LMFDB - Embedded newform 287.3.d.c.286.1

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			286.1
Root			$-9.49661i$ of defining polynomial
Character	$\chi$	$=$	287.286
Dual form			287.3.d.c.286.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} -4.37780 q^{3} -3.00000 q^{4} -3.17602i q^{5} +4.37780 q^{6} +(0.818350 - 6.95200i) q^{7} +7.00000 q^{8} +10.1652 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} -4.37780 q^{3} -3.00000 q^{4} -3.17602i q^{5} +4.37780 q^{6} +(0.818350 - 6.95200i) q^{7} +7.00000 q^{8} +10.1652 q^{9} +3.17602i q^{10} -19.4050i q^{11} +13.1334 q^{12} +4.37780 q^{13} +(-0.818350 + 6.95200i) q^{14} +13.9040i q^{15} +5.00000 q^{16} -25.3531 q^{17} -10.1652 q^{18} -23.3350 q^{19} +9.52807i q^{20} +(-3.58258 + 30.4345i) q^{21} +19.4050i q^{22} +0.747727 q^{23} -30.6446 q^{24} +14.9129 q^{25} -4.37780 q^{26} -5.10080 q^{27} +(-2.45505 + 20.8560i) q^{28} +11.3049i q^{29} -13.9040i q^{30} -17.7304i q^{31} -33.0000 q^{32} +84.9514i q^{33} +25.3531 q^{34} +(-22.0797 - 2.59910i) q^{35} -30.4955 q^{36} -37.1652 q^{37} +23.3350 q^{38} -19.1652 q^{39} -22.2322i q^{40} +(-28.1896 + 29.7716i) q^{41} +(3.58258 - 30.4345i) q^{42} +35.4955 q^{43} +58.2151i q^{44} -32.2848i q^{45} -0.747727 q^{46} +52.0013 q^{47} -21.8890 q^{48} +(-47.6606 - 11.3783i) q^{49} -14.9129 q^{50} +110.991 q^{51} -13.1334 q^{52} -69.2172i q^{53} +5.10080 q^{54} -61.6308 q^{55} +(5.72845 - 48.6640i) q^{56} +102.156 q^{57} -11.3049i q^{58} +20.9064i q^{59} -41.7120i q^{60} +75.4233i q^{61} +17.7304i q^{62} +(8.31865 - 70.6681i) q^{63} +13.0000 q^{64} -13.9040i q^{65} -84.9514i q^{66} +61.1170i q^{67} +76.0593 q^{68} -3.27340 q^{69} +(22.0797 + 2.59910i) q^{70} +107.724i q^{71} +71.1561 q^{72} +19.0561i q^{73} +37.1652 q^{74} -65.2856 q^{75} +70.0050 q^{76} +(-134.904 - 15.8801i) q^{77} +19.1652 q^{78} -46.9102i q^{79} -15.8801i q^{80} -69.1561 q^{81} +(28.1896 - 29.7716i) q^{82} -165.401i q^{83} +(10.7477 - 91.3034i) q^{84} +80.5221i q^{85} -35.4955 q^{86} -49.4906i q^{87} -135.835i q^{88} +70.9187 q^{89} +32.2848i q^{90} +(3.58258 - 30.4345i) q^{91} -2.24318 q^{92} +77.6201i q^{93} -52.0013 q^{94} +74.1125i q^{95} +144.467 q^{96} -100.539 q^{97} +(47.6606 + 11.3783i) q^{98} -197.255i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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	$0.580431\pi$
$3$	−4.37780			−1.45927			−0.729634	−	0.683838i	$-0.760309\pi$
$3$	−4.37780			−1.45927			−0.729634	+	0.683838i	$0.760309\pi$
$4$	−3.00000			−0.750000
$5$		−	3.17602i		−	0.635205i	−0.948224	−	0.317602i	$-0.897122\pi$
$5$		−	3.17602i		−	0.635205i	0.948224	−	0.317602i	$-0.102878\pi$
$6$	4.37780			0.729634
$7$	0.818350	−	6.95200i	0.116907	−	0.993143i
$7$	0.818350	−	6.95200i	0.116907	−	0.993143i
$8$	7.00000			0.875000
$9$	10.1652			1.12946
$10$			3.17602i			0.317602i
$11$		−	19.4050i		−	1.76409i	−0.471162	−	0.882047i	$-0.656165\pi$
$11$		−	19.4050i		−	1.76409i	0.471162	−	0.882047i	$-0.343835\pi$
$12$	13.1334			1.09445
$13$	4.37780			0.336754			0.168377	−	0.985723i	$-0.446147\pi$
$13$	4.37780			0.336754			0.168377	+	0.985723i	$0.446147\pi$
$14$	−0.818350	+	6.95200i	−0.0584536	+	0.496571i
$15$			13.9040i			0.926933i
$16$	5.00000			0.312500
$17$	−25.3531			−1.49136			−0.745680	−	0.666304i	$-0.767875\pi$
$17$	−25.3531			−1.49136			−0.745680	+	0.666304i	$0.767875\pi$
$18$	−10.1652			−0.564731
$19$	−23.3350			−1.22816			−0.614079	−	0.789244i	$-0.710472\pi$
$19$	−23.3350			−1.22816			−0.614079	+	0.789244i	$0.710472\pi$
$20$			9.52807i			0.476403i
$21$	−3.58258	+	30.4345i	−0.170599	+	1.44926i
$22$			19.4050i			0.882047i
$23$	0.747727			0.0325099			0.0162549	−	0.999868i	$-0.494826\pi$
$23$	0.747727			0.0325099			0.0162549	+	0.999868i	$0.494826\pi$
$24$	−30.6446			−1.27686
$25$	14.9129			0.596515
$26$	−4.37780			−0.168377
$27$	−5.10080			−0.188919
$28$	−2.45505	+	20.8560i	−0.0876804	+	0.744857i
$29$			11.3049i			0.389824i	0.980821	+	0.194912i	$0.0624422\pi$
$29$			11.3049i			0.389824i	−0.980821	+	0.194912i	$0.937558\pi$
$30$		−	13.9040i		−	0.463467i
$31$		−	17.7304i		−	0.571948i	−0.958237	−	0.285974i	$-0.907683\pi$
$31$		−	17.7304i		−	0.571948i	0.958237	−	0.285974i	$-0.0923171\pi$
$32$	−33.0000			−1.03125
$33$			84.9514i			2.57428i
$34$	25.3531			0.745680
$35$	−22.0797	−	2.59910i	−0.630849	−	0.0742600i
$36$	−30.4955			−0.847096
$37$	−37.1652			−1.00446			−0.502232	−	0.864733i	$-0.667488\pi$
$37$	−37.1652			−1.00446			−0.502232	+	0.864733i	$0.667488\pi$
$38$	23.3350			0.614079
$39$	−19.1652			−0.491414
$40$		−	22.2322i		−	0.555804i
$41$	−28.1896	+	29.7716i	−0.687550	+	0.726137i
$41$	−28.1896	+	29.7716i	−0.687550	+	0.726137i
$42$	3.58258	−	30.4345i	0.0852994	−	0.724630i
$43$	35.4955			0.825476			0.412738	−	0.910850i	$-0.364573\pi$
$43$	35.4955			0.825476			0.412738	+	0.910850i	$0.364573\pi$
$44$			58.2151i			1.32307i
$45$		−	32.2848i		−	0.717439i
$46$	−0.747727			−0.0162549
$47$	52.0013			1.10641			0.553206	−	0.833045i	$-0.313404\pi$
$47$	52.0013			1.10641			0.553206	+	0.833045i	$0.313404\pi$
$48$	−21.8890			−0.456021
$49$	−47.6606	−	11.3783i	−0.972665	−	0.232211i
$50$	−14.9129			−0.298258
$51$	110.991			2.17629
$52$	−13.1334			−0.252566
$53$		−	69.2172i		−	1.30598i	−0.757365	−	0.652992i	$-0.773513\pi$
$53$		−	69.2172i		−	1.30598i	0.757365	−	0.652992i	$-0.226487\pi$
$54$	5.10080			0.0944593
$55$	−61.6308			−1.12056
$56$	5.72845	−	48.6640i	0.102294	−	0.869000i
$57$	102.156			1.79221
$58$		−	11.3049i		−	0.194912i
$59$			20.9064i			0.354346i	0.984180	+	0.177173i	$0.0566952\pi$
$59$			20.9064i			0.354346i	−0.984180	+	0.177173i	$0.943305\pi$
$60$		−	41.7120i		−	0.695200i
$61$			75.4233i			1.23645i	0.786002	+	0.618224i	$0.212148\pi$
$61$			75.4233i			1.23645i	−0.786002	+	0.618224i	$0.787852\pi$
$62$			17.7304i			0.285974i
$63$	8.31865	−	70.6681i	0.132042	−	1.12172i
$64$	13.0000			0.203125
$65$		−	13.9040i		−	0.213908i
$66$		−	84.9514i		−	1.28714i
$67$			61.1170i			0.912195i	0.889930	+	0.456097i	$0.150753\pi$
$67$			61.1170i			0.912195i	−0.889930	+	0.456097i	$0.849247\pi$
$68$	76.0593			1.11852
$69$	−3.27340			−0.0474406
$70$	22.0797	+	2.59910i	0.315424	+	0.0371300i
$71$			107.724i			1.51725i	0.651530	+	0.758623i	$0.274127\pi$
$71$			107.724i			1.51725i	−0.651530	+	0.758623i	$0.725873\pi$
$72$	71.1561			0.988279
$73$			19.0561i			0.261043i	0.991445	+	0.130521i	$0.0416652\pi$
$73$			19.0561i			0.261043i	−0.991445	+	0.130521i	$0.958335\pi$
$74$	37.1652			0.502232
$75$	−65.2856			−0.870475
$76$	70.0050			0.921119
$77$	−134.904	−	15.8801i	−1.75200	−	0.206235i
$78$	19.1652			0.245707
$79$		−	46.9102i		−	0.593800i	−0.954909	−	0.296900i	$-0.904047\pi$
$79$		−	46.9102i		−	0.593800i	0.954909	−	0.296900i	$-0.0959528\pi$
