LMFDB - Embedded newform 12.4.b.a.11.4

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			11.4
Root			$0.866025 + 1.11803i$ of defining polynomial
Character	$\chi$	$=$	12.11
Dual form			12.4.b.a.11.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.73205 + 2.23607i) q^{2} +(-3.46410 - 3.87298i) q^{3} +(-2.00000 + 7.74597i) q^{4} -8.94427i q^{5} +(2.66025 - 14.4542i) q^{6} +7.74597i q^{7} +(-20.7846 + 8.94427i) q^{8} +(-3.00000 + 26.8328i) q^{9} +O(q^{10})$	\(q+(1.73205 + 2.23607i) q^{2} +(-3.46410 - 3.87298i) q^{3} +(-2.00000 + 7.74597i) q^{4} -8.94427i q^{5} +(2.66025 - 14.4542i) 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} +(36.9282 - 19.0868i) 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} +(-65.1962 + 39.7676i) 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} +(106.641 + 49.5146i) 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} +(-129.282 - 23.7940i) 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} +(-201.846 - 76.9035i) 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} +(111.962 + 20.6062i) 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} +(73.9897 + 324.218i) 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} +(379.865 + 114.745i) 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} +(-170.718 - 330.296i) 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} +(92.1539 - 500.707i) 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} +(-177.646 - 584.542i) 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} +(-26.6025 + 144.542i) 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} +(147.846 + 286.045i) 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} +(355.692 + 583.132i) 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} +(-596.820 + 727.009i) 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	$-0.130990\pi$
$6$	2.66025	−	14.4542i	0.181007	−	0.983482i
$7$			7.74597i			0.418243i	0.977890	+	0.209121i	$0.0670604\pi$
$7$			7.74597i			0.418243i	−0.977890	+	0.209121i	$0.932940\pi$
$8$	−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	$-0.342536\pi$
$11$	34.6410			0.949514			0.474757	+	0.880117i	$0.342536\pi$
$12$	36.9282	−	19.0868i	0.888355	−	0.459158i
$13$	−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	$-0.0821454\pi$
$18$	−65.1962	+	39.7676i	−0.853716	+	0.520740i
$19$		−	69.7137i		−	0.841759i	−0.907117	−	0.420879i	$-0.861722\pi$
$19$		−	69.7137i		−	0.841759i	0.907117	−	0.420879i	$-0.138278\pi$
$20$	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	$-0.644905\pi$
$23$	−96.9948			−0.879340			−0.439670	+	0.898159i	$0.644905\pi$
$24$	106.641	+	49.5146i	0.907000	+	0.421130i
$25$	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	$0.838157\pi$
$30$	−129.282	−	23.7940i	−0.786785	−	0.144806i
$31$			224.633i			1.30146i	0.759309	+	0.650730i	$0.225537\pi$
$31$			224.633i			1.30146i	−0.759309	+	0.650730i	$0.774463\pi$
$32$	−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
$36$	−201.846	−	76.9035i	−0.934473	−	0.356035i
$37$	−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	$0.923348\pi$
$42$	111.962	+	20.6062i	0.411334	+	0.0757050i
$43$		−	224.633i		−	0.796656i	−0.917243	−	0.398328i	$-0.869591\pi$
$43$		−	224.633i		−	0.796656i	0.917243	−	0.398328i	$-0.130409\pi$
$44$	−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	$-0.597329\pi$
$47$	−193.990			−0.602049			−0.301025	+	0.953616i	$0.597329\pi$
$48$	73.9897	+	324.218i	0.222489	+	0.974935i
$49$	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	$-0.249960\pi$
$54$	379.865	+	114.745i	0.957280	+	0.289162i
$55$		−	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	$-0.438796\pi$
$59$	173.205			0.382193			0.191096	+	0.981571i	$0.438796\pi$
$60$	−170.718	−	330.296i	−0.367327	−	0.710684i
$61$	−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
$66$	92.1539	−	500.707i	0.171869	−	0.933830i
$67$			735.867i			1.34180i	0.741549	+	0.670899i	$0.234092\pi$
$67$			735.867i			1.34180i	−0.741549	+	0.670899i	$0.765908\pi$
$68$	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	$-0.165053\pi$
$71$	1039.23			1.73710			0.868549	+	0.495603i	$0.165053\pi$
$72$	−177.646	−	584.542i	−0.290775	−	0.956791i
$73$	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
