LMFDB - Embedded newform 690.2.e.b.551.15

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			551.15
Root			$-0.462710 + 1.66910i$ of defining polynomial
Character	$\chi$	$=$	690.551
Dual form			690.2.e.b.551.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000i q^{2} +(1.66910 + 0.462710i) q^{3} -1.00000 q^{4} +1.00000 q^{5} +(-0.462710 + 1.66910i) q^{6} +2.82123i q^{7} -1.00000i q^{8} +(2.57180 + 1.54462i) q^{9} +O(q^{10})$	\(q+1.00000i q^{2} +(1.66910 + 0.462710i) q^{3} -1.00000 q^{4} +1.00000 q^{5} +(-0.462710 + 1.66910i) q^{6} +2.82123i q^{7} -1.00000i q^{8} +(2.57180 + 1.54462i) q^{9} +1.00000i q^{10} -0.0884736 q^{11} +(-1.66910 - 0.462710i) q^{12} +5.38812 q^{13} -2.82123 q^{14} +(1.66910 + 0.462710i) q^{15} +1.00000 q^{16} -2.84233 q^{17} +(-1.54462 + 2.57180i) q^{18} -5.08924i q^{19} -1.00000 q^{20} +(-1.30541 + 4.70893i) q^{21} -0.0884736i q^{22} +(-4.45994 + 1.76321i) q^{23} +(0.462710 - 1.66910i) q^{24} +1.00000 q^{25} +5.38812i q^{26} +(3.57789 + 3.76812i) q^{27} -2.82123i q^{28} +1.48542i q^{29} +(-0.462710 + 1.66910i) q^{30} -5.56059 q^{31} +1.00000i q^{32} +(-0.147671 - 0.0409376i) q^{33} -2.84233i q^{34} +2.82123i q^{35} +(-2.57180 - 1.54462i) q^{36} +6.20488i q^{37} +5.08924 q^{38} +(8.99332 + 2.49313i) q^{39} -1.00000i q^{40} -0.519960i q^{41} +(-4.70893 - 1.30541i) q^{42} -0.907222i q^{43} +0.0884736 q^{44} +(2.57180 + 1.54462i) q^{45} +(-1.76321 - 4.45994i) q^{46} -0.0243495i q^{47} +(1.66910 + 0.462710i) q^{48} -0.959358 q^{49} +1.00000i q^{50} +(-4.74413 - 1.31517i) q^{51} -5.38812 q^{52} +10.2028 q^{53} +(-3.76812 + 3.57789i) q^{54} -0.0884736 q^{55} +2.82123 q^{56} +(2.35484 - 8.49445i) q^{57} -1.48542 q^{58} -8.85335i q^{59} +(-1.66910 - 0.462710i) q^{60} +10.4775i q^{61} -5.56059i q^{62} +(-4.35773 + 7.25565i) q^{63} -1.00000 q^{64} +5.38812 q^{65} +(0.0409376 - 0.147671i) q^{66} -3.80095i q^{67} +2.84233 q^{68} +(-8.25995 + 0.879316i) q^{69} -2.82123 q^{70} -10.9253i q^{71} +(1.54462 - 2.57180i) q^{72} -5.85816 q^{73} -6.20488 q^{74} +(1.66910 + 0.462710i) q^{75} +5.08924i q^{76} -0.249605i q^{77} +(-2.49313 + 8.99332i) q^{78} -9.17572i q^{79} +1.00000 q^{80} +(4.22831 + 7.94490i) q^{81} +0.519960 q^{82} +7.55626 q^{83} +(1.30541 - 4.70893i) q^{84} -2.84233 q^{85} +0.907222 q^{86} +(-0.687318 + 2.47932i) q^{87} +0.0884736i q^{88} -12.3408 q^{89} +(-1.54462 + 2.57180i) q^{90} +15.2011i q^{91} +(4.45994 - 1.76321i) q^{92} +(-9.28119 - 2.57294i) q^{93} +0.0243495 q^{94} -5.08924i q^{95} +(-0.462710 + 1.66910i) q^{96} -7.83418i q^{97} -0.959358i q^{98} +(-0.227536 - 0.136658i) 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} - 22 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 - 22 * 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
$3$	1.66910	+	0.462710i	0.963656	+	0.267145i
$3$	1.66910	+	0.462710i	0.963656	+	0.267145i
$4$	−1.00000			−0.500000
$5$	1.00000			0.447214
$5$	1.00000			0.447214
$6$	−0.462710	+	1.66910i	−0.188900	+	0.681408i
$7$			2.82123i			1.06633i	0.846013	+	0.533163i	$0.178997\pi$
$7$			2.82123i			1.06633i	−0.846013	+	0.533163i	$0.821003\pi$
$8$		−	1.00000i		−	0.353553i
$9$	2.57180	+	1.54462i	0.857267	+	0.514873i
$10$			1.00000i			0.316228i
$11$	−0.0884736			−0.0266758			−0.0133379	−	0.999911i	$-0.504246\pi$
$11$	−0.0884736			−0.0266758			−0.0133379	+	0.999911i	$0.504246\pi$
$12$	−1.66910	−	0.462710i	−0.481828	−	0.133573i
$13$	5.38812			1.49440			0.747198	−	0.664602i	$-0.231399\pi$
$13$	5.38812			1.49440			0.747198	+	0.664602i	$0.231399\pi$
$14$	−2.82123			−0.754006
$15$	1.66910	+	0.462710i	0.430960	+	0.119471i
$16$	1.00000			0.250000
$17$	−2.84233			−0.689365			−0.344683	−	0.938719i	$-0.612013\pi$
$17$	−2.84233			−0.689365			−0.344683	+	0.938719i	$0.612013\pi$
$18$	−1.54462	+	2.57180i	−0.364070	+	0.606179i
$19$		−	5.08924i		−	1.16755i	−0.811915	−	0.583775i	$-0.801575\pi$
$19$		−	5.08924i		−	1.16755i	0.811915	−	0.583775i	$-0.198425\pi$
$20$	−1.00000			−0.223607
$21$	−1.30541	+	4.70893i	−0.284864	+	1.02757i
$22$		−	0.0884736i		−	0.0188626i
$23$	−4.45994	+	1.76321i	−0.929963	+	0.367654i
$23$	−4.45994	+	1.76321i	−0.929963	+	0.367654i
$24$	0.462710	−	1.66910i	0.0944502	−	0.340704i
$25$	1.00000			0.200000
$26$			5.38812i			1.05670i
$27$	3.57789	+	3.76812i	0.688564	+	0.725175i
$28$		−	2.82123i		−	0.533163i
$29$			1.48542i			0.275836i	0.990444	+	0.137918i	$0.0440410\pi$
$29$			1.48542i			0.275836i	−0.990444	+	0.137918i	$0.955959\pi$
$30$	−0.462710	+	1.66910i	−0.0844788	+	0.304735i
$31$	−5.56059			−0.998712			−0.499356	−	0.866397i	$-0.666430\pi$
$31$	−5.56059			−0.998712			−0.499356	+	0.866397i	$0.666430\pi$
$32$			1.00000i			0.176777i
$33$	−0.147671	−	0.0409376i	−0.0257063	−	0.00712631i
$34$		−	2.84233i		−	0.487455i
$35$			2.82123i			0.476875i
$36$	−2.57180	−	1.54462i	−0.428633	−	0.257436i
$37$			6.20488i			1.02008i	0.860152	+	0.510038i	$0.170369\pi$
$37$			6.20488i			1.02008i	−0.860152	+	0.510038i	$0.829631\pi$
$38$	5.08924			0.825583
$39$	8.99332	+	2.49313i	1.44008	+	0.399221i
$40$		−	1.00000i		−	0.158114i
$41$		−	0.519960i		−	0.0812040i	−0.999175	−	0.0406020i	$-0.987072\pi$
$41$		−	0.519960i		−	0.0812040i	0.999175	−	0.0406020i	$-0.0129276\pi$
$42$	−4.70893	−	1.30541i	−0.726603	−	0.201429i
$43$		−	0.907222i		−	0.138350i	−0.997605	−	0.0691750i	$-0.977963\pi$
$43$		−	0.907222i		−	0.138350i	0.997605	−	0.0691750i	$-0.0220367\pi$
$44$	0.0884736			0.0133379
$45$	2.57180	+	1.54462i	0.383381	+	0.230258i
$46$	−1.76321	−	4.45994i	−0.259971	−	0.657583i
$47$		−	0.0243495i		−	0.00355174i	−0.999998	−	0.00177587i	$-0.999435\pi$
$47$		−	0.0243495i		−	0.00355174i	0.999998	−	0.00177587i	$-0.000565277\pi$
$48$	1.66910	+	0.462710i	0.240914	+	0.0667864i
$49$	−0.959358			−0.137051
$50$			1.00000i			0.141421i
$51$	−4.74413	−	1.31517i	−0.664311	−	0.184161i
$52$	−5.38812			−0.747198
$53$	10.2028			1.40147			0.700733	−	0.713424i	$-0.252857\pi$
$53$	10.2028			1.40147			0.700733	+	0.713424i	$0.252857\pi$
$54$	−3.76812	+	3.57789i	−0.512776	+	0.486889i
$55$	−0.0884736			−0.0119298
$56$	2.82123			0.377003
$57$	2.35484	−	8.49445i	0.311906	−	1.12512i
$58$	−1.48542			−0.195045
$59$		−	8.85335i		−	1.15261i	−0.817235	−	0.576304i	$-0.804494\pi$
$59$		−	8.85335i		−	1.15261i	0.817235	−	0.576304i	$-0.195506\pi$
$60$	−1.66910	−	0.462710i	−0.215480	−	0.0597355i
$61$			10.4775i			1.34150i	0.741682	+	0.670751i	$0.234028\pi$
$61$			10.4775i			1.34150i	−0.741682	+	0.670751i	$0.765972\pi$
$62$		−	5.56059i		−	0.706196i
$63$	−4.35773	+	7.25565i	−0.549022	+	0.914126i
$64$	−1.00000			−0.125000
$65$	5.38812			0.668314
$66$	0.0409376	−	0.147671i	0.00503907	−	0.0181771i
$67$		−	3.80095i		−	0.464360i	−0.972673	−	0.232180i	$-0.925414\pi$
$67$		−	3.80095i		−	0.464360i	0.972673	−	0.232180i	$-0.0745859\pi$
$68$	2.84233			0.344683
$69$	−8.25995	+	0.879316i	−0.994381	+	0.105857i
$70$	−2.82123			−0.337202
$71$		−	10.9253i		−	1.29659i	−0.761389	−	0.648295i	$-0.775482\pi$
$71$		−	10.9253i		−	1.29659i	0.761389	−	0.648295i	$-0.224518\pi$
$72$	1.54462	−	2.57180i	0.182035	−	0.303090i
$73$	−5.85816			−0.685646			−0.342823	−	0.939400i	$-0.611383\pi$
$73$	−5.85816			−0.685646			−0.342823	+	0.939400i	$0.611383\pi$
$74$	−6.20488			−0.721302
$75$	1.66910	+	0.462710i	0.192731	+	0.0534291i
$76$			5.08924i			0.583775i
$77$		−	0.249605i		−	0.0284451i
$78$	−2.49313	+	8.99332i	−0.282292	+	1.01829i
$79$		−	9.17572i		−	1.03235i	−0.856483	−	0.516175i	$-0.827356\pi$
