LMFDB - Embedded newform 273.2.bd.a.127.4

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} + 22x^{14} + 187x^{12} + 774x^{10} + 1619x^{8} + 1618x^{6} + 690x^{4} + 96x^{2} + 1 $ x^16 + 22x^14 + 187x^12 + 774x^10 + 1619x^8 + 1618x^6 + 690x^4 + 96*x^2 + 1
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			127.4
Root			$0.485989i$ of defining polynomial
Character	$\chi$	$=$	273.127
Dual form			273.2.bd.a.43.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.420879 + 0.242995i) q^{2} +(-0.500000 - 0.866025i) q^{3} +(-0.881907 + 1.52751i) q^{4} -1.06536i q^{5} +(0.420879 + 0.242995i) q^{6} +(-0.866025 - 0.500000i) q^{7} -1.82917i q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})$	\(q+(-0.420879 + 0.242995i) q^{2} +(-0.500000 - 0.866025i) q^{3} +(-0.881907 + 1.52751i) q^{4} -1.06536i q^{5} +(0.420879 + 0.242995i) q^{6} +(-0.866025 - 0.500000i) q^{7} -1.82917i q^{8} +(-0.500000 + 0.866025i) q^{9} +(0.258876 + 0.448387i) q^{10} +(4.98494 - 2.87806i) q^{11} +1.76381 q^{12} +(1.77592 - 3.13785i) q^{13} +0.485989 q^{14} +(-0.922628 + 0.532679i) q^{15} +(-1.31934 - 2.28516i) q^{16} +(1.17266 - 2.03111i) q^{17} -0.485989i q^{18} +(-5.36979 - 3.10025i) q^{19} +(1.62734 + 0.939548i) q^{20} +1.00000i q^{21} +(-1.39870 + 2.42263i) q^{22} +(2.75674 + 4.77481i) q^{23} +(-1.58411 + 0.914587i) q^{24} +3.86501 q^{25} +(0.0150320 + 1.75219i) q^{26} +1.00000 q^{27} +(1.52751 - 0.881907i) q^{28} +(-2.80215 - 4.85347i) q^{29} +(0.258876 - 0.448387i) q^{30} -5.46420i q^{31} +(4.27878 + 2.47036i) q^{32} +(-4.98494 - 2.87806i) q^{33} +1.13980i q^{34} +(-0.532679 + 0.922628i) q^{35} +(-0.881907 - 1.52751i) q^{36} +(-4.08375 + 2.35775i) q^{37} +3.01337 q^{38} +(-3.60542 + 0.0309306i) q^{39} -1.94873 q^{40} +(7.69141 - 4.44064i) q^{41} +(-0.242995 - 0.420879i) q^{42} +(-4.77851 + 8.27662i) q^{43} +10.1527i q^{44} +(0.922628 + 0.532679i) q^{45} +(-2.32051 - 1.33975i) q^{46} +5.21864i q^{47} +(-1.31934 + 2.28516i) q^{48} +(0.500000 + 0.866025i) q^{49} +(-1.62670 + 0.939177i) q^{50} -2.34533 q^{51} +(3.22689 + 5.48003i) q^{52} +1.52870 q^{53} +(-0.420879 + 0.242995i) q^{54} +(-3.06616 - 5.31075i) q^{55} +(-0.914587 + 1.58411i) q^{56} +6.20049i q^{57} +(2.35873 + 1.36181i) q^{58} +(-9.06406 - 5.23314i) q^{59} -1.87910i q^{60} +(-3.82305 + 6.62171i) q^{61} +(1.32777 + 2.29977i) q^{62} +(0.866025 - 0.500000i) q^{63} +2.87621 q^{64} +(-3.34294 - 1.89199i) q^{65} +2.79741 q^{66} +(2.83779 - 1.63840i) q^{67} +(2.06836 + 3.58251i) q^{68} +(2.75674 - 4.77481i) q^{69} -0.517753i q^{70} +(7.50761 + 4.33452i) q^{71} +(1.58411 + 0.914587i) q^{72} +7.63941i q^{73} +(1.14584 - 1.98466i) q^{74} +(-1.93251 - 3.34720i) q^{75} +(9.47131 - 5.46826i) q^{76} -5.75611 q^{77} +(1.50993 - 0.889115i) q^{78} -15.6147 q^{79} +(-2.43451 + 1.40557i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(-2.15810 + 3.73794i) q^{82} +2.63313i q^{83} +(-1.52751 - 0.881907i) q^{84} +(-2.16387 - 1.24931i) q^{85} -4.64461i q^{86} +(-2.80215 + 4.85347i) q^{87} +(-5.26447 - 9.11832i) q^{88} +(10.4502 - 6.03343i) q^{89} -0.517753 q^{90} +(-3.10692 + 1.82950i) q^{91} -9.72476 q^{92} +(-4.73214 + 2.73210i) q^{93} +(-1.26810 - 2.19642i) q^{94} +(-3.30288 + 5.72075i) q^{95} -4.94071i q^{96} +(14.5156 + 8.38057i) q^{97} +(-0.420879 - 0.242995i) q^{98} +5.75611i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 8 q^{3} + 6 q^{4} - 8 q^{9}+O(q^{10}) $ 16 * q - 8 * q^3 + 6 * q^4 - 8 * q^9	$ 16 q - 8 q^{3} + 6 q^{4} - 8 q^{9} - 4 q^{10} - 12 q^{11} - 12 q^{12} + 4 q^{13} + 4 q^{14} - 10 q^{16} + 10 q^{17} + 6 q^{20} - 2 q^{22} - 2 q^{23} + 12 q^{25} + 20 q^{26} + 16 q^{27} + 12 q^{29} - 4 q^{30} + 30 q^{32} + 12 q^{33} - 2 q^{35} + 6 q^{36} + 18 q^{37} - 32 q^{38} - 8 q^{39} - 60 q^{40} + 18 q^{41} - 2 q^{42} - 10 q^{43} + 30 q^{46} - 10 q^{48} + 8 q^{49} - 24 q^{50} - 20 q^{51} - 26 q^{52} + 12 q^{53} + 10 q^{55} + 12 q^{56} - 54 q^{58} - 60 q^{59} - 6 q^{61} + 16 q^{62} + 16 q^{64} - 20 q^{65} + 4 q^{66} - 18 q^{67} - 20 q^{68} - 2 q^{69} + 6 q^{71} + 18 q^{74} - 6 q^{75} + 72 q^{76} - 16 q^{77} + 14 q^{78} - 4 q^{79} + 30 q^{80} - 8 q^{81} - 18 q^{82} - 24 q^{85} + 12 q^{87} - 2 q^{88} + 78 q^{89} + 8 q^{90} - 8 q^{91} - 20 q^{92} + 6 q^{93} + 16 q^{94} - 4 q^{95} - 54 q^{97}+O(q^{100}) $ 16 * q - 8 * q^3 + 6 * q^4 - 8 * q^9 - 4 * q^10 - 12 * q^11 - 12 * q^12 + 4 * q^13 + 4 * q^14 - 10 * q^16 + 10 * q^17 + 6 * q^20 - 2 * q^22 - 2 * q^23 + 12 * q^25 + 20 * q^26 + 16 * q^27 + 12 * q^29 - 4 * q^30 + 30 * q^32 + 12 * q^33 - 2 * q^35 + 6 * q^36 + 18 * q^37 - 32 * q^38 - 8 * q^39 - 60 * q^40 + 18 * q^41 - 2 * q^42 - 10 * q^43 + 30 * q^46 - 10 * q^48 + 8 * q^49 - 24 * q^50 - 20 * q^51 - 26 * q^52 + 12 * q^53 + 10 * q^55 + 12 * q^56 - 54 * q^58 - 60 * q^59 - 6 * q^61 + 16 * q^62 + 16 * q^64 - 20 * q^65 + 4 * q^66 - 18 * q^67 - 20 * q^68 - 2 * q^69 + 6 * q^71 + 18 * q^74 - 6 * q^75 + 72 * q^76 - 16 * q^77 + 14 * q^78 - 4 * q^79 + 30 * q^80 - 8 * q^81 - 18 * q^82 - 24 * q^85 + 12 * q^87 - 2 * q^88 + 78 * q^89 + 8 * q^90 - 8 * q^91 - 20 * q^92 + 6 * q^93 + 16 * q^94 - 4 * q^95 - 54 * 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 $

$2$	−0.420879	+	0.242995i	−0.297606	+	0.171823i	−0.641367	−	0.767234i	$-0.721632\pi$
$2$	−0.420879	+	0.242995i	−0.297606	+	0.171823i	0.343761	+	0.939057i	$0.388299\pi$
$3$	−0.500000	−	0.866025i	−0.288675	−	0.500000i
$3$	−0.500000	−	0.866025i	−0.288675	−	0.500000i
$4$	−0.881907	+	1.52751i	−0.440954	+	0.763754i
$5$		−	1.06536i		−	0.476443i	−0.971211	−	0.238221i	$-0.923436\pi$
$5$		−	1.06536i		−	0.476443i	0.971211	−	0.238221i	$-0.0765644\pi$
$6$	0.420879	+	0.242995i	0.171823	+	0.0992021i
$7$	−0.866025	−	0.500000i	−0.327327	−	0.188982i
$7$	−0.866025	−	0.500000i	−0.327327	−	0.188982i
$8$		−	1.82917i		−	0.646710i
$9$	−0.500000	+	0.866025i	−0.166667	+	0.288675i
$10$	0.258876	+	0.448387i	0.0818639	+	0.141792i
$11$	4.98494	−	2.87806i	1.50302	−	0.867767i	0.503022	−	0.864273i	$-0.332221\pi$
$11$	4.98494	−	2.87806i	1.50302	−	0.867767i	0.999994	−	0.00349358i	$-0.00111204\pi$
$12$	1.76381			0.509169
$13$	1.77592	−	3.13785i	0.492552	−	0.870283i
$13$	1.77592	−	3.13785i	0.492552	−	0.870283i
$14$	0.485989			0.129886
$15$	−0.922628	+	0.532679i	−0.238221	+	0.137537i
$16$	−1.31934	−	2.28516i	−0.329834	−	0.571289i
$17$	1.17266	−	2.03111i	0.284413	−	0.492618i	−0.688054	−	0.725660i	$-0.741535\pi$
$17$	1.17266	−	2.03111i	0.284413	−	0.492618i	0.972467	+	0.233042i	$0.0748680\pi$
$18$		−	0.485989i		−	0.114549i
$19$	−5.36979	−	3.10025i	−1.23191	−	0.711246i	−0.264485	−	0.964390i	$-0.585202\pi$
$19$	−5.36979	−	3.10025i	−1.23191	−	0.711246i	−0.967429	+	0.253144i	$0.918535\pi$
$20$	1.62734	+	0.939548i	0.363885	+	0.210089i
$21$			1.00000i			0.218218i
$22$	−1.39870	+	2.42263i	−0.298205	+	0.516506i
$23$	2.75674	+	4.77481i	0.574820	+	0.995618i	0.996061	+	0.0886690i	$0.0282613\pi$
$23$	2.75674	+	4.77481i	0.574820	+	0.995618i	−0.421241	+	0.906949i	$0.638405\pi$
$24$	−1.58411	+	0.914587i	−0.323355	+	0.186689i
$25$	3.86501			0.773002
$26$	0.0150320	+	1.75219i	0.00294801	+	0.343634i
$27$	1.00000			0.192450
$28$	1.52751	−	0.881907i	0.288672	−	0.166665i
$29$	−2.80215	−	4.85347i	−0.520346	−	0.901266i	−0.999720	−	0.0236554i	$-0.992470\pi$
$29$	−2.80215	−	4.85347i	−0.520346	−	0.901266i	0.479374	−	0.877611i	$-0.340864\pi$
$30$	0.258876	−	0.448387i	0.0472642	−	0.0818639i
$31$		−	5.46420i		−	0.981400i	−0.871329	−	0.490700i	$-0.836741\pi$
$31$		−	5.46420i		−	0.981400i	0.871329	−	0.490700i	$-0.163259\pi$
$32$	4.27878	+	2.47036i	0.756389	+	0.436701i
$33$	−4.98494	−	2.87806i	−0.867767	−	0.501005i
$34$			1.13980i			0.195475i
$35$	−0.532679	+	0.922628i	−0.0900393	+	0.155953i
$36$	−0.881907	−	1.52751i	−0.146985	−	0.254585i
$37$	−4.08375	+	2.35775i	−0.671364	+	0.387612i	−0.796593	−	0.604515i	$-0.793367\pi$
$37$	−4.08375	+	2.35775i	−0.671364	+	0.387612i	0.125229	+	0.992128i	$0.460033\pi$
$38$	3.01337			0.488834
$39$	−3.60542	+	0.0309306i	−0.577329	+	0.00495286i
$40$	−1.94873			−0.308121
$41$	7.69141	−	4.44064i	1.20120	−	0.693511i	0.240375	−	0.970680i	$-0.422730\pi$
$41$	7.69141	−	4.44064i	1.20120	−	0.693511i	0.960821	+	0.277169i	$0.0893963\pi$
$42$	−0.242995	−	0.420879i	−0.0374949	−	0.0649430i
$43$	−4.77851	+	8.27662i	−0.728716	+	1.26217i	0.228710	+	0.973495i	$0.426549\pi$
$43$	−4.77851	+	8.27662i	−0.728716	+	1.26217i	−0.957426	+	0.288679i	$0.906784\pi$
$44$			10.1527i			1.53058i
$45$	0.922628	+	0.532679i	0.137537	+	0.0794072i
$46$	−2.32051	−	1.33975i	−0.342140	−	0.197535i
$47$			5.21864i			0.761217i	0.924736	+	0.380608i	$0.124285\pi$
$47$			5.21864i			0.761217i	−0.924736	+	0.380608i	$0.875715\pi$
$48$	−1.31934	+	2.28516i	−0.190430	+	0.329834i
$49$	0.500000	+	0.866025i	0.0714286	+	0.123718i
$50$	−1.62670	+	0.939177i	−0.230050	+	0.132820i
$51$	−2.34533			−0.328412
$52$	3.22689	+	5.48003i	0.447489	+	0.759943i
$53$	1.52870			0.209982			0.104991	−	0.994473i	$-0.466519\pi$
$53$	1.52870			0.209982			0.104991	+	0.994473i	$0.466519\pi$