$80$		−	15.8801i		−	0.198501i
$81$	−69.1561			−0.853779
$82$	28.1896	−	29.7716i	0.343775	−	0.363068i
$83$		−	165.401i		−	1.99278i	−0.0848743	−	0.996392i	$-0.527049\pi$
$83$		−	165.401i		−	1.99278i	0.0848743	−	0.996392i	$-0.472951\pi$
$84$	10.7477	−	91.3034i	0.127949	−	1.08695i
$85$			80.5221i			0.947318i
$86$	−35.4955			−0.412738
$87$		−	49.4906i		−	0.568858i
$88$		−	135.835i		−	1.54358i
$89$	70.9187			0.796840			0.398420	−	0.917203i	$-0.369559\pi$
$89$	70.9187			0.796840			0.398420	+	0.917203i	$0.369559\pi$
$90$			32.2848i			0.358719i
$91$	3.58258	−	30.4345i	0.0393690	−	0.334445i
$92$	−2.24318			−0.0243824
$93$			77.6201i			0.834625i
$94$	−52.0013			−0.553206
$95$			74.1125i			0.780132i
$96$	144.467			1.50487
$97$	−100.539			−1.03648			−0.518240	−	0.855235i	$-0.673413\pi$
$97$	−100.539			−1.03648			−0.518240	+	0.855235i	$0.673413\pi$
$98$	47.6606	+	11.3783i	0.486333	+	0.116106i
$99$		−	197.255i		−	1.99248i
$100$	−44.7386			−0.447386
$101$	87.5162			0.866497			0.433249	−	0.901274i	$-0.357367\pi$
$101$	87.5162			0.866497			0.433249	+	0.901274i	$0.357367\pi$
$102$	−110.991			−1.08815
$103$			112.734i			1.09451i	0.836966	+	0.547254i	$0.184327\pi$
$103$			112.734i			1.09451i	−0.836966	+	0.547254i	$0.815673\pi$
$104$	30.6446			0.294660
$105$	96.6606	+	11.3783i	0.920577	+	0.108365i
$106$			69.2172i			0.652992i
$107$	−89.6515			−0.837865			−0.418932	−	0.908017i	$-0.637596\pi$
$107$	−89.6515			−0.837865			−0.418932	+	0.908017i	$0.637596\pi$
$108$	15.3024			0.141689
$109$			170.053i			1.56012i	0.625707	+	0.780059i	$0.284811\pi$
$109$			170.053i			1.56012i	−0.625707	+	0.780059i	$0.715189\pi$
$110$	61.6308			0.560280
$111$	162.702			1.46578
$112$	4.09175	−	34.7600i	0.0365335	−	0.310357i
$113$	61.4083			0.543437			0.271718	−	0.962377i	$-0.412408\pi$
$113$	61.4083			0.543437			0.271718	+	0.962377i	$0.412408\pi$
$114$	−102.156			−0.896106
$115$		−	2.37480i		−	0.0206504i
$116$		−	33.9147i		−	0.292368i
$117$	44.5010			0.380351
$118$		−	20.9064i		−	0.177173i
$119$	−20.7477	+	176.255i	−0.174351	+	1.48113i
$120$			97.3280i			0.811067i
$121$	−255.555			−2.11203
$122$		−	75.4233i		−	0.618224i
$123$	123.408	−	130.334i	1.00332	−	1.05963i
$124$			53.1912i			0.428961i
$125$		−	126.764i		−	1.01411i
$126$	−8.31865	+	70.6681i	−0.0660211	+	0.560858i
$127$	71.5644			0.563499			0.281750	−	0.959488i	$-0.409085\pi$
$127$	71.5644			0.563499			0.281750	+	0.959488i	$0.409085\pi$
$128$	119.000			0.929688
$129$	−155.392			−1.20459
$130$			13.9040i			0.106954i
$131$		−	242.951i		−	1.85459i	−0.374331	−	0.927295i	$-0.622128\pi$
$131$		−	242.951i		−	1.85459i	0.374331	−	0.927295i	$-0.377872\pi$
$132$		−	254.854i		−	1.93071i
$133$	−19.0962	+	162.225i	−0.143581	+	1.21974i
$134$		−	61.1170i		−	0.456097i
$135$			16.2003i			0.120002i
$136$	−177.472			−1.30494
$137$			60.8142i			0.443899i	0.975058	+	0.221950i	$0.0712421\pi$
$137$			60.8142i			0.443899i	−0.975058	+	0.221950i	$0.928758\pi$
$138$	3.27340			0.0237203
$139$			24.8837i			0.179019i	0.995986	+	0.0895096i	$0.0285300\pi$
$139$			24.8837i			0.179019i	−0.995986	+	0.0895096i	$0.971470\pi$
$140$	66.2391	+	7.79730i	0.473137	+	0.0556950i
$141$	−227.652			−1.61455
$142$		−	107.724i		−	0.758623i
$143$		−	84.9514i		−	0.594066i
$144$	50.8258			0.352957
$145$	35.9046			0.247618
$146$		−	19.0561i		−	0.130521i
$147$	208.649	+	49.8121i	1.41938	+	0.338858i
$148$	111.495			0.753348
$149$		−	15.8974i		−	0.106694i	−0.998576	−	0.0533471i	$-0.983011\pi$
$149$		−	15.8974i		−	0.106694i	0.998576	−	0.0533471i	$-0.0169890\pi$
$150$	65.2856			0.435238
$151$			100.230i			0.663774i	0.943319	+	0.331887i	$0.107685\pi$
$151$			100.230i			0.663774i	−0.943319	+	0.331887i	$0.892315\pi$
$152$	−163.345			−1.07464
$153$	−257.718			−1.68443
$154$	134.904	+	15.8801i	0.875999	+	0.103118i
$155$	−56.3121			−0.363304
$156$	57.4955			0.368561
$157$	−24.4792			−0.155919			−0.0779593	−	0.996957i	$-0.524840\pi$
$157$	−24.4792			−0.155919			−0.0779593	+	0.996957i	$0.524840\pi$
$158$			46.9102i			0.296900i
$159$			303.019i			1.90578i
$160$			104.809i			0.655055i
$161$	0.611903	−	5.19820i	0.00380064	−	0.0322869i
$162$	69.1561			0.426889
$163$	199.808			1.22581			0.612907	−	0.790155i	$-0.290000\pi$
$163$	199.808			1.22581			0.612907	+	0.790155i	$0.290000\pi$
$164$	84.5687	−	89.3148i	0.515663	−	0.544603i
$165$	269.808			1.63520
$166$			165.401i			0.996392i
$167$	−6.13391			−0.0367300			−0.0183650	−	0.999831i	$-0.505846\pi$
$167$	−6.13391			−0.0367300			−0.0183650	+	0.999831i	$0.505846\pi$
$168$	−25.0780	+	213.041i	−0.149274	+	1.26810i
$169$	−149.835			−0.886597
$170$		−	80.5221i		−	0.473659i
$171$	−237.204			−1.38716
$172$	−106.486			−0.619107
$173$		−	117.236i		−	0.677666i	−0.940847	−	0.338833i	$-0.889968\pi$
$173$		−	117.236i		−	0.677666i	0.940847	−	0.338833i	$-0.110032\pi$
$174$			49.4906i			0.284429i
$175$	12.2040	−	103.674i	0.0697369	−	0.592425i
$176$		−	97.0252i		−	0.551279i
$177$		−	91.5241i		−	0.517085i
$178$	−70.9187			−0.398420
$179$			44.9168i			0.250932i	0.992098	+	0.125466i	$0.0400425\pi$
$179$			44.9168i			0.250932i	−0.992098	+	0.125466i	$0.959957\pi$
$180$			96.8543i			0.538079i
$181$	−143.705			−0.793948			−0.396974	−	0.917830i	$-0.629940\pi$
$181$	−143.705			−0.793948			−0.396974	+	0.917830i	$0.629940\pi$
$182$	−3.58258	+	30.4345i	−0.0196845	+	0.167222i
$183$		−	330.188i		−	1.80431i
$184$	5.23409			0.0284461
$185$			118.037i			0.638040i
$186$		−	77.6201i		−	0.417313i
$187$			491.978i			2.63090i
$188$	−156.004			−0.829808
$189$	−4.17424	+	35.4608i	−0.0220859	+	0.187623i
$190$		−	74.1125i		−	0.390066i
$191$			225.366i			1.17993i	0.807430	+	0.589963i	$0.200858\pi$
$191$			225.366i			1.17993i	−0.807430	+	0.589963i	$0.799142\pi$
$192$	−56.9114			−0.296414
$193$			81.7334i			0.423489i	0.977325	+	0.211745i	$0.0679145\pi$
$193$			81.7334i			0.423489i	−0.977325	+	0.211745i	$0.932086\pi$
$194$	100.539			0.518240
$195$			60.8690i			0.312149i
$196$	142.982	+	34.1350i	0.729499	+	0.174158i
$197$	−49.6879			−0.252223			−0.126111	−	0.992016i	$-0.540250\pi$
$197$	−49.6879			−0.252223			−0.126111	+	0.992016i	$0.540250\pi$
$198$			197.255i			0.996238i
$199$	−361.339			−1.81578			−0.907888	−	0.419213i	$-0.862306\pi$
$199$	−361.339			−1.81578			−0.907888	+	0.419213i	$0.862306\pi$
$200$	104.390			0.521951
$201$		−	267.558i		−	1.33114i
$202$	−87.5162			−0.433249
$203$	78.5917	+	9.25137i	0.387151	+	0.0455732i
$204$	−332.973			−1.63222
$205$	94.5553	+	89.5307i	0.461245	+	0.436735i
$206$		−	112.734i		−	0.547254i
$207$	7.60076			0.0367186
$208$	21.8890			0.105236
$209$			452.817i			2.16659i
$210$	−96.6606	−	11.3783i	−0.460289	−	0.0541826i
$211$		−	130.031i		−	0.616262i	−0.951344	−	0.308131i	$-0.900296\pi$
