LMFDB - Embedded newform 160.4.z.a.29.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [160,4,Mod(29,160)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(160, base_ring=CyclotomicField(8))

chi = DirichletCharacter(H, H._module([0, 3, 4]))

N = Newforms(chi, 4, names="a")

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

chi := DirichletCharacter("160.29");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 160 = 2^{5} \cdot 5 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	160.z (of order $8$, degree $4$, 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:	$9.44030560092$
Analytic rank:	$0$
Dimension:	$280$
Relative dimension:	$70$ over $\Q(\zeta_{8})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{8}]$

Embedding invariants

Embedding label			29.6
Character	$\chi$	$=$	160.29
Dual form			160.4.z.a.149.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-2.71925 - 0.778249i) q^{2} +(0.155312 - 0.374956i) q^{3} +(6.78866 + 4.23251i) q^{4} +(-1.64450 - 11.0587i) q^{5} +(-0.714142 + 0.898729i) q^{6} +(-8.18573 - 8.18573i) q^{7} +(-15.1661 - 16.7925i) q^{8} +(18.9754 + 18.9754i) q^{9} +(-4.13465 + 31.3513i) q^{10} +(16.3186 - 6.75938i) q^{11} +(2.64137 - 1.88809i) q^{12} +(-55.5847 - 23.0239i) q^{13} +(15.8885 + 28.6296i) q^{14} +(-4.40195 - 1.10094i) q^{15} +(28.1717 + 57.4661i) q^{16} +6.99500 q^{17} +(-36.8313 - 66.3665i) q^{18} +(23.8850 - 57.6634i) q^{19} +(35.6423 - 82.0343i) q^{20} +(-4.34063 + 1.79795i) q^{21} +(-49.6348 + 5.68052i) q^{22} +(-31.1187 + 31.1187i) q^{23} +(-8.65194 + 3.07855i) q^{24} +(-119.591 + 36.3721i) q^{25} +(133.230 + 105.867i) q^{26} +(20.1859 - 8.36127i) q^{27} +(-20.9239 - 90.2163i) q^{28} +(-223.315 - 92.4999i) q^{29} +(11.1132 + 6.41955i) q^{30} -324.218 q^{31} +(-31.8830 - 178.189i) q^{32} -7.16857i q^{33} +(-19.0212 - 5.44385i) q^{34} +(-77.0624 + 103.985i) q^{35} +(48.5039 + 209.131i) q^{36} +(-340.670 + 141.110i) q^{37} +(-109.826 + 138.213i) q^{38} +(-17.2659 + 17.2659i) q^{39} +(-160.763 + 195.333i) q^{40} +(28.8054 + 28.8054i) q^{41} +(13.2025 - 1.51098i) q^{42} +(-85.4797 - 206.366i) q^{43} +(139.390 + 23.1815i) q^{44} +(178.639 - 241.049i) q^{45} +(108.838 - 60.4014i) q^{46} +404.846 q^{47} +(25.9227 - 1.63798i) q^{48} -208.988i q^{49} +(353.505 - 5.83320i) q^{50} +(1.08641 - 2.62282i) q^{51} +(-279.896 - 391.564i) q^{52} +(130.250 + 314.451i) q^{53} +(-61.3976 + 7.02674i) q^{54} +(-101.586 - 169.347i) q^{55} +(-13.3134 + 261.605i) q^{56} +(-17.9116 - 17.9116i) q^{57} +(535.261 + 425.325i) q^{58} +(-139.925 - 337.809i) q^{59} +(-25.2236 - 26.1052i) q^{60} +(224.274 + 92.8973i) q^{61} +(881.630 + 252.322i) q^{62} -310.655i q^{63} +(-51.9780 + 509.355i) q^{64} +(-163.207 + 652.559i) q^{65} +(-5.57893 + 19.4931i) q^{66} +(309.648 - 747.556i) q^{67} +(47.4866 + 29.6064i) q^{68} +(6.83504 + 16.5012i) q^{69} +(290.478 - 222.788i) q^{70} +(80.6945 - 80.6945i) q^{71} +(30.8619 - 606.428i) q^{72} +(-404.775 + 404.775i) q^{73} +(1036.19 - 118.588i) q^{74} +(-4.93599 + 50.4905i) q^{75} +(406.208 - 290.364i) q^{76} +(-188.910 - 78.2491i) q^{77} +(60.3876 - 33.5132i) q^{78} -735.297i q^{79} +(589.174 - 406.046i) q^{80} +715.685i q^{81} +(-55.9113 - 100.747i) q^{82} +(1133.81 + 469.638i) q^{83} +(-37.0769 - 6.16612i) q^{84} +(-11.5033 - 77.3559i) q^{85} +(71.8364 + 627.686i) q^{86} +(-69.3669 + 69.3669i) q^{87} +(-360.996 - 171.517i) q^{88} +(-117.324 + 117.324i) q^{89} +(-673.361 + 516.447i) q^{90} +(266.533 + 643.469i) q^{91} +(-342.964 + 79.5438i) q^{92} +(-50.3549 + 121.568i) q^{93} +(-1100.88 - 315.071i) q^{94} +(-676.963 - 169.310i) q^{95} +(-71.7651 - 15.7202i) q^{96} -23.2157i q^{97} +(-162.644 + 568.290i) q^{98} +(437.914 + 181.390i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 280 q - 8 q^{4} - 4 q^{5} - 8 q^{6} - 8 q^{9} - 4 q^{10} - 8 q^{11} + 200 q^{14} - 8 q^{16} - 8 q^{19} - 4 q^{20} - 8 q^{21} - 464 q^{24} - 4 q^{25} - 48 q^{26} - 8 q^{29} + 1124 q^{30} + 1472 q^{31} - 72 q^{34}+ \cdots + 5520 q^{99}+O(q^{100}) $ 280 * q - 8 * q^4 - 4 * q^5 - 8 * q^6 - 8 * q^9 - 4 * q^10 - 8 * q^11 + 200 * q^14 - 8 * q^16 - 8 * q^19 - 4 * q^20 - 8 * q^21 - 464 * q^24 - 4 * q^25 - 48 * q^26 - 8 * q^29 + 1124 * q^30 + 1472 * q^31 - 72 * q^34 - 460 * q^35 - 888 * q^36 - 8 * q^39 - 1112 * q^40 - 8 * q^41 - 8 * q^44 - 112 * q^45 - 8 * q^46 + 3556 * q^50 - 1712 * q^51 + 856 * q^54 + 284 * q^55 + 328 * q^56 - 1384 * q^59 - 5248 * q^60 - 1832 * q^61 + 832 * q^64 - 8 * q^65 + 6088 * q^66 + 1048 * q^69 - 616 * q^70 + 216 * q^71 - 2064 * q^74 + 2204 * q^75 - 5128 * q^76 - 656 * q^80 - 6904 * q^84 - 504 * q^85 - 1192 * q^86 - 8 * q^89 + 2720 * q^90 - 8 * q^91 - 920 * q^94 - 8 * q^95 - 4152 * q^96 + 5520 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/160\mathbb{Z}\right)^\times$.

$n$	$31$	$97$	$101$
$\chi(n)$	$1$	$-1$	$e\left(\frac{3}{8}\right)$

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 $

$2$	−2.71925	−	0.778249i	−0.961401	−	0.275153i
$2$	−2.71925	−	0.778249i	−0.961401	−	0.275153i
$3$	0.155312	−	0.374956i	0.0298898	−	0.0721604i	−0.908230	−	0.418472i	$-0.862566\pi$
$3$	0.155312	−	0.374956i	0.0298898	−	0.0721604i	0.938120	+	0.346311i	$0.112566\pi$
$4$	6.78866	+	4.23251i	0.848582	+	0.529064i
$5$	−1.64450	−	11.0587i	−0.147088	−	0.989123i
$5$	−1.64450	−	11.0587i	−0.147088	−	0.989123i
$6$	−0.714142	+	0.898729i	−0.0485912	+	0.0611508i
$7$	−8.18573	−	8.18573i	−0.441988	−	0.441988i	0.450692	−	0.892680i	$-0.351177\pi$
$7$	−8.18573	−	8.18573i	−0.441988	−	0.441988i	−0.892680	+	0.450692i	$0.851177\pi$
$8$	−15.1661	−	16.7925i	−0.670254	−	0.742132i
$9$	18.9754	+	18.9754i	0.702793	+	0.702793i
$10$	−4.13465	+	31.3513i	−0.130749	+	0.991415i
$11$	16.3186	−	6.75938i	0.447294	−	0.185275i	−0.147654	−	0.989039i	$-0.547172\pi$
$11$	16.3186	−	6.75938i	0.447294	−	0.185275i	0.594949	+	0.803764i	$0.297172\pi$
$12$	2.64137	−	1.88809i	0.0635414	−	0.0454204i
$13$	−55.5847	−	23.0239i	−1.18588	−	0.491207i	−0.299467	−	0.954107i	$-0.596809\pi$
$13$	−55.5847	−	23.0239i	−1.18588	−	0.491207i	−0.886410	+	0.462900i	$0.846809\pi$
$14$	15.8885	+	28.6296i	0.303313	+	0.546542i
$15$	−4.40195	−	1.10094i	−0.0757720	−	0.0189508i
$16$	28.1717	+	57.4661i	0.440183	+	0.897908i
$17$	6.99500			0.0997963			0.0498981	−	0.998754i	$-0.484110\pi$
$17$	6.99500			0.0997963			0.0498981	+	0.998754i	$0.484110\pi$
$18$	−36.8313	−	66.3665i	−0.482290	−	0.869041i
$19$	23.8850	−	57.6634i	0.288399	−	0.696257i	−0.711581	−	0.702604i	$-0.752020\pi$
$19$	23.8850	−	57.6634i	0.288399	−	0.696257i	0.999980	+	0.00634714i	$0.00202037\pi$
$20$	35.6423	−	82.0343i	0.398493	−	0.917171i
$21$	−4.34063	+	1.79795i	−0.0451049	+	0.0186831i
$22$	−49.6348	+	5.68052i	−0.481008	+	0.0550496i
$23$	−31.1187	+	31.1187i	−0.282117	+	0.282117i	−0.833953	−	0.551836i	$-0.813928\pi$
$23$	−31.1187	+	31.1187i	−0.282117	+	0.282117i	0.551836	+	0.833953i	$0.313928\pi$
$24$	−8.65194	+	3.07855i	−0.0735863	+	0.0261836i
$25$	−119.591	+	36.3721i	−0.956730	+	0.290977i
$26$	133.230	+	105.867i	1.00495	+	0.798544i
$27$	20.1859	−	8.36127i	0.143881	−	0.0595973i
$28$	−20.9239	−	90.2163i	−0.141223	−	0.608903i
$29$	−223.315	−	92.4999i	−1.42995	−	0.592304i	−0.472609	−	0.881272i	$-0.656688\pi$
$29$	−223.315	−	92.4999i	−1.42995	−	0.592304i	−0.957339	+	0.288968i	$0.906688\pi$
$30$	11.1132	+	6.41955i	0.0676329	+	0.0390681i
$31$	−324.218			−1.87843			−0.939214	−	0.343332i	$-0.888444\pi$
$31$	−324.218			−1.87843			−0.939214	+	0.343332i	$0.888444\pi$
$32$	−31.8830	−	178.189i	−0.176130	−	0.984367i
$33$		−	7.16857i		−	0.0378148i
$34$	−19.0212	−	5.44385i	−0.0959442	−	0.0274592i
$35$	−77.0624	+	103.985i	−0.372169	+	0.502192i
$36$	48.5039	+	209.131i	0.224555	+	0.968200i
$37$	−340.670	+	141.110i	−1.51367	+	0.626982i	−0.976311	−	0.216372i	$-0.930578\pi$
$37$	−340.670	+	141.110i	−1.51367	+	0.626982i	−0.537358	+	0.843354i	$0.680578\pi$
$38$	−109.826	+	138.213i	−0.468844	+	0.590028i
$39$	−17.2659	+	17.2659i	−0.0708913	+	0.0708913i
$40$	−160.763	+	195.333i	−0.635473	+	0.772123i
$41$	28.8054	+	28.8054i	0.109723	+	0.109723i	0.759837	−	0.650114i	$-0.225279\pi$
$41$	28.8054	+	28.8054i	0.109723	+	0.109723i	−0.650114	+	0.759837i	$0.725279\pi$
$42$	13.2025	−	1.51098i	0.0485046	−	0.00555118i
$43$	−85.4797	−	206.366i	−0.303152	−	0.731874i	−0.999894	−	0.0145520i	$-0.995368\pi$
$43$	−85.4797	−	206.366i	−0.303152	−	0.731874i	0.696742	−	0.717322i	$-0.254632\pi$
$44$	139.390	+	23.1815i	0.477588	+	0.0794259i
$45$	178.639	−	241.049i	0.591776	−	0.798522i
$46$	108.838	−	60.4014i	0.348853	−	0.193602i
$47$	404.846			1.25644			0.628221	−	0.778035i	$-0.283783\pi$
$47$	404.846			1.25644			0.628221	+	0.778035i	$0.283783\pi$
$48$	25.9227	−	1.63798i	0.0779504	−	0.00492546i
$49$		−	208.988i		−	0.609293i
$50$	353.505	−	5.83320i	0.999864	−	0.0164988i
$51$	1.08641	−	2.62282i	0.00298289	−	0.00720134i
$52$	−279.896	−	391.564i	−0.746435	−	1.04423i
$53$	130.250	+	314.451i	0.337570	+	0.814965i	0.997948	+	0.0640319i	$0.0203959\pi$
$53$	130.250	+	314.451i	0.337570	+	0.814965i	−0.660378	+	0.750933i	$0.729604\pi$
$54$	−61.3976	+	7.02674i	−0.154725	+	0.0177077i
$55$	−101.586	−	169.347i	−0.249052	−	0.415177i
$56$	−13.3134	+	261.605i	−0.0317692	+	0.624257i
$57$	−17.9116	−	17.9116i	−0.0416220	−	0.0416220i
$58$	535.261	+	425.325i	1.21178	+	0.962895i
$59$	−139.925	−	337.809i	−0.308757	−	0.745405i	−0.999746	−	0.0225401i	$-0.992825\pi$
$59$	−139.925	−	337.809i	−0.308757	−	0.745405i	0.690989	−	0.722865i	$-0.257175\pi$
