LMFDB - Embedded newform 207.2.o.a.11.11

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [207,2,Mod(5,207)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(207, base_ring=CyclotomicField(66))

chi = DirichletCharacter(H, H._module([55, 3]))

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

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

chi := DirichletCharacter("207.5");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 207 = 3^{2} \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	207.o (of order $66$, degree $20$, 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:	$1.65290332184$
Analytic rank:	$0$
Dimension:	$440$
Relative dimension:	$22$ over $\Q(\zeta_{66})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{66}]$

Embedding invariants

Embedding label			11.11
Character	$\chi$	$=$	207.11
Dual form			207.2.o.a.113.11

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.412156 + 0.0196334i) q^{2} +(1.15855 - 1.28754i) q^{3} +(-1.82146 + 0.173928i) q^{4} +(2.81788 + 2.68684i) q^{5} +(-0.452223 + 0.553415i) q^{6} +(0.539603 + 2.79973i) q^{7} +(1.56416 - 0.224892i) q^{8} +(-0.315538 - 2.98336i) q^{9} +O(q^{10})$	\(q+(-0.412156 + 0.0196334i) q^{2} +(1.15855 - 1.28754i) q^{3} +(-1.82146 + 0.173928i) q^{4} +(2.81788 + 2.68684i) q^{5} +(-0.452223 + 0.553415i) q^{6} +(0.539603 + 2.79973i) q^{7} +(1.56416 - 0.224892i) q^{8} +(-0.315538 - 2.98336i) q^{9} +(-1.21416 - 1.05207i) q^{10} +(-1.68703 + 0.869723i) q^{11} +(-1.88630 + 2.54671i) q^{12} +(2.45673 + 0.473497i) q^{13} +(-0.277369 - 1.14333i) q^{14} +(6.72407 - 0.515310i) q^{15} +(2.95309 - 0.569162i) q^{16} +(-2.19831 - 4.81363i) q^{17} +(0.188625 + 1.22342i) q^{18} +(2.26539 + 1.03457i) q^{19} +(-5.59996 - 4.40386i) q^{20} +(4.22993 + 2.54885i) q^{21} +(0.678243 - 0.391584i) q^{22} +(1.47338 - 4.56390i) q^{23} +(1.52259 - 2.27447i) q^{24} +(0.483411 + 10.1480i) q^{25} +(-1.02185 - 0.146921i) q^{26} +(-4.20677 - 3.05009i) q^{27} +(-1.46982 - 5.00573i) q^{28} +(0.293166 - 3.07018i) q^{29} +(-2.76125 + 0.344405i) q^{30} +(-7.06488 + 5.55588i) q^{31} +(-4.27735 + 1.03767i) q^{32} +(-0.834694 + 3.17974i) q^{33} +(1.00056 + 1.94081i) q^{34} +(-6.00189 + 9.33912i) q^{35} +(1.09363 + 5.37918i) q^{36} +(1.48644 - 5.06234i) q^{37} +(-0.954008 - 0.381927i) q^{38} +(3.45589 - 2.61459i) q^{39} +(5.01185 + 3.56892i) q^{40} +(-3.86707 + 4.05566i) q^{41} +(-1.79343 - 0.967478i) q^{42} +(-0.990237 + 1.25919i) q^{43} +(2.92158 - 1.87758i) q^{44} +(7.12667 - 9.25454i) q^{45} +(-0.517659 + 1.90997i) q^{46} +(-3.02178 - 1.74463i) q^{47} +(2.68847 - 4.46163i) q^{48} +(-1.04873 + 0.419849i) q^{49} +(-0.398482 - 4.17309i) q^{50} +(-8.74461 - 2.74640i) q^{51} +(-4.55719 - 0.435159i) q^{52} +(-4.68343 - 5.40497i) q^{53} +(1.79373 + 1.17452i) q^{54} +(-7.09064 - 2.08200i) q^{55} +(1.47366 + 4.25786i) q^{56} +(3.95662 - 1.71819i) q^{57} +(-0.0605523 + 1.27115i) q^{58} +(-0.385512 + 2.00023i) q^{59} +(-12.1580 + 2.10812i) q^{60} +(5.11063 - 12.7657i) q^{61} +(2.80275 - 2.42860i) q^{62} +(8.18233 - 2.49325i) q^{63} +(-4.02867 + 1.18292i) q^{64} +(5.65057 + 7.93511i) q^{65} +(0.281595 - 1.32694i) q^{66} +(-4.41270 + 8.55943i) q^{67} +(4.84136 + 8.38547i) q^{68} +(-4.16923 - 7.18453i) q^{69} +(2.29036 - 3.96701i) q^{70} +(-0.382777 - 0.595613i) q^{71} +(-1.16448 - 4.59548i) q^{72} +(-1.51265 + 3.31223i) q^{73} +(-0.513254 + 2.11566i) q^{74} +(13.6261 + 11.1346i) q^{75} +(-4.30625 - 1.49041i) q^{76} +(-3.34531 - 4.25391i) q^{77} +(-1.37303 + 1.14547i) q^{78} +(-8.46405 + 2.92944i) q^{79} +(9.85069 + 6.33066i) q^{80} +(-8.80087 + 1.88273i) q^{81} +(1.51421 - 1.74749i) q^{82} +(9.59700 - 9.15072i) q^{83} +(-8.14795 - 3.90692i) q^{84} +(6.73889 - 19.4707i) q^{85} +(0.383410 - 0.538424i) q^{86} +(-3.61334 - 3.93441i) q^{87} +(-2.44318 + 1.73978i) q^{88} +(2.44096 - 16.9773i) q^{89} +(-2.75560 + 3.95424i) q^{90} +7.13369i q^{91} +(-1.88991 + 8.56920i) q^{92} +(-1.03155 + 15.5331i) q^{93} +(1.27970 + 0.659731i) q^{94} +(3.60387 + 9.00204i) q^{95} +(-3.61946 + 6.70948i) q^{96} +(17.4427 + 4.23155i) q^{97} +(0.423998 - 0.193633i) q^{98} +(3.12702 + 4.75858i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 440 q - 27 q^{2} - 16 q^{3} - 29 q^{4} - 33 q^{5} - 25 q^{6} - 11 q^{7} - 16 q^{9}+O(q^{10}) $ 440 * q - 27 * q^2 - 16 * q^3 - 29 * q^4 - 33 * q^5 - 25 * q^6 - 11 * q^7 - 16 * q^9	$ 440 q - 27 q^{2} - 16 q^{3} - 29 q^{4} - 33 q^{5} - 25 q^{6} - 11 q^{7} - 16 q^{9} - 44 q^{10} - 33 q^{11} - 22 q^{12} - 9 q^{13} - 33 q^{14} + 3 q^{16} - 39 q^{18} - 44 q^{19} - 33 q^{20} - 55 q^{21} - 27 q^{23} + 52 q^{24} + 11 q^{25} - 79 q^{27} - 44 q^{28} + 27 q^{29} - 66 q^{30} - 3 q^{31} - 33 q^{32} - 11 q^{34} + 23 q^{36} - 44 q^{37} - 33 q^{38} - 40 q^{39} - 77 q^{40} + 9 q^{41} - 22 q^{42} - 11 q^{43} - 36 q^{46} - 120 q^{47} - 56 q^{48} + 35 q^{49} - 3 q^{50} - 22 q^{51} - 38 q^{52} + 42 q^{54} - 44 q^{55} + 165 q^{56} + 11 q^{57} - 10 q^{58} - 9 q^{59} + 88 q^{60} - 11 q^{61} + 33 q^{63} - 22 q^{64} + 198 q^{65} + 33 q^{66} - 11 q^{67} + 3 q^{69} - 70 q^{70} + 14 q^{72} - 36 q^{73} + 231 q^{74} - 13 q^{75} - 11 q^{76} + 39 q^{77} + 3 q^{78} - 11 q^{79} + 172 q^{81} - 10 q^{82} + 66 q^{83} - 110 q^{84} + q^{85} - 33 q^{86} - 196 q^{87} - 99 q^{88} + 418 q^{90} + 63 q^{92} - 188 q^{93} - 42 q^{94} - 93 q^{95} - 82 q^{96} + 22 q^{97} + 242 q^{99}+O(q^{100}) $ 440 * q - 27 * q^2 - 16 * q^3 - 29 * q^4 - 33 * q^5 - 25 * q^6 - 11 * q^7 - 16 * q^9 - 44 * q^10 - 33 * q^11 - 22 * q^12 - 9 * q^13 - 33 * q^14 + 3 * q^16 - 39 * q^18 - 44 * q^19 - 33 * q^20 - 55 * q^21 - 27 * q^23 + 52 * q^24 + 11 * q^25 - 79 * q^27 - 44 * q^28 + 27 * q^29 - 66 * q^30 - 3 * q^31 - 33 * q^32 - 11 * q^34 + 23 * q^36 - 44 * q^37 - 33 * q^38 - 40 * q^39 - 77 * q^40 + 9 * q^41 - 22 * q^42 - 11 * q^43 - 36 * q^46 - 120 * q^47 - 56 * q^48 + 35 * q^49 - 3 * q^50 - 22 * q^51 - 38 * q^52 + 42 * q^54 - 44 * q^55 + 165 * q^56 + 11 * q^57 - 10 * q^58 - 9 * q^59 + 88 * q^60 - 11 * q^61 + 33 * q^63 - 22 * q^64 + 198 * q^65 + 33 * q^66 - 11 * q^67 + 3 * q^69 - 70 * q^70 + 14 * q^72 - 36 * q^73 + 231 * q^74 - 13 * q^75 - 11 * q^76 + 39 * q^77 + 3 * q^78 - 11 * q^79 + 172 * q^81 - 10 * q^82 + 66 * q^83 - 110 * q^84 + q^85 - 33 * q^86 - 196 * q^87 - 99 * q^88 + 418 * q^90 + 63 * q^92 - 188 * q^93 - 42 * q^94 - 93 * q^95 - 82 * q^96 + 22 * q^97 + 242 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/207\mathbb{Z}\right)^\times$.

$n$	$28$	$47$
$\chi(n)$	$e\left(\frac{9}{22}\right)$	$e\left(\frac{1}{6}\right)$

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 $

$2$	−0.412156	+	0.0196334i	−0.291438	+	0.0138829i	−0.192792	−	0.981240i	$-0.561754\pi$
$2$	−0.412156	+	0.0196334i	−0.291438	+	0.0138829i	−0.0986464	+	0.995123i	$0.531451\pi$
$3$	1.15855	−	1.28754i	0.668887	−	0.743364i
$3$	1.15855	−	1.28754i	0.668887	−	0.743364i
$4$	−1.82146	+	0.173928i	−0.910728	+	0.0869640i
$5$	2.81788	+	2.68684i	1.26019	+	1.20159i	0.969586	+	0.244749i	$0.0787057\pi$
$5$	2.81788	+	2.68684i	1.26019	+	1.20159i	0.290607	+	0.956843i	$0.406143\pi$
$6$	−0.452223	+	0.553415i	−0.184619	+	0.225931i
$7$	0.539603	+	2.79973i	0.203951	+	1.05820i	0.929162	+	0.369672i	$0.120530\pi$
$7$	0.539603	+	2.79973i	0.203951	+	1.05820i	−0.725212	+	0.688526i	$0.758258\pi$
$8$	1.56416	−	0.224892i	0.553013	−	0.0795113i
$9$	−0.315538	−	2.98336i	−0.105179	−	0.994453i
$10$	−1.21416	−	1.05207i	−0.383950	−	0.332695i
$11$	−1.68703	+	0.869723i	−0.508658	+	0.262231i	−0.693396	−	0.720556i	$-0.743886\pi$
$11$	−1.68703	+	0.869723i	−0.508658	+	0.262231i	0.184739	+	0.982788i	$0.440856\pi$
$12$	−1.88630	+	2.54671i	−0.544529	+	0.735172i
$13$	2.45673	+	0.473497i	0.681376	+	0.131324i	0.518183	−	0.855270i	$-0.326609\pi$
$13$	2.45673	+	0.473497i	0.681376	+	0.131324i	0.163193	+	0.986594i	$0.447821\pi$
$14$	−0.277369	−	1.14333i	−0.0741300	−	0.305568i
$15$	6.72407	−	0.515310i	1.73615	−	0.133052i
$16$	2.95309	−	0.569162i	0.738273	−	0.142290i
$17$	−2.19831	−	4.81363i	−0.533169	−	1.16748i	−0.964209	−	0.265144i	$-0.914580\pi$
$17$	−2.19831	−	4.81363i	−0.533169	−	1.16748i	0.431040	−	0.902333i	$-0.358147\pi$
$18$	0.188625	+	1.22342i	0.0444593	+	0.288362i
$19$	2.26539	+	1.03457i	0.519717	+	0.237347i	0.657962	−	0.753051i	$-0.271419\pi$
$19$	2.26539	+	1.03457i	0.519717	+	0.237347i	−0.138245	+	0.990398i	$0.544146\pi$
$20$	−5.59996	−	4.40386i	−1.25219	−	0.984732i
$21$	4.22993	+	2.54885i	0.923046	+	0.556205i
$22$	0.678243	−	0.391584i	0.144602	−	0.0834859i
$23$	1.47338	−	4.56390i	0.307221	−	0.951638i
$23$	1.47338	−	4.56390i	0.307221	−	0.951638i
$24$	1.52259	−	2.27447i	0.310798	−	0.464274i
$25$	0.483411	+	10.1480i	0.0966822	+	2.02961i
$26$	−1.02185	−	0.146921i	−0.200402	−	0.0288135i
$27$	−4.20677	−	3.05009i	−0.809594	−	0.586991i
$28$	−1.46982	−	5.00573i	−0.277769	−	0.945994i
$29$	0.293166	−	3.07018i	0.0544396	−	0.570118i	−0.926565	−	0.376134i	$-0.877253\pi$
$29$	0.293166	−	3.07018i	0.0544396	−	0.570118i	0.981005	−	0.193983i	$-0.0621408\pi$
$30$	−2.76125	+	0.344405i	−0.504133	+	0.0628794i
$31$	−7.06488	+	5.55588i	−1.26889	+	0.997866i	−0.269498	+	0.963001i	$0.586858\pi$
$31$	−7.06488	+	5.55588i	−1.26889	+	0.997866i	−0.999392	+	0.0348655i	$0.988900\pi$
$32$	−4.27735	+	1.03767i	−0.756137	+	0.183437i
$33$	−0.834694	+	3.17974i	−0.145301	+	0.553521i
$34$	1.00056	+	1.94081i	0.171594	+	0.332846i
$35$	−6.00189	+	9.33912i	−1.01450	+	1.57860i
$36$	1.09363	+	5.37918i	0.182272	+	0.896530i
$37$	1.48644	−	5.06234i	0.244369	−	0.832244i	−0.742378	−	0.669981i	$-0.766302\pi$
$37$	1.48644	−	5.06234i	0.244369	−	0.832244i	0.986747	−	0.162264i	$-0.0518795\pi$
$38$	−0.954008	−	0.381927i	−0.154760	−	0.0619568i
$39$	3.45589	−	2.61459i	0.553385	−	0.418669i
$40$	5.01185	+	3.56892i	0.792443	+	0.564296i
$41$	−3.86707	+	4.05566i	−0.603934	+	0.633388i	−0.952733	−	0.303810i	$-0.901741\pi$
$41$	−3.86707	+	4.05566i	−0.603934	+	0.633388i	0.348799	+	0.937198i	$0.386590\pi$
$42$	−1.79343	−	0.967478i	−0.276733	−	0.149285i
$43$	−0.990237	+	1.25919i	−0.151010	+	0.192024i	−0.855672	−	0.517518i	$-0.826856\pi$
$43$	−0.990237	+	1.25919i	−0.151010	+	0.192024i	0.704663	+	0.709543i	$0.251098\pi$
$44$	2.92158	−	1.87758i	0.440444	−	0.283056i
