LMFDB - Embedded newform 138.4.d.a.137.15

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			137.15
Character	$\chi$	$=$	138.137
Dual form			138.4.d.a.137.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+2.00000i q^{2} +(-3.26555 - 4.04180i) q^{3} -4.00000 q^{4} -6.82316 q^{5} +(8.08360 - 6.53111i) q^{6} +3.09939i q^{7} -8.00000i q^{8} +(-5.67231 + 26.3974i) q^{9} +O(q^{10})$	\(q+2.00000i q^{2} +(-3.26555 - 4.04180i) q^{3} -4.00000 q^{4} -6.82316 q^{5} +(8.08360 - 6.53111i) q^{6} +3.09939i q^{7} -8.00000i q^{8} +(-5.67231 + 26.3974i) q^{9} -13.6463i q^{10} +50.4927 q^{11} +(13.0622 + 16.1672i) q^{12} +6.18710 q^{13} -6.19878 q^{14} +(22.2814 + 27.5779i) q^{15} +16.0000 q^{16} +118.176 q^{17} +(-52.7949 - 11.3446i) q^{18} +92.8440i q^{19} +27.2926 q^{20} +(12.5271 - 10.1212i) q^{21} +100.985i q^{22} +(109.125 - 16.0867i) q^{23} +(-32.3344 + 26.1244i) q^{24} -78.4445 q^{25} +12.3742i q^{26} +(125.216 - 63.2760i) q^{27} -12.3976i q^{28} +108.478i q^{29} +(-55.1557 + 44.5628i) q^{30} -49.4045 q^{31} +32.0000i q^{32} +(-164.887 - 204.082i) q^{33} +236.353i q^{34} -21.1476i q^{35} +(22.6892 - 105.590i) q^{36} -55.2490i q^{37} -185.688 q^{38} +(-20.2043 - 25.0070i) q^{39} +54.5853i q^{40} -136.636i q^{41} +(20.2425 + 25.0542i) q^{42} +211.875i q^{43} -201.971 q^{44} +(38.7031 - 180.114i) q^{45} +(32.1734 + 218.250i) q^{46} +451.774i q^{47} +(-52.2489 - 64.6688i) q^{48} +333.394 q^{49} -156.889i q^{50} +(-385.912 - 477.646i) q^{51} -24.7484 q^{52} +265.883 q^{53} +(126.552 + 250.433i) q^{54} -344.520 q^{55} +24.7951 q^{56} +(375.257 - 303.187i) q^{57} -216.957 q^{58} -653.373i q^{59} +(-89.1256 - 110.311i) q^{60} -687.646i q^{61} -98.8090i q^{62} +(-81.8160 - 17.5807i) q^{63} -64.0000 q^{64} -42.2156 q^{65} +(408.163 - 329.774i) q^{66} +10.5578i q^{67} -472.706 q^{68} +(-421.372 - 388.529i) q^{69} +42.2953 q^{70} +314.914i q^{71} +(211.180 + 45.3785i) q^{72} +795.294 q^{73} +110.498 q^{74} +(256.165 + 317.057i) q^{75} -371.376i q^{76} +156.497i q^{77} +(50.0141 - 40.4086i) q^{78} +1223.44i q^{79} -109.171 q^{80} +(-664.650 - 299.469i) q^{81} +273.272 q^{82} -403.836 q^{83} +(-50.1085 + 40.4849i) q^{84} -806.337 q^{85} -423.751 q^{86} +(438.448 - 354.242i) q^{87} -403.942i q^{88} -29.6522 q^{89} +(360.228 + 77.4061i) q^{90} +19.1762i q^{91} +(-436.499 + 64.3467i) q^{92} +(161.333 + 199.683i) q^{93} -903.547 q^{94} -633.489i q^{95} +(129.338 - 104.498i) q^{96} +1165.71i q^{97} +666.788i q^{98} +(-286.410 + 1332.88i) 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
$3$	−3.26555	−	4.04180i	−0.628456	−	0.777845i
$3$	−3.26555	−	4.04180i	−0.628456	−	0.777845i
$4$	−4.00000			−0.500000
$5$	−6.82316			−0.610282			−0.305141	−	0.952307i	$-0.598704\pi$
$5$	−6.82316			−0.610282			−0.305141	+	0.952307i	$0.598704\pi$
$6$	8.08360	−	6.53111i	0.550019	−	0.444386i
$7$			3.09939i			0.167351i	0.996493	+	0.0836757i	$0.0266660\pi$
$7$			3.09939i			0.167351i	−0.996493	+	0.0836757i	$0.973334\pi$
$8$		−	8.00000i		−	0.353553i
$9$	−5.67231	+	26.3974i	−0.210085	+	0.977683i
$10$		−	13.6463i		−	0.431535i
$11$	50.4927			1.38401			0.692006	−	0.721892i	$-0.256727\pi$
$11$	50.4927			1.38401			0.692006	+	0.721892i	$0.256727\pi$
$12$	13.0622	+	16.1672i	0.314228	+	0.388922i
$13$	6.18710			0.132000			0.0659998	−	0.997820i	$-0.478976\pi$
$13$	6.18710			0.132000			0.0659998	+	0.997820i	$0.478976\pi$
$14$	−6.19878			−0.118335
$15$	22.2814	+	27.5779i	0.383536	+	0.474705i
$16$	16.0000			0.250000
$17$	118.176			1.68600			0.843000	−	0.537913i	$-0.180787\pi$
$17$	118.176			1.68600			0.843000	+	0.537913i	$0.180787\pi$
$18$	−52.7949	−	11.3446i	−0.691326	−	0.148553i
$19$			92.8440i			1.12105i	0.828139	+	0.560523i	$0.189400\pi$
$19$			92.8440i			1.12105i	−0.828139	+	0.560523i	$0.810600\pi$
$20$	27.2926			0.305141
$21$	12.5271	−	10.1212i	0.130173	−	0.105173i
$22$			100.985i			0.978644i
$23$	109.125	−	16.0867i	0.989308	−	0.145839i
$23$	109.125	−	16.0867i	0.989308	−	0.145839i
$24$	−32.3344	+	26.1244i	−0.275010	+	0.222193i
$25$	−78.4445			−0.627556
$26$			12.3742i			0.0933377i
$27$	125.216	−	63.2760i	0.892515	−	0.451017i
$28$		−	12.3976i		−	0.0836757i
$29$			108.478i			0.694618i	0.937751	+	0.347309i	$0.112904\pi$
$29$			108.478i			0.694618i	−0.937751	+	0.347309i	$0.887096\pi$
$30$	−55.1557	+	44.5628i	−0.335667	+	0.271201i
$31$	−49.4045			−0.286236			−0.143118	−	0.989706i	$-0.545713\pi$
$31$	−49.4045			−0.286236			−0.143118	+	0.989706i	$0.545713\pi$
$32$			32.0000i			0.176777i
$33$	−164.887	−	204.082i	−0.869791	−	1.07655i
$34$			236.353i			1.19218i
$35$		−	21.1476i		−	0.102131i
$36$	22.6892	−	105.590i	0.105043	−	0.488842i
$37$		−	55.2490i		−	0.245483i	−0.992439	−	0.122742i	$-0.960831\pi$
$37$		−	55.2490i		−	0.245483i	0.992439	−	0.122742i	$-0.0391686\pi$
$38$	−185.688			−0.792699
$39$	−20.2043	−	25.0070i	−0.0829559	−	0.102675i
$40$			54.5853i			0.215767i
$41$		−	136.636i		−	0.520463i	−0.965546	−	0.260231i	$-0.916201\pi$
$41$		−	136.636i		−	0.520463i	0.965546	−	0.260231i	$-0.0837989\pi$
$42$	20.2425	+	25.0542i	0.0743685	+	0.0920465i
$43$			211.875i			0.751411i	0.926739	+	0.375706i	$0.122600\pi$
$43$			211.875i			0.751411i	−0.926739	+	0.375706i	$0.877400\pi$
$44$	−201.971			−0.692006
$45$	38.7031	−	180.114i	0.128211	−	0.596662i
$46$	32.1734	+	218.250i	0.103124	+	0.699547i
$47$			451.774i			1.40208i	0.713120	+	0.701042i	$0.247281\pi$
$47$			451.774i			1.40208i	−0.713120	+	0.701042i	$0.752719\pi$
$48$	−52.2489	−	64.6688i	−0.157114	−	0.194461i
$49$	333.394			0.971994
$50$		−	156.889i		−	0.443749i
$51$	−385.912	−	477.646i	−1.05958	−	1.31145i
$52$	−24.7484			−0.0659998
$53$	265.883			0.689091			0.344545	−	0.938770i	$-0.388033\pi$
$53$	265.883			0.689091			0.344545	+	0.938770i	$0.388033\pi$
$54$	126.552	+	250.433i	0.318917	+	0.631104i
$55$	−344.520			−0.844638
$56$	24.7951			0.0591676
$57$	375.257	−	303.187i	0.872000	−	0.704528i
$58$	−216.957			−0.491169
$59$		−	653.373i		−	1.44173i	−0.693077	−	0.720864i	$-0.743745\pi$
$59$		−	653.373i		−	1.44173i	0.693077	−	0.720864i	$-0.256255\pi$
$60$	−89.1256	−	110.311i	−0.191768	−	0.237352i
$61$		−	687.646i		−	1.44335i	−0.692234	−	0.721673i	$-0.743374\pi$
$61$		−	687.646i		−	1.44335i	0.692234	−	0.721673i	$-0.256626\pi$
$62$		−	98.8090i		−	0.202399i
$63$	−81.8160	−	17.5807i	−0.163617	−	0.0351581i
$64$	−64.0000			−0.125000
$65$	−42.2156			−0.0805569
$66$	408.163	−	329.774i	0.761233	−	0.615035i
$67$			10.5578i			0.0192513i	0.999954	+	0.00962564i	$0.00306398\pi$
$67$			10.5578i			0.0192513i	−0.999954	+	0.00962564i	$0.996936\pi$
$68$	−472.706			−0.843000
$69$	−421.372	−	388.529i	−0.735177	−	0.677875i
$70$	42.2953			0.0722179
$71$			314.914i			0.526385i	0.964743	+	0.263193i	$0.0847755\pi$
$71$			314.914i			0.526385i	−0.964743	+	0.263193i	$0.915224\pi$
$72$	211.180	+	45.3785i	0.345663	+	0.0742764i
$73$	795.294			1.27510			0.637549	−	0.770410i	$-0.279949\pi$
$73$	795.294			1.27510			0.637549	+	0.770410i	$0.279949\pi$
$74$	110.498			0.173583
$75$	256.165	+	317.057i	0.394391	+	0.488141i
$76$		−	371.376i		−	0.560523i
$77$			156.497i			0.231616i
$78$	50.0141	−	40.4086i	0.0726023	−	0.0586587i
$79$			1223.44i			1.74238i	0.490949	+	0.871188i	$0.336650\pi$
$79$			1223.44i			1.74238i	−0.490949	+	0.871188i	$0.663350\pi$
$80$	−109.171			−0.152570
