LMFDB - Embedded newform 309.2.i.b.100.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [309,2,Mod(13,309)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(309, base_ring=CyclotomicField(34))

chi = DirichletCharacter(H, H._module([0, 24]))

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

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

chi := DirichletCharacter("309.13");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 309 = 3 \cdot 103 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	309.i (of order $17$, degree $16$, 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:	$2.46737742246$
Analytic rank:	$0$
Dimension:	$160$
Relative dimension:	$10$ over $\Q(\zeta_{17})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{17}]$

Embedding invariants

Embedding label			100.8
Character	$\chi$	$=$	309.100
Dual form			309.2.i.b.34.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.953159 - 0.590171i) q^{2} +(-0.273663 - 0.961826i) q^{3} +(-0.331266 + 0.665272i) q^{4} +(-3.48587 + 1.35043i) q^{5} +(-0.828486 - 0.755265i) q^{6} +(-0.264645 + 2.85597i) q^{7} +(0.283755 + 3.06220i) q^{8} +(-0.850217 + 0.526432i) q^{9} +O(q^{10})$	\(q+(0.953159 - 0.590171i) q^{2} +(-0.273663 - 0.961826i) q^{3} +(-0.331266 + 0.665272i) q^{4} +(-3.48587 + 1.35043i) q^{5} +(-0.828486 - 0.755265i) q^{6} +(-0.264645 + 2.85597i) q^{7} +(0.283755 + 3.06220i) q^{8} +(-0.850217 + 0.526432i) q^{9} +(-2.52561 + 3.34444i) q^{10} +(-2.73195 + 1.69155i) q^{11} +(0.730531 + 0.136560i) q^{12} +(0.635585 - 6.85906i) q^{13} +(1.43327 + 2.87838i) q^{14} +(2.25284 + 2.98324i) q^{15} +(1.18195 + 1.56515i) q^{16} +(-3.36538 + 3.06795i) q^{17} +(-0.499707 + 1.00355i) q^{18} +(-0.242795 + 0.853336i) q^{19} +(0.256346 - 2.76641i) q^{20} +(2.81937 - 0.527032i) q^{21} +(-1.60568 + 3.22463i) q^{22} +(6.61282 + 4.09448i) q^{23} +(2.86765 - 1.11093i) q^{24} +(6.63260 - 6.04642i) q^{25} +(-3.44220 - 6.91288i) q^{26} +(0.739009 + 0.673696i) q^{27} +(-1.81233 - 1.12215i) q^{28} +(-0.972524 + 0.376758i) q^{29} +(3.90793 + 1.51394i) q^{30} +(0.378376 + 0.501051i) q^{31} +(-3.68501 - 1.42758i) q^{32} +(2.37461 + 2.16474i) q^{33} +(-1.39713 + 4.91039i) q^{34} +(-2.93429 - 10.3130i) q^{35} +(-0.0685725 - 0.740015i) q^{36} +(-3.90612 - 0.730179i) q^{37} +(0.272192 + 0.956655i) q^{38} +(-6.77115 + 1.26575i) q^{39} +(-5.12444 - 10.2913i) q^{40} +(7.57828 + 2.93584i) q^{41} +(2.37627 - 2.16626i) q^{42} +(-0.298389 + 0.0557786i) q^{43} +(-0.220340 - 2.37784i) q^{44} +(2.25284 - 2.98324i) q^{45} +8.71951 q^{46} -4.10162 q^{47} +(1.18195 - 1.56515i) q^{48} +(-1.20574 - 0.225393i) q^{49} +(2.75351 - 9.67757i) q^{50} +(3.87181 + 2.39732i) q^{51} +(4.35259 + 2.69501i) q^{52} +(-3.61905 + 12.7196i) q^{53} +(1.10199 + 0.205997i) q^{54} +(7.23890 - 9.58585i) q^{55} -8.82067 q^{56} +0.887204 q^{57} +(-0.704618 + 0.933065i) q^{58} +(-0.797466 - 8.60602i) q^{59} +(-2.73096 + 0.510504i) q^{60} +(-7.92436 + 7.22401i) q^{61} +(0.656358 + 0.254275i) q^{62} +(-1.27847 - 2.56752i) q^{63} +(-8.21074 + 1.53485i) q^{64} +(7.04714 + 24.7681i) q^{65} +(3.54095 + 0.661918i) q^{66} +(0.895858 + 9.66785i) q^{67} +(-0.926184 - 3.25520i) q^{68} +(2.12850 - 7.48089i) q^{69} +(-8.88325 - 8.09816i) q^{70} +(-1.72073 - 0.666614i) q^{71} +(-1.85330 - 2.45416i) q^{72} +(4.50861 + 1.74665i) q^{73} +(-4.15408 + 1.60930i) q^{74} +(-7.63070 - 4.72473i) q^{75} +(-0.487271 - 0.444206i) q^{76} +(-4.10803 - 8.25004i) q^{77} +(-5.70698 + 5.20260i) q^{78} +(8.46861 - 3.28076i) q^{79} +(-6.23377 - 3.85979i) q^{80} +(0.445738 - 0.895163i) q^{81} +(8.95596 - 1.67416i) q^{82} +(0.241176 - 2.60271i) q^{83} +(-0.583343 + 2.05024i) q^{84} +(7.58822 - 15.2392i) q^{85} +(-0.251493 + 0.229266i) q^{86} +(0.628519 + 0.832293i) q^{87} +(-5.95508 - 7.88580i) q^{88} +(-5.56322 - 11.1725i) q^{89} +(0.386691 - 4.17306i) q^{90} +(19.4211 + 3.63043i) q^{91} +(-4.91455 + 3.04296i) q^{92} +(0.378376 - 0.501051i) q^{93} +(-3.90949 + 2.42066i) q^{94} +(-0.306022 - 3.30250i) q^{95} +(-0.364633 + 3.93501i) q^{96} +(9.64205 + 8.78989i) q^{97} +(-1.28229 + 0.496760i) q^{98} +(1.43226 - 2.87637i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 160 q - q^{2} - 10 q^{3} - 17 q^{4} - 4 q^{5} - q^{6} - 12 q^{7} + 36 q^{8} - 10 q^{9}+O(q^{10}) $ 160 * q - q^2 - 10 * q^3 - 17 * q^4 - 4 * q^5 - q^6 - 12 * q^7 + 36 * q^8 - 10 * q^9	\( 160 q - q^{2} - 10 q^{3} - 17 q^{4} - 4 q^{5} - q^{6} - 12 q^{7} + 36 q^{8} - 10 q^{9} + 12 q^{10} + q^{11} + 17 q^{12} - 18 q^{13} + 31 q^{14} - 4 q^{15} - 39 q^{16} - 14 q^{17} - q^{18} - 11 q^{19} + 31 q^{20} + 5 q^{21} + 3 q^{23} - 15 q^{24} - 8 q^{25} - 33 q^{26} - 10 q^{27} - 2 q^{28} - 28 q^{29} + 12 q^{30} - 20 q^{31} - 46 q^{32} + 18 q^{33} + 5 q^{34} - 3 q^{35} - 17 q^{36} - 34 q^{37} - 14 q^{38} - 18 q^{39} - 56 q^{40} + 40 q^{41} + 14 q^{42} - 42 q^{43} - 26 q^{44} - 4 q^{45} + 112 q^{46} - 40 q^{47} - 39 q^{48} + 30 q^{49} - 10 q^{50} + 3 q^{51} - 58 q^{52} - 48 q^{53} - q^{54} - 64 q^{55} + 86 q^{56} + 6 q^{57} - 36 q^{58} + 76 q^{59} - 20 q^{60} - 28 q^{61} - 66 q^{62} - 12 q^{63} + 88 q^{64} - 14 q^{65} - 34 q^{66} - 84 q^{67} - 107 q^{68} - 14 q^{69} + 8 q^{70} + 41 q^{71} - 15 q^{72} - 32 q^{73} + 3 q^{74} - 42 q^{75} - 68 q^{76} + 93 q^{77} + 18 q^{78} - 100 q^{79} - 168 q^{80} - 10 q^{81} + 99 q^{82} - 28 q^{83} + 151 q^{84} + 15 q^{85} + 64 q^{86} - 11 q^{87} - 25 q^{88} - 19 q^{89} - 5 q^{90} + 122 q^{91} - 78 q^{92} - 20 q^{93} + 138 q^{94} - 15 q^{95} + 56 q^{96} + 161 q^{97} + 65 q^{98} + q^{99}+O(q^{100}) \) 160 * q - q^2 - 10 * q^3 - 17 * q^4 - 4 * q^5 - q^6 - 12 * q^7 + 36 * q^8 - 10 * q^9 + 12 * q^10 + q^11 + 17 * q^12 - 18 * q^13 + 31 * q^14 - 4 * q^15 - 39 * q^16 - 14 * q^17 - q^18 - 11 * q^19 + 31 * q^20 + 5 * q^21 + 3 * q^23 - 15 * q^24 - 8 * q^25 - 33 * q^26 - 10 * q^27 - 2 * q^28 - 28 * q^29 + 12 * q^30 - 20 * q^31 - 46 * q^32 + 18 * q^33 + 5 * q^34 - 3 * q^35 - 17 * q^36 - 34 * q^37 - 14 * q^38 - 18 * q^39 - 56 * q^40 + 40 * q^41 + 14 * q^42 - 42 * q^43 - 26 * q^44 - 4 * q^45 + 112 * q^46 - 40 * q^47 - 39 * q^48 + 30 * q^49 - 10 * q^50 + 3 * q^51 - 58 * q^52 - 48 * q^53 - q^54 - 64 * q^55 + 86 * q^56 + 6 * q^57 - 36 * q^58 + 76 * q^59 - 20 * q^60 - 28 * q^61 - 66 * q^62 - 12 * q^63 + 88 * q^64 - 14 * q^65 - 34 * q^66 - 84 * q^67 - 107 * q^68 - 14 * q^69 + 8 * q^70 + 41 * q^71 - 15 * q^72 - 32 * q^73 + 3 * q^74 - 42 * q^75 - 68 * q^76 + 93 * q^77 + 18 * q^78 - 100 * q^79 - 168 * q^80 - 10 * q^81 + 99 * q^82 - 28 * q^83 + 151 * q^84 + 15 * q^85 + 64 * q^86 - 11 * q^87 - 25 * q^88 - 19 * q^89 - 5 * q^90 + 122 * q^91 - 78 * q^92 - 20 * q^93 + 138 * q^94 - 15 * q^95 + 56 * q^96 + 161 * q^97 + 65 * q^98 + q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/309\mathbb{Z}\right)^\times$.

