LMFDB - Embedded newform 650.2.ba.b.73.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [650,2,Mod(73,650)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(650, base_ring=CyclotomicField(20))

chi = DirichletCharacter(H, H._module([11, 5]))

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

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

chi := DirichletCharacter("650.73");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 650 = 2 \cdot 5^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	650.ba (of order $20$, degree $8$, 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:	$5.19027613138$
Analytic rank:	$0$
Dimension:	$144$
Relative dimension:	$18$ over $\Q(\zeta_{20})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{20}]$

Embedding invariants

Embedding label			73.1
Character	$\chi$	$=$	650.73
Dual form			650.2.ba.b.187.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.809017 - 0.587785i) q^{2} +(-2.86287 + 1.45871i) q^{3} +(0.309017 - 0.951057i) q^{4} +(-2.06627 + 0.854710i) q^{5} +(-1.45871 + 2.86287i) q^{6} -2.35225i q^{7} +(-0.309017 - 0.951057i) q^{8} +(4.30486 - 5.92513i) q^{9} +O(q^{10})$	\(q+(0.809017 - 0.587785i) q^{2} +(-2.86287 + 1.45871i) q^{3} +(0.309017 - 0.951057i) q^{4} +(-2.06627 + 0.854710i) q^{5} +(-1.45871 + 2.86287i) q^{6} -2.35225i q^{7} +(-0.309017 - 0.951057i) q^{8} +(4.30486 - 5.92513i) q^{9} +(-1.16926 + 1.90600i) q^{10} +(-0.0589691 + 0.372316i) q^{11} +(0.502636 + 3.17352i) q^{12} +(-2.34964 + 2.73481i) q^{13} +(-1.38262 - 1.90301i) q^{14} +(4.66870 - 5.46101i) q^{15} +(-0.809017 - 0.587785i) q^{16} +(1.22811 - 2.41030i) q^{17} -7.32387i q^{18} +(7.16915 + 3.65286i) q^{19} +(0.174366 + 2.22926i) q^{20} +(3.43124 + 6.73419i) q^{21} +(0.171135 + 0.335871i) q^{22} +(-0.798580 + 5.04203i) q^{23} +(2.27199 + 2.27199i) q^{24} +(3.53894 - 3.53212i) q^{25} +(-0.293413 + 3.59359i) q^{26} +(-2.17333 + 13.7219i) q^{27} +(-2.23712 - 0.726884i) q^{28} +(6.87916 + 2.23517i) q^{29} +(0.567154 - 7.16224i) q^{30} +(-2.48518 + 4.87743i) q^{31} -1.00000 q^{32} +(-0.374279 - 1.15191i) q^{33} +(-0.423178 - 2.67184i) q^{34} +(2.01049 + 4.86038i) q^{35} +(-4.30486 - 5.92513i) q^{36} +(5.23039 - 7.19902i) q^{37} +(7.94706 - 1.25869i) q^{38} +(2.73742 - 11.2569i) q^{39} +(1.45139 + 1.70102i) q^{40} +(-0.0555382 - 0.350654i) q^{41} +(6.73419 + 3.43124i) q^{42} +(4.51155 - 4.51155i) q^{43} +(0.335871 + 0.171135i) q^{44} +(-3.83073 + 15.9223i) q^{45} +(2.31757 + 4.54848i) q^{46} +(5.20991 + 1.69280i) q^{47} +(3.17352 + 0.502636i) q^{48} +1.46693 q^{49} +(0.786932 - 4.93769i) q^{50} +8.69184i q^{51} +(1.87488 + 3.07974i) q^{52} +(-7.83802 + 3.99367i) q^{53} +(6.30725 + 12.3787i) q^{54} +(-0.196376 - 0.819707i) q^{55} +(-2.23712 + 0.726884i) q^{56} -25.8528 q^{57} +(6.87916 - 2.23517i) q^{58} +(0.0162404 + 0.102538i) q^{59} +(-3.75102 - 6.12774i) q^{60} +(6.85871 - 4.98314i) q^{61} +(0.856334 + 5.40668i) q^{62} +(-13.9374 - 10.1261i) q^{63} +(-0.809017 + 0.587785i) q^{64} +(2.51751 - 7.65912i) q^{65} +(-0.979875 - 0.711921i) q^{66} +(2.47933 + 7.63060i) q^{67} +(-1.91283 - 1.91283i) q^{68} +(-5.06861 - 15.5996i) q^{69} +(4.48338 + 2.75039i) q^{70} +(5.58704 - 2.84674i) q^{71} +(-6.96541 - 2.26320i) q^{72} +(5.92676 - 4.30604i) q^{73} -8.89847i q^{74} +(-4.97920 + 15.2743i) q^{75} +(5.68947 - 5.68947i) q^{76} +(0.875779 + 0.138710i) q^{77} +(-4.40199 - 10.7160i) q^{78} +(-15.7552 - 5.11917i) q^{79} +(2.17403 + 0.523047i) q^{80} +(-7.00461 - 21.5580i) q^{81} +(-0.251041 - 0.251041i) q^{82} +(-3.72800 + 1.21130i) q^{83} +(7.46490 - 1.18232i) q^{84} +(-0.477496 + 6.03001i) q^{85} +(0.998098 - 6.30174i) q^{86} +(-22.9546 + 3.63566i) q^{87} +(0.372316 - 0.0589691i) q^{88} +(4.69015 + 0.742847i) q^{89} +(6.25978 + 15.1331i) q^{90} +(6.43296 + 5.52693i) q^{91} +(4.54848 + 2.31757i) q^{92} -17.5886i q^{93} +(5.20991 - 1.69280i) q^{94} +(-17.9355 - 1.42025i) q^{95} +(2.86287 - 1.45871i) q^{96} +(0.0172223 - 0.0530049i) q^{97} +(1.18677 - 0.862241i) q^{98} +(1.95217 + 1.95217i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 144 q + 36 q^{2} - 36 q^{4} + 36 q^{8} - 20 q^{9}+O(q^{10}) $ 144 * q + 36 * q^2 - 36 * q^4 + 36 * q^8 - 20 * q^9	$ 144 q + 36 q^{2} - 36 q^{4} + 36 q^{8} - 20 q^{9} + 6 q^{13} + 8 q^{15} - 36 q^{16} - 6 q^{17} - 20 q^{19} - 6 q^{21} + 12 q^{23} + 2 q^{25} + 14 q^{26} - 24 q^{27} + 20 q^{29} + 12 q^{30} - 6 q^{31} - 144 q^{32} - 54 q^{33} + 6 q^{34} + 40 q^{35} + 20 q^{36} - 60 q^{37} + 20 q^{39} + 52 q^{41} + 6 q^{42} - 12 q^{43} - 6 q^{45} + 28 q^{46} + 50 q^{47} - 160 q^{49} - 22 q^{50} + 6 q^{52} + 20 q^{53} - 6 q^{54} - 32 q^{55} - 28 q^{57} + 20 q^{58} - 16 q^{59} - 12 q^{60} + 12 q^{61} + 6 q^{62} - 70 q^{63} - 36 q^{64} + 44 q^{65} - 16 q^{66} - 8 q^{67} - 6 q^{68} + 26 q^{69} + 10 q^{70} + 72 q^{71} - 52 q^{73} + 32 q^{75} - 56 q^{77} - 50 q^{78} - 20 q^{79} + 124 q^{81} - 22 q^{82} + 70 q^{83} - 6 q^{84} - 18 q^{85} - 8 q^{86} + 8 q^{87} + 28 q^{89} - 14 q^{90} - 26 q^{91} + 12 q^{92} + 50 q^{94} - 46 q^{95} + 28 q^{97} - 20 q^{98} + 40 q^{99}+O(q^{100}) $ 144 * q + 36 * q^2 - 36 * q^4 + 36 * q^8 - 20 * q^9 + 6 * q^13 + 8 * q^15 - 36 * q^16 - 6 * q^17 - 20 * q^19 - 6 * q^21 + 12 * q^23 + 2 * q^25 + 14 * q^26 - 24 * q^27 + 20 * q^29 + 12 * q^30 - 6 * q^31 - 144 * q^32 - 54 * q^33 + 6 * q^34 + 40 * q^35 + 20 * q^36 - 60 * q^37 + 20 * q^39 + 52 * q^41 + 6 * q^42 - 12 * q^43 - 6 * q^45 + 28 * q^46 + 50 * q^47 - 160 * q^49 - 22 * q^50 + 6 * q^52 + 20 * q^53 - 6 * q^54 - 32 * q^55 - 28 * q^57 + 20 * q^58 - 16 * q^59 - 12 * q^60 + 12 * q^61 + 6 * q^62 - 70 * q^63 - 36 * q^64 + 44 * q^65 - 16 * q^66 - 8 * q^67 - 6 * q^68 + 26 * q^69 + 10 * q^70 + 72 * q^71 - 52 * q^73 + 32 * q^75 - 56 * q^77 - 50 * q^78 - 20 * q^79 + 124 * q^81 - 22 * q^82 + 70 * q^83 - 6 * q^84 - 18 * q^85 - 8 * q^86 + 8 * q^87 + 28 * q^89 - 14 * q^90 - 26 * q^91 + 12 * q^92 + 50 * q^94 - 46 * q^95 + 28 * q^97 - 20 * q^98 + 40 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/650\mathbb{Z}\right)^\times$.

$n$	$27$	$301$
$\chi(n)$	$e\left(\frac{11}{20}\right)$	$e\left(\frac{1}{4}\right)$

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 $

$2$	0.809017	−	0.587785i	0.572061	−	0.415627i
$2$	0.809017	−	0.587785i	0.572061	−	0.415627i
$3$	−2.86287	+	1.45871i	−1.65288	+	0.842185i	−0.656768	+	0.754093i	$0.728077\pi$
$3$	−2.86287	+	1.45871i	−1.65288	+	0.842185i	−0.996112	+	0.0880920i	$0.971923\pi$
$4$	0.309017	−	0.951057i	0.154508	−	0.475528i
$5$	−2.06627	+	0.854710i	−0.924064	+	0.382238i
$5$	−2.06627	+	0.854710i	−0.924064	+	0.382238i
$6$	−1.45871	+	2.86287i	−0.595514	+	1.16876i
$7$		−	2.35225i		−	0.889066i	−0.895762	−	0.444533i	$-0.853370\pi$
$7$		−	2.35225i		−	0.889066i	0.895762	−	0.444533i	$-0.146630\pi$
$8$	−0.309017	−	0.951057i	−0.109254	−	0.336249i
$9$	4.30486	−	5.92513i	1.43495	−	1.97504i
$10$	−1.16926	+	1.90600i	−0.369753	+	0.602730i
$11$	−0.0589691	+	0.372316i	−0.0177798	+	0.112258i	−0.994982	−	0.100053i	$-0.968099\pi$
$11$	−0.0589691	+	0.372316i	−0.0177798	+	0.112258i	0.977202	+	0.212310i	$0.0680988\pi$
$12$	0.502636	+	3.17352i	0.145099	+	0.916116i
$13$	−2.34964	+	2.73481i	−0.651672	+	0.758501i
$13$	−2.34964	+	2.73481i	−0.651672	+	0.758501i
$14$	−1.38262	−	1.90301i	−0.369520	−	0.508600i
$15$	4.66870	−	5.46101i	1.20545	−	1.41003i
$16$	−0.809017	−	0.587785i	−0.202254	−	0.146946i
$17$	1.22811	−	2.41030i	0.297860	−	0.584584i	−0.692769	−	0.721159i	$-0.743610\pi$
$17$	1.22811	−	2.41030i	0.297860	−	0.584584i	0.990630	+	0.136575i	$0.0436096\pi$
$18$		−	7.32387i		−	1.72625i
$19$	7.16915	+	3.65286i	1.64471	+	0.838024i	0.997104	+	0.0760529i	$0.0242318\pi$
$19$	7.16915	+	3.65286i	1.64471	+	0.838024i	0.647611	+	0.761971i	$0.275768\pi$
$20$	0.174366	+	2.22926i	0.0389893	+	0.498478i
$21$	3.43124	+	6.73419i	0.748758	+	1.46952i
$22$	0.171135	+	0.335871i	0.0364861	+	0.0716080i
$23$	−0.798580	+	5.04203i	−0.166515	+	1.05134i	0.752925	+	0.658107i	$0.228642\pi$
$23$	−0.798580	+	5.04203i	−0.166515	+	1.05134i	−0.919440	+	0.393230i	$0.871358\pi$
$24$	2.27199	+	2.27199i	0.463768	+	0.463768i
$25$	3.53894	−	3.53212i	0.707788	−	0.706425i
$26$	−0.293413	+	3.59359i	−0.0575431	+	0.704762i
$27$	−2.17333	+	13.7219i	−0.418258	+	2.64077i
$28$	−2.23712	−	0.726884i	−0.422776	−	0.137368i
$29$	6.87916	+	2.23517i	1.27743	+	0.415061i	0.867674	−	0.497134i	$-0.165614\pi$
$29$	6.87916	+	2.23517i	1.27743	+	0.415061i	0.409754	+	0.912196i	$0.365614\pi$
$30$	0.567154	−	7.16224i	0.103548	−	1.30764i
$31$	−2.48518	+	4.87743i	−0.446351	+	0.876013i	0.552739	+	0.833355i	$0.313583\pi$
$31$	−2.48518	+	4.87743i	−0.446351	+	0.876013i	−0.999090	+	0.0426585i	$0.986417\pi$
$32$	−1.00000			−0.176777
$33$	−0.374279	−	1.15191i	−0.0651536	−	0.200522i
$34$	−0.423178	−	2.67184i	−0.0725744	−	0.458217i
$35$	2.01049	+	4.86038i	0.339835	+	0.821554i
$36$	−4.30486	−	5.92513i	−0.717477	−	0.987522i
$37$	5.23039	−	7.19902i	0.859871	−	1.18351i	−0.121729	−	0.992563i	$-0.538844\pi$
$37$	5.23039	−	7.19902i	0.859871	−	1.18351i	0.981600	−	0.190948i	$-0.0611560\pi$
$38$	7.94706	−	1.25869i	1.28918	−	0.204187i
$39$	2.73742	−	11.2569i	0.438338	−	1.80254i
$40$	1.45139	+	1.70102i	0.229485	+	0.268955i
$41$	−0.0555382	−	0.350654i	−0.00867361	−	0.0547630i	0.982972	−	0.183756i	$-0.0588256\pi$
$41$	−0.0555382	−	0.350654i	−0.00867361	−	0.0547630i	−0.991646	+	0.128993i	$0.958826\pi$
$42$	6.73419	+	3.43124i	1.03911	+	0.529452i
$43$	4.51155	−	4.51155i	0.688005	−	0.688005i	−0.273786	−	0.961791i	$-0.588276\pi$
$43$	4.51155	−	4.51155i	0.688005	−	0.688005i	0.961791	+	0.273786i	$0.0882760\pi$
$44$	0.335871	+	0.171135i	0.0506345	+	0.0257996i
$45$	−3.83073	+	15.9223i	−0.571051	+	2.37356i
$46$	2.31757	+	4.54848i	0.341707	+	0.670637i
$47$	5.20991	+	1.69280i	0.759943	+	0.246921i	0.663254	−	0.748394i	$-0.269175\pi$
