LMFDB - Embedded newform 731.2.e.a.681.2

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			681.2
Character	$\chi$	$=$	731.681
Dual form			731.2.e.a.307.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.66184 q^{2} +(-1.22526 - 2.12222i) q^{3} +5.08540 q^{4} +(-0.351592 - 0.608975i) q^{5} +(3.26146 + 5.64901i) q^{6} +(-1.71463 + 2.96983i) q^{7} -8.21285 q^{8} +(-1.50254 + 2.60247i) q^{9} +O(q^{10})$	\(q-2.66184 q^{2} +(-1.22526 - 2.12222i) q^{3} +5.08540 q^{4} +(-0.351592 - 0.608975i) q^{5} +(3.26146 + 5.64901i) q^{6} +(-1.71463 + 2.96983i) q^{7} -8.21285 q^{8} +(-1.50254 + 2.60247i) q^{9} +(0.935881 + 1.62099i) q^{10} -2.92598 q^{11} +(-6.23095 - 10.7923i) q^{12} +(-0.158863 + 0.275158i) q^{13} +(4.56408 - 7.90521i) q^{14} +(-0.861584 + 1.49231i) q^{15} +11.6905 q^{16} +(0.500000 - 0.866025i) q^{17} +(3.99952 - 6.92737i) q^{18} +(1.88935 + 3.27246i) q^{19} +(-1.78798 - 3.09688i) q^{20} +8.40349 q^{21} +7.78849 q^{22} +(0.112918 + 0.195579i) q^{23} +(10.0629 + 17.4295i) q^{24} +(2.25277 - 3.90191i) q^{25} +(0.422867 - 0.732428i) q^{26} +0.0124367 q^{27} +(-8.71959 + 15.1028i) q^{28} +(-1.31084 + 2.27043i) q^{29} +(2.29340 - 3.97229i) q^{30} +(2.45321 + 4.24908i) q^{31} -14.6926 q^{32} +(3.58509 + 6.20956i) q^{33} +(-1.33092 + 2.30522i) q^{34} +2.41140 q^{35} +(-7.64101 + 13.2346i) q^{36} +(-3.33013 - 5.76795i) q^{37} +(-5.02916 - 8.71077i) q^{38} +0.778594 q^{39} +(2.88757 + 5.00142i) q^{40} +8.73268 q^{41} -22.3688 q^{42} +(4.71201 + 4.56036i) q^{43} -14.8798 q^{44} +2.11312 q^{45} +(-0.300569 - 0.520601i) q^{46} +0.129653 q^{47} +(-14.3239 - 24.8098i) q^{48} +(-2.37992 - 4.12214i) q^{49} +(-5.99651 + 10.3863i) q^{50} -2.45053 q^{51} +(-0.807880 + 1.39929i) q^{52} +(-5.43802 - 9.41893i) q^{53} -0.0331044 q^{54} +(1.02875 + 1.78185i) q^{55} +(14.0820 - 24.3908i) q^{56} +(4.62991 - 8.01924i) q^{57} +(3.48924 - 6.04353i) q^{58} +8.37738 q^{59} +(-4.38150 + 7.58898i) q^{60} +(-0.201600 + 0.349182i) q^{61} +(-6.53006 - 11.3104i) q^{62} +(-5.15259 - 8.92456i) q^{63} +15.7283 q^{64} +0.223419 q^{65} +(-9.54295 - 16.5289i) q^{66} +(5.79001 + 10.0286i) q^{67} +(2.54270 - 4.40409i) q^{68} +(0.276708 - 0.479272i) q^{69} -6.41876 q^{70} +(1.66521 - 2.88422i) q^{71} +(12.3401 - 21.3737i) q^{72} +(2.18343 - 3.78181i) q^{73} +(8.86428 + 15.3534i) q^{74} -11.0409 q^{75} +(9.60813 + 16.6418i) q^{76} +(5.01698 - 8.68966i) q^{77} -2.07249 q^{78} +(8.40824 - 14.5635i) q^{79} +(-4.11028 - 7.11922i) q^{80} +(4.49237 + 7.78102i) q^{81} -23.2450 q^{82} +(-0.983722 - 1.70386i) q^{83} +42.7351 q^{84} -0.703183 q^{85} +(-12.5426 - 12.1390i) q^{86} +6.42447 q^{87} +24.0306 q^{88} +(-4.27897 - 7.41139i) q^{89} -5.62479 q^{90} +(-0.544782 - 0.943589i) q^{91} +(0.574232 + 0.994600i) q^{92} +(6.01165 - 10.4125i) q^{93} -0.345116 q^{94} +(1.32856 - 2.30114i) q^{95} +(18.0023 + 31.1808i) q^{96} -18.3370 q^{97} +(6.33497 + 10.9725i) q^{98} +(4.39639 - 7.61478i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 58 q - 6 q^{2} + 3 q^{3} + 54 q^{4} - q^{5} + 12 q^{6} + 7 q^{7} - 12 q^{8} - 22 q^{9}+O(q^{10}) $ 58 * q - 6 * q^2 + 3 * q^3 + 54 * q^4 - q^5 + 12 * q^6 + 7 * q^7 - 12 * q^8 - 22 * q^9	\( 58 q - 6 q^{2} + 3 q^{3} + 54 q^{4} - q^{5} + 12 q^{6} + 7 q^{7} - 12 q^{8} - 22 q^{9} + 4 q^{10} + 16 q^{11} + 12 q^{12} + 2 q^{13} - 11 q^{14} + 7 q^{15} + 30 q^{16} + 29 q^{17} + 8 q^{18} + 8 q^{19} - 33 q^{20} - 26 q^{21} - 22 q^{22} - 5 q^{23} + 12 q^{24} - 36 q^{25} - 12 q^{27} + 15 q^{28} + 2 q^{29} + 11 q^{30} + 3 q^{31} - 40 q^{32} + 17 q^{33} - 3 q^{34} + 38 q^{35} - 7 q^{36} + 2 q^{37} + q^{38} - 54 q^{39} + 5 q^{40} + 14 q^{41} - 112 q^{42} + 31 q^{43} - 24 q^{44} - 46 q^{45} - 13 q^{46} - 28 q^{47} - 28 q^{49} - 13 q^{50} + 6 q^{51} + 85 q^{52} - 10 q^{53} + 34 q^{54} + 36 q^{55} - 54 q^{56} - 23 q^{57} + 3 q^{58} + 12 q^{59} + 2 q^{60} - q^{61} - q^{62} - 14 q^{63} + 28 q^{64} + 80 q^{65} - 74 q^{66} + 11 q^{67} + 27 q^{68} - 11 q^{69} + 2 q^{70} + 16 q^{71} + 21 q^{72} + 14 q^{73} + 21 q^{74} - 54 q^{75} + 44 q^{76} + 25 q^{77} + 88 q^{78} - 4 q^{79} - 112 q^{80} + 11 q^{81} - 176 q^{82} - 3 q^{83} + 100 q^{84} - 2 q^{85} + 44 q^{86} + 8 q^{87} - 106 q^{88} + 82 q^{89} + 54 q^{90} - 15 q^{91} + 42 q^{92} + 88 q^{94} + 29 q^{95} + 20 q^{96} + 20 q^{97} + 44 q^{98} - 54 q^{99}+O(q^{100}) \) 58 * q - 6 * q^2 + 3 * q^3 + 54 * q^4 - q^5 + 12 * q^6 + 7 * q^7 - 12 * q^8 - 22 * q^9 + 4 * q^10 + 16 * q^11 + 12 * q^12 + 2 * q^13 - 11 * q^14 + 7 * q^15 + 30 * q^16 + 29 * q^17 + 8 * q^18 + 8 * q^19 - 33 * q^20 - 26 * q^21 - 22 * q^22 - 5 * q^23 + 12 * q^24 - 36 * q^25 - 12 * q^27 + 15 * q^28 + 2 * q^29 + 11 * q^30 + 3 * q^31 - 40 * q^32 + 17 * q^33 - 3 * q^34 + 38 * q^35 - 7 * q^36 + 2 * q^37 + q^38 - 54 * q^39 + 5 * q^40 + 14 * q^41 - 112 * q^42 + 31 * q^43 - 24 * q^44 - 46 * q^45 - 13 * q^46 - 28 * q^47 - 28 * q^49 - 13 * q^50 + 6 * q^51 + 85 * q^52 - 10 * q^53 + 34 * q^54 + 36 * q^55 - 54 * q^56 - 23 * q^57 + 3 * q^58 + 12 * q^59 + 2 * q^60 - q^61 - q^62 - 14 * q^63 + 28 * q^64 + 80 * q^65 - 74 * q^66 + 11 * q^67 + 27 * q^68 - 11 * q^69 + 2 * q^70 + 16 * q^71 + 21 * q^72 + 14 * q^73 + 21 * q^74 - 54 * q^75 + 44 * q^76 + 25 * q^77 + 88 * q^78 - 4 * q^79 - 112 * q^80 + 11 * q^81 - 176 * q^82 - 3 * q^83 + 100 * q^84 - 2 * q^85 + 44 * q^86 + 8 * q^87 - 106 * q^88 + 82 * q^89 + 54 * q^90 - 15 * q^91 + 42 * q^92 + 88 * q^94 + 29 * q^95 + 20 * q^96 + 20 * q^97 + 44 * q^98 - 54 * q^99

Display 100 coefficients 10 coefficients

Character values

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

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

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 $

$2$	−2.66184			−1.88221			−0.941103	−	0.338120i	$-0.890209\pi$
$2$	−2.66184			−1.88221			−0.941103	+	0.338120i	$0.890209\pi$
$3$	−1.22526	−	2.12222i	−0.707406	−	1.22526i	−0.965816	−	0.259228i	$-0.916532\pi$
$3$	−1.22526	−	2.12222i	−0.707406	−	1.22526i	0.258411	−	0.966035i	$-0.416801\pi$
$4$	5.08540			2.54270
$5$	−0.351592	−	0.608975i	−0.157237	−	0.272342i	0.776635	−	0.629951i	$-0.216925\pi$
$5$	−0.351592	−	0.608975i	−0.157237	−	0.272342i	−0.933871	+	0.357610i	$0.883592\pi$
$6$	3.26146	+	5.64901i	1.33148	+	2.30620i
$7$	−1.71463	+	2.96983i	−0.648070	+	1.12249i	0.335514	+	0.942035i	$0.391090\pi$
$7$	−1.71463	+	2.96983i	−0.648070	+	1.12249i	−0.983583	+	0.180454i	$0.942243\pi$
$8$	−8.21285			−2.90368
$9$	−1.50254	+	2.60247i	−0.500846	+	0.867490i
$10$	0.935881	+	1.62099i	0.295952	+	0.512603i
$11$	−2.92598			−0.882216			−0.441108	−	0.897454i	$-0.645414\pi$
$11$	−2.92598			−0.882216			−0.441108	+	0.897454i	$0.645414\pi$
$12$	−6.23095	−	10.7923i	−1.79872	−	3.11548i
$13$	−0.158863	+	0.275158i	−0.0440606	+	0.0763151i	−0.887215	−	0.461357i	$-0.847363\pi$
$13$	−0.158863	+	0.275158i	−0.0440606	+	0.0763151i	0.843154	+	0.537672i	$0.180696\pi$
$14$	4.56408	−	7.90521i	1.21980	−	2.11276i
$15$	−0.861584	+	1.49231i	−0.222460	+	0.385312i
$16$	11.6905			2.92263
$17$	0.500000	−	0.866025i	0.121268	−	0.210042i
$17$	0.500000	−	0.866025i	0.121268	−	0.210042i
$18$	3.99952	−	6.92737i	0.942695	−	1.63280i
$19$	1.88935	+	3.27246i	0.433448	+	0.750753i	0.997168	−	0.0752127i	$-0.0239636\pi$
$19$	1.88935	+	3.27246i	0.433448	+	0.750753i	−0.563720	+	0.825966i	$0.690630\pi$
$20$	−1.78798	−	3.09688i	−0.399806	−	0.692484i
$21$	8.40349			1.83379
$22$	7.78849			1.66051
$23$	0.112918	+	0.195579i	0.0235450	+	0.0407811i	0.877558	−	0.479471i	$-0.159171\pi$
$23$	0.112918	+	0.195579i	0.0235450	+	0.0407811i	−0.854013	+	0.520252i	$0.825838\pi$
$24$	10.0629	+	17.4295i	2.05408	+	3.55777i
$25$	2.25277	−	3.90191i	0.450553	−	0.780381i
$26$	0.422867	−	0.732428i	0.0829311	−	0.143641i
$27$	0.0124367			0.00239344
$28$	−8.71959	+	15.1028i	−1.64785	+	2.85415i
$29$	−1.31084	+	2.27043i	−0.243416	+	0.421609i	−0.961685	−	0.274157i	$-0.911601\pi$
$29$	−1.31084	+	2.27043i	−0.243416	+	0.421609i	0.718269	+	0.695765i	$0.244935\pi$
$30$	2.29340	−	3.97229i	0.418716	−	0.725237i
$31$	2.45321	+	4.24908i	0.440610	+	0.763158i	0.997735	−	0.0672703i	$-0.0214290\pi$
$31$	2.45321	+	4.24908i	0.440610	+	0.763158i	−0.557125	+	0.830428i	$0.688096\pi$
$32$	−14.6926			−2.59730
$33$	3.58509	+	6.20956i	0.624085	+	1.08095i
$34$	−1.33092	+	2.30522i	−0.228251	+	0.395342i
$35$	2.41140			0.407601
$36$	−7.64101	+	13.2346i	−1.27350	+	2.20577i
$37$	−3.33013	−	5.76795i	−0.547470	−	0.948246i	−0.998447	−	0.0557103i	$-0.982258\pi$
$37$	−3.33013	−	5.76795i	−0.547470	−	0.948246i	0.450977	−	0.892536i	$-0.351076\pi$
$38$	−5.02916	−	8.71077i	−0.815838	−	1.41307i
$39$	0.778594			0.124675
$40$	2.88757	+	5.00142i	0.456565	+	0.790794i
$41$	8.73268			1.36382			0.681908	−	0.731438i	$-0.261150\pi$
$41$	8.73268			1.36382			0.681908	+	0.731438i	$0.261150\pi$
$42$	−22.3688			−3.45158
$43$	4.71201	+	4.56036i	0.718576	+	0.695449i
$43$	4.71201	+	4.56036i	0.718576	+	0.695449i
$44$	−14.8798			−2.24321
$45$	2.11312			0.315005
