LMFDB - Embedded newform 144.3.o.c.79.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [144,3,Mod(31,144)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(144, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([3, 0, 2])) N = Newforms(chi, 3, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("144.31"); S:= CuspForms(chi, 3); N := Newforms(S);

Level:	$ N $	$=$	$ 144 = 2^{4} \cdot 3^{2} $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	144.o (of order $6$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [8,0,3] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(3)] == traces)

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

Self dual:	no
Analytic conductor:	$3.92371580679$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{6})$
Coefficient field:	8.0.856615824.2
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} + 11x^{6} + 36x^{4} + 32x^{2} + 4 $ x^8 + 11x^6 + 36x^4 + 32*x^2 + 4
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 2^{2}\cdot 3^{4} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			79.1
Root			$2.33086i$ of defining polynomial
Character	$\chi$	$=$	144.79
Dual form			144.3.o.c.31.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-2.89248 + 0.795973i) q^{3} +(0.355304 + 0.615405i) q^{5} +(-2.70480 - 1.56162i) q^{7} +(7.73285 - 4.60467i) q^{9} +(-14.3822 - 8.30359i) q^{11} +(-9.17743 - 15.8958i) q^{13} +(-1.51756 - 1.49723i) q^{15} -9.69321 q^{17} -8.20686i q^{19} +(9.06659 + 2.36400i) q^{21} +(-1.94815 + 1.12477i) q^{23} +(12.2475 - 21.2133i) q^{25} +(-18.7019 + 19.4740i) q^{27} +(-20.8217 + 36.0642i) q^{29} +(21.6298 - 12.4879i) q^{31} +(48.2097 + 12.5701i) q^{33} -2.21940i q^{35} -40.3888 q^{37} +(39.1981 + 38.6732i) q^{39} +(25.6944 + 44.5040i) q^{41} +(56.6621 + 32.7139i) q^{43} +(5.58126 + 3.12278i) q^{45} +(-29.2894 - 16.9102i) q^{47} +(-19.6227 - 33.9875i) q^{49} +(28.0374 - 7.71554i) q^{51} -90.6691 q^{53} -11.8012i q^{55} +(6.53244 + 23.7382i) q^{57} +(66.2243 - 38.2346i) q^{59} +(1.35822 - 2.35250i) q^{61} +(-28.1066 + 0.378955i) q^{63} +(6.52157 - 11.2957i) q^{65} +(34.5422 - 19.9429i) q^{67} +(4.73970 - 4.80403i) q^{69} +102.923i q^{71} +38.1741 q^{73} +(-18.5404 + 71.1078i) q^{75} +(25.9341 + 44.9192i) q^{77} +(-94.4994 - 54.5593i) q^{79} +(38.5940 - 71.2145i) q^{81} +(-113.503 - 65.5311i) q^{83} +(-3.44404 - 5.96526i) q^{85} +(31.5201 - 120.888i) q^{87} +38.0903 q^{89} +57.3266i q^{91} +(-52.6235 + 53.3378i) q^{93} +(5.05055 - 2.91593i) q^{95} +(-12.1961 + 21.1243i) q^{97} +(-149.451 + 2.01501i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 3 q^{3} + 3 q^{5} - 3 q^{7} - 3 q^{9} - 18 q^{11} + 5 q^{13} + 21 q^{15} + 6 q^{17} - 33 q^{21} + 81 q^{23} - 23 q^{25} - 108 q^{27} + 69 q^{29} - 45 q^{31} + 72 q^{33} - 20 q^{37} + 141 q^{39} + 54 q^{41}+ \cdots - 585 q^{99}+O(q^{100}) $ 8 * q + 3 * q^3 + 3 * q^5 - 3 * q^7 - 3 * q^9 - 18 * q^11 + 5 * q^13 + 21 * q^15 + 6 * q^17 - 33 * q^21 + 81 * q^23 - 23 * q^25 - 108 * q^27 + 69 * q^29 - 45 * q^31 + 72 * q^33 - 20 * q^37 + 141 * q^39 + 54 * q^41 - 117 * q^45 - 207 * q^47 + 41 * q^49 + 141 * q^51 - 252 * q^53 - 273 * q^57 + 306 * q^59 + 7 * q^61 - 441 * q^63 + 93 * q^65 - 12 * q^67 + 189 * q^69 + 74 * q^73 + 387 * q^75 + 207 * q^77 - 33 * q^79 + 117 * q^81 - 549 * q^83 - 30 * q^85 + 87 * q^87 - 168 * q^89 - 27 * q^93 + 684 * q^95 - 10 * q^97 - 585 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/144\mathbb{Z}\right)^\times$.

$n$	$37$	$65$	$127$
$\chi(n)$	$1$	$e\left(\frac{2}{3}\right)$	$-1$

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			0
$2$		0			0
$3$	−2.89248	+	0.795973i	−0.964159	+	0.265324i
$3$	−2.89248	+	0.795973i	−0.964159	+	0.265324i
$4$		0			0
$5$	0.355304	+	0.615405i	0.0710609	+	0.123081i	0.899367	−	0.437195i	$-0.144028\pi$
$5$	0.355304	+	0.615405i	0.0710609	+	0.123081i	−0.828306	+	0.560277i	$0.810695\pi$
$6$		0			0
$7$	−2.70480	−	1.56162i	−0.386401	−	0.223088i	0.294199	−	0.955744i	$-0.404947\pi$
$7$	−2.70480	−	1.56162i	−0.386401	−	0.223088i	−0.680599	+	0.732656i	$0.738281\pi$
$8$		0			0
$9$	7.73285	−	4.60467i	0.859206	−	0.511630i
$10$		0			0
$11$	−14.3822	−	8.30359i	−1.30748	−	0.754872i	−0.325802	−	0.945438i	$-0.605634\pi$
$11$	−14.3822	−	8.30359i	−1.30748	−	0.754872i	−0.981674	+	0.190566i	$0.938968\pi$
$12$		0			0
$13$	−9.17743	−	15.8958i	−0.705956	−	1.22275i	−0.966345	−	0.257248i	$-0.917184\pi$
$13$	−9.17743	−	15.8958i	−0.705956	−	1.22275i	0.260389	−	0.965504i	$-0.416149\pi$
$14$		0			0
$15$	−1.51756	−	1.49723i	−0.101170	−	0.0998156i
$16$		0			0
$17$	−9.69321			−0.570189			−0.285095	−	0.958499i	$-0.592025\pi$
$17$	−9.69321			−0.570189			−0.285095	+	0.958499i	$0.592025\pi$
$18$		0			0
$19$		−	8.20686i		−	0.431940i	−0.976400	−	0.215970i	$-0.930709\pi$
$19$		−	8.20686i		−	0.431940i	0.976400	−	0.215970i	$-0.0692913\pi$
$20$		0			0
$21$	9.06659	+	2.36400i	0.431742	+	0.112571i
$22$		0			0
$23$	−1.94815	+	1.12477i	−0.0847022	+	0.0489028i	−0.541753	−	0.840538i	$-0.682239\pi$
$23$	−1.94815	+	1.12477i	−0.0847022	+	0.0489028i	0.457051	+	0.889441i	$0.348906\pi$
$24$		0			0
$25$	12.2475	−	21.2133i	0.489901	−	0.848533i
$26$		0			0
$27$	−18.7019	+	19.4740i	−0.692663	+	0.721261i
$28$		0			0
$29$	−20.8217	+	36.0642i	−0.717989	+	1.24359i	0.243806	+	0.969824i	$0.421604\pi$
$29$	−20.8217	+	36.0642i	−0.717989	+	1.24359i	−0.961795	+	0.273770i	$0.911729\pi$
$30$		0			0
$31$	21.6298	−	12.4879i	0.697734	−	0.402837i	−0.108769	−	0.994067i	$-0.534691\pi$
$31$	21.6298	−	12.4879i	0.697734	−	0.402837i	0.806503	+	0.591230i	$0.201358\pi$
$32$		0			0
$33$	48.2097	+	12.5701i	1.46090	+	0.380911i
$34$		0			0
$35$		−	2.21940i		−	0.0634115i
$36$		0			0
$37$	−40.3888			−1.09159			−0.545794	−	0.837919i	$-0.683772\pi$
$37$	−40.3888			−1.09159			−0.545794	+	0.837919i	$0.683772\pi$
$38$		0			0
$39$	39.1981	+	38.6732i	1.00508	+	0.991620i
$40$		0			0
$41$	25.6944	+	44.5040i	0.626692	+	1.08546i	0.988211	+	0.153098i	$0.0489251\pi$
$41$	25.6944	+	44.5040i	0.626692	+	1.08546i	−0.361519	+	0.932365i	$0.617742\pi$
$42$		0			0
$43$	56.6621	+	32.7139i	1.31772	+	0.760787i	0.983362	−	0.181658i	$-0.0581464\pi$
$43$	56.6621	+	32.7139i	1.31772	+	0.760787i	0.334360	+	0.942445i	$0.391480\pi$
$44$		0			0
$45$	5.58126	+	3.12278i	0.124028	+	0.0693951i
$46$		0			0
$47$	−29.2894	−	16.9102i	−0.623179	−	0.359793i	0.154927	−	0.987926i	$-0.450486\pi$
$47$	−29.2894	−	16.9102i	−0.623179	−	0.359793i	−0.778106	+	0.628133i	$0.783819\pi$
$48$		0			0
$49$	−19.6227	−	33.9875i	−0.400463	−	0.693622i
$50$		0			0
$51$	28.0374	−	7.71554i	0.549753	−	0.151285i
$52$		0			0
$53$	−90.6691			−1.71074			−0.855369	−	0.518019i	$-0.826670\pi$
$53$	−90.6691			−1.71074			−0.855369	+	0.518019i	$0.826670\pi$
$54$		0			0
$55$		−	11.8012i		−	0.214567i
$56$		0			0
$57$	6.53244	+	23.7382i	0.114604	+	0.416459i
$58$		0			0
$59$	66.2243	−	38.2346i	1.12245	−	0.648045i	0.180422	−	0.983589i	$-0.442254\pi$