$79$		−	9.17572i		−	1.03235i	0.856483	−	0.516175i	$-0.172644\pi$
$80$	1.00000			0.111803
$81$	4.22831	+	7.94490i	0.469812	+	0.882766i
$82$	0.519960			0.0574199
$83$	7.55626			0.829407			0.414703	−	0.909957i	$-0.363885\pi$
$83$	7.55626			0.829407			0.414703	+	0.909957i	$0.363885\pi$
$84$	1.30541	−	4.70893i	0.142432	−	0.513786i
$85$	−2.84233			−0.308293
$86$	0.907222			0.0978283
$87$	−0.687318	+	2.47932i	−0.0736883	+	0.265811i
$88$			0.0884736i			0.00943131i
$89$	−12.3408			−1.30813			−0.654063	−	0.756440i	$-0.726937\pi$
$89$	−12.3408			−1.30813			−0.654063	+	0.756440i	$0.726937\pi$
$90$	−1.54462	+	2.57180i	−0.162817	+	0.271091i
$91$			15.2011i			1.59351i
$92$	4.45994	−	1.76321i	0.464981	−	0.183827i
$93$	−9.28119	−	2.57294i	−0.962415	−	0.266801i
$94$	0.0243495			0.00251146
$95$		−	5.08924i		−	0.522145i
$96$	−0.462710	+	1.66910i	−0.0472251	+	0.170352i
$97$		−	7.83418i		−	0.795440i	−0.917507	−	0.397720i	$-0.869802\pi$
$97$		−	7.83418i		−	0.795440i	0.917507	−	0.397720i	$-0.130198\pi$
$98$		−	0.959358i		−	0.0969098i
$99$	−0.227536	−	0.136658i	−0.0228683	−	0.0137346i
$100$	−1.00000			−0.100000
$101$		−	11.3714i		−	1.13149i	−0.824579	−	0.565747i	$-0.808588\pi$
$101$		−	11.3714i		−	1.13149i	0.824579	−	0.565747i	$-0.191412\pi$
$102$	1.31517	−	4.74413i	0.130221	−	0.469739i
$103$		−	15.3014i		−	1.50770i	−0.657049	−	0.753848i	$-0.728195\pi$
$103$		−	15.3014i		−	1.50770i	0.657049	−	0.753848i	$-0.271805\pi$
$104$		−	5.38812i		−	0.528349i
$105$	−1.30541	+	4.70893i	−0.127395	+	0.459544i
$106$			10.2028i			0.990986i
$107$	2.15054			0.207901			0.103950	−	0.994582i	$-0.466852\pi$
$107$	2.15054			0.207901			0.103950	+	0.994582i	$0.466852\pi$
$108$	−3.57789	−	3.76812i	−0.344282	−	0.362588i
$109$		−	9.04331i		−	0.866192i	−0.901348	−	0.433096i	$-0.857421\pi$
$109$		−	9.04331i		−	0.866192i	0.901348	−	0.433096i	$-0.142579\pi$
$110$		−	0.0884736i		−	0.00843562i
$111$	−2.87106	+	10.3566i	−0.272509	+	0.983002i
$112$			2.82123i			0.266582i
$113$	−5.46926			−0.514505			−0.257252	−	0.966344i	$-0.582817\pi$
$113$	−5.46926			−0.514505			−0.257252	+	0.966344i	$0.582817\pi$
$114$	8.49445	+	2.35484i	0.795578	+	0.220551i
$115$	−4.45994	+	1.76321i	−0.415892	+	0.164420i
$116$		−	1.48542i		−	0.137918i
$117$	13.8572	+	8.32259i	1.28110	+	0.769424i
$118$	8.85335			0.815017
$119$		−	8.01886i		−	0.735088i
$120$	0.462710	−	1.66910i	0.0422394	−	0.152367i
$121$	−10.9922			−0.999288
$122$	−10.4775			−0.948585
$123$	0.240590	−	0.867865i	0.0216933	−	0.0782528i
$124$	5.56059			0.499356
$125$	1.00000			0.0894427
$126$	−7.25565	−	4.35773i	−0.646384	−	0.388217i
$127$	−1.22410			−0.108621			−0.0543105	−	0.998524i	$-0.517296\pi$
$127$	−1.22410			−0.108621			−0.0543105	+	0.998524i	$0.517296\pi$
$128$		−	1.00000i		−	0.0883883i
$129$	0.419780	−	1.51425i	0.0369596	−	0.133322i
$130$			5.38812i			0.472569i
$131$			17.3758i			1.51813i	0.651014	+	0.759066i	$0.274344\pi$
$131$			17.3758i			1.51813i	−0.651014	+	0.759066i	$0.725656\pi$
$132$	0.147671	+	0.0409376i	0.0128531	+	0.00356316i
$133$	14.3579			1.24499
$134$	3.80095			0.328352
$135$	3.57789	+	3.76812i	0.307935	+	0.324308i
$136$			2.84233i			0.243727i
$137$	18.2067			1.55550			0.777751	−	0.628573i	$-0.216361\pi$
$137$	18.2067			1.55550			0.777751	+	0.628573i	$0.216361\pi$
$138$	−0.879316	−	8.25995i	−0.0748523	−	0.703134i
$139$	−7.87519			−0.667965			−0.333982	−	0.942579i	$-0.608393\pi$
$139$	−7.87519			−0.667965			−0.333982	+	0.942579i	$0.608393\pi$
$140$		−	2.82123i		−	0.238438i
$141$	0.0112667	−	0.0406418i	0.000948831	−	0.00342265i
$142$	10.9253			0.916828
$143$	−0.476706			−0.0398642
$144$	2.57180	+	1.54462i	0.214317	+	0.128718i
$145$			1.48542i			0.123357i
$146$		−	5.85816i		−	0.484825i
$147$	−1.60127	−	0.443904i	−0.132070	−	0.0366126i
$148$		−	6.20488i		−	0.510038i
$149$	7.85015			0.643110			0.321555	−	0.946891i	$-0.395795\pi$
$149$	7.85015			0.643110			0.321555	+	0.946891i	$0.395795\pi$
$150$	−0.462710	+	1.66910i	−0.0377801	+	0.136282i
$151$	8.89534			0.723892			0.361946	−	0.932199i	$-0.382112\pi$
$151$	8.89534			0.723892			0.361946	+	0.932199i	$0.382112\pi$
$152$	−5.08924			−0.412792
$153$	−7.30989	−	4.39031i	−0.590970	−	0.354935i
$154$	0.249605			0.0201137
$155$	−5.56059			−0.446637
$156$	−8.99332	−	2.49313i	−0.720042	−	0.199611i
$157$		−	13.4878i		−	1.07644i	−0.842803	−	0.538222i	$-0.819096\pi$
$157$		−	13.4878i		−	1.07644i	0.842803	−	0.538222i	$-0.180904\pi$
$158$	9.17572			0.729981
$159$	17.0295	+	4.72094i	1.35053	+	0.374395i
$160$			1.00000i			0.0790569i
$161$	−4.97442	−	12.5825i	−0.392039	−	0.991643i
$162$	−7.94490	+	4.22831i	−0.624210	+	0.332207i
$163$	−7.19796			−0.563788			−0.281894	−	0.959446i	$-0.590963\pi$
$163$	−7.19796			−0.563788			−0.281894	+	0.959446i	$0.590963\pi$
$164$			0.519960i			0.0406020i
$165$	−0.147671	−	0.0409376i	−0.0114962	−	0.00318698i
$166$			7.55626i			0.586479i
$167$		−	15.7105i		−	1.21572i	−0.794045	−	0.607859i	$-0.792029\pi$
$167$		−	15.7105i		−	1.21572i	0.794045	−	0.607859i	$-0.207971\pi$
$168$	4.70893	+	1.30541i	0.363301	+	0.100715i
$169$	16.0318			1.23322
$170$		−	2.84233i		−	0.217996i
$171$	7.86093	−	13.0885i	0.601140	−	1.00090i
$172$			0.907222i			0.0691750i
$173$			0.427486i			0.0325012i	0.999868	+	0.0162506i	$0.00517295\pi$
$173$			0.427486i			0.0325012i	−0.999868	+	0.0162506i	$0.994827\pi$
$174$	−2.47932	−	0.687318i	−0.187957	−	0.0521055i
$175$			2.82123i			0.213265i
$176$	−0.0884736			−0.00666895
$177$	4.09653	−	14.7771i	0.307914	−	1.11072i
$178$		−	12.3408i		−	0.924984i
$179$		−	12.9141i		−	0.965244i	−0.875829	−	0.482622i	$-0.839684\pi$
$179$		−	12.9141i		−	0.965244i	0.875829	−	0.482622i	$-0.160316\pi$
$180$	−2.57180	−	1.54462i	−0.191691	−	0.115129i
$181$			24.7502i			1.83967i	0.392308	+	0.919834i	$0.371677\pi$
$181$			24.7502i			1.83967i	−0.392308	+	0.919834i	$0.628323\pi$
$182$	−15.2011			−1.12678
$183$	−4.84802	+	17.4880i	−0.358376	+	1.29275i
$184$	1.76321	+	4.45994i	0.129985	+	0.328791i
$185$			6.20488i			0.456192i
$186$	2.57294	−	9.28119i	0.188657	−	0.680530i
$187$	0.251471			0.0183894
$188$			0.0243495i			0.00177587i
$189$	−10.6307	+	10.0940i	−0.773273	+	0.734234i
$190$	5.08924			0.369212
$191$	15.4356			1.11688			0.558441	−	0.829544i	$-0.311400\pi$
$191$	15.4356			1.11688			0.558441	+	0.829544i	$0.311400\pi$
$192$	−1.66910	−	0.462710i	−0.120457	−	0.0333932i
$193$	3.49474			0.251557			0.125779	−	0.992058i	$-0.459857\pi$
$193$	3.49474			0.251557			0.125779	+	0.992058i	$0.459857\pi$
$194$	7.83418			0.562461
$195$	8.99332	+	2.49313i	0.644025	+	0.178537i
$196$	0.959358			0.0685256
$197$		−	15.4600i		−	1.10148i	−0.834677	−	0.550739i	$-0.814346\pi$
$197$		−	15.4600i		−	1.10148i	0.834677	−	0.550739i	$-0.185654\pi$
$198$	0.136658	−	0.227536i	0.00971185	−	0.0161703i
$199$			1.10416i			0.0782715i	0.999234	+	0.0391357i	$0.0124605\pi$
$199$			1.10416i			0.0782715i	−0.999234	+	0.0391357i	$0.987540\pi$
$200$		−	1.00000i		−	0.0707107i
$201$	1.75874	−	6.34417i	0.124052	−	0.447483i
$202$	11.3714			0.800087
$203$	−4.19072			−0.294131
$204$	4.74413	+	1.31517i	0.332156	+	0.0920804i
$205$		−	0.519960i		−	0.0363155i
$206$	15.3014			1.06610
$207$	−14.1936	−	2.35429i	−0.986521	−	0.163635i
$208$	5.38812			0.373599
$209$			0.450263i			0.0311453i
$210$	−4.70893	−	1.30541i	−0.324947	−	0.0900820i
$211$	−27.0611			−1.86297			−0.931483	−	0.363785i	$-0.881484\pi$
$211$	−27.0611			−1.86297			−0.931483	+	0.363785i	$0.881484\pi$
$212$	−10.2028			−0.700733
$213$	5.05523	−	18.2354i	0.346378	−	1.24947i
