LMFDB - Embedded newform 538.3.c.b.187.19

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [538,3,Mod(187,538)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(538, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([1]))

N = Newforms(chi, 3, names="a")

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

chi := DirichletCharacter("538.187");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 538 = 2 \cdot 269 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	538.c (of order $4$, degree $2$, 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:	$14.6594382226$
Analytic rank:	$0$
Dimension:	$46$
Relative dimension:	$23$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			187.19
Character	$\chi$	$=$	538.187
Dual form			538.3.c.b.351.19

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.00000 - 1.00000i) q^{2} +(2.50903 + 2.50903i) q^{3} +2.00000i q^{4} -9.33859 q^{5} -5.01806i q^{6} +(7.56973 - 7.56973i) q^{7} +(2.00000 - 2.00000i) q^{8} +3.59045i q^{9} +(9.33859 + 9.33859i) q^{10} -2.77741i q^{11} +(-5.01806 + 5.01806i) q^{12} +21.9868i q^{13} -15.1395 q^{14} +(-23.4308 - 23.4308i) q^{15} -4.00000 q^{16} +(5.95995 + 5.95995i) q^{17} +(3.59045 - 3.59045i) q^{18} +(-11.5053 + 11.5053i) q^{19} -18.6772i q^{20} +37.9854 q^{21} +(-2.77741 + 2.77741i) q^{22} -38.8588 q^{23} +10.0361 q^{24} +62.2093 q^{25} +(21.9868 - 21.9868i) q^{26} +(13.5727 - 13.5727i) q^{27} +(15.1395 + 15.1395i) q^{28} +(-33.4036 + 33.4036i) q^{29} +46.8616i q^{30} +(-0.994331 + 0.994331i) q^{31} +(4.00000 + 4.00000i) q^{32} +(6.96860 - 6.96860i) q^{33} -11.9199i q^{34} +(-70.6907 + 70.6907i) q^{35} -7.18090 q^{36} -37.3683 q^{37} +23.0106 q^{38} +(-55.1656 + 55.1656i) q^{39} +(-18.6772 + 18.6772i) q^{40} -73.7321 q^{41} +(-37.9854 - 37.9854i) q^{42} -3.77063i q^{43} +5.55482 q^{44} -33.5298i q^{45} +(38.8588 + 38.8588i) q^{46} +5.27937 q^{47} +(-10.0361 - 10.0361i) q^{48} -65.6017i q^{49} +(-62.2093 - 62.2093i) q^{50} +29.9074i q^{51} -43.9736 q^{52} +30.4928 q^{53} -27.1454 q^{54} +25.9371i q^{55} -30.2789i q^{56} -57.7343 q^{57} +66.8072 q^{58} +(-13.9942 + 13.9942i) q^{59} +(46.8616 - 46.8616i) q^{60} +13.1154 q^{61} +1.98866 q^{62} +(27.1788 + 27.1788i) q^{63} -8.00000i q^{64} -205.326i q^{65} -13.9372 q^{66} -109.169 q^{67} +(-11.9199 + 11.9199i) q^{68} +(-97.4979 - 97.4979i) q^{69} +141.381 q^{70} +(-59.9574 + 59.9574i) q^{71} +(7.18090 + 7.18090i) q^{72} -22.8934i q^{73} +(37.3683 + 37.3683i) q^{74} +(156.085 + 156.085i) q^{75} +(-23.0106 - 23.0106i) q^{76} +(-21.0242 - 21.0242i) q^{77} +110.331 q^{78} -15.5383i q^{79} +37.3544 q^{80} +100.423 q^{81} +(73.7321 + 73.7321i) q^{82} +(-1.13888 + 1.13888i) q^{83} +75.9707i q^{84} +(-55.6576 - 55.6576i) q^{85} +(-3.77063 + 3.77063i) q^{86} -167.621 q^{87} +(-5.55482 - 5.55482i) q^{88} +5.33762i q^{89} +(-33.5298 + 33.5298i) q^{90} +(166.434 + 166.434i) q^{91} -77.7177i q^{92} -4.98961 q^{93} +(-5.27937 - 5.27937i) q^{94} +(107.443 - 107.443i) q^{95} +20.0722i q^{96} +133.029i q^{97} +(-65.6017 + 65.6017i) q^{98} +9.97215 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 46 q - 46 q^{2} - 6 q^{3} - 32 q^{5} + 4 q^{7} + 92 q^{8} + 32 q^{10} + 12 q^{12} - 8 q^{14} - 10 q^{15} - 184 q^{16} - 50 q^{17} + 118 q^{18} + 10 q^{19} + 16 q^{21} + 8 q^{22} - 124 q^{23} - 24 q^{24}+ \cdots + 508 q^{99}+O(q^{100}) $ 46 * q - 46 * q^2 - 6 * q^3 - 32 * q^5 + 4 * q^7 + 92 * q^8 + 32 * q^10 + 12 * q^12 - 8 * q^14 - 10 * q^15 - 184 * q^16 - 50 * q^17 + 118 * q^18 + 10 * q^19 + 16 * q^21 + 8 * q^22 - 124 * q^23 - 24 * q^24 + 178 * q^25 + 4 * q^26 + 90 * q^27 + 8 * q^28 + 40 * q^29 + 40 * q^31 + 184 * q^32 - 64 * q^33 - 14 * q^35 - 236 * q^36 - 32 * q^37 - 20 * q^38 - 54 * q^39 - 64 * q^40 - 132 * q^41 - 16 * q^42 - 16 * q^44 + 124 * q^46 - 60 * q^47 + 24 * q^48 - 178 * q^50 - 8 * q^52 - 188 * q^53 - 180 * q^54 - 40 * q^57 - 80 * q^58 + 190 * q^59 + 20 * q^60 - 80 * q^62 - 266 * q^63 + 128 * q^66 - 164 * q^67 + 100 * q^68 + 170 * q^69 + 28 * q^70 - 92 * q^71 + 236 * q^72 + 32 * q^74 - 190 * q^75 + 20 * q^76 + 20 * q^77 + 108 * q^78 + 128 * q^80 - 298 * q^81 + 132 * q^82 + 190 * q^83 + 298 * q^85 + 228 * q^86 - 92 * q^87 + 16 * q^88 - 528 * q^90 + 2 * q^91 + 232 * q^93 + 60 * q^94 - 280 * q^95 - 226 * q^98 + 508 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/538\mathbb{Z}\right)^\times$.

$n$	$271$
$\chi(n)$	$e\left(\frac{1}{4}\right)$

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 $

$2$	−1.00000	−	1.00000i	−0.500000	−	0.500000i
$2$	−1.00000	−	1.00000i	−0.500000	−	0.500000i
$3$	2.50903	+	2.50903i	0.836343	+	0.836343i	0.988375	−	0.152033i	$-0.0485819\pi$
$3$	2.50903	+	2.50903i	0.836343	+	0.836343i	−0.152033	+	0.988375i	$0.548582\pi$
$4$			2.00000i			0.500000i
$5$	−9.33859			−1.86772			−0.933859	−	0.357640i	$-0.883581\pi$
$5$	−9.33859			−1.86772			−0.933859	+	0.357640i	$0.883581\pi$
$6$		−	5.01806i		−	0.836343i
$7$	7.56973	−	7.56973i	1.08139	−	1.08139i	0.0850105	−	0.996380i	$-0.472908\pi$
$7$	7.56973	−	7.56973i	1.08139	−	1.08139i	0.996380	−	0.0850105i	$-0.0270924\pi$
$8$	2.00000	−	2.00000i	0.250000	−	0.250000i
$9$			3.59045i			0.398939i
$10$	9.33859	+	9.33859i	0.933859	+	0.933859i
$11$		−	2.77741i		−	0.252492i	−0.991999	−	0.126246i	$-0.959707\pi$
$11$		−	2.77741i		−	0.252492i	0.991999	−	0.126246i	$-0.0402928\pi$
$12$	−5.01806	+	5.01806i	−0.418171	+	0.418171i
$13$			21.9868i			1.69129i	0.533743	+	0.845647i	$0.320785\pi$
$13$			21.9868i			1.69129i	−0.533743	+	0.845647i	$0.679215\pi$
$14$	−15.1395			−1.08139
$15$	−23.4308	−	23.4308i	−1.56205	−	1.56205i
$16$	−4.00000			−0.250000
$17$	5.95995	+	5.95995i	0.350586	+	0.350586i	0.860327	−	0.509742i	$-0.170259\pi$
$17$	5.95995	+	5.95995i	0.350586	+	0.350586i	−0.509742	+	0.860327i	$0.670259\pi$
$18$	3.59045	−	3.59045i	0.199470	−	0.199470i
$19$	−11.5053	+	11.5053i	−0.605543	+	0.605543i	−0.941778	−	0.336235i	$-0.890846\pi$
$19$	−11.5053	+	11.5053i	−0.605543	+	0.605543i	0.336235	+	0.941778i	$0.390846\pi$
$20$		−	18.6772i		−	0.933859i
$21$	37.9854			1.80883
$22$	−2.77741	+	2.77741i	−0.126246	+	0.126246i
$23$	−38.8588			−1.68951			−0.844757	−	0.535150i	$-0.820255\pi$
$23$	−38.8588			−1.68951			−0.844757	+	0.535150i	$0.820255\pi$
$24$	10.0361			0.418171
$25$	62.2093			2.48837
$26$	21.9868	−	21.9868i	0.845647	−	0.845647i
$27$	13.5727	−	13.5727i	0.502693	−	0.502693i
$28$	15.1395	+	15.1395i	0.540695	+	0.540695i
$29$	−33.4036	+	33.4036i	−1.15185	+	1.15185i	−0.165667	+	0.986182i	$0.552978\pi$
$29$	−33.4036	+	33.4036i	−1.15185	+	1.15185i	−0.986182	+	0.165667i	$0.947022\pi$
$30$			46.8616i			1.56205i
$31$	−0.994331	+	0.994331i	−0.0320752	+	0.0320752i	−0.722962	−	0.690887i	$-0.757220\pi$
$31$	−0.994331	+	0.994331i	−0.0320752	+	0.0320752i	0.690887	+	0.722962i	$0.257220\pi$
$32$	4.00000	+	4.00000i	0.125000	+	0.125000i
$33$	6.96860	−	6.96860i	0.211170	−	0.211170i
$34$		−	11.9199i		−	0.350586i
$35$	−70.6907	+	70.6907i	−2.01973	+	2.01973i
$36$	−7.18090			−0.199470
$37$	−37.3683			−1.00995			−0.504977	−	0.863133i	$-0.668499\pi$
$37$	−37.3683			−1.00995			−0.504977	+	0.863133i	$0.668499\pi$
$38$	23.0106			0.605543
$39$	−55.1656	+	55.1656i	−1.41450	+	1.41450i
$40$	−18.6772	+	18.6772i	−0.466930	+	0.466930i
$41$	−73.7321			−1.79834			−0.899172	−	0.437595i	$-0.855830\pi$
$41$	−73.7321			−1.79834			−0.899172	+	0.437595i	$0.855830\pi$
$42$	−37.9854	−	37.9854i	−0.904413	−	0.904413i
$43$		−	3.77063i		−	0.0876891i	−0.999038	−	0.0438445i	$-0.986039\pi$
$43$		−	3.77063i		−	0.0876891i	0.999038	−	0.0438445i	$-0.0139606\pi$
$44$	5.55482			0.126246
$45$		−	33.5298i		−	0.745106i
$46$	38.8588	+	38.8588i	0.844757	+	0.844757i
$47$	5.27937			0.112327			0.0561635	−	0.998422i	$-0.482113\pi$
$47$	5.27937			0.112327			0.0561635	+	0.998422i	$0.482113\pi$
$48$	−10.0361	−	10.0361i	−0.209086	−	0.209086i
$49$		−	65.6017i		−	1.33881i
$50$	−62.2093	−	62.2093i	−1.24419	−	1.24419i
$51$			29.9074i			0.586420i
$52$	−43.9736			−0.845647
$53$	30.4928			0.575336			0.287668	−	0.957730i	$-0.407120\pi$
$53$	30.4928			0.575336			0.287668	+	0.957730i	$0.407120\pi$
$54$	−27.1454			−0.502693
$55$			25.9371i			0.471584i
$56$		−	30.2789i		−	0.540695i
$57$	−57.7343			−1.01288
