LMFDB - Embedded newform 207.2.o.a.149.13

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			149.13
Character	$\chi$	$=$	207.149
Dual form			207.2.o.a.182.13

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.180230 - 0.349597i) q^{2} +(1.34645 - 1.08953i) q^{3} +(1.07038 + 1.50314i) q^{4} +(0.578937 - 2.38641i) q^{5} +(-0.138227 - 0.667079i) q^{6} +(-3.53667 - 1.22405i) q^{7} +(1.49704 - 0.215242i) q^{8} +(0.625841 - 2.93399i) q^{9} +O(q^{10})$	\(q+(0.180230 - 0.349597i) q^{2} +(1.34645 - 1.08953i) q^{3} +(1.07038 + 1.50314i) q^{4} +(0.578937 - 2.38641i) q^{5} +(-0.138227 - 0.667079i) q^{6} +(-3.53667 - 1.22405i) q^{7} +(1.49704 - 0.215242i) q^{8} +(0.625841 - 2.93399i) q^{9} +(-0.729939 - 0.632496i) q^{10} +(-0.0639269 + 1.34199i) q^{11} +(3.07892 + 0.857683i) q^{12} +(1.59924 + 4.62071i) q^{13} +(-1.06534 + 1.01580i) q^{14} +(-1.82056 - 3.84394i) q^{15} +(-1.01251 + 2.92547i) q^{16} +(1.26232 + 2.76408i) q^{17} +(-0.912919 - 0.747584i) q^{18} +(-4.64144 - 2.11967i) q^{19} +(4.20678 - 1.68414i) q^{20} +(-6.09559 + 2.20519i) q^{21} +(0.457634 + 0.264215i) q^{22} +(4.78526 - 0.318308i) q^{23} +(1.78117 - 1.92088i) q^{24} +(-0.915604 - 0.472027i) q^{25} +(1.90361 + 0.273698i) q^{26} +(-2.35402 - 4.63234i) q^{27} +(-1.94566 - 6.62631i) q^{28} +(-1.12939 - 0.804232i) q^{29} +(-1.67195 - 0.0563305i) q^{30} +(0.316159 + 0.126571i) q^{31} +(2.92764 + 3.07042i) q^{32} +(1.37607 + 1.87657i) q^{33} +(1.19382 + 0.0568687i) q^{34} +(-4.96860 + 7.73130i) q^{35} +(5.08008 - 2.19976i) q^{36} +(-2.58296 + 8.79676i) q^{37} +(-1.57755 + 1.24060i) q^{38} +(7.18770 + 4.47911i) q^{39} +(0.353036 - 3.69716i) q^{40} +(-4.74940 - 1.15219i) q^{41} +(-0.327678 + 2.52844i) q^{42} +(-2.11981 - 5.29503i) q^{43} +(-2.08562 + 1.34035i) q^{44} +(-6.63939 - 3.19211i) q^{45} +(0.751165 - 1.73028i) q^{46} +(-5.27943 + 3.04808i) q^{47} +(1.82409 + 5.04215i) q^{48} +(5.50738 + 4.33105i) q^{49} +(-0.330038 + 0.235019i) q^{50} +(4.71120 + 2.34636i) q^{51} +(-5.23376 + 7.34978i) q^{52} +(0.820706 + 0.947145i) q^{53} +(-2.04372 - 0.0119284i) q^{54} +(3.16553 + 0.929483i) q^{55} +(-5.55800 - 1.07122i) q^{56} +(-8.55890 + 2.20296i) q^{57} +(-0.484705 + 0.249883i) q^{58} +(12.1348 - 4.19991i) q^{59} +(3.82928 - 6.85103i) q^{60} +(0.140899 + 0.179167i) q^{61} +(0.101230 - 0.0877163i) q^{62} +(-5.80476 + 9.61052i) q^{63} +(-4.33960 + 1.27422i) q^{64} +(11.9528 - 1.14135i) q^{65} +(0.904050 - 0.142855i) q^{66} +(-4.67876 + 0.222877i) q^{67} +(-2.80364 + 4.85605i) q^{68} +(6.09629 - 5.64227i) q^{69} +(1.80735 + 3.13042i) q^{70} +(-7.13238 - 11.0982i) q^{71} +(0.305390 - 4.52701i) q^{72} +(-1.37981 + 3.02136i) q^{73} +(2.60979 + 2.48843i) q^{74} +(-1.74710 + 0.362021i) q^{75} +(-1.78194 - 9.24556i) q^{76} +(1.86876 - 4.66793i) q^{77} +(2.86132 - 1.70553i) q^{78} +(-2.34942 + 12.1899i) q^{79} +(6.39518 + 4.10993i) q^{80} +(-8.21665 - 3.67243i) q^{81} +(-1.25878 + 1.45271i) q^{82} +(-1.65193 - 6.80935i) q^{83} +(-9.83930 - 6.80211i) q^{84} +(7.32704 - 1.41217i) q^{85} +(-2.23318 - 0.213242i) q^{86} +(-2.39689 + 0.147646i) q^{87} +(0.193151 + 2.02277i) q^{88} +(2.56329 - 17.8281i) q^{89} +(-2.31256 + 1.74580i) q^{90} -18.2995i q^{91} +(5.60050 + 6.85218i) q^{92} +(0.563594 - 0.174044i) q^{93} +(0.114089 + 2.39503i) q^{94} +(-7.74550 + 9.84921i) q^{95} +(7.28724 + 0.944404i) q^{96} +(5.06377 - 5.31073i) q^{97} +(2.50671 - 1.14478i) q^{98} +(3.89738 + 1.02743i) 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 $\left(\mathbb{Z}/207\mathbb{Z}\right)^\times$.

$n$	$28$	$47$
$\chi(n)$	$e\left(\frac{9}{22}\right)$	$e\left(\frac{5}{6}\right)$

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 $

$2$	0.180230	−	0.349597i	0.127442	−	0.247202i	−0.816479	−	0.577375i	$-0.804077\pi$
$2$	0.180230	−	0.349597i	0.127442	−	0.247202i	0.943920	+	0.330173i	$0.107107\pi$
$3$	1.34645	−	1.08953i	0.777372	−	0.629041i
$3$	1.34645	−	1.08953i	0.777372	−	0.629041i
$4$	1.07038	+	1.50314i	0.535189	+	0.751568i
$5$	0.578937	−	2.38641i	0.258908	−	1.06723i	−0.682747	−	0.730655i	$-0.739215\pi$
$5$	0.578937	−	2.38641i	0.258908	−	1.06723i	0.941655	−	0.336580i	$-0.109270\pi$
$6$	−0.138227	−	0.667079i	−0.0564309	−	0.272334i
$7$	−3.53667	−	1.22405i	−1.33674	−	0.462649i	−0.437149	−	0.899389i	$-0.644012\pi$
$7$	−3.53667	−	1.22405i	−1.33674	−	0.462649i	−0.899588	+	0.436740i	$0.856133\pi$
$8$	1.49704	−	0.215242i	0.529283	−	0.0760994i
$9$	0.625841	−	2.93399i	0.208614	−	0.977998i
$10$	−0.729939	−	0.632496i	−0.230827	−	0.200013i
$11$	−0.0639269	+	1.34199i	−0.0192747	+	0.404625i	0.968527	+	0.248908i	$0.0800718\pi$
$11$	−0.0639269	+	1.34199i	−0.0192747	+	0.404625i	−0.987802	+	0.155717i	$0.950231\pi$
$12$	3.07892	+	0.857683i	0.888809	+	0.247592i
$13$	1.59924	+	4.62071i	0.443550	+	1.28155i	0.916348	+	0.400383i	$0.131123\pi$
$13$	1.59924	+	4.62071i	0.443550	+	1.28155i	−0.472798	+	0.881171i	$0.656756\pi$
$14$	−1.06534	+	1.01580i	−0.284724	+	0.271484i
$15$	−1.82056	−	3.84394i	−0.470067	−	0.992502i
$16$	−1.01251	+	2.92547i	−0.253128	+	0.731367i
$17$	1.26232	+	2.76408i	0.306156	+	0.670389i	0.998699	−	0.0509877i	$-0.0162369\pi$
$17$	1.26232	+	2.76408i	0.306156	+	0.670389i	−0.692543	+	0.721377i	$0.743510\pi$
$18$	−0.912919	−	0.747584i	−0.215177	−	0.176207i
$19$	−4.64144	−	2.11967i	−1.06482	−	0.486286i	−0.195584	−	0.980687i	$-0.562660\pi$
$19$	−4.64144	−	2.11967i	−1.06482	−	0.486286i	−0.869234	+	0.494401i	$0.835388\pi$
$20$	4.20678	−	1.68414i	0.940665	−	0.376585i
$21$	−6.09559	+	2.20519i	−1.33017	+	0.481213i
$22$	0.457634	+	0.264215i	0.0975679	+	0.0563308i
$23$	4.78526	−	0.318308i	0.997795	−	0.0663718i
$23$	4.78526	−	0.318308i	0.997795	−	0.0663718i
$24$	1.78117	−	1.92088i	0.363580	−	0.392098i
$25$	−0.915604	−	0.472027i	−0.183121	−	0.0944053i
$26$	1.90361	+	0.273698i	0.373329	+	0.0536767i
$27$	−2.35402	−	4.63234i	−0.453031	−	0.891495i
$28$	−1.94566	−	6.62631i	−0.367695	−	1.25225i
$29$	−1.12939	−	0.804232i	−0.209722	−	0.149342i	0.470370	−	0.882469i	$-0.344121\pi$
$29$	−1.12939	−	0.804232i	−0.209722	−	0.149342i	−0.680091	+	0.733127i	$0.738060\pi$
$30$	−1.67195	−	0.0563305i	−0.305255	−	0.0102845i
$31$	0.316159	+	0.126571i	0.0567838	+	0.0227328i	0.399881	−	0.916567i	$-0.369052\pi$
$31$	0.316159	+	0.126571i	0.0567838	+	0.0227328i	−0.343097	+	0.939300i	$0.611476\pi$
$32$	2.92764	+	3.07042i	0.517539	+	0.542780i
$33$	1.37607	+	1.87657i	0.239543	+	0.326669i
$34$	1.19382	+	0.0568687i	0.204739	+	0.00975290i
$35$	−4.96860	+	7.73130i	−0.839848	+	1.30683i
$36$	5.08008	−	2.19976i	0.846680	−	0.366627i
$37$	−2.58296	+	8.79676i	−0.424636	+	1.44618i	0.418371	+	0.908276i	$0.362601\pi$
$37$	−2.58296	+	8.79676i	−0.424636	+	1.44618i	−0.843007	+	0.537902i	$0.819217\pi$
$38$	−1.57755	+	1.24060i	−0.255913	+	0.201252i
$39$	7.18770	+	4.47911i	1.15095	+	0.717232i
$40$	0.353036	−	3.69716i	0.0558198	−	0.584572i
$41$	−4.74940	−	1.15219i	−0.741731	−	0.179942i	−0.152949	−	0.988234i	$-0.548877\pi$
$41$	−4.74940	−	1.15219i	−0.741731	−	0.179942i	−0.588782	+	0.808292i	$0.700392\pi$
$42$	−0.327678	+	2.52844i	−0.0505618	+	0.390147i
$43$	−2.11981	−	5.29503i	−0.323268	−	0.807484i	−0.997612	−	0.0690668i	$-0.977998\pi$
$43$	−2.11981	−	5.29503i	−0.323268	−	0.807484i	0.674344	−	0.738417i	$-0.264426\pi$
$44$	−2.08562	+	1.34035i	−0.314419	+	0.202065i
$45$	−6.63939	−	3.19211i	−0.989742	−	0.475852i
$46$	0.751165	−	1.73028i	0.110753	−	0.255116i
$47$	−5.27943	+	3.04808i	−0.770085	+	0.444609i	−0.832905	−	0.553416i	$-0.813324\pi$
$47$	−5.27943	+	3.04808i	−0.770085	+	0.444609i	0.0628202	+	0.998025i	$0.479991\pi$
$48$	1.82409	+	5.04215i	0.263285	+	0.727772i
$49$	5.50738	+	4.33105i	0.786768	+	0.618721i
$50$	−0.330038	+	0.235019i	−0.0466744	+	0.0332367i
$51$	4.71120	+	2.34636i	0.659700	+	0.328556i
$52$	−5.23376	+	7.34978i	−0.725792	+	1.01923i
$53$	0.820706	+	0.947145i	0.112733	+	0.130100i	0.809311	−	0.587380i	$-0.199841\pi$
$53$	0.820706	+	0.947145i	0.112733	+	0.130100i	−0.696579	+	0.717481i	$0.745295\pi$
$54$	−2.04372	−	0.0119284i	−0.278114	−	0.00162325i
$55$	3.16553	+	0.929483i	0.426840	+	0.125331i
$56$	−5.55800	−	1.07122i	−0.742719	−	0.143147i
$57$	−8.55890	+	2.20296i	−1.13365	+	0.291790i
$58$	−0.484705	+	0.249883i	−0.0636449	+	0.0328113i
$59$	12.1348	−	4.19991i	1.57982	−	0.546782i	0.610382	−	0.792107i	$-0.291016\pi$
$59$	12.1348	−	4.19991i	1.57982	−	0.546782i	0.969441	+	0.245325i	$0.0788947\pi$
$60$	3.82928	−	6.85103i	0.494358	−	0.884464i
$61$	0.140899	+	0.179167i	0.0180402	+	0.0229400i	0.794990	−	0.606623i	$-0.207476\pi$
$61$	0.140899	+	0.179167i	0.0180402	+	0.0229400i	−0.776949	+	0.629563i	$0.783234\pi$
$62$	0.101230	−	0.0877163i	0.0128562	−	0.0111400i
$63$	−5.80476	+	9.61052i	−0.731332	+	1.21081i
$64$	−4.33960	+	1.27422i	−0.542450	+	0.159278i
$65$	11.9528	−	1.14135i	1.48256	−	0.141567i
$66$	0.904050	−	0.142855i	0.111281	−	0.0175842i
$67$	−4.67876	+	0.222877i	−0.571601	+	0.0272287i	−0.331393	−	0.943493i	$-0.607519\pi$
$67$	−4.67876	+	0.222877i	−0.571601	+	0.0272287i	−0.240208	+	0.970721i	$0.577216\pi$
$68$	−2.80364	+	4.85605i	−0.339991	+	0.588883i
$69$	6.09629	−	5.64227i	0.733907	−	0.679250i
$70$	1.80735	+	3.13042i	0.216019	+	0.374156i
$71$	−7.13238	−	11.0982i	−0.846458	−	1.31711i	−0.946689	−	0.322150i	$-0.895595\pi$
$71$	−7.13238	−	11.0982i	−0.846458	−	1.31711i	0.100231	−	0.994964i	$-0.468042\pi$
$72$	0.305390	−	4.52701i	0.0359906	−	0.533513i
$73$	−1.37981	+	3.02136i	−0.161495	+	0.353624i	−0.973030	−	0.230680i	$-0.925905\pi$
$73$	−1.37981	+	3.02136i	−0.161495	+	0.353624i	0.811535	+	0.584304i	$0.198632\pi$
