LMFDB - Embedded newform 1386.2.bk.b.703.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1386,2,Mod(703,1386)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1386, 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("1386.703");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1386 = 2 \cdot 3^{2} \cdot 7 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1386.bk (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:	$11.0672657201$
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:	no (minimal twist has level 462)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			703.1
Root			$0.500000 + 2.40229i$ of defining polynomial
Character	$\chi$	$=$	1386.703
Dual form			1386.2.bk.b.901.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

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

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1386\mathbb{Z}\right)^\times$.

$n$	$155$	$199$	$1135$
$\chi(n)$	$1$	$e\left(\frac{1}{6}\right)$	$-1$

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			0
$3$		0			0
$4$	0.500000	−	0.866025i	0.250000	−	0.433013i
$5$	−2.83045	+	1.63416i	−1.26581	+	0.730818i	−0.974193	−	0.225716i	$-0.927528\pi$
$5$	−2.83045	+	1.63416i	−1.26581	+	0.730818i	−0.291621	+	0.956534i	$0.594195\pi$
$6$		0			0
$7$	2.54243	+	0.732142i	0.960950	+	0.276724i
$7$	2.54243	+	0.732142i	0.960950	+	0.276724i
$8$			1.00000i			0.353553i
$9$		0			0
$10$	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			0
$13$	−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
$15$		0			0
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	2.66290	−	4.61228i	0.645848	−	1.11864i	−0.338257	−	0.941054i	$-0.609837\pi$
$17$	2.66290	−	4.61228i	0.645848	−	1.11864i	0.984105	−	0.177587i	$-0.0568292\pi$
$18$		0			0
$19$	−2.13745	−	3.70217i	−0.490364	−	0.849336i	0.509574	−	0.860427i	$-0.329803\pi$
$19$	−2.13745	−	3.70217i	−0.490364	−	0.849336i	−0.999938	+	0.0110907i	$0.996470\pi$
$20$			3.26832i			0.730818i
$21$		0			0
$22$	−1.14045	+	3.11438i	−0.243145	+	0.663988i
$23$	2.68593	+	4.65217i	0.560055	+	0.970044i	0.997491	+	0.0707942i	$0.0225533\pi$
$23$	2.68593	+	4.65217i	0.560055	+	0.970044i	−0.437436	+	0.899250i	$0.644113\pi$
$24$		0			0
$25$	2.84095	−	4.92067i	0.568190	−	0.984135i
$26$	4.43853	−	2.56259i	0.870468	−	0.502565i
$27$		0			0
$28$	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	$-0.146333\pi$
$30$		0			0
$31$	5.59873	+	3.23243i	1.00556	+	0.580561i	0.909889	−	0.414852i	$-0.136167\pi$
$31$	5.59873	+	3.23243i	1.00556	+	0.580561i	0.0956723	+	0.995413i	$0.469500\pi$
$32$	0.866025	+	0.500000i	0.153093	+	0.0883883i
$33$		0			0
$34$			5.32580i			0.913367i
$35$	−8.39266	+	2.08245i	−1.41862	+	0.351999i
$36$		0			0
$37$	−1.06546	−	1.84544i	−0.175161	−	0.303388i	0.765056	−	0.643964i	$-0.222711\pi$
$37$	−1.06546	−	1.84544i	−0.175161	−	0.303388i	−0.940217	+	0.340576i	$0.889378\pi$
$38$	3.70217	+	2.13745i	0.600571	+	0.346740i
$39$		0			0
$40$	−1.63416	−	2.83045i	−0.258383	−	0.447533i
$41$	−0.949652			−0.148311			−0.0741554	−	0.997247i	$-0.523626\pi$
$41$	−0.949652			−0.148311			−0.0741554	+	0.997247i	$0.523626\pi$
$42$		0			0
$43$		−	6.20483i		−	0.946228i	−0.881001	−	0.473114i	$-0.843130\pi$
$43$		−	6.20483i		−	0.946228i	0.881001	−	0.473114i	$-0.156870\pi$
$44$	−0.569529	−	3.26736i	−0.0858597	−	0.492573i
$45$		0			0
$46$	−4.65217	−	2.68593i	−0.685925	−	0.396019i
$47$	−10.4185	+	6.01513i	−1.51970	+	0.877397i	−0.519965	+	0.854188i	$0.674055\pi$
$47$	−10.4185	+	6.01513i	−1.51970	+	0.877397i	−0.999731	+	0.0232091i	$0.992612\pi$
$48$		0			0
$49$	5.92794	+	3.72284i	0.846848	+	0.531835i
$50$			5.68190i			0.803543i
$51$		0			0
$52$	−2.56259	+	4.43853i	−0.355367	+	0.615514i
$53$	6.26996	−	10.8599i	0.861246	−	1.49172i	−0.00948193	−	0.999955i	$-0.503018\pi$
$53$	6.26996	−	10.8599i	0.861246	−	1.49172i	0.870727	−	0.491766i	$-0.163648\pi$
$54$		0			0
$55$	−3.72736	+	10.1788i	−0.502598	+	1.37251i
$56$	−0.732142	+	2.54243i	−0.0978366	+	0.339747i
$57$		0			0
$58$	2.38937	+	4.13851i	0.313740	+	0.543413i
$59$	11.6778	+	6.74219i	1.52032	+	0.877758i	0.999713	+	0.0239621i	$0.00762810\pi$
$59$	11.6778	+	6.74219i	1.52032	+	0.877758i	0.520608	+	0.853796i	$0.325705\pi$
$60$		0			0
$61$	2.67030	+	4.62509i	0.341897	+	0.592183i	0.984785	−	0.173778i	$-0.0555974\pi$
$61$	2.67030	+	4.62509i	0.341897	+	0.592183i	−0.642888	+	0.765960i	$0.722264\pi$
$62$	−6.46485			−0.821037
$63$		0			0
$64$	−1.00000			−0.125000
$65$	14.5065	−	8.37536i	1.79931	−	1.03883i
$66$		0			0
$67$	−3.09675	+	5.36373i	−0.378328	+	0.655284i	−0.990819	−	0.135194i	$-0.956834\pi$
$67$	−3.09675	+	5.36373i	−0.378328	+	0.655284i	0.612491	+	0.790478i	$0.290168\pi$
$68$	−2.66290	−	4.61228i	−0.322924	−	0.559321i
$69$		0			0
$70$	6.22703	−	5.99979i	0.744272	−	0.717112i
$71$	10.8061			1.28245			0.641226	−	0.767352i	$-0.278426\pi$
$71$	10.8061			1.28245			0.641226	+	0.767352i	$0.278426\pi$
$72$		0			0
$73$	6.61476	−	11.4571i	0.774199	−	1.34095i	−0.161045	−	0.986947i	$-0.551486\pi$
$73$	6.61476	−	11.4571i	0.774199	−	1.34095i	0.935244	−	0.354005i	$-0.115180\pi$
$74$	1.84544	+	1.06546i	0.214528	+	0.123858i
$75$		0			0
$76$	−4.27490			−0.490364
$77$	8.02731	−	3.54433i	0.914797	−	0.403913i
$78$		0			0
$79$	7.93887	−	4.58351i	0.893193	−	0.515685i	0.0182072	−	0.999834i	$-0.494204\pi$
$79$	7.93887	−	4.58351i	0.893193	−	0.515685i	0.874985	+	0.484149i	$0.160871\pi$
$80$	2.83045	+	1.63416i	0.316454	+	0.182705i
$81$		0			0
$82$	0.822423	−	0.474826i	0.0908214	−	0.0524358i
$83$	−0.835847			−0.0917462			−0.0458731	−	0.998947i	$-0.514607\pi$
$83$	−0.835847			−0.0917462			−0.0458731	+	0.998947i	$0.514607\pi$
$84$		0			0
$85$			17.4064i			1.88799i
$86$	3.10242	+	5.37354i	0.334542	+	0.579444i
$87$		0			0
$88$	2.12691	+	2.54485i	0.226729	+	0.271282i
$89$	5.39021	−	3.11204i	0.571361	−	0.329875i	−0.186332	−	0.982487i	$-0.559660\pi$
$89$	5.39021	−	3.11204i	0.571361	−	0.329875i	0.757693	+	0.652611i	$0.226327\pi$
$90$		0			0
$91$	−13.0304	−	3.75236i	−1.36596	−	0.393354i
$92$	5.37186			0.560055
$93$		0			0
$94$	6.01513	−	10.4185i	0.620413	−	1.07459i
$95$	12.0999	+	6.98586i	1.24142	+	0.716734i
$96$		0			0
$97$			0.624337i			0.0633919i	0.999498	+	0.0316959i	$0.0100908\pi$
$97$			0.624337i			0.0633919i	−0.999498	+	0.0316959i	$0.989909\pi$
