LMFDB - Embedded newform 273.2.l.b.256.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [273,2,Mod(16,273)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(273, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 2, 2]))

N = Newforms(chi, 2, names="a")

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

chi := DirichletCharacter("273.16");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 273 = 3 \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	273.l (of order $3$, 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:	$2.17991597518$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} + 11 x^{14} - 4 x^{13} + 87 x^{12} - 35 x^{11} + 326 x^{10} - 205 x^{9} + 895 x^{8} - 481 x^{7} + \cdots + 1 $ x^16 + 11x^14 - 4x^13 + 87x^12 - 35x^11 + 326x^10 - 205x^9 + 895x^8 - 481x^7 + 1005x^6 - 544x^5 + 811x^4 - 312x^3 + 195x^2 + 13x + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			256.1
Root			$1.21707 - 2.10803i$ of defining polynomial
Character	$\chi$	$=$	273.256
Dual form			273.2.l.b.16.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.43414 q^{2} +(0.500000 + 0.866025i) q^{3} +3.92506 q^{4} +(-0.613891 - 1.06329i) q^{5} +(-1.21707 - 2.10803i) q^{6} +(2.20121 - 1.46788i) q^{7} -4.68588 q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})$	\(q-2.43414 q^{2} +(0.500000 + 0.866025i) q^{3} +3.92506 q^{4} +(-0.613891 - 1.06329i) q^{5} +(-1.21707 - 2.10803i) q^{6} +(2.20121 - 1.46788i) q^{7} -4.68588 q^{8} +(-0.500000 + 0.866025i) q^{9} +(1.49430 + 2.58820i) q^{10} +(-1.74628 - 3.02464i) q^{11} +(1.96253 + 3.39920i) q^{12} +(-2.87580 - 2.17480i) q^{13} +(-5.35806 + 3.57304i) q^{14} +(0.613891 - 1.06329i) q^{15} +3.55599 q^{16} +4.52705 q^{17} +(1.21707 - 2.10803i) q^{18} +(-0.677706 + 1.17382i) q^{19} +(-2.40956 - 4.17348i) q^{20} +(2.37183 + 1.17236i) q^{21} +(4.25069 + 7.36241i) q^{22} -0.673327 q^{23} +(-2.34294 - 4.05809i) q^{24} +(1.74628 - 3.02464i) q^{25} +(7.00012 + 5.29378i) q^{26} -1.00000 q^{27} +(8.63988 - 5.76153i) q^{28} +(2.64824 - 4.58688i) q^{29} +(-1.49430 + 2.58820i) q^{30} +(4.99846 - 8.65759i) q^{31} +0.715973 q^{32} +(1.74628 - 3.02464i) q^{33} -11.0195 q^{34} +(-2.91209 - 1.43940i) q^{35} +(-1.96253 + 3.39920i) q^{36} -3.08236 q^{37} +(1.64963 - 2.85725i) q^{38} +(0.445532 - 3.57792i) q^{39} +(2.87662 + 4.98245i) q^{40} +(3.61102 - 6.25447i) q^{41} +(-5.77337 - 2.85370i) q^{42} +(4.48886 + 7.77494i) q^{43} +(-6.85424 - 11.8719i) q^{44} +1.22778 q^{45} +1.63898 q^{46} +(2.58008 + 4.46883i) q^{47} +(1.77799 + 3.07957i) q^{48} +(2.69064 - 6.46223i) q^{49} +(-4.25069 + 7.36241i) q^{50} +(2.26353 + 3.92054i) q^{51} +(-11.2877 - 8.53623i) q^{52} +(-4.95271 + 8.57835i) q^{53} +2.43414 q^{54} +(-2.14405 + 3.71360i) q^{55} +(-10.3146 + 6.87832i) q^{56} -1.35541 q^{57} +(-6.44620 + 11.1651i) q^{58} +0.803443 q^{59} +(2.40956 - 4.17348i) q^{60} +(-2.32487 + 4.02680i) q^{61} +(-12.1670 + 21.0738i) q^{62} +(0.170619 + 2.64024i) q^{63} -8.85475 q^{64} +(-0.547016 + 4.39290i) q^{65} +(-4.25069 + 7.36241i) q^{66} +(1.06068 + 1.83715i) q^{67} +17.7690 q^{68} +(-0.336664 - 0.583119i) q^{69} +(7.08845 + 3.50372i) q^{70} +(-2.52793 - 4.37850i) q^{71} +(2.34294 - 4.05809i) q^{72} +(-6.04227 + 10.4655i) q^{73} +7.50291 q^{74} +3.49255 q^{75} +(-2.66004 + 4.60732i) q^{76} +(-8.28373 - 4.09453i) q^{77} +(-1.08449 + 8.70917i) q^{78} +(-5.90140 - 10.2215i) q^{79} +(-2.18299 - 3.78105i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(-8.78975 + 15.2243i) q^{82} +12.6805 q^{83} +(9.30957 + 4.60159i) q^{84} +(-2.77912 - 4.81357i) q^{85} +(-10.9265 - 18.9253i) q^{86} +5.29648 q^{87} +(8.18284 + 14.1731i) q^{88} -3.10466 q^{89} -2.98860 q^{90} +(-9.52259 - 0.565851i) q^{91} -2.64285 q^{92} +9.99692 q^{93} +(-6.28029 - 10.8778i) q^{94} +1.66415 q^{95} +(0.357986 + 0.620050i) q^{96} +(-3.59585 - 6.22820i) q^{97} +(-6.54941 + 15.7300i) q^{98} +3.49255 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 8 q^{3} + 12 q^{4} + q^{7} + 12 q^{8} - 8 q^{9}+O(q^{10}) $ 16 * q + 8 * q^3 + 12 * q^4 + q^7 + 12 * q^8 - 8 * q^9	\( 16 q + 8 q^{3} + 12 q^{4} + q^{7} + 12 q^{8} - 8 q^{9} - 4 q^{10} - 2 q^{11} + 6 q^{12} + 5 q^{13} - 7 q^{14} + 12 q^{16} + 4 q^{17} - 11 q^{19} - 20 q^{20} - q^{21} + 7 q^{22} - 8 q^{23} + 6 q^{24} + 2 q^{25} + 33 q^{26} - 16 q^{27} - q^{28} + 15 q^{29} + 4 q^{30} + 3 q^{31} - 6 q^{32} + 2 q^{33} - 68 q^{34} - 6 q^{36} - 8 q^{37} + 2 q^{38} + 4 q^{39} - 25 q^{40} + 19 q^{41} - 17 q^{42} + 11 q^{43} - 16 q^{44} - 4 q^{46} + 5 q^{47} + 6 q^{48} + 7 q^{49} - 7 q^{50} + 2 q^{51} - 18 q^{52} + 36 q^{53} - 15 q^{55} - 51 q^{56} - 22 q^{57} + 20 q^{58} + 34 q^{59} + 20 q^{60} - 22 q^{61} - 6 q^{62} - 2 q^{63} - 20 q^{64} - 24 q^{65} - 7 q^{66} + 26 q^{67} - 10 q^{68} - 4 q^{69} + 46 q^{70} + 9 q^{71} - 6 q^{72} - 6 q^{73} - 30 q^{74} + 4 q^{75} - 16 q^{76} - 36 q^{77} + 6 q^{78} + 16 q^{79} - 28 q^{80} - 8 q^{81} - q^{82} + 36 q^{83} - 8 q^{84} - 4 q^{85} + 16 q^{86} + 30 q^{87} + 24 q^{88} - 40 q^{89} + 8 q^{90} - 10 q^{91} - 94 q^{92} + 6 q^{93} - 20 q^{94} - 3 q^{96} + 7 q^{97} + 18 q^{98} + 4 q^{99}+O(q^{100}) \) 16 * q + 8 * q^3 + 12 * q^4 + q^7 + 12 * q^8 - 8 * q^9 - 4 * q^10 - 2 * q^11 + 6 * q^12 + 5 * q^13 - 7 * q^14 + 12 * q^16 + 4 * q^17 - 11 * q^19 - 20 * q^20 - q^21 + 7 * q^22 - 8 * q^23 + 6 * q^24 + 2 * q^25 + 33 * q^26 - 16 * q^27 - q^28 + 15 * q^29 + 4 * q^30 + 3 * q^31 - 6 * q^32 + 2 * q^33 - 68 * q^34 - 6 * q^36 - 8 * q^37 + 2 * q^38 + 4 * q^39 - 25 * q^40 + 19 * q^41 - 17 * q^42 + 11 * q^43 - 16 * q^44 - 4 * q^46 + 5 * q^47 + 6 * q^48 + 7 * q^49 - 7 * q^50 + 2 * q^51 - 18 * q^52 + 36 * q^53 - 15 * q^55 - 51 * q^56 - 22 * q^57 + 20 * q^58 + 34 * q^59 + 20 * q^60 - 22 * q^61 - 6 * q^62 - 2 * q^63 - 20 * q^64 - 24 * q^65 - 7 * q^66 + 26 * q^67 - 10 * q^68 - 4 * q^69 + 46 * q^70 + 9 * q^71 - 6 * q^72 - 6 * q^73 - 30 * q^74 + 4 * q^75 - 16 * q^76 - 36 * q^77 + 6 * q^78 + 16 * q^79 - 28 * q^80 - 8 * q^81 - q^82 + 36 * q^83 - 8 * q^84 - 4 * q^85 + 16 * q^86 + 30 * q^87 + 24 * q^88 - 40 * q^89 + 8 * q^90 - 10 * q^91 - 94 * q^92 + 6 * q^93 - 20 * q^94 - 3 * q^96 + 7 * q^97 + 18 * q^98 + 4 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/273\mathbb{Z}\right)^\times$.

$n$	$92$	$106$	$157$
$\chi(n)$	$1$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{2}{3}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−2.43414			−1.72120			−0.860600	−	0.509281i	$-0.829911\pi$
$2$	−2.43414			−1.72120			−0.860600	+	0.509281i	$0.829911\pi$
$3$	0.500000	+	0.866025i	0.288675	+	0.500000i
$3$	0.500000	+	0.866025i	0.288675	+	0.500000i
$4$	3.92506			1.96253
$5$	−0.613891	−	1.06329i	−0.274540	−	0.475518i	0.695479	−	0.718547i	$-0.255192\pi$
$5$	−0.613891	−	1.06329i	−0.274540	−	0.475518i	−0.970019	+	0.243029i	$0.921859\pi$
$6$	−1.21707	−	2.10803i	−0.496868	−	0.860600i
$7$	2.20121	−	1.46788i	0.831979	−	0.554807i
$7$	2.20121	−	1.46788i	0.831979	−	0.554807i
$8$	−4.68588			−1.65671
$9$	−0.500000	+	0.866025i	−0.166667	+	0.288675i
$10$	1.49430	+	2.58820i	0.472539	+	0.818462i
$11$	−1.74628	−	3.02464i	−0.526522	−	0.911963i	−0.999522	−	0.0309005i	$-0.990162\pi$
$11$	−1.74628	−	3.02464i	−0.526522	−	0.911963i	0.473001	−	0.881062i	$-0.343171\pi$
$12$	1.96253	+	3.39920i	0.566534	+	0.981265i
$13$	−2.87580	−	2.17480i	−0.797604	−	0.603181i
$13$	−2.87580	−	2.17480i	−0.797604	−	0.603181i
$14$	−5.35806	+	3.57304i	−1.43200	+	0.954935i
$15$	0.613891	−	1.06329i	0.158506	−	0.274540i
$16$	3.55599			0.888997
$17$	4.52705			1.09797			0.548986	−	0.835832i	$-0.315014\pi$
$17$	4.52705			1.09797			0.548986	+	0.835832i	$0.315014\pi$
$18$	1.21707	−	2.10803i	0.286867	−	0.496868i
$19$	−0.677706	+	1.17382i	−0.155476	+	0.269293i	−0.933232	−	0.359273i	$-0.883025\pi$
$19$	−0.677706	+	1.17382i	−0.155476	+	0.269293i	0.777756	+	0.628566i	$0.216358\pi$
$20$	−2.40956	−	4.17348i	−0.538794	−	0.933219i
$21$	2.37183	+	1.17236i	0.517575	+	0.255830i
$22$	4.25069	+	7.36241i	0.906250	+	1.56967i
$23$	−0.673327			−0.140398			−0.0701992	−	0.997533i	$-0.522364\pi$
$23$	−0.673327			−0.140398			−0.0701992	+	0.997533i	$0.522364\pi$
$24$	−2.34294	−	4.05809i	−0.478251	−	0.828354i
$25$	1.74628	−	3.02464i	0.349255	−	0.604928i
$26$	7.00012	+	5.29378i	1.37284	+	1.03820i
$27$	−1.00000			−0.192450
$28$	8.63988	−	5.76153i	1.63278	−	1.08883i
$29$	2.64824	−	4.58688i	0.491766	−	0.851763i	−0.508189	−	0.861245i	$-0.669685\pi$
$29$	2.64824	−	4.58688i	0.491766	−	0.851763i	0.999955	+	0.00948238i	$0.00301838\pi$
$30$	−1.49430	+	2.58820i	−0.272821	+	0.472539i
$31$	4.99846	−	8.65759i	0.897750	−	1.55495i	0.0673864	−	0.997727i	$-0.478534\pi$
$31$	4.99846	−	8.65759i	0.897750	−	1.55495i	0.830364	−	0.557222i	$-0.188133\pi$
$32$	0.715973			0.126567
$33$	1.74628	−	3.02464i	0.303988	−	0.526522i
$34$	−11.0195			−1.88983
$35$	−2.91209	−	1.43940i	−0.492233	−	0.243304i
$36$	−1.96253	+	3.39920i	−0.327088	+	0.566534i
$37$	−3.08236			−0.506737			−0.253368	−	0.967370i	$-0.581538\pi$
$37$	−3.08236			−0.506737			−0.253368	+	0.967370i	$0.581538\pi$
$38$	1.64963	−	2.85725i	0.267606	−	0.463507i
$39$	0.445532	−	3.57792i	0.0713421	−	0.572926i
$40$	2.87662	+	4.98245i	0.454834	+	0.787795i
$41$	3.61102	−	6.25447i	0.563947	−	0.976784i	−0.433200	−	0.901298i	$-0.642616\pi$
