LMFDB - Embedded newform 360.3.g.c.91.7

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [360,3,Mod(91,360)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("360.91"); S:= CuspForms(chi, 3); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(360, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([1, 1, 0, 0])) N = Newforms(chi, 3, names="a")

Level:	$ N $	$=$	$ 360 = 2^{3} \cdot 3^{2} \cdot 5 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	360.g (of order $2$, degree $1$, minimal)

Newform invariants

comment:select newform

sage:traces = [16,4] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(2)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$9.80928951697$
Analytic rank:	$0$
Dimension:	$16$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 4 x^{15} + x^{14} + 24 x^{13} - 44 x^{12} - 32 x^{11} + 180 x^{10} - 64 x^{9} - 352 x^{8} + \cdots + 65536 $ x^16 - 4x^15 + x^14 + 24x^13 - 44x^12 - 32x^11 + 180x^10 - 64x^9 - 352x^8 - 256x^7 + 2880x^6 - 2048x^5 - 11264x^4 + 24576x^3 + 4096x^2 - 65536x + 65536
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 2^{18} $
Twist minimal:	no (minimal twist has level 120)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			91.7
Root			$0.444906 - 1.94989i$ of defining polynomial
Character	$\chi$	$=$	360.91
Dual form			360.3.g.c.91.8

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.444906 - 1.94989i) q^{2} +(-3.60412 - 1.73503i) q^{4} +2.23607i q^{5} -5.48395i q^{7} +(-4.98661 + 6.25570i) q^{8} +(4.36008 + 0.994839i) q^{10} -1.62564 q^{11} -18.0504i q^{13} +(-10.6931 - 2.43984i) q^{14} +(9.97933 + 12.5065i) q^{16} -24.0180 q^{17} -34.4282 q^{19} +(3.87965 - 8.05905i) q^{20} +(-0.723259 + 3.16982i) q^{22} +30.7256i q^{23} -5.00000 q^{25} +(-35.1962 - 8.03071i) q^{26} +(-9.51482 + 19.7648i) q^{28} +8.33039i q^{29} +5.48491i q^{31} +(28.8262 - 13.8943i) q^{32} +(-10.6858 + 46.8324i) q^{34} +12.2625 q^{35} -42.8951i q^{37} +(-15.3173 + 67.1311i) q^{38} +(-13.9882 - 11.1504i) q^{40} +6.22670 q^{41} -57.2727 q^{43} +(5.85901 + 2.82054i) q^{44} +(59.9113 + 13.6700i) q^{46} -41.5525i q^{47} +18.9263 q^{49} +(-2.22453 + 9.74943i) q^{50} +(-31.3180 + 65.0556i) q^{52} -38.1670i q^{53} -3.63505i q^{55} +(34.3059 + 27.3463i) q^{56} +(16.2433 + 3.70624i) q^{58} -70.7342 q^{59} +63.5799i q^{61} +(10.6950 + 2.44027i) q^{62} +(-14.2675 - 62.3894i) q^{64} +40.3618 q^{65} +59.4604 q^{67} +(86.5638 + 41.6720i) q^{68} +(5.45565 - 23.9104i) q^{70} -48.4629i q^{71} +93.1375 q^{73} +(-83.6407 - 19.0843i) q^{74} +(124.083 + 59.7340i) q^{76} +8.91495i q^{77} -60.2424i q^{79} +(-27.9654 + 22.3145i) q^{80} +(2.77030 - 12.1414i) q^{82} -5.69214 q^{83} -53.7060i q^{85} +(-25.4809 + 111.675i) q^{86} +(8.10645 - 10.1695i) q^{88} -49.1046 q^{89} -98.9872 q^{91} +(53.3098 - 110.739i) q^{92} +(-81.0226 - 18.4869i) q^{94} -76.9838i q^{95} +35.9229 q^{97} +(8.42044 - 36.9042i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 4 q^{2} + 14 q^{4} - 20 q^{8} + 10 q^{10} - 64 q^{11} + 20 q^{14} - 14 q^{16} - 32 q^{19} + 40 q^{20} + 28 q^{22} - 80 q^{25} - 36 q^{26} - 28 q^{28} - 36 q^{32} - 72 q^{34} + 240 q^{38} + 10 q^{40}+ \cdots - 428 q^{98}+O(q^{100}) $ 16 * q + 4 * q^2 + 14 * q^4 - 20 * q^8 + 10 * q^10 - 64 * q^11 + 20 * q^14 - 14 * q^16 - 32 * q^19 + 40 * q^20 + 28 * q^22 - 80 * q^25 - 36 * q^26 - 28 * q^28 - 36 * q^32 - 72 * q^34 + 240 * q^38 + 10 * q^40 - 192 * q^43 + 100 * q^44 + 212 * q^46 - 80 * q^49 - 20 * q^50 + 232 * q^52 + 116 * q^56 + 140 * q^58 - 128 * q^59 - 104 * q^62 + 14 * q^64 - 64 * q^67 + 576 * q^68 - 180 * q^70 - 160 * q^73 - 300 * q^74 + 420 * q^76 - 80 * q^80 + 160 * q^82 - 312 * q^86 + 604 * q^88 - 192 * q^91 - 216 * q^92 + 460 * q^94 - 224 * q^97 - 428 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/360\mathbb{Z}\right)^\times$.

$n$	$181$	$217$	$271$	$281$
$\chi(n)$	$-1$	$1$	$-1$	$1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	0.444906	−	1.94989i	0.222453	−	0.974943i
$2$	0.444906	−	1.94989i	0.222453	−	0.974943i
$3$		0			0
$3$		0			0
$4$	−3.60412	−	1.73503i	−0.901029	−	0.433758i
$5$			2.23607i			0.447214i
$5$			2.23607i			0.447214i
$6$		0			0
$7$		−	5.48395i		−	0.783421i	−0.920089	−	0.391710i	$-0.871884\pi$
$7$		−	5.48395i		−	0.783421i	0.920089	−	0.391710i	$-0.128116\pi$
$8$	−4.98661	+	6.25570i	−0.623326	+	0.781962i
$9$		0			0
$10$	4.36008	+	0.994839i	0.436008	+	0.0994839i
$11$	−1.62564			−0.147786			−0.0738929	−	0.997266i	$-0.523542\pi$
$11$	−1.62564			−0.147786			−0.0738929	+	0.997266i	$0.523542\pi$
$12$		0			0
$13$		−	18.0504i		−	1.38849i	−0.719739	−	0.694245i	$-0.755739\pi$
$13$		−	18.0504i		−	1.38849i	0.719739	−	0.694245i	$-0.244261\pi$
$14$	−10.6931	−	2.43984i	−0.763791	−	0.174274i
$15$		0			0
$16$	9.97933	+	12.5065i	0.623708	+	0.781657i
$17$	−24.0180			−1.41283			−0.706413	−	0.707800i	$-0.749688\pi$
$17$	−24.0180			−1.41283			−0.706413	+	0.707800i	$0.749688\pi$
$18$		0			0
$19$	−34.4282			−1.81201			−0.906005	−	0.423267i	$-0.860883\pi$
$19$	−34.4282			−1.81201			−0.906005	+	0.423267i	$0.860883\pi$
$20$	3.87965	−	8.05905i	0.193982	−	0.402953i
$21$		0			0
$22$	−0.723259	+	3.16982i	−0.0328754	+	0.144083i
$23$			30.7256i			1.33589i	0.744209	+	0.667947i	$0.232827\pi$
$23$			30.7256i			1.33589i	−0.744209	+	0.667947i	$0.767173\pi$
$24$		0			0
$25$	−5.00000			−0.200000
$26$	−35.1962	−	8.03071i	−1.35370	−	0.308873i
$27$		0			0
$28$	−9.51482	+	19.7648i	−0.339815	+	0.705885i
$29$			8.33039i			0.287255i	0.989632	+	0.143627i	$0.0458767\pi$
$29$			8.33039i			0.287255i	−0.989632	+	0.143627i	$0.954123\pi$
$30$		0			0
$31$			5.48491i			0.176933i	0.996079	+	0.0884663i	$0.0281966\pi$
$31$			5.48491i			0.176933i	−0.996079	+	0.0884663i	$0.971803\pi$
$32$	28.8262	−	13.8943i	0.900817	−	0.434198i
$33$		0			0
$34$	−10.6858	+	46.8324i	−0.314287	+	1.37742i
$35$	12.2625			0.350356
$36$		0			0
$37$		−	42.8951i		−	1.15933i	−0.814856	−	0.579664i	$-0.803184\pi$
$37$		−	42.8951i		−	1.15933i	0.814856	−	0.579664i	$-0.196816\pi$
$38$	−15.3173	+	67.1311i	−0.403087	+	1.76661i
$39$		0			0
$40$	−13.9882	−	11.1504i	−0.349704	−	0.278760i
$41$	6.22670			0.151871			0.0759354	−	0.997113i	$-0.475806\pi$
$41$	6.22670			0.151871			0.0759354	+	0.997113i	$0.475806\pi$
$42$		0			0
$43$	−57.2727			−1.33192			−0.665961	−	0.745986i	$-0.731978\pi$
$43$	−57.2727			−1.33192			−0.665961	+	0.745986i	$0.731978\pi$
$44$	5.85901	+	2.82054i	0.133159	+	0.0641033i
$45$		0			0
$46$	59.9113	+	13.6700i	1.30242	+	0.297173i
$47$		−	41.5525i		−	0.884095i	−0.896992	−	0.442048i	$-0.854252\pi$
$47$		−	41.5525i		−	0.884095i	0.896992	−	0.442048i	$-0.145748\pi$
$48$		0			0
$49$	18.9263			0.386252
$50$	−2.22453	+	9.74943i	−0.0444906	+	0.194989i
$51$		0			0
$52$	−31.3180	+	65.0556i	−0.602268	+	1.25107i
$53$		−	38.1670i		−	0.720132i	−0.932927	−	0.360066i	$-0.882754\pi$
$53$		−	38.1670i		−	0.720132i	0.932927	−	0.360066i	$-0.117246\pi$
