LMFDB - Embedded newform 273.2.t.d.205.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [273,2,Mod(4,273)]

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, 4, 1]))

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

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

chi := DirichletCharacter("273.4");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 273 = 3 \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	273.t (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:	$2.17991597518$
Analytic rank:	$0$
Dimension:	$20$
Relative dimension:	$10$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} + 33 x^{18} + 455 x^{16} + 3403 x^{14} + 15006 x^{12} + 39799 x^{10} + 62505 x^{8} + 55993 x^{6} + \cdots + 576 $ x^20 + 33x^18 + 455x^16 + 3403x^14 + 15006x^12 + 39799x^10 + 62505x^8 + 55993x^6 + 27166x^4 + 6435*x^2 + 576
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 3 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			205.5
Root			$0.493650i$ of defining polynomial
Character	$\chi$	$=$	273.205
Dual form			273.2.t.d.4.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+0.493650i q^{2} +(0.500000 - 0.866025i) q^{3} +1.75631 q^{4} +(2.40375 + 1.38781i) q^{5} +(0.427513 + 0.246825i) q^{6} +(-0.134370 + 2.64234i) q^{7} +1.85430i q^{8} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})$	\(q+0.493650i q^{2} +(0.500000 - 0.866025i) q^{3} +1.75631 q^{4} +(2.40375 + 1.38781i) q^{5} +(0.427513 + 0.246825i) q^{6} +(-0.134370 + 2.64234i) q^{7} +1.85430i q^{8} +(-0.500000 - 0.866025i) q^{9} +(-0.685090 + 1.18661i) q^{10} +(-3.69662 - 2.13424i) q^{11} +(0.878155 - 1.52101i) q^{12} +(-3.60546 - 0.0256188i) q^{13} +(-1.30439 - 0.0663316i) q^{14} +(2.40375 - 1.38781i) q^{15} +2.59724 q^{16} -4.53423 q^{17} +(0.427513 - 0.246825i) q^{18} +(6.72325 - 3.88167i) q^{19} +(4.22173 + 2.43742i) q^{20} +(2.22115 + 1.43754i) q^{21} +(1.05357 - 1.82484i) q^{22} -1.52334 q^{23} +(1.60587 + 0.927151i) q^{24} +(1.35201 + 2.34175i) q^{25} +(0.0126467 - 1.77984i) q^{26} -1.00000 q^{27} +(-0.235995 + 4.64076i) q^{28} +(-2.58391 - 4.47547i) q^{29} +(0.685090 + 1.18661i) q^{30} +(3.83715 - 2.21538i) q^{31} +4.99073i q^{32} +(-3.69662 + 2.13424i) q^{33} -2.23832i q^{34} +(-3.99004 + 6.16504i) q^{35} +(-0.878155 - 1.52101i) q^{36} -6.32954i q^{37} +(1.91618 + 3.31893i) q^{38} +(-1.82492 + 3.10961i) q^{39} +(-2.57341 + 4.45728i) q^{40} +(-0.0911887 + 0.0526478i) q^{41} +(-0.709640 + 1.09647i) q^{42} +(0.997139 - 1.72709i) q^{43} +(-6.49241 - 3.74839i) q^{44} -2.77561i q^{45} -0.751998i q^{46} +(10.6531 + 6.15060i) q^{47} +(1.29862 - 2.24928i) q^{48} +(-6.96389 - 0.710101i) q^{49} +(-1.15601 + 0.667421i) q^{50} +(-2.26712 + 3.92676i) q^{51} +(-6.33231 - 0.0449946i) q^{52} +(-4.99999 - 8.66024i) q^{53} -0.493650i q^{54} +(-5.92383 - 10.2604i) q^{55} +(-4.89969 - 0.249162i) q^{56} -7.76333i q^{57} +(2.20932 - 1.27555i) q^{58} +1.32593i q^{59} +(4.22173 - 2.43742i) q^{60} +(4.77043 + 8.26263i) q^{61} +(1.09362 + 1.89421i) q^{62} +(2.35552 - 1.20480i) q^{63} +2.73081 q^{64} +(-8.63107 - 5.06526i) q^{65} +(-1.05357 - 1.82484i) q^{66} +(3.63550 + 2.09896i) q^{67} -7.96352 q^{68} +(-0.761671 + 1.31925i) q^{69} +(-3.04337 - 1.96968i) q^{70} +(-7.08704 - 4.09170i) q^{71} +(1.60587 - 0.927151i) q^{72} +(-12.7369 + 7.35364i) q^{73} +3.12458 q^{74} +2.70402 q^{75} +(11.8081 - 6.81741i) q^{76} +(6.13611 - 9.48094i) q^{77} +(-1.53506 - 0.900870i) q^{78} +(-2.91099 + 5.04199i) q^{79} +(6.24313 + 3.60447i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(-0.0259896 - 0.0450153i) q^{82} +5.22675i q^{83} +(3.90102 + 2.52476i) q^{84} +(-10.8992 - 6.29264i) q^{85} +(0.852580 + 0.492237i) q^{86} -5.16783 q^{87} +(3.95753 - 6.85465i) q^{88} +8.39590i q^{89} +1.37018 q^{90} +(0.552159 - 9.52340i) q^{91} -2.67546 q^{92} -4.43076i q^{93} +(-3.03624 + 5.25892i) q^{94} +21.5480 q^{95} +(4.32210 + 2.49537i) q^{96} +(7.51885 + 4.34101i) q^{97} +(0.350541 - 3.43772i) q^{98} +4.26849i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q + 10 q^{3} - 26 q^{4} + 6 q^{5} + 3 q^{6} + 2 q^{7} - 10 q^{9}+O(q^{10}) $ 20 * q + 10 * q^3 - 26 * q^4 + 6 * q^5 + 3 * q^6 + 2 * q^7 - 10 * q^9	$ 20 q + 10 q^{3} - 26 q^{4} + 6 q^{5} + 3 q^{6} + 2 q^{7} - 10 q^{9} + 2 q^{10} - 12 q^{11} - 13 q^{12} + 8 q^{13} + 2 q^{14} + 6 q^{15} + 42 q^{16} + 16 q^{17} + 3 q^{18} - 9 q^{19} - 5 q^{21} - 9 q^{22} - 36 q^{23} + 3 q^{24} + 12 q^{25} - 16 q^{26} - 20 q^{27} - 2 q^{28} - 3 q^{29} - 2 q^{30} - 18 q^{31} - 12 q^{33} + 18 q^{35} + 13 q^{36} + 9 q^{38} + 7 q^{39} + 5 q^{40} + 21 q^{41} + 16 q^{42} + 16 q^{43} - 6 q^{44} + 21 q^{47} + 21 q^{48} - 24 q^{49} - 54 q^{50} + 8 q^{51} - 41 q^{52} - 26 q^{53} + 17 q^{55} - 6 q^{56} + 42 q^{58} + 4 q^{62} - 7 q^{63} - 46 q^{64} - 50 q^{65} + 9 q^{66} - 3 q^{67} + 6 q^{68} - 18 q^{69} + 15 q^{71} + 3 q^{72} - 9 q^{73} + 12 q^{74} + 24 q^{75} + 75 q^{76} + 20 q^{77} - 32 q^{78} + 3 q^{79} - 24 q^{80} - 10 q^{81} + 15 q^{82} + 41 q^{84} - 78 q^{85} + 3 q^{86} - 6 q^{87} - 22 q^{88} - 4 q^{90} + 4 q^{91} + 142 q^{92} + 36 q^{94} - 84 q^{95} - 24 q^{96} - 15 q^{97} + 81 q^{98}+O(q^{100}) $ 20 * q + 10 * q^3 - 26 * q^4 + 6 * q^5 + 3 * q^6 + 2 * q^7 - 10 * q^9 + 2 * q^10 - 12 * q^11 - 13 * q^12 + 8 * q^13 + 2 * q^14 + 6 * q^15 + 42 * q^16 + 16 * q^17 + 3 * q^18 - 9 * q^19 - 5 * q^21 - 9 * q^22 - 36 * q^23 + 3 * q^24 + 12 * q^25 - 16 * q^26 - 20 * q^27 - 2 * q^28 - 3 * q^29 - 2 * q^30 - 18 * q^31 - 12 * q^33 + 18 * q^35 + 13 * q^36 + 9 * q^38 + 7 * q^39 + 5 * q^40 + 21 * q^41 + 16 * q^42 + 16 * q^43 - 6 * q^44 + 21 * q^47 + 21 * q^48 - 24 * q^49 - 54 * q^50 + 8 * q^51 - 41 * q^52 - 26 * q^53 + 17 * q^55 - 6 * q^56 + 42 * q^58 + 4 * q^62 - 7 * q^63 - 46 * q^64 - 50 * q^65 + 9 * q^66 - 3 * q^67 + 6 * q^68 - 18 * q^69 + 15 * q^71 + 3 * q^72 - 9 * q^73 + 12 * q^74 + 24 * q^75 + 75 * q^76 + 20 * q^77 - 32 * q^78 + 3 * q^79 - 24 * q^80 - 10 * q^81 + 15 * q^82 + 41 * q^84 - 78 * q^85 + 3 * q^86 - 6 * q^87 - 22 * q^88 - 4 * q^90 + 4 * q^91 + 142 * q^92 + 36 * q^94 - 84 * q^95 - 24 * q^96 - 15 * q^97 + 81 * q^98

Display 100 coefficients 10 coefficients

Character values

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

$n$	$92$	$106$	$157$
$\chi(n)$	$1$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{1}{3}\right)$

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 $

$2$			0.493650i			0.349063i	0.984652	+	0.174532i	$0.0558411\pi$
$2$			0.493650i			0.349063i	−0.984652	+	0.174532i	$0.944159\pi$
$3$	0.500000	−	0.866025i	0.288675	−	0.500000i
$3$	0.500000	−	0.866025i	0.288675	−	0.500000i
$4$	1.75631			0.878155
$5$	2.40375	+	1.38781i	1.07499	+	0.620646i	0.929541	−	0.368720i	$-0.120204\pi$
$5$	2.40375	+	1.38781i	1.07499	+	0.620646i	0.145449	+	0.989366i	$0.453537\pi$
$6$	0.427513	+	0.246825i	0.174532	+	0.100766i
$7$	−0.134370	+	2.64234i	−0.0507870	+	0.998710i
$7$	−0.134370	+	2.64234i	−0.0507870	+	0.998710i
$8$			1.85430i			0.655595i
$9$	−0.500000	−	0.866025i	−0.166667	−	0.288675i
$10$	−0.685090	+	1.18661i	−0.216645	+	0.375239i
$11$	−3.69662	−	2.13424i	−1.11457	−	0.643499i	−0.174563	−	0.984646i	$-0.555851\pi$
$11$	−3.69662	−	2.13424i	−1.11457	−	0.643499i	−0.940010	+	0.341147i	$0.889185\pi$
$12$	0.878155	−	1.52101i	0.253501	−	0.439077i
$13$	−3.60546	−	0.0256188i	−0.999975	−	0.00710538i
$13$	−3.60546	−	0.0256188i	−0.999975	−	0.00710538i
$14$	−1.30439	−	0.0663316i	−0.348613	−	0.0177279i
$15$	2.40375	−	1.38781i	0.620646	−	0.358330i
$16$	2.59724			0.649311
$17$	−4.53423			−1.09971			−0.549857	−	0.835259i	$-0.685318\pi$
$17$	−4.53423			−1.09971			−0.549857	+	0.835259i	$0.685318\pi$
$18$	0.427513	−	0.246825i	0.100766	−	0.0581772i
$19$	6.72325	−	3.88167i	1.54242	−	0.890516i	0.543733	−	0.839258i	$-0.317011\pi$
$19$	6.72325	−	3.88167i	1.54242	−	0.890516i	0.998685	−	0.0512571i	$-0.0163228\pi$
$20$	4.22173	+	2.43742i	0.944008	+	0.545023i
$21$	2.22115	+	1.43754i	0.484694	+	0.313696i
$22$	1.05357	−	1.82484i	0.224622	−	0.389056i
$23$	−1.52334			−0.317639			−0.158819	−	0.987308i	$-0.550769\pi$
$23$	−1.52334			−0.317639			−0.158819	+	0.987308i	$0.550769\pi$
$24$	1.60587	+	0.927151i	0.327797	+	0.189254i
$25$	1.35201	+	2.34175i	0.270402	+	0.468351i
$26$	0.0126467	−	1.77984i	0.00248023	−	0.349054i
$27$	−1.00000			−0.192450
$28$	−0.235995	+	4.64076i	−0.0445989	+	0.877022i
$29$	−2.58391	−	4.47547i	−0.479821	−	0.831074i	0.519911	−	0.854220i	$-0.325965\pi$
$29$	−2.58391	−	4.47547i	−0.479821	−	0.831074i	−0.999732	+	0.0231461i	$0.992632\pi$
$30$	0.685090	+	1.18661i	0.125080	+	0.216645i
$31$	3.83715	−	2.21538i	0.689173	−	0.397894i	−0.114129	−	0.993466i	$-0.536408\pi$
$31$	3.83715	−	2.21538i	0.689173	−	0.397894i	0.803302	+	0.595572i	$0.203074\pi$
$32$			4.99073i			0.882245i
$33$	−3.69662	+	2.13424i	−0.643499	+	0.371524i
$34$		−	2.23832i		−	0.383869i
$35$	−3.99004	+	6.16504i	−0.674440	+	1.04208i
$36$	−0.878155	−	1.52101i	−0.146359	−	0.253501i
$37$		−	6.32954i		−	1.04057i	−0.853993	−	0.520285i	$-0.825826\pi$
$37$		−	6.32954i		−	1.04057i	0.853993	−	0.520285i	$-0.174174\pi$
$38$	1.91618	+	3.31893i	0.310846	+	0.538401i
$39$	−1.82492	+	3.10961i	−0.292221	+	0.497936i
$40$	−2.57341	+	4.45728i	−0.406892	+	0.704758i
$41$	−0.0911887	+	0.0526478i	−0.0142413	+	0.00822221i	−0.507104	−	0.861885i	$-0.669284\pi$
