LMFDB - Embedded newform 209.2.j.b.100.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [209,2,Mod(23,209)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(209, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([0, 2]))

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

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

chi := DirichletCharacter("209.23");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 209 = 11 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	209.j (of order $9$, degree $6$, 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:	$1.66887340224$
Analytic rank:	$0$
Dimension:	$42$
Relative dimension:	$7$ over $\Q(\zeta_{9})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			100.3
Character	$\chi$	$=$	209.100
Dual form			209.2.j.b.23.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.69844 + 0.618183i) q^{2} +(-0.255473 + 1.44886i) q^{3} +(0.970468 - 0.814320i) q^{4} +(1.59794 + 1.34083i) q^{5} +(-0.461753 - 2.61873i) q^{6} +(1.29928 + 2.25041i) q^{7} +(0.662558 - 1.14758i) q^{8} +(0.785155 + 0.285773i) q^{9} +O(q^{10})$	\(q+(-1.69844 + 0.618183i) q^{2} +(-0.255473 + 1.44886i) q^{3} +(0.970468 - 0.814320i) q^{4} +(1.59794 + 1.34083i) q^{5} +(-0.461753 - 2.61873i) q^{6} +(1.29928 + 2.25041i) q^{7} +(0.662558 - 1.14758i) q^{8} +(0.785155 + 0.285773i) q^{9} +(-3.54289 - 1.28951i) q^{10} +(-0.500000 + 0.866025i) q^{11} +(0.931905 + 1.61411i) q^{12} +(-0.0709285 - 0.402256i) q^{13} +(-3.59791 - 3.01900i) q^{14} +(-2.35090 + 1.97264i) q^{15} +(-0.855875 + 4.85391i) q^{16} +(-4.49951 + 1.63769i) q^{17} -1.51020 q^{18} +(1.94741 - 3.89969i) q^{19} +2.64262 q^{20} +(-3.59245 + 1.30755i) q^{21} +(0.313859 - 1.77999i) q^{22} +(-2.47703 + 2.07847i) q^{23} +(1.49342 + 1.25313i) q^{24} +(-0.112656 - 0.638902i) q^{25} +(0.369135 + 0.639361i) q^{26} +(-2.82144 + 4.88688i) q^{27} +(3.09346 + 1.12593i) q^{28} +(-5.93594 - 2.16051i) q^{29} +(2.77342 - 4.80371i) q^{30} +(1.98782 + 3.44301i) q^{31} +(-1.08674 - 6.16320i) q^{32} +(-1.12701 - 0.945675i) q^{33} +(6.62976 - 5.56303i) q^{34} +(-0.941256 + 5.33813i) q^{35} +(0.994678 - 0.362033i) q^{36} +7.56574 q^{37} +(-0.896850 + 7.82726i) q^{38} +0.600931 q^{39} +(2.59745 - 0.945393i) q^{40} +(2.14832 - 12.1838i) q^{41} +(5.29328 - 4.44159i) q^{42} +(7.06867 + 5.93132i) q^{43} +(0.219987 + 1.24761i) q^{44} +(0.871457 + 1.50941i) q^{45} +(2.92221 - 5.06142i) q^{46} +(0.667672 + 0.243013i) q^{47} +(-6.81397 - 2.48008i) q^{48} +(0.123768 - 0.214373i) q^{49} +(0.586297 + 1.01550i) q^{50} +(-1.22327 - 6.93753i) q^{51} +(-0.396398 - 0.332618i) q^{52} +(-2.01458 + 1.69043i) q^{53} +(1.77107 - 10.0443i) q^{54} +(-1.96016 + 0.713441i) q^{55} +3.44338 q^{56} +(5.15259 + 3.81779i) q^{57} +11.4174 q^{58} +(0.0852921 - 0.0310438i) q^{59} +(-0.675116 + 3.82878i) q^{60} +(6.25373 - 5.24750i) q^{61} +(-5.50461 - 4.61892i) q^{62} +(0.377026 + 2.13822i) q^{63} +(0.726959 + 1.25913i) q^{64} +(0.426017 - 0.737884i) q^{65} +(2.49876 + 0.909476i) q^{66} +(-4.71604 - 1.71650i) q^{67} +(-3.03303 + 5.25336i) q^{68} +(-2.37860 - 4.11985i) q^{69} +(-1.70127 - 9.64838i) q^{70} +(2.74040 + 2.29947i) q^{71} +(0.848159 - 0.711690i) q^{72} +(-0.237702 + 1.34808i) q^{73} +(-12.8500 + 4.67701i) q^{74} +0.954459 q^{75} +(-1.28569 - 5.37034i) q^{76} -2.59855 q^{77} +(-1.02065 + 0.371485i) q^{78} +(-0.215660 + 1.22307i) q^{79} +(-7.87591 + 6.60867i) q^{80} +(-4.43941 - 3.72510i) q^{81} +(3.88298 + 22.0215i) q^{82} +(6.75874 + 11.7065i) q^{83} +(-2.42160 + 4.19434i) q^{84} +(-9.38580 - 3.41615i) q^{85} +(-15.6724 - 5.70427i) q^{86} +(4.64674 - 8.04839i) q^{87} +(0.662558 + 1.14758i) q^{88} +(1.06215 + 6.02376i) q^{89} +(-2.41321 - 2.02492i) q^{90} +(0.813085 - 0.682259i) q^{91} +(-0.711336 + 4.03418i) q^{92} +(-5.49627 + 2.00048i) q^{93} -1.28423 q^{94} +(8.34068 - 3.62032i) q^{95} +9.20724 q^{96} +(-1.78667 + 0.650293i) q^{97} +(-0.0776916 + 0.440611i) q^{98} +(-0.640064 + 0.537077i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 42 q - 3 q^{2} + 3 q^{4} - 6 q^{5} + 12 q^{6} - 6 q^{7} - 15 q^{8}+O(q^{10}) $ 42 * q - 3 * q^2 + 3 * q^4 - 6 * q^5 + 12 * q^6 - 6 * q^7 - 15 * q^8	\( 42 q - 3 q^{2} + 3 q^{4} - 6 q^{5} + 12 q^{6} - 6 q^{7} - 15 q^{8} - 15 q^{10} - 21 q^{11} - 30 q^{12} - 18 q^{13} - 3 q^{14} - 9 q^{15} - 3 q^{16} + 12 q^{18} - 6 q^{19} + 30 q^{20} + 9 q^{21} + 6 q^{22} + 15 q^{23} + 3 q^{24} - 6 q^{26} - 24 q^{27} - 9 q^{28} - 15 q^{29} + 30 q^{30} - 54 q^{31} + 42 q^{32} - 45 q^{34} - 12 q^{35} + 6 q^{36} + 114 q^{37} - 60 q^{38} - 48 q^{40} + 15 q^{41} + 84 q^{42} - 6 q^{43} + 3 q^{44} + 3 q^{45} - 15 q^{46} - 42 q^{47} + 12 q^{48} - 21 q^{49} - 33 q^{50} + 93 q^{51} + 3 q^{52} + 48 q^{54} + 3 q^{55} + 114 q^{56} - 15 q^{57} + 60 q^{58} - 33 q^{59} - 81 q^{60} + 63 q^{61} - 24 q^{62} + 87 q^{63} + 15 q^{64} + 24 q^{65} - 15 q^{66} - 51 q^{67} + 48 q^{68} - 54 q^{69} - 84 q^{70} + 9 q^{71} - 51 q^{72} - 27 q^{73} - 33 q^{74} + 54 q^{75} - 60 q^{76} + 12 q^{77} - 87 q^{78} + 24 q^{79} + 120 q^{80} - 36 q^{81} + 111 q^{82} - 12 q^{83} + 48 q^{84} + 39 q^{85} - 60 q^{86} - 75 q^{87} - 15 q^{88} - 21 q^{89} - 63 q^{90} - 3 q^{91} + 6 q^{92} - 72 q^{93} + 84 q^{94} - 72 q^{95} - 6 q^{96} - 18 q^{97} - 120 q^{98}+O(q^{100}) \) 42 * q - 3 * q^2 + 3 * q^4 - 6 * q^5 + 12 * q^6 - 6 * q^7 - 15 * q^8 - 15 * q^10 - 21 * q^11 - 30 * q^12 - 18 * q^13 - 3 * q^14 - 9 * q^15 - 3 * q^16 + 12 * q^18 - 6 * q^19 + 30 * q^20 + 9 * q^21 + 6 * q^22 + 15 * q^23 + 3 * q^24 - 6 * q^26 - 24 * q^27 - 9 * q^28 - 15 * q^29 + 30 * q^30 - 54 * q^31 + 42 * q^32 - 45 * q^34 - 12 * q^35 + 6 * q^36 + 114 * q^37 - 60 * q^38 - 48 * q^40 + 15 * q^41 + 84 * q^42 - 6 * q^43 + 3 * q^44 + 3 * q^45 - 15 * q^46 - 42 * q^47 + 12 * q^48 - 21 * q^49 - 33 * q^50 + 93 * q^51 + 3 * q^52 + 48 * q^54 + 3 * q^55 + 114 * q^56 - 15 * q^57 + 60 * q^58 - 33 * q^59 - 81 * q^60 + 63 * q^61 - 24 * q^62 + 87 * q^63 + 15 * q^64 + 24 * q^65 - 15 * q^66 - 51 * q^67 + 48 * q^68 - 54 * q^69 - 84 * q^70 + 9 * q^71 - 51 * q^72 - 27 * q^73 - 33 * q^74 + 54 * q^75 - 60 * q^76 + 12 * q^77 - 87 * q^78 + 24 * q^79 + 120 * q^80 - 36 * q^81 + 111 * q^82 - 12 * q^83 + 48 * q^84 + 39 * q^85 - 60 * q^86 - 75 * q^87 - 15 * q^88 - 21 * q^89 - 63 * q^90 - 3 * q^91 + 6 * q^92 - 72 * q^93 + 84 * q^94 - 72 * q^95 - 6 * q^96 - 18 * q^97 - 120 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/209\mathbb{Z}\right)^\times$.

$n$	$78$	$134$
$\chi(n)$	$e\left(\frac{8}{9}\right)$	$1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−1.69844	+	0.618183i	−1.20098	+	0.437121i	−0.863566	−	0.504235i	$-0.831774\pi$
$2$	−1.69844	+	0.618183i	−1.20098	+	0.437121i	−0.337414	+	0.941356i	$0.609552\pi$
$3$	−0.255473	+	1.44886i	−0.147497	+	0.836499i	0.817831	+	0.575459i	$0.195176\pi$
$3$	−0.255473	+	1.44886i	−0.147497	+	0.836499i	−0.965328	+	0.261040i	$0.915935\pi$
$4$	0.970468	−	0.814320i	0.485234	−	0.407160i
$5$	1.59794	+	1.34083i	0.714621	+	0.599638i	0.925891	−	0.377790i	$-0.123316\pi$
$5$	1.59794	+	1.34083i	0.714621	+	0.599638i	−0.211271	+	0.977428i	$0.567760\pi$
$6$	−0.461753	−	2.61873i	−0.188510	−	1.06909i
$7$	1.29928	+	2.25041i	0.491080	+	0.850575i	0.999947	−	0.0102697i	$-0.00326899\pi$
$7$	1.29928	+	2.25041i	0.491080	+	0.850575i	−0.508867	+	0.860845i	$0.669936\pi$
$8$	0.662558	−	1.14758i	0.234250	−	0.405732i
$9$	0.785155	+	0.285773i	0.261718	+	0.0952576i
$10$	−3.54289	−	1.28951i	−1.12036	−	0.407778i
$11$	−0.500000	+	0.866025i	−0.150756	+	0.261116i
$11$	−0.500000	+	0.866025i	−0.150756	+	0.261116i
$12$	0.931905	+	1.61411i	0.269018	+	0.465953i
$13$	−0.0709285	−	0.402256i	−0.0196720	−	0.111566i	0.973391	−	0.229152i	$-0.0735953\pi$
$13$	−0.0709285	−	0.402256i	−0.0196720	−	0.111566i	−0.993063	+	0.117587i	$0.962484\pi$
$14$	−3.59791	−	3.01900i	−0.961582	−	0.806863i
$15$	−2.35090	+	1.97264i	−0.607001	+	0.509334i
$16$	−0.855875	+	4.85391i	−0.213969	+	1.21348i
$17$	−4.49951	+	1.63769i	−1.09129	+	0.397197i	−0.824099	−	0.566446i	$-0.808318\pi$
$17$	−4.49951	+	1.63769i	−1.09129	+	0.397197i	−0.267192	+	0.963643i	$0.586096\pi$
$18$	−1.51020			−0.355958
$19$	1.94741	−	3.89969i	0.446767	−	0.894650i
$19$	1.94741	−	3.89969i	0.446767	−	0.894650i
$20$	2.64262			0.590907
$21$	−3.59245	+	1.30755i	−0.783938	+	0.285330i
$22$	0.313859	−	1.77999i	0.0669151	−	0.379494i
$23$	−2.47703	+	2.07847i	−0.516496	+	0.433392i	−0.863408	−	0.504506i	$-0.831675\pi$
$23$	−2.47703	+	2.07847i	−0.516496	+	0.433392i	0.346912	+	0.937898i	$0.387230\pi$
$24$	1.49342	+	1.25313i	0.304843	+	0.255794i
$25$	−0.112656	−	0.638902i	−0.0225311	−	0.127780i
$26$	0.369135	+	0.639361i	0.0723934	+	0.125389i
$27$	−2.82144	+	4.88688i	−0.542987	+	0.940481i
$28$	3.09346	+	1.12593i	0.584609	+	0.212780i
$29$	−5.93594	−	2.16051i	−1.10228	−	0.401196i	−0.274122	−	0.961695i	$-0.588387\pi$
$29$	−5.93594	−	2.16051i	−1.10228	−	0.401196i	−0.828155	+	0.560499i	$0.810609\pi$
$30$	2.77342	−	4.80371i	0.506355	−	0.877033i
$31$	1.98782	+	3.44301i	0.357023	+	0.618383i	0.987462	−	0.157856i	$-0.0504583\pi$
$31$	1.98782	+	3.44301i	0.357023	+	0.618383i	−0.630439	+	0.776239i	$0.717125\pi$
$32$	−1.08674	−	6.16320i	−0.192110	−	1.08951i
$33$	−1.12701	−	0.945675i	−0.196188	−	0.164621i
$34$	6.62976	−	5.56303i	1.13699	−	0.954052i
$35$	−0.941256	+	5.33813i	−0.159101	+	0.902309i
$36$	0.994678	−	0.362033i	0.165780	−	0.0603389i
$37$	7.56574			1.24380			0.621900	−	0.783097i	$-0.286361\pi$
$37$	7.56574			1.24380			0.621900	+	0.783097i	$0.286361\pi$
$38$	−0.896850	+	7.82726i	−0.145488	+	1.26975i
$39$	0.600931			0.0962260
$40$	2.59745	−	0.945393i	0.410692	−	0.149480i
$41$	2.14832	−	12.1838i	0.335512	−	1.90278i	−0.0866085	−	0.996242i	$-0.527603\pi$
$41$	2.14832	−	12.1838i	0.335512	−	1.90278i	0.422120	−	0.906540i	$-0.361286\pi$
$42$	5.29328	−	4.44159i	0.816770	−	0.685352i
$43$	7.06867	+	5.93132i	1.07796	+	0.904517i	0.995750	−	0.0920978i	$-0.0293572\pi$
