LMFDB - Embedded newform 336.3.bv.a.229.63

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [336,3,Mod(61,336)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(336, base_ring=CyclotomicField(12)) chi = DirichletCharacter(H, H._module([0, 9, 0, 10])) N = Newforms(chi, 3, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("336.61"); S:= CuspForms(chi, 3); N := Newforms(S);

Level:	$ N $	$=$	$ 336 = 2^{4} \cdot 3 \cdot 7 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	336.bv (of order $12$, degree $4$, minimal)

Newform invariants

comment:select newform

sage:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$9.15533688251$
Analytic rank:	$0$
Dimension:	$256$
Relative dimension:	$64$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			229.63
Character	$\chi$	$=$	336.229
Dual form			336.3.bv.a.157.63

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.99011 - 0.198630i) q^{2} +(0.448288 - 1.67303i) q^{3} +(3.92109 - 0.790591i) q^{4} +(-2.42988 - 9.06845i) q^{5} +(0.559829 - 3.41857i) q^{6} +(6.77691 + 1.75315i) q^{7} +(7.64638 - 2.35221i) q^{8} +(-2.59808 - 1.50000i) q^{9} +(-6.63701 - 17.5646i) q^{10} +(-4.03581 + 15.0619i) q^{11} +(0.435093 - 6.91453i) q^{12} +(-8.68701 - 8.68701i) q^{13} +(13.8350 + 2.14287i) q^{14} -16.2611 q^{15} +(14.7499 - 6.19996i) q^{16} +(12.8308 - 7.40787i) q^{17} +(-5.46841 - 2.46911i) q^{18} +(-17.5923 + 4.71384i) q^{19} +(-16.6972 - 33.6372i) q^{20} +(5.97108 - 10.5521i) q^{21} +(-5.03998 + 30.7764i) q^{22} +(8.25787 + 4.76768i) q^{23} +(-0.507547 - 13.8471i) q^{24} +(-54.6819 + 31.5706i) q^{25} +(-19.0136 - 15.5626i) q^{26} +(-3.67423 + 3.67423i) q^{27} +(27.9589 + 1.51651i) q^{28} +(28.7528 - 28.7528i) q^{29} +(-32.3614 + 3.22994i) q^{30} +(-3.46843 + 2.00250i) q^{31} +(28.1225 - 15.2684i) q^{32} +(23.3898 + 13.5041i) q^{33} +(24.0633 - 17.2911i) q^{34} +(-0.568726 - 65.7160i) q^{35} +(-11.3732 - 3.82762i) q^{36} +(-0.945732 + 0.253408i) q^{37} +(-34.0743 + 12.8754i) q^{38} +(-18.4279 + 10.6394i) q^{39} +(-39.9107 - 63.6252i) q^{40} +23.1289 q^{41} +(9.78717 - 22.1858i) q^{42} +(21.1443 + 21.1443i) q^{43} +(-3.91702 + 62.2496i) q^{44} +(-7.28965 + 27.2054i) q^{45} +(17.3811 + 7.84796i) q^{46} +(72.7787 + 42.0188i) q^{47} +(-3.76052 - 27.4565i) q^{48} +(42.8529 + 23.7619i) q^{49} +(-102.552 + 73.6905i) q^{50} +(-6.64171 - 24.7872i) q^{51} +(-40.9304 - 27.1947i) q^{52} +(-5.61117 + 20.9412i) q^{53} +(-6.58233 + 8.04195i) q^{54} +146.394 q^{55} +(55.9426 - 2.53545i) q^{56} +31.5456i q^{57} +(51.5101 - 62.9324i) q^{58} +(18.2213 + 4.88238i) q^{59} +(-63.7613 + 12.8559i) q^{60} +(-106.766 + 28.6078i) q^{61} +(-6.50481 + 4.67413i) q^{62} +(-14.9772 - 14.7202i) q^{63} +(52.9342 - 35.9718i) q^{64} +(-57.6693 + 99.8862i) q^{65} +(49.2306 + 22.2287i) q^{66} +(7.92019 + 2.12221i) q^{67} +(44.4542 - 39.1908i) q^{68} +(11.6784 - 11.6784i) q^{69} +(-14.1850 - 130.669i) q^{70} -22.4919i q^{71} +(-23.3942 - 5.35835i) q^{72} +(16.6746 + 28.8813i) q^{73} +(-1.83178 + 0.692161i) q^{74} +(28.3054 + 105.637i) q^{75} +(-65.2543 + 32.3917i) q^{76} +(-53.7560 + 94.9974i) q^{77} +(-34.5604 + 24.8339i) q^{78} +(10.9701 - 19.0007i) q^{79} +(-92.0647 - 118.694i) q^{80} +(4.50000 + 7.79423i) q^{81} +(46.0291 - 4.59409i) q^{82} +(-98.1751 - 98.1751i) q^{83} +(15.0708 - 46.0963i) q^{84} +(-98.3553 - 98.3553i) q^{85} +(46.2793 + 37.8796i) q^{86} +(-35.2148 - 60.9938i) q^{87} +(4.56930 + 124.662i) q^{88} +(46.7566 - 80.9847i) q^{89} +(-9.10344 + 55.5897i) q^{90} +(-43.6414 - 74.1007i) q^{91} +(36.1491 + 12.1659i) q^{92} +(1.79539 + 6.70049i) q^{93} +(153.184 + 69.1661i) q^{94} +(85.4945 + 148.081i) q^{95} +(-12.9375 - 53.8945i) q^{96} +114.643i q^{97} +(90.0019 + 38.7770i) q^{98} +(33.0781 - 33.0781i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 256 q - 12 q^{4} - 24 q^{8} + 108 q^{10} + 32 q^{11} + 32 q^{14} - 4 q^{16} + 12 q^{18} + 48 q^{22} - 64 q^{29} - 96 q^{35} - 96 q^{37} + 60 q^{40} - 60 q^{42} - 192 q^{43} + 228 q^{44} + 180 q^{46} - 32 q^{50}+ \cdots + 192 q^{99}+O(q^{100}) $ 256 * q - 12 * q^4 - 24 * q^8 + 108 * q^10 + 32 * q^11 + 32 * q^14 - 4 * q^16 + 12 * q^18 + 48 * q^22 - 64 * q^29 - 96 * q^35 - 96 * q^37 + 60 * q^40 - 60 * q^42 - 192 * q^43 + 228 * q^44 + 180 * q^46 - 32 * q^50 + 720 * q^52 + 160 * q^53 - 56 * q^56 - 312 * q^58 + 384 * q^59 + 72 * q^60 - 96 * q^64 - 216 * q^66 - 320 * q^67 - 780 * q^68 - 828 * q^70 + 60 * q^72 - 88 * q^74 - 72 * q^78 - 612 * q^80 + 1152 * q^81 + 780 * q^82 - 72 * q^84 - 212 * q^86 - 464 * q^88 - 480 * q^91 - 488 * q^92 - 612 * q^94 + 768 * q^95 - 900 * q^96 - 196 * q^98 + 192 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/336\mathbb{Z}\right)^\times$.

$n$	$85$	$113$	$127$	$241$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$1$	$1$	$e\left(\frac{5}{6}\right)$

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 $

$2$	1.99011	−	0.198630i	0.995056	−	0.0993149i
$2$	1.99011	−	0.198630i	0.995056	−	0.0993149i
$3$	0.448288	−	1.67303i	0.149429	−	0.557678i
$3$	0.448288	−	1.67303i	0.149429	−	0.557678i
$4$	3.92109	−	0.790591i	0.980273	−	0.197648i
$5$	−2.42988	−	9.06845i	−0.485977	−	1.81369i	−0.575621	−	0.817717i	$-0.695239\pi$
$5$	−2.42988	−	9.06845i	−0.485977	−	1.81369i	0.0896436	−	0.995974i	$-0.471427\pi$
$6$	0.559829	−	3.41857i	0.0933048	−	0.569761i
$7$	6.77691	+	1.75315i	0.968129	+	0.250450i
$7$	6.77691	+	1.75315i	0.968129	+	0.250450i
$8$	7.64638	−	2.35221i	0.955797	−	0.294026i
$9$	−2.59808	−	1.50000i	−0.288675	−	0.166667i
$10$	−6.63701	−	17.5646i	−0.663701	−	1.75646i
$11$	−4.03581	+	15.0619i	−0.366892	+	1.36926i	0.497946	+	0.867208i	$0.334088\pi$
$11$	−4.03581	+	15.0619i	−0.366892	+	1.36926i	−0.864838	+	0.502051i	$0.832579\pi$
$12$	0.435093	−	6.91453i	0.0362578	−	0.576211i
$13$	−8.68701	−	8.68701i	−0.668232	−	0.668232i	0.289075	−	0.957306i	$-0.406652\pi$
$13$	−8.68701	−	8.68701i	−0.668232	−	0.668232i	−0.957306	+	0.289075i	$0.906652\pi$
$14$	13.8350	+	2.14287i	0.988217	+	0.153062i
$15$	−16.2611			−1.08407
$16$	14.7499	−	6.19996i	0.921871	−	0.387498i
$17$	12.8308	−	7.40787i	0.754753	−	0.435757i	−0.0726556	−	0.997357i	$-0.523147\pi$
$17$	12.8308	−	7.40787i	0.754753	−	0.435757i	0.827409	+	0.561600i	$0.189814\pi$
$18$	−5.46841	−	2.46911i	−0.303800	−	0.137173i
$19$	−17.5923	+	4.71384i	−0.925910	+	0.248097i	−0.690110	−	0.723705i	$-0.742438\pi$
$19$	−17.5923	+	4.71384i	−0.925910	+	0.248097i	−0.235800	+	0.971802i	$0.575771\pi$
$20$	−16.6972	−	33.6372i	−0.834862	−	1.68186i
$21$	5.97108	−	10.5521i	0.284337	−	0.502479i
$22$	−5.03998	+	30.7764i	−0.229090	+	1.39893i
$23$	8.25787	+	4.76768i	0.359038	+	0.207290i	0.668659	−	0.743570i	$-0.266869\pi$
$23$	8.25787	+	4.76768i	0.359038	+	0.207290i	−0.309621	+	0.950860i	$0.600202\pi$
$24$	−0.507547	−	13.8471i	−0.0211478	−	0.576963i
$25$	−54.6819	+	31.5706i	−2.18728	+	1.26282i
$26$	−19.0136	−	15.5626i	−0.731293	−	0.598563i
$27$	−3.67423	+	3.67423i	−0.136083	+	0.136083i
$28$	27.9589	+	1.51651i	0.998532	+	0.0541610i
$29$	28.7528	−	28.7528i	0.991474	−	0.991474i	−0.00848949	−	0.999964i	$-0.502702\pi$
$29$	28.7528	−	28.7528i	0.991474	−	0.991474i	0.999964	+	0.00848949i	$0.00270232\pi$
$30$	−32.3614	+	3.22994i	−1.07871	+	0.107665i
$31$	−3.46843	+	2.00250i	−0.111885	+	0.0645967i	−0.554898	−	0.831918i	$-0.687243\pi$
$31$	−3.46843	+	2.00250i	−0.111885	+	0.0645967i	0.443013	+	0.896515i	$0.353909\pi$
$32$	28.1225	−	15.2684i	0.878829	−	0.477137i
$33$	23.3898	+	13.5041i	0.708781	+	0.409215i
$34$	24.0633	−	17.2911i	0.707744	−	0.508561i
$35$	−0.568726	−	65.7160i	−0.0162493	−	1.87760i
$36$	−11.3732	−	3.82762i	−0.315922	−	0.106323i
$37$	−0.945732	+	0.253408i	−0.0255603	+	0.00684887i	−0.271577	−	0.962417i	$-0.587545\pi$
$37$	−0.945732	+	0.253408i	−0.0255603	+	0.00684887i	0.246016	+	0.969266i	$0.420878\pi$
$38$	−34.0743	+	12.8754i	−0.896693	+	0.338827i
$39$	−18.4279	+	10.6394i	−0.472511	+	0.272804i
$40$	−39.9107	−	63.6252i	−0.997768	−	1.59063i
$41$	23.1289			0.564120			0.282060	−	0.959397i	$-0.408982\pi$
$41$	23.1289			0.564120			0.282060	+	0.959397i	$0.408982\pi$
$42$	9.78717	−	22.1858i	0.233028	−	0.528234i
$43$	21.1443	+	21.1443i	0.491727	+	0.491727i	0.908850	−	0.417123i	$-0.136962\pi$
$43$	21.1443	+	21.1443i	0.491727	+	0.491727i	−0.417123	+	0.908850i	$0.636962\pi$
$44$	−3.91702	+	62.2496i	−0.0890233	+	1.41476i
$45$	−7.28965	+	27.2054i	−0.161992	+	0.604564i
$46$	17.3811	+	7.84796i	0.377850	+	0.170608i
$47$	72.7787	+	42.0188i	1.54848	+	0.894017i	0.998258	+	0.0589997i	$0.0187911\pi$
$47$	72.7787	+	42.0188i	1.54848	+	0.894017i	0.550224	+	0.835017i	$0.314542\pi$
$48$	−3.76052	−	27.4565i	−0.0783442	−	0.572010i
$49$	42.8529	+	23.7619i	0.874549	+	0.484937i
$50$	−102.552	+	73.6905i	−2.05104	+	1.47381i
$51$	−6.64171	−	24.7872i	−0.130230	−	0.486024i
$52$	−40.9304	−	27.1947i	−0.787124	−	0.522975i
$53$	−5.61117	+	20.9412i	−0.105871	+	0.395117i	−0.998443	−	0.0557896i	$-0.982232\pi$
$53$	−5.61117	+	20.9412i	−0.105871	+	0.395117i	0.892571	+	0.450906i	$0.148899\pi$
$54$	−6.58233	+	8.04195i	−0.121895	+	0.148925i
$55$	146.394			2.66171
$56$	55.9426	−	2.53545i	0.998975	−	0.0452758i
$57$			31.5456i			0.553432i
$58$	51.5101	−	62.9324i	0.888105	−	1.08504i
$59$	18.2213	+	4.88238i	0.308836	+	0.0827523i	0.409908	−	0.912127i	$-0.365561\pi$
$59$	18.2213	+	4.88238i	0.308836	+	0.0827523i	−0.101073	+	0.994879i	$0.532227\pi$
$60$	−63.7613	+	12.8559i	−1.06269	+	0.214265i