$47$	5.20991	+	1.69280i	0.759943	+	0.246921i	0.0966891	+	0.995315i	$0.469175\pi$
$48$	3.17352	+	0.502636i	0.458058	+	0.0725493i
$49$	1.46693			0.209562
$50$	0.786932	−	4.93769i	0.111289	−	0.698294i
$51$			8.69184i			1.21710i
$52$	1.87488	+	3.07974i	0.260000	+	0.427083i
$53$	−7.83802	+	3.99367i	−1.07663	+	0.548573i	−0.900083	−	0.435718i	$-0.856494\pi$
$53$	−7.83802	+	3.99367i	−1.07663	+	0.548573i	−0.176552	+	0.984291i	$0.556494\pi$
$54$	6.30725	+	12.3787i	0.858308	+	1.68452i
$55$	−0.196376	−	0.819707i	−0.0264794	−	0.110529i
$56$	−2.23712	+	0.726884i	−0.298948	+	0.0971340i
$57$	−25.8528			−3.42429
$58$	6.87916	−	2.23517i	0.903278	−	0.293493i
$59$	0.0162404	+	0.102538i	0.00211432	+	0.0133493i	0.988723	−	0.149756i	$-0.0478489\pi$
$59$	0.0162404	+	0.102538i	0.00211432	+	0.0133493i	−0.986609	+	0.163106i	$0.947849\pi$
$60$	−3.75102	−	6.12774i	−0.484255	−	0.791087i
$61$	6.85871	−	4.98314i	0.878168	−	0.638026i	−0.0545985	−	0.998508i	$-0.517388\pi$
$61$	6.85871	−	4.98314i	0.878168	−	0.638026i	0.932766	+	0.360482i	$0.117388\pi$
$62$	0.856334	+	5.40668i	0.108754	+	0.686649i
$63$	−13.9374	−	10.1261i	−1.75594	−	1.27577i
$64$	−0.809017	+	0.587785i	−0.101127	+	0.0734732i
$65$	2.51751	−	7.65912i	0.312259	−	0.949997i
$66$	−0.979875	−	0.711921i	−0.120614	−	0.0876314i
$67$	2.47933	+	7.63060i	0.302899	+	0.932226i	0.980453	+	0.196753i	$0.0630398\pi$
$67$	2.47933	+	7.63060i	0.302899	+	0.932226i	−0.677554	+	0.735473i	$0.736960\pi$
$68$	−1.91283	−	1.91283i	−0.231964	−	0.231964i
$69$	−5.06861	−	15.5996i	−0.610189	−	1.87797i
$70$	4.48338	+	2.75039i	0.535866	+	0.328735i
$71$	5.58704	−	2.84674i	0.663059	−	0.337846i	−0.0898638	−	0.995954i	$-0.528643\pi$
$71$	5.58704	−	2.84674i	0.663059	−	0.337846i	0.752923	+	0.658108i	$0.228643\pi$
$72$	−6.96541	−	2.26320i	−0.820881	−	0.266721i
$73$	5.92676	−	4.30604i	0.693675	−	0.503984i	−0.184191	−	0.982890i	$-0.558967\pi$
$73$	5.92676	−	4.30604i	0.693675	−	0.503984i	0.877866	+	0.478906i	$0.158967\pi$
$74$		−	8.89847i		−	1.03443i
$75$	−4.97920	+	15.2743i	−0.574949	+	1.76372i
$76$	5.68947	−	5.68947i	0.652627	−	0.652627i
$77$	0.875779	+	0.138710i	0.0998043	+	0.0158075i
$78$	−4.40199	−	10.7160i	−0.498427	−	1.21335i
$79$	−15.7552	−	5.11917i	−1.77260	−	0.575951i	−0.774219	−	0.632918i	$-0.781857\pi$
$79$	−15.7552	−	5.11917i	−1.77260	−	0.575951i	−0.998376	+	0.0569665i	$0.981857\pi$
$80$	2.17403	+	0.523047i	0.243064	+	0.0584785i
$81$	−7.00461	−	21.5580i	−0.778291	−	2.39533i
$82$	−0.251041	−	0.251041i	−0.0277228	−	0.0277228i
$83$	−3.72800	+	1.21130i	−0.409201	+	0.132957i	−0.506382	−	0.862309i	$-0.669017\pi$
$83$	−3.72800	+	1.21130i	−0.409201	+	0.132957i	0.0971811	+	0.995267i	$0.469017\pi$
$84$	7.46490	−	1.18232i	0.814488	−	0.129002i
$85$	−0.477496	+	6.03001i	−0.0517917	+	0.654047i
$86$	0.998098	−	6.30174i	0.107628	−	0.679534i
$87$	−22.9546	+	3.63566i	−2.46099	+	0.389783i
$88$	0.372316	−	0.0589691i	0.0396890	−	0.00628612i
$89$	4.69015	+	0.742847i	0.497155	+	0.0787416i	0.399977	−	0.916525i	$-0.369018\pi$
$89$	4.69015	+	0.742847i	0.497155	+	0.0787416i	0.0971783	+	0.995267i	$0.469018\pi$
$90$	6.25978	+	15.1331i	0.659839	+	1.59517i
$91$	6.43296	+	5.52693i	0.674357	+	0.579379i
$92$	4.54848	+	2.31757i	0.474212	+	0.241623i
$93$		−	17.5886i		−	1.82385i
$94$	5.20991	−	1.69280i	0.537361	−	0.174599i
$95$	−17.9355	−	1.42025i	−1.84015	−	0.145715i
$96$	2.86287	−	1.45871i	0.292191	−	0.148879i
$97$	0.0172223	−	0.0530049i	0.00174866	−	0.00538183i	−0.950178	−	0.311707i	$-0.899099\pi$
$97$	0.0172223	−	0.0530049i	0.00174866	−	0.00538183i	0.951927	+	0.306325i	$0.0990994\pi$
$98$	1.18677	−	0.862241i	0.119882	−	0.0870995i
$99$	1.95217	+	1.95217i	0.196200	+	0.196200i
$100$	−2.26566	−	4.45722i	−0.226566	−	0.445722i
$101$		−	11.8727i		−	1.18138i	−0.806898	−	0.590691i	$-0.798855\pi$
$101$		−	11.8727i		−	1.18138i	0.806898	−	0.590691i	$-0.201145\pi$
$102$	5.10893	+	7.03185i	0.505860	+	0.696256i
$103$	4.06902	+	7.98589i	0.400932	+	0.786874i	0.999903	−	0.0138969i	$-0.00442366\pi$
$103$	4.06902	+	7.98589i	0.400932	+	0.786874i	−0.598971	+	0.800770i	$0.704424\pi$
$104$	3.32704	+	1.38953i	0.326243	+	0.136255i
$105$	−12.8456	−	10.9819i	−1.25361	−	1.07173i
$106$	−3.99367	+	7.83802i	−0.387900	+	0.761296i
$107$	−7.37555	+	7.37555i	−0.713022	+	0.713022i	−0.967166	−	0.254145i	$-0.918206\pi$
$107$	−7.37555	+	7.37555i	−0.713022	+	0.713022i	0.254145	+	0.967166i	$0.418206\pi$
$108$	12.3787	+	6.30725i	1.19114	+	0.606916i
$109$	2.42557	−	0.384172i	0.232327	−	0.0367970i	−0.0391850	−	0.999232i	$-0.512476\pi$
$109$	2.42557	−	0.384172i	0.232327	−	0.0367970i	0.271512	+	0.962435i	$0.412476\pi$
$110$	−0.640683	−	0.547730i	−0.0610868	−	0.0522240i
$111$	−4.47269	+	28.2395i	−0.424529	+	2.68037i
$112$	−1.38262	+	1.90301i	−0.130645	+	0.179817i
$113$	−0.724544	−	4.57459i	−0.0681594	−	0.430342i	−0.998045	−	0.0624936i	$-0.980095\pi$
$113$	−0.724544	−	4.57459i	−0.0681594	−	0.430342i	0.929886	−	0.367848i	$-0.119905\pi$
$114$	−20.9154	+	15.1959i	−1.95890	+	1.42323i
$115$	−2.65940	−	11.1008i	−0.247990	−	1.03515i
$116$	4.25155	−	5.85176i	0.394747	−	0.543323i
$117$	6.08927	+	25.6949i	0.562953	+	2.37549i
$118$	0.0734090	+	0.0734090i	0.00675785	+	0.00675785i
$119$	−5.66963	−	2.88882i	−0.519734	−	0.264818i
$120$	−6.63643	−	2.75265i	−0.605821	−	0.251281i
$121$	10.3265	+	3.35528i	0.938771	+	0.305025i
$122$	2.61979	−	8.06289i	0.237185	−	0.729980i
$123$	0.670501	+	0.922865i	0.0604570	+	0.0832119i
$124$	3.87075	+	3.87075i	0.347604	+	0.347604i
$125$	−4.29346	+	10.3231i	−0.384019	+	0.923325i
$126$	−17.2275			−1.53475
$127$	3.47228	+	0.549955i	0.308115	+	0.0488006i	0.308577	−	0.951199i	$-0.400147\pi$
$127$	3.47228	+	0.549955i	0.308115	+	0.0488006i	−0.000462332		1.00000i	$0.500147\pi$
$128$	−0.309017	+	0.951057i	−0.0273135	+	0.0840623i
$129$	−6.33497	+	19.4970i	−0.557763	+	1.71662i
$130$	−2.46521	−	7.67611i	−0.216213	−	0.673240i
$131$	4.60756	+	14.1806i	0.402565	+	1.23897i	0.922912	+	0.385012i	$0.125803\pi$
$131$	4.60756	+	14.1806i	0.402565	+	1.23897i	−0.520347	+	0.853955i	$0.674197\pi$
$132$	−1.21119			−0.105421
$133$	8.59244	−	16.8636i	0.745059	−	1.46226i
$134$	6.49097	+	4.71597i	0.560735	+	0.407398i
$135$	−7.23754	−	30.2106i	−0.622908	−	2.60012i
$136$	−2.67184	−	0.423178i	−0.229108	−	0.0362872i
$137$	2.88278	−	3.96780i	0.246292	−	0.338992i	−0.667916	−	0.744237i	$-0.732813\pi$
$137$	2.88278	−	3.96780i	0.246292	−	0.338992i	0.914208	+	0.405244i	$0.132813\pi$
$138$	−13.2698	−	9.64108i	−1.12960	−	0.820703i
$139$	8.20166	+	11.2886i	0.695656	+	0.957488i	0.999988	+	0.00492223i	$0.00156680\pi$
$139$	8.20166	+	11.2886i	0.695656	+	0.957488i	−0.304332	+	0.952566i	$0.598433\pi$
$140$	5.24377	−	0.410151i	0.443179	−	0.0346641i
$141$	−17.3846	+	2.75345i	−1.46405	+	0.231882i
$142$	2.84674	−	5.58704i	0.238893	−	0.468854i
$143$	−0.879659	−	1.03608i	−0.0735608	−	0.0866411i
$144$	−6.96541	+	2.26320i	−0.580451	+	0.188600i
$145$	−16.1246	+	1.26122i	−1.33908	+	0.104738i
$146$	2.26382	−	6.96732i	0.187355	−	0.576620i
$147$	−4.19964	+	2.13982i	−0.346380	+	0.176490i
$148$	−5.23039	−	7.19902i	−0.429935	−	0.591755i
$149$	−5.17250	+	5.17250i	−0.423748	+	0.423748i	−0.886492	−	0.462744i	$-0.846865\pi$
$149$	−5.17250	+	5.17250i	−0.423748	+	0.423748i	0.462744	+	0.886492i	$0.346865\pi$
$150$	4.94975	+	15.2839i	0.404145	+	1.24792i
$151$	13.1240	−	13.1240i	1.06801	−	1.06801i	0.0705004	−	0.997512i	$-0.477540\pi$
$151$	13.1240	−	13.1240i	1.06801	−	1.06801i	0.997512	−	0.0705004i	$-0.0224596\pi$
$152$	1.25869	−	7.94706i	0.102093	−	0.644592i
$153$	−8.99451	−	17.6527i	−0.727163	−	1.42714i
$154$	0.790052	−	0.402552i	0.0636642	−	0.0324385i
$155$	0.966251	−	12.2022i	0.0776112	−	0.980104i
$156$	−9.85999	−	6.08200i	−0.789431	−	0.486950i
$157$	15.5108	−	15.5108i	1.23790	−	1.23790i	0.277036	−	0.960860i	$-0.410648\pi$
$157$	15.5108	−	15.5108i	1.23790	−	1.23790i	0.960860	−	0.277036i	$-0.0893521\pi$
$158$	−15.7552	+	5.11917i	−1.25341	+	0.407259i
$159$	16.6137	−	22.8667i	1.31755	−	1.81345i
$160$	2.06627	−	0.854710i	0.163353	−	0.0675708i
$161$	11.8601	+	1.87846i	0.934707	+	0.148043i
$162$	−18.3383	−	13.3236i	−1.44079	−	1.04680i
$163$	4.39760	+	3.19504i	0.344447	+	0.250255i	0.746536	−	0.665345i	$-0.231716\pi$
$163$	4.39760	+	3.19504i	0.344447	+	0.250255i	−0.402089	+	0.915601i	$0.631716\pi$
$164$	−0.350654	−	0.0555382i	−0.0273815	−	0.00433680i
$165$	1.75791	+	2.06026i	0.136853	+	0.160391i
$166$	−2.30403	+	3.17122i	−0.178827	+	0.246135i
$167$	−16.9392	+	5.50389i	−1.31080	+	0.425904i	−0.879325	−	0.476223i	$-0.842006\pi$
$167$	−16.9392	+	5.50389i	−1.31080	+	0.425904i	−0.431472	+	0.902126i	$0.642006\pi$
$168$	5.34428	−	5.34428i	0.412320	−	0.412320i
$169$	−1.95841	−	12.8516i	−0.150647	−	0.988588i
$170$	3.15805	+	5.15905i	0.242211	+	0.395681i
$171$	52.5059	−	26.7531i	4.01522	−	2.04586i
$172$	−2.89659	−	5.68488i	−0.220863	−	0.433468i
$173$	−3.60027	+	22.7312i	−0.273724	+	1.72822i	0.341510	+	0.939878i	$0.389062\pi$
$173$	−3.60027	+	22.7312i	−0.273724	+	1.72822i	−0.615233	+	0.788345i	$0.710938\pi$
$174$	−16.4337	+	16.4337i	−1.24584	+	1.24584i
$175$	−8.30843	−	8.32446i	−0.628058	−	0.629270i
$176$	0.266549	−	0.266549i	0.0200919	−	0.0200919i
$177$	−0.196067	−	0.269863i	−0.0147373	−	0.0202841i
$178$	4.23105	−	2.15583i	0.317130	−	0.161586i
$179$	−0.853317	+	2.62624i	−0.0637799	+	0.196294i	−0.977869	−	0.209220i	$-0.932908\pi$
$179$	−0.853317	+	2.62624i	−0.0637799	+	0.196294i	0.914089	+	0.405514i	$0.132908\pi$
$180$	13.9593	+	8.56351i	1.04046	+	0.638286i
$181$	−19.6273	+	6.37728i	−1.45888	+	0.474020i	−0.927729	−	0.373255i	$-0.878242\pi$
$181$	−19.6273	+	6.37728i	−1.45888	+	0.474020i	−0.531154	+	0.847275i	$0.678242\pi$
$182$	8.45302	+	0.690181i	0.626579	+	0.0511596i
$183$	−12.3667	+	24.2709i	−0.914170	+	1.79416i
$184$	5.04203	−	0.798580i	0.371704	−	0.0588721i
$185$	−4.65432	+	19.3456i	−0.342193	+	1.42232i
$186$	−10.3383	−	14.2295i	−0.758043	−	1.04336i
