LMFDB - Embedded newform 731.2.e.b.307.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [731,2,Mod(307,731)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(731, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 4]))

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

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

chi := DirichletCharacter("731.307");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 731 = 17 \cdot 43 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	731.e (of order $3$, 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:	$5.83706438776$
Analytic rank:	$0$
Dimension:	$58$
Relative dimension:	$29$ over $\Q(\zeta_{3})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			307.3
Character	$\chi$	$=$	731.307
Dual form			731.2.e.b.681.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.46652 q^{2} +(0.742625 - 1.28626i) q^{3} +4.08373 q^{4} +(0.428499 - 0.742181i) q^{5} +(-1.83170 + 3.17260i) q^{6} +(-2.43048 - 4.20972i) q^{7} -5.13956 q^{8} +(0.397017 + 0.687654i) q^{9} +O(q^{10})$	\(q-2.46652 q^{2} +(0.742625 - 1.28626i) q^{3} +4.08373 q^{4} +(0.428499 - 0.742181i) q^{5} +(-1.83170 + 3.17260i) q^{6} +(-2.43048 - 4.20972i) q^{7} -5.13956 q^{8} +(0.397017 + 0.687654i) q^{9} +(-1.05690 + 1.83061i) q^{10} +6.05985 q^{11} +(3.03268 - 5.25275i) q^{12} +(0.875156 + 1.51581i) q^{13} +(5.99483 + 10.3834i) q^{14} +(-0.636427 - 1.10232i) q^{15} +4.50938 q^{16} +(-0.500000 - 0.866025i) q^{17} +(-0.979251 - 1.69611i) q^{18} +(2.26398 - 3.92132i) q^{19} +(1.74987 - 3.03087i) q^{20} -7.21974 q^{21} -14.9467 q^{22} +(4.28730 - 7.42582i) q^{23} +(-3.81676 + 6.61083i) q^{24} +(2.13278 + 3.69408i) q^{25} +(-2.15859 - 3.73879i) q^{26} +5.63509 q^{27} +(-9.92542 - 17.1913i) q^{28} +(-1.39854 - 2.42234i) q^{29} +(1.56976 + 2.71891i) q^{30} +(-2.36665 + 4.09915i) q^{31} -0.843355 q^{32} +(4.50019 - 7.79456i) q^{33} +(1.23326 + 2.13607i) q^{34} -4.16583 q^{35} +(1.62131 + 2.80819i) q^{36} +(-4.58473 + 7.94098i) q^{37} +(-5.58415 + 9.67203i) q^{38} +2.59965 q^{39} +(-2.20229 + 3.81449i) q^{40} -2.70589 q^{41} +17.8076 q^{42} +(4.05456 - 5.15369i) q^{43} +24.7468 q^{44} +0.680485 q^{45} +(-10.5747 + 18.3159i) q^{46} +1.27282 q^{47} +(3.34877 - 5.80025i) q^{48} +(-8.31447 + 14.4011i) q^{49} +(-5.26054 - 9.11153i) q^{50} -1.48525 q^{51} +(3.57390 + 6.19017i) q^{52} +(4.59828 - 7.96446i) q^{53} -13.8991 q^{54} +(2.59664 - 4.49751i) q^{55} +(12.4916 + 21.6361i) q^{56} +(-3.36257 - 5.82415i) q^{57} +(3.44953 + 5.97477i) q^{58} -7.62547 q^{59} +(-2.59900 - 4.50159i) q^{60} +(2.05511 + 3.55956i) q^{61} +(5.83739 - 10.1106i) q^{62} +(1.92988 - 3.34266i) q^{63} -6.93860 q^{64} +1.50001 q^{65} +(-11.0998 + 19.2255i) q^{66} +(-5.41099 + 9.37210i) q^{67} +(-2.04186 - 3.53661i) q^{68} +(-6.36771 - 11.0292i) q^{69} +10.2751 q^{70} +(-2.66225 - 4.61115i) q^{71} +(-2.04049 - 3.53424i) q^{72} +(-5.78506 - 10.0200i) q^{73} +(11.3083 - 19.5866i) q^{74} +6.33541 q^{75} +(9.24547 - 16.0136i) q^{76} +(-14.7283 - 25.5102i) q^{77} -6.41209 q^{78} +(-3.54591 - 6.14170i) q^{79} +(1.93226 - 3.34678i) q^{80} +(2.99370 - 5.18525i) q^{81} +6.67413 q^{82} +(-0.350368 + 0.606856i) q^{83} -29.4834 q^{84} -0.856997 q^{85} +(-10.0007 + 12.7117i) q^{86} -4.15437 q^{87} -31.1449 q^{88} +(-4.96902 + 8.60659i) q^{89} -1.67843 q^{90} +(4.25410 - 7.36831i) q^{91} +(17.5082 - 30.3250i) q^{92} +(3.51506 + 6.08826i) q^{93} -3.13943 q^{94} +(-1.94022 - 3.36056i) q^{95} +(-0.626296 + 1.08478i) q^{96} -4.70746 q^{97} +(20.5078 - 35.5206i) q^{98} +(2.40586 + 4.16707i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 58 q + 2 q^{2} - 5 q^{3} + 54 q^{4} - 3 q^{5} - 8 q^{6} - 13 q^{7} + 12 q^{8} - 30 q^{9}+O(q^{10}) $ 58 * q + 2 * q^2 - 5 * q^3 + 54 * q^4 - 3 * q^5 - 8 * q^6 - 13 * q^7 + 12 * q^8 - 30 * q^9	\( 58 q + 2 q^{2} - 5 q^{3} + 54 q^{4} - 3 q^{5} - 8 q^{6} - 13 q^{7} + 12 q^{8} - 30 q^{9} + 4 q^{10} - 8 q^{12} + 2 q^{13} + 5 q^{14} - 5 q^{15} + 30 q^{16} - 29 q^{17} + 16 q^{18} - 4 q^{19} - 7 q^{20} - 26 q^{21} - 10 q^{22} + 5 q^{23} - 28 q^{24} - 24 q^{25} - 8 q^{26} + 28 q^{27} - 25 q^{28} + 10 q^{29} - 5 q^{30} + 3 q^{31} + 16 q^{32} - 23 q^{33} - q^{34} - 26 q^{35} - 39 q^{36} - 16 q^{37} + q^{38} + 130 q^{39} + 15 q^{40} - 22 q^{41} + 112 q^{42} + 7 q^{43} + 24 q^{44} + 2 q^{45} - 61 q^{46} + 12 q^{47} + 22 q^{48} - 36 q^{49} - 17 q^{50} + 10 q^{51} - 35 q^{52} - 10 q^{53} - 10 q^{54} - 20 q^{55} - 4 q^{56} + 9 q^{57} - 17 q^{58} - 36 q^{59} + 22 q^{60} - 35 q^{61} + 3 q^{62} - 22 q^{63} + 28 q^{64} - 28 q^{65} + 14 q^{66} - 17 q^{67} - 27 q^{68} - 23 q^{69} + 10 q^{70} - 6 q^{71} + 17 q^{72} - 14 q^{73} + 21 q^{74} + 70 q^{75} - 44 q^{76} - 11 q^{77} - 184 q^{78} - 10 q^{79} + 8 q^{80} - 13 q^{81} + 184 q^{82} + 9 q^{83} - 36 q^{84} + 6 q^{85} - 76 q^{86} + 8 q^{87} + 50 q^{88} - 54 q^{89} - 34 q^{90} - 23 q^{91} - 66 q^{92} + 96 q^{94} - 3 q^{95} - 60 q^{96} + 36 q^{97} - 16 q^{98} + 20 q^{99}+O(q^{100}) \) 58 * q + 2 * q^2 - 5 * q^3 + 54 * q^4 - 3 * q^5 - 8 * q^6 - 13 * q^7 + 12 * q^8 - 30 * q^9 + 4 * q^10 - 8 * q^12 + 2 * q^13 + 5 * q^14 - 5 * q^15 + 30 * q^16 - 29 * q^17 + 16 * q^18 - 4 * q^19 - 7 * q^20 - 26 * q^21 - 10 * q^22 + 5 * q^23 - 28 * q^24 - 24 * q^25 - 8 * q^26 + 28 * q^27 - 25 * q^28 + 10 * q^29 - 5 * q^30 + 3 * q^31 + 16 * q^32 - 23 * q^33 - q^34 - 26 * q^35 - 39 * q^36 - 16 * q^37 + q^38 + 130 * q^39 + 15 * q^40 - 22 * q^41 + 112 * q^42 + 7 * q^43 + 24 * q^44 + 2 * q^45 - 61 * q^46 + 12 * q^47 + 22 * q^48 - 36 * q^49 - 17 * q^50 + 10 * q^51 - 35 * q^52 - 10 * q^53 - 10 * q^54 - 20 * q^55 - 4 * q^56 + 9 * q^57 - 17 * q^58 - 36 * q^59 + 22 * q^60 - 35 * q^61 + 3 * q^62 - 22 * q^63 + 28 * q^64 - 28 * q^65 + 14 * q^66 - 17 * q^67 - 27 * q^68 - 23 * q^69 + 10 * q^70 - 6 * q^71 + 17 * q^72 - 14 * q^73 + 21 * q^74 + 70 * q^75 - 44 * q^76 - 11 * q^77 - 184 * q^78 - 10 * q^79 + 8 * q^80 - 13 * q^81 + 184 * q^82 + 9 * q^83 - 36 * q^84 + 6 * q^85 - 76 * q^86 + 8 * q^87 + 50 * q^88 - 54 * q^89 - 34 * q^90 - 23 * q^91 - 66 * q^92 + 96 * q^94 - 3 * q^95 - 60 * q^96 + 36 * q^97 - 16 * q^98 + 20 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/731\mathbb{Z}\right)^\times$.

$n$	$173$	$562$
$\chi(n)$	$1$	$e\left(\frac{2}{3}\right)$

Coefficient data

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

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

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

$2$	−2.46652			−1.74409			−0.872047	−	0.489422i	$-0.837208\pi$
$2$	−2.46652			−1.74409			−0.872047	+	0.489422i	$0.837208\pi$
$3$	0.742625	−	1.28626i	0.428755	−	0.742625i	−0.568008	−	0.823023i	$-0.692286\pi$
$3$	0.742625	−	1.28626i	0.428755	−	0.742625i	0.996763	+	0.0803981i	$0.0256192\pi$
$4$	4.08373			2.04186
$5$	0.428499	−	0.742181i	0.191630	−	0.331914i	−0.754160	−	0.656690i	$-0.771956\pi$
$5$	0.428499	−	0.742181i	0.191630	−	0.331914i	0.945791	+	0.324777i	$0.105289\pi$
$6$	−1.83170	+	3.17260i	−0.747788	+	1.29521i
$7$	−2.43048	−	4.20972i	−0.918635	−	1.59112i	−0.801490	−	0.598008i	$-0.795959\pi$
$7$	−2.43048	−	4.20972i	−0.918635	−	1.59112i	−0.117145	−	0.993115i	$-0.537374\pi$
$8$	−5.13956			−1.81711
$9$	0.397017	+	0.687654i	0.132339	+	0.229218i
$10$	−1.05690	+	1.83061i	−0.334221	+	0.578889i
$11$	6.05985			1.82711			0.913556	−	0.406712i	$-0.133325\pi$
$11$	6.05985			1.82711			0.913556	+	0.406712i	$0.133325\pi$
$12$	3.03268	−	5.25275i	0.875459	−	1.51634i
$13$	0.875156	+	1.51581i	0.242724	+	0.420411i	0.961489	−	0.274842i	$-0.0886256\pi$
$13$	0.875156	+	1.51581i	0.242724	+	0.420411i	−0.718765	+	0.695253i	$0.755292\pi$
$14$	5.99483	+	10.3834i	1.60219	+	2.77507i
$15$	−0.636427	−	1.10232i	−0.164325	−	0.284619i
$16$	4.50938			1.12734
$17$	−0.500000	−	0.866025i	−0.121268	−	0.210042i
$17$	−0.500000	−	0.866025i	−0.121268	−	0.210042i
$18$	−0.979251	−	1.69611i	−0.230812	−	0.399777i
$19$	2.26398	−	3.92132i	0.519392	−	0.899614i	−0.480354	−	0.877075i	$-0.659492\pi$
$19$	2.26398	−	3.92132i	0.519392	−	0.899614i	0.999746	−	0.0225388i	$-0.00717492\pi$
$20$	1.74987	−	3.03087i	0.391283	−	0.677722i
$21$	−7.21974			−1.57548
$22$	−14.9467			−3.18666
$23$	4.28730	−	7.42582i	0.893963	−	1.54839i	0.0588811	−	0.998265i	$-0.481247\pi$
$23$	4.28730	−	7.42582i	0.893963	−	1.54839i	0.835082	−	0.550125i	$-0.185420\pi$
$24$	−3.81676	+	6.61083i	−0.779094	+	1.34943i
$25$	2.13278	+	3.69408i	0.426556	+	0.738816i
$26$	−2.15859	−	3.73879i	−0.423334	−	0.733236i
$27$	5.63509			1.08447
$28$	−9.92542	−	17.1913i	−1.87573	−	3.24886i
$29$	−1.39854	−	2.42234i	−0.259703	−	0.449818i	0.706460	−	0.707753i	$-0.250291\pi$
$29$	−1.39854	−	2.42234i	−0.259703	−	0.449818i	−0.966162	+	0.257935i	$0.916958\pi$
$30$	1.56976	+	2.71891i	0.286598	+	0.496402i
$31$	−2.36665	+	4.09915i	−0.425062	+	0.736230i	−0.996426	−	0.0844672i	$-0.973081\pi$
$31$	−2.36665	+	4.09915i	−0.425062	+	0.736230i	0.571364	+	0.820697i	$0.306415\pi$
$32$	−0.843355			−0.149085
$33$	4.50019	−	7.79456i	0.783383	−	1.35686i
$34$	1.23326	+	2.13607i	0.211502	+	0.366333i