$46$	−0.300569	−	0.520601i	−0.0443165	−	0.0767585i
$47$	0.129653			0.0189119			0.00945594	−	0.999955i	$-0.496990\pi$
$47$	0.129653			0.0189119			0.00945594	+	0.999955i	$0.496990\pi$
$48$	−14.3239	−	24.8098i	−2.06748	−	3.58099i
$49$	−2.37992	−	4.12214i	−0.339988	−	0.588877i
$50$	−5.99651	+	10.3863i	−0.848034	+	1.46884i
$51$	−2.45053			−0.343142
$52$	−0.807880	+	1.39929i	−0.112033	+	0.194047i
$53$	−5.43802	−	9.41893i	−0.746970	−	1.29379i	−0.949269	−	0.314466i	$-0.898175\pi$
$53$	−5.43802	−	9.41893i	−0.746970	−	1.29379i	0.202299	−	0.979324i	$-0.435159\pi$
$54$	−0.0331044			−0.00450494
$55$	1.02875	+	1.78185i	0.138717	+	0.240264i
$56$	14.0820	−	24.3908i	1.88179	−	3.25935i
$57$	4.62991	−	8.01924i	0.613247	−	1.06217i
$58$	3.48924	−	6.04353i	0.458159	−	0.793555i
$59$	8.37738			1.09064			0.545321	−	0.838227i	$-0.316408\pi$
$59$	8.37738			1.09064			0.545321	+	0.838227i	$0.316408\pi$
$60$	−4.38150	+	7.58898i	−0.565650	+	0.979734i
$61$	−0.201600	+	0.349182i	−0.0258123	+	0.0447082i	−0.878643	−	0.477479i	$-0.841551\pi$
$61$	−0.201600	+	0.349182i	−0.0258123	+	0.0447082i	0.852831	+	0.522187i	$0.174884\pi$
$62$	−6.53006	−	11.3104i	−0.829318	−	1.43642i
$63$	−5.15259	−	8.92456i	−0.649166	−	1.12439i
$64$	15.7283			1.96604
$65$	0.223419			0.0277117
$66$	−9.54295	−	16.5289i	−1.17466	−	2.03456i
$67$	5.79001	+	10.0286i	0.707362	+	1.22519i	0.965832	+	0.259168i	$0.0834483\pi$
$67$	5.79001	+	10.0286i	0.707362	+	1.22519i	−0.258470	+	0.966019i	$0.583218\pi$
$68$	2.54270	−	4.40409i	0.308348	−	0.534074i
$69$	0.276708	−	0.479272i	0.0333117	−	0.0576976i
$70$	−6.41876			−0.767189
$71$	1.66521	−	2.88422i	0.197624	−	0.342294i	−0.750134	−	0.661286i	$-0.770011\pi$
$71$	1.66521	−	2.88422i	0.197624	−	0.342294i	0.947757	+	0.318992i	$0.103344\pi$
$72$	12.3401	−	21.3737i	1.45430	−	2.51892i
$73$	2.18343	−	3.78181i	0.255551	−	0.442627i	−0.709494	−	0.704711i	$-0.751077\pi$
$73$	2.18343	−	3.78181i	0.255551	−	0.442627i	0.965045	+	0.262084i	$0.0844099\pi$
$74$	8.86428	+	15.3534i	1.03045	+	1.78479i
$75$	−11.0409			−1.27490
$76$	9.60813	+	16.6418i	1.10213	+	1.90894i
$77$	5.01698	−	8.68966i	0.571737	−	0.990278i
$78$	−2.07249			−0.234664
$79$	8.40824	−	14.5635i	0.946000	−	1.63852i	0.192265	−	0.981343i	$-0.438417\pi$
$79$	8.40824	−	14.5635i	0.946000	−	1.63852i	0.753736	−	0.657178i	$-0.228250\pi$
$80$	−4.11028	−	7.11922i	−0.459544	−	0.795953i
$81$	4.49237	+	7.78102i	0.499153	+	0.864558i
$82$	−23.2450			−2.56698
$83$	−0.983722	−	1.70386i	−0.107977	−	0.187023i	0.806973	−	0.590588i	$-0.201104\pi$
$83$	−0.983722	−	1.70386i	−0.107977	−	0.187023i	−0.914951	+	0.403565i	$0.867771\pi$
$84$	42.7351			4.66279
$85$	−0.703183			−0.0762709
$86$	−12.5426	−	12.1390i	−1.35251	−	1.30898i
$87$	6.42447			0.688776
$88$	24.0306			2.56167
$89$	−4.27897	−	7.41139i	−0.453570	−	0.785605i	0.545035	−	0.838413i	$-0.316516\pi$
$89$	−4.27897	−	7.41139i	−0.453570	−	0.785605i	−0.998605	+	0.0528077i	$0.983183\pi$
$90$	−5.62479			−0.592905
$91$	−0.544782	−	0.943589i	−0.0571086	−	0.0989150i
$92$	0.574232	+	0.994600i	0.0598679	+	0.103694i
$93$	6.01165	−	10.4125i	0.623380	−	1.07972i
$94$	−0.345116			−0.0355960
$95$	1.32856	−	2.30114i	0.136308	−	0.236092i
$96$	18.0023	+	31.1808i	1.83735	+	3.18238i
$97$	−18.3370			−1.86184			−0.930922	−	0.365218i	$-0.880994\pi$
$97$	−18.3370			−1.86184			−0.930922	+	0.365218i	$0.880994\pi$
$98$	6.33497	+	10.9725i	0.639928	+	1.10839i
$99$	4.39639	−	7.61478i	0.441854	−	0.765314i
$100$	11.4562	−	19.8428i	1.14562	−	1.98428i
$101$	6.97043	−	12.0731i	0.693583	−	1.20132i	−0.277073	−	0.960849i	$-0.589364\pi$
$101$	6.97043	−	12.0731i	0.693583	−	1.20132i	0.970656	−	0.240472i	$-0.0773024\pi$
$102$	6.52291			0.645864
$103$	2.77074	−	4.79906i	0.273009	−	0.472865i	−0.696622	−	0.717438i	$-0.745314\pi$
$103$	2.77074	−	4.79906i	0.273009	−	0.472865i	0.969631	+	0.244573i	$0.0786478\pi$
$104$	1.30472	−	2.25983i	0.127938	−	0.221595i
$105$	−2.95460	−	5.11751i	−0.288339	−	0.499418i
$106$	14.4752	+	25.0717i	1.40595	+	2.43518i
$107$	−3.70336			−0.358017			−0.179009	−	0.983847i	$-0.557289\pi$
$107$	−3.70336			−0.358017			−0.179009	+	0.983847i	$0.557289\pi$
$108$	0.0632454			0.00608579
$109$	−0.186327	−	0.322727i	−0.0178469	−	0.0309117i	0.856964	−	0.515376i	$-0.172348\pi$
$109$	−0.186327	−	0.322727i	−0.0178469	−	0.0309117i	−0.874811	+	0.484465i	$0.839014\pi$
$110$	−2.73837	−	4.74300i	−0.261093	−	0.452227i
$111$	−8.16057	+	14.1345i	−0.774567	+	1.34159i
$112$	−20.0449	+	34.7188i	−1.89407	+	3.28062i
$113$	15.6535			1.47255			0.736277	−	0.676681i	$-0.236582\pi$
$113$	15.6535			1.47255			0.736277	+	0.676681i	$0.236582\pi$
$114$	−12.3241	+	21.3460i	−1.15426	+	1.99923i
$115$	0.0794019	−	0.137528i	0.00740427	−	0.0128246i
$116$	−6.66612	+	11.5461i	−0.618934	+	1.07203i
$117$	−0.477394	−	0.826871i	−0.0441351	−	0.0764442i
$118$	−22.2993			−2.05281
$119$	1.71463	+	2.96983i	0.157180	+	0.272244i
$120$	7.07606	−	12.2561i	0.645953	−	1.11882i
$121$	−2.43864			−0.221695
$122$	0.536628	−	0.929467i	0.0485840	−	0.0841500i
$123$	−10.6998	−	18.5326i	−0.964771	−	1.67103i
$124$	12.4756	+	21.6083i	1.12034	+	1.94048i
$125$	−6.68413			−0.597847
$126$	13.7154	+	23.7558i	1.22186	+	2.11633i
$127$	17.4681			1.55004			0.775019	−	0.631937i	$-0.217740\pi$
$127$	17.4681			1.55004			0.775019	+	0.631937i	$0.217740\pi$
$128$	−12.4811			−1.10318
$129$	3.90463	−	15.5876i	0.343783	−	1.37241i
$130$	−0.594706			−0.0521592
$131$	−11.1527			−0.974417			−0.487208	−	0.873286i	$-0.661985\pi$
$131$	−11.1527			−0.974417			−0.487208	+	0.873286i	$0.661985\pi$
$132$	18.2316	+	31.5781i	1.58686	+	2.74852i
$133$	−12.9582			−1.12362
$134$	−15.4121	−	26.6945i	−1.33140	−	2.30606i
$135$	−0.00437262	−	0.00757361i	−0.000376336	−	0.000651832i
$136$	−4.10643	+	7.11254i	−0.352123	+	0.609895i
$137$	−18.8214			−1.60802			−0.804012	−	0.594614i	$-0.797305\pi$
$137$	−18.8214			−1.60802			−0.804012	+	0.594614i	$0.797305\pi$
$138$	−0.736553	+	1.27575i	−0.0626995	+	0.108599i
$139$	−6.55596	−	11.3553i	−0.556069	−	0.963140i	−0.997819	−	0.0660021i	$-0.978976\pi$
$139$	−6.55596	−	11.3553i	−0.556069	−	0.963140i	0.441750	−	0.897138i	$-0.354358\pi$
$140$	12.2629			1.03641
$141$	−0.158859	−	0.275152i	−0.0133784	−	0.0231720i
$142$	−4.43252	+	7.67735i	−0.371969	+	0.644269i
$143$	0.464829	−	0.805107i	0.0388709	−	0.0673264i
$144$	−17.5654	+	30.4242i	−1.46379	+	2.53535i
$145$	1.84352			0.153096
$146$	−5.81194	+	10.0666i	−0.480999	+	0.833115i
$147$	−5.83205	+	10.1014i	−0.481019	+	0.833150i
$148$	−16.9350	−	29.3324i	−1.39205	−	2.41111i
$149$	9.32239	+	16.1469i	0.763720	+	1.32280i	0.940921	+	0.338627i	$0.109963\pi$
$149$	9.32239	+	16.1469i	0.763720	+	1.32280i	−0.177200	+	0.984175i	$0.556704\pi$
$150$	29.3892			2.39962
$151$	5.61810			0.457195			0.228597	−	0.973521i	$-0.426586\pi$
$151$	5.61810			0.457195			0.228597	+	0.973521i	$0.426586\pi$
$152$	−15.5170	−	26.8762i	−1.25859	−	2.17995i
$153$	1.50254	+	2.60247i	0.121473	+	0.210397i
$154$	−13.3544	+	23.1305i	−1.07613	+	1.86391i
$155$	1.72506	−	2.98789i	0.138560	−	0.239993i
$156$	3.95946			0.317011
$157$	2.23349	−	3.86853i	0.178252	−	0.308742i	−0.763030	−	0.646363i	$-0.776289\pi$
$157$	2.23349	−	3.86853i	0.178252	−	0.308742i	0.941282	+	0.337621i	$0.109622\pi$
$158$	−22.3814	+	38.7657i	−1.78057	+	3.08403i
$159$	−13.3260	+	23.0813i	−1.05682	+	1.83047i
$160$	5.16579	+	8.94741i	0.408391	+	0.707354i
$161$	−0.774450			−0.0610352
$162$	−11.9580	−	20.7118i	−0.939508	−	1.62728i
$163$	6.87124	−	11.9013i	0.538197	−	0.932184i	−0.460804	−	0.887502i	$-0.652439\pi$
$163$	6.87124	−	11.9013i	0.538197	−	0.932184i	0.999001	−	0.0446826i	$-0.0142277\pi$
$164$	44.4092			3.46778
$165$	2.52098	−	4.36646i	0.196258	−	0.339929i
$166$	2.61851	+	4.53540i	0.203236	+	0.352015i
$167$	10.5790	+	18.3234i	0.818629	+	1.41791i	0.906692	+	0.421793i	$0.138599\pi$
$167$	10.5790	+	18.3234i	0.818629	+	1.41791i	−0.0880631	+	0.996115i	$0.528068\pi$
$168$	−69.0166			−5.32475
$169$	6.44953	+	11.1709i	0.496117	+	0.859300i
$170$	1.87176			0.143558
$171$	−11.3553			−0.868362
$172$	23.9625	+	23.1913i	1.82712	+	1.76832i
$173$	−3.09221			−0.235096			−0.117548	−	0.993067i	$-0.537503\pi$
$173$	−3.09221			−0.235096			−0.117548	+	0.993067i	$0.537503\pi$
$174$	−17.1009			−1.29642
$175$	7.72533	+	13.3807i	0.583980	+	1.01148i
$176$	−34.2062			−2.57839
$177$	−10.2645	−	17.7786i	−0.771526	−	1.33632i
$178$	11.3899	+	19.7279i	0.853711	+	1.47867i
$179$	8.00272	−	13.8611i	0.598152	−	1.03603i	−0.394942	−	0.918706i	$-0.629235\pi$
$179$	8.00272	−	13.8611i	0.598152	−	1.03603i	0.993094	−	0.117323i	$-0.0374313\pi$
$180$	10.7461			0.800964
$181$	−3.95342	+	6.84752i	−0.293855	+	0.508972i	−0.974718	−	0.223439i	$-0.928272\pi$
$181$	−3.95342	+	6.84752i	−0.293855	+	0.508972i	0.680863	+	0.732411i	$0.261605\pi$
$182$	1.45012	+	2.51169i	0.107490	+	0.186179i
$183$	0.988053			0.0730390
$184$	−0.927377	−	1.60626i	−0.0683672	−	0.118415i
$185$	−2.34169	+	4.05593i	−0.172165	+	0.298198i
$186$	−16.0021	+	27.7164i	−1.17333	+	2.03227i
