LMFDB - Embedded newform 462.2.p.b.439.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [462,2,Mod(241,462)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(462, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 1, 3]))

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

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

chi := DirichletCharacter("462.241");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 462 = 2 \cdot 3 \cdot 7 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	462.p (of order $6$, degree $2$, 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:	$3.68908857338$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(\zeta_{6})$
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} - 8 x^{15} + 74 x^{14} - 378 x^{13} + 1878 x^{12} - 6718 x^{11} + 22086 x^{10} - 56904 x^{9} + \cdots + 13417 $ x^16 - 8x^15 + 74x^14 - 378x^13 + 1878x^12 - 6718x^11 + 22086x^10 - 56904x^9 + 130215x^8 - 239606x^7 + 378750x^6 - 477124x^5 + 493030x^4 - 386266x^3 + 223844x^2 - 82874*x + 13417
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			439.8
Root			$0.500000 - 2.40229i$ of defining polynomial
Character	$\chi$	$=$	462.439
Dual form			462.2.p.b.241.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.866025 + 0.500000i) q^{2} +(0.866025 - 0.500000i) q^{3} +(0.500000 + 0.866025i) q^{4} +(2.83045 + 1.63416i) q^{5} +1.00000 q^{6} +(2.54243 - 0.732142i) q^{7} +1.00000i q^{8} +(0.500000 - 0.866025i) q^{9} +O(q^{10})$	\(q+(0.866025 + 0.500000i) q^{2} +(0.866025 - 0.500000i) q^{3} +(0.500000 + 0.866025i) q^{4} +(2.83045 + 1.63416i) q^{5} +1.00000 q^{6} +(2.54243 - 0.732142i) q^{7} +1.00000i q^{8} +(0.500000 - 0.866025i) q^{9} +(1.63416 + 2.83045i) q^{10} +(-2.54485 - 2.12691i) q^{11} +(0.866025 + 0.500000i) q^{12} -5.12518 q^{13} +(2.56788 + 0.637163i) q^{14} +3.26832 q^{15} +(-0.500000 + 0.866025i) q^{16} +(-2.66290 - 4.61228i) q^{17} +(0.866025 - 0.500000i) q^{18} +(-2.13745 + 3.70217i) q^{19} +3.26832i q^{20} +(1.83574 - 1.90527i) q^{21} +(-1.14045 - 3.11438i) q^{22} +(-2.68593 + 4.65217i) q^{23} +(0.500000 + 0.866025i) q^{24} +(2.84095 + 4.92067i) q^{25} +(-4.43853 - 2.56259i) q^{26} -1.00000i q^{27} +(1.90527 + 1.83574i) q^{28} -4.77874i q^{29} +(2.83045 + 1.63416i) q^{30} +(5.59873 - 3.23243i) q^{31} +(-0.866025 + 0.500000i) q^{32} +(-3.26736 - 0.569529i) q^{33} -5.32580i q^{34} +(8.39266 + 2.08245i) q^{35} +1.00000 q^{36} +(-1.06546 + 1.84544i) q^{37} +(-3.70217 + 2.13745i) q^{38} +(-4.43853 + 2.56259i) q^{39} +(-1.63416 + 2.83045i) q^{40} +0.949652 q^{41} +(2.54243 - 0.732142i) q^{42} +6.20483i q^{43} +(0.569529 - 3.26736i) q^{44} +(2.83045 - 1.63416i) q^{45} +(-4.65217 + 2.68593i) q^{46} +(10.4185 + 6.01513i) q^{47} +1.00000i q^{48} +(5.92794 - 3.72284i) q^{49} +5.68190i q^{50} +(-4.61228 - 2.66290i) q^{51} +(-2.56259 - 4.43853i) q^{52} +(-6.26996 - 10.8599i) q^{53} +(0.500000 - 0.866025i) q^{54} +(-3.72736 - 10.1788i) q^{55} +(0.732142 + 2.54243i) q^{56} +4.27490i q^{57} +(2.38937 - 4.13851i) q^{58} +(-11.6778 + 6.74219i) q^{59} +(1.63416 + 2.83045i) q^{60} +(2.67030 - 4.62509i) q^{61} +6.46485 q^{62} +(0.637163 - 2.56788i) q^{63} -1.00000 q^{64} +(-14.5065 - 8.37536i) q^{65} +(-2.54485 - 2.12691i) q^{66} +(-3.09675 - 5.36373i) q^{67} +(2.66290 - 4.61228i) q^{68} +5.37186i q^{69} +(6.22703 + 5.99979i) q^{70} -10.8061 q^{71} +(0.866025 + 0.500000i) q^{72} +(6.61476 + 11.4571i) q^{73} +(-1.84544 + 1.06546i) q^{74} +(4.92067 + 2.84095i) q^{75} -4.27490 q^{76} +(-8.02731 - 3.54433i) q^{77} -5.12518 q^{78} +(7.93887 + 4.58351i) q^{79} +(-2.83045 + 1.63416i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(0.822423 + 0.474826i) q^{82} +0.835847 q^{83} +(2.56788 + 0.637163i) q^{84} -17.4064i q^{85} +(-3.10242 + 5.37354i) q^{86} +(-2.38937 - 4.13851i) q^{87} +(2.12691 - 2.54485i) q^{88} +(-5.39021 - 3.11204i) q^{89} +3.26832 q^{90} +(-13.0304 + 3.75236i) q^{91} -5.37186 q^{92} +(3.23243 - 5.59873i) q^{93} +(6.01513 + 10.4185i) q^{94} +(-12.0999 + 6.98586i) q^{95} +(-0.500000 + 0.866025i) q^{96} -0.624337i q^{97} +(6.99517 - 0.260109i) q^{98} +(-3.11438 + 1.14045i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 8 q^{4} + 12 q^{5} + 16 q^{6} + 6 q^{7} + 8 q^{9}+O(q^{10}) $ 16 * q + 8 * q^4 + 12 * q^5 + 16 * q^6 + 6 * q^7 + 8 * q^9	$ 16 q + 8 q^{4} + 12 q^{5} + 16 q^{6} + 6 q^{7} + 8 q^{9} - 2 q^{10} - 4 q^{11} + 8 q^{14} - 4 q^{15} - 8 q^{16} + 10 q^{19} + 4 q^{21} + 2 q^{22} - 4 q^{23} + 8 q^{24} + 10 q^{25} + 12 q^{26} + 12 q^{30} + 6 q^{31} + 4 q^{33} + 8 q^{35} + 16 q^{36} + 14 q^{37} - 12 q^{38} + 12 q^{39} + 2 q^{40} - 32 q^{41} + 6 q^{42} + 4 q^{44} + 12 q^{45} - 18 q^{46} - 24 q^{47} - 6 q^{49} - 6 q^{51} + 8 q^{54} + 14 q^{55} + 4 q^{56} - 2 q^{60} - 28 q^{61} + 8 q^{62} + 6 q^{63} - 16 q^{64} - 72 q^{65} - 4 q^{66} - 16 q^{67} - 30 q^{70} - 56 q^{71} + 44 q^{73} - 24 q^{74} - 12 q^{75} + 20 q^{76} - 52 q^{77} + 30 q^{79} - 12 q^{80} - 8 q^{81} - 12 q^{82} - 8 q^{83} + 8 q^{84} - 12 q^{86} - 2 q^{88} - 36 q^{89} - 4 q^{90} - 8 q^{91} - 8 q^{92} + 4 q^{93} - 14 q^{94} - 72 q^{95} - 8 q^{96} + 40 q^{98} - 8 q^{99}+O(q^{100}) $ 16 * q + 8 * q^4 + 12 * q^5 + 16 * q^6 + 6 * q^7 + 8 * q^9 - 2 * q^10 - 4 * q^11 + 8 * q^14 - 4 * q^15 - 8 * q^16 + 10 * q^19 + 4 * q^21 + 2 * q^22 - 4 * q^23 + 8 * q^24 + 10 * q^25 + 12 * q^26 + 12 * q^30 + 6 * q^31 + 4 * q^33 + 8 * q^35 + 16 * q^36 + 14 * q^37 - 12 * q^38 + 12 * q^39 + 2 * q^40 - 32 * q^41 + 6 * q^42 + 4 * q^44 + 12 * q^45 - 18 * q^46 - 24 * q^47 - 6 * q^49 - 6 * q^51 + 8 * q^54 + 14 * q^55 + 4 * q^56 - 2 * q^60 - 28 * q^61 + 8 * q^62 + 6 * q^63 - 16 * q^64 - 72 * q^65 - 4 * q^66 - 16 * q^67 - 30 * q^70 - 56 * q^71 + 44 * q^73 - 24 * q^74 - 12 * q^75 + 20 * q^76 - 52 * q^77 + 30 * q^79 - 12 * q^80 - 8 * q^81 - 12 * q^82 - 8 * q^83 + 8 * q^84 - 12 * q^86 - 2 * q^88 - 36 * q^89 - 4 * q^90 - 8 * q^91 - 8 * q^92 + 4 * q^93 - 14 * q^94 - 72 * q^95 - 8 * q^96 + 40 * q^98 - 8 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/462\mathbb{Z}\right)^\times$.

$n$	$155$	$199$	$211$
$\chi(n)$	$1$	$e\left(\frac{5}{6}\right)$	$-1$

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 $

$2$	0.866025	+	0.500000i	0.612372	+	0.353553i
$2$	0.866025	+	0.500000i	0.612372	+	0.353553i
$3$	0.866025	−	0.500000i	0.500000	−	0.288675i
$3$	0.866025	−	0.500000i	0.500000	−	0.288675i
$4$	0.500000	+	0.866025i	0.250000	+	0.433013i
$5$	2.83045	+	1.63416i	1.26581	+	0.730818i	0.974193	−	0.225716i	$-0.0724721\pi$
$5$	2.83045	+	1.63416i	1.26581	+	0.730818i	0.291621	+	0.956534i	$0.405805\pi$
$6$	1.00000			0.408248
$7$	2.54243	−	0.732142i	0.960950	−	0.276724i
$7$	2.54243	−	0.732142i	0.960950	−	0.276724i
$8$			1.00000i			0.353553i
$9$	0.500000	−	0.866025i	0.166667	−	0.288675i
$10$	1.63416	+	2.83045i	0.516767	+	0.895066i
$11$	−2.54485	−	2.12691i	−0.767302	−	0.641286i
$11$	−2.54485	−	2.12691i	−0.767302	−	0.641286i
$12$	0.866025	+	0.500000i	0.250000	+	0.144338i
$13$	−5.12518			−1.42147			−0.710734	−	0.703461i	$-0.751637\pi$
$13$	−5.12518			−1.42147			−0.710734	+	0.703461i	$0.751637\pi$
$14$	2.56788	+	0.637163i	0.686296	+	0.170289i
$15$	3.26832			0.843876
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	−2.66290	−	4.61228i	−0.645848	−	1.11864i	−0.984105	−	0.177587i	$-0.943171\pi$
$17$	−2.66290	−	4.61228i	−0.645848	−	1.11864i	0.338257	−	0.941054i	$-0.390163\pi$
$18$	0.866025	−	0.500000i	0.204124	−	0.117851i
$19$	−2.13745	+	3.70217i	−0.490364	+	0.849336i	−0.999938	−	0.0110907i	$-0.996470\pi$
$19$	−2.13745	+	3.70217i	−0.490364	+	0.849336i	0.509574	+	0.860427i	$0.329803\pi$
$20$			3.26832i			0.730818i
$21$	1.83574	−	1.90527i	0.400592	−	0.415764i
$22$	−1.14045	−	3.11438i	−0.243145	−	0.663988i
$23$	−2.68593	+	4.65217i	−0.560055	+	0.970044i	0.437436	+	0.899250i	$0.355887\pi$
$23$	−2.68593	+	4.65217i	−0.560055	+	0.970044i	−0.997491	+	0.0707942i	$0.977447\pi$
$24$	0.500000	+	0.866025i	0.102062	+	0.176777i
$25$	2.84095	+	4.92067i	0.568190	+	0.984135i
$26$	−4.43853	−	2.56259i	−0.870468	−	0.502565i
$27$		−	1.00000i		−	0.192450i
$28$	1.90527	+	1.83574i	0.360062	+	0.346922i
$29$		−	4.77874i		−	0.887389i	−0.896178	−	0.443695i	$-0.853667\pi$
$29$		−	4.77874i		−	0.887389i	0.896178	−	0.443695i	$-0.146333\pi$
$30$	2.83045	+	1.63416i	0.516767	+	0.298355i
$31$	5.59873	−	3.23243i	1.00556	−	0.580561i	0.0956723	−	0.995413i	$-0.469500\pi$
$31$	5.59873	−	3.23243i	1.00556	−	0.580561i	0.909889	+	0.414852i	$0.136167\pi$
$32$	−0.866025	+	0.500000i	−0.153093	+	0.0883883i
$33$	−3.26736	−	0.569529i	−0.568774	−	0.0991423i
$34$		−	5.32580i		−	0.913367i
$35$	8.39266	+	2.08245i	1.41862	+	0.351999i
$36$	1.00000			0.166667
$37$	−1.06546	+	1.84544i	−0.175161	+	0.303388i	−0.940217	−	0.340576i	$-0.889378\pi$
$37$	−1.06546	+	1.84544i	−0.175161	+	0.303388i	0.765056	+	0.643964i	$0.222711\pi$
$38$	−3.70217	+	2.13745i	−0.600571	+	0.346740i
$39$	−4.43853	+	2.56259i	−0.710734	+	0.410343i
$40$	−1.63416	+	2.83045i	−0.258383	+	0.447533i
$41$	0.949652			0.148311			0.0741554	−	0.997247i	$-0.476374\pi$
$41$	0.949652			0.148311			0.0741554	+	0.997247i	$0.476374\pi$
$42$	2.54243	−	0.732142i	0.392306	−	0.112972i
$43$			6.20483i			0.946228i	0.881001	+	0.473114i	$0.156870\pi$
$43$			6.20483i			0.946228i	−0.881001	+	0.473114i	$0.843130\pi$