$43$	7.06867	+	5.93132i	1.07796	+	0.904517i	0.0822115	+	0.996615i	$0.473802\pi$
$44$	0.219987	+	1.24761i	0.0331643	+	0.188084i
$45$	0.871457	+	1.50941i	0.129909	+	0.225009i
$46$	2.92221	−	5.06142i	0.430857	−	0.746266i
$47$	0.667672	+	0.243013i	0.0973899	+	0.0354470i	0.390256	−	0.920707i	$-0.372387\pi$
$47$	0.667672	+	0.243013i	0.0973899	+	0.0354470i	−0.292866	+	0.956154i	$0.594609\pi$
$48$	−6.81397	−	2.48008i	−0.983512	−	0.357969i
$49$	0.123768	−	0.214373i	0.0176812	−	0.0306247i
$50$	0.586297	+	1.01550i	0.0829150	+	0.143613i
$51$	−1.22327	−	6.93753i	−0.171293	−	0.971448i
$52$	−0.396398	−	0.332618i	−0.0549706	−	0.0461258i
$53$	−2.01458	+	1.69043i	−0.276723	+	0.232198i	−0.770578	−	0.637346i	$-0.780032\pi$
$53$	−2.01458	+	1.69043i	−0.276723	+	0.232198i	0.493854	+	0.869545i	$0.335588\pi$
$54$	1.77107	−	10.0443i	0.241013	−	1.36685i
$55$	−1.96016	+	0.713441i	−0.264308	+	0.0962004i
$56$	3.44338			0.460141
$57$	5.15259	+	3.81779i	0.682477	+	0.505679i
$58$	11.4174			1.49918
$59$	0.0852921	−	0.0310438i	0.0111041	−	0.00404155i	−0.336462	−	0.941697i	$-0.609230\pi$
$59$	0.0852921	−	0.0310438i	0.0111041	−	0.00404155i	0.347566	+	0.937655i	$0.387008\pi$
$60$	−0.675116	+	3.82878i	−0.0871571	+	0.494293i
$61$	6.25373	−	5.24750i	0.800708	−	0.671874i	−0.147663	−	0.989038i	$-0.547175\pi$
$61$	6.25373	−	5.24750i	0.800708	−	0.671874i	0.948371	+	0.317164i	$0.102731\pi$
$62$	−5.50461	−	4.61892i	−0.699086	−	0.586603i
$63$	0.377026	+	2.13822i	0.0475008	+	0.269390i
$64$	0.726959	+	1.25913i	0.0908698	+	0.157391i
$65$	0.426017	−	0.737884i	0.0528409	−	0.0915232i
$66$	2.49876	+	0.909476i	0.307577	+	0.111949i
$67$	−4.71604	−	1.71650i	−0.576156	−	0.209704i	0.0374738	−	0.999298i	$-0.488069\pi$
$67$	−4.71604	−	1.71650i	−0.576156	−	0.209704i	−0.613629	+	0.789594i	$0.710291\pi$
$68$	−3.03303	+	5.25336i	−0.367809	+	0.637063i
$69$	−2.37860	−	4.11985i	−0.286350	−	0.495972i
$70$	−1.70127	−	9.64838i	−0.203341	−	1.15320i
$71$	2.74040	+	2.29947i	0.325226	+	0.272897i	0.790751	−	0.612138i	$-0.209690\pi$
$71$	2.74040	+	2.29947i	0.325226	+	0.272897i	−0.465526	+	0.885034i	$0.654135\pi$
$72$	0.848159	−	0.711690i	0.0999565	−	0.0838735i
$73$	−0.237702	+	1.34808i	−0.0278209	+	0.157780i	−0.995553	−	0.0941999i	$-0.969971\pi$
$73$	−0.237702	+	1.34808i	−0.0278209	+	0.157780i	0.967732	+	0.251980i	$0.0810818\pi$
$74$	−12.8500	+	4.67701i	−1.49378	+	0.543691i
$75$	0.954459			0.110211
$76$	−1.28569	−	5.37034i	−0.147479	−	0.616021i
$77$	−2.59855			−0.296132
$78$	−1.02065	+	0.371485i	−0.115566	+	0.0420624i
$79$	−0.215660	+	1.22307i	−0.0242636	+	0.137606i	−0.994533	−	0.104421i	$-0.966701\pi$
$79$	−0.215660	+	1.22307i	−0.0242636	+	0.137606i	0.970270	+	0.242027i	$0.0778122\pi$
$80$	−7.87591	+	6.60867i	−0.880553	+	0.738872i
$81$	−4.43941	−	3.72510i	−0.493267	−	0.413900i
$82$	3.88298	+	22.0215i	0.428803	+	2.43186i
$83$	6.75874	+	11.7065i	0.741868	+	1.28495i	0.951644	+	0.307204i	$0.0993934\pi$
$83$	6.75874	+	11.7065i	0.741868	+	1.28495i	−0.209775	+	0.977750i	$0.567273\pi$
$84$	−2.42160	+	4.19434i	−0.264219	+	0.457640i
$85$	−9.38580	−	3.41615i	−1.01803	−	0.370534i
$86$	−15.6724	−	5.70427i	−1.68999	−	0.615107i
$87$	4.64674	−	8.04839i	0.498183	−	0.862878i
$88$	0.662558	+	1.14758i	0.0706289	+	0.122333i
$89$	1.06215	+	6.02376i	0.112588	+	0.638517i	0.987916	+	0.154989i	$0.0495341\pi$
$89$	1.06215	+	6.02376i	0.112588	+	0.638517i	−0.875328	+	0.483529i	$0.839355\pi$
$90$	−2.41321	−	2.02492i	−0.254375	−	0.213446i
$91$	0.813085	−	0.682259i	0.0852344	−	0.0715202i
$92$	−0.711336	+	4.03418i	−0.0741619	+	0.420593i
$93$	−5.49627	+	2.00048i	−0.569936	+	0.207440i
$94$	−1.28423			−0.132458
$95$	8.34068	−	3.62032i	0.855735	−	0.371437i
$96$	9.20724			0.939710
$97$	−1.78667	+	0.650293i	−0.181408	+	0.0660273i	−0.431127	−	0.902291i	$-0.641884\pi$
$97$	−1.78667	+	0.650293i	−0.181408	+	0.0660273i	0.249719	+	0.968318i	$0.419662\pi$
$98$	−0.0776916	+	0.440611i	−0.00784804	+	0.0445084i
$99$	−0.640064	+	0.537077i	−0.0643289	+	0.0539783i
$100$	−0.629599	−	0.528296i	−0.0629599	−	0.0528296i
$101$	2.25477	+	12.7874i	0.224358	+	1.27240i	0.863908	+	0.503649i	$0.168010\pi$
$101$	2.25477	+	12.7874i	0.224358	+	1.27240i	−0.639550	+	0.768749i	$0.720879\pi$
$102$	6.36632	+	11.0268i	0.630359	+	1.09181i
$103$	1.91967	−	3.32496i	0.189150	−	0.327618i	−0.755817	−	0.654783i	$-0.772760\pi$
$103$	1.91967	−	3.32496i	0.189150	−	0.327618i	0.944967	+	0.327165i	$0.106093\pi$
$104$	−0.508616	−	0.185121i	−0.0498740	−	0.0181526i
$105$	−7.49373	−	2.72749i	−0.731313	−	0.266176i
$106$	2.37665	−	4.11647i	0.230840	−	0.399827i
$107$	−8.11576	−	14.0569i	−0.784580	−	1.35893i	−0.929249	−	0.369453i	$-0.879545\pi$
$107$	−8.11576	−	14.0569i	−0.784580	−	1.35893i	0.144669	−	0.989480i	$-0.453788\pi$
$108$	1.24136	+	7.04012i	0.119450	+	0.677436i
$109$	−11.9014	−	9.98642i	−1.13994	−	0.956526i	−0.140506	−	0.990080i	$-0.544873\pi$
$109$	−11.9014	−	9.98642i	−1.13994	−	0.956526i	−0.999437	+	0.0335540i	$0.989317\pi$
$110$	2.88819	−	2.42348i	0.275378	−	0.231070i
$111$	−1.93284	+	10.9617i	−0.183457	+	1.04044i
$112$	−12.0353	+	4.38049i	−1.13723	+	0.413918i
$113$	15.7519			1.48181			0.740906	−	0.671608i	$-0.234396\pi$
$113$	15.7519			1.48181			0.740906	+	0.671608i	$0.234396\pi$
$114$	−11.1115	−	3.29906i	−1.04068	−	0.308985i
$115$	−6.74502			−0.628977
$116$	−7.51999	+	2.73705i	−0.698213	+	0.254129i
$117$	0.0592639	−	0.336102i	0.00547895	−	0.0310727i
$118$	−0.125673	+	0.105452i	−0.0115691	+	0.00970765i
$119$	−9.53156	−	7.99793i	−0.873757	−	0.733169i
$120$	0.706163	+	4.00485i	0.0644636	+	0.365591i
$121$	−0.500000	−	0.866025i	−0.0454545	−	0.0787296i
$122$	−7.37768	+	12.7785i	−0.667944	+	1.15691i
$123$	17.1037	+	6.22523i	1.54219	+	0.561310i
$124$	4.73283	+	1.72261i	0.425021	+	0.154695i
$125$	5.89155	−	10.2045i	0.526956	−	0.912715i
$126$	−1.96217	−	3.39857i	−0.174804	−	0.302769i
$127$	2.85105	+	16.1691i	0.252989	+	1.43477i	0.801181	+	0.598422i	$0.204205\pi$
$127$	2.85105	+	16.1691i	0.252989	+	1.43477i	−0.548192	+	0.836353i	$0.684684\pi$
$128$	7.57517	+	6.35632i	0.669557	+	0.561825i
$129$	−10.3995	+	8.72620i	−0.915624	+	0.768299i
$130$	−0.267419	+	1.51661i	−0.0234542	+	0.133015i
$131$	−0.873562	+	0.317951i	−0.0763235	+	0.0277795i	−0.379900	−	0.925028i	$-0.624042\pi$
$131$	−0.873562	+	0.317951i	−0.0763235	+	0.0277795i	0.303576	+	0.952807i	$0.401819\pi$
$132$	−1.86381			−0.162224
$133$	11.3061	−	0.684290i	0.980366	−	0.0593355i
$134$	9.07103			0.783617
$135$	−11.0610	+	4.02587i	−0.951978	+	0.346492i
$136$	−1.10180	+	6.24863i	−0.0944787	+	0.535815i
$137$	9.91545	−	8.32005i	0.847134	−	0.710830i	−0.112023	−	0.993706i	$-0.535733\pi$
$137$	9.91545	−	8.32005i	0.847134	−	0.710830i	0.959156	+	0.282876i	$0.0912885\pi$
$138$	6.58674	+	5.52693i	0.560700	+	0.470483i
$139$	−0.697914	−	3.95807i	−0.0591963	−	0.335719i	0.940798	−	0.338967i	$-0.110077\pi$
$139$	−0.697914	−	3.95807i	−0.0591963	−	0.335719i	−0.999995	+	0.00324761i	$0.998966\pi$
$140$	3.43349	+	5.94697i	0.290182	+	0.502611i
$141$	−0.522663	+	0.905279i	−0.0440161	+	0.0762382i
$142$	−6.07590	−	2.21145i	−0.509878	−	0.185581i
$143$	0.383828	+	0.139702i	0.0320973	+	0.0116825i
$144$	−2.05911	+	3.56648i	−0.171592	+	0.297207i
$145$	−6.58841	−	11.4115i	−0.547137	−	0.947670i
$146$	−0.429634	−	2.43657i	−0.0355567	−	0.201652i
$147$	0.278976	+	0.234089i	0.0230096	+	0.0193073i
$148$	7.34231	−	6.16093i	0.603534	−	0.506425i
$149$	3.48934	−	19.7890i	0.285858	−	1.62118i	−0.416349	−	0.909205i	$-0.636690\pi$
$149$	3.48934	−	19.7890i	0.285858	−	1.62118i	0.702206	−	0.711974i	$-0.252198\pi$
$150$	−1.62109	+	0.590030i	−0.132362	+	0.0481757i
$151$	10.9681			0.892570			0.446285	−	0.894891i	$-0.352747\pi$
$151$	10.9681			0.892570			0.446285	+	0.894891i	$0.352747\pi$
$152$	−3.18495	−	4.81859i	−0.258333	−	0.390839i
$153$	−4.00081			−0.323447
$154$	4.41349	−	1.60638i	0.355649	−	0.129446i
$155$	−1.44007	+	8.16706i	−0.115669	+	0.655994i
$156$	0.583185	−	0.489350i	0.0466922	−	0.0391794i
$157$	−7.52967	−	6.31814i	−0.600933	−	0.504243i	0.290812	−	0.956780i	$-0.406074\pi$
$157$	−7.52967	−	6.31814i	−0.600933	−	0.504243i	−0.891745	+	0.452538i	$0.850519\pi$
$158$	−0.389793	−	2.21062i	−0.0310102	−	0.175868i
$159$	−1.93452	−	3.35069i	−0.153418	−	0.265727i
$160$	6.52727	−	11.3056i	0.516026	−	0.893783i
$161$	−7.89576	−	2.87382i	−0.622273	−	0.226489i
$162$	9.84287	+	3.58251i	0.773329	+	0.281469i
$163$	8.27616	−	14.3347i	0.648239	−	1.12278i	−0.335305	−	0.942110i	$-0.608839\pi$
$163$	8.27616	−	14.3347i	0.648239	−	1.12278i	0.983543	−	0.180673i	$-0.0578274\pi$
$164$	−7.83659	−	13.5734i	−0.611935	−	1.05990i
$165$	−0.532907	−	3.02226i	−0.0414867	−	0.235283i
$166$	−18.7161	−	15.7047i	−1.45265	−	1.21892i
$167$	−1.48522	+	1.24624i	−0.114930	+	0.0964373i	−0.698441	−	0.715667i	$-0.746123\pi$
$167$	−1.48522	+	1.24624i	−0.114930	+	0.0964373i	0.583512	+	0.812105i	$0.301678\pi$
$168$	−0.879690	+	4.98897i	−0.0678696	+	0.384907i
$169$	12.0592	−	4.38920i	0.927633	−	0.337631i
$170$	18.0531			1.38461
$171$	2.64345	−	2.50534i	0.202149	−	0.191588i
$172$	11.6899			0.891347
$173$	8.77583	−	3.19414i	0.667214	−	0.242846i	0.0138660	−	0.999904i	$-0.495586\pi$
$173$	8.77583	−	3.19414i	0.667214	−	0.242846i	0.653348	+	0.757058i	$0.273364\pi$
$174$	−2.91685	+	16.5423i	−0.221126	+	1.25407i
$175$	1.29142	−	1.08363i	0.0976223	−	0.0819148i
$176$	−3.77567	−	3.16816i	−0.284602	−	0.238809i
$177$	0.0231882	+	0.131507i	0.00174293	+	0.00988466i
$178$	−5.52779	−	9.57441i	−0.414325	−	0.717632i
$179$	0.0415473	−	0.0719621i	0.00310539	−	0.00537870i	−0.864469	−	0.502687i	$-0.832345\pi$
$179$	0.0415473	−	0.0719621i	0.00310539	−	0.00537870i	0.867574	+	0.497308i	$0.165678\pi$
$180$	2.07486	+	0.755188i	0.154651	+	0.0562884i
$181$	−4.18798	−	1.52430i	−0.311290	−	0.113300i	0.181651	−	0.983363i	$-0.441856\pi$
$181$	−4.18798	−	1.52430i	−0.311290	−	0.113300i	−0.492941	+	0.870063i	$0.664078\pi$