$45$	7.12667	−	9.25454i	1.06238	−	1.37959i
$46$	−0.517659	+	1.90997i	−0.0763246	+	0.281609i
$47$	−3.02178	−	1.74463i	−0.440772	−	0.254480i	0.263153	−	0.964754i	$-0.415238\pi$
$47$	−3.02178	−	1.74463i	−0.440772	−	0.254480i	−0.703925	+	0.710274i	$0.748571\pi$
$48$	2.68847	−	4.46163i	0.388048	−	0.643981i
$49$	−1.04873	+	0.419849i	−0.149819	+	0.0599784i
$50$	−0.398482	−	4.17309i	−0.0563538	−	0.590164i
$51$	−8.74461	−	2.74640i	−1.22449	−	0.384572i
$52$	−4.55719	−	0.435159i	−0.631969	−	0.0603457i
$53$	−4.68343	−	5.40497i	−0.643319	−	0.742430i	0.336639	−	0.941634i	$-0.390710\pi$
$53$	−4.68343	−	5.40497i	−0.643319	−	0.742430i	−0.979958	+	0.199204i	$0.936164\pi$
$54$	1.79373	+	1.17452i	0.244096	+	0.159832i
$55$	−7.09064	−	2.08200i	−0.956102	−	0.280737i
$56$	1.47366	+	4.25786i	0.196926	+	0.568981i
$57$	3.95662	−	1.71819i	0.524067	−	0.227580i
$58$	−0.0605523	+	1.27115i	−0.00795090	+	0.166910i
$59$	−0.385512	+	2.00023i	−0.0501894	+	0.260408i	−0.998353	−	0.0573763i	$-0.981727\pi$
$59$	−0.385512	+	2.00023i	−0.0501894	+	0.260408i	0.948163	+	0.317784i	$0.102939\pi$
$60$	−12.1580	+	2.10812i	−1.56959	+	0.272157i
$61$	5.11063	−	12.7657i	0.654349	−	1.63448i	−0.113260	−	0.993565i	$-0.536129\pi$
$61$	5.11063	−	12.7657i	0.654349	−	1.63448i	0.767609	−	0.640919i	$-0.221446\pi$
$62$	2.80275	−	2.42860i	0.355950	−	0.308433i
$63$	8.18233	−	2.49325i	1.03088	−	0.314120i
$64$	−4.02867	+	1.18292i	−0.503583	+	0.147865i
$65$	5.65057	+	7.93511i	0.700867	+	0.984230i
$66$	0.281595	−	1.32694i	0.0346620	−	0.163335i
$67$	−4.41270	+	8.55943i	−0.539097	+	1.04570i	0.449239	+	0.893411i	$0.351695\pi$
$67$	−4.41270	+	8.55943i	−0.539097	+	1.04570i	−0.988336	+	0.152290i	$0.951335\pi$
$68$	4.84136	+	8.38547i	0.587101	+	1.01689i
$69$	−4.16923	−	7.18453i	−0.501917	−	0.864916i
$70$	2.29036	−	3.96701i	0.273750	−	0.474149i
$71$	−0.382777	−	0.595613i	−0.0454273	−	0.0706863i	0.817797	−	0.575507i	$-0.195195\pi$
$71$	−0.382777	−	0.595613i	−0.0454273	−	0.0706863i	−0.863224	+	0.504820i	$0.831559\pi$
$72$	−1.16448	−	4.59548i	−0.137236	−	0.541583i
$73$	−1.51265	+	3.31223i	−0.177042	+	0.387668i	−0.977261	−	0.212040i	$-0.931989\pi$
$73$	−1.51265	+	3.31223i	−0.177042	+	0.387668i	0.800219	+	0.599708i	$0.204717\pi$
$74$	−0.513254	+	2.11566i	−0.0596645	+	0.245941i
$75$	13.6261	+	11.1346i	1.57341	+	1.28571i
$76$	−4.30625	−	1.49041i	−0.493961	−	0.170962i
$77$	−3.34531	−	4.25391i	−0.381234	−	0.484778i
$78$	−1.37303	+	1.14547i	−0.155465	+	0.129699i
$79$	−8.46405	+	2.92944i	−0.952280	+	0.329587i	−0.758658	−	0.651489i	$-0.774145\pi$
$79$	−8.46405	+	2.92944i	−0.952280	+	0.329587i	−0.193622	+	0.981076i	$0.562023\pi$
$80$	9.85069	+	6.33066i	1.10134	+	0.707789i
$81$	−8.80087	+	1.88273i	−0.977875	+	0.209192i
$82$	1.51421	−	1.74749i	0.167216	−	0.192978i
$83$	9.59700	−	9.15072i	1.05341	−	1.00442i	0.0534245	−	0.998572i	$-0.482986\pi$
$83$	9.59700	−	9.15072i	1.05341	−	1.00442i	0.999983	−	0.00585005i	$-0.00186214\pi$
$84$	−8.14795	−	3.90692i	−0.889014	−	0.426280i
$85$	6.73889	−	19.4707i	0.730935	−	2.11190i
$86$	0.383410	−	0.538424i	0.0413442	−	0.0580598i
$87$	−3.61334	−	3.93441i	−0.387391	−	0.421813i
$88$	−2.44318	+	1.73978i	−0.260444	+	0.185461i
$89$	2.44096	−	16.9773i	0.258742	−	1.79959i	−0.283083	−	0.959096i	$-0.591357\pi$
$89$	2.44096	−	16.9773i	0.258742	−	1.79959i	0.541824	−	0.840492i	$-0.317734\pi$
$90$	−2.75560	+	3.95424i	−0.290466	+	0.416813i
$91$			7.13369i			0.747814i
$92$	−1.88991	+	8.56920i	−0.197037	+	0.893401i
$93$	−1.03155	+	15.5331i	−0.106967	+	1.61071i
$94$	1.27970	+	0.659731i	0.131991	+	0.0680460i
$95$	3.60387	+	9.00204i	0.369750	+	0.923590i
$96$	−3.61946	+	6.70948i	−0.369410	+	0.684783i
$97$	17.4427	+	4.23155i	1.77104	+	0.429649i	0.982641	−	0.185519i	$-0.0593968\pi$
$97$	17.4427	+	4.23155i	1.77104	+	0.429649i	0.788396	+	0.615168i	$0.210912\pi$
$98$	0.423998	−	0.193633i	0.0428303	−	0.0195599i
$99$	3.12702	+	4.75858i	0.314277	+	0.478255i
$100$	−2.64554	−	18.4001i	−0.264554	−	1.84001i
$101$	6.88320	+	7.21890i	0.684904	+	0.718307i	0.970783	−	0.239959i	$-0.0771339\pi$
$101$	6.88320	+	7.21890i	0.684904	+	0.718307i	−0.285879	+	0.958266i	$0.592285\pi$
$102$	3.65807	+	0.960257i	0.362203	+	0.0950796i
$103$	−5.40186	−	0.257322i	−0.532261	−	0.0253547i	−0.220269	−	0.975439i	$-0.570693\pi$
$103$	−5.40186	−	0.257322i	−0.532261	−	0.0253547i	−0.311993	+	0.950085i	$0.600996\pi$
$104$	3.94920	+	0.188124i	0.387251	+	0.0184471i
$105$	5.07106	+	18.5475i	0.494885	+	1.81005i
$106$	2.03642	+	2.13574i	0.197795	+	0.207441i
$107$	0.313712	+	2.18191i	0.0303277	+	0.210933i	0.999350	−	0.0360379i	$-0.0114737\pi$
$107$	0.313712	+	2.18191i	0.0303277	+	0.210933i	−0.969023	+	0.246971i	$0.920565\pi$
$108$	8.19295	+	4.82394i	0.788367	+	0.464183i
$109$	1.91450	−	0.874322i	0.183376	−	0.0837449i	−0.321611	−	0.946872i	$-0.604224\pi$
$109$	1.91450	−	0.874322i	0.183376	−	0.0837449i	0.504987	+	0.863127i	$0.331497\pi$
$110$	2.96333	+	0.718896i	0.282542	+	0.0685440i
$111$	−4.79588	−	7.77882i	−0.455205	−	0.738333i
$112$	3.18700	+	7.96073i	0.301143	+	0.752218i
$113$	−8.00063	−	4.12461i	−0.752636	−	0.388011i	0.0388126	−	0.999247i	$-0.487642\pi$
$113$	−8.00063	−	4.12461i	−0.752636	−	0.388011i	−0.791449	+	0.611236i	$0.790673\pi$
$114$	−1.59701	+	0.785846i	−0.149574	+	0.0736013i
$115$	16.4143	−	8.90176i	1.53064	−	0.830093i
$116$			5.64319i			0.523957i
$117$	0.637417	−	7.47873i	0.0589293	−	0.691409i
$118$	0.119620	−	0.831975i	0.0110119	−	0.0765895i
$119$	12.2906	−	8.75213i	1.12668	−	0.802306i
$120$	10.4016	−	2.31821i	0.949533	−	0.211623i
$121$	−4.29098	+	6.02584i	−0.390089	+	0.547804i
$122$	−1.85574	+	5.36181i	−0.168011	+	0.485436i
$123$	0.741665	+	9.67769i	0.0668737	+	0.872608i
$124$	11.9021	−	11.3486i	1.06884	−	1.01913i
$125$	−13.1554	+	15.1821i	−1.17665	+	1.35793i
$126$	−3.32345	+	1.18826i	−0.296076	+	0.105858i
$127$	12.9965	+	8.35233i	1.15325	+	0.741150i	0.970284	−	0.241969i	$-0.0777933\pi$
$127$	12.9965	+	8.35233i	1.15325	+	0.741150i	0.182967	+	0.983119i	$0.441430\pi$
$128$	9.95591	−	3.44577i	0.879987	−	0.304566i
$129$	0.474025	+	2.73380i	0.0417355	+	0.240698i
$130$	−2.48471	−	3.15957i	−0.217923	−	0.277112i
$131$	−8.21538	−	2.84337i	−0.717781	−	0.248426i	−0.0563273	−	0.998412i	$-0.517939\pi$
$131$	−8.21538	−	2.84337i	−0.717781	−	0.248426i	−0.661454	+	0.749986i	$0.730060\pi$
$132$	0.967313	−	5.93693i	0.0841938	−	0.516743i
$133$	−1.67410	+	6.90074i	−0.145163	+	0.598370i
$134$	1.65067	−	3.61446i	0.142596	−	0.312242i
$135$	−3.65906	−	19.8977i	−0.314921	−	1.71252i
$136$	−4.52105	−	7.03490i	−0.387677	−	0.603237i
$137$	−3.66836	+	6.35378i	−0.313409	+	0.542840i	−0.979098	−	0.203389i	$-0.934804\pi$
$137$	−3.66836	+	6.35378i	−0.313409	+	0.542840i	0.665689	+	0.746229i	$0.268138\pi$
$138$	1.85943	+	2.87929i	0.158285	+	0.245102i
$139$	−5.07885	−	8.79682i	−0.430782	−	0.746137i	0.566159	−	0.824296i	$-0.308429\pi$
$139$	−5.07885	−	8.79682i	−0.430782	−	0.746137i	−0.996941	+	0.0781594i	$0.975096\pi$
$140$	9.30784	−	18.0547i	0.786656	−	1.52590i
$141$	−5.74716	+	1.86944i	−0.483998	+	0.157436i
$142$	0.169458	+	0.237971i	0.0142206	+	0.0199700i
$143$	−4.55639	+	1.33788i	−0.381024	+	0.111879i
$144$	−2.62983	−	8.63054i	−0.219152	−	0.719212i
$145$	9.07519	−	7.86370i	0.753653	−	0.653044i
$146$	0.558416	−	1.39486i	0.0462149	−	0.115439i
$147$	−0.674431	+	1.83670i	−0.0556261	+	0.151489i
$148$	−1.82700	+	9.47937i	−0.150178	+	0.779200i
$149$	0.0190670	−	0.400267i	0.00156203	−	0.0327911i	−0.997952	−	0.0639711i	$-0.979623\pi$
$149$	0.0190670	−	0.400267i	0.00156203	−	0.0327911i	0.999514	+	0.0311799i	$0.00992649\pi$
$150$	−5.83469	−	4.32166i	−0.476401	−	0.352862i
$151$	−2.85563	−	8.25080i	−0.232388	−	0.671441i	−0.999550	−	0.0299878i	$-0.990453\pi$
$151$	−2.85563	−	8.25080i	−0.232388	−	0.671441i	0.767162	−	0.641453i	$-0.221668\pi$
$152$	3.77610	+	1.10876i	0.306282	+	0.0899325i
$153$	−13.6671	+	8.07724i	−1.10492	+	0.653006i
$154$	1.46231	+	1.68760i	0.117836	+	0.135990i
$155$	−34.8358	−	3.32641i	−2.79808	−	0.267184i
$156$	−5.84000	+	5.36343i	−0.467575	+	0.429418i
$157$	0.561998	+	5.88551i	0.0448524	+	0.469715i	0.989797	+	0.142485i	$0.0455092\pi$
$157$	0.561998	+	5.88551i	0.0448524	+	0.469715i	−0.944945	+	0.327230i	$0.893885\pi$
$158$	3.43100	−	1.37356i	0.272955	−	0.109275i
$159$	−12.3851	−	0.231786i	−0.982204	−	0.0183818i
$160$	−14.8411	−	8.56853i	−1.17329	−	0.677402i
$161$	13.5727	+	1.66238i	1.06968	+	0.131014i
$162$	3.59037	−	0.948769i	0.282086	−	0.0745424i
$163$	−11.9294	+	7.66656i	−0.934383	+	0.600491i	−0.916797	−	0.399354i	$-0.869234\pi$
$163$	−11.9294	+	7.66656i	−0.934383	+	0.600491i	−0.0175860	+	0.999845i	$0.505598\pi$
$164$	6.33830	−	8.05980i	0.494938	−	0.629365i
$165$	−10.8955	+	6.71742i	−0.848214	+	0.522950i
$166$	−3.77580	+	3.95995i	−0.293059	+	0.307352i
$167$	−0.456629	−	0.325164i	−0.0353350	−	0.0251620i	0.562253	−	0.826965i	$-0.309935\pi$
$167$	−0.456629	−	0.325164i	−0.0353350	−	0.0251620i	−0.597588	+	0.801803i	$0.703874\pi$
$168$	7.18949	+	3.03553i	0.554681	+	0.234196i
$169$	−6.25744	−	2.50510i	−0.481341	−	0.192700i
$170$	−2.39520	+	8.15730i	−0.183703	+	0.625636i
$171$	2.37168	−	7.08493i	0.181367	−	0.541798i
$172$	1.58467	−	2.46579i	0.120830	−	0.188015i
$173$	−0.0263099	−	0.0510341i	−0.00200031	−	0.00388005i	0.887833	−	0.460165i	$-0.152210\pi$
$173$	−0.0263099	−	0.0510341i	−0.00200031	−	0.00388005i	−0.889833	+	0.456285i	$0.849180\pi$
$174$	1.56651	+	1.55065i	0.118757	+	0.117554i
$175$	−28.1509	+	6.82934i	−2.12801	+	0.516249i
$176$	−4.48693	+	3.52856i	−0.338215	+	0.265975i
$177$	2.12875	+	2.81372i	0.160006	+	0.211492i
$178$	−0.672736	+	7.04521i	−0.0504237	+	0.528061i
$179$	0.0316032	+	0.107631i	0.00236213	+	0.00804469i	0.960666	−	0.277708i	$-0.0895747\pi$
$179$	0.0316032	+	0.107631i	0.00236213	+	0.00804469i	−0.958303	+	0.285752i	$0.907757\pi$
$180$	−11.3713	+	18.0963i	−0.847566	+	1.34882i
$181$	14.9883	+	2.15499i	1.11407	+	0.160179i	0.674676	−	0.738114i	$-0.264283\pi$
$181$	14.9883	+	2.15499i	1.11407	+	0.160179i	0.439396	+	0.898293i	$0.355192\pi$
$182$	−0.140059	−	2.94019i	−0.0103818	−	0.217942i
$183$	−10.5155	−	21.3699i	−0.777331	−	1.57970i
$184$	1.27822	−	7.47000i	0.0942315	−	0.550696i
