LMFDB - Embedded newform 287.3.b.a.83.14

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [287,3,Mod(83,287)]

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, 0]))

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

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

chi := DirichletCharacter("287.83");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 287 = 7 \cdot 41 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	287.b (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:	$52$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			83.14
Character	$\chi$	$=$	287.83
Dual form			287.3.b.a.83.13

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.91914 q^{2} +2.33237i q^{3} -0.316896 q^{4} +6.26237i q^{5} -4.47614i q^{6} +(-1.97015 + 6.71703i) q^{7} +8.28473 q^{8} +3.56006 q^{9} +O(q^{10})$	\(q-1.91914 q^{2} +2.33237i q^{3} -0.316896 q^{4} +6.26237i q^{5} -4.47614i q^{6} +(-1.97015 + 6.71703i) q^{7} +8.28473 q^{8} +3.56006 q^{9} -12.0184i q^{10} +12.5496 q^{11} -0.739117i q^{12} +23.6377i q^{13} +(3.78100 - 12.8909i) q^{14} -14.6061 q^{15} -14.6320 q^{16} +9.94729i q^{17} -6.83227 q^{18} -24.1194i q^{19} -1.98452i q^{20} +(-15.6666 - 4.59512i) q^{21} -24.0845 q^{22} +6.30871 q^{23} +19.3230i q^{24} -14.2172 q^{25} -45.3640i q^{26} +29.2947i q^{27} +(0.624333 - 2.12860i) q^{28} -26.6427 q^{29} +28.0312 q^{30} -5.57725i q^{31} -5.05807 q^{32} +29.2704i q^{33} -19.0903i q^{34} +(-42.0645 - 12.3378i) q^{35} -1.12817 q^{36} +71.0302 q^{37} +46.2886i q^{38} -55.1317 q^{39} +51.8820i q^{40} -6.40312i q^{41} +(30.0664 + 8.81869i) q^{42} -60.7101 q^{43} -3.97693 q^{44} +22.2944i q^{45} -12.1073 q^{46} -50.6819i q^{47} -34.1272i q^{48} +(-41.2370 - 26.4672i) q^{49} +27.2849 q^{50} -23.2007 q^{51} -7.49067i q^{52} -86.4120 q^{53} -56.2206i q^{54} +78.5905i q^{55} +(-16.3222 + 55.6488i) q^{56} +56.2554 q^{57} +51.1311 q^{58} +37.3809i q^{59} +4.62862 q^{60} -73.3194i q^{61} +10.7035i q^{62} +(-7.01388 + 23.9131i) q^{63} +68.2351 q^{64} -148.028 q^{65} -56.1740i q^{66} +110.569 q^{67} -3.15225i q^{68} +14.7142i q^{69} +(80.7277 + 23.6780i) q^{70} +103.259 q^{71} +29.4942 q^{72} +81.2730i q^{73} -136.317 q^{74} -33.1598i q^{75} +7.64335i q^{76} +(-24.7247 + 84.2963i) q^{77} +105.806 q^{78} +94.1852 q^{79} -91.6309i q^{80} -36.2854 q^{81} +12.2885i q^{82} +0.958746i q^{83} +(4.96467 + 1.45617i) q^{84} -62.2936 q^{85} +116.511 q^{86} -62.1405i q^{87} +103.970 q^{88} -115.196i q^{89} -42.7862i q^{90} +(-158.775 - 46.5698i) q^{91} -1.99920 q^{92} +13.0082 q^{93} +97.2657i q^{94} +151.045 q^{95} -11.7973i q^{96} -76.5913i q^{97} +(79.1396 + 50.7942i) q^{98} +44.6775 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 52 q + 2 q^{2} + 90 q^{4} + 12 q^{7} - 2 q^{8} - 140 q^{9}+O(q^{10}) $ 52 * q + 2 * q^2 + 90 * q^4 + 12 * q^7 - 2 * q^8 - 140 * q^9	$ 52 q + 2 q^{2} + 90 q^{4} + 12 q^{7} - 2 q^{8} - 140 q^{9} + 24 q^{11} - 14 q^{14} + 44 q^{15} + 194 q^{16} + 70 q^{18} - 16 q^{21} - 48 q^{22} - 80 q^{23} - 304 q^{25} + 64 q^{28} - 12 q^{29} + 64 q^{30} - 166 q^{32} + 30 q^{35} - 70 q^{36} + 36 q^{37} - 68 q^{39} + 164 q^{42} - 172 q^{43} + 72 q^{44} + 68 q^{46} - 172 q^{49} - 234 q^{50} + 156 q^{51} + 64 q^{53} - 234 q^{56} + 140 q^{57} - 556 q^{58} + 152 q^{60} - 130 q^{63} + 334 q^{64} - 76 q^{65} + 160 q^{67} + 202 q^{70} - 408 q^{71} - 40 q^{72} + 398 q^{74} - 248 q^{77} + 390 q^{78} + 264 q^{79} - 116 q^{81} - 418 q^{84} + 232 q^{85} + 368 q^{86} - 220 q^{88} + 32 q^{91} - 74 q^{92} + 240 q^{93} - 44 q^{95} + 838 q^{98} - 24 q^{99}+O(q^{100}) $ 52 * q + 2 * q^2 + 90 * q^4 + 12 * q^7 - 2 * q^8 - 140 * q^9 + 24 * q^11 - 14 * q^14 + 44 * q^15 + 194 * q^16 + 70 * q^18 - 16 * q^21 - 48 * q^22 - 80 * q^23 - 304 * q^25 + 64 * q^28 - 12 * q^29 + 64 * q^30 - 166 * q^32 + 30 * q^35 - 70 * q^36 + 36 * q^37 - 68 * q^39 + 164 * q^42 - 172 * q^43 + 72 * q^44 + 68 * q^46 - 172 * q^49 - 234 * q^50 + 156 * q^51 + 64 * q^53 - 234 * q^56 + 140 * q^57 - 556 * q^58 + 152 * q^60 - 130 * q^63 + 334 * q^64 - 76 * q^65 + 160 * q^67 + 202 * q^70 - 408 * q^71 - 40 * q^72 + 398 * q^74 - 248 * q^77 + 390 * q^78 + 264 * q^79 - 116 * q^81 - 418 * q^84 + 232 * q^85 + 368 * q^86 - 220 * q^88 + 32 * q^91 - 74 * q^92 + 240 * q^93 - 44 * q^95 + 838 * q^98 - 24 * q^99

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 $

$2$	−1.91914			−0.959571			−0.479785	−	0.877386i	$-0.659285\pi$
$2$	−1.91914			−0.959571			−0.479785	+	0.877386i	$0.659285\pi$
$3$			2.33237i			0.777456i	0.921353	+	0.388728i	$0.127085\pi$
$3$			2.33237i			0.777456i	−0.921353	+	0.388728i	$0.872915\pi$
$4$	−0.316896			−0.0792239
$5$			6.26237i			1.25247i	0.779633	+	0.626237i	$0.215406\pi$
$5$			6.26237i			1.25247i	−0.779633	+	0.626237i	$0.784594\pi$
$6$		−	4.47614i		−	0.746024i
$7$	−1.97015	+	6.71703i	−0.281451	+	0.959576i
$7$	−1.97015	+	6.71703i	−0.281451	+	0.959576i
$8$	8.28473			1.03559
$9$	3.56006			0.395563
$10$		−	12.0184i		−	1.20184i
$11$	12.5496			1.14088			0.570438	−	0.821340i	$-0.306773\pi$
$11$	12.5496			1.14088			0.570438	+	0.821340i	$0.306773\pi$
$12$		−	0.739117i		−	0.0615931i
$13$			23.6377i			1.81828i	0.416488	+	0.909141i	$0.363261\pi$
$13$			23.6377i			1.81828i	−0.416488	+	0.909141i	$0.636739\pi$
$14$	3.78100	−	12.8909i	0.270072	−	0.920781i
$15$	−14.6061			−0.973742
$16$	−14.6320			−0.914500
$17$			9.94729i			0.585135i	0.956245	+	0.292567i	$0.0945096\pi$
$17$			9.94729i			0.585135i	−0.956245	+	0.292567i	$0.905490\pi$
$18$	−6.83227			−0.379570
$19$		−	24.1194i		−	1.26944i	−0.772740	−	0.634722i	$-0.781115\pi$
$19$		−	24.1194i		−	1.26944i	0.772740	−	0.634722i	$-0.218885\pi$
$20$		−	1.98452i		−	0.0992258i
$21$	−15.6666	−	4.59512i	−0.746028	−	0.218815i
$22$	−24.0845			−1.09475
$23$	6.30871			0.274292			0.137146	−	0.990551i	$-0.456207\pi$
$23$	6.30871			0.274292			0.137146	+	0.990551i	$0.456207\pi$
$24$			19.3230i			0.805127i
$25$	−14.2172			−0.568689
$26$		−	45.3640i		−	1.74477i
$27$			29.2947i			1.08499i
$28$	0.624333	−	2.12860i	0.0222976	−	0.0760213i
$29$	−26.6427			−0.918713			−0.459356	−	0.888252i	$-0.651920\pi$
$29$	−26.6427			−0.918713			−0.459356	+	0.888252i	$0.651920\pi$
$30$	28.0312			0.934375
$31$		−	5.57725i		−	0.179911i	−0.995946	−	0.0899557i	$-0.971327\pi$
$31$		−	5.57725i		−	0.179911i	0.995946	−	0.0899557i	$-0.0286725\pi$
$32$	−5.05807			−0.158065
$33$			29.2704i			0.886981i
$34$		−	19.0903i		−	0.561478i
$35$	−42.0645	−	12.3378i	−1.20184	−	0.352509i
$36$	−1.12817			−0.0313380
$37$	71.0302			1.91974			0.959868	−	0.280453i	$-0.0904848\pi$
$37$	71.0302			1.91974			0.959868	+	0.280453i	$0.0904848\pi$
$38$			46.2886i			1.21812i
$39$	−55.1317			−1.41363
$40$			51.8820i			1.29705i
$41$		−	6.40312i		−	0.156174i
$41$		−	6.40312i		−	0.156174i
$42$	30.0664	+	8.81869i	0.715866	+	0.209969i
$43$	−60.7101			−1.41186			−0.705931	−	0.708281i	$-0.749471\pi$
$43$	−60.7101			−1.41186			−0.705931	+	0.708281i	$0.749471\pi$
$44$	−3.97693			−0.0903847
$45$			22.2944i			0.495432i
$46$	−12.1073			−0.263202
$47$		−	50.6819i		−	1.07834i	−0.842198	−	0.539169i	$-0.818739\pi$