$214$			2.15054i			0.147008i
$215$		−	0.907222i		−	0.0618720i
$216$	3.76812	−	3.57789i	0.256388	−	0.243444i
$217$		−	15.6877i		−	1.06495i
$218$	9.04331			0.612490
$219$	−9.77787	−	2.71063i	−0.660727	−	0.183167i
$220$	0.0884736			0.00596489
$221$	−15.3148			−1.03018
$222$	−10.3566	−	2.87106i	−0.695088	−	0.192693i
$223$	−9.23318			−0.618299			−0.309150	−	0.951013i	$-0.600044\pi$
$223$	−9.23318			−0.618299			−0.309150	+	0.951013i	$0.600044\pi$
$224$	−2.82123			−0.188502
$225$	2.57180	+	1.54462i	0.171453	+	0.102975i
$226$		−	5.46926i		−	0.363810i
$227$	14.7794			0.980945			0.490473	−	0.871457i	$-0.336824\pi$
$227$	14.7794			0.980945			0.490473	+	0.871457i	$0.336824\pi$
$228$	−2.35484	+	8.49445i	−0.155953	+	0.562559i
$229$			26.9323i			1.77974i	0.456216	+	0.889869i	$0.349204\pi$
$229$			26.9323i			1.77974i	−0.456216	+	0.889869i	$0.650796\pi$
$230$	−1.76321	−	4.45994i	−0.116263	−	0.294080i
$231$	0.115494	−	0.416615i	0.00759897	−	0.0274113i
$232$	1.48542			0.0975226
$233$		−	18.5217i		−	1.21340i	−0.794932	−	0.606698i	$-0.792494\pi$
$233$		−	18.5217i		−	1.21340i	0.794932	−	0.606698i	$-0.207506\pi$
$234$	−8.32259	+	13.8572i	−0.544065	+	0.905871i
$235$		−	0.0243495i		−	0.00158839i
$236$			8.85335i			0.576304i
$237$	4.24569	−	15.3152i	0.275787	−	0.994830i
$238$	8.01886			0.519786
$239$			23.2974i			1.50698i	0.657457	+	0.753492i	$0.271632\pi$
$239$			23.2974i			1.50698i	−0.657457	+	0.753492i	$0.728368\pi$
$240$	1.66910	+	0.462710i	0.107740	+	0.0298678i
$241$			10.7446i			0.692122i	0.938212	+	0.346061i	$0.112481\pi$
$241$			10.7446i			0.692122i	−0.938212	+	0.346061i	$0.887519\pi$
$242$		−	10.9922i		−	0.706604i
$243$	3.38130	+	15.2173i	0.216910	+	0.976192i
$244$		−	10.4775i		−	0.670751i
$245$	−0.959358			−0.0612911
$246$	0.867865	+	0.240590i	0.0553331	+	0.0153395i
$247$		−	27.4214i		−	1.74478i
$248$			5.56059i			0.353098i
$249$	12.6122	+	3.49635i	0.799263	+	0.221572i
$250$			1.00000i			0.0632456i
$251$	10.1577			0.641147			0.320573	−	0.947224i	$-0.396124\pi$
$251$	10.1577			0.641147			0.320573	+	0.947224i	$0.396124\pi$
$252$	4.35773	−	7.25565i	0.274511	−	0.457063i
$253$	0.394587	−	0.155997i	0.0248075	−	0.00980747i
$254$		−	1.22410i		−	0.0768067i
$255$	−4.74413	−	1.31517i	−0.297089	−	0.0823592i
$256$	1.00000			0.0625000
$257$			14.7723i			0.921468i	0.887538	+	0.460734i	$0.152414\pi$
$257$			14.7723i			0.921468i	−0.887538	+	0.460734i	$0.847586\pi$
$258$	1.51425	+	0.419780i	0.0942728	+	0.0261344i
$259$	−17.5054			−1.08773
$260$	−5.38812			−0.334157
$261$	−2.29441	+	3.82020i	−0.142020	+	0.236465i
$262$	−17.3758			−1.07348
$263$	−24.0408			−1.48242			−0.741209	−	0.671275i	$-0.765747\pi$
$263$	−24.0408			−1.48242			−0.741209	+	0.671275i	$0.765747\pi$
$264$	−0.0409376	+	0.147671i	−0.00251953	+	0.00908854i
$265$	10.2028			0.626754
$266$			14.3579i			0.880341i
$267$	−20.5981	−	5.71022i	−1.26058	−	0.349460i
$268$			3.80095i			0.232180i
$269$		−	4.74366i		−	0.289226i	−0.989488	−	0.144613i	$-0.953806\pi$
$269$		−	4.74366i		−	0.289226i	0.989488	−	0.144613i	$-0.0461937\pi$
$270$	−3.76812	+	3.57789i	−0.229321	+	0.217743i
$271$	−0.303443			−0.0184329			−0.00921643	−	0.999958i	$-0.502934\pi$
$271$	−0.303443			−0.0184329			−0.00921643	+	0.999958i	$0.502934\pi$
$272$	−2.84233			−0.172341
$273$	−7.03372	+	25.3723i	−0.425700	+	1.53560i
$274$			18.2067i			1.09991i
$275$	−0.0884736			−0.00533516
$276$	8.25995	−	0.879316i	0.497191	−	0.0529286i
$277$	23.1558			1.39129			0.695647	−	0.718383i	$-0.255118\pi$
$277$	23.1558			1.39129			0.695647	+	0.718383i	$0.255118\pi$
$278$		−	7.87519i		−	0.472322i
$279$	−14.3007	−	8.58899i	−0.856162	−	0.514210i
$280$	2.82123			0.168601
$281$	−1.79749			−0.107229			−0.0536146	−	0.998562i	$-0.517074\pi$
$281$	−1.79749			−0.107229			−0.0536146	+	0.998562i	$0.517074\pi$
$282$	0.0406418	+	0.0112667i	0.00242018	+	0.000670925i
$283$		−	25.5875i		−	1.52102i	−0.649328	−	0.760509i	$-0.724950\pi$
$283$		−	25.5875i		−	1.52102i	0.649328	−	0.760509i	$-0.275050\pi$
$284$			10.9253i			0.648295i
$285$	2.35484	−	8.49445i	0.139489	−	0.503168i
$286$		−	0.476706i		−	0.0281882i
$287$	1.46693			0.0865900
$288$	−1.54462	+	2.57180i	−0.0910175	+	0.151545i
$289$	−8.92119			−0.524776
$290$	−1.48542			−0.0872269
$291$	3.62495	−	13.0760i	0.212498	−	0.766531i
$292$	5.85816			0.342823
$293$	24.0774			1.40662			0.703308	−	0.710885i	$-0.251705\pi$
$293$	24.0774			1.40662			0.703308	+	0.710885i	$0.251705\pi$
$294$	0.443904	−	1.60127i	0.0258890	−	0.0933877i
$295$		−	8.85335i		−	0.515462i
$296$	6.20488			0.360651
$297$	−0.316548	−	0.333379i	−0.0183680	−	0.0193446i
$298$			7.85015i			0.454747i
$299$	−24.0307	+	9.50038i	−1.38973	+	0.549421i
$300$	−1.66910	−	0.462710i	−0.0963656	−	0.0267145i
$301$	2.55949			0.147526
$302$			8.89534i			0.511869i
$303$	5.26164	−	18.9800i	0.302273	−	1.09037i
$304$		−	5.08924i		−	0.291888i
$305$			10.4775i			0.599938i
$306$	4.39031	−	7.30989i	0.250977	−	0.417879i
$307$	−18.5284			−1.05747			−0.528735	−	0.848787i	$-0.677333\pi$
$307$	−18.5284			−1.05747			−0.528735	+	0.848787i	$0.677333\pi$
$308$			0.249605i			0.0142225i
$309$	7.08013	−	25.5397i	0.402774	−	1.45290i
$310$		−	5.56059i		−	0.315820i
$311$			29.6815i			1.68308i	0.540193	+	0.841541i	$0.318351\pi$
$311$			29.6815i			1.68308i	−0.540193	+	0.841541i	$0.681649\pi$
$312$	2.49313	−	8.99332i	0.141146	−	0.509146i
$313$		−	8.20686i		−	0.463879i	−0.972730	−	0.231939i	$-0.925493\pi$
$313$		−	8.20686i		−	0.463879i	0.972730	−	0.231939i	$-0.0745071\pi$
$314$	13.4878			0.761161
$315$	−4.35773	+	7.25565i	−0.245530	+	0.408809i
$316$			9.17572i			0.516175i
$317$			30.8326i			1.73173i	0.500274	+	0.865867i	$0.333232\pi$
$317$			30.8326i			1.73173i	−0.500274	+	0.865867i	$0.666768\pi$
$318$	−4.72094	+	17.0295i	−0.264737	+	0.954970i
$319$		−	0.131420i		−	0.00735813i
$320$	−1.00000			−0.0559017
$321$	3.58947	+	0.995077i	0.200345	+	0.0555398i
$322$	12.5825	−	4.97442i	0.701198	−	0.277214i
$323$			14.4653i			0.804869i
$324$	−4.22831	−	7.94490i	−0.234906	−	0.441383i
$325$	5.38812			0.298879
$326$		−	7.19796i		−	0.398658i
$327$	4.18443	−	15.0942i	0.231399	−	0.834711i
$328$	−0.519960			−0.0287100
$329$	0.0686956			0.00378731
$330$	0.0409376	−	0.147671i	0.00225354	−	0.00812904i
$331$	−18.1025			−0.995004			−0.497502	−	0.867463i	$-0.665749\pi$
$331$	−18.1025			−0.995004			−0.497502	+	0.867463i	$0.665749\pi$
$332$	−7.55626			−0.414703
$333$	−9.58417	+	15.9577i	−0.525209	+	0.874477i
$334$	15.7105			0.859642
$335$		−	3.80095i		−	0.207668i
$336$	−1.30541	+	4.70893i	−0.0712160	+	0.256893i
$337$			19.1719i			1.04436i	0.852835	+	0.522181i	$0.174882\pi$
$337$			19.1719i			1.04436i	−0.852835	+	0.522181i	$0.825118\pi$
$338$			16.0318i			0.872017i
$339$	−9.12875	−	2.53068i	−0.495806	−	0.137448i
$340$	2.84233			0.154147
$341$	0.491965			0.0266414
$342$	13.0885	+	7.86093i	0.707745	+	0.425070i
$343$			17.0421i			0.920185i
$344$	−0.907222			−0.0489141
$345$	−8.25995	+	0.879316i	−0.444701	+	0.0473408i
$346$	−0.427486			−0.0229818
$347$			24.7654i			1.32947i	0.747077	+	0.664737i	$0.231457\pi$
$347$			24.7654i			1.32947i	−0.747077	+	0.664737i	$0.768543\pi$
$348$	0.687318	−	2.47932i	0.0368441	−	0.132905i
$349$	29.5558			1.58209			0.791043	−	0.611760i	$-0.209538\pi$
$349$	29.5558			1.58209			0.791043	+	0.611760i	$0.209538\pi$
$350$	−2.82123			−0.150801
$351$	19.2781	+	20.3031i	1.02899	+	1.08370i
$352$		−	0.0884736i		−	0.00471566i
