LMFDB - Embedded newform 230.3.c.a.229.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [230,3,Mod(229,230)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(230, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("230.229");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 230 = 2 \cdot 5 \cdot 23 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	230.c (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:	$6.26704608029$
Analytic rank:	$0$
Dimension:	$24$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			229.1
Character	$\chi$	$=$	230.229
Dual form			230.3.c.a.229.23

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.41421i q^{2} -5.45221i q^{3} -2.00000 q^{4} +(-3.90521 + 3.12239i) q^{5} -7.71059 q^{6} +0.770899 q^{7} +2.82843i q^{8} -20.7266 q^{9} +O(q^{10})$	\(q-1.41421i q^{2} -5.45221i q^{3} -2.00000 q^{4} +(-3.90521 + 3.12239i) q^{5} -7.71059 q^{6} +0.770899 q^{7} +2.82843i q^{8} -20.7266 q^{9} +(4.41573 + 5.52280i) q^{10} +8.45857i q^{11} +10.9044i q^{12} -4.15908i q^{13} -1.09022i q^{14} +(17.0239 + 21.2920i) q^{15} +4.00000 q^{16} -32.2680 q^{17} +29.3118i q^{18} -23.8163i q^{19} +(7.81042 - 6.24479i) q^{20} -4.20310i q^{21} +11.9622 q^{22} +(19.8603 + 11.6004i) q^{23} +15.4212 q^{24} +(5.50131 - 24.3872i) q^{25} -5.88182 q^{26} +63.9359i q^{27} -1.54180 q^{28} +21.7473 q^{29} +(30.1115 - 24.0755i) q^{30} -31.8764 q^{31} -5.65685i q^{32} +46.1179 q^{33} +45.6339i q^{34} +(-3.01052 + 2.40705i) q^{35} +41.4532 q^{36} -6.03947 q^{37} -33.6814 q^{38} -22.6762 q^{39} +(-8.83146 - 11.0456i) q^{40} +16.9449 q^{41} -5.94408 q^{42} -61.7107 q^{43} -16.9171i q^{44} +(80.9417 - 64.7166i) q^{45} +(16.4055 - 28.0866i) q^{46} -45.0037i q^{47} -21.8088i q^{48} -48.4057 q^{49} +(-34.4887 - 7.78003i) q^{50} +175.932i q^{51} +8.31815i q^{52} -45.8817 q^{53} +90.4190 q^{54} +(-26.4110 - 33.0325i) q^{55} +2.18043i q^{56} -129.852 q^{57} -30.7553i q^{58} -93.6903 q^{59} +(-34.0479 - 42.5840i) q^{60} +37.1088i q^{61} +45.0801i q^{62} -15.9781 q^{63} -8.00000 q^{64} +(12.9863 + 16.2421i) q^{65} -65.2206i q^{66} +44.2092 q^{67} +64.5360 q^{68} +(63.2481 - 108.282i) q^{69} +(3.40408 + 4.25752i) q^{70} +77.7931 q^{71} -58.6237i q^{72} -101.411i q^{73} +8.54110i q^{74} +(-132.964 - 29.9943i) q^{75} +47.6326i q^{76} +6.52070i q^{77} +32.0689i q^{78} +14.4772i q^{79} +(-15.6208 + 12.4896i) q^{80} +162.052 q^{81} -23.9637i q^{82} +44.9529 q^{83} +8.40621i q^{84} +(126.013 - 100.753i) q^{85} +87.2720i q^{86} -118.571i q^{87} -23.9245 q^{88} -74.0570i q^{89} +(-91.5231 - 114.469i) q^{90} -3.20623i q^{91} +(-39.7205 - 23.2009i) q^{92} +173.797i q^{93} -63.6448 q^{94} +(74.3639 + 93.0077i) q^{95} -30.8424 q^{96} +42.2048 q^{97} +68.4560i q^{98} -175.317i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q - 48 q^{4} + 8 q^{6} - 96 q^{9}+O(q^{10}) $ 24 * q - 48 * q^4 + 8 * q^6 - 96 * q^9	$ 24 q - 48 q^{4} + 8 q^{6} - 96 q^{9} + 96 q^{16} - 16 q^{24} - 48 q^{25} - 32 q^{26} + 100 q^{29} - 124 q^{31} - 28 q^{35} + 192 q^{36} + 192 q^{39} - 116 q^{41} + 148 q^{46} - 76 q^{49} - 144 q^{50} - 16 q^{54} - 224 q^{55} + 84 q^{59} - 192 q^{64} - 340 q^{69} + 328 q^{70} + 196 q^{71} - 496 q^{75} + 1360 q^{81} + 316 q^{85} - 376 q^{94} - 368 q^{95} + 32 q^{96}+O(q^{100}) $ 24 * q - 48 * q^4 + 8 * q^6 - 96 * q^9 + 96 * q^16 - 16 * q^24 - 48 * q^25 - 32 * q^26 + 100 * q^29 - 124 * q^31 - 28 * q^35 + 192 * q^36 + 192 * q^39 - 116 * q^41 + 148 * q^46 - 76 * q^49 - 144 * q^50 - 16 * q^54 - 224 * q^55 + 84 * q^59 - 192 * q^64 - 340 * q^69 + 328 * q^70 + 196 * q^71 - 496 * q^75 + 1360 * q^81 + 316 * q^85 - 376 * q^94 - 368 * q^95 + 32 * q^96

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/230\mathbb{Z}\right)^\times$.

$n$	$47$	$51$
$\chi(n)$	$-1$	$-1$

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 $

$2$		−	1.41421i		−	0.707107i
$2$		−	1.41421i		−	0.707107i
$3$		−	5.45221i		−	1.81740i	−0.417446	−	0.908702i	$-0.637075\pi$
$3$		−	5.45221i		−	1.81740i	0.417446	−	0.908702i	$-0.362925\pi$
$4$	−2.00000			−0.500000
$5$	−3.90521	+	3.12239i	−0.781042	+	0.624479i
$5$	−3.90521	+	3.12239i	−0.781042	+	0.624479i
$6$	−7.71059			−1.28510
$7$	0.770899			0.110128			0.0550642	−	0.998483i	$-0.482464\pi$
$7$	0.770899			0.110128			0.0550642	+	0.998483i	$0.482464\pi$
$8$			2.82843i			0.353553i
$9$	−20.7266			−2.30296
$10$	4.41573	+	5.52280i	0.441573	+	0.552280i
$11$			8.45857i			0.768961i	0.923133	+	0.384481i	$0.125619\pi$
$11$			8.45857i			0.768961i	−0.923133	+	0.384481i	$0.874381\pi$
$12$			10.9044i			0.908702i
$13$		−	4.15908i		−	0.319929i	−0.987123	−	0.159964i	$-0.948862\pi$
$13$		−	4.15908i		−	0.319929i	0.987123	−	0.159964i	$-0.0511380\pi$
$14$		−	1.09022i		−	0.0778725i
$15$	17.0239	+	21.2920i	1.13493	+	1.41947i
$16$	4.00000			0.250000
$17$	−32.2680			−1.89812			−0.949059	−	0.315097i	$-0.897963\pi$
$17$	−32.2680			−1.89812			−0.949059	+	0.315097i	$0.897963\pi$
$18$			29.3118i			1.62844i
$19$		−	23.8163i		−	1.25349i	−0.779224	−	0.626745i	$-0.784387\pi$
$19$		−	23.8163i		−	1.25349i	0.779224	−	0.626745i	$-0.215613\pi$
$20$	7.81042	−	6.24479i	0.390521	−	0.312239i
$21$		−	4.20310i		−	0.200148i
$22$	11.9622			0.543738
$23$	19.8603	+	11.6004i	0.863489	+	0.504367i
$23$	19.8603	+	11.6004i	0.863489	+	0.504367i
$24$	15.4212			0.642549
$25$	5.50131	−	24.3872i	0.220052	−	0.975488i
$26$	−5.88182			−0.226224
$27$			63.9359i			2.36800i
$28$	−1.54180			−0.0550642
$29$	21.7473			0.749907			0.374953	−	0.927044i	$-0.377659\pi$
$29$	21.7473			0.749907			0.374953	+	0.927044i	$0.377659\pi$
$30$	30.1115	−	24.0755i	1.00372	−	0.802517i
$31$	−31.8764			−1.02827			−0.514136	−	0.857709i	$-0.671887\pi$
$31$	−31.8764			−1.02827			−0.514136	+	0.857709i	$0.671887\pi$
$32$		−	5.65685i		−	0.176777i
$33$	46.1179			1.39751
$34$			45.6339i			1.34217i
$35$	−3.01052	+	2.40705i	−0.0860149	+	0.0687729i
$36$	41.4532			1.15148
$37$	−6.03947			−0.163229			−0.0816145	−	0.996664i	$-0.526008\pi$
$37$	−6.03947			−0.163229			−0.0816145	+	0.996664i	$0.526008\pi$
$38$	−33.6814			−0.886352
$39$	−22.6762			−0.581440
$40$	−8.83146	−	11.0456i	−0.220787	−	0.276140i
$41$	16.9449			0.413289			0.206645	−	0.978416i	$-0.433746\pi$
$41$	16.9449			0.413289			0.206645	+	0.978416i	$0.433746\pi$
$42$	−5.94408			−0.141526
$43$	−61.7107			−1.43513			−0.717566	−	0.696491i	$-0.754744\pi$
$43$	−61.7107			−1.43513			−0.717566	+	0.696491i	$0.754744\pi$
$44$		−	16.9171i		−	0.384481i
$45$	80.9417	−	64.7166i	1.79870	−	1.43815i
$46$	16.4055	−	28.0866i	0.356641	−	0.610579i
$47$		−	45.0037i		−	0.957525i	−0.877945	−	0.478762i	$-0.841086\pi$
$47$		−	45.0037i		−	0.957525i	0.877945	−	0.478762i	$-0.158914\pi$
$48$		−	21.8088i		−	0.454351i
$49$	−48.4057			−0.987872
$50$	−34.4887	−	7.78003i	−0.689774	−	0.155601i
$51$			175.932i			3.44965i
$52$			8.31815i			0.159964i
$53$	−45.8817			−0.865692			−0.432846	−	0.901468i	$-0.642491\pi$
$53$	−45.8817			−0.865692			−0.432846	+	0.901468i	$0.642491\pi$
$54$	90.4190			1.67443
$55$	−26.4110	−	33.0325i	−0.480200	−	0.600591i
$56$			2.18043i			0.0389363i
$57$	−129.852			−2.27810
$58$		−	30.7553i		−	0.530264i
$59$	−93.6903			−1.58797			−0.793986	−	0.607937i	$-0.791997\pi$
$59$	−93.6903			−1.58797			−0.793986	+	0.607937i	$0.791997\pi$