$58$	66.8072			1.15185
$59$	−13.9942	+	13.9942i	−0.237189	+	0.237189i	−0.815685	−	0.578496i	$-0.803640\pi$
$59$	−13.9942	+	13.9942i	−0.237189	+	0.237189i	0.578496	+	0.815685i	$0.303640\pi$
$60$	46.8616	−	46.8616i	0.781027	−	0.781027i
$61$	13.1154			0.215006			0.107503	−	0.994205i	$-0.465714\pi$
$61$	13.1154			0.215006			0.107503	+	0.994205i	$0.465714\pi$
$62$	1.98866			0.0320752
$63$	27.1788	+	27.1788i	0.431409	+	0.431409i
$64$		−	8.00000i		−	0.125000i
$65$		−	205.326i		−	3.15886i
$66$	−13.9372			−0.211170
$67$	−109.169			−1.62939			−0.814694	−	0.579891i	$-0.803095\pi$
$67$	−109.169			−1.62939			−0.814694	+	0.579891i	$0.803095\pi$
$68$	−11.9199	+	11.9199i	−0.175293	+	0.175293i
$69$	−97.4979	−	97.4979i	−1.41301	−	1.41301i
$70$	141.381			2.01973
$71$	−59.9574	+	59.9574i	−0.844470	+	0.844470i	−0.989437	−	0.144966i	$-0.953693\pi$
$71$	−59.9574	+	59.9574i	−0.844470	+	0.844470i	0.144966	+	0.989437i	$0.453693\pi$
$72$	7.18090	+	7.18090i	0.0997348	+	0.0997348i
$73$		−	22.8934i		−	0.313609i	−0.987630	−	0.156804i	$-0.949881\pi$
$73$		−	22.8934i		−	0.313609i	0.987630	−	0.156804i	$-0.0501192\pi$
$74$	37.3683	+	37.3683i	0.504977	+	0.504977i
$75$	156.085	+	156.085i	2.08113	+	2.08113i
$76$	−23.0106	−	23.0106i	−0.302771	−	0.302771i
$77$	−21.0242	−	21.0242i	−0.273042	−	0.273042i
$78$	110.331			1.41450
$79$		−	15.5383i		−	0.196687i	−0.995153	−	0.0983437i	$-0.968646\pi$
$79$		−	15.5383i		−	0.196687i	0.995153	−	0.0983437i	$-0.0313544\pi$
$80$	37.3544			0.466930
$81$	100.423			1.23979
$82$	73.7321	+	73.7321i	0.899172	+	0.899172i
$83$	−1.13888	+	1.13888i	−0.0137214	+	0.0137214i	−0.713934	−	0.700213i	$-0.753088\pi$
$83$	−1.13888	+	1.13888i	−0.0137214	+	0.0137214i	0.700213	+	0.713934i	$0.253088\pi$
$84$			75.9707i			0.904413i
$85$	−55.6576	−	55.6576i	−0.654795	−	0.654795i
$86$	−3.77063	+	3.77063i	−0.0438445	+	0.0438445i
$87$	−167.621			−1.92668
$88$	−5.55482	−	5.55482i	−0.0631229	−	0.0631229i
$89$			5.33762i			0.0599732i	0.999550	+	0.0299866i	$0.00954647\pi$
$89$			5.33762i			0.0599732i	−0.999550	+	0.0299866i	$0.990454\pi$
$90$	−33.5298	+	33.5298i	−0.372553	+	0.372553i
$91$	166.434	+	166.434i	1.82895	+	1.82895i
$92$		−	77.7177i		−	0.844757i
$93$	−4.98961			−0.0536517
$94$	−5.27937	−	5.27937i	−0.0561635	−	0.0561635i
$95$	107.443	−	107.443i	1.13098	−	1.13098i
$96$			20.0722i			0.209086i
$97$			133.029i			1.37143i	0.727871	+	0.685715i	$0.240510\pi$
$97$			133.029i			1.37143i	−0.727871	+	0.685715i	$0.759490\pi$
$98$	−65.6017	+	65.6017i	−0.669406	+	0.669406i
$99$	9.97215			0.100729
$100$			124.419i			1.24419i
$101$	101.492	+	101.492i	1.00487	+	1.00487i	0.999988	+	0.00487932i	$0.00155314\pi$
$101$	101.492	+	101.492i	1.00487	+	1.00487i	0.00487932	+	0.999988i	$0.498447\pi$
$102$	29.9074	−	29.9074i	0.293210	−	0.293210i
$103$			185.242i			1.79847i	0.437468	+	0.899234i	$0.355875\pi$
$103$			185.242i			1.79847i	−0.437468	+	0.899234i	$0.644125\pi$
$104$	43.9736	+	43.9736i	0.422823	+	0.422823i
$105$	−354.730			−3.37838
$106$	−30.4928	−	30.4928i	−0.287668	−	0.287668i
$107$	−27.9295	+	27.9295i	−0.261024	+	0.261024i	−0.825470	−	0.564446i	$-0.809090\pi$
$107$	−27.9295	+	27.9295i	−0.261024	+	0.261024i	0.564446	+	0.825470i	$0.309090\pi$
$108$	27.1454	+	27.1454i	0.251347	+	0.251347i
$109$	−110.515	+	110.515i	−1.01390	+	1.01390i	−0.0139955	+	0.999902i	$0.504455\pi$
$109$	−110.515	+	110.515i	−1.01390	+	1.01390i	−0.999902	+	0.0139955i	$0.995545\pi$
$110$	25.9371	−	25.9371i	0.235792	−	0.235792i
$111$	−93.7582	−	93.7582i	−0.844668	−	0.844668i
$112$	−30.2789	+	30.2789i	−0.270348	+	0.270348i
$113$	158.480	−	158.480i	1.40248	−	1.40248i	0.610346	−	0.792135i	$-0.291030\pi$
$113$	158.480	−	158.480i	1.40248	−	1.40248i	0.792135	−	0.610346i	$-0.208970\pi$
$114$	57.7343	+	57.7343i	0.506441	+	0.506441i
$115$	362.887			3.15554
$116$	−66.8072	−	66.8072i	−0.575924	−	0.575924i
$117$	−78.9426			−0.674723
$118$	27.9884			0.237189
$119$	90.2305			0.758240
$120$	−93.7232			−0.781027
$121$	113.286			0.936248
$122$	−13.1154	−	13.1154i	−0.107503	−	0.107503i
$123$	−184.996	−	184.996i	−1.50403	−	1.50403i
$124$	−1.98866	−	1.98866i	−0.0160376	−	0.0160376i
$125$	−347.483			−2.77986
$126$		−	54.3575i		−	0.431409i
$127$		−	137.028i		−	1.07896i	−0.841999	−	0.539479i	$-0.818621\pi$
$127$		−	137.028i		−	1.07896i	0.841999	−	0.539479i	$-0.181379\pi$
$128$	−8.00000	+	8.00000i	−0.0625000	+	0.0625000i
$129$	9.46062	−	9.46062i	0.0733381	−	0.0733381i
$130$	−205.326	+	205.326i	−1.57943	+	1.57943i
$131$	3.72007			0.0283975			0.0141987	−	0.999899i	$-0.495480\pi$
$131$	3.72007			0.0283975			0.0141987	+	0.999899i	$0.495480\pi$
$132$	13.9372	+	13.9372i	0.105585	+	0.105585i
$133$			174.184i			1.30966i
$134$	109.169	+	109.169i	0.814694	+	0.814694i
$135$	−126.750	+	126.750i	−0.938889	+	0.938889i
$136$	23.8398			0.175293
$137$	165.955	−	165.955i	1.21135	−	1.21135i	0.240764	−	0.970584i	$-0.422602\pi$
$137$	165.955	−	165.955i	1.21135	−	1.21135i	0.970584	−	0.240764i	$-0.0773979\pi$
$138$			194.996i			1.41301i
$139$	−55.4492	−	55.4492i	−0.398915	−	0.398915i	0.478935	−	0.877850i	$-0.341023\pi$
$139$	−55.4492	−	55.4492i	−0.398915	−	0.398915i	−0.877850	+	0.478935i	$0.841023\pi$
$140$	−141.381	−	141.381i	−1.00987	−	1.00987i
$141$	13.2461	+	13.2461i	0.0939439	+	0.0939439i
$142$	119.915			0.844470
$143$	61.0664			0.427038
$144$		−	14.3618i		−	0.0997348i
$145$	311.943	−	311.943i	2.15133	−	2.15133i
$146$	−22.8934	+	22.8934i	−0.156804	+	0.156804i
$147$	164.597	−	164.597i	1.11971	−	1.11971i
$148$		−	74.7366i		−	0.504977i
$149$			215.861i			1.44873i	0.689417	+	0.724365i	$0.257867\pi$
$149$			215.861i			1.44873i	−0.689417	+	0.724365i	$0.742133\pi$
$150$		−	312.170i		−	2.08113i
$151$			17.4767i			0.115740i	0.998324	+	0.0578698i	$0.0184308\pi$
$151$			17.4767i			0.115740i	−0.998324	+	0.0578698i	$0.981569\pi$
$152$			46.0213i			0.302771i
$153$	−21.3989	+	21.3989i	−0.139862	+	0.139862i
$154$			42.0485i			0.273042i
$155$	9.28565	−	9.28565i	0.0599074	−	0.0599074i
$156$	−110.331	−	110.331i	−0.707251	−	0.707251i
$157$	127.982	+	127.982i	0.815175	+	0.815175i	0.985404	−	0.170230i	$-0.0544510\pi$
$157$	127.982	+	127.982i	0.815175	+	0.815175i	−0.170230	+	0.985404i	$0.554451\pi$
$158$	−15.5383	+	15.5383i	−0.0983437	+	0.0983437i
$159$	76.5073	+	76.5073i	0.481178	+	0.481178i
$160$	−37.3544	−	37.3544i	−0.233465	−	0.233465i
$161$	−294.151	+	294.151i	−1.82702	+	1.82702i
$162$	−100.423	−	100.423i	−0.619893	−	0.619893i
$163$	48.9605	−	48.9605i	0.300371	−	0.300371i	−0.540788	−	0.841159i	$-0.681874\pi$
$163$	48.9605	−	48.9605i	0.300371	−	0.300371i	0.841159	+	0.540788i	$0.181874\pi$
$164$		−	147.464i		−	0.899172i
$165$	−65.0769	+	65.0769i	−0.394406	+	0.394406i
$166$	2.27776			0.0137214
$167$	−102.936	−	102.936i	−0.616386	−	0.616386i	0.328217	−	0.944603i	$-0.393552\pi$
$167$	−102.936	−	102.936i	−0.616386	−	0.616386i	−0.944603	+	0.328217i	$0.893552\pi$
$168$	75.9707	−	75.9707i	0.452207	−	0.452207i
$169$	−314.420			−1.86047
$170$			111.315i			0.654795i
$171$	−41.3093	−	41.3093i	−0.241575	−	0.241575i
$172$	7.54126			0.0438445
$173$	103.881			0.600467			0.300234	−	0.953866i	$-0.402935\pi$
$173$	103.881			0.600467			0.300234	+	0.953866i	$0.402935\pi$
$174$	167.621	+	167.621i	0.963340	+	0.963340i
$175$	470.908	−	470.908i	2.69090	−	2.69090i
$176$			11.1096i			0.0631229i
$177$	−70.2236			−0.396743
$178$	5.33762	−	5.33762i	0.0299866	−	0.0299866i
$179$	−175.102	−	175.102i	−0.978223	−	0.978223i	0.0215452	−	0.999768i	$-0.493141\pi$
$179$	−175.102	−	175.102i	−0.978223	−	0.978223i	−0.999768	+	0.0215452i	$0.993141\pi$
$180$	67.0595			0.372553
$181$	109.980	−	109.980i	0.607624	−	0.607624i	−0.334700	−	0.942325i	$-0.608635\pi$
$181$	109.980	−	109.980i	0.607624	−	0.607624i	0.942325	+	0.334700i	$0.108635\pi$
$182$		−	332.869i		−	1.82895i
$183$	32.9069	+	32.9069i	0.179819	+	0.179819i
$184$	−77.7177	+	77.7177i	−0.422379	+	0.422379i
$185$	348.967			1.88631
$186$	4.98961	+	4.98961i	0.0268259	+	0.0268259i
$187$	16.5532	−	16.5532i	0.0885199	−	0.0885199i
$188$			10.5587i			0.0561635i
$189$		−	205.484i		−	1.08722i
$190$	−214.887			−1.13098
$191$			188.656i			0.987726i	0.869540	+	0.493863i	$0.164416\pi$
$191$			188.656i			0.987726i	−0.869540	+	0.493863i	$0.835584\pi$
