LMFDB - Embedded newform 273.2.bd.b.127.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [273,2,Mod(43,273)]

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, 0, 1]))

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

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

chi := DirichletCharacter("273.43");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 273 = 3 \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	273.bd (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:	$16$
Relative dimension:	$8$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 4 x^{15} + 10 x^{14} - 8 x^{13} - 3 x^{12} + 32 x^{11} - 5 x^{10} - 44 x^{9} + 214 x^{8} + \cdots + 6561 $ x^16 - 4x^15 + 10x^14 - 8x^13 - 3x^12 + 32x^11 - 5x^10 - 44x^9 + 214x^8 - 132x^7 - 45x^6 + 864x^5 - 243x^4 - 1944x^3 + 7290x^2 - 8748*x + 6561
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			127.1
Root			$-1.67549 - 0.438998i$ of defining polynomial
Character	$\chi$	$=$	273.127
Dual form			273.2.bd.b.43.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.20165 + 1.27113i) q^{2} +(0.500000 + 0.866025i) q^{3} +(2.23152 - 3.86511i) q^{4} +4.07309i q^{5} +(-2.20165 - 1.27113i) q^{6} +(0.866025 + 0.500000i) q^{7} +6.26168i q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})$	\(q+(-2.20165 + 1.27113i) q^{2} +(0.500000 + 0.866025i) q^{3} +(2.23152 - 3.86511i) q^{4} +4.07309i q^{5} +(-2.20165 - 1.27113i) q^{6} +(0.866025 + 0.500000i) q^{7} +6.26168i q^{8} +(-0.500000 + 0.866025i) q^{9} +(-5.17741 - 8.96754i) q^{10} +(3.35856 - 1.93907i) q^{11} +4.46304 q^{12} +(1.02114 + 3.45793i) q^{13} -2.54225 q^{14} +(-3.52740 + 2.03654i) q^{15} +(-3.49633 - 6.05583i) q^{16} +(-1.23657 + 2.14181i) q^{17} -2.54225i q^{18} +(2.32035 + 1.33965i) q^{19} +(15.7429 + 9.08919i) q^{20} +1.00000i q^{21} +(-4.92960 + 8.53831i) q^{22} +(-2.42463 - 4.19958i) q^{23} +(-5.42277 + 3.13084i) q^{24} -11.5901 q^{25} +(-6.64367 - 6.31516i) q^{26} -1.00000 q^{27} +(3.86511 - 2.23152i) q^{28} +(-2.88198 - 4.99174i) q^{29} +(5.17741 - 8.96754i) q^{30} -4.35651i q^{31} +(4.54990 + 2.62688i) q^{32} +(3.35856 + 1.93907i) q^{33} -6.28736i q^{34} +(-2.03654 + 3.52740i) q^{35} +(2.23152 + 3.86511i) q^{36} +(-1.95262 + 1.12734i) q^{37} -6.81147 q^{38} +(-2.48408 + 2.61330i) q^{39} -25.5044 q^{40} +(-4.19367 + 2.42121i) q^{41} +(-1.27113 - 2.20165i) q^{42} +(1.84786 - 3.20059i) q^{43} -17.3083i q^{44} +(-3.52740 - 2.03654i) q^{45} +(10.6764 + 6.16402i) q^{46} +10.0772i q^{47} +(3.49633 - 6.05583i) q^{48} +(0.500000 + 0.866025i) q^{49} +(25.5173 - 14.7324i) q^{50} -2.47315 q^{51} +(15.6440 + 3.76961i) q^{52} +11.2374 q^{53} +(2.20165 - 1.27113i) q^{54} +(7.89800 + 13.6797i) q^{55} +(-3.13084 + 5.42277i) q^{56} +2.67931i q^{57} +(12.6903 + 7.32672i) q^{58} +(-7.27129 - 4.19808i) q^{59} +18.1784i q^{60} +(3.51417 - 6.08672i) q^{61} +(5.53768 + 9.59154i) q^{62} +(-0.866025 + 0.500000i) q^{63} +0.628931 q^{64} +(-14.0845 + 4.15921i) q^{65} -9.85919 q^{66} +(4.44955 - 2.56895i) q^{67} +(5.51888 + 9.55899i) q^{68} +(2.42463 - 4.19958i) q^{69} -10.3548i q^{70} +(8.49523 + 4.90473i) q^{71} +(-5.42277 - 3.13084i) q^{72} +8.54270i q^{73} +(2.86599 - 4.96405i) q^{74} +(-5.79503 - 10.0373i) q^{75} +(10.3558 - 5.97893i) q^{76} +3.87813 q^{77} +(2.14726 - 8.91116i) q^{78} +0.0251142 q^{79} +(24.6659 - 14.2409i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(6.15533 - 10.6614i) q^{82} -0.202640i q^{83} +(3.86511 + 2.23152i) q^{84} +(-8.72378 - 5.03668i) q^{85} +9.39546i q^{86} +(2.88198 - 4.99174i) q^{87} +(12.1418 + 21.0302i) q^{88} +(15.8356 - 9.14267i) q^{89} +10.3548 q^{90} +(-0.844628 + 3.50523i) q^{91} -21.6425 q^{92} +(3.77285 - 2.17826i) q^{93} +(-12.8093 - 22.1864i) q^{94} +(-5.45653 + 9.45098i) q^{95} +5.25377i q^{96} +(-9.20599 - 5.31508i) q^{97} +(-2.20165 - 1.27113i) q^{98} +3.87813i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 8 q^{3} + 14 q^{4} - 8 q^{9}+O(q^{10}) $ 16 * q + 8 * q^3 + 14 * q^4 - 8 * q^9	$ 16 q + 8 q^{3} + 14 q^{4} - 8 q^{9} - 4 q^{10} + 28 q^{12} - 12 q^{13} - 4 q^{14} - 12 q^{15} - 10 q^{16} - 2 q^{17} + 18 q^{20} - 18 q^{22} - 6 q^{23} - 20 q^{25} + 20 q^{26} - 16 q^{27} - 12 q^{29} + 4 q^{30} - 30 q^{32} + 6 q^{35} + 14 q^{36} - 6 q^{37} - 24 q^{38} - 28 q^{40} - 30 q^{41} - 2 q^{42} + 14 q^{43} - 12 q^{45} - 42 q^{46} + 10 q^{48} + 8 q^{49} + 84 q^{50} - 4 q^{51} + 30 q^{52} + 28 q^{53} + 2 q^{55} - 12 q^{56} + 66 q^{58} - 24 q^{59} + 2 q^{61} - 20 q^{62} - 48 q^{64} - 44 q^{65} - 36 q^{66} + 30 q^{67} + 36 q^{68} + 6 q^{69} - 6 q^{71} + 6 q^{74} - 10 q^{75} - 24 q^{76} + 32 q^{77} + 10 q^{78} + 92 q^{79} + 114 q^{80} - 8 q^{81} - 42 q^{82} + 48 q^{85} + 12 q^{87} + 62 q^{88} + 18 q^{89} + 8 q^{90} - 116 q^{92} - 6 q^{93} - 24 q^{94} - 24 q^{95} - 6 q^{97}+O(q^{100}) $ 16 * q + 8 * q^3 + 14 * q^4 - 8 * q^9 - 4 * q^10 + 28 * q^12 - 12 * q^13 - 4 * q^14 - 12 * q^15 - 10 * q^16 - 2 * q^17 + 18 * q^20 - 18 * q^22 - 6 * q^23 - 20 * q^25 + 20 * q^26 - 16 * q^27 - 12 * q^29 + 4 * q^30 - 30 * q^32 + 6 * q^35 + 14 * q^36 - 6 * q^37 - 24 * q^38 - 28 * q^40 - 30 * q^41 - 2 * q^42 + 14 * q^43 - 12 * q^45 - 42 * q^46 + 10 * q^48 + 8 * q^49 + 84 * q^50 - 4 * q^51 + 30 * q^52 + 28 * q^53 + 2 * q^55 - 12 * q^56 + 66 * q^58 - 24 * q^59 + 2 * q^61 - 20 * q^62 - 48 * q^64 - 44 * q^65 - 36 * q^66 + 30 * q^67 + 36 * q^68 + 6 * q^69 - 6 * q^71 + 6 * q^74 - 10 * q^75 - 24 * q^76 + 32 * q^77 + 10 * q^78 + 92 * q^79 + 114 * q^80 - 8 * q^81 - 42 * q^82 + 48 * q^85 + 12 * q^87 + 62 * q^88 + 18 * q^89 + 8 * q^90 - 116 * q^92 - 6 * q^93 - 24 * q^94 - 24 * q^95 - 6 * q^97

