LMFDB - Embedded newform 287.3.d.c.286.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [287,3,Mod(286,287)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(287, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 3, names="a")

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

chi := DirichletCharacter("287.286");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 287 = 7 \cdot 41 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	287.d (of order $2$, degree $1$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$7.82018358714$
Analytic rank:	$0$
Dimension:	$8$
Coefficient field:	$\mathbb{Q}[x]/(x^{8} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} + 120x^{6} + 2874x^{4} + 16920x^{2} + 19881 $ x^8 + 120x^6 + 2874x^4 + 16920*x^2 + 19881
Coefficient ring:	$\Z[a_1, \ldots, a_{41}]$
Coefficient ring index:	$ 2^{5} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			286.4
Root			$-1.25038i$ of defining polynomial
Character	$\chi$	$=$	287.286
Dual form			287.3.d.c.286.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} -0.913701 q^{3} -3.00000 q^{4} +7.47749i q^{5} +0.913701 q^{6} +(-6.10985 + 3.41609i) q^{7} +7.00000 q^{8} -8.16515 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} -0.913701 q^{3} -3.00000 q^{4} +7.47749i q^{5} +0.913701 q^{6} +(-6.10985 + 3.41609i) q^{7} +7.00000 q^{8} -8.16515 q^{9} -7.47749i q^{10} -6.11921i q^{11} +2.74110 q^{12} +0.913701 q^{13} +(6.10985 - 3.41609i) q^{14} -6.83219i q^{15} +5.00000 q^{16} -1.10440 q^{17} +8.16515 q^{18} +28.6265 q^{19} -22.4325i q^{20} +(5.58258 - 3.12129i) q^{21} +6.11921i q^{22} -26.7477 q^{23} -6.39590 q^{24} -30.9129 q^{25} -0.913701 q^{26} +15.6838 q^{27} +(18.3296 - 10.2483i) q^{28} -52.5186i q^{29} +6.83219i q^{30} -26.7887i q^{31} -33.0000 q^{32} +5.59112i q^{33} +1.10440 q^{34} +(-25.5438 - 45.6864i) q^{35} +24.4955 q^{36} -18.8348 q^{37} -28.6265 q^{38} -0.834849 q^{39} +52.3424i q^{40} +(-24.7255 + 32.7055i) q^{41} +(-5.58258 + 3.12129i) q^{42} -19.4955 q^{43} +18.3576i q^{44} -61.0548i q^{45} +26.7477 q^{46} +48.5372 q^{47} -4.56850 q^{48} +(25.6606 - 41.7437i) q^{49} +30.9129 q^{50} +1.00909 q^{51} -2.74110 q^{52} -44.2604i q^{53} -15.6838 q^{54} +45.7563 q^{55} +(-42.7690 + 23.9127i) q^{56} -26.1561 q^{57} +52.5186i q^{58} +19.3112i q^{59} +20.4966i q^{60} +28.0236i q^{61} +26.7887i q^{62} +(49.8879 - 27.8929i) q^{63} +13.0000 q^{64} +6.83219i q^{65} -5.59112i q^{66} -14.3774i q^{67} +3.31320 q^{68} +24.4394 q^{69} +(25.5438 + 45.6864i) q^{70} +134.920i q^{71} -57.1561 q^{72} -44.8649i q^{73} +18.8348 q^{74} +28.2451 q^{75} -85.8795 q^{76} +(20.9038 + 37.3875i) q^{77} +0.834849 q^{78} -70.8762i q^{79} +37.3875i q^{80} +59.1561 q^{81} +(24.7255 - 32.7055i) q^{82} -90.3134i q^{83} +(-16.7477 + 9.36386i) q^{84} -8.25815i q^{85} +19.4955 q^{86} +47.9862i q^{87} -42.8345i q^{88} -81.5017 q^{89} +61.0548i q^{90} +(-5.58258 + 3.12129i) q^{91} +80.2432 q^{92} +24.4768i q^{93} -48.5372 q^{94} +214.055i q^{95} +30.1521 q^{96} -100.539 q^{97} +(-25.6606 + 41.7437i) q^{98} +49.9643i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 8 q^{2} - 24 q^{4} + 56 q^{8} + 8 q^{9}+O(q^{10}) $ 8 * q - 8 * q^2 - 24 * q^4 + 56 * q^8 + 8 * q^9	$ 8 q - 8 q^{2} - 24 q^{4} + 56 q^{8} + 8 q^{9} + 40 q^{16} - 8 q^{18} + 8 q^{21} - 104 q^{23} - 64 q^{25} - 264 q^{32} - 24 q^{36} - 224 q^{37} - 80 q^{39} - 8 q^{42} + 64 q^{43} + 104 q^{46} - 88 q^{49} + 64 q^{50} + 448 q^{51} + 304 q^{57} + 104 q^{64} + 56 q^{72} + 224 q^{74} - 456 q^{77} + 80 q^{78} - 40 q^{81} - 24 q^{84} - 64 q^{86} - 8 q^{91} + 312 q^{92} + 88 q^{98}+O(q^{100}) $ 8 * q - 8 * q^2 - 24 * q^4 + 56 * q^8 + 8 * q^9 + 40 * q^16 - 8 * q^18 + 8 * q^21 - 104 * q^23 - 64 * q^25 - 264 * q^32 - 24 * q^36 - 224 * q^37 - 80 * q^39 - 8 * q^42 + 64 * q^43 + 104 * q^46 - 88 * q^49 + 64 * q^50 + 448 * q^51 + 304 * q^57 + 104 * q^64 + 56 * q^72 + 224 * q^74 - 456 * q^77 + 80 * q^78 - 40 * q^81 - 24 * q^84 - 64 * q^86 - 8 * q^91 + 312 * q^92 + 88 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/287\mathbb{Z}\right)^\times$.

$n$	$206$	$211$
$\chi(n)$	$-1$	$-1$

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 $

$2$	−1.00000			−0.500000			−0.250000	−	0.968246i	$-0.580431\pi$
$2$	−1.00000			−0.500000			−0.250000	+	0.968246i	$0.580431\pi$
$3$	−0.913701			−0.304567			−0.152283	−	0.988337i	$-0.548663\pi$
$3$	−0.913701			−0.304567			−0.152283	+	0.988337i	$0.548663\pi$
$4$	−3.00000			−0.750000
$5$			7.47749i			1.49550i	0.663981	+	0.747749i	$0.268865\pi$
$5$			7.47749i			1.49550i	−0.663981	+	0.747749i	$0.731135\pi$
$6$	0.913701			0.152283
$7$	−6.10985	+	3.41609i	−0.872836	+	0.488013i
$7$	−6.10985	+	3.41609i	−0.872836	+	0.488013i
$8$	7.00000			0.875000
$9$	−8.16515			−0.907239
$10$		−	7.47749i		−	0.747749i
$11$		−	6.11921i		−	0.556292i	−0.960539	−	0.278146i	$-0.910280\pi$
$11$		−	6.11921i		−	0.556292i	0.960539	−	0.278146i	$-0.0897198\pi$
$12$	2.74110			0.228425
$13$	0.913701			0.0702847			0.0351423	−	0.999382i	$-0.488812\pi$
$13$	0.913701			0.0702847			0.0351423	+	0.999382i	$0.488812\pi$
$14$	6.10985	−	3.41609i	0.436418	−	0.244007i
$15$		−	6.83219i		−	0.455479i
$16$	5.00000			0.312500
$17$	−1.10440			−0.0649648			−0.0324824	−	0.999472i	$-0.510341\pi$
$17$	−1.10440			−0.0649648			−0.0324824	+	0.999472i	$0.510341\pi$
$18$	8.16515			0.453620
$19$	28.6265			1.50666			0.753329	−	0.657643i	$-0.228447\pi$
$19$	28.6265			1.50666			0.753329	+	0.657643i	$0.228447\pi$
$20$		−	22.4325i		−	1.12162i
$21$	5.58258	−	3.12129i	0.265837	−	0.148633i
$22$			6.11921i			0.278146i
$23$	−26.7477			−1.16294			−0.581472	−	0.813566i	$-0.697523\pi$
$23$	−26.7477			−1.16294			−0.581472	+	0.813566i	$0.697523\pi$
$24$	−6.39590			−0.266496
$25$	−30.9129			−1.23652
$26$	−0.913701			−0.0351423
$27$	15.6838			0.580882
$28$	18.3296	−	10.2483i	0.654627	−	0.366010i
$29$		−	52.5186i		−	1.81098i	−0.424362	−	0.905492i	$-0.639502\pi$
$29$		−	52.5186i		−	1.81098i	0.424362	−	0.905492i	$-0.360498\pi$
$30$			6.83219i			0.227740i
$31$		−	26.7887i		−	0.864151i	−0.901837	−	0.432075i	$-0.857781\pi$
$31$		−	26.7887i		−	0.864151i	0.901837	−	0.432075i	$-0.142219\pi$
$32$	−33.0000			−1.03125
$33$			5.59112i			0.169428i
$34$	1.10440			0.0324824
$35$	−25.5438	−	45.6864i	−0.729823	−	1.30532i
$36$	24.4955			0.680429
$37$	−18.8348			−0.509050			−0.254525	−	0.967066i	$-0.581919\pi$
$37$	−18.8348			−0.509050			−0.254525	+	0.967066i	$0.581919\pi$
$38$	−28.6265			−0.753329
$39$	−0.834849			−0.0214064
$40$			52.3424i			1.30856i
$41$	−24.7255	+	32.7055i	−0.603060	+	0.797696i
$41$	−24.7255	+	32.7055i	−0.603060	+	0.797696i
$42$	−5.58258	+	3.12129i	−0.132918	+	0.0743163i
$43$	−19.4955			−0.453383			−0.226691	−	0.973967i	$-0.572791\pi$
$43$	−19.4955			−0.453383			−0.226691	+	0.973967i	$0.572791\pi$
$44$			18.3576i			0.417219i
$45$		−	61.0548i		−	1.35677i
$46$	26.7477			0.581472
$47$	48.5372			1.03271			0.516353	−	0.856376i	$-0.327289\pi$
$47$	48.5372			1.03271			0.516353	+	0.856376i	$0.327289\pi$
$48$	−4.56850			−0.0951771
$49$	25.6606	−	41.7437i	0.523686	−	0.851911i