$60$	−25.2236	−	26.1052i	−0.0542726	−	0.0561695i
$61$	224.274	+	92.8973i	0.470743	+	0.194988i	0.605428	−	0.795900i	$-0.293002\pi$
$61$	224.274	+	92.8973i	0.470743	+	0.194988i	−0.134684	+	0.990889i	$0.543002\pi$
$62$	881.630	+	252.322i	1.80592	+	0.516854i
$63$		−	310.655i		−	0.621252i
$64$	−51.9780	+	509.355i	−0.101519	+	0.994834i
$65$	−163.207	+	652.559i	−0.311435	+	1.24523i
$66$	−5.57893	+	19.4931i	−0.0104048	+	0.0363551i
$67$	309.648	−	747.556i	0.564620	−	1.36311i	−0.341417	−	0.939912i	$-0.610907\pi$
$67$	309.648	−	747.556i	0.564620	−	1.36311i	0.906036	−	0.423200i	$-0.139093\pi$
$68$	47.4866	+	29.6064i	0.0846853	+	0.0527986i
$69$	6.83504	+	16.5012i	0.0119252	+	0.0287901i
$70$	290.478	−	222.788i	0.495983	−	0.380404i
$71$	80.6945	−	80.6945i	0.134883	−	0.134883i	−0.636442	−	0.771325i	$-0.719595\pi$
$71$	80.6945	−	80.6945i	0.134883	−	0.134883i	0.771325	+	0.636442i	$0.219595\pi$
$72$	30.8619	−	606.428i	0.0505154	−	0.992615i
$73$	−404.775	+	404.775i	−0.648977	+	0.648977i	−0.952746	−	0.303769i	$-0.901755\pi$
$73$	−404.775	+	404.775i	−0.648977	+	0.648977i	0.303769	+	0.952746i	$0.401755\pi$
$74$	1036.19	−	118.588i	1.62776	−	0.186291i
$75$	−4.93599	+	50.4905i	−0.00759945	+	0.0777353i
$76$	406.208	−	290.364i	0.613095	−	0.438250i
$77$	−188.910	−	78.2491i	−0.279588	−	0.115809i
$78$	60.3876	−	33.5132i	0.0876609	−	0.0486490i
$79$		−	735.297i		−	1.04718i	−0.851970	−	0.523591i	$-0.824592\pi$
$79$		−	735.297i		−	1.04718i	0.851970	−	0.523591i	$-0.175408\pi$
$80$	589.174	−	406.046i	0.823396	−	0.567467i
$81$			715.685i			0.981736i
$82$	−55.9113	−	100.747i	−0.0752971	−	0.135678i
$83$	1133.81	+	469.638i	1.49941	+	0.621078i	0.973341	−	0.229361i	$-0.0736637\pi$
$83$	1133.81	+	469.638i	1.49941	+	0.621078i	0.526073	+	0.850439i	$0.323664\pi$
$84$	−37.0769	−	6.16612i	−0.0481598	−	0.00800927i
$85$	−11.5033	−	77.3559i	−0.0146789	−	0.0987108i
$86$	71.8364	+	627.686i	0.0900735	+	0.787037i
$87$	−69.3669	+	69.3669i	−0.0854817	+	0.0854817i
$88$	−360.996	−	171.517i	−0.437299	−	0.207770i
$89$	−117.324	+	117.324i	−0.139734	+	0.139734i	−0.773514	−	0.633780i	$-0.781503\pi$
$89$	−117.324	+	117.324i	−0.139734	+	0.139734i	0.633780	+	0.773514i	$0.281503\pi$
$90$	−673.361	+	516.447i	−0.788649	+	0.604870i
$91$	266.533	+	643.469i	0.307036	+	0.741251i
$92$	−342.964	+	79.5438i	−0.388657	+	0.0901415i
$93$	−50.3549	+	121.568i	−0.0561459	+	0.135548i
$94$	−1100.88	−	315.071i	−1.20794	−	0.345714i
$95$	−676.963	−	169.310i	−0.731105	−	0.182851i
$96$	−71.7651	−	15.7202i	−0.0762968	−	0.0167129i
$97$		−	23.2157i		−	0.0243010i	−0.999926	−	0.0121505i	$-0.996132\pi$
$97$		−	23.2157i		−	0.0243010i	0.999926	−	0.0121505i	$-0.00386772\pi$
$98$	−162.644	+	568.290i	−0.167649	+	0.585775i
$99$	437.914	+	181.390i	0.444566	+	0.184145i
$100$	−965.809	−	259.253i	−0.965809	−	0.259253i
$101$	−126.622	−	305.693i	−0.124746	−	0.301165i	0.849152	−	0.528148i	$-0.177114\pi$
$101$	−126.622	−	305.693i	−0.124746	−	0.301165i	−0.973899	+	0.226984i	$0.927114\pi$
$102$	−4.99542	+	6.28661i	−0.00484922	+	0.00610262i
$103$	1072.29	+	1072.29i	1.02578	+	1.02578i	0.999659	+	0.0261218i	$0.00831577\pi$
$103$	1072.29	+	1072.29i	1.02578	+	1.02578i	0.0261218	+	0.999659i	$0.491684\pi$
$104$	456.373	+	1282.59i	0.430299	+	1.20931i
$105$	27.0212	+	45.0452i	0.0251143	+	0.0418663i
$106$	−109.461	−	956.438i	−0.100300	−	0.876391i
$107$	−332.349	−	802.362i	−0.300275	−	0.724927i	−0.999945	−	0.0104617i	$-0.996670\pi$
$107$	−332.349	−	802.362i	−0.300275	−	0.724927i	0.699671	−	0.714466i	$-0.253330\pi$
$108$	172.424	+	28.6752i	0.153625	+	0.0255488i
$109$	229.675	−	554.484i	0.201824	−	0.487247i	−0.790267	−	0.612762i	$-0.790058\pi$
$109$	229.675	−	554.484i	0.201824	−	0.487247i	0.992092	+	0.125515i	$0.0400583\pi$
$110$	144.444	+	539.557i	0.125202	+	0.467679i
$111$			149.652i			0.127967i
$112$	239.796	−	701.008i	0.202309	−	0.591420i
$113$	−944.182			−0.786028			−0.393014	−	0.919533i	$-0.628568\pi$
$113$	−944.182			−0.786028			−0.393014	+	0.919533i	$0.628568\pi$
$114$	34.7665	+	62.6460i	0.0285630	+	0.0514678i
$115$	395.308	+	292.959i	0.320545	+	0.237552i
$116$	−1124.50	−	1573.13i	−0.900061	−	1.25915i
$117$	−617.853	−	1491.63i	−0.488210	−	1.17864i
$118$	117.592	+	1027.48i	0.0917389	+	0.801589i
$119$	−57.2592	−	57.2592i	−0.0441087	−	0.0441087i
$120$	48.2730	+	90.6169i	0.0367225	+	0.0689346i
$121$	−720.552	+	720.552i	−0.541362	+	0.541362i
$122$	−537.560	−	427.152i	−0.398921	−	0.316988i
$123$	15.2746	−	6.32693i	0.0111972	−	0.00463805i
$124$	−2201.00	−	1372.26i	−1.59400	−	0.993808i
$125$	598.898	+	1262.71i	0.428536	+	0.903525i
$126$	−241.767	+	844.750i	−0.170939	+	0.597272i
$127$		−	1848.45i		−	1.29152i	−0.763539	−	0.645761i	$-0.776540\pi$
$127$		−	1848.45i		−	1.29152i	0.763539	−	0.645761i	$-0.223460\pi$
$128$	537.746	−	1344.61i	0.371332	−	0.928500i
$129$	−90.6544			−0.0618734
$130$	951.653	−	1647.46i	0.642042	−	1.11147i
$131$	1125.30	+	466.114i	0.750518	+	0.310875i	0.724953	−	0.688799i	$-0.241862\pi$
$131$	1125.30	+	466.114i	0.750518	+	0.310875i	0.0255650	+	0.999673i	$0.491862\pi$
$132$	30.3410	−	48.6649i	0.0200064	−	0.0320889i
$133$	−667.533	+	276.501i	−0.435206	+	0.180268i
$134$	−1423.80	+	1791.81i	−0.917889	+	1.15514i
$135$	−125.661	−	209.480i	−0.0801122	−	0.133550i
$136$	−106.087	−	117.464i	−0.0668888	−	0.0740620i
$137$	421.450	−	421.450i	0.262824	−	0.262824i	−0.563376	−	0.826200i	$-0.690498\pi$
$137$	421.450	−	421.450i	0.262824	−	0.262824i	0.826200	+	0.563376i	$0.190498\pi$
$138$	−5.74411	−	50.1904i	−0.00354327	−	0.0309601i
$139$	565.929	−	234.415i	0.345334	−	0.143042i	−0.203273	−	0.979122i	$-0.565158\pi$
$139$	565.929	−	234.415i	0.345334	−	0.143042i	0.548608	+	0.836080i	$0.315158\pi$
$140$	−963.269	+	379.753i	−0.581508	+	0.229250i
$141$	62.8774	−	151.799i	0.0375548	−	0.0906654i
$142$	−282.229	+	156.628i	−0.166790	+	0.0925629i
$143$	−1062.69			−0.621445
$144$	−555.874	+	1625.01i	−0.321686	+	0.940401i
$145$	−655.692	+	2621.69i	−0.375533	+	1.50152i
$146$	1415.70	−	785.669i	0.802495	−	0.445359i
$147$	−78.3612	−	32.4583i	−0.0439668	−	0.0182117i
$148$	−2909.94	−	483.941i	−1.61619	−	0.268782i
$149$	2372.89	−	982.884i	1.30466	−	0.540409i	0.381341	−	0.924435i	$-0.375463\pi$
$149$	2372.89	−	982.884i	1.30466	−	0.540409i	0.923322	+	0.384025i	$0.125463\pi$
$150$	52.7164	−	133.455i	0.0286952	−	0.0726437i
$151$	−1029.38	−	1029.38i	−0.554764	−	0.554764i	0.373048	−	0.927812i	$-0.378313\pi$
$151$	−1029.38	−	1029.38i	−0.554764	−	0.554764i	−0.927812	+	0.373048i	$0.878313\pi$
$152$	−1330.56	+	473.441i	−0.710015	+	0.252639i
$153$	132.733	+	132.733i	0.0701361	+	0.0701361i
$154$	452.796	+	359.798i	0.236931	+	0.188268i
$155$	533.176	+	3585.44i	0.276295	+	1.85800i
$156$	−190.291	+	44.1342i	−0.0976631	+	0.0226511i
$157$	−802.704	+	1937.90i	−0.408043	+	0.985104i	0.577609	+	0.816314i	$0.303986\pi$
$157$	−802.704	+	1937.90i	−0.408043	+	0.985104i	−0.985652	+	0.168790i	$0.946014\pi$
$158$	−572.244	+	1999.46i	−0.288135	+	1.00676i
$159$	138.135			0.0688981
$160$	−1918.12	+	645.618i	−0.947754	+	0.319003i
$161$	509.458			0.249385
$162$	556.982	−	1946.13i	0.270127	−	0.943841i
$163$	1162.59	−	2806.74i	0.558658	−	1.34872i	−0.352171	−	0.935936i	$-0.614557\pi$
$163$	1162.59	−	2806.74i	0.558658	−	1.34872i	0.910829	−	0.412784i	$-0.135443\pi$
$164$	73.6307	+	317.469i	0.0350585	+	0.151159i
$165$	−79.2753	+	11.7887i	−0.0374035	+	0.00556211i
$166$	−2717.61	−	2159.45i	−1.27065	−	1.00967i
$167$	−140.070	−	140.070i	−0.0649037	−	0.0649037i	0.673910	−	0.738814i	$-0.264614\pi$
$167$	−140.070	−	140.070i	−0.0649037	−	0.0649037i	−0.738814	+	0.673910i	$0.764614\pi$
$168$	96.0227	+	45.6223i	0.0440971	+	0.0209514i
$169$	1006.04	+	1006.04i	0.457915	+	0.457915i
$170$	−28.9219	+	219.302i	−0.0130483	+	0.0989396i
$171$	1547.41	−	640.960i	0.692010	−	0.286640i
$172$	293.155	−	1762.74i	0.129959	−	0.781442i
$173$	−1918.49	−	794.666i	−0.843124	−	0.349233i	−0.0810393	−	0.996711i	$-0.525824\pi$
$173$	−1918.49	−	794.666i	−0.843124	−	0.349233i	−0.762084	+	0.647478i	$0.775824\pi$
$174$	242.611	−	134.641i	0.105703	−	0.0586617i
$175$	1276.67	+	681.209i	0.551471	+	0.294255i
$176$	848.157	+	747.342i	0.363252	+	0.320074i
$177$	−148.395			−0.0630174
$178$	410.341	−	227.726i	0.172789	−	0.0958923i
$179$	635.261	−	1533.65i	0.265260	−	0.640395i	−0.733988	−	0.679163i	$-0.762343\pi$
$179$	635.261	−	1533.65i	0.265260	−	0.640395i	0.999248	+	0.0387674i	$0.0123431\pi$
$180$	2232.96	−	880.308i	0.924640	−	0.364524i
$181$	1059.98	−	439.060i	0.435293	−	0.180304i	−0.154266	−	0.988029i	$-0.549301\pi$
$181$	1059.98	−	439.060i	0.435293	−	0.180304i	0.589559	+	0.807725i	$0.299301\pi$
$182$	−223.992	−	1957.18i	−0.0912276	−	0.797121i
$183$	69.6649	−	69.6649i	0.0281409	−	0.0281409i
$184$	994.510	+	50.6118i	0.398458	+	0.0202780i
$185$	2120.73	+	3535.32i	0.842806	+	1.40498i
$186$	231.538	−	291.384i	0.0912751	−	0.114867i
$187$	114.148	−	47.2818i	0.0446383	−	0.0184898i
$188$	2748.36	+	1713.51i	1.06619	+	0.664739i
$189$	−233.679	−	96.7931i	−0.0899347	−	0.0372522i
$190$	1709.07	+	987.243i	0.652572	+	0.376958i
$191$	−3258.74			−1.23452			−0.617262	−	0.786758i	$-0.711758\pi$
$191$	−3258.74			−1.23452			−0.617262	+	0.786758i	$0.711758\pi$
$192$	182.913	+	98.5984i	0.0687532	+	0.0370611i
$193$		−	3037.57i		−	1.13290i	−0.824098	−	0.566448i	$-0.808317\pi$
$193$		−	3037.57i		−	1.13290i	0.824098	−	0.566448i	$-0.191683\pi$
$194$	−18.0676	+	63.1294i	−0.00668649	+	0.0233630i