$211$		−	130.031i		−	0.616262i	0.951344	−	0.308131i	$-0.0997036\pi$
$212$			207.651i			0.979488i
$213$		−	471.596i		−	2.21407i
$214$	89.6515			0.418932
$215$		−	112.734i		−	0.524346i
$216$	−35.7056			−0.165304
$217$	−123.262	−	14.5097i	−0.568026	−	0.0668648i
$218$		−	170.053i		−	0.780059i
$219$		−	83.4240i		−	0.380932i
$220$	184.892			0.840420
$221$	−110.991			−0.502221
$222$	−162.702			−0.732890
$223$		−	159.850i		−	0.716817i	−0.933565	−	0.358409i	$-0.883320\pi$
$223$		−	159.850i		−	0.716817i	0.933565	−	0.358409i	$-0.116680\pi$
$224$	−27.0056	+	229.416i	−0.120561	+	1.02418i
$225$	151.592			0.673741
$226$	−61.4083			−0.271718
$227$	41.3072			0.181970			0.0909851	−	0.995852i	$-0.470998\pi$
$227$	41.3072			0.181970			0.0909851	+	0.995852i	$0.470998\pi$
$228$	−306.468			−1.34416
$229$	−240.096			−1.04845			−0.524227	−	0.851579i	$-0.675646\pi$
$229$	−240.096			−1.04845			−0.524227	+	0.851579i	$0.675646\pi$
$230$			2.37480i			0.0103252i
$231$	590.582	+	69.5200i	2.55663	+	0.300952i
$232$			79.1343i			0.341096i
$233$		−	406.118i		−	1.74300i	−0.490400	−	0.871498i	$-0.663149\pi$
$233$		−	406.118i		−	1.74300i	0.490400	−	0.871498i	$-0.336851\pi$
$234$	−44.5010			−0.190175
$235$		−	165.157i		−	0.702797i
$236$		−	62.7192i		−	0.265759i
$237$			205.364i			0.866513i
$238$	20.7477	−	176.255i	0.0871753	−	0.740567i
$239$			121.628i			0.508905i	0.967085	+	0.254453i	$0.0818953\pi$
$239$			121.628i			0.508905i	−0.967085	+	0.254453i	$0.918105\pi$
$240$			69.5200i			0.289667i
$241$			266.509i			1.10585i	0.833232	+	0.552924i	$0.186488\pi$
$241$			266.509i			1.10585i	−0.833232	+	0.552924i	$0.813512\pi$
$242$	255.555			1.05601
$243$	348.659			1.43481
$244$		−	226.270i		−	0.927336i
$245$	−36.1379	+	151.371i	−0.147502	+	0.617842i
$246$	−123.408	+	130.334i	−0.501660	+	0.529814i
$247$	−102.156			−0.413587
$248$		−	124.113i		−	0.500455i
$249$			724.093i			2.90800i
$250$			126.764i			0.507057i
$251$		−	187.109i		−	0.745453i	−0.927941	−	0.372726i	$-0.878423\pi$
$251$		−	187.109i		−	0.745453i	0.927941	−	0.372726i	$-0.121577\pi$
$252$	−24.9560	+	212.004i	−0.0990316	+	0.841287i
$253$		−	14.5097i		−	0.0573505i
$254$	−71.5644			−0.281750
$255$		−	352.510i		−	1.38239i
$256$	−171.000			−0.667969
$257$	397.387			1.54625			0.773126	−	0.634253i	$-0.218692\pi$
$257$	397.387			1.54625			0.773126	+	0.634253i	$0.218692\pi$
$258$	155.392			0.602295
$259$	−30.4141	+	258.372i	−0.117429	+	0.997576i
$260$			41.7120i			0.160431i
$261$			114.916i			0.440291i
$262$			242.951i			0.927295i
$263$		−	281.588i		−	1.07068i	−0.844638	−	0.535338i	$-0.820184\pi$
$263$		−	281.588i		−	1.07068i	0.844638	−	0.535338i	$-0.179816\pi$
$264$			594.660i			2.25250i
$265$	−219.835			−0.829567
$266$	19.0962	−	162.225i	0.0717903	−	0.609868i
$267$	−310.468			−1.16280
$268$		−	183.351i		−	0.684146i
$269$			207.214i			0.770312i	0.922852	+	0.385156i	$0.125852\pi$
$269$			207.214i			0.770312i	−0.922852	+	0.385156i	$0.874148\pi$
$270$		−	16.2003i		−	0.0600010i
$271$		−	169.626i		−	0.625927i	−0.949765	−	0.312963i	$-0.898678\pi$
$271$		−	169.626i		−	0.625927i	0.949765	−	0.312963i	$-0.101322\pi$
$272$	−126.766			−0.466050
$273$	−15.6838	+	133.236i	−0.0574498	+	0.488044i
$274$		−	60.8142i		−	0.221950i
$275$		−	289.385i		−	1.05231i
$276$	9.82020			0.0355804
$277$	−85.9636			−0.310338			−0.155169	−	0.987888i	$-0.549592\pi$
$277$	−85.9636			−0.310338			−0.155169	+	0.987888i	$0.549592\pi$
$278$		−	24.8837i		−	0.0895096i
$279$		−	180.232i		−	0.645993i
$280$	−154.558	−	18.1937i	−0.551993	−	0.0649775i
$281$			245.074i			0.872149i	0.899911	+	0.436074i	$0.143632\pi$
$281$			245.074i			0.872149i	−0.899911	+	0.436074i	$0.856368\pi$
$282$	227.652			0.807275
$283$		−	203.790i		−	0.720106i	−0.932932	−	0.360053i	$-0.882759\pi$
$283$		−	203.790i		−	0.720106i	0.932932	−	0.360053i	$-0.117241\pi$
$284$		−	323.173i		−	1.13793i
$285$		−	324.450i		−	1.13842i
$286$			84.9514i			0.297033i
$287$	183.903	+	220.337i	0.640778	+	0.767726i
$288$	−335.450			−1.16476
$289$	353.780			1.22415
$290$	−35.9046			−0.123809
$291$	440.138			1.51250
$292$		−	57.1684i		−	0.195782i
$293$	422.057			1.44047			0.720233	−	0.693732i	$-0.244035\pi$
$293$	422.057			1.44047			0.720233	+	0.693732i	$0.244035\pi$
$294$	−208.649	−	49.8121i	−0.709689	−	0.169429i
$295$	66.3992			0.225082
$296$	−260.156			−0.878906
$297$			98.9812i			0.333270i
$298$			15.8974i			0.0533471i
$299$	3.27340			0.0109478
$300$	195.857			0.652856
$301$	29.0477	−	246.764i	0.0965040	−	0.819815i
$302$		−	100.230i		−	0.331887i
$303$	−383.129			−1.26445
$304$	−116.675			−0.383800
$305$	239.546			0.785397
$306$	257.718			0.842216
$307$		−	402.802i		−	1.31206i	−0.754736	−	0.656029i	$-0.772235\pi$
$307$		−	402.802i		−	1.31206i	0.754736	−	0.656029i	$-0.227765\pi$
$308$	404.711	+	47.6403i	1.31400	+	0.154676i
$309$		−	493.529i		−	1.59718i
$310$	56.3121			0.181652
$311$	112.670			0.362284			0.181142	−	0.983457i	$-0.442021\pi$
$311$	112.670			0.362284			0.181142	+	0.983457i	$0.442021\pi$
$312$	−134.156			−0.429987
$313$	−412.188			−1.31690			−0.658448	−	0.752626i	$-0.728787\pi$
$313$	−412.188			−1.31690			−0.658448	+	0.752626i	$0.728787\pi$
$314$	24.4792			0.0779593
$315$	−224.444	−	26.4202i	−0.712519	−	0.0838738i
$316$			140.731i			0.445350i
$317$		−	322.391i		−	1.01701i	−0.861060	−	0.508503i	$-0.830199\pi$
$317$		−	322.391i		−	1.01701i	0.861060	−	0.508503i	$-0.169801\pi$
$318$		−	303.019i		−	0.952890i
$319$	219.372			0.687686
$320$		−	41.2883i		−	0.129026i
$321$	392.477			1.22267
$322$	−0.611903	+	5.19820i	−0.00190032	+	0.0161435i
$323$	591.615			1.83163
$324$	207.468			0.640334
$325$	65.2856			0.200879
$326$	−199.808			−0.612907
$327$		−	744.457i		−	2.27663i
$328$	−197.327	+	208.401i	−0.601607	+	0.635370i
$329$	42.5553	−	361.513i	0.129347	−	1.09882i
$330$	−269.808			−0.817599
$331$		−	320.574i		−	0.968502i	−0.874929	−	0.484251i	$-0.839092\pi$
$331$		−	320.574i		−	0.968502i	0.874929	−	0.484251i	$-0.160908\pi$
$332$			496.203i			1.49459i
$333$	−377.789			−1.13450
$334$	6.13391			0.0183650
$335$	194.109			0.579430
$336$	−17.9129	+	152.172i	−0.0533121	+	0.452894i
$337$	264.018			0.783437			0.391718	−	0.920085i	$-0.371881\pi$
$337$	264.018			0.783437			0.391718	+	0.920085i	$0.371881\pi$
$338$	149.835			0.443298
$339$	−268.834			−0.793019
$340$		−	241.566i		−	0.710489i
$341$	−344.059			−1.00897
$342$	237.204			0.693579
$343$	−118.105	+	322.025i	−0.344330	+	0.938849i
$344$	248.468			0.722291
$345$			10.3964i			0.0301345i
$346$			117.236i			0.338833i
$347$		−	70.4285i		−	0.202964i	−0.994837	−	0.101482i	$-0.967642\pi$
$347$		−	70.4285i		−	0.202964i	0.994837	−	0.101482i	$-0.0323584\pi$
$348$			148.472i			0.426643i
$349$			516.862i			1.48098i	0.672068	+	0.740489i	$0.265406\pi$
