LMFDB - Embedded newform 273.2.bl.d.88.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [273,2,Mod(88,273)]

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, 5]))

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

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

chi := DirichletCharacter("273.88");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 273 = 3 \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	273.bl (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:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 3 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			88.6
Root			$-0.493650i$ of defining polynomial
Character	$\chi$	$=$	273.88
Dual form			273.2.bl.d.121.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.427513 - 0.246825i) q^{2} -1.00000 q^{3} +(-0.878155 - 1.52101i) q^{4} +(-2.40375 + 1.38781i) q^{5} +(0.427513 + 0.246825i) q^{6} +(2.22115 - 1.43754i) q^{7} +1.85430i q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+(-0.427513 - 0.246825i) q^{2} -1.00000 q^{3} +(-0.878155 - 1.52101i) q^{4} +(-2.40375 + 1.38781i) q^{5} +(0.427513 + 0.246825i) q^{6} +(2.22115 - 1.43754i) q^{7} +1.85430i q^{8} +1.00000 q^{9} +1.37018 q^{10} +4.26849i 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} +(-1.29862 + 2.24928i) q^{16} +(2.26712 + 3.92676i) q^{17} +(-0.427513 - 0.246825i) q^{18} +7.76333i q^{19} +(4.22173 + 2.43742i) q^{20} +(-2.22115 + 1.43754i) q^{21} +(1.05357 - 1.82484i) q^{22} +(0.761671 - 1.31925i) q^{23} -1.85430i q^{24} +(1.35201 - 2.34175i) q^{25} +(1.53506 + 0.900870i) q^{26} -1.00000 q^{27} +(-4.13702 - 2.11600i) q^{28} +(-2.58391 - 4.47547i) q^{29} -1.37018 q^{30} +(-3.83715 - 2.21538i) q^{31} +(4.32210 - 2.49537i) q^{32} -4.26849i q^{33} -2.23832i q^{34} +(-3.34406 + 6.53800i) q^{35} +(-0.878155 - 1.52101i) q^{36} +(5.48154 + 3.16477i) q^{37} +(1.91618 - 3.31893i) q^{38} +(3.60546 + 0.0256188i) q^{39} +(-2.57341 - 4.45728i) q^{40} +(-0.0911887 + 0.0526478i) q^{41} +(1.30439 - 0.0663316i) q^{42} +(0.997139 - 1.72709i) q^{43} +(6.49241 - 3.74839i) q^{44} +(-2.40375 + 1.38781i) q^{45} +(-0.651249 + 0.375999i) q^{46} +(-10.6531 + 6.15060i) q^{47} +(1.29862 - 2.24928i) q^{48} +(2.86698 - 6.38596i) q^{49} +(-1.15601 + 0.667421i) q^{50} +(-2.26712 - 3.92676i) q^{51} +(3.12719 + 5.50643i) q^{52} +(-4.99999 + 8.66024i) q^{53} +(0.427513 + 0.246825i) q^{54} +(-5.92383 - 10.2604i) q^{55} +(2.66563 + 4.11868i) q^{56} -7.76333i q^{57} +2.55110i q^{58} +(1.14829 - 0.662967i) q^{59} +(-4.22173 - 2.43742i) q^{60} -9.54086 q^{61} +(1.09362 + 1.89421i) q^{62} +(2.22115 - 1.43754i) q^{63} +2.73081 q^{64} +(8.70218 - 4.94210i) q^{65} +(-1.05357 + 1.82484i) q^{66} -4.19791i q^{67} +(3.98176 - 6.89661i) q^{68} +(-0.761671 + 1.31925i) q^{69} +(3.04337 - 1.96968i) q^{70} +(-7.08704 - 4.09170i) q^{71} +1.85430i q^{72} +(12.7369 + 7.35364i) q^{73} +(-1.56229 - 2.70596i) q^{74} +(-1.35201 + 2.34175i) 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} -7.20894i q^{80} +1.00000 q^{81} +0.0519792 q^{82} +5.22675i q^{83} +(4.13702 + 2.11600i) q^{84} +(-10.8992 - 6.29264i) q^{85} +(-0.852580 + 0.492237i) q^{86} +(2.58391 + 4.47547i) q^{87} -7.91507 q^{88} +(-7.27106 - 4.19795i) q^{89} +1.37018 q^{90} +(-8.04508 + 5.12608i) q^{91} -2.67546 q^{92} +(3.83715 + 2.21538i) q^{93} +6.07248 q^{94} +(-10.7740 - 18.6611i) q^{95} +(-4.32210 + 2.49537i) q^{96} +(7.51885 + 4.34101i) q^{97} +(-2.80189 + 2.02244i) q^{98} +4.26849i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q - 3 q^{2} - 20 q^{3} + 13 q^{4} - 6 q^{5} + 3 q^{6} - 5 q^{7} + 20 q^{9}+O(q^{10}) $ 20 * q - 3 * q^2 - 20 * q^3 + 13 * q^4 - 6 * q^5 + 3 * q^6 - 5 * q^7 + 20 * q^9	$ 20 q - 3 q^{2} - 20 q^{3} + 13 q^{4} - 6 q^{5} + 3 q^{6} - 5 q^{7} + 20 q^{9} - 4 q^{10} - 13 q^{12} + 8 q^{13} + 2 q^{14} + 6 q^{15} - 21 q^{16} - 8 q^{17} - 3 q^{18} + 5 q^{21} - 9 q^{22} + 18 q^{23} + 12 q^{25} + 32 q^{26} - 20 q^{27} - 43 q^{28} - 3 q^{29} + 4 q^{30} + 18 q^{31} - 24 q^{32} - 24 q^{35} + 13 q^{36} - 12 q^{37} + 9 q^{38} - 8 q^{39} + 5 q^{40} + 21 q^{41} - 2 q^{42} + 16 q^{43} + 6 q^{44} - 6 q^{45} + 6 q^{46} - 21 q^{47} + 21 q^{48} + 3 q^{49} - 54 q^{50} + 8 q^{51} + 13 q^{52} - 26 q^{53} + 3 q^{54} + 17 q^{55} + 6 q^{56} + 15 q^{59} + 4 q^{62} - 5 q^{63} - 46 q^{64} + 37 q^{65} + 9 q^{66} - 3 q^{68} - 18 q^{69} + 15 q^{71} + 9 q^{73} - 6 q^{74} - 12 q^{75} + 75 q^{76} + 20 q^{77} - 32 q^{78} + 3 q^{79} + 20 q^{81} - 30 q^{82} + 43 q^{84} - 78 q^{85} - 3 q^{86} + 3 q^{87} + 44 q^{88} - 24 q^{89} - 4 q^{90} - 4 q^{91} + 142 q^{92} - 18 q^{93} - 72 q^{94} + 42 q^{95} + 24 q^{96} - 15 q^{97} - 33 q^{98}+O(q^{100}) $ 20 * q - 3 * q^2 - 20 * q^3 + 13 * q^4 - 6 * q^5 + 3 * q^6 - 5 * q^7 + 20 * q^9 - 4 * q^10 - 13 * q^12 + 8 * q^13 + 2 * q^14 + 6 * q^15 - 21 * q^16 - 8 * q^17 - 3 * q^18 + 5 * q^21 - 9 * q^22 + 18 * q^23 + 12 * q^25 + 32 * q^26 - 20 * q^27 - 43 * q^28 - 3 * q^29 + 4 * q^30 + 18 * q^31 - 24 * q^32 - 24 * q^35 + 13 * q^36 - 12 * q^37 + 9 * q^38 - 8 * q^39 + 5 * q^40 + 21 * q^41 - 2 * q^42 + 16 * q^43 + 6 * q^44 - 6 * q^45 + 6 * q^46 - 21 * q^47 + 21 * q^48 + 3 * q^49 - 54 * q^50 + 8 * q^51 + 13 * q^52 - 26 * q^53 + 3 * q^54 + 17 * q^55 + 6 * q^56 + 15 * q^59 + 4 * q^62 - 5 * q^63 - 46 * q^64 + 37 * q^65 + 9 * q^66 - 3 * q^68 - 18 * q^69 + 15 * q^71 + 9 * q^73 - 6 * q^74 - 12 * q^75 + 75 * q^76 + 20 * q^77 - 32 * q^78 + 3 * q^79 + 20 * q^81 - 30 * q^82 + 43 * q^84 - 78 * q^85 - 3 * q^86 + 3 * q^87 + 44 * q^88 - 24 * q^89 - 4 * q^90 - 4 * q^91 + 142 * q^92 - 18 * q^93 - 72 * q^94 + 42 * q^95 + 24 * q^96 - 15 * q^97 - 33 * q^98

Display 100 coefficients 10 coefficients

Character values

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

$n$	$92$	$106$	$157$
$\chi(n)$	$1$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{2}{3}\right)$

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 $

$2$	−0.427513	−	0.246825i	−0.302298	−	0.174532i	0.341177	−	0.939999i	$-0.389174\pi$
$2$	−0.427513	−	0.246825i	−0.302298	−	0.174532i	−0.643475	+	0.765467i	$0.722508\pi$
$3$	−1.00000			−0.577350
$3$	−1.00000			−0.577350
$4$	−0.878155	−	1.52101i	−0.439077	−	0.760504i
$5$	−2.40375	+	1.38781i	−1.07499	+	0.620646i	−0.929541	−	0.368720i	$-0.879796\pi$
$5$	−2.40375	+	1.38781i	−1.07499	+	0.620646i	−0.145449	+	0.989366i	$0.546463\pi$
$6$	0.427513	+	0.246825i	0.174532	+	0.100766i
$7$	2.22115	−	1.43754i	0.839514	−	0.543338i
$7$	2.22115	−	1.43754i	0.839514	−	0.543338i
$8$			1.85430i			0.655595i
$9$	1.00000			0.333333
$10$	1.37018			0.433289
$11$			4.26849i			1.28700i	0.765447	+	0.643499i	$0.222518\pi$
$11$			4.26849i			1.28700i	−0.765447	+	0.643499i	$0.777482\pi$
$12$	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
$16$	−1.29862	+	2.24928i	−0.324655	+	0.562320i
$17$	2.26712	+	3.92676i	0.549857	+	0.952380i	0.998284	+	0.0585603i	$0.0186510\pi$
$17$	2.26712	+	3.92676i	0.549857	+	0.952380i	−0.448427	+	0.893819i	$0.648016\pi$
$18$	−0.427513	−	0.246825i	−0.100766	−	0.0581772i
$19$			7.76333i			1.78103i	0.454953	+	0.890516i	$0.349656\pi$
$19$			7.76333i			1.78103i	−0.454953	+	0.890516i	$0.650344\pi$
$20$	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
$23$	0.761671	−	1.31925i	0.158819	−	0.275083i	−0.775624	−	0.631196i	$-0.782565\pi$
$23$	0.761671	−	1.31925i	0.158819	−	0.275083i	0.934443	+	0.356112i	$0.115898\pi$
$24$		−	1.85430i		−	0.378508i
$25$	1.35201	−	2.34175i	0.270402	−	0.468351i
$26$	1.53506	+	0.900870i	0.301050	+	0.176675i
$27$	−1.00000			−0.192450
$28$	−4.13702	−	2.11600i	−0.781822	−	0.399887i
$29$	−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	$0.992632\pi$
$30$	−1.37018			−0.250160
$31$	−3.83715	−	2.21538i	−0.689173	−	0.397894i	0.114129	−	0.993466i	$-0.463592\pi$
$31$	−3.83715	−	2.21538i	−0.689173	−	0.397894i	−0.803302	+	0.595572i	$0.796926\pi$
$32$	4.32210	−	2.49537i	0.764047	−	0.441123i
$33$		−	4.26849i		−	0.743048i
$34$		−	2.23832i		−	0.383869i
$35$	−3.34406	+	6.53800i	−0.565249	+	1.10512i
$36$	−0.878155	−	1.52101i	−0.146359	−	0.253501i
