LMFDB - Embedded newform 900.3.p.c.401.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [900,3,Mod(101,900)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(900, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 1, 0]))

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

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

chi := DirichletCharacter("900.101");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 900 = 2^{2} \cdot 3^{2} \cdot 5^{2} $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	900.p (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:	$24.5232237924$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$6$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 2 x^{11} - 11 x^{10} + 60 x^{9} - 120 x^{8} - 342 x^{7} + 2709 x^{6} - 3078 x^{5} + \cdots + 531441 $ x^12 - 2x^11 - 11x^10 + 60x^9 - 120x^8 - 342x^7 + 2709x^6 - 3078x^5 - 9720x^4 + 43740x^3 - 72171x^2 - 118098*x + 531441
Coefficient ring:	$\Z[a_1, \ldots, a_{17}]$
Coefficient ring index:	$ 3^{6} $
Twist minimal:	no (minimal twist has level 180)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			401.2
Root			$2.65605 + 1.39478i$ of defining polynomial
Character	$\chi$	$=$	900.401
Dual form			900.3.p.c.101.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.65605 - 1.39478i) q^{3} +(-1.41583 - 2.45229i) q^{7} +(5.10917 + 7.40921i) q^{9} +O(q^{10})$	\(q+(-2.65605 - 1.39478i) q^{3} +(-1.41583 - 2.45229i) q^{7} +(5.10917 + 7.40921i) q^{9} +(-0.949152 + 0.547993i) q^{11} +(-2.09634 + 3.63097i) q^{13} -7.85770i q^{17} +13.3580 q^{19} +(0.340105 + 8.48818i) q^{21} +(21.4218 + 12.3679i) q^{23} +(-3.23598 - 26.8054i) q^{27} +(-2.43628 + 1.40659i) q^{29} +(12.0630 - 20.8937i) q^{31} +(3.28532 - 0.131636i) q^{33} -49.9138 q^{37} +(10.6324 - 6.72010i) q^{39} +(-18.9104 - 10.9179i) q^{41} +(24.5149 + 42.4611i) q^{43} +(58.5815 - 33.8220i) q^{47} +(20.4908 - 35.4912i) q^{49} +(-10.9598 + 20.8704i) q^{51} +49.8418i q^{53} +(-35.4795 - 18.6315i) q^{57} +(-86.8838 - 50.1624i) q^{59} +(-41.5597 - 71.9835i) q^{61} +(10.9358 - 23.0194i) q^{63} +(28.7754 - 49.8405i) q^{67} +(-39.6468 - 62.7284i) q^{69} -14.2317i q^{71} -71.5532 q^{73} +(2.68768 + 1.55173i) q^{77} +(-54.4107 - 94.2421i) q^{79} +(-28.7927 + 75.7098i) q^{81} +(69.7793 - 40.2871i) q^{83} +(8.43276 - 0.337884i) q^{87} -65.6139i q^{89} +11.8723 q^{91} +(-61.1820 + 38.6694i) q^{93} +(-77.4238 - 134.102i) q^{97} +(-8.90957 - 4.23267i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 2 q^{3} + 6 q^{7} + 26 q^{9}+O(q^{10}) $ 12 * q - 2 * q^3 + 6 * q^7 + 26 * q^9	$ 12 q - 2 q^{3} + 6 q^{7} + 26 q^{9} + 48 q^{11} + 30 q^{13} + 72 q^{19} - 128 q^{21} + 78 q^{23} + 106 q^{27} + 150 q^{29} - 12 q^{31} - 96 q^{33} + 12 q^{37} + 40 q^{39} + 90 q^{41} - 114 q^{43} - 12 q^{47} + 48 q^{49} - 144 q^{51} + 158 q^{57} + 48 q^{59} - 78 q^{61} + 212 q^{63} + 168 q^{67} - 150 q^{69} + 24 q^{73} + 258 q^{77} + 120 q^{79} + 434 q^{81} - 114 q^{83} + 330 q^{87} + 120 q^{91} - 82 q^{93} - 96 q^{97} - 120 q^{99}+O(q^{100}) $ 12 * q - 2 * q^3 + 6 * q^7 + 26 * q^9 + 48 * q^11 + 30 * q^13 + 72 * q^19 - 128 * q^21 + 78 * q^23 + 106 * q^27 + 150 * q^29 - 12 * q^31 - 96 * q^33 + 12 * q^37 + 40 * q^39 + 90 * q^41 - 114 * q^43 - 12 * q^47 + 48 * q^49 - 144 * q^51 + 158 * q^57 + 48 * q^59 - 78 * q^61 + 212 * q^63 + 168 * q^67 - 150 * q^69 + 24 * q^73 + 258 * q^77 + 120 * q^79 + 434 * q^81 - 114 * q^83 + 330 * q^87 + 120 * q^91 - 82 * q^93 - 96 * q^97 - 120 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/900\mathbb{Z}\right)^\times$.

$n$	$101$	$451$	$577$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$1$	$1$

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
$3$	−2.65605	−	1.39478i	−0.885349	−	0.464927i
$3$	−2.65605	−	1.39478i	−0.885349	−	0.464927i
$4$		0			0
$5$		0			0
$5$		0			0
$6$		0			0
$7$	−1.41583	−	2.45229i	−0.202262	−	0.350327i	0.746995	−	0.664829i	$-0.231496\pi$
$7$	−1.41583	−	2.45229i	−0.202262	−	0.350327i	−0.949257	+	0.314502i	$0.898162\pi$
$8$		0			0
$9$	5.10917	+	7.40921i	0.567686	+	0.823245i
$10$		0			0
$11$	−0.949152	+	0.547993i	−0.0862865	+	0.0498175i	−0.542522	−	0.840041i	$-0.682531\pi$
$11$	−0.949152	+	0.547993i	−0.0862865	+	0.0498175i	0.456236	+	0.889859i	$0.349197\pi$
$12$		0			0
$13$	−2.09634	+	3.63097i	−0.161257	+	0.279306i	−0.935320	−	0.353803i	$-0.884888\pi$
$13$	−2.09634	+	3.63097i	−0.161257	+	0.279306i	0.774063	+	0.633109i	$0.218222\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$		−	7.85770i		−	0.462218i	−0.972928	−	0.231109i	$-0.925765\pi$
$17$		−	7.85770i		−	0.462218i	0.972928	−	0.231109i	$-0.0742353\pi$
$18$		0			0
$19$	13.3580			0.703053			0.351527	−	0.936178i	$-0.385663\pi$
$19$	13.3580			0.703053			0.351527	+	0.936178i	$0.385663\pi$
$20$		0			0
$21$	0.340105	+	8.48818i	0.0161955	+	0.404199i
$22$		0			0
$23$	21.4218	+	12.3679i	0.931383	+	0.537734i	0.887249	−	0.461292i	$-0.152614\pi$
$23$	21.4218	+	12.3679i	0.931383	+	0.537734i	0.0441340	+	0.999026i	$0.485947\pi$
$24$		0			0
$25$		0			0
$26$		0			0
$27$	−3.23598	−	26.8054i	−0.119851	−	0.992792i
$28$		0			0
$29$	−2.43628	+	1.40659i	−0.0840097	+	0.0485030i	−0.541416	−	0.840755i	$-0.682112\pi$
$29$	−2.43628	+	1.40659i	−0.0840097	+	0.0485030i	0.457407	+	0.889258i	$0.348778\pi$
$30$		0			0
$31$	12.0630	−	20.8937i	0.389128	−	0.673990i	−0.603204	−	0.797587i	$-0.706110\pi$
$31$	12.0630	−	20.8937i	0.389128	−	0.673990i	0.992333	+	0.123597i	$0.0394429\pi$
$32$		0			0
$33$	3.28532	−	0.131636i	0.0995552	−	0.00398898i
$34$		0			0
$35$		0			0
$36$		0			0
$37$	−49.9138			−1.34902			−0.674511	−	0.738264i	$-0.735646\pi$
$37$	−49.9138			−1.34902			−0.674511	+	0.738264i	$0.735646\pi$
$38$		0			0
$39$	10.6324	−	6.72010i	0.272626	−	0.172310i
$40$		0			0
$41$	−18.9104	−	10.9179i	−0.461229	−	0.266291i	0.251332	−	0.967901i	$-0.419131\pi$
$41$	−18.9104	−	10.9179i	−0.461229	−	0.266291i	−0.712561	+	0.701610i	$0.752465\pi$
$42$		0			0
$43$	24.5149	+	42.4611i	0.570114	+	0.987467i	0.996554	+	0.0829506i	$0.0264344\pi$
$43$	24.5149	+	42.4611i	0.570114	+	0.987467i	−0.426439	+	0.904516i	$0.640232\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	58.5815	−	33.8220i	1.24641	−	0.719618i	0.276022	−	0.961151i	$-0.410984\pi$
$47$	58.5815	−	33.8220i	1.24641	−	0.719618i	0.970393	+	0.241533i	$0.0776503\pi$
$48$		0			0
$49$	20.4908	−	35.4912i	0.418180	−	0.724310i
$50$		0			0
$51$	−10.9598	+	20.8704i	−0.214897	+	0.409224i
$52$		0			0
$53$			49.8418i			0.940412i	0.882557	+	0.470206i	$0.155820\pi$
$53$			49.8418i			0.940412i	−0.882557	+	0.470206i	$0.844180\pi$