$35$	−4.16583			−0.704154
$36$	1.62131	+	2.80819i	0.270218	+	0.468032i
$37$	−4.58473	+	7.94098i	−0.753725	+	1.30549i	0.192281	+	0.981340i	$0.438411\pi$
$37$	−4.58473	+	7.94098i	−0.753725	+	1.30549i	−0.946006	+	0.324150i	$0.894922\pi$
$38$	−5.58415	+	9.67203i	−0.905869	+	1.56901i
$39$	2.59965			0.416277
$40$	−2.20229	+	3.81449i	−0.348213	+	0.603123i
$41$	−2.70589			−0.422589			−0.211294	−	0.977422i	$-0.567768\pi$
$41$	−2.70589			−0.422589			−0.211294	+	0.977422i	$0.567768\pi$
$42$	17.8076			2.74778
$43$	4.05456	−	5.15369i	0.618315	−	0.785931i
$43$	4.05456	−	5.15369i	0.618315	−	0.785931i
$44$	24.7468			3.73071
$45$	0.680485			0.101441
$46$	−10.5747	+	18.3159i	−1.55916	+	2.70054i
$47$	1.27282			0.185659			0.0928297	−	0.995682i	$-0.470409\pi$
$47$	1.27282			0.185659			0.0928297	+	0.995682i	$0.470409\pi$
$48$	3.34877	−	5.80025i	0.483354	−	0.837194i
$49$	−8.31447	+	14.4011i	−1.18778	+	2.05730i
$50$	−5.26054	−	9.11153i	−0.743953	−	1.28856i
$51$	−1.48525			−0.207977
$52$	3.57390	+	6.19017i	0.495610	+	0.858422i
$53$	4.59828	−	7.96446i	0.631623	−	1.09400i	−0.355597	−	0.934639i	$-0.615722\pi$
$53$	4.59828	−	7.96446i	0.631623	−	1.09400i	0.987220	−	0.159364i	$-0.0509442\pi$
$54$	−13.8991			−1.89142
$55$	2.59664	−	4.49751i	0.350130	−	0.606444i
$56$	12.4916	+	21.6361i	1.66926	+	2.89124i
$57$	−3.36257	−	5.82415i	−0.445384	−	0.771427i
$58$	3.44953	+	5.97477i	0.452946	+	0.784525i
$59$	−7.62547			−0.992752			−0.496376	−	0.868108i	$-0.665336\pi$
$59$	−7.62547			−0.992752			−0.496376	+	0.868108i	$0.665336\pi$
$60$	−2.59900	−	4.50159i	−0.335529	−	0.581153i
$61$	2.05511	+	3.55956i	0.263131	+	0.455755i	0.967072	−	0.254502i	$-0.0819117\pi$
$61$	2.05511	+	3.55956i	0.263131	+	0.455755i	−0.703942	+	0.710258i	$0.748578\pi$
$62$	5.83739	−	10.1106i	0.741349	−	1.28405i
$63$	1.92988	−	3.34266i	0.243142	−	0.421135i
$64$	−6.93860			−0.867325
$65$	1.50001			0.186054
$66$	−11.0998	+	19.2255i	−1.36629	+	2.36649i
$67$	−5.41099	+	9.37210i	−0.661057	+	1.14498i	0.319281	+	0.947660i	$0.396559\pi$
$67$	−5.41099	+	9.37210i	−0.661057	+	1.14498i	−0.980338	+	0.197324i	$0.936775\pi$
$68$	−2.04186	−	3.53661i	−0.247612	−	0.428877i
$69$	−6.36771	−	11.0292i	−0.766582	−	1.32776i
$70$	10.2751			1.22811
$71$	−2.66225	−	4.61115i	−0.315951	−	0.547243i	0.663688	−	0.748009i	$-0.268990\pi$
$71$	−2.66225	−	4.61115i	−0.315951	−	0.547243i	−0.979639	+	0.200767i	$0.935657\pi$
$72$	−2.04049	−	3.53424i	−0.240474	−	0.416514i
$73$	−5.78506	−	10.0200i	−0.677090	−	1.17275i	−0.975853	−	0.218426i	$-0.929908\pi$
$73$	−5.78506	−	10.0200i	−0.677090	−	1.17275i	0.298764	−	0.954327i	$-0.403426\pi$
$74$	11.3083	−	19.5866i	1.31457	−	2.27690i
$75$	6.33541			0.731551
$76$	9.24547	−	16.0136i	1.06053	−	1.83689i
$77$	−14.7283	−	25.5102i	−1.67845	−	2.90716i
$78$	−6.41209			−0.726026
$79$	−3.54591	−	6.14170i	−0.398947	−	0.690996i	0.594650	−	0.803985i	$-0.297291\pi$
$79$	−3.54591	−	6.14170i	−0.398947	−	0.690996i	−0.993596	+	0.112989i	$0.963957\pi$
$80$	1.93226	−	3.34678i	0.216033	−	0.374181i
$81$	2.99370	−	5.18525i	0.332634	−	0.576139i
$82$	6.67413			0.737034
$83$	−0.350368	+	0.606856i	−0.0384579	+	0.0666111i	−0.884614	−	0.466325i	$-0.845578\pi$
$83$	−0.350368	+	0.606856i	−0.0384579	+	0.0666111i	0.846156	+	0.532936i	$0.178911\pi$
$84$	−29.4834			−3.21691
$85$	−0.856997			−0.0929544
$86$	−10.0007	+	12.7117i	−1.07840	+	1.37074i
$87$	−4.15437			−0.445395
$88$	−31.1449			−3.32006
$89$	−4.96902	+	8.60659i	−0.526715	+	0.912297i	0.472801	+	0.881169i	$0.343243\pi$
$89$	−4.96902	+	8.60659i	−0.526715	+	0.912297i	−0.999515	+	0.0311273i	$0.990090\pi$
$90$	−1.67843			−0.176922
$91$	4.25410	−	7.36831i	0.445950	−	0.772409i
$92$	17.5082	−	30.3250i	1.82535	−	3.16160i
$93$	3.51506	+	6.08826i	0.364495	+	0.631324i
$94$	−3.13943			−0.323808
$95$	−1.94022	−	3.36056i	−0.199063	−	0.344787i
$96$	−0.626296	+	1.08478i	−0.0639211	+	0.110715i
$97$	−4.70746			−0.477971			−0.238985	−	0.971023i	$-0.576815\pi$
$97$	−4.70746			−0.477971			−0.238985	+	0.971023i	$0.576815\pi$
$98$	20.5078	−	35.5206i	2.07160	−	3.58812i
$99$	2.40586	+	4.16707i	0.241798	+	0.418807i
$100$	8.70968	+	15.0856i	0.870968	+	1.50856i
$101$	1.05832	+	1.83307i	0.105307	+	0.182397i	0.913864	−	0.406021i	$-0.133084\pi$
$101$	1.05832	+	1.83307i	0.105307	+	0.182397i	−0.808556	+	0.588419i	$0.799751\pi$
$102$	3.66340			0.362731
$103$	−3.43231	−	5.94494i	−0.338196	−	0.585772i	0.645898	−	0.763424i	$-0.276483\pi$
$103$	−3.43231	−	5.94494i	−0.338196	−	0.585772i	−0.984093	+	0.177652i	$0.943150\pi$
$104$	−4.49791	−	7.79061i	−0.441057	−	0.763933i
$105$	−3.09365	+	5.35836i	−0.301909	+	0.522922i
$106$	−11.3418	+	19.6445i	−1.10161	+	1.90804i
$107$	4.90980			0.474649			0.237324	−	0.971430i	$-0.423730\pi$
$107$	4.90980			0.474649			0.237324	+	0.971430i	$0.423730\pi$
$108$	23.0122			2.21435
$109$	6.72905	−	11.6551i	0.644526	−	1.11635i	−0.339884	−	0.940467i	$-0.610388\pi$
$109$	6.72905	−	11.6551i	0.644526	−	1.11635i	0.984411	−	0.175885i	$-0.0562788\pi$
$110$	−6.40466	+	11.0932i	−0.610660	+	1.05769i
$111$	6.80947	+	11.7943i	0.646326	+	1.11947i
$112$	−10.9599	−	18.9832i	−1.03562	−	1.79374i
$113$	−3.50120			−0.329365			−0.164683	−	0.986347i	$-0.552660\pi$
$113$	−3.50120			−0.329365			−0.164683	+	0.986347i	$0.552660\pi$
$114$	8.29386	+	14.3654i	0.776791	+	1.34544i
$115$	−3.67420	−	6.36391i	−0.342621	−	0.593437i
$116$	−5.71126	−	9.89220i	−0.530277	−	0.918467i
$117$	−0.694903	+	1.20361i	−0.0642438	+	0.111274i
$118$	18.8084			1.73145
$119$	−2.43048	+	4.20972i	−0.222802	+	0.385904i
$120$	3.27096	+	5.66546i	0.298596	+	0.517184i
$121$	25.7217			2.33834
$122$	−5.06898	−	8.77974i	−0.458924	−	0.794880i
$123$	−2.00946	+	3.48049i	−0.181187	+	0.313825i
$124$	−9.66474	+	16.7398i	−0.867919	+	1.50328i
$125$	7.94056			0.710225
$126$	−4.76010	+	8.24473i	−0.424063	+	0.734499i
$127$	−13.7604			−1.22103			−0.610517	−	0.792003i	$-0.709038\pi$
$127$	−13.7604			−1.22103			−0.610517	+	0.792003i	$0.709038\pi$
$128$	18.8009			1.66178
$129$	−3.61799	−	9.04249i	−0.318546	−	0.796147i
$130$	−3.69981			−0.324495
$131$	20.7164			1.81000			0.904999	−	0.425413i	$-0.139871\pi$
$131$	20.7164			1.81000			0.904999	+	0.425413i	$0.139871\pi$
$132$	18.3776	−	31.8309i	1.59956	−	2.77052i
$133$	−22.0102			−1.90853
$134$	13.3463	−	23.1165i	1.15295	−	1.99696i
$135$	2.41463	−	4.18226i	0.207818	−	0.359951i
$136$	2.56978	+	4.45099i	0.220357	+	0.381669i
$137$	−9.58510			−0.818910			−0.409455	−	0.912330i	$-0.634281\pi$
$137$	−9.58510			−0.818910			−0.409455	+	0.912330i	$0.634281\pi$
$138$	15.7061	+	27.2037i	1.33699	+	2.31574i
$139$	−9.32195	+	16.1461i	−0.790678	+	1.36949i	0.134870	+	0.990863i	$0.456938\pi$
$139$	−9.32195	+	16.1461i	−0.790678	+	1.36949i	−0.925548	+	0.378630i	$0.876395\pi$
$140$	−17.0121			−1.43779
$141$	0.945226	−	1.63718i	0.0796024	−	0.137875i
$142$	6.56649	+	11.3735i	0.551048	+	0.954442i
$143$	5.30331	+	9.18560i	0.443485	+	0.768138i
$144$	1.79030	+	3.10089i	0.149192	+	0.258407i
$145$	−2.39709			−0.199068
$146$	14.2690	+	24.7146i	1.18091	+	2.04539i
$147$	12.3491	+	21.3892i	1.01853	+	1.76415i
$148$	−18.7228	+	32.4288i	−1.53900	+	2.66563i
$149$	3.57420	−	6.19070i	0.292810	−	0.507162i	−0.681663	−	0.731666i	$-0.738743\pi$
$149$	3.57420	−	6.19070i	0.292810	−	0.507162i	0.974473	+	0.224504i	$0.0720763\pi$
$150$	−15.6264			−1.27589
$151$	−18.1400			−1.47621			−0.738107	−	0.674684i	$-0.764280\pi$
$151$	−18.1400			−1.47621			−0.738107	+	0.674684i	$0.764280\pi$
$152$	−11.6358	+	20.1539i	−0.943792	+	1.63470i
$153$	0.397017	−	0.687654i	0.0320969	−	0.0555935i
$154$	36.3278	+	62.9215i	2.92737	+	5.07036i
$155$	2.02821	+	3.51296i	0.162910	+	0.282168i
$156$	10.6163			0.849981
$157$	−3.30807	−	5.72975i	−0.264013	−	0.457284i	0.703292	−	0.710901i	$-0.251713\pi$
$157$	−3.30807	−	5.72975i	−0.264013	−	0.457284i	−0.967304	+	0.253618i	$0.918379\pi$
$158$	8.74607	+	15.1486i	0.695800	+	1.20516i
$159$	−6.82960	−	11.8292i	−0.541622	−	0.938118i
$160$	−0.361376	+	0.625922i	−0.0285693	+	0.0494835i
$161$	−41.6808			−3.28490
$162$	−7.38404	+	12.7895i	−0.580145	+	1.00484i
$163$	4.09343	+	7.09003i	0.320622	+	0.555334i	0.980617	−	0.195937i	$-0.0627747\pi$
$163$	4.09343	+	7.09003i	0.320622	+	0.555334i	−0.659994	+	0.751271i	$0.729441\pi$
$164$	−11.0501			−0.862869
$165$	−3.85665	−	6.67992i	−0.300240	−	0.520031i
$166$	0.864191	−	1.49682i	0.0670742	−	0.116176i
$167$	−1.08847	+	1.88529i	−0.0842286	+	0.145888i	−0.905062	−	0.425279i	$-0.860176\pi$
$167$	−1.08847	+	1.88529i	−0.0842286	+	0.145888i	0.820834	+	0.571167i	$0.193509\pi$
$168$	37.1063			2.86281
$169$	4.96821	−	8.60518i	0.382170	−	0.661937i
$170$	2.11380			0.162121
$171$	3.59535			0.274943
$172$	16.5577	−	21.0463i	1.26251	−	1.60476i
$173$	3.77252			0.286819			0.143410	−	0.989663i	$-0.454193\pi$
$173$	3.77252			0.286819			0.143410	+	0.989663i	$0.454193\pi$
$174$	10.2468			0.776810
$175$	10.3673	−	17.9568i	0.783698	−	1.35740i
$176$	27.3261			2.05978
$177$	−5.66287	+	9.80837i	−0.425647	+	0.737242i
$178$	12.2562	−	21.2283i	0.918640	−	1.59113i