$187$	0.824973	+	0.599378i	0.0603280	+	0.0438309i
$188$	3.21990	−	4.43181i	0.234835	−	0.323223i
$189$	32.2772	+	5.11221i	2.34782	+	0.371859i
$190$	−15.3450	+	9.39323i	−1.11324	+	0.681456i
$191$	13.3388	+	9.69122i	0.965163	+	0.701232i	0.954344	−	0.298709i	$-0.0965561\pi$
$191$	13.3388	+	9.69122i	0.965163	+	0.701232i	0.0108192	+	0.999941i	$0.496556\pi$
$192$	1.45871	−	2.86287i	0.105273	−	0.206610i
$193$	−2.43896			−0.175560			−0.0877800	−	0.996140i	$-0.527977\pi$
$193$	−2.43896			−0.175560			−0.0877800	+	0.996140i	$0.527977\pi$
$194$	−0.0172223	−	0.0530049i	−0.00123649	−	0.00380553i
$195$	3.96510	+	25.5994i	0.283947	+	1.83321i
$196$	0.453307	−	1.39514i	0.0323791	−	0.0996525i
$197$	1.89938	−	5.84570i	0.135326	−	0.416489i	−0.860315	−	0.509763i	$-0.829733\pi$
$197$	1.89938	−	5.84570i	0.135326	−	0.416489i	0.995641	+	0.0932737i	$0.0297332\pi$
$198$	2.72679	+	0.431881i	0.193785	+	0.0306925i
$199$	−4.12099			−0.292129			−0.146065	−	0.989275i	$-0.546661\pi$
$199$	−4.12099			−0.292129			−0.146065	+	0.989275i	$0.546661\pi$
$200$	−4.45284	−	2.27425i	−0.314864	−	0.160813i
$201$	−18.2288	−	18.2288i	−1.28576	−	1.28576i
$202$	−6.97862	−	9.60525i	−0.491014	−	0.675823i
$203$	5.25768	−	16.1815i	0.369017	−	1.13572i
$204$	8.26643	+	2.68593i	0.578766	+	0.188052i
$205$	0.414465	+	0.677077i	0.0289475	+	0.0472891i
$206$	7.98589	+	4.06902i	0.556404	+	0.283502i
$207$	26.4369	+	26.4369i	1.83749	+	1.83749i
$208$	3.50838	−	0.831429i	0.243262	−	0.0576492i
$209$	−1.78278	+	2.45378i	−0.123317	+	0.169732i
$210$	−16.8474	−	1.33409i	−1.16258	−	0.0920606i
$211$	−1.10715	+	0.804395i	−0.0762197	+	0.0553768i	−0.625243	−	0.780430i	$-0.715000\pi$
$211$	−1.10715	+	0.804395i	−0.0762197	+	0.0553768i	0.549023	+	0.835807i	$0.315000\pi$
$212$	1.37613	+	8.68851i	0.0945127	+	0.596729i
$213$	−11.8424	+	16.2997i	−0.811429	+	1.11684i
$214$	−1.63171	+	10.3022i	−0.111541	+	0.704243i
$215$	−5.46601	+	13.1781i	−0.372779	+	0.898742i
$216$	13.7219	−	2.17333i	0.933655	−	0.147876i
$217$	11.4729	+	5.84575i	0.778833	+	0.396835i
$218$	1.73652	−	1.73652i	0.117612	−	0.117612i
$219$	−10.6863	+	20.9730i	−0.722113	+	1.41723i
$220$	−0.840271	−	0.0665382i	−0.0566511	−	0.00448601i
$221$	3.70611	+	9.02199i	0.249300	+	0.606884i
$222$	12.9803	+	25.4752i	0.871178	+	1.70978i
$223$	2.34973	+	3.23413i	0.157350	+	0.216573i	0.880412	−	0.474209i	$-0.157266\pi$
$223$	2.34973	+	3.23413i	0.157350	+	0.216573i	−0.723062	+	0.690783i	$0.757266\pi$
$224$			2.35225i			0.157166i
$225$	−5.69366	−	36.1740i	−0.379577	−	2.41160i
$226$	−3.27505	−	3.27505i	−0.217853	−	0.217853i
$227$	9.61019	−	6.98222i	0.637851	−	0.463426i	−0.221260	−	0.975215i	$-0.571017\pi$
$227$	9.61019	−	6.98222i	0.637851	−	0.463426i	0.859111	+	0.511789i	$0.171017\pi$
$228$	−7.98896	+	24.5875i	−0.529082	+	1.62835i
$229$	7.14364	−	3.63986i	0.472065	−	0.240529i	−0.201739	−	0.979439i	$-0.564659\pi$
$229$	7.14364	−	3.63986i	0.472065	−	0.240529i	0.673804	+	0.738910i	$0.264659\pi$
$230$	−8.67636	−	7.41754i	−0.572102	−	0.489098i
$231$	−2.70958	+	0.880397i	−0.178277	+	0.0579258i
$232$		−	7.23318i		−	0.474881i
$233$	23.2995	+	11.8717i	1.52640	+	0.777739i	0.997481	−	0.0709336i	$-0.0225979\pi$
$233$	23.2995	+	11.8717i	1.52640	+	0.777739i	0.528918	+	0.848673i	$0.322598\pi$
$234$	20.0294	+	17.2084i	1.30936	+	1.12495i
$235$	−12.2119	+	0.955179i	−0.796619	+	0.0623090i
$236$	0.102538	+	0.0162404i	0.00667465	+	0.00105716i
$237$	52.5724	−	8.32665i	3.41495	−	0.540874i
$238$	−6.28483	+	0.995419i	−0.407385	+	0.0645234i
$239$	2.29581	−	14.4952i	0.148504	−	0.937614i	−0.795086	−	0.606497i	$-0.792574\pi$
$239$	2.29581	−	14.4952i	0.148504	−	0.937614i	0.943589	−	0.331118i	$-0.107426\pi$
$240$	−6.98695	+	1.67386i	−0.451006	+	0.108047i
$241$	−26.8374	+	4.25062i	−1.72875	+	0.273807i	−0.940065	−	0.340995i	$-0.889236\pi$
$241$	−26.8374	+	4.25062i	−1.72875	+	0.273807i	−0.788682	+	0.614802i	$0.789236\pi$
$242$	10.3265	−	3.35528i	0.663811	−	0.215685i
$243$	22.0288	+	22.0288i	1.41315	+	1.41315i
$244$	−2.61979	−	8.06289i	−0.167715	−	0.516174i
$245$	−3.03108	+	1.25380i	−0.193648	+	0.0801025i
$246$	1.08489	+	0.352503i	0.0691702	+	0.0224748i
$247$	−26.8348	+	11.0234i	−1.70746	+	0.701401i
$248$	5.40668	+	0.856334i	0.343324	+	0.0543772i
$249$	8.90585	−	8.90585i	0.564385	−	0.564385i
$250$	2.59428	+	10.8752i	0.164077	+	0.687807i
$251$		−	5.17509i		−	0.326649i	−0.986572	−	0.163325i	$-0.947778\pi$
$251$		−	5.17509i		−	0.326649i	0.986572	−	0.163325i	$-0.0522218\pi$
$252$	−13.9374	+	10.1261i	−0.877972	+	0.637884i
$253$	−1.83014	−	0.594648i	−0.115060	−	0.0373852i
$254$	3.13239	−	1.59603i	0.196544	−	0.100144i
$255$	−7.42901	−	17.9597i	−0.465222	−	1.12468i
$256$	0.309017	+	0.951057i	0.0193136	+	0.0594410i
$257$	−6.95348	−	6.95348i	−0.433746	−	0.433746i	0.456154	−	0.889901i	$-0.349227\pi$
$257$	−6.95348	−	6.95348i	−0.433746	−	0.433746i	−0.889901	+	0.456154i	$0.849227\pi$
$258$	6.33497	+	19.4970i	0.394398	+	1.21383i
$259$	−16.9339	−	12.3032i	−1.05222	−	0.764482i
$260$	−6.50630	−	4.76109i	−0.403504	−	0.295270i
$261$	42.8575	−	31.1378i	2.65281	−	1.92738i
$262$	12.0628	+	8.76410i	0.745239	+	0.541448i
$263$	1.33877	+	8.45266i	0.0825521	+	0.521213i	0.993963	+	0.109716i	$0.0349941\pi$
$263$	1.33877	+	8.45266i	0.0825521	+	0.521213i	−0.911411	+	0.411498i	$0.865006\pi$
$264$	−0.979875	+	0.711921i	−0.0603071	+	0.0438157i
$265$	12.7820	−	14.9512i	0.785194	−	0.918447i
$266$	−2.96075	−	18.6934i	−0.181535	−	1.14617i
$267$	−14.5109	+	4.71488i	−0.888052	+	0.288546i
$268$	8.02328			0.490100
$269$	−22.1120	+	7.18464i	−1.34820	+	0.438055i	−0.892085	−	0.451868i	$-0.850758\pi$
$269$	−22.1120	+	7.18464i	−1.34820	+	0.438055i	−0.456110	+	0.889923i	$0.650758\pi$
$270$	−23.6127	−	20.1868i	−1.43702	−	1.22853i
$271$	−13.0917	−	25.6939i	−0.795263	−	1.56079i	−0.827603	−	0.561314i	$-0.810296\pi$
$271$	−13.0917	−	25.6939i	−0.795263	−	1.56079i	0.0323400	−	0.999477i	$-0.489704\pi$
$272$	−2.41030	+	1.22811i	−0.146146	+	0.0744651i
$273$	−26.4789	−	6.43909i	−1.60258	−	0.389712i
$274$		−	4.90448i		−	0.296290i
$275$	1.10638	+	1.52589i	0.0667171	+	0.0920146i
$276$	−16.4024			−0.987307
$277$	2.80618	+	0.444455i	0.168607	+	0.0267047i	0.240167	−	0.970732i	$-0.422798\pi$
$277$	2.80618	+	0.444455i	0.168607	+	0.0267047i	−0.0715601	+	0.997436i	$0.522798\pi$
$278$	13.2706	+	4.31187i	0.795916	+	0.258609i
$279$	18.2011	+	35.7217i	1.08967	+	2.13860i
$280$	4.00122	−	3.41403i	0.239119	−	0.204027i
$281$	12.0950	+	6.16272i	0.721528	+	0.367637i	0.775876	−	0.630885i	$-0.217308\pi$
$281$	12.0950	+	6.16272i	0.721528	+	0.367637i	−0.0543481	+	0.998522i	$0.517308\pi$
$282$	−12.4460	+	12.4460i	−0.741149	+	0.741149i
$283$	2.75011	+	1.40125i	0.163477	+	0.0832958i	0.533815	−	0.845601i	$-0.320758\pi$
$283$	2.75011	+	1.40125i	0.163477	+	0.0832958i	−0.370338	+	0.928897i	$0.620758\pi$
$284$	−0.980919	−	6.19328i	−0.0582068	−	0.367503i
$285$	53.4189	−	22.0967i	3.16426	−	1.30889i
$286$	−1.32065	−	0.321153i	−0.0780917	−	0.0189902i
$287$	−0.824826	+	0.130640i	−0.0486879	+	0.00771141i
$288$	−4.30486	+	5.92513i	−0.253666	+	0.349142i
$289$	5.69105	+	7.83306i	0.334768	+	0.460768i
$290$	−12.3038	+	10.4982i	−0.722502	+	0.616473i
$291$	0.0280132	+	0.176869i	0.00164217	+	0.0103682i
$292$	−2.26382	−	6.96732i	−0.132480	−	0.407732i
$293$	−3.11230			−0.181822			−0.0909111	−	0.995859i	$-0.528978\pi$
$293$	−3.11230			−0.181822			−0.0909111	+	0.995859i	$0.528978\pi$
$294$	−2.13982	+	4.19964i	−0.124797	+	0.244928i
$295$	−0.121197	−	0.197990i	−0.00705638	−	0.0115274i
$296$	−8.46295	−	2.74978i	−0.491899	−	0.159828i
$297$	−4.98071	−	1.61833i	−0.289010	−	0.0939051i
$298$	−1.14432	+	7.22496i	−0.0662888	+	0.418531i
$299$	−11.9126	−	14.0309i	−0.688926	−	0.811429i
$300$	12.9881	+	9.45552i	0.749866	+	0.545915i
$301$	−10.6123	−	10.6123i	−0.611682	−	0.611682i
$302$	2.90343	−	18.3316i	0.167074	−	1.05486i
$303$	17.3188	+	33.9901i	0.994942	+	1.95268i
$304$	−3.65286	−	7.16915i	−0.209506	−	0.411179i
$305$	−9.91279	+	16.1587i	−0.567605	+	0.925246i
$306$	−17.6527	−	8.99451i	−1.00914	−	0.514182i
$307$		−	15.4033i		−	0.879111i	−0.898215	−	0.439556i	$-0.855136\pi$
$307$		−	15.4033i		−	0.879111i	0.898215	−	0.439556i	$-0.144864\pi$
$308$	0.402552	−	0.790052i	0.0229375	−	0.0450174i
$309$	−23.2982	−	16.9271i	−1.32539	−	0.962949i
$310$	−6.39056	−	10.4397i	−0.362959	−	0.592937i
$311$	5.10437	+	7.02556i	0.289442	+	0.398383i	0.928833	−	0.370499i	$-0.120813\pi$
$311$	5.10437	+	7.02556i	0.289442	+	0.398383i	−0.639391	+	0.768882i	$0.720813\pi$
$312$	−11.5518	+	0.875116i	−0.653993	+	0.0495437i
$313$	0.815258	+	5.14734i	0.0460811	+	0.290945i	0.999957	−	0.00925605i	$-0.00294633\pi$
$313$	0.815258	+	5.14734i	0.0460811	+	0.290945i	−0.953876	+	0.300201i	$0.902946\pi$
$314$	3.43148	−	21.6655i	0.193650	−	1.22265i
$315$	37.4533	+	9.01082i	2.11025	+	0.507702i
$316$	−9.73723	+	13.4021i	−0.547762	+	0.753930i
$317$	3.72653	+	11.4691i	0.209303	+	0.644168i	0.999509	+	0.0313269i	$0.00997330\pi$
$317$	3.72653	+	11.4691i	0.209303	+	0.644168i	−0.790206	+	0.612841i	$0.790027\pi$
$318$		−	28.2648i		−	1.58501i
$319$	−1.23785	+	2.42942i	−0.0693062	+	0.136021i
$320$	1.16926	−	1.90600i	0.0653637	−	0.106549i
$321$	10.3565	−	31.8740i	0.578044	−	1.77904i
$322$	10.6992	−	5.45149i	0.596241	−	0.303800i
$323$	17.6090	−	12.7937i	0.979791	−	0.711860i
$324$	−22.6674			−1.25930
$325$	1.34448	+	17.9776i	0.0745782	+	0.997215i
$326$	5.43573			0.301057
$327$	−6.38370	+	4.63803i	−0.353020	+	0.256484i
$328$	−0.316330	+	0.161178i	−0.0174664	+	0.00889957i
$329$	3.98189	−	12.2550i	0.219529	−	0.675640i
$330$	2.63317	+	0.633511i	0.144951	+	0.0348736i
$331$	7.11625	−	13.9664i	0.391144	−	0.767664i	−0.608521	−	0.793538i	$-0.708237\pi$
$331$	7.11625	−	13.9664i	0.391144	−	0.767664i	0.999665	+	0.0258740i	$0.00823688\pi$
$332$			3.91985i			0.215130i
$333$	−20.1390	−	61.9815i	−1.10361	−	3.39657i
