LMFDB - Embedded newform 360.3.g.c.91.10

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			91.10
Root			$1.13200 + 1.64881i$ of defining polynomial
Character	$\chi$	$=$	360.91
Dual form			360.3.g.c.91.9

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.13200 + 1.64881i) q^{2} +(-1.43715 + 3.73291i) q^{4} -2.23607i q^{5} -11.6935i q^{7} +(-7.78171 + 1.85607i) q^{8} +(3.68685 - 2.53123i) q^{10} -19.3398 q^{11} -12.9092i q^{13} +(19.2803 - 13.2370i) q^{14} +(-11.8692 - 10.7295i) q^{16} -3.08243 q^{17} -10.1462 q^{19} +(8.34704 + 3.21356i) q^{20} +(-21.8926 - 31.8876i) q^{22} -12.5038i q^{23} -5.00000 q^{25} +(21.2849 - 14.6133i) q^{26} +(43.6507 + 16.8053i) q^{28} +0.924932i q^{29} +32.5955i q^{31} +(4.25493 - 31.7159i) q^{32} +(-3.48931 - 5.08233i) q^{34} -26.1474 q^{35} +3.15307i q^{37} +(-11.4855 - 16.7292i) q^{38} +(4.15030 + 17.4004i) q^{40} +68.9305 q^{41} +69.7882 q^{43} +(27.7941 - 72.1936i) q^{44} +(20.6164 - 14.1543i) q^{46} -46.2730i q^{47} -87.7376 q^{49} +(-5.66000 - 8.24405i) q^{50} +(48.1890 + 18.5525i) q^{52} +16.7503i q^{53} +43.2451i q^{55} +(21.7039 + 90.9953i) q^{56} +(-1.52504 + 1.04702i) q^{58} -72.0926 q^{59} +37.8730i q^{61} +(-53.7438 + 36.8981i) q^{62} +(57.1100 - 28.8868i) q^{64} -28.8660 q^{65} -121.224 q^{67} +(4.42990 - 11.5064i) q^{68} +(-29.5989 - 43.1121i) q^{70} -67.4107i q^{71} -14.7754 q^{73} +(-5.19881 + 3.56928i) q^{74} +(14.5816 - 37.8748i) q^{76} +226.149i q^{77} -132.433i q^{79} +(-23.9919 + 26.5404i) q^{80} +(78.0294 + 113.653i) q^{82} +33.3714 q^{83} +6.89251i q^{85} +(79.0003 + 115.068i) q^{86} +(150.497 - 35.8960i) q^{88} +60.3607 q^{89} -150.954 q^{91} +(46.6755 + 17.9698i) q^{92} +(76.2953 - 52.3810i) q^{94} +22.6876i q^{95} -13.2188 q^{97} +(-99.3190 - 144.663i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	1.13200	+	1.64881i	0.566000	+	0.824405i
$2$	1.13200	+	1.64881i	0.566000	+	0.824405i
$3$		0			0
$3$		0			0
$4$	−1.43715	+	3.73291i	−0.359287	+	0.933227i
$5$		−	2.23607i		−	0.447214i
$5$		−	2.23607i		−	0.447214i
$6$		0			0
$7$		−	11.6935i		−	1.67050i	−0.549872	−	0.835249i	$-0.685324\pi$
$7$		−	11.6935i		−	1.67050i	0.549872	−	0.835249i	$-0.314676\pi$
$8$	−7.78171	+	1.85607i	−0.972714	+	0.232009i
$9$		0			0
$10$	3.68685	−	2.53123i	0.368685	−	0.253123i
$11$	−19.3398			−1.75816			−0.879081	−	0.476673i	$-0.841843\pi$
$11$	−19.3398			−1.75816			−0.879081	+	0.476673i	$0.841843\pi$
$12$		0			0
$13$		−	12.9092i		−	0.993019i	−0.868031	−	0.496510i	$-0.834615\pi$
$13$		−	12.9092i		−	0.993019i	0.868031	−	0.496510i	$-0.165385\pi$
$14$	19.2803	−	13.2370i	1.37717	−	0.945502i
$15$		0			0
$16$	−11.8692	−	10.7295i	−0.741826	−	0.670593i
$17$	−3.08243			−0.181319			−0.0906596	−	0.995882i	$-0.528898\pi$
$17$	−3.08243			−0.181319			−0.0906596	+	0.995882i	$0.528898\pi$
$18$		0			0
$19$	−10.1462			−0.534010			−0.267005	−	0.963695i	$-0.586034\pi$
$19$	−10.1462			−0.534010			−0.267005	+	0.963695i	$0.586034\pi$
$20$	8.34704	+	3.21356i	0.417352	+	0.160678i
$21$		0			0
$22$	−21.8926	−	31.8876i	−0.995120	−	1.44944i
$23$		−	12.5038i		−	0.543643i	−0.962348	−	0.271821i	$-0.912374\pi$
$23$		−	12.5038i		−	0.543643i	0.962348	−	0.271821i	$-0.0876260\pi$
$24$		0			0
$25$	−5.00000			−0.200000
$26$	21.2849	−	14.6133i	0.818650	−	0.562049i
$27$		0			0
$28$	43.6507	+	16.8053i	1.55895	+	0.600188i
$29$			0.924932i			0.0318942i	0.999873	+	0.0159471i	$0.00507633\pi$
$29$			0.924932i			0.0318942i	−0.999873	+	0.0159471i	$0.994924\pi$
$30$		0			0
$31$			32.5955i			1.05147i	0.850649	+	0.525734i	$0.176209\pi$
$31$			32.5955i			1.05147i	−0.850649	+	0.525734i	$0.823791\pi$
$32$	4.25493	−	31.7159i	0.132966	−	0.991121i
$33$		0			0
$34$	−3.48931	−	5.08233i	−0.102627	−	0.149480i
$35$	−26.1474			−0.747069
$36$		0			0
$37$			3.15307i			0.0852181i	0.999092	+	0.0426090i	$0.0135670\pi$
$37$			3.15307i			0.0852181i	−0.999092	+	0.0426090i	$0.986433\pi$
$38$	−11.4855	−	16.7292i	−0.302250	−	0.440241i
$39$		0			0
$40$	4.15030	+	17.4004i	0.103758	+	0.435011i
$41$	68.9305			1.68123			0.840616	−	0.541631i	$-0.182193\pi$
$41$	68.9305			1.68123			0.840616	+	0.541631i	$0.182193\pi$
$42$		0			0
$43$	69.7882			1.62298			0.811491	−	0.584365i	$-0.198656\pi$
$43$	69.7882			1.62298			0.811491	+	0.584365i	$0.198656\pi$
$44$	27.7941	−	72.1936i	0.631685	−	1.64076i
$45$		0			0
$46$	20.6164	−	14.1543i	0.448182	−	0.307702i
$47$		−	46.2730i		−	0.984531i	−0.870445	−	0.492265i	$-0.836169\pi$
$47$		−	46.2730i		−	0.984531i	0.870445	−	0.492265i	$-0.163831\pi$
$48$		0			0
$49$	−87.7376			−1.79056
$50$	−5.66000	−	8.24405i	−0.113200	−	0.164881i
$51$		0			0
$52$	48.1890	+	18.5525i	0.926712	+	0.356779i
$53$			16.7503i			0.316043i	0.987436	+	0.158021i	$0.0505115\pi$
$53$			16.7503i			0.316043i	−0.987436	+	0.158021i	$0.949488\pi$
$54$		0			0
$55$			43.2451i			0.786274i
$56$	21.7039	+	90.9953i	0.387570	+	1.62492i
$57$		0			0
$58$	−1.52504	+	1.04702i	−0.0262937	+	0.0180521i
$59$	−72.0926			−1.22191			−0.610954	−	0.791666i	$-0.709214\pi$
$59$	−72.0926			−1.22191			−0.610954	+	0.791666i	$0.709214\pi$
$60$		0			0
$61$			37.8730i			0.620869i	0.950595	+	0.310434i	$0.100474\pi$
$61$			37.8730i			0.620869i	−0.950595	+	0.310434i	$0.899526\pi$
$62$	−53.7438	+	36.8981i	−0.866835	+	0.595131i
$63$		0			0
$64$	57.1100	−	28.8868i	0.892344	−	0.451356i
$65$	−28.8660			−0.444092
$66$		0			0
$67$	−121.224			−1.80931			−0.904654	−	0.426148i	$-0.859870\pi$
$67$	−121.224			−1.80931			−0.904654	+	0.426148i	$0.859870\pi$
$68$	4.42990	−	11.5064i	0.0651456	−	0.169212i
$69$		0			0
$70$	−29.5989	−	43.1121i	−0.422842	−	0.615888i
$71$		−	67.4107i		−	0.949447i	−0.880135	−	0.474724i	$-0.842548\pi$
$71$		−	67.4107i		−	0.949447i	0.880135	−	0.474724i	$-0.157452\pi$
$72$		0			0
$73$	−14.7754			−0.202402			−0.101201	−	0.994866i	$-0.532269\pi$
$73$	−14.7754			−0.202402			−0.101201	+	0.994866i	$0.532269\pi$
$74$	−5.19881	+	3.56928i	−0.0702542	+	0.0482335i
$75$		0			0
$76$	14.5816	−	37.8748i	0.191863	−	0.498353i
$77$			226.149i			2.93701i
$78$		0			0
$79$		−	132.433i		−	1.67637i	−0.545390	−	0.838183i	$-0.683618\pi$
$79$		−	132.433i		−	1.67637i	0.545390	−	0.838183i	$-0.316382\pi$
$80$	−23.9919	+	26.5404i	−0.299898	+	0.331755i
$81$		0			0
$82$	78.0294	+	113.653i	0.951578	+	1.38602i
$83$	33.3714			0.402065			0.201033	−	0.979585i	$-0.435570\pi$
$83$	33.3714			0.402065			0.201033	+	0.979585i	$0.435570\pi$
$84$		0			0
$85$			6.89251i			0.0810884i
$86$	79.0003	+	115.068i	0.918608	+	1.33799i
$87$		0			0
$88$	150.497	−	35.8960i	1.71019	−	0.407909i