$44$	0.569529	−	3.26736i	0.0858597	−	0.492573i
$45$	2.83045	−	1.63416i	0.421938	−	0.243606i
$46$	−4.65217	+	2.68593i	−0.685925	+	0.396019i
$47$	10.4185	+	6.01513i	1.51970	+	0.877397i	0.999731	+	0.0232091i	$0.00738833\pi$
$47$	10.4185	+	6.01513i	1.51970	+	0.877397i	0.519965	+	0.854188i	$0.325945\pi$
$48$			1.00000i			0.144338i
$49$	5.92794	−	3.72284i	0.846848	−	0.531835i
$50$			5.68190i			0.803543i
$51$	−4.61228	−	2.66290i	−0.645848	−	0.372880i
$52$	−2.56259	−	4.43853i	−0.355367	−	0.615514i
$53$	−6.26996	−	10.8599i	−0.861246	−	1.49172i	−0.870727	−	0.491766i	$-0.836352\pi$
$53$	−6.26996	−	10.8599i	−0.861246	−	1.49172i	0.00948193	−	0.999955i	$-0.496982\pi$
$54$	0.500000	−	0.866025i	0.0680414	−	0.117851i
$55$	−3.72736	−	10.1788i	−0.502598	−	1.37251i
$56$	0.732142	+	2.54243i	0.0978366	+	0.339747i
$57$			4.27490i			0.566224i
$58$	2.38937	−	4.13851i	0.313740	−	0.543413i
$59$	−11.6778	+	6.74219i	−1.52032	+	0.877758i	−0.520608	+	0.853796i	$0.674295\pi$
$59$	−11.6778	+	6.74219i	−1.52032	+	0.877758i	−0.999713	+	0.0239621i	$0.992372\pi$
$60$	1.63416	+	2.83045i	0.210969	+	0.365409i
$61$	2.67030	−	4.62509i	0.341897	−	0.592183i	−0.642888	−	0.765960i	$-0.722264\pi$
$61$	2.67030	−	4.62509i	0.341897	−	0.592183i	0.984785	+	0.173778i	$0.0555974\pi$
$62$	6.46485			0.821037
$63$	0.637163	−	2.56788i	0.0802750	−	0.323523i
$64$	−1.00000			−0.125000
$65$	−14.5065	−	8.37536i	−1.79931	−	1.03883i
$66$	−2.54485	−	2.12691i	−0.313250	−	0.261804i
$67$	−3.09675	−	5.36373i	−0.378328	−	0.655284i	0.612491	−	0.790478i	$-0.290168\pi$
$67$	−3.09675	−	5.36373i	−0.378328	−	0.655284i	−0.990819	+	0.135194i	$0.956834\pi$
$68$	2.66290	−	4.61228i	0.322924	−	0.559321i
$69$			5.37186i			0.646696i
$70$	6.22703	+	5.99979i	0.744272	+	0.717112i
$71$	−10.8061			−1.28245			−0.641226	−	0.767352i	$-0.721574\pi$
$71$	−10.8061			−1.28245			−0.641226	+	0.767352i	$0.721574\pi$
$72$	0.866025	+	0.500000i	0.102062	+	0.0589256i
$73$	6.61476	+	11.4571i	0.774199	+	1.34095i	0.935244	+	0.354005i	$0.115180\pi$
$73$	6.61476	+	11.4571i	0.774199	+	1.34095i	−0.161045	+	0.986947i	$0.551486\pi$
$74$	−1.84544	+	1.06546i	−0.214528	+	0.123858i
$75$	4.92067	+	2.84095i	0.568190	+	0.328045i
$76$	−4.27490			−0.490364
$77$	−8.02731	−	3.54433i	−0.914797	−	0.403913i
$78$	−5.12518			−0.580312
$79$	7.93887	+	4.58351i	0.893193	+	0.515685i	0.874985	−	0.484149i	$-0.160871\pi$
$79$	7.93887	+	4.58351i	0.893193	+	0.515685i	0.0182072	+	0.999834i	$0.494204\pi$
$80$	−2.83045	+	1.63416i	−0.316454	+	0.182705i
$81$	−0.500000	−	0.866025i	−0.0555556	−	0.0962250i
$82$	0.822423	+	0.474826i	0.0908214	+	0.0524358i
$83$	0.835847			0.0917462			0.0458731	−	0.998947i	$-0.485393\pi$
$83$	0.835847			0.0917462			0.0458731	+	0.998947i	$0.485393\pi$
$84$	2.56788	+	0.637163i	0.280179	+	0.0695202i
$85$		−	17.4064i		−	1.88799i
$86$	−3.10242	+	5.37354i	−0.334542	+	0.579444i
$87$	−2.38937	−	4.13851i	−0.256167	−	0.443695i
$88$	2.12691	−	2.54485i	0.226729	−	0.271282i
$89$	−5.39021	−	3.11204i	−0.571361	−	0.329875i	0.186332	−	0.982487i	$-0.440340\pi$
$89$	−5.39021	−	3.11204i	−0.571361	−	0.329875i	−0.757693	+	0.652611i	$0.773673\pi$
$90$	3.26832			0.344511
$91$	−13.0304	+	3.75236i	−1.36596	+	0.393354i
$92$	−5.37186			−0.560055
$93$	3.23243	−	5.59873i	0.335187	−	0.580561i
$94$	6.01513	+	10.4185i	0.620413	+	1.07459i
$95$	−12.0999	+	6.98586i	−1.24142	+	0.716734i
$96$	−0.500000	+	0.866025i	−0.0510310	+	0.0883883i
$97$		−	0.624337i		−	0.0633919i	−0.999498	−	0.0316959i	$-0.989909\pi$
$97$		−	0.624337i		−	0.0633919i	0.999498	−	0.0316959i	$-0.0100908\pi$
$98$	6.99517	−	0.260109i	0.706618	−	0.0262750i
$99$	−3.11438	+	1.14045i	−0.313007	+	0.114620i
$100$	−2.84095	+	4.92067i	−0.284095	+	0.492067i
$101$	6.58462	+	11.4049i	0.655194	+	1.13483i	0.981845	+	0.189685i	$0.0607466\pi$
$101$	6.58462	+	11.4049i	0.655194	+	1.13483i	−0.326651	+	0.945145i	$0.605920\pi$
$102$	−2.66290	−	4.61228i	−0.263666	−	0.456683i
$103$	11.4421	+	6.60608i	1.12742	+	0.650916i	0.943285	−	0.331985i	$-0.107718\pi$
$103$	11.4421	+	6.60608i	1.12742	+	0.650916i	0.184135	+	0.982901i	$0.441052\pi$
$104$		−	5.12518i		−	0.502565i
$105$	8.30948	−	2.39287i	0.810922	−	0.233520i
$106$		−	12.5399i		−	1.21799i
$107$	−9.62104	−	5.55471i	−0.930101	−	0.536994i	−0.0432576	−	0.999064i	$-0.513774\pi$
$107$	−9.62104	−	5.55471i	−0.930101	−	0.536994i	−0.886844	+	0.462070i	$0.847107\pi$
$108$	0.866025	−	0.500000i	0.0833333	−	0.0481125i
$109$	6.17596	−	3.56569i	0.591549	−	0.341531i	−0.174161	−	0.984717i	$-0.555721\pi$
$109$	6.17596	−	3.56569i	0.591549	−	0.341531i	0.765710	+	0.643186i	$0.222388\pi$
$110$	1.86140	−	10.6788i	0.177478	−	1.01818i
$111$			2.13093i			0.202259i
$112$	−0.637163	+	2.56788i	−0.0602063	+	0.242642i
$113$	2.41436			0.227124			0.113562	−	0.993531i	$-0.463774\pi$
$113$	2.41436			0.227124			0.113562	+	0.993531i	$0.463774\pi$
$114$	−2.13745	+	3.70217i	−0.200190	+	0.346740i
$115$	−15.2048	+	8.77847i	−1.41785	+	0.818597i
$116$	4.13851	−	2.38937i	0.384251	−	0.221847i
$117$	−2.56259	+	4.43853i	−0.236911	+	0.410343i
$118$	−13.4844			−1.24134
$119$	−10.1471	−	9.77678i	−0.930181	−	0.896236i
$120$			3.26832i			0.298355i
$121$	1.95254	+	10.8253i	0.177504	+	0.984120i
$122$	4.62509	−	2.67030i	0.418736	−	0.241758i
$123$	0.822423	−	0.474826i	0.0741554	−	0.0428136i
$124$	5.59873	+	3.23243i	0.502781	+	0.290281i
$125$			2.22868i			0.199339i
$126$	1.83574	−	1.90527i	0.163541	−	0.169735i
$127$		−	13.8100i		−	1.22544i	−0.790301	−	0.612719i	$-0.790076\pi$
$127$		−	13.8100i		−	1.22544i	0.790301	−	0.612719i	$-0.209924\pi$
$128$	−0.866025	−	0.500000i	−0.0765466	−	0.0441942i
$129$	3.10242	+	5.37354i	0.273152	+	0.473114i
$130$	−8.37536	−	14.5065i	−0.734567	−	1.27231i
$131$	5.89332	−	10.2075i	0.514902	−	0.891836i	−0.484949	−	0.874543i	$-0.661162\pi$
$131$	5.89332	−	10.2075i	0.514902	−	0.891836i	0.999850	−	0.0172935i	$-0.00550496\pi$
$132$	−1.14045	−	3.11438i	−0.0992637	−	0.271072i
$133$	−2.72381	+	10.9774i	−0.236184	+	0.951864i
$134$		−	6.19350i		−	0.535037i
$135$	1.63416	−	2.83045i	0.140646	−	0.243606i
$136$	4.61228	−	2.66290i	0.395499	−	0.228342i
$137$	−2.43055	−	4.20984i	−0.207656	−	0.359671i	0.743320	−	0.668936i	$-0.233250\pi$
$137$	−2.43055	−	4.20984i	−0.207656	−	0.359671i	−0.950976	+	0.309265i	$0.899917\pi$
$138$	−2.68593	+	4.65217i	−0.228642	+	0.396019i
$139$	16.7827			1.42349			0.711744	−	0.702439i	$-0.247906\pi$
$139$	16.7827			1.42349			0.711744	+	0.702439i	$0.247906\pi$
$140$	2.39287	+	8.30948i	0.202235	+	0.702279i
$141$	12.0303			1.01313
$142$	−9.35838	−	5.40306i	−0.785338	−	0.453415i
$143$	13.0428	+	10.9008i	1.09069	+	0.911568i
$144$	0.500000	+	0.866025i	0.0416667	+	0.0721688i
$145$	7.80922	−	13.5260i	0.648520	−	1.12327i
$146$			13.2295i			1.09488i
$147$	3.27232	−	6.18805i	0.269897	−	0.510381i
$148$	−2.13093			−0.175161
$149$	−6.25672	−	3.61232i	−0.512571	−	0.295933i	0.221319	−	0.975201i	$-0.428964\pi$
$149$	−6.25672	−	3.61232i	−0.512571	−	0.295933i	−0.733890	+	0.679269i	$0.762297\pi$
$150$	2.84095	+	4.92067i	0.231963	+	0.401771i
$151$	−4.22644	+	2.44014i	−0.343943	+	0.198576i	−0.662014	−	0.749491i	$-0.730298\pi$
$151$	−4.22644	+	2.44014i	−0.343943	+	0.198576i	0.318071	+	0.948067i	$0.396965\pi$
$152$	−3.70217	−	2.13745i	−0.300286	−	0.173370i
$153$	−5.32580			−0.430565
$154$	−5.17969	−	7.08313i	−0.417392	−	0.570775i
$155$	21.1292			1.69714
$156$	−4.43853	−	2.56259i	−0.355367	−	0.205171i
$157$	−2.85996	+	1.65120i	−0.228249	+	0.131780i	−0.609764	−	0.792583i	$-0.708736\pi$
$157$	−2.85996	+	1.65120i	−0.228249	+	0.131780i	0.381515	+	0.924363i	$0.375403\pi$
$158$	4.58351	+	7.93887i	0.364644	+	0.631583i
$159$	−10.8599	−	6.26996i	−0.861246	−	0.497240i
$160$	−3.26832			−0.258383
$161$	−3.42275	+	13.7943i	−0.269751	+	1.08714i
$162$		−	1.00000i		−	0.0785674i
$163$	2.42268	−	4.19621i	0.189759	−	0.328672i	−0.755411	−	0.655252i	$-0.772563\pi$
$163$	2.42268	−	4.19621i	0.189759	−	0.328672i	0.945170	+	0.326579i	$0.105896\pi$
$164$	0.474826	+	0.822423i	0.0370777	+	0.0642205i
$165$	−8.31739	−	6.95141i	−0.647508	−	0.541166i
$166$	0.723865	+	0.417924i	0.0561828	+	0.0324372i
$167$	2.13922			0.165538			0.0827688	−	0.996569i	$-0.473624\pi$
$167$	2.13922			0.165538			0.0827688	+	0.996569i	$0.473624\pi$
$168$	1.90527	+	1.83574i	0.146995	+	0.141631i
$169$	13.2674			1.02057
$170$	8.70320	−	15.0744i	0.667505	−	1.15615i
$171$	2.13745	+	3.70217i	0.163455	+	0.283112i
$172$	−5.37354	+	3.10242i	−0.409729	+	0.236557i
$173$	8.87458	−	15.3712i	0.674722	−	1.16865i	−0.301828	−	0.953362i	$-0.597597\pi$
$173$	8.87458	−	15.3712i	0.674722	−	1.16865i	0.976550	−	0.215290i	$-0.0690697\pi$
$174$		−	4.77874i		−	0.362275i
$175$	10.8256	+	10.4305i	0.818336	+	0.788472i
$176$	3.11438	−	1.14045i	0.234755	−	0.0859649i
$177$	−6.74219	+	11.6778i	−0.506774	+	0.877758i
$178$	−3.11204	−	5.39021i	−0.233257	−	0.404013i
$179$	−1.44235	−	2.49822i	−0.107806	−	0.186726i	0.807075	−	0.590449i	$-0.201049\pi$
$179$	−1.44235	−	2.49822i	−0.107806	−	0.186726i	−0.914881	+	0.403723i	$0.867716\pi$
$180$	2.83045	+	1.63416i	0.210969	+	0.121803i
$181$		−	10.9351i		−	0.812803i	−0.913695	−	0.406401i	$-0.866783\pi$
$181$		−	10.9351i		−	0.812803i	0.913695	−	0.406401i	$-0.133217\pi$
$182$	−13.1609	−	3.26558i	−0.975547	−	0.242061i
$183$		−	5.34060i		−	0.394788i
$184$	−4.65217	−	2.68593i	−0.342962	−	0.198009i
