LMFDB - Embedded newform 459.3.i.a.305.5

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [459,3,Mod(152,459)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("459.152"); S:= CuspForms(chi, 3); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(459, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([5, 3])) N = Newforms(chi, 3, names="a")

Level:	$ N $	$=$	$ 459 = 3^{3} \cdot 17 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	459.i (of order $6$, degree $2$, not minimal)

Newform invariants

comment:select newform

sage:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$12.5068441341$
Analytic rank:	$0$
Dimension:	$68$
Relative dimension:	$34$ over $\Q(\zeta_{6})$
Twist minimal:	no (minimal twist has level 153)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			305.5
Character	$\chi$	$=$	459.305
Dual form			459.3.i.a.152.5

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-2.65135 - 1.53076i) q^{2} +(2.68643 + 4.65303i) q^{4} +(-4.03905 - 6.99584i) q^{5} +(-8.17722 - 4.72112i) q^{7} -4.20301i q^{8} +24.7312i q^{10} +(-5.27158 + 9.13064i) q^{11} +(10.9174 + 18.9095i) q^{13} +(14.4538 + 25.0347i) q^{14} +(4.31192 - 7.46847i) q^{16} +(-15.3418 - 7.32324i) q^{17} -14.6494 q^{19} +(21.7012 - 37.5877i) q^{20} +(27.9536 - 16.1390i) q^{22} +(-3.86711 - 6.69802i) q^{23} +(-20.1279 + 34.8625i) q^{25} -66.8475i q^{26} -50.7318i q^{28} +(3.81538 - 6.60843i) q^{29} +(15.0154 - 8.66912i) q^{31} +(-37.4245 + 21.6070i) q^{32} +(29.4663 + 42.9010i) q^{34} +76.2754i q^{35} -13.8739i q^{37} +(38.8408 + 22.4247i) q^{38} +(-29.4036 + 16.9762i) q^{40} +(23.1373 + 40.0749i) q^{41} +(27.7975 - 48.1467i) q^{43} -56.6468 q^{44} +23.6784i q^{46} +(-18.6323 - 10.7574i) q^{47} +(20.0780 + 34.7761i) q^{49} +(106.732 - 61.6218i) q^{50} +(-58.6576 + 101.598i) q^{52} +61.3273i q^{53} +85.1687 q^{55} +(-19.8429 + 34.3690i) q^{56} +(-20.2318 + 11.6808i) q^{58} +(76.3789 - 44.0974i) q^{59} +(-34.9764 - 20.1936i) q^{61} -53.0812 q^{62} +97.8050 q^{64} +(88.1919 - 152.753i) q^{65} +(-36.3540 - 62.9669i) q^{67} +(-7.13935 - 91.0591i) q^{68} +(116.759 - 202.233i) q^{70} +10.1569 q^{71} +34.6373i q^{73} +(-21.2375 + 36.7845i) q^{74} +(-39.3547 - 68.1643i) q^{76} +(86.2137 - 49.7755i) q^{77} +(96.7823 + 55.8773i) q^{79} -69.6643 q^{80} -141.670i q^{82} +(3.77295 + 2.17831i) q^{83} +(10.7340 + 136.908i) q^{85} +(-147.402 + 85.1025i) q^{86} +(38.3762 + 22.1565i) q^{88} +67.1458i q^{89} -206.169i q^{91} +(20.7774 - 35.9875i) q^{92} +(32.9339 + 57.0431i) q^{94} +(59.1699 + 102.485i) q^{95} +(-89.7342 - 51.8080i) q^{97} -122.938i q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 68 q + 6 q^{2} + 62 q^{4} - 2 q^{13} - 106 q^{16} - 32 q^{19} - 132 q^{25} - 27 q^{34} + 102 q^{38} + 58 q^{43} + 312 q^{47} + 152 q^{49} + 90 q^{50} + 70 q^{52} + 92 q^{55} + 258 q^{59} - 16 q^{64} + 82 q^{67}+ \cdots - 18 q^{94}+O(q^{100}) $ 68 * q + 6 * q^2 + 62 * q^4 - 2 * q^13 - 106 * q^16 - 32 * q^19 - 132 * q^25 - 27 * q^34 + 102 * q^38 + 58 * q^43 + 312 * q^47 + 152 * q^49 + 90 * q^50 + 70 * q^52 + 92 * q^55 + 258 * q^59 - 16 * q^64 + 82 * q^67 + 333 * q^68 + 204 * q^70 + 34 * q^76 + 60 * q^77 + 690 * q^83 - 44 * q^85 + 1248 * q^86 - 18 * q^94

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/459\mathbb{Z}\right)^\times$.

$n$	$137$	$190$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$-1$

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 $

$2$	−2.65135	−	1.53076i	−1.32567	−	0.765378i	−0.341046	−	0.940046i	$-0.610781\pi$
$2$	−2.65135	−	1.53076i	−1.32567	−	0.765378i	−0.984627	+	0.174668i	$0.944115\pi$
$3$		0			0
$3$		0			0
$4$	2.68643	+	4.65303i	0.671607	+	1.16326i
$5$	−4.03905	−	6.99584i	−0.807811	−	1.39917i	−0.914377	−	0.404863i	$-0.867319\pi$
$5$	−4.03905	−	6.99584i	−0.807811	−	1.39917i	0.106567	−	0.994306i	$-0.466014\pi$
$6$		0			0
$7$	−8.17722	−	4.72112i	−1.16817	−	0.674446i	−0.214925	−	0.976631i	$-0.568951\pi$
$7$	−8.17722	−	4.72112i	−1.16817	−	0.674446i	−0.953249	+	0.302185i	$0.902284\pi$
$8$		−	4.20301i		−	0.525377i
$9$		0			0
$10$			24.7312i			2.47312i
$11$	−5.27158	+	9.13064i	−0.479234	+	0.830058i	−0.999716	−	0.0238145i	$-0.992419\pi$
$11$	−5.27158	+	9.13064i	−0.479234	+	0.830058i	0.520482	+	0.853873i	$0.325752\pi$
$12$		0			0
$13$	10.9174	+	18.9095i	0.839800	+	1.45458i	0.890062	+	0.455840i	$0.150661\pi$
$13$	10.9174	+	18.9095i	0.839800	+	1.45458i	−0.0502618	+	0.998736i	$0.516006\pi$
$14$	14.4538	+	25.0347i	1.03241	+	1.78819i
$15$		0			0
$16$	4.31192	−	7.46847i	0.269495	−	0.466779i
$17$	−15.3418	−	7.32324i	−0.902458	−	0.430779i
$17$	−15.3418	−	7.32324i	−0.902458	−	0.430779i
$18$		0			0
$19$	−14.6494			−0.771023			−0.385512	−	0.922703i	$-0.625975\pi$
$19$	−14.6494			−0.771023			−0.385512	+	0.922703i	$0.625975\pi$
$20$	21.7012	−	37.5877i	1.08506	−	1.87938i
$21$		0			0
$22$	27.9536	−	16.1390i	1.27062	−	0.733591i
$23$	−3.86711	−	6.69802i	−0.168135	−	0.291218i	0.769629	−	0.638491i	$-0.220441\pi$
$23$	−3.86711	−	6.69802i	−0.168135	−	0.291218i	−0.937764	+	0.347273i	$0.887108\pi$
$24$		0			0
$25$	−20.1279	+	34.8625i	−0.805116	+	1.39450i
$26$		−	66.8475i		−	2.57106i
$27$		0			0
$28$		−	50.7318i		−	1.81185i
$29$	3.81538	−	6.60843i	0.131565	−	0.227877i	−0.792715	−	0.609592i	$-0.791333\pi$
$29$	3.81538	−	6.60843i	0.131565	−	0.227877i	0.924280	+	0.381715i	$0.124667\pi$
$30$		0			0
$31$	15.0154	−	8.66912i	0.484366	−	0.279649i	−0.237868	−	0.971297i	$-0.576449\pi$
$31$	15.0154	−	8.66912i	0.484366	−	0.279649i	0.722234	+	0.691648i	$0.243115\pi$
$32$	−37.4245	+	21.6070i	−1.16951	+	0.675220i
$33$		0			0
$34$	29.4663	+	42.9010i	0.866656	+	1.26179i
$35$			76.2754i			2.17930i
$36$		0			0
$37$		−	13.8739i		−	0.374970i	−0.982267	−	0.187485i	$-0.939966\pi$
$37$		−	13.8739i		−	0.374970i	0.982267	−	0.187485i	$-0.0600336\pi$
$38$	38.8408	+	22.4247i	1.02213	+	0.590124i
$39$		0			0
$40$	−29.4036	+	16.9762i	−0.735091	+	0.424405i
$41$	23.1373	+	40.0749i	0.564324	+	0.977437i	0.997112	+	0.0759417i	$0.0241963\pi$
$41$	23.1373	+	40.0749i	0.564324	+	0.977437i	−0.432789	+	0.901495i	$0.642470\pi$
$42$		0			0
$43$	27.7975	−	48.1467i	0.646454	−	1.11969i	−0.337509	−	0.941322i	$-0.609584\pi$
$43$	27.7975	−	48.1467i	0.646454	−	1.11969i	0.983964	−	0.178370i	$-0.0570823\pi$
$44$	−56.6468			−1.28743
$45$		0			0
$46$			23.6784i			0.514747i
$47$	−18.6323	−	10.7574i	−0.396433	−	0.228881i	0.288511	−	0.957477i	$-0.406840\pi$
$47$	−18.6323	−	10.7574i	−0.396433	−	0.228881i	−0.684944	+	0.728596i	$0.740173\pi$
$48$		0			0
$49$	20.0780	+	34.7761i	0.409754	+	0.709716i
$50$	106.732	−	61.6218i	2.13464	−	1.23244i
$51$		0			0
$52$	−58.6576	+	101.598i	−1.12803	+	1.95381i
$53$			61.3273i			1.15712i	0.815640	+	0.578559i	$0.196385\pi$
$53$			61.3273i			1.15712i	−0.815640	+	0.578559i	$0.803615\pi$
$54$		0			0
$55$	85.1687			1.54852
$56$	−19.8429	+	34.3690i	−0.354338	+	0.613732i
$57$		0			0
$58$	−20.2318	+	11.6808i	−0.348824	+	0.201394i
$59$	76.3789	−	44.0974i	1.29456	−	0.747413i	0.315099	−	0.949059i	$-0.397962\pi$
$59$	76.3789	−	44.0974i	1.29456	−	0.747413i	0.979459	+	0.201645i	$0.0646289\pi$
$60$		0			0
$61$	−34.9764	−	20.1936i	−0.573383	−	0.331043i	0.185116	−	0.982717i	$-0.440734\pi$
$61$	−34.9764	−	20.1936i	−0.573383	−	0.331043i	−0.758499	+	0.651674i	$0.774067\pi$