$187$	−1.46299	+	2.53397i	−0.106984	+	0.185302i
$188$	0.659339			0.0480872
$189$	−0.0213243	+	0.0369347i	−0.00155111	+	0.00268661i
$190$	−3.53642	+	6.12527i	−0.256559	+	0.444373i
$191$	7.55464	+	13.0850i	0.546635	+	0.946799i	0.998502	+	0.0547138i	$0.0174246\pi$
$191$	7.55464	+	13.0850i	0.546635	+	0.946799i	−0.451867	+	0.892085i	$0.649242\pi$
$192$	−19.2713	−	33.3789i	−1.39079	−	2.40891i
$193$	20.6195			1.48423			0.742114	−	0.670274i	$-0.233823\pi$
$193$	20.6195			1.48423			0.742114	+	0.670274i	$0.233823\pi$
$194$	48.8103			3.50437
$195$	−0.273747	−	0.474144i	−0.0196034	−	0.0339542i
$196$	−12.1028	−	20.9627i	−0.864488	−	1.49734i
$197$	−3.77914	+	6.54565i	−0.269252	+	0.466359i	−0.968669	−	0.248356i	$-0.920110\pi$
$197$	−3.77914	+	6.54565i	−0.269252	+	0.466359i	0.699417	+	0.714714i	$0.253443\pi$
$198$	−11.7025	+	20.2693i	−0.831661	+	1.44048i
$199$	18.2105			1.29091			0.645455	−	0.763799i	$-0.276668\pi$
$199$	18.2105			1.29091			0.645455	+	0.763799i	$0.276668\pi$
$200$	−18.5016	+	32.0458i	−1.30826	+	2.26598i
$201$	14.1886	−	24.5753i	1.00078	−	1.73341i
$202$	−18.5542	+	32.1368i	−1.30547	+	2.26113i
$203$	−4.49520	−	7.78591i	−0.315501	−	0.546464i
$204$	−12.4619			−0.872508
$205$	−3.07034	−	5.31798i	−0.214442	−	0.371424i
$206$	−7.37527	+	12.7743i	−0.513859	+	0.890030i
$207$	−0.678653			−0.0471696
$208$	−1.85718	+	3.21674i	−0.128773	+	0.223041i
$209$	−5.52821	−	9.57515i	−0.382394	−	0.662327i
$210$	7.86467	+	13.6220i	0.542714	+	0.940008i
$211$	−19.5051			−1.34279			−0.671393	−	0.741101i	$-0.734304\pi$
$211$	−19.5051			−1.34279			−0.671393	+	0.741101i	$0.734304\pi$
$212$	−27.6545	−	47.8990i	−1.89932	−	3.28972i
$213$	−8.16127			−0.559201
$214$	9.85776			0.673863
$215$	1.12044	−	4.47288i	0.0764134	−	0.305048i
$216$	−0.102140			−0.00694977
$217$	−16.8254			−1.14218
$218$	0.495972	+	0.859049i	0.0335915	+	0.0581821i
$219$	−10.7011			−0.723112
$220$	5.23161	+	9.06141i	0.352715	+	0.610920i
$221$	0.158863	+	0.275158i	0.0106863	+	0.0185091i
$222$	21.7221	−	37.6239i	1.45789	−	2.52515i
$223$	15.6232			1.04621			0.523104	−	0.852269i	$-0.324774\pi$
$223$	15.6232			1.04621			0.523104	+	0.852269i	$0.324774\pi$
$224$	25.1923	−	43.6344i	1.68323	−	2.91545i
$225$	6.76973	+	11.7255i	0.451316	+	0.781701i
$226$	−41.6670			−2.77165
$227$	9.89831	+	17.1444i	0.656974	+	1.13791i	0.981395	+	0.192000i	$0.0614973\pi$
$227$	9.89831	+	17.1444i	0.656974	+	1.13791i	−0.324421	+	0.945913i	$0.605169\pi$
$228$	23.5450	−	40.7811i	1.55930	−	2.70079i
$229$	9.87030	−	17.0959i	0.652248	−	1.12973i	−0.330328	−	0.943866i	$-0.607159\pi$
$229$	9.87030	−	17.0959i	0.652248	−	1.12973i	0.982576	−	0.185860i	$-0.0595072\pi$
$230$	−0.211355	+	0.366078i	−0.0139364	+	0.0241385i
$231$	−24.5885			−1.61780
$232$	10.7657	−	18.6467i	0.706803	−	1.22422i
$233$	7.66226	−	13.2714i	0.501972	−	0.869440i	−0.498026	−	0.867162i	$-0.665942\pi$
$233$	7.66226	−	13.2714i	0.501972	−	0.869440i	0.999997	−	0.00227815i	$-0.000725158\pi$
$234$	1.27075	+	2.20100i	0.0830714	+	0.143884i
$235$	−0.0455850	−	0.0789555i	−0.00297364	−	0.00515049i
$236$	42.6023			2.77318
$237$	−41.2092			−2.67682
$238$	−4.56408	−	7.90521i	−0.295845	−	0.512419i
$239$	1.04026	+	1.80178i	0.0672886	+	0.116547i	0.897707	−	0.440593i	$-0.145232\pi$
$239$	1.04026	+	1.80178i	0.0672886	+	0.116547i	−0.830418	+	0.557140i	$0.811899\pi$
$240$	−10.0724	+	17.4458i	−0.650168	+	1.12612i
$241$	5.81674	−	10.0749i	0.374689	−	0.648981i	−0.615591	−	0.788066i	$-0.711083\pi$
$241$	5.81674	−	10.0749i	0.374689	−	0.648981i	0.990280	+	0.139085i	$0.0444161\pi$
$242$	6.49128			0.417275
$243$	11.0273	−	19.0999i	0.707404	−	1.22526i
$244$	−1.02522	+	1.77573i	−0.0656329	+	0.113679i
$245$	−1.67352	+	2.89862i	−0.106917	+	0.185186i
$246$	28.4813	+	49.3310i	1.81590	+	3.14523i
$247$	−1.20059			−0.0763918
$248$	−20.1478	−	34.8971i	−1.27939	−	2.21597i
$249$	−2.41064	+	4.17534i	−0.152768	+	0.264602i
$250$	17.7921			1.12527
$251$	−12.2201	+	21.1658i	−0.771326	+	1.33598i	0.165511	+	0.986208i	$0.447073\pi$
$251$	−12.2201	+	21.1658i	−0.771326	+	1.33598i	−0.936837	+	0.349767i	$0.886261\pi$
$252$	−26.2030	−	45.3849i	−1.65063	−	2.85898i
$253$	−0.330395	−	0.572261i	−0.0207718	−	0.0359778i
$254$	−46.4972			−2.91749
$255$	0.861584	+	1.49231i	0.0539545	+	0.0934519i
$256$	1.76609			0.110381
$257$	8.35513			0.521179			0.260589	−	0.965450i	$-0.416083\pi$
$257$	8.35513			0.521179			0.260589	+	0.965450i	$0.416083\pi$
$258$	−10.3935	+	41.4916i	−0.647071	+	2.58316i
$259$	22.8398			1.41919
$260$	1.13618			0.0704626
$261$	−3.93916	−	6.82282i	−0.243828	−	0.422322i
$262$	29.6867			1.83405
$263$	5.35592	+	9.27673i	0.330260	+	0.572028i	0.982563	−	0.185931i	$-0.0595301\pi$
$263$	5.35592	+	9.27673i	0.330260	+	0.572028i	−0.652302	+	0.757959i	$0.726197\pi$
$264$	−29.4438	−	50.9982i	−1.81214	−	3.13872i
$265$	−3.82393	+	6.62324i	−0.234902	+	0.406862i
$266$	34.4926			2.11488
$267$	−10.4857	+	18.1618i	−0.641715	+	1.11148i
$268$	29.4445	+	50.9994i	1.79861	+	3.11528i
$269$	5.36873			0.327337			0.163669	−	0.986515i	$-0.447667\pi$
$269$	5.36873			0.327337			0.163669	+	0.986515i	$0.447667\pi$
$270$	0.0116392	+	0.0201597i	0.000708341	+	0.00122688i
$271$	3.56136	−	6.16845i	0.216337	−	0.374707i	−0.737348	−	0.675513i	$-0.763922\pi$
$271$	3.56136	−	6.16845i	0.216337	−	0.374707i	0.953685	+	0.300806i	$0.0972557\pi$
$272$	5.84525	−	10.1243i	0.354421	−	0.613874i
$273$	−1.33500	+	2.31229i	−0.0807979	+	0.139946i
$274$	50.0997			3.02663
$275$	−6.59155	+	11.4169i	−0.397485	+	0.688465i
$276$	1.40717	−	2.43729i	0.0847018	−	0.146708i
$277$	8.64831	+	14.9793i	0.519626	+	0.900019i	0.999740	+	0.0228129i	$0.00726220\pi$
$277$	8.64831	+	14.9793i	0.519626	+	0.900019i	−0.480113	+	0.877206i	$0.659404\pi$
$278$	17.4509	+	30.2259i	1.04664	+	1.81283i
$279$	−14.7442			−0.882710
$280$	−19.8045			−1.18354
$281$	4.63359	+	8.02561i	0.276417	+	0.478768i	0.970492	−	0.241135i	$-0.0775197\pi$
$281$	4.63359	+	8.02561i	0.276417	+	0.478768i	−0.694075	+	0.719903i	$0.744186\pi$
$282$	0.422858	+	0.732412i	0.0251808	+	0.0436145i
$283$	−1.99006	+	3.44688i	−0.118297	+	0.204896i	−0.919093	−	0.394041i	$-0.871077\pi$
$283$	−1.99006	+	3.44688i	−0.118297	+	0.204896i	0.800796	+	0.598937i	$0.204410\pi$
$284$	8.46825	−	14.6674i	0.502498	−	0.870352i
$285$	−6.51135			−0.385699
$286$	−1.23730	+	2.14307i	−0.0731631	+	0.126722i
$287$	−14.9733	+	25.9346i	−0.883847	+	1.53087i
$288$	22.0761	−	38.2370i	1.30085	−	2.25314i
$289$	−0.500000	−	0.866025i	−0.0294118	−	0.0509427i
$290$	−4.90715			−0.288158
$291$	22.4677	+	38.9152i	1.31708	+	2.28125i
$292$	11.1036	−	19.2320i	0.649789	−	1.12547i
$293$	26.9318			1.57337			0.786687	−	0.617352i	$-0.211794\pi$
$293$	26.9318			1.57337			0.786687	+	0.617352i	$0.211794\pi$
$294$	15.5240	−	26.8883i	0.905378	−	1.56816i
$295$	−2.94542	−	5.10161i	−0.171489	−	0.297027i
$296$	27.3499	+	47.3713i	1.58968	+	2.75340i
$297$	−0.0363894			−0.00211153
$298$	−24.8147	−	42.9804i	−1.43748	−	2.48979i
$299$	−0.0717537			−0.00414962
$300$	−56.1475			−3.24168
$301$	−21.6229	+	6.17453i	−1.24632	+	0.355894i
$302$	−14.9545			−0.860535
$303$	−34.1624			−1.96258
$304$	22.0875	+	38.2567i	1.26681	+	2.19417i
$305$	0.283524			0.0162345
$306$	−3.99952	−	6.92737i	−0.228637	−	0.396011i
$307$	−5.60546	−	9.70894i	−0.319921	−	0.554119i	0.660551	−	0.750782i	$-0.270323\pi$
$307$	−5.60546	−	9.70894i	−0.319921	−	0.554119i	−0.980471	+	0.196663i	$0.936990\pi$
$308$	25.5133	−	44.1904i	1.45376	−	2.51798i
$309$	−13.5795			−0.772512
$310$	−4.59183	+	7.95328i	−0.260798	+	0.451716i
$311$	4.26099	+	7.38025i	0.241618	+	0.418495i	0.961175	−	0.275938i	$-0.0889884\pi$
$311$	4.26099	+	7.38025i	0.241618	+	0.418495i	−0.719557	+	0.694433i	$0.755655\pi$
$312$	−6.39448			−0.362016
$313$	2.83823	+	4.91596i	0.160426	+	0.277867i	0.935022	−	0.354591i	$-0.115380\pi$
$313$	2.83823	+	4.91596i	0.160426	+	0.277867i	−0.774595	+	0.632457i	$0.782046\pi$
$314$	−5.94521	+	10.2974i	−0.335508	+	0.581116i
$315$	−3.62322	+	6.27560i	−0.204145	+	0.353590i
$316$	42.7593	−	74.0612i	2.40540	−	4.16627i
$317$	26.4575			1.48600			0.743001	−	0.669290i	$-0.233402\pi$
$317$	26.4575			1.48600			0.743001	+	0.669290i	$0.233402\pi$
$318$	35.4717	−	61.4389i	1.98916	−	3.44532i
$319$	3.83548	−	6.64324i	0.214746	−	0.371950i
$320$	−5.52994	−	9.57813i	−0.309133	−	0.535434i
$321$	4.53759	+	7.85934i	0.253264	+	0.438665i
$322$	2.06146			0.114881
$323$	3.77871			0.210253
$324$	22.8455	+	39.5696i	1.26920	+	2.19831i
$325$	0.715761	+	1.23973i	0.0397033	+	0.0687681i
$326$	−18.2901	+	31.6795i	−1.01300	+	1.75456i
$327$	−0.456598	+	0.790851i	−0.0252499	+	0.0437342i
$328$	−71.7202			−3.96009
$329$	−0.222307	+	0.385048i	−0.0122562	+	0.0212284i
$330$	−6.71045	+	11.6228i	−0.369398	+	0.639816i
$331$	12.5582	−	21.7515i	0.690261	−	1.19557i	−0.281491	−	0.959564i	$-0.590829\pi$
$331$	12.5582	−	21.7515i	0.690261	−	1.19557i	0.971752	−	0.236004i	$-0.0758378\pi$
$332$	−5.00262	−	8.66479i	−0.274554	−	0.475542i
$333$	20.0146			1.09679
