LMFDB - Embedded newform 230.3.c.a.229.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("230.229");

S:= CuspForms(chi, 3);

N := Newforms(S);

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

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$6.26704608029$
Analytic rank:	$0$
Dimension:	$24$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			229.3
Character	$\chi$	$=$	230.229
Dual form			230.3.c.a.229.21

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.41421i q^{2} -2.29017i q^{3} -2.00000 q^{4} +(-2.28201 - 4.44887i) q^{5} -3.23879 q^{6} -9.92340 q^{7} +2.82843i q^{8} +3.75511 q^{9} +O(q^{10})$	\(q-1.41421i q^{2} -2.29017i q^{3} -2.00000 q^{4} +(-2.28201 - 4.44887i) q^{5} -3.23879 q^{6} -9.92340 q^{7} +2.82843i q^{8} +3.75511 q^{9} +(-6.29165 + 3.22725i) q^{10} +3.77166i q^{11} +4.58035i q^{12} +6.77647i q^{13} +14.0338i q^{14} +(-10.1887 + 5.22619i) q^{15} +4.00000 q^{16} -8.36352 q^{17} -5.31052i q^{18} +3.59141i q^{19} +(4.56402 + 8.89774i) q^{20} +22.7263i q^{21} +5.33394 q^{22} +(-1.76487 - 22.9322i) q^{23} +6.47759 q^{24} +(-14.5849 + 20.3047i) q^{25} +9.58338 q^{26} -29.2114i q^{27} +19.8468 q^{28} +5.85684 q^{29} +(7.39096 + 14.4090i) q^{30} -42.7430 q^{31} -5.65685i q^{32} +8.63776 q^{33} +11.8278i q^{34} +(22.6453 + 44.1479i) q^{35} -7.51021 q^{36} +4.28977 q^{37} +5.07902 q^{38} +15.5193 q^{39} +(12.5833 - 6.45449i) q^{40} -25.3700 q^{41} +32.1399 q^{42} -65.1140 q^{43} -7.54332i q^{44} +(-8.56918 - 16.7060i) q^{45} +(-32.4310 + 2.49590i) q^{46} -5.16843i q^{47} -9.16069i q^{48} +49.4739 q^{49} +(28.7152 + 20.6261i) q^{50} +19.1539i q^{51} -13.5529i q^{52} +8.63917 q^{53} -41.3112 q^{54} +(16.7796 - 8.60696i) q^{55} -28.0676i q^{56} +8.22495 q^{57} -8.28282i q^{58} +82.3317 q^{59} +(20.3774 - 10.4524i) q^{60} -108.297i q^{61} +60.4477i q^{62} -37.2634 q^{63} -8.00000 q^{64} +(30.1477 - 15.4640i) q^{65} -12.2156i q^{66} -30.7493 q^{67} +16.7270 q^{68} +(-52.5187 + 4.04186i) q^{69} +(62.4346 - 32.0253i) q^{70} -117.687 q^{71} +10.6210i q^{72} -81.8929i q^{73} -6.06665i q^{74} +(46.5013 + 33.4019i) q^{75} -7.18282i q^{76} -37.4277i q^{77} -21.9476i q^{78} -138.608i q^{79} +(-9.12803 - 17.7955i) q^{80} -33.1032 q^{81} +35.8787i q^{82} +33.5348 q^{83} -45.4526i q^{84} +(19.0856 + 37.2082i) q^{85} +92.0850i q^{86} -13.4132i q^{87} -10.6679 q^{88} +49.1683i q^{89} +(-23.6258 + 12.1187i) q^{90} -67.2457i q^{91} +(3.52974 + 45.8644i) q^{92} +97.8888i q^{93} -7.30926 q^{94} +(15.9777 - 8.19562i) q^{95} -12.9552 q^{96} +138.450 q^{97} -69.9666i q^{98} +14.1630i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q - 48 q^{4} + 8 q^{6} - 96 q^{9}+O(q^{10}) $ 24 * q - 48 * q^4 + 8 * q^6 - 96 * q^9	$ 24 q - 48 q^{4} + 8 q^{6} - 96 q^{9} + 96 q^{16} - 16 q^{24} - 48 q^{25} - 32 q^{26} + 100 q^{29} - 124 q^{31} - 28 q^{35} + 192 q^{36} + 192 q^{39} - 116 q^{41} + 148 q^{46} - 76 q^{49} - 144 q^{50} - 16 q^{54} - 224 q^{55} + 84 q^{59} - 192 q^{64} - 340 q^{69} + 328 q^{70} + 196 q^{71} - 496 q^{75} + 1360 q^{81} + 316 q^{85} - 376 q^{94} - 368 q^{95} + 32 q^{96}+O(q^{100}) $ 24 * q - 48 * q^4 + 8 * q^6 - 96 * q^9 + 96 * q^16 - 16 * q^24 - 48 * q^25 - 32 * q^26 + 100 * q^29 - 124 * q^31 - 28 * q^35 + 192 * q^36 + 192 * q^39 - 116 * q^41 + 148 * q^46 - 76 * q^49 - 144 * q^50 - 16 * q^54 - 224 * q^55 + 84 * q^59 - 192 * q^64 - 340 * q^69 + 328 * q^70 + 196 * q^71 - 496 * q^75 + 1360 * q^81 + 316 * q^85 - 376 * q^94 - 368 * q^95 + 32 * q^96

Display 100 coefficients 10 coefficients

Character values

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

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

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$		−	1.41421i		−	0.707107i
$2$		−	1.41421i		−	0.707107i
$3$		−	2.29017i		−	0.763391i	−0.924288	−	0.381696i	$-0.875340\pi$
$3$		−	2.29017i		−	0.763391i	0.924288	−	0.381696i	$-0.124660\pi$
$4$	−2.00000			−0.500000
$5$	−2.28201	−	4.44887i	−0.456402	−	0.889774i
$5$	−2.28201	−	4.44887i	−0.456402	−	0.889774i
$6$	−3.23879			−0.539799
$7$	−9.92340			−1.41763			−0.708814	−	0.705395i	$-0.750770\pi$
$7$	−9.92340			−1.41763			−0.708814	+	0.705395i	$0.750770\pi$
$8$			2.82843i			0.353553i
$9$	3.75511			0.417234
$10$	−6.29165	+	3.22725i	−0.629165	+	0.322725i
$11$			3.77166i			0.342878i	0.985195	+	0.171439i	$0.0548417\pi$
$11$			3.77166i			0.342878i	−0.985195	+	0.171439i	$0.945158\pi$
$12$			4.58035i			0.381696i
$13$			6.77647i			0.521267i	0.965438	+	0.260634i	$0.0839315\pi$
$13$			6.77647i			0.521267i	−0.965438	+	0.260634i	$0.916069\pi$
$14$			14.0338i			1.00241i
$15$	−10.1887	+	5.22619i	−0.679246	+	0.348413i
$16$	4.00000			0.250000
$17$	−8.36352			−0.491972			−0.245986	−	0.969273i	$-0.579112\pi$
$17$	−8.36352			−0.491972			−0.245986	+	0.969273i	$0.579112\pi$
$18$		−	5.31052i		−	0.295029i
$19$			3.59141i			0.189022i	0.995524	+	0.0945108i	$0.0301287\pi$
$19$			3.59141i			0.189022i	−0.995524	+	0.0945108i	$0.969871\pi$
$20$	4.56402	+	8.89774i	0.228201	+	0.444887i
$21$			22.7263i			1.08221i
$22$	5.33394			0.242452
$23$	−1.76487	−	22.9322i	−0.0767335	−	0.997052i
$23$	−1.76487	−	22.9322i	−0.0767335	−	0.997052i
$24$	6.47759			0.269900
$25$	−14.5849	+	20.3047i	−0.583395	+	0.812188i
$26$	9.58338			0.368592
$27$		−	29.2114i		−	1.08190i
$28$	19.8468			0.708814
$29$	5.85684			0.201960			0.100980	−	0.994888i	$-0.467802\pi$
$29$	5.85684			0.201960			0.100980	+	0.994888i	$0.467802\pi$
$30$	7.39096	+	14.4090i	0.246365	+	0.480299i
$31$	−42.7430			−1.37881			−0.689403	−	0.724378i	$-0.742127\pi$
$31$	−42.7430			−1.37881			−0.689403	+	0.724378i	$0.742127\pi$
$32$		−	5.65685i		−	0.176777i
$33$	8.63776			0.261750
$34$			11.8278i			0.347876i
$35$	22.6453	+	44.1479i	0.647008	+	1.26137i
$36$	−7.51021			−0.208617
$37$	4.28977			0.115940			0.0579699	−	0.998318i	$-0.481537\pi$
$37$	4.28977			0.115940			0.0579699	+	0.998318i	$0.481537\pi$
$38$	5.07902			0.133658
$39$	15.5193			0.397931
$40$	12.5833	−	6.45449i	0.314583	−	0.161362i
$41$	−25.3700			−0.618781			−0.309391	−	0.950935i	$-0.600125\pi$
$41$	−25.3700			−0.618781			−0.309391	+	0.950935i	$0.600125\pi$
$42$	32.1399			0.765235
$43$	−65.1140			−1.51428			−0.757139	−	0.653254i	$-0.773404\pi$
$43$	−65.1140			−1.51428			−0.757139	+	0.653254i	$0.773404\pi$
$44$		−	7.54332i		−	0.171439i
$45$	−8.56918	−	16.7060i	−0.190426	−	0.371244i
$46$	−32.4310	+	2.49590i	−0.705022	+	0.0542587i
$47$		−	5.16843i		−	0.109966i	−0.998487	−	0.0549832i	$-0.982489\pi$
$47$		−	5.16843i		−	0.109966i	0.998487	−	0.0549832i	$-0.0175105\pi$
$48$		−	9.16069i		−	0.190848i
$49$	49.4739			1.00967
$50$	28.7152	+	20.6261i	0.574304	+	0.412523i
$51$			19.1539i			0.375567i
$52$		−	13.5529i		−	0.260634i
$53$	8.63917			0.163003			0.0815016	−	0.996673i	$-0.474028\pi$
$53$	8.63917			0.163003			0.0815016	+	0.996673i	$0.474028\pi$
$54$	−41.3112			−0.765022
$55$	16.7796	−	8.60696i	0.305084	−	0.156490i
$56$		−	28.0676i		−	0.501207i
$57$	8.22495			0.144297
$58$		−	8.28282i		−	0.142807i
$59$	82.3317			1.39545			0.697726	−	0.716365i	$-0.254195\pi$
$59$	82.3317			1.39545			0.697726	+	0.716365i	$0.254195\pi$
$60$	20.3774	−	10.4524i	0.339623	−	0.174206i
$61$		−	108.297i		−	1.77536i	−0.460462	−	0.887680i	$-0.652316\pi$