$47$		−	50.6819i		−	1.07834i	0.842198	−	0.539169i	$-0.181261\pi$
$48$		−	34.1272i		−	0.710983i
$49$	−41.2370	−	26.4672i	−0.841571	−	0.540146i
$50$	27.2849			0.545697
$51$	−23.2007			−0.454916
$52$		−	7.49067i		−	0.144051i
$53$	−86.4120			−1.63042			−0.815208	−	0.579168i	$-0.803377\pi$
$53$	−86.4120			−1.63042			−0.815208	+	0.579168i	$0.803377\pi$
$54$		−	56.2206i		−	1.04112i
$55$			78.5905i			1.42892i
$56$	−16.3222	+	55.6488i	−0.291468	+	0.993729i
$57$	56.2554			0.986937
$58$	51.1311			0.881570
$59$			37.3809i			0.633574i	0.948497	+	0.316787i	$0.102604\pi$
$59$			37.3809i			0.633574i	−0.948497	+	0.316787i	$0.897396\pi$
$60$	4.62862			0.0771437
$61$		−	73.3194i		−	1.20196i	−0.799265	−	0.600979i	$-0.794778\pi$
$61$		−	73.3194i		−	1.20196i	0.799265	−	0.600979i	$-0.205222\pi$
$62$			10.7035i			0.172638i
$63$	−7.01388	+	23.9131i	−0.111331	+	0.379572i
$64$	68.2351			1.06617
$65$	−148.028			−2.27735
$66$		−	56.1740i		−	0.851121i
$67$	110.569			1.65028			0.825139	−	0.564930i	$-0.191097\pi$
$67$	110.569			1.65028			0.825139	+	0.564930i	$0.191097\pi$
$68$		−	3.15225i		−	0.0463567i
$69$			14.7142i			0.213249i
$70$	80.7277	+	23.6780i	1.15325	+	0.338258i
$71$	103.259			1.45435			0.727176	−	0.686451i	$-0.240832\pi$
$71$	103.259			1.45435			0.727176	+	0.686451i	$0.240832\pi$
$72$	29.4942			0.409642
$73$			81.2730i			1.11333i	0.830737	+	0.556665i	$0.187919\pi$
$73$			81.2730i			1.11333i	−0.830737	+	0.556665i	$0.812081\pi$
$74$	−136.317			−1.84212
$75$		−	33.1598i		−	0.442130i
$76$			7.64335i			0.100570i
$77$	−24.7247	+	84.2963i	−0.321100	+	1.09476i
$78$	105.806			1.35648
$79$	94.1852			1.19222			0.596109	−	0.802904i	$-0.296713\pi$
$79$	94.1852			1.19222			0.596109	+	0.802904i	$0.296713\pi$
$80$		−	91.6309i		−	1.14539i
$81$	−36.2854			−0.447967
$82$			12.2885i			0.149860i
$83$			0.958746i			0.0115512i	0.999983	+	0.00577558i	$0.00183843\pi$
$83$			0.958746i			0.0115512i	−0.999983	+	0.00577558i	$0.998162\pi$
$84$	4.96467	+	1.45617i	0.0591032	+	0.0173354i
$85$	−62.2936			−0.732866
$86$	116.511			1.35478
$87$		−	62.1405i		−	0.714258i
$88$	103.970			1.18148
$89$		−	115.196i		−	1.29433i	−0.762349	−	0.647166i	$-0.775954\pi$
$89$		−	115.196i		−	1.29433i	0.762349	−	0.647166i	$-0.224046\pi$
$90$		−	42.7862i		−	0.475402i
$91$	−158.775	−	46.5698i	−1.74478	−	0.511757i
$92$	−1.99920			−0.0217304
$93$	13.0082			0.139873
$94$			97.2657i			1.03474i
$95$	151.045			1.58994
$96$		−	11.7973i		−	0.122888i
$97$		−	76.5913i		−	0.789601i	−0.918767	−	0.394800i	$-0.870814\pi$
$97$		−	76.5913i		−	0.789601i	0.918767	−	0.394800i	$-0.129186\pi$
$98$	79.1396	+	50.7942i	0.807547	+	0.518309i
$99$	44.6775			0.451288
$100$	4.50538			0.0450538
$101$		−	79.9095i		−	0.791183i	−0.918426	−	0.395592i	$-0.870540\pi$
$101$		−	79.9095i		−	0.791183i	0.918426	−	0.395592i	$-0.129460\pi$
$102$	44.5255			0.436524
$103$		−	125.144i		−	1.21499i	−0.794322	−	0.607497i	$-0.792174\pi$
$103$		−	125.144i		−	1.21499i	0.794322	−	0.607497i	$-0.207826\pi$
$104$			195.832i			1.88300i
$105$	28.7763	−	98.1098i	0.274060	−	0.934379i
$106$	165.837			1.56450
$107$	−87.0240			−0.813308			−0.406654	−	0.913582i	$-0.633305\pi$
$107$	−87.0240			−0.813308			−0.406654	+	0.913582i	$0.633305\pi$
$108$		−	9.28336i		−	0.0859570i
$109$	110.409			1.01292			0.506462	−	0.862262i	$-0.330953\pi$
$109$	110.409			1.01292			0.506462	+	0.862262i	$0.330953\pi$
$110$		−	150.826i		−	1.37115i
$111$			165.668i			1.49251i
$112$	28.8273	−	98.2835i	0.257386	−	0.877532i
$113$	−30.3267			−0.268378			−0.134189	−	0.990956i	$-0.542843\pi$
$113$	−30.3267			−0.268378			−0.134189	+	0.990956i	$0.542843\pi$
$114$	−107.962			−0.947036
$115$			39.5074i			0.343543i
$116$	8.44294			0.0727840
$117$			84.1516i			0.719245i
$118$		−	71.7392i		−	0.607959i
$119$	−66.8163	−	19.5977i	−0.561481	−	0.164687i
$120$	−121.008			−1.00840
$121$	36.4936			0.301600
$122$			140.710i			1.15336i
$123$	14.9344			0.121418
$124$			1.76741i			0.0142533i
$125$			67.5257i			0.540206i
$126$	13.4606	−	45.8926i	0.106830	−	0.364227i
$127$	124.814			0.982791			0.491396	−	0.870937i	$-0.336487\pi$
$127$	124.814			0.982791			0.491396	+	0.870937i	$0.336487\pi$
$128$	−110.721			−0.865005
$129$		−	141.598i		−	1.09766i
$130$	284.086			2.18528
$131$			137.852i			1.05231i	0.850390	+	0.526153i	$0.176366\pi$
$131$			137.852i			1.05231i	−0.850390	+	0.526153i	$0.823634\pi$
$132$		−	9.27565i		−	0.0702701i
$133$	162.011	+	47.5190i	1.21813	+	0.357286i
$134$	−212.197			−1.58356
$135$	−183.454			−1.35892
$136$			82.4107i			0.605961i
$137$	−116.122			−0.847603			−0.423801	−	0.905755i	$-0.639305\pi$
$137$	−116.122			−0.847603			−0.423801	+	0.905755i	$0.639305\pi$
$138$		−	28.2387i		−	0.204628i
$139$			88.5284i			0.636895i	0.947941	+	0.318447i	$0.103161\pi$
$139$			88.5284i			0.636895i	−0.947941	+	0.318447i	$0.896839\pi$
$140$	13.3301	+	3.90980i	0.0952147	+	0.0279272i
$141$	118.209			0.838359
$142$	−198.169			−1.39555
$143$			296.644i			2.07444i
$144$	−52.0909			−0.361742
$145$		−	166.846i		−	1.15066i
$146$		−	155.974i		−	1.06832i
$147$	61.7311	−	96.1798i	0.419940	−	0.654284i
$148$	−22.5092			−0.152089
$149$	49.4951			0.332182			0.166091	−	0.986110i	$-0.446885\pi$
$149$	49.4951			0.332182			0.166091	+	0.986110i	$0.446885\pi$
$150$			63.6383i			0.424255i
$151$	39.0932			0.258895			0.129448	−	0.991586i	$-0.458680\pi$
$151$	39.0932			0.258895			0.129448	+	0.991586i	$0.458680\pi$
$152$		−	199.823i		−	1.31463i
$153$			35.4130i			0.231458i
$154$	47.4503	−	161.777i	0.308119	−	1.05050i
$155$	34.9268			0.225334
$156$	17.4710			0.111994
$157$		−	84.1980i		−	0.536293i	−0.963378	−	0.268146i	$-0.913589\pi$
$157$		−	84.1980i		−	0.536293i	0.963378	−	0.268146i	$-0.0864111\pi$
$158$	−180.755			−1.14402
$159$		−	201.545i		−	1.26758i
$160$		−	31.6755i		−	0.197972i
$161$	−12.4291	+	42.3758i	−0.0771995	+	0.263203i
$162$	69.6367			0.429856
$163$	−87.0446			−0.534016			−0.267008	−	0.963694i	$-0.586035\pi$
$163$	−87.0446			−0.534016			−0.267008	+	0.963694i	$0.586035\pi$
$164$			2.02912i			0.0123727i
$165$	−183.302			−1.11092
$166$		−	1.83997i		−	0.0110842i
$167$			181.375i			1.08608i	0.839708	+	0.543038i	$0.182726\pi$
$167$			181.375i			1.08608i	−0.839708	+	0.543038i	$0.817274\pi$
$168$	−129.793	−	38.0694i	−0.772580	−	0.226603i
$169$	−389.739			−2.30615
$170$	119.550			0.703236
$171$		−	85.8668i		−	0.502145i
$172$	19.2387			0.111853
$173$			173.842i			1.00487i	0.864616	+	0.502433i	$0.167562\pi$
$173$			173.842i			1.00487i	−0.864616	+	0.502433i	$0.832438\pi$
$174$			119.256i			0.685381i
$175$	28.0101	−	95.4975i	0.160058	−	0.545700i
$176$	−183.626			−1.04333
$177$	−87.1859			−0.492576
$178$			221.077i			1.24200i
$179$	−336.692			−1.88096			−0.940481	−	0.339846i	$-0.889625\pi$
$179$	−336.692			−1.88096			−0.940481	+	0.339846i	$0.889625\pi$
$180$		−	7.06501i		−	0.0392500i
$181$			137.033i			0.757087i	0.925583	+	0.378544i	$0.123575\pi$
$181$			137.033i			0.757087i	−0.925583	+	0.378544i	$0.876425\pi$
$182$	304.712	+	89.3741i	1.67424	+	0.491067i
$183$	171.008			0.934468
$184$	52.2659			0.284054
$185$			444.817i			2.40442i
$186$	−24.9646			−0.134218
