LMFDB - Embedded newform 144.3.o.c.31.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [144,3,Mod(31,144)]

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

lf = mfeigenbasis(mf)

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")

//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: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$3.92371580679$
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			31.1
Root			$-2.33086i$ of defining polynomial
Character	$\chi$	$=$	144.31
Dual form			144.3.o.c.79.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

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

Display 100 coefficients 10 coefficients

Character values

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

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

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	−0.828306	−	0.560277i	$-0.810695\pi$
$5$	0.355304	−	0.615405i	0.0710609	−	0.123081i	0.899367	+	0.437195i	$0.144028\pi$
$6$		0			0
$7$	−2.70480	+	1.56162i	−0.386401	+	0.223088i	−0.680599	−	0.732656i	$-0.738281\pi$
$7$	−2.70480	+	1.56162i	−0.386401	+	0.223088i	0.294199	+	0.955744i	$0.404947\pi$
$8$		0			0
$9$	7.73285	+	4.60467i	0.859206	+	0.511630i
$10$		0			0
$11$	−14.3822	+	8.30359i	−1.30748	+	0.754872i	−0.981674	−	0.190566i	$-0.938968\pi$
$11$	−14.3822	+	8.30359i	−1.30748	+	0.754872i	−0.325802	+	0.945438i	$0.605634\pi$
$12$		0			0
$13$	−9.17743	+	15.8958i	−0.705956	+	1.22275i	0.260389	+	0.965504i	$0.416149\pi$
$13$	−9.17743	+	15.8958i	−0.705956	+	1.22275i	−0.966345	+	0.257248i	$0.917184\pi$
$14$		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	$0.0692913\pi$
$19$			8.20686i			0.431940i	−0.976400	+	0.215970i	$0.930709\pi$
$20$		0			0
$21$	9.06659	−	2.36400i	0.431742	−	0.112571i
$22$		0			0
$23$	−1.94815	−	1.12477i	−0.0847022	−	0.0489028i	0.457051	−	0.889441i	$-0.348906\pi$
$23$	−1.94815	−	1.12477i	−0.0847022	−	0.0489028i	−0.541753	+	0.840538i	$0.682239\pi$
$24$		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	−0.961795	−	0.273770i	$-0.911729\pi$
$29$	−20.8217	−	36.0642i	−0.717989	−	1.24359i	0.243806	−	0.969824i	$-0.421604\pi$
$30$		0			0
$31$	21.6298	+	12.4879i	0.697734	+	0.402837i	0.806503	−	0.591230i	$-0.201358\pi$
$31$	21.6298	+	12.4879i	0.697734	+	0.402837i	−0.108769	+	0.994067i	$0.534691\pi$
$32$		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	−0.361519	−	0.932365i	$-0.617742\pi$
$41$	25.6944	−	44.5040i	0.626692	−	1.08546i	0.988211	−	0.153098i	$-0.0489251\pi$
$42$		0			0
$43$	56.6621	−	32.7139i	1.31772	−	0.760787i	0.334360	−	0.942445i	$-0.391480\pi$
$43$	56.6621	−	32.7139i	1.31772	−	0.760787i	0.983362	+	0.181658i	$0.0581464\pi$
$44$		0			0
$45$	5.58126	−	3.12278i	0.124028	−	0.0693951i
$46$		0			0
$47$	−29.2894	+	16.9102i	−0.623179	+	0.359793i	−0.778106	−	0.628133i	$-0.783819\pi$
$47$	−29.2894	+	16.9102i	−0.623179	+	0.359793i	0.154927	+	0.987926i	$0.450486\pi$
$48$		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	0.942024	−	0.335545i	$-0.108920\pi$
$59$	66.2243	+	38.2346i	1.12245	+	0.648045i	0.180422	+	0.983589i	$0.442254\pi$
$60$		0			0
$61$	1.35822	+	2.35250i	0.0222659	+	0.0385656i	0.876944	−	0.480593i	$-0.159579\pi$
$61$	1.35822	+	2.35250i	0.0222659	+	0.0385656i	−0.854678	+	0.519159i	$0.826245\pi$
$62$		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	0.735114	−	0.677943i	$-0.237129\pi$
$67$	34.5422	+	19.9429i	0.515555	+	0.297656i	−0.219559	+	0.975599i	$0.570462\pi$
$68$		0			0
$69$	4.73970	+	4.80403i	0.0686913	+	0.0696237i
$70$		0			0