$195$	219.333	+	162.546i	0.0805475	+	0.0596930i
$196$	884.542	−	1418.75i	0.322355	−	0.517035i
$197$	4657.46	−	1929.18i	1.68442	−	0.697709i	0.684897	−	0.728640i	$-0.259847\pi$
$197$	4657.46	−	1929.18i	1.68442	−	0.697709i	0.999522	+	0.0309314i	$0.00984733\pi$
$198$	−1049.63	−	834.051i	−0.376738	−	0.299361i
$199$	−993.987	+	993.987i	−0.354080	+	0.354080i	−0.861625	−	0.507545i	$-0.830553\pi$
$199$	−993.987	+	993.987i	−0.354080	+	0.354080i	0.507545	+	0.861625i	$0.330553\pi$
$200$	2424.51	+	1456.62i	0.857195	+	0.514991i
$201$	−232.209	−	232.209i	−0.0814863	−	0.0814863i
$202$	106.412	+	929.801i	0.0370651	+	0.323864i
$203$	1070.81	+	2585.17i	0.370228	+	0.893811i
$204$	18.4764	−	13.2072i	0.00634120	−	0.00453279i
$205$	271.180	−	365.921i	0.0923905	−	0.124668i
$206$	−2081.31	−	3750.32i	−0.703940	−	1.26843i
$207$	−1180.98			−0.396540
$208$	−242.819	−	3842.86i	−0.0809446	−	1.28103i
$209$		−	1102.43i		−	0.364865i
$210$	−38.4211	−	143.518i	−0.0126253	−	0.0471605i
$211$	−207.176	+	500.166i	−0.0675950	+	0.163189i	−0.954067	−	0.299594i	$-0.903149\pi$
$211$	−207.176	+	500.166i	−0.0675950	+	0.163189i	0.886472	+	0.462782i	$0.153149\pi$
$212$	−446.695	+	2685.98i	−0.144713	+	0.870160i
$213$	−17.7241	−	42.7897i	−0.00570157	−	0.0137648i
$214$	279.303	+	2440.47i	0.0892186	+	0.779567i
$215$	−2141.58	+	1284.67i	−0.679323	+	0.407505i
$216$	−446.548	−	212.164i	−0.140666	−	0.0668330i
$217$	2653.96	+	2653.96i	0.830242	+	0.830242i
$218$	−1056.07	+	1329.04i	−0.328102	+	0.412907i
$219$	88.9066	+	214.639i	0.0274326	+	0.0662283i
$220$	27.1306	−	1579.60i	0.00831430	−	0.484076i
$221$	−388.815	−	161.052i	−0.118346	−	0.0490206i
$222$	116.467	−	406.942i	0.0352105	−	0.123028i
$223$			1802.31i			0.541218i	0.962689	+	0.270609i	$0.0872251\pi$
$223$			1802.31i			0.541218i	−0.962689	+	0.270609i	$0.912775\pi$
$224$	−1197.63	+	1719.60i	−0.357231	+	0.512926i
$225$	−2959.47	−	1579.12i	−0.876880	−	0.467886i
$226$	2567.47	+	734.809i	0.755688	+	0.216278i
$227$	−1048.26	+	2530.72i	−0.306499	+	0.739954i	0.693315	+	0.720635i	$0.256150\pi$
$227$	−1048.26	+	2530.72i	−0.306499	+	0.739954i	−0.999813	+	0.0193185i	$0.993850\pi$
$228$	−45.7847	−	197.407i	−0.0132990	−	0.0573404i
$229$	−1742.01	−	4205.59i	−0.502688	−	1.21360i	−0.948014	−	0.318227i	$-0.896912\pi$
$229$	−1742.01	−	4205.59i	−0.502688	−	1.21360i	0.445327	−	0.895368i	$-0.353088\pi$
$230$	−846.946	−	1104.28i	−0.242809	−	0.316582i
$231$	−58.6800	+	58.6800i	−0.0167137	+	0.0167137i
$232$	1833.51	+	5152.88i	0.518860	+	1.45820i
$233$	−570.178	+	570.178i	−0.160316	+	0.160316i	−0.782707	−	0.622391i	$-0.786161\pi$
$233$	−570.178	+	570.178i	−0.160316	+	0.160316i	0.622391	+	0.782707i	$0.286161\pi$
$234$	519.239	+	4536.96i	0.145059	+	1.26748i
$235$	−665.768	−	4477.08i	−0.184808	−	1.24278i
$236$	479.876	−	2885.50i	0.132361	−	0.795890i
$237$	−275.704	−	114.200i	−0.0755650	−	0.0313001i
$238$	111.140	+	200.264i	0.0302695	+	0.0545428i
$239$		−	4426.38i		−	1.19799i	−0.800754	−	0.598993i	$-0.795568\pi$
$239$		−	4426.38i		−	1.19799i	0.800754	−	0.598993i	$-0.204432\pi$
$240$	−60.7438	−	283.979i	−0.0163375	−	0.0763781i
$241$			5713.00i			1.52700i	0.645809	+	0.763499i	$0.276520\pi$
$241$			5713.00i			1.52700i	−0.645809	+	0.763499i	$0.723480\pi$
$242$	2520.13	−	1398.59i	0.669422	−	0.371508i
$243$	813.370	+	336.909i	0.214723	+	0.0889412i
$244$	1129.33	+	1579.89i	0.296303	+	0.414517i
$245$	−2311.14	+	343.680i	−0.602666	+	0.0896200i
$246$	−46.4593	+	5.31710i	−0.0120412	+	0.00137807i
$247$	−2655.27	+	2655.27i	−0.684012	+	0.684012i
$248$	4917.13	+	5444.44i	1.25902	+	1.39404i
$249$	352.188	−	352.188i	0.0896344	−	0.0896344i
$250$	−645.847	−	3899.73i	−0.163388	−	0.986562i
$251$	−705.172	−	1702.44i	−0.177331	−	0.428115i	0.810074	−	0.586328i	$-0.199427\pi$
$251$	−705.172	−	1702.44i	−0.177331	−	0.428115i	−0.987405	+	0.158213i	$0.949427\pi$
$252$	1314.85	−	2108.93i	0.328682	−	0.527183i
$253$	−297.470	+	718.155i	−0.0739200	+	0.178459i
$254$	−1438.55	+	5026.40i	−0.355366	+	1.24167i
$255$	−30.7917	−	7.70107i	−0.00756176	−	0.00189121i
$256$	−2508.71	+	3237.84i	−0.612478	+	0.790488i
$257$		−	2806.74i		−	0.681243i	−0.940201	−	0.340621i	$-0.889363\pi$
$257$		−	2806.74i		−	0.681243i	0.940201	−	0.340621i	$-0.110637\pi$
$258$	246.512	+	70.5517i	0.0594852	+	0.0170246i
$259$	3943.72	+	1633.54i	0.946142	+	0.391905i
$260$	−3869.92	+	3739.22i	−0.923084	+	0.891911i
$261$	−2482.26	−	5992.71i	−0.588690	−	1.42122i
$262$	−2697.22	−	2143.24i	−0.636010	−	0.505382i
$263$	4261.11	+	4261.11i	0.999055	+	0.999055i	1.00000		0.000944982i	$-0.000300797\pi$
$263$	4261.11	+	4261.11i	0.999055	+	0.999055i	−0.000944982		1.00000i	$0.500301\pi$
$264$	−120.378	+	108.719i	−0.0280635	+	0.0253455i
$265$	3263.23	−	1957.51i	0.756448	−	0.453770i
$266$	2030.38	−	232.369i	0.468009	−	0.0535619i
$267$	25.7696	+	62.2133i	0.00590664	+	0.0142599i
$268$	5266.13	−	3764.31i	1.20030	−	0.857993i
$269$	2655.71	−	6411.44i	0.601938	−	1.45321i	−0.269646	−	0.962959i	$-0.586907\pi$
$269$	2655.71	−	6411.44i	0.601938	−	1.45321i	0.871584	−	0.490246i	$-0.163093\pi$
$270$	178.675	+	667.425i	0.0402734	+	0.150438i
$271$			3572.98i			0.800897i	0.916319	+	0.400449i	$0.131146\pi$
$271$			3572.98i			0.800897i	−0.916319	+	0.400449i	$0.868854\pi$
$272$	197.061	+	401.976i	0.0439286	+	0.0896079i
$273$	282.668			0.0626662
$274$	−1474.02	+	818.035i	−0.324996	+	0.180362i
$275$	−1705.71	+	1401.90i	−0.374029	+	0.307411i
$276$	−23.4410	+	140.951i	−0.00511225	+	0.0307400i
$277$	−526.889	−	1272.02i	−0.114288	−	0.275915i	0.856377	−	0.516350i	$-0.172710\pi$
$277$	−526.889	−	1272.02i	−0.114288	−	0.275915i	−0.970665	+	0.240435i	$0.922710\pi$
$278$	−1721.34	+	197.001i	−0.371363	+	0.0425011i
$279$	−6152.17	−	6152.17i	−1.32015	−	1.32015i
$280$	2914.91	−	282.980i	0.622140	−	0.0603974i
$281$	109.510	−	109.510i	0.0232485	−	0.0232485i	−0.695387	−	0.718635i	$-0.744767\pi$
$281$	109.510	−	109.510i	0.0232485	−	0.0232485i	0.718635	+	0.695387i	$0.244767\pi$
$282$	−289.117	+	363.847i	−0.0610521	+	0.0768325i
$283$	−4776.35	+	1978.43i	−1.00327	+	0.415567i	−0.822994	−	0.568050i	$-0.807698\pi$
$283$	−4776.35	+	1978.43i	−1.00327	+	0.415567i	−0.180273	+	0.983617i	$0.557698\pi$
$284$	889.347	−	206.267i	0.185821	−	0.0430975i
$285$	−168.624	+	227.536i	−0.0350472	+	0.0472914i
$286$	2889.72	+	827.038i	0.597457	+	0.170992i
$287$		−	471.586i		−	0.0969924i
$288$	2776.23	−	3986.21i	0.568023	−	0.815589i
$289$	−4864.07			−0.990041
$290$	3823.32	−	6618.75i	0.774183	−	1.34023i
$291$	−8.70488	−	3.60568i	−0.00175357	−	0.000726353i
$292$	−4461.09	+	1034.66i	−0.894061	+	0.207360i
$293$	5880.40	−	2435.74i	1.17248	−	0.485657i	0.290468	−	0.956885i	$-0.406189\pi$
$293$	5880.40	−	2435.74i	1.17248	−	0.485657i	0.882012	+	0.471228i	$0.156189\pi$
$294$	187.823	+	149.247i	0.0372588	+	0.0296063i
$295$	−3505.63	+	2102.92i	−0.691883	+	0.415039i
$296$	7536.23	+	3580.61i	1.47985	+	0.703105i
$297$	272.888	−	272.888i	0.0533150	−	0.0533150i
$298$	−7217.42	+	826.007i	−1.40300	+	0.160568i
$299$	2446.19	−	1013.25i	0.473134	−	0.195978i
$300$	−247.210	+	321.871i	−0.0475757	+	0.0619441i
$301$	−989.545	+	2388.97i	−0.189490	+	0.457469i
$302$	1998.02	+	3600.24i	0.380706	+	0.685996i
$303$	−134.288			−0.0254608
$304$	3986.57	−	251.900i	0.752123	−	0.0475245i
$305$	658.509	−	2632.96i	0.123627	−	0.494304i
$306$	−257.635	−	464.234i	−0.0481308	−	0.0867271i
$307$	2472.13	+	1023.99i	0.459582	+	0.190365i	0.600448	−	0.799663i	$-0.294989\pi$
$307$	2472.13	+	1023.99i	0.459582	+	0.190365i	−0.140866	+	0.990029i	$0.544989\pi$
$308$	−951.255	−	1330.77i	−0.175983	−	0.246194i
$309$	568.599	−	235.521i	0.104681	−	0.0433603i
$310$	1340.53	−	10164.7i	0.245603	−	1.86230i
$311$	5529.74	+	5529.74i	1.00824	+	1.00824i	0.999966	+	0.00827558i	$0.00263423\pi$
$311$	5529.74	+	5529.74i	1.00824	+	1.00824i	0.00827558	+	0.999966i	$0.497366\pi$
$312$	551.796	+	28.0815i	0.100126	+	0.00509553i
$313$	433.439	+	433.439i	0.0782729	+	0.0782729i	0.745159	−	0.666886i	$-0.232373\pi$
$313$	433.439	+	433.439i	0.0782729	+	0.0782729i	−0.666886	+	0.745159i	$0.732373\pi$
$314$	3690.92	−	4644.93i	0.663347	−	0.834805i
$315$	−3435.45	+	510.872i	−0.614495	+	0.0913790i
$316$	3112.15	−	4991.68i	0.554026	−	0.888619i
$317$	−2053.68	+	4958.03i	−0.363869	+	0.878456i	0.630858	+	0.775898i	$0.282703\pi$
$317$	−2053.68	+	4958.03i	−0.363869	+	0.878456i	−0.994727	+	0.102558i	$0.967297\pi$
$318$	−375.623	−	107.503i	−0.0662386	−	0.0189575i
$319$	−4269.42			−0.749347
$320$	5718.30	−	262.823i	0.998945	−	0.0459132i
$321$	−352.468			−0.0612862
$322$	−1385.34	−	396.485i	−0.239758	−	0.0686188i
$323$	167.075	−	403.355i	0.0287812	−	0.0694839i
$324$	−3029.15	+	4858.54i	−0.519401	+	0.833083i
$325$	7484.87	+	731.726i	1.27749	+	0.124889i
$326$	−5345.73	+	6727.46i	−0.908198	+	1.14294i
$327$	−172.236	−	172.236i	−0.0291275	−	0.0291275i
$328$	46.8494	−	920.580i	0.00788667	−	0.154971i
$329$	−3313.96	−	3313.96i	−0.555333	−	0.555333i
$330$	224.744	+	29.6395i	0.0374902	+	0.00494425i
$331$	−2684.19	+	1111.83i	−0.445730	+	0.184627i	−0.594247	−	0.804283i	$-0.702550\pi$
$331$	−2684.19	+	1111.83i	−0.445730	+	0.184627i	0.148518	+	0.988910i	$0.452550\pi$
$332$	5709.27	+	7987.06i	0.943787	+	1.32032i
$333$	−9141.97	−	3786.73i	−1.50443	−	0.623157i
$334$	271.875	+	489.894i	0.0445400	+	0.0802568i
$335$	−8776.24	−	2194.96i	−1.43134	−	0.357980i
$336$	−225.604	−	198.788i	−0.0366301	−	0.0322761i
$337$	−5916.97			−0.956433			−0.478216	−	0.878242i	$-0.658717\pi$
