LMFDB - Embedded newform 287.3.b.a.83.15

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			83.15
Character	$\chi$	$=$	287.83
Dual form			287.3.b.a.83.16

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.45610 q^{2} -1.32130i q^{3} -1.87978 q^{4} +7.87741i q^{5} +1.92394i q^{6} +(-0.510666 - 6.98135i) q^{7} +8.56153 q^{8} +7.25417 q^{9} +O(q^{10})$	\(q-1.45610 q^{2} -1.32130i q^{3} -1.87978 q^{4} +7.87741i q^{5} +1.92394i q^{6} +(-0.510666 - 6.98135i) q^{7} +8.56153 q^{8} +7.25417 q^{9} -11.4703i q^{10} -14.9743 q^{11} +2.48375i q^{12} +17.8748i q^{13} +(0.743580 + 10.1655i) q^{14} +10.4084 q^{15} -4.94732 q^{16} -31.3052i q^{17} -10.5628 q^{18} +3.88622i q^{19} -14.8078i q^{20} +(-9.22445 + 0.674743i) q^{21} +21.8040 q^{22} -31.4353 q^{23} -11.3123i q^{24} -37.0537 q^{25} -26.0274i q^{26} -21.4766i q^{27} +(0.959939 + 13.1234i) q^{28} -25.4865 q^{29} -15.1557 q^{30} +28.3835i q^{31} -27.0423 q^{32} +19.7855i q^{33} +45.5835i q^{34} +(54.9950 - 4.02273i) q^{35} -13.6362 q^{36} -55.2687 q^{37} -5.65872i q^{38} +23.6179 q^{39} +67.4428i q^{40} +6.40312i q^{41} +(13.4317 - 0.982492i) q^{42} -35.3624 q^{43} +28.1483 q^{44} +57.1441i q^{45} +45.7729 q^{46} -32.0142i q^{47} +6.53689i q^{48} +(-48.4784 + 7.13028i) q^{49} +53.9538 q^{50} -41.3636 q^{51} -33.6006i q^{52} -29.9533 q^{53} +31.2721i q^{54} -117.959i q^{55} +(-4.37209 - 59.7710i) q^{56} +5.13486 q^{57} +37.1109 q^{58} -71.2624i q^{59} -19.5655 q^{60} +35.0491i q^{61} -41.3292i q^{62} +(-3.70446 - 50.6439i) q^{63} +59.1656 q^{64} -140.807 q^{65} -28.8096i q^{66} +69.4294 q^{67} +58.8469i q^{68} +41.5355i q^{69} +(-80.0781 + 5.85749i) q^{70} -65.7118 q^{71} +62.1068 q^{72} -3.48586i q^{73} +80.4767 q^{74} +48.9590i q^{75} -7.30523i q^{76} +(7.64685 + 104.541i) q^{77} -34.3900 q^{78} +127.692 q^{79} -38.9721i q^{80} +36.9105 q^{81} -9.32358i q^{82} -78.7499i q^{83} +(17.3399 - 1.26837i) q^{84} +246.604 q^{85} +51.4911 q^{86} +33.6754i q^{87} -128.203 q^{88} -12.3819i q^{89} -83.2074i q^{90} +(124.790 - 9.12803i) q^{91} +59.0914 q^{92} +37.5031 q^{93} +46.6159i q^{94} -30.6134 q^{95} +35.7310i q^{96} -64.6638i q^{97} +(70.5894 - 10.3824i) q^{98} -108.626 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−1.45610			−0.728049			−0.364025	−	0.931389i	$-0.618598\pi$
$2$	−1.45610			−0.728049			−0.364025	+	0.931389i	$0.618598\pi$
$3$		−	1.32130i		−	0.440433i	−0.975451	−	0.220217i	$-0.929324\pi$
$3$		−	1.32130i		−	0.440433i	0.975451	−	0.220217i	$-0.0706764\pi$
$4$	−1.87978			−0.469944
$5$			7.87741i			1.57548i	0.616006	+	0.787741i	$0.288750\pi$
$5$			7.87741i			1.57548i	−0.616006	+	0.787741i	$0.711250\pi$
$6$			1.92394i			0.320657i
$7$	−0.510666	−	6.98135i	−0.0729523	−	0.997335i
$7$	−0.510666	−	6.98135i	−0.0729523	−	0.997335i
$8$	8.56153			1.07019
$9$	7.25417			0.806019
$10$		−	11.4703i		−	1.14703i
$11$	−14.9743			−1.36130			−0.680649	−	0.732610i	$-0.738302\pi$
$11$	−14.9743			−1.36130			−0.680649	+	0.732610i	$0.738302\pi$
$12$			2.48375i			0.206979i
$13$			17.8748i			1.37498i	0.726193	+	0.687490i	$0.241288\pi$
$13$			17.8748i			1.37498i	−0.726193	+	0.687490i	$0.758712\pi$
$14$	0.743580	+	10.1655i	0.0531129	+	0.726109i
$15$	10.4084			0.693895
$16$	−4.94732			−0.309208
$17$		−	31.3052i		−	1.84148i	−0.390172	−	0.920742i	$-0.627585\pi$
$17$		−	31.3052i		−	1.84148i	0.390172	−	0.920742i	$-0.372415\pi$
$18$	−10.5628			−0.586821
$19$			3.88622i			0.204538i	0.994757	+	0.102269i	$0.0326102\pi$
$19$			3.88622i			0.204538i	−0.994757	+	0.102269i	$0.967390\pi$
$20$		−	14.8078i		−	0.740390i
$21$	−9.22445	+	0.674743i	−0.439259	+	0.0321306i
$22$	21.8040			0.991091
$23$	−31.4353			−1.36675			−0.683377	−	0.730066i	$-0.739489\pi$
$23$	−31.4353			−1.36675			−0.683377	+	0.730066i	$0.739489\pi$
$24$		−	11.3123i		−	0.471348i
$25$	−37.0537			−1.48215
$26$		−	26.0274i		−	1.00105i
$27$		−	21.4766i		−	0.795430i
$28$	0.959939	+	13.1234i	0.0342835	+	0.468692i
$29$	−25.4865			−0.878846			−0.439423	−	0.898280i	$-0.644817\pi$
$29$	−25.4865			−0.878846			−0.439423	+	0.898280i	$0.644817\pi$
$30$	−15.1557			−0.505189
$31$			28.3835i			0.915598i	0.889056	+	0.457799i	$0.151362\pi$
$31$			28.3835i			0.915598i	−0.889056	+	0.457799i	$0.848638\pi$
$32$	−27.0423			−0.845073
$33$			19.7855i			0.599560i
$34$			45.5835i			1.34069i
$35$	54.9950	−	4.02273i	1.57129	−	0.114935i
$36$	−13.6362			−0.378784
$37$	−55.2687			−1.49375			−0.746875	−	0.664965i	$-0.768447\pi$
$37$	−55.2687			−1.49375			−0.746875	+	0.664965i	$0.768447\pi$
$38$		−	5.65872i		−	0.148914i
$39$	23.6179			0.605587
$40$			67.4428i			1.68607i
$41$			6.40312i			0.156174i
$41$			6.40312i			0.156174i
$42$	13.4317	−	0.982492i	0.319802	−	0.0233927i
$43$	−35.3624			−0.822382			−0.411191	−	0.911549i	$-0.634887\pi$
$43$	−35.3624			−0.822382			−0.411191	+	0.911549i	$0.634887\pi$
$44$	28.1483			0.639734
$45$			57.1441i			1.26987i
$46$	45.7729			0.995064
$47$		−	32.0142i		−	0.681154i	−0.940217	−	0.340577i	$-0.889378\pi$
$47$		−	32.0142i		−	0.681154i	0.940217	−	0.340577i	$-0.110622\pi$
$48$			6.53689i			0.136185i
$49$	−48.4784	+	7.13028i	−0.989356	+	0.145516i
$50$	53.9538			1.07908
$51$	−41.3636			−0.811050
$52$		−	33.6006i		−	0.646165i
$53$	−29.9533			−0.565157			−0.282578	−	0.959244i	$-0.591190\pi$
$53$	−29.9533			−0.565157			−0.282578	+	0.959244i	$0.591190\pi$
$54$			31.2721i			0.579112i
$55$		−	117.959i		−	2.14470i
$56$	−4.37209	−	59.7710i	−0.0780730	−	1.06734i
$57$	5.13486			0.0900853
$58$	37.1109			0.639843
$59$		−	71.2624i		−	1.20784i	−0.797046	−	0.603918i	$-0.793605\pi$
$59$		−	71.2624i		−	1.20784i	0.797046	−	0.603918i	$-0.206395\pi$
$60$	−19.5655			−0.326092
$61$			35.0491i			0.574576i	0.957844	+	0.287288i	$0.0927536\pi$
$61$			35.0491i			0.574576i	−0.957844	+	0.287288i	$0.907246\pi$
$62$		−	41.3292i		−	0.666600i
$63$	−3.70446	−	50.6439i	−0.0588009	−	0.803871i
$64$	59.1656			0.924463
$65$	−140.807			−2.16626
$66$		−	28.8096i		−	0.436509i
$67$	69.4294			1.03626			0.518130	−	0.855302i	$-0.326628\pi$
$67$	69.4294			1.03626			0.518130	+	0.855302i	$0.326628\pi$
$68$			58.8469i			0.865395i
$69$			41.5355i			0.601963i
$70$	−80.0781	+	5.85749i	−1.14397	+	0.0836784i
$71$	−65.7118			−0.925519			−0.462759	−	0.886484i	$-0.653141\pi$
$71$	−65.7118			−0.925519			−0.462759	+	0.886484i	$0.653141\pi$
$72$	62.1068			0.862595
$73$		−	3.48586i		−	0.0477516i	−0.999715	−	0.0238758i	$-0.992399\pi$
$73$		−	3.48586i		−	0.0477516i	0.999715	−	0.0238758i	$-0.00760062\pi$
$74$	80.4767			1.08752
$75$			48.9590i			0.652786i
$76$		−	7.30523i		−	0.0961215i
$77$	7.64685	+	104.541i	0.0993098	+	1.35767i
$78$	−34.3900			−0.440897
$79$	127.692			1.61635			0.808176	−	0.588941i	$-0.200455\pi$
