LMFDB - Embedded newform 231.2.p.a.208.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [231,2,Mod(10,231)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(231, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 1, 3]))

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

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

chi := DirichletCharacter("231.10");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 231 = 3 \cdot 7 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	231.p (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:	$1.84454428669$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$16$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			208.3
Character	$\chi$	$=$	231.208
Dual form			231.2.p.a.10.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.71613 - 0.990810i) q^{2} +(0.866025 - 0.500000i) q^{3} +(0.963407 + 1.66867i) q^{4} +(0.315938 + 0.182407i) q^{5} -1.98162 q^{6} +(0.143176 - 2.64187i) q^{7} +0.145025i q^{8} +(0.500000 - 0.866025i) q^{9} +O(q^{10})$	\(q+(-1.71613 - 0.990810i) q^{2} +(0.866025 - 0.500000i) q^{3} +(0.963407 + 1.66867i) q^{4} +(0.315938 + 0.182407i) q^{5} -1.98162 q^{6} +(0.143176 - 2.64187i) q^{7} +0.145025i q^{8} +(0.500000 - 0.866025i) q^{9} +(-0.361461 - 0.626069i) q^{10} +(-2.10292 - 2.56471i) q^{11} +(1.66867 + 0.963407i) q^{12} +5.43170 q^{13} +(-2.86330 + 4.39195i) q^{14} +0.364814 q^{15} +(2.07051 - 3.58622i) q^{16} +(-2.93710 - 5.08721i) q^{17} +(-1.71613 + 0.990810i) q^{18} +(-1.11224 + 1.92646i) q^{19} +0.702929i q^{20} +(-1.19694 - 2.35952i) q^{21} +(1.06774 + 6.48497i) q^{22} +(-1.38495 + 2.39880i) q^{23} +(0.0725127 + 0.125596i) q^{24} +(-2.43346 - 4.21487i) q^{25} +(-9.32152 - 5.38178i) q^{26} -1.00000i q^{27} +(4.54636 - 2.30629i) q^{28} -2.01743i q^{29} +(-0.626069 - 0.361461i) q^{30} +(-4.99947 + 2.88645i) q^{31} +(-6.85534 + 3.95793i) q^{32} +(-3.10353 - 1.16965i) q^{33} +11.6404i q^{34} +(0.527131 - 0.808553i) q^{35} +1.92681 q^{36} +(4.00554 - 6.93780i) q^{37} +(3.81751 - 2.20404i) q^{38} +(4.70399 - 2.71585i) q^{39} +(-0.0264536 + 0.0458191i) q^{40} +8.88534 q^{41} +(-0.283721 + 5.23519i) q^{42} +5.90706i q^{43} +(2.25369 - 5.97994i) q^{44} +(0.315938 - 0.182407i) q^{45} +(4.75351 - 2.74444i) q^{46} +(5.45165 + 3.14751i) q^{47} -4.14101i q^{48} +(-6.95900 - 0.756509i) q^{49} +9.64436i q^{50} +(-5.08721 - 2.93710i) q^{51} +(5.23294 + 9.06372i) q^{52} +(6.47002 + 11.2064i) q^{53} +(-0.990810 + 1.71613i) q^{54} +(-0.196570 - 1.19388i) q^{55} +(0.383139 + 0.0207642i) q^{56} +2.22448i q^{57} +(-1.99888 + 3.46217i) q^{58} +(7.39894 - 4.27178i) q^{59} +(0.351465 + 0.608755i) q^{60} +(1.35352 - 2.34437i) q^{61} +11.4397 q^{62} +(-2.21634 - 1.44493i) q^{63} +7.40420 q^{64} +(1.71608 + 0.990781i) q^{65} +(4.16718 + 5.08228i) q^{66} +(7.30735 + 12.6567i) q^{67} +(5.65925 - 9.80210i) q^{68} +2.76990i q^{69} +(-1.70575 + 0.865297i) q^{70} +2.64558 q^{71} +(0.125596 + 0.0725127i) q^{72} +(2.91182 + 5.04342i) q^{73} +(-13.7481 + 7.93746i) q^{74} +(-4.21487 - 2.43346i) q^{75} -4.28617 q^{76} +(-7.07673 + 5.18844i) q^{77} -10.7636 q^{78} +(-1.59178 - 0.919015i) q^{79} +(1.30831 - 0.755350i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(-15.2484 - 8.80368i) q^{82} -5.21418 q^{83} +(2.78412 - 4.27048i) q^{84} -2.14299i q^{85} +(5.85278 - 10.1373i) q^{86} +(-1.00871 - 1.74714i) q^{87} +(0.371948 - 0.304976i) q^{88} +(-0.367796 - 0.212347i) q^{89} -0.722923 q^{90} +(0.777692 - 14.3499i) q^{91} -5.33708 q^{92} +(-2.88645 + 4.99947i) q^{93} +(-6.23717 - 10.8031i) q^{94} +(-0.702799 + 0.405761i) q^{95} +(-3.95793 + 6.85534i) q^{96} +10.0948i q^{97} +(11.1930 + 8.19331i) q^{98} +(-3.27256 + 0.538824i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q + 12 q^{4} - 12 q^{5} + 16 q^{9}+O(q^{10}) $ 32 * q + 12 * q^4 - 12 * q^5 + 16 * q^9	$ 32 q + 12 q^{4} - 12 q^{5} + 16 q^{9} + 2 q^{11} - 32 q^{14} + 8 q^{15} - 20 q^{16} + 8 q^{22} + 24 q^{23} - 24 q^{26} - 12 q^{31} - 18 q^{33} + 24 q^{36} - 32 q^{37} + 24 q^{38} - 24 q^{42} - 28 q^{44} - 12 q^{45} + 24 q^{47} - 36 q^{49} + 36 q^{53} - 56 q^{56} + 12 q^{58} - 48 q^{59} + 8 q^{64} - 36 q^{66} + 20 q^{67} + 24 q^{70} + 72 q^{71} + 24 q^{75} - 48 q^{78} + 72 q^{80} - 16 q^{81} - 48 q^{82} + 64 q^{86} + 24 q^{88} + 60 q^{89} - 28 q^{91} - 16 q^{92} + 16 q^{93} + 4 q^{99}+O(q^{100}) $ 32 * q + 12 * q^4 - 12 * q^5 + 16 * q^9 + 2 * q^11 - 32 * q^14 + 8 * q^15 - 20 * q^16 + 8 * q^22 + 24 * q^23 - 24 * q^26 - 12 * q^31 - 18 * q^33 + 24 * q^36 - 32 * q^37 + 24 * q^38 - 24 * q^42 - 28 * q^44 - 12 * q^45 + 24 * q^47 - 36 * q^49 + 36 * q^53 - 56 * q^56 + 12 * q^58 - 48 * q^59 + 8 * q^64 - 36 * q^66 + 20 * q^67 + 24 * q^70 + 72 * q^71 + 24 * q^75 - 48 * q^78 + 72 * q^80 - 16 * q^81 - 48 * q^82 + 64 * q^86 + 24 * q^88 + 60 * q^89 - 28 * q^91 - 16 * q^92 + 16 * q^93 + 4 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/231\mathbb{Z}\right)^\times$.

$n$	$155$	$199$	$211$
$\chi(n)$	$1$	$e\left(\frac{5}{6}\right)$	$-1$

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 $

$2$	−1.71613	−	0.990810i	−1.21349	−	0.700608i	−0.249971	−	0.968253i	$-0.580421\pi$
$2$	−1.71613	−	0.990810i	−1.21349	−	0.700608i	−0.963518	+	0.267645i	$0.913755\pi$
$3$	0.866025	−	0.500000i	0.500000	−	0.288675i
$3$	0.866025	−	0.500000i	0.500000	−	0.288675i
$4$	0.963407	+	1.66867i	0.481704	+	0.834335i
$5$	0.315938	+	0.182407i	0.141292	+	0.0815749i	0.568980	−	0.822352i	$-0.307338\pi$
$5$	0.315938	+	0.182407i	0.141292	+	0.0815749i	−0.427688	+	0.903927i	$0.640672\pi$
$6$	−1.98162			−0.808993
$7$	0.143176	−	2.64187i	0.0541156	−	0.998535i
$7$	0.143176	−	2.64187i	0.0541156	−	0.998535i
$8$			0.145025i			0.0512742i
$9$	0.500000	−	0.866025i	0.166667	−	0.288675i
$10$	−0.361461	−	0.626069i	−0.114304	−	0.197981i
$11$	−2.10292	−	2.56471i	−0.634053	−	0.773289i
$11$	−2.10292	−	2.56471i	−0.634053	−	0.773289i
$12$	1.66867	+	0.963407i	0.481704	+	0.278112i
$13$	5.43170			1.50648			0.753242	−	0.657744i	$-0.228489\pi$
$13$	5.43170			1.50648			0.753242	+	0.657744i	$0.228489\pi$
$14$	−2.86330	+	4.39195i	−0.765250	+	1.17380i
$15$	0.364814			0.0941946
$16$	2.07051	−	3.58622i	0.517627	−	0.896556i
$17$	−2.93710	−	5.08721i	−0.712351	−	1.23383i	−0.963972	−	0.266003i	$-0.914297\pi$
$17$	−2.93710	−	5.08721i	−0.712351	−	1.23383i	0.251621	−	0.967826i	$-0.419036\pi$
$18$	−1.71613	+	0.990810i	−0.404496	+	0.233536i
$19$	−1.11224	+	1.92646i	−0.255166	+	0.441960i	−0.964940	−	0.262469i	$-0.915463\pi$
$19$	−1.11224	+	1.92646i	−0.255166	+	0.441960i	0.709775	+	0.704429i	$0.248797\pi$
$20$			0.702929i			0.157180i
$21$	−1.19694	−	2.35952i	−0.261194	−	0.514889i
$22$	1.06774	+	6.48497i	0.227644	+	1.38260i
$23$	−1.38495	+	2.39880i	−0.288782	+	0.500185i	−0.973519	−	0.228605i	$-0.926584\pi$
$23$	−1.38495	+	2.39880i	−0.288782	+	0.500185i	0.684737	+	0.728790i	$0.259917\pi$
$24$	0.0725127	+	0.125596i	0.0148016	+	0.0256371i
$25$	−2.43346	−	4.21487i	−0.486691	−	0.842974i
$26$	−9.32152	−	5.38178i	−1.82810	−	1.05545i
$27$		−	1.00000i		−	0.192450i
$28$	4.54636	−	2.30629i	0.859180	−	0.435847i
$29$		−	2.01743i		−	0.374627i	−0.982300	−	0.187313i	$-0.940022\pi$
$29$		−	2.01743i		−	0.374627i	0.982300	−	0.187313i	$-0.0599779\pi$
$30$	−0.626069	−	0.361461i	−0.114304	−	0.0659935i
$31$	−4.99947	+	2.88645i	−0.897931	+	0.518421i	−0.876528	−	0.481350i	$-0.840147\pi$
$31$	−4.99947	+	2.88645i	−0.897931	+	0.518421i	−0.0214029	+	0.999771i	$0.506813\pi$
$32$	−6.85534	+	3.95793i	−1.21186	+	0.699670i
$33$	−3.10353	−	1.16965i	−0.540256	−	0.203609i
$34$			11.6404i			1.99632i
$35$	0.527131	−	0.808553i	0.0891015	−	0.136670i
$36$	1.92681			0.321136
$37$	4.00554	−	6.93780i	0.658507	−	1.14057i	−0.322495	−	0.946571i	$-0.604521\pi$
$37$	4.00554	−	6.93780i	0.658507	−	1.14057i	0.981002	−	0.193997i	$-0.0621452\pi$
$38$	3.81751	−	2.20404i	0.619281	−	0.357542i
$39$	4.70399	−	2.71585i	0.753242	−	0.434884i
$40$	−0.0264536	+	0.0458191i	−0.00418269	+	0.00724463i
$41$	8.88534			1.38766			0.693829	−	0.720140i	$-0.255922\pi$
$41$	8.88534			1.38766			0.693829	+	0.720140i	$0.255922\pi$
$42$	−0.283721	+	5.23519i	−0.0437791	+	0.807807i
$43$			5.90706i			0.900819i	0.892822	+	0.450409i	$0.148722\pi$
$43$			5.90706i			0.900819i	−0.892822	+	0.450409i	$0.851278\pi$
$44$	2.25369	−	5.97994i	0.339757	−	0.901509i
$45$	0.315938	−	0.182407i	0.0470973	−	0.0271916i
$46$	4.75351	−	2.74444i	0.700867	−	0.404646i
$47$	5.45165	+	3.14751i	0.795205	+	0.459112i	0.841792	−	0.539802i	$-0.181501\pi$
$47$	5.45165	+	3.14751i	0.795205	+	0.459112i	−0.0465868	+	0.998914i	$0.514834\pi$
$48$		−	4.14101i		−	0.597704i
$49$	−6.95900	−	0.756509i	−0.994143	−	0.108073i
$50$			9.64436i			1.36392i
$51$	−5.08721	−	2.93710i	−0.712351	−	0.411276i
$52$	5.23294	+	9.06372i	0.725679	+	1.25691i
$53$	6.47002	+	11.2064i	0.888725	+	1.53932i	0.841384	+	0.540438i	$0.181742\pi$
$53$	6.47002	+	11.2064i	0.888725	+	1.53932i	0.0473417	+	0.998879i	$0.484925\pi$
$54$	−0.990810	+	1.71613i	−0.134832	+	0.233536i
$55$	−0.196570	−	1.19388i	−0.0265056	−	0.160982i
$56$	0.383139	+	0.0207642i	0.0511991	+	0.00277474i
$57$			2.22448i			0.294640i