$50$	30.9129			0.618258
$51$	1.00909			0.0197861
$52$	−2.74110			−0.0527135
$53$		−	44.2604i		−	0.835102i	−0.908653	−	0.417551i	$-0.862888\pi$
$53$		−	44.2604i		−	0.835102i	0.908653	−	0.417551i	$-0.137112\pi$
$54$	−15.6838			−0.290441
$55$	45.7563			0.831933
$56$	−42.7690	+	23.9127i	−0.763732	+	0.427012i
$57$	−26.1561			−0.458878
$58$			52.5186i			0.905492i
$59$			19.3112i			0.327308i	0.986518	+	0.163654i	$0.0523281\pi$
$59$			19.3112i			0.327308i	−0.986518	+	0.163654i	$0.947672\pi$
$60$			20.4966i			0.341609i
$61$			28.0236i			0.459403i	0.973261	+	0.229702i	$0.0737750\pi$
$61$			28.0236i			0.459403i	−0.973261	+	0.229702i	$0.926225\pi$
$62$			26.7887i			0.432075i
$63$	49.8879	−	27.8929i	0.791871	−	0.442745i
$64$	13.0000			0.203125
$65$			6.83219i			0.105111i
$66$		−	5.59112i		−	0.0847140i
$67$		−	14.3774i		−	0.214587i	−0.994227	−	0.107294i	$-0.965781\pi$
$67$		−	14.3774i		−	0.214587i	0.994227	−	0.107294i	$-0.0342185\pi$
$68$	3.31320			0.0487236
$69$	24.4394			0.354194
$70$	25.5438	+	45.6864i	0.364912	+	0.652662i
$71$			134.920i			1.90028i	0.311817	+	0.950142i	$0.399062\pi$
$71$			134.920i			1.90028i	−0.311817	+	0.950142i	$0.600938\pi$
$72$	−57.1561			−0.793834
$73$		−	44.8649i		−	0.614588i	−0.951615	−	0.307294i	$-0.900576\pi$
$73$		−	44.8649i		−	0.614588i	0.951615	−	0.307294i	$-0.0994236\pi$
$74$	18.8348			0.254525
$75$	28.2451			0.376602
$76$	−85.8795			−1.12999
$77$	20.9038	+	37.3875i	0.271478	+	0.485551i
$78$	0.834849			0.0107032
$79$		−	70.8762i		−	0.897167i	−0.893741	−	0.448583i	$-0.851929\pi$
$79$		−	70.8762i		−	0.897167i	0.893741	−	0.448583i	$-0.148071\pi$
$80$			37.3875i			0.467343i
$81$	59.1561			0.730322
$82$	24.7255	−	32.7055i	0.301530	−	0.398848i
$83$		−	90.3134i		−	1.08811i	−0.839049	−	0.544056i	$-0.816888\pi$
$83$		−	90.3134i		−	1.08811i	0.839049	−	0.544056i	$-0.183112\pi$
$84$	−16.7477	+	9.36386i	−0.199378	+	0.111475i
$85$		−	8.25815i		−	0.0971547i
$86$	19.4955			0.226691
$87$			47.9862i			0.551566i
$88$		−	42.8345i		−	0.486755i
$89$	−81.5017			−0.915750			−0.457875	−	0.889017i	$-0.651389\pi$
$89$	−81.5017			−0.915750			−0.457875	+	0.889017i	$0.651389\pi$
$90$			61.0548i			0.678387i
$91$	−5.58258	+	3.12129i	−0.0613470	+	0.0342999i
$92$	80.2432			0.872208
$93$			24.4768i			0.263192i
$94$	−48.5372			−0.516353
$95$			214.055i			2.25321i
$96$	30.1521			0.314085
$97$	−100.539			−1.03648			−0.518240	−	0.855235i	$-0.673413\pi$
$97$	−100.539			−1.03648			−0.518240	+	0.855235i	$0.673413\pi$
$98$	−25.6606	+	41.7437i	−0.261843	+	0.425956i
$99$			49.9643i			0.504689i
$100$	92.7386			0.927386
$101$	−82.2247			−0.814106			−0.407053	−	0.913404i	$-0.633444\pi$
$101$	−82.2247			−0.814106			−0.407053	+	0.913404i	$0.633444\pi$
$102$	−1.00909			−0.00989306
$103$			145.777i			1.41531i	0.706557	+	0.707656i	$0.250247\pi$
$103$			145.777i			1.41531i	−0.706557	+	0.707656i	$0.749753\pi$
$104$	6.39590			0.0614991
$105$	23.3394	+	41.7437i	0.222280	+	0.397559i
$106$			44.2604i			0.417551i
$107$	93.6515			0.875248			0.437624	−	0.899158i	$-0.355820\pi$
$107$	93.6515			0.875248			0.437624	+	0.899158i	$0.355820\pi$
$108$	−47.0514			−0.435661
$109$		−	193.143i		−	1.77195i	−0.463733	−	0.885975i	$-0.653490\pi$
$109$		−	193.143i		−	1.77195i	0.463733	−	0.885975i	$-0.346510\pi$
$110$	−45.7563			−0.415967
$111$	17.2094			0.155040
$112$	−30.5493	+	17.0805i	−0.272761	+	0.152504i
$113$	−39.4083			−0.348746			−0.174373	−	0.984680i	$-0.555790\pi$
$113$	−39.4083			−0.348746			−0.174373	+	0.984680i	$0.555790\pi$
$114$	26.1561			0.229439
$115$		−	200.006i		−	1.73918i
$116$			157.556i			1.35824i
$117$	−7.46050			−0.0637650
$118$		−	19.3112i		−	0.163654i
$119$	6.74773	−	3.77274i	0.0567036	−	0.0317037i
$120$		−	47.8253i		−	0.398544i
$121$	83.5553			0.690540
$122$		−	28.0236i		−	0.229702i
$123$	22.5917	−	29.8831i	0.183672	−	0.242952i
$124$			80.3660i			0.648113i
$125$		−	44.2135i		−	0.353708i
$126$	−49.8879	+	27.8929i	−0.395936	+	0.221372i
$127$	−157.564			−1.24066			−0.620332	−	0.784339i	$-0.713002\pi$
$127$	−157.564			−1.24066			−0.620332	+	0.784339i	$0.713002\pi$
$128$	119.000			0.929688
$129$	17.8130			0.138085
$130$		−	6.83219i		−	0.0525553i
$131$			160.800i			1.22748i	0.789508	+	0.613741i	$0.210336\pi$
$131$			160.800i			1.22748i	−0.789508	+	0.613741i	$0.789664\pi$
$132$		−	16.7734i		−	0.127071i
$133$	−174.904	+	97.7909i	−1.31507	+	0.735270i
$134$			14.3774i			0.107294i
$135$			117.276i			0.868708i
$136$	−7.73081			−0.0568442
$137$			64.0440i			0.467474i	0.972300	+	0.233737i	$0.0750955\pi$
$137$			64.0440i			0.467474i	−0.972300	+	0.233737i	$0.924904\pi$
$138$	−24.4394			−0.177097
$139$		−	195.650i		−	1.40755i	−0.710422	−	0.703776i	$-0.751496\pi$
$139$		−	195.650i		−	1.40755i	0.710422	−	0.703776i	$-0.248504\pi$
$140$	76.6314	+	137.059i	0.547367	+	0.978994i
$141$	−44.3485			−0.314528
$142$		−	134.920i		−	0.950142i
$143$		−	5.59112i		−	0.0390988i
$144$	−40.8258			−0.283512
$145$	392.707			2.70832
$146$			44.8649i			0.307294i
$147$	−23.4461	+	38.1412i	−0.159497	+	0.259464i
$148$	56.5045			0.381787
$149$		−	195.697i		−	1.31340i	−0.754151	−	0.656701i	$-0.771951\pi$
$149$		−	195.697i		−	1.31340i	0.754151	−	0.656701i	$-0.228049\pi$
$150$	−28.2451			−0.188301
$151$		−	80.5603i		−	0.533512i	−0.963764	−	0.266756i	$-0.914048\pi$
$151$		−	80.5603i		−	0.533512i	0.963764	−	0.266756i	$-0.0859518\pi$
$152$	200.386			1.31833
$153$	9.01760			0.0589386
$154$	−20.9038	−	37.3875i	−0.135739	−	0.242776i
$155$	200.312			1.29234
$156$	2.50455			0.0160548
$157$	−97.2253			−0.619270			−0.309635	−	0.950856i	$-0.600207\pi$
$157$	−97.2253			−0.619270			−0.309635	+	0.950856i	$0.600207\pi$
$158$			70.8762i			0.448583i
$159$			40.4408i			0.254344i
$160$		−	246.757i		−	1.54223i
$161$	163.425	−	91.3727i	1.01506	−	0.567533i
$162$	−59.1561			−0.365161
$163$	−111.808			−0.685936			−0.342968	−	0.939347i	$-0.611432\pi$
$163$	−111.808			−0.685936			−0.342968	+	0.939347i	$0.611432\pi$
$164$	74.1764	−	98.1166i	0.452295	−	0.598272i
$165$	−41.8076			−0.253379
$166$			90.3134i			0.544056i
$167$	−290.190			−1.73767			−0.868833	−	0.495105i	$-0.835130\pi$
$167$	−290.190			−1.73767			−0.868833	+	0.495105i	$0.835130\pi$
$168$	39.0780	−	21.8490i	0.232607	−	0.130054i
$169$	−168.165			−0.995060
$170$			8.25815i			0.0485773i
$171$	−233.740			−1.36690
$172$	58.4864			0.340037
$173$		−	66.6460i		−	0.385237i	−0.981274	−	0.192618i	$-0.938302\pi$
$173$		−	66.6460i		−	0.385237i	0.981274	−	0.192618i	$-0.0616980\pi$
$174$		−	47.9862i		−	0.275783i
$175$	188.873	−	105.601i	1.07928	−	0.603436i
$176$		−	30.5960i		−	0.173841i
$177$		−	17.6446i		−	0.0996872i
$178$	81.5017			0.457875
$179$		−	131.653i		−	0.735491i	−0.929926	−	0.367746i	$-0.880130\pi$
$179$		−	131.653i		−	0.735491i	0.929926	−	0.367746i	$-0.119870\pi$
$180$			183.165i			1.01758i
$181$	53.7491			0.296956			0.148478	−	0.988916i	$-0.452563\pi$
$181$	53.7491			0.296956			0.148478	+	0.988916i	$0.452563\pi$
$182$	5.58258	−	3.12129i	0.0306735	−	0.0171499i
$183$		−	25.6052i		−	0.139919i
$184$	−187.234			−1.01758
$185$		−	140.837i		−	0.761283i
$186$		−	24.4768i		−	0.131596i