$98$	−6.99517	−	0.260109i	−0.706618	−	0.0262750i
$99$		0			0
$100$	−2.84095	−	4.92067i	−0.284095	−	0.492067i
$101$	−6.58462	+	11.4049i	−0.655194	+	1.13483i	0.326651	+	0.945145i	$0.394080\pi$
$101$	−6.58462	+	11.4049i	−0.655194	+	1.13483i	−0.981845	+	0.189685i	$0.939253\pi$
$102$		0			0
$103$	11.4421	−	6.60608i	1.12742	−	0.650916i	0.184135	−	0.982901i	$-0.441052\pi$
$103$	11.4421	−	6.60608i	1.12742	−	0.650916i	0.943285	+	0.331985i	$0.107718\pi$
$104$		−	5.12518i		−	0.502565i
$105$		0			0
$106$			12.5399i			1.21799i
$107$	9.62104	−	5.55471i	0.930101	−	0.536994i	0.0432576	−	0.999064i	$-0.486226\pi$
$107$	9.62104	−	5.55471i	0.930101	−	0.536994i	0.886844	+	0.462070i	$0.152893\pi$
$108$		0			0
$109$	6.17596	+	3.56569i	0.591549	+	0.341531i	0.765710	−	0.643186i	$-0.222388\pi$
$109$	6.17596	+	3.56569i	0.591549	+	0.341531i	−0.174161	+	0.984717i	$0.555721\pi$
$110$	−1.86140	−	10.6788i	−0.177478	−	1.01818i
$111$		0			0
$112$	−0.637163	−	2.56788i	−0.0602063	−	0.242642i
$113$	−2.41436			−0.227124			−0.113562	−	0.993531i	$-0.536226\pi$
$113$	−2.41436			−0.227124			−0.113562	+	0.993531i	$0.536226\pi$
$114$		0			0
$115$	−15.2048	−	8.77847i	−1.41785	−	0.818597i
$116$	−4.13851	−	2.38937i	−0.384251	−	0.221847i
$117$		0			0
$118$	−13.4844			−1.24134
$119$	10.1471	−	9.77678i	0.930181	−	0.896236i
$120$		0			0
$121$	1.95254	−	10.8253i	0.177504	−	0.984120i
$122$	−4.62509	−	2.67030i	−0.418736	−	0.241758i
$123$		0			0
$124$	5.59873	−	3.23243i	0.502781	−	0.290281i
$125$			2.22868i			0.199339i
$126$		0			0
$127$			13.8100i			1.22544i	0.790301	+	0.612719i	$0.209924\pi$
$127$			13.8100i			1.22544i	−0.790301	+	0.612719i	$0.790076\pi$
$128$	0.866025	−	0.500000i	0.0765466	−	0.0441942i
$129$		0			0
$130$	−8.37536	+	14.5065i	−0.734567	+	1.27231i
$131$	−5.89332	−	10.2075i	−0.514902	−	0.891836i	−0.999850	−	0.0172935i	$-0.994495\pi$
$131$	−5.89332	−	10.2075i	−0.514902	−	0.891836i	0.484949	−	0.874543i	$-0.338838\pi$
$132$		0			0
$133$	−2.72381	−	10.9774i	−0.236184	−	0.951864i
$134$		−	6.19350i		−	0.535037i
$135$		0			0
$136$	4.61228	+	2.66290i	0.395499	+	0.228342i
$137$	2.43055	−	4.20984i	0.207656	−	0.359671i	−0.743320	−	0.668936i	$-0.766750\pi$
$137$	2.43055	−	4.20984i	0.207656	−	0.359671i	0.950976	+	0.309265i	$0.100083\pi$
$138$		0			0
$139$	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
$141$		0			0
$142$	−9.35838	+	5.40306i	−0.785338	+	0.453415i
$143$	−13.0428	+	10.9008i	−1.09069	+	0.911568i
$144$		0			0
$145$	7.80922	+	13.5260i	0.648520	+	1.12327i
$146$			13.2295i			1.09488i
$147$		0			0
$148$	−2.13093			−0.175161
$149$	6.25672	−	3.61232i	0.512571	−	0.295933i	−0.221319	−	0.975201i	$-0.571036\pi$
$149$	6.25672	−	3.61232i	0.512571	−	0.295933i	0.733890	+	0.679269i	$0.237703\pi$
$150$		0			0
$151$	−4.22644	−	2.44014i	−0.343943	−	0.198576i	0.318071	−	0.948067i	$-0.396965\pi$
$151$	−4.22644	−	2.44014i	−0.343943	−	0.198576i	−0.662014	+	0.749491i	$0.730298\pi$
$152$	3.70217	−	2.13745i	0.300286	−	0.173370i
$153$		0			0
$154$	−5.17969	+	7.08313i	−0.417392	+	0.570775i
$155$	−21.1292			−1.69714
$156$		0			0
$157$	−2.85996	−	1.65120i	−0.228249	−	0.131780i	0.381515	−	0.924363i	$-0.375403\pi$
$157$	−2.85996	−	1.65120i	−0.228249	−	0.131780i	−0.609764	+	0.792583i	$0.708736\pi$
$158$	−4.58351	+	7.93887i	−0.364644	+	0.631583i
$159$		0			0
$160$	−3.26832			−0.258383
$161$	3.42275	+	13.7943i	0.269751	+	1.08714i
$162$		0			0
$163$	2.42268	+	4.19621i	0.189759	+	0.328672i	0.945170	−	0.326579i	$-0.105896\pi$
$163$	2.42268	+	4.19621i	0.189759	+	0.328672i	−0.755411	+	0.655252i	$0.772563\pi$
$164$	−0.474826	+	0.822423i	−0.0370777	+	0.0642205i
$165$		0			0
$166$	0.723865	−	0.417924i	0.0561828	−	0.0324372i
$167$	−2.13922			−0.165538			−0.0827688	−	0.996569i	$-0.526376\pi$
$167$	−2.13922			−0.165538			−0.0827688	+	0.996569i	$0.526376\pi$
$168$		0			0
$169$	13.2674			1.02057
$170$	−8.70320	−	15.0744i	−0.667505	−	1.15615i
$171$		0			0
$172$	−5.37354	−	3.10242i	−0.409729	−	0.236557i
$173$	−8.87458	−	15.3712i	−0.674722	−	1.16865i	−0.976550	−	0.215290i	$-0.930930\pi$
$173$	−8.87458	−	15.3712i	−0.674722	−	1.16865i	0.301828	−	0.953362i	$-0.402403\pi$
$174$		0			0
$175$	10.8256	−	10.4305i	0.818336	−	0.788472i
$176$	−3.11438	−	1.14045i	−0.234755	−	0.0859649i
$177$		0			0
$178$	−3.11204	+	5.39021i	−0.233257	+	0.404013i
$179$	1.44235	−	2.49822i	0.107806	−	0.186726i	−0.807075	−	0.590449i	$-0.798951\pi$
$179$	1.44235	−	2.49822i	0.107806	−	0.186726i	0.914881	+	0.403723i	$0.132284\pi$
$180$		0			0
$181$			10.9351i			0.812803i	0.913695	+	0.406401i	$0.133217\pi$
$181$			10.9351i			0.812803i	−0.913695	+	0.406401i	$0.866783\pi$
$182$	13.1609	−	3.26558i	0.975547	−	0.242061i
$183$		0			0
$184$	−4.65217	+	2.68593i	−0.342962	+	0.198009i
$185$	6.03148	+	3.48228i	0.443443	+	0.256022i
$186$		0			0
$187$	−3.03320	−	17.4013i	−0.221809	−	1.27251i
$188$			12.0303i			0.877397i
$189$		0			0
$190$	−13.9717			−1.01362
$191$	6.43848	+	11.1518i	0.465872	+	0.806914i	0.999240	−	0.0389690i	$-0.0124074\pi$
$191$	6.43848	+	11.1518i	0.465872	+	0.806914i	−0.533368	+	0.845883i	$0.679074\pi$
$192$		0			0
$193$	−5.23494	−	3.02239i	−0.376819	−	0.217557i	0.299614	−	0.954060i	$-0.403142\pi$
$193$	−5.23494	−	3.02239i	−0.376819	−	0.217557i	−0.676433	+	0.736504i	$0.736475\pi$
$194$	−0.312169	−	0.540692i	−0.0224124	−	0.0388194i
$195$		0			0
$196$	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	$0.929317\pi$
$198$		0			0
$199$	−3.36231	−	1.94123i	−0.238348	−	0.137610i	0.376069	−	0.926591i	$-0.377275\pi$
$199$	−3.36231	−	1.94123i	−0.238348	−	0.137610i	−0.614417	+	0.788981i	$0.710609\pi$
$200$	4.92067	+	2.84095i	0.347944	+	0.200886i
$201$		0			0
$202$		−	13.1692i		−	0.926585i
$203$	3.49871	−	12.1496i	0.245562	−	0.852736i
$204$		0			0
$205$	2.68794	−	1.55188i	0.187734	−	0.108388i
$206$	−6.60608	+	11.4421i	−0.460267	+	0.797206i
$207$		0			0
$208$	2.56259	+	4.43853i	0.177684	+	0.307757i
$209$	−13.3137	−	4.87532i	−0.920925	−	0.337233i
$210$		0			0
$211$		−	9.04700i		−	0.622821i	−0.950276	−	0.311410i	$-0.899199\pi$
$211$		−	9.04700i		−	0.622821i	0.950276	−	0.311410i	$-0.100801\pi$
$212$	−6.26996	−	10.8599i	−0.430623	−	0.745860i
$213$		0			0
$214$	−5.55471	+	9.62104i	−0.379712	+	0.657681i
$215$	10.1397	+	17.5624i	0.691521	+	1.19775i