$349$			516.862i			1.48098i	−0.672068	+	0.740489i	$0.734594\pi$
$350$	−12.2040	+	103.674i	−0.0348685	+	0.296212i
$351$	−22.3303			−0.0636191
$352$			640.366i			1.81922i
$353$		−	289.266i		−	0.819450i	−0.912209	−	0.409725i	$-0.865625\pi$
$353$		−	289.266i		−	0.819450i	0.912209	−	0.409725i	$-0.134375\pi$
$354$			91.5241i			0.258543i
$355$	342.135			0.963761
$356$	−212.756			−0.597630
$357$	90.8294	−	771.609i	0.254424	−	2.16137i
$358$		−	44.9168i		−	0.125466i
$359$	−606.450			−1.68928			−0.844638	−	0.535338i	$-0.820184\pi$
$359$	−606.450			−1.68928			−0.844638	+	0.535338i	$0.820184\pi$
$360$		−	225.993i		−	0.627759i
$361$	183.523			0.508373
$362$	143.705			0.396974
$363$	1118.77			3.08201
$364$	−10.7477	+	91.3034i	−0.0295267	+	0.250834i
$365$	60.5227			0.165816
$366$			330.188i			0.902154i
$367$		−	443.813i		−	1.20930i	−0.796491	−	0.604650i	$-0.793313\pi$
$367$		−	443.813i		−	1.20930i	0.796491	−	0.604650i	$-0.206687\pi$
$368$	3.73864			0.0101593
$369$	−286.551	+	302.633i	−0.776561	+	0.820143i
$370$		−	118.037i		−	0.319020i
$371$	−481.198	−	56.6439i	−1.29703	−	0.152679i
$372$		−	232.860i		−	0.625969i
$373$	92.4682			0.247904			0.123952	−	0.992288i	$-0.460443\pi$
$373$	92.4682			0.247904			0.123952	+	0.992288i	$0.460443\pi$
$374$		−	491.978i		−	1.31545i
$375$			554.949i			1.47986i
$376$	364.009			0.968110
$377$			49.4906i			0.131275i
$378$	4.17424	−	35.4608i	0.0110430	−	0.0938116i
$379$	−325.441			−0.858683			−0.429342	−	0.903142i	$-0.641254\pi$
$379$	−325.441			−0.858683			−0.429342	+	0.903142i	$0.641254\pi$
$380$		−	222.338i		−	0.585099i
$381$	−313.295			−0.822296
$382$		−	225.366i		−	0.589963i
$383$	−545.025			−1.42304			−0.711521	−	0.702665i	$-0.751993\pi$
$383$	−545.025			−1.42304			−0.711521	+	0.702665i	$0.751993\pi$
$384$	−520.958			−1.35666
$385$	−50.4356	+	428.458i	−0.131002	+	1.11288i
$386$		−	81.7334i		−	0.211745i
$387$	360.817			0.932343
$388$	301.616			0.777360
$389$	137.964			0.354662			0.177331	−	0.984151i	$-0.443254\pi$
$389$	137.964			0.354662			0.177331	+	0.984151i	$0.443254\pi$
$390$		−	60.8690i		−	0.156074i
$391$	−18.9572			−0.0484839
$392$	−333.624	−	79.6484i	−0.851082	−	0.203185i
$393$			1063.59i			2.70634i
$394$	49.6879			0.126111
$395$	−148.988			−0.377184
$396$			591.765i			1.49436i
$397$	509.231			1.28270			0.641349	−	0.767249i	$-0.278375\pi$
$397$	509.231			1.28270			0.641349	+	0.767249i	$0.278375\pi$
$398$	361.339			0.907888
$399$	83.5994	−	710.189i	0.209522	−	1.77992i
$400$	74.5644			0.186411
$401$	29.7568			0.0742065			0.0371033	−	0.999311i	$-0.488187\pi$
$401$	29.7568			0.0742065			0.0371033	+	0.999311i	$0.488187\pi$
$402$			267.558i			0.665568i
$403$		−	77.6201i		−	0.192606i
$404$	−262.549			−0.649873
$405$			219.641i			0.542324i
$406$	−78.5917	−	9.25137i	−0.193576	−	0.0227866i
$407$			721.191i			1.77197i
$408$	776.936			1.90426
$409$			9.28024i			0.0226901i	0.999936	+	0.0113450i	$0.00361132\pi$
$409$			9.28024i			0.0226901i	−0.999936	+	0.0113450i	$0.996389\pi$
$410$	−94.5553	−	89.5307i	−0.230623	−	0.218368i
$411$		−	266.233i		−	0.647768i
$412$		−	338.203i		−	0.820881i
$413$	145.341	+	17.1088i	0.351916	+	0.0414256i
$414$	−7.60076			−0.0183593
$415$	−525.317			−1.26583
$416$	−144.467			−0.347278
$417$		−	108.936i		−	0.261237i
$418$		−	452.817i		−	1.08329i
$419$		−	156.674i		−	0.373924i	−0.982367	−	0.186962i	$-0.940136\pi$
$419$		−	156.674i		−	0.373924i	0.982367	−	0.186962i	$-0.0598641\pi$
$420$	−289.982	−	34.1350i	−0.690433	−	0.0812739i
$421$			149.739i			0.355675i	0.984060	+	0.177838i	$0.0569102\pi$
$421$			149.739i			0.355675i	−0.984060	+	0.177838i	$0.943090\pi$
$422$			130.031i			0.308131i
$423$	528.601			1.24965
$424$		−	484.520i		−	1.14274i
$425$	−378.088			−0.889619
$426$			471.596i			1.10703i
$427$	524.343	+	61.7227i	1.22797	+	0.144550i
$428$	268.955			0.628398
$429$			371.900i			0.866901i
$430$			112.734i			0.262173i
$431$	−489.408			−1.13552			−0.567759	−	0.823195i	$-0.692189\pi$
$431$	−489.408			−1.13552			−0.567759	+	0.823195i	$0.692189\pi$
$432$	−25.5040			−0.0590371
$433$			626.973i			1.44798i	0.689813	+	0.723988i	$0.257693\pi$
$433$			626.973i			1.44798i	−0.689813	+	0.723988i	$0.742307\pi$
$434$	123.262	+	14.5097i	0.284013	+	0.0334324i
$435$	−157.183			−0.361341
$436$		−	510.158i		−	1.17009i
$437$	−17.4482			−0.0399273
$438$			83.4240i			0.190466i
$439$	−245.911			−0.560163			−0.280081	−	0.959976i	$-0.590361\pi$
$439$	−245.911			−0.560163			−0.280081	+	0.959976i	$0.590361\pi$
$440$	−431.416			−0.980490
$441$	−484.477	−	115.663i	−1.09859	−	0.262273i
$442$	110.991			0.251111
$443$	−664.744			−1.50055			−0.750275	−	0.661126i	$-0.770079\pi$
$443$	−664.744			−1.50055			−0.750275	+	0.661126i	$0.770079\pi$
$444$	−488.105			−1.09934
$445$		−	225.240i		−	0.506156i
$446$			159.850i			0.358409i
$447$			69.5958i			0.155695i
$448$	10.6386	−	90.3760i	0.0237468	−	0.201732i
$449$	2.79848			0.00623270			0.00311635	−	0.999995i	$-0.499008\pi$
$449$	2.79848			0.00623270			0.00311635	+	0.999995i	$0.499008\pi$
$450$	−151.592			−0.336870
$451$	577.719	+	547.019i	1.28097	+	1.21290i
$452$	−184.225			−0.407577
$453$		−	438.787i		−	0.968624i
$454$	−41.3072			−0.0909851
$455$	−96.6606	−	11.3783i	−0.212441	−	0.0250073i
$456$	715.092			1.56819
$457$			736.912i			1.61250i	0.591576	+	0.806249i	$0.298506\pi$
$457$			736.912i			1.61250i	−0.591576	+	0.806249i	$0.701494\pi$
$458$	240.096			0.524227
$459$	129.321			0.281746
$460$			7.12440i			0.0154878i
$461$			304.316i			0.660121i	0.943960	+	0.330061i	$0.107069\pi$
$461$			304.316i			0.660121i	−0.943960	+	0.330061i	$0.892931\pi$
$462$	−590.582	−	69.5200i	−1.27832	−	0.150476i
$463$			438.392i			0.946851i	0.880834	+	0.473426i	$0.156983\pi$
$463$			438.392i			0.946851i	−0.880834	+	0.473426i	$0.843017\pi$
$464$			56.5245i			0.121820i
$465$	246.523			0.530158
$466$			406.118i			0.871498i
$467$			205.116i			0.439220i	0.975588	+	0.219610i	$0.0704785\pi$
$467$			205.116i			0.439220i	−0.975588	+	0.219610i	$0.929522\pi$
$468$	−133.503			−0.285263
$469$	424.886	+	50.0151i	0.905939	+	0.106642i
$470$			165.157i			0.351399i
$471$	107.165			0.227527
$472$			146.345i			0.310053i
$473$		−	688.790i		−	1.45622i
$474$		−	205.364i		−	0.433256i
$475$	−347.992			−0.732615
$476$	62.2432	−	528.765i	0.130763	−	1.11085i
$477$		−	703.603i		−	1.47506i
$478$		−	121.628i		−	0.254453i
$479$	−181.269			−0.378433			−0.189216	−	0.981935i	$-0.560595\pi$
$479$	−181.269			−0.378433			−0.189216	+	0.981935i	$0.560595\pi$
$480$		−	458.832i		−	0.955900i
$481$	−162.702			−0.338257
$482$		−	266.509i		−	0.552924i
$483$	−2.67879	+	22.7567i	−0.00554615	+	0.0471153i
$484$	766.666			1.58402
$485$			319.313i			0.658377i
$486$	−348.659			−0.717405
