LMFDB - Embedded newform 12.4.b.a.11.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [12,4,Mod(11,12)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(12, 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("12.11");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 12 = 2^{2} \cdot 3 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	12.b (of order $2$, degree $1$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$0.708022920069$
Analytic rank:	$0$
Dimension:	$4$
Coefficient field:	$\Q(\sqrt{3}, \sqrt{-5})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} + x^{2} + 4 $ x^4 + x^2 + 4
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 2^{4} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			11.2
Root			$-0.866025 + 1.11803i$ of defining polynomial
Character	$\chi$	$=$	12.11
Dual form			12.4.b.a.11.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.73205 + 2.23607i) q^{2} +(3.46410 + 3.87298i) q^{3} +(-2.00000 - 7.74597i) q^{4} -8.94427i q^{5} +(-14.6603 + 1.03776i) q^{6} -7.74597i q^{7} +(20.7846 + 8.94427i) q^{8} +(-3.00000 + 26.8328i) q^{9} +O(q^{10})$	\(q+(-1.73205 + 2.23607i) q^{2} +(3.46410 + 3.87298i) q^{3} +(-2.00000 - 7.74597i) q^{4} -8.94427i q^{5} +(-14.6603 + 1.03776i) q^{6} -7.74597i q^{7} +(20.7846 + 8.94427i) q^{8} +(-3.00000 + 26.8328i) q^{9} +(20.0000 + 15.4919i) q^{10} -34.6410 q^{11} +(23.0718 - 34.5788i) q^{12} -10.0000 q^{13} +(17.3205 + 13.4164i) q^{14} +(34.6410 - 30.9839i) q^{15} +(-56.0000 + 30.9839i) q^{16} -35.7771i q^{17} +(-54.8038 - 53.1840i) q^{18} +69.7137i q^{19} +(-69.2820 + 17.8885i) q^{20} +(30.0000 - 26.8328i) q^{21} +(60.0000 - 77.4597i) q^{22} +96.9948 q^{23} +(37.3590 + 111.482i) q^{24} +45.0000 q^{25} +(17.3205 - 22.3607i) q^{26} +(-114.315 + 81.3327i) q^{27} +(-60.0000 + 15.4919i) q^{28} +152.053i q^{29} +(9.28203 + 131.125i) q^{30} -224.633i q^{31} +(27.7128 - 178.885i) q^{32} +(-120.000 - 134.164i) q^{33} +(80.0000 + 61.9677i) q^{34} -69.2820 q^{35} +(213.846 - 30.4277i) q^{36} -130.000 q^{37} +(-155.885 - 120.748i) q^{38} +(-34.6410 - 38.7298i) q^{39} +(80.0000 - 185.903i) q^{40} +125.220i q^{41} +(8.03848 + 113.558i) q^{42} +224.633i q^{43} +(69.2820 + 268.328i) q^{44} +(240.000 + 26.8328i) q^{45} +(-168.000 + 216.887i) q^{46} +193.990 q^{47} +(-313.990 - 109.556i) q^{48} +283.000 q^{49} +(-77.9423 + 100.623i) q^{50} +(138.564 - 123.935i) q^{51} +(20.0000 + 77.4597i) q^{52} -545.601i q^{53} +(16.1347 - 396.489i) q^{54} +309.839i q^{55} +(69.2820 - 160.997i) q^{56} +(-270.000 + 241.495i) q^{57} +(-340.000 - 263.363i) q^{58} -173.205 q^{59} +(-309.282 - 206.360i) q^{60} -442.000 q^{61} +(502.295 + 389.076i) q^{62} +(207.846 + 23.2379i) q^{63} +(352.000 + 371.806i) q^{64} +89.4427i q^{65} +(507.846 - 35.9492i) q^{66} -735.867i q^{67} +(-277.128 + 71.5542i) q^{68} +(336.000 + 375.659i) q^{69} +(120.000 - 154.919i) q^{70} -1039.23 q^{71} +(-302.354 + 530.877i) q^{72} +410.000 q^{73} +(225.167 - 290.689i) q^{74} +(155.885 + 174.284i) q^{75} +(540.000 - 139.427i) q^{76} +268.328i q^{77} +(146.603 - 10.3776i) q^{78} +85.2056i q^{79} +(277.128 + 500.879i) q^{80} +(-711.000 - 160.997i) q^{81} +(-280.000 - 216.887i) q^{82} +1254.00 q^{83} +(-267.846 - 178.713i) q^{84} -320.000 q^{85} +(-502.295 - 389.076i) q^{86} +(-588.897 + 526.726i) q^{87} +(-720.000 - 309.839i) q^{88} -840.762i q^{89} +(-475.692 + 490.181i) q^{90} +77.4597i q^{91} +(-193.990 - 751.319i) q^{92} +(870.000 - 778.152i) q^{93} +(-336.000 + 433.774i) q^{94} +623.538 q^{95} +(788.820 - 512.346i) q^{96} +770.000 q^{97} +(-490.170 + 632.807i) q^{98} +(103.923 - 929.516i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 8 q^{4} - 24 q^{6} - 12 q^{9}+O(q^{10}) $ 4 * q - 8 * q^4 - 24 * q^6 - 12 * q^9	$ 4 q - 8 q^{4} - 24 q^{6} - 12 q^{9} + 80 q^{10} + 120 q^{12} - 40 q^{13} - 224 q^{16} - 240 q^{18} + 120 q^{21} + 240 q^{22} + 288 q^{24} + 180 q^{25} - 240 q^{28} - 240 q^{30} - 480 q^{33} + 320 q^{34} + 24 q^{36} - 520 q^{37} + 320 q^{40} + 240 q^{42} + 960 q^{45} - 672 q^{46} - 480 q^{48} + 1132 q^{49} + 80 q^{52} + 792 q^{54} - 1080 q^{57} - 1360 q^{58} - 960 q^{60} - 1768 q^{61} + 1408 q^{64} + 1200 q^{66} + 1344 q^{69} + 480 q^{70} - 960 q^{72} + 1640 q^{73} + 2160 q^{76} + 240 q^{78} - 2844 q^{81} - 1120 q^{82} - 240 q^{84} - 1280 q^{85} - 2880 q^{88} - 240 q^{90} + 3480 q^{93} - 1344 q^{94} + 384 q^{96} + 3080 q^{97}+O(q^{100}) $ 4 * q - 8 * q^4 - 24 * q^6 - 12 * q^9 + 80 * q^10 + 120 * q^12 - 40 * q^13 - 224 * q^16 - 240 * q^18 + 120 * q^21 + 240 * q^22 + 288 * q^24 + 180 * q^25 - 240 * q^28 - 240 * q^30 - 480 * q^33 + 320 * q^34 + 24 * q^36 - 520 * q^37 + 320 * q^40 + 240 * q^42 + 960 * q^45 - 672 * q^46 - 480 * q^48 + 1132 * q^49 + 80 * q^52 + 792 * q^54 - 1080 * q^57 - 1360 * q^58 - 960 * q^60 - 1768 * q^61 + 1408 * q^64 + 1200 * q^66 + 1344 * q^69 + 480 * q^70 - 960 * q^72 + 1640 * q^73 + 2160 * q^76 + 240 * q^78 - 2844 * q^81 - 1120 * q^82 - 240 * q^84 - 1280 * q^85 - 2880 * q^88 - 240 * q^90 + 3480 * q^93 - 1344 * q^94 + 384 * q^96 + 3080 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/12\mathbb{Z}\right)^\times$.

$n$	$5$	$7$
$\chi(n)$	$-1$	$-1$

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 $

$2$	−1.73205	+	2.23607i	−0.612372	+	0.790569i
$2$	−1.73205	+	2.23607i	−0.612372	+	0.790569i
$3$	3.46410	+	3.87298i	0.666667	+	0.745356i
$3$	3.46410	+	3.87298i	0.666667	+	0.745356i
$4$	−2.00000	−	7.74597i	−0.250000	−	0.968246i
$5$		−	8.94427i		−	0.800000i	−0.916515	−	0.400000i	$-0.869010\pi$
$5$		−	8.94427i		−	0.800000i	0.916515	−	0.400000i	$-0.130990\pi$
$6$	−14.6603	+	1.03776i	−0.997504	+	0.0706108i
$7$		−	7.74597i		−	0.418243i	−0.977890	−	0.209121i	$-0.932940\pi$
$7$		−	7.74597i		−	0.418243i	0.977890	−	0.209121i	$-0.0670604\pi$
$8$	20.7846	+	8.94427i	0.918559	+	0.395285i
$9$	−3.00000	+	26.8328i	−0.111111	+	0.993808i
$10$	20.0000	+	15.4919i	0.632456	+	0.489898i
$11$	−34.6410			−0.949514			−0.474757	−	0.880117i	$-0.657464\pi$
$11$	−34.6410			−0.949514			−0.474757	+	0.880117i	$0.657464\pi$
$12$	23.0718	−	34.5788i	0.555021	−	0.831836i
$13$	−10.0000			−0.213346			−0.106673	−	0.994294i	$-0.534020\pi$
$13$	−10.0000			−0.213346			−0.106673	+	0.994294i	$0.534020\pi$
$14$	17.3205	+	13.4164i	0.330650	+	0.256120i
$15$	34.6410	−	30.9839i	0.596285	−	0.533333i
$16$	−56.0000	+	30.9839i	−0.875000	+	0.484123i
$17$		−	35.7771i		−	0.510425i	−0.966885	−	0.255212i	$-0.917855\pi$
$17$		−	35.7771i		−	0.510425i	0.966885	−	0.255212i	$-0.0821454\pi$
$18$	−54.8038	−	53.1840i	−0.717633	−	0.696422i
$19$			69.7137i			0.841759i	0.907117	+	0.420879i	$0.138278\pi$
$19$			69.7137i			0.841759i	−0.907117	+	0.420879i	$0.861722\pi$
$20$	−69.2820	+	17.8885i	−0.774597	+	0.200000i
$21$	30.0000	−	26.8328i	0.311740	−	0.278829i
$22$	60.0000	−	77.4597i	0.581456	−	0.750657i
$23$	96.9948			0.879340			0.439670	−	0.898159i	$-0.355095\pi$