$192$	20.0722	−	20.0722i	0.104543	−	0.104543i
$193$	−88.6898	+	88.6898i	−0.459533	+	0.459533i	−0.898502	−	0.438969i	$-0.855344\pi$
$193$	−88.6898	+	88.6898i	−0.459533	+	0.459533i	0.438969	+	0.898502i	$0.355344\pi$
$194$	133.029	−	133.029i	0.685715	−	0.685715i
$195$	515.169	−	515.169i	2.64189	−	2.64189i
$196$	131.203			0.669406
$197$	123.136	−	123.136i	0.625057	−	0.625057i	−0.321763	−	0.946820i	$-0.604275\pi$
$197$	123.136	−	123.136i	0.625057	−	0.625057i	0.946820	+	0.321763i	$0.104275\pi$
$198$	−9.97215	−	9.97215i	−0.0503644	−	0.0503644i
$199$		−	278.717i		−	1.40059i	−0.713855	−	0.700294i	$-0.753052\pi$
$199$		−	278.717i		−	1.40059i	0.713855	−	0.700294i	$-0.246948\pi$
$200$	124.419	−	124.419i	0.622093	−	0.622093i
$201$	−273.908	−	273.908i	−1.36273	−	1.36273i
$202$		−	202.983i		−	1.00487i
$203$			505.713i			2.49120i
$204$	−59.8148			−0.293210
$205$	688.554			3.35880
$206$	185.242	−	185.242i	0.899234	−	0.899234i
$207$		−	139.521i		−	0.674013i
$208$		−	87.9473i		−	0.422823i
$209$	31.9550	+	31.9550i	0.152895	+	0.152895i
$210$	354.730	+	354.730i	1.68919	+	1.68919i
$211$			135.519i			0.642270i	0.947033	+	0.321135i	$0.104064\pi$
$211$			135.519i			0.642270i	−0.947033	+	0.321135i	$0.895936\pi$
$212$			60.9856i			0.287668i
$213$	−300.870			−1.41253
$214$	55.8591			0.261024
$215$			35.2124i			0.163779i
$216$		−	54.2909i		−	0.251347i
$217$			15.0536i			0.0693716i
$218$	221.030			1.01390
$219$	57.4403	−	57.4403i	0.262284	−	0.262284i
$220$	−51.8742			−0.235792
$221$	−131.040	+	131.040i	−0.592943	+	0.592943i
$222$			187.516i			0.844668i
$223$	−28.1268	+	28.1268i	−0.126129	+	0.126129i	−0.767353	−	0.641224i	$-0.778427\pi$
$223$	−28.1268	+	28.1268i	−0.126129	+	0.126129i	0.641224	+	0.767353i	$0.278427\pi$
$224$	60.5579			0.270348
$225$			223.360i			0.992710i
$226$	−316.961			−1.40248
$227$	104.606	−	104.606i	0.460818	−	0.460818i	−0.438105	−	0.898924i	$-0.644350\pi$
$227$	104.606	−	104.606i	0.460818	−	0.460818i	0.898924	+	0.438105i	$0.144350\pi$
$228$		−	115.469i		−	0.506441i
$229$	−79.7578	−	79.7578i	−0.348287	−	0.348287i	0.511184	−	0.859471i	$-0.329207\pi$
$229$	−79.7578	−	79.7578i	−0.348287	−	0.348287i	−0.859471	+	0.511184i	$0.829207\pi$
$230$	−362.887	−	362.887i	−1.57777	−	1.57777i
$231$		−	105.501i		−	0.456714i
$232$			133.614i			0.575924i
$233$		−	64.4090i		−	0.276433i	−0.990402	−	0.138217i	$-0.955863\pi$
$233$		−	64.4090i		−	0.276433i	0.990402	−	0.138217i	$-0.0441370\pi$
$234$	78.9426	+	78.9426i	0.337362	+	0.337362i
$235$	−49.3019			−0.209795
$236$	−27.9884	−	27.9884i	−0.118595	−	0.118595i
$237$	38.9860	−	38.9860i	0.164498	−	0.164498i
$238$	−90.2305	−	90.2305i	−0.379120	−	0.379120i
$239$	−263.585			−1.10286			−0.551432	−	0.834220i	$-0.685919\pi$
$239$	−263.585			−1.10286			−0.551432	+	0.834220i	$0.685919\pi$
$240$	93.7232	+	93.7232i	0.390513	+	0.390513i
$241$	131.894	−	131.894i	0.547280	−	0.547280i	−0.378373	−	0.925653i	$-0.623516\pi$
$241$	131.894	−	131.894i	0.547280	−	0.547280i	0.925653	+	0.378373i	$0.123516\pi$
$242$	−113.286	−	113.286i	−0.468124	−	0.468124i
$243$	129.809	+	129.809i	0.534194	+	0.534194i
$244$			26.2308i			0.107503i
$245$			612.628i			2.50052i
$246$			369.992i			1.50403i
$247$	−252.965	−	252.965i	−1.02415	−	1.02415i
$248$			3.97732i			0.0160376i
$249$	−5.71496			−0.0229517
$250$	347.483	+	347.483i	1.38993	+	1.38993i
$251$	−120.640	−	120.640i	−0.480639	−	0.480639i	0.424696	−	0.905336i	$-0.360381\pi$
$251$	−120.640	−	120.640i	−0.480639	−	0.480639i	−0.905336	+	0.424696i	$0.860381\pi$
$252$	−54.3575	+	54.3575i	−0.215704	+	0.215704i
$253$			107.927i			0.426588i
$254$	−137.028	+	137.028i	−0.539479	+	0.539479i
$255$		−	279.293i		−	1.09527i
$256$	16.0000			0.0625000
$257$	−21.7398	−	21.7398i	−0.0845905	−	0.0845905i	0.663545	−	0.748136i	$-0.269051\pi$
$257$	−21.7398	−	21.7398i	−0.0845905	−	0.0845905i	−0.748136	+	0.663545i	$0.769051\pi$
$258$	−18.9212			−0.0733381
$259$	−282.868	+	282.868i	−1.09216	+	1.09216i
$260$	410.652			1.57943
$261$	−119.934	−	119.934i	−0.459517	−	0.459517i
$262$	−3.72007	−	3.72007i	−0.0141987	−	0.0141987i
$263$	−320.777			−1.21968			−0.609842	−	0.792523i	$-0.708767\pi$
$263$	−320.777			−1.21968			−0.609842	+	0.792523i	$0.708767\pi$
$264$		−	27.8744i		−	0.105585i
$265$	−284.760			−1.07457
$266$	174.184	−	174.184i	0.654828	−	0.654828i
$267$	−13.3922	+	13.3922i	−0.0501582	+	0.0501582i
$268$		−	218.338i		−	0.814694i
$269$	−65.5521	+	260.891i	−0.243688	+	0.969854i
$269$	−65.5521	+	260.891i	−0.243688	+	0.969854i
$270$	253.500			0.938889
$271$	−183.006	−	183.006i	−0.675298	−	0.675298i	0.283634	−	0.958932i	$-0.408460\pi$
$271$	−183.006	−	183.006i	−0.675298	−	0.675298i	−0.958932	+	0.283634i	$0.908460\pi$
$272$	−23.8398	−	23.8398i	−0.0876464	−	0.0876464i
$273$			835.177i			3.05926i
$274$	−331.909			−1.21135
$275$		−	172.781i		−	0.628294i
$276$	194.996	−	194.996i	0.706507	−	0.706507i
$277$	154.379	−	154.379i	0.557323	−	0.557323i	−0.371221	−	0.928545i	$-0.621061\pi$
$277$	154.379	−	154.379i	0.557323	−	0.557323i	0.928545	+	0.371221i	$0.121061\pi$
$278$			110.898i			0.398915i
$279$	−3.57010	−	3.57010i	−0.0127960	−	0.0127960i
$280$			282.763i			1.00987i
$281$	−175.992	+	175.992i	−0.626305	+	0.626305i	−0.947136	−	0.320831i	$-0.896038\pi$
$281$	−175.992	+	175.992i	−0.626305	+	0.626305i	0.320831	+	0.947136i	$0.396038\pi$
$282$		−	26.4922i		−	0.0939439i
$283$	−4.04793			−0.0143037			−0.00715183	−	0.999974i	$-0.502277\pi$
$283$	−4.04793			−0.0143037			−0.00715183	+	0.999974i	$0.502277\pi$
$284$	−119.915	−	119.915i	−0.422235	−	0.422235i
$285$	539.157			1.89178
$286$	−61.0664	−	61.0664i	−0.213519	−	0.213519i
$287$	−558.133	+	558.133i	−1.94471	+	1.94471i
$288$	−14.3618	+	14.3618i	−0.0498674	+	0.0498674i
$289$		−	217.958i		−	0.754180i
$290$	−623.886			−2.15133
$291$	−333.773	+	333.773i	−1.14699	+	1.14699i
$292$	45.7869			0.156804
$293$	161.191			0.550141			0.275071	−	0.961424i	$-0.411299\pi$
$293$	161.191			0.550141			0.275071	+	0.961424i	$0.411299\pi$
$294$	−329.193			−1.11971
$295$	130.686	−	130.686i	0.443003	−	0.443003i
$296$	−74.7366	+	74.7366i	−0.252489	+	0.252489i
$297$	−37.6970	−	37.6970i	−0.126926	−	0.126926i
$298$	215.861	−	215.861i	0.724365	−	0.724365i
$299$		−	854.382i		−	2.85746i
$300$	−312.170	+	312.170i	−1.04057	+	1.04057i
$301$	−28.5427	−	28.5427i	−0.0948261	−	0.0948261i
$302$	17.4767	−	17.4767i	0.0578698	−	0.0578698i
$303$			509.291i			1.68083i
$304$	46.0213	−	46.0213i	0.151386	−	0.151386i
$305$	−122.479			−0.401571
$306$	42.7979			0.139862
$307$	142.393			0.463820			0.231910	−	0.972737i	$-0.425503\pi$
$307$	142.393			0.463820			0.231910	+	0.972737i	$0.425503\pi$
$308$	42.0485	−	42.0485i	0.136521	−	0.136521i
$309$	−464.778	+	464.778i	−1.50414	+	1.50414i
$310$	−18.5713			−0.0599074
$311$	275.032	+	275.032i	0.884347	+	0.884347i	0.993973	−	0.109626i	$-0.0349653\pi$
$311$	275.032	+	275.032i	0.884347	+	0.884347i	−0.109626	+	0.993973i	$0.534965\pi$
$312$			220.662i			0.707251i
$313$	102.897			0.328743			0.164372	−	0.986398i	$-0.447440\pi$
$313$	102.897			0.328743			0.164372	+	0.986398i	$0.447440\pi$
$314$		−	255.965i		−	0.815175i
$315$	−253.811	−	253.811i	−0.805751	−	0.805751i
$316$	31.0766			0.0983437
$317$	−276.703	−	276.703i	−0.872879	−	0.872879i	0.119906	−	0.992785i	$-0.461741\pi$
$317$	−276.703	−	276.703i	−0.872879	−	0.872879i	−0.992785	+	0.119906i	$0.961741\pi$
$318$		−	153.015i		−	0.481178i
$319$	92.7755	+	92.7755i	0.290832	+	0.290832i
$320$			74.7088i			0.233465i
$321$	−140.152			−0.436611
$322$	588.302			1.82702
$323$	−137.142			−0.424589
$324$			200.845i			0.619893i
$325$			1367.79i			4.20857i
$326$	−97.9209			−0.300371
$327$	−554.570			−1.69593
$328$	−147.464	+	147.464i	−0.449586	+	0.449586i
$329$	39.9634	−	39.9634i	0.121469	−	0.121469i
$330$	130.154			0.394406
$331$	338.119			1.02151			0.510754	−	0.859727i	$-0.329366\pi$
$331$	338.119			1.02151			0.510754	+	0.859727i	$0.329366\pi$
$332$	−2.27776	−	2.27776i	−0.00686072	−	0.00686072i
$333$		−	134.169i		−	0.402910i
$334$			205.873i			0.616386i
$335$	1019.49			3.04324
$336$	−151.941			−0.452207
$337$	−103.394	+	103.394i	−0.306808	+	0.306808i	−0.843670	−	0.536862i	$-0.819609\pi$
