LMFDB - Embedded newform 287.3.b.a.83.18

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			83.18
Character	$\chi$	$=$	287.83
Dual form			287.3.b.a.83.17

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.37538 q^{2} +3.94905i q^{3} -2.10832 q^{4} -8.96232i q^{5} -5.43145i q^{6} +(-6.93022 - 0.985899i) q^{7} +8.40128 q^{8} -6.59497 q^{9} +O(q^{10})$	\(q-1.37538 q^{2} +3.94905i q^{3} -2.10832 q^{4} -8.96232i q^{5} -5.43145i q^{6} +(-6.93022 - 0.985899i) q^{7} +8.40128 q^{8} -6.59497 q^{9} +12.3266i q^{10} +7.89140 q^{11} -8.32586i q^{12} +22.1274i q^{13} +(9.53171 + 1.35599i) q^{14} +35.3926 q^{15} -3.12169 q^{16} -13.9450i q^{17} +9.07061 q^{18} +17.3372i q^{19} +18.8954i q^{20} +(3.89336 - 27.3678i) q^{21} -10.8537 q^{22} +20.7786 q^{23} +33.1771i q^{24} -55.3231 q^{25} -30.4336i q^{26} +9.49758i q^{27} +(14.6111 + 2.07859i) q^{28} +9.76346 q^{29} -48.6784 q^{30} +41.4010i q^{31} -29.3116 q^{32} +31.1635i q^{33} +19.1797i q^{34} +(-8.83594 + 62.1109i) q^{35} +13.9043 q^{36} -24.7505 q^{37} -23.8453i q^{38} -87.3821 q^{39} -75.2949i q^{40} -6.40312i q^{41} +(-5.35486 + 37.6412i) q^{42} +62.4860 q^{43} -16.6376 q^{44} +59.1062i q^{45} -28.5786 q^{46} +20.4869i q^{47} -12.3277i q^{48} +(47.0560 + 13.6650i) q^{49} +76.0905 q^{50} +55.0693 q^{51} -46.6517i q^{52} +74.7238 q^{53} -13.0628i q^{54} -70.7252i q^{55} +(-58.2228 - 8.28281i) q^{56} -68.4655 q^{57} -13.4285 q^{58} +25.1146i q^{59} -74.6190 q^{60} +105.606i q^{61} -56.9423i q^{62} +(45.7046 + 6.50197i) q^{63} +52.8014 q^{64} +198.313 q^{65} -42.8618i q^{66} +108.141 q^{67} +29.4005i q^{68} +82.0558i q^{69} +(12.1528 - 85.4262i) q^{70} -22.8434 q^{71} -55.4062 q^{72} +2.88823i q^{73} +34.0414 q^{74} -218.474i q^{75} -36.5524i q^{76} +(-54.6892 - 7.78012i) q^{77} +120.184 q^{78} -43.3707 q^{79} +27.9776i q^{80} -96.8611 q^{81} +8.80675i q^{82} +53.2469i q^{83} +(-8.20846 + 57.7001i) q^{84} -124.979 q^{85} -85.9422 q^{86} +38.5564i q^{87} +66.2979 q^{88} -155.247i q^{89} -81.2937i q^{90} +(21.8154 - 153.348i) q^{91} -43.8081 q^{92} -163.495 q^{93} -28.1773i q^{94} +155.382 q^{95} -115.753i q^{96} +43.7566i q^{97} +(-64.7200 - 18.7946i) q^{98} -52.0435 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−1.37538			−0.687691			−0.343846	−	0.939026i	$-0.611730\pi$
$2$	−1.37538			−0.687691			−0.343846	+	0.939026i	$0.611730\pi$
$3$			3.94905i			1.31635i	0.752865	+	0.658174i	$0.228671\pi$
$3$			3.94905i			1.31635i	−0.752865	+	0.658174i	$0.771329\pi$
$4$	−2.10832			−0.527081
$5$		−	8.96232i		−	1.79246i	−0.443586	−	0.896232i	$-0.646294\pi$
$5$		−	8.96232i		−	1.79246i	0.443586	−	0.896232i	$-0.353706\pi$
$6$		−	5.43145i		−	0.905242i
$7$	−6.93022	−	0.985899i	−0.990032	−	0.140843i
$7$	−6.93022	−	0.985899i	−0.990032	−	0.140843i
$8$	8.40128			1.05016
$9$	−6.59497			−0.732774
$10$			12.3266i			1.23266i
$11$	7.89140			0.717400			0.358700	−	0.933453i	$-0.383220\pi$
$11$	7.89140			0.717400			0.358700	+	0.933453i	$0.383220\pi$
$12$		−	8.32586i		−	0.693822i
$13$			22.1274i			1.70211i	0.525078	+	0.851054i	$0.324036\pi$
$13$			22.1274i			1.70211i	−0.525078	+	0.851054i	$0.675964\pi$
$14$	9.53171	+	1.35599i	0.680837	+	0.0968563i
$15$	35.3926			2.35951
$16$	−3.12169			−0.195106
$17$		−	13.9450i		−	0.820292i	−0.912020	−	0.410146i	$-0.865478\pi$
$17$		−	13.9450i		−	0.820292i	0.912020	−	0.410146i	$-0.134522\pi$
$18$	9.07061			0.503923
$19$			17.3372i			0.912485i	0.889855	+	0.456243i	$0.150805\pi$
$19$			17.3372i			0.912485i	−0.889855	+	0.456243i	$0.849195\pi$
$20$			18.8954i			0.944772i
$21$	3.89336	−	27.3678i	0.185398	−	1.30323i
$22$	−10.8537			−0.493350
$23$	20.7786			0.903419			0.451710	−	0.892165i	$-0.350814\pi$
$23$	20.7786			0.903419			0.451710	+	0.892165i	$0.350814\pi$
$24$			33.1771i			1.38238i
$25$	−55.3231			−2.21292
$26$		−	30.4336i		−	1.17052i
$27$			9.49758i			0.351762i
$28$	14.6111	+	2.07859i	0.521827	+	0.0742354i
$29$	9.76346			0.336671			0.168336	−	0.985730i	$-0.446161\pi$
$29$	9.76346			0.336671			0.168336	+	0.985730i	$0.446161\pi$
$30$	−48.6784			−1.62261
$31$			41.4010i			1.33552i	0.744378	+	0.667759i	$0.232746\pi$
$31$			41.4010i			1.33552i	−0.744378	+	0.667759i	$0.767254\pi$
$32$	−29.3116			−0.915988
$33$			31.1635i			0.944349i
$34$			19.1797i			0.564108i
$35$	−8.83594	+	62.1109i	−0.252455	+	1.77460i
$36$	13.9043			0.386231
$37$	−24.7505			−0.668931			−0.334466	−	0.942408i	$-0.608556\pi$
$37$	−24.7505			−0.668931			−0.334466	+	0.942408i	$0.608556\pi$
$38$		−	23.8453i		−	0.627508i
$39$	−87.3821			−2.24057
$40$		−	75.2949i		−	1.88237i
$41$		−	6.40312i		−	0.156174i
$41$		−	6.40312i		−	0.156174i
$42$	−5.35486	+	37.6412i	−0.127497	+	0.896218i
$43$	62.4860			1.45316			0.726582	−	0.687080i	$-0.241108\pi$
$43$	62.4860			1.45316			0.726582	+	0.687080i	$0.241108\pi$
$44$	−16.6376			−0.378128
$45$			59.1062i			1.31347i
$46$	−28.5786			−0.621274
$47$			20.4869i			0.435891i	0.975961	+	0.217946i	$0.0699356\pi$
$47$			20.4869i			0.435891i	−0.975961	+	0.217946i	$0.930064\pi$
$48$		−	12.3277i		−	0.256827i
$49$	47.0560	+	13.6650i	0.960327	+	0.278878i
$50$	76.0905			1.52181
$51$	55.0693			1.07979
$52$		−	46.6517i		−	0.897148i
$53$	74.7238			1.40988			0.704941	−	0.709266i	$-0.250973\pi$
$53$	74.7238			1.40988			0.704941	+	0.709266i	$0.250973\pi$
$54$		−	13.0628i		−	0.241904i
$55$		−	70.7252i		−	1.28591i
$56$	−58.2228	−	8.28281i	−1.03969	−	0.147907i
$57$	−68.4655			−1.20115
$58$	−13.4285			−0.231526
$59$			25.1146i			0.425672i	0.977088	+	0.212836i	$0.0682699\pi$
$59$			25.1146i			0.425672i	−0.977088	+	0.212836i	$0.931730\pi$
$60$	−74.6190			−1.24365
$61$			105.606i			1.73124i	0.500703	+	0.865619i	$0.333075\pi$
$61$			105.606i			1.73124i	−0.500703	+	0.865619i	$0.666925\pi$
$62$		−	56.9423i		−	0.918424i
$63$	45.7046	+	6.50197i	0.725470	+	0.103206i
$64$	52.8014			0.825023
$65$	198.313			3.05097
$66$		−	42.8618i		−	0.649420i
$67$	108.141			1.61405			0.807026	−	0.590516i	$-0.201076\pi$
$67$	108.141			1.61405			0.807026	+	0.590516i	$0.201076\pi$
$68$			29.4005i			0.432360i
$69$			82.0558i			1.18921i
$70$	12.1528	−	85.4262i	0.173611	−	1.22037i
$71$	−22.8434			−0.321738			−0.160869	−	0.986976i	$-0.551430\pi$
$71$	−22.8434			−0.321738			−0.160869	+	0.986976i	$0.551430\pi$
$72$	−55.4062			−0.769530
$73$			2.88823i			0.0395648i	0.999804	+	0.0197824i	$0.00629735\pi$
$73$			2.88823i			0.0395648i	−0.999804	+	0.0197824i	$0.993703\pi$
$74$	34.0414			0.460018
$75$		−	218.474i		−	2.91298i
$76$		−	36.5524i		−	0.480953i
$77$	−54.6892	−	7.78012i	−0.710249	−	0.101041i
$78$	120.184			1.54082
$79$	−43.3707			−0.548997			−0.274498	−	0.961588i	$-0.588512\pi$