$185$	−6.03148	+	3.48228i	−0.443443	+	0.256022i
$186$	5.59873	−	3.23243i	0.410519	−	0.237013i
$187$	−3.03320	+	17.4013i	−0.221809	+	1.27251i
$188$			12.0303i			0.877397i
$189$	−0.732142	−	2.54243i	−0.0532555	−	0.184935i
$190$	−13.9717			−1.01362
$191$	−6.43848	+	11.1518i	−0.465872	+	0.806914i	−0.999240	−	0.0389690i	$-0.987593\pi$
$191$	−6.43848	+	11.1518i	−0.465872	+	0.806914i	0.533368	+	0.845883i	$0.320926\pi$
$192$	−0.866025	+	0.500000i	−0.0625000	+	0.0360844i
$193$	−5.23494	+	3.02239i	−0.376819	+	0.217557i	−0.676433	−	0.736504i	$-0.736475\pi$
$193$	−5.23494	+	3.02239i	−0.376819	+	0.217557i	0.299614	+	0.954060i	$0.403142\pi$
$194$	0.312169	−	0.540692i	0.0224124	−	0.0388194i
$195$	−16.7507			−1.19954
$196$	6.18805	+	3.27232i	0.442003	+	0.233737i
$197$			6.18237i			0.440476i	0.975446	+	0.220238i	$0.0706833\pi$
$197$			6.18237i			0.440476i	−0.975446	+	0.220238i	$0.929317\pi$
$198$	−3.26736	−	0.569529i	−0.232201	−	0.0404747i
$199$	−3.36231	+	1.94123i	−0.238348	+	0.137610i	−0.614417	−	0.788981i	$-0.710609\pi$
$199$	−3.36231	+	1.94123i	−0.238348	+	0.137610i	0.376069	+	0.926591i	$0.377275\pi$
$200$	−4.92067	+	2.84095i	−0.347944	+	0.200886i
$201$	−5.36373	−	3.09675i	−0.378328	−	0.218428i
$202$			13.1692i			0.926585i
$203$	−3.49871	−	12.1496i	−0.245562	−	0.852736i
$204$		−	5.32580i		−	0.372880i
$205$	2.68794	+	1.55188i	0.187734	+	0.108388i
$206$	6.60608	+	11.4421i	0.460267	+	0.797206i
$207$	2.68593	+	4.65217i	0.186685	+	0.323348i
$208$	2.56259	−	4.43853i	0.177684	−	0.307757i
$209$	13.3137	−	4.87532i	0.920925	−	0.337233i
$210$	8.39266	+	2.08245i	0.579148	+	0.143703i
$211$			9.04700i			0.622821i	0.950276	+	0.311410i	$0.100801\pi$
$211$			9.04700i			0.622821i	−0.950276	+	0.311410i	$0.899199\pi$
$212$	6.26996	−	10.8599i	0.430623	−	0.745860i
$213$	−9.35838	+	5.40306i	−0.641226	+	0.370212i
$214$	−5.55471	−	9.62104i	−0.379712	−	0.657681i
$215$	−10.1397	+	17.5624i	−0.691521	+	1.19775i
$216$	1.00000			0.0680414
$217$	11.8678	−	12.3173i	0.805639	−	0.836152i
$218$	7.13138			0.482998
$219$	11.4571	+	6.61476i	0.774199	+	0.446984i
$220$	6.95141	−	8.31739i	0.468664	−	0.560758i
$221$	13.6478	+	23.6387i	0.918052	+	1.59011i
$222$	−1.06546	+	1.84544i	−0.0715093	+	0.123858i
$223$			5.42935i			0.363576i	0.983338	+	0.181788i	$0.0581885\pi$
$223$			5.42935i			0.363576i	−0.983338	+	0.181788i	$0.941812\pi$
$224$	−1.83574	+	1.90527i	−0.122656	+	0.127301i
$225$	5.68190			0.378794
$226$	2.09090	+	1.20718i	0.139084	+	0.0803004i
$227$	5.92818	+	10.2679i	0.393467	+	0.681505i	0.992904	−	0.118917i	$-0.0379422\pi$
$227$	5.92818	+	10.2679i	0.393467	+	0.681505i	−0.599437	+	0.800422i	$0.704609\pi$
$228$	−3.70217	+	2.13745i	−0.245182	+	0.141556i
$229$	−5.56595	−	3.21350i	−0.367808	−	0.212354i	0.304692	−	0.952451i	$-0.401446\pi$
$229$	−5.56595	−	3.21350i	−0.367808	−	0.212354i	−0.672501	+	0.740097i	$0.734780\pi$
$230$	−17.5569			−1.15767
$231$	−8.72402	+	0.944181i	−0.573998	+	0.0621225i
$232$	4.77874			0.313740
$233$	1.73972	+	1.00443i	0.113973	+	0.0658023i	0.555903	−	0.831247i	$-0.312373\pi$
$233$	1.73972	+	1.00443i	0.113973	+	0.0658023i	−0.441930	+	0.897050i	$0.645706\pi$
$234$	−4.43853	+	2.56259i	−0.290156	+	0.167522i
$235$	19.6594	+	34.0510i	1.28243	+	2.22124i
$236$	−11.6778	−	6.74219i	−0.760161	−	0.438879i
$237$	9.16702			0.595462
$238$	−3.89924	−	13.5405i	−0.252750	−	0.877699i
$239$			4.65869i			0.301346i	0.988584	+	0.150673i	$0.0481440\pi$
$239$			4.65869i			0.301346i	−0.988584	+	0.150673i	$0.951856\pi$
$240$	−1.63416	+	2.83045i	−0.105485	+	0.182705i
$241$	−2.98498	−	5.17014i	−0.192279	−	0.333038i	0.753726	−	0.657189i	$-0.228255\pi$
$241$	−2.98498	−	5.17014i	−0.192279	−	0.333038i	−0.946005	+	0.324151i	$0.894921\pi$
$242$	−3.72171	+	10.3513i	−0.239241	+	0.665405i
$243$	−0.866025	−	0.500000i	−0.0555556	−	0.0320750i
$244$	5.34060			0.341897
$245$	22.8624	−	0.850118i	1.46063	−	0.0543121i
$246$	0.949652			0.0605476
$247$	10.9548	−	18.9743i	0.697037	−	1.20730i
$248$	3.23243	+	5.59873i	0.205259	+	0.355520i
$249$	0.723865	−	0.417924i	0.0458731	−	0.0264848i
$250$	−1.11434	+	1.93010i	−0.0704771	+	0.122070i
$251$			1.45699i			0.0919645i	0.998942	+	0.0459822i	$0.0146418\pi$
$251$			1.45699i			0.0919645i	−0.998942	+	0.0459822i	$0.985358\pi$
$252$	2.54243	−	0.732142i	0.160158	−	0.0461206i
$253$	16.7300	−	6.12635i	1.05181	−	0.385161i
$254$	6.90499	−	11.9598i	0.433258	−	0.750424i
$255$	−8.70320	−	15.0744i	−0.545015	−	0.943994i
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	22.8407	+	13.1871i	1.42477	+	0.822589i	0.996701	−	0.0811588i	$-0.0258621\pi$
$257$	22.8407	+	13.1871i	1.42477	+	0.822589i	0.428065	+	0.903748i	$0.359195\pi$
$258$			6.20483i			0.386296i
$259$	−1.35775	+	5.47198i	−0.0843665	+	0.340012i
$260$		−	16.7507i		−	1.03883i
$261$	−4.13851	−	2.38937i	−0.256167	−	0.147898i
$262$	10.2075	−	5.89332i	0.630623	−	0.364091i
$263$	−27.1221	+	15.6589i	−1.67242	+	0.965571i	−0.706138	+	0.708074i	$0.749564\pi$
$263$	−27.1221	+	15.6589i	−1.67242	+	0.965571i	−0.966279	+	0.257497i	$0.917102\pi$
$264$	0.569529	−	3.26736i	0.0350521	−	0.201092i
$265$		−	40.9845i		−	2.51766i
$266$	−7.84761	+	8.14484i	−0.481168	+	0.499392i
$267$	−6.22408			−0.380907
$268$	3.09675	−	5.36373i	0.189164	−	0.327642i
$269$	2.64139	−	1.52501i	0.161049	−	0.0929815i	−0.417310	−	0.908764i	$-0.637027\pi$
$269$	2.64139	−	1.52501i	0.161049	−	0.0929815i	0.578358	+	0.815783i	$0.303694\pi$
$270$	2.83045	−	1.63416i	0.172256	−	0.0994518i
$271$	−11.2246	+	19.4416i	−0.681847	+	1.18099i	0.292569	+	0.956244i	$0.405490\pi$
$271$	−11.2246	+	19.4416i	−0.681847	+	1.18099i	−0.974417	+	0.224750i	$0.927844\pi$
$272$	5.32580			0.322924
$273$	−9.40850	+	9.76485i	−0.569428	+	0.590995i
$274$		−	4.86111i		−	0.293670i
$275$	3.23601	−	18.5648i	0.195139	−	1.11950i
$276$	−4.65217	+	2.68593i	−0.280028	+	0.161674i
$277$	−17.7724	+	10.2609i	−1.06784	+	0.616518i	−0.927591	−	0.373598i	$-0.878124\pi$
$277$	−17.7724	+	10.2609i	−1.06784	+	0.616518i	−0.140250	+	0.990116i	$0.544791\pi$
$278$	14.5342	+	8.39134i	0.871705	+	0.503279i
$279$		−	6.46485i		−	0.387041i
$280$	−2.08245	+	8.39266i	−0.124450	+	0.501557i
$281$		−	13.8822i		−	0.828141i	−0.910245	−	0.414071i	$-0.864107\pi$
$281$		−	13.8822i		−	0.828141i	0.910245	−	0.414071i	$-0.135893\pi$
$282$	10.4185	+	6.01513i	0.620413	+	0.358196i
$283$	14.8931	+	25.7956i	0.885304	+	1.53339i	0.845365	+	0.534189i	$0.179383\pi$
$283$	14.8931	+	25.7956i	0.885304	+	1.53339i	0.0399386	+	0.999202i	$0.487284\pi$
$284$	−5.40306	−	9.35838i	−0.320613	−	0.555318i
$285$	−6.98586	+	12.0999i	−0.413807	+	0.716734i
$286$	5.84502	+	15.9618i	0.345624	+	0.943838i
$287$	2.41443	−	0.695280i	0.142519	−	0.0410411i
$288$			1.00000i			0.0589256i
$289$	−5.68205	+	9.84161i	−0.334238	+	0.578918i
$290$	13.5260	−	7.80922i	0.794272	−	0.458573i
$291$	−0.312169	−	0.540692i	−0.0182997	−	0.0316959i
$292$	−6.61476	+	11.4571i	−0.387099	+	0.670476i
$293$	10.3943			0.607243			0.303621	−	0.952793i	$-0.401804\pi$
$293$	10.3943			0.607243			0.303621	+	0.952793i	$0.401804\pi$
$294$	5.92794	−	3.72284i	0.345724	−	0.217121i
$295$	−44.0712			−2.56593
$296$	−1.84544	−	1.06546i	−0.107264	−	0.0619289i
$297$	−2.12691	+	2.54485i	−0.123416	+	0.147667i
$298$	−3.61232	−	6.25672i	−0.209256	−	0.362442i
$299$	13.7659	−	23.8432i	0.796100	−	1.37889i
$300$			5.68190i			0.328045i
$301$	4.54282	+	15.7754i	0.261844	+	0.909277i
$302$	−4.88028			−0.280828
$303$	11.4049	+	6.58462i	0.655194	+	0.378277i
$304$	−2.13745	−	3.70217i	−0.122591	−	0.212334i
$305$	15.1163	−	8.72739i	0.865556	−	0.499729i
$306$	−4.61228	−	2.66290i	−0.263666	−	0.152228i
$307$	−1.37847			−0.0786736			−0.0393368	−	0.999226i	$-0.512525\pi$
$307$	−1.37847			−0.0786736			−0.0393368	+	0.999226i	$0.512525\pi$
$308$	−0.944181	−	8.72402i	−0.0537997	−	0.497097i
$309$	13.2122			0.751613
$310$	18.2984	+	10.5646i	1.03928	+	0.600029i
$311$	9.11149	−	5.26052i	0.516665	−	0.298297i	−0.218904	−	0.975746i	$-0.570248\pi$
$311$	9.11149	−	5.26052i	0.516665	−	0.298297i	0.735569	+	0.677450i	$0.236915\pi$
$312$	−2.56259	−	4.43853i	−0.145078	−	0.251282i
$313$	1.96323	+	1.13347i	0.110968	+	0.0640676i	0.554457	−	0.832212i	$-0.312926\pi$
$313$	1.96323	+	1.13347i	0.110968	+	0.0640676i	−0.443489	+	0.896280i	$0.646259\pi$
$314$	−3.30239			−0.186365
$315$	5.99979	−	6.22703i	0.338050	−	0.350853i
$316$			9.16702i			0.515685i
$317$	2.47085	−	4.27963i	0.138777	−	0.240368i	−0.788257	−	0.615346i	$-0.789016\pi$
$317$	2.47085	−	4.27963i	0.138777	−	0.240368i	0.927034	+	0.374978i	$0.122350\pi$
$318$	−6.26996	−	10.8599i	−0.351602	−	0.608993i
$319$	−10.1639	+	12.1612i	−0.569071	+	0.680895i
$320$	−2.83045	−	1.63416i	−0.158227	−	0.0913523i
$321$	−11.1094			−0.620067
$322$	−9.86134	+	10.2348i	−0.549551	+	0.570365i
$323$	22.7672			1.26680
$324$	0.500000	−	0.866025i	0.0277778	−	0.0481125i
$325$	−14.5604	−	25.2193i	−0.807665	−	1.39892i
$326$	4.19621	−	2.42268i	0.232406	−	0.134180i
$327$	3.56569	−	6.17596i	0.197183	−	0.341531i
$328$			0.949652i			0.0524358i
$329$	30.8923	+	7.66524i	1.70315	+	0.422598i
$330$	−3.72736	−	10.1788i	−0.205185	−	0.560324i
$331$	−6.47446	+	11.2141i	−0.355869	+	0.616383i	−0.987266	−	0.159077i	$-0.949148\pi$
$331$	−6.47446	+	11.2141i	−0.355869	+	0.616383i	0.631398	+	0.775459i	$0.282482\pi$
$332$	0.417924	+	0.723865i	0.0229365	+	0.0397272i