$337$	−5916.97			−0.956433			−0.478216	+	0.878242i	$0.658717\pi$
$338$	−1952.72	−	3518.62i	−0.314243	−	0.566236i
$339$	−146.643	+	354.027i	−0.0234942	+	0.0567201i
$340$	249.318	−	573.830i	0.0397681	−	0.0915303i
$341$	−5290.78	+	2191.51i	−0.840210	+	0.348026i
$342$	−4706.63	+	538.657i	−0.744168	+	0.0851674i
$343$	−4518.42	+	4518.42i	−0.711288	+	0.711288i
$344$	−2169.02	+	4565.20i	−0.339958	+	0.715520i
$345$	171.243	−	102.723i	0.0267229	−	0.0160302i
$346$	4598.42	+	3653.96i	0.714487	+	0.567741i
$347$	−8870.37	+	3674.23i	−1.37230	+	0.568423i	−0.942410	−	0.334460i	$-0.891446\pi$
$347$	−8870.37	+	3674.23i	−1.37230	+	0.568423i	−0.429885	+	0.902884i	$0.641446\pi$
$348$	−764.504	+	177.312i	−0.117764	+	0.0273130i
$349$	4523.35	+	1873.63i	0.693780	+	0.287373i	0.701574	−	0.712596i	$-0.252481\pi$
$349$	4523.35	+	1873.63i	0.693780	+	0.287373i	−0.00779399	+	0.999970i	$0.502481\pi$
$350$	−2941.45	−	2845.95i	−0.449220	−	0.434635i
$351$	−1314.53			−0.199899
$352$	−1724.73	−	2692.29i	−0.261161	−	0.407669i
$353$		−	5717.13i		−	0.862018i	−0.902348	−	0.431009i	$-0.858158\pi$
$353$		−	5717.13i		−	0.862018i	0.902348	−	0.431009i	$-0.141842\pi$
$354$	403.525	+	115.489i	0.0605850	+	0.0173394i
$355$	−1025.08	−	759.677i	−0.153255	−	0.113576i
$356$	−1293.05	+	299.898i	−0.192504	+	0.0446476i
$357$	−30.3627	+	12.5767i	−0.00450131	+	0.00186450i
$358$	−2921.00	+	3676.00i	−0.431228	+	0.542689i
$359$	8158.62	−	8158.62i	1.19943	−	1.19943i	0.225092	−	0.974337i	$-0.427732\pi$
$359$	8158.62	−	8158.62i	1.19943	−	1.19943i	0.974337	−	0.225092i	$-0.0722684\pi$
$360$	−6757.08	+	655.977i	−0.989249	+	0.0960362i
$361$	2095.47	+	2095.47i	0.305507	+	0.305507i
$362$	−3224.06	+	368.982i	−0.468102	+	0.0535726i
$363$	158.265	+	382.086i	0.0228837	+	0.0552461i
$364$	−914.084	+	5496.39i	−0.131624	+	0.791454i
$365$	5141.95	+	3810.65i	0.737376	+	0.546462i
$366$	−243.653	+	135.220i	−0.0347977	+	0.0193116i
$367$	−378.023			−0.0537673			−0.0268837	−	0.999639i	$-0.508558\pi$
$367$	−378.023			−0.0537673			−0.0268837	+	0.999639i	$0.508558\pi$
$368$	−2664.93	−	911.603i	−0.377498	−	0.129132i
$369$			1093.19i			0.154225i
$370$	−3015.43	−	11263.9i	−0.423689	−	1.58265i
$371$	1507.82	−	3640.20i	0.211003	−	0.509406i
$372$	−856.379	+	612.153i	−0.119358	+	0.0853189i
$373$	−4755.38	−	11480.5i	−0.660119	−	1.59367i	−0.797616	−	0.603166i	$-0.793906\pi$
$373$	−4755.38	−	11480.5i	−0.660119	−	1.59367i	0.137497	−	0.990502i	$-0.456094\pi$
$374$	−347.195	+	39.7353i	−0.0480028	+	0.00549375i
$375$	566.479	−	28.4458i	0.0780076	−	0.00391716i
$376$	−6139.94	−	6798.38i	−0.842136	−	0.932446i
$377$	10283.2	+	10283.2i	1.40480	+	1.40480i
$378$	560.103	+	445.066i	0.0762133	+	0.0605601i
$379$	3275.00	+	7906.55i	0.443867	+	1.07159i	0.974580	+	0.224038i	$0.0719240\pi$
$379$	3275.00	+	7906.55i	0.443867	+	1.07159i	−0.530714	+	0.847551i	$0.678076\pi$
$380$	−3879.06	−	4014.64i	−0.523662	−	0.541965i
$381$	−693.088	−	287.086i	−0.0931967	−	0.0386034i
$382$	8861.33	+	2536.11i	1.18687	+	0.339683i
$383$		−	14206.8i		−	1.89538i	−0.319188	−	0.947691i	$-0.603410\pi$
$383$		−	14206.8i		−	1.89538i	0.319188	−	0.947691i	$-0.396590\pi$
$384$	−420.652	−	410.466i	−0.0559019	−	0.0545482i
$385$	−554.674	+	2217.79i	−0.0734254	+	0.293581i
$386$	−2363.98	+	8259.91i	−0.311719	+	1.08917i
$387$	2293.87	−	5537.90i	0.301303	−	0.727409i
$388$	98.2608	−	157.604i	0.0128568	−	0.0206214i
$389$	788.251	+	1903.01i	0.102740	+	0.248037i	0.966888	−	0.255202i	$-0.0821418\pi$
$389$	788.251	+	1903.01i	0.102740	+	0.248037i	−0.864148	+	0.503238i	$0.832142\pi$
$390$	−469.921	−	612.698i	−0.0610138	−	0.0795517i
$391$	−217.675	+	217.675i	−0.0281542	+	0.0281542i
$392$	−3509.43	+	3169.53i	−0.452176	+	0.408381i
$393$	349.545	−	349.545i	0.0448657	−	0.0448657i
$394$	−14166.2	+	1621.27i	−1.81138	+	0.207306i
$395$	−8131.45	+	1209.19i	−1.03579	+	0.154028i
$396$	2205.11	+	3084.87i	0.279826	+	0.391466i
$397$	6563.62	+	2718.74i	0.829770	+	0.343702i	0.756812	−	0.653633i	$-0.226756\pi$
$397$	6563.62	+	2718.74i	0.829770	+	0.343702i	0.0729585	+	0.997335i	$0.476756\pi$
$398$	3476.47	−	1929.33i	0.437838	−	0.242986i
$399$			293.240i			0.0367928i
$400$	−5459.26	−	5847.78i	−0.682407	−	0.730972i
$401$		−	8252.03i		−	1.02765i	−0.857896	−	0.513824i	$-0.828229\pi$
$401$		−	8252.03i		−	1.02765i	0.857896	−	0.513824i	$-0.171771\pi$
$402$	450.718	+	812.151i	0.0559198	+	0.100762i
$403$	18021.5	+	7464.77i	2.22759	+	0.922696i
$404$	434.255	−	2611.18i	0.0534777	−	0.321562i
$405$	7914.57	−	1176.94i	0.971058	−	0.144402i
$406$	−899.903	−	7863.09i	−0.110003	−	0.961179i
$407$	−4605.43	+	4605.43i	−0.560891	+	0.560891i
$408$	−60.5204	+	21.5345i	−0.00734364	+	0.00261303i
$409$	1552.62	−	1552.62i	0.187706	−	0.187706i	−0.606997	−	0.794704i	$-0.707626\pi$
$409$	1552.62	−	1552.62i	0.187706	−	0.187706i	0.794704	+	0.606997i	$0.207626\pi$
$410$	−1022.19	+	783.986i	−0.123127	+	0.0944348i
$411$	−92.5691	−	223.482i	−0.0111097	−	0.0268212i
$412$	2740.92	+	11817.8i	0.327756	+	1.41316i
$413$	−1619.82	+	3910.60i	−0.192993	+	0.465927i
$414$	3211.38	+	919.096i	0.381234	+	0.109109i
$415$	3329.06	−	13310.8i	0.393776	−	1.57446i
$416$	−2330.41	+	10638.7i	−0.274659	+	1.25385i
$417$		−	248.606i		−	0.0291950i
$418$	−857.967	+	2997.79i	−0.100394	+	0.350782i
$419$	−11750.0	−	4867.01i	−1.36999	−	0.567468i	−0.428204	−	0.903682i	$-0.640854\pi$
$419$	−11750.0	−	4867.01i	−1.36999	−	0.567468i	−0.941786	+	0.336214i	$0.890854\pi$
$420$	−7.21656	+	420.164i	−0.000838410	+	0.0488140i
$421$	3477.18	+	8394.66i	0.402536	+	0.971807i	0.987048	+	0.160423i	$0.0512857\pi$
$421$	3477.18	+	8394.66i	0.402536	+	0.971807i	−0.584513	+	0.811385i	$0.698714\pi$
$422$	952.616	−	1198.84i	0.109888	−	0.138291i
$423$	7682.11	+	7682.11i	0.883019	+	0.883019i
$424$	3305.04	−	6956.22i	0.378554	−	0.796755i
$425$	−836.541	+	254.423i	−0.0954781	+	0.0290384i
$426$	14.8952	+	130.150i	0.00169407	+	0.0148023i
$427$	−1075.41	−	2596.28i	−0.121880	−	0.294245i
$428$	1139.80	−	6853.63i	0.128725	−	0.774025i
$429$	−165.049	+	398.462i	−0.0185749	+	0.0448437i
$430$	6823.28	−	1826.65i	0.765228	−	0.204858i
$431$			7330.20i			0.819219i	0.912261	+	0.409610i	$0.134335\pi$
$431$			7330.20i			0.819219i	−0.912261	+	0.409610i	$0.865665\pi$
$432$	1049.16	+	924.453i	0.116847	+	0.102958i
$433$	−13402.9			−1.48753			−0.743765	−	0.668441i	$-0.766962\pi$
$433$	−13402.9			−1.48753			−0.743765	+	0.668441i	$0.766962\pi$
$434$	−5151.34	−	9282.23i	−0.569752	−	1.02664i
$435$	881.184	+	653.036i	0.0971253	+	0.0719786i
$436$	3906.04	−	2792.10i	0.429050	−	0.306691i
$437$	1051.14	+	2537.68i	0.115064	+	0.277788i
$438$	−74.7163	−	652.850i	−0.00815088	−	0.0712200i
$439$	11925.8	+	11925.8i	1.29655	+	1.29655i	0.930657	+	0.365893i	$0.119236\pi$
$439$	11925.8	+	11925.8i	1.29655	+	1.29655i	0.365893	+	0.930657i	$0.380764\pi$
$440$	−1303.10	+	4274.22i	−0.141188	+	0.463104i
$441$	3965.63	−	3965.63i	0.428207	−	0.428207i
$442$	931.946	+	740.536i	0.100290	+	0.0796917i
$443$	−6233.97	+	2582.19i	−0.668589	+	0.276939i	−0.691048	−	0.722809i	$-0.742851\pi$
$443$	−6233.97	+	2582.19i	−0.668589	+	0.276939i	0.0224589	+	0.999748i	$0.492851\pi$
$444$	−633.405	+	1015.94i	−0.0677029	+	0.108591i
$445$	1490.40	+	1104.52i	0.158768	+	0.117661i
$446$	1402.65	−	4900.94i	0.148918	−	0.520327i
$447$		−	1042.38i		−	0.110298i
$448$	4594.92	−	3743.96i	0.484575	−	0.394834i
$449$	577.190			0.0606665			0.0303333	−	0.999540i	$-0.490343\pi$
$449$	577.190			0.0606665			0.0303333	+	0.999540i	$0.490343\pi$
$450$	6818.60	+	6597.22i	0.714293	+	0.691102i
$451$	664.769	+	275.356i	0.0694074	+	0.0287495i
$452$	−6409.72	−	3996.26i	−0.667009	−	0.415859i
$453$	−545.845	+	226.097i	−0.0566138	+	0.0234502i
$454$	4820.00	−	6065.85i	0.498268	−	0.627058i
$455$	6677.63	−	4005.71i	0.688027	−	0.412726i
$456$	−29.1317	+	572.431i	−0.00299171	+	0.0587863i
$457$	6069.59	−	6069.59i	0.621276	−	0.621276i	−0.324581	−	0.945858i	$-0.605223\pi$
$457$	6069.59	−	6069.59i	0.621276	−	0.621276i	0.945858	+	0.324581i	$0.105223\pi$
$458$	1463.97	+	12791.8i	0.149360	+	1.30507i
$459$	141.200	−	58.4871i	0.0143587	−	0.00594759i
$460$	1443.66	+	3661.94i	0.146328	+	0.371171i
$461$	−3743.29	+	9037.09i	−0.378183	+	0.913014i	0.614124	+	0.789210i	$0.289509\pi$
$461$	−3743.29	+	9037.09i	−0.378183	+	0.913014i	−0.992307	+	0.123804i	$0.960491\pi$
$462$	205.233	−	113.898i	0.0206673	−	0.0114697i
$463$	17095.0			1.71592			0.857960	−	0.513717i	$-0.171732\pi$
$463$	17095.0			1.71592			0.857960	+	0.513717i	$0.171732\pi$
$464$	−975.540	−	15438.9i	−0.0976041	−	1.54468i
$465$	1427.19	+	356.944i	0.142332	+	0.0355976i
$466$	1994.20	−	1106.72i	0.198239	−	0.110016i
$467$	2292.43	+	949.557i	0.227155	+	0.0940905i	0.493358	−	0.869826i	$-0.335769\pi$
$467$	2292.43	+	949.557i	0.227155	+	0.0940905i	−0.266203	+	0.963917i	$0.585769\pi$
$468$	2118.95	−	12741.2i	0.209291	−	1.25847i
$469$	−8653.99	+	3584.60i	−0.852034	+	0.352924i
$470$	−1673.89	+	12692.4i	−0.164279	+	1.24566i
$471$	601.958	+	601.958i	0.0588891	+	0.0588891i
$472$	−3550.54	+	7472.93i	−0.346244	+	0.728749i
$473$	−2789.82	−	2789.82i	−0.271196	−	0.271196i
$474$	660.832	+	525.106i	0.0640359	+	0.0508838i
$475$	−759.091	+	7764.78i	−0.0733252	+	0.750048i
$476$	−146.363	−	631.063i	−0.0140935	−	0.0607662i
$477$	−3495.29	+	8438.38i	−0.335510	+	0.809993i
$478$	−3444.83	+	12036.4i	−0.329629	+	1.15174i
$479$	2658.72			0.253611			0.126806	−	0.991928i	$-0.459528\pi$
$479$	2658.72			0.253611			0.126806	+	0.991928i	$0.459528\pi$