$n$	$104$	$211$
$\chi(n)$	$1$	$e\left(\frac{15}{17}\right)$

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 $

$2$	0.953159	−	0.590171i	0.673985	−	0.417314i	−0.146322	−	0.989237i	$-0.546744\pi$
$2$	0.953159	−	0.590171i	0.673985	−	0.417314i	0.820307	+	0.571923i	$0.193802\pi$
$3$	−0.273663	−	0.961826i	−0.157999	−	0.555310i
$3$	−0.273663	−	0.961826i	−0.157999	−	0.555310i
$4$	−0.331266	+	0.665272i	−0.165633	+	0.332636i
$5$	−3.48587	+	1.35043i	−1.55893	+	0.603933i	−0.977737	−	0.209833i	$-0.932708\pi$
$5$	−3.48587	+	1.35043i	−1.55893	+	0.603933i	−0.581193	+	0.813766i	$0.697414\pi$
$6$	−0.828486	−	0.755265i	−0.338228	−	0.308336i
$7$	−0.264645	+	2.85597i	−0.100026	+	1.07946i	0.786754	+	0.617266i	$0.211760\pi$
$7$	−0.264645	+	2.85597i	−0.100026	+	1.07946i	−0.886781	+	0.462191i	$0.847064\pi$
$8$	0.283755	+	3.06220i	0.100323	+	1.08265i
$9$	−0.850217	+	0.526432i	−0.283406	+	0.175477i
$10$	−2.52561	+	3.34444i	−0.798667	+	1.05761i
$11$	−2.73195	+	1.69155i	−0.823713	+	0.510022i	−0.872400	−	0.488792i	$-0.837438\pi$
$11$	−2.73195	+	1.69155i	−0.823713	+	0.510022i	0.0486867	+	0.998814i	$0.484496\pi$
$12$	0.730531	+	0.136560i	0.210886	+	0.0394215i
$13$	0.635585	−	6.85906i	0.176280	−	1.90236i	−0.206381	−	0.978472i	$-0.566169\pi$
$13$	0.635585	−	6.85906i	0.176280	−	1.90236i	0.382661	−	0.923889i	$-0.375008\pi$
$14$	1.43327	+	2.87838i	0.383056	+	0.769281i
$15$	2.25284	+	2.98324i	0.581680	+	0.770269i
$16$	1.18195	+	1.56515i	0.295487	+	0.391289i
$17$	−3.36538	+	3.06795i	−0.816224	+	0.744086i	−0.969761	−	0.244057i	$-0.921522\pi$
$17$	−3.36538	+	3.06795i	−0.816224	+	0.744086i	0.153537	+	0.988143i	$0.450933\pi$
$18$	−0.499707	+	1.00355i	−0.117782	+	0.236538i
$19$	−0.242795	+	0.853336i	−0.0557010	+	0.195769i	−0.984682	−	0.174358i	$-0.944215\pi$
$19$	−0.242795	+	0.853336i	−0.0557010	+	0.195769i	0.928981	+	0.370126i	$0.120686\pi$
$20$	0.256346	−	2.76641i	0.0573206	−	0.618588i
$21$	2.81937	−	0.527032i	0.615238	−	0.115008i
$22$	−1.60568	+	3.22463i	−0.342332	+	0.687494i
$23$	6.61282	+	4.09448i	1.37887	+	0.853759i	0.997500	−	0.0706646i	$-0.0225120\pi$
$23$	6.61282	+	4.09448i	1.37887	+	0.853759i	0.381368	+	0.924423i	$0.375453\pi$
$24$	2.86765	−	1.11093i	0.585357	−	0.226769i
$25$	6.63260	−	6.04642i	1.32652	−	1.20928i
$26$	−3.44220	−	6.91288i	−0.675072	−	1.35573i
$27$	0.739009	+	0.673696i	0.142222	+	0.129653i
$28$	−1.81233	−	1.12215i	−0.342499	−	0.212066i
$29$	−0.972524	+	0.376758i	−0.180593	+	0.0699621i	−0.449841	−	0.893109i	$-0.648519\pi$
$29$	−0.972524	+	0.376758i	−0.180593	+	0.0699621i	0.269247	+	0.963071i	$0.413225\pi$
$30$	3.90793	+	1.51394i	0.713488	+	0.276407i
$31$	0.378376	+	0.501051i	0.0679583	+	0.0899914i	0.830727	−	0.556680i	$-0.187925\pi$
$31$	0.378376	+	0.501051i	0.0679583	+	0.0899914i	−0.762769	+	0.646672i	$0.776160\pi$
$32$	−3.68501	−	1.42758i	−0.651424	−	0.252363i
$33$	2.37461	+	2.16474i	0.413367	+	0.376833i
$34$	−1.39713	+	4.91039i	−0.239605	+	0.842125i
$35$	−2.93429	−	10.3130i	−0.495985	−	1.74321i
$36$	−0.0685725	−	0.740015i	−0.0114288	−	0.123336i
$37$	−3.90612	−	0.730179i	−0.642161	−	0.120041i	−0.147410	−	0.989075i	$-0.547094\pi$
$37$	−3.90612	−	0.730179i	−0.642161	−	0.120041i	−0.494751	+	0.869035i	$0.664741\pi$
$38$	0.272192	+	0.956655i	0.0441554	+	0.155190i
$39$	−6.77115	+	1.26575i	−1.08425	+	0.202682i
$40$	−5.12444	−	10.2913i	−0.810245	−	1.62719i
$41$	7.57828	+	2.93584i	1.18353	+	0.458501i	0.870941	−	0.491388i	$-0.163510\pi$
$41$	7.57828	+	2.93584i	1.18353	+	0.458501i	0.312587	+	0.949889i	$0.398804\pi$
$42$	2.37627	−	2.16626i	0.366667	−	0.334261i
$43$	−0.298389	+	0.0557786i	−0.0455039	+	0.00850615i	−0.206452	−	0.978457i	$-0.566192\pi$
$43$	−0.298389	+	0.0557786i	−0.0455039	+	0.00850615i	0.160948	+	0.986963i	$0.448545\pi$
$44$	−0.220340	−	2.37784i	−0.0332175	−	0.358473i
$45$	2.25284	−	2.98324i	0.335833	−	0.444715i
$46$	8.71951			1.28562
$47$	−4.10162			−0.598282			−0.299141	−	0.954209i	$-0.596700\pi$
$47$	−4.10162			−0.598282			−0.299141	+	0.954209i	$0.596700\pi$
$48$	1.18195	−	1.56515i	0.170600	−	0.225911i
$49$	−1.20574	−	0.225393i	−0.172249	−	0.0321989i
$50$	2.75351	−	9.67757i	0.389404	−	1.36861i
$51$	3.87181	+	2.39732i	0.542162	+	0.335692i
$52$	4.35259	+	2.69501i	0.603596	+	0.373731i
$53$	−3.61905	+	12.7196i	−0.497114	+	1.74718i	0.153876	+	0.988090i	$0.450824\pi$
$53$	−3.61905	+	12.7196i	−0.497114	+	1.74718i	−0.650991	+	0.759086i	$0.725646\pi$
$54$	1.10199	+	0.205997i	0.149962	+	0.0280327i
$55$	7.23890	−	9.58585i	0.976093	−	1.29256i
$56$	−8.82067			−1.17871
$57$	0.887204			0.117513
$58$	−0.704618	+	0.933065i	−0.0925209	+	0.122517i
$59$	−0.797466	−	8.60602i	−0.103821	−	1.12041i	−0.875110	−	0.483924i	$-0.839211\pi$
$59$	−0.797466	−	8.60602i	−0.103821	−	1.12041i	0.771289	−	0.636485i	$-0.219612\pi$
$60$	−2.73096	+	0.510504i	−0.352565	+	0.0659058i
$61$	−7.92436	+	7.22401i	−1.01461	+	0.924940i	−0.997190	−	0.0749084i	$-0.976134\pi$
$61$	−7.92436	+	7.22401i	−1.01461	+	0.924940i	−0.0174203	+	0.999848i	$0.505545\pi$
$62$	0.656358	+	0.254275i	0.0833576	+	0.0322929i
$63$	−1.27847	−	2.56752i	−0.161072	−	0.323477i
$64$	−8.21074	+	1.53485i	−1.02634	+	0.191857i
$65$	7.04714	+	24.7681i	0.874090	+	3.07211i
$66$	3.54095	+	0.661918i	0.435861	+	0.0814765i
$67$	0.895858	+	9.66785i	0.109447	+	1.18112i	0.856426	+	0.516269i	$0.172680\pi$
$67$	0.895858	+	9.66785i	0.109447	+	1.18112i	−0.746980	+	0.664847i	$0.768497\pi$
$68$	−0.926184	−	3.25520i	−0.112316	−	0.394751i
$69$	2.12850	−	7.48089i	0.256241	−	0.900593i
$70$	−8.88325	−	8.09816i	−1.06175	−	0.967915i
$71$	−1.72073	−	0.666614i	−0.204213	−	0.0791126i	0.256963	−	0.966421i	$-0.417278\pi$
$71$	−1.72073	−	0.666614i	−0.204213	−	0.0791126i	−0.461176	+	0.887309i	$0.652572\pi$
$72$	−1.85330	−	2.45416i	−0.218413	−	0.289226i
$73$	4.50861	+	1.74665i	0.527693	+	0.204430i	0.610326	−	0.792151i	$-0.291039\pi$
$73$	4.50861	+	1.74665i	0.527693	+	0.204430i	−0.0826323	+	0.996580i	$0.526333\pi$
$74$	−4.15408	+	1.60930i	−0.482902	+	0.187077i
$75$	−7.63070	−	4.72473i	−0.881117	−	0.545564i
$76$	−0.487271	−	0.444206i	−0.0558938	−	0.0509539i
$77$	−4.10803	−	8.25004i	−0.468153	−	0.940179i
$78$	−5.70698	+	5.20260i	−0.646188	+	0.589078i
$79$	8.46861	−	3.28076i	0.952793	−	0.369114i	0.165858	−	0.986150i	$-0.446961\pi$
$79$	8.46861	−	3.28076i	0.952793	−	0.369114i	0.786935	+	0.617036i	$0.211667\pi$
$80$	−6.23377	−	3.85979i	−0.696956	−	0.431537i
$81$	0.445738	−	0.895163i	0.0495265	−	0.0994626i
$82$	8.95596	−	1.67416i	0.989020	−	0.184880i
$83$	0.241176	−	2.60271i	0.0264725	−	0.285684i	−0.972199	−	0.234156i	$-0.924767\pi$
$83$	0.241176	−	2.60271i	0.0264725	−	0.285684i	0.998672	−	0.0515280i	$-0.0164091\pi$
$84$	−0.583343	+	2.05024i	−0.0636480	+	0.223699i
$85$	7.58822	−	15.2392i	0.823058	−	1.65292i
$86$	−0.251493	+	0.229266i	−0.0271192	+	0.0247224i
$87$	0.628519	+	0.832293i	0.0673843	+	0.0892312i
$88$	−5.95508	−	7.88580i	−0.634814	−	0.840629i
$89$	−5.56322	−	11.1725i	−0.589700	−	1.18428i	−0.966184	−	0.257855i	$-0.916984\pi$
$89$	−5.56322	−	11.1725i	−0.589700	−	1.18428i	0.376483	−	0.926423i	$-0.377133\pi$
$90$	0.386691	−	4.17306i	0.0407608	−	0.439879i
$91$	19.4211	+	3.63043i	2.03588	+	0.380573i
$92$	−4.91455	+	3.04296i	−0.512377	+	0.317251i
$93$	0.378376	−	0.501051i	0.0392358	−	0.0519566i
$94$	−3.90949	+	2.42066i	−0.403233	+	0.249672i
$95$	−0.306022	−	3.30250i	−0.0313972	−	0.338829i
$96$	−0.364633	+	3.93501i	−0.0372152	+	0.401616i
$97$	9.64205	+	8.78989i	0.979002	+	0.892478i	0.994215	−	0.107406i	$-0.0342544\pi$
$97$	9.64205	+	8.78989i	0.979002	+	0.892478i	−0.0152131	+	0.999884i	$0.504843\pi$
$98$	−1.28229	+	0.496760i	−0.129530	+	0.0501804i
$99$	1.43226	−	2.87637i	0.143948	−	0.289086i
$100$	1.82536	+	6.41546i	0.182536	+	0.641546i
$101$	−7.33789	+	4.54343i	−0.730147	+	0.452088i	−0.840505	−	0.541804i	$-0.817742\pi$
$101$	−7.33789	+	4.54343i	−0.730147	+	0.452088i	0.110358	+	0.993892i	$0.464800\pi$
$102$	5.10528			0.505498
$103$	9.68140	+	3.04474i	0.953937	+	0.300007i
$103$	9.68140	+	3.04474i	0.953937	+	0.300007i
$104$	21.1842			2.07728
$105$	−9.11626	+	5.64455i	−0.889656	+	0.550852i
$106$	4.05723	+	14.2597i	0.394073	+	1.38502i
$107$	1.83851	−	3.69222i	0.177735	−	0.356940i	−0.788324	−	0.615260i	$-0.789051\pi$
$107$	1.83851	−	3.69222i	0.177735	−	0.356940i	0.966059	+	0.258320i	$0.0831688\pi$
$108$	−0.693000	+	0.268470i	−0.0666839	+	0.0258335i
$109$	7.15958	+	6.52682i	0.685763	+	0.625156i	0.939674	−	0.342072i	$-0.111129\pi$
$109$	7.15958	+	6.52682i	0.685763	+	0.625156i	−0.253911	+	0.967228i	$0.581717\pi$
$110$	1.24253	−	13.4090i	0.118471	−	1.27850i
$111$	0.366654	+	3.95682i	0.0348012	+	0.375565i
$112$	−4.78284	+	2.96141i	−0.451936	+	0.279827i
$113$	2.33446	−	3.09132i	0.219607	−	0.290807i	−0.674855	−	0.737950i	$-0.735794\pi$
$113$	2.33446	−	3.09132i	0.219607	−	0.290807i	0.894462	+	0.447143i	$0.147559\pi$
$114$	0.845647	−	0.523602i	0.0792021	−	0.0490398i
$115$	−28.5808	−	5.34268i	−2.66517	−	0.498207i
$116$	0.0715178	−	0.771800i	0.00664026	−	0.0716599i
$117$	3.07044	+	6.16628i	0.283863	+	0.570073i
$118$	−5.83914	−	7.73227i	−0.537536	−	0.711813i
$119$	−7.87135	−	10.4233i	−0.721565	−	0.955507i
$120$	−8.49603	+	7.74516i	−0.775578	+	0.707033i
$121$	−0.300924	+	0.604336i	−0.0273567	+	0.0549397i
$122$	−3.28978	+	11.5624i	−0.297842	+	1.04681i
$123$	0.749873	−	8.09241i	0.0676137	−	0.729668i
$124$	−0.458679	+	0.0857419i	−0.0411906	+	0.00769985i
$125$	−6.62358	+	13.3019i	−0.592431	+	1.18976i
$126$	−2.73386	−	1.69273i	−0.243552	−	0.150801i
$127$	5.39427	−	2.08975i	0.478664	−	0.185436i	−0.109808	−	0.993953i	$-0.535024\pi$
$127$	5.39427	−	2.08975i	0.478664	−	0.185436i	0.588473	+	0.808517i	$0.299730\pi$
$128$	−1.07938	+	0.983981i	−0.0954042	+	0.0869725i
$129$	0.135307	+	0.271734i	0.0119131	+	0.0239248i
$130$	21.3345	+	19.4490i	1.87116	+	1.70579i
$131$	11.6263	+	7.19872i	1.01580	+	0.628955i	0.930077	−	0.367364i	$-0.119740\pi$
$131$	11.6263	+	7.19872i	1.01580	+	0.628955i	0.0857198	+	0.996319i	$0.472681\pi$
$132$	−2.22677	+	0.862656i	−0.193816	+	0.0750846i
$133$	−2.37285	−	0.919247i	−0.205752	−	0.0797088i
$134$	6.55958	+	8.68629i	0.566662	+	0.750381i
$135$	−3.48587	−	1.35043i	−0.300016	−	0.116227i
$136$	−10.3496	−	9.43493i	−0.887473	−	0.809038i
$137$	1.22788	−	4.31555i	0.104905	−	0.368703i	−0.891541	−	0.452941i	$-0.850375\pi$
$137$	1.22788	−	4.31555i	0.104905	−	0.368703i	0.996446	+	0.0842379i	$0.0268456\pi$
$138$	−2.38621	−	8.38665i	−0.203128	−	0.713919i
$139$	−1.03239	−	11.1413i	−0.0875661	−	0.944989i	−0.920274	−	0.391275i	$-0.872034\pi$
$139$	−1.03239	−	11.1413i	−0.0875661	−	0.944989i	0.832708	−	0.553713i	$-0.186790\pi$
$140$	7.83296	+	1.46423i	0.662006	+	0.123750i
$141$	1.12246	+	3.94504i	0.0945282	+	0.332232i
$142$	−2.03355	+	0.380136i	−0.170651	+	0.0319003i
$143$	9.86606	+	19.8137i	0.825041	+	1.65691i
$144$	−1.82886	−	0.708505i	−0.152405	−	0.0590421i
$145$	2.88131	−	2.62666i	0.239280	−	0.218132i
$146$	5.32825	−	0.996022i	0.440969	−	0.0824314i
$147$	0.113179	+	1.22140i	0.00933485	+	0.100739i
$148$	1.77973	−	2.35675i	0.146293	−	0.193723i
$149$	14.4962			1.18757			0.593786	−	0.804623i	$-0.297633\pi$
$149$	14.4962			1.18757			0.593786	+	0.804623i	$0.297633\pi$
$150$	−10.0617			−0.821531
$151$	−7.86393	+	10.4135i	−0.639958	+	0.847441i	−0.996213	−	0.0869475i	$-0.972289\pi$