$61$		−	108.297i		−	1.77536i	0.460462	−	0.887680i	$-0.347684\pi$
$62$			60.4477i			0.974963i
$63$	−37.2634			−0.591483
$64$	−8.00000			−0.125000
$65$	30.1477	−	15.4640i	0.463810	−	0.237907i
$66$		−	12.2156i		−	0.185085i
$67$	−30.7493			−0.458945			−0.229472	−	0.973315i	$-0.573700\pi$
$67$	−30.7493			−0.458945			−0.229472	+	0.973315i	$0.573700\pi$
$68$	16.7270			0.245986
$69$	−52.5187	+	4.04186i	−0.761140	+	0.0585776i
$70$	62.4346	−	32.0253i	0.891922	−	0.457504i
$71$	−117.687			−1.65756			−0.828779	−	0.559576i	$-0.810964\pi$
$71$	−117.687			−1.65756			−0.828779	+	0.559576i	$0.810964\pi$
$72$			10.6210i			0.147514i
$73$		−	81.8929i		−	1.12182i	−0.827877	−	0.560910i	$-0.810451\pi$
$73$		−	81.8929i		−	1.12182i	0.827877	−	0.560910i	$-0.189549\pi$
$74$		−	6.06665i		−	0.0819818i
$75$	46.5013	+	33.4019i	0.620018	+	0.445359i
$76$		−	7.18282i		−	0.0945108i
$77$		−	37.4277i		−	0.486074i
$78$		−	21.9476i		−	0.281380i
$79$		−	138.608i		−	1.75453i	−0.480007	−	0.877265i	$-0.659366\pi$
$79$		−	138.608i		−	1.75453i	0.480007	−	0.877265i	$-0.340634\pi$
$80$	−9.12803	−	17.7955i	−0.114100	−	0.222443i
$81$	−33.1032			−0.408682
$82$			35.8787i			0.437545i
$83$	33.5348			0.404034			0.202017	−	0.979382i	$-0.435250\pi$
$83$	33.5348			0.404034			0.202017	+	0.979382i	$0.435250\pi$
$84$		−	45.4526i		−	0.541103i
$85$	19.0856	+	37.2082i	0.224537	+	0.437743i
$86$			92.0850i			1.07076i
$87$		−	13.4132i		−	0.154174i
$88$	−10.6679			−0.121226
$89$			49.1683i			0.552453i	0.961093	+	0.276226i	$0.0890839\pi$
$89$			49.1683i			0.552453i	−0.961093	+	0.276226i	$0.910916\pi$
$90$	−23.6258	+	12.1187i	−0.262509	+	0.134652i
$91$		−	67.2457i		−	0.738963i
$92$	3.52974	+	45.8644i	0.0383667	+	0.498526i
$93$			97.8888i			1.05257i
$94$	−7.30926			−0.0777581
$95$	15.9777	−	8.19562i	0.168186	−	0.0862697i
$96$	−12.9552			−0.134950
$97$	138.450			1.42732			0.713658	−	0.700495i	$-0.247037\pi$
$97$	138.450			1.42732			0.713658	+	0.700495i	$0.247037\pi$
$98$		−	69.9666i		−	0.713945i
$99$			14.1630i			0.143060i
$100$	29.1698	−	40.6094i	0.291698	−	0.406094i
$101$	−118.002			−1.16834			−0.584168	−	0.811633i	$-0.698579\pi$
$101$	−118.002			−1.16834			−0.584168	+	0.811633i	$0.698579\pi$
$102$	27.0877			0.265566
$103$	93.5481			0.908234			0.454117	−	0.890942i	$-0.349955\pi$
$103$	93.5481			0.908234			0.454117	+	0.890942i	$0.349955\pi$
$104$	−19.1668			−0.184296
$105$	101.106	−	51.8616i	0.962918	−	0.493920i
$106$		−	12.2176i		−	0.115261i
$107$	−94.3250			−0.881542			−0.440771	−	0.897620i	$-0.645295\pi$
$107$	−94.3250			−0.881542			−0.440771	+	0.897620i	$0.645295\pi$
$108$			58.4228i			0.540952i
$109$		−	39.6045i		−	0.363344i	−0.983359	−	0.181672i	$-0.941849\pi$
$109$		−	39.6045i		−	0.363344i	0.983359	−	0.181672i	$-0.0581509\pi$
$110$	−12.1721	−	23.7300i	−0.110655	−	0.215727i
$111$		−	9.82432i		−	0.0885074i
$112$	−39.6936			−0.354407
$113$	139.567			1.23511			0.617555	−	0.786528i	$-0.288123\pi$
$113$	139.567			1.23511			0.617555	+	0.786528i	$0.288123\pi$
$114$		−	11.6318i		−	0.102034i
$115$	−97.9949	+	60.1831i	−0.852129	+	0.523331i
$116$	−11.7137			−0.100980
$117$			25.4464i			0.217490i
$118$		−	116.435i		−	0.986733i
$119$	82.9945			0.697433
$120$	−14.7819	−	28.8179i	−0.123183	−	0.240150i
$121$	106.775			0.882434
$122$	−153.155			−1.25537
$123$			58.1018i			0.472372i
$124$	85.4860			0.689403
$125$	123.616	+	18.5507i	0.988927	+	0.148406i
$126$			52.6984i			0.418241i
$127$			97.7645i			0.769799i	0.922958	+	0.384900i	$0.125764\pi$
$127$			97.7645i			0.769799i	−0.922958	+	0.384900i	$0.874236\pi$
$128$			11.3137i			0.0883883i
$129$			149.122i			1.15599i
$130$	−21.8694	−	42.6352i	−0.168226	−	0.327963i
$131$	−39.3002			−0.300002			−0.150001	−	0.988686i	$-0.547928\pi$
$131$	−39.3002			−0.300002			−0.150001	+	0.988686i	$0.547928\pi$
$132$	−17.2755			−0.130875
$133$		−	35.6390i		−	0.267962i
$134$			43.4861i			0.324523i
$135$	−129.958	+	66.6607i	−0.962650	+	0.493783i
$136$		−	23.6556i		−	0.173938i
$137$	65.5953			0.478798			0.239399	−	0.970921i	$-0.423050\pi$
$137$	65.5953			0.478798			0.239399	+	0.970921i	$0.423050\pi$
$138$	5.71605	+	74.2726i	0.0414206	+	0.538208i
$139$	−109.952			−0.791022			−0.395511	−	0.918461i	$-0.629432\pi$
$139$	−109.952			−0.791022			−0.395511	+	0.918461i	$0.629432\pi$
$140$	−45.2906	−	88.2958i	−0.323504	−	0.630684i
$141$	−11.8366			−0.0839475
$142$			166.434i			1.17207i
$143$	−25.5586			−0.178731
$144$	15.0204			0.104308
$145$	−13.3653	−	26.0563i	−0.0921748	−	0.179699i
$146$	−115.814			−0.793247
$147$		−	113.304i		−	0.770774i
$148$	−8.57955			−0.0579699
$149$			241.014i			1.61754i	0.588124	+	0.808771i	$0.299867\pi$
$149$			241.014i			1.61754i	−0.588124	+	0.808771i	$0.700133\pi$
$150$	47.2374	−	65.7628i	0.314916	−	0.438419i
$151$	−215.991			−1.43041			−0.715203	−	0.698917i	$-0.753666\pi$
$151$	−215.991			−1.43041			−0.715203	+	0.698917i	$0.753666\pi$
$152$	−10.1580			−0.0668292
$153$	−31.4059			−0.205267
$154$	−52.9308			−0.343706
$155$	97.5398	+	190.158i	0.629289	+	1.22683i
$156$	−31.0386			−0.198965
$157$	−29.1218			−0.185489			−0.0927445	−	0.995690i	$-0.529564\pi$
$157$	−29.1218			−0.185489			−0.0927445	+	0.995690i	$0.529564\pi$
$158$	−196.021			−1.24064
$159$		−	19.7852i		−	0.124435i
$160$	−25.1666	+	12.9090i	−0.157291	+	0.0806812i
$161$	17.5135	+	227.565i	0.108780	+	1.41345i
$162$			46.8150i			0.288982i
$163$			80.6418i			0.494735i	0.968922	+	0.247367i	$0.0795655\pi$
$163$			80.6418i			0.494735i	−0.968922	+	0.247367i	$0.920435\pi$
$164$	50.7401			0.309391
$165$	−19.7114	−	38.4283i	−0.119463	−	0.232899i
$166$		−	47.4254i		−	0.285695i
$167$		−	150.797i		−	0.902975i	−0.892277	−	0.451487i	$-0.850894\pi$
$167$		−	150.797i		−	0.902975i	0.892277	−	0.451487i	$-0.149106\pi$
$168$	−64.2797			−0.382617
$169$	123.079			0.728280
$170$	52.6203	−	26.9911i	0.309531	−	0.158771i
$171$			13.4861i			0.0788662i
$172$	130.228			0.757139
$173$			19.4076i			0.112182i	0.998426	+	0.0560912i	$0.0178638\pi$
$173$			19.4076i			0.112182i	−0.998426	+	0.0560912i	$0.982136\pi$
$174$	−18.9691			−0.109018
$175$	144.732	−	201.492i	0.827038	−	1.15138i
$176$			15.0866i			0.0857196i
$177$		−	188.554i		−	1.06528i
$178$	69.5345			0.390643
$179$	131.190			0.732906			0.366453	−	0.930437i	$-0.380572\pi$
$179$	131.190			0.732906			0.366453	+	0.930437i	$0.380572\pi$
$180$	17.1384	+	33.4119i	0.0952131	+	0.185622i
$181$			119.940i			0.662652i	0.943516	+	0.331326i	$0.107496\pi$
$181$			119.940i			0.662652i	−0.943516	+	0.331326i	$0.892504\pi$
$182$	−95.0997			−0.522526
$183$	−248.019			−1.35529
$184$	64.8620	−	4.99180i	0.352511	−	0.0271294i
$185$	−9.78930	−	19.0846i	−0.0529151	−	0.103160i
$186$	138.436			0.744278
$187$		−	31.5444i		−	0.168686i
$188$			10.3369i			0.0549832i
$189$			289.876i			1.53374i
$190$	−11.5904	−	22.5959i	−0.0610019	−	0.118926i
$191$			40.1019i			0.209957i	0.994474	+	0.104979i	$0.0334774\pi$
$191$			40.1019i			0.209957i	−0.994474	+	0.104979i	$0.966523\pi$
$192$			18.3214i			0.0954239i
$193$			214.452i			1.11115i	0.831466	+	0.555575i	$0.187502\pi$
$193$			214.452i			1.11115i	−0.831466	+	0.555575i	$0.812498\pi$
$194$		−	195.797i		−	1.00926i
$195$	−35.4152	−	69.0434i	−0.181616	−	0.354068i
$196$	−98.9477			−0.504835