$54$		0			0
$55$		0			0
$56$		0			0
$57$	−35.4795	−	18.6315i	−0.622448	−	0.326869i
$58$		0			0
$59$	−86.8838	−	50.1624i	−1.47261	−	0.850210i	−0.473081	−	0.881019i	$-0.656858\pi$
$59$	−86.8838	−	50.1624i	−1.47261	−	0.850210i	−0.999525	+	0.0308088i	$0.990192\pi$
$60$		0			0
$61$	−41.5597	−	71.9835i	−0.681307	−	1.18006i	−0.974582	−	0.224030i	$-0.928079\pi$
$61$	−41.5597	−	71.9835i	−0.681307	−	1.18006i	0.293276	−	0.956028i	$-0.405255\pi$
$62$		0			0
$63$	10.9358	−	23.0194i	0.173584	−	0.365387i
$64$		0			0
$65$		0			0
$66$		0			0
$67$	28.7754	−	49.8405i	0.429484	−	0.743888i	−0.567343	−	0.823481i	$-0.692029\pi$
$67$	28.7754	−	49.8405i	0.429484	−	0.743888i	0.996827	+	0.0795931i	$0.0253621\pi$
$68$		0			0
$69$	−39.6468	−	62.7284i	−0.574592	−	0.909107i
$70$		0			0
$71$		−	14.2317i		−	0.200446i	−0.994965	−	0.100223i	$-0.968044\pi$
$71$		−	14.2317i		−	0.200446i	0.994965	−	0.100223i	$-0.0319556\pi$
$72$		0			0
$73$	−71.5532			−0.980180			−0.490090	−	0.871672i	$-0.663036\pi$
$73$	−71.5532			−0.980180			−0.490090	+	0.871672i	$0.663036\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	2.68768	+	1.55173i	0.0349049	+	0.0201524i
$78$		0			0
$79$	−54.4107	−	94.2421i	−0.688743	−	1.19294i	−0.972245	−	0.233966i	$-0.924830\pi$
$79$	−54.4107	−	94.2421i	−0.688743	−	1.19294i	0.283502	−	0.958972i	$-0.408504\pi$
$80$		0			0
$81$	−28.7927	+	75.7098i	−0.355466	+	0.934689i
$82$		0			0
$83$	69.7793	−	40.2871i	0.840715	−	0.485387i	−0.0167923	−	0.999859i	$-0.505345\pi$
$83$	69.7793	−	40.2871i	0.840715	−	0.485387i	0.857507	+	0.514472i	$0.172012\pi$
$84$		0			0
$85$		0			0
$86$		0			0
$87$	8.43276	−	0.337884i	0.0969283	−	0.00388373i
$88$		0			0
$89$		−	65.6139i		−	0.737235i	−0.929581	−	0.368617i	$-0.879831\pi$
$89$		−	65.6139i		−	0.737235i	0.929581	−	0.368617i	$-0.120169\pi$
$90$		0			0
$91$	11.8723			0.130465
$92$		0			0
$93$	−61.1820	+	38.6694i	−0.657871	+	0.415800i
$94$		0			0
$95$		0			0
$96$		0			0
$97$	−77.4238	−	134.102i	−0.798184	−	1.38249i	−0.920798	−	0.390040i	$-0.872461\pi$
$97$	−77.4238	−	134.102i	−0.798184	−	1.38249i	0.122614	−	0.992454i	$-0.460872\pi$
$98$		0			0
$99$	−8.90957	−	4.23267i	−0.0899957	−	0.0427543i
$100$		0			0
$101$	124.917	−	72.1209i	1.23680	−	0.714068i	0.268363	−	0.963318i	$-0.413517\pi$
$101$	124.917	−	72.1209i	1.23680	−	0.714068i	0.968439	+	0.249250i	$0.0801841\pi$
$102$		0			0
$103$	10.1445	−	17.5708i	0.0984901	−	0.170590i	−0.812570	−	0.582864i	$-0.801932\pi$
$103$	10.1445	−	17.5708i	0.0984901	−	0.170590i	0.911060	+	0.412274i	$0.135265\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$		−	156.290i		−	1.46065i	−0.683100	−	0.730325i	$-0.739369\pi$
$107$		−	156.290i		−	1.46065i	0.683100	−	0.730325i	$-0.260631\pi$
$108$		0			0
$109$	55.5439			0.509577			0.254788	−	0.966997i	$-0.417994\pi$
$109$	55.5439			0.509577			0.254788	+	0.966997i	$0.417994\pi$
$110$		0			0
$111$	132.574	+	69.6189i	1.19436	+	0.627197i
$112$		0			0
$113$	−96.5164	−	55.7238i	−0.854127	−	0.493131i	0.00791409	−	0.999969i	$-0.497481\pi$
$113$	−96.5164	−	55.7238i	−0.854127	−	0.493131i	−0.862041	+	0.506838i	$0.830814\pi$
$114$		0			0
$115$		0			0
$116$		0			0
$117$	−37.6132	+	3.01902i	−0.321481	+	0.0258036i
$118$		0			0
$119$	−19.2694	+	11.1252i	−0.161928	+	0.0934889i
$120$		0			0
$121$	−59.8994	+	103.749i	−0.495036	+	0.857428i
$122$		0			0
$123$	34.9988	+	55.3743i	0.284543	+	0.450198i
$124$		0			0
$125$		0			0
$126$		0			0
$127$	−144.448			−1.13739			−0.568694	−	0.822549i	$-0.692551\pi$
$127$	−144.448			−1.13739			−0.568694	+	0.822549i	$0.692551\pi$
$128$		0			0
$129$	−5.88886	−	146.972i	−0.0456501	−	1.13931i
$130$		0			0
$131$	166.658	+	96.2201i	1.27220	+	0.734504i	0.975401	−	0.220436i	$-0.0707480\pi$
$131$	166.658	+	96.2201i	1.27220	+	0.734504i	0.296797	+	0.954940i	$0.404081\pi$
$132$		0			0
$133$	−18.9127	−	32.7578i	−0.142201	−	0.246299i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	28.4931	−	16.4505i	0.207979	−	0.120077i	−0.392393	−	0.919798i	$-0.628353\pi$
$137$	28.4931	−	16.4505i	0.207979	−	0.120077i	0.600372	+	0.799721i	$0.295019\pi$
$138$		0			0
$139$	−80.1236	+	138.778i	−0.576429	+	0.998404i	0.419456	+	0.907776i	$0.362221\pi$
$139$	−80.1236	+	138.778i	−0.576429	+	0.998404i	−0.995885	+	0.0906285i	$0.971112\pi$
$140$		0			0
$141$	−202.770	+	8.12458i	−1.43808	+	0.0576211i
$142$		0			0
$143$		−	4.59513i		−	0.0321338i
$144$		0			0
$145$		0			0
$146$		0			0
$147$	−103.927	+	65.6860i	−0.706987	+	0.446844i
$148$		0			0
$149$	39.1186	+	22.5851i	0.262541	+	0.151578i	0.625493	−	0.780230i	$-0.284898\pi$
$149$	39.1186	+	22.5851i	0.262541	+	0.151578i	−0.362952	+	0.931808i	$0.618231\pi$
$150$		0			0
$151$	−134.134	−	232.328i	−0.888307	−	1.53859i	−0.841875	−	0.539672i	$-0.818548\pi$
$151$	−134.134	−	232.328i	−0.888307	−	1.53859i	−0.0464318	−	0.998921i	$-0.514785\pi$
$152$		0			0
$153$	58.2193	−	40.1463i	0.380519	−	0.262394i
$154$		0			0
$155$		0			0
$156$		0			0
$157$	104.156	−	180.403i	0.663412	−	1.14906i	−0.316302	−	0.948659i	$-0.602441\pi$
$157$	104.156	−	180.403i	0.663412	−	1.14906i	0.979713	−	0.200404i	$-0.0642255\pi$
$158$		0			0
$159$	69.5184	−	132.382i	0.437223	−	0.832593i
$160$		0			0
$161$		−	70.0433i		−	0.435052i
$162$		0			0
$163$	24.6396			0.151163			0.0755815	−	0.997140i	$-0.475919\pi$
$163$	24.6396			0.151163			0.0755815	+	0.997140i	$0.475919\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	77.3116	+	44.6359i	0.462944	+	0.267281i	0.713281	−	0.700878i	$-0.247208\pi$
$167$	77.3116	+	44.6359i	0.462944	+	0.267281i	−0.250337	+	0.968159i	$0.580542\pi$
$168$		0			0
$169$	75.7107	+	131.135i	0.447992	+	0.775945i
$170$		0			0
$171$	68.2484	+	98.9723i	0.399113	+	0.578785i
$172$		0			0
$173$	−52.9937	+	30.5959i	−0.306322	+	0.176855i	−0.645279	−	0.763947i	$-0.723259\pi$
$173$	−52.9937	+	30.5959i	−0.306322	+	0.176855i	0.338958	+	0.940802i	$0.389926\pi$
$174$		0			0
$175$		0			0
$176$		0			0
$177$	160.802	+	254.418i	0.908485	+	1.43739i
$178$		0			0
$179$			131.909i			0.736924i	0.929643	+	0.368462i	$0.120115\pi$
$179$			131.909i			0.736924i	−0.929643	+	0.368462i	$0.879885\pi$
$180$		0			0
$181$	−311.741			−1.72233			−0.861163	−	0.508328i	$-0.830264\pi$
$181$	−311.741			−1.72233			−0.861163	+	0.508328i	$0.830264\pi$
$182$		0			0
$183$	9.98329	+	249.158i	0.0545535	+	1.36152i
$184$		0			0
$185$		0			0
$186$		0			0
$187$	4.30596	+	7.45815i	0.0230265	+	0.0398832i
$188$		0			0
$189$	−61.1530	+	45.8875i	−0.323561	+	0.242791i
$190$		0			0
$191$	303.129	−	175.012i	1.58706	−	0.916291i	0.593274	−	0.805000i	$-0.297835\pi$