$182$	−0.959217	+	1.66141i	−0.0711019	+	0.123152i
$183$	6.00523	+	10.4014i	0.443919	+	0.768890i
$184$	0.744048	+	4.21971i	0.0548520	+	0.311081i
$185$	12.0896	+	10.1444i	0.888845	+	0.745830i
$186$	8.09843	−	6.79539i	0.593806	−	0.498262i
$187$	0.831475	−	4.71553i	0.0608035	−	0.344834i
$188$	0.845844	−	0.307862i	0.0616895	−	0.0224532i
$189$	−14.6633			−1.06660
$190$	−11.9281	+	11.3050i	−0.865358	+	0.820148i
$191$	10.1388			0.733617			0.366809	−	0.930296i	$-0.380450\pi$
$191$	10.1388			0.733617			0.366809	+	0.930296i	$0.380450\pi$
$192$	−2.01002	+	0.731587i	−0.145061	+	0.0527977i
$193$	−3.73481	+	21.1811i	−0.268837	+	1.52465i	0.489044	+	0.872259i	$0.337346\pi$
$193$	−3.73481	+	21.1811i	−0.268837	+	1.52465i	−0.757881	+	0.652392i	$0.773765\pi$
$194$	2.63255	−	2.20897i	0.189006	−	0.158595i
$195$	0.960253	+	0.805748i	0.0687651	+	0.0577008i
$196$	−0.0544548	−	0.308829i	−0.00388963	−	0.0220592i
$197$	−0.164773	−	0.285395i	−0.0117396	−	0.0203335i	0.860096	−	0.510132i	$-0.170404\pi$
$197$	−0.164773	−	0.285395i	−0.0117396	−	0.0203335i	−0.871836	+	0.489799i	$0.837070\pi$
$198$	0.755100	−	1.30787i	0.0536626	−	0.0929464i
$199$	8.50692	+	3.09627i	0.603040	+	0.219489i	0.625455	−	0.780260i	$-0.284913\pi$
$199$	8.50692	+	3.09627i	0.603040	+	0.219489i	−0.0224153	+	0.999749i	$0.507136\pi$
$200$	−0.807835	−	0.294028i	−0.0571226	−	0.0207909i
$201$	3.69178	−	6.39435i	0.260398	−	0.451023i
$202$	−11.7346	−	20.3249i	−0.825642	−	1.43005i
$203$	−2.85040	−	16.1654i	−0.200059	−	1.13459i
$204$	−6.83651	−	5.73652i	−0.478652	−	0.401637i
$205$	19.7692	−	16.5884i	1.38074	−	1.15858i
$206$	−1.20501	+	6.83396i	−0.0839572	+	0.476145i
$207$	−2.53882	+	0.924055i	−0.176460	+	0.0642263i
$208$	2.01322			0.139592
$209$	2.40352	+	3.63635i	0.166255	+	0.251532i
$210$	14.4138			0.994644
$211$	−4.56382	+	1.66109i	−0.314186	+	0.114354i	−0.494300	−	0.869291i	$-0.664576\pi$
$211$	−4.56382	+	1.66109i	−0.314186	+	0.114354i	0.180114	+	0.983646i	$0.442353\pi$
$212$	−0.578532	+	3.28102i	−0.0397337	+	0.225341i
$213$	−4.03170	+	3.38300i	−0.276247	+	0.231799i
$214$	22.4739	+	18.8578i	1.53628	+	1.28910i
$215$	3.34241	+	18.9558i	0.227951	+	1.29277i
$216$	3.73874	+	6.47569i	0.254389	+	0.440615i
$217$	−5.16546	+	8.94683i	−0.350654	+	0.607351i
$218$	26.3872	+	9.60416i	1.78717	+	0.650475i
$219$	−1.89244	−	0.688793i	−0.127880	−	0.0465444i
$220$	−1.32131	+	2.28857i	−0.0890826	+	0.154296i
$221$	0.977912	+	1.69379i	0.0657815	+	0.113937i
$222$	−3.49350	−	19.8126i	−0.234468	−	1.32974i
$223$	2.60868	+	2.18894i	0.174690	+	0.146582i	0.725941	−	0.687757i	$-0.241405\pi$
$223$	2.60868	+	2.18894i	0.174690	+	0.146582i	−0.551250	+	0.834340i	$0.685849\pi$
$224$	12.4578	−	10.4533i	0.832369	−	0.698441i
$225$	0.0941288	−	0.533831i	0.00627525	−	0.0355887i
$226$	−26.7537	+	9.73754i	−1.77963	+	0.647732i
$227$	−25.6797			−1.70442			−0.852212	−	0.523196i	$-0.824740\pi$
$227$	−25.6797			−1.70442			−0.852212	+	0.523196i	$0.824740\pi$
$228$	8.10932	−	0.490807i	0.537053	−	0.0325045i
$229$	−25.0124			−1.65287			−0.826433	−	0.563036i	$-0.809633\pi$
$229$	−25.0124			−1.65287			−0.826433	+	0.563036i	$0.809633\pi$
$230$	11.4560	−	4.16966i	0.755389	−	0.274939i
$231$	0.663859	−	3.76493i	0.0436787	−	0.247714i
$232$	−6.41227	+	5.38053i	−0.420986	+	0.353249i
$233$	−3.98211	−	3.34138i	−0.260876	−	0.218901i	0.502963	−	0.864308i	$-0.332243\pi$
$233$	−3.98211	−	3.34138i	−0.260876	−	0.218901i	−0.763839	+	0.645407i	$0.776688\pi$
$234$	0.107116	+	0.607486i	0.00700241	+	0.0397126i
$235$	0.741061	+	1.28355i	0.0483415	+	0.0837299i
$236$	0.0574937	−	0.0995820i	0.00374252	−	0.00648224i
$237$	−1.71695	−	0.624920i	−0.111528	−	0.0405929i
$238$	21.1330	+	7.69178i	1.36985	+	0.498584i
$239$	−5.60150	+	9.70208i	−0.362331	+	0.627575i	−0.988344	−	0.152237i	$-0.951352\pi$
$239$	−5.60150	+	9.70208i	−0.362331	+	0.627575i	0.626013	+	0.779812i	$0.284686\pi$
$240$	−7.56295	−	13.0994i	−0.488186	−	0.845563i
$241$	5.10700	+	28.9632i	0.328971	+	1.86569i	0.480158	+	0.877182i	$0.340579\pi$
$241$	5.10700	+	28.9632i	0.328971	+	1.86569i	−0.151188	+	0.988505i	$0.548310\pi$
$242$	1.38458	+	1.16180i	0.0890044	+	0.0746835i
$243$	−6.43681	+	5.40113i	−0.412922	+	0.346482i
$244$	1.79590	−	10.1851i	0.114971	−	0.652032i
$245$	0.485212	−	0.176603i	0.0309990	−	0.0112827i
$246$	−32.8980			−2.09750
$247$	−1.70680	−	0.506759i	−0.108601	−	0.0322443i
$248$	5.26819			0.334531
$249$	−18.6877	+	6.80177i	−1.18429	+	0.431045i
$250$	−3.69824	+	20.9737i	−0.233897	+	1.32650i
$251$	13.0878	−	10.9820i	0.826096	−	0.693177i	−0.128295	−	0.991736i	$-0.540950\pi$
$251$	13.0878	−	10.9820i	0.826096	−	0.693177i	0.954391	+	0.298559i	$0.0965060\pi$
$252$	2.10708	+	1.76805i	0.132734	+	0.111377i
$253$	−0.561497	−	3.18441i	−0.0353010	−	0.200202i
$254$	−14.8378	−	25.6998i	−0.931005	−	1.61255i
$255$	7.34734	−	12.7260i	0.460108	−	0.796931i
$256$	−19.5278	−	7.10755i	−1.22049	−	0.444222i
$257$	−11.6832	−	4.25234i	−0.728779	−	0.265254i	−0.0491311	−	0.998792i	$-0.515645\pi$
$257$	−11.6832	−	4.25234i	−0.728779	−	0.265254i	−0.679648	+	0.733538i	$0.737867\pi$
$258$	12.2685	−	21.2497i	0.763806	−	1.32295i
$259$	9.82998	+	17.0260i	0.610805	+	1.05795i
$260$	−0.187437	−	1.06301i	−0.0116243	−	0.0659249i
$261$	−4.04322	−	3.39266i	−0.250269	−	0.210001i
$262$	1.28714	−	1.08004i	0.0795200	−	0.0667252i
$263$	2.49620	−	14.1567i	0.153922	−	0.872938i	−0.805842	−	0.592131i	$-0.798287\pi$
$263$	2.49620	−	14.1567i	0.153922	−	0.872938i	0.959764	−	0.280807i	$-0.0906020\pi$
$264$	−1.83195	+	0.666776i	−0.112749	+	0.0410372i
$265$	−5.48575			−0.336987
$266$	−18.7798	+	8.15148i	−1.15146	+	0.499799i
$267$	−8.99893			−0.550725
$268$	−5.97454	+	2.17456i	−0.364953	+	0.132832i
$269$	5.34770	−	30.3283i	0.326055	−	1.84915i	−0.176099	−	0.984372i	$-0.556348\pi$
$269$	5.34770	−	30.3283i	0.326055	−	1.84915i	0.502154	−	0.864778i	$-0.332541\pi$
$270$	16.2977	−	13.6754i	0.991848	−	0.832259i
$271$	−7.04129	−	5.90834i	−0.427728	−	0.358906i	0.403366	−	0.915039i	$-0.367840\pi$
$271$	−7.04129	−	5.90834i	−0.427728	−	0.358906i	−0.831094	+	0.556133i	$0.812285\pi$
$272$	−4.09816	−	23.2418i	−0.248488	−	1.40924i
$273$	0.780775	+	1.35234i	0.0472547	+	0.0818475i
$274$	−11.6975	+	20.2607i	−0.706672	+	1.22399i
$275$	0.609633	+	0.221888i	0.0367623	+	0.0133804i
$276$	−5.66323	−	2.06125i	−0.340887	−	0.124073i
$277$	4.86244	−	8.42200i	0.292156	−	0.506029i	−0.682163	−	0.731200i	$-0.738961\pi$
$277$	4.86244	−	8.42200i	0.292156	−	0.506029i	0.974319	+	0.225171i	$0.0722941\pi$
$278$	3.63218	+	6.29111i	0.217843	+	0.377316i
$279$	0.576829	+	3.27136i	0.0345339	+	0.195851i
$280$	5.50232	+	4.61699i	0.328826	+	0.275918i
$281$	−7.64341	+	6.41358i	−0.455968	+	0.382602i	−0.841645	−	0.540031i	$-0.818412\pi$
$281$	−7.64341	+	6.41358i	−0.455968	+	0.382602i	0.385677	+	0.922634i	$0.373968\pi$
$282$	0.328085	−	1.86066i	0.0195372	−	0.110801i
$283$	−17.8110	+	6.48268i	−1.05876	+	0.385355i	−0.811960	−	0.583712i	$-0.801600\pi$
$283$	−17.8110	+	6.48268i	−1.05876	+	0.385355i	−0.246795	+	0.969068i	$0.579377\pi$
$284$	4.53197			0.268923
$285$	3.11451	+	13.0093i	0.184488	+	0.770607i
$286$	−0.738271			−0.0436549
$287$	30.2097	−	10.9954i	1.78322	−	0.649040i
$288$	0.908018	−	5.14963i	0.0535055	−	0.303445i
$289$	4.54078	−	3.81017i	0.267105	−	0.224127i
$290$	18.2444	+	15.3089i	1.07135	+	0.898967i
$291$	−0.485738	−	2.75476i	−0.0284745	−	0.161487i
$292$	0.867082	+	1.50183i	0.0507422	+	0.0878880i
$293$	−13.3714	+	23.1600i	−0.781168	+	1.35302i	0.150094	+	0.988672i	$0.452042\pi$
$293$	−13.3714	+	23.1600i	−0.781168	+	1.35302i	−0.931262	+	0.364350i	$0.881291\pi$
$294$	−0.618535	−	0.225128i	−0.0360737	−	0.0131297i
$295$	0.177916	+	0.0647562i	0.0103587	+	0.00377025i
$296$	5.01274	−	8.68232i	0.291360	−	0.504650i
$297$	−2.82144	−	4.88688i	−0.163717	−	0.283566i
$298$	6.30678	+	35.7675i	0.365342	+	2.07196i
$299$	1.01177	+	0.848975i	0.0585121	+	0.0490975i
$300$	0.926272	−	0.777235i	0.0534783	−	0.0448737i
$301$	−4.16375	+	23.6138i	−0.239995	+	1.36108i
$302$	−18.6287	+	6.78027i	−1.07196	+	0.390161i
$303$	−19.1032			−1.09745
$304$	17.2620	+	12.7902i	0.990043	+	0.733569i
$305$	17.0291			0.975083
$306$	6.79515	−	2.47323i	0.388453	−	0.141385i
$307$	2.21479	−	12.5607i	0.126405	−	0.716878i	−0.854059	−	0.520177i	$-0.825866\pi$
$307$	2.21479	−	12.5607i	0.126405	−	0.716878i	0.980463	−	0.196701i	$-0.0630229\pi$
$308$	−2.52181	+	2.11605i	−0.143694	+	0.120573i
$309$	4.32697	+	3.63076i	0.246153	+	0.206547i
$310$	−2.60285	−	14.7615i	−0.147832	−	0.838397i
$311$	14.6980	+	25.4577i	0.833447	+	1.44357i	0.895289	+	0.445486i	$0.146969\pi$
$311$	14.6980	+	25.4577i	0.833447	+	1.44357i	−0.0618419	+	0.998086i	$0.519697\pi$
$312$	0.398152	−	0.689620i	0.0225409	−	0.0390420i
$313$	−27.0499	−	9.84537i	−1.52895	−	0.556493i	−0.565588	−	0.824688i	$-0.691351\pi$
$313$	−27.0499	−	9.84537i	−1.52895	−	0.556493i	−0.963365	+	0.268195i	$0.913573\pi$
$314$	16.6945	+	6.07629i	0.942124	+	0.342905i
$315$	−2.26453	+	3.92227i	−0.127592	+	0.220995i
$316$	0.786676	+	1.36256i	0.0442540	+	0.0766501i
$317$	2.50489	+	14.2059i	0.140689	+	0.797884i	0.970728	+	0.240180i	$0.0772065\pi$
$317$	2.50489	+	14.2059i	0.140689	+	0.797884i	−0.830040	+	0.557704i	$0.811682\pi$
$318$	5.35702	+	4.49507i	0.300407	+	0.252071i
$319$	4.83902	−	4.06042i	0.270933	−	0.227340i
$320$	−0.526643	+	2.98674i	−0.0294403	+	0.166964i
$321$	22.4398	−	8.16743i	1.25247	−	0.455861i
$322$	15.1870			0.846340
$323$	−2.37593	+	20.7359i	−0.132200	+	1.15378i
$324$	−7.34173			−0.407874
$325$	−0.249011	+	0.0906327i	−0.0138127	+	0.00502740i
$326$	−5.19510	+	29.4629i	−0.287730	+	1.63180i
$327$	17.5094	−	14.6921i	0.968271	−	0.812476i
$328$	−12.5585	−	10.5378i	−0.693427	−	0.581854i
$329$	0.320611	+	1.81828i	0.0176759	+	0.100245i
$330$	2.77342	+	4.80371i	0.152672	+	0.264435i
$331$	13.2083	−	22.8775i	0.725996	−	1.25746i	−0.232567	−	0.972580i	$-0.574713\pi$
