LMFDB - Embedded newform 547.2.c.a.40.15

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [547,2,Mod(40,547)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(547, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([2]))

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

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

chi := DirichletCharacter("547.40");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 547 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	547.c (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:	$4.36781699056$
Analytic rank:	$0$
Dimension:	$90$
Relative dimension:	$45$ over $\Q(\zeta_{3})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			40.15
Character	$\chi$	$=$	547.40
Dual form			547.2.c.a.506.15

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.557049 - 0.964838i) q^{2} -2.42664 q^{3} +(0.379392 - 0.657126i) q^{4} +(1.11858 - 1.93744i) q^{5} +(1.35176 + 2.34132i) q^{6} +(1.58983 + 2.75366i) q^{7} -3.07356 q^{8} +2.88859 q^{9} +O(q^{10})$	\(q+(-0.557049 - 0.964838i) q^{2} -2.42664 q^{3} +(0.379392 - 0.657126i) q^{4} +(1.11858 - 1.93744i) q^{5} +(1.35176 + 2.34132i) q^{6} +(1.58983 + 2.75366i) q^{7} -3.07356 q^{8} +2.88859 q^{9} -2.49243 q^{10} +(2.51664 + 4.35894i) q^{11} +(-0.920648 + 1.59461i) q^{12} +(2.79491 + 4.84092i) q^{13} +(1.77123 - 3.06785i) q^{14} +(-2.71440 + 4.70148i) q^{15} +(0.953339 + 1.65123i) q^{16} +(-3.02454 - 5.23865i) q^{17} +(-1.60909 - 2.78702i) q^{18} +(-4.02321 + 6.96840i) q^{19} +(-0.848764 - 1.47010i) q^{20} +(-3.85794 - 6.68216i) q^{21} +(2.80378 - 4.85629i) q^{22} +(-0.0829682 + 0.143705i) q^{23} +7.45842 q^{24} +(-0.00245873 - 0.00425865i) q^{25} +(3.11380 - 5.39326i) q^{26} +0.270358 q^{27} +2.41267 q^{28} +9.35411 q^{29} +6.04822 q^{30} +1.54761 q^{31} +(-2.01144 + 3.48392i) q^{32} +(-6.10697 - 10.5776i) q^{33} +(-3.36963 + 5.83638i) q^{34} +7.11343 q^{35} +(1.09591 - 1.89817i) q^{36} +(-1.58729 - 2.74928i) q^{37} +8.96450 q^{38} +(-6.78224 - 11.7472i) q^{39} +(-3.43803 + 5.95485i) q^{40} +(5.01978 + 8.69451i) q^{41} +(-4.29813 + 7.44458i) q^{42} +(-2.51340 - 4.35334i) q^{43} +3.81917 q^{44} +(3.23113 - 5.59648i) q^{45} +0.184869 q^{46} +(-1.16776 + 2.02263i) q^{47} +(-2.31341 - 4.00695i) q^{48} +(-1.55511 + 2.69353i) q^{49} +(-0.00273927 + 0.00474455i) q^{50} +(7.33947 + 12.7123i) q^{51} +4.24146 q^{52} +(-2.99865 - 5.19381i) q^{53} +(-0.150603 - 0.260852i) q^{54} +11.2603 q^{55} +(-4.88643 - 8.46355i) q^{56} +(9.76288 - 16.9098i) q^{57} +(-5.21070 - 9.02520i) q^{58} +(-2.58081 - 4.47009i) q^{59} +(2.05964 + 3.56741i) q^{60} +(-0.236136 - 0.409000i) q^{61} +(-0.862093 - 1.49319i) q^{62} +(4.59236 + 7.95420i) q^{63} +8.29525 q^{64} +12.5054 q^{65} +(-6.80377 + 11.7845i) q^{66} +(2.86270 + 4.95834i) q^{67} -4.58994 q^{68} +(0.201334 - 0.348721i) q^{69} +(-3.96253 - 6.86330i) q^{70} +(-0.589868 - 1.02168i) q^{71} -8.87824 q^{72} +(-2.12263 - 3.67650i) q^{73} +(-1.76840 + 3.06296i) q^{74} +(0.00596646 + 0.0103342i) q^{75} +(3.05275 + 5.28751i) q^{76} +(-8.00204 + 13.8599i) q^{77} +(-7.55608 + 13.0875i) q^{78} +7.91227 q^{79} +4.26556 q^{80} -9.32182 q^{81} +(5.59253 - 9.68654i) q^{82} +(-1.80276 - 3.12247i) q^{83} -5.85469 q^{84} -13.5328 q^{85} +(-2.80018 + 4.85005i) q^{86} -22.6991 q^{87} +(-7.73503 - 13.3975i) q^{88} +6.08215 q^{89} -7.19959 q^{90} +(-8.88685 + 15.3925i) q^{91} +(0.0629549 + 0.109041i) q^{92} -3.75548 q^{93} +2.60201 q^{94} +(9.00059 + 15.5895i) q^{95} +(4.88105 - 8.45423i) q^{96} +(-4.75534 + 8.23649i) q^{97} +3.46509 q^{98} +(7.26952 + 12.5912i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 90 q - q^{2} - 4 q^{3} - 47 q^{4} + q^{5} - 3 q^{6} + 2 q^{7} - 30 q^{8} + 82 q^{9}+O(q^{10}) $ 90 * q - q^2 - 4 * q^3 - 47 * q^4 + q^5 - 3 * q^6 + 2 * q^7 - 30 * q^8 + 82 * q^9	\( 90 q - q^{2} - 4 q^{3} - 47 q^{4} + q^{5} - 3 q^{6} + 2 q^{7} - 30 q^{8} + 82 q^{9} - 10 q^{10} + q^{11} + 4 q^{12} - 3 q^{13} + 2 q^{14} - 7 q^{15} - 39 q^{16} - 4 q^{17} - 11 q^{18} - 2 q^{19} + 25 q^{20} - 27 q^{21} - 7 q^{22} + q^{23} + 32 q^{24} - 40 q^{25} - 10 q^{26} - 34 q^{27} - 28 q^{28} + 26 q^{29} - 40 q^{30} - 24 q^{31} + 19 q^{32} + q^{33} - 6 q^{34} - 8 q^{35} - 36 q^{36} - 10 q^{37} + 24 q^{38} + 22 q^{39} + 20 q^{40} + 3 q^{41} + 38 q^{42} - 12 q^{43} - 30 q^{44} - 2 q^{45} - 40 q^{46} + 32 q^{47} + 14 q^{48} - 43 q^{49} + 14 q^{50} + 13 q^{51} + 46 q^{52} + 9 q^{53} - 8 q^{54} + 4 q^{55} - 8 q^{56} - 8 q^{57} + 4 q^{58} + 22 q^{59} - 2 q^{60} - 12 q^{61} + 11 q^{62} + 8 q^{63} + 22 q^{64} + 18 q^{65} + 12 q^{66} - 22 q^{67} + 6 q^{68} - q^{69} - 6 q^{70} - 4 q^{71} - 140 q^{72} + 17 q^{73} + 17 q^{74} + 39 q^{75} + 84 q^{76} - 4 q^{77} + 33 q^{78} - 72 q^{79} - 40 q^{80} + 18 q^{81} - 9 q^{82} + 24 q^{83} + 114 q^{84} + 40 q^{85} - 72 q^{86} - 78 q^{87} - 22 q^{88} + 14 q^{89} + 96 q^{90} - 8 q^{92} - 76 q^{93} + 108 q^{94} - 11 q^{95} - 34 q^{96} - 74 q^{98} - 62 q^{99}+O(q^{100}) \) 90 * q - q^2 - 4 * q^3 - 47 * q^4 + q^5 - 3 * q^6 + 2 * q^7 - 30 * q^8 + 82 * q^9 - 10 * q^10 + q^11 + 4 * q^12 - 3 * q^13 + 2 * q^14 - 7 * q^15 - 39 * q^16 - 4 * q^17 - 11 * q^18 - 2 * q^19 + 25 * q^20 - 27 * q^21 - 7 * q^22 + q^23 + 32 * q^24 - 40 * q^25 - 10 * q^26 - 34 * q^27 - 28 * q^28 + 26 * q^29 - 40 * q^30 - 24 * q^31 + 19 * q^32 + q^33 - 6 * q^34 - 8 * q^35 - 36 * q^36 - 10 * q^37 + 24 * q^38 + 22 * q^39 + 20 * q^40 + 3 * q^41 + 38 * q^42 - 12 * q^43 - 30 * q^44 - 2 * q^45 - 40 * q^46 + 32 * q^47 + 14 * q^48 - 43 * q^49 + 14 * q^50 + 13 * q^51 + 46 * q^52 + 9 * q^53 - 8 * q^54 + 4 * q^55 - 8 * q^56 - 8 * q^57 + 4 * q^58 + 22 * q^59 - 2 * q^60 - 12 * q^61 + 11 * q^62 + 8 * q^63 + 22 * q^64 + 18 * q^65 + 12 * q^66 - 22 * q^67 + 6 * q^68 - q^69 - 6 * q^70 - 4 * q^71 - 140 * q^72 + 17 * q^73 + 17 * q^74 + 39 * q^75 + 84 * q^76 - 4 * q^77 + 33 * q^78 - 72 * q^79 - 40 * q^80 + 18 * q^81 - 9 * q^82 + 24 * q^83 + 114 * q^84 + 40 * q^85 - 72 * q^86 - 78 * q^87 - 22 * q^88 + 14 * q^89 + 96 * q^90 - 8 * q^92 - 76 * q^93 + 108 * q^94 - 11 * q^95 - 34 * q^96 - 74 * q^98 - 62 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/547\mathbb{Z}\right)^\times$.

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

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 $

$2$	−0.557049	−	0.964838i	−0.393893	−	0.682243i	0.599066	−	0.800700i	$-0.295539\pi$
$2$	−0.557049	−	0.964838i	−0.393893	−	0.682243i	−0.992959	+	0.118456i	$0.962205\pi$
$3$	−2.42664			−1.40102			−0.700511	−	0.713642i	$-0.747045\pi$
$3$	−2.42664			−1.40102			−0.700511	+	0.713642i	$0.747045\pi$
$4$	0.379392	−	0.657126i	0.189696	−	0.328563i
$5$	1.11858	−	1.93744i	0.500246	−	0.866451i	−0.499754	−	0.866167i	$-0.666576\pi$
$5$	1.11858	−	1.93744i	0.500246	−	0.866451i	1.00000		0.000283863i	$-9.03565e-5\pi$
$6$	1.35176	+	2.34132i	0.551853	+	0.955838i
$7$	1.58983	+	2.75366i	0.600899	+	1.04079i	0.992685	+	0.120731i	$0.0385239\pi$
$7$	1.58983	+	2.75366i	0.600899	+	1.04079i	−0.391786	+	0.920056i	$0.628143\pi$
$8$	−3.07356			−1.08667
$9$	2.88859			0.962863
$10$	−2.49243			−0.788174
$11$	2.51664	+	4.35894i	0.758794	+	1.31427i	0.943466	+	0.331470i	$0.107545\pi$
$11$	2.51664	+	4.35894i	0.758794	+	1.31427i	−0.184672	+	0.982800i	$0.559122\pi$
$12$	−0.920648	+	1.59461i	−0.265768	+	0.460324i
$13$	2.79491	+	4.84092i	0.775168	+	1.34263i	0.934700	+	0.355437i	$0.115668\pi$
$13$	2.79491	+	4.84092i	0.775168	+	1.34263i	−0.159532	+	0.987193i	$0.550999\pi$
$14$	1.77123	−	3.06785i	0.473380	−	0.819918i
$15$	−2.71440	+	4.70148i	−0.700855	+	1.21392i
$16$	0.953339	+	1.65123i	0.238335	+	0.412808i
$17$	−3.02454	−	5.23865i	−0.733558	−	1.27056i	−0.955353	−	0.295467i	$-0.904525\pi$
$17$	−3.02454	−	5.23865i	−0.733558	−	1.27056i	0.221795	−	0.975093i	$-0.428809\pi$
$18$	−1.60909	−	2.78702i	−0.379265	−	0.656907i
$19$	−4.02321	+	6.96840i	−0.922987	+	1.59866i	−0.128220	+	0.991746i	$0.540926\pi$
$19$	−4.02321	+	6.96840i	−0.922987	+	1.59866i	−0.794767	+	0.606914i	$0.792407\pi$
$20$	−0.848764	−	1.47010i	−0.189789	−	0.328725i
$21$	−3.85794	−	6.68216i	−0.841872	−	1.45817i
$22$	2.80378	−	4.85629i	0.597768	−	1.03536i
$23$	−0.0829682	+	0.143705i	−0.0173001	+	0.0299646i	−0.874546	−	0.484943i	$-0.838840\pi$
$23$	−0.0829682	+	0.143705i	−0.0173001	+	0.0299646i	0.857246	+	0.514907i	$0.172174\pi$
$24$	7.45842			1.52244
$25$	−0.00245873	−	0.00425865i	−0.000491746	−	0.000851730i
$26$	3.11380	−	5.39326i	0.610667	−	1.05771i
$27$	0.270358			0.0520304
$28$	2.41267			0.455952
$29$	9.35411			1.73701			0.868507	−	0.495677i	$-0.165080\pi$
$29$	9.35411			1.73701			0.868507	+	0.495677i	$0.165080\pi$
$30$	6.04822			1.10425
$31$	1.54761			0.277958			0.138979	−	0.990295i	$-0.455618\pi$
$31$	1.54761			0.277958			0.138979	+	0.990295i	$0.455618\pi$
$32$	−2.01144	+	3.48392i	−0.355576	+	0.615876i
$33$	−6.10697	−	10.5776i	−1.06309	−	1.84132i
$34$	−3.36963	+	5.83638i	−0.577888	+	1.00093i
$35$	7.11343			1.20239
$36$	1.09591	−	1.89817i	0.182651	−	0.316361i
$37$	−1.58729	−	2.74928i	−0.260950	−	0.451978i	0.705545	−	0.708665i	$-0.250702\pi$