$81$	−664.650	−	299.469i	−0.911728	−	0.410794i
$82$	273.272			0.368023
$83$	−403.836			−0.534058			−0.267029	−	0.963688i	$-0.586042\pi$
$83$	−403.836			−0.534058			−0.267029	+	0.963688i	$0.586042\pi$
$84$	−50.1085	+	40.4849i	−0.0650867	+	0.0525865i
$85$	−806.337			−1.02894
$86$	−423.751			−0.531328
$87$	438.448	−	354.242i	0.540305	−	0.436537i
$88$		−	403.942i		−	0.489322i
$89$	−29.6522			−0.0353161			−0.0176580	−	0.999844i	$-0.505621\pi$
$89$	−29.6522			−0.0353161			−0.0176580	+	0.999844i	$0.505621\pi$
$90$	360.228	+	77.4061i	0.421904	+	0.0906591i
$91$			19.1762i			0.0220903i
$92$	−436.499	+	64.3467i	−0.494654	+	0.0729197i
$93$	161.333	+	199.683i	0.179887	+	0.222647i
$94$	−903.547			−0.991423
$95$		−	633.489i		−	0.684154i
$96$	129.338	−	104.498i	0.137505	−	0.111096i
$97$			1165.71i			1.22020i	0.792324	+	0.610101i	$0.208871\pi$
$97$			1165.71i			1.22020i	−0.792324	+	0.610101i	$0.791129\pi$
$98$			666.788i			0.687303i
$99$	−286.410	+	1332.88i	−0.290761	+	1.35313i
$100$	313.778			0.313778
$101$		−	35.8082i		−	0.0352777i	−0.999844	−	0.0176389i	$-0.994385\pi$
$101$		−	35.8082i		−	0.0352777i	0.999844	−	0.0176389i	$-0.00561492\pi$
$102$	955.291	−	771.823i	0.927333	−	0.749234i
$103$			775.880i			0.742230i	0.928587	+	0.371115i	$0.121024\pi$
$103$			775.880i			0.742230i	−0.928587	+	0.371115i	$0.878976\pi$
$104$		−	49.4968i		−	0.0466689i
$105$	−85.4745	+	69.0587i	−0.0794425	+	0.0641852i
$106$			531.766i			0.487261i
$107$	136.147			0.123008			0.0615040	−	0.998107i	$-0.480410\pi$
$107$	136.147			0.123008			0.0615040	+	0.998107i	$0.480410\pi$
$108$	−500.866	+	253.104i	−0.446258	+	0.225509i
$109$		−	352.915i		−	0.310121i	−0.987905	−	0.155060i	$-0.950443\pi$
$109$		−	352.915i		−	0.310121i	0.987905	−	0.155060i	$-0.0495572\pi$
$110$		−	689.040i		−	0.597249i
$111$	−223.305	+	180.419i	−0.190948	+	0.154275i
$112$			49.5902i			0.0418378i
$113$	−713.290			−0.593811			−0.296906	−	0.954907i	$-0.595955\pi$
$113$	−713.290			−0.593811			−0.296906	+	0.954907i	$0.595955\pi$
$114$	606.374	+	750.514i	0.498177	+	0.616597i
$115$	−744.576	+	109.762i	−0.603757	+	0.0890031i
$116$		−	433.913i		−	0.347309i
$117$	−35.0951	+	163.324i	−0.0277312	+	0.129054i
$118$	1306.75			1.01946
$119$			366.275i			0.282154i
$120$	220.623	−	178.251i	0.167833	−	0.135600i
$121$	1218.52			0.915489
$122$	1375.29			1.02060
$123$	−552.256	+	446.193i	−0.404839	+	0.327088i
$124$	197.618			0.143118
$125$	1388.13			0.993268
$126$	35.1614	−	163.632i	0.0248605	−	0.115694i
$127$	−2054.40			−1.43542			−0.717711	−	0.696341i	$-0.754810\pi$
$127$	−2054.40			−1.43542			−0.717711	+	0.696341i	$0.754810\pi$
$128$		−	128.000i		−	0.0883883i
$129$	856.358	−	691.891i	0.584482	−	0.472229i
$130$		−	84.4312i		−	0.0569623i
$131$			1631.00i			1.08780i	0.839151	+	0.543898i	$0.183052\pi$
$131$			1631.00i			1.08780i	−0.839151	+	0.543898i	$0.816948\pi$
$132$	659.547	+	816.326i	0.434896	+	0.538273i
$133$	−287.760			−0.187608
$134$	−21.1155			−0.0136127
$135$	−854.372	+	431.742i	−0.544686	+	0.275248i
$136$		−	945.412i		−	0.596091i
$137$	3115.35			1.94279			0.971395	−	0.237471i	$-0.0763184\pi$
$137$	3115.35			1.94279			0.971395	+	0.237471i	$0.0763184\pi$
$138$	777.057	−	842.744i	0.479330	−	0.519849i
$139$	1889.56			1.15303			0.576513	−	0.817088i	$-0.304413\pi$
$139$	1889.56			1.15303			0.576513	+	0.817088i	$0.304413\pi$
$140$			84.5905i			0.0510657i
$141$	1825.98	−	1475.29i	1.09060	−	0.881149i
$142$	−629.827			−0.372211
$143$	312.404			0.182689
$144$	−90.7569	+	422.359i	−0.0525214	+	0.244421i
$145$		−	740.165i		−	0.423913i
$146$			1590.59i			0.901630i
$147$	−1088.72	−	1347.51i	−0.610855	−	0.756060i
$148$			220.996i			0.122742i
$149$	−647.849			−0.356200			−0.178100	−	0.984012i	$-0.556995\pi$
$149$	−647.849			−0.356200			−0.178100	+	0.984012i	$0.556995\pi$
$150$	−634.114	+	512.330i	−0.345168	+	0.278877i
$151$	1408.70			0.759195			0.379597	−	0.925152i	$-0.376063\pi$
$151$	1408.70			0.759195			0.379597	+	0.925152i	$0.376063\pi$
$152$	742.752			0.396349
$153$	−670.333	+	3119.56i	−0.354204	+	1.64837i
$154$	−312.993			−0.163777
$155$	337.095			0.174684
$156$	80.8173	+	100.028i	0.0414780	+	0.0513376i
$157$		−	837.809i		−	0.425888i	−0.977064	−	0.212944i	$-0.931695\pi$
$157$		−	837.809i		−	0.425888i	0.977064	−	0.212944i	$-0.0683053\pi$
$158$	−2446.88			−1.23205
$159$	−868.255	−	1074.65i	−0.433063	−	0.536006i
$160$		−	218.341i		−	0.107884i
$161$	49.8589	+	338.220i	0.0244064	+	0.165562i
$162$	598.938	−	1329.30i	0.290475	−	0.644689i
$163$	−1919.58			−0.922410			−0.461205	−	0.887294i	$-0.652583\pi$
$163$	−1919.58			−0.922410			−0.461205	+	0.887294i	$0.652583\pi$
$164$			546.544i			0.260231i
$165$	1125.05	+	1392.48i	0.530818	+	0.656997i
$166$		−	807.673i		−	0.377636i
$167$			420.600i			0.194892i	0.995241	+	0.0974462i	$0.0310674\pi$
$167$			420.600i			0.194892i	−0.995241	+	0.0974462i	$0.968933\pi$
$168$	−80.9698	−	100.217i	−0.0371843	−	0.0460232i
$169$	−2158.72			−0.982576
$170$		−	1612.67i		−	0.727567i
$171$	−2450.84	−	526.639i	−1.09603	−	0.235515i
$172$		−	847.501i		−	0.375706i
$173$		−	3160.75i		−	1.38906i	−0.719464	−	0.694529i	$-0.755613\pi$
$173$		−	3160.75i		−	1.38906i	0.719464	−	0.694529i	$-0.244387\pi$
$174$	708.484	+	876.896i	0.308678	+	0.382053i
$175$		−	243.130i		−	0.105022i
$176$	807.884			0.346003
$177$	−2640.80	+	2133.63i	−1.12144	+	0.906063i
$178$		−	59.3045i		−	0.0249722i
$179$		−	3316.12i		−	1.38469i	−0.721569	−	0.692343i	$-0.756579\pi$
$179$		−	3316.12i		−	1.38469i	0.721569	−	0.692343i	$-0.243421\pi$
$180$	−154.812	+	720.456i	−0.0641057	+	0.298331i
$181$		−	2990.38i		−	1.22803i	−0.789295	−	0.614014i	$-0.789554\pi$
$181$		−	2990.38i		−	1.22803i	0.789295	−	0.614014i	$-0.210446\pi$
$182$	−38.3525			−0.0156202
$183$	−2779.33	+	2245.55i	−1.12270	+	0.907079i
$184$	−128.693	−	872.998i	−0.0515620	−	0.349773i
$185$			376.973i			0.149814i
$186$	−399.366	+	322.666i	−0.157435	+	0.127199i
$187$	5967.05			2.33344
$188$		−	1807.09i		−	0.701042i
$189$	196.117	+	388.094i	0.0754783	+	0.149364i
$190$	1266.98			0.483770
$191$	−3767.16			−1.42713			−0.713565	−	0.700589i	$-0.752921\pi$
$191$	−3767.16			−1.42713			−0.713565	+	0.700589i	$0.752921\pi$
$192$	208.995	+	258.675i	0.0785570	+	0.0972306i
$193$	−989.248			−0.368951			−0.184476	−	0.982837i	$-0.559059\pi$
$193$	−989.248			−0.368951			−0.184476	+	0.982837i	$0.559059\pi$
$194$	−2331.41			−0.862813
$195$	137.857	+	170.627i	0.0506265	+	0.0626608i
$196$	−1333.58			−0.485997
$197$			2987.20i			1.08035i	0.841552	+	0.540176i	$0.181642\pi$
$197$			2987.20i			1.08035i	−0.841552	+	0.540176i	$0.818358\pi$
$198$	−2665.76	−	572.821i	−0.956804	−	0.205599i
$199$		−	2811.84i		−	1.00164i	−0.865552	−	0.500819i	$-0.833032\pi$
$199$		−	2811.84i		−	1.00164i	0.865552	−	0.500819i	$-0.166968\pi$
$200$			627.556i			0.221875i
$201$	42.6724	−	34.4769i	0.0149745	−	0.0120986i
$202$	71.6164			0.0249451
$203$	−336.217			−0.116245
$204$	1543.65	+	1910.58i	0.529789	+	0.655723i
$205$			932.290i			0.317629i
$206$	−1551.76			−0.524836
$207$	−194.342	+	2971.86i	−0.0652546	+	0.997869i
$208$	98.9936			0.0329999
$209$			4687.95i			1.55154i
$210$	−138.117	−	170.949i	−0.0453858	−	0.0561743i
$211$	265.079			0.0864873			0.0432436	−	0.999065i	$-0.486231\pi$
$211$	265.079			0.0864873			0.0432436	+	0.999065i	$0.486231\pi$
