LMFDB - Embedded newform 138.4.d.a.137.17

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [138,4,Mod(137,138)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(138, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 4, names="a")

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

chi := DirichletCharacter("138.137");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 138 = 2 \cdot 3 \cdot 23 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	138.d (of order $2$, degree $1$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$8.14226358079$
Analytic rank:	$0$
Dimension:	$24$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			137.17
Character	$\chi$	$=$	138.137
Dual form			138.4.d.a.137.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+2.00000i q^{2} +(-1.34717 + 5.01848i) q^{3} -4.00000 q^{4} -4.58818 q^{5} +(-10.0370 - 2.69433i) q^{6} -31.2911i q^{7} -8.00000i q^{8} +(-23.3703 - 13.5215i) q^{9} +O(q^{10})$	\(q+2.00000i q^{2} +(-1.34717 + 5.01848i) q^{3} -4.00000 q^{4} -4.58818 q^{5} +(-10.0370 - 2.69433i) q^{6} -31.2911i q^{7} -8.00000i q^{8} +(-23.3703 - 13.5215i) q^{9} -9.17636i q^{10} +0.810436 q^{11} +(5.38867 - 20.0739i) q^{12} -14.3839 q^{13} +62.5821 q^{14} +(6.18104 - 23.0257i) q^{15} +16.0000 q^{16} +45.4043 q^{17} +(27.0429 - 46.7406i) q^{18} +11.6461i q^{19} +18.3527 q^{20} +(157.034 + 42.1543i) q^{21} +1.62087i q^{22} +(-83.7373 - 71.7988i) q^{23} +(40.1478 + 10.7773i) q^{24} -103.949 q^{25} -28.7678i q^{26} +(99.3408 - 99.0677i) q^{27} +125.164i q^{28} -98.1902i q^{29} +(46.0514 + 12.3621i) q^{30} -56.6639 q^{31} +32.0000i q^{32} +(-1.09179 + 4.06716i) q^{33} +90.8086i q^{34} +143.569i q^{35} +(93.4811 + 54.0858i) q^{36} -398.887i q^{37} -23.2922 q^{38} +(19.3775 - 72.1854i) q^{39} +36.7055i q^{40} +97.5633i q^{41} +(-84.3085 + 314.067i) q^{42} -323.530i q^{43} -3.24174 q^{44} +(107.227 + 62.0389i) q^{45} +(143.598 - 167.475i) q^{46} +341.716i q^{47} +(-21.5547 + 80.2957i) q^{48} -636.131 q^{49} -207.897i q^{50} +(-61.1671 + 227.861i) q^{51} +57.5356 q^{52} -500.795 q^{53} +(198.135 + 198.682i) q^{54} -3.71843 q^{55} -250.329 q^{56} +(-58.4457 - 15.6892i) q^{57} +196.380 q^{58} +37.2842i q^{59} +(-24.7242 + 92.1028i) q^{60} -667.826i q^{61} -113.328i q^{62} +(-423.101 + 731.281i) q^{63} -64.0000 q^{64} +65.9960 q^{65} +(-8.13431 - 2.18358i) q^{66} +791.951i q^{67} -181.617 q^{68} +(473.129 - 323.509i) q^{69} -287.138 q^{70} +854.014i q^{71} +(-108.172 + 186.962i) q^{72} +119.587 q^{73} +797.774 q^{74} +(140.036 - 521.664i) q^{75} -46.5844i q^{76} -25.3594i q^{77} +(144.371 + 38.7550i) q^{78} -604.342i q^{79} -73.4109 q^{80} +(363.340 + 632.001i) q^{81} -195.127 q^{82} -813.864 q^{83} +(-628.134 - 168.617i) q^{84} -208.323 q^{85} +647.059 q^{86} +(492.766 + 132.279i) q^{87} -6.48349i q^{88} -460.781 q^{89} +(-124.078 + 214.454i) q^{90} +450.088i q^{91} +(334.949 + 287.195i) q^{92} +(76.3357 - 284.367i) q^{93} -683.432 q^{94} -53.4344i q^{95} +(-160.591 - 43.1093i) q^{96} +710.377i q^{97} -1272.26i q^{98} +(-18.9401 - 10.9583i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 8 q^{3} - 96 q^{4} + 8 q^{6} + 36 q^{9}+O(q^{10}) $ 24 * q + 8 * q^3 - 96 * q^4 + 8 * q^6 + 36 * q^9	$ 24 q + 8 q^{3} - 96 q^{4} + 8 q^{6} + 36 q^{9} - 32 q^{12} + 96 q^{13} + 384 q^{16} + 128 q^{18} - 32 q^{24} + 144 q^{25} + 188 q^{27} + 72 q^{31} - 144 q^{36} - 660 q^{39} - 96 q^{46} + 128 q^{48} - 504 q^{49} - 384 q^{52} + 88 q^{54} - 672 q^{55} + 816 q^{58} - 1536 q^{64} + 352 q^{69} + 624 q^{70} - 512 q^{72} - 2688 q^{73} - 1072 q^{75} + 80 q^{78} - 2356 q^{81} + 1344 q^{82} + 4872 q^{85} + 3748 q^{87} - 2924 q^{93} - 1296 q^{94} + 128 q^{96}+O(q^{100}) $ 24 * q + 8 * q^3 - 96 * q^4 + 8 * q^6 + 36 * q^9 - 32 * q^12 + 96 * q^13 + 384 * q^16 + 128 * q^18 - 32 * q^24 + 144 * q^25 + 188 * q^27 + 72 * q^31 - 144 * q^36 - 660 * q^39 - 96 * q^46 + 128 * q^48 - 504 * q^49 - 384 * q^52 + 88 * q^54 - 672 * q^55 + 816 * q^58 - 1536 * q^64 + 352 * q^69 + 624 * q^70 - 512 * q^72 - 2688 * q^73 - 1072 * q^75 + 80 * q^78 - 2356 * q^81 + 1344 * q^82 + 4872 * q^85 + 3748 * q^87 - 2924 * q^93 - 1296 * q^94 + 128 * q^96

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/138\mathbb{Z}\right)^\times$.

$n$	$47$	$97$
$\chi(n)$	$-1$	$-1$

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 $

$2$			2.00000i			0.707107i
$2$			2.00000i			0.707107i
$3$	−1.34717	+	5.01848i	−0.259262	+	0.965807i
$3$	−1.34717	+	5.01848i	−0.259262	+	0.965807i
$4$	−4.00000			−0.500000
$5$	−4.58818			−0.410379			−0.205190	−	0.978722i	$-0.565781\pi$
$5$	−4.58818			−0.410379			−0.205190	+	0.978722i	$0.565781\pi$
$6$	−10.0370	−	2.69433i	−0.682929	−	0.183326i
$7$		−	31.2911i		−	1.68956i	−0.535115	−	0.844779i	$-0.679732\pi$
$7$		−	31.2911i		−	1.68956i	0.535115	−	0.844779i	$-0.320268\pi$
$8$		−	8.00000i		−	0.353553i
$9$	−23.3703	−	13.5215i	−0.865566	−	0.500795i
$10$		−	9.17636i		−	0.290182i
$11$	0.810436			0.0222141			0.0111071	−	0.999938i	$-0.496464\pi$
$11$	0.810436			0.0222141			0.0111071	+	0.999938i	$0.496464\pi$
$12$	5.38867	−	20.0739i	0.129631	−	0.482903i
$13$	−14.3839			−0.306875			−0.153438	−	0.988158i	$-0.549034\pi$
$13$	−14.3839			−0.306875			−0.153438	+	0.988158i	$0.549034\pi$
$14$	62.5821			1.19470
$15$	6.18104	−	23.0257i	0.106396	−	0.396347i
$16$	16.0000			0.250000
$17$	45.4043			0.647774			0.323887	−	0.946096i	$-0.395010\pi$
$17$	45.4043			0.647774			0.323887	+	0.946096i	$0.395010\pi$
$18$	27.0429	−	46.7406i	0.354115	−	0.612048i
$19$			11.6461i			0.140621i	0.997525	+	0.0703105i	$0.0223990\pi$
$19$			11.6461i			0.140621i	−0.997525	+	0.0703105i	$0.977601\pi$
$20$	18.3527			0.205190
$21$	157.034	+	42.1543i	1.63179	+	0.438039i
$22$			1.62087i			0.0157078i
$23$	−83.7373	−	71.7988i	−0.759149	−	0.650916i
$23$	−83.7373	−	71.7988i	−0.759149	−	0.650916i
$24$	40.1478	+	10.7773i	0.341464	+	0.0916631i
$25$	−103.949			−0.831589
$26$		−	28.7678i		−	0.216994i
$27$	99.3408	−	99.0677i	0.708080	−	0.706133i
$28$			125.164i			0.844779i
$29$		−	98.1902i		−	0.628740i	−0.949301	−	0.314370i	$-0.898207\pi$
$29$		−	98.1902i		−	0.628740i	0.949301	−	0.314370i	$-0.101793\pi$
$30$	46.0514	+	12.3621i	0.280260	+	0.0752333i
$31$	−56.6639			−0.328295			−0.164147	−	0.986436i	$-0.552487\pi$
$31$	−56.6639			−0.328295			−0.164147	+	0.986436i	$0.552487\pi$
$32$			32.0000i			0.176777i
$33$	−1.09179	+	4.06716i	−0.00575929	+	0.0214546i
$34$			90.8086i			0.458045i
$35$			143.569i			0.693360i
$36$	93.4811	+	54.0858i	0.432783	+	0.250397i
$37$		−	398.887i		−	1.77234i	−0.463359	−	0.886171i	$-0.653356\pi$
$37$		−	398.887i		−	1.77234i	0.463359	−	0.886171i	$-0.346644\pi$
$38$	−23.2922			−0.0994341
$39$	19.3775	−	72.1854i	0.0795612	−	0.296382i
$40$			36.7055i			0.145091i
$41$			97.5633i			0.371630i	0.982585	+	0.185815i	$0.0594925\pi$
$41$			97.5633i			0.371630i	−0.982585	+	0.185815i	$0.940507\pi$
$42$	−84.3085	+	314.067i	−0.309740	+	1.15385i
$43$		−	323.530i		−	1.14739i	−0.819069	−	0.573696i	$-0.805509\pi$
$43$		−	323.530i		−	1.14739i	0.819069	−	0.573696i	$-0.194491\pi$
$44$	−3.24174			−0.0111071
$45$	107.227	+	62.0389i	0.355211	+	0.205516i
$46$	143.598	−	167.475i	0.460267	−	0.536800i
$47$			341.716i			1.06052i	0.847835	+	0.530260i	$0.177906\pi$
$47$			341.716i			1.06052i	−0.847835	+	0.530260i	$0.822094\pi$
$48$	−21.5547	+	80.2957i	−0.0648156	+	0.241452i
$49$	−636.131			−1.85461
$50$		−	207.897i		−	0.588022i
$51$	−61.1671	+	227.861i	−0.167943	+	0.625625i
$52$	57.5356			0.153438
$53$	−500.795			−1.29791			−0.648957	−	0.760825i	$-0.724795\pi$
$53$	−500.795			−1.29791			−0.648957	+	0.760825i	$0.724795\pi$
$54$	198.135	+	198.682i	0.499311	+	0.500688i