$62$	−53.0812			−0.856149
$63$		0			0
$64$	97.8050			1.52820
$65$	88.1919	−	152.753i	1.35680	−	2.35004i
$66$		0			0
$67$	−36.3540	−	62.9669i	−0.542596	−	0.939805i	−0.998754	−	0.0499055i	$-0.984108\pi$
$67$	−36.3540	−	62.9669i	−0.542596	−	0.939805i	0.456158	−	0.889899i	$-0.349225\pi$
$68$	−7.13935	−	91.0591i	−0.104990	−	1.33910i
$69$		0			0
$70$	116.759	−	202.233i	1.66799	−	2.88904i
$71$	10.1569			0.143054			0.0715272	−	0.997439i	$-0.477213\pi$
$71$	10.1569			0.143054			0.0715272	+	0.997439i	$0.477213\pi$
$72$		0			0
$73$			34.6373i			0.474484i	0.971451	+	0.237242i	$0.0762435\pi$
$73$			34.6373i			0.474484i	−0.971451	+	0.237242i	$0.923757\pi$
$74$	−21.2375	+	36.7845i	−0.286994	+	0.497088i
$75$		0			0
$76$	−39.3547	−	68.1643i	−0.517825	−	0.896899i
$77$	86.2137	−	49.7755i	1.11966	−	0.646435i
$78$		0			0
$79$	96.7823	+	55.8773i	1.22509	+	0.707308i	0.965999	−	0.258545i	$-0.0832429\pi$
$79$	96.7823	+	55.8773i	1.22509	+	0.707308i	0.259093	+	0.965852i	$0.416576\pi$
$80$	−69.6643			−0.870804
$81$		0			0
$82$		−	141.670i		−	1.72768i
$83$	3.77295	+	2.17831i	0.0454572	+	0.0262447i	0.522556	−	0.852605i	$-0.324978\pi$
$83$	3.77295	+	2.17831i	0.0454572	+	0.0262447i	−0.477099	+	0.878849i	$0.658312\pi$
$84$		0			0
$85$	10.7340	+	136.908i	0.126283	+	1.61068i
$86$	−147.402	+	85.1025i	−1.71397	+	0.989564i
$87$		0			0
$88$	38.3762	+	22.1565i	0.436093	+	0.251779i
$89$			67.1458i			0.754447i	0.926122	+	0.377224i	$0.123121\pi$
$89$			67.1458i			0.754447i	−0.926122	+	0.377224i	$0.876879\pi$
$90$		0			0
$91$		−	206.169i		−	2.26560i
$92$	20.7774	−	35.9875i	0.225841	−	0.391169i
$93$		0			0
$94$	32.9339	+	57.0431i	0.350360	+	0.606842i
$95$	59.1699	+	102.485i	0.622841	+	1.07879i
$96$		0			0
$97$	−89.7342	−	51.8080i	−0.925094	−	0.534104i	−0.0398377	−	0.999206i	$-0.512684\pi$
$97$	−89.7342	−	51.8080i	−0.925094	−	0.534104i	−0.885257	+	0.465103i	$0.846017\pi$
$98$		−	122.938i		−	1.25447i
$99$		0			0
$100$	−216.289			−2.16289
$101$	87.3324	+	50.4214i	0.864677	+	0.499222i	0.865576	−	0.500778i	$-0.166953\pi$
$101$	87.3324	+	50.4214i	0.864677	+	0.499222i	−0.000898689		1.00000i	$0.500286\pi$
$102$		0			0
$103$	44.1151	+	76.4097i	0.428302	+	0.741841i	0.996722	−	0.0808971i	$-0.0257785\pi$
$103$	44.1151	+	76.4097i	0.428302	+	0.741841i	−0.568420	+	0.822738i	$0.692445\pi$
$104$	79.4769	−	45.8860i	0.764201	−	0.441211i
$105$		0			0
$106$	93.8771	−	162.600i	0.885633	−	1.53396i
$107$	169.171			1.58103			0.790517	−	0.612439i	$-0.209812\pi$
$107$	169.171			1.58103			0.790517	+	0.612439i	$0.209812\pi$
$108$		0			0
$109$			87.9613i			0.806984i	0.914983	+	0.403492i	$0.132204\pi$
$109$			87.9613i			0.806984i	−0.914983	+	0.403492i	$0.867796\pi$
$110$	−225.812	−	130.373i	−2.05283	−	1.18520i
$111$		0			0
$112$	−70.5191	+	40.7142i	−0.629635	+	0.363520i
$113$	−15.6861	−	27.1692i	−0.138815	−	0.240435i	0.788233	−	0.615377i	$-0.210996\pi$
$113$	−15.6861	−	27.1692i	−0.138815	−	0.240435i	−0.927048	+	0.374942i	$0.877663\pi$
$114$		0			0
$115$	−31.2389	+	54.1073i	−0.271642	+	0.470499i
$116$	40.9990			0.353439
$117$		0			0
$118$	−270.009			−2.28821
$119$	90.8792	+	132.314i	0.763691	+	1.11188i
$120$		0			0
$121$	4.92097	+	8.52337i	0.0406692	+	0.0704410i
$122$	61.8230	+	107.081i	0.506746	+	0.877710i
$123$		0			0
$124$	80.6754	+	46.5779i	0.650608	+	0.375629i
$125$	123.238			0.985903
$126$		0			0
$127$	70.3705			0.554098			0.277049	−	0.960856i	$-0.410644\pi$
$127$	70.3705			0.554098			0.277049	+	0.960856i	$0.410644\pi$
$128$	−109.617	−	63.2875i	−0.856384	−	0.494433i
$129$		0			0
$130$	−467.655	+	270.001i	−3.59734	+	2.07693i
$131$	16.3054	+	28.2417i	0.124468	+	0.215586i	0.921525	−	0.388319i	$-0.126944\pi$
$131$	16.3054	+	28.2417i	0.124468	+	0.215586i	−0.797057	+	0.603905i	$0.793611\pi$
$132$		0			0
$133$	119.792	+	69.1618i	0.900690	+	0.520013i
$134$			222.596i			1.66117i
$135$		0			0
$136$	−30.7797	+	64.4817i	−0.226321	+	0.474130i
$137$	−102.728	−	59.3098i	−0.749836	−	0.432918i	0.0757984	−	0.997123i	$-0.475849\pi$
$137$	−102.728	−	59.3098i	−0.749836	−	0.432918i	−0.825635	+	0.564205i	$0.809183\pi$
$138$		0			0
$139$	79.2798	−	45.7722i	0.570358	−	0.329297i	−0.186934	−	0.982372i	$-0.559855\pi$
$139$	79.2798	−	45.7722i	0.570358	−	0.329297i	0.757292	+	0.653076i	$0.226522\pi$
$140$	−354.912	+	204.908i	−2.53508	+	1.46363i
$141$		0			0
$142$	−26.9294	−	15.5477i	−0.189644	−	0.109491i
$143$	−230.208			−1.60984
$144$		0			0
$145$	−61.6421			−0.425118
$146$	53.0213	−	91.8356i	0.363160	−	0.629011i
$147$		0			0
$148$	64.5556	−	37.2712i	0.436187	−	0.251832i
$149$	−143.387	+	82.7847i	−0.962331	+	0.555602i	−0.896890	−	0.442255i	$-0.854179\pi$
$149$	−143.387	+	82.7847i	−0.962331	+	0.555602i	−0.0654411	+	0.997856i	$0.520845\pi$
$150$		0			0
$151$	−109.267	+	189.256i	−0.723621	+	1.25335i	0.235918	+	0.971773i	$0.424190\pi$
$151$	−109.267	+	189.256i	−0.723621	+	1.25335i	−0.959539	+	0.281576i	$0.909143\pi$
$152$			61.5718i			0.405078i
$153$		0			0
$154$	−304.777			−1.97907
$155$	−121.296	−	70.0301i	−0.782553	−	0.451807i
$156$		0			0
$157$	−134.982	−	233.796i	−0.859758	−	1.48914i	−0.872160	−	0.489221i	$-0.837281\pi$
$157$	−134.982	−	233.796i	−0.859758	−	1.48914i	0.0124018	−	0.999923i	$-0.496052\pi$
$158$	−171.069	−	296.300i	−1.08272	−	1.87532i
$159$		0			0
$160$	302.319	+	174.544i	1.88949	+	1.09090i
$161$			73.0283i			0.453592i
$162$		0			0
$163$			76.0320i			0.466454i	0.972422	+	0.233227i	$0.0749285\pi$
$163$			76.0320i			0.466454i	−0.972422	+	0.233227i	$0.925071\pi$
$164$	−124.313	+	215.317i	−0.758007	+	1.31291i
$165$		0			0
$166$	−6.66893	−	11.5509i	−0.0401743	−	0.0695839i
$167$	28.7854	+	49.8577i	0.172368	+	0.298549i	0.939247	−	0.343242i	$-0.111525\pi$
$167$	28.7854	+	49.8577i	0.172368	+	0.298549i	−0.766880	+	0.641791i	$0.778192\pi$
$168$		0			0
$169$	−153.879	+	266.527i	−0.910528	+	1.57708i
$170$	181.113	−	379.421i	1.06537	−	2.23189i
$171$		0			0
$172$	298.704			1.73665
$173$	−18.4535	+	31.9624i	−0.106667	+	0.184754i	−0.914418	−	0.404771i	$-0.867351\pi$
$173$	−18.4535	+	31.9624i	−0.106667	+	0.184754i	0.807751	+	0.589524i	$0.200685\pi$
$174$		0			0
$175$	329.181	−	190.052i	1.88103	−	1.08601i
$176$	45.4612	+	78.7412i	0.258303	+	0.447393i
$177$		0			0
$178$	102.784	−	178.027i	0.577437	−	1.00015i
$179$			109.553i			0.612029i	0.952027	+	0.306015i	$0.0989956\pi$
$179$			109.553i			0.612029i	−0.952027	+	0.306015i	$0.901004\pi$
$180$		0			0
$181$			0.415424i			0.00229516i	0.999999	+	0.00114758i	$0.000365286\pi$
$181$			0.415424i			0.00229516i	−0.999999	+	0.00114758i	$0.999635\pi$
$182$	−315.595	+	546.627i	−1.73404	+	3.00344i
$183$		0			0
$184$	−28.1519	+	16.2535i	−0.152999	+	0.0883342i
$185$	−97.0596	+	56.0374i	−0.524646	+	0.302905i
$186$		0			0
$187$	147.741	−	101.475i	0.790060	−	0.542648i
$188$		−	115.596i		−	0.614871i
$189$		0			0
$190$		−	362.299i		−	1.90683i
$191$	135.260	+	78.0927i	0.708170	+	0.408862i	0.810383	−	0.585900i	$-0.199259\pi$
$191$	135.260	+	78.0927i	0.708170	+	0.408862i	−0.102213	+	0.994763i	$0.532592\pi$
$192$		0			0
$193$	−144.878	+	83.6451i	−0.750661	+	0.433394i	−0.825933	−	0.563769i	$-0.809351\pi$
$193$	−144.878	+	83.6451i	−0.750661	+	0.433394i	0.0752717	+	0.997163i	$0.476018\pi$