$89$	60.3607			0.678210			0.339105	−	0.940749i	$-0.389876\pi$
$89$	60.3607			0.678210			0.339105	+	0.940749i	$0.389876\pi$
$90$		0			0
$91$	−150.954			−1.65884
$92$	46.6755	+	17.9698i	0.507342	+	0.195324i
$93$		0			0
$94$	76.2953	−	52.3810i	0.811652	−	0.557245i
$95$			22.6876i			0.238817i
$96$		0			0
$97$	−13.2188			−0.136277			−0.0681383	−	0.997676i	$-0.521706\pi$
$97$	−13.2188			−0.136277			−0.0681383	+	0.997676i	$0.521706\pi$
$98$	−99.3190	−	144.663i	−1.01346	−	1.47615i
$99$		0			0
$100$	7.18574	−	18.6645i	0.0718574	−	0.186645i
$101$		−	148.736i		−	1.47263i	−0.676636	−	0.736317i	$-0.736563\pi$
$101$		−	148.736i		−	1.47263i	0.676636	−	0.736317i	$-0.263437\pi$
$102$		0			0
$103$			133.780i			1.29883i	0.760434	+	0.649416i	$0.224986\pi$
$103$			133.780i			1.29883i	−0.760434	+	0.649416i	$0.775014\pi$
$104$	23.9605	+	100.456i	0.230389	+	0.965923i
$105$		0			0
$106$	−27.6180	+	18.9613i	−0.260547	+	0.178880i
$107$	−55.2036			−0.515921			−0.257961	−	0.966155i	$-0.583051\pi$
$107$	−55.2036			−0.515921			−0.257961	+	0.966155i	$0.583051\pi$
$108$		0			0
$109$			77.6680i			0.712550i	0.934381	+	0.356275i	$0.115953\pi$
$109$			77.6680i			0.712550i	−0.934381	+	0.356275i	$0.884047\pi$
$110$	−71.3029	+	48.9534i	−0.648208	+	0.445031i
$111$		0			0
$112$	−125.465	+	138.792i	−1.12022	+	1.23922i
$113$	90.7924			0.803472			0.401736	−	0.915755i	$-0.368407\pi$
$113$	90.7924			0.803472			0.401736	+	0.915755i	$0.368407\pi$
$114$		0			0
$115$	−27.9593			−0.243124
$116$	−3.45268	−	1.32926i	−0.0297645	−	0.0114592i
$117$		0			0
$118$	−81.6088	−	118.867i	−0.691600	−	1.00735i
$119$			36.0443i			0.302893i
$120$		0			0
$121$	253.027			2.09113
$122$	−62.4454	+	42.8723i	−0.511847	+	0.351412i
$123$		0			0
$124$	−121.676	−	46.8446i	−0.981258	−	0.377779i
$125$			11.1803i			0.0894427i
$126$		0			0
$127$		−	45.7755i		−	0.360437i	−0.983627	−	0.180219i	$-0.942319\pi$
$127$		−	45.7755i		−	0.360437i	0.983627	−	0.180219i	$-0.0576805\pi$
$128$	112.277	+	61.4636i	0.877167	+	0.480185i
$129$		0			0
$130$	−32.6763	−	47.5945i	−0.251356	−	0.366111i
$131$	−186.279			−1.42197			−0.710987	−	0.703205i	$-0.751752\pi$
$131$	−186.279			−1.42197			−0.710987	+	0.703205i	$0.751752\pi$
$132$		0			0
$133$			118.644i			0.892063i
$134$	−137.225	−	199.875i	−1.02407	−	1.49160i
$135$		0			0
$136$	23.9865	−	5.72120i	0.176372	−	0.0420677i
$137$	−32.9523			−0.240528			−0.120264	−	0.992742i	$-0.538374\pi$
$137$	−32.9523			−0.240528			−0.120264	+	0.992742i	$0.538374\pi$
$138$		0			0
$139$	−83.8571			−0.603289			−0.301644	−	0.953421i	$-0.597536\pi$
$139$	−83.8571			−0.603289			−0.301644	+	0.953421i	$0.597536\pi$
$140$	37.5777	−	97.6059i	0.268412	−	0.697185i
$141$		0			0
$142$	111.148	−	76.3090i	0.782729	−	0.537387i
$143$			249.662i			1.74589i
$144$		0			0
$145$	2.06821			0.0142635
$146$	−16.7257	−	24.3618i	−0.114560	−	0.166861i
$147$		0			0
$148$	−11.7701	−	4.53143i	−0.0795278	−	0.0306178i
$149$		−	81.4421i		−	0.546591i	−0.961930	−	0.273296i	$-0.911886\pi$
$149$		−	81.4421i		−	0.546591i	0.961930	−	0.273296i	$-0.0881137\pi$
$150$		0			0
$151$		−	84.7219i		−	0.561072i	−0.959843	−	0.280536i	$-0.909488\pi$
$151$		−	84.7219i		−	0.561072i	0.959843	−	0.280536i	$-0.0905123\pi$
$152$	78.9548	−	18.8321i	0.519439	−	0.123895i
$153$		0			0
$154$	−372.877	+	256.001i	−2.42128	+	1.66235i
$155$	72.8858			0.470231
$156$		0			0
$157$		−	167.846i		−	1.06908i	−0.845143	−	0.534540i	$-0.820485\pi$
$157$		−	167.846i		−	1.06908i	0.845143	−	0.534540i	$-0.179515\pi$
$158$	218.357	−	149.914i	1.38200	−	0.948823i
$159$		0			0
$160$	−70.9188	−	9.51430i	−0.443243	−	0.0594644i
$161$	−146.213			−0.908154
$162$		0			0
$163$	82.8713			0.508413			0.254206	−	0.967150i	$-0.418186\pi$
$163$	82.8713			0.508413			0.254206	+	0.967150i	$0.418186\pi$
$164$	−99.0634	+	257.311i	−0.604045	+	1.56897i
$165$		0			0
$166$	37.7765	+	55.0231i	0.227569	+	0.331464i
$167$		−	37.2973i		−	0.223337i	−0.993746	−	0.111669i	$-0.964380\pi$
$167$		−	37.2973i		−	0.223337i	0.993746	−	0.111669i	$-0.0356195\pi$
$168$		0			0
$169$	2.35134			0.0139132
$170$	−11.3644	+	7.80233i	−0.0668497	+	0.0458961i
$171$		0			0
$172$	−100.296	+	260.513i	−0.583116	+	1.51461i
$173$			211.828i			1.22444i	0.790689	+	0.612218i	$0.209723\pi$
$173$			211.828i			1.22444i	−0.790689	+	0.612218i	$0.790277\pi$
$174$		0			0
$175$			58.4674i			0.334100i
$176$	229.548	+	207.506i	1.30425	+	1.17901i
$177$		0			0
$178$	68.3283	+	99.5233i	0.383867	+	0.559120i
$179$	−86.4715			−0.483081			−0.241540	−	0.970391i	$-0.577653\pi$
$179$	−86.4715			−0.483081			−0.241540	+	0.970391i	$0.577653\pi$
$180$		0			0
$181$			79.4036i			0.438694i	0.975647	+	0.219347i	$0.0703926\pi$
$181$			79.4036i			0.438694i	−0.975647	+	0.219347i	$0.929607\pi$
$182$	−170.880	−	248.895i	−0.938902	−	1.36755i
$183$		0			0
$184$	23.2079	+	97.3008i	0.126130	+	0.528809i
$185$	7.05048			0.0381107
$186$		0			0
$187$	59.6134			0.318788
$188$	172.733	+	66.5011i	0.918791	+	0.353729i
$189$		0			0
$190$	−37.4075	+	25.6824i	−0.196882	+	0.135170i
$191$		−	290.341i		−	1.52011i	−0.649858	−	0.760056i	$-0.725172\pi$
$191$		−	290.341i		−	1.52011i	0.649858	−	0.760056i	$-0.274828\pi$
$192$		0			0
$193$	182.850			0.947408			0.473704	−	0.880684i	$-0.342917\pi$
$193$	182.850			0.947408			0.473704	+	0.880684i	$0.342917\pi$
$194$	−14.9637	−	21.7953i	−0.0771326	−	0.112347i
$195$		0			0
$196$	126.092	−	327.516i	0.643326	−	1.67100i
$197$		−	98.1640i		−	0.498295i	−0.968466	−	0.249147i	$-0.919850\pi$
$197$		−	98.1640i		−	0.498295i	0.968466	−	0.249147i	$-0.0801503\pi$
$198$		0			0
$199$		−	225.355i		−	1.13244i	−0.824255	−	0.566218i	$-0.808406\pi$
$199$		−	225.355i		−	1.13244i	0.824255	−	0.566218i	$-0.191594\pi$
$200$	38.9085	−	9.28036i	0.194543	−	0.0464018i
$201$		0			0
$202$	245.238	−	168.369i	1.21405	−	0.833512i
$203$	10.8157			0.0532792
$204$		0			0
$205$		−	154.133i		−	0.751870i
$206$	−220.577	+	151.439i	−1.07076	+	0.735139i
$207$		0			0
$208$	−138.510	+	153.223i	−0.665911	+	0.736647i
$209$	196.225			0.938877
$210$		0			0
$211$	302.658			1.43440			0.717199	−	0.696869i	$-0.245424\pi$
$211$	302.658			1.43440			0.717199	+	0.696869i	$0.245424\pi$
$212$	−62.5272	−	24.0726i	−0.294940	−	0.113550i
$213$		0			0
$214$	−62.4905	−	91.0202i	−0.292012	−	0.425328i
$215$		−	156.051i		−	0.725820i
$216$		0			0
$217$	381.155			1.75647
$218$	−128.060	+	87.9202i	−0.587430	+	0.403304i
$219$		0			0
$220$	−161.430	−	62.1496i	−0.733772	−	0.282498i
$221$			39.7918i			0.180053i
$222$		0			0
$223$		−	432.537i		−	1.93963i	−0.243842	−	0.969815i	$-0.578408\pi$
