LMFDB - Embedded newform 690.2.e.a.551.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [690,2,Mod(551,690)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(690, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("690.551");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 690 = 2 \cdot 3 \cdot 5 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	690.e (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:	$5.50967773947$
Analytic rank:	$0$
Dimension:	$16$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 2 x^{15} + 3 x^{14} - 12 x^{13} + 15 x^{12} - 4 x^{11} + 45 x^{10} - 66 x^{9} - 32 x^{8} + \cdots + 6561 $ x^16 - 2x^15 + 3x^14 - 12x^13 + 15x^12 - 4x^11 + 45x^10 - 66x^9 - 32x^8 - 198x^7 + 405x^6 - 108x^5 + 1215x^4 - 2916x^3 + 2187x^2 - 4374*x + 6561
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{3} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			551.3
Root			$1.53677 + 0.798958i$ of defining polynomial
Character	$\chi$	$=$	690.551
Dual form			690.2.e.a.551.11

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000i q^{2} +(-0.798958 + 1.53677i) q^{3} -1.00000 q^{4} -1.00000 q^{5} +(1.53677 + 0.798958i) q^{6} -0.145234i q^{7} +1.00000i q^{8} +(-1.72333 - 2.45563i) q^{9} +O(q^{10})$	\(q-1.00000i q^{2} +(-0.798958 + 1.53677i) q^{3} -1.00000 q^{4} -1.00000 q^{5} +(1.53677 + 0.798958i) q^{6} -0.145234i q^{7} +1.00000i q^{8} +(-1.72333 - 2.45563i) q^{9} +1.00000i q^{10} -3.35877 q^{11} +(0.798958 - 1.53677i) q^{12} +2.96087 q^{13} -0.145234 q^{14} +(0.798958 - 1.53677i) q^{15} +1.00000 q^{16} +5.54307 q^{17} +(-2.45563 + 1.72333i) q^{18} -6.91126i q^{19} +1.00000 q^{20} +(0.223191 + 0.116036i) q^{21} +3.35877i q^{22} +(-3.26171 - 3.51586i) q^{23} +(-1.53677 - 0.798958i) q^{24} +1.00000 q^{25} -2.96087i q^{26} +(5.15061 - 0.686420i) q^{27} +0.145234i q^{28} +3.58666i q^{29} +(-1.53677 - 0.798958i) q^{30} +10.6138 q^{31} -1.00000i q^{32} +(2.68352 - 5.16167i) q^{33} -5.54307i q^{34} +0.145234i q^{35} +(1.72333 + 2.45563i) q^{36} -6.04149i q^{37} -6.91126 q^{38} +(-2.36561 + 4.55019i) q^{39} -1.00000i q^{40} +8.84450i q^{41} +(0.116036 - 0.223191i) q^{42} -8.40616i q^{43} +3.35877 q^{44} +(1.72333 + 2.45563i) q^{45} +(-3.51586 + 3.26171i) q^{46} -9.98664i q^{47} +(-0.798958 + 1.53677i) q^{48} +6.97891 q^{49} -1.00000i q^{50} +(-4.42868 + 8.51843i) q^{51} -2.96087 q^{52} -3.83589 q^{53} +(-0.686420 - 5.15061i) q^{54} +3.35877 q^{55} +0.145234 q^{56} +(10.6210 + 5.52181i) q^{57} +3.58666 q^{58} -7.91338i q^{59} +(-0.798958 + 1.53677i) q^{60} -4.14107i q^{61} -10.6138i q^{62} +(-0.356641 + 0.250286i) q^{63} -1.00000 q^{64} -2.96087 q^{65} +(-5.16167 - 2.68352i) q^{66} -13.0680i q^{67} -5.54307 q^{68} +(8.00904 - 2.20347i) q^{69} +0.145234 q^{70} -1.26558i q^{71} +(2.45563 - 1.72333i) q^{72} -9.24658 q^{73} -6.04149 q^{74} +(-0.798958 + 1.53677i) q^{75} +6.91126i q^{76} +0.487808i q^{77} +(4.55019 + 2.36561i) q^{78} +13.2148i q^{79} -1.00000 q^{80} +(-3.06025 + 8.46374i) q^{81} +8.84450 q^{82} +9.71029 q^{83} +(-0.223191 - 0.116036i) q^{84} -5.54307 q^{85} -8.40616 q^{86} +(-5.51188 - 2.86559i) q^{87} -3.35877i q^{88} -15.3774 q^{89} +(2.45563 - 1.72333i) q^{90} -0.430019i q^{91} +(3.26171 + 3.51586i) q^{92} +(-8.47998 + 16.3110i) q^{93} -9.98664 q^{94} +6.91126i q^{95} +(1.53677 + 0.798958i) q^{96} +11.6097i q^{97} -6.97891i q^{98} +(5.78828 + 8.24791i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 16 q^{4} - 16 q^{5} + 2 q^{6} + 2 q^{9}+O(q^{10}) $ 16 * q - 16 * q^4 - 16 * q^5 + 2 * q^6 + 2 * q^9	$ 16 q - 16 q^{4} - 16 q^{5} + 2 q^{6} + 2 q^{9} - 12 q^{11} - 12 q^{14} + 16 q^{16} + 8 q^{18} + 16 q^{20} - 4 q^{21} + 4 q^{23} - 2 q^{24} + 16 q^{25} + 24 q^{27} - 2 q^{30} + 4 q^{31} - 28 q^{33} - 2 q^{36} - 16 q^{38} - 8 q^{39} + 12 q^{44} - 2 q^{45} - 4 q^{46} - 4 q^{49} - 2 q^{51} - 8 q^{53} - 26 q^{54} + 12 q^{55} + 12 q^{56} + 28 q^{57} - 8 q^{58} - 16 q^{64} + 10 q^{66} + 30 q^{69} + 12 q^{70} - 8 q^{72} - 16 q^{73} - 24 q^{74} - 12 q^{78} - 16 q^{80} + 22 q^{81} - 16 q^{82} - 40 q^{83} + 4 q^{84} - 40 q^{86} + 20 q^{87} + 80 q^{89} - 8 q^{90} - 4 q^{92} - 4 q^{93} - 24 q^{94} + 2 q^{96} - 8 q^{99}+O(q^{100}) $ 16 * q - 16 * q^4 - 16 * q^5 + 2 * q^6 + 2 * q^9 - 12 * q^11 - 12 * q^14 + 16 * q^16 + 8 * q^18 + 16 * q^20 - 4 * q^21 + 4 * q^23 - 2 * q^24 + 16 * q^25 + 24 * q^27 - 2 * q^30 + 4 * q^31 - 28 * q^33 - 2 * q^36 - 16 * q^38 - 8 * q^39 + 12 * q^44 - 2 * q^45 - 4 * q^46 - 4 * q^49 - 2 * q^51 - 8 * q^53 - 26 * q^54 + 12 * q^55 + 12 * q^56 + 28 * q^57 - 8 * q^58 - 16 * q^64 + 10 * q^66 + 30 * q^69 + 12 * q^70 - 8 * q^72 - 16 * q^73 - 24 * q^74 - 12 * q^78 - 16 * q^80 + 22 * q^81 - 16 * q^82 - 40 * q^83 + 4 * q^84 - 40 * q^86 + 20 * q^87 + 80 * q^89 - 8 * q^90 - 4 * q^92 - 4 * q^93 - 24 * q^94 + 2 * q^96 - 8 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/690\mathbb{Z}\right)^\times$.

$n$	$277$	$461$	$511$
$\chi(n)$	$1$	$-1$	$-1$

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
$3$	−0.798958	+	1.53677i	−0.461279	+	0.887255i
$3$	−0.798958	+	1.53677i	−0.461279	+	0.887255i
$4$	−1.00000			−0.500000
$5$	−1.00000			−0.447214
$5$	−1.00000			−0.447214
$6$	1.53677	+	0.798958i	0.627384	+	0.326173i
$7$		−	0.145234i		−	0.0548933i	−0.999623	−	0.0274466i	$-0.991262\pi$
$7$		−	0.145234i		−	0.0548933i	0.999623	−	0.0274466i	$-0.00873763\pi$
$8$			1.00000i			0.353553i
$9$	−1.72333	−	2.45563i	−0.574444	−	0.818544i
$10$			1.00000i			0.316228i
$11$	−3.35877			−1.01271			−0.506354	−	0.862326i	$-0.669007\pi$
$11$	−3.35877			−1.01271			−0.506354	+	0.862326i	$0.669007\pi$
$12$	0.798958	−	1.53677i	0.230639	−	0.443628i
$13$	2.96087			0.821199			0.410599	−	0.911816i	$-0.365320\pi$
$13$	2.96087			0.821199			0.410599	+	0.911816i	$0.365320\pi$
$14$	−0.145234			−0.0388154
$15$	0.798958	−	1.53677i	0.206290	−	0.396793i
$16$	1.00000			0.250000
$17$	5.54307			1.34439			0.672196	−	0.740373i	$-0.265351\pi$
$17$	5.54307			1.34439			0.672196	+	0.740373i	$0.265351\pi$
$18$	−2.45563	+	1.72333i	−0.578798	+	0.406193i
$19$		−	6.91126i		−	1.58555i	−0.609513	−	0.792776i	$-0.708635\pi$
$19$		−	6.91126i		−	1.58555i	0.609513	−	0.792776i	$-0.291365\pi$
$20$	1.00000			0.223607
$21$	0.223191	+	0.116036i	0.0487043	+	0.0253211i
$22$			3.35877i			0.716093i
$23$	−3.26171	−	3.51586i	−0.680113	−	0.733107i
$23$	−3.26171	−	3.51586i	−0.680113	−	0.733107i
$24$	−1.53677	−	0.798958i	−0.313692	−	0.163087i
$25$	1.00000			0.200000
$26$		−	2.96087i		−	0.580675i
$27$	5.15061	−	0.686420i	0.991236	−	0.132102i
$28$			0.145234i			0.0274466i
$29$			3.58666i			0.666026i	0.942922	+	0.333013i	$0.108065\pi$
$29$			3.58666i			0.666026i	−0.942922	+	0.333013i	$0.891935\pi$
$30$	−1.53677	−	0.798958i	−0.280575	−	0.145869i
$31$	10.6138			1.90629			0.953147	−	0.302506i	$-0.0978233\pi$
$31$	10.6138			1.90629			0.953147	+	0.302506i	$0.0978233\pi$
$32$		−	1.00000i		−	0.176777i
$33$	2.68352	−	5.16167i	0.467141	−	0.898531i
$34$		−	5.54307i		−	0.950628i
$35$			0.145234i			0.0245490i
$36$	1.72333	+	2.45563i	0.287222	+	0.409272i
$37$		−	6.04149i		−	0.993214i	−0.867975	−	0.496607i	$-0.834579\pi$
$37$		−	6.04149i		−	0.993214i	0.867975	−	0.496607i	$-0.165421\pi$
$38$	−6.91126			−1.12115
$39$	−2.36561	+	4.55019i	−0.378801	+	0.728613i
$40$		−	1.00000i		−	0.158114i
$41$			8.84450i			1.38128i	0.723199	+	0.690639i	$0.242671\pi$
$41$			8.84450i			1.38128i	−0.723199	+	0.690639i	$0.757329\pi$
$42$	0.116036	−	0.223191i	0.0179047	−	0.0344392i
$43$		−	8.40616i		−	1.28193i	−0.767571	−	0.640964i	$-0.778535\pi$
$43$		−	8.40616i		−	1.28193i	0.767571	−	0.640964i	$-0.221465\pi$
$44$	3.35877			0.506354
$45$	1.72333	+	2.45563i	0.256899	+	0.366064i
$46$	−3.51586	+	3.26171i	−0.518385	+	0.480912i
$47$		−	9.98664i		−	1.45670i	−0.685205	−	0.728351i	$-0.740287\pi$