$71$		−	102.923i		−	1.44962i	−0.688950	−	0.724809i	$-0.741928\pi$
$71$		−	102.923i		−	1.44962i	0.688950	−	0.724809i	$-0.258072\pi$
$72$		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	−0.959705	−	0.281010i	$-0.909331\pi$
$79$	−94.4994	+	54.5593i	−1.19620	+	0.690624i	−0.236491	+	0.971634i	$0.575997\pi$
$80$		0			0
$81$	38.5940	+	71.2145i	0.476470	+	0.879191i
$82$		0			0
$83$	−113.503	+	65.5311i	−1.36751	+	0.789531i	−0.990609	−	0.136723i	$-0.956343\pi$
$83$	−113.503	+	65.5311i	−1.36751	+	0.789531i	−0.376899	+	0.926254i	$0.623010\pi$
$84$		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	0.796286	−	0.604920i	$-0.206795\pi$
$97$	−12.1961	−	21.1243i	−0.125733	−	0.217776i	−0.922019	+	0.387144i	$0.873462\pi$
$98$		0			0
$99$	−149.451	−	2.01501i	−1.50961	−	0.0203537i
$100$		0			0
$101$	98.1305	+	169.967i	0.971589	+	1.68284i	0.690760	+	0.723084i	$0.257276\pi$
$101$	98.1305	+	169.967i	0.971589	+	1.68284i	0.280829	+	0.959758i	$0.409391\pi$
$102$		0			0
$103$	−104.472	−	60.3172i	−1.01430	−	0.585604i	−0.101849	−	0.994800i	$-0.532476\pi$
$103$	−104.472	−	60.3172i	−1.01430	−	0.585604i	−0.912446	+	0.409196i	$0.865809\pi$
$104$		0			0
$105$	1.76658	−	6.41957i	0.0168246	−	0.0611387i
$106$		0			0
$107$			6.52440i			0.0609757i	0.999535	+	0.0304878i	$0.00970609\pi$
$107$			6.52440i			0.0609757i	−0.999535	+	0.0304878i	$0.990294\pi$
$108$		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	−0.999541	−	0.0303032i	$-0.990353\pi$
$113$	−53.5086	+	92.6795i	−0.473527	+	0.820173i	0.526014	+	0.850476i	$0.323686\pi$
$114$		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	$0.130766\pi$
$127$			101.437i			0.798713i	−0.916796	+	0.399357i	$0.869234\pi$
$128$		0			0
$129$	−189.933	+	49.5226i	−1.47235	+	0.383896i
$130$		0			0
$131$	162.820	+	94.0042i	1.24290	+	0.717589i	0.969684	−	0.244363i	$-0.0785790\pi$
$131$	162.820	+	94.0042i	1.24290	+	0.717589i	0.273217	+	0.961952i	$0.411912\pi$
$132$		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	0.957413	−	0.288723i	$-0.0932307\pi$
$137$	31.3271	+	54.2601i	0.228665	+	0.396059i	−0.728748	+	0.684782i	$0.759897\pi$
$138$		0			0
$139$	−40.5801	−	23.4289i	−0.291943	−	0.168553i	0.346875	−	0.937911i	$-0.387243\pi$
$139$	−40.5801	−	23.4289i	−0.291943	−	0.168553i	−0.638818	+	0.769358i	$0.720576\pi$
$140$		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	−0.626021	−	0.779806i	$-0.715317\pi$
$149$	53.9860	−	93.5064i	0.362322	−	0.627560i	0.988343	+	0.152247i	$0.0486508\pi$
$150$		0			0
$151$	2.75240	−	1.58910i	0.0182278	−	0.0105238i	−0.490858	−	0.871239i	$-0.663317\pi$
$151$	2.75240	−	1.58910i	0.0182278	−	0.0105238i	0.509086	+	0.860716i	$0.329983\pi$
$152$		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	−0.0914764	−	0.995807i	$-0.529159\pi$
$157$	128.215	−	222.075i	0.816656	−	1.41449i	0.908133	−	0.418683i	$-0.137508\pi$
$158$		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	$-0.788400\pi$
$163$		−	201.100i		−	1.23374i	0.787065	−	0.616870i	$-0.211600\pi$
$164$		0			0
$165$	9.39345	−	34.1347i	0.0569300	−	0.206877i
$166$		0			0
$167$	110.689	+	63.9062i	0.662807	+	0.382672i	0.793346	−	0.608771i	$-0.208337\pi$
$167$	110.689	+	63.9062i	0.662807	+	0.382672i	−0.130538	+	0.991443i	$0.541671\pi$
$168$		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	0.995220	+	0.0976562i	$0.0311346\pi$
$173$	100.718	+	174.448i	0.582183	+	1.00837i	−0.413037	+	0.910714i	$0.635532\pi$
$174$		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	$-0.994814\pi$
$179$		−	5.83187i		−	0.0325803i	0.999867	−	0.0162901i	$-0.00518554\pi$