$41$	−0.0911887	+	0.0526478i	−0.0142413	+	0.00822221i	0.492862	+	0.870107i	$0.335951\pi$
$42$	−0.709640	+	1.09647i	−0.109500	+	0.169189i
$43$	0.997139	−	1.72709i	0.152062	−	0.263379i	−0.779923	−	0.625875i	$-0.784742\pi$
$43$	0.997139	−	1.72709i	0.152062	−	0.263379i	0.931985	+	0.362496i	$0.118075\pi$
$44$	−6.49241	−	3.74839i	−0.978767	−	0.565092i
$45$		−	2.77561i		−	0.413764i
$46$		−	0.751998i		−	0.110876i
$47$	10.6531	+	6.15060i	1.55392	+	0.897157i	0.997817	+	0.0660438i	$0.0210377\pi$
$47$	10.6531	+	6.15060i	1.55392	+	0.897157i	0.556104	+	0.831113i	$0.312296\pi$
$48$	1.29862	−	2.24928i	0.187440	−	0.324655i
$49$	−6.96389	−	0.710101i	−0.994841	−	0.101443i
$50$	−1.15601	+	0.667421i	−0.163484	+	0.0943875i
$51$	−2.26712	+	3.92676i	−0.317460	+	0.549857i
$52$	−6.33231	−	0.0449946i	−0.878133	−	0.00623963i
$53$	−4.99999	−	8.66024i	−0.686801	−	1.18958i	−0.972867	−	0.231365i	$-0.925681\pi$
$53$	−4.99999	−	8.66024i	−0.686801	−	1.18958i	0.286066	−	0.958210i	$-0.407652\pi$
$54$		−	0.493650i		−	0.0671772i
$55$	−5.92383	−	10.2604i	−0.798770	−	1.38351i
$56$	−4.89969	−	0.249162i	−0.654749	−	0.0332957i
$57$		−	7.76333i		−	1.02828i
$58$	2.20932	−	1.27555i	0.290097	−	0.167488i
$59$			1.32593i			0.172622i	0.996268	+	0.0863110i	$0.0275079\pi$
$59$			1.32593i			0.172622i	−0.996268	+	0.0863110i	$0.972492\pi$
$60$	4.22173	−	2.43742i	0.545023	−	0.314669i
$61$	4.77043	+	8.26263i	0.610791	+	1.05792i	0.991107	+	0.133064i	$0.0424817\pi$
$61$	4.77043	+	8.26263i	0.610791	+	1.05792i	−0.380317	+	0.924856i	$0.624185\pi$
$62$	1.09362	+	1.89421i	0.138890	+	0.240565i
$63$	2.35552	−	1.20480i	0.296767	−	0.151791i
$64$	2.73081			0.341351
$65$	−8.63107	−	5.06526i	−1.07055	−	0.628268i
$66$	−1.05357	−	1.82484i	−0.129685	−	0.224622i
$67$	3.63550	+	2.09896i	0.444147	+	0.256428i	0.705355	−	0.708854i	$-0.250788\pi$
$67$	3.63550	+	2.09896i	0.444147	+	0.256428i	−0.261208	+	0.965283i	$0.584121\pi$
$68$	−7.96352			−0.965719
$69$	−0.761671	+	1.31925i	−0.0916945	+	0.158819i
$70$	−3.04337	−	1.96968i	−0.363752	−	0.235422i
$71$	−7.08704	−	4.09170i	−0.841076	−	0.485596i	0.0165536	−	0.999863i	$-0.494731\pi$
$71$	−7.08704	−	4.09170i	−0.841076	−	0.485596i	−0.857630	+	0.514267i	$0.828064\pi$
$72$	1.60587	−	0.927151i	0.189254	−	0.109266i
$73$	−12.7369	+	7.35364i	−1.49074	+	0.860679i	−0.999944	−	0.0105964i	$-0.996627\pi$
$73$	−12.7369	+	7.35364i	−1.49074	+	0.860679i	−0.490795	+	0.871275i	$0.663294\pi$
$74$	3.12458			0.363225
$75$	2.70402			0.312234
$76$	11.8081	−	6.81741i	1.35448	−	0.782011i
$77$	6.13611	−	9.48094i	0.699274	−	1.08045i
$78$	−1.53506	−	0.900870i	−0.173811	−	0.102003i
$79$	−2.91099	+	5.04199i	−0.327512	+	0.567268i	−0.982018	−	0.188789i	$-0.939544\pi$
$79$	−2.91099	+	5.04199i	−0.327512	+	0.567268i	0.654505	+	0.756058i	$0.272877\pi$
$80$	6.24313	+	3.60447i	0.698003	+	0.402992i
$81$	−0.500000	+	0.866025i	−0.0555556	+	0.0962250i
$82$	−0.0259896	−	0.0450153i	−0.00287007	−	0.00497111i
$83$			5.22675i			0.573710i	0.957974	+	0.286855i	$0.0926099\pi$
$83$			5.22675i			0.573710i	−0.957974	+	0.286855i	$0.907390\pi$
$84$	3.90102	+	2.52476i	0.425636	+	0.275474i
$85$	−10.8992	−	6.29264i	−1.18218	−	0.682532i
$86$	0.852580	+	0.492237i	0.0919361	+	0.0530793i
$87$	−5.16783			−0.554049
$88$	3.95753	−	6.85465i	0.421874	−	0.730708i
$89$			8.39590i			0.889963i	0.895540	+	0.444982i	$0.146790\pi$
$89$			8.39590i			0.889963i	−0.895540	+	0.444982i	$0.853210\pi$
$90$	1.37018			0.144430
$91$	0.552159	−	9.52340i	0.0578819	−	0.998323i
$92$	−2.67546			−0.278936
$93$		−	4.43076i		−	0.459449i
$94$	−3.03624	+	5.25892i	−0.313164	+	0.542417i
$95$	21.5480			2.21078
$96$	4.32210	+	2.49537i	0.441123	+	0.254682i
$97$	7.51885	+	4.34101i	0.763423	+	0.440763i	0.830524	−	0.556984i	$-0.188041\pi$
$97$	7.51885	+	4.34101i	0.763423	+	0.440763i	−0.0671001	+	0.997746i	$0.521375\pi$
$98$	0.350541	−	3.43772i	0.0354100	−	0.347263i
$99$			4.26849i			0.428999i
$100$	2.37455	+	4.11284i	0.237455	+	0.411284i
$101$	−1.76672	+	3.06005i	−0.175795	+	0.304486i	−0.940436	−	0.339970i	$-0.889583\pi$
$101$	−1.76672	+	3.06005i	−0.175795	+	0.304486i	0.764641	+	0.644457i	$0.222916\pi$
$102$	−1.93845	−	1.11916i	−0.191935	−	0.110814i
$103$	1.55849	−	2.69939i	0.153563	−	0.265979i	−0.778972	−	0.627059i	$-0.784259\pi$
$103$	1.55849	−	2.69939i	0.153563	−	0.265979i	0.932535	+	0.361080i	$0.117592\pi$
$104$	0.0475050	−	6.68561i	0.00465825	−	0.655578i
$105$	3.34406	+	6.53800i	0.326347	+	0.638043i
$106$	4.27513	−	2.46824i	0.415237	−	0.239737i
$107$	−0.987204			−0.0954366			−0.0477183	−	0.998861i	$-0.515195\pi$
$107$	−0.987204			−0.0954366			−0.0477183	+	0.998861i	$0.515195\pi$
$108$	−1.75631			−0.169001
$109$	−10.8749	+	6.27865i	−1.04163	+	0.601385i	−0.920294	−	0.391226i	$-0.872051\pi$
$109$	−10.8749	+	6.27865i	−1.04163	+	0.601385i	−0.121335	+	0.992612i	$0.538718\pi$
$110$	5.06504	−	2.92430i	0.482932	−	0.278821i
$111$	−5.48154	−	3.16477i	−0.520285	−	0.300387i
$112$	−0.348991	+	6.86279i	−0.0329766	+	0.648473i
$113$	−6.46070	+	11.1903i	−0.607771	+	1.05269i	0.383836	+	0.923401i	$0.374603\pi$
$113$	−6.46070	+	11.1903i	−0.607771	+	1.05269i	−0.991607	+	0.129289i	$0.958730\pi$
$114$	3.83237			0.358934
$115$	−3.66174	−	2.11410i	−0.341459	−	0.197141i
$116$	−4.53815	−	7.86031i	−0.421357	−	0.729812i
$117$	1.78054	+	3.13523i	0.164611	+	0.289852i
$118$	−0.654548			−0.0602560
$119$	0.609264	−	11.9810i	0.0558512	−	1.09829i
$120$	2.57341	+	4.45728i	0.234919	+	0.406892i
$121$	3.60999	+	6.25269i	0.328181	+	0.568427i
$122$	−4.07884	+	2.35492i	−0.369281	+	0.213205i
$123$			0.105296i			0.00949419i
$124$	6.73923	−	3.89090i	0.605201	−	0.349413i
$125$		−	6.37274i		−	0.569995i
$126$	0.594750	+	1.16280i	0.0529845	+	0.103590i
$127$	1.62994	+	2.82315i	0.144634	+	0.250514i	0.929236	−	0.369486i	$-0.120466\pi$
$127$	1.62994	+	2.82315i	0.144634	+	0.250514i	−0.784602	+	0.619999i	$0.787133\pi$
$128$			11.3295i			1.00140i
$129$	−0.997139	−	1.72709i	−0.0877932	−	0.152062i
$130$	2.50047	−	4.26073i	0.219305	−	0.373691i
$131$	−0.605523	+	1.04880i	−0.0529048	+	0.0916338i	−0.891265	−	0.453483i	$-0.850181\pi$
$131$	−0.605523	+	1.04880i	−0.0529048	+	0.0916338i	0.838360	+	0.545117i	$0.183515\pi$
$132$	−6.49241	+	3.74839i	−0.565092	+	0.326256i
$133$	9.35327	+	18.2867i	0.811032	+	1.58565i
$134$	−1.03615	+	1.79466i	−0.0895097	+	0.155035i
$135$	−2.40375	−	1.38781i	−0.206882	−	0.119443i
$136$		−	8.40784i		−	0.720966i
$137$			13.7639i			1.17593i	0.808887	+	0.587964i	$0.200070\pi$
$137$			13.7639i			1.17593i	−0.808887	+	0.587964i	$0.799930\pi$
$138$	−0.651249	−	0.375999i	−0.0554380	−	0.0320072i
$139$	−7.90937	+	13.6994i	−0.670864	+	1.16197i	0.306796	+	0.951775i	$0.400743\pi$
$139$	−7.90937	+	13.6994i	−0.670864	+	1.16197i	−0.977659	+	0.210195i	$0.932590\pi$
$140$	−7.00775	+	10.8277i	−0.592263	+	0.915109i
$141$	10.6531	−	6.15060i	0.897157	−	0.517974i
$142$	2.01987	−	3.49851i	0.169504	−	0.293589i
$143$	13.2733	+	7.78963i	1.10997	+	0.651402i
$144$	−1.29862	−	2.24928i	−0.108218	−	0.187440i
$145$		−	14.3439i		−	1.19120i
$146$	−3.63012	−	6.28756i	−0.300431	−	0.520362i
$147$	−4.09691	+	5.67585i	−0.337907	+	0.468137i
$148$		−	11.1166i		−	0.913782i
$149$	14.2445	−	8.22407i	1.16696	−	0.673742i	0.213995	−	0.976835i	$-0.431352\pi$
$149$	14.2445	−	8.22407i	1.16696	−	0.673742i	0.952961	+	0.303093i	$0.0980192\pi$
$150$			1.33484i			0.108989i
$151$	6.57823	−	3.79794i	0.535329	−	0.309072i	−0.207855	−	0.978160i	$-0.566648\pi$
$151$	6.57823	−	3.79794i	0.535329	−	0.309072i	0.743184	+	0.669087i	$0.233315\pi$
$152$	7.19778	+	12.4669i	0.583817	+	1.01120i
$153$	2.26712	+	3.92676i	0.183286	+	0.317460i
$154$	4.68026	+	3.02909i	0.377146	+	0.244091i
$155$	12.2981			0.987805
$156$	−3.20512	+	5.46144i	−0.256615	+	0.437265i
$157$	1.94950	+	3.37664i	0.155587	+	0.269485i	0.933273	−	0.359169i	$-0.116940\pi$
$157$	1.94950	+	3.37664i	0.155587	+	0.269485i	−0.777686	+	0.628653i	$0.783606\pi$
$158$	−2.48898	−	1.43701i	−0.198012	−	0.114323i
$159$	−9.99998			−0.793050
$160$	−6.92617	+	11.9965i	−0.547562	+	0.948405i
$161$	0.204691	−	4.02519i	0.0161319	−	0.317229i
$162$	−0.427513	−	0.246825i	−0.0335886	−	0.0193924i
$163$	−10.3098	+	5.95235i	−0.807524	+	0.466224i	−0.846095	−	0.533032i	$-0.821053\pi$
$163$	−10.3098	+	5.95235i	−0.807524	+	0.466224i	0.0385712	+	0.999256i	$0.487719\pi$
$164$	−0.160156	+	0.0924659i	−0.0125061	+	0.00722038i
$165$	−11.8477			−0.922340
$166$	−2.58018			−0.200261
$167$	17.8391	−	10.2994i	1.38043	−	0.796992i	0.388220	−	0.921567i	$-0.373090\pi$
$167$	17.8391	−	10.2994i	1.38043	−	0.796992i	0.992210	+	0.124575i	$0.0397567\pi$
$168$	−2.66563	+	4.11868i	−0.205658	+	0.317763i
$169$	12.9987	+	0.184735i	0.999899	+	0.0142104i
$170$	3.10636	−	5.38037i	0.238247	−	0.412656i
$171$	−6.72325	−	3.88167i	−0.514139	−	0.296839i
$172$	1.75128	−	3.03331i	0.133534	−	0.231288i
$173$	−0.155012	−	0.268489i	−0.0117854	−	0.0204129i	0.860073	−	0.510172i	$-0.170418\pi$
$173$	−0.155012	−	0.268489i	−0.0117854	−	0.0204129i	−0.871858	+	0.489759i	$0.837085\pi$
$174$		−	2.55110i		−	0.193398i
$175$	−6.36937	+	3.25781i	−0.481479	+	0.246267i
$176$	−9.60102	−	5.54315i	−0.723704	−	0.417831i
$177$	1.14829	+	0.662967i	0.0863110	+	0.0498317i
$178$	−4.14463			−0.310653
$179$	6.85580	−	11.8746i	0.512426	−	0.887549i	−0.487470	−	0.873140i	$-0.662080\pi$
$179$	6.85580	−	11.8746i	0.512426	−	0.887549i	0.999896	−	0.0144087i	$-0.00458660\pi$
$180$		−	4.87484i		−	0.363349i