$47$		−	9.98664i		−	1.45670i	0.685205	−	0.728351i	$-0.259713\pi$
$48$	−0.798958	+	1.53677i	−0.115320	+	0.221814i
$49$	6.97891			0.996987
$50$		−	1.00000i		−	0.141421i
$51$	−4.42868	+	8.51843i	−0.620139	+	1.19282i
$52$	−2.96087			−0.410599
$53$	−3.83589			−0.526900			−0.263450	−	0.964673i	$-0.584860\pi$
$53$	−3.83589			−0.526900			−0.263450	+	0.964673i	$0.584860\pi$
$54$	−0.686420	−	5.15061i	−0.0934099	−	0.700910i
$55$	3.35877			0.452897
$56$	0.145234			0.0194077
$57$	10.6210	+	5.52181i	1.40679	+	0.731382i
$58$	3.58666			0.470952
$59$		−	7.91338i		−	1.03023i	−0.857120	−	0.515117i	$-0.827748\pi$
$59$		−	7.91338i		−	1.03023i	0.857120	−	0.515117i	$-0.172252\pi$
$60$	−0.798958	+	1.53677i	−0.103145	+	0.198396i
$61$		−	4.14107i		−	0.530209i	−0.964220	−	0.265105i	$-0.914594\pi$
$61$		−	4.14107i		−	0.530209i	0.964220	−	0.265105i	$-0.0854065\pi$
$62$		−	10.6138i		−	1.34795i
$63$	−0.356641	+	0.250286i	−0.0449325	+	0.0315331i
$64$	−1.00000			−0.125000
$65$	−2.96087			−0.367251
$66$	−5.16167	−	2.68352i	−0.635357	−	0.330318i
$67$		−	13.0680i		−	1.59651i	−0.602322	−	0.798253i	$-0.705758\pi$
$67$		−	13.0680i		−	1.59651i	0.602322	−	0.798253i	$-0.294242\pi$
$68$	−5.54307			−0.672196
$69$	8.00904	−	2.20347i	0.964175	−	0.265267i
$70$	0.145234			0.0173588
$71$		−	1.26558i		−	0.150196i	−0.997176	−	0.0750981i	$-0.976073\pi$
$71$		−	1.26558i		−	0.150196i	0.997176	−	0.0750981i	$-0.0239270\pi$
$72$	2.45563	−	1.72333i	0.289399	−	0.203097i
$73$	−9.24658			−1.08223			−0.541115	−	0.840948i	$-0.681998\pi$
$73$	−9.24658			−1.08223			−0.541115	+	0.840948i	$0.681998\pi$
$74$	−6.04149			−0.702309
$75$	−0.798958	+	1.53677i	−0.0922557	+	0.177451i
$76$			6.91126i			0.792776i
$77$			0.487808i			0.0555909i
$78$	4.55019	+	2.36561i	0.515207	+	0.267853i
$79$			13.2148i			1.48678i	0.668857	+	0.743391i	$0.266784\pi$
$79$			13.2148i			1.48678i	−0.668857	+	0.743391i	$0.733216\pi$
$80$	−1.00000			−0.111803
$81$	−3.06025	+	8.46374i	−0.340028	+	0.940415i
$82$	8.84450			0.976711
$83$	9.71029			1.06584			0.532921	−	0.846165i	$-0.321094\pi$
$83$	9.71029			1.06584			0.532921	+	0.846165i	$0.321094\pi$
$84$	−0.223191	−	0.116036i	−0.0243522	−	0.0126605i
$85$	−5.54307			−0.601230
$86$	−8.40616			−0.906460
$87$	−5.51188	−	2.86559i	−0.590935	−	0.307224i
$88$		−	3.35877i		−	0.358046i
$89$	−15.3774			−1.63000			−0.815001	−	0.579459i	$-0.803264\pi$
$89$	−15.3774			−1.63000			−0.815001	+	0.579459i	$0.803264\pi$
$90$	2.45563	−	1.72333i	0.258846	−	0.181655i
$91$		−	0.430019i		−	0.0450783i
$92$	3.26171	+	3.51586i	0.340056	+	0.366554i
$93$	−8.47998	+	16.3110i	−0.879333	+	1.69137i
$94$	−9.98664			−1.03004
$95$			6.91126i			0.709081i
$96$	1.53677	+	0.798958i	0.156846	+	0.0815433i
$97$			11.6097i			1.17879i	0.807845	+	0.589395i	$0.200634\pi$
$97$			11.6097i			1.17879i	−0.807845	+	0.589395i	$0.799366\pi$
$98$		−	6.97891i		−	0.704976i
$99$	5.78828	+	8.24791i	0.581744	+	0.828946i
$100$	−1.00000			−0.100000
$101$		−	5.20471i		−	0.517888i	−0.965892	−	0.258944i	$-0.916625\pi$
$101$		−	5.20471i		−	0.517888i	0.965892	−	0.258944i	$-0.0833745\pi$
$102$	8.51843	+	4.42868i	0.843450	+	0.438505i
$103$			8.68617i			0.855874i	0.903809	+	0.427937i	$0.140759\pi$
$103$			8.68617i			0.855874i	−0.903809	+	0.427937i	$0.859241\pi$
$104$			2.96087i			0.290338i
$105$	−0.223191	−	0.116036i	−0.0217812	−	0.0113239i
$106$			3.83589i			0.372574i
$107$	−11.1465			−1.07757			−0.538785	−	0.842443i	$-0.681116\pi$
$107$	−11.1465			−1.07757			−0.538785	+	0.842443i	$0.681116\pi$
$108$	−5.15061	+	0.686420i	−0.495618	+	0.0660508i
$109$			7.19631i			0.689282i	0.938735	+	0.344641i	$0.111999\pi$
$109$			7.19631i			0.689282i	−0.938735	+	0.344641i	$0.888001\pi$
$110$		−	3.35877i		−	0.320246i
$111$	9.28438	+	4.82690i	0.881235	+	0.458149i
$112$		−	0.145234i		−	0.0137233i
$113$	13.1580			1.23780			0.618902	−	0.785468i	$-0.287578\pi$
$113$	13.1580			1.23780			0.618902	+	0.785468i	$0.287578\pi$
$114$	5.52181	−	10.6210i	0.517165	−	0.994751i
$115$	3.26171	+	3.51586i	0.304156	+	0.327856i
$116$		−	3.58666i		−	0.333013i
$117$	−5.10257	−	7.27082i	−0.471733	−	0.672187i
$118$	−7.91338			−0.728486
$119$		−	0.805042i		−	0.0737980i
$120$	1.53677	+	0.798958i	0.140287	+	0.0729346i
$121$	0.281357			0.0255779
$122$	−4.14107			−0.374915
$123$	−13.5920	−	7.06638i	−1.22555	−	0.637154i
$124$	−10.6138			−0.953147
$125$	−1.00000			−0.0894427
$126$	0.250286	+	0.356641i	0.0222973	+	0.0317721i
$127$	−13.8601			−1.22989			−0.614943	−	0.788572i	$-0.710821\pi$
$127$	−13.8601			−1.22989			−0.614943	+	0.788572i	$0.710821\pi$
$128$			1.00000i			0.0883883i
$129$	12.9184	+	6.71617i	1.13740	+	0.591326i
$130$			2.96087i			0.259686i
$131$			3.17761i			0.277629i	0.990318	+	0.138815i	$0.0443292\pi$
$131$			3.17761i			0.277629i	−0.990318	+	0.138815i	$0.955671\pi$
$132$	−2.68352	+	5.16167i	−0.233570	+	0.449265i
$133$	−1.00375			−0.0870362
$134$	−13.0680			−1.12890
$135$	−5.15061	+	0.686420i	−0.443294	+	0.0590776i
$136$			5.54307i			0.475314i
$137$	19.0473			1.62732			0.813661	−	0.581340i	$-0.197471\pi$
$137$	19.0473			1.62732			0.813661	+	0.581340i	$0.197471\pi$
$138$	−2.20347	−	8.00904i	−0.187572	−	0.681775i
$139$	10.1337			0.859531			0.429766	−	0.902940i	$-0.358596\pi$
$139$	10.1337			0.859531			0.429766	+	0.902940i	$0.358596\pi$
$140$		−	0.145234i		−	0.0122745i
$141$	15.3472	+	7.97891i	1.29247	+	0.671945i
$142$	−1.26558			−0.106205
$143$	−9.94490			−0.831635
$144$	−1.72333	−	2.45563i	−0.143611	−	0.204636i
$145$		−	3.58666i		−	0.297856i
$146$			9.24658i			0.765253i
$147$	−5.57585	+	10.7250i	−0.459889	+	0.884582i
$148$			6.04149i			0.496607i
$149$	19.7755			1.62008			0.810038	−	0.586378i	$-0.199447\pi$
$149$	19.7755			1.62008			0.810038	+	0.586378i	$0.199447\pi$
$150$	1.53677	+	0.798958i	0.125477	+	0.0652347i
$151$	−9.13517			−0.743409			−0.371705	−	0.928351i	$-0.621227\pi$
$151$	−9.13517			−0.743409			−0.371705	+	0.928351i	$0.621227\pi$
$152$	6.91126			0.560577
$153$	−9.55255	−	13.6117i	−0.772278	−	1.10044i
$154$	0.487808			0.0393087
$155$	−10.6138			−0.852521
$156$	2.36561	−	4.55019i	0.189401	−	0.364306i
$157$		−	10.3178i		−	0.823451i	−0.911308	−	0.411726i	$-0.864926\pi$
$157$		−	10.3178i		−	0.823451i	0.911308	−	0.411726i	$-0.135074\pi$
$158$	13.2148			1.05131
$159$	3.06471	−	5.89488i	0.243048	−	0.467494i
$160$			1.00000i			0.0790569i
$161$	−0.510622	+	0.473711i	−0.0402427	+	0.0373336i
$162$	8.46374	+	3.06025i	0.664974	+	0.240436i
$163$	11.8046			0.924607			0.462303	−	0.886722i	$-0.347023\pi$
$163$	11.8046			0.924607			0.462303	+	0.886722i	$0.347023\pi$
$164$		−	8.84450i		−	0.690639i
$165$	−2.68352	+	5.16167i	−0.208912	+	0.401835i
$166$		−	9.71029i		−	0.753664i
$167$		−	11.8429i		−	0.916428i	−0.888842	−	0.458214i	$-0.848489\pi$
$167$		−	11.8429i		−	0.916428i	0.888842	−	0.458214i	$-0.151511\pi$
$168$	−0.116036	+	0.223191i	−0.00895236	+	0.0172196i
$169$	−4.23323			−0.325633
$170$			5.54307i			0.425134i
$171$	−16.9715	+	11.9104i	−1.29784	+	0.910811i
$172$			8.40616i			0.640964i
$173$		−	9.94482i		−	0.756090i	−0.925787	−	0.378045i	$-0.876596\pi$
$173$		−	9.94482i		−	0.756090i	0.925787	−	0.378045i	$-0.123404\pi$
$174$	−2.86559	+	5.51188i	−0.217240	+	0.417854i
$175$		−	0.145234i		−	0.0109787i
$176$	−3.35877			−0.253177
$177$	12.1611	+	6.32246i	0.914081	+	0.475225i
$178$			15.3774i			1.15259i
$179$		−	3.37701i		−	0.252409i	−0.992004	−	0.126205i	$-0.959720\pi$
$179$		−	3.37701i		−	0.252409i	0.992004	−	0.126205i	$-0.0402796\pi$
$180$	−1.72333	−	2.45563i	−0.128450	−	0.183032i
$181$		−	5.28230i		−	0.392630i	−0.980541	−	0.196315i	$-0.937102\pi$
$181$		−	5.28230i		−	0.392630i	0.980541	−	0.196315i	$-0.0628976\pi$
$182$	−0.430019			−0.0318752
$183$	6.36387	+	3.30854i	0.470431	+	0.244574i
$184$	3.51586	−	3.26171i	0.259193	−	0.240456i
$185$			6.04149i			0.444179i