$194$	158.611	+	274.722i	0.817582	+	1.41609i
$195$		0			0
$196$	−107.876	+	186.847i	−0.550388	+	0.953300i
$197$	−168.129			−0.853449			−0.426724	−	0.904382i	$-0.640333\pi$
$197$	−168.129			−0.853449			−0.426724	+	0.904382i	$0.640333\pi$
$198$		0			0
$199$			143.847i			0.722849i	0.932401	+	0.361424i	$0.117709\pi$
$199$			143.847i			0.722849i	−0.932401	+	0.361424i	$0.882291\pi$
$200$	146.528	+	84.5978i	0.732639	+	0.422989i
$201$		0			0
$202$	−154.366	−	267.369i	−0.764186	−	1.32361i
$203$	−62.3984	+	36.0257i	−0.307381	+	0.177467i
$204$		0			0
$205$	186.905	−	323.729i	0.911733	−	1.57917i
$206$		−	270.118i		−	1.31125i
$207$		0			0
$208$	188.300			0.905288
$209$	77.2257	−	133.759i	0.369501	−	0.639994i
$210$		0			0
$211$	−57.1214	+	32.9791i	−0.270718	+	0.156299i	−0.629214	−	0.777232i	$-0.716623\pi$
$211$	−57.1214	+	32.9791i	−0.270718	+	0.156299i	0.358496	+	0.933531i	$0.383290\pi$
$212$	−285.358	+	164.751i	−1.34603	+	0.777129i
$213$		0			0
$214$	−448.530	−	258.959i	−2.09594	−	1.21009i
$215$	−449.103			−2.08885
$216$		0			0
$217$	−163.712			−0.754433
$218$	134.647	−	233.216i	0.617648	−	1.06980i
$219$		0			0
$220$	228.800	+	396.292i	1.04000	+	1.80133i
$221$	−29.0137	−	370.056i	−0.131284	−	1.67446i
$222$		0			0
$223$	−63.9158	+	110.705i	−0.286618	+	0.496437i	−0.973000	−	0.230804i	$-0.925864\pi$
$223$	−63.9158	+	110.705i	−0.286618	+	0.496437i	0.686382	+	0.727241i	$0.259198\pi$
$224$	408.038			1.82160
$225$		0			0
$226$			96.0465i			0.424985i
$227$	15.6179	−	27.0510i	0.0688014	−	0.119168i	−0.829573	−	0.558399i	$-0.811416\pi$
$227$	15.6179	−	27.0510i	0.0688014	−	0.119168i	0.898374	+	0.439231i	$0.144749\pi$
$228$		0			0
$229$	197.416	+	341.934i	0.862078	+	1.49316i	0.869919	+	0.493194i	$0.164171\pi$
$229$	197.416	+	341.934i	0.862078	+	1.49316i	−0.00784094	+	0.999969i	$0.502496\pi$
$230$	165.650	−	95.6382i	0.720219	−	0.415818i
$231$		0			0
$232$	−27.7753	−	16.0361i	−0.119721	−	0.0691211i
$233$	46.9497			0.201501			0.100750	−	0.994912i	$-0.467876\pi$
$233$	46.9497			0.201501			0.100750	+	0.994912i	$0.467876\pi$
$234$		0			0
$235$			173.799i			0.739569i
$236$	410.373	+	236.929i	1.73887	+	1.00394i
$237$		0			0
$238$	−38.4118	−	489.925i	−0.161394	−	2.05851i
$239$	291.961	−	168.564i	1.22159	−	0.705288i	0.256336	−	0.966588i	$-0.417484\pi$
$239$	291.961	−	168.564i	1.22159	−	0.705288i	0.965258	+	0.261300i	$0.0841511\pi$
$240$		0			0
$241$	11.1211	+	6.42077i	0.0461457	+	0.0266422i	0.522895	−	0.852397i	$-0.324852\pi$
$241$	11.1211	+	6.42077i	0.0461457	+	0.0266422i	−0.476750	+	0.879039i	$0.658185\pi$
$242$		−	30.1312i		−	0.124509i
$243$		0			0
$244$		−	216.995i		−	0.889323i
$245$	162.192	−	280.925i	0.662008	−	1.14663i
$246$		0			0
$247$	−159.934	−	277.013i	−0.647505	−	1.12151i
$248$	−36.4364	−	63.1098i	−0.146921	−	0.254475i
$249$		0			0
$250$	−326.746	−	188.647i	−1.30699	−	0.754589i
$251$		−	48.3962i		−	0.192814i	−0.995342	−	0.0964068i	$-0.969265\pi$
$251$		−	48.3962i		−	0.192814i	0.995342	−	0.0964068i	$-0.0307350\pi$
$252$		0			0
$253$	81.5430			0.322304
$254$	−186.577	−	107.720i	−0.734553	−	0.424095i
$255$		0			0
$256$	−1.85466	−	3.21237i	−0.00724478	−	0.0125483i
$257$	−49.7329	+	28.7133i	−0.193513	+	0.111725i	−0.593626	−	0.804741i	$-0.702304\pi$
$257$	−49.7329	+	28.7133i	−0.193513	+	0.111725i	0.400113	+	0.916466i	$0.368971\pi$
$258$		0			0
$259$	−65.5003	+	113.450i	−0.252897	+	0.438030i
$260$	947.685			3.64494
$261$		0			0
$262$		−	99.8381i		−	0.381061i
$263$	206.973	+	119.496i	0.786970	+	0.454357i	0.838895	−	0.544294i	$-0.183202\pi$
$263$	206.973	+	119.496i	0.786970	+	0.454357i	−0.0519251	+	0.998651i	$0.516536\pi$
$264$		0			0
$265$	429.036	−	247.704i	1.61900	−	0.934733i
$266$	−211.740	−	366.744i	−0.796014	−	1.37874i
$267$		0			0
$268$	195.325	−	338.312i	0.728823	−	1.26236i
$269$	194.989			0.724867			0.362434	−	0.932010i	$-0.381946\pi$
$269$	194.989			0.724867			0.362434	+	0.932010i	$0.381946\pi$
$270$		0			0
$271$	8.67112			0.0319967			0.0159984	−	0.999872i	$-0.494907\pi$
$271$	8.67112			0.0319967			0.0159984	+	0.999872i	$0.494907\pi$
$272$	−120.846	+	83.0024i	−0.444286	+	0.305156i
$273$		0			0
$274$	181.578	+	314.502i	0.662692	+	1.14782i
$275$	−212.211	−	367.561i	−0.771678	−	1.33659i
$276$		0			0
$277$	4.04307	+	2.33427i	0.0145959	+	0.00842695i	0.507280	−	0.861781i	$-0.330651\pi$
$277$	4.04307	+	2.33427i	0.0145959	+	0.00842695i	−0.492684	+	0.870208i	$0.663984\pi$
$278$	−280.264			−1.00815
$279$		0			0
$280$	320.587			1.14495
$281$	−112.493	−	64.9476i	−0.400329	−	0.231130i	0.286297	−	0.958141i	$-0.407576\pi$
$281$	−112.493	−	64.9476i	−0.400329	−	0.231130i	−0.686626	+	0.727011i	$0.740909\pi$
$282$		0			0
$283$	−302.468	+	174.630i	−1.06879	+	0.617066i	−0.927851	−	0.372952i	$-0.878346\pi$
$283$	−302.468	+	174.630i	−1.06879	+	0.617066i	−0.140939	+	0.990018i	$0.545012\pi$
$284$	27.2857	+	47.2602i	0.0960764	+	0.166409i
$285$		0			0
$286$	610.360	+	352.392i	2.13413	+	1.23214i
$287$		−	436.935i		−	1.52242i
$288$		0			0
$289$	181.740	+	224.703i	0.628860	+	0.777519i
$290$	163.434	+	94.3589i	0.563567	+	0.325376i
$291$		0			0
$292$	−161.169	+	93.0507i	−0.551947	+	0.318667i
$293$	−153.145	+	88.4185i	−0.522680	+	0.301770i	−0.738031	−	0.674767i	$-0.764244\pi$
$293$	−153.145	+	88.4185i	−0.522680	+	0.301770i	0.215350	+	0.976537i	$0.430911\pi$
$294$		0			0
$295$	−616.997	−	356.223i	−2.09151	−	1.20754i
$296$	−58.3122			−0.197001
$297$		0			0
$298$	506.893			1.70098
$299$	84.4375	−	146.250i	0.282400	−	0.489130i
$300$		0			0
$301$	−454.613	+	262.471i	−1.51034	+	0.871997i
$302$	579.408	−	334.522i	1.91857	−	1.10769i
$303$		0			0
$304$	−63.1672	+	109.409i	−0.207787	+	0.359898i
$305$			326.252i			1.06968i
$306$		0			0
$307$	337.549			1.09951			0.549754	−	0.835327i	$-0.314722\pi$
$307$	337.549			1.09951			0.549754	+	0.835327i	$0.314722\pi$
$308$	463.214	+	267.437i	1.50394	+	0.868301i
$309$		0			0
$310$	214.398	+	371.348i	0.691606	+	1.19790i
$311$	287.876	+	498.615i	0.925645	+	1.60327i	0.790520	+	0.612437i	$0.209811\pi$
$311$	287.876	+	498.615i	0.925645	+	1.60327i	0.135126	+	0.990828i	$0.456856\pi$
$312$		0			0
$313$	431.908	+	249.362i	1.37990	+	0.796685i	0.992147	−	0.125078i	$-0.0399182\pi$
$313$	431.908	+	249.362i	1.37990	+	0.796685i	0.387752	+	0.921764i	$0.373252\pi$
$314$			826.498i			2.63216i
$315$		0			0
$316$			600.441i			1.90013i
$317$	−231.112	+	400.297i	−0.729060	+	1.26277i	0.228222	+	0.973609i	$0.426709\pi$
$317$	−231.112	+	400.297i	−0.729060	+	1.26277i	−0.957281	+	0.289159i	$0.906624\pi$
$318$		0			0
$319$	40.2261	+	69.6737i	0.126101	+	0.218413i
$320$	−395.040	−	684.229i	−1.23450	−	2.13821i
$321$		0			0
$322$	111.788	−	193.623i	0.347169	−	0.601315i
$323$	224.749	+	107.281i	0.695816	+	0.332140i
$324$		0			0
$325$	−878.977			−2.70454
$326$	116.386	−	201.587i	0.357014	−	0.618366i
$327$		0			0
$328$	168.435	−	97.2463i	0.513523	−	0.296483i
$329$	101.574	+	175.931i	0.308735	+	0.534745i
$330$		0			0
$331$	−17.8432	+	30.9053i	−0.0539068	+	0.0933694i	−0.891720	−	0.452588i	$-0.850501\pi$
$331$	−17.8432	+	30.9053i	−0.0539068	+	0.0933694i	0.837813	+	0.545958i	$0.183834\pi$
$332$			23.4075i			0.0705046i
$333$		0			0
$334$		−	176.254i		−	0.527705i
$335$	−293.671	+	508.653i	−0.876630	+	1.51837i
$336$		0			0