$37$	−1.58729	−	2.74928i	−0.260950	−	0.451978i	−0.966495	+	0.256687i	$0.917369\pi$
$38$	8.96450			1.45423
$39$	−6.78224	−	11.7472i	−1.08603	−	1.88105i
$40$	−3.43803	+	5.95485i	−0.543600	+	0.941544i
$41$	5.01978	+	8.69451i	0.783958	+	1.35785i	0.929620	+	0.368520i	$0.120135\pi$
$41$	5.01978	+	8.69451i	0.783958	+	1.35785i	−0.145662	+	0.989334i	$0.546531\pi$
$42$	−4.29813	+	7.44458i	−0.663216	+	1.14872i
$43$	−2.51340	−	4.35334i	−0.383290	−	0.663878i	0.608240	−	0.793753i	$-0.291876\pi$
$43$	−2.51340	−	4.35334i	−0.383290	−	0.663878i	−0.991530	+	0.129875i	$0.958542\pi$
$44$	3.81917			0.575761
$45$	3.23113	−	5.59648i	0.481668	−	0.834273i
$46$	0.184869			0.0272575
$47$	−1.16776	+	2.02263i	−0.170336	+	0.295030i	−0.938537	−	0.345178i	$-0.887819\pi$
$47$	−1.16776	+	2.02263i	−0.170336	+	0.295030i	0.768201	+	0.640208i	$0.221152\pi$
$48$	−2.31341	−	4.00695i	−0.333912	−	0.578353i
$49$	−1.55511	+	2.69353i	−0.222159	+	0.384790i
$50$	−0.00273927	+	0.00474455i	−0.000387391	+	0.000670981i
$51$	7.33947	+	12.7123i	1.02773	+	1.78008i
$52$	4.24146			0.588185
$53$	−2.99865	−	5.19381i	−0.411896	−	0.713425i	0.583201	−	0.812328i	$-0.301800\pi$
$53$	−2.99865	−	5.19381i	−0.411896	−	0.713425i	−0.995097	+	0.0989029i	$0.968467\pi$
$54$	−0.150603	−	0.260852i	−0.0204944	−	0.0354974i
$55$	11.2603			1.51833
$56$	−4.88643	−	8.46355i	−0.652977	−	1.13099i
$57$	9.76288	−	16.9098i	1.29312	−	2.23976i
$58$	−5.21070	−	9.02520i	−0.684198	−	1.18507i
$59$	−2.58081	−	4.47009i	−0.335993	−	0.581957i	0.647682	−	0.761911i	$-0.275738\pi$
$59$	−2.58081	−	4.47009i	−0.335993	−	0.581957i	−0.983675	+	0.179954i	$0.942405\pi$
$60$	2.05964	+	3.56741i	0.265899	+	0.460551i
$61$	−0.236136	−	0.409000i	−0.0302341	−	0.0523671i	0.850512	−	0.525955i	$-0.176292\pi$
$61$	−0.236136	−	0.409000i	−0.0302341	−	0.0523671i	−0.880747	+	0.473588i	$0.842959\pi$
$62$	−0.862093	−	1.49319i	−0.109486	−	0.189635i
$63$	4.59236	+	7.95420i	0.578583	+	1.00214i
$64$	8.29525			1.03691
$65$	12.5054			1.55110
$66$	−6.80377	+	11.7845i	−0.837486	+	1.45057i
$67$	2.86270	+	4.95834i	0.349734	+	0.605757i	0.986202	−	0.165546i	$-0.0529386\pi$
$67$	2.86270	+	4.95834i	0.349734	+	0.605757i	−0.636468	+	0.771303i	$0.719605\pi$
$68$	−4.58994			−0.556612
$69$	0.201334	−	0.348721i	0.0242378	−	0.0419810i
$70$	−3.96253	−	6.86330i	−0.473613	−	0.820321i
$71$	−0.589868	−	1.02168i	−0.0700045	−	0.121251i	0.828899	−	0.559399i	$-0.188968\pi$
$71$	−0.589868	−	1.02168i	−0.0700045	−	0.121251i	−0.898903	+	0.438148i	$0.855635\pi$
$72$	−8.87824			−1.04631
$73$	−2.12263	−	3.67650i	−0.248435	−	0.430301i	0.714657	−	0.699475i	$-0.246583\pi$
$73$	−2.12263	−	3.67650i	−0.248435	−	0.430301i	−0.963092	+	0.269174i	$0.913249\pi$
$74$	−1.76840	+	3.06296i	−0.205573	+	0.356062i
$75$	0.00596646	+	0.0103342i	0.000688947	+	0.00119329i
$76$	3.05275	+	5.28751i	0.350174	+	0.606519i
$77$	−8.00204	+	13.8599i	−0.911917	+	1.57949i
$78$	−7.55608	+	13.0875i	−0.855558	+	1.48187i
$79$	7.91227			0.890200			0.445100	−	0.895481i	$-0.353168\pi$
$79$	7.91227			0.890200			0.445100	+	0.895481i	$0.353168\pi$
$80$	4.26556			0.476904
$81$	−9.32182			−1.03576
$82$	5.59253	−	9.68654i	0.617591	−	1.06970i
$83$	−1.80276	−	3.12247i	−0.197878	−	0.342735i	0.749962	−	0.661481i	$-0.230072\pi$
$83$	−1.80276	−	3.12247i	−0.197878	−	0.342735i	−0.947840	+	0.318746i	$0.896738\pi$
$84$	−5.85469			−0.638799
$85$	−13.5328			−1.46784
$86$	−2.80018	+	4.85005i	−0.301951	+	0.522994i
$87$	−22.6991			−2.43360
$88$	−7.73503	−	13.3975i	−0.824556	−	1.42817i
$89$	6.08215			0.644707			0.322354	−	0.946619i	$-0.395526\pi$
$89$	6.08215			0.644707			0.322354	+	0.946619i	$0.395526\pi$
$90$	−7.19959			−0.758903
$91$	−8.88685	+	15.3925i	−0.931595	+	1.61357i
$92$	0.0629549	+	0.109041i	0.00656351	+	0.0113683i
$93$	−3.75548			−0.389426
$94$	2.60201			0.268377
$95$	9.00059	+	15.5895i	0.923441	+	1.59945i
$96$	4.88105	−	8.45423i	0.498170	−	0.862856i
$97$	−4.75534	+	8.23649i	−0.482832	+	0.836289i	−0.999806	−	0.0197121i	$-0.993725\pi$
$97$	−4.75534	+	8.23649i	−0.482832	+	0.836289i	0.516974	+	0.856001i	$0.327058\pi$
$98$	3.46509			0.350027
$99$	7.26952	+	12.5912i	0.730615	+	1.26546i
$100$	−0.00373129			−0.000373129
$101$	−16.6890			−1.66061			−0.830307	−	0.557306i	$-0.811835\pi$
$101$	−16.6890			−1.66061			−0.830307	+	0.557306i	$0.811835\pi$
$102$	8.17689	−	14.1628i	0.809633	−	1.40233i
$103$	−3.05231			−0.300753			−0.150377	−	0.988629i	$-0.548049\pi$
$103$	−3.05231			−0.300753			−0.150377	+	0.988629i	$0.548049\pi$
$104$	−8.59031	−	14.8789i	−0.842349	−	1.45899i
$105$	−17.2617			−1.68457
$106$	−3.34079	+	5.78642i	−0.324486	+	0.562027i
$107$	17.5432			1.69597			0.847984	−	0.530022i	$-0.177816\pi$
$107$	17.5432			1.69597			0.847984	+	0.530022i	$0.177816\pi$
$108$	0.102572	−	0.177659i	0.00986996	−	0.0170953i
$109$	0.268261	−	0.464641i	0.0256947	−	0.0445046i	−0.852892	−	0.522087i	$-0.825154\pi$
$109$	0.268261	−	0.464641i	0.0256947	−	0.0445046i	0.878587	+	0.477583i	$0.158487\pi$
$110$	−6.27253	−	10.8643i	−0.598062	−	1.03587i
$111$	3.85180	+	6.67151i	0.365596	+	0.633231i
$112$	−3.03129	+	5.25035i	−0.286430	+	0.496112i
$113$	−5.29595	+	9.17285i	−0.498201	+	0.862909i	−0.999998	−	0.00207605i	$-0.999339\pi$
$113$	−5.29595	+	9.17285i	−0.498201	+	0.862909i	0.501797	+	0.864986i	$0.332673\pi$
$114$	−21.7536			−2.03741
$115$	0.185614	+	0.321492i	0.0173086	+	0.0299793i
$116$	3.54887	−	6.14683i	0.329505	−	0.570719i
$117$	8.07334	+	13.9834i	0.746380	+	1.29277i
$118$	−2.87528	+	4.98013i	−0.264691	+	0.458458i
$119$	9.61700	−	16.6571i	0.881589	−	1.52696i
$120$	8.34287	−	14.4503i	0.761596	−	1.31912i
$121$	−7.16691	+	12.4135i	−0.651537	+	1.12850i
$122$	−0.263079	+	0.455666i	−0.0238181	+	0.0412541i
$123$	−12.1812	−	21.0985i	−1.09834	−	1.90238i
$124$	0.587149	−	1.01697i	0.0527276	−	0.0913268i
$125$	11.1748			0.999508
$126$	5.11634	−	8.86176i	0.455800	−	0.789469i
$127$	−5.89210	+	10.2054i	−0.522840	+	0.905585i	0.476807	+	0.879008i	$0.341794\pi$
$127$	−5.89210	+	10.2054i	−0.522840	+	0.905585i	−0.999647	+	0.0265767i	$0.991539\pi$
$128$	−0.597976	−	1.03573i	−0.0528541	−	0.0915460i
$129$	6.09912	+	10.5640i	0.536998	+	0.930108i
$130$	−6.96610	−	12.0656i	−0.610967	−	1.05823i
$131$	6.88482			0.601530			0.300765	−	0.953698i	$-0.402758\pi$
$131$	6.88482			0.601530			0.300765	+	0.953698i	$0.402758\pi$
$132$	−9.26775			−0.806654
$133$	−25.5848			−2.21849
$134$	3.18933	−	5.52407i	0.275516	−	0.477207i
$135$	0.302418	−	0.523803i	0.0260280	−	0.0450818i
$136$	9.29609	+	16.1013i	0.797133	+	1.38068i
$137$	−2.82441	−	4.89202i	−0.241305	−	0.417953i	0.719781	−	0.694201i	$-0.244242\pi$
$137$	−2.82441	−	4.89202i	−0.241305	−	0.417953i	−0.961086	+	0.276248i	$0.910909\pi$
$138$	−0.448612			−0.0381884
$139$	4.04564	+	7.00725i	0.343147	+	0.594347i	0.985015	−	0.172467i	$-0.0551739\pi$
$139$	4.04564	+	7.00725i	0.343147	+	0.594347i	−0.641869	+	0.766815i	$0.721841\pi$
$140$	2.69878	−	4.67442i	0.228088	−	0.395061i
$141$	2.83374	−	4.90819i	0.238644	−	0.413344i
$142$	−0.657172	+	1.13825i	−0.0551486	+	0.0955202i
$143$	−14.0675	+	24.3657i	−1.17639	+	2.03756i
$144$	2.75380	+	4.76973i	0.229484	+	0.397477i
$145$	10.4634	−	18.1231i	0.868934	−	1.50504i
$146$	−2.36481	+	4.09598i	−0.195713	+	0.338986i
$147$	3.77370	−	6.53623i	0.311249	−	0.539099i
$148$	−2.40883			−0.198004
$149$	6.00715			0.492125			0.246063	−	0.969254i	$-0.420863\pi$
$149$	6.00715			0.492125			0.246063	+	0.969254i	$0.420863\pi$
$150$	0.00664723	−	0.0115133i	0.000542744	−	0.000940060i
$151$	−2.35800			−0.191891			−0.0959457	−	0.995387i	$-0.530588\pi$
$151$	−2.35800			−0.191891			−0.0959457	+	0.995387i	$0.530588\pi$
$152$	12.3656	−	21.4178i	1.00298	−	1.73721i
$153$	−8.73664	−	15.1323i	−0.706316	−	1.22337i
$154$	17.8301			1.43679
$155$	1.73113	−	2.99840i	0.139047	−	0.240837i
$156$	−10.2925			−0.824060
$157$	9.53016	+	16.5067i	0.760589	+	1.31738i	0.942547	+	0.334073i	$0.108423\pi$
$157$	9.53016	+	16.5067i	0.760589	+	1.31738i	−0.181958	+	0.983306i	$0.558243\pi$
$158$	−4.40752	−	7.63405i	−0.350644	−	0.607333i
$159$	7.27665	+	12.6035i	0.577076	+	0.999524i
$160$	4.49994	+	7.79412i	0.355751	+	0.616179i
$161$	−0.527621			−0.0415823
$162$	5.19272	+	8.99405i	0.407978	+	0.706639i
$163$	−4.02211	−	6.96650i	−0.315036	−	0.545658i	0.664409	−	0.747369i	$-0.268683\pi$
$163$	−4.02211	−	6.96650i	−0.315036	−	0.545658i	−0.979445	+	0.201711i	$0.935350\pi$
$164$	7.61786			0.594855
$165$	−27.3246			−2.12722
$166$	−2.00845	+	3.47874i	−0.155886	+	0.270002i
$167$	11.6161			0.898882			0.449441	−	0.893310i	$-0.351623\pi$
$167$	11.6161			0.898882			0.449441	+	0.893310i	$0.351623\pi$
$168$	11.8576	+	20.5380i	0.914835	+	1.58454i
$169$	−9.12302	+	15.8015i	−0.701770	+	1.21550i
$170$	7.53844	+	13.0570i	0.578172	+	1.00142i
$171$	−11.6214	+	20.1288i	−0.888709	+	1.53929i
$172$	−3.81426			−0.290835
$173$	−15.3441			−1.16659			−0.583295	−	0.812260i	$-0.698237\pi$
$173$	−15.3441			−1.16659			−0.583295	+	0.812260i	$0.698237\pi$
$174$	12.6445	+	21.9009i	0.958577	+	1.66030i
$175$	0.00781793	−	0.0135410i	0.000590980	−	0.00102361i
$176$	−4.79841	+	8.31110i	−0.361694	+	0.626473i