$180$		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	−0.402555	−	0.915396i	$-0.631878\pi$
$191$	36.0843	−	20.8333i	0.188923	−	0.109075i	0.591478	+	0.806321i	$0.298545\pi$
$192$		0			0
$193$	−69.1927	+	119.845i	−0.358511	+	0.620960i	−0.987712	−	0.156283i	$-0.950049\pi$
$193$	−69.1927	+	119.845i	−0.358511	+	0.620960i	0.629201	+	0.777242i	$0.283382\pi$
$194$		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	$0.0701666\pi$
$199$			87.0243i			0.437308i	−0.975802	+	0.218654i	$0.929833\pi$
$200$		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	0.950875	−	0.309574i	$-0.100186\pi$
$211$	244.383	+	141.095i	1.15821	+	0.668695i	0.207339	+	0.978269i	$0.433520\pi$
$212$		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	−0.947691	−	0.319190i	$-0.896589\pi$
$223$	−255.359	+	147.432i	−1.14511	+	0.661129i	−0.197419	+	0.980319i	$0.563256\pi$
$224$		0			0
$225$	−2.97208	+	220.435i	−0.0132092	+	0.979712i
$226$		0			0
$227$	−124.390	+	71.8164i	−0.547972	+	0.316372i	−0.748304	−	0.663356i	$-0.769131\pi$
$227$	−124.390	+	71.8164i	−0.547972	+	0.316372i	0.200332	+	0.979728i	$0.435798\pi$
$228$		0			0
$229$	−141.426	+	244.958i	−0.617583	+	1.06968i	0.372343	+	0.928095i	$0.378555\pi$
$229$	−141.426	+	244.958i	−0.617583	+	1.06968i	−0.989925	+	0.141590i	$0.954779\pi$
$230$		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	−0.319966	−	0.947429i	$-0.603672\pi$
$239$	−310.807	−	179.444i	−1.30045	−	0.750813i	−0.980481	+	0.196616i	$0.937005\pi$
$240$		0			0
$241$	87.7048	+	151.909i	0.363920	+	0.630328i	0.988602	−	0.150551i	$-0.0481048\pi$
$241$	87.7048	+	151.909i	0.363920	+	0.630328i	−0.624682	+	0.780879i	$0.714771\pi$
$242$		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	$0.304266\pi$
$251$			410.044i			1.63364i	−0.576891	+	0.816821i	$0.695734\pi$
$252$		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	−0.983733	−	0.179638i	$-0.942507\pi$
$257$	−86.4280	+	149.698i	−0.336296	+	0.582481i	0.647437	+	0.762119i	$0.275841\pi$
$258$		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	−0.730589	−	0.682818i	$-0.760754\pi$
$263$	−132.696	+	76.6118i	−0.504546	+	0.291300i	0.226043	+	0.974117i	$0.427421\pi$
$264$		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	$0.0239311\pi$
$271$			40.7101i			0.150222i	−0.997175	+	0.0751108i	$0.976069\pi$
$272$		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	0.979346	+	0.202191i	$0.0648063\pi$
$277$	184.143	+	318.945i	0.664776	+	1.15143i	−0.314570	+	0.949234i	$0.601860\pi$
$278$		0			0
$279$	109.757	+	196.165i	0.393394	+	0.703101i
$280$		0			0
$281$	−238.310	−	412.765i	−0.848078	−	1.46891i	−0.882921	−	0.469521i	$-0.844427\pi$
$281$	−238.310	−	412.765i	−0.848078	−	1.46891i	0.0348433	−	0.999393i	$-0.488907\pi$
$282$		0			0
$283$	−150.052	−	86.6323i	−0.530217	−	0.306121i	0.210888	−	0.977510i	$-0.432365\pi$
$283$	−150.052	−	86.6323i	−0.530217	−	0.306121i	−0.741105	+	0.671389i	$0.765698\pi$
$284$		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	−0.870963	−	0.491349i	$-0.836504\pi$
$293$	−2.91833	+	5.05470i	−0.00996017	+	0.0172515i	0.861002	+	0.508601i	$0.169837\pi$
$294$		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	$0.206988\pi$
$307$			371.717i			1.21080i	−0.795920	+	0.605402i	$0.793012\pi$
$308$		0			0
$309$	254.173	+	257.623i	0.822567	+	0.833733i
$310$		0			0
$311$	193.964	+	111.985i	0.623679	+	0.360081i	0.778300	−	0.627892i	$-0.216082\pi$
$311$	193.964	+	111.985i	0.623679	+	0.360081i	−0.154621	+	0.987974i	$0.549416\pi$
$312$		0			0