$187$			6.75806i			0.0361393i
$188$	−145.612			−0.774530
$189$	−95.8258	+	53.5774i	−0.507015	+	0.283478i
$190$		−	214.055i		−	1.12660i
$191$		−	142.050i		−	0.743717i	−0.928289	−	0.371859i	$-0.878721\pi$
$191$		−	142.050i		−	0.743717i	0.928289	−	0.371859i	$-0.121279\pi$
$192$	−11.8781			−0.0618651
$193$		−	321.944i		−	1.66810i	−0.551688	−	0.834051i	$-0.686016\pi$
$193$		−	321.944i		−	1.66810i	0.551688	−	0.834051i	$-0.313984\pi$
$194$	100.539			0.518240
$195$		−	6.24257i		−	0.0320132i
$196$	−76.9818	+	125.231i	−0.392764	+	0.638934i
$197$	−306.312			−1.55488			−0.777442	−	0.628955i	$-0.783483\pi$
$197$	−306.312			−1.55488			−0.777442	+	0.628955i	$0.783483\pi$
$198$		−	49.9643i		−	0.252345i
$199$	−46.1062			−0.231690			−0.115845	−	0.993267i	$-0.536958\pi$
$199$	−46.1062			−0.231690			−0.115845	+	0.993267i	$0.536958\pi$
$200$	−216.390			−1.08195
$201$			13.1366i			0.0653562i
$202$	82.2247			0.407053
$203$	179.408	+	320.881i	0.883785	+	1.58069i
$204$	−3.02727			−0.0148396
$205$	−244.555	−	184.884i	−1.19295	−	0.901875i
$206$		−	145.777i		−	0.707656i
$207$	218.399			1.05507
$208$	4.56850			0.0219640
$209$		−	175.172i		−	0.838141i
$210$	−23.3394	−	41.7437i	−0.111140	−	0.198779i
$211$		−	108.304i		−	0.513291i	−0.966506	−	0.256646i	$-0.917383\pi$
$211$		−	108.304i		−	0.513291i	0.966506	−	0.256646i	$-0.0826173\pi$
$212$			132.781i			0.626327i
$213$		−	123.277i		−	0.578764i
$214$	−93.6515			−0.437624
$215$		−	145.777i		−	0.678033i
$216$	109.787			0.508272
$217$	91.5126	+	163.675i	0.421717	+	0.754262i
$218$			193.143i			0.885975i
$219$			40.9931i			0.187183i
$220$	−137.269			−0.623950
$221$	−1.00909			−0.00456603
$222$	−17.2094			−0.0775199
$223$			102.215i			0.458363i	0.973384	+	0.229182i	$0.0736050\pi$
$223$			102.215i			0.458363i	−0.973384	+	0.229182i	$0.926395\pi$
$224$	201.625	−	112.731i	0.900112	−	0.503264i
$225$	252.408			1.12181
$226$	39.4083			0.174373
$227$	217.976			0.960248			0.480124	−	0.877200i	$-0.340592\pi$
$227$	217.976			0.960248			0.480124	+	0.877200i	$0.340592\pi$
$228$	78.4682			0.344159
$229$	−167.350			−0.730785			−0.365393	−	0.930854i	$-0.619065\pi$
$229$	−167.350			−0.730785			−0.365393	+	0.930854i	$0.619065\pi$
$230$			200.006i			0.869591i
$231$	−19.0998	−	34.1609i	−0.0826831	−	0.147883i
$232$		−	367.630i		−	1.58461i
$233$			230.868i			0.990852i	0.868650	+	0.495426i	$0.164988\pi$
$233$			230.868i			0.990852i	−0.868650	+	0.495426i	$0.835012\pi$
$234$	7.46050			0.0318825
$235$			362.937i			1.54441i
$236$		−	57.9336i		−	0.245481i
$237$			64.7596i			0.273247i
$238$	−6.74773	+	3.77274i	−0.0283518	+	0.0158518i
$239$			128.088i			0.535933i	0.963428	+	0.267967i	$0.0863517\pi$
$239$			128.088i			0.535933i	−0.963428	+	0.267967i	$0.913648\pi$
$240$		−	34.1609i		−	0.142337i
$241$		−	284.796i		−	1.18173i	−0.806772	−	0.590863i	$-0.798787\pi$
$241$		−	284.796i		−	1.18173i	0.806772	−	0.590863i	$-0.201213\pi$
$242$	−83.5553			−0.345270
$243$	−195.205			−0.803314
$244$		−	84.0708i		−	0.344552i
$245$	312.138	+	191.877i	1.27403	+	0.783171i
$246$	−22.5917	+	29.8831i	−0.0918360	+	0.121476i
$247$	26.1561			0.105895
$248$		−	187.521i		−	0.756132i
$249$			82.5194i			0.331403i
$250$			44.2135i			0.176854i
$251$			97.8588i			0.389876i	0.980816	+	0.194938i	$0.0624505\pi$
$251$			97.8588i			0.389876i	−0.980816	+	0.194938i	$0.937549\pi$
$252$	−149.664	+	83.6788i	−0.593903	+	0.332059i
$253$			163.675i			0.646936i
$254$	157.564			0.620332
$255$			7.54547i			0.0295901i
$256$	−171.000			−0.667969
$257$	−122.229			−0.475597			−0.237799	−	0.971314i	$-0.576426\pi$
$257$	−122.229			−0.475597			−0.237799	+	0.971314i	$0.576426\pi$
$258$	−17.8130			−0.0690427
$259$	115.078	−	64.3416i	0.444317	−	0.248423i
$260$		−	20.4966i		−	0.0788329i
$261$			428.822i			1.64300i
$262$		−	160.800i		−	0.613741i
$263$			326.221i			1.24039i	0.784449	+	0.620193i	$0.212946\pi$
$263$			326.221i			1.24039i	−0.784449	+	0.620193i	$0.787054\pi$
$264$			39.1379i			0.148249i
$265$	330.957			1.24889
$266$	174.904	−	97.7909i	0.657533	−	0.367635i
$267$	74.4682			0.278907
$268$			43.1321i			0.160941i
$269$			128.936i			0.479315i	0.970857	+	0.239658i	$0.0770352\pi$
$269$			128.936i			0.479315i	−0.970857	+	0.239658i	$0.922965\pi$
$270$		−	117.276i		−	0.434354i
$271$		−	354.495i		−	1.30810i	−0.756451	−	0.654051i	$-0.773068\pi$
$271$		−	354.495i		−	1.30810i	0.756451	−	0.654051i	$-0.226932\pi$
$272$	−5.52200			−0.0203015
$273$	5.10080	−	2.85192i	0.0186843	−	0.0104466i
$274$		−	64.0440i		−	0.233737i
$275$			189.162i			0.687863i
$276$	−73.3182			−0.265646
$277$	353.964			1.27785			0.638924	−	0.769270i	$-0.279380\pi$
$277$	353.964			1.27785			0.638924	+	0.769270i	$0.279380\pi$
$278$			195.650i			0.703776i
$279$			218.734i			0.783991i
$280$	−178.807	−	319.805i	−0.638595	−	1.14216i
$281$		−	214.352i		−	0.762819i	−0.924406	−	0.381409i	$-0.875439\pi$
$281$		−	214.352i		−	0.762819i	0.924406	−	0.381409i	$-0.124561\pi$
$282$	44.3485			0.157264
$283$			342.730i			1.21106i	0.795823	+	0.605529i	$0.207039\pi$
$283$			342.730i			1.21106i	−0.795823	+	0.605529i	$0.792961\pi$
$284$		−	404.761i		−	1.42521i
$285$		−	195.582i		−	0.686252i
$286$			5.59112i			0.0195494i
$287$	39.3438	−	284.290i	0.137086	−	0.990559i
$288$	269.450			0.935590
$289$	−287.780			−0.995780
$290$	−392.707			−1.35416
$291$	91.8621			0.315677
$292$			134.595i			0.460941i
$293$	−4.02790			−0.0137471			−0.00687354	−	0.999976i	$-0.502188\pi$
$293$	−4.02790			−0.0137471			−0.00687354	+	0.999976i	$0.502188\pi$
$294$	23.4461	−	38.1412i	0.0797487	−	0.129732i
$295$	−144.399			−0.489489
$296$	−131.844			−0.445419
$297$		−	95.9725i		−	0.323140i
$298$			195.697i			0.656701i
$299$	−24.4394			−0.0817372
$300$	−84.7353			−0.282451
$301$	119.114	−	66.5983i	0.395729	−	0.221257i
$302$			80.5603i			0.266756i
$303$	75.1288			0.247950
$304$	143.133			0.470831
$305$	−209.546			−0.687037
$306$	−9.01760			−0.0294693
$307$			263.015i			0.856727i	0.903607	+	0.428363i	$0.140910\pi$
$307$			263.015i			0.856727i	−0.903607	+	0.428363i	$0.859090\pi$
$308$	−62.7114	−	112.162i	−0.203608	−	0.364164i
$309$		−	133.197i		−	0.431057i
$310$	−200.312			−0.646168
$311$	−583.614			−1.87657			−0.938286	−	0.345860i	$-0.887587\pi$
$311$	−583.614			−1.87657			−0.938286	+	0.345860i	$0.887587\pi$
$312$	−5.84394			−0.0187306
$313$	512.727			1.63810			0.819052	−	0.573719i	$-0.194500\pi$
$313$	512.727			1.63810			0.819052	+	0.573719i	$0.194500\pi$
$314$	97.2253			0.309635
$315$	208.569	+	373.036i	0.662124	+	1.18424i
$316$			212.629i			0.672875i
$317$			111.454i			0.351590i	0.984427	+	0.175795i	$0.0562495\pi$
$317$			111.454i			0.351590i	−0.984427	+	0.175795i	$0.943750\pi$
$318$		−	40.4408i		−	0.127172i
$319$	−321.372			−1.00744
$320$			97.2074i			0.303773i
$321$	−85.5694			−0.266571
$322$	−163.425	+	91.3727i	−0.507530	+	0.283766i
$323$	−31.6151			−0.0978797
$324$	−177.468			−0.547741
$325$	−28.2451			−0.0869080
$326$	111.808			0.342968
$327$			176.474i			0.539677i
$328$	−173.078	+	228.939i	−0.527678	+	0.697984i
$329$	−296.555	+	165.808i	−0.901384	+	0.503975i
$330$	41.8076			0.126690