$54$	−0.420879	+	0.242995i	−0.0572744	+	0.0330674i
$55$	−3.06616	−	5.31075i	−0.413441	−	0.716102i
$56$	−0.914587	+	1.58411i	−0.122217	+	0.211686i
$57$			6.20049i			0.821276i
$58$	2.35873	+	1.36181i	0.309717	+	0.178815i
$59$	−9.06406	−	5.23314i	−1.18004	−	0.681297i	−0.224016	−	0.974585i	$-0.571917\pi$
$59$	−9.06406	−	5.23314i	−1.18004	−	0.681297i	−0.956024	+	0.293289i	$0.905250\pi$
$60$		−	1.87910i		−	0.242590i
$61$	−3.82305	+	6.62171i	−0.489491	+	0.847823i	−0.999927	−	0.0120926i	$-0.996151\pi$
$61$	−3.82305	+	6.62171i	−0.489491	+	0.847823i	0.510436	+	0.859916i	$0.329484\pi$
$62$	1.32777	+	2.29977i	0.168627	+	0.292071i
$63$	0.866025	−	0.500000i	0.109109	−	0.0629941i
$64$	2.87621			0.359526
$65$	−3.34294	−	1.89199i	−0.414640	−	0.234673i
$66$	2.79741			0.344337
$67$	2.83779	−	1.63840i	0.346691	−	0.200162i	−0.316536	−	0.948581i	$-0.602520\pi$
$67$	2.83779	−	1.63840i	0.346691	−	0.200162i	0.663227	+	0.748418i	$0.269186\pi$
$68$	2.06836	+	3.58251i	0.250826	+	0.434443i
$69$	2.75674	−	4.77481i	0.331873	−	0.574820i
$70$		−	0.517753i		−	0.0618833i
$71$	7.50761	+	4.33452i	0.890990	+	0.514413i	0.874266	−	0.485447i	$-0.161343\pi$
$71$	7.50761	+	4.33452i	0.890990	+	0.514413i	0.0167238	+	0.999860i	$0.494676\pi$
$72$	1.58411	+	0.914587i	0.186689	+	0.107785i
$73$			7.63941i			0.894126i	0.894503	+	0.447063i	$0.147530\pi$
$73$			7.63941i			0.894126i	−0.894503	+	0.447063i	$0.852470\pi$
$74$	1.14584	−	1.98466i	0.133202	−	0.230712i
$75$	−1.93251	−	3.34720i	−0.223146	−	0.386501i
$76$	9.47131	−	5.46826i	1.08643	−	0.627253i
$77$	−5.75611			−0.655970
$78$	1.50993	−	0.889115i	0.170966	−	0.100672i
$79$	−15.6147			−1.75679			−0.878397	−	0.477932i	$-0.841387\pi$
$79$	−15.6147			−1.75679			−0.878397	+	0.477932i	$0.841387\pi$
$80$	−2.43451	+	1.40557i	−0.272187	+	0.157147i
$81$	−0.500000	−	0.866025i	−0.0555556	−	0.0962250i
$82$	−2.15810	+	3.73794i	−0.238322	+	0.412786i
$83$			2.63313i			0.289024i	0.989503	+	0.144512i	$0.0461612\pi$
$83$			2.63313i			0.289024i	−0.989503	+	0.144512i	$0.953839\pi$
$84$	−1.52751	−	0.881907i	−0.166665	−	0.0962240i
$85$	−2.16387	−	1.24931i	−0.234704	−	0.135507i
$86$		−	4.64461i		−	0.500841i
$87$	−2.80215	+	4.85347i	−0.300422	+	0.520346i
$88$	−5.26447	−	9.11832i	−0.561194	−	0.972016i
$89$	10.4502	−	6.03343i	1.10772	−	0.639542i	0.169481	−	0.985533i	$-0.445791\pi$
$89$	10.4502	−	6.03343i	1.10772	−	0.639542i	0.938238	+	0.345991i	$0.112457\pi$
$90$	−0.517753			−0.0545759
$91$	−3.10692	+	1.82950i	−0.325694	+	0.191783i
$92$	−9.72476			−1.01388
$93$	−4.73214	+	2.73210i	−0.490700	+	0.283306i
$94$	−1.26810	−	2.19642i	−0.130795	−	0.226543i
$95$	−3.30288	+	5.72075i	−0.338868	+	0.586936i
$96$		−	4.94071i		−	0.504259i
$97$	14.5156	+	8.38057i	1.47383	+	0.850918i	0.999566	−	0.0294624i	$-0.00937954\pi$
$97$	14.5156	+	8.38057i	1.47383	+	0.850918i	0.474268	+	0.880381i	$0.342713\pi$
$98$	−0.420879	−	0.242995i	−0.0425152	−	0.0245462i
$99$			5.75611i			0.578511i
$100$	−3.40858	+	5.90384i	−0.340858	+	0.590384i
$101$	−1.28815	−	2.23115i	−0.128176	−	0.222008i	0.794794	−	0.606880i	$-0.207579\pi$
$101$	−1.28815	−	2.23115i	−0.128176	−	0.222008i	−0.922970	+	0.384872i	$0.874246\pi$
$102$	0.987100	−	0.569902i	0.0977375	−	0.0564287i
$103$	10.3824			1.02301			0.511506	−	0.859280i	$-0.329088\pi$
$103$	10.3824			1.02301			0.511506	+	0.859280i	$0.329088\pi$
$104$	−5.73967	−	3.24847i	−0.562821	−	0.318539i
$105$	1.06536			0.103968
$106$	−0.643396	+	0.371465i	−0.0624921	+	0.0360798i
$107$	−8.51774	−	14.7532i	−0.823441	−	1.42624i	−0.903105	−	0.429420i	$-0.858718\pi$
$107$	−8.51774	−	14.7532i	−0.823441	−	1.42624i	0.0796637	−	0.996822i	$-0.474615\pi$
$108$	−0.881907	+	1.52751i	−0.0848616	+	0.146985i
$109$		−	1.86126i		−	0.178276i	−0.996019	−	0.0891380i	$-0.971589\pi$
$109$		−	1.86126i		−	0.178276i	0.996019	−	0.0891380i	$-0.0284112\pi$
$110$	2.58097	+	1.49012i	0.246086	+	0.142078i
$111$	4.08375	+	2.35775i	0.387612	+	0.223788i
$112$			2.63867i			0.249331i
$113$	2.38371	−	4.12870i	0.224240	−	0.388396i	−0.731851	−	0.681465i	$-0.761343\pi$
$113$	2.38371	−	4.12870i	0.224240	−	0.388396i	0.956091	+	0.293069i	$0.0946766\pi$
$114$	−1.50669	−	2.60966i	−0.141114	−	0.244417i
$115$	5.08689	−	2.93692i	0.474355	−	0.273869i
$116$	9.88495			0.917794
$117$	1.82950	+	3.10692i	0.169137	+	0.287235i
$118$	5.08650			0.468250
$119$	−2.03111	+	1.17266i	−0.186192	+	0.107498i
$120$	0.974363	+	1.68765i	0.0889468	+	0.154060i
$121$	11.0664	−	19.1676i	1.00604	−	1.74251i
$122$		−	3.71592i		−	0.336423i
$123$	−7.69141	−	4.44064i	−0.693511	−	0.400399i
$124$	8.34662	+	4.81892i	0.749548	+	0.432752i
$125$		−	9.44442i		−	0.844734i
$126$	−0.242995	+	0.420879i	−0.0216477	+	0.0374949i
$127$	−0.593804	−	1.02850i	−0.0526916	−	0.0912645i	0.838477	−	0.544938i	$-0.183447\pi$
$127$	−0.593804	−	1.02850i	−0.0526916	−	0.0912645i	−0.891168	+	0.453673i	$0.850113\pi$
$128$	−9.76810	+	5.63962i	−0.863386	+	0.498476i
$129$	9.55702			0.841449
$130$	1.86672	−	0.0160144i	0.163722	−	0.00140456i
$131$	−14.8261			−1.29537			−0.647683	−	0.761910i	$-0.724262\pi$
$131$	−14.8261			−1.29537			−0.647683	+	0.761910i	$0.724262\pi$
$132$	8.79251	−	5.07636i	0.765290	−	0.441840i
$133$	3.10025	+	5.36979i	0.268826	+	0.465619i
$134$	−0.796244	+	1.37914i	−0.0687850	+	0.119139i
$135$		−	1.06536i		−	0.0916915i
$136$	−3.71526	−	2.14501i	−0.318581	−	0.183933i
$137$	5.69247	+	3.28655i	0.486341	+	0.280789i	0.723055	−	0.690790i	$-0.242737\pi$
$137$	5.69247	+	3.28655i	0.486341	+	0.280789i	−0.236714	+	0.971579i	$0.576071\pi$
$138$			2.67949i			0.228094i
$139$	0.367315	−	0.636208i	0.0311553	−	0.0539625i	−0.850027	−	0.526739i	$-0.823415\pi$
$139$	0.367315	−	0.636208i	0.0311553	−	0.0539625i	0.881183	+	0.472776i	$0.156748\pi$
$140$	−0.939548	−	1.62734i	−0.0794063	−	0.137536i
$141$	4.51947	−	2.60932i	0.380608	−	0.219744i
$142$	−4.21306			−0.353552
$143$	−0.178040	−	20.7532i	−0.0148885	−	1.73547i
$144$	2.63867			0.219889
$145$	−5.17068	+	2.98530i	−0.429402	+	0.247915i
$146$	−1.85634	−	3.21527i	−0.153631	−	0.266097i
$147$	0.500000	−	0.866025i	0.0412393	−	0.0714286i
$148$		−	8.31728i		−	0.683676i
$149$	19.6065	+	11.3198i	1.60622	+	0.927354i	0.990205	+	0.139622i	$0.0445887\pi$
$149$	19.6065	+	11.3198i	1.60622	+	0.927354i	0.616019	+	0.787732i	$0.288745\pi$
$150$	1.62670	+	0.939177i	0.132820	+	0.0766835i
$151$			7.94508i			0.646561i	0.946303	+	0.323281i	$0.104786\pi$
$151$			7.94508i			0.646561i	−0.946303	+	0.323281i	$0.895214\pi$
$152$	−5.67089	+	9.82227i	−0.459970	+	0.796691i
$153$	1.17266	+	2.03111i	0.0948043	+	0.164206i
$154$	2.42263	−	1.39870i	0.195221	−	0.112711i
$155$	−5.82134			−0.467581
$156$	3.13240	−	5.53458i	0.250793	−	0.443121i
$157$	15.4868			1.23598			0.617991	−	0.786185i	$-0.287947\pi$
$157$	15.4868			1.23598			0.617991	+	0.786185i	$0.287947\pi$
$158$	6.57191	−	3.79429i	0.522833	−	0.301858i
$159$	−0.764348	−	1.32389i	−0.0606167	−	0.104991i
$160$	2.63182	−	4.55844i	0.208063	−	0.360376i
$161$		−	5.51348i		−	0.434523i
$162$	0.420879	+	0.242995i	0.0330674	+	0.0190915i
$163$	5.10619	+	2.94806i	0.399947	+	0.230910i	0.686461	−	0.727166i	$-0.259163\pi$
$163$	5.10619	+	2.94806i	0.399947	+	0.230910i	−0.286514	+	0.958076i	$0.592496\pi$
$164$			15.6649i			1.22322i
$165$	−3.06616	+	5.31075i	−0.238701	+	0.413441i
$166$	−0.639837	−	1.10823i	−0.0496609	−	0.0860153i
$167$	8.23496	−	4.75446i	0.637241	−	0.367911i	−0.146310	−	0.989239i	$-0.546740\pi$
$167$	8.23496	−	4.75446i	0.637241	−	0.367911i	0.783551	+	0.621328i	$0.213406\pi$
$168$	1.82917			0.141124
$169$	−6.69220	−	11.1452i	−0.514784	−	0.857320i
$170$	1.21430			0.0931326
$171$	5.36979	−	3.10025i	0.410638	−	0.237082i
$172$	−8.42841	−	14.5984i	−0.642660	−	1.11312i
$173$	−0.812324	+	1.40699i	−0.0617599	+	0.106971i	−0.895252	−	0.445560i	$-0.853005\pi$
$173$	−0.812324	+	1.40699i	−0.0617599	+	0.106971i	0.833492	+	0.552531i	$0.186338\pi$
$174$		−	2.72363i		−	0.206478i
$175$	−3.34720	−	1.93251i	−0.253024	−	0.146084i
$176$	−13.1536	−	7.59424i	−0.991491	−	0.572438i
$177$			10.4663i			0.786694i
$178$	−2.93218	+	5.07869i	−0.219776	+	0.380664i
$179$	9.87735	+	17.1081i	0.738268	+	1.27872i	0.953275	+	0.302105i	$0.0976892\pi$
$179$	9.87735	+	17.1081i	0.738268	+	1.27872i	−0.215007	+	0.976612i	$0.568977\pi$
$180$	−1.62734	+	0.939548i	−0.121295	+	0.0700297i
$181$	−0.589428			−0.0438118			−0.0219059	−	0.999760i	$-0.506973\pi$
$181$	−0.589428			−0.0438118			−0.0219059	+	0.999760i	$0.506973\pi$
$182$	0.863079	−	1.52496i	0.0639757	−	0.113038i
$183$	7.64609			0.565215
$184$	8.73396	−	5.04256i	0.643876	−	0.371742i
$185$	2.51185	+	4.35066i	0.184675	+	0.319867i
$186$	1.32777	−	2.29977i	0.0973570	−	0.168627i
$187$		−	13.5000i		−	0.987217i
$188$	−7.97152	−	4.60236i	−0.581383	−	0.335661i
$189$	−0.866025	−	0.500000i	−0.0629941	−	0.0363696i
$190$		−	3.21032i		−	0.232901i
$191$	−4.58812	+	7.94686i	−0.331985	+	0.575015i	−0.982901	−	0.184135i	$-0.941052\pi$
$191$	−4.58812	+	7.94686i	−0.331985	+	0.575015i	0.650916	+	0.759150i	$0.274385\pi$
$192$	−1.43810	−	2.49087i	−0.103786	−	0.179763i