$334$	−28.1597	−	48.7740i	−1.54083	−	2.66879i
$335$	4.07144	−	7.05194i	0.222446	−	0.385289i
$336$	98.2411			5.35949
$337$	6.61043	−	11.4496i	0.360093	−	0.623700i	−0.627883	−	0.778308i	$-0.716078\pi$
$337$	6.61043	−	11.4496i	0.360093	−	0.623700i	0.987976	+	0.154608i	$0.0494115\pi$
$338$	−17.1676	−	29.7352i	−0.933795	−	1.61738i
$339$	−19.1796	−	33.2200i	−1.04169	−	1.80426i
$340$	−3.57597			−0.193934
$341$	−7.17804	−	12.4327i	−0.388713	−	0.673270i
$342$	30.2260			1.63444
$343$	−7.68211			−0.414795
$344$	−38.6991	−	37.4536i	−2.08651	−	2.01936i
$345$	−0.389153			−0.0209513
$346$	8.23098			0.442500
$347$	−8.37594	−	14.5076i	−0.449644	−	0.778807i	0.548718	−	0.836007i	$-0.315116\pi$
$347$	−8.37594	−	14.5076i	−0.449644	−	0.778807i	−0.998363	+	0.0572005i	$0.981783\pi$
$348$	32.6710			1.75135
$349$	−3.67932	−	6.37276i	−0.196949	−	0.341126i	0.750588	−	0.660770i	$-0.229770\pi$
$349$	−3.67932	−	6.37276i	−0.196949	−	0.341126i	−0.947538	+	0.319644i	$0.896437\pi$
$350$	−20.5636	−	35.6172i	−1.09917	−	1.90382i
$351$	−0.00197572	+	0.00342205i	−0.000105456	+	0.000182655i
$352$	42.9902			2.29138
$353$	6.14561	−	10.6445i	0.327098	−	0.566550i	−0.654837	−	0.755770i	$-0.727263\pi$
$353$	6.14561	−	10.6445i	0.327098	−	0.566550i	0.981935	+	0.189220i	$0.0605959\pi$
$354$	27.3225	+	47.3239i	1.45217	+	2.51524i
$355$	−2.34189			−0.124295
$356$	−21.7603	−	37.6899i	−1.15329	−	1.99756i
$357$	4.20175	−	7.27764i	0.222380	−	0.385173i
$358$	−21.3020	+	36.8961i	−1.12584	+	1.95002i
$359$	−16.5754	+	28.7094i	−0.874814	+	1.51522i	−0.0178541	+	0.999841i	$0.505683\pi$
$359$	−16.5754	+	28.7094i	−0.874814	+	1.51522i	−0.856960	+	0.515382i	$0.827650\pi$
$360$	−17.3547			−0.914674
$361$	2.36068	−	4.08882i	0.124246	−	0.215201i
$362$	10.5234	−	18.2270i	0.553096	−	0.957991i
$363$	2.98798	+	5.17533i	0.156828	+	0.271634i
$364$	−2.77043	−	4.79853i	−0.145210	−	0.251511i
$365$	−3.07070			−0.160728
$366$	−2.63004			−0.137474
$367$	0.423423	+	0.733390i	0.0221025	+	0.0382827i	0.876865	−	0.480737i	$-0.159631\pi$
$367$	0.423423	+	0.733390i	0.0221025	+	0.0382827i	−0.854763	+	0.519019i	$0.826297\pi$
$368$	1.32007	+	2.28642i	0.0688132	+	0.119188i
$369$	−13.1212	+	22.7266i	−0.683061	+	1.18310i
$370$	6.23321	−	10.7962i	0.324049	−	0.561270i
$371$	37.2968			1.93635
$372$	30.5717	−	52.9517i	1.58507	−	2.74542i
$373$	1.49305	−	2.58603i	0.0773070	−	0.133900i	−0.824780	−	0.565454i	$-0.808701\pi$
$373$	1.49305	−	2.58603i	0.0773070	−	0.133900i	0.902087	+	0.431554i	$0.142034\pi$
$374$	3.89425	−	6.74503i	0.201367	−	0.348777i
$375$	8.18982	+	14.1852i	0.422920	+	0.732520i
$376$	−1.06482			−0.0549140
$377$	−0.416486	−	0.721374i	−0.0214501	−	0.0371527i
$378$	0.0567618	−	0.0983144i	0.00291951	−	0.00505675i
$379$	−32.7797			−1.68378			−0.841890	−	0.539649i	$-0.818557\pi$
$379$	−32.7797			−1.68378			−0.841890	+	0.539649i	$0.818557\pi$
$380$	6.75627	−	11.7022i	0.346590	−	0.600311i
$381$	−21.4030	−	37.0710i	−1.09651	−	1.89920i
$382$	−20.1093	−	34.8303i	−1.02888	−	1.78207i
$383$	33.3246			1.70281			0.851403	−	0.524512i	$-0.175752\pi$
$383$	33.3246			1.70281			0.851403	+	0.524512i	$0.175752\pi$
$384$	15.2926	+	26.4876i	0.780398	+	1.35169i
$385$	−7.05571			−0.359592
$386$	−54.8860			−2.79362
$387$	−18.9482	+	5.41077i	−0.963191	+	0.275045i
$388$	−93.2512			−4.73411
$389$	14.7578			0.748248			0.374124	−	0.927379i	$-0.377943\pi$
$389$	14.7578			0.748248			0.374124	+	0.927379i	$0.377943\pi$
$390$	0.728672	+	1.26210i	0.0368977	+	0.0639087i
$391$	0.225836			0.0114210
$392$	19.5459	+	33.8545i	0.987218	+	1.70991i
$393$	13.6650	+	23.6685i	0.689308	+	1.19392i
$394$	10.0595	−	17.4235i	0.506788	−	0.877783i
$395$	−11.8251			−0.594983
$396$	22.3574	−	38.7242i	1.12350	−	1.94596i
$397$	6.87590	+	11.9094i	0.345092	+	0.597716i	0.985370	−	0.170426i	$-0.0545145\pi$
$397$	6.87590	+	11.9094i	0.345092	+	0.597716i	−0.640279	+	0.768143i	$0.721181\pi$
$398$	−48.4735			−2.42976
$399$	15.8772	+	27.5001i	0.794853	+	1.37673i
$400$	26.3360	−	45.6153i	1.31680	−	2.28076i
$401$	−17.8172	+	30.8604i	−0.889751	+	1.54109i	−0.0495811	+	0.998770i	$0.515789\pi$
$401$	−17.8172	+	30.8604i	−0.889751	+	1.54109i	−0.840170	+	0.542324i	$0.817545\pi$
$402$	−37.7677	+	65.4156i	−1.88368	+	3.26263i
$403$	−1.55889			−0.0776540
$404$	35.4474	−	61.3967i	1.76357	−	3.05460i
$405$	3.15896	−	5.47148i	0.156970	−	0.271880i
$406$	11.9655	+	20.7249i	0.593838	+	1.02856i
$407$	9.74389	+	16.8769i	0.482987	+	0.836558i
$408$	20.1258			0.996376
$409$	36.1870			1.78933			0.894667	−	0.446734i	$-0.147413\pi$
$409$	36.1870			1.78933			0.894667	+	0.446734i	$0.147413\pi$
$410$	8.17275	+	14.1556i	0.403624	+	0.699096i
$411$	23.0612	+	39.9432i	1.13752	+	1.97025i
$412$	14.0903	−	24.4051i	0.694180	−	1.20235i
$413$	−14.3641	+	24.8794i	−0.706812	+	1.22423i
$414$	1.80647			0.0887830
$415$	−0.691737	+	1.19812i	−0.0339560	+	0.0588136i
$416$	2.33410	−	4.04278i	0.114439	−	0.198214i
$417$	−16.0655	+	27.8263i	−0.786733	+	1.36266i
$418$	14.7152	+	25.4875i	0.719745	+	1.24664i
$419$	−32.9566			−1.61003			−0.805017	−	0.593252i	$-0.797844\pi$
$419$	−32.9566			−1.61003			−0.805017	+	0.593252i	$0.797844\pi$
$420$	−15.0253	−	26.0246i	−0.733160	−	1.26987i
$421$	6.60220	−	11.4353i	0.321772	−	0.557325i	−0.659082	−	0.752071i	$-0.729055\pi$
$421$	6.60220	−	11.4353i	0.321772	−	0.557325i	0.980854	+	0.194746i	$0.0623883\pi$
$422$	51.9195			2.52740
$423$	−0.194809	+	0.337419i	−0.00947193	+	0.0164059i
$424$	44.6617	+	77.3563i	2.16896	+	3.75675i
$425$	−2.25277	−	3.90191i	−0.109275	−	0.189270i
$426$	21.7240			1.05253
$427$	−0.691340	−	1.19744i	−0.0334563	−	0.0579480i
$428$	−18.8331			−0.910331
$429$	−2.27815			−0.109990
$430$	−2.98244	+	11.9061i	−0.143826	+	0.574163i
$431$	17.1406			0.825633			0.412817	−	0.910814i	$-0.364545\pi$
$431$	17.1406			0.825633			0.412817	+	0.910814i	$0.364545\pi$
$432$	0.145391			0.00699512
$433$	−9.73627	−	16.8637i	−0.467895	−	0.810419i	0.531432	−	0.847101i	$-0.321654\pi$
$433$	−9.73627	−	16.8637i	−0.467895	−	0.810419i	−0.999327	+	0.0366826i	$0.988321\pi$
$434$	44.7866			2.14982
$435$	−2.25879	−	3.91234i	−0.108301	−	0.187582i
$436$	−0.947546	−	1.64120i	−0.0453792	−	0.0785991i
$437$	−0.426684	+	0.739038i	−0.0204110	+	0.0353530i
$438$	28.4846			1.36105
$439$	−7.11030	+	12.3154i	−0.339356	+	0.587782i	−0.984312	−	0.176438i	$-0.943542\pi$
$439$	−7.11030	+	12.3154i	−0.339356	+	0.587782i	0.644956	+	0.764220i	$0.276876\pi$
$440$	−8.44897	−	14.6340i	−0.402789	−	0.697651i
$441$	14.3037			0.681127
$442$	−0.422867	−	0.732428i	−0.0201137	−	0.0348380i
$443$	−11.2184	+	19.4308i	−0.533002	+	0.923187i	0.466255	+	0.884650i	$0.345603\pi$
$443$	−11.2184	+	19.4308i	−0.533002	+	0.923187i	−0.999257	+	0.0385364i	$0.987730\pi$
$444$	−41.4998	+	71.8797i	−1.96949	+	3.41126i
$445$	−3.00890	+	5.21156i	−0.142635	+	0.247052i
$446$	−41.5866			−1.96918
$447$	22.8448	−	39.5683i	1.08052	−	1.87152i
$448$	−26.9682	+	46.7103i	−1.27413	+	2.20686i
$449$	−13.7128	−	23.7513i	−0.647149	−	1.12089i	−0.983801	−	0.179265i	$-0.942628\pi$
$449$	−13.7128	−	23.7513i	−0.647149	−	1.12089i	0.336652	−	0.941629i	$-0.390705\pi$
$450$	−18.0200	−	31.2115i	−0.849469	−	1.47132i
$451$	−25.5516			−1.20318
$452$	79.6041			3.74426
$453$	−6.88365	−	11.9228i	−0.323422	−	0.560184i
$454$	−26.3477	−	45.6356i	−1.23656	−	2.14179i
$455$	−0.383081	+	0.663516i	−0.0179591	+	0.0311061i
$456$	−38.0248	+	65.8608i	−1.78067	+	3.08422i
$457$	−14.3885			−0.673066			−0.336533	−	0.941672i	$-0.609254\pi$
$457$	−14.3885			−0.673066			−0.336533	+	0.941672i	$0.609254\pi$
$458$	−26.2732	+	45.5065i	−1.22766	+	2.12638i
$459$	0.00621833	−	0.0107705i	0.000290247	−	0.000502722i
$460$	0.403791	−	0.699386i	0.0188268	−	0.0326090i
$461$	−2.24942	−	3.89611i	−0.104766	−	0.181460i	0.808877	−	0.587978i	$-0.200076\pi$
$461$	−2.24942	−	3.89611i	−0.104766	−	0.181460i	−0.913643	+	0.406519i	$0.866743\pi$
$462$	65.4506			3.04504
$463$	11.2886	+	19.5524i	0.524625	+	0.908677i	0.999589	+	0.0286715i	$0.00912769\pi$
$463$	11.2886	+	19.5524i	0.524625	+	0.908677i	−0.474964	+	0.880005i	$0.657539\pi$
$464$	−15.3243	+	26.5425i	−0.711414	+	1.23221i
$465$	−8.45459			−0.392072
$466$	−20.3957	+	35.3265i	−0.944814	+	1.63647i
$467$	6.12367	+	10.6065i	0.283370	+	0.490811i	0.972212	−	0.234100i	$-0.0752144\pi$
$467$	6.12367	+	10.6065i	0.283370	+	0.490811i	−0.688843	+	0.724911i	$0.741881\pi$
$468$	−2.42774	−	4.20497i	−0.112222	−	0.194375i
$469$	−39.7109			−1.83368
$470$	0.121340	+	0.210167i	0.00559700	+	0.00969429i
$471$	−10.9465			−0.504387
$472$	−68.8022			−3.16688
$473$	−13.7873	−	13.3435i	−0.633939	−	0.613536i
$474$	109.692			5.03834
$475$	17.0251			0.781165
$476$	8.71959	+	15.1028i	0.399662	+	0.692234i
$477$	32.6833			1.49647
$478$	−2.76900	−	4.79605i	−0.126651	−	0.219366i
$479$	−16.3519	−	28.3224i	−0.747139	−	1.29408i	−0.949189	−	0.314707i	$-0.898094\pi$
$479$	−16.3519	−	28.3224i	−0.747139	−	1.29408i	0.202050	−	0.979375i	$-0.435240\pi$
$480$	12.6589	−	21.9258i	0.577797	−	1.00077i