$187$			124.835i			0.667567i
$188$			16.0609i			0.0854301i
$189$	−196.773	−	57.7150i	−1.04113	−	0.305370i
$190$	−289.876			−1.52566
$191$	199.348			1.04371			0.521853	−	0.853036i	$-0.325241\pi$
$191$	199.348			1.04371			0.521853	+	0.853036i	$0.325241\pi$
$192$			159.149i			0.828903i
$193$	−27.2603			−0.141245			−0.0706225	−	0.997503i	$-0.522499\pi$
$193$	−27.2603			−0.141245			−0.0706225	+	0.997503i	$0.522499\pi$
$194$			146.989i			0.757678i
$195$		−	345.255i		−	1.77054i
$196$	13.0678	+	8.38733i	0.0666726	+	0.0427925i
$197$	5.25957			0.0266983			0.0133492	−	0.999911i	$-0.495751\pi$
$197$	5.25957			0.0266983			0.0133492	+	0.999911i	$0.495751\pi$
$198$	−85.7425			−0.433043
$199$			138.232i			0.694633i	0.937748	+	0.347317i	$0.112907\pi$
$199$			138.232i			0.694633i	−0.937748	+	0.347317i	$0.887093\pi$
$200$	−117.786			−0.588929
$201$			257.887i			1.28302i
$202$			153.358i			0.759197i
$203$	52.4901	−	178.960i	0.258572	−	0.881574i
$204$	7.35221			0.0360402
$205$	40.0987			0.195603
$206$			240.170i			1.16587i
$207$	22.4594			0.108500
$208$		−	345.866i		−	1.66282i
$209$		−	302.690i		−	1.44828i
$210$	−55.2258	+	188.287i	−0.262980	+	0.896603i
$211$	74.6085			0.353595			0.176797	−	0.984247i	$-0.443426\pi$
$211$	74.6085			0.353595			0.176797	+	0.984247i	$0.443426\pi$
$212$	27.3836			0.129168
$213$			240.838i			1.13069i
$214$	167.011			0.780427
$215$		−	380.189i		−	1.76832i
$216$			242.699i			1.12360i
$217$	37.4626	+	10.9880i	0.172639	+	0.0506361i
$218$	−211.890			−0.971972
$219$	−189.559			−0.865564
$220$		−	24.9050i		−	0.113204i
$221$	−235.131			−1.06394
$222$		−	317.941i		−	1.43217i
$223$		−	124.442i		−	0.558035i	−0.960286	−	0.279017i	$-0.909991\pi$
$223$		−	124.442i		−	0.558035i	0.960286	−	0.279017i	$-0.0900087\pi$
$224$	9.96517	−	33.9752i	0.0444874	−	0.151675i
$225$	−50.6142			−0.224952
$226$	58.2013			0.257528
$227$		−	206.291i		−	0.908770i	−0.890806	−	0.454385i	$-0.849859\pi$
$227$		−	206.291i		−	0.908770i	0.890806	−	0.454385i	$-0.150141\pi$
$228$	−17.8271			−0.0781890
$229$			182.464i			0.796786i	0.917215	+	0.398393i	$0.130432\pi$
$229$			182.464i			0.796786i	−0.917215	+	0.398393i	$0.869568\pi$
$230$		−	75.8203i		−	0.329654i
$231$	−196.610	−	57.6671i	−0.851125	−	0.249641i
$232$	−220.727			−0.951411
$233$	−17.4469			−0.0748795			−0.0374397	−	0.999299i	$-0.511920\pi$
$233$	−17.4469			−0.0748795			−0.0374397	+	0.999299i	$0.511920\pi$
$234$		−	161.499i		−	0.690166i
$235$	317.388			1.35059
$236$		−	11.8458i		−	0.0501942i
$237$			219.674i			0.926896i
$238$	128.230	+	37.6107i	0.538781	+	0.158028i
$239$	262.008			1.09627			0.548133	−	0.836391i	$-0.315339\pi$
$239$	262.008			1.09627			0.548133	+	0.836391i	$0.315339\pi$
$240$	213.717			0.890487
$241$		−	227.647i		−	0.944595i	−0.881439	−	0.472297i	$-0.843425\pi$
$241$		−	227.647i		−	0.944595i	0.881439	−	0.472297i	$-0.156575\pi$
$242$	−70.0363			−0.289406
$243$			179.021i			0.736713i
$244$			23.2346i			0.0952237i
$245$	165.747	−	258.241i	0.676519	−	1.05405i
$246$	−28.6613			−0.116509
$247$	570.127			2.30821
$248$		−	46.2060i		−	0.186315i
$249$	−2.23615			−0.00898051
$250$		−	129.591i		−	0.518366i
$251$		−	34.8554i		−	0.138866i	−0.997587	−	0.0694331i	$-0.977881\pi$
$251$		−	34.8554i		−	0.138866i	0.997587	−	0.0694331i	$-0.0221190\pi$
$252$	2.22267	−	7.57795i	0.00882010	−	0.0300712i
$253$	79.1720			0.312933
$254$	−239.537			−0.943058
$255$		−	145.291i		−	0.569770i
$256$	−60.4520			−0.236141
$257$		−	300.434i		−	1.16900i	−0.811393	−	0.584501i	$-0.801290\pi$
$257$		−	300.434i		−	1.16900i	0.811393	−	0.584501i	$-0.198710\pi$
$258$			271.747i			1.05328i
$259$	−139.940	+	477.112i	−0.540311	+	1.84213i
$260$	46.9093			0.180421
$261$	−94.8496			−0.363409
$262$		−	264.558i		−	1.00976i
$263$	108.913			0.414120			0.207060	−	0.978328i	$-0.433611\pi$
$263$	108.913			0.414120			0.207060	+	0.978328i	$0.433611\pi$
$264$			242.497i			0.918550i
$265$		−	541.144i		−	2.04205i
$266$	−310.922	−	91.1957i	−1.16888	−	0.342841i
$267$	268.678			1.00629
$268$	−35.0387			−0.130741
$269$			63.7950i			0.237156i	0.992945	+	0.118578i	$0.0378336\pi$
$269$			63.7950i			0.237156i	−0.992945	+	0.118578i	$0.962166\pi$
$270$	352.074			1.30398
$271$			242.093i			0.893332i	0.894701	+	0.446666i	$0.147389\pi$
$271$			242.093i			0.893332i	−0.894701	+	0.446666i	$0.852611\pi$
$272$		−	145.549i		−	0.535106i
$273$	108.618	−	370.321i	0.397868	−	1.35649i
$274$	222.854			0.813335
$275$	−178.421			−0.648804
$276$		−	4.66287i		−	0.0168945i
$277$	361.928			1.30660			0.653299	−	0.757100i	$-0.273385\pi$
$277$	361.928			1.30660			0.653299	+	0.757100i	$0.273385\pi$
$278$		−	169.898i		−	0.611146i
$279$		−	19.8554i		−	0.0711662i
$280$	−348.493	−	102.216i	−1.24462	−	0.365056i
$281$	−541.998			−1.92882			−0.964409	−	0.264415i	$-0.914821\pi$
$281$	−541.998			−1.92882			−0.964409	+	0.264415i	$0.914821\pi$
$282$	−226.859			−0.804465
$283$		−	86.7364i		−	0.306489i	−0.988188	−	0.153244i	$-0.951028\pi$
$283$		−	86.7364i		−	0.306489i	0.988188	−	0.153244i	$-0.0489722\pi$
$284$	−32.7223			−0.115219
$285$			352.292i			1.23611i
$286$		−	569.303i		−	1.99057i
$287$	43.0100	+	12.6151i	0.149861	+	0.0439552i
$288$	−18.0070			−0.0625245
$289$	190.051			0.657617
$290$			320.201i			1.10414i
$291$	178.639			0.613880
$292$		−	25.7551i		−	0.0882023i
$293$			33.1630i			0.113184i	0.998397	+	0.0565921i	$0.0180234\pi$
$293$			33.1630i			0.113184i	−0.998397	+	0.0565921i	$0.981977\pi$
$294$	−118.471	+	184.583i	−0.402962	+	0.627832i
$295$	−234.093			−0.793534
$296$	588.466			1.98806
$297$			367.638i			1.23784i
$298$	−94.9881			−0.318752
$299$			149.123i			0.498739i
$300$			10.5082i			0.0350273i
$301$	119.608	−	407.791i	0.397369	−	1.35479i
$302$	−75.0254			−0.248428
$303$	186.378			0.615110
$304$			352.916i			1.16091i
$305$	459.153			1.50542
$306$		−	67.9626i		−	0.222100i
$307$			208.508i			0.679178i	0.940574	+	0.339589i	$0.110288\pi$
$307$			208.508i			0.679178i	−0.940574	+	0.339589i	$0.889712\pi$
$308$	7.83516	−	26.7131i	0.0254388	−	0.0867310i
$309$	291.883			0.944604
$310$	−67.0294			−0.216224
$311$		−	177.856i		−	0.571885i	−0.958247	−	0.285942i	$-0.907693\pi$
$311$		−	177.856i		−	0.571885i	0.958247	−	0.285942i	$-0.0923066\pi$
$312$	−456.752			−1.46395
$313$			458.915i			1.46618i	0.680131	+	0.733091i	$0.261923\pi$
$313$			458.915i			1.46618i	−0.680131	+	0.733091i	$0.738077\pi$
$314$			161.588i			0.514611i
$315$	−149.752	−	43.9234i	−0.475404	−	0.139440i
$316$	−29.8469			−0.0944521
$317$	−142.874			−0.450707			−0.225354	−	0.974277i	$-0.572354\pi$
$317$	−142.874			−0.450707			−0.225354	+	0.974277i	$0.572354\pi$
$318$			386.793i			1.21633i
$319$	−334.356			−1.04814
$320$			427.313i			1.33535i
$321$		−	202.972i		−	0.632311i
$322$	23.8532	−	81.3251i	0.0740784	−	0.252562i
$323$	239.923			0.742796
$324$	11.4987			0.0354897
$325$		−	336.062i		−	1.03404i
$326$	167.051			0.512426
$327$			257.514i			0.787504i
$328$		−	53.0482i		−	0.161732i
$329$	340.432	+	99.8510i	1.03475	+	0.303499i
$330$	351.782			1.06601
$331$	376.714			1.13811			0.569054	−	0.822300i	$-0.307309\pi$
$331$	376.714			1.13811			0.569054	+	0.822300i	$0.307309\pi$