$223$		−	432.537i		−	1.93963i	0.243842	−	0.969815i	$-0.421592\pi$
$224$	−370.869	−	49.7549i	−1.65566	−	0.222120i
$225$		0			0
$226$	102.777	+	149.699i	0.454766	+	0.662387i
$227$	359.320			1.58291			0.791453	−	0.611230i	$-0.209325\pi$
$227$	359.320			1.58291			0.791453	+	0.611230i	$0.209325\pi$
$228$		0			0
$229$			212.212i			0.926688i	0.886179	+	0.463344i	$0.153351\pi$
$229$			212.212i			0.926688i	−0.886179	+	0.463344i	$0.846649\pi$
$230$	−31.6500	−	46.0996i	−0.137609	−	0.200433i
$231$		0			0
$232$	−1.71674	−	7.19755i	−0.00739974	−	0.0310239i
$233$	276.656			1.18736			0.593682	−	0.804699i	$-0.297674\pi$
$233$	276.656			1.18736			0.593682	+	0.804699i	$0.297674\pi$
$234$		0			0
$235$	−103.469			−0.440296
$236$	103.608	−	269.115i	0.439016	−	1.14032i
$237$		0			0
$238$	−59.4302	+	40.8022i	−0.249707	+	0.171438i
$239$		−	27.9106i		−	0.116781i	−0.998294	−	0.0583904i	$-0.981403\pi$
$239$		−	27.9106i		−	0.116781i	0.998294	−	0.0583904i	$-0.0185968\pi$
$240$		0			0
$241$	−115.420			−0.478920			−0.239460	−	0.970906i	$-0.576970\pi$
$241$	−115.420			−0.478920			−0.239460	+	0.970906i	$0.576970\pi$
$242$	286.427	+	417.194i	1.18358	+	1.72394i
$243$		0			0
$244$	−141.376	−	54.4291i	−0.579411	−	0.223070i
$245$			196.187i			0.800764i
$246$		0			0
$247$			130.980i			0.530282i
$248$	−60.4996	−	253.649i	−0.243950	−	1.02278i
$249$		0			0
$250$	−18.4343	+	12.6562i	−0.0737370	+	0.0506246i
$251$	26.6696			0.106253			0.0531267	−	0.998588i	$-0.483081\pi$
$251$	26.6696			0.106253			0.0531267	+	0.998588i	$0.483081\pi$
$252$		0			0
$253$			241.820i			0.955812i
$254$	75.4752	−	51.8179i	0.297146	−	0.204008i
$255$		0			0
$256$	25.7563	+	254.701i	0.100610	+	0.994926i
$257$	−170.155			−0.662082			−0.331041	−	0.943616i	$-0.607400\pi$
$257$	−170.155			−0.662082			−0.331041	+	0.943616i	$0.607400\pi$
$258$		0			0
$259$	36.8704			0.142357
$260$	41.4847	−	107.754i	0.159556	−	0.414438i
$261$		0			0
$262$	−210.868	−	307.138i	−0.804838	−	1.17228i
$263$			105.658i			0.401741i	0.979618	+	0.200870i	$0.0643770\pi$
$263$			105.658i			0.401741i	−0.979618	+	0.200870i	$0.935623\pi$
$264$		0			0
$265$	37.4547			0.141339
$266$	−195.622	+	134.306i	−0.735421	+	0.504908i
$267$		0			0
$268$	174.216	−	452.517i	0.650061	−	1.68849i
$269$		−	206.889i		−	0.769103i	−0.923104	−	0.384551i	$-0.874356\pi$
$269$		−	206.889i		−	0.769103i	0.923104	−	0.384551i	$-0.125644\pi$
$270$		0			0
$271$			247.759i			0.914241i	0.889405	+	0.457120i	$0.151119\pi$
$271$			247.759i			0.914241i	−0.889405	+	0.457120i	$0.848881\pi$
$272$	36.5860	+	33.0728i	0.134507	+	0.121591i
$273$		0			0
$274$	−37.3020	−	54.3321i	−0.136139	−	0.198292i
$275$	96.6989			0.351632
$276$		0			0
$277$		−	26.9487i		−	0.0972879i	−0.998816	−	0.0486439i	$-0.984510\pi$
$277$		−	26.9487i		−	0.0972879i	0.998816	−	0.0486439i	$-0.0154900\pi$
$278$	−94.9264	−	138.264i	−0.341462	−	0.497354i
$279$		0			0
$280$	203.472	−	48.5315i	0.726685	−	0.173327i
$281$	289.489			1.03021			0.515106	−	0.857127i	$-0.327753\pi$
$281$	289.489			1.03021			0.515106	+	0.857127i	$0.327753\pi$
$282$		0			0
$283$	3.01272			0.0106457			0.00532283	−	0.999986i	$-0.498306\pi$
$283$	3.01272			0.0106457			0.00532283	+	0.999986i	$0.498306\pi$
$284$	251.638	+	96.8792i	0.886050	+	0.341124i
$285$		0			0
$286$	−411.645	+	282.618i	−1.43932	+	0.988173i
$287$		−	806.038i		−	2.80849i
$288$		0			0
$289$	−279.499			−0.967123
$290$	2.34122	+	3.41009i	0.00807316	+	0.0117589i
$291$		0			0
$292$	21.2344	−	55.1551i	0.0727205	−	0.188887i
$293$		−	95.1952i		−	0.324898i	−0.986717	−	0.162449i	$-0.948061\pi$
$293$		−	95.1952i		−	0.324898i	0.986717	−	0.162449i	$-0.0519393\pi$
$294$		0			0
$295$			161.204i			0.546454i
$296$	−5.85232	−	24.5363i	−0.0197714	−	0.0828928i
$297$		0			0
$298$	134.282	−	92.1925i	0.450612	−	0.309371i
$299$	−161.414			−0.539848
$300$		0			0
$301$		−	816.068i		−	2.71119i
$302$	139.690	−	95.9053i	0.462551	−	0.317567i
$303$		0			0
$304$	120.427	+	108.863i	0.396143	+	0.358104i
$305$	84.6866			0.277661
$306$		0			0
$307$	167.348			0.545108			0.272554	−	0.962140i	$-0.412132\pi$
$307$	167.348			0.545108			0.272554	+	0.962140i	$0.412132\pi$
$308$	−844.195	−	325.010i	−2.74089	−	1.05523i
$309$		0			0
$310$	82.5067	+	120.175i	0.266151	+	0.387661i
$311$			299.478i			0.962951i	0.876460	+	0.481475i	$0.159899\pi$
$311$			299.478i			0.962951i	−0.876460	+	0.481475i	$0.840101\pi$
$312$		0			0
$313$	−123.623			−0.394963			−0.197481	−	0.980307i	$-0.563276\pi$
$313$	−123.623			−0.394963			−0.197481	+	0.980307i	$0.563276\pi$
$314$	276.746	−	190.001i	0.881356	−	0.605100i
$315$		0			0
$316$	494.360	+	190.326i	1.56443	+	0.602296i
$317$		−	135.949i		−	0.428862i	−0.976739	−	0.214431i	$-0.931210\pi$
$317$		−	135.949i		−	0.428862i	0.976739	−	0.214431i	$-0.0687896\pi$
$318$		0			0
$319$		−	17.8880i		−	0.0560752i
$320$	−64.5929	−	127.702i	−0.201853	−	0.399068i
$321$		0			0
$322$	−165.513	−	241.077i	−0.514016	−	0.748687i
$323$	31.2749			0.0968263
$324$		0			0
$325$			64.5462i			0.198604i
$326$	93.8104	+	136.639i	0.287762	+	0.419138i
$327$		0			0
$328$	−536.397	+	127.940i	−1.63536	+	0.390061i
$329$	−541.092			−1.64466
$330$		0			0
$331$	−41.1886			−0.124437			−0.0622185	−	0.998063i	$-0.519818\pi$
$331$	−41.1886			−0.124437			−0.0622185	+	0.998063i	$0.519818\pi$
$332$	−47.9597	+	124.572i	−0.144457	+	0.375218i
$333$		0			0
$334$	61.4962	−	42.2206i	0.184120	−	0.126409i
$335$			271.064i			0.809147i
$336$		0			0
$337$	−565.599			−1.67834			−0.839168	−	0.543873i	$-0.816957\pi$
$337$	−565.599			−1.67834			−0.839168	+	0.543873i	$0.816957\pi$
$338$	2.66171	+	3.87690i	0.00787489	+	0.0114701i
$339$		0			0
$340$	−25.7291	−	9.90556i	−0.0756739	−	0.0291340i
$341$		−	630.390i		−	1.84865i
$342$		0			0
$343$			452.977i			1.32063i
$344$	−543.072	+	129.532i	−1.57870	+	0.376546i
$345$		0			0
$346$	−349.263	+	239.789i	−1.00943	+	0.693032i
$347$	−134.668			−0.388092			−0.194046	−	0.980992i	$-0.562161\pi$
$347$	−134.668			−0.388092			−0.194046	+	0.980992i	$0.562161\pi$
$348$		0			0
$349$		−	461.309i		−	1.32180i	−0.750473	−	0.660901i	$-0.770174\pi$
$349$		−	461.309i		−	1.32180i	0.750473	−	0.660901i	$-0.229826\pi$
$350$	−96.4017	+	66.1852i	−0.275433	+	0.189100i
$351$		0			0
$352$	−82.2893	+	613.378i	−0.233777	+	1.74255i
$353$	429.790			1.21754			0.608768	−	0.793349i	$-0.291664\pi$
$353$	429.790			1.21754			0.608768	+	0.793349i	$0.291664\pi$
$354$		0			0
$355$	−150.735			−0.424606
$356$	−86.7473	+	225.321i	−0.243672	+	0.632924i
$357$		0			0
$358$	−97.8858	−	142.575i	−0.273424	−	0.398254i