$186$	16.3110	+	8.47998i	1.19598	+	0.621782i
$187$	−18.6179			−1.36148
$188$			9.98664i			0.728351i
$189$	−0.0996915	−	0.748044i	−0.00725149	−	0.0544122i
$190$	6.91126			0.501396
$191$	−22.1062			−1.59955			−0.799775	−	0.600300i	$-0.795048\pi$
$191$	−22.1062			−1.59955			−0.799775	+	0.600300i	$0.795048\pi$
$192$	0.798958	−	1.53677i	0.0576598	−	0.110907i
$193$	5.62469			0.404874			0.202437	−	0.979295i	$-0.435114\pi$
$193$	5.62469			0.404874			0.202437	+	0.979295i	$0.435114\pi$
$194$	11.6097			0.833530
$195$	2.36561	−	4.55019i	0.169405	−	0.325846i
$196$	−6.97891			−0.498493
$197$			4.97721i			0.354611i	0.984156	+	0.177306i	$0.0567381\pi$
$197$			4.97721i			0.354611i	−0.984156	+	0.177306i	$0.943262\pi$
$198$	8.24791	−	5.78828i	0.586153	−	0.411355i
$199$		−	5.07219i		−	0.359558i	−0.983707	−	0.179779i	$-0.942462\pi$
$199$		−	5.07219i		−	0.359558i	0.983707	−	0.179779i	$-0.0575382\pi$
$200$			1.00000i			0.0707107i
$201$	20.0825	+	10.4408i	1.41651	+	0.736434i
$202$	−5.20471			−0.366202
$203$	0.520905			0.0365603
$204$	4.42868	−	8.51843i	0.310070	−	0.596409i
$205$		−	8.84450i		−	0.617727i
$206$	8.68617			0.605194
$207$	−3.01265	+	14.0685i	−0.209394	+	0.977831i
$208$	2.96087			0.205300
$209$			23.2134i			1.60570i
$210$	−0.116036	+	0.223191i	−0.00800723	+	0.0154017i
$211$	−9.58459			−0.659830			−0.329915	−	0.944011i	$-0.607020\pi$
$211$	−9.58459			−0.659830			−0.329915	+	0.944011i	$0.607020\pi$
$212$	3.83589			0.263450
$213$	1.94490	+	1.01114i	0.133262	+	0.0692823i
$214$			11.1465i			0.761957i
$215$			8.40616i			0.573296i
$216$	0.686420	+	5.15061i	0.0467050	+	0.350455i
$217$		−	1.54148i		−	0.104643i
$218$	7.19631			0.487396
$219$	7.38763	−	14.2099i	0.499210	−	0.960215i
$220$	−3.35877			−0.226448
$221$	16.4123			1.10401
$222$	4.82690	−	9.28438i	0.323960	−	0.623127i
$223$	17.7150			1.18628			0.593142	−	0.805098i	$-0.297887\pi$
$223$	17.7150			1.18628			0.593142	+	0.805098i	$0.297887\pi$
$224$	−0.145234			−0.00970385
$225$	−1.72333	−	2.45563i	−0.114889	−	0.163709i
$226$		−	13.1580i		−	0.875260i
$227$	−3.72255			−0.247074			−0.123537	−	0.992340i	$-0.539424\pi$
$227$	−3.72255			−0.247074			−0.123537	+	0.992340i	$0.539424\pi$
$228$	−10.6210	−	5.52181i	−0.703395	−	0.365691i
$229$			4.59060i			0.303355i	0.988430	+	0.151678i	$0.0484676\pi$
$229$			4.59060i			0.303355i	−0.988430	+	0.151678i	$0.951532\pi$
$230$	3.51586	−	3.26171i	0.231829	−	0.215071i
$231$	−0.749649	−	0.389738i	−0.0493233	−	0.0256429i
$232$	−3.58666			−0.235476
$233$		−	3.65041i		−	0.239147i	−0.992825	−	0.119573i	$-0.961847\pi$
$233$		−	3.65041i		−	0.239147i	0.992825	−	0.119573i	$-0.0381526\pi$
$234$	−7.27082	+	5.10257i	−0.475308	+	0.333565i
$235$			9.98664i			0.651457i
$236$			7.91338i			0.515117i
$237$	−20.3081	−	10.5581i	−1.31916	−	0.685821i
$238$	−0.805042			−0.0521831
$239$		−	2.23114i		−	0.144321i	−0.997393	−	0.0721603i	$-0.977011\pi$
$239$		−	2.23114i		−	0.144321i	0.997393	−	0.0721603i	$-0.0229893\pi$
$240$	0.798958	−	1.53677i	0.0515725	−	0.0991982i
$241$			14.8025i			0.953511i	0.879036	+	0.476756i	$0.158187\pi$
$241$			14.8025i			0.953511i	−0.879036	+	0.476756i	$0.841813\pi$
$242$		−	0.281357i		−	0.0180863i
$243$	−10.5618	−	11.4651i	−0.677541	−	0.735485i
$244$			4.14107i			0.265105i
$245$	−6.97891			−0.445866
$246$	−7.06638	+	13.5920i	−0.450536	+	0.866592i
$247$		−	20.4634i		−	1.30205i
$248$			10.6138i			0.673977i
$249$	−7.75811	+	14.9225i	−0.491650	+	0.945674i
$250$			1.00000i			0.0632456i
$251$	−13.8618			−0.874948			−0.437474	−	0.899231i	$-0.644127\pi$
$251$	−13.8618			−0.874948			−0.437474	+	0.899231i	$0.644127\pi$
$252$	0.356641	−	0.250286i	0.0224663	−	0.0157666i
$253$	10.9553	+	11.8090i	0.688756	+	0.742424i
$254$			13.8601i			0.869660i
$255$	4.42868	−	8.51843i	0.277335	−	0.533445i
$256$	1.00000			0.0625000
$257$		−	1.86957i		−	0.116621i	−0.998298	−	0.0583104i	$-0.981429\pi$
$257$		−	1.86957i		−	0.116621i	0.998298	−	0.0583104i	$-0.0185713\pi$
$258$	6.71617	−	12.9184i	0.418131	−	0.804261i
$259$	−0.877429			−0.0545208
$260$	2.96087			0.183626
$261$	8.80752	−	6.18101i	0.545172	−	0.382595i
$262$	3.17761			0.196313
$263$	21.2810			1.31224			0.656120	−	0.754656i	$-0.272196\pi$
$263$	21.2810			1.31224			0.656120	+	0.754656i	$0.272196\pi$
$264$	5.16167	+	2.68352i	0.317679	+	0.165159i
$265$	3.83589			0.235637
$266$			1.00375i			0.0615439i
$267$	12.2859	−	23.6316i	0.751885	−	1.44623i
$268$			13.0680i			0.798253i
$269$		−	21.9822i		−	1.34028i	−0.742237	−	0.670138i	$-0.766235\pi$
$269$		−	21.9822i		−	1.34028i	0.742237	−	0.670138i	$-0.233765\pi$
$270$	0.686420	+	5.15061i	0.0417742	+	0.313456i
$271$	18.8975			1.14794			0.573971	−	0.818876i	$-0.305402\pi$
$271$	18.8975			1.14794			0.573971	+	0.818876i	$0.305402\pi$
$272$	5.54307			0.336098
$273$	0.660841	+	0.343567i	0.0399959	+	0.0207936i
$274$		−	19.0473i		−	1.15069i
$275$	−3.35877			−0.202542
$276$	−8.00904	+	2.20347i	−0.482088	+	0.132633i
$277$	−8.26393			−0.496532			−0.248266	−	0.968692i	$-0.579861\pi$
$277$	−8.26393			−0.496532			−0.248266	+	0.968692i	$0.579861\pi$
$278$		−	10.1337i		−	0.607780i
$279$	−18.2911	−	26.0636i	−1.09506	−	1.56039i
$280$	−0.145234			−0.00867939
$281$	−13.4017			−0.799475			−0.399738	−	0.916630i	$-0.630899\pi$
$281$	−13.4017			−0.799475			−0.399738	+	0.916630i	$0.630899\pi$
$282$	7.97891	−	15.3472i	0.475137	−	0.913911i
$283$			30.2552i			1.79849i	0.437450	+	0.899243i	$0.355882\pi$
$283$			30.2552i			1.79849i	−0.437450	+	0.899243i	$0.644118\pi$
$284$			1.26558i			0.0750981i
$285$	−10.6210	−	5.52181i	−0.629136	−	0.327084i
$286$			9.94490i			0.588054i
$287$	1.28452			0.0758229
$288$	−2.45563	+	1.72333i	−0.144699	+	0.101548i
$289$	13.7256			0.807389
$290$	−3.58666			−0.210616
$291$	−17.8415	−	9.27569i	−1.04589	−	0.543750i
$292$	9.24658			0.541115
$293$	7.09896			0.414725			0.207363	−	0.978264i	$-0.433512\pi$
$293$	7.09896			0.414725			0.207363	+	0.978264i	$0.433512\pi$
$294$	10.7250	+	5.57585i	0.625494	+	0.325190i
$295$			7.91338i			0.460735i
$296$	6.04149			0.351154
$297$	−17.2997	+	2.30553i	−1.00383	+	0.133780i
$298$		−	19.7755i		−	1.14557i
$299$	−9.65750	−	10.4100i	−0.558508	−	0.602027i
$300$	0.798958	−	1.53677i	0.0461279	−	0.0887255i
$301$	−1.22086			−0.0703692
$302$			9.13517i			0.525670i
$303$	7.99845	+	4.15834i	0.459499	+	0.238891i
$304$		−	6.91126i		−	0.396388i
$305$			4.14107i			0.237117i
$306$	−13.6117	+	9.55255i	−0.778131	+	0.546083i
$307$	−27.6286			−1.57685			−0.788423	−	0.615133i	$-0.789102\pi$
$307$	−27.6286			−1.57685			−0.788423	+	0.615133i	$0.789102\pi$
$308$		−	0.487808i		−	0.0277954i
$309$	−13.3487	−	6.93989i	−0.759379	−	0.394796i
$310$			10.6138i			0.602823i
$311$			30.1469i			1.70948i	0.519060	+	0.854738i	$0.326282\pi$
$311$			30.1469i			1.70948i	−0.519060	+	0.854738i	$0.673718\pi$
$312$	−4.55019	−	2.36561i	−0.257604	−	0.133927i
$313$		−	5.35060i		−	0.302434i	−0.988501	−	0.151217i	$-0.951681\pi$
$313$		−	5.35060i		−	0.302434i	0.988501	−	0.151217i	$-0.0483192\pi$
$314$	−10.3178			−0.582268
$315$	0.356641	−	0.250286i	0.0200944	−	0.0141020i
$316$		−	13.2148i		−	0.743391i
$317$		−	20.5865i		−	1.15625i	−0.815947	−	0.578127i	$-0.803784\pi$
$317$		−	20.5865i		−	1.15625i	0.815947	−	0.578127i	$-0.196216\pi$
$318$	−5.89488	−	3.06471i	−0.330568	−	0.171861i
$319$		−	12.0468i		−	0.674490i
$320$	1.00000			0.0559017
$321$	8.90556	−	17.1296i	0.497060	−	0.956079i
$322$	0.473711	+	0.510622i	0.0263989	+	0.0284559i
$323$		−	38.3096i		−	2.13160i
$324$	3.06025	−	8.46374i	0.170014	−	0.470208i
$325$	2.96087			0.164240
$326$		−	11.8046i		−	0.653796i
$327$	−11.0591	−	5.74955i	−0.611569	−	0.317951i
$328$	−8.84450			−0.488356
$329$	−1.45040			−0.0799631
$330$	5.16167	+	2.68352i	0.284140	+	0.147723i
$331$	0.146593			0.00805747			0.00402874	−	0.999992i	$-0.498718\pi$