$212$	−1063.53			−0.344545
$213$	1272.82	−	1028.37i	0.409446	−	0.330810i
$214$			272.295i			0.0869798i
$215$		−	1445.66i		−	0.458573i
$216$	−506.208	−	1001.73i	−0.159459	−	0.315552i
$217$		−	153.124i		−	0.0479019i
$218$	705.830			0.219288
$219$	−2597.08	−	3214.42i	−0.801343	−	0.991828i
$220$	1378.08			0.422319
$221$	731.170			0.222551
$222$	−360.837	−	446.611i	−0.109089	−	0.135020i
$223$	−3189.10			−0.957659			−0.478830	−	0.877908i	$-0.658939\pi$
$223$	−3189.10			−0.957659			−0.478830	+	0.877908i	$0.658939\pi$
$224$	−99.1805			−0.0295838
$225$	444.961	−	2070.73i	0.131840	−	0.613551i
$226$		−	1426.58i		−	0.419888i
$227$	4687.01			1.37043			0.685216	−	0.728340i	$-0.259708\pi$
$227$	4687.01			1.37043			0.685216	+	0.728340i	$0.259708\pi$
$228$	−1501.03	+	1212.75i	−0.436000	+	0.352264i
$229$		−	6067.92i		−	1.75100i	−0.483216	−	0.875501i	$-0.660531\pi$
$229$		−	6067.92i		−	1.75100i	0.483216	−	0.875501i	$-0.339469\pi$
$230$	−219.524	−	1489.15i	−0.0629347	−	0.426921i
$231$	632.528	−	511.048i	0.180161	−	0.145561i
$232$	867.827			0.245585
$233$		−	1827.91i		−	0.513950i	−0.966418	−	0.256975i	$-0.917274\pi$
$233$		−	1827.91i		−	0.513950i	0.966418	−	0.256975i	$-0.0827258\pi$
$234$	−326.647	−	70.1903i	−0.0912547	−	0.0196089i
$235$		−	3082.52i		−	0.855667i
$236$			2613.49i			0.720864i
$237$	4944.90	−	3995.21i	1.35530	−	1.09501i
$238$	−732.550			−0.199513
$239$			3454.47i			0.934942i	0.884008	+	0.467471i	$0.154835\pi$
$239$			3454.47i			0.934942i	−0.884008	+	0.467471i	$0.845165\pi$
$240$	356.502	+	441.246i	0.0958839	+	0.118676i
$241$		−	780.677i		−	0.208663i	−0.994543	−	0.104332i	$-0.966730\pi$
$241$		−	780.677i		−	0.208663i	0.994543	−	0.104332i	$-0.0332703\pi$
$242$			2437.03i			0.647349i
$243$	960.057	+	3664.31i	0.253447	+	0.967349i
$244$			2750.58i			0.721673i
$245$	−2274.80			−0.593190
$246$	−892.385	−	1104.51i	−0.231286	−	0.286265i
$247$			574.435i			0.147977i
$248$			395.236i			0.101200i
$249$	1318.75	+	1632.23i	0.335632	+	0.415414i
$250$			2776.27i			0.702347i
$251$	5708.15			1.43544			0.717720	−	0.696332i	$-0.245186\pi$
$251$	5708.15			1.43544			0.717720	+	0.696332i	$0.245186\pi$
$252$	327.264	+	70.3228i	0.0818083	+	0.0175790i
$253$	5510.01	−	812.260i	1.36921	−	0.201843i
$254$		−	4108.80i		−	1.01500i
$255$	2633.14	+	3259.05i	0.646641	+	0.800352i
$256$	256.000			0.0625000
$257$		−	5609.13i		−	1.36143i	−0.732548	−	0.680715i	$-0.761669\pi$
$257$		−	5609.13i		−	1.36143i	0.732548	−	0.680715i	$-0.238331\pi$
$258$	1383.78	+	1712.72i	0.333916	+	0.413291i
$259$	171.238			0.0410819
$260$	168.862			0.0402785
$261$	−2863.55	−	615.322i	−0.679116	−	0.145929i
$262$	−3262.00			−0.769188
$263$	706.383			0.165618			0.0828088	−	0.996565i	$-0.473611\pi$
$263$	706.383			0.165618			0.0828088	+	0.996565i	$0.473611\pi$
$264$	−1632.65	+	1319.09i	−0.380617	+	0.307518i
$265$	−1814.16			−0.420540
$266$		−	575.519i		−	0.132659i
$267$	96.8310	+	119.848i	0.0221946	+	0.0274704i
$268$		−	42.2310i		−	0.00962564i
$269$			1817.30i			0.411905i	0.978562	+	0.205953i	$0.0660292\pi$
$269$			1817.30i			0.411905i	−0.978562	+	0.205953i	$0.933971\pi$
$270$	−863.484	−	1708.74i	−0.194629	−	0.385151i
$271$	−4857.57			−1.08884			−0.544422	−	0.838812i	$-0.683251\pi$
$271$	−4857.57			−1.08884			−0.544422	+	0.838812i	$0.683251\pi$
$272$	1890.82			0.421500
$273$	77.5065	−	62.6211i	0.0171828	−	0.0138828i
$274$			6230.70i			1.37376i
$275$	−3960.88			−0.868545
$276$	1685.49	+	1554.11i	0.367589	+	0.338937i
$277$	−623.733			−0.135294			−0.0676471	−	0.997709i	$-0.521549\pi$
$277$	−623.733			−0.135294			−0.0676471	+	0.997709i	$0.521549\pi$
$278$			3779.13i			0.815313i
$279$	280.237	−	1304.15i	0.0601339	−	0.279848i
$280$	−169.181			−0.0361089
$281$	−422.486			−0.0896918			−0.0448459	−	0.998994i	$-0.514280\pi$
$281$	−422.486			−0.0896918			−0.0448459	+	0.998994i	$0.514280\pi$
$282$	2950.58	+	3651.96i	0.623066	+	0.771173i
$283$			5963.94i			1.25272i	0.779534	+	0.626360i	$0.215456\pi$
$283$			5963.94i			1.25272i	−0.779534	+	0.626360i	$0.784544\pi$
$284$		−	1259.65i		−	0.263193i
$285$	−2560.44	+	2068.69i	−0.532166	+	0.429961i
$286$			624.807i			0.129181i
$287$	423.489			0.0871001
$288$	−844.718	−	181.514i	−0.172832	−	0.0371382i
$289$	9052.68			1.84260
$290$	1480.33			0.299752
$291$	4711.55	−	3806.68i	0.949127	−	0.766843i
$292$	−3181.18			−0.637549
$293$	−3560.06			−0.709832			−0.354916	−	0.934898i	$-0.615491\pi$
$293$	−3560.06			−0.709832			−0.354916	+	0.934898i	$0.615491\pi$
$294$	2695.02	−	2177.43i	0.534615	−	0.431940i
$295$			4458.07i			0.879860i
$296$	−441.992			−0.0867914
$297$	6322.52	−	3194.98i	1.23525	−	0.624213i
$298$		−	1295.70i		−	0.251872i
$299$	675.166	−	99.5299i	0.130588	−	0.0192507i
$300$	−1024.66	−	1268.23i	−0.197196	−	0.244071i
$301$	−656.684			−0.125750
$302$			2817.40i			0.536832i
$303$	−144.730	+	116.934i	−0.0274406	+	0.0221705i
$304$			1485.50i			0.280261i
$305$			4691.92i			0.880848i
$306$	−6239.11	−	1340.67i	−1.16558	−	0.250460i
$307$	1409.77			0.262085			0.131042	−	0.991377i	$-0.458168\pi$
$307$	1409.77			0.262085			0.131042	+	0.991377i	$0.458168\pi$
$308$		−	625.987i		−	0.115808i
$309$	3135.95	−	2533.68i	0.577340	−	0.466459i
$310$			674.189i			0.123521i
$311$		−	9394.27i		−	1.71286i	−0.516262	−	0.856431i	$-0.672677\pi$
$311$		−	9394.27i		−	1.71286i	0.516262	−	0.856431i	$-0.327323\pi$
$312$	−200.056	+	161.635i	−0.0363011	+	0.0293293i
$313$			1657.79i			0.299373i	0.988734	+	0.149687i	$0.0478264\pi$
$313$			1657.79i			0.299373i	−0.988734	+	0.149687i	$0.952174\pi$
$314$	1675.62			0.301149
$315$	558.243	+	119.956i	0.0998522	+	0.0214563i
$316$		−	4893.76i		−	0.871188i
$317$		−	5647.64i		−	1.00064i	−0.865840	−	0.500321i	$-0.833215\pi$
$317$		−	5647.64i		−	1.00064i	0.865840	−	0.500321i	$-0.166785\pi$
$318$	2149.29	−	1736.51i	0.379013	−	0.306222i
$319$			5477.37i			0.961360i
$320$	436.682			0.0762852
$321$	−444.596	−	550.280i	−0.0773051	−	0.0956811i
$322$	−676.440	+	99.7178i	−0.117070	+	0.0172579i
$323$			10972.0i			1.89008i
$324$	2658.60	+	1197.88i	0.455864	+	0.205397i
$325$	−485.344			−0.0828371
$326$		−	3839.15i		−	0.652242i
$327$	−1426.41	+	1152.46i	−0.241226	+	0.194897i
$328$	−1093.09			−0.184011
$329$	−1400.22			−0.234641
$330$	−2784.96	+	2250.10i	−0.464567	+	0.375345i
$331$	−7210.43			−1.19735			−0.598673	−	0.800994i	$-0.704305\pi$
$331$	−7210.43			−1.19735			−0.598673	+	0.800994i	$0.704305\pi$
$332$	1615.35			0.267029
$333$	1458.43	+	313.389i	0.240005	+	0.0515724i
$334$	−841.201			−0.137810
$335$		−	72.0373i		−	0.0117487i
$336$	200.434	−	161.940i	0.0325433	−	0.0262932i
$337$			10749.1i			1.73752i	0.495237	+	0.868758i	$0.335081\pi$
$337$			10749.1i			1.73752i	−0.495237	+	0.868758i	$0.664919\pi$
$338$		−	4317.44i		−	0.694786i
$339$	2329.29	+	2882.97i	0.373184	+	0.461893i
$340$	3225.35			0.514468
$341$	−2494.57			−0.396154
$342$	1053.28	−	4901.69i	0.166534	−	0.775008i
$343$			2096.41i			0.330016i
$344$	1695.00			0.265664
$345$	2875.09	+	2650.99i	0.448665	+	0.413695i
$346$	6321.49			0.982213
$347$			5044.62i			0.780431i	0.920724	+	0.390215i	$0.127599\pi$
$347$			5044.62i			0.780431i	−0.920724	+	0.390215i	$0.872401\pi$
$348$	−1753.79	+	1416.97i	−0.270153	+	0.218268i
$349$	−11006.0			−1.68807			−0.844034	−	0.536290i	$-0.819825\pi$
