LMFDB - Embedded newform 690.2.e.a.551.7

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

$q$-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} +(6.62825 - 5.00663i) 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} + 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
$3$	1.66910	−	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	$-0.495754\pi$
$11$	0.0884736			0.0266758			0.0133379	+	0.999911i	$0.495754\pi$
$12$	−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	$-0.387987\pi$
$17$	2.84233			0.689365			0.344683	+	0.938719i	$0.387987\pi$
$18$	−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	$-0.955959\pi$
$29$		−	1.48542i		−	0.275836i	0.990444	−	0.137918i	$-0.0440410\pi$
$30$	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	$0.0129276\pi$
$41$			0.519960i			0.0812040i	−0.999175	+	0.0406020i	$0.987072\pi$
$42$	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	$0.000565277\pi$
$47$			0.0243495i			0.00355174i	−0.999998	+	0.00177587i	$0.999435\pi$
$48$	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	$-0.747143\pi$
$53$	−10.2028			−1.40147			−0.700733	+	0.713424i	$0.747143\pi$
$54$	−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	$0.195506\pi$
$59$			8.85335i			1.15261i	−0.817235	+	0.576304i	$0.804494\pi$
$60$	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
$69$	6.62825	−	5.00663i	0.797947	−	0.602728i
$70$	−2.82123			−0.337202
$71$			10.9253i			1.29659i	0.761389	+	0.648295i	$0.224518\pi$
$71$			10.9253i			1.29659i	−0.761389	+	0.648295i	$0.775482\pi$
$72$	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	$-0.636115\pi$
$83$	−7.55626			−0.829407			−0.414703	+	0.909957i	$0.636115\pi$
$84$	−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	$-0.273063\pi$
$89$	12.3408			1.30813			0.654063	+	0.756440i	$0.273063\pi$
$90$	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	$0.191412\pi$
$101$			11.3714i			1.13149i	−0.824579	+	0.565747i	$0.808588\pi$
$102$	−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	$-0.533148\pi$
$107$	−2.15054			−0.207901			−0.103950	+	0.994582i	$0.533148\pi$
$108$	−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	$-0.417183\pi$
$113$	5.46926			0.514505			0.257252	+	0.966344i	$0.417183\pi$
$114$	−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	$-0.725656\pi$
$131$		−	17.3758i		−	1.51813i	0.651014	−	0.759066i	$-0.274344\pi$
$132$	−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	$-0.783639\pi$
$137$	−18.2067			−1.55550			−0.777751	+	0.628573i	$0.783639\pi$
$138$	−5.00663	−	6.62825i	−0.426193	−	0.564234i
$139$	−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	$-0.604205\pi$
$149$	−7.85015			−0.643110			−0.321555	+	0.946891i	$0.604205\pi$
$150$	−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	$0.207971\pi$
$167$			15.7105i			1.21572i	−0.794045	+	0.607859i	$0.792029\pi$
$168$	−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	$-0.994827\pi$
$173$		−	0.427486i		−	0.0325012i	0.999868	−	0.0162506i	$-0.00517295\pi$
$174$	−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	$0.160316\pi$
$179$			12.9141i			0.965244i	−0.875829	+	0.482622i	$0.839684\pi$
$180$	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	$-0.688600\pi$
$191$	−15.4356			−1.11688			−0.558441	+	0.829544i	$0.688600\pi$
$192$	−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	$0.185654\pi$
$197$			15.4600i			1.10148i	−0.834677	+	0.550739i	$0.814346\pi$
$198$	−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
$207$	8.74660	−	11.4235i	0.607931	−	0.793990i
$208$	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	$-0.663176\pi$
$227$	−14.7794			−0.980945			−0.490473	+	0.871457i	$0.663176\pi$
$228$	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	$0.207506\pi$
$233$			18.5217i			1.21340i	−0.794932	+	0.606698i	$0.792494\pi$