$181$	−0.968409			−0.0719813			−0.0359907	−	0.999352i	$-0.511459\pi$
$181$	−0.968409			−0.0719813			−0.0359907	+	0.999352i	$0.511459\pi$
$182$	4.70122	+	0.272573i	0.348478	+	0.0202045i
$183$	9.54086			0.705281
$184$		−	2.82474i		−	0.208242i
$185$	8.78418	−	15.2146i	0.645826	−	1.11860i
$186$	2.18725			0.160377
$187$	16.7613	+	9.67716i	1.22571	+	0.707664i
$188$	18.7102	+	10.8024i	1.36458	+	0.787842i
$189$	0.134370	−	2.64234i	0.00977396	−	0.192202i
$190$			10.6372i			0.771702i
$191$	−0.538508	−	0.932724i	−0.0389651	−	0.0674895i	0.845885	−	0.533365i	$-0.179073\pi$
$191$	−0.538508	−	0.932724i	−0.0389651	−	0.0674895i	−0.884850	+	0.465876i	$0.845739\pi$
$192$	1.36541	−	2.36495i	0.0985397	−	0.170676i
$193$	−11.1787	−	6.45400i	−0.804657	−	0.464569i	0.0404400	−	0.999182i	$-0.487124\pi$
$193$	−11.1787	−	6.45400i	−0.804657	−	0.464569i	−0.845097	+	0.534613i	$0.820457\pi$
$194$	−2.14294	+	3.71168i	−0.153854	+	0.266483i
$195$	−8.70218	+	4.94210i	−0.623176	+	0.353911i
$196$	−12.2307	−	1.24716i	−0.873625	−	0.0890826i
$197$	13.8632	−	8.00395i	0.987716	−	0.570258i	0.0831250	−	0.996539i	$-0.473510\pi$
$197$	13.8632	−	8.00395i	0.987716	−	0.570258i	0.904591	+	0.426281i	$0.140177\pi$
$198$	−2.10714			−0.149748
$199$	8.52029			0.603987			0.301994	−	0.953310i	$-0.402348\pi$
$199$	8.52029			0.603987			0.301994	+	0.953310i	$0.402348\pi$
$200$	−4.34232	+	2.50704i	−0.307048	+	0.177274i
$201$	3.63550	−	2.09896i	0.256428	−	0.148049i
$202$	−1.51059	−	0.872142i	−0.106285	−	0.0613637i
$203$	12.1729	−	6.22621i	0.854370	−	0.436994i
$204$	−3.98176	+	6.89661i	−0.278779	+	0.482859i
$205$	−0.292260			−0.0204123
$206$	1.33255	+	0.769350i	0.0928434	+	0.0536031i
$207$	0.761671	+	1.31925i	0.0529398	+	0.0916945i
$208$	−9.36426	−	0.0665383i	−0.649294	−	0.00461360i
$209$	−33.1377			−2.29218
$210$	−3.22748	+	1.65079i	−0.222717	+	0.113916i
$211$	−10.3435	−	17.9155i	−0.712078	−	1.23336i	−0.964076	−	0.265628i	$-0.914421\pi$
$211$	−10.3435	−	17.9155i	−0.712078	−	1.23336i	0.251997	−	0.967728i	$-0.418913\pi$
$212$	−8.78153	−	15.2101i	−0.603118	−	1.04463i
$213$	−7.08704	+	4.09170i	−0.485596	+	0.280359i
$214$		−	0.487333i		−	0.0333134i
$215$	4.79375	−	2.76767i	0.326931	−	0.188754i
$216$		−	1.85430i		−	0.126169i
$217$	5.33819	+	10.4367i	0.362380	+	0.708491i
$218$	−3.09945	−	5.36841i	−0.209921	−	0.363595i
$219$			14.7073i			0.993826i
$220$	−10.4041	−	18.0204i	−0.701443	−	1.21494i
$221$	16.3480	+	0.116162i	1.09969	+	0.00781389i
$222$	1.56229	−	2.70596i	0.104854	−	0.181612i
$223$	−8.25498	+	4.76602i	−0.552795	+	0.319156i	−0.750248	−	0.661156i	$-0.770066\pi$
$223$	−8.25498	+	4.76602i	−0.552795	+	0.319156i	0.197454	+	0.980312i	$0.436733\pi$
$224$	−13.1872	−	0.670604i	−0.881107	−	0.0448066i
$225$	1.35201	−	2.34175i	0.0901341	−	0.156117i
$226$	−5.52407	−	3.18932i	−0.367456	−	0.212151i
$227$			10.9513i			0.726860i	0.931621	+	0.363430i	$0.118394\pi$
$227$			10.9513i			0.726860i	−0.931621	+	0.363430i	$0.881606\pi$
$228$		−	13.6348i		−	0.902988i
$229$	−22.9511	−	13.2508i	−1.51665	−	0.875640i	−0.999809	−	0.0195616i	$-0.993773\pi$
$229$	−22.9511	−	13.2508i	−1.51665	−	0.875640i	−0.516845	−	0.856079i	$-0.672894\pi$
$230$	1.04363	−	1.80762i	0.0688148	−	0.119191i
$231$	−5.14268	−	10.0545i	−0.338363	−	0.661537i
$232$	8.29888	−	4.79136i	0.544848	−	0.314568i
$233$	5.33371	−	9.23825i	0.349423	−	0.605218i	−0.636724	−	0.771092i	$-0.719711\pi$
$233$	5.33371	−	9.23825i	0.349423	−	0.605218i	0.986147	+	0.165874i	$0.0530444\pi$
$234$	−1.54771	+	0.878965i	−0.101177	+	0.0574598i
$235$	17.0717	+	29.5690i	1.11363	+	1.92887i
$236$			2.32875i			0.151589i
$237$	2.91099	+	5.04199i	0.189089	+	0.327512i
$238$	5.91441	+	0.300763i	0.383374	+	0.0194956i
$239$			25.5584i			1.65323i	0.562765	+	0.826617i	$0.309738\pi$
$239$			25.5584i			1.65323i	−0.562765	+	0.826617i	$0.690262\pi$
$240$	6.24313	−	3.60447i	0.402992	−	0.232668i
$241$			0.459225i			0.0295813i	0.999891	+	0.0147907i	$0.00470818\pi$
$241$			0.459225i			0.0295813i	−0.999891	+	0.0147907i	$0.995292\pi$
$242$	−3.08664	+	1.78207i	−0.198417	+	0.114556i
$243$	0.500000	+	0.866025i	0.0320750	+	0.0555556i
$244$	8.37835	+	14.5117i	0.536369	+	0.929018i
$245$	−15.7540	−	11.3714i	−1.00648	−	0.726494i
$246$	−0.0519792			−0.00331407
$247$	−24.3398	+	13.8230i	−1.54871	+	0.879534i
$248$	4.10799	+	7.11524i	0.260857	+	0.451818i
$249$	4.52650	+	2.61338i	0.286855	+	0.165616i
$250$	3.14590			0.198964
$251$	11.2929	−	19.5598i	0.712800	−	1.23461i	−0.251001	−	0.967987i	$-0.580760\pi$
$251$	11.2929	−	19.5598i	0.712800	−	1.23461i	0.963802	−	0.266620i	$-0.0859068\pi$
$252$	4.13702	−	2.11600i	0.260607	−	0.133296i
$253$	5.63122	+	3.25119i	0.354032	+	0.204400i
$254$	−1.39365	+	0.804622i	−0.0874451	+	0.0504865i
$255$	−10.8992	+	6.29264i	−0.682532	+	0.394060i
$256$	−0.131198			−0.00819989
$257$	−24.4625			−1.52593			−0.762964	−	0.646441i	$-0.776257\pi$
$257$	−24.4625			−1.52593			−0.762964	+	0.646441i	$0.776257\pi$
$258$	0.852580	−	0.492237i	0.0530793	−	0.0306454i
$259$	16.7248	+	0.850499i	1.03923	+	0.0528475i
$260$	−15.1588	−	8.89617i	−0.940111	−	0.551717i
$261$	−2.58391	+	4.47547i	−0.159940	+	0.277025i
$262$	−0.517739	−	0.298917i	−0.0319860	−	0.0184671i
$263$	0.570488	−	0.988115i	0.0351778	−	0.0609298i	−0.847900	−	0.530155i	$-0.822134\pi$
$263$	0.570488	−	0.988115i	0.0351778	−	0.0609298i	0.883078	+	0.469226i	$0.155467\pi$
$264$	−3.95753	−	6.85465i	−0.243569	−	0.421874i
$265$		−	27.7561i		−	1.70504i
$266$	−9.02721	+	4.61724i	−0.553494	+	0.283101i
$267$	7.27106	+	4.19795i	0.444982	+	0.256910i
$268$	6.38506	+	3.68642i	0.390030	+	0.225184i
$269$	24.9242			1.51965			0.759826	−	0.650126i	$-0.225284\pi$
$269$	24.9242			1.51965			0.759826	+	0.650126i	$0.225284\pi$
$270$	0.685090	−	1.18661i	0.0416933	−	0.0722149i
$271$			0.238152i			0.0144667i	0.999974	+	0.00723336i	$0.00230247\pi$
$271$			0.238152i			0.0144667i	−0.999974	+	0.00723336i	$0.997698\pi$
$272$	−11.7765			−0.714056
$273$	−7.97143	−	5.23988i	−0.482453	−	0.317132i
$274$	−6.79454			−0.410473
$275$		−	11.5421i		−	0.696014i
$276$	−1.33773	+	2.31702i	−0.0805219	+	0.139468i
$277$	−25.4403			−1.52856			−0.764281	−	0.644883i	$-0.776906\pi$
$277$	−25.4403			−1.52856			−0.764281	+	0.644883i	$0.776906\pi$
$278$	−6.76272	−	3.90446i	−0.405601	−	0.234174i
$279$	−3.83715	−	2.21538i	−0.229724	−	0.132631i
$280$	−11.4318	−	7.39874i	−0.683184	−	0.442160i
$281$			5.77285i			0.344379i	0.985064	+	0.172190i	$0.0550842\pi$
$281$			5.77285i			0.344379i	−0.985064	+	0.172190i	$0.944916\pi$
$282$	3.03624	+	5.25892i	0.180806	+	0.313164i
$283$	4.03435	−	6.98771i	0.239817	−	0.415376i	−0.720844	−	0.693097i	$-0.756246\pi$
$283$	4.03435	−	6.98771i	0.239817	−	0.415376i	0.960662	+	0.277721i	$0.0895791\pi$
$284$	−12.4470	−	7.18630i	−0.738595	−	0.426428i
$285$	10.7740	−	18.6611i	0.638197	−	1.10539i
$286$	−3.84535	+	6.55238i	−0.227380	+	0.387450i
$287$	−0.126860	−	0.248026i	−0.00748833	−	0.0146405i
$288$	4.32210	−	2.49537i	0.254682	−	0.147041i
$289$	3.55928			0.209369
$290$	7.08086			0.415802
$291$	7.51885	−	4.34101i	0.440763	−	0.254474i
$292$	−22.3699	+	12.9153i	−1.30910	+	0.755809i
$293$	−10.7719	−	6.21915i	−0.629300	−	0.363327i	0.151181	−	0.988506i	$-0.451692\pi$
$293$	−10.7719	−	6.21915i	−0.629300	−	0.363327i	−0.780481	+	0.625180i	$0.785026\pi$
$294$	−2.80189	−	2.02244i	−0.163409	−	0.117951i
$295$	−1.84014	+	3.18722i	−0.107137	+	0.185567i
$296$	11.7369			0.682192
$297$	3.69662	+	2.13424i	0.214500	+	0.123841i
$298$	4.05981	+	7.03180i	0.235179	+	0.407341i
$299$	5.49235	+	0.0390263i	0.317631	+	0.00225695i
$300$	4.74910			0.274190
$301$	4.42958	+	2.86685i	0.255317	+	0.165242i
$302$	1.87485	+	3.24734i	0.107886	+	0.186864i
$303$	1.76672	+	3.06005i	0.101495	+	0.175795i
$304$	17.4619	−	10.0816i	1.00151	−	0.578221i
$305$			26.4817i			1.51634i
$306$	−1.93845	+	1.11916i	−0.110814	+	0.0639782i
$307$			21.2894i			1.21505i	0.794299	+	0.607527i	$0.207838\pi$
$307$			21.2894i			1.21505i	−0.794299	+	0.607527i	$0.792162\pi$
$308$	10.7769	−	16.6515i	0.614071	−	0.948805i
$309$	−1.55849	−	2.69939i	−0.0886595	−	0.153563i
$310$			6.07094i			0.344807i
$311$	−4.95963	−	8.59033i	−0.281235	−	0.487113i	0.690454	−	0.723376i	$-0.257411\pi$
$311$	−4.95963	−	8.59033i	−0.281235	−	0.487113i	−0.971689	+	0.236263i	$0.924077\pi$
$312$	−5.76616	−	3.38395i	−0.326444	−	0.191578i
$313$	14.1334	−	24.4797i	0.798866	−	1.38368i	−0.121489	−	0.992593i	$-0.538767\pi$
$313$	14.1334	−	24.4797i	0.798866	−	1.38368i	0.920355	−	0.391084i	$-0.127900\pi$
$314$	−1.66688	+	0.962371i	−0.0940672	+	0.0543097i
$315$	7.33410	+	0.372958i	0.413230	+	0.0210138i
$316$	−5.11261	+	8.85530i	−0.287607	+	0.498149i
$317$	0.874001	+	0.504605i	0.0490888	+	0.0283414i	0.524344	−	0.851507i	$-0.324311\pi$
$317$	0.874001	+	0.504605i	0.0490888	+	0.0283414i	−0.475255	+	0.879848i	$0.657644\pi$
$318$		−	4.93649i		−	0.276825i
$319$			22.0588i			1.23506i
$320$	6.56419	+	3.78984i	0.366949	+	0.211858i
$321$	−0.493602	+	0.854944i	−0.0275502	+	0.0477183i
$322$	1.98703	+	0.101046i	0.110733	+	0.00563106i
$323$	−30.4848	+	17.6004i	−1.69622	+	0.979312i
$324$	−0.878155	+	1.52101i	−0.0487864	+	0.0845005i
$325$	−4.81463	−	8.47774i	−0.267068	−	0.470260i
$326$	−2.93838	−	5.08942i	−0.162742	−	0.281877i
$327$			12.5573i			0.694420i
$328$	−0.0976250	−	0.169091i	−0.00539044	−	0.00933651i
$329$	−17.6834	+	27.3227i	−0.974918	+	1.50635i