$55$	−3.71843			−0.00911623
$56$	−250.329			−0.597349
$57$	−58.4457	−	15.6892i	−0.135813	−	0.0364577i
$58$	196.380			0.444586
$59$			37.2842i			0.0822711i	0.999154	+	0.0411356i	$0.0130975\pi$
$59$			37.2842i			0.0822711i	−0.999154	+	0.0411356i	$0.986902\pi$
$60$	−24.7242	+	92.1028i	−0.0531980	+	0.198174i
$61$		−	667.826i		−	1.40174i	−0.713287	−	0.700872i	$-0.752794\pi$
$61$		−	667.826i		−	1.40174i	0.713287	−	0.700872i	$-0.247206\pi$
$62$		−	113.328i		−	0.232139i
$63$	−423.101	+	731.281i	−0.846122	+	1.46242i
$64$	−64.0000			−0.125000
$65$	65.9960			0.125935
$66$	−8.13431	−	2.18358i	−0.0151707	−	0.00407243i
$67$			791.951i			1.44406i	0.691860	+	0.722031i	$0.256791\pi$
$67$			791.951i			1.44406i	−0.691860	+	0.722031i	$0.743209\pi$
$68$	−181.617			−0.323887
$69$	473.129	−	323.509i	0.825478	−	0.564434i
$70$	−287.138			−0.490280
$71$			854.014i			1.42750i	0.700398	+	0.713752i	$0.253006\pi$
$71$			854.014i			1.42750i	−0.700398	+	0.713752i	$0.746994\pi$
$72$	−108.172	+	186.962i	−0.177058	+	0.306024i
$73$	119.587			0.191734			0.0958669	−	0.995394i	$-0.469438\pi$
$73$	119.587			0.191734			0.0958669	+	0.995394i	$0.469438\pi$
$74$	797.774			1.25323
$75$	140.036	−	521.664i	0.215600	−	0.803154i
$76$		−	46.5844i		−	0.0703105i
$77$		−	25.3594i		−	0.0375321i
$78$	144.371	+	38.7550i	0.209574	+	0.0562583i
$79$		−	604.342i		−	0.860681i	−0.902667	−	0.430341i	$-0.858393\pi$
$79$		−	604.342i		−	0.860681i	0.902667	−	0.430341i	$-0.141607\pi$
$80$	−73.4109			−0.102595
$81$	363.340	+	632.001i	0.498409	+	0.866942i
$82$	−195.127			−0.262782
$83$	−813.864			−1.07630			−0.538152	−	0.842848i	$-0.680877\pi$
$83$	−813.864			−1.07630			−0.538152	+	0.842848i	$0.680877\pi$
$84$	−628.134	−	168.617i	−0.815894	−	0.219019i
$85$	−208.323			−0.265833
$86$	647.059			0.811328
$87$	492.766	+	132.279i	0.607242	+	0.163009i
$88$		−	6.48349i		−	0.00785388i
$89$	−460.781			−0.548795			−0.274397	−	0.961616i	$-0.588478\pi$
$89$	−460.781			−0.548795			−0.274397	+	0.961616i	$0.588478\pi$
$90$	−124.078	+	214.454i	−0.145322	+	0.251172i
$91$			450.088i			0.518484i
$92$	334.949	+	287.195i	0.379575	+	0.325458i
$93$	76.3357	−	284.367i	0.0851145	−	0.317069i
$94$	−683.432			−0.749901
$95$		−	53.4344i		−	0.0577080i
$96$	−160.591	−	43.1093i	−0.170732	−	0.0458315i
$97$			710.377i			0.743587i	0.928316	+	0.371793i	$0.121257\pi$
$97$			710.377i			0.743587i	−0.928316	+	0.371793i	$0.878743\pi$
$98$		−	1272.26i		−	1.31141i
$99$	−18.9401	−	10.9583i	−0.0192278	−	0.0111247i
$100$	415.794			0.415794
$101$		−	1397.57i		−	1.37687i	−0.725300	−	0.688433i	$-0.758299\pi$
$101$		−	1397.57i		−	1.37687i	0.725300	−	0.688433i	$-0.241701\pi$
$102$	−455.721	−	122.334i	−0.442383	−	0.118754i
$103$			321.220i			0.307288i	0.988126	+	0.153644i	$0.0491010\pi$
$103$			321.220i			0.307288i	−0.988126	+	0.153644i	$0.950899\pi$
$104$			115.071i			0.108497i
$105$	−720.499	−	193.411i	−0.669652	−	0.179762i
$106$		−	1001.59i		−	0.917764i
$107$	1705.86			1.54123			0.770613	−	0.637303i	$-0.219950\pi$
$107$	1705.86			1.54123			0.770613	+	0.637303i	$0.219950\pi$
$108$	−397.363	+	396.271i	−0.354040	+	0.353066i
$109$		−	673.915i		−	0.592196i	−0.955158	−	0.296098i	$-0.904315\pi$
$109$		−	673.915i		−	0.592196i	0.955158	−	0.296098i	$-0.0956855\pi$
$110$		−	7.43685i		−	0.00644615i
$111$	2001.81	+	537.367i	1.71174	+	0.459501i
$112$		−	500.657i		−	0.422390i
$113$	544.693			0.453455			0.226728	−	0.973958i	$-0.427197\pi$
$113$	544.693			0.453455			0.226728	+	0.973958i	$0.427197\pi$
$114$	31.3785	−	116.891i	0.0257795	−	0.0960341i
$115$	384.202	+	329.426i	0.311539	+	0.267123i
$116$			392.761i			0.314370i
$117$	336.156	+	194.491i	0.265621	+	0.153682i
$118$	−74.5685			−0.0581745
$119$		−	1420.75i		−	1.09445i
$120$	−184.206	−	49.4484i	−0.140130	−	0.0376166i
$121$	−1330.34			−0.999507
$122$	1335.65			0.991183
$123$	−489.620	−	131.434i	−0.358923	−	0.0963497i
$124$	226.656			0.164147
$125$	1050.46			0.751646
$126$	−1462.56	−	846.202i	−1.03409	−	0.598299i
$127$	2661.94			1.85991			0.929957	−	0.367667i	$-0.119843\pi$
$127$	2661.94			1.85991			0.929957	+	0.367667i	$0.119843\pi$
$128$		−	128.000i		−	0.0883883i
$129$	1623.63	+	435.848i	1.10816	+	0.297475i
$130$			131.992i			0.0890497i
$131$			337.091i			0.224822i	0.993662	+	0.112411i	$0.0358574\pi$
$131$			337.091i			0.224822i	−0.993662	+	0.112411i	$0.964143\pi$
$132$	4.36717	−	16.2686i	0.00287964	−	0.0107273i
$133$	364.419			0.237587
$134$	−1583.90			−1.02111
$135$	−455.794	+	454.540i	−0.290581	+	0.289782i
$136$		−	363.234i		−	0.229023i
$137$	−1963.95			−1.22476			−0.612379	−	0.790565i	$-0.709787\pi$
$137$	−1963.95			−1.22476			−0.612379	+	0.790565i	$0.709787\pi$
$138$	647.018	+	946.257i	0.399115	+	0.583701i
$139$	1044.68			0.637471			0.318736	−	0.947844i	$-0.396742\pi$
$139$	1044.68			0.637471			0.318736	+	0.947844i	$0.396742\pi$
$140$		−	574.276i		−	0.346680i
$141$	−1714.90	−	460.349i	−1.02426	−	0.274953i
$142$	−1708.03			−1.00940
$143$	−11.6572			−0.00681697
$144$	−373.925	−	216.343i	−0.216392	−	0.125199i
$145$			450.515i			0.258022i
$146$			239.173i			0.135576i
$147$	856.974	−	3192.41i	0.480830	−	1.79119i
$148$			1595.55i			0.886171i
$149$	1119.27			0.615398			0.307699	−	0.951484i	$-0.400441\pi$
$149$	1119.27			0.615398			0.307699	+	0.951484i	$0.400441\pi$
$150$	1043.33	+	280.072i	0.567916	+	0.152452i
$151$	−889.980			−0.479639			−0.239820	−	0.970817i	$-0.577088\pi$
$151$	−889.980			−0.479639			−0.239820	+	0.970817i	$0.577088\pi$
$152$	93.1688			0.0497170
$153$	−1061.11	−	613.932i	−0.560691	−	0.324402i
$154$	50.7188			0.0265392
$155$	259.984			0.134725
$156$	−77.5101	+	288.741i	−0.0397806	+	0.148191i
$157$		−	1637.20i		−	0.832247i	−0.909308	−	0.416123i	$-0.863388\pi$
$157$		−	1637.20i		−	0.832247i	0.909308	−	0.416123i	$-0.136612\pi$
$158$	1208.68			0.608594
$159$	674.654	−	2513.23i	0.336500	−	1.25354i
$160$		−	146.822i		−	0.0725455i
$161$	−2246.66	+	2620.23i	−1.09976	+	1.28263i
$162$	−1264.00	+	726.681i	−0.613020	+	0.352429i
$163$	515.592			0.247756			0.123878	−	0.992297i	$-0.460467\pi$
$163$	515.592			0.247756			0.123878	+	0.992297i	$0.460467\pi$
$164$		−	390.253i		−	0.185815i
$165$	5.00934	−	18.6608i	0.00236349	−	0.00880451i
$166$		−	1627.73i		−	0.761062i
$167$		−	1940.45i		−	0.899142i	−0.893245	−	0.449571i	$-0.851577\pi$
$167$		−	1940.45i		−	0.899142i	0.893245	−	0.449571i	$-0.148423\pi$
$168$	337.234	−	1256.27i	0.154870	−	0.576924i
$169$	−1990.10			−0.905828
$170$		−	416.646i		−	0.187972i
$171$	157.472	−	272.173i	0.0704222	−	0.121717i
$172$			1294.12i			0.573696i
$173$			3537.82i			1.55477i	0.629025	+	0.777385i	$0.283454\pi$
$173$			3537.82i			1.55477i	−0.629025	+	0.777385i	$0.716546\pi$
$174$	−264.557	+	985.531i	−0.115265	+	0.429385i
$175$			3252.66i			1.40502i
$176$	12.9670			0.00555353
$177$	−187.110	−	50.2281i	−0.0794580	−	0.0213298i
$178$		−	921.563i		−	0.388056i
$179$			2748.49i			1.14766i	0.818974	+	0.573831i	$0.194544\pi$
$179$			2748.49i			1.14766i	−0.818974	+	0.573831i	$0.805456\pi$
$180$	−428.908	−	248.156i	−0.177605	−	0.102758i
$181$			2382.46i			0.978381i	0.872177	+	0.489190i	$0.162708\pi$
$181$			2382.46i			0.978381i	−0.872177	+	0.489190i	$0.837292\pi$
$182$	−900.176			−0.366623
$183$	3351.47	+	899.673i	1.35381	+	0.363420i
$184$	−574.390	+	669.899i	−0.230134	+	0.268400i
$185$			1830.17i			0.727332i
$186$	568.733	+	152.671i	0.224202	+	0.0601850i
$187$	36.7973			0.0143897
$188$		−	1366.86i		−	0.530260i
$189$	−3099.93	−	3108.48i	−1.19305	−	1.19634i
$190$	106.869			0.0408057
$191$	−4596.66			−1.74137			−0.870687	−	0.491837i	$-0.836326\pi$
$191$	−4596.66			−1.74137			−0.870687	+	0.491837i	$0.836326\pi$
$192$	86.2187	−	321.183i	0.0324078	−	0.120726i