$37$	5.48154	+	3.16477i	0.901160	+	0.520285i	0.877576	−	0.479437i	$-0.159159\pi$
$37$	5.48154	+	3.16477i	0.901160	+	0.520285i	0.0235839	+	0.999722i	$0.492492\pi$
$38$	1.91618	−	3.31893i	0.310846	−	0.538401i
$39$	3.60546	+	0.0256188i	0.577336	+	0.00410230i
$40$	−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	$0.335951\pi$
$42$	1.30439	−	0.0663316i	0.201272	−	0.0102352i
$43$	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
$45$	−2.40375	+	1.38781i	−0.358330	+	0.206882i
$46$	−0.651249	+	0.375999i	−0.0960215	+	0.0554380i
$47$	−10.6531	+	6.15060i	−1.55392	+	0.897157i	−0.556104	+	0.831113i	$0.687704\pi$
$47$	−10.6531	+	6.15060i	−1.55392	+	0.897157i	−0.997817	+	0.0660438i	$0.978962\pi$
$48$	1.29862	−	2.24928i	0.187440	−	0.324655i
$49$	2.86698	−	6.38596i	0.409569	−	0.912279i
$50$	−1.15601	+	0.667421i	−0.163484	+	0.0943875i
$51$	−2.26712	−	3.92676i	−0.317460	−	0.549857i
$52$	3.12719	+	5.50643i	0.433663	+	0.763605i
$53$	−4.99999	+	8.66024i	−0.686801	+	1.18958i	0.286066	+	0.958210i	$0.407652\pi$
$53$	−4.99999	+	8.66024i	−0.686801	+	1.18958i	−0.972867	+	0.231365i	$0.925681\pi$
$54$	0.427513	+	0.246825i	0.0581772	+	0.0335886i
$55$	−5.92383	−	10.2604i	−0.798770	−	1.38351i
$56$	2.66563	+	4.11868i	0.356209	+	0.550381i
$57$		−	7.76333i		−	1.02828i
$58$			2.55110i			0.334976i
$59$	1.14829	−	0.662967i	0.149495	−	0.0863110i	−0.423387	−	0.905949i	$-0.639159\pi$
$59$	1.14829	−	0.662967i	0.149495	−	0.0863110i	0.572882	+	0.819638i	$0.305825\pi$
$60$	−4.22173	−	2.43742i	−0.545023	−	0.314669i
$61$	−9.54086			−1.22158			−0.610791	−	0.791792i	$-0.709148\pi$
$61$	−9.54086			−1.22158			−0.610791	+	0.791792i	$0.709148\pi$
$62$	1.09362	+	1.89421i	0.138890	+	0.240565i
$63$	2.22115	−	1.43754i	0.279838	−	0.181113i
$64$	2.73081			0.341351
$65$	8.70218	−	4.94210i	1.07937	−	0.612992i
$66$	−1.05357	+	1.82484i	−0.129685	+	0.224622i
$67$		−	4.19791i		−	0.512857i	−0.966563	−	0.256428i	$-0.917454\pi$
$67$		−	4.19791i		−	0.512857i	0.966563	−	0.256428i	$-0.0825458\pi$
$68$	3.98176	−	6.89661i	0.482859	−	0.836337i
$69$	−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	$0.828064\pi$
$72$			1.85430i			0.218532i
$73$	12.7369	+	7.35364i	1.49074	+	0.860679i	0.999944	−	0.0105964i	$-0.00337300\pi$
$73$	12.7369	+	7.35364i	1.49074	+	0.860679i	0.490795	+	0.871275i	$0.336706\pi$
$74$	−1.56229	−	2.70596i	−0.181612	−	0.314562i
$75$	−1.35201	+	2.34175i	−0.156117	+	0.270402i
$76$	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	0.654505	−	0.756058i	$-0.272877\pi$
$79$	−2.91099	−	5.04199i	−0.327512	−	0.567268i	−0.982018	+	0.188789i	$0.939544\pi$
$80$		−	7.20894i		−	0.805984i
$81$	1.00000			0.111111
$82$	0.0519792			0.00574014
$83$			5.22675i			0.573710i	0.957974	+	0.286855i	$0.0926099\pi$
$83$			5.22675i			0.573710i	−0.957974	+	0.286855i	$0.907390\pi$
$84$	4.13702	+	2.11600i	0.451385	+	0.230875i
$85$	−10.8992	−	6.29264i	−1.18218	−	0.682532i
$86$	−0.852580	+	0.492237i	−0.0919361	+	0.0530793i
$87$	2.58391	+	4.47547i	0.277025	+	0.479821i
$88$	−7.91507			−0.843749
$89$	−7.27106	−	4.19795i	−0.770731	−	0.444982i	0.0624045	−	0.998051i	$-0.480123\pi$
$89$	−7.27106	−	4.19795i	−0.770731	−	0.444982i	−0.833135	+	0.553069i	$0.813456\pi$
$90$	1.37018			0.144430
$91$	−8.04508	+	5.12608i	−0.843354	+	0.537359i
$92$	−2.67546			−0.278936
$93$	3.83715	+	2.21538i	0.397894	+	0.229724i
$94$	6.07248			0.626329
$95$	−10.7740	−	18.6611i	−1.10539	−	1.91459i
$96$	−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	$0.521375\pi$
$98$	−2.80189	+	2.02244i	−0.283033	+	0.204297i
$99$			4.26849i			0.428999i
$100$	−4.74910			−0.474910
$101$	3.53344			0.351591			0.175795	−	0.984427i	$-0.443750\pi$
$101$	3.53344			0.351591			0.175795	+	0.984427i	$0.443750\pi$
$102$			2.23832i			0.221627i
$103$	1.55849	+	2.69939i	0.153563	+	0.265979i	0.932535	−	0.361080i	$-0.117592\pi$
$103$	1.55849	+	2.69939i	0.153563	+	0.265979i	−0.778972	+	0.627059i	$0.784259\pi$
$104$	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
$107$	0.493602	−	0.854944i	0.0477183	−	0.0826505i	−0.841180	−	0.540756i	$-0.818138\pi$
$107$	0.493602	−	0.854944i	0.0477183	−	0.0826505i	0.888898	+	0.458105i	$0.151472\pi$
$108$	0.878155	+	1.52101i	0.0845005	+	0.146359i
$109$	10.8749	+	6.27865i	1.04163	+	0.601385i	0.920294	−	0.391226i	$-0.127949\pi$
$109$	10.8749	+	6.27865i	1.04163	+	0.601385i	0.121335	+	0.992612i	$0.461282\pi$
$110$			5.84860i			0.557642i
$111$	−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	$0.958730\pi$
$114$	−1.91618	+	3.31893i	−0.179467	+	0.310846i
$115$			4.22821i			0.394283i
$116$	−4.53815	+	7.86031i	−0.421357	+	0.729812i
$117$	−3.60546	−	0.0256188i	−0.333325	−	0.00236846i
$118$	−0.654548			−0.0602560
$119$	10.6805	+	5.46285i	0.979076	+	0.500779i
$120$	2.57341	+	4.45728i	0.234919	+	0.406892i
$121$	−7.21999			−0.656363
$122$	4.07884	+	2.35492i	0.369281	+	0.213205i
$123$	0.0911887	−	0.0526478i	0.00822221	−	0.00474710i
$124$			7.78179i			0.698825i
$125$		−	6.37274i		−	0.569995i
$126$	−1.30439	+	0.0663316i	−0.116204	+	0.00590929i
$127$	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	$0.787133\pi$
$128$	−9.81166	−	5.66477i	−0.867237	−	0.500699i
$129$	−0.997139	+	1.72709i	−0.0877932	+	0.152062i
$130$	−4.94013	−	0.0351024i	−0.433278	−	0.00307869i
$131$	−0.605523	−	1.04880i	−0.0529048	−	0.0916338i	0.838360	−	0.545117i	$-0.183515\pi$
$131$	−0.605523	−	1.04880i	−0.0529048	−	0.0916338i	−0.891265	+	0.453483i	$0.850181\pi$
$132$	−6.49241	+	3.74839i	−0.565092	+	0.326256i
$133$	11.1601	+	17.2435i	0.967701	+	1.49520i
$134$	−1.03615	+	1.79466i	−0.0895097	+	0.155035i
$135$	2.40375	−	1.38781i	0.206882	−	0.119443i
$136$	−7.28140	+	4.20392i	−0.624375	+	0.360483i
$137$	11.9199	−	6.88194i	1.01838	−	0.587964i	0.104748	−	0.994499i	$-0.466597\pi$
$137$	11.9199	−	6.88194i	1.01838	−	0.587964i	0.913635	+	0.406535i	$0.133263\pi$
$138$	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	$0.932590\pi$
$140$	12.8810	−	0.655031i	1.08864	−	0.0553602i
$141$	10.6531	−	6.15060i	0.897157	−	0.517974i
$142$	2.01987	+	3.49851i	0.169504	+	0.293589i
$143$	0.109354	−	15.3899i	0.00914461	−	1.28697i
$144$	−1.29862	+	2.24928i	−0.108218	+	0.187440i
$145$	12.4222	+	7.17195i	1.03161	+	0.595598i
$146$	−3.63012	−	6.28756i	−0.300431	−	0.520362i
$147$	−2.86698	+	6.38596i	−0.236464	+	0.526705i
$148$		−	11.1166i		−	0.913782i
$149$			16.4481i			1.34748i	0.738966	+	0.673742i	$0.235314\pi$
$149$			16.4481i			1.34748i	−0.738966	+	0.673742i	$0.764686\pi$
$150$	1.15601	−	0.667421i	0.0943875	−	0.0544947i
$151$	−6.57823	−	3.79794i	−0.535329	−	0.309072i	0.207855	−	0.978160i	$-0.433352\pi$
$151$	−6.57823	−	3.79794i	−0.535329	−	0.309072i	−0.743184	+	0.669087i	$0.766685\pi$
$152$	−14.3956			−1.16763
$153$	2.26712	+	3.92676i	0.183286	+	0.317460i
$154$	−0.283136	−	5.56777i	−0.0228157	−	0.448664i
$155$	12.2981			0.987805
$156$	−3.12719	−	5.50643i	−0.250375	−	0.440868i
$157$	1.94950	−	3.37664i	0.155587	−	0.269485i	−0.777686	−	0.628653i	$-0.783606\pi$
$157$	1.94950	−	3.37664i	0.155587	−	0.269485i	0.933273	+	0.359169i	$0.116940\pi$
$158$			2.87402i			0.228645i
$159$	4.99999	−	8.66024i	0.396525	−	0.686801i
$160$	−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
$163$		−	11.9047i		−	0.932449i	−0.884667	−	0.466224i	$-0.845614\pi$
$163$		−	11.9047i		−	0.932449i	0.884667	−	0.466224i	$-0.154386\pi$
$164$	0.160156	+	0.0924659i	0.0125061	+	0.00722038i
$165$	5.92383	+	10.2604i	0.461170	+	0.798770i
$166$	1.29009	−	2.23451i	0.100131	−	0.173431i
$167$	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
$171$			7.76333i			0.593677i
$172$	−3.50257			−0.267068
$173$	0.310025			0.0235707			0.0117854	−	0.999931i	$-0.496249\pi$
$173$	0.310025			0.0235707			0.0117854	+	0.999931i	$0.496249\pi$
$174$		−	2.55110i		−	0.193398i
$175$	−0.363339	−	7.14494i	−0.0274659	−	0.540107i
$176$	−9.60102	−	5.54315i	−0.723704	−	0.417831i
$177$	−1.14829	+	0.662967i	−0.0863110	+	0.0498317i
$178$	2.07232	+	3.58936i	0.155327	+	0.269034i
$179$	−13.7116			−1.02485			−0.512426	−	0.858731i	$-0.671253\pi$
$179$	−13.7116			−1.02485			−0.512426	+	0.858731i	$0.671253\pi$