$353$			28.0481i			1.49285i	0.665469	+	0.746425i	$0.268231\pi$
$353$			28.0481i			1.49285i	−0.665469	+	0.746425i	$0.731769\pi$
$354$	14.7771	+	4.09653i	0.785396	+	0.217728i
$355$		−	10.9253i		−	0.579853i
$356$	12.3408			0.654063
$357$	3.71040	−	13.3843i	0.196375	−	0.708372i
$358$	12.9141			0.682531
$359$	−11.9019			−0.628160			−0.314080	−	0.949396i	$-0.601696\pi$
$359$	−11.9019			−0.628160			−0.314080	+	0.949396i	$0.601696\pi$
$360$	1.54462	−	2.57180i	0.0814085	−	0.135546i
$361$	−6.90033			−0.363175
$362$	−24.7502			−1.30084
$363$	−18.3471	−	5.08618i	−0.962970	−	0.266955i
$364$		−	15.2011i		−	0.796757i
$365$	−5.85816			−0.306630
$366$	−17.4880	−	4.84802i	−0.914110	−	0.253410i
$367$			31.6802i			1.65369i	0.562427	+	0.826847i	$0.309868\pi$
$367$			31.6802i			1.65369i	−0.562427	+	0.826847i	$0.690132\pi$
$368$	−4.45994	+	1.76321i	−0.232491	+	0.0919136i
$369$	0.803139	−	1.33723i	0.0418097	−	0.0696135i
$370$	−6.20488			−0.322576
$371$			28.7845i			1.49442i
$372$	9.28119	+	2.57294i	0.481207	+	0.133401i
$373$		−	8.32570i		−	0.431088i	−0.976494	−	0.215544i	$-0.930847\pi$
$373$		−	8.32570i		−	0.431088i	0.976494	−	0.215544i	$-0.0691525\pi$
$374$			0.251471i			0.0130032i
$375$	1.66910	+	0.462710i	0.0861920	+	0.0238942i
$376$	−0.0243495			−0.00125573
$377$			8.00363i			0.412208i
$378$	−10.0940	−	10.6307i	−0.519182	−	0.546787i
$379$			9.50248i			0.488110i	0.969761	+	0.244055i	$0.0784777\pi$
$379$			9.50248i			0.488110i	−0.969761	+	0.244055i	$0.921522\pi$
$380$			5.08924i			0.261072i
$381$	−2.04314	−	0.566402i	−0.104673	−	0.0290176i
$382$			15.4356i			0.789755i
$383$	−37.1871			−1.90017			−0.950087	−	0.311985i	$-0.899006\pi$
$383$	−37.1871			−1.90017			−0.950087	+	0.311985i	$0.899006\pi$
$384$	0.462710	−	1.66910i	0.0236125	−	0.0851760i
$385$		−	0.249605i		−	0.0127210i
$386$			3.49474i			0.177878i
$387$	1.40131	−	2.33319i	0.0712327	−	0.118603i
$388$			7.83418i			0.397720i
$389$	−18.6520			−0.945696			−0.472848	−	0.881144i	$-0.656774\pi$
$389$	−18.6520			−0.945696			−0.472848	+	0.881144i	$0.656774\pi$
$390$	−2.49313	+	8.99332i	−0.126245	+	0.455394i
$391$	12.6766	−	5.01161i	0.641084	−	0.253448i
$392$			0.959358i			0.0484549i
$393$	−8.03996	+	29.0020i	−0.405562	+	1.46296i
$394$	15.4600			0.778863
$395$		−	9.17572i		−	0.461681i
$396$	0.227536	+	0.136658i	0.0114341	+	0.00686732i
$397$	2.78953			0.140003			0.0700013	−	0.997547i	$-0.477700\pi$
$397$	2.78953			0.140003			0.0700013	+	0.997547i	$0.477700\pi$
$398$	−1.10416			−0.0553463
$399$	23.9648	+	6.64355i	1.19974	+	0.332593i
$400$	1.00000			0.0500000
$401$	−34.5221			−1.72395			−0.861976	−	0.506949i	$-0.830773\pi$
$401$	−34.5221			−1.72395			−0.861976	+	0.506949i	$0.830773\pi$
$402$	6.34417	+	1.75874i	0.316419	+	0.0877178i
$403$	−29.9611			−1.49247
$404$			11.3714i			0.565747i
$405$	4.22831	+	7.94490i	0.210106	+	0.394785i
$406$		−	4.19072i		−	0.207982i
$407$		−	0.548968i		−	0.0272113i
$408$	−1.31517	+	4.74413i	−0.0651107	+	0.234869i
$409$	−13.4130			−0.663233			−0.331616	−	0.943414i	$-0.607594\pi$
$409$	−13.4130			−0.663233			−0.331616	+	0.943414i	$0.607594\pi$
$410$	0.519960			0.0256790
$411$	30.3888	+	8.42440i	1.49897	+	0.415545i
$412$			15.3014i			0.753848i
$413$	24.9774			1.22906
$414$	2.35429	−	14.1936i	0.115707	−	0.697576i
$415$	7.55626			0.370922
$416$			5.38812i			0.264174i
$417$	−13.1445	−	3.64392i	−0.643688	−	0.178444i
$418$	−0.450263			−0.0220231
$419$	−39.6632			−1.93767			−0.968837	−	0.247698i	$-0.920326\pi$
$419$	−39.6632			−1.93767			−0.968837	+	0.247698i	$0.920326\pi$
$420$	1.30541	−	4.70893i	0.0636976	−	0.229772i
$421$		−	8.88923i		−	0.433234i	−0.976257	−	0.216617i	$-0.930498\pi$
$421$		−	8.88923i		−	0.433234i	0.976257	−	0.216617i	$-0.0695024\pi$
$422$		−	27.0611i		−	1.31732i
$423$	0.0376107	−	0.0626220i	0.00182869	−	0.00304479i
$424$		−	10.2028i		−	0.495493i
$425$	−2.84233			−0.137873
$426$	18.2354	+	5.05523i	0.883507	+	0.244926i
$427$	−29.5594			−1.43048
$428$	−2.15054			−0.103950
$429$	−0.795671	−	0.220577i	−0.0384154	−	0.0106495i
$430$	0.907222			0.0437501
$431$	40.0125			1.92733			0.963666	−	0.267110i	$-0.0860686\pi$
$431$	40.0125			1.92733			0.963666	+	0.267110i	$0.0860686\pi$
$432$	3.57789	+	3.76812i	0.172141	+	0.181294i
$433$		−	24.6079i		−	1.18258i	−0.806459	−	0.591289i	$-0.798619\pi$
$433$		−	24.6079i		−	1.18258i	0.806459	−	0.591289i	$-0.201381\pi$
$434$	15.6877			0.753035
$435$	−0.687318	+	2.47932i	−0.0329544	+	0.118874i
$436$			9.04331i			0.433096i
$437$	8.97339	+	22.6977i	0.429255	+	1.08578i
$438$	2.71063	−	9.77787i	0.129519	−	0.467205i
$439$	−28.9558			−1.38199			−0.690993	−	0.722861i	$-0.742827\pi$
$439$	−28.9558			−1.38199			−0.690993	+	0.722861i	$0.742827\pi$
$440$			0.0884736i			0.00421781i
$441$	−2.46728	−	1.48184i	−0.117489	−	0.0705639i
$442$		−	15.3148i		−	0.728450i
$443$		−	3.91361i		−	0.185941i	−0.995669	−	0.0929706i	$-0.970364\pi$
$443$		−	3.91361i		−	0.185941i	0.995669	−	0.0929706i	$-0.0296362\pi$
$444$	2.87106	−	10.3566i	0.136254	−	0.491501i
$445$	−12.3408			−0.585011
$446$		−	9.23318i		−	0.437204i
$447$	13.1027	+	3.63234i	0.619737	+	0.171804i
$448$		−	2.82123i		−	0.133291i
$449$		−	16.9735i		−	0.801029i	−0.916290	−	0.400514i	$-0.868831\pi$
$449$		−	16.9735i		−	0.801029i	0.916290	−	0.400514i	$-0.131169\pi$
$450$	−1.54462	+	2.57180i	−0.0728140	+	0.121236i
$451$			0.0460027i			0.00216618i
$452$	5.46926			0.257252
$453$	14.8472	+	4.11596i	0.697583	+	0.193385i
$454$			14.7794i			0.693633i
$455$			15.2011i			0.712641i
$456$	−8.49445	−	2.35484i	−0.397789	−	0.110275i
$457$			16.4848i			0.771129i	0.922681	+	0.385564i	$0.125993\pi$
$457$			16.4848i			0.771129i	−0.922681	+	0.385564i	$0.874007\pi$
$458$	−26.9323			−1.25846
$459$	−10.1695	−	10.7102i	−0.474672	−	0.499911i
$460$	4.45994	−	1.76321i	0.207946	−	0.0822100i
$461$		−	42.6536i		−	1.98657i	−0.115674	−	0.993287i	$-0.536903\pi$
$461$		−	42.6536i		−	1.98657i	0.115674	−	0.993287i	$-0.463097\pi$
$462$	0.416615	+	0.115494i	0.0193827	+	0.00537329i
$463$	9.52088			0.442473			0.221236	−	0.975220i	$-0.428991\pi$
$463$	9.52088			0.442473			0.221236	+	0.975220i	$0.428991\pi$
$464$			1.48542i			0.0689589i
$465$	−9.28119	−	2.57294i	−0.430405	−	0.119317i
$466$	18.5217			0.858001
$467$	18.2551			0.844744			0.422372	−	0.906423i	$-0.361198\pi$
$467$	18.2551			0.844744			0.422372	+	0.906423i	$0.361198\pi$
$468$	−13.8572	−	8.32259i	−0.640548	−	0.384712i
$469$	10.7234			0.495159
$470$	0.0243495			0.00112316
$471$	6.24094	−	22.5125i	0.287567	−	1.03732i
$472$	−8.85335			−0.407509
$473$			0.0802652i			0.00369060i
$474$	15.3152	+	4.24569i	0.703451	+	0.195011i
$475$		−	5.08924i		−	0.233510i
$476$			8.01886i			0.367544i
$477$	26.2396	+	15.7595i	1.20143	+	0.721576i
$478$	−23.2974			−1.06560
$479$	6.28781			0.287298			0.143649	−	0.989629i	$-0.454116\pi$
$479$	6.28781			0.287298			0.143649	+	0.989629i	$0.454116\pi$
$480$	−0.462710	+	1.66910i	−0.0211197	+	0.0761837i
$481$			33.4326i			1.52440i
$482$	−10.7446			−0.489404
$483$	−2.48075	−	23.3033i	−0.112878	−	1.06033i
$484$	10.9922			0.499644
$485$		−	7.83418i		−	0.355732i
$486$	−15.2173	+	3.38130i	−0.690272	+	0.153379i
$487$	−2.55380			−0.115724			−0.0578618	−	0.998325i	$-0.518428\pi$
$487$	−2.55380			−0.115724			−0.0578618	+	0.998325i	$0.518428\pi$
$488$	10.4775			0.474293
$489$	−12.0141	−	3.33057i	−0.543298	−	0.150613i
$490$		−	0.959358i		−	0.0433394i
$491$		−	16.8062i		−	0.758452i	−0.925304	−	0.379226i	$-0.876190\pi$
$491$		−	16.8062i		−	0.758452i	0.925304	−	0.379226i	$-0.123810\pi$
