1729	−	45.3327i	0.0654322	−	0.113332i
$401$	−187.786	−	108.418i	−0.468294	−	0.270370i	0.247231	−	0.968956i	$-0.420479\pi$
$401$	−187.786	−	108.418i	−0.468294	−	0.270370i	−0.715525	+	0.698587i	$0.753813\pi$
$402$		0			0
$403$	0.0415653	+	0.0719932i	0.000103140	+	0.000178643i
$404$			113.018i			0.279748i
$405$		0			0
$406$	−279.371			−0.688106
$407$	344.275	−	198.767i	0.845883	−	0.488371i
$408$		0			0
$409$	199.674	−	345.845i	0.488200	−	0.845587i	−0.511708	−	0.859159i	$-0.670987\pi$
$409$	199.674	−	345.845i	0.488200	−	0.845587i	0.999908	+	0.0135724i	$0.00432036\pi$
$410$	−12.9349	−	7.46794i	−0.0315484	−	0.0182145i
$411$		0			0
$412$	236.939	+	410.390i	0.575094	+	0.996092i
$413$		−	1131.71i		−	2.74022i
$414$		0			0
$415$	−132.616			−0.319556
$416$	42.1276	−	24.3224i	0.101268	−	0.0584673i
$417$		0			0
$418$	77.7355	−	134.642i	0.185970	−	0.322110i
$419$	84.0379	+	48.5193i	0.200568	+	0.115798i	0.596920	−	0.802301i	$-0.296391\pi$
$419$	84.0379	+	48.5193i	0.200568	+	0.115798i	−0.396353	+	0.918098i	$0.629724\pi$
$420$		0			0
$421$	−196.281	−	339.968i	−0.466225	−	0.807525i	0.533031	−	0.846096i	$-0.321053\pi$
$421$	−196.281	−	339.968i	−0.466225	−	0.807525i	−0.999256	+	0.0385706i	$0.987720\pi$
$422$		−	135.457i		−	0.320988i
$423$		0			0
$424$	−154.349			−0.364030
$425$	25.3132	−	14.6146i	0.0595604	−	0.0343872i
$426$		0			0
$427$	122.946	−	212.949i	0.287930	−	0.498710i
$428$	−553.575	−	319.607i	−1.29340	−	0.746745i
$429$		0			0
$430$	−13.0988	−	22.6878i	−0.0304623	−	0.0527623i
$431$			59.7762i			0.138692i	0.997593	+	0.0693459i	$0.0220912\pi$
$431$			59.7762i			0.138692i	−0.997593	+	0.0693459i	$0.977909\pi$
$432$		0			0
$433$	−11.3594			−0.0262341			−0.0131171	−	0.999914i	$-0.504175\pi$
$433$	−11.3594			−0.0262341			−0.0131171	+	0.999914i	$0.504175\pi$
$434$	−0.353878	+	0.204312i	−0.000815388	+	0.000470764i
$435$		0			0
$436$	270.367	−	468.289i	0.620107	−	1.07406i
$437$	485.820	+	280.488i	1.11172	+	0.641850i
$438$		0			0
$439$	−167.351	−	289.860i	−0.381209	−	0.660273i	0.610026	−	0.792381i	$-0.291159\pi$
$439$	−167.351	−	289.860i	−0.381209	−	0.660273i	−0.991235	+	0.132108i	$0.957825\pi$
$440$			155.499i			0.353408i
$441$		0			0
$442$	7.01302			0.0158666
$443$	466.284	−	269.209i	1.05256	−	0.607696i	0.129196	−	0.991619i	$-0.458760\pi$
$443$	466.284	−	269.209i	1.05256	−	0.607696i	0.923365	+	0.383923i	$0.125427\pi$
$444$		0			0
$445$	−52.2768	+	90.5461i	−0.117476	+	0.203474i
$446$	182.723	+	105.495i	0.409693	+	0.236536i
$447$		0			0
$448$	−137.614	−	238.355i	−0.307174	−	0.532042i
$449$		−	17.7036i		−	0.0394290i	−0.999806	−	0.0197145i	$-0.993724\pi$
$449$		−	17.7036i		−	0.0394290i	0.999806	−	0.0197145i	$-0.00627572\pi$
$450$		0			0
$451$	−128.657			−0.285271
$452$	−29.1549	+	16.8326i	−0.0645019	+	0.0372402i
$453$		0			0
$454$	−128.678	+	222.877i	−0.283432	+	0.490918i
$455$	41.1795	+	23.7750i	0.0905044	+	0.0522527i
$456$		0			0
$457$	−45.3152	−	78.4883i	−0.0991580	−	0.171747i	0.812178	−	0.583409i	$-0.198282\pi$
$457$	−45.3152	−	78.4883i	−0.0991580	−	0.171747i	−0.911336	+	0.411662i	$0.864948\pi$
$458$			262.995i			0.574226i
$459$		0			0
$460$	−262.628			−0.570931
$461$	339.780	−	196.172i	0.737050	−	0.425536i	−0.0839455	−	0.996470i	$-0.526752\pi$
$461$	339.780	−	196.172i	0.737050	−	0.425536i	0.820996	+	0.570934i	$0.193419\pi$
$462$		0			0
$463$	206.709	−	358.031i	0.446457	−	0.773285i	−0.551696	−	0.834045i	$-0.686019\pi$
$463$	206.709	−	358.031i	0.446457	−	0.773285i	0.998152	+	0.0607600i	$0.0193524\pi$
$464$	297.628	+	171.836i	0.641439	+	0.370335i
$465$		0			0
$466$	−13.7966	−	23.8963i	−0.0296063	−	0.0512797i
$467$		−	700.469i		−	1.49993i	−0.661475	−	0.749967i	$-0.730069\pi$
$467$		−	700.469i		−	1.49993i	0.661475	−	0.749967i	$-0.269931\pi$
$468$		0			0
$469$	−428.743			−0.914165
$470$	9.76621	−	5.63853i	0.0207792	−	0.0119969i
$471$		0			0
$472$	240.055	−	415.787i	0.508590	−	0.880904i
$473$	−195.432	−	112.833i	−0.413175	−	0.238547i
$474$		0			0
$475$	−42.0298	−	72.7977i	−0.0884838	−	0.153258i
$476$		−	252.727i		−	0.530940i
$477$		0			0
$478$	199.674			0.417728
$479$	−158.875	+	91.7265i	−0.331680	+	0.191496i	−0.656587	−	0.754250i	$-0.728000\pi$
$479$	−158.875	+	91.7265i	−0.331680	+	0.191496i	0.324906	+	0.945746i	$0.394667\pi$
$480$		0			0
$481$	25.7853	−	44.6614i	0.0536076	−	0.0928511i
$482$	−118.522	−	68.4286i	−0.245896	−	0.141968i