$332$		−	0.303822i		−	0.000915128i
$333$	252.872			0.759376
$334$		−	348.084i		−	1.04217i
$335$			692.421i			2.06693i
$336$	229.233	+	67.2358i	0.682242	+	0.200107i
$337$	−164.261			−0.487422			−0.243711	−	0.969848i	$-0.578365\pi$
$337$	−164.261			−0.487422			−0.243711	+	0.969848i	$0.578365\pi$
$338$	747.965			2.21291
$339$		−	70.7331i		−	0.208652i
$340$	19.7406			0.0580605
$341$		−	69.9925i		−	0.205257i
$342$			164.791i			0.481844i
$343$	259.024	−	224.846i	0.755172	−	0.655527i
$344$	−502.967			−1.46211
$345$	−92.1458			−0.267089
$346$		−	333.627i		−	0.964241i
$347$	605.958			1.74628			0.873138	−	0.487472i	$-0.162081\pi$
$347$	605.958			1.74628			0.873138	+	0.487472i	$0.162081\pi$
$348$			19.6920i			0.0565863i
$349$			525.313i			1.50520i	0.658480	+	0.752598i	$0.271200\pi$
$349$			525.313i			1.50520i	−0.658480	+	0.752598i	$0.728800\pi$
$350$	−53.7554	+	183.273i	−0.153587	+	0.523638i
$351$	−692.458			−1.97281
$352$	−63.4769			−0.180332
$353$		−	24.1046i		−	0.0682849i	−0.999417	−	0.0341425i	$-0.989130\pi$
$353$		−	24.1046i		−	0.0682849i	0.999417	−	0.0341425i	$-0.0108700\pi$
$354$	167.322			0.472661
$355$			646.645i			1.82154i
$356$			36.5050i			0.102542i
$357$	45.7090	−	155.840i	0.128036	−	0.436527i
$358$	646.160			1.80492
$359$	−643.332			−1.79201			−0.896005	−	0.444043i	$-0.853544\pi$
$359$	−643.332			−1.79201			−0.896005	+	0.444043i	$0.853544\pi$
$360$			184.703i			0.513065i
$361$	−220.747			−0.611489
$362$		−	262.985i		−	0.726479i
$363$			85.1164i			0.234480i
$364$	50.3151	+	14.7578i	0.138228	+	0.0405434i
$365$	−508.961			−1.39441
$366$	−328.188			−0.896689
$367$		−	441.151i		−	1.20205i	−0.799232	−	0.601023i	$-0.794760\pi$
$367$		−	441.151i		−	1.20205i	0.799232	−	0.601023i	$-0.205240\pi$
$368$	−92.3089			−0.250840
$369$		−	22.7955i		−	0.0617765i
$370$		−	853.667i		−	2.30721i
$371$	170.245	−	580.432i	0.458881	−	1.56451i
$372$	−4.12224			−0.0110813
$373$	−105.057			−0.281653			−0.140827	−	0.990034i	$-0.544976\pi$
$373$	−105.057			−0.281653			−0.140827	+	0.990034i	$0.544976\pi$
$374$		−	239.576i		−	0.640578i
$375$	−157.495			−0.419986
$376$		−	419.886i		−	1.11672i
$377$		−	629.771i		−	1.67048i
$378$	377.636	+	110.763i	0.999036	+	0.293025i
$379$	450.275			1.18806			0.594030	−	0.804443i	$-0.297536\pi$
$379$	450.275			1.18806			0.594030	+	0.804443i	$0.297536\pi$
$380$	−47.8654			−0.125962
$381$			291.113i			0.764076i
$382$	−382.576			−1.00151
$383$		−	332.244i		−	0.867478i	−0.901039	−	0.433739i	$-0.857194\pi$
$383$		−	332.244i		−	0.867478i	0.901039	−	0.433739i	$-0.142806\pi$
$384$		−	258.241i		−	0.672503i
$385$	−527.894	−	154.835i	−1.37115	−	0.402170i
$386$	52.3163			0.135535
$387$	−216.132			−0.558480
$388$			24.2714i			0.0625553i
$389$	−370.646			−0.952818			−0.476409	−	0.879224i	$-0.658062\pi$
$389$	−370.646			−0.952818			−0.476409	+	0.879224i	$0.658062\pi$
$390$			662.593i			1.69896i
$391$			62.7545i			0.160498i
$392$	−341.637	−	219.273i	−0.871524	−	0.559371i
$393$	−321.522			−0.818121
$394$	−10.0939			−0.0256189
$395$			589.822i			1.49322i
$396$	−14.1581			−0.0357528
$397$		−	92.3514i		−	0.232623i	−0.993213	−	0.116312i	$-0.962893\pi$
$397$		−	92.3514i		−	0.232623i	0.993213	−	0.116312i	$-0.0371071\pi$
$398$		−	265.287i		−	0.666550i
$399$	−110.832	+	377.869i	−0.277774	+	0.947040i
$400$	208.026			0.520066
$401$	273.963			0.683199			0.341600	−	0.939846i	$-0.389031\pi$
$401$	273.963			0.683199			0.341600	+	0.939846i	$0.389031\pi$
$402$		−	494.921i		−	1.23115i
$403$	131.833			0.327130
$404$			25.3230i			0.0626806i
$405$		−	227.232i		−	0.561067i
$406$	−100.736	+	343.449i	−0.248118	+	0.845933i
$407$	891.404			2.19018
$408$	−192.212			−0.471108
$409$			318.314i			0.778273i	0.921180	+	0.389136i	$0.127226\pi$
$409$			318.314i			0.778273i	−0.921180	+	0.389136i	$0.872774\pi$
$410$	−76.9551			−0.187695
$411$		−	270.838i		−	0.658973i
$412$			39.6577i			0.0962566i
$413$	−251.088	−	73.6460i	−0.607962	−	0.178320i
$414$	−43.1028			−0.104113
$415$	−6.00402			−0.0144675
$416$		−	119.561i		−	0.287406i
$417$	−206.481			−0.495157
$418$			580.906i			1.38973i
$419$		−	346.276i		−	0.826435i	−0.910632	−	0.413218i	$-0.864405\pi$
$419$		−	346.276i		−	0.826435i	0.910632	−	0.413218i	$-0.135595\pi$
$420$	−9.11909	+	31.0906i	−0.0217121	+	0.0740252i
$421$	−68.8057			−0.163434			−0.0817170	−	0.996656i	$-0.526040\pi$
$421$	−68.8057			−0.163434			−0.0817170	+	0.996656i	$0.526040\pi$
$422$	−143.184			−0.339299
$423$		−	180.431i		−	0.426550i
$424$	−715.901			−1.68845
$425$		−	141.423i		−	0.332760i
$426$		−	462.202i		−	1.08498i
$427$	492.489	+	144.450i	1.15337	+	0.338291i
$428$	27.5775			0.0644335
$429$	−691.883			−1.61278
$430$			729.636i			1.69683i
$431$	336.942			0.781769			0.390884	−	0.920440i	$-0.372169\pi$
$431$	336.942			0.781769			0.390884	+	0.920440i	$0.372169\pi$
$432$		−	428.640i		−	0.992221i
$433$			114.453i			0.264326i	0.991228	+	0.132163i	$0.0421922\pi$
$433$			114.453i			0.264326i	−0.991228	+	0.132163i	$0.957808\pi$
$434$	−71.8960	−	21.0876i	−0.165659	−	0.0485890i
$435$	389.146			0.894589
$436$	−34.9880			−0.0802478
$437$		−	152.162i		−	0.348198i
$438$	363.790			0.830570
$439$		−	602.341i		−	1.37208i	−0.727566	−	0.686038i	$-0.759349\pi$
$439$		−	602.341i		−	1.37208i	0.727566	−	0.686038i	$-0.240651\pi$
$440$			651.101i			1.47978i
$441$	−146.806	−	94.2248i	−0.332894	−	0.213662i
$442$	451.249			1.02093
$443$	116.447			0.262860			0.131430	−	0.991325i	$-0.458043\pi$
$443$	116.447			0.262860			0.131430	+	0.991325i	$0.458043\pi$
$444$		−	52.4996i		−	0.118242i
$445$	721.397			1.62112
$446$			238.821i			0.535474i
$447$			115.441i			0.258257i
$448$	−134.434	+	458.337i	−0.300075	+	1.02307i
$449$	40.7385			0.0907317			0.0453658	−	0.998970i	$-0.485555\pi$
$449$	40.7385			0.0907317			0.0453658	+	0.998970i	$0.485555\pi$
$450$	97.1359			0.215858
$451$		−	80.3569i		−	0.178175i
$452$	9.61041			0.0212620
$453$			91.1797i			0.201280i
$454$			395.901i			0.872029i
$455$	291.637	−	994.307i	0.640961	−	2.18529i
$456$	466.061			1.02206
$457$	106.407			0.232837			0.116419	−	0.993200i	$-0.462859\pi$
$457$	106.407			0.232837			0.116419	+	0.993200i	$0.462859\pi$
$458$		−	350.174i		−	0.764572i
$459$	−291.403			−0.634864
$460$		−	12.5197i		−	0.0272168i
$461$		−	452.191i		−	0.980892i	−0.871472	−	0.490446i	$-0.836834\pi$
$461$		−	452.191i		−	0.980892i	0.871472	−	0.490446i	$-0.163166\pi$
$462$	377.322	+	110.671i	0.816715	+	0.239548i
$463$	427.700			0.923759			0.461879	−	0.886943i	$-0.347175\pi$
$463$	427.700			0.923759			0.461879	+	0.886943i	$0.347175\pi$
$464$	389.835			0.840162
$465$			81.4621i			0.175187i
$466$	33.4831			0.0718521
$467$			318.878i			0.682822i	0.939914	+	0.341411i	$0.110905\pi$
$467$			318.878i			0.682822i	−0.939914	+	0.341411i	$0.889095\pi$
$468$		−	26.6673i		−	0.0569814i
$469$	−217.837	+	742.693i	−0.464471	+	1.58357i
$470$	−609.113			−1.29599
$471$	196.381			0.416944
$472$			309.690i			0.656124i
$473$	−761.890			−1.61076
$474$		−	421.586i		−	0.889422i
$475$			342.911i			0.721919i
$476$	21.1738	+	6.21042i	0.0444827	+	0.0130471i
$477$	−307.632			−0.644932