$197$		−	38.6221i		−	0.196051i	−0.995184	−	0.0980257i	$-0.968747\pi$
$197$		−	38.6221i		−	0.196051i	0.995184	−	0.0980257i	$-0.0312527\pi$
$198$	20.0295			0.101159
$199$		−	334.055i		−	1.67867i	−0.543617	−	0.839333i	$-0.682946\pi$
$199$		−	334.055i		−	1.67867i	0.543617	−	0.839333i	$-0.317054\pi$
$200$	−57.4304	−	41.2523i	−0.287152	−	0.206261i
$201$			70.4213i			0.350355i
$202$			166.880i			0.826138i
$203$	−58.1197			−0.286304
$204$		−	38.3078i		−	0.187783i
$205$	57.8946	+	112.868i	0.282413	+	0.550576i
$206$		−	132.297i		−	0.642219i
$207$	−6.62727	−	86.1128i	−0.0320158	−	0.416004i
$208$			27.1059i			0.130317i
$209$	−13.5456			−0.0648114
$210$	−73.3434	−	142.986i	−0.349254	−	0.680886i
$211$	17.2731			0.0818630			0.0409315	−	0.999162i	$-0.486967\pi$
$211$	17.2731			0.0818630			0.0409315	+	0.999162i	$0.486967\pi$
$212$	−17.2783			−0.0815016
$213$			269.523i			1.26536i
$214$			133.396i			0.623344i
$215$	148.591	+	289.684i	0.691119	+	1.34737i
$216$	82.6223			0.382511
$217$	424.156			1.95463
$218$	−56.0092			−0.256923
$219$	−187.549			−0.856388
$220$	−33.5593	+	17.2139i	−0.152542	+	0.0782451i
$221$		−	56.6752i		−	0.256449i
$222$	−13.8937			−0.0625842
$223$		−	218.370i		−	0.979239i	−0.871936	−	0.489620i	$-0.837136\pi$
$223$		−	218.370i		−	0.979239i	0.871936	−	0.489620i	$-0.162864\pi$
$224$			56.1352i			0.250604i
$225$	−54.7678	+	76.2463i	−0.243412	+	0.338873i
$226$		−	197.378i		−	0.873355i
$227$	−170.495			−0.751078			−0.375539	−	0.926807i	$-0.622542\pi$
$227$	−170.495			−0.751078			−0.375539	+	0.926807i	$0.622542\pi$
$228$	−16.4499			−0.0721487
$229$		−	373.215i		−	1.62976i	−0.579629	−	0.814881i	$-0.696802\pi$
$229$		−	373.215i		−	1.62976i	0.579629	−	0.814881i	$-0.303198\pi$
$230$	85.1118	+	138.586i	0.370051	+	0.602546i
$231$	−85.7160			−0.371065
$232$			16.5656i			0.0714036i
$233$			308.084i			1.32225i	0.750276	+	0.661124i	$0.229920\pi$
$233$			308.084i			1.32225i	−0.750276	+	0.661124i	$0.770080\pi$
$234$	35.9866			0.153789
$235$	−22.9936	+	11.7944i	−0.0978453	+	0.0501889i
$236$	−164.663			−0.697726
$237$	−317.436			−1.33939
$238$		−	117.372i		−	0.493160i
$239$	141.838			0.593463			0.296732	−	0.954961i	$-0.404103\pi$
$239$	141.838			0.593463			0.296732	+	0.954961i	$0.404103\pi$
$240$	−40.7547	+	20.9048i	−0.169811	+	0.0871032i
$241$		−	171.606i		−	0.712060i	−0.934475	−	0.356030i	$-0.884130\pi$
$241$		−	171.606i		−	0.712060i	0.934475	−	0.356030i	$-0.115870\pi$
$242$		−	151.002i		−	0.623975i
$243$		−	187.090i		−	0.769920i
$244$			216.594i			0.887680i
$245$	−112.900	−	220.103i	−0.460815	−	0.898379i
$246$	82.1683			0.334018
$247$	−24.3371			−0.0985307
$248$		−	120.895i		−	0.487481i
$249$		−	76.8005i		−	0.308436i
$250$	26.2347	−	174.819i	0.104939	−	0.699277i
$251$		−	48.8673i		−	0.194691i	−0.995251	−	0.0973453i	$-0.968965\pi$
$251$		−	48.8673i		−	0.194691i	0.995251	−	0.0973453i	$-0.0310351\pi$
$252$	74.5268			0.295741
$253$	86.4925	−	6.65649i	0.341867	−	0.0263102i
$254$	138.260			0.544330
$255$	85.2132	−	43.7094i	0.334170	−	0.171409i
$256$	16.0000			0.0625000
$257$		−	319.787i		−	1.24431i	−0.782894	−	0.622155i	$-0.786258\pi$
$257$		−	319.787i		−	1.24431i	0.782894	−	0.622155i	$-0.213742\pi$
$258$	210.891			0.817406
$259$	−42.5691			−0.164360
$260$	−60.2953	+	30.9279i	−0.231905	+	0.118954i
$261$	21.9930			0.0842645
$262$			55.5789i			0.212133i
$263$	390.798			1.48593			0.742963	−	0.669333i	$-0.233420\pi$
$263$	390.798			1.48593			0.742963	+	0.669333i	$0.233420\pi$
$264$			24.4313i			0.0925427i
$265$	−19.7146	−	38.4345i	−0.0743949	−	0.145036i
$266$	−50.4011			−0.189478
$267$	112.604			0.421738
$268$	61.4986			0.229472
$269$	−364.221			−1.35398			−0.676992	−	0.735991i	$-0.736717\pi$
$269$	−364.221			−1.35398			−0.676992	+	0.735991i	$0.736717\pi$
$270$	94.2724	+	183.788i	0.349157	+	0.680696i
$271$	301.823			1.11374			0.556869	−	0.830601i	$-0.312003\pi$
$271$	301.823			1.11374			0.556869	+	0.830601i	$0.312003\pi$
$272$	−33.4541			−0.122993
$273$	−154.004			−0.564118
$274$		−	92.7657i		−	0.338561i
$275$	−76.5825	−	55.0092i	−0.278482	−	0.200034i
$276$	105.037	−	8.08371i	0.380570	−	0.0292888i
$277$		−	362.800i		−	1.30975i	−0.755739	−	0.654873i	$-0.772722\pi$
$277$		−	362.800i		−	1.30975i	0.755739	−	0.654873i	$-0.227278\pi$
$278$			155.496i			0.559337i
$279$	−160.504			−0.575285
$280$	−124.869	+	64.0505i	−0.445961	+	0.228752i
$281$		−	86.2564i		−	0.306962i	−0.988152	−	0.153481i	$-0.950952\pi$
$281$		−	86.2564i		−	0.306962i	0.988152	−	0.153481i	$-0.0490484\pi$
$282$			16.7395i			0.0593598i
$283$	−371.739			−1.31357			−0.656783	−	0.754079i	$-0.728083\pi$
$283$	−371.739			−1.31357			−0.656783	+	0.754079i	$0.728083\pi$
$284$	235.373			0.828779
$285$	−18.7694	−	36.5917i	−0.0658576	−	0.128392i
$286$			36.1453i			0.126382i
$287$	251.757			0.877202
$288$		−	21.2421i		−	0.0737572i
$289$	−219.052			−0.757964
$290$	−36.8492	+	18.9015i	−0.127066	+	0.0651774i
$291$		−	317.074i		−	1.08960i
$292$			163.786i			0.560910i
$293$	159.208			0.543371			0.271685	−	0.962386i	$-0.412419\pi$
$293$	159.208			0.543371			0.271685	+	0.962386i	$0.412419\pi$
$294$	−160.236			−0.545019
$295$	−187.882	−	366.283i	−0.636886	−	1.24164i
$296$			12.1333i			0.0409909i
$297$	110.176			0.370961
$298$	340.845			1.14377
$299$	155.399	−	11.9596i	0.519730	−	0.0399986i
$300$	−93.0026	−	66.8038i	−0.310009	−	0.222679i
$301$	646.152			2.14668
$302$			305.458i			1.01145i
$303$			270.245i			0.891897i
$304$			14.3656i			0.0472554i
$305$	−481.799	+	247.134i	−1.57967	+	0.810277i
$306$			44.4146i			0.145146i
$307$			10.1864i			0.0331804i	0.999862	+	0.0165902i	$0.00528106\pi$
$307$			10.1864i			0.0331804i	−0.999862	+	0.0165902i	$0.994719\pi$
$308$			74.8554i			0.243037i
$309$		−	214.241i		−	0.693338i
$310$	268.924	−	137.942i	0.867497	−	0.444975i
$311$	390.702			1.25628			0.628138	−	0.778102i	$-0.283817\pi$
$311$	390.702			1.25628			0.628138	+	0.778102i	$0.283817\pi$
$312$			43.8952i			0.140690i
$313$	536.465			1.71395			0.856973	−	0.515361i	$-0.172342\pi$
$313$	536.465			1.71395			0.856973	+	0.515361i	$0.172342\pi$
$314$			41.1844i			0.131160i
$315$	85.0354	+	165.780i	0.269954	+	0.526286i
$316$			277.216i			0.877265i
$317$			295.497i			0.932167i	0.884741	+	0.466083i	$0.154335\pi$
$317$			295.497i			0.932167i	−0.884741	+	0.466083i	$0.845665\pi$
$318$	−27.9805			−0.0879890
$319$			22.0900i			0.0692477i
$320$	18.2561	+	35.5910i	0.0570502	+	0.111222i
$321$			216.021i			0.672961i
$322$	321.826	−	24.7678i	0.999459	−	0.0769187i
$323$		−	30.0368i		−	0.0929932i
$324$	66.2065			0.204341
$325$	−137.594	−	98.8341i	−0.423367	−	0.304105i
$326$	114.045			0.349830
$327$	−90.7011			−0.277373
$328$		−	71.7573i		−	0.218772i
$329$			51.2884i			0.155892i
$330$	−54.3458	+	27.8762i	−0.164684	+	0.0844733i
$331$	−199.717			−0.603374			−0.301687	−	0.953407i	$-0.597550\pi$
$331$	−199.717			−0.603374			−0.301687	+	0.953407i	$0.597550\pi$
$332$	−67.0696			−0.202017
$333$	16.1085			0.0483740
$334$	−213.259			−0.638500
$335$	70.1702	+	136.800i	0.209463	+	0.408357i
$336$			90.9052i			0.270551i
$337$	−367.909			−1.09172			−0.545860	−	0.837877i	$-0.683797\pi$
$337$	−367.909			−1.09172			−0.545860	+	0.837877i	$0.683797\pi$
$338$		−	174.061i		−	0.514972i
$339$		−	319.634i		−	0.942872i