$79$	−43.3707			−0.548997			−0.274498	+	0.961588i	$0.588512\pi$
$80$			27.9776i			0.349720i
$81$	−96.8611			−1.19582
$82$			8.80675i			0.107399i
$83$			53.2469i			0.641529i	0.947159	+	0.320765i	$0.103940\pi$
$83$			53.2469i			0.641529i	−0.947159	+	0.320765i	$0.896060\pi$
$84$	−8.20846	+	57.7001i	−0.0977197	+	0.686906i
$85$	−124.979			−1.47034
$86$	−85.9422			−0.999328
$87$			38.5564i			0.443177i
$88$	66.2979			0.753385
$89$		−	155.247i		−	1.74435i	−0.489196	−	0.872174i	$-0.662710\pi$
$89$		−	155.247i		−	1.74435i	0.489196	−	0.872174i	$-0.337290\pi$
$90$		−	81.2937i		−	0.903263i
$91$	21.8154	−	153.348i	0.239729	−	1.68514i
$92$	−43.8081			−0.476175
$93$	−163.495			−1.75801
$94$		−	28.1773i		−	0.299759i
$95$	155.382			1.63560
$96$		−	115.753i		−	1.20576i
$97$			43.7566i			0.451099i	0.974232	+	0.225550i	$0.0724178\pi$
$97$			43.7566i			0.451099i	−0.974232	+	0.225550i	$0.927582\pi$
$98$	−64.7200	−	18.7946i	−0.660408	−	0.191782i
$99$	−52.0435			−0.525692
$100$	116.639			1.16639
$101$			164.397i			1.62770i	0.581078	+	0.813848i	$0.302631\pi$
$101$			164.397i			1.62770i	−0.581078	+	0.813848i	$0.697369\pi$
$102$	−75.7414			−0.742562
$103$		−	37.3990i		−	0.363097i	−0.983382	−	0.181549i	$-0.941889\pi$
$103$		−	37.3990i		−	0.363097i	0.983382	−	0.181549i	$-0.0581109\pi$
$104$			185.899i			1.78749i
$105$	−245.279	−	34.8935i	−2.33599	−	0.332319i
$106$	−102.774			−0.969564
$107$	−14.3184			−0.133817			−0.0669084	−	0.997759i	$-0.521314\pi$
$107$	−14.3184			−0.133817			−0.0669084	+	0.997759i	$0.521314\pi$
$108$		−	20.0240i		−	0.185407i
$109$	21.4456			0.196748			0.0983742	−	0.995149i	$-0.468636\pi$
$109$	21.4456			0.196748			0.0983742	+	0.995149i	$0.468636\pi$
$110$			97.2743i			0.884311i
$111$		−	97.7407i		−	0.880547i
$112$	21.6340	+	3.07767i	0.193161	+	0.0274792i
$113$	−102.615			−0.908100			−0.454050	−	0.890976i	$-0.650021\pi$
$113$	−102.615			−0.908100			−0.454050	+	0.890976i	$0.650021\pi$
$114$	94.1662			0.826020
$115$		−	186.225i		−	1.61935i
$116$	−20.5845			−0.177453
$117$		−	145.930i		−	1.24726i
$118$		−	34.5422i		−	0.292731i
$119$	−13.7483	+	96.6417i	−0.115532	+	0.812115i
$120$	297.343			2.47786
$121$	−58.7258			−0.485337
$122$		−	145.248i		−	1.19056i
$123$	25.2862			0.205579
$124$		−	87.2867i		−	0.703925i
$125$			271.765i			2.17412i
$126$	−62.8613	−	8.94270i	−0.498900	−	0.0709738i
$127$	115.208			0.907150			0.453575	−	0.891218i	$-0.350148\pi$
$127$	115.208			0.907150			0.453575	+	0.891218i	$0.350148\pi$
$128$	44.6242			0.348627
$129$			246.760i			1.91287i
$130$	−272.756			−2.09812
$131$		−	101.692i		−	0.776271i	−0.921602	−	0.388136i	$-0.873119\pi$
$131$		−	101.692i		−	0.776271i	0.921602	−	0.388136i	$-0.126881\pi$
$132$		−	65.7027i		−	0.497748i
$133$	17.0927	−	120.151i	0.128517	−	0.903389i
$134$	−148.736			−1.10997
$135$	85.1203			0.630521
$136$		−	117.156i		−	0.861438i
$137$	227.407			1.65990			0.829952	−	0.557835i	$-0.188368\pi$
$137$	227.407			1.65990			0.829952	+	0.557835i	$0.188368\pi$
$138$		−	112.858i		−	0.817813i
$139$		−	71.1707i		−	0.512020i	−0.966674	−	0.256010i	$-0.917592\pi$
$139$		−	71.1707i		−	0.512020i	0.966674	−	0.256010i	$-0.0824080\pi$
$140$	18.6290	−	130.950i	0.133064	−	0.935355i
$141$	−80.9037			−0.573785
$142$	31.4184			0.221256
$143$			174.616i			1.22109i
$144$	20.5875			0.142968
$145$		−	87.5032i		−	0.603471i
$146$		−	3.97243i		−	0.0272084i
$147$	−53.9637	+	185.826i	−0.367100	+	1.26412i
$148$	52.1819			0.352581
$149$	−172.348			−1.15670			−0.578350	−	0.815789i	$-0.696303\pi$
$149$	−172.348			−1.15670			−0.578350	+	0.815789i	$0.696303\pi$
$150$			300.485i			2.00323i
$151$	−124.449			−0.824163			−0.412082	−	0.911147i	$-0.635198\pi$
$151$	−124.449			−0.824163			−0.412082	+	0.911147i	$0.635198\pi$
$152$			145.655i			0.958255i
$153$			91.9666i			0.601089i
$154$	75.2185	+	10.7006i	0.488432	+	0.0694847i
$155$	371.049			2.39387
$156$	184.230			1.18096
$157$		−	124.348i		−	0.792023i	−0.918246	−	0.396011i	$-0.870394\pi$
$157$		−	124.348i		−	0.792023i	0.918246	−	0.396011i	$-0.129606\pi$
$158$	59.6514			0.377540
$159$			295.088i			1.85590i
$160$			262.700i			1.64187i
$161$	−144.001	−	20.4856i	−0.894414	−	0.127240i
$162$	133.221			0.822352
$163$	149.522			0.917311			0.458655	−	0.888614i	$-0.348331\pi$
$163$	149.522			0.917311			0.458655	+	0.888614i	$0.348331\pi$
$164$			13.4998i			0.0823161i
$165$	279.297			1.69271
$166$		−	73.2349i		−	0.441174i
$167$		−	247.222i		−	1.48037i	−0.672401	−	0.740187i	$-0.734737\pi$
$167$		−	247.222i		−	1.48037i	0.672401	−	0.740187i	$-0.265263\pi$
$168$	32.7092	−	229.924i	0.194698	−	1.36860i
$169$	−320.622			−1.89717
$170$	171.894			1.01114
$171$		−	114.338i		−	0.668646i
$172$	−131.741			−0.765934
$173$			140.654i			0.813026i	0.913645	+	0.406513i	$0.133255\pi$
$173$			140.654i			0.813026i	−0.913645	+	0.406513i	$0.866745\pi$
$174$		−	53.0298i		−	0.304769i
$175$	383.402	+	54.5430i	2.19087	+	0.311674i
$176$	−24.6345			−0.139969
$177$	−99.1788			−0.560332
$178$			213.524i			1.19957i
$179$	−93.9794			−0.525024			−0.262512	−	0.964929i	$-0.584551\pi$
$179$	−93.9794			−0.525024			−0.262512	+	0.964929i	$0.584551\pi$
$180$		−	124.615i		−	0.692305i
$181$			123.872i			0.684377i	0.939631	+	0.342189i	$0.111168\pi$
$181$			123.872i			0.684377i	−0.939631	+	0.342189i	$0.888832\pi$
$182$	−30.0045	+	210.912i	−0.164860	+	1.15886i
$183$	−417.041			−2.27891
$184$	174.567			0.948735
$185$			221.821i			1.19903i
$186$	224.868			1.20897
$187$		−	110.045i		−	0.588477i
$188$		−	43.1930i		−	0.229750i
$189$	9.36365	−	65.8203i	0.0495431	−	0.348256i
$190$	−213.709			−1.12479
$191$	70.1694			0.367379			0.183690	−	0.982984i	$-0.441196\pi$
$191$	70.1694			0.367379			0.183690	+	0.982984i	$0.441196\pi$
$192$			208.515i			1.08602i
$193$	321.836			1.66755			0.833773	−	0.552108i	$-0.186176\pi$
$193$	321.836			1.66755			0.833773	+	0.552108i	$0.186176\pi$
$194$		−	60.1821i		−	0.310217i
$195$			783.146i			4.01614i
$196$	−99.2092	−	28.8102i	−0.506169	−	0.146991i
$197$	−334.975			−1.70038			−0.850189	−	0.526477i	$-0.823513\pi$
$197$	−334.975			−1.70038			−0.850189	+	0.526477i	$0.823513\pi$
$198$	71.5798			0.361514
$199$			47.7786i			0.240094i	0.992768	+	0.120047i	$0.0383045\pi$
$199$			47.7786i			0.240094i	−0.992768	+	0.120047i	$0.961696\pi$
$200$	−464.785			−2.32393
$201$			427.056i			2.12465i
$202$		−	226.109i		−	1.11935i
$203$	−67.6630	−	9.62578i	−0.333315	−	0.0474177i
$204$	−116.104			−0.569136
$205$	−57.3868			−0.279936
$206$			51.4379i			0.249699i
$207$	−137.035			−0.662002
$208$		−	69.0749i		−	0.332091i
$209$			136.815i			0.654617i
$210$	337.352	+	47.9920i	1.60644	+	0.228533i