$330$		−	5.84860i		−	0.321955i
$331$	16.7277	−	9.65775i	0.919438	−	0.530838i	0.0359824	−	0.999352i	$-0.488544\pi$
$331$	16.7277	−	9.65775i	0.919438	−	0.530838i	0.883456	+	0.468515i	$0.155211\pi$
$332$			9.17979i			0.503807i
$333$	−5.48154	+	3.16477i	−0.300387	+	0.173428i
$334$	5.08430	+	8.80627i	0.278201	+	0.481857i
$335$	5.82589	+	10.0907i	0.318302	+	0.551316i
$336$	5.76886	+	3.73363i	0.314717	+	0.203686i
$337$	15.2586			0.831188			0.415594	−	0.909550i	$-0.363574\pi$
$337$	15.2586			0.831188			0.415594	+	0.909550i	$0.363574\pi$
$338$	−0.0911946	+	6.41680i	−0.00496033	+	0.349028i
$339$	6.46070	+	11.1903i	0.350897	+	0.607771i
$340$	−19.1423	−	11.0518i	−1.03814	−	0.599369i
$341$	−18.9127			−1.02418
$342$	1.91618	−	3.31893i	0.103615	−	0.179467i
$343$	2.81206	−	18.3055i	0.151837	−	0.988406i
$344$	3.20255	+	1.84900i	0.172670	+	0.0996912i
$345$	−3.66174	+	2.11410i	−0.197141	+	0.113820i
$346$	0.132540	−	0.0765218i	0.00712538	−	0.00411384i
$347$	−8.98206			−0.482182			−0.241091	−	0.970502i	$-0.577505\pi$
$347$	−8.98206			−0.482182			−0.241091	+	0.970502i	$0.577505\pi$
$348$	−9.07631			−0.486541
$349$	7.65902	−	4.42194i	0.409978	−	0.236701i	−0.280802	−	0.959766i	$-0.590601\pi$
$349$	7.65902	−	4.42194i	0.409978	−	0.236701i	0.690780	+	0.723065i	$0.257267\pi$
$350$	−1.60822	−	3.14424i	−0.0859629	−	0.168067i
$351$	3.60546	+	0.0256188i	0.192445	+	0.00136743i
$352$	10.6514	−	18.4488i	0.567724	−	0.983326i
$353$	20.8217	+	12.0214i	1.10823	+	0.639836i	0.938370	−	0.345633i	$-0.112336\pi$
$353$	20.8217	+	12.0214i	1.10823	+	0.639836i	0.169858	+	0.985468i	$0.445669\pi$
$354$	−0.327274	+	0.566855i	−0.0173944	+	0.0301280i
$355$	−11.3570	−	19.6709i	−0.602766	−	1.04402i
$356$			14.7458i			0.781526i
$357$	−10.0712	−	6.51813i	−0.533024	−	0.344976i
$358$	5.86189	+	3.38436i	0.309811	+	0.178869i
$359$	−8.49648	−	4.90544i	−0.448427	−	0.258899i	0.258739	−	0.965947i	$-0.416693\pi$
$359$	−8.49648	−	4.90544i	−0.448427	−	0.258899i	−0.707166	+	0.707048i	$0.750026\pi$
$360$	5.14682			0.271261
$361$	20.6347	−	35.7403i	1.08604	−	1.88107i
$362$		−	0.478055i		−	0.0251260i
$363$	7.21999			0.378951
$364$	0.969761	−	16.7260i	0.0508293	−	0.876683i
$365$	−40.8217			−2.13671
$366$			4.70984i			0.246187i
$367$	2.92174	−	5.06061i	0.152514	−	0.264162i	−0.779637	−	0.626232i	$-0.784596\pi$
$367$	2.92174	−	5.06061i	0.152514	−	0.264162i	0.932151	+	0.362070i	$0.117930\pi$
$368$	−3.95649			−0.206246
$369$	0.0911887	+	0.0526478i	0.00474710	+	0.00274074i
$370$	7.51071	+	4.33631i	0.390463	+	0.225434i
$371$	23.5551	−	12.0480i	1.22292	−	0.625500i
$372$		−	7.78179i		−	0.403467i
$373$	−6.16662	−	10.6809i	−0.319296	−	0.553036i	0.661046	−	0.750346i	$-0.270113\pi$
$373$	−6.16662	−	10.6809i	−0.319296	−	0.553036i	−0.980341	+	0.197310i	$0.936780\pi$
$374$	−4.77713	+	8.27423i	−0.247020	+	0.427850i
$375$	−5.51895	−	3.18637i	−0.284998	−	0.164543i
$376$	−11.4051	+	19.7541i	−0.588171	+	1.01874i
$377$	9.20155	+	16.2023i	0.473904	+	0.834463i
$378$	1.30439	+	0.0663316i	0.0670906	+	0.00341173i
$379$	−4.87528	+	2.81475i	−0.250426	+	0.144584i	−0.619960	−	0.784634i	$-0.712851\pi$
$379$	−4.87528	+	2.81475i	−0.250426	+	0.144584i	0.369533	+	0.929218i	$0.379518\pi$
$380$	37.8450			1.94141
$381$	3.25989			0.167009
$382$	0.460439	−	0.265835i	0.0235581	−	0.0136013i
$383$	17.0194	−	9.82618i	0.869653	−	0.502094i	0.00241978	−	0.999997i	$-0.499230\pi$
$383$	17.0194	−	9.82618i	0.869653	−	0.502094i	0.867233	+	0.497903i	$0.165896\pi$
$384$	9.81166	+	5.66477i	0.500699	+	0.289079i
$385$	27.9074	−	14.2741i	1.42229	−	0.727474i
$386$	3.18602	−	5.51834i	0.162164	−	0.280876i
$387$	−1.99428			−0.101375
$388$	13.2054	+	7.62416i	0.670404	+	0.387058i
$389$	16.4825	+	28.5486i	0.835697	+	1.44747i	0.893461	+	0.449140i	$0.148270\pi$
$389$	16.4825	+	28.5486i	0.835697	+	1.44747i	−0.0577640	+	0.998330i	$0.518397\pi$
$390$	−2.43967	−	4.29583i	−0.123537	−	0.217528i
$391$	6.90719			0.349312
$392$	1.31674	−	12.9132i	0.0665055	−	0.652213i
$393$	0.605523	+	1.04880i	0.0305446	+	0.0529048i
$394$	3.95115	+	6.84359i	0.199056	+	0.344775i
$395$	−13.9946	+	8.07979i	−0.704145	+	0.406538i
$396$			7.49679i			0.376728i
$397$	17.8263	−	10.2920i	0.894677	−	0.516542i	0.0192077	−	0.999816i	$-0.493886\pi$
$397$	17.8263	−	10.2920i	0.894677	−	0.516542i	0.875469	+	0.483273i	$0.160552\pi$
$398$			4.20604i			0.210830i
$399$	20.5133	+	1.04316i	1.02695	+	0.0522232i
$400$	3.51150	+	6.08210i	0.175575	+	0.304105i
$401$		−	2.67850i		−	0.133758i	−0.997761	−	0.0668789i	$-0.978696\pi$
$401$		−	2.67850i		−	0.133758i	0.997761	−	0.0668789i	$-0.0213041\pi$
$402$	1.03615	+	1.79466i	0.0516785	+	0.0895097i
$403$	−13.8915	+	7.88916i	−0.691983	+	0.392987i
$404$	−3.10291	+	5.37440i	−0.154376	+	0.267386i
$405$	−2.40375	+	1.38781i	−0.119443	+	0.0689606i
$406$	3.07357	+	6.00915i	0.152539	+	0.298229i
$407$	−13.5088	+	23.3979i	−0.669606	+	1.15979i
$408$	−7.28140	−	4.20392i	−0.360483	−	0.208125i
$409$		−	8.27042i		−	0.408946i	−0.978872	−	0.204473i	$-0.934452\pi$
$409$		−	8.27042i		−	0.408946i	0.978872	−	0.204473i	$-0.0655481\pi$
$410$		−	0.144274i		−	0.00712519i
$411$	11.9199	+	6.88194i	0.587964	+	0.339461i
$412$	2.73720	−	4.74096i	0.134852	−	0.233570i
$413$	−3.50357	−	0.178166i	−0.172399	−	0.00876696i
$414$	−0.651249	+	0.375999i	−0.0320072	+	0.0184793i
$415$	−7.25372	+	12.5638i	−0.356071	+	0.616733i
$416$	0.127857	−	17.9939i	0.00626869	−	0.882223i
$417$	7.90937	+	13.6994i	0.387323	+	0.670864i
$418$		−	16.3584i		−	0.800117i
$419$	3.97996	+	6.89350i	0.194434	+	0.336769i	0.946715	−	0.322073i	$-0.104380\pi$
$419$	3.97996	+	6.89350i	0.194434	+	0.336769i	−0.752281	+	0.658843i	$0.771046\pi$
$420$	5.87321	+	11.4828i	0.286583	+	0.560301i
$421$			1.97435i			0.0962238i	0.998842	+	0.0481119i	$0.0153204\pi$
$421$			1.97435i			0.0962238i	−0.998842	+	0.0481119i	$0.984680\pi$
$422$	8.84400	−	5.10608i	0.430519	−	0.248560i
$423$		−	12.3012i		−	0.598104i
$424$	16.0587	−	9.27149i	0.779879	−	0.450263i
$425$	−6.13034	−	10.6181i	−0.297365	−	0.515052i
$426$	−2.01987	−	3.49851i	−0.0978629	−	0.169504i
$427$	−22.4736	+	11.4948i	−1.08758	+	0.556274i
$428$	−1.73384			−0.0838081
$429$	13.3827	−	7.60023i	0.646122	−	0.366943i
$430$	1.36626	+	2.36643i	0.0658869	+	0.114119i
$431$	−3.86442	−	2.23112i	−0.186143	−	0.107469i	0.404033	−	0.914744i	$-0.367608\pi$
$431$	−3.86442	−	2.23112i	−0.186143	−	0.107469i	−0.590176	+	0.807275i	$0.700941\pi$
$432$	−2.59724			−0.124960
$433$	1.32626	−	2.29715i	0.0637360	−	0.110394i	−0.832397	−	0.554180i	$-0.813032\pi$
$433$	1.32626	−	2.29715i	0.0637360	−	0.110394i	0.896133	+	0.443786i	$0.146365\pi$
$434$	−5.15209	+	2.63519i	−0.247308	+	0.126493i
$435$	−12.4222	−	7.17195i	−0.595598	−	0.343868i
$436$	−19.0997	+	11.0272i	−0.914712	+	0.528109i
$437$	−10.2418	+	5.91311i	−0.489932	+	0.282862i
$438$	−7.26025			−0.346908
$439$	−2.16049			−0.103115			−0.0515574	−	0.998670i	$-0.516419\pi$
$439$	−2.16049			−0.103115			−0.0515574	+	0.998670i	$0.516419\pi$
$440$	19.0258	−	10.9846i	0.907022	−	0.523669i
$441$	2.86698	+	6.38596i	0.136523	+	0.304093i
$442$	−0.0573433	+	8.07019i	−0.00272754	+	0.383860i
$443$	7.62546	−	13.2077i	0.362296	−	0.627516i	−0.626042	−	0.779789i	$-0.715326\pi$
$443$	7.62546	−	13.2077i	0.362296	−	0.627516i	0.988338	+	0.152274i	$0.0486595\pi$
$444$	−9.62729	−	5.55832i	−0.456891	−	0.263786i
$445$	−11.6519	+	20.1816i	−0.552352	+	0.956702i
$446$	−2.35274	−	4.07507i	−0.111406	−	0.192960i
$447$		−	16.4481i		−	0.777970i
$448$	−0.366939	+	7.21573i	−0.0173362	+	0.340911i
$449$	23.7035	+	13.6852i	1.11864	+	0.645847i	0.941053	−	0.338258i	$-0.109838\pi$
$449$	23.7035	+	13.6852i	1.11864	+	0.645847i	0.177586	+	0.984105i	$0.443171\pi$
$450$	1.15601	+	0.667421i	0.0544947	+	0.0314625i
$451$	0.449453			0.0211639
$452$	−11.3470	+	19.6536i	−0.533717	+	0.924426i
$453$		−	7.59589i		−	0.356886i
$454$	−5.40609			−0.253720
$455$	14.5439	−	22.1256i	0.681828	−	1.03726i
$456$	14.3956			0.674134
$457$			27.0928i			1.26735i	0.773600	+	0.633675i	$0.218454\pi$
$457$			27.0928i			1.26735i	−0.773600	+	0.633675i	$0.781546\pi$
$458$	6.54128	−	11.3298i	0.305654	−	0.529408i
$459$	4.53423			0.211640
$460$	−6.43114	−	3.71302i	−0.299854	−	0.173121i
$461$	−19.5829	−	11.3062i	−0.912065	−	0.526581i	−0.0309699	−	0.999520i	$-0.509860\pi$
$461$	−19.5829	−	11.3062i	−0.912065	−	0.526581i	−0.881095	+	0.472939i	$0.843193\pi$
$462$	4.96340	−	2.53868i	0.230918	−	0.118110i
$463$			9.70369i			0.450969i	0.974247	+	0.225484i	$0.0723965\pi$
$463$			9.70369i			0.450969i	−0.974247	+	0.225484i	$0.927604\pi$
$464$	−6.71106	−	11.6239i	−0.311553	−	0.539626i
$465$	6.14904	−	10.6504i	0.285155	−	0.493903i
$466$	4.56046	+	2.63298i	0.211259	+	0.121971i
$467$	−7.49852	+	12.9878i	−0.346990	+	0.601004i	−0.985713	−	0.168432i	$-0.946130\pi$
$467$	−7.49852	+	12.9878i	−0.346990	+	0.601004i	0.638723	+	0.769437i	$0.279463\pi$
$468$	3.12719	+	5.50643i	0.144554	+	0.254535i
$469$	−6.03465	+	9.32418i	−0.278654	+	0.430551i
$470$	−14.5967	+	8.42743i	−0.673297	+	0.388728i
$471$	3.89900			0.179657
$472$	−2.45868			−0.113170
$473$	−7.37208	+	4.25627i	−0.338969	+	0.195704i
$474$	−2.48898	+	1.43701i	−0.114323	+	0.0660041i
$475$	18.1798	+	10.4961i	0.834147	+	0.481595i
$476$	1.07006	−	21.0423i	0.0490460	−	0.964472i
$477$	−4.99999	+	8.66024i	−0.228934	+	0.396525i
$478$	−12.6169			−0.577083
$479$	−24.2739	−	14.0145i	−1.10910	−	0.640341i	−0.170506	−	0.985357i	$-0.554540\pi$