$216$		0			0
$217$	11.8678	+	12.3173i	0.805639	+	0.836152i
$218$	−7.13138			−0.482998
$219$		0			0
$220$	6.95141	+	8.31739i	0.468664	+	0.560758i
$221$	−13.6478	+	23.6387i	−0.918052	+	1.59011i
$222$		0			0
$223$		−	5.42935i		−	0.363576i	−0.983338	−	0.181788i	$-0.941812\pi$
$223$		−	5.42935i		−	0.363576i	0.983338	−	0.181788i	$-0.0581885\pi$
$224$	1.83574	+	1.90527i	0.122656	+	0.127301i
$225$		0			0
$226$	2.09090	−	1.20718i	0.139084	−	0.0803004i
$227$	−5.92818	+	10.2679i	−0.393467	+	0.681505i	−0.992904	−	0.118917i	$-0.962058\pi$
$227$	−5.92818	+	10.2679i	−0.393467	+	0.681505i	0.599437	+	0.800422i	$0.295391\pi$
$228$		0			0
$229$	−5.56595	+	3.21350i	−0.367808	+	0.212354i	−0.672501	−	0.740097i	$-0.734780\pi$
$229$	−5.56595	+	3.21350i	−0.367808	+	0.212354i	0.304692	+	0.952451i	$0.401446\pi$
$230$	17.5569			1.15767
$231$		0			0
$232$	4.77874			0.313740
$233$	−1.73972	+	1.00443i	−0.113973	+	0.0658023i	−0.555903	−	0.831247i	$-0.687627\pi$
$233$	−1.73972	+	1.00443i	−0.113973	+	0.0658023i	0.441930	+	0.897050i	$0.354294\pi$
$234$		0			0
$235$	19.6594	−	34.0510i	1.28243	−	2.22124i
$236$	11.6778	−	6.74219i	0.760161	−	0.438879i
$237$		0			0
$238$	−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	$0.951856\pi$
$240$		0			0
$241$	−2.98498	+	5.17014i	−0.192279	+	0.333038i	−0.946005	−	0.324151i	$-0.894921\pi$
$241$	−2.98498	+	5.17014i	−0.192279	+	0.333038i	0.753726	+	0.657189i	$0.228255\pi$
$242$	3.72171	+	10.3513i	0.239241	+	0.665405i
$243$		0			0
$244$	5.34060			0.341897
$245$	−22.8624	−	0.850118i	−1.46063	−	0.0543121i
$246$		0			0
$247$	10.9548	+	18.9743i	0.697037	+	1.20730i
$248$	−3.23243	+	5.59873i	−0.205259	+	0.355520i
$249$		0			0
$250$	−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	$0.985358\pi$
$252$		0			0
$253$	16.7300	+	6.12635i	1.05181	+	0.385161i
$254$	−6.90499	−	11.9598i	−0.433258	−	0.750424i
$255$		0			0
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	−22.8407	+	13.1871i	−1.42477	+	0.822589i	−0.996701	−	0.0811588i	$-0.974138\pi$
$257$	−22.8407	+	13.1871i	−1.42477	+	0.822589i	−0.428065	+	0.903748i	$0.640805\pi$
$258$		0			0
$259$	−1.35775	−	5.47198i	−0.0843665	−	0.340012i
$260$		−	16.7507i		−	1.03883i
$261$		0			0
$262$	10.2075	+	5.89332i	0.630623	+	0.364091i
$263$	27.1221	+	15.6589i	1.67242	+	0.965571i	0.966279	+	0.257497i	$0.0828977\pi$
$263$	27.1221	+	15.6589i	1.67242	+	0.965571i	0.706138	+	0.708074i	$0.250436\pi$
$264$		0			0
$265$			40.9845i			2.51766i
$266$	7.84761	+	8.14484i	0.481168	+	0.499392i
$267$		0			0
$268$	3.09675	+	5.36373i	0.189164	+	0.327642i
$269$	−2.64139	−	1.52501i	−0.161049	−	0.0929815i	0.417310	−	0.908764i	$-0.362973\pi$
$269$	−2.64139	−	1.52501i	−0.161049	−	0.0929815i	−0.578358	+	0.815783i	$0.696306\pi$
$270$		0			0
$271$	−11.2246	−	19.4416i	−0.681847	−	1.18099i	−0.974417	−	0.224750i	$-0.927844\pi$
$271$	−11.2246	−	19.4416i	−0.681847	−	1.18099i	0.292569	−	0.956244i	$-0.405490\pi$
$272$	−5.32580			−0.322924
$273$		0			0
$274$			4.86111i			0.293670i
$275$	−3.23601	−	18.5648i	−0.195139	−	1.11950i
$276$		0			0
$277$	−17.7724	−	10.2609i	−1.06784	−	0.616518i	−0.140250	−	0.990116i	$-0.544791\pi$
$277$	−17.7724	−	10.2609i	−1.06784	−	0.616518i	−0.927591	+	0.373598i	$0.878124\pi$
$278$	−14.5342	+	8.39134i	−0.871705	+	0.503279i
$279$		0			0
$280$	−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	$-0.135893\pi$
$282$		0			0
$283$	14.8931	−	25.7956i	0.885304	−	1.53339i	0.0399386	−	0.999202i	$-0.487284\pi$
$283$	14.8931	−	25.7956i	0.885304	−	1.53339i	0.845365	−	0.534189i	$-0.179383\pi$
$284$	5.40306	−	9.35838i	0.320613	−	0.555318i
$285$		0			0
$286$	5.84502	−	15.9618i	0.345624	−	0.943838i
$287$	−2.41443	−	0.695280i	−0.142519	−	0.0410411i
$288$		0			0
$289$	−5.68205	−	9.84161i	−0.334238	−	0.578918i
$290$	−13.5260	−	7.80922i	−0.794272	−	0.458573i
$291$		0			0
$292$	−6.61476	−	11.4571i	−0.387099	−	0.670476i
$293$	−10.3943			−0.607243			−0.303621	−	0.952793i	$-0.598196\pi$
$293$	−10.3943			−0.607243			−0.303621	+	0.952793i	$0.598196\pi$
$294$		0			0
$295$	−44.0712			−2.56593
$296$	1.84544	−	1.06546i	0.107264	−	0.0619289i
$297$		0			0
$298$	−3.61232	+	6.25672i	−0.209256	+	0.362442i
$299$	−13.7659	−	23.8432i	−0.796100	−	1.37889i
$300$		0			0
$301$	4.54282	−	15.7754i	0.261844	−	0.909277i
$302$	4.88028			0.280828
$303$		0			0
$304$	−2.13745	+	3.70217i	−0.122591	+	0.212334i
$305$	−15.1163	−	8.72739i	−0.865556	−	0.499729i
$306$		0			0
$307$	−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
$309$		0			0
$310$	18.2984	−	10.5646i	1.03928	−	0.600029i
$311$	−9.11149	−	5.26052i	−0.516665	−	0.298297i	0.218904	−	0.975746i	$-0.429752\pi$
$311$	−9.11149	−	5.26052i	−0.516665	−	0.298297i	−0.735569	+	0.677450i	$0.763085\pi$
$312$		0			0
$313$	1.96323	−	1.13347i	0.110968	−	0.0640676i	−0.443489	−	0.896280i	$-0.646259\pi$
$313$	1.96323	−	1.13347i	0.110968	−	0.0640676i	0.554457	+	0.832212i	$0.312926\pi$
$314$	3.30239			0.186365
$315$		0			0
$316$		−	9.16702i		−	0.515685i
$317$	−2.47085	−	4.27963i	−0.138777	−	0.240368i	0.788257	−	0.615346i	$-0.210984\pi$
$317$	−2.47085	−	4.27963i	−0.138777	−	0.240368i	−0.927034	+	0.374978i	$0.877650\pi$
$318$		0			0
$319$	−10.1639	−	12.1612i	−0.569071	−	0.680895i
$320$	2.83045	−	1.63416i	0.158227	−	0.0913523i
$321$		0			0
$322$	−9.86134	−	10.2348i	−0.549551	−	0.570365i
$323$	−22.7672			−1.26680
$324$		0			0
$325$	−14.5604	+	25.2193i	−0.807665	+	1.39892i
$326$	−4.19621	−	2.42268i	−0.232406	−	0.134180i
$327$		0			0
$328$		−	0.949652i		−	0.0524358i
$329$	−30.8923	+	7.66524i	−1.70315	+	0.422598i
$330$		0			0
$331$	−6.47446	−	11.2141i	−0.355869	−	0.616383i	0.631398	−	0.775459i	$-0.282482\pi$
$331$	−6.47446	−	11.2141i	−0.355869	−	0.616383i	−0.987266	+	0.159077i	$0.949148\pi$
$332$	−0.417924	+	0.723865i	−0.0229365	+	0.0397272i
$333$		0			0
$334$	1.85262	−	1.06961i	0.101371	−	0.0585264i
$335$		−	20.2423i		−	1.10596i
$336$		0			0
$337$			8.22142i			0.447849i	0.974606	+	0.223925i	$0.0718869\pi$
$337$			8.22142i			0.447849i	−0.974606	+	0.223925i	$0.928113\pi$
$338$	−11.4899	+	6.63372i	−0.624970	+	0.360827i
$339$		0			0
$340$	15.0744	+	8.70320i	0.817523	+	0.471997i
$341$	21.1230	−	3.68192i	1.14387	−	0.199387i
$342$		0			0
$343$	12.3457	+	13.8052i	0.666607	+	0.745409i
$344$	6.20483			0.334542
$345$		0			0