$54$		0			0
$55$		−	3.63505i		−	0.0660918i
$56$	34.3059	+	27.3463i	0.612605	+	0.488327i
$57$		0			0
$58$	16.2433	+	3.70624i	0.280057	+	0.0639006i
$59$	−70.7342			−1.19889			−0.599443	−	0.800418i	$-0.704611\pi$
$59$	−70.7342			−1.19889			−0.599443	+	0.800418i	$0.704611\pi$
$60$		0			0
$61$			63.5799i			1.04229i	0.853467	+	0.521147i	$0.174496\pi$
$61$			63.5799i			1.04229i	−0.853467	+	0.521147i	$0.825504\pi$
$62$	10.6950	+	2.44027i	0.172499	+	0.0393592i
$63$		0			0
$64$	−14.2675	−	62.3894i	−0.222929	−	0.974835i
$65$	40.3618			0.620951
$66$		0			0
$67$	59.4604			0.887468			0.443734	−	0.896159i	$-0.353654\pi$
$67$	59.4604			0.887468			0.443734	+	0.896159i	$0.353654\pi$
$68$	86.5638	+	41.6720i	1.27300	+	0.612824i
$69$		0			0
$70$	5.45565	−	23.9104i	0.0779378	−	0.341578i
$71$		−	48.4629i		−	0.682576i	−0.939959	−	0.341288i	$-0.889137\pi$
$71$		−	48.4629i		−	0.682576i	0.939959	−	0.341288i	$-0.110863\pi$
$72$		0			0
$73$	93.1375			1.27586			0.637928	−	0.770096i	$-0.279792\pi$
$73$	93.1375			1.27586			0.637928	+	0.770096i	$0.279792\pi$
$74$	−83.6407	−	19.0843i	−1.13028	−	0.257896i
$75$		0			0
$76$	124.083	+	59.7340i	1.63267	+	0.785974i
$77$			8.91495i			0.115779i
$78$		0			0
$79$		−	60.2424i		−	0.762562i	−0.924459	−	0.381281i	$-0.875483\pi$
$79$		−	60.2424i		−	0.762562i	0.924459	−	0.381281i	$-0.124517\pi$
$80$	−27.9654	+	22.3145i	−0.349568	+	0.278931i
$81$		0			0
$82$	2.77030	−	12.1414i	0.0337841	−	0.148065i
$83$	−5.69214			−0.0685800			−0.0342900	−	0.999412i	$-0.510917\pi$
$83$	−5.69214			−0.0685800			−0.0342900	+	0.999412i	$0.510917\pi$
$84$		0			0
$85$		−	53.7060i		−	0.631835i
$86$	−25.4809	+	111.675i	−0.296290	+	1.29855i
$87$		0			0
$88$	8.10645	−	10.1695i	0.0921188	−	0.115563i
$89$	−49.1046			−0.551737			−0.275868	−	0.961195i	$-0.588965\pi$
$89$	−49.1046			−0.551737			−0.275868	+	0.961195i	$0.588965\pi$
$90$		0			0
$91$	−98.9872			−1.08777
$92$	53.3098	−	110.739i	0.579454	−	1.20368i
$93$		0			0
$94$	−81.0226	−	18.4869i	−0.861943	−	0.196670i
$95$		−	76.9838i		−	0.810356i
$96$		0			0
$97$	35.9229			0.370339			0.185170	−	0.982707i	$-0.440717\pi$
$97$	35.9229			0.370339			0.185170	+	0.982707i	$0.440717\pi$
$98$	8.42044	−	36.9042i	0.0859228	−	0.376574i
$99$		0			0
$100$	18.0206	+	8.67516i	0.180206	+	0.0867516i
$101$		−	67.3302i		−	0.666635i	−0.942815	−	0.333318i	$-0.891832\pi$
$101$		−	67.3302i		−	0.666635i	0.942815	−	0.333318i	$-0.108168\pi$
$102$		0			0
$103$		−	73.3368i		−	0.712008i	−0.934484	−	0.356004i	$-0.884139\pi$
$103$		−	73.3368i		−	0.712008i	0.934484	−	0.356004i	$-0.115861\pi$
$104$	112.918	+	90.0101i	1.08575	+	0.865482i
$105$		0			0
$106$	−74.4214	−	16.9807i	−0.702088	−	0.160196i
$107$	−154.194			−1.44107			−0.720533	−	0.693421i	$-0.756103\pi$
$107$	−154.194			−1.44107			−0.720533	+	0.693421i	$0.756103\pi$
$108$		0			0
$109$		−	120.753i		−	1.10782i	−0.832575	−	0.553912i	$-0.813134\pi$
$109$		−	120.753i		−	1.10782i	0.832575	−	0.553912i	$-0.186866\pi$
$110$	−7.08794	−	1.61726i	−0.0644358	−	0.0147023i
$111$		0			0
$112$	68.5851	−	54.7261i	0.612367	−	0.488626i
$113$	209.411			1.85320			0.926599	−	0.376050i	$-0.122718\pi$
$113$	209.411			1.85320			0.926599	+	0.376050i	$0.122718\pi$
$114$		0			0
$115$	−68.7044			−0.597430
$116$	14.4535	−	30.0237i	0.124599	−	0.258825i
$117$		0			0
$118$	−31.4701	+	137.924i	−0.266696	+	1.16885i
$119$			131.714i			1.10684i
$120$		0			0
$121$	−118.357			−0.978159
$122$	123.974	+	28.2871i	1.01618	+	0.231861i
$123$		0			0
$124$	9.51650	−	19.7683i	0.0767459	−	0.159422i
$125$		−	11.1803i		−	0.0894427i
$126$		0			0
$127$			137.663i			1.08396i	0.840391	+	0.541981i	$0.182326\pi$
$127$			137.663i			1.08396i	−0.840391	+	0.541981i	$0.817674\pi$
$128$	−128.000	+	0.0625616i	−1.00000	+	0.000488762i
$129$		0			0
$130$	17.9572	−	78.7010i	0.138132	−	0.605393i
$131$	−30.3019			−0.231312			−0.115656	−	0.993289i	$-0.536897\pi$
$131$	−30.3019			−0.231312			−0.115656	+	0.993289i	$0.536897\pi$
$132$		0			0
$133$			188.802i			1.41957i
$134$	26.4543	−	115.941i	0.197420	−	0.865231i
$135$		0			0
$136$	119.769	−	150.250i	0.880651	−	1.10478i
$137$	186.067			1.35815			0.679076	−	0.734068i	$-0.262381\pi$
$137$	186.067			1.35815			0.679076	+	0.734068i	$0.262381\pi$
$138$		0			0
$139$	5.92262			0.0426087			0.0213044	−	0.999773i	$-0.493218\pi$
$139$	5.92262			0.0426087			0.0213044	+	0.999773i	$0.493218\pi$
$140$	−44.1954	−	21.2758i	−0.315681	−	0.151970i
$141$		0			0
$142$	−94.4972	−	21.5614i	−0.665473	−	0.151841i
$143$			29.3435i			0.205199i
$144$		0			0
$145$	−18.6273			−0.128464
$146$	41.4374	−	181.608i	0.283818	−	1.24389i
$147$		0			0
$148$	−74.4244	+	154.599i	−0.502868	+	1.04459i
$149$		−	235.886i		−	1.58313i	−0.611086	−	0.791564i	$-0.709267\pi$
$149$		−	235.886i		−	1.58313i	0.611086	−	0.791564i	$-0.290733\pi$
$150$		0			0
$151$		−	56.9382i		−	0.377074i	−0.982066	−	0.188537i	$-0.939625\pi$
$151$		−	56.9382i		−	0.377074i	0.982066	−	0.188537i	$-0.0603745\pi$
$152$	171.680	−	215.372i	1.12947	−	1.41692i
$153$		0			0
$154$	17.3831	+	3.96631i	0.112878	+	0.0257553i
$155$	−12.2646			−0.0791267
$156$		0			0
$157$		−	304.162i		−	1.93734i	−0.248351	−	0.968670i	$-0.579889\pi$
$157$		−	304.162i		−	1.93734i	0.248351	−	0.968670i	$-0.420111\pi$
$158$	−117.466	−	26.8022i	−0.743455	−	0.169634i
$159$		0			0
$160$	31.0687	+	64.4572i	0.194179	+	0.402858i
$161$	168.497			1.04657
$162$		0			0
$163$	248.671			1.52559			0.762796	−	0.646640i	$-0.223826\pi$
$163$	248.671			1.52559			0.762796	+	0.646640i	$0.223826\pi$
$164$	−22.4418	−	10.8035i	−0.136840	−	0.0658752i
$165$		0			0
$166$	−2.53246	+	11.0990i	−0.0152558	+	0.0668616i
$167$			20.4759i			0.122610i	0.998119	+	0.0613051i	$0.0195263\pi$
$167$			20.4759i			0.122610i	−0.998119	+	0.0613051i	$0.980474\pi$
$168$		0			0
$169$	−156.816			−0.927903
$170$	−104.721	−	23.8941i	−0.616003	−	0.140553i
$171$		0			0
$172$	206.417	+	99.3699i	1.20010	+	0.577732i
$173$			10.9926i			0.0635410i	0.999495	+	0.0317705i	$0.0101146\pi$
$173$			10.9926i			0.0635410i	−0.999495	+	0.0317705i	$0.989885\pi$
$174$		0			0
$175$			27.4197i			0.156684i
$176$	−16.2228	−	20.3312i	−0.0921752	−	0.115518i
$177$		0			0
$178$	−21.8469	+	95.7484i	−0.122735	+	0.537912i
$179$	−177.062			−0.989173			−0.494587	−	0.869128i	$-0.664681\pi$
$179$	−177.062			−0.989173			−0.494587	+	0.869128i	$0.664681\pi$
$180$		0			0
$181$			194.021i			1.07194i	0.844237	+	0.535969i	$0.180054\pi$
$181$			194.021i			1.07194i	−0.844237	+	0.535969i	$0.819946\pi$
$182$	−44.0400	+	193.014i	−0.241978	+	1.06052i
$183$		0			0
$184$	−192.210	−	153.216i	−1.04462	−	0.832697i
$185$	95.9164			0.518467
$186$		0			0
$187$	39.0448			0.208796
$188$	−72.0949	+	149.760i	−0.383483	+	0.796596i
$189$		0			0
$190$	−150.110	−	34.2505i	−0.790051	−	0.180266i
$191$			326.808i			1.71104i	0.517772	+	0.855519i	$0.326762\pi$
$191$			326.808i			1.71104i	−0.517772	+	0.855519i	$0.673238\pi$
$192$		0			0