$23$	96.9948			0.879340			0.439670	+	0.898159i	$0.355095\pi$
$24$	37.3590	+	111.482i	0.317745	+	0.948176i
$25$	45.0000			0.360000
$26$	17.3205	−	22.3607i	0.130647	−	0.168665i
$27$	−114.315	+	81.3327i	−0.814815	+	0.579721i
$28$	−60.0000	+	15.4919i	−0.404962	+	0.104561i
$29$			152.053i			0.973637i	0.873503	+	0.486818i	$0.161843\pi$
$29$			152.053i			0.973637i	−0.873503	+	0.486818i	$0.838157\pi$
$30$	9.28203	+	131.125i	0.0564886	+	0.798003i
$31$		−	224.633i		−	1.30146i	−0.759309	−	0.650730i	$-0.774463\pi$
$31$		−	224.633i		−	1.30146i	0.759309	−	0.650730i	$-0.225537\pi$
$32$	27.7128	−	178.885i	0.153093	−	0.988212i
$33$	−120.000	−	134.164i	−0.633010	−	0.707726i
$34$	80.0000	+	61.9677i	0.403526	+	0.312570i
$35$	−69.2820			−0.334594
$36$	213.846	−	30.4277i	0.990028	−	0.140869i
$37$	−130.000			−0.577618			−0.288809	−	0.957387i	$-0.593259\pi$
$37$	−130.000			−0.577618			−0.288809	+	0.957387i	$0.593259\pi$
$38$	−155.885	−	120.748i	−0.665469	−	0.515470i
$39$	−34.6410	−	38.7298i	−0.142231	−	0.159019i
$40$	80.0000	−	185.903i	0.316228	−	0.734847i
$41$			125.220i			0.476977i	0.971145	+	0.238488i	$0.0766519\pi$
$41$			125.220i			0.476977i	−0.971145	+	0.238488i	$0.923348\pi$
$42$	8.03848	+	113.558i	0.0295325	+	0.417199i
$43$			224.633i			0.796656i	0.917243	+	0.398328i	$0.130409\pi$
$43$			224.633i			0.796656i	−0.917243	+	0.398328i	$0.869591\pi$
$44$	69.2820	+	268.328i	0.237379	+	0.919363i
$45$	240.000	+	26.8328i	0.795046	+	0.0888889i
$46$	−168.000	+	216.887i	−0.538484	+	0.695179i
$47$	193.990			0.602049			0.301025	−	0.953616i	$-0.402671\pi$
$47$	193.990			0.602049			0.301025	+	0.953616i	$0.402671\pi$
$48$	−313.990	−	109.556i	−0.944177	−	0.329438i
$49$	283.000			0.825073
$50$	−77.9423	+	100.623i	−0.220454	+	0.284605i
$51$	138.564	−	123.935i	0.380448	−	0.340283i
$52$	20.0000	+	77.4597i	0.0533366	+	0.206572i
$53$		−	545.601i		−	1.41404i	−0.707195	−	0.707019i	$-0.750040\pi$
$53$		−	545.601i		−	1.41404i	0.707195	−	0.707019i	$-0.249960\pi$
$54$	16.1347	−	396.489i	0.0406602	−	0.999173i
$55$			309.839i			0.759612i
$56$	69.2820	−	160.997i	0.165325	−	0.384181i
$57$	−270.000	+	241.495i	−0.627410	+	0.561173i
$58$	−340.000	−	263.363i	−0.769727	−	0.596228i
$59$	−173.205			−0.382193			−0.191096	−	0.981571i	$-0.561204\pi$
$59$	−173.205			−0.382193			−0.191096	+	0.981571i	$0.561204\pi$
$60$	−309.282	−	206.360i	−0.665469	−	0.444017i
$61$	−442.000			−0.927743			−0.463871	−	0.885903i	$-0.653540\pi$
$61$	−442.000			−0.927743			−0.463871	+	0.885903i	$0.653540\pi$
$62$	502.295	+	389.076i	1.02890	+	0.796979i
$63$	207.846	+	23.2379i	0.415653	+	0.0464714i
$64$	352.000	+	371.806i	0.687500	+	0.726184i
$65$			89.4427i			0.170677i
$66$	507.846	−	35.9492i	0.947144	−	0.0670460i
$67$		−	735.867i		−	1.34180i	−0.741549	−	0.670899i	$-0.765908\pi$
$67$		−	735.867i		−	1.34180i	0.741549	−	0.670899i	$-0.234092\pi$
$68$	−277.128	+	71.5542i	−0.494217	+	0.127606i
$69$	336.000	+	375.659i	0.586227	+	0.655421i
$70$	120.000	−	154.919i	0.204896	−	0.264520i
$71$	−1039.23			−1.73710			−0.868549	−	0.495603i	$-0.834947\pi$
$71$	−1039.23			−1.73710			−0.868549	+	0.495603i	$0.834947\pi$
$72$	−302.354	+	530.877i	−0.494899	+	0.868950i
$73$	410.000			0.657354			0.328677	−	0.944442i	$-0.393397\pi$
$73$	410.000			0.657354			0.328677	+	0.944442i	$0.393397\pi$
$74$	225.167	−	290.689i	0.353717	−	0.456647i
$75$	155.885	+	174.284i	0.240000	+	0.268328i
$76$	540.000	−	139.427i	0.815030	−	0.210440i
$77$			268.328i			0.397128i
$78$	146.603	−	10.3776i	0.212814	−	0.0150646i
$79$			85.2056i			0.121347i	0.998158	+	0.0606733i	$0.0193248\pi$
$79$			85.2056i			0.121347i	−0.998158	+	0.0606733i	$0.980675\pi$
$80$	277.128	+	500.879i	0.387298	+	0.700000i
$81$	−711.000	−	160.997i	−0.975309	−	0.220846i
$82$	−280.000	−	216.887i	−0.377083	−	0.292087i
$83$	1254.00			1.65837			0.829186	−	0.558973i	$-0.188804\pi$
$83$	1254.00			1.65837			0.829186	+	0.558973i	$0.188804\pi$
$84$	−267.846	−	178.713i	−0.347910	−	0.232134i
$85$	−320.000			−0.408340
$86$	−502.295	−	389.076i	−0.629812	−	0.487850i
$87$	−588.897	+	526.726i	−0.725706	+	0.649091i
$88$	−720.000	−	309.839i	−0.872185	−	0.375329i
$89$		−	840.762i		−	1.00135i	−0.865634	−	0.500677i	$-0.833084\pi$
$89$		−	840.762i		−	1.00135i	0.865634	−	0.500677i	$-0.166916\pi$
$90$	−475.692	+	490.181i	−0.557137	+	0.574106i
$91$			77.4597i			0.0892305i
$92$	−193.990	−	751.319i	−0.219835	−	0.851417i
$93$	870.000	−	778.152i	0.970052	−	0.867641i
$94$	−336.000	+	433.774i	−0.368678	+	0.475962i
$95$	623.538			0.673407
$96$	788.820	−	512.346i	0.838632	−	0.544699i
$97$	770.000			0.805996			0.402998	−	0.915201i	$-0.367968\pi$
$97$	770.000			0.805996			0.402998	+	0.915201i	$0.367968\pi$
$98$	−490.170	+	632.807i	−0.505252	+	0.652277i
$99$	103.923	−	929.516i	0.105502	−	0.943635i
$100$	−90.0000	−	348.569i	−0.0900000	−	0.348569i
$101$			1493.69i			1.47156i	0.677218	+	0.735782i	$0.263185\pi$
$101$			1493.69i			1.47156i	−0.677218	+	0.735782i	$0.736815\pi$
$102$	37.1281	+	524.501i	0.0360415	+	0.509151i
$103$			1355.54i			1.29675i	0.761319	+	0.648377i	$0.224552\pi$
$103$			1355.54i			1.29675i	−0.761319	+	0.648377i	$0.775448\pi$
$104$	−207.846	−	89.4427i	−0.195971	−	0.0843325i
$105$	−240.000	−	268.328i	−0.223063	−	0.249392i
$106$	1220.00	+	945.008i	1.11790	+	0.865918i
$107$	−644.323			−0.582141			−0.291070	−	0.956702i	$-0.594011\pi$
$107$	−644.323			−0.582141			−0.291070	+	0.956702i	$0.594011\pi$
$108$	858.631	+	722.818i	0.765016	+	0.644011i
$109$	−1066.00			−0.936737			−0.468368	−	0.883533i	$-0.655158\pi$
$109$	−1066.00			−0.936737			−0.468368	+	0.883533i	$0.655158\pi$
$110$	−692.820	−	536.656i	−0.600526	−	0.465165i
$111$	−450.333	−	503.488i	−0.385079	−	0.430531i
$112$	240.000	+	433.774i	0.202481	+	0.365963i
$113$			1037.54i			0.863745i	0.901935	+	0.431872i	$0.142147\pi$
$113$			1037.54i			0.863745i	−0.901935	+	0.431872i	$0.857853\pi$
$114$	−72.3463	−	1022.02i	−0.0594373	−	0.839658i
$115$		−	867.548i		−	0.703472i
$116$	1177.79	−	304.105i	0.942720	−	0.243409i
$117$	30.0000	−	268.328i	0.0237051	−	0.212025i
$118$	300.000	−	387.298i	0.234044	−	0.302150i
$119$	−277.128			−0.213481
$120$	997.128	−	334.149i	0.758541	−	0.254196i
$121$	−131.000			−0.0984222
$122$	765.566	−	988.342i	0.568124	−	0.733445i
$123$	−484.974	+	433.774i	−0.355518	+	0.317985i
$124$	−1740.00	+	449.266i	−1.26013	+	0.325365i
$125$		−	1520.53i		−	1.08800i
$126$	−411.962	+	424.509i	−0.291273	+	0.300145i
$127$		−	1835.79i		−	1.28268i	−0.767257	−	0.641340i	$-0.778379\pi$
$127$		−	1835.79i		−	1.28268i	0.767257	−	0.641340i	$-0.221621\pi$
$128$	−1441.07	+	143.108i	−0.995105	+	0.0988212i
$129$	−870.000	+	778.152i	−0.593792	+	0.531104i
$130$	−200.000	−	154.919i	−0.134932	−	0.104518i
$131$	450.333			0.300350			0.150175	−	0.988659i	$-0.452016\pi$
$131$	450.333			0.300350			0.150175	+	0.988659i	$0.452016\pi$
$132$	−799.230	+	1197.84i	−0.527001	+	0.789841i
$133$	540.000			0.352060
$134$	1645.45	+	1274.56i	1.06078	+	0.821680i