$74$	2.60979	+	2.48843i	0.303382	+	0.289274i
$75$	−1.74710	+	0.362021i	−0.201738	+	0.0418025i
$76$	−1.78194	−	9.24556i	−0.204402	−	1.06054i
$77$	1.86876	−	4.66793i	0.212965	−	0.531960i
$78$	2.86132	−	1.70553i	0.323981	−	0.193113i
$79$	−2.34942	+	12.1899i	−0.264330	+	1.37148i	0.570649	+	0.821194i	$0.306692\pi$
$79$	−2.34942	+	12.1899i	−0.264330	+	1.37148i	−0.834979	+	0.550281i	$0.814520\pi$
$80$	6.39518	+	4.10993i	0.715003	+	0.459504i
$81$	−8.21665	−	3.67243i	−0.912961	−	0.408048i
$82$	−1.25878	+	1.45271i	−0.139009	+	0.160425i
$83$	−1.65193	−	6.80935i	−0.181323	−	0.747423i	−0.987744	−	0.156082i	$-0.950114\pi$
$83$	−1.65193	−	6.80935i	−0.181323	−	0.747423i	0.806421	−	0.591341i	$-0.201401\pi$
$84$	−9.83930	−	6.80211i	−1.07356	−	0.742172i
$85$	7.32704	−	1.41217i	0.794729	−	0.153171i
$86$	−2.23318	−	0.213242i	−0.240810	−	0.0229945i
$87$	−2.39689	+	0.147646i	−0.256974	+	0.0158293i
$88$	0.193151	+	2.02277i	0.0205900	+	0.215628i
$89$	2.56329	−	17.8281i	0.271708	−	1.88977i	−0.159000	−	0.987279i	$-0.550827\pi$
$89$	2.56329	−	17.8281i	0.271708	−	1.88977i	0.430708	−	0.902491i	$-0.358264\pi$
$90$	−2.31256	+	1.74580i	−0.243766	+	0.184023i
$91$		−	18.2995i		−	1.91831i
$92$	5.60050	+	6.85218i	0.583892	+	0.714390i
$93$	0.563594	−	0.174044i	0.0584420	−	0.0180475i
$94$	0.114089	+	2.39503i	0.0117674	+	0.247028i
$95$	−7.74550	+	9.84921i	−0.794672	+	1.01051i
$96$	7.28724	+	0.944404i	0.743751	+	0.0963878i
$97$	5.06377	−	5.31073i	0.514148	−	0.539223i	−0.414566	−	0.910019i	$-0.636067\pi$
$97$	5.06377	−	5.31073i	0.514148	−	0.539223i	0.928714	+	0.370796i	$0.120915\pi$
$98$	2.50671	−	1.14478i	0.253216	−	0.115640i
$99$	3.89738	+	1.02743i	0.391702	+	0.103261i
$100$	−0.270522	−	1.88153i	−0.0270522	−	0.188153i
$101$	−13.8519	+	3.36044i	−1.37832	+	0.334376i	−0.855382	−	0.517997i	$-0.826678\pi$
$101$	−13.8519	+	3.36044i	−1.37832	+	0.334376i	−0.522934	+	0.852373i	$0.675163\pi$
$102$	1.66938	−	1.22414i	0.165293	−	0.121207i
$103$	3.97570	+	7.71178i	0.391737	+	0.759864i	0.999411	−	0.0343226i	$-0.0109274\pi$
$103$	3.97570	+	7.71178i	0.391737	+	0.759864i	−0.607674	+	0.794187i	$0.707897\pi$
$104$	3.38869	+	6.57315i	0.332289	+	0.644550i
$105$	1.73353	+	15.8232i	0.169175	+	1.54419i
$106$	0.479034	−	0.116212i	0.0465279	−	0.0112875i
$107$	0.753083	+	5.23781i	0.0728033	+	0.506358i	0.993296	+	0.115598i	$0.0368785\pi$
$107$	0.753083	+	5.23781i	0.0728033	+	0.506358i	−0.920493	+	0.390760i	$0.872212\pi$
$108$	4.44335	−	8.49677i	0.427562	−	0.817602i
$109$	13.3881	−	6.11415i	1.28235	−	0.585629i	0.346507	−	0.938047i	$-0.387368\pi$
$109$	13.3881	−	6.11415i	1.28235	−	0.585629i	0.935843	+	0.352418i	$0.114640\pi$
$110$	0.895466	−	0.939138i	0.0853793	−	0.0895433i
$111$	6.10653	+	14.6586i	0.579606	+	1.39133i
$112$	7.16186	−	9.10705i	0.676732	−	0.860535i
$113$	−0.309369	−	6.49445i	−0.0291030	−	0.610947i	−0.965563	−	0.260171i	$-0.916221\pi$
$113$	−0.309369	−	6.49445i	−0.0291030	−	0.610947i	0.936460	−	0.350776i	$-0.114082\pi$
$114$	−0.772418	+	3.38920i	−0.0723436	+	0.317428i
$115$	2.01075	−	11.6039i	0.187503	−	1.08207i
$116$		−	2.55845i		−	0.237546i
$117$	14.5580	−	1.80034i	1.34589	−	0.166441i
$118$	0.718784	−	4.99925i	0.0661694	−	0.460218i
$119$	−1.08101	−	11.3208i	−0.0990957	−	1.03778i
$120$	−3.55283	−	5.36267i	−0.324327	−	0.489543i
$121$	9.15334	+	0.874038i	0.832122	+	0.0794580i
$122$	0.0880303	−	0.0169664i	0.00796989	−	0.00153607i
$123$	−7.65016	+	3.62325i	−0.689792	+	0.326698i
$124$	0.148156	+	0.610709i	0.0133048	+	0.0548433i
$125$	6.38395	−	7.36747i	0.570998	−	0.658967i
$126$	2.31361	+	3.76143i	0.206113	+	0.335094i
$127$	−5.30715	−	3.41070i	−0.470933	−	0.302650i	0.283564	−	0.958953i	$-0.408483\pi$
$127$	−5.30715	−	3.41070i	−0.470933	−	0.302650i	−0.754498	+	0.656303i	$0.772119\pi$
$128$	−1.94245	+	10.0784i	−0.171690	+	0.890812i
$129$	−8.62331	−	4.81988i	−0.759240	−	0.424366i
$130$	1.75523	−	4.38435i	0.153944	−	0.384533i
$131$	−3.64196	−	18.8963i	−0.318200	−	1.65098i	−0.690845	−	0.723003i	$-0.742761\pi$
$131$	−3.64196	−	18.8963i	−0.318200	−	1.65098i	0.372646	−	0.927974i	$-0.378451\pi$
$132$	−1.34783	+	4.07706i	−0.117313	+	0.354862i
$133$	13.8206	+	13.1780i	1.19840	+	1.14267i
$134$	−0.765333	+	1.67585i	−0.0661147	+	0.144771i
$135$	−12.4175	+	2.93582i	−1.06873	+	0.252675i
$136$	2.48468	+	3.86624i	0.213060	+	0.331527i
$137$	4.51672	+	7.82319i	0.385889	+	0.668380i	0.991892	−	0.127083i	$-0.0405613\pi$
$137$	4.51672	+	7.82319i	0.385889	+	0.668380i	−0.606003	+	0.795462i	$0.707228\pi$
$138$	−0.873788	−	3.14815i	−0.0743818	−	0.267988i
$139$	9.15903	−	15.8639i	0.776859	−	1.34556i	−0.156885	−	0.987617i	$-0.550145\pi$
$139$	9.15903	−	15.8639i	0.776859	−	1.34556i	0.933744	−	0.357942i	$-0.116521\pi$
$140$	−16.9395	+	0.806927i	−1.43165	+	0.0681978i
$141$	−3.78750	+	9.85619i	−0.318965	+	0.830041i
$142$	−5.16536	+	0.493232i	−0.433467	+	0.0413911i
$143$	−6.30318	+	1.85078i	−0.527098	+	0.154770i
$144$	7.94963	+	4.80159i	0.662469	+	0.400132i
$145$	−2.57307	+	2.22958i	−0.213682	+	0.185156i
$146$	0.807576	+	1.02692i	0.0668355	+	0.0849882i
$147$	12.1342	−	0.168933i	1.00081	−	0.0139333i
$148$	−15.9875	+	5.53332i	−1.31416	+	0.454836i
$149$	−18.4643	+	9.51901i	−1.51265	+	0.779827i	−0.997032	−	0.0769887i	$-0.975469\pi$
$149$	−18.4643	+	9.51901i	−1.51265	+	0.779827i	−0.515622	+	0.856816i	$0.672439\pi$
$150$	−0.188318	+	0.676027i	−0.0153761	+	0.0551974i
$151$	−8.67208	−	1.67141i	−0.705724	−	0.136017i	−0.176253	−	0.984345i	$-0.556398\pi$
$151$	−8.67208	−	1.67141i	−0.705724	−	0.136017i	−0.529471	+	0.848328i	$0.677610\pi$
$152$	−7.40465	−	2.17420i	−0.600596	−	0.176351i
$153$	8.89982	−	1.97375i	0.719508	−	0.159568i
$154$	−1.29509	−	1.49461i	−0.104361	−	0.120439i
$155$	0.485086	−	0.681208i	0.0389630	−	0.0547159i
$156$	0.960844	+	15.5984i	0.0769291	+	1.24888i
$157$	−1.61273	+	1.14842i	−0.128710	+	0.0916539i	−0.642599	−	0.766203i	$-0.722144\pi$
$157$	−1.61273	+	1.14842i	−0.128710	+	0.0916539i	0.513889	+	0.857857i	$0.328204\pi$
$158$	3.83813	+	3.01834i	0.305345	+	0.240126i
$159$	2.13698	+	0.381096i	0.169474	+	0.0302229i
$160$	9.02221	−	5.20898i	0.713268	−	0.411806i
$161$	−17.3135	−	4.73166i	−1.36450	−	0.372907i
$162$	−2.76475	+	2.21063i	−0.217219	+	0.173684i
$163$	2.50907	−	1.61248i	0.196526	−	0.126299i	−0.438677	−	0.898645i	$-0.644553\pi$
$163$	2.50907	−	1.61248i	0.196526	−	0.126299i	0.635203	+	0.772345i	$0.280916\pi$
$164$	−3.35175	−	8.37227i	−0.261728	−	0.653765i
$165$	5.27492	−	2.19744i	0.410652	−	0.171071i
$166$	−2.67825	−	0.649737i	−0.207873	−	0.0504294i
$167$	1.05931	−	11.0936i	0.0819717	−	0.858447i	−0.857197	−	0.514989i	$-0.827796\pi$
$167$	1.05931	−	11.0936i	0.0819717	−	0.858447i	0.939168	−	0.343457i	$-0.111598\pi$
$168$	−8.65068	+	4.61328i	−0.667415	+	0.355923i
$169$	−8.57466	+	6.74319i	−0.659589	+	0.518707i
$170$	0.826859	−	2.81602i	0.0634172	−	0.215979i
$171$	−9.12391	+	12.2914i	−0.697723	+	0.939944i
$172$	5.69015	−	8.85405i	0.433870	−	0.675115i
$173$	1.33755	+	0.0637155i	0.101692	+	0.00484420i	0.0983663	−	0.995150i	$-0.468638\pi$
$173$	1.33755	+	0.0637155i	0.101692	+	0.00484420i	0.00332588	+	0.999994i	$0.498941\pi$
$174$	−0.380375	+	0.864556i	−0.0288361	+	0.0655419i
$175$	2.66041	+	2.79015i	0.201108	+	0.210916i
$176$	−3.86122	−	1.54580i	−0.291051	−	0.116519i
$177$	11.7630	−	18.8763i	0.884161	−	1.41883i
$178$	−5.77065	−	4.10926i	−0.432528	−	0.308002i
$179$	4.65532	+	15.8546i	0.347955	+	1.18503i	0.928666	+	0.370916i	$0.120956\pi$
$179$	4.65532	+	15.8546i	0.347955	+	1.18503i	−0.580712	+	0.814109i	$0.697226\pi$
$180$	−2.30848	−	13.3967i	−0.172064	−	0.998529i
$181$	10.0022	+	1.43811i	0.743461	+	0.106894i	0.503628	−	0.863921i	$-0.331998\pi$
$181$	10.0022	+	1.43811i	0.743461	+	0.106894i	0.239833	+	0.970814i	$0.422907\pi$
$182$	−6.39744	−	3.29811i	−0.474210	−	0.244472i
$183$	0.384921	+	0.0877256i	0.0284542	+	0.00648486i
$184$	7.09520	−	1.50651i	0.523065	−	0.111061i
$185$	19.4973	+	11.2568i	1.43347	+	0.827614i
$186$	0.0407312	−	0.228399i	0.00298655	−	0.0167470i
$187$	−3.79007	+	1.51732i	−0.277157	+	0.110957i
$188$	−10.2327	−	4.67311i	−0.746295	−	0.340821i
$189$	2.65515	+	19.2645i	0.193134	+	1.40129i
$190$	2.04728	+	4.48292i	0.148525	+	0.325225i
$191$	2.57616	−	7.44332i	0.186404	−	0.538580i	−0.812618	−	0.582797i	$-0.801958\pi$
$191$	2.57616	−	7.44332i	0.186404	−	0.538580i	0.999022	+	0.0442174i	$0.0140794\pi$
$192$	−4.45474	+	6.44381i	−0.321493	+	0.465042i
$193$	−18.5387	+	17.6766i	−1.33445	+	1.27239i	−0.399897	+	0.916560i	$0.630954\pi$
$193$	−18.5387	+	17.6766i	−1.33445	+	1.27239i	−0.934550	+	0.355832i	$0.884197\pi$
$194$	−0.943971	−	2.72743i	−0.0677732	−	0.195818i
$195$	14.8502	−	14.5597i	1.06345	−	1.04264i
$196$	−0.615179	+	12.9142i	−0.0439414	+	0.922443i
$197$	20.9697	+	18.1703i	1.49403	+	1.29458i	0.846293	+	0.532718i	$0.178829\pi$
$197$	20.9697	+	18.1703i	1.49403	+	1.29458i	0.647736	+	0.761865i	$0.275716\pi$
$198$	1.06161	−	1.17734i	0.0754454	−	0.0836698i
$199$	14.1918	−	2.04047i	1.00603	−	0.144645i	0.380447	−	0.924803i	$-0.375770\pi$
$199$	14.1918	−	2.04047i	1.00603	−	0.144645i	0.625583	+	0.780157i	$0.284861\pi$
$200$	−1.47229	−	0.509566i	−0.104107	−	0.0360317i
$201$	−6.05687	+	5.39775i	−0.427219	+	0.380728i
$202$	−1.32173	+	5.44823i	−0.0929963	+	0.383336i
$203$	3.00984	+	4.22674i	0.211250	+	0.296659i
$204$	1.51586	+	9.59307i	0.106132	+	0.671649i
$205$	−5.49920	+	10.6670i	−0.384081	+	0.745013i
$206$	3.41255			0.237764
$207$	2.06090	−	14.2391i	0.143242	−	0.989688i
$208$	−15.1370			−1.04956
$209$	3.14129	−	6.09326i	0.217288	−	0.421480i
