LMFDB - Embedded newform 690.2.e.a.551.16

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			551.16
Root			$-0.157845 + 1.72484i$ of defining polynomial
Character	$\chi$	$=$	690.551
Dual form			690.2.e.a.551.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000i q^{2} +(1.72484 + 0.157845i) q^{3} -1.00000 q^{4} -1.00000 q^{5} +(-0.157845 + 1.72484i) q^{6} +4.77029i q^{7} -1.00000i q^{8} +(2.95017 + 0.544517i) q^{9} +O(q^{10})$	\(q+1.00000i q^{2} +(1.72484 + 0.157845i) q^{3} -1.00000 q^{4} -1.00000 q^{5} +(-0.157845 + 1.72484i) q^{6} +4.77029i q^{7} -1.00000i q^{8} +(2.95017 + 0.544517i) q^{9} -1.00000i q^{10} -5.68772 q^{11} +(-1.72484 - 0.157845i) q^{12} -5.86303 q^{13} -4.77029 q^{14} +(-1.72484 - 0.157845i) q^{15} +1.00000 q^{16} +1.96521 q^{17} +(-0.544517 + 2.95017i) q^{18} +3.08903i q^{19} +1.00000 q^{20} +(-0.752968 + 8.22800i) q^{21} -5.68772i q^{22} +(1.22009 - 4.63804i) q^{23} +(0.157845 - 1.72484i) q^{24} +1.00000 q^{25} -5.86303i q^{26} +(5.00263 + 1.40488i) q^{27} -4.77029i q^{28} +4.66722i q^{29} +(0.157845 - 1.72484i) q^{30} +7.74501 q^{31} +1.00000i q^{32} +(-9.81042 - 0.897780i) q^{33} +1.96521i q^{34} -4.77029i q^{35} +(-2.95017 - 0.544517i) q^{36} +3.13987i q^{37} -3.08903 q^{38} +(-10.1128 - 0.925453i) q^{39} +1.00000i q^{40} +8.70541i q^{41} +(-8.22800 - 0.752968i) q^{42} -7.75780i q^{43} +5.68772 q^{44} +(-2.95017 - 0.544517i) q^{45} +(4.63804 + 1.22009i) q^{46} +8.55477i q^{47} +(1.72484 + 0.157845i) q^{48} -15.7556 q^{49} +1.00000i q^{50} +(3.38968 + 0.310200i) q^{51} +5.86303 q^{52} +2.37670 q^{53} +(-1.40488 + 5.00263i) q^{54} +5.68772 q^{55} +4.77029 q^{56} +(-0.487590 + 5.32810i) q^{57} -4.66722 q^{58} +2.47606i q^{59} +(1.72484 + 0.157845i) q^{60} -2.31175i q^{61} +7.74501i q^{62} +(-2.59750 + 14.0732i) q^{63} -1.00000 q^{64} +5.86303 q^{65} +(0.897780 - 9.81042i) q^{66} -9.67337i q^{67} -1.96521 q^{68} +(2.83655 - 7.80730i) q^{69} +4.77029 q^{70} +1.59802i q^{71} +(0.544517 - 2.95017i) q^{72} +3.25573 q^{73} -3.13987 q^{74} +(1.72484 + 0.157845i) q^{75} -3.08903i q^{76} -27.1320i q^{77} +(0.925453 - 10.1128i) q^{78} +6.19457i q^{79} -1.00000 q^{80} +(8.40700 + 3.21284i) q^{81} -8.70541 q^{82} +14.7833 q^{83} +(0.752968 - 8.22800i) q^{84} -1.96521 q^{85} +7.75780 q^{86} +(-0.736699 + 8.05022i) q^{87} +5.68772i q^{88} +7.42799 q^{89} +(0.544517 - 2.95017i) q^{90} -27.9683i q^{91} +(-1.22009 + 4.63804i) q^{92} +(13.3589 + 1.22251i) q^{93} -8.55477 q^{94} -3.08903i q^{95} +(-0.157845 + 1.72484i) q^{96} -6.65323i q^{97} -15.7556i q^{98} +(-16.7797 - 3.09706i) 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
$3$	1.72484	+	0.157845i	0.995839	+	0.0911321i
$3$	1.72484	+	0.157845i	0.995839	+	0.0911321i
$4$	−1.00000			−0.500000
$5$	−1.00000			−0.447214
$5$	−1.00000			−0.447214
$6$	−0.157845	+	1.72484i	−0.0644401	+	0.704164i
$7$			4.77029i			1.80300i	0.432780	+	0.901500i	$0.357533\pi$
$7$			4.77029i			1.80300i	−0.432780	+	0.901500i	$0.642467\pi$
$8$		−	1.00000i		−	0.353553i
$9$	2.95017	+	0.544517i	0.983390	+	0.181506i
$10$		−	1.00000i		−	0.316228i
$11$	−5.68772			−1.71491			−0.857455	−	0.514558i	$-0.827956\pi$
$11$	−5.68772			−1.71491			−0.857455	+	0.514558i	$0.827956\pi$
$12$	−1.72484	−	0.157845i	−0.497919	−	0.0455660i
$13$	−5.86303			−1.62611			−0.813056	−	0.582185i	$-0.802198\pi$
$13$	−5.86303			−1.62611			−0.813056	+	0.582185i	$0.802198\pi$
$14$	−4.77029			−1.27491
$15$	−1.72484	−	0.157845i	−0.445353	−	0.0407555i
$16$	1.00000			0.250000
$17$	1.96521			0.476634			0.238317	−	0.971187i	$-0.423404\pi$
$17$	1.96521			0.476634			0.238317	+	0.971187i	$0.423404\pi$
$18$	−0.544517	+	2.95017i	−0.128344	+	0.695362i
$19$			3.08903i			0.708673i	0.935118	+	0.354337i	$0.115293\pi$
$19$			3.08903i			0.708673i	−0.935118	+	0.354337i	$0.884707\pi$
$20$	1.00000			0.223607
$21$	−0.752968	+	8.22800i	−0.164311	+	1.79550i
$22$		−	5.68772i		−	1.21262i
$23$	1.22009	−	4.63804i	0.254405	−	0.967098i
$23$	1.22009	−	4.63804i	0.254405	−	0.967098i
$24$	0.157845	−	1.72484i	0.0322201	−	0.352082i
$25$	1.00000			0.200000
$26$		−	5.86303i		−	1.14984i
$27$	5.00263	+	1.40488i	0.962757	+	0.270369i
$28$		−	4.77029i		−	0.901500i
$29$			4.66722i			0.866681i	0.901230	+	0.433341i	$0.142665\pi$
$29$			4.66722i			0.866681i	−0.901230	+	0.433341i	$0.857335\pi$
$30$	0.157845	−	1.72484i	0.0288185	−	0.314912i
$31$	7.74501			1.39105			0.695523	−	0.718504i	$-0.255173\pi$
$31$	7.74501			1.39105			0.695523	+	0.718504i	$0.255173\pi$
$32$			1.00000i			0.176777i
$33$	−9.81042	−	0.897780i	−1.70777	−	0.156283i
$34$			1.96521i			0.337031i
$35$		−	4.77029i		−	0.806326i
$36$	−2.95017	−	0.544517i	−0.491695	−	0.0907529i
$37$			3.13987i			0.516192i	0.966119	+	0.258096i	$0.0830950\pi$
$37$			3.13987i			0.516192i	−0.966119	+	0.258096i	$0.916905\pi$
$38$	−3.08903			−0.501108
$39$	−10.1128	−	0.925453i	−1.61935	−	0.148191i
$40$			1.00000i			0.158114i
$41$			8.70541i			1.35956i	0.733417	+	0.679779i	$0.237924\pi$
$41$			8.70541i			1.35956i	−0.733417	+	0.679779i	$0.762076\pi$
$42$	−8.22800	−	0.752968i	−1.26961	−	0.116185i
$43$		−	7.75780i		−	1.18305i	−0.806285	−	0.591527i	$-0.798525\pi$
$43$		−	7.75780i		−	1.18305i	0.806285	−	0.591527i	$-0.201475\pi$
$44$	5.68772			0.857455
$45$	−2.95017	−	0.544517i	−0.439785	−	0.0811718i
$46$	4.63804	+	1.22009i	0.683841	+	0.179892i
$47$			8.55477i			1.24784i	0.781488	+	0.623921i	$0.214461\pi$
$47$			8.55477i			1.24784i	−0.781488	+	0.623921i	$0.785539\pi$
$48$	1.72484	+	0.157845i	0.248960	+	0.0227830i
$49$	−15.7556			−2.25081
$50$			1.00000i			0.141421i
$51$	3.38968	+	0.310200i	0.474651	+	0.0434366i
$52$	5.86303			0.813056
$53$	2.37670			0.326465			0.163233	−	0.986588i	$-0.447808\pi$
$53$	2.37670			0.326465			0.163233	+	0.986588i	$0.447808\pi$
$54$	−1.40488	+	5.00263i	−0.191180	+	0.680772i
$55$	5.68772			0.766931
$56$	4.77029			0.637456
$57$	−0.487590	+	5.32810i	−0.0645829	+	0.705724i
$58$	−4.66722			−0.612836
$59$			2.47606i			0.322355i	0.986925	+	0.161178i	$0.0515292\pi$
$59$			2.47606i			0.322355i	−0.986925	+	0.161178i	$0.948471\pi$
$60$	1.72484	+	0.157845i	0.222676	+	0.0203778i
$61$		−	2.31175i		−	0.295989i	−0.988988	−	0.147994i	$-0.952718\pi$
$61$		−	2.31175i		−	0.295989i	0.988988	−	0.147994i	$-0.0472818\pi$
$62$			7.74501i			0.983618i
$63$	−2.59750	+	14.0732i	−0.327255	+	1.77305i
$64$	−1.00000			−0.125000
$65$	5.86303			0.727220
$66$	0.897780	−	9.81042i	0.110509	−	1.20758i
$67$		−	9.67337i		−	1.18179i	−0.806748	−	0.590895i	$-0.798775\pi$
$67$		−	9.67337i		−	1.18179i	0.806748	−	0.590895i	$-0.201225\pi$
$68$	−1.96521			−0.238317
$69$	2.83655	−	7.80730i	0.341480	−	0.939889i
$70$	4.77029			0.570158
$71$			1.59802i			0.189650i	0.995494	+	0.0948252i	$0.0302292\pi$
$71$			1.59802i			0.189650i	−0.995494	+	0.0948252i	$0.969771\pi$
$72$	0.544517	−	2.95017i	0.0641720	−	0.347681i
$73$	3.25573			0.381054			0.190527	−	0.981682i	$-0.438980\pi$
$73$	3.25573			0.381054			0.190527	+	0.981682i	$0.438980\pi$
$74$	−3.13987			−0.365003
$75$	1.72484	+	0.157845i	0.199168	+	0.0182264i
$76$		−	3.08903i		−	0.354337i
$77$		−	27.1320i		−	3.09198i
$78$	0.925453	−	10.1128i	0.104787	−	1.14505i
$79$			6.19457i			0.696944i	0.937319	+	0.348472i	$0.113299\pi$
$79$			6.19457i			0.696944i	−0.937319	+	0.348472i	$0.886701\pi$
$80$	−1.00000			−0.111803