$60$	−34.0479	−	42.5840i	−0.567465	−	0.709734i
$61$			37.1088i			0.608341i	0.952618	+	0.304170i	$0.0983792\pi$
$61$			37.1088i			0.608341i	−0.952618	+	0.304170i	$0.901621\pi$
$62$			45.0801i			0.727099i
$63$	−15.9781			−0.253621
$64$	−8.00000			−0.125000
$65$	12.9863	+	16.2421i	0.199789	+	0.249878i
$66$		−	65.2206i		−	0.988191i
$67$	44.2092			0.659838			0.329919	−	0.944009i	$-0.392978\pi$
$67$	44.2092			0.659838			0.329919	+	0.944009i	$0.392978\pi$
$68$	64.5360			0.949059
$69$	63.2481	−	108.282i	0.916639	−	1.56931i
$70$	3.40408	+	4.25752i	0.0486298	+	0.0608217i
$71$	77.7931			1.09568			0.547839	−	0.836584i	$-0.315451\pi$
$71$	77.7931			1.09568			0.547839	+	0.836584i	$0.315451\pi$
$72$		−	58.6237i		−	0.814218i
$73$		−	101.411i		−	1.38919i	−0.719401	−	0.694595i	$-0.755584\pi$
$73$		−	101.411i		−	1.38919i	0.719401	−	0.694595i	$-0.244416\pi$
$74$			8.54110i			0.115420i
$75$	−132.964	−	29.9943i	−1.77286	−	0.399924i
$76$			47.6326i			0.626745i
$77$			6.52070i			0.0846845i
$78$			32.0689i			0.411140i
$79$			14.4772i			0.183256i	0.995793	+	0.0916278i	$0.0292070\pi$
$79$			14.4772i			0.183256i	−0.995793	+	0.0916278i	$0.970793\pi$
$80$	−15.6208	+	12.4896i	−0.195260	+	0.156120i
$81$	162.052			2.00065
$82$		−	23.9637i		−	0.292240i
$83$	44.9529			0.541602			0.270801	−	0.962635i	$-0.412712\pi$
$83$	44.9529			0.541602			0.270801	+	0.962635i	$0.412712\pi$
$84$			8.40621i			0.100074i
$85$	126.013	−	100.753i	1.48251	−	1.18534i
$86$			87.2720i			1.01479i
$87$		−	118.571i		−	1.36288i
$88$	−23.9245			−0.271869
$89$		−	74.0570i		−	0.832102i	−0.909341	−	0.416051i	$-0.863414\pi$
$89$		−	74.0570i		−	0.832102i	0.909341	−	0.416051i	$-0.136586\pi$
$90$	−91.5231	−	114.469i	−1.01692	−	1.27188i
$91$		−	3.20623i		−	0.0352333i
$92$	−39.7205	−	23.2009i	−0.431745	−	0.252184i
$93$			173.797i			1.86879i
$94$	−63.6448			−0.677072
$95$	74.3639	+	93.0077i	0.782778	+	0.979028i
$96$	−30.8424			−0.321275
$97$	42.2048			0.435101			0.217551	−	0.976049i	$-0.430193\pi$
$97$	42.2048			0.435101			0.217551	+	0.976049i	$0.430193\pi$
$98$			68.4560i			0.698531i
$99$		−	175.317i		−	1.77088i
$100$	−11.0026	+	48.7744i	−0.110026	+	0.487744i
$101$	42.3218			0.419027			0.209514	−	0.977806i	$-0.432812\pi$
$101$	42.3218			0.419027			0.209514	+	0.977806i	$0.432812\pi$
$102$	248.805			2.43927
$103$	−203.560			−1.97632			−0.988158	−	0.153443i	$-0.950964\pi$
$103$	−203.560			−1.97632			−0.988158	+	0.153443i	$0.950964\pi$
$104$	11.7636			0.113112
$105$	13.1237	+	16.4140i	0.124988	+	0.156324i
$106$			64.8865i			0.612137i
$107$	141.946			1.32660			0.663301	−	0.748353i	$-0.269155\pi$
$107$	141.946			1.32660			0.663301	+	0.748353i	$0.269155\pi$
$108$		−	127.872i		−	1.18400i
$109$		−	82.8396i		−	0.759997i	−0.924987	−	0.379998i	$-0.875925\pi$
$109$		−	82.8396i		−	0.759997i	0.924987	−	0.379998i	$-0.124075\pi$
$110$	−46.7150	+	37.3508i	−0.424682	+	0.339553i
$111$			32.9285i			0.296653i
$112$	3.08360			0.0275321
$113$	−88.6557			−0.784564			−0.392282	−	0.919845i	$-0.628314\pi$
$113$	−88.6557			−0.784564			−0.392282	+	0.919845i	$0.628314\pi$
$114$			183.638i			1.61086i
$115$	−113.780	+	16.7094i	−0.989388	+	0.145299i
$116$	−43.4946			−0.374953
$117$			86.2035i			0.736782i
$118$			132.498i			1.12287i
$119$	−24.8754			−0.209037
$120$	−60.2229	+	48.1510i	−0.501858	+	0.401258i
$121$	49.4526			0.408699
$122$	52.4797			0.430162
$123$		−	92.3870i		−	0.751114i
$124$	63.7529			0.514136
$125$	54.6627	+	112.414i	0.437301	+	0.899315i
$126$			22.5965i			0.179337i
$127$		−	211.003i		−	1.66144i	−0.556689	−	0.830721i	$-0.687929\pi$
$127$		−	211.003i		−	1.66144i	0.556689	−	0.830721i	$-0.312071\pi$
$128$			11.3137i			0.0883883i
$129$			336.459i			2.60821i
$130$	22.9697	−	18.3654i	0.176690	−	0.141272i
$131$	−17.0037			−0.129799			−0.0648997	−	0.997892i	$-0.520673\pi$
$131$	−17.0037			−0.129799			−0.0648997	+	0.997892i	$0.520673\pi$
$132$	−92.2358			−0.698756
$133$		−	18.3600i		−	0.138045i
$134$		−	62.5212i		−	0.466576i
$135$	−199.633	−	249.683i	−1.47876	−	1.84950i
$136$		−	91.2677i		−	0.671086i
$137$	93.2792			0.680870			0.340435	−	0.940268i	$-0.389426\pi$
$137$	93.2792			0.680870			0.340435	+	0.940268i	$0.389426\pi$
$138$	−153.134	−	89.4463i	−1.10967	−	0.648161i
$139$	46.0137			0.331034			0.165517	−	0.986207i	$-0.447071\pi$
$139$	46.0137			0.331034			0.165517	+	0.986207i	$0.447071\pi$
$140$	6.02104	−	4.81410i	0.0430074	−	0.0343864i
$141$	−245.369			−1.74021
$142$		−	110.016i		−	0.774761i
$143$	35.1798			0.246013
$144$	−82.9064			−0.575739
$145$	−84.9278	+	67.9036i	−0.585709	+	0.468301i
$146$	−143.417			−0.982305
$147$			263.918i			1.79536i
$148$	12.0789			0.0816145
$149$		−	173.780i		−	1.16631i	−0.812362	−	0.583154i	$-0.801818\pi$
$149$		−	173.780i		−	1.16631i	0.812362	−	0.583154i	$-0.198182\pi$
$150$	−42.4183	+	188.040i	−0.282789	+	1.25360i
$151$	65.7314			0.435307			0.217654	−	0.976026i	$-0.430160\pi$
$151$	65.7314			0.435307			0.217654	+	0.976026i	$0.430160\pi$
$152$	67.3627			0.443176
$153$	668.806			4.37128
$154$	9.22167			0.0598810
$155$	124.484	−	99.5308i	0.803124	−	0.642134i
$156$	45.3523			0.290720
$157$	−141.661			−0.902301			−0.451151	−	0.892448i	$-0.648986\pi$
$157$	−141.661			−0.902301			−0.451151	+	0.892448i	$0.648986\pi$
$158$	20.4738			0.129581
$159$			250.157i			1.57331i
$160$	17.6629	+	22.0912i	0.110393	+	0.138070i
$161$	15.3102	+	8.94277i	0.0950947	+	0.0555452i
$162$		−	229.177i		−	1.41467i
$163$			165.811i			1.01724i	0.860990	+	0.508621i	$0.169845\pi$
$163$			165.811i			1.01724i	−0.860990	+	0.508621i	$0.830155\pi$
$164$	−33.8897			−0.206645
$165$	−180.100	+	143.998i	−1.09152	+	0.872717i
$166$		−	63.5730i		−	0.382970i
$167$			197.607i			1.18328i	0.806203	+	0.591639i	$0.201519\pi$
$167$			197.607i			1.18328i	−0.806203	+	0.591639i	$0.798481\pi$
$168$	11.8882			0.0707629
$169$	151.702			0.897645
$170$	−142.487	−	178.210i	−0.838158	−	1.04829i
$171$			493.631i			2.88673i
$172$	123.421			0.717566
$173$			129.325i			0.747545i	0.927520	+	0.373773i	$0.121936\pi$
$173$			129.325i			0.747545i	−0.927520	+	0.373773i	$0.878064\pi$
$174$	−167.685			−0.963704
$175$	4.24095	−	18.8001i	0.0242340	−	0.107429i
$176$			33.8343i			0.192240i
$177$			510.819i			2.88598i
$178$	−104.732			−0.588385
$179$	−53.7876			−0.300489			−0.150245	−	0.988649i	$-0.548006\pi$
$179$	−53.7876			−0.300489			−0.150245	+	0.988649i	$0.548006\pi$
$180$	−161.883	+	129.433i	−0.899352	+	0.719073i
$181$		−	294.478i		−	1.62695i	−0.581599	−	0.813476i	$-0.697573\pi$
$181$		−	294.478i		−	1.62695i	0.581599	−	0.813476i	$-0.302427\pi$
$182$	−4.53429			−0.0249137
$183$	202.325			1.10560
$184$	−32.8110	+	56.1733i	−0.178321	+	0.305290i
$185$	23.5854	−	18.8576i	0.127489	−	0.101933i
$186$	245.786			1.32143
$187$		−	272.941i		−	1.45958i
$188$			90.0073i			0.478762i
$189$			49.2881i			0.260784i
$190$	131.533	−	105.166i	0.692278	−	0.553508i
$191$			10.1786i			0.0532913i	0.999645	+	0.0266456i	$0.00848258\pi$
$191$			10.1786i			0.0532913i	−0.999645	+	0.0266456i	$0.991517\pi$
$192$			43.6177i			0.227175i
$193$		−	6.11467i		−	0.0316822i	−0.999875	−	0.0158411i	$-0.994957\pi$
$193$		−	6.11467i		−	0.0316822i	0.999875	−	0.0158411i	$-0.00504259\pi$
$194$		−	59.6866i		−	0.307663i
$195$	88.5551	−	70.8039i	0.454129	−	0.363097i