$337$	−103.394	+	103.394i	−0.306808	+	0.306808i	0.536862	+	0.843670i	$0.319609\pi$
$338$	314.420	+	314.420i	0.930237	+	0.930237i
$339$	795.264			2.34591
$340$	111.315	−	111.315i	0.327398	−	0.327398i
$341$	2.76166	+	2.76166i	0.00809872	+	0.00809872i
$342$			82.6185i			0.241575i
$343$	−125.671	−	125.671i	−0.366387	−	0.366387i
$344$	−7.54126	−	7.54126i	−0.0219223	−	0.0219223i
$345$	910.494	+	910.494i	2.63911	+	2.63911i
$346$	−103.881	−	103.881i	−0.300234	−	0.300234i
$347$	−102.188			−0.294489			−0.147245	−	0.989100i	$-0.547040\pi$
$347$	−102.188			−0.294489			−0.147245	+	0.989100i	$0.547040\pi$
$348$		−	335.242i		−	0.963340i
$349$	−59.7928			−0.171326			−0.0856631	−	0.996324i	$-0.527301\pi$
$349$	−59.7928			−0.171326			−0.0856631	+	0.996324i	$0.527301\pi$
$350$	−941.816			−2.69090
$351$	298.421	+	298.421i	0.850202	+	0.850202i
$352$	11.1096	−	11.1096i	0.0315615	−	0.0315615i
$353$		−	267.041i		−	0.756489i	−0.925706	−	0.378244i	$-0.876528\pi$
$353$		−	267.041i		−	0.756489i	0.925706	−	0.378244i	$-0.123472\pi$
$354$	70.2236	+	70.2236i	0.198372	+	0.198372i
$355$	559.918	−	559.918i	1.57723	−	1.57723i
$356$	−10.6752			−0.0299866
$357$	226.391	+	226.391i	0.634149	+	0.634149i
$358$			350.204i			0.978223i
$359$	21.6116	−	21.6116i	0.0601993	−	0.0601993i	−0.676366	−	0.736566i	$-0.736446\pi$
$359$	21.6116	−	21.6116i	0.0601993	−	0.0601993i	0.736566	+	0.676366i	$0.236446\pi$
$360$	−67.0595	−	67.0595i	−0.186277	−	0.186277i
$361$			96.2555i			0.266636i
$362$	−219.960			−0.607624
$363$	284.238	+	284.238i	0.783024	+	0.783024i
$364$	−332.869	+	332.869i	−0.914474	+	0.914474i
$365$			213.793i			0.585733i
$366$		−	65.8138i		−	0.179819i
$367$	66.8642	−	66.8642i	0.182191	−	0.182191i	−0.610119	−	0.792310i	$-0.708878\pi$
$367$	66.8642	−	66.8642i	0.182191	−	0.182191i	0.792310	+	0.610119i	$0.208878\pi$
$368$	155.435			0.422379
$369$		−	264.732i		−	0.717430i
$370$	−348.967	−	348.967i	−0.943155	−	0.943155i
$371$	230.822	−	230.822i	0.622163	−	0.622163i
$372$		−	9.97922i		−	0.0268259i
$373$	53.7768	+	53.7768i	0.144174	+	0.144174i	0.775510	−	0.631336i	$-0.217493\pi$
$373$	53.7768	+	53.7768i	0.144174	+	0.144174i	−0.631336	+	0.775510i	$0.717493\pi$
$374$	−33.1065			−0.0885199
$375$	−871.845	−	871.845i	−2.32492	−	2.32492i
$376$	10.5587	−	10.5587i	0.0280818	−	0.0280818i
$377$	−734.439	−	734.439i	−1.94811	−	1.94811i
$378$	−205.484	+	205.484i	−0.543608	+	0.543608i
$379$	264.542	−	264.542i	0.697999	−	0.697999i	−0.265979	−	0.963979i	$-0.585695\pi$
$379$	264.542	−	264.542i	0.697999	−	0.697999i	0.963979	+	0.265979i	$0.0856953\pi$
$380$	214.887	+	214.887i	0.565492	+	0.565492i
$381$	343.806	−	343.806i	0.902379	−	0.902379i
$382$	188.656	−	188.656i	0.493863	−	0.493863i
$383$	−258.722	−	258.722i	−0.675514	−	0.675514i	0.283467	−	0.958982i	$-0.408515\pi$
$383$	−258.722	−	258.722i	−0.675514	−	0.675514i	−0.958982	+	0.283467i	$0.908515\pi$
$384$	−40.1445			−0.104543
$385$	196.337	+	196.337i	0.509966	+	0.509966i
$386$	177.380			0.459533
$387$	13.5383			0.0349826
$388$	−266.057			−0.685715
$389$	345.517			0.888219			0.444110	−	0.895972i	$-0.353520\pi$
$389$	345.517			0.888219			0.444110	+	0.895972i	$0.353520\pi$
$390$	−1030.34			−2.64189
$391$	−231.597	−	231.597i	−0.592319	−	0.592319i
$392$	−131.203	−	131.203i	−0.334703	−	0.334703i
$393$	9.33377	+	9.33377i	0.0237500	+	0.0237500i
$394$	−246.272			−0.625057
$395$			145.106i			0.367357i
$396$			19.9443i			0.0503644i
$397$	−260.780	+	260.780i	−0.656876	+	0.656876i	−0.954640	−	0.297763i	$-0.903759\pi$
$397$	−260.780	+	260.780i	−0.656876	+	0.656876i	0.297763	+	0.954640i	$0.403759\pi$
$398$	−278.717	+	278.717i	−0.700294	+	0.700294i
$399$	−437.034	+	437.034i	−1.09532	+	1.09532i
$400$	−248.837			−0.622093
$401$	288.615	+	288.615i	0.719738	+	0.719738i	0.968551	−	0.248814i	$-0.0800407\pi$
$401$	288.615	+	288.615i	0.719738	+	0.719738i	−0.248814	+	0.968551i	$0.580041\pi$
$402$			547.816i			1.36273i
$403$	−21.8622	−	21.8622i	−0.0542486	−	0.0542486i
$404$	−202.983	+	202.983i	−0.502434	+	0.502434i
$405$	−937.807			−2.31557
$406$	505.713	−	505.713i	1.24560	−	1.24560i
$407$			103.787i			0.255005i
$408$	59.8148	+	59.8148i	0.146605	+	0.146605i
$409$	162.708	+	162.708i	0.397819	+	0.397819i	0.877463	−	0.479644i	$-0.159234\pi$
$409$	162.708	+	162.708i	0.397819	+	0.397819i	−0.479644	+	0.877463i	$0.659234\pi$
$410$	−688.554	−	688.554i	−1.67940	−	1.67940i
$411$	832.770			2.02620
$412$	−370.484			−0.899234
$413$			211.864i			0.512989i
$414$	−139.521	+	139.521i	−0.337007	+	0.337007i
$415$	10.6355	−	10.6355i	0.0256278	−	0.0256278i
$416$	−87.9473	+	87.9473i	−0.211412	+	0.211412i
$417$		−	278.247i		−	0.667260i
$418$		−	63.9099i		−	0.152895i
$419$		−	24.0825i		−	0.0574762i	−0.999587	−	0.0287381i	$-0.990851\pi$
$419$		−	24.0825i		−	0.0574762i	0.999587	−	0.0287381i	$-0.00914888\pi$
$420$		−	709.460i		−	1.68919i
$421$			76.3924i			0.181455i	0.995876	+	0.0907274i	$0.0289192\pi$
$421$			76.3924i			0.181455i	−0.995876	+	0.0907274i	$0.971081\pi$
$422$	135.519	−	135.519i	0.321135	−	0.321135i
$423$			18.9553i			0.0448116i
$424$	60.9856	−	60.9856i	0.143834	−	0.143834i
$425$	370.765	+	370.765i	0.872388	+	0.872388i
$426$	300.870	+	300.870i	0.706267	+	0.706267i
$427$	99.2800	−	99.2800i	0.232506	−	0.232506i
$428$	−55.8591	−	55.8591i	−0.130512	−	0.130512i
$429$	153.217	+	153.217i	0.357150	+	0.357150i
$430$	35.2124	−	35.2124i	0.0818893	−	0.0818893i
$431$	−590.726	−	590.726i	−1.37060	−	1.37060i	−0.859560	−	0.511035i	$-0.829262\pi$
$431$	−590.726	−	590.726i	−1.37060	−	1.37060i	−0.511035	−	0.859560i	$-0.670738\pi$
$432$	−54.2909	+	54.2909i	−0.125673	+	0.125673i
$433$		−	193.848i		−	0.447686i	−0.974625	−	0.223843i	$-0.928140\pi$
$433$		−	193.848i		−	0.447686i	0.974625	−	0.223843i	$-0.0718603\pi$
$434$	15.0536	−	15.0536i	0.0346858	−	0.0346858i
$435$	1565.35			3.59850
$436$	−221.030	−	221.030i	−0.506949	−	0.506949i
$437$	447.083	−	447.083i	1.02307	−	1.02307i
$438$	−114.881			−0.262284
$439$		−	368.874i		−	0.840260i	−0.907464	−	0.420130i	$-0.861984\pi$
$439$		−	368.874i		−	0.840260i	0.907464	−	0.420130i	$-0.138016\pi$
$440$	51.8742	+	51.8742i	0.117896	+	0.117896i
$441$	235.540			0.534104
$442$	262.081			0.592943
$443$	527.286	+	527.286i	1.19026	+	1.19026i	0.976994	+	0.213267i	$0.0684103\pi$
$443$	527.286	+	527.286i	1.19026	+	1.19026i	0.213267	+	0.976994i	$0.431590\pi$
$444$	187.516	−	187.516i	0.422334	−	0.422334i
$445$		−	49.8459i		−	0.112013i
$446$	56.2536			0.126129
$447$	−541.601	+	541.601i	−1.21164	+	1.21164i
$448$	−60.5579	−	60.5579i	−0.135174	−	0.135174i
$449$	54.8607			0.122184			0.0610921	−	0.998132i	$-0.480542\pi$
$449$	54.8607			0.122184			0.0610921	+	0.998132i	$0.480542\pi$
$450$	223.360	−	223.360i	0.496355	−	0.496355i
$451$			204.784i			0.454067i
$452$	316.961	+	316.961i	0.701240	+	0.701240i
$453$	−43.8495	+	43.8495i	−0.0967980	+	0.0967980i
$454$	−209.211			−0.460818
$455$	−1554.26	−	1554.26i	−3.41596	−	3.41596i
$456$	−115.469	+	115.469i	−0.253221	+	0.253221i
$457$			866.664i			1.89642i	0.317645	+	0.948210i	$0.397108\pi$
$457$			866.664i			1.89642i	−0.317645	+	0.948210i	$0.602892\pi$
$458$			159.516i			0.348287i
$459$	161.786			0.352474
$460$			725.774i			1.57777i
$461$	371.947	−	371.947i	0.806827	−	0.806827i	−0.177325	−	0.984152i	$-0.556744\pi$
$461$	371.947	−	371.947i	0.806827	−	0.806827i	0.984152	+	0.177325i	$0.0567443\pi$
$462$	−105.501	+	105.501i	−0.228357	+	0.228357i
$463$	−357.605	+	357.605i	−0.772365	+	0.772365i	−0.978520	−	0.206154i	$-0.933905\pi$
$463$	−357.605	+	357.605i	−0.772365	+	0.772365i	0.206154	+	0.978520i	$0.433905\pi$
$464$	133.614	−	133.614i	0.287962	−	0.287962i
$465$	46.5959			0.100206
$466$	−64.4090	+	64.4090i	−0.138217	+	0.138217i
$467$	559.522	+	559.522i	1.19812	+	1.19812i	0.974729	+	0.223392i	$0.0717130\pi$
$467$	559.522	+	559.522i	1.19812	+	1.19812i	0.223392	+	0.974729i	$0.428287\pi$
$468$		−	157.885i		−	0.337362i
$469$	−826.381	+	826.381i	−1.76201	+	1.76201i
$470$	49.3019	+	49.3019i	0.104898	+	0.104898i
$471$			642.223i			1.36353i
$472$			55.9767i			0.118595i
$473$	−10.4726			−0.0221408
$474$	−77.9721			−0.164498
$475$	−715.738	+	715.738i	−1.50682	+	1.50682i
$476$			180.461i			0.379120i
$477$			109.483i			0.229524i