$185$	17.7903	−	10.2712i	1.30797	−	0.755157i
$186$	0.120193	−	6.42232i	0.00881295	−	0.470907i
$187$	7.89514	+	6.20881i	0.577350	+	0.454033i
$188$	5.80748	+	2.65219i	0.423554	+	0.193431i
$189$	6.26944	−	13.4237i	0.456035	−	0.976428i
$190$	−1.66210	−	3.63949i	−0.120581	−	0.264036i
$191$	3.04518	−	0.586910i	0.220341	−	0.0424673i	−0.0778856	−	0.996962i	$-0.524817\pi$
$191$	3.04518	−	0.586910i	0.220341	−	0.0424673i	0.298227	+	0.954495i	$0.403605\pi$
$192$	−3.14433	+	6.55756i	−0.226923	+	0.473251i
$193$	−2.33717	−	9.63397i	−0.168234	−	0.693468i	−0.991968	−	0.126492i	$-0.959628\pi$
$193$	−2.33717	−	9.63397i	−0.168234	−	0.693468i	0.823734	−	0.566976i	$-0.191887\pi$
$194$	−7.27219	−	1.40160i	−0.522113	−	0.100629i
$195$	16.7633	+	1.91785i	1.20044	+	0.137340i
$196$	1.83719	−	0.947140i	0.131228	−	0.0676528i
$197$	18.3799	+	15.9263i	1.30952	+	1.13470i	0.981798	+	0.189928i	$0.0608253\pi$
$197$	18.3799	+	15.9263i	1.30952	+	1.13470i	0.327719	+	0.944775i	$0.393720\pi$
$198$	−1.38225	−	1.89988i	−0.0982320	−	0.135019i
$199$	−6.67327	+	0.959471i	−0.473055	+	0.0680151i	−0.374720	−	0.927138i	$-0.622261\pi$
$199$	−6.67327	+	0.959471i	−0.473055	+	0.0680151i	−0.0983357	+	0.995153i	$0.531352\pi$
$200$	3.03834	+	15.7644i	0.214843	+	1.11471i
$201$	5.90833	+	15.5980i	0.416742	+	1.10020i
$202$	−2.97869	−	2.84017i	−0.209580	−	0.199834i
$203$	8.75386	−	0.835892i	0.614400	−	0.0586681i
$204$	16.4056	+	3.48151i	1.14862	+	0.243754i
$205$	−21.7938	+	1.03817i	−1.52215	+	0.0725088i
$206$	2.23146			0.155473
$207$	−14.0807	−	2.95555i	−0.978673	−	0.205425i
$208$	7.52446			0.521727
$209$	−4.72157	+	0.224916i	−0.326598	+	0.0155578i
$210$	−2.45422	−	7.54491i	−0.169357	−	0.520648i
$211$	24.4711	−	2.33671i	1.68466	−	0.160866i	0.791674	−	0.610944i	$-0.209210\pi$
$211$	24.4711	−	2.33671i	1.68466	−	0.160866i	0.892989	+	0.450078i	$0.148604\pi$
$212$	9.47075	+	9.03034i	0.650454	+	0.620206i
$213$	−1.21034	−	0.197203i	−0.0829314	−	0.0135121i
$214$	−0.172137	−	0.893130i	−0.0117670	−	0.0610531i
$215$	−6.17361	+	0.887631i	−0.421036	+	0.0605359i
$216$	−7.26599	−	3.82476i	−0.494388	−	0.260242i
$217$	−19.3672	−	16.7818i	−1.31473	−	1.13922i
$218$	−0.771906	+	0.397945i	−0.0522801	+	0.0269523i
$219$	2.51217	+	5.78498i	0.169757	+	0.390913i
$220$	13.2774	+	2.55901i	0.895163	+	0.172529i
$221$	−3.12143	−	12.8667i	−0.209970	−	0.865509i
$222$	2.12938	+	3.11193i	0.142914	+	0.208859i
$223$	−13.1037	+	2.52554i	−0.877492	+	0.169123i	−0.608055	−	0.793895i	$-0.708050\pi$
$223$	−13.1037	+	2.52554i	−0.877492	+	0.169123i	−0.269437	+	0.963018i	$0.586838\pi$
$224$	−5.21328	−	11.4155i	−0.348327	−	0.762730i
$225$	30.1227	−	4.64429i	2.00818	−	0.309619i
$226$	3.37849	+	1.54290i	0.224734	+	0.102632i
$227$	−3.28026	−	2.57962i	−0.217718	−	0.171216i	0.503343	−	0.864087i	$-0.332103\pi$
$227$	−3.28026	−	2.57962i	−0.217718	−	0.171216i	−0.721062	+	0.692871i	$0.756346\pi$
$228$	−6.90797	+	3.81778i	−0.457491	+	0.252839i
$229$	0.135177	−	0.0780442i	0.00893272	−	0.00515731i	−0.495527	−	0.868593i	$-0.665025\pi$
$229$	0.135177	−	0.0780442i	0.00893272	−	0.00515731i	0.504460	+	0.863435i	$0.331692\pi$
$230$	−6.59047	+	3.99118i	−0.434563	+	0.263171i
$231$	−9.35280	−	0.621119i	−0.615369	−	0.0408666i
$232$	−0.231900	−	4.86817i	−0.0152250	−	0.319611i
$233$	−10.2631	−	1.47562i	−0.672360	−	0.0966708i	−0.202325	−	0.979318i	$-0.564850\pi$
$233$	−10.2631	−	1.47562i	−0.672360	−	0.0966708i	−0.470035	+	0.882648i	$0.655759\pi$
$234$	−0.115883	+	3.09492i	−0.00757548	+	0.202321i
$235$	−3.82748	−	13.0352i	−0.249677	−	0.850322i
$236$	0.354298	−	3.71038i	0.0230629	−	0.241525i
$237$	−6.03422	+	14.2917i	−0.391965	+	0.928347i
$238$	−4.89383	+	3.84855i	−0.317220	+	0.249465i
$239$	8.54758	−	2.07362i	0.552897	−	0.134131i	0.0504299	−	0.998728i	$-0.483941\pi$
$239$	8.54758	−	2.07362i	0.552897	−	0.134131i	0.502467	+	0.864596i	$0.332426\pi$
$240$	19.5635	−	5.34884i	1.26282	−	0.345266i
$241$	10.0070	+	19.4108i	0.644607	+	1.25036i	0.954108	+	0.299463i	$0.0968077\pi$
$241$	10.0070	+	19.4108i	0.644607	+	1.25036i	−0.309501	+	0.950899i	$0.600162\pi$
$242$	1.65025	−	2.56784i	0.106082	−	0.165067i
$243$	−7.77213	+	13.5127i	−0.498582	+	0.866842i
$244$	−7.08847	+	24.1411i	−0.453793	+	1.54548i
$245$	−4.08326	−	1.63469i	−0.260870	−	0.104437i
$246$	−0.495688	−	3.97416i	−0.0316039	−	0.253383i
$247$	5.07560	+	3.61432i	0.322953	+	0.229974i
$248$	−9.80111	+	10.2791i	−0.622371	+	0.652724i
$249$	−0.663380	−	22.9581i	−0.0420400	−	1.45491i
$250$	5.12400	−	6.51570i	0.324070	−	0.412089i
$251$	−19.9712	+	12.8347i	−1.26057	+	0.810119i	−0.988362	−	0.152120i	$-0.951390\pi$
$251$	−19.9712	+	12.8347i	−1.26057	+	0.810119i	−0.272207	+	0.962239i	$0.587754\pi$
$252$	−14.4701	+	5.96449i	−0.911532	+	0.375727i
$253$	1.48369	+	8.98085i	0.0932787	+	0.564621i
$254$	−5.52057	−	3.18730i	−0.346391	−	0.199989i
$255$	−17.2621	−	31.2344i	−1.08100	−	1.95597i
$256$	3.76022	−	1.50537i	0.235014	−	0.0940854i
$257$	2.02811	+	21.2393i	0.126510	+	1.32487i	0.806319	+	0.591481i	$0.201457\pi$
$257$	2.02811	+	21.2393i	0.126510	+	1.32487i	−0.679809	+	0.733389i	$0.737937\pi$
$258$	−0.249046	−	1.11745i	−0.0155049	−	0.0695692i
$259$	14.9753	+	1.42997i	0.930518	+	0.0888537i
$260$	−11.6724	−	13.4707i	−0.723892	−	0.835416i
$261$	−9.25195	+	0.0941378i	−0.572681	+	0.00582698i
$262$	3.44185	+	1.01062i	0.212638	+	0.0624361i
$263$	0.0103775	+	0.0299839i	0.000639905	+	0.00184889i	0.945320	−	0.326143i	$-0.105749\pi$
$263$	0.0103775	+	0.0299839i	0.000639905	+	0.00184889i	−0.944680	+	0.327992i	$0.893628\pi$
$264$	−0.590495	+	5.16132i	−0.0363425	+	0.317657i
$265$	1.32495	−	27.8142i	0.0813912	−	1.70861i
$266$	0.554506	−	2.87705i	0.0339990	−	0.176403i
$267$	−19.0310	−	22.8118i	−1.16468	−	1.39606i
$268$	6.54881	−	16.3581i	0.400032	−	0.999232i
$269$	−6.25253	+	5.41785i	−0.381224	+	0.330332i	−0.824302	−	0.566151i	$-0.808432\pi$
$269$	−6.25253	+	5.41785i	−0.381224	+	0.330332i	0.443078	+	0.896483i	$0.353886\pi$
$270$	1.89876	+	8.12913i	0.115555	+	0.494723i
$271$	20.7664	−	6.09758i	1.26147	−	0.370401i	0.418430	−	0.908249i	$-0.362581\pi$
$271$	20.7664	−	6.09758i	1.26147	−	0.370401i	0.843042	+	0.537848i	$0.180762\pi$
$272$	−9.23155	−	12.9639i	−0.559745	−	0.786052i
$273$	9.18494	+	8.26471i	0.555898	+	0.500203i
$274$	1.38719	−	2.69077i	0.0838032	−	0.162555i
$275$	−9.64151	−	16.6996i	−0.581405	−	1.00702i
$276$	8.84367	+	12.3612i	0.532326	+	0.744055i
$277$	−12.6723	+	21.9491i	−0.761405	+	1.31879i	0.180722	+	0.983534i	$0.442157\pi$
$277$	−12.6723	+	21.9491i	−0.761405	+	1.31879i	−0.942127	+	0.335257i	$0.891177\pi$
$278$	2.26599	+	3.52595i	0.135905	+	0.211472i
$279$	18.8044	+	19.3240i	1.12579	+	1.15690i
$280$	−7.28760	+	15.9576i	−0.435518	+	0.953651i
$281$	−2.00902	+	8.28129i	−0.119848	+	0.494020i	0.879972	+	0.475026i	$0.157561\pi$
$281$	−2.00902	+	8.28129i	−0.119848	+	0.494020i	−0.999820	+	0.0189939i	$0.993954\pi$
$282$	2.33202	−	0.883339i	0.138870	−	0.0526021i
$283$	17.6109	+	6.09521i	1.04686	+	0.362323i	0.795744	−	0.605634i	$-0.207080\pi$
$283$	17.6109	+	6.09521i	1.04686	+	0.362323i	0.251119	+	0.967956i	$0.419202\pi$
$284$	0.800806	+	1.01831i	0.0475191	+	0.0604255i
$285$	15.7658	+	5.78914i	0.933884	+	0.342919i
$286$	1.85168	−	0.640872i	0.109492	−	0.0378955i
$287$	−13.4414	−	8.63828i	−0.793423	−	0.509902i
$288$	4.44543	+	12.4335i	0.261949	+	0.732649i
$289$	−7.20585	+	8.31599i	−0.423873	+	0.489176i
$290$	−3.58600	+	3.41925i	−0.210577	+	0.200785i
$291$	25.6565	−	17.5558i	1.50401	−	1.02914i
$292$	2.17913	−	6.29618i	0.127524	−	0.368456i
$293$	5.26116	−	7.38826i	0.307360	−	0.431627i	−0.631787	−	0.775142i	$-0.717678\pi$
$293$	5.26116	−	7.38826i	0.307360	−	0.431627i	0.939147	+	0.343515i	$0.111618\pi$
$294$	0.241910	−	0.770249i	0.0141085	−	0.0449218i
$295$	−6.46062	+	4.60059i	−0.376152	+	0.267857i
$296$	1.18654	−	8.25259i	0.0689664	−	0.479672i
$297$	9.74967	+	1.48686i	0.565733	+	0.0862765i
$298$			0.165347i			0.00957828i
$299$	5.78070	−	10.5146i	0.334307	−	0.608077i
$300$	−26.7560	−	17.9112i	−1.54476	−	1.03410i
$301$	−4.05972	−	2.09293i	−0.233998	−	0.120635i
$302$	1.33896	+	3.34455i	0.0770483	+	0.192457i
$303$	17.2692	−	0.498997i	0.992087	−	0.0286666i
$304$	7.27875	+	1.76580i	0.417465	+	0.101276i
$305$	48.7006	−	22.2408i	2.78859	−	1.27351i
$306$	5.47442	−	3.59742i	0.312951	−	0.205651i
$307$	−0.383791	−	2.66932i	−0.0219041	−	0.152346i	0.975934	−	0.218066i	$-0.0699748\pi$
$307$	−0.383791	−	2.66932i	−0.0219041	−	0.152346i	−0.997838	+	0.0657196i	$0.979066\pi$
$308$	6.83322	+	7.16647i	0.389359	+	0.408348i
$309$	−6.58963	+	6.65702i	−0.374871	+	0.378704i
$310$	14.4231	+	0.687056i	0.819176	+	0.0390222i
$311$	−8.84883	−	0.421522i	−0.501771	−	0.0239023i	−0.204829	−	0.978798i	$-0.565664\pi$
$311$	−8.84883	−	0.421522i	−0.501771	−	0.0239023i	−0.296942	+	0.954895i	$0.595967\pi$
$312$	4.81756	−	4.86682i	0.272740	−	0.275530i
$313$	−1.56228	−	1.63847i	−0.0883052	−	0.0926118i	0.678099	−	0.734971i	$-0.262804\pi$
$313$	−1.56228	−	1.63847i	−0.0883052	−	0.0926118i	−0.766404	+	0.642359i	$0.777956\pi$
$314$	−0.347184	−	2.41472i	−0.0195927	−	0.136270i
$315$	29.7558	+	14.9589i	1.67655	+	0.842841i
$316$	14.9074	−	6.80797i	0.838606	−	0.382979i
$317$	20.3384	+	4.93404i	1.14232	+	0.277124i	0.761902	−	0.647692i	$-0.224266\pi$
$317$	20.3384	+	4.93404i	1.14232	+	0.277124i	0.380416	+	0.924815i	$0.375781\pi$
$318$	5.10915	−	0.147630i	0.286507	−	0.00827870i
$319$	2.17562	+	5.43445i	0.121812	+	0.304271i
$320$	−14.5306	−	7.49106i	−0.812286	−	0.418763i
$321$	3.17276	+	2.12393i	0.177086	+	0.118546i
$322$	−5.62671	−	0.418680i	−0.313565	−	0.0233321i
$323$		−	13.1791i		−	0.733303i
$324$	15.7029	−	4.96003i	0.872386	−	0.275557i
$325$	−3.61745	+	25.1599i	−0.200660	+	1.39562i
$326$	4.76626	−	3.39404i	0.263978	−	0.187978i
$327$	1.09231	−	3.47794i	0.0604048	−	0.192331i
$328$	−5.13661	+	7.21336i	−0.283622	+	0.398291i
$329$	3.25392	−	9.40157i	0.179394	−	0.518325i
$330$	4.35877	−	2.98254i	0.239942	−	0.164184i
$331$	−19.6691	+	18.7544i	−1.08111	+	1.03084i	−0.0816955	+	0.996657i	$0.526033\pi$
$331$	−19.6691	+	18.7544i	−1.08111	+	1.03084i	−0.999416	+	0.0341801i	$0.989118\pi$
$332$	−15.8889	+	18.3368i	−0.872019	+	1.00636i
$333$	−15.5718	−	2.83722i	−0.853331	−	0.155479i