$334$	−10.4690	+	14.4094i	−0.572839	+	0.788445i
$335$	−11.6449	−	13.6478i	−0.636230	−	0.745657i
$336$	1.18232	−	7.46490i	0.0645011	−	0.407244i
$337$	−0.695981	−	4.39425i	−0.0379125	−	0.239370i	0.961454	−	0.274967i	$-0.0886668\pi$
$337$	−0.695981	−	4.39425i	−0.0379125	−	0.239370i	−0.999366	+	0.0355967i	$0.988667\pi$
$338$	−9.13839	−	9.24607i	−0.497063	−	0.502920i
$339$	8.74727	+	12.0396i	0.475086	+	0.653900i
$340$	5.58733	+	2.31750i	0.303015	+	0.125684i
$341$	−1.66940	−	1.21289i	−0.0904030	−	0.0656816i
$342$	26.7531	−	52.5059i	1.44664	−	2.83919i
$343$		−	19.9163i		−	1.07538i
$344$	−5.68488	−	2.89659i	−0.306508	−	0.156174i
$345$	23.8063	+	27.9008i	1.28169	+	1.50213i
$346$	10.4484	+	20.5061i	0.561709	+	1.10242i
$347$	2.41884	+	4.74724i	0.129850	+	0.254845i	0.946773	−	0.321902i	$-0.104322\pi$
$347$	2.41884	+	4.74724i	0.129850	+	0.254845i	−0.816923	+	0.576747i	$0.804322\pi$
$348$	−3.63566	+	22.9546i	−0.194892	+	1.23050i
$349$	−0.170859	−	0.170859i	−0.00914586	−	0.00914586i	0.702519	−	0.711665i	$-0.252059\pi$
$349$	−0.170859	−	0.170859i	−0.00914586	−	0.00914586i	−0.711665	+	0.702519i	$0.752059\pi$
$350$	−11.6147	−	1.85106i	−0.620830	−	0.0989432i
$351$	−32.4202	−	38.1851i	−1.73046	−	2.03817i
$352$	0.0589691	−	0.372316i	0.00314306	−	0.0198445i
$353$	−11.0830	−	3.60109i	−0.589890	−	0.191667i	−0.00116351	−	0.999999i	$-0.500370\pi$
$353$	−11.0830	−	3.60109i	−0.589890	−	0.191667i	−0.588726	+	0.808333i	$0.700370\pi$
$354$	−0.317243	−	0.103078i	−0.0168613	−	0.00547856i
$355$	−9.11119	+	10.6574i	−0.483572	+	0.565638i
$356$	2.15583	−	4.23105i	0.114259	−	0.224245i
$357$	20.4454			1.08208
$358$	0.853317	+	2.62624i	0.0450992	+	0.138801i
$359$	4.67684	+	29.5284i	0.246834	+	1.55845i	0.730324	+	0.683100i	$0.239369\pi$
$359$	4.67684	+	29.5284i	0.246834	+	1.55845i	−0.483490	+	0.875350i	$0.660631\pi$
$360$	16.3268	−	1.27703i	0.860498	−	0.0673054i
$361$	26.8853	+	37.0045i	1.41502	+	1.94760i
$362$	−12.1303	+	16.6959i	−0.637555	+	0.877519i
$363$	−34.4578	+	5.45757i	−1.80856	+	0.286448i
$364$	7.24431	−	4.41019i	0.379705	−	0.231157i
$365$	−8.56586	+	13.9631i	−0.448358	+	0.730862i
$366$	4.26126	+	26.9046i	0.222740	+	1.40632i
$367$	19.4489	+	9.90970i	1.01522	+	0.517282i	0.880723	−	0.473631i	$-0.157057\pi$
$367$	19.4489	+	9.90970i	1.01522	+	0.517282i	0.134501	+	0.990914i	$0.457057\pi$
$368$	3.60970	−	3.60970i	0.188168	−	0.188168i
$369$	−2.31676	−	1.18045i	−0.120606	−	0.0614516i
$370$	7.60562	+	18.3866i	0.395397	+	0.955876i
$371$	9.39410	+	18.4370i	0.487717	+	0.957199i
$372$	−16.7278	−	5.43518i	−0.867294	−	0.281801i
$373$	−8.05018	−	1.27502i	−0.416823	−	0.0660182i	−0.0554991	−	0.998459i	$-0.517675\pi$
$373$	−8.05018	−	1.27502i	−0.416823	−	0.0660182i	−0.361323	+	0.932441i	$0.617675\pi$
$374$	1.01972			0.0527286
$375$	−2.76673	−	35.8166i	−0.142873	−	1.84956i
$376$		−	5.47802i		−	0.282507i
$377$	−22.2763	+	13.5614i	−1.14729	+	0.698446i
$378$	29.1177	−	14.8362i	1.49765	−	0.763093i
$379$	−11.7770	−	23.1137i	−0.604945	−	1.18727i	−0.966919	−	0.255083i	$-0.917897\pi$
$379$	−11.7770	−	23.1137i	−0.604945	−	1.18727i	0.361975	−	0.932188i	$-0.382103\pi$
$380$	−6.89312	+	16.6188i	−0.353610	+	0.852527i
$381$	−10.7429	+	3.49058i	−0.550376	+	0.178828i
$382$	16.4877			0.843584
$383$	8.39059	−	2.72627i	0.428739	−	0.139306i	−0.0866951	−	0.996235i	$-0.527631\pi$
$383$	8.39059	−	2.72627i	0.428739	−	0.139306i	0.515434	+	0.856929i	$0.327631\pi$
$384$	−0.502636	−	3.17352i	−0.0256500	−	0.161948i
$385$	−1.92815	+	0.461926i	−0.0982678	+	0.0235419i
$386$	−1.97316	+	1.43358i	−0.100431	+	0.0729675i
$387$	−7.30993	−	46.1531i	−0.371585	−	2.34609i
$388$	−0.0450887	−	0.0327588i	−0.00228903	−	0.00166308i
$389$	−26.3615	+	19.1528i	−1.33658	+	0.971084i	−0.337020	+	0.941497i	$0.609419\pi$
$389$	−26.3615	+	19.1528i	−1.33658	+	0.971084i	−0.999562	+	0.0295864i	$0.990581\pi$
$390$	18.2548	+	18.3797i	0.924367	+	0.930693i
$391$	11.1721	+	8.11699i	0.564996	+	0.410494i
$392$	−0.453307	−	1.39514i	−0.0228955	−	0.0704650i
$393$	−33.8762	−	33.8762i	−1.70883	−	1.70883i
$394$	−1.89938	−	5.84570i	−0.0956896	−	0.294502i
$395$	36.9298	−	2.88853i	1.85814	−	0.145338i
$396$	2.45987	−	1.25337i	0.123613	−	0.0629842i
$397$	13.0585	+	4.24295i	0.655385	+	0.212948i	0.617787	−	0.786345i	$-0.288029\pi$
$397$	13.0585	+	4.24295i	0.655385	+	0.212948i	0.0375980	+	0.999293i	$0.488029\pi$
$398$	−3.33395	+	2.42226i	−0.167116	+	0.121417i
$399$			60.8122i			3.04442i
$400$	−4.93919	+	0.777412i	−0.246960	+	0.0388706i
$401$	15.6108	−	15.6108i	0.779567	−	0.779567i	−0.200190	−	0.979757i	$-0.564156\pi$
$401$	15.6108	−	15.6108i	0.779567	−	0.779567i	0.979757	+	0.200190i	$0.0641560\pi$
$402$	−25.4620	−	4.03279i	−1.26993	−	0.201137i
$403$	−7.49961	−	18.2567i	−0.373582	−	0.909431i
$404$	−11.2916	−	3.66888i	−0.561780	−	0.182534i
$405$	32.8993	+	38.5577i	1.63478	+	1.91595i
$406$	−5.25768	−	16.1815i	−0.260934	−	0.803074i
$407$	2.37188	+	2.37188i	0.117570	+	0.117570i
$408$	8.26643	−	2.68593i	0.409249	−	0.132973i
$409$	23.8158	−	3.77205i	1.17762	−	0.186516i	0.463210	−	0.886248i	$-0.346697\pi$
$409$	23.8158	−	3.77205i	1.17762	−	0.186516i	0.714405	+	0.699732i	$0.246697\pi$
$410$	0.733285	+	0.304151i	0.0362144	+	0.0150209i
$411$	−2.46517	+	15.5644i	−0.121598	+	0.767738i
$412$	8.85243	−	1.40209i	0.436128	−	0.0690759i
$413$	0.241195	−	0.0382015i	0.0118684	−	0.00187977i
$414$	36.9272	+	5.84869i	1.81487	+	0.287447i
$415$	6.66774	−	5.68923i	0.327306	−	0.279273i
$416$	2.34964	−	2.73481i	0.115200	−	0.134085i
$417$	−39.9471	−	20.3541i	−1.95622	−	0.996743i
$418$			3.03304i			0.148351i
$419$	−19.5673	+	6.35779i	−0.955924	+	0.310599i	−0.745120	−	0.666930i	$-0.767608\pi$
$419$	−19.5673	+	6.35779i	−0.955924	+	0.310599i	−0.210804	+	0.977528i	$0.567608\pi$
$420$	−14.4140	+	8.82333i	−0.703329	+	0.430534i
$421$	−31.7098	+	16.1570i	−1.54544	+	0.787442i	−0.998754	−	0.0498946i	$-0.984111\pi$
$421$	−31.7098	+	16.1570i	−1.54544	+	0.787442i	−0.546688	+	0.837337i	$0.684111\pi$
$422$	−0.422895	+	1.30154i	−0.0205862	+	0.0633579i
$423$	32.4580	−	23.5821i	1.57816	−	1.14660i
$424$	6.22029	+	6.22029i	0.302084	+	0.302084i
$425$	−4.16728	−	12.8678i	−0.202143	−	0.624178i
$426$			20.1475i			0.976151i
$427$	−11.7216	−	16.1334i	−0.567247	−	0.780749i
$428$	4.73540	+	9.29374i	0.228894	+	0.449230i
$429$	4.02968	+	1.68299i	0.194555	+	0.0812556i
$430$	3.32383	+	13.8742i	0.160289	+	0.669073i
$431$	1.47766	−	2.90008i	0.0711766	−	0.139692i	−0.852676	−	0.522439i	$-0.825022\pi$
$431$	1.47766	−	2.90008i	0.0711766	−	0.139692i	0.923853	+	0.382748i	$0.125022\pi$
$432$	9.82377	−	9.82377i	0.472647	−	0.472647i
$433$	−1.83165	−	0.933271i	−0.0880233	−	0.0448501i	0.409425	−	0.912344i	$-0.365729\pi$
$433$	−1.83165	−	0.933271i	−0.0880233	−	0.0448501i	−0.497448	+	0.867494i	$0.665729\pi$
$434$	12.7178	−	2.01431i	0.610476	−	0.0966899i
$435$	44.3230	−	27.1318i	2.12513	−	1.30087i
$436$	0.384172	−	2.42557i	0.0183985	−	0.116164i
$437$	−24.1430	+	33.2300i	−1.15492	+	1.58960i
$438$	3.68225	+	23.2488i	0.175945	+	1.11087i
$439$	−0.240961	+	0.175069i	−0.0115005	+	0.00835557i	−0.593521	−	0.804819i	$-0.702262\pi$
$439$	−0.240961	+	0.175069i	−0.0115005	+	0.00835557i	0.582020	+	0.813174i	$0.302262\pi$
$440$	−0.718904	+	0.440068i	−0.0342724	+	0.0209794i
$441$	6.31494	−	8.69176i	0.300711	−	0.413894i
$442$	8.30130	+	5.12054i	0.394852	+	0.243559i
$443$	−1.01108	−	1.01108i	−0.0480377	−	0.0480377i	0.682680	−	0.730718i	$-0.260814\pi$
$443$	−1.01108	−	1.01108i	−0.0480377	−	0.0480377i	−0.730718	+	0.682680i	$0.760814\pi$
$444$	25.4752	+	12.9803i	1.20900	+	0.616016i
$445$	−10.3260	+	2.47380i	−0.489501	+	0.117269i
$446$	3.80195	+	1.23533i	0.180028	+	0.0584945i
$447$	7.26305	−	22.3534i	0.343531	−	1.05728i
$448$	1.38262	+	1.90301i	0.0653225	+	0.0899087i
$449$	−13.6543	−	13.6543i	−0.644384	−	0.644384i	0.307246	−	0.951630i	$-0.400593\pi$
$449$	−13.6543	−	13.6543i	−0.644384	−	0.644384i	−0.951630	+	0.307246i	$0.900593\pi$
$450$	−25.8688	−	25.9187i	−1.21947	−	1.22182i
$451$	0.133829			0.00630177
$452$	−4.57459	−	0.724544i	−0.215171	−	0.0340797i
$453$	−18.4282	+	56.7162i	−0.865833	+	2.66476i
$454$	3.67077	−	11.2975i	0.172278	−	0.530216i
$455$	−18.0161	−	5.92181i	−0.844610	−	0.277619i
$456$	7.98896	+	24.5875i	0.374117	+	1.15141i
$457$	23.5459			1.10143			0.550715	−	0.834693i	$-0.314355\pi$
$457$	23.5459			1.10143			0.550715	+	0.834693i	$0.314355\pi$
$458$	3.63986	−	7.14364i	0.170080	−	0.333800i
$459$	30.4048	+	22.0903i	1.41917	+	1.03109i
$460$	−11.3792	−	0.901084i	−0.530560	−	0.0420133i
$461$	−9.85545	−	1.56095i	−0.459014	−	0.0727007i	−0.0773546	−	0.997004i	$-0.524647\pi$
$461$	−9.85545	−	1.56095i	−0.459014	−	0.0727007i	−0.381660	+	0.924303i	$0.624647\pi$
$462$	−1.67461	+	2.30491i	−0.0779101	+	0.107234i
$463$	7.21217	+	5.23995i	0.335178	+	0.243521i	0.742625	−	0.669708i	$-0.233581\pi$
$463$	7.21217	+	5.23995i	0.335178	+	0.243521i	−0.407447	+	0.913229i	$0.633581\pi$
$464$	−4.25155	−	5.85176i	−0.197373	−	0.271661i
$465$	15.0332	+	36.3428i	0.697147	+	1.68536i
$466$	25.8277	−	4.09070i	1.19644	−	0.189498i
$467$	14.1719	−	27.8139i	0.655797	−	1.28707i	−0.288343	−	0.957527i	$-0.593104\pi$
$467$	14.1719	−	27.8139i	0.655797	−	1.28707i	0.944139	−	0.329546i	$-0.106896\pi$
$468$	26.3190	+	2.14892i	1.21660	+	0.0993339i
$469$	17.9491	−	5.83200i	0.828810	−	0.269297i
$470$	−9.31822	+	7.95075i	−0.429818	+	0.366741i
$471$	−21.7797	+	67.0311i	−1.00356	+	3.08863i
$472$	0.0925008	−	0.0471315i	0.00425769	−	0.00216940i
$473$	1.41368	+	1.94576i	0.0650011	+	0.0894663i
$474$	37.6377	−	37.6377i	1.72876	−	1.72876i
$475$	38.2735	−	12.3951i	1.75611	−	0.568724i
$476$	−4.49944	+	4.49944i	−0.206232	+	0.206232i
$477$	−10.0786	+	63.6335i	−0.461465	+	2.91358i
$478$	−6.66270	−	13.0763i	−0.304745	−	0.598095i
$479$	−7.27592	+	3.70726i	−0.332445	+	0.169389i	−0.612243	−	0.790670i	$-0.709733\pi$