$349$	−11006.0			−1.68807			−0.844034	+	0.536290i	$0.819825\pi$
$350$	486.260			0.0742620
$351$	774.727	−	391.495i	0.117812	−	0.0595340i
$352$			1615.77i			0.244661i
$353$		−	6049.33i		−	0.912106i	−0.889953	−	0.456053i	$-0.849263\pi$
$353$		−	6049.33i		−	0.912106i	0.889953	−	0.456053i	$-0.150737\pi$
$354$	−4267.25	−	5281.61i	−0.640683	−	0.792978i
$355$		−	2148.71i		−	0.321244i
$356$	118.609			0.0176580
$357$	1480.41	−	1196.09i	0.219472	−	0.177322i
$358$	6632.25			0.979121
$359$	−2394.19			−0.351979			−0.175989	−	0.984392i	$-0.556312\pi$
$359$	−2394.19			−0.351979			−0.175989	+	0.984392i	$0.556312\pi$
$360$	−1440.91	−	309.624i	−0.210952	−	0.0453296i
$361$	−1761.00			−0.256743
$362$	5980.76			0.868347
$363$	−3979.13	−	4925.00i	−0.575345	−	0.712109i
$364$		−	76.7050i		−	0.0110451i
$365$	−5426.42			−0.778169
$366$	−4491.09	−	5558.66i	−0.641402	−	0.793868i
$367$			10274.1i			1.46131i	0.682744	+	0.730657i	$0.260786\pi$
$367$			10274.1i			1.46131i	−0.682744	+	0.730657i	$0.739214\pi$
$368$	1746.00	−	257.387i	0.247327	−	0.0364598i
$369$	3606.84	+	775.042i	0.508848	+	0.109342i
$370$	−753.945			−0.105934
$371$			824.074i			0.115320i
$372$	−645.332	−	798.732i	−0.0899433	−	0.111323i
$373$			5217.63i			0.724286i	0.932123	+	0.362143i	$0.117955\pi$
$373$			5217.63i			0.724286i	−0.932123	+	0.362143i	$0.882045\pi$
$374$			11934.1i			1.64999i
$375$	−4533.03	−	5610.56i	−0.624226	−	0.772608i
$376$	3614.19			0.495712
$377$			671.167i			0.0916892i
$378$	−776.189	+	392.234i	−0.105616	+	0.0533712i
$379$		−	10040.7i		−	1.36084i	−0.732823	−	0.680419i	$-0.761798\pi$
$379$		−	10040.7i		−	1.36084i	0.732823	−	0.680419i	$-0.238202\pi$
$380$			2533.96i			0.342077i
$381$	6708.76	+	8303.48i	0.902100	+	1.11654i
$382$		−	7534.31i		−	1.00913i
$383$	1660.73			0.221565			0.110782	−	0.993845i	$-0.464664\pi$
$383$	1660.73			0.221565			0.110782	+	0.993845i	$0.464664\pi$
$384$	−517.350	+	417.991i	−0.0687524	+	0.0555482i
$385$		−	1067.80i		−	0.141351i
$386$		−	1978.50i		−	0.260888i
$387$	−5592.97	−	1201.82i	−0.734642	−	0.157861i
$388$		−	4662.82i		−	0.610101i
$389$	−14704.5			−1.91658			−0.958291	−	0.285796i	$-0.907742\pi$
$389$	−14704.5			−1.91658			−0.958291	+	0.285796i	$0.907742\pi$
$390$	−341.254	+	275.715i	−0.0443079	+	0.0357983i
$391$	12896.0	−	1901.07i	1.66797	−	0.245885i
$392$		−	2667.15i		−	0.343652i
$393$	6592.18	−	5326.13i	0.846137	−	0.683632i
$394$	−5974.40			−0.763924
$395$		−	8347.73i		−	1.06334i
$396$	1145.64	−	5331.52i	0.145380	−	0.676563i
$397$	3102.07			0.392162			0.196081	−	0.980588i	$-0.437178\pi$
$397$	3102.07			0.392162			0.196081	+	0.980588i	$0.437178\pi$
$398$	5623.68			0.708265
$399$	939.695	+	1163.07i	0.117904	+	0.145930i
$400$	−1255.11			−0.156889
$401$	−10808.9			−1.34606			−0.673031	−	0.739614i	$-0.735008\pi$
$401$	−10808.9			−1.34606			−0.673031	+	0.739614i	$0.735008\pi$
$402$	68.9539	+	85.3447i	0.00855499	+	0.0105886i
$403$	−305.671			−0.0377830
$404$			143.233i			0.0176389i
$405$	4535.01	+	2043.32i	0.556411	+	0.250700i
$406$		−	672.433i		−	0.0821978i
$407$		−	2789.67i		−	0.339752i
$408$	−3821.17	+	3087.29i	−0.463666	+	0.374617i
$409$	−13861.0			−1.67575			−0.837873	−	0.545865i	$-0.816201\pi$
$409$	−13861.0			−1.67575			−0.837873	+	0.545865i	$0.816201\pi$
$410$	−1864.58			−0.224598
$411$	−10173.3	−	12591.6i	−1.22096	−	1.51119i
$412$		−	3103.52i		−	0.371115i
$413$	2025.06			0.241275
$414$	−5943.73	−	388.684i	−0.705600	−	0.0461420i
$415$	2755.44			0.325926
$416$			197.987i			0.0233344i
$417$	−6170.48	−	7637.24i	−0.724627	−	0.896876i
$418$	−9375.89			−1.09710
$419$	8102.73			0.944736			0.472368	−	0.881401i	$-0.343399\pi$
$419$	8102.73			0.944736			0.472368	+	0.881401i	$0.343399\pi$
$420$	341.898	−	276.235i	0.0397212	−	0.0320926i
$421$		−	1825.10i		−	0.211282i	−0.994404	−	0.105641i	$-0.966310\pi$
$421$		−	1825.10i		−	0.211282i	0.994404	−	0.105641i	$-0.0336895\pi$
$422$			530.159i			0.0611557i
$423$	−11925.7	−	2562.60i	−1.37079	−	0.294557i
$424$		−	2127.06i		−	0.243630i
$425$	−9270.29			−1.05806
$426$	2056.73	+	2545.64i	0.233918	+	0.289522i
$427$	2131.28			0.241546
$428$	−544.589			−0.0615040
$429$	−1020.17	−	1262.67i	−0.114812	−	0.142104i
$430$	2891.32			0.324260
$431$	−1126.53			−0.125901			−0.0629504	−	0.998017i	$-0.520051\pi$
$431$	−1126.53			−0.125901			−0.0629504	+	0.998017i	$0.520051\pi$
$432$	2003.46	−	1012.42i	0.223129	−	0.112754i
$433$		−	6781.15i		−	0.752613i	−0.926495	−	0.376306i	$-0.877194\pi$
$433$		−	6781.15i		−	0.752613i	0.926495	−	0.376306i	$-0.122806\pi$
$434$	306.247			0.0338718
$435$	−2991.60	+	2417.05i	−0.329738	+	0.266411i
$436$			1411.66i			0.155060i
$437$	1493.55	+	10131.6i	0.163493	+	1.10906i
$438$	6428.84	−	5194.15i	0.701328	−	0.566635i
$439$	13687.2			1.48806			0.744028	−	0.668149i	$-0.232913\pi$
$439$	13687.2			1.48806			0.744028	+	0.668149i	$0.232913\pi$
$440$			2756.16i			0.298624i
$441$	−1891.11	+	8800.74i	−0.204202	+	0.950302i
$442$			1462.34i			0.157367i
$443$			9550.89i			1.02433i	0.858888	+	0.512163i	$0.171156\pi$
$443$			9550.89i			1.02433i	−0.858888	+	0.512163i	$0.828844\pi$
$444$	893.221	−	721.674i	0.0954739	−	0.0771377i
$445$	202.322			0.0215528
$446$		−	6378.20i		−	0.677167i
$447$	2115.59	+	2618.48i	0.223856	+	0.277069i
$448$		−	198.361i		−	0.0209189i
$449$		−	15829.0i		−	1.66373i	−0.554975	−	0.831867i	$-0.687272\pi$
$449$		−	15829.0i		−	1.66373i	0.554975	−	0.831867i	$-0.312728\pi$
$450$	4141.47	+	889.922i	0.433846	+	0.0932252i
$451$		−	6899.13i		−	0.720327i
$452$	2853.16			0.296906
$453$	−4600.19	−	5693.69i	−0.477121	−	0.590536i
$454$			9374.03i			0.969042i
$455$		−	130.843i		−	0.0134813i
$456$	−2425.50	−	3002.05i	−0.249088	−	0.308298i
$457$			12373.0i			1.26648i	0.773954	+	0.633242i	$0.218276\pi$
$457$			12373.0i			1.26648i	−0.773954	+	0.633242i	$0.781724\pi$
$458$	12135.8			1.23815
$459$	14797.6	−	7477.73i	1.50478	−	0.760415i
$460$	2978.30	−	439.048i	0.301879	−	0.0445016i
$461$			6444.45i			0.651080i	0.945528	+	0.325540i	$0.105546\pi$
$461$			6444.45i			0.651080i	−0.945528	+	0.325540i	$0.894454\pi$
$462$	1022.10	+	1265.06i	0.102927	+	0.127393i
$463$	125.291			0.0125762			0.00628808	−	0.999980i	$-0.497998\pi$
$463$	125.291			0.0125762			0.00628808	+	0.999980i	$0.497998\pi$
$464$			1735.65i			0.173654i
$465$	−1100.80	−	1362.47i	−0.109782	−	0.135877i
$466$	3655.82			0.363418
$467$	6489.03			0.642990			0.321495	−	0.946911i	$-0.395815\pi$
$467$	6489.03			0.642990			0.321495	+	0.946911i	$0.395815\pi$
$468$	140.381	−	653.295i	0.0138656	−	0.0645268i
$469$	−32.7226			−0.00322173
$470$	6165.05			0.605048
$471$	−3386.26	+	2735.91i	−0.331275	+	0.267652i
$472$	−5226.98			−0.509728
$473$			10698.2i			1.03996i
$474$	7990.42	+	9889.80i	0.774287	+	0.958341i
$475$		−	7283.10i		−	0.703519i
$476$		−	1465.10i		−	0.141077i
$477$	−1508.17	+	7018.63i	−0.144768	+	0.673712i
$478$	−6908.94			−0.661104
$479$	11843.7			1.12976			0.564879	−	0.825174i	$-0.308923\pi$
$479$	11843.7			1.12976			0.564879	+	0.825174i	$0.308923\pi$
$480$	−882.491	+	713.005i	−0.0839167	+	0.0678001i
$481$		−	341.831i		−	0.0324036i
$482$	1561.35			0.147547
$483$	1204.20	−	1306.00i	0.113443	−	0.123033i
$484$	−4874.06			−0.457745
$485$		−	7953.80i		−	0.744667i
$486$	−7328.63	+	1920.11i	−0.684019	+	0.179214i
$487$	−14770.3			−1.37435			−0.687173	−	0.726494i	$-0.741149\pi$