$346$	15.3712	+	8.87458i	0.826362	+	0.477100i
$347$	−27.1635	−	15.6829i	−1.45821	−	0.841901i	−0.459291	−	0.888286i	$-0.651897\pi$
$347$	−27.1635	−	15.6829i	−1.45821	−	0.841901i	−0.998924	+	0.0463849i	$0.985230\pi$
$348$		0			0
$349$	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
$351$		0			0
$352$	3.26736	−	0.569529i	0.174151	−	0.0303560i
$353$	7.06177	+	4.07712i	0.375860	+	0.217003i	0.676016	−	0.736887i	$-0.263705\pi$
$353$	7.06177	+	4.07712i	0.375860	+	0.217003i	−0.300155	+	0.953890i	$0.597039\pi$
$354$		0			0
$355$	−30.5862	+	17.6589i	−1.62335	+	0.937239i
$356$		−	6.22408i		−	0.329875i
$357$		0			0
$358$			2.88470i			0.152461i
$359$	8.26228	−	4.77023i	0.436067	−	0.251763i	−0.265861	−	0.964011i	$-0.585656\pi$
$359$	8.26228	−	4.77023i	0.436067	−	0.251763i	0.701928	+	0.712248i	$0.252323\pi$
$360$		0			0
$361$	0.362625	−	0.628085i	0.0190855	−	0.0330571i
$362$	−5.46757	−	9.47011i	−0.287369	−	0.497738i
$363$		0			0
$364$	−9.76485	+	9.40850i	−0.511817	+	0.493139i
$365$			43.2383i			2.26319i
$366$		0			0
$367$	−5.86022	−	3.38340i	−0.305901	−	0.176612i	0.339190	−	0.940718i	$-0.389847\pi$
$367$	−5.86022	−	3.38340i	−0.305901	−	0.176612i	−0.645091	+	0.764106i	$0.723180\pi$
$368$	2.68593	−	4.65217i	0.140014	−	0.242511i
$369$		0			0
$370$	−6.96456			−0.362070
$371$	23.8919	−	23.0201i	1.24041	−	1.19514i
$372$		0			0
$373$	−0.412900	+	0.238388i	−0.0213791	+	0.0123433i	−0.510651	−	0.859788i	$-0.670596\pi$
$373$	−0.412900	+	0.238388i	−0.0213791	+	0.0123433i	0.489272	+	0.872131i	$0.337262\pi$
$374$	11.3275	+	13.5534i	0.585730	+	0.700828i
$375$		0			0
$376$	−6.01513	−	10.4185i	−0.310207	−	0.537294i
$377$			24.4919i			1.26140i
$378$		0			0
$379$	−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
$381$		0			0
$382$	−11.1518	−	6.43848i	−0.570574	−	0.329421i
$383$	−10.5825	+	6.10983i	−0.540743	+	0.312198i	−0.745380	−	0.666640i	$-0.767732\pi$
$383$	−10.5825	+	6.10983i	−0.540743	+	0.312198i	0.204637	+	0.978838i	$0.434399\pi$
$384$		0			0
$385$	−16.9289	+	23.1499i	−0.862776	+	1.17983i
$386$	6.04479			0.307672
$387$		0			0
$388$	0.540692	+	0.312169i	0.0274495	+	0.0158480i
$389$	14.0160	−	24.2765i	0.710641	−	1.23087i	−0.253975	−	0.967211i	$-0.581738\pi$
$389$	14.0160	−	24.2765i	0.710641	−	1.23087i	0.964617	−	0.263656i	$-0.0849285\pi$
$390$		0			0
$391$	28.6094			1.44684
$392$	−3.72284	+	5.92794i	−0.188032	+	0.299406i
$393$		0			0
$394$	−3.09118	−	5.35409i	−0.155732	−	0.269735i
$395$	−14.9804	+	25.9468i	−0.753744	+	1.30552i
$396$		0			0
$397$	−26.1090	+	15.0741i	−1.31038	+	0.756546i	−0.982158	−	0.188057i	$-0.939781\pi$
$397$	−26.1090	+	15.0741i	−1.31038	+	0.756546i	−0.328217	+	0.944602i	$0.606448\pi$
$398$	3.88246			0.194610
$399$		0			0
$400$	−5.68190			−0.284095
$401$	−1.60532	−	2.78050i	−0.0801661	−	0.138852i	0.823155	−	0.567817i	$-0.192212\pi$
$401$	−1.60532	−	2.78050i	−0.0801661	−	0.138852i	−0.903321	+	0.428965i	$0.858878\pi$
$402$		0			0
$403$	−28.6945	−	16.5668i	−1.42937	−	0.825249i
$404$	6.58462	+	11.4049i	0.327597	+	0.567415i
$405$		0			0
$406$	3.04484	+	12.2712i	0.151113	+	0.609011i
$407$	−6.63653	−	2.43023i	−0.328960	−	0.120462i
$408$		0			0
$409$	−17.1522	+	29.7084i	−0.848120	+	1.46899i	0.0347647	+	0.999396i	$0.488932\pi$
$409$	−17.1522	+	29.7084i	−0.848120	+	1.46899i	−0.882884	+	0.469591i	$0.844402\pi$
$410$	−1.55188	+	2.68794i	−0.0766420	+	0.132748i
$411$		0			0
$412$		−	13.2122i		−	0.650916i
$413$	24.7538	+	25.6914i	1.21806	+	1.26419i
$414$		0			0
$415$	2.36582	−	1.36591i	0.116134	−	0.0670498i
$416$	−4.43853	−	2.56259i	−0.217617	−	0.125641i
$417$		0			0
$418$	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	$-0.101195\pi$
$420$		0			0
$421$	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
$423$		0			0
$424$	10.8599	+	6.26996i	0.527403	+	0.304496i
$425$	−15.1303	−	26.2065i	−0.733929	−	1.27120i
$426$		0			0
$427$	3.40283	+	13.7140i	0.164675	+	0.663668i
$428$		−	11.1094i		−	0.536994i
$429$		0			0
$430$	−17.5624	−	10.1397i	−0.846936	−	0.488979i
$431$	−22.4488	−	12.9608i	−1.08132	−	0.624302i	−0.150070	−	0.988675i	$-0.547950\pi$
$431$	−22.4488	−	12.9608i	−1.08132	−	0.624302i	−0.931253	+	0.364374i	$0.881283\pi$
$432$		0			0
$433$		−	29.5108i		−	1.41820i	−0.705110	−	0.709098i	$-0.749102\pi$
$433$		−	29.5108i		−	1.41820i	0.705110	−	0.709098i	$-0.250898\pi$
$434$	−16.4365	−	4.73319i	−0.788975	−	0.227200i
$435$		0			0
$436$	6.17596	−	3.56569i	0.295775	−	0.170766i
$437$	11.4821	−	19.8875i	0.549262	−	0.951350i
$438$		0			0
$439$	−5.71039	−	9.89069i	−0.272542	−	0.472057i	0.696970	−	0.717100i	$-0.254531\pi$
$439$	−5.71039	−	9.89069i	−0.272542	−	0.472057i	−0.969512	+	0.245043i	$0.921198\pi$
$440$	−10.1788	−	3.72736i	−0.485255	−	0.177695i
$441$		0			0
$442$		−	27.2956i		−	1.29832i
$443$	12.7606	+	22.1020i	0.606273	+	1.05010i	0.991849	+	0.127420i	$0.0406696\pi$
$443$	12.7606	+	22.1020i	0.606273	+	1.05010i	−0.385575	+	0.922676i	$0.625997\pi$
$444$		0			0
$445$	−10.1711	+	17.6169i	−0.482158	+	0.835122i
$446$	2.71468	+	4.70196i	0.128544	+	0.222644i
$447$		0			0
$448$	−2.54243	−	0.732142i	−0.120119	−	0.0345904i
$449$	−25.9959			−1.22682			−0.613412	−	0.789763i	$-0.710203\pi$
$449$	−25.9959			−1.22682			−0.613412	+	0.789763i	$0.710203\pi$
$450$		0			0
$451$	−2.41672	+	2.01982i	−0.113799	+	0.0951097i
$452$	−1.20718	+	2.09090i	−0.0567809	+	0.0983474i
$453$		0			0
$454$		−	11.8564i		−	0.556446i
$455$	43.0139	−	10.6729i	2.01652	−	0.500355i
$456$		0			0
$457$	−6.95633	+	4.01624i	−0.325403	+	0.187872i	−0.653798	−	0.756669i	$-0.726826\pi$
$457$	−6.95633	+	4.01624i	−0.325403	+	0.187872i	0.328395	+	0.944540i	$0.393492\pi$
$458$	3.21350	−	5.56595i	0.150157	−	0.260080i
$459$		0			0
$460$	−15.2048	+	8.77847i	−0.708926	+	0.409298i
$461$	33.5115			1.56078			0.780392	−	0.625290i	$-0.215019\pi$
$461$	33.5115			1.56078			0.780392	+	0.625290i	$0.215019\pi$
$462$		0			0
$463$	−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
$465$		0			0
$466$	1.00443	−	1.73972i	0.0465293	−	0.0805911i
$467$	−8.86193	+	5.11644i	−0.410081	+	0.236760i	−0.690825	−	0.723022i	$-0.742752\pi$
$467$	−8.86193	+	5.11644i	−0.410081	+	0.236760i	0.280743	+	0.959783i	$0.409419\pi$
$468$		0			0
$469$	−11.8003	+	11.3697i	−0.544887	+	0.525002i
$470$			39.3187i			1.81364i
$471$		0			0