$331$	0.146593			0.00805747			0.00402874	+	0.999992i	$0.498718\pi$
$332$	−9.71029			−0.532921
$333$	−14.8357	+	10.4115i	−0.812990	+	0.570546i
$334$	−11.8429			−0.648012
$335$			13.0680i			0.713979i
$336$	0.223191	+	0.116036i	0.0121761	+	0.00633027i
$337$		−	24.5559i		−	1.33764i	−0.743423	−	0.668821i	$-0.766799\pi$
$337$		−	24.5559i		−	1.33764i	0.743423	−	0.668821i	$-0.233201\pi$
$338$			4.23323i			0.230257i
$339$	−10.5127	+	20.2209i	−0.570973	+	1.09825i
$340$	5.54307			0.300615
$341$	−35.6493			−1.93052
$342$	11.9104	+	16.9715i	0.644041	+	0.917715i
$343$		−	2.03021i		−	0.109621i
$344$	8.40616			0.453230
$345$	−8.00904	+	2.20347i	−0.431192	+	0.118631i
$346$	−9.94482			−0.534637
$347$		−	9.62040i		−	0.516450i	−0.966085	−	0.258225i	$-0.916862\pi$
$347$		−	9.62040i		−	0.516450i	0.966085	−	0.258225i	$-0.0831376\pi$
$348$	5.51188	+	2.86559i	0.295468	+	0.153612i
$349$	23.1850			1.24106			0.620532	−	0.784181i	$-0.286917\pi$
$349$	23.1850			1.24106			0.620532	+	0.784181i	$0.286917\pi$
$350$	−0.145234			−0.00776308
$351$	15.2503	−	2.03240i	0.814002	−	0.108482i
$352$			3.35877i			0.179023i
$353$		−	9.38131i		−	0.499317i	−0.968334	−	0.249658i	$-0.919682\pi$
$353$		−	9.38131i		−	0.499317i	0.968334	−	0.249658i	$-0.0803183\pi$
$354$	6.32246	−	12.1611i	0.336035	−	0.646353i
$355$			1.26558i			0.0671698i
$356$	15.3774			0.815001
$357$	1.23716	+	0.643195i	0.0654777	+	0.0340415i
$358$	−3.37701			−0.178480
$359$	13.9686			0.737234			0.368617	−	0.929581i	$-0.379831\pi$
$359$	13.9686			0.737234			0.368617	+	0.929581i	$0.379831\pi$
$360$	−2.45563	+	1.72333i	−0.129423	+	0.0908276i
$361$	−28.7656			−1.51398
$362$	−5.28230			−0.277632
$363$	−0.224792	+	0.432381i	−0.0117985	+	0.0226941i
$364$			0.430019i			0.0225391i
$365$	9.24658			0.483988
$366$	3.30854	−	6.36387i	0.172940	−	0.332645i
$367$		−	11.2257i		−	0.585976i	−0.956116	−	0.292988i	$-0.905350\pi$
$367$		−	11.2257i		−	0.585976i	0.956116	−	0.292988i	$-0.0946496\pi$
$368$	−3.26171	−	3.51586i	−0.170028	−	0.183277i
$369$	21.7188	−	15.2420i	1.13064	−	0.793467i
$370$	6.04149			0.314082
$371$			0.557101i			0.0289232i
$372$	8.47998	−	16.3110i	0.439667	−	0.845685i
$373$		−	6.04006i		−	0.312743i	−0.987698	−	0.156371i	$-0.950020\pi$
$373$		−	6.04006i		−	0.312743i	0.987698	−	0.156371i	$-0.0499797\pi$
$374$			18.6179i			0.962709i
$375$	0.798958	−	1.53677i	0.0412580	−	0.0793585i
$376$	9.98664			0.515022
$377$			10.6196i			0.546940i
$378$	−0.748044	+	0.0996915i	−0.0384752	+	0.00512758i
$379$			6.58693i			0.338348i	0.985586	+	0.169174i	$0.0541099\pi$
$379$			6.58693i			0.338348i	−0.985586	+	0.169174i	$0.945890\pi$
$380$		−	6.91126i		−	0.354540i
$381$	11.0736	−	21.2998i	0.567320	−	1.09122i
$382$			22.1062i			1.13105i
$383$	−25.9655			−1.32677			−0.663387	−	0.748277i	$-0.730882\pi$
$383$	−25.9655			−1.32677			−0.663387	+	0.748277i	$0.730882\pi$
$384$	−1.53677	−	0.798958i	−0.0784230	−	0.0407717i
$385$		−	0.487808i		−	0.0248610i
$386$		−	5.62469i		−	0.286289i
$387$	−20.6424	+	14.4866i	−1.04931	+	0.736396i
$388$		−	11.6097i		−	0.589395i
$389$	25.9332			1.31486			0.657432	−	0.753514i	$-0.271643\pi$
$389$	25.9332			1.31486			0.657432	+	0.753514i	$0.271643\pi$
$390$	−4.55019	−	2.36561i	−0.230408	−	0.119788i
$391$	−18.0799	−	19.4887i	−0.914338	−	0.985583i
$392$			6.97891i			0.352488i
$393$	−4.88326	−	2.53878i	−0.246328	−	0.128064i
$394$	4.97721			0.250748
$395$		−	13.2148i		−	0.664909i
$396$	−5.78828	−	8.24791i	−0.290872	−	0.414473i
$397$	11.2187			0.563049			0.281524	−	0.959554i	$-0.409160\pi$
$397$	11.2187			0.563049			0.281524	+	0.959554i	$0.409160\pi$
$398$	−5.07219			−0.254246
$399$	0.801954	−	1.54253i	0.0401479	−	0.0772233i
$400$	1.00000			0.0500000
$401$	16.0468			0.801337			0.400669	−	0.916223i	$-0.368778\pi$
$401$	16.0468			0.801337			0.400669	+	0.916223i	$0.368778\pi$
$402$	10.4408	−	20.0825i	0.520738	−	1.00162i
$403$	31.4261			1.56545
$404$			5.20471i			0.258944i
$405$	3.06025	−	8.46374i	0.152065	−	0.420566i
$406$		−	0.520905i		−	0.0258521i
$407$			20.2920i			1.00584i
$408$	−8.51843	−	4.42868i	−0.421725	−	0.219252i
$409$	−25.0421			−1.23825			−0.619127	−	0.785291i	$-0.712513\pi$
$409$	−25.0421			−1.23825			−0.619127	+	0.785291i	$0.712513\pi$
$410$	−8.84450			−0.436799
$411$	−15.2180	+	29.2714i	−0.750649	+	1.44385i
$412$		−	8.68617i		−	0.427937i
$413$	−1.14929			−0.0565529
$414$	14.0685	+	3.01265i	0.691431	+	0.148064i
$415$	−9.71029			−0.476659
$416$		−	2.96087i		−	0.145169i
$417$	−8.09642	+	15.5732i	−0.396483	+	0.762624i
$418$	23.2134			1.13540
$419$	0.170219			0.00831576			0.00415788	−	0.999991i	$-0.498677\pi$
$419$	0.170219			0.00831576			0.00415788	+	0.999991i	$0.498677\pi$
$420$	0.223191	+	0.116036i	0.0108906	+	0.00566197i
$421$		−	3.35189i		−	0.163361i	−0.996659	−	0.0816807i	$-0.973971\pi$
$421$		−	3.35189i		−	0.163361i	0.996659	−	0.0816807i	$-0.0260288\pi$
$422$			9.58459i			0.466571i
$423$	−24.5235	+	17.2103i	−1.19237	+	0.836793i
$424$		−	3.83589i		−	0.186287i
$425$	5.54307			0.268878
$426$	1.01114	−	1.94490i	0.0489900	−	0.0942307i
$427$	−0.601423			−0.0291049
$428$	11.1465			0.538785
$429$	7.94556	−	15.2830i	0.383615	−	0.737872i
$430$	8.40616			0.405381
$431$	21.5603			1.03852			0.519262	−	0.854615i	$-0.326207\pi$
$431$	21.5603			1.03852			0.519262	+	0.854615i	$0.326207\pi$
$432$	5.15061	−	0.686420i	0.247809	−	0.0330254i
$433$			25.3255i			1.21707i	0.793529	+	0.608533i	$0.208242\pi$
$433$			25.3255i			1.21707i	−0.793529	+	0.608533i	$0.791758\pi$
$434$	−1.54148			−0.0739936
$435$	5.51188	+	2.86559i	0.264274	+	0.137395i
$436$		−	7.19631i		−	0.344641i
$437$	−24.2990	+	22.5425i	−1.16238	+	1.07835i
$438$	−14.2099	−	7.38763i	−0.678974	−	0.352995i
$439$	−0.917239			−0.0437774			−0.0218887	−	0.999760i	$-0.506968\pi$
$439$	−0.917239			−0.0437774			−0.0218887	+	0.999760i	$0.506968\pi$
$440$			3.35877i			0.160123i
$441$	−12.0270	−	17.1376i	−0.572713	−	0.816077i
$442$		−	16.4123i		−	0.780655i
$443$			4.08632i			0.194147i	0.995277	+	0.0970734i	$0.0309482\pi$
$443$			4.08632i			0.194147i	−0.995277	+	0.0970734i	$0.969052\pi$
$444$	−9.28438	−	4.82690i	−0.440617	−	0.229074i
$445$	15.3774			0.728959
$446$		−	17.7150i		−	0.838829i
$447$	−15.7998	+	30.3905i	−0.747306	+	1.43742i
$448$			0.145234i			0.00686166i
$449$		−	5.31513i		−	0.250836i	−0.992104	−	0.125418i	$-0.959973\pi$
$449$		−	5.31513i		−	0.250836i	0.992104	−	0.125418i	$-0.0400273\pi$
$450$	−2.45563	+	1.72333i	−0.115760	+	0.0812386i
$451$		−	29.7067i		−	1.39883i
$452$	−13.1580			−0.618902
$453$	7.29861	−	14.0387i	0.342919	−	0.659594i
$454$			3.72255i			0.174708i
$455$			0.430019i			0.0201596i
$456$	−5.52181	+	10.6210i	−0.258582	+	0.497375i
$457$		−	17.8678i		−	0.835822i	−0.908488	−	0.417911i	$-0.862762\pi$
$457$		−	17.8678i		−	0.835822i	0.908488	−	0.417911i	$-0.137238\pi$
$458$	4.59060			0.214505
$459$	28.5502	−	3.80487i	1.33261	−	0.177596i
$460$	−3.26171	−	3.51586i	−0.152078	−	0.163928i
$461$			0.958482i			0.0446410i	0.999751	+	0.0223205i	$0.00710542\pi$
$461$			0.958482i			0.0446410i	−0.999751	+	0.0223205i	$0.992895\pi$
$462$	−0.389738	+	0.749649i	−0.0181323	+	0.0348768i
$463$	41.6838			1.93721			0.968606	−	0.248603i	$-0.0799714\pi$
$463$	41.6838			1.93721			0.968606	+	0.248603i	$0.0799714\pi$
$464$			3.58666i			0.166507i
$465$	8.47998	−	16.3110i	0.393250	−	0.756404i
$466$	−3.65041			−0.169102
$467$	7.07758			0.327511			0.163756	−	0.986501i	$-0.447639\pi$
$467$	7.07758			0.327511			0.163756	+	0.986501i	$0.447639\pi$
$468$	5.10257	+	7.27082i	0.235866	+	0.336094i
$469$	−1.89791			−0.0876375
$470$	9.98664			0.460649
$471$	15.8561	+	8.24350i	0.730611	+	0.379840i
$472$	7.91338			0.364243
$473$			28.2344i			1.29822i
$474$	−10.5581	+	20.3081i	−0.484949	+	0.932784i
$475$		−	6.91126i		−	0.317111i
$476$			0.805042i			0.0368990i