$483$		0			0
$484$	100.534	+	174.129i	0.207714	+	0.359771i
$485$			51.7632i			0.106728i
$486$		0			0
$487$	247.290			0.507783			0.253891	−	0.967233i	$-0.418289\pi$
$487$	247.290			0.507783			0.253891	+	0.967233i	$0.418289\pi$
$488$	90.3402	−	52.1579i	0.185123	−	0.106881i
$489$		0			0
$490$	−78.9047	+	136.667i	−0.161030	+	0.278912i
$491$	−641.600	−	370.428i	−1.30672	−	0.754436i	−0.325174	−	0.945654i	$-0.605423\pi$
$491$	−641.600	−	370.428i	−1.30672	−	0.754436i	−0.981548	+	0.191218i	$0.938756\pi$
$492$		0			0
$493$	95.9506	+	166.191i	0.194626	+	0.337102i
$494$		−	20.1686i		−	0.0408272i
$495$		0			0
$496$	0.502672			0.00101345
$497$	−891.143	+	514.502i	−1.79305	+	1.03522i
$498$		0			0
$499$	−433.389	+	750.651i	−0.868514	+	1.50431i	−0.00499918	+	0.999988i	$0.501591\pi$
$499$	−433.389	+	750.651i	−0.868514	+	1.50431i	−0.863515	+	0.504323i	$0.831742\pi$
$500$	34.0812	+	19.6768i	0.0681623	+	0.0393535i
$501$		0			0
$502$	93.9531	+	162.732i	0.187158	+	0.324166i
$503$		−	515.541i		−	1.02493i	−0.858708	−	0.512466i	$-0.828732\pi$
$503$		−	515.541i		−	1.02493i	0.858708	−	0.512466i	$-0.171268\pi$
$504$		0			0
$505$	−71.7968			−0.142172
$506$	267.233	−	154.287i	0.528129	−	0.304915i
$507$		0			0
$508$	150.816	−	261.221i	0.296882	−	0.514215i
$509$	−19.7738	−	11.4164i	−0.0388483	−	0.0224291i	0.480450	−	0.877022i	$-0.340473\pi$
$509$	−19.7738	−	11.4164i	−0.0388483	−	0.0224291i	−0.519298	+	0.854593i	$0.673807\pi$
$510$		0			0
$511$	45.3897	+	78.6172i	0.0888252	+	0.153850i
$512$		−	512.344i		−	1.00067i
$513$		0			0
$514$	41.5880			0.0809105
$515$	−260.707	+	150.519i	−0.506228	+	0.292271i
$516$		0			0
$517$	48.5701	−	84.1259i	0.0939460	−	0.162719i
$518$	219.530	+	126.746i	0.423804	+	0.244683i
$519$		0			0
$520$	10.0862	+	17.4697i	0.0193965	+	0.0335957i
$521$			717.049i			1.37629i	0.725572	+	0.688147i	$0.241575\pi$
$521$			717.049i			1.37629i	−0.725572	+	0.688147i	$0.758425\pi$
$522$		0			0
$523$	−116.101			−0.221991			−0.110995	−	0.993821i	$-0.535404\pi$
$523$	−116.101			−0.221991			−0.110995	+	0.993821i	$0.535404\pi$
$524$	−277.745	+	160.356i	−0.530049	+	0.306024i
$525$		0			0
$526$	92.6991	−	160.560i	0.176234	−	0.305246i
$527$	0.243080	+	0.140343i	0.000461253	+	0.000266305i
$528$		0			0
$529$	292.205	+	506.113i	0.552372	+	0.956736i
$530$		−	45.8962i		−	0.0865967i
$531$		0			0
$532$	−726.815			−1.36619
$533$	−14.4541	+	8.34510i	−0.0271185	+	0.0156568i
$534$		0			0
$535$	203.036	−	351.668i	0.379506	−	0.657323i
$536$	−157.519	−	90.9437i	−0.293879	−	0.169671i
$537$		0			0
$538$	39.1606	+	67.8281i	0.0727892	+	0.126075i
$539$			1359.37i			2.52202i
$540$		0			0
$541$	645.219			1.19264			0.596321	−	0.802746i	$-0.296629\pi$
$541$	645.219			1.19264			0.596321	+	0.802746i	$0.296629\pi$
$542$	−258.750	+	149.390i	−0.477399	+	0.275627i
$543$		0			0
$544$	82.1230	−	142.241i	0.150961	−	0.261473i
$545$	297.489	+	171.755i	0.545851	+	0.315147i
$546$		0			0
$547$	−197.004	−	341.222i	−0.360154	−	0.623806i	0.627832	−	0.778349i	$-0.283943\pi$
$547$	−197.004	−	341.222i	−0.360154	−	0.623806i	−0.987986	+	0.154544i	$0.950609\pi$
$548$			117.567i			0.214539i
$549$		0			0
$550$	−46.2383			−0.0840697
$551$	477.947	−	275.943i	0.867417	−	0.500803i
$552$		0			0
$553$	−130.240	+	225.583i	−0.235516	+	0.407925i
$554$	88.4657	+	51.0757i	0.159685	+	0.0921944i
$555$		0			0
$556$	438.306	+	759.168i	0.788319	+	1.36541i
$557$		−	62.6871i		−	0.112544i	−0.998415	−	0.0562721i	$-0.982079\pi$
$557$		−	62.6871i		−	0.112544i	0.998415	−	0.0562721i	$-0.0179214\pi$
$558$		0			0
$559$	−29.2747			−0.0523697
$560$	249.003	−	143.762i	0.444648	−	0.256718i
$561$		0			0
$562$	−20.6099	+	35.6974i	−0.0366725	+	0.0635186i
$563$	903.058	+	521.381i	1.60401	+	0.926076i	0.990674	+	0.136254i	$0.0435063\pi$
$563$	903.058	+	521.381i	1.60401	+	0.926076i	0.613336	+	0.789822i	$0.289827\pi$
$564$		0			0
$565$	−10.6932	−	18.5211i	−0.0189260	−	0.0327808i
$566$		−	125.642i		−	0.221982i
$567$		0			0
$568$	−436.538			−0.768553
$569$	679.400	−	392.252i	1.19402	−	0.689370i	0.234808	−	0.972042i	$-0.424554\pi$
$569$	679.400	−	392.252i	1.19402	−	0.689370i	0.959217	+	0.282671i	$0.0912206\pi$
$570$		0			0
$571$	20.8407	−	36.0971i	0.0364986	−	0.0632174i	−0.847199	−	0.531276i	$-0.821713\pi$
$571$	20.8407	−	36.0971i	0.0364986	−	0.0632174i	0.883698	+	0.468058i	$0.155046\pi$