$472$	−6.74219	+	11.6778i	−0.310334	+	0.537515i
$473$	−13.1971	−	15.7904i	−0.606803	−	0.726042i
$474$		0			0
$475$	−24.2896			−1.11448
$476$	−3.39340	−	13.6760i	−0.155536	−	0.626839i
$477$		0			0
$478$	−2.32934	−	4.03454i	−0.106542	−	0.184536i
$479$	2.59813	−	4.50009i	0.118712	−	0.205614i	−0.800546	−	0.599272i	$-0.795457\pi$
$479$	2.59813	−	4.50009i	0.118712	−	0.205614i	0.919257	+	0.393657i	$0.128790\pi$
$480$		0			0
$481$	5.46070	+	9.45820i	0.248986	+	0.431257i
$482$		−	5.96996i		−	0.271924i
$483$		0			0
$484$	−8.39873	−	7.10361i	−0.381761	−	0.322891i
$485$	−1.02027	−	1.76715i	−0.0463279	−	0.0802423i
$486$		0			0
$487$	15.7741	−	27.3216i	0.714794	−	1.23806i	−0.248245	−	0.968697i	$-0.579854\pi$
$487$	15.7741	−	27.3216i	0.714794	−	1.23806i	0.963039	−	0.269362i	$-0.0868128\pi$
$488$	−4.62509	+	2.67030i	−0.209368	+	0.120879i
$489$		0			0
$490$	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			0
$493$	−22.0409	−	12.7253i	−0.992670	−	0.573118i
$494$	−18.9743	−	10.9548i	−0.853693	−	0.492880i
$495$		0			0
$496$		−	6.46485i		−	0.290281i
$497$	27.4739	+	7.91162i	1.23237	+	0.354885i
$498$		0			0
$499$	17.3818	+	30.1061i	0.778114	+	1.34773i	0.933027	+	0.359805i	$0.117157\pi$
$499$	17.3818	+	30.1061i	0.778114	+	1.34773i	−0.154913	+	0.987928i	$0.549510\pi$
$500$	1.93010	+	1.11434i	0.0863165	+	0.0498349i
$501$		0			0
$502$	−0.728495	−	1.26179i	−0.0325143	−	0.0563165i
$503$	3.06150			0.136506			0.0682529	−	0.997668i	$-0.478258\pi$
$503$	3.06150			0.136506			0.0682529	+	0.997668i	$0.478258\pi$
$504$		0			0
$505$		−	43.0413i		−	1.91531i
$506$	−17.5518	+	3.05943i	−0.780272	+	0.136008i
$507$		0			0
$508$	11.9598	+	6.90499i	0.530630	+	0.306360i
$509$	24.6258	−	14.2177i	1.09152	−	0.630188i	0.157538	−	0.987513i	$-0.449644\pi$
$509$	24.6258	−	14.2177i	1.09152	−	0.630188i	0.933980	+	0.357325i	$0.116311\pi$
$510$		0			0
$511$	25.2058	−	24.2860i	1.11504	−	1.07435i
$512$		−	1.00000i		−	0.0441942i
$513$		0			0
$514$	13.1871	−	22.8407i	0.581658	−	1.00746i
$515$	−21.5908	+	37.3963i	−0.951403	+	1.64788i
$516$		0			0
$517$	−13.7199	+	37.4668i	−0.603402	+	1.64779i
$518$	3.91184	+	4.06000i	0.171876	+	0.178386i
$519$		0			0
$520$	8.37536	+	14.5065i	0.367284	+	0.636154i
$521$	3.15741	+	1.82293i	0.138329	+	0.0798642i	0.567567	−	0.823327i	$-0.307885\pi$
$521$	3.15741	+	1.82293i	0.138329	+	0.0798642i	−0.429238	+	0.903191i	$0.641218\pi$
$522$		0			0
$523$	−11.9730	−	20.7378i	−0.523542	−	0.906801i	−0.999625	−	0.0274006i	$-0.991277\pi$
$523$	−11.9730	−	20.7378i	−0.523542	−	0.906801i	0.476083	−	0.879401i	$-0.342056\pi$
$524$	−11.7866			−0.514902
$525$		0			0
$526$	−31.3179			−1.36552
$527$	29.8177	−	17.2152i	1.29888	−	0.749908i
$528$		0			0
$529$	−2.92843	+	5.07220i	−0.127323	+	0.220530i
$530$	−20.4922	−	35.4936i	−0.890126	−	1.54174i
$531$		0			0
$532$	−10.8686	−	3.12983i	−0.471215	−	0.135695i
$533$	4.86714			0.210819
$534$		0			0
$535$	−18.1546	+	31.4446i	−0.784890	+	1.35947i
$536$	−5.36373	−	3.09675i	−0.231678	−	0.133759i
$537$		0			0
$538$	3.05002			0.131496
$539$	23.0039	−	3.13408i	0.990846	−	0.134994i
$540$		0			0
$541$	−37.2883	+	21.5284i	−1.60315	+	0.925580i	−0.612299	+	0.790626i	$0.709755\pi$
$541$	−37.2883	+	21.5284i	−1.60315	+	0.925580i	−0.990852	+	0.134954i	$0.956911\pi$
$542$	19.4416	+	11.2246i	0.835089	+	0.482139i
$543$		0			0
$544$	4.61228	−	2.66290i	0.197750	−	0.114171i
$545$	−23.3076			−0.998389
$546$		0			0
$547$		−	8.00013i		−	0.342061i	−0.985266	−	0.171030i	$-0.945290\pi$
$547$		−	8.00013i		−	0.342061i	0.985266	−	0.171030i	$-0.0547097\pi$
$548$	−2.43055	−	4.20984i	−0.103828	−	0.179836i
$549$		0			0
$550$	12.0849	+	14.4596i	0.515301	+	0.616560i
$551$	−17.6917	+	10.2143i	−0.753692	+	0.435144i
$552$		0			0
$553$	23.5398	−	5.84089i	1.00102	−	0.248380i
$554$	20.5218			0.871888
$555$		0			0
$556$	8.39134	−	14.5342i	0.355872	−	0.616388i
$557$	20.2134	+	11.6702i	0.856471	+	0.494484i	0.862829	−	0.505496i	$-0.168691\pi$
$557$	20.2134	+	11.6702i	0.856471	+	0.494484i	−0.00635822	+	0.999980i	$0.502024\pi$
$558$		0			0
$559$			31.8009i			1.34503i
$560$	5.99979	+	6.22703i	0.253537	+	0.263140i
$561$		0			0
$562$	6.94109	+	12.0223i	0.292792	+	0.507131i
$563$	13.2190	−	22.8960i	0.557116	−	0.964953i	−0.440620	−	0.897694i	$-0.645241\pi$
$563$	13.2190	−	22.8960i	0.557116	−	0.964953i	0.997736	−	0.0672592i	$-0.0214254\pi$
$564$		0			0
$565$	6.83371	−	3.94545i	0.287496	−	0.165986i
$566$			29.7862i			1.25201i
$567$		0			0
$568$			10.8061i			0.453415i
$569$	−21.6494	+	12.4993i	−0.907590	+	0.523997i	−0.879655	−	0.475612i	$-0.842227\pi$
$569$	−21.6494	+	12.4993i	−0.907590	+	0.523997i	−0.0279352	+	0.999610i	$0.508893\pi$
$570$		0			0
$571$	37.6593	+	21.7426i	1.57599	+	0.909899i	0.995411	+	0.0956961i	$0.0305077\pi$
$571$	37.6593	+	21.7426i	1.57599	+	0.909899i	0.580581	+	0.814203i	$0.302826\pi$
$572$	2.91894	+	16.7458i	0.122047	+	0.700177i
$573$		0			0
$574$	2.43860	−	0.605084i	0.101785	−	0.0252557i
$575$	30.5224			1.27287
$576$		0			0
$577$	24.0746	+	13.8995i	1.00224	+	0.578643i	0.908910	−	0.416992i	$-0.136916\pi$
$577$	24.0746	+	13.8995i	1.00224	+	0.578643i	0.0933293	+	0.995635i	$0.470249\pi$
$578$	9.84161	+	5.68205i	0.409357	+	0.236342i
$579$		0			0
$580$	15.6184			0.648520
$581$	−2.12509	−	0.611959i	−0.0881634	−	0.0253883i
$582$		0			0
$583$	−7.14185	−	40.9724i	−0.295785	−	1.69690i
$584$	11.4571	+	6.61476i	0.474098	+	0.273721i
$585$		0			0
$586$	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	$0.925294\pi$
$588$		0			0
$589$		−	27.6366i		−	1.13875i
$590$	38.1668	−	22.0356i	1.57130	−	0.907192i
$591$		0			0
$592$	−1.06546	+	1.84544i	−0.0437903	+	0.0758471i
$593$	7.85106	+	13.5984i	0.322405	+	0.558421i	0.980984	−	0.194090i	$-0.0621755\pi$
$593$	7.85106	+	13.5984i	0.322405	+	0.558421i	−0.658579	+	0.752512i	$0.728842\pi$
$594$		0			0
$595$	−12.7440	+	44.2546i	−0.522451	+	1.81426i
$596$		−	7.22464i		−	0.295933i
$597$		0			0
$598$	23.8432	+	13.7659i	0.975020	+	0.562928i
$599$	4.79001	−	8.29654i	0.195714	−	0.338987i	−0.751420	−	0.659824i	$-0.770631\pi$
$599$	4.79001	−	8.29654i	0.195714	−	0.338987i	0.947134	+	0.320837i	$0.103964\pi$
$600$		0			0
$601$	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
$603$		0			0
$604$	−4.22644	+	2.44014i	−0.171972	+	0.0992878i
$605$	12.1637	+	33.8313i	0.494526	+	1.37544i