Display 100 coefficients 10 coefficients

Character values

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

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

Coefficient data

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

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

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

$2$	−2.20165	+	1.27113i	−1.55680	+	0.898822i	−0.559245	+	0.829002i	$0.688909\pi$
$2$	−2.20165	+	1.27113i	−1.55680	+	0.898822i	−0.997560	+	0.0698193i	$0.977758\pi$
$3$	0.500000	+	0.866025i	0.288675	+	0.500000i
$3$	0.500000	+	0.866025i	0.288675	+	0.500000i
$4$	2.23152	−	3.86511i	1.11576	−	1.93255i
$5$			4.07309i			1.82154i	0.412913	+	0.910771i	$0.364511\pi$
$5$			4.07309i			1.82154i	−0.412913	+	0.910771i	$0.635489\pi$
$6$	−2.20165	−	1.27113i	−0.898822	−	0.518935i
$7$	0.866025	+	0.500000i	0.327327	+	0.188982i
$7$	0.866025	+	0.500000i	0.327327	+	0.188982i
$8$			6.26168i			2.21384i
$9$	−0.500000	+	0.866025i	−0.166667	+	0.288675i
$10$	−5.17741	−	8.96754i	−1.63724	−	2.83578i
$11$	3.35856	−	1.93907i	1.01264	−	0.584651i	0.100680	−	0.994919i	$-0.467898\pi$
$11$	3.35856	−	1.93907i	1.01264	−	0.584651i	0.911965	+	0.410268i	$0.134565\pi$
$12$	4.46304			1.28837
$13$	1.02114	+	3.45793i	0.283214	+	0.959057i
$13$	1.02114	+	3.45793i	0.283214	+	0.959057i
$14$	−2.54225			−0.679445
$15$	−3.52740	+	2.03654i	−0.910771	+	0.525834i
$16$	−3.49633	−	6.05583i	−0.874083	−	1.51396i
$17$	−1.23657	+	2.14181i	−0.299913	+	0.519465i	−0.976116	−	0.217251i	$-0.930291\pi$
$17$	−1.23657	+	2.14181i	−0.299913	+	0.519465i	0.676203	+	0.736716i	$0.263624\pi$
$18$		−	2.54225i		−	0.599214i
$19$	2.32035	+	1.33965i	0.532324	+	0.307337i	0.741962	−	0.670442i	$-0.233895\pi$
$19$	2.32035	+	1.33965i	0.532324	+	0.307337i	−0.209638	+	0.977779i	$0.567229\pi$
$20$	15.7429	+	9.08919i	3.52023	+	2.03240i
$21$			1.00000i			0.218218i
$22$	−4.92960	+	8.53831i	−1.05099	+	1.82037i
$23$	−2.42463	−	4.19958i	−0.505570	−	0.875674i	−0.999979	−	0.00644419i	$-0.997949\pi$
$23$	−2.42463	−	4.19958i	−0.505570	−	0.875674i	0.494409	−	0.869230i	$-0.335385\pi$
$24$	−5.42277	+	3.13084i	−1.10692	+	0.639080i
$25$	−11.5901			−2.31801
$26$	−6.64367	−	6.31516i	−1.30293	−	1.23850i
$27$	−1.00000			−0.192450
$28$	3.86511	−	2.23152i	0.730437	−	0.421718i
$29$	−2.88198	−	4.99174i	−0.535171	−	0.926943i	−0.999155	−	0.0410994i	$-0.986914\pi$
$29$	−2.88198	−	4.99174i	−0.535171	−	0.926943i	0.463984	−	0.885843i	$-0.346419\pi$
$30$	5.17741	−	8.96754i	0.945261	−	1.63724i
$31$		−	4.35651i		−	0.782453i	−0.920294	−	0.391226i	$-0.872051\pi$
$31$		−	4.35651i		−	0.782453i	0.920294	−	0.391226i	$-0.127949\pi$
$32$	4.54990	+	2.62688i	0.804316	+	0.464372i
$33$	3.35856	+	1.93907i	0.584651	+	0.337548i
$34$		−	6.28736i		−	1.07827i
$35$	−2.03654	+	3.52740i	−0.344239	+	0.596239i
$36$	2.23152	+	3.86511i	0.371920	+	0.644185i
$37$	−1.95262	+	1.12734i	−0.321008	+	0.185334i	−0.651842	−	0.758355i	$-0.726003\pi$
$37$	−1.95262	+	1.12734i	−0.321008	+	0.185334i	0.330834	+	0.943689i	$0.392670\pi$
$38$	−6.81147			−1.10497
$39$	−2.48408	+	2.61330i	−0.397771	+	0.418463i
$40$	−25.5044			−4.03259
$41$	−4.19367	+	2.42121i	−0.654940	+	0.378130i	−0.790346	−	0.612660i	$-0.790099\pi$
$41$	−4.19367	+	2.42121i	−0.654940	+	0.378130i	0.135406	+	0.990790i	$0.456766\pi$
$42$	−1.27113	−	2.20165i	−0.196139	−	0.339723i
$43$	1.84786	−	3.20059i	0.281796	−	0.488085i	−0.690031	−	0.723780i	$-0.742403\pi$
$43$	1.84786	−	3.20059i	0.281796	−	0.488085i	0.971827	+	0.235694i	$0.0757364\pi$
$44$		−	17.3083i		−	2.60932i
$45$	−3.52740	−	2.03654i	−0.525834	−	0.303590i
$46$	10.6764	+	6.16402i	1.57415	+	0.908835i
$47$			10.0772i			1.46991i	0.678119	+	0.734953i	$0.262796\pi$
$47$			10.0772i			1.46991i	−0.678119	+	0.734953i	$0.737204\pi$
$48$	3.49633	−	6.05583i	0.504652	−	0.874083i
$49$	0.500000	+	0.866025i	0.0714286	+	0.123718i
$50$	25.5173	−	14.7324i	3.60869	−	2.08348i
$51$	−2.47315			−0.346310
$52$	15.6440	+	3.76961i	2.16943	+	0.522751i
$53$	11.2374			1.54358			0.771789	−	0.635878i	$-0.219362\pi$
$53$	11.2374			1.54358			0.771789	+	0.635878i	$0.219362\pi$
$54$	2.20165	−	1.27113i	0.299607	−	0.172978i
$55$	7.89800	+	13.6797i	1.06497	+	1.84457i
$56$	−3.13084	+	5.42277i	−0.418376	+	0.724648i
$57$			2.67931i			0.354883i
$58$	12.6903	+	7.32672i	1.66631	+	0.962046i
$59$	−7.27129	−	4.19808i	−0.946642	−	0.546544i	−0.0546057	−	0.998508i	$-0.517390\pi$
$59$	−7.27129	−	4.19808i	−0.946642	−	0.546544i	−0.892036	+	0.451964i	$0.850724\pi$
$60$			18.1784i			2.34682i
$61$	3.51417	−	6.08672i	0.449943	−	0.779324i	−0.548439	−	0.836191i	$-0.684778\pi$
$61$	3.51417	−	6.08672i	0.449943	−	0.779324i	0.998382	+	0.0568665i	$0.0181109\pi$
$62$	5.53768	+	9.59154i	0.703286	+	1.21813i
$63$	−0.866025	+	0.500000i	−0.109109	+	0.0629941i
$64$	0.628931			0.0786164
$65$	−14.0845	+	4.15921i	−1.74696	+	0.515886i
$66$	−9.85919			−1.21358
$67$	4.44955	−	2.56895i	0.543599	−	0.313847i	−0.202937	−	0.979192i	$-0.565049\pi$
$67$	4.44955	−	2.56895i	0.543599	−	0.313847i	0.746536	+	0.665345i	$0.231715\pi$
$68$	5.51888	+	9.55899i	0.669263	+	1.15920i
$69$	2.42463	−	4.19958i	0.291891	−	0.505570i
$70$		−	10.3548i		−	1.23764i
$71$	8.49523	+	4.90473i	1.00820	+	0.582084i	0.910664	−	0.413148i	$-0.135571\pi$
$71$	8.49523	+	4.90473i	1.00820	+	0.582084i	0.0975351	+	0.995232i	$0.468904\pi$
$72$	−5.42277	−	3.13084i	−0.639080	−	0.368973i
$73$			8.54270i			0.999847i	0.866069	+	0.499924i	$0.166639\pi$
$73$			8.54270i			0.999847i	−0.866069	+	0.499924i	$0.833361\pi$
$74$	2.86599	−	4.96405i	0.333165	−	0.577059i
$75$	−5.79503	−	10.0373i	−0.669152	−	1.15901i
$76$	10.3558	−	5.97893i	1.18789	−	0.685830i
$77$	3.87813			0.441954
$78$	2.14726	−	8.91116i	0.243129	−	1.00899i
$79$	0.0251142			0.00282556			0.00141278	−	0.999999i	$-0.499550\pi$
$79$	0.0251142			0.00282556			0.00141278	+	0.999999i	$0.499550\pi$
$80$	24.6659	−	14.2409i	2.75773	−	1.59218i
$81$	−0.500000	−	0.866025i	−0.0555556	−	0.0962250i
$82$	6.15533	−	10.6614i	0.679743	−	1.17735i
$83$		−	0.202640i		−	0.0222427i	−0.999938	−	0.0111213i	$-0.996460\pi$
$83$		−	0.202640i		−	0.0222427i	0.999938	−	0.0111213i	$-0.00354011\pi$
$84$	3.86511	+	2.23152i	0.421718	+	0.243479i
$85$	−8.72378	−	5.03668i	−0.946227	−	0.546304i
$86$			9.39546i			1.01314i
$87$	2.88198	−	4.99174i	0.308981	−	0.535171i
$88$	12.1418	+	21.0302i	1.29432	+	2.24183i
$89$	15.8356	−	9.14267i	1.67857	−	0.969121i	0.715992	−	0.698109i	$-0.245975\pi$
$89$	15.8356	−	9.14267i	1.67857	−	0.969121i	0.962576	−	0.271013i	$-0.0873585\pi$
$90$	10.3548			1.09149
$91$	−0.844628	+	3.50523i	−0.0885410	+	0.367447i
$92$	−21.6425			−2.25638
$93$	3.77285	−	2.17826i	0.391226	−	0.225875i
$94$	−12.8093	−	22.1864i	−1.32118	−	2.28836i
$95$	−5.45653	+	9.45098i	−0.559828	+	0.969650i
$96$			5.25377i			0.536211i
$97$	−9.20599	−	5.31508i	−0.934727	−	0.539665i	−0.0464233	−	0.998922i	$-0.514782\pi$
$97$	−9.20599	−	5.31508i	−0.934727	−	0.539665i	−0.888303	+	0.459257i	$0.848116\pi$
$98$	−2.20165	−	1.27113i	−0.222401	−	0.128403i
$99$			3.87813i			0.389767i
$100$	−25.8635	+	44.7968i	−2.58635	+	4.47968i
$101$	4.53123	+	7.84832i	0.450874	+	0.780938i	0.998441	−	0.0558249i	$-0.0177789\pi$
$101$	4.53123	+	7.84832i	0.450874	+	0.780938i	−0.547566	+	0.836762i	$0.684446\pi$
$102$	5.44502	−	3.14368i	0.539137	−	0.311271i
$103$	13.2895			1.30945			0.654725	−	0.755867i	$-0.272784\pi$
$103$	13.2895			1.30945			0.654725	+	0.755867i	$0.272784\pi$
$104$	−21.6524	+	6.39407i	−2.12319	+	0.626990i
$105$	−4.07309			−0.397493
$106$	−24.7409	+	14.2842i	−2.40305	+	1.38740i
$107$	−1.43560	−	2.48654i	−0.138785	−	0.240382i	0.788252	−	0.615353i	$-0.210986\pi$
$107$	−1.43560	−	2.48654i	−0.138785	−	0.240382i	−0.927037	+	0.374970i	$0.877653\pi$
$108$	−2.23152	+	3.86511i	−0.214728	+	0.371920i
$109$			9.54925i			0.914652i	0.889299	+	0.457326i	$0.151193\pi$
$109$			9.54925i			0.914652i	−0.889299	+	0.457326i	$0.848807\pi$
$110$	−34.7773	−	20.0787i	−3.31589	−	1.91443i
$111$	−1.95262	−	1.12734i	−0.185334	−	0.107003i
$112$		−	6.99267i		−	0.660745i
$113$	9.06391	−	15.6992i	0.852661	−	1.47685i	−0.0261374	−	0.999658i	$-0.508321\pi$
$113$	9.06391	−	15.6992i	0.852661	−	1.47685i	0.878798	−	0.477194i	$-0.158346\pi$
$114$	−3.40573	−	5.89891i	−0.318976	−	0.552483i
$115$	17.1053	−	9.87574i	1.59508	−	0.920917i
$116$	−25.7248			−2.38849
$117$	−3.50523	−	0.844628i	−0.324058	−	0.0780859i
$118$	21.3452			1.96498
$119$	−2.14181	+	1.23657i	−0.196339	+	0.113357i
$120$	−12.7522	−	22.0874i	−1.16411	−	2.01630i
$121$	2.01996	−	3.49868i	0.183633	−	0.318062i
$122$			17.8678i			1.61767i
$123$	−4.19367	−	2.42121i	−0.378130	−	0.218313i
$124$	−16.8384	−	9.72165i	−1.51213	−	0.873030i
$125$		−	26.8419i		−	2.40081i
$126$	1.27113	−	2.20165i	0.113241	−	0.196139i
$127$	4.47860	+	7.75716i	0.397412	+	0.688337i	0.993406	−	0.114652i	$-0.0365752\pi$
$127$	4.47860	+	7.75716i	0.397412	+	0.688337i	−0.595994	+	0.802989i	$0.703242\pi$
$128$	−10.4845	+	6.05322i	−0.926706	+	0.535034i
$129$	3.69572			0.325390
$130$	25.7222	−	27.0603i	2.25599	−	2.37334i
$131$	−11.8752			−1.03754			−0.518772	−	0.854912i	$-0.673611\pi$
$131$	−11.8752			−1.03754			−0.518772	+	0.854912i	$0.673611\pi$
$132$	14.9894	−	8.65414i	1.30466	−	0.753246i
$133$	1.33965	+	2.32035i	0.116163	+	0.201200i
$134$	−6.53092	+	11.3119i	−0.564185	+	0.977197i
$135$		−	4.07309i		−	0.350556i
$136$	−13.4113	−	7.74302i	−1.15001	−	0.663959i
$137$	−13.8568	−	8.00021i	−1.18386	−	0.683504i	−0.226959	−	0.973904i	$-0.572878\pi$
$137$	−13.8568	−	8.00021i	−1.18386	−	0.683504i	−0.956905	+	0.290400i	$0.906212\pi$
$138$			12.3280i			1.04943i
$139$	−7.56874	+	13.1094i	−0.641972	+	1.11193i	0.343020	+	0.939328i	$0.388550\pi$
$139$	−7.56874	+	13.1094i	−0.641972	+	1.11193i	−0.984992	+	0.172600i	$0.944783\pi$
$140$	9.08919	+	15.7429i	0.768177	+	1.33052i
$141$	−8.72708	+	5.03858i	−0.734953	+	0.424325i
$142$	−24.9381			−2.09276
$143$	10.1347	+	9.63360i	0.847509	+	0.805602i
$144$	6.99267			0.582722
$145$	20.3318	−	11.7386i	1.68846	−	0.974835i
$146$	−10.8588	−	18.8081i	−0.898685	−	1.55657i
$147$	−0.500000	+	0.866025i	−0.0412393	+	0.0714286i
$148$			10.0628i			0.827155i
$149$	9.18568	+	5.30335i	0.752520	+	0.434468i	0.826604	−	0.562784i	$-0.190270\pi$
$149$	9.18568	+	5.30335i	0.752520	+	0.434468i	−0.0740836	+	0.997252i	$0.523603\pi$
$150$	25.5173	+	14.7324i	2.08348	+	1.20290i
