LMFDB - Embedded newform 310.2.b.a.249.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [310,2,Mod(249,310)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(310, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([1, 0]))

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

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

chi := DirichletCharacter("310.249");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 310 = 2 \cdot 5 \cdot 31 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	310.b (of order $2$, degree $1$, 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:	$2.47536246266$
Analytic rank:	$0$
Dimension:	$8$
Coefficient field:	8.0.619810816.2
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 2x^{5} + 14x^{4} - 8x^{3} + 2x^{2} + 2x + 1 $ x^8 - 2x^5 + 14x^4 - 8x^3 + 2x^2 + 2*x + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			249.4
Root			$-0.252709 - 0.252709i$ of defining polynomial
Character	$\chi$	$=$	310.249
Dual form			310.2.b.a.249.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000i q^{2} +0.872276i q^{3} -1.00000 q^{4} +(-2.23127 - 0.146426i) q^{5} +0.872276 q^{6} +2.79827i q^{7} +1.00000i q^{8} +2.23913 q^{9} +O(q^{10})$	\(q-1.00000i q^{2} +0.872276i q^{3} -1.00000 q^{4} +(-2.23127 - 0.146426i) q^{5} +0.872276 q^{6} +2.79827i q^{7} +1.00000i q^{8} +2.23913 q^{9} +(-0.146426 + 2.23127i) q^{10} -6.53654 q^{11} -0.872276i q^{12} +3.33481i q^{13} +2.79827 q^{14} +(0.127724 - 1.94628i) q^{15} +1.00000 q^{16} +6.39798i q^{17} -2.23913i q^{18} +1.45170 q^{19} +(2.23127 + 0.146426i) q^{20} -2.44086 q^{21} +6.53654i q^{22} -2.50542i q^{23} -0.872276 q^{24} +(4.95712 + 0.653431i) q^{25} +3.33481 q^{26} +4.56997i q^{27} -2.79827i q^{28} -5.98824 q^{29} +(-1.94628 - 0.127724i) q^{30} -1.00000 q^{31} -1.00000i q^{32} -5.70167i q^{33} +6.39798 q^{34} +(0.409739 - 6.24369i) q^{35} -2.23913 q^{36} +2.11689i q^{37} -1.45170i q^{38} -2.90888 q^{39} +(0.146426 - 2.23127i) q^{40} +3.81228 q^{41} +2.44086i q^{42} -10.3240i q^{43} +6.53654 q^{44} +(-4.99611 - 0.327867i) q^{45} -2.50542 q^{46} -6.12680i q^{47} +0.872276i q^{48} -0.830315 q^{49} +(0.653431 - 4.95712i) q^{50} -5.58081 q^{51} -3.33481i q^{52} +9.07937i q^{53} +4.56997 q^{54} +(14.5848 + 0.957119i) q^{55} -2.79827 q^{56} +1.26628i q^{57} +5.98824i q^{58} -1.59654 q^{59} +(-0.127724 + 1.94628i) q^{60} +3.23286 q^{61} +1.00000i q^{62} +6.26570i q^{63} -1.00000 q^{64} +(0.488303 - 7.44086i) q^{65} -5.70167 q^{66} +7.87683i q^{67} -6.39798i q^{68} +2.18542 q^{69} +(-6.24369 - 0.409739i) q^{70} -0.841151 q^{71} +2.23913i q^{72} -12.7374i q^{73} +2.11689 q^{74} +(-0.569972 + 4.32398i) q^{75} -1.45170 q^{76} -18.2910i q^{77} +2.90888i q^{78} -8.24449 q^{79} +(-2.23127 - 0.146426i) q^{80} +2.73112 q^{81} -3.81228i q^{82} +5.02029i q^{83} +2.44086 q^{84} +(0.936830 - 14.2756i) q^{85} -10.3240 q^{86} -5.22340i q^{87} -6.53654i q^{88} +5.93591 q^{89} +(-0.327867 + 4.99611i) q^{90} -9.33171 q^{91} +2.50542i q^{92} -0.872276i q^{93} -6.12680 q^{94} +(-3.23913 - 0.212567i) q^{95} +0.872276 q^{96} +13.5942i q^{97} +0.830315i q^{98} -14.6362 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 8 q^{4} - 2 q^{5} - 8 q^{6} - 8 q^{9}+O(q^{10}) $ 8 * q - 8 * q^4 - 2 * q^5 - 8 * q^6 - 8 * q^9	$ 8 q - 8 q^{4} - 2 q^{5} - 8 q^{6} - 8 q^{9} + 2 q^{10} - 16 q^{11} + 12 q^{14} + 16 q^{15} + 8 q^{16} - 12 q^{19} + 2 q^{20} - 4 q^{21} + 8 q^{24} + 12 q^{25} - 20 q^{26} + 12 q^{29} + 4 q^{30} - 8 q^{31} + 8 q^{34} + 20 q^{35} + 8 q^{36} - 40 q^{39} - 2 q^{40} + 16 q^{44} + 30 q^{45} - 16 q^{46} - 32 q^{49} - 8 q^{50} - 44 q^{51} + 44 q^{54} + 36 q^{55} - 12 q^{56} + 8 q^{59} - 16 q^{60} + 4 q^{61} - 8 q^{64} + 12 q^{65} + 12 q^{66} - 28 q^{69} - 20 q^{70} - 24 q^{71} + 40 q^{74} - 12 q^{75} + 12 q^{76} + 32 q^{79} - 2 q^{80} + 88 q^{81} + 4 q^{84} + 4 q^{85} - 44 q^{86} - 24 q^{89} - 34 q^{90} - 20 q^{91} + 4 q^{94} - 8 q^{96} + 20 q^{99}+O(q^{100}) $ 8 * q - 8 * q^4 - 2 * q^5 - 8 * q^6 - 8 * q^9 + 2 * q^10 - 16 * q^11 + 12 * q^14 + 16 * q^15 + 8 * q^16 - 12 * q^19 + 2 * q^20 - 4 * q^21 + 8 * q^24 + 12 * q^25 - 20 * q^26 + 12 * q^29 + 4 * q^30 - 8 * q^31 + 8 * q^34 + 20 * q^35 + 8 * q^36 - 40 * q^39 - 2 * q^40 + 16 * q^44 + 30 * q^45 - 16 * q^46 - 32 * q^49 - 8 * q^50 - 44 * q^51 + 44 * q^54 + 36 * q^55 - 12 * q^56 + 8 * q^59 - 16 * q^60 + 4 * q^61 - 8 * q^64 + 12 * q^65 + 12 * q^66 - 28 * q^69 - 20 * q^70 - 24 * q^71 + 40 * q^74 - 12 * q^75 + 12 * q^76 + 32 * q^79 - 2 * q^80 + 88 * q^81 + 4 * q^84 + 4 * q^85 - 44 * q^86 - 24 * q^89 - 34 * q^90 - 20 * q^91 + 4 * q^94 - 8 * q^96 + 20 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/310\mathbb{Z}\right)^\times$.