$313$	79.0960	+	136.998i	0.252703	+	0.437694i	0.964269	−	0.264925i	$-0.0853472\pi$
$313$	79.0960	+	136.998i	0.252703	+	0.437694i	−0.711566	+	0.702619i	$0.752014\pi$
$314$		0			0
$315$	−10.2196	+	17.1623i	−0.0324432	+	0.0544835i
$316$		0			0
$317$	−206.428	−	357.543i	−0.651191	−	1.12790i	−0.982834	−	0.184491i	$-0.940936\pi$
$317$	−206.428	−	357.543i	−0.651191	−	1.12790i	0.331643	−	0.943405i	$-0.392397\pi$
$318$		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	−0.295843	−	0.955237i	$-0.595600\pi$
$331$	126.937	−	73.2871i	0.383495	−	0.221411i	0.679338	+	0.733826i	$0.262267\pi$
$332$		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	−0.927687	−	0.373360i	$-0.878206\pi$
$337$	−47.3499	+	82.0124i	−0.140504	+	0.243360i	0.787182	+	0.616720i	$0.211539\pi$
$338$		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	0.612609	−	0.790386i	$-0.290120\pi$
$347$	81.3438	+	46.9639i	0.234420	+	0.135343i	−0.378189	+	0.925728i	$0.623453\pi$
$348$		0			0
$349$	−115.579	−	200.188i	−0.331171	−	0.573605i	0.651571	−	0.758588i	$-0.274110\pi$
$349$	−115.579	−	200.188i	−0.331171	−	0.573605i	−0.982742	+	0.184983i	$0.940777\pi$
$350$		0			0
$351$	481.191	−	118.560i	1.37091	−	0.337777i
$352$		0			0
$353$	−48.9623	−	84.8052i	−0.138703	−	0.240241i	0.788303	−	0.615288i	$-0.210960\pi$
$353$	−48.9623	−	84.8052i	−0.138703	−	0.240241i	−0.927006	+	0.375046i	$0.877627\pi$
$354$		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	$0.110506\pi$
$359$			244.287i			0.680465i	−0.940341	+	0.340233i	$0.889494\pi$
$360$		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	0.0942999	−	0.995544i	$-0.469939\pi$
$367$	368.327	−	212.654i	1.00362	−	0.579438i	0.909316	+	0.416106i	$0.136605\pi$
$368$		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	−0.799611	−	0.600519i	$-0.794961\pi$
$373$	44.8567	−	77.6941i	0.120259	−	0.208295i	0.919870	+	0.392224i	$0.128294\pi$
$374$		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	$-0.820008\pi$
$379$		−	406.140i		−	1.07161i	0.844342	−	0.535805i	$-0.179992\pi$
$380$		0			0
$381$	80.7408	−	293.403i	0.211918	−	0.770087i
$382$		0			0
$383$	−280.901	−	162.178i	−0.733423	−	0.423442i	0.0862502	−	0.996274i	$-0.472512\pi$
$383$	−280.901	−	162.178i	−0.733423	−	0.423442i	−0.819673	+	0.572832i	$0.805845\pi$
$384$		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	0.826810	−	0.562481i	$-0.190153\pi$
$389$	−28.6761	−	49.6685i	−0.0737176	−	0.127683i	−0.900528	+	0.434798i	$0.856820\pi$
$390$		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	−0.994760	−	0.102242i	$-0.967398\pi$
$401$	−163.943	+	283.958i	−0.408836	+	0.708124i	0.585924	+	0.810366i	$0.300732\pi$
$402$		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	−0.907375	−	0.420321i	$-0.861917\pi$
$409$	−36.6786	+	63.5292i	−0.0896787	+	0.155328i	0.817697	+	0.575649i	$0.195251\pi$
$410$		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	−0.344943	−	0.938624i	$-0.612102\pi$
$419$	−557.390	−	321.809i	−1.33029	−	0.768041i	−0.985343	+	0.170582i	$0.945435\pi$
$420$		0			0
$421$	−280.151	−	485.236i	−0.665441	−	1.15258i	−0.979165	−	0.203064i	$-0.934910\pi$
$421$	−280.151	−	485.236i	−0.665441	−	1.15258i	0.313724	−	0.949514i	$-0.398423\pi$
$422$		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	$0.213809\pi$
$431$			536.437i			1.24463i	−0.782765	+	0.622317i	$0.786191\pi$
$432$		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	−0.596082	−	0.802924i	$-0.703277\pi$
$439$	−87.2604	+	50.3798i	−0.198771	+	0.114760i	0.397311	+	0.917684i	$0.369943\pi$
$440$		0			0
$441$	−308.241	+	172.464i	−0.698958	+	0.391076i