$58$	−1.99888	+	3.46217i	−0.262466	+	0.454605i
$59$	7.39894	−	4.27178i	0.963260	−	0.556139i	0.0660854	−	0.997814i	$-0.478949\pi$
$59$	7.39894	−	4.27178i	0.963260	−	0.556139i	0.897175	+	0.441675i	$0.145616\pi$
$60$	0.351465	+	0.608755i	0.0453739	+	0.0785899i
$61$	1.35352	−	2.34437i	0.173301	−	0.300166i	−0.766271	−	0.642517i	$-0.777890\pi$
$61$	1.35352	−	2.34437i	0.173301	−	0.300166i	0.939572	+	0.342352i	$0.111223\pi$
$62$	11.4397			1.45284
$63$	−2.21634	−	1.44493i	−0.279233	−	0.182044i
$64$	7.40420			0.925525
$65$	1.71608	+	0.990781i	0.212854	+	0.122891i
$66$	4.16718	+	5.08228i	0.512944	+	0.625585i
$67$	7.30735	+	12.6567i	0.892735	+	1.54626i	0.836583	+	0.547840i	$0.184550\pi$
$67$	7.30735	+	12.6567i	0.892735	+	1.54626i	0.0561520	+	0.998422i	$0.482117\pi$
$68$	5.65925	−	9.80210i	0.686285	−	1.18868i
$69$			2.76990i			0.333457i
$70$	−1.70575	+	0.865297i	−0.203876	+	0.103423i
$71$	2.64558			0.313973			0.156987	−	0.987601i	$-0.449822\pi$
$71$	2.64558			0.313973			0.156987	+	0.987601i	$0.449822\pi$
$72$	0.125596	+	0.0725127i	0.0148016	+	0.00854570i
$73$	2.91182	+	5.04342i	0.340802	+	0.590287i	0.984582	−	0.174924i	$-0.0559679\pi$
$73$	2.91182	+	5.04342i	0.340802	+	0.590287i	−0.643779	+	0.765211i	$0.722635\pi$
$74$	−13.7481	+	7.93746i	−1.59818	+	0.922711i
$75$	−4.21487	−	2.43346i	−0.486691	−	0.280991i
$76$	−4.28617			−0.491657
$77$	−7.07673	+	5.18844i	−0.806469	+	0.591277i
$78$	−10.7636			−1.21873
$79$	−1.59178	−	0.919015i	−0.179089	−	0.103397i	0.407775	−	0.913082i	$-0.366305\pi$
$79$	−1.59178	−	0.919015i	−0.179089	−	0.103397i	−0.586865	+	0.809685i	$0.699638\pi$
$80$	1.30831	−	0.755350i	0.146273	−	0.0844507i
$81$	−0.500000	−	0.866025i	−0.0555556	−	0.0962250i
$82$	−15.2484	−	8.80368i	−1.68391	−	0.972204i
$83$	−5.21418			−0.572330			−0.286165	−	0.958180i	$-0.592381\pi$
$83$	−5.21418			−0.572330			−0.286165	+	0.958180i	$0.592381\pi$
$84$	2.78412	−	4.27048i	0.303772	−	0.465948i
$85$		−	2.14299i		−	0.232440i
$86$	5.85278	−	10.1373i	0.631121	−	1.09313i
$87$	−1.00871	−	1.74714i	−0.108145	−	0.187313i
$88$	0.371948	−	0.304976i	0.0396498	−	0.0325106i
$89$	−0.367796	−	0.212347i	−0.0389863	−	0.0225087i	0.480380	−	0.877060i	$-0.340499\pi$
$89$	−0.367796	−	0.212347i	−0.0389863	−	0.0225087i	−0.519366	+	0.854552i	$0.673832\pi$
$90$	−0.722923			−0.0762027
$91$	0.777692	−	14.3499i	0.0815243	−	1.50428i
$92$	−5.33708			−0.556429
$93$	−2.88645	+	4.99947i	−0.299310	+	0.518421i
$94$	−6.23717	−	10.8031i	−0.643315	−	1.11425i
$95$	−0.702799	+	0.405761i	−0.0721057	+	0.0416302i
$96$	−3.95793	+	6.85534i	−0.403955	+	0.699670i
$97$			10.0948i			1.02497i	0.858695	+	0.512487i	$0.171276\pi$
$97$			10.0948i			1.02497i	−0.858695	+	0.512487i	$0.828724\pi$
$98$	11.1930	+	8.19331i	1.13066	+	0.827650i
$99$	−3.27256	+	0.538824i	−0.328905	+	0.0541538i
$100$	4.68882	−	8.12127i	0.468882	−	0.812127i
$101$	−7.62305	−	13.2035i	−0.758522	−	1.31380i	−0.943604	−	0.331075i	$-0.892589\pi$
$101$	−7.62305	−	13.2035i	−0.758522	−	1.31380i	0.185083	−	0.982723i	$-0.440745\pi$
$102$	5.82021	+	10.0809i	0.576287	+	0.998159i
$103$	−4.57538	−	2.64160i	−0.450826	−	0.260284i	0.257353	−	0.966317i	$-0.417150\pi$
$103$	−4.57538	−	2.64160i	−0.450826	−	0.260284i	−0.708179	+	0.706033i	$0.750483\pi$
$104$			0.787735i			0.0772438i
$105$	0.0522328	−	0.963793i	0.00509740	−	0.0940566i
$106$		−	25.6422i		−	2.49059i
$107$	3.38728	+	1.95565i	0.327461	+	0.189060i	0.654713	−	0.755877i	$-0.272789\pi$
$107$	3.38728	+	1.95565i	0.327461	+	0.189060i	−0.327252	+	0.944937i	$0.606123\pi$
$108$	1.66867	−	0.963407i	0.160568	−	0.0927039i
$109$	5.50618	−	3.17899i	0.527396	−	0.304492i	−0.212559	−	0.977148i	$-0.568180\pi$
$109$	5.50618	−	3.17899i	0.527396	−	0.304492i	0.739955	+	0.672656i	$0.234847\pi$
$110$	−0.845564	+	2.24362i	−0.0806214	+	0.213920i
$111$		−	8.01109i		−	0.760379i
$112$	−9.17790	−	5.98348i	−0.867230	−	0.565386i
$113$	4.20066			0.395165			0.197582	−	0.980286i	$-0.436691\pi$
$113$	4.20066			0.395165			0.197582	+	0.980286i	$0.436691\pi$
$114$	2.20404	−	3.81751i	0.206427	−	0.357542i
$115$	−0.875117	+	0.505249i	−0.0816051	+	0.0471147i
$116$	3.36642	−	1.94360i	0.312564	−	0.180459i
$117$	2.71585	−	4.70399i	0.251081	−	0.434884i
$118$	−16.9301			−1.55854
$119$	−13.8603	+	7.03108i	−1.27057	+	0.644538i
$120$			0.0529073i			0.00482975i
$121$	−2.15548	+	10.7867i	−0.195953	+	0.980613i
$122$	−4.64565	+	2.68216i	−0.420597	+	0.242832i
$123$	7.69493	−	4.44267i	0.693829	−	0.400582i
$124$	−9.63305	−	5.56165i	−0.865074	−	0.499451i
$125$		−	3.59959i		−	0.321957i
$126$	2.37188	+	4.67567i	0.211304	+	0.416542i
$127$			14.3427i			1.27271i	0.771396	+	0.636356i	$0.219559\pi$
$127$			14.3427i			1.27271i	−0.771396	+	0.636356i	$0.780441\pi$
$128$	1.00409	+	0.579713i	0.0887501	+	0.0512399i
$129$	2.95353	+	5.11567i	0.260044	+	0.450409i
$130$	−1.96335	−	3.40062i	−0.172197	−	0.298254i
$131$	−2.55274	+	4.42148i	−0.223034	+	0.386307i	−0.955728	−	0.294252i	$-0.904930\pi$
$131$	−2.55274	+	4.42148i	−0.223034	+	0.386307i	0.732694	+	0.680559i	$0.238263\pi$
$132$	−1.03821	−	6.30562i	−0.0903649	−	0.548834i
$133$	4.93021	+	3.21423i	0.427504	+	0.278709i
$134$		−	28.9608i		−	2.50183i
$135$	0.182407	−	0.315938i	0.0156991	−	0.0271916i
$136$	0.737774	−	0.425954i	0.0632636	−	0.0365253i
$137$	1.19506	+	2.06991i	0.102101	+	0.176845i	0.912550	−	0.408965i	$-0.134110\pi$
$137$	1.19506	+	2.06991i	0.102101	+	0.176845i	−0.810449	+	0.585809i	$0.800777\pi$
$138$	2.74444	−	4.75351i	0.233622	−	0.404646i
$139$	−16.1644			−1.37104			−0.685522	−	0.728052i	$-0.740426\pi$
$139$	−16.1644			−1.37104			−0.685522	+	0.728052i	$0.740426\pi$
$140$	1.85705	+	0.100643i	0.156949	+	0.00850588i
$141$	6.29502			0.530137
$142$	−4.54017	−	2.62127i	−0.381003	−	0.219972i
$143$	−11.4224	−	13.9308i	−0.955191	−	1.16495i
$144$	−2.07051	−	3.58622i	−0.172542	−	0.298852i
$145$	0.367993	−	0.637382i	0.0305601	−	0.0529317i
$146$		−	11.5402i		−	0.955076i
$147$	−6.40493	+	2.82434i	−0.528269	+	0.232948i
$148$	15.4359			1.26882
$149$	15.9785	+	9.22518i	1.30901	+	0.755756i	0.981931	−	0.189241i	$-0.0606029\pi$
$149$	15.9785	+	9.22518i	1.30901	+	0.755756i	0.327077	+	0.944998i	$0.393936\pi$
$150$	4.82218	+	8.35226i	0.393729	+	0.681959i
$151$	−8.36660	+	4.83046i	−0.680864	+	0.393097i	−0.800180	−	0.599759i	$-0.795263\pi$
$151$	−8.36660	+	4.83046i	−0.680864	+	0.393097i	0.119317	+	0.992856i	$0.461930\pi$
$152$	−0.279385	−	0.161303i	−0.0226611	−	0.0130834i
$153$	−5.87420			−0.474901
$154$	17.2854	−	1.89235i	1.39289	−	0.152490i
$155$	−2.10603			−0.169161
$156$	9.06372	+	5.23294i	0.725679	+	0.418971i
$157$	−11.4917	+	6.63471i	−0.917134	+	0.529508i	−0.882720	−	0.469900i	$-0.844290\pi$
$157$	−11.4917	+	6.63471i	−0.917134	+	0.529508i	−0.0344145	+	0.999408i	$0.510957\pi$
$158$	1.82114	+	3.15430i	0.144882	+	0.250943i
$159$	11.2064	+	6.47002i	0.888725	+	0.513106i
$160$	−2.88782			−0.228302
$161$	6.13904	+	4.00231i	0.483824	+	0.315427i
$162$			1.98162i			0.155691i
$163$	3.96651	−	6.87020i	0.310681	−	0.538115i	−0.667829	−	0.744315i	$-0.732776\pi$
$163$	3.96651	−	6.87020i	0.310681	−	0.538115i	0.978510	+	0.206199i	$0.0661096\pi$
$164$	8.56020	+	14.8267i	0.668440	+	1.15777i
$165$	−0.767174	−	0.935643i	−0.0597244	−	0.0728397i
$166$	8.94822	+	5.16626i	0.694516	+	0.400979i
$167$	0.682227			0.0527923			0.0263961	−	0.999652i	$-0.491597\pi$
$167$	0.682227			0.0527923			0.0263961	+	0.999652i	$0.491597\pi$
$168$	0.342190	−	0.173587i	0.0264005	−	0.0133925i
$169$	16.5034			1.26949
$170$	−2.12330	+	3.67766i	−0.162849	+	0.282063i
$171$	1.11224	+	1.92646i	0.0850552	+	0.147320i
$172$	−9.85694	+	5.69091i	−0.751585	+	0.433928i
$173$	−0.749385	+	1.29797i	−0.0569747	+	0.0986831i	−0.893106	−	0.449846i	$-0.851479\pi$
$173$	−0.749385	+	1.29797i	−0.0569747	+	0.0986831i	0.836131	+	0.548529i	$0.184812\pi$
$174$			3.99777i			0.303070i
$175$	−11.4836	+	5.82541i	−0.868076	+	0.440360i
$176$	−13.5517	+	2.23128i	−1.02150	+	0.168189i
$177$	4.27178	−	7.39894i	0.321087	−	0.556139i
$178$	0.420791	+	0.728832i	0.0315396	+	0.0546282i
$179$	3.10621	+	5.38012i	0.232169	+	0.402129i	0.958446	−	0.285273i	$-0.0920844\pi$
$179$	3.10621	+	5.38012i	0.232169	+	0.402129i	−0.726277	+	0.687402i	$0.758751\pi$
$180$	0.608755	+	0.351465i	0.0453739	+	0.0261966i
$181$		−	9.87854i		−	0.734266i	−0.930168	−	0.367133i	$-0.880339\pi$
$181$		−	9.87854i		−	0.734266i	0.930168	−	0.367133i	$-0.119661\pi$
$182$	−15.5526	+	23.8558i	−1.15284	+	1.76831i
$183$		−	2.70704i		−	0.200110i
$184$	−0.347887	−	0.200853i	−0.0256466	−	0.0148071i
$185$	2.53101	−	1.46128i	0.186083	−	0.107435i
$186$	9.90705	−	5.71984i	0.726420	−	0.419399i
$187$	−6.87074	+	18.2308i	−0.502438	+	1.33317i
$188$			12.1293i			0.884623i
$189$	−2.64187	−	0.143176i	−0.192168	−	0.0104146i
$190$	1.60813			0.116666
$191$	−0.439746	+	0.761663i	−0.0318189	+	0.0551120i	−0.881496	−	0.472191i	$-0.843463\pi$
$191$	−0.439746	+	0.761663i	−0.0318189	+	0.0551120i	0.849677	+	0.527303i	$0.176797\pi$
$192$	6.41222	−	3.70210i	0.462762	−	0.267176i
$193$	19.3467	−	11.1698i	1.39261	−	0.804022i	0.399003	−	0.916950i	$-0.369356\pi$
$193$	19.3467	−	11.1698i	1.39261	−	0.804022i	0.993603	+	0.112928i	$0.0360229\pi$