$151$			6.19426i			0.504082i	0.967717	+	0.252041i	$0.0811017\pi$
$151$			6.19426i			0.504082i	−0.967717	+	0.252041i	$0.918898\pi$
$152$	−8.38847	+	14.5293i	−0.680395	+	1.17848i
$153$	−1.23657	−	2.14181i	−0.0999711	−	0.173155i
$154$	−8.53831	+	4.92960i	−0.688037	+	0.397238i
$155$	17.7445			1.42527
$156$	4.55741	+	15.4329i	0.364885	+	1.23562i
$157$	−5.84784			−0.466709			−0.233354	−	0.972392i	$-0.574970\pi$
$157$	−5.84784			−0.466709			−0.233354	+	0.972392i	$0.574970\pi$
$158$	−0.0552927	+	0.0319233i	−0.00439885	+	0.00253968i
$159$	5.61871	+	9.73189i	0.445593	+	0.771789i
$160$	−10.6995	+	18.5321i	−0.845873	+	1.46509i
$161$		−	4.84926i		−	0.382175i
$162$	2.20165	+	1.27113i	0.172978	+	0.0998691i
$163$	11.2524	+	6.49659i	0.881358	+	0.508853i	0.871106	−	0.491095i	$-0.163403\pi$
$163$	11.2524	+	6.49659i	0.881358	+	0.508853i	0.0102523	+	0.999947i	$0.496737\pi$
$164$			21.6120i			1.68761i
$165$	−7.89800	+	13.6797i	−0.614858	+	1.06497i
$166$	0.257582	+	0.446144i	0.0199922	+	0.0346275i
$167$	1.08897	−	0.628718i	0.0842672	−	0.0486517i	−0.457274	−	0.889326i	$-0.651174\pi$
$167$	1.08897	−	0.628718i	0.0842672	−	0.0486517i	0.541541	+	0.840674i	$0.317841\pi$
$168$	−6.26168			−0.483099
$169$	−10.9145	+	7.06208i	−0.839579	+	0.543237i
$170$	25.6090			1.96412
$171$	−2.32035	+	1.33965i	−0.177441	+	0.102446i
$172$	−8.24709	−	14.2844i	−0.628834	−	1.08917i
$173$	7.12973	−	12.3490i	0.542063	−	0.938881i	−0.456722	−	0.889609i	$-0.650977\pi$
$173$	7.12973	−	12.3490i	0.542063	−	0.938881i	0.998785	−	0.0492715i	$-0.0156900\pi$
$174$			14.6534i			1.11087i
$175$	−10.0373	−	5.79503i	−0.758748	−	0.438063i
$176$	−23.4853	−	13.5593i	−1.77027	−	1.02207i
$177$		−	8.39617i		−	0.631095i
$178$	−23.2430	+	40.2580i	−1.74213	+	3.01747i
$179$	−3.83996	−	6.65101i	−0.287012	−	0.497120i	0.686083	−	0.727523i	$-0.259329\pi$
$179$	−3.83996	−	6.65101i	−0.287012	−	0.497120i	−0.973095	+	0.230403i	$0.925995\pi$
$180$	−15.7429	+	9.08919i	−1.17341	+	0.677468i
$181$	5.08753			0.378153			0.189077	−	0.981962i	$-0.439451\pi$
$181$	5.08753			0.378153			0.189077	+	0.981962i	$0.439451\pi$
$182$	−2.59600	−	8.79092i	−0.192429	−	0.651627i
$183$	7.02833			0.519549
$184$	26.2964	−	15.1822i	1.93860	−	1.11925i
$185$	−4.59178	−	7.95319i	−0.337594	−	0.584730i
$186$	−5.53768	+	9.59154i	−0.406042	+	0.703286i
$187$			9.59120i			0.701378i
$188$	38.9493	+	22.4874i	2.84067	+	1.64006i
$189$	−0.866025	−	0.500000i	−0.0629941	−	0.0363696i
$190$		−	27.7437i		−	2.01274i
$191$	9.98913	−	17.3017i	0.722788	−	1.25191i	−0.237090	−	0.971488i	$-0.576194\pi$
$191$	9.98913	−	17.3017i	0.722788	−	1.25191i	0.959878	−	0.280418i	$-0.0904730\pi$
$192$	0.314465	+	0.544670i	0.0226946	+	0.0393082i
$193$	1.43383	−	0.827823i	0.103209	−	0.0595880i	−0.447507	−	0.894281i	$-0.647688\pi$
$193$	1.43383	−	0.827823i	0.103209	−	0.0595880i	0.550716	+	0.834693i	$0.314355\pi$
$194$	27.0245			1.94025
$195$	−10.6442	−	10.1179i	−0.762247	−	0.724557i
$196$	4.46304			0.318789
$197$	−8.30642	+	4.79572i	−0.591808	+	0.341681i	−0.765812	−	0.643064i	$-0.777663\pi$
$197$	−8.30642	+	4.79572i	−0.591808	+	0.341681i	0.174004	+	0.984745i	$0.444329\pi$
$198$	−4.92960	−	8.53831i	−0.350331	−	0.606791i
$199$	0.239520	−	0.414860i	0.0169791	−	0.0294086i	−0.857411	−	0.514632i	$-0.827928\pi$
$199$	0.239520	−	0.414860i	0.0169791	−	0.0294086i	0.874390	+	0.485224i	$0.161262\pi$
$200$		−	72.5732i		−	5.13170i
$201$	4.44955	+	2.56895i	0.313847	+	0.181200i
$202$	−19.9524	−	11.5195i	−1.40385	−	0.810512i
$203$		−	5.76396i		−	0.404551i
$204$	−5.51888	+	9.55899i	−0.386399	+	0.669263i
$205$	−9.86182	−	17.0812i	−0.688779	−	1.19300i
$206$	−29.2588	+	16.8926i	−2.03856	+	1.17696i
$207$	4.84926			0.337047
$208$	17.3704	−	18.2739i	1.20442	−	1.26707i
$209$	10.3907			0.718740
$210$	8.96754	−	5.17741i	0.618819	−	0.357275i
$211$	−5.01468	−	8.68568i	−0.345225	−	0.597947i	0.640170	−	0.768233i	$-0.278864\pi$
$211$	−5.01468	−	8.68568i	−0.345225	−	0.597947i	−0.985395	+	0.170287i	$0.945531\pi$
$212$	25.0765	−	43.4339i	1.72226	−	2.98305i
$213$			9.80945i			0.672133i
$214$	6.32140	+	3.64966i	0.432122	+	0.249486i
$215$	13.0363	+	7.52651i	0.889068	+	0.513303i
$216$		−	6.26168i		−	0.426053i
$217$	2.17826	−	3.77285i	0.147870	−	0.256118i
$218$	−12.1383	−	21.0242i	−0.822109	−	1.42394i
$219$	−7.39820	+	4.27135i	−0.499924	+	0.288631i
$220$	70.4982			4.75299
$221$	−8.66894	−	2.08889i	−0.583136	−	0.140514i
$222$	5.73199			0.384706
$223$	2.88727	−	1.66697i	0.193346	−	0.111628i	−0.400202	−	0.916427i	$-0.631060\pi$
$223$	2.88727	−	1.66697i	0.193346	−	0.111628i	0.593548	+	0.804799i	$0.297727\pi$
$224$	2.62688	+	4.54990i	0.175516	+	0.304003i
$225$	5.79503	−	10.0373i	0.386335	−	0.669152i
$226$			46.0855i			3.06556i
$227$	0.709367	+	0.409553i	0.0470824	+	0.0271830i	0.523356	−	0.852114i	$-0.324680\pi$
$227$	0.709367	+	0.409553i	0.0470824	+	0.0271830i	−0.476274	+	0.879297i	$0.658013\pi$
$228$	10.3558	+	5.97893i	0.685830	+	0.395964i
$229$		−	11.8844i		−	0.785342i	−0.919679	−	0.392671i	$-0.871551\pi$
$229$		−	11.8844i		−	0.785342i	0.919679	−	0.392671i	$-0.128449\pi$
$230$	−25.1066	+	43.4859i	−1.65548	+	2.86738i
$231$	1.93907	+	3.35856i	0.127581	+	0.220977i
$232$	31.2567	−	18.0460i	2.05210	−	1.18478i
$233$	2.81216			0.184231			0.0921154	−	0.995748i	$-0.470637\pi$
$233$	2.81216			0.184231			0.0921154	+	0.995748i	$0.470637\pi$
$234$	8.79092	−	2.59600i	0.574681	−	0.169706i
$235$	−41.0452			−2.67749
$236$	−32.4521	+	18.7362i	−2.11245	+	1.21962i
$237$	0.0125571	+	0.0217495i	0.000815670	+	0.00141278i
$238$	3.14368	−	5.44502i	0.203775	−	0.352948i
$239$			22.4961i			1.45515i	0.686027	+	0.727576i	$0.259353\pi$
$239$			22.4961i			1.45515i	−0.686027	+	0.727576i	$0.740647\pi$
$240$	24.6659	+	14.2409i	1.59218	+	0.919245i
$241$	−22.1610	−	12.7947i	−1.42752	−	0.824177i	−0.430593	−	0.902546i	$-0.641695\pi$
$241$	−22.1610	−	12.7947i	−1.42752	−	0.824177i	−0.996924	+	0.0783691i	$0.975029\pi$
$242$			10.2705i			0.660214i
$243$	0.500000	−	0.866025i	0.0320750	−	0.0555556i
$244$	−15.6839	−	27.1653i	−1.00406	−	1.73908i
$245$	−3.52740	+	2.03654i	−0.225357	+	0.130110i
$246$	12.3107			0.784900
$247$	−2.26302	+	9.39157i	−0.143992	+	0.597571i
$248$	27.2791			1.73222
$249$	0.175492	−	0.101320i	0.0111213	−	0.00642091i
$250$	34.1194	+	59.0966i	2.15790	+	3.73760i
$251$	0.754196	−	1.30631i	0.0476044	−	0.0824533i	−0.841241	−	0.540660i	$-0.818175\pi$
$251$	0.754196	−	1.30631i	0.0476044	−	0.0824533i	0.888846	+	0.458206i	$0.151508\pi$
$252$			4.46304i			0.281145i
$253$	−16.2866	−	9.40304i	−1.02393	−	0.591164i
$254$	−19.7207	−	11.3857i	−1.23738	−	0.714404i
$255$		−	10.0734i		−	0.630818i
$256$	14.7599	−	25.5649i	0.922492	−	1.59780i
$257$	6.54927	+	11.3437i	0.408532	+	0.707599i	0.994726	−	0.102573i	$-0.0327074\pi$
$257$	6.54927	+	11.3437i	0.408532	+	0.707599i	−0.586193	+	0.810171i	$0.699374\pi$
$258$	−8.13670	+	4.69773i	−0.506569	+	0.292468i
$259$	−2.25469			−0.140100
$260$	−15.3540	+	63.7193i	−0.952212	+	3.95170i
$261$	5.76396			0.356780
$262$	26.1452	−	15.0949i	1.61525	−	0.932568i
$263$	4.10869	+	7.11646i	0.253353	+	0.438820i	0.964447	−	0.264277i	$-0.0851334\pi$
$263$	4.10869	+	7.11646i	0.253353	+	0.438820i	−0.711094	+	0.703097i	$0.751800\pi$
$264$	−12.1418	+	21.0302i	−0.747277	+	1.29432i
$265$			45.7710i			2.81169i
$266$	−5.89891	−	3.40573i	−0.361685	−	0.208819i
$267$	15.8356	+	9.14267i	0.969121	+	0.559522i
$268$		−	22.9307i		−	1.40071i
$269$	8.90910	−	15.4310i	0.543197	−	0.940845i	−0.455521	−	0.890225i	$-0.650547\pi$
$269$	8.90910	−	15.4310i	0.543197	−	0.940845i	0.998718	−	0.0506200i	$-0.0161197\pi$
$270$	5.17741	+	8.96754i	0.315087	+	0.545747i
$271$	7.09376	−	4.09559i	0.430916	−	0.248789i	−0.268821	−	0.963190i	$-0.586634\pi$
$271$	7.09376	−	4.09559i	0.430916	−	0.248789i	0.699737	+	0.714401i	$0.253301\pi$
$272$	17.2939			1.04860
$273$	−3.45793	+	1.02114i	−0.209283	+	0.0618024i
$274$	40.6771			2.45739
$275$	−38.9260	+	22.4739i	−2.34732	+	1.35523i
$276$	−10.8212	−	18.7429i	−0.651362	−	1.12819i
$277$	1.99478	−	3.45506i	0.119855	−	0.207594i	−0.799855	−	0.600193i	$-0.795090\pi$
$277$	1.99478	−	3.45506i	0.119855	−	0.207594i	0.919710	+	0.392599i	$0.128424\pi$
$278$		−	38.4833i		−	2.30807i
$279$	3.77285	+	2.17826i	0.225875	+	0.130409i
$280$	−22.0874	−	12.7522i	−1.31998	−	0.762089i
$281$			18.1416i			1.08224i	0.840946	+	0.541119i	$0.181999\pi$
$281$			18.1416i			1.08224i	−0.840946	+	0.541119i	$0.818001\pi$
$282$	12.8093	−	22.1864i	0.762785	−	1.32118i
$283$	−0.561670	−	0.972840i	−0.0333878	−	0.0578293i	0.848849	−	0.528636i	$-0.177296\pi$
$283$	−0.561670	−	0.972840i	−0.0333878	−	0.0578293i	−0.882236	+	0.470807i	$0.843963\pi$
$284$	37.9146	−	21.8900i	2.24982	−	1.29893i
$285$	−10.9131			−0.646434
$286$	−34.5587	−	8.32735i	−2.04350	−	0.492406i
$287$	−4.84243			−0.285839
$288$	−4.54990	+	2.62688i	−0.268105	+	0.154791i
$289$	5.44177	+	9.42542i	0.320104	+	0.554437i
$290$	−29.8424	+	51.6886i	−1.75241	+	3.03526i
$291$		−	10.6302i		−	0.623151i
$292$	33.0185	+	19.0632i	1.93226	+	1.11559i
$293$	−5.49574	−	3.17297i	−0.321064	−	0.185367i	0.330803	−	0.943700i	$-0.392681\pi$
$293$	−5.49574	−	3.17297i	−0.321064	−	0.185367i	−0.651867	+	0.758333i	$0.726014\pi$
$294$		−	2.54225i		−	0.148267i
$295$	17.0992	−	29.6166i	0.995552	−	1.72435i
$296$	−7.05907	−	12.2267i	−0.410300	−	0.710660i
$297$	−3.35856	+	1.93907i	−0.194884	+	0.112516i
$298$	−26.9649			−1.56204
$299$	12.0460	−	12.6726i	0.696636	−	0.732874i
$300$	−51.7269			−2.98646
$301$	3.20059	−	1.84786i	0.184479	−	0.106509i
$302$	−7.87368	−	13.6376i	−0.453080	−	0.784757i
$303$	−4.53123	+	7.84832i	−0.260313	+	0.450874i
$304$		−	18.7355i		−	1.07455i
$305$	24.7917	+	14.3135i	1.41957	+	0.819590i
$306$	5.44502	+	3.14368i	0.311271	+	0.179712i
$307$		−	16.3235i		−	0.931630i	−0.884882	−	0.465815i	$-0.845761\pi$
$307$		−	16.3235i		−	0.931630i	0.884882	−	0.465815i	$-0.154239\pi$
$308$	8.65414	−	14.9894i	0.493115	−	0.854101i
$309$	6.64473	+	11.5090i	0.378006	+	0.654725i
$310$	−39.0672	+	22.5555i	−2.21887	+	1.28106i
$311$	21.8715			1.24022			0.620110	−	0.784515i	$-0.287088\pi$
$311$	21.8715			1.24022			0.620110	+	0.784515i	$0.287088\pi$
$312$	−16.3636	−	15.5545i	−0.926409	−	0.880601i
$313$	−17.4005			−0.983535			−0.491768	−	0.870726i	$-0.663649\pi$
$313$	−17.4005			−0.983535			−0.491768	+	0.870726i	$0.663649\pi$