$59$	66.2243	−	38.2346i	1.12245	−	0.648045i	0.942024	+	0.335545i	$0.108920\pi$
$60$		0			0
$61$	1.35822	−	2.35250i	0.0222659	−	0.0385656i	−0.854678	−	0.519159i	$-0.826245\pi$
$61$	1.35822	−	2.35250i	0.0222659	−	0.0385656i	0.876944	+	0.480593i	$0.159579\pi$
$62$		0			0
$63$	−28.1066	+	0.378955i	−0.446136	+	0.00601516i
$64$		0			0
$65$	6.52157	−	11.2957i	0.100332	−	0.173780i
$66$		0			0
$67$	34.5422	−	19.9429i	0.515555	−	0.297656i	−0.219559	−	0.975599i	$-0.570462\pi$
$67$	34.5422	−	19.9429i	0.515555	−	0.297656i	0.735114	+	0.677943i	$0.237129\pi$
$68$		0			0
$69$	4.73970	−	4.80403i	0.0686913	−	0.0696237i
$70$		0			0
$71$			102.923i			1.44962i	0.688950	+	0.724809i	$0.258072\pi$
$71$			102.923i			1.44962i	−0.688950	+	0.724809i	$0.741928\pi$
$72$		0			0
$73$	38.1741			0.522933			0.261466	−	0.965213i	$-0.415794\pi$
$73$	38.1741			0.522933			0.261466	+	0.965213i	$0.415794\pi$
$74$		0			0
$75$	−18.5404	+	71.1078i	−0.247206	+	0.948103i
$76$		0			0
$77$	25.9341	+	44.9192i	0.336806	+	0.583366i
$78$		0			0
$79$	−94.4994	−	54.5593i	−1.19620	−	0.690624i	−0.236491	−	0.971634i	$-0.575997\pi$
$79$	−94.4994	−	54.5593i	−1.19620	−	0.690624i	−0.959705	+	0.281010i	$0.909331\pi$
$80$		0			0
$81$	38.5940	−	71.2145i	0.476470	−	0.879191i
$82$		0			0
$83$	−113.503	−	65.5311i	−1.36751	−	0.789531i	−0.376899	−	0.926254i	$-0.623010\pi$
$83$	−113.503	−	65.5311i	−1.36751	−	0.789531i	−0.990609	+	0.136723i	$0.956343\pi$
$84$		0			0
$85$	−3.44404	−	5.96526i	−0.0405181	−	0.0701795i
$86$		0			0
$87$	31.5201	−	120.888i	0.362300	−	1.38952i
$88$		0			0
$89$	38.0903			0.427981			0.213991	−	0.976836i	$-0.431354\pi$
$89$	38.0903			0.427981			0.213991	+	0.976836i	$0.431354\pi$
$90$		0			0
$91$			57.3266i			0.629963i
$92$		0			0
$93$	−52.6235	+	53.3378i	−0.565844	+	0.573525i
$94$		0			0
$95$	5.05055	−	2.91593i	0.0531636	−	0.0306940i
$96$		0			0
$97$	−12.1961	+	21.1243i	−0.125733	+	0.217776i	−0.922019	−	0.387144i	$-0.873462\pi$
$97$	−12.1961	+	21.1243i	−0.125733	+	0.217776i	0.796286	+	0.604920i	$0.206795\pi$
$98$		0			0
$99$	−149.451	+	2.01501i	−1.50961	+	0.0203537i
$100$		0			0
$101$	98.1305	−	169.967i	0.971589	−	1.68284i	0.280829	−	0.959758i	$-0.409391\pi$
$101$	98.1305	−	169.967i	0.971589	−	1.68284i	0.690760	−	0.723084i	$-0.257276\pi$
$102$		0			0
$103$	−104.472	+	60.3172i	−1.01430	+	0.585604i	−0.912446	−	0.409196i	$-0.865809\pi$
$103$	−104.472	+	60.3172i	−1.01430	+	0.585604i	−0.101849	+	0.994800i	$0.532476\pi$
$104$		0			0
$105$	1.76658	+	6.41957i	0.0168246	+	0.0611387i
$106$		0			0
$107$		−	6.52440i		−	0.0609757i	−0.999535	−	0.0304878i	$-0.990294\pi$
$107$		−	6.52440i		−	0.0609757i	0.999535	−	0.0304878i	$-0.00970609\pi$
$108$		0			0
$109$	38.0272			0.348873			0.174437	−	0.984668i	$-0.444190\pi$
$109$	38.0272			0.348873			0.174437	+	0.984668i	$0.444190\pi$
$110$		0			0
$111$	116.824	−	32.1484i	1.05247	−	0.289625i
$112$		0			0
$113$	−53.5086	−	92.6795i	−0.473527	−	0.820173i	0.526014	−	0.850476i	$-0.323686\pi$
$113$	−53.5086	−	92.6795i	−0.473527	−	0.820173i	−0.999541	+	0.0303032i	$0.990353\pi$
$114$		0			0
$115$	−1.38437	−	0.799268i	−0.0120380	−	0.00695016i
$116$		0			0
$117$	−144.163	−	80.6607i	−1.23216	−	0.689408i
$118$		0			0
$119$	26.2182	+	15.1371i	0.220321	+	0.127203i
$120$		0			0
$121$	77.3992	+	134.059i	0.639662	+	1.10793i
$122$		0			0
$123$	−109.744	−	108.275i	−0.892231	−	0.880282i
$124$		0			0
$125$	35.1716			0.281373
$126$		0			0
$127$		−	101.437i		−	0.798713i	−0.916796	−	0.399357i	$-0.869234\pi$
$127$		−	101.437i		−	0.798713i	0.916796	−	0.399357i	$-0.130766\pi$
$128$		0			0
$129$	−189.933	−	49.5226i	−1.47235	−	0.383896i
$130$		0			0
$131$	162.820	−	94.0042i	1.24290	−	0.717589i	0.273217	−	0.961952i	$-0.411912\pi$
$131$	162.820	−	94.0042i	1.24290	−	0.717589i	0.969684	+	0.244363i	$0.0785790\pi$
$132$		0			0
$133$	−12.8160	+	22.1979i	−0.0963608	+	0.166902i
$134$		0			0
$135$	−18.6293	−	4.59004i	−0.137995	−	0.0340003i
$136$		0			0
$137$	31.3271	−	54.2601i	0.228665	−	0.396059i	−0.728748	−	0.684782i	$-0.759897\pi$
$137$	31.3271	−	54.2601i	0.228665	−	0.396059i	0.957413	+	0.288723i	$0.0932307\pi$
$138$		0			0
$139$	−40.5801	+	23.4289i	−0.291943	+	0.168553i	−0.638818	−	0.769358i	$-0.720576\pi$
$139$	−40.5801	+	23.4289i	−0.291943	+	0.168553i	0.346875	+	0.937911i	$0.387243\pi$
$140$		0			0
$141$	98.1791	+	25.5989i	0.696305	+	0.181553i
$142$		0			0
$143$			304.822i			2.13163i
$144$		0			0
$145$	−29.5922			−0.204084
$146$		0			0
$147$	83.8113	+	82.6889i	0.570145	+	0.562510i
$148$		0			0
$149$	53.9860	+	93.5064i	0.362322	+	0.627560i	0.988343	−	0.152247i	$-0.0486508\pi$
$149$	53.9860	+	93.5064i	0.362322	+	0.627560i	−0.626021	+	0.779806i	$0.715317\pi$
$150$		0			0
$151$	2.75240	+	1.58910i	0.0182278	+	0.0105238i	0.509086	−	0.860716i	$-0.329983\pi$
$151$	2.75240	+	1.58910i	0.0182278	+	0.0105238i	−0.490858	+	0.871239i	$0.663317\pi$
$152$		0			0
$153$	−74.9562	+	44.6340i	−0.489910	+	0.291726i
$154$		0			0
$155$	15.3703	+	8.87405i	0.0991632	+	0.0572519i
$156$		0			0
$157$	128.215	+	222.075i	0.816656	+	1.41449i	0.908133	+	0.418683i	$0.137508\pi$
$157$	128.215	+	222.075i	0.816656	+	1.41449i	−0.0914764	+	0.995807i	$0.529159\pi$
$158$		0			0
$159$	262.258	−	72.1702i	1.64942	−	0.453901i
$160$		0			0
$161$	7.02582			0.0436386
$162$		0			0
$163$			201.100i			1.23374i	0.787065	+	0.616870i	$0.211600\pi$
$163$			201.100i			1.23374i	−0.787065	+	0.616870i	$0.788400\pi$
$164$		0			0
$165$	9.39345	+	34.1347i	0.0569300	+	0.206877i
$166$		0			0
$167$	110.689	−	63.9062i	0.662807	−	0.382672i	−0.130538	−	0.991443i	$-0.541671\pi$
$167$	110.689	−	63.9062i	0.662807	−	0.382672i	0.793346	+	0.608771i	$0.208337\pi$
$168$		0			0
$169$	−83.9505	+	145.407i	−0.496749	+	0.860394i
$170$		0			0
$171$	−37.7899	−	63.4624i	−0.220993	−	0.371125i
$172$		0			0
$173$	100.718	−	174.448i	0.582183	−	1.00837i	−0.413037	−	0.910714i	$-0.635532\pi$
$173$	100.718	−	174.448i	0.582183	−	1.00837i	0.995220	−	0.0976562i	$-0.0311346\pi$
$174$		0			0
$175$	−66.2543	+	38.2519i	−0.378596	+	0.218582i
$176$		0			0
$177$	−161.119	+	163.306i	−0.910275	+	0.922630i
$178$		0			0
$179$			5.83187i			0.0325803i	0.999867	+	0.0162901i	$0.00518554\pi$
$179$			5.83187i			0.0325803i	−0.999867	+	0.0162901i	$0.994814\pi$
$180$		0			0
$181$	132.737			0.733353			0.366677	−	0.930348i	$-0.380496\pi$
$181$	132.737			0.733353			0.366677	+	0.930348i	$0.380496\pi$
$182$		0			0
$183$	−2.05608	+	7.88566i	−0.0112354	+	0.0430910i
$184$		0			0
$185$	−14.3503	−	24.8555i	−0.0775693	−	0.134354i
$186$		0			0
$187$	139.410	+	80.4885i	0.745509	+	0.430420i
$188$		0			0
$189$	80.9960	−	23.4682i	0.428551	−	0.124170i
$190$		0			0
$191$	36.0843	+	20.8333i	0.188923	+	0.109075i	0.591478	−	0.806321i	$-0.298545\pi$
$191$	36.0843	+	20.8333i	0.188923	+	0.109075i	−0.402555	+	0.915396i	$0.631878\pi$
$192$		0			0
$193$	−69.1927	−	119.845i	−0.358511	−	0.620960i	0.629201	−	0.777242i	$-0.283382\pi$