$442$		0			0
$443$	519.799	−	300.106i	1.17336	−	0.677440i	0.218891	−	0.975749i	$-0.429756\pi$
$443$	519.799	−	300.106i	1.17336	−	0.677440i	0.954469	+	0.298309i	$0.0964227\pi$
$444$		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	0.945208	−	0.326469i	$-0.105859\pi$
$457$	86.7721	+	150.294i	0.189873	+	0.328870i	−0.755334	+	0.655339i	$0.772526\pi$
$458$		0			0
$459$	181.282	+	188.766i	0.394949	+	0.411255i
$460$		0			0
$461$	361.655	+	626.406i	0.784502	+	1.35880i	0.929296	+	0.369336i	$0.120415\pi$
$461$	361.655	+	626.406i	0.784502	+	1.35880i	−0.144794	+	0.989462i	$0.546252\pi$
$462$		0			0
$463$	−643.880	−	371.744i	−1.39067	−	0.802903i	−0.397280	−	0.917698i	$-0.630046\pi$
$463$	−643.880	−	371.744i	−1.39067	−	0.802903i	−0.993389	+	0.114794i	$0.963379\pi$
$464$		0			0
$465$	−51.5217	+	13.4336i	−0.110799	+	0.0288895i
$466$		0			0
$467$		−	98.0700i		−	0.210000i	−0.994472	−	0.105000i	$-0.966516\pi$
$467$		−	98.0700i		−	0.210000i	0.994472	−	0.105000i	$-0.0334842\pi$
$468$		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	−0.774156	−	0.632995i	$-0.781825\pi$
$479$	−293.648	+	169.538i	−0.613043	+	0.353941i	0.161112	+	0.986936i	$0.448492\pi$
$480$		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	$-0.705638\pi$
$487$		−	777.718i		−	1.59696i	0.602023	−	0.798479i	$-0.294362\pi$
$488$		0			0
$489$	−160.070	+	581.676i	−0.327341	+	1.18952i
$490$		0			0
$491$	52.0054	+	30.0254i	0.105917	+	0.0611514i	0.552023	−	0.833829i	$-0.313856\pi$
$491$	52.0054	+	30.0254i	0.105917	+	0.0611514i	−0.446106	+	0.894980i	$0.647189\pi$
$492$		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	0.227996	−	0.973662i	$-0.426783\pi$
$499$	−250.110	−	144.401i	−0.501222	−	0.289381i	−0.729218	+	0.684281i	$0.760116\pi$
$500$		0			0
$501$	−269.297	−	272.953i	−0.537520	−	0.544816i
$502$		0			0
$503$			567.389i			1.12801i	0.825772	+	0.564005i	$0.190740\pi$
$503$			567.389i			1.12801i	−0.825772	+	0.564005i	$0.809260\pi$
$504$		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	−0.667603	−	0.744517i	$-0.732680\pi$
$509$	158.283	−	274.155i	0.310970	−	0.538615i	0.978573	+	0.205902i	$0.0660130\pi$
$510$		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	$-0.793931\pi$
$523$		−	630.846i		−	1.20621i	0.797663	−	0.603103i	$-0.206069\pi$
$524$		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	−0.969401	−	0.245484i	$-0.921053\pi$
$547$	−679.104	+	392.081i	−1.24151	+	0.716784i	−0.272105	+	0.962268i	$0.587720\pi$
$548$		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	0.368619	−	0.929581i	$-0.379831\pi$
$563$	−141.939	−	81.9485i	−0.252112	−	0.145557i	−0.620731	+	0.784024i	$0.713164\pi$
$564$		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	−0.989666	−	0.143392i	$-0.954199\pi$
$569$	−352.219	−	610.061i	−0.619014	−	1.07216i	0.370652	−	0.928772i	$-0.379134\pi$
$570$		0			0
$571$	−413.817	−	238.917i	−0.724723	−	0.418419i	0.0917653	−	0.995781i	$-0.470749\pi$
$571$	−413.817	−	238.917i	−0.724723	−	0.418419i	−0.816489	+	0.577361i	$0.804082\pi$
$572$		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	0.215522	−	0.976499i	$-0.430855\pi$
$587$	686.177	−	396.164i	1.16896	−	0.674897i	0.953434	+	0.301602i	$0.0975215\pi$
$588$		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	0.987053	−	0.160396i	$-0.0512770\pi$
$599$	803.662	+	463.994i	1.34167	+	0.774615i	0.354620	+	0.935011i	$0.384610\pi$
$600$		0			0
$601$	−66.4316	−	115.063i	−0.110535	−	0.191452i	0.805451	−	0.592662i	$-0.201923\pi$
$601$	−66.4316	−	115.063i	−0.110535	−	0.191452i	−0.915986	+	0.401210i	$0.868590\pi$