$478$	−502.830			−1.05195
$479$			647.142i			1.35103i	0.737347	+	0.675514i	$0.236078\pi$
$479$			647.142i			1.35103i	−0.737347	+	0.675514i	$0.763922\pi$
$480$	73.8788			0.153914
$481$			1678.99i			3.49062i
$482$			436.888i			0.906406i
$483$	−98.8358	−	28.9893i	−0.204629	−	0.0600192i
$484$	−11.5647			−0.0238939
$485$	479.643			0.988954
$486$		−	343.567i		−	0.706929i
$487$	16.2233			0.0333127			0.0166564	−	0.999861i	$-0.494698\pi$
$487$	16.2233			0.0333127			0.0166564	+	0.999861i	$0.494698\pi$
$488$		−	607.432i		−	1.24474i
$489$		−	203.020i		−	0.415174i
$490$	−318.092	+	495.601i	−0.649167	+	1.01143i
$491$	325.023			0.661961			0.330981	−	0.943638i	$-0.392621\pi$
$491$	325.023			0.661961			0.330981	+	0.943638i	$0.392621\pi$
$492$	−4.73266			−0.00961922
$493$		−	265.022i		−	0.537571i
$494$	−1094.16			−2.21489
$495$			279.787i			0.565227i
$496$			81.6063i			0.164529i
$497$	−203.436	+	693.594i	−0.409328	+	1.39556i
$498$	4.29148			0.00861744
$499$	−351.499			−0.704408			−0.352204	−	0.935923i	$-0.614568\pi$
$499$	−351.499			−0.704408			−0.352204	+	0.935923i	$0.614568\pi$
$500$		−	21.3986i		−	0.0427972i
$501$	−423.032			−0.844375
$502$			66.8924i			0.133252i
$503$		−	217.196i		−	0.431800i	−0.976415	−	0.215900i	$-0.930731\pi$
$503$		−	217.196i		−	0.431800i	0.976415	−	0.215900i	$-0.0692686\pi$
$504$	−58.1081	+	198.113i	−0.115294	+	0.393082i
$505$	500.423			0.990936
$506$	−151.942			−0.300281
$507$		−	909.015i		−	1.79293i
$508$	−39.5532			−0.0778605
$509$			195.548i			0.384182i	0.981377	+	0.192091i	$0.0615268\pi$
$509$			195.548i			0.384182i	−0.981377	+	0.192091i	$0.938473\pi$
$510$			278.835i			0.546735i
$511$	−545.913	−	160.120i	−1.06832	−	0.313347i
$512$	558.898			1.09160
$513$	706.571			1.37733
$514$			576.575i			1.12174i
$515$	783.700			1.52175
$516$			44.8718i			0.0869609i
$517$		−	636.039i		−	1.23025i
$518$	268.565	−	915.646i	0.518466	−	1.76766i
$519$	−405.463			−0.781239
$520$	−1226.37			−2.35840
$521$		−	340.384i		−	0.653329i	−0.945140	−	0.326665i	$-0.894075\pi$
$521$		−	340.384i		−	0.653329i	0.945140	−	0.326665i	$-0.105925\pi$
$522$	182.030			0.348716
$523$		−	640.004i		−	1.22372i	−0.790967	−	0.611859i	$-0.790422\pi$
$523$		−	640.004i		−	1.22372i	0.790967	−	0.611859i	$-0.209578\pi$
$524$		−	43.6847i		−	0.0833678i
$525$	222.735	+	65.3299i	0.424258	+	0.124438i
$526$	−209.020			−0.397377
$527$	55.4785			0.105272
$528$		−	428.284i		−	0.811144i
$529$	−489.200			−0.924764
$530$			1038.53i			1.95949i
$531$			133.078i			0.250618i
$532$	−51.3406	−	15.0586i	−0.0965049	−	0.0283056i
$533$	151.355			0.283968
$534$	−515.632			−0.965602
$535$		−	544.976i		−	1.01865i
$536$	916.031			1.70901
$537$		−	785.290i		−	1.46236i
$538$		−	122.432i		−	0.227568i
$539$	−517.510	−	332.153i	−0.960129	−	0.616240i
$540$	58.1358			0.107659
$541$	593.808			1.09761			0.548806	−	0.835950i	$-0.315083\pi$
$541$	593.808			1.09761			0.548806	+	0.835950i	$0.315083\pi$
$542$		−	464.611i		−	0.857216i
$543$	−319.611			−0.588602
$544$		−	50.3141i		−	0.0924891i
$545$			691.420i			1.26866i
$546$	−208.453	+	710.699i	−0.381782	+	1.30165i
$547$	−335.435			−0.613226			−0.306613	−	0.951834i	$-0.599196\pi$
$547$	−335.435			−0.613226			−0.306613	+	0.951834i	$0.599196\pi$
$548$	36.7984			0.0671504
$549$		−	261.022i		−	0.475449i
$550$	342.415			0.622573
$551$			642.606i			1.16625i
$552$			121.903i			0.220839i
$553$	−185.559	+	632.645i	−0.335550	+	1.14402i
$554$	−694.590			−1.25377
$555$	−1037.48			−1.86933
$556$		−	28.0543i		−	0.0504573i
$557$	21.3334			0.0383005			0.0191502	−	0.999817i	$-0.493904\pi$
$557$	21.3334			0.0383005			0.0191502	+	0.999817i	$0.493904\pi$
$558$			38.1053i			0.0682890i
$559$		−	1435.04i		−	2.56716i
$560$	615.488	+	180.527i	1.09908	+	0.322370i
$561$	−291.161			−0.519003
$562$	1040.17			1.85084
$563$			329.597i			0.585430i	0.956200	+	0.292715i	$0.0945588\pi$
$563$			329.597i			0.585430i	−0.956200	+	0.292715i	$0.905441\pi$
$564$	−37.4598			−0.0664181
$565$		−	189.917i		−	0.336136i
$566$			166.459i			0.294098i
$567$	71.4877	−	243.730i	0.126081	−	0.429859i
$568$	855.473			1.50611
$569$	−689.582			−1.21192			−0.605960	−	0.795495i	$-0.707211\pi$
$569$	−689.582			−1.21192			−0.605960	+	0.795495i	$0.707211\pi$
$570$		−	676.098i		−	1.18614i
$571$	616.853			1.08030			0.540152	−	0.841568i	$-0.318367\pi$
$571$	616.853			1.08030			0.540152	+	0.841568i	$0.318367\pi$
$572$		−	94.0053i		−	0.164345i
$573$			464.952i			0.811434i
$574$	−82.5422	−	24.2102i	−0.143802	−	0.0421781i
$575$	−89.6923			−0.155987
$576$	242.921			0.421739
$577$		−	519.333i		−	0.900058i	−0.893014	−	0.450029i	$-0.851414\pi$
$577$		−	519.333i		−	0.900058i	0.893014	−	0.450029i	$-0.148586\pi$
$578$	−364.736			−0.631030
$579$		−	63.5810i		−	0.109812i
$580$			52.8728i			0.0911600i
$581$	−6.43993	−	1.88888i	−0.0110842	−	0.00325108i
$582$	−342.833			−0.589061
$583$	−1084.44			−1.86010
$584$			673.325i			1.15295i
$585$	−526.988			−0.900835
$586$		−	63.6444i		−	0.108608i
$587$			580.967i			0.989722i	0.868972	+	0.494861i	$0.164781\pi$
$587$			580.967i			0.989722i	−0.868972	+	0.494861i	$0.835219\pi$
$588$	−19.5623	+	30.4790i	−0.0332693	+	0.0518350i
$589$	−134.520			−0.228387
$590$	449.257			0.761452
$591$			12.2672i			0.0207567i
$592$	−1039.31			−1.75560
$593$		−	410.000i		−	0.691400i	−0.938345	−	0.345700i	$-0.887641\pi$
$593$		−	410.000i		−	0.691400i	0.938345	−	0.345700i	$-0.112359\pi$
$594$		−	705.549i		−	1.18779i
$595$	122.728	−	418.428i	0.206265	−	0.703240i
$596$	−15.6848			−0.0263168
$597$	−322.408			−0.540046
$598$		−	286.188i		−	0.478576i
$599$	320.956			0.535820			0.267910	−	0.963444i	$-0.413667\pi$
$599$	320.956			0.535820			0.267910	+	0.963444i	$0.413667\pi$
$600$		−	274.720i		−	0.457867i
$601$			1047.43i			1.74281i	0.490567	+	0.871403i	$0.336790\pi$
$601$			1047.43i			1.74281i	−0.490567	+	0.871403i	$0.663210\pi$
$602$	−229.545	+	782.609i	−0.381304	+	1.30002i
$603$	393.631			0.652788
$604$	−12.3885			−0.0205107
$605$			228.536i			0.377746i
$606$	−357.686			−0.590242
$607$			482.244i			0.794471i	0.917717	+	0.397235i	$0.130030\pi$
$607$			482.244i			0.794471i	−0.917717	+	0.397235i	$0.869970\pi$
$608$			121.998i			0.200654i
$609$	417.399	+	122.426i	0.685385	+	0.201028i
$610$	−881.179			−1.44456
$611$	1198.00			1.96072
$612$		−	11.2222i		−	0.0183370i
$613$	−563.500			−0.919250			−0.459625	−	0.888113i	$-0.652016\pi$
$613$	−563.500			−0.919250			−0.459625	+	0.888113i	$0.652016\pi$
$614$		−	400.156i		−	0.651719i
$615$			93.5249i			0.152073i
$616$	−204.838	+	698.373i	−0.332529	+	1.13372i
$617$	−215.409			−0.349122			−0.174561	−	0.984646i	$-0.555851\pi$
$617$	−215.409			−0.349122			−0.174561	+	0.984646i	$0.555851\pi$
$618$	−560.164			−0.906414
$619$			532.376i			0.860058i	0.902815	+	0.430029i	$0.141497\pi$
$619$			532.376i			0.860058i	−0.902815	+	0.430029i	$0.858503\pi$
$620$	−11.0681			−0.0178518
$621$			184.811i			0.297603i
$622$			341.331i			0.548764i
$623$	773.772	+	226.953i	1.24201	+	0.364290i
$624$	806.687			1.29277
$625$	−778.301			−1.24528
$626$		−	880.723i		−	1.40691i
$627$	705.985			1.12597
$628$			26.6820i			0.0424872i