$78$	−26.6025	+	144.542i	−0.0386172	+	0.209822i
$79$		−	85.2056i		−	0.121347i	−0.998158	−	0.0606733i	$-0.980675\pi$
$79$		−	85.2056i		−	0.121347i	0.998158	−	0.0606733i	$-0.0193248\pi$
$80$	−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	$-0.811196\pi$
$83$	−1254.00			−1.65837			−0.829186	+	0.558973i	$0.811196\pi$
$84$	147.846	+	286.045i	0.192040	+	0.371548i
$85$	−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	$-0.166916\pi$
$90$	355.692	+	583.132i	0.416592	+	0.682972i
$91$		−	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
$96$	−596.820	+	727.009i	−0.634507	+	0.772917i
$97$	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	$0.736815\pi$
$102$	−517.128	−	95.1761i	−0.501993	−	0.0923906i
$103$		−	1355.54i		−	1.29675i	−0.761319	−	0.648377i	$-0.775448\pi$
$103$		−	1355.54i		−	1.29675i	0.761319	−	0.648377i	$-0.224552\pi$
$104$	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	$-0.405989\pi$
$107$	644.323			0.582141			0.291070	+	0.956702i	$0.405989\pi$
$108$	401.369	+	1048.15i	0.357609	+	0.933871i
$109$	−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	$0.857853\pi$
$114$	−1007.65	−	185.456i	−0.827855	−	0.152365i
$115$			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
$120$	442.872	−	953.826i	0.336904	−	0.725600i
$121$	−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
$126$	−308.038	−	505.007i	−0.217796	−	0.357060i
$127$			1835.79i			1.28268i	0.767257	+	0.641340i	$0.221621\pi$
$127$			1835.79i			1.28268i	−0.767257	+	0.641340i	$0.778379\pi$
$128$	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	$-0.547984\pi$
$131$	−450.333			−0.300350			−0.150175	+	0.988659i	$0.547984\pi$
$132$	1279.23	−	661.188i	0.843505	−	0.435977i
$133$	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	$-0.00887852\pi$
$138$	−258.031	+	1401.98i	−0.159167	+	0.864815i
$139$		−	1959.73i		−	1.19584i	−0.801555	−	0.597921i	$-0.795994\pi$
$139$		−	1959.73i		−	1.19584i	0.801555	−	0.597921i	$-0.204006\pi$
$140$	−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
$144$	999.384	−	1409.69i	0.578347	−	0.815791i
$145$	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	$-0.146816\pi$
$150$	119.711	−	650.438i	0.0651626	−	0.354053i
$151$			565.456i			0.304743i	0.988323	+	0.152371i	$0.0486909\pi$
$151$			565.456i			0.304743i	−0.988323	+	0.152371i	$0.951309\pi$
$152$	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
$156$	−369.282	+	190.868i	−0.189527	+	0.0979597i
$157$	−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
$162$	−871.488	−	1868.70i	−0.422658	−	0.906289i
$163$		−	255.617i		−	0.122831i	−0.998112	−	0.0614155i	$-0.980439\pi$
$163$		−	255.617i		−	0.122831i	0.998112	−	0.0614155i	$-0.0195615\pi$
$164$	−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	$-0.501022\pi$
$167$	−13.8564			−0.00642060			−0.00321030	+	0.999995i	$0.501022\pi$
$168$	−383.538	+	826.038i	−0.176135	+	0.379346i
$169$	−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	$0.920991\pi$
$174$	2197.79	+	404.499i	0.957554	+	0.176235i
$175$			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	$-0.408981\pi$
$179$	1351.00			0.564125			0.282063	+	0.959396i	$0.408981\pi$
$180$	−687.846	+	1805.37i	−0.284828	+	0.747578i
$181$	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
$186$	3246.88	+	597.581i	1.27996	+	0.235574i
$187$		−	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	$-0.675908\pi$
$191$	−2771.28			−1.04986			−0.524929	+	0.851146i	$0.675908\pi$
$192$	−2659.36	−	75.3150i	−0.999599	−	0.0283093i
$193$	−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	$0.873664\pi$
$198$	−2258.46	+	1377.59i	−0.810615	+	0.494450i
$199$			255.617i			0.0910563i	0.998963	+	0.0455281i	$0.0144971\pi$
$199$			255.617i			0.0910563i	−0.998963	+	0.0455281i	$0.985503\pi$
$200$	−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
$204$	−682.872	−	1321.18i	−0.234366	−	0.453438i
$205$	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
$210$	184.308	−	1001.41i	0.0605640	−	0.329067i
$211$			549.964i			0.179436i	0.995967	+	0.0897181i	$0.0285966\pi$
$211$			549.964i			0.179436i	−0.995967	+	0.0897181i	$0.971403\pi$
$212$	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
$216$	−1648.54	+	2712.93i	−0.519300	+	0.854592i