$193$	−2.84691	+	1.64367i	−0.204925	+	0.118314i	−0.598951	−	0.800786i	$-0.704416\pi$
$193$	−2.84691	+	1.64367i	−0.204925	+	0.118314i	0.394025	+	0.919100i	$0.371082\pi$
$194$	−8.14574			−0.584830
$195$	0.0329522	+	3.84106i	0.00235976	+	0.275064i
$196$	−1.76381			−0.125987
$197$	−13.2678	+	7.66017i	−0.945292	+	0.545765i	−0.891615	−	0.452793i	$-0.850427\pi$
$197$	−13.2678	+	7.66017i	−0.945292	+	0.545765i	−0.0536771	+	0.998558i	$0.517094\pi$
$198$	−1.39870	−	2.42263i	−0.0994016	−	0.172169i
$199$	−7.26150	+	12.5773i	−0.514754	+	0.891581i	0.485099	+	0.874459i	$0.338784\pi$
$199$	−7.26150	+	12.5773i	−0.514754	+	0.891581i	−0.999853	+	0.0171214i	$0.994550\pi$
$200$		−	7.06977i		−	0.499909i
$201$	−2.83779	−	1.63840i	−0.200162	−	0.115564i
$202$	1.08431	+	0.626029i	0.0762921	+	0.0440473i
$203$			5.60430i			0.393345i
$204$	2.06836	−	3.58251i	0.144814	−	0.250826i
$205$	−4.73087	−	8.19411i	−0.330418	−	0.572301i
$206$	−4.36975	+	2.52288i	−0.304455	+	0.175777i
$207$	−5.51348			−0.383213
$208$	−9.51351	+	0.0816157i	−0.659643	+	0.00565903i
$209$	−35.6908			−2.46878
$210$	−0.448387	+	0.258876i	−0.0309417	+	0.0178642i
$211$	8.26364	+	14.3130i	0.568892	+	0.985350i	0.996676	+	0.0814692i	$0.0259612\pi$
$211$	8.26364	+	14.3130i	0.568892	+	0.985350i	−0.427783	+	0.903881i	$0.640705\pi$
$212$	−1.34817	+	2.33509i	−0.0925925	+	0.160375i
$213$		−	8.66905i		−	0.593993i
$214$	7.16988	+	4.13953i	0.490123	+	0.282972i
$215$	8.81757	+	5.09083i	0.601354	+	0.347192i
$216$		−	1.82917i		−	0.124459i
$217$	−2.73210	+	4.73214i	−0.185467	+	0.321239i
$218$	0.452275	+	0.783363i	0.0306319	+	0.0530561i
$219$	6.61593	−	3.81971i	0.447063	−	0.258112i
$220$	10.8163			0.729234
$221$	−4.29077	−	7.28675i	−0.288628	−	0.490160i
$222$	−2.29169			−0.153808
$223$	−18.7844	+	10.8452i	−1.25789	+	0.726246i	−0.972665	−	0.232213i	$-0.925403\pi$
$223$	−18.7844	+	10.8452i	−1.25789	+	0.726246i	−0.285230	+	0.958459i	$0.592070\pi$
$224$	−2.47036	−	4.27878i	−0.165058	−	0.285888i
$225$	−1.93251	+	3.34720i	−0.128834	+	0.223146i
$226$			2.31691i			0.154119i
$227$	−4.70729	−	2.71776i	−0.312434	−	0.180384i	0.335581	−	0.942011i	$-0.391067\pi$
$227$	−4.70729	−	2.71776i	−0.312434	−	0.180384i	−0.648015	+	0.761627i	$0.724401\pi$
$228$	−9.47131	−	5.46826i	−0.627253	−	0.362144i
$229$		−	9.99668i		−	0.660599i	−0.943876	−	0.330300i	$-0.892850\pi$
$229$		−	9.99668i		−	0.660599i	0.943876	−	0.330300i	$-0.107150\pi$
$230$	−1.42731	+	2.47217i	−0.0941141	+	0.163010i
$231$	2.87806	+	4.98494i	0.189362	+	0.327985i
$232$	−8.87783	+	5.12562i	−0.582858	+	0.336513i
$233$	1.72553			0.113043			0.0565217	−	0.998401i	$-0.481999\pi$
$233$	1.72553			0.113043			0.0565217	+	0.998401i	$0.481999\pi$
$234$	−1.52496	−	0.863079i	−0.0996898	−	0.0564213i
$235$	5.55972			0.362676
$236$	15.9873	−	9.23029i	1.04069	−	0.600840i
$237$	7.80736	+	13.5228i	0.507143	+	0.878397i
$238$	0.569902	−	0.987100i	0.0369413	−	0.0639842i
$239$			5.80837i			0.375712i	0.982197	+	0.187856i	$0.0601539\pi$
$239$			5.80837i			0.375712i	−0.982197	+	0.187856i	$0.939846\pi$
$240$	2.43451	+	1.40557i	0.157147	+	0.0907289i
$241$	9.63038	+	5.56010i	0.620348	+	0.358158i	0.777004	−	0.629495i	$-0.216738\pi$
$241$	9.63038	+	5.56010i	0.620348	+	0.358158i	−0.156657	+	0.987653i	$0.550072\pi$
$242$			10.7563i			0.691443i
$243$	−0.500000	+	0.866025i	−0.0320750	+	0.0555556i
$244$	−6.74315	−	11.6795i	−0.431686	−	0.747701i
$245$	0.922628	−	0.532679i	0.0589445	−	0.0340316i
$246$	4.31620			0.275191
$247$	−19.2644	+	11.3438i	−1.22577	+	0.721787i
$248$	−9.99498			−0.634682
$249$	2.28036	−	1.31657i	0.144512	−	0.0834339i
$250$	2.29494	+	3.97496i	0.145145	+	0.251398i
$251$	4.87634	−	8.44607i	0.307792	−	0.533111i	−0.670087	−	0.742283i	$-0.733743\pi$
$251$	4.87634	−	8.44607i	0.307792	−	0.533111i	0.977879	+	0.209171i	$0.0670766\pi$
$252$			1.76381i			0.111110i
$253$	27.4844	+	15.8681i	1.72793	+	0.997620i
$254$	0.499839	+	0.288582i	0.0313627	+	0.0181073i
$255$			2.49862i			0.156469i
$256$	−0.135416	+	0.234547i	−0.00846350	+	0.0146592i
$257$	5.19710	+	9.00164i	0.324186	+	0.561507i	0.981347	−	0.192243i	$-0.0615762\pi$
$257$	5.19710	+	9.00164i	0.324186	+	0.561507i	−0.657161	+	0.753750i	$0.728243\pi$
$258$	−4.02235	+	2.32230i	−0.250421	+	0.144580i
$259$	4.71551			0.293007
$260$	5.83820	−	3.43780i	0.362070	−	0.213203i
$261$	5.60430			0.346898
$262$	6.24001	−	3.60267i	0.385509	−	0.222574i
$263$	12.2395	+	21.1994i	0.754717	+	1.30721i	0.945515	+	0.325579i	$0.105559\pi$
$263$	12.2395	+	21.1994i	0.754717	+	1.30721i	−0.190798	+	0.981629i	$0.561107\pi$
$264$	−5.26447	+	9.11832i	−0.324005	+	0.561194i
$265$		−	1.62861i		−	0.100045i
$266$	−2.60966	−	1.50669i	−0.160008	−	0.0923809i
$267$	−10.4502	−	6.03343i	−0.639542	−	0.369240i
$268$			5.77966i			0.353049i
$269$	−2.52910	+	4.38052i	−0.154202	+	0.267085i	−0.932768	−	0.360477i	$-0.882614\pi$
$269$	−2.52910	+	4.38052i	−0.154202	+	0.267085i	0.778566	+	0.627562i	$0.215947\pi$
$270$	0.258876	+	0.448387i	0.0157547	+	0.0272880i
$271$	11.7523	−	6.78518i	0.713900	−	0.412170i	−0.0986037	−	0.995127i	$-0.531438\pi$
$271$	11.7523	−	6.78518i	0.713900	−	0.412170i	0.812503	+	0.582957i	$0.198104\pi$
$272$	−6.18855			−0.375236
$273$	3.13785	+	1.77592i	0.189911	+	0.107484i
$274$	−3.19446			−0.192984
$275$	19.2669	−	11.1237i	1.16183	−	0.670786i
$276$	4.86238	+	8.42189i	0.292681	+	0.506938i
$277$	−11.7870	+	20.4156i	−0.708210	+	1.22666i	0.257311	+	0.966329i	$0.417164\pi$
$277$	−11.7870	+	20.4156i	−0.708210	+	1.22666i	−0.965521	+	0.260327i	$0.916170\pi$
$278$			0.357022i			0.0214128i
$279$	4.73214	+	2.73210i	0.283306	+	0.163567i
$280$	1.68765	+	0.974363i	0.100856	+	0.0582293i
$281$		−	14.8688i		−	0.886996i	−0.896275	−	0.443498i	$-0.853737\pi$
$281$		−	14.8688i		−	0.886996i	0.896275	−	0.443498i	$-0.146263\pi$
$282$	−1.26810	+	2.19642i	−0.0755143	+	0.130795i
$283$	−10.4948	−	18.1776i	−0.623852	−	1.08054i	−0.988762	−	0.149500i	$-0.952233\pi$
$283$	−10.4948	−	18.1776i	−0.623852	−	1.08054i	0.364910	−	0.931043i	$-0.381100\pi$
$284$	−13.2420	+	7.64530i	−0.785770	+	0.453665i
$285$	6.60575			0.391291
$286$	5.11785	+	8.69132i	0.302625	+	0.513929i
$287$	−8.88127			−0.524245
$288$	−4.27878	+	2.47036i	−0.252130	+	0.145567i
$289$	5.74972	+	9.95880i	0.338219	+	0.585812i
$290$	1.45082	−	2.51290i	0.0851952	−	0.147562i
$291$		−	16.7611i		−	0.982556i
$292$	−11.6693	−	6.73725i	−0.682892	−	0.394268i
$293$	6.39182	+	3.69032i	0.373414	+	0.215591i	0.674949	−	0.737864i	$-0.264166\pi$
$293$	6.39182	+	3.69032i	0.373414	+	0.215591i	−0.301535	+	0.953455i	$0.597499\pi$
$294$			0.485989i			0.0283435i
$295$	−5.57517	+	9.65648i	−0.324599	+	0.562222i
$296$	4.31274	+	7.46989i	0.250673	+	0.434178i
$297$	4.98494	−	2.87806i	0.289256	−	0.167002i
$298$	−11.0026			−0.637363
$299$	19.8784	−	0.170535i	1.14960	−	0.00986232i
$300$	6.81716			0.393589
$301$	8.27662	−	4.77851i	0.477057	−	0.275429i
$302$	−1.93061	−	3.34392i	−0.111094	−	0.192421i
$303$	−1.28815	+	2.23115i	−0.0740026	+	0.128176i
$304$			16.3611i			0.938371i
$305$	7.05450	+	4.07292i	0.403939	+	0.233215i
$306$	−0.987100	−	0.569902i	−0.0564287	−	0.0325792i
$307$			26.2172i			1.49629i	0.663534	+	0.748146i	$0.269056\pi$
$307$			26.2172i			1.49629i	−0.663534	+	0.748146i	$0.730944\pi$
$308$	5.07636	−	8.79251i	0.289252	−	0.501000i
$309$	−5.19122	−	8.99146i	−0.295318	−	0.511506i
$310$	2.45008	−	1.41455i	0.139155	−	0.0803413i
$311$	−23.3730			−1.32536			−0.662681	−	0.748902i	$-0.730581\pi$
$311$	−23.3730			−1.32536			−0.662681	+	0.748902i	$0.730581\pi$
$312$	0.0565775	+	6.59494i	0.00320307	+	0.373365i
$313$	−20.5337			−1.16064			−0.580318	−	0.814390i	$-0.697072\pi$
$313$	−20.5337			−1.16064			−0.580318	+	0.814390i	$0.697072\pi$
$314$	−6.51807	+	3.76321i	−0.367836	+	0.212370i
$315$	−0.532679	−	0.922628i	−0.0300131	−	0.0519842i
$316$	13.7707	−	23.8516i	0.774665	−	1.34176i
$317$			2.73722i			0.153738i	0.997041	+	0.0768689i	$0.0244923\pi$
$317$			2.73722i			0.153738i	−0.997041	+	0.0768689i	$0.975508\pi$
$318$	0.643396	+	0.371465i	0.0360798	+	0.0208307i
$319$	−27.9371	−	16.1295i	−1.56418	−	0.903079i
$320$		−	3.06419i		−	0.171294i
$321$	−8.51774	+	14.7532i	−0.475414	+	0.823441i
$322$	1.33975	+	2.32051i	0.0746611	+	0.129317i
$323$	−12.5939	+	7.27110i	−0.700744	+	0.404575i
$324$	1.76381			0.0979897
$325$	6.86396	−	12.1278i	0.380744	−	0.672730i
$326$	−2.86545			−0.158703
$327$	−1.61189	+	0.930628i	−0.0891380	+	0.0514638i
$328$	−8.12269	−	14.0689i	−0.448501	−	0.776826i
$329$	2.60932	−	4.51947i	0.143856	−	0.249167i
$330$		−	2.98024i		−	0.164057i
$331$	−8.35843	−	4.82574i	−0.459421	−	0.265247i	0.252380	−	0.967628i	$-0.418787\pi$
$331$	−8.35843	−	4.82574i	−0.459421	−	0.265247i	−0.711801	+	0.702382i	$0.752120\pi$
$332$	−4.02213	−	2.32218i	−0.220743	−	0.127446i
$333$		−	4.71551i		−	0.258408i
$334$	−2.31062	+	4.00210i	−0.126431	+	0.218985i
$335$	−1.74548	−	3.02327i	−0.0953659	−	0.165179i
$336$	2.28516	−	1.31934i	0.124665	−	0.0719756i
$337$	11.3368			0.617555			0.308778	−	0.951134i	$-0.400080\pi$
$337$	11.3368			0.617555			0.308778	+	0.951134i	$0.400080\pi$