$193$	4019.38			1.49907			0.749537	−	0.661963i	$-0.230276\pi$
$193$	4019.38			1.49907			0.749537	+	0.661963i	$0.230276\pi$
$194$	−1420.75			−0.525795
$195$	−88.9076	+	331.200i	−0.0326503	+	0.121629i
$196$	2544.52			0.927304
$197$		−	1042.02i		−	0.376857i	−0.982087	−	0.188428i	$-0.939661\pi$
$197$		−	1042.02i		−	0.376857i	0.982087	−	0.188428i	$-0.0603393\pi$
$198$	21.9165	−	37.8802i	0.00786637	−	0.0135961i
$199$			4356.75i			1.55197i	0.630751	+	0.775985i	$0.282747\pi$
$199$			4356.75i			1.55197i	−0.630751	+	0.775985i	$0.717253\pi$
$200$			831.589i			0.294011i
$201$	−3974.39	−	1066.89i	−1.39469	−	0.374391i
$202$	2795.14			0.973592
$203$	−3072.48			−1.06229
$204$	244.669	−	911.442i	0.0839717	−	0.312812i
$205$		−	447.638i		−	0.152509i
$206$	−642.439			−0.217286
$207$	986.141	+	2810.21i	0.331119	+	0.943589i
$208$	−230.143			−0.0767188
$209$			9.43842i			0.00312377i
$210$	386.823	−	1441.00i	0.127111	−	0.473515i
$211$	808.276			0.263716			0.131858	−	0.991269i	$-0.457906\pi$
$211$	808.276			0.263716			0.131858	+	0.991269i	$0.457906\pi$
$212$	2003.18			0.648957
$213$	−4285.85	−	1150.50i	−1.37869	−	0.370098i
$214$			3411.71i			1.08981i
$215$			1484.41i			0.470866i
$216$	−792.541	−	794.727i	−0.249656	−	0.250344i
$217$			1773.07i			0.554673i
$218$	1347.83			0.418746
$219$	−161.103	+	600.143i	−0.0497093	+	0.185178i
$220$	14.8737			0.00455811
$221$	−653.091			−0.198786
$222$	−1074.73	+	4003.61i	−0.324917	+	1.21038i
$223$	4202.65			1.26202			0.631010	−	0.775775i	$-0.282641\pi$
$223$	4202.65			1.26202			0.631010	+	0.775775i	$0.282641\pi$
$224$	1001.31			0.298675
$225$	2429.31	+	1405.54i	0.719795	+	0.416455i
$226$			1089.39i			0.320641i
$227$	2701.93			0.790014			0.395007	−	0.918678i	$-0.370742\pi$
$227$	2701.93			0.790014			0.395007	+	0.918678i	$0.370742\pi$
$228$	233.783	+	62.7570i	0.0679064	+	0.0182289i
$229$		−	4059.77i		−	1.17152i	−0.810486	−	0.585759i	$-0.800797\pi$
$229$		−	4059.77i		−	1.17152i	0.810486	−	0.585759i	$-0.199203\pi$
$230$	−658.851	+	768.404i	−0.188884	+	0.220292i
$231$	127.266	+	34.1633i	0.0362488	+	0.00973066i
$232$	−785.522			−0.222293
$233$			3175.56i			0.892866i	0.894817	+	0.446433i	$0.147306\pi$
$233$			3175.56i			0.892866i	−0.894817	+	0.446433i	$0.852694\pi$
$234$	−388.983	+	672.312i	−0.108669	+	0.187822i
$235$		−	1567.86i		−	0.435216i
$236$		−	149.137i		−	0.0411356i
$237$	3032.88	+	814.150i	0.831252	+	0.223142i
$238$	2841.50			0.773895
$239$		−	4079.75i		−	1.10417i	−0.833787	−	0.552087i	$-0.813832\pi$
$239$		−	4079.75i		−	1.10417i	0.833787	−	0.552087i	$-0.186168\pi$
$240$	98.8967	−	368.411i	0.0265990	−	0.0990868i
$241$		−	4134.54i		−	1.10510i	−0.833479	−	0.552551i	$-0.813655\pi$
$241$		−	4134.54i		−	1.10510i	0.833479	−	0.552551i	$-0.186345\pi$
$242$		−	2660.69i		−	0.706758i
$243$	−3661.16	+	972.007i	−0.966517	+	0.256602i
$244$			2671.31i			0.700872i
$245$	2918.68			0.761093
$246$	262.868	−	979.239i	0.0681295	−	0.253797i
$247$		−	167.516i		−	0.0431531i
$248$			453.311i			0.116070i
$249$	1096.41	−	4084.36i	0.279045	−	1.03950i
$250$			2100.92i			0.531494i
$251$	−3797.24			−0.954898			−0.477449	−	0.878659i	$-0.658438\pi$
$251$	−3797.24			−0.954898			−0.477449	+	0.878659i	$0.658438\pi$
$252$	1692.40	−	2925.12i	0.423061	−	0.731212i
$253$	−67.8637	−	58.1883i	−0.0168639	−	0.0144595i
$254$			5323.88i			1.31516i
$255$	280.646	−	1045.47i	0.0689205	−	0.256743i
$256$	256.000			0.0625000
$257$		−	6268.13i		−	1.52138i	−0.649114	−	0.760691i	$-0.724860\pi$
$257$		−	6268.13i		−	1.52138i	0.649114	−	0.760691i	$-0.275140\pi$
$258$	−871.697	+	3247.25i	−0.210347	+	0.783586i
$259$	−12481.6			−2.99447
$260$	−263.984			−0.0629677
$261$	−1327.67	+	2294.73i	−0.314870	+	0.544216i
$262$	−674.181			−0.158973
$263$	2160.75			0.506606			0.253303	−	0.967387i	$-0.418483\pi$
$263$	2160.75			0.506606			0.253303	+	0.967387i	$0.418483\pi$
$264$	32.5372	+	8.73433i	0.00758534	+	0.00203622i
$265$	2297.74			0.532637
$266$			728.838i			0.168000i
$267$	620.749	−	2312.42i	0.142282	−	0.530030i
$268$		−	3167.80i		−	0.722031i
$269$		−	8400.13i		−	1.90396i	−0.306162	−	0.951979i	$-0.599045\pi$
$269$		−	8400.13i		−	1.90396i	0.306162	−	0.951979i	$-0.400955\pi$
$270$	−909.081	−	911.587i	−0.204907	−	0.205472i
$271$	1857.07			0.416269			0.208134	−	0.978100i	$-0.433261\pi$
$271$	1857.07			0.416269			0.208134	+	0.978100i	$0.433261\pi$
$272$	726.469			0.161943
$273$	−2258.76	−	606.343i	−0.500755	−	0.134423i
$274$		−	3927.90i		−	0.866034i
$275$	−84.2436			−0.0184730
$276$	−1892.51	+	1294.04i	−0.412739	+	0.282217i
$277$	−4910.32			−1.06510			−0.532550	−	0.846399i	$-0.678766\pi$
$277$	−4910.32			−1.06510			−0.532550	+	0.846399i	$0.678766\pi$
$278$			2089.36i			0.450760i
$279$	1324.25	+	766.179i	0.284161	+	0.164408i
$280$	1148.55			0.245140
$281$	−58.7011			−0.0124620			−0.00623099	−	0.999981i	$-0.501983\pi$
$281$	−58.7011			−0.0124620			−0.00623099	+	0.999981i	$0.501983\pi$
$282$	920.697	−	3429.79i	0.194421	−	0.724259i
$283$		−	4610.48i		−	0.968425i	−0.874950	−	0.484213i	$-0.839106\pi$
$283$		−	4610.48i		−	0.968425i	0.874950	−	0.484213i	$-0.160894\pi$
$284$		−	3416.06i		−	0.713752i
$285$	268.160	+	71.9851i	0.0557348	+	0.0149615i
$286$		−	23.3145i		−	0.00482033i
$287$	3052.86			0.627891
$288$	432.687	−	747.849i	0.0885288	−	0.153012i
$289$	−2851.45			−0.580389
$290$	−901.029			−0.182449
$291$	−3565.01	−	956.997i	−0.718161	−	0.192784i
$292$	−478.347			−0.0958669
$293$	9883.89			1.97073			0.985364	−	0.170466i	$-0.0545272\pi$
$293$	9883.89			1.97073			0.985364	+	0.170466i	$0.0545272\pi$
$294$	6384.82	+	1713.95i	1.26657	+	0.339998i
$295$		−	171.067i		−	0.0337624i
$296$	−3191.10			−0.626617
$297$	80.5093	−	80.2880i	0.0157294	−	0.0156861i
$298$			2238.54i			0.435152i
$299$	1204.47	+	1032.75i	0.232964	+	0.199750i
$300$	−560.144	+	2086.66i	−0.107800	+	0.401577i
$301$	−10123.6			−1.93858
$302$		−	1779.96i		−	0.339156i
$303$	7013.68	+	1882.76i	1.32979	+	0.356970i
$304$			186.338i			0.0351553i
$305$			3064.11i			0.575247i
$306$	1227.86	−	2122.22i	0.229387	−	0.396469i
$307$	2482.33			0.461479			0.230740	−	0.973016i	$-0.425885\pi$
$307$	2482.33			0.461479			0.230740	+	0.973016i	$0.425885\pi$
$308$			101.438i			0.0187660i
$309$	−1612.03	−	432.736i	−0.296781	−	0.0796683i
$310$			519.969i			0.0952653i
$311$			2610.33i			0.475944i	0.971272	+	0.237972i	$0.0764826\pi$
$311$			2610.33i			0.475944i	−0.971272	+	0.237972i	$0.923517\pi$
$312$	−577.483	−	155.020i	−0.104787	−	0.0281291i
$313$		−	1446.18i		−	0.261160i	−0.991438	−	0.130580i	$-0.958316\pi$
$313$		−	1446.18i		−	0.261160i	0.991438	−	0.130580i	$-0.0416839\pi$
$314$	3274.40			0.588487
$315$	1941.26	−	3355.25i	0.347231	−	0.600149i
$316$			2417.37i			0.430341i
$317$		−	4606.38i		−	0.816152i	−0.912948	−	0.408076i	$-0.866200\pi$
$317$		−	4606.38i		−	0.816152i	0.912948	−	0.408076i	$-0.133800\pi$
$318$	5026.46	+	1349.31i	0.886383	+	0.237942i
$319$		−	79.5768i		−	0.0139669i
$320$	293.644			0.0512974
$321$	−2298.07	+	8560.80i	−0.399582	+	1.48853i
$322$	−5240.46	−	4493.32i	−0.906955	−	0.777649i
$323$			528.783i			0.0910906i
$324$	−1453.36	−	2528.00i	−0.249205	−	0.433471i
$325$	1495.19			0.255194
$326$			1031.18i			0.175190i
$327$	3382.03	+	907.876i	0.571947	+	0.153534i
$328$	780.507			0.131391
$329$	10692.7			1.79181
$330$	37.3217	+	10.0187i	0.00622573	+	0.00167124i
$331$	8414.60			1.39731			0.698653	−	0.715461i	$-0.253783\pi$
$331$	8414.60			1.39731			0.698653	+	0.715461i	$0.253783\pi$
$332$	3255.46			0.538152
$333$	−5393.53	+	9322.10i	−0.887579	+	1.53408i
$334$	3880.91			0.635790
$335$		−	3633.61i		−	0.592614i
$336$	2512.54	+	674.468i	0.407947	+	0.109510i