$61$	−106.766	+	28.6078i	−1.75026	+	0.468980i	−0.984681	−	0.174366i	$-0.944212\pi$
$61$	−106.766	+	28.6078i	−1.75026	+	0.468980i	−0.765575	+	0.643346i	$0.777546\pi$
$62$	−6.50481	+	4.67413i	−0.104916	+	0.0753892i
$63$	−14.9772	−	14.7202i	−0.237733	−	0.233654i
$64$	52.9342	−	35.9718i	0.827097	−	0.562059i
$65$	−57.6693	+	99.8862i	−0.887220	+	1.53671i
$66$	49.2306	+	22.2287i	0.745918	+	0.336799i
$67$	7.92019	+	2.12221i	0.118212	+	0.0316748i	0.317440	−	0.948278i	$-0.397177\pi$
$67$	7.92019	+	2.12221i	0.118212	+	0.0316748i	−0.199228	+	0.979953i	$0.563843\pi$
$68$	44.4542	−	39.1908i	0.653738	−	0.576336i
$69$	11.6784	−	11.6784i	0.169252	−	0.169252i
$70$	−14.1850	−	130.669i	−0.202643	−	1.86670i
$71$		−	22.4919i		−	0.316787i	−0.987376	−	0.158394i	$-0.949369\pi$
$71$		−	22.4919i		−	0.316787i	0.987376	−	0.158394i	$-0.0506315\pi$
$72$	−23.3942	−	5.35835i	−0.324919	−	0.0744215i
$73$	16.6746	+	28.8813i	0.228419	+	0.395634i	0.957340	−	0.288964i	$-0.0933109\pi$
$73$	16.6746	+	28.8813i	0.228419	+	0.395634i	−0.728920	+	0.684598i	$0.759978\pi$
$74$	−1.83178	+	0.692161i	−0.0247538	+	0.00935353i
$75$	28.3054	+	105.637i	0.377406	+	1.40850i
$76$	−65.2543	+	32.3917i	−0.858609	+	0.426207i
$77$	−53.7560	+	94.9974i	−0.698130	+	1.23373i
$78$	−34.5604	+	24.8339i	−0.443082	+	0.318383i
$79$	10.9701	−	19.0007i	0.138862	−	0.240515i	−0.788204	−	0.615414i	$-0.788989\pi$
$79$	10.9701	−	19.0007i	0.138862	−	0.240515i	0.927066	+	0.374898i	$0.122322\pi$
$80$	−92.0647	−	118.694i	−1.15081	−	1.48367i
$81$	4.50000	+	7.79423i	0.0555556	+	0.0962250i
$82$	46.0291	−	4.59409i	0.561331	−	0.0560255i
$83$	−98.1751	−	98.1751i	−1.18283	−	1.18283i	−0.979007	−	0.203825i	$-0.934663\pi$
$83$	−98.1751	−	98.1751i	−1.18283	−	1.18283i	−0.203825	−	0.979007i	$-0.565337\pi$
$84$	15.0708	−	46.0963i	0.179414	−	0.548766i
$85$	−98.3553	−	98.3553i	−1.15712	−	1.15712i
$86$	46.2793	+	37.8796i	0.538132	+	0.440460i
$87$	−35.2148	−	60.9938i	−0.404768	−	0.701078i
$88$	4.56930	+	124.662i	0.0519239	+	1.41661i
$89$	46.7566	−	80.9847i	0.525354	−	0.909941i	−0.474209	−	0.880412i	$-0.657266\pi$
$89$	46.7566	−	80.9847i	0.525354	−	0.909941i	0.999564	−	0.0295286i	$-0.00940062\pi$
$90$	−9.10344	+	55.5897i	−0.101149	+	0.617663i
$91$	−43.6414	−	74.1007i	−0.479576	−	0.814294i
$92$	36.1491	+	12.1659i	0.392925	+	0.132238i
$93$	1.79539	+	6.70049i	0.0193053	+	0.0720483i
$94$	153.184	+	69.1661i	1.62962	+	0.735809i
$95$	85.4945	+	148.081i	0.899942	+	1.55875i
$96$	−12.9375	−	53.8945i	−0.134766	−	0.561401i
$97$			114.643i			1.18188i	0.806714	+	0.590942i	$0.201244\pi$
$97$			114.643i			1.18188i	−0.806714	+	0.590942i	$0.798756\pi$
$98$	90.0019	+	38.7770i	0.918387	+	0.395683i
$99$	33.0781	−	33.0781i	0.334122	−	0.334122i
$100$	−189.453	+	167.022i	−1.89453	+	1.67022i
$101$	168.787	+	45.2263i	1.67116	+	0.447785i	0.965423	−	0.260690i	$-0.0839501\pi$
$101$	168.787	+	45.2263i	1.67116	+	0.447785i	0.705735	+	0.708475i	$0.250617\pi$
$102$	−18.1412	−	48.0101i	−0.177855	−	0.470687i
$103$	−96.0431	+	166.352i	−0.932457	+	1.61506i	−0.153351	+	0.988172i	$0.549007\pi$
$103$	−96.0431	+	166.352i	−0.932457	+	1.61506i	−0.779106	+	0.626892i	$0.784327\pi$
$104$	−86.8579	−	45.9905i	−0.835172	−	0.442216i
$105$	−110.200	−	28.5082i	−1.04952	−	0.271507i
$106$	−7.00732	+	42.7898i	−0.0661068	+	0.403678i
$107$	28.9133	−	7.74731i	0.270218	−	0.0724048i	−0.121166	−	0.992632i	$-0.538663\pi$
$107$	28.9133	−	7.74731i	0.270218	−	0.0724048i	0.391384	+	0.920228i	$0.371997\pi$
$108$	−11.5022	+	17.3118i	−0.106502	+	0.160295i
$109$	34.5025	+	9.24491i	0.316537	+	0.0848157i	0.413589	−	0.910464i	$-0.364275\pi$
$109$	34.5025	+	9.24491i	0.316537	+	0.0848157i	−0.0970528	+	0.995279i	$0.530942\pi$
$110$	291.341	−	29.0783i	2.64855	−	0.264348i
$111$			1.69584i			0.0152778i
$112$	110.828	−	16.1577i	0.989539	−	0.144265i
$113$	−165.343			−1.46321			−0.731605	−	0.681729i	$-0.761228\pi$
$113$	−165.343			−1.46321			−0.731605	+	0.681729i	$0.761228\pi$
$114$	6.26590	+	62.7794i	0.0549641	+	0.550696i
$115$	23.1698	−	86.4710i	0.201477	−	0.751922i
$116$	90.0106	−	135.474i	0.775953	−	1.16788i
$117$	9.53900	+	35.6000i	0.0815299	+	0.304274i
$118$	37.2322	+	6.09720i	0.315527	+	0.0516712i
$119$	99.9403	−	27.7081i	0.839834	−	0.232841i
$120$	−124.339	+	38.2495i	−1.03615	+	0.318746i
$121$	−105.783	−	61.0736i	−0.874236	−	0.504740i
$122$	−206.793	+	78.1395i	−1.69503	+	0.640488i
$123$	10.3684	−	38.6954i	0.0842960	−	0.314597i
$124$	−12.0169	+	10.5941i	−0.0969103	+	0.0854362i
$125$	253.203	+	253.203i	2.02562	+	2.02562i
$126$	−32.7302	−	26.3199i	−0.259763	−	0.208888i
$127$	149.192			1.17474			0.587371	−	0.809318i	$-0.300163\pi$
$127$	149.192			1.17474			0.587371	+	0.809318i	$0.300163\pi$
$128$	98.2000	−	82.1022i	0.767187	−	0.641423i
$129$	44.8538	−	25.8963i	0.347704	−	0.200747i
$130$	−94.9280	+	210.240i	−0.730216	+	1.61723i
$131$	−78.2278	+	20.9611i	−0.597159	+	0.160008i	−0.544723	−	0.838616i	$-0.683365\pi$
$131$	−78.2278	+	20.9611i	−0.597159	+	0.160008i	−0.0524358	+	0.998624i	$0.516698\pi$
$132$	102.390	+	34.4590i	0.775679	+	0.261053i
$133$	−127.485	+	1.10330i	−0.958537	+	0.00829546i
$134$	16.1836	+	2.65025i	0.120773	+	0.0197780i
$135$	42.2476	+	24.3917i	0.312945	+	0.180679i
$136$	80.6843	−	86.8241i	0.593267	−	0.638413i
$137$	6.24491	−	3.60550i	0.0455833	−	0.0263175i	−0.477035	−	0.878884i	$-0.658289\pi$
$137$	6.24491	−	3.60550i	0.0455833	−	0.0263175i	0.522618	+	0.852567i	$0.324955\pi$
$138$	20.9216	−	25.5610i	0.151606	−	0.185224i
$139$	0.896461	−	0.896461i	0.00644936	−	0.00644936i	−0.703875	−	0.710324i	$-0.748548\pi$
$139$	0.896461	−	0.896461i	0.00644936	−	0.00644936i	0.710324	+	0.703875i	$0.248548\pi$
$140$	−54.1845	−	257.229i	−0.387032	−	1.83735i
$141$	102.925	−	102.925i	0.729962	−	0.729962i
$142$	−4.46756	−	44.7614i	−0.0314617	−	0.315221i
$143$	165.902	−	95.7833i	1.16015	−	0.669814i
$144$	−47.6214	−	6.01693i	−0.330704	−	0.0417842i
$145$	−330.609	−	190.877i	−2.28006	−	1.31639i
$146$	38.9210	+	54.1649i	0.266582	+	0.370993i
$147$	58.9649	−	61.0422i	0.401121	−	0.415253i
$148$	−3.50796	+	1.74132i	−0.0237024	+	0.0117657i
$149$	−228.006	+	61.0940i	−1.53024	+	0.410027i	−0.923098	−	0.384566i	$-0.874351\pi$
$149$	−228.006	+	61.0940i	−1.53024	+	0.410027i	−0.607143	+	0.794592i	$0.707685\pi$
$150$	77.3137	+	204.608i	0.515425	+	1.36405i
$151$	−99.6326	+	57.5229i	−0.659818	+	0.380946i	−0.792208	−	0.610251i	$-0.791068\pi$
$151$	−99.6326	+	57.5229i	−0.659818	+	0.380946i	0.132389	+	0.991198i	$0.457735\pi$
$152$	−123.429	+	77.4246i	−0.812035	+	0.509372i
$153$	−44.4472			−0.290505
$154$	−88.1112	+	199.733i	−0.572151	+	1.29697i
$155$	26.5875	+	26.5875i	0.171532	+	0.171532i
$156$	−63.8462	+	56.2869i	−0.409271	+	0.360814i
$157$	11.3133	−	42.2217i	0.0720590	−	0.268928i	−0.920491	−	0.390763i	$-0.872211\pi$
$157$	11.3133	−	42.2217i	0.0720590	−	0.268928i	0.992550	+	0.121835i	$0.0388779\pi$
$158$	18.0575	−	39.9925i	0.114288	−	0.253117i
$159$	32.5198	+	18.7753i	0.204527	+	0.118084i
$160$	−206.795	−	217.927i	−1.29247	−	1.36205i
$161$	47.6043	+	46.7874i	0.295679	+	0.290605i
$162$	10.5037	+	14.6176i	0.0648375	+	0.0902318i
$163$	−10.1237	−	37.7822i	−0.0621086	−	0.231793i	0.927893	−	0.372846i	$-0.121618\pi$
$163$	−10.1237	−	37.7822i	−0.0621086	−	0.231793i	−0.990002	+	0.141053i	$0.954951\pi$
$164$	90.6906	−	18.2855i	0.552991	−	0.111497i
$165$	65.6268	−	244.922i	0.397738	−	1.48438i
$166$	−214.880	−	175.879i	−1.29446	−	1.05951i
$167$	36.7194			0.219877			0.109938	−	0.993938i	$-0.464935\pi$
$167$	36.7194			0.219877			0.109938	+	0.993938i	$0.464935\pi$
$168$	20.8365	−	94.7304i	0.124027	−	0.563871i
$169$		−	18.0717i		−	0.106933i
$170$	−215.274	−	176.202i	−1.26632	−	1.03648i
$171$	52.7769	+	14.1415i	0.308637	+	0.0826990i
$172$	99.6251	+	66.1922i	0.579216	+	0.384838i
$173$	−86.5719	+	23.1969i	−0.500416	+	0.134086i	−0.500193	−	0.865914i	$-0.666738\pi$
$173$	−86.5719	+	23.1969i	−0.500416	+	0.134086i	−0.000222833		1.00000i	$0.500071\pi$
$174$	−82.1966	−	114.390i	−0.472394	−	0.657413i
$175$	−425.922	+	118.085i	−2.43384	+	0.674773i
$176$	33.8549	+	247.183i	0.192358	+	1.40445i
$177$	16.3368	−	28.2961i	0.0922982	−	0.159865i
$178$	76.9648	−	170.456i	0.432387	−	0.957618i
$179$	83.6432	+	22.4121i	0.467281	+	0.125207i	0.484774	−	0.874640i	$-0.338902\pi$
$179$	83.6432	+	22.4121i	0.467281	+	0.125207i	−0.0174933	+	0.999847i	$0.505569\pi$
$180$	−7.07510	+	112.438i	−0.0393061	+	0.624655i
$181$	160.895	−	160.895i	0.888925	−	0.888925i	−0.105495	−	0.994420i	$-0.533643\pi$
$181$	160.895	−	160.895i	0.888925	−	0.888925i	0.994420	+	0.105495i	$0.0336426\pi$
$182$	−101.570	−	138.800i	−0.558076	−	0.762639i
$183$			191.447i			1.04616i
$184$	74.3574	+	17.0313i	0.404116	+	0.0925612i
$185$	4.59604	+	7.96057i	0.0248435	+	0.0430301i
$186$	4.90395	+	12.9781i	0.0263653	+	0.0697748i
$187$	59.7935	+	223.152i	0.319751	+	1.19333i
$188$	318.592	+	107.221i	1.69464	+	0.570326i
$189$	−31.3414	+	18.4585i	−0.165828	+	0.0976638i
$190$	199.557	+	277.716i	1.05030	+	1.46166i
$191$	48.2319	−	83.5401i	0.252523	−	0.437383i	−0.711697	−	0.702487i	$-0.752073\pi$
$191$	48.2319	−	83.5401i	0.252523	−	0.437383i	0.964220	+	0.265104i	$0.0854063\pi$
$192$	−36.4522	−	104.686i	−0.189855	−	0.545242i
$193$	22.2068	+	38.4632i	0.115061	+	0.199291i	0.917804	−	0.397034i	$-0.129960\pi$
$193$	22.2068	+	38.4632i	0.115061	+	0.199291i	−0.802743	+	0.596325i	$0.796627\pi$
$194$	22.7715	+	228.152i	0.117379	+	1.17604i
$195$	141.260	+	141.260i	0.724412	+	0.724412i
$196$	186.816	+	59.2934i	0.953144	+	0.302518i