$340$	−38.1712	−	74.4164i	−0.112268	−	0.218872i
$341$		−	161.212i		−	0.472763i
$342$	19.0723			0.0557668
$343$	−4.70237			−0.0137095
$344$		−	184.170i		−	0.535378i
$345$	137.830	+	224.425i	0.399507	+	0.650508i
$346$	27.4464			0.0793250
$347$		−	206.127i		−	0.594025i	−0.954874	−	0.297012i	$-0.904010\pi$
$347$		−	206.127i		−	0.594025i	0.954874	−	0.297012i	$-0.0959902\pi$
$348$			26.8263i			0.0770872i
$349$	−195.800			−0.561032			−0.280516	−	0.959849i	$-0.590506\pi$
$349$	−195.800			−0.561032			−0.280516	+	0.959849i	$0.590506\pi$
$350$	−284.952	−	204.681i	−0.814150	−	0.584804i
$351$	197.950			0.563961
$352$	21.3357			0.0606129
$353$		−	335.246i		−	0.949706i	−0.880065	−	0.474853i	$-0.842501\pi$
$353$		−	335.246i		−	0.949706i	0.880065	−	0.474853i	$-0.157499\pi$
$354$	−266.655			−0.753264
$355$	268.562	+	523.572i	0.756512	+	1.47485i
$356$		−	98.3366i		−	0.276226i
$357$		−	190.072i		−	0.532414i
$358$		−	185.531i		−	0.518243i
$359$			562.219i			1.56607i	0.621978	+	0.783035i	$0.286329\pi$
$359$			562.219i			1.56607i	−0.621978	+	0.783035i	$0.713671\pi$
$360$	47.2516	−	24.2373i	0.131255	−	0.0673258i
$361$	348.102			0.964271
$362$	169.621			0.468565
$363$		−	244.532i		−	0.673643i
$364$			134.491i			0.369482i
$365$	−364.331	+	186.880i	−0.998167	+	0.512001i
$366$			350.751i			0.958337i
$367$	−402.041			−1.09548			−0.547740	−	0.836649i	$-0.684512\pi$
$367$	−402.041			−1.09548			−0.547740	+	0.836649i	$0.684512\pi$
$368$	−7.05948	−	91.7288i	−0.0191834	−	0.249263i
$369$	−95.2672			−0.258177
$370$	−26.9898	+	13.8442i	−0.0729453	+	0.0374166i
$371$	−85.7299			−0.231078
$372$		−	195.778i		−	0.526284i
$373$	−476.171			−1.27660			−0.638299	−	0.769789i	$-0.720362\pi$
$373$	−476.171			−1.27660			−0.638299	+	0.769789i	$0.720362\pi$
$374$	−44.6105			−0.119279
$375$	42.4843	−	283.102i	0.113292	−	0.754938i
$376$	14.6185			0.0388790
$377$			39.6887i			0.105275i
$378$	409.947			1.08452
$379$			522.262i			1.37800i	0.724762	+	0.688999i	$0.241950\pi$
$379$			522.262i			1.37800i	−0.724762	+	0.688999i	$0.758050\pi$
$380$	−31.9554	+	16.3912i	−0.0840932	+	0.0431349i
$381$	223.898			0.587658
$382$	56.7126			0.148462
$383$	−562.573			−1.46886			−0.734429	−	0.678685i	$-0.762550\pi$
$383$	−562.573			−1.46886			−0.734429	+	0.678685i	$0.762550\pi$
$384$	25.9104			0.0674749
$385$	−166.511	+	85.4103i	−0.432496	+	0.221845i
$386$	303.281			0.785702
$387$	−244.510			−0.631808
$388$	−276.899			−0.713658
$389$		−	700.851i		−	1.80167i	−0.434158	−	0.900837i	$-0.642954\pi$
$389$		−	700.851i		−	1.80167i	0.434158	−	0.900837i	$-0.357046\pi$
$390$	−97.6420	+	50.0846i	−0.250364	+	0.128422i
$391$	14.7605	+	191.794i	0.0377507	+	0.490521i
$392$			139.933i			0.356973i
$393$			90.0043i			0.229019i
$394$	−54.6200			−0.138629
$395$	−616.648	+	316.304i	−1.56113	+	0.800770i
$396$		−	28.3260i		−	0.0715302i
$397$		−	87.9617i		−	0.221566i	−0.993845	−	0.110783i	$-0.964664\pi$
$397$		−	87.9617i		−	0.221566i	0.993845	−	0.110783i	$-0.0353359\pi$
$398$	−472.425			−1.18700
$399$	−81.6195			−0.204560
$400$	−58.3395	+	81.2188i	−0.145849	+	0.203047i
$401$			422.433i			1.05345i	0.850036	+	0.526725i	$0.176580\pi$
$401$			422.433i			1.05345i	−0.850036	+	0.526725i	$0.823420\pi$
$402$	99.5907			0.247738
$403$		−	289.647i		−	0.718726i
$404$	236.004			0.584168
$405$	75.5419	+	147.272i	0.186523	+	0.363635i
$406$			82.1937i			0.202448i
$407$			16.1796i			0.0397532i
$408$	−54.1754			−0.132783
$409$	−153.708			−0.375814			−0.187907	−	0.982187i	$-0.560170\pi$
$409$	−153.708			−0.375814			−0.187907	+	0.982187i	$0.560170\pi$
$410$	159.619	−	81.8754i	0.389316	−	0.199696i
$411$		−	150.225i		−	0.365510i
$412$	−187.096			−0.454117
$413$	−817.010			−1.97823
$414$	−121.782	+	9.37238i	−0.294159	+	0.0226386i
$415$	−76.5267	−	149.192i	−0.184402	−	0.359499i
$416$	38.3335			0.0921479
$417$			251.809i			0.603859i
$418$			19.1563i			0.0458286i
$419$			715.672i			1.70805i	0.520233	+	0.854024i	$0.325845\pi$
$419$			715.672i			1.70805i	−0.520233	+	0.854024i	$0.674155\pi$
$420$	−202.213	+	103.723i	−0.481459	+	0.246960i
$421$		−	201.138i		−	0.477762i	−0.971049	−	0.238881i	$-0.923219\pi$
$421$		−	201.138i		−	0.477762i	0.971049	−	0.238881i	$-0.0767806\pi$
$422$		−	24.4279i		−	0.0578859i
$423$		−	19.4080i		−	0.0458818i
$424$			24.4353i			0.0576303i
$425$	121.981	−	169.819i	0.287014	−	0.399574i
$426$	381.163			0.894748
$427$			1074.67i			2.51680i
$428$	188.650			0.440771
$429$			58.5336i			0.136442i
$430$	409.674	−	210.139i	0.952731	−	0.488695i
$431$			81.1508i			0.188285i	0.995559	+	0.0941425i	$0.0300109\pi$
$431$			81.1508i			0.188285i	−0.995559	+	0.0941425i	$0.969989\pi$
$432$		−	116.846i		−	0.270476i
$433$	260.642			0.601944			0.300972	−	0.953633i	$-0.402689\pi$
$433$	260.642			0.601944			0.300972	+	0.953633i	$0.402689\pi$
$434$		−	599.847i		−	1.38214i
$435$	−59.6735	+	30.6090i	−0.137180	+	0.0703654i
$436$			79.2089i			0.181672i
$437$	82.3589	−	6.33837i	0.188464	−	0.0145043i
$438$			265.234i			0.605558i
$439$	−668.702			−1.52324			−0.761620	−	0.648024i	$-0.775596\pi$
$439$	−668.702			−1.52324			−0.761620	+	0.648024i	$0.775596\pi$
$440$	24.3442	+	47.4600i	0.0553277	+	0.107864i
$441$	185.780			0.421269
$442$	−80.1508			−0.181337
$443$		−	592.784i		−	1.33811i	−0.743212	−	0.669056i	$-0.766698\pi$
$443$		−	592.784i		−	1.33811i	0.743212	−	0.669056i	$-0.233302\pi$
$444$			19.6486i			0.0442537i
$445$	218.743	−	112.202i	0.491558	−	0.252140i
$446$	−308.822			−0.692427
$447$	551.963			1.23482
$448$	79.3872			0.177204
$449$	326.176			0.726449			0.363225	−	0.931702i	$-0.381676\pi$
$449$	326.176			0.726449			0.363225	+	0.931702i	$0.381676\pi$
$450$	107.829	+	77.4533i	0.239619	+	0.172118i
$451$		−	95.6872i		−	0.212167i
$452$	−279.135			−0.617555
$453$			494.658i			1.09196i
$454$			241.116i			0.531092i
$455$	−299.167	+	153.455i	−0.657510	+	0.337264i
$456$			23.2637i			0.0510168i
$457$	−724.352			−1.58501			−0.792507	−	0.609862i	$-0.791225\pi$
$457$	−724.352			−1.58501			−0.792507	+	0.609862i	$0.791225\pi$
$458$	−527.806			−1.15242
$459$			244.310i			0.532266i
$460$	195.990	−	120.366i	0.426065	−	0.261666i
$461$	509.925			1.10613			0.553064	−	0.833138i	$-0.313458\pi$
$461$	509.925			1.10613			0.553064	+	0.833138i	$0.313458\pi$
$462$			121.221i			0.262382i
$463$		−	639.749i		−	1.38175i	−0.722975	−	0.690874i	$-0.757226\pi$
$463$		−	639.749i		−	1.38175i	0.722975	−	0.690874i	$-0.242774\pi$
$464$	23.4273			0.0504900
$465$	435.495	−	223.383i	0.936548	−	0.480394i
$466$	435.696			0.934971
$467$	163.138			0.349332			0.174666	−	0.984628i	$-0.444115\pi$
$467$	163.138			0.349332			0.174666	+	0.984628i	$0.444115\pi$
$468$		−	50.8928i		−	0.108745i
$469$	305.138			0.650613
$470$	16.6798	+	32.5179i	0.0354889	+	0.0691871i
$471$			66.6939i			0.141601i
$472$			232.869i			0.493367i
$473$		−	245.588i		−	0.519213i
$474$			448.922i			0.947093i
$475$	−72.9225	−	52.3803i	−0.153521	−	0.110274i
$476$	−165.989			−0.348716
$477$	32.4410			0.0680104
$478$		−	200.589i		−	0.419642i
$479$		−	141.599i		−	0.295613i	−0.989016	−	0.147807i	$-0.952779\pi$
$479$		−	141.599i		−	0.295613i	0.989016	−	0.147807i	$-0.0472213\pi$
$480$	29.5638	+	57.6359i	0.0615913	+	0.120075i
$481$			29.0695i			0.0604356i
$482$	−242.688			−0.503502