$606$		0			0
$607$	20.2326	+	35.0438i	0.821215	+	1.42239i	0.904778	+	0.425883i	$0.140037\pi$
$607$	20.2326	+	35.0438i	0.821215	+	1.42239i	−0.0835632	+	0.996502i	$0.526630\pi$
$608$		−	4.27490i		−	0.173370i
$609$		0			0
$610$	17.4548			0.706723
$611$	53.3967	−	30.8286i	2.16020	−	1.24719i
$612$		0			0
$613$	−9.07028	−	5.23673i	−0.366345	−	0.211509i	0.305515	−	0.952187i	$-0.401171\pi$
$613$	−9.07028	−	5.23673i	−0.366345	−	0.211509i	−0.671860	+	0.740678i	$0.734505\pi$
$614$	1.19379	−	0.689237i	0.0481776	−	0.0278153i
$615$		0			0
$616$	3.54433	+	8.02731i	0.142805	+	0.323430i
$617$	14.4244			0.580706			0.290353	−	0.956920i	$-0.406227\pi$
$617$	14.4244			0.580706			0.290353	+	0.956920i	$0.406227\pi$
$618$		0			0
$619$	38.7932	+	22.3973i	1.55923	+	0.900223i	0.997331	+	0.0730178i	$0.0232630\pi$
$619$	38.7932	+	22.3973i	1.55923	+	0.900223i	0.561901	+	0.827205i	$0.310070\pi$
$620$	−10.5646	+	18.2984i	−0.424285	+	0.734882i
$621$		0			0
$622$	10.5210			0.421855
$623$	15.9827	−	3.96575i	0.640333	−	0.158885i
$624$		0			0
$625$	10.5627	+	18.2952i	0.422510	+	0.731808i
$626$	−1.13347	+	1.96323i	−0.0453026	+	0.0784664i
$627$		0			0
$628$	−2.85996	+	1.65120i	−0.114125	+	0.0658900i
$629$	−11.3489			−0.452510
$630$		0			0
$631$	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
$633$		0			0
$634$	4.27963	+	2.47085i	0.169966	+	0.0981298i
$635$	−22.5677	−	39.0884i	−0.895572	−	1.55118i
$636$		0			0
$637$	−30.3817	−	19.0802i	−1.20377	−	0.755986i
$638$	14.8828	+	5.44993i	0.589216	+	0.215765i
$639$		0			0
$640$	−1.63416	+	2.83045i	−0.0645958	+	0.111883i
$641$	10.7925	−	18.6931i	0.426278	−	0.738335i	−0.570261	−	0.821463i	$-0.693158\pi$
$641$	10.7925	−	18.6931i	0.426278	−	0.738335i	0.996539	+	0.0831289i	$0.0264913\pi$
$642$		0			0
$643$		−	28.9651i		−	1.14227i	−0.820855	−	0.571137i	$-0.806503\pi$
$643$		−	28.9651i		−	1.14227i	0.820855	−	0.571137i	$-0.193497\pi$
$644$	13.6576	+	3.93296i	0.538185	+	0.154980i
$645$		0			0
$646$	19.7170	−	11.3836i	0.775755	−	0.447882i
$647$	−25.4299	−	14.6820i	−0.999753	−	0.577208i	−0.0915779	−	0.995798i	$-0.529191\pi$
$647$	−25.4299	−	14.6820i	−0.999753	−	0.577208i	−0.908175	+	0.418590i	$0.862524\pi$
$648$		0			0
$649$	44.0583	−	7.67974i	1.72944	−	0.301456i
$650$		−	29.1208i		−	1.14221i
$651$		0			0
$652$	4.84536			0.189759
$653$	−19.1225	−	33.1211i	−0.748320	−	1.29613i	−0.948628	−	0.316395i	$-0.897528\pi$
$653$	−19.1225	−	33.1211i	−0.748320	−	1.29613i	0.200308	−	0.979733i	$-0.435806\pi$
$654$		0			0
$655$	33.3615	+	19.2612i	1.30354	+	0.752599i
$656$	0.474826	+	0.822423i	0.0185388	+	0.0321102i
$657$		0			0
$658$	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	$0.998696\pi$
$660$		0			0
$661$	8.07735	+	4.66346i	0.314172	+	0.181388i	0.648792	−	0.760966i	$-0.275274\pi$
$661$	8.07735	+	4.66346i	0.314172	+	0.181388i	−0.334620	+	0.942353i	$0.608608\pi$
$662$	11.2141	+	6.47446i	0.435848	+	0.251637i
$663$		0			0
$664$		−	0.835847i		−	0.0324372i
$665$	25.6485	+	26.6199i	0.994605	+	1.03228i
$666$		0			0
$667$	22.2315	−	12.8354i	0.860807	−	0.496987i
$668$	−1.06961	+	1.85262i	−0.0413844	+	0.0716799i
$669$		0			0
$670$	10.1212	+	17.5304i	0.391015	+	0.677257i
$671$	16.6327	+	6.09070i	0.642096	+	0.235129i
$672$		0			0
$673$			15.7351i			0.606545i	0.952904	+	0.303273i	$0.0980793\pi$
$673$			15.7351i			0.606545i	−0.952904	+	0.303273i	$0.901921\pi$
$674$	−4.11071	−	7.11996i	−0.158339	−	0.274251i
$675$		0			0
$676$	6.63372	−	11.4899i	0.255143	−	0.441921i
$677$	6.53943	+	11.3266i	0.251331	+	0.435318i	0.963892	−	0.266292i	$-0.0857985\pi$
$677$	6.53943	+	11.3266i	0.251331	+	0.435318i	−0.712562	+	0.701609i	$0.752465\pi$
$678$		0			0
$679$	−0.457103	+	1.58734i	−0.0175420	+	0.0609164i
$680$	−17.4064			−0.667505
$681$		0			0
$682$	−16.4521	+	13.7501i	−0.629983	+	0.526520i
$683$	−12.5854	+	21.7986i	−0.481568	+	0.834101i	−0.999776	−	0.0211540i	$-0.993266\pi$
$683$	−12.5854	+	21.7986i	−0.481568	+	0.834101i	0.518208	+	0.855255i	$0.326599\pi$
$684$		0			0
$685$			15.8876i			0.607036i
$686$	−17.5943	−	5.78276i	−0.671754	−	0.220787i
$687$		0			0
$688$	−5.37354	+	3.10242i	−0.204864	+	0.118278i
$689$	−32.1347	+	55.6589i	−1.22423	+	2.12043i
$690$		0			0
$691$	0.686294	−	0.396232i	0.0261079	−	0.0150734i	−0.486889	−	0.873464i	$-0.661868\pi$
$691$	0.686294	−	0.396232i	0.0261079	−	0.0150734i	0.512997	+	0.858390i	$0.328535\pi$
$692$	−17.7492			−0.674722
$693$		0			0
$694$	31.3657			1.19063
$695$	−47.5025	+	27.4256i	−1.80187	+	1.04031i
$696$		0			0
$697$	−2.52883	+	4.38006i	−0.0957862	+	0.165907i
$698$	−2.73094	+	1.57671i	−0.103368	+	0.0596793i
$699$		0			0
$700$	−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	$0.731315\pi$
$702$		0			0
$703$	−4.55475	+	7.88906i	−0.171786	+	0.297542i
$704$	−2.54485	+	2.12691i	−0.0959127	+	0.0801608i
$705$		0			0
$706$	−8.15423			−0.306889
$707$	−25.0910	+	24.1753i	−0.943643	+	0.909206i
$708$		0			0
$709$	−18.2211	−	31.5598i	−0.684307	−	1.18525i	−0.973654	−	0.228030i	$-0.926771\pi$
$709$	−18.2211	−	31.5598i	−0.684307	−	1.18525i	0.289347	−	0.957224i	$-0.406562\pi$
$710$	17.6589	−	30.5862i	0.662728	−	1.14788i
$711$		0			0
$712$	3.11204	+	5.39021i	0.116629	+	0.202007i
$713$			34.7283i			1.30058i
$714$		0			0
$715$	19.1034	−	52.1681i	0.714427	−	1.95098i
$716$	−1.44235	−	2.49822i	−0.0539031	−	0.0933629i
$717$		0			0
$718$	−4.77023	+	8.26228i	−0.178023	+	0.308346i
$719$	12.2632	−	7.08018i	0.457341	−	0.264046i	−0.253584	−	0.967313i	$-0.581610\pi$
$719$	12.2632	−	7.08018i	0.457341	−	0.264046i	0.710926	+	0.703267i	$0.248276\pi$
$720$		0			0
$721$	33.9273	−	8.41830i	1.26352	−	0.313514i
$722$			0.725250i			0.0269910i
$723$		0			0
$724$	9.47011	+	5.46757i	0.351954	+	0.203201i
$725$	−23.5146	−	13.5762i	−0.873311	−	0.504206i
$726$		0			0
$727$		−	8.58699i		−	0.318474i	−0.987240	−	0.159237i	$-0.949097\pi$
$727$		−	8.58699i		−	0.318474i	0.987240	−	0.159237i	$-0.0509033\pi$
$728$	3.75236	−	13.0304i	0.139072	−	0.482940i
$729$		0			0
$730$	−21.6191	−	37.4454i	−0.800160	−	1.38592i
$731$	−28.6184	−	16.5228i	−1.05849	−	0.611119i
$732$		0			0
$733$	−21.3598	−	36.9962i	−0.788942	−	1.36649i	−0.926616	−	0.376010i	$-0.877296\pi$
$733$	−21.3598	−	36.9962i	−0.788942	−	1.36649i	0.137674	−	0.990478i	$-0.456037\pi$
$734$	6.76680			0.249767
$735$		0			0