$331$		−	359.074i		−	1.08482i	−0.840115	−	0.542408i	$-0.817513\pi$
$331$		−	359.074i		−	1.08482i	0.840115	−	0.542408i	$-0.182487\pi$
$332$			270.940i			0.816085i
$333$	153.789			0.461830
$334$	290.190			0.868833
$335$	107.507			0.320915
$336$	27.9129	−	15.6064i	0.0830740	−	0.0464477i
$337$	483.982			1.43615			0.718074	−	0.695967i	$-0.245024\pi$
$337$	483.982			1.43615			0.718074	+	0.695967i	$0.245024\pi$
$338$	168.165			0.497530
$339$	36.0074			0.106217
$340$			24.7744i			0.0728660i
$341$	−163.925			−0.480720
$342$	233.740			0.683450
$343$	−14.1823	+	342.707i	−0.0413477	+	0.999145i
$344$	−136.468			−0.396710
$345$			182.745i			0.529697i
$346$			66.6460i			0.192618i
$347$			269.425i			0.776441i	0.921567	+	0.388220i	$0.126910\pi$
$347$			269.425i			0.776441i	−0.921567	+	0.388220i	$0.873090\pi$
$348$		−	143.959i		−	0.413674i
$349$		−	188.892i		−	0.541237i	−0.962687	−	0.270618i	$-0.912772\pi$
$349$		−	188.892i		−	0.541237i	0.962687	−	0.270618i	$-0.0872282\pi$
$350$	−188.873	+	105.601i	−0.539638	+	0.301718i
$351$	14.3303			0.0408271
$352$			201.934i			0.573676i
$353$			201.309i			0.570280i	0.958486	+	0.285140i	$0.0920401\pi$
$353$			201.309i			0.570280i	−0.958486	+	0.285140i	$0.907960\pi$
$354$			17.6446i			0.0498436i
$355$	−1008.86			−2.84187
$356$	244.505			0.686812
$357$	−6.16540	+	3.44715i	−0.0172700	+	0.00965589i
$358$			131.653i			0.367746i
$359$	−1.55000			−0.00431756			−0.00215878	−	0.999998i	$-0.500687\pi$
$359$	−1.55000			−0.00431756			−0.00215878	+	0.999998i	$0.500687\pi$
$360$		−	427.384i		−	1.18718i
$361$	458.477			1.27002
$362$	−53.7491			−0.148478
$363$	−76.3445			−0.210315
$364$	16.7477	−	9.36386i	0.0460102	−	0.0257249i
$365$	335.477			0.919116
$366$			25.6052i			0.0699595i
$367$			16.9093i			0.0460745i	0.999735	+	0.0230372i	$0.00733363\pi$
$367$			16.9093i			0.0460745i	−0.999735	+	0.0230372i	$0.992666\pi$
$368$	−133.739			−0.363420
$369$	201.887	−	267.046i	0.547120	−	0.723701i
$370$			140.837i			0.380642i
$371$	151.198	+	270.425i	0.407541	+	0.728907i
$372$		−	73.4305i		−	0.197394i
$373$	−292.468			−0.784097			−0.392048	−	0.919945i	$-0.628233\pi$
$373$	−292.468			−0.784097			−0.392048	+	0.919945i	$0.628233\pi$
$374$		−	6.75806i		−	0.0180697i
$375$			40.3979i			0.107728i
$376$	339.761			0.903619
$377$		−	47.9862i		−	0.127284i
$378$	95.8258	−	53.5774i	0.253507	−	0.141739i
$379$	389.441			1.02755			0.513774	−	0.857925i	$-0.328247\pi$
$379$	389.441			1.02755			0.513774	+	0.857925i	$0.328247\pi$
$380$		−	642.164i		−	1.68990i
$381$	143.967			0.377865
$382$			142.050i			0.371859i
$383$	−545.025			−1.42304			−0.711521	−	0.702665i	$-0.751993\pi$
$383$	−545.025			−1.42304			−0.711521	+	0.702665i	$0.751993\pi$
$384$	−108.730			−0.283152
$385$	−279.564	+	156.308i	−0.726141	+	0.405995i
$386$			321.944i			0.834051i
$387$	159.183			0.411326
$388$	301.616			0.777360
$389$	−301.964			−0.776256			−0.388128	−	0.921605i	$-0.626878\pi$
$389$	−301.964			−0.776256			−0.388128	+	0.921605i	$0.626878\pi$
$390$			6.24257i			0.0160066i
$391$	29.5402			0.0755504
$392$	179.624	−	292.206i	0.458225	−	0.745423i
$393$		−	146.923i		−	0.373850i
$394$	306.312			0.777442
$395$	529.976			1.34171
$396$		−	149.893i		−	0.378517i
$397$	−27.7045			−0.0697846			−0.0348923	−	0.999391i	$-0.511109\pi$
$397$	−27.7045			−0.0697846			−0.0348923	+	0.999391i	$0.511109\pi$
$398$	46.1062			0.115845
$399$	159.810	−	89.3516i	0.400526	−	0.223939i
$400$	−154.564			−0.386411
$401$	112.243			0.279908			0.139954	−	0.990158i	$-0.455305\pi$
$401$	112.243			0.279908			0.139954	+	0.990158i	$0.455305\pi$
$402$		−	13.1366i		−	0.0326781i
$403$		−	24.4768i		−	0.0607365i
$404$	246.674			0.610580
$405$			442.339i			1.09219i
$406$	−179.408	−	320.881i	−0.441892	−	0.790347i
$407$			115.254i			0.283180i
$408$	7.06364			0.0173128
$409$		−	501.575i		−	1.22635i	−0.789949	−	0.613173i	$-0.789893\pi$
$409$		−	501.575i		−	1.22635i	0.789949	−	0.613173i	$-0.210107\pi$
$410$	244.555	+	184.884i	0.596476	+	0.450938i
$411$		−	58.5170i		−	0.142377i
$412$		−	437.331i		−	1.06148i
$413$	−65.9688	−	117.989i	−0.159731	−	0.285686i
$414$	−218.399			−0.527534
$415$	675.317			1.62727
$416$	−30.1521			−0.0724810
$417$			178.765i			0.428694i
$418$			175.172i			0.419071i
$419$			94.7376i			0.226104i	0.993589	+	0.113052i	$0.0360627\pi$
$419$			94.7376i			0.226104i	−0.993589	+	0.113052i	$0.963937\pi$
$420$	−70.0182	−	125.231i	−0.166710	−	0.298169i
$421$			36.0023i			0.0855161i	0.999085	+	0.0427580i	$0.0136145\pi$
$421$			36.0023i			0.0855161i	−0.999085	+	0.0427580i	$0.986386\pi$
$422$			108.304i			0.256646i
$423$	−396.314			−0.936912
$424$		−	309.823i		−	0.730714i
$425$	34.1402			0.0803299
$426$			123.277i			0.289382i
$427$	−95.7312	−	171.220i	−0.224195	−	0.400984i
$428$	−280.955			−0.656436
$429$			5.10861i			0.0119082i
$430$			145.777i			0.339016i
$431$	−388.592			−0.901605			−0.450802	−	0.892624i	$-0.648862\pi$
$431$	−388.592			−0.901605			−0.450802	+	0.892624i	$0.648862\pi$
$432$	78.4190			0.181526
$433$		−	722.263i		−	1.66804i	−0.551731	−	0.834022i	$-0.686032\pi$
$433$		−	722.263i		−	1.66804i	0.551731	−	0.834022i	$-0.313968\pi$
$434$	−91.5126	−	163.675i	−0.210859	−	0.377131i
$435$	−358.817			−0.824866
$436$			579.428i			1.32896i
$437$	−765.694			−1.75216
$438$		−	40.9931i		−	0.0935916i
$439$	346.450			0.789180			0.394590	−	0.918857i	$-0.370887\pi$
$439$	346.450			0.789180			0.394590	+	0.918857i	$0.370887\pi$
$440$	320.294			0.727941
$441$	−209.523	+	340.843i	−0.475108	+	0.772887i
$442$	1.00909			0.00228301
$443$	416.744			0.940731			0.470366	−	0.882472i	$-0.344122\pi$
$443$	416.744			0.940731			0.470366	+	0.882472i	$0.344122\pi$
$444$	−51.6282			−0.116280
$445$		−	609.429i		−	1.36950i
$446$		−	102.215i		−	0.229182i
$447$			178.808i			0.400019i
$448$	−79.4281	+	44.4092i	−0.177295	+	0.0991277i
$449$	−418.798			−0.932736			−0.466368	−	0.884591i	$-0.654438\pi$
$449$	−418.798			−0.932736			−0.466368	+	0.884591i	$0.654438\pi$
$450$	−252.408			−0.560907
$451$	200.132	+	151.300i	0.443751	+	0.335477i
$452$	118.225			0.261560
$453$			73.6080i			0.162490i
$454$	−217.976			−0.480124
$455$	−23.3394	−	41.7437i	−0.0512954	−	0.0917443i
$456$	−183.092			−0.401518
$457$		−	362.106i		−	0.792354i	−0.918174	−	0.396177i	$-0.870337\pi$
$457$		−	362.106i		−	0.792354i	0.918174	−	0.396177i	$-0.129663\pi$
$458$	167.350			0.365393
$459$	−17.3212			−0.0377368
$460$			600.018i			1.30439i
$461$			791.243i			1.71636i	0.513347	+	0.858181i	$0.328406\pi$
$461$			791.243i			1.71636i	−0.513347	+	0.858181i	$0.671594\pi$
$462$	19.0998	+	34.1609i	0.0413416	+	0.0739414i
$463$			755.161i			1.63102i	0.578745	+	0.815509i	$0.303543\pi$
$463$			755.161i			1.63102i	−0.578745	+	0.815509i	$0.696457\pi$
$464$		−	262.593i		−	0.565933i
$465$	−183.025			−0.393603
$466$		−	230.868i		−	0.495426i
$467$		−	414.383i		−	0.887330i	−0.896193	−	0.443665i	$-0.853678\pi$
$467$		−	414.383i		−	0.887330i	0.896193	−	0.443665i	$-0.146322\pi$
$468$	22.3815			0.0478237
$469$	49.1144	+	87.8435i	0.104722	+	0.187300i
$470$		−	362.937i		−	0.772206i
$471$	88.8348			0.188609