$337$	436.273	−	251.882i	1.29458	−	0.747425i	0.315116	−	0.949053i	$-0.397957\pi$
$337$	436.273	−	251.882i	1.29458	−	0.747425i	0.979462	+	0.201628i	$0.0646232\pi$
$338$	815.974	−	471.103i	2.41413	−	1.39380i
$339$		0			0
$340$	−608.199	+	417.738i	−1.78882	+	1.22864i
$341$			182.800i			0.536070i
$342$		0			0
$343$			83.5078i			0.243463i
$344$	−202.362	−	116.833i	−0.588260	−	0.339632i
$345$		0			0
$346$	97.8531	−	56.4955i	0.282813	−	0.163282i
$347$	100.785	+	174.564i	0.290446	+	0.503067i	0.973915	−	0.226912i	$-0.0728630\pi$
$347$	100.785	+	174.564i	0.290446	+	0.503067i	−0.683469	+	0.729979i	$0.739530\pi$
$348$		0			0
$349$	−103.083	+	178.544i	−0.295366	+	0.511588i	−0.975070	−	0.221898i	$-0.928775\pi$
$349$	−103.083	+	178.544i	−0.295366	+	0.511588i	0.679704	+	0.733486i	$0.262108\pi$
$350$	−1163.70			−3.32485
$351$		0			0
$352$		−	455.612i		−	1.29435i
$353$	−387.685	−	223.830i	−1.09826	−	0.634080i	−0.162496	−	0.986709i	$-0.551954\pi$
$353$	−387.685	−	223.830i	−1.09826	−	0.634080i	−0.935763	+	0.352629i	$0.885288\pi$
$354$		0			0
$355$	−41.0241	−	71.0559i	−0.115561	−	0.200157i
$356$	−312.432	+	180.382i	−0.877617	+	0.506692i
$357$		0			0
$358$	167.699	−	290.464i	0.468434	−	0.811351i
$359$		−	366.344i		−	1.02046i	−0.860039	−	0.510228i	$-0.829561\pi$
$359$		−	366.344i		−	1.02046i	0.860039	−	0.510228i	$-0.170439\pi$
$360$		0			0
$361$	−146.394			−0.405523
$362$	0.635913	−	1.10143i	0.00175666	−	0.00304263i
$363$		0			0
$364$	959.313	−	553.859i	2.63547	−	1.52159i
$365$	242.317	−	139.902i	0.663884	−	0.383293i
$366$		0			0
$367$	−236.295	−	136.425i	−0.643855	−	0.371730i	0.142243	−	0.989832i	$-0.454568\pi$
$367$	−236.295	−	136.425i	−0.643855	−	0.371730i	−0.786098	+	0.618102i	$0.787902\pi$
$368$	−66.6986			−0.181246
$369$		0			0
$370$	343.118			0.927346
$371$	289.534	−	501.487i	0.780414	−	1.35172i
$372$		0			0
$373$	−126.588	−	219.258i	−0.339379	−	0.587822i	0.644937	−	0.764236i	$-0.276884\pi$
$373$	−126.588	−	219.258i	−0.339379	−	0.587822i	−0.984316	+	0.176414i	$0.943550\pi$
$374$	−547.047	+	42.8904i	−1.46269	+	0.114680i
$375$		0			0
$376$	−45.2135	+	78.3120i	−0.120249	+	0.208277i
$377$	166.616			0.441952
$378$		0			0
$379$		−	497.597i		−	1.31292i	−0.754360	−	0.656461i	$-0.772053\pi$
$379$		−	497.597i		−	1.31292i	0.754360	−	0.656461i	$-0.227947\pi$
$380$	−317.911	+	550.638i	−0.836608	+	1.44905i
$381$		0			0
$382$	−239.082	−	414.101i	−0.625868	−	1.08404i
$383$	643.789	−	371.692i	1.68091	−	0.970474i	0.719854	−	0.694126i	$-0.244209\pi$
$383$	643.789	−	371.692i	1.68091	−	0.970474i	0.961057	−	0.276349i	$-0.0891244\pi$
$384$		0			0
$385$	−696.443	−	402.092i	−1.80894	−	1.04439i
$386$	512.161			1.32684
$387$		0			0
$388$		−	556.714i		−	1.43483i
$389$	−502.792	−	290.287i	−1.29252	−	0.746240i	−0.313424	−	0.949613i	$-0.601476\pi$
$389$	−502.792	−	290.287i	−1.29252	−	0.746240i	−0.979101	+	0.203374i	$0.934809\pi$
$390$		0			0
$391$	10.2771	+	131.079i	0.0262841	+	0.335241i
$392$	146.164	−	84.3880i	0.372868	−	0.215276i
$393$		0			0
$394$	445.769	+	257.365i	1.13139	+	0.653211i
$395$		−	902.765i		−	2.28548i
$396$		0			0
$397$			752.926i			1.89654i	0.317465	+	0.948270i	$0.397168\pi$
$397$			752.926i			1.89654i	−0.317465	+	0.948270i	$0.602832\pi$
$398$	220.194	−	381.388i	0.553252	−	0.958261i
$399$		0			0
$400$	173.580	+	300.649i	0.433950	+	0.751623i
$401$	16.6360	+	28.8144i	0.0414863	+	0.0718564i	0.886023	−	0.463641i	$-0.153457\pi$
$401$	16.6360	+	28.8144i	0.0414863	+	0.0718564i	−0.844537	+	0.535498i	$0.820124\pi$
$402$		0			0
$403$	327.857	+	189.288i	0.813542	+	0.469698i
$404$			541.814i			1.34112i
$405$		0			0
$406$	220.586			0.543316
$407$	126.677	+	73.1373i	0.311247	+	0.179698i
$408$		0			0
$409$	55.9973	+	96.9902i	0.136913	+	0.237140i	0.926327	−	0.376722i	$-0.122949\pi$
$409$	55.9973	+	96.9902i	0.136913	+	0.237140i	−0.789414	+	0.613862i	$0.789615\pi$
$410$	−991.102	+	572.213i	−2.41732	+	1.39564i
$411$		0			0
$412$	−237.024	+	410.538i	−0.575302	+	0.996452i
$413$	−832.756			−2.01636
$414$		0			0
$415$		−	35.1933i		−	0.0848031i
$416$	−817.156	−	471.785i	−1.96432	−	1.13410i
$417$		0			0
$418$	−409.504	+	236.427i	−0.979675	+	0.565616i
$419$	210.700	+	364.943i	0.502864	+	0.870986i	0.999995	+	0.00331046i	$0.00105376\pi$
$419$	210.700	+	364.943i	0.502864	+	0.870986i	−0.497130	+	0.867676i	$0.665613\pi$
$420$		0			0
$421$	200.328	−	346.979i	0.475839	−	0.824178i	−0.523778	−	0.851855i	$-0.675478\pi$
$421$	200.328	−	346.979i	0.475839	−	0.824178i	0.999617	+	0.0276772i	$0.00881106\pi$
$422$	201.932			0.478511
$423$		0			0
$424$	257.760			0.607923
$425$	564.104	−	387.452i	1.32730	−	0.911652i
$426$		0			0
$427$	190.673	+	330.255i	0.446541	+	0.773432i
$428$	454.465	+	787.156i	1.06183	+	1.83915i
$429$		0			0
$430$	1190.73	+	687.467i	2.76913	+	1.59876i
$431$	−769.605			−1.78563			−0.892814	−	0.450426i	$-0.851272\pi$
$431$	−769.605			−1.78563			−0.892814	+	0.450426i	$0.851272\pi$
$432$		0			0
$433$	212.894			0.491671			0.245836	−	0.969312i	$-0.420938\pi$
$433$	212.894			0.491671			0.245836	+	0.969312i	$0.420938\pi$
$434$	434.057	+	250.603i	1.00013	+	0.577426i
$435$		0			0
$436$	−409.286	+	236.302i	−0.938730	+	0.541976i
$437$	56.6509	+	98.1223i	0.129636	+	0.224536i
$438$		0			0
$439$	32.0975	+	18.5315i	0.0731150	+	0.0422130i	0.536112	−	0.844147i	$-0.319893\pi$
$439$	32.0975	+	18.5315i	0.0731150	+	0.0422130i	−0.462997	+	0.886360i	$0.653226\pi$
$440$		−	357.965i		−	0.813558i
$441$		0			0
$442$	−489.540	+	1025.56i	−1.10756	+	2.32027i
$443$	−356.817	−	206.009i	−0.805457	−	0.465031i	0.0399189	−	0.999203i	$-0.487290\pi$
$443$	−356.817	−	206.009i	−0.805457	−	0.465031i	−0.845376	+	0.534172i	$0.820623\pi$
$444$		0			0
$445$	469.742	−	271.206i	1.05560	−	0.609451i
$446$	338.926	−	195.679i	0.759924	−	0.438742i
$447$		0			0
$448$	−799.773	−	461.749i	−1.78521	−	1.03069i
$449$	629.945			1.40300			0.701498	−	0.712672i	$-0.252515\pi$
$449$	629.945			1.40300			0.701498	+	0.712672i	$0.252515\pi$
$450$		0			0
$451$	−487.879			−1.08177
$452$	84.2793	−	145.976i	0.186459	−	0.322956i
$453$		0			0
$454$	−82.8171	+	47.8145i	−0.182417	+	0.105318i
$455$	−1442.33	+	832.729i	−3.16995	+	1.83017i
$456$		0			0
$457$	−399.682	+	692.270i	−0.874579	+	1.51481i	−0.0173675	+	0.999849i	$0.505529\pi$
$457$	−399.682	+	692.270i	−0.874579	+	1.51481i	−0.857211	+	0.514965i	$0.827805\pi$
$458$		−	1208.78i		−	2.63926i
$459$		0			0
$460$	−335.684			−0.729748
$461$	487.175	+	281.271i	1.05678	+	0.610131i	0.924539	−	0.381086i	$-0.124450\pi$
$461$	487.175	+	281.271i	1.05678	+	0.610131i	0.132239	+	0.991218i	$0.457783\pi$
$462$		0			0
$463$	−39.1962	−	67.8898i	−0.0846570	−	0.146630i	0.820588	−	0.571520i	$-0.193646\pi$
$463$	−39.1962	−	67.8898i	−0.0846570	−	0.146630i	−0.905245	+	0.424890i	$0.860313\pi$
$464$	−32.9032	−	56.9901i	−0.0709121	−	0.122823i
$465$		0			0
$466$	−124.480	−	71.8685i	−0.267124	−	0.154224i
$467$		−	427.234i		−	0.914849i	−0.889249	−	0.457424i	$-0.848772\pi$
$467$		−	427.234i		−	0.914849i	0.889249	−	0.457424i	$-0.151228\pi$
$468$		0			0
$469$			686.526i			1.46381i
$470$	266.043	−	460.801i	0.566050	−	0.980427i
$471$		0			0
$472$	−185.342	−	321.022i	−0.392674	−	0.680131i
$473$	293.074	+	507.619i	0.619606	+	1.07319i
$474$		0			0
$475$	294.862	−	510.717i	0.620763	−	1.07519i