$338$	5.52482	+	3.06459i	0.300511	+	0.166692i
$339$	−4.76742			−0.258930
$340$	3.81666	−	2.20355i	0.206987	−	0.119504i
$341$	−15.7263	−	27.2387i	−0.851627	−	1.47506i
$342$	−1.50669	+	2.60966i	−0.0814723	+	0.141114i
$343$		−	1.00000i		−	0.0539949i
$344$	15.1394	+	8.74072i	0.816261	+	0.471268i
$345$	−5.08689	−	2.93692i	−0.273869	−	0.158118i
$346$		−	0.789562i		−	0.0424471i
$347$	9.83667	−	17.0376i	0.528060	−	0.914627i	−0.471405	−	0.881917i	$-0.656253\pi$
$347$	9.83667	−	17.0376i	0.528060	−	0.914627i	0.999465	−	0.0327100i	$-0.0104138\pi$
$348$	−4.94247	−	8.56062i	−0.264944	−	0.458897i
$349$	6.82990	−	3.94324i	0.365596	−	0.211077i	−0.305937	−	0.952052i	$-0.598970\pi$
$349$	6.82990	−	3.94324i	0.365596	−	0.211077i	0.671533	+	0.740975i	$0.265636\pi$
$350$	1.87835			0.100402
$351$	1.77592	−	3.13785i	0.0947917	−	0.167486i
$352$	28.4393			1.51582
$353$	12.7151	−	7.34104i	0.676754	−	0.390724i	−0.121877	−	0.992545i	$-0.538891\pi$
$353$	12.7151	−	7.34104i	0.676754	−	0.390724i	0.798631	+	0.601821i	$0.205558\pi$
$354$	−2.54325	−	4.40504i	−0.135172	−	0.234125i
$355$	4.61782	−	7.99830i	0.245089	−	0.424506i
$356$			21.2837i			1.12803i
$357$	2.03111	+	1.17266i	0.107498	+	0.0620640i
$358$	−8.31434	−	4.80028i	−0.439426	−	0.253703i
$359$		−	16.7725i		−	0.885220i	−0.896714	−	0.442610i	$-0.854053\pi$
$359$		−	16.7725i		−	0.885220i	0.896714	−	0.442610i	$-0.145947\pi$
$360$	0.974363	−	1.68765i	0.0513534	−	0.0889468i
$361$	9.72307	+	16.8408i	0.511740	+	0.886360i
$362$	0.248078	−	0.143228i	0.0130387	−	0.00752789i
$363$	−22.1329			−1.16167
$364$	−0.0545559	−	6.35929i	−0.00285951	−	0.333317i
$365$	8.13871			0.426000
$366$	−3.21808	+	1.85796i	−0.168212	+	0.0971171i
$367$	5.47023	+	9.47471i	0.285543	+	0.494576i	0.972741	−	0.231895i	$-0.0744926\pi$
$367$	5.47023	+	9.47471i	0.285543	+	0.494576i	−0.687197	+	0.726471i	$0.741159\pi$
$368$	7.27413	−	12.5992i	0.379190	−	0.656777i
$369$			8.88127i			0.462341i
$370$	−2.11437	−	1.22073i	−0.109921	−	0.0634629i
$371$	−1.32389	−	0.764348i	−0.0687329	−	0.0396830i
$372$		−	9.63784i		−	0.499699i
$373$	3.61767	−	6.26599i	0.187316	−	0.324441i	−0.757039	−	0.653370i	$-0.773355\pi$
$373$	3.61767	−	6.26599i	0.187316	−	0.324441i	0.944354	+	0.328930i	$0.106688\pi$
$374$	3.28042	+	5.68186i	0.169627	+	0.293802i
$375$	−8.17911	+	4.72221i	−0.422367	+	0.243854i
$376$	9.54580			0.492287
$377$	−20.2059	+	0.173345i	−1.04065	+	0.00892770i
$378$	0.485989			0.0249966
$379$	2.28182	−	1.31741i	0.117209	−	0.0676707i	−0.440249	−	0.897876i	$-0.645110\pi$
$379$	2.28182	−	1.31741i	0.117209	−	0.0676707i	0.557458	+	0.830205i	$0.311777\pi$
$380$	−5.82566	−	10.0903i	−0.298850	−	0.517623i
$381$	−0.593804	+	1.02850i	−0.0304215	+	0.0526916i
$382$		−	4.45956i		−	0.228171i
$383$	7.45530	+	4.30432i	0.380948	+	0.219941i	0.678231	−	0.734849i	$-0.262747\pi$
$383$	7.45530	+	4.30432i	0.380948	+	0.219941i	−0.297283	+	0.954790i	$0.596080\pi$
$384$	9.76810	+	5.63962i	0.498476	+	0.287795i
$385$			6.13233i			0.312532i
$386$	0.798804	−	1.38357i	0.0406581	−	0.0704218i
$387$	−4.77851	−	8.27662i	−0.242905	−	0.420724i
$388$	−25.6028	+	14.7818i	−1.29978	+	0.750431i
$389$	19.9726			1.01265			0.506325	−	0.862343i	$-0.331004\pi$
$389$	19.9726			1.01265			0.506325	+	0.862343i	$0.331004\pi$
$390$	−0.947227	−	1.60862i	−0.0479647	−	0.0814554i
$391$	12.9309			0.653945
$392$	1.58411	−	0.914587i	0.0800097	−	0.0461936i
$393$	7.41307	+	12.8398i	0.373940	+	0.647683i
$394$	3.72276	−	6.44801i	0.187550	−	0.324846i
$395$			16.6353i			0.837012i
$396$	−8.79251	−	5.07636i	−0.441840	−	0.255097i
$397$	−2.47610	−	1.42958i	−0.124272	−	0.0717485i	0.436575	−	0.899668i	$-0.356191\pi$
$397$	−2.47610	−	1.42958i	−0.124272	−	0.0717485i	−0.560847	+	0.827919i	$0.689525\pi$
$398$		−	7.05802i		−	0.353787i
$399$	3.10025	−	5.36979i	0.155206	−	0.268826i
$400$	−5.09924	−	8.83215i	−0.254962	−	0.441608i
$401$	15.6107	−	9.01285i	0.779562	−	0.450080i	−0.0567132	−	0.998391i	$-0.518062\pi$
$401$	15.6107	−	9.01285i	0.779562	−	0.450080i	0.836275	+	0.548310i	$0.184729\pi$
$402$	1.59249			0.0794261
$403$	−17.1459	−	9.70400i	−0.854096	−	0.483391i
$404$	4.54413			0.226079
$405$	−0.922628	+	0.532679i	−0.0458457	+	0.0264691i
$406$	−1.36181	−	2.35873i	−0.0675857	−	0.117062i
$407$	−13.5715	+	23.5065i	−0.672714	+	1.16518i
$408$			4.29001i			0.212387i
$409$	−7.58420	−	4.37874i	−0.375015	−	0.216515i	0.300632	−	0.953740i	$-0.402802\pi$
$409$	−7.58420	−	4.37874i	−0.375015	−	0.216515i	−0.675647	+	0.737225i	$0.736136\pi$
$410$	3.98225	+	2.29915i	0.196669	+	0.113547i
$411$		−	6.57310i		−	0.324227i
$412$	−9.15635	+	15.8593i	−0.451101	+	0.781330i
$413$	5.23314	+	9.06406i	0.257506	+	0.446013i
$414$	2.32051	−	1.33975i	0.114047	−	0.0658449i
$415$	2.80523			0.137703
$416$	15.3504	−	9.03901i	0.752615	−	0.443174i
$417$	−0.734630			−0.0359750
$418$	15.0215	−	8.67266i	0.734725	−	0.424194i
$419$	0.864446	+	1.49726i	0.0422310	+	0.0731462i	0.886368	−	0.462981i	$-0.153220\pi$
$419$	0.864446	+	1.49726i	0.0422310	+	0.0731462i	−0.844137	+	0.536127i	$0.819887\pi$
$420$	−0.939548	+	1.62734i	−0.0458452	+	0.0794063i
$421$		−	25.6427i		−	1.24975i	−0.780726	−	0.624874i	$-0.785150\pi$
$421$		−	25.6427i		−	1.24975i	0.780726	−	0.624874i	$-0.214850\pi$
$422$	−6.95598	−	4.01604i	−0.338612	−	0.195498i
$423$	−4.51947	−	2.60932i	−0.219744	−	0.126869i
$424$		−	2.79625i		−	0.135798i
$425$	4.53236	−	7.85028i	0.219852	−	0.380795i
$426$	2.10653	+	3.64862i	0.102062	+	0.176776i
$427$	6.62171	−	3.82305i	0.320447	−	0.185010i
$428$	30.0474			1.45240
$429$	−17.8838	+	10.5308i	−0.863437	+	0.508431i
$430$	−4.94818			−0.238622
$431$	0.222971	−	0.128733i	0.0107402	−	0.00620083i	−0.494620	−	0.869109i	$-0.664693\pi$
$431$	0.222971	−	0.128733i	0.0107402	−	0.00620083i	0.505360	+	0.862908i	$0.331360\pi$
$432$	−1.31934	−	2.28516i	−0.0634765	−	0.109945i
$433$	−12.1641	+	21.0688i	−0.584570	+	1.01250i	0.410359	+	0.911924i	$0.365403\pi$
$433$	−12.1641	+	21.0688i	−0.584570	+	1.01250i	−0.994929	+	0.100580i	$0.967930\pi$
$434$		−	2.65554i		−	0.127470i
$435$	5.17068	+	2.98530i	0.247915	+	0.143134i
$436$	2.84308	+	1.64145i	0.136159	+	0.0786114i
$437$		−	34.1863i		−	1.63535i
$438$	−1.85634	+	3.21527i	−0.0886992	+	0.153631i
$439$	8.50900	+	14.7380i	0.406112	+	0.703407i	0.994450	−	0.105208i	$-0.0335509\pi$
$439$	8.50900	+	14.7380i	0.406112	+	0.703407i	−0.588338	+	0.808615i	$0.700218\pi$
$440$	−9.71428	+	5.60854i	−0.463110	+	0.267377i
$441$	−1.00000			−0.0476190
$442$	3.57654	+	2.02421i	0.170118	+	0.0962816i
$443$	38.1564			1.81287			0.906433	−	0.422349i	$-0.138794\pi$
$443$	38.1564			1.81287			0.906433	+	0.422349i	$0.138794\pi$
$444$	−7.20298	+	4.15864i	−0.341838	+	0.197360i
$445$	−6.42776	−	11.1332i	−0.304705	−	0.527765i
$446$	5.27063	−	9.12900i	0.249572	−	0.432271i
$447$		−	22.6396i		−	1.07082i
$448$	−2.49087	−	1.43810i	−0.117683	−	0.0679440i
$449$	35.7959	+	20.6668i	1.68931	+	0.975325i	0.955043	+	0.296468i	$0.0958087\pi$
$449$	35.7959	+	20.6668i	1.68931	+	0.975325i	0.734270	+	0.678858i	$0.237525\pi$
$450$		−	1.87835i		−	0.0885464i
$451$	25.5608	−	44.2726i	1.20361	−	2.08472i
$452$	4.20442	+	7.28227i	0.197759	+	0.342529i
$453$	6.88064	−	3.97254i	0.323281	−	0.186646i
$454$	2.64160			0.123976
$455$	1.94907	+	3.30998i	0.0913738	+	0.155174i
$456$	11.3418			0.531127
$457$	−16.1281	+	9.31158i	−0.754442	+	0.435578i	−0.827297	−	0.561765i	$-0.810123\pi$
$457$	−16.1281	+	9.31158i	−0.754442	+	0.435578i	0.0728544	+	0.997343i	$0.476789\pi$
$458$	2.42914	+	4.20739i	0.113506	+	0.196599i
$459$	1.17266	−	2.03111i	0.0547353	−	0.0948043i
$460$			10.3604i			0.483054i
$461$	−6.58984	−	3.80465i	−0.306919	−	0.177200i	0.338628	−	0.940920i	$-0.390037\pi$
$461$	−6.58984	−	3.80465i	−0.306919	−	0.177200i	−0.645547	+	0.763720i	$0.723371\pi$
$462$	−2.42263	−	1.39870i	−0.112711	−	0.0650736i
$463$		−	25.2029i		−	1.17128i	−0.810571	−	0.585640i	$-0.800843\pi$
$463$		−	25.2029i		−	1.17128i	0.810571	−	0.585640i	$-0.199157\pi$
$464$	−7.39395	+	12.8067i	−0.343256	+	0.594536i
$465$	2.91067	+	5.04143i	0.134979	+	0.233791i
$466$	−0.726241	+	0.419295i	−0.0336425	+	0.0194235i
$467$	18.6005			0.860727			0.430364	−	0.902656i	$-0.358385\pi$
$467$	18.6005			0.860727			0.430364	+	0.902656i	$0.358385\pi$
$468$	−6.35929	+	0.0545559i	−0.293958	+	0.00252185i
$469$	−3.27680			−0.151308
$470$	−2.33997	+	1.35098i	−0.107935	+	0.0623162i
$471$	−7.74340	−	13.4120i	−0.356797	−	0.617991i
$472$	−9.57232	+	16.5797i	−0.440602	+	0.763144i
$473$			55.0113i			2.52942i
$474$	−6.57191	−	3.79429i	−0.301858	−	0.174278i
$475$	−20.7543	−	11.9825i	−0.952272	−	0.549794i
$476$		−	4.13673i		−	0.189607i
$477$	−0.764348	+	1.32389i	−0.0349971	+	0.0606167i
$478$	−1.41140	−	2.44462i	−0.0645561	−	0.111814i
$479$	−21.2514	+	12.2695i	−0.971001	+	0.560608i	−0.899541	−	0.436836i	$-0.856099\pi$
$479$	−21.2514	+	12.2695i	−0.971001	+	0.560608i	−0.0714598	+	0.997443i	$0.522766\pi$
$480$	−5.26363			−0.240251
$481$	0.145854	+	17.0014i	0.00665035	+	0.775196i
$482$	−5.40430			−0.246159
$483$	−4.77481	+	2.75674i	−0.217262	+	0.125436i