$177$	6.26270	+	10.8473i	0.470733	+	0.815334i
$178$	−3.38806	−	5.86829i	−0.253946	−	0.439847i
$179$	14.0744			1.05197			0.525985	−	0.850494i	$-0.323697\pi$
$179$	14.0744			1.05197			0.525985	+	0.850494i	$0.323697\pi$
$180$	−2.45173	−	4.24652i	−0.182741	−	0.316517i
$181$	13.2350	−	22.9237i	0.983751	−	1.70391i	0.336389	−	0.941723i	$-0.390794\pi$
$181$	13.2350	−	22.9237i	0.983751	−	1.70391i	0.647361	−	0.762183i	$-0.275872\pi$
$182$	19.8017			1.46780
$183$	0.573018	+	0.992496i	0.0423587	+	0.0733674i
$184$	0.255008	−	0.441686i	0.0187994	−	0.0325615i
$185$	−7.10209			−0.522156
$186$	2.09199	+	3.62343i	0.153392	+	0.265683i
$187$	15.2233	−	26.3676i	1.11324	−	1.92819i
$188$	0.886080	+	1.53474i	0.0646240	+	0.111932i
$189$	0.429823	+	0.744475i	0.0312650	+	0.0541526i
$190$	10.0275	−	17.3682i	0.727474	−	1.26002i
$191$	−0.173457	+	0.300437i	−0.0125509	+	0.0217388i	−0.872233	−	0.489091i	$-0.837329\pi$
$191$	−0.173457	+	0.300437i	−0.0125509	+	0.0217388i	0.859682	+	0.510830i	$0.170662\pi$
$192$	−20.1296			−1.45273
$193$	9.92007	−	17.1821i	0.714063	−	1.23679i	−0.249257	−	0.968437i	$-0.580187\pi$
$193$	9.92007	−	17.1821i	0.714063	−	1.23679i	0.963320	−	0.268355i	$-0.0864801\pi$
$194$	10.5958			0.760737
$195$	−30.3460			−2.17312
$196$	1.17999	+	2.04381i	0.0842853	+	0.145986i
$197$	3.07984			0.219429			0.109715	−	0.993963i	$-0.465006\pi$
$197$	3.07984			0.219429			0.109715	+	0.993963i	$0.465006\pi$
$198$	8.09897	−	14.0278i	0.575568	−	0.996914i
$199$	−10.1219	+	17.5316i	−0.717521	+	1.24278i	0.244459	+	0.969660i	$0.421390\pi$
$199$	−10.1219	+	17.5316i	−0.717521	+	1.24278i	−0.961979	+	0.273123i	$0.911944\pi$
$200$	0.00755705	+	0.0130892i	0.000534364	+	0.000925546i
$201$	−6.94674	−	12.0321i	−0.489985	−	0.848679i
$202$	9.29658	+	16.1021i	0.654105	+	1.13294i
$203$	14.8714	+	25.7581i	1.04377	+	1.80786i
$204$	11.1381			0.779826
$205$	22.4602			1.56869
$206$	1.70029	+	2.94499i	0.118465	+	0.205187i
$207$	−0.239661	+	0.415105i	−0.0166576	+	0.0288518i
$208$	−5.32899	+	9.23008i	−0.369499	+	0.639991i
$209$	−40.4998			−2.80143
$210$	9.61564	+	16.6548i	0.663542	+	1.14929i
$211$	−3.52222	+	6.10066i	−0.242479	+	0.419987i	−0.961420	−	0.275085i	$-0.911294\pi$
$211$	−3.52222	+	6.10066i	−0.242479	+	0.419987i	0.718940	+	0.695072i	$0.244627\pi$
$212$	−4.55066			−0.312540
$213$	1.43140	+	2.47926i	0.0980778	+	0.169876i
$214$	−9.77244	−	16.9264i	−0.668030	−	1.15706i
$215$	−11.2458			−0.766957
$216$	−0.830961			−0.0565397
$217$	2.46043	+	4.26159i	0.167025	+	0.289295i
$218$	−0.597738			−0.0404839
$219$	5.15085	+	8.92154i	0.348062	+	0.602861i
$220$	4.27206	−	7.39942i	0.288022	−	0.498869i
$221$	16.9066	−	29.2831i	1.13726	−	1.96980i
$222$	4.29128	−	7.43272i	0.288012	−	0.498851i
$223$	−5.69225	+	9.85927i	−0.381181	+	0.660225i	−0.991231	−	0.132138i	$-0.957816\pi$
$223$	−5.69225	+	9.85927i	−0.381181	+	0.660225i	0.610050	+	0.792363i	$0.291149\pi$
$224$	−12.7914			−0.854662
$225$	−0.00710226	−	0.0123015i	−0.000473484	−	0.000820099i
$226$	11.8004			0.784952
$227$	12.2962	−	21.2977i	0.816131	−	1.41358i	−0.0923824	−	0.995724i	$-0.529448\pi$
$227$	12.2962	−	21.2977i	0.816131	−	1.41358i	0.908513	−	0.417856i	$-0.137218\pi$
$228$	−7.40792	−	12.8309i	−0.490601	−	0.849746i
$229$	5.13149	−	8.88800i	0.339098	−	0.587335i	−0.645165	−	0.764043i	$-0.723211\pi$
$229$	5.13149	−	8.88800i	0.339098	−	0.587335i	0.984263	+	0.176708i	$0.0565447\pi$
$230$	0.206792	−	0.358174i	0.0136355	−	0.0236173i
$231$	19.4181	−	33.6331i	1.27762	−	2.21290i
$232$	−28.7504			−1.88756
$233$	7.03200	−	12.1798i	0.460682	−	0.797924i	−0.538313	−	0.842745i	$-0.680938\pi$
$233$	7.03200	−	12.1798i	0.460682	−	0.797924i	0.998995	+	0.0448206i	$0.0142716\pi$
$234$	8.99449	−	15.5789i	0.587988	−	1.01843i
$235$	2.61248	+	4.52495i	0.170420	+	0.295175i
$236$	−3.91656			−0.254946
$237$	−19.2002			−1.24719
$238$	−21.4286			−1.38901
$239$	−11.6344	−	20.1514i	−0.752567	−	1.30349i	−0.946575	−	0.322485i	$-0.895482\pi$
$239$	−11.6344	−	20.1514i	−0.752567	−	1.30349i	0.194007	−	0.981000i	$-0.437851\pi$
$240$	−10.3510			−0.668153
$241$	6.01996	−	10.4269i	0.387780	−	0.671654i	−0.604371	−	0.796703i	$-0.706576\pi$
$241$	6.01996	−	10.4269i	0.387780	−	0.671654i	0.992151	+	0.125049i	$0.0399089\pi$
$242$	15.9693			1.02654
$243$	21.8096			1.39909
$244$	−0.358353			−0.0229412
$245$	3.47904	+	6.02588i	0.222268	+	0.384979i
$246$	−13.5711	+	23.5058i	−0.865259	+	1.49867i
$247$	−44.9780			−2.86188
$248$	−4.75666			−0.302048
$249$	4.37465	+	7.57711i	0.277232	+	0.480180i
$250$	−6.22493	−	10.7819i	−0.393699	−	0.681907i
$251$	9.74296	+	16.8753i	0.614970	+	1.06516i	0.990390	+	0.138305i	$0.0441654\pi$
$251$	9.74296	+	16.8753i	0.614970	+	1.06516i	−0.375419	+	0.926855i	$0.622501\pi$
$252$	6.96922			0.439020
$253$	−0.835203			−0.0525088
$254$	13.1288			0.823772
$255$	32.8392			2.05647
$256$	7.62905	−	13.2139i	0.476815	−	0.825868i
$257$	−12.0811			−0.753599			−0.376800	−	0.926295i	$-0.622975\pi$
$257$	−12.0811			−0.753599			−0.376800	+	0.926295i	$0.622975\pi$
$258$	6.79503	−	11.7693i	0.423040	−	0.732727i
$259$	5.04705	−	8.74175i	0.313609	−	0.543186i
$260$	4.74443	−	8.21760i	0.294237	−	0.509634i
$261$	27.0202			1.67251
$262$	−3.83519	−	6.64274i	−0.236939	−	0.410390i
$263$	−12.9880			−0.800876			−0.400438	−	0.916324i	$-0.631142\pi$
$263$	−12.9880			−0.800876			−0.400438	+	0.916324i	$0.631142\pi$
$264$	18.7701	+	32.5108i	1.15522	+	2.00090i
$265$	−13.4170			−0.824197
$266$	14.2520	+	24.6852i	0.873847	+	1.51355i
$267$	−14.7592			−0.903249
$268$	4.34434			0.265373
$269$	−6.79673	+	11.7723i	−0.414404	+	0.717769i	−0.995366	−	0.0961619i	$-0.969343\pi$
$269$	−6.79673	+	11.7723i	−0.414404	+	0.717769i	0.580961	+	0.813931i	$0.302677\pi$
$270$	−0.673847			−0.0410090
$271$	4.17863	+	7.23760i	0.253834	+	0.439653i	0.964578	−	0.263797i	$-0.0849750\pi$
$271$	4.17863	+	7.23760i	0.253834	+	0.439653i	−0.710744	+	0.703450i	$0.751642\pi$
$272$	5.76682	−	9.98843i	0.349665	−	0.605637i
$273$	21.5652	−	37.3520i	1.30518	−	2.26065i
$274$	−3.14667	+	5.45019i	−0.190097	+	0.329258i
$275$	0.0123755	−	0.0214349i	0.000746269	−	0.00129258i
$276$	−0.152769	−	0.264604i	−0.00919562	−	0.0159273i
$277$	16.9294			1.01719			0.508596	−	0.861005i	$-0.330165\pi$
$277$	16.9294			1.01719			0.508596	+	0.861005i	$0.330165\pi$
$278$	4.50724	−	7.80677i	0.270326	−	0.468219i
$279$	4.47040			0.267636
$280$	−21.8635			−1.30660
$281$	−0.0808757	−	0.140081i	−0.00482464	−	0.00835652i	0.863603	−	0.504172i	$-0.168202\pi$
$281$	−0.0808757	−	0.140081i	−0.00482464	−	0.00835652i	−0.868428	+	0.495816i	$0.834869\pi$
$282$	−6.31414			−0.376001
$283$	−14.6679	−	25.4055i	−0.871916	−	1.51020i	−0.860012	−	0.510274i	$-0.829544\pi$
$283$	−14.6679	−	25.4055i	−0.871916	−	1.51020i	−0.0119043	−	0.999929i	$-0.503789\pi$
$284$	−0.895166			−0.0531183
$285$	−21.8412	−	37.8301i	−1.29376	−	2.24086i
$286$	31.3452			1.85348
$287$	−15.9612	+	27.6456i	−0.942158	+	1.63187i
$288$	−5.81023	+	10.0636i	−0.342371	+	0.593004i
$289$	−9.79567	+	16.9666i	−0.576216	+	0.998035i
$290$	−23.3144			−1.36907
$291$	11.5395	−	19.9870i	0.676458	−	1.17166i
$292$	−3.22123			−0.188508
$293$	8.83018			0.515865			0.257932	−	0.966163i	$-0.416959\pi$
$293$	8.83018			0.515865			0.257932	+	0.966163i	$0.416959\pi$
$294$	−8.40854			−0.490396
$295$	−11.5474			−0.672316
$296$	4.87864	+	8.45006i	0.283565	+	0.491150i
$297$	0.680392	+	1.17847i	0.0394804	+	0.0683820i
$298$	−3.34628	−	5.79593i	−0.193845	−	0.335749i
$299$	−0.927554			−0.0536418
$300$	0.00905451			0.000522762
$301$	7.99176	−	13.8421i	0.460637	−	0.797847i
$302$	1.31352	+	2.27509i	0.0755848	+	0.130917i
$303$	40.4981			2.32656
$304$	−15.3419			−0.879920
$305$	−1.05655			−0.0604980
$306$	−9.73348	+	16.8589i	−0.556426	+	0.963759i
$307$	−18.7583			−1.07059			−0.535295	−	0.844665i	$-0.679800\pi$
$307$	−18.7583			−1.07059			−0.535295	+	0.844665i	$0.679800\pi$
$308$	6.07182	+	10.5167i	0.345974	+	0.599245i
$309$	7.40687			0.421362
$310$	−3.85729			−0.219079
$311$	−19.2973			−1.09425			−0.547125	−	0.837051i	$-0.684278\pi$
$311$	−19.2973			−1.09425			−0.547125	+	0.837051i	$0.684278\pi$
$312$	20.8456	+	36.1056i	1.18015	+	2.04408i
$313$	−14.7301	+	25.5133i	−0.832594	+	1.44210i	0.0633796	+	0.997989i	$0.479812\pi$
$313$	−14.7301	+	25.5133i	−0.832594	+	1.44210i	−0.895974	+	0.444106i	$0.853521\pi$
$314$	10.6175	−	18.3901i	0.599182	−	1.03781i
$315$	20.5478			1.15773
$316$	3.00185	−	5.19936i	0.168867	−	0.292487i
$317$	1.92751	−	3.33855i	0.108260	−	0.187512i	−0.806806	−	0.590817i	$-0.798805\pi$
$317$	1.92751	−	3.33855i	0.108260	−	0.187512i	0.915065	+	0.403306i	$0.132139\pi$
$318$	8.10690	−	14.0416i	0.454612	−	0.787412i
$319$	23.5409	+	40.7740i	1.31804	+	2.28291i
$320$	9.27893	−	16.0716i	0.518708	−	0.898429i
$321$	−42.5711			−2.37609
$322$	0.293911	+	0.509069i	0.0163790	+	0.0283693i
$323$	48.6734			2.70826
$324$	−3.53663	+	6.12562i	−0.196479	+	0.340312i
$325$	0.0137439	−	0.0238051i	0.000762372	−	0.00132047i
$326$	−4.48103	+	7.76137i	−0.248181	+	0.429862i
$327$	−0.650972	+	1.12752i	−0.0359989	+	0.0623519i