$472$			135.178i			0.286395i
$473$			119.297i			0.252213i
$474$		−	64.7596i		−	0.136624i
$475$	−884.928			−1.86301
$476$	−20.2432	+	11.3182i	−0.0425277	+	0.0237778i
$477$			361.393i			0.757637i
$478$		−	128.088i		−	0.267967i
$479$	535.800			1.11858			0.559290	−	0.828972i	$-0.311074\pi$
$479$	535.800			1.11858			0.559290	+	0.828972i	$0.311074\pi$
$480$			225.462i			0.469713i
$481$	−17.2094			−0.0357784
$482$			284.796i			0.590863i
$483$	−149.321	+	83.4873i	−0.309154	+	0.172852i
$484$	−250.666			−0.517905
$485$		−	751.776i		−	1.55005i
$486$	195.205			0.401657
$487$	164.083			0.336927			0.168463	−	0.985708i	$-0.446120\pi$
$487$	164.083			0.336927			0.168463	+	0.985708i	$0.446120\pi$
$488$			196.165i			0.401978i
$489$	102.159			0.208913
$490$	−312.138	−	191.877i	−0.637016	−	0.391586i
$491$	180.541			0.367700			0.183850	−	0.982954i	$-0.441144\pi$
$491$	180.541			0.367700			0.183850	+	0.982954i	$0.441144\pi$
$492$	−67.7750	+	89.6492i	−0.137754	+	0.182214i
$493$			58.0015i			0.117650i
$494$	−26.1561			−0.0529475
$495$	−373.607			−0.754762
$496$		−	133.943i		−	0.270047i
$497$	−460.900	−	824.342i	−0.927364	−	1.65864i
$498$		−	82.5194i		−	0.165702i
$499$		−	90.0645i		−	0.180490i	−0.995920	−	0.0902450i	$-0.971235\pi$
$499$		−	90.0645i		−	0.180490i	0.995920	−	0.0902450i	$-0.0287650\pi$
$500$			132.640i			0.265281i
$501$	265.147			0.529235
$502$		−	97.8588i		−	0.194938i
$503$	212.375			0.422216			0.211108	−	0.977463i	$-0.432293\pi$
$503$	212.375			0.422216			0.211108	+	0.977463i	$0.432293\pi$
$504$	349.215	−	195.250i	0.692887	−	0.387402i
$505$		−	614.835i		−	1.21749i
$506$		−	163.675i		−	0.323468i
$507$	153.653			0.303062
$508$	472.693			0.930498
$509$	196.651			0.386348			0.193174	−	0.981165i	$-0.438122\pi$
$509$	196.651			0.386348			0.193174	+	0.981165i	$0.438122\pi$
$510$		−	7.54547i		−	0.0147950i
$511$	153.263	+	274.118i	0.299927	+	0.536435i
$512$	−305.000			−0.595703
$513$	448.973			0.875190
$514$	122.229			0.237799
$515$	−1090.05			−2.11660
$516$	−53.4390			−0.103564
$517$		−	297.009i		−	0.574486i
$518$	−115.078	+	64.3416i	−0.222159	+	0.124212i
$519$			60.8945i			0.117330i
$520$			47.8253i			0.0919718i
$521$	540.440			1.03731			0.518656	−	0.854983i	$-0.326433\pi$
$521$	540.440			1.03731			0.518656	+	0.854983i	$0.326433\pi$
$522$		−	428.822i		−	0.821498i
$523$		−	586.434i		−	1.12129i	−0.828057	−	0.560644i	$-0.810554\pi$
$523$		−	586.434i		−	1.12129i	0.828057	−	0.560644i	$-0.189446\pi$
$524$		−	482.400i		−	0.920611i
$525$	−172.573	+	96.4880i	−0.328711	+	0.183787i
$526$		−	326.221i		−	0.620193i
$527$			29.5854i			0.0561394i
$528$			27.9556i			0.0529462i
$529$	186.441			0.352440
$530$	−330.957			−0.624447
$531$		−	157.679i		−	0.296947i
$532$	524.711	−	293.373i	0.986300	−	0.551452i
$533$	−22.5917	+	29.8831i	−0.0423859	+	0.0560658i
$534$	−74.4682			−0.139454
$535$			700.278i			1.30893i
$536$		−	100.641i		−	0.187764i
$537$			120.291i			0.224006i
$538$		−	128.936i		−	0.239658i
$539$	−255.438	−	157.023i	−0.473911	−	0.291322i
$540$		−	351.827i		−	0.651531i
$541$	−235.248			−0.434840			−0.217420	−	0.976078i	$-0.569764\pi$
$541$	−235.248			−0.434840			−0.217420	+	0.976078i	$0.569764\pi$
$542$			354.495i			0.654051i
$543$	−49.1106			−0.0904431
$544$	36.4452			0.0669949
$545$	1444.22			2.64995
$546$	−5.10080	+	2.85192i	−0.00934213	+	0.00522330i
$547$			488.290i			0.892670i	0.894866	+	0.446335i	$0.147271\pi$
$547$			488.290i			0.892670i	−0.894866	+	0.446335i	$0.852729\pi$
$548$		−	192.132i		−	0.350606i
$549$		−	228.817i		−	0.416789i
$550$		−	189.162i		−	0.343931i
$551$		−	1503.42i		−	2.72854i
$552$	171.076			0.309920
$553$	242.120	+	433.043i	0.437829	+	0.783080i
$554$	−353.964			−0.638924
$555$			128.683i			0.231862i
$556$			586.949i			1.05566i
$557$		−	629.212i		−	1.12964i	−0.825213	−	0.564822i	$-0.808945\pi$
$557$		−	629.212i		−	1.12964i	0.825213	−	0.564822i	$-0.191055\pi$
$558$		−	218.734i		−	0.391996i
$559$	−17.8130			−0.0318658
$560$	−127.719	−	228.432i	−0.228070	−	0.407914i
$561$		−	6.17484i		−	0.0110068i
$562$			214.352i			0.381409i
$563$	964.650			1.71341			0.856705	−	0.515806i	$-0.172507\pi$
$563$	964.650			1.71341			0.856705	+	0.515806i	$0.172507\pi$
$564$	133.045			0.235896
$565$		−	294.675i		−	0.521550i
$566$		−	342.730i		−	0.605529i
$567$	−361.435	+	202.083i	−0.637451	+	0.356407i
$568$			944.441i			1.66275i
$569$	−544.207			−0.956427			−0.478213	−	0.878244i	$-0.658715\pi$
$569$	−544.207			−0.956427			−0.478213	+	0.878244i	$0.658715\pi$
$570$			195.582i			0.343126i
$571$			425.970i			0.746007i	0.927830	+	0.373004i	$0.121672\pi$
$571$			425.970i			0.746007i	−0.927830	+	0.373004i	$0.878328\pi$
$572$			16.7734i			0.0293241i
$573$			129.791i			0.226512i
$574$	−39.3438	+	284.290i	−0.0685432	+	0.495280i
$575$	826.849			1.43800
$576$	−106.147			−0.184283
$577$	514.349			0.891419			0.445709	−	0.895178i	$-0.352951\pi$
$577$	514.349			0.891419			0.445709	+	0.895178i	$0.352951\pi$
$578$	287.780			0.497890
$579$			294.160i			0.508048i
$580$	−1178.12			−2.03124
$581$	308.519	+	551.801i	0.531014	+	0.949744i
$582$	−91.8621			−0.157839
$583$	−270.839			−0.464560
$584$		−	314.055i		−	0.537765i
$585$		−	55.7858i		−	0.0953604i
$586$	4.02790			0.00687354
$587$	543.602			0.926068			0.463034	−	0.886341i	$-0.346761\pi$
$587$	543.602			0.926068			0.463034	+	0.886341i	$0.346761\pi$
$588$	70.3383	−	114.424i	0.119623	−	0.194598i
$589$		−	766.866i		−	1.30198i
$590$	144.399			0.244744
$591$	279.878			0.473566
$592$	−94.1742			−0.159078
$593$	−1166.75			−1.96754			−0.983771	−	0.179429i	$-0.942575\pi$
$593$	−1166.75			−1.96754			−0.983771	+	0.179429i	$0.942575\pi$
$594$			95.9725i			0.161570i
$595$	28.2106	+	50.4561i	0.0474128	+	0.0848001i
$596$			587.091i			0.985051i
$597$	42.1273			0.0705650
$598$	24.4394			0.0408686
$599$	801.405			1.33790			0.668952	−	0.743306i	$-0.266743\pi$
$599$	801.405			1.33790			0.668952	+	0.743306i	$0.266743\pi$
$600$	197.716			0.329526
$601$	−778.685			−1.29565			−0.647824	−	0.761790i	$-0.724321\pi$
$601$	−778.685			−1.29565			−0.647824	+	0.761790i	$0.724321\pi$
$602$	−119.114	+	66.5983i	−0.197864	+	0.110628i
$603$			117.393i			0.194682i
$604$			241.681i			0.400134i
$605$			624.784i			1.03270i
$606$	−75.1288			−0.123975
$607$			794.568i			1.30901i	0.756058	+	0.654504i	$0.227123\pi$
$607$			794.568i			1.30901i	−0.756058	+	0.654504i	$0.772877\pi$
$608$	−944.675			−1.55374
$609$	−163.925	−	293.189i	−0.269172	−	0.481427i
$610$	209.546			0.343518
$611$	44.3485			0.0725834
$612$	−27.0528			−0.0442039
$613$	−743.982			−1.21367			−0.606837	−	0.794827i	$-0.707562\pi$
$613$	−743.982			−1.21367			−0.606837	+	0.794827i	$0.707562\pi$
$614$		−	263.015i		−	0.428363i
$615$	223.450	+	168.929i	0.363334	+	0.274681i
$616$	146.327	+	261.712i	0.237543	+	0.424857i
$617$	−100.316			−0.162587			−0.0812933	−	0.996690i	$-0.525905\pi$
$617$	−100.316			−0.162587			−0.0812933	+	0.996690i	$0.525905\pi$
$618$			133.197i			0.215528i
$619$			398.261i			0.643395i	0.946843	+	0.321697i	$0.104253\pi$
$619$			398.261i			0.643395i	−0.946843	+	0.321697i	$0.895747\pi$