$572$	70.4380	+	40.6674i	0.123143	+	0.0710969i
$573$		0			0
$574$	−41.0198	−	71.0484i	−0.0714631	−	0.123778i
$575$		−	166.839i		−	0.290155i
$576$		0			0
$577$	995.520			1.72534			0.862669	−	0.505769i	$-0.168791\pi$
$577$	995.520			1.72534			0.862669	+	0.505769i	$0.168791\pi$
$578$	−152.914	+	88.2848i	−0.264557	+	0.152742i
$579$		0			0
$580$	−129.186	+	223.757i	−0.222734	+	0.385787i
$581$	−630.839	−	364.215i	−1.08578	−	0.626877i
$582$		0			0
$583$	−197.674	−	342.382i	−0.339064	−	0.587276i
$584$			38.5117i			0.0659447i
$585$		0			0
$586$	23.9471			0.0408653
$587$	−319.043	+	184.200i	−0.543515	+	0.313799i	−0.746502	−	0.665383i	$-0.768268\pi$
$587$	−319.043	+	184.200i	−0.543515	+	0.313799i	0.202987	+	0.979181i	$0.434935\pi$
$588$		0			0
$589$	0.403609	−	0.699071i	0.000685244	−	0.00118688i
$590$	123.636	+	71.3812i	0.209552	+	0.120985i
$591$		0			0
$592$	−155.918	−	270.057i	−0.263374	−	0.456178i
$593$			789.968i			1.33216i	0.745882	+	0.666078i	$0.232028\pi$
$593$			789.968i			1.33216i	−0.745882	+	0.666078i	$0.767972\pi$
$594$		0			0
$595$	160.549			0.269831
$596$	−360.937	+	208.387i	−0.605599	+	0.349643i
$597$		0			0
$598$	20.0151	−	34.6671i	0.0334700	−	0.0579717i
$599$	−387.181	−	223.539i	−0.646379	−	0.373187i	0.140689	−	0.990054i	$-0.455068\pi$
$599$	−387.181	−	223.539i	−0.646379	−	0.373187i	−0.787068	+	0.616867i	$0.788402\pi$
$600$		0			0
$601$	110.559	+	191.494i	0.183959	+	0.318626i	0.943225	−	0.332154i	$-0.107775\pi$
$601$	110.559	+	191.494i	0.183959	+	0.318626i	−0.759267	+	0.650780i	$0.774442\pi$
$602$		−	143.898i		−	0.239033i
$603$		0			0
$604$	−568.660			−0.941489
$605$	−110.619	+	63.8657i	−0.182841	+	0.105563i
$606$		0			0
$607$	−260.263	+	450.788i	−0.428769	+	0.742649i	−0.996764	−	0.0803827i	$-0.974386\pi$
$607$	−260.263	+	450.788i	−0.428769	+	0.742649i	0.567996	+	0.823032i	$0.307719\pi$
$608$	−409.069	−	236.176i	−0.672811	−	0.388448i
$609$		0			0
$610$	15.5094	+	26.8630i	0.0254252	+	0.0440377i
$611$		−	12.6016i		−	0.0206246i
$612$		0			0
$613$	238.301			0.388746			0.194373	−	0.980928i	$-0.437733\pi$
$613$	238.301			0.388746			0.194373	+	0.980928i	$0.437733\pi$
$614$	−25.5150	+	14.7311i	−0.0415554	+	0.0239920i
$615$		0			0
$616$	−427.062	+	739.694i	−0.693283	+	1.20080i
$617$	953.150	+	550.301i	1.54481	+	0.891898i	0.998525	+	0.0543012i	$0.0172931\pi$
$617$	953.150	+	550.301i	1.54481	+	0.891898i	0.546288	+	0.837597i	$0.316040\pi$
$618$		0			0
$619$	14.1127	+	24.4439i	0.0227992	+	0.0394894i	0.877200	−	0.480125i	$-0.159409\pi$
$619$	14.1127	+	24.4439i	0.0227992	+	0.0394894i	−0.854401	+	0.519615i	$0.826075\pi$
$620$			0.377909i			0.000609531i
$621$		0			0
$622$	−370.212			−0.595196
$623$	−497.351	+	287.146i	−0.798316	+	0.460908i
$624$		0			0
$625$	−12.5000	+	21.6506i	−0.0200000	+	0.0346410i
$626$	43.4372	+	25.0785i	0.0693886	+	0.0400615i
$627$		0			0
$628$	261.755	+	453.372i	0.416807	+	0.721931i
$629$		−	174.125i		−	0.276828i
$630$		0			0
$631$	452.702			0.717437			0.358718	−	0.933446i	$-0.383214\pi$
$631$	452.702			0.717437			0.358718	+	0.933446i	$0.383214\pi$
$632$	−95.6998	+	55.2523i	−0.151424	+	0.0874245i
$633$		0			0
$634$	106.788	−	184.963i	0.168436	−	0.291740i
$635$	165.945	+	95.8085i	0.261331	+	0.150879i
$636$		0			0
$637$	88.1726	+	152.719i	0.138419	+	0.239748i
$638$		−	303.573i		−	0.475820i
$639$		0			0
$640$	286.020			0.446906
$641$	139.324	−	80.4388i	0.217354	−	0.125489i	−0.387370	−	0.921924i	$-0.626617\pi$
$641$	139.324	−	80.4388i	0.217354	−	0.125489i	0.604725	+	0.796435i	$0.293283\pi$
$642$		0			0
$643$	−209.233	+	362.401i	−0.325401	+	0.563610i	−0.981593	−	0.190983i	$-0.938832\pi$
$643$	−209.233	+	362.401i	−0.325401	+	0.563610i	0.656193	+	0.754593i	$0.272166\pi$
$644$	−1249.29	−	721.280i	−1.93990	−	1.12000i
$645$		0			0
$646$	−34.0491	−	58.9747i	−0.0527075	−	0.0912921i
$647$			943.607i			1.45843i	0.684282	+	0.729217i	$0.260116\pi$
$647$			943.607i			1.45843i	−0.684282	+	0.729217i	$0.739884\pi$
$648$		0			0
$649$	1229.75			1.89484
$650$	−5.19470	+	2.99916i	−0.00799184	+	0.00461409i
$651$		0			0
$652$	−155.066	+	268.581i	−0.237831	+	0.411935i
$653$	34.9700	+	20.1899i	0.0535528	+	0.0309187i	0.526537	−	0.850152i	$-0.323490\pi$
$653$	34.9700	+	20.1899i	0.0535528	+	0.0309187i	−0.472985	+	0.881071i	$0.656823\pi$
$654$		0			0
$655$	−101.869	−	176.443i	−0.155525	−	0.269378i
$656$			100.922i			0.153844i