$210$	5.84419	+	2.24578i	0.403287	+	0.154973i
$211$	7.45693	+	10.4718i	0.513356	+	0.720907i	0.987162	−	0.159722i	$-0.0510597\pi$
$211$	7.45693	+	10.4718i	0.513356	+	0.720907i	−0.473806	+	0.880629i	$0.657120\pi$
$212$	−0.545222	+	2.24744i	−0.0374460	+	0.154355i
$213$	−21.6952	−	7.17219i	−1.48653	−	0.491430i
$214$	1.96685	+	0.680733i	0.134451	+	0.0465339i
$215$	−13.8633	+	1.99325i	−0.945472	+	0.135938i
$216$	−4.52113	−	6.42811i	−0.307624	−	0.437378i
$217$	−0.963221	−	0.834636i	−0.0653877	−	0.0566588i
$218$	0.275449	−	5.78239i	0.0186558	−	0.391633i
$219$	1.43403	+	5.57145i	0.0969027	+	0.376484i
$220$	1.99117	+	5.75312i	0.134245	+	0.387875i
$221$	−10.7533	+	10.2532i	−0.723344	+	0.689707i
$222$	6.22517	+	0.507091i	0.417806	+	0.0340337i
$223$	−3.77192	+	10.8983i	−0.252587	+	0.729801i	0.745414	+	0.666601i	$0.232252\pi$
$223$	−3.77192	+	10.8983i	−0.252587	+	0.729801i	−0.998001	+	0.0631996i	$0.979870\pi$
$224$	−6.59575	−	14.4427i	−0.440697	−	0.964993i
$225$	−1.95795	+	2.39096i	−0.130530	+	0.159398i
$226$	−2.32620	−	1.06234i	−0.154736	−	0.0706657i
$227$	1.91859	−	0.768089i	0.127341	−	0.0509798i	−0.307117	−	0.951672i	$-0.599364\pi$
$227$	1.91859	−	0.768089i	0.127341	−	0.0509798i	0.434458	+	0.900692i	$0.356940\pi$
$228$	−12.4726	−	10.5072i	−0.826019	−	0.695856i
$229$	−10.8821	−	6.28278i	−0.719109	−	0.415178i	0.0953158	−	0.995447i	$-0.469614\pi$
$229$	−10.8821	−	6.28278i	−0.719109	−	0.415178i	−0.814425	+	0.580269i	$0.802947\pi$
$230$	−3.69427	−	2.79431i	−0.243593	−	0.184251i
$231$	−2.56968	−	8.32120i	−0.169072	−	0.547495i
$232$	−1.86384	−	0.960875i	−0.122367	−	0.0630845i
$233$	21.4266	+	3.08068i	1.40370	+	0.201822i	0.802203	−	0.597052i	$-0.203661\pi$
$233$	21.4266	+	3.08068i	1.40370	+	0.201822i	0.601499	+	0.798873i	$0.294570\pi$
$234$	1.99439	−	5.41390i	0.130377	−	0.353918i
$235$	4.21751	+	14.3635i	0.275120	+	0.936974i
$236$	19.3019	+	13.7448i	1.25645	+	0.894713i
$237$	10.1180	+	18.9729i	0.657232	+	1.23242i
$238$	−4.15255	−	1.66243i	−0.269170	−	0.107759i
$239$	−5.57783	−	5.84986i	−0.360800	−	0.378396i	0.518167	−	0.855280i	$-0.326615\pi$
$239$	−5.57783	−	5.84986i	−0.360800	−	0.378396i	−0.878966	+	0.476884i	$0.841766\pi$
$240$	13.0887	−	1.43394i	0.844870	−	0.0925607i
$241$	5.03385	+	0.239792i	0.324259	+	0.0154463i	0.209080	−	0.977898i	$-0.432953\pi$
$241$	5.03385	+	0.239792i	0.324259	+	0.0154463i	0.115178	+	0.993345i	$0.463256\pi$
$242$	1.95526	−	3.04245i	0.125689	−	0.195576i
$243$	−15.0645	+	4.00757i	−0.966389	+	0.257085i
$244$	−0.118498	+	0.403566i	−0.00758604	+	0.0258357i
$245$	13.5241	−	10.6355i	0.864022	−	0.679474i
$246$	−0.112108	+	3.32749i	−0.00714775	+	0.212153i
$247$	2.37161	−	24.8366i	0.150902	−	1.58031i
$248$	0.500545	+	0.121431i	0.0317847	+	0.00771088i
$249$	−9.64324	−	7.36860i	−0.611115	−	0.466966i
$250$	−1.42507	−	3.55964i	−0.0901291	−	0.225132i
$251$	−6.51350	+	4.18597i	−0.411129	+	0.264216i	−0.729816	−	0.683644i	$-0.760394\pi$
$251$	−6.51350	+	4.18597i	−0.411129	+	0.264216i	0.318687	+	0.947860i	$0.396758\pi$
$252$	−20.6592	+	1.56154i	−1.30141	+	0.0983677i
$253$	0.121259	+	6.44212i	0.00762352	+	0.405012i
$254$	−2.14887	+	1.24065i	−0.134832	+	0.0778455i
$255$	8.32687	−	9.88445i	0.521449	−	0.618989i
$256$	−3.93705	−	3.09613i	−0.246066	−	0.193508i
$257$	−11.0665	+	7.88042i	−0.690310	+	0.491567i	−0.870566	−	0.492052i	$-0.836247\pi$
$257$	−11.0665	+	7.88042i	−0.690310	+	0.491567i	0.180256	+	0.983620i	$0.442307\pi$
$258$	−3.23919	+	2.14600i	−0.201663	+	0.133604i
$259$	19.9028	−	27.9496i	1.23670	−	1.73670i
$260$	14.5096	+	16.7449i	0.899846	+	1.03848i
$261$	−3.06643	+	2.81029i	−0.189807	+	0.173953i
$262$	−7.26247	−	2.13245i	−0.448677	−	0.131743i
$263$	−19.2039	−	3.70125i	−1.18416	−	0.228229i	−0.441105	−	0.897455i	$-0.645413\pi$
$263$	−19.2039	−	3.70125i	−1.18416	−	0.228229i	−0.743058	+	0.669227i	$0.766625\pi$
$264$	2.46394	+	2.51311i	0.151645	+	0.154671i
$265$	2.73541	−	1.41020i	0.168035	−	0.0866280i
$266$	7.09786	−	2.45659i	0.435198	−	0.150623i
$267$	−15.9729	−	26.7973i	−0.977526	−	1.63997i
$268$	−5.34306	−	6.79425i	−0.326379	−	0.415025i
$269$	3.89084	−	3.37143i	0.237229	−	0.205560i	−0.528130	−	0.849163i	$-0.677107\pi$
$269$	3.89084	−	3.37143i	0.237229	−	0.205560i	0.765359	+	0.643603i	$0.222561\pi$
$270$	−1.21165	+	4.87023i	−0.0737385	+	0.296393i
$271$	−8.42993	+	2.47525i	−0.512082	+	0.150361i	−0.527557	−	0.849519i	$-0.676892\pi$
$271$	−8.42993	+	2.47525i	−0.512082	+	0.150361i	0.0154755	+	0.999880i	$0.495074\pi$
$272$	−9.36435	+	0.894187i	−0.567797	+	0.0542181i
$273$	−19.9379	−	24.6393i	−1.20670	−	1.49124i
$274$	3.54901	−	0.169060i	0.214403	−	0.0102133i
$275$	0.691987	−	1.19856i	0.0417284	−	0.0722757i
$276$	15.0064	+	3.12419i	0.903282	+	0.188054i
$277$	−7.10493	−	12.3061i	−0.426894	−	0.739402i	0.569701	−	0.821852i	$-0.307059\pi$
$277$	−7.10493	−	12.3061i	−0.426894	−	0.739402i	−0.996595	+	0.0824500i	$0.973726\pi$
$278$	−3.89524	−	6.06111i	−0.233621	−	0.363521i
$279$	0.569224	−	0.848395i	0.0340785	−	0.0507921i
$280$	−5.77409	+	12.6435i	−0.345068	+	0.755594i
$281$	1.28175	+	1.22215i	0.0764630	+	0.0729073i	0.727347	−	0.686270i	$-0.240753\pi$
$281$	1.28175	+	1.22215i	0.0764630	+	0.0729073i	−0.650884	+	0.759177i	$0.725602\pi$
$282$	2.76307	+	3.10047i	0.164539	+	0.184631i
$283$	0.0528824	+	0.274380i	0.00314353	+	0.0163102i	0.983467	−	0.181090i	$-0.0579624\pi$
$283$	0.0528824	+	0.274380i	0.00314353	+	0.0163102i	−0.980323	+	0.197400i	$0.936750\pi$
$284$	9.04776	−	22.6002i	0.536886	−	1.34108i
$285$	0.302113	+	21.7004i	0.0178956	+	1.28542i
$286$	−0.488993	+	2.53714i	−0.0289147	+	0.150024i
$287$	15.3867	+	9.88844i	0.908249	+	0.583696i
$288$	10.8408	−	6.66809i	0.638803	−	0.392921i
$289$	5.08591	−	5.86945i	0.299171	−	0.345262i
$290$	0.315709	+	1.30137i	0.0185391	+	0.0764192i
$291$	1.03189	−	12.6678i	0.0604905	−	0.742597i
$292$	−6.01844	+	1.15996i	−0.352203	+	0.0678815i
$293$	28.0548	+	2.67891i	1.63898	+	0.156503i	0.873455	−	0.486906i	$-0.161874\pi$
$293$	28.0548	+	2.67891i	1.63898	+	0.156503i	0.765523	+	0.643409i	$0.222481\pi$
$294$	2.12789	−	4.27253i	0.124101	−	0.249179i
$295$	−2.99740	−	31.3902i	−0.174515	−	1.82761i
$296$	−1.97336	+	13.7250i	−0.114699	+	0.797752i
$297$	6.36704	−	2.86294i	0.369453	−	0.166125i
$298$			8.17066i			0.473314i
$299$	9.12359	+	21.6022i	0.527631	+	1.24929i
$300$	−2.41423	−	2.23863i	−0.139385	−	0.129247i
$301$	1.01567	+	21.3215i	0.0585423	+	1.22895i
$302$	−2.14728	+	2.73049i	−0.123562	+	0.157122i
$303$	−14.9896	+	19.6167i	−0.861128	+	1.12695i
$304$	10.9005	−	11.4322i	0.625189	−	0.655680i
$305$	0.509137	−	0.232515i	0.0291531	−	0.0133138i
$306$	0.913995	−	3.46707i	0.0522496	−	0.198199i
$307$	1.30791	+	9.09669i	0.0746462	+	0.519176i	0.992499	+	0.122254i	$0.0390123\pi$
$307$	1.30791	+	9.09669i	0.0746462	+	0.519176i	−0.917853	+	0.396921i	$0.870079\pi$
$308$	9.01682	−	2.18746i	0.513781	−	0.124642i
$309$	13.7553	+	6.05186i	0.782512	+	0.344278i
$310$	−0.150721	−	0.292358i	−0.00856039	−	0.0166048i
$311$	3.46112	+	6.71365i	0.196262	+	0.380696i	0.966346	−	0.257248i	$-0.0828156\pi$
$311$	3.46112	+	6.71365i	0.196262	+	0.380696i	−0.770083	+	0.637944i	$0.779785\pi$
$312$	11.7244	+	5.15831i	0.663761	+	0.292032i
$313$	18.7926	−	4.55903i	1.06222	−	0.257692i	0.333674	−	0.942689i	$-0.391712\pi$
$313$	18.7926	−	4.55903i	1.06222	−	0.257692i	0.728546	+	0.684997i	$0.240197\pi$
$314$	0.110822	+	0.770784i	0.00625405	+	0.0434979i
$315$	19.5740	+	19.4164i	1.10287	+	1.09399i
$316$	−20.8379	+	9.51636i	−1.17222	+	0.535337i
$317$	−7.83069	+	8.21259i	−0.439815	+	0.461265i	−0.905910	−	0.423470i	$-0.860812\pi$
$317$	−7.83069	+	8.21259i	−0.439815	+	0.461265i	0.466095	+	0.884735i	$0.345661\pi$
$318$	0.518377	−	0.678397i	0.0290691	−	0.0380426i
$319$	1.15147	−	1.46421i	0.0644699	−	0.0819802i
$320$	0.528461	+	11.0938i	0.0295419	+	0.620160i
$321$	6.72074	+	6.23192i	0.375115	+	0.347832i
$322$	−4.77458	+	5.19996i	−0.266077	+	0.289782i
$323$		−	15.5050i		−	0.862722i
$324$	−3.27476	−	16.2816i	−0.181931	−	0.904535i
$325$	0.716824	−	4.98562i	0.0397623	−	0.276553i
$326$	−0.111510	−	1.16778i	−0.00617594	−	0.0646774i
$327$	11.3648	−	22.8192i	0.628477	−	1.26190i
$328$	−7.35803	−	0.702606i	−0.406279	−	0.0387949i
$329$	22.4027	−	4.31776i	1.23510	−	0.238046i
$330$	0.182477	−	2.24014i	0.0100451	−	0.123316i
$331$	−4.00353	−	16.5028i	−0.220054	−	0.907074i	−0.969516	−	0.245027i	$-0.921203\pi$
$331$	−4.00353	−	16.5028i	−0.220054	−	0.907074i	0.749462	−	0.662047i	$-0.230312\pi$
$332$	8.46719	−	9.77166i	0.464697	−	0.536289i
$333$	24.1931	+	13.0838i	1.32577	+	0.716986i
$334$	−3.68736	−	2.36972i	−0.201763	−	0.129665i
$335$	−2.17683	+	11.2945i	−0.118933	+	0.617082i
$336$	−0.279348	−	20.0652i	−0.0152397	−	1.09465i
$337$	−6.06579	+	15.1516i	−0.330424	+	0.825360i	0.666390	+	0.745603i	$0.267839\pi$
$337$	−6.06579	+	15.1516i	−0.330424	+	0.825360i	−0.996814	+	0.0797568i	$0.974586\pi$
$338$	0.811988	+	4.21299i	0.0441663	+	0.229157i
$339$	−7.49246	−	8.40737i	−0.406935	−	0.456626i
$340$	9.96539	+	9.50198i	0.540449	+	0.515317i
$341$	−0.190068	+	0.416191i	−0.0102928	+	0.0225380i
$342$	2.65262	+	5.40496i	0.143437	+	0.292267i
$343$	−0.0128878	−	0.0200538i	−0.000695877	−	0.00108281i
$344$	−4.31314	−	7.47059i	−0.232549	−	0.402787i
$345$	−9.93541	−	17.8148i	−0.534904	−	0.959114i
$346$	0.263341	−	0.456120i	0.0141573	−	0.0245212i
$347$	7.25952	−	0.345813i	0.389711	−	0.0185642i	0.148188	−	0.988959i	$-0.452656\pi$
$347$	7.25952	−	0.345813i	0.389711	−	0.0185642i	0.241523	+	0.970395i	$0.422353\pi$
$348$	−2.78752	−	3.44482i	−0.149427	−	0.184662i