$602$		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	0.840294	−	0.542131i	$-0.182382\pi$
$607$	480.102	+	277.187i	0.790942	+	0.456651i	−0.0493520	+	0.998781i	$0.515716\pi$
$608$		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	0.494900	+	0.868950i	$0.335205\pi$
$617$	−311.636	+	539.770i	−0.505083	+	0.874829i	−0.999983	+	0.00587917i	$0.998129\pi$
$618$		0			0
$619$	−613.432	+	354.165i	−0.991005	+	0.572157i	−0.905575	−	0.424187i	$-0.860560\pi$
$619$	−613.432	+	354.165i	−0.991005	+	0.572157i	−0.0854305	+	0.996344i	$0.527227\pi$
$620$		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	$-0.639423\pi$
$631$		−	1142.86i		−	1.81119i	0.424139	−	0.905597i	$-0.360577\pi$
$632$		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	0.737489	−	0.675359i	$-0.236011\pi$
$641$	−138.542	−	239.961i	−0.216134	−	0.374354i	−0.953623	+	0.301005i	$0.902678\pi$
$642$		0			0
$643$	737.236	+	425.644i	1.14656	+	0.661965i	0.948046	−	0.318133i	$-0.103056\pi$
$643$	737.236	+	425.644i	1.14656	+	0.661965i	0.198511	+	0.980099i	$0.436389\pi$
$644$		0			0
$645$	−37.0076	+	134.481i	−0.0573761	+	0.208498i
$646$		0			0
$647$			706.622i			1.09215i	0.837736	+	0.546076i	$0.183879\pi$
$647$			706.622i			1.09215i	−0.837736	+	0.546076i	$0.816121\pi$
$648$		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	0.395383	+	0.918516i	$0.370612\pi$
$653$	−390.342	+	676.092i	−0.597767	+	1.03536i	−0.993150	+	0.116846i	$0.962722\pi$
$654$		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	−0.824086	−	0.566465i	$-0.808311\pi$
$659$	−491.322	+	283.665i	−0.745557	+	0.430447i	0.0785296	+	0.996912i	$0.474977\pi$
$660$		0			0
$661$	46.9164	−	81.2615i	0.0709778	−	0.122937i	−0.828352	−	0.560208i	$-0.810721\pi$
$661$	46.9164	−	81.2615i	0.0709778	−	0.122937i	0.899330	+	0.437270i	$0.144055\pi$
$662$		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	0.931113	−	0.364730i	$-0.118839\pi$
$673$	100.742	+	174.490i	0.149691	+	0.259272i	−0.781422	+	0.624003i	$0.785505\pi$
$674$		0			0
$675$	184.057	−	635.238i	0.272677	−	0.941094i
$676$		0			0
$677$	−336.988	−	583.680i	−0.497766	−	0.862157i	0.502230	−	0.864734i	$-0.332513\pi$
$677$	−336.988	−	583.680i	−0.497766	−	0.862157i	−0.999997	+	0.00257723i	$0.999180\pi$
$678$		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	$0.0363450\pi$
$683$			155.633i			0.227867i	−0.993488	+	0.113933i	$0.963655\pi$
$684$		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	0.0940588	−	0.995567i	$-0.470016\pi$
$691$	693.263	−	400.255i	1.00327	−	0.579241i	0.909215	+	0.416326i	$0.136682\pi$
$692$		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	0.999977	+	0.00674353i	$0.00214655\pi$
$709$	358.633	+	621.170i	0.505829	+	0.876121i	−0.494149	+	0.869377i	$0.664520\pi$
$710$		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	$-0.884071\pi$
$719$		−	512.219i		−	0.712404i	0.934409	−	0.356202i	$-0.115929\pi$
$720$		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	−0.840044	−	0.542518i	$-0.817471\pi$
$727$	−574.499	+	331.687i	−0.790232	+	0.456241i	0.0498122	+	0.998759i	$0.484138\pi$
$728$		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	−0.948653	−	0.316320i	$-0.897553\pi$
$733$	−146.883	+	254.408i	−0.200386	+	0.347078i	0.748267	+	0.663398i	$0.230886\pi$
$734$		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	$0.358959\pi$
$739$			1335.27i			1.80686i	−0.428736	+	0.903430i	$0.641041\pi$
$740$		0			0
$741$	317.385	+	321.694i	0.428320	+	0.434134i
$742$		0			0
$743$	488.188	+	281.855i	0.657050	+	0.379348i	0.791152	−	0.611620i	$-0.209482\pi$