$193$	255.564			1.32416			0.662082	−	0.749431i	$-0.269673\pi$
$193$	255.564			1.32416			0.662082	+	0.749431i	$0.269673\pi$
$194$	15.9823	−	70.0456i	0.0823830	−	0.361060i
$195$		0			0
$196$	−68.2127	−	32.8378i	−0.348024	−	0.167540i
$197$			266.053i			1.35053i	0.737577	+	0.675263i	$0.235970\pi$
$197$			266.053i			1.35053i	−0.737577	+	0.675263i	$0.764030\pi$
$198$		0			0
$199$		−	266.589i		−	1.33964i	−0.742521	−	0.669822i	$-0.766370\pi$
$199$		−	266.589i		−	1.33964i	0.742521	−	0.669822i	$-0.233630\pi$
$200$	24.9330	−	31.2785i	0.124665	−	0.156392i
$201$		0			0
$202$	−131.286	−	29.9556i	−0.649932	−	0.148295i
$203$	45.6834			0.225041
$204$		0			0
$205$			13.9233i			0.0679187i
$206$	−142.998	−	32.6280i	−0.694167	−	0.158388i
$207$		0			0
$208$	225.747	−	180.131i	1.08532	−	0.866012i
$209$	55.9680			0.267790
$210$		0			0
$211$	−50.6253			−0.239930			−0.119965	−	0.992778i	$-0.538278\pi$
$211$	−50.6253			−0.239930			−0.119965	+	0.992778i	$0.538278\pi$
$212$	−66.2210	+	137.558i	−0.312363	+	0.648861i
$213$		0			0
$214$	−68.6018	+	300.661i	−0.320569	+	1.40496i
$215$		−	128.066i		−	0.595654i
$216$		0			0
$217$	30.0790			0.138613
$218$	−235.454	−	53.7236i	−1.08007	−	0.246439i
$219$		0			0
$220$	−6.30693	+	13.1012i	−0.0286679	+	0.0595507i
$221$			433.534i			1.96169i
$222$		0			0
$223$			357.193i			1.60176i	0.598825	+	0.800880i	$0.295635\pi$
$223$			357.193i			1.60176i	−0.598825	+	0.800880i	$0.704365\pi$
$224$	−76.1958	−	158.081i	−0.340160	−	0.705719i
$225$		0			0
$226$	93.1684	−	408.329i	0.412249	−	1.80676i
$227$	−135.900			−0.598680			−0.299340	−	0.954146i	$-0.596767\pi$
$227$	−135.900			−0.598680			−0.299340	+	0.954146i	$0.596767\pi$
$228$		0			0
$229$			396.479i			1.73135i	0.500608	+	0.865674i	$0.333110\pi$
$229$			396.479i			1.73135i	−0.500608	+	0.865674i	$0.666890\pi$
$230$	−30.5670	+	133.966i	−0.132900	+	0.582460i
$231$		0			0
$232$	−52.1124	−	41.5404i	−0.224622	−	0.179053i
$233$	95.1970			0.408571			0.204285	−	0.978911i	$-0.434513\pi$
$233$	95.1970			0.408571			0.204285	+	0.978911i	$0.434513\pi$
$234$		0			0
$235$	92.9142			0.395379
$236$	254.935	+	122.726i	1.08023	+	0.520026i
$237$		0			0
$238$	256.827	+	58.6001i	1.07910	+	0.246219i
$239$			96.9914i			0.405822i	0.979197	+	0.202911i	$0.0650402\pi$
$239$			96.9914i			0.405822i	−0.979197	+	0.202911i	$0.934960\pi$
$240$		0			0
$241$	36.2570			0.150444			0.0752220	−	0.997167i	$-0.476033\pi$
$241$	36.2570			0.150444			0.0752220	+	0.997167i	$0.476033\pi$
$242$	−52.6578	+	230.783i	−0.217594	+	0.953650i
$243$		0			0
$244$	110.313	−	229.149i	0.452103	−	0.939137i
$245$			42.3206i			0.172737i
$246$		0			0
$247$			621.442i			2.51596i
$248$	−34.3119	−	27.3511i	−0.138355	−	0.110287i
$249$		0			0
$250$	−21.8004	−	4.97420i	−0.0872016	−	0.0198968i
$251$	−323.513			−1.28890			−0.644449	−	0.764647i	$-0.722913\pi$
$251$	−323.513			−1.28890			−0.644449	+	0.764647i	$0.722913\pi$
$252$		0			0
$253$		−	49.9488i		−	0.197426i
$254$	268.428	+	61.2471i	1.05680	+	0.241130i
$255$		0			0
$256$	−56.8259	+	249.613i	−0.221976	+	0.975052i
$257$	−403.216			−1.56893			−0.784467	−	0.620171i	$-0.787063\pi$
$257$	−403.216			−1.56893			−0.784467	+	0.620171i	$0.787063\pi$
$258$		0			0
$259$	−235.235			−0.908242
$260$	−145.469	−	70.0291i	−0.559496	−	0.269343i
$261$		0			0
$262$	−13.4815	+	59.0853i	−0.0514561	+	0.225516i
$263$			16.0314i			0.0609561i	0.999535	+	0.0304780i	$0.00970296\pi$
$263$			16.0314i			0.0609561i	−0.999535	+	0.0304780i	$0.990297\pi$
$264$		0			0
$265$	85.3441			0.322053
$266$	368.143	+	83.9993i	1.38400	+	0.315787i
$267$		0			0
$268$	−214.302	−	103.166i	−0.799635	−	0.384946i
$269$		−	261.953i		−	0.973804i	−0.873457	−	0.486902i	$-0.838127\pi$
$269$		−	261.953i		−	0.973804i	0.873457	−	0.486902i	$-0.161873\pi$
$270$		0			0
$271$			25.2639i			0.0932246i	0.998913	+	0.0466123i	$0.0148425\pi$
$271$			25.2639i			0.0932246i	−0.998913	+	0.0466123i	$0.985157\pi$
$272$	−239.684	−	300.382i	−0.881191	−	1.10435i
$273$		0			0
$274$	82.7822	−	362.809i	0.302125	−	1.32412i
$275$	8.12822			0.0295572
$276$		0			0
$277$		−	2.48104i		−	0.00895683i	−0.999990	−	0.00447842i	$-0.998574\pi$
$277$		−	2.48104i		−	0.00895683i	0.999990	−	0.00447842i	$-0.00142553\pi$
$278$	2.63501	−	11.5484i	0.00947844	−	0.0415411i
$279$		0			0
$280$	−61.1482	+	76.7103i	−0.218386	+	0.273965i
$281$	−386.378			−1.37501			−0.687505	−	0.726180i	$-0.741294\pi$
$281$	−386.378			−1.37501			−0.687505	+	0.726180i	$0.741294\pi$
$282$		0			0
$283$	115.917			0.409600			0.204800	−	0.978804i	$-0.434346\pi$
$283$	115.917			0.409600			0.204800	+	0.978804i	$0.434346\pi$
$284$	−84.0847	+	174.666i	−0.296073	+	0.615021i
$285$		0			0
$286$	57.2165	+	13.0551i	0.200058	+	0.0456471i
$287$		−	34.1469i		−	0.118979i
$288$		0			0
$289$	287.866			0.996076
$290$	−8.28740	+	36.3211i	−0.0285772	+	0.125245i
$291$		0			0
$292$	−335.678	−	161.596i	−1.14958	−	0.553413i
$293$		−	536.585i		−	1.83135i	−0.401922	−	0.915674i	$-0.631658\pi$
$293$		−	536.585i		−	1.83135i	0.401922	−	0.915674i	$-0.368342\pi$
$294$		0			0
$295$		−	158.167i		−	0.536158i
$296$	268.339	+	213.901i	0.906550	+	0.722639i
$297$		0			0
$298$	−459.951	−	104.947i	−1.54346	−	0.352171i
$299$	554.607			1.85487
$300$		0			0
$301$			314.080i			1.04346i
$302$	−111.023	−	25.3321i	−0.367626	−	0.0838812i
$303$		0			0
$304$	−343.570	−	430.577i	−1.13017	−	1.41637i
$305$	−142.169			−0.466128
$306$		0			0
$307$	−332.415			−1.08279			−0.541393	−	0.840770i	$-0.682103\pi$
$307$	−332.415			−1.08279			−0.541393	+	0.840770i	$0.682103\pi$
$308$	15.4677	−	32.1305i	0.0502199	−	0.104320i
$309$		0			0
$310$	−5.45661	+	23.9147i	−0.0176020	+	0.0771441i
$311$		−	523.655i		−	1.68378i	−0.539651	−	0.841889i	$-0.681444\pi$
$311$		−	523.655i		−	1.68378i	0.539651	−	0.841889i	$-0.318556\pi$
$312$		0			0
$313$	−188.357			−0.601781			−0.300890	−	0.953659i	$-0.597284\pi$
$313$	−188.357			−0.601781			−0.300890	+	0.953659i	$0.597284\pi$
$314$	−593.082	−	135.324i	−1.88880	−	0.430967i
$315$		0			0
$316$	−104.523	+	217.121i	−0.330768	+	0.687091i
$317$			393.769i			1.24217i	0.783742	+	0.621087i	$0.213308\pi$
$317$			393.769i			1.24217i	−0.783742	+	0.621087i	$0.786692\pi$
$318$		0			0
$319$		−	13.5422i		−	0.0424522i
$320$	139.507	−	31.9031i	0.435959	−	0.0996970i
$321$		0			0
$322$	74.9654	−	328.551i	0.232812	−	1.02034i
$323$	826.897			2.56005
$324$		0			0
$325$			90.2518i			0.277698i
$326$	110.635	−	484.881i	0.339372	−	1.48737i
$327$		0			0
$328$	−31.0501	+	38.9524i	−0.0946650	+	0.118757i
$329$	−227.872			−0.692619
$330$		0			0
$331$	−94.6057			−0.285818			−0.142909	−	0.989736i	$-0.545646\pi$
$331$	−94.6057			−0.285818			−0.142909	+	0.989736i	$0.545646\pi$
$332$	20.5151	+	9.87604i	0.0617926	+	0.0297471i
$333$		0			0
$334$	39.9257	+	9.10984i	0.119538	+	0.0272750i
$335$			132.957i			0.396888i
$336$		0			0
$337$	−520.784			−1.54535			−0.772676	−	0.634800i	$-0.781082\pi$