$328$	−15.4286	−	26.7231i	−0.851901	−	1.47554i
$329$	−7.42617			−0.409418
$330$	15.2212	+	26.3638i	0.837898	+	1.45128i
$331$	11.4361			0.628584			0.314292	−	0.949326i	$-0.398233\pi$
$331$	11.4361			0.628584			0.314292	+	0.949326i	$0.398233\pi$
$332$	−2.73581			−0.150147
$333$	−4.58504	−	7.94152i	−0.251259	−	0.435193i
$334$	−6.47075	−	11.2077i	−0.354064	−	0.613256i
$335$	12.8087			0.699812
$336$	7.35586	−	12.7407i	0.401295	−	0.695063i
$337$	5.79859	+	10.0435i	0.315870	+	0.547102i	0.979622	−	0.200850i	$-0.0643705\pi$
$337$	5.79859	+	10.0435i	0.315870	+	0.547102i	−0.663752	+	0.747952i	$0.731037\pi$
$338$	20.3279			1.10569
$339$	12.8514	−	22.2592i	0.697991	−	1.20896i
$340$	−5.13424	+	8.89276i	−0.278443	+	0.482277i
$341$	3.89476	+	6.74592i	0.210913	+	0.365312i
$342$	25.8947			1.40023
$343$	12.3682			0.667818
$344$	7.72509	+	13.3802i	0.416509	+	0.721414i
$345$	−0.450418	−	0.780147i	−0.0242497	−	0.0420017i
$346$	8.54742	+	14.8046i	0.459512	+	0.795899i
$347$	12.8419	+	22.2429i	0.689390	+	1.19406i	0.972035	+	0.234835i	$0.0754549\pi$
$347$	12.8419	+	22.2429i	0.689390	+	1.19406i	−0.282645	+	0.959225i	$0.591212\pi$
$348$	−8.61184	+	14.9162i	−0.461643	+	0.799590i
$349$	−2.22827	+	3.85948i	−0.119277	+	0.206593i	−0.919481	−	0.393134i	$-0.871391\pi$
$349$	−2.22827	+	3.85948i	−0.119277	+	0.206593i	0.800205	+	0.599727i	$0.204724\pi$
$350$	−0.0174199			−0.000931132
$351$	0.755625	+	1.30878i	0.0403323	+	0.0698576i
$352$	−20.2483			−1.07924
$353$	−32.1081			−1.70894			−0.854472	−	0.519498i	$-0.826119\pi$
$353$	−32.1081			−1.70894			−0.854472	+	0.519498i	$0.826119\pi$
$354$	6.97727	−	12.0850i	0.370838	−	0.642309i
$355$	−2.63927			−0.140078
$356$	2.30752	−	3.99674i	0.122298	−	0.211827i
$357$	−23.3370	+	40.4209i	−1.23513	+	2.13930i
$358$	−7.84013	−	13.5795i	−0.414364	−	0.717699i
$359$	−12.0022	−	20.7884i	−0.633450	−	1.09717i	−0.986841	−	0.161692i	$-0.948305\pi$
$359$	−12.0022	−	20.7884i	−0.633450	−	1.09717i	0.353391	−	0.935476i	$-0.385029\pi$
$360$	−9.93105	+	17.2011i	−0.523413	+	0.906577i
$361$	−22.8724	−	39.6161i	−1.20381	−	2.08506i
$362$	−29.4902			−1.54997
$363$	17.3915	−	30.1230i	0.912818	−	1.58105i
$364$	6.74320	+	11.6796i	0.353440	+	0.612176i
$365$	−9.49734			−0.497113
$366$	0.638398	−	1.10574i	0.0333696	−	0.0577979i
$367$	−8.90242	−	15.4194i	−0.464703	−	0.804889i	0.534485	−	0.845178i	$-0.320505\pi$
$367$	−8.90242	−	15.4194i	−0.464703	−	0.804889i	−0.999188	+	0.0402891i	$0.987172\pi$
$368$	−0.316387			−0.0164928
$369$	14.5001	+	25.1149i	0.754844	+	1.30743i
$370$	3.95621	+	6.85236i	0.205674	+	0.356237i
$371$	9.53468	−	16.5145i	0.495016	−	0.857393i
$372$	−1.42480	+	2.46783i	−0.0738725	+	0.127951i
$373$	11.0521	+	19.1428i	0.572257	+	0.991179i	0.996334	+	0.0855525i	$0.0272655\pi$
$373$	11.0521	+	19.1428i	0.572257	+	0.991179i	−0.424076	+	0.905627i	$0.639401\pi$
$374$	−33.9206			−1.75399
$375$	−27.1173			−1.40033
$376$	3.58919	−	6.21666i	0.185098	−	0.320600i
$377$	26.1439	+	45.2825i	1.34648	+	2.33217i
$378$	0.478865	−	0.829419i	0.0246302	−	0.0426607i
$379$	−11.3705	−	19.6943i	−0.584064	−	1.01163i	−0.994991	−	0.0999605i	$-0.968128\pi$
$379$	−11.3705	−	19.6943i	−0.584064	−	1.01163i	0.410927	−	0.911668i	$-0.365205\pi$
$380$	13.6590			0.700692
$381$	14.2980	−	24.7649i	0.732510	−	1.26874i
$382$	0.386497			0.0197749
$383$	−12.9935			−0.663937			−0.331968	−	0.943291i	$-0.607713\pi$
$383$	−12.9935			−0.663937			−0.331968	+	0.943291i	$0.607713\pi$
$384$	1.45107	+	2.51333i	0.0740498	+	0.128258i
$385$	17.9019	+	31.0070i	0.912365	+	1.58026i
$386$	−22.1039			−1.12506
$387$	−7.26018	−	12.5750i	−0.369056	−	0.639223i
$388$	3.60828	+	6.24972i	0.183183	+	0.317281i
$389$	−17.0162	−	29.4729i	−0.862754	−	1.49433i	−0.869260	−	0.494356i	$-0.835404\pi$
$389$	−17.0162	−	29.4729i	−0.862754	−	1.49433i	0.00650533	−	0.999979i	$-0.497929\pi$
$390$	16.9042	+	29.2790i	0.855978	+	1.48260i
$391$	1.00376			0.0507624
$392$	4.77972	−	8.27872i	0.241412	−	0.418139i
$393$	−16.7070			−0.842756
$394$	−1.71562	−	2.97154i	−0.0864317	−	0.149704i
$395$	8.85053	−	15.3296i	0.445319	−	0.771315i
$396$	11.0320			0.554379
$397$	−0.110568	+	0.191510i	−0.00554927	+	0.00961162i	−0.868787	−	0.495186i	$-0.835100\pi$
$397$	−0.110568	+	0.191510i	−0.00554927	+	0.00961162i	0.863237	+	0.504798i	$0.168433\pi$
$398$	22.5535			1.13051
$399$	62.0852			3.10815
$400$	0.00468801	−	0.00811987i	0.000234401	−	0.000405994i
$401$	5.61531	−	9.72600i	0.280415	−	0.485693i	−0.691072	−	0.722786i	$-0.742861\pi$
$401$	5.61531	−	9.72600i	0.280415	−	0.485693i	0.971487	+	0.237093i	$0.0761945\pi$
$402$	−7.73935	+	13.4049i	−0.386004	+	0.668578i
$403$	4.32542	+	7.49184i	0.215464	+	0.373195i
$404$	−6.33166	+	10.9668i	−0.315012	+	0.545617i
$405$	−10.4272	+	18.0605i	−0.518134	+	0.897434i
$406$	16.5682	−	28.6970i	0.822268	−	1.42421i
$407$	7.98929	−	13.8378i	0.396014	−	0.685917i
$408$	−22.5583	−	39.0721i	−1.11680	−	1.93436i
$409$	15.5701			0.769892			0.384946	−	0.922939i	$-0.374220\pi$
$409$	15.5701			0.769892			0.384946	+	0.922939i	$0.374220\pi$
$410$	−12.5114	−	21.6704i	−0.617895	−	1.07023i
$411$	6.85382	+	11.8712i	0.338074	+	0.585562i
$412$	−1.15802	+	2.00576i	−0.0570517	+	0.0988165i
$413$	8.20609	−	14.2134i	0.403795	−	0.699394i
$414$	0.534012			0.0262452
$415$	−8.06614			−0.395951
$416$	−22.4872			−1.10253
$417$	−9.81732	−	17.0041i	−0.480756	−	0.832694i
$418$	22.5604	+	39.0757i	1.10346	+	1.91126i
$419$	−5.28097	−	9.14692i	−0.257992	−	0.446856i	0.707712	−	0.706502i	$-0.249728\pi$
$419$	−5.28097	−	9.14692i	−0.257992	−	0.446856i	−0.965704	+	0.259645i	$0.916394\pi$
$420$	−6.54896	+	11.3431i	−0.319557	+	0.553489i
$421$	0.188113	−	0.325820i	0.00916804	−	0.0158795i	−0.861405	−	0.507919i	$-0.830415\pi$
$421$	0.188113	−	0.325820i	0.00916804	−	0.0158795i	0.870573	+	0.492039i	$0.163748\pi$
$422$	7.84820			0.382044
$423$	−3.37319	+	5.84253i	−0.164010	+	0.284074i
$424$	9.21652	+	15.9635i	0.447594	+	0.775255i
$425$	−0.0148731	+	0.0257609i	−0.000721449	+	0.00124959i
$426$	1.59472	−	2.76214i	0.0772644	−	0.133826i
$427$	0.750832	−	1.30048i	0.0363353	−	0.0629346i
$428$	6.65576	−	11.5281i	0.321718	−	0.557232i
$429$	34.1368	−	59.1267i	1.64814	−	2.85467i
$430$	6.26447	+	10.8504i	0.302099	+	0.523251i
$431$	3.69166	−	6.39414i	0.177821	−	0.307995i	−0.763313	−	0.646029i	$-0.776429\pi$
$431$	3.69166	−	6.39414i	0.177821	−	0.307995i	0.941134	+	0.338034i	$0.109762\pi$
$432$	0.257743	+	0.446424i	0.0124007	+	0.0214786i
$433$	3.71980			0.178762			0.0893811	−	0.995997i	$-0.471511\pi$
$433$	3.71980			0.178762			0.0893811	+	0.995997i	$0.471511\pi$
$434$	2.74116	−	4.74783i	0.131580	−	0.227903i
$435$	−25.3908	+	43.9782i	−1.21740	+	2.10859i
$436$	−0.203552	−	0.352562i	−0.00974837	−	0.0168847i
$437$	−0.667596	−	1.15631i	−0.0319355	−	0.0553138i
$438$	5.73856	−	9.93947i	0.274199	−	0.474926i
$439$	2.27784	−	3.94534i	0.108715	−	0.188301i	−0.806535	−	0.591187i	$-0.798660\pi$
$439$	2.27784	−	3.94534i	0.108715	−	0.188301i	0.915250	+	0.402886i	$0.131993\pi$
$440$	−34.6091			−1.64992
$441$	−4.49207	+	7.78050i	−0.213908	+	0.370500i
$442$	−37.6713			−1.79184
$443$	4.69514	+	8.13223i	0.223073	+	0.386374i	0.955740	−	0.294214i	$-0.0950578\pi$
$443$	4.69514	+	8.13223i	0.223073	+	0.386374i	−0.732667	+	0.680588i	$0.761725\pi$
$444$	5.84536			0.277409
$445$	6.80340	−	11.7838i	0.322512	−	0.558607i
$446$	12.6835			0.600579
$447$	−14.5772			−0.689478
$448$	13.1880	+	22.8423i	0.623076	+	1.07920i
$449$	40.9017			1.93027			0.965135	−	0.261751i	$-0.0843001\pi$
$449$	40.9017			1.93027			0.965135	+	0.261751i	$0.0843001\pi$
$450$	−0.00791262	+	0.0137051i	−0.000373005	+	0.000646063i
$451$	−25.2659	+	43.7618i	−1.18973	+	2.06066i
$452$	4.01848	+	6.96022i	0.189014	+	0.327381i
$453$	5.72202			0.268844
$454$	−27.3985			−1.28587
$455$	19.8814	+	34.4355i	0.932053	+	1.61436i
$456$	−30.0068	+	51.9733i	−1.40520	+	2.43387i
$457$	19.3583			0.905541			0.452771	−	0.891627i	$-0.350436\pi$
$457$	19.3583			0.905541			0.452771	+	0.891627i	$0.350436\pi$
$458$	−11.4340			−0.534274
$459$	−0.817708	−	1.41631i	−0.0381673	−	0.0661078i
$460$	0.281681			0.0131335
$461$	5.04173	−	8.73253i	0.234817	−	0.406714i	−0.724403	−	0.689377i	$-0.757884\pi$
$461$	5.04173	−	8.73253i	0.234817	−	0.406714i	0.959219	+	0.282663i	$0.0912177\pi$
$462$	−43.2673			−2.01298
$463$	−21.1847			−0.984539			−0.492269	−	0.870443i	$-0.663832\pi$
$463$	−21.1847			−0.984539			−0.492269	+	0.870443i	$0.663832\pi$
$464$	8.91764	+	15.4458i	0.413991	+	0.717053i
$465$	−4.20082	+	7.27604i	−0.194809	+	0.337418i
$466$	−15.6687			−0.725838
$467$	11.8439			0.548071			0.274035	−	0.961720i	$-0.411641\pi$
$467$	11.8439			0.548071			0.274035	+	0.961720i	$0.411641\pi$
$468$	12.2518			0.566341
$469$	−9.10239	+	15.7658i	−0.420309	+	0.727997i
$470$	2.91056	−	5.04124i	0.134254	−	0.232535i
$471$	−23.1263	−	40.0559i	−1.06560	−	1.84568i
$472$	7.93227	+	13.7391i	0.365112	+	0.632393i
$473$	12.6506	−	21.9115i	0.581677	−	1.00749i
$474$	10.6955	+	18.5251i	0.491260	+	0.850887i
$475$	0.0395679			0.00181550
$476$	−7.29722	−	12.6392i	−0.334468	−	0.579315i
$477$	−8.66186	−	15.0028i	−0.396599	−	0.686930i