$479$	−7.27592	+	3.70726i	−0.332445	+	0.169389i	0.279798	+	0.960059i	$0.409733\pi$
$480$	−4.66870	+	5.46101i	−0.213096	+	0.249260i
$481$	7.39844	+	31.2192i	0.337340	+	1.42347i
$482$	−19.2134	+	19.2134i	−0.875148	+	0.875148i
$483$	−36.6941	+	11.9226i	−1.66964	+	0.542499i
$484$	6.38212	−	8.78423i	0.290096	−	0.399283i
$485$	0.00971786	+	0.124243i	0.000441265	+	0.00564156i
$486$	30.7698	+	4.87347i	1.39575	+	0.221065i
$487$	5.59662	+	4.06618i	0.253607	+	0.184256i	0.707324	−	0.706890i	$-0.249902\pi$
$487$	5.59662	+	4.06618i	0.253607	+	0.184256i	−0.453717	+	0.891146i	$0.649902\pi$
$488$	−6.85871	−	4.98314i	−0.310479	−	0.225576i
$489$	−17.2504	−	2.73219i	−0.780090	−	0.123554i
$490$	−1.71523	+	2.79597i	−0.0774860	+	0.126309i
$491$	−20.5693	+	28.3112i	−0.928280	+	1.27767i	0.0322468	+	0.999480i	$0.489734\pi$
$491$	−20.5693	+	28.3112i	−0.928280	+	1.27767i	−0.960527	+	0.278188i	$0.910266\pi$
$492$	1.08489	−	0.352503i	0.0489107	−	0.0158921i
$493$	13.8358	−	13.8358i	0.623134	−	0.623134i
$494$	−15.2304	+	24.6912i	−0.685249	+	1.11091i
$495$	−5.70224	−	2.36517i	−0.256297	−	0.106306i
$496$	4.87743	−	2.48518i	0.219003	−	0.111588i
$497$	−6.69623	−	13.1421i	−0.300367	−	0.589504i
$498$	1.97026	−	12.4397i	0.0882893	−	0.557437i
$499$	−1.68724	+	1.68724i	−0.0755312	+	0.0755312i	−0.743863	−	0.668332i	$-0.767009\pi$
$499$	−1.68724	+	1.68724i	−0.0755312	+	0.0755312i	0.668332	+	0.743863i	$0.267009\pi$
$500$	8.49109	+	7.27333i	0.379733	+	0.325273i
$501$	40.4663	−	40.4663i	1.80790	−	1.80790i
$502$	−3.04184	−	4.18674i	−0.135764	−	0.186863i
$503$	24.1309	−	12.2953i	1.07594	−	0.548221i	0.176073	−	0.984377i	$-0.443661\pi$
$503$	24.1309	−	12.2953i	1.07594	−	0.548221i	0.899871	+	0.436157i	$0.143661\pi$
$504$	−5.32360	+	16.3844i	−0.237132	+	0.729818i
$505$	10.1478	+	24.5323i	0.451569	+	1.09167i
$506$	−1.83014	+	0.594648i	−0.0813596	+	0.0264353i
$507$	24.3534	+	33.9359i	1.08157	+	1.50714i
$508$	1.59603	−	3.13239i	0.0708124	−	0.138977i
$509$	11.8346	−	1.87442i	0.524561	−	0.0830823i	0.111462	−	0.993769i	$-0.464447\pi$
$509$	11.8346	−	1.87442i	0.524561	−	0.0830823i	0.413098	+	0.910686i	$0.364447\pi$
$510$	−16.5666	−	10.1630i	−0.733583	−	0.450026i
$511$	−10.1289	−	13.9412i	−0.448075	−	0.616722i
$512$	0.809017	+	0.587785i	0.0357538	+	0.0259767i
$513$	−65.7050	+	90.4352i	−2.90095	+	3.99281i
$514$	−9.71264	−	1.53833i	−0.428406	−	0.0678529i
$515$	−15.2333	−	13.0232i	−0.671260	−	0.573870i
$516$	16.5852	+	12.0498i	0.730121	+	0.530464i
$517$	−0.937481	+	1.83991i	−0.0412304	+	0.0809191i
$518$	−20.9314			−0.919673
$519$	−22.8511	−	70.3284i	−1.00305	−	3.08707i
$520$	−8.06221	−	0.0274955i	−0.353551	−	0.00120576i
$521$	−0.946349	+	2.91256i	−0.0414603	+	0.127602i	−0.969644	−	0.244520i	$-0.921370\pi$
$521$	−0.946349	+	2.91256i	−0.0414603	+	0.127602i	0.928184	+	0.372122i	$0.121370\pi$
$522$	16.3701	−	50.3820i	0.716501	−	2.20516i
$523$	−23.7995	−	3.76947i	−1.04068	−	0.164827i	−0.387374	−	0.921923i	$-0.626618\pi$
$523$	−23.7995	−	3.76947i	−1.04068	−	0.164827i	−0.653305	+	0.757095i	$0.726618\pi$
$524$	14.9104			0.651363
$525$	35.9289	+	11.7123i	1.56807	+	0.511167i
$526$	6.05144	+	6.05144i	0.263855	+	0.263855i
$527$	8.70402	+	11.9801i	0.379153	+	0.521859i
$528$	−0.374279	+	1.15191i	−0.0162884	+	0.0501305i
$529$	−2.91006	−	0.945537i	−0.126525	−	0.0411103i
$530$	1.55276	−	19.6089i	0.0674477	−	0.851756i
$531$	0.677463	+	0.345185i	0.0293994	+	0.0149797i
$532$	−13.3830	−	13.3830i	−0.580228	−	0.580228i
$533$	1.08947	+	0.672024i	0.0471901	+	0.0291086i
$534$	−8.96823	+	12.3437i	−0.388093	+	0.534164i
$535$	8.93592	−	21.5438i	0.386333	−	0.931422i
$536$	6.49097	−	4.71597i	0.280367	−	0.203699i
$537$	−1.38797	−	8.76333i	−0.0598955	−	0.378166i
$538$	−13.6660	+	18.8096i	−0.589183	+	0.810941i
$539$	−0.0865036	+	0.546162i	−0.00372597	+	0.0235249i
$540$	−30.9686	−	2.45230i	−1.33267	−	0.105530i
$541$	5.80264	−	0.919048i	0.249475	−	0.0395130i	−0.0304444	−	0.999536i	$-0.509692\pi$
$541$	5.80264	−	0.919048i	0.249475	−	0.0395130i	0.279919	+	0.960023i	$0.409692\pi$
$542$	−25.6939	−	13.0917i	−1.10365	−	0.562336i
$543$	46.8878	−	46.8878i	2.01215	−	2.01215i
$544$	−1.22811	+	2.41030i	−0.0526548	+	0.103341i
$545$	−4.68352	+	2.86696i	−0.200620	+	0.122807i
$546$	−25.2067	+	10.3546i	−1.07875	+	0.443135i
$547$	−10.7931	−	21.1826i	−0.461479	−	0.905703i	−0.998084	−	0.0618698i	$-0.980294\pi$
$547$	−10.7931	−	21.1826i	−0.461479	−	0.905703i	0.536605	−	0.843833i	$-0.319706\pi$
$548$	−2.88278	−	3.96780i	−0.123146	−	0.169496i
$549$		−	62.0905i		−	2.64996i
$550$	1.79197	+	0.584158i	0.0764101	+	0.0249086i
$551$	41.1529	+	41.1529i	1.75317	+	1.75317i
$552$	−13.2698	+	9.64108i	−0.564800	+	0.410352i
$553$	−12.0415	+	37.0601i	−0.512059	+	1.57595i
$554$	2.53149	−	1.28986i	0.107553	−	0.0548008i
$555$	−14.8948	−	62.1732i	−0.632248	−	2.63911i
$556$	13.2706	−	4.31187i	0.562797	−	0.182864i
$557$		−	6.54798i		−	0.277447i	−0.990331	−	0.138723i	$-0.955700\pi$
$557$		−	6.54798i		−	0.277447i	0.990331	−	0.138723i	$-0.0442999\pi$
$558$	35.7217	+	18.2011i	1.51222	+	0.770514i
$559$	1.73774	+	22.9387i	0.0734987	+	0.970206i
$560$	1.23034	−	5.11386i	0.0519912	−	0.216100i
$561$	−3.23611	−	0.512550i	−0.136629	−	0.0216399i
$562$	13.4074	−	2.12353i	0.565558	−	0.0895756i
$563$	17.1872	−	2.72219i	0.724354	−	0.114726i	0.216639	−	0.976252i	$-0.430490\pi$
$563$	17.1872	−	2.72219i	0.724354	−	0.114726i	0.507715	+	0.861525i	$0.330490\pi$
$564$	−2.75345	+	17.3846i	−0.115941	+	0.732024i
$565$	5.40706	+	8.83307i	0.227477	+	0.371610i
$566$	3.04852	−	0.482838i	0.128139	−	0.0202952i
$567$	−50.7097	+	16.4766i	−2.12961	+	0.691952i
$568$	−4.43390	−	4.43390i	−0.186042	−	0.186042i
$569$	−5.26633	−	16.2081i	−0.220776	−	0.679479i	−0.998693	−	0.0511120i	$-0.983723\pi$
$569$	−5.26633	−	16.2081i	−0.220776	−	0.679479i	0.777917	−	0.628367i	$-0.216277\pi$
$570$	30.2287	−	49.2754i	1.26614	−	2.06392i
$571$	−25.5103	−	8.28881i	−1.06757	−	0.346876i	−0.278032	−	0.960572i	$-0.589682\pi$
$571$	−25.5103	−	8.28881i	−1.06757	−	0.346876i	−0.789543	+	0.613696i	$0.789682\pi$
$572$	−1.25720	+	0.516440i	−0.0525661	+	0.0215934i
$573$	−52.3240	−	8.28731i	−2.18587	−	0.346207i
$574$	−0.590510	+	0.590510i	−0.0246474	+	0.0246474i
$575$	14.9830	+	20.6641i	0.624833	+	0.861754i
$576$			7.32387i			0.305161i
$577$	30.7704	−	22.3560i	1.28099	−	0.930693i	0.281407	−	0.959589i	$-0.409199\pi$
$577$	30.7704	−	22.3560i	1.28099	−	0.930693i	0.999582	+	0.0288954i	$0.00919898\pi$
$578$	9.20831	+	2.99196i	0.383015	+	0.124449i
$579$	6.98243	−	3.55773i	0.290180	−	0.147854i
$580$	−3.78329	+	15.7252i	−0.157093	+	0.652952i
$581$	2.84928	+	8.76917i	0.118208	+	0.363806i
$582$	0.126624	+	0.126624i	0.00524873	+	0.00524873i
$583$	−1.02471	−	3.15372i	−0.0424390	−	0.130614i
$584$	−5.92676	−	4.30604i	−0.245251	−	0.178185i
$585$	−34.5438	−	47.8880i	−1.42821	−	1.97993i
$586$	−2.51790	+	1.82936i	−0.104014	+	0.0755702i
$587$	−8.92905	−	6.48734i	−0.368542	−	0.267761i	0.388064	−	0.921632i	$-0.373144\pi$
$587$	−8.92905	−	6.48734i	−0.368542	−	0.267761i	−0.756606	+	0.653871i	$0.773144\pi$
$588$	0.737333	+	4.65534i	0.0304071	+	0.191983i
$589$	−35.6332	+	25.8890i	−1.46824	+	1.06674i
$590$	−0.214426	−	0.0889394i	−0.00882779	−	0.00366158i
$591$	3.08947	+	19.5062i	0.127084	+	0.802376i
$592$	−8.46295	+	2.74978i	−0.347825	+	0.113015i
$593$	−17.0492			−0.700127			−0.350064	−	0.936726i	$-0.613840\pi$
$593$	−17.0492			−0.700127			−0.350064	+	0.936726i	$0.613840\pi$
$594$	−4.98071	+	1.61833i	−0.204361	+	0.0664009i
$595$	14.1841	+	1.12319i	0.581491	+	0.0460463i
$596$	3.32095	+	6.51773i	0.136031	+	0.266977i
$597$	11.7979	−	6.01132i	0.482855	−	0.246027i
$598$	−17.8847	−	4.34917i	−0.731360	−	0.177851i
$599$		−	23.8233i		−	0.973393i	−0.873571	−	0.486696i	$-0.838202\pi$
$599$		−	23.8233i		−	0.973393i	0.873571	−	0.486696i	$-0.161798\pi$
$600$	16.0654	+	0.0154844i	0.655866	+	0.000632147i
$601$	5.45550			0.222535			0.111267	−	0.993791i	$-0.464509\pi$
$601$	5.45550			0.222535			0.111267	+	0.993791i	$0.464509\pi$
$602$	−14.8233	−	2.34777i	−0.604151	−	0.0956881i
$603$	55.8855	+	18.1583i	2.27583	+	0.739463i
$604$	−8.42610	−	16.5371i	−0.342853	−	0.672887i
$605$	−24.2051	+	1.89324i	−0.984076	+	0.0769713i
$606$	33.9901	+	17.3188i	1.38076	+	0.703530i
$607$	−10.8725	+	10.8725i	−0.441301	+	0.441301i	−0.892449	−	0.451148i	$-0.851015\pi$
$607$	−10.8725	+	10.8725i	−0.441301	+	0.441301i	0.451148	+	0.892449i	$0.351015\pi$
$608$	−7.16915	−	3.65286i	−0.290747	−	0.148143i
$609$	8.55196	+	53.9950i	0.346543	+	2.18799i
$610$	1.47824	+	18.8993i	0.0598522	+	0.765209i
$611$	−16.8709	+	10.2707i	−0.682523	+	0.415506i
$612$	−19.5682	+	3.09930i	−0.790997	+	0.125282i
$613$	19.7322	−	27.1590i	0.796975	−	1.09694i	−0.196229	−	0.980558i	$-0.562870\pi$
$613$	19.7322	−	27.1590i	0.796975	−	1.09694i	0.993204	−	0.116384i	$-0.0371303\pi$
$614$	−9.05382	−	12.4615i	−0.365382	−	0.502906i
$615$	−2.17422	−	1.33380i	−0.0876729	−	0.0537842i
$616$	−0.138710	−	0.875779i	−0.00558878	−	0.0352862i
$617$	−1.86357	−	5.73548i	−0.0750246	−	0.230902i	0.906511	−	0.422183i	$-0.138736\pi$
$617$	−1.86357	−	5.73548i	−0.0750246	−	0.230902i	−0.981535	+	0.191281i	$0.938736\pi$
$618$	−28.7981			−1.15843
$619$	−8.44666	+	16.5775i	−0.339500	+	0.666306i	−0.996129	−	0.0879080i	$-0.971982\pi$
$619$	−8.44666	+	16.5775i	−0.339500	+	0.666306i	0.656629	+	0.754214i	$0.271982\pi$
$620$	−11.3064	−	4.68965i	−0.454076	−	0.188341i
$621$	−67.4505	−	21.9160i	−2.70670	−	0.879459i
$622$	8.25905	+	2.68353i	0.331158	+	0.107600i
$623$	1.74736	−	11.0324i	0.0700065	−	0.442003i
$624$	−8.83123	+	7.49797i	−0.353532	+	0.300159i
$625$	0.0481917	−	25.0000i	0.00192767	−	0.999998i
$626$	3.68509	+	3.68509i	0.147286	+	0.147286i
$627$	1.52452	−	9.62541i	0.0608833	−	0.384402i
$628$	−9.95854	−	19.5447i	−0.397389	−	0.779920i
$629$	−10.9283	−	21.4480i	−0.435740	−	0.855188i
$630$	35.5968	−	14.7246i	1.41821	−	0.586641i