$337$	−520.784			−1.54535			−0.772676	+	0.634800i	$0.781082\pi$
$338$	−69.7682	+	305.773i	−0.206415	+	0.904653i
$339$		0			0
$340$	−93.1815	+	193.563i	−0.274063	+	0.569302i
$341$		−	8.91652i		−	0.0261481i
$342$		0			0
$343$		−	372.504i		−	1.08602i
$344$	285.596	−	358.280i	0.830222	−	1.04151i
$345$		0			0
$346$	21.4343	+	4.89067i	0.0619489	+	0.0141349i
$347$	21.6254			0.0623210			0.0311605	−	0.999514i	$-0.490080\pi$
$347$	21.6254			0.0623210			0.0311605	+	0.999514i	$0.490080\pi$
$348$		0			0
$349$		−	241.608i		−	0.692286i	−0.938182	−	0.346143i	$-0.887491\pi$
$349$		−	241.608i		−	0.692286i	0.938182	−	0.346143i	$-0.112509\pi$
$350$	53.4654	+	12.1992i	0.152758	+	0.0348548i
$351$		0			0
$352$	−46.8611	+	22.5873i	−0.133128	+	0.0641684i
$353$	100.887			0.285799			0.142899	−	0.989737i	$-0.454357\pi$
$353$	100.887			0.285799			0.142899	+	0.989737i	$0.454357\pi$
$354$		0			0
$355$	108.366			0.305257
$356$	176.979	+	85.1980i	0.497131	+	0.239320i
$357$		0			0
$358$	−78.7759	+	345.251i	−0.220044	+	0.964388i
$359$			161.368i			0.449494i	0.974417	+	0.224747i	$0.0721556\pi$
$359$			161.368i			0.449494i	−0.974417	+	0.224747i	$0.927844\pi$
$360$		0			0
$361$	824.301			2.28338
$362$	378.319	+	86.3210i	1.04508	+	0.238456i
$363$		0			0
$364$	356.762	+	171.746i	0.980114	+	0.471830i
$365$			208.262i			0.570580i
$366$		0			0
$367$			301.732i			0.822157i	0.911600	+	0.411079i	$0.134848\pi$
$367$			301.732i			0.822157i	−0.911600	+	0.411079i	$0.865152\pi$
$368$	−384.270	+	306.620i	−1.04421	+	0.833208i
$369$		0			0
$370$	42.6738	−	187.026i	0.115335	−	0.505476i
$371$	−209.306			−0.564167
$372$		0			0
$373$		−	263.001i		−	0.705097i	−0.935794	−	0.352548i	$-0.885315\pi$
$373$		−	263.001i		−	0.705097i	0.935794	−	0.352548i	$-0.114685\pi$
$374$	17.3712	−	76.1329i	0.0464472	−	0.203564i
$375$		0			0
$376$	259.940	+	207.206i	0.691329	+	0.551080i
$377$	150.367			0.398850
$378$		0			0
$379$	−9.55298			−0.0252057			−0.0126029	−	0.999921i	$-0.504012\pi$
$379$	−9.55298			−0.0252057			−0.0126029	+	0.999921i	$0.504012\pi$
$380$	−133.569	+	277.459i	−0.351498	+	0.730154i
$381$		0			0
$382$	637.239	+	145.399i	1.66816	+	0.380625i
$383$		−	319.027i		−	0.832968i	−0.909143	−	0.416484i	$-0.863262\pi$
$383$		−	319.027i		−	0.832968i	0.909143	−	0.416484i	$-0.136738\pi$
$384$		0			0
$385$	−19.9344			−0.0517777
$386$	113.702	−	498.320i	0.294564	−	1.29098i
$387$		0			0
$388$	−129.470	−	62.3274i	−0.333687	−	0.160638i
$389$			108.219i			0.278198i	0.990278	+	0.139099i	$0.0444206\pi$
$389$			108.219i			0.278198i	−0.990278	+	0.139099i	$0.955579\pi$
$390$		0			0
$391$		−	737.967i		−	1.88738i
$392$	−94.3782	+	118.397i	−0.240761	+	0.302034i
$393$		0			0
$394$	518.774	+	118.369i	1.31669	+	0.300428i
$395$	134.706			0.341028
$396$		0			0
$397$		−	533.165i		−	1.34299i	−0.741011	−	0.671493i	$-0.765654\pi$
$397$		−	533.165i		−	1.34299i	0.741011	−	0.671493i	$-0.234346\pi$
$398$	−519.819	−	118.607i	−1.30608	−	0.298008i
$399$		0			0
$400$	−49.8967	−	62.5326i	−0.124742	−	0.156331i
$401$	−610.423			−1.52225			−0.761126	−	0.648604i	$-0.775353\pi$
$401$	−610.423			−1.52225			−0.761126	+	0.648604i	$0.775353\pi$
$402$		0			0
$403$	99.0047			0.245669
$404$	−116.820	+	242.666i	−0.289158	+	0.600658i
$405$		0			0
$406$	20.3248	−	89.0774i	0.0500611	−	0.219403i
$407$			69.7322i			0.171332i
$408$		0			0
$409$	−174.487			−0.426618			−0.213309	−	0.976985i	$-0.568424\pi$
$409$	−174.487			−0.426618			−0.213309	+	0.976985i	$0.568424\pi$
$410$	27.1489	+	6.19457i	0.0662169	+	0.0151087i
$411$		0			0
$412$	−127.242	+	264.314i	−0.308839	+	0.641540i
$413$			387.903i			0.939232i
$414$		0			0
$415$		−	12.7280i		−	0.0306699i
$416$	−250.798	−	520.323i	−0.602880	−	1.25078i
$417$		0			0
$418$	24.9005	−	109.131i	0.0595705	−	0.261080i
$419$	−35.8925			−0.0856622			−0.0428311	−	0.999082i	$-0.513638\pi$
$419$	−35.8925			−0.0856622			−0.0428311	+	0.999082i	$0.513638\pi$
$420$		0			0
$421$			236.757i			0.562368i	0.959654	+	0.281184i	$0.0907271\pi$
$421$			236.757i			0.562368i	−0.959654	+	0.281184i	$0.909273\pi$
$422$	−22.5235	+	98.7136i	−0.0533732	+	0.233918i
$423$		0			0
$424$	238.761	+	190.324i	0.563116	+	0.448877i
$425$	120.090			0.282565
$426$		0			0
$427$	348.669			0.816554
$428$	555.733	+	267.532i	1.29844	+	0.625074i
$429$		0			0
$430$	−249.713	−	56.9771i	−0.580729	−	0.132505i
$431$			195.847i			0.454403i	0.973848	+	0.227201i	$0.0729575\pi$
$431$			195.847i			0.454403i	−0.973848	+	0.227201i	$0.927042\pi$
$432$		0			0
$433$	−66.2067			−0.152902			−0.0764512	−	0.997073i	$-0.524359\pi$
$433$	−66.2067			−0.152902			−0.0764512	+	0.997073i	$0.524359\pi$
$434$	13.3823	−	58.6506i	0.0308348	−	0.135140i
$435$		0			0
$436$	−209.510	+	435.208i	−0.480528	+	0.998183i
$437$		−	1057.83i		−	2.42065i
$438$		0			0
$439$			551.797i			1.25694i	0.777834	+	0.628470i	$0.216319\pi$
$439$			551.797i			1.25694i	−0.777834	+	0.628470i	$0.783681\pi$
$440$	22.7398	+	18.1266i	0.0516813	+	0.0411968i
$441$		0			0
$442$	845.343	+	192.882i	1.91254	+	0.436384i
$443$	277.959			0.627446			0.313723	−	0.949515i	$-0.398424\pi$
$443$	277.959			0.627446			0.313723	+	0.949515i	$0.398424\pi$
$444$		0			0
$445$		−	109.801i		−	0.246744i
$446$	696.485	+	158.917i	1.56163	+	0.356316i
$447$		0			0
$448$	−342.140	+	78.2421i	−0.763706	+	0.174647i
$449$	147.609			0.328752			0.164376	−	0.986398i	$-0.447439\pi$
$449$	147.609			0.328752			0.164376	+	0.986398i	$0.447439\pi$
$450$		0			0
$451$	−10.1224			−0.0224444
$452$	−754.744	−	363.336i	−1.66979	−	0.803840i
$453$		0			0
$454$	−60.4629	+	264.990i	−0.133178	+	0.583679i
$455$		−	221.342i		−	0.486466i
$456$		0			0
$457$	−485.661			−1.06272			−0.531358	−	0.847147i	$-0.678318\pi$
$457$	−485.661			−1.06272			−0.531358	+	0.847147i	$0.678318\pi$
$458$	773.089	+	176.396i	1.68797	+	0.385143i
$459$		0			0
$460$	247.619	+	119.204i	0.538302	+	0.259140i
$461$			447.963i			0.971721i	0.874036	+	0.485861i	$0.161494\pi$
$461$			447.963i			0.971721i	−0.874036	+	0.485861i	$0.838506\pi$
$462$		0			0
$463$		−	762.712i		−	1.64733i	−0.567080	−	0.823663i	$-0.691927\pi$
$463$		−	762.712i		−	1.64733i	0.567080	−	0.823663i	$-0.308073\pi$
$464$	−104.184	+	83.1317i	−0.224535	+	0.179163i
$465$		0			0
$466$	42.3537	−	185.623i	0.0908877	−	0.398333i
$467$	838.223			1.79491			0.897455	−	0.441106i	$-0.145414\pi$
$467$	838.223			1.79491			0.897455	+	0.441106i	$0.145414\pi$
$468$		0			0
$469$		−	326.077i		−	0.695261i
$470$	41.3380	−	181.172i	0.0879533	−	0.385473i
$471$		0			0
$472$	352.724	−	442.492i	0.747297	−	0.937483i
$473$	93.1050			0.196839
$474$		0			0
$475$	172.141			0.362402
$476$	228.527	−	474.711i	0.480099	−	0.997293i
$477$		0			0
$478$	189.122	+	43.1520i	0.395653	+	0.0902762i
$479$			150.795i			0.314812i	0.987534	+	0.157406i	$0.0503131\pi$
$479$			150.795i			0.314812i	−0.987534	+	0.157406i	$0.949687\pi$
$480$		0			0
$481$	−774.273			−1.60971
$482$	16.1309	−	70.6970i	0.0334667	−	0.146674i
$483$		0			0