$234$	−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	$-0.728368\pi$
$239$		−	23.2974i		−	1.50698i	0.657457	−	0.753492i	$-0.271632\pi$
$240$	−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	$-0.603876\pi$
$251$	−10.1577			−0.641147			−0.320573	+	0.947224i	$0.603876\pi$
$252$	−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	$-0.847586\pi$
$257$		−	14.7723i		−	0.921468i	0.887538	−	0.460734i	$-0.152414\pi$
$258$	−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	$-0.234253\pi$
$263$	24.0408			1.48242			0.741209	+	0.671275i	$0.234253\pi$
$264$	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	$0.0461937\pi$
$269$			4.74366i			0.289226i	−0.989488	+	0.144613i	$0.953806\pi$
$270$	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
$276$	−6.62825	+	5.00663i	−0.398973	+	0.301364i
$277$	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	$-0.482926\pi$
$281$	1.79749			0.107229			0.0536146	+	0.998562i	$0.482926\pi$
$282$	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	$-0.748295\pi$
$293$	−24.0774			−1.40662			−0.703308	+	0.710885i	$0.748295\pi$
$294$	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	$-0.681649\pi$
$311$		−	29.6815i		−	1.68308i	0.540193	−	0.841541i	$-0.318351\pi$
$312$	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	$-0.666768\pi$
$317$		−	30.8326i		−	1.73173i	0.500274	−	0.865867i	$-0.333232\pi$
$318$	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
$345$	−6.62825	+	5.00663i	−0.356853	+	0.269548i
$346$	−0.427486			−0.0229818
$347$		−	24.7654i		−	1.32947i	−0.747077	−	0.664737i	$-0.768543\pi$
$347$		−	24.7654i		−	1.32947i	0.747077	−	0.664737i	$-0.231457\pi$
$348$	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	$-0.731769\pi$
$353$		−	28.0481i		−	1.49285i	0.665469	−	0.746425i	$-0.268231\pi$
$354$	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	$-0.398304\pi$
$359$	11.9019			0.628160			0.314080	+	0.949396i	$0.398304\pi$
$360$	−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	$-0.100994\pi$
$383$	37.1871			1.90017			0.950087	+	0.311985i	$0.100994\pi$
$384$	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	$-0.343226\pi$
$389$	18.6520			0.945696			0.472848	+	0.881144i	$0.343226\pi$
$390$	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	$-0.169227\pi$
$401$	34.5221			1.72395			0.861976	+	0.506949i	$0.169227\pi$
$402$	−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
$414$	−11.4235	−	8.74660i	−0.561436	−	0.429872i
$415$	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	$-0.0796741\pi$
$419$	39.6632			1.93767			0.968837	+	0.247698i	$0.0796741\pi$
$420$	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	$-0.913931\pi$
$431$	−40.0125			−1.92733			−0.963666	+	0.267110i	$0.913931\pi$
$432$	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	$0.0296362\pi$
$443$			3.91361i			0.185941i	−0.995669	+	0.0929706i	$0.970364\pi$
$444$	−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	$0.131169\pi$
$449$			16.9735i			0.801029i	−0.916290	+	0.400514i	$0.868831\pi$
$450$	−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	$0.463097\pi$
$461$			42.6536i			1.98657i	−0.115674	+	0.993287i	$0.536903\pi$
$462$	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	$-0.638802\pi$
$467$	−18.2551			−0.844744			−0.422372	+	0.906423i	$0.638802\pi$
$468$	−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	$-0.545884\pi$
$479$	−6.28781			−0.287298			−0.143649	+	0.989629i	$0.545884\pi$
$480$	0.462710	+	1.66910i	0.0211197	+	0.0761837i
$481$			33.4326i			1.52440i
$482$	10.7446			0.489404
$483$	14.1249	+	18.6998i	0.642704	+	0.850872i
$484$	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	$0.123810\pi$
$491$			16.8062i			0.758452i	−0.925304	+	0.379226i	$0.876190\pi$