$n$	$187$	$251$
$\chi(n)$	$-1$	$1$

Coefficient data

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

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

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

$2$		−	1.00000i		−	0.707107i
$2$		−	1.00000i		−	0.707107i
$3$			0.872276i			0.503609i	0.967778	+	0.251804i	$0.0810240\pi$
$3$			0.872276i			0.503609i	−0.967778	+	0.251804i	$0.918976\pi$
$4$	−1.00000			−0.500000
$5$	−2.23127	−	0.146426i	−0.997854	−	0.0654836i
$5$	−2.23127	−	0.146426i	−0.997854	−	0.0654836i
$6$	0.872276			0.356105
$7$			2.79827i			1.05765i	0.848732	+	0.528823i	$0.177367\pi$
$7$			2.79827i			1.05765i	−0.848732	+	0.528823i	$0.822633\pi$
$8$			1.00000i			0.353553i
$9$	2.23913			0.746378
$10$	−0.146426	+	2.23127i	−0.0463039	+	0.705589i
$11$	−6.53654			−1.97084			−0.985421	−	0.170134i	$-0.945580\pi$
$11$	−6.53654			−1.97084			−0.985421	+	0.170134i	$0.945580\pi$
$12$		−	0.872276i		−	0.251804i
$13$			3.33481i			0.924911i	0.886643	+	0.462455i	$0.153031\pi$
$13$			3.33481i			0.924911i	−0.886643	+	0.462455i	$0.846969\pi$
$14$	2.79827			0.747869
$15$	0.127724	−	1.94628i	0.0329781	−	0.502528i
$16$	1.00000			0.250000
$17$			6.39798i			1.55174i	0.630894	+	0.775869i	$0.282688\pi$
$17$			6.39798i			1.55174i	−0.630894	+	0.775869i	$0.717312\pi$
$18$		−	2.23913i		−	0.527769i
$19$	1.45170			0.333043			0.166521	−	0.986038i	$-0.446746\pi$
$19$	1.45170			0.333043			0.166521	+	0.986038i	$0.446746\pi$
$20$	2.23127	+	0.146426i	0.498927	+	0.0327418i
$21$	−2.44086			−0.532640
$22$			6.53654i			1.39360i
$23$		−	2.50542i		−	0.522416i	−0.965283	−	0.261208i	$-0.915879\pi$
$23$		−	2.50542i		−	0.522416i	0.965283	−	0.261208i	$-0.0841208\pi$
$24$	−0.872276			−0.178053
$25$	4.95712	+	0.653431i	0.991424	+	0.130686i
$26$	3.33481			0.654011
$27$			4.56997i			0.879492i
$28$		−	2.79827i		−	0.528823i
$29$	−5.98824			−1.11199			−0.555995	−	0.831186i	$-0.687662\pi$
$29$	−5.98824			−1.11199			−0.555995	+	0.831186i	$0.687662\pi$
$30$	−1.94628	−	0.127724i	−0.355341	−	0.0233191i
$31$	−1.00000			−0.179605
$31$	−1.00000			−0.179605
$32$		−	1.00000i		−	0.176777i
$33$		−	5.70167i		−	0.992534i
$34$	6.39798			1.09725
$35$	0.409739	−	6.24369i	0.0692585	−	1.05538i
$36$	−2.23913			−0.373189
$37$			2.11689i			0.348014i	0.984744	+	0.174007i	$0.0556716\pi$
$37$			2.11689i			0.348014i	−0.984744	+	0.174007i	$0.944328\pi$
$38$		−	1.45170i		−	0.235497i
$39$	−2.90888			−0.465793
$40$	0.146426	−	2.23127i	0.0231520	−	0.352795i
$41$	3.81228			0.595378			0.297689	−	0.954663i	$-0.403784\pi$
$41$	3.81228			0.595378			0.297689	+	0.954663i	$0.403784\pi$
$42$			2.44086i			0.376634i
$43$		−	10.3240i		−	1.57439i	−0.616703	−	0.787196i	$-0.711532\pi$
$43$		−	10.3240i		−	1.57439i	0.616703	−	0.787196i	$-0.288468\pi$
$44$	6.53654			0.985421
$45$	−4.99611	−	0.327867i	−0.744776	−	0.0488755i
$46$	−2.50542			−0.369404
$47$		−	6.12680i		−	0.893686i	−0.894612	−	0.446843i	$-0.852548\pi$
$47$		−	6.12680i		−	0.893686i	0.894612	−	0.446843i	$-0.147452\pi$
$48$			0.872276i			0.125902i
$49$	−0.830315			−0.118616
$50$	0.653431	−	4.95712i	0.0924091	−	0.701042i
$51$	−5.58081			−0.781470
$52$		−	3.33481i		−	0.462455i
$53$			9.07937i			1.24715i	0.781765	+	0.623573i	$0.214320\pi$
$53$			9.07937i			1.24715i	−0.781765	+	0.623573i	$0.785680\pi$
$54$	4.56997			0.621894
$55$	14.5848	+	0.957119i	1.96661	+	0.129058i
$56$	−2.79827			−0.373935
$57$			1.26628i			0.167723i
$58$			5.98824i			0.786295i
$59$	−1.59654			−0.207852			−0.103926	−	0.994585i	$-0.533140\pi$
$59$	−1.59654			−0.207852			−0.103926	+	0.994585i	$0.533140\pi$
$60$	−0.127724	+	1.94628i	−0.0164891	+	0.251264i
$61$	3.23286			0.413925			0.206962	−	0.978349i	$-0.433642\pi$
$61$	3.23286			0.413925			0.206962	+	0.978349i	$0.433642\pi$
$62$			1.00000i			0.127000i
$63$			6.26570i			0.789404i
$64$	−1.00000			−0.125000
$65$	0.488303	−	7.44086i	0.0605665	−	0.922926i
$66$	−5.70167			−0.701827
$67$			7.87683i			0.962308i	0.876636	+	0.481154i	$0.159782\pi$
$67$			7.87683i			0.962308i	−0.876636	+	0.481154i	$0.840218\pi$
$68$		−	6.39798i		−	0.775869i
$69$	2.18542			0.263093
$70$	−6.24369	−	0.409739i	−0.746264	−	0.0489732i
$71$	−0.841151			−0.0998263			−0.0499131	−	0.998754i	$-0.515894\pi$
$71$	−0.841151			−0.0998263			−0.0499131	+	0.998754i	$0.515894\pi$
$72$			2.23913i			0.263884i
$73$		−	12.7374i		−	1.49079i	−0.666621	−	0.745397i	$-0.732260\pi$
$73$		−	12.7374i		−	1.49079i	0.666621	−	0.745397i	$-0.267740\pi$
$74$	2.11689			0.246083
$75$	−0.569972	+	4.32398i	−0.0658147	+	0.499290i
$76$	−1.45170			−0.166521
$77$		−	18.2910i		−	2.08445i
$78$			2.90888i			0.329366i
$79$	−8.24449			−0.927578			−0.463789	−	0.885946i	$-0.653510\pi$
$79$	−8.24449			−0.927578			−0.463789	+	0.885946i	$0.653510\pi$
$80$	−2.23127	−	0.146426i	−0.249463	−	0.0163709i
$81$	2.73112			0.303458
$82$		−	3.81228i		−	0.420996i
$83$			5.02029i			0.551048i	0.961294	+	0.275524i	$0.0888514\pi$
$83$			5.02029i			0.551048i	−0.961294	+	0.275524i	$0.911149\pi$
$84$	2.44086			0.266320
$85$	0.936830	−	14.2756i	0.101613	−	1.54841i
$86$	−10.3240			−1.11326
$87$		−	5.22340i		−	0.560008i
$88$		−	6.53654i		−	0.696798i
$89$	5.93591			0.629205			0.314603	−	0.949223i	$-0.398129\pi$
$89$	5.93591			0.629205			0.314603	+	0.949223i	$0.398129\pi$
$90$	−0.327867	+	4.99611i	−0.0345602	+	0.526636i
$91$	−9.33171			−0.978229
$92$			2.50542i			0.261208i
$93$		−	0.872276i		−	0.0904508i
$94$	−6.12680			−0.631932
$95$	−3.23913	−	0.212567i	−0.332328	−	0.0218089i
$96$	0.872276			0.0890263
$97$			13.5942i			1.38029i	0.723673	+	0.690143i	$0.242452\pi$
$97$			13.5942i			1.38029i	−0.723673	+	0.690143i	$0.757548\pi$
$98$			0.830315i			0.0838744i
$99$	−14.6362			−1.47099
$100$	−4.95712	−	0.653431i	−0.495712	−	0.0653431i
$101$	13.7820			1.37136			0.685678	−	0.727905i	$-0.259506\pi$
$101$	13.7820			1.37136			0.685678	+	0.727905i	$0.259506\pi$
$102$			5.58081i			0.552582i
$103$		−	3.57487i		−	0.352242i	−0.984369	−	0.176121i	$-0.943645\pi$
$103$		−	3.57487i		−	0.352242i	0.984369	−	0.176121i	$-0.0563550\pi$
$104$	−3.33481			−0.327005
$105$	5.44622	+	0.357406i	0.531497	+	0.0348792i
$106$	9.07937			0.881866
$107$		−	1.04824i		−	0.101337i	−0.998716	−	0.0506686i	$-0.983865\pi$
$107$		−	1.04824i		−	0.101337i	0.998716	−	0.0506686i	$-0.0161352\pi$
$108$		−	4.56997i		−	0.439746i
$109$	−8.03740			−0.769844			−0.384922	−	0.922949i	$-0.625772\pi$
$109$	−8.03740			−0.769844			−0.384922	+	0.922949i	$0.625772\pi$
$110$	0.957119	−	14.5848i	0.0912577	−	1.39060i
$111$	−1.84651			−0.175263
$112$			2.79827i			0.264412i
$113$			9.00853i			0.847451i	0.905791	+	0.423726i	$0.139278\pi$
$113$			9.00853i			0.847451i	−0.905791	+	0.423726i	$0.860722\pi$
$114$	1.26628			0.118598
$115$	−0.366858	+	5.59026i	−0.0342097	+	0.521295i
$116$	5.98824			0.555995
$117$			7.46709i			0.690333i
$118$			1.59654i			0.146973i
$119$	−17.9033			−1.64119
$120$	1.94628	+	0.127724i	0.177670	+	0.0116595i
$121$	31.7264			2.88422
$122$		−	3.23286i		−	0.292689i
$123$			3.32536i			0.299838i
$124$	1.00000			0.0898027
$125$	−10.9650	−	2.18383i	−0.980738	−	0.195328i
$126$	6.26570			0.558193
$127$			21.7265i			1.92792i	0.266053	+	0.963958i	$0.414280\pi$
$127$			21.7265i			1.92792i	−0.266053	+	0.963958i	$0.585720\pi$
$128$			1.00000i			0.0883883i
$129$	9.00536			0.792878
$130$	−7.44086	−	0.488303i	−0.652607	−	0.0428270i
$131$	2.61055			0.228085			0.114042	−	0.993476i	$-0.463620\pi$
$131$	2.61055			0.228085			0.114042	+	0.993476i	$0.463620\pi$
$132$			5.70167i			0.496267i
$133$			4.06225i			0.352242i
$134$	7.87683			0.680455
$135$	0.669162	−	10.1968i	0.0575923	−	0.877604i
$136$	−6.39798			−0.548623
$137$		−	7.49458i		−	0.640305i	−0.947366	−	0.320153i	$-0.896266\pi$
$137$		−	7.49458i		−	0.640305i	0.947366	−	0.320153i	$-0.103734\pi$
$138$		−	2.18542i		−	0.186035i
$139$	12.6579			1.07363			0.536813	−	0.843701i	$-0.319628\pi$
$139$	12.6579			1.07363			0.536813	+	0.843701i	$0.319628\pi$
$140$	−0.409739	+	6.24369i	−0.0346293	+	0.527688i
$141$	5.34427			0.450068
$142$			0.841151i			0.0705878i
$143$		−	21.7982i		−	1.82285i
$144$	2.23913			0.186595
$145$	13.3614	+	0.876834i	1.10960	+	0.0728171i
$146$	−12.7374			−1.05415
$147$		−	0.724264i		−	0.0597363i
$148$		−	2.11689i		−	0.174007i
$149$	14.6354			1.19898			0.599489	−	0.800383i	$-0.295370\pi$
$149$	14.6354			1.19898			0.599489	+	0.800383i	$0.295370\pi$