$314$	12.8749	−	7.43334i	0.726574	−	0.419488i
$315$	−2.03654	−	3.52740i	−0.114746	−	0.198746i
$316$	0.0560428	−	0.0970690i	0.00315265	−	0.00546056i
$317$			19.1824i			1.07739i	0.842501	+	0.538695i	$0.181082\pi$
$317$			19.1824i			1.07739i	−0.842501	+	0.538695i	$0.818918\pi$
$318$	−24.7409	−	14.2842i	−1.38740	−	0.801017i
$319$	−19.3586	−	11.1767i	−1.08388	−	0.625776i
$320$			2.56169i			0.143203i
$321$	1.43560	−	2.48654i	0.0801275	−	0.138785i
$322$	6.16402	+	10.6764i	0.343507	+	0.594972i
$323$	−5.73856	+	3.31316i	−0.319302	+	0.184349i
$324$	−4.46304			−0.247947
$325$	−11.8351	−	40.0776i	−0.656494	−	2.22310i
$326$	−33.0320			−1.82947
$327$	−8.26989	+	4.77463i	−0.457326	+	0.264037i
$328$	−15.1609	−	26.2594i	−0.837118	−	1.44993i
$329$	−5.03858	+	8.72708i	−0.277786	+	0.481139i
$330$		−	40.1574i		−	2.21059i
$331$	17.2867	+	9.98046i	0.950161	+	0.548576i	0.893131	−	0.449797i	$-0.148504\pi$
$331$	17.2867	+	9.98046i	0.950161	+	0.548576i	0.0570302	+	0.998372i	$0.481837\pi$
$332$	−0.783228	−	0.452197i	−0.0429852	−	0.0248175i
$333$		−	2.25469i		−	0.123556i
$334$	−1.59836	+	2.76844i	−0.0874584	+	0.151482i
$335$	10.4636	+	18.1234i	0.571685	+	0.990188i
$336$	6.05583	−	3.49633i	0.330372	−	0.190741i
$337$	−10.9850			−0.598391			−0.299196	−	0.954192i	$-0.596718\pi$
$337$	−10.9850			−0.598391			−0.299196	+	0.954192i	$0.596718\pi$
$338$	15.0532	−	29.4220i	0.818788	−	1.60035i
$339$	18.1278			0.984568
$340$	−38.9346	+	22.4789i	−2.11153	+	1.21909i
$341$	−8.44757	−	14.6316i	−0.457462	−	0.792347i
$342$	3.40573	−	5.89891i	0.184161	−	0.318976i
$343$			1.00000i			0.0539949i
$344$	20.0411	+	11.5707i	1.08054	+	0.623851i
$345$	17.1053	+	9.87574i	0.920917	+	0.531692i
$346$			36.2511i			1.94887i
$347$	−6.85922	+	11.8805i	−0.368222	+	0.637779i	−0.989288	−	0.145979i	$-0.953367\pi$
$347$	−6.85922	+	11.8805i	−0.368222	+	0.637779i	0.621066	+	0.783759i	$0.286700\pi$
$348$	−12.8624	−	22.2783i	−0.689498	−	1.19424i
$349$	17.5786	−	10.1490i	0.940961	−	0.543264i	0.0506997	−	0.998714i	$-0.483855\pi$
$349$	17.5786	−	10.1490i	0.940961	−	0.543264i	0.890262	+	0.455450i	$0.150522\pi$
$350$	29.4649			1.57496
$351$	−1.02114	−	3.45793i	−0.0545046	−	0.184571i
$352$	20.3748			1.08598
$353$	1.01371	−	0.585267i	0.0539544	−	0.0311506i	−0.472780	−	0.881180i	$-0.656750\pi$
$353$	1.01371	−	0.585267i	0.0539544	−	0.0311506i	0.526735	+	0.850030i	$0.323416\pi$
$354$	10.6726	+	18.4855i	0.567242	+	0.982491i
$355$	−19.9774	+	34.6019i	−1.06029	+	1.83648i
$356$		−	81.6083i		−	4.32523i
$357$	−2.14181	−	1.23657i	−0.113357	−	0.0654464i
$358$	16.9086	+	9.76216i	0.893645	+	0.515946i
$359$		−	20.1459i		−	1.06326i	−0.846977	−	0.531630i	$-0.821580\pi$
$359$		−	20.1459i		−	1.06326i	0.846977	−	0.531630i	$-0.178420\pi$
$360$	12.7522	−	22.0874i	0.672099	−	1.16411i
$361$	−5.91066	−	10.2376i	−0.311087	−	0.538819i
$362$	−11.2010	+	6.46690i	−0.588711	+	0.339892i
$363$	4.03993			0.212041
$364$	11.6633	+	11.0866i	0.611322	+	0.581094i
$365$	−34.7952			−1.82126
$366$	−15.4740	+	8.93390i	−0.808837	+	0.466982i
$367$	3.16211	+	5.47693i	0.165061	+	0.285893i	0.936677	−	0.350195i	$-0.113885\pi$
$367$	3.16211	+	5.47693i	0.165061	+	0.285893i	−0.771616	+	0.636088i	$0.780551\pi$
$368$	−16.9546	+	29.3663i	−0.883822	+	1.53082i
$369$		−	4.84243i		−	0.252087i
$370$	20.2190	+	11.6734i	1.05114	+	0.606874i
$371$	9.73189	+	5.61871i	0.505255	+	0.291709i
$372$		−	19.4433i		−	1.00809i
$373$	7.04276	−	12.1984i	0.364661	−	0.631611i	−0.624061	−	0.781376i	$-0.714518\pi$
$373$	7.04276	−	12.1984i	0.364661	−	0.631611i	0.988722	+	0.149765i	$0.0478517\pi$
$374$	−12.1916	−	21.1165i	−0.630414	−	1.09191i
$375$	23.2458	−	13.4210i	1.20041	−	0.693055i
$376$	−63.0999			−3.25413
$377$	14.3182	−	15.0630i	0.737423	−	0.775782i
$378$	2.54225			0.130759
$379$	7.83453	−	4.52327i	0.402433	−	0.232345i	−0.285100	−	0.958498i	$-0.592027\pi$
$379$	7.83453	−	4.52327i	0.402433	−	0.232345i	0.687533	+	0.726153i	$0.258694\pi$
$380$	24.3527	+	42.1801i	1.24927	+	2.16380i
$381$	−4.47860	+	7.75716i	−0.229446	+	0.397412i
$382$			50.7898i			2.59863i
$383$	−8.31170	−	4.79876i	−0.424708	−	0.245205i	0.272382	−	0.962189i	$-0.412189\pi$
$383$	−8.31170	−	4.79876i	−0.424708	−	0.245205i	−0.697090	+	0.716984i	$0.745522\pi$
$384$	−10.4845	−	6.05322i	−0.535034	−	0.308902i
$385$			15.7960i			0.805038i
$386$	−2.10453	+	3.64516i	−0.107118	+	0.185534i
$387$	1.84786	+	3.20059i	0.0939321	+	0.162695i
$388$	−41.0867	+	23.7214i	−2.08586	+	1.20427i
$389$	−20.1151			−1.01988			−0.509938	−	0.860211i	$-0.670332\pi$
$389$	−20.1151			−1.01988			−0.509938	+	0.860211i	$0.670332\pi$
$390$	36.2960	+	8.74597i	1.83792	+	0.442869i
$391$	11.9929			0.606509
$392$	−5.42277	+	3.13084i	−0.273891	+	0.158131i
$393$	−5.93762	−	10.2843i	−0.299513	−	0.518772i
$394$	12.1919	−	21.1170i	0.614220	−	1.06386i
$395$			0.102292i			0.00514688i
$396$	14.9894	+	8.65414i	0.753246	+	0.434887i
$397$	−4.96061	−	2.86401i	−0.248966	−	0.143740i	0.370325	−	0.928902i	$-0.379246\pi$
$397$	−4.96061	−	2.86401i	−0.248966	−	0.143740i	−0.619291	+	0.785162i	$0.712580\pi$
$398$			1.21784i			0.0610447i
$399$	−1.33965	+	2.32035i	−0.0670665	+	0.116163i
$400$	40.5227	+	70.1874i	2.02614	+	3.50937i
$401$	5.91153	−	3.41302i	0.295208	−	0.170438i	−0.345080	−	0.938573i	$-0.612148\pi$
$401$	5.91153	−	3.41302i	0.295208	−	0.170438i	0.640288	+	0.768135i	$0.278815\pi$
$402$	−13.0618			−0.651465
$403$	15.0645	−	4.44863i	0.750417	−	0.221602i
$404$	40.4462			2.01227
$405$	3.52740	−	2.03654i	0.175278	−	0.101197i
$406$	7.32672	+	12.6903i	0.363619	+	0.629807i
$407$	−4.37199	+	7.57252i	−0.216712	+	0.375356i
$408$		−	15.4860i		−	0.766674i
$409$	−19.1956	−	11.0826i	−0.949162	−	0.547999i	−0.0563417	−	0.998412i	$-0.517944\pi$
$409$	−19.1956	−	11.0826i	−0.949162	−	0.547999i	−0.892821	+	0.450412i	$0.851277\pi$
$410$	43.4246	+	25.0712i	2.14459	+	1.23818i
$411$		−	16.0004i		−	0.789243i
$412$	29.6557	−	51.3652i	1.46103	−	2.53058i
$413$	−4.19808	−	7.27129i	−0.206574	−	0.357797i
$414$	−10.6764	+	6.16402i	−0.524716	+	0.302945i
$415$	0.825373			0.0405160
$416$	−4.43748	+	18.4156i	−0.217565	+	0.902901i
$417$	−15.1375			−0.741286
$418$	−22.8768	+	13.2079i	−1.11894	+	0.646019i
$419$	6.85981	+	11.8815i	0.335124	+	0.580451i	0.983509	−	0.180861i	$-0.0578885\pi$
$419$	6.85981	+	11.8815i	0.335124	+	0.580451i	−0.648385	+	0.761313i	$0.724555\pi$
$420$	−9.08919	+	15.7429i	−0.443507	+	0.768177i
$421$		−	10.9099i		−	0.531718i	−0.964012	−	0.265859i	$-0.914344\pi$
$421$		−	10.9099i		−	0.531718i	0.964012	−	0.265859i	$-0.0856555\pi$
$422$	22.0812	+	12.7486i	1.07490	+	0.620591i
$423$	−8.72708	−	5.03858i	−0.424325	−	0.244984i
$424$			70.3651i			3.41723i
$425$	14.3320	−	24.8237i	0.695203	−	1.20413i
$426$	−12.4690	−	21.5970i	−0.604127	−	1.04638i
$427$	6.08672	−	3.51417i	0.294557	−	0.170062i
$428$	−12.8143			−0.619403
$429$	−3.27558	+	13.5937i	−0.158146	+	0.656312i
$430$	−38.2685			−1.84547
$431$	7.14105	−	4.12289i	0.343972	−	0.198592i	−0.318055	−	0.948072i	$-0.603030\pi$
$431$	7.14105	−	4.12289i	0.343972	−	0.198592i	0.662027	+	0.749480i	$0.269696\pi$
$432$	3.49633	+	6.05583i	0.168217	+	0.291361i
$433$	−10.8228	+	18.7457i	−0.520112	+	0.900861i	0.479614	+	0.877479i	$0.340777\pi$
$433$	−10.8228	+	18.7457i	−0.520112	+	0.900861i	−0.999727	+	0.0233817i	$0.992557\pi$
$434$			11.0754i			0.531634i
$435$	20.3318	+	11.7386i	0.974835	+	0.562821i
$436$	36.9089	+	21.3094i	1.76762	+	1.02053i
$437$		−	12.9927i		−	0.621523i
$438$	10.8588	−	18.8081i	0.518856	−	0.898685i
$439$	8.10230	+	14.0336i	0.386702	+	0.669787i	0.992004	−	0.126209i	$-0.0402810\pi$
$439$	8.10230	+	14.0336i	0.386702	+	0.669787i	−0.605302	+	0.795996i	$0.706948\pi$
$440$	−85.6580	+	49.4547i	−4.08359	+	2.35766i
$441$	−1.00000			−0.0476190
$442$	21.7413	−	6.42030i	1.03413	−	0.305383i
$443$	8.19296			0.389259			0.194630	−	0.980877i	$-0.437650\pi$
$443$	8.19296			0.389259			0.194630	+	0.980877i	$0.437650\pi$
$444$	−8.71462	+	5.03139i	−0.413578	+	0.238779i
$445$	37.2389	+	64.4997i	1.76529	+	3.05758i
$446$	−4.23785	+	7.34017i	−0.200668	+	0.347567i
$447$			10.6067i			0.501680i
$448$	0.544670	+	0.314465i	0.0257332	+	0.0148571i
$449$	7.10630	+	4.10282i	0.335367	+	0.193624i	0.658221	−	0.752824i	$-0.271309\pi$
$449$	7.10630	+	4.10282i	0.335367	+	0.193624i	−0.322854	+	0.946449i	$0.604642\pi$
$450$			29.4649i			1.38899i
$451$	−9.38979	+	16.2636i	−0.442148	+	0.765823i
$452$	−40.4526	−	70.0660i	−1.90273	−	3.29563i
$453$	−5.36439	+	3.09713i	−0.252041	+	0.145516i
$454$	−2.08238			−0.0977307
$455$	−14.2771	−	3.44024i	−0.669321	−	0.161281i
$456$	−16.7769			−0.785652
$457$	−13.2743	+	7.66392i	−0.620946	+	0.358503i	−0.777237	−	0.629208i	$-0.783379\pi$
$457$	−13.2743	+	7.66392i	−0.620946	+	0.358503i	0.156291	+	0.987711i	$0.450046\pi$
$458$	15.1065	+	26.1653i	0.705882	+	1.22262i
$459$	1.23657	−	2.14181i	0.0577183	−	0.0999711i
$460$		−	88.1517i		−	4.11009i
$461$	−31.5683	−	18.2260i	−1.47028	−	0.848867i	−0.470837	−	0.882220i	$-0.656048\pi$
$461$	−31.5683	−	18.2260i	−1.47028	−	0.848867i	−0.999444	+	0.0333528i	$0.989381\pi$
$462$	−8.53831	−	4.92960i	−0.397238	−	0.229346i
$463$		−	35.7314i		−	1.66058i	−0.557333	−	0.830289i	$-0.688175\pi$
$463$		−	35.7314i		−	1.66058i	0.557333	−	0.830289i	$-0.311825\pi$
$464$	−20.1527	+	34.9056i	−0.935568	+	1.62045i
$465$	8.87224	+	15.3672i	0.411440	+	0.712635i
$466$	−6.19141	+	3.57461i	−0.286811	+	0.165591i
$467$	13.9609			0.646033			0.323017	−	0.946393i	$-0.395303\pi$
$467$	13.9609			0.646033			0.323017	+	0.946393i	$0.395303\pi$
$468$	−11.0866	+	11.6633i	−0.512477	+	0.539135i
$469$	5.13790			0.237246
$470$	90.3673	−	52.1736i	4.16833	−	2.40659i
$471$	−2.92392	−	5.06438i	−0.134727	−	0.233354i
$472$	26.2870	−	45.5305i	1.20996	−	2.09571i
$473$		−	14.3325i		−	0.659010i
$474$	−0.0552927	−	0.0319233i	−0.00253968	−	0.00146628i
$475$	−26.8930	−	15.5267i	−1.23393	−	0.712412i
$476$			11.0378i			0.505915i
$477$	−5.61871	+	9.73189i	−0.257263	+	0.445593i
$478$	−28.5954	−	49.5287i	−1.30792	−	2.26539i
$479$	27.2338	−	15.7235i	1.24435	−	0.718423i	0.274370	−	0.961624i	$-0.411531\pi$
$479$	27.2338	−	15.7235i	1.24435	−	0.718423i	0.969976	+	0.243201i	$0.0781974\pi$
$480$	−21.3991			−0.976730
$481$	−5.89218	−	5.60083i	−0.268660	−	0.255376i
$482$	65.0546			2.96315
$483$	4.19958	−	2.42463i	0.191088	−	0.110325i
$484$	−9.01519	−	15.6148i	−0.409781	−	0.709762i