$191$	303.129	−	175.012i	1.58706	−	0.916291i	0.993788	−	0.111290i	$-0.0354983\pi$
$192$		0			0
$193$	99.0214	−	171.510i	0.513064	−	0.888653i	−0.486821	−	0.873502i	$-0.661844\pi$
$193$	99.0214	−	171.510i	0.513064	−	0.888653i	0.999885	−	0.0151517i	$-0.00482311\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$			32.5493i			0.165225i	0.996582	+	0.0826124i	$0.0263263\pi$
$197$			32.5493i			0.165225i	−0.996582	+	0.0826124i	$0.973674\pi$
$198$		0			0
$199$	128.299			0.644717			0.322358	−	0.946618i	$-0.395524\pi$
$199$	128.299			0.644717			0.322358	+	0.946618i	$0.395524\pi$
$200$		0			0
$201$	−145.946	+	92.2433i	−0.726097	+	0.458922i
$202$		0			0
$203$	6.89873	+	3.98298i	0.0339839	+	0.0196206i
$204$		0			0
$205$		0			0
$206$		0			0
$207$	17.8115	+	221.908i	0.0860457	+	1.07202i
$208$		0			0
$209$	−12.6788	+	7.32010i	−0.0606640	+	0.0350244i
$210$		0			0
$211$	18.0757	−	31.3080i	0.0856668	−	0.148379i	−0.820008	−	0.572352i	$-0.806031\pi$
$211$	18.0757	−	31.3080i	0.0856668	−	0.148379i	0.905675	+	0.423972i	$0.139365\pi$
$212$		0			0
$213$	−19.8500	+	37.8000i	−0.0931927	+	0.177465i
$214$		0			0
$215$		0			0
$216$		0			0
$217$	−68.3166			−0.314823
$218$		0			0
$219$	190.049	+	99.8010i	0.867802	+	0.455712i
$220$		0			0
$221$	28.5311	+	16.4724i	0.129100	+	0.0745359i
$222$		0			0
$223$	87.4685	+	151.500i	0.392236	+	0.679372i	0.992744	−	0.120246i	$-0.0383685\pi$
$223$	87.4685	+	151.500i	0.392236	+	0.679372i	−0.600508	+	0.799618i	$0.705035\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	118.004	−	68.1296i	0.519841	−	0.300130i	−0.217028	−	0.976165i	$-0.569636\pi$
$227$	118.004	−	68.1296i	0.519841	−	0.300130i	0.736870	+	0.676035i	$0.236303\pi$
$228$		0			0
$229$	−97.1240	+	168.224i	−0.424122	+	0.734601i	−0.996338	−	0.0855017i	$-0.972751\pi$
$229$	−97.1240	+	168.224i	−0.424122	+	0.734601i	0.572216	+	0.820103i	$0.306084\pi$
$230$		0			0
$231$	−4.97427	−	7.87019i	−0.0215336	−	0.0340701i
$232$		0			0
$233$			196.013i			0.841258i	0.907233	+	0.420629i	$0.138191\pi$
$233$			196.013i			0.841258i	−0.907233	+	0.420629i	$0.861809\pi$
$234$		0			0
$235$		0			0
$236$		0			0
$237$	13.0703	+	326.202i	0.0551489	+	1.37638i
$238$		0			0
$239$	43.8109	+	25.2943i	0.183309	+	0.105834i	0.588847	−	0.808245i	$-0.299582\pi$
$239$	43.8109	+	25.2943i	0.183309	+	0.105834i	−0.405537	+	0.914079i	$0.632916\pi$
$240$		0			0
$241$	−104.678	−	181.308i	−0.434351	−	0.752317i	0.562892	−	0.826531i	$-0.309689\pi$
$241$	−104.678	−	181.308i	−0.434351	−	0.752317i	−0.997242	+	0.0742134i	$0.976355\pi$
$242$		0			0
$243$	182.073	−	160.929i	0.749273	−	0.662261i
$244$		0			0
$245$		0			0
$246$		0			0
$247$	−28.0030	+	48.5026i	−0.113372	+	0.196367i
$248$		0			0
$249$	−241.529	+	9.67759i	−0.969996	+	0.0388658i
$250$		0			0
$251$			179.480i			0.715061i	0.933901	+	0.357531i	$0.116381\pi$
$251$			179.480i			0.715061i	−0.933901	+	0.357531i	$0.883619\pi$
$252$		0			0
$253$	−27.1100			−0.107154
$254$		0			0
$255$		0			0
$256$		0			0
$257$	390.047	+	225.194i	1.51769	+	0.876241i	0.999784	+	0.0208064i	$0.00662337\pi$
$257$	390.047	+	225.194i	1.51769	+	0.876241i	0.517911	+	0.855435i	$0.326710\pi$
$258$		0			0
$259$	70.6696	+	122.403i	0.272856	+	0.472600i
$260$		0			0
$261$	−22.8691	−	10.8644i	−0.0876210	−	0.0416261i
$262$		0			0
$263$	342.665	−	197.837i	1.30291	−	0.752234i	0.322005	−	0.946738i	$-0.395643\pi$
$263$	342.665	−	197.837i	1.30291	−	0.752234i	0.980902	+	0.194504i	$0.0623098\pi$
$264$		0			0
$265$		0			0
$266$		0			0
$267$	−91.5170	+	174.274i	−0.342760	+	0.652710i
$268$		0			0
$269$			374.710i			1.39298i	0.717569	+	0.696488i	$0.245255\pi$
$269$			374.710i			1.39298i	−0.717569	+	0.696488i	$0.754745\pi$
$270$		0			0
$271$	41.1748			0.151936			0.0759682	−	0.997110i	$-0.475795\pi$
$271$	41.1748			0.151936			0.0759682	+	0.997110i	$0.475795\pi$
$272$		0			0
$273$	−31.5333	−	16.5592i	−0.115507	−	0.0606565i
$274$		0			0
$275$		0			0
$276$		0			0
$277$	−9.81388	−	16.9981i	−0.0354292	−	0.0613651i	0.847767	−	0.530369i	$-0.177946\pi$
$277$	−9.81388	−	16.9981i	−0.0354292	−	0.0613651i	−0.883196	+	0.469004i	$0.844613\pi$
$278$		0			0
$279$	216.438	−	17.3724i	0.775762	−	0.0622665i
$280$		0			0
$281$	316.627	−	182.805i	1.12679	−	0.650551i	0.183663	−	0.982989i	$-0.441205\pi$
$281$	316.627	−	182.805i	1.12679	−	0.650551i	0.943125	+	0.332438i	$0.107871\pi$
$282$		0			0
$283$	12.0391	−	20.8524i	0.0425410	−	0.0736832i	−0.843971	−	0.536389i	$-0.819788\pi$
$283$	12.0391	−	20.8524i	0.0425410	−	0.0736832i	0.886512	+	0.462706i	$0.153121\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$			61.8317i			0.215441i
$288$		0			0
$289$	227.257			0.786355
$290$		0			0
$291$	18.5984	+	464.171i	0.0639121	+	1.59509i
$292$		0			0
$293$	−295.058	−	170.352i	−1.00703	−	0.581406i	−0.0967059	−	0.995313i	$-0.530831\pi$
$293$	−295.058	−	170.352i	−1.00703	−	0.581406i	−0.910319	+	0.413907i	$0.864164\pi$
$294$		0			0
$295$		0			0
$296$		0			0
$297$	17.7606	+	23.6691i	0.0598000	+	0.0796939i
$298$		0			0
$299$	−89.8149	+	51.8547i	−0.300384	+	0.173427i
$300$		0			0
$301$	69.4180	−	120.235i	0.230624	−	0.399453i
$302$		0			0
$303$	−432.378	+	17.3246i	−1.42699	+	0.0571767i
$304$		0			0
$305$		0			0
$306$		0			0
$307$	−401.187			−1.30680			−0.653399	−	0.757014i	$-0.726658\pi$
$307$	−401.187			−1.30680			−0.653399	+	0.757014i	$0.726658\pi$
$308$		0			0
$309$	−51.4516	+	32.5194i	−0.166510	+	0.105241i
$310$		0			0
$311$	78.7894	+	45.4891i	0.253342	+	0.146267i	0.621294	−	0.783578i	$-0.286607\pi$
$311$	78.7894	+	45.4891i	0.253342	+	0.146267i	−0.367951	+	0.929845i	$0.619941\pi$
$312$		0			0
$313$	−232.638	−	402.942i	−0.743254	−	1.28735i	−0.951006	−	0.309172i	$-0.899948\pi$
$313$	−232.638	−	402.942i	−0.743254	−	1.28735i	0.207752	−	0.978181i	$-0.433385\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	167.607	−	96.7678i	0.528728	−	0.305261i	−0.211770	−	0.977319i	$-0.567923\pi$
$317$	167.607	−	96.7678i	0.528728	−	0.305261i	0.740498	+	0.672058i	$0.234590\pi$
$318$		0			0
$319$	1.54160	−	2.67013i	0.00483261	−	0.00837032i
$320$		0			0
$321$	−217.990	+	415.112i	−0.679096	+	1.29318i
$322$		0			0
$323$		−	104.963i		−	0.324964i
$324$		0			0
$325$		0			0
$326$		0			0
$327$	−147.527	−	77.4715i	−0.451153	−	0.236916i
$328$		0			0
$329$	−165.883	−	95.7726i	−0.504204	−	0.291102i
$330$		0			0
$331$	−65.9739	−	114.270i	−0.199317	−	0.345227i	0.748990	−	0.662581i	$-0.230539\pi$
$331$	−65.9739	−	114.270i	−0.199317	−	0.345227i	−0.948307	+	0.317354i	$0.897206\pi$
$332$		0			0
$333$	−255.018	−	369.822i	−0.765821	−	1.11058i
$334$		0			0