$217$	−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
$222$	−345.833	+	1879.04i	−0.104553	+	0.568077i
$223$			472.504i			0.141889i	0.997480	+	0.0709444i	$0.0226013\pi$
$223$			472.504i			0.141889i	−0.997480	+	0.0709444i	$0.977399\pi$
$224$	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	$-0.523557\pi$
$227$	−505.759			−0.147878			−0.0739392	+	0.997263i	$0.523557\pi$
$228$	−1330.61	−	2574.40i	−0.386501	−	0.747780i
$229$	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	$0.733935\pi$
$234$	651.962	−	397.676i	0.182137	−	0.111098i
$235$			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	$-0.220859\pi$
$239$	5681.13			1.53758			0.768790	+	0.639502i	$0.220859\pi$
$240$	2899.90	−	661.784i	0.779948	−	0.177992i
$241$	−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
$246$	1809.95	+	333.116i	0.469098	+	0.0863363i
$247$			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	$-0.679968\pi$
$251$	−4260.84			−1.07148			−0.535741	+	0.844382i	$0.679968\pi$
$252$	595.692	−	1563.49i	0.148909	−	0.390837i
$253$	−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	$-0.124793\pi$
$258$	−3246.88	−	597.581i	−0.783497	−	0.144201i
$259$		−	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	$-0.333817\pi$
$263$	4253.92			0.997368			0.498684	+	0.866784i	$0.333817\pi$
$264$	3694.15	+	1715.24i	0.861210	+	0.399869i
$265$	−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	$0.998387\pi$
$270$	1026.31	−	3397.62i	0.231330	−	0.765824i
$271$		−	8760.69i		−	1.96374i	−0.189552	−	0.981871i	$-0.560704\pi$
$271$		−	8760.69i		−	1.96374i	0.189552	−	0.981871i	$-0.439296\pi$
$272$	−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
$276$	−3581.85	+	1851.33i	−0.781166	+	0.403756i
$277$	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	$-0.201083\pi$
$282$	−516.062	+	2803.96i	−0.108975	+	0.592104i
$283$			6777.72i			1.42365i	0.702356	+	0.711826i	$0.252132\pi$
$283$			6777.72i			1.42365i	−0.702356	+	0.711826i	$0.747868\pi$
$284$	−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
$288$	4883.14	−	206.956i	0.999103	−	0.0423438i
$289$	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	$-0.0207345\pi$
$294$	752.852	−	4090.53i	0.149344	−	0.811444i
$295$		−	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
$300$	1661.77	−	858.908i	0.319808	−	0.165297i
$301$	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
$306$	1422.77	+	2332.53i	0.265798	+	0.435757i
$307$		−	1556.94i		−	0.289444i	−0.989472	−	0.144722i	$-0.953771\pi$
$307$		−	1556.94i		−	0.289444i	0.989472	−	0.144722i	$-0.0462287\pi$
$308$	−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	$-0.595939\pi$
$311$	−3256.26			−0.593715			−0.296857	+	0.954922i	$0.595939\pi$
$312$	−1066.41	−	495.146i	−0.193505	−	0.0898465i
$313$	−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	$-0.0138764\pi$
$318$	−7886.20	−	1451.44i	−1.39068	−	0.255951i
$319$			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
$324$	2669.08	−	5185.39i	0.457661	−	0.889127i
$325$	−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
$330$	−4478.46	−	824.250i	−0.747064	−	0.137495i
$331$			4237.04i			0.703592i	0.936077	+	0.351796i	$0.114429\pi$
$331$			4237.04i			0.703592i	−0.936077	+	0.351796i	$0.885571\pi$
$332$	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
$336$	−2511.38	+	573.122i	−0.407760	+	0.0930546i
$337$	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
$342$	2772.35	+	4545.07i	0.438337	+	0.718623i
$343$			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	$-0.549154\pi$
$347$	−1988.39			−0.307616			−0.153808	+	0.988101i	$0.549154\pi$
$348$	2902.21	+	5615.03i	0.447053	+	0.864935i
$349$	−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	$0.773627\pi$
$354$	460.770	−	2503.54i	0.0691797	−	0.375880i
$355$		−	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	$-0.703184\pi$
$359$	−8106.00			−1.19169			−0.595847	+	0.803098i	$0.703184\pi$
$360$	−5228.31	+	1588.92i	−0.765433	+	0.232620i
$361$	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
$366$	−1175.83	+	6388.74i	−0.167928	+	0.912418i
$367$		−	7893.14i		−	1.12267i	−0.827590	−	0.561333i	$-0.810289\pi$
$367$		−	7893.14i		−	1.12267i	0.827590	−	0.561333i	$-0.189711\pi$