$179$	3.30603	+	5.72620i	0.247104	+	0.427997i	0.962721	−	0.270496i	$-0.0871877\pi$
$179$	3.30603	+	5.72620i	0.247104	+	0.427997i	−0.715617	+	0.698493i	$0.753854\pi$
$180$	2.77892			0.207128
$181$	5.06434	+	8.77169i	0.376429	+	0.651994i	0.990540	−	0.137226i	$-0.0438185\pi$
$181$	5.06434	+	8.77169i	0.376429	+	0.651994i	−0.614111	+	0.789220i	$0.710485\pi$
$182$	−10.4928	+	18.1741i	−0.777780	+	1.34715i
$183$	6.10472			0.451274
$184$	−22.0348	+	38.1654i	−1.62443	+	2.81359i
$185$	3.92910	+	6.80540i	0.288873	+	0.500343i
$186$	−8.66997	−	15.0168i	−0.635713	−	1.10109i
$187$	−3.02992	−	5.24798i	−0.221570	−	0.383770i
$188$	5.19784			0.379091
$189$	−13.6960	−	23.7221i	−0.996235	−	1.72553i
$190$	4.78560	+	8.28891i	0.347184	+	0.601340i
$191$	4.57251	−	7.91982i	0.330855	−	0.573058i	−0.651824	−	0.758370i	$-0.725996\pi$
$191$	4.57251	−	7.91982i	0.330855	−	0.573058i	0.982680	+	0.185312i	$0.0593294\pi$
$192$	−5.15278	+	8.92487i	−0.371870	+	0.644097i
$193$	5.95482			0.428637			0.214319	−	0.976764i	$-0.431247\pi$
$193$	5.95482			0.428637			0.214319	+	0.976764i	$0.431247\pi$
$194$	11.6111			0.833626
$195$	1.11395	−	1.92941i	0.0797713	−	0.138168i
$196$	−33.9540	+	58.8101i	−2.42529	+	4.20072i
$197$	12.4998	+	21.6502i	0.890570	+	1.54251i	0.839193	+	0.543834i	$0.183028\pi$
$197$	12.4998	+	21.6502i	0.890570	+	1.54251i	0.0513776	+	0.998679i	$0.483639\pi$
$198$	−5.93411	−	10.2782i	−0.421719	−	0.730438i
$199$	21.9092			1.55310			0.776550	−	0.630055i	$-0.216968\pi$
$199$	21.9092			1.55310			0.776550	+	0.630055i	$0.216968\pi$
$200$	−10.9615	−	18.9859i	−0.775098	−	1.34251i
$201$	8.03666	+	13.9199i	0.566863	+	0.981835i
$202$	−2.61038	−	4.52131i	−0.183666	−	0.318118i
$203$	−6.79825	+	11.7749i	−0.477144	+	0.826438i
$204$	−6.06535			−0.424660
$205$	−1.15947	+	2.00826i	−0.0809809	+	0.140263i
$206$	8.46587	+	14.6633i	0.589845	+	1.02164i
$207$	6.80852			0.473225
$208$	3.94641	+	6.83537i	0.273634	+	0.473948i
$209$	13.7194	−	23.7626i	0.948988	−	1.64370i
$210$	7.63055	−	13.2165i	0.526558	−	0.912025i
$211$	1.70694			0.117511			0.0587553	−	0.998272i	$-0.481287\pi$
$211$	1.70694			0.117511			0.0587553	+	0.998272i	$0.481287\pi$
$212$	18.7781	−	32.5247i	1.28969	−	2.23380i
$213$	−7.90820			−0.541861
$214$	−12.1101			−0.827832
$215$	−2.08760	−	5.21757i	−0.142373	−	0.355835i
$216$	−28.9619			−1.97060
$217$	23.0084			1.56191
$218$	−16.5974	+	28.7475i	−1.12411	+	1.94702i
$219$	−17.1845			−1.16122
$220$	10.6040	−	18.3666i	0.714919	−	1.23828i
$221$	0.875156	−	1.51581i	0.0588693	−	0.101965i
$222$	−16.7957	−	29.0910i	−1.12725	−	1.95246i
$223$	−19.2650			−1.29008			−0.645039	−	0.764150i	$-0.723159\pi$
$223$	−19.2650			−1.29008			−0.645039	+	0.764150i	$0.723159\pi$
$224$	2.04976	+	3.55028i	0.136955	+	0.237213i
$225$	−1.69350	+	2.93322i	−0.112900	+	0.195548i
$226$	8.63579			0.574444
$227$	−13.9956	+	24.2410i	−0.928918	+	1.60893i	−0.143783	+	0.989609i	$0.545927\pi$
$227$	−13.9956	+	24.2410i	−0.928918	+	1.60893i	−0.785135	+	0.619324i	$0.787407\pi$
$228$	−13.7318	−	23.7842i	−0.909413	−	1.57515i
$229$	8.72065	+	15.1046i	0.576277	+	0.998141i	0.995902	+	0.0904433i	$0.0288284\pi$
$229$	8.72065	+	15.1046i	0.576277	+	0.998141i	−0.419625	+	0.907698i	$0.637838\pi$
$230$	9.06250	+	15.6967i	0.597564	+	1.03501i
$231$	−43.7505			−2.87857
$232$	7.18789	+	12.4498i	0.471908	+	0.817368i
$233$	3.43121	+	5.94303i	0.224786	+	0.389341i	0.956255	−	0.292534i	$-0.0944984\pi$
$233$	3.43121	+	5.94303i	0.224786	+	0.389341i	−0.731469	+	0.681874i	$0.761165\pi$
$234$	1.71399	−	2.96872i	0.112047	−	0.194072i
$235$	0.545401	−	0.944661i	0.0355780	−	0.0616229i
$236$	−31.1404			−2.02706
$237$	−10.5331			−0.684201
$238$	5.99483	−	10.3834i	0.388587	−	0.673053i
$239$	1.81199	−	3.13845i	0.117208	−	0.203009i	−0.801452	−	0.598058i	$-0.795939\pi$
$239$	1.81199	−	3.13845i	0.117208	−	0.203009i	0.918660	+	0.395049i	$0.129272\pi$
$240$	−2.86989	−	4.97080i	−0.185251	−	0.320864i
$241$	5.94814	+	10.3025i	0.383154	+	0.663641i	0.991511	−	0.130022i	$-0.0415047\pi$
$241$	5.94814	+	10.3025i	0.383154	+	0.663641i	−0.608358	+	0.793663i	$0.708171\pi$
$242$	−63.4432			−4.07829
$243$	4.00623	+	6.93900i	0.257000	+	0.445137i
$244$	8.39253	+	14.5363i	0.537277	+	0.930590i
$245$	7.12548	+	12.3417i	0.455230	+	0.788482i
$246$	4.95637	−	8.58469i	0.316007	−	0.547340i
$247$	7.92533			0.504277
$248$	12.1635	−	21.0678i	0.772384	−	1.33781i
$249$	0.520384	+	0.901332i	0.0329780	+	0.0571196i
$250$	−19.5856			−1.23870
$251$	8.04457	+	13.9336i	0.507769	+	0.879482i	0.999960	+	0.00899420i	$0.00286298\pi$
$251$	8.04457	+	13.9336i	0.507769	+	0.879482i	−0.492191	+	0.870487i	$0.663804\pi$
$252$	7.88112	−	13.6505i	0.496464	−	0.859901i
$253$	25.9804	−	44.9993i	1.63337	−	2.82908i
$254$	33.9402			2.12960
$255$	−0.636427	+	1.10232i	−0.0398546	+	0.0690303i
$256$	−32.4957			−2.03098
$257$	1.90268			0.118686			0.0593429	−	0.998238i	$-0.481099\pi$
$257$	1.90268			0.118686			0.0593429	+	0.998238i	$0.481099\pi$
$258$	8.92385	+	22.3035i	0.555574	+	1.38856i
$259$	44.5724			2.76959
$260$	6.12564			0.379896
$261$	1.11049	−	1.92342i	0.0687376	−	0.119057i
$262$	−51.0974			−3.15681
$263$	1.99586	−	3.45692i	0.123070	−	0.213163i	−0.797907	−	0.602780i	$-0.794059\pi$
$263$	1.99586	−	3.45692i	0.123070	−	0.213163i	0.920977	+	0.389618i	$0.127393\pi$
$264$	−23.1290	+	40.0606i	−1.42349	+	2.46556i
$265$	−3.94072	−	6.82552i	−0.242076	−	0.419288i
$266$	54.2887			3.32865
$267$	7.38023	+	12.7829i	0.451663	+	0.782303i
$268$	−22.0970	+	38.2731i	−1.34979	+	2.33790i
$269$	13.3698			0.815172			0.407586	−	0.913167i	$-0.366371\pi$
$269$	13.3698			0.815172			0.407586	+	0.913167i	$0.366371\pi$
$270$	−5.95573	+	10.3156i	−0.362454	+	0.627789i
$271$	−7.43452	−	12.8770i	−0.451615	−	0.782220i	0.546872	−	0.837216i	$-0.315819\pi$
$271$	−7.43452	−	12.8770i	−0.451615	−	0.782220i	−0.998487	+	0.0549967i	$0.982485\pi$
$272$	−2.25469	−	3.90523i	−0.136711	−	0.236790i
$273$	−6.31839	−	10.9438i	−0.382407	−	0.662348i
$274$	23.6418			1.42826
$275$	12.9243	+	22.3856i	0.779365	+	1.34990i
$276$	−26.0040	−	45.0402i	−1.56526	−	2.71110i
$277$	−12.5897	+	21.8060i	−0.756442	+	1.31020i	0.188212	+	0.982128i	$0.439731\pi$
$277$	−12.5897	+	21.8060i	−0.756442	+	1.31020i	−0.944654	+	0.328068i	$0.893602\pi$
$278$	22.9928	−	39.8247i	1.37902	−	2.38853i
$279$	−3.75840			−0.225009
$280$	21.4105			1.27952
$281$	0.684462	−	1.18552i	0.0408316	−	0.0707224i	−0.844887	−	0.534944i	$-0.820333\pi$
$281$	0.684462	−	1.18552i	0.0408316	−	0.0707224i	0.885719	+	0.464222i	$0.153666\pi$
$282$	−2.33142	+	4.03814i	−0.138834	+	0.240468i
$283$	−6.72457	−	11.6473i	−0.399734	−	0.692360i	0.593959	−	0.804495i	$-0.297564\pi$
$283$	−6.72457	−	11.6473i	−0.399734	−	0.692360i	−0.993693	+	0.112136i	$0.964231\pi$
$284$	−10.8719	−	18.8307i	−0.645128	−	1.11739i
$285$	−5.76343			−0.341396
$286$	−13.0807	−	22.6565i	−0.773479	−	1.33971i
$287$	6.57661	+	11.3910i	0.388205	+	0.672390i
$288$	−0.334826	−	0.579936i	−0.0197298	−	0.0341730i
$289$	−0.500000	+	0.866025i	−0.0294118	+	0.0509427i
$290$	5.91248			0.347193
$291$	−3.49588	+	6.05504i	−0.204932	+	0.354953i
$292$	−23.6246	−	40.9190i	−1.38252	−	2.39460i
$293$	5.61563			0.328068			0.164034	−	0.986455i	$-0.447549\pi$
$293$	5.61563			0.328068			0.164034	+	0.986455i	$0.447549\pi$
$294$	−30.4592	−	52.7569i	−1.77642	−	3.07685i
$295$	−3.26751	+	5.65949i	−0.190242	+	0.329508i
$296$	23.5635	−	40.8131i	1.36960	−	2.37222i
$297$	34.1478			1.98145
$298$	−8.81585	+	15.2695i	−0.510689	+	0.884538i
$299$	15.0082			0.867947
$300$	25.8721			1.49373
$301$	−31.5501	−	4.54261i	−1.81852	−	0.261831i
$302$	44.7427			2.57466
$303$	3.14375			0.180604
$304$	10.2091	−	17.6827i	0.585534	−	1.01417i
$305$	3.52246			0.201695
$306$	−0.979251	+	1.69611i	−0.0559800	+	0.0969603i
$307$	11.5797	−	20.0567i	0.660890	−	1.14470i	−0.319492	−	0.947589i	$-0.603512\pi$
$307$	11.5797	−	20.0567i	0.660890	−	1.14470i	0.980382	−	0.197106i	$-0.0631544\pi$
$308$	−60.1465	−	104.177i	−3.42717	−	5.93603i
$309$	−10.1957			−0.580012
$310$	−5.00262	−	8.66480i	−0.284130	−	0.492128i
$311$	−8.72666	+	15.1150i	−0.494843	+	0.857094i	−0.999982	−	0.00594409i	$-0.998108\pi$
$311$	−8.72666	+	15.1150i	−0.494843	+	0.857094i	0.505139	+	0.863038i	$0.331441\pi$
$312$	−13.3610			−0.756420
$313$	−12.6106	+	21.8422i	−0.712793	+	1.23459i	0.251012	+	0.967984i	$0.419237\pi$
$313$	−12.6106	+	21.8422i	−0.712793	+	1.23459i	−0.963805	+	0.266609i	$0.914097\pi$
$314$	8.15943	+	14.1325i	0.460463	+	0.797545i
$315$	−1.65391	−	2.86465i	−0.0931870	−	0.161405i
$316$	−14.4805	−	25.0810i	−0.814595	−	1.41092i
$317$	12.6194			0.708779			0.354389	−	0.935098i	$-0.384689\pi$
$317$	12.6194			0.708779			0.354389	+	0.935098i	$0.384689\pi$
$318$	16.8454	+	29.1770i	0.944640	+	1.63617i
$319$	−8.47495	−	14.6790i	−0.474506	−	0.821868i
$320$	−2.97318	+	5.14970i	−0.166206	+	0.287877i
$321$	3.64614	−	6.31530i	0.203508	−	0.352486i
$322$	102.807			5.72918
$323$	−4.52796			−0.251942
$324$	12.2255	−	21.1751i	0.679193	−	1.17640i
$325$	−3.73302	+	6.46579i	−0.207071	+	0.358657i
$326$	−10.0965	−	17.4877i	−0.559195	−	0.968555i