$484$	426.574	+	205.354i	0.881350	+	0.424284i
$485$			80.3261i			0.165621i
$486$		0			0
$487$		−	148.464i		−	0.304855i	−0.988315	−	0.152427i	$-0.951291\pi$
$487$		−	148.464i		−	0.304855i	0.988315	−	0.152427i	$-0.0487090\pi$
$488$	−397.736	−	317.048i	−0.815034	−	0.649688i
$489$		0			0
$490$	82.5203	+	18.8287i	0.168409	+	0.0384259i
$491$	−76.8116			−0.156439			−0.0782196	−	0.996936i	$-0.524924\pi$
$491$	−76.8116			−0.156439			−0.0782196	+	0.996936i	$0.524924\pi$
$492$		0			0
$493$		−	200.079i		−	0.405841i
$494$	1211.74	+	276.483i	2.45292	+	0.559682i
$495$		0			0
$496$	−68.5972	+	54.7358i	−0.138301	+	0.110354i
$497$	−265.768			−0.534744
$498$		0			0
$499$	564.248			1.13076			0.565379	−	0.824832i	$-0.308730\pi$
$499$	564.248			1.13076			0.565379	+	0.824832i	$0.308730\pi$
$500$	−19.3982	+	40.2953i	−0.0387965	+	0.0805905i
$501$		0			0
$502$	−143.933	+	630.815i	−0.286719	+	1.25660i
$503$		−	223.999i		−	0.445327i	−0.974895	−	0.222663i	$-0.928525\pi$
$503$		−	223.999i		−	0.445327i	0.974895	−	0.222663i	$-0.0714750\pi$
$504$		0			0
$505$	150.555			0.298128
$506$	−97.3946	−	22.2225i	−0.192479	−	0.0439180i
$507$		0			0
$508$	238.850	−	496.154i	0.470177	−	0.976682i
$509$		−	174.435i		−	0.342701i	−0.985210	−	0.171350i	$-0.945187\pi$
$509$		−	174.435i		−	0.342701i	0.985210	−	0.171350i	$-0.0548130\pi$
$510$		0			0
$511$		−	510.761i		−	0.999532i
$512$	461.436	+	221.859i	0.901241	+	0.433317i
$513$		0			0
$514$	−179.393	+	786.226i	−0.349014	+	1.52962i
$515$	163.986			0.318420
$516$		0			0
$517$			67.5496i			0.130657i
$518$	−104.657	+	458.681i	−0.202041	+	0.885484i
$519$		0			0
$520$	−201.269	+	252.491i	−0.387055	+	0.485560i
$521$	−478.465			−0.918358			−0.459179	−	0.888344i	$-0.651856\pi$
$521$	−478.465			−0.918358			−0.459179	+	0.888344i	$0.651856\pi$
$522$		0			0
$523$	−491.609			−0.939979			−0.469990	−	0.882672i	$-0.655742\pi$
$523$	−491.609			−0.939979			−0.469990	+	0.882672i	$0.655742\pi$
$524$	109.212	+	52.5748i	0.208419	+	0.100334i
$525$		0			0
$526$	31.2595	+	7.13248i	0.0594287	+	0.0135599i
$527$		−	131.737i		−	0.249975i
$528$		0			0
$529$	−415.059			−0.784611
$530$	37.9701	−	166.411i	0.0716416	−	0.313983i
$531$		0			0
$532$	327.578	−	680.466i	0.615748	−	1.27907i
$533$		−	112.394i		−	0.210871i
$534$		0			0
$535$		−	344.788i		−	0.644464i
$536$	−296.505	+	371.966i	−0.553182	+	0.693966i
$537$		0			0
$538$	−510.779	−	116.545i	−0.949404	−	0.216625i
$539$	−30.7675			−0.0570826
$540$		0			0
$541$			166.802i			0.308322i	0.988046	+	0.154161i	$0.0492674\pi$
$541$			166.802i			0.308322i	−0.988046	+	0.154161i	$0.950733\pi$
$542$	49.2617	+	11.2400i	0.0908887	+	0.0207381i
$543$		0			0
$544$	−692.347	+	333.715i	−1.27270	+	0.613446i
$545$	270.012			0.495434
$546$		0			0
$547$	166.395			0.304195			0.152098	−	0.988365i	$-0.451397\pi$
$547$	166.395			0.304195			0.152098	+	0.988365i	$0.451397\pi$
$548$	−670.606	−	322.832i	−1.22373	−	0.589109i
$549$		0			0
$550$	3.61629	−	15.8491i	0.00657508	−	0.0288166i
$551$		−	286.800i		−	0.520508i
$552$		0			0
$553$	−330.366			−0.597407
$554$	−4.83775	−	1.10383i	−0.00873240	−	0.00199247i
$555$		0			0
$556$	−21.3458	−	10.2759i	−0.0383917	−	0.0184819i
$557$		−	267.280i		−	0.479856i	−0.970791	−	0.239928i	$-0.922876\pi$
$557$		−	267.280i		−	0.479856i	0.970791	−	0.239928i	$-0.0771238\pi$
$558$		0			0
$559$			1033.79i			1.84936i
$560$	122.371	+	153.361i	0.218520	+	0.273859i
$561$		0			0
$562$	−171.902	+	753.393i	−0.305875	+	1.34056i
$563$	−637.679			−1.13264			−0.566322	−	0.824184i	$-0.691634\pi$
$563$	−637.679			−1.13264			−0.566322	+	0.824184i	$0.691634\pi$
$564$		0			0
$565$			468.258i			0.828776i
$566$	51.5720	−	226.024i	0.0911166	−	0.399337i
$567$		0			0
$568$	303.169	+	241.666i	0.533749	+	0.425467i
$569$	−58.7735			−0.103293			−0.0516463	−	0.998665i	$-0.516447\pi$
$569$	−58.7735			−0.103293			−0.0516463	+	0.998665i	$0.516447\pi$
$570$		0			0
$571$	−3.25216			−0.00569555			−0.00284778	−	0.999996i	$-0.500906\pi$
$571$	−3.25216			−0.00569555			−0.00284778	+	0.999996i	$0.500906\pi$
$572$	50.9119	−	105.757i	0.0890068	−	0.184890i
$573$		0			0
$574$	−66.5826	−	15.1922i	−0.115998	−	0.0264672i
$575$		−	153.628i		−	0.267179i
$576$		0			0
$577$	366.712			0.635549			0.317775	−	0.948166i	$-0.397064\pi$
$577$	366.712			0.635549			0.317775	+	0.948166i	$0.397064\pi$
$578$	128.073	−	561.306i	0.221580	−	0.971117i
$579$		0			0
$580$	67.1350	+	32.3190i	0.115750	+	0.0557224i
$581$			31.2154i			0.0537270i
$582$		0			0
$583$			62.0460i			0.106425i
$584$	−464.440	+	582.640i	−0.795274	+	0.997671i
$585$		0			0
$586$	−1046.28	−	238.730i	−1.78546	−	0.407389i
$587$	−203.754			−0.347111			−0.173556	−	0.984824i	$-0.555526\pi$
$587$	−203.754			−0.347111			−0.173556	+	0.984824i	$0.555526\pi$
$588$		0			0
$589$		−	188.836i		−	0.320604i
$590$	−308.407	−	70.3692i	−0.522724	−	0.119270i
$591$		0			0
$592$	536.469	−	428.065i	0.906197	−	0.723082i
$593$	−291.378			−0.491362			−0.245681	−	0.969351i	$-0.579012\pi$
$593$	−291.378			−0.491362			−0.245681	+	0.969351i	$0.579012\pi$
$594$		0			0
$595$	−294.521			−0.494992
$596$	−409.270	+	850.161i	−0.686694	+	1.42644i
$597$		0			0
$598$	246.748	−	1081.42i	0.412622	−	1.80840i
$599$		−	855.966i		−	1.42899i	−0.699640	−	0.714495i	$-0.746656\pi$
$599$		−	855.966i		−	1.42899i	0.699640	−	0.714495i	$-0.253344\pi$
$600$		0			0
$601$	−426.264			−0.709258			−0.354629	−	0.935007i	$-0.615393\pi$
$601$	−426.264			−0.709258			−0.354629	+	0.935007i	$0.615393\pi$
$602$	612.421	+	139.736i	1.01731	+	0.232120i
$603$		0			0
$604$	−98.7895	+	205.212i	−0.163559	+	0.339755i
$605$		−	264.655i		−	0.437446i
$606$		0			0
$607$			410.035i			0.675510i	0.941234	+	0.337755i	$0.109668\pi$
$607$			410.035i			0.675510i	−0.941234	+	0.337755i	$0.890332\pi$
$608$	−992.433	+	478.357i	−1.63229	+	0.786772i
$609$		0			0
$610$	−63.2518	+	277.213i	−0.103691	+	0.454448i
$611$	−750.037			−1.22756
$612$		0			0
$613$		−	252.628i		−	0.412118i	−0.978540	−	0.206059i	$-0.933936\pi$
$613$		−	252.628i		−	0.412118i	0.978540	−	0.206059i	$-0.0660639\pi$
$614$	−147.893	+	648.172i	−0.240869	+	1.05565i
$615$		0			0
$616$	−55.7692	−	44.4553i	−0.0905344	−	0.0721678i
$617$	−234.903			−0.380718			−0.190359	−	0.981715i	$-0.560965\pi$
$617$	−234.903			−0.380718			−0.190359	+	0.981715i	$0.560965\pi$
$618$		0			0
$619$	412.764			0.666824			0.333412	−	0.942781i	$-0.391800\pi$
$619$	412.764			0.666824			0.333412	+	0.942781i	$0.391800\pi$
$620$	44.2032	+	21.2795i	0.0712955	+	0.0343218i
$621$		0			0
$622$	−1021.07	−	232.977i	−1.64159	−	0.374561i
$623$			269.287i			0.432242i
$624$		0			0
$625$	25.0000			0.0400000
$626$	−83.8013	+	367.276i	−0.133868	+	0.586702i
$627$		0			0
$628$	−527.731	+	1096.24i	−0.840337	+	1.74560i
$629$			1030.26i			1.63793i
$630$		0			0
$631$		−	969.308i		−	1.53615i	−0.640363	−	0.768073i	$-0.721216\pi$
$631$		−	969.308i		−	1.53615i	0.640363	−	0.768073i	$-0.278784\pi$