$193$	−69.1927	−	119.845i	−0.358511	−	0.620960i	−0.987712	+	0.156283i	$0.950049\pi$
$194$		0			0
$195$	−9.87242	+	37.8635i	−0.0506278	+	0.194172i
$196$		0			0
$197$	−109.421			−0.555438			−0.277719	−	0.960662i	$-0.589578\pi$
$197$	−109.421			−0.555438			−0.277719	+	0.960662i	$0.589578\pi$
$198$		0			0
$199$		−	87.0243i		−	0.437308i	−0.975802	−	0.218654i	$-0.929833\pi$
$199$		−	87.0243i		−	0.437308i	0.975802	−	0.218654i	$-0.0701666\pi$
$200$		0			0
$201$	−84.0385	+	85.1792i	−0.418102	+	0.423777i
$202$		0			0
$203$	112.637	−	65.0311i	0.554863	−	0.320350i
$204$		0			0
$205$	−18.2587	+	31.6249i	−0.0890666	+	0.154268i
$206$		0			0
$207$	−9.88559	+	17.6682i	−0.0477565	+	0.0853538i
$208$		0			0
$209$	−68.1464	+	118.033i	−0.326059	+	0.564751i
$210$		0			0
$211$	244.383	−	141.095i	1.15821	−	0.668695i	0.207339	−	0.978269i	$-0.433520\pi$
$211$	244.383	−	141.095i	1.15821	−	0.668695i	0.950875	+	0.309574i	$0.100186\pi$
$212$		0			0
$213$	−81.9239	−	297.702i	−0.384619	−	1.39766i
$214$		0			0
$215$			46.4935i			0.216249i
$216$		0			0
$217$	−78.0057			−0.359473
$218$		0			0
$219$	−110.418	+	30.3855i	−0.504190	+	0.138747i
$220$		0			0
$221$	88.9588	+	154.081i	0.402529	+	0.697200i
$222$		0			0
$223$	−255.359	−	147.432i	−1.14511	−	0.661129i	−0.197419	−	0.980319i	$-0.563256\pi$
$223$	−255.359	−	147.432i	−1.14511	−	0.661129i	−0.947691	+	0.319190i	$0.896589\pi$
$224$		0			0
$225$	−2.97208	−	220.435i	−0.0132092	−	0.979712i
$226$		0			0
$227$	−124.390	−	71.8164i	−0.547972	−	0.316372i	0.200332	−	0.979728i	$-0.435798\pi$
$227$	−124.390	−	71.8164i	−0.547972	−	0.316372i	−0.748304	+	0.663356i	$0.769131\pi$
$228$		0			0
$229$	−141.426	−	244.958i	−0.617583	−	1.06968i	−0.989925	−	0.141590i	$-0.954779\pi$
$229$	−141.426	−	244.958i	−0.617583	−	1.06968i	0.372343	−	0.928095i	$-0.378555\pi$
$230$		0			0
$231$	−110.768	−	109.285i	−0.479516	−	0.473094i
$232$		0			0
$233$	−25.9127			−0.111213			−0.0556067	−	0.998453i	$-0.517709\pi$
$233$	−25.9127			−0.111213			−0.0556067	+	0.998453i	$0.517709\pi$
$234$		0			0
$235$		−	24.0331i		−	0.102269i
$236$		0			0
$237$	316.765	+	82.5925i	1.33656	+	0.348491i
$238$		0			0
$239$	−310.807	+	179.444i	−1.30045	+	0.750813i	−0.980481	−	0.196616i	$-0.937005\pi$
$239$	−310.807	+	179.444i	−1.30045	+	0.750813i	−0.319966	+	0.947429i	$0.603672\pi$
$240$		0			0
$241$	87.7048	−	151.909i	0.363920	−	0.630328i	−0.624682	−	0.780879i	$-0.714771\pi$
$241$	87.7048	−	151.909i	0.363920	−	0.630328i	0.988602	+	0.150551i	$0.0481048\pi$
$242$		0			0
$243$	−54.9476	+	236.706i	−0.226122	+	0.974099i
$244$		0			0
$245$	13.9441	−	24.1518i	0.0569145	−	0.0985789i
$246$		0			0
$247$	−130.454	+	75.3179i	−0.528156	+	0.304931i
$248$		0			0
$249$	380.466	+	99.2017i	1.52798	+	0.398401i
$250$		0			0
$251$		−	410.044i		−	1.63364i	−0.576891	−	0.816821i	$-0.695734\pi$
$251$		−	410.044i		−	1.63364i	0.576891	−	0.816821i	$-0.304266\pi$
$252$		0			0
$253$	37.3583			0.147661
$254$		0			0
$255$	14.7100	+	14.5130i	0.0576863	+	0.0569137i
$256$		0			0
$257$	−86.4280	−	149.698i	−0.336296	−	0.582481i	0.647437	−	0.762119i	$-0.275841\pi$
$257$	−86.4280	−	149.698i	−0.336296	−	0.582481i	−0.983733	+	0.179638i	$0.942507\pi$
$258$		0			0
$259$	109.244	+	63.0719i	0.421790	+	0.243521i
$260$		0			0
$261$	5.05276	+	374.756i	0.0193592	+	1.43585i
$262$		0			0
$263$	−132.696	−	76.6118i	−0.504546	−	0.291300i	0.226043	−	0.974117i	$-0.427421\pi$
$263$	−132.696	−	76.6118i	−0.504546	−	0.291300i	−0.730589	+	0.682818i	$0.760754\pi$
$264$		0			0
$265$	−32.2151	−	55.7983i	−0.121567	−	0.210559i
$266$		0			0
$267$	−110.175	+	30.3189i	−0.412642	+	0.113554i
$268$		0			0
$269$	12.6752			0.0471198			0.0235599	−	0.999722i	$-0.492500\pi$
$269$	12.6752			0.0471198			0.0235599	+	0.999722i	$0.492500\pi$
$270$		0			0
$271$		−	40.7101i		−	0.150222i	−0.997175	−	0.0751108i	$-0.976069\pi$
$271$		−	40.7101i		−	0.150222i	0.997175	−	0.0751108i	$-0.0239311\pi$
$272$		0			0
$273$	−45.6305	−	165.816i	−0.167145	−	0.607385i
$274$		0			0
$275$	−352.293	+	203.397i	−1.28107	+	0.739624i
$276$		0			0
$277$	184.143	−	318.945i	0.664776	−	1.15143i	−0.314570	−	0.949234i	$-0.601860\pi$
$277$	184.143	−	318.945i	0.664776	−	1.15143i	0.979346	−	0.202191i	$-0.0648063\pi$
$278$		0			0
$279$	109.757	−	196.165i	0.393394	−	0.703101i
$280$		0			0
$281$	−238.310	+	412.765i	−0.848078	+	1.46891i	0.0348433	+	0.999393i	$0.488907\pi$
$281$	−238.310	+	412.765i	−0.848078	+	1.46891i	−0.882921	+	0.469521i	$0.844427\pi$
$282$		0			0
$283$	−150.052	+	86.6323i	−0.530217	+	0.306121i	−0.741105	−	0.671389i	$-0.765698\pi$
$283$	−150.052	+	86.6323i	−0.530217	+	0.306121i	0.210888	+	0.977510i	$0.432365\pi$
$284$		0			0
$285$	−12.2876	+	12.4544i	−0.0431143	+	0.0436995i
$286$		0			0
$287$		−	160.499i		−	0.559231i
$288$		0			0
$289$	−195.042			−0.674884
$290$		0			0
$291$	18.4626	−	70.8094i	0.0634455	−	0.243331i
$292$		0			0
$293$	−2.91833	−	5.05470i	−0.00996017	−	0.0172515i	0.861002	−	0.508601i	$-0.169837\pi$
$293$	−2.91833	−	5.05470i	−0.00996017	−	0.0172515i	−0.870963	+	0.491349i	$0.836504\pi$
$294$		0			0
$295$	47.0596	+	27.1699i	0.159524	+	0.0921013i
$296$		0			0
$297$	430.680	−	124.787i	1.45010	−	0.420160i
$298$		0			0
$299$	35.7580	+	20.6449i	0.119592	+	0.0690465i
$300$		0			0
$301$	−102.173	−	176.969i	−0.339446	−	0.587937i
$302$		0			0
$303$	−148.551	+	569.735i	−0.490268	+	1.88031i
$304$		0			0
$305$	1.93032			0.00632893
$306$		0			0
$307$		−	371.717i		−	1.21080i	−0.795920	−	0.605402i	$-0.793012\pi$
$307$		−	371.717i		−	1.21080i	0.795920	−	0.605402i	$-0.206988\pi$
$308$		0			0
$309$	254.173	−	257.623i	0.822567	−	0.833733i
$310$		0			0
$311$	193.964	−	111.985i	0.623679	−	0.360081i	−0.154621	−	0.987974i	$-0.549416\pi$
$311$	193.964	−	111.985i	0.623679	−	0.360081i	0.778300	+	0.627892i	$0.216082\pi$
$312$		0			0
$313$	79.0960	−	136.998i	0.252703	−	0.437694i	−0.711566	−	0.702619i	$-0.752014\pi$
$313$	79.0960	−	136.998i	0.252703	−	0.437694i	0.964269	+	0.264925i	$0.0853472\pi$
$314$		0			0
$315$	−10.2196	−	17.1623i	−0.0324432	−	0.0544835i
$316$		0			0
$317$	−206.428	+	357.543i	−0.651191	+	1.12790i	0.331643	+	0.943405i	$0.392397\pi$
$317$	−206.428	+	357.543i	−0.651191	+	1.12790i	−0.982834	+	0.184491i	$0.940936\pi$
$318$		0			0
$319$	598.925	−	345.789i	1.87751	−	1.08398i
$320$		0			0
$321$	5.19325	+	18.8717i	0.0161783	+	0.0587903i
$322$		0			0
$323$			79.5508i			0.246287i
$324$		0			0
$325$	−449.603			−1.38339
$326$		0			0
$327$	−109.993	+	30.2686i	−0.336370	+	0.0925646i
$328$		0			0
$329$	52.8147	+	91.4778i	0.160531	+	0.278048i
$330$		0			0
$331$	126.937	+	73.2871i	0.383495	+	0.221411i	0.679338	−	0.733826i	$-0.262267\pi$
$331$	126.937	+	73.2871i	0.383495	+	0.221411i	−0.295843	+	0.955237i	$0.595600\pi$
$332$		0			0
$333$	−312.320	+	185.977i	−0.937899	+	0.558489i
$334$		0			0
$335$	24.5460	+	14.1716i	0.0732716	+	0.0423034i
$336$		0			0
$337$	−47.3499	−	82.0124i	−0.140504	−	0.243360i	0.787182	−	0.616720i	$-0.211539\pi$