$492$	−0.240590	+	0.867865i	−0.0108466	+	0.0391264i
$493$		−	4.22205i		−	0.190152i
$494$	27.4214			1.23375
$495$	−0.227536	−	0.136658i	−0.0102270	−	0.00614232i
$496$	−5.56059			−0.249678
$497$	30.8227			1.38259
$498$	−3.49635	+	12.6122i	−0.156675	+	0.565164i
$499$	−9.17252			−0.410619			−0.205309	−	0.978697i	$-0.565820\pi$
$499$	−9.17252			−0.410619			−0.205309	+	0.978697i	$0.565820\pi$
$500$	−1.00000			−0.0447214
$501$	7.26941	−	26.2225i	0.324773	−	1.17153i
$502$			10.1577i			0.453359i
$503$	5.33773			0.237997			0.118999	−	0.992894i	$-0.462032\pi$
$503$	5.33773			0.237997			0.118999	+	0.992894i	$0.462032\pi$
$504$	7.25565	+	4.35773i	0.323192	+	0.194109i
$505$		−	11.3714i		−	0.506019i
$506$	0.155997	+	0.394587i	0.00693493	+	0.0175415i
$507$	26.7588	+	7.41809i	1.18840	+	0.329449i
$508$	1.22410			0.0543105
$509$			4.91462i			0.217837i	0.994051	+	0.108918i	$0.0347387\pi$
$509$			4.91462i			0.217837i	−0.994051	+	0.108918i	$0.965261\pi$
$510$	1.31517	−	4.74413i	0.0582368	−	0.210074i
$511$		−	16.5272i		−	0.731122i
$512$			1.00000i			0.0441942i
$513$	19.1769	−	18.2087i	0.846679	−	0.803934i
$514$	−14.7723			−0.651576
$515$		−	15.3014i		−	0.674262i
$516$	−0.419780	+	1.51425i	−0.0184798	+	0.0666610i
$517$			0.00215429i			9.47454e-5i
$518$		−	17.5054i		−	0.769144i
$519$	−0.197802	+	0.713518i	−0.00868255	+	0.0313200i
$520$		−	5.38812i		−	0.236285i
$521$	−39.5006			−1.73055			−0.865276	−	0.501296i	$-0.832857\pi$
$521$	−39.5006			−1.73055			−0.865276	+	0.501296i	$0.832857\pi$
$522$	−3.82020	−	2.29441i	−0.167206	−	0.100424i
$523$		−	9.23575i		−	0.403851i	−0.979401	−	0.201926i	$-0.935280\pi$
$523$		−	9.23575i		−	0.403851i	0.979401	−	0.201926i	$-0.0647199\pi$
$524$		−	17.3758i		−	0.759066i
$525$	−1.30541	+	4.70893i	−0.0569728	+	0.205514i
$526$		−	24.0408i		−	1.04823i
$527$	15.8050			0.688477
$528$	−0.147671	−	0.0409376i	−0.00642657	−	0.00178158i
$529$	16.7822	−	15.7276i	0.729661	−	0.683810i
$530$			10.2028i			0.443182i
$531$	13.6751	−	22.7691i	0.593447	−	0.988093i
$532$	−14.3579			−0.622495
$533$		−	2.80160i		−	0.121351i
$534$	5.71022	−	20.5981i	0.247105	−	0.891367i
$535$	2.15054			0.0929761
$536$	−3.80095			−0.164176
$537$	5.97547	−	21.5549i	0.257861	−	0.930164i
$538$	4.74366			0.204514
$539$	0.0848778			0.00365595
$540$	−3.57789	−	3.76812i	−0.153968	−	0.162154i
$541$	36.8369			1.58374			0.791870	−	0.610689i	$-0.209108\pi$
$541$	36.8369			1.58374			0.791870	+	0.610689i	$0.209108\pi$
$542$		−	0.303443i		−	0.0130340i
$543$	−11.4522	+	41.3106i	−0.491459	+	1.77281i
$544$		−	2.84233i		−	0.121864i
$545$		−	9.04331i		−	0.387373i
$546$	−25.3723	−	7.03372i	−1.08583	−	0.301015i
$547$	5.76966			0.246693			0.123347	−	0.992364i	$-0.460637\pi$
$547$	5.76966			0.246693			0.123347	+	0.992364i	$0.460637\pi$
$548$	−18.2067			−0.777751
$549$	−16.1837	+	26.9460i	−0.690703	+	1.15003i
$550$		−	0.0884736i		−	0.00377253i
$551$	7.55966			0.322052
$552$	0.879316	+	8.25995i	0.0374262	+	0.351567i
$553$	25.8868			1.10082
$554$			23.1558i			0.983794i
$555$	−2.87106	+	10.3566i	−0.121870	+	0.439612i
$556$	7.87519			0.333982
$557$	7.85492			0.332823			0.166412	−	0.986056i	$-0.446782\pi$
$557$	7.85492			0.332823			0.166412	+	0.986056i	$0.446782\pi$
$558$	8.58899	−	14.3007i	0.363601	−	0.605398i
$559$		−	4.88822i		−	0.206750i
$560$			2.82123i			0.119219i
$561$	0.419730	+	0.116358i	0.0177210	+	0.00491263i
$562$		−	1.79749i		−	0.0758226i
$563$	−9.90300			−0.417362			−0.208681	−	0.977984i	$-0.566917\pi$
$563$	−9.90300			−0.417362			−0.208681	+	0.977984i	$0.566917\pi$
$564$	−0.0112667	+	0.0406418i	−0.000474415	+	0.00171133i
$565$	−5.46926			−0.230094
$566$	25.5875			1.07552
$567$	−22.4144	+	11.9290i	−0.941317	+	0.500973i
$568$	−10.9253			−0.458414
$569$	7.04866			0.295495			0.147748	−	0.989025i	$-0.452798\pi$
$569$	7.04866			0.295495			0.147748	+	0.989025i	$0.452798\pi$
$570$	8.49445	+	2.35484i	0.355793	+	0.0986333i
$571$		−	31.1060i		−	1.30175i	−0.759186	−	0.650874i	$-0.774403\pi$
$571$		−	31.1060i		−	1.30175i	0.759186	−	0.650874i	$-0.225597\pi$
$572$	0.476706			0.0199321
$573$	25.7636	+	7.14221i	1.07629	+	0.298370i
$574$			1.46693i			0.0612284i
$575$	−4.45994	+	1.76321i	−0.185993	+	0.0735309i
$576$	−2.57180	−	1.54462i	−0.107158	−	0.0643591i
$577$	8.95481			0.372794			0.186397	−	0.982475i	$-0.440319\pi$
$577$	8.95481			0.372794			0.186397	+	0.982475i	$0.440319\pi$
$578$		−	8.92119i		−	0.371072i
$579$	5.83308	+	1.61705i	0.242415	+	0.0672023i
$580$		−	1.48542i		−	0.0616787i
$581$			21.3180i			0.884418i
$582$	13.0760	+	3.62495i	0.542019	+	0.150259i
$583$	−0.902680			−0.0373852
$584$			5.85816i			0.242412i
$585$	13.8572	+	8.32259i	0.572923	+	0.344097i
$586$			24.0774i			0.994628i
$587$		−	13.8103i		−	0.570014i	−0.958525	−	0.285007i	$-0.908004\pi$
$587$		−	13.8103i		−	0.570014i	0.958525	−	0.285007i	$-0.0919959\pi$
$588$	1.60127	+	0.443904i	0.0660351	+	0.0183063i
$589$			28.2992i			1.16605i
$590$	8.85335			0.364487
$591$	7.15348	−	25.8043i	0.294255	−	1.06145i
$592$			6.20488i			0.255019i
$593$		−	2.50124i		−	0.102714i	−0.998680	−	0.0513568i	$-0.983645\pi$
$593$		−	2.50124i		−	0.102714i	0.998680	−	0.0513568i	$-0.0163546\pi$
$594$	0.333379	−	0.316548i	0.0136787	−	0.0129881i
$595$		−	8.01886i		−	0.328741i
$596$	−7.85015			−0.321555
$597$	−0.510903	+	1.84295i	−0.0209099	+	0.0754268i
$598$	−9.50038	−	24.0307i	−0.388499	−	0.982689i
$599$		−	0.571210i		−	0.0233390i	−0.999932	−	0.0116695i	$-0.996285\pi$
$599$		−	0.571210i		−	0.0233390i	0.999932	−	0.0116695i	$-0.00371460\pi$
$600$	0.462710	−	1.66910i	0.0188900	−	0.0681408i
$601$	−16.9300			−0.690588			−0.345294	−	0.938494i	$-0.612221\pi$
$601$	−16.9300			−0.690588			−0.345294	+	0.938494i	$0.612221\pi$
$602$			2.55949i			0.104317i
$603$	5.87102	−	9.77529i	0.239086	−	0.398080i
$604$	−8.89534			−0.361946
$605$	−10.9922			−0.446895
$606$	18.9800	+	5.26164i	0.771009	+	0.213740i
$607$	1.41388			0.0573878			0.0286939	−	0.999588i	$-0.490865\pi$
$607$	1.41388			0.0573878			0.0286939	+	0.999588i	$0.490865\pi$
$608$	5.08924			0.206396
$609$	−6.99473	−	1.93909i	−0.283441	−	0.0785757i
$610$	−10.4775			−0.424220
$611$		−	0.131198i		−	0.00530770i
$612$	7.30989	+	4.39031i	0.295485	+	0.177468i
$613$		−	3.59479i		−	0.145192i	−0.997361	−	0.0725961i	$-0.976872\pi$
$613$		−	3.59479i		−	0.145192i	0.997361	−	0.0725961i	$-0.0231284\pi$
$614$		−	18.5284i		−	0.747744i
$615$	0.240590	−	0.867865i	0.00970153	−	0.0349957i
$616$	−0.249605			−0.0100569
$617$	−5.75072			−0.231515			−0.115758	−	0.993277i	$-0.536930\pi$
$617$	−5.75072			−0.231515			−0.115758	+	0.993277i	$0.536930\pi$
$618$	25.5397	+	7.08013i	1.02736	+	0.284804i
$619$			37.6313i			1.51253i	0.654265	+	0.756265i	$0.272978\pi$
$619$			37.6313i			1.51253i	−0.654265	+	0.756265i	$0.727022\pi$
$620$	5.56059			0.223319
$621$	−22.6011	−	10.4970i	−0.906953	−	0.421232i
$622$	−29.6815			−1.19012
$623$		−	34.8164i		−	1.39489i
$624$	8.99332	+	2.49313i	0.360021	+	0.0998053i
$625$	1.00000			0.0400000
$626$	8.20686			0.328012
$627$	−0.208341	+	0.751534i	−0.00832034	+	0.0300134i
$628$			13.4878i			0.538222i
$629$		−	17.6363i		−	0.703205i
$630$	−7.25565	−	4.35773i	−0.289072	−	0.173616i
$631$		−	18.9775i		−	0.755482i	−0.925911	−	0.377741i	$-0.876701\pi$
$631$		−	18.9775i		−	0.755482i	0.925911	−	0.377741i	$-0.123299\pi$
$632$	−9.17572			−0.364991
$633$	−45.1678	−	12.5214i	−1.79526	−	0.497683i
$634$	−30.8326			−1.22452
$635$	−1.22410			−0.0485768