$41$	3.61102	−	6.25447i	0.563947	−	0.976784i	0.997147	−	0.0754865i	$-0.0240510\pi$
$42$	−5.77337	−	2.85370i	−0.890851	−	0.440335i
$43$	4.48886	+	7.77494i	0.684545	+	1.18567i	0.973579	+	0.228348i	$0.0733325\pi$
$43$	4.48886	+	7.77494i	0.684545	+	1.18567i	−0.289034	+	0.957319i	$0.593334\pi$
$44$	−6.85424	−	11.8719i	−1.03332	−	1.78975i
$45$	1.22778			0.183027
$46$	1.63898			0.241654
$47$	2.58008	+	4.46883i	0.376344	+	0.651846i	0.990527	−	0.137317i	$-0.0438479\pi$
$47$	2.58008	+	4.46883i	0.376344	+	0.651846i	−0.614184	+	0.789163i	$0.710515\pi$
$48$	1.77799	+	3.07957i	0.256631	+	0.444498i
$49$	2.69064	−	6.46223i	0.384377	−	0.923176i
$50$	−4.25069	+	7.36241i	−0.601138	+	1.04120i
$51$	2.26353	+	3.92054i	0.316957	+	0.548986i
$52$	−11.2877	−	8.53623i	−1.56532	−	1.18376i
$53$	−4.95271	+	8.57835i	−0.680308	+	1.17833i	0.294579	+	0.955627i	$0.404820\pi$
$53$	−4.95271	+	8.57835i	−0.680308	+	1.17833i	−0.974887	+	0.222700i	$0.928513\pi$
$54$	2.43414			0.331245
$55$	−2.14405	+	3.71360i	−0.289103	+	0.500741i
$56$	−10.3146	+	6.87832i	−1.37835	+	0.919154i
$57$	−1.35541			−0.179529
$58$	−6.44620	+	11.1651i	−0.846427	+	1.46605i
$59$	0.803443			0.104599			0.0522997	−	0.998631i	$-0.483345\pi$
$59$	0.803443			0.104599			0.0522997	+	0.998631i	$0.483345\pi$
$60$	2.40956	−	4.17348i	0.311073	−	0.538794i
$61$	−2.32487	+	4.02680i	−0.297669	+	0.515579i	−0.975602	−	0.219545i	$-0.929543\pi$
$61$	−2.32487	+	4.02680i	−0.297669	+	0.515579i	0.677933	+	0.735124i	$0.262876\pi$
$62$	−12.1670	+	21.0738i	−1.54521	+	2.67638i
$63$	0.170619	+	2.64024i	0.0214960	+	0.332639i
$64$	−8.85475			−1.10684
$65$	−0.547016	+	4.39290i	−0.0678490	+	0.544873i
$66$	−4.25069	+	7.36241i	−0.523223	+	0.906250i
$67$	1.06068	+	1.83715i	0.129583	+	0.224444i	0.923515	−	0.383563i	$-0.125303\pi$
$67$	1.06068	+	1.83715i	0.129583	+	0.224444i	−0.793932	+	0.608006i	$0.791970\pi$
$68$	17.7690			2.15480
$69$	−0.336664	−	0.583119i	−0.0405295	−	0.0701992i
$70$	7.08845	+	3.50372i	0.847231	+	0.418775i
$71$	−2.52793	−	4.37850i	−0.300010	−	0.519632i	0.676128	−	0.736784i	$-0.263657\pi$
$71$	−2.52793	−	4.37850i	−0.300010	−	0.519632i	−0.976138	+	0.217152i	$0.930323\pi$
$72$	2.34294	−	4.05809i	0.276118	−	0.478251i
$73$	−6.04227	+	10.4655i	−0.707194	+	1.22490i	0.258699	+	0.965958i	$0.416706\pi$
$73$	−6.04227	+	10.4655i	−0.707194	+	1.22490i	−0.965894	+	0.258939i	$0.916627\pi$
$74$	7.50291			0.872195
$75$	3.49255			0.403285
$76$	−2.66004	+	4.60732i	−0.305127	+	0.528496i
$77$	−8.28373	−	4.09453i	−0.944019	−	0.466615i
$78$	−1.08449	+	8.70917i	−0.122794	+	0.986120i
$79$	−5.90140	−	10.2215i	−0.663960	−	1.15001i	−0.979566	−	0.201122i	$-0.935541\pi$
$79$	−5.90140	−	10.2215i	−0.663960	−	1.15001i	0.315607	−	0.948890i	$-0.397792\pi$
$80$	−2.18299	−	3.78105i	−0.244066	−	0.422734i
$81$	−0.500000	−	0.866025i	−0.0555556	−	0.0962250i
$82$	−8.78975	+	15.2243i	−0.970665	+	1.68124i
$83$	12.6805			1.39187			0.695935	−	0.718105i	$-0.254990\pi$
$83$	12.6805			1.39187			0.695935	+	0.718105i	$0.254990\pi$
$84$	9.30957	+	4.60159i	1.01576	+	0.502075i
$85$	−2.77912	−	4.81357i	−0.301438	−	0.522105i
$86$	−10.9265	−	18.9253i	−1.17824	−	2.04077i
$87$	5.29648			0.567842
$88$	8.18284	+	14.1731i	0.872293	+	1.51086i
$89$	−3.10466			−0.329093			−0.164546	−	0.986369i	$-0.552616\pi$
$89$	−3.10466			−0.329093			−0.164546	+	0.986369i	$0.552616\pi$
$90$	−2.98860			−0.315026
$91$	−9.52259	−	0.565851i	−0.998239	−	0.0593173i
$92$	−2.64285			−0.275536
$93$	9.99692			1.03663
$94$	−6.28029	−	10.8778i	−0.647763	−	1.12196i
$95$	1.66415			0.170738
$96$	0.357986	+	0.620050i	0.0365368	+	0.0632836i
$97$	−3.59585	−	6.22820i	−0.365104	−	0.632378i	0.623689	−	0.781672i	$-0.285633\pi$
$97$	−3.59585	−	6.22820i	−0.365104	−	0.632378i	−0.988793	+	0.149294i	$0.952300\pi$
$98$	−6.54941	+	15.7300i	−0.661590	+	1.58897i
$99$	3.49255			0.351015
$100$	6.85424	−	11.8719i	0.685424	−	1.18719i
$101$	0.772886	+	1.33868i	0.0769050	+	0.133203i	0.901913	−	0.431918i	$-0.142163\pi$
$101$	0.772886	+	1.33868i	0.0769050	+	0.133203i	−0.825008	+	0.565121i	$0.808830\pi$
$102$	−5.50975	−	9.54317i	−0.545547	−	0.944914i
$103$	−2.75895	−	4.77865i	−0.271848	−	0.470854i	0.697487	−	0.716597i	$-0.254301\pi$
$103$	−2.75895	−	4.77865i	−0.271848	−	0.470854i	−0.969335	+	0.245743i	$0.920968\pi$
$104$	13.4757	+	10.1909i	1.32140	+	0.999296i
$105$	−0.209483	−	3.24164i	−0.0204435	−	0.316352i
$106$	12.0556	−	20.8810i	1.17095	−	2.02814i
$107$	1.44837			0.140020			0.0700098	−	0.997546i	$-0.477697\pi$
$107$	1.44837			0.140020			0.0700098	+	0.997546i	$0.477697\pi$
$108$	−3.92506			−0.377689
$109$	−8.20485	+	14.2112i	−0.785882	+	1.36119i	0.142588	+	0.989782i	$0.454458\pi$
$109$	−8.20485	+	14.2112i	−0.785882	+	1.36119i	−0.928471	+	0.371406i	$0.878876\pi$
$110$	5.21892	−	9.03943i	0.497604	−	0.861876i
$111$	−1.54118	−	2.66940i	−0.146282	−	0.253368i
$112$	7.82747	−	5.21977i	0.739626	−	0.493222i
$113$	5.38049	+	9.31929i	0.506154	+	0.876685i	0.999975	+	0.00712097i	$0.00226669\pi$
$113$	5.38049	+	9.31929i	0.506154	+	0.876685i	−0.493820	+	0.869564i	$0.664400\pi$
$114$	3.29927			0.309005
$115$	0.413350	+	0.715943i	0.0385451	+	0.0667620i
$116$	10.3945	−	18.0038i	0.965105	−	1.67161i
$117$	3.32133	−	1.40312i	0.307057	−	0.129718i
$118$	−1.95570			−0.180036
$119$	9.96499	−	6.64518i	0.913489	−	0.609163i
$120$	−2.87662	+	4.98245i	−0.262598	+	0.454834i
$121$	−0.598956	+	1.03742i	−0.0544505	+	0.0943111i
$122$	5.65908	−	9.80181i	0.512349	−	0.887414i
$123$	7.22204			0.651189
$124$	19.6193	−	33.9816i	1.76186	−	3.05164i
$125$	−10.4270			−0.932619
$126$	−0.415312	−	6.42674i	−0.0369989	−	0.572539i
$127$	8.24568	−	14.2819i	0.731686	−	1.26732i	−0.224476	−	0.974480i	$-0.572067\pi$
$127$	8.24568	−	14.2819i	0.731686	−	1.26732i	0.956162	−	0.292838i	$-0.0945996\pi$
$128$	20.1218			1.77853
$129$	−4.48886	+	7.77494i	−0.395222	+	0.684545i
$130$	1.33152	−	10.6930i	0.116782	−	0.937835i
$131$	3.52172	+	6.09979i	0.307694	+	0.532942i	0.977857	−	0.209272i	$-0.0671094\pi$
$131$	3.52172	+	6.09979i	0.307694	+	0.532942i	−0.670164	+	0.742213i	$0.733776\pi$
$132$	6.85424	−	11.8719i	0.596585	−	1.03332i
$133$	0.231259	+	3.57862i	0.0200527	+	0.310306i
$134$	−2.58185	−	4.47189i	−0.223038	−	0.386312i
$135$	0.613891	+	1.06329i	0.0528353	+	0.0915135i
$136$	−21.2132			−1.81902
$137$	−19.3213			−1.65073			−0.825365	−	0.564600i	$-0.809031\pi$
$137$	−19.3213			−1.65073			−0.825365	+	0.564600i	$0.809031\pi$
$138$	0.819488	+	1.41940i	0.0697595	+	0.120827i
$139$	7.76176	+	13.4438i	0.658343	+	1.14028i	0.981044	+	0.193783i	$0.0620759\pi$
$139$	7.76176	+	13.4438i	0.658343	+	1.14028i	−0.322701	+	0.946501i	$0.604591\pi$
$140$	−11.4301	−	5.64975i	−0.966022	−	0.477491i
$141$	−2.58008	+	4.46883i	−0.217282	+	0.376344i
$142$	6.15334	+	10.6579i	0.516377	+	0.894392i
$143$	−1.55604	+	12.4961i	−0.130123	+	1.04497i
$144$	−1.77799	+	3.07957i	−0.148166	+	0.256631i
$145$	−6.50292			−0.540038
$146$	14.7078	−	25.4746i	1.21722	−	2.10829i
$147$	6.94178	−	0.900953i	0.572548	−	0.0743093i
$148$	−12.0984			−0.994486
$149$	−8.76659	+	15.1842i	−0.718187	+	1.24394i	0.243530	+	0.969893i	$0.421694\pi$
$149$	−8.76659	+	15.1842i	−0.718187	+	1.24394i	−0.961717	+	0.274043i	$0.911639\pi$
$150$	−8.50138			−0.694134
$151$	−7.01950	+	12.1581i	−0.571239	+	0.989415i	0.425200	+	0.905099i	$0.360204\pi$
$151$	−7.01950	+	12.1581i	−0.571239	+	0.989415i	−0.996439	+	0.0843154i	$0.973130\pi$
$152$	3.17565	−	5.50038i	0.257579	−	0.446140i
$153$	−2.26353	+	3.92054i	−0.182995	+	0.316957i
$154$	20.1638	+	9.96669i	1.62485	+	0.803138i
$155$	−12.2740			−0.985875
$156$	1.74874	−	14.0436i	0.140011	−	1.12438i
$157$	5.62295	−	9.73923i	0.448760	−	0.777275i	−0.549545	−	0.835464i	$-0.685199\pi$
$157$	5.62295	−	9.73923i	0.448760	−	0.777275i	0.998306	+	0.0581884i	$0.0185324\pi$
$158$	14.3649	+	24.8807i	1.14281	+	1.97940i
$159$	−9.90543			−0.785551
$160$	−0.439529	−	0.761287i	−0.0347478	−	0.0601850i
$161$	−1.48213	+	0.988365i	−0.116809	+	0.0778941i
$162$	1.21707	+	2.10803i	0.0956222	+	0.165623i
$163$	−5.80397	+	10.0528i	−0.454602	+	0.787394i	−0.998665	−	0.0516501i	$-0.983552\pi$
$163$	−5.80397	+	10.0528i	−0.454602	+	0.787394i	0.544063	+	0.839044i	$0.316885\pi$
$164$	14.1735	−	24.5492i	1.10676	−	1.91697i
$165$	−4.28809			−0.333827
$166$	−30.8662			−2.39569
$167$	3.44594	−	5.96855i	0.266655	−	0.461860i	−0.701341	−	0.712826i	$-0.747415\pi$
$167$	3.44594	−	5.96855i	0.266655	−	0.461860i	0.967996	+	0.250966i	$0.0807482\pi$
$168$	−11.1141	−	5.49354i	−0.857471	−	0.423836i
$169$	3.54048	+	12.5086i	0.272345	+	0.962200i
$170$	6.76477	+	11.7169i	0.518834	+	0.898648i
$171$	−0.677706	−	1.17382i	−0.0518255	−	0.0897644i
$172$	17.6191	+	30.5171i	1.34344	+	2.32691i
$173$	7.91930	−	13.7166i	0.602093	−	1.04286i	−0.390411	−	0.920641i	$-0.627667\pi$
$173$	7.91930	−	13.7166i	0.602093	−	1.04286i	0.992504	−	0.122215i	$-0.0389997\pi$
$174$	−12.8924			−0.977370
$175$	−0.595896	−	9.22119i	−0.0450455	−	0.697056i
$176$	−6.20973	−	10.7556i	−0.468076	−	0.810732i
$177$	0.401721	+	0.695802i	0.0301952	+	0.0522997i
$178$	7.55718			0.566435
$179$	−10.5515	−	18.2758i	−0.788658	−	1.36600i	−0.926789	−	0.375582i	$-0.877443\pi$
$179$	−10.5515	−	18.2758i	−0.788658	−	1.36600i	0.138131	−	0.990414i	$-0.455891\pi$