$337$	−47.3499	−	82.0124i	−0.140504	−	0.243360i	−0.927687	+	0.373360i	$0.878206\pi$
$338$		0			0
$339$	228.543	+	225.482i	0.674167	+	0.665139i
$340$		0			0
$341$	−414.779			−1.21636
$342$		0			0
$343$			275.611i			0.803532i
$344$		0			0
$345$	4.64046	+	1.20994i	0.0134506	+	0.00350708i
$346$		0			0
$347$	81.3438	−	46.9639i	0.234420	−	0.135343i	−0.378189	−	0.925728i	$-0.623453\pi$
$347$	81.3438	−	46.9639i	0.234420	−	0.135343i	0.612609	+	0.790386i	$0.290120\pi$
$348$		0			0
$349$	−115.579	+	200.188i	−0.331171	+	0.573605i	−0.982742	−	0.184983i	$-0.940777\pi$
$349$	−115.579	+	200.188i	−0.331171	+	0.573605i	0.651571	+	0.758588i	$0.274110\pi$
$350$		0			0
$351$	481.191	+	118.560i	1.37091	+	0.337777i
$352$		0			0
$353$	−48.9623	+	84.8052i	−0.138703	+	0.240241i	−0.927006	−	0.375046i	$-0.877627\pi$
$353$	−48.9623	+	84.8052i	−0.138703	+	0.240241i	0.788303	+	0.615288i	$0.210960\pi$
$354$		0			0
$355$	−63.3393	+	36.5690i	−0.178421	+	0.103011i
$356$		0			0
$357$	−87.8844	−	22.9147i	−0.246175	−	0.0641869i
$358$		0			0
$359$		−	244.287i		−	0.680465i	−0.940341	−	0.340233i	$-0.889494\pi$
$359$		−	244.287i		−	0.680465i	0.940341	−	0.340233i	$-0.110506\pi$
$360$		0			0
$361$	293.647			0.813428
$362$		0			0
$363$	−330.583	−	326.156i	−0.910697	−	0.898501i
$364$		0			0
$365$	13.5634	+	23.4925i	0.0371601	+	0.0643631i
$366$		0			0
$367$	368.327	+	212.654i	1.00362	+	0.579438i	0.909316	−	0.416106i	$-0.136605\pi$
$367$	368.327	+	212.654i	1.00362	+	0.579438i	0.0942999	+	0.995544i	$0.469939\pi$
$368$		0			0
$369$	403.617	+	225.829i	1.09381	+	0.612002i
$370$		0			0
$371$	245.242	+	141.591i	0.661030	+	0.381646i
$372$		0			0
$373$	44.8567	+	77.6941i	0.120259	+	0.208295i	0.919870	−	0.392224i	$-0.128294\pi$
$373$	44.8567	+	77.6941i	0.120259	+	0.208295i	−0.799611	+	0.600519i	$0.794961\pi$
$374$		0			0
$375$	−101.733	+	27.9957i	−0.271288	+	0.0746551i
$376$		0			0
$377$	764.359			2.02748
$378$		0			0
$379$			406.140i			1.07161i	0.844342	+	0.535805i	$0.179992\pi$
$379$			406.140i			1.07161i	−0.844342	+	0.535805i	$0.820008\pi$
$380$		0			0
$381$	80.7408	+	293.403i	0.211918	+	0.770087i
$382$		0			0
$383$	−280.901	+	162.178i	−0.733423	+	0.423442i	−0.819673	−	0.572832i	$-0.805845\pi$
$383$	−280.901	+	162.178i	−0.733423	+	0.423442i	0.0862502	+	0.996274i	$0.472512\pi$
$384$		0			0
$385$	−18.4290	+	31.9200i	−0.0478675	+	0.0829090i
$386$		0			0
$387$	588.796	−	7.93860i	1.52144	−	0.0205132i
$388$		0			0
$389$	−28.6761	+	49.6685i	−0.0737176	+	0.127683i	−0.900528	−	0.434798i	$-0.856820\pi$
$389$	−28.6761	+	49.6685i	−0.0737176	+	0.127683i	0.826810	+	0.562481i	$0.190153\pi$
$390$		0			0
$391$	18.8838	−	10.9026i	0.0482963	−	0.0278839i
$392$		0			0
$393$	−396.128	+	401.505i	−1.00796	+	1.02164i
$394$		0			0
$395$		−	77.5406i		−	0.196305i
$396$		0			0
$397$	194.475			0.489861			0.244931	−	0.969541i	$-0.421235\pi$
$397$	194.475			0.489861			0.244931	+	0.969541i	$0.421235\pi$
$398$		0			0
$399$	19.4010	−	74.4082i	0.0486240	−	0.186487i
$400$		0			0
$401$	−163.943	−	283.958i	−0.408836	−	0.708124i	0.585924	−	0.810366i	$-0.300732\pi$
$401$	−163.943	−	283.958i	−0.408836	−	0.708124i	−0.994760	+	0.102242i	$0.967398\pi$
$402$		0			0
$403$	−397.011	−	229.215i	−0.985140	−	0.568771i
$404$		0			0
$405$	57.5384	−	1.55184i	0.142070	−	0.00383170i
$406$		0			0
$407$	580.881	+	335.372i	1.42723	+	0.824009i
$408$		0			0
$409$	−36.6786	−	63.5292i	−0.0896787	−	0.155328i	0.817697	−	0.575649i	$-0.195251\pi$
$409$	−36.6786	−	63.5292i	−0.0896787	−	0.155328i	−0.907375	+	0.420321i	$0.861917\pi$
$410$		0			0
$411$	−47.4233	+	181.882i	−0.115385	+	0.442534i
$412$		0			0
$413$	−238.832			−0.578285
$414$		0			0
$415$		−	93.1340i		−	0.224419i
$416$		0			0
$417$	98.7282	−	100.068i	0.236758	−	0.239972i
$418$		0			0
$419$	−557.390	+	321.809i	−1.33029	+	0.768041i	−0.985343	−	0.170582i	$-0.945435\pi$
$419$	−557.390	+	321.809i	−1.33029	+	0.768041i	−0.344943	+	0.938624i	$0.612102\pi$
$420$		0			0
$421$	−280.151	+	485.236i	−0.665441	+	1.15258i	0.313724	+	0.949514i	$0.398423\pi$
$421$	−280.151	+	485.236i	−0.665441	+	1.15258i	−0.979165	+	0.203064i	$0.934910\pi$
$422$		0			0
$423$	−304.357	+	4.10358i	−0.719520	+	0.00970112i
$424$		0			0
$425$	−118.718	+	205.625i	−0.279336	+	0.483824i
$426$		0			0
$427$	−7.34742	+	4.24204i	−0.0172071	+	0.00993451i
$428$		0			0
$429$	−242.631	−	881.692i	−0.565572	−	2.05523i
$430$		0			0
$431$		−	536.437i		−	1.24463i	−0.782765	−	0.622317i	$-0.786191\pi$
$431$		−	536.437i		−	1.24463i	0.782765	−	0.622317i	$-0.213809\pi$
$432$		0			0
$433$	281.999			0.651268			0.325634	−	0.945496i	$-0.394422\pi$
$433$	281.999			0.651268			0.325634	+	0.945496i	$0.394422\pi$
$434$		0			0
$435$	85.5947	−	23.5546i	0.196769	−	0.0541484i
$436$		0			0
$437$	9.23079	+	15.9882i	0.0211231	+	0.0365863i
$438$		0			0
$439$	−87.2604	−	50.3798i	−0.198771	−	0.114760i	0.397311	−	0.917684i	$-0.369943\pi$
$439$	−87.2604	−	50.3798i	−0.198771	−	0.114760i	−0.596082	+	0.802924i	$0.703277\pi$
$440$		0			0
$441$	−308.241	−	172.464i	−0.698958	−	0.391076i
$442$		0			0
$443$	519.799	+	300.106i	1.17336	+	0.677440i	0.954469	−	0.298309i	$-0.0964227\pi$
$443$	519.799	+	300.106i	1.17336	+	0.677440i	0.218891	+	0.975749i	$0.429756\pi$
$444$		0			0
$445$	13.5337	+	23.4410i	0.0304127	+	0.0526764i
$446$		0			0
$447$	−230.582	−	227.494i	−0.515843	−	0.508935i
$448$		0			0
$449$	639.843			1.42504			0.712520	−	0.701651i	$-0.247554\pi$
$449$	639.843			1.42504			0.712520	+	0.701651i	$0.247554\pi$
$450$		0			0
$451$		−	853.422i		−	1.89229i
$452$		0			0
$453$	−9.22612	−	2.40559i	−0.0203667	−	0.00531036i
$454$		0			0
$455$	−35.2791	+	20.3684i	−0.0775365	+	0.0447657i
$456$		0			0
$457$	86.7721	−	150.294i	0.189873	−	0.328870i	−0.755334	−	0.655339i	$-0.772526\pi$
$457$	86.7721	−	150.294i	0.189873	−	0.328870i	0.945208	+	0.326469i	$0.105859\pi$
$458$		0			0
$459$	181.282	−	188.766i	0.394949	−	0.411255i
$460$		0			0
$461$	361.655	−	626.406i	0.784502	−	1.35880i	−0.144794	−	0.989462i	$-0.546252\pi$
$461$	361.655	−	626.406i	0.784502	−	1.35880i	0.929296	−	0.369336i	$-0.120415\pi$
$462$		0			0
$463$	−643.880	+	371.744i	−1.39067	+	0.802903i	−0.993389	−	0.114794i	$-0.963379\pi$
$463$	−643.880	+	371.744i	−1.39067	+	0.802903i	−0.397280	+	0.917698i	$0.630046\pi$
$464$		0			0
$465$	−51.5217	−	13.4336i	−0.110799	−	0.0288895i
$466$		0			0
$467$			98.0700i			0.210000i	0.994472	+	0.105000i	$0.0334842\pi$
$467$			98.0700i			0.210000i	−0.994472	+	0.105000i	$0.966516\pi$
$468$		0			0
$469$	−124.573			−0.265614
$470$		0			0
$471$	−547.625	−	540.291i	−1.16269	−	1.14711i
$472$		0			0
$473$	−543.285	−	940.997i	−1.14859	−	1.98942i
$474$		0			0
$475$	−174.095	−	100.514i	−0.366515	−	0.211608i
$476$		0			0
$477$	−701.131	+	417.501i	−1.46988	+	0.875265i
$478$		0			0
$479$	−293.648	−	169.538i	−0.613043	−	0.353941i	0.161112	−	0.986936i	$-0.448492\pi$
$479$	−293.648	−	169.538i	−0.613043	−	0.353941i	−0.774156	+	0.632995i	$0.781825\pi$