$481$	2.11613			0.0964874
$482$	−15.4832	+	26.8178i	−0.705242	+	1.22152i
$483$	0.948904	+	1.64355i	0.0431766	+	0.0747841i
$484$	−12.4015			−0.563704
$485$	6.44715	+	11.1668i	0.292750	+	0.507058i
$486$	−29.3530	+	50.8409i	−1.33148	+	2.30619i
$487$	−13.8728	+	24.0283i	−0.628634	+	1.08883i	0.359192	+	0.933264i	$0.383052\pi$
$487$	−13.8728	+	24.0283i	−0.628634	+	1.08883i	−0.987826	+	0.155563i	$0.950281\pi$
$488$	1.65571	−	2.86778i	0.0749506	−	0.129818i
$489$	−33.6763			−1.52289
$490$	4.45464	−	7.71567i	0.201240	−	0.348558i
$491$	−1.72602	+	2.98956i	−0.0778943	+	0.134917i	−0.902341	−	0.431022i	$-0.858153\pi$
$491$	−1.72602	+	2.98956i	−0.0778943	+	0.134917i	0.824447	+	0.565939i	$0.191486\pi$
$492$	−54.4129	−	94.2460i	−2.45312	−	4.24894i
$493$	1.31084	+	2.27043i	0.0590371	+	0.102255i
$494$	3.19578			0.143785
$495$	−6.18294			−0.277903
$496$	28.6793	+	49.6740i	1.28774	+	2.23043i
$497$	5.71043	+	9.89076i	0.256148	+	0.443661i
$498$	6.41673	−	11.1141i	0.287541	−	0.498035i
$499$	−0.993084	+	1.72007i	−0.0444565	+	0.0770010i	−0.887397	−	0.461005i	$-0.847489\pi$
$499$	−0.993084	+	1.72007i	−0.0444565	+	0.0770010i	0.842941	+	0.538006i	$0.180822\pi$
$500$	−33.9915			−1.52015
$501$	25.9242	−	44.9020i	1.15821	−	2.00607i
$502$	32.5280	−	56.3401i	1.45179	−	2.51458i
$503$	13.9002	−	24.0759i	0.619779	−	1.07349i	−0.369746	−	0.929133i	$-0.620555\pi$
$503$	13.9002	−	24.0759i	0.619779	−	1.07349i	0.989526	−	0.144357i	$-0.0461112\pi$
$504$	42.3175	+	73.2960i	1.88497	+	3.26487i
$505$	−9.80297			−0.436227
$506$	0.879460	+	1.52327i	0.0390968	+	0.0677176i
$507$	15.8047	−	27.3746i	0.701913	−	1.21575i
$508$	88.8321			3.94129
$509$	0.630573	−	1.09219i	0.0279497	−	0.0484103i	−0.851712	−	0.524010i	$-0.824436\pi$
$509$	0.630573	−	1.09219i	0.0279497	−	0.0484103i	0.879662	+	0.475600i	$0.157769\pi$
$510$	−2.29340	−	3.97229i	−0.101554	−	0.175896i
$511$	7.48754	+	12.9688i	0.331229	+	0.573706i
$512$	20.2611			0.895424
$513$	0.0234973	+	0.0406984i	0.00103743	+	0.00179688i
$514$	−22.2400			−0.980966
$515$	−3.89667			−0.171708
$516$	19.8566	−	79.2690i	0.874138	−	3.48962i
$517$	−0.379363			−0.0166844
$518$	−60.7959			−2.67122
$519$	3.78877	+	6.56234i	0.166309	+	0.288055i
$520$	−1.83491			−0.0804660
$521$	16.4658	+	28.5196i	0.721379	+	1.24946i	0.960447	+	0.278462i	$0.0898246\pi$
$521$	16.4658	+	28.5196i	0.721379	+	1.24946i	−0.239068	+	0.971003i	$0.576842\pi$
$522$	10.4854	+	18.1613i	0.458934	+	0.794897i
$523$	−6.49964	+	11.2577i	−0.284209	+	0.492265i	−0.972417	−	0.233248i	$-0.925064\pi$
$523$	−6.49964	+	11.2577i	−0.284209	+	0.492265i	0.688208	+	0.725514i	$0.258398\pi$
$524$	−56.7160			−2.47765
$525$	18.9311	−	32.7896i	0.826221	−	1.43106i
$526$	−14.2566	−	24.6932i	−0.621618	−	1.07667i
$527$	4.90642			0.213727
$528$	41.9116	+	72.5930i	1.82397	+	3.15920i
$529$	11.4745	−	19.8744i	0.498891	−	0.864105i
$530$	10.1787	−	17.6300i	0.442134	−	0.765798i
$531$	−12.5873	+	21.8019i	−0.546244	+	0.946122i
$532$	−65.8976			−2.85702
$533$	−1.38730	+	2.40287i	−0.0600905	+	0.104080i
$534$	27.9113	−	48.3438i	1.20784	−	2.09204i
$535$	1.30207	+	2.25525i	0.0562934	+	0.0975031i
$536$	−47.5525	−	82.3633i	−2.05395	−	3.55755i
$537$	−39.2218			−1.69254
$538$	−14.2907			−0.616116
$539$	6.96359	+	12.0613i	0.299943	+	0.519517i
$540$	−0.0222366	−	0.0385148i	−0.000956909	−	0.00165741i
$541$	−1.99732	+	3.45946i	−0.0858714	+	0.148734i	−0.905762	−	0.423786i	$-0.860701\pi$
$541$	−1.99732	+	3.45946i	−0.0858714	+	0.148734i	0.819891	+	0.572520i	$0.194034\pi$
$542$	−9.47977	+	16.4194i	−0.407191	+	0.705275i
$543$	19.3759			0.831500
$544$	−7.34629	+	12.7241i	−0.314969	+	0.545543i
$545$	−0.131022	+	0.226936i	−0.00561236	+	0.00972089i
$546$	3.55356	−	6.15495i	0.152078	−	0.263408i
$547$	−7.25034	−	12.5580i	−0.310002	−	0.536939i	0.668360	−	0.743838i	$-0.266996\pi$
$547$	−7.25034	−	12.5580i	−0.310002	−	0.536939i	−0.978362	+	0.206898i	$0.933663\pi$
$548$	−95.7145			−4.08872
$549$	−0.605824	−	1.04932i	−0.0258559	−	0.0447838i
$550$	17.5457	−	30.3900i	0.748150	−	1.29583i
$551$	−9.90653			−0.422032
$552$	−2.27256	+	3.93619i	−0.0967266	+	0.167535i
$553$	28.8340	+	49.9420i	1.22615	+	2.12375i
$554$	−23.0204	−	39.8725i	−0.978044	−	1.69402i
$555$	11.4768			0.487161
$556$	−33.3397	−	57.7460i	−1.41392	−	2.44898i
$557$	−14.6700			−0.621589			−0.310795	−	0.950477i	$-0.600595\pi$
$557$	−14.6700			−0.621589			−0.310795	+	0.950477i	$0.600595\pi$
$558$	39.2466			1.66144
$559$	−2.00338	+	0.572078i	−0.0847341	+	0.0241963i
$560$	28.1905			1.19127
$561$	7.17019			0.302726
$562$	−12.3339	−	21.3629i	−0.520273	−	0.901139i
$563$	−6.21691			−0.262011			−0.131006	−	0.991382i	$-0.541821\pi$
$563$	−6.21691			−0.262011			−0.131006	+	0.991382i	$0.541821\pi$
$564$	−0.807863	−	1.39926i	−0.0340172	−	0.0589195i
$565$	−5.50362	−	9.53256i	−0.231539	−	0.401038i
$566$	5.29722	−	9.17506i	0.222659	−	0.385656i
$567$	−30.8111			−1.29394
$568$	−13.6761	+	23.6877i	−0.573836	+	0.993914i
$569$	4.31537	+	7.47444i	0.180910	+	0.313345i	0.942191	−	0.335077i	$-0.108762\pi$
$569$	4.31537	+	7.47444i	0.180910	+	0.313345i	−0.761281	+	0.648422i	$0.775429\pi$
$570$	17.3322			0.725966
$571$	−4.66111	−	8.07327i	−0.195061	−	0.337856i	0.751859	−	0.659323i	$-0.229157\pi$
$571$	−4.66111	−	8.07327i	−0.195061	−	0.337856i	−0.946921	+	0.321468i	$0.895824\pi$
$572$	2.36384	−	4.09429i	0.0988372	−	0.171191i
$573$	18.5128	−	32.0652i	0.773385	−	1.33954i
$574$	39.8566	−	69.0337i	1.66358	−	2.88141i
$575$	1.01751			0.0424331
$576$	−23.6324	+	40.9324i	−0.984682	+	1.70552i
$577$	4.36270	−	7.55642i	0.181622	−	0.314578i	−0.760811	−	0.648973i	$-0.775199\pi$
$577$	4.36270	−	7.55642i	0.181622	−	0.314578i	0.942433	+	0.334395i	$0.108532\pi$
$578$	1.33092	+	2.30522i	0.0553590	+	0.0958846i
$579$	−25.2644	−	43.7591i	−1.04995	−	1.81857i
$580$	9.37502			0.389276
$581$	6.74688			0.279908
$582$	−59.8054	−	103.586i	−2.47902	−	4.29378i
$583$	15.9115	+	27.5596i	0.658989	+	1.14140i
$584$	−17.9322	+	31.0594i	−0.742038	+	1.28525i
$585$	−0.335696	+	0.581442i	−0.0138793	+	0.0240397i
$586$	−71.6883			−2.96142
$587$	12.5113	−	21.6702i	0.516398	−	0.894427i	−0.483421	−	0.875388i	$-0.660606\pi$
$587$	12.5113	−	21.6702i	0.516398	−	0.894427i	0.999819	−	0.0190389i	$-0.00606064\pi$
$588$	−29.6583	+	51.3697i	−1.22309	+	2.11845i
$589$	−9.26997	+	16.0561i	−0.381962	+	0.661578i
$590$	7.84023	+	13.5797i	0.322777	+	0.559067i
$591$	18.5217			0.761882
$592$	−38.9309	−	67.4303i	−1.60005	−	2.77137i
$593$	−15.3787	+	26.6367i	−0.631528	+	1.09384i	0.355712	+	0.934596i	$0.384238\pi$
$593$	−15.3787	+	26.6367i	−0.631528	+	1.09384i	−0.987240	+	0.159242i	$0.949095\pi$
$594$	0.0968628			0.00397433
$595$	1.20570	−	2.08833i	0.0494289	−	0.0856133i
$596$	47.4081	+	82.1133i	1.94191	+	3.36349i
$597$	−22.3127	−	38.6467i	−0.913197	−	1.58170i
$598$	0.190997			0.00781045
$599$	−7.11657	−	12.3263i	−0.290775	−	0.503637i	0.683218	−	0.730214i	$-0.260580\pi$
$599$	−7.11657	−	12.3263i	−0.290775	−	0.503637i	−0.973993	+	0.226577i	$0.927247\pi$
$600$	90.6775			3.70189
$601$	15.2760			0.623122			0.311561	−	0.950226i	$-0.399148\pi$
$601$	15.2760			0.623122			0.311561	+	0.950226i	$0.399148\pi$
$602$	57.5566	−	16.4356i	2.34583	−	0.669866i
$603$	−34.7988			−1.41712
$604$	28.5703			1.16251
$605$	0.857407	+	1.48507i	0.0348585	+	0.0603767i
$606$	90.9349			3.69398
$607$	22.3753	+	38.7552i	0.908186	+	1.57302i	0.816583	+	0.577228i	$0.195866\pi$
$607$	22.3753	+	38.7552i	0.908186	+	1.57302i	0.0916029	+	0.995796i	$0.470801\pi$
$608$	−27.7595	−	48.0808i	−1.12580	−	1.94994i
$609$	−11.0156	+	19.0796i	−0.446374	+	0.773143i
$610$	−0.754696			−0.0305567
$611$	−0.0205971	+	0.0356752i	−0.000833268	+	0.00144326i
$612$	7.64101	+	13.2346i	0.308869	+	0.534977i
$613$	34.9046			1.40978			0.704891	−	0.709316i	$-0.250996\pi$
$613$	34.9046			1.40978			0.704891	+	0.709316i	$0.250996\pi$
$614$	14.9209	+	25.8437i	0.602157	+	1.04297i
$615$	−7.52394	+	13.0318i	−0.303395	+	0.525495i
$616$	−41.2037	+	71.3668i	−1.66014	+	2.87545i
$617$	−14.7279	+	25.5095i	−0.592924	+	1.02698i	0.400912	+	0.916117i	$0.368693\pi$
$617$	−14.7279	+	25.5095i	−0.592924	+	1.02698i	−0.993836	+	0.110858i	$0.964640\pi$
$618$	36.1466			1.45403
$619$	16.7430	−	28.9997i	0.672957	−	1.16560i	−0.304105	−	0.952639i	$-0.598357\pi$
$619$	16.7430	−	28.9997i	0.672957	−	1.16560i	0.977062	−	0.212957i	$-0.0683094\pi$
$620$	8.77261	−	15.1946i	0.352316	−	0.610230i
$621$	0.00140432	+	0.00243235i	5.63534e−5	+	9.76070e-5i
$622$	−11.3421	−	19.6450i	−0.454776	−	0.787695i
$623$	29.3474			1.17578
$624$	9.10216			0.364378
$625$	−8.91375	−	15.4391i	−0.356550	−	0.617563i
$626$	−7.55492	−	13.0855i	−0.301956	−	0.523002i
$627$	−13.5470	+	23.4641i	−0.541016	+	0.937067i
$628$	11.3582	−	19.6730i	0.453242	−	0.785038i
$629$	−6.66026			−0.265562
$630$	9.64443	−	16.7047i	0.384243	−	0.665529i
$631$	−11.6191	+	20.1249i	−0.462549	+	0.801159i	−0.999087	−	0.0427175i	$-0.986398\pi$
$631$	−11.6191	+	20.1249i	−0.462549	+	0.801159i	0.536538	+	0.843876i	$0.319732\pi$