$631$	−36.8674	−	18.7849i	−1.46767	−	0.747813i	−0.476343	−	0.879259i	$-0.658038\pi$
$631$	−36.8674	−	18.7849i	−1.46767	−	0.747813i	−0.991323	+	0.131446i	$0.958038\pi$
$632$			16.5660i			0.658959i
$633$	1.99627	−	3.91789i	0.0793445	−	0.155722i
$634$	9.75618	+	7.08828i	0.387467	+	0.281512i
$635$	−7.64472	+	1.83144i	−0.303371	+	0.0726784i
$636$	−16.6137	−	22.8667i	−0.658775	−	0.906725i
$637$	−3.44676	+	4.01179i	−0.136566	+	0.158953i
$638$	0.426534	+	2.69303i	0.0168866	+	0.106618i
$639$	7.18412	−	45.3587i	0.284199	−	1.79436i
$640$	−0.174366	−	2.22926i	−0.00689240	−	0.0881192i
$641$	−28.4542	+	39.1638i	−1.12387	+	1.54688i	−0.324656	+	0.945832i	$0.605249\pi$
$641$	−28.4542	+	39.1638i	−1.12387	+	1.54688i	−0.799216	+	0.601044i	$0.794751\pi$
$642$	−10.3565	−	31.8740i	−0.408739	−	1.25797i
$643$			5.02797i			0.198284i	0.995073	+	0.0991419i	$0.0316098\pi$
$643$			5.02797i			0.198284i	−0.995073	+	0.0991419i	$0.968390\pi$
$644$	5.45149	−	10.6992i	0.214819	−	0.421606i
$645$	−3.57456	−	45.7007i	−0.140748	−	1.79946i
$646$	6.72604	−	20.7006i	0.264632	−	0.814455i
$647$	−33.3778	+	17.0068i	−1.31222	+	0.668607i	−0.963270	−	0.268535i	$-0.913460\pi$
$647$	−33.3778	+	17.0068i	−1.31222	+	0.668607i	−0.348946	+	0.937143i	$0.613460\pi$
$648$	−18.3383	+	13.3236i	−0.720397	+	0.523399i
$649$	−0.0391342			−0.00153615
$650$	11.6546	+	13.7539i	0.457133	+	0.539472i
$651$	−41.3728			−1.62153
$652$	4.39760	−	3.19504i	0.172223	−	0.125128i
$653$	−11.9438	+	6.08567i	−0.467397	+	0.238151i	−0.671795	−	0.740737i	$-0.734476\pi$
$653$	−11.9438	+	6.08567i	−0.467397	+	0.238151i	0.204398	+	0.978888i	$0.434476\pi$
$654$	−2.43836	+	7.50449i	−0.0953473	+	0.293449i
$655$	−21.6408	−	25.3628i	−0.845576	−	0.991008i
$656$	−0.161178	+	0.316330i	−0.00629295	+	0.0123506i
$657$		−	53.6537i		−	2.09323i
$658$	−3.98189	−	12.2550i	−0.155230	−	0.477750i
$659$	21.0169	−	28.9272i	0.818700	−	1.12684i	−0.171222	−	0.985232i	$-0.554772\pi$
$659$	21.0169	−	28.9272i	0.818700	−	1.12684i	0.989922	−	0.141612i	$-0.0452285\pi$
$660$	2.50265	−	1.03522i	0.0974155	−	0.0402958i
$661$	−6.79394	+	42.8952i	−0.264254	+	1.66843i	0.396657	+	0.917967i	$0.370170\pi$
$661$	−6.79394	+	42.8952i	−0.264254	+	1.66843i	−0.660911	+	0.750465i	$0.729830\pi$
$662$	−2.45209	−	15.4819i	−0.0953032	−	0.601721i
$663$	−23.7706	−	20.4227i	−0.923172	−	0.793151i
$664$	2.30403	+	3.17122i	0.0894136	+	0.123067i
$665$	−3.34079	+	42.1888i	−0.129550	+	1.63601i
$666$	−52.7246	−	38.3067i	−2.04304	−	1.48435i
$667$	−16.7634	+	32.9000i	−0.649081	+	1.27389i
$668$			17.8110i			0.689126i
$669$	−11.4446	−	5.83133i	−0.442475	−	0.225452i
$670$	−17.4429	−	4.19656i	−0.673878	−	0.162127i
$671$	1.45085	+	2.84746i	0.0560095	+	0.109925i
$672$	−3.43124	−	6.73419i	−0.132363	−	0.259777i
$673$	1.47733	−	9.32752i	0.0569470	−	0.359549i	−0.942716	−	0.333596i	$-0.891738\pi$
$673$	1.47733	−	9.32752i	0.0569470	−	0.359549i	0.999663	−	0.0259533i	$-0.00826213\pi$
$674$	−3.14594	−	3.14594i	−0.121177	−	0.121177i
$675$	40.7761	+	56.2373i	1.56947	+	2.16458i
$676$	−12.8278	−	2.10882i	−0.493378	−	0.0811083i
$677$	2.39068	−	15.0942i	0.0918813	−	0.580115i	−0.898196	−	0.439594i	$-0.855122\pi$
$677$	2.39068	−	15.0942i	0.0918813	−	0.580115i	0.990078	−	0.140521i	$-0.0448778\pi$
$678$	14.1534	+	4.59871i	0.543557	+	0.176612i
$679$	−0.124681	−	0.0405112i	−0.00478481	−	0.00155468i
$680$	5.88244	−	1.40925i	0.225581	−	0.0540423i
$681$	−17.3278	+	34.0076i	−0.664001	+	1.30318i
$682$	−2.06349			−0.0790151
$683$	−7.52138	−	23.1484i	−0.287798	−	0.885750i	−0.985546	−	0.169407i	$-0.945815\pi$
$683$	−7.52138	−	23.1484i	−0.287798	−	0.885750i	0.697749	−	0.716343i	$-0.254185\pi$
$684$	−9.21848	−	58.2032i	−0.352477	−	2.22545i
$685$	−2.56527	+	10.6625i	−0.0980141	+	0.407393i
$686$	−11.7065	−	16.1126i	−0.446957	−	0.615183i
$687$	−15.1418	+	20.8409i	−0.577697	+	0.795131i
$688$	−6.30174	+	0.998098i	−0.240252	+	0.0380521i
$689$	7.49456	−	30.8192i	0.285520	−	1.17412i
$690$	35.6593	+	8.57922i	1.35753	+	0.326605i
$691$	−3.12605	−	19.7371i	−0.118920	−	0.750834i	−0.973019	−	0.230724i	$-0.925891\pi$
$691$	−3.12605	−	19.7371i	−0.118920	−	0.750834i	0.854099	−	0.520111i	$-0.174109\pi$
$692$	20.5061	+	10.4484i	0.779526	+	0.397188i
$693$	4.59198	−	4.59198i	0.174435	−	0.174435i
$694$	4.74724	+	2.41884i	0.180203	+	0.0918179i
$695$	−26.5953	−	16.3153i	−1.00882	−	0.618874i
$696$	10.5511	+	20.7077i	0.399938	+	0.784922i
$697$	−0.913390	−	0.296778i	−0.0345971	−	0.0112413i
$698$	−0.238656	−	0.0377994i	−0.00903326	−	0.00143073i
$699$	−84.0207			−3.17796
$700$	−10.4845	+	5.32939i	−0.396276	+	0.201432i
$701$			25.4195i			0.960082i	0.877246	+	0.480041i	$0.159378\pi$
$701$			25.4195i			0.960082i	−0.877246	+	0.480041i	$0.840622\pi$
$702$	−48.6731	−	11.8362i	−1.83705	−	0.446730i
$703$	63.7944	−	32.5049i	2.40605	−	1.22595i
$704$	−0.171135	−	0.335871i	−0.00644989	−	0.0126586i
$705$	33.5679	−	20.5482i	1.26424	−	0.773889i
$706$	−11.0830	+	3.60109i	−0.417115	+	0.135529i
$707$	−27.9276			−1.05033
$708$	−0.317243	+	0.103078i	−0.0119227	+	0.00387393i
$709$	5.51684	+	34.8319i	0.207189	+	1.30814i	0.843676	+	0.536853i	$0.180387\pi$
$709$	5.51684	+	34.8319i	0.207189	+	1.30814i	−0.636487	+	0.771288i	$0.719613\pi$
$710$	−1.10683	+	13.9775i	−0.0415385	+	0.524565i
$711$	−98.1555	+	71.3142i	−3.68112	+	2.67449i
$712$	−0.742847	−	4.69015i	−0.0278394	−	0.175771i
$713$	−22.6076	−	16.4254i	−0.846660	−	0.615135i
$714$	16.5406	−	12.0175i	0.619018	−	0.449743i
$715$	2.70316	+	1.38896i	0.101092	+	0.0519442i
$716$	2.23401	+	1.62311i	0.0834890	+	0.0606583i
$717$	14.5716	+	44.8467i	0.544186	+	1.67483i
$718$	21.1400	+	21.1400i	0.788938	+	0.788938i
$719$	−9.56014	−	29.4231i	−0.356533	−	1.09730i	−0.955115	−	0.296234i	$-0.904269\pi$
$719$	−9.56014	−	29.4231i	−0.356533	−	1.09730i	0.598582	−	0.801061i	$-0.295731\pi$
$720$	12.4580	−	10.6298i	0.464284	−	0.396149i
$721$	18.7848	−	9.57133i	0.699583	−	0.356455i
$722$	43.5014	+	14.1345i	1.61895	+	0.526030i
$723$	70.6316	−	51.3168i	2.62682	−	1.90849i
$724$			20.6373i			0.766980i
$725$	32.2398	−	16.3879i	1.19736	−	0.608631i
$726$	−24.6690	+	24.6690i	−0.915554	+	0.915554i
$727$	−3.85037	−	0.609839i	−0.142802	−	0.0226177i	0.0846240	−	0.996413i	$-0.473031\pi$
$727$	−3.85037	−	0.609839i	−0.142802	−	0.0226177i	−0.227426	+	0.973795i	$0.573031\pi$
$728$	3.26853	−	7.82602i	0.121140	−	0.290052i
$729$	−30.5252	−	9.91822i	−1.13056	−	0.367342i
$730$	1.27738	+	16.3313i	0.0472780	+	0.604448i
$731$	−5.33352	−	16.4149i	−0.197267	−	0.607126i
$732$	19.2615	+	19.2615i	0.711927	+	0.711927i
$733$	46.3281	−	15.0529i	1.71117	−	0.555992i	0.720641	−	0.693308i	$-0.243847\pi$
$733$	46.3281	−	15.0529i	1.71117	−	0.555992i	0.990527	+	0.137316i	$0.0438475\pi$
$734$	21.5593	−	3.41465i	0.795767	−	0.126037i
$735$	6.84866	−	8.01093i	0.252617	−	0.295487i
$736$	0.798580	−	5.04203i	0.0294360	−	0.185852i
$737$	−2.98720	+	0.473126i	−0.110035	+	0.0174278i
$738$	−2.56815	+	0.406754i	−0.0945347	+	0.0149728i
$739$	44.9780	+	7.12381i	1.65454	+	0.262054i	0.912733	−	0.408557i	$-0.133968\pi$
$739$	44.9780	+	7.12381i	1.65454	+	0.262054i	0.741809	+	0.670611i	$0.233968\pi$
$740$	16.9605	+	10.4046i	0.623479	+	0.382482i
$741$	60.7447	−	70.7026i	2.23151	−	2.59733i
$742$	18.4370	+	9.39410i	0.676842	+	0.344868i
$743$			24.3495i			0.893298i	0.894709	+	0.446649i	$0.147383\pi$
$743$			24.3495i			0.893298i	−0.894709	+	0.446649i	$0.852617\pi$
$744$	−16.7278	+	5.43518i	−0.613270	+	0.199263i
$745$	6.26679	−	15.1088i	0.229598	−	0.553543i
$746$	−7.26217	+	3.70026i	−0.265887	+	0.135476i
$747$	−8.87139	+	27.3033i	−0.324587	+	0.998977i
$748$	0.824973	−	0.599378i	0.0301640	−	0.0219154i
$749$	17.3491	+	17.3491i	0.633923	+	0.633923i
$750$	−23.2908	−	27.3500i	−0.850460	−	0.998680i
$751$			4.44015i			0.162023i	0.996713	+	0.0810117i	$0.0258151\pi$
$751$			4.44015i			0.162023i	−0.996713	+	0.0810117i	$0.974185\pi$
$752$	−3.21990	−	4.43181i	−0.117418	−	0.161612i
$753$	7.54894	+	14.8156i	0.275099	+	0.539912i
$754$	−10.0507	+	24.0651i	−0.366027	+	0.876398i
$755$	−15.9004	+	38.3348i	−0.578676	+	1.39515i
$756$	14.8362	−	29.1177i	0.539588	−	1.05900i
$757$	−19.6841	+	19.6841i	−0.715430	+	0.715430i	−0.967666	−	0.252235i	$-0.918834\pi$
$757$	−19.6841	+	19.6841i	−0.715430	+	0.715430i	0.252235	+	0.967666i	$0.418834\pi$
$758$	−23.1137	−	11.7770i	−0.839527	−	0.427760i
$759$	6.10687	−	0.967233i	0.221665	−	0.0351083i
$760$	4.19164	+	17.4966i	0.152047	+	0.634668i
$761$	6.51032	−	41.1045i	0.235999	−	1.49004i	−0.530441	−	0.847722i	$-0.677973\pi$
$761$	6.51032	−	41.1045i	0.235999	−	1.49004i	0.766439	−	0.642317i	$-0.222027\pi$
$762$	−6.63949	+	9.13847i	−0.240523	+	0.331052i
$763$	−0.903669	−	5.70554i	−0.0327150	−	0.206554i
$764$	13.3388	−	9.69122i	0.482582	−	0.350616i
$765$	33.6731	+	28.7876i	1.21745	+	1.04082i
$766$	5.18567	−	7.13746i	0.187366	−	0.257887i
$767$	−0.318581	−	0.196512i	−0.0115033	−	0.00709565i
$768$	−2.27199	−	2.27199i	−0.0819833	−	0.0819833i
$769$	−10.9426	−	5.57553i	−0.394600	−	0.201059i	0.245420	−	0.969417i	$-0.421074\pi$
$769$	−10.9426	−	5.57553i	−0.394600	−	0.201059i	−0.640020	+	0.768358i	$0.721074\pi$
$770$	−1.28840	+	1.50705i	−0.0464305	+	0.0543102i
$771$	30.0500	+	9.76385i	1.08223	+	0.351636i
$772$	−0.753680	+	2.31959i	−0.0271255	+	0.0834838i
$773$	−16.0252	−	22.0568i	−0.576386	−	0.793328i	0.416907	−	0.908949i	$-0.363114\pi$
$773$	−16.0252	−	22.0568i	−0.576386	−	0.793328i	−0.993293	+	0.115621i	$0.963114\pi$
$774$	−33.0420	−	33.0420i	−1.18767	−	1.18767i
$775$	8.43281	+	26.0389i	0.302916	+	0.935345i
$776$	−0.0557327			−0.00200069
$777$	66.4262	+	10.5209i	2.38303	+	0.377434i
$778$	−10.0692	+	30.9898i	−0.360999	+	1.11104i
$779$	0.882731	−	2.71677i	0.0316271	−	0.0973382i
$780$	25.5718	+	4.13962i	0.915616	+	0.148222i
$781$	0.730424	+	2.24801i	0.0261366	+	0.0804402i
$782$	13.8094			0.493825
$783$	−45.6215	+	89.5372i	−1.63038	+	3.19980i