$327$	−9.99432	−	17.3107i	−0.552687	−	0.957283i
$328$	13.9071			0.767889
$329$	−3.09356	−	5.35820i	−0.170553	−	0.295407i
$330$	9.51252	+	16.4762i	0.523647	+	0.906983i
$331$	−5.12471	−	8.87626i	−0.281680	−	0.487883i	0.690119	−	0.723696i	$-0.257558\pi$
$331$	−5.12471	−	8.87626i	−0.281680	−	0.487883i	−0.971799	+	0.235813i	$0.924225\pi$
$332$	−1.43081	+	2.47823i	−0.0785258	+	0.136011i
$333$	−7.28086			−0.398989
$334$	2.68474	−	4.65011i	0.146903	−	0.254443i
$335$	4.63720	+	8.03187i	0.253357	+	0.438828i
$336$	−32.5565			−1.77610
$337$	5.14044	+	8.90350i	0.280017	+	0.485004i	0.971389	−	0.237495i	$-0.0763264\pi$
$337$	5.14044	+	8.90350i	0.280017	+	0.485004i	−0.691371	+	0.722500i	$0.742993\pi$
$338$	−12.2542	+	21.2249i	−0.666540	+	1.15448i
$339$	−2.60008	+	4.50347i	−0.141217	+	0.244595i
$340$	−3.49974			−0.189800
$341$	−14.3415	+	24.8402i	−0.776637	+	1.34517i
$342$	−8.86801			−0.479527
$343$	46.8059			2.52728
$344$	−20.8387	+	26.4877i	−1.12355	+	1.42812i
$345$	−10.9142			−0.587602
$346$	−9.30500			−0.500240
$347$	2.91463	−	5.04828i	0.156465	−	0.271006i	−0.777126	−	0.629345i	$-0.783323\pi$
$347$	2.91463	−	5.04828i	0.156465	−	0.271006i	0.933592	+	0.358339i	$0.116657\pi$
$348$	−16.9653			−0.909436
$349$	−8.47194	+	14.6738i	−0.453493	+	0.785472i	−0.998600	−	0.0528938i	$-0.983156\pi$
$349$	−8.47194	+	14.6738i	−0.453493	+	0.785472i	0.545107	+	0.838366i	$0.316489\pi$
$350$	−25.5713	+	44.2908i	−1.36684	+	2.36744i
$351$	4.93158	+	8.54174i	0.263228	+	0.455924i
$352$	−5.11060			−0.272396
$353$	−9.81905	−	17.0071i	−0.522615	−	0.905196i	−0.999654	−	0.0263138i	$-0.991623\pi$
$353$	−9.81905	−	17.0071i	−0.522615	−	0.905196i	0.477038	−	0.878882i	$-0.341710\pi$
$354$	13.9676	−	24.1926i	0.742369	−	1.28582i
$355$	−4.56308			−0.242183
$356$	−20.2921	+	35.1470i	−1.07548	+	1.86279i
$357$	3.60987	+	6.25248i	0.191055	+	0.330916i
$358$	−8.15438	−	14.1238i	−0.430973	−	0.746466i
$359$	−0.370894	−	0.642408i	−0.0195751	−	0.0339050i	0.856072	−	0.516857i	$-0.172898\pi$
$359$	−0.370894	−	0.642408i	−0.0195751	−	0.0339050i	−0.875647	+	0.482952i	$0.839565\pi$
$360$	−3.49739			−0.184329
$361$	−0.751192	−	1.30110i	−0.0395364	−	0.0684790i
$362$	−12.4913	−	21.6356i	−0.656528	−	1.13714i
$363$	19.1016	−	33.0849i	1.00257	−	1.73651i
$364$	17.3726	−	30.0902i	0.910570	−	1.57715i
$365$	−9.91556			−0.519004
$366$	−15.0574			−0.787064
$367$	7.65072	−	13.2514i	0.399364	−	0.691719i	−0.594283	−	0.804256i	$-0.702564\pi$
$367$	7.65072	−	13.2514i	0.399364	−	0.691719i	0.993648	+	0.112537i	$0.0358975\pi$
$368$	19.3330	−	33.4858i	1.00780	−	1.74557i
$369$	−1.07428	−	1.86071i	−0.0559250	−	0.0968649i
$370$	−9.69121	−	16.7857i	−0.503822	−	0.872645i
$371$	−44.7042			−2.32092
$372$	14.3546	+	24.8628i	0.744249	+	1.28908i
$373$	−7.42932	−	12.8680i	−0.384676	−	0.666278i	0.607048	−	0.794665i	$-0.292353\pi$
$373$	−7.42932	−	12.8680i	−0.384676	−	0.666278i	−0.991724	+	0.128387i	$0.959020\pi$
$374$	7.47337	+	12.9443i	0.386439	+	0.669332i
$375$	5.89685	−	10.2137i	0.304512	−	0.527431i
$376$	−6.54172			−0.337363
$377$	2.44788	−	4.23986i	0.126072	−	0.218364i
$378$	33.7814	+	58.5111i	1.73753	+	3.00949i
$379$	35.4666			1.82180			0.910900	−	0.412628i	$-0.135389\pi$
$379$	35.4666			1.82180			0.910900	+	0.412628i	$0.135389\pi$
$380$	−7.92334	−	13.7236i	−0.406459	−	0.704007i
$381$	−10.2188	+	17.6994i	−0.523524	+	0.906770i
$382$	−11.2782	+	19.5344i	−0.577043	+	0.999467i
$383$	−9.68269			−0.494762			−0.247381	−	0.968918i	$-0.579570\pi$
$383$	−9.68269			−0.494762			−0.247381	+	0.968918i	$0.579570\pi$
$384$	13.9620	−	24.1829i	0.712497	−	1.23408i
$385$	−25.2443			−1.28657
$386$	−14.6877			−0.747584
$387$	5.15368	+	0.742031i	0.261976	+	0.0377195i
$388$	−19.2240			−0.975951
$389$	15.2437			0.772887			0.386443	−	0.922313i	$-0.373704\pi$
$389$	15.2437			0.772887			0.386443	+	0.922313i	$0.373704\pi$
$390$	−2.74757	+	4.75893i	−0.139129	+	0.240978i
$391$	−8.57460			−0.433636
$392$	42.7327	−	74.0152i	2.15833	−	3.73833i
$393$	15.3845	−	26.6467i	0.776045	−	1.34415i
$394$	−30.8309	−	53.4007i	−1.55324	−	2.69029i
$395$	−6.07768			−0.305801
$396$	9.82488	+	17.0172i	0.493719	+	0.855146i
$397$	3.41766	−	5.91957i	0.171528	−	0.297095i	−0.767427	−	0.641137i	$-0.778463\pi$
$397$	3.41766	−	5.91957i	0.171528	−	0.297095i	0.938954	+	0.344042i	$0.111796\pi$
$398$	−54.0394			−2.70875
$399$	−16.3453	+	28.3109i	−0.818290	+	1.41732i
$400$	9.61750	+	16.6580i	0.480875	+	0.832900i
$401$	−3.06047	−	5.30089i	−0.152832	−	0.264714i	0.779435	−	0.626483i	$-0.215506\pi$
$401$	−3.06047	−	5.30089i	−0.152832	−	0.264714i	−0.932268	+	0.361769i	$0.882173\pi$
$402$	−19.8226	−	34.3338i	−0.988662	−	1.71241i
$403$	−8.28474			−0.412692
$404$	4.32191	+	7.48576i	0.215023	+	0.372431i
$405$	−2.56560	−	4.44374i	−0.127486	−	0.220811i
$406$	16.7680	−	29.0431i	0.832184	−	1.44138i
$407$	−27.7828	+	48.1211i	−1.37714	+	2.38528i
$408$	7.63353			0.377916
$409$	−1.11227			−0.0549982			−0.0274991	−	0.999622i	$-0.508754\pi$
$409$	−1.11227			−0.0549982			−0.0274991	+	0.999622i	$0.508754\pi$
$410$	2.85986	−	4.95342i	0.141238	−	0.244632i
$411$	−7.11813	+	12.3290i	−0.351111	+	0.608143i
$412$	−14.0166	−	24.2775i	−0.690550	−	1.19607i
$413$	18.5336	+	32.1011i	0.911977	+	1.57959i
$414$	−16.7934			−0.825349
$415$	0.300265	+	0.520074i	0.0147394	+	0.0255294i
$416$	−0.738066	−	1.27837i	−0.0361867	−	0.0626772i
$417$	13.8454	+	23.9810i	0.678013	+	1.17435i
$418$	−33.8391	+	58.6110i	−1.65512	+	2.86676i
$419$	−2.58513			−0.126292			−0.0631459	−	0.998004i	$-0.520113\pi$
$419$	−2.58513			−0.126292			−0.0631459	+	0.998004i	$0.520113\pi$
$420$	−12.6336	+	21.8821i	−0.616457	+	1.06774i
$421$	−8.63285	−	14.9525i	−0.420739	−	0.728742i	0.575273	−	0.817962i	$-0.304896\pi$
$421$	−8.63285	−	14.9525i	−0.420739	−	0.728742i	−0.996012	+	0.0892198i	$0.971563\pi$
$422$	−4.21020			−0.204950
$423$	0.505330	+	0.875257i	0.0245700	+	0.0425565i
$424$	−23.6331	+	40.9338i	−1.14773	+	1.98792i
$425$	2.13278	−	3.69408i	0.103455	−	0.179189i
$426$	19.5058			0.945057
$427$	9.98983	−	17.3029i	0.483442	−	0.837346i
$428$	20.0503			0.969168
$429$	15.7535			0.760585
$430$	5.14911	+	12.8692i	0.248312	+	0.620610i
$431$	−2.22097			−0.106980			−0.0534902	−	0.998568i	$-0.517035\pi$
$431$	−2.22097			−0.106980			−0.0534902	+	0.998568i	$0.517035\pi$
$432$	25.4107			1.22257
$433$	−20.0830	+	34.7847i	−0.965125	+	1.67165i	−0.255847	+	0.966717i	$0.582354\pi$
$433$	−20.0830	+	34.7847i	−0.965125	+	1.67165i	−0.709278	+	0.704929i	$0.750979\pi$
$434$	−56.7506			−2.72412
$435$	−1.78014	+	3.08329i	−0.0853512	+	0.147833i
$436$	27.4796	−	47.5961i	1.31604	−	2.27944i
$437$	−19.4127	−	33.6238i	−0.928635	−	1.60844i
$438$	42.3859			2.02528
$439$	3.54785	+	6.14506i	0.169330	+	0.293288i	0.938184	−	0.346136i	$-0.112506\pi$
$439$	3.54785	+	6.14506i	0.169330	+	0.293288i	−0.768855	+	0.639424i	$0.779173\pi$
$440$	−13.3456	+	23.1152i	−0.636225	+	1.10197i
$441$	−13.2039			−0.628759
$442$	−2.15859	+	3.73879i	−0.102674	+	0.177836i
$443$	−0.111399	−	0.192948i	−0.00529272	−	0.00916725i	0.863367	−	0.504577i	$-0.168351\pi$
$443$	−0.111399	−	0.192948i	−0.00529272	−	0.00916725i	−0.868660	+	0.495409i	$0.835018\pi$
$444$	27.8080	+	48.1649i	1.31971	+	2.28580i
$445$	4.25843	+	7.37583i	0.201869	+	0.349648i
$446$	47.5175			2.25002
$447$	−5.30859	−	9.19474i	−0.251087	−	0.434896i
$448$	16.8641	+	29.2095i	0.796755	+	1.38002i
$449$	11.0104	−	19.0706i	0.519613	−	0.899996i	−0.480127	−	0.877199i	$-0.659410\pi$
$449$	11.0104	−	19.0706i	0.519613	−	0.899996i	0.999740	−	0.0227970i	$-0.00725713\pi$
$450$	4.17705	−	7.23486i	0.196908	−	0.341055i
$451$	−16.3973			−0.772117
$452$	−14.2980			−0.672519
$453$	−13.4712	+	23.3328i	−0.632933	+	1.09627i
$454$	34.5204	−	59.7910i	1.62012	−	2.80613i
$455$	−3.64575	−	6.31462i	−0.170915	−	0.296034i
$456$	17.2821	+	29.9335i	0.809310	+	1.40177i
$457$	26.0286			1.21757			0.608784	−	0.793336i	$-0.291658\pi$
$457$	26.0286			1.21757			0.608784	+	0.793336i	$0.291658\pi$
$458$	−21.5097	−	37.2559i	−1.00508	−	1.74085i
$459$	−2.81754	−	4.88013i	−0.131512	−	0.227785i
$460$	−15.0044	−	25.9885i	−0.699586	−	1.21172i
$461$	−2.47306	+	4.28346i	−0.115182	+	0.199501i	−0.917852	−	0.396922i	$-0.870078\pi$
$461$	−2.47306	+	4.28346i	−0.115182	+	0.199501i	0.802671	+	0.596422i	$0.203412\pi$
$462$	107.912			5.02050
$463$	−1.72500	+	2.98778i	−0.0801674	+	0.138854i	−0.903322	−	0.428964i	$-0.858879\pi$
$463$	−1.72500	+	2.98778i	−0.0801674	+	0.138854i	0.823154	+	0.567818i	$0.192212\pi$
$464$	−6.30655	−	10.9233i	−0.292774	−	0.507100i
$465$	6.02480			0.279393
$466$	−8.46315	−	14.6586i	−0.392048	−	0.679047i
$467$	14.0814	−	24.3896i	0.651608	−	1.12862i	−0.331125	−	0.943587i	$-0.607428\pi$
$467$	14.0814	−	24.3896i	0.651608	−	1.12862i	0.982733	−	0.185031i	$-0.0592384\pi$
$468$	−2.83780	+	4.91521i	−0.131177	+	0.227205i
$469$	52.6052			2.42908
$470$	−1.34524	+	2.33003i	−0.0620514	+	0.107476i
$471$	−9.82662			−0.452787
$472$	39.1916			1.80394
$473$	24.5700	−	31.2306i	1.12973	−	1.43598i
$474$	25.9802			1.19331
$475$	19.3142			0.886198