$657$		0			0
$658$	61.9425			0.0941375
$659$	−381.612	+	220.324i	−0.579077	+	0.334330i	−0.760767	−	0.649026i	$-0.775177\pi$
$659$	−381.612	+	220.324i	−0.579077	+	0.334330i	0.181689	+	0.983356i	$0.441843\pi$
$660$		0			0
$661$	604.773	−	1047.50i	0.914937	−	1.58472i	0.107943	−	0.994157i	$-0.465574\pi$
$661$	604.773	−	1047.50i	0.914937	−	1.58472i	0.806994	−	0.590560i	$-0.201093\pi$
$662$	37.2899	+	21.5293i	0.0563292	+	0.0325217i
$663$		0			0
$664$	−154.512	−	267.623i	−0.232700	−	0.403047i
$665$		−	461.721i		−	0.694318i
$666$		0			0
$667$	1095.37			1.64223
$668$	436.985	−	252.294i	0.654170	−	0.377685i
$669$		0			0
$670$	27.0425	−	46.8390i	0.0403619	−	0.0699089i
$671$	231.397	+	133.597i	0.344854	+	0.199102i
$672$		0			0
$673$	−365.400	−	632.891i	−0.542941	−	0.940402i	−0.998733	−	0.0503157i	$-0.983977\pi$
$673$	−365.400	−	632.891i	−0.542941	−	0.940402i	0.455792	−	0.890086i	$-0.349356\pi$
$674$		−	82.3586i		−	0.122194i
$675$		0			0
$676$	−584.310			−0.864363
$677$	809.236	−	467.213i	1.19533	−	0.690122i	0.235817	−	0.971798i	$-0.424224\pi$
$677$	809.236	−	467.213i	1.19533	−	0.690122i	0.959510	+	0.281676i	$0.0908902\pi$
$678$		0			0
$679$	−142.162	+	246.232i	−0.209370	+	0.362639i
$680$	58.9854	+	34.0553i	0.0867433	+	0.0500813i
$681$		0			0
$682$	−0.222012	−	0.384535i	−0.000325530	−	0.000563835i
$683$			1.73043i			0.00253358i	0.999999	+	0.00126679i	$0.000403231\pi$
$683$			1.73043i			0.00253358i	−0.999999	+	0.00126679i	$0.999597\pi$
$684$		0			0
$685$	−74.6866			−0.109032
$686$	−389.542	+	224.902i	−0.567846	+	0.327846i
$687$		0			0
$688$	−88.5087	+	153.302i	−0.128646	+	0.222822i
$689$	−44.4159	−	25.6435i	−0.0644643	−	0.0372185i
$690$		0			0
$691$	−3.42602	−	5.93403i	−0.00495805	−	0.00858760i	0.863536	−	0.504288i	$-0.168245\pi$
$691$	−3.42602	−	5.93403i	−0.00495805	−	0.00858760i	−0.868494	+	0.495700i	$0.834912\pi$
$692$		−	854.461i		−	1.23477i
$693$		0			0
$694$	420.440			0.605821
$695$	−482.274	+	278.441i	−0.693920	+	0.400635i
$696$		0			0
$697$	−28.1767	+	48.8034i	−0.0404257	+	0.0700193i
$698$	−186.720	−	107.803i	−0.267507	−	0.154445i
$699$		0			0
$700$	108.080	+	187.201i	0.154400	+	0.267429i
$701$			60.8542i			0.0868105i	0.999058	+	0.0434053i	$0.0138207\pi$
$701$			60.8542i			0.0868105i	−0.999058	+	0.0434053i	$0.986179\pi$
$702$		0			0
$703$	−500.762			−0.712321
$704$	259.004	−	149.536i	0.367903	−	0.212409i
$705$		0			0
$706$	73.3611	−	127.065i	0.103911	−	0.179979i
$707$	−341.530	−	197.182i	−0.483069	−	0.278900i
$708$		0			0
$709$	−427.005	−	739.595i	−0.602264	−	1.04315i	−0.992477	−	0.122428i	$-0.960932\pi$
$709$	−427.005	−	739.595i	−0.602264	−	1.04315i	0.390213	−	0.920725i	$-0.372401\pi$
$710$		−	129.806i		−	0.182826i
$711$		0			0
$712$	−243.634			−0.342182
$713$	1.38750	−	0.801071i	0.00194600	−	0.00112352i
$714$		0			0
$715$	−25.8347	+	44.7470i	−0.0361324	+	0.0625832i
$716$	1042.49	+	601.884i	1.45600	+	0.840621i
$717$		0			0
$718$	−186.381	−	322.821i	−0.259583	−	0.449612i
$719$		−	712.375i		−	0.990786i	−0.868669	−	0.495393i	$-0.835024\pi$
$719$		−	712.375i		−	0.990786i	0.868669	−	0.495393i	$-0.164976\pi$
$720$		0			0
$721$	−1653.54			−2.29340
$722$	47.0212	−	27.1477i	0.0651263	−	0.0376007i
$723$		0			0
$724$	316.369	−	547.967i	0.436973	−	0.756860i
$725$	−142.145	−	82.0676i	−0.196062	−	0.113197i
$726$		0			0
$727$	−64.4633	−	111.654i	−0.0886703	−	0.153582i	0.818279	−	0.574821i	$-0.194928\pi$
$727$	−64.4633	−	111.654i	−0.0886703	−	0.153582i	−0.906949	+	0.421240i	$0.861595\pi$
$728$			110.802i			0.152201i
$729$		0			0
$730$	−11.4516			−0.0156871
$731$	−85.6014	+	49.4220i	−0.117102	+	0.0676088i
$732$		0			0
$733$	−85.3955	+	147.909i	−0.116501	+	0.201786i	−0.918379	−	0.395702i	$-0.870501\pi$
$733$	−85.3955	+	147.909i	−0.116501	+	0.201786i	0.801878	+	0.597488i	$0.203835\pi$
$734$	−136.346	−	78.7193i	−0.185757	−	0.107247i
$735$		0			0
$736$	−468.755	−	811.908i	−0.636896	−	1.10314i
$737$		−	465.886i		−	0.632139i
$738$		0			0
$739$	−279.938			−0.378806			−0.189403	−	0.981899i	$-0.560655\pi$
$739$	−279.938			−0.378806			−0.189403	+	0.981899i	$0.560655\pi$
$740$	203.029	−	117.219i	0.274364	−	0.158404i
$741$		0			0
$742$	126.049	−	218.323i	0.169878	−	0.294236i
$743$	−548.419	−	316.630i	−0.738115	−	0.426151i	0.0832687	−	0.996527i	$-0.473464\pi$
$743$	−548.419	−	316.630i	−0.738115	−	0.426151i	−0.821383	+	0.570376i	$0.806797\pi$