$194$	10.0020	−	17.3240i	0.718105	−	1.24379i
$195$	1.98156			0.141903
$196$	−5.44199	−	12.3411i	−0.388714	−	0.881508i
$197$			1.93301i			0.137721i	0.997626	+	0.0688607i	$0.0219364\pi$
$197$			1.93301i			0.137721i	−0.997626	+	0.0688607i	$0.978064\pi$
$198$	6.15002	+	2.31779i	0.437063	+	0.164718i
$199$	−1.75591	+	1.01378i	−0.124473	+	0.0718648i	−0.560944	−	0.827854i	$-0.689562\pi$
$199$	−1.75591	+	1.01378i	−0.124473	+	0.0718648i	0.436470	+	0.899719i	$0.356228\pi$
$200$	0.611263	−	0.352913i	0.0432228	−	0.0249547i
$201$	12.6567	+	7.30735i	0.892735	+	0.515421i
$202$			30.2120i			2.12571i
$203$	−5.32978	−	0.288848i	−0.374078	−	0.0202731i
$204$		−	11.3185i		−	0.792453i
$205$	2.80722	+	1.62075i	0.196065	+	0.113198i
$206$	5.23464	+	9.06666i	0.364715	+	0.631704i
$207$	1.38495	+	2.39880i	0.0962606	+	0.166728i
$208$	11.2464	−	19.4793i	0.779796	−	1.35065i
$209$	7.27976	−	1.19860i	0.503551	−	0.0829092i
$210$	−1.04457	+	1.60224i	−0.0720824	+	0.110565i
$211$			8.17186i			0.562574i	0.959624	+	0.281287i	$0.0907612\pi$
$211$			8.17186i			0.562574i	−0.959624	+	0.281287i	$0.909239\pi$
$212$	−12.4665	+	21.5927i	−0.856204	+	1.48299i
$213$	2.29114	−	1.32279i	0.156987	−	0.0906362i
$214$	−3.87535	−	6.71230i	−0.264913	−	0.458844i
$215$	−1.07749	+	1.86627i	−0.0734842	+	0.127278i
$216$	0.145025			0.00986773
$217$	6.90982	+	13.6212i	0.469069	+	0.924670i
$218$	−12.5991			−0.853319
$219$	5.04342	+	2.91182i	0.340802	+	0.196762i
$220$	1.80281	−	1.47820i	0.121545	−	0.0996603i
$221$	−15.9535	−	27.6322i	−1.07315	−	1.85874i
$222$	−7.93746	+	13.7481i	−0.532728	+	0.922711i
$223$		−	24.2491i		−	1.62384i	−0.583767	−	0.811921i	$-0.698422\pi$
$223$		−	24.2491i		−	1.62384i	0.583767	−	0.811921i	$-0.301578\pi$
$224$	9.47483	+	18.6776i	0.633064	+	1.24795i
$225$	−4.86691			−0.324461
$226$	−7.20889	−	4.16205i	−0.479528	−	0.276856i
$227$	1.68016	+	2.91012i	0.111516	+	0.193151i	0.916382	−	0.400306i	$-0.131096\pi$
$227$	1.68016	+	2.91012i	0.111516	+	0.193151i	−0.804866	+	0.593457i	$0.797763\pi$
$228$	−3.71193	+	2.14308i	−0.245828	+	0.141929i
$229$	−18.9480	−	10.9396i	−1.25212	−	0.722910i	−0.280587	−	0.959828i	$-0.590529\pi$
$229$	−18.9480	−	10.9396i	−1.25212	−	0.722910i	−0.971530	+	0.236918i	$0.923863\pi$
$230$	2.00242			0.132036
$231$	−3.53441	+	8.03168i	−0.232547	+	0.528446i
$232$	0.292578			0.0192087
$233$	6.88201	+	3.97333i	0.450856	+	0.260302i	0.708192	−	0.706020i	$-0.249511\pi$
$233$	6.88201	+	3.97333i	0.450856	+	0.260302i	−0.257336	+	0.966322i	$0.582845\pi$
$234$	−9.32152	+	5.38178i	−0.609367	+	0.351818i
$235$	1.14826	+	1.98884i	0.0749040	+	0.129738i
$236$	14.2564	+	8.23093i	0.928012	+	0.535788i
$237$	−1.83803			−0.119393
$238$	30.7526	+	1.66664i	1.99339	+	0.108032i
$239$		−	18.3659i		−	1.18799i	−0.804467	−	0.593997i	$-0.797549\pi$
$239$		−	18.3659i		−	1.18799i	0.804467	−	0.593997i	$-0.202451\pi$
$240$	0.755350	−	1.30831i	0.0487576	−	0.0844507i
$241$	4.58938	+	7.94904i	0.295628	+	0.512043i	0.975131	−	0.221630i	$-0.0711378\pi$
$241$	4.58938	+	7.94904i	0.295628	+	0.512043i	−0.679503	+	0.733673i	$0.737804\pi$
$242$	14.3867	−	16.3758i	0.924813	−	1.05268i
$243$	−0.866025	−	0.500000i	−0.0555556	−	0.0320750i
$244$	5.21597			0.333918
$245$	−2.06062	−	1.50838i	−0.131648	−	0.0963669i
$246$	−17.6074			−1.12260
$247$	−6.04137	+	10.4640i	−0.384403	+	0.665805i
$248$	−0.418608	−	0.725050i	−0.0265816	−	0.0460407i
$249$	−4.51561	+	2.60709i	−0.286165	+	0.165218i
$250$	−3.56651	+	6.17737i	−0.225566	+	0.390691i
$251$		−	25.7949i		−	1.62816i	−0.580752	−	0.814080i	$-0.697242\pi$
$251$		−	25.7949i		−	1.62816i	0.580752	−	0.814080i	$-0.302758\pi$
$252$	0.275875	−	5.09040i	0.0173785	−	0.320665i
$253$	9.06467	−	1.49249i	0.569891	−	0.0938318i
$254$	14.2109	−	24.6140i	0.891672	−	1.54442i
$255$	−1.07150	−	1.85588i	−0.0670997	−	0.116220i
$256$	−8.55297	−	14.8142i	−0.534561	−	0.925886i
$257$	−5.11786	−	2.95480i	−0.319243	−	0.184315i	0.331812	−	0.943346i	$-0.392340\pi$
$257$	−5.11786	−	2.95480i	−0.319243	−	0.184315i	−0.651055	+	0.759030i	$0.725673\pi$
$258$		−	11.7056i		−	0.728756i
$259$	−17.7553	−	11.5755i	−1.10326	−	0.719265i
$260$			3.81810i			0.236789i
$261$	−1.74714	−	1.00871i	−0.108145	−	0.0624378i
$262$	8.76170	−	5.05857i	0.541299	−	0.312519i
$263$	−16.8128	+	9.70685i	−1.03672	+	0.598550i	−0.918902	−	0.394485i	$-0.870923\pi$
$263$	−16.8128	+	9.70685i	−1.03672	+	0.598550i	−0.117817	+	0.993035i	$0.537590\pi$
$264$	0.169628	−	0.450091i	0.0104399	−	0.0277012i
$265$			4.72071i			0.289991i
$266$	−5.27622	−	10.4009i	−0.323506	−	0.637723i
$267$	−0.424694			−0.0259909
$268$	−14.0799	+	24.3871i	−0.860067	+	1.48968i
$269$	−24.5994	+	14.2025i	−1.49985	+	0.865940i	−1.00000		0.000170607i	$-0.999946\pi$
$269$	−24.5994	+	14.2025i	−1.49985	+	0.865940i	−0.499852	+	0.866111i	$0.666612\pi$
$270$	−0.626069	+	0.361461i	−0.0381014	+	0.0219978i
$271$	7.89059	−	13.6669i	0.479319	−	0.830205i	−0.520399	−	0.853923i	$-0.674217\pi$
$271$	7.89059	−	13.6669i	0.479319	−	0.830205i	0.999719	+	0.0237176i	$0.00755024\pi$
$272$	−24.3251			−1.47493
$273$	−6.50144	−	12.8162i	−0.393485	−	0.775672i
$274$		−	4.73633i		−	0.286132i
$275$	−5.69257	+	15.1046i	−0.343275	+	0.910843i
$276$	−4.62205	+	2.66854i	−0.278215	+	0.160627i
$277$	14.7731	−	8.52924i	0.887628	−	0.512472i	0.0144621	−	0.999895i	$-0.495396\pi$
$277$	14.7731	−	8.52924i	0.887628	−	0.512472i	0.873166	+	0.487423i	$0.162063\pi$
$278$	27.7402	+	16.0158i	1.66375	+	0.960565i
$279$			5.77289i			0.345614i
$280$	0.117261	+	0.0764474i	0.00700767	+	0.00456861i
$281$			26.5761i			1.58540i	0.609612	+	0.792700i	$0.291325\pi$
$281$			26.5761i			1.58540i	−0.609612	+	0.792700i	$0.708675\pi$
$282$	−10.8031	−	6.23717i	−0.643315	−	0.371418i
$283$	4.78709	+	8.29148i	0.284563	+	0.492877i	0.972503	−	0.232890i	$-0.0748182\pi$
$283$	4.78709	+	8.29148i	0.284563	+	0.492877i	−0.687940	+	0.725767i	$0.741485\pi$
$284$	2.54878	+	4.41461i	0.151242	+	0.261959i
$285$	−0.405761	+	0.702799i	−0.0240352	+	0.0416302i
$286$	5.79967	+	35.2245i	0.342941	+	2.08287i
$287$	1.27217	−	23.4740i	0.0750940	−	1.38562i
$288$			7.91586i			0.466447i
$289$	−8.75312	+	15.1608i	−0.514889	+	0.891814i
$290$	−1.26305	+	0.729221i	−0.0741688	+	0.0428213i
$291$	5.04741	+	8.74237i	0.295884	+	0.512487i
$292$	−5.61053	+	9.71773i	−0.328332	+	0.568687i
$293$	−16.8865			−0.986518			−0.493259	−	0.869883i	$-0.664194\pi$
$293$	−16.8865			−0.986518			−0.493259	+	0.869883i	$0.664194\pi$
$294$	13.7901	+	1.49911i	0.804254	+	0.0874300i
$295$	3.11681			0.181468
$296$	1.00616	+	0.580905i	0.0584817	+	0.0337644i
$297$	−2.56471	+	2.10292i	−0.148820	+	0.122024i
$298$	−18.2808	−	31.6633i	−1.05898	−	1.83420i
$299$	−7.52263	+	13.0296i	−0.435045	+	0.753520i
$300$		−	9.37764i		−	0.541418i
$301$	15.6057	+	0.845753i	0.899499	+	0.0487484i
$302$	19.1443			1.10163
$303$	−13.2035	−	7.62305i	−0.758522	−	0.437933i
$304$	4.60581	+	7.97749i	0.264161	+	0.457541i
$305$	0.855259	−	0.493784i	0.0489720	−	0.0282740i
$306$	10.0809	+	5.82021i	0.576287	+	0.332720i
$307$	−1.57027			−0.0896199			−0.0448099	−	0.998996i	$-0.514268\pi$
$307$	−1.57027			−0.0896199			−0.0448099	+	0.998996i	$0.514268\pi$
$308$	−15.4756	−	6.81016i	−0.881802	−	0.388045i
$309$	−5.28319			−0.300550
$310$	3.61423	+	2.08668i	0.205274	+	0.118515i
$311$	20.8470	−	12.0360i	1.18212	−	0.682499i	0.225619	−	0.974216i	$-0.427560\pi$
$311$	20.8470	−	12.0360i	1.18212	−	0.682499i	0.956505	+	0.291716i	$0.0942264\pi$
$312$	0.393867	+	0.682198i	0.0222984	+	0.0386219i
$313$	0.413571	+	0.238775i	0.0233764	+	0.0134964i	0.511643	−	0.859198i	$-0.329037\pi$
$313$	0.413571	+	0.238775i	0.0233764	+	0.0134964i	−0.488266	+	0.872695i	$0.662371\pi$
$314$	26.2949			1.48391
$315$	−0.436662	−	0.860786i	−0.0246031	−	0.0484998i
$316$		−	3.54154i		−	0.199227i
$317$	4.70710	−	8.15293i	0.264377	−	0.457914i	−0.703023	−	0.711167i	$-0.748167\pi$
$317$	4.70710	−	8.15293i	0.264377	−	0.457914i	0.967400	+	0.253253i	$0.0815004\pi$
$318$	−12.8211	−	22.2068i	−0.718972	−	1.24530i
$319$	−5.17411	+	4.24248i	−0.289695	+	0.237533i
$320$	2.33927	+	1.35058i	0.130769	+	0.0754996i
$321$	3.91130			0.218307
$322$	−6.56988	−	12.9511i	−0.366125	−	0.721738i
$323$	13.0671			0.727070
$324$	0.963407	−	1.66867i	0.0535226	−	0.0927039i
$325$	−13.2178	−	22.8939i	−0.733192	−	1.26993i
$326$	−13.6141	+	7.86011i	−0.754016	+	0.435331i
$327$	3.17899	−	5.50618i	0.175799	−	0.304492i
$328$			1.28860i			0.0711510i
$329$	9.09588	−	13.9519i	0.501472	−	0.769195i
$330$	0.389528	+	2.36581i	0.0214428	+	0.130234i
$331$	−9.39932	+	16.2801i	−0.516633	+	0.894835i	0.483180	+	0.875521i	$0.339482\pi$
$331$	−9.39932	+	16.2801i	−0.516633	+	0.894835i	−0.999813	+	0.0193142i	$0.993852\pi$
$332$	−5.02338	−	8.70074i	−0.275694	−	0.477515i
$333$	−4.00554	−	6.93780i	−0.219502	−	0.380189i
$334$	−1.17079	−	0.675957i	−0.0640629	−	0.0369867i
$335$			5.33165i			0.291299i
$336$	−10.9400	−	0.592896i	−0.596828	−	0.0323451i
$337$			5.47186i			0.298071i	0.988832	+	0.149036i	$0.0476169\pi$
$337$			5.47186i			0.298071i	−0.988832	+	0.149036i	$0.952383\pi$
$338$	−28.3220	−	16.3517i	−1.54052	−	0.889417i
$339$	3.63788	−	2.10033i	0.197582	−	0.114074i