$478$	263.585	+	263.585i	0.551432	+	0.551432i
$479$	348.719	+	348.719i	0.728016	+	0.728016i	0.970224	−	0.242209i	$-0.0778718\pi$
$479$	348.719	+	348.719i	0.728016	+	0.728016i	−0.242209	+	0.970224i	$0.577872\pi$
$480$		−	187.446i		−	0.390513i
$481$		−	821.610i		−	1.70813i
$482$	−263.789			−0.547280
$483$	−1476.07			−3.05604
$484$			226.572i			0.468124i
$485$		−	1242.30i		−	2.56144i
$486$		−	259.618i		−	0.534194i
$487$	−383.219			−0.786897			−0.393448	−	0.919347i	$-0.628718\pi$
$487$	−383.219			−0.786897			−0.393448	+	0.919347i	$0.628718\pi$
$488$	26.2308	−	26.2308i	0.0537516	−	0.0537516i
$489$	245.686			0.502426
$490$	612.628	−	612.628i	1.25026	−	1.25026i
$491$			63.1198i			0.128554i	0.997932	+	0.0642768i	$0.0204740\pi$
$491$			63.1198i			0.128554i	−0.997932	+	0.0642768i	$0.979526\pi$
$492$	369.992	−	369.992i	0.752016	−	0.752016i
$493$	−398.168			−0.807643
$494$			505.930i			1.02415i
$495$	−93.1259			−0.188133
$496$	3.97732	−	3.97732i	0.00801880	−	0.00801880i
$497$			907.723i			1.82640i
$498$	5.71496	+	5.71496i	0.0114758	+	0.0114758i
$499$	−228.174	−	228.174i	−0.457262	−	0.457262i	0.440494	−	0.897756i	$-0.354803\pi$
$499$	−228.174	−	228.174i	−0.457262	−	0.457262i	−0.897756	+	0.440494i	$0.854803\pi$
$500$		−	694.966i		−	1.38993i
$501$		−	516.541i		−	1.03102i
$502$			241.281i			0.480639i
$503$	536.557	+	536.557i	1.06671	+	1.06671i	0.997609	+	0.0691036i	$0.0220139\pi$
$503$	536.557	+	536.557i	1.06671	+	1.06671i	0.0691036	+	0.997609i	$0.477986\pi$
$504$	108.715			0.215704
$505$	−947.789	−	947.789i	−1.87681	−	1.87681i
$506$	107.927	−	107.927i	0.213294	−	0.213294i
$507$	−788.889	−	788.889i	−1.55599	−	1.55599i
$508$	274.055			0.539479
$509$	374.080	+	374.080i	0.734932	+	0.734932i	0.971592	−	0.236660i	$-0.0760529\pi$
$509$	374.080	+	374.080i	0.734932	+	0.734932i	−0.236660	+	0.971592i	$0.576053\pi$
$510$	−279.293	+	279.293i	−0.547633	+	0.547633i
$511$	−173.297	−	173.297i	−0.339134	−	0.339134i
$512$	−16.0000	−	16.0000i	−0.0312500	−	0.0312500i
$513$			312.317i			0.608804i
$514$			43.4795i			0.0845905i
$515$		−	1729.90i		−	3.35903i
$516$	18.9212	+	18.9212i	0.0366691	+	0.0366691i
$517$		−	14.6630i		−	0.0283616i
$518$	565.736			1.09216
$519$	260.640	+	260.640i	0.502196	+	0.502196i
$520$	−410.652	−	410.652i	−0.789715	−	0.789715i
$521$	15.1103	−	15.1103i	0.0290024	−	0.0290024i	−0.692457	−	0.721459i	$-0.743472\pi$
$521$	15.1103	−	15.1103i	0.0290024	−	0.0290024i	0.721459	+	0.692457i	$0.243472\pi$
$522$			239.868i			0.459517i
$523$	−140.109	+	140.109i	−0.267895	+	0.267895i	−0.828251	−	0.560357i	$-0.810664\pi$
$523$	−140.109	+	140.109i	−0.267895	+	0.267895i	0.560357	+	0.828251i	$0.310664\pi$
$524$			7.44014i			0.0141987i
$525$	2363.04			4.50104
$526$	320.777	+	320.777i	0.609842	+	0.609842i
$527$	−11.8523			−0.0224902
$528$	−27.8744	+	27.8744i	−0.0527924	+	0.0527924i
$529$	981.009			1.85446
$530$	284.760	+	284.760i	0.537283	+	0.537283i
$531$	−50.2454	−	50.2454i	−0.0946241	−	0.0946241i
$532$	−348.369			−0.654828
$533$		−	1621.13i		−	3.04153i
$534$	26.7845			0.0501582
$535$	260.823	−	260.823i	0.487519	−	0.487519i
$536$	−218.338	+	218.338i	−0.407347	+	0.407347i
$537$		−	878.671i		−	1.63626i
$538$	326.443	−	195.338i	0.606771	−	0.363083i
$539$	−182.203			−0.338039
$540$	−253.500	−	253.500i	−0.469445	−	0.469445i
$541$	−30.6541	−	30.6541i	−0.0566620	−	0.0566620i	0.678208	−	0.734870i	$-0.262757\pi$
$541$	−30.6541	−	30.6541i	−0.0566620	−	0.0566620i	−0.734870	+	0.678208i	$0.762757\pi$
$542$			366.012i			0.675298i
$543$	551.886			1.01636
$544$			47.6796i			0.0876464i
$545$	1032.05	−	1032.05i	1.89368	−	1.89368i
$546$	835.177	−	835.177i	1.52963	−	1.52963i
$547$		−	279.861i		−	0.511629i	−0.966726	−	0.255814i	$-0.917656\pi$
$547$		−	279.861i		−	0.511629i	0.966726	−	0.255814i	$-0.0823436\pi$
$548$	331.909	+	331.909i	0.605674	+	0.605674i
$549$			47.0901i			0.0857744i
$550$	−172.781	+	172.781i	−0.314147	+	0.314147i
$551$		−	768.638i		−	1.39499i
$552$	−389.992			−0.706507
$553$	−117.621	−	117.621i	−0.212696	−	0.212696i
$554$	−308.757			−0.557323
$555$	875.569	+	875.569i	1.57760	+	1.57760i
$556$	110.898	−	110.898i	0.199458	−	0.199458i
$557$	−536.790	+	536.790i	−0.963716	+	0.963716i	−0.999364	−	0.0356484i	$-0.988650\pi$
$557$	−536.790	+	536.790i	−0.963716	+	0.963716i	0.0356484	+	0.999364i	$0.488650\pi$
$558$			7.14019i			0.0127960i
$559$	82.9041			0.148308
$560$	282.763	−	282.763i	0.504933	−	0.504933i
$561$	83.0651			0.148066
$562$	351.983			0.626305
$563$	−602.327			−1.06985			−0.534926	−	0.844899i	$-0.679661\pi$
$563$	−602.327			−1.06985			−0.534926	+	0.844899i	$0.679661\pi$
$564$	−26.4922	+	26.4922i	−0.0469719	+	0.0469719i
$565$	−1479.98	+	1479.98i	−2.61944	+	2.61944i
$566$	4.04793	+	4.04793i	0.00715183	+	0.00715183i
$567$	760.173	−	760.173i	1.34069	−	1.34069i
$568$			239.830i			0.422235i
$569$	425.615	−	425.615i	0.748005	−	0.748005i	−0.226100	−	0.974104i	$-0.572598\pi$
$569$	425.615	−	425.615i	0.748005	−	0.748005i	0.974104	+	0.226100i	$0.0725975\pi$
$570$	−539.157	−	539.157i	−0.945890	−	0.945890i
$571$	−44.0568	+	44.0568i	−0.0771573	+	0.0771573i	−0.744632	−	0.667475i	$-0.767375\pi$
$571$	−44.0568	+	44.0568i	−0.0771573	+	0.0771573i	0.667475	+	0.744632i	$0.267375\pi$
$572$			122.133i			0.213519i
$573$	−473.343	+	473.343i	−0.826078	+	0.826078i
$574$	1116.27			1.94471
$575$	−2417.38			−4.20414
$576$	28.7236			0.0498674
$577$	−236.020	+	236.020i	−0.409048	+	0.409048i	−0.881406	−	0.472359i	$-0.843403\pi$
$577$	−236.020	+	236.020i	−0.409048	+	0.409048i	0.472359	+	0.881406i	$0.343403\pi$
$578$	−217.958	+	217.958i	−0.377090	+	0.377090i
$579$	−445.051			−0.768654
$580$	623.886	+	623.886i	1.07566	+	1.07566i
$581$			17.2420i			0.0296765i
$582$	667.545			1.14699
$583$		−	84.6910i		−	0.145268i
$584$	−45.7869	−	45.7869i	−0.0784022	−	0.0784022i
$585$	737.213			1.26019
$586$	−161.191	−	161.191i	−0.275071	−	0.275071i
$587$		−	214.417i		−	0.365275i	−0.983180	−	0.182638i	$-0.941536\pi$
$587$		−	214.417i		−	0.365275i	0.983180	−	0.182638i	$-0.0584635\pi$
$588$	329.193	+	329.193i	0.559853	+	0.559853i
$589$		−	22.8802i		−	0.0388458i
$590$	−261.372			−0.443003
$591$	617.905			1.04552
$592$	149.473			0.252489
$593$			56.2579i			0.0948700i	0.998874	+	0.0474350i	$0.0151047\pi$
$593$			56.2579i			0.0948700i	−0.998874	+	0.0474350i	$0.984895\pi$
$594$			75.3939i			0.126926i
$595$	−842.626			−1.41618
$596$	−431.722			−0.724365
$597$	699.309	−	699.309i	1.17137	−	1.17137i
$598$	−854.382	+	854.382i	−1.42873	+	1.42873i
$599$	−386.191			−0.644727			−0.322363	−	0.946616i	$-0.604477\pi$
$599$	−386.191			−0.644727			−0.322363	+	0.946616i	$0.604477\pi$
$600$	624.340			1.04057
$601$	137.404	+	137.404i	0.228626	+	0.228626i	0.812119	−	0.583492i	$-0.198314\pi$
$601$	137.404	+	137.404i	0.228626	+	0.228626i	−0.583492	+	0.812119i	$0.698314\pi$
$602$			57.0853i			0.0948261i
$603$		−	391.966i		−	0.650027i
$604$	−34.9533			−0.0578698
$605$	−1057.93			−1.74865
$606$	509.291	−	509.291i	0.840414	−	0.840414i
$607$	−67.1390	−	67.1390i	−0.110608	−	0.110608i	0.649637	−	0.760245i	$-0.274921\pi$
$607$	−67.1390	−	67.1390i	−0.110608	−	0.110608i	−0.760245	+	0.649637i	$0.774921\pi$
$608$	−92.0425			−0.151386
$609$	−1268.85	+	1268.85i	−2.08349	+	2.08349i
$610$	122.479	+	122.479i	0.200786	+	0.200786i
$611$			116.077i			0.189978i
$612$	−42.7979	−	42.7979i	−0.0699311	−	0.0699311i
$613$	412.459	+	412.459i	0.672853	+	0.672853i	0.958373	−	0.285520i	$-0.0921663\pi$
$613$	412.459	+	412.459i	0.672853	+	0.672853i	−0.285520	+	0.958373i	$0.592166\pi$
$614$	−142.393	−	142.393i	−0.231910	−	0.231910i
$615$	1727.60	+	1727.60i	2.80911	+	2.80911i
$616$	−84.0970			−0.136521
$617$			1059.74i			1.71757i	0.512336	+	0.858785i	$0.328780\pi$
$617$			1059.74i			1.71757i	−0.512336	+	0.858785i	$0.671220\pi$
$618$	929.556			1.50414
$619$	−246.774			−0.398665			−0.199332	−	0.979932i	$-0.563877\pi$
$619$	−246.774			−0.398665			−0.199332	+	0.979932i	$0.563877\pi$
$620$	18.5713	+	18.5713i	0.0299537	+	0.0299537i
$621$	−527.420	+	527.420i	−0.849307	+	0.849307i
$622$		−	550.064i		−	0.884347i
$623$	40.4044	+	40.4044i	0.0648545	+	0.0648545i
$624$	220.662	−	220.662i	0.353625	−	0.353625i
$625$	1689.77			2.70363
$626$	−102.897	−	102.897i	−0.164372	−	0.164372i