$636$	−17.0295	−	4.72094i	−0.675265	−	0.187198i
$637$	−5.16914			−0.204809
$638$	0.131420			0.00520299
$639$	16.8754	−	28.0976i	0.667579	−	1.11152i
$640$		−	1.00000i		−	0.0395285i
$641$	−39.5864			−1.56357			−0.781785	−	0.623548i	$-0.785691\pi$
$641$	−39.5864			−1.56357			−0.781785	+	0.623548i	$0.785691\pi$
$642$	−0.995077	+	3.58947i	−0.0392725	+	0.141665i
$643$			8.50938i			0.335577i	0.985823	+	0.167789i	$0.0536626\pi$
$643$			8.50938i			0.335577i	−0.985823	+	0.167789i	$0.946337\pi$
$644$	4.97442	+	12.5825i	0.196020	+	0.495822i
$645$	0.419780	−	1.51425i	0.0165288	−	0.0596234i
$646$	−14.4653			−0.569128
$647$			18.9221i			0.743903i	0.928252	+	0.371951i	$0.121311\pi$
$647$			18.9221i			0.743903i	−0.928252	+	0.371951i	$0.878689\pi$
$648$	7.94490	−	4.22831i	0.312105	−	0.166104i
$649$			0.783288i			0.0307467i
$650$			5.38812i			0.211339i
$651$	7.25886	−	26.1844i	0.284497	−	1.02625i
$652$	7.19796			0.281894
$653$			10.9104i			0.426956i	0.976948	+	0.213478i	$0.0684791\pi$
$653$			10.9104i			0.426956i	−0.976948	+	0.213478i	$0.931521\pi$
$654$	15.0942	+	4.18443i	0.590230	+	0.163624i
$655$			17.3758i			0.678929i
$656$		−	0.519960i		−	0.0203010i
$657$	−15.0660	−	9.04863i	−0.587781	−	0.353021i
$658$			0.0686956i			0.00267803i
$659$	9.42907			0.367304			0.183652	−	0.982991i	$-0.441208\pi$
$659$	9.42907			0.367304			0.183652	+	0.982991i	$0.441208\pi$
$660$	0.147671	+	0.0409376i	0.00574810	+	0.00159349i
$661$		−	10.2837i		−	0.399991i	−0.979797	−	0.199995i	$-0.935907\pi$
$661$		−	10.2837i		−	0.399991i	0.979797	−	0.199995i	$-0.0640927\pi$
$662$		−	18.1025i		−	0.703574i
$663$	−25.5619	−	7.08630i	−0.992744	−	0.275209i
$664$		−	7.55626i		−	0.293240i
$665$	14.3579			0.556776
$666$	−15.9577	−	9.58417i	−0.618348	−	0.371379i
$667$	−2.61911	−	6.62489i	−0.101412	−	0.256517i
$668$			15.7105i			0.607859i
$669$	−15.4111	−	4.27228i	−0.595828	−	0.165176i
$670$	3.80095			0.146844
$671$		−	0.926979i		−	0.0357856i
$672$	−4.70893	−	1.30541i	−0.181651	−	0.0503573i
$673$	34.9603			1.34762			0.673811	−	0.738904i	$-0.264656\pi$
$673$	34.9603			1.34762			0.673811	+	0.738904i	$0.264656\pi$
$674$	−19.1719			−0.738476
$675$	3.57789	+	3.76812i	0.137713	+	0.145035i
$676$	−16.0318			−0.616609
$677$	−20.1189			−0.773231			−0.386615	−	0.922241i	$-0.626356\pi$
$677$	−20.1189			−0.773231			−0.386615	+	0.922241i	$0.626356\pi$
$678$	2.53068	−	9.12875i	0.0971902	−	0.350588i
$679$	22.1020			0.848198
$680$			2.84233i			0.108998i
$681$	24.6684	+	6.83858i	0.945294	+	0.262055i
$682$			0.491965i			0.0188383i
$683$			16.5961i			0.635030i	0.948253	+	0.317515i	$0.102848\pi$
$683$			16.5961i			0.635030i	−0.948253	+	0.317515i	$0.897152\pi$
$684$	−7.86093	+	13.0885i	−0.300570	+	0.500451i
$685$	18.2067			0.695641
$686$	−17.0421			−0.650669
$687$	−12.4618	+	44.9528i	−0.475449	+	1.71506i
$688$		−	0.907222i		−	0.0345875i
$689$	54.9740			2.09434
$690$	−0.879316	−	8.25995i	−0.0334750	−	0.314451i
$691$	−44.3960			−1.68890			−0.844452	−	0.535630i	$-0.820074\pi$
$691$	−44.3960			−1.68890			−0.844452	+	0.535630i	$0.820074\pi$
$692$		−	0.427486i		−	0.0162506i
$693$	0.385544	−	0.641933i	0.0146456	−	0.0243850i
$694$	−24.7654			−0.940081
$695$	−7.87519			−0.298723
$696$	2.47932	+	0.687318i	0.0939783	+	0.0260527i
$697$			1.47789i			0.0559792i
$698$			29.5558i			1.11870i
$699$	8.57017	−	30.9146i	0.324153	−	1.16930i
$700$		−	2.82123i		−	0.106633i
$701$	−4.03643			−0.152454			−0.0762269	−	0.997090i	$-0.524287\pi$
$701$	−4.03643			−0.152454			−0.0762269	+	0.997090i	$0.524287\pi$
$702$	−20.3031	+	19.2781i	−0.766291	+	0.727604i
$703$	31.5781			1.19099
$704$	0.0884736			0.00333447
$705$	0.0112667	−	0.0406418i	0.000424330	−	0.00153066i
$706$	−28.0481			−1.05560
$707$	32.0813			1.20654
$708$	−4.09653	+	14.7771i	−0.153957	+	0.555359i
$709$		−	32.9635i		−	1.23797i	−0.785402	−	0.618986i	$-0.787544\pi$
$709$		−	32.9635i		−	1.23797i	0.785402	−	0.618986i	$-0.212456\pi$
$710$	10.9253			0.410018
$711$	14.1730	−	23.5981i	0.531528	−	0.884998i
$712$			12.3408i			0.462492i
$713$	24.7999	−	9.80448i	0.928764	−	0.367181i
$714$	13.3843	+	3.71040i	0.500895	+	0.138858i
$715$	−0.476706			−0.0178278
$716$			12.9141i			0.482622i
$717$	−10.7799	+	38.8857i	−0.402584	+	1.45221i
$718$		−	11.9019i		−	0.444177i
$719$			9.37917i			0.349784i	0.984588	+	0.174892i	$0.0559576\pi$
$719$			9.37917i			0.349784i	−0.984588	+	0.174892i	$0.944042\pi$
$720$	2.57180	+	1.54462i	0.0958453	+	0.0575645i
$721$	43.1690			1.60770
$722$		−	6.90033i		−	0.256804i
$723$	−4.97164	+	17.9339i	−0.184897	+	0.666968i
$724$		−	24.7502i		−	0.919834i
$725$			1.48542i			0.0551671i
$726$	5.08618	−	18.3471i	0.188766	−	0.680923i
$727$			37.6346i			1.39579i	0.716199	+	0.697896i	$0.245880\pi$
$727$			37.6346i			1.39579i	−0.716199	+	0.697896i	$0.754120\pi$
$728$	15.2011			0.563392
$729$	−1.39747	+	26.9638i	−0.0517583	+	0.998660i
$730$		−	5.85816i		−	0.216820i
$731$			2.57862i			0.0953737i
$732$	4.84802	−	17.4880i	0.179188	−	0.646374i
$733$		−	48.8726i		−	1.80515i	−0.430533	−	0.902575i	$-0.641674\pi$
$733$		−	48.8726i		−	1.80515i	0.430533	−	0.902575i	$-0.358326\pi$
$734$	−31.6802			−1.16934
$735$	−1.60127	−	0.443904i	−0.0590636	−	0.0163737i
$736$	−1.76321	−	4.45994i	−0.0649927	−	0.164396i
$737$			0.336284i			0.0123872i
$738$	1.33723	+	0.803139i	0.0492242	+	0.0295640i
$739$	−4.24348			−0.156099			−0.0780495	−	0.996949i	$-0.524869\pi$
$739$	−4.24348			−0.156099			−0.0780495	+	0.996949i	$0.524869\pi$
$740$		−	6.20488i		−	0.228096i
$741$	12.6882	−	45.7691i	0.466111	−	1.68137i
$742$	−28.7845			−1.05671
$743$	13.3090			0.488261			0.244130	−	0.969742i	$-0.421498\pi$
$743$	13.3090			0.488261			0.244130	+	0.969742i	$0.421498\pi$
$744$	−2.57294	+	9.28119i	−0.0943285	+	0.340265i
$745$	7.85015			0.287607
$746$	8.32570			0.304826
$747$	19.4332	+	11.6715i	0.711023	+	0.427039i
$748$	−0.251471			−0.00919468
$749$			6.06718i			0.221690i
$750$	−0.462710	+	1.66910i	−0.0168958	+	0.0609470i
$751$			36.2427i			1.32251i	0.750159	+	0.661257i	$0.229977\pi$
$751$			36.2427i			1.32251i	−0.750159	+	0.661257i	$0.770023\pi$
$752$		−	0.0243495i		−	0.000887934i
$753$	16.9542	+	4.70005i	0.617845	+	0.171279i
$754$	−8.00363			−0.291475
$755$	8.89534			0.323735
$756$	10.6307	−	10.0940i	0.386637	−	0.367117i
$757$			38.6987i			1.40653i	0.710929	+	0.703264i	$0.248275\pi$
$757$			38.6987i			1.40653i	−0.710929	+	0.703264i	$0.751725\pi$
$758$	−9.50248			−0.345146
$759$	0.730787	−	0.0777962i	0.0265259	−	0.00282382i
$760$	−5.08924			−0.184606
$761$			33.2491i			1.20528i	0.798014	+	0.602639i	$0.205884\pi$
$761$			33.2491i			1.20528i	−0.798014	+	0.602639i	$0.794116\pi$
$762$	0.566402	−	2.04314i	0.0205186	−	0.0740153i
$763$	25.5133			0.923643
$764$	−15.4356			−0.558441
$765$	−7.30989	−	4.39031i	−0.264290	−	0.158732i
$766$		−	37.1871i		−	1.34363i
$767$		−	47.7029i		−	1.72245i
$768$	1.66910	+	0.462710i	0.0602285	+	0.0166966i
$769$			5.52635i			0.199285i	0.995023	+	0.0996426i	$0.0317700\pi$
$769$			5.52635i			0.199285i	−0.995023	+	0.0996426i	$0.968230\pi$
$770$	0.249605			0.00899512
$771$	−6.83526	+	24.6564i	−0.246166	+	0.887978i
$772$	−3.49474			−0.125779
$773$	−13.0486			−0.469327			−0.234663	−	0.972077i	$-0.575399\pi$
$773$	−13.0486			−0.469327			−0.234663	+	0.972077i	$0.575399\pi$
$774$	2.33319	+	1.40131i	0.0838649	+	0.0503691i
$775$	−5.56059			−0.199742
$776$	−7.83418			−0.281230
$777$	−29.2183	−	8.09992i	−1.04820	−	0.290583i
$778$		−	18.6520i		−	0.668708i