$483$	521.164	−	40.1090i	1.07901	−	0.0830413i
$484$	−213.549			−0.441217
$485$	−315.943	−	615.944i	−0.651429	−	1.26999i
$486$	−264.586			−0.544415
$487$			861.286i			1.76855i	0.466963	+	0.884277i	$0.345348\pi$
$487$			861.286i			1.76855i	−0.466963	+	0.884277i	$0.654652\pi$
$488$	306.310			0.627684
$489$	184.684			0.377676
$490$	−311.272	+	159.664i	−0.635250	+	0.325846i
$491$	−714.739			−1.45568			−0.727840	−	0.685747i	$-0.759476\pi$
$491$	−714.739			−1.45568			−0.727840	+	0.685747i	$0.759476\pi$
$492$		−	116.204i		−	0.236186i
$493$	−48.9838			−0.0993585
$494$			34.4178i			0.0696718i
$495$	63.0093	−	32.3201i	0.127291	−	0.0652930i
$496$	−170.972			−0.344701
$497$	1167.85			2.34980
$498$	−108.612			−0.218097
$499$	531.913			1.06596			0.532979	−	0.846128i	$-0.321072\pi$
$499$	531.913			1.06596			0.532979	+	0.846128i	$0.321072\pi$
$500$	−247.232	−	37.1014i	−0.494463	−	0.0742028i
$501$	−345.351			−0.689323
$502$	−69.1089			−0.137667
$503$	721.625			1.43464			0.717321	−	0.696743i	$-0.245368\pi$
$503$	721.625			1.43464			0.717321	+	0.696743i	$0.245368\pi$
$504$		−	105.397i		−	0.209121i
$505$	269.281	+	524.975i	0.533230	+	1.03955i
$506$	−9.41370	−	122.319i	−0.0186041	−	0.241737i
$507$		−	281.873i		−	0.555963i
$508$		−	195.529i		−	0.384900i
$509$	829.610			1.62988			0.814941	−	0.579544i	$-0.196769\pi$
$509$	829.610			1.62988			0.814941	+	0.579544i	$0.196769\pi$
$510$	−61.8144	−	120.510i	−0.121205	−	0.236294i
$511$			812.656i			1.59033i
$512$		−	22.6274i		−	0.0441942i
$513$	104.910			0.204503
$514$	−452.248			−0.879859
$515$	−213.478	−	416.183i	−0.414520	−	0.808123i
$516$		−	298.245i		−	0.577993i
$517$	19.4936			0.0377051
$518$			60.2018i			0.116220i
$519$	44.4467			0.0856391
$520$	43.7387	+	85.2704i	0.0841129	+	0.163982i
$521$		−	431.800i		−	0.828790i	−0.910097	−	0.414395i	$-0.863993\pi$
$521$		−	431.800i		−	0.828790i	0.910097	−	0.414395i	$-0.136007\pi$
$522$		−	31.1029i		−	0.0595840i
$523$	419.527			0.802155			0.401078	−	0.916044i	$-0.368636\pi$
$523$	419.527			0.802155			0.401078	+	0.916044i	$0.368636\pi$
$524$	78.6004			0.150001
$525$	−461.451	−	331.460i	−0.878955	−	0.631353i
$526$		−	552.672i		−	1.05071i
$527$	357.482			0.678333
$528$	34.5510			0.0654376
$529$	−522.770	+	80.9446i	−0.988224	+	0.153014i
$530$	−54.3546	+	27.8807i	−0.102556	+	0.0526051i
$531$	309.164			0.582230
$532$			71.2780i			0.133981i
$533$		−	171.919i		−	0.322551i
$534$		−	159.246i		−	0.298213i
$535$	215.250	+	419.640i	0.402337	+	0.784373i
$536$		−	86.9722i		−	0.162262i
$537$		−	300.448i		−	0.559494i
$538$			515.087i			0.957411i
$539$			186.599i			0.346194i
$540$	259.915	−	133.321i	0.481325	−	0.246891i
$541$	311.858			0.576448			0.288224	−	0.957563i	$-0.406935\pi$
$541$	311.858			0.576448			0.288224	+	0.957563i	$0.406935\pi$
$542$		−	426.842i		−	0.787531i
$543$	274.683			0.505862
$544$			47.3112i			0.0869691i
$545$	−176.195	+	90.3777i	−0.323294	+	0.165831i
$546$			217.795i			0.398892i
$547$		−	248.962i		−	0.455141i	−0.973762	−	0.227570i	$-0.926922\pi$
$547$		−	248.962i		−	0.455141i	0.973762	−	0.227570i	$-0.0730782\pi$
$548$	−131.191			−0.239399
$549$		−	406.666i		−	0.740740i
$550$	−77.7948	+	108.304i	−0.141445	+	0.196916i
$551$			21.0343i			0.0381748i
$552$	−11.4321	−	148.545i	−0.0207103	−	0.269104i
$553$			1375.46i			2.48727i
$554$	−513.076			−0.926131
$555$	−43.7071	+	22.4192i	−0.0787516	+	0.0403949i
$556$	219.904			0.395511
$557$	−309.966			−0.556492			−0.278246	−	0.960510i	$-0.589753\pi$
$557$	−309.966			−0.556492			−0.278246	+	0.960510i	$0.589753\pi$
$558$			226.987i			0.406788i
$559$		−	441.243i		−	0.789344i
$560$	90.5811	+	176.592i	0.161752	+	0.315342i
$561$	−72.2421			−0.128774
$562$	−121.985			−0.217055
$563$	1076.21			1.91156			0.955782	−	0.294075i	$-0.0950114\pi$
$563$	1076.21			1.91156			0.955782	+	0.294075i	$0.0950114\pi$
$564$	23.6732			0.0419737
$565$	−318.494	−	620.917i	−0.563706	−	1.09897i
$566$			525.719i			0.928832i
$567$	328.497			0.579359
$568$		−	332.868i		−	0.586035i
$569$		−	670.488i		−	1.17836i	−0.808001	−	0.589181i	$-0.799450\pi$
$569$		−	670.488i		−	1.17836i	0.808001	−	0.589181i	$-0.200550\pi$
$570$	−51.7485	+	26.5439i	−0.0907869	+	0.0465683i
$571$		−	487.987i		−	0.854618i	−0.904106	−	0.427309i	$-0.859462\pi$
$571$		−	487.987i		−	0.854618i	0.904106	−	0.427309i	$-0.140538\pi$
$572$	51.1171			0.0893656
$573$	91.8402			0.160280
$574$		−	356.038i		−	0.620276i
$575$	491.372	+	298.628i	0.854560	+	0.519353i
$576$	−30.0408			−0.0521542
$577$			435.218i			0.754278i	0.926157	+	0.377139i	$0.123092\pi$
$577$			435.218i			0.754278i	−0.926157	+	0.377139i	$0.876908\pi$
$578$			309.786i			0.535961i
$579$	491.132			0.848242
$580$	26.7307	+	52.1126i	0.0460874	+	0.0898493i
$581$	−332.779			−0.572770
$582$	−448.410			−0.770463
$583$			32.5840i			0.0558903i
$584$	231.628			0.396624
$585$	113.208	−	58.0688i	0.193517	−	0.0992630i
$586$		−	225.154i		−	0.384221i
$587$			634.204i			1.08042i	0.841532	+	0.540208i	$0.181654\pi$
$587$			634.204i			1.08042i	−0.841532	+	0.540208i	$0.818346\pi$
$588$			226.607i			0.385387i
$589$		−	153.508i		−	0.260624i
$590$	−518.002	+	265.705i	−0.877970	+	0.450347i
$591$	−88.4514			−0.149664
$592$	17.1591			0.0289850
$593$			201.595i			0.339957i	0.985448	+	0.169979i	$0.0543699\pi$
$593$			201.595i			0.339957i	−0.985448	+	0.169979i	$0.945630\pi$
$594$		−	155.812i		−	0.262309i
$595$	−189.394	−	369.232i	−0.318310	−	0.620558i
$596$		−	482.027i		−	0.808771i
$597$	−765.043			−1.28148
$598$	−16.9134	−	219.768i	−0.0282833	−	0.367505i
$599$	522.791			0.872773			0.436387	−	0.899759i	$-0.356258\pi$
$599$	522.791			0.872773			0.436387	+	0.899759i	$0.356258\pi$
$600$	−94.4748	+	131.526i	−0.157458	+	0.219209i
$601$	−568.503			−0.945929			−0.472965	−	0.881081i	$-0.656816\pi$
$601$	−568.503			−0.945929			−0.472965	+	0.881081i	$0.656816\pi$
$602$		−	913.797i		−	1.51793i
$603$	−115.467			−0.191487
$604$	431.983			0.715203
$605$	−243.660	−	475.026i	−0.402744	−	0.785167i
$606$	382.184			0.630666
$607$		−	686.871i		−	1.13158i	−0.824549	−	0.565791i	$-0.808571\pi$
$607$		−	686.871i		−	1.13158i	0.824549	−	0.565791i	$-0.191429\pi$
$608$	20.3161			0.0334146
$609$			133.104i			0.218562i
$610$	349.501	+	681.366i	0.572952	+	1.11699i
$611$	35.0237			0.0573219
$612$	62.8118			0.102634
$613$	−900.475			−1.46896			−0.734482	−	0.678628i	$-0.762575\pi$
$613$	−900.475			−1.46896			−0.734482	+	0.678628i	$0.762575\pi$
$614$	14.4057			0.0234621
$615$	258.487	−	132.589i	0.420305	−	0.215591i
$616$	105.862			0.171853
$617$	18.4606			0.0299199			0.0149599	−	0.999888i	$-0.495238\pi$
$617$	18.4606			0.0299199			0.0149599	+	0.999888i	$0.495238\pi$
$618$	−302.983			−0.490264
$619$		−	228.644i		−	0.369377i	−0.982797	−	0.184689i	$-0.940872\pi$
$619$		−	228.644i		−	0.369377i	0.982797	−	0.184689i	$-0.0591276\pi$
$620$	−195.080	−	380.316i	−0.314645	−	0.613413i
$621$	−669.881	+	51.5543i	−1.07871	+	0.0830182i
$622$		−	552.536i		−	0.888321i
$623$		−	487.917i		−	0.783173i
$624$	62.0772			0.0994827
$625$	−199.563	−	592.284i	−0.319300	−	0.947654i
$626$		−	758.676i		−	1.21194i
$627$			31.0217i			0.0494764i
$628$	58.2435			0.0927445
$629$	−35.8776			−0.0570391
$630$	234.448	−	120.258i	0.372140	−	0.190886i
$631$			1089.20i			1.72615i	0.505075	+	0.863075i	$0.331465\pi$