$487$	−844.083			−1.73323			−0.866615	−	0.498977i	$-0.833709\pi$
$487$	−844.083			−1.73323			−0.866615	+	0.498977i	$0.833709\pi$
$488$			527.963i			1.08189i
$489$	−874.718			−1.78879
$490$	36.1379	−	151.371i	0.0737508	−	0.308921i
$491$	675.459			1.37568			0.687840	−	0.725862i	$-0.258559\pi$
$491$	675.459			1.37568			0.687840	+	0.725862i	$0.258559\pi$
$492$	−370.225	+	391.003i	−0.752490	+	0.794721i
$493$		−	286.614i		−	0.581368i
$494$	102.156			0.206794
$495$	−626.487			−1.26563
$496$		−	88.6519i		−	0.178734i
$497$	748.900	+	88.1563i	1.50684	+	0.177377i
$498$		−	724.093i		−	1.45400i
$499$		−	676.880i		−	1.35647i	−0.734844	−	0.678236i	$-0.762745\pi$
$499$		−	676.880i		−	1.35647i	0.734844	−	0.678236i	$-0.237255\pi$
$500$			380.293i			0.760585i
$501$	26.8530			0.0535989
$502$			187.109i			0.372726i
$503$	−286.456			−0.569495			−0.284747	−	0.958603i	$-0.591910\pi$
$503$	−286.456			−0.569495			−0.284747	+	0.958603i	$0.591910\pi$
$504$	58.2306	−	494.677i	0.115537	−	0.981502i
$505$		−	277.954i		−	0.550403i
$506$			14.5097i			0.0286752i
$507$	655.947			1.29378
$508$	−214.693			−0.422624
$509$	−381.854			−0.750204			−0.375102	−	0.926984i	$-0.622392\pi$
$509$	−381.854			−0.750204			−0.375102	+	0.926984i	$0.622392\pi$
$510$			352.510i			0.691195i
$511$	132.478	+	15.5946i	0.259253	+	0.0305178i
$512$	−305.000			−0.595703
$513$	119.027			0.232022
$514$	−397.387			−0.773126
$515$	358.047			0.695237
$516$	466.176			0.903442
$517$		−	1009.09i		−	1.95181i
$518$	30.4141	−	258.372i	0.0587145	−	0.498788i
$519$			513.237i			0.988895i
$520$		−	97.3280i		−	0.187169i
$521$	−439.901			−0.844340			−0.422170	−	0.906517i	$-0.638731\pi$
$521$	−439.901			−0.844340			−0.422170	+	0.906517i	$0.638731\pi$
$522$		−	114.916i		−	0.220146i
$523$			627.498i			1.19980i	0.800073	+	0.599902i	$0.204794\pi$
$523$			627.498i			1.19980i	−0.800073	+	0.599902i	$0.795206\pi$
$524$			728.854i			1.39094i
$525$	−53.4265	+	453.866i	−0.101765	+	0.864506i
$526$			281.588i			0.535338i
$527$			449.521i			0.852980i
$528$			424.757i			0.804464i
$529$	−528.441			−0.998943
$530$	219.835			0.414784
$531$			212.517i			0.400220i
$532$	57.2886	−	486.675i	0.107685	−	0.914803i
$533$	−123.408	+	130.334i	−0.231535	+	0.244529i
$534$	310.468			0.581401
$535$			284.735i			0.532215i
$536$			427.819i			0.798170i
$537$		−	196.637i		−	0.366176i
$538$		−	207.214i		−	0.385156i
$539$	−220.797	+	924.856i	−0.409642	+	1.71587i
$540$		−	48.6008i		−	0.0900015i
$541$	791.248			1.46257			0.731283	−	0.682074i	$-0.238922\pi$
$541$	791.248			1.46257			0.731283	+	0.682074i	$0.238922\pi$
$542$			169.626i			0.312963i
$543$	629.111			1.15858
$544$	836.653			1.53796
$545$	540.091			0.990994
$546$	15.6838	−	133.236i	0.0287249	−	0.244022i
$547$			694.771i			1.27015i	0.772451	+	0.635074i	$0.219030\pi$
$547$			694.771i			1.27015i	−0.772451	+	0.635074i	$0.780970\pi$
$548$		−	182.443i		−	0.332924i
$549$			766.690i			1.39652i
$550$			289.385i			0.526154i
$551$		−	263.800i		−	0.478766i
$552$	−22.9138			−0.0415105
$553$	−326.120	−	38.3890i	−0.589728	−	0.0694195i
$554$	85.9636			0.155169
$555$		−	516.744i		−	0.931071i
$556$		−	74.6510i		−	0.134264i
$557$		−	216.837i		−	0.389294i	−0.980873	−	0.194647i	$-0.937644\pi$
$557$		−	216.837i		−	0.389294i	0.980873	−	0.194647i	$-0.0623561\pi$
$558$			180.232i			0.322997i
$559$	155.392			0.277982
$560$	−110.399	−	12.9955i	−0.197140	−	0.0232062i
$561$		−	2153.78i		−	3.83918i
$562$		−	245.074i		−	0.436074i
$563$	850.335			1.51036			0.755182	−	0.655515i	$-0.227548\pi$
$563$	850.335			1.51036			0.755182	+	0.655515i	$0.227548\pi$
$564$	682.955			1.21091
$565$		−	195.034i		−	0.345193i
$566$			203.790i			0.360053i
$567$	−56.5939	+	480.773i	−0.0998128	+	0.847924i
$568$			754.071i			1.32759i
$569$	−21.7932			−0.0383009			−0.0191504	−	0.999817i	$-0.506096\pi$
$569$	−21.7932			−0.0383009			−0.0191504	+	0.999817i	$0.506096\pi$
$570$			324.450i			0.569211i
$571$			248.152i			0.434592i	0.976106	+	0.217296i	$0.0697237\pi$
$571$			248.152i			0.434592i	−0.976106	+	0.217296i	$0.930276\pi$
$572$			254.854i			0.445549i
$573$		−	986.607i		−	1.72183i
$574$	−183.903	−	220.337i	−0.320389	−	0.383863i
$575$	11.1508			0.0193926
$576$	132.147			0.229422
$577$	919.649			1.59384			0.796922	−	0.604082i	$-0.206460\pi$
$577$	919.649			1.59384			0.796922	+	0.604082i	$0.206460\pi$
$578$	−353.780			−0.612077
$579$		−	357.813i		−	0.617984i
$580$	−107.714			−0.185714
$581$	−1149.87	−	135.356i	−1.97912	−	0.232971i
$582$	−440.138			−0.756251
$583$	−1343.16			−2.30388
$584$			133.393i			0.228413i
$585$		−	141.336i		−	0.241600i
$586$	−422.057			−0.720233
$587$	−284.318			−0.484358			−0.242179	−	0.970232i	$-0.577862\pi$
$587$	−284.318			−0.484358			−0.242179	+	0.970232i	$0.577862\pi$
$588$	−625.946	−	149.436i	−1.06453	−	0.254144i
$589$			413.739i			0.702443i
$590$	−66.3992			−0.112541
$591$	217.524			0.368060
$592$	−185.826			−0.313895
$593$	−875.768			−1.47684			−0.738421	−	0.674340i	$-0.764428\pi$
$593$	−875.768			−1.47684			−0.738421	+	0.674340i	$0.764428\pi$
$594$		−	98.9812i		−	0.166635i
$595$	559.789	+	65.8953i	0.940823	+	0.110748i
$596$			47.6923i			0.0800206i
$597$	1581.87			2.64970
$598$	−3.27340			−0.00547392
$599$	−353.405			−0.589991			−0.294995	−	0.955499i	$-0.595318\pi$
$599$	−353.405			−0.589991			−0.294995	+	0.955499i	$0.595318\pi$
$600$	−456.999			−0.761666
$601$	−581.231			−0.967107			−0.483553	−	0.875315i	$-0.660654\pi$
$601$	−581.231			−0.967107			−0.483553	+	0.875315i	$0.660654\pi$
$602$	−29.0477	+	246.764i	−0.0482520	+	0.409908i
$603$			621.264i			1.03029i
$604$		−	300.690i		−	0.497831i
$605$			811.649i			1.34157i
$606$	383.129			0.632226
$607$		−	774.119i		−	1.27532i	−0.770318	−	0.637660i	$-0.779902\pi$
$607$		−	774.119i		−	1.27532i	0.770318	−	0.637660i	$-0.220098\pi$
$608$	770.055			1.26654
$609$	−344.059	−	40.5007i	−0.564957	−	0.0665035i
$610$	−239.546			−0.392699
$611$	227.652			0.372588
$612$	773.155			1.26332
$613$	−524.018			−0.854842			−0.427421	−	0.904053i	$-0.640578\pi$
$613$	−524.018			−0.854842			−0.427421	+	0.904053i	$0.640578\pi$
$614$			402.802i			0.656029i
$615$	−413.944	−	391.948i	−0.673080	−	0.637313i
$616$	−944.327	−	111.161i	−1.53300	−	0.180456i
$617$	−897.684			−1.45492			−0.727459	−	0.686151i	$-0.759299\pi$
$617$	−897.684			−1.45492			−0.727459	+	0.686151i	$0.759299\pi$
$618$			493.529i			0.798590i
$619$		−	605.790i		−	0.978660i	−0.872099	−	0.489330i	$-0.837241\pi$
$619$		−	605.790i		−	0.978660i	0.872099	−	0.489330i	$-0.162759\pi$
$620$	168.936			0.272478
$621$	−3.81401			−0.00614172
$622$	−112.670			−0.181142
$623$	58.0364	−	493.027i	0.0931563	−	0.791376i
$624$	−95.8258			−0.153567
$625$	−29.7841			−0.0476545
$626$	412.188			0.658448