$744$		0			0
$745$	−132.381	−	229.291i	−0.177693	−	0.307774i
$746$			275.484i			0.369282i
$747$		0			0
$748$	274.622			0.367141
$749$	1931.64	−	1115.23i	2.57896	−	1.48896i
$750$		0			0
$751$	−633.828	+	1097.82i	−0.843978	+	1.46181i	0.0425269	+	0.999095i	$0.486459\pi$
$751$	−633.828	+	1097.82i	−0.843978	+	1.46181i	−0.886505	+	0.462718i	$0.846874\pi$
$752$	−65.9904	−	38.0996i	−0.0877532	−	0.0506643i
$753$		0			0
$754$	−19.6907	−	34.1053i	−0.0261150	−	0.0452325i
$755$		−	361.251i		−	0.478478i
$756$		0			0
$757$	−573.185			−0.757179			−0.378590	−	0.925565i	$-0.623591\pi$
$757$	−573.185			−0.757179			−0.378590	+	0.925565i	$0.623591\pi$
$758$	350.288	−	202.239i	0.462122	−	0.266806i
$759$		0			0
$760$	97.9390	−	169.635i	0.128867	−	0.223204i
$761$	395.528	+	228.358i	0.519747	+	0.300076i	0.736831	−	0.676077i	$-0.236321\pi$
$761$	395.528	+	228.358i	0.519747	+	0.300076i	−0.217084	+	0.976153i	$0.569655\pi$
$762$		0			0
$763$	943.414	+	1634.04i	1.23645	+	2.14160i
$764$			791.290i			1.03572i
$765$		0			0
$766$	143.711			0.187613
$767$	138.158	−	79.7654i	0.180127	−	0.103997i
$768$		0			0
$769$	88.1986	−	152.765i	0.114693	−	0.198653i	−0.802964	−	0.596027i	$-0.796745\pi$
$769$	88.1986	−	152.765i	0.114693	−	0.198653i	0.917657	+	0.397374i	$0.130078\pi$
$770$	−219.951	−	126.989i	−0.285650	−	0.164920i
$771$		0			0
$772$	−477.219	−	826.568i	−0.618159	−	1.07068i
$773$			1310.88i			1.69583i	0.530133	+	0.847915i	$0.322142\pi$
$773$			1310.88i			1.69583i	−0.530133	+	0.847915i	$0.677858\pi$
$774$		0			0
$775$	−0.240073			−0.000309772
$776$	−104.460	+	60.3100i	−0.134613	+	0.0777191i
$777$		0			0
$778$	−124.302	+	215.297i	−0.159771	+	0.276732i
$779$	140.353	+	81.0329i	0.180171	+	0.104022i
$780$		0			0
$781$	−559.074	−	968.345i	−0.715844	−	1.23988i
$782$		−	135.159i		−	0.172838i
$783$		0			0
$784$	1066.32			1.36010
$785$	−288.013	+	166.284i	−0.366895	+	0.211827i
$786$		0			0
$787$	−150.589	+	260.828i	−0.191346	+	0.331421i	−0.945697	−	0.325051i	$-0.894619\pi$
$787$	−150.589	+	260.828i	−0.191346	+	0.331421i	0.754350	+	0.656472i	$0.227952\pi$
$788$	35.6346	+	20.5737i	0.0452216	+	0.0261087i
$789$		0			0
$790$	−16.4295	−	28.4567i	−0.0207968	−	0.0360211i
$791$		−	117.471i		−	0.148509i
$792$		0			0
$793$	34.6621			0.0437101
$794$	400.590	−	231.281i	0.504522	−	0.291286i
$795$		0			0
$796$	−406.251	+	703.647i	−0.510365	+	0.883978i
$797$	33.9335	+	19.5915i	0.0425765	+	0.0245816i	0.521137	−	0.853473i	$-0.325508\pi$
$797$	33.9335	+	19.5915i	0.0425765	+	0.0245816i	−0.478561	+	0.878054i	$0.658841\pi$
$798$		0			0
$799$	−21.2743	−	36.8481i	−0.0266261	−	0.0461178i
$800$			140.481i			0.175602i
$801$		0			0
$802$	150.246			0.187340
$803$	−85.4280	+	49.3219i	−0.106386	+	0.0614220i
$804$		0			0
$805$	458.205	−	793.635i	0.569199	−	0.985882i
$806$	−0.0498843	−	0.0288007i	−6.18912e−5	−	3.57329e-5i
$807$		0			0
$808$	−83.6514	−	144.888i	−0.103529	−	0.179317i
$809$		−	1079.90i		−	1.33485i	−0.744676	−	0.667426i	$-0.767396\pi$
$809$		−	1079.90i		−	1.33485i	0.744676	−	0.667426i	$-0.232604\pi$
$810$		0			0
$811$	376.329			0.464030			0.232015	−	0.972712i	$-0.425468\pi$
$811$	376.329			0.464030			0.232015	+	0.972712i	$0.425468\pi$
$812$	−1229.05	+	709.591i	−1.51361	+	0.873880i
$813$		0			0
$814$	−137.726	+	238.549i	−0.169197	+	0.293057i
$815$	−170.621	−	98.5081i	−0.209351	−	0.120869i
$816$		0			0
$817$	142.132	+	246.180i	0.173968	+	0.301322i
$818$			276.709i			0.338275i
$819$		0			0
$820$	−75.8731			−0.0925281
$821$	−277.118	+	159.994i	−0.337537	+	0.194877i	−0.659182	−	0.751983i	$-0.729097\pi$
$821$	−277.118	+	159.994i	−0.337537	+	0.194877i	0.321645	+	0.946860i	$0.395764\pi$
$822$		0			0
$823$	−773.986	+	1340.58i	−0.940445	+	1.62890i	−0.175821	+	0.984422i	$0.556258\pi$
$823$	−773.986	+	1340.58i	−0.940445	+	1.62890i	−0.764624	+	0.644476i	$0.777075\pi$
$824$	−607.507	−	350.744i	−0.737266	−	0.425661i
$825$		0			0
$826$	392.082	+	679.106i	0.474675	+	0.822162i
$827$			95.9042i			0.115966i	0.998318	+	0.0579832i	$0.0184670\pi$
$827$			95.9042i			0.115966i	−0.998318	+	0.0579832i	$0.981533\pi$
$828$		0			0
$829$	664.409			0.801459			0.400729	−	0.916196i	$-0.368757\pi$
$829$	664.409			0.801459			0.400729	+	0.916196i	$0.368757\pi$
$830$	79.5789	−	45.9449i	0.0958782	−	0.0553553i
$831$		0			0
$832$	19.3987	−	33.5995i	0.0233158	−	0.0403841i