$478$	−12.9619	+	22.4506i	−0.592863	+	1.02687i
$479$	−26.7810			−1.22365			−0.611827	−	0.790991i	$-0.709565\pi$
$479$	−26.7810			−1.22365			−0.611827	+	0.790991i	$0.709565\pi$
$480$	−10.9197	−	18.9135i	−0.498415	−	0.863281i
$481$	8.87269	−	15.3679i	0.404560	−	0.700718i
$482$	−13.4137			−0.610975
$483$	1.28035			0.0582578
$484$	5.43814	+	9.41913i	0.247188	+	0.428142i
$485$	10.6385	+	18.4264i	0.483069	+	0.836700i
$486$	−12.1491	−	21.0428i	−0.551092	−	0.954520i
$487$	−6.75170	−	11.6943i	−0.305949	−	0.529919i	0.671523	−	0.740984i	$-0.265640\pi$
$487$	−6.75170	−	11.6943i	−0.305949	−	0.529919i	−0.977472	+	0.211064i	$0.932307\pi$
$488$	0.725778	+	1.25708i	0.0328544	+	0.0569056i
$489$	9.76022	+	16.9052i	0.441372	+	0.764479i
$490$	3.87600	−	6.71343i	0.175100	−	0.303282i
$491$	−20.7483	−	35.9371i	−0.936358	−	1.62182i	−0.772195	−	0.635386i	$-0.780841\pi$
$491$	−20.7483	−	35.9371i	−0.936358	−	1.62182i	−0.164163	−	0.986433i	$-0.552492\pi$
$492$	−18.4858			−0.833404
$493$	−28.2919	−	49.0029i	−1.27420	−	2.20698i
$494$	25.0549	+	43.3964i	1.12728	+	1.95250i
$495$	32.5263			1.46195
$496$	1.47539	+	2.55546i	0.0662471	+	0.114743i
$497$	1.87558	−	3.24860i	0.0841312	−	0.145720i
$498$	4.87379	−	8.44165i	0.218400	−	0.378279i
$499$	20.0219	+	34.6789i	0.896303	+	1.55244i	0.832184	+	0.554500i	$0.187090\pi$
$499$	20.0219	+	34.6789i	0.896303	+	1.55244i	0.0641191	+	0.997942i	$0.479576\pi$
$500$	4.23964	−	7.34328i	0.189603	−	0.328401i
$501$	−28.1882			−1.25935
$502$	10.8546	−	18.8008i	0.484466	−	0.839119i
$503$	−16.2488			−0.724496			−0.362248	−	0.932082i	$-0.617991\pi$
$503$	−16.2488			−0.724496			−0.362248	+	0.932082i	$0.617991\pi$
$504$	−14.1149	−	24.4477i	−0.628727	−	1.08899i
$505$	−18.6680	+	32.3339i	−0.830715	+	1.43884i
$506$	0.465249	+	0.805835i	0.0206828	+	0.0358237i
$507$	22.1383	−	38.3446i	0.983196	−	1.70295i
$508$	4.47083	+	7.74371i	0.198361	+	0.343572i
$509$	−24.0709			−1.06692			−0.533462	−	0.845824i	$-0.679109\pi$
$509$	−24.0709			−1.06692			−0.533462	+	0.845824i	$0.679109\pi$
$510$	−18.2931	−	31.6845i	−0.810031	−	1.40302i
$511$	6.74922	−	11.6900i	0.298568	−	0.517135i
$512$	−19.3909			−0.856966
$513$	−1.08771	+	1.88396i	−0.0480234	+	0.0831789i
$514$	6.72978	+	11.6563i	0.296838	+	0.514138i
$515$	−3.41427	+	5.91368i	−0.150451	+	0.260588i
$516$	9.25584			0.407466
$517$	−11.7553			−0.516999
$518$	−11.2458			−0.494114
$519$	37.2346			1.63442
$520$	−38.4359			−1.68553
$521$	0.614158	−	1.06375i	0.0269067	−	0.0466038i	−0.852258	−	0.523121i	$-0.824768\pi$
$521$	0.614158	−	1.06375i	0.0269067	−	0.0466038i	0.879165	+	0.476517i	$0.158101\pi$
$522$	−15.0516	−	26.0701i	−0.658789	−	1.14106i
$523$	−35.2668			−1.54211			−0.771054	−	0.636770i	$-0.780270\pi$
$523$	−35.2668			−1.54211			−0.771054	+	0.636770i	$0.780270\pi$
$524$	2.61205	−	4.52420i	0.114108	−	0.197641i
$525$	−0.0189713	+	0.0328593i	−0.000827975	+	0.00143410i
$526$	7.23497	+	12.5313i	0.315460	+	0.546392i
$527$	−4.68079	−	8.10737i	−0.203899	−	0.353163i
$528$	11.6440	−	20.1681i	0.506741	−	0.877702i
$529$	11.4862	+	19.8947i	0.499401	+	0.864989i
$530$	7.47391	+	12.9452i	0.324646	+	0.562303i
$531$	−7.45490	−	12.9123i	−0.323515	−	0.560344i
$532$	−9.70668	+	16.8125i	−0.420838	+	0.728913i
$533$	−28.0596	+	48.6007i	−1.21540	+	2.10513i
$534$	8.22161	+	14.2402i	0.355784	+	0.616235i
$535$	19.6236	−	33.9890i	0.848401	−	1.46947i
$536$	−8.79866	−	15.2397i	−0.380044	−	0.658256i
$537$	−34.1535			−1.47383
$538$	15.1445			0.652924
$539$	−15.6546			−0.674291
$540$	−0.229470	−	0.397454i	−0.00987481	−	0.0171037i
$541$	−9.65631	−	16.7252i	−0.415157	−	0.719074i	0.580288	−	0.814412i	$-0.302940\pi$
$541$	−9.65631	−	16.7252i	−0.415157	−	0.719074i	−0.995445	+	0.0953379i	$0.969607\pi$
$542$	4.65541	−	8.06340i	0.199967	−	0.346353i
$543$	−32.1166	+	55.6276i	−1.37826	+	2.38721i
$544$	24.3348			1.04334
$545$	−0.600144	−	1.03948i	−0.0257073	−	0.0445264i
$546$	−48.0515			−2.05641
$547$	22.3964	−	6.73820i	0.957599	−	0.288105i
$547$	22.3964	−	6.73820i	0.957599	−	0.288105i
$548$	−4.28623			−0.183099
$549$	−0.682100	−	1.18143i	−0.0291113	−	0.0504223i
$550$	−0.0275750			−0.00117580
$551$	−37.6335	+	65.1831i	−1.60324	+	2.77690i
$552$	−0.618812	+	1.07181i	−0.0263384	+	0.0456194i
$553$	12.5792	+	21.7877i	0.534920	+	0.926508i
$554$	−9.43053	−	16.3342i	−0.400665	−	0.693972i
$555$	17.2342			0.731552
$556$	6.13953			0.260374
$557$	−6.11257			−0.258998			−0.129499	−	0.991580i	$-0.541337\pi$
$557$	−6.11257			−0.258998			−0.129499	+	0.991580i	$0.541337\pi$
$558$	−2.49023	−	4.31321i	−0.105420	−	0.182593i
$559$	14.0495	−	24.3344i	0.594229	−	1.02923i
$560$	6.78151	+	11.7459i	0.286571	+	0.496356i
$561$	−36.9415	+	63.9846i	−1.55967	+	2.70143i
$562$	−0.0901035	+	0.156064i	−0.00380079	+	0.00658316i
$563$	0.829695	+	1.43707i	0.0349675	+	0.0605654i	0.882980	−	0.469412i	$-0.155534\pi$
$563$	0.829695	+	1.43707i	0.0349675	+	0.0605654i	−0.848012	+	0.529977i	$0.822201\pi$
$564$	−2.15020	−	3.72425i	−0.0905397	−	0.156819i
$565$	11.8479	+	20.5212i	0.498446	+	0.863334i
$566$	−16.3415	+	28.3043i	−0.686884	+	1.18972i
$567$	−14.8201	−	25.6692i	−0.622386	−	1.07800i
$568$	1.81299	+	3.14020i	0.0760716	+	0.131760i
$569$	2.80703	−	4.86192i	0.117677	−	0.203822i	−0.801170	−	0.598437i	$-0.795789\pi$
$569$	2.80703	−	4.86192i	0.117677	−	0.203822i	0.918847	+	0.394615i	$0.129122\pi$
$570$	−24.3332	+	42.1464i	−1.01921	+	1.76532i
$571$	23.3253			0.976133			0.488067	−	0.872806i	$-0.337702\pi$
$571$	23.3253			0.976133			0.488067	+	0.872806i	$0.337702\pi$
$572$	10.6742	+	18.4883i	0.446311	+	0.773034i
$573$	0.420918	−	0.729052i	0.0175841	−	0.0304566i
$574$	35.5647			1.48444
$575$	0.000815986	0		3.40290e−5	0
$576$	23.9616			0.998398
$577$	33.4483			1.39247			0.696236	−	0.717813i	$-0.254857\pi$
$577$	33.4483			1.39247			0.696236	+	0.717813i	$0.254857\pi$
$578$	21.8267			0.907870
$579$	−24.0725	+	41.6947i	−1.00042	+	1.73277i
$580$	−7.93943	−	13.7515i	−0.329667	−	0.570999i
$581$	5.73215	−	9.92838i	0.237810	−	0.411899i
$582$	−25.7123			−1.06581
$583$	15.0930	−	26.1419i	0.625089	−	1.08269i
$584$	6.52401	+	11.2999i	0.269966	+	0.467594i
$585$	36.1228			1.49349
$586$	−4.91885	−	8.51969i	−0.203196	−	0.351945i
$587$	19.3702	−	33.5501i	0.799493	−	1.38476i	−0.120454	−	0.992719i	$-0.538435\pi$
$587$	19.3702	−	33.5501i	0.799493	−	1.38476i	0.919947	−	0.392043i	$-0.128232\pi$
$588$	−2.86342	−	4.95959i	−0.118085	−	0.204530i
$589$	−6.22634	+	10.7843i	−0.256552	+	0.444361i
$590$	6.43248	+	11.1414i	0.264821	+	0.458683i
$591$	−7.47366			−0.307425
$592$	3.02646	−	5.24198i	0.124387	−	0.215444i
$593$	−12.8413			−0.527330			−0.263665	−	0.964614i	$-0.584931\pi$
$593$	−12.8413			−0.527330			−0.263665	+	0.964614i	$0.584931\pi$
$594$	0.758024	−	1.31294i	0.0311021	−	0.0538704i
$595$	−21.5148	−	37.2648i	−0.882022	−	1.52771i
$596$	2.27907	−	3.94746i	0.0933542	−	0.161694i
$597$	24.5622	−	42.5429i	1.00526	−	1.74117i
$598$	0.516693	+	0.894939i	0.0211292	+	0.0365968i
$599$	10.5691			0.431844			0.215922	−	0.976411i	$-0.430724\pi$
$599$	10.5691			0.431844			0.215922	+	0.976411i	$0.430724\pi$
$600$	−0.0183383	−	0.0317628i	−0.000748656	−	0.00129671i
$601$	4.75497	+	8.23584i	0.193959	+	0.335947i	0.946559	−	0.322531i	$-0.104534\pi$
$601$	4.75497	+	8.23584i	0.193959	+	0.335947i	−0.752600	+	0.658478i	$0.771200\pi$
$602$	−17.8072			−0.725768
$603$	8.26915	+	14.3226i	0.336746	+	0.583261i
$604$	−0.894607	+	1.54951i	−0.0364011	+	0.0630485i
$605$	16.0336	+	27.7710i	0.651858	+	1.12905i
$606$	−22.5595	−	39.0741i	−0.916415	−	1.58728i
$607$	−9.06609	−	15.7029i	−0.367981	−	0.637362i	0.621269	−	0.783598i	$-0.286618\pi$
$607$	−9.06609	−	15.7029i	−0.367981	−	0.637362i	−0.989250	+	0.146236i	$0.953284\pi$
$608$	−16.1849	−	28.0331i	−0.656385	−	1.13689i
$609$	−36.0876	−	62.5056i	−1.46234	−	2.53285i
$610$	0.588552	+	1.01940i	0.0238298	+	0.0412744i
$611$	−13.0552			−0.528155
$612$	−13.2585			−0.535941
$613$	17.5138	−	30.3348i	0.707377	−	1.22521i	−0.258450	−	0.966025i	$-0.583212\pi$
$613$	17.5138	−	30.3348i	0.707377	−	1.22521i	0.965827	−	0.259188i	$-0.0834549\pi$
$614$	10.4493	+	18.0987i	0.421699	+	0.730403i
$615$	−54.5028			−2.19776
$616$	24.5947	−	42.5993i	0.990950	−	1.71638i
$617$	11.3520	+	19.6623i	0.457015	+	0.791573i	0.998802	−	0.0489431i	$-0.0155853\pi$
$617$	11.3520	+	19.6623i	0.457015	+	0.791573i	−0.541787	+	0.840516i	$0.682252\pi$
$618$	−4.12599	−	7.14643i	−0.165972	−	0.287471i
$619$	−45.5626			−1.83132			−0.915659	−	0.401957i	$-0.868330\pi$
$619$	−45.5626			−1.83132			−0.915659	+	0.401957i	$0.868330\pi$
$620$	−1.31355	−	2.27514i	−0.0527535	−	0.0913717i
$621$	−0.0224311	+	0.0388518i	−0.000900129	+	0.00155907i
$622$	10.7496	+	18.6188i	0.431018	+	0.746545i
$623$	9.66958	+	16.7482i	0.387404	+	0.671003i
$624$	12.9315	−	22.3981i	0.517676	−	0.896641i
$625$	12.5123	−	21.6719i	0.500491	−	0.866876i
$626$	32.8216			1.31181
$627$	98.2784			3.92486
$628$	14.4627			0.577123
$629$	−9.60167	+	16.6306i	−0.382844	+	0.663105i
$630$	−11.4461	−	19.8252i	−0.456024	−	0.789857i
$631$	−1.58883			−0.0632503			−0.0316252	−	0.999500i	$-0.510068\pi$