$196$	96.8114			0.493936
$197$			176.222i			0.894527i	0.894402	+	0.447264i	$0.147601\pi$
$197$			176.222i			0.894527i	−0.894402	+	0.447264i	$0.852399\pi$
$198$	−247.936			−1.25220
$199$		−	248.127i		−	1.24687i	−0.781875	−	0.623435i	$-0.785737\pi$
$199$		−	248.127i		−	1.24687i	0.781875	−	0.623435i	$-0.214263\pi$
$200$	68.9774	+	15.5601i	0.344887	+	0.0778003i
$201$		−	241.038i		−	1.19919i
$202$		−	59.8520i		−	0.296297i
$203$	16.7650			0.0825861
$204$		−	351.864i		−	1.72482i
$205$	−66.1732	+	52.9085i	−0.322796	+	0.258090i
$206$			287.878i			1.39747i
$207$	−411.635	−	240.438i	−1.98858	−	1.16154i
$208$		−	16.6363i		−	0.0799822i
$209$	201.452			0.963885
$210$	23.2129	−	18.5598i	0.110538	−	0.0883799i
$211$	247.820			1.17450			0.587250	−	0.809405i	$-0.300210\pi$
$211$	247.820			1.17450			0.587250	+	0.809405i	$0.300210\pi$
$212$	91.7633			0.432846
$213$		−	424.145i		−	1.99129i
$214$		−	200.743i		−	0.938049i
$215$	240.993	−	192.685i	1.12090	−	0.896209i
$216$	−180.838			−0.837213
$217$	−24.5735			−0.113242
$218$	−117.153			−0.537399
$219$	−552.913			−2.52472
$220$	52.8220	+	66.0650i	0.240100	+	0.300295i
$221$			134.205i			0.607263i
$222$	46.5679			0.209765
$223$		−	290.264i		−	1.30163i	−0.759235	−	0.650817i	$-0.774427\pi$
$223$		−	290.264i		−	1.30163i	0.759235	−	0.650817i	$-0.225573\pi$
$224$		−	4.36086i		−	0.0194681i
$225$	−114.023	+	505.464i	−0.506771	+	2.24651i
$226$			125.378i			0.554770i
$227$	−310.686			−1.36866			−0.684331	−	0.729171i	$-0.739906\pi$
$227$	−310.686			−1.36866			−0.684331	+	0.729171i	$0.739906\pi$
$228$	259.703			1.13905
$229$			267.722i			1.16909i	0.811361	+	0.584545i	$0.198727\pi$
$229$			267.722i			1.16909i	−0.811361	+	0.584545i	$0.801273\pi$
$230$	23.6306	+	160.909i	0.102742	+	0.699603i
$231$	35.5522			0.153906
$232$			61.5107i			0.265132i
$233$			82.0593i			0.352186i	0.984374	+	0.176093i	$0.0563459\pi$
$233$			82.0593i			0.352186i	−0.984374	+	0.176093i	$0.943654\pi$
$234$	121.910			0.520984
$235$	140.519	+	175.749i	0.597954	+	0.747867i
$236$	187.381			0.793986
$237$	78.9327			0.333049
$238$			35.1791i			0.147811i
$239$	15.0646			0.0630316			0.0315158	−	0.999503i	$-0.489967\pi$
$239$	15.0646			0.0630316			0.0315158	+	0.999503i	$0.489967\pi$
$240$	68.0958	+	85.1681i	0.283732	+	0.354867i
$241$		−	70.4867i		−	0.292476i	−0.989249	−	0.146238i	$-0.953283\pi$
$241$		−	70.4867i		−	0.292476i	0.989249	−	0.146238i	$-0.0467165\pi$
$242$		−	69.9365i		−	0.288994i
$243$		−	308.121i		−	1.26799i
$244$		−	74.2176i		−	0.304170i
$245$	189.034	−	151.142i	0.771569	−	0.616905i
$246$	−130.655			−0.531117
$247$	−99.0539			−0.401028
$248$		−	90.1602i		−	0.363549i
$249$		−	245.093i		−	0.984309i
$250$	158.978	−	77.3047i	0.635912	−	0.309219i
$251$			210.853i			0.840053i	0.907512	+	0.420027i	$0.137979\pi$
$251$			210.853i			0.840053i	−0.907512	+	0.420027i	$0.862021\pi$
$252$	31.9562			0.126810
$253$	−98.1232	+	167.989i	−0.387839	+	0.663990i
$254$	−298.403			−1.17482
$255$	−549.329	−	687.051i	−2.15423	−	2.69432i
$256$	16.0000			0.0625000
$257$			224.082i			0.871914i	0.899967	+	0.435957i	$0.143590\pi$
$257$			224.082i			0.871914i	−0.899967	+	0.435957i	$0.856410\pi$
$258$	475.826			1.84428
$259$	−4.65582			−0.0179761
$260$	−25.9726	−	32.4841i	−0.0998944	−	0.124939i
$261$	−450.748			−1.72700
$262$			24.0469i			0.0917820i
$263$	−141.086			−0.536448			−0.268224	−	0.963357i	$-0.586437\pi$
$263$	−141.086			−0.536448			−0.268224	+	0.963357i	$0.586437\pi$
$264$			130.441i			0.494095i
$265$	179.177	−	143.261i	0.676141	−	0.540606i
$266$	−25.9649			−0.0976125
$267$	−403.775			−1.51226
$268$	−88.4183			−0.329919
$269$	−192.441			−0.715394			−0.357697	−	0.933838i	$-0.616438\pi$
$269$	−192.441			−0.715394			−0.357697	+	0.933838i	$0.616438\pi$
$270$	−353.105	+	282.324i	−1.30780	+	1.04564i
$271$	138.386			0.510649			0.255324	−	0.966855i	$-0.417818\pi$
$271$	138.386			0.510649			0.255324	+	0.966855i	$0.417818\pi$
$272$	−129.072			−0.474530
$273$	−17.4810			−0.0640331
$274$		−	131.917i		−	0.481448i
$275$	206.281	+	46.5332i	0.750112	+	0.169212i
$276$	−126.496	+	216.565i	−0.458319	+	0.784654i
$277$		−	443.283i		−	1.60030i	−0.599799	−	0.800151i	$-0.704753\pi$
$277$		−	443.283i		−	1.60030i	0.599799	−	0.800151i	$-0.295247\pi$
$278$		−	65.0732i		−	0.234076i
$279$	660.690			2.36807
$280$	−6.80817	−	8.51504i	−0.0243149	−	0.0304109i
$281$		−	405.142i		−	1.44178i	−0.693047	−	0.720892i	$-0.743732\pi$
$281$		−	405.142i		−	1.44178i	0.693047	−	0.720892i	$-0.256268\pi$
$282$			347.005i			1.23051i
$283$	−161.101			−0.569263			−0.284631	−	0.958637i	$-0.591871\pi$
$283$	−161.101			−0.569263			−0.284631	+	0.958637i	$0.591871\pi$
$284$	−155.586			−0.547839
$285$	507.098	−	405.448i	1.77929	−	1.42262i
$286$		−	49.7518i		−	0.173957i
$287$	13.0628			0.0455149
$288$			117.247i			0.407109i
$289$	752.225			2.60286
$290$	96.0303	+	120.106i	0.331139	+	0.414159i
$291$		−	230.109i		−	0.790754i
$292$			202.822i			0.694595i
$293$	−187.936			−0.641419			−0.320709	−	0.947178i	$-0.603921\pi$
$293$	−187.936			−0.641419			−0.320709	+	0.947178i	$0.603921\pi$
$294$	373.237			1.26951
$295$	365.880	−	292.538i	1.24027	−	0.991654i
$296$		−	17.0822i		−	0.0577102i
$297$	−540.806			−1.82090
$298$	−245.762			−0.824704
$299$	48.2471	−	82.6003i	0.161362	−	0.276255i
$300$	265.928	+	59.9886i	0.886428	+	0.199962i
$301$	−47.5727			−0.158049
$302$		−	92.9583i		−	0.307809i
$303$		−	230.747i		−	0.761542i
$304$		−	95.2653i		−	0.313373i
$305$	−115.868	−	144.918i	−0.379896	−	0.475139i
$306$		−	945.835i		−	3.09096i
$307$			357.974i			1.16604i	0.812458	+	0.583020i	$0.198129\pi$
$307$			357.974i			1.16604i	−0.812458	+	0.583020i	$0.801871\pi$
$308$		−	13.0414i		−	0.0423422i
$309$			1109.85i			3.59176i
$310$	−140.758	−	176.047i	−0.454058	−	0.567894i
$311$	88.3106			0.283957			0.141978	−	0.989870i	$-0.454654\pi$
$311$	88.3106			0.283957			0.141978	+	0.989870i	$0.454654\pi$
$312$		−	64.1379i		−	0.205570i
$313$	451.978			1.44402			0.722009	−	0.691883i	$-0.243219\pi$
$313$	451.978			1.44402			0.722009	+	0.691883i	$0.243219\pi$
$314$			200.339i			0.638023i
$315$	62.3979	−	49.8900i	0.198088	−	0.158381i
$316$		−	28.9544i		−	0.0916278i
$317$		−	545.035i		−	1.71935i	−0.510838	−	0.859677i	$-0.670665\pi$
$317$		−	545.035i		−	1.71935i	0.510838	−	0.859677i	$-0.329335\pi$
$318$	353.775			1.11250
$319$			183.951i			0.576649i
$320$	31.2417	−	24.9792i	0.0976302	−	0.0780599i
$321$		−	773.922i		−	2.41097i
$322$	12.6470	−	21.6520i	0.0392764	−	0.0672421i
$323$			768.506i			2.37927i
$324$	−324.105			−1.00032
$325$	−101.428	−	22.8804i	−0.312087	−	0.0704011i
$326$	234.492			0.719299
$327$	−451.659			−1.38122
$328$			47.9273i			0.146120i
$329$		−	34.6933i		−	0.105451i
$330$	203.644	+	254.700i	0.617104	+	0.771818i
$331$	−529.975			−1.60113			−0.800566	−	0.599244i	$-0.795468\pi$
$331$	−529.975			−1.60113			−0.800566	+	0.599244i	$0.795468\pi$
$332$	−89.9059			−0.270801
$333$	125.178			0.375909
$334$	279.459			0.836704
$335$	−172.646	+	138.038i	−0.515361	+	0.412055i
$336$		−	16.8124i		−	0.0500369i
$337$	278.285			0.825771			0.412886	−	0.910783i	$-0.364521\pi$
$337$	278.285			0.825771			0.412886	+	0.910783i	$0.364521\pi$
$338$		−	214.539i		−	0.634731i
$339$			483.369i			1.42587i