$620$	−600.936			−0.969252
$621$	−419.506			−0.675533
$622$	583.614			0.938286
$623$	497.964	−	278.418i	0.799300	−	0.446898i
$624$	−4.17424			−0.00668949
$625$	−442.216			−0.707545
$626$	−512.727			−0.819052
$627$			160.054i			0.255270i
$628$	291.676			0.464452
$629$	20.8012			0.0330703
$630$	−208.569	−	373.036i	−0.331062	−	0.592121i
$631$	−285.492			−0.452443			−0.226222	−	0.974076i	$-0.572637\pi$
$631$	−285.492			−0.452443			−0.226222	+	0.974076i	$0.572637\pi$
$632$		−	496.133i		−	0.785021i
$633$			98.9578i			0.156331i
$634$		−	111.454i		−	0.175795i
$635$		−	1178.19i		−	1.85541i
$636$		−	121.322i		−	0.190758i
$637$	23.4461	−	38.1412i	0.0368071	−	0.0598763i
$638$	321.372			0.503718
$639$		−	1101.64i		−	1.72401i
$640$			889.821i			1.39035i
$641$			54.3599i			0.0848048i	0.999101	+	0.0424024i	$0.0135012\pi$
$641$			54.3599i			0.0848048i	−0.999101	+	0.0424024i	$0.986499\pi$
$642$	85.5694			0.133286
$643$	376.244			0.585138			0.292569	−	0.956244i	$-0.405490\pi$
$643$	376.244			0.585138			0.292569	+	0.956244i	$0.405490\pi$
$644$	−490.274	+	274.118i	−0.761295	+	0.425649i
$645$			133.197i			0.206506i
$646$	31.6151			0.0489399
$647$			1066.47i			1.64833i	0.566347	+	0.824167i	$0.308356\pi$
$647$			1066.47i			1.64833i	−0.566347	+	0.824167i	$0.691644\pi$
$648$	414.092			0.639032
$649$	118.169			0.182079
$650$	28.2451			0.0434540
$651$	−83.6151	−	149.550i	−0.128441	−	0.229723i
$652$	335.423			0.514452
$653$			525.303i			0.804446i	0.915542	+	0.402223i	$0.131762\pi$
$653$			525.303i			0.804446i	−0.915542	+	0.402223i	$0.868238\pi$
$654$		−	176.474i		−	0.269839i
$655$	−1202.38			−1.83570
$656$	−123.627	+	163.528i	−0.188456	+	0.249280i
$657$			366.329i			0.557579i
$658$	296.555	−	165.808i	0.450692	−	0.251987i
$659$		−	995.831i		−	1.51113i	−0.655076	−	0.755563i	$-0.727364\pi$
$659$		−	995.831i		−	1.51113i	0.655076	−	0.755563i	$-0.272636\pi$
$660$	125.423			0.190034
$661$			355.594i			0.537964i	0.963145	+	0.268982i	$0.0866873\pi$
$661$			355.594i			0.537964i	−0.963145	+	0.268982i	$0.913313\pi$
$662$			359.074i			0.542408i
$663$	0.922008			0.00139066
$664$		−	632.194i		−	0.952099i
$665$	−731.230	−	1307.84i	−1.09959	−	1.96668i
$666$	−153.789			−0.230915
$667$			1404.75i			2.10608i
$668$	870.571			1.30325
$669$		−	93.3939i		−	0.139602i
$670$	−107.507			−0.160458
$671$	171.482			0.255562
$672$	−184.225	+	103.002i	−0.274144	+	0.153277i
$673$		−	1134.02i		−	1.68502i	−0.538680	−	0.842510i	$-0.681077\pi$
$673$		−	1134.02i		−	1.68502i	0.538680	−	0.842510i	$-0.318923\pi$
$674$	−483.982			−0.718074
$675$	−484.832			−0.718269
$676$	504.495			0.746295
$677$		−	57.2821i		−	0.0846117i	−0.999105	−	0.0423058i	$-0.986530\pi$
$677$		−	57.2821i		−	0.0846117i	0.999105	−	0.0423058i	$-0.0134704\pi$
$678$	−36.0074			−0.0531083
$679$	614.276	−	343.449i	0.904677	−	0.505816i
$680$		−	57.8070i		−	0.0850104i
$681$	−199.165			−0.292460
$682$	163.925			0.240360
$683$			207.340i			0.303573i	0.988413	+	0.151786i	$0.0485025\pi$
$683$			207.340i			0.303573i	−0.988413	+	0.151786i	$0.951497\pi$
$684$	701.219			1.02517
$685$	−478.888			−0.699107
$686$	14.1823	−	342.707i	0.0206738	−	0.499572i
$687$	152.908			0.222573
$688$	−97.4773			−0.141682
$689$		−	40.4408i		−	0.0586949i
$690$		−	182.745i		−	0.264849i
$691$	−792.271			−1.14656			−0.573279	−	0.819360i	$-0.694329\pi$
$691$	−792.271			−1.14656			−0.573279	+	0.819360i	$0.694329\pi$
$692$			199.938i			0.288928i
$693$	−170.683	−	305.274i	−0.246295	−	0.440511i
$694$		−	269.425i		−	0.388220i
$695$	1462.97			2.10499
$696$			335.904i			0.482620i
$697$	27.3068	−	36.1200i	0.0391777	−	0.0518221i
$698$			188.892i			0.270618i
$699$		−	210.945i		−	0.301781i
$700$	−566.619	+	316.804i	−0.809456	+	0.452577i
$701$	1100.36			1.56970			0.784850	−	0.619686i	$-0.212740\pi$
$701$	1100.36			1.56970			0.784850	+	0.619686i	$0.212740\pi$
$702$	−14.3303			−0.0204135
$703$	−539.176			−0.766965
$704$		−	79.5497i		−	0.112997i
$705$		−	331.615i		−	0.470376i
$706$		−	201.309i		−	0.285140i
$707$	502.381	−	280.887i	0.710581	−	0.397295i
$708$			52.9339i			0.0747654i
$709$			332.638i			0.469165i	0.972096	+	0.234583i	$0.0753724\pi$
$709$			332.638i			0.469165i	−0.972096	+	0.234583i	$0.924628\pi$
$710$	1008.86			1.42094
$711$			578.715i			0.813945i
$712$	−570.512			−0.801281
$713$			716.536i			1.00496i
$714$	6.16540	−	3.44715i	0.00863502	−	0.00482794i
$715$	41.8076			0.0584721
$716$			394.959i			0.551618i
$717$		−	117.034i		−	0.163227i
$718$	1.55000			0.00215878
$719$	690.961			0.961003			0.480502	−	0.876994i	$-0.340455\pi$
$719$	690.961			0.961003			0.480502	+	0.876994i	$0.340455\pi$
$720$		−	305.274i		−	0.423992i
$721$	−497.988	−	890.677i	−0.690691	−	1.23534i
$722$	−458.477			−0.635010
$723$			260.218i			0.359915i
$724$	−161.247			−0.222717
$725$			1623.50i			2.23931i
$726$	76.3445			0.105158
$727$	−227.773			−0.313306			−0.156653	−	0.987654i	$-0.550070\pi$
$727$	−227.773			−0.313306			−0.156653	+	0.987654i	$0.550070\pi$
$728$	−39.0780	+	21.8490i	−0.0536786	+	0.0300124i
$729$	−354.045			−0.485659
$730$	−335.477			−0.459558
$731$	21.5308			0.0294539
$732$			76.8155i			0.104939i
$733$		−	444.673i		−	0.606648i	−0.952888	−	0.303324i	$-0.901904\pi$
$733$		−	444.673i		−	0.606648i	0.952888	−	0.303324i	$-0.0980964\pi$
$734$		−	16.9093i		−	0.0230372i
$735$	−285.201	−	175.318i	−0.388028	−	0.238528i
$736$	882.675			1.19929
$737$	−87.9780			−0.119373
$738$	−201.887	+	267.046i	−0.273560	+	0.361850i
$739$	187.670			0.253951			0.126975	−	0.991906i	$-0.459473\pi$
$739$	187.670			0.253951			0.126975	+	0.991906i	$0.459473\pi$
$740$			422.512i			0.570963i
$741$	−23.8988			−0.0322521
$742$	−151.198	−	270.425i	−0.203771	−	0.364454i
$743$	277.339			0.373270			0.186635	−	0.982429i	$-0.440242\pi$
$743$	277.339			0.373270			0.186635	+	0.982429i	$0.440242\pi$
$744$			171.338i			0.230293i
$745$	1463.32			1.96419
$746$	292.468			0.392048
$747$			737.422i			0.987178i
$748$		−	20.2742i		−	0.0271045i
$749$	−572.197	+	319.922i	−0.763948	+	0.427133i
$750$		−	40.3979i		−	0.0538639i
$751$			374.047i			0.498065i	0.968495	+	0.249032i	$0.0801126\pi$
$751$			374.047i			0.498065i	−0.968495	+	0.249032i	$0.919887\pi$
$752$	242.686			0.322721
$753$		−	89.4137i		−	0.118743i
$754$			47.9862i			0.0636422i
$755$	602.389			0.797866
$756$	287.477	−	160.732i	0.380261	−	0.212609i
$757$			798.355i			1.05463i	0.849670	+	0.527315i	$0.176801\pi$
$757$			798.355i			1.05463i	−0.849670	+	0.527315i	$0.823199\pi$
$758$	−389.441			−0.513774
$759$		−	149.550i		−	0.197035i
$760$			1498.38i			1.97155i
$761$			1155.44i			1.51832i	0.650903	+	0.759161i	$0.274390\pi$
$761$			1155.44i			1.51832i	−0.650903	+	0.759161i	$0.725610\pi$
$762$	−143.967			−0.188933
$763$	659.793	+	1180.07i	0.864735	+	1.54662i
$764$			426.150i			0.557788i
$765$			67.4290i			0.0881425i
$766$	545.025			0.711521
$767$			17.6446i			0.0230047i
$768$	156.243			0.203441
$769$			300.131i			0.390287i	0.980775	+	0.195143i	$0.0625172\pi$
$769$			300.131i			0.390287i	−0.980775	+	0.195143i	$0.937483\pi$
$770$	279.564	−	156.308i	0.363071	−	0.202997i
$771$	111.680			0.144851