$150$	4.32398	+	0.569972i	0.353051	+	0.0465380i
$151$	4.01256			0.326537			0.163269	−	0.986582i	$-0.447796\pi$
$151$	4.01256			0.326537			0.163269	+	0.986582i	$0.447796\pi$
$152$			1.45170i			0.117748i
$153$			14.3259i			1.15818i
$154$	−18.2910			−1.47393
$155$	2.23127	+	0.146426i	0.179220	+	0.0117612i
$156$	2.90888			0.232897
$157$			24.4981i			1.95516i	0.210561	+	0.977581i	$0.432471\pi$
$157$			24.4981i			1.95516i	−0.210561	+	0.977581i	$0.567529\pi$
$158$			8.24449i			0.655897i
$159$	−7.91971			−0.628074
$160$	−0.146426	+	2.23127i	−0.0115760	+	0.176397i
$161$	7.01084			0.552531
$162$		−	2.73112i		−	0.214577i
$163$			19.1696i			1.50148i	0.660600	+	0.750738i	$0.270302\pi$
$163$			19.1696i			1.50148i	−0.660600	+	0.750738i	$0.729698\pi$
$164$	−3.81228			−0.297689
$165$	−0.834872	+	12.7220i	−0.0649947	+	0.990403i
$166$	5.02029			0.389650
$167$			18.0693i			1.39825i	0.715001	+	0.699123i	$0.246426\pi$
$167$			18.0693i			1.39825i	−0.715001	+	0.699123i	$0.753574\pi$
$168$		−	2.44086i		−	0.188317i
$169$	1.87902			0.144540
$170$	−14.2756	−	0.936830i	−1.09489	−	0.0718516i
$171$	3.25055			0.248576
$172$			10.3240i			0.787196i
$173$		−	13.0948i		−	0.995576i	−0.867299	−	0.497788i	$-0.834146\pi$
$173$		−	13.0948i		−	0.995576i	0.867299	−	0.497788i	$-0.165854\pi$
$174$	−5.22340			−0.395985
$175$	−1.82848	+	13.8714i	−0.138220	+	1.04858i
$176$	−6.53654			−0.492711
$177$		−	1.39262i		−	0.104676i
$178$		−	5.93591i		−	0.444915i
$179$	17.4899			1.30726			0.653629	−	0.756816i	$-0.273246\pi$
$179$	17.4899			1.30726			0.653629	+	0.756816i	$0.273246\pi$
$180$	4.99611	+	0.327867i	0.372388	+	0.0244378i
$181$	2.63486			0.195848			0.0979239	−	0.995194i	$-0.468780\pi$
$181$	2.63486			0.195848			0.0979239	+	0.995194i	$0.468780\pi$
$182$			9.33171i			0.691712i
$183$			2.81994i			0.208456i
$184$	2.50542			0.184702
$185$	0.309967	−	4.72334i	0.0227892	−	0.347267i
$186$	−0.872276			−0.0639584
$187$		−	41.8207i		−	3.05823i
$188$			6.12680i			0.446843i
$189$	−12.7880			−0.930191
$190$	−0.212567	+	3.23913i	−0.0154212	+	0.234991i
$191$	−14.9837			−1.08418			−0.542091	−	0.840320i	$-0.682367\pi$
$191$	−14.9837			−1.08418			−0.542091	+	0.840320i	$0.682367\pi$
$192$		−	0.872276i		−	0.0629511i
$193$		−	14.6605i		−	1.05529i	−0.849466	−	0.527643i	$-0.823076\pi$
$193$		−	14.6605i		−	1.05529i	0.849466	−	0.527643i	$-0.176924\pi$
$194$	13.5942			0.976009
$195$	6.49049	+	0.425935i	0.464794	+	0.0305018i
$196$	0.830315			0.0593082
$197$		−	7.33799i		−	0.522810i	−0.965229	−	0.261405i	$-0.915814\pi$
$197$		−	7.33799i		−	0.522810i	0.965229	−	0.261405i	$-0.0841858\pi$
$198$			14.6362i			1.04015i
$199$	1.48910			0.105560			0.0527799	−	0.998606i	$-0.483192\pi$
$199$	1.48910			0.105560			0.0527799	+	0.998606i	$0.483192\pi$
$200$	−0.653431	+	4.95712i	−0.0462045	+	0.350521i
$201$	−6.87077			−0.484627
$202$		−	13.7820i		−	0.969695i
$203$		−	16.7567i		−	1.17609i
$204$	5.58081			0.390735
$205$	−8.50622	−	0.558216i	−0.594100	−	0.0389875i
$206$	−3.57487			−0.249073
$207$		−	5.60997i		−	0.389920i
$208$			3.33481i			0.231228i
$209$	−9.48910			−0.656375
$210$	0.357406	−	5.44622i	0.0246633	−	0.375825i
$211$	−3.71971			−0.256075			−0.128038	−	0.991769i	$-0.540868\pi$
$211$	−3.71971			−0.256075			−0.128038	+	0.991769i	$0.540868\pi$
$212$		−	9.07937i		−	0.623573i
$213$		−	0.733716i		−	0.0502734i
$214$	−1.04824			−0.0716562
$215$	−1.51170	+	23.0356i	−0.103097	+	1.57101i
$216$	−4.56997			−0.310947
$217$		−	2.79827i		−	0.189959i
$218$			8.03740i			0.544362i
$219$	11.1105			0.750777
$220$	−14.5848	−	0.957119i	−0.983306	−	0.0645289i
$221$	−21.3361			−1.43522
$222$			1.84651i			0.123930i
$223$			3.37459i			0.225979i	0.993596	+	0.112990i	$0.0360427\pi$
$223$			3.37459i			0.225979i	−0.993596	+	0.112990i	$0.963957\pi$
$224$	2.79827			0.186967
$225$	11.0997	+	1.46312i	0.739977	+	0.0975413i
$226$	9.00853			0.599239
$227$		−	18.1462i		−	1.20440i	−0.798344	−	0.602202i	$-0.794290\pi$
$227$		−	18.1462i		−	1.20440i	0.798344	−	0.602202i	$-0.205710\pi$
$228$		−	1.26628i		−	0.0838617i
$229$	−22.4647			−1.48451			−0.742254	−	0.670119i	$-0.766243\pi$
$229$	−22.4647			−1.48451			−0.742254	+	0.670119i	$0.766243\pi$
$230$	5.59026	+	0.366858i	0.368611	+	0.0241899i
$231$	15.9548			1.04975
$232$		−	5.98824i		−	0.393147i
$233$			0.298329i			0.0195442i	0.999952	+	0.00977208i	$0.00311060\pi$
$233$			0.298329i			0.0195442i	−0.999952	+	0.00977208i	$0.996889\pi$
$234$	7.46709			0.488139
$235$	−0.897123	+	13.6705i	−0.0585218	+	0.891768i
$236$	1.59654			0.103926
$237$		−	7.19148i		−	0.467137i
$238$			17.9033i			1.16050i
$239$	−16.4016			−1.06093			−0.530466	−	0.847706i	$-0.677983\pi$
$239$	−16.4016			−1.06093			−0.530466	+	0.847706i	$0.677983\pi$
$240$	0.127724	−	1.94628i	0.00824454	−	0.125632i
$241$	−22.8302			−1.47062			−0.735311	−	0.677730i	$-0.762964\pi$
$241$	−22.8302			−1.47062			−0.735311	+	0.677730i	$0.762964\pi$
$242$		−	31.7264i		−	2.03945i
$243$			16.0922i			1.03232i
$244$	−3.23286			−0.206962
$245$	1.85265	+	0.121580i	0.118362	+	0.00776743i
$246$	3.32536			0.212017
$247$			4.84115i			0.308035i
$248$		−	1.00000i		−	0.0635001i
$249$	−4.37908			−0.277513
$250$	−2.18383	+	10.9650i	−0.138118	+	0.693487i
$251$	18.9742			1.19764			0.598822	−	0.800883i	$-0.295636\pi$
$251$	18.9742			1.19764			0.598822	+	0.800883i	$0.295636\pi$
$252$		−	6.26570i		−	0.394702i
$253$			16.3768i			1.02960i
$254$	21.7265			1.36324
$255$	12.4523	+	0.817175i	0.779792	+	0.0511735i
$256$	1.00000			0.0625000
$257$			26.4422i			1.64942i	0.565557	+	0.824710i	$0.308661\pi$
$257$			26.4422i			1.64942i	−0.565557	+	0.824710i	$0.691339\pi$
$258$		−	9.00536i		−	0.560649i
$259$	−5.92362			−0.368076
$260$	−0.488303	+	7.44086i	−0.0302833	+	0.461463i
$261$	−13.4085			−0.829964
$262$		−	2.61055i		−	0.161280i
$263$		−	13.7699i		−	0.849086i	−0.905408	−	0.424543i	$-0.860435\pi$
$263$		−	13.7699i		−	0.849086i	0.905408	−	0.424543i	$-0.139565\pi$
$264$	5.70167			0.350914
$265$	1.32945	−	20.2585i	0.0816677	−	1.24447i
$266$	4.06225			0.249073
$267$			5.17775i			0.316873i
$268$		−	7.87683i		−	0.481154i
$269$	0.495966			0.0302396			0.0151198	−	0.999886i	$-0.495187\pi$
$269$	0.495966			0.0302396			0.0151198	+	0.999886i	$0.495187\pi$
$270$	−10.1968	−	0.669162i	−0.620560	−	0.0407239i
$271$	−1.40518			−0.0853587			−0.0426793	−	0.999089i	$-0.513589\pi$
$271$	−1.40518			−0.0853587			−0.0426793	+	0.999089i	$0.513589\pi$
$272$			6.39798i			0.387935i
$273$		−	8.13983i		−	0.492645i
$274$	−7.49458			−0.452764
$275$	−32.4024	−	4.27118i	−1.95394	−	0.257562i
$276$	−2.18542			−0.131547
$277$		−	6.10116i		−	0.366583i	−0.983059	−	0.183291i	$-0.941325\pi$
$277$		−	6.10116i		−	0.366583i	0.983059	−	0.183291i	$-0.0586752\pi$
$278$		−	12.6579i		−	0.759169i
$279$	−2.23913			−0.134053
$280$	6.24369	+	0.409739i	0.373132	+	0.0244866i
$281$	20.8113			1.24150			0.620749	−	0.784010i	$-0.286829\pi$
$281$	20.8113			1.24150			0.620749	+	0.784010i	$0.286829\pi$
$282$		−	5.34427i		−	0.318246i
$283$		−	14.5280i		−	0.863598i	−0.901970	−	0.431799i	$-0.857879\pi$
$283$		−	14.5280i		−	0.863598i	0.901970	−	0.431799i	$-0.142121\pi$
$284$	0.841151			0.0499131
$285$	0.185417	−	2.82542i	0.0109831	−	0.167363i
$286$	−21.7982			−1.28895
$287$			10.6678i			0.629700i
$288$		−	2.23913i		−	0.131942i
$289$	−23.9342			−1.40789
$290$	0.876834	−	13.3614i	0.0514895	−	0.784607i
$291$	−11.8579			−0.695124
$292$			12.7374i			0.745397i
$293$		−	5.90830i		−	0.345166i	−0.984995	−	0.172583i	$-0.944789\pi$
$293$		−	5.90830i		−	0.345166i	0.984995	−	0.172583i	$-0.0552114\pi$
$294$	−0.724264			−0.0422399
$295$	3.56231	+	0.233775i	0.207406	+	0.0136109i
$296$	−2.11689			−0.123042
$297$		−	29.8718i		−	1.73334i
$298$		−	14.6354i		−	0.847806i
$299$	8.35510			0.483188
$300$	0.569972	−	4.32398i	0.0329074	−	0.249645i
$301$	28.8893			1.66515
$302$		−	4.01256i		−	0.230897i
$303$			12.0217i			0.690627i
$304$	1.45170			0.0832607
$305$	−7.21337	−	0.473374i	−0.413036	−	0.0271053i
$306$	14.3259			0.818960
$307$		−	32.8035i		−	1.87220i	−0.351740	−	0.936098i	$-0.614410\pi$
$307$		−	32.8035i		−	1.87220i	0.351740	−	0.936098i	$-0.385590\pi$
$308$			18.2910i			1.04223i
$309$	3.11827			0.177392
$310$	0.146426	−	2.23127i	0.00831643	−	0.126728i
$311$	−4.45936			−0.252867			−0.126434	−	0.991975i	$-0.540353\pi$
$311$	−4.45936			−0.252867			−0.126434	+	0.991975i	$0.540353\pi$