$340$	3.57595	−	2.06457i	0.193933	−	0.111967i
$341$	17.9164	+	6.75224i	0.970226	+	0.365654i
$342$		−	4.40808i		−	0.238362i
$343$	−2.99497	+	18.2765i	−0.161713	+	0.986838i
$344$	−0.856674			−0.0461888
$345$	−0.505249	+	0.875117i	−0.0272017	+	0.0471147i
$346$	2.57209	−	1.48500i	0.138276	−	0.0798339i
$347$	15.3867	−	8.88350i	0.826000	−	0.476891i	−0.0264813	−	0.999649i	$-0.508430\pi$
$347$	15.3867	−	8.88350i	0.826000	−	0.476891i	0.852481	+	0.522758i	$0.175097\pi$
$348$	1.94360	−	3.36642i	0.104188	−	0.180459i
$349$	30.5643			1.63607			0.818035	−	0.575169i	$-0.195064\pi$
$349$	30.5643			1.63607			0.818035	+	0.575169i	$0.195064\pi$
$350$	25.4792	+	1.38085i	1.36192	+	0.0738093i
$351$		−	5.43170i		−	0.289923i
$352$	24.5672	+	9.25876i	1.30943	+	0.493494i
$353$	14.2411	−	8.22211i	0.757978	−	0.437619i	−0.0705915	−	0.997505i	$-0.522489\pi$
$353$	14.2411	−	8.22211i	0.757978	−	0.437619i	0.828569	+	0.559887i	$0.189155\pi$
$354$	−14.6619	+	8.46504i	−0.779271	+	0.449912i
$355$	0.835841	+	0.482573i	0.0443619	+	0.0256123i
$356$		−	0.818307i		−	0.0433702i
$357$	−8.48782	+	13.0192i	−0.449223	+	0.689051i
$358$		−	12.3107i		−	0.650639i
$359$	−29.0708	−	16.7841i	−1.53430	−	0.885828i	−0.999156	−	0.0410671i	$-0.986924\pi$
$359$	−29.0708	−	16.7841i	−1.53430	−	0.885828i	−0.535143	−	0.844761i	$-0.679742\pi$
$360$	0.0264536	+	0.0458191i	0.00139423	+	0.00241488i
$361$	7.02584	+	12.1691i	0.369781	+	0.640479i
$362$	−9.78775	+	16.9529i	−0.514433	+	0.891024i
$363$	3.52667	+	10.4193i	0.185102	+	0.546873i
$364$	24.6945	−	12.5271i	1.29434	−	0.656597i
$365$			2.12454i			0.111204i
$366$	−2.68216	+	4.64565i	−0.140199	+	0.242832i
$367$	5.26096	−	3.03742i	0.274620	−	0.158552i	−0.356365	−	0.934347i	$-0.615984\pi$
$367$	5.26096	−	3.03742i	0.274620	−	0.158552i	0.630985	+	0.775795i	$0.282651\pi$
$368$	5.73509	+	9.93348i	0.298962	+	0.517818i
$369$	4.44267	−	7.69493i	0.231276	−	0.400582i
$370$	−5.79140			−0.301080
$371$	30.5323	−	15.4885i	1.58516	−	0.804122i
$372$	−11.1233			−0.576716
$373$	−30.2576	−	17.4692i	−1.56668	−	0.904522i	−0.996553	−	0.0829641i	$-0.973561\pi$
$373$	−30.2576	−	17.4692i	−1.56668	−	0.904522i	−0.570125	−	0.821558i	$-0.693105\pi$
$374$	29.8543	−	24.4788i	1.54373	−	1.26577i
$375$	−1.79979	−	3.11733i	−0.0929410	−	0.160978i
$376$	−0.456469	+	0.790628i	−0.0235406	+	0.0407735i
$377$		−	10.9581i		−	0.564369i
$378$	4.39195	+	2.86330i	0.225897	+	0.147272i
$379$	−14.1967			−0.729235			−0.364617	−	0.931157i	$-0.618800\pi$
$379$	−14.1967			−0.729235			−0.364617	+	0.931157i	$0.618800\pi$
$380$	−1.35416	−	0.781827i	−0.0694671	−	0.0401069i
$381$	7.17137	+	12.4212i	0.367400	+	0.636356i
$382$	1.50933	−	0.871409i	0.0772238	−	0.0445852i
$383$	16.3497	+	9.43952i	0.835432	+	0.482337i	0.855709	−	0.517458i	$-0.173121\pi$
$383$	16.3497	+	9.43952i	0.835432	+	0.482337i	−0.0202770	+	0.999794i	$0.506455\pi$
$384$	1.15943			0.0591667
$385$	−3.18222	+	0.348379i	−0.162181	+	0.0177551i
$386$	−44.2687			−2.25322
$387$	5.11567	+	2.95353i	0.260044	+	0.150136i
$388$	−16.8449	+	9.72542i	−0.855172	+	0.493734i
$389$	1.82144	+	3.15483i	0.0923508	+	0.159956i	0.908500	−	0.417885i	$-0.137229\pi$
$389$	1.82144	+	3.15483i	0.0923508	+	0.159956i	−0.816149	+	0.577841i	$0.803895\pi$
$390$	−3.40062	−	1.96335i	−0.172197	−	0.0994181i
$391$	16.2709			0.822857
$392$	0.109713	−	1.00923i	0.00554134	−	0.0509739i
$393$			5.10549i			0.257538i
$394$	1.91525	−	3.31731i	0.0964888	−	0.167123i
$395$	−0.335270	−	0.580704i	−0.0168692	−	0.0292184i
$396$	−4.05193	−	4.94172i	−0.203617	−	0.248331i
$397$	16.2129	+	9.36051i	0.813701	+	0.469790i	0.848239	−	0.529613i	$-0.177663\pi$
$397$	16.2129	+	9.36051i	0.813701	+	0.469790i	−0.0345385	+	0.999403i	$0.510996\pi$
$398$	4.01784			0.201396
$399$	5.87680	+	0.318494i	0.294208	+	0.0159446i
$400$	−20.1539			−1.00770
$401$	−9.72588	+	16.8457i	−0.485687	+	0.841235i	−0.999865	−	0.0164490i	$-0.994764\pi$
$401$	−9.72588	+	16.8457i	−0.485687	+	0.841235i	0.514178	+	0.857684i	$0.328097\pi$
$402$	−14.4804	−	25.0808i	−0.722216	−	1.25091i
$403$	−27.1556	+	15.6783i	−1.35272	+	0.780993i
$404$	14.6882	−	25.4407i	0.730765	−	1.26572i
$405$		−	0.364814i		−	0.0181278i
$406$	8.86042	+	5.77650i	0.439735	+	0.286683i
$407$	−26.2168	+	4.31656i	−1.29952	+	0.213964i
$408$	0.425954	−	0.737774i	0.0210879	−	0.0365253i
$409$	2.00889	+	3.47950i	0.0993331	+	0.172050i	0.911409	−	0.411502i	$-0.134996\pi$
$409$	2.00889	+	3.47950i	0.0993331	+	0.172050i	−0.812076	+	0.583552i	$0.801662\pi$
$410$	−3.21171	−	5.56284i	−0.158615	−	0.274729i
$411$	2.06991	+	1.19506i	0.102101	+	0.0589482i
$412$		−	10.1797i		−	0.501519i
$413$	−10.2262	−	20.1587i	−0.503196	−	0.991945i
$414$		−	5.48888i		−	0.269764i
$415$	−1.64736	−	0.951103i	−0.0808656	−	0.0466878i
$416$	−37.2362	+	21.4983i	−1.82565	+	1.05404i
$417$	−13.9988	+	8.08218i	−0.685522	+	0.395786i
$418$	−13.6806	−	5.15589i	−0.669141	−	0.252183i
$419$			18.7760i			0.917268i	0.888625	+	0.458634i	$0.151661\pi$
$419$			18.7760i			0.917268i	−0.888625	+	0.458634i	$0.848339\pi$
$420$	1.65857	−	0.841366i	0.0809301	−	0.0410545i
$421$	37.7836			1.84146			0.920730	−	0.390201i	$-0.127594\pi$
$421$	37.7836			1.84146			0.920730	+	0.390201i	$0.127594\pi$
$422$	8.09675	−	14.0240i	0.394144	−	0.682677i
$423$	5.45165	−	3.14751i	0.265068	−	0.153037i
$424$	−1.62521	+	0.938317i	−0.0789273	+	0.0455687i
$425$	−14.2946	+	24.7590i	−0.693390	+	1.20099i
$426$	−5.24254			−0.254002
$427$	−5.99974	−	3.91149i	−0.290348	−	0.189290i
$428$			7.53634i			0.364283i
$429$	−16.8575	−	6.35317i	−0.813887	−	0.306734i
$430$	3.69823	−	2.13517i	0.178345	−	0.102967i
$431$	10.5902	−	6.11424i	0.510111	−	0.294512i	−0.222769	−	0.974871i	$-0.571509\pi$
$431$	10.5902	−	6.11424i	0.510111	−	0.294512i	0.732879	+	0.680359i	$0.238176\pi$
$432$	−3.58622	−	2.07051i	−0.172542	−	0.0996173i
$433$		−	15.0598i		−	0.723726i	−0.932231	−	0.361863i	$-0.882141\pi$
$433$		−	15.0598i		−	0.723726i	0.932231	−	0.361863i	$-0.117859\pi$
$434$	1.63789	−	30.2222i	0.0786213	−	1.45071i
$435$		−	0.735985i		−	0.0352878i
$436$	10.6094	+	6.12533i	0.508097	+	0.293350i
$437$	−3.08080	−	5.33609i	−0.147374	−	0.255260i
$438$	−5.77011	−	9.99413i	−0.275707	−	0.477538i
$439$	7.66796	−	13.2813i	0.365972	−	0.633882i	−0.622960	−	0.782254i	$-0.714070\pi$
$439$	7.66796	−	13.2813i	0.365972	−	0.633882i	0.988932	+	0.148372i	$0.0474033\pi$
$440$	0.173142	−	0.0285077i	0.00825424	−	0.00135905i
$441$	−4.13466	+	5.64842i	−0.196888	+	0.268972i
$442$			63.2274i			3.00742i
$443$	−7.86874	+	13.6291i	−0.373855	+	0.647536i	−0.990155	−	0.139975i	$-0.955298\pi$
$443$	−7.86874	+	13.6291i	−0.373855	+	0.647536i	0.616300	+	0.787512i	$0.288631\pi$
$444$	13.3679	−	7.71794i	0.634411	−	0.366277i
$445$	−0.0774672	−	0.134177i	−0.00367230	−	0.00636061i
$446$	−24.0263	+	41.6147i	−1.13768	+	1.97051i
$447$	18.4504			0.872672
$448$	1.06011	−	19.5610i	0.0500854	−	0.924169i
$449$	−14.0305			−0.662142			−0.331071	−	0.943606i	$-0.607410\pi$
$449$	−14.0305			−0.662142			−0.331071	+	0.943606i	$0.607410\pi$
$450$	8.35226	+	4.82218i	0.393729	+	0.227320i
$451$	−18.6851	−	22.7883i	−0.879849	−	1.07306i
$452$	4.04695	+	7.00951i	0.190352	+	0.329700i
$453$	−4.83046	+	8.36660i	−0.226955	+	0.393097i
$454$		−	6.65886i		−	0.312516i
$455$	2.86322	−	4.39182i	0.134230	−	0.205892i
$456$	−0.322606			−0.0151074
$457$	28.3403	+	16.3623i	1.32570	+	0.765396i	0.984632	−	0.174642i	$-0.0558767\pi$
$457$	28.3403	+	16.3623i	1.32570	+	0.765396i	0.341072	+	0.940037i	$0.389210\pi$
$458$	21.6782	+	37.5477i	1.01295	+	1.75449i
$459$	−5.08721	+	2.93710i	−0.237450	+	0.137092i
$460$	−1.68619	−	0.973521i	−0.0786189	−	0.0453907i
$461$	−17.3441			−0.807795			−0.403897	−	0.914804i	$-0.632345\pi$
$461$	−17.3441			−0.807795			−0.403897	+	0.914804i	$0.632345\pi$
$462$	14.0234	−	10.2815i	0.652427	−	0.478339i
$463$	−28.3707			−1.31850			−0.659250	−	0.751924i	$-0.729126\pi$
$463$	−28.3707			−1.31850			−0.659250	+	0.751924i	$0.729126\pi$
$464$	−7.23494	−	4.17709i	−0.335874	−	0.193917i
$465$	−1.82388	+	1.05302i	−0.0845803	+	0.0488325i
$466$	−7.87363	−	13.6375i	−0.364739	−	0.631746i
$467$	−30.8759	−	17.8262i	−1.42877	−	0.824899i	−0.431744	−	0.901996i	$-0.642102\pi$
$467$	−30.8759	−	17.8262i	−1.42877	−	0.824899i	−0.997024	+	0.0770966i	$0.975435\pi$
$468$	10.4659			0.483786
$469$	34.4837	−	17.4930i	1.59231	−	0.807750i
$470$		−	4.55082i		−	0.209913i
$471$	−6.63471	+	11.4917i	−0.305711	+	0.529508i
$472$	0.619517	+	1.07303i	0.0285156	+	0.0493904i
$473$	15.1499	−	12.4221i	0.696594	−	0.571167i
$474$	3.15430	+	1.82114i	0.144882	+	0.0836476i
$475$	10.8264			0.496747
$476$	−25.0857	−	16.3545i	−1.14980	−	0.749605i
$477$	12.9400			0.592483
$478$	−18.1972	+	31.5184i	−0.832318	+	1.44162i
$479$	13.1341	+	22.7489i	0.600111	+	1.03942i	0.992804	+	0.119753i	$0.0382103\pi$
$479$	13.1341	+	22.7489i	0.600111	+	1.03942i	−0.392693	+	0.919670i	$0.628456\pi$
$480$	−2.50092	+	1.44391i	−0.114151	+	0.0659051i
$481$	21.7569	−	37.6841i	0.992031	−	1.71825i
$482$		−	18.1888i		−	0.828478i
$483$	7.31772	+	0.396584i	0.332968	+	0.0180452i
$484$	−20.0761	+	6.79524i	−0.912552	+	0.308874i
$485$	−1.84137	+	3.18934i	−0.0836121	+	0.144820i