$476$	−9.92542	+	17.1913i	−0.454931	+	0.787963i
$477$	7.30239			0.334353
$478$	−4.46930	+	7.74105i	−0.204421	+	0.354068i
$479$	6.65004	−	11.5182i	0.303848	−	0.526280i	−0.673156	−	0.739500i	$-0.735062\pi$
$479$	6.65004	−	11.5182i	0.303848	−	0.526280i	0.977004	+	0.213220i	$0.0683951\pi$
$480$	0.536734	+	0.929651i	0.0244984	+	0.0424325i
$481$	−16.0494			−0.731790
$482$	−14.6712	−	25.4113i	−0.668256	−	1.15745i
$483$	−30.9532	+	53.6125i	−1.40842	+	2.43945i
$484$	105.041			4.77457
$485$	−2.01714	+	3.49379i	−0.0915937	+	0.158645i
$486$	−9.88146	−	17.1152i	−0.448232	−	0.776361i
$487$	−7.08585	−	12.2731i	−0.321091	−	0.556145i	0.659623	−	0.751597i	$-0.270716\pi$
$487$	−7.08585	−	12.2731i	−0.321091	−	0.556145i	−0.980713	+	0.195452i	$0.937383\pi$
$488$	−10.5624	−	18.2946i	−0.478137	−	0.828157i
$489$	12.1595			0.549873
$490$	−17.5751	−	30.4410i	−0.793964	−	1.37519i
$491$	12.2611	+	21.2369i	0.553337	+	0.958407i	0.998031	+	0.0627246i	$0.0199790\pi$
$491$	12.2611	+	21.2369i	0.553337	+	0.958407i	−0.444694	+	0.895682i	$0.646688\pi$
$492$	−8.20608	+	14.2134i	−0.369959	+	0.640788i
$493$	−1.39854	+	2.42234i	−0.0629871	+	0.109097i
$494$	−19.5480			−0.879506
$495$	4.12363			0.185344
$496$	−10.6721	+	18.4846i	−0.479191	+	0.829984i
$497$	−12.9411	+	22.4146i	−0.580487	+	1.00543i
$498$	−1.28354	−	2.22316i	−0.0575168	−	0.0996220i
$499$	12.4613	+	21.5837i	0.557846	+	0.966218i	0.997676	+	0.0681370i	$0.0217055\pi$
$499$	12.4613	+	21.5837i	0.557846	+	0.966218i	−0.439830	+	0.898081i	$0.644961\pi$
$500$	32.4271			1.45018
$501$	1.61665	+	2.80013i	0.0722268	+	0.125100i
$502$	−19.8421	−	34.3675i	−0.885597	−	1.53390i
$503$	4.29789	+	7.44417i	0.191634	+	0.331919i	0.945792	−	0.324774i	$-0.105288\pi$
$503$	4.29789	+	7.44417i	0.191634	+	0.331919i	−0.754158	+	0.656693i	$0.771955\pi$
$504$	−9.91875	+	17.1798i	−0.441816	+	0.765248i
$505$	1.81396			0.0807202
$506$	−64.0811	+	110.992i	−2.84875	+	4.93419i
$507$	−7.37903	−	12.7808i	−0.327714	−	0.567617i
$508$	−56.1935			−2.49319
$509$	−0.525420	−	0.910055i	−0.0232889	−	0.0403375i	0.854146	−	0.520033i	$-0.174080\pi$
$509$	−0.525420	−	0.910055i	−0.0232889	−	0.0403375i	−0.877435	+	0.479696i	$0.840747\pi$
$510$	1.56976	−	2.71891i	0.0695102	−	0.120395i
$511$	−28.1209	+	48.7069i	−1.24400	+	2.15467i
$512$	42.5494			1.88044
$513$	12.7577	−	22.0970i	0.563267	−	0.975607i
$514$	−4.69299			−0.206999
$515$	−5.88297			−0.259234
$516$	−14.7749	−	36.9271i	−0.650428	−	1.62562i
$517$	7.71308			0.339221
$518$	−109.939			−4.83043
$519$	2.80157	−	4.85246i	0.122975	−	0.212999i
$520$	−7.70940			−0.338080
$521$	20.0113	−	34.6606i	0.876711	−	1.51851i	0.0217816	−	0.999763i	$-0.493066\pi$
$521$	20.0113	−	34.6606i	0.876711	−	1.51851i	0.854929	−	0.518745i	$-0.173601\pi$
$522$	−2.73905	+	4.74417i	−0.119885	+	0.207647i
$523$	11.0656	+	19.1662i	0.483864	+	0.838078i	0.999828	−	0.0185327i	$-0.00589947\pi$
$523$	11.0656	+	19.1662i	0.483864	+	0.838078i	−0.515964	+	0.856610i	$0.672566\pi$
$524$	84.6000			3.69577
$525$	−15.3981	−	26.6703i	−0.672028	−	1.16399i
$526$	−4.92282	+	8.52657i	−0.214645	+	0.371776i
$527$	4.73329			0.206186
$528$	20.2931	−	35.1486i	0.883142	−	1.52965i
$529$	−25.2618	−	43.7548i	−1.09834	−	1.90238i
$530$	9.71986	+	16.8353i	0.422204	+	0.731279i
$531$	−3.02744	−	5.24368i	−0.131380	−	0.227557i
$532$	−89.8837			−3.89695
$533$	−2.36807	−	4.10162i	−0.102573	−	0.177661i
$534$	−18.2035	−	31.5294i	−0.787742	−	1.36441i
$535$	2.10384	−	3.64397i	0.0909571	−	0.157542i
$536$	27.8101	−	48.1685i	1.20121	−	2.08056i
$537$	9.82055			0.423788
$538$	−32.9769			−1.42174
$539$	−50.3844	+	87.2683i	−2.17021	+	3.75891i
$540$	9.86068	−	17.0792i	0.424336	−	0.734972i
$541$	8.77806	+	15.2040i	0.377398	+	0.653673i	0.990683	−	0.136189i	$-0.0434854\pi$
$541$	8.77806	+	15.2040i	0.377398	+	0.653673i	−0.613285	+	0.789862i	$0.710152\pi$
$542$	18.3374	+	31.7613i	0.787659	+	1.36426i
$543$	15.0436			0.645583
$544$	0.421677	+	0.730366i	0.0180793	+	0.0313142i
$545$	−5.76678	−	9.98836i	−0.247022	−	0.427854i
$546$	15.5845	+	26.9931i	0.666953	+	1.15520i
$547$	−5.85241	+	10.1367i	−0.250231	+	0.433413i	−0.963589	−	0.267387i	$-0.913840\pi$
$547$	−5.85241	+	10.1367i	−0.250231	+	0.433413i	0.713358	+	0.700799i	$0.247173\pi$
$548$	−39.1429			−1.67210
$549$	−1.63183	+	2.82641i	−0.0696448	+	0.120628i
$550$	−31.8781	−	55.2144i	−1.35929	−	2.35435i
$551$	−12.6651			−0.539550
$552$	32.7272	+	56.6852i	1.39296	+	2.41268i
$553$	−17.2366	+	29.8546i	−0.732973	+	1.26955i
$554$	31.0528	−	53.7850i	1.31931	−	2.28511i
$555$	11.6714			0.495423
$556$	−38.0683	+	65.9362i	−1.61446	+	2.79632i
$557$	−11.9744			−0.507370			−0.253685	−	0.967287i	$-0.581643\pi$
$557$	−11.9744			−0.507370			−0.253685	+	0.967287i	$0.581643\pi$
$558$	9.27016			0.392437
$559$	11.3604	+	1.63568i	0.480494	+	0.0691819i
$560$	−18.7853			−0.793824
$561$	−9.00038			−0.379997
$562$	−1.68824	+	2.92412i	−0.0712141	+	0.123347i
$563$	−10.8070			−0.455460			−0.227730	−	0.973724i	$-0.573130\pi$
$563$	−10.8070			−0.455460			−0.227730	+	0.973724i	$0.573130\pi$
$564$	3.86004	−	6.68579i	0.162537	−	0.281523i
$565$	−1.50026	+	2.59853i	−0.0631164	+	0.109321i
$566$	16.5863	+	28.7283i	0.697174	+	1.20754i
$567$	−29.1046			−1.22228
$568$	13.6828	+	23.6993i	0.574117	+	0.994399i
$569$	7.38597	−	12.7929i	0.309636	−	0.536305i	−0.668647	−	0.743580i	$-0.733126\pi$
$569$	7.38597	−	12.7929i	0.309636	−	0.536305i	0.978283	+	0.207275i	$0.0664595\pi$
$570$	14.2156			0.595427
$571$	0.412767	−	0.714934i	0.0172738	−	0.0299190i	−0.857259	−	0.514885i	$-0.827835\pi$
$571$	0.412767	−	0.714934i	0.0172738	−	0.0299190i	0.874533	+	0.484966i	$0.161168\pi$
$572$	21.6573	+	37.5115i	0.905536	+	1.56843i
$573$	−6.79132	−	11.7629i	−0.283712	−	0.491403i
$574$	−16.2213	−	28.0962i	−0.677066	−	1.17271i
$575$	36.5754			1.52530
$576$	−2.75474	−	4.77135i	−0.114781	−	0.198806i
$577$	18.8361	+	32.6250i	0.784156	+	1.35820i	0.929502	+	0.368817i	$0.120237\pi$
$577$	18.8361	+	32.6250i	0.784156	+	1.35820i	−0.145346	+	0.989381i	$0.546429\pi$
$578$	1.23326	−	2.13607i	0.0512969	−	0.0888488i
$579$	4.42220	−	7.65947i	0.183780	−	0.318317i
$580$	−9.78907			−0.406469
$581$	3.40625			0.141315
$582$	8.62266	−	14.9349i	0.357421	−	0.619071i
$583$	27.8649	−	48.2634i	1.15405	−	1.99887i
$584$	29.7326	+	51.4984i	1.23035	+	2.13102i
$585$	0.595530	+	1.03149i	0.0246221	+	0.0426468i
$586$	−13.8511			−0.572182
$587$	−1.02827	−	1.78102i	−0.0424414	−	0.0735107i	0.844024	−	0.536305i	$-0.180180\pi$
$587$	−1.02827	−	1.78102i	−0.0424414	−	0.0735107i	−0.886466	+	0.462794i	$0.846847\pi$
$588$	50.4302	+	87.3477i	2.07971	+	3.60216i
$589$	10.7161	+	18.5608i	0.441548	+	0.764784i
$590$	8.05937	−	13.9592i	0.331799	−	0.574693i
$591$	37.1305			1.52734
$592$	−20.6743	+	35.8089i	−0.849707	+	1.47174i
$593$	−10.0552	−	17.4161i	−0.412918	−	0.715195i	0.582290	−	0.812981i	$-0.302157\pi$
$593$	−10.0552	−	17.4161i	−0.412918	−	0.715195i	−0.995207	+	0.0977868i	$0.968824\pi$
$594$	−84.2262			−3.45584
$595$	2.08292	+	3.60771i	0.0853912	+	0.147902i
$596$	14.5961	−	25.2811i	0.597879	−	1.03556i
$597$	16.2703	−	28.1810i	0.665899	−	1.15337i
$598$	−37.0181			−1.51378
$599$	−9.31183	+	16.1286i	−0.380471	+	0.658995i	−0.991130	−	0.132899i	$-0.957572\pi$
$599$	−9.31183	+	16.1286i	−0.380471	+	0.658995i	0.610658	+	0.791894i	$0.290905\pi$
$600$	−32.5612			−1.32931
$601$	15.4768			0.631312			0.315656	−	0.948874i	$-0.397776\pi$
$601$	15.4768			0.631312			0.315656	+	0.948874i	$0.397776\pi$
$602$	77.8190	+	11.2044i	3.17167	+	0.456659i
$603$	−8.59301			−0.349934
$604$	−74.0789			−3.01423
$605$	11.0217	−	19.0902i	0.448097	−	0.776127i
$606$	−7.75413			−0.314990
$607$	−18.5792	+	32.1802i	−0.754107	+	1.30615i	0.191710	+	0.981452i	$0.438597\pi$
$607$	−18.5792	+	32.1802i	−0.754107	+	1.30615i	−0.945817	+	0.324701i	$0.894736\pi$
$608$	−1.90934	+	3.30707i	−0.0774338	+	0.134119i
$609$	10.0971	+	17.4887i	0.409155	+	0.708678i
$610$	−8.68821			−0.351775
$611$	1.11391	+	1.92935i	0.0450641	+	0.0780533i
$612$	1.62131	−	2.80819i	0.0655375	−	0.113514i
$613$	−0.666538			−0.0269212			−0.0134606	−	0.999909i	$-0.504285\pi$
$613$	−0.666538			−0.0269212			−0.0134606	+	0.999909i	$0.504285\pi$
$614$	−28.5617	+	49.4702i	−1.15265	+	1.99646i
$615$	1.72210	+	2.98277i	0.0694418	+	0.120277i
$616$	75.6972	+	131.111i	3.04993	+	5.28263i
$617$	9.02543	+	15.6325i	0.363350	+	0.629341i	0.988510	−	0.151156i	$-0.0482995\pi$
$617$	9.02543	+	15.6325i	0.363350	+	0.629341i	−0.625160	+	0.780497i	$0.714966\pi$
$618$	25.1479			1.01160
$619$	−9.90836	−	17.1618i	−0.398251	−	0.689790i	0.595260	−	0.803533i	$-0.297049\pi$
$619$	−9.90836	−	17.1618i	−0.398251	−	0.689790i	−0.993510	+	0.113743i	$0.963716\pi$
$620$	8.28266	+	14.3460i	0.332640	+	0.576149i
$621$	24.1593	−	41.8451i	0.969479	−	1.67919i
$622$	21.5245	−	37.2815i	0.863053	−	1.49485i
$623$	48.3084			1.93543
$624$	11.7228			0.469287
$625$	−7.26137	+	12.5771i	−0.290455	+	0.503083i
$626$	31.1043	−	53.8742i	1.24318	−	2.15325i
$627$	−20.3767	−	35.2934i	−0.813766	−	1.40948i
$628$	−13.5093	−	23.3987i	−0.539078	−	0.933711i
$629$	9.16946			0.365610