$135$	727.461	+	1022.47i	0.463777	+	0.651852i
$136$	320.000	−	743.613i	0.201763	−	0.468855i
$137$		−	89.4427i		−	0.0557782i	−0.999611	−	0.0278891i	$-0.991121\pi$
$137$		−	89.4427i		−	0.0557782i	0.999611	−	0.0278891i	$-0.00887852\pi$
$138$	−1421.97	+	100.658i	−0.877145	+	0.0620909i
$139$			1959.73i			1.19584i	0.801555	+	0.597921i	$0.204006\pi$
$139$			1959.73i			1.19584i	−0.801555	+	0.597921i	$0.795994\pi$
$140$	138.564	+	536.656i	0.0836486	+	0.323970i
$141$	672.000	+	751.319i	0.401366	+	0.448741i
$142$	1800.00	−	2323.79i	1.06375	−	1.37330i
$143$	346.410			0.202575
$144$	−663.384	−	1595.59i	−0.383903	−	0.923373i
$145$	1360.00			0.778909
$146$	−710.141	+	916.788i	−0.402546	+	0.519684i
$147$	980.341	+	1096.05i	0.550049	+	0.614973i
$148$	260.000	+	1006.98i	0.144405	+	0.559276i
$149$		−	1618.91i		−	0.890111i	−0.895503	−	0.445055i	$-0.853184\pi$
$149$		−	1618.91i		−	0.890111i	0.895503	−	0.445055i	$-0.146816\pi$
$150$	−659.711	+	46.6993i	−0.359101	+	0.0254199i
$151$		−	565.456i		−	0.304743i	−0.988323	−	0.152371i	$-0.951309\pi$
$151$		−	565.456i		−	0.304743i	0.988323	−	0.152371i	$-0.0486909\pi$
$152$	−623.538	+	1448.97i	−0.332734	+	0.773205i
$153$	960.000	+	107.331i	0.507264	+	0.0567138i
$154$	−600.000	−	464.758i	−0.313957	−	0.243190i
$155$	−2009.18			−1.04117
$156$	−230.718	+	345.788i	−0.118412	+	0.177469i
$157$	−730.000			−0.371085			−0.185542	−	0.982636i	$-0.559404\pi$
$157$	−730.000			−0.371085			−0.185542	+	0.982636i	$0.559404\pi$
$158$	−190.526	−	147.580i	−0.0959329	−	0.0743093i
$159$	2113.10	−	1890.02i	1.05396	−	0.942692i
$160$	−1600.00	−	247.871i	−0.790569	−	0.122474i
$161$		−	751.319i		−	0.367778i
$162$	1591.49	−	1310.99i	0.771846	−	0.635809i
$163$			255.617i			0.122831i	0.998112	+	0.0614155i	$0.0195615\pi$
$163$			255.617i			0.122831i	−0.998112	+	0.0614155i	$0.980439\pi$
$164$	969.948	−	250.440i	0.461831	−	0.119244i
$165$	−1200.00	+	1073.31i	−0.566181	+	0.506408i
$166$	−2172.00	+	2804.04i	−1.01554	+	1.31106i
$167$	13.8564			0.00642060			0.00321030	−	0.999995i	$-0.498978\pi$
$167$	13.8564			0.00642060			0.00321030	+	0.999995i	$0.498978\pi$
$168$	863.538	−	289.381i	0.396568	−	0.132894i
$169$	−2097.00			−0.954483
$170$	554.256	−	715.542i	0.250056	−	0.322821i
$171$	−1870.61	−	209.141i	−0.836547	−	0.0935288i
$172$	1740.00	−	449.266i	0.771359	−	0.199164i
$173$			1118.03i			0.491344i	0.969353	+	0.245672i	$0.0790086\pi$
$173$			1118.03i			0.491344i	−0.969353	+	0.245672i	$0.920991\pi$
$174$	−157.795	−	2229.13i	−0.0687493	−	0.971206i
$175$		−	348.569i		−	0.150567i
$176$	1939.90	−	1073.31i	0.830825	−	0.459682i
$177$	−600.000	−	670.820i	−0.254795	−	0.284870i
$178$	1880.00	+	1456.24i	0.791640	+	0.613202i
$179$	−1351.00			−0.564125			−0.282063	−	0.959396i	$-0.591019\pi$
$179$	−1351.00			−0.564125			−0.282063	+	0.959396i	$0.591019\pi$
$180$	−272.154	−	1912.70i	−0.112695	−	0.792023i
$181$	1262.00			0.518253			0.259126	−	0.965843i	$-0.416565\pi$
$181$	1262.00			0.518253			0.259126	+	0.965843i	$0.416565\pi$
$182$	−173.205	−	134.164i	−0.0705429	−	0.0546423i
$183$	−1531.13	−	1711.86i	−0.618495	−	0.691499i
$184$	2016.00	+	867.548i	0.807725	+	0.347590i
$185$			1162.76i			0.462094i
$186$	233.116	+	3293.18i	0.0918972	+	1.29821i
$187$			1239.35i			0.484656i
$188$	−387.979	−	1502.64i	−0.150512	−	0.582931i
$189$	630.000	+	885.483i	0.242464	+	0.340791i
$190$	−1080.00	+	1394.27i	−0.412376	+	0.532375i
$191$	2771.28			1.04986			0.524929	−	0.851146i	$-0.324092\pi$
$191$	2771.28			1.04986			0.524929	+	0.851146i	$0.324092\pi$
$192$	−220.636	+	2651.27i	−0.0829325	+	0.996555i
$193$	−190.000			−0.0708627			−0.0354313	−	0.999372i	$-0.511281\pi$
$193$	−190.000			−0.0708627			−0.0354313	+	0.999372i	$0.511281\pi$
$194$	−1333.68	+	1721.77i	−0.493570	+	0.637196i
$195$	−346.410	+	309.839i	−0.127215	+	0.113785i
$196$	−566.000	−	2192.11i	−0.206268	−	0.798873i
$197$			2137.68i			0.773114i	0.922266	+	0.386557i	$0.126336\pi$
$197$			2137.68i			0.773114i	−0.922266	+	0.386557i	$0.873664\pi$
$198$	1898.46	+	1842.35i	0.681403	+	0.661262i
$199$		−	255.617i		−	0.0910563i	−0.998963	−	0.0455281i	$-0.985503\pi$
$199$		−	255.617i		−	0.0910563i	0.998963	−	0.0455281i	$-0.0144971\pi$
$200$	935.307	+	402.492i	0.330681	+	0.142302i
$201$	2850.00	−	2549.12i	1.00012	−	0.894532i
$202$	−3340.00	−	2587.15i	−1.16337	−	0.901146i
$203$	1177.79			0.407217
$204$	−1237.13	−	825.442i	−0.424590	−	0.283296i
$205$	1120.00			0.381581
$206$	−3031.09	−	2347.87i	−1.02517	−	0.794097i
$207$	−290.985	+	2602.64i	−0.0977045	+	0.873895i
$208$	560.000	−	309.839i	0.186678	−	0.103286i
$209$		−	2414.95i		−	0.799262i
$210$	1015.69	−	71.8983i	0.333759	−	0.0236260i
$211$		−	549.964i		−	0.179436i	−0.995967	−	0.0897181i	$-0.971403\pi$
$211$		−	549.964i		−	0.179436i	0.995967	−	0.0897181i	$-0.0285966\pi$
$212$	−4226.20	+	1091.20i	−1.36914	+	0.353509i
$213$	−3600.00	−	4024.92i	−1.15807	−	1.29476i
$214$	1116.00	−	1440.75i	0.356487	−	0.460223i
$215$	2009.18			0.637325
$216$	−3103.46	+	668.000i	−0.977610	+	0.210424i
$217$	−1740.00			−0.544327
$218$	1846.37	−	2383.65i	0.573632	−	0.740555i
$219$	1420.28	+	1587.92i	0.438236	+	0.489963i
$220$	2400.00	−	619.677i	0.735491	−	0.189903i
$221$			357.771i			0.108897i
$222$	1905.83	−	134.909i	0.576176	−	0.0407861i
$223$		−	472.504i		−	0.141889i	−0.997480	−	0.0709444i	$-0.977399\pi$
$223$		−	472.504i		−	0.141889i	0.997480	−	0.0709444i	$-0.0226013\pi$
$224$	−1385.64	−	214.663i	−0.413313	−	0.0640301i
$225$	−135.000	+	1207.48i	−0.0400000	+	0.357771i
$226$	−2320.00	−	1797.06i	−0.682850	−	0.528933i
$227$	505.759			0.147878			0.0739392	−	0.997263i	$-0.476443\pi$
$227$	505.759			0.147878			0.0739392	+	0.997263i	$0.476443\pi$
$228$	2410.61	+	1608.42i	0.700206	+	0.467194i
$229$	4094.00			1.18139			0.590697	−	0.806894i	$-0.298853\pi$
$229$	4094.00			1.18139			0.590697	+	0.806894i	$0.298853\pi$
$230$	1939.90	+	1502.64i	0.556144	+	0.430787i
$231$	−1039.23	+	929.516i	−0.296001	+	0.264752i
$232$	−1360.00	+	3160.35i	−0.384864	+	0.894342i
$233$			5277.12i			1.48376i	0.670534	+	0.741879i	$0.266065\pi$
$233$			5277.12i			1.48376i	−0.670534	+	0.741879i	$0.733935\pi$
$234$	548.038	+	531.840i	0.153104	+	0.148579i
$235$		−	1735.10i		−	0.481639i
$236$	346.410	+	1341.64i	0.0955482	+	0.370057i
$237$	−330.000	+	295.161i	−0.0904464	+	0.0808977i
$238$	480.000	−	619.677i	0.130730	−	0.168772i
$239$	−5681.13			−1.53758			−0.768790	−	0.639502i	$-0.779141\pi$
$239$	−5681.13			−1.53758			−0.768790	+	0.639502i	$0.779141\pi$
$240$	−979.897	+	2808.41i	−0.263550	+	0.755342i
$241$	−1198.00			−0.320207			−0.160104	−	0.987100i	$-0.551183\pi$
$241$	−1198.00			−0.320207			−0.160104	+	0.987100i	$0.551183\pi$
$242$	226.899	−	292.925i	0.0602711	−	0.0778096i
$243$	−1839.44	−	3311.40i	−0.485597	−	0.874183i
$244$	884.000	+	3423.72i	0.231936	+	0.898283i
$245$		−	2531.23i		−	0.660058i
$246$	−129.948	−	1835.75i	−0.0336797	−	0.475786i
$247$		−	697.137i		−	0.179586i