$312$		−	2.90888i		−	0.164683i
$313$		−	20.2591i		−	1.14511i	−0.819866	−	0.572556i	$-0.805952\pi$
$313$		−	20.2591i		−	1.14511i	0.819866	−	0.572556i	$-0.194048\pi$
$314$	24.4981			1.38251
$315$	0.917461	−	13.9805i	0.0516931	−	0.787710i
$316$	8.24449			0.463789
$317$		−	10.7834i		−	0.605657i	−0.953045	−	0.302828i	$-0.902069\pi$
$317$		−	10.7834i		−	0.605657i	0.953045	−	0.302828i	$-0.0979309\pi$
$318$			7.91971i			0.444116i
$319$	39.1424			2.19155
$320$	2.23127	+	0.146426i	0.124732	+	0.00818545i
$321$	0.914355			0.0510343
$322$		−	7.01084i		−	0.390699i
$323$			9.28796i			0.516796i
$324$	−2.73112			−0.151729
$325$	−2.17907	+	16.5311i	−0.120873	+	0.916979i
$326$	19.1696			1.06170
$327$		−	7.01084i		−	0.387700i
$328$			3.81228i			0.210498i
$329$	17.1445			0.945204
$330$	12.7220	+	0.834872i	0.700321	+	0.0459582i
$331$	−3.54605			−0.194908			−0.0974541	−	0.995240i	$-0.531070\pi$
$331$	−3.54605			−0.194908			−0.0974541	+	0.995240i	$0.531070\pi$
$332$		−	5.02029i		−	0.275524i
$333$			4.73999i			0.259750i
$334$	18.0693			0.988710
$335$	1.15337	−	17.5753i	0.0630154	−	0.960243i
$336$	−2.44086			−0.133160
$337$			22.6236i			1.23238i	0.787596	+	0.616192i	$0.211326\pi$
$337$			22.6236i			1.23238i	−0.787596	+	0.616192i	$0.788674\pi$
$338$		−	1.87902i		−	0.102205i
$339$	−7.85793			−0.426784
$340$	−0.936830	+	14.2756i	−0.0508067	+	0.774204i
$341$	6.53654			0.353974
$342$		−	3.25055i		−	0.175770i
$343$			17.2644i			0.932192i
$344$	10.3240			0.556632
$345$	−4.87625	−	0.320002i	−0.262529	−	0.0172283i
$346$	−13.0948			−0.703979
$347$			15.6475i			0.840002i	0.907524	+	0.420001i	$0.137970\pi$
$347$			15.6475i			0.840002i	−0.907524	+	0.420001i	$0.862030\pi$
$348$			5.22340i			0.280004i
$349$	−10.3708			−0.555138			−0.277569	−	0.960706i	$-0.589529\pi$
$349$	−10.3708			−0.555138			−0.277569	+	0.960706i	$0.589529\pi$
$350$	13.8714	+	1.82848i	0.741455	+	0.0977361i
$351$	−15.2400			−0.813451
$352$			6.53654i			0.348399i
$353$		−	9.02703i		−	0.480460i	−0.970716	−	0.240230i	$-0.922777\pi$
$353$		−	9.02703i		−	0.480460i	0.970716	−	0.240230i	$-0.0772229\pi$
$354$	−1.39262			−0.0740171
$355$	1.87683	+	0.123166i	0.0996120	+	0.00653699i
$356$	−5.93591			−0.314603
$357$		−	15.6166i		−	0.826519i
$358$		−	17.4899i		−	0.924370i
$359$	−32.3635			−1.70808			−0.854041	−	0.520206i	$-0.825855\pi$
$359$	−32.3635			−1.70808			−0.854041	+	0.520206i	$0.825855\pi$
$360$	0.327867	−	4.99611i	0.0172801	−	0.263318i
$361$	−16.8926			−0.889082
$362$		−	2.63486i		−	0.138485i
$363$			27.6742i			1.45252i
$364$	9.33171			0.489114
$365$	−1.86508	+	28.4205i	−0.0976226	+	1.48759i
$366$	2.81994			0.147401
$367$		−	13.9927i		−	0.730412i	−0.930927	−	0.365206i	$-0.880999\pi$
$367$		−	13.9927i		−	0.730412i	0.930927	−	0.365206i	$-0.119001\pi$
$368$		−	2.50542i		−	0.130604i
$369$	8.53621			0.444377
$370$	−4.72334	−	0.309967i	−0.245555	−	0.0161144i
$371$	−25.4065			−1.31904
$372$			0.872276i			0.0452254i
$373$			1.42091i			0.0735721i	0.999323	+	0.0367860i	$0.0117120\pi$
$373$			1.42091i			0.0735721i	−0.999323	+	0.0367860i	$0.988288\pi$
$374$	−41.8207			−2.16250
$375$	1.90490	−	9.56450i	0.0983688	−	0.493908i
$376$	6.12680			0.315966
$377$		−	19.9697i		−	1.02849i
$378$			12.7880i			0.657745i
$379$	29.1912			1.49945			0.749727	−	0.661748i	$-0.230185\pi$
$379$	29.1912			1.49945			0.749727	+	0.661748i	$0.230185\pi$
$380$	3.23913	+	0.212567i	0.166164	+	0.0109044i
$381$	−18.9515			−0.970916
$382$			14.9837i			0.766632i
$383$			26.9070i			1.37489i	0.726239	+	0.687443i	$0.241267\pi$
$383$			26.9070i			1.37489i	−0.726239	+	0.687443i	$0.758733\pi$
$384$	−0.872276			−0.0445132
$385$	−2.67828	+	40.8122i	−0.136498	+	2.07998i
$386$	−14.6605			−0.746200
$387$		−	23.1168i		−	1.17509i
$388$		−	13.5942i		−	0.690143i
$389$	0.0274871			0.00139365			0.000696825	−	1.00000i	$-0.499778\pi$
$389$	0.0274871			0.00139365			0.000696825		1.00000i	$0.499778\pi$
$390$	0.425935	−	6.49049i	0.0215681	−	0.328659i
$391$	16.0296			0.810653
$392$		−	0.830315i		−	0.0419372i
$393$			2.27712i			0.114866i
$394$	−7.33799			−0.369682
$395$	18.3957	+	1.20721i	0.925587	+	0.0607412i
$396$	14.6362			0.735497
$397$		−	15.7021i		−	0.788068i	−0.919096	−	0.394034i	$-0.871079\pi$
$397$		−	15.7021i		−	0.788068i	0.919096	−	0.394034i	$-0.128921\pi$
$398$		−	1.48910i		−	0.0746421i
$399$	−3.54340			−0.177392
$400$	4.95712	+	0.653431i	0.247856	+	0.0326715i
$401$	30.6370			1.52994			0.764969	−	0.644067i	$-0.222754\pi$
$401$	30.6370			1.52994			0.764969	+	0.644067i	$0.222754\pi$
$402$			6.87077i			0.342683i
$403$		−	3.33481i		−	0.166119i
$404$	−13.7820			−0.685678
$405$	−6.09387	−	0.399907i	−0.302807	−	0.0198716i
$406$	−16.7567			−0.831622
$407$		−	13.8371i		−	0.685881i
$408$		−	5.58081i		−	0.276291i
$409$	−10.3519			−0.511870			−0.255935	−	0.966694i	$-0.582383\pi$
$409$	−10.3519			−0.511870			−0.255935	+	0.966694i	$0.582383\pi$
$410$	−0.558216	+	8.50622i	−0.0275683	+	0.420092i
$411$	6.53735			0.322463
$412$			3.57487i			0.176121i
$413$		−	4.46755i		−	0.219834i
$414$	−5.60997			−0.275715
$415$	0.735100	−	11.2016i	0.0360846	−	0.549866i
$416$	3.33481			0.163503
$417$			11.0412i			0.540688i
$418$			9.48910i			0.464127i
$419$	16.1496			0.788960			0.394480	−	0.918904i	$-0.370925\pi$
$419$	16.1496			0.788960			0.394480	+	0.918904i	$0.370925\pi$
$420$	−5.44622	−	0.357406i	−0.265749	−	0.0174396i
$421$	−26.1804			−1.27595			−0.637977	−	0.770055i	$-0.720229\pi$
$421$	−26.1804			−1.27595			−0.637977	+	0.770055i	$0.720229\pi$
$422$			3.71971i			0.181072i
$423$		−	13.7187i		−	0.667028i
$424$	−9.07937			−0.440933
$425$	−4.18064	+	31.7156i	−0.202791	+	1.53843i
$426$	−0.733716			−0.0355487
$427$			9.04640i			0.437786i
$428$			1.04824i			0.0506686i
$429$	19.0140			0.918005
$430$	23.0356	+	1.51170i	1.11087	+	0.0729005i
$431$	−24.7248			−1.19095			−0.595476	−	0.803373i	$-0.703036\pi$
$431$	−24.7248			−1.19095			−0.595476	+	0.803373i	$0.703036\pi$
$432$			4.56997i			0.219873i
$433$		−	1.26265i		−	0.0606789i	−0.999540	−	0.0303394i	$-0.990341\pi$
$433$		−	1.26265i		−	0.0606789i	0.999540	−	0.0303394i	$-0.00965883\pi$
$434$	−2.79827			−0.134321
$435$	−0.764841	+	11.6548i	−0.0366713	+	0.558806i
$436$	8.03740			0.384922
$437$		−	3.63712i		−	0.173987i
$438$		−	11.1105i		−	0.530880i
$439$	28.0379			1.33817			0.669087	−	0.743184i	$-0.266685\pi$
$439$	28.0379			1.33817			0.669087	+	0.743184i	$0.266685\pi$
$440$	−0.957119	+	14.5848i	−0.0456289	+	0.695302i
$441$	−1.85919			−0.0885327
$442$			21.3361i			1.01485i
$443$			20.3095i			0.964934i	0.875914	+	0.482467i	$0.160259\pi$
$443$			20.3095i			0.964934i	−0.875914	+	0.482467i	$0.839741\pi$
$444$	1.84651			0.0876315
$445$	−13.2446	−	0.869171i	−0.627855	−	0.0412026i
$446$	3.37459			0.159791
$447$			12.7661i			0.603816i
$448$		−	2.79827i		−	0.132206i
$449$	−0.298793			−0.0141009			−0.00705046	−	0.999975i	$-0.502244\pi$
$449$	−0.298793			−0.0141009			−0.00705046	+	0.999975i	$0.502244\pi$
$450$	1.46312	−	11.0997i	0.0689721	−	0.523243i
$451$	−24.9191			−1.17340
$452$		−	9.00853i		−	0.423726i
$453$			3.50006i			0.164447i
$454$	−18.1462			−0.851642
$455$	20.8215	+	1.36640i	0.976129	+	0.0640580i
$456$	−1.26628			−0.0592992
$457$		−	21.3105i		−	0.996863i	−0.866929	−	0.498432i	$-0.833910\pi$
$457$		−	21.3105i		−	0.996863i	0.866929	−	0.498432i	$-0.166090\pi$
$458$			22.4647i			1.04971i
$459$	−29.2386			−1.36474
$460$	0.366858	−	5.59026i	0.0171048	−	0.260647i
$461$	24.5165			1.14185			0.570923	−	0.821004i	$-0.306585\pi$
$461$	24.5165			1.14185			0.570923	+	0.821004i	$0.306585\pi$
$462$		−	15.9548i		−	0.742285i
$463$		−	5.45400i		−	0.253469i	−0.991937	−	0.126735i	$-0.959550\pi$
$463$		−	5.45400i		−	0.253469i	0.991937	−	0.126735i	$-0.0404496\pi$
$464$	−5.98824			−0.277997
$465$	−0.127724	+	1.94628i	−0.00592305	+	0.0902567i
$466$	0.298329			0.0138198
$467$		−	10.4345i		−	0.482852i	−0.970419	−	0.241426i	$-0.922385\pi$
$467$		−	10.4345i		−	0.482852i	0.970419	−	0.241426i	$-0.0776151\pi$
$468$		−	7.46709i		−	0.345167i
$469$	−22.0415			−1.01778
$470$	13.6705	+	0.897123i	0.630575	+	0.0413812i
$471$	−21.3691			−0.984637
$472$		−	1.59654i		−	0.0734867i
$473$			67.4831i			3.10288i
$474$	−7.19148			−0.330315
$475$	7.19625	+	0.948586i	0.330187	+	0.0435241i
$476$	17.9033			0.820596
$477$			20.3299i			0.930843i
$478$			16.4016i			0.750193i
$479$	23.3691			1.06776			0.533881	−	0.845560i	$-0.320733\pi$