$180$	4.81912			0.359196
$181$	15.0685			1.12003			0.560015	−	0.828483i	$-0.310796\pi$
$181$	15.0685			1.12003			0.560015	+	0.828483i	$0.310796\pi$
$182$	23.1794	+	1.37736i	1.71817	+	0.102097i
$183$	−4.64974			−0.343719
$184$	3.15513			0.232599
$185$	1.89223	+	3.27744i	0.139120	+	0.240962i
$186$	−24.3340			−1.78425
$187$	−7.90548	−	13.6927i	−0.578106	−	1.00131i
$188$	10.1270	+	17.5404i	0.738586	+	1.27927i
$189$	−2.20121	+	1.46788i	−0.160114	+	0.106773i
$190$	−4.05078			−0.293875
$191$	4.74903	−	8.22556i	0.343628	−	0.595180i	−0.641476	−	0.767143i	$-0.721678\pi$
$191$	4.74903	−	8.22556i	0.343628	−	0.595180i	0.985103	+	0.171963i	$0.0550109\pi$
$192$	−4.42738	−	7.66844i	−0.319518	−	0.553422i
$193$	9.27175	+	16.0591i	0.667395	+	1.15596i	0.978630	+	0.205629i	$0.0659241\pi$
$193$	9.27175	+	16.0591i	0.667395	+	1.15596i	−0.311235	+	0.950333i	$0.600743\pi$
$194$	8.75283	+	15.1603i	0.628416	+	1.08845i
$195$	−4.07787	+	1.72272i	−0.292023	+	0.123367i
$196$	10.5609	−	25.3647i	0.754352	−	1.81176i
$197$	−12.8786	+	22.3065i	−0.917565	+	1.58927i	−0.114463	+	0.993427i	$0.536515\pi$
$197$	−12.8786	+	22.3065i	−0.917565	+	1.58927i	−0.803102	+	0.595842i	$0.796819\pi$
$198$	−8.50138			−0.604166
$199$	17.6956			1.25441			0.627203	−	0.778856i	$-0.284200\pi$
$199$	17.6956			1.25441			0.627203	+	0.778856i	$0.284200\pi$
$200$	−8.18284	+	14.1731i	−0.578614	+	1.00219i
$201$	−1.06068	+	1.83715i	−0.0748145	+	0.129583i
$202$	−1.88132	−	3.25854i	−0.132369	−	0.229270i
$203$	−0.903681	−	13.9840i	−0.0634259	−	0.981484i
$204$	8.88448	+	15.3884i	0.622038	+	1.07740i
$205$	−8.86709			−0.619305
$206$	6.71569	+	11.6319i	0.467905	+	0.810434i
$207$	0.336664	−	0.583119i	0.0233997	−	0.0405295i
$208$	−10.2263	−	7.73356i	−0.709067	−	0.536226i
$209$	4.73385			0.327447
$210$	0.509912	+	7.89063i	0.0351873	+	0.544505i
$211$	−6.23896	+	10.8062i	−0.429508	+	0.743929i	−0.996830	−	0.0795669i	$-0.974646\pi$
$211$	−6.23896	+	10.8062i	−0.429508	+	0.743929i	0.567322	+	0.823496i	$0.307980\pi$
$212$	−19.4397	+	33.6706i	−1.33512	+	2.31250i
$213$	2.52793	−	4.37850i	0.173211	−	0.300010i
$214$	−3.52555			−0.241002
$215$	5.51135	−	9.54593i	0.375871	−	0.651027i
$216$	4.68588			0.318834
$217$	−1.70567	−	26.3943i	−0.115788	−	1.79176i
$218$	19.9718	−	34.5922i	1.35266	−	2.34288i
$219$	−12.0845			−0.816598
$220$	−8.41551	+	14.5761i	−0.567374	+	0.982720i
$221$	−13.0189	−	9.84544i	−0.875746	−	0.662276i
$222$	3.75145	+	6.49771i	0.251781	+	0.436098i
$223$	−4.65232	+	8.05805i	−0.311542	+	0.539607i	−0.978696	−	0.205313i	$-0.934179\pi$
$223$	−4.65232	+	8.05805i	−0.311542	+	0.539607i	0.667154	+	0.744920i	$0.267512\pi$
$224$	1.57601	−	1.05096i	0.105301	−	0.0702205i
$225$	1.74628	+	3.02464i	0.116418	+	0.201643i
$226$	−13.0969	−	22.6845i	−0.871193	−	1.50895i
$227$	9.53301			0.632728			0.316364	−	0.948638i	$-0.397538\pi$
$227$	9.53301			0.632728			0.316364	+	0.948638i	$0.397538\pi$
$228$	−5.32008			−0.352331
$229$	3.22423	+	5.58453i	0.213063	+	0.369036i	0.952672	−	0.304001i	$-0.0983226\pi$
$229$	3.22423	+	5.58453i	0.213063	+	0.369036i	−0.739608	+	0.673037i	$0.764989\pi$
$230$	−1.00615	−	1.74271i	−0.0663438	−	0.114911i
$231$	−0.595896	−	9.22119i	−0.0392071	−	0.606710i
$232$	−12.4093	+	21.4936i	−0.814712	+	1.41112i
$233$	12.2379	+	21.1967i	0.801733	+	1.38864i	0.918475	+	0.395479i	$0.129421\pi$
$233$	12.2379	+	21.1967i	0.801733	+	1.38864i	−0.116742	+	0.993162i	$0.537245\pi$
$234$	−8.08461	+	3.41539i	−0.528507	+	0.223271i
$235$	3.16778	−	5.48675i	0.206643	−	0.357916i
$236$	3.15356			0.205279
$237$	5.90140	−	10.2215i	0.383337	−	0.663960i
$238$	−24.2562	+	16.1753i	−1.57230	+	1.04849i
$239$	3.62130			0.234242			0.117121	−	0.993118i	$-0.462633\pi$
$239$	3.62130			0.234242			0.117121	+	0.993118i	$0.462633\pi$
$240$	2.18299	−	3.78105i	0.140911	−	0.244066i
$241$	25.1298			1.61875			0.809377	−	0.587289i	$-0.199805\pi$
$241$	25.1298			1.61875			0.809377	+	0.587289i	$0.199805\pi$
$242$	1.45795	−	2.52524i	0.0937203	−	0.162328i
$243$	0.500000	−	0.866025i	0.0320750	−	0.0555556i
$244$	−9.12527	+	15.8054i	−0.584185	+	1.01184i
$245$	−8.52299	+	1.10617i	−0.544514	+	0.0706708i
$246$	−17.5795			−1.12083
$247$	4.50178	−	1.90180i	0.286441	−	0.121009i
$248$	−23.4222	+	40.5684i	−1.48731	+	2.57610i
$249$	6.34027	+	10.9817i	0.401798	+	0.695935i
$250$	25.3808			1.60523
$251$	0.280269	+	0.485440i	0.0176904	+	0.0306407i	0.874735	−	0.484601i	$-0.161035\pi$
$251$	0.280269	+	0.485440i	0.0176904	+	0.0306407i	−0.857045	+	0.515242i	$0.827702\pi$
$252$	0.669691	+	10.3631i	0.0421866	+	0.652815i
$253$	1.17581	+	2.03657i	0.0739229	+	0.128038i
$254$	−20.0712	+	34.7643i	−1.25938	+	2.18131i
$255$	2.77912	−	4.81357i	0.174035	−	0.301438i
$256$	−31.2699			−1.95437
$257$	−23.7587			−1.48203			−0.741013	−	0.671490i	$-0.765655\pi$
$257$	−23.7587			−1.48203			−0.741013	+	0.671490i	$0.765655\pi$
$258$	10.9265	−	18.9253i	0.680257	−	1.17824i
$259$	−6.78491	+	4.52454i	−0.421594	+	0.281141i
$260$	−2.14707	+	17.2424i	−0.133156	+	1.06933i
$261$	2.64824	+	4.58688i	0.163922	+	0.283921i
$262$	−8.57237	−	14.8478i	−0.529603	−	0.917299i
$263$	3.53761	+	6.12732i	0.218138	+	0.377827i	0.954239	−	0.299046i	$-0.0966683\pi$
$263$	3.53761	+	6.12732i	0.218138	+	0.377827i	−0.736100	+	0.676872i	$0.763335\pi$
$264$	−8.18284	+	14.1731i	−0.503619	+	0.872293i
$265$	12.1617			0.747088
$266$	−0.562919	−	8.71088i	−0.0345148	−	0.534098i
$267$	−1.55233	−	2.68871i	−0.0950009	−	0.164546i
$268$	4.16323	+	7.21093i	0.254310	+	0.440478i
$269$	−10.3884			−0.633394			−0.316697	−	0.948527i	$-0.602574\pi$
$269$	−10.3884			−0.633394			−0.316697	+	0.948527i	$0.602574\pi$
$270$	−1.49430	−	2.58820i	−0.0909402	−	0.157513i
$271$	−0.122772			−0.00745789			−0.00372894	−	0.999993i	$-0.501187\pi$
$271$	−0.122772			−0.00745789			−0.00372894	+	0.999993i	$0.501187\pi$
$272$	16.0981			0.976093
$273$	−4.27126	−	8.52973i	−0.258508	−	0.516243i
$274$	47.0308			2.84124
$275$	−12.1979			−0.735562
$276$	−1.32143	−	2.28878i	−0.0795405	−	0.137768i
$277$	−5.37199			−0.322771			−0.161386	−	0.986891i	$-0.551596\pi$
$277$	−5.37199			−0.322771			−0.161386	+	0.986891i	$0.551596\pi$
$278$	−18.8932	−	32.7240i	−1.13314	−	1.96266i
$279$	4.99846	+	8.65759i	0.299250	+	0.518316i
$280$	13.6457	+	6.74488i	0.815486	+	0.403083i
$281$	−14.8847			−0.887945			−0.443972	−	0.896040i	$-0.646431\pi$
$281$	−14.8847			−0.887945			−0.443972	+	0.896040i	$0.646431\pi$
$282$	6.28029	−	10.8778i	0.373986	−	0.647763i
$283$	−2.24269	−	3.88445i	−0.133314	−	0.230906i	0.791638	−	0.610990i	$-0.209229\pi$
$283$	−2.24269	−	3.88445i	−0.133314	−	0.230906i	−0.924952	+	0.380084i	$0.875895\pi$
$284$	−9.92228	−	17.1859i	−0.588779	−	1.01979i
$285$	0.832075	+	1.44120i	0.0492879	+	0.0853691i
$286$	3.78763	−	30.4172i	0.223967	−	1.79861i
$287$	−1.23222	−	19.0680i	−0.0727356	−	1.12555i
$288$	−0.357986	+	0.620050i	−0.0210945	+	0.0365368i
$289$	3.49420			0.205541
$290$	15.8291			0.929514
$291$	3.59585	−	6.22820i	0.210793	−	0.365104i
$292$	−23.7163	+	41.0778i	−1.38789	+	2.40390i
$293$	−11.0016	−	19.0553i	−0.642719	−	1.11322i	−0.984823	−	0.173560i	$-0.944473\pi$
$293$	−11.0016	−	19.0553i	−0.642719	−	1.11322i	0.342105	−	0.939662i	$-0.388860\pi$
$294$	−16.8973	+	2.19305i	−0.985470	+	0.127901i
$295$	−0.493226	−	0.854293i	−0.0287168	−	0.0497389i
$296$	14.4436			0.839515
$297$	1.74628	+	3.02464i	0.101329	+	0.175507i
$298$	21.3392	−	36.9605i	1.23614	−	2.14106i
$299$	1.93636	+	1.46435i	0.111982	+	0.0846857i
$300$	13.7085			0.791459
$301$	21.2936	+	10.5251i	1.22734	+	0.606659i
$302$	17.0865	−	29.5947i	0.983217	−	1.70298i
$303$	−0.772886	+	1.33868i	−0.0444011	+	0.0769050i
$304$	−2.40991	+	4.17409i	−0.138218	+	0.239401i
$305$	5.70887			0.326889
$306$	5.50975	−	9.54317i	0.314971	−	0.545547i
$307$	32.9959			1.88318			0.941589	−	0.336764i	$-0.109333\pi$
$307$	32.9959			1.88318			0.941589	+	0.336764i	$0.109333\pi$
$308$	−32.5142	−	16.0713i	−1.85267	−	0.915747i
$309$	2.75895	−	4.77865i	0.156951	−	0.271848i
$310$	29.8768			1.69689
$311$	4.11532	−	7.12794i	0.233358	−	0.404188i	−0.725436	−	0.688290i	$-0.758362\pi$
$311$	4.11532	−	7.12794i	0.233358	−	0.404188i	0.958794	+	0.284101i	$0.0916952\pi$
$312$	−2.08771	+	16.7657i	−0.118193	+	0.949171i
$313$	7.14348	+	12.3729i	0.403773	+	0.699356i	0.994178	−	0.107752i	$-0.0343651\pi$
$313$	7.14348	+	12.3729i	0.403773	+	0.699356i	−0.590405	+	0.807107i	$0.701032\pi$
$314$	−13.6871	+	23.7067i	−0.772406	+	1.33785i
$315$	2.70261	−	1.80224i	0.152275	−	0.101545i
$316$	−23.1634	−	40.1201i	−1.30304	−	2.25693i
$317$	4.68195	+	8.10938i	0.262965	+	0.455468i	0.967028	−	0.254669i	$-0.0819664\pi$
$317$	4.68195	+	8.10938i	0.262965	+	0.455468i	−0.704064	+	0.710137i	$0.748633\pi$
$318$	24.1112			1.35209
$319$	−18.4982			−1.03570
$320$	5.43585	+	9.41518i	0.303874	+	0.526324i
$321$	0.724187	+	1.25433i	0.0404202	+	0.0700098i
$322$	3.60773	−	2.40582i	0.201051	−	0.134071i
$323$	−3.06801	+	5.31395i	−0.170709	+	0.295676i
$324$	−1.96253	−	3.39920i	−0.109029	−	0.188845i
$325$	−11.5999	+	4.90046i	−0.643448	+	0.271829i
$326$	14.1277	−	24.4699i	0.782462	−	1.35526i
$327$	−16.4097			−0.907459
$328$	−16.9208	+	29.3077i	−0.934295	+	1.61825i
$329$	12.2390	+	6.04958i	0.674759	+	0.333524i
$330$	10.4378			0.574584