$349$	5.14045	−	0.490854i	0.275162	−	0.0262748i	0.0434372	−	0.999056i	$-0.486169\pi$
$349$	5.14045	−	0.490854i	0.275162	−	0.0262748i	0.231725	+	0.972781i	$0.425563\pi$
$350$	1.45491	−	0.427201i	0.0777683	−	0.0228348i
$351$	17.6401	−	18.2855i	0.941556	−	0.976006i
$352$	−4.30764	+	3.73259i	−0.229598	+	0.198948i
$353$	−13.0541	−	16.5996i	−0.694800	−	0.883510i	0.302779	−	0.953061i	$-0.402086\pi$
$353$	−13.0541	−	16.5996i	−0.694800	−	0.883510i	−0.997578	+	0.0695513i	$0.977843\pi$
$354$	−4.47904	−	7.51437i	−0.238058	−	0.399384i
$355$	−30.6140	+	10.5956i	−1.62482	+	0.562357i
$356$	29.5417	−	15.2298i	1.56571	−	0.807178i
$357$	−13.7899	−	14.0651i	−0.729839	−	0.744403i
$358$	6.38172	+	1.22998i	0.337285	+	0.0650063i
$359$	−22.7885	−	6.69129i	−1.20273	−	0.353153i	−0.381833	−	0.924231i	$-0.624707\pi$
$359$	−22.7885	−	6.69129i	−1.20273	−	0.353153i	−0.820896	+	0.571078i	$0.806525\pi$
$360$	−10.6265	−	3.34964i	−0.560065	−	0.176541i
$361$	4.60756	+	5.31741i	0.242503	+	0.279864i
$362$	2.30546	−	3.23756i	0.121172	−	0.170162i
$363$	13.2768	−	8.79601i	0.696850	−	0.461671i
$364$	27.5066	−	19.5874i	1.44174	−	1.02666i
$365$	6.41139	+	5.04197i	0.335587	+	0.263909i
$366$	0.100043	−	0.118756i	0.00522931	−	0.00620749i
$367$	−23.6545	+	13.6569i	−1.23476	+	0.712887i	−0.968018	−	0.250882i	$-0.919279\pi$
$367$	−23.6545	+	13.6569i	−1.23476	+	0.712887i	−0.266739	+	0.963769i	$0.585946\pi$
$368$	−3.91394	+	14.3214i	−0.204028	+	0.746555i
$369$	−6.35289	+	13.2136i	−0.330718	+	0.687873i
$370$	7.44932	−	4.78739i	0.387272	−	0.248884i
$371$	−1.74321	−	4.35433i	−0.0905030	−	0.226066i
$372$	0.864872	+	0.660866i	0.0448415	+	0.0342643i
$373$	−9.18019	−	2.22709i	−0.475332	−	0.115314i	−0.00906612	−	0.999959i	$-0.502886\pi$
$373$	−9.18019	−	2.22709i	−0.475332	−	0.115314i	−0.466266	+	0.884645i	$0.654401\pi$
$374$	−0.152635	+	1.59846i	−0.00789254	+	0.0826545i
$375$	0.568559	−	16.8754i	0.0293603	−	0.871444i
$376$	−7.24744	+	5.69945i	−0.373758	+	0.293927i
$377$	1.90996	−	6.50472i	0.0983679	−	0.335010i
$378$	7.21335	+	2.54381i	0.371015	+	0.130839i
$379$	−18.4502	+	28.7091i	−0.947724	+	1.47469i	−0.0688530	+	0.997627i	$0.521934\pi$
$379$	−18.4502	+	28.7091i	−0.947724	+	1.47469i	−0.878871	+	0.477060i	$0.841702\pi$
$380$	−23.0953	−	1.10017i	−1.18477	−	0.0564373i
$381$	−10.8619	+	1.18998i	−0.556470	+	0.0609647i
$382$	−2.13786	−	2.24212i	−0.109382	−	0.114717i
$383$	−13.9277	−	5.57581i	−0.711672	−	0.284911i	−0.0125585	−	0.999921i	$-0.503998\pi$
$383$	−13.9277	−	5.57581i	−0.711672	−	0.284911i	−0.699114	+	0.715011i	$0.746422\pi$
$384$	8.36531	+	15.6864i	0.426891	+	0.800492i
$385$	−10.0577	−	7.16206i	−0.512588	−	0.365012i
$386$	2.83847	+	9.66693i	0.144474	+	0.492034i
$387$	−16.8622	+	2.90566i	−0.857156	+	0.147703i
$388$	13.4029	+	1.92705i	0.680429	+	0.0978309i
$389$	12.7507	+	6.57342i	0.646484	+	0.333286i	0.750093	−	0.661332i	$-0.230009\pi$
$389$	12.7507	+	6.57342i	0.646484	+	0.333286i	−0.103609	+	0.994618i	$0.533039\pi$
$390$	−2.41356	−	7.81567i	−0.122216	−	0.395762i
$391$	6.92033	+	12.8251i	0.349976	+	0.648591i
$392$	9.17698	+	5.29833i	0.463507	+	0.267606i
$393$	−25.4918	−	21.4748i	−1.28589	−	1.08326i
$394$	10.1316	−	4.05610i	0.510425	−	0.204343i
$395$	27.7300	+	12.6639i	1.39525	+	0.637189i
$396$	2.62730	+	6.95804i	0.132027	+	0.349655i
$397$	0.320425	+	0.701633i	0.0160817	+	0.0352139i	0.917502	−	0.397730i	$-0.130202\pi$
$397$	0.320425	+	0.701633i	0.0160817	+	0.0352139i	−0.901421	+	0.432944i	$0.857475\pi$
$398$	1.84444	−	5.32916i	0.0924535	−	0.267127i
$399$	32.9666	+	2.68540i	1.65039	+	0.134438i
$400$	2.30796	−	2.20064i	0.115398	−	0.110032i
$401$	−1.42943	−	4.13005i	−0.0713821	−	0.206245i	0.903666	−	0.428237i	$-0.140865\pi$
$401$	−1.42943	−	4.13005i	−0.0713821	−	0.206245i	−0.975048	+	0.221992i	$0.928744\pi$
$402$	0.795407	+	3.09029i	0.0396713	+	0.154130i
$403$	−0.0792325	+	1.66330i	−0.00394685	+	0.0828546i
$404$	−19.8780	−	17.2244i	−0.988966	−	0.856944i
$405$	−13.5208	+	17.4822i	−0.671856	+	0.868696i
$406$	2.02012	−	0.290449i	0.100257	−	0.0144147i
$407$	−11.6400	−	4.02866i	−0.576976	−	0.199693i
$408$	7.55788	+	2.49855i	0.374171	+	0.123697i
$409$	0.970403	−	4.00006i	0.0479833	−	0.197790i	−0.942775	−	0.333430i	$-0.891794\pi$
$409$	0.970403	−	4.00006i	0.0479833	−	0.197790i	0.990758	+	0.135640i	$0.0433091\pi$
$410$	2.73801	+	3.84500i	0.135221	+	0.189891i
$411$	14.6051	+	5.61240i	0.720418	+	0.276839i
$412$	−7.33636	+	14.2305i	−0.361436	+	0.701089i
$413$	−48.0579			−2.36478
$414$	−4.60652	−	3.28679i	−0.226398	−	0.161537i
$415$	−17.2063			−0.844622
$416$	−9.50552	+	18.4381i	−0.466046	+	0.904004i
$417$	−4.95208	−	31.3390i	−0.242504	−	1.53468i
$418$	−1.56403	−	2.19637i	−0.0764991	−	0.107428i
$419$	−5.07503	+	20.9196i	−0.247932	+	1.02199i	0.702656	+	0.711530i	$0.251997\pi$
$419$	−5.07503	+	20.9196i	−0.247932	+	1.02199i	−0.950587	+	0.310458i	$0.899518\pi$
$420$	−21.9290	+	19.5426i	−1.07002	+	0.953581i
$421$	−29.8071	−	10.3163i	−1.45271	−	0.502788i	−0.517131	−	0.855906i	$-0.673000\pi$
$421$	−29.8071	−	10.3163i	−1.45271	−	0.502788i	−0.935579	+	0.353118i	$0.885121\pi$
$422$	5.00486	−	0.719590i	0.243633	−	0.0350291i
$423$	5.63897	+	17.3974i	0.274176	+	0.845893i
$424$	1.43249	+	1.24126i	0.0695680	+	0.0602810i
$425$	0.148941	−	3.12665i	0.00722469	−	0.151665i
$426$	−6.41749	+	6.29193i	−0.310928	+	0.304845i
$427$	−0.279002	−	0.806123i	−0.0135018	−	0.0390110i
$428$	−7.06706	+	6.73842i	−0.341599	+	0.325714i
$429$	−6.47041	+	9.35949i	−0.312395	+	0.451880i
$430$	−1.80175	+	5.20582i	−0.0868881	+	0.251047i
$431$	9.96858	+	21.8282i	0.480170	+	1.05143i	0.982417	+	0.186701i	$0.0597795\pi$
$431$	9.96858	+	21.8282i	0.480170	+	1.05143i	−0.502247	+	0.864724i	$0.667493\pi$
$432$	15.9352	−	2.19629i	0.766685	−	0.105669i
$433$	1.08449	+	0.495269i	0.0521172	+	0.0238011i	0.441303	−	0.897358i	$-0.354516\pi$
$433$	1.08449	+	0.495269i	0.0521172	+	0.0238011i	−0.389186	+	0.921159i	$0.627244\pi$
$434$	−0.465387	+	0.186313i	−0.0223393	+	0.00894330i
$435$	−1.03531	+	5.80545i	−0.0496392	+	0.278350i
$436$	23.5208	+	13.5797i	1.12644	+	0.650351i
$437$	−22.8852	−	8.66577i	−1.09475	−	0.414540i
$438$	2.20622	+	0.502809i	0.105417	+	0.0240251i
$439$	28.5868	+	14.7375i	1.36437	+	0.703384i	0.975929	−	0.218089i	$-0.0699822\pi$
$439$	28.5868	+	14.7375i	1.36437	+	0.703384i	0.388445	+	0.921472i	$0.373012\pi$
$440$	4.93898	+	0.710118i	0.235457	+	0.0338536i
$441$	16.1540	−	13.4481i	0.769239	−	0.640384i
$442$	1.64644	+	5.60724i	0.0783129	+	0.266709i
$443$	10.5153	+	7.48791i	0.499597	+	0.355761i	0.801908	−	0.597448i	$-0.203819\pi$
$443$	10.5153	+	7.48791i	0.499597	+	0.355761i	−0.302311	+	0.953209i	$0.597758\pi$
$444$	−15.4976	+	24.8692i	−0.735482	+	1.18024i
$445$	−41.0611	−	16.4384i	−1.94648	−	0.779253i
$446$	3.13018	+	3.28284i	0.148218	+	0.155447i
$447$	−14.4899	+	32.9343i	−0.685351	+	1.55774i
$448$	16.9075	+	0.805402i	0.798803	+	0.0380517i
$449$	15.4954	−	24.1114i	0.731275	−	1.13789i	−0.254048	−	0.967192i	$-0.581762\pi$
$449$	15.4954	−	24.1114i	0.731275	−	1.13789i	0.985324	−	0.170695i	$-0.0546014\pi$
$450$	0.482993	+	1.11541i	0.0227685	+	0.0525811i
$451$	1.84984	−	6.29999i	0.0871057	−	0.296655i
$452$	9.43091	−	7.41655i	0.443592	−	0.348845i
$453$	−13.4976	+	7.19805i	−0.634170	+	0.338194i
$454$	0.0772660	−	0.809166i	0.00362627	−	0.0379760i
$455$	−43.6701	−	10.5942i	−2.04728	−	0.496666i
$456$	−12.3388	+	5.14015i	−0.577819	+	0.240710i
$457$	−0.435069	−	1.08675i	−0.0203517	−	0.0508360i	0.917844	−	0.396941i	$-0.129928\pi$
$457$	−0.435069	−	1.08675i	−0.0203517	−	0.0508360i	−0.938196	+	0.346105i	$0.887504\pi$
$458$	−4.15771	+	2.67200i	−0.194277	+	0.124854i
$459$	9.83268	−	12.3542i	0.458950	−	0.576644i
$460$	19.5944	−	9.39810i	0.913596	−	0.438189i
$461$	−6.19576	+	3.57712i	−0.288565	+	0.166603i	−0.637295	−	0.770620i	$-0.719947\pi$
$461$	−6.19576	+	3.57712i	−0.288565	+	0.166603i	0.348729	+	0.937223i	$0.386613\pi$
$462$	−3.37219	−	0.601376i	−0.156889	−	0.0279785i
$463$	1.47041	+	1.15634i	0.0683356	+	0.0537397i	0.651743	−	0.758440i	$-0.274038\pi$
$463$	1.47041	+	1.15634i	0.0683356	+	0.0537397i	−0.583407	+	0.812180i	$0.698281\pi$
$464$	3.49627	−	2.48968i	0.162310	−	0.115581i
$465$	−0.0890550	−	1.44573i	−0.00412983	−	0.0670440i
$466$	4.93870	−	6.93543i	0.228781	−	0.321278i
$467$	9.87831	+	11.4002i	0.457114	+	0.527537i	0.936782	−	0.349912i	$-0.113789\pi$
$467$	9.87831	+	11.4002i	0.457114	+	0.527537i	−0.479669	+	0.877450i	$0.659243\pi$
$468$	18.2887	+	19.9556i	0.845397	+	0.922449i
$469$	16.8200	+	4.93881i	0.776678	+	0.228053i
$470$	5.78156	+	1.11431i	0.266684	+	0.0513991i
$471$	−0.920216	+	3.30341i	−0.0424013	+	0.152213i
$472$	17.2623	−	8.89935i	0.794563	−	0.409626i
$473$	7.24139	−	2.50627i	0.332959	−	0.115238i
$474$	8.45641	−	0.117730i	0.388416	−	0.00540753i
$475$	3.24917	+	4.13166i	0.149082	+	0.189574i
$476$	15.8596	−	13.7425i	0.726925	−	0.629884i
$477$	3.29255	−	1.81518i	0.150755	−	0.0831115i
$478$	−3.05038	+	0.895673i	−0.139521	+	0.0409671i
$479$	11.7386	−	1.12090i	0.536352	−	0.0512154i	0.176634	−	0.984277i	$-0.443479\pi$
$479$	11.7386	−	1.12090i	0.536352	−	0.0512154i	0.359718	+	0.933061i	$0.382873\pi$
$480$	6.47259	−	16.8436i	0.295432	−	0.768801i
$481$	−44.7780	+	2.13304i	−2.04170	+	0.0972582i
$482$	0.991079	−	1.71660i	0.0451424	−	0.0781889i
$483$	−28.4670	+	12.4927i	−1.29530	+	0.568437i
$484$	8.48374	+	14.6943i	0.385625	+	0.667921i
$485$	−9.74197	−	15.1588i	−0.442360	−	0.688326i
$486$	−1.31404	+	5.98878i	−0.0596060	+	0.271657i
$487$	16.0089	−	35.0545i	0.725431	−	1.58847i	−0.0807024	−	0.996738i	$-0.525716\pi$