$631$			1089.20i			1.72615i	−0.505075	+	0.863075i	$0.668535\pi$
$632$	392.042			0.620320
$633$		−	39.5584i		−	0.0624935i
$634$	417.896			0.659141
$635$	434.942	−	223.099i	0.684947	−	0.351338i
$636$			39.5704i			0.0622176i
$637$			335.258i			0.526308i
$638$	31.2400			0.0489655
$639$	−441.925			−0.691589
$640$	50.3332	−	25.8180i	0.0786456	−	0.0403406i
$641$		−	16.8364i		−	0.0262659i	−0.999914	−	0.0131329i	$-0.995820\pi$
$641$		−	16.8364i		−	0.0262659i	0.999914	−	0.0131329i	$-0.00418046\pi$
$642$	305.499			0.475856
$643$	−472.059			−0.734150			−0.367075	−	0.930191i	$-0.619641\pi$
$643$	−472.059			−0.734150			−0.367075	+	0.930191i	$0.619641\pi$
$644$	−35.0270	−	455.131i	−0.0543898	−	0.706724i
$645$	663.426	−	340.298i	1.02857	−	0.527594i
$646$	−42.4785			−0.0657561
$647$		−	175.941i		−	0.271933i	−0.990713	−	0.135967i	$-0.956586\pi$
$647$		−	175.941i		−	0.271933i	0.990713	−	0.135967i	$-0.0434140\pi$
$648$		−	93.6301i		−	0.144491i
$649$			310.527i			0.478470i
$650$	−139.772	+	194.588i	−0.215035	+	0.299366i
$651$		−	971.390i		−	1.49215i
$652$		−	161.284i		−	0.247367i
$653$			698.137i			1.06912i	0.845130	+	0.534561i	$0.179523\pi$
$653$			698.137i			1.06912i	−0.845130	+	0.534561i	$0.820477\pi$
$654$			128.271i			0.196133i
$655$	89.6834	+	174.842i	0.136921	+	0.266934i
$656$	−101.480			−0.154695
$657$		−	307.517i		−	0.468062i
$658$	72.5327			0.110232
$659$			30.4888i			0.0462652i	0.999732	+	0.0231326i	$0.00736399\pi$
$659$			30.4888i			0.0462652i	−0.999732	+	0.0231326i	$0.992636\pi$
$660$	39.4229	+	76.8565i	0.0597316	+	0.116449i
$661$		−	749.974i		−	1.13461i	−0.823509	−	0.567303i	$-0.807987\pi$
$661$		−	749.974i		−	1.13461i	0.823509	−	0.567303i	$-0.192013\pi$
$662$			282.442i			0.426650i
$663$	−129.796			−0.195771
$664$			94.8508i			0.142848i
$665$	−158.553	+	81.3285i	−0.238426	+	0.122298i
$666$		−	22.7809i		−	0.0342056i
$667$	−10.3366	−	134.310i	−0.0154971	−	0.201364i
$668$			301.594i			0.451487i
$669$	−500.106			−0.747543
$670$	193.464	−	99.2356i	0.288752	−	0.148113i
$671$	408.459			0.608732
$672$	128.559			0.191309
$673$		−	375.227i		−	0.557543i	−0.960357	−	0.278772i	$-0.910073\pi$
$673$		−	375.227i		−	0.557543i	0.960357	−	0.278772i	$-0.0899273\pi$
$674$			520.303i			0.771962i
$675$	593.129	+	426.045i	0.878710	+	0.631177i
$676$	−246.159			−0.364140
$677$	−119.598			−0.176659			−0.0883296	−	0.996091i	$-0.528153\pi$
$677$	−119.598			−0.176659			−0.0883296	+	0.996091i	$0.528153\pi$
$678$	−452.030			−0.666711
$679$	−1373.89			−2.02340
$680$	−105.241	+	53.9823i	−0.154766	+	0.0793857i
$681$			390.462i			0.573366i
$682$	−227.988			−0.334294
$683$			149.185i			0.218427i	0.994018	+	0.109213i	$0.0348332\pi$
$683$			149.185i			0.218427i	−0.994018	+	0.109213i	$0.965167\pi$
$684$		−	26.9722i		−	0.0394331i
$685$	−149.689	−	291.825i	−0.218524	−	0.426022i
$686$			6.65016i			0.00969411i
$687$	−854.728			−1.24415
$688$	−260.456			−0.378570
$689$			58.5431i			0.0849682i
$690$	317.385	−	194.921i	0.459979	−	0.282494i
$691$	45.1261			0.0653055			0.0326528	−	0.999467i	$-0.489604\pi$
$691$	45.1261			0.0653055			0.0326528	+	0.999467i	$0.489604\pi$
$692$		−	38.8151i		−	0.0560912i
$693$		−	140.545i		−	0.202807i
$694$	−291.507			−0.420039
$695$	250.911	+	489.162i	0.361024	+	0.703830i
$696$	37.9382			0.0545089
$697$	212.183			0.304423
$698$			276.903i			0.396709i
$699$	705.566			1.00939
$700$	−289.463	+	402.984i	−0.413519	+	0.575691i
$701$			775.256i			1.10593i	0.833205	+	0.552964i	$0.186503\pi$
$701$			775.256i			1.10593i	−0.833205	+	0.552964i	$0.813497\pi$
$702$		−	279.944i		−	0.398781i
$703$			15.4063i			0.0219151i
$704$		−	30.1733i		−	0.0428598i
$705$	27.0112	+	52.6594i	0.0383138	+	0.0746943i
$706$	−474.110			−0.671544
$707$	1170.98			1.65627
$708$			377.108i			0.532638i
$709$			959.884i			1.35386i	0.736049	+	0.676928i	$0.236689\pi$
$709$			959.884i			1.35386i	−0.736049	+	0.676928i	$0.763311\pi$
$710$	740.443	−	379.804i	1.04288	−	0.534935i
$711$		−	520.487i		−	0.732049i
$712$	−139.069			−0.195322
$713$	75.4358	+	980.190i	0.105801	+	1.37474i
$714$	−268.802			−0.376474
$715$	58.3249	+	113.707i	0.0815732	+	0.159030i
$716$	−262.380			−0.366453
$717$		−	324.833i		−	0.453045i
$718$	795.098			1.10738
$719$	50.3372			0.0700101			0.0350050	−	0.999387i	$-0.488855\pi$
$719$	50.3372			0.0700101			0.0350050	+	0.999387i	$0.488855\pi$
$720$	−34.2767	−	66.8239i	−0.0476066	−	0.0928110i
$721$	−928.316			−1.28754
$722$		−	492.290i		−	0.681842i
$723$	−393.009			−0.543580
$724$		−	239.880i		−	0.331326i
$725$	−85.4213	+	118.921i	−0.117822	+	0.164030i
$726$	−345.821			−0.476337
$727$	313.655			0.431438			0.215719	−	0.976456i	$-0.430791\pi$
$727$	313.655			0.431438			0.215719	+	0.976456i	$0.430791\pi$
$728$	190.199			0.261263
$729$	−726.399			−0.996432
$730$	264.289	+	515.242i	0.362039	+	0.705811i
$731$	544.582			0.744982
$732$	496.037			0.677647
$733$	−1032.82			−1.40903			−0.704516	−	0.709688i	$-0.748836\pi$
$733$	−1032.82			−1.40903			−0.704516	+	0.709688i	$0.748836\pi$
$734$			568.572i			0.774621i
$735$	−504.074	+	258.560i	−0.685814	+	0.351782i
$736$	−129.724	+	9.98361i	−0.176255	+	0.0135647i
$737$		−	115.976i		−	0.157362i
$738$			134.728i			0.182558i
$739$	1033.23			1.39815			0.699075	−	0.715049i	$-0.253595\pi$
$739$	1033.23			1.39815			0.699075	+	0.715049i	$0.253595\pi$
$740$	19.5786	+	38.1693i	0.0264576	+	0.0515801i
$741$			55.7362i			0.0752175i
$742$			121.240i			0.163397i
$743$	−378.634			−0.509602			−0.254801	−	0.966994i	$-0.582010\pi$
$743$	−378.634			−0.509602			−0.254801	+	0.966994i	$0.582010\pi$
$744$	−276.871			−0.372139
$745$	1072.24	−	549.995i	1.43925	−	0.738249i
$746$			673.407i			0.902691i
$747$	125.927			0.168577
$748$			63.0887i			0.0843432i
$749$	936.025			1.24970
$750$	−400.366	−	60.0819i	−0.533822	−	0.0801092i
$751$			1031.32i			1.37327i	0.727004	+	0.686633i	$0.240912\pi$
$751$			1031.32i			1.37327i	−0.727004	+	0.686633i	$0.759088\pi$
$752$		−	20.6737i		−	0.0274916i
$753$	−111.915			−0.148625
$754$	56.1283			0.0744407
$755$	492.894	+	960.917i	0.652840	+	1.27274i
$756$		−	579.753i		−	0.766869i
$757$	−456.485			−0.603018			−0.301509	−	0.953463i	$-0.597490\pi$
$757$	−456.485			−0.603018			−0.301509	+	0.953463i	$0.597490\pi$
$758$	738.589			0.974392
$759$	−15.2445	−	198.083i	−0.0200850	−	0.260979i
$760$	23.1807	+	45.1918i	0.0305010	+	0.0594629i
$761$	363.034			0.477049			0.238525	−	0.971136i	$-0.423336\pi$
$761$	363.034			0.477049			0.238525	+	0.971136i	$0.423336\pi$
$762$		−	316.639i		−	0.415537i
$763$			393.011i			0.515086i
$764$		−	80.2037i		−	0.104979i
$765$	71.6685	+	139.721i	0.0936843	+	0.182641i
$766$			795.598i			1.03864i
$767$			557.918i			0.727403i
$768$		−	36.6428i		−	0.0477119i
$769$			1390.41i			1.80807i	0.427455	+	0.904037i	$0.359410\pi$
$769$			1390.41i			1.80807i	−0.427455	+	0.904037i	$0.640590\pi$
$770$	120.788	+	235.482i	0.156868	+	0.305821i
$771$	−732.369			−0.949895
$772$		−	428.904i		−	0.555575i
$773$	−197.113			−0.254998			−0.127499	−	0.991839i	$-0.540695\pi$
$773$	−197.113			−0.254998			−0.127499	+	0.991839i	$0.540695\pi$
$774$			345.789i			0.446756i
$775$	623.401	−	867.884i	0.804389	−	1.11985i
$776$			391.595i			0.504632i
$777$			97.4907i			0.125471i