$485$	21.6488	−	37.4968i	0.983021	−	1.70264i
$486$			2.54225i			0.115319i
$487$	−29.1752	−	16.8443i	−1.32205	−	0.763288i	−0.337997	−	0.941147i	$-0.609749\pi$
$487$	−29.1752	−	16.8443i	−1.32205	−	0.763288i	−0.984056	+	0.177860i	$0.943083\pi$
$488$	38.1130	+	22.0046i	1.72530	+	0.996100i
$489$			12.9932i			0.587572i
$490$	5.17741	−	8.96754i	0.233892	−	0.405112i
$491$	−6.10451	−	10.5733i	−0.275493	−	0.477167i	0.694767	−	0.719235i	$-0.255508\pi$
$491$	−6.10451	−	10.5733i	−0.275493	−	0.477167i	−0.970259	+	0.242068i	$0.922174\pi$
$492$	−18.7165	+	10.8060i	−0.843805	+	0.487171i
$493$	14.2551			0.642019
$494$	−6.95549	−	23.5536i	−0.312942	−	1.05973i
$495$	−15.7960			−0.709977
$496$	−26.3823	+	15.2318i	−1.18460	+	0.683929i
$497$	4.90473	+	8.49523i	0.220007	+	0.381063i
$498$	−0.257582	+	0.446144i	−0.0115425	+	0.0199922i
$499$		−	33.1624i		−	1.48455i	−0.670094	−	0.742276i	$-0.733746\pi$
$499$		−	33.1624i		−	1.48455i	0.670094	−	0.742276i	$-0.266254\pi$
$500$	−103.747	−	59.8983i	−4.63970	−	2.67873i
$501$	1.08897	+	0.628718i	0.0486517	+	0.0280891i
$502$			3.83471i			0.171152i
$503$	−12.7393	+	22.0651i	−0.568017	+	0.983834i	0.428745	+	0.903425i	$0.358956\pi$
$503$	−12.7393	+	22.0651i	−0.568017	+	0.983834i	−0.996762	+	0.0804085i	$0.974378\pi$
$504$	−3.13084	−	5.42277i	−0.139459	−	0.241549i
$505$	−31.9669	+	18.4561i	−1.42251	+	0.821286i
$506$	47.8098			2.12541
$507$	−11.5732	−	5.92122i	−0.513984	−	0.262971i
$508$	39.9764			1.77366
$509$	−5.95979	+	3.44089i	−0.264163	+	0.152515i	−0.626232	−	0.779637i	$-0.715404\pi$
$509$	−5.95979	+	3.44089i	−0.264163	+	0.152515i	0.362069	+	0.932151i	$0.382070\pi$
$510$	12.8045	+	22.1780i	0.566993	+	0.982060i
$511$	−4.27135	+	7.39820i	−0.188953	+	0.327277i
$512$			50.8338i			2.24656i
$513$	−2.32035	−	1.33965i	−0.102446	−	0.0591471i
$514$	−28.8385	−	16.6499i	−1.27201	−	0.734395i
$515$			54.1292i			2.38522i
$516$	8.24709	−	14.2844i	0.363058	−	0.628834i
$517$	19.5403	+	33.8448i	0.859381	+	1.48849i
$518$	4.96405	−	2.86599i	0.218108	−	0.125925i
$519$	14.2595			0.625921
$520$	−26.0436	−	88.1923i	−1.14209	−	3.86749i
$521$	5.42730			0.237774			0.118887	−	0.992908i	$-0.462067\pi$
$521$	5.42730			0.237774			0.118887	+	0.992908i	$0.462067\pi$
$522$	−12.6903	+	7.32672i	−0.555437	+	0.320682i
$523$	−14.7960	−	25.6274i	−0.646983	−	1.12061i	−0.983840	−	0.179051i	$-0.942697\pi$
$523$	−14.7960	−	25.6274i	−0.646983	−	1.12061i	0.336857	−	0.941556i	$-0.390636\pi$
$524$	−26.4999	+	45.8991i	−1.15765	+	2.00511i
$525$		−	11.5901i		−	0.505832i
$526$	−18.0918	−	10.4453i	−0.788841	−	0.455438i
$527$	9.33082	+	5.38715i	0.406457	+	0.234668i
$528$		−	27.1185i		−	1.18018i
$529$	−0.257668	+	0.446294i	−0.0112030	+	0.0194041i
$530$	−58.1807	−	100.772i	−2.52721	−	4.37726i
$531$	7.27129	−	4.19808i	0.315547	−	0.182181i
$532$	11.9579			0.518439
$533$	−12.6547	−	12.0290i	−0.548137	−	0.521033i
$534$	−46.4859			−2.01164
$535$	10.1279	−	5.84734i	0.437867	−	0.252802i
$536$	16.0859	+	27.8616i	0.694806	+	1.20344i
$537$	3.83996	−	6.65101i	0.165707	−	0.287012i
$538$			45.2983i			1.95295i
$539$	3.35856	+	1.93907i	0.144664	+	0.0835215i
$540$	−15.7429	−	9.08919i	−0.677468	−	0.391136i
$541$			38.2583i			1.64485i	0.568872	+	0.822426i	$0.307380\pi$
$541$			38.2583i			1.64485i	−0.568872	+	0.822426i	$0.692620\pi$
$542$	−10.4120	+	18.0341i	−0.447234	+	0.774632i
$543$	2.54377	+	4.40593i	0.109163	+	0.189077i
$544$	−11.2526	+	6.49667i	−0.482450	+	0.278543i
$545$	−38.8950			−1.66608
$546$	6.31516	−	6.64367i	0.270264	−	0.284323i
$547$	−21.8681			−0.935013			−0.467507	−	0.883990i	$-0.654848\pi$
$547$	−21.8681			−0.935013			−0.467507	+	0.883990i	$0.654848\pi$
$548$	−61.8434	+	35.7053i	−2.64182	+	1.52525i
$549$	3.51417	+	6.08672i	0.149981	+	0.259775i
$550$	57.1343	−	98.9596i	2.43622	−	4.21965i
$551$		−	15.4434i		−	0.657912i
$552$	26.2964	+	15.1822i	1.11925	+	0.646199i
$553$	0.0217495	+	0.0125571i	0.000924883	+	0.000533981i
$554$			10.1425i			0.430912i
$555$	4.59178	−	7.95319i	0.194910	−	0.337594i
$556$	33.7796	+	58.5080i	1.43257	+	2.48129i
$557$	−25.2629	+	14.5856i	−1.07043	+	0.618010i	−0.928298	−	0.371838i	$-0.878728\pi$
$557$	−25.2629	+	14.5856i	−1.07043	+	0.618010i	−0.142128	+	0.989848i	$0.545394\pi$
$558$	−11.0754			−0.468857
$559$	12.9543	+	3.12151i	0.547910	+	0.132026i
$560$	28.4818			1.20357
$561$	−8.30622	+	4.79560i	−0.350689	+	0.202470i
$562$	−23.0603	−	39.9416i	−0.972739	−	1.68483i
$563$	15.9712	−	27.6629i	0.673104	−	1.16585i	−0.303915	−	0.952699i	$-0.598294\pi$
$563$	15.9712	−	27.6629i	0.673104	−	1.16585i	0.977019	−	0.213152i	$-0.0683728\pi$
$564$			44.9748i			1.89378i
$565$	63.9441	+	36.9181i	2.69015	+	1.55316i
$566$	2.47320	+	1.42791i	0.103957	+	0.0600193i
$567$		−	1.00000i		−	0.0419961i
$568$	−30.7118	+	53.1944i	−1.28864	+	2.23199i
$569$	3.95674	+	6.85327i	0.165875	+	0.287304i	0.936966	−	0.349421i	$-0.113622\pi$
$569$	3.95674	+	6.85327i	0.165875	+	0.287304i	−0.771091	+	0.636725i	$0.780289\pi$
$570$	24.0268	−	13.8719i	1.00637	−	0.581028i
$571$	16.2883			0.681644			0.340822	−	0.940128i	$-0.389295\pi$
$571$	16.2883			0.681644			0.340822	+	0.940128i	$0.389295\pi$
$572$	59.8508	−	17.6742i	2.50249	−	0.738997i
$573$	19.9783			0.834604
$574$	10.6614	−	6.15533i	0.444996	−	0.256919i
$575$	28.1016	+	48.6734i	1.17192	+	2.02982i
$576$	−0.314465	+	0.544670i	−0.0131027	+	0.0226946i
$577$			14.5408i			0.605343i	0.953095	+	0.302671i	$0.0978784\pi$
$577$			14.5408i			0.605343i	−0.953095	+	0.302671i	$0.902122\pi$
$578$	−23.9618	−	13.8343i	−0.996679	−	0.575433i
$579$	1.43383	+	0.827823i	0.0595880	+	0.0344032i
$580$		−	104.780i		−	4.35073i
$581$	0.101320	−	0.175492i	0.00420347	−	0.00728063i
$582$	13.5123	+	23.4039i	0.560102	+	0.970125i
$583$	37.7416	−	21.7901i	1.56310	−	0.902454i
$584$	−53.4916			−2.21350
$585$	3.44024	−	14.2771i	0.142237	−	0.590285i
$586$	16.1330			0.666446
$587$	−25.7902	+	14.8900i	−1.06448	+	0.614576i	−0.926667	−	0.375883i	$-0.877339\pi$
$587$	−25.7902	+	14.8900i	−1.06448	+	0.614576i	−0.137809	+	0.990459i	$0.544006\pi$
$588$	2.23152	+	3.86511i	0.0920264	+	0.159394i
$589$	5.83622	−	10.1086i	0.240477	−	0.416519i
$590$			86.9408i			3.57930i
$591$	−8.30642	−	4.79572i	−0.341681	−	0.197269i
$592$	13.6540	+	7.88315i	0.561176	+	0.323995i
$593$			23.7723i			0.976210i	0.872785	+	0.488105i	$0.162312\pi$
$593$			23.7723i			0.976210i	−0.872785	+	0.488105i	$0.837688\pi$
$594$	4.92960	−	8.53831i	0.202264	−	0.350331i
$595$	−5.03668	−	8.72378i	−0.206484	−	0.357640i
$596$	40.9961	−	23.6691i	1.67927	−	0.969524i
$597$	0.479039			0.0196058
$598$	−10.4126	+	43.2126i	−0.425803	+	1.76709i
$599$	37.6443			1.53810			0.769052	−	0.639186i	$-0.220729\pi$
$599$	37.6443			1.53810			0.769052	+	0.639186i	$0.220729\pi$
$600$	62.8502	−	36.2866i	2.56585	−	1.48139i
$601$	−4.62772	−	8.01544i	−0.188769	−	0.326957i	0.756071	−	0.654489i	$-0.227116\pi$
$601$	−4.62772	−	8.01544i	−0.188769	−	0.326957i	−0.944840	+	0.327532i	$0.893783\pi$
$602$	−4.69773	+	8.13670i	−0.191465	+	0.331627i
$603$			5.13790i			0.209231i
$604$	23.9415	+	13.8226i	0.974165	+	0.562435i
$605$	14.2504	+	8.22750i	0.579363	+	0.334495i
$606$		−	23.0391i		−	0.935898i
$607$	1.57081	−	2.72072i	0.0637572	−	0.110431i	−0.832385	−	0.554198i	$-0.813025\pi$
$607$	1.57081	−	2.72072i	0.0637572	−	0.110431i	0.896142	+	0.443767i	$0.146358\pi$
$608$	7.03823	+	12.1906i	0.285438	+	0.494393i
$609$	4.99174	−	2.88198i	0.202275	−	0.116784i
$610$	−72.7771			−2.94666
$611$	−34.8461	+	10.2902i	−1.40972	+	0.416298i
$612$	−11.0378			−0.446175
$613$	−11.5175	+	6.64963i	−0.465187	+	0.268576i	−0.714223	−	0.699918i	$-0.753220\pi$
$613$	−11.5175	+	6.64963i	−0.465187	+	0.268576i	0.249036	+	0.968494i	$0.419886\pi$
$614$	20.7492	+	35.9386i	0.837369	+	1.45037i
$615$	9.86182	−	17.0812i	0.397667	−	0.688779i
$616$			24.2836i			0.978415i
$617$	4.95426	+	2.86034i	0.199451	+	0.115153i	0.596399	−	0.802688i	$-0.296597\pi$
$617$	4.95426	+	2.86034i	0.199451	+	0.115153i	−0.396948	+	0.917841i	$0.629931\pi$
$618$	−29.2588	−	16.8926i	−1.17696	−	0.679519i
$619$			10.8582i			0.436426i	0.975901	+	0.218213i	$0.0700228\pi$
$619$			10.8582i			0.436426i	−0.975901	+	0.218213i	$0.929977\pi$
$620$	39.5972	−	68.5843i	1.59026	−	2.75441i
$621$	2.42463	+	4.19958i	0.0972971	+	0.168523i
$622$	−48.1535	+	27.8015i	−1.93078	+	1.11474i
$623$	18.2853			0.732587
$624$	24.5109	+	5.90620i	0.981220	+	0.236437i
$625$	51.3792			2.05517
$626$	38.3099	−	22.1182i	1.53117	−	0.884023i
$627$	5.19535	+	8.99862i	0.207482	+	0.359370i
$628$	−13.0496	+	22.6025i	−0.520735	+	0.901940i
$629$		−	5.57618i		−	0.222337i
$630$	8.96754	+	5.17741i	0.357275	+	0.206273i
$631$	18.5025	+	10.6824i	0.736575	+	0.425262i	0.820823	−	0.571183i	$-0.193515\pi$
$631$	18.5025	+	10.6824i	0.736575	+	0.425262i	−0.0842480	+	0.996445i	$0.526849\pi$
$632$			0.157257i			0.00625534i
$633$	5.01468	−	8.68568i	0.199316	−	0.345225i
$634$	−24.3832	−	42.2329i	−0.968381	−	1.67728i
$635$	−31.5956	+	18.2417i	−1.25383	+	0.723901i
$636$	50.1531			1.98870
$637$	−2.48408	+	2.61330i	−0.0984229	+	0.103543i
$638$	56.8280			2.24984
$639$	−8.49523	+	4.90473i	−0.336066	+	0.194028i
$640$	−24.6553	−	42.7042i	−0.974587	−	1.68803i
$641$	19.9055	−	34.4773i	0.786218	−	1.36177i	−0.142050	−	0.989859i	$-0.545369\pi$
$641$	19.9055	−	34.4773i	0.786218	−	1.36177i	0.928269	−	0.371911i	$-0.121297\pi$
$642$			7.29932i			0.288081i
$643$	−5.04309	−	2.91163i	−0.198880	−	0.114823i	0.397253	−	0.917709i	$-0.369964\pi$
$643$	−5.04309	−	2.91163i	−0.198880	−	0.114823i	−0.596133	+	0.802886i	$0.703297\pi$
$644$	−18.7429	−	10.8212i	−0.738575	−	0.426416i
$645$			15.0530i			0.592712i
$646$	8.42289	−	14.5889i	0.331394	−	0.573991i
$647$	−4.99313	−	8.64836i	−0.196300	−	0.340002i	0.751026	−	0.660273i	$-0.229559\pi$
$647$	−4.99313	−	8.64836i	−0.196300	−	0.340002i	−0.947326	+	0.320271i	$0.896226\pi$
$648$	5.42277	−	3.13084i	0.213027	−	0.122991i
$649$	−32.5615			−1.27815
$650$	77.0005	+	73.1931i	3.02021	+	2.87087i
$651$	4.35651			0.170745
$652$	50.2201	−	28.9946i	1.96677	−	1.13552i
$653$	−16.9124	−	29.2931i	−0.661834	−	1.14633i	−0.980133	−	0.198339i	$-0.936445\pi$
$653$	−16.9124	−	29.2931i	−0.661834	−	1.14633i	0.318300	−	0.947990i	$-0.396888\pi$
$654$	12.1383	−	21.0242i	0.474645	−	0.822109i
$655$		−	48.3689i		−	1.88993i
$656$	29.3249	+	16.9307i	1.14495	+	0.661034i