$476$	−371.521	+	778.316i	−0.780506	+	1.63512i
$477$		0			0
$478$	−1032.12			−2.15925
$479$	11.2455	−	19.4777i	0.0234770	−	0.0406633i	−0.854048	−	0.520194i	$-0.825860\pi$
$479$	11.2455	−	19.4777i	0.0234770	−	0.0406633i	0.877525	+	0.479531i	$0.159193\pi$
$480$		0			0
$481$	262.348	−	151.467i	0.545422	−	0.314900i
$482$	−19.6573	−	34.0474i	−0.0407827	−	0.0706378i
$483$		0			0
$484$	−26.4396	+	45.7948i	−0.0546274	+	0.0946174i
$485$			837.022i			1.72582i
$486$		0			0
$487$		−	507.974i		−	1.04307i	−0.853230	−	0.521534i	$-0.825360\pi$
$487$		−	507.974i		−	1.04307i	0.853230	−	0.521534i	$-0.174640\pi$
$488$	−84.8741	+	147.006i	−0.173922	+	0.301242i
$489$		0			0
$490$	−860.054	+	496.553i	−1.75521	+	1.01337i
$491$	−122.685	+	70.8320i	−0.249867	+	0.144261i	−0.619703	−	0.784836i	$-0.712747\pi$
$491$	−122.685	+	70.8320i	−0.249867	+	0.144261i	0.369837	+	0.929097i	$0.379414\pi$
$492$		0			0
$493$	−106.930	+	73.4441i	−0.216896	+	0.148974i
$494$			979.279i			1.98235i
$495$		0			0
$496$		−	149.522i		−	0.301456i
$497$	−83.0550	−	47.9518i	−0.167113	−	0.0964825i
$498$		0			0
$499$	161.668	−	93.3388i	0.323983	−	0.187052i	−0.329183	−	0.944266i	$-0.606773\pi$
$499$	161.668	−	93.3388i	0.323983	−	0.187052i	0.653167	+	0.757214i	$0.273440\pi$
$500$	331.070	+	573.430i	0.662139	+	1.14686i
$501$		0			0
$502$	−74.0828	+	128.315i	−0.147575	+	0.255608i
$503$	228.337			0.453950			0.226975	−	0.973901i	$-0.427116\pi$
$503$	228.337			0.453950			0.226975	+	0.973901i	$0.427116\pi$
$504$		0			0
$505$		−	814.618i		−	1.61311i
$506$	−216.199	−	124.822i	−0.427270	−	0.246685i
$507$		0			0
$508$	189.045	+	327.436i	0.372136	+	0.644559i
$509$	−26.2022	+	15.1279i	−0.0514778	+	0.0297207i	−0.525518	−	0.850782i	$-0.676128\pi$
$509$	−26.2022	+	15.1279i	−0.0514778	+	0.0297207i	0.474040	+	0.880503i	$0.342795\pi$
$510$		0			0
$511$	163.527	−	283.237i	0.320014	−	0.554280i
$512$			517.656i			1.01105i
$513$		0			0
$514$	175.812			0.342047
$515$	356.367	−	617.245i	0.691974	−	1.19853i
$516$		0			0
$517$	196.444	−	113.417i	0.379968	−	0.219375i
$518$	347.328	−	200.530i	0.670518	−	0.387124i
$519$		0			0
$520$	−642.023	−	370.672i	−1.23466	−	0.712831i
$521$	38.9717			0.0748017			0.0374009	−	0.999300i	$-0.488092\pi$
$521$	38.9717			0.0748017			0.0374009	+	0.999300i	$0.488092\pi$
$522$		0			0
$523$	383.762			0.733771			0.366886	−	0.930266i	$-0.380424\pi$
$523$	383.762			0.733771			0.366886	+	0.930266i	$0.380424\pi$
$524$	−87.6063	+	151.739i	−0.167188	+	0.289578i
$525$		0			0
$526$	−365.838	−	633.650i	−0.695510	−	1.20466i
$527$	−293.848	+	23.0387i	−0.557587	+	0.0437167i
$528$		0			0
$529$	234.591	−	406.324i	0.443461	−	0.768097i
$530$	−1516.70			−2.86170
$531$		0			0
$532$			743.193i			1.39698i
$533$	−505.197	+	875.028i	−0.947838	+	1.64170i
$534$		0			0
$535$	−683.290	−	1183.49i	−1.27718	−	2.21213i
$536$	−264.651	+	152.796i	−0.493752	+	0.285068i
$537$		0			0
$538$	−516.984	−	298.481i	−0.960938	−	0.554798i
$539$	−423.370			−0.785473
$540$		0			0
$541$			991.043i			1.83187i	0.401324	+	0.915936i	$0.368550\pi$
$541$			991.043i			1.83187i	−0.401324	+	0.915936i	$0.631450\pi$
$542$	−22.9901	−	13.2734i	−0.0424172	−	0.0244896i
$543$		0			0
$544$	732.391	−	57.4220i	1.34631	−	0.105555i
$545$	615.363	−	355.280i	1.12911	−	0.651890i
$546$		0			0
$547$	−464.221	−	268.018i	−0.848667	−	0.489978i	0.0115342	−	0.999933i	$-0.496328\pi$
$547$	−464.221	−	268.018i	−0.848667	−	0.489978i	−0.860201	+	0.509956i	$0.829662\pi$
$548$		−	637.326i		−	1.16300i
$549$		0			0
$550$			1299.38i			2.36250i
$551$	−55.8932	+	96.8098i	−0.101440	+	0.175698i
$552$		0			0
$553$	−527.607	−	913.842i	−0.954081	−	1.65252i
$554$	−7.14638	−	12.3779i	−0.0128996	−	0.0223428i
$555$		0			0
$556$	425.959	+	245.928i	0.766113	+	0.442316i
$557$			798.037i			1.43274i	0.697720	+	0.716370i	$0.254198\pi$
$557$			798.037i			1.43274i	−0.697720	+	0.716370i	$0.745802\pi$
$558$		0			0
$559$	1213.91			2.17157
$560$	569.661	+	328.894i	1.01725	+	0.587310i
$561$		0			0
$562$	198.838	+	344.397i	0.353804	+	0.612806i
$563$	856.083	−	494.260i	1.52057	−	0.877904i	0.520869	−	0.853637i	$-0.325608\pi$
$563$	856.083	−	494.260i	1.52057	−	0.877904i	0.999706	−	0.0242674i	$-0.00772532\pi$
$564$		0			0
$565$	−126.714	+	219.475i	−0.224273	+	0.388452i
$566$	1069.26			1.88916
$567$		0			0
$568$		−	42.6895i		−	0.0751575i
$569$	581.846	+	335.929i	1.02258	+	0.590384i	0.914849	−	0.403796i	$-0.132309\pi$
$569$	581.846	+	335.929i	1.02258	+	0.590384i	0.107727	+	0.994181i	$0.465643\pi$
$570$		0			0
$571$	−873.895	+	504.543i	−1.53046	+	0.883614i	−0.531124	+	0.847294i	$0.678230\pi$
$571$	−873.895	+	504.543i	−1.53046	+	0.883614i	−0.999340	+	0.0363195i	$0.988437\pi$
$572$	−618.436	−	1071.16i	−1.08118	−	1.87266i
$573$		0			0
$574$	−668.841	+	1158.47i	−1.16523	+	2.01824i
$575$	311.347			0.541473
$576$		0			0
$577$	365.156			0.632852			0.316426	−	0.948617i	$-0.397517\pi$
$577$	365.156			0.632852			0.316426	+	0.948617i	$0.397517\pi$
$578$	−137.892	−	873.966i	−0.238567	−	1.51205i
$579$		0			0
$580$	−165.597	−	286.822i	−0.285512	−	0.494521i
$581$	−20.5682	−	35.6251i	−0.0354013	−	0.0613169i
$582$		0			0
$583$	−559.957	−	323.291i	−0.960476	−	0.554531i
$584$	145.581			0.249283
$585$		0			0
$586$	541.388			0.923871
$587$	−388.428	−	224.259i	−0.661718	−	0.382043i	0.131213	−	0.991354i	$-0.458113\pi$
$587$	−388.428	−	224.259i	−0.661718	−	0.382043i	−0.792931	+	0.609311i	$0.791446\pi$
$588$		0			0
$589$	−219.967	+	126.998i	−0.373458	+	0.215616i
$590$	1090.58	+	1888.94i	1.84844	+	3.20160i
$591$		0			0
$592$	−103.617	−	59.8231i	−0.175028	−	0.101053i
$593$		−	65.3628i		−	0.110224i	−0.998480	−	0.0551120i	$-0.982448\pi$
$593$		−	65.3628i		−	0.110224i	0.998480	−	0.0551120i	$-0.0175516\pi$
$594$		0			0
$595$	558.583	−	1170.20i	0.938795	−	1.96672i
$596$	−770.399	−	444.790i	−1.29262	−	0.746292i
$597$		0			0
$598$	−447.746	+	258.506i	−0.748739	+	0.432285i
$599$	−854.077	+	493.102i	−1.42584	+	0.823208i	−0.996789	−	0.0800729i	$-0.974485\pi$
$599$	−854.077	+	493.102i	−1.42584	+	0.823208i	−0.429049	+	0.903281i	$0.641151\pi$
$600$		0			0
$601$	−107.558	−	62.0987i	−0.178965	−	0.103326i	0.407841	−	0.913053i	$-0.366282\pi$
$601$	−107.558	−	62.0987i	−0.178965	−	0.103326i	−0.586806	+	0.809727i	$0.699615\pi$
$602$	1607.12			2.66963
$603$		0			0
$604$	−1174.15			−1.94396
$605$	39.7521	−	68.8526i	0.0657059	−	0.113806i
$606$		0			0
$607$	839.562	−	484.721i	1.38313	−	0.798552i	0.390604	−	0.920559i	$-0.372266\pi$
$607$	839.562	−	484.721i	1.38313	−	0.798552i	0.992529	+	0.122007i	$0.0389330\pi$
$608$	548.248	−	316.531i	0.901723	−	0.520610i
$609$		0			0
$610$	499.413	−	865.008i	0.818709	−	1.41805i
$611$		−	469.771i		−	0.768856i
$612$		0			0
$613$	730.706			1.19202			0.596008	−	0.802978i	$-0.296753\pi$
$613$	730.706			1.19202			0.596008	+	0.802978i	$0.296753\pi$
$614$	−894.959	−	516.705i	−1.45759	−	0.841539i
$615$		0			0
$616$	−209.207	−	362.357i	−0.339622	−	0.588243i
$617$	−283.553	−	491.128i	−0.459567	−	0.795994i	0.539371	−	0.842069i	$-0.318662\pi$
$617$	−283.553	−	491.128i	−0.459567	−	0.795994i	−0.998938	+	0.0460743i	$0.985329\pi$
$618$		0			0
$619$	246.723	+	142.446i	0.398583	+	0.230122i	0.685872	−	0.727722i	$-0.259421\pi$
$619$	246.723	+	142.446i	0.398583	+	0.230122i	−0.287289	+	0.957844i	$0.592754\pi$