$479$	23.3691			1.06776			0.533881	+	0.845560i	$0.320733\pi$
$480$	−1.94628	−	0.127724i	−0.0888352	−	0.00582977i
$481$	−7.05942			−0.321882
$482$			22.8302i			1.03989i
$483$			6.11539i			0.278260i
$484$	−31.7264			−1.44211
$485$	1.99055	−	30.3324i	0.0903861	−	1.37732i
$486$	16.0922			0.729958
$487$			10.9504i			0.496209i	0.968733	+	0.248105i	$0.0798077\pi$
$487$			10.9504i			0.496209i	−0.968733	+	0.248105i	$0.920192\pi$
$488$			3.23286i			0.146344i
$489$	−16.7212			−0.756157
$490$	0.121580	−	1.85265i	0.00549240	−	0.0836944i
$491$	−27.6705			−1.24875			−0.624377	−	0.781123i	$-0.714647\pi$
$491$	−27.6705			−1.24875			−0.624377	+	0.781123i	$0.714647\pi$
$492$		−	3.32536i		−	0.149919i
$493$		−	38.3127i		−	1.72552i
$494$	4.84115			0.217814
$495$	32.6573	+	2.14312i	1.46784	+	0.0963260i
$496$	−1.00000			−0.0449013
$497$		−	2.35377i		−	0.105581i
$498$			4.37908i			0.196231i
$499$	−6.90577			−0.309145			−0.154572	−	0.987981i	$-0.549400\pi$
$499$	−6.90577			−0.309145			−0.154572	+	0.987981i	$0.549400\pi$
$500$	10.9650	+	2.18383i	0.490369	+	0.0976638i
$501$	−15.7614			−0.704170
$502$		−	18.9742i		−	0.846862i
$503$			7.26812i			0.324070i	0.986785	+	0.162035i	$0.0518057\pi$
$503$			7.26812i			0.324070i	−0.986785	+	0.162035i	$0.948194\pi$
$504$	−6.26570			−0.279097
$505$	−30.7512	−	2.01803i	−1.36841	−	0.0898014i
$506$	16.3768			0.728036
$507$			1.63902i			0.0727916i
$508$		−	21.7265i		−	0.963958i
$509$	7.37953			0.327092			0.163546	−	0.986536i	$-0.447707\pi$
$509$	7.37953			0.327092			0.163546	+	0.986536i	$0.447707\pi$
$510$	0.817175	−	12.4523i	0.0361851	−	0.551396i
$511$	35.6426			1.57673
$512$		−	1.00000i		−	0.0441942i
$513$			6.63423i			0.292908i
$514$	26.4422			1.16632
$515$	−0.523453	+	7.97649i	−0.0230661	+	0.351486i
$516$	−9.00536			−0.396439
$517$			40.0481i			1.76131i
$518$			5.92362i			0.260269i
$519$	11.4222			0.501381
$520$	7.44086	+	0.488303i	0.326303	+	0.0214135i
$521$	29.1570			1.27739			0.638696	−	0.769459i	$-0.279474\pi$
$521$	29.1570			1.27739			0.638696	+	0.769459i	$0.279474\pi$
$522$			13.4085i			0.586873i
$523$		−	9.09032i		−	0.397492i	−0.980051	−	0.198746i	$-0.936313\pi$
$523$		−	9.09032i		−	0.397492i	0.980051	−	0.198746i	$-0.0636869\pi$
$524$	−2.61055			−0.114042
$525$	−12.0997	−	1.59494i	−0.528072	−	0.0696087i
$526$	−13.7699			−0.600395
$527$		−	6.39798i		−	0.278701i
$528$		−	5.70167i		−	0.248133i
$529$	16.7229			0.727082
$530$	−20.2585	−	1.32945i	−0.879973	−	0.0577478i
$531$	−3.57487			−0.155136
$532$		−	4.06225i		−	0.176121i
$533$			12.7132i			0.550672i
$534$	5.17775			0.224063
$535$	−0.153490	+	2.33891i	−0.00663593	+	0.101120i
$536$	−7.87683			−0.340227
$537$			15.2560i			0.658346i
$538$		−	0.495966i		−	0.0213826i
$539$	5.42739			0.233774
$540$	−0.669162	+	10.1968i	−0.0287962	+	0.438802i
$541$	−14.7693			−0.634981			−0.317491	−	0.948261i	$-0.602840\pi$
$541$	−14.7693			−0.634981			−0.317491	+	0.948261i	$0.602840\pi$
$542$			1.40518i			0.0603577i
$543$			2.29833i			0.0986307i
$544$	6.39798			0.274311
$545$	17.9336	+	1.17688i	0.768191	+	0.0504122i
$546$	−8.13983			−0.348352
$547$		−	16.3284i		−	0.698153i	−0.937094	−	0.349076i	$-0.886495\pi$
$547$		−	16.3284i		−	0.698153i	0.937094	−	0.349076i	$-0.113505\pi$
$548$			7.49458i			0.320153i
$549$	7.23880			0.308944
$550$	−4.27118	+	32.4024i	−0.182124	+	1.38164i
$551$	−8.69314			−0.370340
$552$			2.18542i			0.0930175i
$553$		−	23.0703i		−	0.981050i
$554$	−6.10116			−0.259213
$555$	4.12006	+	0.270377i	0.174887	+	0.0114769i
$556$	−12.6579			−0.536813
$557$			29.6447i			1.25609i	0.778178	+	0.628044i	$0.216144\pi$
$557$			29.6447i			1.25609i	−0.778178	+	0.628044i	$0.783856\pi$
$558$			2.23913i			0.0947901i
$559$	34.4285			1.45617
$560$	0.409739	−	6.24369i	0.0173146	−	0.263844i
$561$	36.4792			1.54015
$562$		−	20.8113i		−	0.877871i
$563$		−	17.0357i		−	0.717968i	−0.933344	−	0.358984i	$-0.883123\pi$
$563$		−	17.0357i		−	0.717968i	0.933344	−	0.358984i	$-0.116877\pi$
$564$	−5.34427			−0.225034
$565$	1.31908	−	20.1005i	0.0554942	−	0.845633i
$566$	−14.5280			−0.610656
$567$			7.64242i			0.320952i
$568$		−	0.841151i		−	0.0352939i
$569$	−31.3050			−1.31237			−0.656187	−	0.754598i	$-0.727832\pi$
$569$	−31.3050			−1.31237			−0.656187	+	0.754598i	$0.727832\pi$
$570$	−2.82542	−	0.185417i	−0.118344	−	0.00776625i
$571$	−4.47152			−0.187127			−0.0935637	−	0.995613i	$-0.529826\pi$
$571$	−4.47152			−0.187127			−0.0935637	+	0.995613i	$0.529826\pi$
$572$			21.7982i			0.911427i
$573$		−	13.0699i		−	0.546003i
$574$	10.6678			0.445265
$575$	1.63712	−	12.4197i	0.0682725	−	0.517935i
$576$	−2.23913			−0.0932973
$577$		−	12.6377i		−	0.526114i	−0.964780	−	0.263057i	$-0.915269\pi$
$577$		−	12.6377i		−	0.526114i	0.964780	−	0.263057i	$-0.0847308\pi$
$578$			23.9342i			0.995531i
$579$	12.7880			0.531452
$580$	−13.3614	−	0.876834i	−0.554801	−	0.0364085i
$581$	−14.0481			−0.582814
$582$			11.8579i			0.491527i
$583$		−	59.3477i		−	2.45793i
$584$	12.7374			0.527075
$585$	1.09338	−	16.6611i	0.0452055	−	0.688851i
$586$	−5.90830			−0.244069
$587$			35.4169i			1.46181i	0.682478	+	0.730906i	$0.260902\pi$
$587$			35.4169i			1.46181i	−0.682478	+	0.730906i	$0.739098\pi$
$588$			0.724264i			0.0298681i
$589$	−1.45170			−0.0598163
$590$	0.233775	−	3.56231i	0.00962435	−	0.146658i
$591$	6.40075			0.263292
$592$			2.11689i			0.0870035i
$593$			12.8046i			0.525823i	0.964820	+	0.262911i	$0.0846827\pi$
$593$			12.8046i			0.525823i	−0.964820	+	0.262911i	$0.915317\pi$
$594$	−29.8718			−1.22566
$595$	39.9470	+	2.62150i	1.63767	+	0.107471i
$596$	−14.6354			−0.599489
$597$			1.29891i			0.0531609i
$598$		−	8.35510i		−	0.341666i
$599$	25.8104			1.05459			0.527293	−	0.849684i	$-0.323207\pi$
$599$	25.8104			1.05459			0.527293	+	0.849684i	$0.323207\pi$
$600$	−4.32398	−	0.569972i	−0.176526	−	0.0232690i
$601$	41.6353			1.69834			0.849169	−	0.528121i	$-0.177103\pi$
$601$	41.6353			1.69834			0.849169	+	0.528121i	$0.177103\pi$
$602$		−	28.8893i		−	1.17744i
$603$			17.6373i			0.718246i
$604$	−4.01256			−0.163269
$605$	−70.7901	−	4.64557i	−2.87803	−	0.188869i
$606$	12.0217			0.488347
$607$		−	12.1822i		−	0.494462i	−0.968957	−	0.247231i	$-0.920479\pi$
$607$		−	12.1822i		−	0.494462i	0.968957	−	0.247231i	$-0.0795207\pi$
$608$		−	1.45170i		−	0.0588742i
$609$	14.6165			0.592290
$610$	−0.473374	+	7.21337i	−0.0191663	+	0.292061i
$611$	20.4317			0.826580
$612$		−	14.3259i		−	0.579092i
$613$		−	2.12945i		−	0.0860075i	−0.999075	−	0.0430037i	$-0.986307\pi$
$613$		−	2.12945i		−	0.0860075i	0.999075	−	0.0430037i	$-0.0136927\pi$
$614$	−32.8035			−1.32384
$615$	0.486919	−	7.41977i	0.0196345	−	0.299194i
$616$	18.2910			0.736966
$617$		−	17.3176i		−	0.697180i	−0.937275	−	0.348590i	$-0.886661\pi$
$617$		−	17.3176i		−	0.697180i	0.937275	−	0.348590i	$-0.113339\pi$
$618$		−	3.11827i		−	0.125435i
$619$	43.1295			1.73352			0.866761	−	0.498724i	$-0.166198\pi$
$619$	43.1295			1.73352			0.866761	+	0.498724i	$0.166198\pi$
$620$	−2.23127	−	0.146426i	−0.0896099	−	0.00588060i
$621$	11.4497			0.459460
$622$			4.45936i			0.178804i
$623$			16.6103i			0.665477i
$624$	−2.90888			−0.116448
$625$	24.1461	+	6.47827i	0.965842	+	0.259131i
$626$	−20.2591			−0.809716
$627$		−	8.27712i		−	0.330556i
$628$		−	24.4981i		−	0.977581i
$629$	−13.5438			−0.540027
$630$	−13.9805	−	0.917461i	−0.556995	−	0.0365525i
$631$	13.2446			0.527260			0.263630	−	0.964624i	$-0.415080\pi$
$631$	13.2446			0.527260			0.263630	+	0.964624i	$0.415080\pi$
$632$		−	8.24449i		−	0.327948i
$633$		−	3.24461i		−	0.128962i
$634$	−10.7834			−0.428264
$635$	3.18132	−	48.4777i	0.126247	−	1.92378i
$636$	7.91971			0.314037
$637$		−	2.76894i		−	0.109710i
$638$		−	39.1424i		−	1.54966i
$639$	−1.88345			−0.0745081
$640$	0.146426	−	2.23127i	0.00578799	−	0.0881986i
$641$	−8.89084			−0.351167			−0.175584	−	0.984465i	$-0.556181\pi$
$641$	−8.89084			−0.351167			−0.175584	+	0.984465i	$0.556181\pi$
$642$		−	0.914355i		−	0.0360867i
$643$		−	21.1384i		−	0.833619i	−0.908994	−	0.416809i	$-0.863148\pi$
$643$		−	21.1384i		−	0.833619i	0.908994	−	0.416809i	$-0.136852\pi$
$644$	−7.01084			−0.276266
$645$	−20.0934	−	1.31862i	−0.791176	−	0.0519205i
$646$	9.28796			0.365430
$647$			27.1443i			1.06715i	0.845752	+	0.533575i	$0.179152\pi$
$647$			27.1443i			1.06715i	−0.845752	+	0.533575i	$0.820848\pi$
$648$			2.73112i			0.107289i