$335$		0			0
$336$		0			0
$337$	−175.261	+	303.562i	−0.520064	+	0.900777i	0.479664	+	0.877452i	$0.340758\pi$
$337$	−175.261	+	303.562i	−0.520064	+	0.900777i	−0.999728	+	0.0233245i	$0.992575\pi$
$338$		0			0
$339$	178.630	+	282.624i	0.526931	+	0.833699i
$340$		0			0
$341$			26.4417i			0.0775417i
$342$		0			0
$343$	−254.798			−0.742851
$344$		0			0
$345$		0			0
$346$		0			0
$347$	198.620	+	114.673i	0.572392	+	0.330470i	0.758104	−	0.652134i	$-0.226126\pi$
$347$	198.620	+	114.673i	0.572392	+	0.330470i	−0.185712	+	0.982604i	$0.559459\pi$
$348$		0			0
$349$	167.325	+	289.815i	0.479440	+	0.830415i	0.999722	−	0.0235800i	$-0.00750645\pi$
$349$	167.325	+	289.815i	0.479440	+	0.830415i	−0.520282	+	0.853995i	$0.674173\pi$
$350$		0			0
$351$	104.113	+	44.4435i	0.296619	+	0.126620i
$352$		0			0
$353$	−25.1509	+	14.5209i	−0.0712489	+	0.0411356i	−0.535201	−	0.844725i	$-0.679764\pi$
$353$	−25.1509	+	14.5209i	−0.0712489	+	0.0411356i	0.463952	+	0.885860i	$0.346431\pi$
$354$		0			0
$355$		0			0
$356$		0			0
$357$	66.6976	−	2.67244i	0.186828	−	0.00748583i
$358$		0			0
$359$		−	293.412i		−	0.817304i	−0.912690	−	0.408652i	$-0.865999\pi$
$359$		−	293.412i		−	0.817304i	0.912690	−	0.408652i	$-0.134001\pi$
$360$		0			0
$361$	−182.563			−0.505716
$362$		0			0
$363$	303.803	−	192.015i	0.836922	−	0.528967i
$364$		0			0
$365$		0			0
$366$		0			0
$367$	−28.6259	−	49.5815i	−0.0779997	−	0.135099i	0.824387	−	0.566026i	$-0.191520\pi$
$367$	−28.6259	−	49.5815i	−0.0779997	−	0.135099i	−0.902387	+	0.430927i	$0.858187\pi$
$368$		0			0
$369$	−15.7233	−	195.892i	−0.0426106	−	0.530874i
$370$		0			0
$371$	122.227	−	70.5676i	0.329452	−	0.190209i
$372$		0			0
$373$	−150.282	+	260.297i	−0.402902	+	0.697847i	−0.994075	−	0.108698i	$-0.965332\pi$
$373$	−150.282	+	260.297i	−0.402902	+	0.697847i	0.591173	+	0.806545i	$0.298665\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$		−	11.7948i		−	0.0312859i
$378$		0			0
$379$	−198.314			−0.523255			−0.261627	−	0.965169i	$-0.584259\pi$
$379$	−198.314			−0.523255			−0.261627	+	0.965169i	$0.584259\pi$
$380$		0			0
$381$	383.662	+	201.474i	1.00699	+	0.528803i
$382$		0			0
$383$	48.8088	+	28.1798i	0.127438	+	0.0735765i	0.562364	−	0.826890i	$-0.309892\pi$
$383$	48.8088	+	28.1798i	0.127438	+	0.0735765i	−0.434926	+	0.900466i	$0.643225\pi$
$384$		0			0
$385$		0			0
$386$		0			0
$387$	−189.352	+	398.577i	−0.489282	+	1.02991i
$388$		0			0
$389$	−620.660	+	358.338i	−1.59553	+	0.921179i	−0.603194	+	0.797595i	$0.706105\pi$
$389$	−620.660	+	358.338i	−1.59553	+	0.921179i	−0.992334	+	0.123584i	$0.960561\pi$
$390$		0			0
$391$	97.1831	−	168.326i	0.248550	−	0.430501i
$392$		0			0
$393$	−308.446	−	488.017i	−0.784849	−	1.24177i
$394$		0			0
$395$		0			0
$396$		0			0
$397$	310.467			0.782032			0.391016	−	0.920384i	$-0.372124\pi$
$397$	310.467			0.782032			0.391016	+	0.920384i	$0.372124\pi$
$398$		0			0
$399$	4.54313	+	113.385i	0.0113863	+	0.284173i
$400$		0			0
$401$	−426.833	−	246.432i	−1.06442	−	0.614544i	−0.137770	−	0.990464i	$-0.543993\pi$
$401$	−426.833	−	246.432i	−1.06442	−	0.614544i	−0.926652	+	0.375920i	$0.877327\pi$
$402$		0			0
$403$	50.5763	+	87.6008i	0.125500	+	0.217372i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	47.3758	−	27.3524i	0.116402	−	0.0672050i
$408$		0			0
$409$	341.160	−	590.906i	0.834132	−	1.44476i	−0.0606037	−	0.998162i	$-0.519303\pi$
$409$	341.160	−	590.906i	0.834132	−	1.44476i	0.894735	−	0.446597i	$-0.147364\pi$
$410$		0			0
$411$	−98.6240	+	3.95167i	−0.239961	+	0.00961477i
$412$		0			0
$413$			284.086i			0.687859i
$414$		0			0
$415$		0			0
$416$		0			0
$417$	406.377	−	256.847i	0.974526	−	0.615939i
$418$		0			0
$419$	−192.209	−	110.972i	−0.458732	−	0.264849i	0.252779	−	0.967524i	$-0.418655\pi$
$419$	−192.209	−	110.972i	−0.458732	−	0.264849i	−0.711511	+	0.702675i	$0.751989\pi$
$420$		0			0
$421$	−76.5614	−	132.608i	−0.181856	−	0.314984i	0.760657	−	0.649155i	$-0.224877\pi$
$421$	−76.5614	−	132.608i	−0.181856	−	0.314984i	−0.942513	+	0.334171i	$0.891544\pi$
$422$		0			0
$423$	549.898	+	261.240i	1.29999	+	0.617588i
$424$		0			0
$425$		0			0
$426$		0			0
$427$	−117.683	+	203.833i	−0.275604	+	0.477361i
$428$		0			0
$429$	−6.40920	+	12.2049i	−0.0149399	+	0.0284496i
$430$		0			0
$431$			328.398i			0.761944i	0.924587	+	0.380972i	$0.124411\pi$
$431$			328.398i			0.761944i	−0.924587	+	0.380972i	$0.875589\pi$
$432$		0			0
$433$	171.691			0.396515			0.198258	−	0.980150i	$-0.436472\pi$
$433$	171.691			0.396515			0.198258	+	0.980150i	$0.436472\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	286.153	+	165.210i	0.654812	+	0.378056i
$438$		0			0
$439$	−49.2459	−	85.2965i	−0.112178	−	0.194297i	0.804470	−	0.593993i	$-0.202449\pi$
$439$	−49.2459	−	85.2965i	−0.112178	−	0.194297i	−0.916648	+	0.399695i	$0.869116\pi$
$440$		0			0
$441$	367.653	−	29.5096i	0.833680	−	0.0669153i
$442$		0			0
$443$	654.554	−	377.907i	1.47755	−	0.853063i	0.477871	−	0.878430i	$-0.341409\pi$
$443$	654.554	−	377.907i	1.47755	−	0.853063i	0.999678	+	0.0253671i	$0.00807546\pi$
$444$		0			0
$445$		0			0
$446$		0			0
$447$	−72.3994	−	114.549i	−0.161967	−	0.256262i
$448$		0			0
$449$		−	167.336i		−	0.372686i	−0.982485	−	0.186343i	$-0.940336\pi$
$449$		−	167.336i		−	0.372686i	0.982485	−	0.186343i	$-0.0596635\pi$
$450$		0			0
$451$	23.9318			0.0530638
$452$		0			0
$453$	32.2212	+	804.161i	0.0711284	+	1.77519i
$454$		0			0
$455$		0			0
$456$		0			0
$457$	−183.553	−	317.924i	−0.401648	−	0.695676i	0.592277	−	0.805735i	$-0.298229\pi$
$457$	−183.553	−	317.924i	−0.401648	−	0.695676i	−0.993925	+	0.110059i	$0.964896\pi$
$458$		0			0
$459$	−210.629	+	25.4274i	−0.458886	+	0.0553973i
$460$		0			0
$461$	467.957	−	270.175i	1.01509	−	0.586063i	0.102413	−	0.994742i	$-0.467344\pi$
$461$	467.957	−	270.175i	1.01509	−	0.586063i	0.912678	+	0.408679i	$0.134010\pi$
$462$		0			0
$463$	−89.8654	+	155.651i	−0.194094	+	0.336180i	−0.946603	−	0.322401i	$-0.895510\pi$
$463$	−89.8654	+	155.651i	−0.194094	+	0.336180i	0.752509	+	0.658582i	$0.228843\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$		−	56.0646i		−	0.120053i	−0.998197	−	0.0600264i	$-0.980882\pi$
$467$		−	56.0646i		−	0.120053i	0.998197	−	0.0600264i	$-0.0191185\pi$
$468$		0			0
$469$	−162.965			−0.347473
$470$		0			0
$471$	−528.265	+	333.884i	−1.12158	+	0.708884i
$472$		0			0
$473$	−46.5367	−	26.8680i	−0.0983863	−	0.0568034i
$474$		0			0
$475$		0			0
$476$		0			0
$477$	−369.288	+	254.650i	−0.774190	+	0.533858i
$478$		0			0
$479$	497.782	−	287.395i	1.03921	−	0.599989i	0.119601	−	0.992822i	$-0.461838\pi$