$779$	−2.64620			−0.0948098
$780$	−8.99332	−	2.49313i	−0.322013	−	0.0892685i
$781$			0.966597i			0.0345876i
$782$	5.01161	+	12.6766i	0.179215	+	0.453315i
$783$	−5.59724	+	5.31466i	−0.200029	+	0.189931i
$784$	−0.959358			−0.0342628
$785$		−	13.4878i		−	0.481401i
$786$	−29.0020	−	8.03996i	−1.03447	−	0.286776i
$787$			51.4300i			1.83328i	0.399714	+	0.916640i	$0.369110\pi$
$787$			51.4300i			1.83328i	−0.399714	+	0.916640i	$0.630890\pi$
$788$			15.4600i			0.550739i
$789$	−40.1265	−	11.1239i	−1.42854	−	0.396021i
$790$	9.17572			0.326457
$791$		−	15.4301i		−	0.548630i
$792$	−0.136658	+	0.227536i	−0.00485593	+	0.00808515i
$793$			56.4539i			2.00474i
$794$			2.78953i			0.0989968i
$795$	17.0295	+	4.72094i	0.603976	+	0.167435i
$796$		−	1.10416i		−	0.0391357i
$797$	18.9958			0.672867			0.336434	−	0.941707i	$-0.390779\pi$
$797$	18.9958			0.672867			0.336434	+	0.941707i	$0.390779\pi$
$798$	−6.64355	+	23.9648i	−0.235179	+	0.848346i
$799$			0.0692092i			0.00244844i
$800$			1.00000i			0.0353553i
$801$	−31.7381	−	19.0619i	−1.12141	−	0.673518i
$802$		−	34.5221i		−	1.21902i
$803$	0.518293			0.0182901
$804$	−1.75874	+	6.34417i	−0.0620258	+	0.223742i
$805$	−4.97442	−	12.5825i	−0.175325	−	0.443476i
$806$		−	29.9611i		−	1.05534i
$807$	2.19494	−	7.91765i	0.0772655	−	0.278715i
$808$	−11.3714			−0.400043
$809$		−	10.0723i		−	0.354123i	−0.984200	−	0.177061i	$-0.943341\pi$
$809$		−	10.0723i		−	0.354123i	0.984200	−	0.177061i	$-0.0566591\pi$
$810$	−7.94490	+	4.22831i	−0.279155	+	0.148568i
$811$	39.9165			1.40166			0.700829	−	0.713330i	$-0.252814\pi$
$811$	39.9165			1.40166			0.700829	+	0.713330i	$0.252814\pi$
$812$	4.19072			0.147065
$813$	−0.506478	−	0.140406i	−0.0177629	−	0.00492426i
$814$	0.548968			0.0192413
$815$	−7.19796			−0.252134
$816$	−4.74413	−	1.31517i	−0.166078	−	0.0460402i
$817$	−4.61707			−0.161531
$818$		−	13.4130i		−	0.468976i
$819$	−23.4800	+	39.0943i	−0.820457	+	1.36607i
$820$			0.519960i			0.0181578i
$821$		−	42.9606i		−	1.49934i	−0.661814	−	0.749668i	$-0.730213\pi$
$821$		−	42.9606i		−	1.49934i	0.661814	−	0.749668i	$-0.269787\pi$
$822$	−8.42440	+	30.3888i	−0.293835	+	1.05993i
$823$	−20.1098			−0.700985			−0.350493	−	0.936565i	$-0.613986\pi$
$823$	−20.1098			−0.700985			−0.350493	+	0.936565i	$0.613986\pi$
$824$	−15.3014			−0.533051
$825$	−0.147671	−	0.0409376i	−0.00514126	−	0.00142526i
$826$			24.9774i			0.869074i
$827$	−17.6733			−0.614559			−0.307280	−	0.951619i	$-0.599419\pi$
$827$	−17.6733			−0.614559			−0.307280	+	0.951619i	$0.599419\pi$
$828$	14.1936	+	2.35429i	0.493261	+	0.0818173i
$829$	−39.6740			−1.37793			−0.688967	−	0.724793i	$-0.741935\pi$
$829$	−39.6740			−1.37793			−0.688967	+	0.724793i	$0.741935\pi$
$830$			7.55626i			0.262282i
$831$	38.6493	+	10.7144i	1.34073	+	0.371678i
$832$	−5.38812			−0.186799
$833$	2.72681			0.0944783
$834$	3.64392	−	13.1445i	0.126179	−	0.455156i
$835$		−	15.7105i		−	0.543685i
$836$		−	0.450263i		−	0.0155727i
$837$	−19.8952	−	20.9530i	−0.687677	−	0.724241i
$838$		−	39.6632i		−	1.37014i
$839$	31.0921			1.07342			0.536710	−	0.843767i	$-0.319667\pi$
$839$	31.0921			1.07342			0.536710	+	0.843767i	$0.319667\pi$
$840$	4.70893	+	1.30541i	0.162473	+	0.0450410i
$841$	26.7935			0.923915
$842$	8.88923			0.306343
$843$	−3.00019	−	0.831716i	−0.103332	−	0.0286458i
$844$	27.0611			0.931483
$845$	16.0318			0.551512
$846$	0.0626220	+	0.0376107i	0.00215299	+	0.00129308i
$847$		−	31.0115i		−	1.06557i
$848$	10.2028			0.350366
$849$	11.8396	−	42.7081i	0.406333	−	1.46574i
$850$		−	2.84233i		−	0.0974910i
$851$	−10.9405	−	27.6734i	−0.375035	−	0.948632i
$852$	−5.05523	+	18.2354i	−0.173189	+	0.624734i
$853$	16.9564			0.580578			0.290289	−	0.956939i	$-0.406249\pi$
$853$	16.9564			0.580578			0.290289	+	0.956939i	$0.406249\pi$
$854$		−	29.5594i		−	1.01150i
$855$	7.86093	−	13.0885i	0.268838	−	0.447617i
$856$		−	2.15054i		−	0.0735040i
$857$		−	41.8620i		−	1.42998i	−0.699135	−	0.714990i	$-0.746431\pi$
$857$		−	41.8620i		−	1.42998i	0.699135	−	0.714990i	$-0.253569\pi$
$858$	0.220577	−	0.795671i	0.00753036	−	0.0271638i
$859$	−8.38489			−0.286089			−0.143044	−	0.989716i	$-0.545689\pi$
$859$	−8.38489			−0.286089			−0.143044	+	0.989716i	$0.545689\pi$
$860$			0.907222i			0.0309360i
$861$	2.44845	+	0.678761i	0.0834430	+	0.0231321i
$862$			40.0125i			1.36283i
$863$		−	11.9040i		−	0.405216i	−0.979260	−	0.202608i	$-0.935058\pi$
$863$		−	11.9040i		−	0.405216i	0.979260	−	0.202608i	$-0.0649416\pi$
$864$	−3.76812	+	3.57789i	−0.128194	+	0.121722i
$865$			0.427486i			0.0145350i
$866$	24.6079			0.836209
$867$	−14.8904	−	4.12792i	−0.505703	−	0.140191i
$868$			15.6877i			0.532476i
$869$			0.811809i			0.0275387i
$870$	−2.47932	−	0.687318i	−0.0840567	−	0.0233023i
$871$		−	20.4800i		−	0.693938i
$872$	−9.04331			−0.306245
$873$	12.1008	−	20.1479i	0.409550	−	0.681904i
$874$	−22.6977	+	8.97339i	−0.767761	+	0.303529i
$875$			2.82123i			0.0953751i
$876$	9.77787	+	2.71063i	0.330364	+	0.0915836i
$877$	12.2166			0.412524			0.206262	−	0.978497i	$-0.433870\pi$
$877$	12.2166			0.412524			0.206262	+	0.978497i	$0.433870\pi$
$878$		−	28.9558i		−	0.977212i
$879$	40.1876	+	11.1408i	1.35549	+	0.375771i
$880$	−0.0884736			−0.00298244
$881$	−24.0770			−0.811174			−0.405587	−	0.914056i	$-0.632933\pi$
$881$	−24.0770			−0.811174			−0.405587	+	0.914056i	$0.632933\pi$
$882$	1.48184	−	2.46728i	0.0498962	−	0.0830775i
$883$	0.670650			0.0225692			0.0112846	−	0.999936i	$-0.496408\pi$
$883$	0.670650			0.0225692			0.0112846	+	0.999936i	$0.496408\pi$
$884$	15.3148			0.515092
$885$	4.09653	−	14.7771i	0.137703	−	0.496728i
$886$	3.91361			0.131480
$887$			49.6106i			1.66576i	0.553453	+	0.832880i	$0.313310\pi$
$887$			49.6106i			1.66576i	−0.553453	+	0.832880i	$0.686690\pi$
$888$	10.3566	+	2.87106i	0.347544	+	0.0963463i
$889$		−	3.45346i		−	0.115825i
$890$		−	12.3408i		−	0.413666i
$891$	−0.374093	−	0.702913i	−0.0125326	−	0.0235485i
$892$	9.23318			0.309150
$893$	−0.123920			−0.00414683
$894$	−3.63234	+	13.1027i	−0.121484	+	0.438220i
$895$		−	12.9141i		−	0.431670i
$896$	2.82123			0.0942508
$897$	−44.5056	+	4.73786i	−1.48600	+	0.158192i
$898$	16.9735			0.566413
$899$		−	8.25982i		−	0.275480i
$900$	−2.57180	−	1.54462i	−0.0857267	−	0.0514873i
$901$	−28.9997			−0.966122
$902$	−0.0460027			−0.00153172
$903$	4.27204	+	1.18430i	0.142165	+	0.0394110i
$904$			5.46926i			0.181905i
$905$			24.7502i			0.822724i
$906$	−4.11596	+	14.8472i	−0.136744	+	0.493266i
$907$		−	6.74337i		−	0.223910i	−0.993713	−	0.111955i	$-0.964289\pi$
$907$		−	6.74337i		−	0.223910i	0.993713	−	0.111955i	$-0.0357112\pi$
$908$	−14.7794			−0.490473
$909$	17.5644	−	29.2449i	0.582575	−	0.969992i
$910$	−15.2011			−0.503913
$911$	−22.2997			−0.738821			−0.369411	−	0.929266i	$-0.620440\pi$
$911$	−22.2997			−0.738821			−0.369411	+	0.929266i	$0.620440\pi$
$912$	2.35484	−	8.49445i	0.0779765	−	0.281279i
$913$	−0.668529			−0.0221251
$914$	−16.4848			−0.545270
$915$	−4.84802	+	17.4880i	−0.160271	+	0.578134i
$916$		−	26.9323i		−	0.889869i
$917$	−49.0212			−1.61882
$918$	10.7102	−	10.1695i	0.353490	−	0.335644i
$919$			31.6892i			1.04533i	0.852538	+	0.522665i	$0.175062\pi$
$919$			31.6892i			1.04533i	−0.852538	+	0.522665i	$0.824938\pi$
$920$	1.76321	+	4.45994i	0.0581313	+	0.147040i
$921$	−30.9257	−	8.57325i	−1.01904	−	0.282498i
$922$	42.6536			1.40472
$923$		−	58.8667i		−	1.93762i
$924$	−0.115494	+	0.416615i	−0.00379949	+	0.0137056i
$925$			6.20488i			0.204015i
$926$			9.52088i			0.312875i