$487$	16.0089	−	35.0545i	0.725431	−	1.58847i	0.806133	−	0.591734i	$-0.201556\pi$
$488$	0.249495	+	0.237893i	0.0112941	+	0.0107689i
$489$	1.62148	−	4.90484i	0.0733260	−	0.221804i
$490$	−1.28068	−	6.64480i	−0.0578552	−	0.300181i
$491$	2.93995	−	7.34364i	0.132678	−	0.331414i	−0.847121	−	0.531401i	$-0.821666\pi$
$491$	2.93995	−	7.34364i	0.132678	−	0.331414i	0.979799	+	0.199987i	$0.0640901\pi$
$492$	−13.6348	−	7.62098i	−0.614705	−	0.343580i
$493$	0.797324	−	4.13691i	0.0359097	−	0.186317i
$494$	−8.25535	−	5.30539i	−0.371426	−	0.238701i
$495$	4.70822	−	8.70593i	0.211619	−	0.391303i
$496$	−0.690394	+	0.796758i	−0.0309996	+	0.0357755i
$497$	11.6401	+	47.9811i	0.522130	+	2.15225i
$498$	−4.31403	+	2.04320i	−0.193317	+	0.0915582i
$499$	−37.7730	+	7.28016i	−1.69095	+	0.325905i	−0.941719	−	0.336401i	$-0.890790\pi$
$499$	−37.7730	+	7.28016i	−1.69095	+	0.325905i	−0.749234	+	0.662305i	$0.769578\pi$
$500$	17.9076	+	1.70997i	0.800851	+	0.0764720i
$501$	−10.6605	−	16.0911i	−0.476276	−	0.718896i
$502$	0.289476	+	3.03153i	0.0129200	+	0.135304i
$503$	−1.13526	+	7.89593i	−0.0506189	+	0.352062i	0.948733	+	0.316077i	$0.102366\pi$
$503$	−1.13526	+	7.89593i	−0.0506189	+	0.352062i	−0.999352	+	0.0359849i	$0.988543\pi$
$504$	−6.62137	+	15.6367i	−0.294939	+	0.696516i
$505$			35.0018i			1.55756i
$506$	2.27400	+	1.11867i	0.101091	+	0.0497309i
$507$	−4.19841	+	18.4217i	−0.186458	+	0.818137i
$508$	−0.553915	−	11.6281i	−0.0245760	−	0.515914i
$509$	−8.90554	+	11.3243i	−0.394731	+	0.501942i	−0.942277	−	0.334834i	$-0.891320\pi$
$509$	−8.90554	+	11.3243i	−0.394731	+	0.501942i	0.547546	+	0.836776i	$0.315562\pi$
$510$	−1.95482	−	4.69252i	−0.0865611	−	0.207788i
$511$	8.57825	−	8.99661i	0.379480	−	0.397987i
$512$	−20.4646	+	9.34589i	−0.904418	+	0.413034i
$513$	1.10697	+	26.4905i	0.0488741	+	1.16958i
$514$	0.760458	+	5.28910i	0.0335423	+	0.233292i
$515$	20.7051	−	5.02301i	0.912378	−	0.221340i
$516$	−1.98528	−	18.1211i	−0.0873970	−	0.797737i
$517$	−3.75300	−	7.27980i	−0.165057	−	0.320165i
$518$	−6.18400	−	11.9953i	−0.271710	−	0.527043i
$519$	1.87036	−	1.37152i	0.0820999	−	0.0602029i
$520$	17.6481	−	4.28137i	0.773919	−	0.187751i
$521$	−1.30246	−	9.05880i	−0.0570618	−	0.396873i	−0.998257	−	0.0590110i	$-0.981205\pi$
$521$	−1.30246	−	9.05880i	−0.0570618	−	0.396873i	0.941196	−	0.337862i	$-0.109704\pi$
$522$	0.429807	+	1.57851i	0.0188121	+	0.0690895i
$523$	−1.84322	+	0.841770i	−0.0805983	+	0.0368080i	−0.455306	−	0.890335i	$-0.650470\pi$
$523$	−1.84322	+	0.841770i	−0.0805983	+	0.0368080i	0.374708	+	0.927143i	$0.377743\pi$
$524$	24.5054	−	25.7005i	1.07052	−	1.12273i
$525$	6.62206	+	0.858198i	0.289010	+	0.0374548i
$526$	−4.75506	+	6.04654i	−0.207330	+	0.263642i
$527$	0.0492394	+	1.03366i	0.00214490	+	0.0450270i
$528$	−6.88313	+	2.12559i	−0.299550	+	0.0925042i
$529$	22.7974	−	3.04637i	0.991190	−	0.132451i
$530$		−	1.21045i		−	0.0525786i
$531$	−4.72803	−	38.2321i	−0.205179	−	1.65913i
$532$	−5.01495	+	34.8797i	−0.217426	+	1.51223i
$533$	−2.27150	−	23.7882i	−0.0983895	−	1.03038i
$534$	−12.2470	+	0.754402i	−0.529981	+	0.0326462i
$535$	12.9355	+	1.23519i	0.559252	+	0.0534021i
$536$	−6.95630	+	1.34072i	−0.300467	+	0.0579102i
$537$	23.5422	+	16.2752i	1.01592	+	0.702327i
$538$	−0.477397	−	1.96786i	−0.0205820	−	0.0848403i
$539$	−6.16430	+	7.11398i	−0.265515	+	0.306421i
$540$	−17.7044	−	15.5228i	−0.761874	−	0.667993i
$541$	12.2763	+	7.88953i	0.527801	+	0.339197i	0.777251	−	0.629190i	$-0.216613\pi$
$541$	12.2763	+	7.88953i	0.527801	+	0.339197i	−0.249450	+	0.968388i	$0.580250\pi$
$542$	−0.653983	+	3.39319i	−0.0280910	+	0.145750i
$543$	15.0344	−	8.96143i	0.645186	−	0.384572i
$544$	−4.79131	+	11.9681i	−0.205426	+	0.513128i
$545$	−6.83999	−	35.4892i	−0.292993	−	1.52019i
$546$	−12.2072	+	2.52948i	−0.522420	+	0.108252i
$547$	5.73878	+	5.47192i	0.245373	+	0.233962i	0.802778	−	0.596278i	$-0.203354\pi$
$547$	5.73878	+	5.47192i	0.245373	+	0.233962i	−0.557405	+	0.830241i	$0.688203\pi$
$548$	−6.92472	+	15.1630i	−0.295809	+	0.647732i
$549$	0.613855	−	0.301265i	0.0261987	−	0.0128577i
$550$	−0.294295	−	0.457932i	−0.0125488	−	0.0195263i
$551$	3.53726	+	6.12672i	0.150692	+	0.261007i
$552$	7.91193	−	9.75887i	0.336754	−	0.415365i
$553$	23.2303	−	40.2360i	0.987852	−	1.71101i
$554$	−5.58269	+	0.265936i	−0.237186	+	0.0112985i
$555$	38.5167	−	6.08628i	1.63494	−	0.258348i
$556$	33.6492	−	3.21311i	1.42705	−	0.136266i
$557$	25.7430	−	7.55883i	1.09077	−	0.320278i	0.313589	−	0.949559i	$-0.398469\pi$
$557$	25.7430	−	7.55883i	1.09077	−	0.320278i	0.777178	+	0.629281i	$0.216650\pi$
$558$	−0.194005	−	0.351905i	−0.00821289	−	0.0148973i
$559$	21.0767	−	18.2630i	0.891448	−	0.772444i
$560$	−17.5869	−	22.3635i	−0.743181	−	0.945032i
$561$	−3.44997	+	6.17239i	−0.145658	+	0.260598i
$562$	0.658269	−	0.227829i	0.0277674	−	0.00961039i
$563$	−31.7139	+	16.3497i	−1.33658	+	0.689057i	−0.970404	−	0.241488i	$-0.922365\pi$
$563$	−31.7139	+	16.3497i	−1.33658	+	0.689057i	−0.366180	+	0.930544i	$0.619334\pi$
$564$	−18.8693	+	4.85673i	−0.794539	+	0.204505i
$565$	−15.6775	−	3.02159i	−0.659558	−	0.127119i
$566$	0.105453	+	0.0309639i	0.00443253	+	0.00130151i
$567$	24.5643	+	23.0458i	1.03161	+	0.967833i
$568$	−13.0662	−	15.0792i	−0.548247	−	0.632711i
$569$	1.93569	−	2.71830i	0.0811484	−	0.113957i	−0.772007	−	0.635615i	$-0.780747\pi$
$569$	1.93569	−	2.71830i	0.0811484	−	0.113957i	0.853155	+	0.521658i	$0.174686\pi$
$570$	7.64084	+	3.80544i	0.320040	+	0.159392i
$571$	−6.96344	+	4.95864i	−0.291411	+	0.207513i	−0.716407	−	0.697682i	$-0.754215\pi$
$571$	−6.96344	+	4.95864i	−0.291411	+	0.207513i	0.424997	+	0.905195i	$0.360275\pi$
$572$	−9.52876	−	7.49350i	−0.398418	−	0.313319i
$573$	−4.64107	−	12.8288i	−0.193884	−	0.535933i
$574$	6.23011	−	3.59695i	0.260040	−	0.150134i
$575$	−4.53165	−	1.96732i	−0.188983	−	0.0820431i
$576$	1.02266	+	13.5298i	0.0426108	+	0.563743i
$577$	−8.44447	+	5.42693i	−0.351548	+	0.225926i	−0.704482	−	0.709722i	$-0.748820\pi$
$577$	−8.44447	+	5.42693i	−0.351548	+	0.225926i	0.352934	+	0.935648i	$0.385184\pi$
$578$	−1.13531	−	2.83586i	−0.0472226	−	0.117956i
$579$	−5.70216	+	43.9992i	−0.236974	+	1.82854i
$580$	−6.10552	−	1.48118i	−0.253518	−	0.0615028i
$581$	−2.49268	+	26.1045i	−0.103414	+	1.08300i
$582$	−4.24263	−	2.64385i	−0.175862	−	0.109591i
$583$	−1.32352	+	1.04083i	−0.0548148	+	0.0431068i
$584$	−1.41531	+	4.82009i	−0.0585658	+	0.199457i
$585$	4.13181	−	35.7836i	0.170829	−	1.47947i
$586$	5.99284	−	9.32503i	0.247562	−	0.385214i
$587$	−8.49883	−	0.404849i	−0.350784	−	0.0167099i	−0.128549	−	0.991703i	$-0.541032\pi$
$587$	−8.49883	−	0.404849i	−0.350784	−	0.0167099i	−0.222235	+	0.974993i	$0.571335\pi$
$588$	13.2421	+	18.0586i	0.546096	+	0.744722i
$589$	−1.19914	−	1.25762i	−0.0494098	−	0.0518195i
$590$	−11.5141	−	4.60956i	−0.474029	−	0.189773i
$591$	48.0317	+	1.61826i	1.97576	+	0.0665664i
$592$	−23.1193	−	16.4632i	−0.950199	−	0.676634i
$593$	−1.92025	−	6.53979i	−0.0788554	−	0.268557i	0.910623	−	0.413238i	$-0.135602\pi$
$593$	−1.92025	−	6.53979i	−0.0788554	−	0.268557i	−0.989478	+	0.144682i	$0.953784\pi$
$594$	0.146656	−	2.74188i	0.00601737	−	0.112501i
$595$	−27.6419	−	3.97431i	−1.13321	−	0.162931i
$596$	−34.0722	−	17.5654i	−1.39565	−	0.719508i
$597$	16.8854	−	18.2098i	0.691072	−	0.745278i
$598$	9.19640	+	0.703782i	0.376069	+	0.0287798i
$599$	26.4110	+	15.2484i	1.07913	+	0.623033i	0.930660	−	0.365884i	$-0.119233\pi$
$599$	26.4110	+	15.2484i	1.07913	+	0.623033i	0.148465	+	0.988918i	$0.452567\pi$
$600$	−2.53755	+	0.918007i	−0.103595	+	0.0374775i
$601$	10.8368	−	4.33839i	0.442041	−	0.176966i	−0.139956	−	0.990158i	$-0.544696\pi$
$601$	10.8368	−	4.33839i	0.442041	−	0.176966i	0.581996	+	0.813191i	$0.302272\pi$
$602$	7.63699	+	3.48770i	0.311261	+	0.142148i
$603$	−2.27424	+	13.8669i	−0.0926142	+	0.564705i
$604$	−6.77006	−	14.8244i	−0.275470	−	0.603195i
$605$	7.38502	−	21.3376i	0.300244	−	0.867497i
$606$	4.15638	+	8.77582i	0.168842	+	0.356493i
$607$	30.9618	−	29.5220i	1.25670	−	1.19826i	0.285929	−	0.958251i	$-0.407698\pi$
$607$	30.9618	−	29.5220i	1.25670	−	1.19826i	0.970770	−	0.240010i	$-0.0771507\pi$
$608$	−7.08018	−	20.4568i	−0.287139	−	0.829634i
$609$	8.65776	+	2.41176i	0.350830	+	0.0977293i
$610$	0.0104751	−	0.219899i	0.000424123	−	0.00890344i
$611$	−22.5274	−	19.5201i	−0.911361	−	0.789698i
$612$	12.4930	+	11.2650i	0.504999	+	0.455360i
$613$	17.0432	−	2.45045i	0.688369	−	0.0989725i	0.210751	−	0.977540i	$-0.432409\pi$
$613$	17.0432	−	2.45045i	0.688369	−	0.0989725i	0.477619	+	0.878567i	$0.341500\pi$
$614$	3.41590	+	1.18225i	0.137854	+	0.0477119i
$615$	4.21761	+	20.3540i	0.170070	+	0.820754i
$616$	1.79287	−	7.39031i	0.0722368	−	0.297764i
$617$	5.01009	+	7.03569i	0.201699	+	0.283246i	0.903019	−	0.429600i	$-0.141345\pi$
$617$	5.01009	+	7.03569i	0.201699	+	0.283246i	−0.701321	+	0.712846i	$0.747406\pi$
$618$	4.59482	−	3.71808i	0.184831	−	0.149563i
$619$	15.3406	−	29.7567i	0.616592	−	1.19602i	−0.349284	−	0.937017i	$-0.613575\pi$
$619$	15.3406	−	29.7567i	0.616592	−	1.19602i	0.965876	−	0.259005i	$-0.0833945\pi$
$620$	1.54317			0.0619754
$621$	−12.7391	−	21.4176i	−0.511202	−	0.859461i
$622$	2.97086			0.119121
$623$	−30.8880	+	59.9144i	−1.23750	+	2.40042i
$624$	−20.3811	+	16.4922i	−0.815899	+	0.660217i
$625$	−16.8735	−	23.6956i	−0.674941	−	0.947822i
$626$	1.79316	−	7.39149i	0.0716690	−	0.295424i
$627$	−2.40921	−	11.6268i	−0.0962147	−	0.464329i
$628$	−3.45246	−	1.19491i	−0.137768	−	0.0476821i
$629$	−27.5755	+	3.96476i	−1.09951	+	0.158085i
$630$	10.3157	−	3.34360i	0.410989	−	0.133212i