$480$	−55.8284	+	819.483i	−0.00530876	+	0.0779252i
$481$	22184.9			2.10300
$482$	4446.14	−	15535.1i	0.420158	−	1.46806i
$483$	79.1249	−	191.025i	0.00745406	−	0.0179957i
$484$	−7941.33	+	1841.84i	−0.745805	+	0.172975i
$485$	−256.737	+	38.1782i	−0.0240367	+	0.00357440i
$486$	−1949.56	−	1549.14i	−0.181962	−	0.144590i
$487$	7016.26	+	7016.26i	0.652848	+	0.652848i	0.953678	−	0.300830i	$-0.0972637\pi$
$487$	7016.26	+	7016.26i	0.652848	+	0.652848i	−0.300830	+	0.953678i	$0.597264\pi$
$488$	−1841.38	−	5175.02i	−0.170811	−	0.480045i
$489$	−871.842	−	871.842i	−0.0806259	−	0.0806259i
$490$	6552.04	+	864.090i	0.604063	+	0.0796645i
$491$	1448.58	−	600.022i	0.133144	−	0.0551499i	−0.315117	−	0.949053i	$-0.602044\pi$
$491$	1448.58	−	600.022i	0.133144	−	0.0551499i	0.448261	+	0.893903i	$0.352044\pi$
$492$	130.473	+	21.6984i	0.0119556	+	0.00198829i
$493$	−1562.09	−	647.037i	−0.142703	−	0.0591097i
$494$	9286.82	−	5153.89i	0.845818	−	0.469402i
$495$	1285.79	−	5141.07i	0.116752	−	0.466816i
$496$	−9133.77	−	18631.5i	−0.826852	−	1.68666i
$497$	−1321.09			−0.119233
$498$	−1231.78	+	683.597i	−0.110838	+	0.0615115i
$499$	3037.27	−	7332.63i	0.272479	−	0.657823i	−0.727109	−	0.686522i	$-0.759137\pi$
$499$	3037.27	−	7332.63i	0.272479	−	0.657823i	0.999588	+	0.0286994i	$0.00913657\pi$
$500$	−1278.74	+	11107.0i	−0.114374	+	0.993438i
$501$	−74.2745	+	30.7655i	−0.00662343	+	0.00274352i
$502$	592.621	+	5178.15i	0.0526892	+	0.460383i
$503$	4863.42	−	4863.42i	0.431111	−	0.431111i	−0.457895	−	0.889006i	$-0.651396\pi$
$503$	4863.42	−	4863.42i	0.431111	−	0.431111i	0.889006	+	0.457895i	$0.151396\pi$
$504$	−5216.69	+	4711.43i	−0.461051	+	0.416397i
$505$	−3172.35	+	1903.00i	−0.279540	+	0.167687i
$506$	1367.80	−	1721.34i	0.120170	−	0.151231i
$507$	533.471	−	220.971i	0.0467303	−	0.0193563i
$508$	7823.58	−	12548.5i	0.683298	−	1.09596i
$509$	7097.77	+	2939.99i	0.618081	+	0.256018i	0.669679	−	0.742650i	$-0.266432\pi$
$509$	7097.77	+	2939.99i	0.618081	+	0.256018i	−0.0515983	+	0.998668i	$0.516432\pi$
$510$	77.7369	+	44.9047i	0.00674951	+	0.00389885i
$511$	6626.76			0.573680
$512$	9341.66	−	6852.09i	0.806342	−	0.591450i
$513$		−	1363.69i		−	0.117366i
$514$	−2184.34	+	7632.22i	−0.187446	+	0.654947i
$515$	10094.7	−	13621.5i	0.863743	−	1.16550i
$516$	−615.422	−	383.696i	−0.0525047	−	0.0327350i
$517$	6606.51	−	2736.50i	0.562000	−	0.232788i
$518$	−9452.66	−	7511.21i	−0.801788	−	0.637111i
$519$	−595.930	+	595.930i	−0.0504016	+	0.0504016i
$520$	13433.3	−	7156.13i	1.13287	−	0.603494i
$521$	2532.56	+	2532.56i	0.212962	+	0.212962i	0.805525	−	0.592562i	$-0.201884\pi$
$521$	2532.56	+	2532.56i	0.212962	+	0.212962i	−0.592562	+	0.805525i	$0.701884\pi$
$522$	2086.07	+	18227.5i	0.174914	+	1.52835i
$523$	835.201	+	2016.35i	0.0698294	+	0.168583i	0.954941	−	0.296796i	$-0.0959181\pi$
$523$	835.201	+	2016.35i	0.0698294	+	0.168583i	−0.885112	+	0.465379i	$0.845918\pi$
$524$	5666.43	+	7927.13i	0.472403	+	0.660874i
$525$	453.707	−	372.897i	0.0377169	−	0.0309992i
$526$	−8270.83	−	14903.2i	−0.685599	−	1.23538i
$527$	−2267.90			−0.187460
$528$	411.950	−	201.951i	0.0339542	−	0.0166454i
$529$			10230.3i			0.840820i
$530$	−10397.0	+	2783.36i	−0.852106	+	0.228116i
$531$	3754.92	−	9065.19i	0.306873	−	0.740858i
$532$	−5701.94	−	948.269i	−0.464682	−	0.0772794i
$533$	−937.923	−	2264.35i	−0.0762213	−	0.184015i
$534$	−21.6565	−	189.229i	−0.00175500	−	0.0153347i
$535$	−8326.56	+	4994.84i	−0.672876	+	0.403637i
$536$	−17249.5	+	6137.75i	−1.39005	+	0.494609i
$537$	−476.390	−	476.390i	−0.0382826	−	0.0382826i
$538$	−12211.2	+	15367.5i	−0.978557	+	1.23149i
$539$	−1412.63	−	3410.38i	−0.112887	−	0.272533i
$540$	33.5602	−	1953.95i	0.00267445	−	0.155712i
$541$	−14557.9	−	6030.09i	−1.15692	−	0.479213i	−0.280073	−	0.959979i	$-0.590359\pi$
$541$	−14557.9	−	6030.09i	−1.15692	−	0.479213i	−0.876849	+	0.480766i	$0.840359\pi$
$542$	2780.67	−	9715.83i	0.220369	−	0.769983i
$543$		−	465.639i		−	0.0368002i
$544$	−223.021	−	1246.44i	−0.0175771	−	0.0982361i
$545$	−6509.59	−	1628.07i	−0.511634	−	0.127961i
$546$	−768.647	−	219.987i	−0.0602473	−	0.0172428i
$547$	−1956.68	+	4723.85i	−0.152946	+	0.369245i	−0.981718	−	0.190342i	$-0.939040\pi$
$547$	−1956.68	+	4723.85i	−0.152946	+	0.369245i	0.828772	+	0.559587i	$0.189040\pi$
$548$	4644.87	−	1077.29i	0.362078	−	0.0839770i
$549$	2492.93	+	6018.46i	0.193799	+	0.467872i
$550$	5729.28	−	2484.67i	0.444177	−	0.192630i
$551$	−10667.7	+	10667.7i	−0.824792	+	0.824792i
$552$	173.437	−	365.037i	0.0133731	−	0.0281468i
$553$	−6018.94	+	6018.94i	−0.462841	+	0.462841i
$554$	442.793	+	3869.00i	0.0339576	+	0.296712i
$555$	1654.97	−	246.103i	0.126575	−	0.0188225i
$556$	4834.06	+	803.935i	0.368723	+	0.0613209i
$557$	−10991.0	−	4552.64i	−0.836096	−	0.346322i	−0.0767830	−	0.997048i	$-0.524465\pi$
$557$	−10991.0	−	4552.64i	−0.836096	−	0.346322i	−0.759313	+	0.650725i	$0.774465\pi$
$558$	11941.4	+	21517.2i	0.905947	+	1.63243i
$559$			13438.9i			1.01682i
$560$	−8146.61	−	1499.04i	−0.614745	−	0.113118i
$561$		−	50.1441i		−	0.00377377i
$562$	−383.012	+	212.560i	−0.0287480	+	0.0159542i
$563$	3186.17	+	1319.76i	0.238510	+	0.0987941i	0.498737	−	0.866753i	$-0.333797\pi$
$563$	3186.17	+	1319.76i	0.238510	+	0.0987941i	−0.260227	+	0.965547i	$0.583797\pi$
$564$	1069.35	−	764.385i	0.0798361	−	0.0570681i
$565$	1552.71	+	10441.5i	0.115616	+	0.777478i
$566$	14527.8	−	1662.65i	1.07889	−	0.123474i
$567$	5858.41	−	5858.41i	0.433915	−	0.433915i
$568$	−2578.89	−	131.243i	−0.190506	−	0.00969510i
$569$	8172.00	−	8172.00i	0.602088	−	0.602088i	−0.338778	−	0.940866i	$-0.610014\pi$
$569$	8172.00	−	8172.00i	0.602088	−	0.602088i	0.940866	+	0.338778i	$0.110014\pi$
$570$	635.611	−	487.495i	0.0467067	−	0.0358227i
$571$	−9476.92	−	22879.3i	−0.694565	−	1.67683i	−0.735374	−	0.677661i	$-0.762994\pi$
$571$	−9476.92	−	22879.3i	−0.694565	−	1.67683i	0.0408094	−	0.999167i	$-0.487006\pi$
$572$	−7214.24	−	4497.85i	−0.527347	−	0.328784i
$573$	−506.121	+	1221.89i	−0.0368997	+	0.0890838i
$574$	−367.011	+	1282.36i	−0.0266877	+	0.0932486i
$575$	2589.67	−	4853.37i	0.187820	−	0.351999i
$576$	−10651.5	+	8678.91i	−0.770509	+	0.627815i
$577$		−	1367.83i		−	0.0986886i	−0.998782	−	0.0493443i	$-0.984287\pi$
$577$		−	1367.83i		−	0.0986886i	0.998782	−	0.0493443i	$-0.0157132\pi$
$578$	13226.6	+	3785.46i	0.951826	+	0.272412i
$579$	−1138.95	−	471.771i	−0.0817502	−	0.0338620i
$580$	−15547.6	+	15022.6i	−1.11307	+	1.07548i
$581$	−5436.70	−	13125.4i	−0.388214	−	0.937232i
$582$	20.8647	+	16.5793i	0.00148603	+	0.00118082i
$583$	4250.98	+	4250.98i	0.301986	+	0.301986i
$584$	12936.1	+	658.332i	0.916606	+	0.0466472i
$585$	−15479.5	+	9285.66i	−1.09401	+	0.656265i
$586$	−17885.9	+	2046.98i	−1.26085	+	0.144300i
$587$	−7527.88	−	18173.9i	−0.529316	−	1.27788i	−0.931972	−	0.362531i	$-0.881913\pi$
$587$	−7527.88	−	18173.9i	−0.529316	−	1.27788i	0.402655	−	0.915352i	$-0.368087\pi$
$588$	−394.588	−	552.013i	−0.0276743	−	0.0387154i
$589$	−7743.93	+	18695.5i	−0.541737	+	1.30787i
$590$	11169.3	−	2990.11i	0.779376	−	0.208645i
$591$		−	2045.97i		−	0.142403i
$592$	−17706.3	−	15601.7i	−1.22926	−	1.08315i
$593$	−15750.7			−1.09073			−0.545365	−	0.838199i	$-0.683609\pi$
$593$	−15750.7			−1.09073			−0.545365	+	0.838199i	$0.683609\pi$
$594$	−954.426	+	529.676i	−0.0659269	+	0.0365873i
$595$	−539.051	+	727.377i	−0.0371411	+	0.0501169i
$596$	20268.8	+	3370.83i	1.39302	+	0.231669i
$597$	218.324	+	527.080i	0.0149672	+	0.0361339i
$598$	−7440.37	+	851.524i	−0.508795	+	0.0582298i
$599$	−2239.95	−	2239.95i	−0.152791	−	0.152791i	0.626572	−	0.779363i	$-0.284457\pi$
$599$	−2239.95	−	2239.95i	−0.152791	−	0.152791i	−0.779363	+	0.626572i	$0.784457\pi$
$600$	922.723	−	682.857i	0.0627834	−	0.0464626i
$601$	13502.0	−	13502.0i	0.916400	−	0.916400i	−0.0803655	−	0.996765i	$-0.525609\pi$
$601$	13502.0	−	13502.0i	0.916400	−	0.916400i	0.996765	+	0.0803655i	$0.0256087\pi$
$602$	4550.04	−	5726.11i	0.308049	−	0.387672i
$603$	20060.9	−	8309.49i	1.35480	−	0.561175i
$604$	−2631.23	−	11344.9i	−0.177257	−	0.764269i
$605$	9153.34	+	6783.45i	0.615101	+	0.455845i
$606$	365.162	+	104.509i	0.0244780	+	0.00700561i
$607$		−	17139.1i		−	1.14605i	−0.819537	−	0.573026i	$-0.805769\pi$
$607$		−	17139.1i		−	1.14605i	0.819537	−	0.573026i	$-0.194231\pi$
$608$	−11036.5	−	2417.57i	−0.736168	−	0.161259i
$609$	1135.64			0.0755638
$610$	−3839.75	+	6647.19i	−0.254864	+	0.441208i
$611$	−22503.2	−	9321.13i	−1.48999	−	0.617173i
$612$	339.285	+	1462.87i	0.0224098	+	0.0966227i
$613$	−25293.4	+	10476.9i	−1.66654	+	0.690304i	−0.998548	−	0.0538627i	$-0.982847\pi$
$613$	−25293.4	+	10476.9i	−1.66654	+	0.690304i	−0.667994	+	0.744167i	$0.732847\pi$
$614$	−5925.42	−	4708.41i	−0.389463	−	0.309472i
$615$	−95.0869	−	158.513i	−0.00623459	−	0.0103933i
$616$	1551.03	+	4359.01i	0.101449	+	0.285113i
$617$	−7265.90	+	7265.90i	−0.474091	+	0.474091i	−0.903236	−	0.429145i	$-0.858815\pi$
$617$	−7265.90	+	7265.90i	−0.474091	+	0.474091i	0.429145	+	0.903236i	$0.358815\pi$
$618$	−1729.46	+	197.930i	−0.112571	+	0.0128834i
$619$	−22450.9	+	9299.47i	−1.45780	+	0.603841i	−0.964040	−	0.265758i	$-0.914378\pi$
$619$	−22450.9	+	9299.47i	−1.45780	+	0.603841i	−0.493760	+	0.869598i	$0.664378\pi$
$620$	−11555.9	+	26597.0i	−0.748540	+	1.72284i
$621$	−367.966	+	888.349i	−0.0237777	+	0.0574046i
$622$	−10733.2	−	19340.3i	−0.691903	−	1.24674i
$623$	1920.77			0.123522
$624$	−1478.62	−	505.795i	−0.0948590	−	0.0324487i
$625$	12979.1	−	8699.58i	0.830665	−	0.556773i