$620$		−	752.523i		−	1.21375i
$621$		0			0
$622$		−	1762.67i		−	2.83387i
$623$	317.004	−	549.066i	0.508834	−	0.881326i
$624$		0			0
$625$	5.43303	+	9.41029i	0.00869285	+	0.0150565i
$626$	−763.426	−	1322.29i	−1.21953	−	2.11229i
$627$		0			0
$628$	725.239	−	1256.15i	1.15484	−	2.00024i
$629$	−101.602	+	212.850i	−0.161529	+	0.338395i
$630$		0			0
$631$	226.146			0.358394			0.179197	−	0.983813i	$-0.442650\pi$
$631$	226.146			0.358394			0.179197	+	0.983813i	$0.442650\pi$
$632$	234.853	−	406.778i	0.371603	−	0.643635i
$633$		0			0
$634$	1225.52	−	707.552i	1.93299	−	1.11601i
$635$	−284.230	−	492.301i	−0.447606	−	0.775277i
$636$		0			0
$637$	−438.398	+	759.328i	−0.688223	+	1.19204i
$638$		−	246.305i		−	0.386059i
$639$		0			0
$640$			1022.49i			1.59763i
$641$	−112.238	+	194.403i	−0.175099	+	0.303280i	−0.940195	−	0.340635i	$-0.889358\pi$
$641$	−112.238	+	194.403i	−0.175099	+	0.303280i	0.765097	+	0.643915i	$0.222691\pi$
$642$		0			0
$643$	−348.707	+	201.326i	−0.542313	+	0.313105i	−0.746016	−	0.665928i	$-0.768036\pi$
$643$	−348.707	+	201.326i	−0.542313	+	0.313105i	0.203703	+	0.979033i	$0.434702\pi$
$644$	−339.803	+	196.185i	−0.527644	+	0.304635i
$645$		0			0
$646$	−431.665	−	628.475i	−0.668212	−	0.972872i
$647$			669.881i			1.03537i	0.855573	+	0.517683i	$0.173205\pi$
$647$			669.881i			1.03537i	−0.855573	+	0.517683i	$0.826795\pi$
$648$		0			0
$649$			929.851i			1.43274i
$650$	2330.47	+	1345.50i	3.58534	+	2.07000i
$651$		0			0
$652$	−353.779	+	204.255i	−0.542606	+	0.313274i
$653$	258.224	+	447.257i	0.395442	+	0.684926i	0.993158	−	0.116783i	$-0.0372580\pi$
$653$	258.224	+	447.257i	0.395442	+	0.684926i	−0.597715	+	0.801708i	$0.703925\pi$
$654$		0			0
$655$	131.716	−	228.139i	0.201094	−	0.348305i
$656$	399.064			0.608330
$657$		0			0
$658$		−	621.939i		−	0.945196i
$659$	332.304	+	191.856i	0.504255	+	0.291132i	0.730469	−	0.682946i	$-0.239301\pi$
$659$	332.304	+	191.856i	0.504255	+	0.291132i	−0.226214	+	0.974078i	$0.572635\pi$
$660$		0			0
$661$	−370.080	−	640.998i	−0.559879	−	0.969739i	−0.997506	−	0.0705824i	$-0.977514\pi$
$661$	−370.080	−	640.998i	−0.559879	−	0.969739i	0.437627	−	0.899157i	$-0.355819\pi$
$662$	94.6168	−	54.6271i	0.142926	−	0.0825182i
$663$		0			0
$664$	9.15548	−	15.8578i	0.0137884	−	0.0238822i
$665$		−	1117.39i		−	1.68029i
$666$		0			0
$667$	−59.0179			−0.0884826
$668$	−154.660	+	267.878i	−0.231526	+	0.401016i
$669$		0			0
$670$	1557.25	−	899.078i	2.32425	−	1.34191i
$671$	368.761	−	212.904i	0.549570	−	0.317294i
$672$		0			0
$673$	−694.469	−	400.952i	−1.03190	−	0.595768i	−0.114372	−	0.993438i	$-0.536486\pi$
$673$	−694.469	−	400.952i	−1.03190	−	0.595768i	−0.917529	+	0.397670i	$0.869819\pi$
$674$	−1542.28			−2.28825
$675$		0			0
$676$	−1653.54			−2.44607
$677$	−426.164	+	738.138i	−0.629490	+	1.09031i	0.358165	+	0.933658i	$0.383403\pi$
$677$	−426.164	+	738.138i	−0.629490	+	1.09031i	−0.987654	+	0.156649i	$0.949931\pi$
$678$		0			0
$679$	489.184	+	847.292i	0.720448	+	1.24785i
$680$	575.425	−	45.1153i	0.846213	−	0.0663460i
$681$		0			0
$682$	279.822	−	484.666i	0.410296	−	0.710653i
$683$	−281.224			−0.411748			−0.205874	−	0.978579i	$-0.566004\pi$
$683$	−281.224			−0.411748			−0.205874	+	0.978579i	$0.566004\pi$
$684$		0			0
$685$			958.222i			1.39886i
$686$	127.830	−	221.408i	0.186341	−	0.322752i
$687$		0			0
$688$	−239.722	−	415.210i	−0.348433	−	0.603503i
$689$	−1159.67	+	669.534i	−1.68312	+	0.971748i
$690$		0			0
$691$	755.748	+	436.331i	1.09370	+	0.631449i	0.934560	−	0.355807i	$-0.115794\pi$
$691$	755.748	+	436.331i	1.09370	+	0.631449i	0.159142	+	0.987256i	$0.449127\pi$
$692$	−198.296			−0.286555
$693$		0			0
$694$		−	617.108i		−	0.889204i
$695$	−640.431	−	369.753i	−0.921483	−	0.532018i
$696$		0			0
$697$	−61.4887	−	784.260i	−0.0882191	−	1.12519i
$698$	546.616	−	315.589i	0.783117	−	0.452133i
$699$		0			0
$700$	1768.64	+	1021.12i	2.52663	+	1.45875i
$701$			477.598i			0.681309i	0.940189	+	0.340655i	$0.110649\pi$
$701$			477.598i			0.681309i	−0.940189	+	0.340655i	$0.889351\pi$
$702$		0			0
$703$			203.245i			0.289111i
$704$	−515.586	+	893.022i	−0.732367	+	1.26850i
$705$		0			0
$706$	685.259	+	1186.90i	0.970622	+	1.68117i
$707$	−476.091	−	824.613i	−0.673396	−	1.16636i
$708$		0			0
$709$	−749.650	−	432.811i	−1.05733	−	0.610452i	−0.132641	−	0.991164i	$-0.542346\pi$
$709$	−749.650	−	432.811i	−1.05733	−	0.610452i	−0.924694	+	0.380712i	$0.875679\pi$
$710$			251.192i			0.353791i
$711$		0			0
$712$	282.215			0.396369
$713$	−116.132	−	67.0488i	−0.162878	−	0.0940376i
$714$		0			0
$715$	929.821	+	1610.50i	1.30045	+	2.25244i
$716$	−509.754	+	294.307i	−0.711947	+	0.411043i
$717$		0			0
$718$	−560.783	+	971.304i	−0.781035	+	1.35279i
$719$	−875.206			−1.21725			−0.608627	−	0.793456i	$-0.708280\pi$
$719$	−875.206			−1.21725			−0.608627	+	0.793456i	$0.708280\pi$
$720$		0			0
$721$		−	833.092i		−	1.15547i
$722$	388.141	+	224.093i	0.537591	+	0.310378i
$723$		0			0
$724$	−1.93298	+	1.11601i	−0.00266986	+	0.00154145i
$725$	153.591	+	266.028i	0.211850	+	0.366935i
$726$		0			0
$727$	11.7147	−	20.2904i	0.0161137	−	0.0279098i	−0.857856	−	0.513890i	$-0.828204\pi$
$727$	11.7147	−	20.2904i	0.0161137	−	0.0279098i	0.873970	+	0.485980i	$0.161537\pi$
$728$	−866.533			−1.19029
$729$		0			0
$730$	−856.624			−1.17346
$731$	−779.054	+	535.089i	−1.06574	+	0.731996i
$732$		0			0
$733$	405.654	+	702.614i	0.553417	+	0.958546i	0.998025	+	0.0628206i	$0.0200096\pi$
$733$	405.654	+	702.614i	0.553417	+	0.958546i	−0.444608	+	0.895725i	$0.646657\pi$
$734$	417.666	+	723.419i	0.569027	+	0.985584i
$735$		0			0
$736$	289.449	+	167.113i	0.393273	+	0.227056i
$737$	766.571			1.04012
$738$		0			0
$739$	436.655			0.590873			0.295436	−	0.955362i	$-0.404535\pi$
$739$	436.655			0.590873			0.295436	+	0.955362i	$0.404535\pi$
$740$	−521.487	−	301.081i	−0.704712	−	0.406866i
$741$		0			0
$742$	−1535.31	+	886.410i	−2.06915	+	1.19462i
$743$	−694.330	−	1202.61i	−0.934495	−	1.61859i	−0.775532	−	0.631308i	$-0.782518\pi$
$743$	−694.330	−	1202.61i	−0.934495	−	1.61859i	−0.158963	−	0.987285i	$-0.550815\pi$
$744$		0			0
$745$	1158.30	+	668.743i	1.55476	+	0.897642i
$746$			775.104i			1.03901i
$747$		0			0
$748$	869.063	+	414.838i	1.16185	+	0.554597i
$749$	−1383.35	−	798.676i	−1.84692	−	1.06632i
$750$		0			0
$751$	−813.248	+	469.529i	−1.08289	+	0.625205i	−0.931674	−	0.363296i	$-0.881651\pi$
$751$	−813.248	+	469.529i	−1.08289	+	0.625205i	−0.151213	+	0.988501i	$0.548318\pi$
$752$	−160.682	+	92.7700i	−0.213673	+	0.123364i
$753$		0			0
$754$	−441.757	−	255.048i	−0.585884	−	0.338261i
$755$	1765.34			2.33820
$756$		0			0
$757$	−687.805			−0.908594			−0.454297	−	0.890850i	$-0.650109\pi$
$757$	−687.805			−0.908594			−0.454297	+	0.890850i	$0.650109\pi$
$758$	−761.700	+	1319.30i	−1.00488	+	1.74050i
$759$		0			0
$760$	430.747	−	248.692i	0.566772	−	0.327226i
$761$	1278.64	−	738.221i	1.68021	−	0.970067i	0.718685	−	0.695336i	$-0.244745\pi$
$761$	1278.64	−	738.221i	1.68021	−	0.970067i	0.961521	−	0.274731i	$-0.0885888\pi$
$762$		0			0
$763$	415.276	−	719.279i	0.544267	−	0.942698i
$764$			839.161i			1.09838i
$765$		0			0
$766$	−2275.88			−2.97112
$767$	1667.72	+	962.857i	2.17434	+	1.25536i
$768$		0			0