$81$	8.40700	+	3.21284i	0.934111	+	0.356982i
$82$	−8.70541			−0.961352
$83$	14.7833			1.62268			0.811339	−	0.584576i	$-0.198739\pi$
$83$	14.7833			1.62268			0.811339	+	0.584576i	$0.198739\pi$
$84$	0.752968	−	8.22800i	0.0821555	−	0.897748i
$85$	−1.96521			−0.213157
$86$	7.75780			0.836546
$87$	−0.736699	+	8.05022i	−0.0789824	+	0.863075i
$88$			5.68772i			0.606312i
$89$	7.42799			0.787366			0.393683	−	0.919246i	$-0.371201\pi$
$89$	7.42799			0.787366			0.393683	+	0.919246i	$0.371201\pi$
$90$	0.544517	−	2.95017i	0.0573971	−	0.310975i
$91$		−	27.9683i		−	2.93188i
$92$	−1.22009	+	4.63804i	−0.127203	+	0.483549i
$93$	13.3589	+	1.22251i	1.38526	+	0.126769i
$94$	−8.55477			−0.882357
$95$		−	3.08903i		−	0.316928i
$96$	−0.157845	+	1.72484i	−0.0161100	+	0.176041i
$97$		−	6.65323i		−	0.675533i	−0.941230	−	0.337767i	$-0.890329\pi$
$97$		−	6.65323i		−	0.675533i	0.941230	−	0.337767i	$-0.109671\pi$
$98$		−	15.7556i		−	1.59156i
$99$	−16.7797	−	3.09706i	−1.68643	−	0.311266i
$100$	−1.00000			−0.100000
$101$			7.33256i			0.729617i	0.931083	+	0.364808i	$0.118865\pi$
$101$			7.33256i			0.729617i	−0.931083	+	0.364808i	$0.881135\pi$
$102$	−0.310200	+	3.38968i	−0.0307143	+	0.335629i
$103$			9.24100i			0.910543i	0.890353	+	0.455271i	$0.150458\pi$
$103$			9.24100i			0.910543i	−0.890353	+	0.455271i	$0.849542\pi$
$104$			5.86303i			0.574918i
$105$	0.752968	−	8.22800i	0.0734821	−	0.802970i
$106$			2.37670i			0.230846i
$107$	4.05749			0.392252			0.196126	−	0.980579i	$-0.437164\pi$
$107$	4.05749			0.392252			0.196126	+	0.980579i	$0.437164\pi$
$108$	−5.00263	−	1.40488i	−0.481378	−	0.135184i
$109$			12.2955i			1.17769i	0.808245	+	0.588846i	$0.200418\pi$
$109$			12.2955i			1.17769i	−0.808245	+	0.588846i	$0.799582\pi$
$110$			5.68772i			0.542302i
$111$	−0.495614	+	5.41579i	−0.0470416	+	0.514044i
$112$			4.77029i			0.450750i
$113$	−16.8426			−1.58442			−0.792208	−	0.610251i	$-0.791069\pi$
$113$	−16.8426			−1.58442			−0.792208	+	0.610251i	$0.791069\pi$
$114$	−5.32810	−	0.487590i	−0.499022	−	0.0456670i
$115$	−1.22009	+	4.63804i	−0.113774	+	0.432499i
$116$		−	4.66722i		−	0.433341i
$117$	−17.2969	−	3.19252i	−1.59910	−	0.295149i
$118$	−2.47606			−0.227940
$119$			9.37463i			0.859370i
$120$	−0.157845	+	1.72484i	−0.0144092	+	0.157456i
$121$	21.3501			1.94092
$122$	2.31175			0.209296
$123$	−1.37411	+	15.0155i	−0.123899	+	1.35390i
$124$	−7.74501			−0.695523
$125$	−1.00000			−0.0894427
$126$	−14.0732	−	2.59750i	−1.25374	−	0.231404i
$127$	−1.86527			−0.165516			−0.0827580	−	0.996570i	$-0.526373\pi$
$127$	−1.86527			−0.165516			−0.0827580	+	0.996570i	$0.526373\pi$
$128$		−	1.00000i		−	0.0883883i
$129$	1.22453	−	13.3810i	0.107814	−	1.17813i
$130$			5.86303i			0.514222i
$131$		−	16.7197i		−	1.46081i	−0.683016	−	0.730403i	$-0.739332\pi$
$131$		−	16.7197i		−	1.46081i	0.683016	−	0.730403i	$-0.260668\pi$
$132$	9.81042	+	0.897780i	0.853887	+	0.0781417i
$133$	−14.7356			−1.27774
$134$	9.67337			0.835652
$135$	−5.00263	−	1.40488i	−0.430558	−	0.120913i
$136$		−	1.96521i		−	0.168516i
$137$	−8.27644			−0.707104			−0.353552	−	0.935415i	$-0.615026\pi$
$137$	−8.27644			−0.707104			−0.353552	+	0.935415i	$0.615026\pi$
$138$	7.80730	+	2.83655i	0.664602	+	0.241463i
$139$	1.92339			0.163140			0.0815698	−	0.996668i	$-0.474007\pi$
$139$	1.92339			0.163140			0.0815698	+	0.996668i	$0.474007\pi$
$140$			4.77029i			0.403163i
$141$	−1.35033	+	14.7556i	−0.113718	+	1.24265i
$142$	−1.59802			−0.134103
$143$	33.3473			2.78864
$144$	2.95017	+	0.544517i	0.245847	+	0.0453764i
$145$		−	4.66722i		−	0.387592i
$146$			3.25573i			0.269446i
$147$	−27.1760	−	2.48695i	−2.24144	−	0.205121i
$148$		−	3.13987i		−	0.258096i
$149$	15.1957			1.24488			0.622439	−	0.782669i	$-0.286142\pi$
$149$	15.1957			1.24488			0.622439	+	0.782669i	$0.286142\pi$
$150$	−0.157845	+	1.72484i	−0.0128880	+	0.140833i
$151$	8.73197			0.710598			0.355299	−	0.934753i	$-0.384379\pi$
$151$	8.73197			0.710598			0.355299	+	0.934753i	$0.384379\pi$
$152$	3.08903			0.250554
$153$	5.79771	+	1.07009i	0.468717	+	0.0865118i
$154$	27.1320			2.18636
$155$	−7.74501			−0.622095
$156$	10.1128	+	0.925453i	0.809673	+	0.0740955i
$157$		−	1.95674i		−	0.156165i	−0.996947	−	0.0780826i	$-0.975120\pi$
$157$		−	1.95674i		−	0.156165i	0.996947	−	0.0780826i	$-0.0248798\pi$
$158$	−6.19457			−0.492813
$159$	4.09944	+	0.375151i	0.325107	+	0.0297514i
$160$		−	1.00000i		−	0.0790569i
$161$	22.1248	+	5.82016i	1.74368	+	0.458693i
$162$	−3.21284	+	8.40700i	−0.252424	+	0.660516i
$163$	−10.7116			−0.839001			−0.419500	−	0.907755i	$-0.637795\pi$
$163$	−10.7116			−0.839001			−0.419500	+	0.907755i	$0.637795\pi$
$164$		−	8.70541i		−	0.679779i
$165$	9.81042	+	0.897780i	0.763740	+	0.0698921i
$166$			14.7833i			1.14741i
$167$		−	0.164537i		−	0.0127323i	−0.999980	−	0.00636614i	$-0.997974\pi$
$167$		−	0.164537i		−	0.0127323i	0.999980	−	0.00636614i	$-0.00202642\pi$
$168$	8.22800	+	0.752968i	0.634804	+	0.0580927i
$169$	21.3751			1.64424
$170$		−	1.96521i		−	0.150725i
$171$	−1.68203	+	9.11318i	−0.128628	+	0.696902i
$172$			7.75780i			0.591527i
$173$		−	4.40561i		−	0.334953i	−0.985876	−	0.167476i	$-0.946438\pi$
$173$		−	4.40561i		−	0.334953i	0.985876	−	0.167476i	$-0.0535618\pi$
$174$	−8.05022	−	0.736699i	−0.610286	−	0.0558490i
$175$			4.77029i			0.360600i
$176$	−5.68772			−0.428728
$177$	−0.390834	+	4.27081i	−0.0293769	+	0.321014i
$178$			7.42799i			0.556752i
$179$		−	21.8808i		−	1.63545i	−0.575612	−	0.817723i	$-0.695236\pi$
$179$		−	21.8808i		−	1.63545i	0.575612	−	0.817723i	$-0.304764\pi$
$180$	2.95017	+	0.544517i	0.219893	+	0.0405859i
$181$			13.0668i			0.971248i	0.874168	+	0.485624i	$0.161408\pi$
$181$			13.0668i			0.971248i	−0.874168	+	0.485624i	$0.838592\pi$
$182$	27.9683			2.07315
$183$	0.364899	−	3.98740i	0.0269741	−	0.294757i
$184$	−4.63804	−	1.22009i	−0.341921	−	0.0899459i
$185$		−	3.13987i		−	0.230848i
$186$	−1.22251	+	13.3589i	−0.0896391	+	0.979525i
$187$	−11.1776			−0.817385
$188$		−	8.55477i		−	0.623921i
$189$	−6.70167	+	23.8640i	−0.487475	+	1.73585i
$190$	3.08903			0.224102
$191$	6.15903			0.445652			0.222826	−	0.974858i	$-0.428472\pi$
$191$	6.15903			0.445652			0.222826	+	0.974858i	$0.428472\pi$
$192$	−1.72484	−	0.157845i	−0.124480	−	0.0113915i
$193$	7.16580			0.515806			0.257903	−	0.966171i	$-0.416969\pi$
$193$	7.16580			0.515806			0.257903	+	0.966171i	$0.416969\pi$
$194$	6.65323			0.477674
$195$	10.1128	+	0.925453i	0.724194	+	0.0662730i
$196$	15.7556			1.12540
$197$		−	5.95934i		−	0.424585i	−0.977206	−	0.212293i	$-0.931907\pi$
$197$		−	5.95934i		−	0.424585i	0.977206	−	0.212293i	$-0.0680930\pi$
$198$	3.09706	−	16.7797i	0.220098	−	1.19248i
$199$		−	13.4932i		−	0.956509i	−0.878221	−	0.478254i	$-0.841270\pi$
$199$		−	13.4932i		−	0.956509i	0.878221	−	0.478254i	$-0.158730\pi$
$200$		−	1.00000i		−	0.0707107i
$201$	1.52690	−	16.6851i	0.107699	−	1.17687i
$202$	−7.33256			−0.515917
$203$	−22.2640			−1.56263
$204$	−3.38968	−	0.310200i	−0.237325	−	0.0217183i
$205$		−	8.70541i		−	0.608013i
$206$	−9.24100			−0.643851
$207$	6.12495	−	13.0186i	0.425713	−	0.904858i
$208$	−5.86303			−0.406528
$209$		−	17.5695i		−	1.21531i
$210$	8.22800	+	0.752968i	0.567786	+	0.0519597i
$211$	−6.51146			−0.448268			−0.224134	−	0.974558i	$-0.571955\pi$
$211$	−6.51146			−0.448268			−0.224134	+	0.974558i	$0.571955\pi$