$79$	127.692			1.61635			0.808176	+	0.588941i	$0.200455\pi$
$80$		−	38.9721i		−	0.487151i
$81$	36.9105			0.455685
$82$		−	9.32358i		−	0.113702i
$83$		−	78.7499i		−	0.948794i	−0.880311	−	0.474397i	$-0.842666\pi$
$83$		−	78.7499i		−	0.948794i	0.880311	−	0.474397i	$-0.157334\pi$
$84$	17.3399	−	1.26837i	0.206428	−	0.0150996i
$85$	246.604			2.90123
$86$	51.4911			0.598734
$87$			33.6754i			0.387073i
$88$	−128.203			−1.45685
$89$		−	12.3819i		−	0.139123i	−0.997578	−	0.0695614i	$-0.977840\pi$
$89$		−	12.3819i		−	0.139123i	0.997578	−	0.0695614i	$-0.0221600\pi$
$90$		−	83.2074i		−	0.924527i
$91$	124.790	−	9.12803i	1.37132	−	0.100308i
$92$	59.0914			0.642298
$93$	37.5031			0.403259
$94$			46.6159i			0.495914i
$95$	−30.6134			−0.322246
$96$			35.7310i			0.372198i
$97$		−	64.6638i		−	0.666637i	−0.942814	−	0.333319i	$-0.891832\pi$
$97$		−	64.6638i		−	0.666637i	0.942814	−	0.333319i	$-0.108168\pi$
$98$	70.5894	−	10.3824i	0.720300	−	0.105943i
$99$	−108.626			−1.09723
$100$	69.6527			0.696527
$101$			136.285i			1.34936i	0.738111	+	0.674680i	$0.235718\pi$
$101$			136.285i			1.34936i	−0.738111	+	0.674680i	$0.764282\pi$
$102$	60.2294			0.590484
$103$			42.1111i			0.408846i	0.978883	+	0.204423i	$0.0655318\pi$
$103$			42.1111i			0.408846i	−0.978883	+	0.204423i	$0.934468\pi$
$104$			153.035i			1.47149i
$105$	−5.31523	−	72.6648i	−0.0506212	−	0.692046i
$106$	43.6150			0.411462
$107$	40.9960			0.383140			0.191570	−	0.981479i	$-0.438642\pi$
$107$	40.9960			0.383140			0.191570	+	0.981479i	$0.438642\pi$
$108$			40.3713i			0.373808i
$109$	−141.122			−1.29470			−0.647350	−	0.762193i	$-0.724123\pi$
$109$	−141.122			−1.29470			−0.647350	+	0.762193i	$0.724123\pi$
$110$			171.759i			1.56145i
$111$			73.0265i			0.657897i
$112$	2.52643	+	34.5390i	0.0225574	+	0.308384i
$113$	−140.335			−1.24190			−0.620950	−	0.783851i	$-0.713253\pi$
$113$	−140.335			−1.24190			−0.620950	+	0.783851i	$0.713253\pi$
$114$	−7.47686			−0.0655865
$115$		−	247.629i		−	2.15330i
$116$	47.9090			0.413009
$117$			129.666i			1.10826i
$118$			103.765i			0.879365i
$119$	−218.553	+	15.9865i	−1.83658	+	0.134340i
$120$	89.1121			0.742600
$121$	103.229			0.853131
$122$		−	51.0349i		−	0.418319i
$123$	8.46044			0.0687841
$124$		−	53.3547i		−	0.430280i
$125$		−	94.9517i		−	0.759614i
$126$	5.39405	+	73.7425i	0.0428100	+	0.585258i
$127$	−65.5068			−0.515801			−0.257901	−	0.966171i	$-0.583031\pi$
$127$	−65.5068			−0.515801			−0.257901	+	0.966171i	$0.583031\pi$
$128$	22.0185			0.172019
$129$			46.7243i			0.362204i
$130$	205.029			1.57714
$131$			56.0225i			0.427653i	0.976872	+	0.213826i	$0.0685927\pi$
$131$			56.0225i			0.427653i	−0.976872	+	0.213826i	$0.931407\pi$
$132$		−	37.1923i		−	0.281760i
$133$	27.1311	−	1.98456i	0.203993	−	0.0149215i
$134$	−101.096			−0.754448
$135$	169.180			1.25319
$136$		−	268.021i		−	1.97074i
$137$	207.977			1.51808			0.759042	−	0.651042i	$-0.225668\pi$
$137$	207.977			1.51808			0.759042	+	0.651042i	$0.225668\pi$
$138$		−	60.4797i		−	0.438259i
$139$			88.9230i			0.639734i	0.947463	+	0.319867i	$0.103638\pi$
$139$			88.9230i			0.639734i	−0.947463	+	0.319867i	$0.896362\pi$
$140$	−103.378	+	7.56184i	−0.738417	+	0.0540131i
$141$	−42.3004			−0.300003
$142$	95.6829			0.673823
$143$		−	267.661i		−	1.87176i
$144$	−35.8887			−0.249227
$145$		−	200.768i		−	1.38461i
$146$			5.07576i			0.0347655i
$147$	9.42123	+	64.0545i	0.0640900	+	0.435745i
$148$	103.893			0.701979
$149$	−121.086			−0.812659			−0.406329	−	0.913727i	$-0.633191\pi$
$149$	−121.086			−0.812659			−0.406329	+	0.913727i	$0.633191\pi$
$150$		−	71.2891i		−	0.475261i
$151$	−27.5981			−0.182769			−0.0913843	−	0.995816i	$-0.529129\pi$
$151$	−27.5981			−0.182769			−0.0913843	+	0.995816i	$0.529129\pi$
$152$			33.2720i			0.218895i
$153$		−	227.093i		−	1.48427i
$154$	−11.1346	−	152.221i	−0.0723024	−	0.988451i
$155$	−223.589			−1.44251
$156$	−44.3964			−0.284592
$157$			223.047i			1.42068i	0.703857	+	0.710342i	$0.251460\pi$
$157$			223.047i			1.42068i	−0.703857	+	0.710342i	$0.748540\pi$
$158$	−185.932			−1.17678
$159$			39.5773i			0.248914i
$160$		−	213.024i		−	1.33140i
$161$	16.0530	+	219.461i	0.0997078	+	1.36311i
$162$	−53.7453			−0.331761
$163$	199.426			1.22347			0.611735	−	0.791063i	$-0.290472\pi$
$163$	199.426			1.22347			0.611735	+	0.791063i	$0.290472\pi$
$164$		−	12.0365i		−	0.0733930i
$165$	−155.859			−0.944597
$166$			114.668i			0.690769i
$167$		−	50.1567i		−	0.300340i	−0.988660	−	0.150170i	$-0.952018\pi$
$167$		−	50.1567i		−	0.300340i	0.988660	−	0.150170i	$-0.0479820\pi$
$168$	−78.9754	+	5.77683i	−0.470092	+	0.0343859i
$169$	−150.507			−0.890573
$170$	−359.080			−2.11224
$171$			28.1913i			0.164861i
$172$	66.4735			0.386474
$173$			206.813i			1.19545i	0.801701	+	0.597726i	$0.203929\pi$
$173$			206.813i			1.19545i	−0.801701	+	0.597726i	$0.796071\pi$
$174$		−	49.0346i		−	0.281808i
$175$	18.9221	+	258.685i	0.108126	+	1.47820i
$176$	74.0826			0.420924
$177$	−94.1589			−0.531971
$178$			18.0293i			0.101288i
$179$	177.062			0.989176			0.494588	−	0.869128i	$-0.335319\pi$
$179$	177.062			0.989176			0.494588	+	0.869128i	$0.335319\pi$
$180$		−	107.418i		−	0.596768i
$181$			96.2124i			0.531560i	0.964034	+	0.265780i	$0.0856295\pi$
$181$			96.2124i			0.531560i	−0.964034	+	0.265780i	$0.914370\pi$
$182$	−181.706	+	13.2913i	−0.998386	+	0.0730292i
$183$	46.3104			0.253062
$184$	−269.135			−1.46269
$185$		−	435.375i		−	2.35338i
$186$	−54.6082			−0.293593
$187$			468.773i			2.50681i
$188$			60.1797i			0.320105i
$189$	−149.936	+	10.9674i	−0.793311	+	0.0580285i
$190$	44.5761			0.234611
$191$	−261.211			−1.36760			−0.683799	−	0.729671i	$-0.739673\pi$
$191$	−261.211			−1.36760			−0.683799	+	0.729671i	$0.739673\pi$
$192$		−	78.1755i		−	0.407164i
$193$	−58.6810			−0.304047			−0.152023	−	0.988377i	$-0.548579\pi$
$193$	−58.6810			−0.304047			−0.152023	+	0.988377i	$0.548579\pi$
$194$			94.1569i			0.485345i
$195$			186.048i			0.954092i
$196$	91.1287	−	13.4033i	0.464942	−	0.0683844i
$197$	−123.905			−0.628962			−0.314481	−	0.949264i	$-0.601830\pi$
$197$	−123.905			−0.628962			−0.314481	+	0.949264i	$0.601830\pi$
$198$	158.170			0.798838
$199$			10.3149i			0.0518335i	0.999664	+	0.0259167i	$0.00825048\pi$
$199$			10.3149i			0.0518335i	−0.999664	+	0.0259167i	$0.991750\pi$
$200$	−317.236			−1.58618
$201$		−	91.7370i		−	0.456403i
$202$		−	198.445i		−	0.982400i
$203$	13.0151	+	177.930i	0.0641139	+	0.876505i
$204$	77.7543			0.381149
$205$	−50.4401			−0.246049
$206$		−	61.3180i		−	0.297660i
$207$	−228.037			−1.10163
$208$		−	88.4322i		−	0.425155i
$209$		−	58.1933i		−	0.278437i
$210$	7.73949	+	105.807i	0.0368547	+	0.503843i