$480$		0			0
$481$	370.665	+	642.011i	0.770614	+	1.33474i
$482$		0			0
$483$	−20.3220	+	5.59236i	−0.0420746	+	0.0115784i
$484$		0			0
$485$	−17.3334			−0.0357389
$486$		0			0
$487$			777.718i			1.59696i	0.602023	+	0.798479i	$0.294362\pi$
$487$			777.718i			1.59696i	−0.602023	+	0.798479i	$0.705638\pi$
$488$		0			0
$489$	−160.070	−	581.676i	−0.327341	−	1.18952i
$490$		0			0
$491$	52.0054	−	30.0254i	0.105917	−	0.0611514i	−0.446106	−	0.894980i	$-0.647189\pi$
$491$	52.0054	−	30.0254i	0.105917	−	0.0611514i	0.552023	+	0.833829i	$0.313856\pi$
$492$		0			0
$493$	201.829	−	349.578i	0.409390	−	0.709084i
$494$		0			0
$495$	−54.3407	−	91.2570i	−0.109779	−	0.184358i
$496$		0			0
$497$	160.726	−	278.386i	0.323393	−	0.560133i
$498$		0			0
$499$	−250.110	+	144.401i	−0.501222	+	0.289381i	−0.729218	−	0.684281i	$-0.760116\pi$
$499$	−250.110	+	144.401i	−0.501222	+	0.289381i	0.227996	+	0.973662i	$0.426783\pi$
$500$		0			0
$501$	−269.297	+	272.953i	−0.537520	+	0.544816i
$502$		0			0
$503$		−	567.389i		−	1.12801i	−0.825772	−	0.564005i	$-0.809260\pi$
$503$		−	567.389i		−	1.12801i	0.825772	−	0.564005i	$-0.190740\pi$
$504$		0			0
$505$	139.465			0.276168
$506$		0			0
$507$	127.085	−	487.408i	0.250661	−	0.961357i
$508$		0			0
$509$	158.283	+	274.155i	0.310970	+	0.538615i	0.978573	−	0.205902i	$-0.0660130\pi$
$509$	158.283	+	274.155i	0.310970	+	0.538615i	−0.667603	+	0.744517i	$0.732680\pi$
$510$		0			0
$511$	−103.253	−	59.6134i	−0.202061	−	0.116660i
$512$		0			0
$513$	159.821	+	153.484i	0.311541	+	0.299189i
$514$		0			0
$515$	−74.2390	−	42.8619i	−0.144153	−	0.0832271i
$516$		0			0
$517$	280.831	+	486.414i	0.543194	+	0.940840i
$518$		0			0
$519$	−152.468	+	584.756i	−0.293772	+	1.12670i
$520$		0			0
$521$	597.419			1.14668			0.573339	−	0.819318i	$-0.305648\pi$
$521$	597.419			1.14668			0.573339	+	0.819318i	$0.305648\pi$
$522$		0			0
$523$			630.846i			1.20621i	0.797663	+	0.603103i	$0.206069\pi$
$523$			630.846i			1.20621i	−0.797663	+	0.603103i	$0.793931\pi$
$524$		0			0
$525$	161.191	−	163.379i	0.307031	−	0.311199i
$526$		0			0
$527$	−209.662	+	121.048i	−0.397840	+	0.229693i
$528$		0			0
$529$	−261.970	+	453.745i	−0.495217	+	0.857741i
$530$		0			0
$531$	336.045	−	600.604i	0.632853	−	1.13108i
$532$		0			0
$533$	471.617	−	816.865i	0.884835	−	1.53258i
$534$		0			0
$535$	4.01515	−	2.31815i	0.00750495	−	0.00433299i
$536$		0			0
$537$	−4.64201	−	16.8685i	−0.00864434	−	0.0314126i
$538$		0			0
$539$			651.755i			1.20919i
$540$		0			0
$541$	−144.808			−0.267667			−0.133834	−	0.991004i	$-0.542729\pi$
$541$	−144.808			−0.267667			−0.133834	+	0.991004i	$0.542729\pi$
$542$		0			0
$543$	−383.939	+	105.655i	−0.707069	+	0.194577i
$544$		0			0
$545$	13.5112	+	23.4022i	0.0247913	+	0.0429397i
$546$		0			0
$547$	−679.104	−	392.081i	−1.24151	−	0.716784i	−0.272105	−	0.962268i	$-0.587720\pi$
$547$	−679.104	−	392.081i	−1.24151	−	0.716784i	−0.969401	+	0.245484i	$0.921053\pi$
$548$		0			0
$549$	−0.329596	−	24.4457i	−0.000600357	−	0.0445277i
$550$		0			0
$551$	295.974	+	170.881i	0.537158	+	0.310128i
$552$		0			0
$553$	170.402	+	295.144i	0.308140	+	0.533715i
$554$		0			0
$555$	61.2923	+	60.4714i	0.110436	+	0.108958i
$556$		0			0
$557$	92.1884			0.165509			0.0827544	−	0.996570i	$-0.473628\pi$
$557$	92.1884			0.165509			0.0827544	+	0.996570i	$0.473628\pi$
$558$		0			0
$559$		−	1200.92i		−	2.14833i
$560$		0			0
$561$	−467.307	−	121.844i	−0.832990	−	0.217191i
$562$		0			0
$563$	−141.939	+	81.9485i	−0.252112	+	0.145557i	−0.620731	−	0.784024i	$-0.713164\pi$
$563$	−141.939	+	81.9485i	−0.252112	+	0.145557i	0.368619	+	0.929581i	$0.379831\pi$
$564$		0			0
$565$	38.0237	−	65.8589i	0.0672985	−	0.116564i
$566$		0			0
$567$	−215.599	+	132.352i	−0.380245	+	0.233425i
$568$		0			0
$569$	−352.219	+	610.061i	−0.619014	+	1.07216i	0.370652	+	0.928772i	$0.379134\pi$
$569$	−352.219	+	610.061i	−0.619014	+	1.07216i	−0.989666	+	0.143392i	$0.954199\pi$
$570$		0			0
$571$	−413.817	+	238.917i	−0.724723	+	0.418419i	−0.816489	−	0.577361i	$-0.804082\pi$
$571$	−413.817	+	238.917i	−0.724723	+	0.418419i	0.0917653	+	0.995781i	$0.470749\pi$
$572$		0			0
$573$	−120.956	−	31.5377i	−0.211092	−	0.0550396i
$574$		0			0
$575$			55.1023i			0.0958301i
$576$		0			0
$577$	−21.5525			−0.0373527			−0.0186764	−	0.999826i	$-0.505945\pi$
$577$	−21.5525			−0.0373527			−0.0186764	+	0.999826i	$0.505945\pi$
$578$		0			0
$579$	295.532	+	291.574i	0.510418	+	0.503582i
$580$		0			0
$581$	204.669	+	354.498i	0.352271	+	0.610151i
$582$		0			0
$583$	1304.02	+	752.879i	2.23675	+	1.29139i
$584$		0			0
$585$	−1.58257	−	117.378i	−0.00270526	−	0.200645i
$586$		0			0
$587$	686.177	+	396.164i	1.16896	+	0.674897i	0.953434	−	0.301602i	$-0.0975215\pi$
$587$	686.177	+	396.164i	1.16896	+	0.674897i	0.215522	+	0.976499i	$0.430855\pi$
$588$		0			0
$589$	−102.487	−	177.512i	−0.174001	−	0.301379i
$590$		0			0
$591$	316.498	−	87.0964i	0.535530	−	0.147371i
$592$		0			0
$593$	−571.777			−0.964211			−0.482105	−	0.876113i	$-0.660128\pi$
$593$	−571.777			−0.964211			−0.482105	+	0.876113i	$0.660128\pi$
$594$		0			0
$595$			21.5131i			0.0361565i
$596$		0			0
$597$	69.2690	+	251.716i	0.116028	+	0.421635i
$598$		0			0
$599$	803.662	−	463.994i	1.34167	−	0.774615i	0.354620	−	0.935011i	$-0.384610\pi$
$599$	803.662	−	463.994i	1.34167	−	0.774615i	0.987053	+	0.160396i	$0.0512770\pi$
$600$		0			0
$601$	−66.4316	+	115.063i	−0.110535	+	0.191452i	−0.915986	−	0.401210i	$-0.868590\pi$
$601$	−66.4316	+	115.063i	−0.110535	+	0.191452i	0.805451	+	0.592662i	$0.201923\pi$
$602$		0			0
$603$	175.279	−	313.271i	0.290678	−	0.519521i
$604$		0			0
$605$	−55.0005	+	95.2637i	−0.0909100	+	0.157461i
$606$		0			0
$607$	480.102	−	277.187i	0.790942	−	0.456651i	−0.0493520	−	0.998781i	$-0.515716\pi$
$607$	480.102	−	277.187i	0.790942	−	0.456651i	0.840294	+	0.542131i	$0.182382\pi$
$608$		0			0
$609$	−274.037	+	277.757i	−0.449979	+	0.456087i
$610$		0			0
$611$			620.771i			1.01599i
$612$		0			0
$613$	1096.88			1.78937			0.894684	−	0.446700i	$-0.147401\pi$
$613$	1096.88			1.78937			0.894684	+	0.446700i	$0.147401\pi$
$614$		0			0
$615$	27.6402	−	106.008i	0.0449434	−	0.172370i
$616$		0			0
$617$	−311.636	−	539.770i	−0.505083	−	0.874829i	−0.999983	−	0.00587917i	$-0.998129\pi$
$617$	−311.636	−	539.770i	−0.505083	−	0.874829i	0.494900	−	0.868950i	$-0.335205\pi$
$618$		0			0
$619$	−613.432	−	354.165i	−0.991005	−	0.572157i	−0.0854305	−	0.996344i	$-0.527227\pi$
$619$	−613.432	−	354.165i	−0.991005	−	0.572157i	−0.905575	+	0.424187i	$0.860560\pi$
$620$		0			0
$621$	14.5304	−	58.9736i	0.0233984	−	0.0949656i
$622$		0			0
$623$	−103.027	−	59.4826i	−0.165372	−	0.0954777i
$624$		0			0
$625$	−293.691	−	508.688i	−0.469906	−	0.813901i
$626$		0			0
$627$	103.161	−	395.650i	0.164531	−	0.631021i
$628$		0			0
$629$	391.497			0.622412
$630$		0			0
$631$			1142.86i			1.81119i	0.424139	+	0.905597i	$0.360577\pi$