$631$	17.9982	+	15.5955i	0.716498	+	0.620849i	0.934859	−	0.355019i	$-0.115526\pi$
$631$	17.9982	+	15.5955i	0.716498	+	0.620849i	−0.218361	+	0.975868i	$0.570071\pi$
$632$	−0.893387	+	18.7545i	−0.0355370	+	0.746014i
$633$	21.4497	+	5.97515i	0.852549	+	0.237491i
$634$	1.45977	+	4.21774i	0.0579750	+	0.167508i
$635$	−11.2118	+	10.6904i	−0.444928	+	0.424238i
$636$	1.71454	+	3.62009i	0.0679859	+	0.143546i
$637$	−11.2049	+	32.3744i	−0.443954	+	1.28272i
$638$	−0.304355	−	0.666444i	−0.0120495	−	0.0263848i
$639$	−37.0258	+	13.9807i	−1.46472	+	0.553066i
$640$	22.9266	+	10.4702i	0.906253	+	0.413872i
$641$	34.0382	−	13.6268i	1.34443	−	0.538228i	0.415873	−	0.909423i	$-0.363476\pi$
$641$	34.0382	−	13.6268i	1.34443	−	0.538228i	0.928555	+	0.371195i	$0.121052\pi$
$642$	3.38994	−	1.22637i	0.133790	−	0.0484011i
$643$	40.8998	+	23.6135i	1.61293	+	0.931225i	0.988687	+	0.149995i	$0.0479256\pi$
$643$	40.8998	+	23.6135i	1.61293	+	0.931225i	0.624243	+	0.781231i	$0.285408\pi$
$644$	−11.4197	−	31.0893i	−0.449998	−	1.22509i
$645$	−16.4945	+	17.7883i	−0.649472	+	0.700415i
$646$	−5.42050	−	2.79446i	−0.213267	−	0.109947i
$647$	−19.2048	−	2.76124i	−0.755020	−	0.108555i	−0.245952	−	0.969282i	$-0.579101\pi$
$647$	−19.2048	−	2.76124i	−0.755020	−	0.108555i	−0.509068	+	0.860726i	$0.670010\pi$
$648$	−13.0911	−	3.72920i	−0.514267	−	0.146497i
$649$	4.86050	+	16.5533i	0.190791	+	0.649775i
$650$	−1.61376	−	1.14916i	−0.0632970	−	0.0450736i
$651$	−2.20629	−	0.0743332i	−0.0864713	−	0.00291335i
$652$	5.10944	+	2.04551i	0.200101	+	0.0801084i
$653$	−17.3796	−	18.2272i	−0.680117	−	0.713286i	0.289701	−	0.957117i	$-0.406444\pi$
$653$	−17.3796	−	18.2272i	−0.680117	−	0.713286i	−0.969818	+	0.243831i	$0.921596\pi$
$654$	−5.92922	−	8.08580i	−0.231851	−	0.316180i
$655$	−47.2027	−	2.24854i	−1.84436	−	0.0878579i
$656$	8.17953	−	12.7276i	0.319357	−	0.496929i
$657$	8.00112	+	5.93925i	0.312154	+	0.231712i
$658$	2.52815	−	8.61008i	0.0985575	−	0.335656i
$659$	−24.8037	+	19.5058i	−0.966213	+	0.759838i	−0.970735	−	0.240151i	$-0.922803\pi$
$659$	−24.8037	+	19.5058i	−0.966213	+	0.759838i	0.00452228	+	0.999990i	$0.498561\pi$
$660$	8.94922	+	5.57683i	0.348348	+	0.217078i
$661$	−0.522973	+	5.47682i	−0.0203413	+	0.213023i	0.979587	+	0.201022i	$0.0644263\pi$
$661$	−0.522973	+	5.47682i	−0.0203413	+	0.213023i	−0.999928	+	0.0120014i	$0.996180\pi$
$662$	−6.49087	−	1.57467i	−0.252275	−	0.0612012i
$663$	−3.30750	+	25.5215i	−0.128453	+	0.991172i
$664$	−3.93866	−	9.83829i	−0.152850	−	0.381800i
$665$	39.4493	−	25.3525i	1.52978	−	0.983128i
$666$	8.93436	−	6.09975i	0.346199	−	0.236360i
$667$	−5.66039	−	3.48896i	−0.219171	−	0.135093i
$668$	17.8090	−	10.2820i	0.689052	−	0.397824i
$669$	6.79530	+	18.7836i	0.262721	+	0.726214i
$670$	3.55618	+	2.79661i	0.137387	+	0.108042i
$671$	−0.249448	+	0.177631i	−0.00962982	+	0.00685737i
$672$	−24.6166	−	12.2600i	−0.949606	−	0.472941i
$673$	12.7420	−	17.8936i	0.491168	−	0.689748i	−0.492383	−	0.870378i	$-0.663874\pi$
$673$	12.7420	−	17.8936i	0.491168	−	0.689748i	0.983551	+	0.180630i	$0.0578136\pi$
$674$	4.20371	+	4.85134i	0.161921	+	0.186867i
$675$	−0.0312408	+	5.35255i	−0.00120246	+	0.206020i
$676$	−19.3141	−	5.67112i	−0.742849	−	0.218120i
$677$	8.04149	+	1.54987i	0.309060	+	0.0595664i	0.341423	−	0.939910i	$-0.389091\pi$
$677$	8.04149	+	1.54987i	0.309060	+	0.0595664i	−0.0323632	+	0.999476i	$0.510303\pi$
$678$	−4.28955	+	1.10408i	−0.164739	+	0.0424020i
$679$	−24.4095	+	12.5840i	−0.936751	+	0.482929i
$680$	10.6649	−	3.69116i	0.408980	−	0.141549i
$681$	1.74643	−	3.12456i	0.0669232	−	0.119733i
$682$	0.111243	+	0.141457i	0.00425972	+	0.00541667i
$683$	13.9099	−	12.0530i	0.532248	−	0.461195i	−0.346793	−	0.937942i	$-0.612729\pi$
$683$	13.9099	−	12.0530i	0.532248	−	0.461195i	0.879041	+	0.476746i	$0.158184\pi$
$684$	−28.2416	−	0.558062i	−1.07985	−	0.0213380i
$685$	21.2842	−	6.24961i	0.813228	−	0.238785i
$686$	−0.00933352		0.000891243i	−0.000356355		3.40278e-5i
$687$	−21.4974	+	3.39695i	−0.820179	+	0.129602i
$688$	17.6368	−	0.840142i	0.672395	−	0.0320301i
$689$	−3.06397	+	5.30695i	−0.116728	+	0.202179i
$690$	−8.01863	+	0.262638i	−0.305264	+	0.00999848i
$691$	−9.03090	−	15.6420i	−0.343552	−	0.595049i	0.641538	−	0.767091i	$-0.278297\pi$
$691$	−9.03090	−	15.6420i	−0.343552	−	0.595049i	−0.985090	+	0.172042i	$0.944963\pi$
$692$	1.33591	+	2.07872i	0.0507839	+	0.0790212i
$693$	−12.5261	−	8.40431i	−0.475829	−	0.319253i
$694$	1.18748	−	2.60023i	0.0450763	−	0.0987033i
$695$	−32.5553	−	31.0414i	−1.23489	−	1.17747i
$696$	−3.55646	+	0.736943i	−0.134807	+	0.0279337i
$697$	−2.81048	−	14.5822i	−0.106455	−	0.552339i
$698$	0.754861	−	1.88555i	0.0285719	−	0.0713692i
$699$	32.2063	−	19.1970i	1.21815	−	0.726096i
$700$	−1.34634	+	6.98547i	−0.0508869	+	0.264026i
$701$	0.229034	+	0.147191i	0.00865049	+	0.00555933i	0.544959	−	0.838463i	$-0.316545\pi$
$701$	0.229034	+	0.147191i	0.00865049	+	0.00555933i	−0.536308	+	0.844022i	$0.680182\pi$
$702$	−3.21328	−	9.46248i	−0.121277	−	0.357138i
$703$	30.6349	−	35.3546i	1.15542	−	1.33342i
$704$	−1.43258	−	5.90516i	−0.0539923	−	0.222559i
$705$	21.3282	+	14.7446i	0.803266	+	0.555315i
$706$	−8.15591	+	1.57192i	−0.306952	+	0.0591601i
$707$	53.1030	+	5.07072i	1.99714	+	0.190704i
$708$	40.9645	−	2.52336i	1.53954	−	0.0948336i
$709$	2.78644	+	29.1810i	0.104647	+	1.09591i	0.883412	+	0.468598i	$0.155241\pi$
$709$	2.78644	+	29.1810i	0.104647	+	1.09591i	−0.778765	+	0.627316i	$0.784153\pi$
$710$	−1.81336	+	12.6122i	−0.0680542	+	0.473328i
$711$	34.2949	+	14.5221i	1.28616	+	0.544623i
$712$		−	27.2410i		−	1.02090i
$713$	1.55319	+	0.505039i	0.0581674	+	0.0189138i
$714$	−7.40245	+	2.28596i	−0.277030	+	0.0855498i
$715$	0.767578	+	16.1134i	0.0287058	+	0.602609i
$716$	−18.8486	+	23.9680i	−0.704406	+	0.895725i
$717$	−13.8839	−	1.79931i	−0.518502	−	0.0671963i
$718$	−6.44641	+	6.76080i	−0.240578	+	0.252311i
$719$	−24.3963	+	11.1414i	−0.909827	+	0.415504i	−0.814648	−	0.579956i	$-0.803070\pi$
$719$	−24.3963	+	11.1414i	−0.909827	+	0.415504i	−0.0951793	+	0.995460i	$0.530342\pi$
$720$	16.0609	−	16.1913i	0.598554	−	0.603412i
$721$	−4.62111	−	32.1405i	−0.172099	−	1.19698i
$722$	2.68937	−	0.652433i	0.100088	−	0.0242810i
$723$	7.03907	−	5.16167i	0.261786	−	0.191965i
$724$	8.54452	+	16.5741i	0.317555	+	0.615970i
$725$	0.654451	+	1.26946i	0.0243057	+	0.0471465i
$726$	−0.682186	−	6.22682i	−0.0253183	−	0.231099i
$727$	14.3838	−	3.48947i	0.533465	−	0.129417i	0.0400279	−	0.999199i	$-0.487255\pi$
$727$	14.3838	−	3.48947i	0.533465	−	0.129417i	0.493437	+	0.869781i	$0.335740\pi$
$728$	−3.93881	−	27.3950i	−0.145982	−	1.01533i
$729$	−15.9172	+	21.8092i	−0.589526	+	0.807750i
$730$	2.91818	−	1.33269i	0.108007	−	0.0493250i
$731$	11.9600	−	12.5433i	0.442358	−	0.463932i
$732$	0.280147	+	0.672488i	0.0103545	+	0.0248559i
$733$	10.8980	−	13.8580i	0.402529	−	0.511857i	−0.541958	−	0.840405i	$-0.682317\pi$
$733$	10.8980	−	13.8580i	0.402529	−	0.511857i	0.944487	+	0.328548i	$0.106559\pi$
$734$	0.511177	+	10.7309i	0.0188679	+	0.396086i
$735$	6.62180	−	29.0550i	0.244249	−	1.07171i
$736$	14.9869	+	13.7609i	0.552423	+	0.507233i
$737$		−	6.29309i		−	0.231809i
$738$	3.47446	+	4.60243i	0.127896	+	0.169418i
$739$	1.32552	−	9.21921i	0.0487601	−	0.339134i	−0.950809	−	0.309778i	$-0.899745\pi$
$739$	1.32552	−	9.21921i	0.0487601	−	0.339134i	0.999569	−	0.0293561i	$-0.00934569\pi$
$740$	3.94903	+	41.3561i	0.145169	+	1.52028i
$741$	−23.8670	−	36.0251i	−0.876776	−	1.32341i
$742$	−1.83644	−	0.175358i	−0.0674177	−	0.00643761i
$743$	12.5142	−	2.41191i	0.459100	−	0.0884843i	0.0455428	−	0.998962i	$-0.485498\pi$
$743$	12.5142	−	2.41191i	0.459100	−	0.0884843i	0.413557	+	0.910478i	$0.364286\pi$
$744$	0.806261	−	0.381860i	0.0295590	−	0.0139997i
$745$	12.0266	+	49.5743i	0.440620	+	1.81626i
$746$	−2.43312	+	2.80798i	−0.0890830	+	0.102807i
$747$	−21.0124	+	0.585184i	−0.768805	+	0.0214108i
$748$	−6.33754	−	4.07289i	−0.231724	−	0.148920i
$749$	3.74795	−	19.4462i	0.136947	−	0.710550i
$750$	−5.79712	−	3.24022i	−0.211681	−	0.118316i
$751$	−7.94880	+	19.8551i	−0.290056	+	0.724525i	0.709743	+	0.704461i	$0.248811\pi$
$751$	−7.94880	+	19.8551i	−0.290056	+	0.724525i	−0.999799	+	0.0200637i	$0.993613\pi$
$752$	−3.57156	−	18.5310i	−0.130242	−	0.675757i
$753$	−4.20934	+	12.7329i	−0.153397	+	0.464011i
$754$	−1.92980	−	1.84006i	−0.0702791	−	0.0670110i
$755$	−9.00924	+	19.7275i	−0.327880	+	0.717957i
$756$	−26.1152	+	24.6114i	−0.949801	+	0.895108i
$757$	−7.84006	−	12.1994i	−0.284952	−	0.443394i	0.669040	−	0.743226i	$-0.266705\pi$
$757$	−7.84006	−	12.1994i	−0.284952	−	0.443394i	−0.953992	+	0.299833i	$0.903069\pi$
$758$	6.71133	+	11.6244i	0.243766	+	0.422216i
$759$	7.18216	+	8.54186i	0.260696	+	0.310050i
$760$	−9.47536	+	16.4118i	−0.343707	+	0.595318i
$761$	46.0317	−	2.19276i	1.66865	−	0.0794876i	0.808162	−	0.588960i	$-0.200462\pi$
$761$	46.0317	−	2.19276i	1.66865	−	0.0794876i	0.860487	+	0.509472i	$0.170159\pi$
$762$	−1.54161	+	4.01174i	−0.0558468	+	0.145330i
$763$	−54.8335	+	5.23596i	−1.98511	+	0.189555i
$764$	13.9458	−	4.09485i	0.504541	−	0.148147i
$765$	0.442260	−	22.3813i	0.0159899	−	0.809197i
$766$	−4.45947	+	3.86415i	−0.161127	+	0.139617i
$767$	38.8131	+	49.3549i	1.40146	+	1.78210i
$768$	−8.67437	+	0.120765i	−0.313009	+	0.00435772i
$769$	16.9138	−	5.85392i	0.609927	−	0.211098i	−0.00460526	−	0.999989i	$-0.501466\pi$
$769$	16.9138	−	5.85392i	0.609927	−	0.211098i	0.614532	+	0.788892i	$0.289345\pi$
$770$	−4.31653	+	2.22532i	−0.155557	+	0.0801951i
$771$	−6.31450	+	22.6679i	−0.227411	+	0.816364i
$772$	−46.4139	−	8.94554i	−1.67047	−	0.321957i