$180$	4.22173	+	2.43742i	0.314669	+	0.181674i
$181$	−0.968409			−0.0719813			−0.0359907	−	0.999352i	$-0.511459\pi$
$181$	−0.968409			−0.0719813			−0.0359907	+	0.999352i	$0.511459\pi$
$182$	4.70462	−	0.205739i	0.348730	−	0.0152504i
$183$	9.54086			0.705281
$184$	2.44629	+	1.41237i	0.180343	+	0.104121i
$185$	−17.5684			−1.29165
$186$	−1.09362	−	1.89421i	−0.0801883	−	0.138890i
$187$	−16.7613	+	9.67716i	−1.22571	+	0.707664i
$188$	18.7102	+	10.8024i	1.36458	+	0.787842i
$189$	−2.22115	+	1.43754i	−0.161565	+	0.104565i
$190$			10.6372i			0.771702i
$191$	1.07702			0.0779302			0.0389651	−	0.999241i	$-0.487594\pi$
$191$	1.07702			0.0779302			0.0389651	+	0.999241i	$0.487594\pi$
$192$	−2.73081			−0.197079
$193$			12.9080i			0.929138i	0.885537	+	0.464569i	$0.153791\pi$
$193$			12.9080i			0.929138i	−0.885537	+	0.464569i	$0.846209\pi$
$194$	−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	$0.140177\pi$
$198$	1.05357	−	1.82484i	0.0748739	−	0.129685i
$199$	−4.26015	−	7.37879i	−0.301994	−	0.523068i	0.674594	−	0.738189i	$-0.264319\pi$
$199$	−4.26015	−	7.37879i	−0.301994	−	0.523068i	−0.976587	+	0.215121i	$0.930985\pi$
$200$	4.34232	+	2.50704i	0.307048	+	0.177274i
$201$			4.19791i			0.296098i
$202$	−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
$205$	0.146130	−	0.253105i	0.0102062	−	0.0176776i
$206$		−	1.53870i		−	0.107206i
$207$	0.761671	−	1.31925i	0.0529398	−	0.0916945i
$208$	4.73975	−	8.07642i	0.328643	−	0.559999i
$209$	−33.1377			−2.29218
$210$	−3.04337	+	1.96968i	−0.210013	+	0.135921i
$211$	−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	$-0.418913\pi$
$212$	17.5631			1.20624
$213$	7.08704	+	4.09170i	0.485596	+	0.280359i
$214$	−0.422043	+	0.243667i	−0.0288503	+	0.0166567i
$215$			5.53534i			0.377507i
$216$		−	1.85430i		−	0.126169i
$217$	−11.7076	+	0.595361i	−0.794761	+	0.0404157i
$218$	−3.09945	−	5.36841i	−0.209921	−	0.363595i
$219$	−12.7369	−	7.35364i	−0.860679	−	0.496913i
$220$	−10.4041	+	18.0204i	−0.701443	+	1.21494i
$221$	−8.07340	−	14.2159i	−0.543076	−	0.956263i
$222$	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	$0.436733\pi$
$224$	6.01284	−	11.7558i	0.401750	−	0.785464i
$225$	1.35201	−	2.34175i	0.0901341	−	0.156117i
$226$	5.52407	−	3.18932i	0.367456	−	0.212151i
$227$	9.48407	−	5.47563i	0.629480	−	0.363430i	−0.151071	−	0.988523i	$-0.548272\pi$
$227$	9.48407	−	5.47563i	0.629480	−	0.363430i	0.780551	+	0.625093i	$0.214939\pi$
$228$	−11.8081	+	6.81741i	−0.782011	+	0.451494i
$229$	22.9511	−	13.2508i	1.51665	−	0.875640i	0.516845	−	0.856079i	$-0.327106\pi$
$229$	22.9511	−	13.2508i	1.51665	−	0.875640i	0.999809	−	0.0195616i	$-0.00622703\pi$
$230$	1.04363	−	1.80762i	0.0688148	−	0.119191i
$231$	−6.13611	−	9.48094i	−0.403726	−	0.623800i
$232$	8.29888	−	4.79136i	0.544848	−	0.314568i
$233$	5.33371	+	9.23825i	0.349423	+	0.605218i	0.986147	−	0.165874i	$-0.0530444\pi$
$233$	5.33371	+	9.23825i	0.349423	+	0.605218i	−0.636724	+	0.771092i	$0.719711\pi$
$234$	1.53506	+	0.900870i	0.100350	+	0.0588917i
$235$	17.0717	−	29.5690i	1.11363	−	1.92887i
$236$	−2.01676	−	1.16438i	−0.131280	−	0.0757944i
$237$	2.91099	+	5.04199i	0.189089	+	0.327512i
$238$	−3.21767	−	4.97165i	−0.208571	−	0.322264i
$239$			25.5584i			1.65323i	0.562765	+	0.826617i	$0.309738\pi$
$239$			25.5584i			1.65323i	−0.562765	+	0.826617i	$0.690262\pi$
$240$			7.20894i			0.465335i
$241$	0.397701	−	0.229613i	0.0256182	−	0.0147907i	−0.487136	−	0.873326i	$-0.661958\pi$
$241$	0.397701	−	0.229613i	0.0256182	−	0.0147907i	0.512754	+	0.858535i	$0.328625\pi$
$242$	3.08664	+	1.78207i	0.198417	+	0.114556i
$243$	−1.00000			−0.0641500
$244$	8.37835	+	14.5117i	0.536369	+	0.929018i
$245$	1.97096	+	19.3291i	0.125920	+	1.23489i
$246$	−0.0519792			−0.00331407
$247$	0.198888	−	27.9904i	0.0126549	−	1.78099i
$248$	4.10799	−	7.11524i	0.260857	−	0.451818i
$249$		−	5.22675i		−	0.331232i
$250$	−1.57295	+	2.72443i	−0.0994822	+	0.172308i
$251$	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
$254$		−	1.60924i		−	0.100973i
$255$	10.8992	+	6.29264i	0.682532	+	0.394060i
$256$	0.0655991	+	0.113621i	0.00409995	+	0.00710131i
$257$	12.2312	−	21.1851i	0.762964	−	1.32149i	−0.178352	−	0.983967i	$-0.557077\pi$
$257$	12.2312	−	21.1851i	0.762964	−	1.32149i	0.941316	−	0.337526i	$-0.109590\pi$
$258$	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
$262$			0.597833i			0.0369343i
$263$	−1.14098			−0.0703556			−0.0351778	−	0.999381i	$-0.511200\pi$
$263$	−1.14098			−0.0703556			−0.0351778	+	0.999381i	$0.511200\pi$
$264$	7.91507			0.487139
$265$		−	27.7561i		−	1.70504i
$266$	−0.514955	−	10.1264i	−0.0315739	−	0.620890i
$267$	7.27106	+	4.19795i	0.444982	+	0.256910i
$268$	−6.38506	+	3.68642i	−0.390030	+	0.225184i
$269$	−12.4621	−	21.5850i	−0.759826	−	1.31606i	−0.942939	−	0.332966i	$-0.891951\pi$
$269$	−12.4621	−	21.5850i	−0.759826	−	1.31606i	0.183113	−	0.983092i	$-0.441383\pi$
$270$	−1.37018			−0.0833865
$271$	−0.206246	−	0.119076i	−0.0125286	−	0.00723336i	0.493723	−	0.869619i	$-0.335636\pi$
$271$	−0.206246	−	0.119076i	−0.0125286	−	0.00723336i	−0.506251	+	0.862386i	$0.668969\pi$
$272$	−11.7765			−0.714056
$273$	8.04508	−	5.12608i	0.486911	−	0.310244i
$274$	−6.79454			−0.410473
$275$	9.99575	+	5.77105i	0.602766	+	0.348007i
$276$	2.67546			0.161044
$277$	12.7202	+	22.0320i	0.764281	+	1.32377i	0.940626	+	0.339445i	$0.110239\pi$
$277$	12.7202	+	22.0320i	0.764281	+	1.32377i	−0.176345	+	0.984328i	$0.556427\pi$
$278$	6.76272	−	3.90446i	0.405601	−	0.234174i
$279$	−3.83715	−	2.21538i	−0.229724	−	0.132631i
$280$	−12.1234	−	6.20090i	−0.724513	−	0.370574i
$281$			5.77285i			0.344379i	0.985064	+	0.172190i	$0.0550842\pi$
$281$			5.77285i			0.344379i	−0.985064	+	0.172190i	$0.944916\pi$
$282$	−6.07248			−0.361611
$283$	−8.06871			−0.479635			−0.239817	−	0.970818i	$-0.577088\pi$
$283$	−8.06871			−0.479635			−0.239817	+	0.970818i	$0.577088\pi$
$284$			14.3726i			0.852856i
$285$	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
$289$	−1.77964	+	3.08243i	−0.104685	+	0.181319i
$290$	−3.54043	−	6.13221i	−0.207901	−	0.360096i
$291$	−7.51885	−	4.34101i	−0.440763	−	0.254474i
$292$		−	25.8305i		−	1.51162i
$293$	−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
$296$	−5.86844	+	10.1644i	−0.341096	+	0.590796i
$297$		−	4.26849i		−	0.247683i
$298$	4.05981	−	7.03180i	0.235179	−	0.407341i
$299$	−2.77997	+	4.73700i	−0.160770	+	0.273948i
$300$	4.74910			0.274190
$301$	−0.267971	−	5.26955i	−0.0154456	−	0.303732i
$302$	1.87485	+	3.24734i	0.107886	+	0.186864i
$303$	−3.53344			−0.202991
$304$	−17.4619	−	10.0816i	−1.00151	−	0.578221i
$305$	22.9338	−	13.2409i	1.31319	−	0.758170i
$306$		−	2.23832i		−	0.127956i
$307$			21.2894i			1.21505i	0.794299	+	0.607527i	$0.207838\pi$
$307$			21.2894i			1.21505i	−0.794299	+	0.607527i	$0.792162\pi$
$308$	9.03214	−	17.6588i	0.514654	−	1.00620i
$309$	−1.55849	−	2.69939i	−0.0886595	−	0.153563i
$310$	−5.25759	−	3.03547i	−0.298611	−	0.172403i
$311$	−4.95963	+	8.59033i	−0.281235	+	0.487113i	−0.971689	−	0.236263i	$-0.924077\pi$
$311$	−4.95963	+	8.59033i	−0.281235	+	0.487113i	0.690454	+	0.723376i	$0.257411\pi$
$312$	−0.0475050	+	6.68561i	−0.00268944	+	0.378498i
$313$	14.1334	+	24.4797i	0.798866	+	1.38368i	0.920355	+	0.391084i	$0.127900\pi$
$313$	14.1334	+	24.4797i	0.798866	+	1.38368i	−0.121489	+	0.992593i	$0.538767\pi$
$314$	−1.66688	+	0.962371i	−0.0940672	+	0.0543097i
$315$	−3.34406	+	6.53800i	−0.188416	+	0.368375i
$316$	−5.11261	+	8.85530i	−0.287607	+	0.498149i
$317$	−0.874001	+	0.504605i	−0.0490888	+	0.0283414i	−0.524344	−	0.851507i	$-0.675689\pi$
$317$	−0.874001	+	0.504605i	−0.0490888	+	0.0283414i	0.475255	+	0.879848i	$0.342356\pi$
$318$	−4.27513	+	2.46824i	−0.239737	+	0.138412i
$319$	19.1035	−	11.0294i	1.06959	−	0.617528i
$320$	−6.56419	+	3.78984i	−0.366949	+	0.211858i
$321$	−0.493602	+	0.854944i	−0.0275502	+	0.0477183i
$322$	−0.906008	+	1.77134i	−0.0504898	+	0.0987131i
$323$	−30.4848	+	17.6004i	−1.69622	+	0.979312i
$324$	−0.878155	−	1.52101i	−0.0487864	−	0.0845005i
$325$	−4.93462	+	8.40846i	−0.273723	+	0.466418i
$326$	−2.93838	+	5.08942i	−0.162742	+	0.281877i