$359$			312.402i			0.870200i	0.900382	+	0.435100i	$0.143287\pi$
$359$			312.402i			0.870200i	−0.900382	+	0.435100i	$0.856713\pi$
$360$		0			0
$361$	−258.055			−0.714833
$362$	−130.921	+	89.8849i	−0.361661	+	0.248301i
$363$		0			0
$364$	216.943	−	563.498i	0.595998	−	1.54807i
$365$			33.0387i			0.0905170i
$366$		0			0
$367$		−	138.931i		−	0.378558i	−0.981923	−	0.189279i	$-0.939385\pi$
$367$		−	138.931i		−	0.378558i	0.981923	−	0.189279i	$-0.0606151\pi$
$368$	−134.159	+	148.410i	−0.364563	+	0.403288i
$369$		0			0
$370$	7.98114	+	11.6249i	0.0215707	+	0.0314186i
$371$	195.869			0.527949
$372$		0			0
$373$			422.559i			1.13287i	0.824108	+	0.566433i	$0.191677\pi$
$373$			422.559i			1.13287i	−0.824108	+	0.566433i	$0.808323\pi$
$374$	67.4824	+	98.2912i	0.180434	+	0.262811i
$375$		0			0
$376$	85.8859	+	360.083i	0.228420	+	0.957667i
$377$	11.9402			0.0316715
$378$		0			0
$379$	419.245			1.10619			0.553094	−	0.833119i	$-0.313447\pi$
$379$	419.245			1.10619			0.553094	+	0.833119i	$0.313447\pi$
$380$	−84.6907	−	32.6054i	−0.222870	−	0.0858037i
$381$		0			0
$382$	478.718	−	328.667i	1.25319	−	0.860384i
$383$			306.762i			0.800944i	0.916309	+	0.400472i	$0.131154\pi$
$383$			306.762i			0.800944i	−0.916309	+	0.400472i	$0.868846\pi$
$384$		0			0
$385$	505.685			1.31347
$386$	206.986	+	301.485i	0.536234	+	0.781048i
$387$		0			0
$388$	18.9974	−	49.3447i	0.0489624	−	0.127177i
$389$			441.866i			1.13590i	0.823062	+	0.567951i	$0.192264\pi$
$389$			441.866i			1.13590i	−0.823062	+	0.567951i	$0.807736\pi$
$390$		0			0
$391$			38.5420i			0.0985728i
$392$	682.748	−	162.847i	1.74170	−	0.415426i
$393$		0			0
$394$	161.854	−	111.122i	0.410797	−	0.282035i
$395$	−296.129			−0.749693
$396$		0			0
$397$			160.391i			0.404007i	0.979385	+	0.202004i	$0.0647453\pi$
$397$			160.391i			0.404007i	−0.979385	+	0.202004i	$0.935255\pi$
$398$	371.567	−	255.102i	0.933587	−	0.640960i
$399$		0			0
$400$	59.3460	+	53.6474i	0.148365	+	0.134119i
$401$	−193.791			−0.483270			−0.241635	−	0.970367i	$-0.577684\pi$
$401$	−193.791			−0.483270			−0.241635	+	0.970367i	$0.577684\pi$
$402$		0			0
$403$	420.783			1.04413
$404$	555.218	+	213.756i	1.37430	+	0.529099i
$405$		0			0
$406$	12.2434	+	17.8330i	0.0301560	+	0.0439236i
$407$		−	60.9797i		−	0.149827i
$408$		0			0
$409$	−459.509			−1.12349			−0.561747	−	0.827309i	$-0.689870\pi$
$409$	−459.509			−1.12349			−0.561747	+	0.827309i	$0.689870\pi$
$410$	254.137	−	174.479i	0.619845	−	0.425559i
$411$		0			0
$412$	−499.387	−	192.261i	−1.21210	−	0.466653i
$413$			843.013i			2.04119i
$414$		0			0
$415$		−	74.6207i		−	0.179809i
$416$	−409.428	−	54.9279i	−0.984202	−	0.132038i
$417$		0			0
$418$	222.127	+	323.538i	0.531405	+	0.774015i
$419$	−223.442			−0.533274			−0.266637	−	0.963797i	$-0.585912\pi$
$419$	−223.442			−0.533274			−0.266637	+	0.963797i	$0.585912\pi$
$420$		0			0
$421$		−	753.492i		−	1.78977i	−0.446299	−	0.894884i	$-0.647258\pi$
$421$		−	753.492i		−	1.78977i	0.446299	−	0.894884i	$-0.352742\pi$
$422$	342.609	+	499.025i	0.811870	+	1.18252i
$423$		0			0
$424$	−31.0897	−	130.346i	−0.0733247	−	0.307419i
$425$	15.4121			0.0362638
$426$		0			0
$427$	442.867			1.03716
$428$	79.3357	−	206.070i	0.185364	−	0.481472i
$429$		0			0
$430$	257.299	−	176.650i	0.598369	−	0.410814i
$431$			801.595i			1.85985i	0.367752	+	0.929924i	$0.380128\pi$
$431$			801.595i			1.85985i	−0.367752	+	0.929924i	$0.619872\pi$
$432$		0			0
$433$	725.058			1.67450			0.837249	−	0.546822i	$-0.184162\pi$
$433$	725.058			1.67450			0.837249	+	0.546822i	$0.184162\pi$
$434$	431.468	+	628.452i	0.994165	+	1.44805i
$435$		0			0
$436$	−289.927	−	111.620i	−0.664971	−	0.256010i
$437$			126.866i			0.290311i
$438$		0			0
$439$			551.061i			1.25526i	0.778510	+	0.627632i	$0.215976\pi$
$439$			551.061i			1.25526i	−0.778510	+	0.627632i	$0.784024\pi$
$440$	−80.2659	−	336.521i	−0.182423	−	0.764819i
$441$		0			0
$442$	−65.6091	+	45.0443i	−0.148437	+	0.101910i
$443$	−36.7779			−0.0830201			−0.0415100	−	0.999138i	$-0.513217\pi$
$443$	−36.7779			−0.0830201			−0.0415100	+	0.999138i	$0.513217\pi$
$444$		0			0
$445$		−	134.971i		−	0.303305i
$446$	713.172	−	489.633i	1.59904	−	1.09783i
$447$		0			0
$448$	−337.787	−	667.815i	−0.753990	−	1.49066i
$449$	−332.641			−0.740849			−0.370424	−	0.928863i	$-0.620788\pi$
$449$	−332.641			−0.740849			−0.370424	+	0.928863i	$0.620788\pi$
$450$		0			0
$451$	−1333.10			−2.95588
$452$	−130.482	+	338.920i	−0.288677	+	0.749822i
$453$		0			0
$454$	406.750	+	592.450i	0.895926	+	1.30496i
$455$			337.544i			0.741854i
$456$		0			0
$457$	−343.279			−0.751158			−0.375579	−	0.926790i	$-0.622556\pi$
$457$	−343.279			−0.751158			−0.375579	+	0.926790i	$0.622556\pi$
$458$	−349.896	+	240.224i	−0.763966	+	0.524506i
$459$		0			0
$460$	40.1817	−	104.370i	0.0873515	−	0.226890i
$461$		−	208.768i		−	0.452859i	−0.974028	−	0.226429i	$-0.927295\pi$
$461$		−	208.768i		−	0.452859i	0.974028	−	0.226429i	$-0.0727053\pi$
$462$		0			0
$463$			239.500i			0.517278i	0.965974	+	0.258639i	$0.0832740\pi$
$463$			239.500i			0.517278i	−0.965974	+	0.258639i	$0.916726\pi$
$464$	9.92404	−	10.9782i	0.0213880	−	0.0236599i
$465$		0			0
$466$	313.175	+	456.153i	0.672049	+	0.978869i
$467$	295.094			0.631892			0.315946	−	0.948777i	$-0.397678\pi$
$467$	295.094			0.631892			0.315946	+	0.948777i	$0.397678\pi$
$468$		0			0
$469$			1417.53i			3.02244i
$470$	−117.128	−	170.601i	−0.249207	−	0.362982i
$471$		0			0
$472$	561.003	−	133.809i	1.18857	−	0.283493i
$473$	−1349.69			−2.85346
$474$		0			0
$475$	50.7310			0.106802
$476$	−134.550	−	51.8010i	−0.282668	−	0.108826i
$477$		0			0
$478$	46.0193	−	31.5948i	0.0962746	−	0.0660979i
$479$		−	533.361i		−	1.11349i	−0.830684	−	0.556745i	$-0.812050\pi$
$479$		−	533.361i		−	1.11349i	0.830684	−	0.556745i	$-0.187950\pi$
$480$		0			0
$481$	40.7037			0.0846232
$482$	−130.655	−	190.305i	−0.271069	−	0.394824i
$483$		0			0
$484$	−363.637	+	944.527i	−0.751317	+	1.95150i
$485$			29.5582i			0.0609448i
$486$		0			0
$487$		−	285.675i		−	0.586601i	−0.956020	−	0.293301i	$-0.905246\pi$
$487$		−	285.675i		−	0.586601i	0.956020	−	0.293301i	$-0.0947537\pi$
$488$	−70.2950	−	294.717i	−0.144047	−	0.603927i
$489$		0			0
$490$	−323.475	+	222.084i	−0.660154	+	0.453233i
$491$	−188.244			−0.383388			−0.191694	−	0.981455i	$-0.561398\pi$
$491$	−188.244			−0.383388			−0.191694	+	0.981455i	$0.561398\pi$
$492$		0			0
$493$		−	2.85103i		−	0.00578303i
$494$	−215.961	+	148.269i	−0.437167	+	0.300140i
$495$		0			0
$496$	349.733	−	386.883i	0.705107	−	0.780006i
$497$	−788.266			−1.58605
$498$		0			0