$248$	2009.18	−	4668.91i	0.514448	−	1.19547i
$249$	4344.00	+	4856.74i	1.10558	+	1.23608i
$250$	3400.00	+	2633.63i	0.860140	+	0.666261i
$251$	4260.84			1.07148			0.535741	−	0.844382i	$-0.320032\pi$
$251$	4260.84			1.07148			0.535741	+	0.844382i	$0.320032\pi$
$252$	−235.692	−	1656.44i	−0.0589175	−	0.414072i
$253$	−3360.00			−0.834946
$254$	4104.96	+	3179.69i	1.01405	+	0.785478i
$255$	−1108.51	−	1239.35i	−0.272226	−	0.304358i
$256$	2176.00	−	3470.19i	0.531250	−	0.847215i
$257$		−	3148.38i		−	0.764166i	−0.924128	−	0.382083i	$-0.875207\pi$
$257$		−	3148.38i		−	0.764166i	0.924128	−	0.382083i	$-0.124793\pi$
$258$	−233.116	−	3293.18i	−0.0562525	−	0.794668i
$259$			1006.98i			0.241585i
$260$	692.820	−	178.885i	0.165257	−	0.0426692i
$261$	−4080.00	−	456.158i	−0.967608	−	0.108182i
$262$	−780.000	+	1006.98i	−0.183926	+	0.237447i
$263$	−4253.92			−0.997368			−0.498684	−	0.866784i	$-0.666183\pi$
$263$	−4253.92			−0.997368			−0.498684	+	0.866784i	$0.666183\pi$
$264$	−1294.15	−	3861.86i	−0.301703	−	0.900307i
$265$	−4880.00			−1.13123
$266$	−935.307	+	1207.48i	−0.215592	+	0.278328i
$267$	3256.26	−	2912.48i	0.746366	−	0.667570i
$268$	−5700.00	+	1471.73i	−1.29919	+	0.335449i
$269$			44.7214i			0.0101365i	0.999987	+	0.00506823i	$0.00161328\pi$
$269$			44.7214i			0.0101365i	−0.999987	+	0.00506823i	$0.998387\pi$
$270$	−3546.31	−	144.313i	−0.799338	−	0.0325281i
$271$			8760.69i			1.96374i	0.189552	+	0.981871i	$0.439296\pi$
$271$			8760.69i			1.96374i	−0.189552	+	0.981871i	$0.560704\pi$
$272$	1108.51	+	2003.52i	0.247108	+	0.446622i
$273$	−300.000	+	268.328i	−0.0665085	+	0.0594870i
$274$	200.000	+	154.919i	0.0440965	+	0.0341570i
$275$	−1558.85			−0.341825
$276$	2237.85	−	3353.96i	0.488052	−	0.731467i
$277$	6350.00			1.37738			0.688690	−	0.725055i	$-0.258186\pi$
$277$	6350.00			1.37738			0.688690	+	0.725055i	$0.258186\pi$
$278$	−4382.09	−	3394.35i	−0.945396	−	0.732301i
$279$	6027.54	+	673.899i	1.29340	+	0.144607i
$280$	−1440.00	−	619.677i	−0.307344	−	0.132260i
$281$		−	5563.34i		−	1.18107i	−0.807012	−	0.590535i	$-0.798917\pi$
$281$		−	5563.34i		−	1.18107i	0.807012	−	0.590535i	$-0.201083\pi$
$282$	−2843.94	+	201.315i	−0.600546	+	0.0425112i
$283$		−	6777.72i		−	1.42365i	−0.702356	−	0.711826i	$-0.747868\pi$
$283$		−	6777.72i		−	1.42365i	0.702356	−	0.711826i	$-0.252132\pi$
$284$	2078.46	+	8049.84i	0.434275	+	1.68194i
$285$	2160.00	+	2414.95i	0.448938	+	0.501928i
$286$	−600.000	+	774.597i	−0.124052	+	0.160150i
$287$	969.948			0.199492
$288$	4716.86	+	1280.27i	0.965082	+	0.261946i
$289$	3633.00			0.739467
$290$	−2355.59	+	3041.05i	−0.476983	+	0.615782i
$291$	2667.36	+	2982.20i	0.537331	+	0.600754i
$292$	−820.000	−	3175.85i	−0.164339	−	0.636481i
$293$		−	652.932i		−	0.130187i	−0.997879	−	0.0650933i	$-0.979265\pi$
$293$		−	652.932i		−	0.130187i	0.997879	−	0.0650933i	$-0.0207345\pi$
$294$	−4148.85	+	293.687i	−0.823013	+	0.0582591i
$295$			1549.19i			0.305754i
$296$	−2702.00	−	1162.76i	−0.530576	−	0.228324i
$297$	3960.00	−	2817.45i	0.773678	−	0.550454i
$298$	3620.00	+	2804.04i	0.703695	+	0.545079i
$299$	−969.948			−0.187604
$300$	1038.23	−	1556.05i	0.199808	−	0.299461i
$301$	1740.00			0.333196
$302$	1264.40	+	979.398i	0.240920	+	0.186616i
$303$	−5785.05	+	5174.31i	−1.09684	+	0.981043i
$304$	−2160.00	−	3903.97i	−0.407515	−	0.736539i
$305$			3953.37i			0.742194i
$306$	−1902.77	+	1960.72i	−0.355471	+	0.366297i
$307$			1556.94i			0.289444i	0.989472	+	0.144722i	$0.0462287\pi$
$307$			1556.94i			0.289444i	−0.989472	+	0.144722i	$0.953771\pi$
$308$	2078.46	−	536.656i	0.384517	−	0.0992819i
$309$	−5250.00	+	4695.74i	−0.966544	+	0.864503i
$310$	3480.00	−	4492.66i	0.637583	−	0.823116i
$311$	3256.26			0.593715			0.296857	−	0.954922i	$-0.404061\pi$
$311$	3256.26			0.593715			0.296857	+	0.954922i	$0.404061\pi$
$312$	−373.590	−	1114.82i	−0.0677896	−	0.202290i
$313$	−7030.00			−1.26952			−0.634759	−	0.772710i	$-0.718901\pi$
$313$	−7030.00			−1.26952			−0.634759	+	0.772710i	$0.718901\pi$
$314$	1264.40	−	1632.33i	0.227242	−	0.293368i
$315$	207.846	−	1859.03i	0.0371771	−	0.332522i
$316$	660.000	−	170.411i	0.117493	−	0.0303367i
$317$		−	491.935i		−	0.0871603i	−0.999050	−	0.0435802i	$-0.986124\pi$
$317$		−	491.935i		−	0.0871603i	0.999050	−	0.0435802i	$-0.0138764\pi$
$318$	566.204	+	7998.64i	0.0998464	+	1.41051i
$319$		−	5267.26i		−	0.924482i
$320$	3325.54	−	3148.38i	0.580948	−	0.550000i
$321$	−2232.00	−	2495.45i	−0.388094	−	0.433902i
$322$	1680.00	+	1301.32i	0.290754	+	0.225217i
$323$	2494.15			0.429654
$324$	174.923	+	5829.38i	0.0299937	+	0.999550i
$325$	−450.000			−0.0768046
$326$	−571.577	−	442.741i	−0.0971065	−	0.0752183i
$327$	−3692.73	−	4128.60i	−0.624491	−	0.698202i
$328$	−1120.00	+	2602.64i	−0.188542	+	0.438131i
$329$		−	1502.64i		−	0.251803i
$330$	−321.539	−	4542.31i	−0.0536368	−	0.757716i
$331$		−	4237.04i		−	0.703592i	−0.936077	−	0.351796i	$-0.885571\pi$
$331$		−	4237.04i		−	0.703592i	0.936077	−	0.351796i	$-0.114429\pi$
$332$	−2508.01	−	9713.48i	−0.414593	−	1.60571i
$333$	390.000	−	3488.27i	0.0641798	−	0.574041i
$334$	−24.0000	+	30.9839i	−0.00393180	+	0.00507593i
$335$	−6581.79			−1.07344
$336$	−848.616	+	2432.15i	−0.137785	+	0.394895i
$337$	1490.00			0.240847			0.120424	−	0.992723i	$-0.461575\pi$
$337$	1490.00			0.240847			0.120424	+	0.992723i	$0.461575\pi$
$338$	3632.11	−	4689.03i	0.584499	−	0.754585i
$339$	−4018.36	+	3594.13i	−0.643797	+	0.575830i
$340$	640.000	+	2478.71i	0.102085	+	0.395373i
$341$			7781.52i			1.23576i
$342$	3707.65	−	3820.58i	0.586219	−	0.604074i
$343$		−	4848.98i		−	0.763324i
$344$	−2009.18	+	4668.91i	−0.314906	+	0.731775i
$345$	3360.00	−	3005.28i	0.524337	−	0.468981i
$346$	−2500.00	−	1936.49i	−0.388442	−	0.300886i
$347$	1988.39			0.307616			0.153808	−	0.988101i	$-0.450846\pi$
$347$	1988.39			0.307616			0.153808	+	0.988101i	$0.450846\pi$
$348$	5257.79	+	3508.13i	0.809906	+	0.540389i
$349$	−2074.00			−0.318105			−0.159053	−	0.987270i	$-0.550844\pi$
$349$	−2074.00			−0.318105			−0.159053	+	0.987270i	$0.550844\pi$
$350$	779.423	+	603.738i	0.119034	+	0.0922033i
$351$	1143.15	−	813.327i	0.173838	−	0.123681i
$352$	−960.000	+	6196.77i	−0.145364	+	0.938321i
$353$			8658.06i			1.30544i	0.757597	+	0.652722i	$0.226373\pi$
$353$			8658.06i			1.30544i	−0.757597	+	0.652722i	$0.773627\pi$
$354$	2539.23	−	179.746i	0.381239	−	0.0269870i
$355$			9295.16i			1.38968i
$356$	−6512.51	+	1681.52i	−0.969557	+	0.250339i
$357$	−960.000	−	1073.31i	−0.142321	−	0.159120i
$358$	2340.00	−	3020.93i	0.345455	−	0.445980i
$359$	8106.00			1.19169			0.595847	−	0.803098i	$-0.296816\pi$
$359$	8106.00			1.19169			0.595847	+	0.803098i	$0.296816\pi$
$360$	4748.31	+	2704.33i	0.695160	+	0.395919i
$361$	1999.00			0.291442
$362$	−2185.85	+	2821.92i	−0.317364	+	0.409715i
$363$	−453.797	−	507.361i	−0.0656148	−	0.0733596i
$364$	600.000	−	154.919i	0.0863971	−	0.0223076i
$365$		−	3667.15i		−	0.525884i
$366$	6479.83	−	458.691i	0.925427	−	0.0655087i