$477$	6.61051	+	9.41953i	0.302674	+	0.431290i
$478$	−2.23114			−0.102050
$479$	−12.3246			−0.563125			−0.281562	−	0.959543i	$-0.590853\pi$
$479$	−12.3246			−0.563125			−0.281562	+	0.959543i	$0.590853\pi$
$480$	−1.53677	−	0.798958i	−0.0701437	−	0.0364673i
$481$		−	17.8881i		−	0.815626i
$482$	14.8025			0.674234
$483$	−0.320019	−	1.16318i	−0.0145614	−	0.0529267i
$484$	−0.281357			−0.0127890
$485$		−	11.6097i		−	0.527171i
$486$	−11.4651	+	10.5618i	−0.520067	+	0.479094i
$487$	7.63905			0.346159			0.173079	−	0.984908i	$-0.444628\pi$
$487$	7.63905			0.346159			0.173079	+	0.984908i	$0.444628\pi$
$488$	4.14107			0.187457
$489$	−9.43137	+	18.1410i	−0.426501	+	0.820362i
$490$			6.97891i			0.315275i
$491$			30.8151i			1.39067i	0.718688	+	0.695333i	$0.244743\pi$
$491$			30.8151i			1.39067i	−0.718688	+	0.695333i	$0.755257\pi$
$492$	13.5920	+	7.06638i	0.612773	+	0.318577i
$493$			19.8811i			0.895400i
$494$	−20.4634			−0.920691
$495$	−5.78828	−	8.24791i	−0.260164	−	0.370716i
$496$	10.6138			0.476574
$497$	−0.183805			−0.00824476
$498$	14.9225	+	7.75811i	0.668693	+	0.347649i
$499$	−26.4668			−1.18482			−0.592409	−	0.805638i	$-0.701823\pi$
$499$	−26.4668			−1.18482			−0.592409	+	0.805638i	$0.701823\pi$
$500$	1.00000			0.0447214
$501$	18.1998	+	9.46194i	0.813105	+	0.422729i
$502$			13.8618i			0.618682i
$503$	22.6338			1.00919			0.504595	−	0.863356i	$-0.331642\pi$
$503$	22.6338			1.00919			0.504595	+	0.863356i	$0.331642\pi$
$504$	−0.250286	−	0.356641i	−0.0111486	−	0.0158861i
$505$			5.20471i			0.231607i
$506$	11.8090	−	10.9553i	0.524973	−	0.487024i
$507$	3.38217	−	6.50550i	0.150207	−	0.288919i
$508$	13.8601			0.614943
$509$			15.8116i			0.700839i	0.936593	+	0.350419i	$0.113961\pi$
$509$			15.8116i			0.700839i	−0.936593	+	0.350419i	$0.886039\pi$
$510$	−8.51843	−	4.42868i	−0.377202	−	0.196105i
$511$			1.34292i			0.0594072i
$512$		−	1.00000i		−	0.0441942i
$513$	−4.74403	−	35.5973i	−0.209454	−	1.57166i
$514$	−1.86957			−0.0824634
$515$		−	8.68617i		−	0.382758i
$516$	−12.9184	−	6.71617i	−0.568699	−	0.295663i
$517$			33.5429i			1.47521i
$518$			0.877429i			0.0385520i
$519$	15.2829	+	7.94549i	0.670845	+	0.348768i
$520$		−	2.96087i		−	0.129843i
$521$	7.86606			0.344618			0.172309	−	0.985043i	$-0.444877\pi$
$521$	7.86606			0.344618			0.172309	+	0.985043i	$0.444877\pi$
$522$	−6.18101	−	8.80752i	−0.270535	−	0.385495i
$523$			1.97457i			0.0863418i	0.999068	+	0.0431709i	$0.0137460\pi$
$523$			1.97457i			0.0863418i	−0.999068	+	0.0431709i	$0.986254\pi$
$524$		−	3.17761i		−	0.138815i
$525$	0.223191	+	0.116036i	0.00974087	+	0.00506422i
$526$		−	21.2810i		−	0.927894i
$527$	58.8330			2.56281
$528$	2.68352	−	5.16167i	0.116785	−	0.224633i
$529$	−1.72254	+	22.9354i	−0.0748929	+	0.997192i
$530$		−	3.83589i		−	0.166620i
$531$	−19.4323	+	13.6374i	−0.843292	+	0.591812i
$532$	1.00375			0.0435181
$533$			26.1874i			1.13430i
$534$	−23.6316	−	12.2859i	−1.02264	−	0.531663i
$535$	11.1465			0.481904
$536$	13.0680			0.564450
$537$	5.18969	+	2.69809i	0.223952	+	0.116431i
$538$	−21.9822			−0.947718
$539$	−23.4406			−1.00966
$540$	5.15061	−	0.686420i	0.221647	−	0.0295388i
$541$	2.33239			0.100277			0.0501387	−	0.998742i	$-0.484034\pi$
$541$	2.33239			0.100277			0.0501387	+	0.998742i	$0.484034\pi$
$542$		−	18.8975i		−	0.811717i
$543$	8.11769	+	4.22034i	0.348363	+	0.181112i
$544$		−	5.54307i		−	0.237657i
$545$		−	7.19631i		−	0.308256i
$546$	0.343567	−	0.660841i	0.0147033	−	0.0282814i
$547$	−8.51715			−0.364167			−0.182083	−	0.983283i	$-0.558284\pi$
$547$	−8.51715			−0.364167			−0.182083	+	0.983283i	$0.558284\pi$
$548$	−19.0473			−0.813661
$549$	−10.1689	+	7.13643i	−0.434000	+	0.304576i
$550$			3.35877i			0.143219i
$551$	24.7884			1.05602
$552$	2.20347	+	8.00904i	0.0937860	+	0.340887i
$553$	1.91924			0.0816143
$554$			8.26393i			0.351101i
$555$	−9.28438	−	4.82690i	−0.394100	−	0.204890i
$556$	−10.1337			−0.429766
$557$	−2.38292			−0.100967			−0.0504837	−	0.998725i	$-0.516076\pi$
$557$	−2.38292			−0.100967			−0.0504837	+	0.998725i	$0.516076\pi$
$558$	−26.0636	+	18.2911i	−1.10336	+	0.774324i
$559$		−	24.8896i		−	1.05272i
$560$			0.145234i			0.00613725i
$561$	14.8749	−	28.6115i	0.628020	−	1.20798i
$562$			13.4017i			0.565315i
$563$	6.34926			0.267589			0.133795	−	0.991009i	$-0.457284\pi$
$563$	6.34926			0.267589			0.133795	+	0.991009i	$0.457284\pi$
$564$	−15.3472	−	7.97891i	−0.646233	−	0.335973i
$565$	−13.1580			−0.553563
$566$	30.2552			1.27172
$567$	1.22922	+	0.444453i	0.0516225	+	0.0186653i
$568$	1.26558			0.0531024
$569$	25.7123			1.07792			0.538958	−	0.842333i	$-0.318818\pi$
$569$	25.7123			1.07792			0.538958	+	0.842333i	$0.318818\pi$
$570$	−5.52181	+	10.6210i	−0.231283	+	0.444866i
$571$		−	3.97359i		−	0.166290i	−0.996537	−	0.0831448i	$-0.973504\pi$
$571$		−	3.97359i		−	0.166290i	0.996537	−	0.0831448i	$-0.0264964\pi$
$572$	9.94490			0.415817
$573$	17.6619	−	33.9722i	0.737838	−	1.41921i
$574$		−	1.28452i		−	0.0536149i
$575$	−3.26171	−	3.51586i	−0.136023	−	0.146621i
$576$	1.72333	+	2.45563i	0.0718055	+	0.102318i
$577$	3.74728			0.156001			0.0780007	−	0.996953i	$-0.475146\pi$
$577$	3.74728			0.156001			0.0780007	+	0.996953i	$0.475146\pi$
$578$		−	13.7256i		−	0.570910i
$579$	−4.49389	+	8.64386i	−0.186760	+	0.359227i
$580$			3.58666i			0.148928i
$581$		−	1.41026i		−	0.0585076i
$582$	−9.27569	+	17.8415i	−0.384490	+	0.739554i
$583$	12.8839			0.533596
$584$		−	9.24658i		−	0.382626i
$585$	5.10257	+	7.27082i	0.210965	+	0.300611i
$586$		−	7.09896i		−	0.293255i
$587$			14.0119i			0.578333i	0.957279	+	0.289166i	$0.0933781\pi$
$587$			14.0119i			0.578333i	−0.957279	+	0.289166i	$0.906622\pi$
$588$	5.57585	−	10.7250i	0.229944	−	0.442291i
$589$		−	73.3548i		−	3.02253i
$590$	7.91338			0.325789
$591$	−7.64883	−	3.97658i	−0.314631	−	0.163575i
$592$		−	6.04149i		−	0.248304i
$593$			37.3930i			1.53555i	0.640722	+	0.767773i	$0.278635\pi$
$593$			37.3930i			1.53555i	−0.640722	+	0.767773i	$0.721365\pi$
$594$	2.30553	+	17.2997i	0.0945970	+	0.709817i
$595$			0.805042i			0.0330035i
$596$	−19.7755			−0.810038
$597$	7.79479	+	4.05246i	0.319020	+	0.165856i
$598$	−10.4100	+	9.65750i	−0.425697	+	0.394925i
$599$			47.3032i			1.93275i	0.257128	+	0.966377i	$0.417224\pi$
$599$			47.3032i			1.93275i	−0.257128	+	0.966377i	$0.582776\pi$
$600$	−1.53677	−	0.798958i	−0.0627384	−	0.0326173i
$601$	−22.4865			−0.917244			−0.458622	−	0.888631i	$-0.651657\pi$
$601$	−22.4865			−0.917244			−0.458622	+	0.888631i	$0.651657\pi$
$602$			1.22086i			0.0497586i
$603$	−32.0901	+	22.5204i	−1.30681	+	0.917104i
$604$	9.13517			0.371705
$605$	−0.281357			−0.0114388
$606$	4.15834	−	7.99845i	0.168921	−	0.324915i
$607$	37.1285			1.50700			0.753499	−	0.657449i	$-0.228365\pi$
$607$	37.1285			1.50700			0.753499	+	0.657449i	$0.228365\pi$
$608$	−6.91126			−0.280289
$609$	−0.416181	+	0.800512i	−0.0168645	+	0.0324384i
$610$	4.14107			0.167667
$611$		−	29.5692i		−	1.19624i
$612$	9.55255	+	13.6117i	0.386139	+	0.550222i
$613$			2.91171i			0.117603i	0.998270	+	0.0588014i	$0.0187279\pi$
$613$			2.91171i			0.117603i	−0.998270	+	0.0588014i	$0.981272\pi$
$614$			27.6286i			1.11500i
$615$	13.5920	+	7.06638i	0.548081	+	0.284944i
$616$	−0.487808			−0.0196543
$617$	−16.9070			−0.680651			−0.340325	−	0.940308i	$-0.610537\pi$
$617$	−16.9070			−0.680651			−0.340325	+	0.940308i	$0.610537\pi$
$618$	−6.93989	+	13.3487i	−0.279163	+	0.536962i
$619$			30.6140i			1.23048i	0.788339	+	0.615241i	$0.210941\pi$
$619$			30.6140i			1.23048i	−0.788339	+	0.615241i	$0.789059\pi$
$620$	10.6138			0.426260
$621$	−19.2132	−	15.8699i	−0.770997	−	0.636839i
$622$	30.1469			1.20878
$623$			2.23332i			0.0894762i
$624$	−2.36561	+	4.55019i	−0.0947004	+	0.182153i
$625$	1.00000			0.0400000
$626$	−5.35060			−0.213853
$627$	−35.6736	−	18.5465i	−1.42467	−	0.740676i
$628$			10.3178i			0.411726i