$212$	−2.37670			−0.163233
$213$	−0.252241	+	2.75634i	−0.0172832	+	0.188861i
$214$			4.05749i			0.277364i
$215$			7.75780i			0.529078i
$216$	1.40488	−	5.00263i	0.0955898	−	0.340386i
$217$			36.9459i			2.50805i
$218$	−12.2955			−0.832755
$219$	5.61562	+	0.513902i	0.379468	+	0.0347263i
$220$	−5.68772			−0.383466
$221$	−11.5221			−0.775060
$222$	−5.41579	−	0.495614i	−0.363484	−	0.0332634i
$223$	−6.93854			−0.464639			−0.232319	−	0.972640i	$-0.574631\pi$
$223$	−6.93854			−0.464639			−0.232319	+	0.972640i	$0.574631\pi$
$224$	−4.77029			−0.318728
$225$	2.95017	+	0.544517i	0.196678	+	0.0363011i
$226$		−	16.8426i		−	1.12035i
$227$	8.24167			0.547019			0.273509	−	0.961869i	$-0.411816\pi$
$227$	8.24167			0.547019			0.273509	+	0.961869i	$0.411816\pi$
$228$	0.487590	−	5.32810i	0.0322914	−	0.352862i
$229$		−	18.1323i		−	1.19821i	−0.800669	−	0.599107i	$-0.795522\pi$
$229$		−	18.1323i		−	1.19821i	0.800669	−	0.599107i	$-0.204478\pi$
$230$	−4.63804	−	1.22009i	−0.305823	−	0.0804501i
$231$	4.28267	−	46.7985i	0.281779	−	3.07912i
$232$	4.66722			0.306418
$233$			9.01790i			0.590782i	0.955376	+	0.295391i	$0.0954500\pi$
$233$			9.01790i			0.590782i	−0.955376	+	0.295391i	$0.904550\pi$
$234$	3.19252	−	17.2969i	0.208702	−	1.13074i
$235$		−	8.55477i		−	0.558052i
$236$		−	2.47606i		−	0.161178i
$237$	−0.977784	+	10.6847i	−0.0635139	+	0.694043i
$238$	−9.37463			−0.607667
$239$			26.2916i			1.70066i	0.526247	+	0.850331i	$0.323599\pi$
$239$			26.2916i			1.70066i	−0.526247	+	0.850331i	$0.676401\pi$
$240$	−1.72484	−	0.157845i	−0.111338	−	0.0101889i
$241$			6.09867i			0.392850i	0.980519	+	0.196425i	$0.0629332\pi$
$241$			6.09867i			0.392850i	−0.980519	+	0.196425i	$0.937067\pi$
$242$			21.3501i			1.37244i
$243$	13.9936	+	6.86865i	0.897692	+	0.440624i
$244$			2.31175i			0.147994i
$245$	15.7556			1.00659
$246$	−15.0155	−	1.37411i	−0.957352	−	0.0876100i
$247$		−	18.1111i		−	1.15238i
$248$		−	7.74501i		−	0.491809i
$249$	25.4989	+	2.33347i	1.61593	+	0.147878i
$250$		−	1.00000i		−	0.0632456i
$251$	13.8819			0.876215			0.438107	−	0.898923i	$-0.355649\pi$
$251$	13.8819			0.876215			0.438107	+	0.898923i	$0.355649\pi$
$252$	2.59750	−	14.0732i	0.163627	−	0.886526i
$253$	−6.93950	+	26.3798i	−0.436283	+	1.65849i
$254$		−	1.86527i		−	0.117038i
$255$	−3.38968	−	0.310200i	−0.212270	−	0.0194255i
$256$	1.00000			0.0625000
$257$			14.6251i			0.912286i	0.889907	+	0.456143i	$0.150769\pi$
$257$			14.6251i			0.912286i	−0.889907	+	0.456143i	$0.849231\pi$
$258$	13.3810	+	1.22453i	0.833065	+	0.0762361i
$259$	−14.9781			−0.930693
$260$	−5.86303			−0.363610
$261$	−2.54138	+	13.7691i	−0.157308	+	0.852285i
$262$	16.7197			1.03295
$263$	−13.7157			−0.845744			−0.422872	−	0.906189i	$-0.638978\pi$
$263$	−13.7157			−0.845744			−0.422872	+	0.906189i	$0.638978\pi$
$264$	−0.897780	+	9.81042i	−0.0552545	+	0.603790i
$265$	−2.37670			−0.146000
$266$		−	14.7356i		−	0.903496i
$267$	12.8121	+	1.17247i	0.784089	+	0.0717543i
$268$			9.67337i			0.590895i
$269$			31.3415i			1.91092i	0.295116	+	0.955462i	$0.404642\pi$
$269$			31.3415i			1.91092i	−0.295116	+	0.955462i	$0.595358\pi$
$270$	1.40488	−	5.00263i	0.0854981	−	0.304450i
$271$	−4.59208			−0.278949			−0.139475	−	0.990226i	$-0.544541\pi$
$271$	−4.59208			−0.278949			−0.139475	+	0.990226i	$0.544541\pi$
$272$	1.96521			0.119158
$273$	4.41467	−	48.2410i	0.267188	−	2.91968i
$274$		−	8.27644i		−	0.499998i
$275$	−5.68772			−0.342982
$276$	−2.83655	+	7.80730i	−0.170740	+	0.469944i
$277$	−14.1389			−0.849524			−0.424762	−	0.905305i	$-0.639642\pi$
$277$	−14.1389			−0.849524			−0.424762	+	0.905305i	$0.639642\pi$
$278$			1.92339i			0.115357i
$279$	22.8491	+	4.21729i	1.36794	+	0.252483i
$280$	−4.77029			−0.285079
$281$	6.36108			0.379470			0.189735	−	0.981835i	$-0.439237\pi$
$281$	6.36108			0.379470			0.189735	+	0.981835i	$0.439237\pi$
$282$	−14.7556	−	1.35033i	−0.878685	−	0.0804110i
$283$		−	26.0151i		−	1.54644i	−0.634141	−	0.773218i	$-0.718646\pi$
$283$		−	26.0151i		−	1.54644i	0.634141	−	0.773218i	$-0.281354\pi$
$284$		−	1.59802i		−	0.0948252i
$285$	0.487590	−	5.32810i	0.0288823	−	0.315609i
$286$			33.3473i			1.97186i
$287$	−41.5273			−2.45128
$288$	−0.544517	+	2.95017i	−0.0320860	+	0.173840i
$289$	−13.1379			−0.772820
$290$	4.66722			0.274069
$291$	1.05018	−	11.4758i	0.0615627	−	0.672722i
$292$	−3.25573			−0.190527
$293$	8.44627			0.493437			0.246718	−	0.969087i	$-0.420648\pi$
$293$	8.44627			0.493437			0.246718	+	0.969087i	$0.420648\pi$
$294$	2.48695	−	27.1760i	0.145042	−	1.58494i
$295$		−	2.47606i		−	0.144162i
$296$	3.13987			0.182501
$297$	−28.4535	−	7.99054i	−1.65104	−	0.463658i
$298$			15.1957i			0.880261i
$299$	−7.15340	+	27.1930i	−0.413692	+	1.57261i
$300$	−1.72484	−	0.157845i	−0.0995839	−	0.00911321i
$301$	37.0070			2.13305
$302$			8.73197i			0.502469i
$303$	−1.15741	+	12.6475i	−0.0664915	+	0.726581i
$304$			3.08903i			0.177168i
$305$			2.31175i			0.132370i
$306$	−1.07009	+	5.79771i	−0.0611731	+	0.331433i
$307$	−8.46953			−0.483381			−0.241691	−	0.970353i	$-0.577702\pi$
$307$	−8.46953			−0.483381			−0.241691	+	0.970353i	$0.577702\pi$
$308$			27.1320i			1.54599i
$309$	−1.45865	+	15.9393i	−0.0829796	+	0.906754i
$310$		−	7.74501i		−	0.439887i
$311$		−	16.1616i		−	0.916443i	−0.888838	−	0.458221i	$-0.848487\pi$
$311$		−	16.1616i		−	0.916443i	0.888838	−	0.458221i	$-0.151513\pi$
$312$	−0.925453	+	10.1128i	−0.0523934	+	0.572525i
$313$		−	6.86741i		−	0.388169i	−0.980985	−	0.194084i	$-0.937826\pi$
$313$		−	6.86741i		−	0.388169i	0.980985	−	0.194084i	$-0.0621735\pi$
$314$	1.95674			0.110425
$315$	2.59750	−	14.0732i	0.146353	−	0.792933i
$316$		−	6.19457i		−	0.348472i
$317$		−	18.7231i		−	1.05159i	−0.850610	−	0.525797i	$-0.823767\pi$
$317$		−	18.7231i		−	1.05159i	0.850610	−	0.525797i	$-0.176233\pi$
$318$	−0.375151	+	4.09944i	−0.0210374	+	0.229885i
$319$		−	26.5458i		−	1.48628i
$320$	1.00000			0.0559017
$321$	6.99854	+	0.640456i	0.390620	+	0.0357468i
$322$	−5.82016	+	22.1248i	−0.324345	+	1.23297i
$323$			6.07061i			0.337778i
$324$	−8.40700	−	3.21284i	−0.467056	−	0.178491i
$325$	−5.86303			−0.325223
$326$		−	10.7116i		−	0.593263i
$327$	−1.94078	+	21.2078i	−0.107326	+	1.17279i
$328$	8.70541			0.480676
$329$	−40.8087			−2.24986
$330$	−0.897780	+	9.81042i	−0.0494211	+	0.540046i
$331$	13.5890			0.746918			0.373459	−	0.927647i	$-0.378172\pi$
$331$	13.5890			0.746918			0.373459	+	0.927647i	$0.378172\pi$
$332$	−14.7833			−0.811339
$333$	−1.70971	+	9.26315i	−0.0936917	+	0.507618i
$334$	0.164537			0.00900308
$335$			9.67337i			0.528513i
$336$	−0.752968	+	8.22800i	−0.0410778	+	0.448874i
$337$			4.53301i			0.246929i	0.992349	+	0.123464i	$0.0394005\pi$
$337$			4.53301i			0.246929i	−0.992349	+	0.123464i	$0.960599\pi$
$338$			21.3751i			1.16265i
$339$	−29.0508	−	2.65852i	−1.57782	−	0.144391i
$340$	1.96521			0.106579
$341$	−44.0514			−2.38552
$342$	−9.11318	−	1.68203i	−0.492784	−	0.0909539i
$343$		−	41.7669i		−	2.25520i
$344$	−7.75780			−0.418273
$345$	−2.83655	+	7.80730i	−0.152715	+	0.420331i
$346$	4.40561			0.236847
$347$		−	7.21414i		−	0.387275i	−0.981073	−	0.193638i	$-0.937971\pi$
$347$		−	7.21414i		−	0.387275i	0.981073	−	0.193638i	$-0.0620286\pi$
$348$	0.736699	−	8.05022i	0.0394912	−	0.431537i
$349$	−0.988122			−0.0528930			−0.0264465	−	0.999650i	$-0.508419\pi$