$772$			965.831i			1.25108i
$773$	−1141.88			−1.47720			−0.738600	−	0.674144i	$-0.764513\pi$
$773$	−1141.88			−1.47720			−0.738600	+	0.674144i	$0.764513\pi$
$774$	−159.183			−0.205663
$775$			828.115i			1.06854i
$776$	−703.770			−0.906920
$777$	−105.147	+	58.7890i	−0.135324	+	0.0756615i
$778$	301.964			0.388128
$779$	−707.804	+	936.245i	−0.908606	+	1.20186i
$780$			18.7277i			0.0240099i
$781$	825.605			1.05711
$782$	−29.5402			−0.0377752
$783$		−	823.691i		−	1.05197i
$784$	128.303	−	208.718i	0.163652	−	0.266222i
$785$		−	727.002i		−	0.926117i
$786$			146.923i			0.186925i
$787$			688.377i			0.874685i	0.899295	+	0.437342i	$0.144080\pi$
$787$			688.377i			0.874685i	−0.899295	+	0.437342i	$0.855920\pi$
$788$	918.936			1.16616
$789$		−	298.069i		−	0.377780i
$790$	−529.976			−0.670856
$791$	240.779	−	134.623i	0.304398	−	0.170193i
$792$			349.750i			0.441603i
$793$			25.6052i			0.0322890i
$794$	27.7045			0.0348923
$795$	−302.395			−0.380372
$796$	138.319			0.173767
$797$			1528.46i			1.91777i	0.283797	+	0.958884i	$0.408406\pi$
$797$			1528.46i			1.91777i	−0.283797	+	0.958884i	$0.591594\pi$
$798$	−159.810	+	89.3516i	−0.200263	+	0.111969i
$799$	−53.6046			−0.0670896
$800$	1020.12			1.27516
$801$	665.474			0.830804
$802$	−112.243			−0.139954
$803$	−274.538			−0.341890
$804$		−	39.4098i		−	0.0490172i
$805$	683.239	+	1222.01i	0.848744	+	1.51802i
$806$			24.4768i			0.0303683i
$807$		−	117.809i		−	0.145983i
$808$	−575.573			−0.712343
$809$		−	1121.48i		−	1.38626i	−0.720813	−	0.693129i	$-0.756232\pi$
$809$		−	1121.48i		−	1.38626i	0.720813	−	0.693129i	$-0.243768\pi$
$810$		−	442.339i		−	0.546097i
$811$		−	1294.50i		−	1.59618i	−0.602539	−	0.798089i	$-0.705844\pi$
$811$		−	1294.50i		−	1.59618i	0.602539	−	0.798089i	$-0.294156\pi$
$812$	−538.225	−	962.642i	−0.662839	−	1.18552i
$813$			323.903i			0.398404i
$814$		−	115.254i		−	0.141590i
$815$		−	836.040i		−	1.02582i
$816$	5.04546			0.00618316
$817$	−558.087			−0.683093
$818$			501.575i			0.613173i
$819$	45.5826	−	25.4858i	0.0556564	−	0.0311182i
$820$	733.666	+	554.653i	0.894715	+	0.676406i
$821$	−1256.57			−1.53054			−0.765268	−	0.643712i	$-0.777393\pi$
$821$	−1256.57			−1.53054			−0.765268	+	0.643712i	$0.777393\pi$
$822$			58.5170i			0.0711886i
$823$		−	973.556i		−	1.18294i	−0.806329	−	0.591468i	$-0.798549\pi$
$823$		−	973.556i		−	1.18294i	0.806329	−	0.591468i	$-0.201451\pi$
$824$			1020.44i			1.23840i
$825$		−	172.838i		−	0.209500i
$826$	65.9688	+	117.989i	0.0798654	+	0.142843i
$827$			550.140i			0.665224i	0.943064	+	0.332612i	$0.107930\pi$
$827$			550.140i			0.665224i	−0.943064	+	0.332612i	$0.892070\pi$
$828$	−655.198			−0.791302
$829$		−	312.820i		−	0.377346i	−0.982040	−	0.188673i	$-0.939581\pi$
$829$		−	312.820i		−	0.377346i	0.982040	−	0.188673i	$-0.0604186\pi$
$830$	−675.317			−0.813635
$831$	−323.417			−0.389190
$832$	11.8781			0.0142766
$833$	−28.3396	+	46.1017i	−0.0340211	+	0.0553442i
$834$		−	178.765i		−	0.214347i
$835$		−	2169.90i		−	2.59868i
$836$			525.515i			0.628606i
$837$		−	420.148i		−	0.501970i
$838$		−	94.7376i		−	0.113052i
$839$	−1251.01			−1.49107			−0.745536	−	0.666465i	$-0.767807\pi$
$839$	−1251.01			−1.49107			−0.745536	+	0.666465i	$0.767807\pi$
$840$	163.376	+	292.206i	0.194495	+	0.347864i
$841$	−1917.20			−2.27967
$842$		−	36.0023i		−	0.0427580i
$843$			195.854i			0.232329i
$844$			324.913i			0.384968i
$845$		−	1257.45i		−	1.48811i
$846$	396.314			0.468456
$847$	−510.511	+	285.433i	−0.602728	+	0.336993i
$848$		−	221.302i		−	0.260969i
$849$		−	313.152i		−	0.368848i
$850$	−34.1402			−0.0401650
$851$	503.789			0.591997
$852$			369.830i			0.434073i
$853$			313.471i			0.367493i	0.982974	+	0.183746i	$0.0588225\pi$
$853$			313.471i			0.367493i	−0.982974	+	0.183746i	$0.941178\pi$
$854$	95.7312	+	171.220i	0.112097	+	0.200492i
$855$		−	1747.79i		−	2.04420i
$856$	655.561			0.765842
$857$		−	112.746i		−	0.131559i	−0.997834	−	0.0657794i	$-0.979047\pi$
$857$		−	112.746i		−	0.131559i	0.997834	−	0.0657794i	$-0.0209534\pi$
$858$		−	5.10861i		−	0.00595409i
$859$		−	950.944i		−	1.10704i	−0.832837	−	0.553518i	$-0.813285\pi$
$859$		−	950.944i		−	1.10704i	0.832837	−	0.553518i	$-0.186715\pi$
$860$			437.331i			0.508525i
$861$	−35.9484	+	259.756i	−0.0417520	+	0.301691i
$862$	388.592			0.450802
$863$	−661.826			−0.766890			−0.383445	−	0.923564i	$-0.625262\pi$
$863$	−661.826			−0.766890			−0.383445	+	0.923564i	$0.625262\pi$
$864$	−517.566			−0.599034
$865$	498.345			0.576121
$866$			722.263i			0.834022i
$867$	262.945			0.303281
$868$	−274.538	−	491.025i	−0.316288	−	0.565697i
$869$	−433.706			−0.499086
$870$	358.817			0.412433
$871$		−	13.1366i		−	0.0150822i
$872$		−	1352.00i		−	1.55046i
$873$	820.912			0.940335
$874$	765.694			0.876080
$875$	151.037	+	270.138i	0.172614	+	0.308729i
$876$		−	122.979i		−	0.140387i
$877$	430.203			0.490539			0.245270	−	0.969455i	$-0.421123\pi$
$877$	430.203			0.490539			0.245270	+	0.969455i	$0.421123\pi$
$878$	−346.450			−0.394590
$879$	3.68029			0.00418691
$880$	228.782			0.259979
$881$			1181.82i			1.34146i	0.741703	+	0.670728i	$0.234018\pi$
$881$			1181.82i			1.34146i	−0.741703	+	0.670728i	$0.765982\pi$
$882$	209.523	−	340.843i	0.237554	−	0.386444i
$883$			721.775i			0.817413i	0.912666	+	0.408706i	$0.134020\pi$
$883$			721.775i			0.817413i	−0.912666	+	0.408706i	$0.865980\pi$
$884$	3.02727			0.00342452
$885$	131.938			0.149082
$886$	−416.744			−0.470366
$887$	453.806			0.511619			0.255809	−	0.966727i	$-0.417658\pi$
$887$	453.806			0.511619			0.255809	+	0.966727i	$0.417658\pi$
$888$	120.466			0.135660
$889$	962.695	−	538.255i	1.08290	−	0.605461i
$890$			609.429i			0.684751i
$891$		−	361.988i		−	0.406272i
$892$		−	306.645i		−	0.343773i
$893$	1389.45			1.55594
$894$		−	178.808i		−	0.200009i
$895$	984.433			1.09993
$896$	−727.072	+	406.515i	−0.811465	+	0.453700i
$897$	22.3303			0.0248944
$898$	418.798			0.466368
$899$	−1406.90			−1.56496
$900$	−757.225			−0.841361
$901$			48.8812i			0.0542522i
$902$	−200.132	−	151.300i	−0.221876	−	0.167739i
$903$	−108.835	+	60.8509i	−0.120526	+	0.0673875i
$904$	−275.858			−0.305153
$905$			401.909i			0.444098i
$906$		−	73.6080i		−	0.0812450i
$907$	−1040.95			−1.14769			−0.573845	−	0.818964i	$-0.694549\pi$
$907$	−1040.95			−1.14769			−0.573845	+	0.818964i	$0.694549\pi$
$908$	−653.929			−0.720186
$909$	671.377			0.738589
$910$	23.3394	+	41.7437i	0.0256477	+	0.0458722i
$911$	−1189.07			−1.30524			−0.652618	−	0.757687i	$-0.726329\pi$
$911$	−1189.07			−1.30524			−0.652618	+	0.757687i	$0.726329\pi$
$912$	−130.780			−0.143399
$913$	−552.646			−0.605308
$914$			362.106i			0.396177i
$915$	191.462			0.209249
$916$	502.049			0.548089
$917$	−549.308	−	982.465i	−0.599027	−	1.07139i
$918$	17.3212			0.0188684
$919$		−	503.858i		−	0.548268i	−0.961692	−	0.274134i	$-0.911609\pi$
$919$		−	503.858i		−	0.548268i	0.961692	−	0.274134i	$-0.0883912\pi$
$920$		−	1400.04i		−	1.52178i
$921$		−	240.317i		−	0.260931i
$922$		−	791.243i		−	0.858181i
$923$			123.277i			0.133561i
$924$	57.2994	+	102.483i	0.0620123	+	0.110912i
$925$	582.239			0.629448
$926$		−	755.161i		−	0.815509i