$367$			7893.14i			1.12267i	0.827590	+	0.561333i	$0.189711\pi$
$367$			7893.14i			1.12267i	−0.827590	+	0.561333i	$0.810289\pi$
$368$	−5431.71	+	3005.28i	−0.769423	+	0.425709i
$369$	−3360.00	−	375.659i	−0.474023	−	0.0529974i
$370$	−2600.00	−	2013.95i	−0.365318	−	0.282974i
$371$	−4226.20			−0.591411
$372$	−7767.54	−	5182.69i	−1.08260	−	0.722338i
$373$	4910.00			0.681582			0.340791	−	0.940139i	$-0.389305\pi$
$373$	4910.00			0.681582			0.340791	+	0.940139i	$0.389305\pi$
$374$	−2771.28	−	2146.63i	−0.383154	−	0.296790i
$375$	5888.97	−	5267.26i	0.810947	−	0.725333i
$376$	4032.00	+	1735.10i	0.553017	+	0.237981i
$377$		−	1520.53i		−	0.207722i
$378$	−3071.19	−	124.979i	−0.417897	−	0.0170058i
$379$			3137.12i			0.425179i	0.977142	+	0.212590i	$0.0681897\pi$
$379$			3137.12i			0.425179i	−0.977142	+	0.212590i	$0.931810\pi$
$380$	−1247.08	−	4829.91i	−0.168352	−	0.652024i
$381$	7110.00	−	6359.38i	0.956053	−	0.855120i
$382$	−4800.00	+	6196.77i	−0.642904	+	0.829986i
$383$	6207.67			0.828191			0.414095	−	0.910233i	$-0.364098\pi$
$383$	6207.67			0.828191			0.414095	+	0.910233i	$0.364098\pi$
$384$	−5546.26	−	5085.48i	−0.737060	−	0.675827i
$385$	2400.00			0.317702
$386$	329.090	−	424.853i	0.0433944	−	0.0560219i
$387$	−6027.54	−	673.899i	−0.791723	−	0.0885174i
$388$	−1540.00	−	5964.39i	−0.201499	−	0.780403i
$389$		−	9454.10i		−	1.23224i	−0.787652	−	0.616120i	$-0.788703\pi$
$389$		−	9454.10i		−	1.23224i	0.787652	−	0.616120i	$-0.211297\pi$
$390$	−92.8203	−	1311.25i	−0.0120516	−	0.170251i
$391$		−	3470.19i		−	0.448837i
$392$	5882.04	+	2531.23i	0.757878	+	0.326139i
$393$	1560.00	+	1744.13i	0.200233	+	0.223867i
$394$	−4780.00	−	3702.57i	−0.611200	−	0.473434i
$395$	762.102			0.0970773
$396$	−7407.85	+	1054.05i	−0.940046	+	0.133757i
$397$	−10570.0			−1.33625			−0.668127	−	0.744047i	$-0.732904\pi$
$397$	−10570.0			−1.33625			−0.668127	+	0.744047i	$0.732904\pi$
$398$	571.577	+	442.741i	0.0719863	+	0.0557604i
$399$	1870.61	+	2091.41i	0.234706	+	0.262410i
$400$	−2520.00	+	1394.27i	−0.315000	+	0.174284i
$401$			1681.52i			0.209405i	0.994504	+	0.104702i	$0.0333890\pi$
$401$			1681.52i			0.209405i	−0.994504	+	0.104702i	$0.966611\pi$
$402$	763.655	+	10788.0i	0.0947454	+	1.33845i
$403$			2246.33i			0.277662i
$404$	11570.1	−	2987.39i	1.42484	−	0.367891i
$405$	−1440.00	+	6359.38i	−0.176677	+	0.780247i
$406$	−2040.00	+	2633.63i	−0.249368	+	0.321933i
$407$	4503.33			0.548457
$408$	3988.51	−	1336.60i	0.483973	−	0.162185i
$409$	−3574.00			−0.432085			−0.216043	−	0.976384i	$-0.569315\pi$
$409$	−3574.00			−0.432085			−0.216043	+	0.976384i	$0.569315\pi$
$410$	−1939.90	+	2504.40i	−0.233670	+	0.301667i
$411$	346.410	−	309.839i	0.0415746	−	0.0371854i
$412$	10500.0	−	2711.09i	1.25558	−	0.324189i
$413$			1341.64i			0.159849i
$414$	−5315.69	−	5158.57i	−0.631043	−	0.612392i
$415$		−	11216.2i		−	1.32670i
$416$	−277.128	+	1788.85i	−0.0326618	+	0.210831i
$417$	−7590.00	+	6788.70i	−0.891328	+	0.797228i
$418$	5400.00	+	4182.82i	0.631872	+	0.489446i
$419$	−15346.0			−1.78926			−0.894630	−	0.446808i	$-0.852561\pi$
$419$	−15346.0			−1.78926			−0.894630	+	0.446808i	$0.852561\pi$
$420$	−1598.46	+	2395.69i	−0.185707	+	0.278328i
$421$	3518.00			0.407261			0.203630	−	0.979048i	$-0.434726\pi$
$421$	3518.00			0.407261			0.203630	+	0.979048i	$0.434726\pi$
$422$	1229.76	+	952.565i	0.141857	+	0.109882i
$423$	−581.969	+	5205.29i	−0.0668943	+	0.598321i
$424$	4880.00	−	11340.1i	0.558948	−	1.29888i
$425$		−	1609.97i		−	0.183753i
$426$	15235.4	−	1078.47i	1.73276	−	0.122658i
$427$			3423.72i			0.388022i
$428$	1288.65	+	4990.90i	0.145535	+	0.563655i
$429$	1200.00	+	1341.64i	0.135050	+	0.150991i
$430$	−3480.00	+	4492.66i	−0.390280	+	0.503850i
$431$	−12886.5			−1.44018			−0.720091	−	0.693879i	$-0.755900\pi$
$431$	−12886.5			−1.44018			−0.720091	+	0.693879i	$0.755900\pi$
$432$	3881.66	−	8096.56i	0.432307	−	0.901727i
$433$	14450.0			1.60375			0.801874	−	0.597493i	$-0.203837\pi$
$433$	14450.0			1.60375			0.801874	+	0.597493i	$0.203837\pi$
$434$	3013.77	−	3890.76i	0.333331	−	0.430328i
$435$	4711.18	+	5267.26i	0.519273	+	0.580565i
$436$	2132.00	+	8257.20i	0.234184	+	0.906991i
$437$			6761.87i			0.740192i
$438$	−6010.70	+	425.483i	−0.655714	+	0.0464163i
$439$		−	15065.9i		−	1.63794i	−0.573835	−	0.818971i	$-0.694545\pi$
$439$		−	15065.9i		−	1.63794i	0.573835	−	0.818971i	$-0.305455\pi$
$440$	−2771.28	+	6439.88i	−0.300263	+	0.697748i
$441$	−849.000	+	7593.69i	−0.0916748	+	0.819964i
$442$	−800.000	−	619.677i	−0.0860908	−	0.0666856i
$443$	3041.48			0.326197			0.163098	−	0.986610i	$-0.447851\pi$
$443$	3041.48			0.326197			0.163098	+	0.986610i	$0.447851\pi$
$444$	−2999.33	+	4495.24i	−0.320590	+	0.480484i
$445$	−7520.00			−0.801084
$446$	1056.55	+	818.401i	0.112173	+	0.0868888i
$447$	6270.02	−	5608.08i	0.663450	−	0.593407i
$448$	2880.00	−	2726.58i	0.303721	−	0.287542i
$449$		−	14310.8i		−	1.50416i	−0.659069	−	0.752082i	$-0.729049\pi$
$449$		−	14310.8i		−	1.50416i	0.659069	−	0.752082i	$-0.270951\pi$
$450$	−2466.17	−	2393.28i	−0.258348	−	0.250712i
$451$		−	4337.74i		−	0.452896i
$452$	8036.72	−	2075.07i	0.836317	−	0.215936i
$453$	2190.00	−	1958.80i	0.227142	−	0.203162i
$454$	−876.000	+	1130.91i	−0.0905566	+	0.116908i
$455$	692.820			0.0713844
$456$	−7771.84	+	2604.43i	−0.798136	+	0.267464i
$457$	−3430.00			−0.351091			−0.175546	−	0.984471i	$-0.556169\pi$
$457$	−3430.00			−0.351091			−0.175546	+	0.984471i	$0.556169\pi$
$458$	−7091.02	+	9154.46i	−0.723453	+	0.933974i
$459$	2909.85	+	4089.87i	0.295904	+	0.415902i
$460$	−6720.00	+	1735.10i	−0.681134	+	0.175868i
$461$			3908.65i			0.394889i	0.980314	+	0.197445i	$0.0632642\pi$
$461$			3908.65i			0.394889i	−0.980314	+	0.197445i	$0.936736\pi$
$462$	−278.461	−	3933.76i	−0.0280415	−	0.396136i
$463$			18179.8i			1.82481i	0.409291	+	0.912404i	$0.365776\pi$
$463$			18179.8i			1.82481i	−0.409291	+	0.912404i	$0.634224\pi$
$464$	−4711.18	−	8514.95i	−0.471360	−	0.851932i
$465$	−6960.00	−	7781.52i	−0.694112	−	0.776041i
$466$	−11800.0	−	9140.24i	−1.17301	−	0.908613i
$467$	−1849.83			−0.183298			−0.0916488	−	0.995791i	$-0.529214\pi$
$467$	−1849.83			−0.183298			−0.0916488	+	0.995791i	$0.529214\pi$
$468$	−2138.46	+	304.277i	−0.211219	+	0.0300539i
$469$	−5700.00			−0.561197
$470$	3879.79	+	3005.28i	0.380769	+	0.294943i
$471$	−2528.79	−	2827.28i	−0.247390	−	0.276590i
$472$	−3600.00	−	1549.19i	−0.351067	−	0.151075i
$473$		−	7781.52i		−	0.756437i
$474$	−88.4232	−	1249.14i	−0.00856838	−	0.121044i
$475$			3137.12i			0.303033i
$476$	554.256	+	2146.63i	0.0533704	+	0.206703i
$477$	14640.0	+	1636.80i	1.40528	+	0.157115i
$478$	9840.00	−	12703.4i	0.941571	−	1.21556i
$479$	15242.0			1.45392			0.726959	−	0.686681i	$-0.240933\pi$
$479$	15242.0			1.45392			0.726959	+	0.686681i	$0.240933\pi$
$480$	−4582.56	−	7055.42i	−0.435759	−	0.670905i
$481$	1300.00			0.123233
$482$	2075.00	−	2678.81i	0.196086	−	0.253146i
$483$	2909.85	−	2602.64i	0.274125	−	0.245185i