$631$			1142.86i			1.81119i	−0.424139	+	0.905597i	$0.639423\pi$
$632$		0			0
$633$	−594.565	+	602.636i	−0.939282	+	0.952031i
$634$		0			0
$635$	62.4246	−	36.0409i	0.0983065	−	0.0567573i
$636$		0			0
$637$	−360.172	+	623.836i	−0.565419	+	0.979334i
$638$		0			0
$639$	473.926	+	795.888i	0.741668	+	1.24552i
$640$		0			0
$641$	−138.542	+	239.961i	−0.216134	+	0.374354i	−0.953623	−	0.301005i	$-0.902678\pi$
$641$	−138.542	+	239.961i	−0.216134	+	0.374354i	0.737489	+	0.675359i	$0.236011\pi$
$642$		0			0
$643$	737.236	−	425.644i	1.14656	−	0.661965i	0.198511	−	0.980099i	$-0.436389\pi$
$643$	737.236	−	425.644i	1.14656	−	0.661965i	0.948046	+	0.318133i	$0.103056\pi$
$644$		0			0
$645$	−37.0076	−	134.481i	−0.0573761	−	0.208498i
$646$		0			0
$647$		−	706.622i		−	1.09215i	−0.837736	−	0.546076i	$-0.816121\pi$
$647$		−	706.622i		−	1.09215i	0.837736	−	0.546076i	$-0.183879\pi$
$648$		0			0
$649$	−1269.94			−1.95676
$650$		0			0
$651$	225.630	−	62.0904i	0.346589	−	0.0953770i
$652$		0			0
$653$	−390.342	−	676.092i	−0.597767	−	1.03536i	−0.993150	−	0.116846i	$-0.962722\pi$
$653$	−390.342	−	676.092i	−0.597767	−	1.03536i	0.395383	−	0.918516i	$-0.370612\pi$
$654$		0			0
$655$	115.701	+	66.8002i	0.176643	+	0.101985i
$656$		0			0
$657$	295.195	−	175.779i	0.449307	−	0.267548i
$658$		0			0
$659$	−491.322	−	283.665i	−0.745557	−	0.430447i	0.0785296	−	0.996912i	$-0.474977\pi$
$659$	−491.322	−	283.665i	−0.745557	−	0.430447i	−0.824086	+	0.566465i	$0.808311\pi$
$660$		0			0
$661$	46.9164	+	81.2615i	0.0709778	+	0.122937i	0.899330	−	0.437270i	$-0.144055\pi$
$661$	46.9164	+	81.2615i	0.0709778	+	0.122937i	−0.828352	+	0.560208i	$0.810721\pi$
$662$		0			0
$663$	−379.956	−	374.868i	−0.573086	−	0.565411i
$664$		0			0
$665$	−18.2143			−0.0273899
$666$		0			0
$667$		−	93.6780i		−	0.140447i
$668$		0			0
$669$	855.973	+	223.184i	1.27948	+	0.333608i
$670$		0			0
$671$	−39.0684	+	22.5562i	−0.0582241	+	0.0336157i
$672$		0			0
$673$	100.742	−	174.490i	0.149691	−	0.259272i	−0.781422	−	0.624003i	$-0.785505\pi$
$673$	100.742	−	174.490i	0.149691	−	0.259272i	0.931113	+	0.364730i	$0.118839\pi$
$674$		0			0
$675$	184.057	+	635.238i	0.272677	+	0.941094i
$676$		0			0
$677$	−336.988	+	583.680i	−0.497766	+	0.862157i	−0.999997	−	0.00257723i	$-0.999180\pi$
$677$	−336.988	+	583.680i	−0.497766	+	0.862157i	0.502230	+	0.864734i	$0.332513\pi$
$678$		0			0
$679$	65.9763	−	38.0914i	0.0971668	−	0.0560993i
$680$		0			0
$681$	416.958	+	108.716i	0.612273	+	0.159642i
$682$		0			0
$683$		−	155.633i		−	0.227867i	−0.993488	−	0.113933i	$-0.963655\pi$
$683$		−	155.633i		−	0.227867i	0.993488	−	0.113933i	$-0.0363450\pi$
$684$		0			0
$685$	44.5226			0.0649965
$686$		0			0
$687$	604.053	+	595.963i	0.879262	+	0.867487i
$688$		0			0
$689$	832.110	+	1441.26i	1.20771	+	2.09181i
$690$		0			0
$691$	693.263	+	400.255i	1.00327	+	0.579241i	0.909215	−	0.416326i	$-0.136682\pi$
$691$	693.263	+	400.255i	1.00327	+	0.579241i	0.0940588	+	0.995567i	$0.470016\pi$
$692$		0			0
$693$	407.382	+	227.935i	0.587853	+	0.328911i
$694$		0			0
$695$	−28.8366	−	16.6488i	−0.0414915	−	0.0239551i
$696$		0			0
$697$	−249.061	−	431.387i	−0.357333	−	0.618919i
$698$		0			0
$699$	74.9520	−	20.6258i	0.107228	−	0.0295077i
$700$		0			0
$701$	−488.317			−0.696601			−0.348300	−	0.937383i	$-0.613241\pi$
$701$	−488.317			−0.696601			−0.348300	+	0.937383i	$0.613241\pi$
$702$		0			0
$703$			331.465i			0.471501i
$704$		0			0
$705$	19.1297	+	69.5153i	0.0271344	+	0.0986033i
$706$		0			0
$707$	−530.848	+	306.485i	−0.750845	+	0.433501i
$708$		0			0
$709$	358.633	−	621.170i	0.505829	−	0.876121i	−0.494149	−	0.869377i	$-0.664520\pi$
$709$	358.633	−	621.170i	0.505829	−	0.876121i	0.999977	−	0.00674353i	$-0.00214655\pi$
$710$		0			0
$711$	−981.978	+	13.2398i	−1.38112	+	0.0186214i
$712$		0			0
$713$	−28.0920	+	48.6568i	−0.0393997	+	0.0682423i
$714$		0			0
$715$	−187.589	+	108.305i	−0.262363	+	0.151475i
$716$		0			0
$717$	756.169	−	766.433i	1.05463	−	1.06894i
$718$		0			0
$719$			512.219i			0.712404i	0.934409	+	0.356202i	$0.115929\pi$
$719$			512.219i			0.712404i	−0.934409	+	0.356202i	$0.884071\pi$
$720$		0			0
$721$	376.770			0.522566
$722$		0			0
$723$	−132.768	+	509.204i	−0.183636	+	0.704294i
$724$		0			0
$725$	510.028	+	883.394i	0.703487	+	1.21848i
$726$		0			0
$727$	−574.499	−	331.687i	−0.790232	−	0.456241i	0.0498122	−	0.998759i	$-0.484138\pi$
$727$	−574.499	−	331.687i	−0.790232	−	0.456241i	−0.840044	+	0.542518i	$0.817471\pi$
$728$		0			0
$729$	−29.4770	−	728.404i	−0.0404349	−	0.999182i
$730$		0			0
$731$	−549.237	−	317.102i	−0.751351	−	0.433793i
$732$		0			0
$733$	−146.883	−	254.408i	−0.200386	−	0.347078i	0.748267	−	0.663398i	$-0.230886\pi$
$733$	−146.883	−	254.408i	−0.200386	−	0.347078i	−0.948653	+	0.316320i	$0.897553\pi$
$734$		0			0
$735$	−21.1087	+	80.9577i	−0.0287193	+	0.110147i
$736$		0			0
$737$	−662.392			−0.898768
$738$		0			0
$739$		−	1335.27i		−	1.80686i	−0.428736	−	0.903430i	$-0.641041\pi$
$739$		−	1335.27i		−	1.80686i	0.428736	−	0.903430i	$-0.358959\pi$
$740$		0			0
$741$	317.385	−	321.694i	0.428320	−	0.434134i
$742$		0			0
$743$	488.188	−	281.855i	0.657050	−	0.379348i	−0.134102	−	0.990968i	$-0.542815\pi$
$743$	488.188	−	281.855i	0.657050	−	0.379348i	0.791152	+	0.611620i	$0.209482\pi$
$744$		0			0
$745$	−38.3629	+	66.4465i	−0.0514938	+	0.0891899i
$746$		0			0
$747$	−1179.45	+	15.9023i	−1.57892	+	0.0212882i
$748$		0			0
$749$	−10.1886	+	17.6472i	−0.0136030	+	0.0235610i
$750$		0			0
$751$	591.407	−	341.449i	0.787493	−	0.454659i	−0.0515861	−	0.998669i	$-0.516428\pi$
$751$	591.407	−	341.449i	0.787493	−	0.454659i	0.839079	+	0.544009i	$0.183094\pi$
$752$		0			0
$753$	326.384	+	1186.04i	0.433445	+	1.57509i
$754$		0			0
$755$			2.25845i			0.00299133i
$756$		0			0
$757$	−534.746			−0.706401			−0.353201	−	0.935548i	$-0.614907\pi$
$757$	−534.746			−0.706401			−0.353201	+	0.935548i	$0.614907\pi$
$758$		0			0
$759$	−108.058	+	29.7362i	−0.142369	+	0.0391782i
$760$		0			0
$761$	−416.191	−	720.863i	−0.546900	−	0.947258i	−0.998485	−	0.0550300i	$-0.982475\pi$
$761$	−416.191	−	720.863i	−0.546900	−	0.947258i	0.451585	−	0.892228i	$-0.350859\pi$
$762$		0			0
$763$	−102.856	−	59.3840i	−0.134805	−	0.0778296i
$764$		0			0
$765$	−54.1003	−	30.2698i	−0.0707194	−	0.0395683i
$766$		0			0
$767$	−1215.54	−	701.791i	−1.58480	−	0.914982i
$768$		0			0
$769$	−351.020	−	607.985i	−0.456464	−	0.790618i	0.542308	−	0.840180i	$-0.317551\pi$
$769$	−351.020	−	607.985i	−0.456464	−	0.790618i	−0.998771	+	0.0495620i	$0.984217\pi$
$770$		0			0
$771$	369.146	+	364.203i	0.478789	+	0.472377i
$772$		0			0
$773$	−472.477			−0.611225			−0.305612	−	0.952156i	$-0.598861\pi$
$773$	−472.477			−0.611225			−0.305612	+	0.952156i	$0.598861\pi$
$774$		0			0
$775$		−	611.785i		−	0.789400i
$776$		0			0
$777$	−366.189	−	95.4790i	−0.471285	−	0.122882i
$778$		0			0
$779$	365.238	−	210.870i	0.468855	−	0.270693i
$780$		0			0
$781$	854.630	−	1480.26i	1.09428	−	1.89534i