$349$	−0.988122			−0.0528930			−0.0264465	+	0.999650i	$0.508419\pi$
$350$	−4.77029			−0.254983
$351$	−29.3306	−	8.23684i	−1.56555	−	0.439650i
$352$		−	5.68772i		−	0.303156i
$353$		−	12.2940i		−	0.654342i	−0.944965	−	0.327171i	$-0.893905\pi$
$353$		−	12.2940i		−	0.654342i	0.944965	−	0.327171i	$-0.106095\pi$
$354$	−4.27081	−	0.390834i	−0.226991	−	0.0207726i
$355$		−	1.59802i		−	0.0848143i
$356$	−7.42799			−0.393683
$357$	−1.47974	+	16.1698i	−0.0783162	+	0.855794i
$358$	21.8808			1.15644
$359$	0.189672			0.0100105			0.00500526	−	0.999987i	$-0.498407\pi$
$359$	0.189672			0.0100105			0.00500526	+	0.999987i	$0.498407\pi$
$360$	−0.544517	+	2.95017i	−0.0286986	+	0.155488i
$361$	9.45787			0.497782
$362$	−13.0668			−0.686776
$363$	36.8256	+	3.37002i	1.93284	+	0.176880i
$364$			27.9683i			1.46594i
$365$	−3.25573			−0.170413
$366$	3.98740	+	0.364899i	0.208425	+	0.0190736i
$367$		−	20.2545i		−	1.05728i	−0.848847	−	0.528638i	$-0.822703\pi$
$367$		−	20.2545i		−	1.05728i	0.848847	−	0.528638i	$-0.177297\pi$
$368$	1.22009	−	4.63804i	0.0636014	−	0.241774i
$369$	−4.74025	+	25.6824i	−0.246767	+	1.33697i
$370$	3.13987			0.163234
$371$			11.3375i			0.588616i
$372$	−13.3589	−	1.22251i	−0.692629	−	0.0633844i
$373$			31.1346i			1.61209i	0.591854	+	0.806045i	$0.298396\pi$
$373$			31.1346i			1.61209i	−0.591854	+	0.806045i	$0.701604\pi$
$374$		−	11.1776i		−	0.577978i
$375$	−1.72484	−	0.157845i	−0.0890705	−	0.00815110i
$376$	8.55477			0.441179
$377$		−	27.3641i		−	1.40932i
$378$	−23.8640	−	6.70167i	−1.22743	−	0.344697i
$379$		−	21.8934i		−	1.12459i	−0.826937	−	0.562295i	$-0.809919\pi$
$379$		−	21.8934i		−	1.12459i	0.826937	−	0.562295i	$-0.190081\pi$
$380$			3.08903i			0.158464i
$381$	−3.21730	−	0.294424i	−0.164827	−	0.0150838i
$382$			6.15903i			0.315123i
$383$	−20.5229			−1.04867			−0.524334	−	0.851512i	$-0.675686\pi$
$383$	−20.5229			−1.04867			−0.524334	+	0.851512i	$0.675686\pi$
$384$	0.157845	−	1.72484i	0.00805501	−	0.0880205i
$385$			27.1320i			1.38278i
$386$			7.16580i			0.364730i
$387$	4.22426	−	22.8868i	0.214731	−	1.16340i
$388$			6.65323i			0.337767i
$389$	6.78101			0.343811			0.171905	−	0.985113i	$-0.445008\pi$
$389$	6.78101			0.343811			0.171905	+	0.985113i	$0.445008\pi$
$390$	−0.925453	+	10.1128i	−0.0468621	+	0.512082i
$391$	2.39773	−	9.11473i	0.121258	−	0.460952i
$392$			15.7556i			0.795780i
$393$	2.63913	−	28.8388i	0.133126	−	1.45473i
$394$	5.95934			0.300227
$395$		−	6.19457i		−	0.311683i
$396$	16.7797	+	3.09706i	0.843213	+	0.155633i
$397$	−10.4669			−0.525320			−0.262660	−	0.964888i	$-0.584600\pi$
$397$	−10.4669			−0.525320			−0.262660	+	0.964888i	$0.584600\pi$
$398$	13.4932			0.676354
$399$	−25.4166	−	2.32594i	−1.27242	−	0.116443i
$400$	1.00000			0.0500000
$401$	−6.92220			−0.345678			−0.172839	−	0.984950i	$-0.555294\pi$
$401$	−6.92220			−0.345678			−0.172839	+	0.984950i	$0.555294\pi$
$402$	16.6851	+	1.52690i	0.832175	+	0.0761547i
$403$	−45.4093			−2.26200
$404$		−	7.33256i		−	0.364808i
$405$	−8.40700	−	3.21284i	−0.417747	−	0.159647i
$406$		−	22.2640i		−	1.10494i
$407$		−	17.8587i		−	0.885223i
$408$	0.310200	−	3.38968i	0.0153572	−	0.167814i
$409$	−0.551195			−0.0272549			−0.0136274	−	0.999907i	$-0.504338\pi$
$409$	−0.551195			−0.0272549			−0.0136274	+	0.999907i	$0.504338\pi$
$410$	8.70541			0.429930
$411$	−14.2756	−	1.30640i	−0.704162	−	0.0644399i
$412$		−	9.24100i		−	0.455271i
$413$	−11.8115			−0.581206
$414$	13.0186	+	6.12495i	0.639831	+	0.301025i
$415$	−14.7833			−0.725683
$416$		−	5.86303i		−	0.287459i
$417$	3.31754	+	0.303598i	0.162461	+	0.0148673i
$418$	17.5695			0.859355
$419$	−29.7594			−1.45384			−0.726921	−	0.686721i	$-0.759049\pi$
$419$	−29.7594			−1.45384			−0.726921	+	0.686721i	$0.759049\pi$
$420$	−0.752968	+	8.22800i	−0.0367411	+	0.401485i
$421$			25.4818i			1.24191i	0.783847	+	0.620953i	$0.213254\pi$
$421$			25.4818i			1.24191i	−0.783847	+	0.620953i	$0.786746\pi$
$422$		−	6.51146i		−	0.316973i
$423$	−4.65822	+	25.2380i	−0.226490	+	1.22711i
$424$		−	2.37670i		−	0.115423i
$425$	1.96521			0.0953268
$426$	−2.75634	−	0.252241i	−0.133545	−	0.0122211i
$427$	11.0277			0.533668
$428$	−4.05749			−0.196126
$429$	57.5188	+	5.26371i	2.77703	+	0.254134i
$430$	−7.75780			−0.374115
$431$	−25.7344			−1.23958			−0.619791	−	0.784767i	$-0.712783\pi$
$431$	−25.7344			−1.23958			−0.619791	+	0.784767i	$0.712783\pi$
$432$	5.00263	+	1.40488i	0.240689	+	0.0675922i
$433$			39.5558i			1.90093i	0.310827	+	0.950466i	$0.399394\pi$
$433$			39.5558i			1.90093i	−0.310827	+	0.950466i	$0.600606\pi$
$434$	−36.9459			−1.77346
$435$	0.736699	−	8.05022i	0.0353220	−	0.385979i
$436$		−	12.2955i		−	0.588846i
$437$	14.3271	+	3.76889i	0.685356	+	0.180290i
$438$	−0.513902	+	5.61562i	−0.0245552	+	0.268325i
$439$	12.4645			0.594900			0.297450	−	0.954737i	$-0.403864\pi$
$439$	12.4645			0.594900			0.297450	+	0.954737i	$0.403864\pi$
$440$		−	5.68772i		−	0.271151i
$441$	−46.4818	−	8.57922i	−2.21342	−	0.408534i
$442$		−	11.5221i		−	0.548050i
$443$		−	12.1118i		−	0.575450i	−0.957713	−	0.287725i	$-0.907101\pi$
$443$		−	12.1118i		−	0.575450i	0.957713	−	0.287725i	$-0.0928989\pi$
$444$	0.495614	−	5.41579i	0.0235208	−	0.257022i
$445$	−7.42799			−0.352121
$446$		−	6.93854i		−	0.328549i
$447$	26.2101	+	2.39857i	1.23970	+	0.113448i
$448$		−	4.77029i		−	0.225375i
$449$		−	15.0035i		−	0.708060i	−0.935234	−	0.354030i	$-0.884811\pi$
$449$		−	15.0035i		−	0.708060i	0.935234	−	0.354030i	$-0.115189\pi$
$450$	−0.544517	+	2.95017i	−0.0256688	+	0.139072i
$451$		−	49.5139i		−	2.33152i
$452$	16.8426			0.792208
$453$	15.0613	+	1.37830i	0.707641	+	0.0647583i
$454$			8.24167i			0.386801i
$455$			27.9683i			1.31118i
$456$	5.32810	+	0.487590i	0.249511	+	0.0228335i
$457$			1.63920i			0.0766785i	0.999265	+	0.0383392i	$0.0122068\pi$
$457$			1.63920i			0.0766785i	−0.999265	+	0.0383392i	$0.987793\pi$
$458$	18.1323			0.847266
$459$	9.83123	+	2.76088i	0.458883	+	0.128867i
$460$	1.22009	−	4.63804i	0.0568868	−	0.216250i
$461$		−	11.3693i		−	0.529520i	−0.964314	−	0.264760i	$-0.914707\pi$
$461$		−	11.3693i		−	0.529520i	0.964314	−	0.264760i	$-0.0852928\pi$
$462$	46.7985	+	4.28267i	2.17726	+	0.199248i
$463$	33.7826			1.57001			0.785006	−	0.619488i	$-0.212660\pi$
$463$	33.7826			1.57001			0.785006	+	0.619488i	$0.212660\pi$
$464$			4.66722i			0.216670i
$465$	−13.3589	−	1.22251i	−0.619506	−	0.0566928i
$466$	−9.01790			−0.417746
$467$	−16.9801			−0.785747			−0.392873	−	0.919593i	$-0.628519\pi$
$467$	−16.9801			−0.785747			−0.392873	+	0.919593i	$0.628519\pi$
$468$	17.2969	+	3.19252i	0.799551	+	0.147574i
$469$	46.1448			2.13077
$470$	8.55477			0.394602
$471$	0.308863	−	3.37508i	0.0142317	−	0.155515i
$472$	2.47606			0.113970
$473$			44.1242i			2.02883i
$474$	−10.6847	−	0.977784i	−0.490763	−	0.0449111i
$475$			3.08903i			0.141735i
$476$		−	9.37463i		−	0.429685i
$477$	7.01167	+	1.29415i	0.321042	+	0.0592553i
$478$	−26.2916			−1.20255
$479$	21.1756			0.967540			0.483770	−	0.875195i	$-0.339267\pi$
$479$	21.1756			0.967540			0.483770	+	0.875195i	$0.339267\pi$
$480$	0.157845	−	1.72484i	0.00720462	−	0.0787280i
$481$		−	18.4092i		−	0.839386i
$482$	−6.09867			−0.277787
$483$	37.2431	+	13.5312i	1.69462	+	0.615689i
$484$	−21.3501			−0.970459
$485$			6.65323i			0.302108i
$486$	−6.86865	+	13.9936i	−0.311568	+	0.634764i