$333$	1.06546	+	1.84544i	0.0583871	+	0.101129i
$334$	1.85262	+	1.06961i	0.101371	+	0.0585264i
$335$		−	20.2423i		−	1.10596i
$336$	0.732142	+	2.54243i	0.0399416	+	0.138701i
$337$		−	8.22142i		−	0.447849i	−0.974606	−	0.223925i	$-0.928113\pi$
$337$		−	8.22142i		−	0.447849i	0.974606	−	0.223925i	$-0.0718869\pi$
$338$	11.4899	+	6.63372i	0.624970	+	0.360827i
$339$	2.09090	−	1.20718i	0.113562	−	0.0655650i
$340$	15.0744	−	8.70320i	0.817523	−	0.471997i
$341$	−21.1230	−	3.68192i	−1.14387	−	0.199387i
$342$			4.27490i			0.231160i
$343$	12.3457	−	13.8052i	0.666607	−	0.745409i
$344$	−6.20483			−0.334542
$345$	−8.77847	+	15.2048i	−0.472617	+	0.818597i
$346$	15.3712	−	8.87458i	0.826362	−	0.477100i
$347$	27.1635	−	15.6829i	1.45821	−	0.841901i	0.459291	−	0.888286i	$-0.348103\pi$
$347$	27.1635	−	15.6829i	1.45821	−	0.841901i	0.998924	+	0.0463849i	$0.0147701\pi$
$348$	2.38937	−	4.13851i	0.128084	−	0.221847i
$349$	3.15342			0.168799			0.0843993	−	0.996432i	$-0.473103\pi$
$349$	3.15342			0.168799			0.0843993	+	0.996432i	$0.473103\pi$
$350$	4.15996	+	14.4459i	0.222359	+	0.772164i
$351$			5.12518i			0.273562i
$352$	3.26736	+	0.569529i	0.174151	+	0.0303560i
$353$	−7.06177	+	4.07712i	−0.375860	+	0.217003i	−0.676016	−	0.736887i	$-0.736295\pi$
$353$	−7.06177	+	4.07712i	−0.375860	+	0.217003i	0.300155	+	0.953890i	$0.402961\pi$
$354$	−11.6778	+	6.74219i	−0.620668	+	0.358343i
$355$	−30.5862	−	17.6589i	−1.62335	−	0.937239i
$356$		−	6.22408i		−	0.329875i
$357$	−13.6760	−	3.39340i	−0.723812	−	0.179598i
$358$		−	2.88470i		−	0.152461i
$359$	−8.26228	−	4.77023i	−0.436067	−	0.251763i	0.265861	−	0.964011i	$-0.414344\pi$
$359$	−8.26228	−	4.77023i	−0.436067	−	0.251763i	−0.701928	+	0.712248i	$0.747677\pi$
$360$	1.63416	+	2.83045i	0.0861278	+	0.149178i
$361$	0.362625	+	0.628085i	0.0190855	+	0.0330571i
$362$	5.46757	−	9.47011i	0.287369	−	0.497738i
$363$	7.10361	+	8.39873i	0.372843	+	0.440819i
$364$	−9.76485	−	9.40850i	−0.511817	−	0.493139i
$365$			43.2383i			2.26319i
$366$	2.67030	−	4.62509i	0.139579	−	0.241758i
$367$	−5.86022	+	3.38340i	−0.305901	+	0.176612i	−0.645091	−	0.764106i	$-0.723180\pi$
$367$	−5.86022	+	3.38340i	−0.305901	+	0.176612i	0.339190	+	0.940718i	$0.389847\pi$
$368$	−2.68593	−	4.65217i	−0.140014	−	0.242511i
$369$	0.474826	−	0.822423i	0.0247185	−	0.0428136i
$370$	−6.96456			−0.362070
$371$	−23.8919	−	23.0201i	−1.24041	−	1.19514i
$372$	6.46485			0.335187
$373$	−0.412900	−	0.238388i	−0.0213791	−	0.0123433i	0.489272	−	0.872131i	$-0.337262\pi$
$373$	−0.412900	−	0.238388i	−0.0213791	−	0.0123433i	−0.510651	+	0.859788i	$0.670596\pi$
$374$	−11.3275	+	13.5534i	−0.585730	+	0.700828i
$375$	1.11434	+	1.93010i	0.0575443	+	0.0996697i
$376$	−6.01513	+	10.4185i	−0.310207	+	0.537294i
$377$			24.4919i			1.26140i
$378$	0.637163	−	2.56788i	0.0327721	−	0.132078i
$379$	−15.2564			−0.783669			−0.391835	−	0.920036i	$-0.628160\pi$
$379$	−15.2564			−0.783669			−0.391835	+	0.920036i	$0.628160\pi$
$380$	−12.0999	−	6.98586i	−0.620710	−	0.358367i
$381$	−6.90499	−	11.9598i	−0.353753	−	0.612719i
$382$	−11.1518	+	6.43848i	−0.570574	+	0.329421i
$383$	10.5825	+	6.10983i	0.540743	+	0.312198i	0.745380	−	0.666640i	$-0.232268\pi$
$383$	10.5825	+	6.10983i	0.540743	+	0.312198i	−0.204637	+	0.978838i	$0.565601\pi$
$384$	−1.00000			−0.0510310
$385$	−16.9289	−	23.1499i	−0.862776	−	1.17983i
$386$	−6.04479			−0.307672
$387$	5.37354	+	3.10242i	0.273152	+	0.157705i
$388$	0.540692	−	0.312169i	0.0274495	−	0.0158480i
$389$	−14.0160	−	24.2765i	−0.710641	−	1.23087i	−0.964617	−	0.263656i	$-0.915072\pi$
$389$	−14.0160	−	24.2765i	−0.710641	−	1.23087i	0.253975	−	0.967211i	$-0.418262\pi$
$390$	−14.5065	−	8.37536i	−0.734567	−	0.424103i
$391$	28.6094			1.44684
$392$	3.72284	+	5.92794i	0.188032	+	0.299406i
$393$		−	11.7866i		−	0.594557i
$394$	−3.09118	+	5.35409i	−0.155732	+	0.269735i
$395$	14.9804	+	25.9468i	0.753744	+	1.30552i
$396$	−2.54485	−	2.12691i	−0.127884	−	0.106881i
$397$	−26.1090	−	15.0741i	−1.31038	−	0.756546i	−0.328217	−	0.944602i	$-0.606448\pi$
$397$	−26.1090	−	15.0741i	−1.31038	−	0.756546i	−0.982158	+	0.188057i	$0.939781\pi$
$398$	−3.88246			−0.194610
$399$	3.12983	+	10.8686i	0.156688	+	0.544113i
$400$	−5.68190			−0.284095
$401$	1.60532	−	2.78050i	0.0801661	−	0.138852i	−0.823155	−	0.567817i	$-0.807788\pi$
$401$	1.60532	−	2.78050i	0.0801661	−	0.138852i	0.903321	+	0.428965i	$0.141122\pi$
$402$	−3.09675	−	5.36373i	−0.154452	−	0.267518i
$403$	−28.6945	+	16.5668i	−1.42937	+	0.825249i
$404$	−6.58462	+	11.4049i	−0.327597	+	0.567415i
$405$		−	3.26832i		−	0.162404i
$406$	3.04484	−	12.2712i	0.151113	−	0.609011i
$407$	6.63653	−	2.43023i	0.328960	−	0.120462i
$408$	2.66290	−	4.61228i	0.131833	−	0.228342i
$409$	−17.1522	−	29.7084i	−0.848120	−	1.46899i	−0.882884	−	0.469591i	$-0.844402\pi$
$409$	−17.1522	−	29.7084i	−0.848120	−	1.46899i	0.0347647	−	0.999396i	$-0.488932\pi$
$410$	1.55188	+	2.68794i	0.0766420	+	0.132748i
$411$	−4.20984	−	2.43055i	−0.207656	−	0.119890i
$412$			13.2122i			0.650916i
$413$	−24.7538	+	25.6914i	−1.21806	+	1.26419i
$414$			5.37186i			0.264012i
$415$	2.36582	+	1.36591i	0.116134	+	0.0670498i
$416$	4.43853	−	2.56259i	0.217617	−	0.125641i
$417$	14.5342	−	8.39134i	0.711744	−	0.410925i
$418$	13.9676	+	2.43468i	0.683179	+	0.119084i
$419$		−	12.7969i		−	0.625168i	−0.949890	−	0.312584i	$-0.898805\pi$
$419$		−	12.7969i		−	0.625168i	0.949890	−	0.312584i	$-0.101195\pi$
$420$	6.22703	+	5.99979i	0.303848	+	0.292760i
$421$	35.0356			1.70753			0.853766	−	0.520657i	$-0.174313\pi$
$421$	35.0356			1.70753			0.853766	+	0.520657i	$0.174313\pi$
$422$	−4.52350	+	7.83493i	−0.220200	+	0.381398i
$423$	10.4185	−	6.01513i	0.506565	−	0.292466i
$424$	10.8599	−	6.26996i	0.527403	−	0.304496i
$425$	15.1303	−	26.2065i	0.733929	−	1.27120i
$426$	−10.8061			−0.523559
$427$	3.40283	−	13.7140i	0.164675	−	0.663668i
$428$		−	11.1094i		−	0.536994i
$429$	16.7458	+	2.91894i	0.808495	+	0.140928i
$430$	−17.5624	+	10.1397i	−0.846936	+	0.488979i
$431$	22.4488	−	12.9608i	1.08132	−	0.624302i	0.150070	−	0.988675i	$-0.452050\pi$
$431$	22.4488	−	12.9608i	1.08132	−	0.624302i	0.931253	+	0.364374i	$0.118717\pi$
$432$	0.866025	+	0.500000i	0.0416667	+	0.0240563i
$433$			29.5108i			1.41820i	0.705110	+	0.709098i	$0.250898\pi$
$433$			29.5108i			1.41820i	−0.705110	+	0.709098i	$0.749102\pi$
$434$	16.4365	−	4.73319i	0.788975	−	0.227200i
$435$		−	15.6184i		−	0.748847i
$436$	6.17596	+	3.56569i	0.295775	+	0.170766i
$437$	−11.4821	−	19.8875i	−0.549262	−	0.951350i
$438$	6.61476	+	11.4571i	0.316065	+	0.547441i
$439$	−5.71039	+	9.89069i	−0.272542	+	0.472057i	−0.969512	−	0.245043i	$-0.921198\pi$
$439$	−5.71039	+	9.89069i	−0.272542	+	0.472057i	0.696970	+	0.717100i	$0.254531\pi$
$440$	10.1788	−	3.72736i	0.485255	−	0.177695i
$441$	−0.260109	−	6.99517i	−0.0123861	−	0.333103i
$442$			27.2956i			1.29832i
$443$	−12.7606	+	22.1020i	−0.606273	+	1.05010i	0.385575	+	0.922676i	$0.374003\pi$
$443$	−12.7606	+	22.1020i	−0.606273	+	1.05010i	−0.991849	+	0.127420i	$0.959330\pi$
$444$	−1.84544	+	1.06546i	−0.0875807	+	0.0505647i
$445$	−10.1711	−	17.6169i	−0.482158	−	0.835122i
$446$	−2.71468	+	4.70196i	−0.128544	+	0.222644i
$447$	−7.22464			−0.341714
$448$	−2.54243	+	0.732142i	−0.120119	+	0.0345904i
$449$	25.9959			1.22682			0.613412	−	0.789763i	$-0.289797\pi$
$449$	25.9959			1.22682			0.613412	+	0.789763i	$0.289797\pi$
$450$	4.92067	+	2.84095i	0.231963	+	0.133924i
$451$	−2.41672	−	2.01982i	−0.113799	−	0.0951097i
$452$	1.20718	+	2.09090i	0.0567809	+	0.0983474i
$453$	−2.44014	+	4.22644i	−0.114648	+	0.198576i
$454$			11.8564i			0.556446i
$455$	−43.0139	−	10.6729i	−2.01652	−	0.500355i
$456$	−4.27490			−0.200190
$457$	−6.95633	−	4.01624i	−0.325403	−	0.187872i	0.328395	−	0.944540i	$-0.393492\pi$
$457$	−6.95633	−	4.01624i	−0.325403	−	0.187872i	−0.653798	+	0.756669i	$0.726826\pi$
$458$	−3.21350	−	5.56595i	−0.150157	−	0.260080i
$459$	−4.61228	+	2.66290i	−0.215283	+	0.124293i
$460$	−15.2048	−	8.77847i	−0.708926	−	0.409298i
$461$	−33.5115			−1.56078			−0.780392	−	0.625290i	$-0.784981\pi$
$461$	−33.5115			−1.56078			−0.780392	+	0.625290i	$0.784981\pi$
$462$	−8.02731	−	3.54433i	−0.373464	−	0.164897i
$463$	−15.7419			−0.731587			−0.365793	−	0.930696i	$-0.619202\pi$
$463$	−15.7419			−0.731587			−0.365793	+	0.930696i	$0.619202\pi$
$464$	4.13851	+	2.38937i	0.192125	+	0.110924i
$465$	18.2984	−	10.5646i	0.848569	−	0.489922i
$466$	1.00443	+	1.73972i	0.0465293	+	0.0805911i
$467$	8.86193	+	5.11644i	0.410081	+	0.236760i	0.690825	−	0.723022i	$-0.257248\pi$
$467$	8.86193	+	5.11644i	0.410081	+	0.236760i	−0.280743	+	0.959783i	$0.590581\pi$
$468$	−5.12518			−0.236911
$469$	−11.8003	−	11.3697i	−0.544887	−	0.525002i
$470$			39.3187i			1.81364i
$471$	−1.65120	+	2.85996i	−0.0760832	+	0.131780i
$472$	−6.74219	−	11.6778i	−0.310334	−	0.537515i
$473$	13.1971	−	15.7904i	0.606803	−	0.726042i
$474$	7.93887	+	4.58351i	0.364644	+	0.210528i
$475$	−24.2896			−1.11448
$476$	3.39340	−	13.6760i	0.155536	−	0.626839i
$477$	−12.5399			−0.574164
$478$	−2.32934	+	4.03454i	−0.106542	+	0.184536i
$479$	−2.59813	−	4.50009i	−0.118712	−	0.205614i	0.800546	−	0.599272i	$-0.204543\pi$
$479$	−2.59813	−	4.50009i	−0.118712	−	0.205614i	−0.919257	+	0.393657i	$0.871210\pi$
$480$	−2.83045	+	1.63416i	−0.129192	+	0.0745888i
$481$	5.46070	−	9.45820i	0.248986	−	0.431257i