$629$			706.558i			1.12330i
$630$	287.396	+	84.2953i	0.456184	+	0.133802i
$631$	120.066			0.190278			0.0951392	−	0.995464i	$-0.469670\pi$
$631$	120.066			0.190278			0.0951392	+	0.995464i	$0.469670\pi$
$632$	780.299			1.23465
$633$			174.014i			0.274904i
$634$	274.196			0.432485
$635$			781.634i			1.23092i
$636$			63.8686i			0.100422i
$637$	625.622	−	974.746i	0.982138	−	1.53021i
$638$	641.676			1.00576
$639$	367.609			0.575287
$640$		−	693.373i		−	1.08340i
$641$	−39.7553			−0.0620207			−0.0310104	−	0.999519i	$-0.509872\pi$
$641$	−39.7553			−0.0620207			−0.0310104	+	0.999519i	$0.509872\pi$
$642$			389.532i			0.606747i
$643$		−	505.693i		−	0.786459i	−0.919440	−	0.393229i	$-0.871358\pi$
$643$		−	505.693i		−	0.786459i	0.919440	−	0.393229i	$-0.128642\pi$
$644$	3.93873	−	13.4287i	0.00611605	−	0.0208520i
$645$	886.739			1.37479
$646$	−460.446			−0.712765
$647$			733.634i			1.13390i	0.823752	+	0.566950i	$0.191877\pi$
$647$			733.634i			1.13390i	−0.823752	+	0.566950i	$0.808123\pi$
$648$	−300.614			−0.463911
$649$			469.116i			0.722830i
$650$			644.951i			0.992232i
$651$	−25.6281	+	87.3764i	−0.0393674	+	0.134219i
$652$	27.5840			0.0423068
$653$	415.918			0.636934			0.318467	−	0.947934i	$-0.396832\pi$
$653$	415.918			0.636934			0.318467	+	0.947934i	$0.396832\pi$
$654$		−	494.205i		−	0.755665i
$655$	−863.280			−1.31798
$656$			93.6905i			0.142821i
$657$			289.337i			0.440392i
$658$	−653.336	−	191.628i	−0.992912	−	0.291228i
$659$	−431.839			−0.655295			−0.327647	−	0.944800i	$-0.606256\pi$
$659$	−431.839			−0.655295			−0.327647	+	0.944800i	$0.606256\pi$
$660$	58.0875			0.0880114
$661$		−	175.664i		−	0.265754i	−0.991133	−	0.132877i	$-0.957578\pi$
$661$		−	175.664i		−	0.265754i	0.991133	−	0.132877i	$-0.0424216\pi$
$662$	−722.967			−1.09210
$663$		−	548.411i		−	0.827166i
$664$			7.94296i			0.0119623i
$665$	−297.581	+	1014.57i	−0.447491	+	1.52567i
$666$	−485.297			−0.728675
$667$	−168.081			−0.251995
$668$		−	57.4768i		−	0.0860431i
$669$	290.244			0.433847
$670$		−	1328.85i		−	1.98336i
$671$		−	920.132i		−	1.37128i
$672$	79.2426	+	23.2424i	0.117921	+	0.0345869i
$673$	−1033.14			−1.53513			−0.767566	−	0.640970i	$-0.778532\pi$
$673$	−1033.14			−1.53513			−0.767566	+	0.640970i	$0.778532\pi$
$674$	315.241			0.467716
$675$		−	416.489i		−	0.617021i
$676$	123.507			0.182702
$677$			1008.04i			1.48898i	0.667633	+	0.744491i	$0.267308\pi$
$677$			1008.04i			1.48898i	−0.667633	+	0.744491i	$0.732692\pi$
$678$			135.747i			0.200216i
$679$	514.466	+	150.897i	0.757682	+	0.222234i
$680$	−516.086			−0.758950
$681$	481.146			0.706528
$682$			134.326i			0.196958i
$683$	212.827			0.311606			0.155803	−	0.987788i	$-0.450204\pi$
$683$	212.827			0.311606			0.155803	+	0.987788i	$0.450204\pi$
$684$			27.2108i			0.0397819i
$685$		−	727.196i		−	1.06160i
$686$	−497.104	+	431.511i	−0.724641	+	0.629024i
$687$	−425.573			−0.619466
$688$	888.309			1.29115
$689$		−	2042.58i		−	2.96456i
$690$	176.841			0.256291
$691$		−	1137.94i		−	1.64680i	−0.567461	−	0.823400i	$-0.692074\pi$
$691$		−	1137.94i		−	1.64680i	0.567461	−	0.823400i	$-0.307926\pi$
$692$		−	55.0897i		−	0.0796094i
$693$	−88.0216	+	300.100i	−0.127015	+	0.433045i
$694$	−1162.92			−1.67568
$695$	−554.397			−0.797694
$696$		−	514.817i		−	0.739680i
$697$	63.6937			0.0913827
$698$		−	1008.15i		−	1.44434i
$699$		−	40.6926i		−	0.0582155i
$700$	−8.87628	+	30.2627i	−0.0126804	+	0.0432325i
$701$	−218.576			−0.311806			−0.155903	−	0.987772i	$-0.549829\pi$
$701$	−218.576			−0.311806			−0.155903	+	0.987772i	$0.549829\pi$
$702$	1328.92			1.89306
$703$		−	1713.21i		−	2.43700i
$704$	856.327			1.21637
$705$			740.266i			1.05002i
$706$			46.2601i			0.0655242i
$707$	536.755	+	157.434i	0.759200	+	0.222679i
$708$	27.6288			0.0390238
$709$	853.299			1.20353			0.601763	−	0.798675i	$-0.294465\pi$
$709$	853.299			1.20353			0.601763	+	0.798675i	$0.294465\pi$
$710$		−	1241.00i		−	1.74789i
$711$	335.305			0.471597
$712$		−	954.365i		−	1.34040i
$713$		−	35.1852i		−	0.0493482i
$714$	−87.7221	+	299.079i	−0.122860	+	0.418878i
$715$	−1857.70			−2.59818
$716$	106.696			0.149017
$717$			611.098i			0.852299i
$718$	1234.64			1.71956
$719$			850.571i			1.18299i	0.806308	+	0.591496i	$0.201462\pi$
$719$			850.571i			1.18299i	−0.806308	+	0.591496i	$0.798538\pi$
$720$		−	326.212i		−	0.453072i
$721$	840.599	+	246.554i	1.16588	+	0.341961i
$722$	423.646			0.586767
$723$	530.957			0.734381
$724$		−	43.4251i		−	0.0599794i
$725$	378.785			0.522462
$726$		−	163.350i		−	0.225001i
$727$		−	218.935i		−	0.301149i	−0.988599	−	0.150574i	$-0.951888\pi$
$727$		−	218.935i		−	0.301149i	0.988599	−	0.150574i	$-0.0481123\pi$
$728$	−1315.41	−	385.819i	−1.80688	−	0.529971i
$729$	−744.112			−1.02073
$730$	976.769			1.33804
$731$		−	603.901i		−	0.826129i
$732$	−54.1916			−0.0740322
$733$			342.892i			0.467793i	0.972262	+	0.233896i	$0.0751477\pi$
$733$			342.892i			0.467793i	−0.972262	+	0.233896i	$0.924852\pi$
$734$			846.631i			1.15345i
$735$	602.313	+	386.583i	0.819473	+	0.525963i
$736$	−31.9098			−0.0433558
$737$	1387.60			1.88276
$738$			43.7479i			0.0592789i
$739$	−338.276			−0.457748			−0.228874	−	0.973456i	$-0.573504\pi$
$739$	−338.276			−0.457748			−0.228874	+	0.973456i	$0.573504\pi$
$740$		−	140.961i		−	0.190487i
$741$			1329.75i			1.79453i
$742$	−326.724	+	1113.93i	−0.440329	+	1.50126i
$743$	−441.475			−0.594180			−0.297090	−	0.954850i	$-0.596016\pi$
$743$	−441.475			−0.594180			−0.297090	+	0.954850i	$0.596016\pi$
$744$	107.769			0.144851
$745$			309.956i			0.416049i
$746$	201.618			0.270266
$747$			3.41320i			0.00456921i
$748$		−	39.5597i		−	0.0528872i
$749$	171.451	−	584.543i	0.228906	−	0.780431i
$750$	302.255			0.403006
$751$	−694.309			−0.924513			−0.462256	−	0.886746i	$-0.652960\pi$
$751$	−694.309			−0.924513			−0.462256	+	0.886746i	$0.652960\pi$
$752$			741.577i			0.986139i
$753$	81.2956			0.107962
$754$			1208.62i			1.60294i
$755$			244.816i			0.324260i
$756$	62.3566	+	18.2896i	0.0824822	+	0.0241926i
$757$	1094.03			1.44522			0.722608	−	0.691258i	$-0.242943\pi$
$757$	1094.03			1.44522			0.722608	+	0.691258i	$0.242943\pi$
$758$	−864.141			−1.14003
$759$			184.658i			0.243291i
$760$	1251.37			1.64653
$761$		−	524.642i		−	0.689411i	−0.938711	−	0.344706i	$-0.887979\pi$
$761$		−	524.642i		−	0.689411i	0.938711	−	0.344706i	$-0.112021\pi$
$762$		−	558.687i		−	0.733185i
$763$	−217.522	+	741.619i	−0.285088	+	0.971977i
$764$	−63.1724			−0.0826864
$765$	−221.769			−0.289894
$766$			637.624i			0.832407i
$767$	−883.596			−1.15202
$768$		−	140.996i		−	0.183589i
$769$		−	576.617i		−	0.749828i	−0.927060	−	0.374914i	$-0.877672\pi$
$769$		−	576.617i		−	0.749828i	0.927060	−	0.374914i	$-0.122328\pi$
$770$	1013.10	+	297.151i	1.31572	+	0.385910i
$771$	700.721			0.908847
$772$	8.63866			0.0111900
$773$			1148.94i			1.48633i	0.669107	+	0.743166i	$0.266677\pi$
$773$			1148.94i			1.48633i	−0.669107	+	0.743166i	$0.733323\pi$
$774$	414.787			0.535901
$775$			79.2930i			0.102314i
$776$		−	634.538i		−	0.817704i
$777$	−1112.80	−	326.392i	−1.43218	−	0.420067i
$778$	711.322			0.914296
$779$	−154.440			−0.198254