$479$	−24.2739	−	14.0145i	−1.10910	−	0.640341i	−0.938597	+	0.345016i	$0.887874\pi$
$480$	6.92617	+	11.9965i	0.316135	+	0.547562i
$481$	−0.162155	+	22.8209i	−0.00739365	+	1.04054i
$482$	−0.226697			−0.0103257
$483$	−3.38357	−	2.18986i	−0.153958	−	0.0996421i
$484$	6.34027	+	10.9817i	0.288194	+	0.499167i
$485$	12.0490	+	20.8694i	0.547115	+	0.947631i
$486$	−0.427513	+	0.246825i	−0.0193924	+	0.0111962i
$487$		−	20.8386i		−	0.944289i	−0.881521	−	0.472144i	$-0.843480\pi$
$487$		−	20.8386i		−	0.944289i	0.881521	−	0.472144i	$-0.156520\pi$
$488$	−15.3214	+	8.84582i	−0.693567	+	0.400431i
$489$			11.9047i			0.538349i
$490$	5.61351	−	7.77695i	0.253592	−	0.351327i
$491$	18.0783	+	31.3125i	0.815862	+	1.41311i	0.908708	+	0.417433i	$0.137070\pi$
$491$	18.0783	+	31.3125i	0.815862	+	1.41311i	−0.0928460	+	0.995680i	$0.529596\pi$
$492$			0.184932i			0.00833737i
$493$	11.7161	+	20.2928i	0.527665	+	0.913943i
$494$	−6.82370	−	12.0154i	−0.307013	−	0.540597i
$495$	−5.92383	+	10.2604i	−0.266257	+	0.461170i
$496$	9.96602	−	5.75388i	0.447487	−	0.258357i
$497$	11.7639	−	18.1765i	0.527685	−	0.815329i
$498$	−1.29009	+	2.23451i	−0.0578104	+	0.100131i
$499$	27.1627	+	15.6824i	1.21597	+	0.702039i	0.964053	−	0.265710i	$-0.0856064\pi$
$499$	27.1627	+	15.6824i	1.21597	+	0.702039i	0.251915	+	0.967749i	$0.418940\pi$
$500$		−	11.1925i		−	0.500544i
$501$		−	20.5988i		−	0.920287i
$502$	9.65572	+	5.57473i	0.430956	+	0.248812i
$503$	7.88988	−	13.6657i	0.351792	−	0.609322i	−0.634771	−	0.772700i	$-0.718906\pi$
$503$	7.88988	−	13.6657i	0.351792	−	0.609322i	0.986564	+	0.163378i	$0.0522390\pi$
$504$	2.23406	+	4.36784i	0.0995131	+	0.194559i
$505$	−8.49352	+	4.90373i	−0.377956	+	0.218213i
$506$	−1.60495	+	2.77985i	−0.0713486	+	0.123579i
$507$	6.65933	−	11.1648i	0.295751	−	0.495847i
$508$	2.86269	+	4.95832i	0.127011	+	0.219990i
$509$			4.81769i			0.213541i	0.994284	+	0.106770i	$0.0340509\pi$
$509$			4.81769i			0.213541i	−0.994284	+	0.106770i	$0.965949\pi$
$510$	−3.10636	−	5.38037i	−0.137552	−	0.238247i
$511$	−17.7193	−	34.6432i	−0.783858	−	1.53253i
$512$			22.5943i			0.998536i
$513$	−6.72325	+	3.88167i	−0.296839	+	0.171380i
$514$		−	12.0759i		−	0.532645i
$515$	7.49246	−	4.32577i	0.330157	−	0.190616i
$516$	−1.75128	−	3.03331i	−0.0770960	−	0.133534i
$517$	−26.2537	−	45.4728i	−1.15464	−	1.99989i
$518$	−0.419849	+	8.25619i	−0.0184471	+	0.362756i
$519$	−0.310025			−0.0136086
$520$	9.39252	−	16.0046i	0.411889	−	0.701849i
$521$	−15.5112	−	26.8662i	−0.679558	−	1.17703i	−0.975114	−	0.221703i	$-0.928838\pi$
$521$	−15.5112	−	26.8662i	−0.679558	−	1.17703i	0.295556	−	0.955325i	$-0.404495\pi$
$522$	−2.20932	−	1.27555i	−0.0966991	−	0.0558293i
$523$	−7.28394			−0.318505			−0.159252	−	0.987238i	$-0.550908\pi$
$523$	−7.28394			−0.318505			−0.159252	+	0.987238i	$0.550908\pi$
$524$	−1.06349	+	1.84201i	−0.0464586	+	0.0804687i
$525$	−0.363339	+	7.14494i	−0.0158574	+	0.311831i
$526$	0.487783	+	0.281622i	0.0212683	+	0.0122793i
$527$	−17.3985	+	10.0451i	−0.757893	+	0.437570i
$528$	−9.60102	+	5.54315i	−0.417831	+	0.241235i
$529$	−20.6794			−0.899106
$530$	13.7018			0.595167
$531$	1.14829	−	0.662967i	0.0498317	−	0.0287703i
$532$	16.4272	+	32.1170i	0.712211	+	1.39245i
$533$	0.330126	−	0.187484i	0.0142994	−	0.00812081i
$534$	−2.07232	+	3.58936i	−0.0896779	+	0.155327i
$535$	−2.37299	−	1.37005i	−0.102593	−	0.0592323i
$536$	−3.89210	+	6.74132i	−0.168113	+	0.291180i
$537$	−6.85580	−	11.8746i	−0.295850	−	0.512426i
$538$			12.3038i			0.530455i
$539$	24.2273	+	17.4876i	1.04354	+	0.753245i
$540$	−4.22173	−	2.43742i	−0.181674	−	0.104890i
$541$	2.73615	+	1.57971i	0.117636	+	0.0679172i	0.557664	−	0.830067i	$-0.311698\pi$
$541$	2.73615	+	1.57971i	0.117636	+	0.0679172i	−0.440027	+	0.897984i	$0.645031\pi$
$542$	−0.117564			−0.00504980
$543$	−0.484205	+	0.838667i	−0.0207792	+	0.0359907i
$544$		−	22.6292i		−	0.970217i
$545$	−34.8542			−1.49299
$546$	2.58667	−	3.93509i	0.110699	−	0.168406i
$547$	40.7547			1.74255			0.871273	−	0.490799i	$-0.163295\pi$
$547$	40.7547			1.74255			0.871273	+	0.490799i	$0.163295\pi$
$548$			24.1736i			1.03265i
$549$	4.77043	−	8.26263i	0.203597	−	0.352640i
$550$	5.69775			0.242953
$551$	−34.7446	−	20.0598i	−1.48017	−	0.854576i
$552$	−2.44629	−	1.41237i	−0.104121	−	0.0601144i
$553$	−12.9315	−	8.36932i	−0.549903	−	0.355900i
$554$		−	12.5586i		−	0.533565i
$555$	−8.78418	−	15.2146i	−0.372868	−	0.645826i
$556$	−13.8913	+	24.0604i	−0.589122	+	1.02039i
$557$	−26.1118	−	15.0757i	−1.10639	−	0.638776i	−0.168500	−	0.985702i	$-0.553892\pi$
$557$	−26.1118	−	15.0757i	−1.10639	−	0.638776i	−0.937893	+	0.346926i	$0.887226\pi$
$558$	1.09362	−	1.89421i	0.0462967	−	0.0801883i
$559$	−3.63939	+	6.20143i	−0.153930	+	0.262292i
$560$	−10.3631	+	16.0121i	−0.437921	+	0.676635i
$561$	16.7613	−	9.67716i	0.707664	−	0.408570i
$562$	−2.84977			−0.120210
$563$	43.0104			1.81267			0.906335	−	0.422560i	$-0.138868\pi$
$563$	43.0104			1.81267			0.906335	+	0.422560i	$0.138868\pi$
$564$	18.7102	−	10.8024i	0.787842	−	0.454861i
$565$	−31.0598	+	17.9324i	−1.30670	+	0.754421i
$566$	3.44948	+	1.99156i	0.144993	+	0.0837115i
$567$	−2.22115	−	1.43754i	−0.0932794	−	0.0603708i
$568$	7.58725	−	13.1415i	0.318354	−	0.551405i
$569$	−19.6564			−0.824038			−0.412019	−	0.911175i	$-0.635176\pi$
$569$	−19.6564			−0.824038			−0.412019	+	0.911175i	$0.635176\pi$
$570$	9.21206	+	5.31859i	0.385851	+	0.222771i
$571$	−19.0236	−	32.9498i	−0.796112	−	1.37891i	−0.922130	−	0.386879i	$-0.873553\pi$
$571$	−19.0236	−	32.9498i	−0.796112	−	1.37891i	0.126018	−	0.992028i	$-0.459780\pi$
$572$	23.3121	+	13.6810i	0.974727	+	0.572032i
$573$	−1.07702			−0.0449930
$574$	0.122438	−	0.0626246i	0.00511046	−	0.00261390i
$575$	−2.05958	−	3.56729i	−0.0858903	−	0.148766i
$576$	−1.36541	−	2.36495i	−0.0568919	−	0.0985397i
$577$	−21.8461	+	12.6129i	−0.909465	+	0.525080i	−0.880259	−	0.474493i	$-0.842631\pi$
$577$	−21.8461	+	12.6129i	−0.909465	+	0.525080i	−0.0292063	+	0.999573i	$0.509298\pi$
$578$			1.75704i			0.0730832i
$579$	−11.1787	+	6.45400i	−0.464569	+	0.268219i
$580$		−	25.1923i		−	1.04605i
$581$	−13.8108	−	0.702317i	−0.572970	−	0.0291370i
$582$	2.14294	+	3.71168i	0.0888277	+	0.153854i
$583$			42.6848i			1.76782i
$584$	−13.6359	−	23.6180i	−0.564256	−	0.977321i
$585$	−0.0711079	+	10.0074i	−0.00293995	+	0.413753i
$586$	3.07008	−	5.31754i	0.126824	−	0.219665i
$587$	11.9487	−	6.89860i	0.493176	−	0.284736i	−0.232715	−	0.972545i	$-0.574761\pi$
$587$	11.9487	−	6.89860i	0.493176	−	0.284736i	0.725891	+	0.687809i	$0.241428\pi$
$588$	−7.19544	+	9.96856i	−0.296735	+	0.411096i
$589$	17.1987	−	29.7891i	0.708662	−	1.22744i
$590$	−1.57337	−	0.908385i	−0.0647746	−	0.0373976i
$591$		−	16.0079i		−	0.658477i
$592$		−	16.4394i		−	0.675654i
$593$	−18.1900	−	10.5020i	−0.746975	−	0.431266i	0.0776251	−	0.996983i	$-0.475266\pi$
$593$	−18.1900	−	10.5020i	−0.746975	−	0.431266i	−0.824600	+	0.565717i	$0.808600\pi$
$594$	−1.05357	+	1.82484i	−0.0432285	+	0.0748739i
$595$	18.0918	−	27.9537i	0.741691	−	1.14599i
$596$	25.0178	−	14.4440i	1.02477	−	0.591650i
$597$	4.26015	−	7.37879i	0.174356	−	0.301994i
$598$	−0.0192653	+	2.71130i	−0.000787817	+	0.110873i
$599$	0.472828	+	0.818962i	0.0193192	+	0.0334619i	0.875523	−	0.483176i	$-0.160517\pi$
$599$	0.472828	+	0.818962i	0.0193192	+	0.0334619i	−0.856204	+	0.516638i	$0.827183\pi$
$600$			5.01408i			0.204699i
$601$	−5.95987	−	10.3228i	−0.243108	−	0.421076i	0.718490	−	0.695537i	$-0.244834\pi$
$601$	−5.95987	−	10.3228i	−0.243108	−	0.421076i	−0.961598	+	0.274462i	$0.911500\pi$
$602$	−1.41522	+	2.18666i	−0.0576800	+	0.0891217i
$603$		−	4.19791i		−	0.170952i
$604$	11.5534	−	6.67037i	0.470102	−	0.271413i
$605$			20.0399i			0.814737i
$606$	−1.51059	+	0.872142i	−0.0613637	+	0.0354283i
$607$	−3.47512	−	6.01909i	−0.141051	−	0.244307i	0.786842	−	0.617155i	$-0.211715\pi$
$607$	−3.47512	−	6.01909i	−0.141051	−	0.244307i	−0.927893	+	0.372848i	$0.878381\pi$
$608$	19.3724	+	33.5539i	0.785653	+	1.36079i
$609$	0.694400	−	13.6551i	0.0281385	−	0.553334i
$610$	−13.0727			−0.529298
$611$	−38.2519	−	22.4486i	−1.54751	−	0.908175i
$612$	3.98176	+	6.89661i	0.160953	+	0.278779i
$613$	−2.74806	−	1.58659i	−0.110993	−	0.0640819i	0.443476	−	0.896286i	$-0.353745\pi$
$613$	−2.74806	−	1.58659i	−0.110993	−	0.0640819i	−0.554469	+	0.832204i	$0.687079\pi$
$614$	−10.5095			−0.424130
$615$	−0.146130	+	0.253105i	−0.00589253	+	0.0102062i
$616$	17.5805	+	11.3782i	0.708339	+	0.458440i
$617$	−20.6929	−	11.9470i	−0.833063	−	0.480969i	0.0218373	−	0.999762i	$-0.493048\pi$
$617$	−20.6929	−	11.9470i	−0.833063	−	0.480969i	−0.854900	+	0.518792i	$0.826382\pi$
$618$	1.33255	−	0.769350i	0.0536031	−	0.0309478i
$619$	−7.56226	+	4.36607i	−0.303953	+	0.175487i	−0.644217	−	0.764843i	$-0.722817\pi$
$619$	−7.56226	+	4.36607i	−0.303953	+	0.175487i	0.340264	+	0.940330i	$0.389483\pi$
$620$	21.5992			0.867446
$621$	1.52334			0.0611296
$622$	4.24062	−	2.44832i	0.170033	−	0.0981688i
$623$	−22.1848	−	1.12815i	−0.888815	−	0.0451986i
$624$	−4.73975	+	8.07642i	−0.189742	+	0.323315i
$625$	15.6042	−	27.0272i	0.624167	−	1.08109i
$626$	12.0844	+	6.97694i	0.482991	+	0.278855i
$627$	−16.5689	+	28.6981i	−0.661696	+	1.14609i
$628$	3.42393	+	5.93042i	0.136630	+	0.236649i
$629$			28.6996i			1.14433i
$630$	−0.184111	+	3.62048i	−0.00733515	+	0.144243i