$197$	229.119	+	229.119i	1.16304	+	1.16304i	0.983807	+	0.179232i	$0.0573613\pi$
$197$	229.119	+	229.119i	1.16304	+	1.16304i	0.179232	+	0.983807i	$0.442639\pi$
$198$	59.2589	−	72.3995i	0.299287	−	0.365654i
$199$	−131.929	−	228.507i	−0.662959	−	1.14828i	−0.979834	−	0.199811i	$-0.935967\pi$
$199$	−131.929	−	228.507i	−0.662959	−	1.14828i	0.316876	−	0.948467i	$-0.397366\pi$
$200$	−343.858	+	370.024i	−1.71929	+	1.85012i
$201$	7.10105	−	12.2994i	0.0353286	−	0.0611909i
$202$	344.888	+	56.4794i	1.70737	+	0.279601i
$203$	245.263	−	144.447i	1.20819	−	0.711561i
$204$	−45.6393	−	91.9421i	−0.223722	−	0.450696i
$205$	−56.2006	−	209.743i	−0.274149	−	1.02314i
$206$	−158.094	+	350.135i	−0.767448	+	1.69969i
$207$	−14.3030	−	24.7736i	−0.0690968	−	0.119679i
$208$	−181.992	−	74.2737i	−0.874961	−	0.357085i
$209$		−	283.997i		−	1.35884i
$210$	−224.973	−	34.8455i	−1.07130	−	0.165931i
$211$	−162.315	+	162.315i	−0.769267	+	0.769267i	−0.977977	−	0.208710i	$-0.933073\pi$
$211$	−162.315	+	162.315i	−0.769267	+	0.769267i	0.208710	+	0.977977i	$0.433073\pi$
$212$	−5.44602	+	86.5484i	−0.0256888	+	0.408247i
$213$	−37.6297	−	10.0828i	−0.176665	−	0.0473373i
$214$	56.0020	−	21.1611i	0.261691	−	0.0988835i
$215$	140.368	−	243.124i	0.652873	−	1.13081i
$216$	−19.4520	+	36.7372i	−0.0900556	+	0.170079i
$217$	−27.0159	+	7.49006i	−0.124497	+	0.0345164i
$218$	70.5001	+	11.5452i	0.323395	+	0.0529596i
$219$	55.7943	−	14.9501i	0.254769	−	0.0682651i
$220$	574.025	−	115.738i	2.60921	−	0.526082i
$221$	−175.814	−	47.1091i	−0.795536	−	0.213163i
$222$	0.336844	+	3.37491i	0.00151732	+	0.0152023i
$223$			200.991i			0.901304i	0.892700	+	0.450652i	$0.148808\pi$
$223$			200.991i			0.901304i	−0.892700	+	0.450652i	$0.851192\pi$
$224$	217.352	−	54.1694i	0.970319	−	0.241828i
$225$	189.424			0.841883
$226$	−329.051	+	32.8420i	−1.45598	+	0.145319i
$227$	25.0657	−	93.5464i	0.110421	−	0.412099i	−0.888482	−	0.458911i	$-0.848240\pi$
$227$	25.0657	−	93.5464i	0.110421	−	0.412099i	0.998904	+	0.0468125i	$0.0149063\pi$
$228$	24.9397	+	123.693i	0.109385	+	0.542515i
$229$	−9.87393	−	36.8500i	−0.0431176	−	0.160917i	0.941010	−	0.338378i	$-0.109878\pi$
$229$	−9.87393	−	36.8500i	−0.0431176	−	0.160917i	−0.984128	+	0.177461i	$0.943212\pi$
$230$	28.9349	−	176.689i	0.125804	−	0.768214i
$231$	134.836	+	132.522i	0.583704	+	0.573687i
$232$	152.222	−	287.487i	0.656129	−	1.23917i
$233$	−361.752	−	208.857i	−1.55258	−	0.896384i	−0.997931	−	0.0643012i	$-0.979518\pi$
$233$	−361.752	−	208.857i	−1.55258	−	0.896384i	−0.554652	−	0.832083i	$-0.687149\pi$
$234$	26.0549	+	68.9533i	0.111346	+	0.294672i
$235$	204.202	−	762.091i	0.868943	−	3.24294i
$236$	75.3074	+	4.73868i	0.319099	+	0.0200792i
$237$	−26.8711	−	26.8711i	−0.113380	−	0.113380i
$238$	193.389	−	74.9933i	0.812557	−	0.315098i
$239$	−243.100			−1.01716			−0.508578	−	0.861016i	$-0.669829\pi$
$239$	−243.100			−1.01716			−0.508578	+	0.861016i	$0.669829\pi$
$240$	−239.850	+	100.818i	−0.999376	+	0.420076i
$241$	−261.466	+	150.958i	−1.08492	+	0.626380i	−0.932220	−	0.361892i	$-0.882131\pi$
$241$	−261.466	+	150.958i	−1.08492	+	0.626380i	−0.152702	+	0.988272i	$0.548798\pi$
$242$	−222.650	−	100.532i	−0.920042	−	0.415420i
$243$	15.0573	−	4.03459i	0.0619642	−	0.0166032i
$244$	−396.021	+	196.582i	−1.62304	+	0.805662i
$245$	111.356	−	446.348i	0.454514	−	1.82183i
$246$	12.9482	−	79.0677i	0.0526351	−	0.321413i
$247$	193.774	+	111.875i	0.784509	+	0.452936i
$248$	−21.8106	+	23.4703i	−0.0879461	+	0.0946385i
$249$	−208.261	+	120.239i	−0.836389	+	0.482889i
$250$	554.196	+	453.609i	2.21678	+	1.81443i
$251$	−77.3684	+	77.3684i	−0.308241	+	0.308241i	−0.844227	−	0.535986i	$-0.819940\pi$
$251$	−77.3684	+	77.3684i	−0.308241	+	0.308241i	0.535986	+	0.844227i	$0.319940\pi$
$252$	−70.3646	−	45.8784i	−0.279225	−	0.182057i
$253$	−105.137	+	105.137i	−0.415562	+	0.415562i
$254$	296.909	−	29.6340i	1.16893	−	0.116669i
$255$	−208.643	+	120.460i	−0.818208	+	0.472393i
$256$	179.121	−	182.898i	0.699691	−	0.714445i
$257$	−146.253	−	84.4390i	−0.569076	−	0.328556i	0.187704	−	0.982226i	$-0.439895\pi$
$257$	−146.253	−	84.4390i	−0.569076	−	0.328556i	−0.756780	+	0.653669i	$0.773229\pi$
$258$	84.1202	−	60.4459i	0.326047	−	0.234286i
$259$	−6.85340	+	0.0593114i	−0.0264610	+	0.000229001i
$260$	−147.158	+	437.256i	−0.565991	+	1.68175i
$261$	−117.831	+	31.5727i	−0.451460	+	0.120968i
$262$	−151.519	+	57.2532i	−0.578315	+	0.218524i
$263$	−181.799	+	104.962i	−0.691251	+	0.399094i	−0.804081	−	0.594520i	$-0.797342\pi$
$263$	−181.799	+	104.962i	−0.691251	+	0.399094i	0.112829	+	0.993614i	$0.464009\pi$
$264$	210.611	+	48.2397i	0.797771	+	0.182726i
$265$	203.539			0.768070
$266$	−253.491	+	27.5181i	−0.952974	+	0.103451i
$267$	−114.530	−	114.530i	−0.428950	−	0.428950i
$268$	32.7336	+	2.05974i	0.122140	+	0.00768562i
$269$	−52.9582	+	197.643i	−0.196871	+	0.734732i	0.794904	+	0.606735i	$0.207521\pi$
$269$	−52.9582	+	197.643i	−0.196871	+	0.734732i	−0.991775	+	0.127996i	$0.959145\pi$
$270$	88.9224	+	40.1505i	0.329342	+	0.148706i
$271$	−167.861	−	96.9144i	−0.619412	−	0.357618i	0.157228	−	0.987562i	$-0.449744\pi$
$271$	−167.861	−	96.9144i	−0.619412	−	0.357618i	−0.776640	+	0.629945i	$0.783078\pi$
$272$	143.325	−	188.816i	0.526930	−	0.694177i
$273$	−143.537	+	39.7951i	−0.525776	+	0.145769i
$274$	11.7119	−	8.41577i	0.0427442	−	0.0307145i
$275$	−254.826	−	951.023i	−0.926640	−	3.45827i
$276$	36.5592	−	55.0249i	0.132461	−	0.199365i
$277$	88.0610	−	328.648i	0.317910	−	1.18646i	−0.603340	−	0.797484i	$-0.706164\pi$
$277$	88.0610	−	328.648i	0.317910	−	1.18646i	0.921250	−	0.388971i	$-0.127169\pi$
$278$	1.60599	−	1.96212i	0.00577696	−	0.00705799i
$279$	12.0150			0.0430645
$280$	−158.927	−	501.152i	−0.567595	−	1.78983i
$281$		−	82.2196i		−	0.292597i	−0.989241	−	0.146298i	$-0.953264\pi$
$281$		−	82.2196i		−	0.292597i	0.989241	−	0.146298i	$-0.0467359\pi$
$282$	184.388	−	225.275i	0.653857	−	0.798849i
$283$	−155.455	−	41.6541i	−0.549312	−	0.147188i	−0.0265203	−	0.999648i	$-0.508443\pi$
$283$	−155.455	−	41.6541i	−0.549312	−	0.147188i	−0.522791	+	0.852461i	$0.675109\pi$
$284$	−17.7819	−	88.1928i	−0.0626123	−	0.310538i
$285$	286.070	−	76.6523i	1.00375	−	0.268955i
$286$	311.137	−	223.573i	1.08789	−	0.781722i
$287$	156.742	+	40.5485i	0.546141	+	0.141284i
$288$	−95.9670	−	2.51534i	−0.333219	−	0.00873381i
$289$	−34.7470	+	60.1836i	−0.120232	+	0.208248i
$290$	−695.863	−	314.198i	−2.39953	−	1.08344i
$291$	191.801	+	51.3929i	0.659110	+	0.176608i
$292$	88.2160	+	100.063i	0.302110	+	0.342683i
$293$	79.5362	−	79.5362i	0.271455	−	0.271455i	−0.558231	−	0.829686i	$-0.688520\pi$
$293$	79.5362	−	79.5362i	0.271455	−	0.271455i	0.829686	+	0.558231i	$0.188520\pi$
$294$	105.222	−	133.193i	0.357898	−	0.453037i
$295$		−	177.103i		−	0.600348i
$296$	−6.63535	+	4.16221i	−0.0224167	+	0.0140615i
$297$	−40.5123	−	70.1693i	−0.136405	−	0.236260i
$298$	−441.622	+	166.873i	−1.48195	+	0.559975i
$299$	−30.3193	−	113.153i	−0.101402	−	0.378438i
$300$	194.504	+	391.836i	0.648347	+	1.30612i
$301$	106.224	+	180.362i	0.352902	+	0.599209i
$302$	−186.854	+	134.267i	−0.618723	+	0.444593i
$303$	151.330	−	262.112i	0.499440	−	0.865055i
$304$	−230.259	+	178.600i	−0.757433	+	0.587501i
$305$	518.856	+	898.686i	1.70117	+	2.94651i
$306$	−88.4549	+	8.82854i	−0.289068	+	0.0288514i
$307$	−417.110	−	417.110i	−1.35866	−	1.35866i	−0.875568	−	0.483095i	$-0.839512\pi$
$307$	−417.110	−	417.110i	−1.35866	−	1.35866i	−0.483095	−	0.875568i	$-0.660488\pi$
$308$	−135.678	+	414.992i	−0.440514	+	1.34738i
$309$	235.257	+	235.257i	0.761348	+	0.761348i
$310$	58.1931	+	47.6310i	0.187720	+	0.153648i
$311$	−295.949	−	512.598i	−0.951604	−	1.64823i	−0.741955	−	0.670450i	$-0.766101\pi$
$311$	−295.949	−	512.598i	−0.951604	−	1.64823i	−0.209649	−	0.977777i	$-0.567232\pi$
$312$	−115.881	+	124.699i	−0.371413	+	0.399676i
$313$	61.4458	−	106.427i	0.196312	−	0.340023i	−0.751018	−	0.660282i	$-0.770437\pi$
$313$	61.4458	−	106.427i	0.196312	−	0.340023i	0.947330	+	0.320259i	$0.103770\pi$
$314$	14.1282	−	86.2730i	0.0449942	−	0.274755i
$315$	−97.0964	+	171.588i	−0.308243	+	0.544725i
$316$	27.9928	−	83.1763i	0.0885849	−	0.263216i
$317$	−30.1936	−	112.684i	−0.0952478	−	0.355470i	0.901809	−	0.432135i	$-0.142240\pi$
$317$	−30.1936	−	112.684i	−0.0952478	−	0.355470i	−0.997057	+	0.0766649i	$0.975573\pi$
$318$	68.4475	+	30.9056i	0.215244	+	0.0971875i
$319$	317.029	+	549.111i	0.993822	+	1.72135i
$320$	−454.832	−	392.624i	−1.42135	−	1.22695i
$321$		−	51.8460i		−	0.161514i
$322$	104.031	+	83.6566i	0.323079	+	0.259803i
$323$	−190.804	+	190.804i	−0.590724	+	0.590724i
$324$	23.8070	+	27.0042i	0.0734783	+	0.0833464i
$325$	749.276	+	200.768i	2.30547	+	0.617748i
$326$	−27.6520	−	73.1799i	−0.0848220	−	0.224478i
$327$	30.9341	−	53.5794i	0.0945996	−	0.163851i
$328$	176.852	−	54.4041i	0.539184	−	0.165866i
$329$	419.549	+	412.349i	1.27522	+	1.25334i
$330$	81.9557	−	500.458i	0.248351	−	1.51654i
$331$	−143.012	+	38.3200i	−0.432062	+	0.115771i	−0.468294	−	0.883573i	$-0.655131\pi$
$331$	−143.012	+	38.3200i	−0.432062	+	0.115771i	0.0362322	+	0.999343i	$0.488464\pi$
$332$	−462.570	−	307.337i	−1.39328	−	0.925715i
$333$	2.83720	+	0.760224i	0.00852011	+	0.00228296i
$334$	73.0758	−	7.29357i	0.218790	−	0.0218370i
$335$		−	76.9806i		−	0.229793i
$336$	22.6507	−	192.663i	0.0674127	−	0.573401i
$337$	337.879			1.00261			0.501304	−	0.865271i	$-0.332854\pi$
$337$	337.879			1.00261			0.501304	+	0.865271i	$0.332854\pi$