$487$	14.8247			0.671772			0.335886	−	0.941903i	$-0.390964\pi$
$487$	14.8247			0.671772			0.335886	+	0.941903i	$0.390964\pi$
$488$	−2.31175			−0.104648
$489$	−18.4759	−	1.69078i	−0.835509	−	0.0764599i
$490$			15.7556i			0.711767i
$491$			39.8929i			1.80034i	0.435536	+	0.900171i	$0.356559\pi$
$491$			39.8929i			1.80034i	−0.435536	+	0.900171i	$0.643441\pi$
$492$	1.37411	−	15.0155i	0.0619496	−	0.676950i
$493$			9.17208i			0.413090i
$494$	18.1111			0.814857
$495$	16.7797	+	3.09706i	0.754193	+	0.139202i
$496$	7.74501			0.347761
$497$	−7.62303			−0.341940
$498$	−2.33347	+	25.4989i	−0.104566	+	1.14263i
$499$	−19.4748			−0.871811			−0.435906	−	0.899992i	$-0.643572\pi$
$499$	−19.4748			−0.871811			−0.435906	+	0.899992i	$0.643572\pi$
$500$	1.00000			0.0447214
$501$	0.0259715	−	0.283801i	0.00116032	−	0.0126793i
$502$			13.8819i			0.619577i
$503$	30.4466			1.35755			0.678774	−	0.734348i	$-0.262512\pi$
$503$	30.4466			1.35755			0.678774	+	0.734348i	$0.262512\pi$
$504$	14.0732	+	2.59750i	0.626868	+	0.115702i
$505$		−	7.33256i		−	0.326294i
$506$	−26.3798	−	6.93950i	−1.17273	−	0.308498i
$507$	36.8688	+	3.37397i	1.63740	+	0.149843i
$508$	1.86527			0.0827580
$509$			3.89849i			0.172798i	0.996261	+	0.0863988i	$0.0275359\pi$
$509$			3.89849i			0.172798i	−0.996261	+	0.0863988i	$0.972464\pi$
$510$	0.310200	−	3.38968i	0.0137359	−	0.150098i
$511$			15.5308i			0.687040i
$512$			1.00000i			0.0441942i
$513$	−4.33972	+	15.4533i	−0.191603	+	0.682280i
$514$	−14.6251			−0.645083
$515$		−	9.24100i		−	0.407207i
$516$	−1.22453	+	13.3810i	−0.0539071	+	0.589066i
$517$		−	48.6571i		−	2.13994i
$518$		−	14.9781i		−	0.658099i
$519$	0.695406	−	7.59899i	0.0305249	−	0.333559i
$520$		−	5.86303i		−	0.257111i
$521$	13.7197			0.601072			0.300536	−	0.953770i	$-0.402834\pi$
$521$	13.7197			0.601072			0.300536	+	0.953770i	$0.402834\pi$
$522$	−13.7691	−	2.54138i	−0.602657	−	0.111233i
$523$			23.2611i			1.01714i	0.861022	+	0.508568i	$0.169825\pi$
$523$			23.2611i			1.01714i	−0.861022	+	0.508568i	$0.830175\pi$
$524$			16.7197i			0.730403i
$525$	−0.752968	+	8.22800i	−0.0328622	+	0.359099i
$526$		−	13.7157i		−	0.598031i
$527$	15.2206			0.663020
$528$	−9.81042	−	0.897780i	−0.426944	−	0.0390708i
$529$	−20.0228	−	11.3176i	−0.870556	−	0.492070i
$530$		−	2.37670i		−	0.103237i
$531$	−1.34826	+	7.30479i	−0.0585093	+	0.317001i
$532$	14.7356			0.638868
$533$		−	51.0401i		−	2.21079i
$534$	−1.17247	+	12.8121i	−0.0507379	+	0.554435i
$535$	−4.05749			−0.175421
$536$	−9.67337			−0.417826
$537$	3.45378	−	37.7409i	0.149042	−	1.62864i
$538$	−31.3415			−1.35123
$539$	89.6136			3.85993
$540$	5.00263	+	1.40488i	0.215279	+	0.0604563i
$541$	−20.3714			−0.875837			−0.437918	−	0.899015i	$-0.644284\pi$
$541$	−20.3714			−0.875837			−0.437918	+	0.899015i	$0.644284\pi$
$542$		−	4.59208i		−	0.197247i
$543$	−2.06254	+	22.5382i	−0.0885119	+	0.967207i
$544$			1.96521i			0.0842578i
$545$		−	12.2955i		−	0.526680i
$546$	48.2410	+	4.41467i	2.06453	+	0.188931i
$547$	22.9836			0.982706			0.491353	−	0.870960i	$-0.336502\pi$
$547$	22.9836			0.982706			0.491353	+	0.870960i	$0.336502\pi$
$548$	8.27644			0.353552
$549$	1.25879	−	6.82005i	0.0537237	−	0.291072i
$550$		−	5.68772i		−	0.242525i
$551$	−14.4172			−0.614194
$552$	−7.80730	−	2.83655i	−0.332301	−	0.120732i
$553$	−29.5499			−1.25659
$554$		−	14.1389i		−	0.600704i
$555$	0.495614	−	5.41579i	0.0210377	−	0.229887i
$556$	−1.92339			−0.0815698
$557$	28.2412			1.19662			0.598310	−	0.801265i	$-0.295839\pi$
$557$	28.2412			1.19662			0.598310	+	0.801265i	$0.295839\pi$
$558$	−4.21729	+	22.8491i	−0.178532	+	0.967280i
$559$			45.4843i			1.92378i
$560$		−	4.77029i		−	0.201581i
$561$	−19.2796	−	1.76433i	−0.813983	−	0.0744900i
$562$			6.36108i			0.268326i
$563$	−26.5126			−1.11737			−0.558687	−	0.829379i	$-0.688695\pi$
$563$	−26.5126			−1.11737			−0.558687	+	0.829379i	$0.688695\pi$
$564$	1.35033	−	14.7556i	0.0568592	−	0.621324i
$565$	16.8426			0.708573
$566$	26.0151			1.09349
$567$	−15.3262	+	40.1038i	−0.643638	+	1.68420i
$568$	1.59802			0.0670516
$569$	−27.8748			−1.16857			−0.584285	−	0.811548i	$-0.698625\pi$
$569$	−27.8748			−1.16857			−0.584285	+	0.811548i	$0.698625\pi$
$570$	5.32810	+	0.487590i	0.223170	+	0.0204229i
$571$			40.1603i			1.68066i	0.542077	+	0.840329i	$0.317638\pi$
$571$			40.1603i			1.68066i	−0.542077	+	0.840329i	$0.682362\pi$
$572$	−33.3473			−1.39432
$573$	10.6234	+	0.972175i	0.443797	+	0.0406132i
$574$		−	41.5273i		−	1.73332i
$575$	1.22009	−	4.63804i	0.0508811	−	0.193420i
$576$	−2.95017	−	0.544517i	−0.122924	−	0.0226882i
$577$	12.9838			0.540523			0.270261	−	0.962787i	$-0.412890\pi$
$577$	12.9838			0.540523			0.270261	+	0.962787i	$0.412890\pi$
$578$		−	13.1379i		−	0.546466i
$579$	12.3599	+	1.13109i	0.513660	+	0.0470065i
$580$			4.66722i			0.193796i
$581$			70.5206i			2.92569i
$582$	11.4758	+	1.05018i	0.475686	+	0.0435314i
$583$	−13.5180			−0.559858
$584$		−	3.25573i		−	0.134723i
$585$	17.2969	+	3.19252i	0.715140	+	0.131995i
$586$			8.44627i			0.348912i
$587$		−	26.6529i		−	1.10008i	−0.835137	−	0.550041i	$-0.814612\pi$
$587$		−	26.6529i		−	1.10008i	0.835137	−	0.550041i	$-0.185388\pi$
$588$	27.1760	+	2.48695i	1.12072	+	0.102560i
$589$			23.9246i			0.985797i
$590$	2.47606			0.101938
$591$	0.940654	−	10.2789i	0.0386933	−	0.422818i
$592$			3.13987i			0.129048i
$593$			13.5281i			0.555534i	0.960648	+	0.277767i	$0.0895943\pi$
$593$			13.5281i			0.555534i	−0.960648	+	0.277767i	$0.910406\pi$
$594$	7.99054	−	28.4535i	0.327856	−	1.16746i
$595$		−	9.37463i		−	0.384322i
$596$	−15.1957			−0.622439
$597$	2.12984	−	23.2737i	0.0871686	−	0.952529i
$598$	−27.1930	−	7.15340i	−1.11200	−	0.292524i
$599$		−	8.13093i		−	0.332221i	−0.986107	−	0.166110i	$-0.946879\pi$
$599$		−	8.13093i		−	0.332221i	0.986107	−	0.166110i	$-0.0531208\pi$
$600$	0.157845	−	1.72484i	0.00644401	−	0.0704164i
$601$	−1.00715			−0.0410827			−0.0205413	−	0.999789i	$-0.506539\pi$
$601$	−1.00715			−0.0410827			−0.0205413	+	0.999789i	$0.506539\pi$
$602$			37.0070i			1.50829i
$603$	5.26732	−	28.5381i	0.214502	−	1.16216i
$604$	−8.73197			−0.355299
$605$	−21.3501			−0.868005
$606$	−12.6475	−	1.15741i	−0.513770	−	0.0470166i
$607$	−32.1949			−1.30675			−0.653375	−	0.757034i	$-0.726648\pi$
$607$	−32.1949			−1.30675			−0.653375	+	0.757034i	$0.726648\pi$
$608$	−3.08903			−0.125277
$609$	−38.4019	−	3.51427i	−1.55612	−	0.142405i
$610$	−2.31175			−0.0935999
$611$		−	50.1569i		−	2.02913i
$612$	−5.79771	−	1.07009i	−0.234358	−	0.0432559i
$613$		−	24.0591i		−	0.971739i	−0.874031	−	0.485869i	$-0.838503\pi$
$613$		−	24.0591i		−	0.971739i	0.874031	−	0.485869i	$-0.161497\pi$
$614$		−	8.46953i		−	0.341802i
$615$	1.37411	−	15.0155i	0.0554094	−	0.605482i
$616$	−27.1320			−1.09318
$617$	10.6333			0.428081			0.214041	−	0.976825i	$-0.431338\pi$
$617$	10.6333			0.428081			0.214041	+	0.976825i	$0.431338\pi$
$618$	−15.9393	−	1.45865i	−0.641172	−	0.0586755i
$619$			12.3292i			0.495553i	0.968817	+	0.247776i	$0.0796999\pi$
$619$			12.3292i			0.495553i	−0.968817	+	0.247776i	$0.920300\pi$
$620$	7.74501			0.311047
$621$	12.6195	−	21.4883i	0.506404	−	0.862297i
$622$	16.1616			0.648023
$623$			35.4337i			1.41962i
$624$	−10.1128	−	0.925453i	−0.404837	−	0.0370478i
$625$	1.00000			0.0400000
$626$	6.86741			0.274477