$631$	−1.58883			−0.0632503			−0.0316252	+	0.999500i	$0.510068\pi$
$632$	−24.3188			−0.967350
$633$	8.54716	−	14.8041i	0.339719	−	0.588411i
$634$	−4.29488			−0.170571
$635$	13.1816	+	22.8312i	0.523097	+	0.906030i
$636$	11.0428			0.437876
$637$	−17.3856			−0.688841
$638$	26.2269	−	45.4263i	1.03833	−	1.79844i
$639$	−1.70389	−	2.95122i	−0.0674047	−	0.116748i
$640$	−2.67555			−0.105760
$641$	−44.4239			−1.75464			−0.877318	−	0.479909i	$-0.840670\pi$
$641$	−44.4239			−1.75464			−0.877318	+	0.479909i	$0.840670\pi$
$642$	23.7142	+	41.0742i	0.935925	+	1.62107i
$643$	2.07904	−	3.60100i	0.0819894	−	0.142010i	−0.822115	−	0.569321i	$-0.807206\pi$
$643$	2.07904	−	3.60100i	0.0819894	−	0.142010i	0.904104	+	0.427312i	$0.140539\pi$
$644$	−0.200175	+	0.346714i	−0.00788801	+	0.0136624i
$645$	27.2895			1.07452
$646$	−27.1135	−	46.9619i	−1.06677	−	1.84769i
$647$	−21.2049			−0.833652			−0.416826	−	0.908986i	$-0.636858\pi$
$647$	−21.2049			−0.833652			−0.416826	+	0.908986i	$0.636858\pi$
$648$	28.6512			1.12552
$649$	12.9899	−	22.4992i	0.509899	−	0.883171i
$650$	−0.0306240			−0.00120117
$651$	−5.97058	−	10.3413i	−0.234005	−	0.405309i
$652$	−6.10383			−0.239044
$653$	15.8964	−	27.5334i	0.622074	−	1.07746i	−0.367024	−	0.930211i	$-0.619623\pi$
$653$	15.8964	−	27.5334i	0.622074	−	1.07746i	0.989099	−	0.147253i	$-0.0470432\pi$
$654$	1.45050			0.0567188
$655$	7.70125	−	13.3390i	0.300913	−	0.521196i
$656$	−9.57110	+	16.5776i	−0.373689	+	0.647248i
$657$	−6.13139	−	10.6199i	−0.239208	−	0.414321i
$658$	4.13675	+	7.16505i	0.161267	+	0.279323i
$659$	−0.480293	+	0.831892i	−0.0187096	+	0.0324059i	−0.875229	−	0.483710i	$-0.839289\pi$
$659$	−0.480293	+	0.831892i	−0.0187096	+	0.0324059i	0.856519	+	0.516115i	$0.172622\pi$
$660$	−10.3667	+	17.9557i	−0.403525	+	0.698926i
$661$	30.4387			1.18393			0.591965	−	0.805964i	$-0.298352\pi$
$661$	30.4387			1.18393			0.591965	+	0.805964i	$0.298352\pi$
$662$	−6.37046	−	11.0340i	−0.247595	−	0.428847i
$663$	−41.0263	+	71.0596i	−1.59333	+	2.75973i
$664$	5.54088	+	9.59709i	0.215028	+	0.372439i
$665$	−28.6188	+	49.5692i	−1.10979	+	1.92221i
$666$	−5.10819	+	8.84764i	−0.197938	+	0.342839i
$667$	−0.776093	+	1.34423i	−0.0300505	+	0.0520489i
$668$	4.40706	−	7.63326i	0.170514	−	0.295340i
$669$	13.8130	−	23.9249i	0.534043	−	0.924990i
$670$	−7.13506	−	12.3583i	−0.275651	−	0.477442i
$671$	1.18854	−	2.05861i	0.0458830	−	0.0794717i
$672$	31.0402			1.19740
$673$	11.9750	−	20.7413i	0.461601	−	0.799517i	−0.537440	−	0.843302i	$-0.680608\pi$
$673$	11.9750	−	20.7413i	0.461601	−	0.799517i	0.999041	+	0.0437851i	$0.0139417\pi$
$674$	6.46021	−	11.1894i	0.248838	−	0.431000i
$675$	−0.000664738	−	0.00115136i	−2.55858e−5	−	4.43158e-5i
$676$	6.92240	+	11.9899i	0.266246	+	0.461152i
$677$	−2.56935	−	4.45024i	−0.0987480	−	0.171037i	0.812419	−	0.583075i	$-0.198150\pi$
$677$	−2.56935	−	4.45024i	−0.0987480	−	0.171037i	−0.911167	+	0.412038i	$0.864817\pi$
$678$	−28.6354			−1.09974
$679$	−30.2407			−1.16053
$680$	41.5938			1.59505
$681$	−29.8386	+	51.6819i	−1.14342	+	1.98046i
$682$	4.33915	−	7.51562i	0.166155	−	0.287788i
$683$	−22.7904	−	39.4741i	−0.872050	−	1.51043i	−0.859872	−	0.510509i	$-0.829457\pi$
$683$	−22.7904	−	39.4741i	−0.872050	−	1.51043i	−0.0121774	−	0.999926i	$-0.503876\pi$
$684$	8.81812	+	15.2734i	0.337169	+	0.583994i
$685$	−12.6373			−0.482848
$686$	−6.88968	−	11.9333i	−0.263049	−	0.455614i
$687$	−12.4523	+	21.5680i	−0.475084	+	0.822870i
$688$	4.79225	−	8.30042i	0.182703	−	0.316451i
$689$	16.7619	−	29.0325i	0.638577	−	1.10605i
$690$	−0.501810	+	0.869160i	−0.0191036	+	0.0330884i
$691$	−10.3258	−	17.8848i	−0.392811	−	0.680368i	0.600008	−	0.799994i	$-0.295164\pi$
$691$	−10.3258	−	17.8848i	−0.392811	−	0.680368i	−0.992819	+	0.119626i	$0.961831\pi$
$692$	−5.82143	+	10.0830i	−0.221298	+	0.383299i
$693$	−23.1146	+	40.0356i	−0.878051	+	1.52083i
$694$	14.3072	−	24.7807i	0.543093	−	0.940664i
$695$	18.1015			0.686631
$696$	69.7669			2.64451
$697$	30.3650	−	52.5938i	1.15016	−	1.99213i
$698$	4.96503			0.187929
$699$	−17.0641	+	29.5560i	−0.645425	+	1.11791i
$700$	−0.00593212	−	0.0102747i	−0.000224213	−	0.000388348i
$701$	32.2878			1.21949			0.609746	−	0.792597i	$-0.291271\pi$
$701$	32.2878			1.21949			0.609746	+	0.792597i	$0.291271\pi$
$702$	0.841841	−	1.45811i	0.0317733	−	0.0550329i
$703$	25.5441			0.963413
$704$	20.8761	+	36.1585i	0.786799	+	1.36277i
$705$	−6.33956	−	10.9804i	−0.238761	−	0.413547i
$706$	17.8858	+	30.9791i	0.673142	+	1.16592i
$707$	−26.5326	−	45.9558i	−0.997861	−	1.72835i
$708$	9.50408			0.357185
$709$	−2.32818	−	4.03252i	−0.0874366	−	0.151445i	0.818990	−	0.573807i	$-0.194534\pi$
$709$	−2.32818	−	4.03252i	−0.0874366	−	0.151445i	−0.906427	+	0.422363i	$0.861201\pi$
$710$	1.47020	+	2.54647i	0.0551757	+	0.0955672i
$711$	22.8553			0.857140
$712$	−18.6939			−0.700582
$713$	−0.128402	+	0.222399i	−0.00480869	+	0.00832890i
$714$	51.9994			1.94603
$715$	31.4714	+	54.5101i	1.17696	+	2.03856i
$716$	5.33971	−	9.24865i	0.199554	−	0.345638i
$717$	28.2325	+	48.9002i	1.05436	+	1.82621i
$718$	−13.3716	+	23.1603i	−0.499024	+	0.864334i
$719$	−46.8533			−1.74733			−0.873667	−	0.486525i	$-0.838264\pi$
$719$	−46.8533			−1.74733			−0.873667	+	0.486525i	$0.838264\pi$
$720$	12.3214			0.459193
$721$	−4.85266	−	8.40505i	−0.180722	−	0.313020i
$722$	−25.4821	+	44.1363i	−0.948345	+	1.64258i
$723$	−14.6083	+	25.3023i	−0.543288	+	0.941002i
$724$	−10.0425	−	17.3941i	−0.373227	−	0.646448i
$725$	−0.0229992	−	0.0398359i	−0.000854170	−	0.00147947i
$726$	−38.7517			−1.43821
$727$	2.02353	+	3.50486i	0.0750487	+	0.129988i	0.901107	−	0.433596i	$-0.142755\pi$
$727$	2.02353	+	3.50486i	0.0750487	+	0.129988i	−0.826059	+	0.563584i	$0.809422\pi$
$728$	27.3142	−	47.3097i	1.01233	−	1.75341i
$729$	−24.9587			−0.924397
$730$	5.29049	+	9.16339i	0.195810	+	0.339152i
$731$	−15.2038	+	26.3337i	−0.562331	+	0.973987i
$732$	0.869594			0.0321411
$733$	−0.0672321	−	0.116449i	−0.00248327	−	0.00430116i	0.864781	−	0.502149i	$-0.167457\pi$
$733$	−0.0672321	−	0.116449i	−0.00248327	−	0.00430116i	−0.867264	+	0.497848i	$0.834124\pi$
$734$	−9.91818	+	17.1788i	−0.366087	+	0.634081i
$735$	−8.44239	−	14.6226i	−0.311402	−	0.539365i
$736$	−0.333772	−	0.578110i	−0.0123030	−	0.0213094i
$737$	−14.4087	+	24.9566i	−0.530752	+	0.919290i
$738$	16.1545	−	27.9804i	0.594656	−	1.02997i
$739$	28.8392			1.06087			0.530434	−	0.847726i	$-0.322029\pi$
$739$	28.8392			1.06087			0.530434	+	0.847726i	$0.322029\pi$
$740$	−2.69448	+	4.66697i	−0.0990509	+	0.171561i
$741$	109.145			4.00956
$742$	−21.2451			−0.779934
$743$	25.2407	+	43.7182i	0.925993	+	1.60387i	0.789957	+	0.613163i	$0.210103\pi$
$743$	25.2407	+	43.7182i	0.925993	+	1.60387i	0.136036	+	0.990704i	$0.456564\pi$
$744$	11.5427			0.423176
$745$	6.71950	−	11.6385i	0.246184	−	0.426403i
$746$	12.3132	−	21.3270i	0.450817	−	0.780838i
$747$	−5.20742	−	9.01952i	−0.190530	−	0.330007i
$748$	−11.5512	−	20.0073i	−0.422354	−	0.731539i
$749$	27.8907	+	48.3082i	1.01910	+	1.76514i
$750$	15.1057	+	26.1638i	0.551582	+	0.955367i
$751$	−1.23050			−0.0449014			−0.0224507	−	0.999748i	$-0.507147\pi$
$751$	−1.23050			−0.0449014			−0.0224507	+	0.999748i	$0.507147\pi$
$752$	−4.45310			−0.162388
$753$	−23.6427	−	40.9503i	−0.861587	−	1.49231i
$754$	29.1268	−	50.4492i	1.06074	−	1.83725i
$755$	−2.63762	+	4.56850i	−0.0959929	+	0.166265i
$756$	0.652285			0.0237234
$757$	−12.4767	−	21.6103i	−0.453473	−	0.785439i	0.545126	−	0.838354i	$-0.316482\pi$
$757$	−12.4767	−	21.6103i	−0.453473	−	0.785439i	−0.998599	+	0.0529153i	$0.983149\pi$
$758$	−12.6679	+	21.9414i	−0.460118	+	0.796948i
$759$	2.02674			0.0735659
$760$	−27.6638	−	47.9151i	−1.00347	−	1.73806i
$761$	2.43149	+	4.21147i	0.0881416	+	0.152666i	0.906726	−	0.421721i	$-0.138574\pi$
$761$	2.43149	+	4.21147i	0.0881416	+	0.152666i	−0.818584	+	0.574387i	$0.805241\pi$
$762$	−31.8588			−1.15412
$763$	1.70595			0.0617597
$764$	0.131617	+	0.227967i	0.00476172	+	0.00824754i
$765$	−39.0907			−1.41333
$766$	7.23802	+	12.5366i	0.261520	+	0.452966i
$767$	14.4263	−	24.9870i	0.520902	−	0.902228i
$768$	−18.5130	+	32.0654i	−0.668029	+	1.15706i
$769$	7.66765	−	13.2808i	0.276502	−	0.478916i	−0.694011	−	0.719965i	$-0.744158\pi$
$769$	7.66765	−	13.2808i	0.276502	−	0.478916i	0.970513	+	0.241048i	$0.0774913\pi$
$770$	19.9445	−	34.5449i	0.718749	−	1.24491i
$771$	29.3165			1.05581
$772$	−7.52719	−	13.0375i	−0.270910	−	0.469229i
$773$	−35.8488			−1.28939			−0.644696	−	0.764439i	$-0.723016\pi$
$773$	−35.8488			−1.28939			−0.644696	+	0.764439i	$0.723016\pi$
$774$	−8.08856	+	14.0098i	−0.290737	+	0.503572i
$775$	−0.00380515	−	0.00659071i	−0.000136685	−	0.000236745i
$776$	14.6158	−	25.3153i	0.524677	−	0.908767i
$777$	−12.2474	+	21.2131i	−0.439373	+	0.761016i
$778$	−18.9577	+	32.8357i	−0.679666	+	1.17722i
$779$	−80.7824			−2.89433
$780$	−11.5130	+	19.9412i	−0.412233	+	0.714008i
$781$	2.96897	−	5.14240i	0.106238	−	0.184010i
$782$	−0.559145	−	0.968467i	−0.0199950	−	0.0346323i
$783$	2.52896			0.0903776
$784$	−5.93019			−0.211793
$785$	42.6411			1.52193
$786$	9.30662	+	16.1195i	0.331956	+	0.574965i