$331$	13.2083	−	22.8775i	0.725996	−	1.25746i	0.958563	−	0.284881i	$-0.0919541\pi$
$332$	16.0920	+	5.85700i	0.883161	+	0.321444i
$333$	5.94028	+	2.16208i	0.325525	+	0.118481i
$334$	1.75215	−	3.03481i	0.0958733	−	0.166057i
$335$	−5.23441	−	9.06627i	−0.285987	−	0.495343i
$336$	−3.27202	−	18.5565i	−0.178503	−	1.01234i
$337$	−6.43096	−	5.39622i	−0.350317	−	0.293951i	0.450600	−	0.892726i	$-0.351210\pi$
$337$	−6.43096	−	5.39622i	−0.350317	−	0.293951i	−0.800917	+	0.598775i	$0.795654\pi$
$338$	−17.7686	+	14.9096i	−0.966483	+	0.810976i
$339$	−4.02418	+	22.8222i	−0.218563	+	1.23953i
$340$	−11.8905	+	4.32778i	−0.644851	+	0.234707i
$341$	−3.97564			−0.215293
$342$	−2.94098	+	5.88931i	−0.159030	+	0.318457i
$343$	18.8331			1.01689
$344$	11.4901	−	4.18205i	0.619504	−	0.225481i
$345$	1.72317	−	9.77258i	0.0927723	−	0.526138i
$346$	−12.9307	+	10.8501i	−0.695157	+	0.583306i
$347$	−22.3270	−	18.7346i	−1.19858	−	1.00573i	−0.999669	−	0.0257090i	$-0.991816\pi$
$347$	−22.3270	−	18.7346i	−1.19858	−	1.00573i	−0.198909	−	0.980018i	$-0.563740\pi$
$348$	−2.04445	−	11.5946i	−0.109594	−	0.621538i
$349$	−2.07795	−	3.59911i	−0.111230	−	0.192656i	0.805036	−	0.593225i	$-0.202146\pi$
$349$	−2.07795	−	3.59911i	−0.111230	−	0.192656i	−0.916266	+	0.400569i	$0.868812\pi$
$350$	−1.52352	+	2.63882i	−0.0814357	+	0.141051i
$351$	2.16590	+	0.788322i	0.115607	+	0.0420775i
$352$	5.88086	+	2.14046i	0.313451	+	0.114087i
$353$	−4.83390	+	8.37257i	−0.257283	+	0.445627i	−0.965513	−	0.260355i	$-0.916161\pi$
$353$	−4.83390	+	8.37257i	−0.257283	+	0.445627i	0.708230	+	0.705981i	$0.249494\pi$
$354$	−0.120679	−	0.209022i	−0.00641402	−	0.0111094i
$355$	1.29580	+	7.34882i	0.0687737	+	0.390035i
$356$	5.93605	+	4.98094i	0.314610	+	0.263989i
$357$	14.0229	−	11.7666i	0.742172	−	0.622756i
$358$	−0.0260800	+	0.147907i	−0.00137837	+	0.00781714i
$359$	−6.52320	+	2.37425i	−0.344281	+	0.125308i	−0.508373	−	0.861137i	$-0.669753\pi$
$359$	−6.52320	+	2.37425i	−0.344281	+	0.125308i	0.164092	+	0.986445i	$0.447531\pi$
$360$	2.30956			0.121725
$361$	−11.4152	−	15.1886i	−0.600798	−	0.799401i
$362$	8.05535			0.423380
$363$	1.38248	−	0.503183i	0.0725616	−	0.0264103i
$364$	0.233496	−	1.32422i	0.0122385	−	0.0694081i
$365$	−2.18738	+	1.83543i	−0.114493	+	0.0960706i
$366$	−16.6295	−	13.9538i	−0.869236	−	0.729376i
$367$	−2.61310	−	14.8197i	−0.136403	−	0.773579i	−0.973872	−	0.227095i	$-0.927077\pi$
$367$	−2.61310	−	14.8197i	−0.136403	−	0.773579i	0.837470	−	0.546484i	$-0.184034\pi$
$368$	−7.96869	−	13.8022i	−0.415397	−	0.719488i
$369$	5.16855	−	8.95220i	0.269064	−	0.466033i
$370$	−26.8046	−	9.75606i	−1.39350	−	0.507194i
$371$	−6.42165	−	2.33729i	−0.333395	−	0.121346i
$372$	−3.70492	+	6.41712i	−0.192091	+	0.332712i
$373$	6.58337	+	11.4027i	0.340874	+	0.590411i	0.984595	−	0.174849i	$-0.0559437\pi$
$373$	6.58337	+	11.4027i	0.340874	+	0.590411i	−0.643721	+	0.765260i	$0.722610\pi$
$374$	1.50285	+	8.52306i	0.0777103	+	0.440717i
$375$	13.2797	+	11.1430i	0.685760	+	0.575421i
$376$	0.721249	−	0.605200i	0.0371956	−	0.0312108i
$377$	−0.448048	+	2.54101i	−0.0230757	+	0.130869i
$378$	24.9048	−	9.06461i	1.28097	−	0.466233i
$379$	−26.6043			−1.36657			−0.683286	−	0.730151i	$-0.739450\pi$
$379$	−26.6043			−1.36657			−0.683286	+	0.730151i	$0.739450\pi$
$380$	5.14627	−	10.3054i	0.263998	−	0.528655i
$381$	−24.1551			−1.23750
$382$	−17.2202	+	6.26763i	−0.881060	+	0.320680i
$383$	0.218396	−	1.23858i	0.0111595	−	0.0632887i	−0.978719	−	0.205203i	$-0.934215\pi$
$383$	0.218396	−	1.23858i	0.0111595	−	0.0632887i	0.989879	+	0.141914i	$0.0453257\pi$
$384$	−11.1447	+	9.35148i	−0.568723	+	0.477216i
$385$	−4.15233	−	3.48422i	−0.211622	−	0.177572i
$386$	−6.75045	−	38.2837i	−0.343589	−	1.94859i
$387$	3.85499	+	6.67703i	0.195960	+	0.339413i
$388$	−1.20436	+	2.08601i	−0.0611419	+	0.105901i
$389$	14.3886	+	5.23701i	0.729529	+	0.265527i	0.679965	−	0.733244i	$-0.261995\pi$
$389$	14.3886	+	5.23701i	0.729529	+	0.265527i	0.0495634	+	0.998771i	$0.484217\pi$
$390$	−2.12903	−	0.774905i	−0.107808	−	0.0392388i
$391$	7.74151	−	13.4087i	0.391505	−	0.678107i
$392$	−0.164007	−	0.284069i	−0.00828361	−	0.0143476i
$393$	−0.237494	−	1.34689i	−0.0119800	−	0.0679419i
$394$	0.456283	+	0.382867i	0.0229872	+	0.0192886i
$395$	−1.98454	+	1.66522i	−0.0998528	+	0.0837865i
$396$	−0.183809	+	1.04243i	−0.00923676	+	0.0523842i
$397$	30.7360	−	11.1870i	1.54259	−	0.561458i	0.575928	−	0.817500i	$-0.304641\pi$
$397$	30.7360	−	11.1870i	1.54259	−	0.561458i	0.966666	+	0.256042i	$0.0824186\pi$
$398$	−16.3626			−0.820182
$399$	−1.89697	+	16.5558i	−0.0949672	+	0.828826i
$400$	3.19759			0.159880
$401$	−0.0361618	+	0.0131618i	−0.00180583	+	0.000657269i	−0.342923	−	0.939364i	$-0.611417\pi$
$401$	−0.0361618	+	0.0131618i	−0.00180583	+	0.000657269i	0.341117	+	0.940021i	$0.389195\pi$
$402$	−2.31740	+	13.1426i	−0.115581	+	0.655495i
$403$	1.24398	−	1.04382i	0.0619669	−	0.0519964i
$404$	12.6013	+	10.5737i	0.626936	+	0.526062i
$405$	−2.09917	−	11.9050i	−0.104309	−	0.591564i
$406$	14.8344	+	25.6939i	0.736219	+	1.27517i
$407$	−3.78287	+	6.55212i	−0.187510	+	0.324777i
$408$	−8.77189	−	3.19271i	−0.434273	−	0.158063i
$409$	1.51338	+	0.550825i	0.0748318	+	0.0272365i	0.379165	−	0.925329i	$-0.376211\pi$
$409$	1.51338	+	0.550825i	0.0748318	+	0.0272365i	−0.304333	+	0.952566i	$0.598434\pi$
$410$	−23.3223	+	40.3954i	−1.15181	+	1.99499i
$411$	9.52144	+	16.4916i	0.469658	+	0.813472i
$412$	−0.844605	−	4.78999i	−0.0416107	−	0.235986i
$413$	0.180679	+	0.151608i	0.00889064	+	0.00746013i
$414$	3.74081	−	3.13891i	0.183851	−	0.154269i
$415$	−4.89635	+	27.7686i	−0.240353	+	1.36311i
$416$	−2.40210	+	0.874293i	−0.117773	+	0.0428658i
$417$	5.91298			0.289560
$418$	−6.33018	−	4.69032i	−0.309619	−	0.229411i
$419$	−18.3955			−0.898677			−0.449339	−	0.893361i	$-0.648340\pi$
$419$	−18.3955			−0.898677			−0.449339	+	0.893361i	$0.648340\pi$
$420$	−9.49348	+	3.45534i	−0.463234	+	0.168603i
$421$	6.21050	−	35.2215i	0.302681	−	1.71659i	−0.331542	−	0.943440i	$-0.607569\pi$
$421$	6.21050	−	35.2215i	0.302681	−	1.71659i	0.634223	−	0.773150i	$-0.281320\pi$
$422$	6.72452	−	5.64254i	0.327344	−	0.274675i
$423$	0.454779	+	0.381605i	0.0221121	+	0.0185543i
$424$	0.605137	+	3.43190i	0.0293881	+	0.166668i
$425$	1.55322	+	2.69025i	0.0753420	+	0.130496i
$426$	4.75630	−	8.23815i	0.230443	−	0.399140i
$427$	19.9343	+	7.25551i	0.964691	+	0.351119i
$428$	−19.3229	−	7.03296i	−0.934008	−	0.339951i
$429$	−0.300466	+	0.520422i	−0.0145066	+	0.0251262i
$430$	−17.3950	−	30.1291i	−0.838863	−	1.45295i
$431$	6.44724	+	36.5641i	0.310553	+	1.76123i	0.596142	+	0.802879i	$0.296700\pi$
$431$	6.44724	+	36.5641i	0.310553	+	1.76123i	−0.285589	+	0.958352i	$0.592189\pi$
$432$	−21.3057	−	17.8776i	−1.02507	−	0.860136i
$433$	−16.4661	+	13.8167i	−0.791312	+	0.663990i	−0.946070	−	0.323963i	$-0.894985\pi$
$433$	−16.4661	+	13.8167i	−0.791312	+	0.663990i	0.154758	+	0.987952i	$0.450540\pi$
$434$	3.24245	−	18.3889i	0.155643	−	0.882694i
$435$	18.2167	−	6.63035i	0.873426	−	0.317901i
$436$	−19.6820			−0.942598
$437$	3.28160	+	13.7073i	0.156980	+	0.655708i
$438$	3.64001			0.173926
$439$	4.63520	−	1.68708i	0.221226	−	0.0805198i	−0.229029	−	0.973420i	$-0.573555\pi$
$439$	4.63520	−	1.68708i	0.221226	−	0.0805198i	0.450255	+	0.892900i	$0.351333\pi$
$440$	−0.479989	+	2.72215i	−0.0228826	+	0.129773i
$441$	0.158439	−	0.132946i	0.00754472	−	0.00633077i
$442$	−2.70800	−	2.27228i	−0.128806	−	0.108081i
$443$	−4.18911	−	23.7576i	−0.199030	−	1.12876i	−0.906561	−	0.422075i	$-0.861302\pi$
$443$	−4.18911	−	23.7576i	−0.199030	−	1.12876i	0.707531	−	0.706683i	$-0.249809\pi$
$444$	7.05055	+	12.2119i	0.334604	+	0.579552i
$445$	−6.37959	+	11.0498i	−0.302422	+	0.523810i
$446$	−5.78386	−	2.10515i	−0.273874	−	0.0996819i
$447$	27.7800	+	10.1111i	1.31395	+	0.478239i
$448$	−1.88904	+	3.27191i	−0.0892487	+	0.154583i
$449$	−2.90083	−	5.02439i	−0.136899	−	0.237115i	0.789422	−	0.613850i	$-0.210380\pi$
$449$	−2.90083	−	5.02439i	−0.136899	−	0.237115i	−0.926321	+	0.376735i	$0.877047\pi$
$450$	0.170133	+	0.964870i	0.00802013	+	0.0454844i
$451$	9.47728	+	7.95238i	0.446267	+	0.374463i
$452$	15.2867	−	12.8271i	0.719026	−	0.603335i
$453$	−2.80205	+	15.8912i	−0.131652	+	0.746633i
$454$	43.6156	−	15.8748i	2.04698	−	0.745040i
$455$	2.21405			0.103796
$456$	7.79512	−	3.38352i	0.365040	−	0.158448i
$457$	−7.91108			−0.370065			−0.185032	−	0.982732i	$-0.559239\pi$
$457$	−7.91108			−0.370065			−0.185032	+	0.982732i	$0.559239\pi$
$458$	42.4821	−	15.4622i	1.98506	−	0.722502i
$459$	4.69192	−	26.6092i	0.219000	−	1.24201i
$460$	−6.54583	+	5.49261i	−0.305201	+	0.256094i
$461$	10.6521	+	8.93820i	0.496119	+	0.416293i	0.856213	−	0.516623i	$-0.172811\pi$
$461$	10.6521	+	8.93820i	0.496119	+	0.416293i	−0.360094	+	0.932916i	$0.617255\pi$
$462$	1.19989	+	6.80490i	0.0558238	+	0.316593i
$463$	−13.3631	−	23.1456i	−0.621036	−	1.07567i	−0.989293	−	0.145942i	$-0.953379\pi$
$463$	−13.3631	−	23.1456i	−0.621036	−	1.07567i	0.368257	−	0.929724i	$-0.379955\pi$
$464$	15.5673	−	26.9634i	0.722695	−	1.25174i
$465$	−11.4650	−	4.17292i	−0.531677	−	0.193515i
$466$	8.82896	+	3.21348i	0.408994	+	0.148862i
$467$	−16.1923	+	28.0459i	−0.749292	+	1.29781i	0.198871	+	0.980026i	$0.436273\pi$
$467$	−16.1923	+	28.0459i	−0.749292	+	1.29781i	−0.948163	+	0.317786i	$0.897061\pi$
$468$	−0.216181	−	0.374436i	−0.00999297	−	0.0173083i
$469$	−2.26461	−	12.8432i	−0.104570	−	0.593045i
$470$	−2.05212	−	1.72193i	−0.0946573	−	0.0794269i
$471$	11.0777	−	9.29531i	0.510434	−	0.428305i
$472$	0.0208856	−	0.118448i	0.000961338	−	0.00545202i
$473$	−8.67100	+	3.15599i	−0.398693	+	0.145112i
$474$	3.30246			0.151687
$475$	−2.71091	−	0.804884i	−0.124385	−	0.0369306i
$476$	−15.7630			−0.722494
$477$	−2.06483	+	0.751538i	−0.0945422	+	0.0344106i
$478$	3.51617	−	19.9412i	0.160826	−	0.912088i
$479$	1.36175	−	1.14264i	0.0622198	−	0.0522087i	−0.611147	−	0.791517i	$-0.709292\pi$