$627$		−	1982.34i		−	3.16163i
$628$	73.4376			0.116939
$629$	942.252			1.49802
$630$	224.444	+	26.4202i	0.356260	+	0.0419369i
$631$	823.492			1.30506			0.652529	−	0.757764i	$-0.273708\pi$
$631$	823.492			1.30506			0.652529	+	0.757764i	$0.273708\pi$
$632$		−	328.371i		−	0.519575i
$633$			569.252i			0.899292i
$634$			322.391i			0.508503i
$635$		−	227.290i		−	0.357937i
$636$		−	909.057i		−	1.42934i
$637$	−208.649	−	49.8121i	−0.327549	−	0.0781980i
$638$	−219.372			−0.343843
$639$			1095.03i			1.71367i
$640$		−	377.947i		−	0.590542i
$641$			207.954i			0.324422i	0.986756	+	0.162211i	$0.0518625\pi$
$641$			207.954i			0.324422i	−0.986756	+	0.162211i	$0.948138\pi$
$642$	−392.477			−0.611334
$643$	−1005.93			−1.56444			−0.782218	−	0.623004i	$-0.785912\pi$
$643$	−1005.93			−1.56444			−0.782218	+	0.623004i	$0.785912\pi$
$644$	−1.83571	+	15.5946i	−0.00285048	+	0.0242152i
$645$			493.529i			0.765161i
$646$	−591.615			−0.915813
$647$			1177.11i			1.81934i	0.415335	+	0.909669i	$0.363664\pi$
$647$			1177.11i			1.81934i	−0.415335	+	0.909669i	$0.636336\pi$
$648$	−484.092			−0.747056
$649$	405.690			0.625100
$650$	−65.2856			−0.100439
$651$	539.615	+	63.5205i	0.828902	+	0.0975737i
$652$	−599.423			−0.919360
$653$			492.015i			0.753468i	0.926321	+	0.376734i	$0.122953\pi$
$653$			492.015i			0.753468i	−0.926321	+	0.376734i	$0.877047\pi$
$654$			744.457i			1.13831i
$655$	−771.619			−1.17804
$656$	−140.948	+	148.858i	−0.214859	+	0.226918i
$657$			193.709i			0.294838i
$658$	−42.5553	+	361.513i	−0.0646737	+	0.549412i
$659$		−	490.198i		−	0.743851i	−0.928263	−	0.371925i	$-0.878698\pi$
$659$		−	490.198i		−	0.743851i	0.928263	−	0.371925i	$-0.121302\pi$
$660$	−809.423			−1.22640
$661$			925.986i			1.40089i	0.713708	+	0.700444i	$0.247014\pi$
$661$			925.986i			1.40089i	−0.713708	+	0.700444i	$0.752986\pi$
$662$			320.574i			0.484251i
$663$	485.896			0.732875
$664$		−	1157.81i		−	1.74369i
$665$	515.230	+	60.6500i	0.774782	+	0.0912030i
$666$	377.789			0.567251
$667$			8.45298i			0.0126731i
$668$	18.4017			0.0275475
$669$			699.793i			1.04603i
$670$	−194.109			−0.289715
$671$	1463.59			2.18121
$672$	118.225	−	1004.34i	0.175930	−	1.49455i
$673$		−	750.563i		−	1.11525i	−0.830093	−	0.557625i	$-0.811713\pi$
$673$		−	750.563i		−	1.11525i	0.830093	−	0.557625i	$-0.188287\pi$
$674$	−264.018			−0.391718
$675$	−76.0676			−0.112693
$676$	449.505			0.664948
$677$		−	208.540i		−	0.308035i	−0.988068	−	0.154017i	$-0.950779\pi$
$677$		−	208.540i		−	0.308035i	0.988068	−	0.154017i	$-0.0492212\pi$
$678$	268.834			0.396510
$679$	−82.2758	+	698.944i	−0.121172	+	1.02937i
$680$			563.654i			0.828904i
$681$	−180.835			−0.265543
$682$	344.059			0.504485
$683$			693.080i			1.01476i	0.861723	+	0.507379i	$0.169386\pi$
$683$			693.080i			1.01476i	−0.861723	+	0.507379i	$0.830614\pi$
$684$	711.612			1.04037
$685$	193.147			0.281967
$686$	118.105	−	322.025i	0.172165	−	0.469424i
$687$	1051.09			1.52997
$688$	177.477			0.257961
$689$		−	303.019i		−	0.439795i
$690$		−	10.3964i		−	0.0150672i
$691$	−345.402			−0.499858			−0.249929	−	0.968264i	$-0.580407\pi$
$691$	−345.402			−0.499858			−0.249929	+	0.968264i	$0.580407\pi$
$692$			351.708i			0.508249i
$693$	−1371.32	−	161.424i	−1.97881	−	0.232935i
$694$			70.4285i			0.101482i
$695$	79.0311			0.113714
$696$		−	346.434i		−	0.497750i
$697$	714.693	−	754.803i	1.02538	−	1.08293i
$698$		−	516.862i		−	0.740489i
$699$			1777.90i			2.54350i
$700$	−36.6119	+	311.023i	−0.0523027	+	0.444319i
$701$	−604.359			−0.862138			−0.431069	−	0.902319i	$-0.641864\pi$
$701$	−604.359			−0.862138			−0.431069	+	0.902319i	$0.641864\pi$
$702$	22.3303			0.0318095
$703$	867.249			1.23364
$704$		−	252.265i		−	0.358332i
$705$			723.026i			1.02557i
$706$			289.266i			0.409725i
$707$	71.6189	−	608.413i	0.101300	−	0.860556i
$708$			274.572i			0.387814i
$709$		−	581.369i		−	0.819984i	−0.912089	−	0.409992i	$-0.865531\pi$
$709$		−	581.369i		−	0.819984i	0.912089	−	0.409992i	$-0.134469\pi$
$710$	−342.135			−0.481880
$711$		−	476.849i		−	0.670674i
$712$	496.431			0.697235
$713$		−	13.2575i		−	0.0185940i
$714$	−90.8294	+	771.609i	−0.127212	+	1.08068i
$715$	−269.808			−0.377353
$716$		−	134.750i		−	0.188199i
$717$		−	532.465i		−	0.742629i
$718$	606.450			0.844638
$719$	−320.556			−0.445836			−0.222918	−	0.974837i	$-0.571558\pi$
$719$	−320.556			−0.445836			−0.222918	+	0.974837i	$0.571558\pi$
$720$		−	161.424i		−	0.224200i
$721$	783.729	+	92.2562i	1.08700	+	0.127956i
$722$	−183.523			−0.254187
$723$		−	1166.72i		−	1.61373i
$724$	431.114			0.595461
$725$			168.589i			0.232536i
$726$	−1118.77			−1.54101
$727$	−830.527			−1.14240			−0.571202	−	0.820810i	$-0.693523\pi$
$727$	−830.527			−1.14240			−0.571202	+	0.820810i	$0.693523\pi$
$728$	25.0780	−	213.041i	0.0344478	−	0.292639i
$729$	−903.955			−1.23999
$730$	−60.5227			−0.0829078
$731$	−899.920			−1.23108
$732$			990.565i			1.35323i
$733$		−	1033.69i		−	1.41022i	−0.709096	−	0.705112i	$-0.750897\pi$
$733$		−	1033.69i		−	1.41022i	0.709096	−	0.705112i	$-0.249103\pi$
$734$			443.813i			0.604650i
$735$	158.204	−	662.673i	0.215244	−	0.901596i
$736$	−24.6750			−0.0335258
$737$	1185.98			1.60920
$738$	286.551	−	302.633i	0.388281	−	0.410072i
$739$	224.330			0.303559			0.151780	−	0.988414i	$-0.451500\pi$
$739$	224.330			0.303559			0.151780	+	0.988414i	$0.451500\pi$
$740$		−	354.112i		−	0.478530i
$741$	447.219			0.603534
$742$	481.198	+	56.6439i	0.648514	+	0.0763395i
$743$	350.661			0.471952			0.235976	−	0.971759i	$-0.424171\pi$
$743$	350.661			0.471952			0.235976	+	0.971759i	$0.424171\pi$
$744$			543.341i			0.730297i
$745$	−50.4906			−0.0677726
$746$	−92.4682			−0.123952
$747$		−	1681.33i		−	2.25077i
$748$		−	1475.93i		−	1.97317i
$749$	−73.3663	+	623.257i	−0.0979524	+	0.832119i
$750$		−	554.949i		−	0.739932i
$751$		−	378.916i		−	0.504548i	−0.967656	−	0.252274i	$-0.918822\pi$
$751$		−	378.916i		−	0.504548i	0.967656	−	0.252274i	$-0.0811784\pi$
$752$	260.007			0.345753
$753$			819.125i			1.08781i
$754$		−	49.4906i		−	0.0656374i
$755$	318.333			0.421633
$756$	12.5227	−	106.382i	0.0165645	−	0.140717i
$757$		−	1274.27i		−	1.68332i	−0.540008	−	0.841660i	$-0.681579\pi$
$757$		−	1274.27i		−	1.68332i	0.540008	−	0.841660i	$-0.318421\pi$
$758$	325.441			0.429342
$759$			63.5205i			0.0836897i
$760$			518.788i			0.682615i
$761$		−	1364.03i		−	1.79242i	−0.443633	−	0.896209i	$-0.646311\pi$
$761$		−	1364.03i		−	1.79242i	0.443633	−	0.896209i	$-0.353689\pi$
$762$	313.295			0.411148
$763$	1182.21	+	139.163i	1.54942	+	0.182389i
$764$		−	676.098i		−	0.884945i
$765$			818.519i			1.06996i
$766$	545.025			0.711521
$767$			91.5241i			0.119327i
$768$	748.604			0.974745
$769$			978.653i			1.27263i	0.771429	+	0.636315i	$0.219542\pi$