$211$	−245.254			−1.16234			−0.581170	−	0.813782i	$-0.697405\pi$
$211$	−245.254			−1.16234			−0.581170	+	0.813782i	$0.697405\pi$
$212$	−157.542			−0.743122
$213$		−	90.2096i		−	0.423519i
$214$	19.6933			0.0920247
$215$		−	560.020i		−	2.60474i
$216$			79.7918i			0.369407i
$217$	40.8172	−	286.918i	0.188098	−	1.32220i
$218$	−29.4959			−0.135302
$219$	−11.4058			−0.0520811
$220$			149.112i			0.677780i
$221$	308.566			1.39622
$222$			134.431i			0.605545i
$223$			13.4263i			0.0602077i	0.999547	+	0.0301038i	$0.00958380\pi$
$223$			13.4263i			0.0602077i	−0.999547	+	0.0301038i	$0.990416\pi$
$224$	203.136	+	28.8983i	0.906857	+	0.129010i
$225$	364.854			1.62157
$226$	141.135			0.624493
$227$			114.190i			0.503039i	0.967852	+	0.251520i	$0.0809303\pi$
$227$			114.190i			0.503039i	−0.967852	+	0.251520i	$0.919070\pi$
$228$	144.347			0.633102
$229$			56.6129i			0.247218i	0.992331	+	0.123609i	$0.0394469\pi$
$229$			56.6129i			0.247218i	−0.992331	+	0.123609i	$0.960553\pi$
$230$			256.130i			1.11361i
$231$	30.7241	−	215.970i	0.133005	−	0.934935i
$232$	82.0256			0.353559
$233$	−148.448			−0.637116			−0.318558	−	0.947903i	$-0.603199\pi$
$233$	−148.448			−0.637116			−0.318558	+	0.947903i	$0.603199\pi$
$234$			200.709i			0.857731i
$235$	183.610			0.781319
$236$		−	52.9497i		−	0.224363i
$237$		−	171.273i		−	0.722671i
$238$	18.9092	−	132.919i	0.0794504	−	0.558485i
$239$	−233.858			−0.978485			−0.489242	−	0.872148i	$-0.662727\pi$
$239$	−233.858			−0.978485			−0.489242	+	0.872148i	$0.662727\pi$
$240$	−110.485			−0.460353
$241$			171.548i			0.711817i	0.934521	+	0.355909i	$0.115829\pi$
$241$			171.548i			0.711817i	−0.934521	+	0.355909i	$0.884171\pi$
$242$	80.7705			0.333762
$243$		−	297.031i		−	1.22235i
$244$		−	222.651i		−	0.912502i
$245$	122.470	−	421.731i	0.499878	−	1.72135i
$246$	−34.7783			−0.141375
$247$	−383.628			−1.55315
$248$			347.822i			1.40251i
$249$	−210.275			−0.844476
$250$		−	373.781i		−	1.49513i
$251$			32.9143i			0.131133i	0.997848	+	0.0655664i	$0.0208854\pi$
$251$			32.9143i			0.131133i	−0.997848	+	0.0655664i	$0.979115\pi$
$252$	−96.3600	−	13.7083i	−0.382381	−	0.0543978i
$253$	163.973			0.648113
$254$	−158.455			−0.623839
$255$		−	493.548i		−	1.93548i
$256$	−272.581			−1.06477
$257$		−	132.738i		−	0.516491i	−0.966079	−	0.258245i	$-0.916856\pi$
$257$		−	132.738i		−	0.516491i	0.966079	−	0.258245i	$-0.0831443\pi$
$258$		−	339.390i		−	1.31546i
$259$	171.526	+	24.4014i	0.662263	+	0.0942141i
$260$	−418.107			−1.60810
$261$	−64.3897			−0.246704
$262$			139.865i			0.533835i
$263$	−131.767			−0.501016			−0.250508	−	0.968115i	$-0.580598\pi$
$263$	−131.767			−0.501016			−0.250508	+	0.968115i	$0.580598\pi$
$264$			261.813i			0.991717i
$265$		−	669.698i		−	2.52716i
$266$	−23.5091	+	165.253i	−0.0883799	+	0.621253i
$267$	613.078			2.29617
$268$	−227.997			−0.850735
$269$			203.366i			0.756008i	0.925804	+	0.378004i	$0.123389\pi$
$269$			203.366i			0.756008i	−0.925804	+	0.378004i	$0.876611\pi$
$270$	−117.073			−0.433604
$271$			151.445i			0.558836i	0.960170	+	0.279418i	$0.0901416\pi$
$271$			151.445i			0.558836i	−0.960170	+	0.279418i	$0.909858\pi$
$272$			43.5318i			0.160044i
$273$	605.578	+	86.1499i	2.21823	+	0.315568i
$274$	−312.772			−1.14150
$275$	−436.577			−1.58755
$276$		−	173.000i		−	0.626812i
$277$	−21.1639			−0.0764039			−0.0382020	−	0.999270i	$-0.512163\pi$
$277$	−21.1639			−0.0764039			−0.0382020	+	0.999270i	$0.512163\pi$
$278$			97.8870i			0.352112i
$279$		−	273.039i		−	0.978633i
$280$	−74.2332	+	521.811i	−0.265119	+	1.86361i
$281$	305.730			1.08801			0.544003	−	0.839083i	$-0.316908\pi$
$281$	305.730			1.08801			0.544003	+	0.839083i	$0.316908\pi$
$282$	111.274			0.394587
$283$			282.643i			0.998739i	0.866389	+	0.499369i	$0.166435\pi$
$283$			282.643i			0.998739i	−0.866389	+	0.499369i	$0.833565\pi$
$284$	48.1612			0.169582
$285$			613.609i			2.15301i
$286$		−	240.164i		−	0.839735i
$287$	−6.31283	+	44.3751i	−0.0219959	+	0.154617i
$288$	193.309			0.671212
$289$	94.5381			0.327121
$290$			120.350i			0.415002i
$291$	−172.797			−0.593804
$292$		−	6.08933i		−	0.0208539i
$293$		−	326.573i		−	1.11458i	−0.830317	−	0.557291i	$-0.811841\pi$
$293$		−	326.573i		−	1.11458i	0.830317	−	0.557291i	$-0.188159\pi$
$294$	74.2208	−	255.582i	0.252452	−	0.869328i
$295$	225.085			0.763001
$296$	−207.936			−0.702485
$297$			74.9492i			0.252354i
$298$	237.045			0.795452
$299$			459.777i			1.53772i
$300$			460.613i			1.53538i
$301$	−433.042	−	61.6049i	−1.43868	−	0.204667i
$302$	171.165			0.566770
$303$	−649.213			−2.14262
$304$		−	54.1214i		−	0.178031i
$305$	946.470			3.10318
$306$		−	126.489i		−	0.413364i
$307$			145.242i			0.473100i	0.971619	+	0.236550i	$0.0760167\pi$
$307$			145.242i			0.473100i	−0.971619	+	0.236550i	$0.923983\pi$
$308$	115.302	+	16.4030i	0.374358	+	0.0532565i
$309$	147.690			0.477962
$310$	−510.335			−1.64624
$311$			95.8615i			0.308236i	0.988052	+	0.154118i	$0.0492536\pi$
$311$			95.8615i			0.308236i	−0.988052	+	0.154118i	$0.950746\pi$
$312$	−734.122			−2.35295
$313$			69.0977i			0.220760i	0.993889	+	0.110380i	$0.0352067\pi$
$313$			69.0977i			0.220760i	−0.993889	+	0.110380i	$0.964793\pi$
$314$			171.026i			0.544667i
$315$	58.2727	−	409.619i	0.184993	−	1.30038i
$316$	91.4395			0.289365
$317$	290.285			0.915726			0.457863	−	0.889023i	$-0.348615\pi$
$317$	290.285			0.915726			0.457863	+	0.889023i	$0.348615\pi$
$318$		−	405.859i		−	1.27628i
$319$	77.0474			0.241528
$320$		−	473.223i		−	1.47882i
$321$		−	56.5440i		−	0.176150i
$322$	198.056	+	28.1756i	0.615081	+	0.0875018i
$323$	241.767			0.748504
$324$	204.214			0.630291
$325$		−	1224.16i		−	3.76664i
$326$	−205.650			−0.630827
$327$			84.6895i			0.258989i
$328$		−	53.7944i		−	0.164007i
$329$	20.1980	−	141.979i	0.0613921	−	0.431546i
$330$	−384.141			−1.16406
$331$	264.594			0.799377			0.399689	−	0.916651i	$-0.369118\pi$
$331$	264.594			0.799377			0.399689	+	0.916651i	$0.369118\pi$
$332$		−	112.262i		−	0.338137i
$333$	163.228			0.490176
$334$			340.025i			1.01804i
$335$		−	969.198i		−	2.89313i
$336$	−12.1539	+	85.4337i	−0.0361722	+	0.254267i
$337$	−389.166			−1.15480			−0.577398	−	0.816463i	$-0.695932\pi$
$337$	−389.166			−1.15480			−0.577398	+	0.816463i	$0.695932\pi$
$338$	440.978			1.30467
$339$		−	405.233i		−	1.19538i
$340$	263.496			0.774989
$341$			326.712i			0.958100i
$342$			157.259i			0.459822i
$343$	−312.636	−	141.094i	−0.911476	−	0.411353i
$344$	524.963			1.52605
$345$	735.410			2.13162
$346$		−	193.452i		−	0.559111i
$347$	74.5067			0.214717			0.107358	−	0.994220i	$-0.465761\pi$
$347$	74.5067			0.214717			0.107358	+	0.994220i	$0.465761\pi$
$348$		−	81.2892i		−	0.233590i