$211$	13.9761			0.0662372			0.0331186	−	0.999451i	$-0.489456\pi$
$211$	13.9761			0.0662372			0.0331186	+	0.999451i	$0.489456\pi$
$212$	56.3056			0.265592
$213$			86.8250i			0.407629i
$214$	−59.6942			−0.278945
$215$		−	278.564i		−	1.29565i
$216$		−	183.873i		−	0.851263i
$217$	198.155	−	14.4945i	0.913158	−	0.0667950i
$218$	205.488			0.942605
$219$	−4.60587			−0.0210314
$220$			221.736i			1.00789i
$221$	559.573			2.53201
$222$		−	106.334i		−	0.478981i
$223$		−	221.071i		−	0.991351i	−0.868508	−	0.495675i	$-0.834921\pi$
$223$		−	221.071i		−	0.991351i	0.868508	−	0.495675i	$-0.165079\pi$
$224$	13.8096	+	188.792i	0.0616501	+	0.842822i
$225$	−268.794			−1.19464
$226$	204.341			0.904164
$227$		−	50.4017i		−	0.222034i	−0.993819	−	0.111017i	$-0.964589\pi$
$227$		−	50.4017i		−	0.222034i	0.993819	−	0.111017i	$-0.0354108\pi$
$228$	−9.65240			−0.0423351
$229$		−	1.09640i		−	0.00478777i	−0.999997	−	0.00239389i	$-0.999238\pi$
$229$		−	1.09640i		−	0.00478777i	0.999997	−	0.00239389i	$-0.000761998\pi$
$230$			360.572i			1.56771i
$231$	138.129	−	10.1038i	0.597963	−	0.0437393i
$232$	−218.204			−0.940534
$233$	−62.0131			−0.266151			−0.133075	−	0.991106i	$-0.542485\pi$
$233$	−62.0131			−0.266151			−0.133075	+	0.991106i	$0.542485\pi$
$234$		−	188.807i		−	0.806868i
$235$	252.189			1.07315
$236$			133.957i			0.567616i
$237$		−	168.719i		−	0.711895i
$238$	318.234	−	23.2779i	1.33712	−	0.0978065i
$239$	−406.937			−1.70266			−0.851332	−	0.524628i	$-0.824204\pi$
$239$	−406.937			−1.70266			−0.851332	+	0.524628i	$0.824204\pi$
$240$	−51.4938			−0.214558
$241$			13.6742i			0.0567396i	0.999597	+	0.0283698i	$0.00903159\pi$
$241$			13.6742i			0.0567396i	−0.999597	+	0.0283698i	$0.990968\pi$
$242$	−150.311			−0.621121
$243$		−	242.059i		−	0.996129i
$244$		−	65.8845i		−	0.270019i
$245$	−56.1681	−	381.885i	−0.229258	−	1.55871i
$246$	−12.3192			−0.0500782
$247$	−69.4652			−0.281236
$248$			243.007i			0.979865i
$249$	−104.052			−0.417880
$250$			138.259i			0.553036i
$251$			92.7847i			0.369660i	0.982770	+	0.184830i	$0.0591735\pi$
$251$			92.7847i			0.369660i	−0.982770	+	0.184830i	$0.940827\pi$
$252$	6.96356	+	95.1992i	0.0276332	+	0.377775i
$253$	470.721			1.86056
$254$	95.3843			0.375529
$255$		−	325.838i		−	1.27780i
$256$	−268.723			−1.04970
$257$			79.9349i			0.311031i	0.987833	+	0.155515i	$0.0497038\pi$
$257$			79.9349i			0.311031i	−0.987833	+	0.155515i	$0.950296\pi$
$258$		−	68.0352i		−	0.263702i
$259$	28.2239	+	385.850i	0.108972	+	1.48977i
$260$	264.686			1.01802
$261$	−184.884			−0.708367
$262$		−	81.5743i		−	0.311352i
$263$	441.120			1.67726			0.838631	−	0.544700i	$-0.183356\pi$
$263$	441.120			1.67726			0.838631	+	0.544700i	$0.183356\pi$
$264$			169.394i			0.641645i
$265$		−	235.955i		−	0.890395i
$266$	−39.5055	+	2.88972i	−0.148517	+	0.0108636i
$267$	−16.3602			−0.0612743
$268$	−130.512			−0.486985
$269$		−	248.875i		−	0.925185i	−0.886571	−	0.462592i	$-0.846919\pi$
$269$		−	248.875i		−	0.925185i	0.886571	−	0.462592i	$-0.153081\pi$
$270$	−246.343			−0.912382
$271$			163.181i			0.602144i	0.953601	+	0.301072i	$0.0973444\pi$
$271$			163.181i			0.602144i	−0.953601	+	0.301072i	$0.902656\pi$
$272$			154.877i			0.569401i
$273$	−12.0609	−	164.885i	−0.0441790	−	0.603973i
$274$	−302.835			−1.10524
$275$	554.852			2.01764
$276$		−	78.0775i		−	0.282889i
$277$	−67.3157			−0.243017			−0.121508	−	0.992590i	$-0.538773\pi$
$277$	−67.3157			−0.243017			−0.121508	+	0.992590i	$0.538773\pi$
$278$		−	129.481i		−	0.465758i
$279$			205.899i			0.737989i
$280$	470.841	−	34.4407i	1.68158	−	0.123003i
$281$	264.913			0.942750			0.471375	−	0.881933i	$-0.343758\pi$
$281$	264.913			0.942750			0.471375	+	0.881933i	$0.343758\pi$
$282$	61.5935			0.218417
$283$			181.793i			0.642380i	0.947015	+	0.321190i	$0.104083\pi$
$283$			181.793i			0.642380i	−0.947015	+	0.321190i	$0.895917\pi$
$284$	123.524			0.434942
$285$			40.4494i			0.141928i
$286$			389.741i			1.36273i
$287$	44.7024	−	3.26986i	0.155758	−	0.0113932i
$288$	−196.170			−0.681145
$289$	−691.017			−2.39106
$290$			292.338i			1.00806i
$291$	−85.4402			−0.293609
$292$			6.55265i			0.0224406i
$293$			501.075i			1.71015i	0.518502	+	0.855077i	$0.326490\pi$
$293$			501.075i			1.71015i	−0.518502	+	0.855077i	$0.673510\pi$
$294$	−13.7182	−	93.2697i	−0.0466607	−	0.317244i
$295$	561.363			1.90293
$296$	−473.185			−1.59860
$297$			321.597i			1.08282i
$298$	176.313			0.591656
$299$		−	561.899i		−	1.87926i
$300$		−	92.0320i		−	0.306773i
$301$	18.0584	+	246.877i	0.0599946	+	0.820190i
$302$	40.1855			0.133064
$303$	180.074			0.594303
$304$		−	19.2264i		−	0.0632447i
$305$	−276.096			−0.905234
$306$			330.670i			1.08062i
$307$		−	214.578i		−	0.698951i	−0.936946	−	0.349475i	$-0.886360\pi$
$307$		−	214.578i		−	0.698951i	0.936946	−	0.349475i	$-0.113640\pi$
$308$	−14.3744	−	196.513i	−0.0466701	−	0.638030i
$309$	55.6414			0.180069
$310$	325.567			1.05022
$311$		−	454.796i		−	1.46237i	−0.682181	−	0.731183i	$-0.738968\pi$
$311$		−	454.796i		−	1.46237i	0.682181	−	0.731183i	$-0.261032\pi$
$312$	202.205			0.648094
$313$		−	116.264i		−	0.371450i	−0.982602	−	0.185725i	$-0.940537\pi$
$313$		−	116.264i		−	0.371450i	0.982602	−	0.185725i	$-0.0594634\pi$
$314$		−	324.779i		−	1.03433i
$315$	398.943	−	29.1816i	1.26649	−	0.0926399i
$316$	−240.032			−0.759596
$317$	242.467			0.764881			0.382441	−	0.923980i	$-0.375084\pi$
$317$	242.467			0.764881			0.382441	+	0.923980i	$0.375084\pi$
$318$		−	57.6284i		−	0.181221i
$319$	381.642			1.19637
$320$			466.072i			1.45648i
$321$		−	54.1680i		−	0.168748i
$322$	−23.3747	−	319.557i	−0.0725922	−	0.992412i
$323$	121.659			0.376653
$324$	−69.3835			−0.214147
$325$		−	662.325i		−	2.03792i
$326$	−290.383			−0.890747
$327$			186.465i			0.570229i
$328$			54.8206i			0.167136i
$329$	−223.503	+	16.3486i	−0.679339	+	0.0496918i
$330$	226.945			0.687713
$331$	−76.9100			−0.232357			−0.116178	−	0.993228i	$-0.537064\pi$
$331$	−76.9100			−0.232357			−0.116178	+	0.993228i	$0.537064\pi$
$332$			148.032i			0.445881i
$333$	−400.929			−1.20399
$334$			73.0331i			0.218662i
$335$			546.924i			1.63261i
$336$	45.6363	−	3.33817i	0.135822	−	0.00993503i
$337$	179.426			0.532422			0.266211	−	0.963915i	$-0.414228\pi$
$337$	179.426			0.532422			0.266211	+	0.963915i	$0.414228\pi$
$338$	219.153			0.648381
$339$			185.424i			0.546973i
$340$	−463.561			−1.36342
$341$		−	425.023i		−	1.24640i
$342$		−	41.0493i		−	0.120027i
$343$	74.5352	+	334.804i	0.217304	+	0.976104i
$344$	−302.756			−0.880106
$345$	−327.192			−0.948383
$346$		−	301.140i		−	0.870348i
$347$	452.745			1.30474			0.652370	−	0.757901i	$-0.273775\pi$