$479$	1.36175	−	1.14264i	0.0622198	−	0.0522087i	0.673367	+	0.739308i	$0.264847\pi$
$480$	14.7126	+	12.3453i	0.671536	+	0.563485i
$481$	−0.536627	−	3.04336i	−0.0244681	−	0.138765i
$482$	−26.5785	−	46.0354i	−1.21062	−	2.09685i
$483$	6.18091	−	10.7056i	0.281241	−	0.487124i
$484$	−1.19046	−	0.433290i	−0.0541116	−	0.0196950i
$485$	−3.72692	−	1.35649i	−0.169231	−	0.0615949i
$486$	7.59367	−	13.1526i	0.344456	−	0.596615i
$487$	−20.7925	−	36.0137i	−0.942198	−	1.63194i	−0.761266	−	0.648440i	$-0.775422\pi$
$487$	−20.7925	−	36.0137i	−0.942198	−	1.63194i	−0.180932	−	0.983496i	$-0.557912\pi$
$488$	−1.87849	−	10.6535i	−0.0850353	−	0.482259i
$489$	18.6546	+	15.6531i	0.843592	+	0.707858i
$490$	−0.714932	+	0.599899i	−0.0322973	+	0.0271007i
$491$	6.50169	−	36.8729i	0.293417	−	1.66405i	−0.380150	−	0.924925i	$-0.624128\pi$
$491$	6.50169	−	36.8729i	0.293417	−	1.66405i	0.673567	−	0.739126i	$-0.264761\pi$
$492$	21.6679	−	7.88648i	0.976865	−	0.355550i
$493$	30.2470			1.36226
$494$	3.21217	−	0.194413i	0.144522	−	0.00874704i
$495$	−1.74291			−0.0783382
$496$	−18.4134	+	6.70192i	−0.826785	+	0.300925i
$497$	−1.61421	+	9.15466i	−0.0724074	+	0.410643i
$498$	27.5353	−	23.1048i	1.23388	−	1.03535i
$499$	−1.44044	−	1.20867i	−0.0644828	−	0.0541075i	0.609977	−	0.792419i	$-0.291179\pi$
$499$	−1.44044	−	1.20867i	−0.0644828	−	0.0541075i	−0.674459	+	0.738312i	$0.735623\pi$
$500$	−2.59213	−	14.7007i	−0.115924	−	0.657436i
$501$	−1.42620	−	2.47025i	−0.0637179	−	0.110363i
$502$	−15.4400	+	26.7429i	−0.689123	+	1.19360i
$503$	22.2215	+	8.08798i	0.990809	+	0.360625i	0.786033	−	0.618184i	$-0.212131\pi$
$503$	22.2215	+	8.08798i	0.990809	+	0.360625i	0.204776	+	0.978809i	$0.434354\pi$
$504$	2.70359	+	0.984025i	0.120427	+	0.0438320i
$505$	−13.5428	+	23.4568i	−0.602647	+	1.04382i
$506$	2.92221	+	5.06142i	0.129908	+	0.225008i
$507$	3.27852	+	18.5934i	0.145604	+	0.825763i
$508$	15.9337	+	13.3699i	0.706942	+	0.593194i
$509$	7.33901	−	6.15816i	0.325296	−	0.272956i	−0.465484	−	0.885056i	$-0.654120\pi$
$509$	7.33901	−	6.15816i	0.325296	−	0.272956i	0.790780	+	0.612101i	$0.209675\pi$
$510$	−4.61206	+	26.1563i	−0.204226	+	1.15822i
$511$	−3.34257	+	1.21659i	−0.147866	+	0.0538190i
$512$	17.7833			0.785918
$513$	13.5628	+	20.5195i	0.598813	+	0.905960i
$514$	22.4720			0.991197
$515$	7.52573	−	2.73914i	0.331623	−	0.120701i
$516$	−2.98645	+	16.9370i	−0.131471	+	0.745610i
$517$	−0.544291	+	0.456714i	−0.0239379	+	0.0200863i
$518$	−27.2208	−	22.8410i	−1.19601	−	1.00358i
$519$	2.38587	+	13.5309i	0.104728	+	0.593942i
$520$	−0.564522	−	0.977782i	−0.0247559	−	0.0428786i
$521$	0.191534	−	0.331747i	0.00839126	−	0.0145341i	−0.861799	−	0.507249i	$-0.830662\pi$
$521$	0.191534	−	0.331747i	0.00839126	−	0.0145341i	0.870191	+	0.492715i	$0.163996\pi$
$522$	8.96446	+	3.26280i	0.392364	+	0.142809i
$523$	−15.9303	−	5.79817i	−0.696585	−	0.253536i	−0.0306331	−	0.999531i	$-0.509752\pi$
$523$	−15.9303	−	5.79817i	−0.696585	−	0.253536i	−0.665952	+	0.745994i	$0.731975\pi$
$524$	−0.588851	+	1.01992i	−0.0257241	+	0.0445554i
$525$	1.24010	+	2.14792i	0.0541226	+	0.0937431i
$526$	4.51175	+	25.5874i	0.196722	+	1.11566i
$527$	−14.5828	−	12.2364i	−0.635236	−	0.533026i
$528$	5.55480	−	4.66103i	0.241742	−	0.202845i
$529$	−2.17829	+	12.3537i	−0.0947084	+	0.537118i
$530$	9.31724	−	3.39120i	0.404715	−	0.147304i
$531$	0.0758389			0.00329113
$532$	10.4150	−	9.87088i	0.451548	−	0.427957i
$533$	−5.05336			−0.218885
$534$	15.2842	−	5.56298i	0.661410	−	0.240734i
$535$	5.87944	−	33.3440i	0.254190	−	1.44159i
$536$	−5.09447	+	4.27477i	−0.220048	+	0.184642i
$537$	0.0936486	+	0.0785805i	0.00404124	+	0.00339100i
$538$	9.66568	+	54.8168i	0.416717	+	2.36332i
$539$	0.123768	+	0.214373i	0.00533107	+	0.00923369i
$540$	−7.45599	+	12.9142i	−0.320855	+	0.555737i
$541$	19.7904	+	7.20311i	0.850855	+	0.309686i	0.730389	−	0.683032i	$-0.239339\pi$
$541$	19.7904	+	7.20311i	0.850855	+	0.309686i	0.120466	+	0.992717i	$0.461561\pi$
$542$	15.6116	+	5.68218i	0.670578	+	0.244070i
$543$	3.27841	−	5.67838i	0.140690	−	0.243682i
$544$	14.9832	+	25.9516i	0.642398	+	1.11267i
$545$	−5.62755	−	31.9154i	−0.241058	−	1.36711i
$546$	−2.16210	−	1.81421i	−0.0925292	−	0.0776412i
$547$	−8.72602	+	7.32200i	−0.373097	+	0.313066i	−0.809985	−	0.586450i	$-0.800525\pi$
$547$	−8.72602	+	7.32200i	−0.373097	+	0.313066i	0.436888	+	0.899516i	$0.356081\pi$
$548$	2.84745	−	16.1487i	0.121637	−	0.689838i
$549$	6.40974	−	2.33295i	0.273561	−	0.0995680i
$550$	−1.17259			−0.0499996
$551$	−19.9850	+	18.9409i	−0.851391	+	0.806911i
$552$	−6.30384			−0.268309
$553$	−3.03260	+	1.10378i	−0.128959	+	0.0469374i
$554$	−3.05225	+	17.3102i	−0.129678	+	0.735438i
$555$	−17.7863	+	14.9245i	−0.754988	+	0.633510i
$556$	−3.90044	−	3.27285i	−0.165415	−	0.138800i
$557$	−2.21225	−	12.5463i	−0.0937362	−	0.531604i	−0.995127	−	0.0985985i	$-0.968564\pi$
$557$	−2.21225	−	12.5463i	−0.0937362	−	0.531604i	0.901391	−	0.433006i	$-0.142547\pi$
$558$	−3.00201	−	5.19963i	−0.127085	−	0.220118i
$559$	1.88453	−	3.26411i	0.0797073	−	0.138057i
$560$	−25.1052	−	9.13755i	−1.06089	−	0.386132i
$561$	6.61971	+	2.40938i	0.279485	+	0.101724i
$562$	9.01713	−	15.6181i	0.380365	−	0.658811i
$563$	4.49252	+	7.78127i	0.189337	+	0.327941i	0.945029	−	0.326985i	$-0.106033\pi$
$563$	4.49252	+	7.78127i	0.189337	+	0.327941i	−0.755692	+	0.654927i	$0.772699\pi$
$564$	0.229958	+	1.30416i	0.00968299	+	0.0549150i
$565$	25.1706	+	21.1206i	1.05893	+	0.888551i
$566$	26.2435	−	22.0209i	1.10310	−	0.925608i
$567$	2.61500	−	14.8304i	0.109820	−	0.622819i
$568$	4.45451	−	1.62131i	0.186907	−	0.0680286i
$569$	19.5041			0.817655			0.408828	−	0.912612i	$-0.365938\pi$
$569$	19.5041			0.817655			0.408828	+	0.912612i	$0.365938\pi$
$570$	−13.3320	−	20.1703i	−0.558415	−	0.844841i
$571$	−46.2277			−1.93457			−0.967285	−	0.253690i	$-0.918356\pi$
$571$	−46.2277			−1.93457			−0.967285	+	0.253690i	$0.918356\pi$
$572$	0.486255	−	0.176982i	0.0203313	−	0.00740000i
$573$	−2.59019	+	14.6897i	−0.108207	+	0.613670i
$574$	−44.5123	+	37.3502i	−1.85791	+	1.55897i
$575$	1.60699	+	1.34843i	0.0670162	+	0.0562333i
$576$	0.210950	+	1.19636i	0.00878958	+	0.0498482i
$577$	8.03917	+	13.9242i	0.334675	+	0.579674i	0.983422	−	0.181330i	$-0.0580402\pi$
$577$	8.03917	+	13.9242i	0.334675	+	0.579674i	−0.648747	+	0.761004i	$0.724707\pi$
$578$	−5.35688	+	9.27838i	−0.222817	+	0.385930i
$579$	−29.7343	−	10.8224i	−1.23572	−	0.449764i
$580$	−15.6864	−	5.70939i	−0.651343	−	0.237069i
$581$	−17.5629	+	30.4199i	−0.728633	+	1.26203i
$582$	2.52794	+	4.37852i	0.104787	+	0.181496i
$583$	−0.456667	−	2.58989i	−0.0189132	−	0.107262i
$584$	1.38954	+	1.16596i	0.0574996	+	0.0482479i
$585$	0.545357	−	0.457609i	0.0225477	−	0.0189198i
$586$	8.39350	−	47.6019i	0.346732	−	1.96642i
$587$	−34.7472	+	12.6470i	−1.43417	+	0.521996i	−0.938124	−	0.346299i	$-0.887438\pi$
$587$	−34.7472	+	12.6470i	−1.43417	+	0.521996i	−0.496048	+	0.868295i	$0.665216\pi$
$588$	0.461361			0.0190262
$589$	17.2978	−	1.04693i	0.712743	−	0.0431379i
$590$	−0.342211			−0.0140886
$591$	0.455592	−	0.165822i	0.0187405	−	0.00682100i
$592$	−6.47533	+	36.7234i	−0.266134	+	1.50932i
$593$	−21.3199	+	17.8895i	−0.875504	+	0.734635i	−0.965250	−	0.261330i	$-0.915839\pi$
$593$	−21.3199	+	17.8895i	−0.875504	+	0.734635i	0.0897455	+	0.995965i	$0.471395\pi$
$594$	7.81305	+	6.55592i	0.320573	+	0.268993i
$595$	−4.50699	−	25.5604i	−0.184769	−	1.04788i
$596$	−12.7283	−	22.0460i	−0.521371	−	0.903041i
$597$	−6.65934	+	11.5343i	−0.272549	+	0.472068i
$598$	−2.24325	−	0.816477i	−0.0917334	−	0.0333882i
$599$	−6.31997	−	2.30028i	−0.258227	−	0.0939870i	0.209663	−	0.977774i	$-0.432763\pi$
$599$	−6.31997	−	2.30028i	−0.258227	−	0.0939870i	−0.467890	+	0.883787i	$0.654986\pi$
$600$	0.632384	−	1.09532i	0.0258170	−	0.0447163i
$601$	5.54180	+	9.59867i	0.226055	+	0.391538i	0.956635	−	0.291288i	$-0.0940839\pi$
$601$	5.54180	+	9.59867i	0.226055	+	0.391538i	−0.730581	+	0.682826i	$0.760751\pi$
$602$	−7.52575	−	42.6807i	−0.306727	−	1.73953i
$603$	−3.21229	−	2.69543i	−0.130815	−	0.109766i
$604$	10.6442	−	8.93152i	0.433105	−	0.363419i
$605$	0.362224	−	2.05427i	0.0147265	−	0.0835181i
$606$	32.4457	−	11.8093i	1.31802	−	0.479719i
$607$	−19.6381			−0.797084			−0.398542	−	0.917150i	$-0.630484\pi$
$607$	−19.6381			−0.797084			−0.398542	+	0.917150i	$0.630484\pi$
$608$	−26.1509	−	7.76436i	−1.06056	−	0.314886i
$609$	24.1496			0.978590
$610$	−28.9229	+	10.5271i	−1.17106	+	0.426229i
$611$	0.0503962	−	0.285811i	0.00203881	−	0.0115627i
$612$	−3.88266	+	3.25794i	−0.156947	+	0.131694i
$613$	−6.79185	−	5.69904i	−0.274320	−	0.230182i	0.495240	−	0.868756i	$-0.335080\pi$
$613$	−6.79185	−	5.69904i	−0.274320	−	0.230182i	−0.769560	+	0.638574i	$0.779525\pi$
$614$	4.00312	+	22.7028i	0.161553	+	0.916211i
$615$	18.9837	+	32.8807i	0.765496	+	1.32588i
$616$	−1.72169	+	2.98206i	−0.0693689	+	0.120150i
$617$	12.3433	+	4.49259i	0.496922	+	0.180865i	0.578309	−	0.815818i	$-0.303713\pi$
$617$	12.3433	+	4.49259i	0.496922	+	0.180865i	−0.0813871	+	0.996683i	$0.525935\pi$
$618$	−9.59359	−	3.49178i	−0.385911	−	0.140460i
$619$	−20.6982	+	35.8504i	−0.831933	+	1.44095i	0.0645708	+	0.997913i	$0.479432\pi$
$619$	−20.6982	+	35.8504i	−0.831933	+	1.44095i	−0.896504	+	0.443037i	$0.853901\pi$
$620$	5.25305	+	9.09855i	0.210968	+	0.365407i
$621$	−3.16846	−	17.9692i	−0.127146	−	0.721081i
$622$	−40.7012	−	34.1524i	−1.63197	−	1.36938i
$623$	−12.1759	+	10.2168i	−0.487818	+	0.409327i
$624$	−0.514322	+	2.91687i	−0.0205894	+	0.116768i
$625$	20.0486	−	7.29711i	0.801946	−	0.291884i
$626$	52.0290			2.07950
$627$	−5.88260	+	2.55337i	−0.234928	+	0.101972i
$628$	−12.4523			−0.496900
$629$	−34.0421	+	12.3903i	−1.35735	+	0.494034i
$630$	1.42149	−	8.06164i	0.0566333	−	0.321184i
$631$	−23.2457	+	19.5055i	−0.925398	+	0.776501i	−0.974986	−	0.222268i	$-0.928654\pi$
$631$	−23.2457	+	19.5055i	−0.925398	+	0.776501i	0.0495872	+	0.998770i	$0.484209\pi$