$927$	23.6349	−	39.3523i	0.776272	−	1.29250i
$928$	−1.48542			−0.0487613
$929$			29.0730i			0.953854i	0.878943	+	0.476927i	$0.158249\pi$
$929$			29.0730i			0.953854i	−0.878943	+	0.476927i	$0.841751\pi$
$930$	2.57294	−	9.28119i	0.0843700	−	0.304342i
$931$			4.88240i			0.160014i
$932$			18.5217i			0.606698i
$933$	−13.7339	+	49.5414i	−0.449628	+	1.62191i
$934$			18.2551i			0.597324i
$935$	0.251471			0.00822397
$936$	8.32259	−	13.8572i	0.272032	−	0.452936i
$937$			24.2016i			0.790630i	0.918546	+	0.395315i	$0.129365\pi$
$937$			24.2016i			0.790630i	−0.918546	+	0.395315i	$0.870635\pi$
$938$			10.7234i			0.350130i
$939$	3.79739	−	13.6981i	0.123923	−	0.447020i
$940$			0.0243495i			0.000794193i
$941$	−21.2153			−0.691598			−0.345799	−	0.938309i	$-0.612392\pi$
$941$	−21.2153			−0.691598			−0.345799	+	0.938309i	$0.612392\pi$
$942$	22.5125	+	6.24094i	0.733498	+	0.203341i
$943$	0.916797	+	2.31899i	0.0298550	+	0.0755167i
$944$		−	8.85335i		−	0.288152i
$945$	−10.6307	+	10.0940i	−0.345818	+	0.328359i
$946$	−0.0802652			−0.00260965
$947$			39.0946i			1.27041i	0.772346	+	0.635203i	$0.219083\pi$
$947$			39.0946i			1.27041i	−0.772346	+	0.635203i	$0.780917\pi$
$948$	−4.24569	+	15.3152i	−0.137894	+	0.497415i
$949$	−31.5645			−1.02463
$950$	5.08924			0.165117
$951$	−14.2666	+	51.4628i	−0.462625	+	1.66880i
$952$	−8.01886			−0.259893
$953$	20.2089			0.654631			0.327316	−	0.944915i	$-0.393856\pi$
$953$	20.2089			0.654631			0.327316	+	0.944915i	$0.393856\pi$
$954$	−15.7595	+	26.2396i	−0.510232	+	0.849539i
$955$	15.4356			0.499485
$956$		−	23.2974i		−	0.753492i
$957$	0.0608095	−	0.219354i	0.00196569	−	0.00709071i
$958$			6.28781i			0.203150i
$959$			51.3653i			1.65867i
$960$	−1.66910	−	0.462710i	−0.0538700	−	0.0149339i
$961$	−0.0798189			−0.00257480
$962$	−33.4326			−1.07791
$963$	5.53076	+	3.32177i	0.178226	+	0.107042i
$964$		−	10.7446i		−	0.346061i
$965$	3.49474			0.112500
$966$	23.3033	−	2.48075i	0.749770	−	0.0798170i
$967$	47.2295			1.51880			0.759398	−	0.650626i	$-0.225493\pi$
$967$	47.2295			1.51880			0.759398	+	0.650626i	$0.225493\pi$
$968$			10.9922i			0.353302i
$969$	−6.69322	+	24.1440i	−0.215017	+	0.775617i
$970$	7.83418			0.251540
$971$	14.3487			0.460470			0.230235	−	0.973135i	$-0.426050\pi$
$971$	14.3487			0.460470			0.230235	+	0.973135i	$0.426050\pi$
$972$	−3.38130	−	15.2173i	−0.108455	−	0.488096i
$973$		−	22.2177i		−	0.712268i
$974$		−	2.55380i		−	0.0818290i
$975$	8.99332	+	2.49313i	0.288017	+	0.0798442i
$976$			10.4775i			0.335376i
$977$	−23.8210			−0.762101			−0.381051	−	0.924554i	$-0.624438\pi$
$977$	−23.8210			−0.762101			−0.381051	+	0.924554i	$0.624438\pi$
$978$	3.33057	−	12.0141i	0.106500	−	0.384170i
$979$	1.09184			0.0348953
$980$	0.959358			0.0306456
$981$	13.9685	−	23.2576i	0.445979	−	0.742557i
$982$	16.8062			0.536306
$983$	24.6498			0.786207			0.393104	−	0.919494i	$-0.371401\pi$
$983$	24.6498			0.786207			0.393104	+	0.919494i	$0.371401\pi$
$984$	−0.867865	−	0.240590i	−0.0276665	−	0.00766974i
$985$		−	15.4600i		−	0.492596i
$986$	4.22205			0.134457
$987$	0.114660	+	0.0317861i	0.00364967	+	0.00101176i
$988$			27.4214i			0.872392i
$989$	1.59962	+	4.04616i	0.0508650	+	0.128660i
$990$	0.136658	−	0.227536i	0.00434327	−	0.00723158i
$991$	41.1146			1.30605			0.653024	−	0.757337i	$-0.273500\pi$
$991$	41.1146			1.30605			0.653024	+	0.757337i	$0.273500\pi$
$992$		−	5.56059i		−	0.176549i
$993$	−30.2149	−	8.37620i	−0.958841	−	0.265811i
$994$			30.8227i			0.977638i
$995$			1.10416i			0.0350041i
$996$	−12.6122	−	3.49635i	−0.399632	−	0.110786i
$997$	−40.8555			−1.29391			−0.646953	−	0.762530i	$-0.723957\pi$
$997$	−40.8555			−1.29391			−0.646953	+	0.762530i	$0.723957\pi$
$998$		−	9.17252i		−	0.290351i
$999$	−23.3807	+	22.2003i	−0.739734	+	0.702388i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	690.2.e.b.551.15	yes	16
3.2	odd	2		690.2.e.a.551.7	✓	16
23.22	odd	2		690.2.e.a.551.15	yes	16
69.68	even	2	inner	690.2.e.b.551.7	yes	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
690.2.e.a.551.7	✓	16	3.2	odd	2
690.2.e.a.551.15	yes	16	23.22	odd	2
690.2.e.b.551.7	yes	16	69.68	even	2	inner
690.2.e.b.551.15	yes	16	1.1	even	1	trivial

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)

\(f(q)\)	\(=\)	\(q+1.00000i q^{2} +(1.66910 + 0.462710i) q^{3} -1.00000 q^{4} +1.00000 q^{5} +(-0.462710 + 1.66910i) q^{6} +2.82123i q^{7} -1.00000i q^{8} +(2.57180 + 1.54462i) q^{9} +O(q^{10})\)	\(q+1.00000i q^{2} +(1.66910 + 0.462710i) q^{3} -1.00000 q^{4} +1.00000 q^{5} +(-0.462710 + 1.66910i) q^{6} +2.82123i q^{7} -1.00000i q^{8} +(2.57180 + 1.54462i) q^{9} +1.00000i q^{10} -0.0884736 q^{11} +(-1.66910 - 0.462710i) q^{12} +5.38812 q^{13} -2.82123 q^{14} +(1.66910 + 0.462710i) q^{15} +1.00000 q^{16} -2.84233 q^{17} +(-1.54462 + 2.57180i) q^{18} -5.08924i q^{19} -1.00000 q^{20} +(-1.30541 + 4.70893i) q^{21} -0.0884736i q^{22} +(-4.45994 + 1.76321i) q^{23} +(0.462710 - 1.66910i) q^{24} +1.00000 q^{25} +5.38812i q^{26} +(3.57789 + 3.76812i) q^{27} -2.82123i q^{28} +1.48542i q^{29} +(-0.462710 + 1.66910i) q^{30} -5.56059 q^{31} +1.00000i q^{32} +(-0.147671 - 0.0409376i) q^{33} -2.84233i q^{34} +2.82123i q^{35} +(-2.57180 - 1.54462i) q^{36} +6.20488i q^{37} +5.08924 q^{38} +(8.99332 + 2.49313i) q^{39} -1.00000i q^{40} -0.519960i q^{41} +(-4.70893 - 1.30541i) q^{42} -0.907222i q^{43} +0.0884736 q^{44} +(2.57180 + 1.54462i) q^{45} +(-1.76321 - 4.45994i) q^{46} -0.0243495i q^{47} +(1.66910 + 0.462710i) q^{48} -0.959358 q^{49} +1.00000i q^{50} +(-4.74413 - 1.31517i) q^{51} -5.38812 q^{52} +10.2028 q^{53} +(-3.76812 + 3.57789i) q^{54} -0.0884736 q^{55} +2.82123 q^{56} +(2.35484 - 8.49445i) q^{57} -1.48542 q^{58} -8.85335i q^{59} +(-1.66910 - 0.462710i) q^{60} +10.4775i q^{61} -5.56059i q^{62} +(-4.35773 + 7.25565i) q^{63} -1.00000 q^{64} +5.38812 q^{65} +(0.0409376 - 0.147671i) q^{66} -3.80095i q^{67} +2.84233 q^{68} +(-8.25995 + 0.879316i) q^{69} -2.82123 q^{70} -10.9253i q^{71} +(1.54462 - 2.57180i) q^{72} -5.85816 q^{73} -6.20488 q^{74} +(1.66910 + 0.462710i) q^{75} +5.08924i q^{76} -0.249605i q^{77} +(-2.49313 + 8.99332i) q^{78} -9.17572i q^{79} +1.00000 q^{80} +(4.22831 + 7.94490i) q^{81} +0.519960 q^{82} +7.55626 q^{83} +(1.30541 - 4.70893i) q^{84} -2.84233 q^{85} +0.907222 q^{86} +(-0.687318 + 2.47932i) q^{87} +0.0884736i q^{88} -12.3408 q^{89} +(-1.54462 + 2.57180i) q^{90} +15.2011i q^{91} +(4.45994 - 1.76321i) q^{92} +(-9.28119 - 2.57294i) q^{93} +0.0243495 q^{94} -5.08924i q^{95} +(-0.462710 + 1.66910i) q^{96} -7.83418i q^{97} -0.959358i q^{98} +(-0.227536 - 0.136658i) 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	\( 16 q - 16 q^{4} + 16 q^{5} + 2 q^{6} + 2 q^{9} + 12 q^{11} + 12 q^{14} + 16 q^{16} + 8 q^{18} - 16 q^{20} + 4 q^{21} - 4 q^{23} - 2 q^{24} + 16 q^{25} + 24 q^{27} + 2 q^{30} + 4 q^{31} + 28 q^{33} - 2 q^{36} + 16 q^{38} - 8 q^{39} - 12 q^{44} + 2 q^{45} - 4 q^{46} - 4 q^{49} + 2 q^{51} + 8 q^{53} - 26 q^{54} + 12 q^{55} - 12 q^{56} - 28 q^{57} - 8 q^{58} - 16 q^{64} - 10 q^{66} - 22 q^{69} + 12 q^{70} - 8 q^{72} - 16 q^{73} + 24 q^{74} - 12 q^{78} + 16 q^{80} + 22 q^{81} - 16 q^{82} + 40 q^{83} - 4 q^{84} + 40 q^{86} + 20 q^{87} - 80 q^{89} + 8 q^{90} + 4 q^{92} - 4 q^{93} - 24 q^{94} + 2 q^{96} + 8 q^{99}+O(q^{100}) \) 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 - 22 * 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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