$482$		−	5.96996i		−	0.271924i
$483$	3.93296	+	13.6576i	0.178956	+	0.621442i
$484$	−8.39873	+	7.10361i	−0.381761	+	0.322891i
$485$	1.02027	−	1.76715i	0.0463279	−	0.0802423i
$486$	−0.500000	−	0.866025i	−0.0226805	−	0.0392837i
$487$	15.7741	+	27.3216i	0.714794	+	1.23806i	0.963039	+	0.269362i	$0.0868128\pi$
$487$	15.7741	+	27.3216i	0.714794	+	1.23806i	−0.248245	+	0.968697i	$0.579854\pi$
$488$	4.62509	+	2.67030i	0.209368	+	0.120879i
$489$		−	4.84536i		−	0.219115i
$490$	20.2245	+	10.6950i	0.913650	+	0.483150i
$491$		−	7.14182i		−	0.322306i	−0.986929	−	0.161153i	$-0.948479\pi$
$491$		−	7.14182i		−	0.322306i	0.986929	−	0.161153i	$-0.0515212\pi$
$492$	0.822423	+	0.474826i	0.0370777	+	0.0214068i
$493$	−22.0409	+	12.7253i	−0.992670	+	0.573118i
$494$	18.9743	−	10.9548i	0.853693	−	0.492880i
$495$	−10.6788	−	1.86140i	−0.479975	−	0.0836638i
$496$			6.46485i			0.290281i
$497$	−27.4739	+	7.91162i	−1.23237	+	0.354885i
$498$	0.835847			0.0374552
$499$	17.3818	−	30.1061i	0.778114	−	1.34773i	−0.154913	−	0.987928i	$-0.549510\pi$
$499$	17.3818	−	30.1061i	0.778114	−	1.34773i	0.933027	−	0.359805i	$-0.117157\pi$
$500$	−1.93010	+	1.11434i	−0.0863165	+	0.0498349i
$501$	1.85262	−	1.06961i	0.0827688	−	0.0477866i
$502$	−0.728495	+	1.26179i	−0.0325143	+	0.0563165i
$503$	−3.06150			−0.136506			−0.0682529	−	0.997668i	$-0.521742\pi$
$503$	−3.06150			−0.136506			−0.0682529	+	0.997668i	$0.521742\pi$
$504$	2.56788	+	0.637163i	0.114383	+	0.0283815i
$505$			43.0413i			1.91531i
$506$	17.5518	+	3.05943i	0.780272	+	0.136008i
$507$	11.4899	−	6.63372i	0.510286	−	0.294614i
$508$	11.9598	−	6.90499i	0.530630	−	0.306360i
$509$	−24.6258	−	14.2177i	−1.09152	−	0.630188i	−0.157538	−	0.987513i	$-0.550356\pi$
$509$	−24.6258	−	14.2177i	−1.09152	−	0.630188i	−0.933980	+	0.357325i	$0.883689\pi$
$510$		−	17.4064i		−	0.770768i
$511$	25.2058	+	24.2860i	1.11504	+	1.07435i
$512$		−	1.00000i		−	0.0441942i
$513$	3.70217	+	2.13745i	0.163455	+	0.0943707i
$514$	13.1871	+	22.8407i	0.581658	+	1.00746i
$515$	21.5908	+	37.3963i	0.951403	+	1.64788i
$516$	−3.10242	+	5.37354i	−0.136576	+	0.236557i
$517$	−13.7199	−	37.4668i	−0.603402	−	1.64779i
$518$	−3.91184	+	4.06000i	−0.171876	+	0.178386i
$519$		−	17.7492i		−	0.779101i
$520$	8.37536	−	14.5065i	0.367284	−	0.636154i
$521$	−3.15741	+	1.82293i	−0.138329	+	0.0798642i	−0.567567	−	0.823327i	$-0.692115\pi$
$521$	−3.15741	+	1.82293i	−0.138329	+	0.0798642i	0.429238	+	0.903191i	$0.358782\pi$
$522$	−2.38937	−	4.13851i	−0.104580	−	0.181138i
$523$	−11.9730	+	20.7378i	−0.523542	+	0.906801i	0.476083	+	0.879401i	$0.342056\pi$
$523$	−11.9730	+	20.7378i	−0.523542	+	0.906801i	−0.999625	+	0.0274006i	$0.991277\pi$
$524$	11.7866			0.514902
$525$	14.5905	+	3.62030i	0.636780	+	0.158003i
$526$	−31.3179			−1.36552
$527$	−29.8177	−	17.2152i	−1.29888	−	0.749908i
$528$	2.12691	−	2.54485i	0.0925617	−	0.110750i
$529$	−2.92843	−	5.07220i	−0.127323	−	0.220530i
$530$	20.4922	−	35.4936i	0.890126	−	1.54174i
$531$			13.4844i			0.585172i
$532$	−10.8686	+	3.12983i	−0.471215	+	0.135695i
$533$	−4.86714			−0.210819
$534$	−5.39021	−	3.11204i	−0.233257	−	0.134671i
$535$	−18.1546	−	31.4446i	−0.784890	−	1.35947i
$536$	5.36373	−	3.09675i	0.231678	−	0.133759i
$537$	−2.49822	−	1.44235i	−0.107806	−	0.0622420i
$538$	3.05002			0.131496
$539$	−23.0039	−	3.13408i	−0.990846	−	0.134994i
$540$	3.26832			0.140646
$541$	−37.2883	−	21.5284i	−1.60315	−	0.925580i	−0.990852	−	0.134954i	$-0.956911\pi$
$541$	−37.2883	−	21.5284i	−1.60315	−	0.925580i	−0.612299	−	0.790626i	$-0.709755\pi$
$542$	−19.4416	+	11.2246i	−0.835089	+	0.482139i
$543$	−5.46757	−	9.47011i	−0.234636	−	0.406401i
$544$	4.61228	+	2.66290i	0.197750	+	0.114171i
$545$	23.3076			0.998389
$546$	−13.0304	+	3.75236i	−0.557651	+	0.160586i
$547$			8.00013i			0.342061i	0.985266	+	0.171030i	$0.0547097\pi$
$547$			8.00013i			0.342061i	−0.985266	+	0.171030i	$0.945290\pi$
$548$	2.43055	−	4.20984i	0.103828	−	0.179836i
$549$	−2.67030	−	4.62509i	−0.113966	−	0.197394i
$550$	12.0849	−	14.4596i	0.515301	−	0.616560i
$551$	17.6917	+	10.2143i	0.753692	+	0.435144i
$552$	−5.37186			−0.228642
$553$	23.5398	+	5.84089i	1.00102	+	0.248380i
$554$	−20.5218			−0.871888
$555$	−3.48228	+	6.03148i	−0.147814	+	0.256022i
$556$	8.39134	+	14.5342i	0.355872	+	0.616388i
$557$	−20.2134	+	11.6702i	−0.856471	+	0.494484i	−0.862829	−	0.505496i	$-0.831309\pi$
$557$	−20.2134	+	11.6702i	−0.856471	+	0.494484i	0.00635822	+	0.999980i	$0.497976\pi$
$558$	3.23243	−	5.59873i	0.136840	−	0.237013i
$559$		−	31.8009i		−	1.34503i
$560$	−5.99979	+	6.22703i	−0.253537	+	0.263140i
$561$	6.07382	+	16.5866i	0.256437	+	0.700285i
$562$	6.94109	−	12.0223i	0.292792	−	0.507131i
$563$	−13.2190	−	22.8960i	−0.557116	−	0.964953i	−0.997736	−	0.0672592i	$-0.978575\pi$
$563$	−13.2190	−	22.8960i	−0.557116	−	0.964953i	0.440620	−	0.897694i	$-0.354759\pi$
$564$	6.01513	+	10.4185i	0.253283	+	0.438698i
$565$	6.83371	+	3.94545i	0.287496	+	0.165986i
$566$			29.7862i			1.25201i
$567$	−1.90527	−	1.83574i	−0.0800138	−	0.0770939i
$568$		−	10.8061i		−	0.453415i
$569$	21.6494	+	12.4993i	0.907590	+	0.523997i	0.879655	−	0.475612i	$-0.157773\pi$
$569$	21.6494	+	12.4993i	0.907590	+	0.523997i	0.0279352	+	0.999610i	$0.491107\pi$
$570$	−12.0999	+	6.98586i	−0.506808	+	0.292606i
$571$	37.6593	−	21.7426i	1.57599	−	0.909899i	0.580581	−	0.814203i	$-0.302826\pi$
$571$	37.6593	−	21.7426i	1.57599	−	0.909899i	0.995411	−	0.0956961i	$-0.0305077\pi$
$572$	−2.91894	+	16.7458i	−0.122047	+	0.700177i
$573$			12.8770i			0.537943i
$574$	2.43860	+	0.605084i	0.101785	+	0.0252557i
$575$	−30.5224			−1.27287
$576$	−0.500000	+	0.866025i	−0.0208333	+	0.0360844i
$577$	24.0746	−	13.8995i	1.00224	−	0.578643i	0.0933293	−	0.995635i	$-0.470249\pi$
$577$	24.0746	−	13.8995i	1.00224	−	0.578643i	0.908910	+	0.416992i	$0.136916\pi$
$578$	−9.84161	+	5.68205i	−0.409357	+	0.236342i
$579$	−3.02239	+	5.23494i	−0.125606	+	0.217557i
$580$	15.6184			0.648520
$581$	2.12509	−	0.611959i	0.0881634	−	0.0253883i
$582$		−	0.624337i		−	0.0258796i
$583$	−7.14185	+	40.9724i	−0.295785	+	1.69690i
$584$	−11.4571	+	6.61476i	−0.474098	+	0.273721i
$585$	−14.5065	+	8.37536i	−0.599772	+	0.346278i
$586$	9.00174	+	5.19716i	0.371859	+	0.214693i
$587$			11.2683i			0.465091i	0.972585	+	0.232546i	$0.0747055\pi$
$587$			11.2683i			0.465091i	−0.972585	+	0.232546i	$0.925294\pi$
$588$	6.99517	−	0.260109i	0.288476	−	0.0107267i
$589$			27.6366i			1.13875i
$590$	−38.1668	−	22.0356i	−1.57130	−	0.907192i
$591$	3.09118	+	5.35409i	0.127154	+	0.220238i
$592$	−1.06546	−	1.84544i	−0.0437903	−	0.0758471i
$593$	−7.85106	+	13.5984i	−0.322405	+	0.558421i	−0.980984	−	0.194090i	$-0.937824\pi$
$593$	−7.85106	+	13.5984i	−0.322405	+	0.558421i	0.658579	+	0.752512i	$0.271158\pi$
$594$	−3.11438	+	1.14045i	−0.127785	+	0.0467934i
$595$	−12.7440	−	44.2546i	−0.522451	−	1.81426i
$596$		−	7.22464i		−	0.295933i
$597$	−1.94123	+	3.36231i	−0.0794492	+	0.137610i
$598$	23.8432	−	13.7659i	0.975020	−	0.562928i
$599$	−4.79001	−	8.29654i	−0.195714	−	0.338987i	0.751420	−	0.659824i	$-0.229369\pi$
$599$	−4.79001	−	8.29654i	−0.195714	−	0.338987i	−0.947134	+	0.320837i	$0.896036\pi$
$600$	−2.84095	+	4.92067i	−0.115981	+	0.200886i
$601$	36.7398			1.49865			0.749324	−	0.662204i	$-0.230379\pi$
$601$	36.7398			1.49865			0.749324	+	0.662204i	$0.230379\pi$
$602$	−3.95349	+	15.9333i	−0.161132	+	0.649392i
$603$	−6.19350			−0.252219
$604$	−4.22644	−	2.44014i	−0.171972	−	0.0992878i
$605$	−12.1637	+	33.8313i	−0.494526	+	1.37544i
$606$	6.58462	+	11.4049i	0.267482	+	0.463292i
$607$	20.2326	−	35.0438i	0.821215	−	1.42239i	−0.0835632	−	0.996502i	$-0.526630\pi$
$607$	20.2326	−	35.0438i	0.821215	−	1.42239i	0.904778	−	0.425883i	$-0.140037\pi$
$608$		−	4.27490i		−	0.173370i
$609$	−9.10479	−	8.77253i	−0.368945	−	0.355481i
$610$	17.4548			0.706723
$611$	−53.3967	−	30.8286i	−2.16020	−	1.24719i
$612$	−2.66290	−	4.61228i	−0.107641	−	0.186440i
$613$	−9.07028	+	5.23673i	−0.366345	+	0.211509i	−0.671860	−	0.740678i	$-0.734505\pi$
$613$	−9.07028	+	5.23673i	−0.366345	+	0.211509i	0.305515	+	0.952187i	$0.401171\pi$
$614$	−1.19379	−	0.689237i	−0.0481776	−	0.0278153i
$615$	3.10377			0.125156
$616$	3.54433	−	8.02731i	0.142805	−	0.323430i
$617$	−14.4244			−0.580706			−0.290353	−	0.956920i	$-0.593773\pi$
$617$	−14.4244			−0.580706			−0.290353	+	0.956920i	$0.593773\pi$
$618$	11.4421	+	6.60608i	0.460267	+	0.265735i
$619$	38.7932	−	22.3973i	1.55923	−	0.900223i	0.561901	−	0.827205i	$-0.310070\pi$
$619$	38.7932	−	22.3973i	1.55923	−	0.900223i	0.997331	−	0.0730178i	$-0.0232630\pi$
$620$	10.5646	+	18.2984i	0.424285	+	0.734882i
$621$	4.65217	+	2.68593i	0.186685	+	0.107783i
$622$	10.5210			0.421855
$623$	−15.9827	−	3.96575i	−0.640333	−	0.158885i
$624$		−	5.12518i		−	0.205171i
$625$	10.5627	−	18.2952i	0.422510	−	0.731808i
$626$	1.13347	+	1.96323i	0.0453026	+	0.0784664i
$627$	9.09231	−	10.8790i	0.363112	−	0.434465i
$628$	−2.85996	−	1.65120i	−0.114125	−	0.0658900i
$629$	11.3489			0.452510
$630$	8.30948	−	2.39287i	0.331058	−	0.0953343i
$631$	13.1975			0.525383			0.262692	−	0.964880i	$-0.415390\pi$
$631$	13.1975			0.525383			0.262692	+	0.964880i	$0.415390\pi$
$632$	−4.58351	+	7.93887i	−0.182322	+	0.315791i
$633$	4.52350	+	7.83493i	0.179793	+	0.311410i
$634$	4.27963	−	2.47085i	0.169966	−	0.0981298i