$657$	−7.39820	−	4.27135i	−0.288631	−	0.166641i
$658$		−	25.6187i		−	0.998720i
$659$	−24.9455	+	43.2068i	−0.971737	+	1.68310i	−0.281431	+	0.959581i	$0.590809\pi$
$659$	−24.9455	+	43.2068i	−0.971737	+	1.68310i	−0.690306	+	0.723517i	$0.742524\pi$
$660$	35.2491	+	61.0532i	1.37207	+	2.37649i
$661$	7.57715	−	4.37467i	0.294717	−	0.170155i	−0.345350	−	0.938474i	$-0.612240\pi$
$661$	7.57715	−	4.37467i	0.294717	−	0.170155i	0.640067	+	0.768319i	$0.278907\pi$
$662$	−50.7457			−1.97229
$663$	−2.52544	−	8.55197i	−0.0980799	−	0.332131i
$664$	1.26887			0.0492417
$665$	−9.45098	+	5.45653i	−0.366493	+	0.211595i
$666$	2.86599	+	4.96405i	0.111055	+	0.192353i
$667$	−13.9755	+	24.2063i	−0.541133	+	0.937270i
$668$		−	5.61199i		−	0.217135i
$669$	2.88727	+	1.66697i	0.111628	+	0.0644487i
$670$	−46.0743	−	26.6010i	−1.78001	−	1.02769i
$671$		−	27.2568i		−	1.05224i
$672$	−2.62688	+	4.54990i	−0.101334	+	0.175516i
$673$	12.5271	+	21.6975i	0.482883	+	0.836377i	0.999807	−	0.0196540i	$-0.00625647\pi$
$673$	12.5271	+	21.6975i	0.482883	+	0.836377i	−0.516924	+	0.856031i	$0.672923\pi$
$674$	24.1852	−	13.9633i	0.931579	−	0.537847i
$675$	11.5901			0.446102
$676$	2.93970	+	57.9450i	0.113066	+	2.22866i
$677$	−14.4632			−0.555866			−0.277933	−	0.960600i	$-0.589649\pi$
$677$	−14.4632			−0.555866			−0.277933	+	0.960600i	$0.589649\pi$
$678$	−39.9112	+	23.0427i	−1.53278	+	0.884951i
$679$	−5.31508	−	9.20599i	−0.203974	−	0.353293i
$680$	31.5380	−	54.6255i	1.20943	−	2.09479i
$681$			0.819107i			0.0313882i
$682$	37.1973	+	21.4759i	1.42436	+	0.822353i
$683$	−33.6296	−	19.4161i	−1.28680	−	0.742935i	−0.308719	−	0.951153i	$-0.599900\pi$
$683$	−33.6296	−	19.4161i	−1.28680	−	0.742935i	−0.978082	+	0.208218i	$0.933234\pi$
$684$			11.9579i			0.457220i
$685$	32.5856	−	56.4399i	1.24503	−	2.15646i
$686$	−1.27113	−	2.20165i	−0.0485318	−	0.0840596i
$687$	10.2922	−	5.94219i	0.392671	−	0.226709i
$688$	−25.8430			−0.985254
$689$	11.4750	+	38.8582i	0.437163	+	1.48038i
$690$	−50.2132			−1.91158
$691$	−15.6376	+	9.02838i	−0.594883	+	0.343456i	−0.767026	−	0.641616i	$-0.778264\pi$
$691$	−15.6376	+	9.02838i	−0.594883	+	0.343456i	0.172143	+	0.985072i	$0.444931\pi$
$692$	−31.8203	−	55.1143i	−1.20963	−	2.09513i
$693$	−1.93907	+	3.35856i	−0.0736591	+	0.127581i
$694$		−	34.8757i		−	1.32386i
$695$	−53.3959	−	30.8282i	−2.02542	−	1.16938i
$696$	31.2567	+	18.0460i	1.18478	+	0.684033i
$697$		−	11.9760i		−	0.453625i
$698$	−25.8013	+	44.6892i	−0.976595	+	1.69151i
$699$	1.40608	+	2.43540i	0.0531828	+	0.0921154i
$700$	−44.7968	+	25.8635i	−1.69316	+	0.977547i
$701$	31.9270			1.20587			0.602934	−	0.797791i	$-0.293998\pi$
$701$	31.9270			1.20587			0.602934	+	0.797791i	$0.293998\pi$
$702$	6.64367	+	6.31516i	0.250749	+	0.238350i
$703$	−6.04100			−0.227841
$704$	2.11230	−	1.21954i	0.0796105	−	0.0459631i
$705$	−20.5226	−	35.5462i	−0.772925	−	1.33875i
$706$	−1.48790	+	2.57711i	−0.0559977	+	0.0969908i
$707$			9.06247i			0.340829i
$708$	−32.4521	−	18.7362i	−1.21962	−	0.704151i
$709$	−1.07691	−	0.621752i	−0.0404441	−	0.0233504i	0.479642	−	0.877464i	$-0.340767\pi$
$709$	−1.07691	−	0.621752i	−0.0404441	−	0.0233504i	−0.520086	+	0.854114i	$0.674100\pi$
$710$		−	101.575i		−	3.81205i
$711$	−0.0125571	+	0.0217495i	−0.000470927	+	0.000815670i
$712$	57.2484	+	99.1572i	2.14548	+	3.71607i
$713$	−18.2955	+	10.5629i	−0.685173	+	0.395585i
$714$	6.28736			0.235299
$715$	−39.2385	+	41.2797i	−1.46744	+	1.54377i
$716$	−34.2759			−1.28095
$717$	−19.4822	+	11.2481i	−0.727576	+	0.420066i
$718$	25.6080	+	44.3543i	0.955681	+	1.65529i
$719$	−10.7219	+	18.5709i	−0.399861	+	0.692579i	−0.993708	−	0.111998i	$-0.964275\pi$
$719$	−10.7219	+	18.5709i	−0.399861	+	0.692579i	0.593848	+	0.804578i	$0.297608\pi$
$720$			28.4818i			1.06145i
$721$	11.5090	+	6.64473i	0.428618	+	0.247463i
$722$	26.0265	+	15.0264i	0.968605	+	0.559224i
$723$		−	25.5893i		−	0.951678i
$724$	11.3529	−	19.6639i	0.421929	−	0.730802i
$725$	33.4023	+	57.8546i	1.24053	+	2.14866i
$726$	−8.89453	+	5.13526i	−0.330107	+	0.190587i
$727$	−21.5002			−0.797397			−0.398699	−	0.917082i	$-0.630538\pi$
$727$	−21.5002			−0.797397			−0.398699	+	0.917082i	$0.630538\pi$
$728$	−21.9486	−	5.28878i	−0.813469	−	0.196015i
$729$	1.00000			0.0370370
$730$	76.6070	−	44.2291i	2.83535	−	1.63699i
$731$	4.57003	+	7.91553i	0.169029	+	0.292767i
$732$	15.6839	−	27.1653i	0.579693	−	1.00406i
$733$		−	23.4454i		−	0.865976i	−0.901400	−	0.432988i	$-0.857459\pi$
$733$		−	23.4454i		−	0.865976i	0.901400	−	0.432988i	$-0.142541\pi$
$734$	−13.9237	−	8.03887i	−0.513934	−	0.296720i
$735$	−3.52740	−	2.03654i	−0.130110	−	0.0751191i
$736$		−	25.4769i		−	0.939091i
$737$	9.96273	−	17.2560i	0.366982	−	0.635631i
$738$	6.15533	+	10.6614i	0.226581	+	0.392450i
$739$	42.9578	−	24.8017i	1.58023	−	0.912346i	0.585405	−	0.810741i	$-0.300935\pi$
$739$	42.9578	−	24.8017i	1.58023	−	0.912346i	0.994825	−	0.101605i	$-0.0323979\pi$
$740$	−40.9866			−1.50670
$741$	−9.26485	+	2.73596i	−0.340353	+	0.100508i
$742$	−28.5684			−1.04878
$743$	−18.8560	+	10.8865i	−0.691760	+	0.399388i	−0.804271	−	0.594263i	$-0.797444\pi$
$743$	−18.8560	+	10.8865i	−0.691760	+	0.399388i	0.112511	+	0.993650i	$0.464111\pi$
$744$	13.6395	+	23.6244i	0.500050	+	0.866111i
$745$	−21.6010	+	37.4141i	−0.791401	+	1.37075i
$746$			35.8090i			1.31106i
$747$	0.175492	+	0.101320i	0.00642091	+	0.00370711i
$748$	37.0710	+	21.4030i	1.35545	+	0.782570i
$749$		−	2.87120i		−	0.104912i
$750$	−34.1194	+	59.0966i	−1.24587	+	2.15790i
$751$	−7.62780	−	13.2117i	−0.278342	−	0.482103i	0.692631	−	0.721293i	$-0.256452\pi$
$751$	−7.62780	−	13.2117i	−0.278342	−	0.482103i	−0.970973	+	0.239189i	$0.923118\pi$
$752$	61.0256	−	35.2331i	2.22537	−	1.28482i
$753$	1.50839			0.0549689
$754$	−12.3767	+	51.3636i	−0.450733	+	1.87055i
$755$	−25.2298			−0.918206
$756$	−3.86511	+	2.23152i	−0.140573	+	0.0811597i
$757$	14.5344	+	25.1743i	0.528261	+	0.914974i	0.999457	+	0.0329461i	$0.0104890\pi$
$757$	14.5344	+	25.1743i	0.528261	+	0.914974i	−0.471196	+	0.882028i	$0.656178\pi$
$758$	−11.4993	+	19.9174i	−0.417673	+	0.723431i
$759$		−	18.8061i		−	0.682618i
$760$	−59.1790	−	34.1670i	−2.14665	−	1.23937i
$761$	−13.3261	−	7.69385i	−0.483072	−	0.278902i	0.238624	−	0.971112i	$-0.423304\pi$
$761$	−13.3261	−	7.69385i	−0.483072	−	0.278902i	−0.721696	+	0.692210i	$0.756637\pi$
$762$		−	22.7715i		−	0.824923i
$763$	−4.77463	+	8.26989i	−0.172853	+	0.299390i
$764$	−44.5819	−	77.2181i	−1.61292	−	2.79365i
$765$	8.72378	−	5.03668i	0.315409	−	0.182101i
$766$	24.3993			0.881583
$767$	7.09164	−	29.4305i	0.256064	−	1.06267i
$768$	29.5198			1.06520
$769$	29.4130	−	16.9816i	1.06066	−	0.612372i	0.135045	−	0.990839i	$-0.456882\pi$
$769$	29.4130	−	16.9816i	1.06066	−	0.612372i	0.925615	+	0.378467i	$0.123549\pi$
$770$	−20.0787	−	34.7773i	−0.723586	−	1.25329i
$771$	−6.54927	+	11.3437i	−0.235866	+	0.408532i
$772$		−	7.38922i		−	0.265944i
$773$	22.2354	+	12.8376i	0.799751	+	0.461737i	0.843384	−	0.537311i	$-0.180560\pi$
$773$	22.2354	+	12.8376i	0.799751	+	0.461737i	−0.0436330	+	0.999048i	$0.513893\pi$
$774$	−8.13670	−	4.69773i	−0.292468	−	0.168856i
$775$			50.4923i			1.81374i
$776$	33.2813	−	57.6449i	1.19473	−	2.06933i
$777$	−1.12734	−	1.95262i	−0.0404433	−	0.0700498i
$778$	44.2865	−	25.5688i	1.58775	−	0.916687i
$779$	−12.9743			−0.464854
$780$	−62.8595	+	18.5627i	−2.25073	+	0.664652i
$781$	38.0424			1.36126
$782$	−26.4043	+	15.2445i	−0.944216	+	0.545143i
$783$	2.88198	+	4.99174i	0.102994	+	0.178390i
$784$	3.49633	−	6.05583i	0.124869	−	0.216280i
$785$		−	23.8188i		−	0.850129i
$786$	26.1452	+	15.0949i	0.932568	+	0.538418i
$787$	−24.9179	−	14.3864i	−0.888228	−	0.512819i	−0.0148655	−	0.999890i	$-0.504732\pi$
$787$	−24.9179	−	14.3864i	−0.888228	−	0.512819i	−0.873362	+	0.487071i	$0.838065\pi$
$788$			42.8070i			1.52494i
$789$	−4.10869	+	7.11646i	−0.146273	+	0.253353i
$790$	−0.130026	−	0.225212i	−0.00462613	−	0.00801269i
$791$	15.6992	−	9.06391i	0.558198	−	0.322275i
$792$	−24.2836			−0.862881
$793$	24.6359	+	5.93633i	0.874846	+	0.210805i
$794$	14.5621			0.516788
$795$	−39.6389	+	22.8855i	−1.40585	+	0.811665i
$796$	−1.06899	−	1.85154i	−0.0378892	−	0.0656260i
$797$	−8.45922	+	14.6518i	−0.299641	+	0.518993i	−0.976054	−	0.217529i	$-0.930200\pi$
$797$	−8.45922	+	14.6518i	−0.299641	+	0.518993i	0.676413	+	0.736523i	$0.263534\pi$
$798$		−	6.81147i		−	0.241123i
$799$	−21.5834	−	12.4612i	−0.763564	−	0.440844i
$800$	−52.7336	−	30.4458i	−1.86441	−	1.07642i
$801$			18.2853i			0.646081i
$802$	−8.67676	+	15.0286i	−0.306387	+	0.530678i
$803$	16.5649	+	28.6912i	0.584562	+	1.01249i
$804$	19.8585	−	11.4653i	0.700357	−	0.404351i
$805$	19.7515			0.696148
$806$	−27.5121	+	28.9432i	−0.969072	+	1.01948i
$807$	17.8182			0.627230
$808$	−49.1437	+	28.3731i	−1.72887	+	0.998162i
$809$	−13.4005	−	23.2104i	−0.471137	−	0.816034i	0.528317	−	0.849047i	$-0.322823\pi$
$809$	−13.4005	−	23.2104i	−0.471137	−	0.816034i	−0.999455	+	0.0330129i	$0.989490\pi$
$810$	−5.17741	+	8.96754i	−0.181916	+	0.315087i
$811$			47.8109i			1.67887i	0.543461	+	0.839435i	$0.317114\pi$
$811$			47.8109i			1.67887i	−0.543461	+	0.839435i	$0.682886\pi$
$812$	−22.2783	−	12.8624i	−0.781817	−	0.451382i
$813$	7.09376	+	4.09559i	0.248789	+	0.143639i
$814$		−	22.2294i		−	0.779141i
$815$	−26.4612	+	45.8322i	−0.926896	+	1.60543i
$816$	8.64695	+	14.9770i	0.302704	+	0.524298i
$817$	8.57536	−	4.95099i	0.300014	−	0.173213i
$818$	56.3495			1.97021
$819$	−2.61330	−	2.48408i	−0.0913161	−	0.0868008i
$820$	−88.0275			−3.07405
$821$	−15.9102	+	9.18576i	−0.555270	+	0.320585i	−0.751245	−	0.660024i	$-0.770546\pi$
$821$	−15.9102	+	9.18576i	−0.555270	+	0.320585i	0.195975	+	0.980609i	$0.437213\pi$
$822$	20.3385	+	35.2274i	0.709388	+	1.22870i
$823$	−21.2087	+	36.7345i	−0.739288	+	1.28049i	0.213528	+	0.976937i	$0.431505\pi$
$823$	−21.2087	+	36.7345i	−0.739288	+	1.28049i	−0.952816	+	0.303548i	$0.901829\pi$
$824$			83.2143i			2.89891i
$825$	−38.9260	−	22.4739i	−1.35523	−	0.782441i
$826$	18.4855	+	10.6726i	0.643191	+	0.371347i
$827$		−	45.3875i		−	1.57828i	−0.614215	−	0.789139i	$-0.710527\pi$
$827$		−	45.3875i		−	1.57828i	0.614215	−	0.789139i	$-0.289473\pi$
$828$	10.8212	−	18.7429i	0.376064	−	0.651362i
$829$	−11.1162	−	19.2539i	−0.386082	−	0.668714i	0.605836	−	0.795589i	$-0.292839\pi$
$829$	−11.1162	−	19.2539i	−0.386082	−	0.668714i	−0.991919	+	0.126875i	$0.959505\pi$