$632$	−69.0556	+	119.608i	−2.74688	+	4.75774i
$633$	23.8989	+	41.3941i	0.949895	+	1.64527i
$634$	−70.4257			−2.79696
$635$	−6.14162	−	10.6376i	−0.243723	−	0.422140i
$636$	−67.7681	+	117.378i	−2.68718	+	4.65433i
$637$	1.51232			0.0599203
$638$	−10.2094	+	17.6833i	−0.404195	+	0.700087i
$639$	5.00407	+	8.66731i	0.197958	+	0.342873i
$640$	4.38825	+	7.60067i	0.173461	+	0.300443i
$641$	−2.06861			−0.0817052			−0.0408526	−	0.999165i	$-0.513007\pi$
$641$	−2.06861			−0.0817052			−0.0408526	+	0.999165i	$0.513007\pi$
$642$	−12.0783	−	20.9203i	−0.476694	−	0.825659i
$643$	−13.1092			−0.516976			−0.258488	−	0.966014i	$-0.583224\pi$
$643$	−13.1092			−0.516976			−0.258488	+	0.966014i	$0.583224\pi$
$644$	−3.93839			−0.155194
$645$	−10.8653	+	3.10264i	−0.427819	+	0.122166i
$646$	−10.0583			−0.395740
$647$	7.35349			0.289095			0.144548	−	0.989498i	$-0.453827\pi$
$647$	7.35349			0.289095			0.144548	+	0.989498i	$0.453827\pi$
$648$	−36.8952	−	63.9044i	−1.44938	−	2.51040i
$649$	−24.5120			−0.962182
$650$	−1.90524	−	3.29998i	−0.0747298	−	0.129436i
$651$	20.6155	+	35.7072i	0.807987	+	1.39947i
$652$	34.9430	−	60.5231i	1.36847	−	2.37027i
$653$	−13.0903			−0.512261			−0.256131	−	0.966642i	$-0.582448\pi$
$653$	−13.0903			−0.512261			−0.256131	+	0.966642i	$0.582448\pi$
$654$	1.21539	−	2.10512i	0.0475256	−	0.0823167i
$655$	3.92120	+	6.79172i	0.153214	+	0.265374i
$656$	102.089			3.98592
$657$	6.56136	+	11.3646i	0.255983	+	0.443376i
$658$	0.591747	−	1.02494i	0.0230687	−	0.0399562i
$659$	20.3639	−	35.2713i	0.793265	−	1.37398i	−0.130670	−	0.991426i	$-0.541713\pi$
$659$	20.3639	−	35.2713i	0.793265	−	1.37398i	0.923935	−	0.382549i	$-0.124954\pi$
$660$	12.8202	−	22.2052i	0.499025	−	0.864337i
$661$	−15.5594			−0.605190			−0.302595	−	0.953119i	$-0.597853\pi$
$661$	−15.5594			−0.605190			−0.302595	+	0.953119i	$0.597853\pi$
$662$	−33.4280	+	57.8989i	−1.29921	+	2.25031i
$663$	0.389297	−	0.674282i	0.0151190	−	0.0261869i
$664$	8.07916	+	13.9935i	0.313532	+	0.543054i
$665$	4.55599	+	7.89120i	0.176674	+	0.306008i
$666$	−53.2757			−2.06439
$667$	−0.592067			−0.0229249
$668$	53.7986	+	93.1819i	2.08153	+	3.60531i
$669$	−19.1426	−	33.1559i	−0.740094	−	1.28188i
$670$	−10.8375	+	18.7711i	−0.418690	+	0.725192i
$671$	0.589878	−	1.02170i	0.0227720	−	0.0394423i
$672$	−123.469			−4.76292
$673$	−5.31343	+	9.20314i	−0.204818	+	0.354755i	−0.950075	−	0.312023i	$-0.898994\pi$
$673$	−5.31343	+	9.20314i	−0.204818	+	0.354755i	0.745257	+	0.666777i	$0.232327\pi$
$674$	−17.5959	+	30.4770i	−0.677770	+	1.17393i
$675$	0.0280169	−	0.0485267i	0.00107837	−	0.00186779i
$676$	32.7984	+	56.8085i	1.26148	+	2.18494i
$677$	23.4113			0.899770			0.449885	−	0.893087i	$-0.351465\pi$
$677$	23.4113			0.899770			0.449885	+	0.893087i	$0.351465\pi$
$678$	51.0531	+	88.4265i	1.96068	+	3.39600i
$679$	31.4413	−	54.4578i	1.20660	−	2.08990i
$680$	5.77514			0.221466
$681$	24.2561	−	42.0127i	0.929495	−	1.60993i
$682$	19.1068	+	33.0940i	0.731638	+	1.26723i
$683$	−13.0234	−	22.5573i	−0.498328	−	0.863130i	0.501670	−	0.865059i	$-0.332719\pi$
$683$	−13.0234	−	22.5573i	−0.498328	−	0.863130i	−0.999998	+	0.00192947i	$0.999386\pi$
$684$	−57.7463			−2.20798
$685$	6.61746	+	11.4618i	0.252840	+	0.437932i
$686$	20.4486			0.780730
$687$	−48.3748			−1.84562
$688$	55.0858	+	53.3130i	2.10013	+	2.03254i
$689$	3.45559			0.131648
$690$	1.03586			0.0394346
$691$	−17.4462	−	30.2177i	−0.663684	−	1.14953i	−0.979640	−	0.200761i	$-0.935659\pi$
$691$	−17.4462	−	30.2177i	−0.663684	−	1.14953i	0.315956	−	0.948774i	$-0.397675\pi$
$692$	−15.7251			−0.597780
$693$	15.0764	+	26.1131i	0.572705	+	0.991953i
$694$	22.2954	+	38.6168i	0.846323	+	1.46587i
$695$	−4.61004	+	7.98483i	−0.174869	+	0.302882i
$696$	−52.7632			−1.99998
$697$	4.36634	−	7.56272i	0.165387	−	0.286459i
$698$	9.79376	+	16.9633i	0.370699	+	0.642070i
$699$	−37.5531			−1.42039
$700$	39.2864	+	68.0460i	1.48489	+	2.57190i
$701$	−7.58640	+	13.1400i	−0.286534	+	0.496292i	−0.972980	−	0.230889i	$-0.925837\pi$
$701$	−7.58640	+	13.1400i	−0.286534	+	0.496292i	0.686446	+	0.727181i	$0.259170\pi$
$702$	0.00525905	−	0.00910895i	0.000198490	−	0.000343795i
$703$	12.5836	−	21.7954i	0.474599	−	0.822030i
$704$	−46.0207			−1.73447
$705$	−0.111707	+	0.193483i	−0.00420714	+	0.00728698i
$706$	−16.3587	+	28.3340i	−0.615666	+	1.06636i
$707$	23.9034	+	41.4019i	0.898980	+	1.55708i
$708$	−52.1991	−	90.4114i	−1.96176	−	3.39787i
$709$	1.67241			0.0628086			0.0314043	−	0.999507i	$-0.490002\pi$
$709$	1.67241			0.0628086			0.0314043	+	0.999507i	$0.490002\pi$
$710$	6.23375			0.233948
$711$	25.2674	+	43.7644i	0.947601	+	1.64129i
$712$	35.1425	+	60.8686i	1.31702	+	2.28115i
$713$	−0.554022	+	0.959595i	−0.0207483	+	0.0359371i
$714$	−11.1844	+	19.3719i	−0.418565	+	0.724976i
$715$	−0.653720			−0.0244477
$716$	40.6971	−	70.4894i	1.52092	−	2.63431i
$717$	2.54918	−	4.41530i	0.0952007	−	0.164892i
$718$	44.1210	−	76.4198i	1.64658	−	2.85196i
$719$	−0.467306	−	0.809398i	−0.0174276	−	0.0301854i	0.857180	−	0.515017i	$-0.172214\pi$
$719$	−0.467306	−	0.809398i	−0.0174276	−	0.0301854i	−0.874608	+	0.484831i	$0.838881\pi$
$720$	24.7034			0.920642
$721$	9.50158	+	16.4572i	0.353858	+	0.612899i
$722$	−6.28375	+	10.8838i	−0.233857	+	0.405052i
$723$	−28.5081			−1.06023
$724$	−20.1047	+	34.8224i	−0.747186	+	1.29416i
$725$	5.90601	+	10.2295i	0.219344	+	0.379915i
$726$	−7.95353	−	13.7759i	−0.295183	−	0.511272i
$727$	−45.5589			−1.68969			−0.844843	−	0.535014i	$-0.820306\pi$
$727$	−45.5589			−1.68969			−0.844843	+	0.535014i	$0.820306\pi$
$728$	4.47421	+	7.74956i	0.165825	+	0.287218i
$729$	−27.0913			−1.00338
$730$	8.17371			0.302523
$731$	6.30540	−	1.80054i	0.233214	−	0.0665955i
$732$	5.02465			0.185716
$733$	42.1164			1.55560			0.777802	−	0.628509i	$-0.216334\pi$
$733$	42.1164			1.55560			0.777802	+	0.628509i	$0.216334\pi$
$734$	−1.12709	−	1.95217i	−0.0416015	−	0.0720559i
$735$	8.20200			0.302535
$736$	−1.65905	−	2.87357i	−0.0611535	−	0.105921i
$737$	−16.9414	−	29.3435i	−0.624046	−	1.08088i
$738$	34.9265	−	60.4945i	1.28566	−	2.22683i
$739$	−48.0025			−1.76580			−0.882899	−	0.469562i	$-0.844412\pi$
$739$	−48.0025			−1.76580			−0.882899	+	0.469562i	$0.844412\pi$
$740$	−11.9084	+	20.6260i	−0.437763	+	0.758228i
$741$	1.47104	+	2.54792i	0.0540400	+	0.0936000i
$742$	−99.2782			−3.64462
$743$	20.0402	+	34.7107i	0.735205	+	1.27341i	0.954633	+	0.297784i	$0.0962475\pi$
$743$	20.0402	+	34.7107i	0.735205	+	1.27341i	−0.219428	+	0.975629i	$0.570419\pi$
$744$	−49.3728	+	85.5162i	−1.81010	+	3.13518i
$745$	6.55535	−	11.3542i	0.240170	−	0.415986i
$746$	−3.97425	+	6.88361i	−0.145508	+	0.252027i
$747$	5.91232			0.216320
$748$	−7.43989	+	12.8863i	−0.272029	+	0.471169i
$749$	6.34990	−	10.9983i	0.232020	−	0.401871i
$750$	−21.8000	−	37.7587i	−0.796023	−	1.37875i
$751$	−6.32589	−	10.9568i	−0.230835	−	0.399818i	0.727219	−	0.686405i	$-0.240812\pi$
$751$	−6.32589	−	10.9568i	−0.230835	−	0.399818i	−0.958054	+	0.286588i	$0.907479\pi$
$752$	1.51571			0.0552723
$753$	59.8913			2.18256
$754$	1.10862	+	1.92018i	0.0403735	+	0.0699290i
$755$	−1.97528	−	3.42128i	−0.0718877	−	0.124513i
$756$	−0.108442	+	0.187828i	−0.00394402	+	0.00683124i
$757$	21.9092	−	37.9478i	0.796303	−	1.37924i	−0.125705	−	0.992068i	$-0.540119\pi$
$757$	21.9092	−	37.9478i	0.796303	−	1.37924i	0.922008	−	0.387170i	$-0.126547\pi$
$758$	87.2544			3.16922
$759$	−0.809642	+	1.40234i	−0.0293881	+	0.0509018i
$760$	−10.9113	+	18.8989i	−0.395794	+	0.685535i
$761$	10.3549	−	17.9352i	0.375365	−	0.650152i	−0.615016	−	0.788514i	$-0.710851\pi$
$761$	10.3549	−	17.9352i	0.375365	−	0.650152i	0.990382	+	0.138362i	$0.0441839\pi$
$762$	56.9713	+	98.6771i	2.06385	+	3.57470i
$763$	1.27793			0.0462640
$764$	38.4184	+	66.5426i	1.38993	+	2.40743i
$765$	1.05656	−	1.83001i	0.0382000	−	0.0661643i
$766$	−88.7047			−3.20503
$767$	−1.33085	+	2.30510i	−0.0480543	+	0.0832325i
$768$	−2.16393	−	3.74803i	−0.0780840	−	0.135245i
$769$	12.8814	+	22.3112i	0.464515	+	0.804563i	0.999179	−	0.0405011i	$-0.0128954\pi$
$769$	12.8814	+	22.3112i	0.464515	+	0.804563i	−0.534665	+	0.845064i	$0.679562\pi$
$770$	18.7812			0.676827
$771$	−10.2372	−	17.7314i	−0.368685	−	0.638581i
$772$	104.859			3.77395
$773$	27.1705			0.977256			0.488628	−	0.872492i	$-0.337497\pi$
$773$	27.1705			0.977256			0.488628	+	0.872492i	$0.337497\pi$
$774$	50.4371	−	14.4026i	1.81292	−	0.517691i
$775$	22.1060			0.794072
$776$	150.599			5.40620
$777$	−27.9847	−	48.4710i	−1.00395	−	1.73889i
$778$	−39.2828			−1.40836
$779$	16.4991	+	28.5773i	0.591143	+	1.02389i
$780$	−1.39211	−	2.41121i	−0.0498457	−	0.0863353i
$781$	−4.87236	+	8.43918i	−0.174347	+	0.301978i
$782$	−0.601139			−0.0214967
$783$	−0.0163024	+	0.0282366i	−0.000582601	+	0.00100909i
$784$	−27.8224	−	48.1899i	−0.993659	−	1.72107i
$785$	−3.14111			−0.112111
$786$	−36.3741	−	63.0017i	−1.29742	−	2.24720i
$787$	2.00748	−	3.47705i	0.0715589	−	0.123944i	−0.828026	−	0.560690i	$-0.810536\pi$