$479$	497.782	−	287.395i	1.03921	−	0.599989i	0.919610	+	0.392833i	$0.128505\pi$
$480$		0			0
$481$	104.637	−	181.236i	0.217540	−	0.376790i
$482$		0			0
$483$	−97.6951	+	186.038i	−0.202267	+	0.385173i
$484$		0			0
$485$		0			0
$486$		0			0
$487$	190.185			0.390524			0.195262	−	0.980751i	$-0.437444\pi$
$487$	190.185			0.390524			0.195262	+	0.980751i	$0.437444\pi$
$488$		0			0
$489$	−65.4438	−	34.3668i	−0.133832	−	0.0702797i
$490$		0			0
$491$	−340.176	−	196.401i	−0.692822	−	0.400001i	0.111846	−	0.993726i	$-0.464324\pi$
$491$	−340.176	−	196.401i	−0.692822	−	0.400001i	−0.804668	+	0.593724i	$0.797657\pi$
$492$		0			0
$493$	11.0525	+	19.1436i	0.0224190	+	0.0388308i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	−34.9002	+	20.1496i	−0.0702217	+	0.0405425i
$498$		0			0
$499$	−150.303	+	260.332i	−0.301208	+	0.521707i	−0.976410	−	0.215926i	$-0.930723\pi$
$499$	−150.303	+	260.332i	−0.301208	+	0.521707i	0.675202	+	0.737633i	$0.264056\pi$
$500$		0			0
$501$	−143.086	−	226.388i	−0.285601	−	0.451872i
$502$		0			0
$503$			484.676i			0.963572i	0.876289	+	0.481786i	$0.160012\pi$
$503$			484.676i			0.963572i	−0.876289	+	0.481786i	$0.839988\pi$
$504$		0			0
$505$		0			0
$506$		0			0
$507$	−18.1869	−	453.900i	−0.0358716	−	0.895266i
$508$		0			0
$509$	467.647	+	269.996i	0.918755	+	0.530444i	0.883238	−	0.468925i	$-0.155359\pi$
$509$	467.647	+	269.996i	0.918755	+	0.530444i	0.0355177	+	0.999369i	$0.488692\pi$
$510$		0			0
$511$	101.307	+	175.469i	0.198253	+	0.343384i
$512$		0			0
$513$	−43.2263	−	358.067i	−0.0842617	−	0.697986i
$514$		0			0
$515$		0			0
$516$		0			0
$517$	−37.0685	+	64.2045i	−0.0716992	+	0.124187i
$518$		0			0
$519$	183.428	−	7.34962i	0.353426	−	0.0141611i
$520$		0			0
$521$			103.769i			0.199172i	0.995029	+	0.0995862i	$0.0317519\pi$
$521$			103.769i			0.199172i	−0.995029	+	0.0995862i	$0.968248\pi$
$522$		0			0
$523$	142.380			0.272237			0.136119	−	0.990693i	$-0.456537\pi$
$523$	142.380			0.272237			0.136119	+	0.990693i	$0.456537\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	−164.176	−	94.7873i	−0.311530	−	0.179862i
$528$		0			0
$529$	41.4290	+	71.7571i	0.0783157	+	0.135647i
$530$		0			0
$531$	−72.2407	−	900.028i	−0.136047	−	1.69497i
$532$		0			0
$533$	79.2853	−	45.7754i	0.148753	−	0.0858826i
$534$		0			0
$535$		0			0
$536$		0			0
$537$	183.985	−	350.357i	0.342616	−	0.652435i
$538$		0			0
$539$			44.9154i			0.0833309i
$540$		0			0
$541$	−708.521			−1.30965			−0.654826	−	0.755780i	$-0.727258\pi$
$541$	−708.521			−1.30965			−0.654826	+	0.755780i	$0.727258\pi$
$542$		0			0
$543$	827.999	+	434.811i	1.52486	+	0.800756i
$544$		0			0
$545$		0			0
$546$		0			0
$547$	−242.130	−	419.382i	−0.442652	−	0.766695i	0.555234	−	0.831694i	$-0.312629\pi$
$547$	−242.130	−	419.382i	−0.442652	−	0.766695i	−0.997885	+	0.0649994i	$0.979295\pi$
$548$		0			0
$549$	321.005	−	675.701i	0.584709	−	1.23078i
$550$		0			0
$551$	−32.5439	+	18.7892i	−0.0590633	+	0.0341002i
$552$		0			0
$553$	−154.073	+	266.862i	−0.278612	+	0.482571i
$554$		0			0
$555$		0			0
$556$		0			0
$557$		−	687.468i		−	1.23423i	−0.786871	−	0.617117i	$-0.788301\pi$
$557$		−	687.468i		−	1.23423i	0.786871	−	0.617117i	$-0.211699\pi$
$558$		0			0
$559$	−205.567			−0.367740
$560$		0			0
$561$	−1.03436	−	25.8151i	−0.00184378	−	0.0460162i
$562$		0			0
$563$	−720.306	−	415.869i	−1.27941	−	0.738666i	−0.302667	−	0.953096i	$-0.597877\pi$
$563$	−720.306	−	415.869i	−1.27941	−	0.738666i	−0.976739	+	0.214431i	$0.931210\pi$
$564$		0			0
$565$		0			0
$566$		0			0
$567$	226.428	−	36.5842i	0.399344	−	0.0645224i
$568$		0			0
$569$	250.103	−	144.397i	0.439548	−	0.253773i	−0.263858	−	0.964562i	$-0.584995\pi$
$569$	250.103	−	144.397i	0.439548	−	0.253773i	0.703406	+	0.710788i	$0.251662\pi$
$570$		0			0
$571$	−164.400	+	284.750i	−0.287917	+	0.498686i	−0.973312	−	0.229485i	$-0.926296\pi$
$571$	−164.400	+	284.750i	−0.287917	+	0.498686i	0.685396	+	0.728171i	$0.259629\pi$
$572$		0			0
$573$	−1049.23	+	42.0405i	−1.83111	+	0.0733691i
$574$		0			0
$575$		0			0
$576$		0			0
$577$	297.033			0.514788			0.257394	−	0.966307i	$-0.417136\pi$
$577$	297.033			0.514788			0.257394	+	0.966307i	$0.417136\pi$
$578$		0			0
$579$	−502.225	+	317.426i	−0.867400	+	0.548231i
$580$		0			0
$581$	−197.592	−	114.080i	−0.340089	−	0.196350i
$582$		0			0
$583$	−27.3130	−	47.3074i	−0.0468490	−	0.0811449i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	−793.373	+	458.054i	−1.35157	+	0.780331i	−0.988470	−	0.151419i	$-0.951616\pi$
$587$	−793.373	+	458.054i	−1.35157	+	0.780331i	−0.363103	+	0.931749i	$0.618283\pi$
$588$		0			0
$589$	161.137	−	279.098i	0.273578	−	0.473851i
$590$		0			0
$591$	45.3991	−	86.4524i	0.0768174	−	0.146282i
$592$		0			0
$593$			620.630i			1.04659i	0.852150	+	0.523297i	$0.175298\pi$
$593$			620.630i			1.04659i	−0.852150	+	0.523297i	$0.824702\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$	−340.767	−	178.948i	−0.570799	−	0.299746i
$598$		0			0
$599$	−230.407	−	133.026i	−0.384653	−	0.222079i	0.295188	−	0.955439i	$-0.404618\pi$
$599$	−230.407	−	133.026i	−0.384653	−	0.222079i	−0.679841	+	0.733360i	$0.737951\pi$
$600$		0			0
$601$	504.140	+	873.197i	0.838836	+	1.45291i	0.890869	+	0.454261i	$0.150097\pi$
$601$	504.140	+	873.197i	0.838836	+	1.45291i	−0.0520330	+	0.998645i	$0.516570\pi$
$602$		0			0
$603$	516.297	−	41.4406i	0.856215	−	0.0687240i
$604$		0			0
$605$		0			0
$606$		0			0
$607$	576.693	−	998.861i	0.950071	−	1.64557i	0.204805	−	0.978803i	$-0.434344\pi$
$607$	576.693	−	998.861i	0.950071	−	1.64557i	0.745265	−	0.666768i	$-0.232323\pi$
$608$		0			0
$609$	−12.7680	−	20.2012i	−0.0209655	−	0.0331711i
$610$		0			0
$611$			283.611i			0.464174i
$612$		0			0
$613$	1168.56			1.90629			0.953145	−	0.302515i	$-0.0978262\pi$
$613$	1168.56			1.90629			0.953145	+	0.302515i	$0.0978262\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	−793.512	−	458.134i	−1.28608	−	0.742519i	−0.308128	−	0.951345i	$-0.599702\pi$
$617$	−793.512	−	458.134i	−1.28608	−	0.742519i	−0.977953	+	0.208826i	$0.933036\pi$
$618$		0			0
$619$	−83.6253	−	144.843i	−0.135097	−	0.233995i	0.790537	−	0.612414i	$-0.209801\pi$
$619$	−83.6253	−	144.843i	−0.135097	−	0.233995i	−0.925635	+	0.378418i	$0.876468\pi$
$620$		0			0
$621$	262.205	−	614.242i	0.422231	−	0.989117i
$622$		0			0
$623$	−160.904	+	92.8982i	−0.258274	+	0.149114i
$624$		0			0
$625$		0			0
$626$		0			0
$627$	43.8854	−	1.75840i	0.0699926	−	0.00280447i
$628$		0			0
$629$			392.208i			0.623542i
$630$		0			0
$631$	542.994			0.860530			0.430265	−	0.902703i	$-0.358420\pi$