$927$		−	1190.29i		−	1.28403i
$928$			1733.11i			1.86758i
$929$	−697.206			−0.750491			−0.375246	−	0.926925i	$-0.622442\pi$
$929$	−697.206			−0.750491			−0.375246	+	0.926925i	$0.622442\pi$
$930$	183.025			0.196801
$931$	734.574	−	1194.98i	0.789016	−	1.28354i
$932$		−	692.605i		−	0.743139i
$933$	533.248			0.571542
$934$			414.383i			0.443665i
$935$	−50.5333			−0.0540463
$936$	−52.2235			−0.0557944
$937$	−1007.23			−1.07495			−0.537475	−	0.843280i	$-0.680622\pi$
$937$	−1007.23			−1.07495			−0.537475	+	0.843280i	$0.680622\pi$
$938$	−49.1144	−	87.8435i	−0.0523608	−	0.0936498i
$939$	−468.479			−0.498912
$940$		−	1088.81i		−	1.15831i
$941$			790.864i			0.840450i	0.907420	+	0.420225i	$0.138049\pi$
$941$			790.864i			0.840450i	−0.907420	+	0.420225i	$0.861951\pi$
$942$	−88.8348			−0.0943045
$943$	661.350	−	874.799i	0.701325	−	0.927676i
$944$			96.5559i			0.102284i
$945$	−400.624	−	716.536i	−0.423941	−	0.758239i
$946$		−	119.297i		−	0.126106i
$947$	−1541.40			−1.62767			−0.813836	−	0.581095i	$-0.802624\pi$
$947$	−1541.40			−1.62767			−0.813836	+	0.581095i	$0.802624\pi$
$948$		−	194.279i		−	0.204935i
$949$		−	40.9931i		−	0.0431961i
$950$	884.928			0.931503
$951$		−	101.836i		−	0.107083i
$952$	47.2341	−	26.4092i	0.0496156	−	0.0277407i
$953$	−54.1599			−0.0568309			−0.0284155	−	0.999596i	$-0.509046\pi$
$953$	−54.1599			−0.0568309			−0.0284155	+	0.999596i	$0.509046\pi$
$954$		−	361.393i		−	0.378819i
$955$	1062.18			1.11223
$956$		−	384.264i		−	0.401950i
$957$	293.638			0.306831
$958$	−535.800			−0.559290
$959$	−218.780	−	391.299i	−0.228134	−	0.408029i
$960$		−	88.8184i		−	0.0925192i
$961$	243.367			0.253243
$962$	17.2094			0.0178892
$963$	−764.679			−0.794059
$964$			854.388i			0.886295i
$965$	2407.33			2.49464
$966$	149.321	−	83.4873i	0.154577	−	0.0864258i
$967$		−	197.836i		−	0.204587i	−0.994754	−	0.102294i	$-0.967382\pi$
$967$		−	197.836i		−	0.204587i	0.994754	−	0.102294i	$-0.0326181\pi$
$968$	584.887			0.604222
$969$	28.8868			0.0298109
$970$			751.776i			0.775027i
$971$	1359.32			1.39992			0.699958	−	0.714184i	$-0.253202\pi$
$971$	1359.32			1.39992			0.699958	+	0.714184i	$0.253202\pi$
$972$	585.616			0.602485
$973$	668.358	+	1195.39i	0.686904	+	1.22856i
$974$	−164.083			−0.168463
$975$	25.8076			0.0264693
$976$			140.118i			0.143564i
$977$		−	1309.40i		−	1.34022i	−0.742260	−	0.670112i	$-0.766246\pi$
$977$		−	1309.40i		−	1.34022i	0.742260	−	0.670112i	$-0.233754\pi$
$978$	−102.159			−0.104457
$979$			498.726i			0.509424i
$980$	−936.414	−	575.631i	−0.955524	−	0.587378i
$981$			1577.04i			1.60758i
$982$	−180.541			−0.183850
$983$		−	418.360i		−	0.425595i	−0.977096	−	0.212798i	$-0.931743\pi$
$983$		−	418.360i		−	0.425595i	0.977096	−	0.212798i	$-0.0682575\pi$
$984$	158.142	−	209.181i	0.160713	−	0.212583i
$985$		−	2290.45i		−	2.32533i
$986$		−	58.0015i		−	0.0588251i
$987$	270.963	−	151.499i	0.274532	−	0.153494i
$988$	−78.4682			−0.0794212
$989$	521.459			0.527259
$990$	373.607			0.377381
$991$		−	661.767i		−	0.667777i	−0.942613	−	0.333889i	$-0.891639\pi$
$991$		−	661.767i		−	0.667777i	0.942613	−	0.333889i	$-0.108361\pi$
$992$			884.026i			0.891156i
$993$			328.086i			0.330399i
$994$	460.900	+	824.342i	0.463682	+	0.829318i
$995$		−	344.759i		−	0.346491i
$996$		−	247.558i		−	0.248552i
$997$	882.417			0.885073			0.442536	−	0.896751i	$-0.354079\pi$
$997$	882.417			0.885073			0.442536	+	0.896751i	$0.354079\pi$
$998$			90.0645i			0.0902450i
$999$	−295.402			−0.295698

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	287.3.d.c.286.4	yes	8
7.6	odd	2	inner	287.3.d.c.286.5	yes	8
41.40	even	2	inner	287.3.d.c.286.6	yes	8
287.286	odd	2	inner	287.3.d.c.286.3	✓	8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
287.3.d.c.286.3	✓	8	287.286	odd	2	inner
287.3.d.c.286.4	yes	8	1.1	even	1	trivial
287.3.d.c.286.5	yes	8	7.6	odd	2	inner
287.3.d.c.286.6	yes	8	41.40	even	2	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 287 = 7 \cdot 41 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	287.d (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} -0.913701 q^{3} -3.00000 q^{4} +7.47749i q^{5} +0.913701 q^{6} +(-6.10985 + 3.41609i) q^{7} +7.00000 q^{8} -8.16515 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} -0.913701 q^{3} -3.00000 q^{4} +7.47749i q^{5} +0.913701 q^{6} +(-6.10985 + 3.41609i) q^{7} +7.00000 q^{8} -8.16515 q^{9} -7.47749i q^{10} -6.11921i q^{11} +2.74110 q^{12} +0.913701 q^{13} +(6.10985 - 3.41609i) q^{14} -6.83219i q^{15} +5.00000 q^{16} -1.10440 q^{17} +8.16515 q^{18} +28.6265 q^{19} -22.4325i q^{20} +(5.58258 - 3.12129i) q^{21} +6.11921i q^{22} -26.7477 q^{23} -6.39590 q^{24} -30.9129 q^{25} -0.913701 q^{26} +15.6838 q^{27} +(18.3296 - 10.2483i) q^{28} -52.5186i q^{29} +6.83219i q^{30} -26.7887i q^{31} -33.0000 q^{32} +5.59112i q^{33} +1.10440 q^{34} +(-25.5438 - 45.6864i) q^{35} +24.4955 q^{36} -18.8348 q^{37} -28.6265 q^{38} -0.834849 q^{39} +52.3424i q^{40} +(-24.7255 + 32.7055i) q^{41} +(-5.58258 + 3.12129i) q^{42} -19.4955 q^{43} +18.3576i q^{44} -61.0548i q^{45} +26.7477 q^{46} +48.5372 q^{47} -4.56850 q^{48} +(25.6606 - 41.7437i) q^{49} +30.9129 q^{50} +1.00909 q^{51} -2.74110 q^{52} -44.2604i q^{53} -15.6838 q^{54} +45.7563 q^{55} +(-42.7690 + 23.9127i) q^{56} -26.1561 q^{57} +52.5186i q^{58} +19.3112i q^{59} +20.4966i q^{60} +28.0236i q^{61} +26.7887i q^{62} +(49.8879 - 27.8929i) q^{63} +13.0000 q^{64} +6.83219i q^{65} -5.59112i q^{66} -14.3774i q^{67} +3.31320 q^{68} +24.4394 q^{69} +(25.5438 + 45.6864i) q^{70} +134.920i q^{71} -57.1561 q^{72} -44.8649i q^{73} +18.8348 q^{74} +28.2451 q^{75} -85.8795 q^{76} +(20.9038 + 37.3875i) q^{77} +0.834849 q^{78} -70.8762i q^{79} +37.3875i q^{80} +59.1561 q^{81} +(24.7255 - 32.7055i) q^{82} -90.3134i q^{83} +(-16.7477 + 9.36386i) q^{84} -8.25815i q^{85} +19.4955 q^{86} +47.9862i q^{87} -42.8345i q^{88} -81.5017 q^{89} +61.0548i q^{90} +(-5.58258 + 3.12129i) q^{91} +80.2432 q^{92} +24.4768i q^{93} -48.5372 q^{94} +214.055i q^{95} +30.1521 q^{96} -100.539 q^{97} +(-25.6606 + 41.7437i) q^{98} +49.9643i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 8 q^{2} - 24 q^{4} + 56 q^{8} + 8 q^{9}+O(q^{10}) \) 8 * q - 8 * q^2 - 24 * q^4 + 56 * q^8 + 8 * q^9	\( 8 q - 8 q^{2} - 24 q^{4} + 56 q^{8} + 8 q^{9} + 40 q^{16} - 8 q^{18} + 8 q^{21} - 104 q^{23} - 64 q^{25} - 264 q^{32} - 24 q^{36} - 224 q^{37} - 80 q^{39} - 8 q^{42} + 64 q^{43} + 104 q^{46} - 88 q^{49} + 64 q^{50} + 448 q^{51} + 304 q^{57} + 104 q^{64} + 56 q^{72} + 224 q^{74} - 456 q^{77} + 80 q^{78} - 40 q^{81} - 24 q^{84} - 64 q^{86} - 8 q^{91} + 312 q^{92} + 88 q^{98}+O(q^{100}) \) 8 * q - 8 * q^2 - 24 * q^4 + 56 * q^8 + 8 * q^9 + 40 * q^16 - 8 * q^18 + 8 * q^21 - 104 * q^23 - 64 * q^25 - 264 * q^32 - 24 * q^36 - 224 * q^37 - 80 * q^39 - 8 * q^42 + 64 * q^43 + 104 * q^46 - 88 * q^49 + 64 * q^50 + 448 * q^51 + 304 * q^57 + 104 * q^64 + 56 * q^72 + 224 * q^74 - 456 * q^77 + 80 * q^78 - 40 * q^81 - 24 * q^84 - 64 * q^86 - 8 * q^91 + 312 * q^92 + 88 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more