$833$	515.647	+	297.709i	0.619024	+	0.357394i
$834$		0			0
$835$	160.274	+	277.602i	0.191945	+	0.332458i
$836$		−	789.780i		−	0.944713i
$837$		0			0
$838$	−67.2382			−0.0802366
$839$	−532.982	+	307.718i	−0.635259	+	0.366767i	−0.782786	−	0.622291i	$-0.786202\pi$
$839$	−532.982	+	307.718i	−0.635259	+	0.366767i	0.147527	+	0.989058i	$0.452869\pi$
$840$		0			0
$841$	118.307	−	204.914i	0.140674	−	0.243655i
$842$	235.565	+	136.003i	0.279768	+	0.161524i
$843$		0			0
$844$	−344.056	−	595.922i	−0.407649	−	0.706068i
$845$		−	371.193i		−	0.439281i
$846$		0			0
$847$	−701.602			−0.828337
$848$	−268.573	+	155.061i	−0.316713	+	0.182855i
$849$		0			0
$850$	−10.1265	+	17.5395i	−0.0119135	+	0.0206348i
$851$	−860.740	−	496.949i	−1.01145	−	0.583958i
$852$		0			0
$853$	−743.721	−	1288.16i	−0.871889	−	1.51016i	−0.860041	−	0.510226i	$-0.829562\pi$
$853$	−743.721	−	1288.16i	−0.871889	−	1.51016i	−0.0118480	−	0.999930i	$-0.503771\pi$
$854$			170.379i			0.199507i
$855$		0			0
$856$	946.238			1.10542
$857$	−385.937	+	222.821i	−0.450335	+	0.260001i	−0.707972	−	0.706241i	$-0.750390\pi$
$857$	−385.937	+	222.821i	−0.450335	+	0.260001i	0.257636	+	0.966242i	$0.417056\pi$
$858$		0			0
$859$	747.122	−	1294.05i	0.869757	−	1.50646i	0.00751307	−	0.999972i	$-0.497608\pi$
$859$	747.122	−	1294.05i	0.869757	−	1.50646i	0.862244	−	0.506492i	$-0.169058\pi$
$860$	−115.252	−	66.5408i	−0.134014	−	0.0773731i
$861$		0			0
$862$	−20.7095	−	35.8699i	−0.0240250	−	0.0416124i
$863$		−	786.584i		−	0.911453i	−0.890120	−	0.455727i	$-0.849379\pi$
$863$		−	786.584i		−	0.911453i	0.890120	−	0.455727i	$-0.150621\pi$
$864$		0			0
$865$	542.811			0.627527
$866$	6.81643	−	3.93547i	0.00787116	−	0.00454442i
$867$		0			0
$868$	−1.03789	+	1.79767i	−0.00119572	+	0.00207105i
$869$	−245.125	−	141.523i	−0.282077	−	0.162857i
$870$		0			0
$871$	−30.2188	−	52.3405i	−0.0346944	−	0.0600924i
$872$			800.457i			0.917955i
$873$		0			0
$874$	−388.702			−0.444739
$875$	−118.922	+	68.6598i	−0.135911	+	0.0784684i
$876$		0			0
$877$	−35.1375	+	60.8600i	−0.0400656	+	0.0693956i	−0.885363	−	0.464901i	$-0.846090\pi$
$877$	−35.1375	+	60.8600i	−0.0400656	+	0.0693956i	0.845297	+	0.534296i	$0.179423\pi$
$878$	200.845	+	115.958i	0.228752	+	0.132070i
$879$		0			0
$880$	156.216	+	270.575i	0.177519	+	0.307471i
$881$			883.875i			1.00326i	0.865081	+	0.501632i	$0.167267\pi$
$881$			883.875i			1.00326i	−0.865081	+	0.501632i	$0.832733\pi$
$882$		0			0
$883$	1413.46			1.60075			0.800373	−	0.599503i	$-0.204635\pi$
$883$	1413.46			1.60075			0.800373	+	0.599503i	$0.204635\pi$
$884$	30.8527	−	17.8128i	0.0349012	−	0.0201502i
$885$		0			0
$886$	−186.536	+	323.089i	−0.210537	+	0.364661i
$887$	1105.31	+	638.152i	1.24612	+	0.719450i	0.970334	−	0.241768i	$-0.0777272\pi$
$887$	1105.31	+	638.152i	1.24612	+	0.719450i	0.275790	+	0.961218i	$0.411061\pi$
$888$		0			0
$889$	526.256	+	911.501i	0.591964	+	1.02531i
$890$		−	72.4455i		−	0.0813994i
$891$		0			0
$892$	1071.81			1.20159
$893$	−105.971	+	61.1823i	−0.118668	+	0.0685132i
$894$		0			0
$895$	−382.357	+	662.262i	−0.427215	+	0.739958i
$896$	1360.57	+	785.524i	1.51849	+	0.876701i
$897$		0			0
$898$	6.13343	+	10.6234i	0.00683010	+	0.0118301i
$899$		−	1.57618i		−	0.00175326i
$900$		0			0
$901$	−173.167			−0.192195
$902$	77.2035	−	44.5734i	0.0855914	−	0.0494162i
$903$		0			0
$904$	24.9175	−	43.1584i	0.0275636	−	0.0477416i
$905$	348.105	+	200.979i	0.384647	+	0.222076i
$906$		0			0
$907$	596.996	+	1034.03i	0.658209	+	1.14005i	0.981079	+	0.193609i	$0.0620192\pi$
$907$	596.996	+	1034.03i	0.658209	+	1.14005i	−0.322869	+	0.946444i	$0.604647\pi$
$908$			1307.35i			1.43981i
$909$		0			0
$910$	−32.9475			−0.0362060
$911$	−128.759	+	74.3388i	−0.141338	+	0.0816013i	−0.569001	−	0.822337i	$-0.692670\pi$
$911$	−128.759	+	74.3388i	−0.141338	+	0.0816013i	0.427664	+	0.903938i	$0.359337\pi$
$912$		0			0
$913$	395.768	−	685.490i	0.433481	−	0.750811i
$914$	54.3847	+	31.3990i	0.0595018	+	0.0343534i
$915$		0			0
$916$	667.998	+	1157.01i	0.729255	+	1.26311i
$917$		−	1119.09i		−	1.22038i
$918$		0			0
$919$	−256.801			−0.279435			−0.139717	−	0.990191i	$-0.544619\pi$
$919$	−256.801			−0.279435			−0.139717	+	0.990191i	$0.544619\pi$
$920$	336.687	−	194.386i	0.365964	−	0.211289i
$921$		0			0
$922$	−135.928	+	235.434i	−0.147427	+	0.255352i
$923$	−125.620	−	72.5265i	−0.136099	−	0.0785769i
$924$		0			0