$773$	25.5646	+	7.50643i	0.919493	+	0.269988i	0.707032	−	0.707182i	$-0.250034\pi$
$773$	25.5646	+	7.50643i	0.919493	+	0.269988i	0.212461	+	0.977169i	$0.431852\pi$
$774$	−2.02326	+	6.41867i	−0.0727248	+	0.230714i
$775$	−0.229732	−	0.265124i	−0.00825220	−	0.00952355i
$776$	6.43756	−	9.04029i	0.231095	−	0.324528i
$777$	−3.65387	−	59.3174i	−0.131082	−	2.12800i
$778$	4.59609	−	3.27286i	0.164778	−	0.117338i
$779$	19.6017	+	15.4150i	0.702306	+	0.552299i
$780$	37.7805	+	6.73754i	1.35276	+	0.241243i
$781$	15.3496	−	8.86211i	0.549253	−	0.317111i
$782$	5.73084	−	0.107871i	0.204935	−	0.00385747i
$783$	−1.06688	+	7.12488i	−0.0381273	+	0.254622i
$784$	−18.2466	+	11.7264i	−0.651666	+	0.418800i
$785$	1.80693	+	4.51350i	0.0644921	+	0.161094i
$786$	−12.1019	+	5.04145i	−0.431661	+	0.179823i
$787$	26.7795	+	6.49665i	0.954588	+	0.231580i	0.682659	−	0.730737i	$-0.260823\pi$
$787$	26.7795	+	6.49665i	0.954588	+	0.231580i	0.271929	+	0.962317i	$0.412339\pi$
$788$	−4.86699	+	50.9695i	−0.173379	+	1.81571i
$789$	−29.8897	+	15.9397i	−1.06410	+	0.567469i
$790$	9.42502	−	7.41192i	0.335327	−	0.263704i
$791$	−6.85543	+	23.3474i	−0.243751	+	0.830139i
$792$	6.05568	+	0.699228i	0.215179	+	0.0248460i
$793$	−0.602548	+	0.937582i	−0.0213971	+	0.0332945i
$794$	0.303039	+	0.0144355i	0.0107544	+	0.000512297i
$795$	2.14663	−	4.87908i	0.0761330	−	0.173043i
$796$	18.2577	+	19.1481i	0.647128	+	0.678688i
$797$	−0.986880	−	0.395087i	−0.0349571	−	0.0139947i	0.354118	−	0.935201i	$-0.384781\pi$
$797$	−0.986880	−	0.395087i	−0.0349571	−	0.0139947i	−0.389075	+	0.921206i	$0.627205\pi$
$798$	6.88036	−	11.0410i	0.243562	−	0.390848i
$799$	−15.0895	−	10.7452i	−0.533827	−	0.380137i
$800$	−1.23124	−	4.19322i	−0.0435309	−	0.148253i
$801$	−50.7032	−	18.6782i	−1.79151	−	0.659962i
$802$	−1.70148	−	0.244635i	−0.0600812	−	0.00863838i
$803$	−3.96643	−	2.04484i	−0.139972	−	0.0721608i
$804$	−14.5967	−	3.32667i	−0.514786	−	0.117323i
$805$	−21.3151	+	38.5778i	−0.751259	+	1.35969i
$806$	0.567202	+	0.327474i	0.0199789	+	0.0115348i
$807$	1.56553	−	8.77865i	0.0551092	−	0.309023i
$808$	−20.0135	+	8.01221i	−0.704073	+	0.281868i
$809$	−16.5628	−	7.56400i	−0.582319	−	0.265936i	0.102400	−	0.994743i	$-0.467348\pi$
$809$	−16.5628	−	7.56400i	−0.582319	−	0.265936i	−0.684719	+	0.728807i	$0.740075\pi$
$810$	3.67486	+	7.87764i	0.129121	+	0.276792i
$811$	9.37690	+	20.5325i	0.329268	+	0.720995i	0.999782	−	0.0209016i	$-0.00665366\pi$
$811$	9.37690	+	20.5325i	0.329268	+	0.720995i	−0.670514	+	0.741897i	$0.733926\pi$
$812$	−3.13169	+	9.04842i	−0.109901	+	0.317537i
$813$	−8.65359	+	12.5175i	−0.303495	+	0.439007i
$814$	−3.50629	+	3.34324i	−0.122895	+	0.117180i
$815$	−2.39545	−	6.92120i	−0.0839090	−	0.242439i
$816$	−11.6344	+	11.4067i	−0.407284	+	0.399316i
$817$	−1.38477	+	29.0698i	−0.0484468	+	1.01702i
$818$	−1.22351	−	1.06018i	−0.0427791	−	0.0370683i
$819$	−53.6906	−	11.4526i	−1.87610	−	0.400185i
$820$	−21.9201	+	3.15164i	−0.765484	+	0.110060i
$821$	−11.2959	−	3.90955i	−0.394230	−	0.136444i	0.122759	−	0.992437i	$-0.460826\pi$
$821$	−11.2959	−	3.90955i	−0.394230	−	0.136444i	−0.516989	+	0.855992i	$0.672947\pi$
$822$	4.59435	−	4.09438i	0.160246	−	0.142808i
$823$	−9.11690	+	37.5804i	−0.317795	+	1.30997i	0.559025	+	0.829151i	$0.311176\pi$
$823$	−9.11690	+	37.5804i	−0.317795	+	1.30997i	−0.876820	+	0.480819i	$0.840339\pi$
$824$	7.61167	+	10.6891i	0.265165	+	0.372372i
$825$	−0.374141	−	2.36774i	−0.0130259	−	0.0824340i
$826$	−8.66146	+	16.8009i	−0.301371	+	0.584578i
$827$	16.0543			0.558263			0.279132	−	0.960253i	$-0.409953\pi$
$827$	16.0543			0.558263			0.279132	+	0.960253i	$0.409953\pi$
$828$	23.6093	−	12.1434i	0.820480	−	0.422014i
$829$	−25.7840			−0.895517			−0.447758	−	0.894155i	$-0.647778\pi$
$829$	−25.7840			−0.895517			−0.447758	+	0.894155i	$0.647778\pi$
$830$	−3.10108	+	6.01525i	−0.107640	+	0.208792i
$831$	−22.9743	−	8.82847i	−0.796970	−	0.306256i
$832$	−12.8279	−	18.0142i	−0.444727	−	0.624531i
$833$	−5.01934	+	20.6900i	−0.173910	+	0.716866i
$834$	−11.8485	−	3.91698i	−0.410280	−	0.135634i
$835$	−25.8605	−	8.95042i	−0.894941	−	0.309742i
$836$	12.5214	−	1.80030i	0.433061	−	0.0622647i
$837$	−0.157924	−	1.76251i	−0.00545865	−	0.0609211i
$838$	6.39874	+	5.54454i	0.221041	+	0.191533i
$839$	2.53155	−	53.1437i	0.0873987	−	1.83472i	−0.351500	−	0.936188i	$-0.614328\pi$
$839$	2.53155	−	53.1437i	0.0873987	−	1.83472i	0.438899	−	0.898536i	$-0.355369\pi$
$840$	6.00098	+	23.3149i	0.207054	+	0.804439i
$841$	−8.85625	−	25.5884i	−0.305388	−	0.882360i
$842$	−8.97868	+	8.56116i	−0.309426	+	0.295037i
$843$	3.05738	+	0.249049i	0.105302	+	0.00857769i
$844$	−7.75879	+	22.4176i	−0.267069	+	0.771644i
$845$	11.1278	+	24.3665i	0.382809	+	0.838234i
$846$	7.09840	+	1.16417i	0.244048	+	0.0400250i
$847$	−31.3025	−	14.2954i	−1.07557	−	0.491195i
$848$	−3.60182	+	1.44195i	−0.123687	+	0.0495168i
$849$	0.370149	+	0.311821i	0.0127035	+	0.0107017i
$850$	−1.06622	−	0.615585i	−0.0365712	−	0.0211144i
$851$	−9.56006	+	42.9169i	−0.327714	+	1.47117i
$852$	−12.4413	−	40.2878i	−0.426233	−	1.38024i
$853$	34.6114	+	17.8434i	1.18507	+	0.610946i	0.934087	−	0.357045i	$-0.116216\pi$
$853$	34.6114	+	17.8434i	1.18507	+	0.610946i	0.250983	+	0.967991i	$0.419246\pi$
$854$	−0.332102	−	0.0477491i	−0.0113643	−	0.00163394i
$855$	24.0501	+	28.8893i	0.822495	+	0.987993i
$856$	2.25479	+	7.67910i	0.0770671	+	0.262466i
$857$	−35.6696	−	25.4002i	−1.21845	−	0.867655i	−0.224180	−	0.974548i	$-0.571970\pi$
$857$	−35.6696	−	25.4002i	−1.21845	−	0.867655i	−0.994271	+	0.106893i	$0.965910\pi$
$858$	2.10589	+	3.94889i	0.0718938	+	0.134813i
$859$	8.31250	+	3.32782i	0.283619	+	0.113544i	0.509110	−	0.860701i	$-0.329975\pi$
$859$	8.31250	+	3.32782i	0.283619	+	0.113544i	−0.225491	+	0.974245i	$0.572399\pi$
$860$	−17.8351	−	18.7050i	−0.608173	−	0.637834i
$861$	31.4912	−	3.45005i	1.07322	−	0.117577i
$862$	9.42768	+	0.449096i	0.321108	+	0.0152963i
$863$	9.53827	−	14.8418i	0.324687	−	0.505222i	−0.640087	−	0.768302i	$-0.721102\pi$
$863$	9.53827	−	14.8418i	0.324687	−	0.505222i	0.964774	+	0.263080i	$0.0847383\pi$
$864$	7.33153	−	20.7897i	0.249424	−	0.707280i
$865$	0.926409	−	3.15506i	0.0314989	−	0.107275i
$866$	0.368601	−	0.289871i	0.0125256	−	0.00985022i
$867$	0.452954	−	13.4442i	0.0153831	−	0.456588i
$868$	0.223560	−	2.34123i	0.00758813	−	0.0794665i
$869$	−16.2086	−	3.93216i	−0.549839	−	0.133389i
$870$	1.84297	+	1.40825i	0.0624826	+	0.0477443i
$871$	−8.51231	−	21.2627i	−0.288429	−	0.720460i
$872$	18.7265	−	12.0348i	0.634160	−	0.407550i
$873$	−12.4125	−	18.1807i	−0.420100	−	0.615325i
$874$	−7.15411	+	6.43875i	−0.241991	+	0.217794i
$875$	−31.5961	+	18.2420i	−1.06814	+	0.616694i
$876$	−6.83970	+	8.11911i	−0.231092	+	0.274319i
$877$	5.01424	+	3.94324i	0.169319	+	0.133154i	0.699223	−	0.714904i	$-0.253530\pi$
$877$	5.01424	+	3.94324i	0.169319	+	0.133154i	−0.529904	+	0.848058i	$0.677772\pi$
$878$	10.3044	−	7.33771i	0.347756	−	0.247636i
$879$	40.6930	−	26.9596i	1.37254	−	0.909323i
$880$	−5.92431	+	8.31953i	−0.199709	+	0.280451i
$881$	−22.2751	−	25.7069i	−0.750469	−	0.866087i	0.244145	−	0.969739i	$-0.421493\pi$
$881$	−22.2751	−	25.7069i	−0.750469	−	0.866087i	−0.994614	+	0.103652i	$0.966947\pi$
$882$	−1.78997	−	8.07113i	−0.0602713	−	0.271769i
$883$	40.5705	+	11.9126i	1.36531	+	0.400890i	0.880631	−	0.473803i	$-0.157119\pi$
$883$	40.5705	+	11.9126i	1.36531	+	0.400890i	0.484677	+	0.874693i	$0.338937\pi$
$884$	−26.9221	−	5.18881i	−0.905488	−	0.174518i
$885$	−38.2365	−	38.9995i	−1.28530	−	1.31095i
$886$	4.51292	−	2.32657i	0.151614	−	0.0781627i
$887$	−10.0969	+	3.49457i	−0.339021	+	0.117336i	−0.491274	−	0.871005i	$-0.663468\pi$
$887$	−10.0969	+	3.49457i	−0.339021	+	0.117336i	0.152253	+	0.988342i	$0.451347\pi$
$888$	12.2968	+	20.6301i	0.412655	+	0.692301i
$889$	14.5948	+	18.5588i	0.489493	+	0.622441i
$890$	−13.1472	+	11.3921i	−0.440696	+	0.381865i
$891$	5.45363	−	10.7919i	0.182703	−	0.361542i
$892$	−20.4189	+	5.99554i	−0.683677	+	0.200746i
$893$	30.9651	−	2.95681i	1.03621	−	0.0989458i
$894$	8.90220	+	11.0014i	0.297734	+	0.367941i
$895$	40.5306	−	1.93071i	1.35479	−	0.0645365i
$896$	19.2063	−	33.2663i	0.641637	−	1.11135i
$897$	35.8207	+	19.1458i	1.19602	+	0.639260i
$898$	−5.63652	−	9.76274i	−0.188093	−	0.325787i
$899$	−0.255273	−	0.397213i	−0.00851383	−	0.0132478i
$900$	−5.68969	−	0.383824i	−0.189656	−	0.0127941i
$901$	−1.58200	+	3.46409i	−0.0527040	+	0.115406i
$902$	−1.86906	−	1.78214i	−0.0622328	−	0.0593389i
$903$	24.5980	+	27.6017i	0.818572	+	0.918528i
$904$	−1.86101	−	9.65585i	−0.0618964	−	0.321149i
$905$	9.22257	−	23.0369i	0.306569	−	0.765772i
$906$	0.0837548	+	6.01600i	0.00278257	+	0.199868i
$907$	−4.44090	+	23.0416i	−0.147458	+	0.765083i	0.830619	+	0.556841i	$0.187987\pi$
$907$	−4.44090	+	23.0416i	−0.147458	+	0.765083i	−0.978077	+	0.208243i	$0.933226\pi$
$908$	3.20816	+	2.06176i	0.106467	+	0.0684220i
$909$	1.19041	+	42.7445i	0.0394834	+	1.41775i
$910$	−11.5744	+	13.3575i	−0.383686	+	0.442797i
$911$	−3.81650	−	15.7318i	−0.126446	−	0.521219i	−0.999439	−	0.0334860i	$-0.989339\pi$
$911$	−3.81650	−	15.7318i	−0.126446	−	0.521219i	0.872993	−	0.487733i	$-0.162176\pi$
$912$	2.22131	−	27.2693i	0.0735548	−	0.902977i
$913$	9.24368	−	1.78157i	0.305921	−	0.0589615i
$914$	−0.458337	−	0.0437658i	−0.0151604	−	0.00144765i
$915$	0.432194	−	0.867791i	0.0142879	−	0.0286883i
$916$	−2.20408	−	23.0822i	−0.0728250	−	0.762658i
$917$	−10.2497	+	71.2880i	−0.338474	+	2.35414i
$918$	−2.54684	−	5.66406i	−0.0840583	−	0.186942i
$919$		−	36.5577i		−	1.20593i	−0.797769	−	0.602964i	$-0.793986\pi$