$338$	−3.58957	−	35.9647i	−0.0106200	−	0.106404i
$339$	−74.1211	+	276.624i	−0.218646	+	0.815999i
$340$	−463.419	−	307.901i	−1.36300	−	0.905592i
$341$	−16.1634	−	60.3227i	−0.0474000	−	0.176899i
$342$	107.841	+	17.6602i	0.315324	+	0.0516379i
$343$	248.752	+	236.160i	0.725225	+	0.688512i
$344$	211.413	+	111.941i	0.614572	+	0.325411i
$345$	−134.282	−	77.5278i	−0.389223	−	0.224718i
$346$	−167.680	+	63.3602i	−0.484625	+	0.183122i
$347$	−111.651	+	416.688i	−0.321762	+	1.20083i	0.595766	+	0.803158i	$0.296849\pi$
$347$	−111.651	+	416.688i	−0.321762	+	1.20083i	−0.917527	+	0.397673i	$0.869818\pi$
$348$	−186.302	−	211.322i	−0.535349	−	0.607247i
$349$	77.9645	+	77.9645i	0.223394	+	0.223394i	0.809926	−	0.586532i	$-0.199507\pi$
$349$	77.9645	+	77.9645i	0.223394	+	0.223394i	−0.586532	+	0.809926i	$0.699507\pi$
$350$	−824.177	+	319.604i	−2.35479	+	0.913154i
$351$	63.8362			0.181870
$352$	116.473	+	485.198i	0.330889	+	1.37840i
$353$	−484.225	+	279.568i	−1.37174	+	0.791976i	−0.991147	−	0.132766i	$-0.957614\pi$
$353$	−484.225	+	279.568i	−1.37174	+	0.791976i	−0.380595	+	0.924742i	$0.624281\pi$
$354$	26.8916	−	59.5574i	0.0759649	−	0.168241i
$355$	−203.967	+	54.6527i	−0.574554	+	0.153951i
$356$	119.311	−	354.514i	0.335143	−	0.995826i
$357$	−1.55452	−	179.625i	−0.00435441	−	0.503150i
$358$	170.911	+	27.9886i	0.477405	+	0.0781805i
$359$	318.844	+	184.085i	0.888146	+	0.512771i	0.873336	−	0.487119i	$-0.161952\pi$
$359$	318.844	+	184.085i	0.888146	+	0.512771i	0.0148102	+	0.999890i	$0.495286\pi$
$360$	8.25327	+	225.169i	0.0229258	+	0.625470i
$361$	−25.3667	+	14.6455i	−0.0702678	+	0.0405692i
$362$	288.241	−	352.159i	0.796247	−	0.972814i
$363$	−149.599	+	149.599i	−0.412119	+	0.412119i
$364$	−229.705	−	256.053i	−0.631059	−	0.703443i
$365$	221.391	−	221.391i	0.606551	−	0.606551i
$366$	38.0270	+	381.001i	0.103899	+	1.04099i
$367$	−87.5912	+	50.5708i	−0.238668	+	0.137795i	−0.614564	−	0.788867i	$-0.710668\pi$
$367$	−87.5912	+	50.5708i	−0.238668	+	0.137795i	0.375896	+	0.926662i	$0.377335\pi$
$368$	151.362	+	19.1245i	0.411311	+	0.0519688i
$369$	−60.0907	−	34.6934i	−0.162847	−	0.0940200i
$370$	10.7278	+	14.9295i	0.0289942	+	0.0403501i
$371$	−74.7394	+	132.079i	−0.201454	+	0.356008i
$372$	12.3372	+	24.8538i	0.0331646	+	0.0668114i
$373$	7.87584	−	2.11033i	0.0211149	−	0.00565771i	−0.248246	−	0.968697i	$-0.579854\pi$
$373$	7.87584	−	2.11033i	0.0211149	−	0.00565771i	0.269361	+	0.963039i	$0.413188\pi$
$374$	163.320	+	432.222i	0.436686	+	1.15567i
$375$	537.125	−	310.109i	1.43233	−	0.826958i
$376$	655.330	+	150.101i	1.74290	+	0.399204i
$377$	−499.551			−1.32507
$378$	−58.7066	+	42.9597i	−0.155308	+	0.113650i
$379$	401.529	+	401.529i	1.05944	+	1.05944i	0.998118	+	0.0613258i	$0.0195329\pi$
$379$	401.529	+	401.529i	1.05944	+	1.05944i	0.0613258	+	0.998118i	$0.480467\pi$
$380$	452.303	+	513.047i	1.19027	+	1.35012i
$381$	66.8811	−	249.604i	0.175541	−	0.655127i
$382$	79.3934	−	175.834i	0.207836	−	0.460300i
$383$	49.5231	+	28.5922i	0.129303	+	0.0746531i	0.563256	−	0.826282i	$-0.309548\pi$
$383$	49.5231	+	28.5922i	0.129303	+	0.0746531i	−0.433953	+	0.900935i	$0.642882\pi$
$384$	−93.3378	−	201.097i	−0.243067	−	0.523690i
$385$	992.100	+	256.651i	2.57688	+	0.666627i
$386$	51.8339	+	72.1352i	0.134285	+	0.186879i
$387$	−23.2180	−	86.6508i	−0.0599949	−	0.223904i
$388$	90.6355	+	449.525i	0.233597	+	1.15857i
$389$	−0.302874	+	1.13034i	−0.000778595	+	0.00290576i	−0.966314	−	0.257366i	$-0.917145\pi$
$389$	−0.302874	+	1.13034i	−0.000778595	+	0.00290576i	0.965535	+	0.260272i	$0.0838121\pi$
$390$	309.183	+	253.066i	0.792776	+	0.648886i
$391$	141.273			0.361313
$392$	383.563	+	80.8933i	0.978476	+	0.206361i
$393$			140.274i			0.356932i
$394$	501.482	+	410.462i	1.27280	+	1.04178i
$395$	−198.963	−	53.3120i	−0.503704	−	0.134967i
$396$	103.551	−	155.854i	0.261493	−	0.393570i
$397$	−182.161	+	48.8099i	−0.458844	+	0.122947i	−0.480835	−	0.876811i	$-0.659666\pi$
$397$	−182.161	+	48.8099i	−0.458844	+	0.122947i	0.0219905	+	0.999758i	$0.493000\pi$
$398$	−307.941	−	428.550i	−0.773722	−	1.07676i
$399$	−55.3043	+	213.782i	−0.138607	+	0.535794i
$400$	−610.818	+	804.690i	−1.52704	+	2.01172i
$401$	43.4263	−	75.2165i	0.108295	−	0.187572i	−0.806785	−	0.590846i	$-0.798794\pi$
$401$	43.4263	−	75.2165i	0.108295	−	0.187572i	0.915080	+	0.403273i	$0.132128\pi$
$402$	11.6889	−	25.8876i	0.0290768	−	0.0643971i
$403$	47.5260	+	12.7346i	0.117931	+	0.0315994i
$404$	697.585	+	43.8952i	1.72670	+	0.108651i
$405$	59.7471	−	59.7471i	0.147524	−	0.147524i
$406$	459.409	−	336.182i	1.13155	−	0.828034i
$407$		−	15.2672i		−	0.0375115i
$408$	−109.090	−	173.910i	−0.267377	−	0.426249i
$409$	−73.8086	−	127.840i	−0.180461	−	0.312568i	0.761577	−	0.648075i	$-0.224426\pi$
$409$	−73.8086	−	127.840i	−0.180461	−	0.312568i	−0.942038	+	0.335507i	$0.891092\pi$
$410$	−153.507	−	406.250i	−0.374407	−	0.990853i
$411$	−3.23260	−	12.0642i	−0.00786521	−	0.0293534i
$412$	−245.078	+	728.211i	−0.594849	+	1.76750i
$413$	114.925	+	65.0322i	0.278268	+	0.157463i
$414$	−33.3854	−	46.4612i	−0.0806411	−	0.112225i
$415$	−651.742	+	1128.85i	−1.57046	+	2.72012i
$416$	−376.937	−	111.664i	−0.906099	−	0.268423i
$417$	−1.09794	−	1.90168i	−0.00263294	−	0.00456039i
$418$	−56.4102	−	565.185i	−0.134953	−	1.35212i
$419$	132.535	+	132.535i	0.316312	+	0.316312i	0.847349	−	0.531037i	$-0.178197\pi$
$419$	132.535	+	132.535i	0.316312	+	0.316312i	−0.531037	+	0.847349i	$0.678197\pi$
$420$	−454.643	−	24.6601i	−1.08248	−	0.0587146i
$421$	132.979	+	132.979i	0.315865	+	0.315865i	0.847177	−	0.531311i	$-0.178301\pi$
$421$	132.979	+	132.979i	0.315865	+	0.315865i	−0.531311	+	0.847177i	$0.678301\pi$
$422$	−290.785	+	355.266i	−0.689064	+	0.841863i
$423$	−126.056	−	218.336i	−0.298006	−	0.516161i
$424$	6.35291	+	173.323i	0.0149833	+	0.408780i
$425$	−467.742	+	810.152i	−1.10057	+	1.90624i
$426$	−76.8900	−	12.5916i	−0.180493	−	0.0295578i
$427$	−773.694	+	6.69578i	−1.81193	+	0.0156810i
$428$	107.247	−	53.2365i	0.250577	−	0.124384i
$429$	−85.8770	−	320.497i	−0.200179	−	0.747080i
$430$	231.056	−	511.725i	0.537339	−	1.19006i
$431$	−375.701	−	650.734i	−0.871697	−	1.50982i	−0.860240	−	0.509889i	$-0.829686\pi$
$431$	−375.701	−	650.734i	−0.871697	−	1.50982i	−0.0114569	−	0.999934i	$-0.503647\pi$
$432$	−31.4146	+	76.9748i	−0.0727190	+	0.178182i
$433$			127.109i			0.293555i	0.989170	+	0.146777i	$0.0468901\pi$
$433$			127.109i			0.293555i	−0.989170	+	0.146777i	$0.953110\pi$
$434$	−52.2769	+	20.2722i	−0.120454	+	0.0467102i
$435$	−467.552	+	467.552i	−1.07483	+	1.07483i
$436$	142.596	+	8.97281i	0.327056	+	0.0205798i
$437$	−167.749	−	44.9482i	−0.383865	−	0.102856i
$438$	108.067	−	40.8347i	0.246729	−	0.0932299i
$439$	−198.342	+	343.539i	−0.451804	+	0.782548i	−0.998498	−	0.0547844i	$-0.982553\pi$
$439$	−198.342	+	343.539i	−0.451804	+	0.782548i	0.546694	+	0.837333i	$0.315886\pi$
$440$	1119.39	−	344.350i	2.54406	−	0.782614i
$441$	−75.6923	−	126.015i	−0.171638	−	0.285747i
$442$	−359.246	−	58.8306i	−0.812774	−	0.133101i
$443$	−216.528	+	58.0185i	−0.488776	+	0.130967i	−0.494786	−	0.869015i	$-0.664754\pi$
$443$	−216.528	+	58.0185i	−0.488776	+	0.130967i	0.00600999	+	0.999982i	$0.498087\pi$
$444$	1.34072	+	6.64955i	0.00301963	+	0.0149765i
$445$	−848.019	−	227.226i	−1.90566	−	0.510620i
$446$	39.9227	+	399.994i	0.0895129	+	0.896848i
$447$			408.849i			0.914651i
$448$	421.794	−	150.976i	0.941505	−	0.336999i
$449$	−105.243			−0.234395			−0.117197	−	0.993109i	$-0.537391\pi$
$449$	−105.243			−0.234395			−0.117197	+	0.993109i	$0.537391\pi$
$450$	376.974	−	37.6252i	0.837720	−	0.0836115i
$451$	−93.3439	+	348.364i	−0.206971	+	0.772426i
$452$	−648.324	+	130.718i	−1.43435	+	0.289200i
$453$	51.5736	+	192.475i	0.113849	+	0.424890i
$454$	31.3024	−	191.147i	0.0689480	−	0.421028i
$455$	−565.935	+	575.816i	−1.24381	+	1.26553i
$456$	74.2020	+	241.210i	0.162724	+	0.528969i
$457$	78.1493	+	45.1195i	0.171005	+	0.0987297i	0.583060	−	0.812429i	$-0.301855\pi$
$457$	78.1493	+	45.1195i	0.171005	+	0.0987297i	−0.412055	+	0.911159i	$0.635189\pi$
$458$	−26.9697	−	71.3744i	−0.0588859	−	0.155839i
$459$	−19.9251	+	74.3616i	−0.0434099	+	0.162008i
$460$	22.4879	−	357.379i	0.0488867	−	0.776910i
$461$	274.248	+	274.248i	0.594897	+	0.594897i	0.938950	−	0.344053i	$-0.111800\pi$
$461$	274.248	+	274.248i	0.594897	+	0.594897i	−0.344053	+	0.938950i	$0.611800\pi$
$462$	294.661	+	236.951i	0.637793	+	0.512880i
$463$	763.416			1.64885			0.824423	−	0.565974i	$-0.191500\pi$
$463$	763.416			1.64885			0.824423	+	0.565974i	$0.191500\pi$
$464$	245.835	−	602.367i	0.529817	−	1.29821i
$465$	56.4005	−	32.5629i	0.121291	−	0.0700276i
$466$	−761.412	−	343.795i	−1.63393	−	0.737758i
$467$	−551.494	+	147.772i	−1.18093	+	0.316429i	−0.795295	−	0.606223i	$-0.792684\pi$
$467$	−551.494	+	147.772i	−1.18093	+	0.316429i	−0.385634	+	0.922652i	$0.626017\pi$
$468$	65.5484	+	132.050i	0.140061	+	0.282157i
$469$	49.9538	+	28.2673i	0.106511	+	0.0602714i
$470$	255.010	−	1557.21i	0.542575	−	3.31321i
$471$	−65.5666	−	37.8549i	−0.139207	−	0.0803713i
$472$	150.811	−	5.52778i	0.319516	−	0.0117114i
$473$	−403.806	+	233.138i	−0.853713	+	0.492891i
$474$	−58.8138	−	48.1390i	−0.124080	−	0.101559i
$475$	813.161	−	813.161i	1.71192	−	1.71192i
$476$	369.969	−	187.658i	0.777246	−	0.394239i
$477$	45.9900	−	45.9900i	0.0964151	−	0.0964151i
$478$	−483.797	+	48.2869i	−1.01213	+	0.101019i
$479$	−176.451	+	101.874i	−0.368375	+	0.212681i	−0.672748	−	0.739872i	$-0.734886\pi$