$635$	22.5677	−	39.0884i	0.895572	−	1.55118i
$636$		−	12.5399i		−	0.497240i
$637$	−30.3817	+	19.0802i	−1.20377	+	0.755986i
$638$	−14.8828	+	5.44993i	−0.589216	+	0.215765i
$639$	−5.40306	+	9.35838i	−0.213742	+	0.370212i
$640$	−1.63416	−	2.83045i	−0.0645958	−	0.111883i
$641$	−10.7925	−	18.6931i	−0.426278	−	0.738335i	0.570261	−	0.821463i	$-0.306842\pi$
$641$	−10.7925	−	18.6931i	−0.426278	−	0.738335i	−0.996539	+	0.0831289i	$0.973509\pi$
$642$	−9.62104	−	5.55471i	−0.379712	−	0.219227i
$643$			28.9651i			1.14227i	0.820855	+	0.571137i	$0.193497\pi$
$643$			28.9651i			1.14227i	−0.820855	+	0.571137i	$0.806503\pi$
$644$	−13.6576	+	3.93296i	−0.538185	+	0.154980i
$645$			20.2794i			0.798499i
$646$	19.7170	+	11.3836i	0.775755	+	0.447882i
$647$	25.4299	−	14.6820i	0.999753	−	0.577208i	0.0915779	−	0.995798i	$-0.470809\pi$
$647$	25.4299	−	14.6820i	0.999753	−	0.577208i	0.908175	+	0.418590i	$0.137476\pi$
$648$	0.866025	−	0.500000i	0.0340207	−	0.0196419i
$649$	44.0583	+	7.67974i	1.72944	+	0.301456i
$650$		−	29.1208i		−	1.14221i
$651$	4.11917	−	16.6010i	0.161443	−	0.650644i
$652$	4.84536			0.189759
$653$	19.1225	−	33.1211i	0.748320	−	1.29613i	−0.200308	−	0.979733i	$-0.564194\pi$
$653$	19.1225	−	33.1211i	0.748320	−	1.29613i	0.948628	−	0.316395i	$-0.102472\pi$
$654$	6.17596	−	3.56569i	0.241499	−	0.139430i
$655$	33.3615	−	19.2612i	1.30354	−	0.752599i
$656$	−0.474826	+	0.822423i	−0.0185388	+	0.0321102i
$657$	13.2295			0.516133
$658$	22.9209	+	22.0844i	0.893549	+	0.860941i
$659$			0.210272i			0.00819105i	0.999992	+	0.00409553i	$0.00130365\pi$
$659$			0.210272i			0.00819105i	−0.999992	+	0.00409553i	$0.998696\pi$
$660$	1.86140	−	10.6788i	0.0724550	−	0.415671i
$661$	8.07735	−	4.66346i	0.314172	−	0.181388i	−0.334620	−	0.942353i	$-0.608608\pi$
$661$	8.07735	−	4.66346i	0.314172	−	0.181388i	0.648792	+	0.760966i	$0.275274\pi$
$662$	−11.2141	+	6.47446i	−0.435848	+	0.251637i
$663$	23.6387	+	13.6478i	0.918052	+	0.530038i
$664$			0.835847i			0.0324372i
$665$	−25.6485	+	26.6199i	−0.994605	+	1.03228i
$666$			2.13093i			0.0825718i
$667$	22.2315	+	12.8354i	0.860807	+	0.496987i
$668$	1.06961	+	1.85262i	0.0413844	+	0.0716799i
$669$	2.71468	+	4.70196i	0.104955	+	0.181788i
$670$	10.1212	−	17.5304i	0.391015	−	0.677257i
$671$	−16.6327	+	6.09070i	−0.642096	+	0.235129i
$672$	−0.637163	+	2.56788i	−0.0245791	+	0.0990582i
$673$		−	15.7351i		−	0.606545i	−0.952904	−	0.303273i	$-0.901921\pi$
$673$		−	15.7351i		−	0.606545i	0.952904	−	0.303273i	$-0.0980793\pi$
$674$	4.11071	−	7.11996i	0.158339	−	0.274251i
$675$	4.92067	−	2.84095i	0.189397	−	0.109348i
$676$	6.63372	+	11.4899i	0.255143	+	0.441921i
$677$	−6.53943	+	11.3266i	−0.251331	+	0.435318i	−0.963892	−	0.266292i	$-0.914202\pi$
$677$	−6.53943	+	11.3266i	−0.251331	+	0.435318i	0.712562	+	0.701609i	$0.247535\pi$
$678$	2.41436			0.0927229
$679$	−0.457103	−	1.58734i	−0.0175420	−	0.0609164i
$680$	17.4064			0.667505
$681$	10.2679	+	5.92818i	0.393467	+	0.227168i
$682$	−16.4521	−	13.7501i	−0.629983	−	0.526520i
$683$	12.5854	+	21.7986i	0.481568	+	0.834101i	0.999776	−	0.0211540i	$-0.00673402\pi$
$683$	12.5854	+	21.7986i	0.481568	+	0.834101i	−0.518208	+	0.855255i	$0.673401\pi$
$684$	−2.13745	+	3.70217i	−0.0817274	+	0.141556i
$685$		−	15.8876i		−	0.607036i
$686$	17.5943	−	5.78276i	0.671754	−	0.220787i
$687$	−6.42701			−0.245206
$688$	−5.37354	−	3.10242i	−0.204864	−	0.118278i
$689$	32.1347	+	55.6589i	1.22423	+	2.12043i
$690$	−15.2048	+	8.77847i	−0.578835	+	0.334191i
$691$	0.686294	+	0.396232i	0.0261079	+	0.0150734i	0.512997	−	0.858390i	$-0.328535\pi$
$691$	0.686294	+	0.396232i	0.0261079	+	0.0150734i	−0.486889	+	0.873464i	$0.661868\pi$
$692$	17.7492			0.674722
$693$	−7.08313	+	5.17969i	−0.269066	+	0.196760i
$694$	31.3657			1.19063
$695$	47.5025	+	27.4256i	1.80187	+	1.04031i
$696$	4.13851	−	2.38937i	0.156870	−	0.0905688i
$697$	−2.52883	−	4.38006i	−0.0957862	−	0.165907i
$698$	2.73094	+	1.57671i	0.103368	+	0.0596793i
$699$	2.00886			0.0759820
$700$	−3.62030	+	14.5905i	−0.136835	+	0.551468i
$701$			39.5754i			1.49474i	0.664406	+	0.747372i	$0.268685\pi$
$701$			39.5754i			1.49474i	−0.664406	+	0.747372i	$0.731315\pi$
$702$	−2.56259	+	4.43853i	−0.0967187	+	0.167522i
$703$	−4.55475	−	7.88906i	−0.171786	−	0.297542i
$704$	2.54485	+	2.12691i	0.0959127	+	0.0801608i
$705$	34.0510	+	19.6594i	1.28243	+	0.740414i
$706$	−8.15423			−0.306889
$707$	25.0910	+	24.1753i	0.943643	+	0.909206i
$708$	−13.4844			−0.506774
$709$	−18.2211	+	31.5598i	−0.684307	+	1.18525i	0.289347	+	0.957224i	$0.406562\pi$
$709$	−18.2211	+	31.5598i	−0.684307	+	1.18525i	−0.973654	+	0.228030i	$0.926771\pi$
$710$	−17.6589	−	30.5862i	−0.662728	−	1.14788i
$711$	7.93887	−	4.58351i	0.297731	−	0.171895i
$712$	3.11204	−	5.39021i	0.116629	−	0.202007i
$713$			34.7283i			1.30058i
$714$	−10.1471	−	9.77678i	−0.379745	−	0.365887i
$715$	19.1034	+	52.1681i	0.714427	+	1.95098i
$716$	1.44235	−	2.49822i	0.0539031	−	0.0933629i
$717$	2.32934	+	4.03454i	0.0869910	+	0.150673i
$718$	−4.77023	−	8.26228i	−0.178023	−	0.308346i
$719$	−12.2632	−	7.08018i	−0.457341	−	0.264046i	0.253584	−	0.967313i	$-0.418390\pi$
$719$	−12.2632	−	7.08018i	−0.457341	−	0.264046i	−0.710926	+	0.703267i	$0.751724\pi$
$720$			3.26832i			0.121803i
$721$	33.9273	+	8.41830i	1.26352	+	0.313514i
$722$			0.725250i			0.0269910i
$723$	−5.17014	−	2.98498i	−0.192279	−	0.111013i
$724$	9.47011	−	5.46757i	0.351954	−	0.203201i
$725$	23.5146	−	13.5762i	0.873311	−	0.504206i
$726$	1.95254	+	10.8253i	0.0724655	+	0.401765i
$727$			8.58699i			0.318474i	0.987240	+	0.159237i	$0.0509033\pi$
$727$			8.58699i			0.318474i	−0.987240	+	0.159237i	$0.949097\pi$
$728$	−3.75236	−	13.0304i	−0.139072	−	0.482940i
$729$	−1.00000			−0.0370370
$730$	−21.6191	+	37.4454i	−0.800160	+	1.38592i
$731$	28.6184	−	16.5228i	1.05849	−	0.611119i
$732$	4.62509	−	2.67030i	0.170948	−	0.0986971i
$733$	−21.3598	+	36.9962i	−0.788942	+	1.36649i	0.137674	+	0.990478i	$0.456037\pi$
$733$	−21.3598	+	36.9962i	−0.788942	+	1.36649i	−0.926616	+	0.376010i	$0.877296\pi$
$734$	−6.76680			−0.249767
$735$	19.3744	−	12.1674i	0.714635	−	0.448803i
$736$		−	5.37186i		−	0.198009i
$737$	−3.52738	+	20.2364i	−0.129933	+	0.745417i
$738$	0.822423	−	0.474826i	0.0302738	−	0.0174786i
$739$	−28.7537	+	16.6009i	−1.05772	+	0.610675i	−0.924801	−	0.380452i	$-0.875769\pi$
$739$	−28.7537	+	16.6009i	−1.05772	+	0.610675i	−0.132920	+	0.991127i	$0.542435\pi$
$740$	−6.03148	−	3.48228i	−0.221722	−	0.128011i
$741$		−	21.9096i		−	0.804870i
$742$	−9.18100	−	31.8819i	−0.337045	−	1.17042i
$743$			8.11448i			0.297691i	0.988860	+	0.148846i	$0.0475557\pi$
$743$			8.11448i			0.297691i	−0.988860	+	0.148846i	$0.952444\pi$
$744$	5.59873	+	3.23243i	0.205259	+	0.118507i
$745$	−11.8062	−	20.4490i	−0.432546	−	0.749192i
$746$	−0.238388	−	0.412900i	−0.00872800	−	0.0151173i
$747$	0.417924	−	0.723865i	0.0152910	−	0.0264848i
$748$	−16.5866	+	6.07382i	−0.606465	+	0.222081i
$749$	−28.5277	−	7.07852i	−1.04238	−	0.258643i
$750$			2.22868i			0.0813800i
$751$	−0.0376756	+	0.0652561i	−0.00137480	+	0.00238123i	−0.866712	−	0.498809i	$-0.833771\pi$
$751$	−0.0376756	+	0.0652561i	−0.00137480	+	0.00238123i	0.865337	+	0.501190i	$0.167104\pi$
$752$	−10.4185	+	6.01513i	−0.379924	+	0.219349i
$753$	0.728495	+	1.26179i	0.0265479	+	0.0459822i
$754$	−12.2459	+	21.2106i	−0.445971	+	0.772444i
$755$	−15.9503			−0.580491
$756$	1.83574	−	1.90527i	0.0667653	−	0.0692940i
$757$	−0.134400			−0.00488484			−0.00244242	−	0.999997i	$-0.500777\pi$
$757$	−0.134400			−0.00488484			−0.00244242	+	0.999997i	$0.500777\pi$
$758$	−13.2124	−	7.62821i	−0.479898	−	0.277069i
$759$	11.4254	−	13.6706i	0.414717	−	0.496211i
$760$	−6.98586	−	12.0999i	−0.253404	−	0.438908i
$761$	−7.35142	+	12.7330i	−0.266489	+	0.461572i	−0.967953	−	0.251133i	$-0.919197\pi$
$761$	−7.35142	+	12.7330i	−0.266489	+	0.461572i	0.701464	+	0.712705i	$0.252530\pi$
$762$		−	13.8100i		−	0.500283i
$763$	13.0914	−	13.5872i	0.473939	−	0.491890i
$764$	−12.8770			−0.465872
$765$	−15.0744	−	8.70320i	−0.545015	−	0.314665i
$766$	6.10983	+	10.5825i	0.220757	+	0.382363i
$767$	59.8508	−	34.5549i	2.16109	−	1.24770i
$768$	−0.866025	−	0.500000i	−0.0312500	−	0.0180422i
$769$	−7.17040			−0.258571			−0.129286	−	0.991607i	$-0.541268\pi$
$769$	−7.17040			−0.258571			−0.129286	+	0.991607i	$0.541268\pi$
$770$	−3.08588	−	28.5129i	−0.111207	−	1.02753i
$771$	26.3742			0.949844
$772$	−5.23494	−	3.02239i	−0.188410	−	0.108778i
$773$	−32.2256	+	18.6055i	−1.15907	+	0.669192i	−0.951082	−	0.308939i	$-0.900026\pi$
$773$	−32.2256	+	18.6055i	−1.15907	+	0.669192i	−0.207992	+	0.978131i	$0.566693\pi$
$774$	3.10242	+	5.37354i	0.111514	+	0.193148i
$775$	31.8114	+	18.3663i	1.14270	+	0.659739i
$776$	0.624337			0.0224124
$777$	1.56014	+	5.41775i	0.0559698	+	0.194361i
$778$		−	28.0321i		−	1.00500i
$779$	−2.02983	+	3.51577i	−0.0727263	+	0.125966i
$780$	−8.37536	−	14.5065i	−0.299886	−	0.519417i
$781$	27.5000	+	22.9836i	0.984027	+	0.822419i
$782$	24.7765	+	14.3047i	0.886006	+	0.511536i
$783$	−4.77874			−0.170778
$784$	0.260109	+	6.99517i	0.00928960	+	0.249827i
$785$	−10.7933			−0.385229
$786$	5.89332	−	10.2075i	0.210208	−	0.364091i
$787$	−21.5599	−	37.3429i	−0.768529	−	1.33113i	−0.938360	−	0.345658i	$-0.887656\pi$
$787$	−21.5599	−	37.3429i	−0.768529	−	1.33113i	0.169831	−	0.985473i	$-0.445678\pi$