$784$	−1.18677	−	0.862241i	−0.0423847	−	0.0307943i
$785$	−18.7922	+	45.3067i	−0.670724	+	1.61707i
$786$	−47.3184	−	7.49450i	−1.68779	−	0.267320i
$787$	2.31604	−	3.18775i	0.0825577	−	0.113631i	−0.765741	−	0.643149i	$-0.777627\pi$
$787$	2.31604	−	3.18775i	0.0825577	−	0.113631i	0.848298	+	0.529519i	$0.177627\pi$
$788$	−4.97265	−	3.61284i	−0.177143	−	0.128702i
$789$	−16.1627	−	22.2460i	−0.575407	−	0.791979i
$790$	28.1790	−	24.0437i	1.00256	−	0.855436i
$791$	−10.7606	+	1.70431i	−0.382602	+	0.0605982i
$792$	1.25337	−	2.45987i	0.0445365	−	0.0874079i
$793$	−2.48751	+	30.4659i	−0.0883340	+	1.08187i
$794$	13.0585	−	4.24295i	0.463427	−	0.150577i
$795$	−14.7839	+	61.4487i	−0.524329	+	2.17936i
$796$	−1.27346	+	3.91930i	−0.0451365	+	0.138916i
$797$	−27.2135	+	13.8660i	−0.963952	+	0.491158i	−0.863811	−	0.503815i	$-0.831929\pi$
$797$	−27.2135	+	13.8660i	−0.963952	+	0.491158i	−0.100141	+	0.994973i	$0.531929\pi$
$798$	35.7445	+	49.1981i	1.26534	+	1.74159i
$799$	10.4785	−	10.4785i	0.370703	−	0.370703i
$800$	−3.53894	+	3.53212i	−0.125120	+	0.124879i
$801$	24.5919	−	24.5919i	0.868912	−	0.868912i
$802$	3.45361	−	21.8052i	0.121951	−	0.769969i
$803$	1.25371	+	2.46055i	0.0442426	+	0.0868309i
$804$	−22.9696	+	11.7036i	−0.810077	+	0.412755i
$805$	−26.1117	+	6.25556i	−0.920317	+	0.220480i
$806$	−16.7983	−	10.3618i	−0.591696	−	0.364979i
$807$	52.8237	−	52.8237i	1.85948	−	1.85948i
$808$	−11.2916	+	3.66888i	−0.397239	+	0.129071i
$809$	14.4281	−	19.8586i	0.507265	−	0.698190i	−0.476190	−	0.879342i	$-0.657983\pi$
$809$	14.4281	−	19.8586i	0.507265	−	0.698190i	0.983455	+	0.181152i	$0.0579826\pi$
$810$	49.2797	+	11.8561i	1.73151	+	0.416582i
$811$	−32.5122	−	5.14942i	−1.14166	−	0.180821i	−0.443166	−	0.896440i	$-0.646145\pi$
$811$	−32.5122	−	5.14942i	−1.14166	−	0.180821i	−0.698491	+	0.715619i	$0.746145\pi$
$812$	−13.7648	−	10.0007i	−0.483050	−	0.350956i
$813$	74.9596	+	54.4614i	2.62895	+	1.91004i
$814$	3.31304	+	0.524735i	0.116122	+	0.0183919i
$815$	−11.8175	−	2.84315i	−0.413948	−	0.0995911i
$816$	5.10893	−	7.03185i	0.178848	−	0.246164i
$817$	48.8240	−	15.8639i	1.70814	−	0.555007i
$818$	17.0502	−	17.0502i	0.596147	−	0.596147i
$819$	60.4408	−	14.3235i	2.11197	−	0.500503i
$820$	0.772015	−	0.184951i	0.0269599	−	0.00645877i
$821$	33.0764	−	16.8533i	1.15437	−	0.588183i	0.231329	−	0.972876i	$-0.425693\pi$
$821$	33.0764	−	16.8533i	1.15437	−	0.588183i	0.923045	+	0.384693i	$0.125693\pi$
$822$	7.15419	+	14.0409i	0.249531	+	0.489732i
$823$	−0.854879	+	5.39749i	−0.0297992	+	0.188145i	−0.998098	−	0.0616509i	$-0.980363\pi$
$823$	−0.854879	+	5.39749i	−0.0297992	+	0.188145i	0.968299	+	0.249796i	$0.0803634\pi$
$824$	6.33764	−	6.33764i	0.220782	−	0.220782i
$825$	−5.39325	−	2.75455i	−0.187769	−	0.0959010i
$826$	0.172676	−	0.172676i	0.00600817	−	0.00600817i
$827$	28.8062	+	39.6483i	1.00169	+	1.37871i	0.924283	+	0.381708i	$0.124664\pi$
$827$	28.8062	+	39.6483i	1.00169	+	1.37871i	0.0774067	+	0.997000i	$0.475336\pi$
$828$	33.3125	−	16.9736i	1.15769	−	0.589872i
$829$	−2.38151	+	7.32954i	−0.0827134	+	0.254566i	−0.983857	−	0.178954i	$-0.942729\pi$
$829$	−2.38151	+	7.32954i	−0.0827134	+	0.254566i	0.901144	+	0.433520i	$0.142729\pi$
$830$	2.05027	−	8.52188i	0.0711658	−	0.295799i
$831$	−8.68206	+	2.82097i	−0.301177	+	0.0978585i
$832$	0.293413	−	3.59359i	0.0101723	−	0.124585i
$833$	1.80155	−	3.53575i	0.0624201	−	0.122506i
$834$	−44.2817	+	7.01353i	−1.53335	+	0.242859i
$835$	30.2968	−	25.8506i	1.04846	−	0.894599i
$836$	1.78278	+	2.45378i	0.0616586	+	0.0848658i
$837$	−61.5264	−	44.7015i	−2.12666	−	1.54511i
$838$	−12.0932	+	16.6449i	−0.417754	+	0.574989i
$839$	−37.0636	−	5.87030i	−1.27958	−	0.202665i	−0.520611	−	0.853794i	$-0.674296\pi$
$839$	−37.0636	−	5.87030i	−1.27958	−	0.202665i	−0.758967	+	0.651129i	$0.774296\pi$
$840$	−6.47491	+	15.6105i	−0.223406	+	0.538615i
$841$	18.8653	+	13.7065i	0.650529	+	0.472637i
$842$	−16.1570	+	31.7098i	−0.556806	+	1.09279i
$843$	−43.6161			−1.50222
$844$	0.422895	+	1.30154i	0.0145567	+	0.0448008i
$845$	15.0310	+	24.8811i	0.517083	+	0.855935i
$846$	12.3979	−	38.1567i	0.426247	−	1.31185i
$847$	7.89244	−	24.2904i	0.271187	−	0.834629i
$848$	8.68851	+	1.37613i	0.298365	+	0.0472563i
$849$	−9.91723			−0.340359
$850$	−10.9349	−	7.96076i	−0.375063	−	0.273052i
$851$	32.1208	+	32.1208i	1.10109	+	1.10109i
$852$	11.8424	+	16.2997i	0.405715	+	0.558418i
$853$	6.33987	−	19.5121i	0.217073	−	0.668082i	−0.781927	−	0.623370i	$-0.785763\pi$
$853$	6.33987	−	19.5121i	0.217073	−	0.668082i	0.999000	−	0.0447117i	$-0.0142369\pi$
$854$	−18.9659	−	6.16240i	−0.649001	−	0.210873i
$855$	−85.6251	+	100.156i	−2.92832	+	3.42528i
$856$	9.29374	+	4.73540i	0.317653	+	0.161853i
$857$	−18.5993	−	18.5993i	−0.635342	−	0.635342i	0.314061	−	0.949403i	$-0.398310\pi$
$857$	−18.5993	−	18.5993i	−0.635342	−	0.635342i	−0.949403	+	0.314061i	$0.898310\pi$
$858$	4.24932	−	1.00702i	0.145069	−	0.0343791i
$859$	−14.0973	+	19.4033i	−0.480993	+	0.662031i	−0.978695	−	0.205318i	$-0.934177\pi$
$859$	−14.0973	+	19.4033i	−0.480993	+	0.662031i	0.497702	+	0.867348i	$0.334177\pi$
$860$	10.8441	+	9.27075i	0.369780	+	0.316130i
$861$	2.17081	−	1.57718i	0.0739809	−	0.0537503i
$862$	−0.509168	−	3.21476i	−0.0173423	−	0.109495i
$863$	−10.1024	+	13.9048i	−0.343891	+	0.473325i	−0.945573	−	0.325410i	$-0.894498\pi$
$863$	−10.1024	+	13.9048i	−0.343891	+	0.473325i	0.601682	+	0.798736i	$0.294498\pi$
$864$	2.17333	−	13.7219i	0.0739382	−	0.466827i
$865$	−11.9895	−	50.0460i	−0.407655	−	1.70162i
$866$	−2.03040	+	0.321583i	−0.0689957	+	0.0109278i
$867$	−27.7189	−	14.1235i	−0.941383	−	0.479658i
$868$	9.10497	−	9.10497i	0.309043	−	0.309043i
$869$	2.83501	−	5.56403i	0.0961713	−	0.188747i
$870$	19.9104	−	48.0025i	0.675026	−	1.62744i
$871$	−26.6938	−	11.1486i	−0.904485	−	0.377757i
$872$	−1.11491	−	2.18814i	−0.0377557	−	0.0740997i
$873$	−0.239921	−	0.330223i	−0.00812011	−	0.0111764i
$874$			41.0745i			1.38937i
$875$	24.2825	+	10.0993i	0.820897	+	0.341418i
$876$	16.6443	+	16.6443i	0.562359	+	0.562359i
$877$	28.4329	−	20.6577i	0.960110	−	0.697561i	0.00693359	−	0.999976i	$-0.497793\pi$
$877$	28.4329	−	20.6577i	0.960110	−	0.697561i	0.953176	+	0.302415i	$0.0977930\pi$
$878$	−0.0920391	+	0.283267i	−0.00310617	+	0.00955980i
$879$	8.91011	−	4.53993i	0.300530	−	0.153128i
$880$	−0.322940	+	0.778584i	−0.0108863	+	0.0262461i
$881$	19.2981	−	6.27034i	0.650170	−	0.211253i	0.0346811	−	0.999398i	$-0.488958\pi$
$881$	19.2981	−	6.27034i	0.650170	−	0.211253i	0.615489	+	0.788145i	$0.288958\pi$
$882$		−	10.7436i		−	0.361756i
$883$	7.98134	+	4.06669i	0.268593	+	0.136855i	0.583101	−	0.812400i	$-0.301839\pi$
$883$	7.98134	+	4.06669i	0.268593	+	0.136855i	−0.314507	+	0.949255i	$0.601839\pi$
$884$	9.72567	−	0.736775i	0.327110	−	0.0247804i
$885$	0.635782	+	0.390029i	0.0213716	+	0.0131107i
$886$	−1.41228	−	0.223682i	−0.0474463	−	0.00751476i
$887$	42.2193	−	6.68689i	1.41759	−	0.224524i	0.599848	−	0.800114i	$-0.295228\pi$
$887$	42.2193	−	6.68689i	1.41759	−	0.224524i	0.817738	+	0.575590i	$0.195228\pi$
$888$	28.2395	−	4.47269i	0.947655	−	0.150094i
$889$	1.29363	−	8.16766i	0.0433870	−	0.273934i
$890$	−6.89987	+	8.07083i	−0.231284	+	0.270535i
$891$	8.43944	−	1.33668i	0.282732	−	0.0447803i
$892$	3.80195	−	1.23533i	0.127299	−	0.0413618i
$893$	31.1670	+	31.1670i	1.04296	+	1.04296i
$894$	−7.26305	−	22.3534i	−0.242913	−	0.747609i
$895$	−0.481492	−	6.15586i	−0.0160945	−	0.205768i
$896$	2.23712	+	0.726884i	0.0747369	+	0.0242835i
$897$	54.5714	+	22.7917i	1.82209	+	0.760992i
$898$	−19.0723	−	3.02076i	−0.636451	−	0.100804i
$899$	−27.9978	+	27.9978i	−0.933780	+	0.933780i
$900$	−36.1629	−	5.76338i	−1.20543	−	0.192113i
$901$			23.7967i			0.792782i
$902$	0.108270	−	0.0786629i	0.00360500	−	0.00261919i
$903$	45.8618	+	14.9014i	1.52619	+	0.495888i
$904$	−4.12680	+	2.10271i	−0.137255	+	0.0699351i
$905$	35.1045	−	29.9528i	1.16691	−	0.995665i
$906$	18.4282	+	56.7162i	0.612236	+	1.88427i
$907$	−29.6139	−	29.6139i	−0.983314	−	0.983314i	0.0165487	−	0.999863i	$-0.494732\pi$
$907$	−29.6139	−	29.6139i	−0.983314	−	0.983314i	−0.999863	+	0.0165487i	$0.994732\pi$
$908$	−3.67077	−	11.2975i	−0.121819	−	0.374919i
$909$	−70.3475	−	51.1105i	−2.33328	−	1.69523i
$910$	−18.0561	+	5.79878i	−0.598555	+	0.192228i
$911$	0.614014	−	0.446108i	0.0203432	−	0.0147802i	−0.577567	−	0.816343i	$-0.695998\pi$
$911$	0.614014	−	0.446108i	0.0203432	−	0.0147802i	0.597910	+	0.801563i	$0.295998\pi$
$912$	20.9154	+	15.1959i	0.692577	+	0.503186i
$913$	−0.231150	−	1.45942i	−0.00764994	−	0.0482998i
$914$	19.0490	−	13.8399i	0.630086	−	0.457784i
$915$	4.80823	−	60.7202i	0.158955	−	2.00735i
$916$	−1.25421	−	7.91878i	−0.0414403	−	0.261644i
$917$	33.3563	−	10.8381i	1.10152	−	0.357906i
$918$	37.5823			1.24040
$919$	−28.5464	+	9.27528i	−0.941658	+	0.305963i	−0.739321	−	0.673353i	$-0.764853\pi$
$919$	−28.5464	+	9.27528i	−0.941658	+	0.305963i	−0.202337	+	0.979316i	$0.564853\pi$
$920$	−9.73564	+	5.95956i	−0.320975	+	0.196481i
$921$	22.4689	+	44.0976i	0.740374	+	1.45307i
$922$	−8.89073	+	4.53005i	−0.292801	+	0.149189i
$923$	−5.34221	+	21.9683i	−0.175841	+	0.723096i
$924$			2.84902i			0.0937260i
$925$	−6.91778	−	43.9513i	−0.227455	−	1.44511i
$926$	8.91473			0.292956
$927$	64.8340	+	10.2687i	2.12943	+	0.337268i
$928$	−6.87916	−	2.23517i	−0.225819	−	0.0733732i
$929$	−13.7905	−	27.0653i	−0.452451	−	0.887985i	−0.998730	−	0.0503817i	$-0.983956\pi$
$929$	−13.7905	−	27.0653i	−0.452451	−	0.887985i	0.546279	−	0.837603i	$-0.316044\pi$
$930$	33.5239	+	20.5657i	1.09929	+	0.674375i
$931$	10.5166	+	5.35850i	0.344669	+	0.175618i
$932$	18.4906	−	18.4906i	0.605679	−	0.605679i
$933$	−24.8614	−	12.6675i	−0.813926	−	0.414716i
$934$	−4.88330	−	30.8319i	−0.159786	−	1.00885i
$935$	−2.21691	−	0.533364i	−0.0725008	−	0.0174429i
$936$	22.5556	−	13.7314i	0.737253	−	0.448825i
$937$	−18.7981	+	2.97733i	−0.614108	+	0.0972651i	−0.455737	−	0.890115i	$-0.650624\pi$