$631$	−22.0675	−	12.7407i	−0.878494	−	0.507199i	−0.00833234	−	0.999965i	$-0.502652\pi$
$631$	−22.0675	−	12.7407i	−0.878494	−	0.507199i	−0.870162	+	0.492767i	$0.835986\pi$
$632$	−9.34937	−	5.39786i	−0.371898	−	0.214715i
$633$	−20.6871			−0.822237
$634$	−0.249098	+	0.431450i	−0.00989295	+	0.0171351i
$635$			9.04818i			0.359066i
$636$	−17.5631			−0.696421
$637$	25.0898	+	2.73865i	0.994095	+	0.108509i
$638$	−10.8893			−0.431113
$639$			8.18340i			0.323730i
$640$	−15.7232	+	27.2334i	−0.621514	+	1.07649i
$641$	−3.73833			−0.147655			−0.0738276	−	0.997271i	$-0.523521\pi$
$641$	−3.73833			−0.147655			−0.0738276	+	0.997271i	$0.523521\pi$
$642$	−0.422043	−	0.243667i	−0.0166567	−	0.00961675i
$643$	−32.2258	−	18.6055i	−1.27086	−	0.733731i	−0.295710	−	0.955278i	$-0.595556\pi$
$643$	−32.2258	−	18.6055i	−1.27086	−	0.733731i	−0.975150	+	0.221547i	$0.928889\pi$
$644$	0.359501	−	7.06947i	0.0141663	−	0.278576i
$645$		−	5.53534i		−	0.217954i
$646$	−8.68843	−	15.0488i	−0.341842	−	0.592087i
$647$	−2.04563	+	3.54313i	−0.0804220	+	0.139295i	−0.903431	−	0.428733i	$-0.858960\pi$
$647$	−2.04563	+	3.54313i	−0.0804220	+	0.139295i	0.823009	+	0.568028i	$0.192293\pi$
$648$	−1.60587	−	0.927151i	−0.0630846	−	0.0364219i
$649$	2.82987	−	4.90148i	0.111082	−	0.192400i
$650$	4.18503	−	2.37674i	0.164151	−	0.0932235i
$651$	11.7076	+	0.595361i	0.458856	+	0.0233340i
$652$	−18.1072	+	10.4542i	−0.709131	+	0.409417i
$653$	11.7416			0.459485			0.229742	−	0.973251i	$-0.426212\pi$
$653$	11.7416			0.459485			0.229742	+	0.973251i	$0.426212\pi$
$654$	−6.19891			−0.242396
$655$	−2.91105	+	1.68070i	−0.113744	+	0.0656703i
$656$	−0.236839	+	0.136739i	−0.00924702	+	0.00533877i
$657$	12.7369	+	7.35364i	0.496913	+	0.286893i
$658$	−13.4879	−	8.72941i	−0.525812	−	0.340308i
$659$	24.4971	−	42.4303i	0.954272	−	1.65285i	0.218247	−	0.975893i	$-0.429966\pi$
$659$	24.4971	−	42.4303i	0.954272	−	1.65285i	0.736025	−	0.676955i	$-0.236701\pi$
$660$	−20.8082			−0.809957
$661$	21.2084	+	12.2447i	0.824910	+	0.476262i	0.852107	−	0.523368i	$-0.175325\pi$
$661$	21.2084	+	12.2447i	0.824910	+	0.476262i	−0.0271967	+	0.999630i	$0.508658\pi$
$662$	4.76755	+	8.25763i	0.185296	+	0.320942i
$663$	8.27460	−	14.0997i	0.321359	−	0.547587i
$664$	−9.69197			−0.376122
$665$	−2.89540	+	56.9371i	−0.112279	+	2.20793i
$666$	−1.56229	−	2.70596i	−0.0605375	−	0.104854i
$667$	3.93619	+	6.81768i	0.152410	+	0.263982i
$668$	31.3310	−	18.0889i	1.21223	−	0.699882i
$669$			9.53203i			0.368530i
$670$	−4.98129	+	2.87595i	−0.192444	+	0.111108i
$671$		−	40.7250i		−	1.57217i
$672$	−7.17436	+	11.0851i	−0.276757	+	0.427619i
$673$	12.1327	+	21.0145i	0.467682	+	0.810049i	0.999318	−	0.0369238i	$-0.0117559\pi$
$673$	12.1327	+	21.0145i	0.467682	+	0.810049i	−0.531636	+	0.846973i	$0.678423\pi$
$674$			7.53239i			0.290137i
$675$	−1.35201	−	2.34175i	−0.0520390	−	0.0901341i
$676$	22.8297	+	0.324452i	0.878066	+	0.0124789i
$677$	9.57985	−	16.5928i	0.368184	−	0.637713i	−0.621098	−	0.783733i	$-0.713313\pi$
$677$	9.57985	−	16.5928i	0.368184	−	0.637713i	0.989282	+	0.146020i	$0.0466464\pi$
$678$	−5.52407	+	3.18932i	−0.212151	+	0.122485i
$679$	−12.4807	+	19.2840i	−0.478966	+	0.740053i
$680$	11.6685	−	20.2104i	0.447465	−	0.775032i
$681$	9.48407	+	5.47563i	0.363430	+	0.209827i
$682$		−	9.33623i		−	0.357503i
$683$		−	36.5325i		−	1.39788i	−0.715182	−	0.698938i	$-0.753656\pi$
$683$		−	36.5325i		−	1.39788i	0.715182	−	0.698938i	$-0.246344\pi$
$684$	−11.8081	−	6.81741i	−0.451494	−	0.260670i
$685$	−19.1016	+	33.0849i	−0.729834	+	1.26411i
$686$	9.03652	+	1.38817i	0.345016	+	0.0530007i
$687$	−22.9511	+	13.2508i	−0.875640	+	0.505551i
$688$	2.58981	−	4.48569i	0.0987356	−	0.171015i
$689$	17.8054	+	31.3522i	0.678332	+	1.19443i
$690$	−1.04363	−	1.80762i	−0.0397302	−	0.0688148i
$691$			24.6588i			0.938067i	0.883180	+	0.469033i	$0.155398\pi$
$691$			24.6588i			0.938067i	−0.883180	+	0.469033i	$0.844602\pi$
$692$	−0.272250	−	0.471550i	−0.0103494	−	0.0179256i
$693$	−11.2788	−	0.573556i	−0.428446	−	0.0217876i
$694$		−	4.43399i		−	0.168312i
$695$	−38.0243	+	21.9533i	−1.44234	+	0.832738i
$696$		−	9.58272i		−	0.363232i
$697$	0.413471	−	0.238718i	0.0156613	−	0.00904208i
$698$	2.18289	+	3.78087i	0.0826236	+	0.143108i
$699$	−5.33371	−	9.23825i	−0.201739	−	0.349423i
$700$	−11.1866	+	5.72172i	−0.422813	+	0.216261i
$701$	−8.12077			−0.306717			−0.153359	−	0.988171i	$-0.549009\pi$
$701$	−8.12077			−0.306717			−0.153359	+	0.988171i	$0.549009\pi$
$702$	−0.0126467	+	1.77984i	−0.000477320	+	0.0671755i
$703$	−24.5692	−	42.5551i	−0.926644	−	1.60499i
$704$	−10.0948	−	5.82822i	−0.380461	−	0.219659i
$705$	34.1433			1.28591
$706$	−5.93438	+	10.2786i	−0.223343	+	0.386842i
$707$	−7.84829	−	5.07945i	−0.295165	−	0.191032i
$708$	2.01676	+	1.16438i	0.0757944	+	0.0437599i
$709$	24.5182	−	14.1556i	0.920801	−	0.531625i	0.0369107	−	0.999319i	$-0.488248\pi$
$709$	24.5182	−	14.1556i	0.920801	−	0.531625i	0.883891	+	0.467694i	$0.154915\pi$
$710$	9.71052	−	5.60637i	0.364429	−	0.210403i
$711$	5.82199			0.218342
$712$	−15.5685			−0.583455
$713$	−5.84530	+	3.37478i	−0.218908	+	0.126387i
$714$	3.21767	−	4.97165i	0.120418	−	0.186059i
$715$	21.0953	+	37.1452i	0.788919	+	1.38915i
$716$	12.0409	−	20.8555i	0.449990	−	0.779405i
$717$	22.1342	+	12.7792i	0.826617	+	0.477248i
$718$	2.42157	−	4.19428i	0.0903722	−	0.156529i
$719$	−2.76468	−	4.78857i	−0.103105	−	0.178584i	0.809857	−	0.586627i	$-0.199545\pi$
$719$	−2.76468	−	4.78857i	−0.103105	−	0.178584i	−0.912963	+	0.408043i	$0.866211\pi$
$720$		−	7.20894i		−	0.268661i
$721$	6.92328	+	4.48078i	0.257836	+	0.166873i
$722$	17.6432	+	10.1863i	0.656612	+	0.379095i
$723$	0.397701	+	0.229613i	0.0147907	+	0.00853939i
$724$	−1.70083			−0.0632107
$725$	6.98697	−	12.1018i	0.259489	−	0.449449i
$726$			3.56415i			0.132278i
$727$	−15.3438			−0.569070			−0.284535	−	0.958666i	$-0.591839\pi$
$727$	−15.3438			−0.569070			−0.284535	+	0.958666i	$0.591839\pi$
$728$	17.6593	+	1.02387i	0.654496	+	0.0379471i
$729$	1.00000			0.0370370
$730$		−	20.1516i		−	0.745846i
$731$	−4.52126	+	7.83105i	−0.167225	+	0.289642i
$732$	16.7567			0.619346
$733$	29.7711	+	17.1883i	1.09962	+	0.634865i	0.936121	−	0.351678i	$-0.114389\pi$
$733$	29.7711	+	17.1883i	1.09962	+	0.634865i	0.163498	+	0.986544i	$0.447722\pi$
$734$	2.49817	+	1.44232i	0.0922091	+	0.0532370i
$735$	−17.7249	+	7.95762i	−0.653794	+	0.293521i
$736$		−	7.60260i		−	0.280235i
$737$	−8.95937	−	15.5181i	−0.330023	−	0.571616i
$738$	−0.0259896	+	0.0450153i	−0.000956691	+	0.00165704i
$739$	17.7790	+	10.2647i	0.654009	+	0.377593i	0.789991	−	0.613119i	$-0.210085\pi$
$739$	17.7790	+	10.2647i	0.654009	+	0.377593i	−0.135981	+	0.990711i	$0.543419\pi$
$740$	15.4277	−	26.7216i	0.567135	−	0.982306i
$741$	−0.198888	+	27.9904i	−0.00730632	+	1.02825i
$742$	5.94749	+	11.6280i	0.218339	+	0.426877i
$743$	17.8282	−	10.2931i	0.654055	−	0.377619i	−0.135953	−	0.990715i	$-0.543410\pi$
$743$	17.8282	−	10.2931i	0.654055	−	0.377619i	0.790008	+	0.613097i	$0.210076\pi$
$744$	8.21597			0.301212
$745$	45.6537			1.67262
$746$	5.27263	−	3.04415i	0.193045	−	0.111454i
$747$	4.52650	−	2.61338i	0.165616	−	0.0956184i
$748$	29.4381	+	16.9961i	1.07636	+	0.621439i
$749$	0.132650	−	2.60853i	0.00484694	−	0.0953135i
$750$	1.57295	−	2.72443i	0.0574361	−	0.0994822i
$751$	7.78602			0.284116			0.142058	−	0.989858i	$-0.454628\pi$
$751$	7.78602			0.284116			0.142058	+	0.989858i	$0.454628\pi$
$752$	27.6688	+	15.9746i	1.00898	+	0.582533i
$753$	−11.2929	−	19.5598i	−0.411535	−	0.712800i
$754$	−7.99828	+	4.54234i	−0.291280	+	0.165422i
$755$	21.0832			0.767298
$756$	0.235995	−	4.64076i	0.00858305	−	0.168783i
$757$	5.22596	+	9.05162i	0.189941	+	0.328987i	0.945230	−	0.326404i	$-0.105837\pi$
$757$	5.22596	+	9.05162i	0.189941	+	0.328987i	−0.755290	+	0.655391i	$0.772504\pi$
$758$	−1.38950	−	2.40668i	−0.0504689	−	0.0874147i
$759$	5.63122	−	3.25119i	0.204400	−	0.118011i
$760$			39.9565i			1.44938i
$761$	22.0233	−	12.7151i	0.798343	−	0.460924i	−0.0445481	−	0.999007i	$-0.514185\pi$
$761$	22.0233	−	12.7151i	0.798343	−	0.460924i	0.842892	+	0.538083i	$0.180851\pi$
$762$			1.60924i			0.0582967i
$763$	−15.1290	−	29.5789i	−0.547708	−	1.07083i
$764$	−0.945788	−	1.63815i	−0.0342174	−	0.0592663i
$765$			12.5853i			0.455022i
$766$	4.85069	+	8.40164i	0.175263	+	0.303564i
$767$	0.0339689	−	4.78061i	0.00122655	−	0.172618i
$768$	−0.0655991	+	0.113621i	−0.00236710	+	0.00409995i
$769$	1.67020	−	0.964291i	0.0602290	−	0.0347732i	−0.469583	−	0.882888i	$-0.655596\pi$
$769$	1.67020	−	0.964291i	0.0602290	−	0.0347732i	0.529812	+	0.848115i	$0.322262\pi$
$770$	7.04640	+	13.7765i	0.253935	+	0.496470i
$771$	−12.2312	+	21.1851i	−0.440497	+	0.762964i
$772$	−19.6332	−	11.3352i	−0.706613	−	0.407963i
$773$			24.7191i			0.889084i	0.895758	+	0.444542i	$0.146634\pi$
$773$			24.7191i			0.889084i	−0.895758	+	0.444542i	$0.853366\pi$
$774$		−	0.984475i		−	0.0353862i
$775$	10.3758	+	5.99044i	0.372708	+	0.215183i
$776$	−8.04954	+	13.9422i	−0.288962	+	0.500496i
$777$	9.09895	−	14.0588i	0.326423	−	0.504358i
$778$	−14.0930	+	8.13660i	−0.505259	+	0.291711i
$779$	−0.408723	+	0.707929i	−0.0146440	+	0.0253642i
$780$	−15.2837	+	8.67986i	−0.547245	+	0.310789i
$781$	17.4654	+	30.2509i	0.624960	+	1.08246i
$782$			3.40974i			0.121932i
$783$	2.58391	+	4.47547i	0.0923416	+	0.159940i
$784$	−18.0869	−	1.84430i	−0.645961	−	0.0658680i
$785$			10.8221i			0.386258i