$632$	1.26068	+	1.05784i	0.0501473	+	0.0420786i
$633$	−1.24076	−	7.03668i	−0.0493157	−	0.279683i
$634$	−13.0363	−	22.5795i	−0.517736	−	0.896745i
$635$	−17.1242	+	29.6600i	−0.679554	+	1.17702i
$636$	−4.60593	−	1.67642i	−0.182637	−	0.0664744i
$637$	−0.0950113	−	0.0345813i	−0.00376449	−	0.00137016i
$638$	−5.70872	+	9.88780i	−0.226010	+	0.391462i
$639$	1.49451	+	2.58857i	0.0591220	+	0.102402i
$640$	3.58191	+	20.3140i	0.141588	+	0.802983i
$641$	2.79311	+	2.34369i	0.110321	+	0.0925704i	0.696280	−	0.717771i	$-0.254837\pi$
$641$	2.79311	+	2.34369i	0.110321	+	0.0925704i	−0.585958	+	0.810341i	$0.699282\pi$
$642$	−33.0638	+	27.7438i	−1.30492	+	1.09496i
$643$	1.83775	−	10.4224i	0.0724739	−	0.411020i	−0.926889	−	0.375335i	$-0.877528\pi$
$643$	1.83775	−	10.4224i	0.0724739	−	0.411020i	0.999363	−	0.0356847i	$-0.0113612\pi$
$644$	−10.0028	+	3.64072i	−0.394165	+	0.143464i
$645$	−28.3181			−1.11503
$646$	−8.78321	−	36.6875i	−0.345571	−	1.44345i
$647$	43.8347			1.72332			0.861660	−	0.507486i	$-0.169425\pi$
$647$	43.8347			1.72332			0.861660	+	0.507486i	$0.169425\pi$
$648$	−7.21624	+	2.62650i	−0.283481	+	0.103178i
$649$	−0.0157613	+	0.0893870i	−0.000618687	+	0.00350875i
$650$	0.366904	−	0.307869i	0.0143912	−	0.0120756i
$651$	−11.6431	−	9.76968i	−0.456327	−	0.382904i
$652$	−3.64130	−	20.6508i	−0.142604	−	0.808749i
$653$	−21.4090	−	37.0815i	−0.837799	−	1.45111i	−0.891731	−	0.452566i	$-0.850509\pi$
$653$	−21.4090	−	37.0815i	−0.837799	−	1.45111i	0.0539316	−	0.998545i	$-0.482825\pi$
$654$	−20.6563	+	35.7777i	−0.807724	+	1.39902i
$655$	−1.82222	−	0.663233i	−0.0711999	−	0.0259147i
$656$	57.3001	+	20.8555i	2.23719	+	0.814272i
$657$	−0.571877	+	0.990520i	−0.0223110	+	0.0386438i
$658$	−1.66857	−	2.89004i	−0.0650475	−	0.112666i
$659$	−4.92151	−	27.9113i	−0.191715	−	1.08727i	−0.917020	−	0.398842i	$-0.869412\pi$
$659$	−4.92151	−	27.9113i	−0.191715	−	1.08727i	0.725305	−	0.688428i	$-0.241699\pi$
$660$	−2.97826	−	2.49906i	−0.115929	−	0.0972756i
$661$	−13.0331	+	10.9360i	−0.506928	+	0.425363i	−0.860047	−	0.510216i	$-0.829566\pi$
$661$	−13.0331	+	10.9360i	−0.506928	+	0.425363i	0.353119	+	0.935579i	$0.385121\pi$
$662$	−8.29112	+	47.0213i	−0.322244	+	1.82753i
$663$	−2.70389	+	0.984137i	−0.105011	+	0.0382207i
$664$	17.9122			0.695130
$665$	18.9840	+	14.0662i	0.736169	+	0.545462i
$666$	−11.4258			−0.442740
$667$	19.1940	−	6.98606i	0.743196	−	0.270501i
$668$	−0.426514	+	2.41888i	−0.0165023	+	0.0935894i
$669$	−3.83791	+	3.22039i	−0.148382	+	0.124508i
$670$	14.4950	+	12.1627i	0.559989	+	0.469887i
$671$	1.41761	+	8.03964i	0.0547260	+	0.310367i
$672$	11.9627	+	20.7201i	0.461472	+	0.799294i
$673$	13.5345	−	23.4424i	0.521715	−	0.903637i	−0.477966	−	0.878378i	$-0.658626\pi$
$673$	13.5345	−	23.4424i	0.521715	−	0.903637i	0.999681	−	0.0252587i	$-0.00804096\pi$
$674$	14.2585	+	5.18966i	0.549216	+	0.199898i
$675$	3.44009	+	1.25209i	0.132409	+	0.0481930i
$676$	8.12889	−	14.0796i	0.312649	−	0.541525i
$677$	−1.85392	−	3.21108i	−0.0712518	−	0.123412i	0.828198	−	0.560435i	$-0.189366\pi$
$677$	−1.85392	−	3.21108i	−0.0712518	−	0.123412i	−0.899450	+	0.437023i	$0.856033\pi$
$678$	−7.27348	−	41.2499i	−0.279336	−	1.58419i
$679$	−3.78480	−	3.17582i	−0.145247	−	0.121877i
$680$	−10.1390	+	8.50760i	−0.388812	+	0.326252i
$681$	6.56048	−	37.2063i	0.251398	−	1.42575i
$682$	6.75240	−	2.45767i	0.258563	−	0.0941092i
$683$	−43.7993			−1.67593			−0.837967	−	0.545721i	$-0.816256\pi$
$683$	−43.7993			−1.67593			−0.837967	+	0.545721i	$0.816256\pi$
$684$	0.525233	−	4.58397i	0.0200828	−	0.175272i
$685$	27.0001			1.03162
$686$	−31.9869	+	11.6423i	−1.22127	+	0.444505i
$687$	6.38998	−	36.2394i	0.243793	−	1.38262i
$688$	−34.8400	+	29.2342i	−1.32826	+	1.11454i
$689$	0.822876	+	0.690475i	0.0313491	+	0.0263050i
$690$	3.11453	+	17.6634i	0.118568	+	0.672434i
$691$	20.5086	+	35.5219i	0.780183	+	1.35132i	0.931835	+	0.362882i	$0.118207\pi$
$691$	20.5086	+	35.5219i	0.780183	+	1.35132i	−0.151652	+	0.988434i	$0.548459\pi$
$692$	5.91561	−	10.2461i	0.224878	−	0.389500i
$693$	−2.04026	−	0.742595i	−0.0775032	−	0.0282089i
$694$	49.5026	+	18.0175i	1.87909	+	0.683934i
$695$	4.19188	−	7.26054i	0.159007	−	0.275408i
$696$	−6.15747	−	10.6650i	−0.233398	−	0.404258i
$697$	10.2868	+	58.3391i	0.389639	+	2.20975i
$698$	5.75418	+	4.82833i	0.217799	+	0.182755i
$699$	5.85851	−	4.91587i	0.221589	−	0.185935i
$700$	0.370861	−	2.10326i	0.0140172	−	0.0794957i
$701$	20.7870	−	7.56586i	0.785116	−	0.285759i	0.0818116	−	0.996648i	$-0.473929\pi$
$701$	20.7870	−	7.56586i	0.785116	−	0.285759i	0.703304	+	0.710889i	$0.251707\pi$
$702$	−4.16598			−0.157235
$703$	14.7336	−	29.5040i	0.555689	−	1.11277i
$704$	−1.45392			−0.0547966
$705$	−2.04901	+	0.745779i	−0.0771702	+	0.0280876i
$706$	3.03433	−	17.2086i	0.114199	−	0.647653i
$707$	−25.8474	+	21.6886i	−0.972093	+	0.815683i
$708$	0.129592	+	0.108741i	0.00487037	+	0.00408672i
$709$	5.36438	+	30.4229i	0.201463	+	1.14256i	0.902909	+	0.429833i	$0.141427\pi$
$709$	5.36438	+	30.4229i	0.201463	+	1.14256i	−0.701445	+	0.712723i	$0.747461\pi$
$710$	−6.74375	−	11.6805i	−0.253088	−	0.438362i
$711$	−0.518845	+	0.898666i	−0.0194582	+	0.0337026i
$712$	7.61651	+	2.77218i	0.285441	+	0.103892i
$713$	−12.0801	−	4.39679i	−0.452403	−	0.164661i
$714$	−16.5432	+	28.6537i	−0.619114	+	1.07234i
$715$	0.426017	+	0.737884i	0.0159321	+	0.0275953i
$716$	−0.0182798	−	0.103670i	−0.000683147	−	0.00387432i
$717$	−12.6259	−	10.5944i	−0.471523	−	0.395655i
$718$	9.61156	−	8.06506i	0.358700	−	0.300985i
$719$	1.20414	−	6.82900i	0.0449067	−	0.254679i	−0.954087	−	0.299530i	$-0.903170\pi$
$719$	1.20414	−	6.82900i	0.0449067	−	0.254679i	0.998994	+	0.0448511i	$0.0142813\pi$
$720$	−8.07239	+	2.93811i	−0.300840	+	0.109497i
$721$	9.97671			0.371552
$722$	28.7773	+	18.7403i	1.07098	+	0.697443i
$723$	−43.2683			−1.60917
$724$	−5.30558	+	1.93107i	−0.197180	+	0.0717677i
$725$	−0.711634	+	4.03588i	−0.0264294	+	0.149889i
$726$	−2.03701	+	1.70926i	−0.0756006	+	0.0634364i
$727$	9.80139	+	8.22434i	0.363513	+	0.305024i	0.806189	−	0.591658i	$-0.201526\pi$
$727$	9.80139	+	8.22434i	0.363513	+	0.305024i	−0.442676	+	0.896682i	$0.645971\pi$
$728$	−0.244234	−	1.38512i	−0.00905191	−	0.0513359i
$729$	−14.8739	−	25.7623i	−0.550885	−	0.954160i
$730$	2.58050	−	4.46957i	0.0955088	−	0.165426i
$731$	−41.5191	−	15.1117i	−1.53564	−	0.558928i
$732$	14.2979	+	5.20401i	0.528466	+	0.192346i
$733$	22.7744	−	39.4464i	0.841190	−	1.45698i	−0.0476986	−	0.998862i	$-0.515189\pi$
$733$	22.7744	−	39.4464i	0.841190	−	1.45698i	0.888889	−	0.458123i	$-0.151478\pi$
$734$	13.5995	+	23.5549i	0.501965	+	0.869429i
$735$	0.131914	+	0.748120i	0.00486571	+	0.0275948i
$736$	15.5019	+	13.0077i	0.571409	+	0.479469i
$737$	3.84455	−	3.22596i	0.141616	−	0.118830i
$738$	−3.24440	+	18.3999i	−0.119428	+	0.677310i
$739$	−1.03723	+	0.377521i	−0.0381551	+	0.0138873i	−0.361027	−	0.932555i	$-0.617574\pi$
$739$	−1.03723	+	0.377521i	−0.0381551	+	0.0138873i	0.322872	+	0.946443i	$0.395352\pi$
$740$	19.9933			0.734970
$741$	1.17026	−	2.34345i	0.0429907	−	0.0860887i
$742$	12.3517			0.453444
$743$	30.4727	−	11.0912i	1.11794	−	0.406895i	0.284037	−	0.958813i	$-0.408326\pi$
$743$	30.4727	−	11.0912i	1.11794	−	0.406895i	0.833899	+	0.551918i	$0.186104\pi$
$744$	−1.34588	+	7.63286i	−0.0493423	+	0.279834i
$745$	32.1095	−	26.9430i	1.17640	−	0.987117i
$746$	−18.2304	−	15.2972i	−0.667464	−	0.560069i
$747$	1.96126	+	11.1229i	0.0717588	+	0.406964i
$748$	−3.03303	−	5.25336i	−0.110898	−	0.192082i
$749$	21.0892	−	36.5276i	0.770583	−	1.33469i
$750$	−29.4432	−	10.7164i	−1.07511	−	0.391309i
$751$	−28.3690	−	10.3255i	−1.03520	−	0.376782i	−0.232142	−	0.972682i	$-0.574573\pi$
$751$	−28.3690	−	10.3255i	−1.03520	−	0.376782i	−0.803059	+	0.595900i	$0.796796\pi$
$752$	−1.75100	+	3.03283i	−0.0638526	+	0.110596i
$753$	12.5678	+	21.7680i	0.457995	+	0.793270i
$754$	−0.809822	−	4.59273i	−0.0294920	−	0.167257i
$755$	17.5263	+	14.7063i	0.637849	+	0.535219i
$756$	−14.2303	+	11.9406i	−0.517551	+	0.434277i
$757$	−7.62806	+	43.2609i	−0.277247	+	1.57234i	0.454488	+	0.890753i	$0.349822\pi$
$757$	−7.62806	+	43.2609i	−0.277247	+	1.57234i	−0.731734	+	0.681590i	$0.761289\pi$
$758$	45.1859	−	16.4463i	1.64123	−	0.597358i
$759$	4.75720			0.172675
$760$	1.37156	−	11.9703i	0.0497518	−	0.434209i
$761$	8.54121			0.309619			0.154809	−	0.987944i	$-0.450524\pi$
$761$	8.54121			0.309619			0.154809	+	0.987944i	$0.450524\pi$
$762$	41.0260	−	14.9322i	1.48622	−	0.540938i
$763$	7.01042	−	39.7580i	0.253794	−	1.43934i
$764$	9.83938	−	8.25622i	0.355976	−	0.298700i
$765$	−6.39306	−	5.36442i	−0.231142	−	0.193951i
$766$	0.394739	+	2.23867i	0.0142625	+	0.0808866i
$767$	−0.0185372	−	0.0321073i	−0.000669338	−	0.00115933i
$768$	15.2867	−	26.4773i	0.551610	−	0.955416i
$769$	2.85059	+	1.03753i	0.102795	+	0.0374143i	0.392906	−	0.919579i	$-0.371470\pi$
$769$	2.85059	+	1.03753i	0.102795	+	0.0374143i	−0.290111	+	0.956993i	$0.593692\pi$
$770$	9.20637	+	3.35085i	0.331775	+	0.120756i
$771$	9.14579	−	15.8410i	0.329377	−	0.570498i
$772$	13.6237	+	23.5969i	0.490328	+	0.849273i
$773$	4.82532	+	27.3657i	0.173555	+	0.984277i	0.939799	+	0.341728i	$0.111012\pi$
$773$	4.82532	+	27.3657i	0.173555	+	0.984277i	−0.766245	+	0.642549i	$0.777877\pi$
$774$	−10.6751	−	8.95747i	−0.383709	−	0.321970i
$775$	1.97581	−	1.65790i	0.0709731	−	0.0595535i
$776$	−0.437504	+	2.48121i	−0.0157055	+	0.0890701i
$777$	−27.1796	+	9.89256i	−0.975062	+	0.354893i
$778$	−27.6756			−0.992217
$779$	−43.3292	−	32.1046i	−1.55243	−	1.15027i
$780$	1.58803			0.0568606
$781$	−3.36160	+	1.22352i	−0.120287	+	0.0437810i
$782$	−4.85949	+	27.5596i	−0.173775	+	0.985528i
$783$	27.3061	−	22.9125i	0.975839	−	0.818826i
$784$	0.934615	+	0.784236i	0.0333791	+	0.0280084i
$785$	−3.56040	−	20.1920i	−0.127076	−	0.720684i
$786$	1.23600	+	2.14081i	0.0440865	+	0.0763601i
$787$	15.0563	−	26.0783i	0.536700	−	0.929591i	−0.462379	−	0.886682i	$-0.653004\pi$