$334$	0.194587	+	0.125053i	0.0106473	+	0.00684261i
$335$	−35.4323	+	12.2632i	−1.93587	+	0.670012i
$336$	13.9421	+	5.11948i	0.760602	+	0.279291i
$337$	8.98979	+	11.4314i	0.489705	+	0.622711i	0.966612	−	0.256243i	$-0.0824847\pi$
$337$	8.98979	+	11.4314i	0.489705	+	0.622711i	−0.476907	+	0.878954i	$0.658242\pi$
$338$	2.62822	+	0.909637i	0.142957	+	0.0494778i
$339$	−14.5797	+	5.52261i	−0.791862	+	0.299947i
$340$	−8.88809	+	36.6372i	−0.482024	+	1.98693i
$341$	7.08657	−	15.5174i	0.383759	−	0.840315i
$342$	−0.838400	+	2.96666i	−0.0453355	+	0.160419i
$343$	9.04917	+	14.0808i	0.488609	+	0.760291i
$344$	−1.26570	+	2.19226i	−0.0682422	+	0.118199i
$345$	7.55531	−	31.4472i	0.406764	−	1.69306i
$346$	0.0118458	+	0.0205175i	0.000636833	+	0.00110303i
$347$	−11.4236	+	22.1587i	−0.613252	+	1.18954i	0.353886	+	0.935289i	$0.384860\pi$
$347$	−11.4236	+	22.1587i	−0.613252	+	1.18954i	−0.967138	+	0.254254i	$0.918170\pi$
$348$	7.26585	+	6.53790i	0.389490	+	0.350468i
$349$	−9.09034	−	12.7656i	−0.486595	−	0.683327i	0.496162	−	0.868230i	$-0.334742\pi$
$349$	−9.09034	−	12.7656i	−0.486595	−	0.683327i	−0.982757	+	0.184903i	$0.940803\pi$
$350$	11.4685	−	3.36745i	0.613017	−	0.179998i
$351$	−8.89072	−	9.48516i	−0.474551	−	0.506281i
$352$	6.31352	−	5.47070i	0.336512	−	0.291589i
$353$	−12.5218	+	31.2779i	−0.666467	+	1.66476i	0.0778800	+	0.996963i	$0.475185\pi$
$353$	−12.5218	+	31.2779i	−0.666467	+	1.66476i	−0.744347	+	0.667793i	$0.767239\pi$
$354$	−0.932619	−	1.11790i	−0.0495682	−	0.0594156i
$355$	0.521698	−	2.70683i	0.0276889	−	0.143664i
$356$	−1.49329	+	31.3479i	−0.0791440	+	1.66144i
$357$	2.97054	−	25.9645i	0.157218	−	1.37419i
$358$	−0.0151386	−	0.0437401i	−0.000800100	−	0.00231174i
$359$	22.5665	+	6.62612i	1.19101	+	0.349713i	0.816411	−	0.577472i	$-0.195961\pi$
$359$	22.5665	+	6.62612i	1.19101	+	0.349713i	0.374604	+	0.927185i	$0.377779\pi$
$360$	9.06595	−	16.0783i	0.477818	−	0.847400i
$361$	−8.38069	−	9.67183i	−0.441089	−	0.509044i
$362$	−6.21984	−	0.593922i	−0.326907	−	0.0312159i
$363$	2.78723	+	12.5061i	0.146292	+	0.656397i
$364$	−1.24075	−	12.9937i	−0.0650329	−	0.681055i
$365$	−13.1619	+	5.26923i	−0.688925	+	0.275804i
$366$	4.75361	+	8.60126i	0.248475	+	0.449595i
$367$	3.18377	+	1.83815i	0.166192	+	0.0959508i	0.580789	−	0.814054i	$-0.302744\pi$
$367$	3.18377	+	1.83815i	0.166192	+	0.0959508i	−0.414597	+	0.910005i	$0.636078\pi$
$368$	1.75344	−	14.3162i	0.0914043	−	0.746283i
$369$	13.3197	+	10.2571i	0.693396	+	0.533965i
$370$	−7.13073	+	4.58264i	−0.370709	+	0.238240i
$371$	12.6053	−	16.0289i	0.654432	−	0.832178i
$372$	−0.822714	−	28.4723i	−0.0426557	−	1.47622i
$373$	−6.53697	+	6.85578i	−0.338471	+	0.354979i	−0.870868	−	0.491516i	$-0.836443\pi$
$373$	−6.53697	+	6.85578i	−0.338471	+	0.354979i	0.532397	+	0.846495i	$0.321291\pi$
$374$	−3.37593	−	2.40399i	−0.174565	−	0.124307i
$375$	4.30652	+	34.5274i	0.222388	+	1.78299i
$376$	−5.11889	−	2.04930i	−0.263987	−	0.105684i
$377$	2.17395	−	7.40380i	0.111964	−	0.381315i
$378$	−2.32044	+	5.65574i	−0.119350	+	0.290900i
$379$	−10.7972	+	16.8008i	−0.554614	+	0.862997i	−0.999468	−	0.0326062i	$-0.989619\pi$
$379$	−10.7972	+	16.8008i	−0.554614	+	0.862997i	0.444854	+	0.895603i	$0.353256\pi$
$380$	−8.13001	−	15.7700i	−0.417061	−	0.808985i
$381$	25.8110	−	7.05697i	1.32234	−	0.361540i
$382$	−1.24357	+	0.301686i	−0.0636264	+	0.0154356i
$383$	−5.59403	+	4.39920i	−0.285842	+	0.224788i	−0.750776	−	0.660557i	$-0.770320\pi$
$383$	−5.59403	+	4.39920i	−0.285842	+	0.224788i	0.464934	+	0.885345i	$0.346078\pi$
$384$	7.09781	−	16.8108i	0.362208	−	0.857871i
$385$	2.00290	−	20.9753i	0.102077	−	1.06900i
$386$	1.15243	+	3.92481i	0.0586571	+	0.199768i
$387$	4.06907	+	2.55691i	0.206842	+	0.129975i
$388$	−32.5071	−	4.67381i	−1.65030	−	0.237277i
$389$	−0.0213200	−	0.447561i	−0.00108097	−	0.0226923i	0.998262	−	0.0589250i	$-0.0187673\pi$
$389$	−0.0213200	−	0.447561i	−0.00108097	−	0.0226923i	−0.999343	+	0.0362327i	$0.988464\pi$
$390$	−6.94673	−	0.461332i	−0.351761	−	0.0233605i
$391$	−25.2079	+	2.94055i	−1.27482	+	0.148710i
$392$	−1.54596	+	0.892560i	−0.0780827	+	0.0450811i
$393$	−13.1789	+	7.28348i	−0.664786	+	0.367403i
$394$	−7.88810	−	6.20327i	−0.397397	−	0.312516i
$395$	−31.7216	−	14.4868i	−1.59609	−	0.728908i
$396$	−6.52338	−	8.12367i	−0.327812	−	0.408230i
$397$	−1.36108	−	2.98036i	−0.0683108	−	0.149580i	0.872397	−	0.488798i	$-0.162565\pi$
$397$	−1.36108	−	2.98036i	−0.0683108	−	0.149580i	−0.940708	+	0.339219i	$0.889837\pi$
$398$	2.73159	−	0.526471i	0.136922	−	0.0263896i
$399$	6.94548	+	10.1503i	0.347709	+	0.508151i
$400$	7.20343	+	29.6930i	0.360172	+	1.48465i
$401$	23.8778	+	4.60208i	1.19240	+	0.229817i	0.746574	−	0.665302i	$-0.231697\pi$
$401$	23.8778	+	4.60208i	1.19240	+	0.229817i	0.445828	+	0.895119i	$0.352909\pi$
$402$	−2.74140	−	6.31283i	−0.136729	−	0.314855i
$403$	−19.9872	+	10.3041i	−0.995635	+	0.513286i
$404$	−13.7930	−	11.9517i	−0.686229	−	0.594621i
$405$	−29.8584	−	18.3412i	−1.48367	−	0.911384i
$406$	−3.59155	+	0.516386i	−0.178245	+	0.0256278i
$407$	1.89518	+	9.83310i	0.0939403	+	0.487409i
$408$	−14.2956	−	2.32920i	−0.707737	−	0.115313i
$409$	−11.1809	−	10.6610i	−0.552860	−	0.527151i	0.361329	−	0.932438i	$-0.382323\pi$
$409$	−11.1809	−	10.6610i	−0.552860	−	0.527151i	−0.914189	+	0.405287i	$0.867172\pi$
$410$	8.96208	−	0.855775i	0.442606	−	0.0422637i
$411$	3.93081	+	12.0843i	0.193892	+	0.596076i
$412$	9.88401	−	0.470834i	0.486950	−	0.0231963i
$413$	−5.80812			−0.285799
$414$	5.86146	+	0.941695i	0.288075	+	0.0462818i
$415$	51.6297			2.53440
$416$	−10.9997	+	0.523978i	−0.539303	+	0.0256902i
$417$	−17.2104	−	3.65229i	−0.842796	−	0.178854i
$418$	1.94161	−	0.185401i	0.0949671	−	0.00906826i
$419$	−6.46416	−	6.16356i	−0.315795	−	0.301110i	0.515558	−	0.856855i	$-0.327585\pi$
$419$	−6.46416	−	6.16356i	−0.315795	−	0.301110i	−0.831353	+	0.555745i	$0.812433\pi$
$420$	−12.4626	−	32.9015i	−0.608115	−	1.60543i
$421$	−2.53056	−	13.1298i	−0.123332	−	0.639906i	−0.990005	−	0.141030i	$-0.954959\pi$
$421$	−2.53056	−	13.1298i	−0.123332	−	0.639906i	0.866674	−	0.498876i	$-0.166254\pi$
$422$	−10.0401	+	1.44354i	−0.488742	+	0.0702705i
$423$	−4.25136	+	9.56556i	−0.206708	+	0.465093i
$424$	−8.54116	−	7.40096i	−0.414795	−	0.359422i
$425$	47.7863	−	24.6355i	2.31797	−	1.19500i
$426$	0.502723	+	0.0575153i	0.0243570	+	0.00278663i
$427$	38.4983	+	7.41994i	1.86306	+	0.359076i
$428$	−0.950908	−	3.91970i	−0.0459639	−	0.189466i
$429$	−3.55622	+	7.41654i	−0.171696	+	0.358074i
$430$	2.52706	−	0.487051i	0.121866	−	0.0234877i
$431$	2.98287	+	6.53158i	0.143680	+	0.314615i	0.967767	−	0.251848i	$-0.0810384\pi$
$431$	2.98287	+	6.53158i	0.143680	+	0.314615i	−0.824087	+	0.566464i	$0.808311\pi$
$432$	−14.1590	−	6.61287i	−0.681224	−	0.318162i
$433$	22.6057	+	10.3237i	1.08636	+	0.496124i	0.876399	−	0.481586i	$-0.159939\pi$
$433$	22.6057	+	10.3237i	1.08636	+	0.496124i	0.209961	+	0.977710i	$0.432666\pi$
$434$	8.31180	+	6.53647i	0.398979	+	0.313761i
$435$	0.389178	−	20.7952i	0.0186597	−	0.997052i
$436$	−3.33511	+	1.92552i	−0.159723	+	0.0922159i
$437$	8.05946	−	8.81470i	0.385536	−	0.421664i
$438$	−1.14899	−	2.33499i	−0.0549007	−	0.111570i
$439$	−1.19517	−	25.0897i	−0.0570424	−	1.19747i	−0.828055	−	0.560648i	$-0.810552\pi$
$439$	−1.19517	−	25.0897i	−0.0570424	−	1.19747i	0.771012	−	0.636821i	$-0.219751\pi$
$440$	−11.5591	−	1.66195i	−0.551059	−	0.0792303i
$441$	1.58347	+	2.99626i	0.0754035	+	0.142679i
$442$	1.53913	+	5.24181i	0.0732092	+	0.249328i
$443$	−1.59548	+	16.7087i	−0.0758038	+	0.793853i	0.875013	+	0.484099i	$0.160853\pi$
$443$	−1.59548	+	16.7087i	−0.0758038	+	0.793853i	−0.950817	+	0.309754i	$0.899753\pi$
$444$	10.0884	+	13.3346i	0.478776	+	0.632834i
$445$	52.4936	−	41.2814i	2.48843	−	1.95693i
$446$	5.35121	−	1.29819i	0.253387	−	0.0614710i
$447$	−0.493271	−	0.488277i	−0.0233309	−	0.0230947i
$448$	−5.48575	−	10.6409i	−0.259177	−	0.502734i
$449$	0.530935	−	0.826150i	0.0250563	−	0.0389884i	−0.828499	−	0.559990i	$-0.810805\pi$
$449$	0.530935	−	0.826150i	0.0250563	−	0.0389884i	0.853556	+	0.521001i	$0.174441\pi$
$450$	−12.3241	+	2.50558i	−0.580963	+	0.118114i
$451$	2.99654	−	10.2053i	0.141102	−	0.480548i
$452$	15.2902	+	6.12127i	0.719190	+	0.287920i
$453$	−13.9317	−	5.88219i	−0.654566	−	0.276370i
$454$	1.40263	+	0.998806i	0.0658285	+	0.0468763i
$455$	−19.1671	+	20.1019i	−0.898567	+	0.942390i
$456$	5.80236	−	3.57734i	0.271721	−	0.167524i
$457$	12.3735	−	15.7342i	0.578808	−	0.736015i	−0.405182	−	0.914236i	$-0.632792\pi$
$457$	12.3735	−	15.7342i	0.578808	−	0.736015i	0.983990	+	0.178221i	$0.0570343\pi$
$458$	−0.0541816	+	0.0348204i	−0.00253174	+	0.00162705i
$459$	−5.43423	+	26.9549i	−0.253648	+	1.25815i
$460$	−28.3496	+	19.0691i	−1.32181	+	0.889100i
$461$	−25.6915	−	14.8330i	−1.19657	−	0.690842i	−0.236784	−	0.971562i	$-0.576093\pi$
$461$	−25.6915	−	14.8330i	−1.19657	−	0.690842i	−0.959790	+	0.280720i	$0.909427\pi$
$462$	3.86701	+	0.0723705i	0.179910	+	0.00336698i
$463$	−7.88481	+	3.15660i	−0.366438	+	0.146700i	−0.547572	−	0.836759i	$-0.684448\pi$
$463$	−7.88481	+	3.15660i	−0.366438	+	0.146700i	0.181134	+	0.983459i	$0.442023\pi$
$464$	−0.881680	−	9.23337i	−0.0409310	−	0.428649i
$465$	−44.6418	+	40.9988i	−2.07021	+	1.90127i
$466$	4.25898	+	0.406684i	0.197294	+	0.0188393i
$467$	0.996120	+	1.14958i	0.0460949	+	0.0531964i	0.778329	−	0.627857i	$-0.216068\pi$
$467$	0.996120	+	1.14958i	0.0460949	+	0.0531964i	−0.732234	+	0.681053i	$0.761522\pi$
$468$	0.139733	+	13.7330i	0.00645914	+	0.634810i
$469$	−26.3452	−	7.73565i	−1.21651	−	0.357199i
$470$	1.83344	+	5.29739i	0.0845704	+	0.244350i
$471$	8.22896	+	6.09505i	0.379170	+	0.280845i
$472$	−0.153167	+	3.21537i	−0.00705008	+	0.147999i
$473$	0.575411	−	2.98552i	0.0264574	−	0.137274i
$474$	2.20645	−	6.00889i	0.101345	−	0.275998i
$475$	−9.40375	+	23.4894i	−0.431474	+	1.07777i
$476$	−20.8646	+	18.0793i	−0.956329	+	0.828664i
$477$	−14.6472	+	15.6778i	−0.670648	+	0.717839i
$478$	−3.48223	+	1.02247i	−0.159273	+	0.0467669i
$479$	−7.76122	−	10.8991i	−0.354619	−	0.497993i	0.598277	−	0.801289i	$-0.295852\pi$
$479$	−7.76122	−	10.8991i	−0.354619	−	0.497993i	−0.952896	+	0.303296i	$0.901913\pi$
$480$	−28.2265	+	9.18156i	−1.28836	+	0.419079i