$487$	−14770.3			−1.37435			−0.687173	+	0.726494i	$0.741149\pi$
$488$	−5501.17			−0.510300
$489$	6268.48	+	7758.54i	0.579694	+	0.717492i
$490$		−	4549.60i		−	0.419449i
$491$		−	89.5204i		−	0.00822811i	−0.999992	−	0.00411405i	$-0.998690\pi$
$491$		−	89.5204i		−	0.00822811i	0.999992	−	0.00411405i	$-0.00130955\pi$
$492$	2209.02	−	1784.77i	0.202420	−	0.163544i
$493$			12819.6i			1.17113i
$494$	−1148.87			−0.104636
$495$	1954.22	−	9094.45i	0.177446	−	0.825788i
$496$	−790.472			−0.0715589
$497$	−976.040			−0.0880913
$498$	−3264.45	+	2637.50i	−0.293742	+	0.237328i
$499$	3686.92			0.330760			0.165380	−	0.986230i	$-0.447115\pi$
$499$	3686.92			0.330760			0.165380	+	0.986230i	$0.447115\pi$
$500$	−5552.54			−0.496634
$501$	1699.98	−	1373.49i	0.151596	−	0.122481i
$502$			11416.3i			1.01501i
$503$	12832.8			1.13755			0.568775	−	0.822493i	$-0.307418\pi$
$503$	12832.8			1.13755			0.568775	+	0.822493i	$0.307418\pi$
$504$	−140.646	+	654.528i	−0.0124303	+	0.0578472i
$505$			244.325i			0.0215294i
$506$	1624.52	+	11020.0i	0.142725	+	0.968181i
$507$	7049.42	+	8725.12i	0.617506	+	0.764292i
$508$	8217.60			0.717711
$509$		−	8382.75i		−	0.729978i	−0.931012	−	0.364989i	$-0.881073\pi$
$509$		−	8382.75i		−	0.729978i	0.931012	−	0.364989i	$-0.118927\pi$
$510$	−6518.11	+	5266.27i	−0.565935	+	0.457244i
$511$			2464.93i			0.213389i
$512$			512.000i			0.0441942i
$513$	5874.79	+	11625.6i	0.505611	+	1.00055i
$514$	11218.3			0.962677
$515$		−	5293.95i		−	0.452970i
$516$	−3425.43	+	2767.56i	−0.292241	+	0.236115i
$517$			22811.3i			1.94050i
$518$			342.476i			0.0290493i
$519$	−12775.1	+	10321.6i	−1.08047	+	0.872963i
$520$			337.725i			0.0284812i
$521$	−8122.81			−0.683046			−0.341523	−	0.939873i	$-0.610943\pi$
$521$	−8122.81			−0.683046			−0.341523	+	0.939873i	$0.610943\pi$
$522$	1230.64	−	5727.10i	0.103187	−	0.480208i
$523$		−	21756.6i		−	1.81902i	−0.415680	−	0.909511i	$-0.636456\pi$
$523$		−	21756.6i		−	1.81902i	0.415680	−	0.909511i	$-0.363544\pi$
$524$		−	6524.01i		−	0.543898i
$525$	−982.683	+	793.954i	−0.0816911	+	0.0660019i
$526$			1412.77i			0.117109i
$527$	−5838.45			−0.482593
$528$	−2638.19	−	3265.31i	−0.217448	−	0.269137i
$529$	11649.4	−	3510.91i	0.957462	−	0.288560i
$530$		−	3628.32i		−	0.297366i
$531$	17247.4	+	3706.13i	1.40955	+	0.302886i
$532$	1151.04			0.0938042
$533$		−	845.382i		−	0.0687008i
$534$	−239.697	+	193.662i	−0.0194245	+	0.0156940i
$535$	−928.955			−0.0750696
$536$	84.4621			0.00680635
$537$	−13403.1	+	10829.0i	−1.07707	+	0.870214i
$538$	−3634.59			−0.291261
$539$	16834.0			1.34525
$540$	3417.49	−	1726.97i	0.272343	−	0.137624i
$541$	−2142.23			−0.170243			−0.0851217	−	0.996371i	$-0.527128\pi$
$541$	−2142.23			−0.170243			−0.0851217	+	0.996371i	$0.527128\pi$
$542$		−	9715.15i		−	0.769929i
$543$	−12086.5	+	9765.25i	−0.955216	+	0.771762i
$544$			3781.65i			0.298046i
$545$			2408.00i			0.189261i
$546$	125.242	+	155.013i	0.00981661	+	0.0121501i
$547$	−19790.3			−1.54693			−0.773465	−	0.633839i	$-0.781478\pi$
$547$	−19790.3			−1.54693			−0.773465	+	0.633839i	$0.781478\pi$
$548$	−12461.4			−0.971395
$549$	18152.1	+	3900.54i	1.41113	+	0.303226i
$550$		−	7921.75i		−	0.614154i
$551$	−10071.6			−0.778698
$552$	−3108.23	+	3370.98i	−0.239665	+	0.259924i
$553$	−3791.92			−0.291589
$554$		−	1247.47i		−	0.0956674i
$555$	1523.65	−	1231.02i	0.116532	−	0.0941515i
$556$	−7558.26			−0.576513
$557$	−9074.29			−0.690287			−0.345144	−	0.938550i	$-0.612170\pi$
$557$	−9074.29			−0.690287			−0.345144	+	0.938550i	$0.612170\pi$
$558$	2608.30	+	560.475i	0.197882	+	0.0425211i
$559$			1310.89i			0.0991859i
$560$		−	338.362i		−	0.0255329i
$561$	−19485.7	−	24117.6i	−1.46647	−	1.81506i
$562$		−	844.971i		−	0.0634217i
$563$	25234.5			1.88900			0.944499	−	0.328514i	$-0.106548\pi$
$563$	25234.5			1.88900			0.944499	+	0.328514i	$0.106548\pi$
$564$	−7303.92	+	5901.17i	−0.545302	+	0.440574i
$565$	4866.89			0.362392
$566$	−11927.9			−0.885806
$567$	928.170	−	2060.01i	0.0687469	−	0.152579i
$568$	2519.31			0.186105
$569$	13272.6			0.977887			0.488944	−	0.872315i	$-0.337382\pi$
$569$	13272.6			0.977887			0.488944	+	0.872315i	$0.337382\pi$
$570$	−4137.39	−	5120.87i	−0.304028	−	0.376298i
$571$		−	17338.2i		−	1.27072i	−0.772216	−	0.635360i	$-0.780852\pi$
$571$		−	17338.2i		−	1.27072i	0.772216	−	0.635360i	$-0.219148\pi$
$572$	−1249.61			−0.0913445
$573$	12301.9	+	15226.1i	0.896889	+	1.11009i
$574$			846.977i			0.0615891i
$575$	−8560.24	+	1261.91i	−0.620846	+	0.0915223i
$576$	363.028	−	1689.44i	0.0262607	−	0.122210i
$577$	18444.3			1.33076			0.665378	−	0.746507i	$-0.268270\pi$
$577$	18444.3			1.33076			0.665378	+	0.746507i	$0.268270\pi$
$578$			18105.4i			1.30291i
$579$	3230.44	+	3998.34i	0.231870	+	0.286987i
$580$			2960.66i			0.211956i
$581$		−	1251.65i		−	0.0893753i
$582$	7613.35	+	9423.10i	0.542240	+	0.671134i
$583$	13425.1			0.953710
$584$		−	6362.35i		−	0.450815i
$585$	239.460	−	1114.38i	0.0169238	−	0.0787591i
$586$		−	7120.12i		−	0.501927i
$587$		−	11823.9i		−	0.831386i	−0.909505	−	0.415693i	$-0.863539\pi$
$587$		−	11823.9i		−	0.831386i	0.909505	−	0.415693i	$-0.136461\pi$
$588$	4354.86	+	5390.05i	0.305428	+	0.378030i
$589$		−	4586.91i		−	0.320883i
$590$	−8916.14			−0.622155
$591$	12073.7	−	9754.87i	0.840346	−	0.678954i
$592$		−	883.983i		−	0.0613708i
$593$			18477.2i			1.27954i	0.768566	+	0.639770i	$0.220971\pi$
$593$			18477.2i			1.27954i	−0.768566	+	0.639770i	$0.779029\pi$
$594$	6389.95	+	12645.0i	0.441385	+	0.873455i
$595$		−	2499.15i		−	0.172194i
$596$	2591.40			0.178100
$597$	−11364.9	+	9182.21i	−0.779119	+	0.629485i
$598$	199.060	+	1350.33i	0.0136123	+	0.0923398i
$599$			21828.3i			1.48895i	0.667650	+	0.744475i	$0.267300\pi$
$599$			21828.3i			1.48895i	−0.667650	+	0.744475i	$0.732700\pi$
$600$	2536.46	−	2049.32i	0.172584	−	0.139438i
$601$	−352.046			−0.0238940			−0.0119470	−	0.999929i	$-0.503803\pi$
$601$	−352.046			−0.0238940			−0.0119470	+	0.999929i	$0.503803\pi$
$602$		−	1313.37i		−	0.0889185i
$603$	−278.698	−	59.8868i	−0.0188216	−	0.00404441i
$604$	−5634.80			−0.379597
$605$	−8314.13			−0.558707
$606$	−233.867	−	289.459i	−0.0156769	−	0.0194034i
$607$	−15282.5			−1.02191			−0.510953	−	0.859609i	$-0.670707\pi$
$607$	−15282.5			−1.02191			−0.510953	+	0.859609i	$0.670707\pi$
$608$	−2971.01			−0.198175
$609$	1097.93	+	1358.92i	0.0730550	+	0.0904207i
$610$	−9383.84			−0.622853
$611$			2795.17i			0.185074i
$612$	2681.33	−	12478.2i	0.177102	−	0.824187i
$613$		−	20870.2i		−	1.37511i	−0.726134	−	0.687553i	$-0.758685\pi$
$613$		−	20870.2i		−	1.37511i	0.726134	−	0.687553i	$-0.241315\pi$
$614$			2819.55i			0.185322i
$615$	3768.13	−	3044.44i	0.247066	−	0.199616i
$616$	1251.97			0.0818887
$617$	11232.5			0.732906			0.366453	−	0.930437i	$-0.380572\pi$
$617$	11232.5			0.732906			0.366453	+	0.930437i	$0.380572\pi$
$618$	5067.36	+	6271.90i	0.329837	+	0.408241i
$619$		−	11245.6i		−	0.730206i	−0.930967	−	0.365103i	$-0.881034\pi$
$619$		−	11245.6i		−	0.730206i	0.930967	−	0.365103i	$-0.118966\pi$
$620$	−1348.38			−0.0873422
$621$	12646.3	−	8919.29i	0.817197	−	0.576359i
$622$	18788.5			1.21118
$623$		−	91.9038i		−	0.00591019i
$624$	−323.269	−	400.113i	−0.0207390	−	0.0256688i
$625$	334.099			0.0213824
$626$	−3315.58			−0.211689