$484$	19.5191	+	33.8081i	0.887233	+	1.53673i
$485$	8.92832	−	15.4643i	0.405414	−	0.702198i
$486$		−	0.485989i		−	0.0220449i
$487$	−26.6423	−	15.3819i	−1.20728	−	0.697022i	−0.245114	−	0.969494i	$-0.578825\pi$
$487$	−26.6423	−	15.3819i	−1.20728	−	0.697022i	−0.962164	+	0.272472i	$0.912159\pi$
$488$	12.1123	+	6.99301i	0.548296	+	0.316559i
$489$		−	5.89612i		−	0.266632i
$490$	−0.258876	+	0.448387i	−0.0116948	+	0.0202561i
$491$	−9.60159	−	16.6304i	−0.433313	−	0.750521i	0.563843	−	0.825882i	$-0.309322\pi$
$491$	−9.60159	−	16.6304i	−0.433313	−	0.750521i	−0.997156	+	0.0753611i	$0.975989\pi$
$492$	13.5662	−	7.83246i	0.611612	−	0.353114i
$493$	−13.1439			−0.591973
$494$	5.35152	−	9.45551i	0.240776	−	0.425424i
$495$	6.13233			0.275628
$496$	−12.4866	+	7.20912i	−0.560663	+	0.323699i
$497$	−4.33452	−	7.50761i	−0.194430	−	0.336763i
$498$	−0.639837	+	1.10823i	−0.0286718	+	0.0496609i
$499$		−	14.0592i		−	0.629376i	−0.949195	−	0.314688i	$-0.898100\pi$
$499$		−	14.0592i		−	0.629376i	0.949195	−	0.314688i	$-0.101900\pi$
$500$	14.4264	+	8.32910i	0.645169	+	0.372489i
$501$	−8.23496	−	4.75446i	−0.367911	−	0.212414i
$502$			4.73970i			0.211543i
$503$	0.301296	−	0.521861i	0.0134341	−	0.0232686i	−0.859230	−	0.511589i	$-0.829057\pi$
$503$	0.301296	−	0.521861i	0.0134341	−	0.0232686i	0.872664	+	0.488321i	$0.162390\pi$
$504$	−0.914587	−	1.58411i	−0.0407389	−	0.0705619i
$505$	−2.37697	+	1.37235i	−0.105774	+	0.0610686i
$506$	−15.4235			−0.685657
$507$	−6.30589	+	11.3682i	−0.280054	+	0.504879i
$508$	2.09472			0.0929382
$509$	−6.81860	+	3.93672i	−0.302229	+	0.174492i	−0.643444	−	0.765493i	$-0.722495\pi$
$509$	−6.81860	+	3.93672i	−0.302229	+	0.174492i	0.341215	+	0.939985i	$0.389162\pi$
$510$	−0.607151	−	1.05162i	−0.0268851	−	0.0465663i
$511$	3.81971	−	6.61593i	0.168974	−	0.292671i
$512$		−	22.6901i		−	1.00277i
$513$	−5.36979	−	3.10025i	−0.237082	−	0.136879i
$514$	−4.37470	−	2.52573i	−0.192960	−	0.111405i
$515$		−	11.0610i		−	0.487407i
$516$	−8.42841	+	14.5984i	−0.371040	+	0.642660i
$517$	15.0195	+	26.0146i	0.660559	+	1.14412i
$518$	−1.98466	+	1.14584i	−0.0872009	+	0.0503455i
$519$	1.62465			0.0713142
$520$	−3.46079	+	6.11481i	−0.151766	+	0.268152i
$521$	−26.5275			−1.16219			−0.581096	−	0.813835i	$-0.697376\pi$
$521$	−26.5275			−1.16219			−0.581096	+	0.813835i	$0.697376\pi$
$522$	−2.35873	+	1.36181i	−0.103239	+	0.0596050i
$523$	3.77968	+	6.54661i	0.165274	+	0.286263i	0.936753	−	0.349992i	$-0.113816\pi$
$523$	3.77968	+	6.54661i	0.165274	+	0.286263i	−0.771479	+	0.636255i	$0.780482\pi$
$524$	13.0753	−	22.6471i	0.571197	−	0.989341i
$525$			3.86501i			0.168683i
$526$	−10.3027	−	5.94824i	−0.449217	−	0.259356i
$527$	−11.0984	−	6.40768i	−0.483455	−	0.279123i
$528$			15.1885i			0.660994i
$529$	−3.69924	+	6.40727i	−0.160836	+	0.278577i
$530$	0.395743	+	0.685447i	0.0171900	+	0.0297739i
$531$	9.06406	−	5.23314i	0.393347	−	0.227099i
$532$	−10.9365			−0.474158
$533$	−0.274703	−	32.0207i	−0.0118987	−	1.38697i
$534$	5.86436			0.253776
$535$	−15.7174	+	9.07445i	−0.679523	+	0.392323i
$536$	−2.99692	−	5.19081i	−0.129447	−	0.224209i
$537$	9.87735	−	17.1081i	0.426239	−	0.738268i
$538$		−	2.45823i		−	0.105982i
$539$	4.98494	+	2.87806i	0.214717	+	0.123967i
$540$	1.62734	+	0.939548i	0.0700297	+	0.0404317i
$541$			13.8116i			0.593807i	0.954907	+	0.296904i	$0.0959540\pi$
$541$			13.8116i			0.593807i	−0.954907	+	0.296904i	$0.904046\pi$
$542$	−3.29752	+	5.71148i	−0.141641	+	0.245329i
$543$	0.294714	+	0.510460i	0.0126474	+	0.0219059i
$544$	10.0352	−	5.79380i	0.430254	−	0.248407i
$545$	−1.98291			−0.0849383
$546$	−1.75219	+	0.0150320i	−0.0749870	+	0.000643308i
$547$	15.3668			0.657039			0.328519	−	0.944497i	$-0.393450\pi$
$547$	15.3668			0.657039			0.328519	+	0.944497i	$0.393450\pi$
$548$	−10.0405	+	5.79687i	−0.428908	+	0.247630i
$549$	−3.82305	−	6.62171i	−0.163164	−	0.282608i
$550$	−5.40601	+	9.36348i	−0.230513	+	0.399260i
$551$			34.7494i			1.48038i
$552$	−8.73396	−	5.04256i	−0.371742	−	0.214625i
$553$	13.5228	+	7.80736i	0.575046	+	0.332003i
$554$		−	11.4567i		−	0.486747i
$555$	2.51185	−	4.35066i	0.106622	−	0.184675i
$556$	0.647876	+	1.12215i	0.0274760	+	0.0475899i
$557$	−22.5868	+	13.0405i	−0.957032	+	0.552542i	−0.895258	−	0.445548i	$-0.853009\pi$
$557$	−22.5868	+	13.0405i	−0.957032	+	0.552542i	−0.0617734	+	0.998090i	$0.519676\pi$
$558$	−2.65554			−0.112418
$559$	17.4845	+	29.6929i	0.739517	+	1.25588i
$560$	2.81113			0.118792
$561$	−11.6913	+	6.74999i	−0.493608	+	0.284985i
$562$	3.61303	+	6.25795i	0.152406	+	0.263976i
$563$	−6.43529	+	11.1462i	−0.271215	+	0.469758i	−0.969173	−	0.246380i	$-0.920759\pi$
$563$	−6.43529	+	11.1462i	−0.271215	+	0.469758i	0.697958	+	0.716138i	$0.254092\pi$
$564$			9.20471i			0.387588i
$565$	−4.39855	−	2.53950i	−0.185048	−	0.106838i
$566$	8.83409	+	5.10037i	0.371325	+	0.214384i
$567$			1.00000i			0.0419961i
$568$	7.92859	−	13.7327i	0.332676	−	0.576212i
$569$	−2.47488	−	4.28662i	−0.103752	−	0.179704i	0.809475	−	0.587154i	$-0.199752\pi$
$569$	−2.47488	−	4.28662i	−0.103752	−	0.179704i	−0.913228	+	0.407449i	$0.866418\pi$
$570$	−2.78022	+	1.60516i	−0.116451	+	0.0672328i
$571$	28.2860			1.18373			0.591865	−	0.806037i	$-0.298392\pi$
$571$	28.2860			1.18373			0.591865	+	0.806037i	$0.298392\pi$
$572$	31.8577	+	18.0304i	1.33204	+	0.753891i
$573$	9.17624			0.383343
$574$	3.73794	−	2.15810i	0.156019	−	0.0900774i
$575$	10.6548	+	18.4547i	0.444337	+	0.769615i
$576$	−1.43810	+	2.49087i	−0.0599210	+	0.103786i
$577$		−	30.1903i		−	1.25684i	−0.777875	−	0.628419i	$-0.783702\pi$
$577$		−	30.1903i		−	1.25684i	0.777875	−	0.628419i	$-0.216298\pi$
$578$	−4.83987	−	2.79430i	−0.201312	−	0.116228i
$579$	2.84691	+	1.64367i	0.118314	+	0.0683084i
$580$		−	10.5310i		−	0.437277i
$581$	1.31657	−	2.28036i	0.0546203	−	0.0946052i
$582$	4.07287	+	7.05441i	0.168826	+	0.292415i
$583$	7.62046	−	4.39967i	0.315607	−	0.182216i
$584$	13.9738			0.578240
$585$	3.30998	−	1.94907i	0.136851	−	0.0805841i
$586$	−3.58691			−0.148174
$587$	−22.5606	+	13.0253i	−0.931174	+	0.537614i	−0.887183	−	0.461418i	$-0.847341\pi$
$587$	−22.5606	+	13.0253i	−0.931174	+	0.537614i	−0.0439914	+	0.999032i	$0.514007\pi$
$588$	0.881907	+	1.52751i	0.0363692	+	0.0629934i
$589$	−16.9404	+	29.3416i	−0.698016	+	1.20900i
$590$		−	5.41895i		−	0.223094i
$591$	13.2678	+	7.66017i	0.545765	+	0.315097i
$592$	10.7757	+	6.22134i	0.442877	+	0.255695i
$593$		−	10.6780i		−	0.438494i	−0.975669	−	0.219247i	$-0.929640\pi$
$593$		−	10.6780i		−	0.438494i	0.975669	−	0.219247i	$-0.0703601\pi$
$594$	−1.39870	+	2.42263i	−0.0573896	+	0.0994016i
$595$	1.24931	+	2.16387i	0.0512167	+	0.0887099i
$596$	−34.5822	+	19.9660i	−1.41654	+	0.817840i
$597$	14.5230			0.594387
$598$	−8.32497	+	4.90212i	−0.340433	+	0.200463i
$599$	−13.3791			−0.546655			−0.273327	−	0.961921i	$-0.588124\pi$
$599$	−13.3791			−0.546655			−0.273327	+	0.961921i	$0.588124\pi$
$600$	−6.12260	+	3.53489i	−0.249954	+	0.144311i
$601$	−17.4475	−	30.2199i	−0.711697	−	1.23270i	−0.964220	−	0.265105i	$-0.914593\pi$
$601$	−17.4475	−	30.2199i	−0.711697	−	1.23270i	0.252522	−	0.967591i	$-0.418740\pi$
$602$	−2.32230	+	4.02235i	−0.0946501	+	0.163939i
$603$			3.27680i			0.133442i
$604$	−12.1362	−	7.00682i	−0.493814	−	0.285104i
$605$	−20.4204	−	11.7897i	−0.830207	−	0.479320i
$606$		−	1.25206i		−	0.0508614i
$607$	17.4463	−	30.2179i	0.708123	−	1.22651i	−0.257429	−	0.966297i	$-0.582875\pi$
$607$	17.4463	−	30.2179i	0.708123	−	1.22651i	0.965553	−	0.260208i	$-0.0837912\pi$
$608$	−15.3174	−	26.5306i	−0.621204	−	1.07596i
$609$	4.85347	−	2.80215i	0.196672	−	0.113549i
$610$	−3.95879			−0.160287
$611$	16.3753	+	9.26790i	0.662474	+	0.374939i
$612$	−4.13673			−0.167217
$613$	−3.51431	+	2.02899i	−0.141942	+	0.0819500i	−0.569289	−	0.822137i	$-0.692781\pi$
$613$	−3.51431	+	2.02899i	−0.141942	+	0.0819500i	0.427347	+	0.904087i	$0.359448\pi$
$614$	−6.37063	−	11.0343i	−0.257098	−	0.445306i
$615$	−4.73087	+	8.19411i	−0.190767	+	0.330418i
$616$			10.5289i			0.424223i
$617$	−1.33035	−	0.768080i	−0.0535580	−	0.0309217i	0.472982	−	0.881072i	$-0.343178\pi$
$617$	−1.33035	−	0.768080i	−0.0535580	−	0.0309217i	−0.526540	+	0.850150i	$0.676511\pi$
$618$	4.36975	+	2.52288i	0.175777	+	0.101485i
$619$			15.0023i			0.602993i	0.953467	+	0.301496i	$0.0974861\pi$
$619$			15.0023i			0.602993i	−0.953467	+	0.301496i	$0.902514\pi$
$620$	5.13388	−	8.89214i	0.206182	−	0.357117i
$621$	2.75674	+	4.77481i	0.110624	+	0.191607i
$622$	9.83721	−	5.67951i	0.394436	−	0.227728i
$623$	−12.0669			−0.483448
$624$	4.82744	+	8.19813i	0.193252	+	0.328188i
$625$	9.26336			0.370534
$626$	8.64222	−	4.98959i	0.345412	−	0.199424i
$627$	17.8454	+	30.9091i	0.712676	+	1.23439i
$628$	−13.6579	+	23.6562i	−0.545011	+	0.943986i
$629$			11.0594i			0.440968i
$630$	0.448387	+	0.258876i	0.0178642	+	0.0103139i
$631$	−8.08574	−	4.66831i	−0.321888	−	0.185842i	0.330346	−	0.943860i	$-0.392835\pi$
$631$	−8.08574	−	4.66831i	−0.321888	−	0.185842i	−0.652234	+	0.758018i	$0.726168\pi$
$632$			28.5620i			1.13614i