$479$	−176.451	+	101.874i	−0.368375	+	0.212681i	0.304373	+	0.952553i	$0.401553\pi$
$480$	−457.303	+	248.281i	−0.952715	+	0.517252i
$481$	10.4169	+	6.01422i	0.0216568	+	0.0125036i
$482$	−490.362	+	352.358i	−1.01735	+	0.731032i
$483$	99.6173	−	58.6693i	0.206247	−	0.121469i
$484$	−463.067	−	155.844i	−0.956751	−	0.321993i
$485$	1039.63	−	278.569i	2.14357	−	0.574368i
$486$	29.1643	−	11.0201i	0.0600089	−	0.0226751i
$487$	528.022	−	304.854i	1.08423	−	0.625983i	0.152199	−	0.988350i	$-0.451365\pi$
$487$	528.022	−	304.854i	1.08423	−	0.625983i	0.932036	+	0.362367i	$0.118031\pi$
$488$	−749.079	+	469.881i	−1.53500	+	0.962871i
$489$	−67.7492			−0.138546
$490$	132.953	−	910.402i	0.271332	−	1.85796i
$491$	372.226	+	372.226i	0.758098	+	0.758098i	0.975976	−	0.217878i	$-0.0699135\pi$
$491$	372.226	+	372.226i	0.758098	+	0.758098i	−0.217878	+	0.975976i	$0.569913\pi$
$492$	10.0632	−	159.925i	0.0204537	−	0.325052i
$493$	155.924	−	581.918i	0.316277	−	1.18036i
$494$	407.853	+	184.155i	0.825613	+	0.372784i
$495$	−380.343	−	219.591i	−0.768371	−	0.443619i
$496$	−38.7437	+	51.0409i	−0.0781123	+	0.102905i
$497$	39.4317	−	152.425i	0.0793394	−	0.306691i
$498$	−390.579	+	280.657i	−0.784296	+	0.563568i
$499$	80.2044	+	299.327i	0.160730	+	0.599853i	0.998546	+	0.0539008i	$0.0171655\pi$
$499$	80.2044	+	299.327i	0.160730	+	0.599853i	−0.837816	+	0.545953i	$0.816168\pi$
$500$	1193.01	+	792.652i	2.38602	+	1.58530i
$501$	16.4609	−	61.4328i	0.0328560	−	0.122620i
$502$	−138.604	+	169.340i	−0.276104	+	0.337330i
$503$	298.261			0.592964			0.296482	−	0.955038i	$-0.404187\pi$
$503$	298.261			0.592964			0.296482	+	0.955038i	$0.404187\pi$
$504$	−149.146	−	77.3266i	−0.295925	−	0.153426i
$505$		−	1640.53i		−	3.24858i
$506$	−188.352	+	230.118i	−0.372236	+	0.454779i
$507$	−30.2345	−	8.10131i	−0.0596341	−	0.0159789i
$508$	584.997	−	117.950i	1.15157	−	0.232185i
$509$	367.451	−	98.4583i	0.721908	−	0.193435i	0.120885	−	0.992666i	$-0.461427\pi$
$509$	367.451	−	98.4583i	0.721908	−	0.193435i	0.601023	+	0.799232i	$0.294760\pi$
$510$	−391.296	+	281.172i	−0.767247	+	0.551317i
$511$	62.3690	+	224.959i	0.122053	+	0.440233i
$512$	320.142	−	399.566i	0.625277	−	0.780403i
$513$	47.3185	−	81.9580i	0.0922387	−	0.159762i
$514$	−307.831	−	138.993i	−0.598893	−	0.270414i
$515$	1741.93	+	466.747i	3.38238	+	0.906306i
$516$	155.402	−	137.003i	0.301167	−	0.265509i
$517$	−926.602	+	926.602i	−1.79227	+	1.79227i
$518$	−13.6273	+	1.47933i	−0.0263074	+	0.00285584i
$519$			155.237i			0.299107i
$520$	−206.008	+	899.418i	−0.396170	+	1.72965i
$521$	177.915	+	308.158i	0.341487	+	0.591473i	0.984709	−	0.174207i	$-0.0557360\pi$
$521$	177.915	+	308.158i	0.341487	+	0.591473i	−0.643222	+	0.765680i	$0.722403\pi$
$522$	−228.226	+	86.2380i	−0.437214	+	0.165207i
$523$	−28.8064	−	107.507i	−0.0550792	−	0.205558i	0.932903	−	0.360129i	$-0.117267\pi$
$523$	−28.8064	−	107.507i	−0.0550792	−	0.205558i	−0.987982	+	0.154570i	$0.950601\pi$
$524$	−290.167	+	144.036i	−0.553753	+	0.274879i
$525$	6.62502	+	765.518i	0.0126191	+	1.45813i
$526$	−340.952	+	244.996i	−0.648198	+	0.465773i
$527$	−29.6685	+	51.3873i	−0.0562970	+	0.0975092i
$528$	428.722	+	54.1687i	0.811974	+	0.102592i
$529$	−219.038	−	379.386i	−0.414061	−	0.717175i
$530$	405.065	−	40.4288i	0.764273	−	0.0762808i
$531$	−40.0168	−	40.0168i	−0.0753611	−	0.0753611i
$532$	−499.010	+	105.115i	−0.937988	+	0.197584i
$533$	−200.921	−	200.921i	−0.376963	−	0.376963i
$534$	−250.676	−	205.178i	−0.469431	−	0.384228i
$535$	−140.512	−	243.374i	−0.262640	−	0.454905i
$536$	65.5526	−	2.40274i	0.122300	−	0.00448273i
$537$	74.9925	−	129.891i	0.139651	−	0.241882i
$538$	−66.1351	+	403.850i	−0.122928	+	0.750651i
$539$	−530.844	+	549.546i	−0.984869	+	1.01957i
$540$	184.941	+	62.2414i	0.342483	+	0.115262i
$541$	−193.342	−	721.561i	−0.357378	−	1.33375i	−0.877465	−	0.479641i	$-0.840767\pi$
$541$	−193.342	−	721.561i	−0.357378	−	1.33375i	0.520087	−	0.854114i	$-0.325900\pi$
$542$	−353.312	−	159.528i	−0.651867	−	0.294333i
$543$	−197.056	−	341.311i	−0.362902	−	0.628565i
$544$	247.728	−	404.234i	0.455383	−	0.743077i
$545$		−	335.348i		−	0.615318i
$546$	−277.750	+	107.707i	−0.508699	+	0.197266i
$547$	−97.8219	+	97.8219i	−0.178833	+	0.178833i	−0.790847	−	0.612014i	$-0.790360\pi$
$547$	−97.8219	+	97.8219i	−0.178833	+	0.178833i	0.612014	+	0.790847i	$0.290360\pi$
$548$	21.6364	−	19.0747i	0.0394825	−	0.0348078i
$549$	320.297	+	85.8233i	0.583419	+	0.156327i
$550$	−696.034	−	1842.03i	−1.26552	−	3.34914i
$551$	−370.291	+	641.363i	−0.672035	+	1.16400i
$552$	61.8273	−	116.767i	0.112006	−	0.211535i
$553$	107.654	−	109.534i	0.194673	−	0.198072i
$554$	109.972	−	671.538i	0.198505	−	1.21216i
$555$	15.3786	−	4.12070i	0.0277093	−	0.00742468i
$556$	2.80637	−	4.22384i	0.00504743	−	0.00759684i
$557$	580.720	+	155.604i	1.04259	+	0.279360i	0.739185	−	0.673503i	$-0.235211\pi$
$557$	580.720	+	155.604i	1.04259	+	0.279360i	0.303401	+	0.952863i	$0.401878\pi$
$558$	23.9112	−	2.38654i	0.0428516	−	0.00427695i
$559$		−	367.361i		−	0.657175i
$560$	−415.825	−	965.781i	−0.742545	−	1.72461i
$561$	400.146			0.713273
$562$	−16.3313	−	163.626i	−0.0290592	−	0.291150i
$563$	92.6690	−	345.845i	0.164599	−	0.614290i	−0.833493	−	0.552531i	$-0.813662\pi$
$563$	92.6690	−	345.845i	0.164599	−	0.614290i	0.998091	−	0.0617594i	$-0.0196712\pi$
$564$	322.206	−	484.948i	0.571286	−	0.859837i
$565$	401.764	+	1499.40i	0.711086	+	2.65381i
$566$	−317.647	−	52.0183i	−0.561214	−	0.0919051i
$567$	16.8316	+	60.7099i	0.0296854	+	0.107072i
$568$	−52.9057	−	171.982i	−0.0931438	−	0.302784i
$569$	638.798	+	368.810i	1.12267	+	0.648172i	0.942081	−	0.335387i	$-0.108867\pi$
$569$	638.798	+	368.810i	1.12267	+	0.648172i	0.180587	+	0.983559i	$0.442200\pi$
$570$	554.086	−	209.369i	0.972081	−	0.367313i
$571$	−17.6027	+	65.6940i	−0.0308278	+	0.115051i	−0.979625	−	0.200834i	$-0.935635\pi$
$571$	−17.6027	+	65.6940i	−0.0308278	+	0.115051i	0.948797	+	0.315885i	$0.102301\pi$
$572$	574.790	−	506.736i	1.00488	−	0.885901i
$573$	−118.144	−	118.144i	−0.206184	−	0.206184i
$574$	319.989	+	49.5623i	0.557472	+	0.0863455i
$575$	−602.074			−1.04709
$576$	−191.485	+	14.0561i	−0.332439	+	0.0244030i
$577$	442.753	−	255.624i	0.767337	−	0.443022i	−0.0645869	−	0.997912i	$-0.520573\pi$
$577$	442.753	−	255.624i	0.767337	−	0.443022i	0.831924	+	0.554890i	$0.187240\pi$
$578$	−57.1962	+	126.674i	−0.0989553	+	0.219159i
$579$	74.3053	−	19.9100i	0.128334	−	0.0343869i
$580$	−1447.25	−	487.071i	−2.49527	−	0.839777i
$581$	−493.208	−	837.439i	−0.848894	−	1.44138i
$582$	391.914	+	64.1803i	0.673391	+	0.110275i
$583$	−292.767	−	169.029i	−0.502174	−	0.289930i
$584$	195.435	+	181.615i	0.334649	+	0.310985i
$585$	299.659	−	173.008i	0.512237	−	0.295740i
$586$	142.488	−	174.084i	0.243153	−	0.297072i
$587$	−426.246	+	426.246i	−0.726143	+	0.726143i	−0.969849	−	0.243706i	$-0.921637\pi$
$587$	−426.246	+	426.246i	−0.726143	+	0.726143i	0.243706	+	0.969849i	$0.421637\pi$
$588$	182.947	−	285.969i	0.311135	−	0.486342i
$589$	51.5782	−	51.5782i	0.0875691	−	0.0875691i
$590$	−35.1779	−	352.454i	−0.0596235	−	0.597380i
$591$	486.034	−	280.612i	0.822393	−	0.474809i
$592$	−12.3784	+	9.60125i	−0.0209094	+	0.0162183i
$593$	459.114	+	265.070i	0.774222	+	0.446997i	0.834379	−	0.551191i	$-0.185827\pi$
$593$	459.114	+	265.070i	0.774222	+	0.446997i	−0.0601564	+	0.998189i	$0.519160\pi$
$594$	−94.5616	−	131.598i	−0.159195	−	0.221545i
$595$	−494.113	−	838.976i	−0.830442	−	1.41004i
$596$	−845.732	+	419.815i	−1.41901	+	0.704387i
$597$	−441.442	+	118.284i	−0.739434	+	0.198131i
$598$	−82.8143	−	219.165i	−0.138485	−	0.366497i
$599$	−157.423	+	90.8882i	−0.262810	+	0.151733i	−0.625616	−	0.780131i	$-0.715152\pi$
$599$	−157.423	+	90.8882i	−0.262810	+	0.151733i	0.362806	+	0.931865i	$0.381819\pi$
$600$	464.915	+	741.162i	0.774859	+	1.23527i
$601$	522.041			0.868621			0.434311	−	0.900763i	$-0.356992\pi$
$601$	522.041			0.868621			0.434311	+	0.900763i	$0.356992\pi$
$602$	247.222	+	337.841i	0.410668	+	0.561198i
$603$	−17.3939	−	17.3939i	−0.0288457	−	0.0288457i
$604$	−345.191	+	304.321i	−0.571509	+	0.503843i
$605$	−296.804	+	1107.69i	−0.490584	+	1.83089i
$606$	249.101	−	551.690i	0.411058	−	0.910380i
$607$	538.593	+	310.957i	0.887303	+	0.512285i	0.873059	−	0.487614i	$-0.162133\pi$
$607$	538.593	+	310.957i	0.887303	+	0.512285i	0.0142438	+	0.999899i	$0.495466\pi$
$608$	−422.767	+	401.171i	−0.695340	+	0.659821i
$609$	−131.716	−	475.086i	−0.216282	−	0.780109i
$610$	1211.09	+	1685.42i	1.98539	+	2.76299i
$611$	−267.211	−	997.247i	−0.437335	−	1.63215i
$612$	−174.282	+	35.1396i	−0.284774	+	0.0574176i
$613$	−188.901	+	704.987i	−0.308158	+	1.15006i	0.622036	+	0.782989i	$0.286306\pi$
$613$	−188.901	+	704.987i	−0.308158	+	1.15006i	−0.930193	+	0.367071i	$0.880361\pi$
$614$	−912.945	−	747.244i	−1.48688	−	1.21701i
$615$	−376.102			−0.611547
$616$	−187.585	+	852.831i	−0.304521	+	1.38447i
$617$		−	1060.66i		−	1.71906i	−0.511082	−	0.859532i	$-0.670755\pi$
$617$		−	1060.66i		−	1.71906i	0.511082	−	0.859532i	$-0.329245\pi$
$618$	514.916	+	421.458i	0.833197	+	0.681971i
$619$	1016.19	+	272.287i	1.64166	+	0.439882i	0.957261	−	0.289224i	$-0.0933973\pi$
$619$	1016.19	+	272.287i	1.64166	+	0.439882i	0.684401	+	0.729106i	$0.260064\pi$
$620$	125.272	+	83.2321i	0.202051	+	0.134245i
$621$	−47.8589	+	12.8238i	−0.0770675	+	0.0206502i
$622$	−690.789	−	961.344i	−1.11059	−	1.54557i
$623$	458.843	−	466.855i	0.736506	−	0.749365i
$624$	−205.847	+	271.182i	−0.329883	+	0.434587i