$630$	4.07939	+	7.06571i	0.162527	+	0.281505i
$631$	3.18978	+	5.52485i	0.126983	+	0.219941i	0.922506	−	0.385982i	$-0.126137\pi$
$631$	3.18978	+	5.52485i	0.126983	+	0.219941i	−0.795523	+	0.605923i	$0.792804\pi$
$632$	18.2244	+	31.5656i	0.724929	+	1.25561i
$633$	1.26762	−	2.19558i	0.0503832	−	0.0872663i
$634$	−31.1261			−1.23618
$635$	−5.89629	+	10.2127i	−0.233987	+	0.405278i
$636$	−27.8902	−	48.3073i	−1.10592	−	1.91551i
$637$	−29.1058			−1.15321
$638$	20.9036	+	36.2062i	0.827583	+	1.43342i
$639$	2.11391	−	3.66141i	0.0836252	−	0.144843i
$640$	8.05617	−	13.9537i	0.318448	−	0.551568i
$641$	−14.0926			−0.556625			−0.278312	−	0.960491i	$-0.589775\pi$
$641$	−14.0926			−0.556625			−0.278312	+	0.960491i	$0.589775\pi$
$642$	−8.99329	+	15.5768i	−0.354937	+	0.614769i
$643$	34.0930			1.34450			0.672248	−	0.740326i	$-0.265329\pi$
$643$	34.0930			1.34450			0.672248	+	0.740326i	$0.265329\pi$
$644$	−170.213			−6.70733
$645$	−8.26148	−	1.18949i	−0.325295	−	0.0468362i
$646$	11.1683			0.439411
$647$	6.82365			0.268265			0.134133	−	0.990963i	$-0.457175\pi$
$647$	6.82365			0.268265			0.134133	+	0.990963i	$0.457175\pi$
$648$	−15.3863	+	26.6499i	−0.604432	+	1.04691i
$649$	−46.2092			−1.81387
$650$	9.20758	−	15.9480i	0.361151	−	0.625532i
$651$	17.0866	−	29.5948i	0.669676	−	1.15991i
$652$	16.7165	+	28.9537i	0.654667	+	1.13392i
$653$	35.1241			1.37451			0.687256	−	0.726415i	$-0.258815\pi$
$653$	35.1241			1.37451			0.687256	+	0.726415i	$0.258815\pi$
$654$	24.6512	+	42.6972i	0.963939	+	1.66959i
$655$	8.87694	−	15.3753i	0.346851	−	0.600763i
$656$	−12.2019			−0.476403
$657$	4.59353	−	7.95623i	0.179211	−	0.310402i
$658$	7.63032	+	13.2161i	0.297461	+	0.515218i
$659$	−5.41357	−	9.37658i	−0.210883	−	0.365260i	0.741108	−	0.671385i	$-0.234300\pi$
$659$	−5.41357	−	9.37658i	−0.210883	−	0.365260i	−0.951991	+	0.306126i	$0.900967\pi$
$660$	−15.7495	−	27.2790i	−0.613049	−	1.06183i
$661$	17.4304			0.677963			0.338981	−	0.940793i	$-0.389918\pi$
$661$	17.4304			0.677963			0.338981	+	0.940793i	$0.389918\pi$
$662$	12.6402	+	21.8935i	0.491276	+	0.850915i
$663$	−1.29982	−	2.25136i	−0.0504810	−	0.0874356i
$664$	1.80074	−	3.11897i	0.0698822	−	0.121040i
$665$	−9.43135	+	16.3356i	−0.365732	+	0.633466i
$666$	17.9584			0.695874
$667$	−23.9839			−0.928659
$668$	−4.44503	+	7.69901i	−0.171983	+	0.297884i
$669$	−14.3066	+	24.7798i	−0.553127	+	0.958044i
$670$	−11.4378	−	19.8108i	−0.441879	−	0.765357i
$671$	12.4537	+	21.5704i	0.480769	+	0.832716i
$672$	6.08880			0.234881
$673$	−16.0682	−	27.8310i	−0.619385	−	1.07281i	−0.989598	−	0.143860i	$-0.954049\pi$
$673$	−16.0682	−	27.8310i	−0.619385	−	1.07281i	0.370213	−	0.928947i	$-0.379285\pi$
$674$	−12.6790	−	21.9607i	−0.488377	−	0.845893i
$675$	12.0184	+	20.8165i	0.462588	+	0.801226i
$676$	20.2888	−	35.1412i	0.780338	−	1.35159i
$677$	−36.1628			−1.38985			−0.694924	−	0.719083i	$-0.744562\pi$
$677$	−36.1628			−1.38985			−0.694924	+	0.719083i	$0.744562\pi$
$678$	6.41315	−	11.1079i	0.246296	−	0.426597i
$679$	11.4414	+	19.8171i	0.439081	+	0.760510i
$680$	4.40459			0.168908
$681$	20.7869	+	36.0040i	0.796556	+	1.37968i
$682$	35.3737	−	61.2690i	1.35453	−	2.34611i
$683$	5.93363	−	10.2773i	0.227044	−	0.393252i	−0.729887	−	0.683568i	$-0.760427\pi$
$683$	5.93363	−	10.2773i	0.227044	−	0.393252i	0.956931	+	0.290316i	$0.0937605\pi$
$684$	14.6824			0.561397
$685$	−4.10720	+	7.11388i	−0.156928	+	0.271807i
$686$	−115.448			−4.40781
$687$	25.9047			0.988326
$688$	18.2835	−	23.2399i	0.697053	−	0.886014i
$689$	16.0969			0.613241
$690$	26.9201			1.02483
$691$	−2.57372	+	4.45782i	−0.0979091	+	0.169584i	−0.910819	−	0.412806i	$-0.864549\pi$
$691$	−2.57372	+	4.45782i	−0.0979091	+	0.169584i	0.812910	+	0.582389i	$0.197882\pi$
$692$	15.4059			0.585646
$693$	11.6948	−	20.2560i	0.444249	−	0.769461i
$694$	−7.18899	+	12.4517i	−0.272890	+	0.472660i
$695$	7.98889	+	13.8372i	0.303036	+	0.524873i
$696$	21.3516			0.809331
$697$	1.35294	+	2.34337i	0.0512464	+	0.0887614i
$698$	20.8962	−	36.1933i	0.790934	−	1.36994i
$699$	10.1924			0.385512
$700$	42.3374	−	73.3306i	1.60020	−	2.77164i
$701$	−16.1751	−	28.0161i	−0.610926	−	1.05815i	−0.991085	−	0.133233i	$-0.957464\pi$
$701$	−16.1751	−	28.0161i	−0.610926	−	1.05815i	0.380159	−	0.924921i	$-0.375869\pi$
$702$	−12.1638	−	21.0684i	−0.459095	−	0.795175i
$703$	20.7594	+	35.9564i	0.782957	+	1.35612i
$704$	−42.0468			−1.58470
$705$	−0.810056	−	1.40306i	−0.0305085	−	0.0528422i
$706$	24.2189	+	41.9484i	0.911490	+	1.57875i
$707$	5.14447	−	8.91049i	0.193478	−	0.335113i
$708$	−23.1256	+	40.0547i	−0.869113	+	1.50535i
$709$	4.53699			0.170390			0.0851951	−	0.996364i	$-0.472849\pi$
$709$	4.53699			0.170390			0.0851951	+	0.996364i	$0.472849\pi$
$710$	11.2549			0.422390
$711$	2.81558	−	4.87672i	0.105592	−	0.182891i
$712$	25.5386	−	44.2341i	0.957098	−	1.65774i
$713$	20.2930	+	35.1486i	0.759980	+	1.31632i
$714$	−8.90382	−	15.4219i	−0.333217	−	0.577149i
$715$	9.08984			0.339941
$716$	13.5009	+	23.3843i	0.504553	+	0.873911i
$717$	−2.69125	−	4.66138i	−0.100507	−	0.174082i
$718$	0.914819	+	1.58451i	0.0341407	+	0.0591335i
$719$	7.14812	−	12.3809i	0.266580	−	0.461730i	−0.701396	−	0.712771i	$-0.747440\pi$
$719$	7.14812	−	12.3809i	0.266580	−	0.461730i	0.967976	+	0.251041i	$0.0807730\pi$
$720$	3.06856			0.114359
$721$	−16.6843	+	28.8981i	−0.621357	+	1.07622i
$722$	1.85283	+	3.20920i	0.0689552	+	0.119434i
$723$	17.6690			0.657115
$724$	20.6814	+	35.8212i	0.768617	+	1.33128i
$725$	5.96556	−	10.3326i	0.221555	−	0.383745i
$726$	−47.1145	+	81.6047i	−1.74858	+	3.02864i
$727$	23.8266			0.883681			0.441840	−	0.897094i	$-0.354326\pi$
$727$	23.8266			0.883681			0.441840	+	0.897094i	$0.354326\pi$
$728$	−21.8642	+	37.8699i	−0.810340	+	1.40355i
$729$	29.8627			1.10603
$730$	24.4569			0.905192
$731$	−6.49051	−	0.934508i	−0.240060	−	0.0345640i
$732$	24.9300			0.921439
$733$	2.27980			0.0842063			0.0421031	−	0.999113i	$-0.486594\pi$
$733$	2.27980			0.0842063			0.0421031	+	0.999113i	$0.486594\pi$
$734$	−18.8707	+	32.6849i	−0.696529	+	1.20642i
$735$	21.1662			0.780728
$736$	−3.61571	+	6.26260i	−0.133277	+	0.230842i
$737$	−32.7897	+	56.7935i	−1.20783	+	2.09202i
$738$	2.64974	+	4.58949i	0.0975384	+	0.168941i
$739$	−27.6319			−1.01646			−0.508228	−	0.861222i	$-0.669699\pi$
$739$	−27.6319			−1.01646			−0.508228	+	0.861222i	$0.669699\pi$
$740$	16.0454	+	27.7914i	0.589840	+	1.02163i
$741$	5.88555	−	10.1941i	0.216211	−	0.374488i
$742$	110.264			4.04791
$743$	10.7834	−	18.6774i	0.395605	−	0.685209i	−0.597573	−	0.801815i	$-0.703868\pi$
$743$	10.7834	−	18.6774i	0.395605	−	0.685209i	0.993178	+	0.116606i	$0.0372015\pi$
$744$	−18.0659	−	31.2910i	−0.662327	−	1.14718i
$745$	−3.06308	−	5.30542i	−0.112223	−	0.194375i
$746$	18.3246	+	31.7391i	0.670910	+	1.16205i
$747$	−0.556409			−0.0203579
$748$	−12.3734	−	21.4313i	−0.452416	−	0.783607i
$749$	−11.9332	−	20.6689i	−0.436029	−	0.755224i
$750$	−14.5447	+	25.1922i	−0.531098	+	0.919889i
$751$	2.45618	−	4.25423i	0.0896273	−	0.155239i	−0.817726	−	0.575607i	$-0.804766\pi$
$751$	2.45618	−	4.25423i	0.0896273	−	0.155239i	0.907354	+	0.420368i	$0.138099\pi$
$752$	5.73961			0.209302
$753$	23.8964			0.870833
$754$	−6.03775	+	10.4577i	−0.219882	+	0.380847i
$755$	−7.77297	+	13.4632i	−0.282887	+	0.489976i
$756$	−55.9306	−	96.8746i	−2.03418	−	3.52330i
$757$	−14.4082	−	24.9557i	−0.523673	−	0.907029i	−0.999620	−	0.0275549i	$-0.991228\pi$
$757$	−14.4082	−	24.9557i	−0.523673	−	0.907029i	0.475947	−	0.879474i	$-0.342105\pi$
$758$	−87.4792			−3.17739
$759$	−38.5873	−	66.8352i	−1.40063	−	2.42596i
$760$	9.97189	+	17.2718i	0.361718	+	0.626515i
$761$	−16.8873	−	29.2497i	−0.612165	−	1.06030i	−0.990875	−	0.134786i	$-0.956965\pi$
$761$	−16.8873	−	29.2497i	−0.612165	−	1.06030i	0.378709	−	0.925516i	$-0.376368\pi$
$762$	25.2048	−	43.6561i	0.913075	−	1.58149i
$763$	−65.4193			−2.36834
$764$	18.6729	−	32.3424i	0.675562	−	1.17011i
$765$	−0.340242	−	0.589317i	−0.0123015	−	0.0213068i
$766$	23.8826			0.862912
$767$	−6.67348	−	11.5588i	−0.240965	−	0.417364i
$768$	−24.1321	+	41.7980i	−0.870791	+	1.50825i
$769$	−7.17339	+	12.4247i	−0.258679	+	0.448046i	−0.965888	−	0.258959i	$-0.916621\pi$
$769$	−7.17339	+	12.4247i	−0.258679	+	0.448046i	0.707209	+	0.707004i	$0.249954\pi$
$770$	62.2656			2.24390
$771$	1.41297	−	2.44734i	0.0508870	−	0.0881389i
$772$	24.3179			0.875219
$773$	−0.116741			−0.00419887			−0.00209943	−	0.999998i	$-0.500668\pi$
$773$	−0.116741			−0.00419887			−0.00209943	+	0.999998i	$0.500668\pi$
$774$	−12.7117	−	1.83023i	−0.456912	−	0.0657864i
$775$	−20.1901			−0.725251
$776$	24.1943			0.868524
$777$	33.1005	−	57.3318i	1.18748	−	2.05677i
$778$	−37.5989			−1.34799
$779$	−6.12607	+	10.6107i	−0.219489	+	0.380167i
$780$	4.54905	−	7.87919i	0.162882	−	0.282120i
$781$	−16.1328	−	27.9428i	−0.577277	−	0.999874i
$782$	21.1494			0.756302
$783$	−7.88090	−	13.6501i	−0.281640	−	0.487816i
$784$	−37.4931	+	64.9399i	−1.33904	+	2.31928i
$785$	−5.67002			−0.202372
$786$	−37.9462	+	65.7247i	−1.35350	+	2.34432i