$327$	−10.8749	−	6.27865i	−0.601385	−	0.347210i
$328$	−0.0976250	−	0.169091i	−0.00539044	−	0.00933651i
$329$	−14.8205	+	28.9756i	−0.817080	+	1.59748i
$330$		−	5.84860i		−	0.321955i
$331$			19.3155i			1.06168i	0.847473	+	0.530838i	$0.178123\pi$
$331$			19.3155i			1.06168i	−0.847473	+	0.530838i	$0.821877\pi$
$332$	7.94993	−	4.58990i	0.436309	−	0.251903i
$333$	5.48154	+	3.16477i	0.300387	+	0.173428i
$334$	−10.1686			−0.556401
$335$	5.82589	+	10.0907i	0.318302	+	0.551316i
$336$	−0.348991	−	6.86279i	−0.0190390	−	0.374396i
$337$	15.2586			0.831188			0.415594	−	0.909550i	$-0.363574\pi$
$337$	15.2586			0.831188			0.415594	+	0.909550i	$0.363574\pi$
$338$	−5.51152	−	3.28738i	−0.299787	−	0.178810i
$339$	6.46070	−	11.1903i	0.350897	−	0.607771i
$340$			22.1036i			1.19874i
$341$	9.45633	−	16.3788i	0.512089	−	0.886964i
$342$	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
$345$		−	4.22821i		−	0.227639i
$346$	−0.132540	−	0.0765218i	−0.00712538	−	0.00411384i
$347$	4.49103	+	7.77869i	0.241091	+	0.417582i	0.961025	−	0.276460i	$-0.0891614\pi$
$347$	4.49103	+	7.77869i	0.241091	+	0.417582i	−0.719934	+	0.694042i	$0.755828\pi$
$348$	4.53815	−	7.86031i	0.243271	−	0.421357i
$349$	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
$353$		−	24.0429i		−	1.27967i	−0.768512	−	0.639836i	$-0.779002\pi$
$353$		−	24.0429i		−	1.27967i	0.768512	−	0.639836i	$-0.220998\pi$
$354$	0.654548			0.0347888
$355$	22.7140			1.20553
$356$			14.7458i			0.781526i
$357$	−10.6805	−	5.46285i	−0.565270	−	0.289125i
$358$	5.86189	+	3.38436i	0.309811	+	0.178869i
$359$	8.49648	−	4.90544i	0.448427	−	0.258899i	−0.258739	−	0.965947i	$-0.583307\pi$
$359$	8.49648	−	4.90544i	0.448427	−	0.258899i	0.707166	+	0.707048i	$0.249974\pi$
$360$	−2.57341	−	4.45728i	−0.135631	−	0.234919i
$361$	−41.2694			−2.17207
$362$	0.414008	+	0.239028i	0.0217598	+	0.0125630i
$363$	7.21999			0.378951
$364$	14.8616	+	7.73515i	0.778961	+	0.405432i
$365$	−40.8217			−2.13671
$366$	−4.07884	−	2.35492i	−0.213205	−	0.123094i
$367$	−5.84349			−0.305028			−0.152514	−	0.988301i	$-0.548737\pi$
$367$	−5.84349			−0.305028			−0.152514	+	0.988301i	$0.548737\pi$
$368$	1.97825	+	3.42642i	0.103123	+	0.178615i
$369$	−0.0911887	+	0.0526478i	−0.00474710	+	0.00274074i
$370$	7.51071	+	4.33631i	0.390463	+	0.225434i
$371$	1.34370	+	26.4233i	0.0697612	+	1.37183i
$372$		−	7.78179i		−	0.403467i
$373$	12.3332			0.638591			0.319296	−	0.947655i	$-0.396554\pi$
$373$	12.3332			0.638591			0.319296	+	0.947655i	$0.396554\pi$
$374$	9.55426			0.494039
$375$			6.37274i			0.329087i
$376$	−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	$0.379518\pi$
$380$	−18.9225	+	32.7747i	−0.970703	+	1.68131i
$381$	−1.62994	−	2.82315i	−0.0835045	−	0.144634i
$382$	−0.460439	−	0.265835i	−0.0235581	−	0.0136013i
$383$			19.6524i			1.00419i	0.864813	+	0.502094i	$0.167437\pi$
$383$			19.6524i			1.00419i	−0.864813	+	0.502094i	$0.832563\pi$
$384$	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
$387$	0.997139	−	1.72709i	0.0506874	−	0.0877932i
$388$		−	15.2483i		−	0.774116i
$389$	16.4825	−	28.5486i	0.835697	−	1.44747i	−0.0577640	−	0.998330i	$-0.518397\pi$
$389$	16.4825	−	28.5486i	0.835697	−	1.44747i	0.893461	−	0.449140i	$-0.148270\pi$
$390$	4.94013	+	0.0351024i	0.250153	+	0.00177748i
$391$	6.90719			0.349312
$392$	11.8415	+	5.31625i	0.598086	+	0.268511i
$393$	0.605523	+	1.04880i	0.0305446	+	0.0529048i
$394$	−7.90230			−0.398112
$395$	13.9946	+	8.07979i	0.704145	+	0.406538i
$396$	6.49241	−	3.74839i	0.326256	−	0.188364i
$397$			20.5841i			1.03308i	0.856262	+	0.516542i	$0.172781\pi$
$397$			20.5841i			1.03308i	−0.856262	+	0.516542i	$0.827219\pi$
$398$			4.20604i			0.210830i
$399$	−11.1601	−	17.2435i	−0.558703	−	0.863255i
$400$	3.51150	+	6.08210i	0.175575	+	0.304105i
$401$	2.31965	+	1.33925i	0.115838	+	0.0668789i	0.556799	−	0.830647i	$-0.312029\pi$
$401$	2.31965	+	1.33925i	0.115838	+	0.0668789i	−0.440962	+	0.897526i	$0.645363\pi$
$402$	1.03615	−	1.79466i	0.0516785	−	0.0895097i
$403$	13.7779	+	8.08577i	0.686328	+	0.402781i
$404$	−3.10291	−	5.37440i	−0.154376	−	0.267386i
$405$	−2.40375	+	1.38781i	−0.119443	+	0.0689606i
$406$	3.66730	+	5.66636i	0.182005	+	0.281217i
$407$	−13.5088	+	23.3979i	−0.669606	+	1.15979i
$408$	7.28140	−	4.20392i	0.360483	−	0.208125i
$409$	−7.16239	+	4.13521i	−0.354158	+	0.204473i	−0.666515	−	0.745492i	$-0.732215\pi$
$409$	−7.16239	+	4.13521i	−0.354158	+	0.204473i	0.312357	+	0.949965i	$0.398881\pi$
$410$	−0.124945	+	0.0721371i	−0.00617060	+	0.00356260i
$411$	−11.9199	+	6.88194i	−0.587964	+	0.339461i
$412$	2.73720	−	4.74096i	0.134852	−	0.233570i
$413$	1.59749	−	3.12326i	0.0786072	−	0.153686i
$414$	−0.651249	+	0.375999i	−0.0320072	+	0.0184793i
$415$	−7.25372	−	12.5638i	−0.356071	−	0.616733i
$416$	−15.6471	+	8.88622i	−0.767162	+	0.435683i
$417$	7.90937	−	13.6994i	0.387323	−	0.670864i
$418$	14.1668	+	8.17921i	0.692921	+	0.400058i
$419$	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	$0.771046\pi$
$420$	−12.8810	+	0.655031i	−0.628526	+	0.0319622i
$421$			1.97435i			0.0962238i	0.998842	+	0.0481119i	$0.0153204\pi$
$421$			1.97435i			0.0962238i	−0.998842	+	0.0481119i	$0.984680\pi$
$422$			10.2122i			0.497121i
$423$	−10.6531	+	6.15060i	−0.517974	+	0.299052i
$424$	−16.0587	−	9.27149i	−0.779879	−	0.450263i
$425$	12.2607			0.594730
$426$	−2.01987	−	3.49851i	−0.0978629	−	0.169504i
$427$	−21.1916	+	13.7153i	−1.02554	+	0.663731i
$428$	−1.73384			−0.0838081
$429$	−0.109354	+	15.3899i	−0.00527964	+	0.743030i
$430$	1.36626	−	2.36643i	0.0658869	−	0.114119i
$431$			4.46225i			0.214939i	0.994208	+	0.107469i	$0.0342748\pi$
$431$			4.46225i			0.214939i	−0.994208	+	0.107469i	$0.965725\pi$
$432$	1.29862	−	2.24928i	0.0624800	−	0.108218i
$433$	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
$436$		−	22.0545i		−	1.05622i
$437$	10.2418	+	5.91311i	0.489932	+	0.282862i
$438$	3.63012	+	6.28756i	0.173454	+	0.300431i
$439$	1.08025	−	1.87104i	0.0515574	−	0.0893000i	−0.839095	−	0.543985i	$-0.816915\pi$
$439$	1.08025	−	1.87104i	0.0515574	−	0.0893000i	0.890652	+	0.454685i	$0.150248\pi$
$440$	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	0.988338	−	0.152274i	$-0.0486595\pi$
$443$	7.62546	+	13.2077i	0.362296	+	0.627516i	−0.626042	+	0.779789i	$0.715326\pi$
$444$			11.1166i			0.527572i
$445$	23.3038			1.10470
$446$	4.70549			0.222811
$447$		−	16.4481i		−	0.777970i
$448$	6.06553	−	3.92564i	0.286569	−	0.185469i
$449$	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
$451$	−0.224727	−	0.389238i	−0.0105820	−	0.0183285i
$452$	22.6940			1.06743
$453$	6.57823	+	3.79794i	0.309072	+	0.178443i
$454$	−5.40609			−0.253720
$455$	12.2244	−	23.4868i	0.573087	−	1.10108i
$456$	14.3956			0.674134
$457$	−23.4631	−	13.5464i	−1.09756	−	0.633675i	−0.161978	−	0.986794i	$-0.551787\pi$
$457$	−23.4631	−	13.5464i	−1.09756	−	0.633675i	−0.935578	+	0.353120i	$0.885121\pi$
$458$	−13.0826			−0.611308
$459$	−2.26712	−	3.92676i	−0.105820	−	0.183286i
$460$	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	$0.843193\pi$
$462$	0.283136	+	5.56777i	0.0131727	+	0.259036i
$463$			9.70369i			0.450969i	0.974247	+	0.225484i	$0.0723965\pi$
$463$			9.70369i			0.450969i	−0.974247	+	0.225484i	$0.927604\pi$
$464$	13.4221			0.623106
$465$	−12.2981			−0.570310
$466$		−	5.26597i		−	0.243941i
$467$	−7.49852	−	12.9878i	−0.346990	−	0.601004i	0.638723	−	0.769437i	$-0.279463\pi$
$467$	−7.49852	−	12.9878i	−0.346990	−	0.601004i	−0.985713	+	0.168432i	$0.946130\pi$
$468$	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
$471$	−1.94950	+	3.37664i	−0.0898283	+	0.155587i
$472$	1.22934	+	2.12928i	0.0565850	+	0.0980082i
$473$	7.37208	+	4.25627i	0.338969	+	0.195704i
$474$		−	2.87402i		−	0.132008i
$475$	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
$478$	6.30845	−	10.9265i	0.288542	−	0.499769i
$479$			28.0291i			1.28068i	0.768091	+	0.640341i	$0.221207\pi$
$479$			28.0291i			1.28068i	−0.768091	+	0.640341i	$0.778793\pi$
$480$	6.92617	−	11.9965i	0.316135	−	0.547562i
$481$	−19.6824	−	11.5509i	−0.897441	−	0.526675i
$482$	−0.226697			−0.0103257