$151$	−7.86393	+	10.4135i	−0.639958	+	0.847441i	0.356255	+	0.934389i	$0.384053\pi$
$152$	−2.68198	−	0.501349i	−0.217537	−	0.0406648i
$153$	1.24624	−	4.38006i	0.100752	−	0.354107i
$154$	−8.78454	−	5.43916i	−0.707878	−	0.438300i
$155$	−1.99561	−	1.23563i	−0.160291	−	0.0992480i
$156$	1.40099	−	4.92396i	0.112169	−	0.394232i
$157$	−3.75878	−	0.702638i	−0.299983	−	0.0560766i	0.0316060	−	0.999500i	$-0.489938\pi$
$157$	−3.75878	−	0.702638i	−0.299983	−	0.0560766i	−0.331589	+	0.943424i	$0.607585\pi$
$158$	6.13573	−	8.12502i	0.488132	−	0.646392i
$159$	13.2245			1.04877
$160$	14.7733			1.16794
$161$	−13.4438	+	17.8025i	−1.05952	+	1.40303i
$162$	−0.103440	−	1.11630i	−0.00812701	−	0.0877044i
$163$	−16.4590	+	3.07673i	−1.28917	+	0.240988i	−0.783313	−	0.621628i	$-0.786472\pi$
$163$	−16.4590	+	3.07673i	−1.28917	+	0.240988i	−0.505860	+	0.862616i	$0.668825\pi$
$164$	−4.46356	+	4.06908i	−0.348546	+	0.317741i
$165$	−11.2009	−	4.33927i	−0.871992	−	0.337811i
$166$	−1.30616	−	2.62313i	−0.101378	−	0.203594i
$167$	−3.47541	+	0.649667i	−0.268935	+	0.0502727i	−0.316490	−	0.948596i	$-0.602504\pi$
$167$	−3.47541	+	0.649667i	−0.268935	+	0.0502727i	0.0475544	+	0.998869i	$0.484857\pi$
$168$	2.41389	+	8.48395i	0.186236	+	0.654551i
$169$	−33.8641	−	6.33029i	−2.60493	−	0.486945i
$170$	−1.76095	−	19.0037i	−0.135059	−	1.45752i
$171$	−0.242795	−	0.853336i	−0.0185670	−	0.0652562i
$172$	0.0617383	−	0.216988i	0.00470750	−	0.0165451i
$173$	−8.82170	−	8.04204i	−0.670701	−	0.611425i	0.264987	−	0.964252i	$-0.414632\pi$
$173$	−8.82170	−	8.04204i	−0.670701	−	0.611425i	−0.935689	+	0.352827i	$0.885220\pi$
$174$	1.09027	+	0.422374i	0.0826535	+	0.0320201i
$175$	15.5131	+	20.5427i	1.17268	+	1.55288i
$176$	−5.87656	−	2.27659i	−0.442963	−	0.171605i
$177$	−8.05926	+	3.12217i	−0.605771	+	0.234677i
$178$	−11.8963	−	7.36588i	−0.891665	−	0.552096i
$179$	7.11273	+	6.48411i	0.531630	+	0.484645i	0.894421	−	0.447225i	$-0.147588\pi$
$179$	7.11273	+	6.48411i	0.531630	+	0.484645i	−0.362791	+	0.931871i	$0.618176\pi$
$180$	1.23838	+	2.48700i	0.0923032	+	0.185370i
$181$	−2.75280	+	2.50951i	−0.204614	+	0.186530i	−0.769516	−	0.638628i	$-0.779502\pi$
$181$	−2.75280	+	2.50951i	−0.204614	+	0.186530i	0.564902	+	0.825158i	$0.308914\pi$
$182$	20.6540	−	8.00139i	1.53097	−	0.593103i
$183$	9.11684	+	5.64491i	0.673937	+	0.417284i
$184$	−10.6617	+	21.4116i	−0.785993	+	1.57849i
$185$	14.6023	−	2.72964i	1.07358	−	0.200687i
$186$	0.0649468	−	0.700888i	0.00476213	−	0.0513916i
$187$	4.00445	−	14.0742i	0.292834	−	1.02921i
$188$	1.35873	−	2.72869i	0.0990954	−	0.199010i
$189$	−2.11963	+	1.93230i	−0.154181	+	0.140554i
$190$	−2.24073	−	2.96720i	−0.162559	−	0.215264i
$191$	−3.19709	−	4.23363i	−0.231333	−	0.306335i	0.667513	−	0.744598i	$-0.267359\pi$
$191$	−3.19709	−	4.23363i	−0.231333	−	0.306335i	−0.898847	+	0.438263i	$0.855594\pi$
$192$	3.72324	+	7.47727i	0.268701	+	0.539625i
$193$	−0.672083	+	7.25293i	−0.0483776	+	0.522078i	0.936720	+	0.350080i	$0.113846\pi$
$193$	−0.672083	+	7.25293i	−0.0483776	+	0.522078i	−0.985097	+	0.171997i	$0.944978\pi$
$194$	14.3780	+	2.68771i	1.03228	+	0.192966i
$195$	21.8941	−	13.5562i	1.56787	−	0.970783i
$196$	0.549370	−	0.727483i	0.0392407	−	0.0519631i
$197$	−17.0769	+	10.5736i	−1.21668	+	0.753335i	−0.976106	−	0.217296i	$-0.930276\pi$
$197$	−17.0769	+	10.5736i	−1.21668	+	0.753335i	−0.240573	+	0.970631i	$0.577335\pi$
$198$	−0.332377	−	3.58692i	−0.0236210	−	0.254911i
$199$	0.394490	−	4.25722i	0.0279646	−	0.301786i	−0.970252	−	0.242096i	$-0.922165\pi$
$199$	0.394490	−	4.25722i	0.0279646	−	0.301786i	0.998217	−	0.0596904i	$-0.0190113\pi$
$200$	20.3974	+	18.5947i	1.44231	+	1.31484i
$201$	9.05362	−	3.50739i	0.638593	−	0.247392i
$202$	−4.31278	+	8.66122i	−0.303446	+	0.609401i
$203$	−0.818637	−	2.87721i	−0.0574570	−	0.201941i
$204$	−2.87747	+	1.78166i	−0.201463	+	0.124741i
$205$	−30.3816			−2.12194
$206$	11.0248	−	2.81156i	0.768137	−	0.195891i
$207$	−7.77780			−0.540594
$208$	11.4867	−	7.11227i	0.796460	−	0.493147i
$209$	−0.780157	−	2.74197i	−0.0539646	−	0.189666i
$210$	−5.35800	+	10.7603i	−0.369737	+	0.742532i
$211$	21.5109	−	8.33338i	1.48087	−	0.573693i	0.520858	−	0.853643i	$-0.325612\pi$
$211$	21.5109	−	8.33338i	1.48087	−	0.573693i	0.960015	+	0.279950i	$0.0903179\pi$
$212$	−7.26315	−	6.62124i	−0.498835	−	0.454749i
$213$	−0.170267	+	1.83747i	−0.0116665	+	0.125901i
$214$	−0.426651	−	4.60430i	−0.0291653	−	0.314744i
$215$	0.964821	−	0.597392i	0.0658003	−	0.0407418i
$216$	−1.85330	+	2.45416i	−0.126101	+	0.166984i
$217$	−1.53112	+	0.948032i	−0.103939	+	0.0643566i
$218$	10.6762	+	1.99572i	0.723081	+	0.135167i
$219$	0.446129	−	4.81449i	0.0301466	−	0.325333i
$220$	3.97920	+	7.99131i	0.268278	+	0.538774i
$221$	18.9042	+	25.0333i	1.27164	+	1.68392i
$222$	2.68468	+	3.55510i	0.180184	+	0.238602i
$223$	−17.7363	+	16.1688i	−1.18771	+	1.08274i	−0.192876	+	0.981223i	$0.561781\pi$
$223$	−17.7363	+	16.1688i	−1.18771	+	1.08274i	−0.994834	+	0.101517i	$0.967630\pi$
$224$	5.05236	−	10.1465i	0.337575	−	0.677941i
$225$	−2.45612	+	8.63238i	−0.163742	+	0.575492i
$226$	0.400701	−	4.32425i	0.0266542	−	0.287645i
$227$	20.7807	−	3.88458i	1.37926	−	0.257829i	0.558692	−	0.829375i	$-0.311304\pi$
$227$	20.7807	−	3.88458i	1.37926	−	0.257829i	0.820569	+	0.571547i	$0.193656\pi$
$228$	−0.293901	+	0.590232i	−0.0194641	+	0.0390891i
$229$	0.129857	+	0.0804040i	0.00858119	+	0.00531325i	0.530716	−	0.847550i	$-0.321923\pi$
$229$	0.129857	+	0.0804040i	0.00858119	+	0.00531325i	−0.522135	+	0.852863i	$0.674864\pi$
$230$	−30.3951	+	11.7751i	−2.00420	+	0.776430i
$231$	−6.81088	+	6.20894i	−0.448123	+	0.408518i
$232$	−1.42967	−	2.87116i	−0.0938623	−	0.188501i
$233$	−17.8841	−	16.3035i	−1.17163	−	1.06808i	−0.996505	−	0.0835314i	$-0.973380\pi$
$233$	−17.8841	−	16.3035i	−1.17163	−	1.06808i	−0.175121	−	0.984547i	$-0.556032\pi$
$234$	6.56578	+	4.06536i	0.429219	+	0.265761i
$235$	14.2977	−	5.53897i	0.932680	−	0.361322i
$236$	5.98952	+	2.32035i	0.389885	+	0.151042i
$237$	−5.47306	−	7.24751i	−0.355514	−	0.470776i
$238$	−13.6542	−	5.28967i	−0.885071	−	0.342878i
$239$	−7.30260	−	6.65720i	−0.472366	−	0.430619i	0.402180	−	0.915561i	$-0.368253\pi$
$239$	−7.30260	−	6.65720i	−0.472366	−	0.430619i	−0.874546	+	0.484942i	$0.838841\pi$
$240$	−2.00649	+	7.05208i	−0.129518	+	0.455210i
$241$	6.76994	+	23.7939i	0.436090	+	1.53270i	0.799266	+	0.600978i	$0.205222\pi$
$241$	6.76994	+	23.7939i	0.436090	+	1.53270i	−0.363175	+	0.931721i	$0.618307\pi$
$242$	0.0698336	+	0.753625i	0.00448908	+	0.0484449i
$243$	−0.982973	−	0.183750i	−0.0630578	−	0.0117875i
$244$	−2.18086	−	7.66493i	−0.139615	−	0.490697i
$245$	4.50745	−	0.842588i	0.287970	−	0.0538310i
$246$	−4.06116	−	8.15591i	−0.258930	−	0.520002i
$247$	5.69876	+	2.20771i	0.362604	+	0.140473i
$248$	−1.42695	+	1.30084i	−0.0906117	+	0.0826035i
$249$	−2.56935	+	0.480295i	−0.162826	+	0.0304374i
$250$	1.53710	+	16.5879i	0.0972145	+	1.04911i
$251$	11.0711	−	14.6604i	0.698799	−	0.925359i	−0.300800	−	0.953687i	$-0.597254\pi$
$251$	11.0711	−	14.6604i	0.698799	−	0.925359i	0.999599	+	0.0283283i	$0.00901837\pi$
$252$	2.13161			0.134279
$253$	−24.9919			−1.57123
$254$	3.90829	−	5.17541i	0.245228	−	0.324734i
$255$	−16.7341	−	3.12814i	−1.04793	−	0.195892i
$256$	4.12369	−	14.4933i	0.257731	−	0.905830i
$257$	−1.34577	−	0.833266i	−0.0839469	−	0.0519777i	0.483817	−	0.875169i	$-0.339250\pi$
$257$	−1.34577	−	0.833266i	−0.0839469	−	0.0519777i	−0.567764	+	0.823192i	$0.692191\pi$
$258$	0.289339	+	0.179151i	0.0180134	+	0.0111535i
$259$	3.11911	−	10.9625i	0.193812	−	0.681178i
$260$	−18.8120	−	3.51658i	−1.16667	−	0.218089i
$261$	0.628519	−	0.832293i	0.0389043	−	0.0515177i
$262$	15.3302			0.947104
$263$	−12.8181			−0.790397			−0.395198	−	0.918596i	$-0.629324\pi$
$263$	−12.8181			−0.790397			−0.395198	+	0.918596i	$0.629324\pi$
$264$	−5.95508	+	7.88580i	−0.366510	+	0.485337i
$265$	−4.56149	−	49.2263i	−0.280210	−	3.02395i
$266$	−2.80422	+	0.524199i	−0.171938	+	0.0321407i
$267$	−9.22351	+	8.40834i	−0.564469	+	0.514582i
$268$	−6.72852	−	2.60664i	−0.411010	−	0.159226i
$269$	12.5120	+	25.1275i	0.762872	+	1.53205i	0.844600	+	0.535398i	$0.179838\pi$
$269$	12.5120	+	25.1275i	0.762872	+	1.53205i	−0.0817283	+	0.996655i	$0.526044\pi$
$270$	−4.11958	+	0.770083i	−0.250710	+	0.0468658i
$271$	3.29350	+	11.5754i	0.200066	+	0.703158i	0.995299	+	0.0968542i	$0.0308780\pi$
$271$	3.29350	+	11.5754i	0.200066	+	0.703158i	−0.795233	+	0.606304i	$0.792651\pi$
$272$	−8.77952	−	1.64118i	−0.532336	−	0.0995109i
$273$	−1.82299	−	19.6732i	−0.110333	−	1.19068i
$274$	−1.37655	−	4.83807i	−0.0831604	−	0.292278i
$275$	−7.89211	+	27.7379i	−0.475912	+	1.67266i
$276$	4.27173	+	3.89420i	0.257128	+	0.234403i
$277$	−16.0290	−	6.20967i	−0.963089	−	0.373103i	−0.172200	−	0.985062i	$-0.555087\pi$
$277$	−16.0290	−	6.20967i	−0.963089	−	0.373103i	−0.790889	+	0.611959i	$0.790382\pi$
$278$	−7.55928	−	10.0101i	−0.453375	−	0.600366i
$279$	−0.585471	−	0.226813i	−0.0350512	−	0.0135789i
$280$	30.7478	−	11.9117i	1.83753	−	0.711863i
$281$	11.5846	+	7.17289i	0.691080	+	0.427899i	0.826535	−	0.562885i	$-0.190308\pi$
$281$	11.5846	+	7.17289i	0.691080	+	0.427899i	−0.135455	+	0.990783i	$0.543250\pi$
$282$	3.39813	+	3.09781i	0.202356	+	0.184472i
$283$	−10.0504	−	20.1839i	−0.597434	−	1.19981i	−0.963120	−	0.269071i	$-0.913283\pi$
$283$	−10.0504	−	20.1839i	−0.597434	−	1.19981i	0.365686	−	0.930738i	$-0.380834\pi$
$284$	1.01350	−	0.923928i	0.0601402	−	0.0548250i
$285$	−3.09268	+	1.19811i	−0.183195	+	0.0709700i
$286$	21.0974	+	13.0630i	1.24752	+	0.772429i
$287$	−10.3902	+	20.8664i	−0.613317	+	1.23171i
$288$	3.88458	−	0.726155i	0.228901	−	0.0427891i
$289$	0.344904	−	3.72211i	0.0202885	−	0.218948i
$290$	1.19617	−	4.20409i	0.0702413	−	0.246873i
$291$	5.81567	−	11.6794i	0.340921	−	0.684661i
$292$	−2.65555	+	2.42085i	−0.155404	+	0.141670i
$293$	−12.7917	−	16.9389i	−0.747297	−	0.989581i	−0.999759	−	0.0219743i	$-0.993005\pi$
$293$	−12.7917	−	16.9389i	−0.747297	−	0.989581i	0.252461	−	0.967607i	$-0.418760\pi$
$294$	0.828711	+	1.09739i	0.0483314	+	0.0640011i
$295$	14.4017	+	28.9226i	0.838502	+	1.68394i
$296$	1.12758	−	12.1685i	0.0655392	−	0.707281i
$297$	−3.15852	−	0.590431i	−0.183276	−	0.0342603i
$298$	13.8172	−	8.55522i	0.800406	−	0.495590i
$299$	32.2873	−	42.7553i	1.86722	−	2.47260i
$300$	5.67102	−	3.51135i	0.327417	−	0.202728i
$301$	−0.0803350	−	0.866953i	−0.00463043	−	0.0499703i
$302$	−1.34981	+	14.5668i	−0.0776731	+	0.838226i
$303$	6.37810	+	5.81440i	0.366412	+	0.334029i
$304$	−1.62257	+	0.628588i	−0.0930610	+	0.0360520i
$305$	17.8678	−	35.8833i	1.02311	−	2.05467i
$306$	−1.39713	−	4.91039i	−0.0798684	−	0.280708i
$307$	9.68145	−	5.99450i	0.552550	−	0.342124i	−0.221589	−	0.975140i	$-0.571124\pi$
$307$	9.68145	−	5.99450i	0.552550	−	0.342124i	0.774139	+	0.633016i	$0.218183\pi$
$308$	6.84937			0.390279
$309$	0.279070	−	10.1451i	0.0158757	−	0.577132i
$310$	−2.63136			−0.149451
$311$	21.8894	−	13.5533i	1.24123	−	0.768540i	0.260801	−	0.965393i	$-0.416013\pi$
$311$	21.8894	−	13.5533i	1.24123	−	0.768540i	0.980433	+	0.196853i	$0.0630721\pi$
$312$	−5.79733	−	20.3755i	−0.328209	−	1.15354i
$313$	−4.78986	+	9.61933i	−0.270739	+	0.543717i	−0.988253	−	0.152827i	$-0.951162\pi$
$313$	−4.78986	+	9.61933i	−0.270739	+	0.543717i	0.717514	+	0.696544i	$0.245280\pi$