$632$	376.858	+	300.405i	0.596295	+	0.475325i
$633$		0			0
$634$	767.805	+	175.190i	1.21105	+	0.276325i
$635$	−307.824			−0.484763
$636$		0			0
$637$		−	341.627i		−	0.536307i
$638$	−26.4058	−	6.02502i	−0.0413885	−	0.00944361i
$639$		0			0
$640$	−0.139892	−	286.217i	−0.000218581	−	0.447214i
$641$	805.292			1.25631			0.628153	−	0.778090i	$-0.283811\pi$
$641$	805.292			1.25631			0.628153	+	0.778090i	$0.283811\pi$
$642$		0			0
$643$	887.377			1.38006			0.690028	−	0.723782i	$-0.257598\pi$
$643$	887.377			1.38006			0.690028	+	0.723782i	$0.257598\pi$
$644$	−607.284	−	292.348i	−0.942988	−	0.453957i
$645$		0			0
$646$	367.891	−	1612.36i	0.569491	−	2.49591i
$647$			1129.74i			1.74612i	0.487614	+	0.873059i	$0.337867\pi$
$647$			1129.74i			1.74612i	−0.487614	+	0.873059i	$0.662133\pi$
$648$		0			0
$649$	114.989			0.177178
$650$	175.981	+	40.1536i	0.270740	+	0.0617747i
$651$		0			0
$652$	−896.241	−	431.453i	−1.37460	−	0.661737i
$653$		−	384.844i		−	0.589348i	−0.955598	−	0.294674i	$-0.904789\pi$
$653$		−	384.844i		−	0.589348i	0.955598	−	0.294674i	$-0.0952111\pi$
$654$		0			0
$655$		−	67.7572i		−	0.103446i
$656$	62.1383	+	77.8744i	0.0947231	+	0.118711i
$657$		0			0
$658$	−101.381	+	444.324i	−0.154075	+	0.675264i
$659$	−38.8992			−0.0590276			−0.0295138	−	0.999564i	$-0.509396\pi$
$659$	−38.8992			−0.0590276			−0.0295138	+	0.999564i	$0.509396\pi$
$660$		0			0
$661$			877.861i			1.32808i	0.747697	+	0.664040i	$0.231159\pi$
$661$			877.861i			1.32808i	−0.747697	+	0.664040i	$0.768841\pi$
$662$	−42.0906	+	184.470i	−0.0635810	+	0.278656i
$663$		0			0
$664$	28.3845	−	35.6083i	0.0427477	−	0.0536269i
$665$	−422.175			−0.634850
$666$		0			0
$667$	−255.956			−0.383742
$668$	35.5263	−	73.7975i	0.0531831	−	0.110475i
$669$		0			0
$670$	259.252	+	59.1535i	0.386943	+	0.0882888i
$671$		−	103.358i		−	0.154036i
$672$		0			0
$673$	−343.747			−0.510768			−0.255384	−	0.966840i	$-0.582202\pi$
$673$	−343.747			−0.510768			−0.255384	+	0.966840i	$0.582202\pi$
$674$	−231.700	+	1015.47i	−0.343768	+	1.50663i
$675$		0			0
$676$	565.182	+	272.080i	0.836068	+	0.402485i
$677$		−	404.932i		−	0.598126i	−0.954233	−	0.299063i	$-0.903326\pi$
$677$		−	404.932i		−	0.598126i	0.954233	−	0.299063i	$-0.0966741\pi$
$678$		0			0
$679$		−	196.999i		−	0.290132i
$680$	335.968	+	267.811i	0.494071	+	0.393839i
$681$		0			0
$682$	−17.3862	−	3.96701i	−0.0254930	−	0.00581673i
$683$	−145.169			−0.212546			−0.106273	−	0.994337i	$-0.533892\pi$
$683$	−145.169			−0.212546			−0.106273	+	0.994337i	$0.533892\pi$
$684$		0			0
$685$			416.058i			0.607384i
$686$	−726.341	−	165.729i	−1.05881	−	0.241588i
$687$		0			0
$688$	−571.543	−	716.282i	−0.830731	−	1.04111i
$689$	−688.929			−0.999896
$690$		0			0
$691$	−104.860			−0.151751			−0.0758757	−	0.997117i	$-0.524175\pi$
$691$	−104.860			−0.151751			−0.0758757	+	0.997117i	$0.524175\pi$
$692$	19.0725	−	39.6186i	0.0275614	−	0.0572523i
$693$		0			0
$694$	9.62126	−	42.1671i	0.0138635	−	0.0607595i
$695$			13.2434i			0.0190552i
$696$		0			0
$697$	−149.553			−0.214567
$698$	−471.108	−	107.493i	−0.674940	−	0.154001i
$699$		0			0
$700$	47.5741	−	98.8239i	0.0679630	−	0.141177i
$701$			88.5728i			0.126352i	0.998002	+	0.0631760i	$0.0201229\pi$
$701$			88.5728i			0.126352i	−0.998002	+	0.0631760i	$0.979877\pi$
$702$		0			0
$703$			1476.80i			2.10071i
$704$	23.1938	+	101.423i	0.0329458	+	0.144067i
$705$		0			0
$706$	44.8852	−	196.718i	0.0635768	−	0.278638i
$707$	−369.235			−0.522256
$708$		0			0
$709$			295.500i			0.416784i	0.978045	+	0.208392i	$0.0668230\pi$
$709$			295.500i			0.416784i	−0.978045	+	0.208392i	$0.933177\pi$
$710$	48.2128	−	211.302i	0.0679054	−	0.297609i
$711$		0			0
$712$	244.865	−	307.183i	0.343912	−	0.431437i
$713$	−168.527			−0.236363
$714$		0			0
$715$	−65.6140			−0.0917678
$716$	638.152	+	307.208i	0.891274	+	0.429062i
$717$		0			0
$718$	314.650	+	71.7937i	0.438231	+	0.0999913i
$719$			464.090i			0.645467i	0.946490	+	0.322733i	$0.104602\pi$
$719$			464.090i			0.645467i	−0.946490	+	0.322733i	$0.895398\pi$
$720$		0			0
$721$	−402.175			−0.557802
$722$	366.736	−	1607.29i	0.507945	−	2.22617i
$723$		0			0
$724$	336.633	−	699.274i	0.464962	−	0.965849i
$725$		−	41.6519i		−	0.0574509i
$726$		0			0
$727$		−	1052.48i		−	1.44771i	−0.689952	−	0.723855i	$-0.742369\pi$
$727$		−	1052.48i		−	1.44771i	0.689952	−	0.723855i	$-0.257631\pi$
$728$	493.611	−	619.234i	0.678036	−	0.850596i
$729$		0			0
$730$	406.087	+	92.6568i	0.556283	+	0.126927i
$731$	1375.58			1.88177
$732$		0			0
$733$		−	82.5148i		−	0.112571i	−0.998415	−	0.0562857i	$-0.982074\pi$
$733$		−	82.5148i		−	0.112571i	0.998415	−	0.0562857i	$-0.0179258\pi$
$734$	588.343	+	134.242i	0.801557	+	0.182891i
$735$		0			0
$736$	426.911	+	885.699i	0.580043	+	1.20340i
$737$	−96.6614			−0.131155
$738$		0			0
$739$	214.733			0.290572			0.145286	−	0.989390i	$-0.453590\pi$
$739$	214.733			0.290572			0.145286	+	0.989390i	$0.453590\pi$
$740$	−345.694	−	166.418i	−0.467154	−	0.224889i
$741$		0			0
$742$	−93.1214	+	408.123i	−0.125501	+	0.550031i
$743$		−	96.3747i		−	0.129710i	−0.997895	−	0.0648551i	$-0.979341\pi$
$743$		−	96.3747i		−	0.129710i	0.997895	−	0.0648551i	$-0.0206585\pi$
$744$		0			0
$745$	527.457			0.707996
$746$	−512.822	−	117.011i	−0.687429	−	0.156851i
$747$		0			0
$748$	−140.722	−	67.7439i	−0.188131	−	0.0905668i
$749$			845.592i			1.12896i
$750$		0			0
$751$			547.767i			0.729384i	0.931128	+	0.364692i	$0.118826\pi$
$751$			547.767i			0.729384i	−0.931128	+	0.364692i	$0.881174\pi$
$752$	519.677	−	414.666i	0.691060	−	0.551417i
$753$		0			0
$754$	66.8989	−	293.198i	0.0887254	−	0.388856i
$755$	127.318			0.168633
$756$		0			0
$757$		−	516.109i		−	0.681782i	−0.940103	−	0.340891i	$-0.889271\pi$
$757$		−	516.109i		−	0.681782i	0.940103	−	0.340891i	$-0.110729\pi$
$758$	−4.25017	+	18.6272i	−0.00560709	+	0.0245742i
$759$		0			0
$760$	481.587	+	383.888i	0.633667	+	0.505116i
$761$	446.601			0.586861			0.293430	−	0.955980i	$-0.405203\pi$
$761$	446.601			0.586861			0.293430	+	0.955980i	$0.405203\pi$
$762$		0			0
$763$	−662.202			−0.867893
$764$	567.023	−	1177.86i	0.742176	−	1.54170i
$765$		0			0
$766$	−622.066	−	141.937i	−0.812097	−	0.185296i
$767$			1276.78i			1.66464i
$768$		0			0
$769$	−253.980			−0.330273			−0.165136	−	0.986271i	$-0.552806\pi$
$769$	−253.980			−0.330273			−0.165136	+	0.986271i	$0.552806\pi$
$770$	−8.86894	+	38.8699i	−0.0115181	+	0.0504804i
$771$		0			0
$772$	−921.081	−	443.411i	−1.19311	−	0.574367i
$773$		−	226.748i		−	0.293335i	−0.989186	−	0.146667i	$-0.953145\pi$
$773$		−	226.748i		−	0.293335i	0.989186	−	0.146667i	$-0.0468547\pi$
$774$		0			0
$775$		−	27.4246i		−	0.0353865i
$776$	−179.134	+	224.723i	−0.230842	+	0.289591i
$777$		0			0
$778$	211.015	+	48.1473i	0.271227	+	0.0618860i
$779$	−214.374			−0.275192
$780$		0			0
$781$			78.7835i			0.100875i
$782$	−1438.95	−	328.326i	−1.84009	−	0.419854i
$783$		0			0
$784$	188.872	+	236.703i	0.240908	+	0.301917i