$483$	0.204691	+	4.02519i	0.00931378	+	0.183152i
$484$	6.34027	+	10.9817i	0.288194	+	0.499167i
$485$	−24.0979			−1.09423
$486$	0.427513	+	0.246825i	0.0193924	+	0.0111962i
$487$	−18.0468	+	10.4193i	−0.817778	+	0.472144i	−0.849650	−	0.527348i	$-0.823187\pi$
$487$	−18.0468	+	10.4193i	−0.817778	+	0.472144i	0.0318716	+	0.999492i	$0.489853\pi$
$488$		−	17.6916i		−	0.800863i
$489$			11.9047i			0.538349i
$490$	3.92828	−	8.74991i	0.177462	−	0.395281i
$491$	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	$0.529596\pi$
$492$	−0.160156	−	0.0924659i	−0.00722038	−	0.00416869i
$493$	11.7161	−	20.2928i	0.527665	−	0.913943i
$494$	−6.99376	+	11.9172i	−0.314664	+	0.536179i
$495$	−5.92383	−	10.2604i	−0.266257	−	0.461170i
$496$	9.96602	−	5.75388i	0.447487	−	0.258357i
$497$	−21.6233	+	1.09960i	−0.969938	+	0.0493239i
$498$	−1.29009	+	2.23451i	−0.0578104	+	0.100131i
$499$	−27.1627	+	15.6824i	−1.21597	+	0.702039i	−0.964053	−	0.265710i	$-0.914394\pi$
$499$	−27.1627	+	15.6824i	−1.21597	+	0.702039i	−0.251915	+	0.967749i	$0.581060\pi$
$500$	−9.69299	+	5.59625i	−0.433484	+	0.250272i
$501$	−17.8391	+	10.2994i	−0.796992	+	0.460143i
$502$	−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	$0.0522390\pi$
$504$	2.66563	+	4.11868i	0.118736	+	0.183460i
$505$	−8.49352	+	4.90373i	−0.377956	+	0.218213i
$506$	−1.60495	−	2.77985i	−0.0713486	−	0.123579i
$507$	−12.9987	−	0.184735i	−0.577292	−	0.00820438i
$508$	2.86269	−	4.95832i	0.127011	−	0.219990i
$509$	−4.17225	−	2.40885i	−0.184932	−	0.106770i	0.404676	−	0.914460i	$-0.367384\pi$
$509$	−4.17225	−	2.40885i	−0.184932	−	0.106770i	−0.589608	+	0.807690i	$0.700718\pi$
$510$	−3.10636	−	5.38037i	−0.137552	−	0.238247i
$511$	38.8616	−	1.97621i	1.71914	−	0.0874226i
$512$			22.5943i			0.998536i
$513$		−	7.76333i		−	0.342760i
$514$	−10.4580	+	6.03795i	−0.461284	+	0.266323i
$515$	−7.49246	−	4.32577i	−0.330157	−	0.190616i
$516$	3.50257			0.154192
$517$	−26.2537	−	45.4728i	−1.15464	−	1.99989i
$518$	−7.35999	−	3.76449i	−0.323380	−	0.165402i
$519$	−0.310025			−0.0136086
$520$	9.16414	+	16.1365i	0.401874	+	0.707631i
$521$	−15.5112	+	26.8662i	−0.679558	+	1.17703i	0.295556	+	0.955325i	$0.404495\pi$
$521$	−15.5112	+	26.8662i	−0.679558	+	1.17703i	−0.975114	+	0.221703i	$0.928838\pi$
$522$			2.55110i			0.111659i
$523$	3.64197	−	6.30808i	0.159252	−	0.275833i	−0.775347	−	0.631536i	$-0.782425\pi$
$523$	3.64197	−	6.30808i	0.159252	−	0.275833i	0.934599	+	0.355702i	$0.115758\pi$
$524$	−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
$527$		−	20.0901i		−	0.875139i
$528$	9.60102	+	5.54315i	0.417831	+	0.241235i
$529$	10.3397	+	17.9089i	0.449553	+	0.778648i
$530$	−6.85089	+	11.8661i	−0.297584	+	0.515430i
$531$	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
$535$			2.74010i			0.118465i
$536$	7.78420			0.336226
$537$	13.7116			0.591699
$538$			12.3038i			0.530455i
$539$	27.2584	+	12.2377i	1.17410	+	0.527114i
$540$	−4.22173	−	2.43742i	−0.181674	−	0.104890i
$541$	−2.73615	+	1.57971i	−0.117636	+	0.0679172i	−0.557664	−	0.830067i	$-0.688302\pi$
$541$	−2.73615	+	1.57971i	−0.117636	+	0.0679172i	0.440027	+	0.897984i	$0.354969\pi$
$542$	0.0587819	+	0.101813i	0.00252490	+	0.00437326i
$543$	0.968409			0.0415584
$544$	19.5974	+	11.3146i	0.840233	+	0.485108i
$545$	−34.8542			−1.49299
$546$	−4.70462	+	0.205739i	−0.201339	+	0.00880482i
$547$	40.7547			1.74255			0.871273	−	0.490799i	$-0.163295\pi$
$547$	40.7547			1.74255			0.871273	+	0.490799i	$0.163295\pi$
$548$	−20.9350	−	12.0868i	−0.894298	−	0.516323i
$549$	−9.54086			−0.407194
$550$	−2.84888	−	4.93440i	−0.121477	−	0.210403i
$551$	34.7446	−	20.0598i	1.48017	−	0.854576i
$552$	−2.44629	−	1.41237i	−0.104121	−	0.0601144i
$553$	−13.7138	−	7.01434i	−0.583169	−	0.298280i
$554$		−	12.5586i		−	0.533565i
$555$	17.5684			0.745735
$556$	27.7826			1.17824
$557$			30.1513i			1.27755i	0.769393	+	0.638776i	$0.220559\pi$
$557$			30.1513i			1.27755i	−0.769393	+	0.638776i	$0.779441\pi$
$558$	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
$562$	1.42488	−	2.46797i	0.0601051	−	0.104105i
$563$	−21.5052	−	37.2481i	−0.906335	−	1.56982i	−0.819115	−	0.573629i	$-0.805535\pi$
$563$	−21.5052	−	37.2481i	−0.906335	−	1.56982i	−0.0872203	−	0.996189i	$-0.527798\pi$
$564$	−18.7102	−	10.8024i	−0.787842	−	0.454861i
$565$		−	35.8648i		−	1.50884i
$566$	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
$569$	9.82819	−	17.0229i	0.412019	−	0.713638i	−0.583091	−	0.812407i	$-0.698157\pi$
$569$	9.82819	−	17.0229i	0.412019	−	0.713638i	0.995110	+	0.0987685i	$0.0314903\pi$
$570$		−	10.6372i		−	0.445542i
$571$	−19.0236	+	32.9498i	−0.796112	+	1.37891i	0.126018	+	0.992028i	$0.459780\pi$
$571$	−19.0236	+	32.9498i	−0.796112	+	1.37891i	−0.922130	+	0.386879i	$0.873553\pi$
$572$	−23.5041	+	13.3484i	−0.982758	+	0.558123i
$573$	−1.07702			−0.0449930
$574$	0.115453	−	0.0747220i	0.00481893	−	0.00311884i
$575$	−2.05958	−	3.56729i	−0.0858903	−	0.148766i
$576$	2.73081			0.113784
$577$	21.8461	+	12.6129i	0.909465	+	0.525080i	0.880259	−	0.474493i	$-0.157369\pi$
$577$	21.8461	+	12.6129i	0.909465	+	0.525080i	0.0292063	+	0.999573i	$0.490702\pi$
$578$	1.52164	−	0.878519i	0.0632919	−	0.0365416i
$579$		−	12.9080i		−	0.536438i
$580$		−	25.1923i		−	1.04605i
$581$	7.51364	+	11.6094i	0.311718	+	0.481638i
$582$	2.14294	+	3.71168i	0.0888277	+	0.153854i
$583$	−36.9661	−	21.3424i	−1.53098	−	0.883912i
$584$	−13.6359	+	23.6180i	−0.564256	+	0.977321i
$585$	8.70218	−	4.94210i	0.359791	−	0.204331i
$586$	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	$0.241428\pi$
$588$	12.2307	−	1.24716i	0.504388	−	0.0514319i
$589$	17.1987	−	29.7891i	0.708662	−	1.22744i
$590$	1.57337	−	0.908385i	0.0647746	−	0.0373976i
$591$	−13.8632	+	8.00395i	−0.570258	+	0.329239i
$592$	−14.2369	+	8.21968i	−0.585133	+	0.337827i
$593$	18.1900	−	10.5020i	0.746975	−	0.431266i	−0.0776251	−	0.996983i	$-0.524734\pi$
$593$	18.1900	−	10.5020i	0.746975	−	0.431266i	0.824600	+	0.565717i	$0.191400\pi$
$594$	−1.05357	+	1.82484i	−0.0432285	+	0.0748739i
$595$	−33.2545	+	1.69108i	−1.36330	+	0.0693276i
$596$	25.0178	−	14.4440i	1.02477	−	0.591650i
$597$	4.26015	+	7.37879i	0.174356	+	0.301994i
$598$	2.35769	−	1.33897i	0.0964130	−	0.0547544i
$599$	0.472828	−	0.818962i	0.0193192	−	0.0334619i	−0.856204	−	0.516638i	$-0.827183\pi$
$599$	0.472828	−	0.818962i	0.0193192	−	0.0334619i	0.875523	+	0.483176i	$0.160517\pi$
$600$	−4.34232	−	2.50704i	−0.177274	−	0.102349i
$601$	−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	$0.911500\pi$
$602$	−1.18610	+	2.31895i	−0.0483417	+	0.0945132i
$603$		−	4.19791i		−	0.170952i
$604$			13.3407i			0.542827i
$605$	17.3551	−	10.0199i	0.705583	−	0.407369i
$606$	1.51059	+	0.872142i	0.0613637	+	0.0354283i
$607$	6.95024			0.282102			0.141051	−	0.990002i	$-0.454952\pi$
$607$	6.95024			0.282102			0.141051	+	0.990002i	$0.454952\pi$
$608$	19.3724	+	33.5539i	0.785653	+	1.36079i
$609$	12.1729	+	6.22621i	0.493271	+	0.252299i
$610$	−13.0727			−0.529298
$611$	38.5671	−	21.9028i	1.56026	−	0.886093i
$612$	3.98176	−	6.89661i	0.160953	−	0.278779i
$613$			3.17318i			0.128164i	0.997945	+	0.0640819i	$0.0204119\pi$
$613$			3.17318i			0.128164i	−0.997945	+	0.0640819i	$0.979588\pi$
$614$	5.25477	−	9.10152i	0.212065	−	0.367308i
$615$	−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	$0.826382\pi$
$618$			1.53870i			0.0618956i
$619$	7.56226	+	4.36607i	0.303953	+	0.175487i	0.644217	−	0.764843i	$-0.277183\pi$
$619$	7.56226	+	4.36607i	0.303953	+	0.175487i	−0.340264	+	0.940330i	$0.610517\pi$
$620$	−10.7996	−	18.7055i	−0.433723	−	0.751230i
$621$	−0.761671	+	1.31925i	−0.0305648	+	0.0529398i
$622$	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
$626$		−	13.9539i		−	0.557709i
$627$	33.1377			1.32339
$628$	−6.84786			−0.273259
$629$			28.6996i			1.14433i
$630$	3.04337	−	1.96968i	0.121251	−	0.0784741i
$631$	−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
$633$	10.3435	+	17.9155i	0.411119	+	0.712078i
$634$	0.498196			0.0197859
$635$	−7.83596	−	4.52409i	−0.310960	−	0.179533i
$636$	−17.5631			−0.696421