$481$	6.04879	−	11.7330i	0.275801	−	0.534979i
$482$	−4.50554	−	7.80383i	−0.205222	−	0.355455i
$483$	17.8650	−	15.5495i	0.812886	−	0.707528i
$484$	6.76778	−	11.7221i	0.307626	−	0.532824i
$485$	37.7819	+	58.7897i	1.71559	+	2.66950i
$486$	2.93803	−	5.72195i	0.133272	−	0.259553i
$487$	13.8495	−	30.3262i	0.627580	−	1.37421i	−0.282295	−	0.959328i	$-0.591096\pi$
$487$	13.8495	−	30.3262i	0.627580	−	1.37421i	0.909875	−	0.414882i	$-0.136177\pi$
$488$	5.12292	−	21.1169i	0.231903	−	0.955919i
$489$	−3.94974	+	24.2417i	−0.178613	+	1.09625i
$490$	1.71504	+	0.593580i	0.0774774	+	0.0268152i
$491$	−22.9830	−	29.2253i	−1.03721	−	1.31892i	−0.946381	−	0.323053i	$-0.895291\pi$
$491$	−22.9830	−	29.2253i	−1.03721	−	1.31892i	−0.0908291	−	0.995866i	$-0.528952\pi$
$492$	−3.03413	−	17.4985i	−0.136789	−	0.788893i
$493$	−15.4232	+	5.33802i	−0.694625	+	0.240412i
$494$	−2.16290	−	1.39001i	−0.0973136	−	0.0625396i
$495$	−3.97399	+	21.8109i	−0.178617	+	0.980327i
$496$	−17.7010	+	20.4281i	−0.794800	+	0.917248i
$497$	1.46101	−	1.39307i	0.0655351	−	0.0624876i
$498$	0.724162	+	9.44930i	0.0324505	+	0.423433i
$499$	6.52021	−	18.8389i	0.291885	−	0.843346i	−0.699764	−	0.714375i	$-0.746711\pi$
$499$	6.52021	−	18.8389i	0.291885	−	0.843346i	0.991648	−	0.128971i	$-0.0411675\pi$
$500$	21.3214	−	29.9417i	0.953522	−	1.33903i
$501$	−0.947689	+	0.211212i	−0.0423396	+	0.00943626i
$502$	7.97925	−	5.68200i	0.356132	−	0.253600i
$503$	−1.17664	+	8.18371i	−0.0524638	+	0.364894i	0.946630	+	0.322323i	$0.104464\pi$
$503$	−1.17664	+	8.18371i	−0.0524638	+	0.364894i	−0.999093	+	0.0425704i	$0.986445\pi$
$504$	12.2377	−	5.73998i	0.545112	−	0.255679i
$505$			38.8360i			1.72818i
$506$	−0.787836	−	3.67238i	−0.0350236	−	0.163257i
$507$	−10.4750	+	5.15445i	−0.465209	+	0.228917i
$508$	−25.1252	−	12.9530i	−1.11475	−	0.574695i
$509$	1.81341	+	4.52968i	0.0803780	+	0.200775i	0.963113	−	0.269096i	$-0.0867249\pi$
$509$	1.81341	+	4.52968i	0.0803780	+	0.200775i	−0.882735	+	0.469870i	$0.844301\pi$
$510$	7.72793	+	12.5345i	0.342198	+	0.555038i
$511$	−10.0896	−	2.44771i	−0.446337	−	0.108280i
$512$	−20.6868	+	9.44736i	−0.914237	+	0.417518i
$513$	−6.37446	−	11.2619i	−0.281439	−	0.497223i
$514$	−1.25290	−	8.71409i	−0.0552629	−	0.384362i
$515$	−14.5304	−	15.2391i	−0.640286	−	0.671513i
$516$	−1.33890	−	4.89706i	−0.0589418	−	0.215581i
$517$	6.61517	+	0.315119i	0.290935	+	0.0138589i
$518$	−6.20023	−	0.295353i	−0.272422	−	0.0129771i
$519$	−0.0961900	−	0.0252503i	−0.00422227	−	0.00110836i
$520$	10.6229	+	11.1410i	0.465846	+	0.488565i
$521$	−3.73147	−	25.9530i	−0.163479	−	1.13702i	−0.892013	−	0.452010i	$-0.850707\pi$
$521$	−3.73147	−	25.9530i	−0.163479	−	1.13702i	0.728534	−	0.685009i	$-0.240202\pi$
$522$	3.81140	−	0.220447i	0.166820	−	0.00964870i
$523$	31.7130	−	14.4828i	1.38671	−	0.633290i	0.424459	−	0.905447i	$-0.360464\pi$
$523$	31.7130	−	14.4828i	1.38671	−	0.633290i	0.962253	+	0.272157i	$0.0877370\pi$
$524$	15.4585	+	3.75019i	0.675308	+	0.163828i
$525$	−23.8211	+	44.1576i	−1.03964	+	1.92720i
$526$	−0.00486585	−	0.0121543i	−0.000212161	−	0.000529953i
$527$	42.2748	+	21.7942i	1.84152	+	0.949369i
$528$	−0.655142	+	9.86512i	−0.0285114	+	0.429324i
$529$	−18.6583	−	13.4487i	−0.811230	−	0.584727i
$530$			11.4898i			0.499085i
$531$	6.08904	+	0.518974i	0.264242	+	0.0225215i
$532$	1.84907	−	12.8606i	0.0801674	−	0.557577i
$533$	−11.4207	+	8.13264i	−0.494685	+	0.352264i
$534$	8.29162	+	9.02839i	0.358814	+	0.390696i
$535$	−4.97845	+	6.99126i	−0.215237	+	0.302258i
$536$	−4.97720	+	14.3807i	−0.214982	+	0.621151i
$537$	0.175193	+	0.0840046i	0.00756013	+	0.00362507i
$538$	2.47065	−	2.35576i	0.106517	−	0.101564i
$539$	1.40409	−	1.62040i	0.0604782	−	0.0697956i
$540$	10.1256	+	35.6064i	0.435736	+	1.53226i
$541$	0.354224	+	0.227646i	0.0152293	+	0.00978727i	0.548233	−	0.836325i	$-0.315301\pi$
$541$	0.354224	+	0.227646i	0.0152293	+	0.00978727i	−0.533004	+	0.846113i	$0.678937\pi$
$542$	−8.43930	+	2.92087i	−0.362499	+	0.125462i
$543$	20.1393	−	16.8015i	0.864261	−	0.721019i
$544$	14.3979	+	18.3085i	0.617307	+	0.784970i
$545$	7.74399	+	2.68022i	0.331716	+	0.114808i
$546$	−3.94789	−	3.22602i	−0.168954	−	0.138061i
$547$	1.80228	−	7.42910i	0.0770599	−	0.317645i	−0.920216	−	0.391412i	$-0.871987\pi$
$547$	1.80228	−	7.42910i	0.0770599	−	0.317645i	0.997276	+	0.0737665i	$0.0235020\pi$
$548$	5.57665	−	12.2112i	0.238223	−	0.521635i
$549$	−39.6974	−	11.2188i	−1.69424	−	0.478805i
$550$	4.30168	+	6.69354i	0.183424	+	0.285414i
$551$	3.84045	−	6.65186i	0.163609	−	0.283379i
$552$	−8.13708	−	10.3001i	−0.346337	−	0.438402i
$553$	−12.7689	−	22.1163i	−0.542987	−	0.940481i
$554$	4.79203	−	9.29524i	0.203594	−	0.394917i
$555$	7.38624	−	34.8055i	0.313528	−	1.47741i
$556$	10.7809	+	15.1397i	0.457213	+	0.642065i
$557$	−5.83299	+	1.71272i	−0.247152	+	0.0725702i	−0.402962	−	0.915217i	$-0.632019\pi$
$557$	−5.83299	+	1.71272i	−0.247152	+	0.0725702i	0.155810	+	0.987787i	$0.450201\pi$
$558$	−8.12976	−	7.59531i	−0.344160	−	0.321535i
$559$	−3.02897	+	2.62462i	−0.128112	+	0.111010i
$560$	−12.4087	+	30.9953i	−0.524361	+	1.30979i
$561$	17.1410	−	2.97214i	0.723693	−	0.125484i
$562$	0.665439	−	3.45263i	0.0280699	−	0.145640i
$563$	1.09539	−	22.9951i	0.0461653	−	0.969128i	−0.850378	−	0.526172i	$-0.823627\pi$
$563$	1.09539	−	22.9951i	0.0461653	−	0.969128i	0.896543	−	0.442956i	$-0.146070\pi$
$564$	10.1430	−	4.40470i	0.427099	−	0.185471i
$565$	−11.4626	−	33.1191i	−0.482236	−	1.39333i
$566$	−7.37813	−	2.16641i	−0.310126	−	0.0910612i
$567$	−10.0201	−	23.6241i	−0.420805	−	0.992120i
$568$	−0.732673	−	0.845549i	−0.0307423	−	0.0354785i
$569$	41.1183	+	3.92633i	1.72377	+	0.164600i	0.909450	−	0.415814i	$-0.136503\pi$
$569$	41.1183	+	3.92633i	1.72377	+	0.164600i	0.814321	+	0.580415i	$0.197109\pi$
$570$	−6.61162	−	2.07649i	−0.276930	−	0.0869748i
$571$	−0.640264	−	6.70515i	−0.0267942	−	0.280602i	−0.998933	−	0.0461937i	$-0.985291\pi$
$571$	−0.640264	−	6.70515i	−0.0267942	−	0.280602i	0.972138	−	0.234408i	$-0.0753152\pi$
$572$	8.06657	−	3.22937i	0.337280	−	0.135027i
$573$	2.77231	−	4.60076i	0.115815	−	0.192200i
$574$	5.70957	+	3.29642i	0.238313	+	0.137590i
$575$	47.0269	+	12.7457i	1.96116	+	0.531533i
$576$	4.80029	+	11.6457i	0.200012	+	0.485238i
$577$	−6.71023	+	4.31240i	−0.279350	+	0.179528i	−0.672812	−	0.739813i	$-0.734914\pi$
$577$	−6.71023	+	4.31240i	−0.279350	+	0.179528i	0.393462	+	0.919341i	$0.371277\pi$
$578$	2.80666	−	3.56896i	0.116742	−	0.148449i
$579$	−15.1119	−	8.15219i	−0.628028	−	0.338793i
$580$	−15.1623	+	15.9018i	−0.629582	+	0.660287i
$581$	30.7981	+	21.9312i	1.27772	+	0.909861i
$582$	−10.2298	+	7.73945i	−0.424039	+	0.320810i
$583$	12.6019	+	5.04504i	0.521918	+	0.208944i
$584$	−1.62112	+	5.52104i	−0.0670825	+	0.228462i
$585$	21.8903	−	19.3615i	0.905054	−	0.800500i
$586$	−2.02336	+	3.14841i	−0.0835843	+	0.130060i
$587$	−3.92604	−	7.61546i	−0.162045	−	0.314324i	0.793808	−	0.608168i	$-0.208095\pi$
$587$	−3.92604	−	7.61546i	−0.162045	−	0.314324i	−0.955853	+	0.293845i	$0.905065\pi$
$588$	0.908992	−	3.46277i	0.0374862	−	0.142802i
$589$	−21.7527	+	5.27714i	−0.896304	+	0.217441i
$590$	2.57246	−	2.02301i	0.105907	−	0.0832858i
$591$	41.7999	−	5.21361i	1.71942	−	0.214459i
$592$	1.50830	−	15.7956i	0.0619906	−	0.649195i
$593$	6.00060	+	20.4362i	0.246415	+	0.839212i	0.986085	+	0.166242i	$0.0531634\pi$
$593$	6.00060	+	20.4362i	0.246415	+	0.839212i	−0.739670	+	0.672970i	$0.765018\pi$
$594$	−4.04758	−	0.421400i	−0.166074	−	0.0172903i
$595$	58.1491	+	8.36058i	2.38388	+	0.342750i
$596$	0.0348878	+	0.732384i	0.00142906	+	0.0299996i
$597$	−6.49593	+	9.70371i	−0.265861	+	0.397147i
$598$	−2.17611	+	4.44717i	−0.0889879	+	0.181858i
$599$	28.0149	−	16.1744i	1.14466	−	0.660868i	0.197077	−	0.980388i	$-0.436855\pi$
$599$	28.0149	−	16.1744i	1.14466	−	0.660868i	0.947580	+	0.319520i	$0.103522\pi$
$600$	23.8174	+	14.3518i	0.972343	+	0.585911i
$601$	−22.2969	−	17.5345i	−0.909510	−	0.715246i	0.0494537	−	0.998776i	$-0.484252\pi$
$601$	−22.2969	−	17.5345i	−0.909510	−	0.715246i	−0.958963	+	0.283530i	$0.908494\pi$
$602$	1.71433	+	0.782909i	0.0698709	+	0.0319090i
$603$	26.9282	+	10.4638i	1.09660	+	0.426120i
$604$	6.63645	+	14.5318i	0.270033	+	0.591291i
$605$	−28.2820	+	5.45090i	−1.14982	+	0.221611i
$606$	−7.10779	+	0.544717i	−0.288734	+	0.0221276i
$607$	−4.11960	−	16.9812i	−0.167210	−	0.689247i	−0.992259	−	0.124186i	$-0.960368\pi$
$607$	−4.11960	−	16.9812i	−0.167210	−	0.689247i	0.825049	−	0.565061i	$-0.191147\pi$
$608$	−10.7634	−	2.07448i	−0.436515	−	0.0841313i
$609$	9.06551	−	12.2394i	0.367353	−	0.495965i
$610$	−19.6356	+	10.1229i	−0.795022	+	0.409862i
$611$	−6.59764	−	5.71689i	−0.266912	−	0.231281i
$612$	23.4893	−	17.0894i	0.949497	−	0.690800i
$613$	−40.2352	+	5.78495i	−1.62508	+	0.233652i	−0.893815	−	0.448436i	$-0.851981\pi$
$613$	−40.2352	+	5.78495i	−1.62508	+	0.233652i	−0.731270	+	0.682088i	$0.761072\pi$
$614$	0.210590	+	1.09264i	0.00849871	+	0.0440955i
$615$	−23.9125	+	29.2633i	−0.964245	+	1.18001i
$616$	−6.18927	−	5.90145i	−0.249373	−	0.237776i
$617$	−29.3860	+	2.80602i	−1.18303	+	0.112966i	−0.667972	−	0.744187i	$-0.732837\pi$
$617$	−29.3860	+	2.80602i	−1.18303	+	0.112966i	−0.515062	+	0.857153i	$0.672231\pi$
$618$	2.58525	−	2.87311i	0.103994	−	0.115573i
$619$	17.4812	−	0.832733i	0.702630	−	0.0334704i	0.306773	−	0.951783i	$-0.400751\pi$
$619$	17.4812	−	0.832733i	0.702630	−	0.0334704i	0.395857	+	0.918312i	$0.370448\pi$
$620$	64.0304			2.57152
$621$	−20.1185	+	14.7053i	−0.807327	+	0.590104i
$622$	3.65538			0.146567
$623$	48.8489	−	2.32696i	1.95709	−	0.0932277i
$624$	8.71743	−	9.68807i	0.348977	−	0.387833i
$625$	−27.2946	+	2.60632i	−1.09178	+	0.104253i
$626$	0.676071	+	0.644633i	0.0270212	+	0.0257647i
$627$	−5.18057	+	6.33980i	−0.206892	+	0.253187i
$628$	−2.04731	−	10.6225i	−0.0816966	−	0.423882i
$629$	−27.6359	+	3.97345i	−1.10192	+	0.158432i
$630$	−12.5577	−	5.58121i	−0.500312	−	0.222361i
$631$	0.744832	+	0.645401i	0.0296513	+	0.0256930i	0.669560	−	0.742758i	$-0.266483\pi$
$631$	0.744832	+	0.645401i	0.0296513	+	0.0256930i	−0.639909	+	0.768451i	$0.721028\pi$
$632$	−12.5803	+	6.48559i	−0.500417	+	0.257983i
$633$	25.3424	−	34.2149i	1.00727	−	1.35992i
$634$	−8.47947	−	1.63428i	−0.336763	−	0.0649057i