$785$	680.128			0.866405
$786$		0			0
$787$	−86.1883			−0.109515			−0.0547575	−	0.998500i	$-0.517439\pi$
$787$	−86.1883			−0.109515			−0.0547575	+	0.998500i	$0.517439\pi$
$788$	461.611	−	958.888i	0.585801	−	1.21686i
$789$		0			0
$790$	59.9315	−	262.662i	0.0758627	−	0.332483i
$791$		−	1148.40i		−	1.45183i
$792$		0			0
$793$	1147.64			1.44721
$794$	−1039.61	−	237.208i	−1.30933	−	0.298751i
$795$		0			0
$796$	−462.541	+	960.819i	−0.581082	+	1.20706i
$797$		−	661.678i		−	0.830211i	−0.909773	−	0.415105i	$-0.863745\pi$
$797$		−	661.678i		−	0.830211i	0.909773	−	0.415105i	$-0.136255\pi$
$798$		0			0
$799$			998.009i			1.24907i
$800$	−144.131	+	69.4717i	−0.180163	+	0.0868397i
$801$		0			0
$802$	−271.581	+	1190.26i	−0.338629	+	1.48411i
$803$	−151.408			−0.188553
$804$		0			0
$805$			376.771i			0.468039i
$806$	44.0477	−	193.048i	0.0546498	−	0.239514i
$807$		0			0
$808$	421.197	+	335.749i	0.521283	+	0.415531i
$809$	1095.50			1.35414			0.677070	−	0.735919i	$-0.263250\pi$
$809$	1095.50			1.35414			0.677070	+	0.735919i	$0.263250\pi$
$810$		0			0
$811$	−743.013			−0.916169			−0.458084	−	0.888909i	$-0.651464\pi$
$811$	−743.013			−0.916169			−0.458084	+	0.888909i	$0.651464\pi$
$812$	−164.648	−	79.2621i	−0.202769	−	0.0976135i
$813$		0			0
$814$	135.970	+	31.0243i	0.167039	+	0.0381134i
$815$			556.046i			0.682265i
$816$		0			0
$817$	1971.79			2.41346
$818$	−77.6301	+	340.229i	−0.0949023	+	0.415928i
$819$		0			0
$820$	24.1574	−	50.1813i	0.0294603	−	0.0611968i
$821$			1269.96i			1.54685i	0.633888	+	0.773425i	$0.281458\pi$
$821$			1269.96i			1.54685i	−0.633888	+	0.773425i	$0.718542\pi$
$822$		0			0
$823$			297.950i			0.362029i	0.983480	+	0.181015i	$0.0579381\pi$
$823$			297.950i			0.362029i	−0.983480	+	0.181015i	$0.942062\pi$
$824$	458.773	+	365.702i	0.556763	+	0.443813i
$825$		0			0
$826$	756.367	+	172.580i	0.915698	+	0.208935i
$827$	386.605			0.467478			0.233739	−	0.972299i	$-0.424904\pi$
$827$	386.605			0.467478			0.233739	+	0.972299i	$0.424904\pi$
$828$		0			0
$829$		−	606.395i		−	0.731478i	−0.930717	−	0.365739i	$-0.880816\pi$
$829$		−	606.395i		−	0.731478i	0.930717	−	0.365739i	$-0.119184\pi$
$830$	−24.8182	−	5.66276i	−0.0299014	−	0.00682261i
$831$		0			0
$832$	−1126.15	+	257.533i	−1.35355	+	0.309535i
$833$	−454.573			−0.545706
$834$		0			0
$835$	−45.7855			−0.0548329
$836$	−201.715	−	97.1063i	−0.241286	−	0.116156i
$837$		0			0
$838$	−15.9688	+	69.9863i	−0.0190558	+	0.0835158i
$839$			634.313i			0.756035i	0.925799	+	0.378017i	$0.123394\pi$
$839$			634.313i			0.756035i	−0.925799	+	0.378017i	$0.876606\pi$
$840$		0			0
$841$	771.605			0.917485
$842$	461.649	+	105.334i	0.548277	+	0.125100i
$843$		0			0
$844$	182.459	+	87.8365i	0.216184	+	0.104072i
$845$		−	350.651i		−	0.414971i
$846$		0			0
$847$			649.065i			0.766310i
$848$	477.336	−	380.881i	0.562897	−	0.449152i
$849$		0			0
$850$	53.4288	−	234.162i	0.0628574	−	0.275485i
$851$	1317.98			1.54874
$852$		0			0
$853$		−	350.351i		−	0.410728i	−0.978686	−	0.205364i	$-0.934162\pi$
$853$		−	350.351i		−	0.410728i	0.978686	−	0.205364i	$-0.0658379\pi$
$854$	155.125	−	679.864i	0.181645	−	0.796094i
$855$		0			0
$856$	768.905	−	964.591i	0.898254	−	1.12686i
$857$	582.739			0.679976			0.339988	−	0.940430i	$-0.389577\pi$
$857$	582.739			0.679976			0.339988	+	0.940430i	$0.389577\pi$
$858$		0			0
$859$	−91.0452			−0.105990			−0.0529948	−	0.998595i	$-0.516877\pi$
$859$	−91.0452			−0.105990			−0.0529948	+	0.998595i	$0.516877\pi$
$860$	−222.198	+	461.563i	−0.258370	+	0.536702i
$861$		0			0
$862$	381.880	+	87.1337i	0.443017	+	0.101083i
$863$			311.660i			0.361135i	0.983563	+	0.180568i	$0.0577935\pi$
$863$			311.660i			0.361135i	−0.983563	+	0.180568i	$0.942207\pi$
$864$		0			0
$865$	−24.5802			−0.0284164
$866$	−29.4557	+	129.096i	−0.0340136	+	0.149071i
$867$		0			0
$868$	−108.408	−	52.1880i	−0.124894	−	0.0601244i
$869$			97.9328i			0.112696i
$870$		0			0
$871$		−	1073.28i		−	1.23224i
$872$	755.393	+	602.147i	0.866277	+	0.690536i
$873$		0			0
$874$	−2062.64	−	470.633i	−2.36000	−	0.538481i
$875$	−61.3124			−0.0700713
$876$		0			0
$877$			1264.84i			1.44223i	0.692815	+	0.721115i	$0.256370\pi$
$877$			1264.84i			1.44223i	−0.692815	+	0.721115i	$0.743630\pi$
$878$	1075.94	+	245.498i	1.22545	+	0.279610i
$879$		0			0
$880$	45.4618	−	36.2754i	0.0516612	−	0.0412220i
$881$	1185.61			1.34576			0.672880	−	0.739752i	$-0.265057\pi$
$881$	1185.61			1.34576			0.672880	+	0.739752i	$0.265057\pi$
$882$		0			0
$883$	−1734.26			−1.96405			−0.982026	−	0.188745i	$-0.939558\pi$
$883$	−1734.26			−1.96405			−0.982026	+	0.188745i	$0.939558\pi$
$884$	752.196	−	1562.51i	0.850900	−	1.76754i
$885$		0			0
$886$	123.665	−	541.988i	0.139577	−	0.611725i
$887$		−	780.604i		−	0.880050i	−0.897986	−	0.440025i	$-0.854970\pi$
$887$		−	780.604i		−	0.880050i	0.897986	−	0.440025i	$-0.145030\pi$
$888$		0			0
$889$	754.937			0.849198
$890$	−214.100	−	48.8512i	−0.240562	−	0.0548889i
$891$		0			0
$892$	619.740	−	1287.36i	0.694776	−	1.44323i
$893$			1430.58i			1.60199i
$894$		0			0
$895$		−	395.923i		−	0.442372i
$896$	0.343084	+	701.945i	0.000382907	+	0.783421i
$897$		0			0
$898$	65.6723	−	287.822i	0.0731317	−	0.320514i
$899$	−45.6914			−0.0508247
$900$		0			0
$901$			916.697i			1.01742i
$902$	−4.50352	+	19.7376i	−0.00499281	+	0.0218820i
$903$		0			0
$904$	−1044.25	+	1310.01i	−1.15515	+	1.44913i
$905$	−433.844			−0.479386
$906$		0			0
$907$	1546.71			1.70531			0.852654	−	0.522476i	$-0.174992\pi$
$907$	1546.71			1.70531			0.852654	+	0.522476i	$0.174992\pi$
$908$	489.801	+	235.792i	0.539429	+	0.259682i
$909$		0			0
$910$	−431.592	−	98.4764i	−0.474277	−	0.108216i
$911$		−	739.818i		−	0.812094i	−0.913852	−	0.406047i	$-0.866907\pi$
$911$		−	739.818i		−	0.812094i	0.913852	−	0.406047i	$-0.133093\pi$
$912$		0			0
$913$	9.25339			0.0101352
$914$	−216.073	+	946.984i	−0.236404	+	1.03609i
$915$		0			0
$916$	687.903	−	1428.96i	0.750986	−	1.56000i
$917$			166.174i			0.181215i
$918$		0			0
$919$			334.138i			0.363589i	0.983337	+	0.181795i	$0.0581906\pi$
$919$			334.138i			0.363589i	−0.983337	+	0.181795i	$0.941809\pi$
$920$	342.602	−	429.794i	0.372394	−	0.467167i
$921$		0			0
$922$	873.478	+	199.302i	0.947373	+	0.216162i
$923$	−874.773			−0.947750
$924$		0			0
$925$			214.476i			0.231866i
$926$	−1487.20	−	339.335i	−1.60605	−	0.366452i
$927$		0			0
$928$	115.745	+	240.133i	0.124725	+	0.258764i
$929$	−668.207			−0.719276			−0.359638	−	0.933092i	$-0.617100\pi$
$929$	−668.207			−0.719276			−0.359638	+	0.933092i	$0.617100\pi$
$930$		0			0
$931$	−651.600			−0.699892
$932$	−343.101	−	165.170i	−0.368134	−	0.177221i
$933$		0			0
$934$	372.930	−	1634.44i	0.399283	−	1.74994i
$935$			87.3068i			0.0933762i
$936$		0			0
$937$	−1204.35			−1.28532			−0.642661	−	0.766151i	$-0.722170\pi$
$937$	−1204.35			−1.28532			−0.642661	+	0.766151i	$0.722170\pi$
$938$	−635.814	−	145.074i	−0.677840	−	0.154663i