$314$	−3.99739	+	1.54860i	−0.225586	+	0.0873925i
$315$	7.92385	+	7.22355i	0.446459	+	0.407001i
$316$	−0.622768	+	6.72074i	−0.0350334	+	0.378071i
$317$	0.922501	+	9.95537i	0.0518128	+	0.559149i	0.981587	+	0.191018i	$0.0611788\pi$
$317$	0.922501	+	9.95537i	0.0518128	+	0.559149i	−0.929774	+	0.368131i	$0.879998\pi$
$318$	12.6050	−	7.80470i	0.706855	−	0.437666i
$319$	2.01958	−	2.67436i	0.113075	−	0.149735i
$320$	26.5489	−	16.4384i	1.48413	−	0.918933i
$321$	−4.05440	−	0.757898i	−0.226294	−	0.0423018i
$322$	−2.30758	+	24.9027i	−0.128596	+	1.38777i
$323$	−1.80089	−	3.61668i	−0.100204	−	0.201237i
$324$	0.447869	+	0.593075i	0.0248816	+	0.0329486i
$325$	−37.2571	−	49.3364i	−2.06665	−	2.73669i
$326$	−13.8723	+	12.6463i	−0.768315	+	0.700412i
$327$	4.31835	−	8.67241i	0.238805	−	0.479586i
$328$	−6.83977	+	24.0393i	−0.377663	+	1.32735i
$329$	1.08547	−	11.7141i	0.0598440	−	0.645820i
$330$	−13.2372	+	2.47446i	−0.728683	+	0.136214i
$331$	10.8651	−	21.8201i	0.597200	−	1.19934i	−0.366016	−	0.930609i	$-0.619278\pi$
$331$	10.8651	−	21.8201i	0.597200	−	1.19934i	0.963216	−	0.268730i	$-0.0866039\pi$
$332$	1.65161	+	1.02264i	0.0906441	+	0.0561245i
$333$	3.70544	−	1.43549i	0.203057	−	0.0786646i
$334$	−2.92920	+	2.67032i	−0.160279	+	0.146114i
$335$	−16.1787	−	32.4911i	−0.883934	−	1.77518i
$336$	4.15724	+	3.78983i	0.226796	+	0.206752i
$337$	−23.4451	−	14.5166i	−1.27714	−	0.790771i	−0.291004	−	0.956722i	$-0.593989\pi$
$337$	−23.4451	−	14.5166i	−1.27714	−	0.790771i	−0.986134	+	0.165951i	$0.946931\pi$
$338$	−36.0138	+	13.9518i	−1.95889	+	0.758879i
$339$	−3.61216	−	1.39936i	−0.196186	−	0.0760028i
$340$	7.62450	+	10.0965i	0.413496	+	0.547558i
$341$	−1.88126	−	0.728803i	−0.101876	−	0.0394669i
$342$	−0.735036	−	0.670074i	−0.0397462	−	0.0362335i
$343$	−4.53165	+	15.9271i	−0.244686	+	0.859983i
$344$	−0.255475	−	0.897901i	−0.0137743	−	0.0484116i
$345$	2.68278	+	28.9518i	0.144436	+	1.55871i
$346$	−13.1547	−	2.45903i	−0.707199	−	0.132198i
$347$	−0.709990	−	2.49535i	−0.0381142	−	0.133958i	0.940434	−	0.339977i	$-0.110419\pi$
$347$	−0.709990	−	2.49535i	−0.0381142	−	0.133958i	−0.978548	+	0.206020i	$0.933949\pi$
$348$	−0.761909	+	0.142425i	−0.0408426	+	0.00763481i
$349$	−3.75968	−	7.55046i	−0.201251	−	0.404167i	0.771429	−	0.636315i	$-0.219542\pi$
$349$	−3.75968	−	7.55046i	−0.201251	−	0.404167i	−0.972680	+	0.232148i	$0.925425\pi$
$350$	26.9102	+	10.4251i	1.43841	+	0.557243i
$351$	5.09062	−	4.64071i	0.271717	−	0.247703i
$352$	12.4821	−	2.33331i	0.665298	−	0.124366i
$353$	0.311617	+	3.36288i	0.0165857	+	0.178988i	0.999997	−	0.00240086i	$-0.000764217\pi$
$353$	0.311617	+	3.36288i	0.0165857	+	0.178988i	−0.983411	+	0.181389i	$0.941941\pi$
$354$	−5.83914	+	7.73227i	−0.310347	+	0.410966i
$355$	6.89847			0.366133
$356$	9.27564			0.491608
$357$	−7.87135	+	10.4233i	−0.416596	+	0.551662i
$358$	10.6063	+	1.98266i	0.560560	+	0.104787i
$359$	−3.76785	+	13.2426i	−0.198859	+	0.698918i	0.796666	+	0.604420i	$0.206595\pi$
$359$	−3.76785	+	13.2426i	−0.198859	+	0.698918i	−0.995525	+	0.0944979i	$0.969875\pi$
$360$	9.77454	+	6.05214i	0.515164	+	0.318976i
$361$	15.4849	+	9.58784i	0.814994	+	0.504623i
$362$	−1.14282	+	4.01659i	−0.0600652	+	0.211107i
$363$	0.663618	+	0.124052i	0.0348309	+	0.00651102i
$364$	−8.84878	+	11.7177i	−0.463802	+	0.614173i
$365$	−18.0752			−0.946099
$366$	12.0213			0.628362
$367$	12.1239	−	16.0546i	0.632863	−	0.838046i	−0.362724	−	0.931897i	$-0.618153\pi$
$367$	12.1239	−	16.0546i	0.632863	−	0.838046i	0.995586	+	0.0938512i	$0.0299178\pi$
$368$	1.40752	+	15.1896i	0.0733720	+	0.791810i
$369$	−7.98870	+	1.49335i	−0.415875	+	0.0777406i
$370$	12.3073	−	11.2196i	0.639829	−	0.583281i
$371$	−35.3692	−	13.7021i	−1.83628	−	0.711377i
$372$	0.207992	+	0.417704i	0.0107839	+	0.0216570i
$373$	22.1497	−	4.14050i	1.14687	−	0.214387i	0.424192	−	0.905572i	$-0.360558\pi$
$373$	22.1497	−	4.14050i	1.14687	−	0.214387i	0.722678	+	0.691185i	$0.242911\pi$
$374$	−4.48930	−	15.7782i	−0.232136	−	0.815873i
$375$	14.6068	+	2.73048i	0.754290	+	0.141001i
$376$	−1.16385	−	12.5600i	−0.0600212	−	0.647732i
$377$	1.96608	+	6.91006i	0.101258	+	0.355886i
$378$	−0.879959	+	3.09274i	−0.0452602	+	0.159073i
$379$	14.1205	+	12.8725i	0.725320	+	0.661217i	0.949656	−	0.313295i	$-0.101433\pi$
$379$	14.1205	+	12.8725i	0.725320	+	0.661217i	−0.224336	+	0.974512i	$0.572021\pi$
$380$	2.29844	+	0.890419i	0.117907	+	0.0456775i
$381$	−3.48619	−	4.61646i	−0.178603	−	0.236509i
$382$	−5.54591	−	2.14850i	−0.283753	−	0.109927i
$383$	−24.8540	+	9.62849i	−1.26998	+	0.491993i	−0.899530	−	0.436860i	$-0.856091\pi$
$383$	−24.8540	+	9.62849i	−1.26998	+	0.491993i	−0.370450	+	0.928852i	$0.620796\pi$
$384$	1.24180	+	0.768892i	0.0633705	+	0.0392374i
$385$	25.4612	+	23.2110i	1.29762	+	1.18294i
$386$	3.63987	+	7.30984i	0.185265	+	0.372061i
$387$	0.224332	−	0.204505i	0.0114034	−	0.0103956i
$388$	−9.04176	+	3.50280i	−0.459026	+	0.177828i
$389$	18.2720	+	11.3135i	0.926425	+	0.573618i	0.904655	−	0.426145i	$-0.140129\pi$
$389$	18.2720	+	11.3135i	0.926425	+	0.573618i	0.0217702	+	0.999763i	$0.493070\pi$
$390$	12.8680	−	25.8425i	0.651599	−	1.30859i
$391$	−34.8163	+	6.50829i	−1.76073	+	0.329138i
$392$	0.348062	−	3.75619i	0.0175798	−	0.189716i
$393$	3.74221	−	13.1525i	0.188770	−	0.663457i
$394$	−10.0368	+	20.1566i	−0.505646	+	1.01547i
$395$	−25.0901	+	22.8726i	−1.26242	+	1.15085i
$396$	1.43911	+	1.90569i	0.0723180	+	0.0957645i
$397$	8.49528	+	11.2496i	0.426366	+	0.564600i	0.959600	−	0.281368i	$-0.0907882\pi$
$397$	8.49528	+	11.2496i	0.426366	+	0.564600i	−0.533234	+	0.845968i	$0.679023\pi$
$398$	−2.13648	−	4.29062i	−0.107092	−	0.215070i
$399$	−0.234794	+	2.53383i	−0.0117544	+	0.126850i
$400$	17.3030	+	3.23449i	0.865149	+	0.161724i
$401$	8.19403	−	5.07353i	0.409190	−	0.253360i	−0.306368	−	0.951913i	$-0.599114\pi$
$401$	8.19403	−	5.07353i	0.409190	−	0.253360i	0.715558	+	0.698553i	$0.246173\pi$
$402$	6.55958	−	8.68629i	0.327162	−	0.433233i
$403$	3.67723	−	2.27684i	0.183176	−	0.113418i
$404$	−0.591822	−	6.38678i	−0.0294443	−	0.317754i
$405$	−0.344928	+	3.72237i	−0.0171396	+	0.184966i
$406$	−2.47834	−	2.25930i	−0.122998	−	0.112127i
$407$	11.9064	−	4.61258i	0.590180	−	0.228637i
$408$	−6.24245	+	12.5365i	−0.309047	+	0.620650i
$409$	−3.01953	−	10.6125i	−0.149306	−	0.524756i	0.850694	−	0.525662i	$-0.176182\pi$
$409$	−3.01953	−	10.6125i	−0.149306	−	0.524756i	−1.00000		0.000905590i	$0.999712\pi$
$410$	−28.9585	+	17.9303i	−1.43016	+	0.885516i
$411$	−4.48684			−0.221319
$412$	−5.23271	+	5.43215i	−0.257797	+	0.267623i
$413$	24.7896			1.21982
$414$	−7.41348	+	4.59023i	−0.364353	+	0.225598i
$415$	2.67407	+	9.39840i	0.131265	+	0.461349i
$416$	−12.1340	+	24.3684i	−0.594918	+	1.19476i
$417$	−10.4334	+	4.04193i	−0.510926	+	0.197934i
$418$	−2.36185	−	2.15311i	−0.115522	−	0.105312i
$419$	1.98613	−	21.4337i	0.0970286	−	1.04711i	−0.798468	−	0.602037i	$-0.794356\pi$
$419$	1.98613	−	21.4337i	0.0970286	−	1.04711i	0.895497	−	0.445068i	$-0.146821\pi$
$420$	−0.735253	−	7.93465i	−0.0358767	−	0.387171i
$421$	−13.7211	+	8.49578i	−0.668728	+	0.414059i	−0.818378	−	0.574680i	$-0.805126\pi$
$421$	−13.7211	+	8.49578i	−0.668728	+	0.414059i	0.149650	+	0.988739i	$0.452185\pi$
$422$	15.5852	−	20.6382i	0.758676	−	1.00465i
$423$	3.48726	−	2.15922i	0.169557	−	0.104985i
$424$	−39.9770	−	7.47300i	−1.94146	−	0.362921i
$425$	−3.77113	+	40.6969i	−0.182926	+	1.97409i
$426$	0.922131	+	1.85189i	0.0446774	+	0.0897243i
$427$	−18.5345	−	24.5436i	−0.896945	−	1.18775i
$428$	1.84729	+	2.44621i	0.0892924	+	0.118242i
$429$	16.3574	−	14.9117i	0.789741	−	0.719944i
$430$	0.567065	−	1.13882i	0.0273463	−	0.0549188i
$431$	−3.05471	+	10.7362i	−0.147140	+	0.517144i	−0.999987	−	0.00501669i	$-0.998403\pi$
$431$	−3.05471	+	10.7362i	−0.147140	+	0.517144i	0.852847	+	0.522160i	$0.174874\pi$
$432$	−0.180966	+	1.95294i	−0.00870675	+	0.0939607i
$433$	27.1315	−	5.07175i	1.30385	−	0.243733i	0.514405	−	0.857548i	$-0.328013\pi$
$433$	27.1315	−	5.07175i	1.30385	−	0.243733i	0.789450	+	0.613815i	$0.210366\pi$
$434$	−0.899904	+	1.80725i	−0.0431968	+	0.0867508i
$435$	−3.31490	−	2.05250i	−0.158937	−	0.0984097i
$436$	−6.71384	+	2.60096i	−0.321535	+	0.124563i
$437$	−5.09953	+	4.64883i	−0.243943	+	0.222384i
$438$	−2.41614	−	4.85227i	−0.115448	−	0.231850i
$439$	19.2079	+	17.5103i	0.916741	+	0.835720i	0.986820	−	0.161822i	$-0.0517370\pi$
$439$	19.2079	+	17.5103i	0.916741	+	0.835720i	−0.0700793	+	0.997541i	$0.522325\pi$
$440$	31.4079	+	19.4470i	1.49731	+	0.927097i
$441$	1.14380	−	0.443110i	0.0544666	−	0.0211005i
$442$	32.7927	+	12.7039i	1.55979	+	0.604265i
$443$	6.28057	+	8.31682i	0.298399	+	0.395144i	0.922373	−	0.386301i	$-0.126248\pi$
$443$	6.28057	+	8.31682i	0.298399	+	0.395144i	−0.623974	+	0.781445i	$0.714483\pi$
$444$	−2.75383	−	1.06684i	−0.130691	−	0.0506299i
$445$	34.4804	+	31.4330i	1.63453	+	1.49007i
$446$	−7.36317	+	25.8788i	−0.348656	+	1.22540i
$447$	−3.96706	−	13.9428i	−0.187636	−	0.659471i
$448$	−2.21057	−	23.8559i	−0.104440	−	1.12708i
$449$	−23.9351	−	4.47424i	−1.12957	−	0.211153i	−0.414392	−	0.910098i	$-0.636006\pi$
$449$	−23.9351	−	4.47424i	−1.12957	−	0.211153i	−0.715175	+	0.698946i	$0.753653\pi$
$450$	2.75351	+	9.67757i	0.129801	+	0.456205i
$451$	−25.6696	+	4.79848i	−1.20873	+	0.225952i
$452$	1.28324	+	2.57710i	0.0603587	+	0.121217i
$453$	12.1681	+	4.71394i	0.571706	+	0.221480i
$454$	17.5147	−	15.9668i	0.822006	−	0.749358i
$455$	−72.6022	+	13.5717i	−3.40364	+	0.636251i
$456$	0.251749	+	2.71680i	0.0117892	+	0.127226i
$457$	2.14960	−	2.84653i	0.100554	−	0.133155i	−0.744958	−	0.667111i	$-0.767531\pi$
$457$	2.14960	−	2.84653i	0.100554	−	0.133155i	0.845512	+	0.533956i	$0.179295\pi$
$458$	0.171226			0.00800089
$459$	−4.55391			−0.212558
$460$	13.0222	−	17.2442i	0.607163	−	0.804013i
$461$	22.4485	+	4.19635i	1.04553	+	0.195444i	0.678375	−	0.734716i	$-0.262684\pi$
$461$	22.4485	+	4.19635i	1.04553	+	0.195444i	0.367156	+	0.930159i	$0.380331\pi$
$462$	−2.82752	+	9.93769i	−0.131548	+	0.462343i
$463$	−5.68579	−	3.52049i	−0.264241	−	0.163611i	0.387917	−	0.921694i	$-0.373195\pi$
$463$	−5.68579	−	3.52049i	−0.264241	−	0.163611i	−0.652158	+	0.758083i	$0.726136\pi$
$464$	−1.73916	−	1.07684i	−0.0807384	−	0.0499911i
$465$	−0.642335	+	2.25757i	−0.0297876	+	0.104692i
$466$	−26.6683	−	4.98516i	−1.23538	−	0.230933i
$467$	0.323962	−	0.428995i	0.0149912	−	0.0198515i	−0.790460	−	0.612514i	$-0.790158\pi$
$467$	0.323962	−	0.428995i	0.0149912	−	0.0198515i	0.805451	+	0.592662i	$0.201923\pi$
$468$	−5.11939			−0.236644
$469$	−27.8482			−1.28591
$470$	10.3591	−	13.7176i	0.477828	−	0.632746i
$471$	0.352824	+	3.80758i	0.0162573	+	0.175444i
$472$	26.1271	−	4.88401i	1.20260	−	0.224805i
$473$	0.720831	−	0.657124i	0.0331439	−	0.0302146i
$474$	−9.49397	−	3.67798i	−0.436072	−	0.168935i
$475$	3.54926	+	7.12787i	0.162851	+	0.327049i
$476$	9.54188	−	1.78369i	0.437351	−	0.0817551i
$477$	−3.61905	−	12.7196i	−0.165705	−	0.582392i
$478$	−10.8894	−	2.03559i	−0.498071	−	0.0931056i
$479$	2.84615	+	30.7149i	0.130044	+	1.40340i	0.771496	+	0.636234i	$0.219509\pi$
$479$	2.84615	+	30.7149i	0.130044	+	1.40340i	−0.641452	+	0.767163i	$0.721668\pi$
$480$	−4.04292	−	14.2094i	−0.184533	−	0.648567i
$481$	−7.49101	+	26.3282i	−0.341561	+	1.20046i
$482$	20.4953	+	18.6839i	0.933535	+	0.851030i