$743$	488.188	+	281.855i	0.657050	+	0.379348i	−0.134102	+	0.990968i	$0.542815\pi$
$744$		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	0.839079	−	0.544009i	$-0.183094\pi$
$751$	591.407	+	341.449i	0.787493	+	0.454659i	−0.0515861	+	0.998669i	$0.516428\pi$
$752$		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	0.451585	+	0.892228i	$0.350859\pi$
$761$	−416.191	+	720.863i	−0.546900	+	0.947258i	−0.998485	+	0.0550300i	$0.982475\pi$
$762$		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	−0.998771	−	0.0495620i	$-0.984217\pi$
$769$	−351.020	+	607.985i	−0.456464	+	0.790618i	0.542308	+	0.840180i	$0.317551\pi$
$770$		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	0.103127	−	0.994668i	$-0.467115\pi$
$787$	−556.186	−	321.114i	−0.706717	−	0.408023i	−0.809844	+	0.586645i	$0.800448\pi$
$788$		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	−0.838256	−	0.545276i	$-0.816425\pi$
$797$	42.3167	−	73.2947i	0.0530950	−	0.0919632i	0.891351	+	0.453313i	$0.149758\pi$
$798$		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	$-0.847981\pi$
$811$		−	745.523i		−	0.919264i	0.888110	−	0.459632i	$-0.152019\pi$
$812$		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	0.999951	+	0.00994363i	$0.00316521\pi$
$821$	417.550	+	723.217i	0.508587	+	0.880898i	−0.491364	+	0.870954i	$0.663501\pi$
$822$		0			0
$823$	−369.777	−	213.491i	−0.449304	−	0.259406i	0.258232	−	0.966083i	$-0.416860\pi$
$823$	−369.777	−	213.491i	−0.449304	−	0.259406i	−0.707536	+	0.706677i	$0.750193\pi$
$824$		0			0
$825$	857.102	+	868.736i	1.03891	+	1.05301i
$826$		0			0
$827$			235.457i			0.284713i	0.989815	+	0.142356i	$0.0454679\pi$
$827$			235.457i			0.284713i	−0.989815	+	0.142356i	$0.954532\pi$
$828$		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	−0.571401	+	0.820671i	$0.693600\pi$
$839$	−1315.40	+	759.449i	−1.56782	+	0.905183i	−0.996422	+	0.0845127i	$0.973067\pi$
$840$		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	0.708083	−	0.706130i	$-0.249560\pi$
$853$	−219.635	−	380.418i	−0.257485	−	0.445977i	−0.965568	+	0.260153i	$0.916227\pi$
$854$		0			0
$855$	25.6282	+	45.8046i	0.0299745	+	0.0535726i
$856$		0			0
$857$	42.9674	+	74.4218i	0.0501370	+	0.0868399i	0.890005	−	0.455951i	$-0.150701\pi$
$857$	42.9674	+	74.4218i	0.0501370	+	0.0868399i	−0.839868	+	0.542791i	$0.817368\pi$
$858$		0			0
$859$	750.391	+	433.239i	0.873564	+	0.504352i	0.868531	−	0.495635i	$-0.165065\pi$
$859$	750.391	+	433.239i	0.873564	+	0.504352i	0.00503295	+	0.999987i	$0.498398\pi$
$860$		0			0
$861$	127.753	−	464.241i	0.148378	−	0.539188i
$862$		0			0
$863$		−	651.682i		−	0.755136i	−0.925982	−	0.377568i	$-0.876760\pi$
$863$		−	651.682i		−	0.755136i	0.925982	−	0.377568i	$-0.123240\pi$
$864$		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	−0.994817	−	0.101678i	$-0.967579\pi$
$877$	−359.003	+	621.811i	−0.409353	+	0.709020i	0.585464	+	0.810698i	$0.300912\pi$
$878$		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	$0.0927109\pi$
$883$			507.123i			0.574318i	−0.957883	+	0.287159i	$0.907289\pi$
$884$		0			0
$885$	−157.745	+	41.1301i	−0.178243	+	0.0464746i
$886$		0			0
$887$	222.320	+	128.356i	0.250642	+	0.144708i	0.620058	−	0.784556i	$-0.287109\pi$
$887$	222.320	+	128.356i	0.250642	+	0.144708i	−0.369416	+	0.929264i	$0.620442\pi$
$888$		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	0.479054	−	0.877785i	$-0.340980\pi$
$907$	1341.24	−	774.365i	1.47877	−	0.853766i	0.999711	+	0.0240198i	$0.00764647\pi$
$908$		0			0
$909$	−23.8131	+	1766.19i	−0.0261971	+	1.94300i