$633$	8.26364	−	14.3130i	0.328450	−	0.568892i
$634$	−0.665131	−	1.15204i	−0.0264157	−	0.0457534i
$635$	−1.09572	+	0.632614i	−0.0434823	+	0.0251045i
$636$	2.69634			0.106917
$637$	3.60542	−	0.0309306i	0.142852	−	0.00122552i
$638$	15.6775			0.620679
$639$	−7.50761	+	4.33452i	−0.296997	+	0.171471i
$640$	6.00821	+	10.4065i	0.237495	+	0.411354i
$641$	−6.54834	+	11.3421i	−0.258644	+	0.447984i	−0.965879	−	0.258994i	$-0.916609\pi$
$641$	−6.54834	+	11.3421i	−0.258644	+	0.447984i	0.707235	+	0.706979i	$0.249942\pi$
$642$		−	8.27906i		−	0.326748i
$643$	−12.0111	−	6.93458i	−0.473670	−	0.273473i	0.244105	−	0.969749i	$-0.421506\pi$
$643$	−12.0111	−	6.93458i	−0.473670	−	0.273473i	−0.717775	+	0.696276i	$0.754839\pi$
$644$	8.42189	+	4.86238i	0.331869	+	0.191605i
$645$		−	10.1817i		−	0.400902i
$646$	3.53368	−	6.12051i	0.139031	−	0.240808i
$647$	5.83908	+	10.1136i	0.229558	+	0.397606i	0.957677	−	0.287845i	$-0.0929387\pi$
$647$	5.83908	+	10.1136i	0.229558	+	0.397606i	−0.728119	+	0.685450i	$0.759605\pi$
$648$	−1.58411	+	0.914587i	−0.0622297	+	0.0359284i
$649$	−60.2451			−2.36483
$650$	0.0580987	+	6.77225i	0.00227882	+	0.265630i
$651$	5.46420			0.214159
$652$	−9.00637	+	5.19983i	−0.352716	+	0.203641i
$653$	−4.34307	−	7.52242i	−0.169958	−	0.294375i	0.768447	−	0.639913i	$-0.221030\pi$
$653$	−4.34307	−	7.52242i	−0.169958	−	0.294375i	−0.938405	+	0.345538i	$0.887696\pi$
$654$	0.452275	−	0.783363i	0.0176854	−	0.0306319i
$655$			15.7952i			0.617168i
$656$	−20.2951	−	11.7174i	−0.792390	−	0.457487i
$657$	−6.61593	−	3.81971i	−0.258112	−	0.149021i
$658$			2.53620i			0.0988715i
$659$	24.1981	−	41.9124i	0.942626	−	1.63268i	0.182190	−	0.983263i	$-0.441681\pi$
$659$	24.1981	−	41.9124i	0.942626	−	1.63268i	0.760436	−	0.649413i	$-0.224985\pi$
$660$	−5.40814	−	9.36718i	−0.210512	−	0.364617i
$661$	−22.0611	+	12.7370i	−0.858076	+	0.495410i	−0.863367	−	0.504576i	$-0.831649\pi$
$661$	−22.0611	+	12.7370i	−0.858076	+	0.495410i	0.00529178	+	0.999986i	$0.498316\pi$
$662$	4.69051			0.182302
$663$	−4.16512	+	7.35929i	−0.161760	+	0.285811i
$664$	4.81645			0.186915
$665$	5.72075	−	3.30288i	0.221841	−	0.128080i
$666$	1.14584	+	1.98466i	0.0444005	+	0.0769040i
$667$	15.4496	−	26.7595i	0.598211	−	1.03613i
$668$			16.7720i			0.648927i
$669$	18.7844	+	10.8452i	0.726246	+	0.419298i
$670$	1.46927	+	0.848286i	0.0567630	+	0.0327721i
$671$			44.0118i			1.69906i
$672$	−2.47036	+	4.27878i	−0.0952961	+	0.165058i
$673$	−0.655263	−	1.13495i	−0.0252585	−	0.0437491i	0.853120	−	0.521715i	$-0.174708\pi$
$673$	−0.655263	−	1.13495i	−0.0252585	−	0.0437491i	−0.878378	+	0.477966i	$0.841374\pi$
$674$	−4.77142	+	2.75478i	−0.183788	+	0.106110i
$675$	3.86501			0.148764
$676$	22.9262	−	0.393394i	0.881777	−	0.0151305i
$677$	−47.4782			−1.82473			−0.912367	−	0.409373i	$-0.865747\pi$
$677$	−47.4782			−1.82473			−0.912367	+	0.409373i	$0.865747\pi$
$678$	2.00650	−	1.15846i	0.0770594	−	0.0444902i
$679$	−8.38057	−	14.5156i	−0.321617	−	0.557057i
$680$	−2.28520	+	3.95809i	−0.0876335	+	0.151786i
$681$			5.43551i			0.208289i
$682$	13.2377	+	7.64281i	0.506899	+	0.292658i
$683$	11.4380	+	6.60376i	0.437665	+	0.252686i	0.702607	−	0.711579i	$-0.252019\pi$
$683$	11.4380	+	6.60376i	0.437665	+	0.252686i	−0.264942	+	0.964264i	$0.585353\pi$
$684$			10.9365i			0.418168i
$685$	3.50136	−	6.06453i	0.133780	−	0.231714i
$686$	0.242995	+	0.420879i	0.00927758	+	0.0160692i
$687$	−8.65738	+	4.99834i	−0.330300	+	0.190699i
$688$	25.2178			0.961421
$689$	2.71484	−	4.79682i	0.103427	−	0.182744i
$690$	2.85462			0.108674
$691$	−5.74831	+	3.31879i	−0.218676	+	0.126253i	−0.605337	−	0.795969i	$-0.706962\pi$
$691$	−5.74831	+	3.31879i	−0.218676	+	0.126253i	0.386661	+	0.922222i	$0.373628\pi$
$692$	−1.43279	−	2.48166i	−0.0544665	−	0.0943387i
$693$	2.87806	−	4.98494i	0.109328	−	0.189362i
$694$			9.56103i			0.362932i
$695$	−0.677790	−	0.391322i	−0.0257100	−	0.0148437i
$696$	8.87783	+	5.12562i	0.336513	+	0.194286i
$697$		−	20.8295i		−	0.788974i
$698$	−1.91637	+	3.31926i	−0.0725358	+	0.125636i
$699$	−0.862767	−	1.49436i	−0.0326328	−	0.0565217i
$700$	5.90384	−	3.40858i	0.223144	−	0.128832i
$701$	−49.2722			−1.86099			−0.930494	−	0.366308i	$-0.880622\pi$
$701$	−49.2722			−1.86099			−0.930494	+	0.366308i	$0.880622\pi$
$702$	0.0150320	+	1.75219i	0.000567344	+	0.0661323i
$703$	29.2385			1.10275
$704$	14.3377	−	8.27789i	0.540373	−	0.311985i
$705$	−2.77986	−	4.81486i	−0.104696	−	0.181338i
$706$	−3.56767	+	6.17938i	−0.134271	+	0.232564i
$707$			2.57631i			0.0968921i
$708$	−15.9873	−	9.23029i	−0.600840	−	0.346895i
$709$	−10.0225	−	5.78651i	−0.376404	−	0.217317i	0.299848	−	0.953987i	$-0.403064\pi$
$709$	−10.0225	−	5.78651i	−0.376404	−	0.217317i	−0.676253	+	0.736670i	$0.736397\pi$
$710$			4.48842i			0.168448i
$711$	7.80736	−	13.5228i	0.292799	−	0.507143i
$712$	−11.0362	−	19.1152i	−0.413598	−	0.716373i
$713$	26.0906	−	15.0634i	0.977099	−	0.564129i
$714$	−1.13980			−0.0426561
$715$	−22.1096	+	0.189677i	−0.826852	+	0.00709351i
$716$	−34.8436			−1.30217
$717$	5.03020	−	2.90419i	0.187856	−	0.108459i
$718$	4.07563	+	7.05920i	0.152101	+	0.263447i
$719$	−6.02564	+	10.4367i	−0.224718	+	0.389224i	−0.956235	−	0.292600i	$-0.905480\pi$
$719$	−6.02564	+	10.4367i	−0.224718	+	0.389224i	0.731516	+	0.681824i	$0.238813\pi$
$720$		−	2.81113i		−	0.104765i
$721$	−8.99146	−	5.19122i	−0.334860	−	0.193331i
$722$	−8.18447	−	4.72531i	−0.304594	−	0.175858i
$723$		−	11.1202i		−	0.413565i
$724$	0.519821	−	0.900356i	0.0193190	−	0.0334615i
$725$	−10.8303	−	18.7587i	−0.402229	−	0.696681i
$726$	9.31525	−	5.37816i	0.345721	−	0.199602i
$727$	−35.1133			−1.30228			−0.651139	−	0.758958i	$-0.725709\pi$
$727$	−35.1133			−1.30228			−0.651139	+	0.758958i	$0.725709\pi$
$728$	3.34647	+	5.68309i	0.124028	+	0.210629i
$729$	1.00000			0.0370370
$730$	−3.42541	+	1.97766i	−0.126780	+	0.0731966i
$731$	11.2072	+	19.4114i	0.414513	+	0.717957i
$732$	−6.74315	+	11.6795i	−0.249234	+	0.431686i
$733$			4.72292i			0.174445i	0.996189	+	0.0872225i	$0.0277991\pi$
$733$			4.72292i			0.174445i	−0.996189	+	0.0872225i	$0.972201\pi$
$734$	−4.60461	−	2.65847i	−0.169959	−	0.0981259i
$735$	−0.922628	−	0.532679i	−0.0340316	−	0.0196482i
$736$			27.2405i			1.00410i
$737$	9.43081	−	16.3346i	0.347388	−	0.601694i
$738$	−2.15810	−	3.73794i	−0.0794408	−	0.137595i
$739$	5.24267	−	3.02686i	0.192855	−	0.111345i	−0.400464	−	0.916313i	$-0.631151\pi$
$739$	5.24267	−	3.02686i	0.192855	−	0.111345i	0.593318	+	0.804968i	$0.297818\pi$
$740$	−8.86089			−0.325733
$741$	19.4562	+	11.0116i	0.714742	+	0.404521i
$742$	0.742930			0.0272738
$743$	20.5317	−	11.8540i	0.753235	−	0.434880i	−0.0736267	−	0.997286i	$-0.523457\pi$
$743$	20.5317	−	11.8540i	0.753235	−	0.434880i	0.826862	+	0.562406i	$0.190124\pi$
$744$	4.99749	+	8.65590i	0.183217	+	0.317341i
$745$	12.0596	−	20.8879i	0.441831	−	0.765274i
$746$			3.51630i			0.128741i
$747$	−2.28036	−	1.31657i	−0.0834339	−	0.0481706i
$748$	20.6213	+	11.9057i	0.753991	+	0.435317i
$749$			17.0355i			0.622463i
$750$	2.29494	−	3.97496i	0.0837994	−	0.145145i
$751$	12.0552	+	20.8801i	0.439899	+	0.761927i	0.997681	−	0.0680602i	$-0.0216810\pi$
$751$	12.0552	+	20.8801i	0.439899	+	0.761927i	−0.557782	+	0.829987i	$0.688348\pi$
$752$	11.9254	−	6.88514i	0.434875	−	0.251075i
$753$	−9.75269			−0.355408
$754$	8.46210	−	4.98287i	0.308171	−	0.181465i
$755$	8.46436			0.308050
$756$	1.52751	−	0.881907i	0.0555549	−	0.0320747i
$757$	18.0820	+	31.3189i	0.657200	+	1.13830i	0.981337	+	0.192294i	$0.0615927\pi$
$757$	18.0820	+	31.3189i	0.657200	+	1.13830i	−0.324137	+	0.946010i	$0.605074\pi$
$758$	−0.640246	+	1.10894i	−0.0232548	+	0.0402785i
$759$		−	31.7362i		−	1.15195i
$760$	10.4642	+	6.04153i	0.379578	+	0.219149i
$761$	−11.8683	−	6.85216i	−0.430225	−	0.248390i	0.269218	−	0.963079i	$-0.413235\pi$
$761$	−11.8683	−	6.85216i	−0.430225	−	0.248390i	−0.699442	+	0.714689i	$0.746568\pi$
$762$		−	0.577165i		−	0.0209085i
$763$	−0.930628	+	1.61189i	−0.0336910	+	0.0583545i
$764$	−8.09260	−	14.0168i	−0.292780	−	0.507110i
$765$	2.16387	−	1.24931i	0.0782347	−	0.0451688i
$766$	−4.18371			−0.151163
$767$	−32.5179	+	19.1480i	−1.17415	+	0.691395i
$768$	0.270832			0.00977281
$769$	36.7196	−	21.2001i	1.32414	−	0.764494i	0.339756	−	0.940513i	$-0.389655\pi$
$769$	36.7196	−	21.2001i	1.32414	−	0.764494i	0.984387	+	0.176019i	$0.0563221\pi$
$770$	−1.49012	−	2.58097i	−0.0537003	−	0.0930116i
$771$	5.19710	−	9.00164i	0.187169	−	0.324186i
$772$		−	5.79825i		−	0.208683i
$773$	−3.66142	−	2.11392i	−0.131692	−	0.0760325i	0.432707	−	0.901535i	$-0.357559\pi$
$773$	−3.66142	−	2.11392i	−0.131692	−	0.0760325i	−0.564399	+	0.825502i	$0.690892\pi$
$774$	4.02235	+	2.32230i	0.144580	+	0.0834735i
$775$		−	21.1192i		−	0.758624i
$776$	15.3295	−	26.5515i	0.550298	−	0.953144i
$777$	−2.35775	−	4.08375i	−0.0845840	−	0.146504i
$778$	−8.40604	+	4.85323i	−0.301371	+	0.173997i
$779$	−55.0683			−1.97303
$780$	−5.89632	−	3.33713i	−0.211122	−	0.119488i
$781$	49.9000			1.78556
$782$	−5.44236	+	3.14215i	−0.194618	+	0.112363i
$783$	−2.80215	−	4.85347i	−0.100141	−	0.173449i