$780$			109.410i			0.140269i
$781$	1295.86			1.65924
$782$		−	120.435i		−	0.154009i
$783$		−	780.488i		−	0.996792i
$784$	603.379	+	387.267i	0.769617	+	0.493964i
$785$	527.278			0.671692
$786$	617.045			0.785045
$787$		−	79.2214i		−	0.100662i	−0.998733	−	0.0503312i	$-0.983972\pi$
$787$		−	79.2214i		−	0.100662i	0.998733	−	0.0503312i	$-0.0160277\pi$
$788$	−1.66673			−0.00211514
$789$			254.026i			0.321960i
$790$		−	1131.95i		−	1.43285i
$791$	59.7483	−	203.706i	0.0755352	−	0.257529i
$792$	370.142			0.467351
$793$	1733.10			2.18550
$794$			177.235i			0.223218i
$795$	1262.15			1.58760
$796$		−	43.8051i		−	0.0550315i
$797$		−	303.090i		−	0.380289i	−0.981756	−	0.190144i	$-0.939104\pi$
$797$		−	303.090i		−	0.380289i	0.981756	−	0.190144i	$-0.0608956\pi$
$798$	212.702	−	725.184i	0.266544	−	0.908752i
$799$	504.147			0.630973
$800$	71.9116			0.0898896
$801$		−	410.104i		−	0.511990i
$802$	−525.773			−0.655578
$803$			1019.95i			1.27017i
$804$		−	81.7231i		−	0.101646i
$805$	−265.373	−	77.8357i	−0.329655	−	0.0966903i
$806$	−253.007			−0.313904
$807$	−148.793			−0.184378
$808$		−	662.029i		−	0.819343i
$809$	406.832			0.502883			0.251441	−	0.967873i	$-0.419095\pi$
$809$	406.832			0.502883			0.251441	+	0.967873i	$0.419095\pi$
$810$			436.091i			0.538384i
$811$			778.970i			0.960505i	0.877130	+	0.480253i	$0.159455\pi$
$811$			778.970i			0.960505i	−0.877130	+	0.480253i	$0.840545\pi$
$812$	−16.6339	+	56.7115i	−0.0204851	+	0.0698418i
$813$	−564.650			−0.694526
$814$	−1710.73			−2.10163
$815$		−	545.105i		−	0.668841i
$816$	339.473			0.416021
$817$			1464.29i			1.79228i
$818$		−	610.889i		−	0.746808i
$819$	−565.249	−	165.792i	−0.690170	−	0.202432i
$820$	−12.7071			−0.0154965
$821$	−1310.45			−1.59616			−0.798079	−	0.602553i	$-0.794150\pi$
$821$	−1310.45			−1.59616			−0.798079	+	0.602553i	$0.794150\pi$
$822$			519.777i			0.632332i
$823$	−211.469			−0.256949			−0.128474	−	0.991713i	$-0.541008\pi$
$823$	−211.469			−0.256949			−0.128474	+	0.991713i	$0.541008\pi$
$824$		−	1036.79i		−	1.25824i
$825$		−	416.143i		−	0.504416i
$826$	481.874	+	141.337i	0.583383	+	0.171110i
$827$	−823.007			−0.995171			−0.497586	−	0.867415i	$-0.665780\pi$
$827$	−823.007			−0.995171			−0.497586	+	0.867415i	$0.665780\pi$
$828$	−7.11729			−0.00859576
$829$		−	80.5479i		−	0.0971627i	−0.998819	−	0.0485813i	$-0.984530\pi$
$829$		−	80.5479i		−	0.0971627i	0.998819	−	0.0485813i	$-0.0154700\pi$
$830$	11.5226			0.0138826
$831$			844.148i			1.01582i
$832$			1612.92i			1.93860i
$833$	263.277	−	410.196i	0.316058	−	0.492433i
$834$	396.266			0.475139
$835$	−1135.83			−1.36028
$836$			95.9213i			0.114738i
$837$	163.384			0.195202
$838$			664.553i			0.793023i
$839$		−	453.611i		−	0.540657i	−0.962768	−	0.270329i	$-0.912868\pi$
$839$		−	453.611i		−	0.540657i	0.962768	−	0.270329i	$-0.0871323\pi$
$840$	238.404	−	812.814i	0.283815	−	0.967636i
$841$	−131.168			−0.155967
$842$	132.048			0.156827
$843$		−	1264.14i		−	1.49957i
$844$	−23.6431			−0.0280132
$845$		−	2440.69i		−	2.88839i
$846$			346.272i			0.409305i
$847$	−71.8979	+	245.128i	−0.0848854	+	0.289408i
$848$	1264.38			1.49101
$849$	202.301			0.238282
$850$			271.410i			0.319306i
$851$	448.109			0.526567
$852$		−	76.3204i		−	0.0895780i
$853$			758.240i			0.888909i	0.895801	+	0.444455i	$0.146603\pi$
$853$			758.240i			0.888909i	−0.895801	+	0.444455i	$0.853397\pi$
$854$	−945.155	−	277.221i	−1.10674	−	0.324615i
$855$	537.729			0.628923
$856$	−720.971			−0.842255
$857$			837.380i			0.977106i	0.872534	+	0.488553i	$0.162475\pi$
$857$			837.380i			0.977106i	−0.872534	+	0.488553i	$0.837525\pi$
$858$	1327.82			1.54758
$859$		−	744.943i		−	0.867221i	−0.901100	−	0.433611i	$-0.857239\pi$
$859$		−	744.943i		−	0.867221i	0.901100	−	0.433611i	$-0.142761\pi$
$860$			120.480i			0.140093i
$861$	−29.4231	+	100.315i	−0.0341732	+	0.116510i
$862$	−646.640			−0.750162
$863$	−1250.20			−1.44867			−0.724334	−	0.689449i	$-0.757853\pi$
$863$	−1250.20			−1.44867			−0.724334	+	0.689449i	$0.757853\pi$
$864$		−	148.174i		−	0.171498i
$865$	−1088.66			−1.25857
$866$		−	219.652i		−	0.253639i
$867$			443.270i			0.511268i
$868$	−11.8717	−	3.48206i	−0.0136771	−	0.00401159i
$869$	1181.99			1.36017
$870$	−746.827			−0.858422
$871$			2613.58i			3.00067i
$872$	914.707			1.04898
$873$		−	272.670i		−	0.312337i
$874$			292.021i			0.334120i
$875$	−453.572	−	133.036i	−0.518368	−	0.152041i
$876$	60.0703			0.0685734
$877$	−484.610			−0.552577			−0.276288	−	0.961075i	$-0.589105\pi$
$877$	−484.610			−0.552577			−0.276288	+	0.961075i	$0.589105\pi$
$878$			1155.98i			1.31660i
$879$	−77.3482			−0.0879956
$880$		−	1149.94i		−	1.30674i
$881$		−	239.634i		−	0.272002i	−0.990709	−	0.136001i	$-0.956575\pi$
$881$		−	239.634i		−	0.272002i	0.990709	−	0.136001i	$-0.0434251\pi$
$882$	281.742	+	180.831i	0.319436	+	0.205024i
$883$	591.365			0.669723			0.334861	−	0.942267i	$-0.391311\pi$
$883$	591.365			0.669723			0.334861	+	0.942267i	$0.391311\pi$
$884$	74.5119			0.0842895
$885$		−	545.990i		−	0.616938i
$886$	−223.478			−0.252233
$887$		−	633.387i		−	0.714078i	−0.934089	−	0.357039i	$-0.883786\pi$
$887$		−	633.387i		−	0.714078i	0.934089	−	0.357039i	$-0.116214\pi$
$888$			1372.52i			1.54563i
$889$	−245.904	+	838.383i	−0.276607	+	0.943062i
$890$	−1384.46			−1.55558
$891$	−455.368			−0.511076
$892$			39.4350i			0.0442097i
$893$	−1222.42			−1.36889
$894$		−	221.547i		−	0.247816i
$895$		−	2108.49i		−	2.35585i
$896$	218.137	−	743.714i	0.243456	−	0.830037i
$897$	−347.810			−0.387748
$898$	−78.1830			−0.0870635
$899$			148.593i			0.165287i
$900$	16.0394			0.0178216
$901$		−	859.566i		−	0.954013i
$902$			154.216i			0.170972i
$903$	951.119	+	278.970i	1.05329	+	0.308937i
$904$	−251.249			−0.277930
$905$	−858.150			−0.948232
$906$		−	174.987i		−	0.193142i
$907$	329.311			0.363077			0.181539	−	0.983384i	$-0.441892\pi$
$907$	329.311			0.363077			0.181539	+	0.983384i	$0.441892\pi$
$908$			65.3726i			0.0719963i
$909$		−	284.483i		−	0.312963i
$910$	−559.693	+	1908.22i	−0.615048	+	2.09694i
$911$	321.874			0.353319			0.176659	−	0.984272i	$-0.443471\pi$
$911$	321.874			0.353319			0.176659	+	0.984272i	$0.443471\pi$
$912$	−823.128			−0.902553
$913$			12.0319i			0.0131784i
$914$	−204.209			−0.223424
$915$			1070.91i			1.17040i
$916$		−	57.8220i		−	0.0631245i
$917$	−925.956	−	271.590i	−1.00977	−	0.296172i
$918$	559.243			0.609197
$919$	927.318			1.00905			0.504525	−	0.863397i	$-0.331667\pi$
$919$	927.318			1.00905			0.504525	+	0.863397i	$0.331667\pi$
$920$			327.308i			0.355770i
$921$	−486.316			−0.528031
$922$			867.819i			0.941235i
$923$			2440.80i			2.64442i
$924$	62.3048	+	18.2745i	0.0674295	+	0.0197776i
$925$	−1009.85			−1.09173
$926$	−820.818			−0.886412
$927$		−	445.522i		−	0.480606i
$928$	134.760			0.145216
$929$		−	567.361i		−	0.610722i	−0.952237	−	0.305361i	$-0.901223\pi$
$929$		−	567.361i		−	0.610722i	0.952237	−	0.305361i	$-0.0987772\pi$
$930$		−	156.337i		−	0.168105i
$931$	−638.373	+	994.613i	−0.685686	+	1.06833i
$932$	5.52885			0.00593224
$933$	414.826			0.444615
$934$		−	611.972i		−	0.655216i
$935$	−781.762			−0.836109
$936$			697.174i			0.744844i