$635$	14.1811	+	58.4553i	0.562760	+	2.31973i
$636$	22.5993	−	1.73193i	0.896119	−	0.0686755i
$637$	−2.77525	+	0.534886i	−0.109959	+	0.0211929i
$638$	−1.00339	−	2.19713i	−0.0397247	−	0.0869851i
$639$	−1.65615	+	1.32990i	−0.0655162	+	0.0526101i
$640$	37.3128	+	17.0402i	1.47492	+	0.673572i
$641$	−3.84013	−	3.01991i	−0.151676	−	0.119279i	0.539437	−	0.842026i	$-0.318637\pi$
$641$	−3.84013	−	3.01991i	−0.151676	−	0.119279i	−0.691113	+	0.722747i	$0.742879\pi$
$642$	−1.34937	−	0.813099i	−0.0532555	−	0.0320905i
$643$	5.96974	−	3.44663i	0.235424	−	0.135922i	−0.377648	−	0.925949i	$-0.623267\pi$
$643$	5.96974	−	3.44663i	0.235424	−	0.135922i	0.613072	+	0.790027i	$0.289934\pi$
$644$	−25.0112	−	0.667273i	−0.985581	−	0.0262942i
$645$	−6.00955	+	8.97715i	−0.236626	+	0.353475i
$646$	0.258750	+	5.43184i	0.0101804	+	0.213713i
$647$	37.3999	+	5.37729i	1.47034	+	0.211403i	0.830463	−	0.557074i	$-0.188076\pi$
$647$	37.3999	+	5.37729i	1.47034	+	0.211403i	0.639878	+	0.768477i	$0.278985\pi$
$648$	−13.3425	+	4.92413i	−0.524144	+	0.193438i
$649$	−1.08927	−	3.70973i	−0.0427578	−	0.145620i
$650$	0.996980	−	10.4409i	0.0391048	−	0.409524i
$651$	−44.0451	+	5.49365i	−1.72626	+	0.215313i
$652$	20.3955	−	16.0392i	0.798748	−	0.628142i
$653$	−23.8169	+	5.77791i	−0.932026	+	0.226107i	−0.672897	−	0.739736i	$-0.734950\pi$
$653$	−23.8169	+	5.77791i	−0.932026	+	0.226107i	−0.259128	+	0.965843i	$0.583435\pi$
$654$	−0.381918	+	1.45490i	−0.0149342	+	0.0568912i
$655$	−15.5103	−	30.0857i	−0.606036	−	1.17555i
$656$	−9.11147	+	14.1777i	−0.355743	+	0.553547i
$657$	10.3589	+	3.46763i	0.404139	+	0.135285i
$658$	−1.15654	+	3.93880i	−0.0450865	+	0.153550i
$659$	27.7656	+	11.1157i	1.08159	+	0.433005i	0.842889	−	0.538088i	$-0.180853\pi$
$659$	27.7656	+	11.1157i	1.08159	+	0.433005i	0.238705	+	0.971092i	$0.423277\pi$
$660$	18.6774	−	14.1305i	0.727015	−	0.550030i
$661$	−13.3217	−	9.48635i	−0.518155	−	0.368976i	0.290859	−	0.956766i	$-0.406059\pi$
$661$	−13.3217	−	9.48635i	−0.518155	−	0.368976i	−0.809014	+	0.587790i	$0.799998\pi$
$662$	7.73853	−	8.11593i	0.300766	−	0.315435i
$663$	−20.1828	−	10.8877i	−0.783834	−	0.422844i
$664$	12.9533	−	16.4714i	0.502685	−	0.639216i
$665$	−23.2586	+	14.9474i	−0.901930	+	0.579635i
$666$	6.47373	+	0.863648i	0.250852	+	0.0334657i
$667$	−13.5800	−	5.86153i	−0.525821	−	0.226959i
$668$	0.888285	+	0.512852i	0.0343688	+	0.0198428i
$669$	−11.9296	+	19.7976i	−0.461224	+	0.765420i
$670$	14.3629	−	5.75002i	0.554886	−	0.222143i
$671$	2.48088	+	25.9810i	0.0957733	+	1.00298i
$672$	−20.7378	−	6.51306i	−0.799977	−	0.251247i
$673$	47.3961	+	4.52578i	1.82699	+	0.174456i	0.951268	−	0.308366i	$-0.0997823\pi$
$673$	47.3961	+	4.52578i	1.82699	+	0.174456i	0.875718	+	0.482822i	$0.160388\pi$
$674$	−3.92964	−	4.53504i	−0.151364	−	0.174683i
$675$	28.9189	−	44.1650i	1.11309	−	1.69991i
$676$	11.8334	+	3.47459i	0.455129	+	0.133638i
$677$	−2.89337	−	8.35984i	−0.111201	−	0.321295i	0.875645	−	0.482955i	$-0.160436\pi$
$677$	−2.89337	−	8.35984i	−0.111201	−	0.321295i	−0.986847	+	0.161660i	$0.948315\pi$
$678$	5.90070	−	2.56243i	0.226615	−	0.0984094i
$679$	−2.43506	+	51.1181i	−0.0934489	+	1.96173i
$680$	6.16187	−	31.9708i	0.236297	−	1.22603i
$681$	−7.12171	+	1.23486i	−0.272905	+	0.0473200i
$682$	−2.61611	+	6.53473i	−0.100176	+	0.250228i
$683$	−10.4612	+	9.06468i	−0.400287	+	0.346850i	−0.831623	−	0.555341i	$-0.812588\pi$
$683$	−10.4612	+	9.06468i	−0.400287	+	0.346850i	0.431336	+	0.902191i	$0.358042\pi$
$684$	−3.08764	+	13.3174i	−0.118059	+	0.509203i
$685$	−27.4086	+	8.04788i	−1.04723	+	0.307494i
$686$	−4.00613	−	5.62582i	−0.152955	−	0.214795i
$687$	0.0561230	−	0.264464i	0.00214123	−	0.0100899i
$688$	−2.20758	+	4.28210i	−0.0841631	+	0.163254i
$689$	−8.94672	−	15.4962i	−0.340843	−	0.590357i
$690$	−2.49655	+	13.1095i	−0.0950420	+	0.499070i
$691$	−24.9509	+	43.2162i	−0.949177	+	1.64402i	−0.202013	+	0.979383i	$0.564748\pi$
$691$	−24.9509	+	43.2162i	−0.949177	+	1.64402i	−0.747164	+	0.664639i	$0.768585\pi$
$692$	0.0567986	+	0.0883804i	0.00215916	+	0.00335972i
$693$	−11.6354	+	11.3225i	−0.441991	+	0.430108i
$694$	4.27326	−	9.35714i	0.162211	−	0.355192i
$695$	9.32409	−	38.4344i	0.353683	−	1.45790i
$696$	−6.53665	−	5.34142i	−0.247771	−	0.202466i
$697$	28.0235	+	9.69902i	1.06146	+	0.367377i
$698$	3.99727	+	5.08295i	0.151299	+	0.192392i
$699$	−13.7902	+	11.5047i	−0.521595	+	0.435146i
$700$	50.0879	−	17.3356i	1.89314	−	0.655223i
$701$	−29.6207	−	19.0361i	−1.11876	−	0.718982i	−0.155574	−	0.987824i	$-0.549723\pi$
$701$	−29.6207	−	19.0361i	−1.11876	−	0.718982i	−0.963184	+	0.268842i	$0.913359\pi$
$702$	3.85059	+	3.73481i	0.145331	+	0.140961i
$703$	8.60472	−	9.93037i	0.324533	−	0.374531i
$704$	5.76766	−	5.49945i	0.217377	−	0.207268i
$705$	−21.2177	−	10.1738i	−0.799104	−	0.383169i
$706$	4.54684	−	13.1372i	0.171123	−	0.494426i
$707$	−16.4967	+	23.1664i	−0.620424	+	0.871264i
$708$	−4.36681	−	4.75482i	−0.164115	−	0.178697i
$709$	−6.12034	+	4.35828i	−0.229854	+	0.163679i	−0.689182	−	0.724588i	$-0.742030\pi$
$709$	−6.12034	+	4.35828i	−0.229854	+	0.163679i	0.459327	+	0.888267i	$0.348090\pi$
$710$	−0.161877	+	1.12588i	−0.00607513	+	0.0422535i
$711$	11.4103	+	24.3270i	0.427919	+	0.912332i
$712$		−	27.1041i		−	1.01577i
$713$	14.9472	+	40.4293i	0.559777	+	1.51409i
$714$	−0.714554	+	10.7598i	−0.0267415	+	0.402674i
$715$	−16.4340	−	8.47232i	−0.614597	−	0.316847i
$716$	−0.0762838	−	0.190548i	−0.00285086	−	0.00712110i
$717$	7.23290	−	13.4078i	0.270118	−	0.500723i
$718$	−9.43102	−	2.28794i	−0.351963	−	0.0853852i
$719$	−30.9786	+	14.1474i	−1.15531	+	0.527610i	−0.898552	−	0.438867i	$-0.855380\pi$
$719$	−30.9786	+	14.1474i	−1.15531	+	0.527610i	−0.256753	+	0.966477i	$0.582653\pi$
$720$	15.7784	−	31.3857i	0.588025	−	1.16968i
$721$	−2.19443	−	15.2626i	−0.0817249	−	0.568409i
$722$	3.64404	+	3.82176i	0.135617	+	0.142231i
$723$	36.5859	+	9.60394i	1.36064	+	0.357174i
$724$	−27.6754	−	1.31834i	−1.02855	−	0.0489958i
$725$	31.2980	+	1.49091i	1.16238	+	0.0553710i
$726$	−1.39431	−	5.09972i	−0.0517478	−	0.189269i
$727$	26.1822	+	27.4591i	0.971043	+	1.01840i	0.999823	+	0.0188149i	$0.00598933\pi$
$727$	26.1822	+	27.4591i	0.971043	+	1.01840i	−0.0287799	+	0.999586i	$0.509162\pi$
$728$	1.60431	+	11.1582i	0.0594596	+	0.413551i
$729$	8.39387	+	25.6621i	0.310884	+	0.950448i
$730$	5.32131	−	2.43016i	0.196950	−	0.0899442i
$731$	8.23812	+	1.99855i	0.304698	+	0.0739189i
$732$	22.8704	+	37.0953i	0.845315	+	1.37108i
$733$	−2.91125	−	7.27196i	−0.107530	−	0.268596i	0.864838	−	0.502051i	$-0.167421\pi$
$733$	−2.91125	−	7.27196i	−0.107530	−	0.268596i	−0.972368	+	0.233455i	$0.924997\pi$
$734$	−1.34830	−	0.695097i	−0.0497667	−	0.0256565i
$735$	−6.83539	+	3.36351i	−0.252127	+	0.124065i
$736$	−1.56634	+	21.0503i	−0.0577360	+	0.775924i
$737$		−	18.2778i		−	0.673272i
$738$	−5.69118	−	3.96603i	−0.209495	−	0.145992i
$739$	0.0759584	−	0.528302i	0.00279417	−	0.0194339i	−0.988377	−	0.152025i	$-0.951421\pi$
$739$	0.0759584	−	0.528302i	0.00279417	−	0.0194339i	0.991171	+	0.132591i	$0.0423297\pi$
$740$	−30.6178	+	21.8029i	−1.12553	+	0.801489i
$741$	10.5339	−	2.34770i	0.386973	−	0.0862450i
$742$	−4.88063	+	6.85389i	−0.179174	+	0.251614i
$743$	13.0343	−	37.6600i	0.478181	−	1.38161i	−0.405745	−	0.913986i	$-0.632988\pi$
$743$	13.0343	−	37.6600i	0.478181	−	1.38161i	0.883926	−	0.467627i	$-0.154891\pi$
$744$	1.87976	+	24.5282i	0.0689153	+	0.899247i
$745$	1.12918	−	1.07667i	0.0413700	−	0.0394462i
$746$	2.55965	−	2.95399i	0.0937155	−	0.108153i
$747$	−30.3281	−	25.7439i	−1.10965	−	0.941920i
$748$	−15.4605	−	9.93588i	−0.565293	−	0.363292i
$749$	−5.93948	+	2.05568i	−0.217024	+	0.0751127i
$750$	−2.45285	−	14.1461i	−0.0895655	−	0.516543i
$751$	−17.9707	−	22.8516i	−0.655759	−	0.833866i	0.338488	−	0.940971i	$-0.390084\pi$
$751$	−17.9707	−	22.8516i	−0.655759	−	0.833866i	−0.994248	+	0.107105i	$0.965842\pi$
$752$	−9.91657	−	3.43216i	−0.361620	−	0.125158i
$753$	−6.61231	+	40.5834i	−0.240966	+	1.47894i
$754$	−0.750646	+	3.09420i	−0.0273369	+	0.112684i
$755$	14.1218	−	30.9224i	0.513944	−	1.12538i
$756$	−9.08477	+	25.5410i	−0.330410	+	0.928919i
$757$	−15.4754	−	24.0802i	−0.562463	−	0.875209i	0.437246	−	0.899342i	$-0.355954\pi$
$757$	−15.4754	−	24.0802i	−0.562463	−	0.875209i	−0.999709	+	0.0241331i	$0.992317\pi$
$758$	4.12027	−	7.13652i	0.149655	−	0.259210i
$759$	13.2822	+	8.49442i	0.482112	+	0.308328i
$760$	7.66151	+	13.2701i	0.277912	+	0.481358i
$761$	13.8824	−	26.9282i	0.503238	−	0.976146i	−0.491222	−	0.871034i	$-0.663450\pi$
$761$	13.8824	−	26.9282i	0.503238	−	0.976146i	0.994460	−	0.105111i	$-0.0335199\pi$
$762$	−10.4996	+	3.41533i	−0.380361	+	0.123724i
$763$	3.48093	+	4.88829i	0.126018	+	0.176968i
$764$	−5.44458	+	1.59867i	−0.196978	+	0.0578379i
$765$	−60.2146	−	13.9608i	−2.17706	−	0.504753i
$766$	2.21924	−	1.92299i	0.0801846	−	0.0694803i
$767$	−1.89420	+	4.73149i	−0.0683957	+	0.170844i
$768$	2.41817	−	6.58549i	0.0872582	−	0.237633i
$769$	3.14775	−	16.3321i	0.113511	−	0.588950i	−0.879977	−	0.475016i	$-0.842442\pi$
$769$	3.14775	−	16.3321i	0.113511	−	0.588950i	0.993488	−	0.113935i	$-0.0363454\pi$
$770$	−0.413691	+	8.68444i	−0.0149084	+	0.312965i
$771$	29.6962	+	21.9954i	1.06948	+	0.792146i
$772$	5.93268	+	17.1414i	0.213522	+	0.616931i
$773$	1.21930	+	0.358019i	0.0438553	+	0.0128771i	0.303587	−	0.952804i	$-0.401816\pi$
$773$	1.21930	+	0.358019i	0.0438553	+	0.0128771i	−0.259731	+	0.965681i	$0.583634\pi$
$774$	−1.72729	−	0.973957i	−0.0620863	−	0.0350082i
$775$	−59.7966	−	69.0090i	−2.14796	−	2.47887i
$776$	28.2347	+	2.69609i	1.01357	+	0.0967840i
$777$	19.1907	−	17.6246i	0.688463	−	0.632281i
$778$	0.0175743	+	0.184047i	0.000630070	+	0.00659839i
$779$	−12.9563	+	5.18691i	−0.464207	+	0.185840i
$780$	−30.8671	−	0.577673i	−1.10522	−	0.0206840i
$781$	1.16377	+	0.671906i	0.0416431	+	0.0240427i
$782$	10.3318	−	1.70688i	0.369466	−	0.0610379i
$783$	−10.5976	+	12.0214i	−0.378728	+	0.429608i
$784$	−2.85804	+	1.83675i	−0.102073	+	0.0655981i
$785$	−14.2298	+	18.0947i	−0.507883	+	0.645826i
$786$	5.28875	−	3.26068i	0.188644	−	0.116305i
$787$	−12.1248	+	12.7161i	−0.432202	+	0.453280i	−0.903433	−	0.428730i	$-0.858961\pi$
$787$	−12.1248	+	12.7161i	−0.432202	+	0.453280i	0.471231	+	0.882010i	$0.343810\pi$