$499$	625.534			1.25357			0.626787	−	0.779190i	$-0.284369\pi$
$499$	625.534			1.25357			0.626787	+	0.779190i	$0.284369\pi$
$500$	−41.7352	−	16.0678i	−0.0834704	−	0.0321356i
$501$		0			0
$502$	30.1900	+	43.9731i	0.0601395	+	0.0875959i
$503$			232.863i			0.462949i	0.972841	+	0.231474i	$0.0743549\pi$
$503$			232.863i			0.462949i	−0.972841	+	0.231474i	$0.925645\pi$
$504$		0			0
$505$	−332.584			−0.658582
$506$	−398.716	+	273.741i	−0.787976	+	0.540990i
$507$		0			0
$508$	170.876	+	65.7862i	0.336370	+	0.129500i
$509$		−	615.343i		−	1.20893i	−0.796633	−	0.604463i	$-0.793388\pi$
$509$		−	615.343i		−	1.20893i	0.796633	−	0.604463i	$-0.206612\pi$
$510$		0			0
$511$			172.775i			0.338112i
$512$	−390.797	+	330.789i	−0.763276	+	0.646072i
$513$		0			0
$514$	−192.616	−	280.553i	−0.374739	−	0.545823i
$515$	299.140			0.580855
$516$		0			0
$517$			894.909i			1.73096i
$518$	41.7373	+	60.7922i	0.0805739	+	0.117359i
$519$		0			0
$520$	224.626	−	53.5773i	0.431974	−	0.103033i
$521$	−132.731			−0.254761			−0.127381	−	0.991854i	$-0.540657\pi$
$521$	−132.731			−0.254761			−0.127381	+	0.991854i	$0.540657\pi$
$522$		0			0
$523$	−911.886			−1.74357			−0.871784	−	0.489890i	$-0.837037\pi$
$523$	−911.886			−1.74357			−0.871784	+	0.489890i	$0.837037\pi$
$524$	267.710	−	695.361i	0.510897	−	1.32703i
$525$		0			0
$526$	−174.210	+	119.605i	−0.331197	+	0.227385i
$527$		−	100.473i		−	0.190651i
$528$		0			0
$529$	372.655			0.704453
$530$	42.3988	+	61.7558i	0.0799977	+	0.116520i
$531$		0			0
$532$	−442.889	−	170.510i	−0.832497	−	0.320507i
$533$		−	889.841i		−	1.66950i
$534$		0			0
$535$			123.439i			0.230727i
$536$	943.327	−	225.000i	1.75994	−	0.419775i
$537$		0			0
$538$	341.120	−	234.198i	0.634052	−	0.435313i
$539$	1696.83			3.14810
$540$		0			0
$541$		−	373.215i		−	0.689861i	−0.938628	−	0.344931i	$-0.887902\pi$
$541$		−	373.215i		−	0.689861i	0.938628	−	0.344931i	$-0.112098\pi$
$542$	−408.508	+	280.464i	−0.753705	+	0.517461i
$543$		0			0
$544$	−13.1155	+	97.7618i	−0.0241094	+	0.179709i
$545$	173.671			0.318662
$546$		0			0
$547$	−175.297			−0.320469			−0.160235	−	0.987079i	$-0.551225\pi$
$547$	−175.297			−0.320469			−0.160235	+	0.987079i	$0.551225\pi$
$548$	47.3573	−	123.008i	0.0864185	−	0.224467i
$549$		0			0
$550$	109.463	+	159.438i	0.199024	+	0.289887i
$551$		−	9.38454i		−	0.0170318i
$552$		0			0
$553$	−1548.60			−2.80036
$554$	44.4334	−	30.5060i	0.0802046	−	0.0550650i
$555$		0			0
$556$	120.515	−	313.031i	0.216754	−	0.563005i
$557$			403.527i			0.724466i	0.932088	+	0.362233i	$0.117985\pi$
$557$			403.527i			0.724466i	−0.932088	+	0.362233i	$0.882015\pi$
$558$		0			0
$559$		−	900.913i		−	1.61165i
$560$	310.349	+	280.548i	0.554195	+	0.500979i
$561$		0			0
$562$	327.702	+	477.313i	0.583100	+	0.849311i
$563$	236.345			0.419796			0.209898	−	0.977723i	$-0.432687\pi$
$563$	236.345			0.419796			0.209898	+	0.977723i	$0.432687\pi$
$564$		0			0
$565$		−	203.018i		−	0.359324i
$566$	3.41041	+	4.96741i	0.00602545	+	0.00877634i
$567$		0			0
$568$	125.119	+	524.571i	0.220280	+	0.923540i
$569$	757.837			1.33187			0.665937	−	0.746008i	$-0.268032\pi$
$569$	757.837			1.33187			0.665937	+	0.746008i	$0.268032\pi$
$570$		0			0
$571$	198.009			0.346775			0.173388	−	0.984854i	$-0.444529\pi$
$571$	198.009			0.346775			0.173388	+	0.984854i	$0.444529\pi$
$572$	−931.965	−	358.801i	−1.62931	−	0.627275i
$573$		0			0
$574$	1329.00	−	912.436i	2.31534	−	1.58961i
$575$			62.5189i			0.108729i
$576$		0			0
$577$	−479.109			−0.830346			−0.415173	−	0.909743i	$-0.636279\pi$
$577$	−479.109			−0.830346			−0.415173	+	0.909743i	$0.636279\pi$
$578$	−316.393	−	460.840i	−0.547392	−	0.797301i
$579$		0			0
$580$	−2.97232	+	7.72044i	−0.00512470	+	0.0133111i
$581$		−	390.228i		−	0.671649i
$582$		0			0
$583$		−	323.947i		−	0.555654i
$584$	114.978	−	27.4241i	0.196879	−	0.0469591i
$585$		0			0
$586$	156.959	−	107.761i	0.267848	−	0.183893i
$587$	658.065			1.12106			0.560532	−	0.828133i	$-0.310597\pi$
$587$	658.065			1.12106			0.560532	+	0.828133i	$0.310597\pi$
$588$		0			0
$589$		−	330.720i		−	0.561495i
$590$	−265.795	+	182.483i	−0.450499	+	0.309293i
$591$		0			0
$592$	33.8308	−	37.4244i	0.0571466	−	0.0632169i
$593$	−202.971			−0.342279			−0.171139	−	0.985247i	$-0.554745\pi$
$593$	−202.971			−0.342279			−0.171139	+	0.985247i	$0.554745\pi$
$594$		0			0
$595$	80.5975			0.135458
$596$	304.016	+	117.044i	0.510094	+	0.196383i
$597$		0			0
$598$	−182.721	−	266.142i	−0.305554	−	0.445053i
$599$			11.7767i			0.0196605i	0.999952	+	0.00983027i	$0.00312912\pi$
$599$			11.7767i			0.0196605i	−0.999952	+	0.00983027i	$0.996871\pi$
$600$		0			0
$601$	206.863			0.344198			0.172099	−	0.985080i	$-0.444945\pi$
$601$	206.863			0.344198			0.172099	+	0.985080i	$0.444945\pi$
$602$	1345.54	−	923.789i	2.23512	−	1.53453i
$603$		0			0
$604$	316.259	+	121.758i	0.523608	+	0.201586i
$605$		−	565.786i		−	0.935183i
$606$		0			0
$607$		−	885.649i		−	1.45906i	−0.683950	−	0.729529i	$-0.739739\pi$
$607$		−	885.649i		−	1.45906i	0.683950	−	0.729529i	$-0.260261\pi$
$608$	−43.1713	+	321.795i	−0.0710055	+	0.529269i
$609$		0			0
$610$	95.8653	+	139.632i	0.157156	+	0.228905i
$611$	−597.349			−0.977658
$612$		0			0
$613$		−	979.091i		−	1.59721i	−0.601855	−	0.798606i	$-0.705571\pi$
$613$		−	979.091i		−	1.59721i	0.601855	−	0.798606i	$-0.294429\pi$
$614$	189.438	+	275.925i	0.308531	+	0.449390i
$615$		0			0
$616$	−419.749	−	1759.83i	−0.681411	−	2.85687i
$617$	−1064.97			−1.72604			−0.863019	−	0.505171i	$-0.831429\pi$
$617$	−1064.97			−1.72604			−0.863019	+	0.505171i	$0.831429\pi$
$618$		0			0
$619$	−658.875			−1.06442			−0.532209	−	0.846613i	$-0.678638\pi$
$619$	−658.875			−1.06442			−0.532209	+	0.846613i	$0.678638\pi$
$620$	−104.748	+	272.076i	−0.168948	+	0.438832i
$621$		0			0
$622$	−493.782	+	339.009i	−0.793861	+	0.545030i
$623$		−	705.827i		−	1.13295i
$624$		0			0
$625$	25.0000			0.0400000
$626$	−139.942	−	203.831i	−0.223549	−	0.325609i
$627$		0			0
$628$	626.553	+	241.219i	0.997695	+	0.384107i
$629$		−	9.71910i		−	0.0154517i
$630$		0			0
$631$			1074.30i			1.70253i	0.524736	+	0.851265i	$0.324164\pi$
$631$			1074.30i			1.70253i	−0.524736	+	0.851265i	$0.675836\pi$
$632$	245.805	+	1030.55i	0.388932	+	1.63062i
$633$		0			0
$634$	224.154	−	153.895i	0.353556	−	0.242736i
$635$	−102.357			−0.161192
$636$		0			0
$637$			1132.63i			1.77806i
$638$	29.4939	−	20.2492i	0.0462286	−	0.0317386i
$639$		0			0
$640$	137.437	−	251.060i	0.214745	−	0.392281i
$641$	−170.402			−0.265838			−0.132919	−	0.991127i	$-0.542435\pi$
$641$	−170.402			−0.265838			−0.132919	+	0.991127i	$0.542435\pi$