$925$	74.4653	+	128.978i	0.0805030	+	0.139435i
$926$			286.459i			0.309351i
$927$		0			0
$928$	−922.317			−0.993876
$929$	−1170.40	+	675.730i	−1.25985	+	0.727373i	−0.973045	−	0.230616i	$-0.925926\pi$
$929$	−1170.40	+	675.730i	−1.25985	+	0.727373i	−0.286803	+	0.957990i	$0.592592\pi$
$930$		0			0
$931$	856.177	−	1482.94i	0.919632	−	1.59285i
$932$	−121.391	−	70.0854i	−0.130248	−	0.0751989i
$933$		0			0
$934$	242.678	+	420.331i	0.259827	+	0.450033i
$935$			174.458i			0.186586i
$936$		0			0
$937$	−1046.51			−1.11687			−0.558437	−	0.829547i	$-0.688599\pi$
$937$	−1046.51			−1.11687			−0.558437	+	0.829547i	$0.688599\pi$
$938$	257.276	−	148.539i	0.274282	−	0.158357i
$939$		0			0
$940$	28.6433	−	49.6116i	0.0304716	−	0.0527783i
$941$	−627.759	−	362.437i	−0.667119	−	0.385161i	0.127865	−	0.991792i	$-0.459187\pi$
$941$	−627.759	−	362.437i	−0.667119	−	0.385161i	−0.794984	+	0.606630i	$0.792521\pi$
$942$		0			0
$943$	160.832	+	278.569i	0.170553	+	0.295407i
$944$		−	964.647i		−	1.02187i
$945$		0			0
$946$	156.364			0.165290
$947$	−851.081	+	491.372i	−0.898713	+	0.518872i	−0.876782	−	0.480887i	$-0.840315\pi$
$947$	−851.081	+	491.372i	−0.898713	+	0.518872i	−0.0219306	+	0.999759i	$0.506981\pi$
$948$		0			0
$949$	−6.39833	+	11.0822i	−0.00674219	+	0.0116778i
$950$	50.4417	+	29.1225i	0.0530965	+	0.0306553i
$951$		0			0
$952$	187.058	+	323.994i	0.196490	+	0.340330i
$953$			1358.28i			1.42527i	0.701535	+	0.712635i	$0.252498\pi$
$953$			1358.28i			1.42527i	−0.701535	+	0.712635i	$0.747502\pi$
$954$		0			0
$955$	−502.680			−0.526367
$956$	878.434	−	507.164i	0.918864	−	0.530506i
$957$		0			0
$958$	63.5575	−	110.085i	0.0663439	−	0.114911i
$959$	−355.276	−	205.119i	−0.370465	−	0.213888i
$960$		0			0
$961$	480.499	+	832.248i	0.499999	+	0.866023i
$962$			35.7333i			0.0371448i
$963$		0			0
$964$	−695.224			−0.721186
$965$	525.091	−	303.162i	0.544136	−	0.314157i
$966$		0			0
$967$	−750.065	+	1299.15i	−0.775662	+	1.34349i	0.158760	+	0.987317i	$0.449250\pi$
$967$	−750.065	+	1299.15i	−0.775662	+	1.34349i	−0.934422	+	0.356169i	$0.884083\pi$
$968$	−257.767	−	148.822i	−0.266288	−	0.153741i
$969$		0			0
$970$	−17.9334	−	31.0616i	−0.0184881	−	0.0320223i
$971$		−	249.859i		−	0.257322i	−0.991689	−	0.128661i	$-0.958932\pi$
$971$		−	249.859i		−	0.257322i	0.991689	−	0.128661i	$-0.0410678\pi$
$972$		0			0
$973$	−3058.84			−3.14372
$974$	−148.392	+	85.6739i	−0.152353	+	0.0879609i
$975$		0			0
$976$	104.797	−	181.514i	0.107374	−	0.185977i
$977$	−227.932	−	131.597i	−0.233298	−	0.134695i	0.378795	−	0.925481i	$-0.376339\pi$
$977$	−227.932	−	131.597i	−0.233298	−	0.134695i	−0.612092	+	0.790786i	$0.709672\pi$
$978$		0			0
$979$	−312.022	−	540.437i	−0.318715	−	0.552030i
$980$			801.659i			0.818020i
$981$		0			0
$982$	513.341			0.522750
$983$	838.243	−	483.960i	0.852739	−	0.492329i	−0.00883500	−	0.999961i	$-0.502812\pi$
$983$	838.243	−	483.960i	0.852739	−	0.492329i	0.861574	+	0.507632i	$0.169479\pi$
$984$		0			0
$985$	−13.0698	+	22.6375i	−0.0132688	+	0.0229822i
$986$	−115.154	−	66.4843i	−0.116789	−	0.0674283i
$987$		0			0
$988$	−51.2275	−	88.7287i	−0.0518497	−	0.0898064i
$989$			564.199i			0.570474i
$990$		0			0
$991$	−1203.88			−1.21481			−0.607405	−	0.794392i	$-0.707790\pi$
$991$	−1203.88			−1.21481			−0.607405	+	0.794392i	$0.707790\pi$
$992$	−1.16830	+	0.674516i	−0.00117772	+	0.000679956i
$993$		0			0
$994$	356.499	−	617.475i	0.358651	−	0.621202i
$995$	−447.003	−	258.078i	−0.449250	−	0.259374i
$996$		0			0
$997$	372.668	+	645.480i	0.373790	+	0.647423i	0.990145	−	0.140046i	$-0.0447249\pi$
$997$	372.668	+	645.480i	0.373790	+	0.647423i	−0.616356	+	0.787468i	$0.711392\pi$
$998$		−	600.592i		−	0.601795i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	135.3.i.a.71.4		16
3.2	odd	2		45.3.i.a.41.5	yes	16
4.3	odd	2		2160.3.bs.c.881.4		16
5.2	odd	4		675.3.i.c.449.7		32
5.3	odd	4		675.3.i.c.449.10		32
5.4	even	2		675.3.j.b.476.5		16
9.2	odd	6	inner	135.3.i.a.116.4		16
9.4	even	3		405.3.c.a.161.7		16
9.5	odd	6		405.3.c.a.161.10		16
9.7	even	3		45.3.i.a.11.5	✓	16
12.11	even	2		720.3.bs.c.401.1		16
15.2	even	4		225.3.i.b.149.10		32
15.8	even	4		225.3.i.b.149.7		32
15.14	odd	2		225.3.j.b.176.4		16
36.7	odd	6		720.3.bs.c.641.1		16
36.11	even	6		2160.3.bs.c.1601.4		16
45.2	even	12		675.3.i.c.224.10		32
45.7	odd	12		225.3.i.b.74.7		32
45.29	odd	6		675.3.j.b.251.5		16