$349$			404.578i			1.15925i	0.814884	+	0.579624i	$0.196801\pi$
$349$			404.578i			1.15925i	−0.814884	+	0.579624i	$0.803199\pi$
$350$	−527.324	−	75.0175i	−1.50664	−	0.214336i
$351$	−210.157			−0.598737
$352$	−231.310			−0.657130
$353$		−	132.266i		−	0.374690i	−0.982294	−	0.187345i	$-0.940012\pi$
$353$		−	132.266i		−	0.374690i	0.982294	−	0.187345i	$-0.0599882\pi$
$354$	136.409			0.385336
$355$			204.730i			0.576704i
$356$			327.311i			0.919412i
$357$	−381.643	−	54.2927i	−1.06903	−	0.152081i
$358$	129.258			0.361055
$359$	316.509			0.881640			0.440820	−	0.897596i	$-0.354688\pi$
$359$	316.509			0.881640			0.440820	+	0.897596i	$0.354688\pi$
$360$			496.568i			1.37936i
$361$	60.4210			0.167371
$362$		−	170.372i		−	0.470640i
$363$		−	231.911i		−	0.638873i
$364$	−45.9938	+	323.307i	−0.126357	+	0.888205i
$365$	25.8853			0.0709185
$366$	573.591			1.56719
$367$			282.021i			0.768448i	0.923240	+	0.384224i	$0.125531\pi$
$367$			282.021i			0.768448i	−0.923240	+	0.384224i	$0.874469\pi$
$368$	−64.8645			−0.176262
$369$			42.2284i			0.114440i
$370$		−	305.089i		−	0.824566i
$371$	−517.852	−	73.6701i	−1.39583	−	0.198572i
$372$	344.699			0.926611
$373$	−396.824			−1.06387			−0.531936	−	0.846785i	$-0.678535\pi$
$373$	−396.824			−1.06387			−0.531936	+	0.846785i	$0.678535\pi$
$374$			151.354i			0.404691i
$375$	−1073.21			−2.86190
$376$			172.116i			0.457756i
$377$			216.040i			0.573050i
$378$	−12.8786	+	90.5282i	−0.0340704	+	0.239492i
$379$	223.506			0.589726			0.294863	−	0.955539i	$-0.404726\pi$
$379$	223.506			0.589726			0.294863	+	0.955539i	$0.404726\pi$
$380$	−327.594			−0.862091
$381$			454.962i			1.19413i
$382$	−96.5098			−0.252643
$383$		−	542.079i		−	1.41535i	−0.706538	−	0.707675i	$-0.749744\pi$
$383$		−	542.079i		−	1.41535i	0.706538	−	0.707675i	$-0.250256\pi$
$384$			176.223i			0.458914i
$385$	−69.7279	+	490.142i	−0.181111	+	1.27310i
$386$	−442.648			−1.14676
$387$	−412.094			−1.06484
$388$		−	92.2531i		−	0.237766i
$389$	138.299			0.355524			0.177762	−	0.984073i	$-0.443114\pi$
$389$	138.299			0.355524			0.177762	+	0.984073i	$0.443114\pi$
$390$		−	1077.13i		−	2.76186i
$391$		−	289.757i		−	0.741067i
$392$	395.331	+	114.803i	1.00850	+	0.292866i
$393$	401.585			1.02184
$394$	460.718			1.16934
$395$			388.702i			0.984056i
$396$	109.725			0.277082
$397$		−	84.9819i		−	0.214060i	−0.994256	−	0.107030i	$-0.965866\pi$
$397$		−	84.9819i		−	0.214060i	0.994256	−	0.107030i	$-0.0341341\pi$
$398$		−	65.7139i		−	0.165110i
$399$	474.481	+	67.5000i	1.18918	+	0.169173i
$400$	172.702			0.431754
$401$	−641.684			−1.60021			−0.800105	−	0.599861i	$-0.795223\pi$
$401$	−641.684			−1.60021			−0.800105	+	0.599861i	$0.795223\pi$
$402$		−	587.365i		−	1.46111i
$403$	−916.097			−2.27319
$404$		−	346.602i		−	0.857927i
$405$			868.100i			2.14346i
$406$	93.0625	+	13.2391i	0.229218	+	0.0326087i
$407$	−195.316			−0.479891
$408$	462.653			1.13395
$409$			205.746i			0.503045i	0.967851	+	0.251523i	$0.0809313\pi$
$409$			205.746i			0.503045i	−0.967851	+	0.251523i	$0.919069\pi$
$410$	78.9289			0.192509
$411$			898.040i			2.18501i
$412$			78.8491i			0.191381i
$413$	24.7605	−	174.050i	0.0599527	−	0.421428i
$414$	188.475			0.455253
$415$	477.216			1.14992
$416$		−	648.590i		−	1.55911i
$417$	281.057			0.673997
$418$		−	188.173i		−	0.450174i
$419$			178.320i			0.425586i	0.977097	+	0.212793i	$0.0682560\pi$
$419$			178.320i			0.425586i	−0.977097	+	0.212793i	$0.931744\pi$
$420$	517.126	+	73.5668i	1.23125	+	0.175159i
$421$	−671.261			−1.59444			−0.797222	−	0.603686i	$-0.793698\pi$
$421$	−671.261			−1.59444			−0.797222	+	0.603686i	$0.793698\pi$
$422$	337.318			0.799331
$423$		−	135.110i		−	0.319410i
$424$	627.775			1.48060
$425$			771.479i			1.81524i
$426$			124.073i			0.291251i
$427$	104.116	−	731.870i	0.243832	−	1.71398i
$428$	30.1878			0.0705323
$429$	−689.567			−1.60738
$430$			770.241i			1.79126i
$431$	485.841			1.12724			0.563620	−	0.826034i	$-0.309408\pi$
$431$	485.841			1.12724			0.563620	+	0.826034i	$0.309408\pi$
$432$		−	29.6485i		−	0.0686308i
$433$		−	412.200i		−	0.951962i	−0.879456	−	0.475981i	$-0.842093\pi$
$433$		−	412.200i		−	0.951962i	0.879456	−	0.475981i	$-0.157907\pi$
$434$	−56.1393	+	394.623i	−0.129353	+	0.909269i
$435$	345.554			0.794378
$436$	−45.2142			−0.103702
$437$			360.244i			0.824356i
$438$	15.6873			0.0358158
$439$		−	257.010i		−	0.585445i	−0.956197	−	0.292722i	$-0.905439\pi$
$439$		−	257.010i		−	0.585445i	0.956197	−	0.292722i	$-0.0945612\pi$
$440$		−	594.182i		−	1.35041i
$441$	−310.333	−	90.1202i	−0.703703	−	0.204354i
$442$	−424.396			−0.960172
$443$	204.239			0.461036			0.230518	−	0.973068i	$-0.425958\pi$
$443$	204.239			0.461036			0.230518	+	0.973068i	$0.425958\pi$
$444$			206.069i			0.464119i
$445$	−1391.37			−3.12668
$446$		−	18.4663i		−	0.0414043i
$447$		−	680.611i		−	1.52262i
$448$	−365.926	−	52.0569i	−0.816799	−	0.116198i
$449$	291.509			0.649240			0.324620	−	0.945845i	$-0.394764\pi$
$449$	291.509			0.649240			0.324620	+	0.945845i	$0.394764\pi$
$450$	−501.814			−1.11514
$451$		−	50.5296i		−	0.112039i
$452$	216.346			0.478642
$453$		−	491.454i		−	1.08489i
$454$		−	157.055i		−	0.345936i
$455$	−1374.35	−	195.516i	−3.02055	−	0.429706i
$456$	−575.198			−1.26140
$457$	516.015			1.12914			0.564568	−	0.825387i	$-0.309043\pi$
$457$	516.015			1.12914			0.564568	+	0.825387i	$0.309043\pi$
$458$		−	77.8644i		−	0.170010i
$459$	132.443			0.288548
$460$			392.622i			0.853526i
$461$		−	31.0350i		−	0.0673209i	−0.999433	−	0.0336605i	$-0.989284\pi$
$461$		−	31.0350i		−	0.0673209i	0.999433	−	0.0336605i	$-0.0107165\pi$
$462$	−42.2573	+	297.042i	−0.0914661	+	0.642947i
$463$	−18.6004			−0.0401736			−0.0200868	−	0.999798i	$-0.506394\pi$
$463$	−18.6004			−0.0401736			−0.0200868	+	0.999798i	$0.506394\pi$
$464$	−30.4785			−0.0656864
$465$			1465.29i			3.15116i
$466$	204.173			0.438139
$467$		−	209.316i		−	0.448214i	−0.974564	−	0.224107i	$-0.928053\pi$
$467$		−	209.316i		−	0.448214i	0.974564	−	0.224107i	$-0.0719466\pi$
$468$			307.666i			0.657407i
$469$	−749.444	−	106.617i	−1.59796	−	0.227327i
$470$	−252.534			−0.537307
$471$	491.054			1.04258
$472$			210.995i			0.447023i
$473$	493.102			1.04250
$474$			235.566i			0.496975i
$475$		−	959.149i		−	2.01926i
$476$	28.9859	−	203.752i	0.0608947	−	0.428050i
$477$	−492.801			−1.03313
$478$	321.644			0.672896
$479$			5.29628i			0.0110569i	0.999985	+	0.00552847i	$0.00175978\pi$
$479$			5.29628i			0.0110569i	−0.999985	+	0.00552847i	$0.998240\pi$
$480$	−1037.41			−2.16128
$481$		−	547.663i		−	1.13859i
$482$		−	235.944i		−	0.489511i
$483$	80.8987	−	568.665i	0.167492	−	1.17736i