$486$	0.990810	+	1.71613i	0.0449440	+	0.0778454i
$487$	13.2119	+	22.8836i	0.598687	+	1.03696i	0.993015	+	0.117987i	$0.0376441\pi$
$487$	13.2119	+	22.8836i	0.598687	+	1.03696i	−0.394328	+	0.918970i	$0.629023\pi$
$488$	0.339993	+	0.196295i	0.0153908	+	0.00888586i
$489$		−	7.93302i		−	0.358744i
$490$	2.04178	+	4.63027i	0.0922383	+	0.209174i
$491$		−	16.9030i		−	0.762823i	−0.924405	−	0.381412i	$-0.875438\pi$
$491$		−	16.9030i		−	0.762823i	0.924405	−	0.381412i	$-0.124562\pi$
$492$	14.8267	+	8.56020i	0.668440	+	0.385924i
$493$	−10.2631	+	5.92538i	−0.462225	+	0.266866i
$494$	20.7356	−	11.9717i	0.932937	−	0.538632i
$495$	−1.13221	−	0.426704i	−0.0508892	−	0.0191789i
$496$			23.9056i			1.07339i
$497$	0.378785	−	6.98930i	0.0169909	−	0.313513i
$498$	10.3325			0.463011
$499$	12.8090	−	22.1859i	0.573411	−	0.993178i	−0.422801	−	0.906223i	$-0.638953\pi$
$499$	12.8090	−	22.1859i	0.573411	−	0.993178i	0.996212	−	0.0869550i	$-0.0277136\pi$
$500$	6.00653	−	3.46787i	0.268620	−	0.155088i
$501$	0.590826	−	0.341113i	0.0263961	−	0.0152398i
$502$	−25.5579	+	44.2675i	−1.14070	+	1.97576i
$503$	11.1759			0.498307			0.249153	−	0.968464i	$-0.419848\pi$
$503$	11.1759			0.498307			0.249153	+	0.968464i	$0.419848\pi$
$504$	0.209552	−	0.321426i	0.00933418	−	0.0143174i
$505$		−	5.56199i		−	0.247505i
$506$	−17.0349	−	6.42005i	−0.757295	−	0.285406i
$507$	14.2924	−	8.25171i	0.634747	−	0.366471i
$508$	−23.9333	+	13.8179i	−1.06187	+	0.613070i
$509$	−14.0836	−	8.13115i	−0.624243	−	0.360407i	0.154276	−	0.988028i	$-0.450695\pi$
$509$	−14.0836	−	8.13115i	−0.624243	−	0.360407i	−0.778519	+	0.627621i	$0.784029\pi$
$510$			4.24659i			0.188042i
$511$	13.7410	−	6.97056i	0.607865	−	0.308359i
$512$			31.5786i			1.39559i
$513$	1.92646	+	1.11224i	0.0850552	+	0.0491066i
$514$	5.85528	+	10.1416i	0.258265	+	0.447329i
$515$	−0.963692	−	1.66916i	−0.0424653	−	0.0735521i
$516$	−5.69091	+	9.85694i	−0.250528	+	0.433928i
$517$	−3.39191	−	20.6009i	−0.149176	−	0.906025i
$518$	19.0014	+	37.4572i	0.834872	+	1.64577i
$519$			1.49877i			0.0657887i
$520$	−0.143688	+	0.248876i	−0.00630115	+	0.0109139i
$521$	−34.1873	+	19.7380i	−1.49777	+	0.864739i	−0.999997	−	0.00256769i	$-0.999183\pi$
$521$	−34.1873	+	19.7380i	−1.49777	+	0.864739i	−0.497775	+	0.867306i	$0.665849\pi$
$522$	1.99888	+	3.46217i	0.0874888	+	0.151535i
$523$	−2.70950	+	4.69299i	−0.118478	+	0.205210i	−0.919165	−	0.393873i	$-0.871135\pi$
$523$	−2.70950	+	4.69299i	−0.118478	+	0.205210i	0.800687	+	0.599083i	$0.204468\pi$
$524$	−9.83733			−0.429746
$525$	−7.03235	+	10.7867i	−0.306917	+	0.470772i
$526$	38.4706			1.67740
$527$	29.3679	+	16.9556i	1.27929	+	0.738596i
$528$	−10.6205	+	8.70821i	−0.462198	+	0.378976i
$529$	7.66383	+	13.2741i	0.333210	+	0.577137i
$530$	4.67732	−	8.10136i	0.203170	−	0.351901i
$531$		−	8.54356i		−	0.370759i
$532$	−0.613678	+	11.3235i	−0.0266063	+	0.490936i
$533$	48.2626			2.09048
$534$	0.728832	+	0.420791i	0.0315396	+	0.0182094i
$535$	0.713448	+	1.23573i	0.0308450	+	0.0534252i
$536$	−1.83554	+	1.05975i	−0.0792834	+	0.0457743i
$537$	5.38012	+	3.10621i	0.232169	+	0.134043i
$538$	56.2878			2.42674
$539$	12.6940	+	19.4387i	0.546768	+	0.837284i
$540$	0.702929			0.0302493
$541$	−34.5920	−	19.9717i	−1.48723	−	0.858651i	−0.487334	−	0.873216i	$-0.662030\pi$
$541$	−34.5920	−	19.9717i	−1.48723	−	0.858651i	−0.999894	+	0.0145646i	$0.995364\pi$
$542$	−27.0826	+	15.6361i	−1.16330	+	0.671630i
$543$	−4.93927	−	8.55507i	−0.211964	−	0.367133i
$544$	40.2696	+	23.2497i	1.72655	+	0.996822i
$545$	2.31948			0.0993557
$546$	−1.54109	+	28.4360i	−0.0659526	+	1.21695i
$547$		−	16.5342i		−	0.706952i	−0.935444	−	0.353476i	$-0.885000\pi$
$547$		−	16.5342i		−	0.706952i	0.935444	−	0.353476i	$-0.115000\pi$
$548$	−2.30267	+	3.98834i	−0.0983651	+	0.170373i
$549$	−1.35352	−	2.34437i	−0.0577669	−	0.100055i
$550$	24.7350	−	20.2813i	1.05470	−	0.864797i
$551$	3.88649	+	2.24386i	0.165570	+	0.0955918i
$552$	−0.401706			−0.0170977
$553$	−2.65583	+	4.07370i	−0.112937	+	0.173232i
$554$	−33.8034			−1.43617
$555$	1.46128	−	2.53101i	0.0620278	−	0.107435i
$556$	−15.5729	−	26.9730i	−0.660437	−	1.14391i
$557$	−17.1555	+	9.90471i	−0.726900	+	0.419676i	−0.817287	−	0.576231i	$-0.804523\pi$
$557$	−17.1555	+	9.90471i	−0.726900	+	0.419676i	0.0903867	+	0.995907i	$0.471190\pi$
$558$	5.71984	−	9.90705i	0.242140	−	0.419399i
$559$			32.0854i			1.35707i
$560$	−1.80822	−	3.56453i	−0.0764113	−	0.150629i
$561$	3.16516	+	19.2237i	0.133633	+	0.811625i
$562$	26.3319	−	45.6082i	1.11074	−	1.92386i
$563$	2.13380	+	3.69585i	0.0899289	+	0.155761i	0.907481	−	0.420093i	$-0.138003\pi$
$563$	2.13380	+	3.69585i	0.0899289	+	0.155761i	−0.817552	+	0.575855i	$0.804669\pi$
$564$	6.06467	+	10.5043i	0.255369	+	0.442312i
$565$	1.32715	+	0.766230i	0.0558336	+	0.0322355i
$566$		−	18.9724i		−	0.797468i
$567$	−2.35952	+	1.19694i	−0.0990905	+	0.0502669i
$568$			0.383677i			0.0160987i
$569$	−10.1806	−	5.87778i	−0.426793	−	0.246409i	0.271186	−	0.962527i	$-0.412584\pi$
$569$	−10.1806	−	5.87778i	−0.426793	−	0.246409i	−0.697980	+	0.716118i	$0.745917\pi$
$570$	1.39268	−	0.804064i	0.0583330	−	0.0336785i
$571$	−17.2181	+	9.94087i	−0.720554	+	0.416012i	−0.814957	−	0.579522i	$-0.803239\pi$
$571$	−17.2181	+	9.94087i	−0.720554	+	0.416012i	0.0944023	+	0.995534i	$0.469906\pi$
$572$	12.2414	−	32.4812i	0.511838	−	1.35811i
$573$			0.879492i			0.0367413i
$574$	−25.4414	+	39.0239i	−1.06191	+	1.62883i
$575$	13.4808			0.562190
$576$	3.70210	−	6.41222i	0.154254	−	0.267176i
$577$	−0.243841	+	0.140782i	−0.0101513	+	0.00586083i	−0.505067	−	0.863080i	$-0.668532\pi$
$577$	−0.243841	+	0.140782i	−0.0101513	+	0.00586083i	0.494916	+	0.868941i	$0.335199\pi$
$578$	30.0430	−	17.3453i	1.24962	−	0.721471i
$579$	11.1698	−	19.3467i	0.464202	−	0.804022i
$580$	1.41811			0.0588837
$581$	−0.746548	+	13.7752i	−0.0309720	+	0.571492i
$582$		−	20.0041i		−	0.829196i
$583$	15.1353	−	40.1598i	0.626839	−	1.66325i
$584$	−0.731423	+	0.422287i	−0.0302665	+	0.0174744i
$585$	1.71608	−	0.990781i	0.0709513	−	0.0409638i
$586$	28.9794	+	16.7313i	1.19713	+	0.691163i
$587$			2.55977i			0.105653i	0.998604	+	0.0528265i	$0.0168230\pi$
$587$			2.55977i			0.105653i	−0.998604	+	0.0528265i	$0.983177\pi$
$588$	−10.8835	−	7.96672i	−0.448826	−	0.328542i
$589$		−	12.8417i		−	0.529133i
$590$	−5.34886	−	3.08817i	−0.220209	−	0.127138i
$591$	0.966506	+	1.67404i	0.0397568	+	0.0688607i
$592$	−16.5870	−	28.7296i	−0.681722	−	1.18078i
$593$	−8.67463	+	15.0249i	−0.356224	+	0.616998i	−0.987327	−	0.158701i	$-0.949269\pi$
$593$	−8.67463	+	15.0249i	−0.356224	+	0.616998i	0.631102	+	0.775699i	$0.282603\pi$
$594$	6.48497	−	1.06774i	0.266082	−	0.0438100i
$595$	−5.66151	−	0.306826i	−0.232099	−	0.0125786i
$596$			35.5504i			1.45620i
$597$	−1.01378	+	1.75591i	−0.0414911	+	0.0718648i
$598$	25.8197	−	14.9070i	1.05585	−	0.609592i
$599$	−3.42921	−	5.93957i	−0.140114	−	0.242684i	0.787426	−	0.616410i	$-0.211414\pi$
$599$	−3.42921	−	5.93957i	−0.140114	−	0.242684i	−0.927539	+	0.373726i	$0.878080\pi$
$600$	0.352913	−	0.611263i	0.0144076	−	0.0249547i
$601$	−1.68577			−0.0687641			−0.0343821	−	0.999409i	$-0.510946\pi$
$601$	−1.68577			−0.0687641			−0.0343821	+	0.999409i	$0.510946\pi$
$602$	−25.9435	−	16.9137i	−1.05738	−	0.689352i
$603$	14.6147			0.595157
$604$	−16.1209	−	9.30740i	−0.655949	−	0.378713i
$605$	−2.64858	+	3.01477i	−0.107680	+	0.122568i
$606$	15.1060	+	26.1643i	0.613638	+	1.06285i
$607$	8.25751	−	14.3024i	0.335162	−	0.580518i	−0.648354	−	0.761339i	$-0.724542\pi$
$607$	8.25751	−	14.3024i	0.335162	−	0.580518i	0.983516	+	0.180821i	$0.0578756\pi$
$608$		−	17.6087i		−	0.714127i
$609$	−4.76015	+	2.41474i	−0.192891	+	0.0978503i
$610$	−1.95698			−0.0792359
$611$	29.6118	+	17.0964i	1.19796	+	0.691644i
$612$	−5.65925	−	9.80210i	−0.228762	−	0.396227i
$613$	−19.5034	+	11.2603i	−0.787733	+	0.454798i	−0.839164	−	0.543879i	$-0.816955\pi$
$613$	−19.5034	+	11.2603i	−0.787733	+	0.454798i	0.0514307	+	0.998677i	$0.483622\pi$
$614$	2.69479	+	1.55584i	0.108753	+	0.0627884i
$615$	3.24150			0.130710
$616$	−0.752455	−	1.02631i	−0.0303173	−	0.0413510i
$617$	28.3379			1.14084			0.570421	−	0.821353i	$-0.306780\pi$
$617$	28.3379			1.14084			0.570421	+	0.821353i	$0.306780\pi$
$618$	9.06666	+	5.23464i	0.364715	+	0.210568i
$619$	−14.5332	+	8.39077i	−0.584140	+	0.337253i	−0.762777	−	0.646662i	$-0.776165\pi$
$619$	−14.5332	+	8.39077i	−0.584140	+	0.337253i	0.178637	+	0.983915i	$0.442831\pi$
$620$	−2.02897	−	3.51427i	−0.0814853	−	0.141137i
$621$	2.39880	+	1.38495i	0.0962606	+	0.0555761i
$622$	−47.7016			−1.91266
$623$	−0.613654	+	0.941268i	−0.0245855	+	0.0377111i
$624$		−	22.4928i		−	0.900431i
$625$	−11.5107	+	19.9371i	−0.460427	+	0.797484i
$626$	−0.473161	−	0.819539i	−0.0189113	−	0.0327554i
$627$	5.70515	−	4.67790i	0.227842	−	0.186817i
$628$	−22.1423	−	12.7839i	−0.883574	−	0.510132i
$629$	−47.0587			−1.87635
$630$	−0.103506	+	1.90987i	−0.00412376	+	0.0760911i
$631$	−11.8060			−0.469991			−0.234995	−	0.971997i	$-0.575507\pi$
$631$	−11.8060			−0.469991			−0.234995	+	0.971997i	$0.575507\pi$
$632$	0.133281	−	0.230849i	0.00530161	−	0.00918266i
$633$	4.08593	+	7.07703i	0.162401	+	0.281287i