$626$	−841.305	−	1515.95i	−0.0537146	−	0.0967885i
$627$	−413.364	−	171.221i	−0.0263288	−	0.0109058i
$628$	−13651.5	+	9758.28i	−0.867441	+	0.620060i
$629$	−2382.98	+	987.064i	−0.151059	+	0.0625705i
$630$	9739.45	+	1284.45i	0.615919	+	0.0812281i
$631$	8653.33	+	8653.33i	0.545933	+	0.545933i	0.925262	−	0.379329i	$-0.123845\pi$
$631$	8653.33	+	8653.33i	0.545933	+	0.545933i	−0.379329	+	0.925262i	$0.623845\pi$
$632$	−12347.5	+	11151.6i	−0.777147	+	0.701877i
$633$	155.364	+	155.364i	0.00975537	+	0.00975537i
$634$	9443.06	−	11883.9i	0.591533	−	0.744429i
$635$	−20441.5	+	3039.77i	−1.27747	+	0.189968i
$636$	937.749	+	584.657i	0.0584657	+	0.0364515i
$637$	−4811.71	+	11616.5i	−0.299289	+	0.722547i
$638$	11609.6	+	3322.67i	0.720422	+	0.206185i
$639$	3062.42			0.189589
$640$	−15754.0	−	3735.58i	−0.973020	−	0.230722i
$641$	−8111.41			−0.499815			−0.249908	−	0.968270i	$-0.580400\pi$
$641$	−8111.41			−0.499815			−0.249908	+	0.968270i	$0.580400\pi$
$642$	958.450	+	274.308i	0.0589206	+	0.0168631i
$643$	−2005.56	+	4841.85i	−0.123004	+	0.296958i	−0.973372	−	0.229230i	$-0.926379\pi$
$643$	−2005.56	+	4841.85i	−0.123004	+	0.296958i	0.850368	+	0.526188i	$0.176379\pi$
$644$	3458.54	+	2156.29i	0.211623	+	0.131940i
$645$	149.081	+	1002.52i	0.00910087	+	0.0612005i
$646$	−768.231	+	966.798i	−0.0467889	+	0.0588826i
$647$	−21480.3	−	21480.3i	−1.30522	−	1.30522i	−0.924822	−	0.380399i	$-0.875787\pi$
$647$	−21480.3	−	21480.3i	−1.30522	−	1.30522i	−0.380399	−	0.924822i	$-0.624213\pi$
$648$	12018.2	−	10854.2i	0.728577	−	0.658012i
$649$	−4566.75	−	4566.75i	−0.276211	−	0.276211i
$650$	−19783.8	−	7814.84i	−1.19382	−	0.471574i
$651$	1407.31	−	582.927i	0.0847264	−	0.0350948i
$652$	19772.0	−	14133.3i	1.18763	−	0.848933i
$653$	5106.75	+	2115.29i	0.306038	+	0.126765i	0.530417	−	0.847737i	$-0.322035\pi$
$653$	5106.75	+	2115.29i	0.306038	+	0.126765i	−0.224379	+	0.974502i	$0.572035\pi$
$654$	334.311	+	602.396i	0.0199887	+	0.0360177i
$655$	3304.08	−	13210.9i	0.197101	−	0.788081i
$656$	−843.836	+	2466.83i	−0.0502230	+	0.146819i
$657$	−15361.5			−0.912193
$658$	6432.40	+	11590.6i	0.381096	+	0.686698i
$659$	−11244.3	+	27146.1i	−0.664666	+	1.60465i	0.125740	+	0.992063i	$0.459869\pi$
$659$	−11244.3	+	27146.1i	−0.664666	+	1.60465i	−0.790406	+	0.612583i	$0.790131\pi$
$660$	−588.069	−	255.504i	−0.0346826	−	0.0150689i
$661$	−24419.8	+	10115.0i	−1.43694	+	0.595202i	−0.959055	−	0.283219i	$-0.908598\pi$
$661$	−24419.8	+	10115.0i	−1.43694	+	0.595202i	−0.477888	+	0.878421i	$0.658598\pi$
$662$	8164.27	−	934.371i	0.479325	−	0.0548570i
$663$	−120.775	+	120.775i	−0.00707469	+	0.00707469i
$664$	−9309.03	−	26162.1i	−0.544067	−	1.52904i
$665$	4155.51	+	6927.36i	0.242321	+	0.403957i
$666$	21912.3	+	17411.8i	1.27490	+	1.01305i
$667$	9827.73	−	4070.78i	0.570511	−	0.236314i
$668$	−358.038	−	1543.73i	−0.0207379	−	0.0894143i
$669$	675.788	+	279.920i	0.0390545	+	0.0161769i
$670$	22156.6	+	12798.7i	1.27759	+	0.737998i
$671$	4287.76			0.246687
$672$	458.768	+	716.131i	0.0263354	+	0.0411092i
$673$			1877.87i			0.107558i	0.998553	+	0.0537790i	$0.0171266\pi$
$673$			1877.87i			0.107558i	−0.998553	+	0.0537790i	$0.982873\pi$
$674$	16089.7	+	4604.88i	0.919515	+	0.263165i
$675$	−2109.94	+	1734.14i	−0.120313	+	0.0988845i
$676$	2571.58	+	11087.7i	0.146312	+	0.630845i
$677$	25019.3	−	10363.3i	1.42034	−	0.588324i	0.465394	−	0.885103i	$-0.345913\pi$
$677$	25019.3	−	10363.3i	1.42034	−	0.588324i	0.954946	+	0.296779i	$0.0959125\pi$
$678$	674.280	−	848.564i	0.0381940	−	0.0480662i
$679$	−190.038	+	190.038i	−0.0107408	+	0.0107408i
$680$	−1124.54	+	1366.36i	−0.0634179	+	0.0770550i
$681$	786.101	+	786.101i	0.0442341	+	0.0442341i
$682$	16092.5	−	1841.73i	0.903539	−	0.103407i
$683$	1363.88	+	3292.70i	0.0764092	+	0.184468i	0.957469	−	0.288538i	$-0.0931690\pi$
$683$	1363.88	+	3292.70i	0.0764092	+	0.184468i	−0.881059	+	0.473006i	$0.843169\pi$
$684$	13217.7	+	2198.19i	0.738878	+	0.122880i
$685$	−5353.78	−	3967.63i	−0.298624	−	0.221307i
$686$	15803.2	−	8770.27i	0.879546	−	0.488120i
$687$	−1847.47			−0.102599
$688$	9450.96	−	10725.9i	0.523713	−	0.594361i
$689$		−	20477.5i		−	1.13227i
$690$	−545.596	+	146.061i	−0.0301022	+	0.00805860i
$691$	8082.22	−	19512.2i	0.444952	−	1.07421i	−0.529236	−	0.848474i	$-0.677522\pi$
$691$	8082.22	−	19512.2i	0.444952	−	1.07421i	0.974189	−	0.225735i	$-0.0724784\pi$
$692$	−9660.56	−	13514.8i	−0.530693	−	0.742419i
$693$	−2099.84	−	5069.45i	−0.115103	−	0.277882i
$694$	26980.2	−	3087.79i	1.47573	−	0.168892i
$695$	−3523.01	−	5872.96i	−0.192281	−	0.320538i
$696$	2216.87	+	112.819i	0.120733	+	0.00614426i
$697$	201.493	+	201.493i	0.0109499	+	0.0109499i
$698$	−10842.0	−	8615.17i	−0.587929	−	0.467176i
$699$	125.236	+	302.347i	0.00677664	+	0.0163603i
$700$	5783.68	+	10028.0i	0.312289	+	0.541463i
$701$	−3951.37	−	1636.71i	−0.212898	−	0.0881851i	0.273686	−	0.961819i	$-0.411757\pi$
$701$	−3951.37	−	1636.71i	−0.212898	−	0.0881851i	−0.486584	+	0.873634i	$0.661757\pi$
$702$	3574.55	+	1023.04i	0.192183	+	0.0550028i
$703$			23014.6i			1.23472i
$704$	2594.71	+	8663.29i	0.138909	+	0.463792i
$705$	−1782.11	−	445.711i	−0.0952031	−	0.0238105i
$706$	−4449.35	+	15546.3i	−0.237186	+	0.828744i
$707$	−1465.83	+	3538.82i	−0.0779747	+	0.188248i
$708$	−1007.41	−	628.085i	−0.0534755	−	0.0333402i
$709$	8029.82	+	19385.7i	0.425340	+	1.02686i	0.980747	+	0.195284i	$0.0625627\pi$
$709$	8029.82	+	19385.7i	0.425340	+	1.02686i	−0.555406	+	0.831579i	$0.687437\pi$
$710$	2196.23	+	2863.52i	0.116089	+	0.151361i
$711$	13952.6	−	13952.6i	0.735952	−	0.735952i
$712$	3749.52	+	190.818i	0.197359	+	0.0100438i
$713$	10089.2	−	10089.2i	0.529936	−	0.529936i
$714$	92.3517	−	10.5693i	0.00484058	−	0.000553987i
$715$	1747.59	+	11752.0i	0.0914073	+	0.614686i
$716$	10803.8	−	7722.71i	0.563905	−	0.403088i
$717$	−1659.70	−	687.470i	−0.0864471	−	0.0358076i
$718$	−28534.8	+	15835.9i	−1.48316	+	0.823106i
$719$		−	7762.84i		−	0.402650i	−0.979525	−	0.201325i	$-0.935475\pi$
$719$		−	7762.84i		−	0.402650i	0.979525	−	0.201325i	$-0.0645247\pi$
$720$	18884.7	+	3474.93i	0.977489	+	0.179865i
$721$		−	17554.9i		−	0.906765i
$722$	−4067.31	−	7328.91i	−0.209653	−	0.377775i
$723$	2142.12	+	887.297i	0.110189	+	0.0456417i
$724$	9054.20	+	1505.77i	0.464774	+	0.0772948i
$725$	30070.9	+	2939.75i	1.54042	+	0.150593i
$726$	−133.005	−	1162.16i	−0.00679927	−	0.0594101i
$727$	21492.6	−	21492.6i	1.09645	−	1.09645i	0.101623	−	0.994823i	$-0.467596\pi$
$727$	21492.6	−	21492.6i	1.09645	−	1.09645i	0.994823	−	0.101623i	$-0.0324036\pi$
$728$	6763.19	−	14234.7i	0.344314	−	0.724688i
$729$	−13411.1	+	13411.1i	−0.681356	+	0.681356i
$730$	−11016.6	−	14363.8i	−0.558553	−	0.728259i
$731$	−597.931	−	1443.53i	−0.0302534	−	0.0730383i
$732$	767.788	−	178.074i	0.0387681	−	0.00899152i
$733$	−4341.79	+	10482.0i	−0.218783	+	0.528188i	−0.994721	−	0.102621i	$-0.967277\pi$
$733$	−4341.79	+	10482.0i	−0.218783	+	0.528188i	0.775938	+	0.630809i	$0.217277\pi$
$734$	1027.94	+	294.196i	0.0516920	+	0.0147942i
$735$	−230.083	+	919.954i	−0.0115466	+	0.0461674i
$736$	6537.17	+	4552.86i	0.327396	+	0.228017i
$737$		−	14292.1i		−	0.714322i
$738$	850.772	−	2972.65i	0.0424354	−	0.148272i
$739$	−11952.7	−	4950.98i	−0.594977	−	0.246448i	0.0648132	−	0.997897i	$-0.479355\pi$
$739$	−11952.7	−	4950.98i	−0.594977	−	0.246448i	−0.659790	+	0.751450i	$0.729355\pi$
$740$	−566.384	+	32976.1i	−0.0281361	+	1.63814i
$741$	583.216	+	1408.01i	0.0289136	+	0.0698036i
$742$	−6933.12	+	8725.16i	−0.343023	+	0.431685i
$743$	−3345.98	−	3345.98i	−0.165211	−	0.165211i	0.619659	−	0.784871i	$-0.287271\pi$
$743$	−3345.98	−	3345.98i	−0.165211	−	0.165211i	−0.784871	+	0.619659i	$0.787271\pi$
$744$	2805.12	−	998.121i	0.138227	−	0.0491840i
$745$	−14771.7	−	24624.8i	−0.726432	−	1.21098i
$746$	3996.38	+	34919.3i	0.196137	+	1.71379i
$747$	12602.9	+	30426.0i	0.617289	+	1.49027i
$748$	975.036	+	162.154i	0.0476615	+	0.00792641i
$749$	−3847.40	+	9288.43i	−0.187691	+	0.453127i
$750$	−1562.54	−	363.510i	−0.0760743	−	0.0176980i
$751$			24527.0i			1.19175i	0.803077	+	0.595875i	$0.203195\pi$
$751$			24527.0i			1.19175i	−0.803077	+	0.595875i	$0.796805\pi$
$752$	11405.2	+	23264.9i	0.553065	+	1.12817i
$753$	−747.861			−0.0361933
$754$	−19959.6	−	35965.3i	−0.964041	−	1.73711i
$755$	−9690.79	+	13076.4i	−0.467131	+	0.630330i
$756$	−1176.69	−	1646.15i	−0.0566082	−	0.0791928i
$757$	−6348.46	−	15326.5i	−0.304807	−	0.735869i	−0.999857	−	0.0169078i	$-0.994618\pi$
$757$	−6348.46	−	15326.5i	−0.304807	−	0.735869i	0.695050	−	0.718961i	$-0.255382\pi$
$758$	−2752.28	−	24048.7i	−0.131883	−	1.15236i
$759$	223.076	+	223.076i	0.0106682	+	0.0106682i
$760$	7423.75	+	13935.7i	0.354326	+	0.665133i
$761$	14406.9	−	14406.9i	0.686269	−	0.686269i	−0.275136	−	0.961405i	$-0.588723\pi$
$761$	14406.9	−	14406.9i	0.686269	−	0.686269i	0.961405	+	0.275136i	$0.0887230\pi$
$762$	1661.26	+	1320.05i	0.0789776	+	0.0627566i
$763$	−6418.92	+	2658.80i	−0.304561	+	0.126153i
$764$	−22122.5	−	13792.7i	−1.04760	−	0.653142i
$765$	1249.58	−	1686.14i	0.0590571	−	0.0796895i
$766$	−11056.4	+	38631.8i	−0.521520	+	1.82222i
$767$			21998.6i			1.03562i
$768$	824.415	+	1443.53i	0.0387350	+	0.0678242i
$769$	−4409.85			−0.206792			−0.103396	−	0.994640i	$-0.532971\pi$
$769$	−4409.85			−0.206792			−0.103396	+	0.994640i	$0.532971\pi$
$770$	3234.29	−	5599.04i	0.151371	−	0.262046i
$771$	−1052.40	−	435.920i	−0.0491587	−	0.0203622i
$772$	12856.5	−	20621.0i	0.599374	−	0.961355i