$484$	123.813			0.255812
$485$	392.161			0.808579
$486$			408.531i			0.840599i
$487$	−526.497			−1.08110			−0.540551	−	0.841311i	$-0.681784\pi$
$487$	−526.497			−1.08110			−0.540551	+	0.841311i	$0.681784\pi$
$488$			887.222i			1.81808i
$489$			590.468i			1.20750i
$490$	−168.443	+	580.041i	−0.343762	+	1.18376i
$491$	138.239			0.281546			0.140773	−	0.990042i	$-0.455041\pi$
$491$	138.239			0.281546			0.140773	+	0.990042i	$0.455041\pi$
$492$	−53.3115			−0.108357
$493$		−	136.151i		−	0.276168i
$494$	527.635			1.06809
$495$			466.431i			0.942284i
$496$		−	129.241i		−	0.260567i
$497$	158.310	+	22.5213i	0.318531	+	0.0453144i
$498$	289.208			0.580739
$499$	253.801			0.508619			0.254309	−	0.967123i	$-0.418152\pi$
$499$	253.801			0.508619			0.254309	+	0.967123i	$0.418152\pi$
$500$		−	572.969i		−	1.14594i
$501$	976.293			1.94869
$502$		−	45.2698i		−	0.0901789i
$503$			882.608i			1.75469i	0.479862	+	0.877344i	$0.340687\pi$
$503$			882.608i			1.75469i	−0.479862	+	0.877344i	$0.659313\pi$
$504$	383.977	+	54.6249i	0.761860	+	0.108383i
$505$	1473.38			2.91759
$506$	−225.525			−0.445702
$507$		−	1266.15i		−	2.49734i
$508$	−242.896			−0.478141
$509$		−	455.242i		−	0.894385i	−0.894438	−	0.447193i	$-0.852424\pi$
$509$		−	455.242i		−	0.894385i	0.894438	−	0.447193i	$-0.147576\pi$
$510$			678.818i			1.33102i
$511$	2.84751	−	20.0161i	0.00557242	−	0.0391705i
$512$	196.407			0.383607
$513$	−164.662			−0.320978
$514$			182.566i			0.355186i
$515$	−335.182			−0.650838
$516$		−	520.250i		−	1.00824i
$517$			161.670i			0.312708i
$518$	−235.914	−	33.5613i	−0.455433	−	0.0647902i
$519$	−555.447			−1.07023
$520$	1666.08			3.20400
$521$		−	562.711i		−	1.08006i	−0.841646	−	0.540030i	$-0.818413\pi$
$521$		−	562.711i		−	1.08006i	0.841646	−	0.540030i	$-0.181587\pi$
$522$	88.5605			0.169656
$523$			483.006i			0.923530i	0.887002	+	0.461765i	$0.152784\pi$
$523$			483.006i			0.923530i	−0.887002	+	0.461765i	$0.847216\pi$
$524$			214.398i			0.409157i
$525$	−215.393	+	1514.07i	−0.410272	+	2.88394i
$526$	181.230			0.344545
$527$	577.336			1.09551
$528$		−	97.2828i		−	0.184248i
$529$	−97.2481			−0.183834
$530$			921.091i			1.73791i
$531$		−	165.630i		−	0.311921i
$532$	−36.0370	+	253.317i	−0.0677387	+	0.476159i
$533$	141.684			0.265825
$534$	−843.216			−1.57906
$535$			128.326i			0.239862i
$536$	908.527			1.69501
$537$		−	371.129i		−	0.691115i
$538$		−	279.706i		−	0.519900i
$539$	371.338	+	107.836i	0.688938	+	0.200067i
$540$	−179.461			−0.332335
$541$	905.358			1.67349			0.836745	−	0.547592i	$-0.184455\pi$
$541$	905.358			1.67349			0.836745	+	0.547592i	$0.184455\pi$
$542$		−	208.294i		−	0.384307i
$543$	−489.177			−0.900879
$544$			408.749i			0.751377i
$545$		−	192.202i		−	0.352664i
$546$	−832.901	−	118.489i	−1.52546	−	0.217013i
$547$	892.245			1.63116			0.815581	−	0.578643i	$-0.196418\pi$
$547$	892.245			1.63116			0.815581	+	0.578643i	$0.196418\pi$
$548$	−479.447			−0.874903
$549$		−	696.465i		−	1.26861i
$550$	600.460			1.09175
$551$			169.271i			0.307207i
$552$			689.374i			1.24887i
$553$	300.569	+	42.7591i	0.543524	+	0.0773222i
$554$	29.1085			0.0525423
$555$	−875.983			−1.57835
$556$			150.051i			0.269876i
$557$	554.619			0.995725			0.497863	−	0.867256i	$-0.334118\pi$
$557$	554.619			0.995725			0.497863	+	0.867256i	$0.334118\pi$
$558$			375.533i			0.672997i
$559$			1382.65i			2.47344i
$560$	27.5831	−	193.891i	0.0492555	−	0.346234i
$561$	434.574			0.774641
$562$	−420.496			−0.748213
$563$		−	811.020i		−	1.44053i	−0.693698	−	0.720266i	$-0.744020\pi$
$563$		−	811.020i		−	1.44053i	0.693698	−	0.720266i	$-0.255980\pi$
$564$	170.571			0.302431
$565$			919.671i			1.62774i
$566$		−	388.743i		−	0.686824i
$567$	671.269	+	95.4952i	1.18390	+	0.168422i
$568$	−191.914			−0.337876
$569$	−371.410			−0.652742			−0.326371	−	0.945242i	$-0.605826\pi$
$569$	−371.410			−0.652742			−0.326371	+	0.945242i	$0.605826\pi$
$570$		−	843.948i		−	1.48061i
$571$	1098.72			1.92421			0.962104	−	0.272682i	$-0.0879107\pi$
$571$	1098.72			1.92421			0.962104	+	0.272682i	$0.0879107\pi$
$572$		−	368.147i		−	0.643614i
$573$			277.102i			0.483599i
$574$	8.68256	−	61.0327i	0.0151264	−	0.106329i
$575$	−1149.54			−1.99920
$576$	−348.224			−0.604555
$577$			373.826i			0.647878i	0.946078	+	0.323939i	$0.105007\pi$
$577$			373.826i			0.647878i	−0.946078	+	0.323939i	$0.894993\pi$
$578$	−130.026			−0.224959
$579$			1270.95i			2.19507i
$580$			184.485i			0.318078i
$581$	52.4961	−	369.013i	0.0903547	−	0.635134i
$582$	237.662			0.408354
$583$	589.675			1.01145
$584$			24.2649i			0.0415494i
$585$	−1307.87			−2.23567
$586$			449.162i			0.766489i
$587$		−	501.271i		−	0.853953i	−0.904263	−	0.426977i	$-0.859579\pi$
$587$		−	501.271i		−	0.853953i	0.904263	−	0.426977i	$-0.140421\pi$
$588$	113.773	−	391.782i	0.193491	−	0.666296i
$589$	−717.779			−1.21864
$590$	−309.578			−0.524709
$591$		−	1322.83i		−	2.23829i
$592$	77.2633			0.130512
$593$		−	95.5479i		−	0.161126i	−0.996750	−	0.0805631i	$-0.974328\pi$
$593$		−	95.5479i		−	0.161126i	0.996750	−	0.0805631i	$-0.0256719\pi$
$594$		−	103.084i		−	0.173542i
$595$	866.133	+	123.217i	1.45569	+	0.207087i
$596$	363.365			0.609674
$597$	−188.680			−0.316047
$598$		−	632.370i		−	1.05747i
$599$	−879.079			−1.46758			−0.733789	−	0.679378i	$-0.762250\pi$
$599$	−879.079			−1.46758			−0.733789	+	0.679378i	$0.762250\pi$
$600$		−	1835.46i		−	3.05910i
$601$		−	782.926i		−	1.30271i	−0.758775	−	0.651353i	$-0.774202\pi$
$601$		−	782.926i		−	1.30271i	0.758775	−	0.651353i	$-0.225798\pi$
$602$	595.599	+	84.7303i	0.989367	+	0.140748i
$603$	−713.190			−1.18274
$604$	262.378			0.434400
$605$			526.319i			0.869949i
$606$	892.916			1.47346
$607$			917.036i			1.51077i	0.655282	+	0.755384i	$0.272550\pi$
$607$			917.036i			1.51077i	−0.655282	+	0.755384i	$0.727450\pi$
$608$		−	508.182i		−	0.835825i
$609$	38.0127	−	267.204i	0.0624182	−	0.438759i
$610$	−1301.76			−2.13403
$611$	−453.322			−0.741934
$612$		−	193.895i		−	0.316822i
$613$	−286.295			−0.467039			−0.233519	−	0.972352i	$-0.575024\pi$
$613$	−286.295			−0.467039			−0.233519	+	0.972352i	$0.575024\pi$
$614$		−	199.763i		−	0.325347i
$615$		−	226.623i		−	0.368493i
$616$	−459.459	−	65.3630i	−0.745875	−	0.106109i
$617$	162.173			0.262842			0.131421	−	0.991327i	$-0.458046\pi$
$617$	162.173			0.262842			0.131421	+	0.991327i	$0.458046\pi$
$618$	−203.131			−0.328691
$619$			698.531i			1.12848i	0.825610	+	0.564241i	$0.190831\pi$
$619$			698.531i			1.12848i	−0.825610	+	0.564241i	$0.809169\pi$
$620$	−782.291			−1.26176
$621$			197.347i			0.317789i
$622$		−	131.846i		−	0.211971i
$623$	−153.058	+	1075.90i	−0.245679	+	1.72696i