$937$	−18.7981	+	2.97733i	−0.614108	+	0.0972651i	−0.158371	+	0.987380i	$0.550624\pi$
$938$	11.0931	−	15.2684i	0.362203	−	0.498530i
$939$	−9.84243	−	13.5469i	−0.321196	−	0.442088i
$940$	−2.86527	+	11.9094i	−0.0934547	+	0.388442i
$941$	−5.02173	−	31.7060i	−0.163704	−	1.03358i	−0.923549	−	0.383481i	$-0.874725\pi$
$941$	−5.02173	−	31.7060i	−0.163704	−	1.03358i	0.759845	−	0.650104i	$-0.225275\pi$
$942$	21.7797	+	67.0311i	0.709622	+	2.18399i
$943$	1.81236			0.0590186
$944$	0.0471315	−	0.0925008i	0.00153400	−	0.00301064i
$945$	−71.0629	+	17.0245i	−2.31168	+	0.553806i
$946$	2.28738	+	0.743216i	0.0743692	+	0.0241640i
$947$	−7.99192	−	2.59673i	−0.259702	−	0.0843824i	0.176272	−	0.984341i	$-0.443596\pi$
$947$	−7.99192	−	2.59673i	−0.259702	−	0.0843824i	−0.435974	+	0.899959i	$0.643596\pi$
$948$	8.32665	−	52.5724i	0.270437	−	1.70747i
$949$	−2.14951	+	26.3262i	−0.0697760	+	0.854585i
$950$	23.6783	−	32.5244i	0.768226	−	1.05523i
$951$	−27.3986	−	27.3986i	−0.888461	−	0.888461i
$952$	−0.995419	+	6.28483i	−0.0322617	+	0.203692i
$953$	20.1010	+	39.4504i	0.651134	+	1.27792i	0.946551	+	0.322555i	$0.104542\pi$
$953$	20.1010	+	39.4504i	0.651134	+	1.27792i	−0.295416	+	0.955369i	$0.595458\pi$
$954$	29.2491	+	57.4046i	0.946975	+	1.85854i
$955$	−35.8448	−	8.62385i	−1.15991	−	0.279061i
$956$	−13.0763	−	6.66270i	−0.422917	−	0.215487i
$957$		−	8.76076i		−	0.283195i
$958$	−3.70726	+	7.27592i	−0.119776	+	0.235074i
$959$	−9.33326	−	6.78101i	−0.301387	−	0.218970i
$960$	−0.567154	+	7.16224i	−0.0183048	+	0.231160i
$961$	0.608083	+	0.836955i	0.0196156	+	0.0269985i
$962$	24.3357	+	20.9082i	0.784613	+	0.674107i
$963$	11.9504	+	75.4518i	0.385096	+	2.43140i
$964$	−4.25062	+	26.8374i	−0.136903	+	0.864373i
$965$	5.03955	−	2.08460i	0.162229	−	0.0671058i
$966$	−22.6782	+	31.2139i	−0.729659	+	1.00429i
$967$	−6.17184	−	18.9950i	−0.198473	−	0.610837i	−0.999918	−	0.0127694i	$-0.995935\pi$
$967$	−6.17184	−	18.9950i	−0.198473	−	0.610837i	0.801445	−	0.598068i	$-0.204065\pi$
$968$		−	10.8579i		−	0.348986i
$969$	−31.7501	+	62.3131i	−1.01996	+	2.00178i
$970$	0.0808899	+	0.0948023i	0.00259722	+	0.00304392i
$971$	13.4652	−	41.4415i	0.432117	−	1.32992i	−0.463894	−	0.885891i	$-0.653548\pi$
$971$	13.4652	−	41.4415i	0.432117	−	1.32992i	0.896012	−	0.444030i	$-0.146452\pi$
$972$	27.7579	−	14.1433i	0.890334	−	0.453648i
$973$	26.5536	−	19.2923i	0.851270	−	0.618484i
$974$	6.91780			0.221661
$975$	−30.0730	−	49.5062i	−0.963108	−	1.58547i
$976$	−8.47783			−0.271369
$977$	20.4665	−	14.8698i	0.654783	−	0.475727i	−0.210114	−	0.977677i	$-0.567384\pi$
$977$	20.4665	−	14.8698i	0.654783	−	0.475727i	0.864897	+	0.501949i	$0.167384\pi$
$978$	−15.5618	+	7.92914i	−0.497612	+	0.253546i
$979$	−0.553147	+	1.70241i	−0.0176787	+	0.0544093i
$980$	0.255782	+	3.27017i	0.00817067	+	0.104462i
$981$	8.16546	−	16.0256i	0.260703	−	0.511659i
$982$			34.9946i			1.11672i
$983$	16.0580	+	49.4216i	0.512172	+	1.57630i	0.788370	+	0.615202i	$0.210926\pi$
$983$	16.0580	+	49.4216i	0.512172	+	1.57630i	−0.276198	+	0.961101i	$0.589074\pi$
$984$	0.670501	−	0.922865i	0.0213748	−	0.0294199i
$985$	1.07174	+	13.7022i	0.0341486	+	0.436589i
$986$	3.06092	−	19.3259i	0.0974796	−	0.615462i
$987$	6.47680	+	40.8929i	0.206159	+	1.30164i
$988$	2.19145	+	28.9278i	0.0697192	+	0.920316i
$989$	19.1445	+	26.3502i	0.608761	+	0.837888i
$990$	−6.00342	+	1.43823i	−0.190801	+	0.0457101i
$991$	−35.8657	−	26.0580i	−1.13931	−	0.827759i	−0.152289	−	0.988336i	$-0.548664\pi$
$991$	−35.8657	−	26.0580i	−1.13931	−	0.827759i	−0.987023	+	0.160577i	$0.948664\pi$
$992$	2.48518	−	4.87743i	0.0789044	−	0.154859i
$993$			50.3646i			1.59827i
$994$	−13.1421	−	6.69623i	−0.416842	−	0.212392i
$995$	8.51508	−	3.52226i	0.269946	−	0.111663i
$996$	−5.71791	−	11.2220i	−0.181179	−	0.355583i
$997$	12.1670	+	23.8790i	0.385332	+	0.756256i	0.999457	−	0.0329528i	$-0.0104911\pi$
$997$	12.1670	+	23.8790i	0.385332	+	0.756256i	−0.614125	+	0.789208i	$0.710491\pi$
$998$	−0.373271	+	2.35674i	−0.0118157	+	0.0746013i
$999$	87.4166	+	87.4166i	2.76574	+	2.76574i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	650.2.ba.b.73.1	✓	144
13.5	odd	4		650.2.bd.b.473.1	yes	144
25.12	odd	20		650.2.bd.b.437.1	yes	144
325.187	even	20	inner	650.2.ba.b.187.1	yes	144

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
650.2.ba.b.73.1	✓	144	1.1	even	1	trivial
650.2.ba.b.187.1	yes	144	325.187	even	20	inner
650.2.bd.b.437.1	yes	144	25.12	odd	20
650.2.bd.b.473.1	yes	144	13.5	odd	4

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:	\( N \)	\(=\)	\( 650 = 2 \cdot 5^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	650.ba (of order \(20\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(0.809017 - 0.587785i) q^{2} +(-2.86287 + 1.45871i) q^{3} +(0.309017 - 0.951057i) q^{4} +(-2.06627 + 0.854710i) q^{5} +(-1.45871 + 2.86287i) q^{6} -2.35225i q^{7} +(-0.309017 - 0.951057i) q^{8} +(4.30486 - 5.92513i) q^{9} +O(q^{10})\)	\(q+(0.809017 - 0.587785i) q^{2} +(-2.86287 + 1.45871i) q^{3} +(0.309017 - 0.951057i) q^{4} +(-2.06627 + 0.854710i) q^{5} +(-1.45871 + 2.86287i) q^{6} -2.35225i q^{7} +(-0.309017 - 0.951057i) q^{8} +(4.30486 - 5.92513i) q^{9} +(-1.16926 + 1.90600i) q^{10} +(-0.0589691 + 0.372316i) q^{11} +(0.502636 + 3.17352i) q^{12} +(-2.34964 + 2.73481i) q^{13} +(-1.38262 - 1.90301i) q^{14} +(4.66870 - 5.46101i) q^{15} +(-0.809017 - 0.587785i) q^{16} +(1.22811 - 2.41030i) q^{17} -7.32387i q^{18} +(7.16915 + 3.65286i) q^{19} +(0.174366 + 2.22926i) q^{20} +(3.43124 + 6.73419i) q^{21} +(0.171135 + 0.335871i) q^{22} +(-0.798580 + 5.04203i) q^{23} +(2.27199 + 2.27199i) q^{24} +(3.53894 - 3.53212i) q^{25} +(-0.293413 + 3.59359i) q^{26} +(-2.17333 + 13.7219i) q^{27} +(-2.23712 - 0.726884i) q^{28} +(6.87916 + 2.23517i) q^{29} +(0.567154 - 7.16224i) q^{30} +(-2.48518 + 4.87743i) q^{31} -1.00000 q^{32} +(-0.374279 - 1.15191i) q^{33} +(-0.423178 - 2.67184i) q^{34} +(2.01049 + 4.86038i) q^{35} +(-4.30486 - 5.92513i) q^{36} +(5.23039 - 7.19902i) q^{37} +(7.94706 - 1.25869i) q^{38} +(2.73742 - 11.2569i) q^{39} +(1.45139 + 1.70102i) q^{40} +(-0.0555382 - 0.350654i) q^{41} +(6.73419 + 3.43124i) q^{42} +(4.51155 - 4.51155i) q^{43} +(0.335871 + 0.171135i) q^{44} +(-3.83073 + 15.9223i) q^{45} +(2.31757 + 4.54848i) q^{46} +(5.20991 + 1.69280i) q^{47} +(3.17352 + 0.502636i) q^{48} +1.46693 q^{49} +(0.786932 - 4.93769i) q^{50} +8.69184i q^{51} +(1.87488 + 3.07974i) q^{52} +(-7.83802 + 3.99367i) q^{53} +(6.30725 + 12.3787i) q^{54} +(-0.196376 - 0.819707i) q^{55} +(-2.23712 + 0.726884i) q^{56} -25.8528 q^{57} +(6.87916 - 2.23517i) q^{58} +(0.0162404 + 0.102538i) q^{59} +(-3.75102 - 6.12774i) q^{60} +(6.85871 - 4.98314i) q^{61} +(0.856334 + 5.40668i) q^{62} +(-13.9374 - 10.1261i) q^{63} +(-0.809017 + 0.587785i) q^{64} +(2.51751 - 7.65912i) q^{65} +(-0.979875 - 0.711921i) q^{66} +(2.47933 + 7.63060i) q^{67} +(-1.91283 - 1.91283i) q^{68} +(-5.06861 - 15.5996i) q^{69} +(4.48338 + 2.75039i) q^{70} +(5.58704 - 2.84674i) q^{71} +(-6.96541 - 2.26320i) q^{72} +(5.92676 - 4.30604i) q^{73} -8.89847i q^{74} +(-4.97920 + 15.2743i) q^{75} +(5.68947 - 5.68947i) q^{76} +(0.875779 + 0.138710i) q^{77} +(-4.40199 - 10.7160i) q^{78} +(-15.7552 - 5.11917i) q^{79} +(2.17403 + 0.523047i) q^{80} +(-7.00461 - 21.5580i) q^{81} +(-0.251041 - 0.251041i) q^{82} +(-3.72800 + 1.21130i) q^{83} +(7.46490 - 1.18232i) q^{84} +(-0.477496 + 6.03001i) q^{85} +(0.998098 - 6.30174i) q^{86} +(-22.9546 + 3.63566i) q^{87} +(0.372316 - 0.0589691i) q^{88} +(4.69015 + 0.742847i) q^{89} +(6.25978 + 15.1331i) q^{90} +(6.43296 + 5.52693i) q^{91} +(4.54848 + 2.31757i) q^{92} -17.5886i q^{93} +(5.20991 - 1.69280i) q^{94} +(-17.9355 - 1.42025i) q^{95} +(2.86287 - 1.45871i) q^{96} +(0.0172223 - 0.0530049i) q^{97} +(1.18677 - 0.862241i) q^{98} +(1.95217 + 1.95217i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 144 q + 36 q^{2} - 36 q^{4} + 36 q^{8} - 20 q^{9}+O(q^{10}) \) 144 * q + 36 * q^2 - 36 * q^4 + 36 * q^8 - 20 * q^9	\( 144 q + 36 q^{2} - 36 q^{4} + 36 q^{8} - 20 q^{9} + 6 q^{13} + 8 q^{15} - 36 q^{16} - 6 q^{17} - 20 q^{19} - 6 q^{21} + 12 q^{23} + 2 q^{25} + 14 q^{26} - 24 q^{27} + 20 q^{29} + 12 q^{30} - 6 q^{31} - 144 q^{32} - 54 q^{33} + 6 q^{34} + 40 q^{35} + 20 q^{36} - 60 q^{37} + 20 q^{39} + 52 q^{41} + 6 q^{42} - 12 q^{43} - 6 q^{45} + 28 q^{46} + 50 q^{47} - 160 q^{49} - 22 q^{50} + 6 q^{52} + 20 q^{53} - 6 q^{54} - 32 q^{55} - 28 q^{57} + 20 q^{58} - 16 q^{59} - 12 q^{60} + 12 q^{61} + 6 q^{62} - 70 q^{63} - 36 q^{64} + 44 q^{65} - 16 q^{66} - 8 q^{67} - 6 q^{68} + 26 q^{69} + 10 q^{70} + 72 q^{71} - 52 q^{73} + 32 q^{75} - 56 q^{77} - 50 q^{78} - 20 q^{79} + 124 q^{81} - 22 q^{82} + 70 q^{83} - 6 q^{84} - 18 q^{85} - 8 q^{86} + 8 q^{87} + 28 q^{89} - 14 q^{90} - 26 q^{91} + 12 q^{92} + 50 q^{94} - 46 q^{95} + 28 q^{97} - 20 q^{98} + 40 q^{99}+O(q^{100}) \) 144 * q + 36 * q^2 - 36 * q^4 + 36 * q^8 - 20 * q^9 + 6 * q^13 + 8 * q^15 - 36 * q^16 - 6 * q^17 - 20 * q^19 - 6 * q^21 + 12 * q^23 + 2 * q^25 + 14 * q^26 - 24 * q^27 + 20 * q^29 + 12 * q^30 - 6 * q^31 - 144 * q^32 - 54 * q^33 + 6 * q^34 + 40 * q^35 + 20 * q^36 - 60 * q^37 + 20 * q^39 + 52 * q^41 + 6 * q^42 - 12 * q^43 - 6 * q^45 + 28 * q^46 + 50 * q^47 - 160 * q^49 - 22 * q^50 + 6 * q^52 + 20 * q^53 - 6 * q^54 - 32 * q^55 - 28 * q^57 + 20 * q^58 - 16 * q^59 - 12 * q^60 + 12 * q^61 + 6 * q^62 - 70 * q^63 - 36 * q^64 + 44 * q^65 - 16 * q^66 - 8 * q^67 - 6 * q^68 + 26 * q^69 + 10 * q^70 + 72 * q^71 - 52 * q^73 + 32 * q^75 - 56 * q^77 - 50 * q^78 - 20 * q^79 + 124 * q^81 - 22 * q^82 + 70 * q^83 - 6 * q^84 - 18 * q^85 - 8 * q^86 + 8 * q^87 + 28 * q^89 - 14 * q^90 - 26 * q^91 + 12 * q^92 + 50 * q^94 - 46 * q^95 + 28 * q^97 - 20 * q^98 + 40 * q^99

Introduction

L-functions

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