$347$	452.745			1.30474			0.652370	+	0.757901i	$0.273775\pi$
$348$		−	63.3022i		−	0.181903i
$349$			369.379i			1.05839i	0.848499	+	0.529197i	$0.177507\pi$
$349$			369.379i			1.05839i	−0.848499	+	0.529197i	$0.822493\pi$
$350$	−27.5524	−	376.670i	−0.0787210	−	1.07620i
$351$	383.889			1.09370
$352$	404.940			1.15040
$353$		−	114.503i		−	0.324370i	−0.986760	−	0.162185i	$-0.948146\pi$
$353$		−	114.503i		−	0.324370i	0.986760	−	0.162185i	$-0.0518541\pi$
$354$	137.105			0.387301
$355$		−	517.639i		−	1.45814i
$356$			23.2753i			0.0653800i
$357$	21.1230	+	288.773i	0.0591680	+	0.808889i
$358$	−257.820			−0.720169
$359$	−402.956			−1.12244			−0.561220	−	0.827667i	$-0.689668\pi$
$359$	−402.956			−1.12244			−0.561220	+	0.827667i	$0.689668\pi$
$360$			489.241i			1.35900i
$361$	345.897			0.958164
$362$		−	140.095i		−	0.387002i
$363$		−	136.396i		−	0.375747i
$364$	−234.577	+	17.1587i	−0.644443	+	0.0471392i
$365$	27.4596			0.0752318
$366$	−67.4324			−0.184242
$367$			103.133i			0.281016i	0.990080	+	0.140508i	$0.0448736\pi$
$367$			103.133i			0.281016i	−0.990080	+	0.140508i	$0.955126\pi$
$368$	155.521			0.422611
$369$			46.4493i			0.125879i
$370$			633.948i			1.71337i
$371$	15.2961	+	209.115i	0.0412295	+	0.563651i
$372$	−70.4976			−0.189510
$373$	17.4499			0.0467825			0.0233912	−	0.999726i	$-0.492554\pi$
$373$	17.4499			0.0467825			0.0233912	+	0.999726i	$0.492554\pi$
$374$		−	682.579i		−	1.82508i
$375$	−125.460			−0.334559
$376$		−	274.091i		−	0.728965i
$377$		−	455.566i		−	1.20840i
$378$	218.321	−	15.9696i	0.577569	−	0.0422476i
$379$	225.752			0.595653			0.297827	−	0.954620i	$-0.403738\pi$
$379$	225.752			0.595653			0.297827	+	0.954620i	$0.403738\pi$
$380$	57.5463			0.151438
$381$			86.5540i			0.227176i
$382$	380.349			0.995678
$383$		−	372.599i		−	0.972843i	−0.873724	−	0.486421i	$-0.838302\pi$
$383$		−	372.599i		−	0.972843i	0.873724	−	0.486421i	$-0.161698\pi$
$384$		−	29.0930i		−	0.0757630i
$385$	−823.510	+	60.2374i	−2.13899	+	0.156461i
$386$	85.4453			0.221361
$387$	−256.525			−0.662855
$388$			121.554i			0.313283i
$389$	209.375			0.538239			0.269119	−	0.963107i	$-0.413267\pi$
$389$	209.375			0.538239			0.269119	+	0.963107i	$0.413267\pi$
$390$		−	270.904i		−	0.694626i
$391$			984.090i			2.51685i
$392$	−415.050	+	61.0461i	−1.05880	+	0.155730i
$393$	74.0225			0.188352
$394$	180.419			0.457915
$395$			1005.88i			2.54654i
$396$	204.193			0.515638
$397$		−	582.691i		−	1.46773i	−0.679293	−	0.733867i	$-0.737713\pi$
$397$		−	582.691i		−	1.46773i	0.679293	−	0.733867i	$-0.262287\pi$
$398$		−	15.0194i		−	0.0377373i
$399$	−2.62220	−	35.8482i	−0.00657193	−	0.0898452i
$400$	183.316			0.458291
$401$	317.065			0.790686			0.395343	−	0.918533i	$-0.370626\pi$
$401$	317.065			0.790686			0.395343	+	0.918533i	$0.370626\pi$
$402$			133.578i			0.332284i
$403$	−507.348			−1.25893
$404$		−	256.186i		−	0.634124i
$405$			290.759i			0.717924i
$406$	−18.9513	−	259.084i	−0.0466780	−	0.638138i
$407$	827.609			2.03344
$408$	−354.136			−0.867979
$409$		−	309.038i		−	0.755595i	−0.925888	−	0.377798i	$-0.876681\pi$
$409$		−	309.038i		−	0.755595i	0.925888	−	0.377798i	$-0.123319\pi$
$410$	73.4457			0.179136
$411$		−	274.800i		−	0.668614i
$412$		−	79.1596i		−	0.192135i
$413$	−497.507	+	36.3913i	−1.20462	+	0.0881145i
$414$	332.045			0.802040
$415$	620.346			1.49481
$416$		−	483.375i		−	1.16196i
$417$	117.494			0.281760
$418$			84.7352i			0.202716i
$419$		−	433.901i		−	1.03556i	−0.855513	−	0.517782i	$-0.826758\pi$
$419$		−	433.901i		−	1.03556i	0.855513	−	0.517782i	$-0.173242\pi$
$420$	9.99145	+	136.594i	0.0237892	+	0.325223i
$421$	244.765			0.581389			0.290695	−	0.956816i	$-0.406114\pi$
$421$	244.765			0.581389			0.290695	+	0.956816i	$0.406114\pi$
$422$	−20.3505			−0.0482240
$423$		−	232.237i		−	0.549023i
$424$	−256.446			−0.604826
$425$			1159.97i			2.72935i
$426$		−	126.426i		−	0.296774i
$427$	244.690	−	17.8984i	0.573045	−	0.0419166i
$428$	−77.0634			−0.180055
$429$	−353.661			−0.824384
$430$			405.617i			0.943295i
$431$	−364.787			−0.846374			−0.423187	−	0.906042i	$-0.639089\pi$
$431$	−364.787			−0.846374			−0.423187	+	0.906042i	$0.639089\pi$
$432$			106.252i			0.245953i
$433$			530.061i			1.22416i	0.790796	+	0.612080i	$0.209667\pi$
$433$			530.061i			1.22416i	−0.790796	+	0.612080i	$0.790333\pi$
$434$	−288.534	+	21.1054i	−0.664824	+	0.0486300i
$435$	−265.275			−0.609827
$436$	265.279			0.608437
$437$		−	122.165i		−	0.279553i
$438$	6.70660			0.0153119
$439$			187.033i			0.426044i	0.977047	+	0.213022i	$0.0683306\pi$
$439$			187.033i			0.426044i	−0.977047	+	0.213022i	$0.931669\pi$
$440$		−	1009.91i		−	2.29524i
$441$	−351.671	+	51.7242i	−0.797439	+	0.117288i
$442$	−814.793			−1.84342
$443$	−313.872			−0.708515			−0.354258	−	0.935148i	$-0.615266\pi$
$443$	−313.872			−0.708515			−0.354258	+	0.935148i	$0.615266\pi$
$444$		−	137.274i		−	0.309175i
$445$	97.5376			0.219186
$446$			321.901i			0.721752i
$447$			159.991i			0.357922i
$448$	−30.2139	−	413.056i	−0.0674417	−	0.921999i
$449$	−737.074			−1.64159			−0.820795	−	0.571223i	$-0.806469\pi$
$449$	−737.074			−1.64159			−0.820795	+	0.571223i	$0.806469\pi$
$450$	391.390			0.869755
$451$		−	95.8821i		−	0.212599i
$452$	263.798			0.583624
$453$			36.4653i			0.0804973i
$454$			73.3899i			0.161652i
$455$	71.9053	+	983.022i	0.158034	+	2.16049i
$456$	43.9623			0.0964085
$457$	766.856			1.67802			0.839011	−	0.544115i	$-0.183135\pi$
$457$	766.856			1.67802			0.839011	+	0.544115i	$0.183135\pi$
$458$			1.59647i			0.00348573i
$459$	−672.330			−1.46477
$460$			465.488i			1.01193i
$461$		−	689.894i		−	1.49652i	−0.663408	−	0.748258i	$-0.730891\pi$
$461$		−	689.894i		−	1.49652i	0.663408	−	0.748258i	$-0.269109\pi$
$462$	−201.130	+	14.7121i	−0.435346	+	0.0318444i
$463$	196.171			0.423696			0.211848	−	0.977303i	$-0.432052\pi$
$463$	196.171			0.423696			0.211848	+	0.977303i	$0.432052\pi$
$464$	126.090			0.271746
$465$			295.428i			0.635328i
$466$	90.2972			0.193771
$467$			739.115i			1.58269i	0.611371	+	0.791344i	$0.290618\pi$
$467$			739.115i			1.58269i	−0.611371	+	0.791344i	$0.709382\pi$
$468$		−	243.744i		−	0.520821i
$469$	−35.4553	−	484.711i	−0.0755976	−	1.03350i
$470$	−367.213			−0.781303
$471$	294.712			0.625716
$472$		−	610.115i		−	1.29262i
$473$	529.526			1.11951
$474$			245.672i			0.518295i
$475$		−	143.999i		−	0.303155i
$476$	410.831	−	30.0511i	0.863089	−	0.0631326i
$477$	−217.286			−0.455527
$478$	592.540			1.23962
$479$		−	97.3743i		−	0.203287i	−0.994821	−	0.101643i	$-0.967590\pi$
$479$		−	97.3743i		−	0.203287i	0.994821	−	0.101643i	$-0.0324100\pi$
$480$	−281.468			−0.586392
$481$		−	987.915i		−	2.05388i
$482$		−	19.9110i		−	0.0413092i