$649$	10.4359			0.409643
$650$	16.5311	+	2.17907i	0.648402	+	0.0854701i
$651$	2.44086			0.0956650
$652$		−	19.1696i		−	0.750738i
$653$			35.9733i			1.40774i	0.710327	+	0.703872i	$0.248547\pi$
$653$			35.9733i			1.40774i	−0.710327	+	0.703872i	$0.751453\pi$
$654$	−7.01084			−0.274145
$655$	−5.82484	−	0.382252i	−0.227595	−	0.0149358i
$656$	3.81228			0.148845
$657$		−	28.5206i		−	1.11270i
$658$		−	17.1445i		−	0.668360i
$659$	−21.8109			−0.849632			−0.424816	−	0.905280i	$-0.639661\pi$
$659$	−21.8109			−0.849632			−0.424816	+	0.905280i	$0.639661\pi$
$660$	0.834872	−	12.7220i	0.0324974	−	0.495202i
$661$	2.54553			0.0990097			0.0495048	−	0.998774i	$-0.484236\pi$
$661$	2.54553			0.0990097			0.0495048	+	0.998774i	$0.484236\pi$
$662$			3.54605i			0.137821i
$663$		−	18.6110i		−	0.722790i
$664$	−5.02029			−0.194825
$665$	0.594818	−	9.06397i	0.0230661	−	0.351486i
$666$	4.73999			0.183671
$667$			15.0031i			0.580921i
$668$		−	18.0693i		−	0.699123i
$669$	−2.94357			−0.113805
$670$	−17.5753	−	1.15337i	−0.678994	−	0.0445587i
$671$	−21.1317			−0.815780
$672$			2.44086i			0.0941584i
$673$		−	14.6785i		−	0.565816i	−0.959147	−	0.282908i	$-0.908701\pi$
$673$		−	14.6785i		−	0.565816i	0.959147	−	0.282908i	$-0.0912992\pi$
$674$	22.6236			0.871427
$675$	−2.98616	+	22.6539i	−0.114937	+	0.871949i
$676$	−1.87902			−0.0722700
$677$			2.86633i			0.110162i	0.998482	+	0.0550811i	$0.0175417\pi$
$677$			2.86633i			0.110162i	−0.998482	+	0.0550811i	$0.982458\pi$
$678$			7.85793i			0.301782i
$679$	−38.0403			−1.45985
$680$	14.2756	+	0.936830i	0.547445	+	0.0359258i
$681$	15.8285			0.606549
$682$		−	6.53654i		−	0.250297i
$683$		−	7.73043i		−	0.295796i	−0.989003	−	0.147898i	$-0.952749\pi$
$683$		−	7.73043i		−	0.295796i	0.989003	−	0.147898i	$-0.0472508\pi$
$684$	−3.25055			−0.124288
$685$	−1.09740	+	16.7224i	−0.0419295	+	0.638931i
$686$	17.2644			0.659160
$687$		−	19.5954i		−	0.747611i
$688$		−	10.3240i		−	0.393598i
$689$	−30.2780			−1.15350
$690$	−0.320002	+	4.87625i	−0.0121822	+	0.185636i
$691$	−15.8583			−0.603279			−0.301640	−	0.953422i	$-0.597534\pi$
$691$	−15.8583			−0.603279			−0.301640	+	0.953422i	$0.597534\pi$
$692$			13.0948i			0.497788i
$693$		−	40.9560i		−	1.55579i
$694$	15.6475			0.593971
$695$	−28.2431	−	1.85344i	−1.07132	−	0.0703050i
$696$	5.22340			0.197993
$697$			24.3909i			0.923871i
$698$			10.3708i			0.392542i
$699$	−0.260225			−0.00984261
$700$	1.82848	−	13.8714i	0.0691099	−	0.524288i
$701$	52.1227			1.96865			0.984323	−	0.176376i	$-0.0564374\pi$
$701$	52.1227			1.96865			0.984323	+	0.176376i	$0.0564374\pi$
$702$			15.2400i			0.575197i
$703$			3.07309i			0.115904i
$704$	6.53654			0.246355
$705$	−11.9245	−	0.782539i	−0.449102	−	0.0294721i
$706$	−9.02703			−0.339737
$707$			38.5656i			1.45041i
$708$			1.39262i			0.0523380i
$709$	−5.77297			−0.216808			−0.108404	−	0.994107i	$-0.534574\pi$
$709$	−5.77297			−0.216808			−0.108404	+	0.994107i	$0.534574\pi$
$710$	0.123166	−	1.87683i	0.00462235	−	0.0704363i
$711$	−18.4605			−0.692324
$712$			5.93591i			0.222458i
$713$			2.50542i			0.0938286i
$714$	−15.6166			−0.584437
$715$	−3.19181	+	48.6375i	−0.119367	+	1.81894i
$716$	−17.4899			−0.653629
$717$		−	14.3067i		−	0.534295i
$718$			32.3635i			1.20780i
$719$	27.6667			1.03180			0.515898	−	0.856650i	$-0.327458\pi$
$719$	27.6667			1.03180			0.515898	+	0.856650i	$0.327458\pi$
$720$	−4.99611	−	0.327867i	−0.186194	−	0.0122189i
$721$	10.0034			0.372548
$722$			16.8926i			0.628676i
$723$		−	19.9142i		−	0.740618i
$724$	−2.63486			−0.0979239
$725$	−29.6844	−	3.91290i	−1.10245	−	0.145322i
$726$	27.6742			1.02709
$727$		−	0.361044i		−	0.0133904i	−0.999978	−	0.00669519i	$-0.997869\pi$
$727$		−	0.361044i		−	0.0133904i	0.999978	−	0.00669519i	$-0.00213116\pi$
$728$		−	9.33171i		−	0.345856i
$729$	−5.84348			−0.216425
$730$	28.4205	+	1.86508i	1.05189	+	0.0690296i
$731$	66.0526			2.44304
$732$		−	2.81994i		−	0.104228i
$733$			2.20299i			0.0813692i	0.999172	+	0.0406846i	$0.0129539\pi$
$733$			2.20299i			0.0813692i	−0.999172	+	0.0406846i	$0.987046\pi$
$734$	−13.9927			−0.516479
$735$	−0.106051	+	1.61603i	−0.00391175	+	0.0596080i
$736$	−2.50542			−0.0923509
$737$		−	51.4873i		−	1.89656i
$738$		−	8.53621i		−	0.314222i
$739$	4.98836			0.183500			0.0917499	−	0.995782i	$-0.470754\pi$
$739$	4.98836			0.183500			0.0917499	+	0.995782i	$0.470754\pi$
$740$	−0.309967	+	4.72334i	−0.0113946	+	0.173634i
$741$	−4.22282			−0.155129
$742$			25.4065i			0.932703i
$743$		−	19.0289i		−	0.698102i	−0.937104	−	0.349051i	$-0.886504\pi$
$743$		−	19.0289i		−	0.698102i	0.937104	−	0.349051i	$-0.113496\pi$
$744$	0.872276			0.0319792
$745$	−32.6555	−	2.14300i	−1.19640	−	0.0785135i
$746$	1.42091			0.0520233
$747$			11.2411i			0.411290i
$748$			41.8207i			1.52912i
$749$	2.93326			0.107179
$750$	−9.56450	−	1.90490i	−0.349246	−	0.0695572i
$751$	−34.9275			−1.27452			−0.637262	−	0.770647i	$-0.719933\pi$
$751$	−34.9275			−1.27452			−0.637262	+	0.770647i	$0.719933\pi$
$752$		−	6.12680i		−	0.223422i
$753$			16.5508i			0.603144i
$754$	−19.9697			−0.727253
$755$	−8.95309	−	0.587542i	−0.325836	−	0.0213828i
$756$	12.7880			0.465096
$757$			11.9481i			0.434262i	0.976142	+	0.217131i	$0.0696699\pi$
$757$			11.9481i			0.434262i	−0.976142	+	0.217131i	$0.930330\pi$
$758$		−	29.1912i		−	1.06027i
$759$	−14.2851			−0.518515
$760$	0.212567	−	3.23913i	0.00771060	−	0.117496i
$761$	−41.8471			−1.51696			−0.758479	−	0.651698i	$-0.774057\pi$
$761$	−41.8471			−1.51696			−0.758479	+	0.651698i	$0.774057\pi$
$762$			18.9515i			0.686541i
$763$		−	22.4908i		−	0.814223i
$764$	14.9837			0.542091
$765$	2.09769	−	31.9650i	0.0758421	−	1.15570i
$766$	26.9070			0.972191
$767$		−	5.32416i		−	0.192244i
$768$			0.872276i			0.0314756i
$769$	21.2373			0.765836			0.382918	−	0.923782i	$-0.374919\pi$
$769$	21.2373			0.765836			0.382918	+	0.923782i	$0.374919\pi$
$770$	40.8122	+	2.67828i	1.47077	+	0.0965184i
$771$	−23.0649			−0.830662
$772$			14.6605i			0.527643i
$773$			13.6776i			0.491950i	0.969276	+	0.245975i	$0.0791081\pi$
$773$			13.6776i			0.491950i	−0.969276	+	0.245975i	$0.920892\pi$
$774$	−23.1168			−0.830915
$775$	−4.95712	−	0.653431i	−0.178065	−	0.0234719i
$776$	−13.5942			−0.488005
$777$		−	5.16703i		−	0.185366i
$778$		−	0.0274871i		−	0.000985460i
$779$	5.53429			0.198286
$780$	−6.49049	−	0.425935i	−0.232397	−	0.0152509i
$781$	5.49822			0.196742
$782$		−	16.0296i		−	0.573218i
$783$		−	27.3661i		−	0.977985i
$784$	−0.830315			−0.0296541
$785$	3.58716	−	54.6618i	0.128031	−	1.95096i
$786$	2.27712			0.0812222
$787$			28.4236i			1.01319i	0.862183	+	0.506597i	$0.169097\pi$
$787$			28.4236i			1.01319i	−0.862183	+	0.506597i	$0.830903\pi$
$788$			7.33799i			0.261405i
$789$	12.0111			0.427607
$790$	1.20721	−	18.3957i	0.0429505	−	0.654489i
$791$	−25.2083			−0.896304
$792$		−	14.6362i		−	0.520075i
$793$			10.7810i			0.382843i
$794$	−15.7021			−0.557248
$795$	17.6710	+	1.15965i	0.626726	+	0.0411286i
$796$	−1.48910			−0.0527799
$797$			2.31459i			0.0819871i	0.999159	+	0.0409935i	$0.0130523\pi$
$797$			2.31459i			0.0819871i	−0.999159	+	0.0409935i	$0.986948\pi$
$798$			3.54340i			0.125435i
$799$	39.1992			1.38677
$800$	0.653431	−	4.95712i	0.0231023	−	0.175261i
$801$	13.2913			0.469625
$802$		−	30.6370i		−	1.08183i
$803$			83.2583i			2.93812i
$804$	6.87077			0.242314
$805$	−15.6431	−	1.02657i	−0.551345	−	0.0361818i
$806$	−3.33481			−0.117464
$807$			0.432619i			0.0152289i
$808$			13.7820i			0.484848i
$809$	32.3156			1.13616			0.568078	−	0.822974i	$-0.307687\pi$
$809$	32.3156			1.13616			0.568078	+	0.822974i	$0.307687\pi$
$810$	−0.399907	+	6.09387i	−0.0140513	+	0.214117i
$811$	43.3249			1.52134			0.760671	−	0.649138i	$-0.224870\pi$
$811$	43.3249			1.52134			0.760671	+	0.649138i	$0.224870\pi$
$812$			16.7567i			0.588046i
$813$		−	1.22571i		−	0.0429874i
$814$	−13.8371			−0.484991
$815$	2.80692	−	42.7725i	0.0983221	−	1.49825i
$816$	−5.58081			−0.195367
$817$		−	14.9873i		−	0.524340i
$818$			10.3519i			0.361947i
$819$	−20.8949			−0.730129
$820$	8.50622	+	0.558216i	0.297050	+	0.0194938i
$821$	−50.1018			−1.74856			−0.874282	−	0.485418i	$-0.838667\pi$
$821$	−50.1018			−1.74856			−0.874282	+	0.485418i	$0.838667\pi$
$822$		−	6.53735i		−	0.228016i
$823$		−	15.7906i		−	0.550426i	−0.961383	−	0.275213i	$-0.911252\pi$
$823$		−	15.7906i		−	0.550426i	0.961383	−	0.275213i	$-0.0887484\pi$