$631$	542.994			0.860530			0.430265	+	0.902703i	$0.358420\pi$
$632$		0			0
$633$	−91.6777	+	57.9439i	−0.144831	+	0.0915386i
$634$		0			0
$635$		0			0
$636$		0			0
$637$	85.9117	+	148.803i	0.134869	+	0.233600i
$638$		0			0
$639$	105.445	−	72.7120i	0.165016	−	0.113790i
$640$		0			0
$641$	−90.6386	+	52.3302i	−0.141402	+	0.0816384i	−0.569032	−	0.822315i	$-0.692682\pi$
$641$	−90.6386	+	52.3302i	−0.141402	+	0.0816384i	0.427630	+	0.903954i	$0.359349\pi$
$642$		0			0
$643$	105.237	−	182.276i	0.163666	−	0.283478i	−0.772515	−	0.634997i	$-0.781001\pi$
$643$	105.237	−	182.276i	0.163666	−	0.283478i	0.936181	+	0.351519i	$0.114335\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$		−	899.002i		−	1.38949i	−0.719254	−	0.694747i	$-0.755516\pi$
$647$		−	899.002i		−	1.38949i	0.719254	−	0.694747i	$-0.244484\pi$
$648$		0			0
$649$	109.955			0.169421
$650$		0			0
$651$	181.452	+	95.2867i	0.278728	+	0.146370i
$652$		0			0
$653$	−381.359	−	220.178i	−0.584011	−	0.337179i	0.178715	−	0.983901i	$-0.442806\pi$
$653$	−381.359	−	220.178i	−0.584011	−	0.337179i	−0.762726	+	0.646722i	$0.776139\pi$
$654$		0			0
$655$		0			0
$656$		0			0
$657$	−365.577	−	530.152i	−0.556434	−	0.806929i
$658$		0			0
$659$	779.837	−	450.239i	1.18336	−	0.683215i	0.226573	−	0.973994i	$-0.427248\pi$
$659$	779.837	−	450.239i	1.18336	−	0.683215i	0.956790	+	0.290779i	$0.0939144\pi$
$660$		0			0
$661$	268.406	−	464.893i	0.406060	−	0.703317i	−0.588384	−	0.808582i	$-0.700236\pi$
$661$	268.406	−	464.893i	0.406060	−	0.703317i	0.994444	+	0.105264i	$0.0335689\pi$
$662$		0			0
$663$	−52.8045	−	83.5462i	−0.0796448	−	0.126012i
$664$		0			0
$665$		0			0
$666$		0			0
$667$	−69.5861			−0.104327
$668$		0			0
$669$	−21.0113	−	524.390i	−0.0314070	−	0.783842i
$670$		0			0
$671$	78.8929	+	45.5488i	0.117575	+	0.0678820i
$672$		0			0
$673$	−73.7299	−	127.704i	−0.109554	−	0.189753i	0.806036	−	0.591867i	$-0.201609\pi$
$673$	−73.7299	−	127.704i	−0.109554	−	0.189753i	−0.915590	+	0.402114i	$0.868276\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	−760.854	+	439.279i	−1.12386	+	0.648861i	−0.942384	−	0.334534i	$-0.891421\pi$
$677$	−760.854	+	439.279i	−1.12386	+	0.648861i	−0.181477	+	0.983395i	$0.558088\pi$
$678$		0			0
$679$	−219.238	+	379.732i	−0.322884	+	0.559251i
$680$		0			0
$681$	−408.450	+	16.3658i	−0.599780	+	0.0240320i
$682$		0			0
$683$			395.518i			0.579090i	0.957164	+	0.289545i	$0.0935039\pi$
$683$			395.518i			0.579090i	−0.957164	+	0.289545i	$0.906496\pi$
$684$		0			0
$685$		0			0
$686$		0			0
$687$	492.601	−	311.343i	0.717032	−	0.453193i
$688$		0			0
$689$	−180.974	−	104.486i	−0.262662	−	0.151648i
$690$		0			0
$691$	370.319	+	641.412i	0.535918	+	0.928237i	0.999118	+	0.0419833i	$0.0133676\pi$
$691$	370.319	+	641.412i	0.535918	+	0.928237i	−0.463201	+	0.886253i	$0.653299\pi$
$692$		0			0
$693$	2.23471	+	27.8416i	0.00322469	+	0.0401755i
$694$		0			0
$695$		0			0
$696$		0			0
$697$	−85.7897	+	148.592i	−0.123084	+	0.213188i
$698$		0			0
$699$	273.395	−	520.620i	0.391124	−	0.744807i
$700$		0			0
$701$			1221.15i			1.74201i	0.491275	+	0.871004i	$0.336531\pi$
$701$			1221.15i			1.74201i	−0.491275	+	0.871004i	$0.663469\pi$
$702$		0			0
$703$	−666.750			−0.948435
$704$		0			0
$705$		0			0
$706$		0			0
$707$	−353.723	−	204.222i	−0.500315	−	0.288857i
$708$		0			0
$709$	−371.624	−	643.672i	−0.524153	−	0.907859i	−0.999605	−	0.0281175i	$-0.991049\pi$
$709$	−371.624	−	643.672i	−0.524153	−	0.907859i	0.475452	−	0.879742i	$-0.342285\pi$
$710$		0			0
$711$	420.265	−	884.639i	0.591091	−	1.24422i
$712$		0			0
$713$	516.822	−	298.387i	0.724855	−	0.418495i
$714$		0			0
$715$		0			0
$716$		0			0
$717$	−81.0840	−	128.289i	−0.113088	−	0.178925i
$718$		0			0
$719$		−	1187.47i		−	1.65156i	−0.563993	−	0.825779i	$-0.690736\pi$
$719$		−	1187.47i		−	1.65156i	0.563993	−	0.825779i	$-0.309264\pi$
$720$		0			0
$721$	−57.4515			−0.0796831
$722$		0			0
$723$	25.1454	+	627.567i	0.0347793	+	0.868005i
$724$		0			0
$725$		0			0
$726$		0			0
$727$	90.5432	+	156.825i	0.124544	+	0.215716i	0.921554	−	0.388249i	$-0.126920\pi$
$727$	90.5432	+	156.825i	0.124544	+	0.215716i	−0.797011	+	0.603965i	$0.793587\pi$
$728$		0			0
$729$	−708.057	+	173.483i	−0.971271	+	0.237974i
$730$		0			0
$731$	333.646	−	192.631i	0.456425	−	0.263517i
$732$		0			0
$733$	253.995	−	439.932i	0.346514	−	0.600180i	−0.639114	−	0.769112i	$-0.720699\pi$
$733$	253.995	−	439.932i	0.346514	−	0.600180i	0.985628	+	0.168932i	$0.0540320\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$			63.0749i			0.0855834i
$738$		0			0
$739$	−1428.58			−1.93313			−0.966566	−	0.256418i	$-0.917458\pi$
$739$	−1428.58			−1.93313			−0.966566	+	0.256418i	$0.917458\pi$
$740$		0			0
$741$	142.028	−	89.7672i	0.191670	−	0.121143i
$742$		0			0
$743$	−620.319	−	358.142i	−0.834885	−	0.482021i	0.0206374	−	0.999787i	$-0.493430\pi$
$743$	−620.319	−	358.142i	−0.834885	−	0.482021i	−0.855522	+	0.517766i	$0.826764\pi$
$744$		0			0
$745$		0			0
$746$		0			0
$747$	655.010	+	311.176i	0.876854	+	0.416567i
$748$		0			0
$749$	−383.268	+	221.280i	−0.511706	+	0.295433i
$750$		0			0
$751$	−265.708	+	460.219i	−0.353805	+	0.612809i	−0.986913	−	0.161255i	$-0.948446\pi$
$751$	−265.708	+	460.219i	−0.353805	+	0.612809i	0.633108	+	0.774064i	$0.281779\pi$
$752$		0			0
$753$	250.336	−	476.708i	0.332451	−	0.633079i
$754$		0			0
$755$		0			0
$756$		0			0
$757$	952.388			1.25811			0.629054	−	0.777362i	$-0.283442\pi$
$757$	952.388			1.25811			0.629054	+	0.777362i	$0.283442\pi$
$758$		0			0
$759$	72.0056	+	37.8126i	0.0948690	+	0.0498189i
$760$		0			0
$761$	−1203.10	−	694.609i	−1.58094	−	0.912758i	−0.994722	−	0.102606i	$-0.967282\pi$
$761$	−1203.10	−	694.609i	−1.58094	−	0.912758i	−0.586220	−	0.810152i	$-0.699385\pi$
$762$		0			0
$763$	−78.6407	−	136.210i	−0.103068	−	0.178519i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	364.277	−	210.315i	0.474937	−	0.274205i
$768$		0			0
$769$	511.731	−	886.345i	0.665450	−	1.15259i	−0.313713	−	0.949518i	$-0.601573\pi$
$769$	511.731	−	886.345i	0.665450	−	1.15259i	0.979163	−	0.203076i	$-0.0650938\pi$
$770$		0			0
$771$	−721.888	−	1142.16i	−0.936301	−	1.48140i
$772$		0			0
$773$			1030.13i			1.33264i	0.745666	+	0.666320i	$0.232132\pi$
$773$			1030.13i			1.33264i	−0.745666	+	0.666320i	$0.767868\pi$
$774$		0			0
$775$		0			0
$776$		0			0
$777$	−16.9759	−	423.678i	−0.0218481	−	0.545274i
$778$		0			0
$779$	−252.605	−	145.842i	−0.324268	−	0.187216i
$780$		0			0
$781$	7.79885	+	13.5080i	0.00998572	+	0.0172958i
$782$		0			0
$783$	45.5879	+	60.7538i	0.0582221	+	0.0775910i
$784$		0			0
$785$		0			0
$786$		0			0