$331$	12.2390	−	21.1985i	0.672714	−	1.16517i	−0.304418	−	0.952539i	$-0.598462\pi$
$331$	12.2390	−	21.1985i	0.672714	−	1.16517i	0.977132	−	0.212636i	$-0.0682047\pi$
$332$	49.7719			2.73159
$333$	1.54118	−	2.66940i	0.0844561	−	0.146282i
$334$	−8.38793	+	14.5283i	−0.458967	+	0.794954i
$335$	1.30228	−	2.25562i	0.0711513	−	0.123238i
$336$	8.43419	+	4.16890i	0.460123	+	0.227432i
$337$	−13.1685			−0.717334			−0.358667	−	0.933466i	$-0.616769\pi$
$337$	−13.1685			−0.717334			−0.358667	+	0.933466i	$0.616769\pi$
$338$	−8.61805	−	30.4477i	−0.468760	−	1.65614i
$339$	−5.38049	+	9.31929i	−0.292228	+	0.506154i
$340$	−10.9082	−	18.8936i	−0.591580	−	1.02465i
$341$	−34.9148			−1.89074
$342$	1.64963	+	2.85725i	0.0892020	+	0.154502i
$343$	−3.56314	−	18.1743i	−0.192391	−	0.981318i
$344$	−21.0343	−	36.4324i	−1.13409	−	1.96430i
$345$	−0.413350	+	0.715943i	−0.0222540	+	0.0385451i
$346$	−19.2767	+	33.3882i	−1.03632	+	1.79496i
$347$	14.6733			0.787705			0.393853	−	0.919174i	$-0.371142\pi$
$347$	14.6733			0.787705			0.393853	+	0.919174i	$0.371142\pi$
$348$	20.7890			1.11441
$349$	12.1698	−	21.0787i	0.651433	−	1.12831i	−0.331342	−	0.943511i	$-0.607502\pi$
$349$	12.1698	−	21.0787i	0.651433	−	1.12831i	0.982775	−	0.184804i	$-0.0591652\pi$
$350$	1.45050	+	22.4457i	0.0775324	+	1.19977i
$351$	2.87580	+	2.17480i	0.153499	+	0.116082i
$352$	−1.25029	−	2.16556i	−0.0666404	−	0.115425i
$353$	0.334813	+	0.579912i	0.0178203	+	0.0308656i	0.874798	−	0.484488i	$-0.160994\pi$
$353$	0.334813	+	0.579912i	0.0178203	+	0.0308656i	−0.856978	+	0.515353i	$0.827661\pi$
$354$	−0.977848	−	1.69368i	−0.0519721	−	0.0900182i
$355$	−3.10375	+	5.37585i	−0.164730	+	0.285320i
$356$	−12.1860			−0.645855
$357$	10.7374	+	5.30734i	0.568283	+	0.280894i
$358$	25.6840	+	44.4859i	1.35744	+	2.35115i
$359$	17.8146	+	30.8557i	0.940216	+	1.62850i	0.765058	+	0.643962i	$0.222710\pi$
$359$	17.8146	+	30.8557i	0.940216	+	1.62850i	0.175158	+	0.984540i	$0.443956\pi$
$360$	−5.75324			−0.303222
$361$	8.58143	+	14.8635i	0.451654	+	0.782288i
$362$	−36.6788			−1.92779
$363$	−1.19791			−0.0628741
$364$	−37.3768	−	2.22100i	−1.95908	−	0.116412i
$365$	14.8372			0.776614
$366$	11.3182			0.591609
$367$	−5.11118	−	8.85282i	−0.266801	−	0.462113i	0.701233	−	0.712932i	$-0.252633\pi$
$367$	−5.11118	−	8.85282i	−0.266801	−	0.462113i	−0.968034	+	0.250819i	$0.919300\pi$
$368$	−2.39434			−0.124814
$369$	3.61102	+	6.25447i	0.187982	+	0.325595i
$370$	−4.60597	−	7.97777i	−0.239453	−	0.414745i
$371$	1.69006	+	26.1527i	0.0877433	+	1.35778i
$372$	39.2385			2.03442
$373$	−2.47554	+	4.28776i	−0.128179	+	0.222012i	−0.922971	−	0.384870i	$-0.874246\pi$
$373$	−2.47554	+	4.28776i	−0.128179	+	0.222012i	0.794792	+	0.606881i	$0.207580\pi$
$374$	19.2431	+	33.3300i	0.995036	+	1.72345i
$375$	−5.21350	−	9.03005i	−0.269224	−	0.466310i
$376$	−12.0900	−	20.9404i	−0.623492	−	1.07992i
$377$	−17.5914	+	7.43158i	−0.906002	+	0.382746i
$378$	5.35806	−	3.57304i	0.275589	−	0.183777i
$379$	6.33641	−	10.9750i	0.325479	−	0.563747i	−0.656130	−	0.754648i	$-0.727808\pi$
$379$	6.33641	−	10.9750i	0.325479	−	0.563747i	0.981609	+	0.190901i	$0.0611410\pi$
$380$	6.53189			0.335079
$381$	16.4914			0.844878
$382$	−11.5598	+	20.0222i	−0.591452	+	1.02442i
$383$	11.8951	−	20.6029i	0.607810	−	1.05276i	−0.383790	−	0.923420i	$-0.625381\pi$
$383$	11.8951	−	20.6029i	0.607810	−	1.05276i	0.991601	−	0.129338i	$-0.0412853\pi$
$384$	10.0609	+	17.4260i	0.513418	+	0.889267i
$385$	0.731631	+	11.3216i	0.0372874	+	0.577003i
$386$	−22.5688	−	39.0903i	−1.14872	−	1.98964i
$387$	−8.97773			−0.456363
$388$	−14.1139	−	24.4461i	−0.716527	−	1.24106i
$389$	12.7721	−	22.1218i	0.647569	−	1.12162i	−0.336133	−	0.941815i	$-0.609119\pi$
$389$	12.7721	−	22.1218i	0.647569	−	1.12162i	0.983702	−	0.179808i	$-0.0575475\pi$
$390$	9.92614	−	4.19336i	0.502630	−	0.212339i
$391$	−3.04819			−0.154153
$392$	−12.6080	+	30.2812i	−0.636801	+	1.52943i
$393$	−3.52172	+	6.09979i	−0.177647	+	0.307694i
$394$	31.3485	−	54.2971i	1.57931	−	2.73545i
$395$	−7.24564	+	12.5498i	−0.364568	+	0.631450i
$396$	13.7085			0.688877
$397$	1.06368	−	1.84235i	0.0533846	−	0.0924648i	−0.838098	−	0.545519i	$-0.816332\pi$
$397$	1.06368	−	1.84235i	0.0533846	−	0.0924648i	0.891483	+	0.453055i	$0.149666\pi$
$398$	−43.0736			−2.15908
$399$	−2.98355	+	1.98959i	−0.149364	+	0.0996039i
$400$	6.20973	−	10.7556i	0.310487	−	0.537779i
$401$	0.587289			0.0293278			0.0146639	−	0.999892i	$-0.495332\pi$
$401$	0.587289			0.0293278			0.0146639	+	0.999892i	$0.495332\pi$
$402$	2.58185	−	4.47189i	0.128771	−	0.223038i
$403$	−33.2031	+	14.0269i	−1.65397	+	0.698728i
$404$	3.03362	+	5.25439i	0.150928	+	0.261416i
$405$	−0.613891	+	1.06329i	−0.0305045	+	0.0528353i
$406$	2.19969	+	34.0391i	0.109169	+	1.68933i
$407$	5.38265	+	9.32302i	0.266808	+	0.462125i
$408$	−10.6066	−	18.3712i	−0.525105	−	0.909509i
$409$	−4.34455			−0.214824			−0.107412	−	0.994215i	$-0.534256\pi$
$409$	−4.34455			−0.214824			−0.107412	+	0.994215i	$0.534256\pi$
$410$	21.5838			1.06595
$411$	−9.66065	−	16.7327i	−0.476525	−	0.825365i
$412$	−10.8291	−	18.7565i	−0.533510	−	0.924066i
$413$	1.76855	−	1.17936i	0.0870244	−	0.0580325i
$414$	−0.819488	+	1.41940i	−0.0402756	+	0.0697595i
$415$	−7.78446	−	13.4831i	−0.382124	−	0.661859i
$416$	−2.05900	−	1.55710i	−0.100951	−	0.0763430i
$417$	−7.76176	+	13.4438i	−0.380095	+	0.658343i
$418$	−11.5229			−0.563602
$419$	−4.72818	+	8.18946i	−0.230987	+	0.400081i	−0.958099	−	0.286438i	$-0.907529\pi$
$419$	−4.72818	+	8.18946i	−0.230987	+	0.400081i	0.727112	+	0.686519i	$0.240862\pi$
$420$	−0.822235	−	12.7237i	−0.0401209	−	0.620851i
$421$	−11.9569			−0.582741			−0.291371	−	0.956610i	$-0.594111\pi$
$421$	−11.9569			−0.582741			−0.291371	+	0.956610i	$0.594111\pi$
$422$	15.1865	−	26.3039i	0.739269	−	1.28045i
$423$	−5.16016			−0.250896
$424$	23.2078	−	40.1971i	1.12707	−	1.95214i
$425$	7.90548	−	13.6927i	0.383472	−	0.664193i
$426$	−6.15334	+	10.6579i	−0.298131	+	0.516377i
$427$	0.793336	+	12.2765i	0.0383922	+	0.594100i
$428$	5.68496			0.274793
$429$	−11.5999	+	4.90046i	−0.560050	+	0.236596i
$430$	−13.4154	+	23.2362i	−0.646949	+	1.12055i
$431$	13.2352	+	22.9241i	0.637519	+	1.10422i	0.985975	+	0.166891i	$0.0533726\pi$
$431$	13.2352	+	22.9241i	0.637519	+	1.10422i	−0.348456	+	0.937325i	$0.613294\pi$
$432$	−3.55599			−0.171087
$433$	4.13088	+	7.15489i	0.198517	+	0.343842i	0.948048	−	0.318128i	$-0.103054\pi$
$433$	4.13088	+	7.15489i	0.198517	+	0.343842i	−0.749531	+	0.661970i	$0.769721\pi$
$434$	4.15184	+	64.2476i	0.199295	+	3.08398i
$435$	−3.25146	−	5.63169i	−0.155896	−	0.270019i
$436$	−32.2046	+	55.7799i	−1.54232	+	2.67137i
$437$	0.456318	−	0.790366i	0.0218286	−	0.0378083i
$438$	29.4155			1.40553
$439$	35.1043			1.67544			0.837719	−	0.546102i	$-0.183889\pi$
$439$	35.1043			1.67544			0.837719	+	0.546102i	$0.183889\pi$
$440$	10.0467	−	17.4015i	0.478960	−	0.829582i
$441$	4.25114	+	5.56128i	0.202435	+	0.264823i
$442$	31.6899	+	23.9652i	1.50734	+	1.13991i
$443$	0.192275	+	0.333030i	0.00913525	+	0.0158227i	0.870557	−	0.492068i	$-0.163759\pi$
$443$	0.192275	+	0.333030i	0.00913525	+	0.0158227i	−0.861422	+	0.507890i	$0.830425\pi$
$444$	−6.04922	−	10.4776i	−0.287083	−	0.497243i
$445$	1.90592	+	3.30115i	0.0903493	+	0.156490i
$446$	11.3244	−	19.6145i	0.536227	−	0.928772i
$447$	−17.5332			−0.829291
$448$	−19.4912	+	12.9977i	−0.920871	+	0.614085i
$449$	−18.9728	−	32.8619i	−0.895382	−	1.55085i	−0.833331	−	0.552774i	$-0.813569\pi$
$449$	−18.9728	−	32.8619i	−0.895382	−	1.55085i	−0.0620505	−	0.998073i	$-0.519764\pi$
$450$	−4.25069	−	7.36241i	−0.200379	−	0.347067i
$451$	−25.2233			−1.18772
$452$	21.1188	+	36.5788i	0.993343	+	1.72052i
$453$	−14.0390			−0.659610
$454$	−23.2047			−1.08905
$455$	5.24417	+	10.4727i	0.245851	+	0.490966i
$456$	6.35130			0.297427
$457$	−14.3895			−0.673112			−0.336556	−	0.941663i	$-0.609262\pi$
$457$	−14.3895			−0.673112			−0.336556	+	0.941663i	$0.609262\pi$
$458$	−7.84825	−	13.5936i	−0.366725	−	0.635186i
$459$	−4.52705			−0.211305
$460$	1.62242	+	2.81012i	0.0756459	+	0.131022i
$461$	1.79501	+	3.10905i	0.0836019	+	0.144803i	0.904795	−	0.425848i	$-0.140024\pi$
$461$	1.79501	+	3.10905i	0.0836019	+	0.144803i	−0.821193	+	0.570651i	$0.806691\pi$
$462$	1.45050	+	22.4457i	0.0674833	+	1.04427i
$463$	4.69484			0.218188			0.109094	−	0.994031i	$-0.465205\pi$
$463$	4.69484			0.218188			0.109094	+	0.994031i	$0.465205\pi$
$464$	9.41710	−	16.3109i	0.437178	−	0.757214i
$465$	−6.13702	−	10.6296i	−0.284598	−	0.492937i
$466$	−29.7889	−	51.5958i	−1.37994	−	2.39013i
$467$	20.0343	+	34.7003i	0.927075	+	1.60574i	0.788190	+	0.615432i	$0.211018\pi$
$467$	20.0343	+	34.7003i	0.927075	+	1.60574i	0.138885	+	0.990309i	$0.455648\pi$
$468$	13.0364	−	5.50732i	0.602610	−	0.254576i
$469$	5.03150	+	2.48700i	0.232333	+	0.114839i
$470$	−7.71083	+	13.3556i	−0.355674	+	0.616046i
$471$	11.2459			0.518184
$472$	−3.76484			−0.173291
$473$	15.6776	−	27.1544i	0.720856	−	1.24856i
$474$	−14.3649	+	24.8807i	−0.659800	+	1.14281i
$475$	2.36692	+	4.09963i	0.108602	+	0.188104i
$476$	39.1132	−	26.0827i	1.79275	−	1.19550i
$477$	−4.95271	−	8.57835i	−0.226769	−	0.392776i
$478$	−8.81476			−0.403178
$479$	−10.2350	−	17.7276i	−0.467650	−	0.809993i	0.531667	−	0.846954i	$-0.321566\pi$