$483$	289.974	−	21.2108i	0.600359	−	0.0439146i
$484$	−194.047			−0.400924
$485$	509.384			1.05028
$486$			352.462i			0.725231i
$487$	−624.316			−1.28196			−0.640982	−	0.767556i	$-0.721473\pi$
$487$	−624.316			−1.28196			−0.640982	+	0.767556i	$0.721473\pi$
$488$			300.074i			0.614906i
$489$		−	263.501i		−	0.538857i
$490$	81.7863	+	556.062i	0.166911	+	1.13482i
$491$	−436.382			−0.888761			−0.444380	−	0.895838i	$-0.646576\pi$
$491$	−436.382			−0.888761			−0.444380	+	0.895838i	$0.646576\pi$
$492$	−15.9038			−0.0323247
$493$			797.862i			1.61838i
$494$	101.148			0.204753
$495$		−	855.691i		−	1.72867i
$496$		−	140.422i		−	0.283110i
$497$	33.5568	+	458.757i	0.0675187	+	0.923053i
$498$	151.510			0.304237
$499$	−201.548			−0.403904			−0.201952	−	0.979395i	$-0.564728\pi$
$499$	−201.548			−0.403904			−0.201952	+	0.979395i	$0.564728\pi$
$500$			178.488i			0.356976i
$501$	−66.2720			−0.132279
$502$		−	135.104i		−	0.269131i
$503$			389.359i			0.774074i	0.922064	+	0.387037i	$0.126501\pi$
$503$			389.359i			0.774074i	−0.922064	+	0.387037i	$0.873499\pi$
$504$	−31.7158	−	433.589i	−0.0629283	−	0.860296i
$505$	−1073.58			−2.12589
$506$	−685.416			−1.35458
$507$			198.864i			0.392238i
$508$	123.138			0.242398
$509$		−	298.276i		−	0.586004i	−0.956112	−	0.293002i	$-0.905346\pi$
$509$		−	298.276i		−	0.586004i	0.956112	−	0.293002i	$-0.0946542\pi$
$510$			474.452i			0.930298i
$511$	−24.3360	+	1.78011i	−0.0476243	+	0.00348359i
$512$	303.214			0.592215
$513$	83.4629			0.162696
$514$		−	116.393i		−	0.226446i
$515$	−331.727			−0.644130
$516$		−	87.8313i		−	0.170216i
$517$			479.390i			0.927253i
$518$	−41.0967	−	561.836i	−0.0793373	−	1.08463i
$519$	273.262			0.526516
$520$	−1205.52			−2.31831
$521$			749.351i			1.43829i	0.694858	+	0.719147i	$0.255467\pi$
$521$			749.351i			1.43829i	−0.694858	+	0.719147i	$0.744533\pi$
$522$	269.209			0.515726
$523$		−	730.100i		−	1.39599i	−0.716105	−	0.697993i	$-0.754077\pi$
$523$		−	730.100i		−	1.39599i	0.716105	−	0.697993i	$-0.245923\pi$
$524$		−	105.310i		−	0.200973i
$525$	341.800	−	25.0017i	0.651047	−	0.0476223i
$526$	−642.314			−1.22113
$527$	888.553			1.68606
$528$		−	97.8852i		−	0.185389i
$529$	459.180			0.868016
$530$			343.573i			0.648251i
$531$		−	516.949i		−	0.973539i
$532$	−51.0004	+	3.73053i	−0.0958653	+	0.00701228i
$533$	−114.454			−0.214736
$534$	23.8221			0.0446107
$535$			322.942i			0.603631i
$536$	594.422			1.10900
$537$		−	233.952i		−	0.435666i
$538$			362.386i			0.673580i
$539$	725.929	−	106.771i	1.34681	−	0.198090i
$540$	−318.021			−0.588928
$541$	−328.785			−0.607736			−0.303868	−	0.952714i	$-0.598278\pi$
$541$	−328.785			−0.607736			−0.303868	+	0.952714i	$0.598278\pi$
$542$		−	237.608i		−	0.438390i
$543$	127.125			0.234117
$544$			846.567i			1.55619i
$545$		−	1111.68i		−	2.03978i
$546$	17.5618	+	240.088i	0.0321645	+	0.439722i
$547$	−936.113			−1.71136			−0.855679	−	0.517507i	$-0.826860\pi$
$547$	−936.113			−1.71136			−0.855679	+	0.517507i	$0.826860\pi$
$548$	−390.951			−0.713415
$549$			254.252i			0.463119i
$550$	−807.919			−1.46894
$551$		−	99.0463i		−	0.179757i
$552$			355.607i			0.644216i
$553$	−65.2079	−	891.461i	−0.117917	−	1.61205i
$554$	98.0182			0.176928
$555$	−575.260			−1.03650
$556$		−	167.155i		−	0.300639i
$557$	−155.016			−0.278305			−0.139152	−	0.990271i	$-0.544438\pi$
$557$	−155.016			−0.278305			−0.139152	+	0.990271i	$0.544438\pi$
$558$		−	299.809i		−	0.537292i
$559$		−	632.094i		−	1.13076i
$560$	−272.078	+	19.9017i	−0.485853	+	0.0355388i
$561$	619.389			1.10408
$562$	−385.739			−0.686368
$563$			85.7911i			0.152382i	0.997093	+	0.0761910i	$0.0242759\pi$
$563$			85.7911i			0.152382i	−0.997093	+	0.0761910i	$0.975724\pi$
$564$	79.5153			0.140985
$565$		−	1105.47i		−	1.95659i
$566$		−	264.709i		−	0.467684i
$567$	−18.8489	−	257.685i	−0.0332433	−	0.454471i
$568$	−562.594			−0.990483
$569$	298.630			0.524833			0.262416	−	0.964955i	$-0.415481\pi$
$569$	298.630			0.524833			0.262416	+	0.964955i	$0.415481\pi$
$570$		−	58.8983i		−	0.103330i
$571$	−329.213			−0.576554			−0.288277	−	0.957547i	$-0.593082\pi$
$571$	−329.213			−0.576554			−0.288277	+	0.957547i	$0.593082\pi$
$572$			503.144i			0.879622i
$573$			345.138i			0.602335i
$574$	−65.0911	+	4.76124i	−0.113399	+	0.00829483i
$575$	1164.79			2.02573
$576$	429.197			0.745134
$577$			324.811i			0.562931i	0.959571	+	0.281465i	$0.0908204\pi$
$577$			324.811i			0.562931i	−0.959571	+	0.281465i	$0.909180\pi$
$578$	1006.19			1.74081
$579$			77.5351i			0.133912i
$580$			377.399i			0.650689i
$581$	−549.781	+	40.2149i	−0.946266	+	0.0692167i
$582$	124.409			0.213762
$583$	448.529			0.769347
$584$		−	29.8443i		−	0.0511033i
$585$	−1021.44			−1.74605
$586$		−	729.614i		−	1.24508i
$587$		−	901.749i		−	1.53620i	−0.640331	−	0.768099i	$-0.721203\pi$
$587$		−	901.749i		−	1.53620i	0.640331	−	0.768099i	$-0.278797\pi$
$588$	−17.7098	−	120.408i	−0.0301187	−	0.204776i
$589$	−110.305			−0.187274
$590$	−817.400			−1.38542
$591$			163.716i			0.277016i
$592$	273.432			0.461879
$593$			444.484i			0.749552i	0.927115	+	0.374776i	$0.122280\pi$
$593$			444.484i			0.749552i	−0.927115	+	0.374776i	$0.877720\pi$
$594$		−	468.276i		−	0.788344i
$595$	−125.932	−	1721.63i	−0.211651	−	2.89350i
$596$	227.615			0.381905
$597$	13.6290			0.0228292
$598$			818.180i			1.36819i
$599$	−1001.31			−1.67164			−0.835818	−	0.549006i	$-0.815006\pi$
$599$	−1001.31			−1.67164			−0.835818	+	0.549006i	$0.815006\pi$
$600$			419.164i			0.698607i
$601$			499.342i			0.830852i	0.909627	+	0.415426i	$0.136367\pi$
$601$			499.342i			0.830852i	−0.909627	+	0.415426i	$0.863633\pi$
$602$	−26.2948	−	359.478i	−0.0436790	−	0.597139i
$603$	503.653			0.835245
$604$	51.8782			0.0858911
$605$			813.176i			1.34409i
$606$	−262.205			−0.432681
$607$		−	390.190i		−	0.642817i	−0.946941	−	0.321409i	$-0.895844\pi$
$607$		−	390.190i		−	0.642817i	0.946941	−	0.321409i	$-0.104156\pi$
$608$		−	105.093i		−	0.172850i
$609$	235.099	−	17.1969i	0.386042	−	0.0282379i
$610$	402.023			0.659055
$611$	572.247			0.936574
$612$			426.885i			0.697525i
$613$	1110.61			1.81177			0.905883	−	0.423528i	$-0.139208\pi$
$613$	1110.61			1.81177			0.905883	+	0.423528i	$0.139208\pi$
$614$			312.446i			0.508870i
$615$			66.6464i			0.108368i
$616$	65.4688	+	895.028i	0.106281	+	1.45297i
$617$	909.843			1.47462			0.737312	−	0.675552i	$-0.236095\pi$
$617$	909.843			1.47462			0.737312	+	0.675552i	$0.236095\pi$
$618$	−81.0194			−0.131099
$619$			789.543i			1.27551i	0.770237	+	0.637757i	$0.220138\pi$
$619$			789.543i			1.27551i	−0.770237	+	0.637757i	$0.779862\pi$
$620$	420.297			0.677899
$621$			675.125i			1.08716i
$622$			662.228i			1.06467i