$787$	−410.738	+	711.419i	−0.521903	+	0.903963i	0.477772	+	0.878484i	$0.341444\pi$
$787$	−410.738	+	711.419i	−0.521903	+	0.903963i	−0.999675	+	0.0254790i	$0.991889\pi$
$788$		0			0
$789$	−1186.07	+	47.5236i	−1.50326	+	0.0602327i
$790$		0			0
$791$			315.582i			0.398966i
$792$		0			0
$793$	348.494			0.439462
$794$		0			0
$795$		0			0
$796$		0			0
$797$	148.193	+	85.5591i	0.185938	+	0.107351i	0.590080	−	0.807345i	$-0.299096\pi$
$797$	148.193	+	85.5591i	0.185938	+	0.107351i	−0.404142	+	0.914696i	$0.632430\pi$
$798$		0			0
$799$	−265.763	−	460.316i	−0.332620	−	0.576115i
$800$		0			0
$801$	486.147	−	335.233i	0.606925	−	0.418518i
$802$		0			0
$803$	67.9148	−	39.2106i	0.0845763	−	0.0488302i
$804$		0			0
$805$		0			0
$806$		0			0
$807$	522.639	−	995.248i	0.647632	−	1.23327i
$808$		0			0
$809$			605.283i			0.748186i	0.927391	+	0.374093i	$0.122046\pi$
$809$			605.283i			0.748186i	−0.927391	+	0.374093i	$0.877954\pi$
$810$		0			0
$811$	1570.18			1.93610			0.968050	−	0.250756i	$-0.0806791\pi$
$811$	1570.18			1.93610			0.968050	+	0.250756i	$0.0806791\pi$
$812$		0			0
$813$	−109.362	−	57.4298i	−0.134517	−	0.0706393i
$814$		0			0
$815$		0			0
$816$		0			0
$817$	327.471	+	567.196i	0.400821	+	0.694242i
$818$		0			0
$819$	60.6575	+	87.9642i	0.0740629	+	0.107404i
$820$		0			0
$821$	−1386.41	+	800.446i	−1.68869	+	0.974965i	−0.733166	+	0.680050i	$0.761958\pi$
$821$	−1386.41	+	800.446i	−1.68869	+	0.974965i	−0.955523	+	0.294915i	$0.904709\pi$
$822$		0			0
$823$	−186.840	+	323.616i	−0.227023	+	0.393215i	−0.956924	−	0.290337i	$-0.906232\pi$
$823$	−186.840	+	323.616i	−0.227023	+	0.393215i	0.729902	+	0.683552i	$0.239566\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$			1490.30i			1.80205i	0.433764	+	0.901027i	$0.357185\pi$
$827$			1490.30i			1.80205i	−0.433764	+	0.901027i	$0.642815\pi$
$828$		0			0
$829$	−85.8287			−0.103533			−0.0517664	−	0.998659i	$-0.516485\pi$
$829$	−85.8287			−0.103533			−0.0517664	+	0.998659i	$0.516485\pi$
$830$		0			0
$831$	2.35745	+	58.8360i	0.00283688	+	0.0708015i
$832$		0			0
$833$	−278.879	−	161.011i	−0.334789	−	0.193290i
$834$		0			0
$835$		0			0
$836$		0			0
$837$	−599.099	−	255.741i	−0.715769	−	0.305545i
$838$		0			0
$839$	1114.95	−	643.717i	1.32890	−	0.767243i	0.343774	−	0.939053i	$-0.388295\pi$
$839$	1114.95	−	643.717i	1.32890	−	0.767243i	0.985130	+	0.171810i	$0.0549614\pi$
$840$		0			0
$841$	−416.543	+	721.474i	−0.495295	+	0.857876i
$842$		0			0
$843$	−1095.95	+	43.9126i	−1.30006	+	0.0520909i
$844$		0			0
$845$		0			0
$846$		0			0
$847$	339.230			0.400508
$848$		0			0
$849$	−61.0609	+	38.5929i	−0.0719210	+	0.0454569i
$850$		0			0
$851$	−1069.24	−	617.329i	−1.25646	−	0.725415i
$852$		0			0
$853$	524.686	+	908.783i	0.615107	+	1.06540i	0.990366	+	0.138477i	$0.0442206\pi$
$853$	524.686	+	908.783i	0.615107	+	1.06540i	−0.375259	+	0.926920i	$0.622446\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	−608.526	+	351.333i	−0.710066	+	0.409957i	−0.811085	−	0.584928i	$-0.801123\pi$
$857$	−608.526	+	351.333i	−0.710066	+	0.409957i	0.101020	+	0.994884i	$0.467789\pi$
$858$		0			0
$859$	−152.845	+	264.735i	−0.177934	+	0.308190i	−0.941173	−	0.337926i	$-0.890275\pi$
$859$	−152.845	+	264.735i	−0.177934	+	0.308190i	0.763239	+	0.646116i	$0.223608\pi$
$860$		0			0
$861$	86.2417	−	164.228i	0.100165	−	0.190741i
$862$		0			0
$863$		−	975.875i		−	1.13079i	−0.824819	−	0.565397i	$-0.808723\pi$
$863$		−	975.875i		−	1.13079i	0.824819	−	0.565397i	$-0.191277\pi$
$864$		0			0
$865$		0			0
$866$		0			0
$867$	−603.604	−	316.973i	−0.696198	−	0.365598i
$868$		0			0
$869$	103.288	+	59.6333i	0.118858	+	0.0686229i
$870$		0			0
$871$	120.646	+	208.966i	0.138515	+	0.239915i
$872$		0			0
$873$	598.018	−	1258.80i	0.685015	−	1.44192i
$874$		0			0
$875$		0			0
$876$		0			0
$877$	−177.660	+	307.716i	−0.202577	+	0.350874i	−0.949358	−	0.314196i	$-0.898265\pi$
$877$	−177.660	+	307.716i	−0.202577	+	0.350874i	0.746781	+	0.665070i	$0.231598\pi$
$878$		0			0
$879$	546.085	+	864.005i	0.621257	+	0.982941i
$880$		0			0
$881$		−	645.657i		−	0.732869i	−0.930444	−	0.366434i	$-0.880578\pi$
$881$		−	645.657i		−	0.732869i	0.930444	−	0.366434i	$-0.119422\pi$
$882$		0			0
$883$	−1069.33			−1.21101			−0.605507	−	0.795840i	$-0.707030\pi$
$883$	−1069.33			−1.21101			−0.605507	+	0.795840i	$0.707030\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	−247.125	−	142.678i	−0.278608	−	0.160854i	0.354185	−	0.935175i	$-0.384758\pi$
$887$	−247.125	−	142.678i	−0.278608	−	0.160854i	−0.632793	+	0.774321i	$0.718092\pi$
$888$		0			0
$889$	204.515	+	354.230i	0.230050	+	0.398459i
$890$		0			0
$891$	−14.1598	−	87.6383i	−0.0158920	−	0.0983595i
$892$		0			0
$893$	782.533	−	451.795i	0.876296	−	0.505930i
$894$		0			0
$895$		0			0
$896$		0			0
$897$	310.879	−	12.4563i	0.346576	−	0.0138866i
$898$		0			0
$899$			67.8706i			0.0754957i
$900$		0			0
$901$	391.642			0.434675
$902$		0			0
$903$	−352.079	+	222.528i	−0.389900	+	0.246432i
$904$		0			0
$905$		0			0
$906$		0			0
$907$	620.865	+	1075.37i	0.684526	+	1.18563i	0.973585	+	0.228323i	$0.0733242\pi$
$907$	620.865	+	1075.37i	0.684526	+	1.18563i	−0.289059	+	0.957311i	$0.593342\pi$
$908$		0			0
$909$	1172.58	+	557.058i	1.28997	+	0.612825i
$910$		0			0
$911$	−123.752	+	71.4483i	−0.135842	+	0.0784285i	−0.566381	−	0.824144i	$-0.691657\pi$
$911$	−123.752	+	71.4483i	−0.135842	+	0.0784285i	0.430539	+	0.902572i	$0.358324\pi$
$912$		0			0
$913$	−44.1541	+	76.4772i	−0.0483616	+	0.0837647i
$914$		0			0
$915$		0			0
$916$		0			0
$917$		−	544.926i		−	0.594248i
$918$		0			0
$919$	976.872			1.06297			0.531487	−	0.847067i	$-0.321634\pi$
$919$	976.872			1.06297			0.531487	+	0.847067i	$0.321634\pi$
$920$		0			0
$921$	1065.57	+	559.568i	1.15697	+	0.607566i
$922$		0			0
$923$	51.6748	+	29.8345i	0.0559857	+	0.0323233i
$924$		0			0
$925$		0			0
$926$		0			0
$927$	182.015	−	14.6094i	0.196349	−	0.0157599i
$928$		0			0
$929$	−784.088	+	452.693i	−0.844013	+	0.487291i	−0.858626	−	0.512602i	$-0.828682\pi$
$929$	−784.088	+	452.693i	−0.844013	+	0.487291i	0.0146135	+	0.999893i	$0.495348\pi$
$930$		0			0
$931$	273.717	−	474.092i	0.294003	−	0.509229i
$932$		0			0
$933$	−145.821	−	230.715i	−0.156293	−	0.247283i
$934$		0			0
$935$		0			0
$936$		0			0
$937$	−601.348			−0.641780			−0.320890	−	0.947116i	$-0.603982\pi$
$937$	−601.348			−0.641780			−0.320890	+	0.947116i	$0.603982\pi$
$938$		0			0
$939$	55.8834	+	1394.71i	0.0595137	+	1.48532i
$940$		0			0
$941$	430.443	+	248.517i	0.457432	+	0.264098i	0.710964	−	0.703229i	$-0.248259\pi$