$627$	18947.7	−	15308.7i	1.20686	−	0.975075i
$628$			3351.24i			0.212944i
$629$		−	6529.13i		−	0.413885i
$630$	−239.912	+	1116.49i	−0.0151719	+	0.0706062i
$631$		−	22890.2i		−	1.44413i	−0.691827	−	0.722064i	$-0.743194\pi$
$631$		−	22890.2i		−	1.44413i	0.691827	−	0.722064i	$-0.256806\pi$
$632$	9787.52			0.616023
$633$	−865.631	−	1071.40i	−0.0543535	−	0.0672737i
$634$	11295.3			0.707560
$635$	14017.5			0.876012
$636$	3473.02	+	4298.58i	0.216532	+	0.268003i
$637$	2062.74			0.128303
$638$	−10954.7			−0.679784
$639$	−8312.91	−	1786.29i	−0.514638	−	0.110586i
$640$			873.364i			0.0539418i
$641$	−18165.2			−1.11931			−0.559657	−	0.828724i	$-0.689067\pi$
$641$	−18165.2			−1.11931			−0.559657	+	0.828724i	$0.689067\pi$
$642$	1100.56	−	889.193i	0.0676568	−	0.0546630i
$643$		−	12929.0i		−	0.792954i	−0.918045	−	0.396477i	$-0.870233\pi$
$643$		−	12929.0i		−	0.792954i	0.918045	−	0.396477i	$-0.129767\pi$
$644$	−199.436	−	1352.88i	−0.0122032	−	0.0827810i
$645$	−5843.07	+	4720.88i	−0.356699	+	0.288193i
$646$	−21943.9			−1.33649
$647$			23926.6i			1.45387i	0.686708	+	0.726933i	$0.259055\pi$
$647$			23926.6i			1.45387i	−0.686708	+	0.726933i	$0.740945\pi$
$648$	−2395.75	+	5317.20i	−0.145238	+	0.322345i
$649$		−	32990.6i		−	1.99537i
$650$		−	970.688i		−	0.0585747i
$651$	−618.896	+	500.034i	−0.0372603	+	0.0301043i
$652$	7678.30			0.461205
$653$		−	16405.2i		−	0.983134i	−0.870840	−	0.491567i	$-0.836424\pi$
$653$		−	16405.2i		−	0.983134i	0.870840	−	0.491567i	$-0.163576\pi$
$654$	−2304.93	−	2852.83i	−0.137813	−	0.170572i
$655$		−	11128.6i		−	0.663862i
$656$		−	2186.18i		−	0.130116i
$657$	−4511.15	+	20993.7i	−0.267879	+	1.24664i
$658$		−	2800.44i		−	0.165916i
$659$	3748.37			0.221572			0.110786	−	0.993844i	$-0.464663\pi$
$659$	3748.37			0.221572			0.110786	+	0.993844i	$0.464663\pi$
$660$	−4500.20	−	5569.92i	−0.265409	−	0.328499i
$661$			20659.5i			1.21568i	0.794060	+	0.607839i	$0.207963\pi$
$661$			20659.5i			1.21568i	−0.794060	+	0.607839i	$0.792037\pi$
$662$		−	14420.9i		−	0.846651i
$663$	−2387.68	−	2955.24i	−0.139864	−	0.173110i
$664$			3230.69i			0.188818i
$665$	1963.43			0.114494
$666$	−626.778	+	2916.86i	−0.0364672	+	0.169709i
$667$	1745.06	+	11837.7i	0.101303	+	0.687191i
$668$		−	1682.40i		−	0.0974462i
$669$	10414.2	+	12889.7i	0.601847	+	0.744910i
$670$	144.075			0.00830759
$671$		−	34721.1i		−	1.99761i
$672$	323.879	+	400.868i	0.0185921	+	0.0230116i
$673$	20270.8			1.16104			0.580521	−	0.814245i	$-0.302849\pi$
$673$	20270.8			1.16104			0.580521	+	0.814245i	$0.302849\pi$
$674$	−21498.3			−1.22861
$675$	−9822.54	+	4963.65i	−0.560103	+	0.283038i
$676$	8634.88			0.491288
$677$	−15499.8			−0.879922			−0.439961	−	0.898017i	$-0.645008\pi$
$677$	−15499.8			−0.879922			−0.439961	+	0.898017i	$0.645008\pi$
$678$	−5765.95	+	4658.57i	−0.326608	+	0.263881i
$679$	−3612.98			−0.204202
$680$			6450.70i			0.363784i
$681$	−15305.7	−	18944.0i	−0.861257	−	1.06598i
$682$		−	4989.13i		−	0.280123i
$683$		−	12938.6i		−	0.724865i	−0.932010	−	0.362433i	$-0.881946\pi$
$683$		−	12938.6i		−	0.724865i	0.932010	−	0.362433i	$-0.118054\pi$
$684$	9803.37	+	2106.56i	0.548014	+	0.117758i
$685$	−21256.5			−1.18565
$686$	−4192.82			−0.233356
$687$	−24525.3	+	19815.1i	−1.36201	+	1.10043i
$688$			3390.01i			0.187853i
$689$	1645.04			0.0909596
$690$	−5301.99	+	5750.18i	−0.292526	+	0.317254i
$691$	−9114.95			−0.501807			−0.250904	−	0.968012i	$-0.580728\pi$
$691$	−9114.95			−0.501807			−0.250904	+	0.968012i	$0.580728\pi$
$692$			12643.0i			0.694529i
$693$	−4131.11	−	887.697i	−0.226447	−	0.0486592i
$694$	−10089.2			−0.551848
$695$	−12892.8			−0.703672
$696$	−2833.94	−	3507.58i	−0.154339	−	0.191027i
$697$		−	16147.2i		−	0.877500i
$698$		−	22011.9i		−	1.19364i
$699$	−7388.05	+	5969.14i	−0.399774	+	0.322995i
$700$			972.520i			0.0525112i
$701$	−10252.8			−0.552417			−0.276209	−	0.961098i	$-0.589078\pi$
$701$	−10252.8			−0.552417			−0.276209	+	0.961098i	$0.589078\pi$
$702$	782.990	+	1549.45i	0.0420969	+	0.0833054i
$703$	5129.53			0.275198
$704$	−3231.53			−0.173002
$705$	−12458.9	+	10066.1i	−0.665576	+	0.537749i
$706$	12098.7			0.644956
$707$	110.984			0.00590377
$708$	10563.2	−	8534.50i	0.560720	−	0.453031i
$709$			30842.0i			1.63370i	0.576848	+	0.816852i	$0.304283\pi$
$709$			30842.0i			1.63370i	−0.576848	+	0.816852i	$0.695717\pi$
$710$	4297.41			0.227153
$711$	−32295.7	−	6939.73i	−1.70349	−	0.366048i
$712$			237.218i			0.0124861i
$713$	−5391.25	+	794.754i	−0.283175	+	0.0417444i
$714$	2392.18	+	2960.82i	0.125385	+	0.155190i
$715$	−2131.58			−0.111492
$716$			13264.5i			0.692343i
$717$	13962.3	−	11280.8i	0.727240	−	0.587570i
$718$		−	4788.38i		−	0.248887i
$719$			14449.8i			0.749496i	0.927127	+	0.374748i	$0.122271\pi$
$719$			14449.8i			0.749496i	−0.927127	+	0.374748i	$0.877729\pi$
$720$	619.249	−	2881.82i	0.0320528	−	0.149166i
$721$	−2404.75			−0.124213
$722$		−	3522.00i		−	0.181545i
$723$	−3155.34	+	2549.34i	−0.162308	+	0.131136i
$724$			11961.5i			0.614014i
$725$		−	8509.53i		−	0.435912i
$726$	9850.00	−	7958.26i	0.503537	−	0.406830i
$727$			32756.4i			1.67107i	0.549437	+	0.835535i	$0.314842\pi$
$727$			32756.4i			1.67107i	−0.549437	+	0.835535i	$0.685158\pi$
$728$	153.410			0.00781010
$729$	11675.3	−	15846.4i	0.593167	−	0.805079i
$730$		−	10852.8i		−	0.550248i
$731$			25038.7i			1.26688i
$732$	11117.3	−	8982.18i	0.561349	−	0.453540i
$733$		−	38694.2i		−	1.94980i	−0.222639	−	0.974901i	$-0.571467\pi$
$733$		−	38694.2i		−	1.94980i	0.222639	−	0.974901i	$-0.428533\pi$
$734$	−20548.2			−1.03331
$735$	7428.48	+	9194.28i	0.372794	+	0.461410i
$736$	514.774	+	3491.99i	0.0257810	+	0.174887i
$737$			533.090i			0.0266440i
$738$	−1550.08	+	7213.69i	−0.0773162	+	0.359810i
$739$	18619.1			0.926813			0.463407	−	0.886146i	$-0.346627\pi$
$739$	18619.1			0.926813			0.463407	+	0.886146i	$0.346627\pi$
$740$		−	1507.89i		−	0.0749070i
$741$	2321.75	−	1875.85i	0.115104	−	0.0929974i
$742$	−1648.15			−0.0815437
$743$	14237.7			0.703003			0.351502	−	0.936187i	$-0.385671\pi$
$743$	14237.7			0.703003			0.351502	+	0.936187i	$0.385671\pi$
$744$	1597.46	−	1290.66i	0.0787176	−	0.0635995i
$745$	4420.38			0.217383
$746$	−10435.3			−0.512147
$747$	2290.68	−	10660.2i	0.112198	−	0.522139i
$748$	−23868.2			−1.16672
$749$			421.973i			0.0205855i
$750$	11221.1	−	9066.06i	0.546317	−	0.441394i
$751$			30448.9i			1.47949i	0.672887	+	0.739745i	$0.265054\pi$
$751$			30448.9i			1.47949i	−0.672887	+	0.739745i	$0.734946\pi$
$752$			7228.38i			0.350521i
$753$	−18640.3	−	23071.2i	−0.902111	−	1.11655i
$754$	−1342.33			−0.0648341
$755$	−9611.79			−0.463323
$756$	−784.467	−	1552.38i	−0.0377392	−	0.0746818i
$757$			1061.16i			0.0509492i	0.999675	+	0.0254746i	$0.00810970\pi$
$757$			1061.16i			0.0509492i	−0.999675	+	0.0254746i	$0.991890\pi$
$758$	20081.5			0.962258
$759$	−21276.2	−	19617.9i	−1.01749	−	0.938187i
$760$	−5067.91			−0.241885
$761$		−	3736.49i		−	0.177986i	−0.996032	−	0.0889932i	$-0.971635\pi$
$761$		−	3736.49i		−	0.177986i	0.996032	−	0.0889932i	$-0.0283649\pi$
$762$	−16607.0	+	13417.5i	−0.789510	+	0.637881i
$763$	1093.82			0.0518991
$764$	15068.6			0.713565
$765$	4573.79	−	21285.2i	0.216164	−	1.00597i
$766$			3321.46i			0.156670i
$767$		−	4042.49i		−	0.190307i
$768$	−835.982	−	1034.70i	−0.0392785	−	0.0486153i