$788$	−5.35409	+	3.09118i	−0.190732	+	0.110119i
$789$	−15.6589	+	27.1221i	−0.557472	+	0.965571i
$790$			29.9607i			1.06596i
$791$	6.13834	−	1.76765i	0.218254	−	0.0628505i
$792$	−1.14045	−	3.11438i	−0.0405242	−	0.110665i
$793$	−13.6858	+	23.7044i	−0.485995	+	0.841769i
$794$	−15.0741	−	26.1090i	−0.534959	−	0.926575i
$795$	−20.4922	−	35.4936i	−0.726785	−	1.25883i
$796$	−3.36231	−	1.94123i	−0.119174	−	0.0688050i
$797$			30.1768i			1.06892i	0.845195	+	0.534458i	$0.179484\pi$
$797$			30.1768i			1.06892i	−0.845195	+	0.534458i	$0.820516\pi$
$798$	−2.72381	+	10.9774i	−0.0964218	+	0.388597i
$799$		−	64.0707i		−	2.26666i
$800$	−4.92067	−	2.84095i	−0.173972	−	0.100443i
$801$	−5.39021	+	3.11204i	−0.190454	+	0.109958i
$802$	2.78050	−	1.60532i	0.0981830	−	0.0566860i
$803$	7.53459	−	43.2256i	0.265890	−	1.52540i
$804$		−	6.19350i		−	0.218428i
$805$	−32.2300	+	33.4507i	−1.13596	+	1.17898i
$806$	−33.1335			−1.16708
$807$	1.52501	−	2.64139i	0.0536829	−	0.0929815i
$808$	−11.4049	+	6.58462i	−0.401223	+	0.231646i
$809$	40.0519	−	23.1240i	1.40815	−	0.812996i	0.412940	−	0.910758i	$-0.364502\pi$
$809$	40.0519	−	23.1240i	1.40815	−	0.812996i	0.995210	+	0.0977627i	$0.0311686\pi$
$810$	1.63416	−	2.83045i	0.0574185	−	0.0994518i
$811$	−22.9534			−0.806003			−0.403001	−	0.915199i	$-0.632033\pi$
$811$	−22.9534			−0.806003			−0.403001	+	0.915199i	$0.632033\pi$
$812$	8.77253	−	9.10479i	0.307855	−	0.319515i
$813$			22.4492i			0.787329i
$814$	6.96251	+	1.21363i	0.244036	+	0.0425376i
$815$	13.7145	−	7.91809i	0.480399	−	0.277359i
$816$	4.61228	−	2.66290i	0.161462	−	0.0932201i
$817$	−22.9713	−	13.2625i	−0.803666	−	0.463997i
$818$		−	34.3043i		−	1.19942i
$819$	−3.26558	+	13.1609i	−0.114108	+	0.459877i
$820$			3.10377i			0.108388i
$821$	14.2638	+	8.23523i	0.497812	+	0.287412i	0.727809	−	0.685780i	$-0.240539\pi$
$821$	14.2638	+	8.23523i	0.497812	+	0.287412i	−0.229998	+	0.973191i	$0.573872\pi$
$822$	−2.43055	−	4.20984i	−0.0847753	−	0.146835i
$823$	−6.10784	−	10.5791i	−0.212906	−	0.368764i	0.739717	−	0.672918i	$-0.234959\pi$
$823$	−6.10784	−	10.5791i	−0.212906	−	0.368764i	−0.952623	+	0.304155i	$0.901626\pi$
$824$	−6.60608	+	11.4421i	−0.230134	+	0.398603i
$825$	−6.47995	−	17.6956i	−0.225603	−	0.616082i
$826$	−34.2831	+	9.87247i	−1.19286	+	0.343507i
$827$			4.55524i			0.158401i	0.996859	+	0.0792007i	$0.0252368\pi$
$827$			4.55524i			0.158401i	−0.996859	+	0.0792007i	$0.974763\pi$
$828$	−2.68593	+	4.65217i	−0.0933425	+	0.161674i
$829$	−32.1952	+	18.5879i	−1.11819	+	0.645585i	−0.940937	−	0.338581i	$-0.890053\pi$
$829$	−32.1952	+	18.5879i	−1.11819	+	0.645585i	−0.177249	+	0.984166i	$0.556720\pi$
$830$	1.36591	+	2.36582i	0.0474113	+	0.0821188i
$831$	−10.2609	+	17.7724i	−0.355947	+	0.616518i
$832$	5.12518			0.177684
$833$	−32.9563	−	17.4277i	−1.14187	−	0.603835i
$834$	16.7827			0.581136
$835$	6.05494	+	3.49582i	0.209540	+	0.120978i
$836$	10.8790	+	9.09231i	0.376257	+	0.314464i
$837$	−3.23243	−	5.59873i	−0.111729	−	0.193520i
$838$	6.39844	−	11.0824i	0.221030	−	0.382836i
$839$		−	39.5086i		−	1.36399i	−0.731358	−	0.681994i	$-0.761113\pi$
$839$		−	39.5086i		−	1.36399i	0.731358	−	0.681994i	$-0.238887\pi$
$840$	2.39287	+	8.30948i	0.0825619	+	0.286704i
$841$	6.16366			0.212540
$842$	30.3417	+	17.5178i	1.04565	+	0.603704i
$843$	−6.94109	−	12.0223i	−0.239064	−	0.414071i
$844$	−7.83493	+	4.52350i	−0.269689	+	0.155705i
$845$	37.5528	+	21.6811i	1.29185	+	0.745853i
$846$	12.0303			0.413609
$847$	12.8899	+	26.0931i	0.442901	+	0.896570i
$848$	12.5399			0.430623
$849$	25.7956	+	14.8931i	0.885304	+	0.511130i
$850$	26.2065	−	15.1303i	0.898876	−	0.518966i
$851$	−5.72353	−	9.91344i	−0.196200	−	0.339828i
$852$	−9.35838	−	5.40306i	−0.320613	−	0.185106i
$853$	−34.2280			−1.17194			−0.585972	−	0.810331i	$-0.699287\pi$
$853$	−34.2280			−1.17194			−0.585972	+	0.810331i	$0.699287\pi$
$854$	9.80396	−	10.1753i	0.335484	−	0.348191i
$855$			13.9717i			0.477823i
$856$	5.55471	−	9.62104i	0.189856	−	0.328840i
$857$	0.822073	+	1.42387i	0.0280815	+	0.0486385i	0.879725	−	0.475484i	$-0.157727\pi$
$857$	0.822073	+	1.42387i	0.0280815	+	0.0486385i	−0.851643	+	0.524122i	$0.824394\pi$
$858$	13.0428	+	10.9008i	0.445274	+	0.372146i
$859$	−19.0267	−	10.9850i	−0.649181	−	0.374805i	0.138961	−	0.990298i	$-0.455624\pi$
$859$	−19.0267	−	10.9850i	−0.649181	−	0.374805i	−0.788142	+	0.615493i	$0.788957\pi$
$860$	−20.2794			−0.691521
$861$	1.74332	−	1.80934i	0.0594120	−	0.0616623i
$862$	25.9217			0.882896
$863$	−4.76103	+	8.24634i	−0.162067	+	0.280709i	−0.935610	−	0.353036i	$-0.885149\pi$
$863$	−4.76103	+	8.24634i	−0.162067	+	0.280709i	0.773543	+	0.633744i	$0.218483\pi$
$864$	0.500000	+	0.866025i	0.0170103	+	0.0294628i
$865$	50.2380	−	29.0049i	1.70814	−	0.986198i
$866$	−14.7554	+	25.5571i	−0.501408	+	0.868464i
$867$			11.3641i			0.385945i
$868$	16.6010	+	4.11917i	0.563474	+	0.139814i
$869$	−10.4546	−	28.5496i	−0.354646	−	0.968478i
$870$	7.80922	−	13.5260i	0.264757	−	0.458573i
$871$	15.8714	+	27.4901i	0.537782	+	0.931465i
$872$	3.56569	+	6.17596i	0.120750	+	0.209144i
$873$	−0.540692	−	0.312169i	−0.0182997	−	0.0105653i
$874$		−	22.9641i		−	0.776774i
$875$	1.63171	+	5.66628i	0.0551619	+	0.191555i
$876$			13.2295i			0.446984i
$877$	30.0244	+	17.3346i	1.01385	+	0.585347i	0.912317	−	0.409485i	$-0.134292\pi$
$877$	30.0244	+	17.3346i	1.01385	+	0.585347i	0.101534	+	0.994832i	$0.467625\pi$
$878$	−9.89069	+	5.71039i	−0.333795	+	0.192716i
$879$	9.00174	−	5.19716i	0.303621	−	0.175296i
$880$	10.6788	+	1.86140i	0.359981	+	0.0627479i
$881$			9.30311i			0.313430i	0.987644	+	0.156715i	$0.0500904\pi$
$881$			9.30311i			0.313430i	−0.987644	+	0.156715i	$0.949910\pi$
$882$	3.27232	−	6.18805i	0.110185	−	0.208362i
$883$	−40.2050			−1.35301			−0.676503	−	0.736440i	$-0.736505\pi$
$883$	−40.2050			−1.35301			−0.676503	+	0.736440i	$0.736505\pi$
$884$	−13.6478	+	23.6387i	−0.459026	+	0.795056i
$885$	−38.1668	+	22.0356i	−1.28296	+	0.740719i
$886$	−22.1020	+	12.7606i	−0.742530	+	0.428700i
$887$	−7.54456	+	13.0676i	−0.253322	+	0.438766i	−0.964438	−	0.264308i	$-0.914856\pi$
$887$	−7.54456	+	13.0676i	−0.253322	+	0.438766i	0.711117	+	0.703074i	$0.248190\pi$
$888$	−2.13093			−0.0715093
$889$	−10.1109	−	35.1110i	−0.339108	−	1.17758i
$890$		−	20.3423i		−	0.681874i
$891$	−0.569529	+	3.26736i	−0.0190799	+	0.109461i
$892$	−4.70196	+	2.71468i	−0.157433	+	0.0908940i
$893$	−44.5381	+	25.7141i	−1.49041	+	0.860488i
$894$	−6.25672	−	3.61232i	−0.209256	−	0.120814i
$895$		−	9.42811i		−	0.315147i
$896$	−2.56788	−	0.637163i	−0.0857869	−	0.0212861i
$897$		−	27.5317i		−	0.919258i
$898$	22.5131	+	12.9980i	0.751273	+	0.433747i
$899$	−15.4469	−	26.7549i	−0.515184	−	0.892324i
$900$	2.84095	+	4.92067i	0.0946984	+	0.164022i
$901$	−33.3925	+	57.8376i	−1.11247	+	1.92685i
$902$	−1.08303	−	2.95758i	−0.0360611	−	0.0984766i
$903$	11.8219	+	11.3905i	0.393408	+	0.379051i
$904$			2.41436i			0.0803004i
$905$	17.8698	−	30.9513i	0.594011	−	1.02886i
$906$	−4.22644	+	2.44014i	−0.140414	+	0.0810682i
$907$	9.26851	+	16.0535i	0.307756	+	0.533049i	0.977871	−	0.209208i	$-0.0670887\pi$
$907$	9.26851	+	16.0535i	0.307756	+	0.533049i	−0.670115	+	0.742257i	$0.733755\pi$
$908$	−5.92818	+	10.2679i	−0.196734	+	0.340752i
$909$	13.1692			0.436796
$910$	−31.9146	−	30.7500i	−1.05796	−	1.01935i
$911$	−33.6539			−1.11500			−0.557502	−	0.830176i	$-0.688240\pi$
$911$	−33.6539			−1.11500			−0.557502	+	0.830176i	$0.688240\pi$
$912$	−3.70217	−	2.13745i	−0.122591	−	0.0707780i
$913$	−2.12711	−	1.77777i	−0.0703970	−	0.0588356i
$914$	−4.01624	−	6.95633i	−0.132845	−	0.230095i
$915$	8.72739	−	15.1163i	0.288519	−	0.499729i
$916$		−	6.42701i		−	0.212354i
$917$	7.51002	−	30.2667i	0.248003	−	0.999495i
$918$	−5.32580			−0.175777
$919$	−11.9496	−	6.89909i	−0.394180	−	0.227580i	0.289790	−	0.957090i	$-0.406415\pi$
$919$	−11.9496	−	6.89909i	−0.394180	−	0.227580i	−0.683970	+	0.729510i	$0.739748\pi$
$920$	−8.77847	−	15.2048i	−0.289418	−	0.501286i
$921$	−1.19379	+	0.689237i	−0.0393368	+	0.0227111i
$922$	−29.0218	−	16.7557i	−0.955781	−	0.551821i
$923$	55.3833			1.82296
$924$	−5.17969	−	7.08313i	−0.170399	−	0.233018i
$925$	−12.1077			−0.398100
$926$	−13.6329	−	7.87094i	−0.448004	−	0.258655i
$927$	11.4421	−	6.60608i	0.375807	−	0.216972i
$928$	2.38937	+	4.13851i	0.0784349	+	0.135853i
$929$	−27.2253	−	15.7186i	−0.893234	−	0.515709i	−0.0182352	−	0.999834i	$-0.505805\pi$
$929$	−27.2253	−	15.7186i	−0.893234	−	0.515709i	−0.874999	+	0.484125i	$0.839138\pi$
$930$	21.1292			0.692854
$931$	1.11194	+	29.9036i	0.0364423	+	0.980051i
$932$			2.00886i			0.0658023i
$933$	5.26052	−	9.11149i	0.172222	−	0.298297i
$934$	5.11644	+	8.86193i	0.167415	+	0.289971i
$935$	−37.0218	+	44.2967i	−1.21074	+	1.44866i
$936$	−4.43853	−	2.56259i	−0.145078	−	0.0837608i
$937$	13.0822			0.427377			0.213689	−	0.976902i	$-0.431452\pi$
$937$	13.0822			0.427377			0.213689	+	0.976902i	$0.431452\pi$
$938$	−4.53452	−	15.7466i	−0.148057	−	0.514143i
$939$	2.26694			0.0739788
$940$	−19.6594	+	34.0510i	−0.641217	+	1.11062i
$941$	−19.1723	−	33.2075i	−0.625001	−	1.08253i	−0.988541	−	0.150954i	$-0.951765\pi$
$941$	−19.1723	−	33.2075i	−0.625001	−	1.08253i	0.363540	−	0.931579i	$-0.381568\pi$
$942$	−2.85996	+	1.65120i	−0.0931825	+	0.0537989i
$943$	−2.55070	+	4.41794i	−0.0830622	+	0.143868i
$944$		−	13.4844i		−	0.438879i