$787$	2.00748	−	3.47705i	0.0715589	−	0.123944i	0.899585	+	0.436746i	$0.143869\pi$
$788$	−19.2184	+	33.2873i	−0.684628	+	1.18581i
$789$	13.1248	−	22.7329i	0.467256	−	0.809312i
$790$	31.4764			1.11988
$791$	−26.8399	+	46.4881i	−0.954317	+	1.65293i
$792$	−36.1069	+	62.5390i	−1.28300	+	2.22223i
$793$	−0.0640535	−	0.110944i	−0.00227461	−	0.00393973i
$794$	−18.3026	−	31.7010i	−0.649534	−	1.12503i
$795$	18.7413			0.664684
$796$	92.6078			3.28240
$797$	−20.1834	−	34.9587i	−0.714934	−	1.23830i	−0.962985	−	0.269555i	$-0.913123\pi$
$797$	−20.1834	−	34.9587i	−0.714934	−	1.23830i	0.248051	−	0.968747i	$-0.420210\pi$
$798$	−42.2625	−	73.2009i	−1.49608	−	2.59128i
$799$	0.0648266	−	0.112283i	0.00229340	−	0.00397229i
$800$	−33.0989	+	57.3290i	−1.17022	+	2.02689i
$801$	25.7172			0.908674
$802$	47.4267	−	82.1454i	1.67469	−	2.90066i
$803$	−6.38866	+	11.0655i	−0.225451	+	0.390493i
$804$	72.1546	−	124.975i	2.54469	−	4.40754i
$805$	0.272290	+	0.471620i	0.00959696	+	0.0166224i
$806$	4.14953			0.146161
$807$	−6.57810	−	11.3936i	−0.231560	−	0.401074i
$808$	−57.2471	+	99.1548i	−2.01394	+	3.48825i
$809$	27.1365			0.954068			0.477034	−	0.878885i	$-0.341712\pi$
$809$	27.1365			0.954068			0.477034	+	0.878885i	$0.341712\pi$
$810$	−8.40866	+	14.5642i	−0.295450	+	0.511735i
$811$	−11.2966	−	19.5662i	−0.396676	−	0.687063i	0.596638	−	0.802511i	$-0.296503\pi$
$811$	−11.2966	−	19.5662i	−0.396676	−	0.687063i	−0.993314	+	0.115448i	$0.963170\pi$
$812$	−22.8599	−	39.5945i	−0.802225	−	1.38949i
$813$	−17.4544			−0.612152
$814$	−25.9367	−	44.9237i	−0.909081	−	1.57457i
$815$	−9.66348			−0.338497
$816$	−28.6479			−1.00288
$817$	−6.02093	+	24.0360i	−0.210646	+	0.840914i
$818$	−96.3242			−3.36790
$819$	3.27422			0.114410
$820$	−15.6139	−	27.0441i	−0.545261	−	0.944420i
$821$	−2.34370			−0.0817956			−0.0408978	−	0.999163i	$-0.513022\pi$
$821$	−2.34370			−0.0817956			−0.0408978	+	0.999163i	$0.513022\pi$
$822$	−61.3853	−	106.322i	−2.14106	−	3.70842i
$823$	−7.21715	−	12.5005i	−0.251574	−	0.435739i	0.712385	−	0.701789i	$-0.247615\pi$
$823$	−7.21715	−	12.5005i	−0.251574	−	0.435739i	−0.963959	+	0.266049i	$0.914282\pi$
$824$	−22.7557	+	39.4140i	−0.792731	+	1.37305i
$825$	32.3055			1.12473
$826$	38.2350	−	66.2250i	1.33037	−	2.30426i
$827$	14.1601	+	24.5261i	0.492396	+	0.852855i	0.999962	−	0.00875814i	$-0.00278784\pi$
$827$	14.1601	+	24.5261i	0.492396	+	0.852855i	−0.507566	+	0.861613i	$0.669455\pi$
$828$	−3.45122			−0.119938
$829$	4.94715	+	8.56872i	0.171822	+	0.297604i	0.939057	−	0.343762i	$-0.111701\pi$
$829$	4.94715	+	8.56872i	0.171822	+	0.297604i	−0.767235	+	0.641366i	$0.778368\pi$
$830$	1.84129	−	3.18921i	0.0639122	−	0.110699i
$831$	21.1929	−	36.7072i	0.735173	−	1.27336i
$832$	−2.49864	+	4.32777i	−0.0866247	+	0.150038i
$833$	−4.75984			−0.164919
$834$	42.7639	−	74.0693i	1.48079	−	2.56481i
$835$	7.43899	−	12.8847i	0.257437	−	0.445894i
$836$	−28.1132	−	48.6935i	−0.972315	−	1.68410i
$837$	0.0305097	+	0.0528444i	0.00105457	+	0.00182657i
$838$	87.7252			3.03042
$839$	−29.0620			−1.00333			−0.501666	−	0.865061i	$-0.667280\pi$
$839$	−29.0620			−1.00333			−0.501666	+	0.865061i	$0.667280\pi$
$840$	24.2657	+	42.0294i	0.837245	+	1.45015i
$841$	11.0634	+	19.1624i	0.381497	+	0.660773i
$842$	−17.5740	+	30.4391i	−0.605641	+	1.04900i
$843$	11.3547	−	19.6670i	0.391077	−	0.677366i
$844$	−99.1913			−3.41430
$845$	4.53520	−	7.85519i	0.156016	−	0.270227i
$846$	0.518550	−	0.898156i	0.0178281	−	0.0308792i
$847$	4.18137	−	7.24235i	0.143674	−	0.248850i
$848$	−63.5732	−	110.112i	−2.18311	−	3.78126i
$849$	9.75338			0.334735
$850$	5.99651	+	10.3863i	0.205679	+	0.356246i
$851$	0.752062	−	1.30261i	0.0257804	−	0.0446529i
$852$	−41.5033			−1.42188
$853$	9.02809	−	15.6371i	0.309116	−	0.535405i	−0.669053	−	0.743214i	$-0.733300\pi$
$853$	9.02809	−	15.6371i	0.309116	−	0.535405i	0.978169	+	0.207810i	$0.0666335\pi$
$854$	1.84024	+	3.18739i	0.0629717	+	0.109070i
$855$	3.99243	+	6.91509i	0.136538	+	0.236491i
$856$	30.4151			1.03957
$857$	6.57956	+	11.3961i	0.224754	+	0.389285i	0.956245	−	0.292565i	$-0.0945090\pi$
$857$	6.57956	+	11.3961i	0.224754	+	0.389285i	−0.731492	+	0.681850i	$0.761176\pi$
$858$	6.06407			0.207024
$859$	−10.2638			−0.350197			−0.175098	−	0.984551i	$-0.556024\pi$
$859$	−10.2638			−0.350197			−0.175098	+	0.984551i	$0.556024\pi$
$860$	5.69789	−	22.7464i	0.194296	−	0.775646i
$861$	73.3850			2.50096
$862$	−45.6256			−1.55401
$863$	23.5586	+	40.8047i	0.801945	+	1.38901i	0.918334	+	0.395806i	$0.129535\pi$
$863$	23.5586	+	40.8047i	0.801945	+	1.38901i	−0.116389	+	0.993204i	$0.537132\pi$
$864$	−0.182727			−0.00621648
$865$	1.08720	+	1.88308i	0.0369658	+	0.0640266i
$866$	25.9164	+	44.8885i	0.880676	+	1.52537i
$867$	−1.22526	+	2.12222i	−0.0416121	+	0.0720743i
$868$	−85.5639			−2.90423
$869$	−24.6023	+	42.6125i	−0.834577	+	1.44553i
$870$	6.01254	+	10.4140i	0.203844	+	0.353069i
$871$	−3.67926			−0.124667
$872$	1.53027	+	2.65051i	0.0518216	+	0.0897576i
$873$	27.5521	−	47.7216i	0.932497	−	1.61513i
$874$	1.13576	−	1.96720i	0.0384178	−	0.0665416i
$875$	11.4608	−	19.8507i	0.387446	−	0.671077i
$876$	−54.4193			−1.83866
$877$	−18.1181	+	31.3815i	−0.611804	+	1.05968i	0.379132	+	0.925343i	$0.376223\pi$
$877$	−18.1181	+	31.3815i	−0.611804	+	1.05968i	−0.990936	+	0.134334i	$0.957111\pi$
$878$	18.9265	−	32.7816i	0.638738	−	1.10633i
$879$	−32.9986	−	57.1552i	−1.11301	−	1.92780i
$880$	12.0266	+	20.8307i	0.405417	+	0.702203i
$881$	−0.266443			−0.00897670			−0.00448835	−	0.999990i	$-0.501429\pi$
$881$	−0.266443			−0.00897670			−0.00448835	+	0.999990i	$0.501429\pi$
$882$	−38.0741			−1.28202
$883$	2.18476	+	3.78411i	0.0735229	+	0.127345i	0.900443	−	0.434974i	$-0.143242\pi$
$883$	2.18476	+	3.78411i	0.0735229	+	0.127345i	−0.826920	+	0.562319i	$0.809909\pi$
$884$	0.807880	+	1.39929i	0.0271720	+	0.0470632i
$885$	−7.21782	+	12.5016i	−0.242624	+	0.420238i
$886$	29.8616	−	51.7218i	1.00322	−	1.73763i
$887$	7.45800			0.250415			0.125208	−	0.992131i	$-0.460040\pi$
$887$	7.45800			0.250415			0.125208	+	0.992131i	$0.460040\pi$
$888$	67.0215	−	116.085i	2.24910	−	3.89555i
$889$	−29.9513	+	51.8771i	−1.00453	+	1.73990i
$890$	8.00921	−	13.8724i	0.268469	−	0.465003i
$891$	−13.1446	−	22.7671i	−0.440361	−	0.762727i
$892$	79.4504			2.66020
$893$	0.244961	+	0.424285i	0.00819731	+	0.0141982i
$894$	−60.8091	+	105.325i	−2.03376	+	3.52258i
$895$	−11.2548			−0.376205
$896$	21.4005	−	37.0667i	0.714939	−	1.23831i
$897$	0.0879171	+	0.152277i	0.00293547	+	0.00508438i
$898$	36.5014	+	63.2223i	1.21807	+	2.10975i
$899$	−12.8630			−0.429006
$900$	34.4268	+	59.6290i	1.14756	+	1.98763i
$901$	−10.8760			−0.362334
$902$	68.0144			2.26463
$903$	39.5974	+	38.3230i	1.31772	+	1.27531i
$904$	−128.560			−4.27583
$905$	5.55996			0.184819
$906$	18.3232	+	31.7367i	0.608747	+	1.05438i
$907$	−3.13536			−0.104108			−0.0520539	−	0.998644i	$-0.516577\pi$
$907$	−3.13536			−0.104108			−0.0520539	+	0.998644i	$0.516577\pi$
$908$	50.3369	+	87.1861i	1.67049	+	2.89337i
$909$	20.9467	+	36.2807i	0.694757	+	1.20335i
$910$	1.01970	−	1.76618i	0.0338028	−	0.0585481i
$911$	−16.8020			−0.556675			−0.278338	−	0.960483i	$-0.589783\pi$
$911$	−16.8020			−0.556675			−0.278338	+	0.960483i	$0.589783\pi$
$912$	54.1260	−	93.7490i	1.79229	−	3.10434i
$913$	2.87835	+	4.98545i	0.0952595	+	0.164994i
$914$	38.2999			1.26685
$915$	−0.347391	−	0.601699i	−0.0114844	−	0.0198916i
$916$	50.1944	−	86.9393i	1.65847	−	2.87256i
$917$	19.1228	−	33.1216i	0.631490	−	1.09377i
$918$	−0.0165522	+	0.0286693i	−0.000546304	+	0.000946227i
$919$	−39.3850			−1.29919			−0.649595	−	0.760280i	$-0.725062\pi$
$919$	−39.3850			−1.29919			−0.649595	+	0.760280i	$0.725062\pi$
$920$	−0.652116	+	1.12950i	−0.0214996	+	0.0372385i
$921$	−13.7363	+	23.7920i	−0.452627	+	0.783974i
$922$	5.98759	+	10.3708i	0.197191	+	0.341545i
$923$	0.529079	+	0.916391i	0.0174148	+	0.0301634i
$924$	−125.042			−4.11358
$925$	−30.0080			−0.986658
$926$	−30.0484	−	52.0454i	−0.987452	−	1.71032i
$927$	8.32628	+	14.4215i	0.273471	+	0.473665i
$928$	19.2595	−	33.3585i	0.632226	−	1.09505i
$929$	−1.80701	+	3.12983i	−0.0592861	+	0.102686i	−0.894145	−	0.447777i	$-0.852216\pi$
$929$	−1.80701	+	3.12983i	−0.0592861	+	0.102686i	0.834859	+	0.550464i	$0.185549\pi$
$930$	22.5048			0.737961
$931$	8.99302	−	15.5764i	0.294734	−	0.510495i
$932$	38.9657	−	67.4906i	1.27636	−	2.21073i
$933$	10.4417	−	18.0855i	0.341844	−	0.592092i
$934$	−16.3002	−	28.2328i	−0.533360	−	0.923807i
$935$	2.05750			0.0672874
$936$	3.92077	+	6.79097i	0.128154	+	0.221970i
$937$	10.7191	−	18.5661i	0.350179	−	0.606527i	−0.636102	−	0.771605i	$-0.719454\pi$
$937$	10.7191	−	18.5661i	0.350179	−	0.606527i	0.986281	+	0.165078i	$0.0527875\pi$
$938$	105.704			3.45136
$939$	6.95516	−	12.0467i	0.226973	−	0.393129i
$940$	−0.231818	−	0.401521i	−0.00756107	−	0.0130962i
$941$	−15.0172	−	26.0105i	−0.489545	−	0.847917i	0.510382	−	0.859948i	$-0.329504\pi$
$941$	−15.0172	−	26.0105i	−0.489545	−	0.847917i	−0.999928	+	0.0120304i	$0.996171\pi$