$769$			13779.4i			0.646160i	0.946372	+	0.323080i	$0.104718\pi$
$769$			13779.4i			0.646160i	−0.946372	+	0.323080i	$0.895282\pi$
$770$	2135.60			0.0999504
$771$	−22671.0	+	18316.9i	−1.05898	+	0.855600i
$772$	3956.99			0.184476
$773$	6676.82			0.310671			0.155336	−	0.987862i	$-0.450354\pi$
$773$	6676.82			0.310671			0.155336	+	0.987862i	$0.450354\pi$
$774$	2403.64	−	11185.9i	0.111624	−	0.519470i
$775$	3875.51			0.179629
$776$	9325.65			0.431406
$777$	−559.187	−	692.110i	−0.0258182	−	0.0319554i
$778$		−	29409.1i		−	1.35523i
$779$	12685.8			0.583463
$780$	−551.429	−	682.508i	−0.0253132	−	0.0313304i
$781$			15900.8i			0.728524i
$782$	3802.13	+	25792.0i	0.173867	+	1.17944i
$783$	6864.07	+	13583.3i	0.313285	+	0.619957i
$784$	5334.30			0.242998
$785$			5716.51i			0.259912i
$786$	10652.3	+	13184.4i	0.483401	+	0.598309i
$787$			36090.5i			1.63467i	0.576160	+	0.817337i	$0.304551\pi$
$787$			36090.5i			1.63467i	−0.576160	+	0.817337i	$0.695449\pi$
$788$		−	11948.8i		−	0.540176i
$789$	−2306.73	−	2855.06i	−0.104083	−	0.128825i
$790$	16695.5			0.751896
$791$		−	2210.76i		−	0.0993750i
$792$	10663.0	+	2291.28i	0.478402	+	0.102799i
$793$		−	4254.54i		−	0.190521i
$794$			6204.14i			0.277300i
$795$	5924.24	+	7332.48i	0.264291	+	0.327115i
$796$			11247.4i			0.500819i
$797$	34615.0			1.53842			0.769212	−	0.638993i	$-0.220649\pi$
$797$	34615.0			1.53842			0.769212	+	0.638993i	$0.220649\pi$
$798$	−2326.13	+	1879.39i	−0.103188	+	0.0833705i
$799$			53389.0i			2.36391i
$800$		−	2510.22i		−	0.110937i
$801$	168.197	−	782.743i	0.00741939	−	0.0345279i
$802$		−	21617.8i		−	0.951810i
$803$	40156.6			1.76475
$804$	−170.689	+	137.908i	−0.00748725	+	0.00604929i
$805$	−340.195	−	2307.73i	−0.0148948	−	0.101040i
$806$		−	611.341i		−	0.0267166i
$807$	7345.15	−	5934.48i	0.320398	−	0.258864i
$808$	−286.466			−0.0124726
$809$		−	32639.7i		−	1.41848i	−0.704966	−	0.709241i	$-0.749038\pi$
$809$		−	32639.7i		−	1.41848i	0.704966	−	0.709241i	$-0.250962\pi$
$810$	−4086.65	+	9070.02i	−0.177272	+	0.393442i
$811$	11072.4			0.479413			0.239707	−	0.970845i	$-0.422949\pi$
$811$	11072.4			0.479413			0.239707	+	0.970845i	$0.422949\pi$
$812$	1344.87			0.0581226
$813$	15862.7	+	19633.3i	0.684290	+	0.846951i
$814$	5579.34			0.240241
$815$	13097.6			0.562930
$816$	−6174.59	−	7642.33i	−0.264894	−	0.327862i
$817$	−19671.3			−0.842366
$818$		−	27721.9i		−	1.18493i
$819$	−506.204	−	108.774i	−0.0215973	−	0.00464085i
$820$		−	3729.16i		−	0.158815i
$821$			36531.8i			1.55295i	0.630150	+	0.776473i	$0.282993\pi$
$821$			36531.8i			1.55295i	−0.630150	+	0.776473i	$0.717007\pi$
$822$	25183.2	−	20346.7i	1.06857	−	0.863348i
$823$	−20802.7			−0.881087			−0.440544	−	0.897731i	$-0.645214\pi$
$823$	−20802.7			−0.881087			−0.440544	+	0.897731i	$0.645214\pi$
$824$	6207.04			0.262418
$825$	12934.5	+	16009.1i	0.545843	+	0.675593i
$826$			4050.11i			0.170607i
$827$	6969.33			0.293044			0.146522	−	0.989207i	$-0.453192\pi$
$827$	6969.33			0.293044			0.146522	+	0.989207i	$0.453192\pi$
$828$	777.368	−	11887.5i	0.0326273	−	0.498934i
$829$	−38446.7			−1.61075			−0.805374	−	0.592767i	$-0.798036\pi$
$829$	−38446.7			−1.61075			−0.805374	+	0.592767i	$0.798036\pi$
$830$			5510.88i			0.230464i
$831$	2036.83	+	2521.01i	0.0850265	+	0.105238i
$832$	−395.975			−0.0164999
$833$	39399.3			1.63878
$834$	15274.5	−	12341.0i	0.634187	−	0.512389i
$835$		−	2869.82i		−	0.118939i
$836$		−	18751.8i		−	0.775770i
$837$	−6186.25	+	3126.12i	−0.255470	+	0.129097i
$838$			16205.5i			0.668029i
$839$	−39708.6			−1.63396			−0.816981	−	0.576665i	$-0.804354\pi$
$839$	−39708.6			−1.63396			−0.816981	+	0.576665i	$0.804354\pi$
$840$	552.470	+	683.796i	0.0226929	+	0.0280871i
$841$	12621.5			0.517506
$842$	3650.20			0.149399
$843$	1379.65	+	1707.60i	0.0563673	+	0.0697663i
$844$	−1060.32			−0.0432436
$845$	14729.3			0.599648
$846$	5125.20	−	23851.3i	0.208284	−	0.969298i
$847$			3776.66i			0.153208i
$848$	4254.12			0.172273
$849$	24105.1	−	19475.6i	0.974421	−	0.787279i
$850$		−	18540.6i		−	0.748161i
$851$	−888.772	−	6029.03i	−0.0358011	−	0.242858i
$852$	−5091.27	+	4113.47i	−0.204723	+	0.165405i
$853$	−32775.6			−1.31561			−0.657804	−	0.753189i	$-0.728515\pi$
$853$	−32775.6			−1.31561			−0.657804	+	0.753189i	$0.728515\pi$
$854$			4262.57i			0.170799i
$855$	16722.5	+	3593.34i	0.668886	+	0.143731i
$856$		−	1089.18i		−	0.0434899i
$857$		−	3793.04i		−	0.151188i	−0.997139	−	0.0755939i	$-0.975915\pi$
$857$		−	3793.04i		−	0.151188i	0.997139	−	0.0755939i	$-0.0240852\pi$
$858$	2525.35	−	2040.34i	0.100482	−	0.0811843i
$859$	−6491.04			−0.257825			−0.128912	−	0.991656i	$-0.541149\pi$
$859$	−6491.04			−0.257825			−0.128912	+	0.991656i	$0.541149\pi$
$860$			5782.64i			0.229286i
$861$	−1382.92	−	1711.66i	−0.0547386	−	0.0677504i
$862$		−	2253.07i		−	0.0890253i
$863$		−	19140.0i		−	0.754962i	−0.926017	−	0.377481i	$-0.876790\pi$
$863$		−	19140.0i		−	0.754962i	0.926017	−	0.377481i	$-0.123210\pi$
$864$	2024.83	+	4006.93i	0.0797293	+	0.157776i
$865$			21566.3i			0.847717i
$866$	13562.3			0.532178
$867$	−29562.0	−	36589.1i	−1.15799	−	1.43325i
$868$			612.495i			0.0239510i
$869$			61774.8i			2.41147i
$870$	−4834.10	−	5983.20i	−0.188381	−	0.233160i
$871$			65.3219i			0.00254116i
$872$	−2823.32			−0.109644
$873$	−30771.7	−	6612.24i	−1.19297	−	0.256347i
$874$	−20263.2	+	2987.10i	−0.784224	+	0.115607i
$875$			4302.37i			0.166225i
$876$	10388.3	+	12857.7i	0.400671	+	0.495914i
$877$	41097.4			1.58240			0.791198	−	0.611561i	$-0.209458\pi$
$877$	41097.4			1.58240			0.791198	+	0.611561i	$0.209458\pi$
$878$			27374.5i			1.05221i
$879$	11625.6	+	14389.0i	0.446098	+	0.552139i
$880$	−5512.32			−0.211159
$881$	16022.8			0.612736			0.306368	−	0.951913i	$-0.400886\pi$
$881$	16022.8			0.612736			0.306368	+	0.951913i	$0.400886\pi$
$882$	−17601.5	−	3782.22i	−0.671965	−	0.144392i
$883$	35431.4			1.35035			0.675177	−	0.737656i	$-0.264067\pi$
$883$	35431.4			1.35035			0.675177	+	0.737656i	$0.264067\pi$
$884$	−2924.68			−0.111276
$885$	18018.6	−	14558.1i	0.684395	−	0.552954i
$886$	−19101.8			−0.724308
$887$		−	8904.23i		−	0.337063i	−0.985696	−	0.168531i	$-0.946098\pi$
$887$		−	8904.23i		−	0.337063i	0.985696	−	0.168531i	$-0.0539024\pi$
$888$	1443.35	+	1786.44i	0.0545446	+	0.0675102i
$889$		−	6367.39i		−	0.240220i
$890$			404.644i			0.0152401i
$891$	−33560.0	−	15121.0i	−1.26184	−	0.568544i
$892$	12756.4			0.478830
$893$	−41944.4			−1.57180
$894$	−5236.95	+	4231.17i	−0.195917	+	0.158290i
$895$			22626.4i			0.845049i
$896$	396.722			0.0147919
$897$	−2607.07	−	2403.87i	−0.0970431	−	0.0894791i
$898$	31658.0			1.17644
$899$		−	5359.32i		−	0.198824i
$900$	−1779.84	+	8282.94i	−0.0659202	+	0.306775i
$901$	31421.1			1.16181
$902$	13798.3			0.509348
$903$	2144.44	+	2654.19i	0.0790282	+	0.0978137i
$904$			5706.32i			0.209944i
$905$			20403.8i			0.749444i
$906$	11387.4	−	9200.38i	0.417572	−	0.337375i
$907$		−	431.477i		−	0.0157960i	−0.999969	−	0.00789799i	$-0.997486\pi$
$907$		−	431.477i		−	0.0157960i	0.999969	−	0.00789799i	$-0.00251404\pi$
$908$	−18748.1			−0.685216
$909$	945.245	+	203.115i	0.0344904	+	0.00741134i
$910$	261.685			0.00953272
$911$	−5895.76			−0.214418			−0.107209	−	0.994236i	$-0.534191\pi$
$911$	−5895.76			−0.214418			−0.107209	+	0.994236i	$0.534191\pi$
$912$	6004.11	−	4850.99i	0.218000	−	0.176132i