$340$	−252.027	+	201.507i	−0.741255	+	0.592668i
$341$		−	269.629i		−	0.790702i
$342$	698.100			2.04123
$343$	−75.0900			−0.218921
$344$		−	174.544i		−	0.507396i
$345$	91.1030	+	620.350i	0.264067	+	1.79812i
$346$	182.894			0.528594
$347$			641.622i			1.84906i	0.381114	+	0.924528i	$0.375540\pi$
$347$			641.622i			1.84906i	−0.381114	+	0.924528i	$0.624460\pi$
$348$			237.142i			0.681442i
$349$	−237.462			−0.680408			−0.340204	−	0.940352i	$-0.610496\pi$
$349$	−237.462			−0.680408			−0.340204	+	0.940352i	$0.610496\pi$
$350$	−26.5873	−	5.99761i	−0.0759637	−	0.0171360i
$351$	265.914			0.757590
$352$	47.8489			0.135934
$353$		−	297.586i		−	0.843020i	−0.906824	−	0.421510i	$-0.861500\pi$
$353$		−	297.586i		−	0.843020i	0.906824	−	0.421510i	$-0.138500\pi$
$354$	722.407			2.04070
$355$	−303.798	+	242.901i	−0.855770	+	0.684228i
$356$			148.114i			0.416051i
$357$			135.626i			0.379904i
$358$			76.0671i			0.212478i
$359$		−	145.988i		−	0.406651i	−0.979111	−	0.203325i	$-0.934825\pi$
$359$		−	145.988i		−	0.406651i	0.979111	−	0.203325i	$-0.0651749\pi$
$360$	183.046	+	228.938i	0.508462	+	0.635938i
$361$	−206.217			−0.571239
$362$	−416.455			−1.15043
$363$		−	269.626i		−	0.742771i
$364$			6.41246i			0.0176166i
$365$	316.645	+	396.030i	0.867519	+	1.08501i
$366$		−	286.131i		−	0.781778i
$367$	687.079			1.87215			0.936075	−	0.351801i	$-0.114431\pi$
$367$	687.079			1.87215			0.936075	+	0.351801i	$0.114431\pi$
$368$	79.4410	+	46.4018i	0.215872	+	0.126092i
$369$	−351.209			−0.951787
$370$	−26.6687	−	33.3548i	−0.0720775	−	0.0901481i
$371$	−35.3701			−0.0953373
$372$		−	347.594i		−	0.934393i
$373$	−703.379			−1.88573			−0.942867	−	0.333170i	$-0.891882\pi$
$373$	−703.379			−1.88573			−0.942867	+	0.333170i	$0.891882\pi$
$374$	−385.997			−1.03208
$375$	612.907	−	298.032i	1.63442	−	0.794753i
$376$	127.290			0.338536
$377$		−	90.4487i		−	0.239917i
$378$	69.7039			0.184402
$379$			602.990i			1.59100i	0.605952	+	0.795501i	$0.292792\pi$
$379$			602.990i			1.59100i	−0.605952	+	0.795501i	$0.707208\pi$
$380$	−148.728	−	186.015i	−0.391389	−	0.489514i
$381$	−1150.43			−3.01951
$382$	14.3948			0.0376826
$383$	−223.793			−0.584315			−0.292158	−	0.956370i	$-0.594373\pi$
$383$	−223.793			−0.584315			−0.292158	+	0.956370i	$0.594373\pi$
$384$	61.6847			0.160637
$385$	−20.3602	−	25.4647i	−0.0528837	−	0.0661421i
$386$	−8.64745			−0.0224027
$387$	1279.05			3.30504
$388$	−84.4096			−0.217551
$389$		−	348.989i		−	0.897145i	−0.893746	−	0.448572i	$-0.851933\pi$
$389$		−	348.989i		−	0.897145i	0.893746	−	0.448572i	$-0.148067\pi$
$390$	−100.132	−	125.236i	−0.256748	−	0.321118i
$391$	−640.851	−	374.323i	−1.63901	−	0.957349i
$392$		−	136.912i		−	0.349265i
$393$			92.7078i			0.235898i
$394$	249.215			0.632526
$395$	−45.2035	−	56.5364i	−0.114439	−	0.143130i
$396$			350.635i			0.885441i
$397$			126.645i			0.319005i	0.987198	+	0.159503i	$0.0509890\pi$
$397$			126.645i			0.319005i	−0.987198	+	0.159503i	$0.949011\pi$
$398$	−350.905			−0.881670
$399$	−100.102			−0.250883
$400$	22.0052	−	97.5488i	0.0550131	−	0.243872i
$401$			330.569i			0.824362i	0.911102	+	0.412181i	$0.135233\pi$
$401$			330.569i			0.824362i	−0.911102	+	0.412181i	$0.864767\pi$
$402$	−340.879			−0.847957
$403$			132.577i			0.328974i
$404$	−84.6435			−0.209514
$405$	−632.849	+	505.992i	−1.56259	+	1.24936i
$406$		−	23.7092i		−	0.0583972i
$407$		−	51.0853i		−	0.125517i
$408$	−497.611			−1.21963
$409$	−381.557			−0.932903			−0.466451	−	0.884547i	$-0.654468\pi$
$409$	−381.557			−0.932903			−0.466451	+	0.884547i	$0.654468\pi$
$410$	74.8240	+	93.5831i	0.182498	+	0.228251i
$411$		−	508.578i		−	1.23742i
$412$	407.121			0.988158
$413$	−72.2257			−0.174881
$414$	−340.030	+	582.140i	−0.821329	+	1.40614i
$415$	−175.551	+	140.361i	−0.423013	+	0.338219i
$416$	−23.5273			−0.0565560
$417$		−	250.876i		−	0.601622i
$418$		−	284.896i		−	0.681570i
$419$		−	125.759i		−	0.300141i	−0.988675	−	0.150070i	$-0.952050\pi$
$419$		−	125.759i		−	0.300141i	0.988675	−	0.150070i	$-0.0479501\pi$
$420$	−26.2475	−	32.8280i	−0.0624940	−	0.0781619i
$421$			88.8050i			0.210938i	0.994423	+	0.105469i	$0.0336344\pi$
$421$			88.8050i			0.210938i	−0.994423	+	0.105469i	$0.966366\pi$
$422$		−	350.470i		−	0.830497i
$423$			932.773i			2.20514i
$424$		−	129.773i		−	0.306068i
$425$	−177.516	+	786.927i	−0.417686	+	1.85159i
$426$	−599.831			−1.40805
$427$			28.6071i			0.0669956i
$428$	−283.893			−0.663301
$429$		−	191.808i		−	0.447105i
$430$	−272.498	−	340.816i	−0.633716	−	0.792594i
$431$			643.839i			1.49383i	0.664922	+	0.746913i	$0.268465\pi$
$431$			643.839i			1.49383i	−0.664922	+	0.746913i	$0.731535\pi$
$432$			255.743i			0.591999i
$433$	137.912			0.318504			0.159252	−	0.987238i	$-0.449092\pi$
$433$	137.912			0.318504			0.159252	+	0.987238i	$0.449092\pi$
$434$			34.7522i			0.0800742i
$435$	370.225	+	463.044i	0.851092	+	1.06447i
$436$			165.679i			0.379998i
$437$	276.280	−	472.998i	0.632220	−	1.08238i
$438$			781.937i			1.78524i
$439$	−300.975			−0.685593			−0.342796	−	0.939410i	$-0.611374\pi$
$439$	−300.975			−0.685593			−0.342796	+	0.939410i	$0.611374\pi$
$440$	93.4300	−	74.7016i	0.212341	−	0.169776i
$441$	1003.29			2.27502
$442$	189.795			0.429400
$443$			248.020i			0.559864i	0.960020	+	0.279932i	$0.0903119\pi$
$443$			248.020i			0.559864i	−0.960020	+	0.279932i	$0.909688\pi$
$444$		−	65.8569i		−	0.148326i
$445$	231.235	+	289.208i	0.519630	+	0.649906i
$446$	−410.496			−0.920394
$447$	−947.484			−2.11965
$448$	−6.16719			−0.0137661
$449$	−576.186			−1.28327			−0.641633	−	0.767012i	$-0.721743\pi$
$449$	−576.186			−1.28327			−0.641633	+	0.767012i	$0.721743\pi$
$450$	714.834	+	161.253i	1.58852	+	0.358341i
$451$			143.329i			0.317803i
$452$	177.311			0.392282
$453$		−	358.381i		−	0.791129i
$454$			439.377i			0.967790i
$455$	10.0111	+	12.5210i	0.0220024	+	0.0275187i
$456$		−	367.276i		−	0.805429i
$457$	−104.755			−0.229224			−0.114612	−	0.993410i	$-0.536563\pi$
$457$	−104.755			−0.229224			−0.114612	+	0.993410i	$0.536563\pi$
$458$	378.616			0.826672
$459$		−	2063.08i		−	4.49474i
$460$	227.559	−	33.4187i	0.494694	−	0.0726494i
$461$	467.711			1.01456			0.507279	−	0.861782i	$-0.330651\pi$
$461$	467.711			1.01456			0.507279	+	0.861782i	$0.330651\pi$
$462$		−	50.2785i		−	0.108828i
$463$			502.838i			1.08604i	0.839719	+	0.543021i	$0.182720\pi$
$463$			502.838i			1.08604i	−0.839719	+	0.543021i	$0.817280\pi$
$464$	86.9892			0.187477
$465$	−542.663	−	678.714i	−1.16702	−	1.45960i
$466$	116.049			0.249033
$467$	209.413			0.448422			0.224211	−	0.974541i	$-0.428020\pi$
$467$	209.413			0.448422			0.224211	+	0.974541i	$0.428020\pi$
$468$		−	172.407i		−	0.368391i
$469$	34.0808			0.0726670
$470$	248.546	−	198.724i	0.528822	−	0.422817i
$471$			772.367i			1.63985i
$472$		−	264.996i		−	0.561433i
$473$		−	521.984i		−	1.10356i
$474$		−	111.628i		−	0.235501i
$475$	−580.813	−	131.021i	−1.22277	−	0.275834i
$476$	49.7508			0.104518
$477$	950.971			1.99365
$478$		−	21.3045i		−	0.0445701i
$479$			446.153i			0.931425i	0.884936	+	0.465713i	$0.154202\pi$
$479$			446.153i			0.931425i	−0.884936	+	0.465713i	$0.845798\pi$
$480$	120.446	−	96.3020i	0.250929	−	0.200629i
$481$			25.1186i			0.0522217i
$482$	−99.6833			−0.206812
$483$	48.7579	−	83.4747i	0.100948	−	0.172825i