$778$	−991.153			−1.27398
$779$		−	91.1142i		−	0.116963i
$780$	70.8303	+	138.087i	0.0908081	+	0.177034i
$781$		−	443.874i		−	0.568341i
$782$	271.237	−	20.8745i	0.346851	−	0.0266938i
$783$		−	171.086i		−	0.218501i
$784$	197.895			0.252418
$785$	66.4561	+	129.559i	0.0846574	+	0.165043i
$786$	127.285			0.161941
$787$	326.291			0.414601			0.207300	−	0.978277i	$-0.433532\pi$
$787$	326.291			0.414601			0.207300	+	0.978277i	$0.433532\pi$
$788$			77.2443i			0.0980257i
$789$		−	894.996i		−	1.13434i
$790$	447.322	+	872.072i	0.566230	+	1.10389i
$791$	−1384.98			−1.75093
$792$	−40.0590			−0.0505795
$793$	733.871			0.925437
$794$	−124.397			−0.156671
$795$	−88.0217	+	45.1500i	−0.110719	+	0.0567924i
$796$			668.109i			0.839333i
$797$	−1370.61			−1.71971			−0.859853	−	0.510542i	$-0.829445\pi$
$797$	−1370.61			−1.71971			−0.859853	+	0.510542i	$0.829445\pi$
$798$			115.427i			0.144646i
$799$			43.2262i			0.0541004i
$800$	114.861	+	82.5045i	0.143576	+	0.103131i
$801$			184.632i			0.230502i
$802$	597.411			0.744902
$803$	308.872			0.384648
$804$		−	140.843i		−	0.175177i
$805$	972.442	−	597.221i	1.20800	−	0.741890i
$806$	−409.622			−0.508216
$807$			834.130i			1.03362i
$808$		−	333.760i		−	0.413069i
$809$	1063.74			1.31488			0.657439	−	0.753508i	$-0.271640\pi$
$809$	1063.74			1.31488			0.657439	+	0.753508i	$0.271640\pi$
$810$	208.274	−	106.832i	0.257128	−	0.131892i
$811$	414.464			0.511053			0.255527	−	0.966802i	$-0.417751\pi$
$811$	414.464			0.511053			0.255527	+	0.966802i	$0.417751\pi$
$812$	116.239			0.143152
$813$		−	691.227i		−	0.850217i
$814$	22.8814			0.0281098
$815$	358.765	−	184.025i	0.440202	−	0.225798i
$816$			76.6156i			0.0938917i
$817$		−	233.851i		−	0.286231i
$818$			217.376i			0.265740i
$819$		−	252.515i		−	0.308321i
$820$	−115.789	−	225.736i	−0.141206	−	0.275288i
$821$	−1214.92			−1.47980			−0.739900	−	0.672717i	$-0.765127\pi$
$821$	−1214.92			−1.47980			−0.739900	+	0.672717i	$0.765127\pi$
$822$	−212.450			−0.258454
$823$		−	1234.78i		−	1.50033i	−0.661248	−	0.750167i	$-0.729973\pi$
$823$		−	1234.78i		−	1.50033i	0.661248	−	0.750167i	$-0.270027\pi$
$824$			264.594i			0.321109i
$825$	−125.981	+	175.387i	−0.152704	+	0.212591i
$826$			1155.43i			1.39882i
$827$	−108.207			−0.130843			−0.0654213	−	0.997858i	$-0.520839\pi$
$827$	−108.207			−0.130843			−0.0654213	+	0.997858i	$0.520839\pi$
$828$	13.2545	+	172.226i	0.0160079	+	0.208002i
$829$	−1028.48			−1.24062			−0.620311	−	0.784356i	$-0.712994\pi$
$829$	−1028.48			−1.24062			−0.620311	+	0.784356i	$0.712994\pi$
$830$	−210.989	+	108.225i	−0.254204	+	0.130392i
$831$	−830.874			−0.999849
$832$		−	54.2118i		−	0.0651584i
$833$	−413.776			−0.496729
$834$	356.112			0.426993
$835$	−670.875	+	344.120i	−0.803444	+	0.412119i
$836$	27.0912			0.0324057
$837$			1248.58i			1.49174i
$838$	1012.11			1.20777
$839$		−	225.069i		−	0.268258i	−0.990964	−	0.134129i	$-0.957176\pi$
$839$		−	225.069i		−	0.268258i	0.990964	−	0.134129i	$-0.0428237\pi$
$840$	146.687	+	285.972i	0.174627	+	0.340443i
$841$	−806.697			−0.959212
$842$	−284.452			−0.337829
$843$	−197.542			−0.234332
$844$	−34.5462			−0.0409315
$845$	−280.868	−	547.564i	−0.332388	−	0.648005i
$846$	−27.4470			−0.0324433
$847$	−1059.57			−1.25096
$848$	34.5567			0.0407508
$849$			851.348i			1.00277i
$850$	−240.160	−	172.507i	−0.282541	−	0.202949i
$851$	−7.57089	−	98.3739i	−0.00889646	−	0.115598i
$852$		−	539.045i		−	0.632682i
$853$			1303.75i			1.52843i	0.644963	+	0.764214i	$0.276873\pi$
$853$			1303.75i			1.52843i	−0.644963	+	0.764214i	$0.723127\pi$
$854$	1519.82			1.77965
$855$	59.9980	−	30.7754i	0.0701731	−	0.0359947i
$856$		−	266.791i		−	0.311672i
$857$		−	590.095i		−	0.688559i	−0.938867	−	0.344279i	$-0.888123\pi$
$857$		−	590.095i		−	0.688559i	0.938867	−	0.344279i	$-0.111877\pi$
$858$	82.7790			0.0964790
$859$	−518.499			−0.603607			−0.301804	−	0.953370i	$-0.597589\pi$
$859$	−518.499			−0.603607			−0.301804	+	0.953370i	$0.597589\pi$
$860$	−297.181	−	579.367i	−0.345559	−	0.673683i
$861$		−	576.567i		−	0.669648i
$862$	114.765			0.133138
$863$		−	718.122i		−	0.832123i	−0.909337	−	0.416061i	$-0.863410\pi$
$863$		−	718.122i		−	0.832123i	0.909337	−	0.416061i	$-0.136590\pi$
$864$	−165.245			−0.191255
$865$	86.3417	−	44.2882i	0.0998170	−	0.0512003i
$866$		−	368.603i		−	0.425639i
$867$			501.666i			0.578623i
$868$	−848.311			−0.977317
$869$	522.782			0.601590
$870$	43.2876	+	84.3910i	0.0497559	+	0.0970012i
$871$		−	208.372i		−	0.239233i
$872$	112.018			0.128461
$873$	519.893			0.595524
$874$	−8.96381	−	116.473i	−0.0102561	−	0.133264i
$875$	−1226.69	−	184.086i	−1.40193	−	0.210384i
$876$	375.098			0.428194
$877$			97.4101i			0.111072i	0.998457	+	0.0555360i	$0.0176868\pi$
$877$			97.4101i			0.111072i	−0.998457	+	0.0555360i	$0.982313\pi$
$878$			945.688i			1.07709i
$879$		−	364.613i		−	0.414804i
$880$	67.1185	−	34.4279i	0.0762711	−	0.0391226i
$881$		−	903.406i		−	1.02543i	−0.858558	−	0.512716i	$-0.828639\pi$
$881$		−	903.406i		−	1.02543i	0.858558	−	0.512716i	$-0.171361\pi$
$882$		−	262.732i		−	0.297882i
$883$			261.231i			0.295844i	0.988999	+	0.147922i	$0.0472585\pi$
$883$			261.231i			0.295844i	−0.988999	+	0.147922i	$0.952741\pi$
$884$			113.350i			0.128224i
$885$	−838.851	+	430.281i	−0.947854	+	0.486194i
$886$	−838.323			−0.946189
$887$			1163.44i			1.31166i	0.754911	+	0.655828i	$0.227680\pi$
$887$			1163.44i			1.31166i	−0.754911	+	0.655828i	$0.772320\pi$
$888$	27.7874			0.0312921
$889$		−	970.156i		−	1.09129i
$890$	−158.678	−	309.350i	−0.178290	−	0.347584i
$891$		−	124.854i		−	0.140128i
$892$			436.741i			0.489620i
$893$	18.5619			0.0207860
$894$		−	780.594i		−	0.873147i
$895$	−299.377	−	583.648i	−0.334499	−	0.652121i
$896$		−	112.270i		−	0.125302i
$897$	−27.3895	−	355.892i	−0.0305346	−	0.396758i
$898$		−	461.282i		−	0.513677i
$899$	−250.339			−0.278463
$900$	109.536	−	152.493i	0.121706	−	0.169436i
$901$	−72.2538			−0.0801929
$902$	−135.322			−0.150025
$903$		−	1479.80i		−	1.63876i
$904$			394.756i			0.436677i
$905$	533.597	−	273.704i	0.589610	−	0.302435i
$906$	699.552			0.772132
$907$	−1170.12			−1.29009			−0.645047	−	0.764143i	$-0.723162\pi$
$907$	−1170.12			−1.29009			−0.645047	+	0.764143i	$0.723162\pi$
$908$	340.989			0.375539
$909$	−443.110			−0.487469
$910$	217.018	+	423.086i	0.238482	+	0.464930i
$911$		−	1409.98i		−	1.54773i	−0.633352	−	0.773864i	$-0.718322\pi$
$911$		−	1409.98i		−	1.54773i	0.633352	−	0.773864i	$-0.281678\pi$
$912$	32.8998			0.0360743
$913$			126.482i			0.138534i
$914$			1024.39i			1.12077i
$915$	565.981	+	1103.40i	0.618558	+	1.20590i
$916$			746.431i			0.814881i
$917$	389.992			0.425291
$918$	345.507			0.376369
$919$			898.968i			0.978202i	0.872227	+	0.489101i	$0.162675\pi$
$919$			898.968i			0.978202i	−0.872227	+	0.489101i	$0.837325\pi$
$920$	−170.224	−	277.171i	−0.185026	−	0.301273i
$921$	23.3286			0.0253296
$922$		−	721.143i		−	0.782151i
$923$		−	797.500i		−	0.864030i
$924$	171.432			0.185532
$925$	−62.5658	+	87.1026i	−0.0676387	+	0.0941650i
$926$	−904.742			−0.977043
$927$	351.283			0.378946
$928$		−	33.1313i		−	0.0357018i
$929$	878.502			0.945643			0.472822	−	0.881158i	$-0.343236\pi$
$929$	878.502			0.945643			0.472822	+	0.881158i	$0.343236\pi$