$634$	−16.1560	+	9.32768i	−0.641637	+	0.370449i
$635$	−2.61622	+	4.53142i	−0.103821	+	0.179824i
$636$			24.9330i			0.988660i
$637$	−37.7992	−	4.10913i	−1.49766	−	0.162810i
$638$	13.0830	−	2.15409i	0.517959	−	0.0852813i
$639$	1.32279	−	2.29114i	0.0523288	−	0.0906362i
$640$	0.211488	+	0.366307i	0.00835978	+	0.0144796i
$641$	−8.90108	−	15.4171i	−0.351572	−	0.608940i	0.634953	−	0.772550i	$-0.281019\pi$
$641$	−8.90108	−	15.4171i	−0.351572	−	0.608940i	−0.986525	+	0.163610i	$0.947686\pi$
$642$	−6.71230	−	3.87535i	−0.264913	−	0.152948i
$643$		−	35.8544i		−	1.41396i	−0.707233	−	0.706980i	$-0.750057\pi$
$643$		−	35.8544i		−	1.41396i	0.707233	−	0.706980i	$-0.249943\pi$
$644$	−0.764145	+	14.0999i	−0.0301115	+	0.555614i
$645$			2.15498i			0.0848523i
$646$	−22.4248	−	12.9470i	−0.882292	−	0.509391i
$647$	34.7363	−	20.0550i	1.36563	−	0.788444i	0.375260	−	0.926920i	$-0.377553\pi$
$647$	34.7363	−	20.0550i	1.36563	−	0.788444i	0.990366	+	0.138475i	$0.0442201\pi$
$648$	0.125596	−	0.0725127i	0.00493386	−	0.00284857i
$649$	−26.5152	−	9.99295i	−1.04081	−	0.392258i
$650$			52.3853i			2.05472i
$651$	12.7947	+	8.34143i	0.501464	+	0.326927i
$652$	15.2855			0.598625
$653$	−4.30668	+	7.45939i	−0.168533	+	0.291908i	−0.937904	−	0.346894i	$-0.887236\pi$
$653$	−4.30668	+	7.45939i	−0.168533	+	0.291908i	0.769371	+	0.638802i	$0.220570\pi$
$654$	−10.9111	+	6.29955i	−0.426660	+	0.246332i
$655$	−1.61302	+	0.931277i	−0.0630259	+	0.0363880i
$656$	18.3972	−	31.8648i	0.718289	−	1.24411i
$657$	5.82364			0.227202
$658$	−29.4334	+	14.9311i	−1.14743	+	0.582074i
$659$		−	16.0122i		−	0.623745i	−0.950124	−	0.311873i	$-0.899044\pi$
$659$		−	16.0122i		−	0.623745i	0.950124	−	0.311873i	$-0.100956\pi$
$660$	0.822179	−	2.18157i	0.0320033	−	0.0849173i
$661$	−29.2549	+	16.8903i	−1.13788	+	0.656958i	−0.945906	−	0.324441i	$-0.894824\pi$
$661$	−29.2549	+	16.8903i	−1.13788	+	0.656958i	−0.191979	+	0.981399i	$0.561491\pi$
$662$	32.2610	−	18.6259i	1.25386	−	0.723915i
$663$	−27.6322	−	15.9535i	−1.07315	−	0.619581i
$664$		−	0.756188i		−	0.0293458i
$665$	0.971346	+	1.91480i	0.0376672	+	0.0742529i
$666$			15.8749i			0.615141i
$667$	4.83941	+	2.79403i	0.187383	+	0.108185i
$668$	0.657262	+	1.13841i	0.0254302	+	0.0440465i
$669$	−12.1246	−	21.0004i	−0.468763	−	0.811921i
$670$	5.28265	−	9.14982i	0.204087	−	0.353488i
$671$	−8.85897	+	1.45862i	−0.341997	+	0.0563094i
$672$	17.5443	+	11.4379i	0.676785	+	0.441226i
$673$		−	39.0078i		−	1.50364i	−0.659368	−	0.751820i	$-0.729176\pi$
$673$		−	39.0078i		−	1.50364i	0.659368	−	0.751820i	$-0.270824\pi$
$674$	5.42157	−	9.39043i	0.208831	−	0.361706i
$675$	−4.21487	+	2.43346i	−0.162230	+	0.0936637i
$676$	15.8995	+	27.5388i	0.611520	+	1.05918i
$677$	11.4527	−	19.8367i	0.440164	−	0.762387i	−0.557537	−	0.830152i	$-0.688253\pi$
$677$	11.4527	−	19.8367i	0.440164	−	0.762387i	0.997701	+	0.0677650i	$0.0215868\pi$
$678$	−8.32411			−0.319685
$679$	26.6692	+	1.44534i	1.02347	+	0.0554671i
$680$	0.310788			0.0119182
$681$	2.91012	+	1.68016i	0.111516	+	0.0643838i
$682$	−24.0567	−	29.3395i	−0.921178	−	1.12347i
$683$	16.3370	+	28.2966i	0.625120	+	1.08274i	0.988518	+	0.151105i	$0.0482831\pi$
$683$	16.3370	+	28.2966i	0.625120	+	1.08274i	−0.363398	+	0.931634i	$0.618384\pi$
$684$	−2.14308	+	3.71193i	−0.0819428	+	0.141929i
$685$			0.871953i			0.0333156i
$686$	23.2483	−	28.3974i	0.887624	−	1.08422i
$687$	−21.8792			−0.834745
$688$	21.1841	+	12.2306i	0.807634	+	0.466288i
$689$	35.1432	+	60.8698i	1.33885	+	2.31896i
$690$	1.73415	−	1.00121i	0.0660179	−	0.0381155i
$691$	20.2148	+	11.6710i	0.769007	+	0.443986i	0.832520	−	0.553995i	$-0.186897\pi$
$691$	20.2148	+	11.6710i	0.769007	+	0.443986i	−0.0635132	+	0.997981i	$0.520230\pi$
$692$	−2.88785			−0.109780
$693$	0.954950	+	8.72285i	0.0362756	+	0.331354i
$694$	−35.2074			−1.33646
$695$	−5.10694	−	2.94849i	−0.193717	−	0.111843i
$696$	0.253380	−	0.146289i	0.00960434	−	0.00554507i
$697$	−26.0971	−	45.2016i	−0.988500	−	1.71213i
$698$	−52.4524	−	30.2834i	−1.98535	−	1.14624i
$699$	7.94667			0.300570
$700$	−20.7840	−	13.5500i	−0.785563	−	0.512143i
$701$		−	41.9176i		−	1.58321i	−0.611036	−	0.791603i	$-0.709247\pi$
$701$		−	41.9176i		−	1.58321i	0.611036	−	0.791603i	$-0.290753\pi$
$702$	−5.38178	+	9.32152i	−0.203122	+	0.351818i
$703$	8.91026	+	15.4330i	0.336057	+	0.582068i
$704$	−15.5704	−	18.9896i	−0.586832	−	0.715698i
$705$	1.98884	+	1.14826i	0.0749040	+	0.0432459i
$706$	−32.5862			−1.22640
$707$	−35.9734	+	18.2487i	−1.35292	+	0.686313i
$708$	16.4619			0.618675
$709$	15.6972	−	27.1883i	0.589519	−	1.02108i	−0.404776	−	0.914416i	$-0.632650\pi$
$709$	15.6972	−	27.1883i	0.589519	−	1.02108i	0.994295	−	0.106662i	$-0.0340162\pi$
$710$	−0.956276	−	1.65632i	−0.0358884	−	0.0621606i
$711$	−1.59178	+	0.919015i	−0.0596965	+	0.0344658i
$712$	0.0307957	−	0.0533397i	0.00115412	−	0.00199899i
$713$		−	15.9903i		−	0.598842i
$714$	27.4658	−	13.9329i	1.02788	−	0.521427i
$715$	−1.06771	−	6.48479i	−0.0399302	−	0.242517i
$716$	−5.98510	+	10.3665i	−0.223674	+	0.387414i
$717$	−9.18297	−	15.9054i	−0.342944	−	0.593997i
$718$	33.2596	+	57.6073i	1.24124	+	2.14989i
$719$	0.570677	+	0.329481i	0.0212827	+	0.0122876i	0.510604	−	0.859816i	$-0.329422\pi$
$719$	0.570677	+	0.329481i	0.0212827	+	0.0122876i	−0.489321	+	0.872104i	$0.662755\pi$
$720$		−	1.51070i		−	0.0563005i
$721$	−7.63385	+	11.7094i	−0.284300	+	0.436079i
$722$		−	27.8451i		−	1.03629i
$723$	7.94904	+	4.58938i	0.295628	+	0.170681i
$724$	16.4840	−	9.51706i	0.612624	−	0.353699i
$725$	−8.50318	+	4.90931i	−0.315800	+	0.182327i
$726$	4.27135	−	21.3752i	0.158525	−	0.793309i
$727$		−	3.90800i		−	0.144940i	−0.997371	−	0.0724698i	$-0.976912\pi$
$727$		−	3.90800i		−	0.144940i	0.997371	−	0.0724698i	$-0.0230881\pi$
$728$	2.08110	+	0.112785i	0.0771306	+	0.00418009i
$729$	−1.00000			−0.0370370
$730$	2.10502	−	3.64600i	0.0779102	−	0.134945i
$731$	30.0505	−	17.3496i	1.11146	−	0.641700i
$732$	4.51716	−	2.60799i	0.166959	−	0.0963939i
$733$	−16.0679	+	27.8304i	−0.593482	+	1.02794i	0.400278	+	0.916394i	$0.368914\pi$
$733$	−16.0679	+	27.8304i	−0.593482	+	1.02794i	−0.993759	+	0.111546i	$0.964420\pi$
$734$	−12.0380			−0.444331
$735$	−2.53874	−	0.275985i	−0.0936429	−	0.0101799i
$736$		−	21.9261i		−	0.808208i
$737$	17.0940	−	45.3572i	0.629667	−	1.67076i
$738$	−15.2484	+	8.80368i	−0.561302	+	0.324068i
$739$	8.70546	−	5.02610i	0.320235	−	0.184888i	−0.331262	−	0.943539i	$-0.607474\pi$
$739$	8.70546	−	5.02610i	0.320235	−	0.184888i	0.651498	+	0.758651i	$0.274141\pi$
$740$	4.87679	+	2.81561i	0.179274	+	0.103504i
$741$			12.0827i			0.443870i
$742$	−67.7435	−	3.67136i	−2.48694	−	0.134780i
$743$			1.22246i			0.0448476i	0.999749	+	0.0224238i	$0.00713831\pi$
$743$			1.22246i			0.0448476i	−0.999749	+	0.0224238i	$0.992862\pi$
$744$	−0.725050	−	0.418608i	−0.0265816	−	0.0153469i
$745$	3.36548	+	5.82917i	0.123301	+	0.213564i
$746$	34.6173	+	59.9590i	1.26743	+	2.19525i
$747$	−2.60709	+	4.51561i	−0.0953884	+	0.165218i
$748$	−37.0405	+	6.09867i	−1.35433	+	0.222990i
$749$	5.65156	−	8.66877i	0.206503	−	0.316750i
$750$			7.13301i			0.260461i
$751$	−3.77946	+	6.54621i	−0.137914	+	0.238875i	−0.926707	−	0.375785i	$-0.877373\pi$
$751$	−3.77946	+	6.54621i	−0.137914	+	0.238875i	0.788793	+	0.614659i	$0.210707\pi$
$752$	22.5754	−	13.0339i	0.823239	−	0.475297i
$753$	−12.8975	−	22.3391i	−0.470009	−	0.814080i
$754$	−10.8573	+	18.8055i	−0.395401	+	0.684855i
$755$	−3.52444			−0.128267
$756$	−2.30629	−	4.54636i	−0.0838788	−	0.165349i
$757$	−12.3734			−0.449721			−0.224860	−	0.974391i	$-0.572193\pi$
$757$	−12.3734			−0.449721			−0.224860	+	0.974391i	$0.572193\pi$
$758$	24.3634	+	14.0662i	0.884918	+	0.510908i
$759$	7.10399	−	5.82487i	0.257858	−	0.211429i
$760$	−0.0588457	−	0.101924i	−0.00213456	−	0.00369716i
$761$	−26.9061	+	46.6027i	−0.975346	+	1.68935i	−0.296555	+	0.955016i	$0.595838\pi$
$761$	−26.9061	+	46.6027i	−0.975346	+	1.68935i	−0.678790	+	0.734332i	$0.737495\pi$
$762$		−	28.4218i		−	1.02961i
$763$	−7.61015	−	15.0018i	−0.275506	−	0.543101i
$764$	−1.69462			−0.0613091
$765$	−1.85588	−	1.07150i	−0.0670997	−	0.0387400i
$766$	−18.7055	−	32.3989i	−0.675858	−	1.17062i
$767$	40.1889	−	23.2031i	1.45114	−	0.837814i
$768$	−14.8142	−	8.55297i	−0.534561	−	0.308629i
$769$	−22.8557			−0.824199			−0.412099	−	0.911139i	$-0.635204\pi$
$769$	−22.8557			−0.824199			−0.412099	+	0.911139i	$0.635204\pi$
$770$	5.80629	+	2.55511i	0.209244	+	0.0920797i
$771$	−5.90959			−0.212829
$772$	37.2775	+	21.5222i	1.34165	+	0.774600i
$773$	10.1111	−	5.83765i	0.363671	−	0.209966i	−0.307019	−	0.951703i	$-0.599331\pi$
$773$	10.1111	−	5.83765i	0.363671	−	0.209966i	0.670690	+	0.741738i	$0.265998\pi$
$774$	−5.85278	−	10.1373i	−0.210374	−	0.364378i
$775$	24.3320	+	14.0481i	0.874030	+	0.504622i
$776$	−1.46400			−0.0525547
$777$	−21.1643	−	1.14700i	−0.759265	−	0.0411484i
$778$		−	7.21881i		−	0.258807i
$779$	−9.88264	+	17.1172i	−0.354082	+	0.613289i
$780$	1.90905	+	3.30657i	0.0683550	+	0.118394i
$781$	−5.56344	−	6.78516i	−0.199076	−	0.242792i
$782$	−27.9231	−	16.1214i	−0.998528	−	0.576500i
$783$	−2.01743			−0.0720969
$784$	−17.1217	+	23.3902i	−0.611488	+	0.835363i