$945$	2.08245	−	8.39266i	0.0677422	−	0.273013i
$946$	19.3242	−	7.07632i	0.628284	−	0.230071i
$947$	−20.4702	+	35.4555i	−0.665193	+	1.15215i	0.314040	+	0.949410i	$0.398317\pi$
$947$	−20.4702	+	35.4555i	−0.665193	+	1.15215i	−0.979233	+	0.202738i	$0.935016\pi$
$948$	4.58351	+	7.93887i	0.148865	+	0.257843i
$949$	−33.9018	−	58.7196i	−1.10050	−	1.90612i
$950$	−21.0354	−	12.1448i	−0.682478	−	0.394029i
$951$		−	4.94169i		−	0.160245i
$952$	9.77678	−	10.1471i	0.316867	−	0.328869i
$953$			19.7503i			0.639776i	0.947455	+	0.319888i	$0.103645\pi$
$953$			19.7503i			0.639776i	−0.947455	+	0.319888i	$0.896355\pi$
$954$	−10.8599	−	6.26996i	−0.351602	−	0.202998i
$955$	−36.4475	+	21.0430i	−1.17941	+	0.680936i
$956$	−4.03454	+	2.32934i	−0.130486	+	0.0753364i
$957$	−2.72163	+	15.6139i	−0.0879778	+	0.504724i
$958$		−	5.19626i		−	0.167883i
$959$	−9.26172	−	8.92373i	−0.299077	−	0.288162i
$960$	−3.26832			−0.105485
$961$	5.39717	−	9.34818i	0.174102	−	0.301554i
$962$	9.45820	−	5.46070i	0.304945	−	0.176060i
$963$	−9.62104	+	5.55471i	−0.310034	+	0.178998i
$964$	2.98498	−	5.17014i	0.0961397	−	0.166519i
$965$	−19.7563			−0.635977
$966$	−3.42275	+	13.7943i	−0.110125	+	0.443824i
$967$		−	36.4927i		−	1.17352i	−0.809759	−	0.586762i	$-0.800402\pi$
$967$		−	36.4927i		−	1.17352i	0.809759	−	0.586762i	$-0.199598\pi$
$968$	−10.8253	+	1.95254i	−0.347939	+	0.0627570i
$969$	19.7170	−	11.3836i	0.633401	−	0.365694i
$970$	1.76715	−	1.02027i	0.0567399	−	0.0327588i
$971$	−44.5292	−	25.7089i	−1.42901	−	0.825039i	−0.431967	−	0.901889i	$-0.642180\pi$
$971$	−44.5292	−	25.7089i	−1.42901	−	0.825039i	−0.997043	+	0.0768499i	$0.975514\pi$
$972$		−	1.00000i		−	0.0320750i
$973$	42.6688	−	12.2873i	1.36790	−	0.393913i
$974$			31.5483i			1.01087i
$975$	−25.2193	−	14.5604i	−0.807665	−	0.466305i
$976$	2.67030	+	4.62509i	0.0854742	+	0.148046i
$977$	−3.90814	−	6.76910i	−0.125033	−	0.216563i	0.796713	−	0.604358i	$-0.206570\pi$
$977$	−3.90814	−	6.76910i	−0.125033	−	0.216563i	−0.921746	+	0.387795i	$0.873237\pi$
$978$	2.42268	−	4.19621i	0.0774688	−	0.134180i
$979$	7.09827	+	19.3841i	0.226862	+	0.619520i
$980$	12.1674	+	19.3744i	0.388675	+	0.618892i
$981$		−	7.13138i		−	0.227687i
$982$	3.57091	−	6.18500i	0.113952	−	0.197371i
$983$	12.7959	−	7.38773i	0.408126	−	0.235632i	−0.281858	−	0.959456i	$-0.590951\pi$
$983$	12.7959	−	7.38773i	0.408126	−	0.235632i	0.689984	+	0.723824i	$0.257617\pi$
$984$	0.474826	+	0.822423i	0.0151369	+	0.0262179i
$985$	−10.1030	+	17.4989i	−0.321908	+	0.557560i
$986$	−25.4506			−0.810512
$987$	30.5861	−	8.80785i	0.973567	−	0.280357i
$988$	21.9096			0.697037
$989$	−28.8659	−	16.6657i	−0.917883	−	0.529940i
$990$	−8.31739	−	6.95141i	−0.264344	−	0.220930i
$991$	0.272746	+	0.472410i	0.00866407	+	0.0150066i	0.870325	−	0.492478i	$-0.163909\pi$
$991$	0.272746	+	0.472410i	0.00866407	+	0.0150066i	−0.861661	+	0.507485i	$0.830575\pi$
$992$	−3.23243	+	5.59873i	−0.102630	+	0.177760i
$993$			12.9489i			0.410922i
$994$	−27.7489	−	6.88527i	−0.880141	−	0.218387i
$995$	−12.6891			−0.402272
$996$	0.723865	+	0.417924i	0.0229365	+	0.0132424i
$997$	−18.9612	−	32.8418i	−0.600508	−	1.04011i	−0.992744	−	0.120246i	$-0.961632\pi$
$997$	−18.9612	−	32.8418i	−0.600508	−	1.04011i	0.392236	−	0.919865i	$-0.371702\pi$
$998$	30.1061	−	17.3818i	0.952991	−	0.550210i
$999$	1.84544	+	1.06546i	0.0583871	+	0.0337098i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	462.2.p.b.439.8	yes	16
3.2	odd	2		1386.2.bk.b.901.1		16
7.2	even	3		3234.2.e.b.2155.1		16
7.3	odd	6		462.2.p.a.241.4	✓	16
7.5	odd	6		3234.2.e.a.2155.8		16
11.10	odd	2		462.2.p.a.439.4	yes	16
21.17	even	6		1386.2.bk.a.703.5		16
33.32	even	2		1386.2.bk.a.901.5		16
77.10	even	6	inner	462.2.p.b.241.8	yes	16
77.54	even	6		3234.2.e.b.2155.16		16
77.65	odd	6		3234.2.e.a.2155.9		16
231.164	odd	6		1386.2.bk.b.703.1		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
462.2.p.a.241.4	✓	16	7.3	odd	6
462.2.p.a.439.4	yes	16	11.10	odd	2
462.2.p.b.241.8	yes	16	77.10	even	6	inner
462.2.p.b.439.8	yes	16	1.1	even	1	trivial
1386.2.bk.a.703.5		16	21.17	even	6
1386.2.bk.a.901.5		16	33.32	even	2
1386.2.bk.b.703.1		16	231.164	odd	6
1386.2.bk.b.901.1		16	3.2	odd	2
3234.2.e.a.2155.8		16	7.5	odd	6
3234.2.e.a.2155.9		16	77.65	odd	6
3234.2.e.b.2155.1		16	7.2	even	3
3234.2.e.b.2155.16		16	77.54	even	6

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:	\( N \)	\(=\)	\( 462 = 2 \cdot 3 \cdot 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	462.p (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.866025 + 0.500000i) q^{2} +(0.866025 - 0.500000i) q^{3} +(0.500000 + 0.866025i) q^{4} +(2.83045 + 1.63416i) q^{5} +1.00000 q^{6} +(2.54243 - 0.732142i) q^{7} +1.00000i q^{8} +(0.500000 - 0.866025i) q^{9} +O(q^{10})\)	\(q+(0.866025 + 0.500000i) q^{2} +(0.866025 - 0.500000i) q^{3} +(0.500000 + 0.866025i) q^{4} +(2.83045 + 1.63416i) q^{5} +1.00000 q^{6} +(2.54243 - 0.732142i) q^{7} +1.00000i q^{8} +(0.500000 - 0.866025i) q^{9} +(1.63416 + 2.83045i) q^{10} +(-2.54485 - 2.12691i) q^{11} +(0.866025 + 0.500000i) q^{12} -5.12518 q^{13} +(2.56788 + 0.637163i) q^{14} +3.26832 q^{15} +(-0.500000 + 0.866025i) q^{16} +(-2.66290 - 4.61228i) q^{17} +(0.866025 - 0.500000i) q^{18} +(-2.13745 + 3.70217i) q^{19} +3.26832i q^{20} +(1.83574 - 1.90527i) q^{21} +(-1.14045 - 3.11438i) q^{22} +(-2.68593 + 4.65217i) q^{23} +(0.500000 + 0.866025i) q^{24} +(2.84095 + 4.92067i) q^{25} +(-4.43853 - 2.56259i) q^{26} -1.00000i q^{27} +(1.90527 + 1.83574i) q^{28} -4.77874i q^{29} +(2.83045 + 1.63416i) q^{30} +(5.59873 - 3.23243i) q^{31} +(-0.866025 + 0.500000i) q^{32} +(-3.26736 - 0.569529i) q^{33} -5.32580i q^{34} +(8.39266 + 2.08245i) q^{35} +1.00000 q^{36} +(-1.06546 + 1.84544i) q^{37} +(-3.70217 + 2.13745i) q^{38} +(-4.43853 + 2.56259i) q^{39} +(-1.63416 + 2.83045i) q^{40} +0.949652 q^{41} +(2.54243 - 0.732142i) q^{42} +6.20483i q^{43} +(0.569529 - 3.26736i) q^{44} +(2.83045 - 1.63416i) q^{45} +(-4.65217 + 2.68593i) q^{46} +(10.4185 + 6.01513i) q^{47} +1.00000i q^{48} +(5.92794 - 3.72284i) q^{49} +5.68190i q^{50} +(-4.61228 - 2.66290i) q^{51} +(-2.56259 - 4.43853i) q^{52} +(-6.26996 - 10.8599i) q^{53} +(0.500000 - 0.866025i) q^{54} +(-3.72736 - 10.1788i) q^{55} +(0.732142 + 2.54243i) q^{56} +4.27490i q^{57} +(2.38937 - 4.13851i) q^{58} +(-11.6778 + 6.74219i) q^{59} +(1.63416 + 2.83045i) q^{60} +(2.67030 - 4.62509i) q^{61} +6.46485 q^{62} +(0.637163 - 2.56788i) q^{63} -1.00000 q^{64} +(-14.5065 - 8.37536i) q^{65} +(-2.54485 - 2.12691i) q^{66} +(-3.09675 - 5.36373i) q^{67} +(2.66290 - 4.61228i) q^{68} +5.37186i q^{69} +(6.22703 + 5.99979i) q^{70} -10.8061 q^{71} +(0.866025 + 0.500000i) q^{72} +(6.61476 + 11.4571i) q^{73} +(-1.84544 + 1.06546i) q^{74} +(4.92067 + 2.84095i) q^{75} -4.27490 q^{76} +(-8.02731 - 3.54433i) q^{77} -5.12518 q^{78} +(7.93887 + 4.58351i) q^{79} +(-2.83045 + 1.63416i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(0.822423 + 0.474826i) q^{82} +0.835847 q^{83} +(2.56788 + 0.637163i) q^{84} -17.4064i q^{85} +(-3.10242 + 5.37354i) q^{86} +(-2.38937 - 4.13851i) q^{87} +(2.12691 - 2.54485i) q^{88} +(-5.39021 - 3.11204i) q^{89} +3.26832 q^{90} +(-13.0304 + 3.75236i) q^{91} -5.37186 q^{92} +(3.23243 - 5.59873i) q^{93} +(6.01513 + 10.4185i) q^{94} +(-12.0999 + 6.98586i) q^{95} +(-0.500000 + 0.866025i) q^{96} -0.624337i q^{97} +(6.99517 - 0.260109i) q^{98} +(-3.11438 + 1.14045i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 8 q^{4} + 12 q^{5} + 16 q^{6} + 6 q^{7} + 8 q^{9}+O(q^{10}) \) 16 * q + 8 * q^4 + 12 * q^5 + 16 * q^6 + 6 * q^7 + 8 * q^9	\( 16 q + 8 q^{4} + 12 q^{5} + 16 q^{6} + 6 q^{7} + 8 q^{9} - 2 q^{10} - 4 q^{11} + 8 q^{14} - 4 q^{15} - 8 q^{16} + 10 q^{19} + 4 q^{21} + 2 q^{22} - 4 q^{23} + 8 q^{24} + 10 q^{25} + 12 q^{26} + 12 q^{30} + 6 q^{31} + 4 q^{33} + 8 q^{35} + 16 q^{36} + 14 q^{37} - 12 q^{38} + 12 q^{39} + 2 q^{40} - 32 q^{41} + 6 q^{42} + 4 q^{44} + 12 q^{45} - 18 q^{46} - 24 q^{47} - 6 q^{49} - 6 q^{51} + 8 q^{54} + 14 q^{55} + 4 q^{56} - 2 q^{60} - 28 q^{61} + 8 q^{62} + 6 q^{63} - 16 q^{64} - 72 q^{65} - 4 q^{66} - 16 q^{67} - 30 q^{70} - 56 q^{71} + 44 q^{73} - 24 q^{74} - 12 q^{75} + 20 q^{76} - 52 q^{77} + 30 q^{79} - 12 q^{80} - 8 q^{81} - 12 q^{82} - 8 q^{83} + 8 q^{84} - 12 q^{86} - 2 q^{88} - 36 q^{89} - 4 q^{90} - 8 q^{91} - 8 q^{92} + 4 q^{93} - 14 q^{94} - 72 q^{95} - 8 q^{96} + 40 q^{98} - 8 q^{99}+O(q^{100}) \) 16 * q + 8 * q^4 + 12 * q^5 + 16 * q^6 + 6 * q^7 + 8 * q^9 - 2 * q^10 - 4 * q^11 + 8 * q^14 - 4 * q^15 - 8 * q^16 + 10 * q^19 + 4 * q^21 + 2 * q^22 - 4 * q^23 + 8 * q^24 + 10 * q^25 + 12 * q^26 + 12 * q^30 + 6 * q^31 + 4 * q^33 + 8 * q^35 + 16 * q^36 + 14 * q^37 - 12 * q^38 + 12 * q^39 + 2 * q^40 - 32 * q^41 + 6 * q^42 + 4 * q^44 + 12 * q^45 - 18 * q^46 - 24 * q^47 - 6 * q^49 - 6 * q^51 + 8 * q^54 + 14 * q^55 + 4 * q^56 - 2 * q^60 - 28 * q^61 + 8 * q^62 + 6 * q^63 - 16 * q^64 - 72 * q^65 - 4 * q^66 - 16 * q^67 - 30 * q^70 - 56 * q^71 + 44 * q^73 - 24 * q^74 - 12 * q^75 + 20 * q^76 - 52 * q^77 + 30 * q^79 - 12 * q^80 - 8 * q^81 - 12 * q^82 - 8 * q^83 + 8 * q^84 - 12 * q^86 - 2 * q^88 - 36 * q^89 - 4 * q^90 - 8 * q^91 - 8 * q^92 + 4 * q^93 - 14 * q^94 - 72 * q^95 - 8 * q^96 + 40 * q^98 - 8 * q^99

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