$788$	−36.2483	−	25.8123i	−1.29129	−	0.919525i
$789$	0.0506284	+	0.0213762i	0.00180242	+	0.000761014i
$790$	13.3587	+	5.34801i	0.475280	+	0.190273i
$791$	7.23062	−	24.6252i	0.257091	−	0.875573i
$792$	5.96131	+	6.73992i	0.211826	+	0.239493i
$793$	18.6000	−	28.9421i	0.660505	−	1.02777i
$794$	0.619494	+	1.20165i	0.0219850	+	0.0426450i
$795$	−34.2770	−	33.9300i	−1.21568	−	1.20337i
$796$	11.9882	−	2.90830i	0.424910	−	0.103082i
$797$	−36.2559	+	28.5119i	−1.28425	+	1.00995i	−0.285581	+	0.958354i	$0.592187\pi$
$797$	−36.2559	+	28.5119i	−1.28425	+	1.00995i	−0.998668	+	0.0515906i	$0.983571\pi$
$798$	−3.06191	−	4.04715i	−0.108390	−	0.143268i
$799$	−1.75517	+	18.3810i	−0.0620935	+	0.650272i
$800$	−12.5981	−	42.9052i	−0.445410	−	1.51693i
$801$	−51.4195	−	1.92529i	−1.81682	−	0.0680268i
$802$	−9.93175	−	1.42797i	−0.350702	−	0.0504234i
$803$	−0.328850	−	6.90341i	−0.0116049	−	0.243616i
$804$	−13.4747	−	27.3835i	−0.475216	−	0.965743i
$805$	33.7797	+	41.1521i	1.19058	+	1.45042i
$806$	8.03556	−	4.63933i	0.283040	−	0.163413i
$807$	−0.268132	+	14.3272i	−0.00943870	+	0.504343i
$808$	12.3899	+	9.74351i	0.435875	+	0.342776i
$809$	7.99865	+	3.65286i	0.281218	+	0.128428i	0.551031	−	0.834485i	$-0.314235\pi$
$809$	7.99865	+	3.65286i	0.281218	+	0.128428i	−0.269813	+	0.962913i	$0.586962\pi$
$810$	12.6664	+	6.97324i	0.445052	+	0.245015i
$811$	10.4674	+	22.9204i	0.367560	+	0.804844i	0.999554	+	0.0298704i	$0.00950945\pi$
$811$	10.4674	+	22.9204i	0.367560	+	0.804844i	−0.631994	+	0.774973i	$0.717763\pi$
$812$	−15.7994	+	3.04508i	−0.554450	+	0.106861i
$813$	16.2080	−	33.8020i	0.568439	−	1.18549i
$814$	−0.974166	−	4.01557i	−0.0341445	−	0.140745i
$815$	−54.2144	−	10.4490i	−1.89905	−	0.366012i
$816$	−27.3868	−	3.13326i	−0.958729	−	0.109686i
$817$	−3.54599	+	1.82809i	−0.124059	+	0.0639567i
$818$	4.81759	+	4.17447i	0.168443	+	0.145957i
$819$	21.2824	−	2.25095i	0.743666	−	0.0786546i
$820$	39.5160	−	5.68154i	1.37996	−	0.198408i
$821$	7.84044	+	40.6801i	0.273633	+	1.41974i	0.815245	+	0.579116i	$0.196602\pi$
$821$	7.84044	+	40.6801i	0.273633	+	1.41974i	−0.541612	+	0.840629i	$0.682186\pi$
$822$	−1.85736	−	4.90345i	−0.0647830	−	0.171028i
$823$	−34.6777	−	33.0652i	−1.20879	−	1.15258i	−0.983999	−	0.178172i	$-0.942982\pi$
$823$	−34.6777	−	33.0652i	−1.20879	−	1.15258i	−0.224791	−	0.974407i	$-0.572170\pi$
$824$	−8.50723	+	0.812342i	−0.296363	+	0.0282993i
$825$	−32.6716	−	6.93339i	−1.13748	−	0.241390i
$826$	2.39385	−	0.114033i	0.0832928	−	0.00396772i
$827$	23.7876			0.827177			0.413588	−	0.910464i	$-0.364275\pi$
$827$	23.7876			0.827177			0.413588	+	0.910464i	$0.364275\pi$
$828$	26.1613	+	2.93438i	0.909170	+	0.101977i
$829$	10.6534			0.370006			0.185003	−	0.982738i	$-0.440770\pi$
$829$	10.6534			0.370006			0.185003	+	0.982738i	$0.440770\pi$
$830$	−21.2795	+	1.01367i	−0.738622	+	0.0351849i
$831$	13.5789	+	41.7452i	0.471048	+	1.44812i
$832$	−10.4575	+	0.998568i	−0.362548	+	0.0346191i
$833$	4.32643	+	4.12525i	0.149902	+	0.142931i
$834$	7.16507	+	1.16742i	0.248106	+	0.0404243i
$835$	−0.413061	−	2.14316i	−0.0142946	−	0.0741672i
$836$	8.56101	−	1.23089i	0.296089	−	0.0425711i
$837$	46.6663	−	1.82380i	1.61302	−	0.0630396i
$838$	2.78525	+	2.41344i	0.0962150	+	0.0833708i
$839$	14.9245	−	7.69412i	0.515252	−	0.265631i	−0.180931	−	0.983496i	$-0.557911\pi$
$839$	14.9245	−	7.69412i	0.515252	−	0.265631i	0.696182	+	0.717865i	$0.254881\pi$
$840$	12.1031	+	27.8708i	0.417597	+	0.961633i
$841$	19.1359	+	3.68814i	0.659858	+	0.127177i
$842$	1.30077	+	5.36183i	0.0448274	+	0.184781i
$843$	8.33498	+	12.1810i	0.287072	+	0.419534i
$844$	−44.1667	+	8.51244i	−1.52028	+	0.293010i
$845$	−10.9019	−	23.8718i	−0.375036	−	0.821215i
$846$	1.56442	−	4.02597i	0.0537859	−	0.138416i
$847$	−19.1862	−	8.76202i	−0.659244	−	0.301067i
$848$	−16.9069	−	13.2957i	−0.580586	−	0.456578i
$849$	28.2510	−	15.6133i	0.969570	−	0.535846i
$850$	−19.2117	+	11.0919i	−0.658957	+	0.380449i
$851$	−20.9139	−	14.2427i	−0.716920	−	0.488234i
$852$	2.23889	+	0.148684i	0.0767030	+	0.00509384i
$853$	−0.880891	−	18.4922i	−0.0301611	−	0.633160i	−0.962452	−	0.271451i	$-0.912496\pi$
$853$	−0.880891	−	18.4922i	−0.0301611	−	0.633160i	0.932291	−	0.361709i	$-0.117807\pi$
$854$	−16.0130	−	2.30232i	−0.547953	−	0.0787838i
$855$	25.7192	−	13.5921i	0.879577	−	0.464841i
$856$	0.981389	+	3.34230i	0.0335432	+	0.114238i
$857$	−0.140114	+	1.46734i	−0.00478621	+	0.0501235i	−0.997550	−	0.0699642i	$-0.977712\pi$
$857$	−0.140114	+	1.46734i	−0.00478621	+	0.0501235i	0.992763	+	0.120088i	$0.0383176\pi$
$858$	1.32010	−	3.12660i	0.0450676	−	0.106740i
$859$	−27.9384	+	21.9710i	−0.953245	+	0.749641i	−0.968182	−	0.250248i	$-0.919488\pi$
$859$	−27.9384	+	21.9710i	−0.953245	+	0.749641i	0.0149363	+	0.999888i	$0.495245\pi$
$860$	11.0906	−	2.69054i	0.378185	−	0.0917468i
$861$	−26.6947	+	7.29858i	−0.909753	+	0.248735i
$862$	−1.35765	−	2.63347i	−0.0462416	−	0.0896963i
$863$	0.570000	−	0.886937i	0.0194030	−	0.0301917i	−0.831417	−	0.555650i	$-0.812470\pi$
$863$	0.570000	−	0.886937i	0.0194030	−	0.0301917i	0.850820	+	0.525458i	$0.176106\pi$
$864$	21.1589	+	8.68106i	0.719839	+	0.295336i
$865$	0.0629825	−	0.214499i	0.00214147	−	0.00729317i
$866$	−9.51976	−	3.81114i	−0.323495	−	0.129508i
$867$	2.35889	+	18.9123i	0.0801122	+	0.642296i
$868$	38.1953	+	27.1988i	1.29643	+	0.923187i
$869$	11.7313	−	12.3034i	0.397956	−	0.417365i
$870$	0.247878	+	8.57850i	0.00840385	+	0.290838i
$871$	−14.8937	+	18.9389i	−0.504653	+	0.641719i
$872$	2.79795	−	1.79813i	0.0947505	−	0.0608924i
$873$	7.12040	−	53.3730i	0.240989	−	1.80640i
$874$	−3.14869	+	3.79127i	−0.106506	+	0.128242i
$875$	−49.6046	−	28.6392i	−1.67694	−	0.968182i
$876$	−5.58199	−	10.1001i	−0.188598	−	0.341252i
$877$	−16.0329	+	6.41862i	−0.541394	+	0.216741i	−0.626209	−	0.779655i	$-0.715394\pi$
$877$	−16.0329	+	6.41862i	−0.541394	+	0.216741i	0.0848150	+	0.996397i	$0.472970\pi$
$878$	0.985195	+	10.3174i	0.0332487	+	0.348196i
$879$	−3.41741	−	15.3336i	−0.115267	−	0.517190i
$880$	−22.1243	−	2.11261i	−0.745810	−	0.0712162i
$881$	−29.7522	−	34.3359i	−1.00238	−	1.15681i	−0.987612	−	0.156915i	$-0.949845\pi$
$881$	−29.7522	−	34.3359i	−1.00238	−	1.15681i	−0.0147663	−	0.999891i	$-0.504700\pi$
$882$	−0.711465	−	1.20384i	−0.0239563	−	0.0405354i
$883$	−4.39522	−	1.29055i	−0.147911	−	0.0434306i	0.206939	−	0.978354i	$-0.433650\pi$
$883$	−4.39522	−	1.29055i	−0.147911	−	0.0434306i	−0.354850	+	0.934923i	$0.615468\pi$
$884$	7.92343	+	22.8933i	0.266494	+	0.769983i
$885$	−1.56147	+	13.6483i	−0.0524884	+	0.458784i
$886$	0.329541	−	6.91791i	0.0110711	−	0.232412i
$887$	−0.119055	+	0.617717i	−0.00399748	+	0.0207409i	−0.983873	−	0.178870i	$-0.942756\pi$
$887$	−0.119055	+	0.617717i	−0.00399748	+	0.0207409i	0.979875	+	0.199611i	$0.0639679\pi$
$888$	−9.25091	−	11.0887i	−0.310440	−	0.372114i
$889$	−16.3713	+	40.8936i	−0.549076	+	1.37153i
$890$	−20.8251	+	18.0450i	−0.698057	+	0.604870i
$891$	13.2099	−	10.8305i	0.442547	−	0.362837i
$892$	23.4286	−	6.87927i	0.784449	−	0.230335i
$893$	−5.04058	−	7.07851i	−0.168677	−	0.236873i
$894$	0.212891	+	0.191562i	0.00712014	+	0.00640679i
$895$	−0.200132	+	0.388203i	−0.00668969	+	0.0129762i
$896$	15.0195	+	26.0145i	0.501766	+	0.869083i
$897$	−6.84085	−	19.6246i	−0.228409	−	0.655247i
$898$	−0.202608	+	0.350927i	−0.00676111	+	0.0117106i
$899$	14.9864	+	23.3192i	0.499823	+	0.777740i
$900$	−54.0595	+	13.6986i	−1.80198	+	0.456618i
$901$	−15.7219	+	34.4261i	−0.523772	+	1.14690i
$902$	−1.03468	+	4.26500i	−0.0344510	+	0.142009i
$903$	−7.39812	+	2.80231i	−0.246194	+	0.0932550i
$904$	−13.4418	−	4.65226i	−0.447069	−	0.154732i
$905$	36.4451	+	46.3437i	1.21148	+	1.54052i
$906$	5.85750	+	2.15086i	0.194603	+	0.0714574i
$907$	8.02706	−	2.77819i	0.266534	−	0.0922484i	−0.190532	−	0.981681i	$-0.561021\pi$
$907$	8.02706	−	2.77819i	0.266534	−	0.0922484i	0.457066	+	0.889433i	$0.348900\pi$
$908$	6.42352	+	4.12815i	0.213172	+	0.136997i
$909$	19.3647	−	22.8129i	0.642285	−	0.756657i
$910$	7.50517	−	8.66143i	0.248794	−	0.287123i
$911$	15.7883	−	15.0541i	0.523090	−	0.498765i	−0.381897	−	0.924205i	$-0.624729\pi$
$911$	15.7883	−	15.0541i	0.523090	−	0.498765i	0.904987	+	0.425440i	$0.139881\pi$
$912$	10.7063	−	7.32594i	0.354522	−	0.242586i
$913$	−8.23181	+	23.7842i	−0.272433	+	0.787143i
$914$	−4.79090	+	6.72788i	−0.158469	+	0.222539i
$915$	27.7859	−	88.4712i	0.918574	−	2.92477i
$916$	−0.232644	+	0.165665i	−0.00768678	+	0.00547373i
$917$	3.52762	−	24.5351i	0.116492	−	0.810221i
$918$	1.71053	−	11.2163i	0.0564560	−	0.370194i
$919$			46.3980i			1.53053i	0.643715	+	0.765265i	$0.277392\pi$
$919$			46.3980i			1.53053i	−0.643715	+	0.765265i	$0.722608\pi$
$920$	23.6726	−	17.6152i	0.780462	−	0.580755i
$921$	−3.88151	−	2.59839i	−0.127900	−	0.0856198i
$922$	10.8801	+	5.60910i	0.358318	+	0.184726i
$923$	−0.658362	−	1.64451i	−0.0216702	−	0.0541296i
$924$	17.1437	−	0.495373i	0.563988	−	0.0162966i
$925$	52.0915	+	12.6373i	1.71276	+	0.415510i
$926$	3.18780	−	1.45582i	0.104758	−	0.0478412i
$927$	0.936809	+	16.1969i	0.0307689	+	0.531976i
$928$	1.93187	+	13.4365i	0.0634167	+	0.441073i
$929$	−10.2684	−	10.7692i	−0.336895	−	0.353325i	0.533394	−	0.845867i	$-0.320916\pi$
$929$	−10.2684	−	10.7692i	−0.336895	−	0.353325i	−0.870289	+	0.492542i	$0.836068\pi$
$930$	17.5944	−	17.7744i	0.576944	−	0.582844i
$931$	−2.81015	−	0.133864i	−0.0920989	−	0.00438721i
$932$	18.9505	+	0.902723i	0.620744	+	0.0295697i
$933$	−10.7945	+	10.9049i	−0.353396	+	0.357011i
$934$	−0.433127	−	0.454251i	−0.0141724	−	0.0148635i
$935$	5.56546	+	38.7086i	0.182010	+	1.26591i
$936$	−0.684884	−	11.8413i	−0.0223861	−	0.387044i
$937$	−7.36347	+	3.36278i	−0.240554	+	0.109857i	−0.532045	−	0.846716i	$-0.678576\pi$
$937$	−7.36347	+	3.36278i	−0.240554	+	0.109857i	0.291490	+	0.956574i	$0.405849\pi$
$938$	11.0102	+	2.67105i	0.359496	+	0.0872128i
$939$	−3.91957	+	0.113257i	−0.127910	+	0.00369601i
$940$	9.23877	+	23.0773i	0.301335	+	0.752699i
$941$	−7.56439	−	3.89972i	−0.246592	−	0.127127i	0.330500	−	0.943806i	$-0.392783\pi$
$941$	−7.56439	−	3.89972i	−0.246592	−	0.127127i	−0.577093	+	0.816679i	$0.695813\pi$
$942$	−3.51128	−	2.35055i	−0.114404	−	0.0765850i