$773$	22210.0	−	9199.67i	1.03342	−	0.428059i	0.199477	−	0.979902i	$-0.436076\pi$
$773$	22210.0	−	9199.67i	1.03342	−	0.428059i	0.833947	+	0.551844i	$0.186076\pi$
$774$	−10547.5	+	13273.7i	−0.489821	+	0.616427i
$775$	38773.6	−	11792.5i	1.79715	−	0.546580i
$776$	−389.851	+	352.092i	−0.0180346	+	0.0162879i
$777$	1225.01	−	1225.01i	0.0565600	−	0.0565600i
$778$	−662.440	−	5788.21i	−0.0305265	−	0.266732i
$779$	2349.03	−	973.000i	0.108039	−	0.0447514i
$780$	801.001	+	2031.80i	0.0367698	+	0.0932692i
$781$	771.375	−	1862.26i	0.0353418	−	0.0853227i
$782$	761.319	−	422.508i	0.0348142	−	0.0193208i
$783$	−5281.22			−0.241041
$784$	12009.7	−	5887.54i	0.547090	−	0.268201i
$785$	22750.8	+	5690.02i	1.03441	+	0.258708i
$786$	−1222.53	+	678.467i	−0.0554788	+	0.0307890i
$787$	−18685.5	−	7739.78i	−0.846335	−	0.350563i	−0.0829866	−	0.996551i	$-0.526446\pi$
$787$	−18685.5	−	7739.78i	−0.846335	−	0.350563i	−0.763348	+	0.645987i	$0.776446\pi$
$788$	39783.2	+	6616.19i	1.79850	+	0.299102i
$789$	2259.53	−	935.929i	0.101954	−	0.0422306i
$790$	23052.5	+	3040.19i	1.03819	+	0.136918i
$791$	7728.82	+	7728.82i	0.347415	+	0.347415i
$792$	−3595.46	−	10104.7i	−0.161312	−	0.453350i
$793$	−10327.3	−	10327.3i	−0.462465	−	0.462465i
$794$	−15732.3	−	12501.1i	−0.703171	−	0.558749i
$795$	−227.162	−	1527.59i	−0.0101341	−	0.0681487i
$796$	−10954.9	+	2540.77i	−0.487796	+	0.113135i
$797$	6512.13	−	15721.7i	0.289424	−	0.698733i	−0.710564	−	0.703633i	$-0.751560\pi$
$797$	6512.13	−	15721.7i	0.289424	−	0.698733i	0.999988	+	0.00490055i	$0.00155990\pi$
$798$	228.214	−	797.392i	0.0101236	−	0.0353727i
$799$	2831.90			0.125388
$800$	10294.1	+	20150.2i	0.454937	+	0.890523i
$801$	−4452.55			−0.196408
$802$	−6422.13	+	22439.3i	−0.282760	+	0.987980i
$803$	−3869.33	+	9341.38i	−0.170044	+	0.410523i
$804$	−593.560	−	2559.21i	−0.0260364	−	0.112259i
$805$	−837.803	−	5633.96i	−0.0366816	−	0.246672i
$806$	−43195.7	−	34323.8i	−1.88772	−	1.50001i
$807$	−1991.55	−	1991.55i	−0.0868721	−	0.0868721i
$808$	−3213.00	+	6762.49i	−0.139892	+	0.294435i
$809$	11546.1	+	11546.1i	0.501781	+	0.501781i	0.911991	−	0.410210i	$-0.134545\pi$
$809$	11546.1	+	11546.1i	0.501781	+	0.501781i	−0.410210	+	0.911991i	$0.634545\pi$
$810$	−22437.7	−	2959.11i	−0.973308	−	0.128361i
$811$	14916.1	−	6178.45i	0.645839	−	0.267515i	−0.0356269	−	0.999365i	$-0.511343\pi$
$811$	14916.1	−	6178.45i	0.645839	−	0.267515i	0.681466	+	0.731850i	$0.261343\pi$
$812$	−3672.39	+	22082.1i	−0.158714	+	0.954346i
$813$	1339.71	+	554.927i	0.0577930	+	0.0239387i
$814$	16107.5	−	8939.15i	0.693572	−	0.384910i
$815$	−32950.9	−	8241.11i	−1.41622	−	0.354201i
$816$	181.329	−	11.4577i	0.00777916	−	0.000491543i
$817$	−13941.5			−0.597001
$818$	−5430.28	+	3013.63i	−0.232109	+	0.128813i
$819$	−7152.50	+	17267.7i	−0.305163	+	0.736729i
$820$	3389.72	−	1336.34i	0.144359	−	0.0569109i
$821$	−18559.8	+	7687.73i	−0.788967	+	0.326801i	−0.740528	−	0.672025i	$-0.765425\pi$
$821$	−18559.8	+	7687.73i	−0.788967	+	0.326801i	−0.0484389	+	0.998826i	$0.515425\pi$
$822$	77.7943	+	679.744i	0.00330096	+	0.0288428i
$823$	−6339.81	+	6339.81i	−0.268520	+	0.268520i	−0.828504	−	0.559984i	$-0.810807\pi$
$823$	−6339.81	+	6339.81i	−0.268520	+	0.268520i	0.559984	+	0.828504i	$0.310807\pi$
$824$	1743.98	−	34268.8i	0.0737311	−	1.44880i
$825$	260.736	+	857.298i	0.0110032	+	0.0361785i
$826$	7448.12	−	9373.27i	0.313745	−	0.394840i
$827$	17426.5	−	7218.29i	0.732743	−	0.303512i	0.0150644	−	0.999887i	$-0.495205\pi$
$827$	17426.5	−	7218.29i	0.732743	−	0.303512i	0.717679	+	0.696374i	$0.245205\pi$
$828$	−8017.26	−	4998.51i	−0.336496	−	0.209795i
$829$	−6252.38	−	2589.82i	−0.261947	−	0.108502i	0.247845	−	0.968800i	$-0.420278\pi$
$829$	−6252.38	−	2589.82i	−0.261947	−	0.108502i	−0.509792	+	0.860298i	$0.670278\pi$
$830$	−19411.7	+	33604.5i	−0.811793	+	1.40534i
$831$	−558.786			−0.0233262
$832$	14616.5	−	27115.6i	0.609058	−	1.12988i
$833$		−	1461.87i		−	0.0608052i
$834$	−193.478	+	676.023i	−0.00803307	+	0.0280680i
$835$	−1318.65	+	1779.34i	−0.0546512	+	0.0737443i
$836$	4666.06	−	7484.03i	0.193037	−	0.309618i
$837$	−6544.63	+	2710.87i	−0.270269	+	0.111949i
$838$	28163.5	+	22379.1i	1.16097	+	0.922521i
$839$	−7933.38	+	7933.38i	−0.326449	+	0.326449i	−0.851235	−	0.524785i	$-0.824146\pi$
$839$	−7933.38	+	7933.38i	−0.326449	+	0.326449i	0.524785	+	0.851235i	$0.324146\pi$
$840$	346.616	−	1136.91i	0.0142374	−	0.0466992i
$841$	24067.5	+	24067.5i	0.986820	+	0.986820i
$842$	−2922.20	−	25533.3i	−0.119603	−	1.04505i
$843$	−24.0533	−	58.0698i	−0.000982728	−	0.00237251i
$844$	−3523.40	+	2518.58i	−0.143697	+	0.102717i
$845$	9471.09	−	12780.0i	0.385580	−	0.520288i
$846$	−14911.0	−	26868.2i	−0.605970	−	1.09190i
$847$	11796.5			0.478550
$848$	−14400.9	+	16343.6i	−0.583171	+	0.661840i
$849$			2098.20i			0.0848173i
$850$	2472.77	−	40.8032i	0.0997827	−	0.00164652i
$851$	6210.03	−	14992.3i	0.250149	−	0.603914i
$852$	60.7852	−	365.502i	0.00244421	−	0.0146971i
$853$	859.040	+	2073.91i	0.0344818	+	0.0832464i	0.940182	−	0.340672i	$-0.110654\pi$
$853$	859.040	+	2073.91i	0.0344818	+	0.0832464i	−0.905701	+	0.423918i	$0.860654\pi$
$854$	903.769	+	7896.88i	0.0362135	+	0.316423i
$855$	−9632.92	−	16058.4i	−0.385309	−	0.642322i
$856$	−8433.24	+	17749.7i	−0.336731	+	0.708729i
$857$	24504.7	+	24504.7i	0.976739	+	0.976739i	0.999736	−	0.0229962i	$-0.00732057\pi$
$857$	24504.7	+	24504.7i	0.976739	+	0.976739i	−0.0229962	+	0.999736i	$0.507321\pi$
$858$	758.911	−	955.070i	0.0301967	−	0.0380018i
$859$	−5719.93	−	13809.1i	−0.227196	−	0.548500i	0.768638	−	0.639684i	$-0.220935\pi$
$859$	−5719.93	−	13809.1i	−0.227196	−	0.548500i	−0.995834	+	0.0911838i	$0.970935\pi$
$860$	−19975.8	−	343.096i	−0.792058	−	0.0136041i
$861$	−176.824	−	73.2429i	−0.00699901	−	0.00289908i
$862$	5704.72	−	19932.7i	0.225410	−	0.787598i
$863$		−	5732.17i		−	0.226101i	−0.993589	−	0.113051i	$-0.963938\pi$
$863$		−	5732.17i		−	0.226101i	0.993589	−	0.113051i	$-0.0360622\pi$
$864$	−2133.48	−	3330.33i	−0.0840073	−	0.131134i
$865$	−5633.04	+	22522.9i	−0.221421	+	0.885322i
$866$	36445.8	+	10430.8i	1.43011	+	0.409298i
$867$	−755.448	+	1823.81i	−0.0295921	+	0.0714417i
$868$	6783.91	+	29249.7i	0.265278	+	1.14378i
$869$	−4970.15	−	11999.0i	−0.194017	−	0.468398i
$870$	−1887.94	−	2461.55i	−0.0735713	−	0.0959246i
$871$	−34423.3	+	34423.3i	−1.33914	+	1.33914i
$872$	−12794.5	+	4552.55i	−0.496875	+	0.176799i
$873$	440.528	−	440.528i	0.0170786	−	0.0170786i
$874$	−883.369	−	7718.63i	−0.0341881	−	0.298726i
$875$	5433.82	−	15238.6i	0.209939	−	0.588755i
$876$	−304.908	+	1833.41i	−0.0117601	+	0.0707137i
$877$	27300.9	+	11308.4i	1.05118	+	0.435414i	0.840313	−	0.542101i	$-0.182371\pi$
$877$	27300.9	+	11308.4i	1.05118	+	0.435414i	0.210868	+	0.977515i	$0.432371\pi$
$878$	−23147.9	−	41710.4i	−0.889755	−	1.60325i
$879$		−	2583.19i		−	0.0991228i
$880$	6869.87	−	10608.6i	0.263163	−	0.406380i
$881$			33592.7i			1.28464i	0.766437	+	0.642320i	$0.222028\pi$
$881$			33592.7i			1.28464i	−0.766437	+	0.642320i	$0.777972\pi$
$882$	−13869.8	+	7697.29i	−0.529501	+	0.293856i
$883$	991.395	+	410.649i	0.0377838	+	0.0156506i	0.401495	−	0.915861i	$-0.368491\pi$
$883$	991.395	+	410.649i	0.0377838	+	0.0156506i	−0.363712	+	0.931512i	$0.618491\pi$
$884$	−1957.87	−	2738.99i	−0.0744914	−	0.104211i
$885$	244.036	+	1641.07i	0.00926913	+	0.0623320i
$886$	18961.3	−	2170.05i	0.718982	−	0.0822849i
$887$	−19197.8	+	19197.8i	−0.726717	+	0.726717i	−0.969964	−	0.243247i	$-0.921787\pi$
$887$	−19197.8	+	19197.8i	−0.726717	+	0.726717i	0.243247	+	0.969964i	$0.421787\pi$
$888$	2513.04	−	2269.64i	0.0949686	−	0.0857706i
$889$	−15130.9	+	15130.9i	−0.570837	+	0.570837i
$890$	−3193.17	−	4163.36i	−0.120264	−	0.156805i
$891$	4837.59	+	11679.0i	0.181891	+	0.439125i
$892$	−7628.30	+	12235.3i	−0.286339	+	0.459268i
$893$	9669.72	−	23344.8i	0.362357	−	0.874808i
$894$	−811.235	+	2834.50i	−0.0303487	+	0.106040i
$895$	−18005.0	−	4503.09i	−0.672447	−	0.168181i
$896$	−15408.5	+	6604.78i	−0.574510	+	0.246262i
$897$		−	1074.59i		−	0.0399993i
$898$	−1569.52	−	449.197i	−0.0583248	−	0.0166926i
$899$	72402.6	+	29990.1i	2.68605	+	1.11260i
$900$	−13407.2	−	23246.1i	−0.496563	−	0.860966i
$901$	911.097	+	2199.58i	0.0336882	+	0.0813305i
$902$	−1593.38	−	1266.12i	−0.0588178	−	0.0467374i
$903$	742.072	+	742.072i	0.0273473	+	0.0273473i
$904$	14319.6	+	15855.2i	0.526838	+	0.583336i
$905$	−6598.59	−	11000.1i	−0.242370	−	0.404038i
$906$	1660.25	−	190.010i	0.0608809	−	0.00696760i
$907$	−5485.35	−	13242.8i	−0.200814	−	0.484808i	0.791105	−	0.611680i	$-0.209506\pi$
$907$	−5485.35	−	13242.8i	−0.200814	−	0.484808i	−0.991919	+	0.126873i	$0.959506\pi$
$908$	−17827.5	+	12743.4i	−0.651572	+	0.465754i
$909$	3397.95	−	8203.37i	0.123985	−	0.299327i
$910$	−21275.6	+	5695.66i	−0.775032	+	0.207483i
$911$			19372.7i			0.704550i	0.935897	+	0.352275i	$0.114592\pi$
$911$			19372.7i			0.704550i	−0.935897	+	0.352275i	$0.885408\pi$
$912$	524.711	−	1533.91i	0.0190514	−	0.0556940i
$913$	21676.6			0.785750
$914$	−21228.4	+	11781.1i	−0.768241	+	0.426350i
$915$	−884.970	−	655.842i	−0.0319740	−	0.0236956i
$916$	5974.28	−	35923.4i	0.215498	−	1.29579i
$917$	−5395.91	−	13026.9i	−0.194317	−	0.469123i
$918$	−429.476	+	49.1520i	−0.0154410	+	0.00176717i
$919$	9602.50	+	9602.50i	0.344676	+	0.344676i	0.858122	−	0.513446i	$-0.171631\pi$
$919$	9602.50	+	9602.50i	0.344676	+	0.344676i	−0.513446	+	0.858122i	$0.671631\pi$
$920$	−1075.77	−	11081.3i	−0.0385511	−	0.397107i
$921$	767.902	−	767.902i	0.0274736	−	0.0274736i