$736$			5.37186i			0.198009i
$737$	3.52738	+	20.2364i	0.129933	+	0.745417i
$738$		0			0
$739$	−28.7537	−	16.6009i	−1.05772	−	0.610675i	−0.132920	−	0.991127i	$-0.542435\pi$
$739$	−28.7537	−	16.6009i	−1.05772	−	0.610675i	−0.924801	+	0.380452i	$0.875769\pi$
$740$	6.03148	−	3.48228i	0.221722	−	0.128011i
$741$		0			0
$742$	−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	$0.952444\pi$
$744$		0			0
$745$	−11.8062	+	20.4490i	−0.432546	+	0.749192i
$746$	0.238388	−	0.412900i	0.00872800	−	0.0151173i
$747$		0			0
$748$	−16.5866	−	6.07382i	−0.606465	−	0.222081i
$749$	28.5277	−	7.07852i	1.04238	−	0.258643i
$750$		0			0
$751$	−0.0376756	−	0.0652561i	−0.00137480	−	0.00238123i	0.865337	−	0.501190i	$-0.167104\pi$
$751$	−0.0376756	−	0.0652561i	−0.00137480	−	0.00238123i	−0.866712	+	0.498809i	$0.833771\pi$
$752$	10.4185	+	6.01513i	0.379924	+	0.219349i
$753$		0			0
$754$	−12.2459	−	21.2106i	−0.445971	−	0.772444i
$755$	15.9503			0.580491
$756$		0			0
$757$	−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
$759$		0			0
$760$	−6.98586	+	12.0999i	−0.253404	+	0.438908i
$761$	7.35142	+	12.7330i	0.266489	+	0.461572i	0.967953	−	0.251133i	$-0.0808031\pi$
$761$	7.35142	+	12.7330i	0.266489	+	0.461572i	−0.701464	+	0.712705i	$0.747470\pi$
$762$		0			0
$763$	13.0914	+	13.5872i	0.473939	+	0.491890i
$764$	12.8770			0.465872
$765$		0			0
$766$	6.10983	−	10.5825i	0.220757	−	0.382363i
$767$	−59.8508	−	34.5549i	−2.16109	−	1.24770i
$768$		0			0
$769$	−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
$771$		0			0
$772$	−5.23494	+	3.02239i	−0.188410	+	0.108778i
$773$	32.2256	+	18.6055i	1.15907	+	0.669192i	0.951082	−	0.308939i	$-0.0999739\pi$
$773$	32.2256	+	18.6055i	1.15907	+	0.669192i	0.207992	+	0.978131i	$0.433307\pi$
$774$		0			0
$775$	31.8114	−	18.3663i	1.14270	−	0.659739i
$776$	−0.624337			−0.0224124
$777$		0			0
$778$			28.0321i			1.00500i
$779$	2.02983	+	3.51577i	0.0727263	+	0.125966i
$780$		0			0
$781$	27.5000	−	22.9836i	0.984027	−	0.822419i
$782$	−24.7765	+	14.3047i	−0.886006	+	0.511536i
$783$		0			0
$784$	0.260109	−	6.99517i	0.00928960	−	0.249827i
$785$	10.7933			0.385229
$786$		0			0
$787$	−21.5599	+	37.3429i	−0.768529	+	1.33113i	0.169831	+	0.985473i	$0.445678\pi$
$787$	−21.5599	+	37.3429i	−0.768529	+	1.33113i	−0.938360	+	0.345658i	$0.887656\pi$
$788$	5.35409	+	3.09118i	0.190732	+	0.110119i
$789$		0			0
$790$		−	29.9607i		−	1.06596i
$791$	−6.13834	−	1.76765i	−0.218254	−	0.0628505i
$792$		0			0
$793$	−13.6858	−	23.7044i	−0.485995	−	0.841769i
$794$	15.0741	−	26.1090i	0.534959	−	0.926575i
$795$		0			0
$796$	−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	$0.820516\pi$
$798$		0			0
$799$			64.0707i			2.26666i
$800$	4.92067	−	2.84095i	0.173972	−	0.100443i
$801$		0			0
$802$	2.78050	+	1.60532i	0.0981830	+	0.0566860i
$803$	−7.53459	−	43.2256i	−0.265890	−	1.52540i
$804$		0			0
$805$	−32.2300	−	33.4507i	−1.13596	−	1.17898i
$806$	33.1335			1.16708
$807$		0			0
$808$	−11.4049	−	6.58462i	−0.401223	−	0.231646i
$809$	−40.0519	−	23.1240i	−1.40815	−	0.812996i	−0.412940	−	0.910758i	$-0.635498\pi$
$809$	−40.0519	−	23.1240i	−1.40815	−	0.812996i	−0.995210	+	0.0977627i	$0.968831\pi$
$810$		0			0
$811$	−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
$813$		0			0
$814$	6.96251	−	1.21363i	0.244036	−	0.0425376i
$815$	−13.7145	−	7.91809i	−0.480399	−	0.277359i
$816$		0			0
$817$	−22.9713	+	13.2625i	−0.803666	+	0.463997i
$818$		−	34.3043i		−	1.19942i
$819$		0			0
$820$		−	3.10377i		−	0.108388i
$821$	−14.2638	+	8.23523i	−0.497812	+	0.287412i	−0.727809	−	0.685780i	$-0.759461\pi$
$821$	−14.2638	+	8.23523i	−0.497812	+	0.287412i	0.229998	+	0.973191i	$0.426128\pi$
$822$		0			0
$823$	−6.10784	+	10.5791i	−0.212906	+	0.368764i	−0.952623	−	0.304155i	$-0.901626\pi$
$823$	−6.10784	+	10.5791i	−0.212906	+	0.368764i	0.739717	+	0.672918i	$0.234959\pi$
$824$	6.60608	+	11.4421i	0.230134	+	0.398603i
$825$		0			0
$826$	−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	$0.974763\pi$
$828$		0			0
$829$	−32.1952	−	18.5879i	−1.11819	−	0.645585i	−0.177249	−	0.984166i	$-0.556720\pi$
$829$	−32.1952	−	18.5879i	−1.11819	−	0.645585i	−0.940937	+	0.338581i	$0.890053\pi$
$830$	−1.36591	+	2.36582i	−0.0474113	+	0.0821188i
$831$		0			0
$832$	5.12518			0.177684
$833$	32.9563	−	17.4277i	1.14187	−	0.603835i
$834$		0			0
$835$	6.05494	−	3.49582i	0.209540	−	0.120978i
$836$	−10.8790	+	9.09231i	−0.376257	+	0.314464i
$837$		0			0
$838$	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	$-0.238887\pi$
$840$		0			0
$841$	6.16366			0.212540
$842$	−30.3417	+	17.5178i	−1.04565	+	0.603704i
$843$		0			0
$844$	−7.83493	−	4.52350i	−0.269689	−	0.155705i
$845$	−37.5528	+	21.6811i	−1.29185	+	0.745853i
$846$		0			0
$847$	12.8899	−	26.0931i	0.442901	−	0.896570i
$848$	−12.5399			−0.430623
$849$		0			0
$850$	26.2065	+	15.1303i	0.898876	+	0.518966i
$851$	5.72353	−	9.91344i	0.196200	−	0.339828i
$852$		0			0
$853$	−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
$855$		0			0
$856$	5.55471	+	9.62104i	0.189856	+	0.328840i
$857$	−0.822073	+	1.42387i	−0.0280815	+	0.0486385i	−0.879725	−	0.475484i	$-0.842273\pi$
$857$	−0.822073	+	1.42387i	−0.0280815	+	0.0486385i	0.851643	+	0.524122i	$0.175606\pi$
$858$		0			0
$859$	−19.0267	+	10.9850i	−0.649181	+	0.374805i	−0.788142	−	0.615493i	$-0.788957\pi$
$859$	−19.0267	+	10.9850i	−0.649181	+	0.374805i	0.138961	+	0.990298i	$0.455624\pi$
$860$	20.2794			0.691521
$861$		0			0
$862$	25.9217			0.882896
$863$	4.76103	+	8.24634i	0.162067	+	0.280709i	0.935610	−	0.353036i	$-0.114851\pi$
$863$	4.76103	+	8.24634i	0.162067	+	0.280709i	−0.773543	+	0.633744i	$0.781517\pi$
$864$		0			0
$865$	50.2380	+	29.0049i	1.70814	+	0.986198i
$866$	14.7554	+	25.5571i	0.501408	+	0.868464i
$867$		0			0
$868$	16.6010	−	4.11917i	0.563474	−	0.139814i
$869$	10.4546	−	28.5496i	0.354646	−	0.968478i
$870$		0			0
$871$	15.8714	−	27.4901i	0.537782	−	0.931465i
$872$	−3.56569	+	6.17596i	−0.120750	+	0.209144i
$873$		0			0
$874$			22.9641i			0.776774i
$875$	−1.63171	+	5.66628i	−0.0551619	+	0.191555i
$876$		0			0
$877$	30.0244	−	17.3346i	1.01385	−	0.585347i	0.101534	−	0.994832i	$-0.467625\pi$
$877$	30.0244	−	17.3346i	1.01385	−	0.585347i	0.912317	+	0.409485i	$0.134292\pi$
$878$	9.89069	+	5.71039i	0.333795	+	0.192716i
$879$		0			0