$625$	891.641	−	1544.37i	1.42662	−	2.47099i
$626$	101.144	−	224.007i	0.161573	−	0.357839i
$627$	−475.136	−	127.312i	−0.757792	−	0.203050i
$628$	10.9803	−	174.499i	0.0174845	−	0.277865i
$629$	−10.2573	+	10.2573i	−0.0163073	+	0.0163073i
$630$	−159.150	+	360.766i	−0.252619	+	0.572645i
$631$		−	36.5138i		−	0.0578666i	−0.999581	−	0.0289333i	$-0.990789\pi$
$631$		−	36.5138i		−	0.0578666i	0.999581	−	0.0289333i	$-0.00921103\pi$
$632$	39.1876	−	171.090i	0.0620057	−	0.270713i
$633$	198.795	+	344.323i	0.314052	+	0.543954i
$634$	−82.4710	−	218.256i	−0.130080	−	0.344253i
$635$	−362.520	−	1352.94i	−0.570898	−	2.13062i
$636$	142.357	+	47.9100i	0.223832	+	0.0753301i
$637$	−165.844	−	578.684i	−0.260352	−	0.908451i
$638$	739.993	+	1029.82i	1.15986	+	1.61414i
$639$	−33.7378	+	58.4356i	−0.0527979	+	0.0914486i
$640$	−983.155	−	691.023i	−1.53618	−	1.07972i
$641$	−371.141	−	642.835i	−0.579003	−	1.00286i	−0.995594	−	0.0937683i	$-0.970109\pi$
$641$	−371.141	−	642.835i	−0.579003	−	1.00286i	0.416591	−	0.909094i	$-0.363225\pi$
$642$	−10.2982	−	103.179i	−0.0160407	−	0.160715i
$643$	777.060	+	777.060i	1.20849	+	1.20849i	0.971516	+	0.236976i	$0.0761562\pi$
$643$	777.060	+	777.060i	1.20849	+	1.20849i	0.236976	+	0.971516i	$0.423844\pi$
$644$	223.651	+	145.822i	0.347284	+	0.226432i
$645$	−343.829	−	343.829i	−0.533068	−	0.533068i
$646$	−341.822	+	417.620i	−0.529135	+	0.646471i
$647$	−184.073	−	318.823i	−0.284502	−	0.492772i	0.687986	−	0.725724i	$-0.258495\pi$
$647$	−184.073	−	318.823i	−0.284502	−	0.492772i	−0.972488	+	0.232952i	$0.925162\pi$
$648$	52.7424	+	49.0127i	0.0813925	+	0.0756368i
$649$	−147.075	+	254.742i	−0.226619	+	0.392515i
$650$	1531.02	+	250.722i	2.35542	+	0.385726i
$651$	0.420220	+	48.5562i	0.000645499	+	0.0745871i
$652$	−69.5663	−	140.144i	−0.106697	−	0.214944i
$653$	145.678	+	543.679i	0.223091	+	0.832586i	0.983160	+	0.182745i	$0.0584981\pi$
$653$	145.678	+	543.679i	0.223091	+	0.832586i	−0.760070	+	0.649842i	$0.774835\pi$
$654$	50.9198	−	112.773i	0.0778591	−	0.172436i
$655$	380.169	+	658.472i	0.580411	+	1.00530i
$656$	341.150	−	143.398i	0.520045	−	0.218595i
$657$		−	100.048i		−	0.152280i
$658$	916.854	+	737.287i	1.39340	+	1.12050i
$659$	266.102	−	266.102i	0.403797	−	0.403797i	−0.475772	−	0.879569i	$-0.657831\pi$
$659$	266.102	−	266.102i	0.403797	−	0.403797i	0.879569	+	0.475772i	$0.157831\pi$
$660$	63.6951	−	1012.25i	0.0965078	−	1.53371i
$661$	−686.887	−	184.051i	−1.03916	−	0.278443i	−0.301397	−	0.953499i	$-0.597453\pi$
$661$	−686.887	−	184.051i	−1.03916	−	0.278443i	−0.737767	+	0.675056i	$0.764120\pi$
$662$	−276.999	+	104.668i	−0.418428	+	0.158108i
$663$	−157.630	+	273.023i	−0.237753	+	0.411800i
$664$	−981.613	−	519.756i	−1.47833	−	0.782764i
$665$	319.780	+	1153.41i	0.480872	+	1.73446i
$666$	5.79734	+	0.949380i	0.00870472	+	0.00142550i
$667$	374.520	−	100.352i	0.561500	−	0.150453i
$668$	143.980	−	29.0301i	0.215539	−	0.0434582i
$669$	336.264	+	90.1017i	0.502637	+	0.134681i
$670$	−15.2906	−	153.200i	−0.0228218	−	0.228657i
$671$		−	1723.54i		−	2.56862i
$672$	6.80882	−	387.920i	0.0101322	−	0.577261i
$673$	−840.334			−1.24864			−0.624320	−	0.781169i	$-0.714624\pi$
$673$	−840.334			−1.24864			−0.624320	+	0.781169i	$0.714624\pi$
$674$	672.417	−	67.1128i	0.997651	−	0.0995738i
$675$	84.9163	−	316.912i	0.125802	−	0.469499i
$676$	−14.2873	−	70.8607i	−0.0211351	−	0.104824i
$677$	−283.907	−	1059.56i	−0.419361	−	1.56508i	−0.775937	−	0.630810i	$-0.782723\pi$
$677$	−283.907	−	1059.56i	−0.419361	−	1.56508i	0.356576	−	0.934266i	$-0.383944\pi$
$678$	−92.5636	+	565.235i	−0.136525	+	0.833680i
$679$	−200.986	+	776.923i	−0.296003	+	1.14422i
$680$	−983.414	−	520.709i	−1.44620	−	0.765749i
$681$	−145.270	−	83.8714i	−0.213318	−	0.123159i
$682$	−44.1489	−	116.838i	−0.0647344	−	0.171317i
$683$	251.945	−	940.272i	0.368880	−	1.37668i	−0.493204	−	0.869914i	$-0.664174\pi$
$683$	251.945	−	940.272i	0.368880	−	1.37668i	0.862084	−	0.506765i	$-0.169159\pi$
$684$	218.123	+	13.7253i	0.318894	+	0.0200662i
$685$	−47.8707	−	47.8707i	−0.0698843	−	0.0698843i
$686$	541.953	+	420.575i	0.790019	+	0.613083i
$687$	−66.0776			−0.0961829
$688$	442.970	+	180.783i	0.643852	+	0.262766i
$689$	230.661	−	133.172i	0.334776	−	0.193283i
$690$	−282.636	−	127.617i	−0.409617	−	0.184952i
$691$	−353.816	+	94.8048i	−0.512035	+	0.137199i	−0.505580	−	0.862780i	$-0.668721\pi$
$691$	−353.816	+	94.8048i	−0.512035	+	0.137199i	−0.00645530	+	0.999979i	$0.502055\pi$
$692$	−321.117	+	159.400i	−0.464042	+	0.230347i
$693$	282.158	−	166.176i	0.407155	−	0.239793i
$694$	−139.432	+	851.434i	−0.200911	+	1.22685i
$695$	−10.3078	−	5.95122i	−0.0148314	−	0.00856290i
$696$	−412.736	−	383.549i	−0.593011	−	0.551076i
$697$	296.762	−	171.336i	0.425771	−	0.245819i
$698$	170.644	+	139.672i	0.244476	+	0.200103i
$699$	−511.594	+	511.594i	−0.731894	+	0.731894i
$700$	−1576.72	+	799.754i	−2.25246	+	1.14251i
$701$	491.476	−	491.476i	0.701106	−	0.701106i	−0.263542	−	0.964648i	$-0.584891\pi$
$701$	491.476	−	491.476i	0.701106	−	0.701106i	0.964648	+	0.263542i	$0.0848907\pi$
$702$	127.041	−	12.6798i	0.180970	−	0.0180624i
$703$	15.4431	−	8.91606i	0.0219674	−	0.0126829i
$704$	328.169	+	942.463i	0.466149	+	1.33873i
$705$	−1183.46	−	683.272i	−1.67867	−	0.969180i
$706$	−908.132	+	652.552i	−1.28631	+	0.924295i
$707$	1064.56	+	602.404i	1.50575	+	0.852056i
$708$	41.6873	−	123.867i	0.0588804	−	0.174954i
$709$	−651.459	+	174.558i	−0.918842	+	0.246203i	−0.687090	−	0.726572i	$-0.741112\pi$
$709$	−651.459	+	174.558i	−0.918842	+	0.246203i	−0.231752	+	0.972775i	$0.574446\pi$
$710$	−395.061	+	149.279i	−0.556424	+	0.210252i
$711$	−57.0021	+	32.9102i	−0.0801717	+	0.0462872i
$712$	167.025	−	729.221i	0.234586	−	1.02419i
$713$	−38.1891			−0.0535612
$714$	−38.7725	−	357.164i	−0.0543032	−	0.500230i
$715$	−1271.73	−	1271.73i	−1.77864	−	1.77864i
$716$	345.692	+	21.7525i	0.482809	+	0.0303805i
$717$	−108.979	+	406.715i	−0.151993	+	0.567245i
$718$	671.101	+	303.018i	0.934681	+	0.422030i
$719$	−722.269	−	417.002i	−1.00455	−	0.579975i	−0.0949562	−	0.995481i	$-0.530271\pi$
$719$	−722.269	−	417.002i	−1.00455	−	0.579975i	−0.909590	+	0.415506i	$0.863604\pi$
$720$	61.1503	+	446.473i	0.0849309	+	0.620101i
$721$	−942.515	+	958.971i	−1.30723	+	1.33006i
$722$	−47.5735	+	34.1847i	−0.0658913	+	0.0473472i
$723$	135.345	+	505.114i	0.187199	+	0.698636i
$724$	503.683	−	758.088i	0.695695	−	1.04708i
$725$	−664.513	+	2480.00i	−0.916570	+	3.42069i
$726$	−268.004	+	327.434i	−0.369152	+	0.451011i
$727$	−479.467			−0.659515			−0.329758	−	0.944066i	$-0.606967\pi$
$727$	−479.467			−0.659515			−0.329758	+	0.944066i	$0.606967\pi$
$728$	−507.999	−	463.948i	−0.697801	−	0.637292i
$729$		−	27.0000i		−	0.0370370i
$730$	396.618	−	484.568i	0.543313	−	0.663792i
$731$	427.932	+	114.664i	0.585406	+	0.156859i
$732$	151.356	+	750.681i	0.206771	+	1.02552i
$733$	−646.502	+	173.230i	−0.881995	+	0.236330i	−0.671267	−	0.741215i	$-0.734250\pi$
$733$	−646.502	+	173.230i	−0.881995	+	0.236330i	−0.210727	+	0.977545i	$0.567583\pi$
$734$	−164.271	+	118.040i	−0.223803	+	0.160817i
$735$	−696.836	−	386.395i	−0.948076	−	0.525707i
$736$	305.027	+	7.99488i	0.414439	+	0.0108626i
$737$	−63.9288	+	110.728i	−0.0867419	+	0.150241i
$738$	−126.478	−	57.1079i	−0.171380	−	0.0773820i
$739$	368.021	+	98.6111i	0.497999	+	0.133439i	0.499071	−	0.866561i	$-0.333675\pi$
$739$	368.021	+	98.6111i	0.497999	+	0.133439i	−0.00107204	+	0.999999i	$0.500341\pi$
$740$	24.3151	+	27.5806i	0.0328582	+	0.0372710i
$741$	274.037	−	274.037i	0.369821	−	0.369821i
$742$	−122.505	+	277.698i	−0.165101	+	0.374256i
$743$		−	517.706i		−	0.696777i	−0.937350	−	0.348389i	$-0.886729\pi$
$743$		−	517.706i		−	0.696777i	0.937350	−	0.348389i	$-0.113271\pi$
$744$	29.4892	+	47.0114i	0.0396360	+	0.0631873i
$745$	1108.06	+	1919.21i	1.48732	+	2.57612i
$746$	15.2546	−	5.76416i	0.0204486	−	0.00772676i
$747$	107.804	+	402.329i	0.144316	+	0.538593i
$748$	410.878	+	827.729i	0.549302	+	1.10659i
$749$	209.525	−	1.81329i	0.279740	−	0.00242095i
$750$	1007.34	−	723.841i	1.34312	−	0.965121i
$751$	378.094	−	654.879i	0.503454	−	0.872009i	−0.496538	−	0.868015i	$-0.665396\pi$
$751$	378.094	−	654.879i	0.503454	−	0.872009i	0.999992	−	0.00399348i	$-0.00127117\pi$
$752$	1334.00	+	168.549i	1.77393	+	0.224135i
$753$	94.7566	+	164.123i	0.125839	+	0.217959i
$754$	−994.163	+	99.2257i	−1.31852	+	0.131599i
$755$	763.739	+	763.739i	1.01158	+	1.01158i
$756$	−108.300	+	97.1556i	−0.143253	+	0.128513i
$757$	−890.330	−	890.330i	−1.17613	−	1.17613i	−0.980722	−	0.195408i	$-0.937397\pi$
$757$	−890.330	−	890.330i	−1.17613	−	1.17613i	−0.195408	−	0.980722i	$-0.562603\pi$
$758$	878.844	+	719.332i	1.15942	+	0.948987i
$759$	128.766	+	223.030i	0.169653	+	0.293847i
$760$	1002.04	+	931.181i	1.31847	+	1.22524i
$761$	−75.3853	+	130.571i	−0.0990609	+	0.171578i	−0.911296	−	0.411751i	$-0.864917\pi$
$761$	−75.3853	+	130.571i	−0.0990609	+	0.171578i	0.812235	+	0.583330i	$0.198251\pi$
$762$	83.5221	−	510.024i	0.109609	−	0.669322i
$763$	217.612	+	123.140i	0.285206	+	0.161389i
$764$	123.076	−	365.700i	0.161094	−	0.478665i
$765$	108.002	+	403.067i	0.141179	+	0.526886i
$766$	104.236	+	47.0648i	0.136078	+	0.0614423i
$767$	−115.875	−	200.702i	−0.151076	−	0.261671i
$768$	−225.697	−	381.666i	−0.293876	−	0.496961i
$769$			835.155i			1.08603i	0.839724	+	0.543014i	$0.182717\pi$
$769$			835.155i			1.08603i	−0.839724	+	0.543014i	$0.817283\pi$
$770$	2025.37	+	313.704i	2.63035	+	0.407408i
$771$	−206.832	+	206.832i	−0.268265	+	0.268265i