$919$		−	36.5577i		−	1.20593i	0.797769	−	0.602964i	$-0.206014\pi$
$920$	0.512532	−	17.8042i	0.0168977	−	0.586988i
$921$	11.6722	+	10.8232i	0.384611	+	0.356637i
$922$	0.133891	+	2.81072i	0.00440947	+	0.0925661i
$923$	39.8751	−	50.7053i	1.31251	−	1.66899i
$924$	9.75737	−	12.7694i	0.320994	−	0.420083i
$925$	6.51727	−	6.83512i	0.214287	−	0.224737i
$926$	0.669264	−	0.305643i	0.0219934	−	0.0100440i
$927$	25.1145	−	6.83833i	0.824868	−	0.224600i
$928$	−0.837106	−	5.82220i	−0.0274793	−	0.191123i
$929$	−40.6195	+	9.85419i	−1.33268	+	0.323305i	−0.837953	−	0.545742i	$-0.816248\pi$
$929$	−40.6195	+	9.85419i	−1.33268	+	0.323305i	−0.494729	+	0.869047i	$0.664733\pi$
$930$	−0.521472	−	0.229430i	−0.0170997	−	0.00752329i
$931$	−16.3817	−	31.7761i	−0.536890	−	1.04142i
$932$	18.3039	+	35.5046i	0.599563	+	1.16299i
$933$	11.9750	+	5.26856i	0.392042	+	0.172485i
$934$	5.76583	−	1.39877i	0.188664	−	0.0457693i
$935$	1.42673	+	9.92309i	0.0466589	+	0.324520i
$936$	21.4064	−	5.82866i	0.699689	−	0.190516i
$937$	−24.4417	+	11.1621i	−0.798475	+	0.364651i	−0.772503	−	0.635011i	$-0.780995\pi$
$937$	−24.4417	+	11.1621i	−0.798475	+	0.364651i	−0.0259723	+	0.999663i	$0.508268\pi$
$938$	4.75806	−	4.99011i	0.155356	−	0.162933i
$939$	20.3360	−	26.6136i	0.663641	−	0.868502i
$940$	−17.0760	+	21.7139i	−0.556958	+	0.708230i
$941$	−0.444322	−	9.32746i	−0.0144845	−	0.304067i	−0.994472	−	0.105006i	$-0.966514\pi$
$941$	−0.444322	−	9.32746i	−0.0144845	−	0.304067i	0.979987	−	0.199061i	$-0.0637891\pi$
$942$	0.989010	+	0.917076i	0.0322237	+	0.0298800i
$943$	−23.0938	−	4.00176i	−0.752039	−	0.130315i
$944$			39.7526i			1.29384i
$945$	47.5102	+	4.81666i	1.54551	+	0.156686i
$946$	0.428929	−	2.98327i	0.0139457	−	0.0969944i
$947$	−0.519786	−	5.44344i	−0.0168908	−	0.176888i	0.983090	−	0.183124i	$-0.0586210\pi$
$947$	−0.519786	−	5.44344i	−0.0168908	−	0.176888i	−0.999981	+	0.00623609i	$0.998015\pi$
$948$	−17.6888	+	35.5168i	−0.574505	+	1.15353i
$949$	−16.1675	−	1.54381i	−0.524819	−	0.0501141i
$950$	2.03001	−	0.391253i	0.0658623	−	0.0126939i
$951$	−1.59573	+	19.5896i	−0.0517452	+	0.635237i
$952$	−4.05502	−	16.7150i	−0.131424	−	0.541736i
$953$	3.09201	−	3.56836i	0.100160	−	0.115591i	−0.703456	−	0.710738i	$-0.748361\pi$
$953$	3.09201	−	3.56836i	0.100160	−	0.115591i	0.803616	+	0.595148i	$0.202906\pi$
$954$	−0.0411674	−	1.47821i	−0.00133284	−	0.0478589i
$955$	−16.2714	−	10.4570i	−0.526529	−	0.338380i
$956$	2.82275	−	14.6458i	0.0912942	−	0.473679i
$957$	−0.0449131	−	3.22605i	−0.00145183	−	0.104283i
$958$	1.72379	−	4.30581i	0.0556930	−	0.139114i
$959$	−6.39815	−	33.1968i	−0.206607	−	1.07198i
$960$	12.7986	+	14.3614i	0.413071	+	0.463512i
$961$	−22.3518	−	21.3124i	−0.721026	−	0.687497i
$962$	−7.32462	+	16.0387i	−0.236155	+	0.517108i
$963$	15.8390	+	1.06849i	0.510405	+	0.0344317i
$964$	5.02768	+	7.82323i	0.161931	+	0.251969i
$965$	31.4510	+	54.4746i	1.01244	+	1.75360i
$966$	−0.763200	+	12.2035i	−0.0245556	+	0.392642i
$967$	8.31902	−	14.4090i	0.267522	−	0.463361i	−0.700700	−	0.713456i	$-0.747129\pi$
$967$	8.31902	−	14.4090i	0.267522	−	0.463361i	0.968221	+	0.250095i	$0.0804620\pi$
$968$	13.8910	−	0.661711i	0.446475	−	0.0212682i
$969$	−16.8932	−	20.8767i	−0.542688	−	0.670656i
$970$	−7.05525	+	0.673695i	−0.226531	+	0.0216310i
$971$	−6.30866	+	1.85239i	−0.202454	+	0.0594460i	−0.381387	−	0.924415i	$-0.624554\pi$
$971$	−6.30866	+	1.85239i	−0.202454	+	0.0594460i	0.178933	+	0.983861i	$0.442735\pi$
$972$	−22.1486	−	18.3544i	−0.710418	−	0.588718i
$973$	−51.8108	+	44.8943i	−1.66098	+	1.43924i
$974$	−9.36967	−	11.9145i	−0.300224	−	0.381765i
$975$	−4.46683	−	7.49388i	−0.143053	−	0.239996i
$976$	−0.666809	+	0.230785i	−0.0213440	+	0.00738724i
$977$	−17.2993	+	8.91841i	−0.553454	+	0.285325i	−0.712179	−	0.701998i	$-0.752292\pi$
$977$	−17.2993	+	8.91841i	−0.553454	+	0.285325i	0.158726	+	0.987323i	$0.449261\pi$
$978$	−1.42248	−	1.45086i	−0.0454858	−	0.0463934i
$979$	23.7612	+	4.57960i	0.759412	+	0.146365i
$980$	30.4624	+	8.94458i	0.973087	+	0.285724i
$981$	−9.56005	−	43.1072i	−0.305229	−	1.37631i
$982$	−2.03744	−	2.35134i	−0.0650175	−	0.0750342i
$983$	3.02623	−	4.24974i	0.0965216	−	0.135546i	−0.763491	−	0.645819i	$-0.776516\pi$
$983$	3.02623	−	4.24974i	0.0965216	−	0.135546i	0.860013	+	0.510273i	$0.170456\pi$
$984$	−10.6727	+	7.07078i	−0.340234	+	0.225408i
$985$	55.5020	−	39.5228i	1.76844	−	1.25930i
$986$	−1.30255	−	1.02434i	−0.0414816	−	0.0326215i
$987$	25.4597	−	30.2220i	0.810390	−	0.961978i
$988$	39.8713	−	23.0197i	1.26847	−	0.732354i
$989$	−11.8293	−	24.6633i	−0.376149	−	0.784248i
$990$	−2.19501	−	3.21504i	−0.0697619	−	0.102181i
$991$	11.2304	−	7.21735i	0.356746	−	0.229267i	−0.349975	−	0.936759i	$-0.613810\pi$
$991$	11.2304	−	7.21735i	0.356746	−	0.229267i	0.706721	+	0.707492i	$0.250174\pi$
$992$	0.536974	+	1.34130i	0.0170490	+	0.0425862i
$993$	−23.3708	−	17.8581i	−0.741651	−	0.566711i
$994$	18.8719	+	4.57828i	0.598581	+	0.145214i
$995$	3.34675	−	35.0488i	0.106099	−	1.11112i
$996$	0.754094	−	22.3823i	0.0238944	−	0.709210i
$997$	−19.7340	+	15.5190i	−0.624982	+	0.491491i	−0.879703	−	0.475523i	$-0.842259\pi$
$997$	−19.7340	+	15.5190i	−0.624982	+	0.491491i	0.254721	+	0.967015i	$0.418016\pi$
$998$	−4.26270	+	14.5174i	−0.134933	+	0.459541i
$999$	46.8299	−	8.74257i	1.48163	−	0.276603i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	207.2.o.a.149.13	yes	440
3.2	odd	2		621.2.s.a.287.10		440
9.2	odd	6	inner	207.2.o.a.11.13	✓	440
9.7	even	3		621.2.s.a.494.10		440
23.21	odd	22	inner	207.2.o.a.113.13	yes	440
69.44	even	22		621.2.s.a.44.10		440
207.182	even	66	inner	207.2.o.a.182.13	yes	440
207.205	odd	66		621.2.s.a.251.10		440

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
207.2.o.a.11.13	✓	440	9.2	odd	6	inner
207.2.o.a.113.13	yes	440	23.21	odd	22	inner
207.2.o.a.149.13	yes	440	1.1	even	1	trivial
207.2.o.a.182.13	yes	440	207.182	even	66	inner
621.2.s.a.44.10		440	69.44	even	22
621.2.s.a.251.10		440	207.205	odd	66
621.2.s.a.287.10		440	3.2	odd	2
621.2.s.a.494.10		440	9.7	even	3

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)

\(f(q)\)	\(=\)	\(q+(0.180230 - 0.349597i) q^{2} +(1.34645 - 1.08953i) q^{3} +(1.07038 + 1.50314i) q^{4} +(0.578937 - 2.38641i) q^{5} +(-0.138227 - 0.667079i) q^{6} +(-3.53667 - 1.22405i) q^{7} +(1.49704 - 0.215242i) q^{8} +(0.625841 - 2.93399i) q^{9} +O(q^{10})\)	\(q+(0.180230 - 0.349597i) q^{2} +(1.34645 - 1.08953i) q^{3} +(1.07038 + 1.50314i) q^{4} +(0.578937 - 2.38641i) q^{5} +(-0.138227 - 0.667079i) q^{6} +(-3.53667 - 1.22405i) q^{7} +(1.49704 - 0.215242i) q^{8} +(0.625841 - 2.93399i) q^{9} +(-0.729939 - 0.632496i) q^{10} +(-0.0639269 + 1.34199i) q^{11} +(3.07892 + 0.857683i) q^{12} +(1.59924 + 4.62071i) q^{13} +(-1.06534 + 1.01580i) q^{14} +(-1.82056 - 3.84394i) q^{15} +(-1.01251 + 2.92547i) q^{16} +(1.26232 + 2.76408i) q^{17} +(-0.912919 - 0.747584i) q^{18} +(-4.64144 - 2.11967i) q^{19} +(4.20678 - 1.68414i) q^{20} +(-6.09559 + 2.20519i) q^{21} +(0.457634 + 0.264215i) q^{22} +(4.78526 - 0.318308i) q^{23} +(1.78117 - 1.92088i) q^{24} +(-0.915604 - 0.472027i) q^{25} +(1.90361 + 0.273698i) q^{26} +(-2.35402 - 4.63234i) q^{27} +(-1.94566 - 6.62631i) q^{28} +(-1.12939 - 0.804232i) q^{29} +(-1.67195 - 0.0563305i) q^{30} +(0.316159 + 0.126571i) q^{31} +(2.92764 + 3.07042i) q^{32} +(1.37607 + 1.87657i) q^{33} +(1.19382 + 0.0568687i) q^{34} +(-4.96860 + 7.73130i) q^{35} +(5.08008 - 2.19976i) q^{36} +(-2.58296 + 8.79676i) q^{37} +(-1.57755 + 1.24060i) q^{38} +(7.18770 + 4.47911i) q^{39} +(0.353036 - 3.69716i) q^{40} +(-4.74940 - 1.15219i) q^{41} +(-0.327678 + 2.52844i) q^{42} +(-2.11981 - 5.29503i) q^{43} +(-2.08562 + 1.34035i) q^{44} +(-6.63939 - 3.19211i) q^{45} +(0.751165 - 1.73028i) q^{46} +(-5.27943 + 3.04808i) q^{47} +(1.82409 + 5.04215i) q^{48} +(5.50738 + 4.33105i) q^{49} +(-0.330038 + 0.235019i) q^{50} +(4.71120 + 2.34636i) q^{51} +(-5.23376 + 7.34978i) q^{52} +(0.820706 + 0.947145i) q^{53} +(-2.04372 - 0.0119284i) q^{54} +(3.16553 + 0.929483i) q^{55} +(-5.55800 - 1.07122i) q^{56} +(-8.55890 + 2.20296i) q^{57} +(-0.484705 + 0.249883i) q^{58} +(12.1348 - 4.19991i) q^{59} +(3.82928 - 6.85103i) q^{60} +(0.140899 + 0.179167i) q^{61} +(0.101230 - 0.0877163i) q^{62} +(-5.80476 + 9.61052i) q^{63} +(-4.33960 + 1.27422i) q^{64} +(11.9528 - 1.14135i) q^{65} +(0.904050 - 0.142855i) q^{66} +(-4.67876 + 0.222877i) q^{67} +(-2.80364 + 4.85605i) q^{68} +(6.09629 - 5.64227i) q^{69} +(1.80735 + 3.13042i) q^{70} +(-7.13238 - 11.0982i) q^{71} +(0.305390 - 4.52701i) q^{72} +(-1.37981 + 3.02136i) q^{73} +(2.60979 + 2.48843i) q^{74} +(-1.74710 + 0.362021i) q^{75} +(-1.78194 - 9.24556i) q^{76} +(1.86876 - 4.66793i) q^{77} +(2.86132 - 1.70553i) q^{78} +(-2.34942 + 12.1899i) q^{79} +(6.39518 + 4.10993i) q^{80} +(-8.21665 - 3.67243i) q^{81} +(-1.25878 + 1.45271i) q^{82} +(-1.65193 - 6.80935i) q^{83} +(-9.83930 - 6.80211i) q^{84} +(7.32704 - 1.41217i) q^{85} +(-2.23318 - 0.213242i) q^{86} +(-2.39689 + 0.147646i) q^{87} +(0.193151 + 2.02277i) q^{88} +(2.56329 - 17.8281i) q^{89} +(-2.31256 + 1.74580i) q^{90} -18.2995i q^{91} +(5.60050 + 6.85218i) q^{92} +(0.563594 - 0.174044i) q^{93} +(0.114089 + 2.39503i) q^{94} +(-7.74550 + 9.84921i) q^{95} +(7.28724 + 0.944404i) q^{96} +(5.06377 - 5.31073i) q^{97} +(2.50671 - 1.14478i) q^{98} +(3.89738 + 1.02743i) 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

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Representations

Groups

Database

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