$782$		0			0
$783$	−312.911	−	1079.95i	−0.399631	−	1.37925i
$784$		0			0
$785$	−91.1107	+	157.808i	−0.116065	+	0.201030i
$786$		0			0
$787$	−556.186	+	321.114i	−0.706717	+	0.408023i	−0.809844	−	0.586645i	$-0.800448\pi$
$787$	−556.186	+	321.114i	−0.706717	+	0.408023i	0.103127	+	0.994668i	$0.467115\pi$
$788$		0			0
$789$	444.800	+	115.976i	0.563752	+	0.146991i
$790$		0			0
$791$			334.240i			0.422554i
$792$		0			0
$793$	−49.8598			−0.0628749
$794$		0			0
$795$	137.596	+	135.753i	0.173076	+	0.170758i
$796$		0			0
$797$	42.3167	+	73.2947i	0.0530950	+	0.0919632i	0.891351	−	0.453313i	$-0.149758\pi$
$797$	42.3167	+	73.2947i	0.0530950	+	0.0919632i	−0.838256	+	0.545276i	$0.816425\pi$
$798$		0			0
$799$	283.909	+	163.915i	0.355330	+	0.205150i
$800$		0			0
$801$	294.547	−	175.393i	0.367724	−	0.218968i
$802$		0			0
$803$	−549.029	−	316.982i	−0.683722	−	0.394747i
$804$		0			0
$805$	2.49630	+	4.32373i	0.00310100	+	0.00537109i
$806$		0			0
$807$	−36.6628	+	10.0891i	−0.0454310	+	0.0125020i
$808$		0			0
$809$	−1071.63			−1.32464			−0.662319	−	0.749222i	$-0.730427\pi$
$809$	−1071.63			−1.32464			−0.662319	+	0.749222i	$0.730427\pi$
$810$		0			0
$811$			745.523i			0.919264i	0.888110	+	0.459632i	$0.152019\pi$
$811$			745.523i			0.919264i	−0.888110	+	0.459632i	$0.847981\pi$
$812$		0			0
$813$	32.4041	+	117.753i	0.0398575	+	0.144838i
$814$		0			0
$815$	−123.758	+	71.4516i	−0.151850	+	0.0876707i
$816$		0			0
$817$	268.478	−	465.017i	0.328614	−	0.569177i
$818$		0			0
$819$	263.970	+	443.298i	0.322308	+	0.541268i
$820$		0			0
$821$	417.550	−	723.217i	0.508587	−	0.880898i	−0.491364	−	0.870954i	$-0.663501\pi$
$821$	417.550	−	723.217i	0.508587	−	0.880898i	0.999951	−	0.00994363i	$-0.00316521\pi$
$822$		0			0
$823$	−369.777	+	213.491i	−0.449304	+	0.259406i	−0.707536	−	0.706677i	$-0.750193\pi$
$823$	−369.777	+	213.491i	−0.449304	+	0.259406i	0.258232	+	0.966083i	$0.416860\pi$
$824$		0			0
$825$	857.102	−	868.736i	1.03891	−	1.05301i
$826$		0			0
$827$		−	235.457i		−	0.284713i	−0.989815	−	0.142356i	$-0.954532\pi$
$827$		−	235.457i		−	0.284713i	0.989815	−	0.142356i	$-0.0454679\pi$
$828$		0			0
$829$	−1336.05			−1.61164			−0.805819	−	0.592161i	$-0.798275\pi$
$829$	−1336.05			−1.61164			−0.805819	+	0.592161i	$0.798275\pi$
$830$		0			0
$831$	−278.758	+	1069.11i	−0.335448	+	1.28654i
$832$		0			0
$833$	190.207	+	329.448i	0.228340	+	0.395496i
$834$		0			0
$835$	78.6565	+	45.4123i	0.0941994	+	0.0543860i
$836$		0			0
$837$	−161.327	+	654.767i	−0.192744	+	0.782279i
$838$		0			0
$839$	−1315.40	−	759.449i	−1.56782	−	0.905183i	−0.996422	−	0.0845127i	$-0.973067\pi$
$839$	−1315.40	−	759.449i	−1.56782	−	0.905183i	−0.571401	−	0.820671i	$-0.693600\pi$
$840$		0			0
$841$	−446.586	−	773.509i	−0.531017	−	0.919749i
$842$		0			0
$843$	360.756	−	1383.60i	0.427943	−	1.64128i
$844$		0			0
$845$	−119.312			−0.141198
$846$		0			0
$847$		−	483.472i		−	0.570805i
$848$		0			0
$849$	365.064	−	370.019i	0.429993	−	0.435829i
$850$		0			0
$851$	78.6834	−	45.4279i	0.0924599	−	0.0533818i
$852$		0			0
$853$	−219.635	+	380.418i	−0.257485	+	0.445977i	−0.965568	−	0.260153i	$-0.916227\pi$
$853$	−219.635	+	380.418i	−0.257485	+	0.445977i	0.708083	+	0.706130i	$0.249560\pi$
$854$		0			0
$855$	25.6282	−	45.8046i	0.0299745	−	0.0535726i
$856$		0			0
$857$	42.9674	−	74.4218i	0.0501370	−	0.0868399i	−0.839868	−	0.542791i	$-0.817368\pi$
$857$	42.9674	−	74.4218i	0.0501370	−	0.0868399i	0.890005	+	0.455951i	$0.150701\pi$
$858$		0			0
$859$	750.391	−	433.239i	0.873564	−	0.504352i	0.00503295	−	0.999987i	$-0.498398\pi$
$859$	750.391	−	433.239i	0.873564	−	0.504352i	0.868531	+	0.495635i	$0.165065\pi$
$860$		0			0
$861$	127.753	+	464.241i	0.148378	+	0.539188i
$862$		0			0
$863$			651.682i			0.755136i	0.925982	+	0.377568i	$0.123240\pi$
$863$			651.682i			0.755136i	−0.925982	+	0.377568i	$0.876760\pi$
$864$		0			0
$865$	143.142			0.165482
$866$		0			0
$867$	564.153	−	155.248i	0.650696	−	0.179063i
$868$		0			0
$869$	906.076	+	1569.37i	1.04266	+	1.80595i
$870$		0			0
$871$	−634.017	−	366.050i	−0.727919	−	0.420264i
$872$		0			0
$873$	2.95961	+	219.510i	0.00339016	+	0.251444i
$874$		0			0
$875$	−95.1323	−	54.9247i	−0.108723	−	0.0627711i
$876$		0			0
$877$	−359.003	−	621.811i	−0.409353	−	0.709020i	0.585464	−	0.810698i	$-0.300912\pi$
$877$	−359.003	−	621.811i	−0.409353	−	0.709020i	−0.994817	+	0.101678i	$0.967579\pi$
$878$		0			0
$879$	12.4646	+	12.2977i	0.0141804	+	0.0139905i
$880$		0			0
$881$	292.378			0.331870			0.165935	−	0.986137i	$-0.446936\pi$
$881$	292.378			0.331870			0.165935	+	0.986137i	$0.446936\pi$
$882$		0			0
$883$		−	507.123i		−	0.574318i	−0.957883	−	0.287159i	$-0.907289\pi$
$883$		−	507.123i		−	0.574318i	0.957883	−	0.287159i	$-0.0927109\pi$
$884$		0			0
$885$	−157.745	−	41.1301i	−0.178243	−	0.0464746i
$886$		0			0
$887$	222.320	−	128.356i	0.250642	−	0.144708i	−0.369416	−	0.929264i	$-0.620442\pi$
$887$	222.320	−	128.356i	0.250642	−	0.144708i	0.620058	+	0.784556i	$0.287109\pi$
$888$		0			0
$889$	−158.405	+	274.366i	−0.178184	+	0.308623i
$890$		0			0
$891$	−1146.40	+	703.754i	−1.28665	+	0.789848i
$892$		0			0
$893$	−138.780	+	240.374i	−0.155409	+	0.269176i
$894$		0			0
$895$	−3.58896	+	2.07209i	−0.00401001	+	0.00231518i
$896$		0			0
$897$	−119.862	−	31.2525i	−0.133626	−	0.0348411i
$898$		0			0
$899$			1040.08i			1.15693i
$900$		0			0
$901$	878.875			0.975444
$902$		0			0
$903$	436.396	+	430.552i	0.483274	+	0.476802i
$904$		0			0
$905$	47.1620	+	81.6870i	0.0521127	+	0.0902619i
$906$		0			0
$907$	1341.24	+	774.365i	1.47877	+	0.853766i	0.999711	−	0.0240198i	$-0.00764647\pi$
$907$	1341.24	+	774.365i	1.47877	+	0.853766i	0.479054	+	0.877785i	$0.340980\pi$
$908$		0			0
$909$	−23.8131	−	1766.19i	−0.0261971	−	1.94300i
$910$		0			0
$911$	465.815	+	268.938i	0.511322	+	0.295212i	0.733377	−	0.679822i	$-0.237943\pi$
$911$	465.815	+	268.938i	0.511322	+	0.295212i	−0.222055	+	0.975034i	$0.571276\pi$
$912$		0			0
$913$	1088.29	+	1884.97i	1.19199	+	2.06459i
$914$		0			0
$915$	−5.58342	+	1.53649i	−0.00610209	+	0.00167922i
$916$		0			0
$917$	−587.195			−0.640343
$918$		0			0
$919$			1099.66i			1.19659i	0.801277	+	0.598294i	$0.204155\pi$
$919$			1099.66i			1.19659i	−0.801277	+	0.598294i	$0.795845\pi$
$920$		0			0
$921$	295.877	+	1075.18i	0.321256	+	1.16741i
$922$		0			0
$923$	1636.04	−	944.568i	1.77252	−	1.02337i
$924$		0			0
$925$	−494.662	+	856.780i	−0.534770	+	0.926249i
$926$		0			0
$927$	−530.129	+	947.485i	−0.571876	+	1.02210i
$928$		0			0
$929$	−97.6555	+	169.144i	−0.105119	+	0.182071i	−0.913787	−	0.406194i	$-0.866856\pi$
$929$	−97.6555	+	169.144i	−0.105119	+	0.182071i	0.808668	+	0.588265i	$0.200189\pi$
$930$		0			0
$931$	−278.931	+	161.041i	−0.299603	+	0.172976i
$932$		0			0
$933$	−471.900	+	478.305i	−0.505788	+	0.512653i
$934$		0			0
$935$			114.392i			0.122344i
$936$		0			0
$937$	1286.97			1.37350			0.686752	−	0.726892i	$-0.259036\pi$