$941$	430.443	+	248.517i	0.457432	+	0.264098i	−0.253532	+	0.967327i	$0.581592\pi$
$942$		0			0
$943$	−270.063	−	467.763i	−0.286387	−	0.496037i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	−1102.31	+	636.420i	−1.16400	+	0.672038i	−0.952260	−	0.305287i	$-0.901248\pi$
$947$	−1102.31	+	636.420i	−1.16400	+	0.672038i	−0.211744	+	0.977325i	$0.567914\pi$
$948$		0			0
$949$	150.000	−	259.808i	0.158061	−	0.273770i
$950$		0			0
$951$	−580.141	+	23.2451i	−0.610033	+	0.0244428i
$952$		0			0
$953$			1562.94i			1.64002i	0.572351	+	0.820009i	$0.306032\pi$
$953$			1562.94i			1.64002i	−0.572351	+	0.820009i	$0.693968\pi$
$954$		0			0
$955$		0			0
$956$		0			0
$957$	−7.81881	+	4.94180i	−0.00817013	+	0.00516384i
$958$		0			0
$959$	−80.6829	−	46.5823i	−0.0841324	−	0.0485738i
$960$		0			0
$961$	189.469	+	328.170i	0.197158	+	0.341488i
$962$		0			0
$963$	1157.98	−	798.510i	1.20247	−	0.829190i
$964$		0			0
$965$		0			0
$966$		0			0
$967$	186.219	−	322.540i	0.192574	−	0.333547i	−0.753529	−	0.657415i	$-0.771650\pi$
$967$	186.219	−	322.540i	0.192574	−	0.333547i	0.946102	+	0.323868i	$0.104983\pi$
$968$		0			0
$969$	−146.401	+	278.787i	−0.151084	+	0.287706i
$970$		0			0
$971$			1250.51i			1.28786i	0.765086	+	0.643928i	$0.222696\pi$
$971$			1250.51i			1.28786i	−0.765086	+	0.643928i	$0.777304\pi$
$972$		0			0
$973$	453.766			0.466358
$974$		0			0
$975$		0			0
$976$		0			0
$977$	1259.23	+	727.019i	1.28888	+	0.744134i	0.978454	−	0.206464i	$-0.0661955\pi$
$977$	1259.23	+	727.019i	1.28888	+	0.744134i	0.310424	+	0.950598i	$0.399529\pi$
$978$		0			0
$979$	35.9560	+	62.2775i	0.0367272	+	0.0636134i
$980$		0			0
$981$	283.783	+	411.536i	0.289279	+	0.419507i
$982$		0			0
$983$	1061.17	−	612.665i	1.07952	−	0.623261i	0.148752	−	0.988874i	$-0.452474\pi$
$983$	1061.17	−	612.665i	1.07952	−	0.623261i	0.930767	+	0.365614i	$0.119141\pi$
$984$		0			0
$985$		0			0
$986$		0			0
$987$	307.011	+	485.747i	0.311055	+	0.492145i
$988$		0			0
$989$			1212.79i			1.22628i
$990$		0			0
$991$	847.879			0.855579			0.427790	−	0.903878i	$-0.359292\pi$
$991$	847.879			0.855579			0.427790	+	0.903878i	$0.359292\pi$
$992$		0			0
$993$	15.8480	+	395.526i	0.0159597	+	0.398314i
$994$		0			0
$995$		0			0
$996$		0			0
$997$	589.869	+	1021.68i	0.591644	+	1.02476i	0.994011	+	0.109279i	$0.0348543\pi$
$997$	589.869	+	1021.68i	0.591644	+	1.02476i	−0.402367	+	0.915479i	$0.631812\pi$
$998$		0			0
$999$	161.520	+	1337.96i	0.161682	+	1.33930i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	900.3.p.c.401.2		12
3.2	odd	2		2700.3.p.c.2501.2		12
5.2	odd	4		900.3.u.c.149.3		24
5.3	odd	4		900.3.u.c.149.10		24
5.4	even	2		180.3.o.b.41.5	✓	12
9.2	odd	6	inner	900.3.p.c.101.2		12
9.7	even	3		2700.3.p.c.1601.2		12
15.2	even	4		2700.3.u.c.449.9		24
15.8	even	4		2700.3.u.c.449.4		24
15.14	odd	2		540.3.o.b.341.3		12
20.19	odd	2		720.3.bs.b.401.2		12
45.2	even	12		900.3.u.c.749.10		24
45.4	even	6		1620.3.g.b.161.2		12
45.7	odd	12		2700.3.u.c.2249.4		24
45.14	odd	6		1620.3.g.b.161.8		12
45.29	odd	6		180.3.o.b.101.5	yes	12
45.34	even	6		540.3.o.b.521.3		12
45.38	even	12		900.3.u.c.749.3		24
45.43	odd	12		2700.3.u.c.2249.9		24
60.59	even	2		2160.3.bs.b.881.1		12
180.79	odd	6		2160.3.bs.b.1601.1		12
180.119	even	6		720.3.bs.b.641.2		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
180.3.o.b.41.5	✓	12	5.4	even	2
180.3.o.b.101.5	yes	12	45.29	odd	6
540.3.o.b.341.3		12	15.14	odd	2
540.3.o.b.521.3		12	45.34	even	6
720.3.bs.b.401.2		12	20.19	odd	2
720.3.bs.b.641.2		12	180.119	even	6
900.3.p.c.101.2		12	9.2	odd	6	inner
900.3.p.c.401.2		12	1.1	even	1	trivial
900.3.u.c.149.3		24	5.2	odd	4
900.3.u.c.149.10		24	5.3	odd	4
900.3.u.c.749.3		24	45.38	even	12
900.3.u.c.749.10		24	45.2	even	12
1620.3.g.b.161.2		12	45.4	even	6
1620.3.g.b.161.8		12	45.14	odd	6
2160.3.bs.b.881.1		12	60.59	even	2
2160.3.bs.b.1601.1		12	180.79	odd	6
2700.3.p.c.1601.2		12	9.7	even	3
2700.3.p.c.2501.2		12	3.2	odd	2
2700.3.u.c.449.4		24	15.8	even	4
2700.3.u.c.449.9		24	15.2	even	4
2700.3.u.c.2249.4		24	45.7	odd	12
2700.3.u.c.2249.9		24	45.43	odd	12

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:	\( N \)	\(=\)	\( 900 = 2^{2} \cdot 3^{2} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	900.p (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-2.65605 - 1.39478i) q^{3} +(-1.41583 - 2.45229i) q^{7} +(5.10917 + 7.40921i) q^{9} +O(q^{10})\)	\(q+(-2.65605 - 1.39478i) q^{3} +(-1.41583 - 2.45229i) q^{7} +(5.10917 + 7.40921i) q^{9} +(-0.949152 + 0.547993i) q^{11} +(-2.09634 + 3.63097i) q^{13} -7.85770i q^{17} +13.3580 q^{19} +(0.340105 + 8.48818i) q^{21} +(21.4218 + 12.3679i) q^{23} +(-3.23598 - 26.8054i) q^{27} +(-2.43628 + 1.40659i) q^{29} +(12.0630 - 20.8937i) q^{31} +(3.28532 - 0.131636i) q^{33} -49.9138 q^{37} +(10.6324 - 6.72010i) q^{39} +(-18.9104 - 10.9179i) q^{41} +(24.5149 + 42.4611i) q^{43} +(58.5815 - 33.8220i) q^{47} +(20.4908 - 35.4912i) q^{49} +(-10.9598 + 20.8704i) q^{51} +49.8418i q^{53} +(-35.4795 - 18.6315i) q^{57} +(-86.8838 - 50.1624i) q^{59} +(-41.5597 - 71.9835i) q^{61} +(10.9358 - 23.0194i) q^{63} +(28.7754 - 49.8405i) q^{67} +(-39.6468 - 62.7284i) q^{69} -14.2317i q^{71} -71.5532 q^{73} +(2.68768 + 1.55173i) q^{77} +(-54.4107 - 94.2421i) q^{79} +(-28.7927 + 75.7098i) q^{81} +(69.7793 - 40.2871i) q^{83} +(8.43276 - 0.337884i) q^{87} -65.6139i q^{89} +11.8723 q^{91} +(-61.1820 + 38.6694i) q^{93} +(-77.4238 - 134.102i) q^{97} +(-8.90957 - 4.23267i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 2 q^{3} + 6 q^{7} + 26 q^{9}+O(q^{10}) \) 12 * q - 2 * q^3 + 6 * q^7 + 26 * q^9	\( 12 q - 2 q^{3} + 6 q^{7} + 26 q^{9} + 48 q^{11} + 30 q^{13} + 72 q^{19} - 128 q^{21} + 78 q^{23} + 106 q^{27} + 150 q^{29} - 12 q^{31} - 96 q^{33} + 12 q^{37} + 40 q^{39} + 90 q^{41} - 114 q^{43} - 12 q^{47} + 48 q^{49} - 144 q^{51} + 158 q^{57} + 48 q^{59} - 78 q^{61} + 212 q^{63} + 168 q^{67} - 150 q^{69} + 24 q^{73} + 258 q^{77} + 120 q^{79} + 434 q^{81} - 114 q^{83} + 330 q^{87} + 120 q^{91} - 82 q^{93} - 96 q^{97} - 120 q^{99}+O(q^{100}) \) 12 * q - 2 * q^3 + 6 * q^7 + 26 * q^9 + 48 * q^11 + 30 * q^13 + 72 * q^19 - 128 * q^21 + 78 * q^23 + 106 * q^27 + 150 * q^29 - 12 * q^31 - 96 * q^33 + 12 * q^37 + 40 * q^39 + 90 * q^41 - 114 * q^43 - 12 * q^47 + 48 * q^49 - 144 * q^51 + 158 * q^57 + 48 * q^59 - 78 * q^61 + 212 * q^63 + 168 * q^67 - 150 * q^69 + 24 * q^73 + 258 * q^77 + 120 * q^79 + 434 * q^81 - 114 * q^83 + 330 * q^87 + 120 * q^91 - 82 * q^93 - 96 * q^97 - 120 * q^99

Introduction

L-functions

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