$629$		−	33.4884i		−	1.33527i
$630$	−0.250286	−	0.356641i	−0.00997164	−	0.0142089i
$631$			12.9825i			0.516826i	0.966035	+	0.258413i	$0.0831995\pi$
$631$			12.9825i			0.516826i	−0.966035	+	0.258413i	$0.916800\pi$
$632$	−13.2148			−0.525657
$633$	7.65769	−	14.7293i	0.304366	−	0.585438i
$634$	−20.5865			−0.817595
$635$	13.8601			0.550021
$636$	−3.06471	+	5.89488i	−0.121524	+	0.233747i
$637$	20.6637			0.818724
$638$	−12.0468			−0.476937
$639$	−3.10779	+	2.18101i	−0.122942	+	0.0862793i
$640$		−	1.00000i		−	0.0395285i
$641$	23.4868			0.927675			0.463837	−	0.885920i	$-0.346472\pi$
$641$	23.4868			0.927675			0.463837	+	0.885920i	$0.346472\pi$
$642$	−17.1296	−	8.90556i	−0.676050	−	0.351474i
$643$			50.0206i			1.97262i	0.164902	+	0.986310i	$0.447269\pi$
$643$			50.0206i			1.97262i	−0.164902	+	0.986310i	$0.552731\pi$
$644$	0.510622	−	0.473711i	0.0201213	−	0.0186668i
$645$	−12.9184	−	6.71617i	−0.508660	−	0.264449i
$646$	−38.3096			−1.50727
$647$		−	21.4247i		−	0.842290i	−0.906993	−	0.421145i	$-0.861628\pi$
$647$		−	21.4247i		−	0.842290i	0.906993	−	0.421145i	$-0.138372\pi$
$648$	−8.46374	−	3.06025i	−0.332487	−	0.120218i
$649$			26.5792i			1.04333i
$650$		−	2.96087i		−	0.116135i
$651$	2.36891	+	1.23158i	0.0928448	+	0.0482695i
$652$	−11.8046			−0.462303
$653$			28.4131i			1.11189i	0.831219	+	0.555946i	$0.187644\pi$
$653$			28.4131i			1.11189i	−0.831219	+	0.555946i	$0.812356\pi$
$654$	−5.74955	+	11.0591i	−0.224825	+	0.432444i
$655$		−	3.17761i		−	0.124160i
$656$			8.84450i			0.345320i
$657$	15.9349	+	22.7062i	0.621681	+	0.885853i
$658$			1.45040i			0.0565424i
$659$	−35.0816			−1.36658			−0.683292	−	0.730146i	$-0.739452\pi$
$659$	−35.0816			−1.36658			−0.683292	+	0.730146i	$0.739452\pi$
$660$	2.68352	−	5.16167i	0.104456	−	0.200918i
$661$			13.5864i			0.528450i	0.964461	+	0.264225i	$0.0851162\pi$
$661$			13.5864i			0.528450i	−0.964461	+	0.264225i	$0.914884\pi$
$662$		−	0.146593i		−	0.00569749i
$663$	−13.1128	+	25.2220i	−0.509257	+	0.979541i
$664$			9.71029i			0.376832i
$665$	1.00375			0.0389238
$666$	10.4115	+	14.8357i	0.403437	+	0.574870i
$667$	12.6102	−	11.6986i	0.488269	−	0.452973i
$668$			11.8429i			0.458214i
$669$	−14.1535	+	27.2239i	−0.547207	+	1.05254i
$670$	13.0680			0.504860
$671$			13.9089i			0.536947i
$672$	0.116036	−	0.223191i	0.00447618	−	0.00860979i
$673$	−32.3448			−1.24680			−0.623400	−	0.781903i	$-0.714249\pi$
$673$	−32.3448			−1.24680			−0.623400	+	0.781903i	$0.714249\pi$
$674$	−24.5559			−0.945856
$675$	5.15061	−	0.686420i	0.198247	−	0.0264203i
$676$	4.23323			0.162816
$677$	−17.2030			−0.661164			−0.330582	−	0.943777i	$-0.607245\pi$
$677$	−17.2030			−0.661164			−0.330582	+	0.943777i	$0.607245\pi$
$678$	20.2209	+	10.5127i	0.776579	+	0.403739i
$679$	1.68613			0.0647076
$680$		−	5.54307i		−	0.212567i
$681$	2.97416	−	5.72071i	0.113970	−	0.219218i
$682$			35.6493i			1.36508i
$683$		−	7.02091i		−	0.268648i	−0.990937	−	0.134324i	$-0.957114\pi$
$683$		−	7.02091i		−	0.268648i	0.990937	−	0.134324i	$-0.0428862\pi$
$684$	16.9715	−	11.9104i	0.648922	−	0.455406i
$685$	−19.0473			−0.727760
$686$	−2.03021			−0.0775138
$687$	−7.05470	−	3.66770i	−0.269154	−	0.139931i
$688$		−	8.40616i		−	0.320482i
$689$	−11.3576			−0.432689
$690$	2.20347	+	8.00904i	0.0838848	+	0.304899i
$691$	−42.5068			−1.61703			−0.808517	−	0.588473i	$-0.799729\pi$
$691$	−42.5068			−1.61703			−0.808517	+	0.588473i	$0.799729\pi$
$692$			9.94482i			0.378045i
$693$	1.19788	−	0.840655i	0.0455036	−	0.0319338i
$694$	−9.62040			−0.365185
$695$	−10.1337			−0.384394
$696$	2.86559	−	5.51188i	0.108620	−	0.208927i
$697$			49.0257i			1.85698i
$698$		−	23.1850i		−	0.877565i
$699$	5.60985	+	2.91653i	0.212184	+	0.110313i
$700$			0.145234i			0.00548933i
$701$	9.67785			0.365527			0.182764	−	0.983157i	$-0.441496\pi$
$701$	9.67785			0.365527			0.182764	+	0.983157i	$0.441496\pi$
$702$	−2.03240	−	15.2503i	−0.0767081	−	0.575586i
$703$	−41.7543			−1.57479
$704$	3.35877			0.126589
$705$	−15.3472	−	7.97891i	−0.578008	−	0.300503i
$706$	−9.38131			−0.353070
$707$	−0.755900			−0.0284286
$708$	−12.1611	−	6.32246i	−0.457040	−	0.237613i
$709$			11.1186i			0.417569i	0.977962	+	0.208784i	$0.0669507\pi$
$709$			11.1186i			0.417569i	−0.977962	+	0.208784i	$0.933049\pi$
$710$	1.26558			0.0474962
$711$	32.4507	−	22.7735i	1.21700	−	0.854073i
$712$		−	15.3774i		−	0.576293i
$713$	−34.6191	−	37.3166i	−1.29650	−	1.39752i
$714$	0.643195	−	1.23716i	0.0240710	−	0.0462997i
$715$	9.94490			0.371918
$716$			3.37701i			0.126205i
$717$	3.42876	+	1.78259i	0.128049	+	0.0665721i
$718$		−	13.9686i		−	0.521303i
$719$			6.75338i			0.251859i	0.992039	+	0.125929i	$0.0401913\pi$
$719$			6.75338i			0.251859i	−0.992039	+	0.125929i	$0.959809\pi$
$720$	1.72333	+	2.45563i	0.0642248	+	0.0915160i
$721$	1.26153			0.0469817
$722$			28.7656i			1.07054i
$723$	−22.7480	−	11.8266i	−0.846008	−	0.439834i
$724$			5.28230i			0.196315i
$725$			3.58666i			0.133205i
$726$	0.432381	+	0.224792i	0.0160472	+	0.00834283i
$727$		−	20.3417i		−	0.754432i	−0.926125	−	0.377216i	$-0.876881\pi$
$727$		−	20.3417i		−	0.754432i	0.926125	−	0.377216i	$-0.123119\pi$
$728$	0.430019			0.0159376
$729$	26.0577	−	7.07097i	0.965098	−	0.261888i
$730$		−	9.24658i		−	0.342231i
$731$		−	46.5959i		−	1.72341i
$732$	−6.36387	−	3.30854i	−0.235215	−	0.122287i
$733$		−	38.8545i		−	1.43512i	−0.696496	−	0.717561i	$-0.745258\pi$
$733$		−	38.8545i		−	1.43512i	0.696496	−	0.717561i	$-0.254742\pi$
$734$	−11.2257			−0.414347
$735$	5.57585	−	10.7250i	0.205668	−	0.395597i
$736$	−3.51586	+	3.26171i	−0.129596	+	0.120228i
$737$			43.8923i			1.61680i
$738$	−15.2420	−	21.7188i	−0.561066	−	0.799481i
$739$	1.32758			0.0488359			0.0244179	−	0.999702i	$-0.492227\pi$
$739$	1.32758			0.0488359			0.0244179	+	0.999702i	$0.492227\pi$
$740$		−	6.04149i		−	0.222090i
$741$	31.4475	+	16.3494i	1.15525	+	0.600610i
$742$	0.557101			0.0204518
$743$	6.50411			0.238613			0.119306	−	0.992857i	$-0.461933\pi$
$743$	6.50411			0.238613			0.119306	+	0.992857i	$0.461933\pi$
$744$	−16.3110	−	8.47998i	−0.597990	−	0.310891i
$745$	−19.7755			−0.724520
$746$	−6.04006			−0.221142
$747$	−16.7340	−	23.8449i	−0.612267	−	0.872439i
$748$	18.6179			0.680738
$749$			1.61885i			0.0591513i
$750$	−1.53677	−	0.798958i	−0.0561150	−	0.0291738i
$751$			0.826257i			0.0301506i	0.999886	+	0.0150753i	$0.00479879\pi$
$751$			0.826257i			0.0301506i	−0.999886	+	0.0150753i	$0.995201\pi$
$752$		−	9.98664i		−	0.364175i
$753$	11.0750	−	21.3024i	0.403595	−	0.776303i
$754$	10.6196			0.386745
$755$	9.13517			0.332463
$756$	0.0996915	+	0.748044i	0.00362574	+	0.0272061i
$757$			38.9797i			1.41674i	0.705842	+	0.708370i	$0.250569\pi$
$757$			38.9797i			1.41674i	−0.705842	+	0.708370i	$0.749431\pi$
$758$	6.58693			0.239248
$759$	−26.9005	+	7.40097i	−0.976428	+	0.268638i
$760$	−6.91126			−0.250698
$761$		−	24.3111i		−	0.881276i	−0.897685	−	0.440638i	$-0.854752\pi$
$761$		−	24.3111i		−	0.881276i	0.897685	−	0.440638i	$-0.145248\pi$
$762$	−21.2998	−	11.0736i	−0.771610	−	0.401156i
$763$	1.04515			0.0378369
$764$	22.1062			0.799775
$765$	9.55255	+	13.6117i	0.345373	+	0.492133i
$766$			25.9655i			0.938171i
$767$		−	23.4305i		−	0.846027i
$768$	−0.798958	+	1.53677i	−0.0288299	+	0.0554535i
$769$			32.2264i			1.16211i	0.813863	+	0.581057i	$0.197361\pi$
$769$			32.2264i			1.16211i	−0.813863	+	0.581057i	$0.802639\pi$
$770$	−0.487808			−0.0175794
$771$	2.87311	+	1.49371i	0.103472	+	0.0537947i
$772$	−5.62469			−0.202437
$773$	2.00243			0.0720223			0.0360111	−	0.999351i	$-0.488535\pi$
$773$	2.00243			0.0720223			0.0360111	+	0.999351i	$0.488535\pi$
$774$	14.4866	+	20.6424i	0.520710	+	0.741977i
$775$	10.6138			0.381259
$776$	−11.6097			−0.416765
$777$	0.701029	−	1.34841i	0.0251493	−	0.0483739i
$778$		−	25.9332i		−	0.929750i