$479$	−10.2350	−	17.7276i	−0.467650	−	0.809993i	−0.999317	+	0.0369602i	$0.988233\pi$
$480$	0.439529	−	0.761287i	0.0200617	−	0.0347478i
$481$	8.86425	+	6.70352i	0.404175	+	0.305654i
$482$	−61.1696			−2.78620
$483$	−1.59702	−	0.789383i	−0.0726668	−	0.0359182i
$484$	−2.35094	+	4.07195i	−0.106861	+	0.185088i
$485$	−4.41492	+	7.64687i	−0.200471	+	0.347227i
$486$	−1.21707	+	2.10803i	−0.0552075	+	0.0956222i
$487$	33.5937			1.52228			0.761138	−	0.648590i	$-0.224641\pi$
$487$	33.5937			1.52228			0.761138	+	0.648590i	$0.224641\pi$
$488$	10.8941	−	18.8691i	0.493151	−	0.854163i
$489$	−11.6079			−0.524930
$490$	20.7462	−	2.69259i	0.937218	−	0.121639i
$491$	20.2312	−	35.0415i	0.913021	−	1.58140i	0.103248	−	0.994656i	$-0.467077\pi$
$491$	20.2312	−	35.0415i	0.913021	−	1.58140i	0.809773	−	0.586743i	$-0.199590\pi$
$492$	28.3470			1.27798
$493$	11.9887	−	20.7651i	0.539944	−	0.935211i
$494$	−10.9580	+	4.62926i	−0.493023	+	0.208280i
$495$	−2.14405	−	3.71360i	−0.0963677	−	0.166914i
$496$	17.7745	−	30.7863i	0.798097	−	1.38234i
$497$	−11.9916	−	5.92729i	−0.537898	−	0.265875i
$498$	−15.4331	−	26.7310i	−0.691575	−	1.19784i
$499$	−2.38204	−	4.12581i	−0.106635	−	0.184697i	0.807770	−	0.589498i	$-0.200674\pi$
$499$	−2.38204	−	4.12581i	−0.106635	−	0.184697i	−0.914405	+	0.404801i	$0.867341\pi$
$500$	−40.9266			−1.83029
$501$	6.89189			0.307907
$502$	−0.682215	−	1.18163i	−0.0304487	−	0.0527388i
$503$	−0.350346	−	0.606817i	−0.0156212	−	0.0270567i	0.858109	−	0.513467i	$-0.171639\pi$
$503$	−0.350346	−	0.606817i	−0.0156212	−	0.0270567i	−0.873730	+	0.486411i	$0.838306\pi$
$504$	−0.799501	−	12.3719i	−0.0356126	−	0.551087i
$505$	0.948935	−	1.64360i	0.0422271	−	0.0731394i
$506$	−2.86210	−	4.95731i	−0.127236	−	0.220379i
$507$	−9.06252	+	9.32045i	−0.402481	+	0.413936i
$508$	32.3648	−	56.0575i	1.43596	−	2.48715i
$509$	26.8914			1.19194			0.595970	−	0.803007i	$-0.296768\pi$
$509$	26.8914			1.19194			0.595970	+	0.803007i	$0.296768\pi$
$510$	−6.76477	+	11.7169i	−0.299549	+	0.518834i
$511$	2.06185	+	31.9061i	0.0912111	+	1.41144i
$512$	35.8718			1.58533
$513$	0.677706	−	1.17382i	0.0299215	−	0.0518255i
$514$	57.8321			2.55087
$515$	−3.38739	+	5.86714i	−0.149266	+	0.258537i
$516$	−17.6191	+	30.5171i	−0.775636	+	1.34344i
$517$	9.01107	−	15.6076i	0.396306	−	0.686423i
$518$	16.5155	−	11.0134i	0.725648	−	0.483900i
$519$	15.8386			0.695237
$520$	2.56325	−	20.5846i	0.112406	−	0.902695i
$521$	−15.4700	+	26.7948i	−0.677753	+	1.17390i	0.297903	+	0.954596i	$0.403713\pi$
$521$	−15.4700	+	26.7948i	−0.677753	+	1.17390i	−0.975656	+	0.219306i	$0.929621\pi$
$522$	−6.44620	−	11.1651i	−0.282142	−	0.488685i
$523$	−1.70226			−0.0744347			−0.0372173	−	0.999307i	$-0.511849\pi$
$523$	−1.70226			−0.0744347			−0.0372173	+	0.999307i	$0.511849\pi$
$524$	13.8230	+	23.9421i	0.603859	+	1.04591i
$525$	7.68783	−	5.12665i	0.335525	−	0.223746i
$526$	−8.61105	−	14.9148i	−0.375460	−	0.650315i
$527$	22.6283	−	39.1933i	0.985704	−	1.70729i
$528$	6.20973	−	10.7556i	0.270244	−	0.468076i
$529$	−22.5466			−0.980288
$530$	−29.6034			−1.28589
$531$	−0.401721	+	0.695802i	−0.0174332	+	0.0301952i
$532$	0.907707	+	14.0463i	0.0393541	+	0.608984i
$533$	−23.9868	+	10.1334i	−1.03898	+	0.438925i
$534$	3.77859	+	6.54471i	0.163516	+	0.283217i
$535$	−0.889144	−	1.54004i	−0.0384410	−	0.0665818i
$536$	−4.97021	−	8.60866i	−0.214681	−	0.371838i
$537$	10.5515	−	18.2758i	0.455332	−	0.788658i
$538$	25.2870			1.09020
$539$	−24.2445	+	3.14662i	−1.04429	+	0.135535i
$540$	2.40956	+	4.17348i	0.103691	+	0.179598i
$541$	1.00845	+	1.74668i	0.0433566	+	0.0750958i	0.886889	−	0.461982i	$-0.152862\pi$
$541$	1.00845	+	1.74668i	0.0433566	+	0.0750958i	−0.843533	+	0.537078i	$0.819528\pi$
$542$	0.298846			0.0128365
$543$	7.53423	+	13.0497i	0.323325	+	0.560015i
$544$	3.24124			0.138967
$545$	20.1475			0.863026
$546$	10.3969	+	20.7626i	0.444944	+	0.888558i
$547$	−2.08074			−0.0889658			−0.0444829	−	0.999010i	$-0.514164\pi$
$547$	−2.08074			−0.0889658			−0.0444829	+	0.999010i	$0.514164\pi$
$548$	−75.8373			−3.23961
$549$	−2.32487	−	4.02680i	−0.0992231	−	0.171860i
$550$	29.6915			1.26605
$551$	3.58945	+	6.21712i	0.152916	+	0.264858i
$552$	1.57757	+	2.73242i	0.0671456	+	0.116300i
$553$	−27.9942	−	13.8372i	−1.19044	−	0.588416i
$554$	13.0762			0.555554
$555$	−1.89223	+	3.27744i	−0.0803208	+	0.139120i
$556$	30.4654	+	52.7676i	1.29202	+	2.23784i
$557$	−9.81703	−	17.0036i	−0.415961	−	0.720465i	0.579568	−	0.814924i	$-0.303221\pi$
$557$	−9.81703	−	17.0036i	−0.415961	−	0.720465i	−0.995529	+	0.0944586i	$0.969888\pi$
$558$	−12.1670	−	21.0738i	−0.515069	−	0.892126i
$559$	3.99986	−	32.1216i	0.169176	−	1.35860i
$560$	−10.3553	−	5.11850i	−0.437593	−	0.216296i
$561$	7.90548	−	13.6927i	0.333770	−	0.578106i
$562$	36.2314			1.52833
$563$	−23.3397			−0.983652			−0.491826	−	0.870693i	$-0.663670\pi$
$563$	−23.3397			−0.983652			−0.491826	+	0.870693i	$0.663670\pi$
$564$	−10.1270	+	17.5404i	−0.426423	+	0.738586i
$565$	6.60607	−	11.4421i	0.277920	−	0.481371i
$566$	5.45902	+	9.45531i	0.229460	+	0.397436i
$567$	−2.37183	−	1.17236i	−0.0996074	−	0.0492346i
$568$	11.8456	+	20.5171i	0.497029	+	0.860880i
$569$	−21.6413			−0.907250			−0.453625	−	0.891193i	$-0.649869\pi$
$569$	−21.6413			−0.907250			−0.453625	+	0.891193i	$0.649869\pi$
$570$	−2.02539	−	3.50808i	−0.0848343	−	0.146937i
$571$	−3.91282	+	6.77720i	−0.163746	+	0.283617i	−0.936209	−	0.351443i	$-0.885691\pi$
$571$	−3.91282	+	6.77720i	−0.163746	+	0.283617i	0.772463	+	0.635060i	$0.219025\pi$
$572$	−6.10756	+	49.0478i	−0.255370	+	2.05079i
$573$	9.49806			0.396787
$574$	2.99940	+	46.4142i	0.125193	+	1.93729i
$575$	−1.17581	+	2.03657i	−0.0490349	+	0.0849309i
$576$	4.42738	−	7.66844i	0.184474	−	0.319518i
$577$	5.92244	−	10.2580i	0.246555	−	0.427045i	−0.716013	−	0.698087i	$-0.754035\pi$
$577$	5.92244	−	10.2580i	0.246555	−	0.427045i	0.962568	+	0.271042i	$0.0873682\pi$
$578$	−8.50538			−0.353777
$579$	−9.27175	+	16.0591i	−0.385321	+	0.667395i
$580$	−25.5244			−1.05984
$581$	27.9125	−	18.6135i	1.15801	−	0.772219i
$582$	−8.75283	+	15.1603i	−0.362816	+	0.628416i
$583$	34.5952			1.43279
$584$	28.3134	−	49.0402i	1.17161	−	2.02930i
$585$	−3.53086	−	2.67018i	−0.145983	−	0.110398i
$586$	26.7794	+	46.3833i	1.10625	+	1.91608i
$587$	−2.24869	+	3.89484i	−0.0928134	+	0.160757i	−0.908694	−	0.417463i	$-0.862919\pi$
$587$	−2.24869	+	3.89484i	−0.0928134	+	0.160757i	0.815881	+	0.578220i	$0.196253\pi$
$588$	27.2469	−	3.53629i	1.12364	−	0.145834i
$589$	6.77497	+	11.7346i	0.279158	+	0.483516i
$590$	1.20058	+	2.07947i	0.0494273	+	0.0856106i
$591$	−25.7573			−1.05951
$592$	−10.9608			−0.450487
$593$	17.8835	+	30.9751i	0.734388	+	1.27200i	0.954992	+	0.296633i	$0.0958638\pi$
$593$	17.8835	+	30.9751i	0.734388	+	1.27200i	−0.220604	+	0.975363i	$0.570803\pi$
$594$	−4.25069	−	7.36241i	−0.174408	−	0.302083i
$595$	−13.1832	−	6.51626i	−0.540457	−	0.267141i
$596$	−34.4094	+	59.5988i	−1.40946	+	2.44126i
$597$	8.84779	+	15.3248i	0.362116	+	0.627203i
$598$	−4.71337	−	3.56445i	−0.192744	−	0.145761i
$599$	−9.70429	+	16.8083i	−0.396507	+	0.686769i	−0.993292	−	0.115631i	$-0.963111\pi$
$599$	−9.70429	+	16.8083i	−0.396507	+	0.686769i	0.596786	+	0.802401i	$0.296444\pi$
$600$	−16.3657			−0.668126
$601$	−20.4135	+	35.3571i	−0.832682	+	1.44225i	0.0632213	+	0.998000i	$0.479863\pi$
$601$	−20.4135	+	35.3571i	−0.832682	+	1.44225i	−0.895904	+	0.444248i	$0.853471\pi$
$602$	−51.8318	−	25.6197i	−2.11251	−	1.04418i
$603$	−2.12136			−0.0863884
$604$	−27.5520	+	47.7214i	−1.12107	+	1.94176i
$605$	1.47077			0.0597955
$606$	1.88132	−	3.25854i	0.0764232	−	0.132369i
$607$	−0.471345	+	0.816393i	−0.0191313	+	0.0331364i	−0.875433	−	0.483340i	$-0.839423\pi$
$607$	−0.471345	+	0.816393i	−0.0191313	+	0.0331364i	0.856301	+	0.516477i	$0.172757\pi$
$608$	−0.485219	+	0.840424i	−0.0196782	+	0.0340837i
$609$	11.6587	−	7.77461i	0.472432	−	0.315043i
$610$	−13.8962			−0.562642
$611$	2.29902	−	18.4626i	0.0930082	−	0.746919i
$612$	−8.88448	+	15.3884i	−0.359134	+	0.622038i
$613$	−0.460547	−	0.797690i	−0.0186013	−	0.0322184i	0.856575	−	0.516023i	$-0.172588\pi$
$613$	−0.460547	−	0.797690i	−0.0186013	−	0.0322184i	−0.875176	+	0.483804i	$0.839255\pi$
$614$	−80.3169			−3.24133
$615$	−4.43355	−	7.67913i	−0.178778	−	0.309652i
$616$	38.8166	+	19.1865i	1.56396	+	0.773045i
$617$	12.3732	+	21.4311i	0.498127	+	0.862782i	0.999998	−	0.00216105i	$-0.000687883\pi$
$617$	12.3732	+	21.4311i	0.498127	+	0.862782i	−0.501870	+	0.864943i	$0.667355\pi$
$618$	−6.71569	+	11.6319i	−0.270145	+	0.467905i
$619$	−12.0229	+	20.8243i	−0.483242	+	0.836999i	−0.999815	−	0.0192441i	$-0.993874\pi$
$619$	−12.0229	+	20.8243i	−0.483242	+	0.836999i	0.516573	+	0.856243i	$0.327207\pi$
$620$	−48.1764			−1.93481
$621$	0.673327			0.0270197
$622$	−10.0173	+	17.3504i	−0.401656	+	0.695689i
$623$	−6.83400	+	4.55727i	−0.273798	+	0.182583i
$624$	1.58430	−	12.7230i	0.0634229	−	0.509329i
$625$	−2.33033	−	4.03626i	−0.0932133	−	0.161450i
$626$	−17.3883	−	30.1174i	−0.694975	−	1.20373i
$627$	2.36692	+	4.09963i	0.0945258	+	0.163723i
$628$	22.0704	−	38.2271i	0.880706	−	1.52543i
$629$	−13.9540			−0.556382
$630$	−6.57853	+	4.38691i	−0.262095	+	0.174779i
$631$	−14.7428	−	25.5353i	−0.586902	−	1.01654i	−0.994635	−	0.103443i	$-0.967014\pi$