$772$	117.483	+	133.261i	0.152181	+	0.172618i
$773$	−1373.36	−	367.991i	−1.77666	−	0.476056i	−0.786695	−	0.617341i	$-0.788210\pi$
$773$	−1373.36	−	367.991i	−1.77666	−	0.476056i	−0.989969	+	0.141285i	$0.954876\pi$
$774$	−63.4179	−	167.833i	−0.0819353	−	0.216839i
$775$	126.440	−	219.001i	0.163149	−	0.282582i
$776$	269.664	+	876.602i	0.347505	+	1.12964i
$777$	−2.97306	+	11.4925i	−0.00382634	+	0.0147909i
$778$	−0.378233	+	2.30966i	−0.000486161	+	0.00296872i
$779$	−406.891	+	109.026i	−0.522324	+	0.139956i
$780$	665.574	+	442.216i	0.853300	+	0.566944i
$781$	338.770	+	90.7730i	0.433764	+	0.116227i
$782$	281.150	−	28.0611i	0.359527	−	0.0358838i
$783$			211.289i			0.269845i
$784$	779.400	+	84.7999i	0.994133	+	0.108163i
$785$	−410.375			−0.522771
$786$	27.8626	+	279.161i	0.0354486	+	0.355167i
$787$	88.3383	−	329.683i	0.112247	−	0.418911i	−0.886819	−	0.462116i	$-0.847090\pi$
$787$	88.3383	−	329.683i	0.112247	−	0.418911i	0.999066	+	0.0432053i	$0.0137570\pi$
$788$	1079.53	+	717.256i	1.36997	+	0.910224i
$789$	94.1061	+	351.209i	0.119273	+	0.445132i
$790$	−406.548	−	66.5768i	−0.514618	−	0.0842745i
$791$	−1120.51	−	289.871i	−1.41658	−	0.366461i
$792$	175.121	−	330.735i	0.221113	−	0.417594i
$793$	1175.99	+	678.958i	1.48296	+	0.856189i
$794$	−352.826	+	133.320i	−0.444365	+	0.167909i
$795$	91.2439	−	340.527i	0.114772	−	0.428335i
$796$	−697.961	−	791.697i	−0.876835	−	0.994594i
$797$	−257.753	−	257.753i	−0.323404	−	0.323404i	0.526668	−	0.850071i	$-0.323441\pi$
$797$	−257.753	−	257.753i	−0.323404	−	0.323404i	−0.850071	+	0.526668i	$0.823441\pi$
$798$	−67.5983	+	436.435i	−0.0847097	+	0.546911i
$799$	1245.08			1.55830
$800$	−1055.76	+	1722.75i	−1.31970	+	2.15344i
$801$	−242.954	+	140.270i	−0.303314	+	0.175118i
$802$	71.4829	−	158.315i	0.0891308	−	0.197400i
$803$	−502.301	+	134.591i	−0.625531	+	0.167610i
$804$	18.1201	−	53.8410i	0.0225374	−	0.0669664i
$805$	308.617	−	545.386i	0.383375	−	0.677498i
$806$	97.1116	+	15.9031i	0.120486	+	0.0197309i
$807$	306.922	+	177.202i	0.380325	+	0.219581i
$808$	1396.99	−	51.2048i	1.72895	−	0.0633723i
$809$	1208.30	−	697.611i	1.49357	−	0.862313i	0.493597	−	0.869691i	$-0.335682\pi$
$809$	1208.30	−	697.611i	1.49357	−	0.862313i	0.999973	+	0.00737735i	$0.00234831\pi$
$810$	107.036	−	130.771i	0.132143	−	0.161446i
$811$	115.420	−	115.420i	0.142318	−	0.142318i	−0.632358	−	0.774676i	$-0.717913\pi$
$811$	115.420	−	115.420i	0.142318	−	0.142318i	0.774676	+	0.632358i	$0.217913\pi$
$812$	847.499	−	760.292i	1.04372	−	0.936320i
$813$	−237.391	+	237.391i	−0.291994	+	0.291994i
$814$	−3.03252	−	30.3834i	−0.00372545	−	0.0373260i
$815$	−318.027	+	183.613i	−0.390217	+	0.225292i
$816$	−251.645	−	324.431i	−0.308388	−	0.397587i
$817$	−471.647	−	272.305i	−0.577291	−	0.333299i
$818$	−172.280	−	239.756i	−0.210612	−	0.293100i
$819$	2.23265	+	257.981i	0.00272607	+	0.314996i
$820$	−386.189	−	777.992i	−0.470962	−	0.948770i
$821$	1038.09	−	278.156i	1.26442	−	0.338801i	0.436531	−	0.899689i	$-0.356207\pi$
$821$	1038.09	−	278.156i	1.26442	−	0.338801i	0.827892	+	0.560888i	$0.189540\pi$
$822$	−8.82956	−	23.3671i	−0.0107416	−	0.0284271i
$823$	−371.294	+	214.367i	−0.451147	+	0.260470i	−0.708315	−	0.705897i	$-0.750544\pi$
$823$	−371.294	+	214.367i	−0.451147	+	0.260470i	0.257167	+	0.966367i	$0.417211\pi$
$824$	−343.088	+	1497.90i	−0.416369	+	1.81784i
$825$	−1705.33			−2.06706
$826$	241.630	+	106.594i	0.292530	+	0.129048i
$827$	222.327	+	222.327i	0.268835	+	0.268835i	0.828631	−	0.559796i	$-0.189120\pi$
$827$	222.327	+	222.327i	0.268835	+	0.268835i	−0.559796	+	0.828631i	$0.689120\pi$
$828$	−75.6693	−	85.8317i	−0.0913881	−	0.103661i
$829$	−98.7667	+	368.602i	−0.119140	+	0.444635i	−0.999563	−	0.0295531i	$-0.990592\pi$
$829$	−98.7667	+	368.602i	−0.119140	+	0.444635i	0.880424	+	0.474188i	$0.157258\pi$
$830$	−1072.82	+	2375.99i	−1.29255	+	2.86264i
$831$	−510.362	−	294.658i	−0.614154	−	0.354582i
$832$	−772.327	−	147.353i	−0.928278	−	0.177107i
$833$	725.862	−	12.5646i	0.871383	−	0.0150836i
$834$	−2.56275	−	3.56648i	−0.00307284	−	0.00427635i
$835$	−89.2240	−	332.989i	−0.106855	−	0.398789i
$836$	−224.525	−	1113.58i	−0.268571	−	1.33203i
$837$	5.38617	−	20.1015i	0.00643509	−	0.0240161i
$838$	290.084	+	237.434i	0.346163	+	0.283334i
$839$	899.004			1.07152			0.535759	−	0.844371i	$-0.320025\pi$
$839$	899.004			1.07152			0.535759	+	0.844371i	$0.320025\pi$
$840$	−909.688	+	41.2292i	−1.08296	+	0.0490823i
$841$		−	812.442i		−	0.966043i
$842$	291.057	+	238.230i	0.345674	+	0.282934i
$843$	−137.556	−	36.8581i	−0.163175	−	0.0437225i
$844$	−508.128	+	764.779i	−0.602048	+	0.906136i
$845$	−163.882	+	43.9121i	−0.193943	+	0.0519670i
$846$	−294.234	−	409.475i	−0.347795	−	0.484012i
$847$	−609.807	−	599.343i	−0.719961	−	0.707606i
$848$	47.0701	+	343.670i	0.0555072	+	0.405271i
$849$	−139.377	+	241.409i	−0.164166	+	0.284345i
$850$	−769.938	+	1705.20i	−0.905809	+	2.00612i
$851$	−9.01789	−	2.41634i	−0.0105968	−	0.00283941i
$852$	−155.521	−	9.78607i	−0.182536	−	0.0114860i
$853$	370.003	−	370.003i	0.433766	−	0.433766i	−0.456141	−	0.889907i	$-0.650769\pi$
$853$	370.003	−	370.003i	0.433766	−	0.433766i	0.889907	+	0.456141i	$0.150769\pi$
$854$	−1538.41	+	167.004i	−1.80142	+	0.195555i
$855$		−	512.967i		−	0.599961i
$856$	202.859	−	127.249i	0.236985	−	0.148656i
$857$	−568.661	−	984.951i	−0.663549	−	1.14930i	−0.979677	−	0.200584i	$-0.935716\pi$
$857$	−568.661	−	984.951i	−0.663549	−	1.14930i	0.316128	−	0.948717i	$-0.397617\pi$
$858$	−234.565	−	620.768i	−0.273386	−	0.723506i
$859$	18.1745	+	67.8283i	0.0211578	+	0.0789619i	0.975698	−	0.219122i	$-0.0703192\pi$
$859$	18.1745	+	67.8283i	0.0211578	+	0.0789619i	−0.954540	+	0.298084i	$0.903653\pi$
$860$	358.183	−	1064.28i	0.416492	−	1.23754i
$861$	138.105	−	244.058i	0.160400	−	0.283459i
$862$	−876.943	−	1220.41i	−1.01734	−	1.41579i
$863$	−719.174	+	1245.65i	−0.833341	+	1.44339i	0.0620324	+	0.998074i	$0.480242\pi$
$863$	−719.174	+	1245.65i	−0.833341	+	1.44339i	−0.895374	+	0.445315i	$0.853092\pi$
$864$	−47.2291	+	159.428i	−0.0546633	+	0.184524i
$865$	420.720	+	728.708i	0.486381	+	0.842437i
$866$	25.2477	+	252.962i	0.0291544	+	0.292104i
$867$	85.1124	+	85.1124i	0.0981689	+	0.0981689i
$868$	−100.010	+	50.7278i	−0.115219	+	0.0584421i
$869$	241.913	+	241.913i	0.278381	+	0.278381i
$870$	−837.611	+	1023.35i	−0.962771	+	1.17626i
$871$	−50.3671	−	87.2384i	−0.0578268	−	0.100159i
$872$	285.565	−	10.4670i	0.327483	−	0.0120034i
$873$	171.964	−	297.850i	0.196981	−	0.341180i
$874$	−342.767	−	56.1320i	−0.392182	−	0.0642242i
$875$	1272.03	+	2159.84i	1.45375	+	2.46838i
$876$	206.955	−	102.731i	0.236250	−	0.117273i
$877$	−157.338	−	587.192i	−0.179404	−	0.669546i	−0.995759	−	0.0919958i	$-0.970675\pi$
$877$	−157.338	−	587.192i	−0.179404	−	0.669546i	0.816355	−	0.577550i	$-0.195991\pi$
$878$	−326.486	+	723.077i	−0.371852	+	0.823550i
$879$	−97.4115	−	168.722i	−0.110821	−	0.191947i
$880$	2159.31	−	907.639i	2.45376	−	1.03141i
$881$			238.416i			0.270620i	0.990803	+	0.135310i	$0.0432030\pi$
$881$			238.416i			0.270620i	−0.990803	+	0.135310i	$0.956797\pi$
$882$	−175.666	−	235.748i	−0.199168	−	0.267288i
$883$	468.315	−	468.315i	0.530368	−	0.530368i	−0.390314	−	0.920682i	$-0.627634\pi$
$883$	468.315	−	468.315i	0.530368	−	0.530368i	0.920682	+	0.390314i	$0.127634\pi$
$884$	−726.625	−	45.7225i	−0.821974	−	0.0517223i
$885$	−296.299	−	79.3930i	−0.334801	−	0.0897096i
$886$	−419.390	+	158.472i	−0.473353	+	0.178862i
$887$	695.397	−	1204.46i	0.783988	−	1.35791i	−0.145614	−	0.989341i	$-0.546516\pi$
$887$	695.397	−	1204.46i	0.783988	−	1.35791i	0.929602	−	0.368565i	$-0.120151\pi$
$888$	3.98897	+	12.9670i	0.00449209	+	0.0146025i
$889$	1011.06	+	261.557i	1.13730	+	0.294215i
$890$	−1732.79	−	283.764i	−1.94695	−	0.318835i
$891$	−135.557	+	36.3223i	−0.152140	+	0.0407658i
$892$	158.901	+	788.103i	0.178141	+	0.883524i
$893$	−1478.41	−	396.140i	−1.65556	−	0.443605i
$894$	81.2096	+	813.655i	0.0908384	+	0.910129i
$895$		−	812.974i		−	0.908350i
$896$	809.429	−	384.239i	0.903381	−	0.428839i
$897$	−202.901			−0.226199
$898$	−209.446	+	20.9044i	−0.233236	+	0.0232789i
$899$	−42.1496	+	157.304i	−0.0468849	+	0.174977i
$900$	742.747	−	149.757i	0.825275	−	0.166396i
$901$	83.1336	+	310.259i	0.0922682	+	0.344349i
$902$	−116.569	+	711.825i	−0.129234	+	0.789163i
$903$	349.370	−	96.8616i	0.386899	−	0.107266i
$904$	−1264.27	+	388.921i	−1.39853	+	0.430222i
$905$	−1850.03	−	1068.12i	−2.04423	−	1.18024i
$906$	140.869	+	372.803i	0.155484	+	0.411483i
$907$	−98.6144	+	368.034i	−0.108726	+	0.405771i	−0.998741	−	0.0501601i	$-0.984027\pi$
$907$	−98.6144	+	368.034i	−0.108726	+	0.405771i	0.890015	+	0.455931i	$0.150694\pi$
$908$	24.3279	−	386.621i	0.0267929	−	0.425794i
$909$	−370.682	−	370.682i	−0.407791	−	0.407791i
$910$	−1011.90	+	1258.35i	−1.11198	+	1.38280i
$911$	1296.80			1.42349			0.711745	−	0.702438i	$-0.247905\pi$
$911$	1296.80			1.42349			0.711745	+	0.702438i	$0.247905\pi$
$912$	195.582	+	465.296i	0.214454	+	0.510193i
$913$	1874.92	−	1082.48i	2.05358	−	1.18563i
$914$	164.488	+	74.2701i	0.179965	+	0.0812583i
$915$	1736.13	−	465.194i	1.89741	−	0.508409i
$916$	−67.8499	−	136.686i	−0.0740719	−	0.149221i
$917$	−566.890	+	4.90604i	−0.618201	+	0.00535010i
$918$	−24.8828	+	151.946i	−0.0271055	+	0.165518i
$919$	647.051	+	373.575i	0.704082	+	0.406502i	0.808866	−	0.587993i	$-0.200082\pi$
$919$	647.051	+	373.575i	0.704082	+	0.406502i	−0.104784	+	0.994495i	$0.533415\pi$