$484$	262.000	+	1014.72i	0.0246056	+	0.0952969i
$485$		−	6887.09i		−	0.644797i
$486$	10590.5	+	1622.41i	0.988468	+	0.151428i
$487$			9783.16i			0.910302i	0.890414	+	0.455151i	$0.150415\pi$
$487$			9783.16i			0.910302i	−0.890414	+	0.455151i	$0.849585\pi$
$488$	−9186.80	−	3953.37i	−0.852186	−	0.366722i
$489$	−990.000	+	885.483i	−0.0915529	+	0.0818874i
$490$	5660.00	+	4384.22i	0.521822	+	0.404202i
$491$	6893.56			0.633609			0.316805	−	0.948491i	$-0.397390\pi$
$491$	6893.56			0.633609			0.316805	+	0.948491i	$0.397390\pi$
$492$	4329.95	+	2889.05i	0.396767	+	0.264732i
$493$	5440.00			0.496968
$494$	1558.85	+	1207.48i	0.141975	+	0.109974i
$495$	−8313.84	−	929.516i	−0.754908	−	0.0844013i
$496$	6960.00	+	12579.4i	0.630067	+	1.13878i
$497$			8049.84i			0.726529i
$498$	−18384.0	+	1301.36i	−1.65423	+	0.117099i
$499$			1309.07i			0.117439i	0.998275	+	0.0587194i	$0.0187017\pi$
$499$			1309.07i			0.117439i	−0.998275	+	0.0587194i	$0.981298\pi$
$500$	−11777.9	+	3041.05i	−1.05345	+	0.272000i
$501$	48.0000	+	53.6656i	0.00428040	+	0.00478564i
$502$	−7380.00	+	9527.54i	−0.656146	+	0.847081i
$503$	−7939.72			−0.703806			−0.351903	−	0.936036i	$-0.614465\pi$
$503$	−7939.72			−0.703806			−0.351903	+	0.936036i	$0.614465\pi$
$504$	4112.15	+	2342.02i	0.363432	+	0.206988i
$505$	13360.0			1.17725
$506$	5819.69	−	7513.19i	0.511298	−	0.660083i
$507$	−7264.22	−	8121.65i	−0.636322	−	0.711430i
$508$	−14220.0	+	3671.59i	−1.24195	+	0.320670i
$509$			14534.4i			1.26567i	0.774285	+	0.632837i	$0.218110\pi$
$509$			14534.4i			1.26567i	−0.774285	+	0.632837i	$0.781890\pi$
$510$	4691.28	−	332.084i	0.407320	−	0.0288332i
$511$		−	3175.85i		−	0.274934i
$512$	3990.65	+	10876.2i	0.344459	+	0.938801i
$513$	−5670.00	−	7969.35i	−0.487986	−	0.685878i
$514$	7040.00	+	5453.16i	0.604127	+	0.467954i
$515$	12124.4			1.03740
$516$	7767.54	+	5182.69i	0.662687	+	0.442161i
$517$	−6720.00			−0.571654
$518$	−2251.67	−	1744.13i	−0.190989	−	0.147940i
$519$	−4330.13	+	3872.98i	−0.366226	+	0.327563i
$520$	−800.000	+	1859.03i	−0.0674660	+	0.156777i
$521$			9355.71i			0.786720i	0.919385	+	0.393360i	$0.128687\pi$
$521$			9355.71i			0.786720i	−0.919385	+	0.393360i	$0.871313\pi$
$522$	8086.77	−	8333.07i	0.678062	−	0.698714i
$523$		−	10062.0i		−	0.841264i	−0.907231	−	0.420632i	$-0.861808\pi$
$523$		−	10062.0i		−	0.841264i	0.907231	−	0.420632i	$-0.138192\pi$
$524$	−900.666	−	3488.27i	−0.0750874	−	0.290812i
$525$	1350.00	−	1207.48i	0.112226	−	0.100378i
$526$	7368.00	−	9512.05i	0.610761	−	0.788489i
$527$	−8036.72			−0.664298
$528$	10876.9	+	3795.12i	0.896510	+	0.312806i
$529$	−2759.00			−0.226761
$530$	8452.41	−	10912.0i	0.692734	−	0.894316i
$531$	519.615	−	4647.58i	0.0424659	−	0.379826i
$532$	−1080.00	−	4182.82i	−0.0880149	−	0.340880i
$533$		−	1252.20i		−	0.101761i
$534$	872.511	+	12325.8i	0.0707065	+	0.998855i
$535$			5763.00i			0.465712i
$536$	6581.79	−	15294.7i	0.530392	−	1.23252i
$537$	−4680.00	−	5232.40i	−0.376084	−	0.420474i
$538$	−100.000	−	77.4597i	−0.00801358	−	0.00620729i
$539$	−9803.41			−0.783419
$540$	6465.08	−	7679.83i	0.515209	−	0.612013i
$541$	−23962.0			−1.90426			−0.952132	−	0.305687i	$-0.901114\pi$
$541$	−23962.0			−1.90426			−0.952132	+	0.305687i	$0.901114\pi$
$542$	−19589.5	−	15174.0i	−1.55247	−	1.20254i
$543$	4371.70	+	4887.70i	0.345502	+	0.386283i
$544$	−6400.00	−	991.484i	−0.504408	−	0.0781425i
$545$			9534.59i			0.749389i
$546$	−80.3848	−	1135.58i	−0.00630064	−	0.0890078i
$547$		−	15112.4i		−	1.18128i	−0.806936	−	0.590639i	$-0.798876\pi$
$547$		−	15112.4i		−	1.18128i	0.806936	−	0.590639i	$-0.201124\pi$
$548$	−692.820	+	178.885i	−0.0540070	+	0.0139445i
$549$	1326.00	−	11860.1i	0.103083	−	0.921998i
$550$	2700.00	−	3485.69i	0.209324	−	0.270237i
$551$	−10600.2			−0.819567
$552$	3623.63	+	10813.2i	0.279406	+	0.833770i
$553$	660.000			0.0507524
$554$	−10998.5	+	14199.0i	−0.843470	+	1.08892i
$555$	−4503.33	+	4027.90i	−0.344425	+	0.308063i
$556$	15180.0	−	3919.46i	1.15787	−	0.298961i
$557$		−	16055.0i		−	1.22131i	−0.791896	−	0.610656i	$-0.790906\pi$
$557$		−	16055.0i		−	1.22131i	0.791896	−	0.610656i	$-0.209094\pi$
$558$	−11946.9	+	12310.8i	−0.906365	+	0.933971i
$559$		−	2246.33i		−	0.169964i
$560$	3879.79	−	2146.63i	0.292770	−	0.161985i
$561$	−4800.00	+	4293.25i	−0.361241	+	0.323104i
$562$	12440.0	+	9635.98i	0.933718	+	0.723255i
$563$	25142.4			1.88211			0.941055	−	0.338254i	$-0.109836\pi$
$563$	25142.4			1.88211			0.941055	+	0.338254i	$0.109836\pi$
$564$	4475.69	−	6707.93i	0.334150	−	0.500806i
$565$	9280.00			0.690996
$566$	15155.4	+	11739.4i	1.12550	+	0.871806i
$567$	−1247.08	+	5507.38i	−0.0923674	+	0.407916i
$568$	−21600.0	−	9295.16i	−1.59563	−	0.686648i
$569$			23416.1i			1.72523i	0.505864	+	0.862613i	$0.331174\pi$
$569$			23416.1i			1.72523i	−0.505864	+	0.862613i	$0.668826\pi$
$570$	−9141.23	+	647.085i	−0.671726	+	0.0475498i
$571$		−	4918.69i		−	0.360492i	−0.983622	−	0.180246i	$-0.942311\pi$
$571$		−	4918.69i		−	0.360492i	0.983622	−	0.180246i	$-0.0576893\pi$
$572$	−692.820	−	2683.28i	−0.0506438	−	0.196143i
$573$	9600.00	+	10733.1i	0.699905	+	0.782518i
$574$	−1680.00	+	2168.87i	−0.122163	+	0.157712i
$575$	4364.77			0.316562
$576$	−11032.6	+	8329.73i	−0.798077	+	0.602556i
$577$	19490.0			1.40620			0.703102	−	0.711089i	$-0.251798\pi$
$577$	19490.0			1.40620			0.703102	+	0.711089i	$0.251798\pi$
$578$	−6292.54	+	8123.63i	−0.452829	+	0.584600i
$579$	−658.179	−	735.867i	−0.0472418	−	0.0528179i
$580$	−2720.00	−	10534.5i	−0.194727	−	0.754176i
$581$		−	9713.48i		−	0.693602i
$582$	−11288.4	+	799.077i	−0.803985	+	0.0569121i
$583$			18900.2i			1.34265i
$584$	8521.69	+	3667.15i	0.603819	+	0.259842i
$585$	−2400.00	−	268.328i	−0.169620	−	0.0189641i
$586$	1460.00	+	1130.91i	0.102922	+	0.0797227i
$587$	−1364.86			−0.0959687			−0.0479844	−	0.998848i	$-0.515280\pi$
$587$	−1364.86			−0.0959687			−0.0479844	+	0.998848i	$0.515280\pi$
$588$	6529.32	−	9785.80i	0.457933	−	0.686326i
$589$	15660.0			1.09552
$590$	−3464.10	−	2683.28i	−0.241720	−	0.187236i
$591$	−8279.20	+	7405.14i	−0.576245	+	0.515409i
$592$	7280.00	−	4027.90i	0.505416	−	0.279638i
$593$		−	25795.3i		−	1.78632i	−0.449743	−	0.893158i	$-0.648485\pi$
$593$		−	25795.3i		−	1.78632i	0.449743	−	0.893158i	$-0.351515\pi$
$594$	−558.921	+	13734.8i	−0.0386074	+	0.948729i
$595$			2478.71i			0.170785i
$596$	−12540.0	+	3237.83i	−0.861846	+	0.222528i
$597$	990.000	−	885.483i	0.0678694	−	0.0607042i
$598$	1680.00	−	2168.87i	0.114883	−	0.148314i
$599$	2424.87			0.165405			0.0827025	−	0.996574i	$-0.473645\pi$
$599$	2424.87			0.165405			0.0827025	+	0.996574i	$0.473645\pi$
$600$	1681.15	+	5016.70i	0.114388	+	0.341343i
$601$	−8758.00			−0.594420			−0.297210	−	0.954812i	$-0.596056\pi$
$601$	−8758.00			−0.594420			−0.297210	+	0.954812i	$0.596056\pi$
$602$	−3013.77	+	3890.76i	−0.204040	+	0.263414i
$603$	19745.4	+	2207.60i	1.33349	+	0.149089i
$604$	−4380.00	+	1130.91i	−0.295066	+	0.0761856i