$484$	−98.9051			−0.204349
$485$	−164.819	+	131.780i	−0.339832	+	0.271711i
$486$	−435.749			−0.896603
$487$			150.073i			0.308158i	0.988059	+	0.154079i	$0.0492410\pi$
$487$			150.073i			0.308158i	−0.988059	+	0.154079i	$0.950759\pi$
$488$	−104.959			−0.215081
$489$	904.034			1.84874
$490$	−213.747	−	267.335i	−0.436218	−	0.545582i
$491$	−823.267			−1.67672			−0.838358	−	0.545121i	$-0.816484\pi$
$491$	−823.267			−1.67672			−0.838358	+	0.545121i	$0.816484\pi$
$492$			184.774i			0.375557i
$493$	−701.742			−1.42341
$494$			140.083i			0.283570i
$495$	547.410	+	684.651i	1.10588	+	1.38313i
$496$	−127.506			−0.257068
$497$	59.9706			0.120665
$498$	−346.614			−0.696011
$499$	−403.544			−0.808705			−0.404353	−	0.914603i	$-0.632503\pi$
$499$	−403.544			−0.808705			−0.404353	+	0.914603i	$0.632503\pi$
$500$	−109.325	−	224.829i	−0.218651	−	0.449657i
$501$	1077.40			2.15049
$502$	298.192			0.594007
$503$	467.899			0.930217			0.465108	−	0.885254i	$-0.346015\pi$
$503$	467.899			0.930217			0.465108	+	0.885254i	$0.346015\pi$
$504$		−	45.1929i		−	0.0896685i
$505$	−165.275	+	132.145i	−0.327278	+	0.261674i
$506$	237.573	+	138.767i	0.469512	+	0.274243i
$507$		−	827.112i		−	1.63138i
$508$			422.006i			0.830721i
$509$	52.1092			0.102376			0.0511878	−	0.998689i	$-0.483699\pi$
$509$	52.1092			0.102376			0.0511878	+	0.998689i	$0.483699\pi$
$510$	−971.637	+	776.869i	−1.90517	+	1.52327i
$511$		−	78.1775i		−	0.152989i
$512$		−	22.6274i		−	0.0441942i
$513$	1522.72			2.96826
$514$	316.900			0.616536
$515$	794.946	−	635.596i	1.54358	−	1.23417i
$516$		−	672.919i		−	1.30411i
$517$	380.667			0.736299
$518$			6.58433i			0.0127111i
$519$	705.109			1.35859
$520$	−45.9395	+	36.7307i	−0.0883452	+	0.0706360i
$521$		−	978.566i		−	1.87825i	−0.343581	−	0.939123i	$-0.611640\pi$
$521$		−	978.566i		−	1.87825i	0.343581	−	0.939123i	$-0.388360\pi$
$522$			637.453i			1.22117i
$523$	360.011			0.688358			0.344179	−	0.938904i	$-0.388157\pi$
$523$	360.011			0.688358			0.344179	+	0.938904i	$0.388157\pi$
$524$	34.0074			0.0648997
$525$	−102.502	−	23.1226i	−0.195242	−	0.0440430i
$526$			199.526i			0.379326i
$527$	1028.59			1.95178
$528$	184.472			0.349378
$529$	259.859	+	460.776i	0.491227	+	0.871031i
$530$	−202.601	−	253.395i	−0.382266	−	0.478104i
$531$	1941.88			3.65703
$532$			36.7199i			0.0690225i
$533$		−	70.4750i		−	0.132223i
$534$			571.024i			1.06933i
$535$	−554.330	+	443.213i	−1.03613	+	0.828435i
$536$			125.042i			0.233288i
$537$			293.261i			0.546110i
$538$			272.152i			0.505860i
$539$		−	409.443i		−	0.759635i
$540$	399.266	+	499.366i	0.739381	+	0.924751i
$541$	142.266			0.262969			0.131484	−	0.991318i	$-0.458026\pi$
$541$	142.266			0.262969			0.131484	+	0.991318i	$0.458026\pi$
$542$		−	195.707i		−	0.361083i
$543$	−1605.56			−2.95683
$544$			182.535i			0.335543i
$545$	258.658	+	323.506i	0.474602	+	0.593589i
$546$			24.7219i			0.0452782i
$547$			405.389i			0.741114i	0.928810	+	0.370557i	$0.120833\pi$
$547$			405.389i			0.741114i	−0.928810	+	0.370557i	$0.879167\pi$
$548$	−186.558			−0.340435
$549$		−	769.139i		−	1.40098i
$550$	65.8079	−	291.725i	0.119651	−	0.530410i
$551$		−	517.941i		−	0.940001i
$552$	306.269	+	178.893i	0.554834	+	0.324081i
$553$			11.1604i			0.0201816i
$554$	−626.897			−1.13158
$555$	−102.816	−	128.593i	−0.185253	−	0.231698i
$556$	−92.0274			−0.165517
$557$	−726.195			−1.30376			−0.651881	−	0.758322i	$-0.726020\pi$
$557$	−726.195			−1.30376			−0.651881	+	0.758322i	$0.726020\pi$
$558$		−	934.357i		−	1.67448i
$559$			256.659i			0.459140i
$560$	−12.0421	+	9.62820i	−0.0215037	+	0.0171932i
$561$	−1488.13			−2.65264
$562$	−572.957			−1.01950
$563$	−294.331			−0.522790			−0.261395	−	0.965232i	$-0.584182\pi$
$563$	−294.331			−0.522790			−0.261395	+	0.965232i	$0.584182\pi$
$564$	490.739			0.870104
$565$	346.219	−	276.818i	0.612777	−	0.489943i
$566$			227.832i			0.402529i
$567$	124.926			0.220328
$568$			220.032i			0.387381i
$569$		−	573.397i		−	1.00773i	−0.863783	−	0.503864i	$-0.831911\pi$
$569$		−	573.397i		−	1.00773i	0.863783	−	0.503864i	$-0.168089\pi$
$570$	−573.390	−	717.144i	−1.00595	−	1.25815i
$571$		−	139.152i		−	0.243698i	−0.992549	−	0.121849i	$-0.961118\pi$
$571$		−	139.152i		−	0.243698i	0.992549	−	0.121849i	$-0.0388824\pi$
$572$	−70.3597			−0.123006
$573$	55.4961			0.0968518
$574$		−	18.4736i		−	0.0321839i
$575$	392.160	−	420.518i	0.682017	−	0.731336i
$576$	165.813			0.287869
$577$		−	784.266i		−	1.35921i	−0.733577	−	0.679606i	$-0.762151\pi$
$577$		−	784.266i		−	1.35921i	0.733577	−	0.679606i	$-0.237849\pi$
$578$		−	1063.81i		−	1.84050i
$579$	−33.3385			−0.0575794
$580$	169.856	−	135.807i	0.292854	−	0.234151i
$581$	34.6542			0.0596457
$582$	−325.424			−0.559148
$583$		−	388.093i		−	0.665683i
$584$	286.833			0.491153
$585$	−269.161	−	336.643i	−0.460105	−	0.575458i
$586$			265.781i			0.453552i
$587$			70.9458i			0.120862i	0.998172	+	0.0604308i	$0.0192475\pi$
$587$			70.9458i			0.120862i	−0.998172	+	0.0604308i	$0.980753\pi$
$588$		−	527.836i		−	0.897681i
$589$			759.180i			1.28893i
$590$	−413.711	−	517.433i	−0.701205	−	0.877005i
$591$	960.798			1.62572
$592$	−24.1579			−0.0408072
$593$			519.409i			0.875900i	0.898999	+	0.437950i	$0.144295\pi$
$593$			519.409i			0.875900i	−0.898999	+	0.437950i	$0.855705\pi$
$594$			764.815i			1.28757i
$595$	97.1436	−	77.6707i	0.163266	−	0.130539i
$596$			347.560i			0.583154i
$597$	−1352.84			−2.26607
$598$	−116.814	−	68.2318i	−0.195342	−	0.114100i
$599$	841.749			1.40526			0.702628	−	0.711557i	$-0.252010\pi$
$599$	841.749			1.40526			0.702628	+	0.711557i	$0.252010\pi$
$600$	84.8367	−	376.079i	0.141394	−	0.626799i
$601$	−465.116			−0.773904			−0.386952	−	0.922100i	$-0.626472\pi$
$601$	−465.116			−0.773904			−0.386952	+	0.922100i	$0.626472\pi$
$602$			67.2779i			0.111757i
$603$	−916.306			−1.51958
$604$	−131.463			−0.217654
$605$	−193.123	+	154.410i	−0.319211	+	0.255224i
$606$	−326.326			−0.538491
$607$		−	725.814i		−	1.19574i	−0.801593	−	0.597870i	$-0.796014\pi$
$607$		−	725.814i		−	1.19574i	0.801593	−	0.597870i	$-0.203986\pi$
$608$	−134.725			−0.221588
$609$		−	91.4061i		−	0.150092i
$610$	−204.944	+	163.862i	−0.335974	+	0.268627i
$611$	−187.174			−0.306340
$612$	−1337.61			−2.18564
$613$	1054.37			1.72002			0.860011	−	0.510276i	$-0.170457\pi$
$613$	1054.37			1.72002			0.860011	+	0.510276i	$0.170457\pi$
$614$	506.252			0.824515
$615$	288.469	+	360.790i	0.469055	+	0.586651i
$616$	−18.4433			−0.0299405
$617$	−966.001			−1.56564			−0.782821	−	0.622247i	$-0.786220\pi$
$617$	−966.001			−1.56564			−0.782821	+	0.622247i	$0.786220\pi$
$618$	1569.57			2.53976
$619$			380.125i			0.614096i	0.951694	+	0.307048i	$0.0993412\pi$
$619$			380.125i			0.614096i	−0.951694	+	0.307048i	$0.900659\pi$
$620$	−248.968	+	199.062i	−0.401562	+	0.321067i
$621$	−741.685	+	1269.78i	−1.19434	+	2.04474i
$622$		−	124.890i		−	0.200788i
$623$		−	57.0905i		−	0.0916380i
$624$	−90.7046			−0.145360
$625$	−564.471	−	268.323i	−0.903154	−	0.429317i
$626$		−	639.193i		−	1.02108i
$627$		−	1098.36i		−	1.75177i
$628$	283.323			0.451151
$629$	194.882			0.309828
$630$	−70.5551	−	88.2439i	−0.111992	−	0.140070i
$631$		−	639.891i		−	1.01409i	−0.861920	−	0.507045i	$-0.830738\pi$
$631$		−	639.891i		−	1.01409i	0.861920	−	0.507045i	$-0.169262\pi$