$785$	−4.84087			−0.172778
$786$	5.05857	−	8.76170i	0.180433	−	0.312519i
$787$	−6.06595	−	10.5065i	−0.216228	−	0.374518i	0.737424	−	0.675430i	$-0.236042\pi$
$787$	−6.06595	−	10.5065i	−0.216228	−	0.374518i	−0.953652	+	0.300913i	$0.902709\pi$
$788$	−3.22556	+	1.86228i	−0.114906	+	0.0663409i
$789$	−9.70685	+	16.8128i	−0.345573	+	0.598550i
$790$			1.32875i			0.0472749i
$791$	0.601436	−	11.0976i	0.0213846	−	0.394586i
$792$	−0.0781431	−	0.474605i	−0.00277669	−	0.0168643i
$793$	7.35193	−	12.7339i	0.261075	−	0.452195i
$794$	−18.5490	−	32.1277i	−0.658278	−	1.14017i
$795$	2.36035	+	4.08825i	0.0837131	+	0.144995i
$796$	−3.38332	−	1.95336i	−0.119919	−	0.0692350i
$797$		−	1.57399i		−	0.0557537i	−0.999611	−	0.0278769i	$-0.991125\pi$
$797$		−	1.57399i		−	0.0557537i	0.999611	−	0.0278769i	$-0.00887463\pi$
$798$	−9.76981	−	6.36937i	−0.345847	−	0.225473i
$799$		−	36.9782i		−	1.30820i
$800$	33.3643	+	19.2629i	1.17961	+	0.681046i
$801$	−0.367796	+	0.212347i	−0.0129954	+	0.00750292i
$802$	33.3818	−	19.2730i	1.17875	−	0.680553i
$803$	6.81160	−	18.0739i	0.240376	−	0.637812i
$804$			28.1598i			0.993120i
$805$	1.20951	+	2.38429i	0.0426296	+	0.0840351i
$806$	62.1369			2.18868
$807$	−14.2025	+	24.5994i	−0.499951	+	0.865940i
$808$	1.91484	−	1.10554i	0.0673639	−	0.0388926i
$809$	−42.3484	+	24.4499i	−1.48889	+	0.859612i	−0.999920	−	0.0126872i	$-0.995961\pi$
$809$	−42.3484	+	24.4499i	−1.48889	+	0.859612i	−0.488972	+	0.872299i	$0.662628\pi$
$810$	−0.361461	+	0.626069i	−0.0127005	+	0.0219978i
$811$	−46.4357			−1.63058			−0.815290	−	0.579053i	$-0.803422\pi$
$811$	−46.4357			−1.63058			−0.815290	+	0.579053i	$0.803422\pi$
$812$	−4.65276	−	9.17193i	−0.163280	−	0.321872i
$813$		−	15.7812i		−	0.553470i
$814$	49.2684	+	18.5681i	1.72686	+	0.650810i
$815$	2.50634	−	1.44704i	0.0877934	−	0.0506876i
$816$	−21.0662	+	12.1626i	−0.737464	+	0.425775i
$817$	−11.3797	−	6.57008i	−0.398126	−	0.229858i
$818$		−	7.96170i		−	0.278374i
$819$	−12.0385	−	7.84844i	−0.420660	−	0.274247i
$820$			6.24577i			0.218112i
$821$	17.1993	+	9.93003i	0.600260	+	0.346560i	0.769144	−	0.639076i	$-0.220683\pi$
$821$	17.1993	+	9.93003i	0.600260	+	0.346560i	−0.168884	+	0.985636i	$0.554016\pi$
$822$	−2.36816	−	4.10178i	−0.0825992	−	0.143066i
$823$	9.53005	+	16.5065i	0.332197	+	0.575381i	0.982942	−	0.183914i	$-0.0588769\pi$
$823$	9.53005	+	16.5065i	0.332197	+	0.575381i	−0.650746	+	0.759296i	$0.725544\pi$
$824$	0.383098	−	0.663546i	0.0133459	−	0.0231157i
$825$	2.62241	+	15.9273i	0.0913005	+	0.554516i
$826$	−2.42399	+	44.7272i	−0.0843414	+	1.55626i
$827$			37.0755i			1.28924i	0.764502	+	0.644621i	$0.222985\pi$
$827$			37.0755i			1.28924i	−0.764502	+	0.644621i	$0.777015\pi$
$828$	−2.66854	+	4.62205i	−0.0927382	+	0.160627i
$829$	−5.02798	+	2.90291i	−0.174629	+	0.100822i	−0.584767	−	0.811201i	$-0.698814\pi$
$829$	−5.02798	+	2.90291i	−0.174629	+	0.100822i	0.410138	+	0.912024i	$0.365481\pi$
$830$	1.88472	+	3.26444i	0.0654197	+	0.113310i
$831$	8.52924	−	14.7731i	0.295876	−	0.512472i
$832$	40.2174			1.39429
$833$	16.5908	+	37.6238i	0.574836	+	1.30359i
$834$	32.0316			1.10916
$835$	0.215542	+	0.124443i	0.00745912	+	0.00430653i
$836$	9.01345	+	10.9928i	0.311737	+	0.380193i
$837$	2.88645	+	4.99947i	0.0997702	+	0.172807i
$838$	18.6035	−	32.2221i	0.642646	−	1.11310i
$839$			11.3409i			0.391530i	0.980651	+	0.195765i	$0.0627190\pi$
$839$			11.3409i			0.391530i	−0.980651	+	0.195765i	$0.937281\pi$
$840$	0.139774	+	0.00757508i	0.00482268	+	0.000261365i
$841$	24.9300			0.859655
$842$	−64.8416	−	37.4363i	−2.23459	−	1.29014i
$843$	13.2881	+	23.0156i	0.457665	+	0.792700i
$844$	−13.6361	+	7.87283i	−0.469375	+	0.270994i
$845$	5.21406	+	3.01034i	0.179369	+	0.103559i
$846$	−12.4743			−0.428877
$847$	28.1886	+	7.23893i	0.968572	+	0.248732i
$848$	53.5849			1.84011
$849$	8.29148	+	4.78709i	0.284563	+	0.164292i
$850$	49.0629	−	28.3265i	1.68284	−	0.971590i
$851$	11.0949	+	19.2170i	0.380330	+	0.658751i
$852$	4.41461	+	2.54878i	0.151242	+	0.0873196i
$853$	13.7963			0.472377			0.236189	−	0.971707i	$-0.424102\pi$
$853$	13.7963			0.472377			0.236189	+	0.971707i	$0.424102\pi$
$854$	6.42080	+	12.6572i	0.219715	+	0.433122i
$855$			0.811523i			0.0277535i
$856$	−0.283619	+	0.491242i	−0.00969388	+	0.0167903i
$857$	−15.2865	−	26.4770i	−0.522177	−	0.904438i	−0.999667	−	0.0258003i	$-0.991787\pi$
$857$	−15.2865	−	26.4770i	−0.522177	−	0.904438i	0.477490	−	0.878637i	$-0.341547\pi$
$858$	22.6349	+	27.6054i	0.772742	+	0.942434i
$859$	−35.1496	−	20.2936i	−1.19929	−	0.692410i	−0.238892	−	0.971046i	$-0.576784\pi$
$859$	−35.1496	−	20.2936i	−1.19929	−	0.692410i	−0.960397	+	0.278637i	$0.910117\pi$
$860$	−4.15225			−0.141590
$861$	−10.6352	−	20.9651i	−0.362448	−	0.714490i
$862$	−24.2322			−0.825351
$863$	−14.6033	+	25.2937i	−0.497103	+	0.861008i	−0.999994	−	0.00334172i	$-0.998936\pi$
$863$	−14.6033	+	25.2937i	−0.497103	+	0.861008i	0.502891	+	0.864350i	$0.332270\pi$
$864$	3.95793	+	6.85534i	0.134652	+	0.233223i
$865$	−0.473519	+	0.273386i	−0.0161001	+	0.00929541i
$866$	−14.9214	+	25.8446i	−0.507049	+	0.878234i
$867$			17.5062i			0.594543i
$868$	−16.0724	+	24.6530i	−0.545533	+	0.836778i
$869$	0.990374	+	6.01507i	0.0335961	+	0.204047i
$870$	−0.729221	+	1.26305i	−0.0247229	+	0.0428213i
$871$	39.6914	+	68.7475i	1.34489	+	2.32942i
$872$	0.461035	+	0.798535i	0.0156126	+	0.0270418i
$873$	8.74237	+	5.04741i	0.295884	+	0.170829i
$874$			12.2099i			0.413007i
$875$	−9.50966	−	0.515376i	−0.321485	−	0.0174229i
$876$			11.2211i			0.379125i
$877$	−11.6589	−	6.73125i	−0.393692	−	0.227298i	0.290067	−	0.957006i	$-0.406323\pi$
$877$	−11.6589	−	6.73125i	−0.393692	−	0.227298i	−0.683759	+	0.729708i	$0.739656\pi$
$878$	−26.3185	+	15.1950i	−0.888205	+	0.512806i
$879$	−14.6241	+	8.44323i	−0.493259	+	0.284783i
$880$	−4.68851	−	1.76699i	−0.158050	−	0.0595651i
$881$			47.1355i			1.58803i	0.607896	+	0.794017i	$0.292014\pi$
$881$			47.1355i			1.58803i	−0.607896	+	0.794017i	$0.707986\pi$
$882$	12.6921	−	5.59678i	0.427366	−	0.188453i
$883$	6.67601			0.224666			0.112333	−	0.993671i	$-0.464168\pi$
$883$	6.67601			0.224666			0.112333	+	0.993671i	$0.464168\pi$
$884$	30.7394	−	53.2421i	1.03388	−	1.79073i
$885$	2.69924	−	1.55841i	0.0907339	−	0.0523853i
$886$	27.0076	−	15.5929i	0.907339	−	0.523852i
$887$	3.21635	−	5.57089i	0.107995	−	0.187052i	−0.806963	−	0.590602i	$-0.798890\pi$
$887$	3.21635	−	5.57089i	0.107995	−	0.187052i	0.914958	+	0.403550i	$0.132224\pi$
$888$	1.16181			0.0389878
$889$	37.8917	+	2.05354i	1.27085	+	0.0688736i
$890$			0.307021i			0.0102914i
$891$	−1.16965	+	3.10353i	−0.0391846	+	0.103972i
$892$	40.4638	−	23.3618i	1.35483	−	0.782211i
$893$	−12.1271	+	7.00158i	−0.405818	+	0.234299i
$894$	−31.6633	−	18.2808i	−1.05898	−	0.611401i
$895$			2.26638i			0.0757567i
$896$	1.67529	−	2.56968i	0.0559676	−	0.0858471i
$897$			15.0453i			0.502347i
$898$	24.0783	+	13.9016i	0.803502	+	0.463902i
$899$	5.82319	+	10.0861i	0.194214	+	0.336389i
$900$	−4.68882	−	8.12127i	−0.156294	−	0.270709i
$901$	38.0062	−	65.8286i	1.26617	−	2.19307i
$902$	9.48727	+	57.6212i	0.315891	+	1.91858i
$903$	13.9378	−	7.07042i	0.463822	−	0.235289i
$904$			0.609202i			0.0202618i
$905$	1.80192	−	3.12101i	0.0598977	−	0.103746i
$906$	16.5794	−	9.57213i	0.550814	−	0.318013i
$907$	20.6838	+	35.8254i	0.686795	+	1.18956i	0.972869	+	0.231356i	$0.0743163\pi$
$907$	20.6838	+	35.8254i	0.686795	+	1.18956i	−0.286074	+	0.958208i	$0.592350\pi$
$908$	−3.23735	+	5.60726i	−0.107435	+	0.186083i
$909$	−15.2461			−0.505681
$910$	−9.26513	+	4.70004i	−0.307136	+	0.155805i
$911$	−42.9021			−1.42141			−0.710705	−	0.703490i	$-0.751624\pi$
$911$	−42.9021			−1.42141			−0.710705	+	0.703490i	$0.751624\pi$
$912$	7.97749	+	4.60581i	0.264161	+	0.152514i
$913$	10.9650	+	13.3729i	0.362888	+	0.442577i
$914$	−32.4238	−	56.1597i	−1.07248	−	1.85760i
$915$	0.493784	−	0.855259i	0.0163240	−	0.0282740i
$916$		−	42.1572i		−	1.39291i
$917$	11.3155	+	7.37708i	0.373671	+	0.243613i
$918$	11.6404			0.384191
$919$	21.0723	+	12.1661i	0.695113	+	0.401323i	0.805524	−	0.592562i	$-0.201884\pi$
$919$	21.0723	+	12.1661i	0.695113	+	0.401323i	−0.110412	+	0.993886i	$0.535217\pi$
$920$	−0.0732739	−	0.126914i	−0.00241577	−	0.00418424i
$921$	−1.35989	+	0.785133i	−0.0448099	+	0.0258710i
$922$	29.7648	+	17.1847i	0.980250	+	0.565948i
$923$	14.3700			0.472995
$924$	−16.8073	+	1.84001i	−0.552920	+	0.0605320i
$925$	−38.9892			−1.28196
$926$	48.6879	+	28.1100i	1.59998	+	0.923751i
$927$	−4.57538	+	2.64160i	−0.150275	+	0.0867614i
$928$	7.98483	+	13.8301i	0.262115	+	0.453996i
$929$	32.9012	+	18.9955i	1.07945	+	0.623224i	0.930749	−	0.365658i	$-0.119156\pi$
$929$	32.9012	+	18.9955i	1.07945	+	0.623224i	0.148706	+	0.988882i	$0.452489\pi$
$930$	4.17335			0.136850
$931$	9.19747	−	12.5648i	0.301435	−	0.411795i
$932$			15.3118i			0.501553i
$933$	12.0360	−	20.8470i	0.394041	−	0.682499i
$934$	35.3248	+	61.1843i	1.15586	+	2.00201i
$935$	−5.49615	+	4.50653i	−0.179743	+	0.147379i
$936$	0.682198	+	0.393867i	0.0222984	+	0.0128740i
$937$	31.8024			1.03894			0.519469	−	0.854489i	$-0.326130\pi$
$937$	31.8024			1.03894			0.519469	+	0.854489i	$0.326130\pi$