$631$	−14.7428	−	25.5353i	−0.586902	−	1.01654i	0.407734	−	0.913101i	$-0.366319\pi$
$632$	27.6533	+	47.8969i	1.09999	+	1.90523i
$633$	−12.4779			−0.495953
$634$	−11.3965	−	19.7394i	−0.452615	−	0.783952i
$635$	−20.2478			−0.803510
$636$	−38.8794			−1.54167
$637$	−21.7918	+	12.7325i	−0.863423	+	0.504480i
$638$	45.0273			1.78265
$639$	5.05586			0.200007
$640$	−12.3526	−	21.3953i	−0.488279	−	0.845725i
$641$	2.18539			0.0863178			0.0431589	−	0.999068i	$-0.486258\pi$
$641$	2.18539			0.0863178			0.0431589	+	0.999068i	$0.486258\pi$
$642$	−1.76278	−	3.05322i	−0.0695712	−	0.120501i
$643$	5.19137	+	8.99172i	0.204728	+	0.354599i	0.950046	−	0.312110i	$-0.101036\pi$
$643$	5.19137	+	8.99172i	0.204728	+	0.354599i	−0.745318	+	0.666709i	$0.767702\pi$
$644$	−5.81747	+	3.87940i	−0.229240	+	0.152870i
$645$	11.0227			0.434018
$646$	7.46798	−	12.9349i	0.293824	−	0.508918i
$647$	6.06580	+	10.5063i	0.238471	+	0.413045i	0.960276	−	0.279052i	$-0.0900203\pi$
$647$	6.06580	+	10.5063i	0.238471	+	0.413045i	−0.721804	+	0.692097i	$0.756687\pi$
$648$	2.34294	+	4.05809i	0.0920394	+	0.159417i
$649$	−1.40303	−	2.43012i	−0.0550738	−	0.0953907i
$650$	28.2359	−	11.9284i	1.10750	−	0.467872i
$651$	22.0053	−	14.6743i	0.862456	−	0.575131i
$652$	−22.7810	+	39.4578i	−0.892171	+	1.54529i
$653$	−24.0253			−0.940183			−0.470091	−	0.882618i	$-0.655779\pi$
$653$	−24.0253			−0.940183			−0.470091	+	0.882618i	$0.655779\pi$
$654$	39.9436			1.56192
$655$	4.32390	−	7.48922i	0.168949	−	0.292628i
$656$	12.8407	−	22.2408i	0.501347	−	0.868358i
$657$	−6.04227	−	10.4655i	−0.235731	−	0.408299i
$658$	−29.7916	−	14.7255i	−1.16140	−	0.574062i
$659$	10.4678	+	18.1307i	0.407766	+	0.706272i	0.994639	−	0.103407i	$-0.0329744\pi$
$659$	10.4678	+	18.1307i	0.407766	+	0.706272i	−0.586873	+	0.809679i	$0.699641\pi$
$660$	−16.8310			−0.655147
$661$	10.7390	+	18.6005i	0.417699	+	0.723476i	0.995708	−	0.0925549i	$-0.0295034\pi$
$661$	10.7390	+	18.6005i	0.417699	+	0.723476i	−0.578009	+	0.816031i	$0.696170\pi$
$662$	−29.7914	+	51.6002i	−1.15787	+	2.00550i
$663$	2.01694	−	16.1974i	0.0783316	−	0.629056i
$664$	−59.4194			−2.30592
$665$	3.66314	−	2.44278i	0.142051	−	0.0947269i
$666$	−3.75145	+	6.49771i	−0.145366	+	0.251781i
$667$	−1.78313	+	3.08847i	−0.0690431	+	0.119586i
$668$	13.5255	−	23.4269i	0.523319	−	0.906415i
$669$	−9.30464			−0.359738
$670$	−3.16995	+	5.49051i	−0.122466	+	0.212117i
$671$	16.2395			0.626918
$672$	1.69816	+	0.839379i	0.0655081	+	0.0323797i
$673$	−0.483978	+	0.838274i	−0.0186560	+	0.0323131i	−0.875203	−	0.483756i	$-0.839272\pi$
$673$	−0.483978	+	0.838274i	−0.0186560	+	0.0323131i	0.856547	+	0.516070i	$0.172605\pi$
$674$	32.0541			1.23468
$675$	−1.74628	+	3.02464i	−0.0672142	+	0.116418i
$676$	13.8966	+	49.0970i	0.534485	+	1.88835i
$677$	−23.4146	−	40.5552i	−0.899895	−	1.55866i	−0.827626	−	0.561279i	$-0.810309\pi$
$677$	−23.4146	−	40.5552i	−0.899895	−	1.55866i	−0.0722691	−	0.997385i	$-0.523024\pi$
$678$	13.0969	−	22.6845i	0.502983	−	0.871193i
$679$	−17.0575	−	8.43128i	−0.654606	−	0.323563i
$680$	13.0226	+	22.5558i	0.499394	+	0.864976i
$681$	4.76651	+	8.25583i	0.182653	+	0.316364i
$682$	84.9876			3.25434
$683$	17.8803			0.684170			0.342085	−	0.939669i	$-0.388867\pi$
$683$	17.8803			0.684170			0.342085	+	0.939669i	$0.388867\pi$
$684$	−2.66004	−	4.60732i	−0.101709	−	0.176165i
$685$	11.8612	+	20.5442i	0.453192	+	0.784952i
$686$	8.67319	+	44.2388i	0.331144	+	1.68905i
$687$	−3.22423	+	5.58453i	−0.123012	+	0.213063i
$688$	15.9623	+	27.6476i	0.608558	+	1.05405i
$689$	32.8992	−	13.8985i	1.25336	−	0.529490i
$690$	1.00615	−	1.74271i	0.0383036	−	0.0663438i
$691$	−33.2164			−1.26361			−0.631806	−	0.775127i	$-0.717686\pi$
$691$	−33.2164			−1.26361			−0.631806	+	0.775127i	$0.717686\pi$
$692$	31.0837	−	53.8386i	1.18163	−	2.04664i
$693$	7.68783	−	5.12665i	0.292037	−	0.194746i
$694$	−35.7170			−1.35580
$695$	9.52974	−	16.5060i	0.361484	−	0.626108i
$696$	−24.8187			−0.940749
$697$	16.3473	−	28.3143i	0.619197	−	1.07248i
$698$	−29.6230	+	51.3085i	−1.12125	+	1.94206i
$699$	−12.2379	+	21.1967i	−0.462881	+	0.801733i
$700$	−2.33893	−	36.1937i	−0.0884032	−	1.36799i
$701$	29.1267			1.10010			0.550050	−	0.835132i	$-0.314609\pi$
$701$	29.1267			1.10010			0.550050	+	0.835132i	$0.314609\pi$
$702$	−7.00012	−	5.29378i	−0.264203	−	0.199801i
$703$	2.08893	−	3.61814i	0.0787856	−	0.136461i
$704$	15.4628	+	26.7824i	0.582778	+	1.00940i
$705$	6.33556			0.238611
$706$	−0.814982	−	1.41159i	−0.0306723	−	0.0531259i
$707$	3.66630	+	1.81220i	0.137886	+	0.0681549i
$708$	1.57678	+	2.73107i	0.0592591	+	0.102640i
$709$	−5.70074	+	9.87397i	−0.214096	+	0.370825i	−0.952992	−	0.302994i	$-0.902014\pi$
$709$	−5.70074	+	9.87397i	−0.214096	+	0.370825i	0.738897	+	0.673819i	$0.235347\pi$
$710$	7.55497	−	13.0856i	0.283533	−	0.491093i
$711$	11.8028			0.442640
$712$	14.5480			0.545211
$713$	−3.36560	+	5.82939i	−0.126043	+	0.218312i
$714$	−26.1364	−	12.9188i	−0.978129	−	0.483475i
$715$	14.2422	−	6.01670i	0.532628	−	0.225012i
$716$	−41.4154	−	71.7336i	−1.54777	−	2.68081i
$717$	1.81065	+	3.13614i	0.0676199	+	0.117121i
$718$	−43.3632	−	75.1073i	−1.61830	−	2.80298i
$719$	18.1259	−	31.3949i	0.675980	−	1.17083i	−0.300201	−	0.953876i	$-0.597054\pi$
$719$	18.1259	−	31.3949i	0.675980	−	1.17083i	0.976181	−	0.216956i	$-0.0696129\pi$
$720$	4.36598			0.162710
$721$	−13.0875	−	6.46898i	−0.487405	−	0.240917i
$722$	−20.8884	−	36.1798i	−0.777387	−	1.34647i
$723$	12.5649	+	21.7631i	0.467294	+	0.809377i
$724$	59.1446			2.19809
$725$	−9.24911	−	16.0199i	−0.343503	−	0.594965i
$726$	2.91589			0.108219
$727$	4.46075			0.165440			0.0827200	−	0.996573i	$-0.473639\pi$
$727$	4.46075			0.165440			0.0827200	+	0.996573i	$0.473639\pi$
$728$	44.6217	+	2.65151i	1.65379	+	0.0982714i
$729$	1.00000			0.0370370
$730$	−36.1159			−1.33671
$731$	20.3213	+	35.1975i	0.751611	+	1.30183i
$732$	−18.2505			−0.674559
$733$	5.24983	+	9.09297i	0.193907	+	0.335856i	0.946542	−	0.322582i	$-0.104551\pi$
$733$	5.24983	+	9.09297i	0.193907	+	0.335856i	−0.752635	+	0.658438i	$0.771217\pi$
$734$	12.4413	+	21.5490i	0.459218	+	0.795390i
$735$	−5.21947	−	6.82804i	−0.192523	−	0.251856i
$736$	−0.482084			−0.0177698
$737$	3.70448	−	6.41634i	0.136456	−	0.236349i
$738$	−8.78975	−	15.2243i	−0.323555	−	0.560414i
$739$	2.32461	+	4.02635i	0.0855123	+	0.148112i	0.905609	−	0.424113i	$-0.139414\pi$
$739$	2.32461	+	4.02635i	0.0855123	+	0.148112i	−0.820097	+	0.572224i	$0.806081\pi$
$740$	7.42713	+	12.8642i	0.273027	+	0.472896i
$741$	3.89790	+	2.94775i	0.143193	+	0.108288i
$742$	−4.11384	−	63.6596i	−0.151024	−	2.33702i
$743$	9.95236	−	17.2380i	0.365117	−	0.632400i	−0.623678	−	0.781681i	$-0.714362\pi$
$743$	9.95236	−	17.2380i	0.365117	−	0.632400i	0.988795	+	0.149281i	$0.0476958\pi$
$744$	−46.8444			−1.71740
$745$	21.5269			0.788686
$746$	6.02582	−	10.4370i	0.220621	−	0.382127i
$747$	−6.34027	+	10.9817i	−0.231978	+	0.401798i
$748$	−31.0295	−	53.7447i	−1.13455	−	1.96510i
$749$	3.18817	−	2.12604i	0.116493	−	0.0776839i
$750$	12.6904	+	21.9804i	0.463389	+	0.802613i
$751$	−41.9901			−1.53224			−0.766120	−	0.642697i	$-0.777815\pi$
$751$	−41.9901			−1.53224			−0.766120	+	0.642697i	$0.777815\pi$
$752$	9.17474	+	15.8911i	0.334568	+	0.579489i
$753$	−0.280269	+	0.485440i	−0.0102136	+	0.0176904i
$754$	42.8199	−	18.0895i	1.55941	−	0.658782i
$755$	17.2368			0.627313
$756$	−8.63988	+	5.76153i	−0.314229	+	0.209545i
$757$	21.8795	−	37.8965i	0.795225	−	1.37737i	−0.127471	−	0.991842i	$-0.540686\pi$
$757$	21.8795	−	37.8965i	0.795225	−	1.37737i	0.922696	−	0.385528i	$-0.125981\pi$
$758$	−15.4237	+	26.7147i	−0.560215	+	0.970321i
$759$	−1.17581	+	2.03657i	−0.0426794	+	0.0739229i
$760$	−7.79801			−0.282864
$761$	−6.01947	+	10.4260i	−0.218206	+	0.377943i	−0.954259	−	0.298980i	$-0.903354\pi$
$761$	−6.01947	+	10.4260i	−0.218206	+	0.377943i	0.736054	+	0.676923i	$0.236687\pi$
$762$	−40.1424			−1.45420
$763$	2.79981	+	43.3256i	0.101360	+	1.56849i
$764$	18.6402	−	32.2858i	0.674380	−	1.16806i
$765$	5.55823			0.200958
$766$	−28.9544	+	50.1504i	−1.04616	+	1.81201i
$767$	−2.31054	−	1.74733i	−0.0834289	−	0.0630924i
$768$	−15.6349	−	27.0805i	−0.564178	−	0.977184i
$769$	13.1918	−	22.8489i	0.475708	−	0.823951i	−0.523905	−	0.851777i	$-0.675525\pi$
$769$	13.1918	−	22.8489i	0.475708	−	0.823951i	0.999613	+	0.0278261i	$0.00885848\pi$
$770$	−1.78090	−	27.5584i	−0.0641790	−	0.993137i
$771$	−11.8793	−	20.5756i	−0.427824	−	0.741013i
$772$	36.3922	+	63.0331i	1.30978	+	2.26861i
$773$	−9.88877			−0.355674			−0.177837	−	0.984060i	$-0.556910\pi$
$773$	−9.88877			−0.355674			−0.177837	+	0.984060i	$0.556910\pi$
$774$	21.8531			0.785493
$775$	−17.4574	−	30.2371i	−0.627088	−	1.08615i
$776$	16.8497	+	29.1846i	0.604870	+	1.04767i
$777$	−7.31082	−	3.61364i	−0.262274	−	0.129639i
$778$	−31.0890	+	53.8478i	−1.11460	+	1.93054i
$779$	4.89442	+	8.47738i	0.175361	+	0.303734i
$780$	−16.0059	+	6.76179i	−0.573104	+	0.242111i
$781$	−8.82892	+	15.2921i	−0.315924	+	0.547196i
$782$	7.41973			0.265329
$783$	−2.64824	+	4.58688i	−0.0946403	+	0.163922i
$784$	9.56788	−	22.9796i	0.341710	−	0.820700i
$785$	−13.8075			−0.492811
$786$	8.57237	−	14.8478i	0.305766	−	0.529603i
$787$	−38.4666			−1.37119			−0.685593	−	0.727985i	$-0.740457\pi$
$787$	−38.4666			−1.37119			−0.685593	+	0.727985i	$0.740457\pi$