$483$	20.8019	+	8.05871i	0.946520	+	0.366684i
$484$	−0.302362	−	0.400392i	−0.0137437	−	0.0181997i
$485$	−45.4812	−	17.6195i	−2.06519	−	0.800060i
$486$	−1.04537	+	0.404980i	−0.0474191	+	0.0183703i
$487$	15.5822	+	9.64811i	0.706098	+	0.437197i	0.831949	−	0.554852i	$-0.187225\pi$
$487$	15.5822	+	9.64811i	0.706098	+	0.437197i	−0.125851	+	0.992049i	$0.540166\pi$
$488$	−24.3700	−	22.2162i	−1.10318	−	1.00568i
$489$	7.46351	+	14.9887i	0.337512	+	0.677815i
$490$	3.79904	−	3.46329i	0.171623	−	0.156455i
$491$	21.4556	−	8.31196i	0.968279	−	0.375113i	0.175403	−	0.984497i	$-0.443877\pi$
$491$	21.4556	−	8.31196i	0.968279	−	0.375113i	0.792876	+	0.609383i	$0.208583\pi$
$492$	5.13525	+	3.17961i	0.231515	+	0.143348i
$493$	2.11704	−	4.25158i	0.0953465	−	0.191482i
$494$	6.73476	−	1.25894i	0.303011	−	0.0566426i
$495$	−1.10834	+	11.9608i	−0.0498160	+	0.537600i
$496$	−0.337000	+	1.18443i	−0.0151318	+	0.0531826i
$497$	2.35922	−	4.73795i	0.105825	−	0.212526i
$498$	−2.16554	+	1.97415i	−0.0970403	+	0.0884639i
$499$	19.2130	+	25.4422i	0.860094	+	1.13895i	0.989091	+	0.147304i	$0.0470595\pi$
$499$	19.2130	+	25.4422i	0.860094	+	1.13895i	−0.128997	+	0.991645i	$0.541176\pi$
$500$	−6.65524	−	8.81297i	−0.297632	−	0.394128i
$501$	1.57596	+	3.16495i	0.0704086	+	0.141400i
$502$	1.90030	−	20.5076i	0.0848147	−	0.915297i
$503$	−17.9704	−	3.35925i	−0.801261	−	0.149782i	−0.232835	−	0.972516i	$-0.574800\pi$
$503$	−17.9704	−	3.35925i	−0.801261	−	0.149782i	−0.568426	+	0.822734i	$0.692447\pi$
$504$	7.49949	−	4.64349i	0.334054	−	0.206837i
$505$	19.4434	−	25.7472i	0.865218	−	1.14573i
$506$	−23.8213	+	14.7495i	−1.05898	+	0.655695i
$507$	3.17870	+	34.3037i	0.141171	+	1.52348i
$508$	−0.396686	+	4.28093i	−0.0176001	+	0.189935i
$509$	11.6107	+	10.5845i	0.514634	+	0.469151i	0.888855	−	0.458189i	$-0.151502\pi$
$509$	11.6107	+	10.5845i	0.514634	+	0.469151i	−0.374221	+	0.927340i	$0.622090\pi$
$510$	−17.7964	+	6.89435i	−0.788036	+	0.305287i
$511$	−6.18156	+	12.4142i	−0.273456	+	0.549174i
$512$	−5.42239	−	19.0577i	−0.239638	−	0.842240i
$513$	−0.754316	+	0.467053i	−0.0333039	+	0.0206209i
$514$	−1.77450			−0.0782700
$515$	−37.8599	+	2.46051i	−1.66831	+	0.108423i
$516$	−0.225600			−0.00993147
$517$	11.2054	−	6.93809i	0.492813	−	0.305137i
$518$	−3.49676	−	12.2898i	−0.153639	−	0.539985i
$519$	−5.32087	+	10.6857i	−0.233560	+	0.469052i
$520$	−73.8454	+	28.6079i	−3.23834	+	1.25454i
$521$	−5.65952	−	5.15934i	−0.247948	−	0.226035i	0.540174	−	0.841553i	$-0.318358\pi$
$521$	−5.65952	−	5.15934i	−0.247948	−	0.226035i	−0.788122	+	0.615519i	$0.788947\pi$
$522$	0.107883	−	1.16424i	0.00472191	−	0.0509575i
$523$	−3.06234	−	33.0479i	−0.133907	−	1.44508i	−0.752096	−	0.659053i	$-0.770957\pi$
$523$	−3.06234	−	33.0479i	−0.133907	−	1.44508i	0.618190	−	0.786029i	$-0.287866\pi$
$524$	−8.64052	+	5.34998i	−0.377463	+	0.233715i
$525$	15.5131	−	20.5427i	0.677048	−	0.896557i
$526$	−12.2177	+	7.56486i	−0.532716	+	0.329844i
$527$	−2.81057	−	0.525388i	−0.122431	−	0.0228862i
$528$	−0.581487	+	6.27525i	−0.0253060	+	0.273095i
$529$	16.7126	+	33.5634i	0.726634	+	1.45928i
$530$	−33.3998	−	44.2285i	−1.45079	−	1.92116i
$531$	5.20851	+	6.89718i	0.226030	+	0.299312i
$532$	1.39760	−	1.27408i	0.0605934	−	0.0552382i
$533$	24.9537	−	50.1139i	1.08087	−	2.17067i
$534$	−3.82911	+	13.4579i	−0.165702	+	0.582382i
$535$	−1.42270	+	15.3534i	−0.0615087	+	0.663785i
$536$	−29.3507	+	5.48660i	−1.26776	+	0.236985i
$537$	4.29009	−	8.61567i	0.185131	−	0.371793i
$538$	26.7555	+	16.5663i	1.15351	+	0.714224i
$539$	3.67529	−	1.42382i	0.158306	−	0.0613281i
$540$	2.05316	−	1.87170i	0.0883539	−	0.0805453i
$541$	10.7086	+	21.5057i	0.460398	+	0.924603i	0.996746	+	0.0806065i	$0.0256857\pi$
$541$	10.7086	+	21.5057i	0.460398	+	0.924603i	−0.536348	+	0.843997i	$0.680197\pi$
$542$	9.97072	+	9.08952i	0.428279	+	0.390428i
$543$	3.16705	+	1.96096i	0.135911	+	0.0841527i
$544$	16.7812	−	6.50107i	0.719488	−	0.278731i
$545$	−33.7714	−	13.0831i	−1.44661	−	0.560419i
$546$	−13.3482	−	17.6758i	−0.571249	−	0.756456i
$547$	25.8893	+	10.0296i	1.10694	+	0.428833i	0.844198	−	0.536032i	$-0.180077\pi$
$547$	25.8893	+	10.0296i	1.10694	+	0.428833i	0.262747	+	0.964865i	$0.415371\pi$
$548$	2.46426	+	2.24647i	0.105268	+	0.0959646i
$549$	2.93448	−	10.3136i	0.125240	−	0.440174i
$550$	8.84766	+	31.0963i	0.377266	+	1.32595i
$551$	−0.0853769	−	0.921364i	−0.00363718	−	0.0392514i
$552$	23.5120	+	4.39515i	1.00074	+	0.187070i
$553$	7.12859	+	25.0544i	0.303138	+	1.06542i
$554$	−18.9429	+	3.54105i	−0.804809	+	0.150445i
$555$	−6.62154	−	13.2979i	−0.281069	−	0.564462i
$556$	7.75396	+	3.00390i	0.328841	+	0.127394i
$557$	5.83990	−	5.32377i	0.247444	−	0.225575i	−0.540465	−	0.841366i	$-0.681752\pi$
$557$	5.83990	−	5.32377i	0.247444	−	0.225575i	0.787909	+	0.615791i	$0.211163\pi$
$558$	−0.691905	+	0.129340i	−0.0292907	+	0.00547538i
$559$	0.192937	+	2.08212i	0.00816036	+	0.0880643i
$560$	12.6732	−	16.7820i	0.535540	−	0.709169i
$561$	−14.6328			−0.617796
$562$	15.2752			0.644346
$563$	−6.02690	+	7.98090i	−0.254003	+	0.336355i	−0.907096	−	0.420923i	$-0.861706\pi$
$563$	−6.02690	+	7.98090i	−0.254003	+	0.336355i	0.653093	+	0.757278i	$0.273471\pi$
$564$	−2.99636	−	0.560117i	−0.126169	−	0.0235852i
$565$	−3.96299	+	13.9285i	−0.166724	+	0.585976i
$566$	−21.4916	−	13.3070i	−0.903359	−	0.559336i
$567$	2.43860	+	1.50992i	0.102412	+	0.0634106i
$568$	1.55304	−	5.45838i	0.0651643	−	0.229029i
$569$	−2.18535	−	0.408513i	−0.0916148	−	0.0171258i	0.137743	−	0.990468i	$-0.456015\pi$
$569$	−2.18535	−	0.408513i	−0.0916148	−	0.0171258i	−0.229357	+	0.973342i	$0.573662\pi$
$570$	−2.24073	+	2.96720i	−0.0938537	+	0.124282i
$571$	4.57201			0.191333			0.0956663	−	0.995413i	$-0.469502\pi$
$571$	4.57201			0.191333			0.0956663	+	0.995413i	$0.469502\pi$
$572$	−16.4498			−0.687801
$573$	−3.19709	+	4.23363i	−0.133560	+	0.176863i
$574$	2.41120	+	26.0210i	0.100642	+	1.08610i
$575$	68.6171	−	12.8268i	2.86153	−	0.534913i
$576$	6.17291	−	5.62735i	0.257205	−	0.234473i
$577$	−11.0925	−	4.29724i	−0.461785	−	0.178896i	0.119100	−	0.992882i	$-0.461999\pi$
$577$	−11.0925	−	4.29724i	−0.461785	−	0.178896i	−0.580885	+	0.813986i	$0.697293\pi$
$578$	−1.86793	−	3.75132i	−0.0776958	−	0.156034i
$579$	7.15998	−	1.33843i	0.297559	−	0.0556234i
$580$	0.792964	+	2.78698i	0.0329260	+	0.115723i
$581$	7.36944	+	1.37759i	0.305736	+	0.0571519i
$582$	−1.34961	−	14.5646i	−0.0559431	−	0.603722i
$583$	−11.6289	−	40.8712i	−0.481618	−	1.69271i
$584$	−4.06925	+	14.3019i	−0.168387	+	0.591818i
$585$	−19.0303	−	17.3484i	−0.786808	−	0.717270i
$586$	−22.1893	−	8.59620i	−0.916633	−	0.355106i
$587$	20.9090	+	27.6880i	0.863007	+	1.14281i	0.988576	+	0.150721i	$0.0481594\pi$
$587$	20.9090	+	27.6880i	0.863007	+	1.14281i	−0.125570	+	0.992085i	$0.540076\pi$
$588$	−0.850054	−	0.329313i	−0.0350556	−	0.0135806i
$589$	−0.519432	+	0.201229i	−0.0214028	+	0.00829150i
$590$	30.7964	+	19.0683i	1.26787	+	0.785031i
$591$	14.8432	+	13.5314i	0.610569	+	0.556608i
$592$	−3.47399	−	6.97671i	−0.142780	−	0.286741i
$593$	−27.7528	+	25.3000i	−1.13967	+	1.03895i	−0.140868	+	0.990028i	$0.544989\pi$
$593$	−27.7528	+	25.3000i	−1.13967	+	1.03895i	−0.998803	+	0.0489187i	$0.984422\pi$
$594$	−3.35903	+	1.30130i	−0.137823	+	0.0533928i
$595$	41.5146	+	25.7047i	1.70193	+	1.05379i
$596$	−4.80209	+	9.64390i	−0.196701	+	0.395029i
$597$	−4.20266	+	0.785613i	−0.172003	+	0.0321530i
$598$	5.54200	−	59.8077i	0.226629	−	2.44572i
$599$	10.0133	−	35.1931i	0.409132	−	1.43795i	−0.434327	−	0.900755i	$-0.643014\pi$
$599$	10.0133	−	35.1931i	0.409132	−	1.43795i	0.843459	−	0.537194i	$-0.180516\pi$
$600$	12.3028	−	24.7074i	0.502261	−	1.00868i
$601$	31.6217	−	28.8270i	1.28988	−	1.17588i	0.316009	−	0.948756i	$-0.397657\pi$
$601$	31.6217	−	28.8270i	1.28988	−	1.17588i	0.973866	−	0.227121i	$-0.0729314\pi$
$602$	−0.588223	−	0.778933i	−0.0239742	−	0.0317469i
$603$	−5.85114	−	7.74816i	−0.238277	−	0.315530i
$604$	−4.32278	−	8.68131i	−0.175891	−	0.353238i
$605$	0.232865	−	2.51302i	0.00946732	−	0.102169i
$606$	9.51083	+	1.77788i	0.386351	+	0.0722215i
$607$	2.10736	−	1.30482i	0.0855349	−	0.0529610i	−0.482998	−	0.875621i	$-0.660452\pi$
$607$	2.10736	−	1.30482i	0.0855349	−	0.0529610i	0.568533	+	0.822660i	$0.307511\pi$
$608$	2.11291	−	2.79794i	0.0856897	−	0.113472i
$609$	−2.54334	+	1.57477i	−0.103061	+	0.0638130i
$610$	−4.14647	−	44.7476i	−0.167886	−	1.81178i
$611$	−2.60693	+	28.1332i	−0.105465	+	1.13815i
$612$	2.50110	+	2.28005i	0.101101	+	0.0921657i
$613$	7.23234	−	2.80182i	0.292111	−	0.113165i	−0.210727	−	0.977545i	$-0.567583\pi$
$613$	7.23234	−	2.80182i	0.292111	−	0.113165i	0.502839	+	0.864380i	$0.332289\pi$
$614$	5.69018	−	11.4274i	0.229637	−	0.461174i
$615$	8.31432	+	29.2218i	0.335266	+	1.17834i
$616$	24.0976	−	14.9206i	0.970921	−	0.601169i
$617$	32.0802			1.29150			0.645750	−	0.763549i	$-0.276545\pi$
$617$	32.0802			1.29150			0.645750	+	0.763549i	$0.276545\pi$
$618$	−5.72132	−	9.83455i	−0.230145	−	0.395604i
$619$	−37.1613			−1.49364			−0.746819	−	0.665028i	$-0.768420\pi$
$619$	−37.1613			−1.49364			−0.746819	+	0.665028i	$0.768420\pi$
$620$	1.48311	−	0.918301i	0.0595630	−	0.0368799i
$621$	2.12850	+	7.48089i	0.0854136	+	0.300198i
$622$	12.8653	−	25.8370i	0.515851	−	1.03597i
$623$	33.3805	−	12.9317i	1.33736	−	0.518097i
$624$	−9.98426	−	9.10185i	−0.399690	−	0.364366i
$625$	0.985018	−	10.6300i	0.0394007	−	0.425201i
$626$	1.11156	+	11.9956i	0.0444267	+	0.479440i
$627$	−2.42380	+	1.50075i	−0.0967971	+	0.0599342i
$628$	1.71260	−	2.26785i	0.0683403	−	0.0904972i
$629$	15.3857	−	9.52642i	0.613468	−	0.379843i
$630$	11.8158	+	2.20876i	0.470754	+	0.0879991i
$631$	2.32158	−	25.0539i	0.0924207	−	0.997378i	−0.815646	−	0.578552i	$-0.803618\pi$
$631$	2.32158	−	25.0539i	0.0924207	−	0.997378i	0.908066	−	0.418826i	$-0.137558\pi$
$632$	12.4494	+	25.0017i	0.495209	+	0.994514i
$633$	−13.9020	−	18.4092i	−0.552555	−	0.731701i
$634$	6.75466	+	8.94462i	0.268262	+	0.355236i
$635$	−15.9817	+	14.5692i	−0.634214	+	0.578162i
$636$	−4.38082	+	8.79787i	−0.173711	+	0.348858i
$637$	−2.31233	+	8.12701i	−0.0916180	+	0.322004i
$638$	0.346653	−	3.74098i	0.0137241	−	0.148107i
$639$	1.81392	−	0.339081i	0.0717576	−	0.0134138i
$640$	2.43377	−	4.88766i	0.0962030	−	0.193202i
$641$	−0.485162	−	0.300399i	−0.0191627	−	0.0118651i	0.516817	−	0.856096i	$-0.327117\pi$
$641$	−0.485162	−	0.300399i	−0.0191627	−	0.0118651i	−0.535980	+	0.844231i	$0.680058\pi$
$642$	−4.31178	+	1.67039i	−0.170172	+	0.0659251i
$643$	−12.1002	+	11.0308i	−0.477187	+	0.435013i	−0.876211	−	0.481927i	$-0.839937\pi$
$643$	−12.1002	+	11.0308i	−0.477187	+	0.435013i	0.399025	+	0.916940i	$0.369349\pi$
$644$	−7.39001	−	14.8411i	−0.291207	−	0.584823i
$645$	−0.838623	−	0.764506i	−0.0330207	−	0.0301024i
$646$	−3.85100	−	2.38444i	−0.151515	−	0.0938143i
$647$	22.0584	−	8.54548i	0.867206	−	0.335958i	0.113793	−	0.993504i	$-0.463700\pi$
$647$	22.0584	−	8.54548i	0.867206	−	0.335958i	0.753414	+	0.657547i	$0.228406\pi$
$648$	2.86765	+	1.11093i	0.112652	+	0.0436416i
$649$	16.7362	+	22.1623i	0.656952	+	0.869945i
$650$	−64.6289	−	25.0374i	−2.53495	−	0.982047i
$651$	1.33085	+	1.21323i	0.0521603	+	0.0475504i
$652$	3.40547	−	11.9690i	0.133368	−	0.468741i
$653$	2.11157	+	7.42139i	0.0826321	+	0.290422i	0.992117	−	0.125315i	$-0.0399943\pi$