$769$	−491.435	−	851.191i	−0.639058	−	1.10688i	−0.985640	−	0.168861i	$-0.945991\pi$
$769$	−491.435	−	851.191i	−0.639058	−	1.10688i	0.346582	−	0.938020i	$-0.387342\pi$
$770$	1231.01	+	2132.17i	1.59871	+	2.76905i
$771$		0			0
$772$	−778.406	−	449.413i	−1.00830	−	0.582141i
$773$			1082.93i			1.40095i	0.713679	+	0.700473i	$0.247028\pi$
$773$			1082.93i			1.40095i	−0.713679	+	0.700473i	$0.752972\pi$
$774$		0			0
$775$			697.965i			0.900599i
$776$	−217.750	+	377.154i	−0.280606	+	0.486023i
$777$		0			0
$778$	888.718	+	1539.30i	1.14231	+	1.97854i
$779$	−338.948	−	587.075i	−0.435107	−	0.753627i
$780$		0			0
$781$	−53.5427	+	92.7387i	−0.0685566	+	0.118744i
$782$	173.402	−	363.268i	0.221742	−	0.464538i
$783$		0			0
$784$	346.298			0.441707
$785$	−1090.40	+	1888.63i	−1.38904	+	2.40589i
$786$		0			0
$787$	−108.379	+	62.5729i	−0.137712	+	0.0795081i	−0.567273	−	0.823530i	$-0.692002\pi$
$787$	−108.379	+	62.5729i	−0.137712	+	0.0795081i	0.429561	+	0.903038i	$0.358668\pi$
$788$	−451.668	−	782.311i	−0.573182	−	0.992781i
$789$		0			0
$790$	−1381.91	+	2393.54i	−1.74926	+	3.02980i
$791$			296.224i			0.374494i
$792$		0			0
$793$		−	881.847i		−	1.11204i
$794$	1152.55	−	1996.27i	1.45157	−	2.51419i
$795$		0			0
$796$	−669.324	+	386.434i	−0.840859	+	0.485470i
$797$	−623.250	+	359.834i	−0.781995	+	0.451485i	−0.837137	−	0.546994i	$-0.815772\pi$
$797$	−623.250	+	359.834i	−0.781995	+	0.451485i	0.0551419	+	0.998479i	$0.482439\pi$
$798$		0			0
$799$	207.074	+	301.487i	0.259167	+	0.377330i
$800$		−	1739.62i		−	2.17452i
$801$		0			0
$802$		−	101.863i		−	0.127011i
$803$	−316.261	−	182.593i	−0.393849	−	0.227389i
$804$		0			0
$805$	510.895	−	294.965i	0.634652	−	0.366416i
$806$	−579.509	−	1003.74i	−0.718994	−	1.24533i
$807$		0			0
$808$	211.922	−	367.059i	0.262279	−	0.454281i
$809$	1176.98			1.45486			0.727429	−	0.686183i	$-0.240715\pi$
$809$	1176.98			1.45486			0.727429	+	0.686183i	$0.240715\pi$
$810$		0			0
$811$			423.706i			0.522449i	0.965278	+	0.261225i	$0.0841263\pi$
$811$			423.706i			0.522449i	−0.965278	+	0.261225i	$0.915874\pi$
$812$	−335.258	−	193.561i	−0.412879	−	0.238376i
$813$		0			0
$814$	−223.911	−	387.825i	−0.275074	−	0.476443i
$815$	531.908	−	307.097i	0.652648	−	0.376807i
$816$		0			0
$817$	−407.218	+	705.323i	−0.498431	+	0.863309i
$818$		−	342.873i		−	0.419160i
$819$		0			0
$820$	2008.43			2.44931
$821$	296.427	−	513.427i	0.361057	−	0.625368i	−0.627078	−	0.778956i	$-0.715749\pi$
$821$	296.427	−	513.427i	0.361057	−	0.625368i	0.988135	+	0.153588i	$0.0490828\pi$
$822$		0			0
$823$	537.310	−	310.216i	0.652868	−	0.376933i	−0.136686	−	0.990614i	$-0.543645\pi$
$823$	537.310	−	310.216i	0.652868	−	0.376933i	0.789554	+	0.613681i	$0.210312\pi$
$824$	321.151	−	185.417i	0.389746	−	0.225020i
$825$		0			0
$826$	2207.93	+	1274.75i	2.67303	+	1.54328i
$827$	−411.264			−0.497296			−0.248648	−	0.968594i	$-0.579986\pi$
$827$	−411.264			−0.497296			−0.248648	+	0.968594i	$0.579986\pi$
$828$		0			0
$829$	−861.153			−1.03878			−0.519392	−	0.854536i	$-0.673842\pi$
$829$	−861.153			−1.03878			−0.519392	+	0.854536i	$0.673842\pi$
$830$	−53.8723	+	93.3096i	−0.0649064	+	0.112421i
$831$		0			0
$832$	1067.78	+	1849.44i	1.28338	+	2.22289i
$833$	−53.3584	−	680.562i	−0.0640558	−	0.817002i
$834$		0			0
$835$	232.531	−	402.756i	0.278481	−	0.482343i
$836$	829.845			0.992637
$837$		0			0
$838$		−	1290.12i		−	1.53952i
$839$	329.019	−	569.877i	0.392156	−	0.679234i	−0.600578	−	0.799566i	$-0.705063\pi$
$839$	329.019	−	569.877i	0.392156	−	0.679234i	0.992734	+	0.120333i	$0.0383961\pi$
$840$		0			0
$841$	391.386	+	677.900i	0.465381	+	0.806064i
$842$	−1062.28	+	613.308i	−1.26162	+	0.728394i
$843$		0			0
$844$	−306.905	−	177.192i	−0.363632	−	0.209943i
$845$	2486.10			2.94214
$846$		0			0
$847$		−	92.9299i		−	0.109717i
$848$	458.021	+	264.438i	0.540119	+	0.311838i
$849$		0			0
$850$	−2088.73	+	163.764i	−2.45733	+	0.192663i
$851$	−92.9276	+	53.6518i	−0.109198	+	0.0630456i
$852$		0			0
$853$	−684.590	−	395.248i	−0.802567	−	0.463362i	0.0418011	−	0.999126i	$-0.486690\pi$
$853$	−684.590	−	395.248i	−0.802567	−	0.463362i	−0.844368	+	0.535764i	$0.820024\pi$
$854$		−	1167.50i		−	1.36709i
$855$		0			0
$856$		−	711.027i		−	0.830639i
$857$	204.881	−	354.864i	0.239068	−	0.414077i	−0.721379	−	0.692540i	$-0.756492\pi$
$857$	204.881	−	354.864i	0.239068	−	0.414077i	0.960447	+	0.278463i	$0.0898249\pi$
$858$		0			0
$859$	−110.043	−	190.600i	−0.128106	−	0.221886i	0.794837	−	0.606823i	$-0.207556\pi$
$859$	−110.043	−	190.600i	−0.128106	−	0.221886i	−0.922943	+	0.384937i	$0.874223\pi$
$860$	−1206.48	−	2089.69i	−1.40289	−	2.42987i
$861$		0			0
$862$	2040.49	+	1178.08i	2.36716	+	1.36668i
$863$		−	1689.85i		−	1.95811i	−0.203603	−	0.979053i	$-0.565265\pi$
$863$		−	1689.85i		−	1.95811i	0.203603	−	0.979053i	$-0.434735\pi$
$864$		0			0
$865$	298.138			0.344669
$866$	−564.455	−	325.888i	−0.651795	−	0.376314i
$867$		0			0
$868$	−439.800	−	761.756i	−0.506682	−	0.877599i
$869$	−1020.39	+	589.123i	−1.17421	+	0.677932i
$870$		0			0
$871$	793.781	−	1374.87i	0.911345	−	1.57850i
$872$	369.703			0.423971
$873$		0			0
$874$		−	346.875i		−	0.396882i
$875$	−1007.74	−	581.821i	−1.15171	−	0.664938i
$876$		0			0
$877$	−233.067	+	134.561i	−0.265755	+	0.153434i	−0.626957	−	0.779054i	$-0.715700\pi$
$877$	−233.067	+	134.561i	−0.265755	+	0.153434i	0.361202	+	0.932488i	$0.382366\pi$
$878$	−56.7344	−	98.2669i	−0.0646178	−	0.111921i
$879$		0			0
$880$	367.241	−	636.080i	0.417319	−	0.722818i
$881$	−353.706			−0.401482			−0.200741	−	0.979644i	$-0.564335\pi$
$881$	−353.706			−0.401482			−0.200741	+	0.979644i	$0.564335\pi$
$882$		0			0
$883$	−1123.57			−1.27245			−0.636224	−	0.771504i	$-0.719505\pi$
$883$	−1123.57			−1.27245			−0.636224	+	0.771504i	$0.719505\pi$
$884$	1643.94	−	1129.13i	1.85966	−	1.27730i
$885$		0			0
$886$	630.698	+	1092.40i	0.711848	+	1.23296i
$887$	14.4433	+	25.0166i	0.0162834	+	0.0282036i	0.874052	−	0.485832i	$-0.161483\pi$
$887$	14.4433	+	25.0166i	0.0162834	+	0.0282036i	−0.857769	+	0.514036i	$0.828150\pi$
$888$		0			0
$889$	−575.435	−	332.228i	−0.647283	−	0.373709i
$890$	−1660.60			−1.86584
$891$		0			0
$892$	−686.821			−0.769979
$893$	272.953	+	157.590i	0.305659	+	0.176472i
$894$		0			0
$895$	766.417	−	442.491i	0.856332	−	0.494404i
$896$	597.576	+	1035.03i	0.666937	+	1.15517i
$897$		0			0
$898$	−1670.20	−	964.292i	−1.85991	−	1.07382i
$899$		−	132.304i		−	0.147168i
$900$		0			0
$901$	449.114	−	940.870i	0.498462	−	1.04425i
$902$	1293.54	+	746.824i	1.43408	+	0.827965i
$903$		0			0
$904$	−114.192	+	65.9290i	−0.126319	+	0.0729303i
$905$	2.90624	−	1.67792i	0.00321132	−	0.00185405i
$906$		0			0
$907$	1311.74	+	757.336i	1.44624	+	0.834990i	0.998255	−	0.0590488i	$-0.0188068\pi$
$907$	1311.74	+	757.336i	1.44624	+	0.834990i	0.447990	+	0.894039i	$0.352140\pi$
$908$	167.826			0.184830
$909$		0			0
$910$	5098.82			5.60310
$911$	−68.1335	+	118.011i	−0.0747897	+	0.129540i	−0.900995	−	0.433830i	$-0.857162\pi$
$911$	−68.1335	+	118.011i	−0.0747897	+	0.129540i	0.826205	+	0.563369i	$0.190495\pi$
$912$		0			0
$913$	−39.7788	+	22.9663i	−0.0435693	+	0.0251547i
$914$	2119.39	−	1223.63i	2.31881	−	1.33877i
$915$		0			0
$916$	−1060.69	+	1837.16i	−1.15796	+	2.00564i
$917$		−	307.918i		−	0.335789i
$918$		0			0