$769$			978.653i			1.27263i	−0.771429	+	0.636315i	$0.780458\pi$
$770$	50.4356	−	428.458i	0.0655008	−	0.556438i
$771$	−1739.68			−2.25639
$772$		−	245.200i		−	0.317617i
$773$	226.445			0.292943			0.146472	−	0.989215i	$-0.453208\pi$
$773$	226.445			0.292943			0.146472	+	0.989215i	$0.453208\pi$
$774$	−360.817			−0.466171
$775$		−	264.411i		−	0.341176i
$776$	−703.770			−0.906920
$777$	133.147	−	1131.10i	0.171360	−	1.45573i
$778$	−137.964			−0.177331
$779$	657.804	−	694.721i	0.844421	−	0.891811i
$780$		−	182.607i		−	0.234111i
$781$	2090.40			2.67656
$782$	18.9572			0.0242420
$783$		−	57.6641i		−	0.0736450i
$784$	−238.303	−	56.8917i	−0.303958	−	0.0725660i
$785$			77.7465i			0.0990402i
$786$		−	1063.59i		−	1.35317i
$787$			609.986i			0.775078i	0.921853	+	0.387539i	$0.126675\pi$
$787$			609.986i			0.775078i	−0.921853	+	0.387539i	$0.873325\pi$
$788$	149.064			0.189167
$789$			1232.73i			1.56240i
$790$	148.988			0.188592
$791$	50.2535	−	426.911i	0.0635316	−	0.539710i
$792$		−	1380.79i		−	1.74342i
$793$			330.188i			0.416379i
$794$	−509.231			−0.641349
$795$	962.395			1.21056
$796$	1084.02			1.36183
$797$		−	329.010i		−	0.412810i	−0.978467	−	0.206405i	$-0.933824\pi$
$797$		−	329.010i		−	0.412810i	0.978467	−	0.206405i	$-0.0661764\pi$
$798$	−83.5994	+	710.189i	−0.104761	+	0.889961i
$799$	−1318.40			−1.65006
$800$	−492.125			−0.615156
$801$	720.900			0.900000
$802$	−29.7568			−0.0371033
$803$	369.785			0.460504
$804$			802.675i			0.998352i
$805$	−16.5096	−	1.94342i	−0.0205088	−	0.00241418i
$806$			77.6201i			0.0963029i
$807$		−	907.141i		−	1.12409i
$808$	612.614			0.758185
$809$		−	1030.94i		−	1.27434i	−0.770724	−	0.637169i	$-0.780105\pi$
$809$		−	1030.94i		−	1.27434i	0.770724	−	0.637169i	$-0.219895\pi$
$810$		−	219.641i		−	0.271162i
$811$		−	1254.91i		−	1.54736i	−0.633576	−	0.773680i	$-0.718414\pi$
$811$		−	1254.91i		−	1.54736i	0.633576	−	0.773680i	$-0.281586\pi$
$812$	−235.775	−	27.7541i	−0.290363	−	0.0341799i
$813$			742.589i			0.913394i
$814$		−	721.191i		−	0.885984i
$815$		−	634.593i		−	0.778642i
$816$	554.955			0.680091
$817$	−828.287			−1.01381
$818$		−	9.28024i		−	0.0113450i
$819$	36.4174	−	309.371i	0.0444657	−	0.377742i
$820$	−283.666	−	268.592i	−0.345934	−	0.327551i
$821$	−83.4303			−0.101620			−0.0508102	−	0.998708i	$-0.516180\pi$
$821$	−83.4303			−0.101620			−0.0508102	+	0.998708i	$0.516180\pi$
$822$			266.233i			0.323884i
$823$			1216.66i			1.47833i	0.673526	+	0.739164i	$0.264779\pi$
$823$			1216.66i			1.47833i	−0.673526	+	0.739164i	$0.735221\pi$
$824$			789.141i			0.957695i
$825$			1266.87i			1.53560i
$826$	−145.341	−	17.1088i	−0.175958	−	0.0207128i
$827$		−	1278.87i		−	1.54639i	−0.634168	−	0.773195i	$-0.718657\pi$
$827$		−	1278.87i		−	1.54639i	0.634168	−	0.773195i	$-0.281343\pi$
$828$	−22.8023			−0.0275390
$829$			191.086i			0.230502i	0.993336	+	0.115251i	$0.0367672\pi$
$829$			191.086i			0.230502i	−0.993336	+	0.115251i	$0.963233\pi$
$830$	525.317			0.632913
$831$	376.332			0.452866
$832$	56.9114			0.0684032
$833$	1208.34	+	288.476i	1.45059	+	0.346310i
$834$			108.936i			0.130618i
$835$			19.4814i			0.0233311i
$836$		−	1358.45i		−	1.62494i
$837$			90.4392i			0.108052i
$838$			156.674i			0.186962i
$839$	526.074			0.627025			0.313513	−	0.949584i	$-0.398494\pi$
$839$	526.074			0.627025			0.313513	+	0.949584i	$0.398494\pi$
$840$	676.624	+	79.6484i	0.805505	+	0.0948195i
$841$	713.199			0.848037
$842$		−	149.739i		−	0.177838i
$843$		−	1072.88i		−	1.27270i
$844$			390.094i			0.462197i
$845$			475.879i			0.563170i
$846$	−528.601			−0.624824
$847$	−209.134	+	1776.62i	−0.246911	+	2.09754i
$848$		−	346.086i		−	0.408120i
$849$			892.152i			1.05083i
$850$	378.088			0.444809
$851$	−27.7894			−0.0326550
$852$			1414.79i			1.66055i
$853$		−	336.906i		−	0.394966i	−0.980306	−	0.197483i	$-0.936723\pi$
$853$		−	336.906i		−	0.394966i	0.980306	−	0.197483i	$-0.0632768\pi$
$854$	−524.343	−	61.7227i	−0.613985	−	0.0722748i
$855$			753.365i			0.881129i
$856$	−627.561			−0.733132
$857$		−	155.873i		−	0.181882i	−0.995856	−	0.0909410i	$-0.971013\pi$
$857$		−	155.873i		−	0.181882i	0.995856	−	0.0909410i	$-0.0289875\pi$
$858$		−	371.900i		−	0.433450i
$859$			694.996i			0.809075i	0.914521	+	0.404538i	$0.132568\pi$
$859$			694.996i			0.809075i	−0.914521	+	0.404538i	$0.867432\pi$
$860$			338.203i			0.393259i
$861$	−805.092	−	964.594i	−0.935066	−	1.12032i
$862$	489.408			0.567759
$863$	−570.174			−0.660689			−0.330344	−	0.943861i	$-0.607165\pi$
$863$	−570.174			−0.660689			−0.330344	+	0.943861i	$0.607165\pi$
$864$	168.326			0.194822
$865$	−372.345			−0.430456
$866$		−	626.973i		−	0.723988i
$867$	−1548.78			−1.78637
$868$	369.785	+	43.5290i	0.426020	+	0.0501486i
$869$	−910.294			−1.04752
$870$	157.183			0.180670
$871$			267.558i			0.307185i
$872$			1190.37i			1.36510i
$873$	−1021.99			−1.17066
$874$	17.4482			0.0199636
$875$	−881.265	−	103.738i	−1.00716	−	0.118557i
$876$			250.272i			0.285699i
$877$	−1146.20			−1.30696			−0.653479	−	0.756944i	$-0.726691\pi$
$877$	−1146.20			−1.30696			−0.653479	+	0.756944i	$0.726691\pi$
$878$	245.911			0.280081
$879$	−1847.68			−2.10203
$880$	−308.154			−0.350175
$881$			749.703i			0.850968i	0.904966	+	0.425484i	$0.139896\pi$
$881$			749.703i			0.850968i	−0.904966	+	0.425484i	$0.860104\pi$
$882$	484.477	+	115.663i	0.549294	+	0.131137i
$883$		−	1054.71i		−	1.19446i	−0.802069	−	0.597231i	$-0.796267\pi$
$883$		−	1054.71i		−	1.19446i	0.802069	−	0.597231i	$-0.203733\pi$
$884$	332.973			0.376666
$885$	−290.683			−0.328455
$886$	664.744			0.750275
$887$	27.7211			0.0312527			0.0156263	−	0.999878i	$-0.495026\pi$
$887$	27.7211			0.0312527			0.0156263	+	0.999878i	$0.495026\pi$
$888$	1138.91			1.28256
$889$	58.5647	−	497.516i	0.0658771	−	0.559635i
$890$			225.240i			0.253078i
$891$			1341.98i			1.50615i
$892$			479.551i			0.537613i
$893$	−1213.45			−1.35885
$894$		−	69.5958i		−	0.0778477i
$895$	142.657			0.159393
$896$	97.3837	−	827.288i	0.108687	−	0.923312i
$897$	−14.3303			−0.0159758
$898$	−2.79848			−0.00311635
$899$	200.440			0.222959
$900$	−454.775			−0.505306
$901$			1754.87i			1.94769i
$902$	−577.719	−	547.019i	−0.640487	−	0.606452i
$903$	−127.165	+	1080.29i	−0.140825	+	1.19633i
$904$	429.858			0.475507
$905$			456.409i			0.504320i
$906$			438.787i			0.484312i
$907$	−491.045			−0.541395			−0.270698	−	0.962664i	$-0.587254\pi$
$907$	−491.045			−0.541395			−0.270698	+	0.962664i	$0.587254\pi$
$908$	−123.922			−0.136478
$909$	889.616			0.978675
$910$	96.6606	+	11.3783i	0.106220	+	0.0125037i
$911$	983.070			1.07911			0.539556	−	0.841950i	$-0.318592\pi$
$911$	983.070			1.07911			0.539556	+	0.841950i	$0.318592\pi$
$912$	510.780			0.560066
$913$	−3209.61			−3.51546
$914$		−	736.912i		−	0.806249i