$337$		−	4905.94i		−	0.793008i	−0.918033	−	0.396504i	$-0.870223\pi$
$337$		−	4905.94i		−	0.793008i	0.918033	−	0.396504i	$-0.129777\pi$
$338$		−	3980.21i		−	0.640517i
$339$	−733.793	+	2733.53i	−0.117564	+	0.437950i
$340$	833.292			0.132917
$341$	−45.9224			−0.00729279
$342$	544.345	+	314.945i	0.0860668	+	0.0497960i
$343$			9172.37i			1.44391i
$344$	−2588.24			−0.405664
$345$	−2170.80	+	1484.32i	−0.338759	+	0.231632i
$346$	−7075.64			−1.09939
$347$			263.112i			0.0407049i	0.999793	+	0.0203524i	$0.00647883\pi$
$347$			263.112i			0.0407049i	−0.999793	+	0.0203524i	$0.993521\pi$
$348$	−1971.06	−	529.114i	−0.303621	−	0.0815043i
$349$	7528.85			1.15476			0.577378	−	0.816477i	$-0.304076\pi$
$349$	7528.85			1.15476			0.577378	+	0.816477i	$0.304076\pi$
$350$	−6505.32			−0.993498
$351$	−1428.91	+	1424.98i	−0.217292	+	0.216695i
$352$			25.9339i			0.00392694i
$353$		−	8877.61i		−	1.33855i	−0.743016	−	0.669274i	$-0.766605\pi$
$353$		−	8877.61i		−	1.33855i	0.743016	−	0.669274i	$-0.233395\pi$
$354$	100.456	−	374.221i	0.0150824	−	0.0561853i
$355$		−	3918.37i		−	0.585819i
$356$	1843.13			0.274397
$357$	7130.00	+	1913.98i	1.05703	+	0.283750i
$358$	−5496.98			−0.811520
$359$	−5671.58			−0.833801			−0.416901	−	0.908952i	$-0.636884\pi$
$359$	−5671.58			−0.833801			−0.416901	+	0.908952i	$0.636884\pi$
$360$	496.311	−	857.817i	0.0726608	−	0.125586i
$361$	6723.37			0.980226
$362$	−4764.92			−0.691819
$363$	1792.19	−	6676.30i	0.259134	−	0.965330i
$364$		−	1800.35i		−	0.259242i
$365$	−548.685			−0.0786836
$366$	−1799.35	+	6702.95i	−0.256976	+	0.957291i
$367$		−	3738.28i		−	0.531708i	−0.964013	−	0.265854i	$-0.914346\pi$
$367$		−	3738.28i		−	0.531708i	0.964013	−	0.265854i	$-0.0856539\pi$
$368$	−1339.80	−	1148.78i	−0.189787	−	0.162729i
$369$	1319.20	−	2280.08i	0.186110	−	0.321670i
$370$	−3660.33			−0.514302
$371$			15670.4i			2.19290i
$372$	−305.343	+	1137.47i	−0.0425572	+	0.158535i
$373$			10036.3i			1.39319i	0.717466	+	0.696594i	$0.245302\pi$
$373$			10036.3i			1.39319i	−0.717466	+	0.696594i	$0.754698\pi$
$374$			73.5945i			0.0101751i
$375$	−1415.14	+	5271.70i	−0.194874	+	0.725945i
$376$	2733.73			0.374950
$377$			1412.36i			0.192945i
$378$	6216.96	−	6199.87i	0.845942	−	0.843615i
$379$		−	3941.24i		−	0.534163i	−0.963674	−	0.267082i	$-0.913941\pi$
$379$		−	3941.24i		−	0.534163i	0.963674	−	0.267082i	$-0.0860593\pi$
$380$			213.738i			0.0288540i
$381$	−3586.08	+	13358.9i	−0.482206	+	1.79632i
$382$		−	9193.32i		−	1.23134i
$383$	−9416.89			−1.25635			−0.628173	−	0.778074i	$-0.716197\pi$
$383$	−9416.89			−1.25635			−0.628173	+	0.778074i	$0.716197\pi$
$384$	642.365	+	172.437i	0.0853661	+	0.0229158i
$385$			116.354i			0.0154024i
$386$			8038.76i			1.06000i
$387$	−4374.59	+	7560.98i	−0.574607	+	0.993143i
$388$		−	2841.51i		−	0.371793i
$389$	3759.41			0.489999			0.244999	−	0.969523i	$-0.421212\pi$
$389$	3759.41			0.489999			0.244999	+	0.969523i	$0.421212\pi$
$390$	−662.399	−	177.815i	−0.0860048	−	0.0230872i
$391$	−3802.03	−	3259.97i	−0.491757	−	0.421647i
$392$			5089.05i			0.655703i
$393$	−1691.68	−	454.117i	−0.217135	−	0.0582880i
$394$	2084.04			0.266478
$395$			2772.83i			0.353206i
$396$	75.7604	+	43.8331i	0.00961390	+	0.00556236i
$397$	−7055.62			−0.891968			−0.445984	−	0.895041i	$-0.647146\pi$
$397$	−7055.62			−0.891968			−0.445984	+	0.895041i	$0.647146\pi$
$398$	−8713.50			−1.09741
$399$	−490.933	+	1828.83i	−0.0615975	+	0.229464i
$400$	−1663.18			−0.207897
$401$	−10421.5			−1.29782			−0.648912	−	0.760864i	$-0.724775\pi$
$401$	−10421.5			−1.29782			−0.648912	+	0.760864i	$0.724775\pi$
$402$	2133.78	−	7948.78i	0.264734	−	0.986192i
$403$	815.048			0.100746
$404$			5590.28i			0.688433i
$405$	−1667.07	−	2899.73i	−0.204537	−	0.355775i
$406$		−	6144.95i		−	0.751155i
$407$		−	323.272i		−	0.0393710i
$408$	1822.88	+	489.337i	0.221192	+	0.0593770i
$409$	2654.24			0.320889			0.160445	−	0.987045i	$-0.448707\pi$
$409$	2654.24			0.320889			0.160445	+	0.987045i	$0.448707\pi$
$410$	895.276			0.107840
$411$	2645.77	−	9856.06i	0.317533	−	1.18288i
$412$		−	1284.88i		−	0.153644i
$413$	1166.66			0.139002
$414$	−5620.42	+	1972.28i	−0.667218	+	0.234136i
$415$	3734.16			0.441693
$416$		−	460.285i		−	0.0542484i
$417$	−1407.36	+	5242.70i	−0.165272	+	0.615674i
$418$	−18.8768			−0.00220884
$419$	12206.4			1.42321			0.711603	−	0.702582i	$-0.247970\pi$
$419$	12206.4			1.42321			0.711603	+	0.702582i	$0.247970\pi$
$420$	2881.99	+	773.646i	0.334826	+	0.0898811i
$421$		−	5323.31i		−	0.616252i	−0.951346	−	0.308126i	$-0.900298\pi$
$421$		−	5323.31i		−	0.616252i	0.951346	−	0.308126i	$-0.0997019\pi$
$422$			1616.55i			0.186475i
$423$	4620.50	−	7986.01i	0.531103	−	0.917950i
$424$			4006.36i			0.458882i
$425$	−4719.71			−0.538682
$426$	2301.00	−	8571.71i	0.261699	−	0.974884i
$427$	−20897.0			−2.36833
$428$	−6823.42			−0.770613
$429$	15.7042	−	58.5016i	0.00176738	−	0.00658388i
$430$	−2968.83			−0.332952
$431$	−12175.0			−1.36067			−0.680337	−	0.732900i	$-0.738166\pi$
$431$	−12175.0			−1.36067			−0.680337	+	0.732900i	$0.738166\pi$
$432$	1589.45	−	1585.08i	0.177020	−	0.176533i
$433$			15943.3i			1.76948i	0.466083	+	0.884741i	$0.345665\pi$
$433$			15943.3i			1.76948i	−0.466083	+	0.884741i	$0.654335\pi$
$434$	−3546.15			−0.392213
$435$	−2260.90	−	606.918i	−0.249199	−	0.0668954i
$436$			2695.66i			0.296098i
$437$	836.176	−	975.213i	0.0915325	−	0.106752i
$438$	−1200.29	−	322.206i	−0.130940	−	0.0351498i
$439$	−15528.1			−1.68819			−0.844096	−	0.536192i	$-0.819862\pi$
$439$	−15528.1			−1.68819			−0.844096	+	0.536192i	$0.819862\pi$
$440$			29.7474i			0.00322307i
$441$	14866.6	+	8601.41i	1.60529	+	0.928778i
$442$		−	1306.18i		−	0.140563i
$443$			11096.6i			1.19010i	0.803688	+	0.595050i	$0.202868\pi$
$443$			11096.6i			1.19010i	−0.803688	+	0.595050i	$0.797132\pi$
$444$	−8007.23	−	2149.47i	−0.855870	−	0.229751i
$445$	2114.15			0.225214
$446$			8405.30i			0.892382i
$447$	−1507.84	+	5617.04i	−0.159549	+	0.594355i
$448$			2002.63i			0.211195i
$449$		−	10576.9i		−	1.11170i	−0.831281	−	0.555852i	$-0.812392\pi$
$449$		−	10576.9i		−	1.11170i	0.831281	−	0.555852i	$-0.187608\pi$
$450$	−2811.07	+	4858.62i	−0.294478	+	0.508972i
$451$			79.0688i			0.00825544i
$452$	−2178.77			−0.226728
$453$	1198.95	−	4466.35i	0.124352	−	0.463239i
$454$			5403.86i			0.558624i
$455$		−	2065.08i		−	0.212775i
$456$	−125.514	+	467.566i	−0.0128898	+	0.0480171i
$457$		−	5806.47i		−	0.594344i	−0.954824	−	0.297172i	$-0.903956\pi$
$457$		−	5806.47i		−	0.594344i	0.954824	−	0.297172i	$-0.0960435\pi$
$458$	8119.55			0.828388
$459$	4510.50	−	4498.10i	0.458676	−	0.457414i
$460$	−1536.81	−	1317.70i	−0.155770	−	0.133561i
$461$		−	13333.5i		−	1.34708i	−0.739151	−	0.673540i	$-0.764773\pi$
$461$		−	13333.5i		−	1.34708i	0.739151	−	0.673540i	$-0.235227\pi$
$462$	−68.3267	+	254.531i	−0.00688061	+	0.0256317i
$463$	10069.2			1.01070			0.505349	−	0.862915i	$-0.331364\pi$
$463$	10069.2			1.01070			0.505349	+	0.862915i	$0.331364\pi$
$464$		−	1571.04i		−	0.157185i
$465$	−350.242	+	1304.73i	−0.0349292	+	0.130119i
$466$	−6351.11			−0.631351
$467$	−4461.60			−0.442095			−0.221047	−	0.975263i	$-0.570948\pi$
$467$	−4461.60			−0.442095			−0.221047	+	0.975263i	$0.570948\pi$
$468$	−1344.62	−	777.966i	−0.132810	−	0.0768408i
$469$	24781.0			2.43983
$470$	3135.71			0.307744
$471$	8216.25	+	2205.58i	0.803790	+	0.215770i
$472$	298.274			0.0290872
$473$		−	262.200i		−	0.0254883i
$474$	−1628.30	+	6065.76i	−0.157785	+	0.587784i
$475$		−	1210.60i		−	0.116939i
$476$			5682.99i			0.547226i
$477$	11703.7	+	6771.48i	1.12343	+	0.649989i
$478$	8159.51			0.780768
$479$	4177.67			0.398502			0.199251	−	0.979948i	$-0.436149\pi$
$479$	4177.67			0.398502			0.199251	+	0.979948i	$0.436149\pi$