$627$			160.352i			0.255745i
$628$	−255.965	+	255.965i	−0.407587	+	0.407587i
$629$	−222.713	−	222.713i	−0.354075	−	0.354075i
$630$			507.623i			0.805751i
$631$	837.046			1.32654			0.663269	−	0.748381i	$-0.269168\pi$
$631$	837.046			1.32654			0.663269	+	0.748381i	$0.269168\pi$
$632$	−31.0766	−	31.0766i	−0.0491718	−	0.0491718i
$633$	−340.021	+	340.021i	−0.537158	+	0.537158i
$634$			553.406i			0.872879i
$635$			1279.65i			2.01519i
$636$	−153.015	+	153.015i	−0.240589	+	0.240589i
$637$	1442.37			2.26432
$638$		−	185.551i		−	0.290832i
$639$	−215.274	−	215.274i	−0.336892	−	0.336892i
$640$	74.7088	−	74.7088i	0.116732	−	0.116732i
$641$			381.912i			0.595806i	0.954596	+	0.297903i	$0.0962872\pi$
$641$			381.912i			0.595806i	−0.954596	+	0.297903i	$0.903713\pi$
$642$	140.152	+	140.152i	0.218305	+	0.218305i
$643$	−784.767			−1.22048			−0.610239	−	0.792217i	$-0.708927\pi$
$643$	−784.767			−1.22048			−0.610239	+	0.792217i	$0.708927\pi$
$644$	−588.302	−	588.302i	−0.913512	−	0.913512i
$645$	−88.3489	+	88.3489i	−0.136975	+	0.136975i
$646$	137.142	+	137.142i	0.212295	+	0.212295i
$647$	370.127	−	370.127i	0.572066	−	0.572066i	−0.360639	−	0.932705i	$-0.617442\pi$
$647$	370.127	−	370.127i	0.572066	−	0.572066i	0.932705	+	0.360639i	$0.117442\pi$
$648$	200.845	−	200.845i	0.309947	−	0.309947i
$649$	38.8676	+	38.8676i	0.0598884	+	0.0598884i
$650$	1367.79	−	1367.79i	2.10429	−	2.10429i
$651$	−37.7700	+	37.7700i	−0.0580185	+	0.0580185i
$652$	97.9209	+	97.9209i	0.150185	+	0.150185i
$653$	−573.066			−0.877589			−0.438795	−	0.898587i	$-0.644594\pi$
$653$	−573.066			−0.877589			−0.438795	+	0.898587i	$0.644594\pi$
$654$	554.570	+	554.570i	0.847966	+	0.847966i
$655$	−34.7402			−0.0530385
$656$	294.928			0.449586
$657$	82.1978			0.125111
$658$	−79.9268			−0.121469
$659$	−752.512			−1.14190			−0.570950	−	0.820985i	$-0.693425\pi$
$659$	−752.512			−1.14190			−0.570950	+	0.820985i	$0.693425\pi$
$660$	−130.154	−	130.154i	−0.197203	−	0.197203i
$661$	−509.520	−	509.520i	−0.770833	−	0.770833i	0.207419	−	0.978252i	$-0.433494\pi$
$661$	−509.520	−	509.520i	−0.770833	−	0.770833i	−0.978252	+	0.207419i	$0.933494\pi$
$662$	−338.119	−	338.119i	−0.510754	−	0.510754i
$663$	−657.568			−0.991808
$664$			4.55552i			0.00686072i
$665$		−	1626.64i		−	2.44607i
$666$	−134.169	+	134.169i	−0.201455	+	0.201455i
$667$	1298.03	−	1298.03i	1.94606	−	1.94606i
$668$	205.873	−	205.873i	0.308193	−	0.308193i
$669$	−141.142			−0.210974
$670$	−1019.49	−	1019.49i	−1.52162	−	1.52162i
$671$		−	36.4268i		−	0.0542873i
$672$	151.941	+	151.941i	0.226103	+	0.226103i
$673$	−58.1658	+	58.1658i	−0.0864277	+	0.0864277i	−0.748999	−	0.662571i	$-0.769465\pi$
$673$	−58.1658	+	58.1658i	−0.0864277	+	0.0864277i	0.662571	+	0.748999i	$0.269465\pi$
$674$	206.788			0.306808
$675$	844.350	−	844.350i	1.25089	−	1.25089i
$676$		−	628.840i		−	0.930237i
$677$	−226.391	−	226.391i	−0.334404	−	0.334404i	0.519852	−	0.854256i	$-0.325987\pi$
$677$	−226.391	−	226.391i	−0.334404	−	0.334404i	−0.854256	+	0.519852i	$0.825987\pi$
$678$	−795.264	−	795.264i	−1.17296	−	1.17296i
$679$	1006.99	+	1006.99i	1.48305	+	1.48305i
$680$	−222.630			−0.327398
$681$	524.918			0.770804
$682$		−	5.52333i		−	0.00809872i
$683$	79.6760	−	79.6760i	0.116656	−	0.116656i	−0.646369	−	0.763025i	$-0.723713\pi$
$683$	79.6760	−	79.6760i	0.116656	−	0.116656i	0.763025	+	0.646369i	$0.223713\pi$
$684$	82.6185	−	82.6185i	0.120787	−	0.120787i
$685$	−1549.78	+	1549.78i	−2.26246	+	2.26246i
$686$			251.342i			0.366387i
$687$		−	400.229i		−	0.582575i
$688$			15.0825i			0.0219223i
$689$			670.440i			0.973062i
$690$		−	1820.99i		−	2.63911i
$691$	−15.6743	+	15.6743i	−0.0226835	+	0.0226835i	−0.718358	−	0.695674i	$-0.755106\pi$
$691$	−15.6743	+	15.6743i	−0.0226835	+	0.0226835i	0.695674	+	0.718358i	$0.255106\pi$
$692$			207.762i			0.300234i
$693$	75.4865	−	75.4865i	0.108927	−	0.108927i
$694$	102.188	+	102.188i	0.147245	+	0.147245i
$695$	517.818	+	517.818i	0.745062	+	0.745062i
$696$	−335.242	+	335.242i	−0.481670	+	0.481670i
$697$	−439.440	−	439.440i	−0.630474	−	0.630474i
$698$	59.7928	+	59.7928i	0.0856631	+	0.0856631i
$699$	161.604	−	161.604i	0.231193	−	0.231193i
$700$	941.816	+	941.816i	1.34545	+	1.34545i
$701$	−749.863	+	749.863i	−1.06971	+	1.06971i	−0.0723238	+	0.997381i	$0.523042\pi$
$701$	−749.863	+	749.863i	−1.06971	+	1.06971i	−0.997381	+	0.0723238i	$0.976958\pi$
$702$		−	596.842i		−	0.850202i
$703$	429.934	−	429.934i	0.611571	−	0.611571i
$704$	−22.2193			−0.0315615
$705$	−123.700	−	123.700i	−0.175461	−	0.175461i
$706$	−267.041	+	267.041i	−0.378244	+	0.378244i
$707$	1536.53			2.17331
$708$		−	140.447i		−	0.198372i
$709$	−175.119	−	175.119i	−0.246994	−	0.246994i	0.572742	−	0.819736i	$-0.305880\pi$
$709$	−175.119	−	175.119i	−0.246994	−	0.246994i	−0.819736	+	0.572742i	$0.805880\pi$
$710$	−1119.84			−1.57723
$711$	55.7895			0.0784663
$712$	10.6752	+	10.6752i	0.0149933	+	0.0149933i
$713$	38.6385	−	38.6385i	0.0541915	−	0.0541915i
$714$		−	452.782i		−	0.634149i
$715$	−570.274			−0.797586
$716$	350.204	−	350.204i	0.489111	−	0.489111i
$717$	−661.341	−	661.341i	−0.922373	−	0.922373i
$718$	−43.2231			−0.0601993
$719$	−11.1479	+	11.1479i	−0.0155048	+	0.0155048i	−0.714817	−	0.699312i	$-0.753490\pi$
$719$	−11.1479	+	11.1479i	−0.0155048	+	0.0155048i	0.699312	+	0.714817i	$0.253490\pi$
$720$			134.119i			0.186277i
$721$	1402.23	+	1402.23i	1.94485	+	1.94485i
$722$	96.2555	−	96.2555i	0.133318	−	0.133318i
$723$	661.854			0.915427
$724$	219.960	+	219.960i	0.303812	+	0.303812i
$725$	−2078.02	+	2078.02i	−2.86623	+	2.86623i
$726$		−	568.476i		−	0.783024i
$727$		−	679.096i		−	0.934107i	−0.884229	−	0.467054i	$-0.845316\pi$
$727$		−	679.096i		−	0.934107i	0.884229	−	0.467054i	$-0.154684\pi$
$728$	665.737			0.914474
$729$		−	252.415i		−	0.346248i
$730$	213.793	−	213.793i	0.292867	−	0.292867i
$731$	22.4728	−	22.4728i	0.0307425	−	0.0307425i
$732$	−65.8138	+	65.8138i	−0.0899095	+	0.0899095i
$733$	−512.015	+	512.015i	−0.698520	+	0.698520i	−0.964091	−	0.265571i	$-0.914439\pi$
$733$	−512.015	+	512.015i	−0.698520	+	0.698520i	0.265571	+	0.964091i	$0.414439\pi$
$734$	−133.728			−0.182191
$735$	−1537.10	+	1537.10i	−2.09129	+	2.09129i
$736$	−155.435	−	155.435i	−0.211189	−	0.211189i
$737$			303.207i			0.411407i
$738$	−264.732	+	264.732i	−0.358715	+	0.358715i
$739$	665.613	+	665.613i	0.900694	+	0.900694i	0.995496	−	0.0948019i	$-0.0302218\pi$
$739$	665.613	+	665.613i	0.900694	+	0.900694i	−0.0948019	+	0.995496i	$0.530222\pi$
$740$			697.935i			0.943155i
$741$		−	1269.39i		−	1.71308i
$742$	−461.645			−0.622163
$743$	613.884			0.826224			0.413112	−	0.910680i	$-0.364442\pi$
$743$	613.884			0.826224			0.413112	+	0.910680i	$0.364442\pi$
$744$	−9.97922	+	9.97922i	−0.0134129	+	0.0134129i
$745$		−	2015.84i		−	2.70582i
$746$		−	107.554i		−	0.144174i
$747$	−4.08909	−	4.08909i	−0.00547402	−	0.00547402i
$748$	33.1065	+	33.1065i	0.0442600	+	0.0442600i
$749$			422.839i			0.564537i
$750$			1743.69i			2.32492i
$751$	−55.4038			−0.0737733			−0.0368867	−	0.999319i	$-0.511744\pi$
$751$	−55.4038			−0.0737733			−0.0368867	+	0.999319i	$0.511744\pi$
$752$	−21.1175			−0.0280818
$753$		−	605.381i		−	0.803959i
$754$			1468.88i			1.94811i
$755$		−	163.208i		−	0.216169i
$756$	410.967			0.543608
$757$	228.069	−	228.069i	0.301280	−	0.301280i	−0.540234	−	0.841515i	$-0.681664\pi$
$757$	228.069	−	228.069i	0.301280	−	0.301280i	0.841515	+	0.540234i	$0.181664\pi$
$758$	−529.083			−0.697999
$759$	−270.792	+	270.792i	−0.356774	+	0.356774i
$760$		−	429.774i		−	0.565492i
$761$	481.277	−	481.277i	0.632427	−	0.632427i	−0.316249	−	0.948676i	$-0.602424\pi$
$761$	481.277	−	481.277i	0.632427	−	0.632427i	0.948676	+	0.316249i	$0.102424\pi$
$762$	−687.613			−0.902379
$763$			1673.14i			2.19284i
$764$	−377.311			−0.493863
$765$	199.836	−	199.836i	0.261223	−	0.261223i
$766$			517.444i			0.675514i
$767$	−307.687	−	307.687i	−0.401157	−	0.401157i
$768$	40.1445	+	40.1445i	0.0522714	+	0.0522714i
$769$			378.421i			0.492095i	0.969258	+	0.246048i	$0.0791320\pi$
$769$			378.421i			0.492095i	−0.969258	+	0.246048i	$0.920868\pi$
$770$		−	392.674i		−	0.509966i
$771$		−	109.091i		−	0.141493i
$772$	−177.380	−	177.380i	−0.229766	−	0.229766i