$605$			1171.70i			0.0787378i
$606$	−1550.10	−	21897.9i	−0.103908	−	1.46789i
$607$		−	19558.6i		−	1.30784i	−0.756565	−	0.653919i	$-0.773124\pi$
$607$		−	19558.6i		−	1.30784i	0.756565	−	0.653919i	$-0.226876\pi$
$608$	12470.8	+	1931.96i	0.831836	+	0.128867i
$609$	4080.00	+	4561.58i	0.271478	+	0.303521i
$610$	−8840.00	−	6847.43i	−0.586756	−	0.454499i
$611$	−1939.90			−0.128445
$612$	−1088.62	−	7650.79i	−0.0719031	−	0.505335i
$613$	−16450.0			−1.08386			−0.541932	−	0.840422i	$-0.682307\pi$
$613$	−16450.0			−1.08386			−0.541932	+	0.840422i	$0.682307\pi$
$614$	−3481.42	−	2696.70i	−0.228825	−	0.177247i
$615$	3879.79	+	4337.74i	0.254388	+	0.284414i
$616$	−2400.00	+	5577.10i	−0.156978	+	0.364785i
$617$		−	8461.28i		−	0.552088i	−0.961145	−	0.276044i	$-0.910976\pi$
$617$		−	8461.28i		−	0.552088i	0.961145	−	0.276044i	$-0.0890236\pi$
$618$	−1406.73	−	19872.6i	−0.0915649	−	1.29352i
$619$			19930.4i			1.29413i	0.762433	+	0.647067i	$0.224005\pi$
$619$			19930.4i			1.29413i	−0.762433	+	0.647067i	$0.775995\pi$
$620$	4018.36	+	15563.0i	0.260292	+	1.00811i
$621$	−11088.0	+	7888.85i	−0.716499	+	0.509772i
$622$	−5640.00	+	7281.21i	−0.363575	+	0.469373i
$623$	−6512.51			−0.418809
$624$	3139.90	+	1095.56i	0.201437	+	0.0702843i
$625$	−7975.00			−0.510400
$626$	12176.3	−	15719.6i	0.777418	−	1.00364i
$627$	9353.07	−	8365.64i	0.595735	−	0.532842i
$628$	1460.00	+	5654.56i	0.0927712	+	0.359301i
$629$			4651.02i			0.294830i
$630$	3796.92	+	3684.70i	0.240116	+	0.233019i
$631$			12199.9i			0.769683i	0.922983	+	0.384842i	$0.125744\pi$
$631$			12199.9i			0.769683i	−0.922983	+	0.384842i	$0.874256\pi$
$632$	−762.102	+	1770.97i	−0.0479665	+	0.111464i
$633$	2130.00	−	1905.13i	0.133744	−	0.119624i
$634$	1100.00	+	852.056i	0.0689063	+	0.0533746i
$635$	−16419.8			−1.02614
$636$	−18866.2	−	12588.0i	−1.17625	−	0.784821i
$637$	−2830.00			−0.176026
$638$	11777.9	+	9123.16i	0.730867	+	0.566127i
$639$	3117.69	−	27885.5i	0.193011	−	1.72634i
$640$	1280.00	+	12889.3i	0.0790569	+	0.796084i
$641$		−	7012.31i		−	0.432090i	−0.976383	−	0.216045i	$-0.930684\pi$
$641$		−	7012.31i		−	0.432090i	0.976383	−	0.216045i	$-0.0693158\pi$
$642$	9445.94	−	668.654i	0.580688	−	0.0411054i
$643$		−	15979.9i		−	0.980073i	−0.871702	−	0.490036i	$-0.836983\pi$
$643$		−	15979.9i		−	0.980073i	0.871702	−	0.490036i	$-0.163017\pi$
$644$	−5819.69	+	1502.64i	−0.356099	+	0.0919444i
$645$	6960.00	+	7781.52i	0.424883	+	0.475034i
$646$	−4320.00	+	5577.10i	−0.263109	+	0.339672i
$647$	−17999.5			−1.09371			−0.546856	−	0.837226i	$-0.684176\pi$
$647$	−17999.5			−1.09371			−0.546856	+	0.837226i	$0.684176\pi$
$648$	−13337.9	−	9705.63i	−0.808581	−	0.588385i
$649$	6000.00			0.362898
$650$	779.423	−	1006.23i	0.0470330	−	0.0607194i
$651$	−6027.54	−	6738.99i	−0.362884	−	0.405717i
$652$	1980.00	−	511.234i	0.118931	−	0.0307078i
$653$			5196.62i			0.311423i	0.987803	+	0.155712i	$0.0497671\pi$
$653$			5196.62i			0.311423i	−0.987803	+	0.155712i	$0.950233\pi$
$654$	15627.8	−	1106.26i	0.934398	−	0.0661437i
$655$		−	4027.90i		−	0.240280i
$656$	−3879.79	−	7012.31i	−0.230915	−	0.417355i
$657$	−1230.00	+	11001.5i	−0.0730394	+	0.653284i
$658$	3360.00	+	2602.64i	0.199068	+	0.154197i
$659$	−6062.18			−0.358344			−0.179172	−	0.983818i	$-0.557342\pi$
$659$	−6062.18			−0.358344			−0.179172	+	0.983818i	$0.557342\pi$
$660$	10713.8	+	7148.53i	0.631872	+	0.421601i
$661$	9422.00			0.554423			0.277211	−	0.960809i	$-0.410590\pi$
$661$	9422.00			0.554423			0.277211	+	0.960809i	$0.410590\pi$
$662$	9474.32	+	7338.78i	0.556238	+	0.430860i
$663$	−1385.64	+	1239.35i	−0.0811672	+	0.0725981i
$664$	26064.0	+	11216.2i	1.52331	+	0.655529i
$665$		−	4829.91i		−	0.281648i
$666$	7124.50	+	6913.92i	0.414518	+	0.402266i
$667$			14748.3i			0.856158i
$668$	−27.7128	−	107.331i	−0.00160515	−	0.00621672i
$669$	1830.00	−	1636.80i	0.105758	−	0.0945925i
$670$	11400.0	−	14717.3i	0.657344	−	0.848627i
$671$	15311.3			0.880905
$672$	−3968.62	−	6110.18i	−0.227816	−	0.350752i
$673$	−17470.0			−1.00062			−0.500311	−	0.865846i	$-0.666781\pi$
$673$	−17470.0			−1.00062			−0.500311	+	0.865846i	$0.666781\pi$
$674$	−2580.76	+	3331.74i	−0.147488	+	0.190406i
$675$	−5144.19	+	3659.97i	−0.293333	+	0.208700i
$676$	4194.00	+	16243.3i	0.238621	+	0.924175i
$677$			20813.3i			1.18157i	0.806830	+	0.590784i	$0.201181\pi$
$677$			20813.3i			1.18157i	−0.806830	+	0.590784i	$0.798819\pi$
$678$	−1076.72	−	15210.5i	−0.0609897	−	0.861589i
$679$		−	5964.39i		−	0.337102i
$680$	−6651.08	−	2862.17i	−0.375084	−	0.161410i
$681$	1752.00	+	1958.80i	0.0985856	+	0.110222i
$682$	−17400.0	−	13478.0i	−0.976951	−	0.756743i
$683$	−12616.3			−0.706805			−0.353402	−	0.935471i	$-0.614975\pi$
$683$	−12616.3			−0.706805			−0.353402	+	0.935471i	$0.614975\pi$
$684$	2121.23	+	14908.0i	0.118578	+	0.833365i
$685$	−800.000			−0.0446225
$686$	10842.6	+	8398.67i	0.603460	+	0.467438i
$687$	14182.0	+	15856.0i	0.787596	+	0.880559i
$688$	−6960.00	−	12579.4i	−0.385680	−	0.697074i
$689$			5456.01i			0.301680i
$690$	900.309	+	12718.5i	0.0496727	+	0.701716i
$691$		−	3028.67i		−	0.166738i	−0.996519	−	0.0833691i	$-0.973432\pi$
$691$		−	3028.67i		−	0.166738i	0.996519	−	0.0833691i	$-0.0265681\pi$
$692$	8660.25	−	2236.07i	0.475742	−	0.122836i
$693$	−7200.00	−	804.984i	−0.394669	−	0.0441253i
$694$	−3444.00	+	4446.18i	−0.188375	+	0.243191i
$695$	17528.4			0.956674
$696$	−16951.2	+	5680.53i	−0.923179	+	0.309368i
$697$	4480.00			0.243461
$698$	3592.27	−	4637.60i	0.194799	−	0.251484i
$699$	−20438.2	+	18280.5i	−1.10593	+	0.989172i
$700$	−2700.00	+	697.137i	−0.145786	+	0.0376419i
$701$		−	17664.9i		−	0.951777i	−0.879506	−	0.475888i	$-0.842127\pi$
$701$		−	17664.9i		−	0.951777i	0.879506	−	0.475888i	$-0.157873\pi$
$702$	−161.347	+	3964.89i	−0.00867470	+	0.213170i
$703$		−	9062.78i		−	0.486215i
$704$	−12193.6	−	12879.8i	−0.652791	−	0.689523i
$705$	6720.00	−	6010.55i	0.358993	−	0.321093i
$706$	−19360.0	−	14996.2i	−1.03204	−	0.799418i
$707$	11570.1			0.615472
$708$	−3996.15	+	5989.22i	−0.212125	+	0.317922i
$709$	14174.0			0.750798			0.375399	−	0.926863i	$-0.377506\pi$
$709$	14174.0			0.750798			0.375399	+	0.926863i	$0.377506\pi$
$710$	−20784.6	−	16099.7i	−1.09864	−	0.851001i
$711$	−2286.31	−	255.617i	−0.120595	−	0.0134830i
$712$	7520.00	−	17474.9i	0.395820	−	0.919803i
$713$		−	21788.2i		−	1.14443i
$714$	4062.77	−	287.593i	0.212949	−	0.0150741i
$715$		−	3098.39i		−	0.162060i
$716$	2702.00	+	10464.8i	0.141031	+	0.546212i
$717$	−19680.0	−	22002.9i	−1.02505	−	1.14604i
$718$	−14040.0	+	18125.6i	−0.729761	+	0.942117i
$719$	32839.7			1.70336			0.851678	−	0.524065i	$-0.175585\pi$
$719$	32839.7			1.70336			0.851678	+	0.524065i	$0.175585\pi$
$720$	−14271.4	+	5933.49i	−0.738699	+	0.307122i
$721$	10500.0			0.542358
$722$	−3462.37	+	4469.90i	−0.178471	+	0.230405i
$723$	−4149.99	−	4639.83i	−0.213472	−	0.238668i
$724$	−2524.00	−	9775.41i	−0.129563	−	0.501796i
$725$			6842.37i			0.350509i