$920$	−26.2326	−	715.690i	−0.0285137	−	0.777924i
$921$	−884.823	+	510.853i	−0.960720	+	0.554672i
$922$	600.257	+	491.310i	0.651038	+	0.532874i
$923$	−195.387	+	195.387i	−0.211687	+	0.211687i
$924$	633.473	+	413.030i	0.685577	+	0.447002i
$925$	43.7142	−	43.7142i	0.0472585	−	0.0472585i
$926$	1519.28	−	151.637i	1.64069	−	0.163755i
$927$	499.055	−	288.129i	0.538355	−	0.310819i
$928$	369.592	−	1247.61i	0.398267	−	1.34441i
$929$	−16.9566	−	9.78992i	−0.0182526	−	0.0105381i	0.490846	−	0.871246i	$-0.336688\pi$
$929$	−16.9566	−	9.78992i	−0.0182526	−	0.0105381i	−0.509099	+	0.860708i	$0.670021\pi$
$930$	105.775	−	76.0065i	0.113737	−	0.0817275i
$931$	−865.891	−	216.024i	−0.930065	−	0.232035i
$932$	−1583.58	−	532.952i	−1.69912	−	0.571837i
$933$	−990.264	+	265.340i	−1.06138	+	0.284395i
$934$	−1068.18	+	403.627i	−1.14366	+	0.432149i
$935$	1878.36	−	1084.47i	2.00894	−	1.15986i
$936$	156.678	+	249.774i	0.167391	+	0.266852i
$937$	1.52100			0.00162327			0.000811634	−	1.00000i	$-0.499742\pi$
$937$	1.52100			0.00162327			0.000811634		1.00000i	$0.499742\pi$
$938$	105.028	+	46.3328i	0.111971	+	0.0493953i
$939$	−150.511	−	150.511i	−0.160288	−	0.160288i
$940$	198.191	−	3149.67i	0.210842	−	3.35071i
$941$	89.7265	−	334.864i	0.0953523	−	0.355860i	−0.901720	−	0.432320i	$-0.857695\pi$
$941$	89.7265	−	334.864i	0.0953523	−	0.355860i	0.997073	+	0.0764602i	$0.0243618\pi$
$942$	−138.004	−	62.3120i	−0.146501	−	0.0661486i
$943$	190.995	+	110.271i	0.202540	+	0.116937i
$944$	299.034	−	40.9565i	0.316773	−	0.0433862i
$945$	243.546	+	239.366i	0.257720	+	0.253298i
$946$	−757.311	+	544.178i	−0.800540	+	0.575241i
$947$	206.243	+	769.710i	0.217786	+	0.812788i	0.985167	+	0.171597i	$0.0548926\pi$
$947$	206.243	+	769.710i	0.217786	+	0.812788i	−0.767382	+	0.641191i	$0.778441\pi$
$948$	−126.608	−	84.1199i	−0.133553	−	0.0887340i
$949$	106.039	−	395.745i	0.111738	−	0.417012i
$950$	1456.76	−	1779.80i	1.53344	−	1.87347i
$951$	−202.059			−0.212470
$952$	699.006	−	446.947i	0.734250	−	0.469482i
$953$			632.383i			0.663571i	0.943355	+	0.331785i	$0.107651\pi$
$953$			632.383i			0.663571i	−0.943355	+	0.331785i	$0.892349\pi$
$954$	82.3903	−	100.660i	0.0863630	−	0.105514i
$955$	−874.778	−	234.396i	−0.915998	−	0.245441i
$956$	−953.219	+	192.193i	−0.997091	+	0.201039i
$957$	1060.80	−	284.241i	1.10846	−	0.297012i
$958$	−330.923	+	237.790i	−0.345431	+	0.248215i
$959$	48.6422	−	13.4859i	0.0507217	−	0.0140624i
$960$	−860.769	+	584.941i	−0.896634	+	0.609314i
$961$	−472.480	+	818.359i	−0.491655	+	0.851571i
$962$	21.9255	+	9.89987i	0.0227916	+	0.0102909i
$963$	−86.7400	−	23.2419i	−0.0900727	−	0.0241349i
$964$	−905.888	+	798.632i	−0.939717	+	0.828456i
$965$	294.842	−	294.842i	0.305536	−	0.305536i
$966$	186.596	−	136.546i	0.193164	−	0.141351i
$967$		−	90.6873i		−	0.0937821i	−0.998900	−	0.0468911i	$-0.985069\pi$
$967$		−	90.6873i		−	0.0937821i	0.998900	−	0.0468911i	$-0.0149314\pi$
$968$	−952.511	−	218.169i	−0.983999	−	0.225381i
$969$	233.686	+	404.756i	0.241162	+	0.417705i
$970$	2013.65	−	760.885i	2.07593	−	0.784417i
$971$	133.817	+	499.413i	0.137814	+	0.514328i	0.999970	+	0.00768637i	$0.00244667\pi$
$971$	133.817	+	499.413i	0.137814	+	0.514328i	−0.862157	+	0.506642i	$0.830887\pi$
$972$	55.8513	−	27.7242i	0.0574602	−	0.0285228i
$973$	7.64686	−	4.50360i	0.00785906	−	0.00462857i
$974$	990.270	−	711.574i	1.01670	−	0.730569i
$975$	671.783	−	1163.56i	0.689008	−	1.19340i
$976$	−1397.42	+	1083.91i	−1.43178	+	1.11056i
$977$	−953.270	−	1651.11i	−0.975711	−	1.68998i	−0.677567	−	0.735461i	$-0.736966\pi$
$977$	−953.270	−	1651.11i	−0.975711	−	1.68998i	−0.298144	−	0.954521i	$-0.596368\pi$
$978$	−134.828	+	13.4570i	−0.137861	+	0.0137597i
$979$	1031.08	+	1031.08i	1.05320	+	1.05320i
$980$	83.7580	−	1838.21i	0.0854674	−	1.87572i
$981$	−75.7727	−	75.7727i	−0.0772403	−	0.0772403i
$982$	814.707	+	666.837i	0.829641	+	0.679060i
$983$	190.952	+	330.739i	0.194255	+	0.336459i	0.946656	−	0.322246i	$-0.104438\pi$
$983$	190.952	+	330.739i	0.194255	+	0.336459i	−0.752401	+	0.658705i	$0.771104\pi$
$984$	−11.7390	−	320.268i	−0.0119299	−	0.325476i
$985$	1521.02	−	2634.48i	1.54418	−	2.67460i
$986$	194.721	−	1189.05i	0.197486	−	1.20594i
$987$	877.953	−	517.068i	0.889516	−	0.523878i
$988$	848.252	+	285.478i	0.858555	+	0.288945i
$989$	73.7974	+	275.416i	0.0746182	+	0.278479i
$990$	−800.544	−	361.464i	−0.808630	−	0.365115i
$991$	733.510	+	1270.48i	0.740172	+	1.28202i	0.952417	+	0.304799i	$0.0985893\pi$
$991$	733.510	+	1270.48i	0.740172	+	1.28202i	−0.212245	+	0.977217i	$0.568077\pi$
$992$	−66.9661	+	109.273i	−0.0675061	+	0.110154i
$993$			256.443i			0.258251i
$994$	48.1973	−	311.176i	0.0484882	−	0.313054i
$995$	−1751.64	+	1751.64i	−1.76044	+	1.76044i
$996$	−721.550	+	636.119i	−0.724448	+	0.638674i
$997$	1322.76	+	354.432i	1.32674	+	0.355499i	0.851499	−	0.524356i	$-0.175694\pi$
$997$	1322.76	+	354.432i	1.32674	+	0.355499i	0.475241	+	0.879855i	$0.342361\pi$
$998$	219.071	+	579.763i	0.219510	+	0.580925i
$999$	2.54376	−	4.40592i	0.00254631	−	0.00441033i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	336.3.bv.a.229.63	yes	256
7.3	odd	6	inner	336.3.bv.a.325.21	yes	256
16.13	even	4	inner	336.3.bv.a.61.21	✓	256
112.45	odd	12	inner	336.3.bv.a.157.63	yes	256

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
336.3.bv.a.61.21	✓	256	16.13	even	4	inner
336.3.bv.a.157.63	yes	256	112.45	odd	12	inner
336.3.bv.a.229.63	yes	256	1.1	even	1	trivial
336.3.bv.a.325.21	yes	256	7.3	odd	6	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 336 = 2^{4} \cdot 3 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	336.bv (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(1.99011 - 0.198630i) q^{2} +(0.448288 - 1.67303i) q^{3} +(3.92109 - 0.790591i) q^{4} +(-2.42988 - 9.06845i) q^{5} +(0.559829 - 3.41857i) q^{6} +(6.77691 + 1.75315i) q^{7} +(7.64638 - 2.35221i) q^{8} +(-2.59808 - 1.50000i) q^{9} +(-6.63701 - 17.5646i) q^{10} +(-4.03581 + 15.0619i) q^{11} +(0.435093 - 6.91453i) q^{12} +(-8.68701 - 8.68701i) q^{13} +(13.8350 + 2.14287i) q^{14} -16.2611 q^{15} +(14.7499 - 6.19996i) q^{16} +(12.8308 - 7.40787i) q^{17} +(-5.46841 - 2.46911i) q^{18} +(-17.5923 + 4.71384i) q^{19} +(-16.6972 - 33.6372i) q^{20} +(5.97108 - 10.5521i) q^{21} +(-5.03998 + 30.7764i) q^{22} +(8.25787 + 4.76768i) q^{23} +(-0.507547 - 13.8471i) q^{24} +(-54.6819 + 31.5706i) q^{25} +(-19.0136 - 15.5626i) q^{26} +(-3.67423 + 3.67423i) q^{27} +(27.9589 + 1.51651i) q^{28} +(28.7528 - 28.7528i) q^{29} +(-32.3614 + 3.22994i) q^{30} +(-3.46843 + 2.00250i) q^{31} +(28.1225 - 15.2684i) q^{32} +(23.3898 + 13.5041i) q^{33} +(24.0633 - 17.2911i) q^{34} +(-0.568726 - 65.7160i) q^{35} +(-11.3732 - 3.82762i) q^{36} +(-0.945732 + 0.253408i) q^{37} +(-34.0743 + 12.8754i) q^{38} +(-18.4279 + 10.6394i) q^{39} +(-39.9107 - 63.6252i) q^{40} +23.1289 q^{41} +(9.78717 - 22.1858i) q^{42} +(21.1443 + 21.1443i) q^{43} +(-3.91702 + 62.2496i) q^{44} +(-7.28965 + 27.2054i) q^{45} +(17.3811 + 7.84796i) q^{46} +(72.7787 + 42.0188i) q^{47} +(-3.76052 - 27.4565i) q^{48} +(42.8529 + 23.7619i) q^{49} +(-102.552 + 73.6905i) q^{50} +(-6.64171 - 24.7872i) q^{51} +(-40.9304 - 27.1947i) q^{52} +(-5.61117 + 20.9412i) q^{53} +(-6.58233 + 8.04195i) q^{54} +146.394 q^{55} +(55.9426 - 2.53545i) q^{56} +31.5456i q^{57} +(51.5101 - 62.9324i) q^{58} +(18.2213 + 4.88238i) q^{59} +(-63.7613 + 12.8559i) q^{60} +(-106.766 + 28.6078i) q^{61} +(-6.50481 + 4.67413i) q^{62} +(-14.9772 - 14.7202i) q^{63} +(52.9342 - 35.9718i) q^{64} +(-57.6693 + 99.8862i) q^{65} +(49.2306 + 22.2287i) q^{66} +(7.92019 + 2.12221i) q^{67} +(44.4542 - 39.1908i) q^{68} +(11.6784 - 11.6784i) q^{69} +(-14.1850 - 130.669i) q^{70} -22.4919i q^{71} +(-23.3942 - 5.35835i) q^{72} +(16.6746 + 28.8813i) q^{73} +(-1.83178 + 0.692161i) q^{74} +(28.3054 + 105.637i) q^{75} +(-65.2543 + 32.3917i) q^{76} +(-53.7560 + 94.9974i) q^{77} +(-34.5604 + 24.8339i) q^{78} +(10.9701 - 19.0007i) q^{79} +(-92.0647 - 118.694i) q^{80} +(4.50000 + 7.79423i) q^{81} +(46.0291 - 4.59409i) q^{82} +(-98.1751 - 98.1751i) q^{83} +(15.0708 - 46.0963i) q^{84} +(-98.3553 - 98.3553i) q^{85} +(46.2793 + 37.8796i) q^{86} +(-35.2148 - 60.9938i) q^{87} +(4.56930 + 124.662i) q^{88} +(46.7566 - 80.9847i) q^{89} +(-9.10344 + 55.5897i) q^{90} +(-43.6414 - 74.1007i) q^{91} +(36.1491 + 12.1659i) q^{92} +(1.79539 + 6.70049i) q^{93} +(153.184 + 69.1661i) q^{94} +(85.4945 + 148.081i) q^{95} +(-12.9375 - 53.8945i) q^{96} +114.643i q^{97} +(90.0019 + 38.7770i) q^{98} +(33.0781 - 33.0781i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 256 q - 12 q^{4} - 24 q^{8} + 108 q^{10} + 32 q^{11} + 32 q^{14} - 4 q^{16} + 12 q^{18} + 48 q^{22} - 64 q^{29} - 96 q^{35} - 96 q^{37} + 60 q^{40} - 60 q^{42} - 192 q^{43} + 228 q^{44} + 180 q^{46} - 32 q^{50}+ \cdots + 192 q^{99}+O(q^{100}) \) 256 * q - 12 * q^4 - 24 * q^8 + 108 * q^10 + 32 * q^11 + 32 * q^14 - 4 * q^16 + 12 * q^18 + 48 * q^22 - 64 * q^29 - 96 * q^35 - 96 * q^37 + 60 * q^40 - 60 * q^42 - 192 * q^43 + 228 * q^44 + 180 * q^46 - 32 * q^50 + 720 * q^52 + 160 * q^53 - 56 * q^56 - 312 * q^58 + 384 * q^59 + 72 * q^60 - 96 * q^64 - 216 * q^66 - 320 * q^67 - 780 * q^68 - 828 * q^70 + 60 * q^72 - 88 * q^74 - 72 * q^78 - 612 * q^80 + 1152 * q^81 + 780 * q^82 - 72 * q^84 - 212 * q^86 - 464 * q^88 - 480 * q^91 - 488 * q^92 - 612 * q^94 + 768 * q^95 - 900 * q^96 - 196 * q^98 + 192 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more