$624$	272.780			0.437147
$625$	1052.57			1.68411
$626$		−	95.0358i		−	0.151814i
$627$	−540.288			−0.861704
$628$			262.165i			0.417460i
$629$			345.144i			0.548719i
$630$	−80.1473	+	563.383i	−0.127218	+	0.894259i
$631$	33.7840			0.0535404			0.0267702	−	0.999642i	$-0.491478\pi$
$631$	33.7840			0.0535404			0.0267702	+	0.999642i	$0.491478\pi$
$632$	−364.370			−0.576534
$633$		−	968.519i		−	1.53005i
$634$	−399.253			−0.629737
$635$		−	1032.53i		−	1.62603i
$636$		−	622.140i		−	0.978207i
$637$	−302.371	+	1041.23i	−0.474680	+	1.63458i
$638$	−105.970			−0.166097
$639$	150.652			0.235761
$640$		−	399.936i		−	0.624901i
$641$	312.358			0.487298			0.243649	−	0.969863i	$-0.421656\pi$
$641$	312.358			0.487298			0.243649	+	0.969863i	$0.421656\pi$
$642$			77.7697i			0.121137i
$643$			206.095i			0.320522i	0.987075	+	0.160261i	$0.0512335\pi$
$643$			206.095i			0.320522i	−0.987075	+	0.160261i	$0.948766\pi$
$644$	303.600	+	43.1903i	0.471428	+	0.0670657i
$645$	2211.54			3.42875
$646$	−332.522			−0.514740
$647$		−	602.620i		−	0.931406i	−0.884941	−	0.465703i	$-0.845801\pi$
$647$		−	602.620i		−	0.931406i	0.884941	−	0.465703i	$-0.154199\pi$
$648$	−813.757			−1.25580
$649$			198.190i			0.305377i
$650$			1683.68i			2.59028i
$651$	1133.05	+	161.189i	1.74048	+	0.247602i
$652$	−315.240			−0.483497
$653$	−428.042			−0.655501			−0.327750	−	0.944764i	$-0.606290\pi$
$653$	−428.042			−0.655501			−0.327750	+	0.944764i	$0.606290\pi$
$654$		−	116.481i		−	0.178105i
$655$	−911.391			−1.39144
$656$			19.9886i			0.0304704i
$657$		−	19.0478i		−	0.0289921i
$658$	−27.7800	+	195.275i	−0.0422188	+	0.296771i
$659$	213.214			0.323541			0.161771	−	0.986828i	$-0.448280\pi$
$659$	213.214			0.323541			0.161771	+	0.986828i	$0.448280\pi$
$660$	−588.848			−0.892195
$661$		−	888.753i		−	1.34456i	−0.740298	−	0.672279i	$-0.765316\pi$
$661$		−	888.753i		−	1.34456i	0.740298	−	0.672279i	$-0.234684\pi$
$662$	−363.918			−0.549725
$663$			1218.54i			1.83792i
$664$			447.342i			0.673708i
$665$	−1076.83	−	153.191i	−1.61929	−	0.230362i
$666$	−224.502			−0.337090
$667$	202.871			0.304155
$668$			521.224i			0.780276i
$669$	−53.0211			−0.0792543
$670$			1333.02i			1.98958i
$671$			833.376i			1.24199i
$672$	−114.121	+	802.194i	−0.169822	+	1.19374i
$673$	391.101			0.581131			0.290565	−	0.956855i	$-0.406157\pi$
$673$	391.101			0.581131			0.290565	+	0.956855i	$0.406157\pi$
$674$	535.252			0.794143
$675$		−	525.436i		−	0.778423i
$676$	675.974			0.999962
$677$		−	638.728i		−	0.943468i	−0.881741	−	0.471734i	$-0.843628\pi$
$677$		−	638.728i		−	0.943468i	0.881741	−	0.471734i	$-0.156372\pi$
$678$			557.350i			0.822050i
$679$	43.1396	−	303.243i	0.0635340	−	0.446603i
$680$	−1049.98			−1.54410
$681$	−450.941			−0.662175
$682$		−	449.354i		−	0.658877i
$683$	−354.468			−0.518987			−0.259494	−	0.965745i	$-0.583556\pi$
$683$	−354.468			−0.518987			−0.259494	+	0.965745i	$0.583556\pi$
$684$			241.062i			0.352430i
$685$		−	2038.09i		−	2.97532i
$686$	429.995	+	194.058i	0.626814	+	0.282884i
$687$	−223.567			−0.325425
$688$	−195.062			−0.283520
$689$			1653.44i			2.39977i
$690$	−1011.47			−1.46590
$691$		−	386.612i		−	0.559497i	−0.960073	−	0.279748i	$-0.909749\pi$
$691$		−	386.612i		−	0.559497i	0.960073	−	0.279748i	$-0.0902510\pi$
$692$		−	296.543i		−	0.428530i
$693$	360.673	+	51.3097i	0.520452	+	0.0740399i
$694$	−102.475			−0.147659
$695$	−637.855			−0.917777
$696$			323.923i			0.465406i
$697$	−89.2913			−0.128108
$698$		−	556.449i		−	0.797205i
$699$		−	586.228i		−	0.838667i
$700$	−808.334	−	114.994i	−1.15476	−	0.164277i
$701$	−902.344			−1.28722			−0.643612	−	0.765352i	$-0.722565\pi$
$701$	−902.344			−1.28722			−0.643612	+	0.765352i	$0.722565\pi$
$702$	289.046			0.411746
$703$		−	429.104i		−	0.610390i
$704$	416.677			0.591871
$705$			725.084i			1.02849i
$706$			181.916i			0.257671i
$707$	162.079	−	1139.31i	0.229249	−	1.61147i
$708$	209.101			0.295340
$709$	940.861			1.32703			0.663513	−	0.748165i	$-0.269065\pi$
$709$	940.861			1.32703			0.663513	+	0.748165i	$0.269065\pi$
$710$		−	281.582i		−	0.396594i
$711$	286.029			0.402291
$712$		−	1304.27i		−	1.83185i
$713$			860.257i			1.20653i
$714$	524.905	+	74.6733i	0.735161	+	0.104584i
$715$	1564.97			2.18876
$716$	198.139			0.276730
$717$		−	923.516i		−	1.28803i
$718$	−435.321			−0.606296
$719$		−	699.679i		−	0.973128i	−0.873645	−	0.486564i	$-0.838250\pi$
$719$		−	699.679i		−	0.973128i	0.873645	−	0.486564i	$-0.161750\pi$
$720$		−	184.511i		−	0.256266i
$721$	−36.8716	+	259.183i	−0.0511396	+	0.359478i
$722$	−83.1019			−0.115100
$723$	−677.451			−0.937000
$724$		−	261.163i		−	0.360722i
$725$	−540.145			−0.745028
$726$			318.966i			0.439348i
$727$			114.289i			0.157207i	0.996906	+	0.0786035i	$0.0250461\pi$
$727$			114.289i			0.157207i	−0.996906	+	0.0786035i	$0.974954\pi$
$728$	183.277	−	1288.32i	0.251754	−	1.76967i
$729$	301.239			0.413222
$730$	−35.6022			−0.0487701
$731$		−	871.365i		−	1.19202i
$732$	879.257			1.20117
$733$		−	573.664i		−	0.782625i	−0.920258	−	0.391313i	$-0.872021\pi$
$733$		−	573.664i		−	0.782625i	0.920258	−	0.391313i	$-0.127979\pi$
$734$		−	387.886i		−	0.528455i
$735$	1665.43	+	483.640i	2.26590	+	0.658013i
$736$	−609.055			−0.827521
$737$	853.387			1.15792
$738$		−	58.0802i		−	0.0786995i
$739$	−211.848			−0.286668			−0.143334	−	0.989674i	$-0.545782\pi$
$739$	−211.848			−0.286668			−0.143334	+	0.989674i	$0.545782\pi$
$740$		−	467.671i		−	0.631988i
$741$		−	1514.96i		−	2.04448i
$742$	712.245	+	101.325i	0.959900	+	0.136556i
$743$	653.801			0.879948			0.439974	−	0.898011i	$-0.354988\pi$
$743$	653.801			0.879948			0.439974	+	0.898011i	$0.354988\pi$
$744$	−1373.56			−1.84619
$745$			1544.64i			2.07334i
$746$	545.785			0.731615
$747$		−	351.162i		−	0.470096i
$748$			232.011i			0.310175i
$749$	99.2297	+	14.1165i	0.132483	+	0.0188471i
$750$	1476.08			1.96811
$751$	−25.1680			−0.0335126			−0.0167563	−	0.999860i	$-0.505334\pi$
$751$	−25.1680			−0.0335126			−0.0167563	+	0.999860i	$0.505334\pi$
$752$		−	63.9537i		−	0.0850449i
$753$	−129.980			−0.172616
$754$		−	297.138i		−	0.394082i
$755$			1115.35i			1.47728i
$756$	−19.7416	+	138.770i	−0.0261132	+	0.183559i
$757$	−1156.96			−1.52835			−0.764176	−	0.645008i	$-0.776854\pi$
$757$	−1156.96			−1.52835			−0.764176	+	0.645008i	$0.776854\pi$
$758$	−307.407			−0.405550
$759$			647.535i			0.853143i
$760$	1305.40			1.71764
$761$			187.841i			0.246835i	0.992355	+	0.123417i	$0.0393854\pi$
$761$			187.841i			0.246835i	−0.992355	+	0.123417i	$0.960615\pi$
$762$		−	625.747i		−	0.821190i
$763$	−148.623	−	21.1432i	−0.194787	−	0.0277106i
$764$	−147.940			−0.193638
$765$	824.234			1.07743