$492$	−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	$-0.537968\pi$
$503$	−5.33773			−0.237997			−0.118999	+	0.992894i	$0.537968\pi$
$504$	−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	$-0.965261\pi$
$509$		−	4.91462i		−	0.217837i	0.994051	−	0.108918i	$-0.0347387\pi$
$510$	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	$-0.167143\pi$
$521$	39.5006			1.73055			0.865276	+	0.501296i	$0.167143\pi$
$522$	−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
$552$	5.00663	+	6.62825i	0.213096	+	0.282117i
$553$	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	$-0.553218\pi$
$557$	−7.85492			−0.332823			−0.166412	+	0.986056i	$0.553218\pi$
$558$	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	$-0.433083\pi$
$563$	9.90300			0.417362			0.208681	+	0.977984i	$0.433083\pi$
$564$	−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	$-0.547202\pi$
$569$	−7.04866			−0.295495			−0.147748	+	0.989025i	$0.547202\pi$
$570$	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	$0.0919959\pi$
$587$			13.8103i			0.570014i	−0.958525	+	0.285007i	$0.908004\pi$
$588$	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	$0.0163546\pi$
$593$			2.50124i			0.102714i	−0.998680	+	0.0513568i	$0.983645\pi$
$594$	−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	$0.00371460\pi$
$599$			0.571210i			0.0233390i	−0.999932	+	0.0116695i	$0.996285\pi$
$600$	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	$-0.463070\pi$
$617$	5.75072			0.231515			0.115758	+	0.993277i	$0.463070\pi$
$618$	−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
$621$	9.31318	−	23.1142i	0.373725	−	0.927539i
$622$	−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	$-0.214309\pi$
$641$	39.5864			1.56357			0.781785	+	0.623548i	$0.214309\pi$
$642$	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	$-0.878689\pi$
$647$		−	18.9221i		−	0.743903i	0.928252	−	0.371951i	$-0.121311\pi$
$648$	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	$-0.931521\pi$
$653$		−	10.9104i		−	0.426956i	0.976948	−	0.213478i	$-0.0684791\pi$
$654$	−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	$-0.558792\pi$
$659$	−9.42907			−0.367304			−0.183652	+	0.982991i	$0.558792\pi$
$660$	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	$-0.373644\pi$
$677$	20.1189			0.773231			0.386615	+	0.922241i	$0.373644\pi$
$678$	−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	$-0.897152\pi$
$683$		−	16.5961i		−	0.635030i	0.948253	−	0.317515i	$-0.102848\pi$
$684$	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
$690$	5.00663	+	6.62825i	0.190599	+	0.252333i
$691$	−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	$-0.475713\pi$
$701$	4.03643			0.152454			0.0762269	+	0.997090i	$0.475713\pi$
$702$	−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	$-0.944042\pi$
$719$		−	9.37917i		−	0.349784i	0.984588	−	0.174892i	$-0.0559576\pi$
$720$	−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	$-0.578502\pi$
$743$	−13.3090			−0.488261			−0.244130	+	0.969742i	$0.578502\pi$
$744$	−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
$759$	0.586424	−	0.442955i	0.0212859	−	0.0160782i
$760$	−5.08924			−0.184606
$761$		−	33.2491i		−	1.20528i	−0.798014	−	0.602639i	$-0.794116\pi$
$761$		−	33.2491i		−	1.20528i	0.798014	−	0.602639i	$-0.205884\pi$
$762$	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	$-0.424601\pi$
$773$	13.0486			0.469327			0.234663	+	0.972077i	$0.424601\pi$
$774$	−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	$-0.609221\pi$
$797$	−18.9958			−0.672867			−0.336434	+	0.941707i	$0.609221\pi$
$798$	−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	$0.0566591\pi$
$809$			10.0723i			0.354123i	−0.984200	+	0.177061i	$0.943341\pi$
$810$	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	$0.269787\pi$