$623$	−86.4425	+	6.32303i	−0.138752	+	0.0101493i
$624$	−116.845			−0.187252
$625$	−178.367			−0.285388
$626$			169.292i			0.270434i
$627$	−76.8908			−0.122633
$628$		−	419.279i		−	0.667642i
$629$			1730.20i			2.75072i
$630$	−580.900	+	42.4912i	−0.922063	+	0.0674464i
$631$	−129.683			−0.205520			−0.102760	−	0.994706i	$-0.532767\pi$
$631$	−129.683			−0.205520			−0.102760	+	0.994706i	$0.532767\pi$
$632$	1093.24			1.72981
$633$		−	18.4666i		−	0.0291731i
$634$	−353.056			−0.556871
$635$		−	516.024i		−	0.812636i
$636$		−	74.3965i		−	0.116976i
$637$	−127.452	−	866.540i	−0.200081	−	1.36035i
$638$	−555.709			−0.871017
$639$	−476.685			−0.745986
$640$			173.449i			0.271013i
$641$	−1056.43			−1.64810			−0.824051	−	0.566515i	$-0.808291\pi$
$641$	−1056.43			−1.64810			−0.824051	+	0.566515i	$0.808291\pi$
$642$			78.8739i			0.122857i
$643$			161.719i			0.251506i	0.992062	+	0.125753i	$0.0401347\pi$
$643$			161.719i			0.251506i	−0.992062	+	0.125753i	$0.959865\pi$
$644$	−30.1760	−	412.538i	−0.0468571	−	0.640587i
$645$	−368.067			−0.570646
$646$	−177.147			−0.274222
$647$			338.032i			0.522460i	0.965277	+	0.261230i	$0.0841282\pi$
$647$			338.032i			0.522460i	−0.965277	+	0.261230i	$0.915872\pi$
$648$	316.010			0.487670
$649$			1067.10i			1.64423i
$650$			964.410i			1.48371i
$651$	−19.1516	−	261.822i	−0.0294187	−	0.402185i
$652$	−374.876			−0.574963
$653$	−809.820			−1.24015			−0.620076	−	0.784542i	$-0.712898\pi$
$653$	−809.820			−1.24015			−0.620076	+	0.784542i	$0.712898\pi$
$654$		−	271.511i		−	0.415155i
$655$	−441.312			−0.673759
$656$		−	31.6783i		−	0.0482901i
$657$		−	25.2870i		−	0.0384886i
$658$	325.442	−	23.8051i	0.494592	−	0.0361780i
$659$	89.0519			0.135132			0.0675660	−	0.997715i	$-0.478477\pi$
$659$	89.0519			0.135132			0.0675660	+	0.997715i	$0.478477\pi$
$660$	292.979			0.443908
$661$		−	1248.26i		−	1.88844i	−0.329320	−	0.944218i	$-0.606820\pi$
$661$		−	1248.26i		−	1.88844i	0.329320	−	0.944218i	$-0.393180\pi$
$662$	111.989			0.169167
$663$		−	739.363i		−	1.11518i
$664$		−	674.220i		−	1.01539i
$665$	15.6332	+	213.723i	0.0235086	+	0.321387i
$666$	583.792			0.876564
$667$	801.178			1.20117
$668$			94.2835i			0.141143i
$669$	−292.101			−0.436624
$670$		−	796.376i		−	1.18862i
$671$		−	524.835i		−	0.782168i
$672$	249.451	−	18.2466i	0.371207	−	0.0271527i
$673$	117.757			0.174973			0.0874865	−	0.996166i	$-0.472117\pi$
$673$	117.757			0.174973			0.0874865	+	0.996166i	$0.472117\pi$
$674$	−261.262			−0.387629
$675$			795.787i			1.17894i
$676$	282.919			0.418520
$677$		−	238.601i		−	0.352439i	−0.984351	−	0.176219i	$-0.943613\pi$
$677$		−	238.601i		−	0.352439i	0.984351	−	0.176219i	$-0.0563868\pi$
$678$		−	269.996i		−	0.398224i
$679$	−451.441	+	33.0216i	−0.664861	+	0.0486327i
$680$	2111.31			3.10487
$681$	−66.5958			−0.0977912
$682$			618.875i			0.907441i
$683$	−977.551			−1.43126			−0.715630	−	0.698479i	$-0.753860\pi$
$683$	−977.551			−1.43126			−0.715630	+	0.698479i	$0.753860\pi$
$684$		−	52.9934i		−	0.0774757i
$685$			1638.32i			2.39171i
$686$	−108.531	−	487.507i	−0.158208	−	0.710652i
$687$	−1.44867			−0.00210869
$688$	174.949			0.254287
$689$		−	535.408i		−	0.777080i
$690$	476.424			0.690470
$691$			618.478i			0.895048i	0.894272	+	0.447524i	$0.147694\pi$
$691$			618.478i			0.895048i	−0.894272	+	0.447524i	$0.852306\pi$
$692$		−	388.763i		−	0.561796i
$693$	55.4716	+	758.355i	0.0800455	+	1.09431i
$694$	−659.241			−0.949915
$695$	−700.483			−1.00789
$696$			288.313i			0.414242i
$697$	200.451			0.287591
$698$		−	537.853i		−	0.770562i
$699$			81.9379i			0.117222i
$700$	−35.5693	−	486.270i	−0.0508132	−	0.694671i
$701$	−838.901			−1.19672			−0.598360	−	0.801227i	$-0.704181\pi$
$701$	−838.901			−1.19672			−0.598360	+	0.801227i	$0.704181\pi$
$702$	−558.980			−0.796268
$703$		−	214.786i		−	0.305528i
$704$	−885.962			−1.25847
$705$		−	333.218i		−	0.472649i
$706$			166.727i			0.236157i
$707$	951.455	−	69.5963i	1.34576	−	0.0984389i
$708$	176.998			0.249997
$709$	−604.689			−0.852876			−0.426438	−	0.904517i	$-0.640232\pi$
$709$	−604.689			−0.852876			−0.426438	+	0.904517i	$0.640232\pi$
$710$			753.734i			1.06160i
$711$	926.298			1.30281
$712$		−	106.008i		−	0.148888i
$713$		−	892.246i		−	1.25140i
$714$	−30.7571	−	420.483i	−0.0430772	−	0.588911i
$715$	2108.48			2.94892
$716$	−332.838			−0.464858
$717$			537.685i			0.749909i
$718$	586.743			0.817191
$719$			1058.54i			1.47223i	0.676854	+	0.736117i	$0.263343\pi$
$719$			1058.54i			1.47223i	−0.676854	+	0.736117i	$0.736657\pi$
$720$		−	282.710i		−	0.392653i
$721$	293.993	−	21.5047i	0.407757	−	0.0298263i
$722$	−503.660			−0.697591
$723$	18.0678			0.0249900
$724$		−	180.858i		−	0.249804i
$725$	944.370			1.30258
$726$			198.606i			0.273562i
$727$		−	1107.76i		−	1.52375i	−0.647726	−	0.761873i	$-0.724280\pi$
$727$		−	1107.76i		−	1.52375i	0.647726	−	0.761873i	$-0.275720\pi$
$728$	1068.39	−	78.1499i	1.46757	−	0.107349i
$729$	12.3615			0.0169568
$730$	−39.9839			−0.0547724
$731$			1107.03i			1.51440i
$732$	−87.0532			−0.118925
$733$			949.586i			1.29548i	0.761862	+	0.647739i	$0.224285\pi$
$733$			949.586i			1.29548i	−0.761862	+	0.647739i	$0.775715\pi$
$734$		−	150.172i		−	0.204594i
$735$	−504.584	+	74.2149i	−0.686509	+	0.100973i
$736$	850.085			1.15501
$737$	−1039.66			−1.41066
$738$		−	67.6348i		−	0.0916461i
$739$	−139.798			−0.189171			−0.0945857	−	0.995517i	$-0.530153\pi$
$739$	−139.798			−0.189171			−0.0945857	+	0.995517i	$0.530153\pi$
$740$			818.408i			1.10596i
$741$			91.7843i			0.123866i
$742$	−22.2727	−	304.491i	−0.0300171	−	0.410366i
$743$	64.2328			0.0864507			0.0432253	−	0.999065i	$-0.486237\pi$
$743$	64.2328			0.0864507			0.0432253	+	0.999065i	$0.486237\pi$
$744$	321.084			0.431565
$745$		−	953.846i		−	1.28033i
$746$	−25.4087			−0.0340599
$747$		−	571.265i		−	0.764746i
$748$		−	881.189i		−	1.17806i
$749$	−20.9353	−	286.207i	−0.0279510	−	0.382119i
$750$	182.682			0.243575
$751$	339.344			0.451857			0.225928	−	0.974144i	$-0.427458\pi$
$751$	339.344			0.451857			0.225928	+	0.974144i	$0.427458\pi$
$752$			158.385i			0.210618i
$753$	122.596			0.162811
$754$			663.348i			0.879772i
$755$		−	217.401i		−	0.287949i
$756$	281.846	−	20.6162i	0.372812	−	0.0272702i
$757$	1069.94			1.41339			0.706697	−	0.707517i	$-0.250184\pi$
$757$	1069.94			1.41339			0.706697	+	0.707517i	$0.250184\pi$
$758$	−328.718			−0.433665
$759$		−	621.964i		−	0.819451i
$760$	−262.097			−0.344865
$761$		−	380.247i		−	0.499667i	−0.968289	−	0.249834i	$-0.919624\pi$
$761$		−	380.247i		−	0.499667i	0.968289	−	0.249834i	$-0.0803759\pi$
$762$		−	126.031i		−	0.165395i
$763$	72.0664	+	985.224i	0.0944514	+	1.29125i