$784$	1.31934	−	2.28516i	0.0471191	−	0.0816127i
$785$		−	16.4990i		−	0.588875i
$786$	−6.24001	−	3.60267i	−0.222574	−	0.128503i
$787$	13.3645	+	7.71598i	0.476392	+	0.275045i	0.718912	−	0.695101i	$-0.244641\pi$
$787$	13.3645	+	7.71598i	0.476392	+	0.275045i	−0.242520	+	0.970147i	$0.577974\pi$
$788$		−	27.0223i		−	0.962628i
$789$	12.2395	−	21.1994i	0.435736	−	0.754717i
$790$	−4.04229	−	7.00144i	−0.143818	−	0.249100i
$791$	−4.12870	+	2.38371i	−0.146800	+	0.0847549i
$792$	10.5289			0.374129
$793$	13.9885	+	23.7558i	0.496746	+	0.843593i
$794$	1.38952			0.0493122
$795$	−1.41042	+	0.814305i	−0.0500223	+	0.0288804i
$796$	−12.8079	−	22.1840i	−0.453966	−	0.786291i
$797$	10.0729	−	17.4467i	0.356799	−	0.617994i	−0.630625	−	0.776088i	$-0.717201\pi$
$797$	10.0729	−	17.4467i	0.356799	−	0.617994i	0.987424	+	0.158094i	$0.0505348\pi$
$798$			3.01337i			0.106672i
$799$	10.5997	+	6.11972i	0.374989	+	0.216500i
$800$	16.5375	+	9.54795i	0.584690	+	0.337571i
$801$			12.0669i			0.426361i
$802$	−4.38015	+	7.58664i	−0.154668	+	0.267893i
$803$	21.9867	+	38.0820i	0.775893	+	1.34389i
$804$	5.00534	−	2.88983i	0.176525	−	0.101917i
$805$	−5.87384			−0.207026
$806$	9.57435	−	0.0821377i	0.337242	−	0.00289318i
$807$	5.05819			0.178057
$808$	−4.08116	+	2.35626i	−0.143575	+	0.0828929i
$809$	−17.0108	−	29.4635i	−0.598067	−	1.03588i	−0.993106	−	0.117218i	$-0.962602\pi$
$809$	−17.0108	−	29.4635i	−0.598067	−	1.03588i	0.395040	−	0.918664i	$-0.370731\pi$
$810$	0.258876	−	0.448387i	0.00909599	−	0.0157547i
$811$		−	30.0516i		−	1.05525i	−0.849477	−	0.527626i	$-0.823082\pi$
$811$		−	30.0516i		−	1.05525i	0.849477	−	0.527626i	$-0.176918\pi$
$812$	−8.56062	−	4.94247i	−0.300419	−	0.173447i
$813$	−11.7523	−	6.78518i	−0.412170	−	0.237967i
$814$		−	13.1912i		−	0.462352i
$815$	3.14074	−	5.43992i	0.110015	−	0.190552i
$816$	3.09428	+	5.35944i	0.108321	+	0.187618i
$817$	51.3192	−	29.6291i	1.79543	−	1.03659i
$818$	4.25604			0.148809
$819$	−0.0309306	−	3.60542i	−0.00108080	−	0.125984i
$820$	16.6888			0.582797
$821$	11.7870	−	6.80525i	0.411370	−	0.237505i	−0.280008	−	0.959998i	$-0.590337\pi$
$821$	11.7870	−	6.80525i	0.411370	−	0.237505i	0.691378	+	0.722493i	$0.257004\pi$
$822$	1.59723	+	2.76648i	0.0557098	+	0.0964921i
$823$	20.1300	−	34.8662i	0.701688	−	1.21536i	−0.266186	−	0.963922i	$-0.585763\pi$
$823$	20.1300	−	34.8662i	0.701688	−	1.21536i	0.967874	−	0.251437i	$-0.0809032\pi$
$824$		−	18.9913i		−	0.661593i
$825$	−19.2669	−	11.1237i	−0.670786	−	0.387278i
$826$	−4.40504	−	2.54325i	−0.153271	−	0.0884910i
$827$		−	16.6662i		−	0.579541i	−0.957096	−	0.289771i	$-0.906421\pi$
$827$		−	16.6662i		−	0.579541i	0.957096	−	0.289771i	$-0.0935790\pi$
$828$	4.86238	−	8.42189i	0.168979	−	0.292681i
$829$	6.11891	+	10.5983i	0.212518	+	0.368093i	0.952502	−	0.304532i	$-0.0985001\pi$
$829$	6.11891	+	10.5983i	0.212518	+	0.368093i	−0.739984	+	0.672625i	$0.765167\pi$
$830$	−1.18066	+	0.681655i	−0.0409814	+	0.0236606i
$831$	23.5739			0.817770
$832$	5.10792	−	9.02511i	0.177085	−	0.312889i
$833$	2.34533			0.0812608
$834$	0.309190	−	0.178511i	0.0107064	−	0.00618134i
$835$	−5.06520	−	8.77319i	−0.175289	−	0.303609i
$836$	31.4759	−	54.5179i	1.08862	−	1.88554i
$837$		−	5.46420i		−	0.188871i
$838$	−0.727654	−	0.420111i	−0.0251364	−	0.0145125i
$839$	40.5002	+	23.3828i	1.39822	+	0.807265i	0.994206	−	0.107487i	$-0.0342804\pi$
$839$	40.5002	+	23.3828i	1.39822	+	0.807265i	0.404017	+	0.914752i	$0.367614\pi$
$840$		−	1.94873i		−	0.0672374i
$841$	−1.20410	+	2.08555i	−0.0415205	+	0.0719157i
$842$	6.23103	+	10.7925i	0.214736	+	0.371933i
$843$	−12.8767	+	7.43438i	−0.443498	+	0.256054i
$844$	−29.1511			−1.00342
$845$	−11.8736	+	7.12959i	−0.408464	+	0.245265i
$846$	2.53620			0.0871965
$847$	−19.1676	+	11.0664i	−0.658607	+	0.380247i
$848$	−2.01686	−	3.49331i	−0.0692593	−	0.119961i
$849$	−10.4948	+	18.1776i	−0.360181	+	0.623852i
$850$			4.40536i			0.151103i
$851$	−22.5157	−	12.9994i	−0.771827	−	0.445615i
$852$	13.2420	+	7.64530i	0.453665	+	0.261923i
$853$			4.23317i			0.144941i	0.997371	+	0.0724704i	$0.0230883\pi$
$853$			4.23317i			0.144941i	−0.997371	+	0.0724704i	$0.976912\pi$
$854$	−1.85796	+	3.21808i	−0.0635781	+	0.110120i
$855$	−3.30288	−	5.72075i	−0.112956	−	0.195645i
$856$	−26.9861	+	15.5804i	−0.922366	+	0.532528i
$857$	12.7087			0.434122			0.217061	−	0.976158i	$-0.430353\pi$
$857$	12.7087			0.434122			0.217061	+	0.976158i	$0.430353\pi$
$858$	4.96798	−	8.77785i	0.169604	−	0.299671i
$859$	12.6692			0.432266			0.216133	−	0.976364i	$-0.430655\pi$
$859$	12.6692			0.432266			0.216133	+	0.976364i	$0.430655\pi$
$860$	−15.5526	+	8.97928i	−0.530338	+	0.306191i
$861$	4.44064	+	7.69141i	0.151336	+	0.262122i
$862$	−0.0625626	+	0.108362i	−0.00213089	+	0.00369081i
$863$			27.6136i			0.939979i	0.882672	+	0.469989i	$0.155742\pi$
$863$			27.6136i			0.939979i	−0.882672	+	0.469989i	$0.844258\pi$
$864$	4.27878	+	2.47036i	0.145567	+	0.0840432i
$865$	1.49895	+	0.865417i	0.0509657	+	0.0294251i
$866$		−	11.8232i		−	0.401770i
$867$	5.74972	−	9.95880i	0.195271	−	0.338219i
$868$	−4.81892	−	8.34662i	−0.163565	−	0.283303i
$869$	−77.8385	+	44.9401i	−2.64049	+	1.52449i
$870$	−2.90164			−0.0983749
$871$	−0.101353	−	11.8142i	−0.00343423	−	0.400310i
$872$	−3.40456			−0.115293
$873$	−14.5156	+	8.38057i	−0.491278	+	0.283639i
$874$	8.30709	+	14.3883i	0.280991	+	0.486692i
$875$	−4.72221	+	8.17911i	−0.159640	+	0.276504i
$876$			13.4745i			0.455261i
$877$	−2.23965	−	1.29306i	−0.0756275	−	0.0436636i	0.461709	−	0.887031i	$-0.347236\pi$
$877$	−2.23965	−	1.29306i	−0.0756275	−	0.0436636i	−0.537337	+	0.843368i	$0.680570\pi$
$878$	−7.16252	−	4.13528i	−0.241723	−	0.139559i
$879$		−	7.38064i		−	0.248943i
$880$	−8.09060	+	14.0133i	−0.272734	+	0.472389i
$881$	7.62486	+	13.2067i	0.256888	+	0.444943i	0.965407	−	0.260749i	$-0.0839695\pi$
$881$	7.62486	+	13.2067i	0.256888	+	0.444943i	−0.708518	+	0.705692i	$0.750636\pi$
$882$	0.420879	−	0.242995i	0.0141717	−	0.00818205i
$883$	20.9880			0.706304			0.353152	−	0.935566i	$-0.385110\pi$
$883$	20.9880			0.706304			0.353152	+	0.935566i	$0.385110\pi$
$884$	14.9146	−	0.127952i	0.501633	−	0.00430348i
$885$	11.1503			0.374815
$886$	−16.0592	+	9.27180i	−0.539521	+	0.311492i
$887$	−0.684569	−	1.18571i	−0.0229856	−	0.0398122i	0.854304	−	0.519774i	$-0.173984\pi$
$887$	−0.684569	−	1.18571i	−0.0229856	−	0.0398122i	−0.877289	+	0.479962i	$0.840651\pi$
$888$	4.31274	−	7.46989i	0.144726	−	0.250673i
$889$			1.18761i			0.0398311i
$890$	5.41062	+	3.12382i	0.181364	+	0.104711i
$891$	−4.98494	−	2.87806i	−0.167002	−	0.0964185i
$892$		−	38.2577i		−	1.28096i
$893$	16.1791	−	28.0230i	0.541412	−	0.937753i
$894$	5.50130	+	9.52853i	0.183991	+	0.318682i
$895$	18.2262	−	10.5229i	0.609236	−	0.351742i
$896$	11.2792			0.376813
$897$	−10.0869	−	17.1299i	−0.336792	−	0.571952i
$898$	−20.0877			−0.670334
$899$	−26.5203	+	15.3115i	−0.884503	+	0.510668i
$900$	−3.40858	−	5.90384i	−0.113619	−	0.196795i
$901$	1.79265	−	3.10496i	0.0597217	−	0.103441i
$902$			24.8446i			0.827233i
$903$	−8.27662	−	4.77851i	−0.275429	−	0.159019i
$904$	−7.55211	−	4.36021i	−0.251180	−	0.145019i
$905$			0.627952i			0.0208738i
$906$	−1.93061	+	3.34392i	−0.0641403	+	0.111094i
$907$	−14.3349	−	24.8288i	−0.475984	−	0.824428i	0.523638	−	0.851941i	$-0.324575\pi$
$907$	−14.3349	−	24.8288i	−0.475984	−	0.824428i	−0.999621	+	0.0275130i	$0.991241\pi$
$908$	8.30279	−	4.79362i	0.275538	−	0.159082i
$909$	2.57631			0.0854508
$910$	−1.62463	−	0.919489i	−0.0538560	−	0.0304808i
$911$	11.9761			0.396784			0.198392	−	0.980123i	$-0.436428\pi$
$911$	11.9761			0.396784			0.198392	+	0.980123i	$0.436428\pi$
$912$	14.1691	−	8.18053i	0.469186	−	0.270884i
$913$	7.57830	+	13.1260i	0.250805	+	0.434407i
$914$	4.52533	−	7.83810i	0.149685	−	0.259261i
$915$		−	8.14583i		−	0.269293i
$916$	15.2700	+	8.81614i	0.504535	+	0.291294i
$917$	12.8398	+	7.41307i	0.424008	+	0.244801i
$918$			1.13980i			0.0376192i
$919$	−13.0048	+	22.5249i	−0.428988	+	0.743029i	−0.996784	−	0.0801408i	$-0.974463\pi$
$919$	−13.0048	+	22.5249i	−0.428988	+	0.743029i	0.567796	+	0.823169i	$0.307796\pi$
$920$	−5.37213	−	9.30480i	−0.177114	−	0.306770i
$921$	22.7047	−	13.1086i	0.748146	−	0.431942i
$922$	3.69803			0.121788
$923$	26.9340	−	15.8600i	0.886544	−	0.522038i
$924$	−10.1527			−0.334000
$925$	−15.7837	+	9.11274i	−0.518966	+	0.299625i
$926$	6.12418	+	10.6074i	0.201253	+	0.348580i
$927$	−5.19122	+	8.99146i	−0.170502	+	0.295318i
$928$		−	27.6892i		−	0.908944i
$929$	−24.7855	−	14.3099i	−0.813185	−	0.469492i	0.0348760	−	0.999392i	$-0.488896\pi$
$929$	−24.7855	−	14.3099i	−0.813185	−	0.469492i	−0.848061	+	0.529899i	$0.822230\pi$
$930$	−2.45008	−	1.41455i	−0.0803413	−	0.0463850i
$931$		−	6.20049i		−	0.203213i
$932$	−1.52176	+	2.63577i	−0.0498469	+	0.0863374i
$933$	11.6865	+	20.2416i	0.382599	+	0.662681i
$934$	−7.82855	+	4.51982i	−0.256158	+	0.147893i
$935$	−14.3823			−0.470352
$936$	5.68309	−	3.34647i	0.185758	−	0.109383i
$937$	−45.1573			−1.47522			−0.737612	−	0.675225i	$-0.764047\pi$