$637$	−10.5004	+	22.9509i	−0.416040	+	0.909346i
$638$	−10.8893			−0.431113
$639$	−7.08704	−	4.09170i	−0.280359	−	0.161865i
$640$	31.4464			1.24303
$641$	1.86917	+	3.23749i	0.0738276	+	0.127873i	0.900576	−	0.434699i	$-0.143145\pi$
$641$	1.86917	+	3.23749i	0.0738276	+	0.127873i	−0.826748	+	0.562572i	$0.809812\pi$
$642$	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	$0.928889\pi$
$644$	−5.94259	+	3.84607i	−0.234171	+	0.151557i
$645$		−	5.53534i		−	0.217954i
$646$	17.3769			0.683683
$647$	4.09126			0.160844			0.0804220	−	0.996761i	$-0.474373\pi$
$647$	4.09126			0.160844			0.0804220	+	0.996761i	$0.474373\pi$
$648$			1.85430i			0.0728439i
$649$	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
$653$	−5.87080	+	10.1685i	−0.229742	+	0.397925i	−0.957732	−	0.287663i	$-0.907122\pi$
$653$	−5.87080	+	10.1685i	−0.229742	+	0.397925i	0.727989	+	0.685588i	$0.240455\pi$
$654$	3.09945	+	5.36841i	0.121198	+	0.209921i
$655$	2.91105	+	1.68070i	0.113744	+	0.0656703i
$656$		−	0.273479i		−	0.0106775i
$657$	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	$-0.236701\pi$
$660$	10.4041	−	18.0204i	0.404979	−	0.701443i
$661$		−	24.4893i		−	0.952524i	−0.879303	−	0.476262i	$-0.841991\pi$
$661$		−	24.4893i		−	0.952524i	0.879303	−	0.476262i	$-0.158009\pi$
$662$	4.76755	−	8.25763i	0.185296	−	0.320942i
$663$	8.07340	+	14.2159i	0.313545	+	0.552098i
$664$	−9.69197			−0.376122
$665$	−50.7567	−	25.9611i	−1.96826	−	1.00673i
$666$	−1.56229	−	2.70596i	−0.0605375	−	0.104854i
$667$	−7.87238			−0.304820
$668$	−31.3310	−	18.0889i	−1.21223	−	0.699882i
$669$	8.25498	−	4.76602i	0.319156	−	0.184265i
$670$		−	5.75190i		−	0.222215i
$671$		−	40.7250i		−	1.57217i
$672$	−6.01284	+	11.7558i	−0.231950	+	0.453488i
$673$	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	$0.678423\pi$
$674$	−6.52325	−	3.76620i	−0.251266	−	0.145069i
$675$	−1.35201	+	2.34175i	−0.0520390	+	0.0901341i
$676$	−11.1339	−	19.9333i	−0.428226	−	0.766667i
$677$	9.57985	+	16.5928i	0.368184	+	0.637713i	0.989282	−	0.146020i	$-0.0466464\pi$
$677$	9.57985	+	16.5928i	0.368184	+	0.637713i	−0.621098	+	0.783733i	$0.713313\pi$
$678$	−5.52407	+	3.18932i	−0.212151	+	0.122485i
$679$	22.9408	−	1.16660i	0.880388	−	0.0447700i
$680$	11.6685	−	20.2104i	0.447465	−	0.775032i
$681$	−9.48407	+	5.47563i	−0.363430	+	0.209827i
$682$	−8.08541	+	4.66812i	−0.309606	+	0.178751i
$683$	−31.6381	+	18.2662i	−1.21060	+	0.698938i	−0.962889	−	0.269896i	$-0.913011\pi$
$683$	−31.6381	+	18.2662i	−1.21060	+	0.698938i	−0.247707	+	0.968835i	$0.579677\pi$
$684$	11.8081	−	6.81741i	0.451494	−	0.260670i
$685$	−19.1016	+	33.0849i	−0.729834	+	1.26411i
$686$	−3.31607	+	8.51994i	−0.126608	+	0.325293i
$687$	−22.9511	+	13.2508i	−0.875640	+	0.505551i
$688$	2.58981	+	4.48569i	0.0987356	+	0.171015i
$689$	18.2491	−	31.0960i	0.695237	−	1.18467i
$690$	−1.04363	+	1.80762i	−0.0397302	+	0.0688148i
$691$	−21.3552	−	12.3294i	−0.812390	−	0.469033i	0.0353954	−	0.999373i	$-0.488731\pi$
$691$	−21.3552	−	12.3294i	−0.812390	−	0.469033i	−0.847785	+	0.530340i	$0.822064\pi$
$692$	−0.272250	−	0.471550i	−0.0103494	−	0.0179256i
$693$	6.13611	+	9.48094i	0.233091	+	0.360151i
$694$		−	4.43399i		−	0.168312i
$695$		−	43.9067i		−	1.66548i
$696$	−8.29888	+	4.79136i	−0.314568	+	0.181616i
$697$	−0.413471	−	0.238718i	−0.0156613	−	0.00904208i
$698$	−4.36578			−0.165247
$699$	−5.33371	−	9.23825i	−0.201739	−	0.349423i
$700$	−10.5485	+	6.82701i	−0.398694	+	0.258037i
$701$	−8.12077			−0.306717			−0.153359	−	0.988171i	$-0.549009\pi$
$701$	−8.12077			−0.306717			−0.153359	+	0.988171i	$0.549009\pi$
$702$	−1.53506	−	0.900870i	−0.0579371	−	0.0340011i
$703$	−24.5692	+	42.5551i	−0.926644	+	1.60499i
$704$			11.6564i			0.439319i
$705$	−17.0717	+	29.5690i	−0.642956	+	1.11363i
$706$	−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
$709$			28.3112i			1.06325i	0.846980	+	0.531625i	$0.178418\pi$
$709$			28.3112i			1.06325i	−0.846980	+	0.531625i	$0.821582\pi$
$710$	−9.71052	−	5.60637i	−0.364429	−	0.210403i
$711$	−2.91099	−	5.04199i	−0.109171	−	0.189089i
$712$	7.78426	−	13.4827i	0.291728	−	0.505287i
$713$	−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
$717$		−	25.5584i		−	0.954495i
$718$	−4.84314			−0.180744
$719$	5.52937			0.206211			0.103105	−	0.994670i	$-0.467122\pi$
$719$	5.52937			0.206211			0.103105	+	0.994670i	$0.467122\pi$
$720$		−	7.20894i		−	0.268661i
$721$	7.34211	+	3.75535i	0.273434	+	0.139856i
$722$	17.6432	+	10.1863i	0.656612	+	0.379095i
$723$	−0.397701	+	0.229613i	−0.0147907	+	0.00853939i
$724$	0.850413	+	1.47296i	0.0316054	+	0.0547421i
$725$	−13.9739			−0.518979
$726$	−3.08664	−	1.78207i	−0.114556	−	0.0661390i
$727$	−15.3438			−0.569070			−0.284535	−	0.958666i	$-0.591839\pi$
$727$	−15.3438			−0.569070			−0.284535	+	0.958666i	$0.591839\pi$
$728$	−9.50529	−	14.9180i	−0.352290	−	0.552898i
$729$	1.00000			0.0370370
$730$	17.4518	+	10.0758i	0.645921	+	0.372923i
$731$	9.04252			0.334450
$732$	−8.37835	−	14.5117i	−0.309673	−	0.536369i
$733$	−29.7711	+	17.1883i	−1.09962	+	0.634865i	−0.936121	−	0.351678i	$-0.885611\pi$
$733$	−29.7711	+	17.1883i	−1.09962	+	0.634865i	−0.163498	+	0.986544i	$0.552278\pi$
$734$	2.49817	+	1.44232i	0.0922091	+	0.0532370i
$735$	−1.97096	−	19.3291i	−0.0727001	−	0.712963i
$736$		−	7.60260i		−	0.280235i
$737$	17.9187			0.660046
$738$	0.0519792			0.00191338
$739$		−	20.5294i		−	0.755185i	−0.925972	−	0.377593i	$-0.876752\pi$
$739$		−	20.5294i		−	0.755185i	0.925972	−	0.377593i	$-0.123248\pi$
$740$	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	$0.210076\pi$
$744$	−4.10799	+	7.11524i	−0.150606	+	0.260857i
$745$	−22.8268	−	39.5372i	−0.836311	−	1.44853i
$746$	−5.27263	−	3.04415i	−0.193045	−	0.111454i
$747$			5.22675i			0.191237i
$748$	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
$751$	−3.89301	+	6.74289i	−0.142058	+	0.246051i	−0.928271	−	0.371903i	$-0.878705\pi$
$751$	−3.89301	+	6.74289i	−0.142058	+	0.246051i	0.786214	+	0.617955i	$0.212039\pi$
$752$		−	31.9492i		−	1.16507i
$753$	−11.2929	+	19.5598i	−0.411535	+	0.712800i
$754$	0.0653562	−	9.19788i	0.00238013	−	0.334967i
$755$	21.0832			0.767298
$756$	4.13702	+	2.11600i	0.150462	+	0.0769583i
$757$	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	$0.772504\pi$
$758$	2.77900			0.100938
$759$	−5.63122	−	3.25119i	−0.204400	−	0.118011i
$760$	34.6034	−	19.9783i	1.25520	−	0.724688i
$761$			25.4303i			0.921848i	0.887440	+	0.460924i	$0.152482\pi$
$761$			25.4303i			0.921848i	−0.887440	+	0.460924i	$0.847518\pi$
$762$			1.60924i			0.0582967i
$763$	33.1806	−	1.68732i	1.20122	−	0.0610851i
$764$	−0.945788	−	1.63815i	−0.0342174	−	0.0592663i
$765$	−10.8992	−	6.29264i	−0.394060	−	0.227511i
$766$	4.85069	−	8.40164i	0.175263	−	0.303564i
$767$	−4.15711	+	2.36089i	−0.150105	+	0.0852466i
$768$	−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	$0.322262\pi$
$770$	8.40757	+	12.9906i	0.302988	+	0.468149i
$771$	−12.2312	+	21.1851i	−0.440497	+	0.762964i
$772$	19.6332	−	11.3352i	0.706613	−	0.407963i
$773$	21.4074	−	12.3596i	0.769970	−	0.444542i	−0.0628941	−	0.998020i	$-0.520033\pi$
$773$	21.4074	−	12.3596i	0.769970	−	0.444542i	0.832864	+	0.553478i	$0.186700\pi$
$774$	−0.852580	+	0.492237i	−0.0306454	+	0.0176931i
$775$	−10.3758	+	5.99044i	−0.372708	+	0.215183i
$776$	−8.04954	+	13.9422i	−0.288962	+	0.500496i
$777$	−16.7248	+	0.850499i	−0.599998	+	0.0305115i
$778$	−14.0930	+	8.13660i	−0.505259	+	0.291711i
$779$	−0.408723	−	0.707929i	−0.0146440	−	0.0253642i
$780$	15.1588	+	8.89617i	0.542774	+	0.318534i
$781$	17.4654	−	30.2509i	0.624960	−	1.08246i
$782$	−2.95292	−	1.70487i	−0.105596	−	0.0609659i
$783$	2.58391	+	4.47547i	0.0923416	+	0.159940i
$784$	10.6407	+	14.7416i	0.380024	+	0.526485i
$785$			10.8221i			0.386258i
$786$		−	0.597833i		−	0.0213240i
$787$	16.6018	−	9.58508i	0.591792	−	0.341671i	−0.174014	−	0.984743i	$-0.555674\pi$
$787$	16.6018	−	9.58508i	0.591792	−	0.341671i	0.765806	+	0.643072i	$0.222340\pi$
$788$	−24.3482	−	14.0574i	−0.867367	−	0.500775i
$789$	1.14098			0.0406198
$790$	−3.98859	−	6.90844i	−0.141908	−	0.245791i
$791$	1.73625	+	34.1427i	0.0617338	+	1.21397i