45.34	even	6		225.3.j.b.101.4		16
45.38	even	12		675.3.i.c.224.7		32
45.43	odd	12		225.3.i.b.74.10		32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
45.3.i.a.11.5	✓	16	9.7	even	3
45.3.i.a.41.5	yes	16	3.2	odd	2
135.3.i.a.71.4		16	1.1	even	1	trivial
135.3.i.a.116.4		16	9.2	odd	6	inner
225.3.i.b.74.7		32	45.7	odd	12
225.3.i.b.74.10		32	45.43	odd	12
225.3.i.b.149.7		32	15.8	even	4
225.3.i.b.149.10		32	15.2	even	4
225.3.j.b.101.4		16	45.34	even	6
225.3.j.b.176.4		16	15.14	odd	2
405.3.c.a.161.7		16	9.4	even	3
405.3.c.a.161.10		16	9.5	odd	6
675.3.i.c.224.7		32	45.38	even	12
675.3.i.c.224.10		32	45.2	even	12
675.3.i.c.449.7		32	5.2	odd	4
675.3.i.c.449.10		32	5.3	odd	4
675.3.j.b.251.5		16	45.29	odd	6
675.3.j.b.476.5		16	5.4	even	2
720.3.bs.c.401.1		16	12.11	even	2
720.3.bs.c.641.1		16	36.7	odd	6
2160.3.bs.c.881.4		16	4.3	odd	2
2160.3.bs.c.1601.4		16	36.11	even	6

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:	\( N \)	\(=\)	\( 135 = 3^{3} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	135.i (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.600071 + 0.346451i) q^{2} +(-1.75994 + 3.04831i) q^{4} +(-1.93649 - 1.11803i) q^{5} +(-6.14112 - 10.6367i) q^{7} -5.21055i q^{8} +O(q^{10})\)	\(q+(-0.600071 + 0.346451i) q^{2} +(-1.75994 + 3.04831i) q^{4} +(-1.93649 - 1.11803i) q^{5} +(-6.14112 - 10.6367i) q^{7} -5.21055i q^{8} +1.54938 q^{10} +(11.5582 - 6.67314i) q^{11} +(0.865680 - 1.49940i) q^{13} +(7.37022 + 4.25520i) q^{14} +(-5.23457 - 9.06655i) q^{16} -5.84583i q^{17} -16.8119 q^{19} +(6.81623 - 3.93535i) q^{20} +(-4.62383 + 8.00871i) q^{22} +(-28.8974 - 16.6839i) q^{23} +(2.50000 + 4.33013i) q^{25} +1.19966i q^{26} +43.2321 q^{28} +(-28.4290 + 16.4135i) q^{29} +(-0.0240073 + 0.0415819i) q^{31} +(24.3321 + 14.0481i) q^{32} +(2.02529 + 3.50791i) q^{34} +27.4639i q^{35} +29.7861 q^{37} +(10.0883 - 5.82451i) q^{38} +(-5.82557 + 10.0902i) q^{40} +(-8.34843 - 4.81997i) q^{41} +(-8.45424 - 14.6432i) q^{43} +46.9774i q^{44} +23.1206 q^{46} +(6.30332 - 3.63922i) q^{47} +(-50.9268 + 88.2078i) q^{49} +(-3.00035 - 1.73226i) q^{50} +(3.04710 + 5.27773i) q^{52} -29.6224i q^{53} -29.8432 q^{55} +(-55.4232 + 31.9986i) q^{56} +(11.3730 - 19.6985i) q^{58} +(79.7972 + 46.0709i) q^{59} +(10.0101 + 17.3380i) q^{61} -0.0332694i q^{62} +22.4086 q^{64} +(-3.35277 + 1.93572i) q^{65} +(17.4538 - 30.2308i) q^{67} +(17.8199 + 10.2883i) q^{68} +(-9.51491 - 16.4803i) q^{70} -83.7798i q^{71} -7.39110 q^{73} +(-17.8738 + 10.3194i) q^{74} +(29.5880 - 51.2480i) q^{76} +(-141.961 - 81.9612i) q^{77} +(-10.6039 - 18.3666i) q^{79} +23.4097i q^{80} +6.67953 q^{82} +(51.3619 - 29.6538i) q^{83} +(-6.53583 + 11.3204i) q^{85} +(10.1463 + 5.85796i) q^{86} +(-34.7707 - 60.2246i) q^{88} -46.7578i q^{89} -21.2650 q^{91} +(101.715 - 58.7254i) q^{92} +(-2.52163 + 4.36758i) q^{94} +(32.5561 + 18.7963i) q^{95} +(-11.5746 - 20.0478i) q^{97} -70.5746i q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 16 q^{4} + 2 q^{7}+O(q^{10}) \) 16 * q + 16 * q^4 + 2 * q^7	\( 16 q + 16 q^{4} + 2 q^{7} + 18 q^{11} - 10 q^{13} + 54 q^{14} - 32 q^{16} - 52 q^{19} - 24 q^{22} + 54 q^{23} + 40 q^{25} + 32 q^{28} + 54 q^{29} + 32 q^{31} - 216 q^{32} + 54 q^{34} + 44 q^{37} - 252 q^{38} - 30 q^{40} - 144 q^{41} - 124 q^{43} - 108 q^{46} + 216 q^{47} - 54 q^{49} + 62 q^{52} + 18 q^{56} + 90 q^{58} + 486 q^{59} + 62 q^{61} + 256 q^{64} + 90 q^{65} + 14 q^{67} + 288 q^{68} - 60 q^{70} - 268 q^{73} - 540 q^{74} - 106 q^{76} - 702 q^{77} - 40 q^{79} - 204 q^{82} - 522 q^{83} + 30 q^{85} - 54 q^{86} + 144 q^{88} + 136 q^{91} + 1332 q^{92} - 150 q^{94} - 180 q^{95} - 142 q^{97}+O(q^{100}) \) 16 * q + 16 * q^4 + 2 * q^7 + 18 * q^11 - 10 * q^13 + 54 * q^14 - 32 * q^16 - 52 * q^19 - 24 * q^22 + 54 * q^23 + 40 * q^25 + 32 * q^28 + 54 * q^29 + 32 * q^31 - 216 * q^32 + 54 * q^34 + 44 * q^37 - 252 * q^38 - 30 * q^40 - 144 * q^41 - 124 * q^43 - 108 * q^46 + 216 * q^47 - 54 * q^49 + 62 * q^52 + 18 * q^56 + 90 * q^58 + 486 * q^59 + 62 * q^61 + 256 * q^64 + 90 * q^65 + 14 * q^67 + 288 * q^68 - 60 * q^70 - 268 * q^73 - 540 * q^74 - 106 * q^76 - 702 * q^77 - 40 * q^79 - 204 * q^82 - 522 * q^83 + 30 * q^85 - 54 * q^86 + 144 * q^88 + 136 * q^91 + 1332 * q^92 - 150 * q^94 - 180 * q^95 - 142 * q^97

Introduction

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