$830$	−1.81719	+	1.04915i	−0.0630754	+	0.0364166i
$831$	3.98956			0.138396
$832$	0.642229	+	2.17480i	0.0222653	+	0.0753976i
$833$	−2.47315			−0.0856895
$834$	33.3275	−	19.2416i	1.15404	−	0.666284i
$835$	2.56083	+	4.43548i	0.0886210	+	0.153496i
$836$	23.1871	−	40.1612i	0.801942	−	1.38900i
$837$			4.35651i			0.150583i
$838$	−30.2059	−	17.4394i	−1.04344	−	0.602433i
$839$	−17.3241	−	10.0021i	−0.598095	−	0.345310i	0.170197	−	0.985410i	$-0.445560\pi$
$839$	−17.3241	−	10.0021i	−0.598095	−	0.345310i	−0.768292	+	0.640100i	$0.778893\pi$
$840$		−	25.5044i		−	0.879984i
$841$	−2.11164	+	3.65747i	−0.0728153	+	0.126120i
$842$	13.8679	+	24.0199i	0.477919	+	0.827781i
$843$	−15.7111	+	9.07081i	−0.541119	+	0.312415i
$844$	−44.7615			−1.54075
$845$	−28.7645	−	44.4559i	−0.989529	−	1.52933i
$846$	25.6187			0.880788
$847$	3.49868	−	2.01996i	0.120216	−	0.0694068i
$848$	−39.2898	−	68.0519i	−1.34922	−	2.33691i
$849$	0.561670	−	0.972840i	0.0192764	−	0.0333878i
$850$			72.8709i			2.49945i
$851$	9.46876	+	5.46679i	0.324585	+	0.187399i
$852$	37.9146	+	21.8900i	1.29893	+	0.749939i
$853$		−	5.25317i		−	0.179865i	−0.995948	−	0.0899326i	$-0.971335\pi$
$853$		−	5.25317i		−	0.179865i	0.995948	−	0.0899326i	$-0.0286652\pi$
$854$	−8.93390	+	15.4740i	−0.305712	+	0.529508i
$855$	−5.45653	−	9.45098i	−0.186609	−	0.323217i
$856$	15.5699	−	8.98927i	0.532167	−	0.307247i
$857$	48.2428			1.64794			0.823971	−	0.566632i	$-0.191754\pi$
$857$	48.2428			1.64794			0.823971	+	0.566632i	$0.191754\pi$
$858$	−10.0677	−	34.0924i	−0.343704	−	1.16389i
$859$	7.55274			0.257696			0.128848	−	0.991664i	$-0.458872\pi$
$859$	7.55274			0.257696			0.128848	+	0.991664i	$0.458872\pi$
$860$	58.1815	−	33.5911i	1.98397	−	1.14545i
$861$	−2.42121	−	4.19367i	−0.0825147	−	0.142920i
$862$	−10.4814	+	18.1543i	−0.356998	+	0.618339i
$863$		−	27.8902i		−	0.949394i	−0.880149	−	0.474697i	$-0.842558\pi$
$863$		−	27.8902i		−	0.949394i	0.880149	−	0.474697i	$-0.157442\pi$
$864$	−4.54990	−	2.62688i	−0.154791	−	0.0893684i
$865$	50.2988	+	29.0400i	1.71021	+	0.987390i
$866$		−	55.0288i		−	1.86995i
$867$	−5.44177	+	9.42542i	−0.184812	+	0.320104i
$868$	−9.72165	−	16.8384i	−0.329974	−	0.571533i
$869$	0.0843475	−	0.0486980i	0.00286129	−	0.00165197i
$870$	−59.6848			−2.02350
$871$	13.4269	+	12.7630i	0.454952	+	0.432456i
$872$	−59.7943			−2.02489
$873$	9.20599	−	5.31508i	0.311576	−	0.179888i
$874$	16.5153	+	28.6053i	0.558638	+	0.967590i
$875$	13.4210	−	23.2458i	0.453711	−	0.785851i
$876$			38.1264i			1.28817i
$877$	−36.1171	−	20.8522i	−1.21959	−	0.704129i	−0.254757	−	0.967005i	$-0.581996\pi$
$877$	−36.1171	−	20.8522i	−1.21959	−	0.704129i	−0.964830	+	0.262876i	$0.915329\pi$
$878$	−35.6769	−	20.5981i	−1.20404	−	0.695151i
$879$		−	6.34593i		−	0.214043i
$880$	55.2281	−	95.6578i	1.86174	−	3.22462i
$881$	2.24306	+	3.88509i	0.0755705	+	0.130892i	0.901334	−	0.433124i	$-0.142589\pi$
$881$	2.24306	+	3.88509i	0.0755705	+	0.130892i	−0.825764	+	0.564016i	$0.809256\pi$
$882$	2.20165	−	1.27113i	0.0741336	−	0.0428010i
$883$	−42.6098			−1.43394			−0.716968	−	0.697107i	$-0.754470\pi$
$883$	−42.6098			−1.43394			−0.716968	+	0.697107i	$0.754470\pi$
$884$	−27.4187	+	28.8450i	−0.922191	+	0.970162i
$885$	34.1983			1.14956
$886$	−18.0381	+	10.4143i	−0.606000	+	0.349874i
$887$	−3.33962	−	5.78438i	−0.112133	−	0.194221i	0.804497	−	0.593957i	$-0.202435\pi$
$887$	−3.33962	−	5.78438i	−0.112133	−	0.194221i	−0.916630	+	0.399736i	$0.869102\pi$
$888$	7.05907	−	12.2267i	0.236887	−	0.410300i
$889$			8.95720i			0.300415i
$890$	−163.975	−	94.6707i	−5.49644	−	3.17337i
$891$	−3.35856	−	1.93907i	−0.112516	−	0.0649612i
$892$		−	14.8795i		−	0.498202i
$893$	−13.4999	+	23.3825i	−0.451757	+	0.782466i
$894$	−13.4825	−	23.3523i	−0.450921	−	0.781018i
$895$	27.0902	−	15.6405i	0.905525	−	0.522805i
$896$	−12.1064			−0.404448
$897$	16.9978	+	4.09582i	0.567538	+	0.136755i
$898$	−20.8608			−0.696135
$899$	−21.7466	+	12.5554i	−0.725289	+	0.418746i
$900$	−25.8635	−	44.7968i	−0.862116	−	1.49323i
$901$	−13.8959	+	24.0684i	−0.462940	+	0.801835i
$902$		−	47.7424i		−	1.58965i
$903$	3.20059	+	1.84786i	0.106509	+	0.0614930i
$904$	98.3030	+	56.7553i	3.26951	+	1.88765i
$905$			20.7220i			0.688822i
$906$	7.87368	−	13.6376i	0.261586	−	0.453080i
$907$	−20.1234	−	34.8547i	−0.668185	−	1.15733i	−0.978411	−	0.206668i	$-0.933738\pi$
$907$	−20.1234	−	34.8547i	−0.668185	−	1.15733i	0.310226	−	0.950663i	$-0.399595\pi$
$908$	3.16594	−	1.82785i	0.105065	−	0.0606595i
$909$	−9.06247			−0.300583
$910$	35.8062	−	10.5738i	1.18696	−	0.350517i
$911$	−45.1672			−1.49646			−0.748228	−	0.663441i	$-0.769095\pi$
$911$	−45.1672			−1.49646			−0.748228	+	0.663441i	$0.769095\pi$
$912$	16.2254	−	9.36775i	0.537277	−	0.310197i
$913$	−0.392934	−	0.680581i	−0.0130042	−	0.0225239i
$914$	19.4836	−	33.7466i	0.644461	−	1.11624i
$915$			28.6270i			0.946381i
$916$	−45.9344	−	26.5202i	−1.51772	−	0.876253i
$917$	−10.2843	−	5.93762i	−0.339616	−	0.196078i
$918$			6.28736i			0.207514i
$919$	11.5241	−	19.9603i	0.380145	−	0.658430i	−0.610938	−	0.791679i	$-0.709207\pi$
$919$	11.5241	−	19.9603i	0.380145	−	0.658430i	0.991083	+	0.133248i	$0.0425408\pi$
$920$	61.8387	+	107.108i	2.03876	+	3.53124i
$921$	14.1365	−	8.16174i	0.465815	−	0.268938i
$922$	92.6699			3.05192
$923$	−8.28533	+	34.3843i	−0.272715	+	1.13177i
$924$	17.3083			0.569401
$925$	22.6310	−	13.0660i	0.744102	−	0.429607i
$926$	45.4191	+	78.6681i	1.49256	+	2.58520i
$927$	−6.64473	+	11.5090i	−0.218242	+	0.378006i
$928$		−	30.2825i		−	0.994073i
$929$	−27.6115	−	15.9415i	−0.905905	−	0.523024i	−0.0267935	−	0.999641i	$-0.508530\pi$
$929$	−27.6115	−	15.9415i	−0.905905	−	0.523024i	−0.879111	+	0.476617i	$0.841863\pi$
$930$	−39.0672	−	22.5555i	−1.28106	−	0.739623i
$931$			2.67931i			0.0878107i
$932$	6.27540	−	10.8693i	0.205557	−	0.356036i
$933$	10.9358	+	18.9413i	0.358021	+	0.620110i
$934$	−30.7371	+	17.7461i	−1.00575	+	0.580669i
$935$	−39.0658			−1.27759
$936$	5.28878	−	21.9486i	0.172869	−	0.717412i
$937$	−47.3929			−1.54826			−0.774129	−	0.633028i	$-0.781812\pi$
$937$	−47.3929			−1.54826			−0.774129	+	0.633028i	$0.781812\pi$
$938$	−11.3119	+	6.53092i	−0.369346	+	0.213242i
$939$	−8.70026	−	15.0693i	−0.283922	−	0.491768i
$940$	−91.5932	+	158.644i	−2.98744	+	5.17440i
$941$		−	16.1481i		−	0.526414i	−0.964739	−	0.263207i	$-0.915220\pi$
$941$		−	16.1481i		−	0.526414i	0.964739	−	0.263207i	$-0.0847803\pi$
$942$	12.8749	+	7.43334i	0.419488	+	0.242191i
$943$	20.3362	+	11.7411i	0.662237	+	0.382343i
$944$			58.7116i			1.91090i
$945$	2.03654	−	3.52740i	0.0662488	−	0.114746i
$946$	18.2184	+	31.5552i	0.592332	+	1.02595i
$947$	−5.50997	+	3.18118i	−0.179050	+	0.103374i	−0.586846	−	0.809698i	$-0.699631\pi$
$947$	−5.50997	+	3.18118i	−0.179050	+	0.103374i	0.407796	+	0.913073i	$0.366297\pi$
$948$	0.112086			0.00364037
$949$	−29.5400	+	8.72332i	−0.958910	+	0.283171i
$950$	78.9453			2.56133
$951$	−16.6124	+	9.59118i	−0.538695	+	0.311015i
$952$	−7.74302	−	13.4113i	−0.250953	−	0.434663i
$953$	20.8904	−	36.1833i	0.676708	−	1.17209i	−0.299259	−	0.954172i	$-0.596739\pi$
$953$	20.8904	−	36.1833i	0.676708	−	1.17209i	0.975967	−	0.217921i	$-0.0699274\pi$
$954$		−	28.5684i		−	0.924934i
$955$	70.4713	+	40.6866i	2.28040	+	1.31659i
$956$	86.9499	+	50.2006i	2.81216	+	1.62360i
$957$		−	22.3534i		−	0.722584i
$958$	−39.9730	+	69.2353i	−1.29147	+	2.23689i
$959$	−8.00021	−	13.8568i	−0.258340	−	0.447458i
$960$	−2.21849	+	1.28085i	−0.0716015	+	0.0413391i
$961$	12.0208			0.387767
$962$	20.0919	+	4.84139i	0.647789	+	0.156093i
$963$	2.87120			0.0925232
$964$	−98.9056	+	57.1032i	−3.18553	+	1.83917i
$965$	3.37180	+	5.84012i	0.108542	+	0.188000i
$966$	−6.16402	+	10.6764i	−0.198324	+	0.343507i
$967$		−	14.7446i		−	0.474156i	−0.971491	−	0.237078i	$-0.923810\pi$
$967$		−	14.7446i		−	0.474156i	0.971491	−	0.237078i	$-0.0761897\pi$
$968$	21.9076	+	12.6484i	0.704137	+	0.406534i
$969$	−5.73856	−	3.31316i	−0.184349	−	0.106434i
$970$			110.073i			3.53424i
$971$	−12.1016	+	20.9605i	−0.388357	+	0.672654i	−0.992229	−	0.124427i	$-0.960291\pi$
$971$	−12.1016	+	20.9605i	−0.388357	+	0.672654i	0.603872	+	0.797082i	$0.293624\pi$
$972$	−2.23152	−	3.86511i	−0.0715761	−	0.123973i
$973$	−13.1094	+	7.56874i	−0.420269	+	0.242643i
$974$	85.6448			2.74424
$975$	28.7907	−	30.2883i	0.922039	−	0.970002i
$976$	−49.1468			−1.57315
$977$	48.3549	−	27.9177i	1.54701	−	0.893167i	0.548643	−	0.836057i	$-0.315145\pi$
$977$	48.3549	−	27.9177i	1.54701	−	0.893167i	0.998368	−	0.0571101i	$-0.0181886\pi$
$978$	−16.5160	−	28.6065i	−0.528123	−	0.914735i
$979$	35.4565	−	61.4125i	1.13320	−	1.96275i
$980$			18.1784i			0.580687i
$981$	−8.26989	−	4.77463i	−0.264037	−	0.152442i
$982$	26.8800	+	15.5192i	0.857776	+	0.495237i
$983$		−	18.5213i		−	0.590736i	−0.955383	−	0.295368i	$-0.904558\pi$
$983$		−	18.5213i		−	0.590736i	0.955383	−	0.295368i	$-0.0954423\pi$
$984$	15.1609	−	26.2594i	0.483310	−	0.837118i
$985$	−19.5334	−	33.8328i	−0.622385	−	1.07800i
$986$	−31.3849	+	18.1201i	−0.999498	+	0.577061i
$987$	−10.0772			−0.320760
$988$	31.2495	+	29.7043i	0.994178	+	0.945019i
$989$	−17.9215			−0.569871
$990$	34.7773	−	20.0787i	1.10530	−	0.638143i
$991$	−31.0501	−	53.7804i	−0.986339	−	1.70839i	−0.635828	−	0.771831i	$-0.719341\pi$
$991$	−31.0501	−	53.7804i	−0.986339	−	1.70839i	−0.350511	−	0.936559i	$-0.613992\pi$
$992$	11.4441	−	19.8217i	0.363349	−	0.629339i
$993$			19.9609i			0.633441i
$994$	−21.5970	−	12.4690i	−0.685016	−	0.395494i
$995$	1.68976	+	0.975585i	0.0535691	+	0.0309281i
$996$		−	0.904393i		−	0.0286568i
$997$	22.8533	−	39.5831i	0.723773	−	1.25361i	−0.235705	−	0.971825i	$-0.575740\pi$
$997$	22.8533	−	39.5831i	0.723773	−	1.25361i	0.959477	−	0.281786i	$-0.0909269\pi$
$998$	42.1536	+	73.0121i	1.33435	+	2.31116i
$999$	1.95262	−	1.12734i	0.0617781	−	0.0356676i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	273.2.bd.b.127.1	yes	16
3.2	odd	2		819.2.ct.c.127.8		16
13.2	odd	12		3549.2.a.ba.1.2		8
13.4	even	6	inner	273.2.bd.b.43.1	✓	16
13.11	odd	12		3549.2.a.bc.1.7		8
39.17	odd	6		819.2.ct.c.316.8		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
273.2.bd.b.43.1	✓	16	13.4	even	6	inner
273.2.bd.b.127.1	yes	16	1.1	even	1	trivial
819.2.ct.c.127.8		16	3.2	odd	2
819.2.ct.c.316.8		16	39.17	odd	6
3549.2.a.ba.1.2		8	13.2	odd	12
3549.2.a.bc.1.7		8	13.11	odd	12