$786$	−0.517739	+	0.298917i	−0.0184671	+	0.0106620i
$787$			19.1702i			0.683342i	0.939820	+	0.341671i	$0.110993\pi$
$787$			19.1702i			0.683342i	−0.939820	+	0.341671i	$0.889007\pi$
$788$	24.3482	−	14.0574i	0.867367	−	0.500775i
$789$	−0.570488	−	0.988115i	−0.0203099	−	0.0351778i
$790$	−3.98859	−	6.90844i	−0.141908	−	0.245791i
$791$	−28.7003	−	18.5750i	−1.02047	−	0.660450i
$792$	−7.91507			−0.281250
$793$	−16.9879	−	29.9128i	−0.603259	−	1.06223i
$794$	5.08066	+	8.79996i	0.180306	+	0.312299i
$795$	−24.0375	−	13.8780i	−0.852521	−	0.492203i
$796$	14.9643			0.530394
$797$	22.2987	−	38.6225i	0.789861	−	1.36808i	−0.136191	−	0.990683i	$-0.543486\pi$
$797$	22.2987	−	38.6225i	0.789861	−	1.36808i	0.926052	−	0.377397i	$-0.123181\pi$
$798$	−0.514955	+	10.1264i	−0.0182292	+	0.358471i
$799$	−48.3039	−	27.8882i	−1.70887	−	0.986615i
$800$	−11.6871	+	6.74753i	−0.413200	+	0.238561i
$801$	7.27106	−	4.19795i	0.256910	−	0.148327i
$802$	1.32224			0.0466899
$803$	62.7779			2.21538
$804$	6.38506	−	3.68642i	0.225184	−	0.130010i
$805$	6.07820	−	9.39147i	0.214229	−	0.331006i
$806$	−3.89449	−	6.85752i	−0.137177	−	0.241546i
$807$	12.4621	−	21.5850i	0.438686	−	0.759826i
$808$	−5.67426	−	3.27603i	−0.199620	−	0.115251i
$809$	1.02455	−	1.77457i	0.0360213	−	0.0623906i	−0.847453	−	0.530871i	$-0.821865\pi$
$809$	1.02455	−	1.77457i	0.0360213	−	0.0623906i	0.883474	+	0.468480i	$0.155198\pi$
$810$	−0.685090	−	1.18661i	−0.0240716	−	0.0416933i
$811$			31.8889i			1.11977i	0.828570	+	0.559885i	$0.189155\pi$
$811$			31.8889i			1.11977i	−0.828570	+	0.559885i	$0.810845\pi$
$812$	21.3794	−	10.9351i	0.750270	−	0.383748i
$813$	0.206246	+	0.119076i	0.00723336	+	0.00417618i
$814$	−11.5504	−	6.66861i	−0.404840	−	0.233735i
$815$	−33.0429			−1.15744
$816$	−5.88826	+	10.1988i	−0.206130	+	0.357028i
$817$		−	15.4822i		−	0.541655i
$818$	4.08269			0.142748
$819$	−8.52358	+	4.28352i	−0.297838	+	0.149678i
$820$	−0.513299			−0.0179252
$821$			25.3458i			0.884575i	0.896873	+	0.442288i	$0.145833\pi$
$821$			25.3458i			0.884575i	−0.896873	+	0.442288i	$0.854167\pi$
$822$	−3.39727	+	5.88424i	−0.118493	+	0.205236i
$823$	−45.2385			−1.57692			−0.788458	−	0.615089i	$-0.789120\pi$
$823$	−45.2385			−1.57692			−0.788458	+	0.615089i	$0.789120\pi$
$824$	5.00548	+	2.88992i	0.174374	+	0.100675i
$825$	−9.99575	−	5.77105i	−0.348007	−	0.200922i
$826$	0.0879514	−	1.72954i	0.00306022	−	0.0601782i
$827$			7.55982i			0.262881i	0.991324	+	0.131440i	$0.0419602\pi$
$827$			7.55982i			0.262881i	−0.991324	+	0.131440i	$0.958040\pi$
$828$	1.33773	+	2.31702i	0.0464894	+	0.0805219i
$829$	−14.6456	+	25.3670i	−0.508664	+	0.881031i	0.491286	+	0.870998i	$0.336527\pi$
$829$	−14.6456	+	25.3670i	−0.508664	+	0.881031i	−0.999950	+	0.0100329i	$0.996806\pi$
$830$	−6.20212	−	3.58080i	−0.215279	−	0.124291i
$831$	−12.7202	+	22.0320i	−0.441258	+	0.764281i
$832$	−9.84583	−	0.0699602i	−0.341343	−	0.00242543i
$833$	31.5759	+	3.21976i	1.09404	+	0.111558i
$834$	−6.76272	+	3.90446i	−0.234174	+	0.135200i
$835$	57.1743			1.97860
$836$	−58.2001			−2.01289
$837$	−3.83715	+	2.21538i	−0.132631	+	0.0765748i
$838$	−3.40298	+	1.96471i	−0.117554	+	0.0678697i
$839$	16.2379	+	9.37493i	0.560593	+	0.323658i	0.753383	−	0.657581i	$-0.228420\pi$
$839$	16.2379	+	9.37493i	0.560593	+	0.323658i	−0.192791	+	0.981240i	$0.561754\pi$
$840$	−12.1234	+	6.20090i	−0.418298	+	0.213951i
$841$	1.14677	−	1.98626i	0.0395437	−	0.0684918i
$842$	−0.974636			−0.0335882
$843$	4.99943	+	2.88642i	0.172190	+	0.0994138i
$844$	−18.1664	−	31.4652i	−0.625315	−	1.08308i
$845$	30.9892	+	18.4837i	1.06606	+	0.635859i
$846$	6.07248			0.208776
$847$	−17.0068	+	8.69865i	−0.584361	+	0.298889i
$848$	−12.9862	−	22.4927i	−0.445948	−	0.772404i
$849$	−4.03435	−	6.98771i	−0.138459	−	0.239817i
$850$	5.24160	−	3.02624i	0.179786	−	0.103799i
$851$			9.64206i			0.330526i
$852$	−12.4470	+	7.18630i	−0.426428	+	0.246198i
$853$			38.2109i			1.30832i	0.756358	+	0.654158i	$0.226977\pi$
$853$			38.2109i			1.30832i	−0.756358	+	0.654158i	$0.773023\pi$
$854$	−5.67442	−	11.0941i	−0.194175	−	0.379633i
$855$	−10.7740	−	18.6611i	−0.368463	−	0.638197i
$856$		−	1.83057i		−	0.0625677i
$857$	−10.1911	−	17.6514i	−0.348120	−	0.602962i	0.637795	−	0.770206i	$-0.279847\pi$
$857$	−10.1911	−	17.6514i	−0.348120	−	0.602962i	−0.985916	+	0.167244i	$0.946513\pi$
$858$	3.75185	+	6.60636i	0.128086	+	0.225538i
$859$	−16.4646	+	28.5175i	−0.561765	+	0.973006i	0.435578	+	0.900151i	$0.356544\pi$
$859$	−16.4646	+	28.5175i	−0.561765	+	0.973006i	−0.997343	+	0.0728544i	$0.976789\pi$
$860$	8.41930	−	4.86089i	0.287096	−	0.165755i
$861$	−0.278227	−	0.0141486i	−0.00948194	−	0.000482182i
$862$	1.10139	−	1.90767i	0.0375136	−	0.0649755i
$863$	49.3767	+	28.5077i	1.68080	+	0.970413i	0.961128	+	0.276103i	$0.0890430\pi$
$863$	49.3767	+	28.5077i	1.68080	+	0.970413i	0.719676	+	0.694310i	$0.244290\pi$
$864$		−	4.99073i		−	0.169788i
$865$		−	0.860508i		−	0.0292581i
$866$	1.13399	+	0.654708i	0.0385345	+	0.0222479i
$867$	1.77964	−	3.08243i	0.0604398	−	0.104685i
$868$	9.37551	+	18.3301i	0.318225	+	0.622165i
$869$	21.5217	−	12.4255i	0.730073	−	0.421508i
$870$	3.54043	−	6.13221i	0.120032	−	0.207901i
$871$	−13.0539	−	7.66084i	−0.442314	−	0.259578i
$872$	−11.6425	−	20.1654i	−0.394265	−	0.682887i
$873$		−	8.68202i		−	0.293842i
$874$	−2.91901	−	5.05587i	−0.0987369	−	0.171017i
$875$	16.8389	+	0.856304i	0.569260	+	0.0289483i
$876$			25.8305i			0.872733i
$877$	8.70497	−	5.02582i	0.293946	−	0.169710i	−0.345774	−	0.938318i	$-0.612384\pi$
$877$	8.70497	−	5.02582i	0.293946	−	0.169710i	0.639720	+	0.768608i	$0.279050\pi$
$878$		−	1.06653i		−	0.0359936i
$879$	−10.7719	+	6.21915i	−0.363327	+	0.209767i
$880$	−15.3856	−	26.6487i	−0.518650	−	0.898328i
$881$	10.1992	+	17.6655i	0.343619	+	0.595166i	0.985102	−	0.171972i	$-0.0550138\pi$
$881$	10.1992	+	17.6655i	0.343619	+	0.595166i	−0.641483	+	0.767137i	$0.721680\pi$
$882$	−3.15243	+	1.41528i	−0.106148	+	0.0476551i
$883$	−3.18616			−0.107223			−0.0536114	−	0.998562i	$-0.517073\pi$
$883$	−3.18616			−0.107223			−0.0536114	+	0.998562i	$0.517073\pi$
$884$	28.7122	+	0.204016i	0.965694	+	0.00686180i
$885$	1.84014	+	3.18722i	0.0618557	+	0.107137i
$886$	6.51997	+	3.76431i	0.219043	+	0.126464i
$887$	−26.1850			−0.879207			−0.439604	−	0.898192i	$-0.644881\pi$
$887$	−26.1850			−0.879207			−0.439604	+	0.898192i	$0.644881\pi$
$888$	5.86844	−	10.1644i	0.196932	−	0.341096i
$889$	−7.67872	+	3.92752i	−0.257536	+	0.131725i
$890$	−9.96267	−	5.75195i	−0.333949	−	0.192806i
$891$	3.69662	−	2.13424i	0.123841	−	0.0714999i
$892$	−14.4983	+	8.37060i	−0.485439	+	0.280269i
$893$	95.4983			3.19573
$894$	8.11962			0.271561
$895$	32.9593	−	19.0290i	1.10171	−	0.636071i
$896$	−29.9364	−	1.52235i	−1.00011	−	0.0508580i
$897$	2.77997	−	4.73700i	0.0928206	−	0.158164i
$898$	−6.75572	+	11.7013i	−0.225441	+	0.390476i
$899$	−19.8297	−	11.4487i	−0.661359	−	0.381836i
$900$	2.37455	−	4.11284i	0.0791517	−	0.137095i
$901$	22.6711	+	39.2675i	0.755285	+	1.30819i
$902$			0.221873i			0.00738755i
$903$	4.69755	−	2.40271i	0.156325	−	0.0799571i
$904$	−20.7501	−	11.9801i	−0.690139	−	0.398452i
$905$	−2.32781	−	1.34396i	−0.0773792	−	0.0446749i
$906$	3.74971			0.124576
$907$	−8.92437	+	15.4575i	−0.296329	+	0.513257i	−0.975293	−	0.220915i	$-0.929096\pi$
$907$	−8.92437	+	15.4575i	−0.296329	+	0.513257i	0.678964	+	0.734171i	$0.262429\pi$
$908$			19.2338i			0.638296i
$909$	3.53344			0.117197
$910$	10.9223	+	7.17959i	0.362071	+	0.238001i
$911$	5.48276			0.181652			0.0908259	−	0.995867i	$-0.471049\pi$
$911$	5.48276			0.181652			0.0908259	+	0.995867i	$0.471049\pi$
$912$		−	20.1633i		−	0.667673i
$913$	11.1552	−	19.3213i	0.369182	−	0.639442i
$914$	−13.3744			−0.442385
$915$	22.9338	+	13.2409i	0.758170	+	0.437729i
$916$	−40.3093	−	23.2726i	−1.33186	−	0.768948i
$917$	−2.68991	−	1.74092i	−0.0888287	−	0.0574904i
$918$			2.23832i			0.0738757i
$919$	−20.0995	−	34.8134i	−0.663022	−	1.14839i	−0.979817	−	0.199894i	$-0.935940\pi$
$919$	−20.0995	−	34.8134i	−0.663022	−	1.14839i	0.316795	−	0.948494i	$-0.397393\pi$
$920$	3.92019	−	6.78997i	0.129245	−	0.223859i
$921$	18.4372	+	10.6447i	0.607527	+	0.350756i
$922$	5.58129	−	9.66708i	0.183810	−	0.318368i
$923$	25.4472	+	14.9340i	0.837605	+	0.491560i
$924$	−9.03214	−	17.6588i	−0.297135	−	0.580932i
$925$	14.8222	−	8.55762i	0.487352	−	0.281373i
$926$	−4.79023			−0.157417
$927$	−3.11699			−0.102375
$928$	22.3359	−	12.8956i	0.733211	−	0.423320i
$929$	−18.0214	+	10.4046i	−0.591262	+	0.341365i	−0.765596	−	0.643321i	$-0.777556\pi$
$929$	−18.0214	+	10.4046i	−0.591262	+	0.341365i	0.174334	+	0.984687i	$0.444223\pi$
$930$	5.25759	+	3.03547i	0.172403	+	0.0995371i
$931$	−49.5763	+	22.2573i	−1.62480	+	0.729454i
$932$	9.36764	−	16.2252i	0.306847	−	0.531475i
$933$	−9.91926			−0.324742
$934$	−6.41143	−	3.70164i	−0.209788	−	0.121121i
$935$	26.8601	+	46.5230i	0.878418	+	1.52146i
$936$	−5.81366	+	3.30167i	−0.190026	+	0.107918i
$937$	−4.03940			−0.131961			−0.0659807	−	0.997821i	$-0.521018\pi$
$937$	−4.03940			−0.131961			−0.0659807	+	0.997821i	$0.521018\pi$
$938$	−4.60288	−	2.97901i	−0.150289	−	0.0972680i
$939$	−14.1334	−	24.4797i	−0.461225	−	0.798866i
$940$	29.9831	+	51.9323i	0.977942	+	1.69385i
$941$	−26.4186	+	15.2528i	−0.861221	+	0.497226i	−0.864421	−	0.502769i	$-0.832315\pi$
$941$	−26.4186	+	15.2528i	−0.861221	+	0.497226i	0.00320007	+	0.999995i	$0.498981\pi$