$480$	736.822	+	197.793i	0.0700650	+	0.0188083i
$481$			5737.56i			0.543888i
$482$	8269.09			0.781425
$483$	−10122.9	−	14804.7i	−0.953644	−	1.39469i
$484$	5321.37			0.499753
$485$		−	3259.34i		−	0.305153i
$486$	−1944.01	−	7322.32i	−0.181445	−	0.683431i
$487$	9833.05			0.914945			0.457472	−	0.889224i	$-0.348755\pi$
$487$	9833.05			0.914945			0.457472	+	0.889224i	$0.348755\pi$
$488$	−5342.61			−0.495592
$489$	−694.588	+	2587.49i	−0.0642338	+	0.239285i
$490$			5837.37i			0.538174i
$491$		−	6410.20i		−	0.589182i	−0.955623	−	0.294591i	$-0.904817\pi$
$491$		−	6410.20i		−	0.589182i	0.955623	−	0.294591i	$-0.0951834\pi$
$492$	1958.48	+	525.736i	0.179461	+	0.0481748i
$493$		−	4458.26i		−	0.407282i
$494$	335.033			0.0305139
$495$	86.9007	+	50.2785i	0.00789070	+	0.00456536i
$496$	−906.623			−0.0820737
$497$	26723.0			2.41185
$498$	8168.72	+	2192.82i	0.735039	+	0.197315i
$499$	−11487.8			−1.03059			−0.515297	−	0.857012i	$-0.672318\pi$
$499$	−11487.8			−1.03059			−0.515297	+	0.857012i	$0.672318\pi$
$500$	−4201.83			−0.375823
$501$	9738.12	+	2614.11i	0.868398	+	0.233114i
$502$		−	7594.47i		−	0.675215i
$503$	11971.2			1.06117			0.530586	−	0.847631i	$-0.321972\pi$
$503$	11971.2			1.06117			0.530586	+	0.847631i	$0.321972\pi$
$504$	5850.25	+	3384.81i	0.517045	+	0.299149i
$505$			6412.31i			0.565038i
$506$	116.377	−	135.727i	0.0102244	−	0.0119245i
$507$	2681.00	−	9987.29i	0.234847	−	0.874855i
$508$	−10647.8			−0.929957
$509$			8556.49i			0.745108i	0.928011	+	0.372554i	$0.121518\pi$
$509$			8556.49i			0.745108i	−0.928011	+	0.372554i	$0.878482\pi$
$510$	2090.93	+	561.292i	0.181545	+	0.0487342i
$511$		−	3742.00i		−	0.323945i
$512$			512.000i			0.0441942i
$513$	1153.75	+	1156.93i	0.0992971	+	0.0995709i
$514$	12536.3			1.07578
$515$		−	1473.81i		−	0.126105i
$516$	−6494.51	−	1743.39i	−0.554079	−	0.148738i
$517$			276.939i			0.0235585i
$518$		−	24963.2i		−	2.11741i
$519$	−17754.5	−	4766.03i	−1.50161	−	0.403093i
$520$		−	527.968i		−	0.0445249i
$521$	−1309.26			−0.110096			−0.0550478	−	0.998484i	$-0.517531\pi$
$521$	−1309.26			−0.110096			−0.0550478	+	0.998484i	$0.517531\pi$
$522$	−4589.47	−	2655.35i	−0.384819	−	0.222647i
$523$		−	15027.8i		−	1.25644i	−0.778034	−	0.628222i	$-0.783783\pi$
$523$		−	15027.8i		−	1.25644i	0.778034	−	0.628222i	$-0.216217\pi$
$524$		−	1348.36i		−	0.112411i
$525$	−16323.4	−	4381.88i	−1.35698	−	0.364268i
$526$			4321.50i			0.358225i
$527$	−2572.78			−0.212661
$528$	−17.4687	+	65.0745i	−0.00143982	+	0.00536364i
$529$	1856.88	+	12024.5i	0.152616	+	0.988286i
$530$			4595.48i			0.376632i
$531$	504.137	−	871.343i	0.0412009	−	0.0712111i
$532$	−1457.68			−0.118794
$533$		−	1403.34i		−	0.114044i
$534$	4624.84	+	1241.50i	0.374788	+	0.100608i
$535$	−7826.77			−0.632488
$536$	6335.61			0.510553
$537$	−13793.2	−	3702.67i	−1.10842	−	0.297546i
$538$	16800.3			1.34630
$539$	−515.543			−0.0411985
$540$	1823.17	−	1818.16i	0.145291	−	0.144891i
$541$	16560.5			1.31607			0.658035	−	0.752988i	$-0.271388\pi$
$541$	16560.5			1.31607			0.658035	+	0.752988i	$0.271388\pi$
$542$			3714.13i			0.294346i
$543$	−11956.3	−	3209.57i	−0.944927	−	0.253657i
$544$			1452.94i			0.114511i
$545$			3092.04i			0.243025i
$546$	1212.69	−	4517.51i	0.0950516	−	0.354087i
$547$	−1879.79			−0.146936			−0.0734680	−	0.997298i	$-0.523407\pi$
$547$	−1879.79			−0.146936			−0.0734680	+	0.997298i	$0.523407\pi$
$548$	7855.81			0.612379
$549$	−9029.99	+	15607.3i	−0.701986	+	1.21330i
$550$		−	168.487i		−	0.0130624i
$551$	1143.53			0.0884141
$552$	−2588.07	−	3785.03i	−0.199557	−	0.291851i
$553$	−18910.5			−1.45417
$554$		−	9820.64i		−	0.753139i
$555$	−9184.65	−	2465.54i	−0.702463	−	0.188570i
$556$	−4178.72			−0.318736
$557$	−16141.5			−1.22789			−0.613946	−	0.789348i	$-0.710419\pi$
$557$	−16141.5			−1.22789			−0.613946	+	0.789348i	$0.710419\pi$
$558$	−1532.36	+	2648.50i	−0.116254	+	0.200932i
$559$			4653.62i			0.352106i
$560$			2297.11i			0.173340i
$561$	−49.5720	+	184.666i	−0.00373072	+	0.0138977i
$562$		−	117.402i		−	0.00881195i
$563$	−17042.1			−1.27573			−0.637867	−	0.770146i	$-0.720183\pi$
$563$	−17042.1			−1.27573			−0.637867	+	0.770146i	$0.720183\pi$
$564$	6859.58	+	1841.39i	0.512129	+	0.137476i
$565$	−2499.15			−0.186089
$566$	9220.95			0.684780
$567$	19776.0	−	11369.3i	1.46475	−	0.842092i
$568$	6832.11			0.504699
$569$	8872.04			0.653665			0.326832	−	0.945082i	$-0.394019\pi$
$569$	8872.04			0.653665			0.326832	+	0.945082i	$0.394019\pi$
$570$	−143.970	+	536.319i	−0.0105794	+	0.0394104i
$571$		−	15508.9i		−	1.13665i	−0.822804	−	0.568326i	$-0.807591\pi$
$571$		−	15508.9i		−	1.13665i	0.822804	−	0.568326i	$-0.192409\pi$
$572$	46.6289			0.00340849
$573$	6192.47	−	23068.2i	0.451473	−	1.68183i
$574$			6105.72i			0.443986i
$575$	8704.38	+	7463.38i	0.631300	+	0.541295i
$576$	1495.70	+	865.373i	0.108196	+	0.0625993i
$577$	−6643.87			−0.479355			−0.239678	−	0.970853i	$-0.577042\pi$
$577$	−6643.87			−0.479355			−0.239678	+	0.970853i	$0.577042\pi$
$578$		−	5702.90i		−	0.410397i
$579$	−5414.77	+	20171.2i	−0.388653	+	1.44782i
$580$		−	1802.06i		−	0.129011i
$581$			25466.7i			1.81848i
$582$	1913.99	−	7130.03i	0.136319	−	0.507817i
$583$	−405.862			−0.0288321
$584$		−	956.694i		−	0.0677881i
$585$	−1542.35	−	892.362i	−0.109005	−	0.0630677i
$586$			19767.8i			1.39351i
$587$		−	12618.0i		−	0.887225i	−0.896219	−	0.443612i	$-0.853697\pi$
$587$		−	12618.0i		−	0.887225i	0.896219	−	0.443612i	$-0.146303\pi$
$588$	−3427.90	+	12769.6i	−0.240415	+	0.895597i
$589$		−	659.914i		−	0.0461651i
$590$	342.134			0.0238736
$591$	5229.35	+	1403.77i	0.363971	+	0.0977047i
$592$		−	6382.19i		−	0.443085i
$593$		−	11691.0i		−	0.809600i	−0.914405	−	0.404800i	$-0.867341\pi$
$593$		−	11691.0i		−	0.809600i	0.914405	−	0.404800i	$-0.132659\pi$
$594$	160.576	+	161.019i	0.0110918	+	0.0111224i
$595$			6518.65i			0.449141i
$596$	−4477.08			−0.307699
$597$	−21864.3	−	5869.27i	−1.49890	−	0.402367i
$598$	−2065.49	+	2408.94i	−0.141245	+	0.164731i
$599$		−	4931.72i		−	0.336402i	−0.985753	−	0.168201i	$-0.946204\pi$
$599$		−	4931.72i		−	0.336402i	0.985753	−	0.168201i	$-0.0537957\pi$
$600$	−4173.31	−	1120.29i	−0.283958	−	0.0762260i
$601$	−13788.2			−0.935829			−0.467915	−	0.883774i	$-0.654995\pi$
$601$	−13788.2			−0.935829			−0.467915	+	0.883774i	$0.654995\pi$
$602$		−	20247.2i		−	1.37079i
$603$	10708.3	−	18508.1i	0.723179	−	1.24993i
$604$	3559.92			0.239820
$605$	6103.86			0.410177
$606$	−3765.52	+	14027.4i	−0.252416	+	0.940301i
$607$	26772.2			1.79020			0.895099	−	0.445868i	$-0.147105\pi$
$607$	26772.2			1.79020			0.895099	+	0.445868i	$0.147105\pi$
$608$	−372.675			−0.0248585
$609$	4139.14	−	15419.2i	0.275413	−	1.02597i
$610$	−6128.22			−0.406761
$611$		−	4915.22i		−	0.325447i
$612$	4244.44	+	2455.73i	0.280346	+	0.162201i
$613$			26337.0i			1.73530i	0.497175	+	0.867651i	$0.334371\pi$
$613$			26337.0i			1.73530i	−0.497175	+	0.867651i	$0.665629\pi$
$614$			4964.66i			0.326315i
$615$	2246.46	+	603.043i	0.147295	+	0.0395399i
$616$	−202.875			−0.0132696
$617$	18410.5			1.20126			0.600631	−	0.799527i	$-0.294916\pi$
$617$	18410.5			1.20126			0.600631	+	0.799527i	$0.294916\pi$
$618$	865.473	−	3224.07i	0.0563340	−	0.209856i
$619$		−	16909.8i		−	1.09800i	−0.835821	−	0.549002i	$-0.815008\pi$
$619$		−	16909.8i		−	1.09800i	0.835821	−	0.549002i	$-0.184992\pi$
$620$	−1039.94			−0.0673627
$621$	−15431.5	+	1163.11i	−0.997172	+	0.0751595i
$622$	−5220.67			−0.336543
$623$			14418.3i			0.927221i
$624$	310.040	−	1154.97i	0.0198903	−	0.0740956i
$625$	8173.88			0.523129
$626$	2892.37			0.184668
$627$	−47.3665	−	12.7151i	−0.00301696	−	0.000809877i
$628$			6548.80i			0.416123i