$787$	15.0563	−	26.0783i	0.536700	−	0.929591i	0.999079	−	0.0429089i	$-0.0136625\pi$
$788$	−0.392310	−	0.142789i	−0.0139754	−	0.00508665i
$789$	19.8733	+	7.23329i	0.707508	+	0.257512i
$790$	2.34121	−	4.05509i	0.0832965	−	0.144274i
$791$	20.4660	+	35.4482i	0.727688	+	1.26039i
$792$	0.192262	+	1.09037i	0.00683174	+	0.0387447i
$793$	−2.55440	−	2.14340i	−0.0907096	−	0.0761144i
$794$	−45.2877	+	38.0009i	−1.60720	+	1.34860i
$795$	1.40146	−	7.94808i	0.0497047	−	0.281889i
$796$	10.7770	−	3.92253i	0.381982	−	0.139030i
$797$	49.8342			1.76522			0.882610	−	0.470107i	$-0.155785\pi$
$797$	49.8342			1.76522			0.882610	+	0.470107i	$0.155785\pi$
$798$	−7.01261	−	29.2917i	−0.248244	−	1.03692i
$799$	−3.40217			−0.120360
$800$	−3.81525	+	1.38864i	−0.134890	+	0.0490958i
$801$	−0.887475	+	5.03312i	−0.0313574	+	0.177837i
$802$	0.0532823	−	0.0447092i	0.00188146	−	0.00157874i
$803$	−1.04862	−	0.879894i	−0.0370049	−	0.0310508i
$804$	−1.62429	−	9.21180i	−0.0572843	−	0.324875i
$805$	−8.76364	−	15.1791i	−0.308878	−	0.534992i
$806$	−1.46755	+	2.54187i	−0.0516923	+	0.0895336i
$807$	42.5752	+	15.4961i	1.49872	+	0.545489i
$808$	16.1686	+	5.88489i	0.568809	+	0.207030i
$809$	4.41999	−	7.65565i	0.155399	−	0.269158i	−0.777805	−	0.628505i	$-0.783667\pi$
$809$	4.41999	−	7.65565i	0.155399	−	0.269158i	0.933204	+	0.359347i	$0.117000\pi$
$810$	10.9248	+	18.9223i	0.383858	+	0.664861i
$811$	−8.41071	−	47.6995i	−0.295340	−	1.67496i	−0.665818	−	0.746115i	$-0.731917\pi$
$811$	−8.41071	−	47.6995i	−0.295340	−	1.67496i	0.370478	−	0.928841i	$-0.379194\pi$
$812$	−15.9300	−	13.3669i	−0.559034	−	0.469085i
$813$	10.3592	−	8.69240i	0.363313	−	0.304856i
$814$	2.37458	−	13.4669i	0.0832289	−	0.472015i
$815$	32.4453	−	11.8091i	1.13651	−	0.413655i
$816$	34.7211			1.21548
$817$	36.8959	−	16.0149i	1.29082	−	0.560290i
$818$	−2.91090			−0.101777
$819$	0.833368	−	0.303321i	0.0291202	−	0.0105989i
$820$	5.67720	−	32.1970i	0.198256	−	1.12437i
$821$	6.37824	−	5.35198i	0.222602	−	0.186785i	−0.524666	−	0.851308i	$-0.675810\pi$
$821$	6.37824	−	5.35198i	0.222602	−	0.186785i	0.747268	+	0.664523i	$0.231365\pi$
$822$	−26.3664	−	22.1241i	−0.919635	−	0.771666i
$823$	−7.42945	−	42.1345i	−0.258974	−	1.46872i	−0.785661	−	0.618658i	$-0.787677\pi$
$823$	−7.42945	−	42.1345i	−0.258974	−	1.46872i	0.526686	−	0.850060i	$-0.323434\pi$
$824$	−2.54378	−	4.40596i	−0.0886169	−	0.153489i
$825$	−0.477229	+	0.826586i	−0.0166150	+	0.0287780i
$826$	−0.400594	−	0.145804i	−0.0139385	−	0.00507318i
$827$	−21.1855	−	7.71090i	−0.736693	−	0.268134i	−0.0536977	−	0.998557i	$-0.517101\pi$
$827$	−21.1855	−	7.71090i	−0.736693	−	0.268134i	−0.682995	+	0.730423i	$0.739323\pi$
$828$	−1.71137	+	2.96418i	−0.0594742	+	0.103012i
$829$	12.3878	+	21.4563i	0.430246	+	0.745207i	0.996894	−	0.0787524i	$-0.0250937\pi$
$829$	12.3878	+	21.4563i	0.430246	+	0.745207i	−0.566649	+	0.823960i	$0.691760\pi$
$830$	−8.84989	−	50.1902i	−0.307184	−	1.74213i
$831$	10.9601	+	9.19658i	0.380200	+	0.319026i
$832$	0.454930	−	0.381731i	0.0157718	−	0.0132342i
$833$	−0.205820	+	1.16726i	−0.00713125	+	0.0404433i
$834$	−10.0429	+	3.65530i	−0.347756	+	0.126573i
$835$	−4.04429			−0.139958
$836$	5.29370	+	1.57173i	0.183086	+	0.0543594i
$837$	−22.4341			−0.775436
$838$	31.2436	−	11.3718i	1.07929	−	0.392831i
$839$	−5.04407	+	28.6063i	−0.174141	+	0.987601i	0.764990	+	0.644042i	$0.222744\pi$
$839$	−5.04407	+	28.6063i	−0.174141	+	0.987601i	−0.939131	+	0.343559i	$0.888367\pi$
$840$	−8.09506	+	6.79256i	−0.279306	+	0.234366i
$841$	8.35233	+	7.00844i	0.288012	+	0.241670i
$842$	11.2251	+	63.6609i	0.386844	+	2.19390i
$843$	−7.33969	−	12.7127i	−0.252792	−	0.437849i
$844$	−3.07638	+	5.32844i	−0.105893	+	0.183413i
$845$	25.1551	+	9.15571i	0.865362	+	0.314966i
$846$	−1.00832	−	0.366998i	−0.0346667	−	0.0126176i
$847$	1.29928	−	2.25041i	0.0446436	−	0.0773250i
$848$	−6.48097	−	11.2254i	−0.222557	−	0.385481i
$849$	−4.84225	−	27.4618i	−0.166186	−	0.942486i
$850$	−4.30111	−	3.60906i	−0.147527	−	0.123790i
$851$	−18.7405	+	15.7252i	−0.642418	+	0.539052i
$852$	−1.15780	+	6.56618i	−0.0396654	+	0.224954i
$853$	−29.5265	+	10.7468i	−1.01097	+	0.367962i	−0.793804	−	0.608173i	$-0.791903\pi$
$853$	−29.5265	+	10.7468i	−1.01097	+	0.367962i	−0.217163	+	0.976135i	$0.569680\pi$
$854$	−38.3426			−1.31206
$855$	7.58331	−	0.458971i	0.259344	−	0.0156965i
$856$	−21.5087			−0.735151
$857$	15.1032	−	5.49713i	0.515916	−	0.187778i	−0.0709226	−	0.997482i	$-0.522594\pi$
$857$	15.1032	−	5.49713i	0.515916	−	0.187778i	0.586839	+	0.809704i	$0.300372\pi$
$858$	0.188608	−	1.06965i	0.00643897	−	0.0365172i
$859$	9.07831	−	7.61761i	0.309748	−	0.259909i	−0.474640	−	0.880180i	$-0.657422\pi$
$859$	9.07831	−	7.61761i	0.309748	−	0.259909i	0.784388	+	0.620271i	$0.212977\pi$
$860$	18.6798	+	15.6742i	0.636975	+	0.534485i
$861$	8.21307	+	46.5786i	0.279901	+	1.58739i
$862$	−33.5536	−	58.1165i	−1.14284	−	1.97945i
$863$	11.2270	−	19.4458i	0.382172	−	0.661941i	−0.609201	−	0.793016i	$-0.708510\pi$
$863$	11.2270	−	19.4458i	0.382172	−	0.661941i	0.991372	+	0.131075i	$0.0418429\pi$
$864$	33.1850	+	12.0784i	1.12898	+	0.410914i
$865$	18.3061	+	6.66286i	0.622424	+	0.226544i
$866$	19.4255	−	33.6460i	0.660106	−	1.14334i
$867$	4.36035	+	7.55234i	0.148085	+	0.256491i
$868$	2.27267	+	12.8890i	0.0771394	+	0.437479i
$869$	−0.951376	−	0.798300i	−0.0322732	−	0.0270805i
$870$	−26.8413	+	22.5225i	−0.910006	+	0.763586i
$871$	−0.355969	+	2.01880i	−0.0120616	+	0.0684045i
$872$	−19.3456	+	7.04122i	−0.655125	+	0.238446i
$873$	−1.58865			−0.0537675
$874$	−14.0472	−	21.2524i	−0.475154	−	0.718873i
$875$	30.6190			1.03511
$876$	−2.39746	+	0.872602i	−0.0810025	+	0.0294825i
$877$	−4.87019	+	27.6202i	−0.164455	+	0.932669i	0.785170	+	0.619280i	$0.212575\pi$
$877$	−4.87019	+	27.6202i	−0.164455	+	0.932669i	−0.949625	+	0.313389i	$0.898536\pi$
$878$	−6.82971	+	5.73080i	−0.230491	+	0.193405i
$879$	−30.1395	−	25.2901i	−1.01658	−	0.853013i
$880$	−1.78532	−	10.1251i	−0.0601832	−	0.341316i
$881$	5.32273	+	9.21924i	0.179327	+	0.310604i	0.941650	−	0.336593i	$-0.109275\pi$
$881$	5.32273	+	9.21924i	0.179327	+	0.310604i	−0.762323	+	0.647197i	$0.775941\pi$
$882$	−0.186915	+	0.323746i	−0.00629374	+	0.0109011i
$883$	−4.86470	−	1.77060i	−0.163710	−	0.0595856i	0.258865	−	0.965914i	$-0.416652\pi$
$883$	−4.86470	−	1.77060i	−0.163710	−	0.0595856i	−0.422575	+	0.906328i	$0.638874\pi$
$884$	2.32832	+	0.847439i	0.0783099	+	0.0285025i
$885$	−0.139275	+	0.241232i	−0.00468168	+	0.00810891i
$886$	21.8015	+	37.7613i	0.732435	+	1.26862i
$887$	−3.54680	−	20.1149i	−0.119090	−	0.675392i	−0.984644	−	0.174576i	$-0.944144\pi$
$887$	−3.54680	−	20.1149i	−0.119090	−	0.675392i	0.865554	−	0.500816i	$-0.166967\pi$
$888$	11.2988	+	9.48085i	0.379164	+	0.318156i
$889$	−32.6828	+	27.4241i	−1.09615	+	0.919775i
$890$	4.00459	−	22.7112i	0.134234	−	0.761280i
$891$	5.44574	−	1.98209i	0.182439	−	0.0664024i
$892$	4.31414			0.144448
$893$	2.24791	−	2.13047i	0.0752233	−	0.0712934i
$894$	−53.4333			−1.78708
$895$	0.162879	−	0.0592831i	0.00544445	−	0.00198162i
$896$	−4.46210	+	25.3059i	−0.149068	+	0.845409i
$897$	−1.48852	+	1.24902i	−0.0497004	+	0.0417036i
$898$	8.03288	+	6.74039i	0.268061	+	0.224930i
$899$	−4.36096	−	24.7322i	−0.145446	−	0.824865i
$900$	−0.343360	−	0.594717i	−0.0114453	−	0.0198239i
$901$	6.29620	−	10.9053i	0.209757	−	0.363310i
$902$	−21.0126	−	7.64797i	−0.699644	−	0.254650i
$903$	−33.1493	−	12.0654i	−1.10314	−	0.401510i
$904$	10.4365	−	18.0766i	0.347114	−	0.601219i
$905$	−4.64832	−	8.05112i	−0.154515	−	0.267628i
$906$	−5.06454	−	28.7224i	−0.168258	−	0.954239i
$907$	−6.30422	−	5.28987i	−0.209328	−	0.175647i	0.532096	−	0.846684i	$-0.321405\pi$
$907$	−6.30422	−	5.28987i	−0.209328	−	0.175647i	−0.741424	+	0.671037i	$0.765849\pi$
$908$	−24.9214	+	20.9115i	−0.827045	+	0.693973i
$909$	−1.88396	+	10.6845i	−0.0624871	+	0.354382i
$910$	−3.76044	+	1.36869i	−0.124658	+	0.0453716i
$911$	25.9796			0.860743			0.430371	−	0.902652i	$-0.358383\pi$
$911$	25.9796			0.860743			0.430371	+	0.902652i	$0.358383\pi$
$912$	−22.9412	+	21.7426i	−0.759658	+	0.719970i
$913$	−13.5175			−0.447363
$914$	13.4365	−	4.89049i	0.444441	−	0.161763i
$915$	−4.35047	+	24.6727i	−0.143822	+	0.815656i
$916$	−24.2737	+	20.3681i	−0.802027	+	0.672980i
$917$	−1.85052	−	1.55277i	−0.0611094	−	0.0512769i
$918$	8.48039	+	48.0947i	0.279894	+	1.58736i
$919$	20.2094	+	35.0038i	0.666648	+	1.15467i	0.978836	+	0.204648i	$0.0656049\pi$
$919$	20.2094	+	35.0038i	0.666648	+	1.15467i	−0.312188	+	0.950020i	$0.601062\pi$
$920$	−4.46897	+	7.74048i	−0.147338	+	0.255196i
$921$	17.6329	+	6.41784i	0.581023	+	0.211475i
$922$	−23.6175	−	8.59605i	−0.777800	−	0.283096i
$923$	0.730601	−	1.26544i	0.0240480	−	0.0416524i
$924$	−2.42160	−	4.19434i	−0.0796649	−	0.137984i
$925$	−0.852323	−	4.83377i	−0.0280242	−	0.158933i
$926$	37.0046	+	31.0506i	1.21605	+	1.02039i
$927$	2.45742	−	2.06202i	0.0807123	−	0.0677256i
$928$	−6.86482	+	38.9323i	−0.225349	+	1.27802i
$929$	−44.4447	+	16.1766i	−1.45818	+	0.530736i	−0.944864	−	0.327462i	$-0.893807\pi$
$929$	−44.4447	+	16.1766i	−1.45818	+	0.530736i	−0.513320	+	0.858197i	$0.671585\pi$
$930$	22.0523			0.723123
$931$	−0.594959	−	0.900130i	−0.0194990	−	0.0295006i
$932$	−6.58546			−0.215714
$933$	−40.6395	+	14.7916i	−1.33048	+	0.484254i
$934$	10.1642	−	57.6442i	0.332584	−	1.88618i
$935$	7.65138	−	6.42027i	0.250227	−	0.209965i
$936$	−0.346440	−	0.290698i	−0.0113237	−	0.00950175i
$937$	−6.88998	−	39.0750i	−0.225086	−	1.27652i	−0.862521	−	0.506021i	$-0.831116\pi$
$937$	−6.88998	−	39.0750i	−0.225086	−	1.27652i	0.637435	−	0.770504i	$-0.279995\pi$
$938$	11.7858	+	20.4135i	0.384819	+	0.666526i
$939$	21.1751	−	36.6763i	0.691022	−	1.19689i
$940$	1.76440	+	0.642189i	0.0575484	+	0.0209459i
$941$	−55.4578	−	20.1850i	−1.80787	−	0.658012i	−0.997386	−	0.0722534i	$-0.976981\pi$
$941$	−55.4578	−	20.1850i	−1.80787	−	0.658012i	−0.810486	−	0.585758i	$-0.800797\pi$