$766$			745.566i			0.973324i
$767$	−555.721			−0.724539
$768$		−	1076.44i		−	1.40161i
$769$			282.206i			0.366978i	0.983022	+	0.183489i	$0.0587392\pi$
$769$			282.206i			0.366978i	−0.983022	+	0.183489i	$0.941261\pi$
$770$	95.9026	−	674.132i	0.124549	−	0.875497i
$771$	524.189			0.679882
$772$	−678.534			−0.878931
$773$		−	858.708i		−	1.11088i	−0.831558	−	0.555438i	$-0.812550\pi$
$773$		−	858.708i		−	1.11088i	0.831558	−	0.555438i	$-0.187450\pi$
$774$	566.786			0.732282
$775$		−	2290.43i		−	2.95540i
$776$			367.612i			0.473727i
$777$	−96.3624	+	677.365i	−0.124019	+	0.871770i
$778$	−190.214			−0.244491
$779$	111.012			0.142506
$780$		−	1651.12i		−	2.11683i
$781$	−180.266			−0.230815
$782$			398.527i			0.509626i
$783$			92.7292i			0.118428i
$784$	−146.894	−	42.6579i	−0.187365	−	0.0544106i
$785$	−1114.44			−1.41967
$786$	−552.332			−0.702713
$787$		−	796.567i		−	1.01216i	−0.862488	−	0.506078i	$-0.831095\pi$
$787$		−	796.567i		−	1.01216i	0.862488	−	0.506078i	$-0.168905\pi$
$788$	706.234			0.896236
$789$		−	520.355i		−	0.659512i
$790$		−	534.614i		−	0.676727i
$791$	711.147	+	101.168i	0.899048	+	0.127899i
$792$	−437.232			−0.552061
$793$	−2336.78			−2.94675
$794$			116.883i			0.147207i
$795$	2644.67			3.32663
$796$		−	100.733i		−	0.126549i
$797$		−	567.684i		−	0.712276i	−0.934433	−	0.356138i	$-0.884093\pi$
$797$		−	567.684i		−	0.712276i	0.934433	−	0.356138i	$-0.115907\pi$
$798$	−652.593	−	92.8384i	−0.817786	−	0.116339i
$799$	285.689			0.357558
$800$	1621.61			2.02701
$801$			1023.85i			1.27821i
$802$	882.561			1.10045
$803$			22.7922i			0.0283838i
$804$		−	900.371i		−	1.11986i
$805$	−183.599	+	1290.58i	−0.228073	+	1.60320i
$806$	1259.98			1.56326
$807$	−803.102			−0.995170
$808$			1381.15i			1.70934i
$809$	65.7634			0.0812897			0.0406449	−	0.999174i	$-0.487059\pi$
$809$	65.7634			0.0812897			0.0406449	+	0.999174i	$0.487059\pi$
$810$		−	1193.97i		−	1.47404i
$811$		−	101.571i		−	0.125242i	−0.998037	−	0.0626208i	$-0.980054\pi$
$811$		−	101.571i		−	0.125242i	0.998037	−	0.0626208i	$-0.0199459\pi$
$812$	142.655	+	20.2943i	0.175684	+	0.0249929i
$813$	−598.062			−0.735624
$814$	268.634			0.330017
$815$		−	1340.06i		−	1.64425i
$816$	−171.909			−0.210673
$817$			1083.33i			1.32599i
$818$		−	282.979i		−	0.345940i
$819$	−143.872	+	1011.32i	−0.175668	+	1.23483i
$820$	120.990			0.147549
$821$	825.103			1.00500			0.502499	−	0.864578i	$-0.332414\pi$
$821$	825.103			1.00500			0.502499	+	0.864578i	$0.332414\pi$
$822$		−	1235.15i		−	1.50261i
$823$	941.093			1.14349			0.571745	−	0.820431i	$-0.306267\pi$
$823$	941.093			1.14349			0.571745	+	0.820431i	$0.306267\pi$
$824$		−	314.199i		−	0.381310i
$825$		−	1724.06i		−	2.08977i
$826$	−34.0551	+	239.385i	−0.0412290	+	0.289813i
$827$	−624.002			−0.754536			−0.377268	−	0.926104i	$-0.623136\pi$
$827$	−624.002			−0.754536			−0.377268	+	0.926104i	$0.623136\pi$
$828$	288.913			0.348929
$829$		−	1390.86i		−	1.67776i	−0.544316	−	0.838880i	$-0.683211\pi$
$829$		−	1390.86i		−	1.67776i	0.544316	−	0.838880i	$-0.316789\pi$
$830$	−656.354			−0.790788
$831$		−	83.5772i		−	0.100574i
$832$			1168.36i			1.40428i
$833$	190.558	−	656.194i	0.228761	−	0.787748i
$834$	−386.560			−0.463502
$835$	−2215.69			−2.65352
$836$		−	288.450i		−	0.345036i
$837$	−393.210			−0.469784
$838$		−	245.259i		−	0.292672i
$839$			1585.09i			1.88926i	0.328140	+	0.944629i	$0.393578\pi$
$839$			1585.09i			1.88926i	−0.328140	+	0.944629i	$0.606422\pi$
$840$	−2060.66	−	293.150i	−2.45316	−	0.348988i
$841$	−745.675			−0.886653
$842$	923.241			1.09649
$843$			1207.34i			1.43220i
$844$	517.074			0.612647
$845$			2873.51i			3.40061i
$846$			185.829i			0.219656i
$847$	406.983	+	57.8977i	0.480499	+	0.0683562i
$848$	−233.264			−0.275076
$849$	−1116.17			−1.31469
$850$		−	1061.08i		−	1.24833i
$851$	−514.281			−0.604325
$852$			190.191i			0.223229i
$853$		−	421.218i		−	0.493808i	−0.969040	−	0.246904i	$-0.920587\pi$
$853$		−	421.218i		−	0.493808i	0.969040	−	0.246904i	$-0.0794132\pi$
$854$	−143.200	+	1006.60i	−0.167681	+	1.17869i
$855$	−1024.74			−1.19852
$856$	−120.293			−0.140529
$857$			771.827i			0.900615i	0.892873	+	0.450308i	$0.148686\pi$
$857$			771.827i			0.900615i	−0.892873	+	0.450308i	$0.851314\pi$
$858$	948.419			1.10538
$859$		−	241.112i		−	0.280690i	−0.990103	−	0.140345i	$-0.955179\pi$
$859$		−	241.112i		−	0.280690i	0.990103	−	0.140345i	$-0.0448211\pi$
$860$			1180.70i			1.37291i
$861$	−175.239	−	24.9297i	−0.203530	−	0.0289543i
$862$	−668.217			−0.775194
$863$	−322.392			−0.373571			−0.186786	−	0.982401i	$-0.559807\pi$
$863$	−322.392			−0.373571			−0.186786	+	0.982401i	$0.559807\pi$
$864$		−	278.389i		−	0.322210i
$865$	1260.58			1.45732
$866$			566.932i			0.654656i
$867$			373.335i			0.430606i
$868$	−86.0559	+	604.916i	−0.0991427	+	0.696908i
$869$	−342.256			−0.393850
$870$	−475.269			−0.546287
$871$			2392.89i			2.74729i
$872$	180.170			0.206617
$873$		−	288.574i		−	0.330554i
$874$		−	495.473i		−	0.566903i
$875$	267.933	−	1883.39i	0.306209	−	2.15245i
$876$	24.0470			0.0274510
$877$	932.943			1.06379			0.531895	−	0.846811i	$-0.321480\pi$
$877$	932.943			1.06379			0.531895	+	0.846811i	$0.321480\pi$
$878$			353.487i			0.402605i
$879$	1289.65			1.46718
$880$			220.782i			0.250889i
$881$			1165.36i			1.32277i	0.750047	+	0.661384i	$0.230031\pi$
$881$			1165.36i			1.32277i	−0.750047	+	0.661384i	$0.769969\pi$
$882$	426.827	+	123.950i	0.483930	+	0.140533i
$883$	−474.423			−0.537286			−0.268643	−	0.963240i	$-0.586575\pi$
$883$	−474.423			−0.537286			−0.268643	+	0.963240i	$0.586575\pi$
$884$	−650.556			−0.735923
$885$			888.872i			1.00437i
$886$	−280.907			−0.317051
$887$			336.075i			0.378890i	0.981891	+	0.189445i	$0.0606688\pi$
$887$			336.075i			0.378890i	−0.981891	+	0.189445i	$0.939331\pi$
$888$		−	821.147i		−	0.924715i
$889$	−798.418	−	113.584i	−0.898108	−	0.127765i
$890$	1913.67			2.15019
$891$	−764.370			−0.857878
$892$		−	28.3070i		−	0.0317343i
$893$	−355.186			−0.397744
$894$			936.101i			1.04709i
$895$			842.273i			0.941087i
$896$	−309.256	−	43.9950i	−0.345152	−	0.0491015i
$897$	−1815.68			−2.02417
$898$	−400.936			−0.446476
$899$			404.217i			0.449630i
$900$	−769.230			−0.854700
$901$		−	1042.02i		−	1.15651i
$902$			69.4976i			0.0770483i
$903$	243.281	−	1710.10i	0.269414	−	1.89380i
$904$	−862.100			−0.953651
$905$	1110.18			1.22672
$906$			675.937i			0.746067i
$907$	1107.46			1.22102			0.610509	−	0.792010i	$-0.290965\pi$
$907$	1107.46			1.22102			0.610509	+	0.792010i	$0.290965\pi$
$908$		−	240.749i		−	0.265142i
$909$		−	1084.20i		−	1.19273i
$910$	1890.26	+	268.910i	2.07721	+	0.295505i