$629$		−	18111.2i		−	1.14808i
$630$	6710.50	+	3882.53i	0.424369	+	0.245529i
$631$			22001.4i			1.38806i	0.719948	+	0.694028i	$0.244166\pi$
$631$			22001.4i			1.38806i	−0.719948	+	0.694028i	$0.755834\pi$
$632$	−4834.74			−0.304297
$633$	−1088.88	+	4056.32i	−0.0683716	+	0.254699i
$634$	9212.77			0.577107
$635$	−12213.5			−0.763271
$636$	−2698.62	+	10052.9i	−0.168250	+	0.626768i
$637$	9150.05			0.569134
$638$	159.154			0.00987611
$639$	11547.5	−	19958.6i	0.714887	−	1.23560i
$640$			587.287i			0.0362728i
$641$	−24385.9			−1.50263			−0.751315	−	0.659943i	$-0.770580\pi$
$641$	−24385.9			−1.50263			−0.751315	+	0.659943i	$0.770580\pi$
$642$	−17121.6	−	4596.14i	−1.05255	−	0.282547i
$643$		−	15326.7i		−	0.940010i	−0.882664	−	0.470005i	$-0.844252\pi$
$643$		−	15326.7i		−	0.940010i	0.882664	−	0.470005i	$-0.155748\pi$
$644$	8986.64	−	10480.9i	0.549881	−	0.641314i
$645$	−7449.50	−	1999.75i	−0.454765	−	0.122078i
$646$	−1057.57			−0.0644108
$647$			2064.11i			0.125423i	0.998032	+	0.0627113i	$0.0199747\pi$
$647$			2064.11i			0.125423i	−0.998032	+	0.0627113i	$0.980025\pi$
$648$	5056.00	−	2906.72i	0.306510	−	0.176214i
$649$			30.2165i			0.00182758i
$650$			2990.37i			0.180449i
$651$	−8898.14	−	2388.63i	−0.535707	−	0.143806i
$652$	−2062.37			−0.123878
$653$			14055.2i			0.842304i	0.906990	+	0.421152i	$0.138374\pi$
$653$			14055.2i			0.842304i	−0.906990	+	0.421152i	$0.861626\pi$
$654$	−1815.75	+	6764.06i	−0.108565	+	0.404428i
$655$		−	1546.63i		−	0.0922625i
$656$			1561.01i			0.0929075i
$657$	−2794.78	−	1616.99i	−0.165958	−	0.0960192i
$658$			21385.3i			1.26700i
$659$	−16192.1			−0.957140			−0.478570	−	0.878050i	$-0.658845\pi$
$659$	−16192.1			−0.957140			−0.478570	+	0.878050i	$0.658845\pi$
$660$	−20.0374	+	74.6434i	−0.00118175	+	0.00440226i
$661$			9266.01i			0.545244i	0.962121	+	0.272622i	$0.0878908\pi$
$661$			9266.01i			0.545244i	−0.962121	+	0.272622i	$0.912109\pi$
$662$			16829.2i			0.988044i
$663$	879.823	−	3277.53i	0.0515377	−	0.191989i
$664$			6510.91i			0.380531i
$665$	−1672.02			−0.0975010
$666$	−18644.2	−	10787.1i	−1.08476	−	0.627613i
$667$	−7049.94	+	8222.18i	−0.409257	+	0.477308i
$668$			7761.81i			0.449571i
$669$	−5661.67	+	21090.9i	−0.327194	+	1.21887i
$670$	7267.23			0.419041
$671$		−	541.230i		−	0.0311385i
$672$	−1348.94	+	5025.07i	−0.0774351	+	0.288462i
$673$	−1920.32			−0.109990			−0.0549948	−	0.998487i	$-0.517514\pi$
$673$	−1920.32			−0.109990			−0.0549948	+	0.998487i	$0.517514\pi$
$674$	9811.88			0.560741
$675$	−10326.3	+	10297.9i	−0.588831	+	0.587212i
$676$	7960.41			0.452914
$677$	16370.4			0.929346			0.464673	−	0.885482i	$-0.346172\pi$
$677$	16370.4			0.929346			0.464673	+	0.885482i	$0.346172\pi$
$678$	−5467.07	−	1467.59i	−0.309678	−	0.0831302i
$679$	22228.5			1.25633
$680$			1666.58i			0.0939862i
$681$	−3639.95	+	13559.6i	−0.204821	+	0.763001i
$682$		−	91.8449i		−	0.00515678i
$683$			33624.6i			1.88376i	0.335950	+	0.941880i	$0.390943\pi$
$683$			33624.6i			1.88376i	−0.335950	+	0.941880i	$0.609057\pi$
$684$	−629.889	+	1088.69i	−0.0352111	+	0.0608584i
$685$	9010.97			0.502615
$686$	−18344.7			−1.02100
$687$	20373.9	+	5469.19i	1.13146	+	0.303730i
$688$		−	5176.48i		−	0.286848i
$689$	7203.39			0.398298
$690$	−2968.64	−	4341.60i	−0.163789	−	0.239539i
$691$	−19803.4			−1.09024			−0.545120	−	0.838358i	$-0.683516\pi$
$691$	−19803.4			−1.09024			−0.545120	+	0.838358i	$0.683516\pi$
$692$		−	14151.3i		−	0.777385i
$693$	−342.896	+	592.656i	−0.0187959	+	0.0324865i
$694$	−526.224			−0.0287827
$695$	−4793.18			−0.261605
$696$	1058.23	−	3942.12i	0.0576323	−	0.214692i
$697$			4429.79i			0.240732i
$698$			15057.7i			0.816536i
$699$	−15936.5	−	4278.00i	−0.862336	−	0.231486i
$700$		−	13010.6i		−	0.702509i
$701$	−8099.55			−0.436399			−0.218200	−	0.975904i	$-0.570018\pi$
$701$	−8099.55			−0.436399			−0.218200	+	0.975904i	$0.570018\pi$
$702$	−2849.96	−	2857.82i	−0.153226	−	0.153649i
$703$	4645.48			0.249228
$704$	−51.8679			−0.00277677
$705$	7868.25	+	2112.16i	0.420334	+	0.112835i
$706$	17755.2			0.946496
$707$	−43731.5			−2.32630
$708$	748.441	+	200.912i	0.0397290	+	0.0106649i
$709$		−	23535.2i		−	1.24666i	−0.781958	−	0.623332i	$-0.785779\pi$
$709$		−	23535.2i		−	1.24666i	0.781958	−	0.623332i	$-0.214221\pi$
$710$	7836.74			0.414236
$711$	−8171.59	+	14123.7i	−0.431025	+	0.744977i
$712$			3686.25i			0.194028i
$713$	4744.88	+	4068.40i	0.249225	+	0.213692i
$714$	−3827.97	+	14260.0i	−0.200642	+	0.747433i
$715$	53.4855			0.00279754
$716$		−	10994.0i		−	0.573831i
$717$	20474.2	+	5496.11i	1.06642	+	0.286270i
$718$		−	11343.2i		−	0.589586i
$719$			19324.1i			1.00232i	0.865355	+	0.501159i	$0.167093\pi$
$719$			19324.1i			1.00232i	−0.865355	+	0.501159i	$0.832907\pi$
$720$	1715.63	+	992.622i	0.0888026	+	0.0513790i
$721$	10051.3			0.519182
$722$			13446.7i			0.693124i
$723$	20749.1	+	5569.92i	1.06731	+	0.286511i
$724$		−	9529.84i		−	0.489190i
$725$			10206.7i			0.522853i
$726$	13352.6	+	3584.39i	0.682592	+	0.183236i
$727$			10458.4i			0.533536i	0.963761	+	0.266768i	$0.0859557\pi$
$727$			10458.4i			0.533536i	−0.963761	+	0.266768i	$0.914044\pi$
$728$	3600.70			0.183312
$729$	54.1985	−	19682.9i	0.00275357	−	0.999996i
$730$		−	1097.37i		−	0.0556377i
$731$		−	14689.6i		−	0.743250i
$732$	−13405.9	−	3598.69i	−0.676907	−	0.181710i
$733$		−	5881.84i		−	0.296386i	−0.988958	−	0.148193i	$-0.952654\pi$
$733$		−	5881.84i		−	0.296386i	0.988958	−	0.148193i	$-0.0473456\pi$
$734$	7476.57			0.375974
$735$	−3931.95	+	14647.4i	−0.197323	+	0.735069i
$736$	2297.56	−	2679.59i	0.115067	−	0.134200i
$737$			641.825i			0.0320786i
$738$	4560.16	+	2638.40i	0.227455	+	0.131600i
$739$	7670.63			0.381825			0.190912	−	0.981607i	$-0.438855\pi$
$739$	7670.63			0.381825			0.190912	+	0.981607i	$0.438855\pi$
$740$		−	7320.67i		−	0.363666i
$741$	840.678	+	225.673i	0.0416776	+	0.0111880i
$742$	−31340.8			−1.55062
$743$	−17622.4			−0.870127			−0.435064	−	0.900400i	$-0.643274\pi$
$743$	−17622.4			−0.870127			−0.435064	+	0.900400i	$0.643274\pi$
$744$	−2274.93	−	610.686i	−0.112101	−	0.0300925i
$745$	−5135.42			−0.252547
$746$	−20072.6			−0.985132
$747$	19020.2	+	11004.6i	0.931612	+	0.539007i
$748$	−147.189			−0.00719487
$749$		−	53378.0i		−	2.60399i
$750$	−10543.4	−	2830.28i	−0.513321	−	0.137796i
$751$			21679.7i			1.05340i	0.850051	+	0.526701i	$0.176571\pi$
$751$			21679.7i			1.05340i	−0.850051	+	0.526701i	$0.823429\pi$
$752$			5467.46i			0.265130i
$753$	5115.51	−	19056.4i	0.247569	−	0.922247i
$754$	−2824.72			−0.136433
$755$	4083.39			0.196834
$756$	12399.7	+	12433.9i	0.596526	+	0.598171i
$757$			5958.14i			0.286067i	0.989718	+	0.143033i	$0.0456856\pi$
$757$			5958.14i			0.286067i	−0.989718	+	0.143033i	$0.954314\pi$
$758$	7882.48			0.377711
$759$	383.440	−	262.183i	0.0183373	−	0.0125384i
$760$	−427.475			−0.0204028
$761$			25113.0i			1.19625i	0.801403	+	0.598124i	$0.204087\pi$
$761$			25113.0i			1.19625i	−0.801403	+	0.598124i	$0.795913\pi$
$762$	−26717.8	−	7172.16i	−1.27019	−	0.340971i
$763$	−21087.5			−1.00055
$764$	18386.6			0.870687
$765$	4868.57	+	2816.83i	0.230096	+	0.133128i
$766$		−	18833.8i		−	0.888371i
$767$		−	536.293i		−	0.0252470i
$768$	−344.875	+	1284.73i	−0.0162039	+	0.0603629i
$769$		−	29527.5i		−	1.38464i	−0.721589	−	0.692322i	$-0.756588\pi$
$769$		−	29527.5i		−	1.38464i	0.721589	−	0.692322i	$-0.243412\pi$
$770$	−232.707			−0.0108911
$771$	31456.5	+	8444.21i	1.46936	+	0.394437i
$772$	−16077.5			−0.749537
$773$	36.2486			0.00168664			0.000843320	−	1.00000i	$-0.499732\pi$
$773$	36.2486			0.00168664			0.000843320		1.00000i	$0.499732\pi$
$774$	−15122.0	−	8749.19i	−0.702258	−	0.406309i
$775$	5890.13			0.273006
$776$	5683.02			0.262898