$653$	2.11157	+	7.42139i	0.0826321	+	0.290422i	−0.909485	+	0.415737i	$0.863524\pi$
$654$	−1.00213	−	10.8148i	−0.0391866	−	0.422890i
$655$	−50.2493	−	9.39322i	−1.96340	−	0.367024i
$656$	4.36210	+	15.3312i	0.170311	+	0.598583i
$657$	−4.75279	+	0.888451i	−0.185424	+	0.0346618i
$658$	−5.87870	−	11.8060i	−0.229176	−	0.460247i
$659$	−24.1180	−	9.34335i	−0.939502	−	0.363965i	−0.157697	−	0.987488i	$-0.550407\pi$
$659$	−24.1180	−	9.34335i	−0.939502	−	0.363965i	−0.781805	+	0.623522i	$0.785701\pi$
$660$	6.59729	−	6.01422i	0.256799	−	0.234103i
$661$	2.48433	−	0.464402i	0.0966293	−	0.0180631i	−0.135213	−	0.990817i	$-0.543172\pi$
$661$	2.48433	−	0.464402i	0.0966293	−	0.0180631i	0.231842	+	0.972753i	$0.425525\pi$
$662$	−2.52140	−	27.2102i	−0.0979970	−	1.05756i
$663$	18.9042	−	25.0333i	0.734180	−	0.972211i
$664$	8.03845			0.311952
$665$	9.51284			0.368892
$666$	2.68468	−	3.55510i	0.104029	−	0.137757i
$667$	−7.97375	−	1.49055i	−0.308745	−	0.0577144i
$668$	0.719081	−	2.52731i	0.0278221	−	0.0977845i
$669$	20.4053	+	12.6344i	0.788914	+	0.488475i
$670$	−34.5962	−	21.4210i	−1.33657	−	0.827567i
$671$	9.42917	−	33.1401i	0.364009	−	1.27936i
$672$	−11.1418	−	2.08276i	−0.429804	−	0.0803444i
$673$	27.9119	−	36.9614i	1.07593	−	1.42476i	0.178311	−	0.983974i	$-0.442937\pi$
$673$	27.9119	−	36.9614i	1.07593	−	1.42476i	0.897614	−	0.440782i	$-0.145299\pi$
$674$	−30.9142			−1.19077
$675$	8.97500			0.345448
$676$	15.4294	−	20.4318i	0.593438	−	0.785839i
$677$	1.84035	+	19.8605i	0.0707304	+	0.763303i	0.955055	+	0.296430i	$0.0957960\pi$
$677$	1.84035	+	19.8605i	0.0707304	+	0.763303i	−0.884324	+	0.466873i	$0.845380\pi$
$678$	−4.26883	+	0.797983i	−0.163943	+	0.0306463i
$679$	−27.6554	+	25.2113i	−1.06132	+	0.967519i
$680$	48.8187	+	18.9125i	1.87211	+	0.725260i
$681$	−9.42319	−	18.9243i	−0.361097	−	0.725181i
$682$	−2.22326	+	0.415599i	−0.0851329	+	0.0159141i
$683$	−0.542581	−	1.90697i	−0.0207613	−	0.0729683i	0.950753	−	0.309950i	$-0.100312\pi$
$683$	−0.542581	−	1.90697i	−0.0207613	−	0.0729683i	−0.971514	+	0.236982i	$0.923842\pi$
$684$	0.648130	+	0.121157i	0.0247819	+	0.00463254i
$685$	1.54764	+	16.7017i	0.0591321	+	0.638137i
$686$	5.08033	+	17.8555i	0.193968	+	0.681727i
$687$	0.0417976	−	0.146903i	0.00159468	−	0.00560471i
$688$	−0.439983	−	0.401097i	−0.0167742	−	0.0152917i
$689$	84.9445	+	32.9077i	3.23613	+	1.25368i
$690$	19.6437	+	26.0124i	0.747821	+	0.990275i
$691$	−19.5310	−	7.56634i	−0.742993	−	0.287837i	−0.0401613	−	0.999193i	$-0.512787\pi$
$691$	−19.5310	−	7.56634i	−0.742993	−	0.287837i	−0.702832	+	0.711356i	$0.748081\pi$
$692$	8.27248	−	3.20478i	0.314473	−	0.121827i
$693$	7.83580	+	4.85172i	0.297658	+	0.184302i
$694$	−2.14942	−	1.95945i	−0.0815908	−	0.0743799i
$695$	18.6443	+	37.4428i	0.707219	+	1.42029i
$696$	−2.37031	+	2.16082i	−0.0898463	+	0.0819057i
$697$	−34.5108	+	13.3695i	−1.30719	+	0.506408i
$698$	−8.03964	−	4.97794i	−0.304305	−	0.188418i
$699$	−10.7869	+	21.6630i	−0.407999	+	0.819372i
$700$	−18.8055	+	3.51535i	−0.710780	+	0.132868i
$701$	−1.56760	+	16.9171i	−0.0592074	+	0.638949i	0.913488	+	0.406865i	$0.133378\pi$
$701$	−1.56760	+	16.9171i	−0.0592074	+	0.638949i	−0.972696	+	0.232084i	$0.925445\pi$
$702$	2.11336	−	7.42768i	0.0797635	−	0.280340i
$703$	1.57147	−	3.15594i	0.0592692	−	0.119029i
$704$	19.8350	−	18.0820i	0.747561	−	0.681492i
$705$	−9.24028	−	12.2361i	−0.348009	−	0.460838i
$706$	2.28170	+	3.02145i	0.0858728	+	0.113714i
$707$	−11.0340	−	22.1592i	−0.414976	−	0.833383i
$708$	0.592665	−	6.39587i	0.0222737	−	0.240372i
$709$	−17.4372	−	3.25958i	−0.654868	−	0.122416i	−0.154178	−	0.988043i	$-0.549273\pi$
$709$	−17.4372	−	3.25958i	−0.654868	−	0.122416i	−0.500689	+	0.865627i	$0.666920\pi$
$710$	6.57534	−	4.07128i	0.246768	−	0.152792i
$711$	−5.47306	+	7.24751i	−0.205256	+	0.271803i
$712$	32.6338	−	20.2060i	1.22300	−	0.757251i
$713$	0.450587	+	4.86261i	0.0168746	+	0.182106i
$714$	−1.35109	+	14.5806i	−0.0505632	+	0.545663i
$715$	−61.1490	−	55.7447i	−2.28684	−	2.08473i
$716$	−6.66991	+	2.58394i	−0.249266	+	0.0965662i
$717$	−4.40462	+	8.84566i	−0.164493	+	0.330347i
$718$	4.22405	+	14.8460i	0.157640	+	0.554047i
$719$	20.1830	−	12.4968i	0.752700	−	0.466052i	−0.0956984	−	0.995410i	$-0.530508\pi$
$719$	20.1830	−	12.4968i	0.752700	−	0.466052i	0.848398	+	0.529358i	$0.177567\pi$
$720$	7.33197			0.273246
$721$	−11.2578	+	26.8441i	−0.419264	+	0.999725i
$722$	20.4180			0.759881
$723$	21.0329	−	13.0230i	0.782221	−	0.484331i
$724$	−0.757598	−	2.66268i	−0.0281559	−	0.0989577i
$725$	−4.17233	+	8.37916i	−0.154956	+	0.311194i
$726$	0.705745	−	0.273407i	0.0261927	−	0.0101471i
$727$	−19.2423	−	17.5416i	−0.713656	−	0.650584i	0.233130	−	0.972445i	$-0.425103\pi$
$727$	−19.2423	−	17.5416i	−0.713656	−	0.650584i	−0.946787	+	0.321862i	$0.895691\pi$
$728$	−5.60629	+	60.5015i	−0.207783	+	2.24234i
$729$	0.0922684	+	0.995734i	0.00341735	+	0.0368790i
$730$	−17.2285	+	10.6675i	−0.637657	+	0.394820i
$731$	0.833066	−	1.10316i	0.0308121	−	0.0408018i
$732$	−6.77551	+	4.19522i	−0.250430	+	0.155060i
$733$	−25.6566	−	4.79605i	−0.947648	−	0.177146i	−0.312831	−	0.949809i	$-0.601277\pi$
$733$	−25.6566	−	4.79605i	−0.947648	−	0.177146i	−0.634817	+	0.772662i	$0.718925\pi$
$734$	2.08102	−	22.4578i	0.0768119	−	0.828933i
$735$	−2.04394	−	4.10479i	−0.0753920	−	0.151408i
$736$	−18.5231	−	24.5286i	−0.682771	−	0.904134i
$737$	−18.8011	−	24.8967i	−0.692547	−	0.917081i
$738$	−6.73318	+	6.13810i	−0.247852	+	0.225947i
$739$	−2.01795	+	4.05259i	−0.0742314	+	0.149077i	−0.929170	−	0.369652i	$-0.879477\pi$
$739$	−2.01795	+	4.05259i	−0.0742314	+	0.149077i	0.854939	+	0.518729i	$0.173595\pi$
$740$	−3.02129	+	10.6187i	−0.111065	+	0.390353i
$741$	0.563894	−	6.08538i	0.0207152	−	0.223552i
$742$	−41.7990	+	7.81360i	−1.53449	+	0.286846i
$743$	1.08767	−	2.18433i	0.0399027	−	0.0801355i	−0.874315	−	0.485359i	$-0.838689\pi$
$743$	1.08767	−	2.18433i	0.0399027	−	0.0801355i	0.914217	+	0.405224i	$0.132806\pi$
$744$	1.64169	+	1.01649i	0.0601871	+	0.0372663i
$745$	−50.5318	+	19.5761i	−1.85134	+	0.717214i
$746$	18.6686	−	17.0187i	0.683506	−	0.623098i
$747$	1.16510	+	2.33983i	0.0426286	+	0.0856098i
$748$	8.03662	+	7.32635i	0.293848	+	0.267878i
$749$	10.0583	+	6.22785i	0.367523	+	0.227561i
$750$	15.5340	−	6.01791i	0.567222	−	0.219743i
$751$	30.6244	+	11.8639i	1.11750	+	0.432922i	0.847956	−	0.530067i	$-0.177833\pi$
$751$	30.6244	+	11.8639i	1.11750	+	0.432922i	0.269543	+	0.962988i	$0.413127\pi$
$752$	−4.84790	−	6.41966i	−0.176785	−	0.234101i
$753$	−17.1305	−	6.63640i	−0.624271	−	0.241844i
$754$	5.95210	+	5.42606i	0.216763	+	0.197605i
$755$	13.3499	−	46.9200i	0.485852	−	1.70759i
$756$	−0.583343	−	2.05024i	−0.0212160	−	0.0745665i
$757$	1.86035	+	20.0764i	0.0676157	+	0.729689i	0.960293	+	0.278993i	$0.0900007\pi$
$757$	1.86035	+	20.0764i	0.0676157	+	0.729689i	−0.892677	+	0.450696i	$0.851176\pi$
$758$	21.0560	+	3.93606i	0.764790	+	0.142964i
$759$	6.83936	+	24.0379i	0.248253	+	0.872519i
$760$	10.0261	−	1.87420i	0.363685	−	0.0679844i
$761$	−10.8459	−	21.7814i	−0.393162	−	0.789576i	0.606824	−	0.794836i	$-0.292443\pi$
$761$	−10.8459	−	21.7814i	−0.393162	−	0.789576i	−0.999986	+	0.00526029i	$0.998326\pi$
$762$	−6.04740	−	2.34277i	−0.219074	−	0.0848698i
$763$	−20.5352	+	18.7203i	−0.743423	+	0.677720i
$764$	3.87561	−	0.724477i	0.140215	−	0.0262107i
$765$	1.57077	+	16.9513i	0.0567913	+	0.612876i
$766$	−18.0074	+	23.8456i	−0.650632	+	0.861576i
$767$	−59.5361			−2.14972
$768$	−15.0685			−0.543738
$769$	0.301143	−	0.398778i	0.0108595	−	0.0143803i	−0.792555	−	0.609800i	$-0.791250\pi$
$769$	0.301143	−	0.398778i	0.0108595	−	0.0143803i	0.803415	+	0.595420i	$0.203014\pi$
$770$	37.9670	+	7.09727i	1.36824	+	0.255768i
$771$	−0.433169	+	1.52243i	−0.0156002	+	0.0548290i
$772$	−4.60254	−	2.84977i	−0.165649	−	0.102566i
$773$	−36.1661	−	22.3931i	−1.30081	−	0.805425i	−0.311355	−	0.950294i	$-0.600783\pi$
$773$	−36.1661	−	22.3931i	−1.30081	−	0.805425i	−0.989451	+	0.144869i	$0.953724\pi$
$774$	0.0931307	−	0.327320i	0.00334751	−	0.0117653i
$775$	5.53918	+	1.03545i	0.198973	+	0.0371945i
$776$	−24.1805	+	32.0201i	−0.868028	+	1.14946i
$777$	−11.3976			−0.408888
$778$	24.0930			0.863776
$779$	−4.34523	+	5.75401i	−0.155684	+	0.206159i
$780$	1.76582	+	19.0563i	0.0632266	+	0.682323i
$781$	5.82856	−	1.08955i	0.208562	−	0.0389870i
$782$	−29.3444	+	26.7510i	−1.04936	+	0.956614i
$783$	−0.972524	−	0.376758i	−0.0347552	−	0.0134642i
$784$	−1.07235	−	2.15358i	−0.0382984	−	0.0769135i
$785$	14.0515	−	2.62668i	0.501520	−	0.0937503i
$786$	−4.19531	−	14.7450i	−0.149642	−	0.525937i
$787$	−29.3404	−	5.48468i	−1.04587	−	0.195508i	−0.367347	−	0.930084i	$-0.619734\pi$
$787$	−29.3404	−	5.48468i	−1.04587	−	0.195508i	−0.678526	+	0.734576i	$0.737381\pi$
$788$	−1.37730	−	14.8635i	−0.0490644	−	0.529489i
$789$	3.50783	+	12.3288i	0.124882	+	0.438915i
$790$	−10.4161	+	36.6087i	−0.370587	+	1.30248i
$791$	8.21093	+	7.48525i	0.291947	+	0.266145i
$792$	9.21445	+	3.56970i	0.327421	+	0.126844i
$793$	44.5133	+	58.9451i	1.58071	+	2.09320i
$794$	14.7365	+	5.70896i	0.522980	+	0.202603i
$795$	−46.0988	+	17.8588i	−1.63496	+	0.633386i
$796$	2.70153	+	1.67272i	0.0957532	+	0.0592879i
$797$	11.0624	+	10.0847i	0.391851	+	0.357219i	0.845513	−	0.533954i	$-0.179295\pi$
$797$	11.0624	+	10.0847i	0.391851	+	0.357219i	−0.453662	+	0.891174i	$0.649883\pi$
$798$	1.27160	+	2.55371i	0.0450141	+	0.0904005i
$799$	13.8035	−	12.5835i	0.488332	−	0.445174i
$800$	−33.0730	+	12.8125i	−1.16931	+	0.452992i
$801$	10.6115	+	6.57035i	0.374938	+	0.232152i
$802$	4.81596	−	9.67176i	0.170058	−	0.341522i
$803$	−15.2718	+	2.85480i	−0.538932	+	0.100744i
$804$	−0.665789	+	7.18501i	−0.0234806	+	0.253396i
$805$	22.8223	−	80.2121i	0.804381	−	2.82710i
$806$	2.16126	−	4.34039i	0.0761270	−	0.152884i
$807$	20.7442	−	18.9109i	0.730231	−	0.665694i
$808$	−15.9951	−	21.1809i	−0.562705	−	0.745141i
$809$	−15.7231	−	20.8207i	−0.552793	−	0.732016i	0.432736	−	0.901521i	$-0.357548\pi$
$809$	−15.7231	−	20.8207i	−0.552793	−	0.732016i	−0.985529	+	0.169504i	$0.945783\pi$
$810$	1.86806	+	3.75158i	0.0656370	+	0.131817i
$811$	2.25466	−	24.3317i	0.0791719	−	0.854400i	−0.859851	−	0.510545i	$-0.829444\pi$
$811$	2.25466	−	24.3317i	0.0791719	−	0.854400i	0.939023	−	0.343855i	$-0.111733\pi$
$812$	2.18532	+	0.408506i	0.0766895	+	0.0143358i
$813$	10.2323	−	6.33554i	0.358861	−	0.222197i
$814$	8.62652	−	11.4234i	0.302359	−	0.400389i
$815$	53.2193	−	32.9520i	1.86419	−	1.15426i
$816$	0.824103	+	8.89349i	0.0288494	+	0.311335i
$817$	0.0248495	−	0.268169i	0.000869374	−	0.00938204i
$818$	−9.14131	−	8.33340i	−0.319618	−	0.291371i
$819$	−18.4233	+	7.13723i	−0.643763	+	0.249395i
$820$	10.0644	−	20.2120i	0.351464	−	0.705835i
$821$	−3.10144	−	10.9004i	−0.108241	−	0.380428i	0.888709	−	0.458472i	$-0.151603\pi$
$821$	−3.10144	−	10.9004i	−0.108241	−	0.380428i	−0.996950	+	0.0780440i	$0.975133\pi$
$822$	−4.27667	+	2.64800i	−0.149166	+	0.0923596i
$823$	29.3735			1.02390			0.511948	−	0.859016i	$-0.328924\pi$
$823$	29.3735			1.02390			0.511948	+	0.859016i	$0.328924\pi$
$824$	−6.57648	+	30.5104i	−0.229102	+	1.06288i
$825$	28.8388			1.00404
$826$	23.6285	−	14.6301i	0.822140	−	0.509047i
$827$	3.53064	+	12.4089i	0.122772	+	0.431500i	0.998702	−	0.0509390i	$-0.0162214\pi$
$827$	3.53064	+	12.4089i	0.122772	+	0.431500i	−0.875929	+	0.482439i	$0.839751\pi$