$632$	−40.9477			−0.0647906
$633$		−	1351.16i		−	2.13454i
$634$	−770.796			−1.21577
$635$	658.835	+	824.011i	1.03753	+	1.29766i
$636$		−	500.313i		−	0.786656i
$637$			201.323i			0.316049i
$638$	260.146			0.407753
$639$	−1612.39			−2.52330
$640$	−35.3259	−	44.1824i	−0.0551967	−	0.0690350i
$641$			871.493i			1.35958i	0.733405	+	0.679792i	$0.237930\pi$
$641$			871.493i			1.35958i	−0.733405	+	0.679792i	$0.762070\pi$
$642$	−1094.49			−1.70481
$643$	−252.302			−0.392383			−0.196191	−	0.980566i	$-0.562857\pi$
$643$	−252.302			−0.392383			−0.196191	+	0.980566i	$0.562857\pi$
$644$	−30.6205	−	17.8855i	−0.0475473	−	0.0277726i
$645$	−1050.56	−	1313.94i	−1.62877	−	2.03712i
$646$	1086.83			1.68240
$647$			502.810i			0.777140i	0.921419	+	0.388570i	$0.127031\pi$
$647$			502.810i			0.777140i	−0.921419	+	0.388570i	$0.872969\pi$
$648$			458.353i			0.707336i
$649$		−	792.486i		−	1.22109i
$650$	−32.3577	+	143.441i	−0.0497811	+	0.220679i
$651$			133.980i			0.205806i
$652$		−	331.621i		−	0.508621i
$653$			325.768i			0.498879i	0.968390	+	0.249439i	$0.0802464\pi$
$653$			325.768i			0.498879i	−0.968390	+	0.249439i	$0.919754\pi$
$654$			638.742i			0.976670i
$655$	66.4030	−	53.0923i	0.101379	−	0.0810569i
$656$	67.7795			0.103322
$657$			2101.90i			3.19924i
$658$	−49.0637			−0.0745649
$659$		−	877.338i		−	1.33132i	−0.746256	−	0.665659i	$-0.768151\pi$
$659$		−	877.338i		−	1.33132i	0.746256	−	0.665659i	$-0.231849\pi$
$660$	360.200	−	287.997i	0.545758	−	0.436358i
$661$		−	471.430i		−	0.713207i	−0.934256	−	0.356603i	$-0.883935\pi$
$661$		−	471.430i		−	0.713207i	0.934256	−	0.356603i	$-0.116065\pi$
$662$			749.498i			1.13217i
$663$	731.715			1.10364
$664$			127.146i			0.191485i
$665$	57.3271	+	71.6995i	0.0862061	+	0.107819i
$666$		−	177.028i		−	0.265808i
$667$	431.907	+	252.278i	0.647537	+	0.378229i
$668$		−	395.215i		−	0.591639i
$669$	−1582.58			−2.36559
$670$	195.216	+	244.158i	0.291367	+	0.364415i
$671$	−313.887			−0.467790
$672$	−23.7763			−0.0353815
$673$			465.176i			0.691198i	0.938382	+	0.345599i	$0.112324\pi$
$673$			465.176i			0.691198i	−0.938382	+	0.345599i	$0.887676\pi$
$674$		−	393.554i		−	0.583908i
$675$	1559.22	+	351.731i	2.30995	+	0.521083i
$676$	−303.404			−0.448823
$677$	−157.617			−0.232816			−0.116408	−	0.993201i	$-0.537138\pi$
$677$	−157.617			−0.232816			−0.116408	+	0.993201i	$0.537138\pi$
$678$	683.588			1.00824
$679$	32.5356			0.0479170
$680$	284.974	+	356.420i	0.419079	+	0.524146i
$681$			1693.93i			2.48741i
$682$	−381.313			−0.559110
$683$			387.721i			0.567674i	0.958873	+	0.283837i	$0.0916074\pi$
$683$			387.721i			0.567674i	−0.958873	+	0.283837i	$0.908393\pi$
$684$		−	987.263i		−	1.44337i
$685$	−364.275	+	291.255i	−0.531788	+	0.425189i
$686$			106.193i			0.154801i
$687$	1459.68			2.12471
$688$	−246.843			−0.358783
$689$			190.825i			0.276960i
$690$	877.308	−	128.839i	1.27146	−	0.186723i
$691$	−443.591			−0.641954			−0.320977	−	0.947087i	$-0.604011\pi$
$691$	−443.591			−0.641954			−0.320977	+	0.947087i	$0.604011\pi$
$692$		−	258.651i		−	0.373773i
$693$		−	135.152i		−	0.195025i
$694$	907.391			1.30748
$695$	−179.693	+	143.673i	−0.258551	+	0.206723i
$696$	335.369			0.481852
$697$	−546.777			−0.784472
$698$			335.822i			0.481121i
$699$	447.405			0.640064
$700$	−8.48191	+	37.6001i	−0.0121170	+	0.0537145i
$701$		−	546.567i		−	0.779696i	−0.920879	−	0.389848i	$-0.872528\pi$
$701$		−	546.567i		−	0.779696i	0.920879	−	0.389848i	$-0.127472\pi$
$702$		−	376.059i		−	0.535697i
$703$			143.838i			0.204606i
$704$		−	67.6686i		−	0.0961201i
$705$	958.219	−	766.140i	1.35918	−	1.08672i
$706$	−420.850			−0.596105
$707$	32.6258			0.0461468
$708$		−	1021.64i		−	1.44299i
$709$			448.985i			0.633265i	0.948548	+	0.316633i	$0.102552\pi$
$709$			448.985i			0.633265i	−0.948548	+	0.316633i	$0.897448\pi$
$710$	343.514	+	429.636i	0.483822	+	0.605121i
$711$		−	300.063i		−	0.422029i
$712$	209.465			0.294192
$713$	−633.074	−	369.781i	−0.887902	−	0.518627i
$714$	191.804			0.268633
$715$	−137.385	+	109.845i	−0.192146	+	0.153630i
$716$	107.575			0.150245
$717$		−	82.1351i		−	0.114554i
$718$	−206.458			−0.287545
$719$	575.714			0.800715			0.400357	−	0.916359i	$-0.368886\pi$
$719$	575.714			0.800715			0.400357	+	0.916359i	$0.368886\pi$
$720$	323.767	−	258.866i	0.449676	−	0.359537i
$721$	−156.925			−0.217648
$722$			291.635i			0.403927i
$723$	−384.308			−0.531547
$724$			588.956i			0.813476i
$725$	119.639	−	530.356i	0.165019	−	0.731525i
$726$	−381.308			−0.525218
$727$	178.666			0.245758			0.122879	−	0.992422i	$-0.460787\pi$
$727$	178.666			0.245758			0.122879	+	0.992422i	$0.460787\pi$
$728$	9.06858			0.0124568
$729$	−221.469			−0.303798
$730$	560.072	−	447.803i	0.767221	−	0.613429i
$731$	1991.28			2.72405
$732$	−404.650			−0.552800
$733$	912.345			1.24467			0.622336	−	0.782750i	$-0.286184\pi$
$733$	912.345			1.24467			0.622336	+	0.782750i	$0.286184\pi$
$734$		−	971.676i		−	1.32381i
$735$	−824.056	−	1030.66i	−1.12117	−	1.40225i
$736$	65.6220	−	112.347i	0.0891604	−	0.152645i
$737$			373.946i			0.507390i
$738$			496.685i			0.673015i
$739$	−274.866			−0.371942			−0.185971	−	0.982555i	$-0.559543\pi$
$739$	−274.866			−0.371942			−0.185971	+	0.982555i	$0.559543\pi$
$740$	−47.1708	+	37.7152i	−0.0637443	+	0.0509665i
$741$			540.063i			0.728830i
$742$			50.0209i			0.0674136i
$743$	−175.014			−0.235550			−0.117775	−	0.993040i	$-0.537576\pi$
$743$	−175.014			−0.235550			−0.117775	+	0.993040i	$0.537576\pi$
$744$	−491.572			−0.660716
$745$	542.609	+	678.647i	0.728335	+	0.910935i
$746$			994.728i			1.33342i
$747$	−931.721			−1.24728
$748$			545.883i			0.729790i
$749$	109.426			0.146097
$750$	−421.482	−	866.781i	−0.561975	−	1.15571i
$751$		−	28.7906i		−	0.0383364i	−0.999816	−	0.0191682i	$-0.993898\pi$
$751$		−	28.7906i		−	0.0383364i	0.999816	−	0.0191682i	$-0.00610180\pi$
$752$		−	180.015i		−	0.239381i
$753$	1149.62			1.52672
$754$	−127.914			−0.169647
$755$	−256.695	+	205.239i	−0.339993	+	0.271840i
$756$		−	98.5762i		−	0.130392i
$757$	522.188			0.689812			0.344906	−	0.938637i	$-0.387911\pi$
$757$	522.188			0.689812			0.344906	+	0.938637i	$0.387911\pi$
$758$	852.756			1.12501
$759$	915.913	+	534.988i	1.20674	+	0.704860i
$760$	−263.066	+	210.333i	−0.346139	+	0.276754i
$761$	613.477			0.806145			0.403073	−	0.915168i	$-0.367942\pi$
$761$	613.477			0.806145			0.403073	+	0.915168i	$0.367942\pi$
$762$			1626.96i			2.13512i
$763$		−	63.8610i		−	0.0836972i
$764$		−	20.3573i		−	0.0266456i
$765$	−2611.83	+	2088.28i	−3.41415	+	2.72977i
$766$			316.491i			0.413173i
$767$			389.665i			0.508038i
$768$		−	87.2354i		−	0.113588i
$769$		−	938.756i		−	1.22075i	−0.792113	−	0.610374i	$-0.791019\pi$
$769$		−	938.756i		−	1.22075i	0.792113	−	0.610374i	$-0.208981\pi$
$770$	−36.0125	+	28.7937i	−0.0467695	+	0.0373944i
$771$	1221.74			1.58462
$772$			12.2293i			0.0158411i
$773$	121.364			0.157004			0.0785020	−	0.996914i	$-0.474986\pi$
$773$	121.364			0.157004			0.0785020	+	0.996914i	$0.474986\pi$
$774$		−	1808.85i		−	2.33702i
$775$	−175.362	+	777.377i	−0.226274	+	1.00307i
$776$			119.373i			0.153831i
$777$			25.3845i			0.0326699i
$778$	−493.546			−0.634377
$779$		−	403.564i		−	0.518054i
$780$	−177.110	+	141.608i	−0.227064	+	0.181548i