$922$	17212.0	−	21660.9i	0.614803	−	0.773714i
$923$	−6343.28	+	2627.47i	−0.226210	+	0.0936991i
$924$	−646.722	+	149.995i	−0.0230255	+	0.00534032i
$925$	35608.6	−	29266.4i	1.26573	−	1.04030i
$926$	−46485.5	−	13304.2i	−1.64969	−	0.472140i
$927$			40694.1i			1.44182i
$928$	−9362.58	+	42741.5i	−0.331187	+	1.51192i
$929$	−19007.8			−0.671288			−0.335644	−	0.941989i	$-0.608954\pi$
$929$	−19007.8			−0.671288			−0.335644	+	0.941989i	$0.608954\pi$
$930$	−3603.10	−	2081.33i	−0.127043	−	0.0733867i
$931$	−12050.9	−	4991.66i	−0.424225	−	0.175720i
$932$	−6284.03	+	1457.46i	−0.220859	+	0.0512238i
$933$	2932.25	−	1214.58i	0.102891	−	0.0426189i
$934$	−5494.71	−	4366.17i	−0.192497	−	0.152961i
$935$	−710.594	−	1184.58i	−0.0248545	−	0.0414332i
$936$	−15677.8	+	32997.6i	−0.547484	+	1.15231i
$937$	24547.2	−	24547.2i	0.855841	−	0.855841i	−0.135004	−	0.990845i	$-0.543105\pi$
$937$	24547.2	−	24547.2i	0.855841	−	0.855841i	0.990845	+	0.135004i	$0.0431047\pi$
$938$	26322.1	−	3012.47i	0.916254	−	0.104862i
$939$	229.839	−	95.2024i	0.00798776	−	0.00330864i
$940$	14429.6	−	33211.2i	0.500683	−	1.15237i
$941$	6782.43	−	16374.2i	0.234964	−	0.567253i	−0.761785	−	0.647830i	$-0.775677\pi$
$941$	6782.43	−	16374.2i	0.234964	−	0.567253i	0.996748	+	0.0805777i	$0.0256765\pi$
$942$	−1168.40	−	2105.35i	−0.0404125	−	0.0728195i
$943$	−1792.77			−0.0619094
$944$	15470.6	−	17557.6i	0.533396	−	0.605350i
$945$	−686.124	+	2743.37i	−0.0236187	+	0.0944359i
$946$	5415.04	+	9757.38i	0.186108	+	0.335349i
$947$	−49250.6	−	20400.2i	−1.69000	−	0.700020i	−0.690275	−	0.723547i	$-0.742510\pi$
$947$	−49250.6	−	20400.2i	−1.69000	−	0.700020i	−0.999723	+	0.0235271i	$0.992510\pi$
$948$	−1388.31	−	1942.19i	−0.0475634	−	0.0665394i
$949$	31818.8	−	13179.8i	1.08839	−	0.450826i
$950$	8107.10	−	20523.6i	0.276873	−	0.700921i
$951$	1540.08	+	1540.08i	0.0525138	+	0.0525138i
$952$	−93.1271	+	1829.93i	−0.00317045	+	0.0622986i
$953$	−18832.4	−	18832.4i	−0.640128	−	0.640128i	0.310458	−	0.950587i	$-0.399517\pi$
$953$	−18832.4	−	18832.4i	−0.640128	−	0.640128i	−0.950587	+	0.310458i	$0.899517\pi$
$954$	16071.7	−	20225.9i	0.545431	−	0.686411i
$955$	5358.99	+	36037.5i	0.181584	+	1.22110i
$956$	18734.7	−	30049.2i	0.633811	−	1.01659i
$957$	−663.092	+	1600.85i	−0.0223978	+	0.0540731i
$958$	−7229.72	−	2069.14i	−0.243822	−	0.0697819i
$959$	−6899.75			−0.232330
$960$	789.573	−	2184.93i	0.0265452	−	0.0734566i
$961$	75326.3			2.52849
$962$	−60326.3	−	17265.4i	−2.02183	−	0.578647i
$963$	8918.68	−	21531.6i	0.298443	−	0.720505i
$964$	−24180.3	+	38783.6i	−0.807879	+	1.29578i
$965$	−33591.6	+	4995.27i	−1.12057	+	0.166636i
$966$	−363.825	+	457.865i	−0.0121179	+	0.0152501i
$967$	−30678.0	−	30678.0i	−1.02021	−	1.02021i	−0.999792	−	0.0204139i	$-0.993502\pi$
$967$	−30678.0	−	30678.0i	−1.02021	−	1.02021i	−0.0204139	−	0.999792i	$-0.506498\pi$
$968$	23027.9	+	1171.92i	0.764611	+	0.0389120i
$969$	−125.292	−	125.292i	−0.00415372	−	0.00415372i
$970$	727.843	+	95.9889i	0.0240924	+	0.00317734i
$971$	14729.7	−	6101.26i	0.486818	−	0.201646i	−0.125754	−	0.992061i	$-0.540135\pi$
$971$	14729.7	−	6101.26i	0.486818	−	0.201646i	0.612572	+	0.790415i	$0.290135\pi$
$972$	4095.72	+	5729.75i	0.135155	+	0.189076i
$973$	−6551.40	−	2713.68i	−0.215856	−	0.0894107i
$974$	−13618.6	−	24539.4i	−0.448015	−	0.807281i
$975$	1436.86	−	2692.85i	0.0471961	−	0.0884516i
$976$	979.732	+	15505.2i	0.0321316	+	0.508515i
$977$	34621.7			1.13372			0.566861	−	0.823813i	$-0.308158\pi$
$977$	34621.7			1.13372			0.566861	+	0.823813i	$0.308158\pi$
$978$	1692.25	+	3049.27i	0.0553294	+	0.0996982i
$979$	−1121.53	+	2707.60i	−0.0366130	+	0.0883916i
$980$	−17144.2	−	7448.80i	−0.558827	−	0.242799i
$981$	14879.7	−	6163.39i	0.484275	−	0.200593i
$982$	−4406.02	+	504.253i	−0.143179	+	0.0163863i
$983$	−19167.0	+	19167.0i	−0.621906	+	0.621906i	−0.946018	−	0.324113i	$-0.894934\pi$
$983$	−19167.0	+	19167.0i	−0.621906	+	0.621906i	0.324113	+	0.946018i	$0.394934\pi$
$984$	−337.901	−	160.544i	−0.0109470	−	0.00520116i
$985$	−28993.5	−	48333.1i	−0.937878	−	1.56347i
$986$	3744.15	+	2975.15i	0.120931	+	0.0960933i
$987$	−1757.29	+	727.892i	−0.0566718	+	0.0234742i
$988$	−29264.2	+	6787.27i	−0.942327	+	0.218554i
$989$	9081.86	+	3761.83i	0.291998	+	0.120950i
$990$	−7497.43	+	12979.2i	−0.240691	+	0.416672i
$991$	34579.7			1.10844			0.554218	−	0.832372i	$-0.313017\pi$
$991$	34579.7			1.10844			0.554218	+	0.832372i	$0.313017\pi$
$992$	10337.0	+	57772.2i	0.330848	+	1.84906i
$993$			1179.13i			0.0376825i
$994$	3592.36	+	1028.13i	0.114631	+	0.0328073i
$995$	12626.8	+	9357.63i	0.402309	+	0.298147i
$996$	3881.52	−	900.243i	0.123485	−	0.0286398i
$997$	−28249.2	+	11701.2i	−0.897353	+	0.371696i	−0.783202	−	0.621768i	$-0.786415\pi$
$997$	−28249.2	+	11701.2i	−0.897353	+	0.371696i	−0.114151	+	0.993463i	$0.536415\pi$
$998$	−13965.7	+	17575.5i	−0.442963	+	0.557458i
$999$	−5696.86	+	5696.86i	−0.180421	+	0.180421i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	160.4.z.a.29.6	✓	280
5.4	even	2	inner	160.4.z.a.29.65	yes	280
32.21	even	8	inner	160.4.z.a.149.65	yes	280
160.149	even	8	inner	160.4.z.a.149.6	yes	280

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
160.4.z.a.29.6	✓	280	1.1	even	1	trivial
160.4.z.a.29.65	yes	280	5.4	even	2	inner
160.4.z.a.149.6	yes	280	160.149	even	8	inner
160.4.z.a.149.65	yes	280	32.21	even	8	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:	\( N \)	\(=\)	\( 160 = 2^{5} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	160.z (of order \(8\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-2.71925 - 0.778249i) q^{2} +(0.155312 - 0.374956i) q^{3} +(6.78866 + 4.23251i) q^{4} +(-1.64450 - 11.0587i) q^{5} +(-0.714142 + 0.898729i) q^{6} +(-8.18573 - 8.18573i) q^{7} +(-15.1661 - 16.7925i) q^{8} +(18.9754 + 18.9754i) q^{9} +(-4.13465 + 31.3513i) q^{10} +(16.3186 - 6.75938i) q^{11} +(2.64137 - 1.88809i) q^{12} +(-55.5847 - 23.0239i) q^{13} +(15.8885 + 28.6296i) q^{14} +(-4.40195 - 1.10094i) q^{15} +(28.1717 + 57.4661i) q^{16} +6.99500 q^{17} +(-36.8313 - 66.3665i) q^{18} +(23.8850 - 57.6634i) q^{19} +(35.6423 - 82.0343i) q^{20} +(-4.34063 + 1.79795i) q^{21} +(-49.6348 + 5.68052i) q^{22} +(-31.1187 + 31.1187i) q^{23} +(-8.65194 + 3.07855i) q^{24} +(-119.591 + 36.3721i) q^{25} +(133.230 + 105.867i) q^{26} +(20.1859 - 8.36127i) q^{27} +(-20.9239 - 90.2163i) q^{28} +(-223.315 - 92.4999i) q^{29} +(11.1132 + 6.41955i) q^{30} -324.218 q^{31} +(-31.8830 - 178.189i) q^{32} -7.16857i q^{33} +(-19.0212 - 5.44385i) q^{34} +(-77.0624 + 103.985i) q^{35} +(48.5039 + 209.131i) q^{36} +(-340.670 + 141.110i) q^{37} +(-109.826 + 138.213i) q^{38} +(-17.2659 + 17.2659i) q^{39} +(-160.763 + 195.333i) q^{40} +(28.8054 + 28.8054i) q^{41} +(13.2025 - 1.51098i) q^{42} +(-85.4797 - 206.366i) q^{43} +(139.390 + 23.1815i) q^{44} +(178.639 - 241.049i) q^{45} +(108.838 - 60.4014i) q^{46} +404.846 q^{47} +(25.9227 - 1.63798i) q^{48} -208.988i q^{49} +(353.505 - 5.83320i) q^{50} +(1.08641 - 2.62282i) q^{51} +(-279.896 - 391.564i) q^{52} +(130.250 + 314.451i) q^{53} +(-61.3976 + 7.02674i) q^{54} +(-101.586 - 169.347i) q^{55} +(-13.3134 + 261.605i) q^{56} +(-17.9116 - 17.9116i) q^{57} +(535.261 + 425.325i) q^{58} +(-139.925 - 337.809i) q^{59} +(-25.2236 - 26.1052i) q^{60} +(224.274 + 92.8973i) q^{61} +(881.630 + 252.322i) q^{62} -310.655i q^{63} +(-51.9780 + 509.355i) q^{64} +(-163.207 + 652.559i) q^{65} +(-5.57893 + 19.4931i) q^{66} +(309.648 - 747.556i) q^{67} +(47.4866 + 29.6064i) q^{68} +(6.83504 + 16.5012i) q^{69} +(290.478 - 222.788i) q^{70} +(80.6945 - 80.6945i) q^{71} +(30.8619 - 606.428i) q^{72} +(-404.775 + 404.775i) q^{73} +(1036.19 - 118.588i) q^{74} +(-4.93599 + 50.4905i) q^{75} +(406.208 - 290.364i) q^{76} +(-188.910 - 78.2491i) q^{77} +(60.3876 - 33.5132i) q^{78} -735.297i q^{79} +(589.174 - 406.046i) q^{80} +715.685i q^{81} +(-55.9113 - 100.747i) q^{82} +(1133.81 + 469.638i) q^{83} +(-37.0769 - 6.16612i) q^{84} +(-11.5033 - 77.3559i) q^{85} +(71.8364 + 627.686i) q^{86} +(-69.3669 + 69.3669i) q^{87} +(-360.996 - 171.517i) q^{88} +(-117.324 + 117.324i) q^{89} +(-673.361 + 516.447i) q^{90} +(266.533 + 643.469i) q^{91} +(-342.964 + 79.5438i) q^{92} +(-50.3549 + 121.568i) q^{93} +(-1100.88 - 315.071i) q^{94} +(-676.963 - 169.310i) q^{95} +(-71.7651 - 15.7202i) q^{96} -23.2157i q^{97} +(-162.644 + 568.290i) q^{98} +(437.914 + 181.390i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 280 q - 8 q^{4} - 4 q^{5} - 8 q^{6} - 8 q^{9} - 4 q^{10} - 8 q^{11} + 200 q^{14} - 8 q^{16} - 8 q^{19} - 4 q^{20} - 8 q^{21} - 464 q^{24} - 4 q^{25} - 48 q^{26} - 8 q^{29} + 1124 q^{30} + 1472 q^{31} - 72 q^{34}+ \cdots + 5520 q^{99}+O(q^{100}) \) 280 * q - 8 * q^4 - 4 * q^5 - 8 * q^6 - 8 * q^9 - 4 * q^10 - 8 * q^11 + 200 * q^14 - 8 * q^16 - 8 * q^19 - 4 * q^20 - 8 * q^21 - 464 * q^24 - 4 * q^25 - 48 * q^26 - 8 * q^29 + 1124 * q^30 + 1472 * q^31 - 72 * q^34 - 460 * q^35 - 888 * q^36 - 8 * q^39 - 1112 * q^40 - 8 * q^41 - 8 * q^44 - 112 * q^45 - 8 * q^46 + 3556 * q^50 - 1712 * q^51 + 856 * q^54 + 284 * q^55 + 328 * q^56 - 1384 * q^59 - 5248 * q^60 - 1832 * q^61 + 832 * q^64 - 8 * q^65 + 6088 * q^66 + 1048 * q^69 - 616 * q^70 + 216 * q^71 - 2064 * q^74 + 2204 * q^75 - 5128 * q^76 - 656 * q^80 - 6904 * q^84 - 504 * q^85 - 1192 * q^86 - 8 * q^89 + 2720 * q^90 - 8 * q^91 - 920 * q^94 - 8 * q^95 - 4152 * q^96 + 5520 * q^99

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