$911$	−355.902			−0.390672			−0.195336	−	0.980736i	$-0.562580\pi$
$911$	−355.902			−0.390672			−0.195336	+	0.980736i	$0.562580\pi$
$912$	213.728			0.234351
$913$			420.193i			0.460233i
$914$	−709.718			−0.776497
$915$			3737.66i			4.08487i
$916$		−	119.358i		−	0.130304i
$917$	−100.258	+	704.745i	−0.109332	+	0.768533i
$918$	−182.160			−0.198432
$919$	−1526.41			−1.66094			−0.830472	−	0.557060i	$-0.811929\pi$
$919$	−1526.41			−1.66094			−0.830472	+	0.557060i	$0.811929\pi$
$920$		−	1564.53i		−	1.70057i
$921$	−573.566			−0.622765
$922$			42.6849i			0.0462960i
$923$		−	505.465i		−	0.547633i
$924$	−64.7762	+	455.334i	−0.0701041	+	0.492786i
$925$	1369.27			1.48029
$926$	25.5827			0.0276271
$927$			246.645i			0.266068i
$928$	−286.183			−0.308387
$929$		−	367.942i		−	0.396062i	−0.980196	−	0.198031i	$-0.936545\pi$
$929$		−	367.942i		−	0.396062i	0.980196	−	0.198031i	$-0.0634547\pi$
$930$		−	2015.34i		−	2.16703i
$931$	−236.913	+	815.820i	−0.254472	+	0.876284i
$932$	312.976			0.335811
$933$	−378.561			−0.405746
$934$			287.890i			0.308233i
$935$	−986.260			−1.05482
$936$		−	1226.00i		−	1.30982i
$937$			167.731i			0.179008i	0.995986	+	0.0895041i	$0.0285282\pi$
$937$			167.731i			0.179008i	−0.995986	+	0.0895041i	$0.971472\pi$
$938$	1030.77	+	146.639i	1.09891	+	0.156331i
$939$	−272.870			−0.290597
$940$	−387.109			−0.411818
$941$			195.582i			0.207845i	0.994585	+	0.103922i	$0.0331394\pi$
$941$			195.582i			0.207845i	−0.994585	+	0.103922i	$0.966861\pi$
$942$	−675.388			−0.716972
$943$		−	133.048i		−	0.141090i
$944$		−	78.4001i		−	0.0830509i
$945$	−589.903	−	83.9200i	−0.624236	−	0.0888042i
$946$	−678.204			−0.716918
$947$	1868.09			1.97264			0.986320	−	0.164844i	$-0.0527122\pi$
$947$	1868.09			1.97264			0.986320	+	0.164844i	$0.0527122\pi$
$948$			361.099i			0.380906i
$949$	−63.9091			−0.0673436
$950$			1319.20i			1.38863i
$951$			1146.35i			1.20542i
$952$	−115.503	+	811.914i	−0.121327	+	0.852851i
$953$	−725.759			−0.761552			−0.380776	−	0.924667i	$-0.624343\pi$
$953$	−725.759			−0.761552			−0.380776	+	0.924667i	$0.624343\pi$
$954$	677.790			0.710472
$955$		−	628.881i		−	0.658514i
$956$	493.048			0.515740
$957$			304.264i			0.317935i
$958$		−	7.28441i		−	0.00760377i
$959$	−1575.98	−	224.200i	−1.64336	−	0.233785i
$960$	1868.78			1.94665
$961$	−753.045			−0.783606
$962$			753.247i			0.783001i
$963$	94.4294			0.0980576
$964$		−	361.678i		−	0.375185i
$965$		−	2884.40i		−	2.98901i
$966$	−111.267	+	782.132i	−0.115183	+	0.809661i
$967$	−967.521			−1.00054			−0.500269	−	0.865870i	$-0.666766\pi$
$967$	−967.521			−1.00054			−0.500269	+	0.865870i	$0.666766\pi$
$968$	−493.372			−0.509682
$969$			954.748i			0.985292i
$970$	−539.371			−0.556053
$971$			408.428i			0.420626i	0.977634	+	0.210313i	$0.0674484\pi$
$971$			408.428i			0.420626i	−0.977634	+	0.210313i	$0.932552\pi$
$972$			626.237i			0.644276i
$973$	−70.1671	+	493.229i	−0.0721142	+	0.506916i
$974$	724.135			0.743465
$975$	4834.25			4.95821
$976$		−	329.668i		−	0.337774i
$977$	−728.326			−0.745472			−0.372736	−	0.927937i	$-0.621580\pi$
$977$	−728.326			−0.745472			−0.372736	+	0.927937i	$0.621580\pi$
$978$		−	812.120i		−	0.830388i
$979$		−	1225.12i		−	1.25140i
$980$	−258.206	+	889.144i	−0.263476	+	0.907290i
$981$	−141.433			−0.144172
$982$	−190.132			−0.193617
$983$			903.056i			0.918674i	0.888262	+	0.459337i	$0.151913\pi$
$983$			903.056i			0.918674i	−0.888262	+	0.459337i	$0.848087\pi$
$984$	212.437			0.215891
$985$			3002.15i			3.04787i
$986$			187.260i			0.189919i
$987$	560.681	+	79.7628i	0.568066	+	0.0808134i
$988$	808.810			0.818634
$989$	1298.37			1.31282
$990$		−	641.521i		−	0.648001i
$991$	9.67122			0.00975905			0.00487953	−	0.999988i	$-0.498447\pi$
$991$	9.67122			0.00975905			0.00487953	+	0.999988i	$0.498447\pi$
$992$		−	1213.53i		−	1.22332i
$993$			1044.89i			1.05226i
$994$	−217.737	−	30.9754i	−0.219051	−	0.0311624i
$995$	428.207			0.430359
$996$	443.326			0.445107
$997$		−	1378.40i		−	1.38254i	−0.722594	−	0.691272i	$-0.757050\pi$
$997$		−	1378.40i		−	1.38254i	0.722594	−	0.691272i	$-0.242950\pi$
$998$	−349.073			−0.349773
$999$		−	235.069i		−	0.235305i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	287.3.b.a.83.18	yes	52
7.6	odd	2	inner	287.3.b.a.83.17	✓	52

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
287.3.b.a.83.17	✓	52	7.6	odd	2	inner
287.3.b.a.83.18	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)

\(f(q)\)	\(=\)	\(q-1.37538 q^{2} +3.94905i q^{3} -2.10832 q^{4} -8.96232i q^{5} -5.43145i q^{6} +(-6.93022 - 0.985899i) q^{7} +8.40128 q^{8} -6.59497 q^{9} +O(q^{10})\)	\(q-1.37538 q^{2} +3.94905i q^{3} -2.10832 q^{4} -8.96232i q^{5} -5.43145i q^{6} +(-6.93022 - 0.985899i) q^{7} +8.40128 q^{8} -6.59497 q^{9} +12.3266i q^{10} +7.89140 q^{11} -8.32586i q^{12} +22.1274i q^{13} +(9.53171 + 1.35599i) q^{14} +35.3926 q^{15} -3.12169 q^{16} -13.9450i q^{17} +9.07061 q^{18} +17.3372i q^{19} +18.8954i q^{20} +(3.89336 - 27.3678i) q^{21} -10.8537 q^{22} +20.7786 q^{23} +33.1771i q^{24} -55.3231 q^{25} -30.4336i q^{26} +9.49758i q^{27} +(14.6111 + 2.07859i) q^{28} +9.76346 q^{29} -48.6784 q^{30} +41.4010i q^{31} -29.3116 q^{32} +31.1635i q^{33} +19.1797i q^{34} +(-8.83594 + 62.1109i) q^{35} +13.9043 q^{36} -24.7505 q^{37} -23.8453i q^{38} -87.3821 q^{39} -75.2949i q^{40} -6.40312i q^{41} +(-5.35486 + 37.6412i) q^{42} +62.4860 q^{43} -16.6376 q^{44} +59.1062i q^{45} -28.5786 q^{46} +20.4869i q^{47} -12.3277i q^{48} +(47.0560 + 13.6650i) q^{49} +76.0905 q^{50} +55.0693 q^{51} -46.6517i q^{52} +74.7238 q^{53} -13.0628i q^{54} -70.7252i q^{55} +(-58.2228 - 8.28281i) q^{56} -68.4655 q^{57} -13.4285 q^{58} +25.1146i q^{59} -74.6190 q^{60} +105.606i q^{61} -56.9423i q^{62} +(45.7046 + 6.50197i) q^{63} +52.8014 q^{64} +198.313 q^{65} -42.8618i q^{66} +108.141 q^{67} +29.4005i q^{68} +82.0558i q^{69} +(12.1528 - 85.4262i) q^{70} -22.8434 q^{71} -55.4062 q^{72} +2.88823i q^{73} +34.0414 q^{74} -218.474i q^{75} -36.5524i q^{76} +(-54.6892 - 7.78012i) q^{77} +120.184 q^{78} -43.3707 q^{79} +27.9776i q^{80} -96.8611 q^{81} +8.80675i q^{82} +53.2469i q^{83} +(-8.20846 + 57.7001i) q^{84} -124.979 q^{85} -85.9422 q^{86} +38.5564i q^{87} +66.2979 q^{88} -155.247i q^{89} -81.2937i q^{90} +(21.8154 - 153.348i) q^{91} -43.8081 q^{92} -163.495 q^{93} -28.1773i q^{94} +155.382 q^{95} -115.753i q^{96} +43.7566i q^{97} +(-64.7200 - 18.7946i) q^{98} -52.0435 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 52 q + 2 q^{2} + 90 q^{4} + 12 q^{7} - 2 q^{8} - 140 q^{9}+O(q^{10}) \) 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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