$788$	−50.5495	+	87.5542i	−1.80075	+	3.11899i
$789$	−3.53761	+	6.12732i	−0.125942	+	0.218138i
$790$	17.6369	−	30.5481i	0.627494	−	1.08685i
$791$	25.5232	+	12.6158i	0.907501	+	0.448565i
$792$	−16.3657			−0.581529
$793$	15.4434	−	6.52414i	0.548410	−	0.231679i
$794$	−2.58915	+	4.48454i	−0.0918856	+	0.159151i
$795$	6.08085	+	10.5323i	0.215666	+	0.373544i
$796$	69.4562			2.46181
$797$	4.91617	+	8.51506i	0.174140	+	0.301619i	0.939863	−	0.341551i	$-0.110952\pi$
$797$	4.91617	+	8.51506i	0.174140	+	0.301619i	−0.765723	+	0.643170i	$0.777619\pi$
$798$	7.26238	−	4.84294i	0.257086	−	0.171438i
$799$	11.6802	+	20.2306i	0.413214	+	0.715709i
$800$	1.25029	−	2.16556i	0.0442043	−	0.0765640i
$801$	1.55233	−	2.68871i	0.0548488	−	0.0950009i
$802$	−1.42955			−0.0504790
$803$	42.2059			1.48941
$804$	−4.16323	+	7.21093i	−0.146826	+	0.254310i
$805$	1.96079	+	0.969190i	0.0691087	+	0.0341595i
$806$	80.8212	−	34.1434i	2.84681	−	1.20265i
$807$	−5.19422	−	8.99665i	−0.182845	−	0.316697i
$808$	−3.62165	−	6.27288i	−0.127409	−	0.220679i
$809$	10.6278	+	18.4078i	0.373653	+	0.647185i	0.990124	−	0.140192i	$-0.0447719\pi$
$809$	10.6278	+	18.4078i	0.373653	+	0.647185i	−0.616472	+	0.787377i	$0.711439\pi$
$810$	1.49430	−	2.58820i	0.0525043	−	0.0909402i
$811$	35.9695			1.26306			0.631531	−	0.775351i	$-0.282427\pi$
$811$	35.9695			1.26306			0.631531	+	0.775351i	$0.282427\pi$
$812$	−3.54700	−	54.8880i	−0.124475	−	1.92619i
$813$	−0.0613862	−	0.106324i	−0.00215291	−	0.00372894i
$814$	−13.1021	−	22.6936i	−0.459230	−	0.795409i
$815$	14.2520			0.499227
$816$	8.04907	+	13.9414i	0.281774	+	0.488046i
$817$	−12.1685			−0.425723
$818$	10.5753			0.369756
$819$	5.25134	−	7.96388i	0.183497	−	0.278281i
$820$	−34.8039			−1.21540
$821$	36.8113			1.28472			0.642362	−	0.766401i	$-0.277955\pi$
$821$	36.8113			1.28472			0.642362	+	0.766401i	$0.277955\pi$
$822$	23.5154	+	40.7299i	0.820194	+	1.42062i
$823$	−37.6324			−1.31178			−0.655892	−	0.754855i	$-0.727707\pi$
$823$	−37.6324			−1.31178			−0.655892	+	0.754855i	$0.727707\pi$
$824$	12.9281	+	22.3922i	0.450373	+	0.780068i
$825$	−6.09896	−	10.5637i	−0.212338	−	0.367781i
$826$	−4.30490	+	2.87073i	−0.149787	+	0.0998856i
$827$	−28.9693			−1.00736			−0.503681	−	0.863890i	$-0.668021\pi$
$827$	−28.9693			−1.00736			−0.503681	+	0.863890i	$0.668021\pi$
$828$	1.32143	−	2.28878i	0.0459227	−	0.0795405i
$829$	−4.43056	−	7.67395i	−0.153880	−	0.266527i	0.778771	−	0.627308i	$-0.215843\pi$
$829$	−4.43056	−	7.67395i	−0.153880	−	0.266527i	−0.932650	+	0.360781i	$0.882510\pi$
$830$	18.9485	+	32.8198i	0.657713	+	1.13919i
$831$	−2.68599	−	4.65228i	−0.0931761	−	0.161386i
$832$	25.4645	+	19.2573i	0.882824	+	0.667628i
$833$	12.1807	−	29.2549i	0.422035	−	1.01362i
$834$	18.8932	−	32.7240i	0.654219	−	1.13314i
$835$	−8.46174			−0.292831
$836$	18.5806			0.642625
$837$	−4.99846	+	8.65759i	−0.172772	+	0.299250i
$838$	11.5091	−	19.9343i	0.397575	−	0.688620i
$839$	15.9655	+	27.6530i	0.551190	+	0.954689i	0.998189	+	0.0601547i	$0.0191594\pi$
$839$	15.9655	+	27.6530i	0.551190	+	0.954689i	−0.446999	+	0.894534i	$0.647507\pi$
$840$	0.981613	+	15.1900i	0.0338689	+	0.524103i
$841$	0.473666	+	0.820413i	0.0163333	+	0.0282901i
$842$	29.1047			1.00301
$843$	−7.44233	−	12.8905i	−0.256328	−	0.443972i
$844$	−24.4883	+	42.4150i	−0.842922	+	1.45998i
$845$	11.1268	−	11.4435i	0.382774	−	0.393668i
$846$	12.5606			0.431842
$847$	0.204387	+	3.16278i	0.00702281	+	0.108674i
$848$	−17.6118	+	30.5045i	−0.604791	+	1.04753i
$849$	2.24269	−	3.88445i	0.0769688	−	0.133314i
$850$	−19.2431	+	33.3300i	−0.660032	+	1.14321i
$851$	2.07544			0.0711450
$852$	9.92228	−	17.1859i	0.339932	−	0.588779i
$853$	5.62395			0.192560			0.0962801	−	0.995354i	$-0.469306\pi$
$853$	5.62395			0.192560			0.0962801	+	0.995354i	$0.469306\pi$
$854$	−1.93109	−	29.8827i	−0.0660807	−	1.02256i
$855$	−0.832075	+	1.44120i	−0.0284564	+	0.0492879i
$856$	−6.78691			−0.231972
$857$	23.8452	−	41.3011i	0.814537	−	1.41082i	−0.0951229	−	0.995466i	$-0.530324\pi$
$857$	23.8452	−	41.3011i	0.814537	−	1.41082i	0.909660	−	0.415354i	$-0.136342\pi$
$858$	28.2359	−	11.9284i	0.963958	−	0.407230i
$859$	−24.8420	−	43.0276i	−0.847598	−	1.46808i	−0.883345	−	0.468723i	$-0.844714\pi$
$859$	−24.8420	−	43.0276i	−0.847598	−	1.46808i	0.0357469	−	0.999361i	$-0.488619\pi$
$860$	21.6324	−	37.4684i	0.737658	−	1.27766i
$861$	15.8972	−	10.6011i	0.541776	−	0.361285i
$862$	−32.2165	−	55.8006i	−1.09730	−	1.90058i
$863$	11.4553	+	19.8412i	0.389944	+	0.675402i	0.992442	−	0.122718i	$-0.0391611\pi$
$863$	11.4553	+	19.8412i	0.389944	+	0.675402i	−0.602498	+	0.798121i	$0.705828\pi$
$864$	−0.715973			−0.0243579
$865$	−19.4463			−0.661195
$866$	−10.0552	−	17.4160i	−0.341688	−	0.591821i
$867$	1.74710	+	3.02606i	0.0593346	+	0.102770i
$868$	−6.69485	−	103.599i	−0.227238	−	3.51639i
$869$	−20.6109	+	35.6992i	−0.699179	+	1.21101i
$870$	7.91453	+	13.7084i	0.268328	+	0.464757i
$871$	0.945132	−	7.59005i	0.0320246	−	0.257179i
$872$	38.4470	−	66.5921i	1.30198	−	2.25509i
$873$	7.19171			0.243402
$874$	−1.11074	+	1.92387i	−0.0375715	+	0.0650757i
$875$	−22.9520	+	15.3056i	−0.775920	+	0.517424i
$876$	−47.4326			−1.60260
$877$	16.1524	−	27.9767i	0.545427	−	0.944707i	−0.453153	−	0.891433i	$-0.649701\pi$
$877$	16.1524	−	27.9767i	0.545427	−	0.944707i	0.998580	−	0.0532742i	$-0.0169657\pi$
$878$	−85.4490			−2.88376
$879$	11.0016	−	19.0553i	0.371074	−	0.642719i
$880$	−7.62420	+	13.2055i	−0.257012	+	0.445157i
$881$	18.8690	−	32.6821i	0.635714	−	1.10109i	−0.350650	−	0.936507i	$-0.614039\pi$
$881$	18.8690	−	32.6821i	0.635714	−	1.10109i	0.986363	−	0.164582i	$-0.0526274\pi$
$882$	−10.3479	−	13.5370i	−0.348431	−	0.455813i
$883$	−34.3867			−1.15720			−0.578602	−	0.815610i	$-0.696401\pi$
$883$	−34.3867			−1.15720			−0.578602	+	0.815610i	$0.696401\pi$
$884$	−51.1000	−	38.6439i	−1.71868	−	1.29974i
$885$	0.493226	−	0.854293i	0.0165796	−	0.0287168i
$886$	−0.468025	−	0.810643i	−0.0157236	−	0.0272341i
$887$	23.6793			0.795073			0.397536	−	0.917586i	$-0.369865\pi$
$887$	23.6793			0.795073			0.397536	+	0.917586i	$0.369865\pi$
$888$	7.22178	+	12.5085i	0.242347	+	0.419757i
$889$	−2.81374	−	43.5412i	−0.0943699	−	1.46033i
$890$	−4.63929	−	8.03548i	−0.155509	−	0.269350i
$891$	−1.74628	+	3.02464i	−0.0585024	+	0.101329i
$892$	−18.2606	+	31.6284i	−0.611412	+	1.05900i
$893$	−6.99415			−0.234050
$894$	42.6783			1.42738
$895$	−12.9550	+	22.4387i	−0.433037	+	0.750043i
$896$	44.2923	−	29.5365i	1.47970	−	0.986744i
$897$	−0.299989	+	2.40911i	−0.0100163	+	0.0804379i
$898$	46.1825	+	79.9905i	1.54113	+	2.66932i
$899$	−26.4742	−	45.8547i	−0.882965	−	1.52934i
$900$	6.85424	+	11.8719i	0.228475	+	0.395730i
$901$	−22.4212	+	38.8346i	−0.746958	+	1.29377i
$902$	61.3973			2.04431
$903$	1.53177	+	23.7034i	0.0509742	+	0.788799i
$904$	−25.2123	−	43.6691i	−0.838550	−	1.45241i
$905$	−9.25039	−	16.0221i	−0.307493	−	0.532594i
$906$	34.1730			1.13532
$907$	4.63367	+	8.02574i	0.153858	+	0.266490i	0.932643	−	0.360801i	$-0.117497\pi$
$907$	4.63367	+	8.02574i	0.153858	+	0.266490i	−0.778784	+	0.627292i	$0.784163\pi$
$908$	37.4177			1.24175
$909$	−1.54577			−0.0512700
$910$	−12.7651	−	25.4920i	−0.423158	−	0.845050i
$911$	−10.2739			−0.340390			−0.170195	−	0.985410i	$-0.554440\pi$
$911$	−10.2739			−0.340390			−0.170195	+	0.985410i	$0.554440\pi$
$912$	−4.81983			−0.159600
$913$	−22.1437	−	38.3540i	−0.732849	−	1.26933i
$914$	35.0261			1.15856
$915$	2.85444	+	4.94403i	0.0943648	+	0.163445i
$916$	12.6553	+	21.9196i	0.418143	+	0.724245i
$917$	16.7058	+	8.25745i	0.551675	+	0.272685i
$918$	11.0195			0.363698
$919$	2.31603	−	4.01148i	0.0763987	−	0.132326i	−0.825295	−	0.564702i	$-0.808991\pi$
$919$	2.31603	−	4.01148i	0.0763987	−	0.132326i	0.901694	+	0.432375i	$0.142324\pi$
$920$	−1.93691	−	3.35482i	−0.0638579	−	0.110605i
$921$	16.4980	+	28.5753i	0.543627	+	0.941589i
$922$	−4.36931	−	7.56787i	−0.143896	−	0.249235i
$923$	−2.25254	+	18.0894i	−0.0741434	+	0.595421i
$924$	−2.33893	−	36.1937i	−0.0769451	−	1.19069i
$925$	−5.38265	+	9.32302i	−0.176980	+	0.306539i
$926$	−11.4279			−0.375545
$927$	5.51791			0.181232
$928$	1.89607	−	3.28408i	0.0622414	−	0.107805i
$929$	−1.54518	+	2.67633i	−0.0506958	+	0.0878076i	−0.890260	−	0.455453i	$-0.849477\pi$
$929$	−1.54518	+	2.67633i	−0.0506958	+	0.0878076i	0.839564	+	0.543261i	$0.182811\pi$
$930$	14.9384	+	25.8741i	0.489849	+	0.848444i
$931$	5.76204	+	7.53783i	0.188843	+	0.247042i
$932$	48.0346	+	83.1983i	1.57342	+	2.72525i
$933$	8.23063			0.269459
$934$	−48.7663	−	84.4657i	−1.59568	−	2.76380i
$935$	−9.70621	+	16.8116i	−0.317427	+	0.549800i
$936$	−15.5634	+	6.57484i	−0.508705	+	0.214905i
$937$	−41.8382			−1.36680			−0.683398	−	0.730046i	$-0.739498\pi$
$937$	−41.8382			−1.36680			−0.683398	+	0.730046i	$0.739498\pi$
$938$	−12.2474	−	6.05372i	−0.399892	−	0.197661i
$939$	−7.14348	+	12.3729i	−0.233119	+	0.403773i
$940$	12.4337	−	21.5358i	0.405543	−	0.702422i
$941$	−18.9382	+	32.8019i	−0.617368	+	1.06931i	0.372596	+	0.927994i	$0.378468\pi$
$941$	−18.9382	+	32.8019i	−0.617368	+	1.06931i	−0.989964	+	0.141319i	$0.954866\pi$
$942$	−27.3741			−0.891898
$943$	−2.43140	+	4.21131i	−0.0791772	+	0.137139i
$944$	2.85703			0.0929885
$945$	2.91209	+	1.43940i	0.0947302	+	0.0468238i