$913$	−20390.8			−0.739143
$914$	−24746.0			−0.895540
$915$	18963.8	−	15321.7i	0.685163	−	0.553574i
$916$			24271.7i			0.875501i
$917$	−5055.11			−0.182044
$918$	14955.5	+	29595.3i	0.537695	+	1.06404i
$919$			5190.53i			0.186311i	0.995652	+	0.0931555i	$0.0296954\pi$
$919$			5190.53i			0.186311i	−0.995652	+	0.0931555i	$0.970305\pi$
$920$	878.096	+	5956.61i	0.0314674	+	0.213460i
$921$	−4603.69	−	5698.02i	−0.164709	−	0.203861i
$922$	−12888.9			−0.460383
$923$			1948.40i			0.0694826i
$924$	−2530.11	+	2044.19i	−0.0900807	+	0.0727803i
$925$			4333.98i			0.154054i
$926$			250.582i			0.00889269i
$927$	−20481.2	−	4401.03i	−0.725666	−	0.155932i
$928$	−3471.31			−0.122792
$929$		−	35347.9i		−	1.24836i	−0.781280	−	0.624181i	$-0.785433\pi$
$929$		−	35347.9i		−	1.24836i	0.781280	−	0.624181i	$-0.214567\pi$
$930$	2724.94	−	2201.60i	0.0960799	−	0.0776273i
$931$			30953.6i			1.08965i
$932$			7311.64i			0.256975i
$933$	−37969.8	+	30677.5i	−1.33234	+	1.07646i
$934$			12978.1i			0.454663i
$935$	−40714.2			−1.42406
$936$	1306.59	+	280.761i	0.0456274	+	0.00980445i
$937$		−	25527.4i		−	0.890016i	−0.895527	−	0.445008i	$-0.853201\pi$
$937$		−	25527.4i		−	0.890016i	0.895527	−	0.445008i	$-0.146799\pi$
$938$		−	65.4452i		−	0.00227810i
$939$	6700.45	−	5413.60i	0.232866	−	0.188143i
$940$			12330.1i			0.427833i
$941$	−22904.6			−0.793484			−0.396742	−	0.917930i	$-0.629859\pi$
$941$	−22904.6			−0.793484			−0.396742	+	0.917930i	$0.629859\pi$
$942$	−5471.83	−	6772.52i	−0.189259	−	0.234247i
$943$	−2198.02	−	14910.4i	−0.0759039	−	0.514898i
$944$		−	10454.0i		−	0.360432i
$945$	−1338.14	−	2648.03i	−0.0460630	−	0.0911539i
$946$	−21396.3			−0.735364
$947$		−	41716.2i		−	1.43146i	−0.698376	−	0.715731i	$-0.746094\pi$
$947$		−	41716.2i		−	1.43146i	0.698376	−	0.715731i	$-0.253906\pi$
$948$	−19779.6	+	15980.8i	−0.677649	+	0.547504i
$949$	4920.56			0.168312
$950$	14566.2			0.497463
$951$	−22826.7	+	18442.7i	−0.778344	+	0.628859i
$952$	2930.20			0.0997566
$953$	31526.7			1.07162			0.535808	−	0.844340i	$-0.320007\pi$
$953$	31526.7			1.07162			0.535808	+	0.844340i	$0.320007\pi$
$954$	−14037.3	−	3016.34i	−0.476387	−	0.102366i
$955$	25703.9			0.870952
$956$		−	13817.9i		−	0.467471i
$957$	22138.4	−	17886.6i	0.747789	−	0.604172i
$958$			23687.5i			0.798860i
$959$			9655.68i			0.325128i
$960$	−1426.01	−	1764.98i	−0.0479419	−	0.0593381i
$961$	−27350.2			−0.918069
$962$	683.662			0.0229128
$963$	−772.269	+	3593.94i	−0.0258422	+	0.120263i
$964$			3122.71i			0.104332i
$965$	6749.79			0.225164
$966$	2611.99	+	2408.40i	0.0869974	+	0.0802165i
$967$	−22749.5			−0.756539			−0.378270	−	0.925695i	$-0.623481\pi$
$967$	−22749.5			−0.756539			−0.378270	+	0.925695i	$0.623481\pi$
$968$		−	9748.13i		−	0.323674i
$969$	44346.5	−	35829.6i	1.47019	−	1.18783i
$970$	15907.6			0.526559
$971$	−37825.3			−1.25013			−0.625063	−	0.780574i	$-0.714927\pi$
$971$	−37825.3			−1.25013			−0.625063	+	0.780574i	$0.714927\pi$
$972$	−3840.23	−	14657.3i	−0.126724	−	0.483675i
$973$			5856.50i			0.192961i
$974$		−	29540.6i		−	0.971810i
$975$	1584.92	+	1961.66i	0.0520595	+	0.0644344i
$976$		−	11002.3i		−	0.360836i
$977$	−7808.43			−0.255695			−0.127847	−	0.991794i	$-0.540807\pi$
$977$	−7808.43			−0.255695			−0.127847	+	0.991794i	$0.540807\pi$
$978$	−15517.1	+	12537.0i	−0.507343	+	0.409906i
$979$	−1497.22			−0.0488779
$980$	9099.20			0.296595
$981$	9316.06	+	2001.84i	0.303200	+	0.0651518i
$982$	179.041			0.00581815
$983$	−31418.9			−1.01944			−0.509719	−	0.860341i	$-0.670251\pi$
$983$	−31418.9			−1.01944			−0.509719	+	0.860341i	$0.670251\pi$
$984$	3569.54	+	4418.05i	0.115643	+	0.143132i
$985$		−	20382.2i		−	0.659319i
$986$	−25639.2			−0.828111
$987$	4572.50	+	5659.42i	0.147461	+	0.182514i
$988$		−	2297.74i		−	0.0739887i
$989$	3408.37	+	23120.9i	0.109585	+	0.743378i
$990$	18188.9	+	3908.45i	0.583920	+	0.125473i
$991$	−22161.3			−0.710370			−0.355185	−	0.934796i	$-0.615582\pi$
$991$	−22161.3			−0.710370			−0.355185	+	0.934796i	$0.615582\pi$
$992$		−	1580.94i		−	0.0505998i
$993$	23546.1	+	29143.1i	0.752479	+	0.931349i
$994$		−	1952.08i		−	0.0622899i
$995$			19185.6i			0.611281i
$996$	−5275.00	−	6528.91i	−0.167816	−	0.207707i
$997$	−8949.91			−0.284299			−0.142150	−	0.989845i	$-0.545401\pi$
$997$	−8949.91			−0.284299			−0.142150	+	0.989845i	$0.545401\pi$
$998$			7373.83i			0.233882i
$999$	−3495.93	−	6918.08i	−0.110717	−	0.219097i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	138.4.d.a.137.15	yes	24
3.2	odd	2	inner	138.4.d.a.137.4	yes	24
23.22	odd	2	inner	138.4.d.a.137.16	yes	24
69.68	even	2	inner	138.4.d.a.137.3	✓	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
138.4.d.a.137.3	✓	24	69.68	even	2	inner
138.4.d.a.137.4	yes	24	3.2	odd	2	inner
138.4.d.a.137.15	yes	24	1.1	even	1	trivial
138.4.d.a.137.16	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)

\(f(q)\)	\(=\)	\(q+2.00000i q^{2} +(-3.26555 - 4.04180i) q^{3} -4.00000 q^{4} -6.82316 q^{5} +(8.08360 - 6.53111i) q^{6} +3.09939i q^{7} -8.00000i q^{8} +(-5.67231 + 26.3974i) q^{9} +O(q^{10})\)	\(q+2.00000i q^{2} +(-3.26555 - 4.04180i) q^{3} -4.00000 q^{4} -6.82316 q^{5} +(8.08360 - 6.53111i) q^{6} +3.09939i q^{7} -8.00000i q^{8} +(-5.67231 + 26.3974i) q^{9} -13.6463i q^{10} +50.4927 q^{11} +(13.0622 + 16.1672i) q^{12} +6.18710 q^{13} -6.19878 q^{14} +(22.2814 + 27.5779i) q^{15} +16.0000 q^{16} +118.176 q^{17} +(-52.7949 - 11.3446i) q^{18} +92.8440i q^{19} +27.2926 q^{20} +(12.5271 - 10.1212i) q^{21} +100.985i q^{22} +(109.125 - 16.0867i) q^{23} +(-32.3344 + 26.1244i) q^{24} -78.4445 q^{25} +12.3742i q^{26} +(125.216 - 63.2760i) q^{27} -12.3976i q^{28} +108.478i q^{29} +(-55.1557 + 44.5628i) q^{30} -49.4045 q^{31} +32.0000i q^{32} +(-164.887 - 204.082i) q^{33} +236.353i q^{34} -21.1476i q^{35} +(22.6892 - 105.590i) q^{36} -55.2490i q^{37} -185.688 q^{38} +(-20.2043 - 25.0070i) q^{39} +54.5853i q^{40} -136.636i q^{41} +(20.2425 + 25.0542i) q^{42} +211.875i q^{43} -201.971 q^{44} +(38.7031 - 180.114i) q^{45} +(32.1734 + 218.250i) q^{46} +451.774i q^{47} +(-52.2489 - 64.6688i) q^{48} +333.394 q^{49} -156.889i q^{50} +(-385.912 - 477.646i) q^{51} -24.7484 q^{52} +265.883 q^{53} +(126.552 + 250.433i) q^{54} -344.520 q^{55} +24.7951 q^{56} +(375.257 - 303.187i) q^{57} -216.957 q^{58} -653.373i q^{59} +(-89.1256 - 110.311i) q^{60} -687.646i q^{61} -98.8090i q^{62} +(-81.8160 - 17.5807i) q^{63} -64.0000 q^{64} -42.2156 q^{65} +(408.163 - 329.774i) q^{66} +10.5578i q^{67} -472.706 q^{68} +(-421.372 - 388.529i) q^{69} +42.2953 q^{70} +314.914i q^{71} +(211.180 + 45.3785i) q^{72} +795.294 q^{73} +110.498 q^{74} +(256.165 + 317.057i) q^{75} -371.376i q^{76} +156.497i q^{77} +(50.0141 - 40.4086i) q^{78} +1223.44i q^{79} -109.171 q^{80} +(-664.650 - 299.469i) q^{81} +273.272 q^{82} -403.836 q^{83} +(-50.1085 + 40.4849i) q^{84} -806.337 q^{85} -423.751 q^{86} +(438.448 - 354.242i) q^{87} -403.942i q^{88} -29.6522 q^{89} +(360.228 + 77.4061i) q^{90} +19.1762i q^{91} +(-436.499 + 64.3467i) q^{92} +(161.333 + 199.683i) q^{93} -903.547 q^{94} -633.489i q^{95} +(129.338 - 104.498i) q^{96} +1165.71i q^{97} +666.788i q^{98} +(-286.410 + 1332.88i) 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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