$642$		0			0
$643$	−387.322			−0.602367			−0.301183	−	0.953566i	$-0.597382\pi$
$643$	−387.322			−0.602367			−0.301183	+	0.953566i	$0.597382\pi$
$644$	210.129	−	545.799i	0.326288	−	0.847514i
$645$		0			0
$646$	35.4032	+	51.5664i	0.0548037	+	0.0798241i
$647$			1098.39i			1.69766i	0.528665	+	0.848830i	$0.322693\pi$
$647$			1098.39i			1.69766i	−0.528665	+	0.848830i	$0.677307\pi$
$648$		0			0
$649$	1394.25			2.14831
$650$	−106.424	+	73.0664i	−0.163730	+	0.112410i
$651$		0			0
$652$	−119.098	+	309.351i	−0.182666	+	0.474465i
$653$			801.196i			1.22695i	0.789716	+	0.613473i	$0.210228\pi$
$653$			801.196i			1.22695i	−0.789716	+	0.613473i	$0.789772\pi$
$654$		0			0
$655$			416.532i			0.635927i
$656$	−818.151	−	739.589i	−1.24718	−	1.12742i
$657$		0			0
$658$	−612.517	−	892.158i	−0.930876	−	1.35586i
$659$	204.225			0.309901			0.154950	−	0.987922i	$-0.450478\pi$
$659$	204.225			0.309901			0.154950	+	0.987922i	$0.450478\pi$
$660$		0			0
$661$		−	283.821i		−	0.429382i	−0.976682	−	0.214691i	$-0.931126\pi$
$661$		−	283.821i		−	0.429382i	0.976682	−	0.214691i	$-0.0688744\pi$
$662$	−46.6255	−	67.9122i	−0.0704313	−	0.102586i
$663$		0			0
$664$	−259.687	+	61.9397i	−0.391094	+	0.0932827i
$665$	265.297			0.398943
$666$		0			0
$667$	11.5651			0.0173390
$668$	139.227	+	53.6018i	0.208424	+	0.0802422i
$669$		0			0
$670$	−446.933	+	306.845i	−0.667065	+	0.457977i
$671$		−	732.455i		−	1.09159i
$672$		0			0
$673$	−371.454			−0.551937			−0.275969	−	0.961167i	$-0.588999\pi$
$673$	−371.454			−0.551937			−0.275969	+	0.961167i	$0.588999\pi$
$674$	−640.258	−	932.565i	−0.949938	−	1.38363i
$675$		0			0
$676$	−3.37922	+	8.77732i	−0.00499884	+	0.0129842i
$677$		−	1084.06i		−	1.60127i	−0.599150	−	0.800637i	$-0.704495\pi$
$677$		−	1084.06i		−	1.60127i	0.599150	−	0.800637i	$-0.295505\pi$
$678$		0			0
$679$			154.574i			0.227650i
$680$	−12.7930	−	53.6355i	−0.0188132	−	0.0788758i
$681$		0			0
$682$	1039.39	−	713.602i	1.52404	−	1.04634i
$683$	580.301			0.849636			0.424818	−	0.905279i	$-0.360338\pi$
$683$	580.301			0.849636			0.424818	+	0.905279i	$0.360338\pi$
$684$		0			0
$685$			73.6836i			0.107567i
$686$	−746.873	+	512.771i	−1.08874	+	0.747479i
$687$		0			0
$688$	−828.331	−	748.792i	−1.20397	−	1.08836i
$689$	216.233			0.313837
$690$		0			0
$691$	−438.911			−0.635183			−0.317592	−	0.948228i	$-0.602874\pi$
$691$	−438.911			−0.635183			−0.317592	+	0.948228i	$0.602874\pi$
$692$	−790.733	−	304.428i	−1.14268	−	0.439924i
$693$		0			0
$694$	−152.444	−	222.042i	−0.219660	−	0.319945i
$695$			187.510i			0.269799i
$696$		0			0
$697$	−212.473			−0.304840
$698$	760.611	−	522.202i	1.08970	−	0.748141i
$699$		0			0
$700$	−218.254	−	84.0264i	−0.311791	−	0.120038i
$701$			173.658i			0.247730i	0.992299	+	0.123865i	$0.0395289\pi$
$701$			173.658i			0.247730i	−0.992299	+	0.123865i	$0.960471\pi$
$702$		0			0
$703$		−	31.9917i		−	0.0455073i
$704$	−1104.49	+	558.665i	−1.56888	+	0.793558i
$705$		0			0
$706$	486.523	+	708.642i	0.689125	+	1.00374i
$707$	−1739.24			−2.46003
$708$		0			0
$709$		−	1231.35i		−	1.73674i	−0.495913	−	0.868372i	$-0.665166\pi$
$709$		−	1231.35i		−	1.73674i	0.495913	−	0.868372i	$-0.334834\pi$
$710$	−170.632	−	248.533i	−0.240327	−	0.350047i
$711$		0			0
$712$	−469.709	+	112.034i	−0.659704	+	0.157351i
$713$	407.567			0.571623
$714$		0			0
$715$	558.261			0.780785
$716$	124.272	−	322.790i	0.173565	−	0.450824i
$717$		0			0
$718$	−515.091	+	353.639i	−0.717397	+	0.492533i
$719$		−	327.782i		−	0.455885i	−0.973675	−	0.227943i	$-0.926800\pi$
$719$		−	327.782i		−	0.455885i	0.973675	−	0.227943i	$-0.0731999\pi$
$720$		0			0
$721$	1564.35			2.16970
$722$	−292.118	−	425.483i	−0.404596	−	0.589312i
$723$		0			0
$724$	−296.406	−	114.115i	−0.409401	−	0.157617i
$725$		−	4.62466i		−	0.00637884i
$726$		0			0
$727$			217.872i			0.299686i	0.988710	+	0.149843i	$0.0478768\pi$
$727$			217.872i			0.299686i	−0.988710	+	0.149843i	$0.952123\pi$
$728$	1174.68	−	280.182i	1.61357	−	0.384865i
$729$		0			0
$730$	−54.4745	+	37.3998i	−0.0746227	+	0.0512327i
$731$	−215.117			−0.294278
$732$		0			0
$733$		−	154.099i		−	0.210231i	−0.994460	−	0.105115i	$-0.966479\pi$
$733$		−	154.099i		−	0.210231i	0.994460	−	0.105115i	$-0.0335212\pi$
$734$	229.071	−	157.270i	0.312085	−	0.214264i
$735$		0			0
$736$	−396.568	−	53.2027i	−0.538815	−	0.0722862i
$737$	2344.44			3.18106
$738$		0			0
$739$	497.686			0.673459			0.336729	−	0.941601i	$-0.390679\pi$
$739$	497.686			0.673459			0.336729	+	0.941601i	$0.390679\pi$
$740$	−10.1326	+	26.3188i	−0.0136927	+	0.0355659i
$741$		0			0
$742$	221.724	+	322.951i	0.298819	+	0.435244i
$743$			657.468i			0.884883i	0.896797	+	0.442441i	$0.145888\pi$
$743$			657.468i			0.884883i	−0.896797	+	0.442441i	$0.854112\pi$
$744$		0			0
$745$	−182.110			−0.244443
$746$	−696.720	+	478.337i	−0.933940	+	0.641203i
$747$		0			0
$748$	−85.6733	+	222.531i	−0.114537	+	0.297502i
$749$			645.522i			0.861846i
$750$		0			0
$751$		−	379.552i		−	0.505396i	−0.967545	−	0.252698i	$-0.918682\pi$
$751$		−	379.552i		−	0.505396i	0.967545	−	0.252698i	$-0.0813179\pi$
$752$	−496.485	+	549.223i	−0.660219	+	0.730350i
$753$		0			0
$754$	13.5163	+	19.6871i	0.0179261	+	0.0261102i
$755$	−189.444			−0.250919
$756$		0			0
$757$		−	195.966i		−	0.258872i	−0.991588	−	0.129436i	$-0.958683\pi$
$757$		−	195.966i		−	0.258872i	0.991588	−	0.129436i	$-0.0413166\pi$
$758$	474.586	+	691.255i	0.626103	+	0.911946i
$759$		0			0
$760$	−42.1098	−	176.548i	−0.0554076	−	0.232300i
$761$	963.030			1.26548			0.632740	−	0.774364i	$-0.281930\pi$
$761$	963.030			1.26548			0.632740	+	0.774364i	$0.281930\pi$
$762$		0			0
$763$	908.209			1.19031
$764$	1083.82	+	417.264i	1.41861	+	0.546156i
$765$		0			0
$766$	−505.792	+	347.254i	−0.660302	+	0.453335i
$767$			930.661i			1.21338i
$768$		0			0
$769$	81.3670			0.105809			0.0529044	−	0.998600i	$-0.483152\pi$
$769$	81.3670			0.105809			0.0529044	+	0.998600i	$0.483152\pi$
$770$	572.436	+	833.779i	0.743424	+	1.08283i
$771$		0			0
$772$	−262.782	+	682.562i	−0.340392	+	0.884147i
$773$		−	781.463i		−	1.01095i	−0.862842	−	0.505474i	$-0.831318\pi$
$773$		−	781.463i		−	1.01095i	0.862842	−	0.505474i	$-0.168682\pi$
$774$		0			0
$775$		−	162.978i		−	0.210294i
$776$	102.865	−	24.5351i	0.132558	−	0.0316174i
$777$		0			0
$778$	−728.553	+	500.193i	−0.936443	+	0.642921i
$779$	−699.383			−0.897795
$780$		0			0
$781$			1303.71i			1.66928i
$782$	−63.5484	+	43.6296i	−0.0812639	+	0.0557923i
$783$		0			0
$784$	1041.38	+	941.379i	1.32829	+	1.20074i
$785$	−375.314			−0.478107