$627$	2.77327	−	30.3047i	0.110754	−	1.21025i
$628$			1.95674i			0.0780826i
$629$			6.17051i			0.246034i
$630$	14.0732	+	2.59750i	0.560688	+	0.103487i
$631$			9.73351i			0.387485i	0.981052	+	0.193742i	$0.0620626\pi$
$631$			9.73351i			0.387485i	−0.981052	+	0.193742i	$0.937937\pi$
$632$	6.19457			0.246407
$633$	−11.2313	−	1.02780i	−0.446402	−	0.0408516i
$634$	18.7231			0.743589
$635$	1.86527			0.0740210
$636$	−4.09944	−	0.375151i	−0.162553	−	0.0148757i
$637$	92.3758			3.66006
$638$	26.5458			1.05096
$639$	−0.870151	+	4.71444i	−0.0344226	+	0.186500i
$640$			1.00000i			0.0395285i
$641$	37.1576			1.46764			0.733819	−	0.679345i	$-0.237736\pi$
$641$	37.1576			1.46764			0.733819	+	0.679345i	$0.237736\pi$
$642$	−0.640456	+	6.99854i	−0.0252768	+	0.276210i
$643$		−	20.5307i		−	0.809652i	−0.914394	−	0.404826i	$-0.867332\pi$
$643$		−	20.5307i		−	0.809652i	0.914394	−	0.404826i	$-0.132668\pi$
$644$	−22.1248	−	5.82016i	−0.871838	−	0.229346i
$645$	−1.22453	+	13.3810i	−0.0482160	+	0.526876i
$646$	−6.07061			−0.238845
$647$		−	10.6897i		−	0.420254i	−0.977674	−	0.210127i	$-0.932612\pi$
$647$		−	10.6897i		−	0.420254i	0.977674	−	0.210127i	$-0.0673878\pi$
$648$	3.21284	−	8.40700i	0.126212	−	0.330258i
$649$		−	14.0831i		−	0.552810i
$650$		−	5.86303i		−	0.229967i
$651$	−5.83175	+	63.7260i	−0.228564	+	2.49762i
$652$	10.7116			0.419500
$653$		−	5.99567i		−	0.234629i	−0.993095	−	0.117314i	$-0.962572\pi$
$653$		−	5.99567i		−	0.234629i	0.993095	−	0.117314i	$-0.0374285\pi$
$654$	−21.2078	−	1.94078i	−0.829289	−	0.0758907i
$655$			16.7197i			0.653292i
$656$			8.70541i			0.339889i
$657$	9.60495	+	1.77280i	0.374725	+	0.0691635i
$658$		−	40.8087i		−	1.59089i
$659$	5.16327			0.201132			0.100566	−	0.994930i	$-0.467935\pi$
$659$	5.16327			0.201132			0.100566	+	0.994930i	$0.467935\pi$
$660$	−9.81042	−	0.897780i	−0.381870	−	0.0349460i
$661$			0.430476i			0.0167436i	0.999965	+	0.00837179i	$0.00266485\pi$
$661$			0.430476i			0.0167436i	−0.999965	+	0.00837179i	$0.997335\pi$
$662$			13.5890i			0.528151i
$663$	−19.8738	−	1.81871i	−0.771835	−	0.0706329i
$664$		−	14.7833i		−	0.573703i
$665$	14.7356			0.571421
$666$	−9.26315	−	1.70971i	−0.358940	−	0.0662501i
$667$	21.6467	+	5.69441i	0.838165	+	0.220488i
$668$			0.164537i			0.00636614i
$669$	−11.9679	−	1.09522i	−0.462705	−	0.0423435i
$670$	−9.67337			−0.373715
$671$			13.1486i			0.507594i
$672$	−8.22800	−	0.752968i	−0.317402	−	0.0290464i
$673$	43.9112			1.69265			0.846327	−	0.532664i	$-0.178809\pi$
$673$	43.9112			1.69265			0.846327	+	0.532664i	$0.178809\pi$
$674$	−4.53301			−0.174605
$675$	5.00263	+	1.40488i	0.192551	+	0.0540738i
$676$	−21.3751			−0.822121
$677$	−27.5574			−1.05912			−0.529558	−	0.848274i	$-0.677642\pi$
$677$	−27.5574			−1.05912			−0.529558	+	0.848274i	$0.677642\pi$
$678$	2.65852	−	29.0508i	0.102100	−	1.11569i
$679$	31.7378			1.21799
$680$			1.96521i			0.0753624i
$681$	14.2156	+	1.30091i	0.544742	+	0.0498509i
$682$		−	44.0514i		−	1.68682i
$683$			26.2484i			1.00437i	0.864761	+	0.502184i	$0.167470\pi$
$683$			26.2484i			1.00437i	−0.864761	+	0.502184i	$0.832530\pi$
$684$	1.68203	−	9.11318i	0.0643141	−	0.348451i
$685$	8.27644			0.316227
$686$	41.7669			1.59467
$687$	2.86210	−	31.2753i	0.109196	−	1.19323i
$688$		−	7.75780i		−	0.295764i
$689$	−13.9347			−0.530869
$690$	−7.80730	−	2.83655i	−0.297219	−	0.107986i
$691$	−38.6282			−1.46948			−0.734742	−	0.678347i	$-0.762697\pi$
$691$	−38.6282			−1.46948			−0.734742	+	0.678347i	$0.762697\pi$
$692$			4.40561i			0.167476i
$693$	14.7739	−	80.0441i	0.561212	−	3.04062i
$694$	7.21414			0.273845
$695$	−1.92339			−0.0729583
$696$	8.05022	+	0.736699i	0.305143	+	0.0279245i
$697$			17.1080i			0.648011i
$698$		−	0.988122i		−	0.0374010i
$699$	−1.42343	+	15.5545i	−0.0538392	+	0.588324i
$700$		−	4.77029i		−	0.180300i
$701$	33.5349			1.26659			0.633297	−	0.773909i	$-0.281701\pi$
$701$	33.5349			1.26659			0.633297	+	0.773909i	$0.281701\pi$
$702$	8.23684	−	29.3306i	0.310880	−	1.10701i
$703$	−9.69917			−0.365811
$704$	5.68772			0.214364
$705$	1.35033	−	14.7556i	0.0508564	−	0.555729i
$706$	12.2940			0.462690
$707$	−34.9784			−1.31550
$708$	0.390834	−	4.27081i	0.0146884	−	0.160507i
$709$			38.3106i			1.43879i	0.694604	+	0.719393i	$0.255580\pi$
$709$			38.3106i			1.43879i	−0.694604	+	0.719393i	$0.744420\pi$
$710$	1.59802			0.0599727
$711$	−3.37305	+	18.2750i	−0.126499	+	0.685367i
$712$		−	7.42799i		−	0.278376i
$713$	9.44958	−	35.9217i	0.353890	−	1.34528i
$714$	−16.1698	−	1.47974i	−0.605138	−	0.0553779i
$715$	−33.3473			−1.24712
$716$			21.8808i			0.817723i
$717$	−4.15001	+	45.3489i	−0.154985	+	1.69359i
$718$			0.189672i			0.00707851i
$719$			17.1239i			0.638612i	0.947652	+	0.319306i	$0.103450\pi$
$719$			17.1239i			0.638612i	−0.947652	+	0.319306i	$0.896550\pi$
$720$	−2.95017	−	0.544517i	−0.109946	−	0.0202930i
$721$	−44.0822			−1.64171
$722$			9.45787i			0.351985i
$723$	−0.962646	+	10.5192i	−0.0358012	+	0.391215i
$724$		−	13.0668i		−	0.485624i
$725$			4.66722i			0.173336i
$726$	−3.37002	+	36.8256i	−0.125073	+	1.36673i
$727$		−	29.1589i		−	1.08144i	−0.841201	−	0.540722i	$-0.818151\pi$
$727$		−	29.1589i		−	1.08144i	0.841201	−	0.540722i	$-0.181849\pi$
$728$	−27.9683			−1.03658
$729$	23.0526	+	14.0562i	0.853801	+	0.520599i
$730$		−	3.25573i		−	0.120500i
$731$		−	15.2457i		−	0.563884i
$732$	−0.364899	+	3.98740i	−0.0134870	+	0.147379i
$733$		−	19.6633i		−	0.726282i	−0.931734	−	0.363141i	$-0.881704\pi$
$733$		−	19.6633i		−	0.726282i	0.931734	−	0.363141i	$-0.118296\pi$
$734$	20.2545			0.747607
$735$	27.1760	+	2.48695i	1.00240	+	0.0917327i
$736$	4.63804	+	1.22009i	0.170960	+	0.0449729i
$737$			55.0194i			2.02667i
$738$	−25.6824	−	4.74025i	−0.945384	−	0.174491i
$739$	2.45920			0.0904632			0.0452316	−	0.998977i	$-0.485597\pi$
$739$	2.45920			0.0904632			0.0452316	+	0.998977i	$0.485597\pi$
$740$			3.13987i			0.115424i
$741$	2.85876	−	31.2388i	0.105019	−	1.14759i
$742$	−11.3375			−0.416214
$743$	30.2633			1.11025			0.555127	−	0.831765i	$-0.312670\pi$
$743$	30.2633			1.11025			0.555127	+	0.831765i	$0.312670\pi$
$744$	1.22251	−	13.3589i	0.0448196	−	0.489762i
$745$	−15.1957			−0.556726
$746$	−31.1346			−1.13992
$747$	43.6132	+	8.04976i	1.59572	+	0.294525i
$748$	11.1776			0.408692
$749$			19.3554i			0.707231i
$750$	0.157845	−	1.72484i	0.00576370	−	0.0629824i
$751$			20.4106i			0.744794i	0.928074	+	0.372397i	$0.121464\pi$
$751$			20.4106i			0.744794i	−0.928074	+	0.372397i	$0.878536\pi$
$752$			8.55477i			0.311960i
$753$	23.9440	+	2.19119i	0.872569	+	0.0798513i
$754$	27.3641			0.996540
$755$	−8.73197			−0.317789
$756$	6.70167	−	23.8640i	0.243737	−	0.867925i
$757$			14.2385i			0.517507i	0.965943	+	0.258754i	$0.0833118\pi$
$757$			14.2385i			0.517507i	−0.965943	+	0.258754i	$0.916688\pi$
$758$	21.8934			0.795205
$759$	−16.1335	+	44.4057i	−0.585608	+	1.61183i
$760$	−3.08903			−0.112051
$761$			26.2699i			0.952284i	0.879368	+	0.476142i	$0.157965\pi$
$761$			26.2699i			0.952284i	−0.879368	+	0.476142i	$0.842035\pi$
$762$	0.294424	−	3.21730i	0.0106659	−	0.116551i
$763$	−58.6529			−2.12338
$764$	−6.15903			−0.222826
$765$	−5.79771	−	1.07009i	−0.209617	−	0.0386892i
$766$		−	20.5229i		−	0.741521i
$767$		−	14.5172i		−	0.524186i
$768$	1.72484	+	0.157845i	0.0622399	+	0.00569576i
$769$		−	16.3030i		−	0.587902i	−0.955820	−	0.293951i	$-0.905030\pi$