$910$		0			0
$911$	465.815	−	268.938i	0.511322	−	0.295212i	−0.222055	−	0.975034i	$-0.571276\pi$
$911$	465.815	−	268.938i	0.511322	−	0.295212i	0.733377	+	0.679822i	$0.237943\pi$
$912$		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	$-0.795845\pi$
$919$		−	1099.66i		−	1.19659i	0.801277	−	0.598294i	$-0.204155\pi$
$920$		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	0.808668	−	0.588265i	$-0.200189\pi$
$929$	−97.6555	−	169.144i	−0.105119	−	0.182071i	−0.913787	+	0.406194i	$0.866856\pi$
$930$		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	0.461652	+	0.887061i	$0.347257\pi$
$941$	−505.685	+	875.873i	−0.537391	+	0.930789i	−0.999043	+	0.0437282i	$0.986076\pi$
$942$		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	−0.149519	−	0.988759i	$-0.547772\pi$
$947$	598.516	−	345.553i	0.632013	−	0.364893i	0.781531	+	0.623866i	$0.214439\pi$
$948$		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	0.912444	−	0.409201i	$-0.134192\pi$
$967$	980.817	+	566.275i	1.01429	+	0.585600i	0.101844	+	0.994800i	$0.467526\pi$
$968$		0			0
$969$	−63.3203	+	230.099i	−0.0653461	+	0.237460i
$970$		0			0
$971$			277.255i			0.285536i	0.989756	+	0.142768i	$0.0456002\pi$
$971$			277.255i			0.285536i	−0.989756	+	0.142768i	$0.954400\pi$
$972$		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	−0.938583	−	0.345053i	$-0.887861\pi$
$977$	−166.546	+	288.467i	−0.170467	+	0.295257i	0.768116	+	0.640310i	$0.221194\pi$
$978$		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	0.327390	−	0.944889i	$-0.393831\pi$
$983$	1287.12	−	743.121i	1.30938	−	0.755973i	0.981993	+	0.188916i	$0.0604975\pi$
$984$		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	$-0.997241\pi$
$991$		−	17.1782i		−	0.0173343i	0.999962	−	0.00866713i	$-0.00275887\pi$
$992$		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	−0.952552	−	0.304377i	$-0.901552\pi$
$997$	−737.655	−	1277.66i	−0.739874	−	1.28150i	0.212677	−	0.977123i	$-0.431782\pi$
$998$		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.31.1	yes	8
3.2	odd	2		432.3.o.a.415.2		8
4.3	odd	2		144.3.o.a.31.4	✓	8
8.3	odd	2		576.3.o.f.319.1		8
8.5	even	2		576.3.o.d.319.4		8
9.2	odd	6		432.3.o.b.127.2		8
9.4	even	3		1296.3.g.j.1135.3		8
9.5	odd	6		1296.3.g.k.1135.5		8
9.7	even	3		144.3.o.a.79.4	yes	8
12.11	even	2		432.3.o.b.415.2		8
24.5	odd	2		1728.3.o.e.1279.3		8
24.11	even	2		1728.3.o.f.1279.3		8
36.7	odd	6	inner	144.3.o.c.79.1	yes	8
36.11	even	6		432.3.o.a.127.2		8
36.23	even	6		1296.3.g.k.1135.6		8
36.31	odd	6		1296.3.g.j.1135.4		8
72.11	even	6		1728.3.o.e.127.3		8
72.29	odd	6		1728.3.o.f.127.3		8
72.43	odd	6		576.3.o.d.511.4		8
72.61	even	6		576.3.o.f.511.1		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
144.3.o.a.31.4	✓	8	4.3	odd	2
144.3.o.a.79.4	yes	8	9.7	even	3
144.3.o.c.31.1	yes	8	1.1	even	1	trivial
144.3.o.c.79.1	yes	8	36.7	odd	6	inner
432.3.o.a.127.2		8	36.11	even	6
432.3.o.a.415.2		8	3.2	odd	2
432.3.o.b.127.2		8	9.2	odd	6
432.3.o.b.415.2		8	12.11	even	2
576.3.o.d.319.4		8	8.5	even	2
576.3.o.d.511.4		8	72.43	odd	6
576.3.o.f.319.1		8	8.3	odd	2
576.3.o.f.511.1		8	72.61	even	6
1296.3.g.j.1135.3		8	9.4	even	3
1296.3.g.j.1135.4		8	36.31	odd	6
1296.3.g.k.1135.5		8	9.5	odd	6
1296.3.g.k.1135.6		8	36.23	even	6
1728.3.o.e.127.3		8	72.11	even	6
1728.3.o.e.1279.3		8	24.5	odd	2
1728.3.o.f.127.3		8	72.29	odd	6
1728.3.o.f.1279.3		8	24.11	even	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

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

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