$946$	−38.1615	+	66.0977i	−1.24074	+	2.14902i
$947$	−0.781555			−0.0253971			−0.0126986	−	0.999919i	$-0.504042\pi$
$947$	−0.781555			−0.0253971			−0.0126986	+	0.999919i	$0.504042\pi$
$948$	23.1634	−	40.1201i	0.752311	−	1.30304i
$949$	40.1368	−	16.9560i	1.30290	−	0.550416i
$950$	−5.76143	−	9.97909i	−0.186926	−	0.323765i
$951$	−4.68195	+	8.10938i	−0.151823	+	0.262965i
$952$	−46.6947	+	31.1385i	−1.51338	+	1.00921i
$953$	14.6233	+	25.3283i	0.473695	+	0.820463i	0.999547	−	0.0301129i	$-0.00958667\pi$
$953$	14.6233	+	25.3283i	0.473695	+	0.820463i	−0.525852	+	0.850576i	$0.676253\pi$
$954$	12.0556	+	20.8810i	0.390315	+	0.676046i
$955$	−11.6615			−0.377359
$956$	14.2138			0.459708
$957$	−9.24911	−	16.0199i	−0.298981	−	0.517851i
$958$	24.9135	+	43.1515i	0.804919	+	1.39416i
$959$	−42.5302	+	28.3614i	−1.37337	+	0.915837i
$960$	−5.43585	+	9.41518i	−0.175441	+	0.303874i
$961$	−34.4692	−	59.7025i	−1.11191	−	1.92589i
$962$	−21.5769	−	16.3173i	−0.695666	−	0.526092i
$963$	−0.724187	+	1.25433i	−0.0233366	+	0.0404202i
$964$	98.6361			3.17686
$965$	11.3837	−	19.7171i	0.366454	−	0.634717i
$966$	3.88737	+	1.92147i	0.125074	+	0.0618224i
$967$	−30.4010			−0.977631			−0.488816	−	0.872387i	$-0.662571\pi$
$967$	−30.4010			−0.977631			−0.488816	+	0.872387i	$0.662571\pi$
$968$	2.80663	−	4.86123i	0.0902087	−	0.156246i
$969$	−6.13602			−0.197117
$970$	10.7466	−	18.6136i	0.345051	−	0.597647i
$971$	−4.45931	+	7.72376i	−0.143106	+	0.247867i	−0.928665	−	0.370920i	$-0.879042\pi$
$971$	−4.45931	+	7.72376i	−0.143106	+	0.247867i	0.785559	+	0.618787i	$0.212376\pi$
$972$	1.96253	−	3.39920i	0.0629482	−	0.109029i
$973$	36.8191	+	18.1992i	1.18037	+	0.583438i
$974$	−81.7719			−2.62014
$975$	−10.0439	−	7.59560i	−0.321662	−	0.243254i
$976$	−8.26721	+	14.3192i	−0.264627	+	0.458348i
$977$	−11.8031	−	20.4436i	−0.377615	−	0.654048i	0.613100	−	0.790005i	$-0.289922\pi$
$977$	−11.8031	−	20.4436i	−0.377615	−	0.654048i	−0.990715	+	0.135957i	$0.956589\pi$
$978$	28.2554			0.903509
$979$	5.42158	+	9.39046i	0.173275	+	0.300120i
$980$	−33.4533	+	4.34180i	−1.06863	+	0.138694i
$981$	−8.20485	−	14.2112i	−0.261961	−	0.453729i
$982$	−49.2457	+	85.2960i	−1.57149	+	2.72190i
$983$	−10.1644	+	17.6053i	−0.324195	+	0.561523i	−0.981349	−	0.192234i	$-0.938427\pi$
$983$	−10.1644	+	17.6053i	−0.324195	+	0.561523i	0.657154	+	0.753756i	$0.271760\pi$
$984$	−33.8416			−1.07883
$985$	31.6243			1.00763
$986$	−29.1823	+	50.5452i	−0.929353	+	1.60969i
$987$	0.880423	+	13.6241i	0.0280242	+	0.433660i
$988$	17.6698	−	7.46469i	0.562150	−	0.237484i
$989$	−3.02247	−	5.23508i	−0.0961091	−	0.166466i
$990$	5.21892	+	9.03943i	0.165868	+	0.287292i
$991$	22.6402	+	39.2140i	0.719190	+	1.24567i	0.961321	+	0.275430i	$0.0888204\pi$
$991$	22.6402	+	39.2140i	0.719190	+	1.24567i	−0.242131	+	0.970244i	$0.577846\pi$
$992$	3.57876	−	6.19860i	0.113626	−	0.196806i
$993$	24.4779			0.776783
$994$	29.1894	+	14.4279i	0.925830	+	0.457625i
$995$	−10.8632	−	18.8155i	−0.344385	−	0.596493i
$996$	24.8859	+	43.1037i	0.788541	+	1.36579i
$997$	−19.3021			−0.611303			−0.305652	−	0.952143i	$-0.598874\pi$
$997$	−19.3021			−0.611303			−0.305652	+	0.952143i	$0.598874\pi$
$998$	5.79823	+	10.0428i	0.183540	+	0.317900i
$999$	3.08236			0.0975215

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	273.2.l.b.256.1	yes	16
3.2	odd	2		819.2.s.e.802.8		16
7.2	even	3		273.2.j.b.100.8	✓	16
13.3	even	3		273.2.j.b.172.8	yes	16
21.2	odd	6		819.2.n.e.100.1		16
39.29	odd	6		819.2.n.e.172.1		16
91.16	even	3	inner	273.2.l.b.16.1	yes	16
273.107	odd	6		819.2.s.e.289.8		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
273.2.j.b.100.8	✓	16	7.2	even	3
273.2.j.b.172.8	yes	16	13.3	even	3
273.2.l.b.16.1	yes	16	91.16	even	3	inner
273.2.l.b.256.1	yes	16	1.1	even	1	trivial
819.2.n.e.100.1		16	21.2	odd	6
819.2.n.e.172.1		16	39.29	odd	6
819.2.s.e.289.8		16	273.107	odd	6
819.2.s.e.802.8		16	3.2	odd	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:	\( N \)	\(=\)	\( 273 = 3 \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	273.l (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q-2.43414 q^{2} +(0.500000 + 0.866025i) q^{3} +3.92506 q^{4} +(-0.613891 - 1.06329i) q^{5} +(-1.21707 - 2.10803i) q^{6} +(2.20121 - 1.46788i) q^{7} -4.68588 q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})\)	\(q-2.43414 q^{2} +(0.500000 + 0.866025i) q^{3} +3.92506 q^{4} +(-0.613891 - 1.06329i) q^{5} +(-1.21707 - 2.10803i) q^{6} +(2.20121 - 1.46788i) q^{7} -4.68588 q^{8} +(-0.500000 + 0.866025i) q^{9} +(1.49430 + 2.58820i) q^{10} +(-1.74628 - 3.02464i) q^{11} +(1.96253 + 3.39920i) q^{12} +(-2.87580 - 2.17480i) q^{13} +(-5.35806 + 3.57304i) q^{14} +(0.613891 - 1.06329i) q^{15} +3.55599 q^{16} +4.52705 q^{17} +(1.21707 - 2.10803i) q^{18} +(-0.677706 + 1.17382i) q^{19} +(-2.40956 - 4.17348i) q^{20} +(2.37183 + 1.17236i) q^{21} +(4.25069 + 7.36241i) q^{22} -0.673327 q^{23} +(-2.34294 - 4.05809i) q^{24} +(1.74628 - 3.02464i) q^{25} +(7.00012 + 5.29378i) q^{26} -1.00000 q^{27} +(8.63988 - 5.76153i) q^{28} +(2.64824 - 4.58688i) q^{29} +(-1.49430 + 2.58820i) q^{30} +(4.99846 - 8.65759i) q^{31} +0.715973 q^{32} +(1.74628 - 3.02464i) q^{33} -11.0195 q^{34} +(-2.91209 - 1.43940i) q^{35} +(-1.96253 + 3.39920i) q^{36} -3.08236 q^{37} +(1.64963 - 2.85725i) q^{38} +(0.445532 - 3.57792i) q^{39} +(2.87662 + 4.98245i) q^{40} +(3.61102 - 6.25447i) q^{41} +(-5.77337 - 2.85370i) q^{42} +(4.48886 + 7.77494i) q^{43} +(-6.85424 - 11.8719i) q^{44} +1.22778 q^{45} +1.63898 q^{46} +(2.58008 + 4.46883i) q^{47} +(1.77799 + 3.07957i) q^{48} +(2.69064 - 6.46223i) q^{49} +(-4.25069 + 7.36241i) q^{50} +(2.26353 + 3.92054i) q^{51} +(-11.2877 - 8.53623i) q^{52} +(-4.95271 + 8.57835i) q^{53} +2.43414 q^{54} +(-2.14405 + 3.71360i) q^{55} +(-10.3146 + 6.87832i) q^{56} -1.35541 q^{57} +(-6.44620 + 11.1651i) q^{58} +0.803443 q^{59} +(2.40956 - 4.17348i) q^{60} +(-2.32487 + 4.02680i) q^{61} +(-12.1670 + 21.0738i) q^{62} +(0.170619 + 2.64024i) q^{63} -8.85475 q^{64} +(-0.547016 + 4.39290i) q^{65} +(-4.25069 + 7.36241i) q^{66} +(1.06068 + 1.83715i) q^{67} +17.7690 q^{68} +(-0.336664 - 0.583119i) q^{69} +(7.08845 + 3.50372i) q^{70} +(-2.52793 - 4.37850i) q^{71} +(2.34294 - 4.05809i) q^{72} +(-6.04227 + 10.4655i) q^{73} +7.50291 q^{74} +3.49255 q^{75} +(-2.66004 + 4.60732i) q^{76} +(-8.28373 - 4.09453i) q^{77} +(-1.08449 + 8.70917i) q^{78} +(-5.90140 - 10.2215i) q^{79} +(-2.18299 - 3.78105i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(-8.78975 + 15.2243i) q^{82} +12.6805 q^{83} +(9.30957 + 4.60159i) q^{84} +(-2.77912 - 4.81357i) q^{85} +(-10.9265 - 18.9253i) q^{86} +5.29648 q^{87} +(8.18284 + 14.1731i) q^{88} -3.10466 q^{89} -2.98860 q^{90} +(-9.52259 - 0.565851i) q^{91} -2.64285 q^{92} +9.99692 q^{93} +(-6.28029 - 10.8778i) q^{94} +1.66415 q^{95} +(0.357986 + 0.620050i) q^{96} +(-3.59585 - 6.22820i) q^{97} +(-6.54941 + 15.7300i) q^{98} +3.49255 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 8 q^{3} + 12 q^{4} + q^{7} + 12 q^{8} - 8 q^{9}+O(q^{10}) \) 16 * q + 8 * q^3 + 12 * q^4 + q^7 + 12 * q^8 - 8 * q^9	\( 16 q + 8 q^{3} + 12 q^{4} + q^{7} + 12 q^{8} - 8 q^{9} - 4 q^{10} - 2 q^{11} + 6 q^{12} + 5 q^{13} - 7 q^{14} + 12 q^{16} + 4 q^{17} - 11 q^{19} - 20 q^{20} - q^{21} + 7 q^{22} - 8 q^{23} + 6 q^{24} + 2 q^{25} + 33 q^{26} - 16 q^{27} - q^{28} + 15 q^{29} + 4 q^{30} + 3 q^{31} - 6 q^{32} + 2 q^{33} - 68 q^{34} - 6 q^{36} - 8 q^{37} + 2 q^{38} + 4 q^{39} - 25 q^{40} + 19 q^{41} - 17 q^{42} + 11 q^{43} - 16 q^{44} - 4 q^{46} + 5 q^{47} + 6 q^{48} + 7 q^{49} - 7 q^{50} + 2 q^{51} - 18 q^{52} + 36 q^{53} - 15 q^{55} - 51 q^{56} - 22 q^{57} + 20 q^{58} + 34 q^{59} + 20 q^{60} - 22 q^{61} - 6 q^{62} - 2 q^{63} - 20 q^{64} - 24 q^{65} - 7 q^{66} + 26 q^{67} - 10 q^{68} - 4 q^{69} + 46 q^{70} + 9 q^{71} - 6 q^{72} - 6 q^{73} - 30 q^{74} + 4 q^{75} - 16 q^{76} - 36 q^{77} + 6 q^{78} + 16 q^{79} - 28 q^{80} - 8 q^{81} - q^{82} + 36 q^{83} - 8 q^{84} - 4 q^{85} + 16 q^{86} + 30 q^{87} + 24 q^{88} - 40 q^{89} + 8 q^{90} - 10 q^{91} - 94 q^{92} + 6 q^{93} - 20 q^{94} - 3 q^{96} + 7 q^{97} + 18 q^{98} + 4 q^{99}+O(q^{100}) \) 16 * q + 8 * q^3 + 12 * q^4 + q^7 + 12 * q^8 - 8 * q^9 - 4 * q^10 - 2 * q^11 + 6 * q^12 + 5 * q^13 - 7 * q^14 + 12 * q^16 + 4 * q^17 - 11 * q^19 - 20 * q^20 - q^21 + 7 * q^22 - 8 * q^23 + 6 * q^24 + 2 * q^25 + 33 * q^26 - 16 * q^27 - q^28 + 15 * q^29 + 4 * q^30 + 3 * q^31 - 6 * q^32 + 2 * q^33 - 68 * q^34 - 6 * q^36 - 8 * q^37 + 2 * q^38 + 4 * q^39 - 25 * q^40 + 19 * q^41 - 17 * q^42 + 11 * q^43 - 16 * q^44 - 4 * q^46 + 5 * q^47 + 6 * q^48 + 7 * q^49 - 7 * q^50 + 2 * q^51 - 18 * q^52 + 36 * q^53 - 15 * q^55 - 51 * q^56 - 22 * q^57 + 20 * q^58 + 34 * q^59 + 20 * q^60 - 22 * q^61 - 6 * q^62 - 2 * q^63 - 20 * q^64 - 24 * q^65 - 7 * q^66 + 26 * q^67 - 10 * q^68 - 4 * q^69 + 46 * q^70 + 9 * q^71 - 6 * q^72 - 6 * q^73 - 30 * q^74 + 4 * q^75 - 16 * q^76 - 36 * q^77 + 6 * q^78 + 16 * q^79 - 28 * q^80 - 8 * q^81 - q^82 + 36 * q^83 - 8 * q^84 - 4 * q^85 + 16 * q^86 + 30 * q^87 + 24 * q^88 - 40 * q^89 + 8 * q^90 - 10 * q^91 - 94 * q^92 + 6 * q^93 - 20 * q^94 - 3 * q^96 + 7 * q^97 + 18 * q^98 + 4 * q^99

Introduction

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