$787$	−6.55228	−	11.3489i	−0.233564	−	0.404544i	0.725291	−	0.688443i	$-0.241705\pi$
$787$	−6.55228	−	11.3489i	−0.233564	−	0.404544i	−0.958854	+	0.283899i	$0.908372\pi$
$788$	51.0456	+	88.4135i	1.81842	+	3.14960i
$789$	−2.96434	−	5.13439i	−0.105533	−	0.182789i
$790$	14.9907			0.533346
$791$	8.50960	+	14.7391i	0.302567	+	0.524061i
$792$	−12.3651	−	21.4169i	−0.439374	−	0.761017i
$793$	−3.59709	+	6.23034i	−0.127736	+	0.221246i
$794$	−8.42974	+	14.6007i	−0.299160	+	0.518161i
$795$	−11.7059			−0.415165
$796$	89.4711			3.17122
$797$	−11.6155	+	20.1186i	−0.411442	+	0.712638i	−0.995048	−	0.0993987i	$-0.968308\pi$
$797$	−11.6155	+	20.1186i	−0.411442	+	0.712638i	0.583606	+	0.812037i	$0.301641\pi$
$798$	40.3161	−	69.8295i	1.42717	−	2.47194i
$799$	−0.636409	−	1.10229i	−0.0225145	−	0.0389963i
$800$	−1.79869	−	3.11542i	−0.0635932	−	0.110147i
$801$	−7.89114			−0.278820
$802$	7.54871	+	13.0747i	0.266554	+	0.461685i
$803$	−35.0566	−	60.7197i	−1.23712	−	2.14275i
$804$	32.8195	+	56.8451i	1.15746	+	2.00477i
$805$	−17.8602	+	30.9347i	−0.629488	+	1.09030i
$806$	20.4345			0.719774
$807$	9.92875	−	17.1971i	0.349509	−	0.605367i
$808$	−5.43932	−	9.42118i	−0.191355	−	0.331436i
$809$	−49.8597			−1.75297			−0.876486	−	0.481427i	$-0.840119\pi$
$809$	−49.8597			−1.75297			−0.876486	+	0.481427i	$0.840119\pi$
$810$	6.32810	+	10.9606i	0.222347	+	0.385116i
$811$	0.311149	−	0.538925i	0.0109259	−	0.0189242i	−0.860511	−	0.509432i	$-0.829855\pi$
$811$	0.311149	−	0.538925i	0.0109259	−	0.0189242i	0.871437	+	0.490508i	$0.163189\pi$
$812$	−27.7622	+	48.0856i	−0.974263	+	1.68747i
$813$	−22.0842			−0.774528
$814$	68.5267	−	118.692i	2.40186	−	4.16015i
$815$	7.01612			0.245764
$816$	−6.69755			−0.234461
$817$	−11.0299	−	27.5671i	−0.385886	−	0.964451i
$818$	2.74344			0.0959220
$819$	6.75579			0.236067
$820$	−4.73496	+	8.20119i	−0.165352	+	0.286398i
$821$	−18.0316			−0.629306			−0.314653	−	0.949207i	$-0.601888\pi$
$821$	−18.0316			−0.629306			−0.314653	+	0.949207i	$0.601888\pi$
$822$	17.5570	−	30.4096i	0.612371	−	1.06066i
$823$	−19.7079	+	34.1351i	−0.686975	+	1.18988i	0.285837	+	0.958278i	$0.407729\pi$
$823$	−19.7079	+	34.1351i	−0.686975	+	1.18988i	−0.972812	+	0.231597i	$0.925605\pi$
$824$	17.6406	+	30.5544i	0.614539	+	1.06441i
$825$	38.3916			1.33663
$826$	−45.7134	−	79.1780i	−1.59057	−	2.75495i
$827$	13.3224	−	23.0751i	0.463266	−	0.802401i	−0.535855	−	0.844310i	$-0.680011\pi$
$827$	13.3224	−	23.0751i	0.463266	−	0.802401i	0.999121	+	0.0419091i	$0.0133440\pi$
$828$	27.8041			0.966261
$829$	6.61456	−	11.4568i	0.229733	−	0.397910i	−0.727996	−	0.685582i	$-0.759548\pi$
$829$	6.61456	−	11.4568i	0.229733	−	0.397910i	0.957729	+	0.287672i	$0.0928813\pi$
$830$	−0.740609	−	1.28277i	−0.0257069	−	0.0445257i
$831$	18.6989	+	32.3874i	0.648656	+	1.12351i
$832$	−6.07235	−	10.5176i	−0.210521	−	0.364633i
$833$	16.6289			0.576158
$834$	−34.1500	−	59.1496i	−1.18252	−	2.04818i
$835$	0.932819	+	1.61569i	0.0322815	+	0.0559132i
$836$	56.0261	−	97.0401i	1.93770	−	3.35620i
$837$	−13.3363	+	23.0991i	−0.460969	+	0.798421i
$838$	6.37627			0.220265
$839$	−10.3966			−0.358930			−0.179465	−	0.983764i	$-0.557437\pi$
$839$	−10.3966			−0.358930			−0.179465	+	0.983764i	$0.557437\pi$
$840$	15.9000	−	27.5396i	0.548602	−	0.950206i
$841$	10.5882	−	18.3392i	0.365109	−	0.632387i
$842$	21.2931	+	36.8807i	0.733809	+	1.27099i
$843$	−1.01660	−	1.76080i	−0.0350135	−	0.0606451i
$844$	6.97068			0.239941
$845$	−4.25774	−	7.37462i	−0.146471	−	0.253695i
$846$	−1.24641	−	2.15884i	−0.0428524	−	0.0742225i
$847$	−62.5162	−	108.281i	−2.14808	−	3.72059i
$848$	20.7354	−	35.9147i	0.712056	−	1.23332i
$849$	−19.9753			−0.685551
$850$	−5.26054	+	9.11153i	−0.180435	+	0.312523i
$851$	39.3122	+	68.0907i	1.34760	+	2.33412i
$852$	−32.2949			−1.10641
$853$	−3.67648	−	6.36784i	−0.125880	−	0.218031i	0.796197	−	0.605038i	$-0.206842\pi$
$853$	−3.67648	−	6.36784i	−0.125880	−	0.218031i	−0.922077	+	0.387007i	$0.873509\pi$
$854$	−24.6401	+	42.6780i	−0.843168	+	1.46041i
$855$	1.54060	−	2.66840i	0.0526875	−	0.0912574i
$856$	−25.2342			−0.862488
$857$	−20.0485	+	34.7250i	−0.684844	+	1.18618i	0.288642	+	0.957437i	$0.406796\pi$
$857$	−20.0485	+	34.7250i	−0.684844	+	1.18618i	−0.973486	+	0.228748i	$0.926537\pi$
$858$	−38.8563			−1.32653
$859$	12.2536			0.418089			0.209044	−	0.977906i	$-0.432965\pi$
$859$	12.2536			0.418089			0.209044	+	0.977906i	$0.432965\pi$
$860$	−8.52519	−	21.3071i	−0.290707	−	0.726567i
$861$	19.5358			0.665778
$862$	5.47807			0.186584
$863$	−1.53879	+	2.66526i	−0.0523810	+	0.0907265i	−0.891027	−	0.453950i	$-0.850014\pi$
$863$	−1.53879	+	2.66526i	−0.0523810	+	0.0907265i	0.838646	+	0.544677i	$0.183348\pi$
$864$	−4.75238			−0.161679
$865$	1.61652	−	2.79989i	0.0549633	−	0.0951993i
$866$	49.5350	−	85.7972i	1.68327	−	2.91551i
$867$	0.742625	+	1.28626i	0.0252209	+	0.0436838i
$868$	93.9599			3.18921
$869$	−21.4877	−	37.2178i	−0.728920	−	1.26253i
$870$	4.39075	−	7.60501i	0.148861	−	0.257834i
$871$	−18.9418			−0.641819
$872$	−34.5844	+	59.9019i	−1.17117	+	2.02853i
$873$	−1.86894	−	3.23710i	−0.0632541	−	0.109559i
$874$	47.8818	+	82.9338i	1.61963	+	2.80528i
$875$	−19.2994	−	33.4275i	−0.652438	−	1.13006i
$876$	−70.1768			−2.37106
$877$	−10.0383	−	17.3869i	−0.338970	−	0.587113i	0.645269	−	0.763955i	$-0.276745\pi$
$877$	−10.0383	−	17.3869i	−0.338970	−	0.587113i	−0.984239	+	0.176842i	$0.943412\pi$
$878$	−8.75085	−	15.1569i	−0.295327	−	0.511521i
$879$	4.17030	−	7.22318i	0.140661	−	0.243632i
$880$	11.7092	−	20.2809i	0.394717	−	0.683671i
$881$	−43.0069			−1.44894			−0.724470	−	0.689307i	$-0.757915\pi$
$881$	−43.0069			−1.44894			−0.724470	+	0.689307i	$0.757915\pi$
$882$	32.5678			1.09661
$883$	0.0219248	−	0.0379749i	0.000737829	−	0.00127796i	−0.865656	−	0.500639i	$-0.833098\pi$
$883$	0.0219248	−	0.0379749i	0.000737829	−	0.00127796i	0.866394	+	0.499361i	$0.166432\pi$
$884$	3.57390	−	6.19017i	0.120203	−	0.208198i
$885$	4.85306	+	8.40575i	0.163134	+	0.282556i
$886$	0.274767	+	0.475911i	0.00923099	+	0.0159886i
$887$	−3.88506			−0.130448			−0.0652238	−	0.997871i	$-0.520776\pi$
$887$	−3.88506			−0.130448			−0.0652238	+	0.997871i	$0.520776\pi$
$888$	−34.9976	−	60.6177i	−1.17444	−	2.03420i
$889$	33.4443	+	57.9272i	1.12168	+	1.94282i
$890$	−10.5035	−	18.1926i	−0.352079	−	0.609818i
$891$	18.1414	−	31.4218i	0.607759	−	1.05267i
$892$	−78.6729			−2.63416
$893$	2.88163	−	4.99113i	0.0964301	−	0.167022i
$894$	13.0937	+	22.6790i	0.437920	+	0.758500i
$895$	5.66651			0.189411
$896$	−45.6952	−	79.1465i	−1.52657	−	2.64410i
$897$	11.1455	−	19.3045i	0.372136	−	0.644559i
$898$	−27.1574	+	47.0380i	−0.906254	+	1.56968i
$899$	13.2394			0.441559
$900$	−6.91578	+	11.9785i	−0.230526	+	0.399283i
$901$	−9.19657			−0.306382
$902$	40.4442			1.34664
$903$	−29.2729	+	37.2083i	−0.974140	+	1.23821i
$904$	17.9946			0.598493
$905$	8.68024			0.288541
$906$	33.2271	−	57.5510i	1.10390	−	1.91200i
$907$	52.5460			1.74476			0.872381	−	0.488827i	$-0.162575\pi$
$907$	52.5460			1.74476			0.872381	+	0.488827i	$0.162575\pi$
$908$	−57.1541	+	98.9937i	−1.89672	+	3.28522i
$909$	−0.840345	+	1.45552i	−0.0278725	+	0.0482766i
$910$	8.99232	+	15.5752i	0.298092	+	0.516311i
$911$	37.2037			1.23261			0.616306	−	0.787507i	$-0.288628\pi$
$911$	37.2037			1.23261			0.616306	+	0.787507i	$0.288628\pi$
$912$	−15.1631	−	26.2633i	−0.502100	−	0.869663i
$913$	−2.12318	+	3.67745i	−0.0702670	+	0.121706i
$914$	−64.2002			−2.12355
$915$	2.61586	−	4.53081i	0.0864778	−	0.149784i
$916$	35.6128	+	61.6831i	1.17668	+	2.03807i
$917$	−50.3507	−	87.2101i	−1.66273	−	2.87993i
$918$	6.94953	+	12.0369i	0.229369	+	0.397278i
$919$	16.2799			0.537026			0.268513	−	0.963276i	$-0.413468\pi$
$919$	16.2799			0.537026			0.268513	+	0.963276i	$0.413468\pi$
$920$	18.8838	+	32.7077i	0.622580	+	1.07834i
$921$	−17.1988	−	29.7892i	−0.566719	−	0.981587i
$922$	6.09984	−	10.5652i	0.200888	−	0.347948i
$923$	4.65976	−	8.07094i	0.153378	−	0.265658i
$924$	−178.665			−5.87765
$925$	−39.1128			−1.28602
$926$	4.25474	−	7.36943i	0.139819	−	0.242174i
$927$	2.72537	−	4.72048i	0.0895130	−	0.155041i
$928$	1.17947	+	2.04290i	0.0387179	+	0.0670613i
$929$	−23.3724	−	40.4822i	−0.766824	−	1.32818i	−0.939277	−	0.343161i	$-0.888502\pi$
$929$	−23.3724	−	40.4822i	−0.766824	−	1.32818i	0.172452	−	0.985018i	$-0.444831\pi$
$930$	−14.8603			−0.487288
$931$	37.6475	+	65.2075i	1.23385	+	2.13709i
$932$	14.0121	+	24.2697i	0.458982	+	0.794981i
$933$	12.9613	+	22.4496i	0.424333	+	0.734966i
$934$	−34.7320	+	60.1575i	−1.13646	+	1.96842i
$935$	−5.19327			−0.169838
$936$	3.57150	−	6.18601i	0.116738	−	0.202196i
$937$	18.9089	+	32.7513i	0.617728	+	1.06994i	0.989899	+	0.141773i	$0.0452802\pi$
$937$	18.9089	+	32.7513i	0.617728	+	1.06994i	−0.372171	+	0.928164i	$0.621386\pi$
$938$	−129.752			−4.23655
$939$	18.7299	+	32.4411i	0.611226	+	1.05868i
$940$	2.22727	−	3.85774i	0.0726454	−	0.125826i
$941$	−14.7068	+	25.4730i	−0.479429	+	0.830395i	−0.999722	−	0.0235926i	$-0.992490\pi$
$941$	−14.7068	+	25.4730i	−0.479429	+	0.830395i	0.520293	+	0.853988i	$0.325823\pi$
$942$	24.2376			0.789703