$764$	491.019			0.642695
$765$	1788.91			2.33844
$766$			542.540i			0.708277i
$767$	1273.80			1.66075
$768$			355.064i			0.462323i
$769$			810.738i			1.05428i	0.849780	+	0.527138i	$0.176735\pi$
$769$			810.738i			1.05428i	−0.849780	+	0.527138i	$0.823265\pi$
$770$	1199.11	−	87.7116i	1.55729	−	0.113911i
$771$	105.618			0.136988
$772$	110.307			0.142885
$773$		−	1031.23i		−	1.33406i	−0.745030	−	0.667031i	$-0.767565\pi$
$773$		−	1031.23i		−	1.33406i	0.745030	−	0.667031i	$-0.232435\pi$
$774$	373.525			0.482591
$775$		−	1051.71i		−	1.35705i
$776$		−	553.622i		−	0.713430i
$777$	509.824	−	37.2922i	0.656144	−	0.0479951i
$778$	−304.870			−0.391864
$779$	−24.8840			−0.0319435
$780$		−	349.729i		−	0.448370i
$781$	983.987			1.25991
$782$		−	1432.93i		−	1.83239i
$783$			547.365i			0.699061i
$784$	239.838	−	35.2758i	0.305916	−	0.0449946i
$785$	−1757.04			−2.23826
$786$	−107.784			−0.137130
$787$		−	1215.13i		−	1.54400i	−0.635623	−	0.772000i	$-0.719257\pi$
$787$		−	1215.13i		−	1.54400i	0.635623	−	0.772000i	$-0.280743\pi$
$788$	232.915			0.295577
$789$		−	582.851i		−	0.738722i
$790$		−	1464.66i		−	1.85400i
$791$	71.6641	+	979.725i	0.0905994	+	1.23859i
$792$	−930.004			−1.17425
$793$	−626.494			−0.790030
$794$			848.455i			1.06858i
$795$	−311.767			−0.392159
$796$		−	19.3896i		−	0.0243589i
$797$		−	1408.15i		−	1.76681i	−0.468606	−	0.883407i	$-0.655244\pi$
$797$		−	1408.15i		−	1.76681i	0.468606	−	0.883407i	$-0.344756\pi$
$798$	3.81818	+	52.1986i	0.00478469	+	0.0654117i
$799$	−1002.21			−1.25433
$800$	1002.02			1.25252
$801$		−	89.8206i		−	0.112136i
$802$	−461.678			−0.575659
$803$			52.1983i			0.0650041i
$804$			172.445i			0.214484i
$805$	−1728.79	+	126.456i	−2.14756	+	0.157088i
$806$	738.749			0.916562
$807$	−328.838			−0.407482
$808$			1166.81i			1.44407i
$809$	688.348			0.850863			0.425432	−	0.904991i	$-0.360122\pi$
$809$	688.348			0.850863			0.425432	+	0.904991i	$0.360122\pi$
$810$		−	423.374i		−	0.522684i
$811$		−	583.581i		−	0.719582i	−0.933033	−	0.359791i	$-0.882848\pi$
$811$		−	583.581i		−	0.719582i	0.933033	−	0.359791i	$-0.117152\pi$
$812$	−24.4655	−	334.470i	−0.0301300	−	0.411909i
$813$	215.611			0.265204
$814$	−1205.08			−1.48044
$815$			1570.96i			1.92756i
$816$	204.639			0.250783
$817$		−	137.426i		−	0.168208i
$818$			449.990i			0.550110i
$819$	905.247	−	66.2163i	1.10531	−	0.0808501i
$820$	94.8161			0.115629
$821$	−113.713			−0.138506			−0.0692529	−	0.997599i	$-0.522062\pi$
$821$	−113.713			−0.138506			−0.0692529	+	0.997599i	$0.522062\pi$
$822$			400.136i			0.486784i
$823$	271.726			0.330166			0.165083	−	0.986280i	$-0.447211\pi$
$823$	271.726			0.330166			0.165083	+	0.986280i	$0.447211\pi$
$824$			360.536i			0.437544i
$825$		−	733.125i		−	0.888636i
$826$	724.420	−	52.9893i	0.877021	−	0.0641517i
$827$	−589.805			−0.713186			−0.356593	−	0.934260i	$-0.616062\pi$
$827$	−589.805			−0.713186			−0.356593	+	0.934260i	$0.616062\pi$
$828$	428.659			0.517705
$829$			1071.46i			1.29247i	0.763137	+	0.646236i	$0.223658\pi$
$829$			1071.46i			1.29247i	−0.763137	+	0.646236i	$0.776342\pi$
$830$	−903.285			−1.08829
$831$			88.9442i			0.107033i
$832$			1057.57i			1.27112i
$833$	223.215	+	1517.63i	0.267965	+	1.82188i
$834$	−171.083			−0.205135
$835$	395.105			0.473180
$836$			109.391i			0.130850i
$837$	609.582			0.728294
$838$			631.803i			0.753941i
$839$			1116.06i			1.33023i	0.746740	+	0.665116i	$0.231618\pi$
$839$			1116.06i			1.33023i	−0.746740	+	0.665116i	$0.768382\pi$
$840$	−45.5065	−	622.122i	−0.0541744	−	0.740622i
$841$	−191.436			−0.227629
$842$	−356.402			−0.423280
$843$		−	350.029i		−	0.415218i
$844$	−26.2719			−0.0311278
$845$		−	1185.60i		−	1.40308i
$846$			338.159i			0.399716i
$847$	−52.7155	−	720.676i	−0.0622379	−	0.850858i
$848$	148.189			0.174751
$849$	240.203			0.282925
$850$		−	1689.04i		−	1.98710i
$851$	1737.39			2.04159
$852$		−	163.212i		−	0.191563i
$853$			1193.28i			1.39892i	0.714669	+	0.699462i	$0.246577\pi$
$853$			1193.28i			1.39892i	−0.714669	+	0.699462i	$0.753423\pi$
$854$	−356.293	+	26.0618i	−0.417205	+	0.0305173i
$855$	−222.075			−0.259736
$856$	350.989			0.410033
$857$		−	215.366i		−	0.251303i	−0.992074	−	0.125651i	$-0.959898\pi$
$857$		−	215.366i		−	0.251303i	0.992074	−	0.125651i	$-0.0401021\pi$
$858$	514.965			0.600192
$859$			822.323i			0.957302i	0.878005	+	0.478651i	$0.158874\pi$
$859$			822.323i			0.957302i	−0.878005	+	0.478651i	$0.841126\pi$
$860$			523.639i			0.608883i
$861$	−4.32046	−	59.0653i	−0.00501796	−	0.0686008i
$862$	531.166			0.616202
$863$	761.095			0.881918			0.440959	−	0.897527i	$-0.354638\pi$
$863$	761.095			0.881918			0.440959	+	0.897527i	$0.354638\pi$
$864$			580.778i			0.672197i
$865$	−1629.15			−1.88341
$866$		−	771.821i		−	0.891248i
$867$			913.040i			1.05310i
$868$	−372.488	+	27.2465i	−0.429134	+	0.0313899i
$869$	−1912.09			−2.20034
$870$	386.266			0.443984
$871$			1241.03i			1.42484i
$872$	−1208.22			−1.38558
$873$		−	469.082i		−	0.537322i
$874$			177.884i			0.203528i
$875$	−662.891	+	48.4886i	−0.757590	+	0.0554156i
$876$	8.65801			0.00988357
$877$	−349.758			−0.398812			−0.199406	−	0.979917i	$-0.563901\pi$
$877$	−349.758			−0.398812			−0.199406	+	0.979917i	$0.563901\pi$
$878$		−	272.339i		−	0.310181i
$879$	662.070			0.753208
$880$			583.579i			0.663158i
$881$		−	772.690i		−	0.877061i	−0.898716	−	0.438530i	$-0.855499\pi$
$881$		−	772.690i		−	0.877061i	0.898716	−	0.438530i	$-0.144501\pi$
$882$	512.067	−	75.3155i	0.580575	−	0.0853918i
$883$	−297.771			−0.337227			−0.168613	−	0.985682i	$-0.553929\pi$
$883$	−297.771			−0.337227			−0.168613	+	0.985682i	$0.553929\pi$
$884$	−1051.87			−1.18990
$885$		−	741.729i		−	0.838112i
$886$	457.029			0.515834
$887$			1392.32i			1.56970i	0.619688	+	0.784848i	$0.287259\pi$
$887$			1392.32i			1.56970i	−0.619688	+	0.784848i	$0.712741\pi$
$888$			625.219i			0.704076i
$889$	33.4521	+	457.326i	0.0376289	+	0.514427i
$890$	−142.024			−0.159578
$891$	−552.708			−0.620323
$892$			415.565i			0.465880i
$893$	124.414			0.139322
$894$		−	232.963i		−	0.260585i
$895$			1394.79i			1.55843i
$896$	−11.2441	−	153.719i	−0.0125492	−	0.171561i
$897$	−742.436			−0.827688
$898$	1073.25			1.19516
$899$		−	723.398i		−	0.804670i
$900$	505.272			0.561414
$901$			937.695i			1.04073i
$902$			139.614i			0.154782i
$903$	326.199	−	23.8605i	0.361239	−	0.0264236i
$904$	−1201.48			−1.32907
$905$	−757.905			−0.837464
$906$		−	53.0970i		−	0.0586060i
$907$	−1450.35			−1.59907			−0.799534	−	0.600621i	$-0.794920\pi$
$907$	−1450.35			−1.59907			−0.799534	+	0.600621i	$0.794920\pi$
$908$			94.7441i			0.104344i
$909$			988.637i			1.08761i
$910$	−104.701	−	1431.38i	−0.115056	−	1.57294i