$938$	−76.5107	−	4.14650i	−2.49816	−	0.135388i
$939$	0.477550			0.0155843
$940$	−2.21248	+	3.83212i	−0.0721631	+	0.124990i
$941$	−2.53829	−	4.39645i	−0.0827460	−	0.143320i	0.821683	−	0.569945i	$-0.193036\pi$
$941$	−2.53829	−	4.39645i	−0.0827460	−	0.143320i	−0.904428	+	0.426625i	$0.859702\pi$
$942$	22.7721	−	13.1475i	0.741955	−	0.428368i
$943$	−12.3057	+	21.3142i	−0.400730	+	0.694085i
$944$		−	35.3790i		−	1.15149i
$945$	−0.808553	−	0.527131i	−0.0263022	−	0.0171476i
$946$	−38.3072	+	6.30723i	−1.24547	+	0.205066i
$947$	20.5441	−	35.5835i	0.667595	−	1.15631i	−0.310980	−	0.950417i	$-0.600657\pi$
$947$	20.5441	−	35.5835i	0.667595	−	1.15631i	0.978575	−	0.205892i	$-0.0660095\pi$
$948$	−1.77077	−	3.06707i	−0.0575120	−	0.0996137i
$949$	15.8161	+	27.3943i	0.513413	+	0.889258i
$950$	−18.5795	−	10.7269i	−0.602797	−	0.348025i
$951$		−	9.41420i		−	0.305276i
$952$	−1.01969	−	2.01009i	−0.0330482	−	0.0651475i
$953$			1.56947i			0.0508402i	0.999677	+	0.0254201i	$0.00809234\pi$
$953$			1.56947i			0.0508402i	−0.999677	+	0.0254201i	$0.991908\pi$
$954$	−22.2068	−	12.8211i	−0.718972	−	0.415099i
$955$	−0.277865	+	0.160426i	−0.00899151	+	0.00519125i
$956$	30.6467	−	17.6939i	0.991185	−	0.572261i
$957$	−2.35967	+	6.26115i	−0.0762775	+	0.202394i
$958$		−	52.0535i		−	1.68177i
$959$	5.63955	−	2.86085i	0.182111	−	0.0923816i
$960$	2.70116			0.0871794
$961$	1.16314	−	2.01461i	0.0375205	−	0.0649874i
$962$	−74.6755	+	43.1139i	−2.40764	+	1.39005i
$963$	3.38728	−	1.95565i	0.109154	−	0.0630199i
$964$	−8.84289	+	15.3163i	−0.284810	+	0.493306i
$965$	8.14982			0.262352
$966$	−12.1652	−	7.93106i	−0.391410	−	0.255178i
$967$			45.6739i			1.46877i	0.678732	+	0.734386i	$0.262530\pi$
$967$			45.6739i			1.46877i	−0.678732	+	0.734386i	$0.737470\pi$
$968$	−1.56435	−	0.312600i	−0.0502802	−	0.0100473i
$969$	11.3164	−	6.53353i	0.363535	−	0.209887i
$970$	6.32006	−	3.64889i	0.202925	−	0.117159i
$971$	−4.86828	−	2.81070i	−0.156231	−	0.0901998i	0.419847	−	0.907595i	$-0.362084\pi$
$971$	−4.86828	−	2.81070i	−0.156231	−	0.0901998i	−0.576077	+	0.817395i	$0.695417\pi$
$972$		−	1.92681i		−	0.0618026i
$973$	−2.31436	+	42.7042i	−0.0741949	+	1.36903i
$974$		−	52.3618i		−	1.67778i
$975$	−22.8939	−	13.2178i	−0.733192	−	0.423309i
$976$	−5.60495	−	9.70806i	−0.179410	−	0.310748i
$977$	−1.98615	−	3.44011i	−0.0635426	−	0.110059i	0.832504	−	0.554019i	$-0.186907\pi$
$977$	−1.98615	−	3.44011i	−0.0635426	−	0.110059i	−0.896047	+	0.443960i	$0.853573\pi$
$978$	−7.86011	+	13.6141i	−0.251339	+	0.435331i
$979$	0.228835	+	1.38984i	0.00731361	+	0.0444194i
$980$	0.531772	−	4.89168i	0.0169868	−	0.156259i
$981$		−	6.35799i		−	0.202995i
$982$	−16.7477	+	29.0079i	−0.534440	+	0.925678i
$983$	−31.0712	+	17.9390i	−0.991019	+	0.572165i	−0.905579	−	0.424178i	$-0.860563\pi$
$983$	−31.0712	+	17.9390i	−0.991019	+	0.572165i	−0.0854402	+	0.996343i	$0.527230\pi$
$984$	0.644300	+	1.11596i	0.0205395	+	0.0355755i
$985$	−0.352595	+	0.610713i	−0.0112346	+	0.0194589i
$986$	23.4837			0.747873
$987$	0.901299	−	16.6307i	0.0286887	−	0.529360i
$988$	−23.2812			−0.740673
$989$	−14.1699	−	8.18098i	−0.450576	−	0.260140i
$990$	1.52025	+	1.85409i	0.0483166	+	0.0589268i
$991$	8.82827	+	15.2910i	0.280439	+	0.485735i	0.971493	−	0.237068i	$-0.0761865\pi$
$991$	8.82827	+	15.2910i	0.280439	+	0.485735i	−0.691054	+	0.722803i	$0.742853\pi$
$992$	22.8487	−	39.5751i	0.725447	−	1.25651i
$993$			18.7986i			0.596557i
$994$	−7.57511	+	11.6193i	−0.240268	+	0.368541i
$995$	−0.739680			−0.0234494
$996$	−8.70074	−	5.02338i	−0.275694	−	0.159172i
$997$	−19.6519	−	34.0381i	−0.622382	−	1.07800i	−0.989041	−	0.147642i	$-0.952832\pi$
$997$	−19.6519	−	34.0381i	−0.622382	−	1.07800i	0.366659	−	0.930356i	$-0.380502\pi$
$998$	−43.9640	+	25.3826i	−1.39166	+	0.803473i
$999$	−6.93780	−	4.00554i	−0.219502	−	0.126730i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	231.2.p.a.208.3	yes	32
3.2	odd	2		693.2.bg.b.208.14		32
7.2	even	3		1617.2.c.a.538.28		32
7.3	odd	6	inner	231.2.p.a.10.14	yes	32
7.5	odd	6		1617.2.c.a.538.27		32
11.10	odd	2	inner	231.2.p.a.208.14	yes	32
21.17	even	6		693.2.bg.b.10.3		32
33.32	even	2		693.2.bg.b.208.3		32
77.10	even	6	inner	231.2.p.a.10.3	✓	32
77.54	even	6		1617.2.c.a.538.5		32
77.65	odd	6		1617.2.c.a.538.6		32
231.164	odd	6		693.2.bg.b.10.14		32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
231.2.p.a.10.3	✓	32	77.10	even	6	inner
231.2.p.a.10.14	yes	32	7.3	odd	6	inner
231.2.p.a.208.3	yes	32	1.1	even	1	trivial
231.2.p.a.208.14	yes	32	11.10	odd	2	inner
693.2.bg.b.10.3		32	21.17	even	6
693.2.bg.b.10.14		32	231.164	odd	6
693.2.bg.b.208.3		32	33.32	even	2
693.2.bg.b.208.14		32	3.2	odd	2
1617.2.c.a.538.5		32	77.54	even	6
1617.2.c.a.538.6		32	77.65	odd	6
1617.2.c.a.538.27		32	7.5	odd	6
1617.2.c.a.538.28		32	7.2	even	3

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:	\( N \)	\(=\)	\( 231 = 3 \cdot 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	231.p (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.71613 - 0.990810i) q^{2} +(0.866025 - 0.500000i) q^{3} +(0.963407 + 1.66867i) q^{4} +(0.315938 + 0.182407i) q^{5} -1.98162 q^{6} +(0.143176 - 2.64187i) q^{7} +0.145025i q^{8} +(0.500000 - 0.866025i) q^{9} +O(q^{10})\)	\(q+(-1.71613 - 0.990810i) q^{2} +(0.866025 - 0.500000i) q^{3} +(0.963407 + 1.66867i) q^{4} +(0.315938 + 0.182407i) q^{5} -1.98162 q^{6} +(0.143176 - 2.64187i) q^{7} +0.145025i q^{8} +(0.500000 - 0.866025i) q^{9} +(-0.361461 - 0.626069i) q^{10} +(-2.10292 - 2.56471i) q^{11} +(1.66867 + 0.963407i) q^{12} +5.43170 q^{13} +(-2.86330 + 4.39195i) q^{14} +0.364814 q^{15} +(2.07051 - 3.58622i) q^{16} +(-2.93710 - 5.08721i) q^{17} +(-1.71613 + 0.990810i) q^{18} +(-1.11224 + 1.92646i) q^{19} +0.702929i q^{20} +(-1.19694 - 2.35952i) q^{21} +(1.06774 + 6.48497i) q^{22} +(-1.38495 + 2.39880i) q^{23} +(0.0725127 + 0.125596i) q^{24} +(-2.43346 - 4.21487i) q^{25} +(-9.32152 - 5.38178i) q^{26} -1.00000i q^{27} +(4.54636 - 2.30629i) q^{28} -2.01743i q^{29} +(-0.626069 - 0.361461i) q^{30} +(-4.99947 + 2.88645i) q^{31} +(-6.85534 + 3.95793i) q^{32} +(-3.10353 - 1.16965i) q^{33} +11.6404i q^{34} +(0.527131 - 0.808553i) q^{35} +1.92681 q^{36} +(4.00554 - 6.93780i) q^{37} +(3.81751 - 2.20404i) q^{38} +(4.70399 - 2.71585i) q^{39} +(-0.0264536 + 0.0458191i) q^{40} +8.88534 q^{41} +(-0.283721 + 5.23519i) q^{42} +5.90706i q^{43} +(2.25369 - 5.97994i) q^{44} +(0.315938 - 0.182407i) q^{45} +(4.75351 - 2.74444i) q^{46} +(5.45165 + 3.14751i) q^{47} -4.14101i q^{48} +(-6.95900 - 0.756509i) q^{49} +9.64436i q^{50} +(-5.08721 - 2.93710i) q^{51} +(5.23294 + 9.06372i) q^{52} +(6.47002 + 11.2064i) q^{53} +(-0.990810 + 1.71613i) q^{54} +(-0.196570 - 1.19388i) q^{55} +(0.383139 + 0.0207642i) q^{56} +2.22448i q^{57} +(-1.99888 + 3.46217i) q^{58} +(7.39894 - 4.27178i) q^{59} +(0.351465 + 0.608755i) q^{60} +(1.35352 - 2.34437i) q^{61} +11.4397 q^{62} +(-2.21634 - 1.44493i) q^{63} +7.40420 q^{64} +(1.71608 + 0.990781i) q^{65} +(4.16718 + 5.08228i) q^{66} +(7.30735 + 12.6567i) q^{67} +(5.65925 - 9.80210i) q^{68} +2.76990i q^{69} +(-1.70575 + 0.865297i) q^{70} +2.64558 q^{71} +(0.125596 + 0.0725127i) q^{72} +(2.91182 + 5.04342i) q^{73} +(-13.7481 + 7.93746i) q^{74} +(-4.21487 - 2.43346i) q^{75} -4.28617 q^{76} +(-7.07673 + 5.18844i) q^{77} -10.7636 q^{78} +(-1.59178 - 0.919015i) q^{79} +(1.30831 - 0.755350i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(-15.2484 - 8.80368i) q^{82} -5.21418 q^{83} +(2.78412 - 4.27048i) q^{84} -2.14299i q^{85} +(5.85278 - 10.1373i) q^{86} +(-1.00871 - 1.74714i) q^{87} +(0.371948 - 0.304976i) q^{88} +(-0.367796 - 0.212347i) q^{89} -0.722923 q^{90} +(0.777692 - 14.3499i) q^{91} -5.33708 q^{92} +(-2.88645 + 4.99947i) q^{93} +(-6.23717 - 10.8031i) q^{94} +(-0.702799 + 0.405761i) q^{95} +(-3.95793 + 6.85534i) q^{96} +10.0948i q^{97} +(11.1930 + 8.19331i) q^{98} +(-3.27256 + 0.538824i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q + 12 q^{4} - 12 q^{5} + 16 q^{9}+O(q^{10}) \) 32 * q + 12 * q^4 - 12 * q^5 + 16 * q^9	\( 32 q + 12 q^{4} - 12 q^{5} + 16 q^{9} + 2 q^{11} - 32 q^{14} + 8 q^{15} - 20 q^{16} + 8 q^{22} + 24 q^{23} - 24 q^{26} - 12 q^{31} - 18 q^{33} + 24 q^{36} - 32 q^{37} + 24 q^{38} - 24 q^{42} - 28 q^{44} - 12 q^{45} + 24 q^{47} - 36 q^{49} + 36 q^{53} - 56 q^{56} + 12 q^{58} - 48 q^{59} + 8 q^{64} - 36 q^{66} + 20 q^{67} + 24 q^{70} + 72 q^{71} + 24 q^{75} - 48 q^{78} + 72 q^{80} - 16 q^{81} - 48 q^{82} + 64 q^{86} + 24 q^{88} + 60 q^{89} - 28 q^{91} - 16 q^{92} + 16 q^{93} + 4 q^{99}+O(q^{100}) \) 32 * q + 12 * q^4 - 12 * q^5 + 16 * q^9 + 2 * q^11 - 32 * q^14 + 8 * q^15 - 20 * q^16 + 8 * q^22 + 24 * q^23 - 24 * q^26 - 12 * q^31 - 18 * q^33 + 24 * q^36 - 32 * q^37 + 24 * q^38 - 24 * q^42 - 28 * q^44 - 12 * q^45 + 24 * q^47 - 36 * q^49 + 36 * q^53 - 56 * q^56 + 12 * q^58 - 48 * q^59 + 8 * q^64 - 36 * q^66 + 20 * q^67 + 24 * q^70 + 72 * q^71 + 24 * q^75 - 48 * q^78 + 72 * q^80 - 16 * q^81 - 48 * q^82 + 64 * q^86 + 24 * q^88 + 60 * q^89 - 28 * q^91 - 16 * q^92 + 16 * q^93 + 4 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more