$939$		0			0
$940$	−334.874	−	161.209i	−0.356248	−	0.171499i
$941$		−	794.818i		−	0.844653i	−0.906444	−	0.422326i	$-0.861214\pi$
$941$		−	794.818i		−	0.844653i	0.906444	−	0.422326i	$-0.138786\pi$
$942$		0			0
$943$			191.319i			0.202883i
$944$	−705.880	−	884.639i	−0.747755	−	0.937118i
$945$		0			0
$946$	41.4229	−	181.544i	0.0437875	−	0.191907i
$947$	−505.479			−0.533769			−0.266884	−	0.963729i	$-0.585994\pi$
$947$	−505.479			−0.533769			−0.266884	+	0.963729i	$0.585994\pi$
$948$		0			0
$949$		−	1681.17i		−	1.77151i
$950$	76.5865	−	335.655i	0.0806174	−	0.353322i
$951$		0			0
$952$	−823.960	−	656.804i	−0.865504	−	0.689920i
$953$	586.218			0.615129			0.307564	−	0.951527i	$-0.400486\pi$
$953$	586.218			0.615129			0.307564	+	0.951527i	$0.400486\pi$
$954$		0			0
$955$	−730.765			−0.765199
$956$	168.283	−	349.568i	0.176028	−	0.365657i
$957$		0			0
$958$	294.033	+	67.0895i	0.306924	+	0.0700308i
$959$		−	1020.38i		−	1.06400i
$960$		0			0
$961$	930.916			0.968695
$962$	−344.478	+	1509.74i	−0.358086	+	1.56938i
$963$		0			0
$964$	−130.674	−	62.9070i	−0.135554	−	0.0652562i
$965$			571.458i			0.592184i
$966$		0			0
$967$		−	598.983i		−	0.619424i	−0.950830	−	0.309712i	$-0.899767\pi$
$967$		−	598.983i		−	0.619424i	0.950830	−	0.309712i	$-0.100233\pi$
$968$	590.201	−	740.407i	0.609712	−	0.764883i
$969$		0			0
$970$	156.627	+	35.7375i	0.161471	+	0.0368428i
$971$	−335.550			−0.345571			−0.172786	−	0.984959i	$-0.555277\pi$
$971$	−335.550			−0.345571			−0.172786	+	0.984959i	$0.555277\pi$
$972$		0			0
$973$		−	32.4793i		−	0.0333806i
$974$	−289.488	−	66.0526i	−0.297216	−	0.0678158i
$975$		0			0
$976$	−795.163	+	634.485i	−0.814716	+	0.650087i
$977$	−1009.81			−1.03359			−0.516794	−	0.856110i	$-0.672875\pi$
$977$	−1009.81			−1.03359			−0.516794	+	0.856110i	$0.672875\pi$
$978$		0			0
$979$	79.8266			0.0815389
$980$	73.4275	−	152.528i	0.0749261	−	0.155641i
$981$		0			0
$982$	−34.1739	+	149.774i	−0.0348003	+	0.152519i
$983$		−	1449.61i		−	1.47468i	−0.675521	−	0.737340i	$-0.736081\pi$
$983$		−	1449.61i		−	1.47468i	0.675521	−	0.737340i	$-0.263919\pi$
$984$		0			0
$985$	−594.914			−0.603973
$986$	−390.132	−	89.0165i	−0.395672	−	0.0902804i
$987$		0			0
$988$	1078.22	−	2239.75i	1.09132	−	2.26695i
$989$		−	1759.73i		−	1.77931i
$990$		0			0
$991$			1085.11i			1.09497i	0.836816	+	0.547485i	$0.184415\pi$
$991$			1085.11i			1.09497i	−0.836816	+	0.547485i	$0.815585\pi$
$992$	76.2093	+	158.109i	0.0768239	+	0.159384i
$993$		0			0
$994$	−118.242	+	518.217i	−0.118955	+	0.521345i
$995$	596.112			0.599107
$996$		0			0
$997$		−	1471.19i		−	1.47561i	−0.675011	−	0.737807i	$-0.735861\pi$
$997$		−	1471.19i		−	1.47561i	0.675011	−	0.737807i	$-0.264139\pi$
$998$	251.037	−	1100.22i	0.251540	−	1.10242i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	360.3.g.c.91.7		16
3.2	odd	2		120.3.g.a.91.10	yes	16
4.3	odd	2		1440.3.g.c.271.14		16
8.3	odd	2	inner	360.3.g.c.91.8		16
8.5	even	2		1440.3.g.c.271.3		16
12.11	even	2		480.3.g.a.271.11		16
15.2	even	4		600.3.p.b.499.1		32
15.8	even	4		600.3.p.b.499.32		32
15.14	odd	2		600.3.g.d.451.7		16
24.5	odd	2		480.3.g.a.271.14		16
24.11	even	2		120.3.g.a.91.9	✓	16
60.23	odd	4		2400.3.p.b.1999.28		32
60.47	odd	4		2400.3.p.b.1999.5		32
60.59	even	2		2400.3.g.b.751.4		16
120.29	odd	2		2400.3.g.b.751.5		16
120.53	even	4		2400.3.p.b.1999.6		32
120.59	even	2		600.3.g.d.451.8		16
120.77	even	4		2400.3.p.b.1999.27		32
120.83	odd	4		600.3.p.b.499.2		32
120.107	odd	4		600.3.p.b.499.31		32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
120.3.g.a.91.9	✓	16	24.11	even	2
120.3.g.a.91.10	yes	16	3.2	odd	2
360.3.g.c.91.7		16	1.1	even	1	trivial
360.3.g.c.91.8		16	8.3	odd	2	inner
480.3.g.a.271.11		16	12.11	even	2
480.3.g.a.271.14		16	24.5	odd	2
600.3.g.d.451.7		16	15.14	odd	2
600.3.g.d.451.8		16	120.59	even	2
600.3.p.b.499.1		32	15.2	even	4
600.3.p.b.499.2		32	120.83	odd	4
600.3.p.b.499.31		32	120.107	odd	4
600.3.p.b.499.32		32	15.8	even	4
1440.3.g.c.271.3		16	8.5	even	2
1440.3.g.c.271.14		16	4.3	odd	2
2400.3.g.b.751.4		16	60.59	even	2
2400.3.g.b.751.5		16	120.29	odd	2
2400.3.p.b.1999.5		32	60.47	odd	4
2400.3.p.b.1999.6		32	120.53	even	4
2400.3.p.b.1999.27		32	120.77	even	4
2400.3.p.b.1999.28		32	60.23	odd	4

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 360 = 2^{3} \cdot 3^{2} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	360.g (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(0.444906 - 1.94989i) q^{2} +(-3.60412 - 1.73503i) q^{4} +2.23607i q^{5} -5.48395i q^{7} +(-4.98661 + 6.25570i) q^{8} +(4.36008 + 0.994839i) q^{10} -1.62564 q^{11} -18.0504i q^{13} +(-10.6931 - 2.43984i) q^{14} +(9.97933 + 12.5065i) q^{16} -24.0180 q^{17} -34.4282 q^{19} +(3.87965 - 8.05905i) q^{20} +(-0.723259 + 3.16982i) q^{22} +30.7256i q^{23} -5.00000 q^{25} +(-35.1962 - 8.03071i) q^{26} +(-9.51482 + 19.7648i) q^{28} +8.33039i q^{29} +5.48491i q^{31} +(28.8262 - 13.8943i) q^{32} +(-10.6858 + 46.8324i) q^{34} +12.2625 q^{35} -42.8951i q^{37} +(-15.3173 + 67.1311i) q^{38} +(-13.9882 - 11.1504i) q^{40} +6.22670 q^{41} -57.2727 q^{43} +(5.85901 + 2.82054i) q^{44} +(59.9113 + 13.6700i) q^{46} -41.5525i q^{47} +18.9263 q^{49} +(-2.22453 + 9.74943i) q^{50} +(-31.3180 + 65.0556i) q^{52} -38.1670i q^{53} -3.63505i q^{55} +(34.3059 + 27.3463i) q^{56} +(16.2433 + 3.70624i) q^{58} -70.7342 q^{59} +63.5799i q^{61} +(10.6950 + 2.44027i) q^{62} +(-14.2675 - 62.3894i) q^{64} +40.3618 q^{65} +59.4604 q^{67} +(86.5638 + 41.6720i) q^{68} +(5.45565 - 23.9104i) q^{70} -48.4629i q^{71} +93.1375 q^{73} +(-83.6407 - 19.0843i) q^{74} +(124.083 + 59.7340i) q^{76} +8.91495i q^{77} -60.2424i q^{79} +(-27.9654 + 22.3145i) q^{80} +(2.77030 - 12.1414i) q^{82} -5.69214 q^{83} -53.7060i q^{85} +(-25.4809 + 111.675i) q^{86} +(8.10645 - 10.1695i) q^{88} -49.1046 q^{89} -98.9872 q^{91} +(53.3098 - 110.739i) q^{92} +(-81.0226 - 18.4869i) q^{94} -76.9838i q^{95} +35.9229 q^{97} +(8.42044 - 36.9042i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 4 q^{2} + 14 q^{4} - 20 q^{8} + 10 q^{10} - 64 q^{11} + 20 q^{14} - 14 q^{16} - 32 q^{19} + 40 q^{20} + 28 q^{22} - 80 q^{25} - 36 q^{26} - 28 q^{28} - 36 q^{32} - 72 q^{34} + 240 q^{38} + 10 q^{40}+ \cdots - 428 q^{98}+O(q^{100}) \) 16 * q + 4 * q^2 + 14 * q^4 - 20 * q^8 + 10 * q^10 - 64 * q^11 + 20 * q^14 - 14 * q^16 - 32 * q^19 + 40 * q^20 + 28 * q^22 - 80 * q^25 - 36 * q^26 - 28 * q^28 - 36 * q^32 - 72 * q^34 + 240 * q^38 + 10 * q^40 - 192 * q^43 + 100 * q^44 + 212 * q^46 - 80 * q^49 - 20 * q^50 + 232 * q^52 + 116 * q^56 + 140 * q^58 - 128 * q^59 - 104 * q^62 + 14 * q^64 - 64 * q^67 + 576 * q^68 - 180 * q^70 - 160 * q^73 - 300 * q^74 + 420 * q^76 - 80 * q^80 + 160 * q^82 - 312 * q^86 + 604 * q^88 - 192 * q^91 - 216 * q^92 + 460 * q^94 - 224 * q^97 - 428 * q^98

Introduction

L-functions

Modular forms

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