$786$		0			0
$787$	1030.41			1.30929			0.654644	−	0.755937i	$-0.272818\pi$
$787$	1030.41			1.30929			0.654644	+	0.755937i	$0.272818\pi$
$788$	366.437	+	141.076i	0.465022	+	0.179031i
$789$		0			0
$790$	−335.218	−	488.260i	−0.424327	−	0.618051i
$791$		−	1061.68i		−	1.34220i
$792$		0			0
$793$	488.912			0.616534
$794$	−264.454	+	181.563i	−0.333066	+	0.228668i
$795$		0			0
$796$	841.229	+	323.868i	1.05682	+	0.406870i
$797$		−	85.4710i		−	0.107241i	−0.998561	−	0.0536205i	$-0.982924\pi$
$797$		−	85.4710i		−	0.107241i	0.998561	−	0.0536205i	$-0.0170761\pi$
$798$		0			0
$799$			142.633i			0.178514i
$800$	−21.2746	+	158.579i	−0.0265933	+	0.198224i
$801$		0			0
$802$	−219.372	−	319.525i	−0.273531	−	0.398410i
$803$	285.752			0.355856
$804$		0			0
$805$			326.942i			0.406139i
$806$	476.327	+	693.792i	0.590977	+	0.860784i
$807$		0			0
$808$	276.065	+	1157.42i	0.341664	+	1.43245i
$809$	−749.874			−0.926915			−0.463458	−	0.886119i	$-0.653391\pi$
$809$	−749.874			−0.926915			−0.463458	+	0.886119i	$0.653391\pi$
$810$		0			0
$811$	−454.606			−0.560550			−0.280275	−	0.959920i	$-0.590426\pi$
$811$	−454.606			−0.560550			−0.280275	+	0.959920i	$0.590426\pi$
$812$	−15.5437	+	40.3739i	−0.0191425	+	0.0497216i
$813$		0			0
$814$	100.544	−	69.0290i	0.123518	−	0.0848022i
$815$		−	185.306i		−	0.227369i
$816$		0			0
$817$	−708.085			−0.866689
$818$	−520.164	−	757.643i	−0.635898	−	0.926214i
$819$		0			0
$820$	575.366	+	221.512i	0.701665	+	0.270137i
$821$			40.2949i			0.0490802i	0.999699	+	0.0245401i	$0.00781214\pi$
$821$			40.2949i			0.0490802i	−0.999699	+	0.0245401i	$0.992188\pi$
$822$		0			0
$823$			1109.53i			1.34815i	0.738662	+	0.674076i	$0.235458\pi$
$823$			1109.53i			1.34815i	−0.738662	+	0.674076i	$0.764542\pi$
$824$	−248.305	−	1041.03i	−0.301340	−	1.26339i
$825$		0			0
$826$	−1389.97	+	954.292i	−1.68277	+	1.15532i
$827$	−750.168			−0.907096			−0.453548	−	0.891232i	$-0.649842\pi$
$827$	−750.168			−0.907096			−0.453548	+	0.891232i	$0.649842\pi$
$828$		0			0
$829$		−	182.949i		−	0.220687i	−0.993894	−	0.110343i	$-0.964805\pi$
$829$		−	182.949i		−	0.220687i	0.993894	−	0.110343i	$-0.0351950\pi$
$830$	123.035	−	84.4707i	0.148235	−	0.101772i
$831$		0			0
$832$	−372.907	−	737.247i	−0.448206	−	0.886114i
$833$	270.445			0.324663
$834$		0			0
$835$	−83.3993			−0.0998794
$836$	−282.005	+	732.491i	−0.337326	+	0.876185i
$837$		0			0
$838$	−252.936	−	368.413i	−0.301833	−	0.439634i
$839$		−	719.345i		−	0.857384i	−0.903451	−	0.428692i	$-0.858975\pi$
$839$		−	719.345i		−	0.857384i	0.903451	−	0.428692i	$-0.141025\pi$
$840$		0			0
$841$	840.145			0.998983
$842$	1242.37	−	852.954i	1.47549	−	1.01301i
$843$		0			0
$844$	−434.964	+	1129.79i	−0.515360	+	1.33862i
$845$		−	5.25774i		−	0.00622218i
$846$		0			0
$847$		−	2958.77i		−	3.49323i
$848$	179.722	−	198.812i	0.211936	−	0.234449i
$849$		0			0
$850$	17.4465	+	25.4117i	0.0205253	+	0.0298961i
$851$	39.4253			0.0463282
$852$		0			0
$853$		−	593.155i		−	0.695375i	−0.937610	−	0.347688i	$-0.886967\pi$
$853$		−	593.155i		−	0.695375i	0.937610	−	0.347688i	$-0.113033\pi$
$854$	501.326	+	730.204i	0.587033	+	0.855040i
$855$		0			0
$856$	429.578	−	102.462i	0.501844	−	0.119698i
$857$	180.069			0.210116			0.105058	−	0.994466i	$-0.466497\pi$
$857$	180.069			0.210116			0.105058	+	0.994466i	$0.466497\pi$
$858$		0			0
$859$	509.587			0.593232			0.296616	−	0.954997i	$-0.404142\pi$
$859$	509.587			0.593232			0.296616	+	0.954997i	$0.404142\pi$
$860$	582.525	+	224.269i	0.677355	+	0.260778i
$861$		0			0
$862$	−1321.68	+	907.406i	−1.53327	+	1.05267i
$863$		−	1430.93i		−	1.65809i	−0.559181	−	0.829046i	$-0.688884\pi$
$863$		−	1430.93i		−	1.65809i	0.559181	−	0.829046i	$-0.311116\pi$
$864$		0			0
$865$	473.661			0.547585
$866$	820.766	+	1195.48i	0.947767	+	1.38046i
$867$		0			0
$868$	−547.776	+	1422.82i	−0.631079	+	1.63919i
$869$			2561.22i			2.94732i
$870$		0			0
$871$			1564.91i			1.79668i
$872$	−144.157	−	604.390i	−0.165318	−	0.693107i
$873$		0			0
$874$	−209.178	+	143.612i	−0.239334	+	0.164316i
$875$	130.737			0.149414
$876$		0			0
$877$		−	905.426i		−	1.03241i	−0.856464	−	0.516207i	$-0.827344\pi$
$877$		−	905.426i		−	1.03241i	0.856464	−	0.516207i	$-0.172656\pi$
$878$	−908.595	+	623.802i	−1.03485	+	0.710480i
$879$		0			0
$880$	463.997	−	513.285i	0.527270	−	0.583278i
$881$	−1479.51			−1.67935			−0.839677	−	0.543086i	$-0.817256\pi$
$881$	−1479.51			−1.67935			−0.839677	+	0.543086i	$0.817256\pi$
$882$		0			0
$883$	360.404			0.408158			0.204079	−	0.978954i	$-0.434580\pi$
$883$	360.404			0.408158			0.204079	+	0.978954i	$0.434580\pi$
$884$	−148.539	−	57.1867i	−0.168031	−	0.0646908i
$885$		0			0
$886$	−41.6326	−	60.6397i	−0.0469894	−	0.0684422i
$887$		−	1106.42i		−	1.24738i	−0.781674	−	0.623688i	$-0.785634\pi$
$887$		−	1106.42i		−	1.24738i	0.781674	−	0.623688i	$-0.214366\pi$
$888$		0			0
$889$	−535.276			−0.602110
$890$	222.541	−	152.787i	0.250046	−	0.171671i
$891$		0			0
$892$	1614.62	+	621.620i	1.81012	+	0.696884i
$893$			469.494i			0.525750i
$894$		0			0
$895$			193.356i			0.216040i
$896$	718.724	−	1312.91i	0.802147	−	1.46531i
$897$		0			0
$898$	−376.550	−	548.462i	−0.419321	−	0.610759i
$899$	−30.1486			−0.0335357
$900$		0			0
$901$		−	51.6315i		−	0.0573046i
$902$	−1509.07	−	2198.03i	−1.67303	−	2.43684i
$903$		0			0
$904$	−706.520	+	168.517i	−0.781549	+	0.186413i
$905$	177.552			0.196190
$906$		0			0
$907$	1467.30			1.61775			0.808876	−	0.587979i	$-0.200076\pi$
$907$	1467.30			1.61775			0.808876	+	0.587979i	$0.200076\pi$
$908$	−516.396	+	1341.31i	−0.568718	+	1.47721i
$909$		0			0
$910$	−556.545	+	382.100i	−0.611588	+	0.419890i
$911$			1188.75i			1.30488i	0.757840	+	0.652441i	$0.226255\pi$
$911$			1188.75i			1.30488i	−0.757840	+	0.652441i	$0.773745\pi$
$912$		0			0
$913$	−645.396			−0.706896
$914$	−388.592	−	566.002i	−0.425156	−	0.619258i
$915$		0			0
$916$	−792.166	−	304.979i	−0.864810	−	0.332947i
$917$			2178.25i			2.37541i
$918$		0			0
$919$			917.844i			0.998743i	0.866388	+	0.499371i	$0.166436\pi$
$919$			917.844i			0.998743i	−0.866388	+	0.499371i	$0.833564\pi$
$920$	217.571	−	51.8945i	0.236490	−	0.0564070i
$921$		0			0
$922$	344.219	−	236.325i	0.373339	−	0.256318i
$923$	−870.222			−0.942819
$924$		0			0
$925$		−	15.7653i		−	0.0170436i
$926$	−394.889	+	271.114i	−0.426447	+	0.292780i
$927$		0			0
$928$	29.3350	+	3.93552i	0.0316110	+	0.00424086i
$929$	326.140			0.351066			0.175533	−	0.984474i	$-0.443835\pi$
$929$	326.140			0.351066			0.175533	+	0.984474i	$0.443835\pi$
$930$		0			0
$931$	890.203			0.956179