$915$	−1048.69			−1.14610
$916$	720.288			0.786340
$917$	−1689.00	−	198.819i	−1.84187	−	0.216815i
$918$	−129.321			−0.140873
$919$			643.092i			0.699773i	0.936792	+	0.349887i	$0.113780\pi$
$919$			643.092i			0.699773i	−0.936792	+	0.349887i	$0.886220\pi$
$920$		−	16.6236i		−	0.0180691i
$921$			1763.39i			1.91464i
$922$		−	304.316i		−	0.330061i
$923$			471.596i			0.510938i
$924$	−1771.75	−	208.560i	−1.91747	−	0.225714i
$925$	−554.239			−0.599178
$926$		−	438.392i		−	0.473426i
$927$			1145.96i			1.23620i
$928$		−	373.062i		−	0.402006i
$929$	210.388			0.226467			0.113234	−	0.993568i	$-0.463879\pi$
$929$	210.388			0.226467			0.113234	+	0.993568i	$0.463879\pi$
$930$	−246.523			−0.265079
$931$	1112.16	+	265.514i	1.19459	+	0.285192i
$932$			1218.35i			1.30725i
$933$	−493.248			−0.528669
$934$		−	205.116i		−	0.219610i
$935$	1562.53			1.67116
$936$	311.507			0.332807
$937$	329.915			0.352098			0.176049	−	0.984381i	$-0.443668\pi$
$937$	329.915			0.352098			0.176049	+	0.984381i	$0.443668\pi$
$938$	−424.886	−	50.0151i	−0.452970	−	0.0533210i
$939$	1804.48			1.92170
$940$			495.472i			0.527098i
$941$		−	947.198i		−	1.00659i	−0.864116	−	0.503293i	$-0.832121\pi$
$941$		−	947.198i		−	1.00659i	0.864116	−	0.503293i	$-0.167879\pi$
$942$	−107.165			−0.113763
$943$	−21.0781	+	22.2610i	−0.0223522	+	0.0236066i
$944$			104.532i			0.110733i
$945$	112.624	+	13.2575i	0.119179	+	0.0140291i
$946$			688.790i			0.728108i
$947$	−386.595			−0.408232			−0.204116	−	0.978947i	$-0.565432\pi$
$947$	−386.595			−0.408232			−0.204116	+	0.978947i	$0.565432\pi$
$948$		−	616.091i		−	0.649885i
$949$			83.4240i			0.0879073i
$950$	347.992			0.366308
$951$			1411.36i			1.48408i
$952$	−145.234	+	1233.78i	−0.152557	+	1.29599i
$953$	−979.840			−1.02816			−0.514082	−	0.857741i	$-0.671867\pi$
$953$	−979.840			−1.02816			−0.514082	+	0.857741i	$0.671867\pi$
$954$			703.603i			0.737529i
$955$	715.767			0.749495
$956$		−	364.885i		−	0.381679i
$957$	−960.367			−1.00352
$958$	181.269			0.189216
$959$	422.780	+	49.7673i	0.440855	+	0.0518950i
$960$			180.752i			0.188283i
$961$	646.633			0.672875
$962$	162.702			0.169129
$963$	−911.321			−0.946336
$964$		−	799.528i		−	0.829386i
$965$	259.587			0.269002
$966$	2.67879	−	22.7567i	0.00277307	−	0.0235576i
$967$			84.0297i			0.0868973i	0.999056	+	0.0434486i	$0.0138345\pi$
$967$			84.0297i			0.0868973i	−0.999056	+	0.0434486i	$0.986166\pi$
$968$	−1788.89			−1.84802
$969$	−2589.97			−2.67283
$970$		−	319.313i		−	0.329188i
$971$	−147.565			−0.151972			−0.0759861	−	0.997109i	$-0.524210\pi$
$971$	−147.565			−0.151972			−0.0759861	+	0.997109i	$0.524210\pi$
$972$	−1045.98			−1.07611
$973$	172.991	+	20.3635i	0.177792	+	0.0209286i
$974$	844.083			0.866615
$975$	−285.808			−0.293136
$976$			377.117i			0.386390i
$977$			116.077i			0.118810i	0.998234	+	0.0594050i	$0.0189203\pi$
$977$			116.077i			0.118810i	−0.998234	+	0.0594050i	$0.981080\pi$
$978$	874.718			0.894395
$979$		−	1376.18i		−	1.40570i
$980$	108.414	−	454.114i	0.110626	−	0.463381i
$981$			1728.61i			1.76209i
$982$	−675.459			−0.687840
$983$			1429.37i			1.45409i	0.686589	+	0.727046i	$0.259107\pi$
$983$			1429.37i			1.45409i	−0.686589	+	0.727046i	$0.740893\pi$
$984$	863.858	−	912.339i	0.877905	−	0.927174i
$985$			157.810i			0.160213i
$986$			286.614i			0.290684i
$987$	−186.299	+	1582.63i	−0.188752	+	1.60348i
$988$	306.468			0.310190
$989$	26.5409			0.0268361
$990$	626.487			0.632815
$991$		−	1138.18i		−	1.14852i	−0.818673	−	0.574261i	$-0.805290\pi$
$991$		−	1138.18i		−	1.14852i	0.818673	−	0.574261i	$-0.194710\pi$
$992$			585.103i			0.589821i
$993$			1403.41i			1.41330i
$994$	−748.900	−	88.1563i	−0.753421	−	0.0886884i
$995$			1147.62i			1.15339i
$996$		−	2172.28i		−	2.18100i
$997$	456.333			0.457706			0.228853	−	0.973461i	$-0.426502\pi$
$997$	456.333			0.457706			0.228853	+	0.973461i	$0.426502\pi$
$998$			676.880i			0.678236i
$999$	189.572			0.189762

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	287.3.d.c.286.1	✓	8
7.6	odd	2	inner	287.3.d.c.286.8	yes	8
41.40	even	2	inner	287.3.d.c.286.7	yes	8
287.286	odd	2	inner	287.3.d.c.286.2	yes	8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
287.3.d.c.286.1	✓	8	1.1	even	1	trivial
287.3.d.c.286.2	yes	8	287.286	odd	2	inner
287.3.d.c.286.7	yes	8	41.40	even	2	inner
287.3.d.c.286.8	yes	8	7.6	odd	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)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} -4.37780 q^{3} -3.00000 q^{4} -3.17602i q^{5} +4.37780 q^{6} +(0.818350 - 6.95200i) q^{7} +7.00000 q^{8} +10.1652 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} -4.37780 q^{3} -3.00000 q^{4} -3.17602i q^{5} +4.37780 q^{6} +(0.818350 - 6.95200i) q^{7} +7.00000 q^{8} +10.1652 q^{9} +3.17602i q^{10} -19.4050i q^{11} +13.1334 q^{12} +4.37780 q^{13} +(-0.818350 + 6.95200i) q^{14} +13.9040i q^{15} +5.00000 q^{16} -25.3531 q^{17} -10.1652 q^{18} -23.3350 q^{19} +9.52807i q^{20} +(-3.58258 + 30.4345i) q^{21} +19.4050i q^{22} +0.747727 q^{23} -30.6446 q^{24} +14.9129 q^{25} -4.37780 q^{26} -5.10080 q^{27} +(-2.45505 + 20.8560i) q^{28} +11.3049i q^{29} -13.9040i q^{30} -17.7304i q^{31} -33.0000 q^{32} +84.9514i q^{33} +25.3531 q^{34} +(-22.0797 - 2.59910i) q^{35} -30.4955 q^{36} -37.1652 q^{37} +23.3350 q^{38} -19.1652 q^{39} -22.2322i q^{40} +(-28.1896 + 29.7716i) q^{41} +(3.58258 - 30.4345i) q^{42} +35.4955 q^{43} +58.2151i q^{44} -32.2848i q^{45} -0.747727 q^{46} +52.0013 q^{47} -21.8890 q^{48} +(-47.6606 - 11.3783i) q^{49} -14.9129 q^{50} +110.991 q^{51} -13.1334 q^{52} -69.2172i q^{53} +5.10080 q^{54} -61.6308 q^{55} +(5.72845 - 48.6640i) q^{56} +102.156 q^{57} -11.3049i q^{58} +20.9064i q^{59} -41.7120i q^{60} +75.4233i q^{61} +17.7304i q^{62} +(8.31865 - 70.6681i) q^{63} +13.0000 q^{64} -13.9040i q^{65} -84.9514i q^{66} +61.1170i q^{67} +76.0593 q^{68} -3.27340 q^{69} +(22.0797 + 2.59910i) q^{70} +107.724i q^{71} +71.1561 q^{72} +19.0561i q^{73} +37.1652 q^{74} -65.2856 q^{75} +70.0050 q^{76} +(-134.904 - 15.8801i) q^{77} +19.1652 q^{78} -46.9102i q^{79} -15.8801i q^{80} -69.1561 q^{81} +(28.1896 - 29.7716i) q^{82} -165.401i q^{83} +(10.7477 - 91.3034i) q^{84} +80.5221i q^{85} -35.4955 q^{86} -49.4906i q^{87} -135.835i q^{88} +70.9187 q^{89} +32.2848i q^{90} +(3.58258 - 30.4345i) q^{91} -2.24318 q^{92} +77.6201i q^{93} -52.0013 q^{94} +74.1125i q^{95} +144.467 q^{96} -100.539 q^{97} +(47.6606 + 11.3783i) q^{98} -197.255i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 8 q^{2} - 24 q^{4} + 56 q^{8} + 8 q^{9}+O(q^{10}) \) 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

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Database

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