$943$	−11.6009	+	20.0934i	−0.377779	+	0.654332i
$944$	−34.3861			−1.11917
$945$	−23.4748			−0.763636
$946$	−60.6025	+	77.0309i	−1.97036	+	2.50449i
$947$	−33.4006			−1.08537			−0.542687	−	0.839935i	$-0.682593\pi$
$947$	−33.4006			−1.08537			−0.542687	+	0.839935i	$0.682593\pi$
$948$	−43.0145			−1.39704
$949$	10.1256	−	17.5381i	0.328692	−	0.569312i
$950$	−47.6390			−1.54561
$951$	9.37151	−	16.2319i	0.303892	−	0.526357i
$952$	12.4916	−	21.6361i	0.404855	−	0.701229i
$953$	9.14829	+	15.8453i	0.296342	+	0.513280i	0.975296	−	0.220901i	$-0.0708998\pi$
$953$	9.14829	+	15.8453i	0.296342	+	0.513280i	−0.678954	+	0.734181i	$0.737566\pi$
$954$	−18.0115			−0.583144
$955$	−3.91863	−	6.78727i	−0.126804	−	0.219631i
$956$	7.39965	−	12.8166i	0.239322	−	0.414518i
$957$	−25.1748			−0.813786
$958$	−16.4025	+	28.4099i	−0.529940	+	0.917882i
$959$	23.2964	+	40.3505i	0.752280	+	1.30299i
$960$	4.41592	+	7.64859i	0.142523	+	0.246857i
$961$	4.29796	+	7.44429i	0.138644	+	0.240138i
$962$	39.5862			1.27631
$963$	1.94928	+	3.37624i	0.0628145	+	0.108798i
$964$	24.2906	+	42.0725i	0.782347	+	1.35507i
$965$	2.55163	−	4.41956i	0.0821399	−	0.142271i
$966$	76.3467	−	132.236i	2.45641	−	4.25463i
$967$	16.0303			0.515499			0.257750	−	0.966212i	$-0.417019\pi$
$967$	16.0303			0.515499			0.257750	+	0.966212i	$0.417019\pi$
$968$	−132.198			−4.24902
$969$	−3.36257	+	5.82415i	−0.108021	+	0.187099i
$970$	4.97532	−	8.61752i	0.159748	−	0.276692i
$971$	19.0441	+	32.9853i	0.611154	+	1.05855i	0.991046	+	0.133519i	$0.0426277\pi$
$971$	19.0441	+	32.9853i	0.611154	+	1.05855i	−0.379892	+	0.925031i	$0.624039\pi$
$972$	16.3604	+	28.3370i	0.524759	+	0.908909i
$973$	90.6273			2.90538
$974$	17.4774	+	30.2718i	0.560012	+	0.969970i
$975$	5.54447	+	9.60331i	0.177565	+	0.307552i
$976$	9.26729	+	16.0514i	0.296639	+	0.513793i
$977$	−26.5719	+	46.0239i	−0.850111	+	1.47244i	0.0309958	+	0.999520i	$0.490132\pi$
$977$	−26.5719	+	46.0239i	−0.850111	+	1.47244i	−0.881107	+	0.472917i	$0.843201\pi$
$978$	−29.9917			−0.959030
$979$	−30.1115	+	52.1546i	−0.962367	+	1.66687i
$980$	29.0985	+	50.4001i	0.929518	+	1.60997i
$981$	10.6862			0.341184
$982$	−30.2423	−	52.3812i	−0.965071	−	1.67155i
$983$	−17.6016	+	30.4869i	−0.561405	+	0.972381i	0.435970	+	0.899961i	$0.356406\pi$
$983$	−17.6016	+	30.4869i	−0.561405	+	0.972381i	−0.997374	+	0.0724200i	$0.976928\pi$
$984$	10.3277	−	17.8882i	0.329236	−	0.570254i
$985$	21.4245			0.682642
$986$	3.44953	−	5.97477i	0.109855	−	0.190275i
$987$	−9.18941			−0.292502
$988$	32.3649			1.02966
$989$	−20.8873	−	52.2038i	−0.664176	−	1.65999i
$990$	−10.1710			−0.323257
$991$	−26.1834			−0.831744			−0.415872	−	0.909423i	$-0.636524\pi$
$991$	−26.1834			−0.831744			−0.415872	+	0.909423i	$0.636524\pi$
$992$	1.99592	−	3.45704i	0.0633706	−	0.109761i
$993$	−15.2230			−0.483086
$994$	31.9194	−	55.2861i	1.01242	−	1.75357i
$995$	9.38805	−	16.2606i	0.297621	−	0.515495i
$996$	2.12511	+	3.68080i	0.0673366	+	0.116630i
$997$	−54.0745			−1.71256			−0.856278	−	0.516516i	$-0.827229\pi$
$997$	−54.0745			−1.71256			−0.856278	+	0.516516i	$0.827229\pi$
$998$	−30.7362	−	53.2366i	−0.972936	−	1.68518i
$999$	−25.8353	+	44.7481i	−0.817394	+	1.41577i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	731.2.e.b.307.3	✓	58
43.36	even	3	inner	731.2.e.b.681.3	yes	58

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
731.2.e.b.307.3	✓	58	1.1	even	1	trivial
731.2.e.b.681.3	yes	58	43.36	even	3	inner

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:	\( N \)	\(=\)	\( 731 = 17 \cdot 43 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	731.e (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q-2.46652 q^{2} +(0.742625 - 1.28626i) q^{3} +4.08373 q^{4} +(0.428499 - 0.742181i) q^{5} +(-1.83170 + 3.17260i) q^{6} +(-2.43048 - 4.20972i) q^{7} -5.13956 q^{8} +(0.397017 + 0.687654i) q^{9} +O(q^{10})\)	\(q-2.46652 q^{2} +(0.742625 - 1.28626i) q^{3} +4.08373 q^{4} +(0.428499 - 0.742181i) q^{5} +(-1.83170 + 3.17260i) q^{6} +(-2.43048 - 4.20972i) q^{7} -5.13956 q^{8} +(0.397017 + 0.687654i) q^{9} +(-1.05690 + 1.83061i) q^{10} +6.05985 q^{11} +(3.03268 - 5.25275i) q^{12} +(0.875156 + 1.51581i) q^{13} +(5.99483 + 10.3834i) q^{14} +(-0.636427 - 1.10232i) q^{15} +4.50938 q^{16} +(-0.500000 - 0.866025i) q^{17} +(-0.979251 - 1.69611i) q^{18} +(2.26398 - 3.92132i) q^{19} +(1.74987 - 3.03087i) q^{20} -7.21974 q^{21} -14.9467 q^{22} +(4.28730 - 7.42582i) q^{23} +(-3.81676 + 6.61083i) q^{24} +(2.13278 + 3.69408i) q^{25} +(-2.15859 - 3.73879i) q^{26} +5.63509 q^{27} +(-9.92542 - 17.1913i) q^{28} +(-1.39854 - 2.42234i) q^{29} +(1.56976 + 2.71891i) q^{30} +(-2.36665 + 4.09915i) q^{31} -0.843355 q^{32} +(4.50019 - 7.79456i) q^{33} +(1.23326 + 2.13607i) q^{34} -4.16583 q^{35} +(1.62131 + 2.80819i) q^{36} +(-4.58473 + 7.94098i) q^{37} +(-5.58415 + 9.67203i) q^{38} +2.59965 q^{39} +(-2.20229 + 3.81449i) q^{40} -2.70589 q^{41} +17.8076 q^{42} +(4.05456 - 5.15369i) q^{43} +24.7468 q^{44} +0.680485 q^{45} +(-10.5747 + 18.3159i) q^{46} +1.27282 q^{47} +(3.34877 - 5.80025i) q^{48} +(-8.31447 + 14.4011i) q^{49} +(-5.26054 - 9.11153i) q^{50} -1.48525 q^{51} +(3.57390 + 6.19017i) q^{52} +(4.59828 - 7.96446i) q^{53} -13.8991 q^{54} +(2.59664 - 4.49751i) q^{55} +(12.4916 + 21.6361i) q^{56} +(-3.36257 - 5.82415i) q^{57} +(3.44953 + 5.97477i) q^{58} -7.62547 q^{59} +(-2.59900 - 4.50159i) q^{60} +(2.05511 + 3.55956i) q^{61} +(5.83739 - 10.1106i) q^{62} +(1.92988 - 3.34266i) q^{63} -6.93860 q^{64} +1.50001 q^{65} +(-11.0998 + 19.2255i) q^{66} +(-5.41099 + 9.37210i) q^{67} +(-2.04186 - 3.53661i) q^{68} +(-6.36771 - 11.0292i) q^{69} +10.2751 q^{70} +(-2.66225 - 4.61115i) q^{71} +(-2.04049 - 3.53424i) q^{72} +(-5.78506 - 10.0200i) q^{73} +(11.3083 - 19.5866i) q^{74} +6.33541 q^{75} +(9.24547 - 16.0136i) q^{76} +(-14.7283 - 25.5102i) q^{77} -6.41209 q^{78} +(-3.54591 - 6.14170i) q^{79} +(1.93226 - 3.34678i) q^{80} +(2.99370 - 5.18525i) q^{81} +6.67413 q^{82} +(-0.350368 + 0.606856i) q^{83} -29.4834 q^{84} -0.856997 q^{85} +(-10.0007 + 12.7117i) q^{86} -4.15437 q^{87} -31.1449 q^{88} +(-4.96902 + 8.60659i) q^{89} -1.67843 q^{90} +(4.25410 - 7.36831i) q^{91} +(17.5082 - 30.3250i) q^{92} +(3.51506 + 6.08826i) q^{93} -3.13943 q^{94} +(-1.94022 - 3.36056i) q^{95} +(-0.626296 + 1.08478i) q^{96} -4.70746 q^{97} +(20.5078 - 35.5206i) q^{98} +(2.40586 + 4.16707i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 58 q + 2 q^{2} - 5 q^{3} + 54 q^{4} - 3 q^{5} - 8 q^{6} - 13 q^{7} + 12 q^{8} - 30 q^{9}+O(q^{10}) \) 58 * q + 2 * q^2 - 5 * q^3 + 54 * q^4 - 3 * q^5 - 8 * q^6 - 13 * q^7 + 12 * q^8 - 30 * q^9	\( 58 q + 2 q^{2} - 5 q^{3} + 54 q^{4} - 3 q^{5} - 8 q^{6} - 13 q^{7} + 12 q^{8} - 30 q^{9} + 4 q^{10} - 8 q^{12} + 2 q^{13} + 5 q^{14} - 5 q^{15} + 30 q^{16} - 29 q^{17} + 16 q^{18} - 4 q^{19} - 7 q^{20} - 26 q^{21} - 10 q^{22} + 5 q^{23} - 28 q^{24} - 24 q^{25} - 8 q^{26} + 28 q^{27} - 25 q^{28} + 10 q^{29} - 5 q^{30} + 3 q^{31} + 16 q^{32} - 23 q^{33} - q^{34} - 26 q^{35} - 39 q^{36} - 16 q^{37} + q^{38} + 130 q^{39} + 15 q^{40} - 22 q^{41} + 112 q^{42} + 7 q^{43} + 24 q^{44} + 2 q^{45} - 61 q^{46} + 12 q^{47} + 22 q^{48} - 36 q^{49} - 17 q^{50} + 10 q^{51} - 35 q^{52} - 10 q^{53} - 10 q^{54} - 20 q^{55} - 4 q^{56} + 9 q^{57} - 17 q^{58} - 36 q^{59} + 22 q^{60} - 35 q^{61} + 3 q^{62} - 22 q^{63} + 28 q^{64} - 28 q^{65} + 14 q^{66} - 17 q^{67} - 27 q^{68} - 23 q^{69} + 10 q^{70} - 6 q^{71} + 17 q^{72} - 14 q^{73} + 21 q^{74} + 70 q^{75} - 44 q^{76} - 11 q^{77} - 184 q^{78} - 10 q^{79} + 8 q^{80} - 13 q^{81} + 184 q^{82} + 9 q^{83} - 36 q^{84} + 6 q^{85} - 76 q^{86} + 8 q^{87} + 50 q^{88} - 54 q^{89} - 34 q^{90} - 23 q^{91} - 66 q^{92} + 96 q^{94} - 3 q^{95} - 60 q^{96} + 36 q^{97} - 16 q^{98} + 20 q^{99}+O(q^{100}) \) 58 * q + 2 * q^2 - 5 * q^3 + 54 * q^4 - 3 * q^5 - 8 * q^6 - 13 * q^7 + 12 * q^8 - 30 * q^9 + 4 * q^10 - 8 * q^12 + 2 * q^13 + 5 * q^14 - 5 * q^15 + 30 * q^16 - 29 * q^17 + 16 * q^18 - 4 * q^19 - 7 * q^20 - 26 * q^21 - 10 * q^22 + 5 * q^23 - 28 * q^24 - 24 * q^25 - 8 * q^26 + 28 * q^27 - 25 * q^28 + 10 * q^29 - 5 * q^30 + 3 * q^31 + 16 * q^32 - 23 * q^33 - q^34 - 26 * q^35 - 39 * q^36 - 16 * q^37 + q^38 + 130 * q^39 + 15 * q^40 - 22 * q^41 + 112 * q^42 + 7 * q^43 + 24 * q^44 + 2 * q^45 - 61 * q^46 + 12 * q^47 + 22 * q^48 - 36 * q^49 - 17 * q^50 + 10 * q^51 - 35 * q^52 - 10 * q^53 - 10 * q^54 - 20 * q^55 - 4 * q^56 + 9 * q^57 - 17 * q^58 - 36 * q^59 + 22 * q^60 - 35 * q^61 + 3 * q^62 - 22 * q^63 + 28 * q^64 - 28 * q^65 + 14 * q^66 - 17 * q^67 - 27 * q^68 - 23 * q^69 + 10 * q^70 - 6 * q^71 + 17 * q^72 - 14 * q^73 + 21 * q^74 + 70 * q^75 - 44 * q^76 - 11 * q^77 - 184 * q^78 - 10 * q^79 + 8 * q^80 - 13 * q^81 + 184 * q^82 + 9 * q^83 - 36 * q^84 + 6 * q^85 - 76 * q^86 + 8 * q^87 + 50 * q^88 - 54 * q^89 - 34 * q^90 - 23 * q^91 - 66 * q^92 + 96 * q^94 - 3 * q^95 - 60 * q^96 + 36 * q^97 - 16 * q^98 + 20 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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