$769$		−	16.3030i		−	0.587902i	0.955820	−	0.293951i	$-0.0949703\pi$
$770$	−27.1320			−0.977771
$771$	−2.30850	+	25.2259i	−0.0831385	+	0.908489i
$772$	−7.16580			−0.257903
$773$	−17.7749			−0.639320			−0.319660	−	0.947532i	$-0.603569\pi$
$773$	−17.7749			−0.639320			−0.319660	+	0.947532i	$0.603569\pi$
$774$	22.8868	+	4.22426i	0.822650	+	0.151838i
$775$	7.74501			0.278209
$776$	−6.65323			−0.238837
$777$	−25.8349	−	2.36422i	−0.926820	−	0.0848160i
$778$			6.78101i			0.243111i
$779$	−26.8913			−0.963482
$780$	−10.1128	−	0.925453i	−0.362097	−	0.0331365i
$781$		−	9.08910i		−	0.325234i
$782$	9.11473	+	2.39773i	0.325942	+	0.0857425i
$783$	−6.55687	+	23.3484i	−0.234324	+	0.834403i
$784$	−15.7556			−0.562701
$785$			1.95674i			0.0698392i
$786$	28.8388	+	2.63913i	1.02865	+	0.0941345i
$787$			19.0599i			0.679413i	0.940531	+	0.339707i	$0.110328\pi$
$787$			19.0599i			0.679413i	−0.940531	+	0.339707i	$0.889672\pi$
$788$			5.95934i			0.212293i
$789$	−23.6574	−	2.16495i	−0.842225	−	0.0770744i
$790$	6.19457			0.220393
$791$		−	80.3440i		−	2.85670i
$792$	−3.09706	+	16.7797i	−0.110049	+	0.596242i
$793$			13.5538i			0.481311i
$794$		−	10.4669i		−	0.371457i
$795$	−4.09944	−	0.375151i	−0.145392	−	0.0133052i
$796$			13.4932i			0.478254i
$797$	33.4483			1.18480			0.592399	−	0.805645i	$-0.298181\pi$
$797$	33.4483			1.18480			0.592399	+	0.805645i	$0.298181\pi$
$798$	2.32594	−	25.4166i	0.0823375	−	0.899737i
$799$			16.8119i			0.594764i
$800$			1.00000i			0.0353553i
$801$	21.9138	+	4.04467i	0.774287	+	0.142911i
$802$		−	6.92220i		−	0.244431i
$803$	−18.5177			−0.653474
$804$	−1.52690	+	16.6851i	−0.0538495	+	0.588436i
$805$	−22.1248	−	5.82016i	−0.779796	−	0.205134i
$806$		−	45.4093i		−	1.59947i
$807$	−4.94711	+	54.0591i	−0.174146	+	1.90297i
$808$	7.33256			0.257958
$809$		−	28.3635i		−	0.997208i	−0.866830	−	0.498604i	$-0.833846\pi$
$809$		−	28.3635i		−	0.997208i	0.866830	−	0.498604i	$-0.166154\pi$
$810$	3.21284	−	8.40700i	0.112888	−	0.295392i
$811$	−3.46425			−0.121646			−0.0608232	−	0.998149i	$-0.519373\pi$
$811$	−3.46425			−0.121646			−0.0608232	+	0.998149i	$0.519373\pi$
$812$	22.2640			0.781313
$813$	−7.92063	−	0.724839i	−0.277788	−	0.0254212i
$814$	17.8587			0.625947
$815$	10.7116			0.375213
$816$	3.38968	+	0.310200i	0.118663	+	0.0108592i
$817$	23.9641			0.838399
$818$		−	0.551195i		−	0.0192721i
$819$	15.2292	−	82.5114i	0.532153	−	2.88318i
$820$			8.70541i			0.304006i
$821$			5.03757i			0.175812i	0.996129	+	0.0879062i	$0.0280176\pi$
$821$			5.03757i			0.175812i	−0.996129	+	0.0879062i	$0.971982\pi$
$822$	1.30640	−	14.2756i	0.0455659	−	0.497918i
$823$	−8.76482			−0.305522			−0.152761	−	0.988263i	$-0.548817\pi$
$823$	−8.76482			−0.305522			−0.152761	+	0.988263i	$0.548817\pi$
$824$	9.24100			0.321925
$825$	−9.81042	−	0.897780i	−0.341555	−	0.0312567i
$826$		−	11.8115i		−	0.410975i
$827$	−35.4433			−1.23249			−0.616243	−	0.787556i	$-0.711346\pi$
$827$	−35.4433			−1.23249			−0.616243	+	0.787556i	$0.711346\pi$
$828$	−6.12495	+	13.0186i	−0.212857	+	0.452429i
$829$	36.1702			1.25624			0.628121	−	0.778116i	$-0.283824\pi$
$829$	36.1702			1.25624			0.628121	+	0.778116i	$0.283824\pi$
$830$		−	14.7833i		−	0.513136i
$831$	−24.3874	−	2.23176i	−0.845989	−	0.0774189i
$832$	5.86303			0.203264
$833$	−30.9632			−1.07281
$834$	−0.303598	+	3.31754i	−0.0105127	+	0.114877i
$835$			0.164537i			0.00569405i
$836$			17.5695i			0.607656i
$837$	38.7455	+	10.8808i	1.33924	+	0.376095i
$838$		−	29.7594i		−	1.02802i
$839$	36.2195			1.25044			0.625219	−	0.780450i	$-0.285010\pi$
$839$	36.2195			1.25044			0.625219	+	0.780450i	$0.285010\pi$
$840$	−8.22800	−	0.752968i	−0.283893	−	0.0259799i
$841$	7.21706			0.248864
$842$	−25.4818			−0.878161
$843$	10.9719	+	1.00407i	0.377891	+	0.0345819i
$844$	6.51146			0.224134
$845$	−21.3751			−0.735327
$846$	−25.2380	−	4.65822i	−0.867701	−	0.160153i
$847$			101.846i			3.49947i
$848$	2.37670			0.0816163
$849$	4.10636	−	44.8719i	0.140930	−	1.54000i
$850$			1.96521i			0.0674062i
$851$	14.5628	+	3.83091i	0.499208	+	0.131322i
$852$	0.252241	−	2.75634i	0.00864162	−	0.0944306i
$853$	30.6307			1.04878			0.524388	−	0.851479i	$-0.324294\pi$
$853$	30.6307			1.04878			0.524388	+	0.851479i	$0.324294\pi$
$854$			11.0277i			0.377360i
$855$	1.68203	−	9.11318i	0.0575243	−	0.311664i
$856$		−	4.05749i		−	0.138682i
$857$		−	46.9029i		−	1.60217i	−0.598548	−	0.801087i	$-0.704255\pi$
$857$		−	46.9029i		−	1.60217i	0.598548	−	0.801087i	$-0.295745\pi$
$858$	−5.26371	+	57.5188i	−0.179700	+	1.96366i
$859$	41.8557			1.42810			0.714049	−	0.700096i	$-0.246860\pi$
$859$	41.8557			1.42810			0.714049	+	0.700096i	$0.246860\pi$
$860$		−	7.75780i		−	0.264539i
$861$	−71.6281	−	6.55490i	−2.44108	−	0.223390i
$862$		−	25.7344i		−	0.876517i
$863$		−	36.8163i		−	1.25324i	−0.779325	−	0.626620i	$-0.784438\pi$
$863$		−	36.8163i		−	1.25324i	0.779325	−	0.626620i	$-0.215562\pi$
$864$	−1.40488	+	5.00263i	−0.0477949	+	0.170193i
$865$			4.40561i			0.149795i
$866$	−39.5558			−1.34416
$867$	−22.6609	−	2.07376i	−0.769604	−	0.0704287i
$868$		−	36.9459i		−	1.25403i
$869$		−	35.2329i		−	1.19520i
$870$	8.05022	+	0.736699i	0.272928	+	0.0249764i
$871$			56.7153i			1.92172i
$872$	12.2955			0.416377
$873$	3.62280	−	19.6282i	0.122613	−	0.664313i
$874$	−3.76889	+	14.3271i	−0.127484	+	0.484620i
$875$		−	4.77029i		−	0.161265i
$876$	−5.61562	−	0.513902i	−0.189734	−	0.0173631i
$877$	−25.1591			−0.849563			−0.424781	−	0.905296i	$-0.639649\pi$
$877$	−25.1591			−0.849563			−0.424781	+	0.905296i	$0.639649\pi$
$878$			12.4645i			0.420658i
$879$	14.5685	+	1.33321i	0.491383	+	0.0449679i
$880$	5.68772			0.191733
$881$	57.3451			1.93201			0.966003	−	0.258529i	$-0.0832378\pi$
$881$	57.3451			1.93201			0.966003	+	0.258529i	$0.0832378\pi$
$882$	8.57922	−	46.4818i	0.288877	−	1.56512i
$883$	28.7600			0.967851			0.483925	−	0.875109i	$-0.339211\pi$
$883$	28.7600			0.967851			0.483925	+	0.875109i	$0.339211\pi$
$884$	11.5221			0.387530
$885$	0.390834	−	4.27081i	0.0131377	−	0.143562i
$886$	12.1118			0.406905
$887$		−	29.1696i		−	0.979421i	−0.871885	−	0.489710i	$-0.837102\pi$
$887$		−	29.1696i		−	0.979421i	0.871885	−	0.489710i	$-0.162898\pi$
$888$	5.41579	+	0.495614i	0.181742	+	0.0166317i
$889$		−	8.89788i		−	0.298425i
$890$		−	7.42799i		−	0.248987i
$891$	−47.8166	−	18.2737i	−1.60192	−	0.612192i
$892$	6.93854			0.232319
$893$	−26.4260			−0.884312
$894$	−2.39857	+	26.2101i	−0.0802200	+	0.876598i
$895$			21.8808i			0.731394i
$896$	4.77029			0.159364
$897$	−16.6308	+	45.7745i	−0.555286	+	1.52837i
$898$	15.0035			0.500674
$899$			36.1477i			1.20559i
$900$	−2.95017	−	0.544517i	−0.0983390	−	0.0181506i
$901$	4.67072			0.155604
$902$	49.5139			1.64863
$903$	63.8312	+	5.84138i	2.12417	+	0.194389i
$904$			16.8426i			0.560176i
$905$		−	13.0668i		−	0.434355i
$906$	−1.37830	+	15.0613i	−0.0457910	+	0.500378i
$907$		−	55.0564i		−	1.82812i	−0.405583	−	0.914058i	$-0.632931\pi$
$907$		−	55.0564i		−	1.82812i	0.405583	−	0.914058i	$-0.367069\pi$
$908$	−8.24167			−0.273509
$909$	−3.99270	+	21.6323i	−0.132430	+	0.717498i
$910$	−27.9683			−0.927142
$911$	24.5235			0.812499			0.406249	−	0.913762i	$-0.366836\pi$
$911$	24.5235			0.812499			0.406249	+	0.913762i	$0.366836\pi$
$912$	−0.487590	+	5.32810i	−0.0161457	+	0.176431i