$930$	−315.911	−	615.882i	−0.339690	−	0.662239i
$931$			177.681i			0.190850i
$932$		−	616.168i		−	0.661124i
$933$		−	894.775i		−	0.959030i
$934$		−	230.712i		−	0.247015i
$935$	−140.337	+	71.9845i	−0.150093	+	0.0769888i
$936$	−71.9732			−0.0768945
$937$	1074.33			1.14656			0.573282	−	0.819358i	$-0.305670\pi$
$937$	1074.33			1.14656			0.573282	+	0.819358i	$0.305670\pi$
$938$		−	431.530i		−	0.460053i
$939$		−	1228.60i		−	1.30841i
$940$	45.9873	−	23.5888i	0.0489227	−	0.0250944i
$941$		−	586.745i		−	0.623533i	−0.950159	−	0.311767i	$-0.899079\pi$
$941$		−	586.745i		−	0.623533i	0.950159	−	0.311767i	$-0.100921\pi$
$942$	94.3194			0.100127
$943$	44.7748	+	581.791i	0.0474812	+	0.616957i
$944$	329.327			0.348863
$945$	1289.62	−	661.500i	1.36468	−	0.700000i
$946$	−347.314			−0.367139
$947$		−	70.3459i		−	0.0742829i	−0.999310	−	0.0371414i	$-0.988175\pi$
$947$		−	70.3459i		−	0.0742829i	0.999310	−	0.0371414i	$-0.0118252\pi$
$948$	634.872			0.669696
$949$	554.945			0.584768
$950$	−74.0769	+	103.128i	−0.0779757	+	0.108556i
$951$	676.739			0.711608
$952$			234.744i			0.246580i
$953$	−446.648			−0.468675			−0.234338	−	0.972155i	$-0.575292\pi$
$953$	−446.648			−0.468675			−0.234338	+	0.972155i	$0.575292\pi$
$954$		−	45.8785i		−	0.0480906i
$955$	178.408	−	91.5127i	0.186815	−	0.0958249i
$956$	−283.676			−0.296732
$957$	50.5900			0.0528631
$958$	−200.251			−0.209030
$959$	−650.928			−0.678757
$960$	81.5095	−	41.8096i	0.0849057	−	0.0435516i
$961$	865.962			0.901105
$962$	41.1105			0.0427344
$963$	−354.200			−0.367809
$964$			343.213i			0.356030i
$965$	954.069	−	489.381i	0.988672	−	0.507131i
$966$	−56.7226	−	737.037i	−0.0587191	−	0.762978i
$967$			24.8727i			0.0257215i	0.999917	+	0.0128608i	$0.00409382\pi$
$967$			24.8727i			0.0257215i	−0.999917	+	0.0128608i	$0.995906\pi$
$968$			302.004i			0.311988i
$969$	−68.7895			−0.0709902
$970$	−871.076	+	446.811i	−0.898017	+	0.460630i
$971$			272.102i			0.280229i	0.990135	+	0.140114i	$0.0447470\pi$
$971$			272.102i			0.280229i	−0.990135	+	0.140114i	$0.955253\pi$
$972$			374.181i			0.384960i
$973$	1091.10			1.12137
$974$	1218.04			1.25056
$975$	−226.347	+	315.115i	−0.232151	+	0.323195i
$976$		−	433.188i		−	0.443840i
$977$	−1948.04			−1.99390			−0.996951	−	0.0780340i	$-0.975136\pi$
$977$	−1948.04			−1.99390			−0.996951	+	0.0780340i	$0.975136\pi$
$978$		−	261.182i		−	0.267057i
$979$	−185.446			−0.189424
$980$	225.800	+	440.206i	0.230408	+	0.449189i
$981$		−	148.719i		−	0.151599i
$982$			1010.79i			1.02932i
$983$	1755.62			1.78598			0.892989	−	0.450079i	$-0.148604\pi$
$983$	1755.62			1.78598			0.892989	+	0.450079i	$0.148604\pi$
$984$	−164.337			−0.167009
$985$	−171.825	+	88.1360i	−0.174441	+	0.0894782i
$986$			69.2735i			0.0702571i
$987$	117.459			0.119006
$988$	48.6742			0.0492654
$989$	114.918	+	1493.21i	0.116196	+	1.50981i
$990$	−45.7075	−	89.1086i	−0.0461691	−	0.0900087i
$991$	249.984			0.252254			0.126127	−	0.992014i	$-0.459745\pi$
$991$	249.984			0.252254			0.126127	+	0.992014i	$0.459745\pi$
$992$			241.791i			0.243741i
$993$			457.386i			0.460610i
$994$		−	1651.59i		−	1.66156i
$995$	−1486.17	+	762.316i	−1.49363	+	0.766146i
$996$			153.601i			0.154218i
$997$			1422.36i			1.42664i	0.700838	+	0.713321i	$0.252810\pi$
$997$			1422.36i			1.42664i	−0.700838	+	0.713321i	$0.747190\pi$
$998$		−	752.239i		−	0.753746i
$999$		−	125.310i		−	0.125436i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	230.3.c.a.229.3	✓	24
5.2	odd	4		1150.3.d.e.551.15		24
5.3	odd	4		1150.3.d.e.551.10		24
5.4	even	2	inner	230.3.c.a.229.22	yes	24
23.22	odd	2	inner	230.3.c.a.229.4	yes	24
115.22	even	4		1150.3.d.e.551.22		24
115.68	even	4		1150.3.d.e.551.3		24
115.114	odd	2	inner	230.3.c.a.229.21	yes	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
230.3.c.a.229.3	✓	24	1.1	even	1	trivial
230.3.c.a.229.4	yes	24	23.22	odd	2	inner
230.3.c.a.229.21	yes	24	115.114	odd	2	inner
230.3.c.a.229.22	yes	24	5.4	even	2	inner
1150.3.d.e.551.3		24	115.68	even	4
1150.3.d.e.551.10		24	5.3	odd	4
1150.3.d.e.551.15		24	5.2	odd	4
1150.3.d.e.551.22		24	115.22	even	4

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q-1.41421i q^{2} -2.29017i q^{3} -2.00000 q^{4} +(-2.28201 - 4.44887i) q^{5} -3.23879 q^{6} -9.92340 q^{7} +2.82843i q^{8} +3.75511 q^{9} +O(q^{10})\)	\(q-1.41421i q^{2} -2.29017i q^{3} -2.00000 q^{4} +(-2.28201 - 4.44887i) q^{5} -3.23879 q^{6} -9.92340 q^{7} +2.82843i q^{8} +3.75511 q^{9} +(-6.29165 + 3.22725i) q^{10} +3.77166i q^{11} +4.58035i q^{12} +6.77647i q^{13} +14.0338i q^{14} +(-10.1887 + 5.22619i) q^{15} +4.00000 q^{16} -8.36352 q^{17} -5.31052i q^{18} +3.59141i q^{19} +(4.56402 + 8.89774i) q^{20} +22.7263i q^{21} +5.33394 q^{22} +(-1.76487 - 22.9322i) q^{23} +6.47759 q^{24} +(-14.5849 + 20.3047i) q^{25} +9.58338 q^{26} -29.2114i q^{27} +19.8468 q^{28} +5.85684 q^{29} +(7.39096 + 14.4090i) q^{30} -42.7430 q^{31} -5.65685i q^{32} +8.63776 q^{33} +11.8278i q^{34} +(22.6453 + 44.1479i) q^{35} -7.51021 q^{36} +4.28977 q^{37} +5.07902 q^{38} +15.5193 q^{39} +(12.5833 - 6.45449i) q^{40} -25.3700 q^{41} +32.1399 q^{42} -65.1140 q^{43} -7.54332i q^{44} +(-8.56918 - 16.7060i) q^{45} +(-32.4310 + 2.49590i) q^{46} -5.16843i q^{47} -9.16069i q^{48} +49.4739 q^{49} +(28.7152 + 20.6261i) q^{50} +19.1539i q^{51} -13.5529i q^{52} +8.63917 q^{53} -41.3112 q^{54} +(16.7796 - 8.60696i) q^{55} -28.0676i q^{56} +8.22495 q^{57} -8.28282i q^{58} +82.3317 q^{59} +(20.3774 - 10.4524i) q^{60} -108.297i q^{61} +60.4477i q^{62} -37.2634 q^{63} -8.00000 q^{64} +(30.1477 - 15.4640i) q^{65} -12.2156i q^{66} -30.7493 q^{67} +16.7270 q^{68} +(-52.5187 + 4.04186i) q^{69} +(62.4346 - 32.0253i) q^{70} -117.687 q^{71} +10.6210i q^{72} -81.8929i q^{73} -6.06665i q^{74} +(46.5013 + 33.4019i) q^{75} -7.18282i q^{76} -37.4277i q^{77} -21.9476i q^{78} -138.608i q^{79} +(-9.12803 - 17.7955i) q^{80} -33.1032 q^{81} +35.8787i q^{82} +33.5348 q^{83} -45.4526i q^{84} +(19.0856 + 37.2082i) q^{85} +92.0850i q^{86} -13.4132i q^{87} -10.6679 q^{88} +49.1683i q^{89} +(-23.6258 + 12.1187i) q^{90} -67.2457i q^{91} +(3.52974 + 45.8644i) q^{92} +97.8888i q^{93} -7.30926 q^{94} +(15.9777 - 8.19562i) q^{95} -12.9552 q^{96} +138.450 q^{97} -69.9666i q^{98} +14.1630i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - 48 q^{4} + 8 q^{6} - 96 q^{9}+O(q^{10}) \) 24 * q - 48 * q^4 + 8 * q^6 - 96 * q^9	\( 24 q - 48 q^{4} + 8 q^{6} - 96 q^{9} + 96 q^{16} - 16 q^{24} - 48 q^{25} - 32 q^{26} + 100 q^{29} - 124 q^{31} - 28 q^{35} + 192 q^{36} + 192 q^{39} - 116 q^{41} + 148 q^{46} - 76 q^{49} - 144 q^{50} - 16 q^{54} - 224 q^{55} + 84 q^{59} - 192 q^{64} - 340 q^{69} + 328 q^{70} + 196 q^{71} - 496 q^{75} + 1360 q^{81} + 316 q^{85} - 376 q^{94} - 368 q^{95} + 32 q^{96}+O(q^{100}) \) 24 * q - 48 * q^4 + 8 * q^6 - 96 * q^9 + 96 * q^16 - 16 * q^24 - 48 * q^25 - 32 * q^26 + 100 * q^29 - 124 * q^31 - 28 * q^35 + 192 * q^36 + 192 * q^39 - 116 * q^41 + 148 * q^46 - 76 * q^49 - 144 * q^50 - 16 * q^54 - 224 * q^55 + 84 * q^59 - 192 * q^64 - 340 * q^69 + 328 * q^70 + 196 * q^71 - 496 * q^75 + 1360 * q^81 + 316 * q^85 - 376 * q^94 - 368 * q^95 + 32 * q^96

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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