$943$	12.8119	+	23.6244i	0.417214	+	0.769317i
$944$			6.12627i			0.199393i
$945$	53.7338	−	20.9812i	1.74796	−	0.682520i
$946$	−0.178543	+	1.24180i	−0.00580495	+	0.0403743i
$947$	−34.6828	+	24.6975i	−1.12704	+	0.802561i	−0.982375	−	0.186920i	$-0.940150\pi$
$947$	−34.6828	+	24.6975i	−1.12704	+	0.802561i	−0.144664	+	0.989481i	$0.546210\pi$
$948$	8.50534	−	27.0813i	0.276241	−	0.879559i
$949$	−5.28450	+	7.42105i	−0.171542	+	0.240897i
$950$	3.41464	−	9.86594i	0.110785	−	0.320093i
$951$	29.9158	−	20.4703i	0.970086	−	0.663794i
$952$	17.2562	−	16.4538i	0.559277	−	0.533270i
$953$	13.6947	−	15.8045i	0.443615	−	0.511960i	−0.489270	−	0.872132i	$-0.662737\pi$
$953$	13.6947	−	15.8045i	0.443615	−	0.511960i	0.932886	+	0.360173i	$0.117282\pi$
$954$	5.72911	−	6.74930i	0.185487	−	0.218517i
$955$	10.1579	+	6.52807i	0.328701	+	0.211243i
$956$	−15.2084	+	5.26368i	−0.491875	+	0.170239i
$957$	9.51765	+	3.49485i	0.307662	+	0.112972i
$958$	3.41282	+	4.33975i	0.110263	+	0.140211i
$959$	−19.7683	−	6.84188i	−0.638352	−	0.220936i
$960$	−26.4795	+	10.0301i	−0.854621	+	0.323719i
$961$	11.7362	−	48.3772i	0.378586	−	1.56055i
$962$	−2.26269	+	4.95459i	−0.0729520	+	0.159742i
$963$	6.41044	−	1.62439i	0.206574	−	0.0523453i
$964$	−21.6034	−	33.6155i	−0.695798	−	1.08268i
$965$	19.2991	−	33.4270i	0.621259	−	1.07605i
$966$	−7.05788	+	6.75958i	−0.227084	+	0.217486i
$967$	16.7702	+	29.0469i	0.539295	+	0.934086i	0.998942	+	0.0459843i	$0.0146424\pi$
$967$	16.7702	+	29.0469i	0.539295	+	0.934086i	−0.459648	+	0.888101i	$0.652024\pi$
$968$	−5.35661	+	10.3904i	−0.172168	+	0.333959i
$969$	−16.9686	−	15.2686i	−0.545111	−	0.490497i
$970$	−16.7263	−	23.4888i	−0.537048	−	0.754179i
$971$	13.7785	−	4.04573i	0.442173	−	0.129834i	−0.0530649	−	0.998591i	$-0.516899\pi$
$971$	13.7785	−	4.04573i	0.442173	−	0.129834i	0.495238	+	0.868757i	$0.335081\pi$
$972$	11.8063	−	25.9647i	0.378689	−	0.832817i
$973$	21.8882	−	18.9662i	0.701702	−	0.608028i
$974$	−5.11275	+	12.7710i	−0.163823	+	0.409210i
$975$	28.2035	+	33.8066i	0.903236	+	1.08268i
$976$	7.82638	−	40.6071i	0.250516	−	1.29980i
$977$	−2.15010	+	45.1362i	−0.0687878	+	1.44403i	0.655843	+	0.754897i	$0.272313\pi$
$977$	−2.15010	+	45.1362i	−0.0687878	+	1.44403i	−0.724631	+	0.689137i	$0.757990\pi$
$978$	1.15196	−	10.0689i	0.0368357	−	0.321968i
$979$	10.6476	+	30.7641i	0.340297	+	0.983224i
$980$	7.72180	+	2.26733i	0.246664	+	0.0724271i
$981$	−3.21251	−	5.43575i	−0.102568	−	0.173550i
$982$	10.0464	+	11.5942i	0.320593	+	0.369984i
$983$	−56.8866	−	5.43201i	−1.81440	−	0.173254i	−0.868067	−	0.496447i	$-0.834638\pi$
$983$	−56.8866	−	5.43201i	−1.81440	−	0.173254i	−0.946333	+	0.323192i	$0.895244\pi$
$984$	3.33651	+	14.9706i	0.106364	+	0.477246i
$985$	9.00097	+	94.2624i	0.286795	+	3.00345i
$986$	6.25196	−	2.50291i	0.199103	−	0.0797088i
$987$	−8.33512	−	15.0817i	−0.265310	−	0.480056i
$988$	−9.87362	−	5.70054i	−0.314122	−	0.181358i
$989$	4.28781	+	6.37460i	0.136344	+	0.202701i
$990$	1.20968	−	9.06752i	0.0384462	−	0.288185i
$991$	10.5824	−	6.80090i	0.336161	−	0.216038i	−0.361659	−	0.932310i	$-0.617790\pi$
$991$	10.5824	−	6.80090i	0.336161	−	0.216038i	0.697821	+	0.716273i	$0.254153\pi$
$992$	24.4538	−	31.0955i	0.776409	−	0.987284i
$993$	1.35960	+	47.0527i	0.0431456	+	1.49317i
$994$	−0.574813	+	0.602846i	−0.0182319	+	0.0191211i
$995$	−21.3824	−	15.2263i	−0.677867	−	0.482707i
$996$	5.20137	+	41.7018i	0.164812	+	1.32137i
$997$	−9.81201	−	3.92814i	−0.310749	−	0.124405i	0.211046	−	0.977476i	$-0.432313\pi$
$997$	−9.81201	−	3.92814i	−0.310749	−	0.124405i	−0.521795	+	0.853071i	$0.674737\pi$
$998$	−2.31747	+	7.89259i	−0.0733583	+	0.249836i
$999$	−21.6937	+	16.7624i	−0.686359	+	0.530337i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	207.2.o.a.11.11	✓	440
3.2	odd	2		621.2.s.a.494.12		440
9.4	even	3		621.2.s.a.287.12		440
9.5	odd	6	inner	207.2.o.a.149.11	yes	440
23.21	odd	22	inner	207.2.o.a.182.11	yes	440
69.44	even	22		621.2.s.a.251.12		440
207.67	odd	66		621.2.s.a.44.12		440
207.113	even	66	inner	207.2.o.a.113.11	yes	440

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
207.2.o.a.11.11	✓	440	1.1	even	1	trivial
207.2.o.a.113.11	yes	440	207.113	even	66	inner
207.2.o.a.149.11	yes	440	9.5	odd	6	inner
207.2.o.a.182.11	yes	440	23.21	odd	22	inner
621.2.s.a.44.12		440	207.67	odd	66
621.2.s.a.251.12		440	69.44	even	22
621.2.s.a.287.12		440	9.4	even	3
621.2.s.a.494.12		440	3.2	odd	2

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:	\( N \)	\(=\)	\( 207 = 3^{2} \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	207.o (of order \(66\), degree \(20\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.412156 + 0.0196334i) q^{2} +(1.15855 - 1.28754i) q^{3} +(-1.82146 + 0.173928i) q^{4} +(2.81788 + 2.68684i) q^{5} +(-0.452223 + 0.553415i) q^{6} +(0.539603 + 2.79973i) q^{7} +(1.56416 - 0.224892i) q^{8} +(-0.315538 - 2.98336i) q^{9} +O(q^{10})\)	\(q+(-0.412156 + 0.0196334i) q^{2} +(1.15855 - 1.28754i) q^{3} +(-1.82146 + 0.173928i) q^{4} +(2.81788 + 2.68684i) q^{5} +(-0.452223 + 0.553415i) q^{6} +(0.539603 + 2.79973i) q^{7} +(1.56416 - 0.224892i) q^{8} +(-0.315538 - 2.98336i) q^{9} +(-1.21416 - 1.05207i) q^{10} +(-1.68703 + 0.869723i) q^{11} +(-1.88630 + 2.54671i) q^{12} +(2.45673 + 0.473497i) q^{13} +(-0.277369 - 1.14333i) q^{14} +(6.72407 - 0.515310i) q^{15} +(2.95309 - 0.569162i) q^{16} +(-2.19831 - 4.81363i) q^{17} +(0.188625 + 1.22342i) q^{18} +(2.26539 + 1.03457i) q^{19} +(-5.59996 - 4.40386i) q^{20} +(4.22993 + 2.54885i) q^{21} +(0.678243 - 0.391584i) q^{22} +(1.47338 - 4.56390i) q^{23} +(1.52259 - 2.27447i) q^{24} +(0.483411 + 10.1480i) q^{25} +(-1.02185 - 0.146921i) q^{26} +(-4.20677 - 3.05009i) q^{27} +(-1.46982 - 5.00573i) q^{28} +(0.293166 - 3.07018i) q^{29} +(-2.76125 + 0.344405i) q^{30} +(-7.06488 + 5.55588i) q^{31} +(-4.27735 + 1.03767i) q^{32} +(-0.834694 + 3.17974i) q^{33} +(1.00056 + 1.94081i) q^{34} +(-6.00189 + 9.33912i) q^{35} +(1.09363 + 5.37918i) q^{36} +(1.48644 - 5.06234i) q^{37} +(-0.954008 - 0.381927i) q^{38} +(3.45589 - 2.61459i) q^{39} +(5.01185 + 3.56892i) q^{40} +(-3.86707 + 4.05566i) q^{41} +(-1.79343 - 0.967478i) q^{42} +(-0.990237 + 1.25919i) q^{43} +(2.92158 - 1.87758i) q^{44} +(7.12667 - 9.25454i) q^{45} +(-0.517659 + 1.90997i) q^{46} +(-3.02178 - 1.74463i) q^{47} +(2.68847 - 4.46163i) q^{48} +(-1.04873 + 0.419849i) q^{49} +(-0.398482 - 4.17309i) q^{50} +(-8.74461 - 2.74640i) q^{51} +(-4.55719 - 0.435159i) q^{52} +(-4.68343 - 5.40497i) q^{53} +(1.79373 + 1.17452i) q^{54} +(-7.09064 - 2.08200i) q^{55} +(1.47366 + 4.25786i) q^{56} +(3.95662 - 1.71819i) q^{57} +(-0.0605523 + 1.27115i) q^{58} +(-0.385512 + 2.00023i) q^{59} +(-12.1580 + 2.10812i) q^{60} +(5.11063 - 12.7657i) q^{61} +(2.80275 - 2.42860i) q^{62} +(8.18233 - 2.49325i) q^{63} +(-4.02867 + 1.18292i) q^{64} +(5.65057 + 7.93511i) q^{65} +(0.281595 - 1.32694i) q^{66} +(-4.41270 + 8.55943i) q^{67} +(4.84136 + 8.38547i) q^{68} +(-4.16923 - 7.18453i) q^{69} +(2.29036 - 3.96701i) q^{70} +(-0.382777 - 0.595613i) q^{71} +(-1.16448 - 4.59548i) q^{72} +(-1.51265 + 3.31223i) q^{73} +(-0.513254 + 2.11566i) q^{74} +(13.6261 + 11.1346i) q^{75} +(-4.30625 - 1.49041i) q^{76} +(-3.34531 - 4.25391i) q^{77} +(-1.37303 + 1.14547i) q^{78} +(-8.46405 + 2.92944i) q^{79} +(9.85069 + 6.33066i) q^{80} +(-8.80087 + 1.88273i) q^{81} +(1.51421 - 1.74749i) q^{82} +(9.59700 - 9.15072i) q^{83} +(-8.14795 - 3.90692i) q^{84} +(6.73889 - 19.4707i) q^{85} +(0.383410 - 0.538424i) q^{86} +(-3.61334 - 3.93441i) q^{87} +(-2.44318 + 1.73978i) q^{88} +(2.44096 - 16.9773i) q^{89} +(-2.75560 + 3.95424i) q^{90} +7.13369i q^{91} +(-1.88991 + 8.56920i) q^{92} +(-1.03155 + 15.5331i) q^{93} +(1.27970 + 0.659731i) q^{94} +(3.60387 + 9.00204i) q^{95} +(-3.61946 + 6.70948i) q^{96} +(17.4427 + 4.23155i) q^{97} +(0.423998 - 0.193633i) q^{98} +(3.12702 + 4.75858i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 440 q - 27 q^{2} - 16 q^{3} - 29 q^{4} - 33 q^{5} - 25 q^{6} - 11 q^{7} - 16 q^{9}+O(q^{10}) \) 440 * q - 27 * q^2 - 16 * q^3 - 29 * q^4 - 33 * q^5 - 25 * q^6 - 11 * q^7 - 16 * q^9	\( 440 q - 27 q^{2} - 16 q^{3} - 29 q^{4} - 33 q^{5} - 25 q^{6} - 11 q^{7} - 16 q^{9} - 44 q^{10} - 33 q^{11} - 22 q^{12} - 9 q^{13} - 33 q^{14} + 3 q^{16} - 39 q^{18} - 44 q^{19} - 33 q^{20} - 55 q^{21} - 27 q^{23} + 52 q^{24} + 11 q^{25} - 79 q^{27} - 44 q^{28} + 27 q^{29} - 66 q^{30} - 3 q^{31} - 33 q^{32} - 11 q^{34} + 23 q^{36} - 44 q^{37} - 33 q^{38} - 40 q^{39} - 77 q^{40} + 9 q^{41} - 22 q^{42} - 11 q^{43} - 36 q^{46} - 120 q^{47} - 56 q^{48} + 35 q^{49} - 3 q^{50} - 22 q^{51} - 38 q^{52} + 42 q^{54} - 44 q^{55} + 165 q^{56} + 11 q^{57} - 10 q^{58} - 9 q^{59} + 88 q^{60} - 11 q^{61} + 33 q^{63} - 22 q^{64} + 198 q^{65} + 33 q^{66} - 11 q^{67} + 3 q^{69} - 70 q^{70} + 14 q^{72} - 36 q^{73} + 231 q^{74} - 13 q^{75} - 11 q^{76} + 39 q^{77} + 3 q^{78} - 11 q^{79} + 172 q^{81} - 10 q^{82} + 66 q^{83} - 110 q^{84} + q^{85} - 33 q^{86} - 196 q^{87} - 99 q^{88} + 418 q^{90} + 63 q^{92} - 188 q^{93} - 42 q^{94} - 93 q^{95} - 82 q^{96} + 22 q^{97} + 242 q^{99}+O(q^{100}) \) 440 * q - 27 * q^2 - 16 * q^3 - 29 * q^4 - 33 * q^5 - 25 * q^6 - 11 * q^7 - 16 * q^9 - 44 * q^10 - 33 * q^11 - 22 * q^12 - 9 * q^13 - 33 * q^14 + 3 * q^16 - 39 * q^18 - 44 * q^19 - 33 * q^20 - 55 * q^21 - 27 * q^23 + 52 * q^24 + 11 * q^25 - 79 * q^27 - 44 * q^28 + 27 * q^29 - 66 * q^30 - 3 * q^31 - 33 * q^32 - 11 * q^34 + 23 * q^36 - 44 * q^37 - 33 * q^38 - 40 * q^39 - 77 * q^40 + 9 * q^41 - 22 * q^42 - 11 * q^43 - 36 * q^46 - 120 * q^47 - 56 * q^48 + 35 * q^49 - 3 * q^50 - 22 * q^51 - 38 * q^52 + 42 * q^54 - 44 * q^55 + 165 * q^56 + 11 * q^57 - 10 * q^58 - 9 * q^59 + 88 * q^60 - 11 * q^61 + 33 * q^63 - 22 * q^64 + 198 * q^65 + 33 * q^66 - 11 * q^67 + 3 * q^69 - 70 * q^70 + 14 * q^72 - 36 * q^73 + 231 * q^74 - 13 * q^75 - 11 * q^76 + 39 * q^77 + 3 * q^78 - 11 * q^79 + 172 * q^81 - 10 * q^82 + 66 * q^83 - 110 * q^84 + q^85 - 33 * q^86 - 196 * q^87 - 99 * q^88 + 418 * q^90 + 63 * q^92 - 188 * q^93 - 42 * q^94 - 93 * q^95 - 82 * q^96 + 22 * q^97 + 242 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

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