$781$			658.019i			0.842534i
$782$	−529.373	+	906.300i	−0.676948	+	1.15895i
$783$			1390.43i			1.77578i
$784$	−193.623			−0.246968
$785$	553.217	−	442.322i	0.704735	−	0.563468i
$786$	131.109			0.166805
$787$	200.567			0.254850			0.127425	−	0.991848i	$-0.459329\pi$
$787$	200.567			0.254850			0.127425	+	0.991848i	$0.459329\pi$
$788$		−	352.444i		−	0.447264i
$789$			769.230i			0.974943i
$790$	−79.9546	+	63.9274i	−0.101208	+	0.0809207i
$791$	−68.3446			−0.0864027
$792$	495.872			0.626102
$793$	154.338			0.194626
$794$	179.103			0.225571
$795$	−781.087	−	976.913i	−0.982500	−	1.22882i
$796$			496.254i			0.623435i
$797$	291.655			0.365941			0.182970	−	0.983118i	$-0.441429\pi$
$797$	291.655			0.365941			0.182970	+	0.983118i	$0.441429\pi$
$798$			141.566i			0.177401i
$799$			1452.18i			1.81750i
$800$	−137.955	−	31.1201i	−0.172444	−	0.0389001i
$801$			1534.95i			1.91629i
$802$	467.496			0.582912
$803$	857.791			1.06823
$804$			482.075i			0.599596i
$805$	−87.7126	+	12.8812i	−0.108960	+	0.0160015i
$806$	187.492			0.232620
$807$			1049.23i			1.30016i
$808$			119.704i			0.148149i
$809$	−1151.04			−1.42279			−0.711394	−	0.702793i	$-0.751936\pi$
$809$	−1151.04			−1.42279			−0.711394	+	0.702793i	$0.751936\pi$
$810$	715.580	+	894.983i	0.883432	+	1.10492i
$811$	−443.021			−0.546266			−0.273133	−	0.961976i	$-0.588060\pi$
$811$	−443.021			−0.546266			−0.273133	+	0.961976i	$0.588060\pi$
$812$	−33.5299			−0.0412930
$813$		−	754.509i		−	0.928055i
$814$	−72.2455			−0.0887537
$815$	−517.726	−	647.525i	−0.635247	−	0.794509i
$816$			703.728i			0.862412i
$817$			1469.72i			1.79892i
$818$			539.603i			0.659662i
$819$			66.4542i			0.0811406i
$820$	132.346	−	105.817i	0.161398	−	0.129045i
$821$	86.5798			0.105456			0.0527282	−	0.998609i	$-0.483208\pi$
$821$	86.5798			0.105456			0.0527282	+	0.998609i	$0.483208\pi$
$822$	−719.238			−0.874985
$823$		−	1231.62i		−	1.49651i	−0.663414	−	0.748253i	$-0.730893\pi$
$823$		−	1231.62i		−	1.49651i	0.663414	−	0.748253i	$-0.269107\pi$
$824$		−	575.756i		−	0.698733i
$825$	253.709	−	1124.69i	0.307526	−	1.36326i
$826$			102.143i			0.123659i
$827$	−174.508			−0.211014			−0.105507	−	0.994419i	$-0.533647\pi$
$827$	−174.508			−0.211014			−0.105507	+	0.994419i	$0.533647\pi$
$828$	823.271	+	480.876i	0.994288	+	0.580768i
$829$	106.709			0.128720			0.0643600	−	0.997927i	$-0.479499\pi$
$829$	106.709			0.128720			0.0643600	+	0.997927i	$0.479499\pi$
$830$	198.500	+	248.266i	0.239157	+	0.299116i
$831$	−2416.87			−2.90839
$832$			33.2726i			0.0399911i
$833$	1561.96			1.87510
$834$	−354.793			−0.425411
$835$	−617.008	−	771.698i	−0.738932	−	0.924190i
$836$	−402.904			−0.481943
$837$		−	2038.05i		−	2.43494i
$838$	−177.850			−0.212232
$839$			62.4957i			0.0744883i	0.999306	+	0.0372441i	$0.0118579\pi$
$839$			62.4957i			0.0744883i	−0.999306	+	0.0372441i	$0.988142\pi$
$840$	−46.4258	+	37.1196i	−0.0552688	+	0.0441899i
$841$	−368.055			−0.437640
$842$	125.589			0.149156
$843$	−2208.92			−2.62030
$844$	−495.639			−0.587250
$845$	−592.428	+	473.674i	−0.701099	+	0.560561i
$846$	1319.14			1.55927
$847$	38.1229			0.0450094
$848$	−183.527			−0.216423
$849$			878.358i			1.03458i
$850$	1112.88	+	251.046i	1.30927	+	0.295348i
$851$	−119.945	−	70.0606i	−0.140946	−	0.0823273i
$852$			848.289i			0.995644i
$853$		−	615.419i		−	0.721476i	−0.932667	−	0.360738i	$-0.882525\pi$
$853$		−	615.419i		−	0.721476i	0.932667	−	0.360738i	$-0.117475\pi$
$854$	40.4566			0.0473730
$855$	−1541.31	−	1927.73i	−1.80270	−	2.25466i
$856$			401.485i			0.469025i
$857$		−	1189.16i		−	1.38758i	−0.720177	−	0.693790i	$-0.755940\pi$
$857$		−	1189.16i		−	1.38758i	0.720177	−	0.693790i	$-0.244060\pi$
$858$	−271.257			−0.316151
$859$	1006.72			1.17196			0.585982	−	0.810324i	$-0.300709\pi$
$859$	1006.72			1.17196			0.585982	+	0.810324i	$0.300709\pi$
$860$	−481.986	+	385.370i	−0.560449	+	0.448105i
$861$		−	71.2210i		−	0.0827189i
$862$	910.526			1.05629
$863$			66.2541i			0.0767719i	0.999263	+	0.0383859i	$0.0122216\pi$
$863$			66.2541i			0.0767719i	−0.999263	+	0.0383859i	$0.987778\pi$
$864$	361.676			0.418606
$865$	−403.805	−	505.042i	−0.466826	−	0.583864i
$866$		−	195.037i		−	0.225216i
$867$		−	4101.29i		−	4.73044i
$868$	49.1470			0.0566210
$869$	−122.456			−0.140916
$870$	654.843	−	523.577i	0.752693	−	0.601813i
$871$		−	183.869i		−	0.211101i
$872$	234.306			0.268699
$873$	−874.762			−1.00202
$874$	−668.920	−	390.719i	−0.765355	−	0.447047i
$875$	42.1394	+	86.6601i	0.0481593	+	0.0990401i
$876$	1105.83			1.26236
$877$			527.609i			0.601607i	0.953686	+	0.300803i	$0.0972548\pi$
$877$			527.609i			0.601607i	−0.953686	+	0.300803i	$0.902745\pi$
$878$			425.643i			0.484787i
$879$			1024.67i			1.16572i
$880$	−105.644	−	132.130i	−0.120050	−	0.150148i
$881$		−	601.457i		−	0.682698i	−0.939937	−	0.341349i	$-0.889116\pi$
$881$		−	601.457i		−	0.682698i	0.939937	−	0.341349i	$-0.110884\pi$
$882$		−	1418.86i		−	1.60869i
$883$			692.293i			0.784024i	0.919960	+	0.392012i	$0.128221\pi$
$883$			692.293i			0.784024i	−0.919960	+	0.392012i	$0.871779\pi$
$884$		−	268.410i		−	0.303632i
$885$	−1594.98	−	1994.86i	−1.80224	−	2.25407i
$886$	350.753			0.395884
$887$		−	658.875i		−	0.742813i	−0.928470	−	0.371406i	$-0.878876\pi$
$887$		−	658.875i		−	0.742813i	0.928470	−	0.371406i	$-0.121124\pi$
$888$	−93.1358			−0.104883
$889$		−	162.662i		−	0.182972i
$890$	409.002	−	327.016i	0.459553	−	0.367434i
$891$			1370.73i			1.53842i
$892$			580.529i			0.650817i
$893$	−1071.82			−1.20025
$894$			1339.95i			1.49882i
$895$	210.052	−	167.946i	0.234695	−	0.187649i
$896$			8.72173i			0.00973407i
$897$	−450.354	−	263.054i	−0.502067	−	0.293259i
$898$			814.850i			0.907406i
$899$	−693.227			−0.771109
$900$	228.047	−	1010.93i	0.253385	−	1.12325i
$901$	1480.51			1.64319
$902$	202.698			0.224721
$903$			259.376i			0.287238i
$904$		−	250.756i		−	0.277385i
$905$	919.477	+	1150.00i	1.01600	+	1.27072i
$906$	−506.828			−0.559413
$907$	−608.891			−0.671324			−0.335662	−	0.941982i	$-0.608960\pi$
$907$	−608.891			−0.671324			−0.335662	+	0.941982i	$0.608960\pi$
$908$	621.373			0.684331
$909$	−877.186			−0.965001
$910$	17.7074	−	14.1578i	0.0194586	−	0.0155581i
$911$		−	1653.04i		−	1.81453i	−0.420557	−	0.907266i	$-0.638165\pi$
$911$		−	1653.04i		−	1.81453i	0.420557	−	0.907266i	$-0.361835\pi$
$912$	−519.406			−0.569525
$913$			380.238i			0.416471i
$914$			148.147i			0.162086i
$915$	−790.121	+	631.738i	−0.863520	+	0.690424i
$916$		−	535.444i		−	0.584545i
$917$	−13.1081			−0.0142946
$918$	−2917.64			−3.17826
$919$			1645.72i			1.79077i	0.445295	+	0.895384i	$0.353099\pi$
$919$			1645.72i			1.79077i	−0.445295	+	0.895384i	$0.646901\pi$
$920$	−47.2612	−	321.817i	−0.0513709	−	0.349801i
$921$	1951.75			2.11917
$922$		−	661.443i		−	0.717401i
$923$		−	323.548i		−	0.350539i
$924$	−71.1045			−0.0769529
$925$	−33.2250	+	147.286i	−0.0359189	+	0.159228i
$926$	711.120			0.767948
$927$	4219.12			4.55137
$928$		−	123.021i		−	0.132566i
$929$	−430.062			−0.462930			−0.231465	−	0.972843i	$-0.574352\pi$
$929$	−430.062			−0.462930			−0.231465	+	0.972843i	$0.574352\pi$
$930$	−959.847	+	767.441i	−1.03209	+	0.825206i
$931$			1152.85i			1.23829i
$932$		−	164.119i		−	0.176093i
$933$		−	481.488i		−	0.516064i