$787$	36.3675			1.29636			0.648180	−	0.761487i	$-0.275530\pi$
$787$	36.3675			1.29636			0.648180	+	0.761487i	$0.275530\pi$
$788$	1.16847	−	2.02384i	0.0416249	−	0.0720964i
$789$	31.5173			1.12204
$790$	−19.7207			−0.701632
$791$	−33.6786			−1.19747
$792$	−22.3433	−	38.6997i	−0.793935	−	1.37513i
$793$	1.31996	−	2.28623i	0.0468731	−	0.0811865i
$794$	0.246368			0.00874329
$795$	32.5581			1.15472
$796$	7.68032	+	13.3027i	0.272222	+	0.471502i
$797$	−1.02112	−	1.76863i	−0.0361699	−	0.0626481i	0.847374	−	0.530997i	$-0.178182\pi$
$797$	−1.02112	−	1.76863i	−0.0361699	−	0.0626481i	−0.883544	+	0.468349i	$0.844849\pi$
$798$	−34.5845	−	59.9022i	−1.22428	−	2.12051i
$799$	14.1278			0.499805
$800$	0.0197824			0.000699414
$801$	17.5688			0.620764
$802$	−12.5120			−0.441815
$803$	10.6838	−	18.5048i	0.377021	−	0.653020i
$804$	−10.5421			−0.371793
$805$	−0.590188	+	1.02224i	−0.0208014	+	0.0360291i
$806$	4.81894	−	8.34665i	0.169740	−	0.293998i
$807$	16.4932	−	28.5671i	0.580589	−	1.00561i
$808$	51.2945			1.80453
$809$	10.3725	+	17.9657i	0.364677	+	0.631639i	0.988724	−	0.149747i	$-0.0478460\pi$
$809$	10.3725	+	17.9657i	0.364677	+	0.631639i	−0.624047	+	0.781387i	$0.714513\pi$
$810$	23.2339			0.816358
$811$	12.4921	+	21.6369i	0.438656	+	0.759774i	0.997586	−	0.0694403i	$-0.0221213\pi$
$811$	12.4921	+	21.6369i	0.438656	+	0.759774i	−0.558930	+	0.829215i	$0.688788\pi$
$812$	22.5684			0.791996
$813$	−10.1400	−	17.5631i	−0.355627	−	0.615963i
$814$	−17.8017			−0.623949
$815$	−17.9963			−0.630382
$816$	−13.9940	+	24.2383i	−0.489888	+	0.848511i
$817$	40.4477			1.41509
$818$	−8.67332	−	15.0226i	−0.303255	−	0.525254i
$819$	−25.6704	+	44.4625i	−0.896998	+	1.55365i
$820$	8.52121	−	14.7592i	0.297574	−	0.515413i
$821$	−3.63533	+	6.29658i	−0.126874	+	0.219752i	−0.922464	−	0.386083i	$-0.873828\pi$
$821$	−3.63533	+	6.29658i	−0.126874	+	0.219752i	0.795590	+	0.605835i	$0.207161\pi$
$822$	7.63584	−	13.2257i	0.266330	−	0.461298i
$823$	18.2134	+	31.5465i	0.634879	+	1.09964i	0.986541	+	0.163515i	$0.0522833\pi$
$823$	18.2134	+	31.5465i	0.634879	+	1.09964i	−0.351662	+	0.936127i	$0.614383\pi$
$824$	9.38146			0.326819
$825$	−0.0300308	+	0.0520149i	−0.00104554	+	0.00181093i
$826$	−18.2848			−0.636209
$827$	26.8134			0.932394			0.466197	−	0.884681i	$-0.345624\pi$
$827$	26.8134			0.932394			0.466197	+	0.884681i	$0.345624\pi$
$828$	0.181851	+	0.314975i	0.00631975	+	0.0109461i
$829$	4.91229			0.170611			0.0853054	−	0.996355i	$-0.472813\pi$
$829$	4.91229			0.170611			0.0853054	+	0.996355i	$0.472813\pi$
$830$	4.49324	+	7.78252i	0.155963	+	0.270135i
$831$	−41.0817			−1.42511
$832$	23.1845	+	40.1567i	0.803776	+	1.39218i
$833$	18.8140			0.651866
$834$	−10.9375	+	18.9442i	−0.378733	+	0.655985i
$835$	12.9936	−	22.5056i	0.449662	−	0.778838i
$836$	−15.3653	+	26.6135i	−0.531420	+	0.920446i
$837$	0.418408			0.0144623
$838$	−5.88353	+	10.1906i	−0.203243	+	0.352027i
$839$	−37.3711			−1.29019			−0.645096	−	0.764101i	$-0.723183\pi$
$839$	−37.3711			−1.29019			−0.645096	+	0.764101i	$0.723183\pi$
$840$	53.0549			1.83057
$841$	58.4993			2.01722
$842$	−0.419152			−0.0144449
$843$	0.196256	+	0.339926i	0.00675943	+	0.0117077i
$844$	2.67260	+	4.62908i	0.0919948	+	0.159340i
$845$	20.4097	+	35.3507i	0.702115	+	1.21610i
$846$	7.51613			0.258410
$847$	−45.5766			−1.56603
$848$	5.71746	−	9.90293i	0.196338	−	0.340068i
$849$	35.5937	+	61.6502i	1.22157	+	2.11583i
$850$	0.0331401			0.00113670
$851$	0.526780			0.0180578
$852$	2.17225			0.0744199
$853$	−17.2980	+	29.9609i	−0.592271	+	1.02584i	0.401655	+	0.915791i	$0.368435\pi$
$853$	−17.2980	+	29.9609i	−0.592271	+	1.02584i	−0.993926	+	0.110052i	$0.964898\pi$
$854$	−1.67300			−0.0572490
$855$	25.9990	+	45.0316i	0.889146	+	1.54005i
$856$	−53.9201			−1.84295
$857$	19.3884			0.662295			0.331148	−	0.943579i	$-0.392564\pi$
$857$	19.3884			0.662295			0.331148	+	0.943579i	$0.392564\pi$
$858$	−76.0636			−2.59677
$859$	−1.13278	−	1.96203i	−0.0386498	−	0.0669435i	0.846053	−	0.533098i	$-0.178972\pi$
$859$	−1.13278	−	1.96203i	−0.0386498	−	0.0669435i	−0.884703	+	0.466155i	$0.845639\pi$
$860$	−4.26657	+	7.38991i	−0.145489	+	0.251994i
$861$	38.7320	−	67.0859i	1.31998	−	2.28628i
$862$	−8.22574			−0.280170
$863$	−1.74099	+	3.01548i	−0.0592640	+	0.102648i	−0.894135	−	0.447797i	$-0.852209\pi$
$863$	−1.74099	+	3.01548i	−0.0592640	+	0.102648i	0.834871	+	0.550445i	$0.185542\pi$
$864$	−0.543810	+	0.941906i	−0.0185008	+	0.0320443i
$865$	−17.1637	+	29.7283i	−0.583582	+	1.01079i
$866$	−2.07211	−	3.58900i	−0.0704133	−	0.121959i
$867$	23.7706	−	41.1718i	0.807291	−	1.39827i
$868$	3.73387			0.126736
$869$	19.9123	+	34.4891i	0.675478	+	1.16996i
$870$	56.5757			1.91810
$871$	−16.0019	+	27.7162i	−0.542205	+	0.939127i
$872$	−0.824515	+	1.42810i	−0.0279216	+	0.0483616i
$873$	−13.7362	+	23.7918i	−0.464901	+	0.805231i
$874$	−0.743768	+	1.28824i	−0.0251583	+	0.0435755i
$875$	17.7661	+	30.7717i	0.600603	+	1.04027i
$876$	7.81677			0.264104
$877$	−6.95419	−	12.0450i	−0.234826	−	0.406731i	0.724396	−	0.689384i	$-0.242119\pi$
$877$	−6.95419	−	12.0450i	−0.234826	−	0.406731i	−0.959222	+	0.282653i	$0.908785\pi$
$878$	−5.07548			−0.171289
$879$	−21.4277			−0.722738
$880$	10.7349	+	18.5933i	0.361872	+	0.626781i
$881$	−14.2143	−	24.6199i	−0.478893	−	0.829467i	0.520814	−	0.853670i	$-0.325628\pi$
$881$	−14.2143	−	24.6199i	−0.478893	−	0.829467i	−0.999707	+	0.0242033i	$0.992295\pi$
$882$	10.0092			0.337028
$883$	7.68738	−	13.3149i	0.258701	−	0.448083i	−0.707193	−	0.707020i	$-0.750039\pi$
$883$	7.68738	−	13.3149i	0.258701	−	0.448083i	0.965894	+	0.258937i	$0.0833722\pi$
$884$	−12.8285	−	22.2196i	−0.431468	−	0.747325i
$885$	28.0214			0.941930
$886$	5.23085	−	9.06010i	0.175734	−	0.304380i
$887$	−7.92204	+	13.7214i	−0.265996	+	0.460719i	−0.967824	−	0.251628i	$-0.919034\pi$
$887$	−7.92204	+	13.7214i	−0.265996	+	0.460719i	0.701828	+	0.712347i	$0.252368\pi$
$888$	−11.8387	−	20.5053i	−0.397281	−	0.688111i
$889$	−37.4697			−1.25669
$890$	−15.1593			−0.508141
$891$	−23.4596	−	40.6333i	−0.785927	−	1.36127i
$892$	4.31919	+	7.48105i	0.144617	+	0.250484i
$893$	−9.39631	−	16.2749i	−0.314435	−	0.544618i
$894$	8.12022	+	14.0646i	0.271581	+	0.470392i
$895$	15.7434	−	27.2683i	0.526243	−	0.911480i
$896$	1.90136	−	3.29325i	0.0635200	−	0.110020i
$897$	2.25084			0.0751534
$898$	−22.7843	−	39.4635i	−0.760321	−	1.31691i
$899$	14.4765			0.482817
$900$	−0.0107782			−0.000359272
$901$	−18.1391	+	31.4178i	−0.604300	+	1.04668i
$902$	56.2974			1.87450
$903$	−19.3931	+	33.5899i	−0.645363	+	1.11780i
$904$	16.2774	−	28.1933i	0.541378	−	0.937695i
$905$	−29.6089	−	51.2842i	−0.984234	−	1.70474i
$906$	−3.18745	−	5.52083i	−0.105896	−	0.183417i
$907$	−18.0909	+	31.3344i	−0.600698	+	1.04044i	0.392017	+	0.919958i	$0.371777\pi$
$907$	−18.0909	+	31.3344i	−0.600698	+	1.04044i	−0.992715	+	0.120482i	$0.961556\pi$
$908$	−9.33020	−	16.1604i	−0.309634	−	0.536301i
$909$	−48.2075			−1.59894
$910$	22.1498	−	38.3646i	0.734259	−	1.27177i
$911$	6.08326	+	10.5365i	0.201547	+	0.349090i	0.949027	−	0.315194i	$-0.102070\pi$
$911$	6.08326	+	10.5365i	0.201547	+	0.349090i	−0.747480	+	0.664284i	$0.768736\pi$
$912$	37.2293			1.23279
$913$	9.07377	−	15.7162i	0.300298	−	0.520131i
$914$	−10.7835	−	18.6776i	−0.356687	−	0.617800i
$915$	2.56387			0.0847591
$916$	−3.89369	−	6.74407i	−0.128651	−	0.222830i
$917$	10.9457	+	18.9585i	0.361459	+	0.626065i
$918$	−0.911007	+	1.57791i	−0.0300677	+	0.0520788i
$919$	−14.2234	+	24.6357i	−0.469188	+	0.812657i	−0.999380	−	0.0352205i	$-0.988787\pi$
$919$	−14.2234	+	24.6357i	−0.469188	+	0.812657i	0.530192	+	0.847878i	$0.322120\pi$
$920$	−0.570494	−	0.988125i	−0.0188086	−	0.0325775i
$921$	45.5196			1.49992
$922$	−11.2340			−0.369971
$923$	3.29726	−	5.71101i	0.108530	−	0.187980i
$924$	−14.7341	−	25.5203i	−0.484717	−	0.839555i
$925$	−0.00780547	+	0.0135195i	−0.000256642	+	0.000444517i
$926$	11.8009	+	20.4398i	0.387803	+	0.671695i
$927$	−8.81687			−0.289584
$928$	−18.8153	+	32.5890i	−0.617641	+	1.06979i
$929$	−27.9854			−0.918172			−0.459086	−	0.888392i	$-0.651823\pi$
$929$	−27.9854			−0.918172			−0.459086	+	0.888392i	$0.651823\pi$
$930$	9.36026			0.306935
$931$	−12.5131	−	21.6733i	−0.410099	−	0.710313i
$932$	−5.33577	−	9.24183i	−0.174779	−	0.302726i
$933$	46.8277			1.53307
$934$	−6.59764	−	11.4275i	−0.215881	−	0.373918i
$935$	−34.0571	−	58.9887i	−1.11379	−	1.92914i
$936$	−24.8139	−	42.9789i	−0.811066	−	1.40481i
$937$	24.8832	+	43.0990i	0.812899	+	1.40798i	0.910826	+	0.412790i	$0.135446\pi$
$937$	24.8832	+	43.0990i	0.812899	+	1.40798i	−0.0979270	+	0.995194i	$0.531221\pi$
$938$	20.2819			0.662228
$939$	35.7447	−	61.9116i	1.16648	−	2.02041i
$940$	3.96462			0.129312
$941$	−8.97999	−	15.5538i	−0.292739	−	0.507039i	0.681717	−	0.731616i	$-0.261233\pi$
$941$	−8.97999	−	15.5538i	−0.292739	−	0.507039i	−0.974456	+	0.224577i	$0.927900\pi$
$942$	−25.7649	+	44.6262i	−0.839467	+	1.45400i
$943$	−1.66593			−0.0542501
$944$	4.92078	−	8.52303i	0.160158	−	0.277401i
$945$	1.92317			0.0625608
$946$	−28.1881			−0.916474