$880$	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	$0.949910\pi$
$882$		0			0
$883$	−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
$885$		0			0
$886$	−22.1020	−	12.7606i	−0.742530	−	0.428700i
$887$	7.54456	+	13.0676i	0.253322	+	0.438766i	0.964438	−	0.264308i	$-0.0851436\pi$
$887$	7.54456	+	13.0676i	0.253322	+	0.438766i	−0.711117	+	0.703074i	$0.751810\pi$
$888$		0			0
$889$	−10.1109	+	35.1110i	−0.339108	+	1.17758i
$890$		−	20.3423i		−	0.681874i
$891$		0			0
$892$	−4.70196	−	2.71468i	−0.157433	−	0.0908940i
$893$	44.5381	+	25.7141i	1.49041	+	0.860488i
$894$		0			0
$895$			9.42811i			0.315147i
$896$	2.56788	−	0.637163i	0.0857869	−	0.0212861i
$897$		0			0
$898$	22.5131	−	12.9980i	0.751273	−	0.433747i
$899$	15.4469	−	26.7549i	0.515184	−	0.892324i
$900$		0			0
$901$	−33.3925	−	57.8376i	−1.11247	−	1.92685i
$902$	1.08303	−	2.95758i	0.0360611	−	0.0984766i
$903$		0			0
$904$		−	2.41436i		−	0.0803004i
$905$	−17.8698	−	30.9513i	−0.594011	−	1.02886i
$906$		0			0
$907$	9.26851	−	16.0535i	0.307756	−	0.533049i	−0.670115	−	0.742257i	$-0.733755\pi$
$907$	9.26851	−	16.0535i	0.307756	−	0.533049i	0.977871	+	0.209208i	$0.0670887\pi$
$908$	5.92818	+	10.2679i	0.196734	+	0.340752i
$909$		0			0
$910$	−31.9146	+	30.7500i	−1.05796	+	1.01935i
$911$	33.6539			1.11500			0.557502	−	0.830176i	$-0.311760\pi$
$911$	33.6539			1.11500			0.557502	+	0.830176i	$0.311760\pi$
$912$		0			0
$913$	−2.12711	+	1.77777i	−0.0703970	+	0.0588356i
$914$	4.01624	−	6.95633i	0.132845	−	0.230095i
$915$		0			0
$916$			6.42701i			0.212354i
$917$	−7.51002	−	30.2667i	−0.248003	−	0.999495i
$918$		0			0
$919$	−11.9496	+	6.89909i	−0.394180	+	0.227580i	−0.683970	−	0.729510i	$-0.739748\pi$
$919$	−11.9496	+	6.89909i	−0.394180	+	0.227580i	0.289790	+	0.957090i	$0.406415\pi$
$920$	8.77847	−	15.2048i	0.289418	−	0.501286i
$921$		0			0
$922$	−29.0218	+	16.7557i	−0.955781	+	0.551821i
$923$	−55.3833			−1.82296
$924$		0			0
$925$	−12.1077			−0.398100
$926$	13.6329	−	7.87094i	0.448004	−	0.258655i
$927$		0			0
$928$	2.38937	−	4.13851i	0.0784349	−	0.135853i
$929$	27.2253	−	15.7186i	0.893234	−	0.515709i	0.0182352	−	0.999834i	$-0.494195\pi$
$929$	27.2253	−	15.7186i	0.893234	−	0.515709i	0.874999	+	0.484125i	$0.160862\pi$
$930$		0			0
$931$	1.11194	−	29.9036i	0.0364423	−	0.980051i
$932$			2.00886i			0.0658023i
$933$		0			0
$934$	5.11644	−	8.86193i	0.167415	−	0.289971i
$935$	37.0218	+	44.2967i	1.21074	+	1.44866i
$936$		0			0
$937$	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
$939$		0			0
$940$	−19.6594	−	34.0510i	−0.641217	−	1.11062i
$941$	19.1723	−	33.2075i	0.625001	−	1.08253i	−0.363540	−	0.931579i	$-0.618432\pi$
$941$	19.1723	−	33.2075i	0.625001	−	1.08253i	0.988541	−	0.150954i	$-0.0482347\pi$
$942$		0			0
$943$	−2.55070	−	4.41794i	−0.0830622	−	0.143868i
$944$		−	13.4844i		−	0.438879i
$945$		0			0
$946$	19.3242	+	7.07632i	0.628284	+	0.230071i
$947$	20.4702	+	35.4555i	0.665193	+	1.15215i	0.979233	+	0.202738i	$0.0649841\pi$
$947$	20.4702	+	35.4555i	0.665193	+	1.15215i	−0.314040	+	0.949410i	$0.601683\pi$
$948$		0			0
$949$	−33.9018	+	58.7196i	−1.10050	+	1.90612i
$950$	21.0354	−	12.1448i	0.682478	−	0.394029i
$951$		0			0
$952$	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	$0.896355\pi$
$954$		0			0
$955$	−36.4475	−	21.0430i	−1.17941	−	0.680936i
$956$	4.03454	+	2.32934i	0.130486	+	0.0753364i
$957$		0			0
$958$			5.19626i			0.167883i
$959$	9.26172	−	8.92373i	0.299077	−	0.288162i
$960$		0			0
$961$	5.39717	+	9.34818i	0.174102	+	0.301554i
$962$	−9.45820	−	5.46070i	−0.304945	−	0.176060i
$963$		0			0
$964$	2.98498	+	5.17014i	0.0961397	+	0.166519i
$965$	19.7563			0.635977
$966$		0			0
$967$			36.4927i			1.17352i	0.809759	+	0.586762i	$0.199598\pi$
$967$			36.4927i			1.17352i	−0.809759	+	0.586762i	$0.800402\pi$
$968$	10.8253	+	1.95254i	0.347939	+	0.0627570i
$969$		0			0
$970$	1.76715	+	1.02027i	0.0567399	+	0.0327588i
$971$	44.5292	−	25.7089i	1.42901	−	0.825039i	0.431967	−	0.901889i	$-0.357820\pi$
$971$	44.5292	−	25.7089i	1.42901	−	0.825039i	0.997043	+	0.0768499i	$0.0244862\pi$
$972$		0			0
$973$	42.6688	+	12.2873i	1.36790	+	0.393913i
$974$			31.5483i			1.01087i
$975$		0			0
$976$	2.67030	−	4.62509i	0.0854742	−	0.148046i
$977$	3.90814	−	6.76910i	0.125033	−	0.216563i	−0.796713	−	0.604358i	$-0.793430\pi$
$977$	3.90814	−	6.76910i	0.125033	−	0.216563i	0.921746	+	0.387795i	$0.126763\pi$
$978$		0			0
$979$	7.09827	−	19.3841i	0.226862	−	0.619520i
$980$	−12.1674	+	19.3744i	−0.388675	+	0.618892i
$981$		0			0
$982$	3.57091	+	6.18500i	0.113952	+	0.197371i
$983$	−12.7959	−	7.38773i	−0.408126	−	0.235632i	0.281858	−	0.959456i	$-0.409049\pi$
$983$	−12.7959	−	7.38773i	−0.408126	−	0.235632i	−0.689984	+	0.723824i	$0.742383\pi$
$984$		0			0
$985$	−10.1030	−	17.4989i	−0.321908	−	0.557560i
$986$	25.4506			0.810512
$987$		0			0
$988$	21.9096			0.697037
$989$	28.8659	−	16.6657i	0.917883	−	0.529940i
$990$		0			0
$991$	0.272746	−	0.472410i	0.00866407	−	0.0150066i	−0.861661	−	0.507485i	$-0.830575\pi$
$991$	0.272746	−	0.472410i	0.00866407	−	0.0150066i	0.870325	+	0.492478i	$0.163909\pi$
$992$	3.23243	+	5.59873i	0.102630	+	0.177760i
$993$		0			0
$994$	−27.7489	+	6.88527i	−0.880141	+	0.218387i
$995$	12.6891			0.402272
$996$		0			0
$997$	−18.9612	+	32.8418i	−0.600508	+	1.04011i	0.392236	+	0.919865i	$0.371702\pi$
$997$	−18.9612	+	32.8418i	−0.600508	+	1.04011i	−0.992744	+	0.120246i	$0.961632\pi$
$998$	−30.1061	−	17.3818i	−0.952991	−	0.550210i
$999$		0			0

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
462.2.p.a.241.4	✓	16	33.32	even	2
462.2.p.a.439.4	yes	16	21.5	even	6
462.2.p.b.241.8	yes	16	3.2	odd	2
462.2.p.b.439.8	yes	16	231.131	odd	6
1386.2.bk.a.703.5		16	11.10	odd	2
1386.2.bk.a.901.5		16	7.5	odd	6
1386.2.bk.b.703.1		16	1.1	even	1	trivial
1386.2.bk.b.901.1		16	77.54	even	6	inner
3234.2.e.a.2155.8		16	231.32	even	6
3234.2.e.a.2155.9		16	21.17	even	6
3234.2.e.b.2155.1		16	231.164	odd	6
3234.2.e.b.2155.16		16	21.11	odd	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:	\( N \)	\(=\)	\( 1386 = 2 \cdot 3^{2} \cdot 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1386.bk (of order \(6\), degree \(2\), minimal)

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

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