$942$			1.92474i			0.0627115i
$943$	0.138912	−	0.0802007i	0.00452359	−	0.00261169i
$944$			3.44378i			0.112085i
$945$	3.99004	−	6.16504i	0.129796	−	0.200549i
$946$	−2.10111	−	3.63923i	−0.0683130	−	0.118322i
$947$			38.4436i			1.24925i	0.780925	+	0.624624i	$0.214748\pi$
$947$			38.4436i			1.24925i	−0.780925	+	0.624624i	$0.785252\pi$
$948$	5.11261	+	8.85530i	0.166050	+	0.287607i
$949$	46.1107	−	26.1870i	1.49682	−	0.850065i
$950$	−5.18141	+	8.97446i	−0.168107	+	0.291170i
$951$	0.874001	−	0.504605i	0.0283414	−	0.0163629i
$952$	22.2163	+	1.12976i	0.720036	+	0.0366157i
$953$	19.3185	−	33.4606i	0.625786	−	1.08389i	−0.362602	−	0.931944i	$-0.618112\pi$
$953$	19.3185	−	33.4606i	0.625786	−	1.08389i	0.988388	−	0.151950i	$-0.0485551\pi$
$954$	−4.27513	−	2.46824i	−0.138412	−	0.0799124i
$955$		−	2.98938i		−	0.0967341i
$956$			44.8884i			1.45180i
$957$	19.1035	+	11.0294i	0.617528	+	0.356530i
$958$	6.91828	−	11.9828i	0.223520	−	0.387147i
$959$	−36.3688	−	1.84945i	−1.17441	−	0.0597218i
$960$	6.56419	−	3.78984i	0.211858	−	0.122316i
$961$	−5.68417	+	9.84528i	−0.183360	+	0.317590i
$962$	−11.2655	−	0.0800480i	−0.363216	−	0.00258085i
$963$	0.493602	+	0.854944i	0.0159061	+	0.0275502i
$964$			0.806542i			0.0259770i
$965$	−17.9138	−	31.0276i	−0.576666	−	0.998814i
$966$	1.08102	−	1.67030i	0.0347814	−	0.0537409i
$967$		−	41.4683i		−	1.33353i	−0.745268	−	0.666765i	$-0.767678\pi$
$967$		−	41.4683i		−	1.33353i	0.745268	−	0.666765i	$-0.232322\pi$
$968$	−11.5944	+	6.69402i	−0.372658	+	0.215154i
$969$			35.2008i			1.13081i
$970$	−10.3022	+	5.94797i	−0.330783	+	0.190978i
$971$	−16.2050	−	28.0679i	−0.520043	−	0.900741i	−0.999729	−	0.0233003i	$-0.992583\pi$
$971$	−16.2050	−	28.0679i	−0.520043	−	0.900741i	0.479686	−	0.877440i	$-0.340751\pi$
$972$	0.878155	+	1.52101i	0.0281668	+	0.0487864i
$973$	−35.1357	−	22.7400i	−1.12640	−	0.729011i
$974$	10.2870			0.329616
$975$	−9.74925	−	0.0692739i	−0.312226	−	0.00221854i
$976$	12.3900	+	21.4601i	0.396593	+	0.686919i
$977$	−19.2615	−	11.1206i	−0.616230	−	0.355780i	0.159170	−	0.987251i	$-0.449118\pi$
$977$	−19.2615	−	11.1206i	−0.616230	−	0.355780i	−0.775400	+	0.631471i	$0.782452\pi$
$978$	−5.87676			−0.187918
$979$	17.9189	−	31.0364i	0.572690	−	0.991929i
$980$	−27.6689	−	19.9718i	−0.883849	−	0.637974i
$981$	10.8749	+	6.27865i	0.347210	+	0.200462i
$982$	−15.4574	+	8.92434i	−0.493266	+	0.284787i
$983$	−44.4432	+	25.6593i	−1.41752	+	0.818404i	−0.996080	−	0.0884530i	$-0.971808\pi$
$983$	−44.4432	+	25.6593i	−1.41752	+	0.818404i	−0.421438	+	0.906857i	$0.638474\pi$
$984$	−0.195250			−0.00622434
$985$	44.4317			1.41571
$986$	−10.0176	+	5.78364i	−0.319024	+	0.184189i
$987$	14.8205	+	28.9756i	0.471741	+	0.922305i
$988$	−42.7483	+	24.2774i	−1.36000	+	0.772367i
$989$	−1.51898	+	2.63096i	−0.0483009	+	0.0836596i
$990$	−5.06504	−	2.92430i	−0.160977	−	0.0929404i
$991$	−7.77646	+	13.4692i	−0.247027	+	0.427864i	−0.962700	−	0.270572i	$-0.912787\pi$
$991$	−7.77646	+	13.4692i	−0.247027	+	0.427864i	0.715672	+	0.698436i	$0.246120\pi$
$992$	11.0564	+	19.1502i	0.351040	+	0.608020i
$993$		−	19.3155i		−	0.612959i
$994$	8.97284	+	5.80727i	0.284601	+	0.184195i
$995$	20.4807	+	11.8245i	0.649280	+	0.374862i
$996$	7.94993	+	4.58990i	0.251903	+	0.145436i
$997$	38.9529			1.23365			0.616826	−	0.787100i	$-0.288418\pi$
$997$	38.9529			1.23365			0.616826	+	0.787100i	$0.288418\pi$
$998$	−7.74160	+	13.4088i	−0.245056	+	0.424450i
$999$			6.32954i			0.200258i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	273.2.t.d.205.5	yes	20
3.2	odd	2		819.2.bm.g.478.6		20
7.4	even	3		273.2.bl.d.88.6	yes	20
13.4	even	6		273.2.bl.d.121.6	yes	20
21.11	odd	6		819.2.do.g.361.5		20
39.17	odd	6		819.2.do.g.667.5		20
91.4	even	6	inner	273.2.t.d.4.6	✓	20
273.95	odd	6		819.2.bm.g.550.5		20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
273.2.t.d.4.6	✓	20	91.4	even	6	inner
273.2.t.d.205.5	yes	20	1.1	even	1	trivial
273.2.bl.d.88.6	yes	20	7.4	even	3
273.2.bl.d.121.6	yes	20	13.4	even	6
819.2.bm.g.478.6		20	3.2	odd	2
819.2.bm.g.550.5		20	273.95	odd	6
819.2.do.g.361.5		20	21.11	odd	6
819.2.do.g.667.5		20	39.17	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 273 = 3 \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	273.t (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+0.493650i q^{2} +(0.500000 - 0.866025i) q^{3} +1.75631 q^{4} +(2.40375 + 1.38781i) q^{5} +(0.427513 + 0.246825i) q^{6} +(-0.134370 + 2.64234i) q^{7} +1.85430i q^{8} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})\)	\(q+0.493650i q^{2} +(0.500000 - 0.866025i) q^{3} +1.75631 q^{4} +(2.40375 + 1.38781i) q^{5} +(0.427513 + 0.246825i) q^{6} +(-0.134370 + 2.64234i) q^{7} +1.85430i q^{8} +(-0.500000 - 0.866025i) q^{9} +(-0.685090 + 1.18661i) q^{10} +(-3.69662 - 2.13424i) q^{11} +(0.878155 - 1.52101i) q^{12} +(-3.60546 - 0.0256188i) q^{13} +(-1.30439 - 0.0663316i) q^{14} +(2.40375 - 1.38781i) q^{15} +2.59724 q^{16} -4.53423 q^{17} +(0.427513 - 0.246825i) q^{18} +(6.72325 - 3.88167i) q^{19} +(4.22173 + 2.43742i) q^{20} +(2.22115 + 1.43754i) q^{21} +(1.05357 - 1.82484i) q^{22} -1.52334 q^{23} +(1.60587 + 0.927151i) q^{24} +(1.35201 + 2.34175i) q^{25} +(0.0126467 - 1.77984i) q^{26} -1.00000 q^{27} +(-0.235995 + 4.64076i) q^{28} +(-2.58391 - 4.47547i) q^{29} +(0.685090 + 1.18661i) q^{30} +(3.83715 - 2.21538i) q^{31} +4.99073i q^{32} +(-3.69662 + 2.13424i) q^{33} -2.23832i q^{34} +(-3.99004 + 6.16504i) q^{35} +(-0.878155 - 1.52101i) q^{36} -6.32954i q^{37} +(1.91618 + 3.31893i) q^{38} +(-1.82492 + 3.10961i) q^{39} +(-2.57341 + 4.45728i) q^{40} +(-0.0911887 + 0.0526478i) q^{41} +(-0.709640 + 1.09647i) q^{42} +(0.997139 - 1.72709i) q^{43} +(-6.49241 - 3.74839i) q^{44} -2.77561i q^{45} -0.751998i q^{46} +(10.6531 + 6.15060i) q^{47} +(1.29862 - 2.24928i) q^{48} +(-6.96389 - 0.710101i) q^{49} +(-1.15601 + 0.667421i) q^{50} +(-2.26712 + 3.92676i) q^{51} +(-6.33231 - 0.0449946i) q^{52} +(-4.99999 - 8.66024i) q^{53} -0.493650i q^{54} +(-5.92383 - 10.2604i) q^{55} +(-4.89969 - 0.249162i) q^{56} -7.76333i q^{57} +(2.20932 - 1.27555i) q^{58} +1.32593i q^{59} +(4.22173 - 2.43742i) q^{60} +(4.77043 + 8.26263i) q^{61} +(1.09362 + 1.89421i) q^{62} +(2.35552 - 1.20480i) q^{63} +2.73081 q^{64} +(-8.63107 - 5.06526i) q^{65} +(-1.05357 - 1.82484i) q^{66} +(3.63550 + 2.09896i) q^{67} -7.96352 q^{68} +(-0.761671 + 1.31925i) q^{69} +(-3.04337 - 1.96968i) q^{70} +(-7.08704 - 4.09170i) q^{71} +(1.60587 - 0.927151i) q^{72} +(-12.7369 + 7.35364i) q^{73} +3.12458 q^{74} +2.70402 q^{75} +(11.8081 - 6.81741i) q^{76} +(6.13611 - 9.48094i) q^{77} +(-1.53506 - 0.900870i) q^{78} +(-2.91099 + 5.04199i) q^{79} +(6.24313 + 3.60447i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(-0.0259896 - 0.0450153i) q^{82} +5.22675i q^{83} +(3.90102 + 2.52476i) q^{84} +(-10.8992 - 6.29264i) q^{85} +(0.852580 + 0.492237i) q^{86} -5.16783 q^{87} +(3.95753 - 6.85465i) q^{88} +8.39590i q^{89} +1.37018 q^{90} +(0.552159 - 9.52340i) q^{91} -2.67546 q^{92} -4.43076i q^{93} +(-3.03624 + 5.25892i) q^{94} +21.5480 q^{95} +(4.32210 + 2.49537i) q^{96} +(7.51885 + 4.34101i) q^{97} +(0.350541 - 3.43772i) q^{98} +4.26849i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q + 10 q^{3} - 26 q^{4} + 6 q^{5} + 3 q^{6} + 2 q^{7} - 10 q^{9}+O(q^{10}) \) 20 * q + 10 * q^3 - 26 * q^4 + 6 * q^5 + 3 * q^6 + 2 * q^7 - 10 * q^9	\( 20 q + 10 q^{3} - 26 q^{4} + 6 q^{5} + 3 q^{6} + 2 q^{7} - 10 q^{9} + 2 q^{10} - 12 q^{11} - 13 q^{12} + 8 q^{13} + 2 q^{14} + 6 q^{15} + 42 q^{16} + 16 q^{17} + 3 q^{18} - 9 q^{19} - 5 q^{21} - 9 q^{22} - 36 q^{23} + 3 q^{24} + 12 q^{25} - 16 q^{26} - 20 q^{27} - 2 q^{28} - 3 q^{29} - 2 q^{30} - 18 q^{31} - 12 q^{33} + 18 q^{35} + 13 q^{36} + 9 q^{38} + 7 q^{39} + 5 q^{40} + 21 q^{41} + 16 q^{42} + 16 q^{43} - 6 q^{44} + 21 q^{47} + 21 q^{48} - 24 q^{49} - 54 q^{50} + 8 q^{51} - 41 q^{52} - 26 q^{53} + 17 q^{55} - 6 q^{56} + 42 q^{58} + 4 q^{62} - 7 q^{63} - 46 q^{64} - 50 q^{65} + 9 q^{66} - 3 q^{67} + 6 q^{68} - 18 q^{69} + 15 q^{71} + 3 q^{72} - 9 q^{73} + 12 q^{74} + 24 q^{75} + 75 q^{76} + 20 q^{77} - 32 q^{78} + 3 q^{79} - 24 q^{80} - 10 q^{81} + 15 q^{82} + 41 q^{84} - 78 q^{85} + 3 q^{86} - 6 q^{87} - 22 q^{88} - 4 q^{90} + 4 q^{91} + 142 q^{92} + 36 q^{94} - 84 q^{95} - 24 q^{96} - 15 q^{97} + 81 q^{98}+O(q^{100}) \) 20 * q + 10 * q^3 - 26 * q^4 + 6 * q^5 + 3 * q^6 + 2 * q^7 - 10 * q^9 + 2 * q^10 - 12 * q^11 - 13 * q^12 + 8 * q^13 + 2 * q^14 + 6 * q^15 + 42 * q^16 + 16 * q^17 + 3 * q^18 - 9 * q^19 - 5 * q^21 - 9 * q^22 - 36 * q^23 + 3 * q^24 + 12 * q^25 - 16 * q^26 - 20 * q^27 - 2 * q^28 - 3 * q^29 - 2 * q^30 - 18 * q^31 - 12 * q^33 + 18 * q^35 + 13 * q^36 + 9 * q^38 + 7 * q^39 + 5 * q^40 + 21 * q^41 + 16 * q^42 + 16 * q^43 - 6 * q^44 + 21 * q^47 + 21 * q^48 - 24 * q^49 - 54 * q^50 + 8 * q^51 - 41 * q^52 - 26 * q^53 + 17 * q^55 - 6 * q^56 + 42 * q^58 + 4 * q^62 - 7 * q^63 - 46 * q^64 - 50 * q^65 + 9 * q^66 - 3 * q^67 + 6 * q^68 - 18 * q^69 + 15 * q^71 + 3 * q^72 - 9 * q^73 + 12 * q^74 + 24 * q^75 + 75 * q^76 + 20 * q^77 - 32 * q^78 + 3 * q^79 - 24 * q^80 - 10 * q^81 + 15 * q^82 + 41 * q^84 - 78 * q^85 + 3 * q^86 - 6 * q^87 - 22 * q^88 - 4 * q^90 + 4 * q^91 + 142 * q^92 + 36 * q^94 - 84 * q^95 - 24 * q^96 - 15 * q^97 + 81 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more