$937$		−	1302.15i		−	1.38970i	−0.719153	−	0.694852i	$-0.755470\pi$
$937$		−	1302.15i		−	1.38970i	0.719153	−	0.694852i	$-0.244530\pi$
$938$	418.060	−	1425.33i	0.445693	−	1.51954i
$939$	−1070.36			−1.13989
$940$	−100.579			−0.106999
$941$			330.430i			0.351147i	0.984466	+	0.175574i	$0.0561780\pi$
$941$			330.430i			0.351147i	−0.984466	+	0.175574i	$0.943822\pi$
$942$	−376.882			−0.400087
$943$		−	40.3954i		−	0.0428371i
$944$		−	546.956i		−	0.579403i
$945$	361.433	−	1232.27i	0.382468	−	1.30399i
$946$	1462.17			1.54564
$947$	519.736			0.548824			0.274412	−	0.961612i	$-0.411517\pi$
$947$	519.736			0.548824			0.274412	+	0.961612i	$0.411517\pi$
$948$		−	69.6138i		−	0.0734323i
$949$	−1921.11			−2.02435
$950$		−	658.096i		−	0.692732i
$951$		−	333.235i		−	0.350405i
$952$	−553.555	−	162.362i	−0.581465	−	0.170548i
$953$	181.682			0.190642			0.0953210	−	0.995447i	$-0.469612\pi$
$953$	181.682			0.190642			0.0953210	+	0.995447i	$0.469612\pi$
$954$	590.390			0.618858
$955$			1248.39i			1.30721i
$956$	−83.0291			−0.0868505
$957$		−	779.841i		−	0.814881i
$958$		−	1241.96i		−	1.29641i
$959$	228.777	−	779.992i	0.238558	−	0.813339i
$960$	−996.651			−1.03818
$961$	929.894			0.967632
$962$		−	3222.22i		−	3.34950i
$963$	−309.811			−0.321715
$964$			72.1405i			0.0748345i
$965$		−	170.714i		−	0.176905i
$966$	189.680	+	55.6345i	0.196356	+	0.0575927i
$967$	−108.396			−0.112095			−0.0560476	−	0.998428i	$-0.517850\pi$
$967$	−108.396			−0.112095			−0.0560476	+	0.998428i	$0.517850\pi$
$968$	302.340			0.312334
$969$			559.589i			0.577491i
$970$	−920.502			−0.948971
$971$		−	921.947i		−	0.949482i	−0.880125	−	0.474741i	$-0.842542\pi$
$971$		−	921.947i		−	0.949482i	0.880125	−	0.474741i	$-0.157458\pi$
$972$		−	56.7311i		−	0.0583653i
$973$	−594.648	−	174.415i	−0.611149	−	0.179254i
$974$	−31.1348			−0.0319659
$975$	783.820			0.803918
$976$			1072.81i			1.09919i
$977$	−1758.98			−1.80039			−0.900196	−	0.435485i	$-0.856577\pi$
$977$	−1758.98			−1.80039			−0.900196	+	0.435485i	$0.856577\pi$
$978$			389.624i			0.398388i
$979$		−	1445.66i		−	1.47667i
$980$	−52.5245	+	81.8355i	−0.0535964	+	0.0835056i
$981$	393.062			0.400675
$982$	−623.765			−0.635199
$983$			482.665i			0.491012i	0.969395	+	0.245506i	$0.0789542\pi$
$983$			482.665i			0.491012i	−0.969395	+	0.245506i	$0.921046\pi$
$984$	123.728			0.125740
$985$			32.9373i			0.0334389i
$986$			508.615i			0.515837i
$987$	−232.889	+	794.011i	−0.235957	+	0.804469i
$988$	−180.671			−0.182865
$989$	−383.002			−0.387262
$990$		−	536.951i		−	0.542375i
$991$	1160.81			1.17136			0.585678	−	0.810544i	$-0.300828\pi$
$991$	1160.81			1.17136			0.585678	+	0.810544i	$0.300828\pi$
$992$			28.2101i			0.0284376i
$993$			878.635i			0.884829i
$994$	390.423	−	1331.10i	0.392779	−	1.33914i
$995$	−865.659			−0.870009
$996$	0.708625			0.000711471
$997$			879.789i			0.882436i	0.897400	+	0.441218i	$0.145453\pi$
$997$			879.789i			0.882436i	−0.897400	+	0.441218i	$0.854547\pi$
$998$	674.577			0.675929
$999$			2080.81i			2.08289i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	287.3.b.a.83.14	yes	52
7.6	odd	2	inner	287.3.b.a.83.13	✓	52

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
287.3.b.a.83.13	✓	52	7.6	odd	2	inner
287.3.b.a.83.14	yes	52	1.1	even	1	trivial

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.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-1.91914 q^{2} +2.33237i q^{3} -0.316896 q^{4} +6.26237i q^{5} -4.47614i q^{6} +(-1.97015 + 6.71703i) q^{7} +8.28473 q^{8} +3.56006 q^{9} +O(q^{10})\)	\(q-1.91914 q^{2} +2.33237i q^{3} -0.316896 q^{4} +6.26237i q^{5} -4.47614i q^{6} +(-1.97015 + 6.71703i) q^{7} +8.28473 q^{8} +3.56006 q^{9} -12.0184i q^{10} +12.5496 q^{11} -0.739117i q^{12} +23.6377i q^{13} +(3.78100 - 12.8909i) q^{14} -14.6061 q^{15} -14.6320 q^{16} +9.94729i q^{17} -6.83227 q^{18} -24.1194i q^{19} -1.98452i q^{20} +(-15.6666 - 4.59512i) q^{21} -24.0845 q^{22} +6.30871 q^{23} +19.3230i q^{24} -14.2172 q^{25} -45.3640i q^{26} +29.2947i q^{27} +(0.624333 - 2.12860i) q^{28} -26.6427 q^{29} +28.0312 q^{30} -5.57725i q^{31} -5.05807 q^{32} +29.2704i q^{33} -19.0903i q^{34} +(-42.0645 - 12.3378i) q^{35} -1.12817 q^{36} +71.0302 q^{37} +46.2886i q^{38} -55.1317 q^{39} +51.8820i q^{40} -6.40312i q^{41} +(30.0664 + 8.81869i) q^{42} -60.7101 q^{43} -3.97693 q^{44} +22.2944i q^{45} -12.1073 q^{46} -50.6819i q^{47} -34.1272i q^{48} +(-41.2370 - 26.4672i) q^{49} +27.2849 q^{50} -23.2007 q^{51} -7.49067i q^{52} -86.4120 q^{53} -56.2206i q^{54} +78.5905i q^{55} +(-16.3222 + 55.6488i) q^{56} +56.2554 q^{57} +51.1311 q^{58} +37.3809i q^{59} +4.62862 q^{60} -73.3194i q^{61} +10.7035i q^{62} +(-7.01388 + 23.9131i) q^{63} +68.2351 q^{64} -148.028 q^{65} -56.1740i q^{66} +110.569 q^{67} -3.15225i q^{68} +14.7142i q^{69} +(80.7277 + 23.6780i) q^{70} +103.259 q^{71} +29.4942 q^{72} +81.2730i q^{73} -136.317 q^{74} -33.1598i q^{75} +7.64335i q^{76} +(-24.7247 + 84.2963i) q^{77} +105.806 q^{78} +94.1852 q^{79} -91.6309i q^{80} -36.2854 q^{81} +12.2885i q^{82} +0.958746i q^{83} +(4.96467 + 1.45617i) q^{84} -62.2936 q^{85} +116.511 q^{86} -62.1405i q^{87} +103.970 q^{88} -115.196i q^{89} -42.7862i q^{90} +(-158.775 - 46.5698i) q^{91} -1.99920 q^{92} +13.0082 q^{93} +97.2657i q^{94} +151.045 q^{95} -11.7973i q^{96} -76.5913i q^{97} +(79.1396 + 50.7942i) q^{98} +44.6775 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 52 q + 2 q^{2} + 90 q^{4} + 12 q^{7} - 2 q^{8} - 140 q^{9}+O(q^{10}) \) 52 * q + 2 * q^2 + 90 * q^4 + 12 * q^7 - 2 * q^8 - 140 * q^9	\( 52 q + 2 q^{2} + 90 q^{4} + 12 q^{7} - 2 q^{8} - 140 q^{9} + 24 q^{11} - 14 q^{14} + 44 q^{15} + 194 q^{16} + 70 q^{18} - 16 q^{21} - 48 q^{22} - 80 q^{23} - 304 q^{25} + 64 q^{28} - 12 q^{29} + 64 q^{30} - 166 q^{32} + 30 q^{35} - 70 q^{36} + 36 q^{37} - 68 q^{39} + 164 q^{42} - 172 q^{43} + 72 q^{44} + 68 q^{46} - 172 q^{49} - 234 q^{50} + 156 q^{51} + 64 q^{53} - 234 q^{56} + 140 q^{57} - 556 q^{58} + 152 q^{60} - 130 q^{63} + 334 q^{64} - 76 q^{65} + 160 q^{67} + 202 q^{70} - 408 q^{71} - 40 q^{72} + 398 q^{74} - 248 q^{77} + 390 q^{78} + 264 q^{79} - 116 q^{81} - 418 q^{84} + 232 q^{85} + 368 q^{86} - 220 q^{88} + 32 q^{91} - 74 q^{92} + 240 q^{93} - 44 q^{95} + 838 q^{98} - 24 q^{99}+O(q^{100}) \) 52 * q + 2 * q^2 + 90 * q^4 + 12 * q^7 - 2 * q^8 - 140 * q^9 + 24 * q^11 - 14 * q^14 + 44 * q^15 + 194 * q^16 + 70 * q^18 - 16 * q^21 - 48 * q^22 - 80 * q^23 - 304 * q^25 + 64 * q^28 - 12 * q^29 + 64 * q^30 - 166 * q^32 + 30 * q^35 - 70 * q^36 + 36 * q^37 - 68 * q^39 + 164 * q^42 - 172 * q^43 + 72 * q^44 + 68 * q^46 - 172 * q^49 - 234 * q^50 + 156 * q^51 + 64 * q^53 - 234 * q^56 + 140 * q^57 - 556 * q^58 + 152 * q^60 - 130 * q^63 + 334 * q^64 - 76 * q^65 + 160 * q^67 + 202 * q^70 - 408 * q^71 - 40 * q^72 + 398 * q^74 - 248 * q^77 + 390 * q^78 + 264 * q^79 - 116 * q^81 - 418 * q^84 + 232 * q^85 + 368 * q^86 - 220 * q^88 + 32 * q^91 - 74 * q^92 + 240 * q^93 - 44 * q^95 + 838 * q^98 - 24 * q^99

Introduction

L-functions

Modular forms

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