$828$	2.57652	−	5.17436i	0.0895404	−	0.179821i
$829$	−25.0905	+	9.72010i	−0.871428	+	0.337593i	−0.755094	−	0.655617i	$-0.772409\pi$
$829$	−25.0905	+	9.72010i	−0.871428	+	0.337593i	−0.116335	+	0.993210i	$0.537114\pi$
$830$	8.09548	+	7.38001i	0.280998	+	0.256164i
$831$	−1.58607	+	17.1165i	−0.0550203	+	0.593763i
$832$	5.30902	+	57.2935i	0.184057	+	1.98629i
$833$	4.74927	−	2.94063i	0.164553	−	0.101887i
$834$	−7.55928	+	10.0101i	−0.261756	+	0.346621i
$835$	11.2375	−	6.95797i	0.388890	−	0.240791i
$836$	2.08260	+	0.389305i	0.0720281	+	0.0134644i
$837$	−0.0579325	+	0.625191i	−0.00200244	+	0.0216098i
$838$	−10.7565	−	21.6019i	−0.371576	−	0.746225i
$839$	−3.65552	−	4.84069i	−0.126202	−	0.167119i	0.730529	−	0.682881i	$-0.239273\pi$
$839$	−3.65552	−	4.84069i	−0.126202	−	0.167119i	−0.856732	+	0.515762i	$0.827509\pi$
$840$	−19.8715	−	26.3142i	−0.685633	−	0.907925i
$841$	−20.6274	+	18.8044i	−0.711290	+	0.648426i
$842$	−8.06448	+	16.1957i	−0.277920	+	0.558139i
$843$	3.72879	−	13.1053i	0.128426	−	0.451372i
$844$	−1.58188	+	17.0712i	−0.0544505	+	0.587615i
$845$	126.595	−	23.6646i	4.35498	−	0.814088i
$846$	2.04961	−	4.11617i	0.0704669	−	0.141517i
$847$	−1.64633	−	1.01936i	−0.0565686	−	0.0350258i
$848$	−24.1857	+	9.36960i	−0.830541	+	0.321753i
$849$	−16.6630	+	15.1903i	−0.571872	+	0.521331i
$850$	20.4237	+	41.0163i	0.700526	+	1.40685i
$851$	−22.8407	−	20.8221i	−0.782970	−	0.713771i
$852$	−1.16601	−	0.721966i	−0.0399470	−	0.0247341i
$853$	−24.0722	+	9.32561i	−0.824216	+	0.319303i	−0.736156	−	0.676812i	$-0.763361\pi$
$853$	−24.0722	+	9.32561i	−0.824216	+	0.319303i	−0.0880602	+	0.996115i	$0.528067\pi$
$854$	−32.1512	−	12.4554i	−1.10019	−	0.426216i
$855$	1.99873	+	2.64674i	0.0683550	+	0.0905167i
$856$	11.8280	+	4.58219i	0.404273	+	0.156616i
$857$	15.3539	+	13.9970i	0.524481	+	0.478127i	0.892093	−	0.451852i	$-0.149236\pi$
$857$	15.3539	+	13.9970i	0.524481	+	0.478127i	−0.367612	+	0.929979i	$0.619825\pi$
$858$	6.79071	−	23.8669i	0.231831	−	0.814802i
$859$	1.03548	+	3.63933i	0.0353300	+	0.124172i	0.977485	−	0.211006i	$-0.0676740\pi$
$859$	1.03548	+	3.63933i	0.0353300	+	0.124172i	−0.942155	+	0.335178i	$0.891203\pi$
$860$	0.0778157	+	0.839765i	0.00265349	+	0.0286357i
$861$	22.9133	+	4.28323i	0.780883	+	0.145972i
$862$	3.42456	+	12.0361i	0.116641	+	0.409951i
$863$	22.0239	−	4.11699i	0.749704	−	0.140144i	0.204988	−	0.978765i	$-0.434285\pi$
$863$	22.0239	−	4.11699i	0.749704	−	0.140144i	0.544716	+	0.838621i	$0.316637\pi$
$864$	−1.76150	−	3.53757i	−0.0599275	−	0.120351i
$865$	41.6116	+	16.1204i	1.41484	+	0.548111i
$866$	22.8674	−	20.8464i	0.777066	−	0.708389i
$867$	−3.67441	+	0.686866i	−0.124789	+	0.0233272i
$868$	−0.123490	−	1.33267i	−0.00419151	−	0.0452336i
$869$	−17.5862	+	23.2880i	−0.596572	+	0.789990i
$870$	−4.37095			−0.148189
$871$	66.8817			2.26620
$872$	−17.9549	+	23.7761i	−0.608029	+	0.805161i
$873$	−12.8251	−	2.39743i	−0.434065	−	0.0811407i
$874$	−2.11705	+	7.44067i	−0.0716104	+	0.251684i
$875$	−36.2371	−	22.4371i	−1.22504	−	0.758511i
$876$	3.05516	+	1.89168i	0.103224	+	0.0639138i
$877$	−12.0373	+	42.3067i	−0.406471	+	1.42860i	0.440881	+	0.897566i	$0.354666\pi$
$877$	−12.0373	+	42.3067i	−0.406471	+	1.42860i	−0.847352	+	0.531032i	$0.821805\pi$
$878$	28.6422	+	5.35415i	0.966627	+	0.180694i
$879$	−12.7917	+	16.9389i	−0.431452	+	0.571335i
$880$	23.5594			0.794186
$881$	49.8006			1.67782			0.838912	−	0.544267i	$-0.183192\pi$
$881$	49.8006			1.67782			0.838912	+	0.544267i	$0.183192\pi$
$882$	0.828711	−	1.09739i	0.0279041	−	0.0369511i
$883$	2.45484	+	26.4919i	0.0826119	+	0.891524i	0.931689	+	0.363256i	$0.118335\pi$
$883$	2.45484	+	26.4919i	0.0826119	+	0.891524i	−0.849078	+	0.528268i	$0.822842\pi$
$884$	−22.9163	+	4.28379i	−0.770758	+	0.144080i
$885$	23.8773	−	21.7670i	0.802626	−	0.731690i
$886$	10.8947	+	4.22064i	0.366015	+	0.141795i
$887$	−19.3533	−	38.8667i	−0.649821	−	1.30502i	−0.937732	−	0.347360i	$-0.887078\pi$
$887$	−19.3533	−	38.8667i	−0.649821	−	1.30502i	0.287910	−	0.957657i	$-0.407039\pi$
$888$	−12.0126	+	2.24554i	−0.403115	+	0.0753553i
$889$	4.54071	+	15.9590i	0.152291	+	0.535246i
$890$	51.4161	+	9.61134i	1.72347	+	0.322173i
$891$	0.296480	+	3.19953i	0.00993245	+	0.107188i
$892$	−4.88120	−	17.1556i	−0.163435	−	0.574413i
$893$	0.995851	−	3.50005i	0.0333249	−	0.117125i
$894$	−12.0099	−	10.9484i	−0.401670	−	0.366171i
$895$	−33.5505	−	12.9975i	−1.12147	−	0.434459i
$896$	−2.52457	−	3.34308i	−0.0843401	−	0.111684i
$897$	−49.9590	−	19.3542i	−1.66808	−	0.646219i
$898$	−25.4545	+	9.86113i	−0.849428	+	0.329070i
$899$	−0.556754	−	0.344728i	−0.0185688	−	0.0114973i
$900$	−4.92925	−	4.49361i	−0.164308	−	0.149787i
$901$	−26.8437	−	53.9094i	−0.894293	−	1.79598i
$902$	−21.6353	+	19.7232i	−0.720376	+	0.656710i
$903$	−0.811873	+	0.314521i	−0.0270174	+	0.0104666i
$904$	10.1287	+	6.27140i	0.336874	+	0.208584i
$905$	6.20699	−	12.4653i	0.206327	−	0.414361i
$906$	14.3801	−	2.68811i	0.477748	−	0.0893066i
$907$	0.372536	−	4.02030i	0.0123698	−	0.133492i	−0.987310	−	0.158807i	$-0.949235\pi$
$907$	0.372536	−	4.02030i	0.0123698	−	0.133492i	0.999680	+	0.0253149i	$0.00805884\pi$
$908$	−4.29963	+	15.1116i	−0.142688	+	0.501497i
$909$	3.84699	−	7.72580i	0.127597	−	0.256249i
$910$	−61.1918	+	55.7837i	−2.02849	+	1.84921i
$911$	−5.52507	−	7.31638i	−0.183054	−	0.242402i	0.697233	−	0.716845i	$-0.254414\pi$
$911$	−5.52507	−	7.31638i	−0.183054	−	0.242402i	−0.880287	+	0.474442i	$0.842650\pi$
$912$	1.04863	+	1.38861i	0.0347236	+	0.0459815i
$913$	3.74373	+	7.51842i	0.123899	+	0.248823i
$914$	0.368971	−	3.98183i	0.0122045	−	0.131707i
$915$	−39.4033	−	7.36575i	−1.30263	−	0.243504i
$916$	−0.0965078	+	0.0597551i	−0.00318871	+	0.00197436i
$917$	−23.6362	+	31.2994i	−0.780536	+	1.03360i
$918$	−4.34060	+	2.68758i	−0.143261	+	0.0887035i
$919$	−1.09828	−	11.8523i	−0.0362290	−	0.390973i	−0.994471	−	0.105014i	$-0.966511\pi$
$919$	−1.09828	−	11.8523i	−0.0362290	−	0.390973i	0.958242	−	0.285959i	$-0.0923122\pi$
$920$	8.25042	−	89.0362i	0.272008	−	2.93544i
$921$	−8.41512	−	7.67140i	−0.277288	−	0.252781i
$922$	23.8736	−	9.24867i	0.786234	−	0.304589i
$923$	−5.66602	+	11.3789i	−0.186499	+	0.374541i
$924$	−1.87442	−	6.58790i	−0.0616639	−	0.216726i
$925$	−30.3227	+	18.7750i	−0.997003	+	0.617318i
$926$	−7.49716			−0.246372
$927$	−9.83414	+	2.50791i	−0.322996	+	0.0823706i
$928$	4.12161			0.135299
$929$	−9.69236	+	6.00126i	−0.317996	+	0.196895i	−0.676143	−	0.736770i	$-0.736350\pi$
$929$	−9.69236	+	6.00126i	−0.317996	+	0.196895i	0.358147	+	0.933665i	$0.383409\pi$
$930$	0.720107	+	2.53091i	0.0236132	+	0.0829919i
$931$	0.485084	−	0.974180i	0.0158980	−	0.0319275i
$932$	16.7707	−	6.49699i	0.549342	−	0.212816i
$933$	−19.0263	−	17.3447i	−0.622892	−	0.567841i
$934$	0.0556068	−	0.600093i	0.00181951	−	0.0196356i
$935$	5.04726	+	54.4686i	0.165063	+	1.78131i
$936$	−18.0112	+	11.1520i	−0.588713	+	0.364516i
$937$	−12.4053	+	16.4273i	−0.405263	+	0.536655i	−0.954185	−	0.299219i	$-0.903274\pi$
$937$	−12.4053	+	16.4273i	−0.405263	+	0.536655i	0.548921	+	0.835874i	$0.315039\pi$
$938$	−26.5438	+	16.4352i	−0.866685	+	0.536629i
$939$	10.5629	+	1.97455i	0.344708	+	0.0644371i
$940$	−1.05143	+	11.3468i	−0.0342939	+	0.370090i
$941$	6.48286	+	13.0193i	0.211335	+	0.424418i	0.975314	−	0.220823i	$-0.0708744\pi$
$941$	6.48286	+	13.0193i	0.211335	+	0.424418i	−0.763979	+	0.645241i	$0.776757\pi$
$942$	2.58342	+	3.42100i	0.0841724	+	0.111462i
$943$	38.0930	+	50.4433i	1.24048	+	1.64266i
$944$	12.5272	−	11.4200i	0.407725	−	0.371691i
$945$	4.77933	−	9.59818i	0.155472	−	0.312229i
$946$	0.299251	−	1.05176i	0.00972949	−	0.0341956i
$947$	0.0281852	−	0.304166i	0.000915894	−	0.00988408i	−0.995264	−	0.0972093i	$-0.969008\pi$
$947$	0.0281852	−	0.304166i	0.000915894	−	0.00988408i	0.996180	+	0.0873252i	$0.0278319\pi$
$948$	6.63461	−	1.24022i	0.215482	−	0.0402806i
$949$	14.8460	−	29.8147i	0.481920	−	0.967826i
$950$	7.58968	+	4.69933i	0.246242	+	0.152466i
$951$	9.32288	−	3.61170i	0.302315	−	0.117117i
$952$	29.6849	−	27.0614i	0.962093	−	0.877063i
$953$	12.5929	+	25.2899i	0.407924	+	0.819222i	0.999912	+	0.0132748i	$0.00422563\pi$
$953$	12.5929	+	25.2899i	0.407924	+	0.819222i	−0.591988	+	0.805947i	$0.701657\pi$
$954$	−10.9563	−	9.98798i	−0.354723	−	0.323373i
$955$	16.8619	+	10.4405i	0.545639	+	0.337845i
$956$	6.84796	−	2.65291i	0.221479	−	0.0858014i
$957$	−3.12495	−	1.21061i	−0.101015	−	0.0391335i
$958$	20.8399	+	27.5964i	0.673305	+	0.891600i
$959$	12.0002	+	4.64889i	0.387505	+	0.150120i
$960$	−23.0763	−	21.0368i	−0.744784	−	0.678961i
$961$	8.37567	−	29.4374i	0.270183	−	0.949594i
$962$	8.39800	+	29.5159i	0.270763	+	0.951632i
$963$	0.380573	+	4.10703i	0.0122638	+	0.132347i
$964$	−18.0721	−	3.37826i	−0.582062	−	0.108806i
$965$	−7.45182	−	26.1904i	−0.239882	−	0.843099i
$966$	24.5836	−	4.59546i	0.790963	−	0.147857i
$967$	6.04612	+	12.1422i	0.194430	+	0.390468i	0.970829	−	0.239774i	$-0.0770733\pi$
$967$	6.04612	+	12.1422i	0.194430	+	0.390468i	−0.776399	+	0.630242i	$0.782956\pi$
$968$	−1.93599	−	0.750006i	−0.0622251	−	0.0241061i
$969$	−2.98578	+	2.72189i	−0.0959169	+	0.0874398i
$970$	−53.7493	+	10.0475i	−1.72579	+	0.322605i
$971$	−0.720981	−	7.78062i	−0.0231374	−	0.249692i	−0.999445	−	0.0333058i	$-0.989396\pi$
$971$	−0.720981	−	7.78062i	−0.0231374	−	0.249692i	0.976308	−	0.216386i	$-0.0694270\pi$
$972$	0.447869	−	0.593075i	0.0143654	−	0.0190229i
$973$	32.0923			1.02883
$974$	20.5464			0.658348
$975$	−37.2571	+	49.3364i	−1.19318	+	1.58003i
$976$	−20.6729	−	3.86443i	−0.661723	−	0.123697i
$977$	−10.6023	+	37.2632i	−0.339197	+	1.19216i	0.585252	+	0.810851i	$0.300995\pi$
$977$	−10.6023	+	37.2632i	−0.339197	+	1.19216i	−0.924450	+	0.381304i	$0.875475\pi$
$978$	15.9598	+	9.88192i	0.510339	+	0.315989i
$979$	34.0972	+	21.1121i	1.08975	+	0.674746i
$980$	−0.932615	+	3.27780i	−0.0297913	+	0.104706i
$981$	−9.52312	−	1.78018i	−0.304050	−	0.0568368i
$982$	15.5452	−	20.5851i	0.496066	−	0.656897i
$983$	−35.5696			−1.13449			−0.567247	−	0.823548i	$-0.691991\pi$
$983$	−35.5696			−1.13449			−0.567247	+	0.823548i	$0.691991\pi$
$984$	24.9934			0.796761
$985$	45.2490	−	59.9194i	1.44175	−	1.90919i
$986$	−0.491288	−	5.30185i	−0.0156458	−	0.168845i
$987$	−11.5640	+	2.16168i	−0.368086	+	0.0688071i
$988$	−3.35654	+	3.05989i	−0.106786	+	0.0973480i
$989$	−2.20158	−	0.852895i	−0.0700061	−	0.0271205i
$990$	6.00253	+	12.0547i	0.190773	+	0.383123i
$991$	0.0862227	−	0.0161178i	0.00273895	−	0.000511999i	−0.182380	−	0.983228i	$-0.558380\pi$
$991$	0.0862227	−	0.0161178i	0.00273895	−	0.000511999i	0.185119	+	0.982716i	$0.440733\pi$
$992$	−0.679029	−	2.38654i	−0.0215592	−	0.0757727i
$993$	−23.9605	−	4.47899i	−0.760362	−	0.142136i
$994$	−0.547490	−	5.90836i	−0.0173653	−	0.187402i
$995$	4.37396	+	15.3729i	0.138664	+	0.487353i
$996$	0.531612	−	1.86842i	0.0168448	−	0.0592033i
$997$	39.5348	+	36.0407i	1.25208	+	1.14142i	0.984028	+	0.178016i	$0.0569678\pi$
$997$	39.5348	+	36.0407i	1.25208	+	1.14142i	0.268051	+	0.963405i	$0.413620\pi$
$998$	33.3283	+	12.9115i	1.05499	+	0.408705i
$999$	−2.39474	−	3.17114i	−0.0757661	−	0.100330i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	309.2.i.b.100.8	yes	160
3.2	odd	2		927.2.u.c.100.3		160
103.34	even	17	inner	309.2.i.b.34.8	✓	160
309.137	odd	34		927.2.u.c.343.3		160