$773$	835.121			1.08036			0.540182	−	0.841548i	$-0.318355\pi$
$773$	835.121			1.08036			0.540182	+	0.841548i	$0.318355\pi$
$774$	−13.5383	−	13.5383i	−0.0174913	−	0.0174913i
$775$	−61.8567	+	61.8567i	−0.0798151	+	0.0798151i
$776$	266.057	+	266.057i	0.342857	+	0.342857i
$777$	−1419.45			−1.82683
$778$	−345.517	−	345.517i	−0.444110	−	0.444110i
$779$	848.311	−	848.311i	1.08897	−	1.08897i
$780$	1030.34	+	1030.34i	1.32095	+	1.32095i
$781$	166.526	+	166.526i	0.213222	+	0.213222i
$782$			463.194i			0.592319i
$783$			906.755i			1.15805i
$784$			262.407i			0.334703i
$785$	−1195.18	−	1195.18i	−1.52252	−	1.52252i
$786$		−	18.6675i		−	0.0237500i
$787$	−16.2916			−0.0207009			−0.0103504	−	0.999946i	$-0.503295\pi$
$787$	−16.2916			−0.0207009			−0.0103504	+	0.999946i	$0.503295\pi$
$788$	246.272	+	246.272i	0.312529	+	0.312529i
$789$	−804.839	−	804.839i	−1.02007	−	1.02007i
$790$	145.106	−	145.106i	0.183678	−	0.183678i
$791$		−	2399.31i		−	3.03326i
$792$	19.9443	−	19.9443i	0.0251822	−	0.0251822i
$793$			288.366i			0.363639i
$794$	521.560			0.656876
$795$	−714.471	−	714.471i	−0.898706	−	0.898706i
$796$	557.434			0.700294
$797$	−718.419	+	718.419i	−0.901403	+	0.901403i	−0.995558	−	0.0941541i	$-0.969985\pi$
$797$	−718.419	+	718.419i	−0.901403	+	0.901403i	0.0941541	+	0.995558i	$0.469985\pi$
$798$	874.067			1.09532
$799$	31.4648	+	31.4648i	0.0393802	+	0.0393802i
$800$	248.837	+	248.837i	0.311047	+	0.311047i
$801$	−19.1645			−0.0239257
$802$		−	577.230i		−	0.719738i
$803$	−63.5844			−0.0791836
$804$	547.816	−	547.816i	0.681364	−	0.681364i
$805$	2746.96	−	2746.96i	3.41237	−	3.41237i
$806$			43.7243i			0.0542486i
$807$	−819.054	+	490.110i	−1.01494	+	0.607323i
$808$	405.966			0.502434
$809$	480.518	+	480.518i	0.593965	+	0.593965i	0.938700	−	0.344735i	$-0.112031\pi$
$809$	480.518	+	480.518i	0.593965	+	0.593965i	−0.344735	+	0.938700i	$0.612031\pi$
$810$	937.807	+	937.807i	1.15779	+	1.15779i
$811$		−	1238.79i		−	1.52749i	−0.645521	−	0.763743i	$-0.723360\pi$
$811$		−	1238.79i		−	1.52749i	0.645521	−	0.763743i	$-0.276640\pi$
$812$	−1011.43			−1.24560
$813$		−	918.334i		−	1.12956i
$814$	103.787	−	103.787i	0.127503	−	0.127503i
$815$	−457.222	+	457.222i	−0.561008	+	0.561008i
$816$		−	119.630i		−	0.146605i
$817$	43.3823	+	43.3823i	0.0530995	+	0.0530995i
$818$		−	325.416i		−	0.397819i
$819$	−597.574	+	597.574i	−0.729639	+	0.729639i
$820$			1377.11i			1.67940i
$821$	542.158			0.660363			0.330182	−	0.943917i	$-0.392890\pi$
$821$	542.158			0.660363			0.330182	+	0.943917i	$0.392890\pi$
$822$	−832.770	−	832.770i	−1.01310	−	1.01310i
$823$	−1303.64			−1.58401			−0.792007	−	0.610512i	$-0.790964\pi$
$823$	−1303.64			−1.58401			−0.792007	+	0.610512i	$0.790964\pi$
$824$	370.484	+	370.484i	0.449617	+	0.449617i
$825$	433.512	−	433.512i	0.525469	−	0.525469i
$826$	211.864	−	211.864i	0.256494	−	0.256494i
$827$			1491.06i			1.80298i	0.432803	+	0.901489i	$0.357525\pi$
$827$			1491.06i			1.80298i	−0.432803	+	0.901489i	$0.642475\pi$
$828$	279.041			0.337007
$829$	−197.949	+	197.949i	−0.238780	+	0.238780i	−0.816345	−	0.577565i	$-0.804003\pi$
$829$	−197.949	+	197.949i	−0.238780	+	0.238780i	0.577565	+	0.816345i	$0.304003\pi$
$830$	−21.2711			−0.0256278
$831$	774.681			0.932227
$832$	175.895			0.211412
$833$	390.983	−	390.983i	0.469368	−	0.469368i
$834$	−278.247	+	278.247i	−0.333630	+	0.333630i
$835$	961.282	+	961.282i	1.15124	+	1.15124i
$836$	−63.9099	+	63.9099i	−0.0764473	+	0.0764473i
$837$			26.9915i			0.0322479i
$838$	−24.0825	+	24.0825i	−0.0287381	+	0.0287381i
$839$	−256.308	−	256.308i	−0.305493	−	0.305493i	0.537665	−	0.843158i	$-0.319306\pi$
$839$	−256.308	−	256.308i	−0.305493	−	0.305493i	−0.843158	+	0.537665i	$0.819306\pi$
$840$	−709.460	+	709.460i	−0.844595	+	0.844595i
$841$		−	1390.60i		−	1.65351i
$842$	76.3924	−	76.3924i	0.0907274	−	0.0907274i
$843$	−883.137			−1.04761
$844$	−271.038			−0.321135
$845$	2936.24			3.47484
$846$	18.9553	−	18.9553i	0.0224058	−	0.0224058i
$847$	857.545	−	857.545i	1.01245	−	1.01245i
$848$	−121.971			−0.143834
$849$	−10.1564	−	10.1564i	−0.0119628	−	0.0119628i
$850$		−	741.530i		−	0.872388i
$851$	1452.09			1.70633
$852$		−	601.739i		−	0.706267i
$853$	−1063.16	−	1063.16i	−1.24638	−	1.24638i	−0.957307	−	0.289072i	$-0.906653\pi$
$853$	−1063.16	−	1063.16i	−1.24638	−	1.24638i	−0.289072	−	0.957307i	$-0.593347\pi$
$854$	−198.560			−0.232506
$855$	385.771	+	385.771i	0.451194	+	0.451194i
$856$			111.718i			0.130512i
$857$	758.076	+	758.076i	0.884569	+	0.884569i	0.993995	−	0.109426i	$-0.0349013\pi$
$857$	758.076	+	758.076i	0.884569	+	0.884569i	−0.109426	+	0.993995i	$0.534901\pi$
$858$		−	306.435i		−	0.357150i
$859$	−241.707			−0.281382			−0.140691	−	0.990054i	$-0.544932\pi$
$859$	−241.707			−0.281382			−0.140691	+	0.990054i	$0.544932\pi$
$860$	−70.4248			−0.0818893
$861$	−2800.74			−3.25289
$862$			1181.45i			1.37060i
$863$			658.396i			0.762915i	0.924386	+	0.381458i	$0.124578\pi$
$863$			658.396i			0.762915i	−0.924386	+	0.381458i	$0.875422\pi$
$864$	108.582			0.125673
$865$	−970.101			−1.12150
$866$	−193.848	+	193.848i	−0.223843	+	0.223843i
$867$	546.863	−	546.863i	0.630753	−	0.630753i
$868$	−30.1073			−0.0346858
$869$	−43.1562			−0.0496619
$870$	−1565.35	−	1565.35i	−1.79925	−	1.79925i
$871$		−	2400.28i		−	2.75577i
$872$			442.059i			0.506949i
$873$	−477.633			−0.547117
$874$	−894.166			−1.02307
$875$	−2630.35	+	2630.35i	−3.00612	+	3.00612i
$876$	114.881	+	114.881i	0.131142	+	0.131142i
$877$	−806.066			−0.919118			−0.459559	−	0.888147i	$-0.651992\pi$
$877$	−806.066			−0.919118			−0.459559	+	0.888147i	$0.651992\pi$
$878$	−368.874	+	368.874i	−0.420130	+	0.420130i
$879$	404.434	+	404.434i	0.460107	+	0.460107i
$880$		−	103.748i		−	0.117896i
$881$	399.262	+	399.262i	0.453192	+	0.453192i	0.896413	−	0.443221i	$-0.146164\pi$
$881$	399.262	+	399.262i	0.453192	+	0.453192i	−0.443221	+	0.896413i	$0.646164\pi$
$882$	−235.540	−	235.540i	−0.267052	−	0.267052i
$883$	−1121.00	−	1121.00i	−1.26954	−	1.26954i	−0.946326	−	0.323212i	$-0.895237\pi$
$883$	−1121.00	−	1121.00i	−1.26954	−	1.26954i	−0.323212	−	0.946326i	$-0.604763\pi$
$884$	−262.081	−	262.081i	−0.296472	−	0.296472i
$885$	655.790			0.741005
$886$		−	1054.57i		−	1.19026i
$887$	−397.616			−0.448271			−0.224136	−	0.974558i	$-0.571956\pi$
$887$	−397.616			−0.448271			−0.224136	+	0.974558i	$0.571956\pi$
$888$	−375.033			−0.422334
$889$	−1037.26	−	1037.26i	−1.16678	−	1.16678i
$890$	−49.8459	+	49.8459i	−0.0560066	+	0.0560066i
$891$		−	278.915i		−	0.313036i
$892$	−56.2536	−	56.2536i	−0.0630645	−	0.0630645i
$893$	−60.7408	+	60.7408i	−0.0680188	+	0.0680188i
$894$	1083.20			1.21164
$895$	1635.21	+	1635.21i	1.82704	+	1.82704i
$896$			121.116i			0.135174i
$897$	2143.67	−	2143.67i	2.38982	−	2.38982i
$898$	−54.8607	−	54.8607i	−0.0610921	−	0.0610921i
$899$		−	66.4285i		−	0.0738915i
$900$	−446.719			−0.496355
$901$	181.736	+	181.736i	0.201704	+	0.201704i
$902$	204.784	−	204.784i	0.227034	−	0.227034i
$903$		−	143.229i		−	0.158614i
$904$		−	633.921i		−	0.701240i
$905$	−1027.06	+	1027.06i	−1.13487	+	1.13487i
$906$	87.6990			0.0967980
$907$			1666.19i			1.83703i	0.395384	+	0.918516i	$0.370612\pi$
$907$			1666.19i			1.83703i	−0.395384	+	0.918516i	$0.629388\pi$
$908$	209.211	+	209.211i	0.230409	+	0.230409i
$909$	−364.401	+	364.401i	−0.400881	+	0.400881i
$910$			3108.53i			3.41596i
$911$	−417.642	−	417.642i	−0.458443	−	0.458443i	0.439701	−	0.898144i	$-0.355084\pi$
$911$	−417.642	−	417.642i	−0.458443	−	0.458443i	−0.898144	+	0.439701i	$0.855084\pi$
$912$	230.937			0.253221
$913$	3.16313	+	3.16313i	0.00346455	+	0.00346455i
$914$	866.664	−	866.664i	0.948210	−	0.948210i
$915$	−307.304	−	307.304i	−0.335851	−	0.335851i
$916$	159.516	−	159.516i	0.174144	−	0.174144i
$917$	28.1600	−	28.1600i	0.0307088	−	0.0307088i
$918$	−161.786	−	161.786i	−0.176237	−	0.176237i
$919$	1185.31	−	1185.31i	1.28979	−	1.28979i	0.354870	−	0.934916i	$-0.384525\pi$
$919$	1185.31	−	1185.31i	1.28979	−	1.28979i	0.934916	−	0.354870i	$-0.115475\pi$
$920$	725.774	−	725.774i	0.788885	−	0.788885i
$921$	357.267	+	357.267i	0.387912	+	0.387912i
$922$	−743.895			−0.806827
$923$	−1318.27	−	1318.27i	−1.42825	−	1.42825i
$924$	211.002			0.228357
$925$	−2324.66			−2.51314