$821$			42.9606i			1.49934i	−0.661814	+	0.749668i	$0.730213\pi$
$822$	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	$-0.400581\pi$
$827$	17.6733			0.614559			0.307280	+	0.951619i	$0.400581\pi$
$828$	−8.74660	+	11.4235i	−0.303965	+	0.396995i
$829$	−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	$-0.680333\pi$
$839$	−31.0921			−1.07342			−0.536710	+	0.843767i	$0.680333\pi$
$840$	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	$0.253569\pi$
$857$			41.8620i			1.42998i	−0.699135	+	0.714990i	$0.746431\pi$
$858$	−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	$0.0649416\pi$
$863$			11.9040i			0.405216i	−0.979260	+	0.202608i	$0.935058\pi$
$864$	−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	$-0.367067\pi$
$881$	24.0770			0.811174			0.405587	+	0.914056i	$0.367067\pi$
$882$	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	$-0.686690\pi$
$887$		−	49.6106i		−	1.66576i	0.553453	−	0.832880i	$-0.313310\pi$
$888$	−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
$897$	35.7138	−	26.9763i	1.19245	−	0.900714i
$898$	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	$-0.379560\pi$
$911$	22.2997			0.738821			0.369411	+	0.929266i	$0.379560\pi$
$912$	−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	$-0.841751\pi$
$929$		−	29.0730i		−	0.953854i	0.878943	−	0.476927i	$-0.158249\pi$
$930$	−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	$-0.387608\pi$
$941$	21.2153			0.691598			0.345799	+	0.938309i	$0.387608\pi$
$942$	−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	$-0.780917\pi$
$947$		−	39.0946i		−	1.27041i	0.772346	−	0.635203i	$-0.219083\pi$
$948$	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	$-0.606144\pi$
$953$	−20.2089			−0.654631			−0.327316	+	0.944915i	$0.606144\pi$
$954$	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
$966$	18.6998	−	14.1249i	0.601657	−	0.454461i
$967$	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	$-0.573950\pi$
$971$	−14.3487			−0.460470			−0.230235	+	0.973135i	$0.573950\pi$
$972$	−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	$-0.375562\pi$
$977$	23.8210			0.762101			0.381051	+	0.924554i	$0.375562\pi$
$978$	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	$-0.628599\pi$
$983$	−24.6498			−0.786207			−0.393104	+	0.919494i	$0.628599\pi$
$984$	−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.a.551.7	✓	16
3.2	odd	2		690.2.e.b.551.15	yes	16
23.22	odd	2		690.2.e.b.551.7	yes	16
69.68	even	2	inner	690.2.e.a.551.15	yes	16

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

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 690 = 2 \cdot 3 \cdot 5 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	690.e (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-1.00000i q^{2} +(1.66910 - 0.462710i) q^{3} -1.00000 q^{4} -1.00000 q^{5} +(-0.462710 - 1.66910i) q^{6} +2.82123i q^{7} +1.00000i q^{8} +(2.57180 - 1.54462i) q^{9} +O(q^{10})\)	\(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} +(6.62825 - 5.00663i) 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	\( 16 q - 16 q^{4} - 16 q^{5} + 2 q^{6} + 2 q^{9} - 12 q^{11} - 12 q^{14} + 16 q^{16} + 8 q^{18} + 16 q^{20} - 4 q^{21} + 4 q^{23} - 2 q^{24} + 16 q^{25} + 24 q^{27} - 2 q^{30} + 4 q^{31} - 28 q^{33} - 2 q^{36} - 16 q^{38} - 8 q^{39} + 12 q^{44} - 2 q^{45} - 4 q^{46} - 4 q^{49} - 2 q^{51} - 8 q^{53} - 26 q^{54} + 12 q^{55} + 12 q^{56} + 28 q^{57} - 8 q^{58} - 16 q^{64} + 10 q^{66} + 30 q^{69} + 12 q^{70} - 8 q^{72} - 16 q^{73} - 24 q^{74} - 12 q^{78} - 16 q^{80} + 22 q^{81} - 16 q^{82} - 40 q^{83} + 4 q^{84} - 40 q^{86} + 20 q^{87} + 80 q^{89} - 8 q^{90} - 4 q^{92} - 4 q^{93} - 24 q^{94} + 2 q^{96} - 8 q^{99}+O(q^{100}) \) 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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