$779$	61.1267			2.19009
$780$	−2.36561	+	4.55019i	−0.0847026	+	0.162923i
$781$			4.25078i			0.152105i
$782$	−19.4887	+	18.0799i	−0.696913	+	0.646535i
$783$	2.46196	+	18.4735i	0.0879831	+	0.660189i
$784$	6.97891			0.249247
$785$			10.3178i			0.368259i
$786$	−2.53878	+	4.88326i	−0.0905552	+	0.174180i
$787$			40.4309i			1.44121i	0.693347	+	0.720603i	$0.256135\pi$
$787$			40.4309i			1.44121i	−0.693347	+	0.720603i	$0.743865\pi$
$788$		−	4.97721i		−	0.177306i
$789$	−17.0026	+	32.7040i	−0.605309	+	1.16429i
$790$	−13.2148			−0.470162
$791$		−	1.91099i		−	0.0679472i
$792$	−8.24791	+	5.78828i	−0.293077	+	0.205678i
$793$		−	12.2612i		−	0.435407i
$794$		−	11.2187i		−	0.398136i
$795$	−3.06471	+	5.89488i	−0.108694	+	0.209070i
$796$			5.07219i			0.179779i
$797$	12.8995			0.456924			0.228462	−	0.973553i	$-0.426630\pi$
$797$	12.8995			0.456924			0.228462	+	0.973553i	$0.426630\pi$
$798$	−1.54253	−	0.801954i	−0.0546051	−	0.0283889i
$799$		−	55.3566i		−	1.95838i
$800$		−	1.00000i		−	0.0353553i
$801$	26.5004	+	37.7613i	0.936345	+	1.33423i
$802$		−	16.0468i		−	0.566631i
$803$	31.0572			1.09598
$804$	−20.0825	−	10.4408i	−0.708254	−	0.368217i
$805$	0.510622	−	0.473711i	0.0179971	−	0.0166961i
$806$		−	31.4261i		−	1.10694i
$807$	33.7815	+	17.5628i	1.18917	+	0.618241i
$808$	5.20471			0.183101
$809$			8.14490i			0.286359i	0.989697	+	0.143180i	$0.0457327\pi$
$809$			8.14490i			0.286359i	−0.989697	+	0.143180i	$0.954267\pi$
$810$	−8.46374	−	3.06025i	−0.297385	−	0.107526i
$811$	18.2134			0.639559			0.319779	−	0.947492i	$-0.396391\pi$
$811$	18.2134			0.639559			0.319779	+	0.947492i	$0.396391\pi$
$812$	−0.520905			−0.0182802
$813$	−15.0983	+	29.0411i	−0.529521	+	1.01852i
$814$	20.2920			0.711234
$815$	−11.8046			−0.413497
$816$	−4.42868	+	8.51843i	−0.155035	+	0.298205i
$817$	−58.0972			−2.03256
$818$			25.0421i			0.875577i
$819$	−1.05597	+	0.741066i	−0.0368985	+	0.0258949i
$820$			8.84450i			0.308863i
$821$			3.90097i			0.136145i	0.997680	+	0.0680724i	$0.0216849\pi$
$821$			3.90097i			0.136145i	−0.997680	+	0.0680724i	$0.978315\pi$
$822$	29.2714	+	15.2180i	1.02096	+	0.530789i
$823$	−1.35194			−0.0471256			−0.0235628	−	0.999722i	$-0.507501\pi$
$823$	−1.35194			−0.0471256			−0.0235628	+	0.999722i	$0.507501\pi$
$824$	−8.68617			−0.302597
$825$	2.68352	−	5.16167i	0.0934281	−	0.179706i
$826$			1.14929i			0.0399890i
$827$	−30.6202			−1.06477			−0.532385	−	0.846502i	$-0.678704\pi$
$827$	−30.6202			−1.06477			−0.532385	+	0.846502i	$0.678704\pi$
$828$	3.01265	−	14.0685i	0.104697	−	0.488916i
$829$	5.29692			0.183970			0.0919848	−	0.995760i	$-0.470679\pi$
$829$	5.29692			0.183970			0.0919848	+	0.995760i	$0.470679\pi$
$830$			9.71029i			0.337049i
$831$	6.60253	−	12.6998i	0.229039	−	0.440550i
$832$	−2.96087			−0.102650
$833$	38.6846			1.34034
$834$	15.5732	+	8.09642i	0.539256	+	0.280356i
$835$			11.8429i			0.409839i
$836$		−	23.2134i		−	0.802851i
$837$	54.6676	−	7.28553i	1.88959	−	0.251825i
$838$		−	0.170219i		−	0.00588013i
$839$	18.2989			0.631749			0.315875	−	0.948801i	$-0.397702\pi$
$839$	18.2989			0.631749			0.315875	+	0.948801i	$0.397702\pi$
$840$	0.116036	−	0.223191i	0.00400362	−	0.00770083i
$841$	16.1359			0.556409
$842$	−3.35189			−0.115514
$843$	10.7074	−	20.5953i	0.368781	−	0.709339i
$844$	9.58459			0.329915
$845$	4.23323			0.145627
$846$	17.2103	+	24.5235i	0.591702	+	0.843136i
$847$		−	0.0408626i		−	0.00140406i
$848$	−3.83589			−0.131725
$849$	−46.4953	−	24.1726i	−1.59572	−	0.829603i
$850$		−	5.54307i		−	0.190126i
$851$	−21.2410	+	19.7056i	−0.728133	+	0.675498i
$852$	−1.94490	−	1.01114i	−0.0666312	−	0.0346411i
$853$	−15.6345			−0.535315			−0.267658	−	0.963514i	$-0.586250\pi$
$853$	−15.6345			−0.535315			−0.267658	+	0.963514i	$0.586250\pi$
$854$			0.601423i			0.0205803i
$855$	16.9715	−	11.9104i	0.580414	−	0.407327i
$856$		−	11.1465i		−	0.380978i
$857$		−	41.9165i		−	1.43184i	−0.698182	−	0.715920i	$-0.746007\pi$
$857$		−	41.9165i		−	1.43184i	0.698182	−	0.715920i	$-0.253993\pi$
$858$	−15.2830	−	7.94556i	−0.521754	−	0.271257i
$859$	−2.84869			−0.0971961			−0.0485981	−	0.998818i	$-0.515475\pi$
$859$	−2.84869			−0.0971961			−0.0485981	+	0.998818i	$0.515475\pi$
$860$		−	8.40616i		−	0.286648i
$861$	−1.02628	+	1.97402i	−0.0349755	+	0.0672743i
$862$		−	21.5603i		−	0.734347i
$863$		−	2.10886i		−	0.0717864i	−0.999356	−	0.0358932i	$-0.988572\pi$
$863$		−	2.10886i		−	0.0717864i	0.999356	−	0.0358932i	$-0.0114276\pi$
$864$	−0.686420	−	5.15061i	−0.0233525	−	0.175227i
$865$			9.94482i			0.338134i
$866$	25.3255			0.860596
$867$	−10.9662	+	21.0931i	−0.372431	+	0.716360i
$868$			1.54148i			0.0523214i
$869$		−	44.3855i		−	1.50568i
$870$	2.86559	−	5.51188i	0.0971526	−	0.186870i
$871$		−	38.6926i		−	1.31105i
$872$	−7.19631			−0.243698
$873$	28.5092	−	20.0074i	0.964891	−	0.677148i
$874$	22.5425	+	24.2990i	0.762512	+	0.821927i
$875$			0.145234i			0.00490980i
$876$	−7.38763	+	14.2099i	−0.249605	+	0.480107i
$877$	−14.4796			−0.488940			−0.244470	−	0.969657i	$-0.578614\pi$
$877$	−14.4796			−0.488940			−0.244470	+	0.969657i	$0.578614\pi$
$878$			0.917239i			0.0309553i
$879$	−5.67177	+	10.9095i	−0.191304	+	0.367967i
$880$	3.35877			0.113224
$881$	6.26949			0.211225			0.105612	−	0.994407i	$-0.466320\pi$
$881$	6.26949			0.211225			0.105612	+	0.994407i	$0.466320\pi$
$882$	−17.1376	+	12.0270i	−0.577054	+	0.404969i
$883$	22.7330			0.765026			0.382513	−	0.923950i	$-0.375059\pi$
$883$	22.7330			0.765026			0.382513	+	0.923950i	$0.375059\pi$
$884$	−16.4123			−0.552006
$885$	−12.1611	−	6.32246i	−0.408789	−	0.212527i
$886$	4.08632			0.137283
$887$			29.2878i			0.983389i	0.870768	+	0.491694i	$0.163622\pi$
$887$			29.2878i			0.983389i	−0.870768	+	0.491694i	$0.836378\pi$
$888$	−4.82690	+	9.28438i	−0.161980	+	0.311564i
$889$			2.01296i			0.0675124i
$890$		−	15.3774i		−	0.515452i
$891$	10.2787	−	28.4278i	0.344349	−	0.952366i
$892$	−17.7150			−0.593142
$893$	−69.0203			−2.30968
$894$	30.3905	+	15.7998i	1.01641	+	0.528425i
$895$			3.37701i			0.112881i
$896$	0.145234			0.00485193
$897$	23.7138	−	6.52420i	0.791779	−	0.217837i
$898$	−5.31513			−0.177368
$899$			38.0681i			1.26964i
$900$	1.72333	+	2.45563i	0.0574444	+	0.0818544i
$901$	−21.2626			−0.708359
$902$	−29.7067			−0.989124
$903$	0.975416	−	1.87618i	0.0324598	−	0.0624355i
$904$			13.1580i			0.437630i
$905$			5.28230i			0.175590i
$906$	−14.0387	−	7.29861i	−0.466403	−	0.242480i
$907$		−	47.6557i		−	1.58238i	−0.611569	−	0.791191i	$-0.709461\pi$
$907$		−	47.6557i		−	1.58238i	0.611569	−	0.791191i	$-0.290539\pi$
$908$	3.72255			0.123537
$909$	−12.7808	+	8.96944i	−0.423914	+	0.297498i
$910$	0.430019			0.0142550
$911$	−20.8392			−0.690432			−0.345216	−	0.938523i	$-0.612194\pi$
$911$	−20.8392			−0.690432			−0.345216	+	0.938523i	$0.612194\pi$
$912$	10.6210	+	5.52181i	0.351697	+	0.182845i
$913$	−32.6146			−1.07939
$914$	−17.8678			−0.591016
$915$	−6.36387	−	3.30854i	−0.210383	−	0.109377i
$916$		−	4.59060i		−	0.151678i
$917$	0.461497			0.0152400
$918$	−3.80487	−	28.5502i	−0.125580	−	0.942297i
$919$			39.5739i			1.30542i	0.757607	+	0.652711i	$0.226368\pi$
$919$			39.5739i			1.30542i	−0.757607	+	0.652711i	$0.773632\pi$
$920$	−3.51586	+	3.26171i	−0.115914	+	0.107535i
$921$	22.0741	−	42.4588i	0.727366	−	1.39907i
$922$	0.958482			0.0315659
$923$		−	3.74721i		−	0.123341i
$924$	0.749649	+	0.389738i	0.0246616	+	0.0128214i
$925$		−	6.04149i		−	0.198643i
$926$		−	41.6838i		−	1.36982i
$927$	21.3300	−	14.9692i	0.700570	−	0.491652i
$928$	3.58666			0.117738
$929$		−	43.9606i		−	1.44230i	−0.692779	−	0.721150i	$-0.743614\pi$
$929$		−	43.9606i		−	1.44230i	0.692779	−	0.721150i	$-0.256386\pi$
$930$	−16.3110	−	8.47998i	−0.534858	−	0.278070i
$931$		−	48.2331i		−	1.58077i
$932$			3.65041i			0.119573i
$933$	−46.3289	−	24.0861i	−1.51674	−	0.788544i