$932$	−397.596	+	1032.73i	−0.426605	+	1.10808i
$933$		0			0
$934$	334.046	+	486.553i	0.357651	+	0.520935i
$935$		−	133.300i		−	0.142566i
$936$		0			0
$937$	803.356			0.857370			0.428685	−	0.903454i	$-0.358977\pi$
$937$	803.356			0.857370			0.428685	+	0.903454i	$0.358977\pi$
$938$	−2337.23	+	1604.64i	−2.49172	+	1.71070i
$939$		0			0
$940$	148.701	−	386.242i	0.158193	−	0.410896i
$941$			617.150i			0.655845i	0.944705	+	0.327922i	$0.106348\pi$
$941$			617.150i			0.655845i	−0.944705	+	0.327922i	$0.893652\pi$
$942$		0			0
$943$		−	861.892i		−	0.913990i
$944$	855.682	+	773.516i	0.906443	+	0.819403i
$945$		0			0
$946$	−1527.85	−	2225.38i	−1.61506	−	2.35241i
$947$	1372.28			1.44908			0.724542	−	0.689231i	$-0.242052\pi$
$947$	1372.28			1.44908			0.724542	+	0.689231i	$0.242052\pi$
$948$		0			0
$949$			190.739i			0.200989i
$950$	57.4275	+	83.6458i	0.0604500	+	0.0880482i
$951$		0			0
$952$	−66.9008	−	280.486i	−0.0702739	−	0.294628i
$953$	313.823			0.329300			0.164650	−	0.986352i	$-0.447351\pi$
$953$	313.823			0.329300			0.164650	+	0.986352i	$0.447351\pi$
$954$		0			0
$955$	−649.223			−0.679815
$956$	104.188	+	40.1117i	0.108983	+	0.0419578i
$957$		0			0
$958$	879.412	−	603.766i	0.917966	−	0.630236i
$959$			385.327i			0.401801i
$960$		0			0
$961$	−101.467			−0.105585
$962$	46.0767	+	67.1127i	0.0478967	+	0.0697638i
$963$		0			0
$964$	165.875	−	430.851i	0.172070	−	0.446941i
$965$		−	408.865i		−	0.423694i
$966$		0			0
$967$		−	191.090i		−	0.197611i	−0.995107	−	0.0988055i	$-0.968498\pi$
$967$		−	191.090i		−	0.197611i	0.995107	−	0.0988055i	$-0.0315022\pi$
$968$	−1968.98	+	469.636i	−2.03407	+	0.485161i
$969$		0			0
$970$	−48.7359	+	33.4599i	−0.0502432	+	0.0344948i
$971$	−88.4914			−0.0911343			−0.0455671	−	0.998961i	$-0.514509\pi$
$971$	−88.4914			−0.0911343			−0.0455671	+	0.998961i	$0.514509\pi$
$972$		0			0
$973$			980.582i			1.00779i
$974$	471.023	−	323.384i	0.483597	−	0.332016i
$975$		0			0
$976$	406.358	−	449.522i	0.416350	−	0.460576i
$977$	1367.80			1.40000			0.700001	−	0.714142i	$-0.253183\pi$
$977$	1367.80			1.40000			0.700001	+	0.714142i	$0.253183\pi$
$978$		0			0
$979$	−1167.36			−1.19240
$980$	−732.349	−	281.950i	−0.747295	−	0.287704i
$981$		0			0
$982$	−213.092	−	310.378i	−0.216998	−	0.316067i
$983$		−	266.437i		−	0.271045i	−0.990774	−	0.135522i	$-0.956729\pi$
$983$		−	266.437i		−	0.271045i	0.990774	−	0.135522i	$-0.0432713\pi$
$984$		0			0
$985$	−219.501			−0.222844
$986$	4.70081	−	3.22737i	0.00476756	−	0.00327320i
$987$		0			0
$988$	−488.935	−	188.237i	−0.494874	−	0.190524i
$989$		−	872.617i		−	0.882322i
$990$		0			0
$991$		−	842.673i		−	0.850326i	−0.905117	−	0.425163i	$-0.860217\pi$
$991$		−	842.673i		−	0.850326i	0.905117	−	0.425163i	$-0.139783\pi$
$992$	1033.79	+	138.691i	1.04213	+	0.139810i
$993$		0			0
$994$	−892.318	−	1299.70i	−0.897705	−	1.30755i
$995$	−503.909			−0.506441
$996$		0			0
$997$			1590.97i			1.59576i	0.602817	+	0.797879i	$0.294045\pi$
$997$			1590.97i			1.59576i	−0.602817	+	0.797879i	$0.705955\pi$
$998$	708.105	+	1031.39i	0.709524	+	1.03345i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	360.3.g.c.91.10		16
3.2	odd	2		120.3.g.a.91.7	✓	16
4.3	odd	2		1440.3.g.c.271.8		16
8.3	odd	2	inner	360.3.g.c.91.9		16
8.5	even	2		1440.3.g.c.271.9		16
12.11	even	2		480.3.g.a.271.8		16
15.2	even	4		600.3.p.b.499.27		32
15.8	even	4		600.3.p.b.499.6		32
15.14	odd	2		600.3.g.d.451.10		16
24.5	odd	2		480.3.g.a.271.1		16
24.11	even	2		120.3.g.a.91.8	yes	16
60.23	odd	4		2400.3.p.b.1999.9		32
60.47	odd	4		2400.3.p.b.1999.22		32
60.59	even	2		2400.3.g.b.751.9		16
120.29	odd	2		2400.3.g.b.751.16		16
120.53	even	4		2400.3.p.b.1999.21		32
120.59	even	2		600.3.g.d.451.9		16
120.77	even	4		2400.3.p.b.1999.10		32
120.83	odd	4		600.3.p.b.499.28		32
120.107	odd	4		600.3.p.b.499.5		32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
120.3.g.a.91.7	✓	16	3.2	odd	2
120.3.g.a.91.8	yes	16	24.11	even	2
360.3.g.c.91.9		16	8.3	odd	2	inner
360.3.g.c.91.10		16	1.1	even	1	trivial
480.3.g.a.271.1		16	24.5	odd	2
480.3.g.a.271.8		16	12.11	even	2
600.3.g.d.451.9		16	120.59	even	2
600.3.g.d.451.10		16	15.14	odd	2
600.3.p.b.499.5		32	120.107	odd	4
600.3.p.b.499.6		32	15.8	even	4
600.3.p.b.499.27		32	15.2	even	4
600.3.p.b.499.28		32	120.83	odd	4
1440.3.g.c.271.8		16	4.3	odd	2
1440.3.g.c.271.9		16	8.5	even	2
2400.3.g.b.751.9		16	60.59	even	2
2400.3.g.b.751.16		16	120.29	odd	2
2400.3.p.b.1999.9		32	60.23	odd	4
2400.3.p.b.1999.10		32	120.77	even	4
2400.3.p.b.1999.21		32	120.53	even	4
2400.3.p.b.1999.22		32	60.47	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)

\(f(q)\)	\(=\)	\(q+(1.13200 + 1.64881i) q^{2} +(-1.43715 + 3.73291i) q^{4} -2.23607i q^{5} -11.6935i q^{7} +(-7.78171 + 1.85607i) q^{8} +(3.68685 - 2.53123i) q^{10} -19.3398 q^{11} -12.9092i q^{13} +(19.2803 - 13.2370i) q^{14} +(-11.8692 - 10.7295i) q^{16} -3.08243 q^{17} -10.1462 q^{19} +(8.34704 + 3.21356i) q^{20} +(-21.8926 - 31.8876i) q^{22} -12.5038i q^{23} -5.00000 q^{25} +(21.2849 - 14.6133i) q^{26} +(43.6507 + 16.8053i) q^{28} +0.924932i q^{29} +32.5955i q^{31} +(4.25493 - 31.7159i) q^{32} +(-3.48931 - 5.08233i) q^{34} -26.1474 q^{35} +3.15307i q^{37} +(-11.4855 - 16.7292i) q^{38} +(4.15030 + 17.4004i) q^{40} +68.9305 q^{41} +69.7882 q^{43} +(27.7941 - 72.1936i) q^{44} +(20.6164 - 14.1543i) q^{46} -46.2730i q^{47} -87.7376 q^{49} +(-5.66000 - 8.24405i) q^{50} +(48.1890 + 18.5525i) q^{52} +16.7503i q^{53} +43.2451i q^{55} +(21.7039 + 90.9953i) q^{56} +(-1.52504 + 1.04702i) q^{58} -72.0926 q^{59} +37.8730i q^{61} +(-53.7438 + 36.8981i) q^{62} +(57.1100 - 28.8868i) q^{64} -28.8660 q^{65} -121.224 q^{67} +(4.42990 - 11.5064i) q^{68} +(-29.5989 - 43.1121i) q^{70} -67.4107i q^{71} -14.7754 q^{73} +(-5.19881 + 3.56928i) q^{74} +(14.5816 - 37.8748i) q^{76} +226.149i q^{77} -132.433i q^{79} +(-23.9919 + 26.5404i) q^{80} +(78.0294 + 113.653i) q^{82} +33.3714 q^{83} +6.89251i q^{85} +(79.0003 + 115.068i) q^{86} +(150.497 - 35.8960i) q^{88} +60.3607 q^{89} -150.954 q^{91} +(46.6755 + 17.9698i) q^{92} +(76.2953 - 52.3810i) q^{94} +22.6876i q^{95} -13.2188 q^{97} +(-99.3190 - 144.663i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 4 q^{2} + 14 q^{4} - 20 q^{8} + 10 q^{10} - 64 q^{11} + 20 q^{14} - 14 q^{16} - 32 q^{19} + 40 q^{20} + 28 q^{22} - 80 q^{25} - 36 q^{26} - 28 q^{28} - 36 q^{32} - 72 q^{34} + 240 q^{38} + 10 q^{40}+ \cdots - 428 q^{98}+O(q^{100}) \) 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

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