$777$	16814.8	−	62638.7i	0.776354	−	2.89208i
$778$			7518.82i			0.346481i
$779$	−1136.23			−0.0522590
$780$	355.630	−	1324.80i	0.0163251	−	0.0608146i
$781$			692.124i			0.0317108i
$782$	6519.94	−	7604.07i	0.298149	−	0.347725i
$783$	−9727.47	−	9754.30i	−0.443974	−	0.445198i
$784$	−10178.1			−0.463652
$785$			7511.77i			0.341537i
$786$	908.234	−	3383.36i	0.0412158	−	0.153538i
$787$		−	12989.0i		−	0.588319i	−0.955756	−	0.294160i	$-0.904960\pi$
$787$		−	12989.0i		−	0.588319i	0.955756	−	0.294160i	$-0.0950397\pi$
$788$			4168.07i			0.188428i
$789$	−2910.89	+	10843.7i	−0.131344	+	0.489284i
$790$	−5545.67			−0.249754
$791$		−	17044.0i		−	0.766139i
$792$	−87.6662	+	151.521i	−0.00393318	+	0.00679806i
$793$			9605.96i			0.430161i
$794$		−	14111.2i		−	0.630717i
$795$	−3095.44	+	11531.2i	−0.138093	+	0.514425i
$796$		−	17427.0i		−	0.775985i
$797$	23810.8			1.05825			0.529123	−	0.848545i	$-0.322521\pi$
$797$	23810.8			1.05825			0.529123	+	0.848545i	$0.322521\pi$
$798$	−3657.66	−	981.866i	−0.162255	−	0.0435560i
$799$			15515.4i			0.686977i
$800$		−	3326.35i		−	0.147006i
$801$	10768.6	+	6230.43i	0.475018	+	0.274833i
$802$		−	20843.1i		−	0.917699i
$803$	96.9173			0.00425920
$804$	15897.6	+	4267.56i	0.697343	+	0.187196i
$805$	10308.1	−	12022.1i	0.451319	−	0.526364i
$806$			1630.10i			0.0712379i
$807$	42155.9	+	11316.4i	1.83886	+	0.493625i
$808$	−11180.6			−0.486796
$809$		−	312.303i		−	0.0135723i	−0.999977	−	0.00678614i	$-0.997840\pi$
$809$		−	312.303i		−	0.0135723i	0.999977	−	0.00678614i	$-0.00216011\pi$
$810$	5799.47	−	3334.14i	0.251571	−	0.144629i
$811$	−5600.26			−0.242481			−0.121240	−	0.992623i	$-0.538687\pi$
$811$	−5600.26			−0.242481			−0.121240	+	0.992623i	$0.538687\pi$
$812$	12289.9			0.531147
$813$	−2501.78	+	9319.65i	−0.107923	+	0.402035i
$814$	646.545			0.0278395
$815$	−2365.63			−0.101674
$816$	−978.674	+	3645.77i	−0.0419858	+	0.156406i
$817$	3767.86			0.161347
$818$			5308.48i			0.226903i
$819$	6085.84	−	10518.7i	0.259654	−	0.448782i
$820$			1790.55i			0.0762547i
$821$			12701.4i			0.539927i	0.962870	+	0.269964i	$0.0870117\pi$
$821$			12701.4i			0.539927i	−0.962870	+	0.269964i	$0.912988\pi$
$822$	19712.1	+	5291.54i	0.836422	+	0.224530i
$823$	−10746.5			−0.455165			−0.227583	−	0.973759i	$-0.573082\pi$
$823$	−10746.5			−0.455165			−0.227583	+	0.973759i	$0.573082\pi$
$824$	2569.76			0.108643
$825$	113.490	−	422.775i	0.00478936	−	0.0178414i
$826$			2333.33i			0.0982892i
$827$	24493.5			1.02989			0.514946	−	0.857223i	$-0.327812\pi$
$827$	24493.5			1.02989			0.514946	+	0.857223i	$0.327812\pi$
$828$	−3944.56	−	11240.8i	−0.165559	−	0.471795i
$829$	−40845.3			−1.71124			−0.855620	−	0.517605i	$-0.826824\pi$
$829$	−40845.3			−1.71124			−0.855620	+	0.517605i	$0.826824\pi$
$830$			7468.31i			0.312324i
$831$	6615.02	−	24642.3i	0.276140	−	1.02868i
$832$	920.570			0.0383594
$833$	−28883.1			−1.20137
$834$	−10485.4	−	2814.71i	−0.435348	−	0.116865i
$835$			8903.15i			0.368990i
$836$		−	37.7537i		−	0.00156189i
$837$	−5629.04	+	5613.56i	−0.232459	+	0.231820i
$838$			24412.9i			1.00636i
$839$	35506.8			1.46106			0.730531	−	0.682879i	$-0.239272\pi$
$839$	35506.8			1.46106			0.730531	+	0.682879i	$0.239272\pi$
$840$	−1547.29	+	5763.99i	−0.0635555	+	0.236758i
$841$	14747.7			0.604686
$842$	10646.6			0.435756
$843$	79.0802	−	294.590i	0.00323092	−	0.0120359i
$844$	−3233.11			−0.131858
$845$	9130.95			0.371733
$846$	15972.0	+	9241.00i	0.649089	+	0.375546i
$847$			41627.9i			1.68872i
$848$	−8012.72			−0.324479
$849$	23137.6	+	6211.08i	0.935312	+	0.251076i
$850$		−	9439.42i		−	0.380905i
$851$	−28639.6	+	33401.7i	−1.15365	+	1.34547i
$852$	17143.4	+	4602.00i	0.689347	+	0.185049i
$853$	−21792.6			−0.874754			−0.437377	−	0.899278i	$-0.644093\pi$
$853$	−21792.6			−0.874754			−0.437377	+	0.899278i	$0.644093\pi$
$854$		−	41794.0i		−	1.67466i
$855$	−722.511	+	1248.78i	−0.0288998	+	0.0499501i
$856$		−	13646.8i		−	0.544906i
$857$		−	2665.02i		−	0.106226i	−0.998589	−	0.0531128i	$-0.983086\pi$
$857$		−	2665.02i		−	0.106226i	0.998589	−	0.0531128i	$-0.0169143\pi$
$858$	117.003	+	31.4085i	0.00465550	+	0.00124973i
$859$	6311.26			0.250684			0.125342	−	0.992114i	$-0.459997\pi$
$859$	6311.26			0.250684			0.125342	+	0.992114i	$0.459997\pi$
$860$		−	5937.65i		−	0.235433i
$861$	−4112.71	+	15320.7i	−0.162788	+	0.606421i
$862$		−	24350.0i		−	0.962141i
$863$			15275.7i			0.602537i	0.953539	+	0.301268i	$0.0974100\pi$
$863$			15275.7i			0.602537i	−0.953539	+	0.301268i	$0.902590\pi$
$864$	3170.17	+	3178.91i	0.124828	+	0.125172i
$865$		−	16232.2i		−	0.638046i
$866$	−31886.6			−1.25121
$867$	3841.38	−	14309.9i	0.150473	−	0.560544i
$868$		−	7092.30i		−	0.277337i
$869$		−	489.781i		−	0.0191193i
$870$	1213.84	−	4521.80i	0.0473022	−	0.176211i
$871$		−	11391.4i		−	0.443147i
$872$	−5391.32			−0.209373
$873$	9605.34	−	16601.7i	0.372384	−	0.643623i
$874$	1950.43	+	1672.35i	0.0754853	+	0.0647233i
$875$		−	32869.9i		−	1.26995i
$876$	644.413	−	2400.57i	0.0248547	−	0.0925889i
$877$	−11570.3			−0.445497			−0.222748	−	0.974876i	$-0.571503\pi$
$877$	−11570.3			−0.445497			−0.222748	+	0.974876i	$0.571503\pi$
$878$		−	31056.2i		−	1.19373i
$879$	−13315.2	+	49602.1i	−0.510935	+	1.90334i
$880$	−59.4948			−0.00227906
$881$	7206.97			0.275606			0.137803	−	0.990460i	$-0.455996\pi$
$881$	7206.97			0.275606			0.137803	+	0.990460i	$0.455996\pi$
$882$	−17202.8	+	29733.1i	−0.656745	+	1.13511i
$883$	20426.2			0.778479			0.389240	−	0.921137i	$-0.372738\pi$
$883$	20426.2			0.778479			0.389240	+	0.921137i	$0.372738\pi$
$884$	2612.36			0.0993929
$885$	858.496	+	230.456i	0.0326079	+	0.00875331i
$886$	−22193.2			−0.841528
$887$		−	18716.2i		−	0.708489i	−0.935153	−	0.354244i	$-0.884738\pi$
$887$		−	18716.2i		−	0.708489i	0.935153	−	0.354244i	$-0.115262\pi$
$888$	4298.94	−	16014.5i	0.162458	−	0.605191i
$889$		−	83295.0i		−	3.14244i
$890$			4228.30i			0.159250i
$891$	294.464	+	512.196i	0.0110717	+	0.0192584i
$892$	−16810.6			−0.631010
$893$	−3979.66			−0.149131
$894$	−11234.1	−	3015.69i	−0.420273	−	0.112819i
$895$		−	12610.6i		−	0.470977i
$896$	−4005.26			−0.149337
$897$	−6805.44	+	4653.33i	−0.253319	+	0.173211i
$898$	21153.8			0.786093
$899$			5563.84i			0.206412i
$900$	−9717.23	−	5622.15i	−0.359898	−	0.208228i
$901$	−22738.2			−0.840755
$902$	−158.138			−0.00583748
$903$	13638.2	−	50805.0i	0.502602	−	1.87230i
$904$		−	4357.55i		−	0.160321i
$905$		−	10931.2i		−	0.401507i
$906$	8932.69	+	2397.90i	0.327559	+	0.0879304i
$907$		−	15153.0i		−	0.554736i	−0.960764	−	0.277368i	$-0.910538\pi$
$907$		−	15153.0i		−	0.554736i	0.960764	−	0.277368i	$-0.0894621\pi$
$908$	−10807.7			−0.395007
$909$	−18897.2	+	32661.6i	−0.689527	+	1.19177i
$910$	4130.17			0.150455
$911$	16030.4			0.582997			0.291498	−	0.956571i	$-0.405846\pi$
$911$	16030.4			0.582997			0.291498	+	0.956571i	$0.405846\pi$
$912$	−935.132	−	251.028i	−0.0339532	−	0.00911443i
$913$	−659.585			−0.0239092
$914$	11612.9			0.420265
$915$	−15377.2	−	4127.86i	−0.555578	−	0.149140i
$916$			16239.1i			0.585759i
$917$	10547.9			0.379851
$918$	8996.19	+	9021.00i	0.323441	+	0.324333i
$919$			18080.2i			0.648978i	0.945889	+	0.324489i	$0.105192\pi$
$919$			18080.2i			0.648978i	−0.945889	+	0.324489i	$0.894808\pi$
$920$	2635.41	−	3073.62i	0.0944421	−	0.110146i
$921$	−3344.11	+	12457.5i	−0.119644	+	0.445700i
$922$	26667.0			0.952529
$923$		−	12284.1i		−	0.438066i
$924$	−509.062	−	136.653i	−0.0181244	−	0.00486533i
$925$			41463.8i			1.47386i
$926$			20138.3i			0.714672i
$927$	4343.36	−	7506.99i	0.153888	−	0.265978i
$928$	3142.09			0.111147
$929$		−	4075.74i		−	0.143940i	−0.997407	−	0.0719702i	$-0.977071\pi$
$929$		−	4075.74i		−	0.143940i	0.997407	−	0.0719702i	$-0.0229287\pi$