$942$	−13.0687	+	22.6356i	−0.425800	+	0.737507i
$943$	20.0021	+	34.6447i	0.651359	+	1.12819i
$944$	0.0776843	+	0.440569i	0.00252841	+	0.0143393i
$945$	−23.4311	−	19.6610i	−0.762214	−	0.639574i
$946$	12.7762	−	10.7205i	0.415391	−	0.348554i
$947$	6.51381	−	36.9417i	0.211670	−	1.20044i	−0.674921	−	0.737890i	$-0.735822\pi$
$947$	6.51381	−	36.9417i	0.211670	−	1.20044i	0.886592	−	0.462553i	$-0.153066\pi$
$948$	−2.17513	+	0.791684i	−0.0706451	+	0.0257127i
$949$	0.559131			0.0181502
$950$	5.10188	−	0.308785i	0.165527	−	0.0100183i
$951$	−21.2223			−0.688180
$952$	−15.4935	+	5.63918i	−0.502148	+	0.182767i
$953$	4.14765	−	23.5225i	0.134356	−	0.761969i	−0.840951	−	0.541112i	$-0.818004\pi$
$953$	4.14765	−	23.5225i	0.134356	−	0.761969i	0.975306	−	0.220857i	$-0.0708853\pi$
$954$	3.04241	−	2.55289i	0.0985018	−	0.0826528i
$955$	16.2012	+	13.5944i	0.524258	+	0.439905i
$956$	2.46452	+	13.9770i	0.0797082	+	0.452048i
$957$	4.64674	+	8.04839i	0.150208	+	0.260167i
$958$	−1.60649	+	2.78252i	−0.0519033	+	0.0898992i
$959$	31.6064	+	11.5038i	1.02062	+	0.371477i
$960$	−4.19282	−	1.52606i	−0.135323	−	0.0492535i
$961$	7.59713	−	13.1586i	0.245069	−	0.424471i
$962$	2.79278	+	4.83724i	0.0900429	+	0.155959i
$963$	−2.35504	−	13.3561i	−0.0758902	−	0.430395i
$964$	28.5415	+	23.9492i	0.919261	+	0.771351i
$965$	−34.3683	+	28.8384i	−1.10636	+	0.928343i
$966$	−3.87987	+	22.0039i	−0.124833	+	0.707963i
$967$	−50.9277	+	18.5362i	−1.63772	+	0.596083i	−0.986639	−	0.162922i	$-0.947908\pi$
$967$	−50.9277	+	18.5362i	−1.63772	+	0.596083i	−0.651085	+	0.759005i	$0.725686\pi$
$968$	−1.32512			−0.0425909
$969$	−29.4364	−	8.73985i	−0.945634	−	0.280764i
$970$	7.16851			0.230167
$971$	23.2267	−	8.45383i	0.745381	−	0.271296i	0.0587201	−	0.998274i	$-0.481298\pi$
$971$	23.2267	−	8.45383i	0.745381	−	0.271296i	0.686661	+	0.726978i	$0.259076\pi$
$972$	−1.84848	+	10.4832i	−0.0592900	+	0.336250i
$973$	8.00050	−	6.71321i	0.256484	−	0.215216i
$974$	57.5779	+	48.3136i	1.84491	+	1.54807i
$975$	−0.0676983	−	0.383936i	−0.00216808	−	0.0122958i
$976$	20.1185	+	34.8462i	0.643977	+	1.11540i
$977$	18.3719	−	31.8210i	0.587769	−	1.01804i	−0.406755	−	0.913537i	$-0.633340\pi$
$977$	18.3719	−	31.8210i	0.587769	−	1.01804i	0.994524	−	0.104508i	$-0.0333268\pi$
$978$	−41.3603	−	15.0539i	−1.32256	−	0.481372i
$979$	−5.74781	−	2.09203i	−0.183701	−	0.0668616i
$980$	0.327072	−	0.566505i	0.0104479	−	0.0180963i
$981$	−6.49056	−	11.2420i	−0.207227	−	0.358929i
$982$	11.7514	+	66.6457i	0.375004	+	2.12675i
$983$	−10.2458	−	8.59726i	−0.326791	−	0.274210i	0.464600	−	0.885521i	$-0.346198\pi$
$983$	−10.2458	−	8.59726i	−0.326791	−	0.274210i	−0.791391	+	0.611311i	$0.790643\pi$
$984$	18.4762	−	15.5033i	0.588999	−	0.494229i
$985$	0.119369	−	0.676977i	0.00380342	−	0.0215703i
$986$	−51.3729	+	18.6982i	−1.63604	+	0.595472i
$987$	−2.71633			−0.0864618
$988$	−2.06906	+	0.898087i	−0.0658255	+	0.0285719i
$989$	−29.8374			−0.948773
$990$	2.96024	−	1.07744i	0.0940826	−	0.0342433i
$991$	−0.151086	+	0.856853i	−0.00479942	+	0.0272188i	−0.987113	−	0.160022i	$-0.948843\pi$
$991$	−0.151086	+	0.856853i	−0.00479942	+	0.0272188i	0.982314	+	0.187241i	$0.0599545\pi$
$992$	19.0597	−	15.9930i	0.605147	−	0.507778i
$993$	29.7719	+	24.9816i	0.944782	+	0.792766i
$994$	−2.91760	−	16.5465i	−0.0925407	−	0.524825i
$995$	9.44198	+	16.3540i	0.299331	+	0.518457i
$996$	−12.5970	+	21.8187i	−0.399152	+	0.691351i
$997$	−25.8113	−	9.39453i	−0.817451	−	0.297528i	−0.100753	−	0.994911i	$-0.532125\pi$
$997$	−25.8113	−	9.39453i	−0.817451	−	0.297528i	−0.716698	+	0.697384i	$0.754347\pi$
$998$	3.19368	+	1.16240i	0.101094	+	0.0367953i
$999$	−21.3463	+	36.9729i	−0.675367	+	1.16977i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	209.2.j.b.100.3	yes	42
19.2	odd	18		3971.2.a.s.1.6		21
19.4	even	9	inner	209.2.j.b.23.3	✓	42
19.17	even	9		3971.2.a.t.1.16		21

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
209.2.j.b.23.3	✓	42	19.4	even	9	inner
209.2.j.b.100.3	yes	42	1.1	even	1	trivial
3971.2.a.s.1.6		21	19.2	odd	18
3971.2.a.t.1.16		21	19.17	even	9

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:	\( N \)	\(=\)	\( 209 = 11 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	209.j (of order \(9\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.69844 + 0.618183i) q^{2} +(-0.255473 + 1.44886i) q^{3} +(0.970468 - 0.814320i) q^{4} +(1.59794 + 1.34083i) q^{5} +(-0.461753 - 2.61873i) q^{6} +(1.29928 + 2.25041i) q^{7} +(0.662558 - 1.14758i) q^{8} +(0.785155 + 0.285773i) q^{9} +O(q^{10})\)	\(q+(-1.69844 + 0.618183i) q^{2} +(-0.255473 + 1.44886i) q^{3} +(0.970468 - 0.814320i) q^{4} +(1.59794 + 1.34083i) q^{5} +(-0.461753 - 2.61873i) q^{6} +(1.29928 + 2.25041i) q^{7} +(0.662558 - 1.14758i) q^{8} +(0.785155 + 0.285773i) q^{9} +(-3.54289 - 1.28951i) q^{10} +(-0.500000 + 0.866025i) q^{11} +(0.931905 + 1.61411i) q^{12} +(-0.0709285 - 0.402256i) q^{13} +(-3.59791 - 3.01900i) q^{14} +(-2.35090 + 1.97264i) q^{15} +(-0.855875 + 4.85391i) q^{16} +(-4.49951 + 1.63769i) q^{17} -1.51020 q^{18} +(1.94741 - 3.89969i) q^{19} +2.64262 q^{20} +(-3.59245 + 1.30755i) q^{21} +(0.313859 - 1.77999i) q^{22} +(-2.47703 + 2.07847i) q^{23} +(1.49342 + 1.25313i) q^{24} +(-0.112656 - 0.638902i) q^{25} +(0.369135 + 0.639361i) q^{26} +(-2.82144 + 4.88688i) q^{27} +(3.09346 + 1.12593i) q^{28} +(-5.93594 - 2.16051i) q^{29} +(2.77342 - 4.80371i) q^{30} +(1.98782 + 3.44301i) q^{31} +(-1.08674 - 6.16320i) q^{32} +(-1.12701 - 0.945675i) q^{33} +(6.62976 - 5.56303i) q^{34} +(-0.941256 + 5.33813i) q^{35} +(0.994678 - 0.362033i) q^{36} +7.56574 q^{37} +(-0.896850 + 7.82726i) q^{38} +0.600931 q^{39} +(2.59745 - 0.945393i) q^{40} +(2.14832 - 12.1838i) q^{41} +(5.29328 - 4.44159i) q^{42} +(7.06867 + 5.93132i) q^{43} +(0.219987 + 1.24761i) q^{44} +(0.871457 + 1.50941i) q^{45} +(2.92221 - 5.06142i) q^{46} +(0.667672 + 0.243013i) q^{47} +(-6.81397 - 2.48008i) q^{48} +(0.123768 - 0.214373i) q^{49} +(0.586297 + 1.01550i) q^{50} +(-1.22327 - 6.93753i) q^{51} +(-0.396398 - 0.332618i) q^{52} +(-2.01458 + 1.69043i) q^{53} +(1.77107 - 10.0443i) q^{54} +(-1.96016 + 0.713441i) q^{55} +3.44338 q^{56} +(5.15259 + 3.81779i) q^{57} +11.4174 q^{58} +(0.0852921 - 0.0310438i) q^{59} +(-0.675116 + 3.82878i) q^{60} +(6.25373 - 5.24750i) q^{61} +(-5.50461 - 4.61892i) q^{62} +(0.377026 + 2.13822i) q^{63} +(0.726959 + 1.25913i) q^{64} +(0.426017 - 0.737884i) q^{65} +(2.49876 + 0.909476i) q^{66} +(-4.71604 - 1.71650i) q^{67} +(-3.03303 + 5.25336i) q^{68} +(-2.37860 - 4.11985i) q^{69} +(-1.70127 - 9.64838i) q^{70} +(2.74040 + 2.29947i) q^{71} +(0.848159 - 0.711690i) q^{72} +(-0.237702 + 1.34808i) q^{73} +(-12.8500 + 4.67701i) q^{74} +0.954459 q^{75} +(-1.28569 - 5.37034i) q^{76} -2.59855 q^{77} +(-1.02065 + 0.371485i) q^{78} +(-0.215660 + 1.22307i) q^{79} +(-7.87591 + 6.60867i) q^{80} +(-4.43941 - 3.72510i) q^{81} +(3.88298 + 22.0215i) q^{82} +(6.75874 + 11.7065i) q^{83} +(-2.42160 + 4.19434i) q^{84} +(-9.38580 - 3.41615i) q^{85} +(-15.6724 - 5.70427i) q^{86} +(4.64674 - 8.04839i) q^{87} +(0.662558 + 1.14758i) q^{88} +(1.06215 + 6.02376i) q^{89} +(-2.41321 - 2.02492i) q^{90} +(0.813085 - 0.682259i) q^{91} +(-0.711336 + 4.03418i) q^{92} +(-5.49627 + 2.00048i) q^{93} -1.28423 q^{94} +(8.34068 - 3.62032i) q^{95} +9.20724 q^{96} +(-1.78667 + 0.650293i) q^{97} +(-0.0776916 + 0.440611i) q^{98} +(-0.640064 + 0.537077i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 42 q - 3 q^{2} + 3 q^{4} - 6 q^{5} + 12 q^{6} - 6 q^{7} - 15 q^{8}+O(q^{10}) \) 42 * q - 3 * q^2 + 3 * q^4 - 6 * q^5 + 12 * q^6 - 6 * q^7 - 15 * q^8	\( 42 q - 3 q^{2} + 3 q^{4} - 6 q^{5} + 12 q^{6} - 6 q^{7} - 15 q^{8} - 15 q^{10} - 21 q^{11} - 30 q^{12} - 18 q^{13} - 3 q^{14} - 9 q^{15} - 3 q^{16} + 12 q^{18} - 6 q^{19} + 30 q^{20} + 9 q^{21} + 6 q^{22} + 15 q^{23} + 3 q^{24} - 6 q^{26} - 24 q^{27} - 9 q^{28} - 15 q^{29} + 30 q^{30} - 54 q^{31} + 42 q^{32} - 45 q^{34} - 12 q^{35} + 6 q^{36} + 114 q^{37} - 60 q^{38} - 48 q^{40} + 15 q^{41} + 84 q^{42} - 6 q^{43} + 3 q^{44} + 3 q^{45} - 15 q^{46} - 42 q^{47} + 12 q^{48} - 21 q^{49} - 33 q^{50} + 93 q^{51} + 3 q^{52} + 48 q^{54} + 3 q^{55} + 114 q^{56} - 15 q^{57} + 60 q^{58} - 33 q^{59} - 81 q^{60} + 63 q^{61} - 24 q^{62} + 87 q^{63} + 15 q^{64} + 24 q^{65} - 15 q^{66} - 51 q^{67} + 48 q^{68} - 54 q^{69} - 84 q^{70} + 9 q^{71} - 51 q^{72} - 27 q^{73} - 33 q^{74} + 54 q^{75} - 60 q^{76} + 12 q^{77} - 87 q^{78} + 24 q^{79} + 120 q^{80} - 36 q^{81} + 111 q^{82} - 12 q^{83} + 48 q^{84} + 39 q^{85} - 60 q^{86} - 75 q^{87} - 15 q^{88} - 21 q^{89} - 63 q^{90} - 3 q^{91} + 6 q^{92} - 72 q^{93} + 84 q^{94} - 72 q^{95} - 6 q^{96} - 18 q^{97} - 120 q^{98}+O(q^{100}) \) 42 * q - 3 * q^2 + 3 * q^4 - 6 * q^5 + 12 * q^6 - 6 * q^7 - 15 * q^8 - 15 * q^10 - 21 * q^11 - 30 * q^12 - 18 * q^13 - 3 * q^14 - 9 * q^15 - 3 * q^16 + 12 * q^18 - 6 * q^19 + 30 * q^20 + 9 * q^21 + 6 * q^22 + 15 * q^23 + 3 * q^24 - 6 * q^26 - 24 * q^27 - 9 * q^28 - 15 * q^29 + 30 * q^30 - 54 * q^31 + 42 * q^32 - 45 * q^34 - 12 * q^35 + 6 * q^36 + 114 * q^37 - 60 * q^38 - 48 * q^40 + 15 * q^41 + 84 * q^42 - 6 * q^43 + 3 * q^44 + 3 * q^45 - 15 * q^46 - 42 * q^47 + 12 * q^48 - 21 * q^49 - 33 * q^50 + 93 * q^51 + 3 * q^52 + 48 * q^54 + 3 * q^55 + 114 * q^56 - 15 * q^57 + 60 * q^58 - 33 * q^59 - 81 * q^60 + 63 * q^61 - 24 * q^62 + 87 * q^63 + 15 * q^64 + 24 * q^65 - 15 * q^66 - 51 * q^67 + 48 * q^68 - 54 * q^69 - 84 * q^70 + 9 * q^71 - 51 * q^72 - 27 * q^73 - 33 * q^74 + 54 * q^75 - 60 * q^76 + 12 * q^77 - 87 * q^78 + 24 * q^79 + 120 * q^80 - 36 * q^81 + 111 * q^82 - 12 * q^83 + 48 * q^84 + 39 * q^85 - 60 * q^86 - 75 * q^87 - 15 * q^88 - 21 * q^89 - 63 * q^90 - 3 * q^91 + 6 * q^92 - 72 * q^93 + 84 * q^94 - 72 * q^95 - 6 * q^96 - 18 * q^97 - 120 * q^98

Introduction

L-functions

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