$934$		−	296.155i		−	0.317082i
$935$	852.231	+	1065.89i	0.911477	+	1.13999i
$936$	−243.820			−0.260492
$937$	−300.016			−0.320188			−0.160094	−	0.987102i	$-0.551180\pi$
$937$	−300.016			−0.320188			−0.160094	+	0.987102i	$0.551180\pi$
$938$		−	48.1975i		−	0.0513833i
$939$		−	2464.28i		−	2.62436i
$940$	−281.038	−	351.497i	−0.298977	−	0.373933i
$941$			1207.88i			1.28361i	0.766867	+	0.641806i	$0.221815\pi$
$941$			1207.88i			1.28361i	−0.766867	+	0.641806i	$0.778185\pi$
$942$	1092.29			1.15955
$943$	336.529	+	196.568i	0.356871	+	0.208450i
$944$	−374.761			−0.396993
$945$	−153.897	−	192.480i	−0.162854	−	0.203683i
$946$	−738.197			−0.780335
$947$		−	146.471i		−	0.154669i	−0.997005	−	0.0773344i	$-0.975359\pi$
$947$		−	146.471i		−	0.154669i	0.997005	−	0.0773344i	$-0.0246409\pi$
$948$	−157.865			−0.166525
$949$	−421.775			−0.444442
$950$	−185.292	+	821.394i	−0.195044	+	0.864625i
$951$	−2971.65			−3.12476
$952$		−	70.3582i		−	0.0739057i
$953$	224.831			0.235919			0.117960	−	0.993018i	$-0.462365\pi$
$953$	224.831			0.235919			0.117960	+	0.993018i	$0.462365\pi$
$954$		−	1344.88i		−	1.40972i
$955$	−31.7817	−	39.7497i	−0.0332793	−	0.0416227i
$956$	−30.1291			−0.0315158
$957$	1002.94			1.04800
$958$	630.955			0.658617
$959$	71.9088			0.0749832
$960$	−136.192	−	170.336i	−0.141866	−	0.177433i
$961$	55.1081			0.0573445
$962$	35.5231			0.0369263
$963$	−2942.07			−3.05510
$964$			140.973i			0.146238i
$965$	19.0924	+	23.8791i	0.0197849	+	0.0247451i
$966$	−118.051	−	68.9540i	−0.122206	−	0.0713810i
$967$			867.622i			0.897230i	0.893725	+	0.448615i	$0.148083\pi$
$967$			867.622i			0.897230i	−0.893725	+	0.448615i	$0.851917\pi$
$968$			139.873i			0.144497i
$969$	4190.05			4.32410
$970$	186.365	+	233.089i	0.192129	+	0.240298i
$971$		−	520.260i		−	0.535799i	−0.963447	−	0.267899i	$-0.913671\pi$
$971$		−	520.260i		−	0.535799i	0.963447	−	0.267899i	$-0.0863295\pi$
$972$			616.242i			0.633994i
$973$	35.4719			0.0364562
$974$	212.235			0.217900
$975$	−124.749	+	553.008i	−0.127947	+	0.567188i
$976$			148.435i			0.152085i
$977$	−324.476			−0.332115			−0.166057	−	0.986116i	$-0.553104\pi$
$977$	−324.476			−0.332115			−0.166057	+	0.986116i	$0.553104\pi$
$978$		−	1278.50i		−	1.30726i
$979$	626.417			0.639854
$980$	−378.069	+	302.283i	−0.385785	+	0.308452i
$981$			1716.98i			1.75024i
$982$			1164.28i			1.18562i
$983$	−1278.01			−1.30011			−0.650055	−	0.759887i	$-0.725254\pi$
$983$	−1278.01			−1.30011			−0.650055	+	0.759887i	$0.725254\pi$
$984$	261.310			0.265559
$985$	−550.234	−	688.183i	−0.558613	−	0.698663i
$986$			992.414i			1.00650i
$987$	−189.155			−0.191646
$988$	198.108			0.200514
$989$	−1225.59	−	715.871i	−1.23922	−	0.723833i
$990$	968.243	−	774.155i	0.978023	−	0.781974i
$991$	977.654			0.986533			0.493266	−	0.869878i	$-0.335803\pi$
$991$	977.654			0.986533			0.493266	+	0.869878i	$0.335803\pi$
$992$			180.320i			0.181775i
$993$			2889.53i			2.90990i
$994$		−	84.8113i		−	0.0853232i
$995$	774.751	+	968.988i	0.778644	+	0.973857i
$996$			490.186i			0.492154i
$997$		−	575.147i		−	0.576877i	−0.957498	−	0.288439i	$-0.906864\pi$
$997$		−	575.147i		−	0.576877i	0.957498	−	0.288439i	$-0.0931362\pi$
$998$			570.697i			0.571841i
$999$		−	386.139i		−	0.386525i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	230.3.c.a.229.1	✓	24
5.2	odd	4		1150.3.d.e.551.21		24
5.3	odd	4		1150.3.d.e.551.4		24
5.4	even	2	inner	230.3.c.a.229.24	yes	24
23.22	odd	2	inner	230.3.c.a.229.2	yes	24
115.22	even	4		1150.3.d.e.551.16		24
115.68	even	4		1150.3.d.e.551.9		24
115.114	odd	2	inner	230.3.c.a.229.23	yes	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
230.3.c.a.229.1	✓	24	1.1	even	1	trivial
230.3.c.a.229.2	yes	24	23.22	odd	2	inner
230.3.c.a.229.23	yes	24	115.114	odd	2	inner
230.3.c.a.229.24	yes	24	5.4	even	2	inner
1150.3.d.e.551.4		24	5.3	odd	4
1150.3.d.e.551.9		24	115.68	even	4
1150.3.d.e.551.16		24	115.22	even	4
1150.3.d.e.551.21		24	5.2	odd	4

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:	\( N \)	\(=\)	\( 230 = 2 \cdot 5 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	230.c (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-1.41421i q^{2} -5.45221i q^{3} -2.00000 q^{4} +(-3.90521 + 3.12239i) q^{5} -7.71059 q^{6} +0.770899 q^{7} +2.82843i q^{8} -20.7266 q^{9} +O(q^{10})\)	\(q-1.41421i q^{2} -5.45221i q^{3} -2.00000 q^{4} +(-3.90521 + 3.12239i) q^{5} -7.71059 q^{6} +0.770899 q^{7} +2.82843i q^{8} -20.7266 q^{9} +(4.41573 + 5.52280i) q^{10} +8.45857i q^{11} +10.9044i q^{12} -4.15908i q^{13} -1.09022i q^{14} +(17.0239 + 21.2920i) q^{15} +4.00000 q^{16} -32.2680 q^{17} +29.3118i q^{18} -23.8163i q^{19} +(7.81042 - 6.24479i) q^{20} -4.20310i q^{21} +11.9622 q^{22} +(19.8603 + 11.6004i) q^{23} +15.4212 q^{24} +(5.50131 - 24.3872i) q^{25} -5.88182 q^{26} +63.9359i q^{27} -1.54180 q^{28} +21.7473 q^{29} +(30.1115 - 24.0755i) q^{30} -31.8764 q^{31} -5.65685i q^{32} +46.1179 q^{33} +45.6339i q^{34} +(-3.01052 + 2.40705i) q^{35} +41.4532 q^{36} -6.03947 q^{37} -33.6814 q^{38} -22.6762 q^{39} +(-8.83146 - 11.0456i) q^{40} +16.9449 q^{41} -5.94408 q^{42} -61.7107 q^{43} -16.9171i q^{44} +(80.9417 - 64.7166i) q^{45} +(16.4055 - 28.0866i) q^{46} -45.0037i q^{47} -21.8088i q^{48} -48.4057 q^{49} +(-34.4887 - 7.78003i) q^{50} +175.932i q^{51} +8.31815i q^{52} -45.8817 q^{53} +90.4190 q^{54} +(-26.4110 - 33.0325i) q^{55} +2.18043i q^{56} -129.852 q^{57} -30.7553i q^{58} -93.6903 q^{59} +(-34.0479 - 42.5840i) q^{60} +37.1088i q^{61} +45.0801i q^{62} -15.9781 q^{63} -8.00000 q^{64} +(12.9863 + 16.2421i) q^{65} -65.2206i q^{66} +44.2092 q^{67} +64.5360 q^{68} +(63.2481 - 108.282i) q^{69} +(3.40408 + 4.25752i) q^{70} +77.7931 q^{71} -58.6237i q^{72} -101.411i q^{73} +8.54110i q^{74} +(-132.964 - 29.9943i) q^{75} +47.6326i q^{76} +6.52070i q^{77} +32.0689i q^{78} +14.4772i q^{79} +(-15.6208 + 12.4896i) q^{80} +162.052 q^{81} -23.9637i q^{82} +44.9529 q^{83} +8.40621i q^{84} +(126.013 - 100.753i) q^{85} +87.2720i q^{86} -118.571i q^{87} -23.9245 q^{88} -74.0570i q^{89} +(-91.5231 - 114.469i) q^{90} -3.20623i q^{91} +(-39.7205 - 23.2009i) q^{92} +173.797i q^{93} -63.6448 q^{94} +(74.3639 + 93.0077i) q^{95} -30.8424 q^{96} +42.2048 q^{97} +68.4560i q^{98} -175.317i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - 48 q^{4} + 8 q^{6} - 96 q^{9}+O(q^{10}) \) 24 * q - 48 * q^4 + 8 * q^6 - 96 * q^9	\( 24 q - 48 q^{4} + 8 q^{6} - 96 q^{9} + 96 q^{16} - 16 q^{24} - 48 q^{25} - 32 q^{26} + 100 q^{29} - 124 q^{31} - 28 q^{35} + 192 q^{36} + 192 q^{39} - 116 q^{41} + 148 q^{46} - 76 q^{49} - 144 q^{50} - 16 q^{54} - 224 q^{55} + 84 q^{59} - 192 q^{64} - 340 q^{69} + 328 q^{70} + 196 q^{71} - 496 q^{75} + 1360 q^{81} + 316 q^{85} - 376 q^{94} - 368 q^{95} + 32 q^{96}+O(q^{100}) \) 24 * q - 48 * q^4 + 8 * q^6 - 96 * q^9 + 96 * q^16 - 16 * q^24 - 48 * q^25 - 32 * q^26 + 100 * q^29 - 124 * q^31 - 28 * q^35 + 192 * q^36 + 192 * q^39 - 116 * q^41 + 148 * q^46 - 76 * q^49 - 144 * q^50 - 16 * q^54 - 224 * q^55 + 84 * q^59 - 192 * q^64 - 340 * q^69 + 328 * q^70 + 196 * q^71 - 496 * q^75 + 1360 * q^81 + 316 * q^85 - 376 * q^94 - 368 * q^95 + 32 * q^96

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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