$930$	−2609.45	−	700.484i	−0.0920078	−	0.0246987i
$931$		−	7408.44i		−	0.260797i
$932$		−	12702.2i		−	0.446433i
$933$	−13099.9	−	3516.55i	−0.459670	−	0.123394i
$934$		−	8923.20i		−	0.312608i
$935$	−168.832			−0.00590525
$936$	1555.93	−	2689.25i	0.0543346	−	0.0939112i
$937$			3607.58i			0.125779i	0.998021	+	0.0628893i	$0.0200315\pi$
$937$			3607.58i			0.125779i	−0.998021	+	0.0628893i	$0.979968\pi$
$938$			49562.0i			1.72522i
$939$	7257.64	+	1948.25i	0.252230	+	0.0677089i
$940$			6271.42i			0.217608i
$941$	−1896.10			−0.0656864			−0.0328432	−	0.999461i	$-0.510456\pi$
$941$	−1896.10			−0.0656864			−0.0328432	+	0.999461i	$0.510456\pi$
$942$	−4411.16	+	16432.5i	−0.152573	+	0.568365i
$943$	7004.92	−	8169.69i	0.241900	−	0.282123i
$944$			596.548i			0.0205678i
$945$	14223.1	+	14262.3i	0.489604	+	0.490954i
$946$	524.400			0.0180230
$947$		−	16331.1i		−	0.560391i	−0.959943	−	0.280195i	$-0.909601\pi$
$947$		−	16331.1i		−	0.560391i	0.959943	−	0.280195i	$-0.0903992\pi$
$948$	−12131.5	−	3256.60i	−0.415626	−	0.111571i
$949$	−1720.12			−0.0588384
$950$	2421.19			0.0826882
$951$	23117.0	+	6205.56i	0.788245	+	0.211597i
$952$	−11366.0			−0.386947
$953$	−541.435			−0.0184038			−0.00920190	−	0.999958i	$-0.502929\pi$
$953$	−541.435			−0.0184038			−0.00920190	+	0.999958i	$0.502929\pi$
$954$	−13543.0	+	23407.4i	−0.459611	+	0.794386i
$955$	21090.3			0.714624
$956$			16319.0i			0.552087i
$957$	399.355	+	107.203i	0.0134894	+	0.00362110i
$958$			8355.34i			0.281784i
$959$			61454.2i			2.06930i
$960$	−395.587	+	1473.64i	−0.0132995	+	0.0495434i
$961$	−26580.2			−0.892223
$962$	−11475.1			−0.384587
$963$	−39866.3	−	23065.7i	−1.33403	−	0.771838i
$964$			16538.2i			0.552551i
$965$	−18441.6			−0.615189
$966$	29609.4	−	20245.9i	0.986198	−	0.674328i
$967$	31482.9			1.04697			0.523486	−	0.852034i	$-0.324631\pi$
$967$	31482.9			1.04697			0.523486	+	0.852034i	$0.324631\pi$
$968$			10642.7i			0.353379i
$969$	−2653.69	−	712.359i	−0.0879760	−	0.0236164i
$970$	6518.68			0.215775
$971$	20128.3			0.665239			0.332619	−	0.943061i	$-0.392068\pi$
$971$	20128.3			0.665239			0.332619	+	0.943061i	$0.392068\pi$
$972$	14644.6	−	3888.03i	0.483259	−	0.128301i
$973$		−	32689.1i		−	1.07705i
$974$			19666.1i			0.646964i
$975$	−2014.27	+	7503.57i	−0.0661622	+	0.246468i
$976$		−	10685.2i		−	0.350436i
$977$	−17316.6			−0.567050			−0.283525	−	0.958965i	$-0.591504\pi$
$977$	−17316.6			−0.567050			−0.283525	+	0.958965i	$0.591504\pi$
$978$	−5174.97	−	1389.18i	−0.169200	−	0.0454202i
$979$	−373.434			−0.0121910
$980$	−11674.7			−0.380547
$981$	−9112.31	+	15749.6i	−0.296569	+	0.512585i
$982$	12820.4			0.416615
$983$	46354.8			1.50406			0.752029	−	0.659130i	$-0.229075\pi$
$983$	46354.8			1.50406			0.752029	+	0.659130i	$0.229075\pi$
$984$	−1051.47	+	3916.96i	−0.0340647	+	0.126898i
$985$			4780.97i			0.154654i
$986$	8916.51			0.287992
$987$	−14404.8	+	53660.9i	−0.464549	+	1.73054i
$988$			670.066i			0.0215766i
$989$	−23229.0	+	27091.5i	−0.746856	+	0.871041i
$990$	−100.557	+	173.801i	−0.00322820	+	0.00557956i
$991$	16767.6			0.537478			0.268739	−	0.963213i	$-0.413393\pi$
$991$	16767.6			0.537478			0.268739	+	0.963213i	$0.413393\pi$
$992$		−	1813.25i		−	0.0580349i
$993$	−11335.9	+	42228.5i	−0.362269	+	1.34953i
$994$			53446.0i			1.70544i
$995$		−	19989.6i		−	0.636896i
$996$	−4385.64	+	16337.4i	−0.139522	+	0.519751i
$997$	28563.5			0.907338			0.453669	−	0.891170i	$-0.350115\pi$
$997$	28563.5			0.907338			0.453669	+	0.891170i	$0.350115\pi$
$998$		−	22975.7i		−	0.728740i
$999$	−39516.8	−	39625.8i	−1.25151	−	1.25496i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	138.4.d.a.137.17	yes	24
3.2	odd	2	inner	138.4.d.a.137.6	yes	24
23.22	odd	2	inner	138.4.d.a.137.18	yes	24
69.68	even	2	inner	138.4.d.a.137.5	✓	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
138.4.d.a.137.5	✓	24	69.68	even	2	inner
138.4.d.a.137.6	yes	24	3.2	odd	2	inner
138.4.d.a.137.17	yes	24	1.1	even	1	trivial
138.4.d.a.137.18	yes	24	23.22	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:	\( N \)	\(=\)	\( 138 = 2 \cdot 3 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	138.d (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+2.00000i q^{2} +(-1.34717 + 5.01848i) q^{3} -4.00000 q^{4} -4.58818 q^{5} +(-10.0370 - 2.69433i) q^{6} -31.2911i q^{7} -8.00000i q^{8} +(-23.3703 - 13.5215i) q^{9} +O(q^{10})\)	\(q+2.00000i q^{2} +(-1.34717 + 5.01848i) q^{3} -4.00000 q^{4} -4.58818 q^{5} +(-10.0370 - 2.69433i) q^{6} -31.2911i q^{7} -8.00000i q^{8} +(-23.3703 - 13.5215i) q^{9} -9.17636i q^{10} +0.810436 q^{11} +(5.38867 - 20.0739i) q^{12} -14.3839 q^{13} +62.5821 q^{14} +(6.18104 - 23.0257i) q^{15} +16.0000 q^{16} +45.4043 q^{17} +(27.0429 - 46.7406i) q^{18} +11.6461i q^{19} +18.3527 q^{20} +(157.034 + 42.1543i) q^{21} +1.62087i q^{22} +(-83.7373 - 71.7988i) q^{23} +(40.1478 + 10.7773i) q^{24} -103.949 q^{25} -28.7678i q^{26} +(99.3408 - 99.0677i) q^{27} +125.164i q^{28} -98.1902i q^{29} +(46.0514 + 12.3621i) q^{30} -56.6639 q^{31} +32.0000i q^{32} +(-1.09179 + 4.06716i) q^{33} +90.8086i q^{34} +143.569i q^{35} +(93.4811 + 54.0858i) q^{36} -398.887i q^{37} -23.2922 q^{38} +(19.3775 - 72.1854i) q^{39} +36.7055i q^{40} +97.5633i q^{41} +(-84.3085 + 314.067i) q^{42} -323.530i q^{43} -3.24174 q^{44} +(107.227 + 62.0389i) q^{45} +(143.598 - 167.475i) q^{46} +341.716i q^{47} +(-21.5547 + 80.2957i) q^{48} -636.131 q^{49} -207.897i q^{50} +(-61.1671 + 227.861i) q^{51} +57.5356 q^{52} -500.795 q^{53} +(198.135 + 198.682i) q^{54} -3.71843 q^{55} -250.329 q^{56} +(-58.4457 - 15.6892i) q^{57} +196.380 q^{58} +37.2842i q^{59} +(-24.7242 + 92.1028i) q^{60} -667.826i q^{61} -113.328i q^{62} +(-423.101 + 731.281i) q^{63} -64.0000 q^{64} +65.9960 q^{65} +(-8.13431 - 2.18358i) q^{66} +791.951i q^{67} -181.617 q^{68} +(473.129 - 323.509i) q^{69} -287.138 q^{70} +854.014i q^{71} +(-108.172 + 186.962i) q^{72} +119.587 q^{73} +797.774 q^{74} +(140.036 - 521.664i) q^{75} -46.5844i q^{76} -25.3594i q^{77} +(144.371 + 38.7550i) q^{78} -604.342i q^{79} -73.4109 q^{80} +(363.340 + 632.001i) q^{81} -195.127 q^{82} -813.864 q^{83} +(-628.134 - 168.617i) q^{84} -208.323 q^{85} +647.059 q^{86} +(492.766 + 132.279i) q^{87} -6.48349i q^{88} -460.781 q^{89} +(-124.078 + 214.454i) q^{90} +450.088i q^{91} +(334.949 + 287.195i) q^{92} +(76.3357 - 284.367i) q^{93} -683.432 q^{94} -53.4344i q^{95} +(-160.591 - 43.1093i) q^{96} +710.377i q^{97} -1272.26i q^{98} +(-18.9401 - 10.9583i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 8 q^{3} - 96 q^{4} + 8 q^{6} + 36 q^{9}+O(q^{10}) \) 24 * q + 8 * q^3 - 96 * q^4 + 8 * q^6 + 36 * q^9	\( 24 q + 8 q^{3} - 96 q^{4} + 8 q^{6} + 36 q^{9} - 32 q^{12} + 96 q^{13} + 384 q^{16} + 128 q^{18} - 32 q^{24} + 144 q^{25} + 188 q^{27} + 72 q^{31} - 144 q^{36} - 660 q^{39} - 96 q^{46} + 128 q^{48} - 504 q^{49} - 384 q^{52} + 88 q^{54} - 672 q^{55} + 816 q^{58} - 1536 q^{64} + 352 q^{69} + 624 q^{70} - 512 q^{72} - 2688 q^{73} - 1072 q^{75} + 80 q^{78} - 2356 q^{81} + 1344 q^{82} + 4872 q^{85} + 3748 q^{87} - 2924 q^{93} - 1296 q^{94} + 128 q^{96}+O(q^{100}) \) 24 * q + 8 * q^3 - 96 * q^4 + 8 * q^6 + 36 * q^9 - 32 * q^12 + 96 * q^13 + 384 * q^16 + 128 * q^18 - 32 * q^24 + 144 * q^25 + 188 * q^27 + 72 * q^31 - 144 * q^36 - 660 * q^39 - 96 * q^46 + 128 * q^48 - 504 * q^49 - 384 * q^52 + 88 * q^54 - 672 * q^55 + 816 * q^58 - 1536 * q^64 + 352 * q^69 + 624 * q^70 - 512 * q^72 - 2688 * q^73 - 1072 * q^75 + 80 * q^78 - 2356 * q^81 + 1344 * q^82 + 4872 * q^85 + 3748 * q^87 - 2924 * q^93 - 1296 * q^94 + 128 * q^96

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