$937$	−45.1573			−1.47522			−0.737612	+	0.675225i	$0.764047\pi$
$938$	1.37914	−	0.796244i	0.0450304	−	0.0259983i
$939$	10.2669	+	17.7827i	0.335046	+	0.580318i
$940$	−4.90316	+	8.49252i	−0.159923	+	0.276996i
$941$			33.5054i			1.09224i	0.837705	+	0.546122i	$0.183897\pi$
$941$			33.5054i			1.09224i	−0.837705	+	0.546122i	$0.816103\pi$
$942$	6.51807	+	3.76321i	0.212370	+	0.122612i
$943$	42.4064	+	24.4834i	1.38094	+	0.797288i
$944$			27.6171i			0.898859i
$945$	−0.532679	+	0.922628i	−0.0173281	+	0.0300131i
$946$	−13.3675	−	23.1531i	−0.434613	−	0.752772i
$947$	35.4712	−	20.4793i	1.15266	−	0.665488i	0.203125	−	0.979153i	$-0.434890\pi$
$947$	35.4712	−	20.4793i	1.15266	−	0.665488i	0.949534	+	0.313665i	$0.101557\pi$
$948$	−27.5415			−0.894506
$949$	23.9713	+	13.5670i	0.778142	+	0.440404i
$950$	11.6467			0.377870
$951$	2.37051	−	1.36861i	0.0768689	−	0.0443803i
$952$	2.14501	+	3.71526i	0.0695201	+	0.120412i
$953$	−13.5406	+	23.4530i	−0.438622	+	0.759716i	−0.997584	−	0.0694777i	$-0.977867\pi$
$953$	−13.5406	+	23.4530i	−0.438622	+	0.759716i	0.558961	+	0.829194i	$0.311200\pi$
$954$		−	0.742930i		−	0.0240532i
$955$	8.46626	+	4.88800i	0.273962	+	0.158172i
$956$	−8.87233	−	5.12244i	−0.286952	−	0.165672i
$957$			32.2590i			1.04279i
$958$	5.96284	−	10.3279i	0.192651	−	0.333681i
$959$	−3.28655	−	5.69247i	−0.106128	−	0.183820i
$960$	−2.65367	+	1.53210i	−0.0856468	+	0.0494482i
$961$	1.14247			0.0368538
$962$	−4.19263	−	7.12008i	−0.135176	−	0.229561i
$963$	17.0355			0.548961
$964$	−16.9862	+	9.80699i	−0.547089	+	0.315862i
$965$	1.75109	+	3.03298i	0.0563697	+	0.0976352i
$966$	1.33975	−	2.32051i	0.0431056	−	0.0746611i
$967$			57.7720i			1.85782i	0.370301	+	0.928912i	$0.379254\pi$
$967$			57.7720i			1.85782i	−0.370301	+	0.928912i	$0.620746\pi$
$968$	−35.0609	−	20.2424i	−1.12690	−	0.650616i
$969$	12.5939	+	7.27110i	0.404575	+	0.233581i
$970$			8.67813i			0.278638i
$971$	−27.8843	+	48.2970i	−0.894849	+	1.54992i	−0.0608566	+	0.998147i	$0.519383\pi$
$971$	−27.8843	+	48.2970i	−0.894849	+	1.54992i	−0.833992	+	0.551777i	$0.813950\pi$
$972$	−0.881907	−	1.52751i	−0.0282872	−	0.0489948i
$973$	−0.636208	+	0.367315i	−0.0203959	+	0.0117756i
$974$	14.9509			0.479058
$975$	−13.9350	+	0.119547i	−0.446277	+	0.00382857i
$976$	20.1755			0.645803
$977$	−25.4683	+	14.7042i	−0.814804	+	0.470427i	−0.848621	−	0.529001i	$-0.822567\pi$
$977$	−25.4683	+	14.7042i	−0.814804	+	0.470427i	0.0338172	+	0.999428i	$0.489234\pi$
$978$	1.43272	+	2.48155i	0.0458135	+	0.0793513i
$979$	34.7291	−	60.1526i	1.10995	−	1.92248i
$980$			1.87910i			0.0600255i
$981$	1.61189	+	0.930628i	0.0514638	+	0.0297127i
$982$	8.08221	+	4.66627i	0.257914	+	0.148907i
$983$		−	43.0253i		−	1.37229i	−0.727464	−	0.686146i	$-0.759301\pi$
$983$		−	43.0253i		−	1.37229i	0.727464	−	0.686146i	$-0.240699\pi$
$984$	−8.12269	+	14.0689i	−0.258942	+	0.448501i
$985$	8.16083	+	14.1350i	0.260026	+	0.450378i
$986$	5.53201	−	3.19390i	0.176175	−	0.101715i
$987$	−5.21864			−0.166111
$988$	−0.338274	−	39.4307i	−0.0107619	−	1.25446i
$989$	−52.6925			−1.67552
$990$	−2.58097	+	1.49012i	−0.0820285	+	0.0473592i
$991$	25.9615	+	44.9666i	0.824693	+	1.42841i	0.902154	+	0.431414i	$0.141985\pi$
$991$	25.9615	+	44.9666i	0.824693	+	1.42841i	−0.0774611	+	0.996995i	$0.524681\pi$
$992$	13.4985	−	23.3801i	0.428579	−	0.742320i
$993$			9.65148i			0.306280i
$994$	3.64862	+	2.10653i	0.115727	+	0.0668151i
$995$	13.3993	+	7.73611i	0.424787	+	0.245251i
$996$			4.64435i			0.147162i
$997$	4.05357	−	7.02099i	0.128378	−	0.222357i	−0.794670	−	0.607041i	$-0.792356\pi$
$997$	4.05357	−	7.02099i	0.128378	−	0.222357i	0.923048	+	0.384684i	$0.125690\pi$
$998$	3.41631	+	5.91722i	0.108141	+	0.187306i
$999$	−4.08375	+	2.35775i	−0.129204	+	0.0745960i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	273.2.bd.a.127.4	yes	16
3.2	odd	2		819.2.ct.b.127.5		16
13.2	odd	12		3549.2.a.bb.1.4		8
13.4	even	6	inner	273.2.bd.a.43.4	✓	16
13.11	odd	12		3549.2.a.bd.1.5		8
39.17	odd	6		819.2.ct.b.316.5		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
273.2.bd.a.43.4	✓	16	13.4	even	6	inner
273.2.bd.a.127.4	yes	16	1.1	even	1	trivial
819.2.ct.b.127.5		16	3.2	odd	2
819.2.ct.b.316.5		16	39.17	odd	6
3549.2.a.bb.1.4		8	13.2	odd	12
3549.2.a.bd.1.5		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)

\(f(q)\)	\(=\)	\(q+(-0.420879 + 0.242995i) q^{2} +(-0.500000 - 0.866025i) q^{3} +(-0.881907 + 1.52751i) q^{4} -1.06536i q^{5} +(0.420879 + 0.242995i) q^{6} +(-0.866025 - 0.500000i) q^{7} -1.82917i q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})\)	\(q+(-0.420879 + 0.242995i) q^{2} +(-0.500000 - 0.866025i) q^{3} +(-0.881907 + 1.52751i) q^{4} -1.06536i q^{5} +(0.420879 + 0.242995i) q^{6} +(-0.866025 - 0.500000i) q^{7} -1.82917i q^{8} +(-0.500000 + 0.866025i) q^{9} +(0.258876 + 0.448387i) q^{10} +(4.98494 - 2.87806i) q^{11} +1.76381 q^{12} +(1.77592 - 3.13785i) q^{13} +0.485989 q^{14} +(-0.922628 + 0.532679i) q^{15} +(-1.31934 - 2.28516i) q^{16} +(1.17266 - 2.03111i) q^{17} -0.485989i q^{18} +(-5.36979 - 3.10025i) q^{19} +(1.62734 + 0.939548i) q^{20} +1.00000i q^{21} +(-1.39870 + 2.42263i) q^{22} +(2.75674 + 4.77481i) q^{23} +(-1.58411 + 0.914587i) q^{24} +3.86501 q^{25} +(0.0150320 + 1.75219i) q^{26} +1.00000 q^{27} +(1.52751 - 0.881907i) q^{28} +(-2.80215 - 4.85347i) q^{29} +(0.258876 - 0.448387i) q^{30} -5.46420i q^{31} +(4.27878 + 2.47036i) q^{32} +(-4.98494 - 2.87806i) q^{33} +1.13980i q^{34} +(-0.532679 + 0.922628i) q^{35} +(-0.881907 - 1.52751i) q^{36} +(-4.08375 + 2.35775i) q^{37} +3.01337 q^{38} +(-3.60542 + 0.0309306i) q^{39} -1.94873 q^{40} +(7.69141 - 4.44064i) q^{41} +(-0.242995 - 0.420879i) q^{42} +(-4.77851 + 8.27662i) q^{43} +10.1527i q^{44} +(0.922628 + 0.532679i) q^{45} +(-2.32051 - 1.33975i) q^{46} +5.21864i q^{47} +(-1.31934 + 2.28516i) q^{48} +(0.500000 + 0.866025i) q^{49} +(-1.62670 + 0.939177i) q^{50} -2.34533 q^{51} +(3.22689 + 5.48003i) q^{52} +1.52870 q^{53} +(-0.420879 + 0.242995i) q^{54} +(-3.06616 - 5.31075i) q^{55} +(-0.914587 + 1.58411i) q^{56} +6.20049i q^{57} +(2.35873 + 1.36181i) q^{58} +(-9.06406 - 5.23314i) q^{59} -1.87910i q^{60} +(-3.82305 + 6.62171i) q^{61} +(1.32777 + 2.29977i) q^{62} +(0.866025 - 0.500000i) q^{63} +2.87621 q^{64} +(-3.34294 - 1.89199i) q^{65} +2.79741 q^{66} +(2.83779 - 1.63840i) q^{67} +(2.06836 + 3.58251i) q^{68} +(2.75674 - 4.77481i) q^{69} -0.517753i q^{70} +(7.50761 + 4.33452i) q^{71} +(1.58411 + 0.914587i) q^{72} +7.63941i q^{73} +(1.14584 - 1.98466i) q^{74} +(-1.93251 - 3.34720i) q^{75} +(9.47131 - 5.46826i) q^{76} -5.75611 q^{77} +(1.50993 - 0.889115i) q^{78} -15.6147 q^{79} +(-2.43451 + 1.40557i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(-2.15810 + 3.73794i) q^{82} +2.63313i q^{83} +(-1.52751 - 0.881907i) q^{84} +(-2.16387 - 1.24931i) q^{85} -4.64461i q^{86} +(-2.80215 + 4.85347i) q^{87} +(-5.26447 - 9.11832i) q^{88} +(10.4502 - 6.03343i) q^{89} -0.517753 q^{90} +(-3.10692 + 1.82950i) q^{91} -9.72476 q^{92} +(-4.73214 + 2.73210i) q^{93} +(-1.26810 - 2.19642i) q^{94} +(-3.30288 + 5.72075i) q^{95} -4.94071i q^{96} +(14.5156 + 8.38057i) q^{97} +(-0.420879 - 0.242995i) q^{98} +5.75611i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 8 q^{3} + 6 q^{4} - 8 q^{9}+O(q^{10}) \) 16 * q - 8 * q^3 + 6 * q^4 - 8 * q^9	\( 16 q - 8 q^{3} + 6 q^{4} - 8 q^{9} - 4 q^{10} - 12 q^{11} - 12 q^{12} + 4 q^{13} + 4 q^{14} - 10 q^{16} + 10 q^{17} + 6 q^{20} - 2 q^{22} - 2 q^{23} + 12 q^{25} + 20 q^{26} + 16 q^{27} + 12 q^{29} - 4 q^{30} + 30 q^{32} + 12 q^{33} - 2 q^{35} + 6 q^{36} + 18 q^{37} - 32 q^{38} - 8 q^{39} - 60 q^{40} + 18 q^{41} - 2 q^{42} - 10 q^{43} + 30 q^{46} - 10 q^{48} + 8 q^{49} - 24 q^{50} - 20 q^{51} - 26 q^{52} + 12 q^{53} + 10 q^{55} + 12 q^{56} - 54 q^{58} - 60 q^{59} - 6 q^{61} + 16 q^{62} + 16 q^{64} - 20 q^{65} + 4 q^{66} - 18 q^{67} - 20 q^{68} - 2 q^{69} + 6 q^{71} + 18 q^{74} - 6 q^{75} + 72 q^{76} - 16 q^{77} + 14 q^{78} - 4 q^{79} + 30 q^{80} - 8 q^{81} - 18 q^{82} - 24 q^{85} + 12 q^{87} - 2 q^{88} + 78 q^{89} + 8 q^{90} - 8 q^{91} - 20 q^{92} + 6 q^{93} + 16 q^{94} - 4 q^{95} - 54 q^{97}+O(q^{100}) \) 16 * q - 8 * q^3 + 6 * q^4 - 8 * q^9 - 4 * q^10 - 12 * q^11 - 12 * q^12 + 4 * q^13 + 4 * q^14 - 10 * q^16 + 10 * q^17 + 6 * q^20 - 2 * q^22 - 2 * q^23 + 12 * q^25 + 20 * q^26 + 16 * q^27 + 12 * q^29 - 4 * q^30 + 30 * q^32 + 12 * q^33 - 2 * q^35 + 6 * q^36 + 18 * q^37 - 32 * q^38 - 8 * q^39 - 60 * q^40 + 18 * q^41 - 2 * q^42 - 10 * q^43 + 30 * q^46 - 10 * q^48 + 8 * q^49 - 24 * q^50 - 20 * q^51 - 26 * q^52 + 12 * q^53 + 10 * q^55 + 12 * q^56 - 54 * q^58 - 60 * q^59 - 6 * q^61 + 16 * q^62 + 16 * q^64 - 20 * q^65 + 4 * q^66 - 18 * q^67 - 20 * q^68 - 2 * q^69 + 6 * q^71 + 18 * q^74 - 6 * q^75 + 72 * q^76 - 16 * q^77 + 14 * q^78 - 4 * q^79 + 30 * q^80 - 8 * q^81 - 18 * q^82 - 24 * q^85 + 12 * q^87 - 2 * q^88 + 78 * q^89 + 8 * q^90 - 8 * q^91 - 20 * q^92 + 6 * q^93 + 16 * q^94 - 4 * q^95 - 54 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more