$947$	−1.60442	+	2.77894i	−0.0521367	+	0.0903033i	−0.890916	−	0.454168i	$-0.849936\pi$
$947$	−1.60442	+	2.77894i	−0.0521367	+	0.0903033i	0.838779	+	0.544472i	$0.183270\pi$
$948$	−7.28442	+	12.6170i	−0.236587	+	0.409780i
$949$	11.8651	−	20.5509i	0.385157	−	0.667111i
$950$	−0.0220413	−	0.0381766i	−0.000715114	−	0.00123861i
$951$	−4.67738	+	8.10146i	−0.151674	+	0.262708i
$952$	−29.5584	+	51.1966i	−0.957993	+	1.65929i
$953$	−28.6136	+	49.5602i	−0.926885	+	1.60541i	−0.138384	+	0.990379i	$0.544191\pi$
$953$	−28.6136	+	49.5602i	−0.926885	+	1.60541i	−0.788501	+	0.615033i	$0.789143\pi$
$954$	−9.65017	+	16.7146i	−0.312436	+	0.541155i
$955$	0.388053	+	0.672127i	0.0125571	+	0.0217495i
$956$	−17.6560			−0.571036
$957$	−57.1253	−	98.9439i	−1.84660	−	3.19840i
$958$	14.9183	+	25.8393i	0.481989	+	0.834830i
$959$	8.98065	−	15.5549i	0.290000	−	0.502295i
$960$	−22.5166	+	39.0000i	−0.726721	+	1.25872i
$961$	−28.6049			−0.922739
$962$	−19.7701			−0.637413
$963$	50.6751			1.63298
$964$	−4.56785	−	7.91174i	−0.147120	−	0.254820i
$965$	−22.1929	−	38.4392i	−0.714414	−	1.23740i
$966$	−0.713216	−	1.23533i	−0.0229474	−	0.0397460i
$967$	23.0326	−	39.8936i	0.740677	−	1.28289i	−0.211510	−	0.977376i	$-0.567838\pi$
$967$	23.0326	−	39.8936i	0.740677	−	1.28289i	0.952187	−	0.305515i	$-0.0988286\pi$
$968$	22.0279	−	38.1535i	0.708004	−	1.22630i
$969$	−118.113			−3.79433
$970$	11.8523	−	20.5288i	0.380555	−	0.659141i
$971$	−5.34102	−	9.25092i	−0.171402	−	0.296876i	0.767508	−	0.641039i	$-0.221496\pi$
$971$	−5.34102	−	9.25092i	−0.171402	−	0.296876i	−0.938910	+	0.344162i	$0.888163\pi$
$972$	8.27441	−	14.3317i	0.265402	−	0.459689i
$973$	−12.8637	+	22.2807i	−0.412393	+	0.714285i
$974$	−7.52207	+	13.0286i	−0.241023	+	0.417463i
$975$	−0.0333514	+	0.0577663i	−0.00106810	+	0.00185000i
$976$	0.450236	−	0.779831i	0.0144117	−	0.0249618i
$977$	−16.9631	−	29.3809i	−0.542696	−	0.939978i	−0.998748	−	0.0500243i	$-0.984070\pi$
$977$	−16.9631	−	29.3809i	−0.542696	−	0.939978i	0.456052	−	0.889953i	$-0.349263\pi$
$978$	10.8738	−	18.8341i	0.347707	−	0.602247i
$979$	15.3066	+	26.5118i	0.489200	+	0.847319i
$980$	5.27969			0.168653
$981$	0.774895	−	1.34216i	0.0247405	−	0.0428518i
$982$	−23.1157	+	40.0375i	−0.737650	+	1.27765i
$983$	7.92807	+	13.7318i	0.252866	+	0.437977i	0.964314	−	0.264762i	$-0.0852934\pi$
$983$	7.92807	+	13.7318i	0.252866	+	0.437977i	−0.711448	+	0.702739i	$0.751960\pi$
$984$	37.4396	+	64.8473i	1.19353	+	2.06726i
$985$	3.44505	−	5.96701i	0.109769	−	0.190125i
$986$	−31.5199	+	54.5941i	−1.00380	+	1.73863i
$987$	18.0207			0.573604
$988$	−17.0643	+	29.5562i	−0.542887	+	0.940308i
$989$	0.834130			0.0265238
$990$	−18.1187	−	31.3826i	−0.575851	−	0.997404i
$991$	21.6546			0.687880			0.343940	−	0.938992i	$-0.388238\pi$
$991$	21.6546			0.687880			0.343940	+	0.938992i	$0.388238\pi$
$992$	−3.11292	+	5.39174i	−0.0988354	+	0.171188i
$993$	−27.7513			−0.880659
$994$	−4.17916			−0.132555
$995$	22.6443	+	39.2211i	0.717873	+	1.24339i
$996$	6.63883			0.210359
$997$	18.3148	−	31.7221i	0.580034	−	1.00465i	−0.415440	−	0.909621i	$-0.636372\pi$
$997$	18.3148	−	31.7221i	0.580034	−	1.00465i	0.995475	−	0.0950286i	$-0.0302942\pi$
$998$	22.3064	−	38.6358i	0.706096	−	1.22299i
$999$	−0.429138	−	0.743288i	−0.0135773	−	0.0235166i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	547.2.c.a.40.15	✓	90
547.506	even	3	inner	547.2.c.a.506.15	yes	90

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
547.2.c.a.40.15	✓	90	1.1	even	1	trivial
547.2.c.a.506.15	yes	90	547.506	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:	\( N \)	\(=\)	\( 547 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	547.c (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.557049 - 0.964838i) q^{2} -2.42664 q^{3} +(0.379392 - 0.657126i) q^{4} +(1.11858 - 1.93744i) q^{5} +(1.35176 + 2.34132i) q^{6} +(1.58983 + 2.75366i) q^{7} -3.07356 q^{8} +2.88859 q^{9} +O(q^{10})\)	\(q+(-0.557049 - 0.964838i) q^{2} -2.42664 q^{3} +(0.379392 - 0.657126i) q^{4} +(1.11858 - 1.93744i) q^{5} +(1.35176 + 2.34132i) q^{6} +(1.58983 + 2.75366i) q^{7} -3.07356 q^{8} +2.88859 q^{9} -2.49243 q^{10} +(2.51664 + 4.35894i) q^{11} +(-0.920648 + 1.59461i) q^{12} +(2.79491 + 4.84092i) q^{13} +(1.77123 - 3.06785i) q^{14} +(-2.71440 + 4.70148i) q^{15} +(0.953339 + 1.65123i) q^{16} +(-3.02454 - 5.23865i) q^{17} +(-1.60909 - 2.78702i) q^{18} +(-4.02321 + 6.96840i) q^{19} +(-0.848764 - 1.47010i) q^{20} +(-3.85794 - 6.68216i) q^{21} +(2.80378 - 4.85629i) q^{22} +(-0.0829682 + 0.143705i) q^{23} +7.45842 q^{24} +(-0.00245873 - 0.00425865i) q^{25} +(3.11380 - 5.39326i) q^{26} +0.270358 q^{27} +2.41267 q^{28} +9.35411 q^{29} +6.04822 q^{30} +1.54761 q^{31} +(-2.01144 + 3.48392i) q^{32} +(-6.10697 - 10.5776i) q^{33} +(-3.36963 + 5.83638i) q^{34} +7.11343 q^{35} +(1.09591 - 1.89817i) q^{36} +(-1.58729 - 2.74928i) q^{37} +8.96450 q^{38} +(-6.78224 - 11.7472i) q^{39} +(-3.43803 + 5.95485i) q^{40} +(5.01978 + 8.69451i) q^{41} +(-4.29813 + 7.44458i) q^{42} +(-2.51340 - 4.35334i) q^{43} +3.81917 q^{44} +(3.23113 - 5.59648i) q^{45} +0.184869 q^{46} +(-1.16776 + 2.02263i) q^{47} +(-2.31341 - 4.00695i) q^{48} +(-1.55511 + 2.69353i) q^{49} +(-0.00273927 + 0.00474455i) q^{50} +(7.33947 + 12.7123i) q^{51} +4.24146 q^{52} +(-2.99865 - 5.19381i) q^{53} +(-0.150603 - 0.260852i) q^{54} +11.2603 q^{55} +(-4.88643 - 8.46355i) q^{56} +(9.76288 - 16.9098i) q^{57} +(-5.21070 - 9.02520i) q^{58} +(-2.58081 - 4.47009i) q^{59} +(2.05964 + 3.56741i) q^{60} +(-0.236136 - 0.409000i) q^{61} +(-0.862093 - 1.49319i) q^{62} +(4.59236 + 7.95420i) q^{63} +8.29525 q^{64} +12.5054 q^{65} +(-6.80377 + 11.7845i) q^{66} +(2.86270 + 4.95834i) q^{67} -4.58994 q^{68} +(0.201334 - 0.348721i) q^{69} +(-3.96253 - 6.86330i) q^{70} +(-0.589868 - 1.02168i) q^{71} -8.87824 q^{72} +(-2.12263 - 3.67650i) q^{73} +(-1.76840 + 3.06296i) q^{74} +(0.00596646 + 0.0103342i) q^{75} +(3.05275 + 5.28751i) q^{76} +(-8.00204 + 13.8599i) q^{77} +(-7.55608 + 13.0875i) q^{78} +7.91227 q^{79} +4.26556 q^{80} -9.32182 q^{81} +(5.59253 - 9.68654i) q^{82} +(-1.80276 - 3.12247i) q^{83} -5.85469 q^{84} -13.5328 q^{85} +(-2.80018 + 4.85005i) q^{86} -22.6991 q^{87} +(-7.73503 - 13.3975i) q^{88} +6.08215 q^{89} -7.19959 q^{90} +(-8.88685 + 15.3925i) q^{91} +(0.0629549 + 0.109041i) q^{92} -3.75548 q^{93} +2.60201 q^{94} +(9.00059 + 15.5895i) q^{95} +(4.88105 - 8.45423i) q^{96} +(-4.75534 + 8.23649i) q^{97} +3.46509 q^{98} +(7.26952 + 12.5912i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 90 q - q^{2} - 4 q^{3} - 47 q^{4} + q^{5} - 3 q^{6} + 2 q^{7} - 30 q^{8} + 82 q^{9}+O(q^{10}) \) 90 * q - q^2 - 4 * q^3 - 47 * q^4 + q^5 - 3 * q^6 + 2 * q^7 - 30 * q^8 + 82 * q^9	\( 90 q - q^{2} - 4 q^{3} - 47 q^{4} + q^{5} - 3 q^{6} + 2 q^{7} - 30 q^{8} + 82 q^{9} - 10 q^{10} + q^{11} + 4 q^{12} - 3 q^{13} + 2 q^{14} - 7 q^{15} - 39 q^{16} - 4 q^{17} - 11 q^{18} - 2 q^{19} + 25 q^{20} - 27 q^{21} - 7 q^{22} + q^{23} + 32 q^{24} - 40 q^{25} - 10 q^{26} - 34 q^{27} - 28 q^{28} + 26 q^{29} - 40 q^{30} - 24 q^{31} + 19 q^{32} + q^{33} - 6 q^{34} - 8 q^{35} - 36 q^{36} - 10 q^{37} + 24 q^{38} + 22 q^{39} + 20 q^{40} + 3 q^{41} + 38 q^{42} - 12 q^{43} - 30 q^{44} - 2 q^{45} - 40 q^{46} + 32 q^{47} + 14 q^{48} - 43 q^{49} + 14 q^{50} + 13 q^{51} + 46 q^{52} + 9 q^{53} - 8 q^{54} + 4 q^{55} - 8 q^{56} - 8 q^{57} + 4 q^{58} + 22 q^{59} - 2 q^{60} - 12 q^{61} + 11 q^{62} + 8 q^{63} + 22 q^{64} + 18 q^{65} + 12 q^{66} - 22 q^{67} + 6 q^{68} - q^{69} - 6 q^{70} - 4 q^{71} - 140 q^{72} + 17 q^{73} + 17 q^{74} + 39 q^{75} + 84 q^{76} - 4 q^{77} + 33 q^{78} - 72 q^{79} - 40 q^{80} + 18 q^{81} - 9 q^{82} + 24 q^{83} + 114 q^{84} + 40 q^{85} - 72 q^{86} - 78 q^{87} - 22 q^{88} + 14 q^{89} + 96 q^{90} - 8 q^{92} - 76 q^{93} + 108 q^{94} - 11 q^{95} - 34 q^{96} - 74 q^{98} - 62 q^{99}+O(q^{100}) \) 90 * q - q^2 - 4 * q^3 - 47 * q^4 + q^5 - 3 * q^6 + 2 * q^7 - 30 * q^8 + 82 * q^9 - 10 * q^10 + q^11 + 4 * q^12 - 3 * q^13 + 2 * q^14 - 7 * q^15 - 39 * q^16 - 4 * q^17 - 11 * q^18 - 2 * q^19 + 25 * q^20 - 27 * q^21 - 7 * q^22 + q^23 + 32 * q^24 - 40 * q^25 - 10 * q^26 - 34 * q^27 - 28 * q^28 + 26 * q^29 - 40 * q^30 - 24 * q^31 + 19 * q^32 + q^33 - 6 * q^34 - 8 * q^35 - 36 * q^36 - 10 * q^37 + 24 * q^38 + 22 * q^39 + 20 * q^40 + 3 * q^41 + 38 * q^42 - 12 * q^43 - 30 * q^44 - 2 * q^45 - 40 * q^46 + 32 * q^47 + 14 * q^48 - 43 * q^49 + 14 * q^50 + 13 * q^51 + 46 * q^52 + 9 * q^53 - 8 * q^54 + 4 * q^55 - 8 * q^56 - 8 * q^57 + 4 * q^58 + 22 * q^59 - 2 * q^60 - 12 * q^61 + 11 * q^62 + 8 * q^63 + 22 * q^64 + 18 * q^65 + 12 * q^66 - 22 * q^67 + 6 * q^68 - q^69 - 6 * q^70 - 4 * q^71 - 140 * q^72 + 17 * q^73 + 17 * q^74 + 39 * q^75 + 84 * q^76 - 4 * q^77 + 33 * q^78 - 72 * q^79 - 40 * q^80 + 18 * q^81 - 9 * q^82 + 24 * q^83 + 114 * q^84 + 40 * q^85 - 72 * q^86 - 78 * q^87 - 22 * q^88 + 14 * q^89 + 96 * q^90 - 8 * q^92 - 76 * q^93 + 108 * q^94 - 11 * q^95 - 34 * q^96 - 74 * q^98 - 62 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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