$726$	1920.49	−	135.947i	0.0981766	−	0.00694967i
$727$		−	8001.58i		−	0.408201i	−0.978950	−	0.204101i	$-0.934573\pi$
$727$		−	8001.58i		−	0.408201i	0.978950	−	0.204101i	$-0.0654270\pi$
$728$	−692.820	+	1609.97i	−0.0352715	+	0.0819635i
$729$	6453.00	−	18595.1i	0.327846	−	0.944731i
$730$	8200.00	+	6351.69i	0.415747	+	0.322037i
$731$	8036.72			0.406633
$732$	−10197.7	+	15283.8i	−0.514917	+	0.771730i
$733$	11750.0			0.592082			0.296041	−	0.955175i	$-0.404333\pi$
$733$	11750.0			0.592082			0.296041	+	0.955175i	$0.404333\pi$
$734$	−17649.6	−	13671.3i	−0.887546	−	0.687490i
$735$	9803.41	−	8768.43i	0.491978	−	0.440039i
$736$	2688.00	−	17351.0i	0.134621	−	0.868974i
$737$			25491.2i			1.27406i
$738$	6659.69	−	6862.53i	0.332177	−	0.342294i
$739$			19961.4i			0.993627i	0.867857	+	0.496814i	$0.165497\pi$
$739$			19961.4i			0.993627i	−0.867857	+	0.496814i	$0.834503\pi$
$740$	9006.66	−	2325.51i	0.447421	−	0.115524i
$741$	2700.00	−	2414.95i	0.133856	−	0.119724i
$742$	7320.00	−	9450.08i	0.362164	−	0.467552i
$743$	−25592.8			−1.26367			−0.631836	−	0.775102i	$-0.717698\pi$
$743$	−25592.8			−1.26367			−0.631836	+	0.775102i	$0.717698\pi$
$744$	25042.6	−	8392.06i	1.23401	−	0.413532i
$745$	−14480.0			−0.712089
$746$	−8504.37	+	10979.1i	−0.417382	+	0.538838i
$747$	−3762.01	+	33648.5i	−0.184264	+	1.64810i
$748$	9600.00	−	2478.71i	0.469266	−	0.121164i
$749$			4990.90i			0.243476i
$750$	1577.95	+	22291.3i	0.0768246	+	1.08528i
$751$		−	5244.02i		−	0.254803i	−0.991851	−	0.127401i	$-0.959336\pi$
$751$		−	5244.02i		−	0.254803i	0.991851	−	0.127401i	$-0.0406637\pi$
$752$	−10863.4	+	6010.55i	−0.526793	+	0.291466i
$753$	14760.0	+	16502.2i	0.714322	+	0.798636i
$754$	3400.00	+	2633.63i	0.164218	+	0.127203i
$755$	−5057.59			−0.243794
$756$	5598.92	−	6650.92i	0.269353	−	0.319963i
$757$	−14290.0			−0.686102			−0.343051	−	0.939317i	$-0.611460\pi$
$757$	−14290.0			−0.686102			−0.343051	+	0.939317i	$0.611460\pi$
$758$	−7014.81	−	5433.65i	−0.336134	−	0.260368i
$759$	−11639.4	−	13013.2i	−0.556631	−	0.622332i
$760$	12960.0	+	5577.10i	0.618564	+	0.266188i
$761$			16976.2i			0.808657i	0.914614	+	0.404328i	$0.132495\pi$
$761$			16976.2i			0.808657i	−0.914614	+	0.404328i	$0.867505\pi$
$762$	1905.12	+	26913.2i	0.0905711	+	1.27948i
$763$			8257.20i			0.391783i
$764$	−5542.56	−	21466.3i	−0.262464	−	1.01652i
$765$	960.000	−	8586.50i	0.0453711	−	0.405811i
$766$	−10752.0	+	13880.8i	−0.507161	+	0.654742i
$767$	1732.05			0.0815394
$768$	20977.9	−	3593.49i	0.985644	−	0.168840i

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:	\( N \)	\(=\)	\( 12 = 2^{2} \cdot 3 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	12.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.73205 + 2.23607i) q^{2} +(3.46410 + 3.87298i) q^{3} +(-2.00000 - 7.74597i) q^{4} -8.94427i q^{5} +(-14.6603 + 1.03776i) q^{6} -7.74597i q^{7} +(20.7846 + 8.94427i) q^{8} +(-3.00000 + 26.8328i) q^{9} +O(q^{10})\)	\(q+(-1.73205 + 2.23607i) q^{2} +(3.46410 + 3.87298i) q^{3} +(-2.00000 - 7.74597i) q^{4} -8.94427i q^{5} +(-14.6603 + 1.03776i) q^{6} -7.74597i q^{7} +(20.7846 + 8.94427i) q^{8} +(-3.00000 + 26.8328i) q^{9} +(20.0000 + 15.4919i) q^{10} -34.6410 q^{11} +(23.0718 - 34.5788i) q^{12} -10.0000 q^{13} +(17.3205 + 13.4164i) q^{14} +(34.6410 - 30.9839i) q^{15} +(-56.0000 + 30.9839i) q^{16} -35.7771i q^{17} +(-54.8038 - 53.1840i) q^{18} +69.7137i q^{19} +(-69.2820 + 17.8885i) q^{20} +(30.0000 - 26.8328i) q^{21} +(60.0000 - 77.4597i) q^{22} +96.9948 q^{23} +(37.3590 + 111.482i) q^{24} +45.0000 q^{25} +(17.3205 - 22.3607i) q^{26} +(-114.315 + 81.3327i) q^{27} +(-60.0000 + 15.4919i) q^{28} +152.053i q^{29} +(9.28203 + 131.125i) q^{30} -224.633i q^{31} +(27.7128 - 178.885i) q^{32} +(-120.000 - 134.164i) q^{33} +(80.0000 + 61.9677i) q^{34} -69.2820 q^{35} +(213.846 - 30.4277i) q^{36} -130.000 q^{37} +(-155.885 - 120.748i) q^{38} +(-34.6410 - 38.7298i) q^{39} +(80.0000 - 185.903i) q^{40} +125.220i q^{41} +(8.03848 + 113.558i) q^{42} +224.633i q^{43} +(69.2820 + 268.328i) q^{44} +(240.000 + 26.8328i) q^{45} +(-168.000 + 216.887i) q^{46} +193.990 q^{47} +(-313.990 - 109.556i) q^{48} +283.000 q^{49} +(-77.9423 + 100.623i) q^{50} +(138.564 - 123.935i) q^{51} +(20.0000 + 77.4597i) q^{52} -545.601i q^{53} +(16.1347 - 396.489i) q^{54} +309.839i q^{55} +(69.2820 - 160.997i) q^{56} +(-270.000 + 241.495i) q^{57} +(-340.000 - 263.363i) q^{58} -173.205 q^{59} +(-309.282 - 206.360i) q^{60} -442.000 q^{61} +(502.295 + 389.076i) q^{62} +(207.846 + 23.2379i) q^{63} +(352.000 + 371.806i) q^{64} +89.4427i q^{65} +(507.846 - 35.9492i) q^{66} -735.867i q^{67} +(-277.128 + 71.5542i) q^{68} +(336.000 + 375.659i) q^{69} +(120.000 - 154.919i) q^{70} -1039.23 q^{71} +(-302.354 + 530.877i) q^{72} +410.000 q^{73} +(225.167 - 290.689i) q^{74} +(155.885 + 174.284i) q^{75} +(540.000 - 139.427i) q^{76} +268.328i q^{77} +(146.603 - 10.3776i) q^{78} +85.2056i q^{79} +(277.128 + 500.879i) q^{80} +(-711.000 - 160.997i) q^{81} +(-280.000 - 216.887i) q^{82} +1254.00 q^{83} +(-267.846 - 178.713i) q^{84} -320.000 q^{85} +(-502.295 - 389.076i) q^{86} +(-588.897 + 526.726i) q^{87} +(-720.000 - 309.839i) q^{88} -840.762i q^{89} +(-475.692 + 490.181i) q^{90} +77.4597i q^{91} +(-193.990 - 751.319i) q^{92} +(870.000 - 778.152i) q^{93} +(-336.000 + 433.774i) q^{94} +623.538 q^{95} +(788.820 - 512.346i) q^{96} +770.000 q^{97} +(-490.170 + 632.807i) q^{98} +(103.923 - 929.516i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 8 q^{4} - 24 q^{6} - 12 q^{9}+O(q^{10}) \) 4 * q - 8 * q^4 - 24 * q^6 - 12 * q^9	\( 4 q - 8 q^{4} - 24 q^{6} - 12 q^{9} + 80 q^{10} + 120 q^{12} - 40 q^{13} - 224 q^{16} - 240 q^{18} + 120 q^{21} + 240 q^{22} + 288 q^{24} + 180 q^{25} - 240 q^{28} - 240 q^{30} - 480 q^{33} + 320 q^{34} + 24 q^{36} - 520 q^{37} + 320 q^{40} + 240 q^{42} + 960 q^{45} - 672 q^{46} - 480 q^{48} + 1132 q^{49} + 80 q^{52} + 792 q^{54} - 1080 q^{57} - 1360 q^{58} - 960 q^{60} - 1768 q^{61} + 1408 q^{64} + 1200 q^{66} + 1344 q^{69} + 480 q^{70} - 960 q^{72} + 1640 q^{73} + 2160 q^{76} + 240 q^{78} - 2844 q^{81} - 1120 q^{82} - 240 q^{84} - 1280 q^{85} - 2880 q^{88} - 240 q^{90} + 3480 q^{93} - 1344 q^{94} + 384 q^{96} + 3080 q^{97}+O(q^{100}) \) 4 * q - 8 * q^4 - 24 * q^6 - 12 * q^9 + 80 * q^10 + 120 * q^12 - 40 * q^13 - 224 * q^16 - 240 * q^18 + 120 * q^21 + 240 * q^22 + 288 * q^24 + 180 * q^25 - 240 * q^28 - 240 * q^30 - 480 * q^33 + 320 * q^34 + 24 * q^36 - 520 * q^37 + 320 * q^40 + 240 * q^42 + 960 * q^45 - 672 * q^46 - 480 * q^48 + 1132 * q^49 + 80 * q^52 + 792 * q^54 - 1080 * q^57 - 1360 * q^58 - 960 * q^60 - 1768 * q^61 + 1408 * q^64 + 1200 * q^66 + 1344 * q^69 + 480 * q^70 - 960 * q^72 + 1640 * q^73 + 2160 * q^76 + 240 * q^78 - 2844 * q^81 - 1120 * q^82 - 240 * q^84 - 1280 * q^85 - 2880 * q^88 - 240 * q^90 + 3480 * q^93 - 1344 * q^94 + 384 * q^96 + 3080 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more