$942$	29.1378			0.949360
$943$	0.986075	+	1.70793i	0.0321110	+	0.0556179i
$944$	97.9358			3.18754
$945$	0.0299897			0.000975567
$946$	36.6995	+	35.5184i	1.19320	+	1.15480i
$947$	−19.7251			−0.640979			−0.320489	−	0.947252i	$-0.603847\pi$
$947$	−19.7251			−0.640979			−0.320489	+	0.947252i	$0.603847\pi$
$948$	−209.565			−6.80636
$949$	0.693730	+	1.20158i	0.0225194	+	0.0390048i
$950$	−45.3181			−1.47031
$951$	−32.4174	−	56.1486i	−1.05121	−	1.82074i
$952$	−14.0820	−	24.3908i	−0.456400	−	0.790509i
$953$	−7.23025	+	12.5232i	−0.234211	+	0.405665i	−0.959043	−	0.283261i	$-0.908584\pi$
$953$	−7.23025	+	12.5232i	−0.234211	+	0.405665i	0.724832	+	0.688925i	$0.241917\pi$
$954$	−86.9979			−2.81666
$955$	5.31230	−	9.20117i	0.171902	−	0.297743i
$956$	5.29012	+	9.16276i	0.171095	+	0.296345i
$957$	−18.7979			−0.607649
$958$	43.5263	+	75.3897i	1.40627	+	2.43573i
$959$	32.2718	−	55.8964i	1.04211	−	1.80499i
$960$	−13.5513	+	23.4715i	−0.437365	+	0.757538i
$961$	3.46352	−	5.99899i	0.111726	−	0.193516i
$962$	−5.63281			−0.181609
$963$	5.56444	−	9.63789i	0.179312	−	0.310577i
$964$	29.5805	−	51.2349i	0.952722	−	1.65016i
$965$	−7.24966	−	12.5568i	−0.233375	−	0.404217i
$966$	−2.52583	−	4.37487i	−0.0812673	−	0.140759i
$967$	−30.6786			−0.986557			−0.493278	−	0.869872i	$-0.664202\pi$
$967$	−30.6786			−0.986557			−0.493278	+	0.869872i	$0.664202\pi$
$968$	20.0282			0.643731
$969$	−4.62991	−	8.01924i	−0.148734	−	0.257615i
$970$	−17.1613	−	29.7242i	−0.551016	−	0.954388i
$971$	22.1044	−	38.2859i	0.709364	−	1.22865i	−0.255730	−	0.966748i	$-0.582316\pi$
$971$	22.1044	−	38.2859i	0.709364	−	1.22865i	0.965093	−	0.261906i	$-0.0843510\pi$
$972$	56.0784	−	97.1307i	1.79872	−	3.11547i
$973$	44.9642			1.44149
$974$	36.9271	−	63.9596i	1.18322	−	2.04940i
$975$	1.75399	−	3.03800i	0.0561726	−	0.0972939i
$976$	−2.35681	+	4.08211i	−0.0754396	+	0.130665i
$977$	−25.7071	−	44.5260i	−0.822443	−	1.42451i	−0.903858	−	0.427832i	$-0.859277\pi$
$977$	−25.7071	−	44.5260i	−0.822443	−	1.42451i	0.0814155	−	0.996680i	$-0.474056\pi$
$978$	89.6410			2.86640
$979$	12.5202	+	21.6856i	0.400146	+	0.693074i
$980$	−8.51051	+	14.7406i	−0.271858	+	0.470873i
$981$	1.11985			0.0357541
$982$	4.59440	−	7.95773i	0.146613	−	0.253941i
$983$	−23.2011	−	40.1855i	−0.740000	−	1.28172i	−0.952495	−	0.304555i	$-0.901492\pi$
$983$	−23.2011	−	40.1855i	−0.740000	−	1.28172i	0.212495	−	0.977162i	$-0.431841\pi$
$984$	87.8761	+	152.206i	2.80139	+	4.85215i
$985$	5.31485			0.169345
$986$	−3.48924	−	6.04353i	−0.111120	−	0.192465i
$987$	1.08954			0.0346804
$988$	−6.10549			−0.194242
$989$	−0.359843	+	1.43652i	−0.0114423	+	0.0456787i
$990$	16.4580			0.523070
$991$	−35.5858			−1.13042			−0.565210	−	0.824947i	$-0.691205\pi$
$991$	−35.5858			−1.13042			−0.565210	+	0.824947i	$0.691205\pi$
$992$	−36.0440	−	62.4300i	−1.14440	−	1.98215i
$993$	−61.5484			−1.95318
$994$	−15.2003	−	26.3276i	−0.482123	−	0.835062i
$995$	−6.40267	−	11.0897i	−0.202978	−	0.351568i
$996$	−12.2590	+	21.2333i	−0.388443	+	0.672803i
$997$	56.5555			1.79113			0.895566	−	0.444929i	$-0.146771\pi$
$997$	56.5555			1.79113			0.895566	+	0.444929i	$0.146771\pi$
$998$	2.64343	−	4.57856i	0.0836764	−	0.144932i
$999$	−0.0414157	−	0.0717341i	−0.00131033	−	0.00226957i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	731.2.e.a.681.2	yes	58
43.6	even	3	inner	731.2.e.a.307.2	✓	58

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
731.2.e.a.307.2	✓	58	43.6	even	3	inner
731.2.e.a.681.2	yes	58	1.1	even	1	trivial

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)

\(f(q)\)	\(=\)	\(q-2.66184 q^{2} +(-1.22526 - 2.12222i) q^{3} +5.08540 q^{4} +(-0.351592 - 0.608975i) q^{5} +(3.26146 + 5.64901i) q^{6} +(-1.71463 + 2.96983i) q^{7} -8.21285 q^{8} +(-1.50254 + 2.60247i) q^{9} +O(q^{10})\)	\(q-2.66184 q^{2} +(-1.22526 - 2.12222i) q^{3} +5.08540 q^{4} +(-0.351592 - 0.608975i) q^{5} +(3.26146 + 5.64901i) q^{6} +(-1.71463 + 2.96983i) q^{7} -8.21285 q^{8} +(-1.50254 + 2.60247i) q^{9} +(0.935881 + 1.62099i) q^{10} -2.92598 q^{11} +(-6.23095 - 10.7923i) q^{12} +(-0.158863 + 0.275158i) q^{13} +(4.56408 - 7.90521i) q^{14} +(-0.861584 + 1.49231i) q^{15} +11.6905 q^{16} +(0.500000 - 0.866025i) q^{17} +(3.99952 - 6.92737i) q^{18} +(1.88935 + 3.27246i) q^{19} +(-1.78798 - 3.09688i) q^{20} +8.40349 q^{21} +7.78849 q^{22} +(0.112918 + 0.195579i) q^{23} +(10.0629 + 17.4295i) q^{24} +(2.25277 - 3.90191i) q^{25} +(0.422867 - 0.732428i) q^{26} +0.0124367 q^{27} +(-8.71959 + 15.1028i) q^{28} +(-1.31084 + 2.27043i) q^{29} +(2.29340 - 3.97229i) q^{30} +(2.45321 + 4.24908i) q^{31} -14.6926 q^{32} +(3.58509 + 6.20956i) q^{33} +(-1.33092 + 2.30522i) q^{34} +2.41140 q^{35} +(-7.64101 + 13.2346i) q^{36} +(-3.33013 - 5.76795i) q^{37} +(-5.02916 - 8.71077i) q^{38} +0.778594 q^{39} +(2.88757 + 5.00142i) q^{40} +8.73268 q^{41} -22.3688 q^{42} +(4.71201 + 4.56036i) q^{43} -14.8798 q^{44} +2.11312 q^{45} +(-0.300569 - 0.520601i) q^{46} +0.129653 q^{47} +(-14.3239 - 24.8098i) q^{48} +(-2.37992 - 4.12214i) q^{49} +(-5.99651 + 10.3863i) q^{50} -2.45053 q^{51} +(-0.807880 + 1.39929i) q^{52} +(-5.43802 - 9.41893i) q^{53} -0.0331044 q^{54} +(1.02875 + 1.78185i) q^{55} +(14.0820 - 24.3908i) q^{56} +(4.62991 - 8.01924i) q^{57} +(3.48924 - 6.04353i) q^{58} +8.37738 q^{59} +(-4.38150 + 7.58898i) q^{60} +(-0.201600 + 0.349182i) q^{61} +(-6.53006 - 11.3104i) q^{62} +(-5.15259 - 8.92456i) q^{63} +15.7283 q^{64} +0.223419 q^{65} +(-9.54295 - 16.5289i) q^{66} +(5.79001 + 10.0286i) q^{67} +(2.54270 - 4.40409i) q^{68} +(0.276708 - 0.479272i) q^{69} -6.41876 q^{70} +(1.66521 - 2.88422i) q^{71} +(12.3401 - 21.3737i) q^{72} +(2.18343 - 3.78181i) q^{73} +(8.86428 + 15.3534i) q^{74} -11.0409 q^{75} +(9.60813 + 16.6418i) q^{76} +(5.01698 - 8.68966i) q^{77} -2.07249 q^{78} +(8.40824 - 14.5635i) q^{79} +(-4.11028 - 7.11922i) q^{80} +(4.49237 + 7.78102i) q^{81} -23.2450 q^{82} +(-0.983722 - 1.70386i) q^{83} +42.7351 q^{84} -0.703183 q^{85} +(-12.5426 - 12.1390i) q^{86} +6.42447 q^{87} +24.0306 q^{88} +(-4.27897 - 7.41139i) q^{89} -5.62479 q^{90} +(-0.544782 - 0.943589i) q^{91} +(0.574232 + 0.994600i) q^{92} +(6.01165 - 10.4125i) q^{93} -0.345116 q^{94} +(1.32856 - 2.30114i) q^{95} +(18.0023 + 31.1808i) q^{96} -18.3370 q^{97} +(6.33497 + 10.9725i) q^{98} +(4.39639 - 7.61478i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 58 q - 6 q^{2} + 3 q^{3} + 54 q^{4} - q^{5} + 12 q^{6} + 7 q^{7} - 12 q^{8} - 22 q^{9}+O(q^{10}) \) 58 * q - 6 * q^2 + 3 * q^3 + 54 * q^4 - q^5 + 12 * q^6 + 7 * q^7 - 12 * q^8 - 22 * q^9	\( 58 q - 6 q^{2} + 3 q^{3} + 54 q^{4} - q^{5} + 12 q^{6} + 7 q^{7} - 12 q^{8} - 22 q^{9} + 4 q^{10} + 16 q^{11} + 12 q^{12} + 2 q^{13} - 11 q^{14} + 7 q^{15} + 30 q^{16} + 29 q^{17} + 8 q^{18} + 8 q^{19} - 33 q^{20} - 26 q^{21} - 22 q^{22} - 5 q^{23} + 12 q^{24} - 36 q^{25} - 12 q^{27} + 15 q^{28} + 2 q^{29} + 11 q^{30} + 3 q^{31} - 40 q^{32} + 17 q^{33} - 3 q^{34} + 38 q^{35} - 7 q^{36} + 2 q^{37} + q^{38} - 54 q^{39} + 5 q^{40} + 14 q^{41} - 112 q^{42} + 31 q^{43} - 24 q^{44} - 46 q^{45} - 13 q^{46} - 28 q^{47} - 28 q^{49} - 13 q^{50} + 6 q^{51} + 85 q^{52} - 10 q^{53} + 34 q^{54} + 36 q^{55} - 54 q^{56} - 23 q^{57} + 3 q^{58} + 12 q^{59} + 2 q^{60} - q^{61} - q^{62} - 14 q^{63} + 28 q^{64} + 80 q^{65} - 74 q^{66} + 11 q^{67} + 27 q^{68} - 11 q^{69} + 2 q^{70} + 16 q^{71} + 21 q^{72} + 14 q^{73} + 21 q^{74} - 54 q^{75} + 44 q^{76} + 25 q^{77} + 88 q^{78} - 4 q^{79} - 112 q^{80} + 11 q^{81} - 176 q^{82} - 3 q^{83} + 100 q^{84} - 2 q^{85} + 44 q^{86} + 8 q^{87} - 106 q^{88} + 82 q^{89} + 54 q^{90} - 15 q^{91} + 42 q^{92} + 88 q^{94} + 29 q^{95} + 20 q^{96} + 20 q^{97} + 44 q^{98} - 54 q^{99}+O(q^{100}) \) 58 * q - 6 * q^2 + 3 * q^3 + 54 * q^4 - q^5 + 12 * q^6 + 7 * q^7 - 12 * q^8 - 22 * q^9 + 4 * q^10 + 16 * q^11 + 12 * q^12 + 2 * q^13 - 11 * q^14 + 7 * q^15 + 30 * q^16 + 29 * q^17 + 8 * q^18 + 8 * q^19 - 33 * q^20 - 26 * q^21 - 22 * q^22 - 5 * q^23 + 12 * q^24 - 36 * q^25 - 12 * q^27 + 15 * q^28 + 2 * q^29 + 11 * q^30 + 3 * q^31 - 40 * q^32 + 17 * q^33 - 3 * q^34 + 38 * q^35 - 7 * q^36 + 2 * q^37 + q^38 - 54 * q^39 + 5 * q^40 + 14 * q^41 - 112 * q^42 + 31 * q^43 - 24 * q^44 - 46 * q^45 - 13 * q^46 - 28 * q^47 - 28 * q^49 - 13 * q^50 + 6 * q^51 + 85 * q^52 - 10 * q^53 + 34 * q^54 + 36 * q^55 - 54 * q^56 - 23 * q^57 + 3 * q^58 + 12 * q^59 + 2 * q^60 - q^61 - q^62 - 14 * q^63 + 28 * q^64 + 80 * q^65 - 74 * q^66 + 11 * q^67 + 27 * q^68 - 11 * q^69 + 2 * q^70 + 16 * q^71 + 21 * q^72 + 14 * q^73 + 21 * q^74 - 54 * q^75 + 44 * q^76 + 25 * q^77 + 88 * q^78 - 4 * q^79 - 112 * q^80 + 11 * q^81 - 176 * q^82 - 3 * q^83 + 100 * q^84 - 2 * q^85 + 44 * q^86 + 8 * q^87 - 106 * q^88 + 82 * q^89 + 54 * q^90 - 15 * q^91 + 42 * q^92 + 88 * q^94 + 29 * q^95 + 20 * q^96 + 20 * q^97 + 44 * q^98 - 54 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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