$824$	3.57487			0.124536
$825$	3.72565	−	28.2639i	0.129710	−	0.984021i
$826$	−4.46755			−0.155446
$827$			51.1633i			1.77912i	0.456817	+	0.889561i	$0.348990\pi$
$827$			51.1633i			1.77912i	−0.456817	+	0.889561i	$0.651010\pi$
$828$			5.60997i			0.194960i
$829$	−36.0238			−1.25116			−0.625579	−	0.780161i	$-0.715137\pi$
$829$	−36.0238			−1.25116			−0.625579	+	0.780161i	$0.715137\pi$
$830$	−11.2016	−	0.735100i	−0.388814	−	0.0255157i
$831$	5.32189			0.184614
$832$		−	3.33481i		−	0.115614i
$833$		−	5.31234i		−	0.184062i
$834$	11.0412			0.382324
$835$	2.64582	−	40.3175i	0.0915623	−	1.39525i
$836$	9.48910			0.328188
$837$		−	4.56997i		−	0.157961i
$838$		−	16.1496i		−	0.557879i
$839$	15.4116			0.532067			0.266034	−	0.963964i	$-0.414287\pi$
$839$	15.4116			0.532067			0.266034	+	0.963964i	$0.414287\pi$
$840$	−0.357406	+	5.44622i	−0.0123317	+	0.187913i
$841$	6.85907			0.236520
$842$			26.1804i			0.902236i
$843$			18.1532i			0.625229i
$844$	3.71971			0.128038
$845$	−4.19260	−	0.275137i	−0.144230	−	0.00946500i
$846$	−13.7187			−0.471660
$847$			88.7790i			3.05048i
$848$			9.07937i			0.311787i
$849$	12.6724			0.434915
$850$	31.7156	+	4.18064i	1.08783	+	0.143395i
$851$	5.30369			0.181808
$852$			0.733716i			0.0251367i
$853$			20.9723i			0.718077i	0.933323	+	0.359038i	$0.116895\pi$
$853$			20.9723i			0.718077i	−0.933323	+	0.359038i	$0.883105\pi$
$854$	9.04640			0.309561
$855$	−7.25286	−	0.475965i	−0.248042	−	0.0162777i
$856$	1.04824			0.0358281
$857$			33.9215i			1.15874i	0.815066	+	0.579368i	$0.196701\pi$
$857$			33.9215i			1.15874i	−0.815066	+	0.579368i	$0.803299\pi$
$858$		−	19.0140i		−	0.649128i
$859$	−4.52582			−0.154419			−0.0772096	−	0.997015i	$-0.524601\pi$
$859$	−4.52582			−0.154419			−0.0772096	+	0.997015i	$0.524601\pi$
$860$	1.51170	−	23.0356i	0.0515484	−	0.785506i
$861$	−9.30526			−0.317122
$862$			24.7248i			0.842130i
$863$		−	37.6298i		−	1.28093i	−0.767986	−	0.640467i	$-0.778741\pi$
$863$		−	37.6298i		−	1.28093i	0.767986	−	0.640467i	$-0.221259\pi$
$864$	4.56997			0.155474
$865$	−1.91741	+	29.2179i	−0.0651939	+	0.993439i
$866$	−1.26265			−0.0429065
$867$		−	20.8772i		−	0.709028i
$868$			2.79827i			0.0949795i
$869$	53.8905			1.82811
$870$	11.6548	+	0.764841i	0.395135	+	0.0259305i
$871$	−26.2678			−0.890049
$872$		−	8.03740i		−	0.272181i
$873$			30.4393i			1.03021i
$874$	−3.63712			−0.123027
$875$	6.11095	−	30.6830i	0.206588	−	1.03727i
$876$	−11.1105			−0.375389
$877$			34.4142i			1.16208i	0.813873	+	0.581042i	$0.197355\pi$
$877$			34.4142i			1.16208i	−0.813873	+	0.581042i	$0.802645\pi$
$878$		−	28.0379i		−	0.946232i
$879$	5.15367			0.173829
$880$	14.5848	+	0.957119i	0.491653	+	0.0322645i
$881$	−51.0060			−1.71844			−0.859218	−	0.511610i	$-0.829049\pi$
$881$	−51.0060			−1.71844			−0.859218	+	0.511610i	$0.829049\pi$
$882$			1.85919i			0.0626020i
$883$		−	3.09694i		−	0.104220i	−0.998641	−	0.0521101i	$-0.983405\pi$
$883$		−	3.09694i		−	0.104220i	0.998641	−	0.0521101i	$-0.0165947\pi$
$884$	21.3361			0.717610
$885$	−0.203916	+	3.10732i	−0.00685457	+	0.104451i
$886$	20.3095			0.682311
$887$		−	33.6546i		−	1.13001i	−0.825087	−	0.565006i	$-0.808874\pi$
$887$		−	33.6546i		−	1.13001i	0.825087	−	0.565006i	$-0.191126\pi$
$888$		−	1.84651i		−	0.0619648i
$889$	−60.7967			−2.03905
$890$	−0.869171	+	13.2446i	−0.0291347	+	0.443960i
$891$	−17.8521			−0.598068
$892$		−	3.37459i		−	0.112990i
$893$		−	8.89429i		−	0.297636i
$894$	12.7661			0.426963
$895$	−39.0247	−	2.56097i	−1.30445	−	0.0856039i
$896$	−2.79827			−0.0934836
$897$			7.28796i			0.243338i
$898$			0.298793i			0.00997086i
$899$	5.98824			0.199719
$900$	−11.0997	−	1.46312i	−0.369988	−	0.0487706i
$901$	−58.0896			−1.93525
$902$			24.9191i			0.829716i
$903$			25.1994i			0.838584i
$904$	−9.00853			−0.299619
$905$	−5.87909	−	0.385812i	−0.195427	−	0.0128248i
$906$	3.50006			0.116282
$907$			13.3757i			0.444134i	0.975031	+	0.222067i	$0.0712803\pi$
$907$			13.3757i			0.444134i	−0.975031	+	0.222067i	$0.928720\pi$
$908$			18.1462i			0.602202i
$909$	30.8597			1.02355
$910$	1.36640	−	20.8215i	0.0452958	−	0.690228i
$911$	−6.83471			−0.226444			−0.113222	−	0.993570i	$-0.536117\pi$
$911$	−6.83471			−0.226444			−0.113222	+	0.993570i	$0.536117\pi$
$912$			1.26628i			0.0419309i
$913$		−	32.8153i		−	1.08603i
$914$	−21.3105			−0.704889
$915$	0.412913	−	6.29205i	0.0136505	−	0.208009i
$916$	22.4647			0.742254
$917$			7.30502i			0.241233i
$918$			29.2386i			0.965018i
$919$	−14.7725			−0.487298			−0.243649	−	0.969863i	$-0.578345\pi$
$919$	−14.7725			−0.487298			−0.243649	+	0.969863i	$0.578345\pi$
$920$	−5.59026	−	0.366858i	−0.184305	−	0.0120949i
$921$	28.6137			0.942854
$922$		−	24.5165i		−	0.807407i
$923$		−	2.80508i		−	0.0923304i
$924$	−15.9548			−0.524875
$925$	−1.38324	+	10.4937i	−0.0454806	+	0.345029i
$926$	−5.45400			−0.179230
$927$		−	8.00461i		−	0.262906i
$928$			5.98824i			0.196574i
$929$	−5.29140			−0.173605			−0.0868026	−	0.996226i	$-0.527665\pi$
$929$	−5.29140			−0.173605			−0.0868026	+	0.996226i	$0.527665\pi$
$930$	1.94628	+	0.127724i	0.0638211	+	0.00418823i
$931$	−1.20537			−0.0395043
$932$		−	0.298329i		−	0.00977208i
$933$		−	3.88980i		−	0.127346i
$934$	−10.4345			−0.341428
$935$	−6.12363	+	93.3132i	−0.200264	+	3.05167i
$936$	−7.46709			−0.244070
$937$			14.4315i			0.471456i	0.971819	+	0.235728i	$0.0757474\pi$
$937$			14.4315i			0.471456i	−0.971819	+	0.235728i	$0.924253\pi$
$938$			22.0415i			0.719681i
$939$	17.6715			0.576688
$940$	0.897123	−	13.6705i	0.0292609	−	0.445884i
$941$	18.4524			0.601531			0.300765	−	0.953698i	$-0.402758\pi$
$941$	18.4524			0.601531			0.300765	+	0.953698i	$0.402758\pi$
$942$			21.3691i			0.696243i
$943$		−	9.55136i		−	0.311035i
$944$	−1.59654			−0.0519629
$945$	28.5335	+	1.87250i	0.928195	+	0.0609123i
$946$	67.4831			2.19407
$947$			16.0330i			0.521001i	0.965474	+	0.260501i	$0.0838876\pi$
$947$			16.0330i			0.521001i	−0.965474	+	0.260501i	$0.916112\pi$
$948$			7.19148i			0.233568i
$949$	42.4767			1.37885
$950$	0.948586	−	7.19625i	0.0307762	−	0.233477i
$951$	9.40611			0.305014
$952$		−	17.9033i		−	0.580249i
$953$		−	3.57851i		−	0.115919i	−0.998319	−	0.0579596i	$-0.981541\pi$
$953$		−	3.57851i		−	0.115919i	0.998319	−	0.0579596i	$-0.0184595\pi$
$954$	20.3299			0.658205
$955$	33.4326	+	2.19400i	1.08185	+	0.0709961i
$956$	16.4016			0.530466
$957$			34.1430i			1.10369i
$958$		−	23.3691i		−	0.755022i
$959$	20.9719			0.677217
$960$	−0.127724	+	1.94628i	−0.00412227	+	0.0628160i
$961$	1.00000			0.0322581
$962$			7.05942i			0.227605i
$963$		−	2.34715i		−	0.0756359i
$964$	22.8302			0.735311
$965$	−2.14668	+	32.7115i	−0.0691040	+	1.05302i
$966$	6.11539			0.196759
$967$		−	8.93055i		−	0.287187i	−0.989637	−	0.143594i	$-0.954134\pi$
$967$		−	8.93055i		−	0.287187i	0.989637	−	0.143594i	$-0.0458658\pi$
$968$			31.7264i			1.01973i
$969$	−8.10166			−0.260263
$970$	−30.3324	−	1.99055i	−0.973914	−	0.0639126i
$971$	12.1040			0.388436			0.194218	−	0.980958i	$-0.437783\pi$
$971$	12.1040			0.388436			0.194218	+	0.980958i	$0.437783\pi$
$972$		−	16.0922i		−	0.516158i
$973$			35.4201i			1.13552i
$974$	10.9504			0.350873
$975$	−14.4197	−	1.90075i	−0.461799	−	0.0608727i
$976$	3.23286			0.103481
$977$			18.1398i			0.580344i	0.956974	+	0.290172i	$0.0937126\pi$
$977$			18.1398i			0.580344i	−0.956974	+	0.290172i	$0.906287\pi$
$978$			16.7212i			0.534684i
$979$	−38.8003			−1.24006
$980$	−1.85265	−	0.121580i	−0.0591809	−	0.00388372i
$981$	−17.9968			−0.574594
$982$			27.6705i			0.883003i
$983$			9.86658i			0.314695i	0.987543	+	0.157348i	$0.0502943\pi$
$983$			9.86658i			0.314695i	−0.987543	+	0.157348i	$0.949706\pi$
$984$	−3.32536			−0.106009
$985$	−1.07447	+	16.3730i	−0.0342355	+	0.521688i
$986$	−38.3127			−1.22012
$987$			14.9547i			0.476013i
$988$		−	4.84115i		−	0.154018i
$989$	−25.8659			−0.822487
$990$	2.14312	−	32.6573i	0.0681128	−	1.03792i
$991$	53.2172			1.69050			0.845250	−	0.534371i	$-0.179452\pi$
$991$	53.2172			1.69050			0.845250	+	0.534371i	$0.179452\pi$
$992$			1.00000i			0.0317500i
$993$		−	3.09313i		−	0.0981575i
$994$	−2.35377			−0.0746570
$995$	−3.32259	−	0.218043i	−0.105333	−	0.00691244i
$996$	4.37908			0.138756
$997$		−	46.5373i		−	1.47385i	−0.675973	−	0.736926i	$-0.736276\pi$
$997$		−	46.5373i		−	1.47385i	0.675973	−	0.736926i	$-0.263724\pi$
$998$			6.90577i			0.218598i
$999$	−9.67412			−0.306075