$792$	−7.91507			−0.281250
$793$	34.3992	+	0.244426i	1.22155	+	0.00867981i
$794$	5.08066	−	8.79996i	0.180306	−	0.312299i
$795$			27.7561i			0.984406i
$796$	−7.48213	+	12.9594i	−0.265197	+	0.459335i
$797$	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
$800$		−	13.4951i		−	0.477122i
$801$	−7.27106	−	4.19795i	−0.256910	−	0.148327i
$802$	−0.661120	−	1.14509i	−0.0233449	−	0.0404346i
$803$	−31.3889	+	54.3672i	−1.10769	+	1.91858i
$804$	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
$808$			6.55207i			0.230501i
$809$	−2.04910			−0.0720425			−0.0360213	−	0.999351i	$-0.511468\pi$
$809$	−2.04910			−0.0720425			−0.0360213	+	0.999351i	$0.511468\pi$
$810$	1.37018			0.0481432
$811$			31.8889i			1.11977i	0.828570	+	0.559885i	$0.189155\pi$
$811$			31.8889i			1.11977i	−0.828570	+	0.559885i	$0.810845\pi$
$812$	1.21958	+	23.9827i	0.0427989	+	0.841627i
$813$	0.206246	+	0.119076i	0.00723336	+	0.00417618i
$814$	11.5504	−	6.66861i	0.404840	−	0.233735i
$815$	16.5214	+	28.6159i	0.578720	+	1.00237i
$816$	11.7765			0.412260
$817$	13.4080	+	7.74112i	0.469087	+	0.270828i
$818$	4.08269			0.142748
$819$	−8.04508	+	5.12608i	−0.281118	+	0.179120i
$820$	−0.513299			−0.0179252
$821$	−21.9501	−	12.6729i	−0.766064	−	0.442288i	0.0654044	−	0.997859i	$-0.479166\pi$
$821$	−21.9501	−	12.6729i	−0.766064	−	0.442288i	−0.831469	+	0.555571i	$0.812500\pi$
$822$	6.79454			0.236987
$823$	22.6193	+	39.1777i	0.788458	+	1.36565i	0.926911	+	0.375280i	$0.122453\pi$
$823$	22.6193	+	39.1777i	0.788458	+	1.36565i	−0.138454	+	0.990369i	$0.544213\pi$
$824$	−5.00548	+	2.88992i	−0.174374	+	0.100675i
$825$	−9.99575	−	5.77105i	−0.348007	−	0.200922i
$826$	−1.45385	+	0.940936i	−0.0505858	+	0.0327393i
$827$			7.55982i			0.262881i	0.991324	+	0.131440i	$0.0419602\pi$
$827$			7.55982i			0.262881i	−0.991324	+	0.131440i	$0.958040\pi$
$828$	−2.67546			−0.0929787
$829$	29.2913			1.01733			0.508664	−	0.860965i	$-0.330140\pi$
$829$	29.2913			1.01733			0.508664	+	0.860965i	$0.330140\pi$
$830$			7.16159i			0.248583i
$831$	−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
$835$	−28.5872	+	49.5144i	−0.989299	+	1.71352i
$836$	29.1000	+	50.4027i	1.00645	+	1.74322i
$837$	3.83715	+	2.21538i	0.132631	+	0.0765748i
$838$		−	3.92942i		−	0.135739i
$839$	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
$842$	0.487318	−	0.844060i	0.0167941	−	0.0290882i
$843$		−	5.77285i		−	0.198828i
$844$	−18.1664	+	31.4652i	−0.625315	+	1.08308i
$845$	−31.5020	+	17.5956i	−1.08370	+	0.605307i
$846$	6.07248			0.208776
$847$	−16.0367	+	10.3790i	−0.551026	+	0.356627i
$848$	−12.9862	−	22.4927i	−0.445948	−	0.772404i
$849$	8.06871			0.276917
$850$	−5.24160	−	3.02624i	−0.179786	−	0.103799i
$851$	8.35027	−	4.82103i	0.286244	−	0.165263i
$852$		−	14.3726i		−	0.492397i
$853$			38.2109i			1.30832i	0.756358	+	0.654158i	$0.226977\pi$
$853$			38.2109i			1.30832i	−0.756358	+	0.654158i	$0.773023\pi$
$854$	12.4450	−	0.632861i	0.425859	−	0.0216561i
$855$	−10.7740	−	18.6611i	−0.368463	−	0.638197i
$856$	1.58532	+	0.915287i	0.0541853	+	0.0312839i
$857$	−10.1911	+	17.6514i	−0.348120	+	0.602962i	−0.985916	−	0.167244i	$-0.946513\pi$
$857$	−10.1911	+	17.6514i	−0.348120	+	0.602962i	0.637795	+	0.770206i	$0.279847\pi$
$858$	3.84535	−	6.55238i	0.131278	−	0.223695i
$859$	−16.4646	−	28.5175i	−0.561765	−	0.973006i	−0.997343	−	0.0728544i	$-0.976789\pi$
$859$	−16.4646	−	28.5175i	−0.561765	−	0.973006i	0.435578	−	0.900151i	$-0.356544\pi$
$860$	8.41930	−	4.86089i	0.287096	−	0.165755i
$861$	0.126860	−	0.248026i	0.00432339	−	0.00845269i
$862$	1.10139	−	1.90767i	0.0375136	−	0.0649755i
$863$	−49.3767	+	28.5077i	−1.68080	+	0.970413i	−0.719676	+	0.694310i	$0.755710\pi$
$863$	−49.3767	+	28.5077i	−1.68080	+	0.970413i	−0.961128	+	0.276103i	$0.910957\pi$
$864$	−4.32210	+	2.49537i	−0.147041	+	0.0848941i
$865$	−0.745222	+	0.430254i	−0.0253383	+	0.0146291i
$866$	−1.13399	+	0.654708i	−0.0385345	+	0.0222479i
$867$	1.77964	−	3.08243i	0.0604398	−	0.104685i
$868$	11.1866	+	17.2845i	0.379698	+	0.586674i
$869$	21.5217	−	12.4255i	0.730073	−	0.421508i
$870$	3.54043	+	6.13221i	0.120032	+	0.207901i
$871$	−0.107546	+	15.1354i	−0.00364405	+	0.512844i
$872$	−11.6425	+	20.1654i	−0.394265	+	0.682887i
$873$	7.51885	+	4.34101i	0.254474	+	0.146921i
$874$	−2.91901	−	5.05587i	−0.0987369	−	0.171017i
$875$	−9.16104	−	14.1548i	−0.309700	−	0.478519i
$876$			25.8305i			0.872733i
$877$			10.0516i			0.339419i	0.985494	+	0.169710i	$0.0542830\pi$
$877$			10.0516i			0.339419i	−0.985494	+	0.169710i	$0.945717\pi$
$878$	−0.923640	+	0.533264i	−0.0311714	+	0.0179968i
$879$	10.7719	+	6.21915i	0.363327	+	0.209767i
$880$	30.7713			1.03730
$881$	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	$0.721680\pi$
$882$	−2.80189	+	2.02244i	−0.0943444	+	0.0680991i
$883$	−3.18616			−0.107223			−0.0536114	−	0.998562i	$-0.517073\pi$
$883$	−3.18616			−0.107223			−0.0536114	+	0.998562i	$0.517073\pi$
$884$	−14.5328	+	24.7634i	−0.488790	+	0.832885i
$885$	1.84014	−	3.18722i	0.0618557	−	0.107137i
$886$		−	7.52861i		−	0.252929i
$887$	13.0925	−	22.6769i	0.439604	−	0.761416i	−0.558055	−	0.829804i	$-0.688452\pi$
$887$	13.0925	−	22.6769i	0.439604	−	0.761416i	0.997659	+	0.0683881i	$0.0217856\pi$
$888$	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
$891$			4.26849i			0.143000i
$892$	14.4983	+	8.37060i	0.485439	+	0.280269i
$893$	−47.7491	−	82.7039i	−1.59786	−	2.76758i
$894$	−4.05981	+	7.03180i	−0.135780	+	0.235179i
$895$	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
$899$			22.8974i			0.763672i
$900$	−4.74910			−0.158303
$901$	−45.3423			−1.51057
$902$			0.221873i			0.00738755i
$903$	0.267971	+	5.26955i	0.00891750	+	0.175360i
$904$	−20.7501	−	11.9801i	−0.690139	−	0.398452i
$905$	2.32781	−	1.34396i	0.0773792	−	0.0446749i
$906$	−1.87485	−	3.24734i	−0.0622879	−	0.107886i
$907$	17.8487			0.592658			0.296329	−	0.955086i	$-0.404238\pi$
$907$	17.8487			0.592658			0.296329	+	0.955086i	$0.404238\pi$
$908$	−16.6570	−	9.61690i	−0.552781	−	0.319148i
$909$	3.53344			0.117197
$910$	−11.0232	+	7.02365i	−0.365416	+	0.232832i
$911$	5.48276			0.181652			0.0908259	−	0.995867i	$-0.471049\pi$
$911$	5.48276			0.181652			0.0908259	+	0.995867i	$0.471049\pi$
$912$	17.4619	+	10.0816i	0.578221	+	0.333836i
$913$	−22.3103			−0.738364
$914$	6.68719	+	11.5825i	0.221192	+	0.383117i
$915$	−22.9338	+	13.2409i	−0.758170	+	0.437729i
$916$	−40.3093	−	23.2726i	−1.33186	−	0.768948i
$917$	−2.85264	−	1.45907i	−0.0942025	−	0.0481827i
$918$			2.23832i			0.0738757i
$919$	40.1991			1.32604			0.663022	−	0.748600i	$-0.269273\pi$
$919$	40.1991			1.32604			0.663022	+	0.748600i	$0.269273\pi$
$920$	−7.84038			−0.258490
$921$		−	21.2894i		−	0.701511i
$922$	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
$926$	2.39511	−	4.14846i	0.0787083	−	0.136327i
$927$	1.55849	+	2.69939i	0.0511876	+	0.0886595i
$928$	−22.3359	−	12.8956i	−0.733211	−	0.423320i
$929$		−	20.8093i		−	0.682731i	−0.939931	−	0.341365i	$-0.889111\pi$
$929$		−	20.8093i		−	0.682731i	0.939931	−	0.341365i	$-0.110889\pi$
$930$	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
$933$	4.95963	−	8.59033i	0.162371	−	0.281235i
$934$			7.40328i			0.242243i
$935$	26.8601	−	46.5230i	0.878418	−	1.52146i
$936$	0.0475050	−	6.68561i	0.00155275	−	0.218526i
$937$	−4.03940			−0.131961			−0.0659807	−	0.997821i	$-0.521018\pi$
$937$	−4.03940			−0.131961			−0.0659807	+	0.997821i	$0.521018\pi$
$938$	0.278455	+	5.47571i	0.00909186	+	0.178788i
$939$	−14.1334	−	24.4797i	−0.461225	−	0.798866i
$940$	−59.9663			−1.95588
$941$	26.4186	+	15.2528i	0.861221	+	0.497226i	0.864421	−	0.502769i	$-0.167685\pi$
$941$	26.4186	+	15.2528i	0.861221	+	0.497226i	−0.00320007	+	0.999995i	$0.501019\pi$
$942$	1.66688	−	0.962371i	0.0543097	−	0.0313557i
$943$			0.160401i			0.00522339i
$944$			3.44378i			0.112085i
$945$	3.34406	−	6.53800i	0.108782	−	0.212681i
$946$	−2.10111	−	3.63923i	−0.0683130	−	0.118322i
$947$	−33.2931	−	19.2218i	−1.08188	−	0.624624i	−0.150478	−	0.988613i	$-0.548081\pi$
$947$	−33.2931	−	19.2218i	−1.08188	−	0.624624i	−0.931403	+	0.363989i	$0.881415\pi$