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
309.2.i.b.34.8	✓	160	103.34	even	17	inner
309.2.i.b.100.8	yes	160	1.1	even	1	trivial
927.2.u.c.100.3		160	3.2	odd	2
927.2.u.c.343.3		160	309.137	odd	34

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:	\( N \)	\(=\)	\( 309 = 3 \cdot 103 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	309.i (of order \(17\), degree \(16\), minimal)

\(f(q)\)	\(=\)	\(q+(0.953159 - 0.590171i) q^{2} +(-0.273663 - 0.961826i) q^{3} +(-0.331266 + 0.665272i) q^{4} +(-3.48587 + 1.35043i) q^{5} +(-0.828486 - 0.755265i) q^{6} +(-0.264645 + 2.85597i) q^{7} +(0.283755 + 3.06220i) q^{8} +(-0.850217 + 0.526432i) q^{9} +O(q^{10})\)	\(q+(0.953159 - 0.590171i) q^{2} +(-0.273663 - 0.961826i) q^{3} +(-0.331266 + 0.665272i) q^{4} +(-3.48587 + 1.35043i) q^{5} +(-0.828486 - 0.755265i) q^{6} +(-0.264645 + 2.85597i) q^{7} +(0.283755 + 3.06220i) q^{8} +(-0.850217 + 0.526432i) q^{9} +(-2.52561 + 3.34444i) q^{10} +(-2.73195 + 1.69155i) q^{11} +(0.730531 + 0.136560i) q^{12} +(0.635585 - 6.85906i) q^{13} +(1.43327 + 2.87838i) q^{14} +(2.25284 + 2.98324i) q^{15} +(1.18195 + 1.56515i) q^{16} +(-3.36538 + 3.06795i) q^{17} +(-0.499707 + 1.00355i) q^{18} +(-0.242795 + 0.853336i) q^{19} +(0.256346 - 2.76641i) q^{20} +(2.81937 - 0.527032i) q^{21} +(-1.60568 + 3.22463i) q^{22} +(6.61282 + 4.09448i) q^{23} +(2.86765 - 1.11093i) q^{24} +(6.63260 - 6.04642i) q^{25} +(-3.44220 - 6.91288i) q^{26} +(0.739009 + 0.673696i) q^{27} +(-1.81233 - 1.12215i) q^{28} +(-0.972524 + 0.376758i) q^{29} +(3.90793 + 1.51394i) q^{30} +(0.378376 + 0.501051i) q^{31} +(-3.68501 - 1.42758i) q^{32} +(2.37461 + 2.16474i) q^{33} +(-1.39713 + 4.91039i) q^{34} +(-2.93429 - 10.3130i) q^{35} +(-0.0685725 - 0.740015i) q^{36} +(-3.90612 - 0.730179i) q^{37} +(0.272192 + 0.956655i) q^{38} +(-6.77115 + 1.26575i) q^{39} +(-5.12444 - 10.2913i) q^{40} +(7.57828 + 2.93584i) q^{41} +(2.37627 - 2.16626i) q^{42} +(-0.298389 + 0.0557786i) q^{43} +(-0.220340 - 2.37784i) q^{44} +(2.25284 - 2.98324i) q^{45} +8.71951 q^{46} -4.10162 q^{47} +(1.18195 - 1.56515i) q^{48} +(-1.20574 - 0.225393i) q^{49} +(2.75351 - 9.67757i) q^{50} +(3.87181 + 2.39732i) q^{51} +(4.35259 + 2.69501i) q^{52} +(-3.61905 + 12.7196i) q^{53} +(1.10199 + 0.205997i) q^{54} +(7.23890 - 9.58585i) q^{55} -8.82067 q^{56} +0.887204 q^{57} +(-0.704618 + 0.933065i) q^{58} +(-0.797466 - 8.60602i) q^{59} +(-2.73096 + 0.510504i) q^{60} +(-7.92436 + 7.22401i) q^{61} +(0.656358 + 0.254275i) q^{62} +(-1.27847 - 2.56752i) q^{63} +(-8.21074 + 1.53485i) q^{64} +(7.04714 + 24.7681i) q^{65} +(3.54095 + 0.661918i) q^{66} +(0.895858 + 9.66785i) q^{67} +(-0.926184 - 3.25520i) q^{68} +(2.12850 - 7.48089i) q^{69} +(-8.88325 - 8.09816i) q^{70} +(-1.72073 - 0.666614i) q^{71} +(-1.85330 - 2.45416i) q^{72} +(4.50861 + 1.74665i) q^{73} +(-4.15408 + 1.60930i) q^{74} +(-7.63070 - 4.72473i) q^{75} +(-0.487271 - 0.444206i) q^{76} +(-4.10803 - 8.25004i) q^{77} +(-5.70698 + 5.20260i) q^{78} +(8.46861 - 3.28076i) q^{79} +(-6.23377 - 3.85979i) q^{80} +(0.445738 - 0.895163i) q^{81} +(8.95596 - 1.67416i) q^{82} +(0.241176 - 2.60271i) q^{83} +(-0.583343 + 2.05024i) q^{84} +(7.58822 - 15.2392i) q^{85} +(-0.251493 + 0.229266i) q^{86} +(0.628519 + 0.832293i) q^{87} +(-5.95508 - 7.88580i) q^{88} +(-5.56322 - 11.1725i) q^{89} +(0.386691 - 4.17306i) q^{90} +(19.4211 + 3.63043i) q^{91} +(-4.91455 + 3.04296i) q^{92} +(0.378376 - 0.501051i) q^{93} +(-3.90949 + 2.42066i) q^{94} +(-0.306022 - 3.30250i) q^{95} +(-0.364633 + 3.93501i) q^{96} +(9.64205 + 8.78989i) q^{97} +(-1.28229 + 0.496760i) q^{98} +(1.43226 - 2.87637i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 160 q - q^{2} - 10 q^{3} - 17 q^{4} - 4 q^{5} - q^{6} - 12 q^{7} + 36 q^{8} - 10 q^{9}+O(q^{10}) \) 160 * q - q^2 - 10 * q^3 - 17 * q^4 - 4 * q^5 - q^6 - 12 * q^7 + 36 * q^8 - 10 * q^9	\( 160 q - q^{2} - 10 q^{3} - 17 q^{4} - 4 q^{5} - q^{6} - 12 q^{7} + 36 q^{8} - 10 q^{9} + 12 q^{10} + q^{11} + 17 q^{12} - 18 q^{13} + 31 q^{14} - 4 q^{15} - 39 q^{16} - 14 q^{17} - q^{18} - 11 q^{19} + 31 q^{20} + 5 q^{21} + 3 q^{23} - 15 q^{24} - 8 q^{25} - 33 q^{26} - 10 q^{27} - 2 q^{28} - 28 q^{29} + 12 q^{30} - 20 q^{31} - 46 q^{32} + 18 q^{33} + 5 q^{34} - 3 q^{35} - 17 q^{36} - 34 q^{37} - 14 q^{38} - 18 q^{39} - 56 q^{40} + 40 q^{41} + 14 q^{42} - 42 q^{43} - 26 q^{44} - 4 q^{45} + 112 q^{46} - 40 q^{47} - 39 q^{48} + 30 q^{49} - 10 q^{50} + 3 q^{51} - 58 q^{52} - 48 q^{53} - q^{54} - 64 q^{55} + 86 q^{56} + 6 q^{57} - 36 q^{58} + 76 q^{59} - 20 q^{60} - 28 q^{61} - 66 q^{62} - 12 q^{63} + 88 q^{64} - 14 q^{65} - 34 q^{66} - 84 q^{67} - 107 q^{68} - 14 q^{69} + 8 q^{70} + 41 q^{71} - 15 q^{72} - 32 q^{73} + 3 q^{74} - 42 q^{75} - 68 q^{76} + 93 q^{77} + 18 q^{78} - 100 q^{79} - 168 q^{80} - 10 q^{81} + 99 q^{82} - 28 q^{83} + 151 q^{84} + 15 q^{85} + 64 q^{86} - 11 q^{87} - 25 q^{88} - 19 q^{89} - 5 q^{90} + 122 q^{91} - 78 q^{92} - 20 q^{93} + 138 q^{94} - 15 q^{95} + 56 q^{96} + 161 q^{97} + 65 q^{98} + q^{99}+O(q^{100}) \) 160 * q - q^2 - 10 * q^3 - 17 * q^4 - 4 * q^5 - q^6 - 12 * q^7 + 36 * q^8 - 10 * q^9 + 12 * q^10 + q^11 + 17 * q^12 - 18 * q^13 + 31 * q^14 - 4 * q^15 - 39 * q^16 - 14 * q^17 - q^18 - 11 * q^19 + 31 * q^20 + 5 * q^21 + 3 * q^23 - 15 * q^24 - 8 * q^25 - 33 * q^26 - 10 * q^27 - 2 * q^28 - 28 * q^29 + 12 * q^30 - 20 * q^31 - 46 * q^32 + 18 * q^33 + 5 * q^34 - 3 * q^35 - 17 * q^36 - 34 * q^37 - 14 * q^38 - 18 * q^39 - 56 * q^40 + 40 * q^41 + 14 * q^42 - 42 * q^43 - 26 * q^44 - 4 * q^45 + 112 * q^46 - 40 * q^47 - 39 * q^48 + 30 * q^49 - 10 * q^50 + 3 * q^51 - 58 * q^52 - 48 * q^53 - q^54 - 64 * q^55 + 86 * q^56 + 6 * q^57 - 36 * q^58 + 76 * q^59 - 20 * q^60 - 28 * q^61 - 66 * q^62 - 12 * q^63 + 88 * q^64 - 14 * q^65 - 34 * q^66 - 84 * q^67 - 107 * q^68 - 14 * q^69 + 8 * q^70 + 41 * q^71 - 15 * q^72 - 32 * q^73 + 3 * q^74 - 42 * q^75 - 68 * q^76 + 93 * q^77 + 18 * q^78 - 100 * q^79 - 168 * q^80 - 10 * q^81 + 99 * q^82 - 28 * q^83 + 151 * q^84 + 15 * q^85 + 64 * q^86 - 11 * q^87 - 25 * q^88 - 19 * q^89 - 5 * q^90 + 122 * q^91 - 78 * q^92 - 20 * q^93 + 138 * q^94 - 15 * q^95 + 56 * q^96 + 161 * q^97 + 65 * q^98 + q^99

Introduction

L-functions

Modular forms

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