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	310.2.b.a.249.4	✓	8
3.2	odd	2		2790.2.d.m.559.8		8
4.3	odd	2		2480.2.d.d.1489.3		8
5.2	odd	4		1550.2.a.p.1.4		4
5.3	odd	4		1550.2.a.o.1.1		4
5.4	even	2	inner	310.2.b.a.249.5	yes	8
15.14	odd	2		2790.2.d.m.559.4		8
20.19	odd	2		2480.2.d.d.1489.6		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
310.2.b.a.249.4	✓	8	1.1	even	1	trivial
310.2.b.a.249.5	yes	8	5.4	even	2	inner
1550.2.a.o.1.1		4	5.3	odd	4
1550.2.a.p.1.4		4	5.2	odd	4
2480.2.d.d.1489.3		8	4.3	odd	2
2480.2.d.d.1489.6		8	20.19	odd	2
2790.2.d.m.559.4		8	15.14	odd	2
2790.2.d.m.559.8		8	3.2	odd	2

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:	\( N \)	\(=\)	\( 310 = 2 \cdot 5 \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	310.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-1.00000i q^{2} +0.872276i q^{3} -1.00000 q^{4} +(-2.23127 - 0.146426i) q^{5} +0.872276 q^{6} +2.79827i q^{7} +1.00000i q^{8} +2.23913 q^{9} +O(q^{10})\)	\(q-1.00000i q^{2} +0.872276i q^{3} -1.00000 q^{4} +(-2.23127 - 0.146426i) q^{5} +0.872276 q^{6} +2.79827i q^{7} +1.00000i q^{8} +2.23913 q^{9} +(-0.146426 + 2.23127i) q^{10} -6.53654 q^{11} -0.872276i q^{12} +3.33481i q^{13} +2.79827 q^{14} +(0.127724 - 1.94628i) q^{15} +1.00000 q^{16} +6.39798i q^{17} -2.23913i q^{18} +1.45170 q^{19} +(2.23127 + 0.146426i) q^{20} -2.44086 q^{21} +6.53654i q^{22} -2.50542i q^{23} -0.872276 q^{24} +(4.95712 + 0.653431i) q^{25} +3.33481 q^{26} +4.56997i q^{27} -2.79827i q^{28} -5.98824 q^{29} +(-1.94628 - 0.127724i) q^{30} -1.00000 q^{31} -1.00000i q^{32} -5.70167i q^{33} +6.39798 q^{34} +(0.409739 - 6.24369i) q^{35} -2.23913 q^{36} +2.11689i q^{37} -1.45170i q^{38} -2.90888 q^{39} +(0.146426 - 2.23127i) q^{40} +3.81228 q^{41} +2.44086i q^{42} -10.3240i q^{43} +6.53654 q^{44} +(-4.99611 - 0.327867i) q^{45} -2.50542 q^{46} -6.12680i q^{47} +0.872276i q^{48} -0.830315 q^{49} +(0.653431 - 4.95712i) q^{50} -5.58081 q^{51} -3.33481i q^{52} +9.07937i q^{53} +4.56997 q^{54} +(14.5848 + 0.957119i) q^{55} -2.79827 q^{56} +1.26628i q^{57} +5.98824i q^{58} -1.59654 q^{59} +(-0.127724 + 1.94628i) q^{60} +3.23286 q^{61} +1.00000i q^{62} +6.26570i q^{63} -1.00000 q^{64} +(0.488303 - 7.44086i) q^{65} -5.70167 q^{66} +7.87683i q^{67} -6.39798i q^{68} +2.18542 q^{69} +(-6.24369 - 0.409739i) q^{70} -0.841151 q^{71} +2.23913i q^{72} -12.7374i q^{73} +2.11689 q^{74} +(-0.569972 + 4.32398i) q^{75} -1.45170 q^{76} -18.2910i q^{77} +2.90888i q^{78} -8.24449 q^{79} +(-2.23127 - 0.146426i) q^{80} +2.73112 q^{81} -3.81228i q^{82} +5.02029i q^{83} +2.44086 q^{84} +(0.936830 - 14.2756i) q^{85} -10.3240 q^{86} -5.22340i q^{87} -6.53654i q^{88} +5.93591 q^{89} +(-0.327867 + 4.99611i) q^{90} -9.33171 q^{91} +2.50542i q^{92} -0.872276i q^{93} -6.12680 q^{94} +(-3.23913 - 0.212567i) q^{95} +0.872276 q^{96} +13.5942i q^{97} +0.830315i q^{98} -14.6362 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 8 q^{4} - 2 q^{5} - 8 q^{6} - 8 q^{9}+O(q^{10}) \) 8 * q - 8 * q^4 - 2 * q^5 - 8 * q^6 - 8 * q^9	\( 8 q - 8 q^{4} - 2 q^{5} - 8 q^{6} - 8 q^{9} + 2 q^{10} - 16 q^{11} + 12 q^{14} + 16 q^{15} + 8 q^{16} - 12 q^{19} + 2 q^{20} - 4 q^{21} + 8 q^{24} + 12 q^{25} - 20 q^{26} + 12 q^{29} + 4 q^{30} - 8 q^{31} + 8 q^{34} + 20 q^{35} + 8 q^{36} - 40 q^{39} - 2 q^{40} + 16 q^{44} + 30 q^{45} - 16 q^{46} - 32 q^{49} - 8 q^{50} - 44 q^{51} + 44 q^{54} + 36 q^{55} - 12 q^{56} + 8 q^{59} - 16 q^{60} + 4 q^{61} - 8 q^{64} + 12 q^{65} + 12 q^{66} - 28 q^{69} - 20 q^{70} - 24 q^{71} + 40 q^{74} - 12 q^{75} + 12 q^{76} + 32 q^{79} - 2 q^{80} + 88 q^{81} + 4 q^{84} + 4 q^{85} - 44 q^{86} - 24 q^{89} - 34 q^{90} - 20 q^{91} + 4 q^{94} - 8 q^{96} + 20 q^{99}+O(q^{100}) \) 8 * q - 8 * q^4 - 2 * q^5 - 8 * q^6 - 8 * q^9 + 2 * q^10 - 16 * q^11 + 12 * q^14 + 16 * q^15 + 8 * q^16 - 12 * q^19 + 2 * q^20 - 4 * q^21 + 8 * q^24 + 12 * q^25 - 20 * q^26 + 12 * q^29 + 4 * q^30 - 8 * q^31 + 8 * q^34 + 20 * q^35 + 8 * q^36 - 40 * q^39 - 2 * q^40 + 16 * q^44 + 30 * q^45 - 16 * q^46 - 32 * q^49 - 8 * q^50 - 44 * q^51 + 44 * q^54 + 36 * q^55 - 12 * q^56 + 8 * q^59 - 16 * q^60 + 4 * q^61 - 8 * q^64 + 12 * q^65 + 12 * q^66 - 28 * q^69 - 20 * q^70 - 24 * q^71 + 40 * q^74 - 12 * q^75 + 12 * q^76 + 32 * q^79 - 2 * q^80 + 88 * q^81 + 4 * q^84 + 4 * q^85 - 44 * q^86 - 24 * q^89 - 34 * q^90 - 20 * q^91 + 4 * q^94 - 8 * q^96 + 20 * q^99

Introduction

L-functions

Modular forms

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Database

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