$948$	5.11261	−	8.85530i	0.166050	−	0.287607i
$949$	−45.7339	−	26.8396i	−1.48459	−	0.871249i
$950$	−5.18141	−	8.97446i	−0.168107	−	0.291170i
$951$	0.874001	−	0.504605i	0.0283414	−	0.0163629i
$952$	−10.1298	+	19.8048i	−0.328308	+	0.641877i
$953$	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
$955$	−2.58888	+	1.49469i	−0.0837742	+	0.0483670i
$956$	38.8745	−	22.4442i	1.25729	−	0.725898i
$957$	−19.1035	+	11.0294i	−0.617528	+	0.356530i
$958$	6.91828	−	11.9828i	0.223520	−	0.387147i
$959$	16.5827	−	32.4210i	0.535484	−	1.04693i
$960$	6.56419	−	3.78984i	0.211858	−	0.122316i
$961$	−5.68417	−	9.84528i	−0.183360	−	0.317590i
$962$	5.56345	+	9.79627i	0.179373	+	0.315844i
$963$	0.493602	−	0.854944i	0.0159061	−	0.0275502i
$964$	−0.698486	−	0.403271i	−0.0224967	−	0.0129885i
$965$	−17.9138	−	31.0276i	−0.576666	−	0.998814i
$966$	0.906008	−	1.77134i	0.0291503	−	0.0569920i
$967$		−	41.4683i		−	1.33353i	−0.745268	−	0.666765i	$-0.767678\pi$
$967$		−	41.4683i		−	1.33353i	0.745268	−	0.666765i	$-0.232322\pi$
$968$		−	13.3880i		−	0.430308i
$969$	30.4848	−	17.6004i	0.979312	−	0.565406i
$970$	10.3022	+	5.94797i	0.330783	+	0.190978i
$971$	32.4100			1.04009			0.520043	−	0.854140i	$-0.325916\pi$
$971$	32.4100			1.04009			0.520043	+	0.854140i	$0.325916\pi$
$972$	0.878155	+	1.52101i	0.0281668	+	0.0487864i
$973$	2.12556	+	41.7984i	0.0681423	+	1.34000i
$974$	10.2870			0.329616
$975$	4.93462	−	8.40846i	0.158034	−	0.269286i
$976$	12.3900	−	21.4601i	0.396593	−	0.686919i
$977$			22.2413i			0.711561i	0.934570	+	0.355780i	$0.115785\pi$
$977$			22.2413i			0.711561i	−0.934570	+	0.355780i	$0.884215\pi$
$978$	2.93838	−	5.08942i	0.0939590	−	0.162742i
$979$	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
$982$		−	17.8487i		−	0.569575i
$983$	44.4432	+	25.6593i	1.41752	+	0.818404i	0.996080	−	0.0884530i	$-0.0281923\pi$
$983$	44.4432	+	25.6593i	1.41752	+	0.818404i	0.421438	+	0.906857i	$0.361526\pi$
$984$	0.0976250	+	0.169091i	0.00311217	+	0.00539044i
$985$	−22.2159	+	38.4790i	−0.707856	+	1.22604i
$986$	−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
$990$			5.84860i			0.185881i
$991$	15.5529			0.494055			0.247027	−	0.969008i	$-0.420546\pi$
$991$	15.5529			0.494055			0.247027	+	0.969008i	$0.420546\pi$
$992$	−22.1127			−0.702081
$993$		−	19.3155i		−	0.612959i
$994$	9.51566	+	4.86708i	0.301819	+	0.154374i
$995$	20.4807	+	11.8245i	0.649280	+	0.374862i
$996$	−7.94993	+	4.58990i	−0.251903	+	0.145436i
$997$	−19.4765	−	33.7342i	−0.616826	−	1.06837i	−0.990061	−	0.140637i	$-0.955085\pi$
$997$	−19.4765	−	33.7342i	−0.616826	−	1.06837i	0.373235	−	0.927737i	$-0.378248\pi$
$998$	15.4832			0.490112
$999$	−5.48154	−	3.16477i	−0.173428	−	0.100129i

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
273.2.t.d.4.6	✓	20	13.4	even	6
273.2.t.d.205.5	yes	20	7.2	even	3
273.2.bl.d.88.6	yes	20	1.1	even	1	trivial
273.2.bl.d.121.6	yes	20	91.30	even	6	inner
819.2.bm.g.478.6		20	21.2	odd	6
819.2.bm.g.550.5		20	39.17	odd	6
819.2.do.g.361.5		20	3.2	odd	2
819.2.do.g.667.5		20	273.212	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.bl (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.427513 - 0.246825i) q^{2} -1.00000 q^{3} +(-0.878155 - 1.52101i) q^{4} +(-2.40375 + 1.38781i) q^{5} +(0.427513 + 0.246825i) q^{6} +(2.22115 - 1.43754i) q^{7} +1.85430i q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+(-0.427513 - 0.246825i) q^{2} -1.00000 q^{3} +(-0.878155 - 1.52101i) q^{4} +(-2.40375 + 1.38781i) q^{5} +(0.427513 + 0.246825i) q^{6} +(2.22115 - 1.43754i) q^{7} +1.85430i q^{8} +1.00000 q^{9} +1.37018 q^{10} +4.26849i 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} +(-1.29862 + 2.24928i) q^{16} +(2.26712 + 3.92676i) q^{17} +(-0.427513 - 0.246825i) q^{18} +7.76333i q^{19} +(4.22173 + 2.43742i) q^{20} +(-2.22115 + 1.43754i) q^{21} +(1.05357 - 1.82484i) q^{22} +(0.761671 - 1.31925i) q^{23} -1.85430i q^{24} +(1.35201 - 2.34175i) q^{25} +(1.53506 + 0.900870i) q^{26} -1.00000 q^{27} +(-4.13702 - 2.11600i) q^{28} +(-2.58391 - 4.47547i) q^{29} -1.37018 q^{30} +(-3.83715 - 2.21538i) q^{31} +(4.32210 - 2.49537i) q^{32} -4.26849i q^{33} -2.23832i q^{34} +(-3.34406 + 6.53800i) q^{35} +(-0.878155 - 1.52101i) q^{36} +(5.48154 + 3.16477i) q^{37} +(1.91618 - 3.31893i) q^{38} +(3.60546 + 0.0256188i) q^{39} +(-2.57341 - 4.45728i) q^{40} +(-0.0911887 + 0.0526478i) q^{41} +(1.30439 - 0.0663316i) q^{42} +(0.997139 - 1.72709i) q^{43} +(6.49241 - 3.74839i) q^{44} +(-2.40375 + 1.38781i) q^{45} +(-0.651249 + 0.375999i) q^{46} +(-10.6531 + 6.15060i) q^{47} +(1.29862 - 2.24928i) q^{48} +(2.86698 - 6.38596i) q^{49} +(-1.15601 + 0.667421i) q^{50} +(-2.26712 - 3.92676i) q^{51} +(3.12719 + 5.50643i) q^{52} +(-4.99999 + 8.66024i) q^{53} +(0.427513 + 0.246825i) q^{54} +(-5.92383 - 10.2604i) q^{55} +(2.66563 + 4.11868i) q^{56} -7.76333i q^{57} +2.55110i q^{58} +(1.14829 - 0.662967i) q^{59} +(-4.22173 - 2.43742i) q^{60} -9.54086 q^{61} +(1.09362 + 1.89421i) q^{62} +(2.22115 - 1.43754i) q^{63} +2.73081 q^{64} +(8.70218 - 4.94210i) q^{65} +(-1.05357 + 1.82484i) q^{66} -4.19791i q^{67} +(3.98176 - 6.89661i) q^{68} +(-0.761671 + 1.31925i) q^{69} +(3.04337 - 1.96968i) q^{70} +(-7.08704 - 4.09170i) q^{71} +1.85430i q^{72} +(12.7369 + 7.35364i) q^{73} +(-1.56229 - 2.70596i) q^{74} +(-1.35201 + 2.34175i) 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} -7.20894i q^{80} +1.00000 q^{81} +0.0519792 q^{82} +5.22675i q^{83} +(4.13702 + 2.11600i) q^{84} +(-10.8992 - 6.29264i) q^{85} +(-0.852580 + 0.492237i) q^{86} +(2.58391 + 4.47547i) q^{87} -7.91507 q^{88} +(-7.27106 - 4.19795i) q^{89} +1.37018 q^{90} +(-8.04508 + 5.12608i) q^{91} -2.67546 q^{92} +(3.83715 + 2.21538i) q^{93} +6.07248 q^{94} +(-10.7740 - 18.6611i) q^{95} +(-4.32210 + 2.49537i) q^{96} +(7.51885 + 4.34101i) q^{97} +(-2.80189 + 2.02244i) q^{98} +4.26849i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q - 3 q^{2} - 20 q^{3} + 13 q^{4} - 6 q^{5} + 3 q^{6} - 5 q^{7} + 20 q^{9}+O(q^{10}) \) 20 * q - 3 * q^2 - 20 * q^3 + 13 * q^4 - 6 * q^5 + 3 * q^6 - 5 * q^7 + 20 * q^9	\( 20 q - 3 q^{2} - 20 q^{3} + 13 q^{4} - 6 q^{5} + 3 q^{6} - 5 q^{7} + 20 q^{9} - 4 q^{10} - 13 q^{12} + 8 q^{13} + 2 q^{14} + 6 q^{15} - 21 q^{16} - 8 q^{17} - 3 q^{18} + 5 q^{21} - 9 q^{22} + 18 q^{23} + 12 q^{25} + 32 q^{26} - 20 q^{27} - 43 q^{28} - 3 q^{29} + 4 q^{30} + 18 q^{31} - 24 q^{32} - 24 q^{35} + 13 q^{36} - 12 q^{37} + 9 q^{38} - 8 q^{39} + 5 q^{40} + 21 q^{41} - 2 q^{42} + 16 q^{43} + 6 q^{44} - 6 q^{45} + 6 q^{46} - 21 q^{47} + 21 q^{48} + 3 q^{49} - 54 q^{50} + 8 q^{51} + 13 q^{52} - 26 q^{53} + 3 q^{54} + 17 q^{55} + 6 q^{56} + 15 q^{59} + 4 q^{62} - 5 q^{63} - 46 q^{64} + 37 q^{65} + 9 q^{66} - 3 q^{68} - 18 q^{69} + 15 q^{71} + 9 q^{73} - 6 q^{74} - 12 q^{75} + 75 q^{76} + 20 q^{77} - 32 q^{78} + 3 q^{79} + 20 q^{81} - 30 q^{82} + 43 q^{84} - 78 q^{85} - 3 q^{86} + 3 q^{87} + 44 q^{88} - 24 q^{89} - 4 q^{90} - 4 q^{91} + 142 q^{92} - 18 q^{93} - 72 q^{94} + 42 q^{95} + 24 q^{96} - 15 q^{97} - 33 q^{98}+O(q^{100}) \) 20 * q - 3 * q^2 - 20 * q^3 + 13 * q^4 - 6 * q^5 + 3 * q^6 - 5 * q^7 + 20 * q^9 - 4 * q^10 - 13 * q^12 + 8 * q^13 + 2 * q^14 + 6 * q^15 - 21 * q^16 - 8 * q^17 - 3 * q^18 + 5 * q^21 - 9 * q^22 + 18 * q^23 + 12 * q^25 + 32 * q^26 - 20 * q^27 - 43 * q^28 - 3 * q^29 + 4 * q^30 + 18 * q^31 - 24 * q^32 - 24 * q^35 + 13 * q^36 - 12 * q^37 + 9 * q^38 - 8 * q^39 + 5 * q^40 + 21 * q^41 - 2 * q^42 + 16 * q^43 + 6 * q^44 - 6 * q^45 + 6 * q^46 - 21 * q^47 + 21 * q^48 + 3 * q^49 - 54 * q^50 + 8 * q^51 + 13 * q^52 - 26 * q^53 + 3 * q^54 + 17 * q^55 + 6 * q^56 + 15 * q^59 + 4 * q^62 - 5 * q^63 - 46 * q^64 + 37 * q^65 + 9 * q^66 - 3 * q^68 - 18 * q^69 + 15 * q^71 + 9 * q^73 - 6 * q^74 - 12 * q^75 + 75 * q^76 + 20 * q^77 - 32 * q^78 + 3 * q^79 + 20 * q^81 - 30 * q^82 + 43 * q^84 - 78 * q^85 - 3 * q^86 + 3 * q^87 + 44 * q^88 - 24 * q^89 - 4 * q^90 - 4 * q^91 + 142 * q^92 - 18 * q^93 - 72 * q^94 + 42 * q^95 + 24 * q^96 - 15 * q^97 - 33 * q^98

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