$926$	715.210			0.772365
$927$	−665.103			−0.717479
$928$	−267.229			−0.287962
$929$	−718.204	−	718.204i	−0.773094	−	0.773094i	0.205552	−	0.978646i	$-0.434101\pi$
$929$	−718.204	−	718.204i	−0.773094	−	0.773094i	−0.978646	+	0.205552i	$0.934101\pi$
$930$	−46.5959	−	46.5959i	−0.0501032	−	0.0501032i
$931$	754.769	+	754.769i	0.810708	+	0.810708i
$932$	128.818			0.138217
$933$			1380.13i			1.47923i
$934$		−	1119.04i		−	1.19812i
$935$	−154.584	+	154.584i	−0.165330	+	0.165330i
$936$	−157.885	+	157.885i	−0.168681	+	0.168681i
$937$	−1136.39	+	1136.39i	−1.21280	+	1.21280i	−0.242694	+	0.970103i	$0.578031\pi$
$937$	−1136.39	+	1136.39i	−1.21280	+	1.21280i	−0.970103	+	0.242694i	$0.921969\pi$
$938$	1652.76			1.76201
$939$	258.171	+	258.171i	0.274942	+	0.274942i
$940$		−	98.6038i		−	0.104898i
$941$	786.546	+	786.546i	0.835862	+	0.835862i	0.988311	−	0.152449i	$-0.0487161\pi$
$941$	786.546	+	786.546i	0.835862	+	0.835862i	−0.152449	+	0.988311i	$0.548716\pi$
$942$	642.223	−	642.223i	0.681766	−	0.681766i
$943$	2865.14			3.03833
$944$	55.9767	−	55.9767i	0.0592974	−	0.0592974i
$945$			1918.93i			2.03061i
$946$	10.4726	+	10.4726i	0.0110704	+	0.0110704i
$947$	15.1563	+	15.1563i	0.0160045	+	0.0160045i	0.715064	−	0.699059i	$-0.246398\pi$
$947$	15.1563	+	15.1563i	0.0160045	+	0.0160045i	−0.699059	+	0.715064i	$0.746398\pi$
$948$	77.9721	+	77.9721i	0.0822490	+	0.0822490i
$949$	503.354			0.530405
$950$	1431.48			1.50682
$951$		−	1388.51i		−	1.46005i
$952$	180.461	−	180.461i	0.189560	−	0.189560i
$953$	−676.964	+	676.964i	−0.710351	+	0.710351i	−0.966609	−	0.256258i	$-0.917510\pi$
$953$	−676.964	+	676.964i	−0.710351	+	0.710351i	0.256258	+	0.966609i	$0.417510\pi$
$954$	109.483	−	109.483i	0.114762	−	0.114762i
$955$		−	1761.78i		−	1.84479i
$956$		−	527.169i		−	0.551432i
$957$			465.553i			0.486471i
$958$		−	697.439i		−	0.728016i
$959$		−	2512.46i		−	2.61988i
$960$	−187.446	+	187.446i	−0.195257	+	0.195257i
$961$			959.023i			0.997942i
$962$	−821.610	+	821.610i	−0.854065	+	0.854065i
$963$	−100.280	−	100.280i	−0.104133	−	0.104133i
$964$	263.789	+	263.789i	0.273640	+	0.273640i
$965$	828.238	−	828.238i	0.858278	−	0.858278i
$966$	1476.07	+	1476.07i	1.52802	+	1.52802i
$967$	−31.4827	−	31.4827i	−0.0325571	−	0.0325571i	0.690641	−	0.723198i	$-0.257329\pi$
$967$	−31.4827	−	31.4827i	−0.0325571	−	0.0325571i	−0.723198	+	0.690641i	$0.757329\pi$
$968$	226.572	−	226.572i	0.234062	−	0.234062i
$969$	−344.094	−	344.094i	−0.355102	−	0.355102i
$970$	−1242.30	+	1242.30i	−1.28072	+	1.28072i
$971$		−	788.282i		−	0.811825i	−0.913912	−	0.405912i	$-0.866954\pi$
$971$		−	788.282i		−	0.811825i	0.913912	−	0.405912i	$-0.133046\pi$
$972$	−259.618	+	259.618i	−0.267097	+	0.267097i
$973$	−839.472			−0.862766
$974$	383.219	+	383.219i	0.393448	+	0.393448i
$975$	−3431.81	+	3431.81i	−3.51981	+	3.51981i
$976$	−52.4615			−0.0537516
$977$			769.724i			0.787844i	0.919144	+	0.393922i	$0.128882\pi$
$977$			769.724i			0.787844i	−0.919144	+	0.393922i	$0.871118\pi$
$978$	−245.686	−	245.686i	−0.251213	−	0.251213i
$979$	14.8247			0.0151427
$980$	−1225.26			−1.25026
$981$	−396.798	−	396.798i	−0.404483	−	0.404483i
$982$	63.1198	−	63.1198i	0.0642768	−	0.0642768i
$983$		−	259.726i		−	0.264218i	−0.991235	−	0.132109i	$-0.957825\pi$
$983$		−	259.726i		−	0.264218i	0.991235	−	0.132109i	$-0.0421749\pi$
$984$	−739.984			−0.752016
$985$	−1149.92	+	1149.92i	−1.16743	+	1.16743i
$986$	398.168	+	398.168i	0.403821	+	0.403821i
$987$	200.539			0.203180
$988$	505.930	−	505.930i	0.512075	−	0.512075i
$989$			146.522i			0.148152i
$990$	93.1259	+	93.1259i	0.0940665	+	0.0940665i
$991$	−514.744	+	514.744i	−0.519419	+	0.519419i	−0.917395	−	0.397977i	$-0.869712\pi$
$991$	−514.744	+	514.744i	−0.519419	+	0.519419i	0.397977	+	0.917395i	$0.369712\pi$
$992$	−7.95465			−0.00801880
$993$	848.351	+	848.351i	0.854331	+	0.854331i
$994$	907.723	−	907.723i	0.913202	−	0.913202i
$995$			2602.82i			2.61590i
$996$		−	11.4299i		−	0.0114758i
$997$	−1495.10			−1.49960			−0.749799	−	0.661666i	$-0.769850\pi$
$997$	−1495.10			−1.49960			−0.749799	+	0.661666i	$0.769850\pi$
$998$			456.348i			0.457262i
$999$	−507.189	+	507.189i	−0.507697	+	0.507697i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	538.3.c.b.187.19	✓	46
269.82	odd	4	inner	538.3.c.b.351.19	yes	46

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
538.3.c.b.187.19	✓	46	1.1	even	1	trivial
538.3.c.b.351.19	yes	46	269.82	odd	4	inner

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:	\( N \)	\(=\)	\( 538 = 2 \cdot 269 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	538.c (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.00000 - 1.00000i) q^{2} +(2.50903 + 2.50903i) q^{3} +2.00000i q^{4} -9.33859 q^{5} -5.01806i q^{6} +(7.56973 - 7.56973i) q^{7} +(2.00000 - 2.00000i) q^{8} +3.59045i q^{9} +(9.33859 + 9.33859i) q^{10} -2.77741i q^{11} +(-5.01806 + 5.01806i) q^{12} +21.9868i q^{13} -15.1395 q^{14} +(-23.4308 - 23.4308i) q^{15} -4.00000 q^{16} +(5.95995 + 5.95995i) q^{17} +(3.59045 - 3.59045i) q^{18} +(-11.5053 + 11.5053i) q^{19} -18.6772i q^{20} +37.9854 q^{21} +(-2.77741 + 2.77741i) q^{22} -38.8588 q^{23} +10.0361 q^{24} +62.2093 q^{25} +(21.9868 - 21.9868i) q^{26} +(13.5727 - 13.5727i) q^{27} +(15.1395 + 15.1395i) q^{28} +(-33.4036 + 33.4036i) q^{29} +46.8616i q^{30} +(-0.994331 + 0.994331i) q^{31} +(4.00000 + 4.00000i) q^{32} +(6.96860 - 6.96860i) q^{33} -11.9199i q^{34} +(-70.6907 + 70.6907i) q^{35} -7.18090 q^{36} -37.3683 q^{37} +23.0106 q^{38} +(-55.1656 + 55.1656i) q^{39} +(-18.6772 + 18.6772i) q^{40} -73.7321 q^{41} +(-37.9854 - 37.9854i) q^{42} -3.77063i q^{43} +5.55482 q^{44} -33.5298i q^{45} +(38.8588 + 38.8588i) q^{46} +5.27937 q^{47} +(-10.0361 - 10.0361i) q^{48} -65.6017i q^{49} +(-62.2093 - 62.2093i) q^{50} +29.9074i q^{51} -43.9736 q^{52} +30.4928 q^{53} -27.1454 q^{54} +25.9371i q^{55} -30.2789i q^{56} -57.7343 q^{57} +66.8072 q^{58} +(-13.9942 + 13.9942i) q^{59} +(46.8616 - 46.8616i) q^{60} +13.1154 q^{61} +1.98866 q^{62} +(27.1788 + 27.1788i) q^{63} -8.00000i q^{64} -205.326i q^{65} -13.9372 q^{66} -109.169 q^{67} +(-11.9199 + 11.9199i) q^{68} +(-97.4979 - 97.4979i) q^{69} +141.381 q^{70} +(-59.9574 + 59.9574i) q^{71} +(7.18090 + 7.18090i) q^{72} -22.8934i q^{73} +(37.3683 + 37.3683i) q^{74} +(156.085 + 156.085i) q^{75} +(-23.0106 - 23.0106i) q^{76} +(-21.0242 - 21.0242i) q^{77} +110.331 q^{78} -15.5383i q^{79} +37.3544 q^{80} +100.423 q^{81} +(73.7321 + 73.7321i) q^{82} +(-1.13888 + 1.13888i) q^{83} +75.9707i q^{84} +(-55.6576 - 55.6576i) q^{85} +(-3.77063 + 3.77063i) q^{86} -167.621 q^{87} +(-5.55482 - 5.55482i) q^{88} +5.33762i q^{89} +(-33.5298 + 33.5298i) q^{90} +(166.434 + 166.434i) q^{91} -77.7177i q^{92} -4.98961 q^{93} +(-5.27937 - 5.27937i) q^{94} +(107.443 - 107.443i) q^{95} +20.0722i q^{96} +133.029i q^{97} +(-65.6017 + 65.6017i) q^{98} +9.97215 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 46 q - 46 q^{2} - 6 q^{3} - 32 q^{5} + 4 q^{7} + 92 q^{8} + 32 q^{10} + 12 q^{12} - 8 q^{14} - 10 q^{15} - 184 q^{16} - 50 q^{17} + 118 q^{18} + 10 q^{19} + 16 q^{21} + 8 q^{22} - 124 q^{23} - 24 q^{24}+ \cdots + 508 q^{99}+O(q^{100}) \) 46 * q - 46 * q^2 - 6 * q^3 - 32 * q^5 + 4 * q^7 + 92 * q^8 + 32 * q^10 + 12 * q^12 - 8 * q^14 - 10 * q^15 - 184 * q^16 - 50 * q^17 + 118 * q^18 + 10 * q^19 + 16 * q^21 + 8 * q^22 - 124 * q^23 - 24 * q^24 + 178 * q^25 + 4 * q^26 + 90 * q^27 + 8 * q^28 + 40 * q^29 + 40 * q^31 + 184 * q^32 - 64 * q^33 - 14 * q^35 - 236 * q^36 - 32 * q^37 - 20 * q^38 - 54 * q^39 - 64 * q^40 - 132 * q^41 - 16 * q^42 - 16 * q^44 + 124 * q^46 - 60 * q^47 + 24 * q^48 - 178 * q^50 - 8 * q^52 - 188 * q^53 - 180 * q^54 - 40 * q^57 - 80 * q^58 + 190 * q^59 + 20 * q^60 - 80 * q^62 - 266 * q^63 + 128 * q^66 - 164 * q^67 + 100 * q^68 + 170 * q^69 + 28 * q^70 - 92 * q^71 + 236 * q^72 + 32 * q^74 - 190 * q^75 + 20 * q^76 + 20 * q^77 + 108 * q^78 + 128 * q^80 - 298 * q^81 + 132 * q^82 + 190 * q^83 + 298 * q^85 + 228 * q^86 - 92 * q^87 + 16 * q^88 - 528 * q^90 + 2 * q^91 + 232 * q^93 + 60 * q^94 - 280 * q^95 - 226 * q^98 + 508 * q^99

Introduction

L-functions

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