$934$		−	7.07758i		−	0.231585i
$935$	18.6179			0.608871
$936$	7.27082	−	5.10257i	0.237654	−	0.166783i
$937$			16.3199i			0.533149i	0.963814	+	0.266575i	$0.0858919\pi$
$937$			16.3199i			0.533149i	−0.963814	+	0.266575i	$0.914108\pi$
$938$			1.89791i			0.0619690i
$939$	8.22265	+	4.27491i	0.268336	+	0.139506i
$940$		−	9.98664i		−	0.325728i
$941$	50.7684			1.65500			0.827502	−	0.561463i	$-0.189761\pi$
$941$	50.7684			1.65500			0.827502	+	0.561463i	$0.189761\pi$
$942$	8.24350	−	15.8561i	0.268588	−	0.516620i
$943$	31.0960	−	28.8482i	1.01263	−	0.939425i
$944$		−	7.91338i		−	0.257559i
$945$	0.0996915	+	0.748044i	0.00324296	+	0.0243339i
$946$	28.2344			0.917979
$947$			24.6666i			0.801557i	0.916175	+	0.400778i	$0.131260\pi$
$947$			24.6666i			0.801557i	−0.916175	+	0.400778i	$0.868740\pi$
$948$	20.3081	+	10.5581i	0.659578	+	0.342910i
$949$	−27.3780			−0.888726
$950$	−6.91126			−0.224231
$951$	31.6368	+	16.4478i	1.02589	+	0.533356i
$952$	0.805042			0.0260916
$953$	−42.3347			−1.37135			−0.685677	−	0.727906i	$-0.740494\pi$
$953$	−42.3347			−1.37135			−0.685677	+	0.727906i	$0.740494\pi$
$954$	9.41953	−	6.61051i	0.304968	−	0.214023i
$955$	22.1062			0.715341
$956$			2.23114i			0.0721603i
$957$	18.5131	+	9.62487i	0.598445	+	0.311128i
$958$			12.3246i			0.398189i
$959$		−	2.76632i		−	0.0893290i
$960$	−0.798958	+	1.53677i	−0.0257863	+	0.0495991i
$961$	81.6528			2.63396
$962$	−17.8881			−0.576735
$963$	19.2091	+	27.3716i	0.619003	+	0.882038i
$964$		−	14.8025i		−	0.476756i
$965$	−5.62469			−0.181065
$966$	−1.16318	+	0.320019i	−0.0374248	+	0.0102964i
$967$	31.0043			0.997030			0.498515	−	0.866881i	$-0.333879\pi$
$967$	31.0043			0.997030			0.498515	+	0.866881i	$0.333879\pi$
$968$			0.281357i			0.00904316i
$969$	58.8731	+	30.6078i	1.89128	+	0.983263i
$970$	−11.6097			−0.372766
$971$	−20.1792			−0.647582			−0.323791	−	0.946129i	$-0.604958\pi$
$971$	−20.1792			−0.647582			−0.323791	+	0.946129i	$0.604958\pi$
$972$	10.5618	+	11.4651i	0.338770	+	0.367743i
$973$		−	1.47176i		−	0.0471825i
$974$		−	7.63905i		−	0.244771i
$975$	−2.36561	+	4.55019i	−0.0757603	+	0.145723i
$976$		−	4.14107i		−	0.132552i
$977$	16.0570			0.513707			0.256854	−	0.966450i	$-0.417314\pi$
$977$	16.0570			0.513707			0.256854	+	0.966450i	$0.417314\pi$
$978$	18.1410	+	9.43137i	0.580084	+	0.301582i
$979$	51.6492			1.65072
$980$	6.97891			0.222933
$981$	17.6715	−	12.4016i	0.564207	−	0.395954i
$982$	30.8151			0.983350
$983$	−34.9165			−1.11366			−0.556831	−	0.830626i	$-0.687983\pi$
$983$	−34.9165			−1.11366			−0.556831	+	0.830626i	$0.687983\pi$
$984$	7.06638	−	13.5920i	0.225268	−	0.433296i
$985$		−	4.97721i		−	0.158587i
$986$	19.8811			0.633143
$987$	1.15881	−	2.22893i	0.0368853	−	0.0709477i
$988$			20.4634i			0.651027i
$989$	−29.5549	+	27.4184i	−0.939791	+	0.871856i
$990$	−8.24791	+	5.78828i	−0.262136	+	0.183964i
$991$	−43.4923			−1.38158			−0.690789	−	0.723056i	$-0.742737\pi$
$991$	−43.4923			−1.38158			−0.690789	+	0.723056i	$0.742737\pi$
$992$		−	10.6138i		−	0.336988i
$993$	−0.117122	+	0.225280i	−0.00371674	+	0.00714903i
$994$			0.183805i			0.00582993i
$995$			5.07219i			0.160799i
$996$	7.75811	−	14.9225i	0.245825	−	0.472837i
$997$	10.9446			0.346619			0.173309	−	0.984867i	$-0.444554\pi$
$997$	10.9446			0.346619			0.173309	+	0.984867i	$0.444554\pi$
$998$			26.4668i			0.837792i
$999$	−4.14700	−	31.1174i	−0.131205	−	0.984510i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	690.2.e.a.551.3	✓	16
3.2	odd	2		690.2.e.b.551.11	yes	16
23.22	odd	2		690.2.e.b.551.3	yes	16
69.68	even	2	inner	690.2.e.a.551.11	yes	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
690.2.e.a.551.3	✓	16	1.1	even	1	trivial
690.2.e.a.551.11	yes	16	69.68	even	2	inner
690.2.e.b.551.3	yes	16	23.22	odd	2
690.2.e.b.551.11	yes	16	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:	\( N \)	\(=\)	\( 690 = 2 \cdot 3 \cdot 5 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	690.e (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-1.00000i q^{2} +(-0.798958 + 1.53677i) q^{3} -1.00000 q^{4} -1.00000 q^{5} +(1.53677 + 0.798958i) q^{6} -0.145234i q^{7} +1.00000i q^{8} +(-1.72333 - 2.45563i) q^{9} +O(q^{10})\)	\(q-1.00000i q^{2} +(-0.798958 + 1.53677i) q^{3} -1.00000 q^{4} -1.00000 q^{5} +(1.53677 + 0.798958i) q^{6} -0.145234i q^{7} +1.00000i q^{8} +(-1.72333 - 2.45563i) q^{9} +1.00000i q^{10} -3.35877 q^{11} +(0.798958 - 1.53677i) q^{12} +2.96087 q^{13} -0.145234 q^{14} +(0.798958 - 1.53677i) q^{15} +1.00000 q^{16} +5.54307 q^{17} +(-2.45563 + 1.72333i) q^{18} -6.91126i q^{19} +1.00000 q^{20} +(0.223191 + 0.116036i) q^{21} +3.35877i q^{22} +(-3.26171 - 3.51586i) q^{23} +(-1.53677 - 0.798958i) q^{24} +1.00000 q^{25} -2.96087i q^{26} +(5.15061 - 0.686420i) q^{27} +0.145234i q^{28} +3.58666i q^{29} +(-1.53677 - 0.798958i) q^{30} +10.6138 q^{31} -1.00000i q^{32} +(2.68352 - 5.16167i) q^{33} -5.54307i q^{34} +0.145234i q^{35} +(1.72333 + 2.45563i) q^{36} -6.04149i q^{37} -6.91126 q^{38} +(-2.36561 + 4.55019i) q^{39} -1.00000i q^{40} +8.84450i q^{41} +(0.116036 - 0.223191i) q^{42} -8.40616i q^{43} +3.35877 q^{44} +(1.72333 + 2.45563i) q^{45} +(-3.51586 + 3.26171i) q^{46} -9.98664i q^{47} +(-0.798958 + 1.53677i) q^{48} +6.97891 q^{49} -1.00000i q^{50} +(-4.42868 + 8.51843i) q^{51} -2.96087 q^{52} -3.83589 q^{53} +(-0.686420 - 5.15061i) q^{54} +3.35877 q^{55} +0.145234 q^{56} +(10.6210 + 5.52181i) q^{57} +3.58666 q^{58} -7.91338i q^{59} +(-0.798958 + 1.53677i) q^{60} -4.14107i q^{61} -10.6138i q^{62} +(-0.356641 + 0.250286i) q^{63} -1.00000 q^{64} -2.96087 q^{65} +(-5.16167 - 2.68352i) q^{66} -13.0680i q^{67} -5.54307 q^{68} +(8.00904 - 2.20347i) q^{69} +0.145234 q^{70} -1.26558i q^{71} +(2.45563 - 1.72333i) q^{72} -9.24658 q^{73} -6.04149 q^{74} +(-0.798958 + 1.53677i) q^{75} +6.91126i q^{76} +0.487808i q^{77} +(4.55019 + 2.36561i) q^{78} +13.2148i q^{79} -1.00000 q^{80} +(-3.06025 + 8.46374i) q^{81} +8.84450 q^{82} +9.71029 q^{83} +(-0.223191 - 0.116036i) q^{84} -5.54307 q^{85} -8.40616 q^{86} +(-5.51188 - 2.86559i) q^{87} -3.35877i q^{88} -15.3774 q^{89} +(2.45563 - 1.72333i) q^{90} -0.430019i q^{91} +(3.26171 + 3.51586i) q^{92} +(-8.47998 + 16.3110i) q^{93} -9.98664 q^{94} +6.91126i q^{95} +(1.53677 + 0.798958i) q^{96} +11.6097i q^{97} -6.97891i q^{98} +(5.78828 + 8.24791i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 16 q^{4} - 16 q^{5} + 2 q^{6} + 2 q^{9}+O(q^{10}) \) 16 * q - 16 * q^4 - 16 * q^5 + 2 * q^6 + 2 * q^9	\( 16 q - 16 q^{4} - 16 q^{5} + 2 q^{6} + 2 q^{9} - 12 q^{11} - 12 q^{14} + 16 q^{16} + 8 q^{18} + 16 q^{20} - 4 q^{21} + 4 q^{23} - 2 q^{24} + 16 q^{25} + 24 q^{27} - 2 q^{30} + 4 q^{31} - 28 q^{33} - 2 q^{36} - 16 q^{38} - 8 q^{39} + 12 q^{44} - 2 q^{45} - 4 q^{46} - 4 q^{49} - 2 q^{51} - 8 q^{53} - 26 q^{54} + 12 q^{55} + 12 q^{56} + 28 q^{57} - 8 q^{58} - 16 q^{64} + 10 q^{66} + 30 q^{69} + 12 q^{70} - 8 q^{72} - 16 q^{73} - 24 q^{74} - 12 q^{78} - 16 q^{80} + 22 q^{81} - 16 q^{82} - 40 q^{83} + 4 q^{84} - 40 q^{86} + 20 q^{87} + 80 q^{89} - 8 q^{90} - 4 q^{92} - 4 q^{93} - 24 q^{94} + 2 q^{96} - 8 q^{99}+O(q^{100}) \) 16 * q - 16 * q^4 - 16 * q^5 + 2 * q^6 + 2 * q^9 - 12 * q^11 - 12 * q^14 + 16 * q^16 + 8 * q^18 + 16 * q^20 - 4 * q^21 + 4 * q^23 - 2 * q^24 + 16 * q^25 + 24 * q^27 - 2 * q^30 + 4 * q^31 - 28 * q^33 - 2 * q^36 - 16 * q^38 - 8 * q^39 + 12 * q^44 - 2 * q^45 - 4 * q^46 - 4 * q^49 - 2 * q^51 - 8 * q^53 - 26 * q^54 + 12 * q^55 + 12 * q^56 + 28 * q^57 - 8 * q^58 - 16 * q^64 + 10 * q^66 + 30 * q^69 + 12 * q^70 - 8 * q^72 - 16 * q^73 - 24 * q^74 - 12 * q^78 - 16 * q^80 + 22 * q^81 - 16 * q^82 - 40 * q^83 + 4 * q^84 - 40 * q^86 + 20 * q^87 + 80 * q^89 - 8 * q^90 - 4 * q^92 - 4 * q^93 - 24 * q^94 + 2 * q^96 - 8 * q^99

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