$911$	−756.503			−0.830409			−0.415205	−	0.909728i	$-0.636290\pi$
$911$	−756.503			−0.830409			−0.415205	+	0.909728i	$0.636290\pi$
$912$	−25.4038			−0.0278551
$913$			1179.22i			1.29159i
$914$	−1116.62			−1.22168
$915$			364.806i			0.398695i
$916$			2.06099i			0.00224999i
$917$	391.113	−	28.6088i	0.426513	−	0.0311982i
$918$	978.979			1.06643
$919$	582.345			0.633673			0.316836	−	0.948480i	$-0.397379\pi$
$919$	582.345			0.633673			0.316836	+	0.948480i	$0.397379\pi$
$920$		−	2120.09i		−	2.30444i
$921$	−283.522			−0.307841
$922$			1004.55i			1.08954i
$923$		−	1174.58i		−	1.27257i
$924$	−259.653	+	18.9929i	−0.281009	+	0.0205550i
$925$	2047.91			2.21396
$926$	−285.645			−0.308472
$927$			305.481i			0.329538i
$928$	689.216			0.742690
$929$		−	1752.86i		−	1.88683i	−0.331615	−	0.943415i	$-0.607594\pi$
$929$		−	1752.86i		−	1.88683i	0.331615	−	0.943415i	$-0.392406\pi$
$930$		−	430.172i		−	0.462550i
$931$	−27.7098	−	188.398i	−0.0297635	−	0.202361i
$932$	116.571			0.125076
$933$	−600.921			−0.644074
$934$		−	1076.22i		−	1.15227i
$935$	−3692.72			−3.94943
$936$			1110.14i			1.18605i
$937$		−	122.902i		−	0.131165i	−0.997847	−	0.0655825i	$-0.979109\pi$
$937$		−	122.902i		−	0.131165i	0.997847	−	0.0655825i	$-0.0208905\pi$
$938$	51.6263	+	705.787i	0.0550387	+	0.752438i
$939$	−153.619			−0.163599
$940$	−474.060			−0.504319
$941$		−	1602.28i		−	1.70274i	−0.524568	−	0.851369i	$-0.675773\pi$
$941$		−	1602.28i		−	1.70274i	0.524568	−	0.851369i	$-0.324227\pi$
$942$	−429.130			−0.455552
$943$		−	201.284i		−	0.213451i
$944$			352.558i			0.373472i
$945$	−86.3946	−	1181.11i	−0.0914229	−	1.24985i
$946$	−771.042			−0.815055
$947$	−173.249			−0.182946			−0.0914728	−	0.995808i	$-0.529157\pi$
$947$	−173.249			−0.182946			−0.0914728	+	0.995808i	$0.529157\pi$
$948$			317.154i			0.334551i
$949$	62.3089			0.0656575
$950$			209.676i			0.220712i
$951$		−	320.372i		−	0.336879i
$952$	−1871.15	+	136.869i	−1.96549	+	0.143770i
$953$	−177.101			−0.185835			−0.0929174	−	0.995674i	$-0.529619\pi$
$953$	−177.101			−0.185835			−0.0929174	+	0.995674i	$0.529619\pi$
$954$	316.390			0.331646
$955$		−	2057.67i		−	2.15463i
$956$	764.950			0.800157
$957$		−	504.264i		−	0.526922i
$958$			141.787i			0.148003i
$959$	−106.207	−	1451.96i	−0.110748	−	1.51404i
$960$	615.821			0.641480
$961$	155.375			0.161681
$962$			1438.50i			1.49532i
$963$	297.392			0.308818
$964$		−	25.7045i		−	0.0266644i
$965$		−	462.254i		−	0.479020i
$966$	−422.230	+	30.8850i	−0.437091	+	0.0319720i
$967$	−1152.74			−1.19208			−0.596040	−	0.802955i	$-0.703260\pi$
$967$	−1152.74			−1.19208			−0.596040	+	0.802955i	$0.703260\pi$
$968$	883.797			0.913014
$969$		−	160.748i		−	0.165891i
$970$	−741.713			−0.764652
$971$			350.030i			0.360484i	0.983622	+	0.180242i	$0.0576882\pi$
$971$			350.030i			0.360484i	−0.983622	+	0.180242i	$0.942312\pi$
$972$			455.018i			0.468125i
$973$	620.802	−	45.4100i	0.638029	−	0.0466700i
$974$	909.066			0.933332
$975$	−875.130			−0.897569
$976$		−	173.399i		−	0.177663i
$977$	765.337			0.783354			0.391677	−	0.920103i	$-0.371895\pi$
$977$	765.337			0.783354			0.391677	+	0.920103i	$0.371895\pi$
$978$			383.683i			0.392314i
$979$			185.410i			0.189387i
$980$	105.584	+	717.859i	0.107738	+	0.732509i
$981$	−1023.73			−1.04355
$982$	635.414			0.647062
$983$			98.2372i			0.0999362i	0.998751	+	0.0499681i	$0.0159120\pi$
$983$			98.2372i			0.0999362i	−0.998751	+	0.0499681i	$0.984088\pi$
$984$	72.4344			0.0736122
$985$		−	976.055i		−	0.990919i
$986$		−	1161.77i		−	1.17826i
$987$	21.6014	+	295.314i	0.0218859	+	0.299203i
$988$	130.579			0.132165
$989$	1111.63			1.12399
$990$			1245.97i			1.25856i
$991$	546.637			0.551602			0.275801	−	0.961215i	$-0.411057\pi$
$991$	546.637			0.551602			0.275801	+	0.961215i	$0.411057\pi$
$992$		−	767.557i		−	0.773747i
$993$			101.621i			0.102337i
$994$	−48.8620	−	667.996i	−0.0491570	−	0.672028i
$995$	−81.2544			−0.0816627
$996$	195.595			0.196381
$997$		−	976.998i		−	0.979938i	−0.871740	−	0.489969i	$-0.837008\pi$
$997$		−	976.998i		−	0.979938i	0.871740	−	0.489969i	$-0.162992\pi$
$998$	293.474			0.294062
$999$			1186.99i			1.18817i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	287.3.b.a.83.15	✓	52
7.6	odd	2	inner	287.3.b.a.83.16	yes	52

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
287.3.b.a.83.15	✓	52	1.1	even	1	trivial
287.3.b.a.83.16	yes	52	7.6	odd	2	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q-1.45610 q^{2} -1.32130i q^{3} -1.87978 q^{4} +7.87741i q^{5} +1.92394i q^{6} +(-0.510666 - 6.98135i) q^{7} +8.56153 q^{8} +7.25417 q^{9} +O(q^{10})\)	\(q-1.45610 q^{2} -1.32130i q^{3} -1.87978 q^{4} +7.87741i q^{5} +1.92394i q^{6} +(-0.510666 - 6.98135i) q^{7} +8.56153 q^{8} +7.25417 q^{9} -11.4703i q^{10} -14.9743 q^{11} +2.48375i q^{12} +17.8748i q^{13} +(0.743580 + 10.1655i) q^{14} +10.4084 q^{15} -4.94732 q^{16} -31.3052i q^{17} -10.5628 q^{18} +3.88622i q^{19} -14.8078i q^{20} +(-9.22445 + 0.674743i) q^{21} +21.8040 q^{22} -31.4353 q^{23} -11.3123i q^{24} -37.0537 q^{25} -26.0274i q^{26} -21.4766i q^{27} +(0.959939 + 13.1234i) q^{28} -25.4865 q^{29} -15.1557 q^{30} +28.3835i q^{31} -27.0423 q^{32} +19.7855i q^{33} +45.5835i q^{34} +(54.9950 - 4.02273i) q^{35} -13.6362 q^{36} -55.2687 q^{37} -5.65872i q^{38} +23.6179 q^{39} +67.4428i q^{40} +6.40312i q^{41} +(13.4317 - 0.982492i) q^{42} -35.3624 q^{43} +28.1483 q^{44} +57.1441i q^{45} +45.7729 q^{46} -32.0142i q^{47} +6.53689i q^{48} +(-48.4784 + 7.13028i) q^{49} +53.9538 q^{50} -41.3636 q^{51} -33.6006i q^{52} -29.9533 q^{53} +31.2721i q^{54} -117.959i q^{55} +(-4.37209 - 59.7710i) q^{56} +5.13486 q^{57} +37.1109 q^{58} -71.2624i q^{59} -19.5655 q^{60} +35.0491i q^{61} -41.3292i q^{62} +(-3.70446 - 50.6439i) q^{63} +59.1656 q^{64} -140.807 q^{65} -28.8096i q^{66} +69.4294 q^{67} +58.8469i q^{68} +41.5355i q^{69} +(-80.0781 + 5.85749i) q^{70} -65.7118 q^{71} +62.1068 q^{72} -3.48586i q^{73} +80.4767 q^{74} +48.9590i q^{75} -7.30523i q^{76} +(7.64685 + 104.541i) q^{77} -34.3900 q^{78} +127.692 q^{79} -38.9721i q^{80} +36.9105 q^{81} -9.32358i q^{82} -78.7499i q^{83} +(17.3399 - 1.26837i) q^{84} +246.604 q^{85} +51.4911 q^{86} +33.6754i q^{87} -128.203 q^{88} -12.3819i q^{89} -83.2074i q^{90} +(124.790 - 9.12803i) q^{91} +59.0914 q^{92} +37.5031 q^{93} +46.6159i q^{94} -30.6134 q^{95} +35.7310i q^{96} -64.6638i q^{97} +(70.5894 - 10.3824i) q^{98} -108.626 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 52 q + 2 q^{2} + 90 q^{4} + 12 q^{7} - 2 q^{8} - 140 q^{9}+O(q^{10}) \) 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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