$937$	1286.97			1.37350			0.686752	+	0.726892i	$0.259036\pi$
$938$		0			0
$939$	−119.736	+	459.223i	−0.127515	+	0.489055i
$940$		0			0
$941$	−505.685	−	875.873i	−0.537391	−	0.930789i	−0.999043	−	0.0437282i	$-0.986076\pi$
$941$	−505.685	−	875.873i	−0.537391	−	0.930789i	0.461652	−	0.887061i	$-0.347257\pi$
$942$		0			0
$943$	−100.113	−	57.8003i	−0.106164	−	0.0612941i
$944$		0			0
$945$	43.2207	+	41.5070i	0.0457362	+	0.0439228i
$946$		0			0
$947$	598.516	+	345.553i	0.632013	+	0.364893i	0.781531	−	0.623866i	$-0.214439\pi$
$947$	598.516	+	345.553i	0.632013	+	0.364893i	−0.149519	+	0.988759i	$0.547772\pi$
$948$		0			0
$949$	−350.340	−	606.807i	−0.369168	−	0.639417i
$950$		0			0
$951$	312.492	−	1198.50i	0.328594	−	1.26025i
$952$		0			0
$953$	659.310			0.691826			0.345913	−	0.938267i	$-0.387569\pi$
$953$	659.310			0.691826			0.345913	+	0.938267i	$0.387569\pi$
$954$		0			0
$955$			29.6086i			0.0310038i
$956$		0			0
$957$	−1457.14	+	1476.92i	−1.52261	+	1.54328i
$958$		0			0
$959$	−169.467	+	97.8419i	−0.176712	+	0.102025i
$960$		0			0
$961$	−168.602	+	292.028i	−0.175445	+	0.303879i
$962$		0			0
$963$	−30.0427	−	50.4522i	−0.0311970	−	0.0523907i
$964$		0			0
$965$	49.1689	−	85.1631i	0.0509522	−	0.0882519i
$966$		0			0
$967$	980.817	−	566.275i	1.01429	−	0.585600i	0.101844	−	0.994800i	$-0.467526\pi$
$967$	980.817	−	566.275i	1.01429	−	0.585600i	0.912444	+	0.409201i	$0.134192\pi$
$968$		0			0
$969$	−63.3203	−	230.099i	−0.0653461	−	0.237460i
$970$		0			0
$971$		−	277.255i		−	0.285536i	−0.989756	−	0.142768i	$-0.954400\pi$
$971$		−	277.255i		−	0.285536i	0.989756	−	0.142768i	$-0.0456002\pi$
$972$		0			0
$973$	146.348			0.150409
$974$		0			0
$975$	1300.47	−	357.872i	1.33381	−	0.367048i
$976$		0			0
$977$	−166.546	−	288.467i	−0.170467	−	0.295257i	0.768116	−	0.640310i	$-0.221194\pi$
$977$	−166.546	−	288.467i	−0.170467	−	0.295257i	−0.938583	+	0.345053i	$0.887861\pi$
$978$		0			0
$979$	−547.824	−	316.286i	−0.559575	−	0.323071i
$980$		0			0
$981$	294.059	−	175.103i	0.299754	−	0.178494i
$982$		0			0
$983$	1287.12	+	743.121i	1.30938	+	0.755973i	0.981993	−	0.188916i	$-0.0604975\pi$
$983$	1287.12	+	743.121i	1.30938	+	0.755973i	0.327390	+	0.944889i	$0.393831\pi$
$984$		0			0
$985$	−38.8778	−	67.3384i	−0.0394699	−	0.0683639i
$986$		0			0
$987$	−225.579	−	222.558i	−0.228551	−	0.225490i
$988$		0			0
$989$	−147.182			−0.148819
$990$		0			0
$991$			17.1782i			0.0173343i	0.999962	+	0.00866713i	$0.00275887\pi$
$991$			17.1782i			0.0173343i	−0.999962	+	0.00866713i	$0.997241\pi$
$992$		0			0
$993$	−425.497	−	110.943i	−0.428496	−	0.111725i
$994$		0			0
$995$	53.5552	−	30.9201i	0.0538243	−	0.0310755i
$996$		0			0
$997$	−737.655	+	1277.66i	−0.739874	+	1.28150i	0.212677	+	0.977123i	$0.431782\pi$
$997$	−737.655	+	1277.66i	−0.739874	+	1.28150i	−0.952552	+	0.304377i	$0.901552\pi$
$998$		0			0
$999$	755.347	−	786.533i	0.756103	−	0.787320i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	144.3.o.c.79.1	yes	8
3.2	odd	2		432.3.o.a.127.2		8
4.3	odd	2		144.3.o.a.79.4	yes	8
8.3	odd	2		576.3.o.f.511.1		8
8.5	even	2		576.3.o.d.511.4		8
9.2	odd	6		1296.3.g.k.1135.6		8
9.4	even	3		144.3.o.a.31.4	✓	8
9.5	odd	6		432.3.o.b.415.2		8
9.7	even	3		1296.3.g.j.1135.4		8
12.11	even	2		432.3.o.b.127.2		8
24.5	odd	2		1728.3.o.e.127.3		8
24.11	even	2		1728.3.o.f.127.3		8
36.7	odd	6		1296.3.g.j.1135.3		8
36.11	even	6		1296.3.g.k.1135.5		8
36.23	even	6		432.3.o.a.415.2		8
36.31	odd	6	inner	144.3.o.c.31.1	yes	8
72.5	odd	6		1728.3.o.f.1279.3		8
72.13	even	6		576.3.o.f.319.1		8
72.59	even	6		1728.3.o.e.1279.3		8
72.67	odd	6		576.3.o.d.319.4		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
144.3.o.a.31.4	✓	8	9.4	even	3
144.3.o.a.79.4	yes	8	4.3	odd	2
144.3.o.c.31.1	yes	8	36.31	odd	6	inner
144.3.o.c.79.1	yes	8	1.1	even	1	trivial
432.3.o.a.127.2		8	3.2	odd	2
432.3.o.a.415.2		8	36.23	even	6
432.3.o.b.127.2		8	12.11	even	2
432.3.o.b.415.2		8	9.5	odd	6
576.3.o.d.319.4		8	72.67	odd	6
576.3.o.d.511.4		8	8.5	even	2
576.3.o.f.319.1		8	72.13	even	6
576.3.o.f.511.1		8	8.3	odd	2
1296.3.g.j.1135.3		8	36.7	odd	6
1296.3.g.j.1135.4		8	9.7	even	3
1296.3.g.k.1135.5		8	36.11	even	6
1296.3.g.k.1135.6		8	9.2	odd	6
1728.3.o.e.127.3		8	24.5	odd	2
1728.3.o.e.1279.3		8	72.59	even	6
1728.3.o.f.127.3		8	24.11	even	2
1728.3.o.f.1279.3		8	72.5	odd	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 144 = 2^{4} \cdot 3^{2} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	144.o (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-2.89248 + 0.795973i) q^{3} +(0.355304 + 0.615405i) q^{5} +(-2.70480 - 1.56162i) q^{7} +(7.73285 - 4.60467i) q^{9} +(-14.3822 - 8.30359i) q^{11} +(-9.17743 - 15.8958i) q^{13} +(-1.51756 - 1.49723i) q^{15} -9.69321 q^{17} -8.20686i q^{19} +(9.06659 + 2.36400i) q^{21} +(-1.94815 + 1.12477i) q^{23} +(12.2475 - 21.2133i) q^{25} +(-18.7019 + 19.4740i) q^{27} +(-20.8217 + 36.0642i) q^{29} +(21.6298 - 12.4879i) q^{31} +(48.2097 + 12.5701i) q^{33} -2.21940i q^{35} -40.3888 q^{37} +(39.1981 + 38.6732i) q^{39} +(25.6944 + 44.5040i) q^{41} +(56.6621 + 32.7139i) q^{43} +(5.58126 + 3.12278i) q^{45} +(-29.2894 - 16.9102i) q^{47} +(-19.6227 - 33.9875i) q^{49} +(28.0374 - 7.71554i) q^{51} -90.6691 q^{53} -11.8012i q^{55} +(6.53244 + 23.7382i) q^{57} +(66.2243 - 38.2346i) q^{59} +(1.35822 - 2.35250i) q^{61} +(-28.1066 + 0.378955i) q^{63} +(6.52157 - 11.2957i) q^{65} +(34.5422 - 19.9429i) q^{67} +(4.73970 - 4.80403i) q^{69} +102.923i q^{71} +38.1741 q^{73} +(-18.5404 + 71.1078i) q^{75} +(25.9341 + 44.9192i) q^{77} +(-94.4994 - 54.5593i) q^{79} +(38.5940 - 71.2145i) q^{81} +(-113.503 - 65.5311i) q^{83} +(-3.44404 - 5.96526i) q^{85} +(31.5201 - 120.888i) q^{87} +38.0903 q^{89} +57.3266i q^{91} +(-52.6235 + 53.3378i) q^{93} +(5.05055 - 2.91593i) q^{95} +(-12.1961 + 21.1243i) q^{97} +(-149.451 + 2.01501i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 3 q^{3} + 3 q^{5} - 3 q^{7} - 3 q^{9} - 18 q^{11} + 5 q^{13} + 21 q^{15} + 6 q^{17} - 33 q^{21} + 81 q^{23} - 23 q^{25} - 108 q^{27} + 69 q^{29} - 45 q^{31} + 72 q^{33} - 20 q^{37} + 141 q^{39} + 54 q^{41}+ \cdots - 585 q^{99}+O(q^{100}) \) 8 * q + 3 * q^3 + 3 * q^5 - 3 * q^7 - 3 * q^9 - 18 * q^11 + 5 * q^13 + 21 * q^15 + 6 * q^17 - 33 * q^21 + 81 * q^23 - 23 * q^25 - 108 * q^27 + 69 * q^29 - 45 * q^31 + 72 * q^33 - 20 * q^37 + 141 * q^39 + 54 * q^41 - 117 * q^45 - 207 * q^47 + 41 * q^49 + 141 * q^51 - 252 * q^53 - 273 * q^57 + 306 * q^59 + 7 * q^61 - 441 * q^63 + 93 * q^65 - 12 * q^67 + 189 * q^69 + 74 * q^73 + 387 * q^75 + 207 * q^77 - 33 * q^79 + 117 * q^81 - 549 * q^83 - 30 * q^85 + 87 * q^87 - 168 * q^89 - 27 * q^93 + 684 * q^95 - 10 * q^97 - 585 * q^99

Introduction

L-functions

Modular forms

Varieties

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Representations

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Database

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