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(-2.20165 + 1.27113i) q^{2} +(0.500000 + 0.866025i) q^{3} +(2.23152 - 3.86511i) q^{4} +4.07309i q^{5} +(-2.20165 - 1.27113i) q^{6} +(0.866025 + 0.500000i) q^{7} +6.26168i q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})\)	\(q+(-2.20165 + 1.27113i) q^{2} +(0.500000 + 0.866025i) q^{3} +(2.23152 - 3.86511i) q^{4} +4.07309i q^{5} +(-2.20165 - 1.27113i) q^{6} +(0.866025 + 0.500000i) q^{7} +6.26168i q^{8} +(-0.500000 + 0.866025i) q^{9} +(-5.17741 - 8.96754i) q^{10} +(3.35856 - 1.93907i) q^{11} +4.46304 q^{12} +(1.02114 + 3.45793i) q^{13} -2.54225 q^{14} +(-3.52740 + 2.03654i) q^{15} +(-3.49633 - 6.05583i) q^{16} +(-1.23657 + 2.14181i) q^{17} -2.54225i q^{18} +(2.32035 + 1.33965i) q^{19} +(15.7429 + 9.08919i) q^{20} +1.00000i q^{21} +(-4.92960 + 8.53831i) q^{22} +(-2.42463 - 4.19958i) q^{23} +(-5.42277 + 3.13084i) q^{24} -11.5901 q^{25} +(-6.64367 - 6.31516i) q^{26} -1.00000 q^{27} +(3.86511 - 2.23152i) q^{28} +(-2.88198 - 4.99174i) q^{29} +(5.17741 - 8.96754i) q^{30} -4.35651i q^{31} +(4.54990 + 2.62688i) q^{32} +(3.35856 + 1.93907i) q^{33} -6.28736i q^{34} +(-2.03654 + 3.52740i) q^{35} +(2.23152 + 3.86511i) q^{36} +(-1.95262 + 1.12734i) q^{37} -6.81147 q^{38} +(-2.48408 + 2.61330i) q^{39} -25.5044 q^{40} +(-4.19367 + 2.42121i) q^{41} +(-1.27113 - 2.20165i) q^{42} +(1.84786 - 3.20059i) q^{43} -17.3083i q^{44} +(-3.52740 - 2.03654i) q^{45} +(10.6764 + 6.16402i) q^{46} +10.0772i q^{47} +(3.49633 - 6.05583i) q^{48} +(0.500000 + 0.866025i) q^{49} +(25.5173 - 14.7324i) q^{50} -2.47315 q^{51} +(15.6440 + 3.76961i) q^{52} +11.2374 q^{53} +(2.20165 - 1.27113i) q^{54} +(7.89800 + 13.6797i) q^{55} +(-3.13084 + 5.42277i) q^{56} +2.67931i q^{57} +(12.6903 + 7.32672i) q^{58} +(-7.27129 - 4.19808i) q^{59} +18.1784i q^{60} +(3.51417 - 6.08672i) q^{61} +(5.53768 + 9.59154i) q^{62} +(-0.866025 + 0.500000i) q^{63} +0.628931 q^{64} +(-14.0845 + 4.15921i) q^{65} -9.85919 q^{66} +(4.44955 - 2.56895i) q^{67} +(5.51888 + 9.55899i) q^{68} +(2.42463 - 4.19958i) q^{69} -10.3548i q^{70} +(8.49523 + 4.90473i) q^{71} +(-5.42277 - 3.13084i) q^{72} +8.54270i q^{73} +(2.86599 - 4.96405i) q^{74} +(-5.79503 - 10.0373i) q^{75} +(10.3558 - 5.97893i) q^{76} +3.87813 q^{77} +(2.14726 - 8.91116i) q^{78} +0.0251142 q^{79} +(24.6659 - 14.2409i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(6.15533 - 10.6614i) q^{82} -0.202640i q^{83} +(3.86511 + 2.23152i) q^{84} +(-8.72378 - 5.03668i) q^{85} +9.39546i q^{86} +(2.88198 - 4.99174i) q^{87} +(12.1418 + 21.0302i) q^{88} +(15.8356 - 9.14267i) q^{89} +10.3548 q^{90} +(-0.844628 + 3.50523i) q^{91} -21.6425 q^{92} +(3.77285 - 2.17826i) q^{93} +(-12.8093 - 22.1864i) q^{94} +(-5.45653 + 9.45098i) q^{95} +5.25377i q^{96} +(-9.20599 - 5.31508i) q^{97} +(-2.20165 - 1.27113i) q^{98} +3.87813i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 8 q^{3} + 14 q^{4} - 8 q^{9}+O(q^{10}) \) 16 * q + 8 * q^3 + 14 * q^4 - 8 * q^9	\( 16 q + 8 q^{3} + 14 q^{4} - 8 q^{9} - 4 q^{10} + 28 q^{12} - 12 q^{13} - 4 q^{14} - 12 q^{15} - 10 q^{16} - 2 q^{17} + 18 q^{20} - 18 q^{22} - 6 q^{23} - 20 q^{25} + 20 q^{26} - 16 q^{27} - 12 q^{29} + 4 q^{30} - 30 q^{32} + 6 q^{35} + 14 q^{36} - 6 q^{37} - 24 q^{38} - 28 q^{40} - 30 q^{41} - 2 q^{42} + 14 q^{43} - 12 q^{45} - 42 q^{46} + 10 q^{48} + 8 q^{49} + 84 q^{50} - 4 q^{51} + 30 q^{52} + 28 q^{53} + 2 q^{55} - 12 q^{56} + 66 q^{58} - 24 q^{59} + 2 q^{61} - 20 q^{62} - 48 q^{64} - 44 q^{65} - 36 q^{66} + 30 q^{67} + 36 q^{68} + 6 q^{69} - 6 q^{71} + 6 q^{74} - 10 q^{75} - 24 q^{76} + 32 q^{77} + 10 q^{78} + 92 q^{79} + 114 q^{80} - 8 q^{81} - 42 q^{82} + 48 q^{85} + 12 q^{87} + 62 q^{88} + 18 q^{89} + 8 q^{90} - 116 q^{92} - 6 q^{93} - 24 q^{94} - 24 q^{95} - 6 q^{97}+O(q^{100}) \) 16 * q + 8 * q^3 + 14 * q^4 - 8 * q^9 - 4 * q^10 + 28 * q^12 - 12 * q^13 - 4 * q^14 - 12 * q^15 - 10 * q^16 - 2 * q^17 + 18 * q^20 - 18 * q^22 - 6 * q^23 - 20 * q^25 + 20 * q^26 - 16 * q^27 - 12 * q^29 + 4 * q^30 - 30 * q^32 + 6 * q^35 + 14 * q^36 - 6 * q^37 - 24 * q^38 - 28 * q^40 - 30 * q^41 - 2 * q^42 + 14 * q^43 - 12 * q^45 - 42 * q^46 + 10 * q^48 + 8 * q^49 + 84 * q^50 - 4 * q^51 + 30 * q^52 + 28 * q^53 + 2 * q^55 - 12 * q^56 + 66 * q^58 - 24 * q^59 + 2 * q^61 - 20 * q^62 - 48 * q^64 - 44 * q^65 - 36 * q^66 + 30 * q^67 + 36 * q^68 + 6 * q^69 - 6 * q^71 + 6 * q^74 - 10 * q^75 - 24 * q^76 + 32 * q^77 + 10 * q^78 + 92 * q^79 + 114 * q^80 - 8 * q^81 - 42 * q^82 + 48 * q^85 + 12 * q^87 + 62 * q^88 + 18 * q^89 + 8 * q^90 - 116 * q^92 - 6 * q^93 - 24 * q^94 - 24 * q^95 - 6 * q^97

Introduction

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