$919$	−1224.19			−1.33209			−0.666046	−	0.745911i	$-0.732015\pi$
$919$	−1224.19			−1.33209			−0.666046	+	0.745911i	$0.732015\pi$
$920$	227.414	+	131.297i	0.247189	+	0.142715i
$921$		0			0
$922$	−861.113	−	1491.49i	−0.933962	−	1.61767i
$923$	110.887	+	192.061i	0.120137	+	0.208084i
$924$		0			0
$925$	483.679	+	279.252i	0.522896	+	0.301894i
$926$			239.999i			0.259178i
$927$		0			0
$928$			329.756i			0.355340i
$929$	403.664	−	699.167i	0.434515	−	0.752601i	−0.562741	−	0.826633i	$-0.690253\pi$
$929$	403.664	−	699.167i	0.434515	−	0.752601i	0.997256	+	0.0740317i	$0.0235866\pi$
$930$		0			0
$931$	−294.131	−	509.450i	−0.315930	−	0.547207i
$932$	126.127	+	218.458i	0.135329	+	0.234397i
$933$		0			0
$934$	−653.992	+	1132.75i	−0.700205	+	1.21279i
$935$	−1306.64	−	623.711i	−1.39748	−	0.667070i
$936$		0			0
$937$	515.871			0.550556			0.275278	−	0.961365i	$-0.411230\pi$
$937$	515.871			0.550556			0.275278	+	0.961365i	$0.411230\pi$
$938$	1050.90	−	1820.22i	1.12037	−	1.94053i
$939$		0			0
$940$	−808.690	+	466.898i	−0.860309	+	0.496700i
$941$	224.355	+	388.594i	0.238422	+	0.412959i	0.960262	−	0.279101i	$-0.0900365\pi$
$941$	224.355	+	388.594i	0.238422	+	0.412959i	−0.721840	+	0.692060i	$0.756703\pi$
$942$		0			0
$943$	178.948	−	309.948i	0.189765	−	0.328683i
$944$		−	760.578i		−	0.805697i
$945$		0			0
$946$		−	1794.50i		−	1.89693i
$947$	−825.128	+	1429.16i	−0.871307	+	1.50915i	−0.0106617	+	0.999943i	$0.503394\pi$
$947$	−825.128	+	1429.16i	−0.871307	+	1.50915i	−0.860645	+	0.509205i	$0.829940\pi$
$948$		0			0
$949$	−654.975	+	378.150i	−0.690173	+	0.398472i
$950$	−1563.57	+	902.725i	−1.64586	+	0.950237i
$951$		0			0
$952$	556.118	−	381.967i	0.584158	−	0.401226i
$953$		−	707.450i		−	0.742340i	−0.928565	−	0.371170i	$-0.878957\pi$
$953$		−	707.450i		−	0.742340i	0.928565	−	0.371170i	$-0.121043\pi$
$954$		0			0
$955$		−	1261.68i		−	1.32113i
$956$	1568.66	+	905.669i	1.64086	+	0.947352i
$957$		0			0
$958$	−59.6313	+	34.4281i	−0.0622456	+	0.0359375i
$959$	560.017	+	969.979i	0.583960	+	1.01145i
$960$		0			0
$961$	−330.193	+	571.911i	−0.343593	+	0.595120i
$962$	−927.435			−0.964069
$963$		0			0
$964$			68.9958i			0.0715724i
$965$	1170.34	+	675.694i	1.21278	+	0.700201i
$966$		0			0
$967$	−47.4516	−	82.1887i	−0.0490710	−	0.0849934i	0.840447	−	0.541894i	$-0.182293\pi$
$967$	−47.4516	−	82.1887i	−0.0490710	−	0.0849934i	−0.889518	+	0.456901i	$0.848959\pi$
$968$	35.8238	−	20.6829i	0.0370081	−	0.0213666i
$969$		0			0
$970$	1281.28	−	2219.24i	1.32090	−	2.28787i
$971$			1370.65i			1.41159i	0.708417	+	0.705794i	$0.249410\pi$
$971$			1370.65i			1.41159i	−0.708417	+	0.705794i	$0.750590\pi$
$972$		0			0
$973$	−864.385			−0.888371
$974$	−777.585	+	1346.82i	−0.798341	+	1.38277i
$975$		0			0
$976$	−301.631	+	174.147i	−0.309048	+	0.178429i
$977$	21.6395	−	12.4936i	0.0221489	−	0.0127877i	−0.488885	−	0.872348i	$-0.662596\pi$
$977$	21.6395	−	12.4936i	0.0221489	−	0.0127877i	0.511034	+	0.859561i	$0.329263\pi$
$978$		0			0
$979$	−613.084	−	353.964i	−0.626235	−	0.361557i
$980$	1742.87			1.77844
$981$		0			0
$982$	433.706			0.441656
$983$	−756.964	+	1311.10i	−0.770055	+	1.33377i	0.167478	+	0.985876i	$0.446438\pi$
$983$	−756.964	+	1311.10i	−0.770055	+	1.33377i	−0.937532	+	0.347898i	$0.886896\pi$
$984$		0			0
$985$	679.084	+	1176.21i	0.689425	+	1.19412i
$986$	395.933	−	31.0425i	0.401555	−	0.0314833i
$987$		0			0
$988$	859.301	−	1488.35i	0.869738	−	1.50643i
$989$	−429.984			−0.434766
$990$		0			0
$991$		−	1110.97i		−	1.12106i	−0.828133	−	0.560531i	$-0.810597\pi$
$991$		−	1110.97i		−	1.12106i	0.828133	−	0.560531i	$-0.189403\pi$
$992$	−374.628	+	648.875i	−0.377649	+	0.654107i
$993$		0			0
$994$	146.805	+	254.274i	0.147691	+	0.255809i
$995$	1006.33	−	581.005i	1.01139	−	0.583925i
$996$		0			0
$997$	−16.8689	−	9.73925i	−0.0169196	−	0.00976856i	0.491516	−	0.870868i	$-0.336443\pi$
$997$	−16.8689	−	9.73925i	−0.0169196	−	0.00976856i	−0.508436	+	0.861100i	$0.669776\pi$
$998$	−571.516			−0.572661
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	459.3.i.a.305.5		68
3.2	odd	2		153.3.i.a.101.29	yes	68
9.4	even	3		153.3.i.a.50.30	yes	68
9.5	odd	6	inner	459.3.i.a.152.6		68
17.16	even	2	inner	459.3.i.a.305.6		68
51.50	odd	2		153.3.i.a.101.30	yes	68
153.50	odd	6	inner	459.3.i.a.152.5		68
153.67	even	6		153.3.i.a.50.29	✓	68

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
153.3.i.a.50.29	✓	68	153.67	even	6
153.3.i.a.50.30	yes	68	9.4	even	3
153.3.i.a.101.29	yes	68	3.2	odd	2
153.3.i.a.101.30	yes	68	51.50	odd	2
459.3.i.a.152.5		68	153.50	odd	6	inner
459.3.i.a.152.6		68	9.5	odd	6	inner
459.3.i.a.305.5		68	1.1	even	1	trivial
459.3.i.a.305.6		68	17.16	even	2	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 459 = 3^{3} \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	459.i (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-2.65135 - 1.53076i) q^{2} +(2.68643 + 4.65303i) q^{4} +(-4.03905 - 6.99584i) q^{5} +(-8.17722 - 4.72112i) q^{7} -4.20301i q^{8} +24.7312i q^{10} +(-5.27158 + 9.13064i) q^{11} +(10.9174 + 18.9095i) q^{13} +(14.4538 + 25.0347i) q^{14} +(4.31192 - 7.46847i) q^{16} +(-15.3418 - 7.32324i) q^{17} -14.6494 q^{19} +(21.7012 - 37.5877i) q^{20} +(27.9536 - 16.1390i) q^{22} +(-3.86711 - 6.69802i) q^{23} +(-20.1279 + 34.8625i) q^{25} -66.8475i q^{26} -50.7318i q^{28} +(3.81538 - 6.60843i) q^{29} +(15.0154 - 8.66912i) q^{31} +(-37.4245 + 21.6070i) q^{32} +(29.4663 + 42.9010i) q^{34} +76.2754i q^{35} -13.8739i q^{37} +(38.8408 + 22.4247i) q^{38} +(-29.4036 + 16.9762i) q^{40} +(23.1373 + 40.0749i) q^{41} +(27.7975 - 48.1467i) q^{43} -56.6468 q^{44} +23.6784i q^{46} +(-18.6323 - 10.7574i) q^{47} +(20.0780 + 34.7761i) q^{49} +(106.732 - 61.6218i) q^{50} +(-58.6576 + 101.598i) q^{52} +61.3273i q^{53} +85.1687 q^{55} +(-19.8429 + 34.3690i) q^{56} +(-20.2318 + 11.6808i) q^{58} +(76.3789 - 44.0974i) q^{59} +(-34.9764 - 20.1936i) q^{61} -53.0812 q^{62} +97.8050 q^{64} +(88.1919 - 152.753i) q^{65} +(-36.3540 - 62.9669i) q^{67} +(-7.13935 - 91.0591i) q^{68} +(116.759 - 202.233i) q^{70} +10.1569 q^{71} +34.6373i q^{73} +(-21.2375 + 36.7845i) q^{74} +(-39.3547 - 68.1643i) q^{76} +(86.2137 - 49.7755i) q^{77} +(96.7823 + 55.8773i) q^{79} -69.6643 q^{80} -141.670i q^{82} +(3.77295 + 2.17831i) q^{83} +(10.7340 + 136.908i) q^{85} +(-147.402 + 85.1025i) q^{86} +(38.3762 + 22.1565i) q^{88} +67.1458i q^{89} -206.169i q^{91} +(20.7774 - 35.9875i) q^{92} +(32.9339 + 57.0431i) q^{94} +(59.1699 + 102.485i) q^{95} +(-89.7342 - 51.8080i) q^{97} -122.938i q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 68 q + 6 q^{2} + 62 q^{4} - 2 q^{13} - 106 q^{16} - 32 q^{19} - 132 q^{25} - 27 q^{34} + 102 q^{38} + 58 q^{43} + 312 q^{47} + 152 q^{49} + 90 q^{50} + 70 q^{52} + 92 q^{55} + 258 q^{59} - 16 q^{64} + 82 q^{67}+ \cdots - 18 q^{94}+O(q^{100}) \) 68 * q + 6 * q^2 + 62 * q^4 - 2 * q^13 - 106 * q^16 - 32 * q^19 - 132 * q^25 - 27 * q^34 + 102 * q^38 + 58 * q^43 + 312 * q^47 + 152 * q^49 + 90 * q^50 + 70 * q^52 + 92 * q^55 + 258 * q^59 - 16 * q^64 + 82 * q^67 + 333 * q^68 + 204 * q^70 + 34 * q^76 + 60 * q^77 + 690 * q^83 - 44 * q^85 + 1248 * q^86 - 18 * q^94

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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