$913$	−84.0832			−2.78275
$914$	−1.63920			−0.0542199
$915$	−0.364899	+	3.98740i	−0.0120632	+	0.131819i
$916$			18.1323i			0.599107i
$917$	79.7577			2.63383
$918$	−2.76088	+	9.83123i	−0.0911227	+	0.324479i
$919$			3.64383i			0.120199i	0.998192	+	0.0600994i	$0.0191418\pi$
$919$			3.64383i			0.120199i	−0.998192	+	0.0600994i	$0.980858\pi$
$920$	4.63804	+	1.22009i	0.152912	+	0.0402250i
$921$	−14.6086	−	1.33688i	−0.481370	−	0.0440516i
$922$	11.3693			0.374428
$923$		−	9.36926i		−	0.308393i
$924$	−4.28267	+	46.7985i	−0.140889	+	1.53956i
$925$			3.13987i			0.103238i
$926$			33.7826i			1.11017i
$927$	−5.03188	+	27.2625i	−0.165269	+	0.895418i
$928$	−4.66722			−0.153209
$929$		−	39.8886i		−	1.30870i	−0.756191	−	0.654351i	$-0.772942\pi$
$929$		−	39.8886i		−	1.30870i	0.756191	−	0.654351i	$-0.227058\pi$
$930$	1.22251	−	13.3589i	0.0400878	−	0.438057i
$931$		−	48.6697i		−	1.59509i
$932$		−	9.01790i		−	0.295391i
$933$	2.55104	−	27.8763i	0.0835173	−	0.912629i
$934$		−	16.9801i		−	0.555607i
$935$	11.1776			0.365545
$936$	−3.19252	+	17.2969i	−0.104351	+	0.565368i
$937$			0.738216i			0.0241165i	0.999927	+	0.0120582i	$0.00383835\pi$
$937$			0.738216i			0.0241165i	−0.999927	+	0.0120582i	$0.996162\pi$
$938$			46.1448i			1.50668i
$939$	1.08399	−	11.8452i	0.0353746	−	0.386553i
$940$			8.55477i			0.279026i
$941$	−13.4338			−0.437929			−0.218965	−	0.975733i	$-0.570268\pi$
$941$	−13.4338			−0.437929			−0.218965	+	0.975733i	$0.570268\pi$
$942$	3.37508	+	0.308863i	0.109966	+	0.0100633i
$943$	40.3760	+	10.6214i	1.31482	+	0.345879i
$944$			2.47606i			0.0805888i
$945$	6.70167	−	23.8640i	0.218005	−	0.776296i
$946$	−44.1242			−1.43460
$947$		−	5.38503i		−	0.174990i	−0.996165	−	0.0874950i	$-0.972114\pi$
$947$		−	5.38503i		−	0.174990i	0.996165	−	0.0874950i	$-0.0278862\pi$
$948$	0.977784	−	10.6847i	0.0317570	−	0.347022i
$949$	−19.0884			−0.619637
$950$	−3.08903			−0.100222
$951$	2.95535	−	32.2944i	0.0958339	−	1.04722i
$952$	9.37463			0.303833
$953$	24.6835			0.799577			0.399788	−	0.916607i	$-0.369084\pi$
$953$	24.6835			0.799577			0.399788	+	0.916607i	$0.369084\pi$
$954$	−1.29415	+	7.01167i	−0.0418998	+	0.227011i
$955$	−6.15903			−0.199302
$956$		−	26.2916i		−	0.850331i
$957$	4.19014	−	45.7874i	0.135448	−	1.48010i
$958$			21.1756i			0.684154i
$959$		−	39.4810i		−	1.27491i
$960$	1.72484	+	0.157845i	0.0556691	+	0.00509444i
$961$	28.9853			0.935008
$962$	18.4092			0.593535
$963$	11.9703	+	2.20937i	0.385737	+	0.0711961i
$964$		−	6.09867i		−	0.196425i
$965$	−7.16580			−0.230675
$966$	−13.5312	+	37.2431i	−0.435358	+	1.19828i
$967$	40.9958			1.31834			0.659168	−	0.751996i	$-0.270909\pi$
$967$	40.9958			1.31834			0.659168	+	0.751996i	$0.270909\pi$
$968$		−	21.3501i		−	0.686218i
$969$	−0.958217	+	10.4708i	−0.0307824	+	0.336372i
$970$	−6.65323			−0.213622
$971$	−9.66722			−0.310236			−0.155118	−	0.987896i	$-0.549576\pi$
$971$	−9.66722			−0.310236			−0.155118	+	0.987896i	$0.549576\pi$
$972$	−13.9936	−	6.86865i	−0.448846	−	0.220312i
$973$			9.17511i			0.294141i
$974$			14.8247i			0.475015i
$975$	−10.1128	−	0.925453i	−0.323869	−	0.0296382i
$976$		−	2.31175i		−	0.0739972i
$977$	−34.0227			−1.08848			−0.544241	−	0.838929i	$-0.683182\pi$
$977$	−34.0227			−1.08848			−0.544241	+	0.838929i	$0.683182\pi$
$978$	1.69078	−	18.4759i	0.0540653	−	0.590794i
$979$	−42.2483			−1.35026
$980$	−15.7556			−0.503295
$981$	−6.69510	+	36.2737i	−0.213758	+	1.15813i
$982$	−39.8929			−1.27303
$983$	14.8967			0.475131			0.237566	−	0.971371i	$-0.423650\pi$
$983$	14.8967			0.475131			0.237566	+	0.971371i	$0.423650\pi$
$984$	15.0155	+	1.37411i	0.478676	+	0.0438050i
$985$			5.95934i			0.189880i
$986$	−9.17208			−0.292098
$987$	−70.3886	−	6.44147i	−2.24049	−	0.205034i
$988$			18.1111i			0.576191i
$989$	−35.9810	−	9.46518i	−1.14413	−	0.300975i
$990$	−3.09706	+	16.7797i	−0.0984310	+	0.533295i
$991$	−15.1230			−0.480398			−0.240199	−	0.970724i	$-0.577213\pi$
$991$	−15.1230			−0.480398			−0.240199	+	0.970724i	$0.577213\pi$
$992$			7.74501i			0.245904i
$993$	23.4389	+	2.14496i	0.743810	+	0.0680682i
$994$		−	7.62303i		−	0.241788i
$995$			13.4932i			0.427764i
$996$	−25.4989	−	2.33347i	−0.807963	−	0.0739390i
$997$	0.414730			0.0131346			0.00656731	−	0.999978i	$-0.497910\pi$
$997$	0.414730			0.0131346			0.00656731	+	0.999978i	$0.497910\pi$
$998$		−	19.4748i		−	0.616464i
$999$	−4.41113	+	15.7076i	−0.139562	+	0.496967i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	690.2.e.a.551.16	yes	16
3.2	odd	2		690.2.e.b.551.8	yes	16
23.22	odd	2		690.2.e.b.551.16	yes	16
69.68	even	2	inner	690.2.e.a.551.8	✓	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
690.2.e.a.551.8	✓	16	69.68	even	2	inner
690.2.e.a.551.16	yes	16	1.1	even	1	trivial
690.2.e.b.551.8	yes	16	3.2	odd	2
690.2.e.b.551.16	yes	16	23.22	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)

\(f(q)\)	\(=\)	\(q+1.00000i q^{2} +(1.72484 + 0.157845i) q^{3} -1.00000 q^{4} -1.00000 q^{5} +(-0.157845 + 1.72484i) q^{6} +4.77029i q^{7} -1.00000i q^{8} +(2.95017 + 0.544517i) q^{9} +O(q^{10})\)	\(q+1.00000i q^{2} +(1.72484 + 0.157845i) q^{3} -1.00000 q^{4} -1.00000 q^{5} +(-0.157845 + 1.72484i) q^{6} +4.77029i q^{7} -1.00000i q^{8} +(2.95017 + 0.544517i) q^{9} -1.00000i q^{10} -5.68772 q^{11} +(-1.72484 - 0.157845i) q^{12} -5.86303 q^{13} -4.77029 q^{14} +(-1.72484 - 0.157845i) q^{15} +1.00000 q^{16} +1.96521 q^{17} +(-0.544517 + 2.95017i) q^{18} +3.08903i q^{19} +1.00000 q^{20} +(-0.752968 + 8.22800i) q^{21} -5.68772i q^{22} +(1.22009 - 4.63804i) q^{23} +(0.157845 - 1.72484i) q^{24} +1.00000 q^{25} -5.86303i q^{26} +(5.00263 + 1.40488i) q^{27} -4.77029i q^{28} +4.66722i q^{29} +(0.157845 - 1.72484i) q^{30} +7.74501 q^{31} +1.00000i q^{32} +(-9.81042 - 0.897780i) q^{33} +1.96521i q^{34} -4.77029i q^{35} +(-2.95017 - 0.544517i) q^{36} +3.13987i q^{37} -3.08903 q^{38} +(-10.1128 - 0.925453i) q^{39} +1.00000i q^{40} +8.70541i q^{41} +(-8.22800 - 0.752968i) q^{42} -7.75780i q^{43} +5.68772 q^{44} +(-2.95017 - 0.544517i) q^{45} +(4.63804 + 1.22009i) q^{46} +8.55477i q^{47} +(1.72484 + 0.157845i) q^{48} -15.7556 q^{49} +1.00000i q^{50} +(3.38968 + 0.310200i) q^{51} +5.86303 q^{52} +2.37670 q^{53} +(-1.40488 + 5.00263i) q^{54} +5.68772 q^{55} +4.77029 q^{56} +(-0.487590 + 5.32810i) q^{57} -4.66722 q^{58} +2.47606i q^{59} +(1.72484 + 0.157845i) q^{60} -2.31175i q^{61} +7.74501i q^{62} +(-2.59750 + 14.0732i) q^{63} -1.00000 q^{64} +5.86303 q^{65} +(0.897780 - 9.81042i) q^{66} -9.67337i q^{67} -1.96521 q^{68} +(2.83655 - 7.80730i) q^{69} +4.77029 q^{70} +1.59802i q^{71} +(0.544517 - 2.95017i) q^{72} +3.25573 q^{73} -3.13987 q^{74} +(1.72484 + 0.157845i) q^{75} -3.08903i q^{76} -27.1320i q^{77} +(0.925453 - 10.1128i) q^{78} +6.19457i q^{79} -1.00000 q^{80} +(8.40700 + 3.21284i) q^{81} -8.70541 q^{82} +14.7833 q^{83} +(0.752968 - 8.22800i) q^{84} -1.96521 q^{85} +7.75780 q^{86} +(-0.736699 + 8.05022i) q^{87} +5.68772i q^{88} +7.42799 q^{89} +(0.544517 - 2.95017i) q^{90} -27.9683i q^{91} +(-1.22009 + 4.63804i) q^{92} +(13.3589 + 1.22251i) q^{93} -8.55477 q^{94} -3.08903i q^{95} +(-0.157845 + 1.72484i) q^{96} -6.65323i q^{97} -15.7556i q^{98} +(-16.7797 - 3.09706i) 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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