$368$	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
$372$	4287.54	+	8295.29i	0.597576	+	1.15616i
$373$	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
$378$	−888.808	+	2942.42i	−0.120940	+	0.400376i
$379$		−	3137.12i		−	0.425179i	−0.977142	−	0.212590i	$-0.931810\pi$
$379$		−	3137.12i		−	0.425179i	0.977142	−	0.212590i	$-0.0681897\pi$
$380$	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	$-0.635902\pi$
$383$	−6207.67			−0.828191			−0.414095	+	0.910233i	$0.635902\pi$
$384$	−4437.74	−	6076.97i	−0.589747	−	0.807588i
$385$	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	$-0.211297\pi$
$390$	1292.82	+	237.940i	0.167858	+	0.0308938i
$391$			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
$396$	−6992.15	−	2664.02i	−0.887295	−	0.338060i
$397$	−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	$0.966611\pi$
$402$	10636.3	+	1957.59i	1.31963	+	0.242875i
$403$		−	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
$408$	1771.49	−	3815.30i	0.214955	−	0.462955i
$409$	−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
$414$	6323.69	−	3857.25i	0.750706	−	0.457907i
$415$			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	$-0.147439\pi$
$419$	15346.0			1.78926			0.894630	+	0.446808i	$0.147439\pi$
$420$	2558.46	−	1322.38i	0.297238	−	0.153632i
$421$	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
$426$	2764.62	−	15021.2i	0.314428	−	1.70840i
$427$		−	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	$-0.244100\pi$
$431$	12886.5			1.44018			0.720091	+	0.693879i	$0.244100\pi$
$432$	−8921.66	+	1012.70i	−0.993619	+	0.112786i
$433$	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
$438$	1090.70	−	5926.21i	0.118986	−	0.646496i
$439$			15065.9i			1.63794i	0.573835	+	0.818971i	$0.305455\pi$
$439$			15065.9i			1.63794i	−0.573835	+	0.818971i	$0.694545\pi$
$440$	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	$-0.552149\pi$
$443$	−3041.48			−0.326197			−0.163098	+	0.986610i	$0.552149\pi$
$444$	−4800.67	+	2481.29i	−0.513130	+	0.265218i
$445$	−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	$-0.270951\pi$
$450$	−2933.83	+	1789.54i	−0.307338	+	0.187466i
$451$			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
$456$	3451.84	−	7434.34i	0.354490	−	0.763476i
$457$	−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	$0.936736\pi$
$462$	3878.46	+	713.821i	0.390568	+	0.0718830i
$463$		−	18179.8i		−	1.82481i	−0.409291	−	0.912404i	$-0.634224\pi$
$463$		−	18179.8i		−	1.82481i	0.409291	−	0.912404i	$-0.365776\pi$
$464$	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	$-0.470786\pi$
$467$	1849.83			0.183298			0.0916488	+	0.995791i	$0.470786\pi$
$468$	2018.46	+	769.035i	0.199366	+	0.0759587i
$469$	−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
$474$	−1231.58	−	226.669i	−0.119342	−	0.0219646i
$475$		−	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	$-0.759067\pi$
$479$	−15242.0			−1.45392			−0.726959	+	0.686681i	$0.759067\pi$
$480$	6502.56	+	5338.12i	0.618333	+	0.507606i
$481$	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
$486$	−4218.52	+	9848.62i	−0.393736	+	0.919223i
$487$		−	9783.16i		−	0.910302i	−0.890414	−	0.455151i	$-0.849585\pi$
$487$		−	9783.16i		−	0.910302i	0.890414	−	0.455151i	$-0.150415\pi$
$488$	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	$-0.602610\pi$
$491$	−6893.56			−0.633609			−0.316805	+	0.948491i	$0.602610\pi$
$492$	2390.05	+	4624.14i	0.219008	+	0.423724i
$493$	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
$498$	−3335.97	+	18125.6i	−0.300178	+	1.63098i
$499$		−	1309.07i		−	0.117439i	−0.998275	−	0.0587194i	$-0.981298\pi$
$499$		−	1309.07i		−	0.117439i	0.998275	−	0.0587194i	$-0.0187017\pi$
$500$	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	$-0.385535\pi$
$503$	7939.72			0.703806			0.351903	+	0.936036i	$0.385535\pi$
$504$	4527.85	−	1376.04i	0.400171	−	0.121615i
$505$	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	$0.781890\pi$
$510$	−851.281	+	4625.33i	−0.0739125	+	0.401595i
$511$			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
$516$	−4287.54	−	8295.29i	−0.365791	−	0.707713i
$517$	−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	$0.871313\pi$
$522$	−6046.77	−	9913.25i	−0.507011	−	0.831209i
$523$			10062.0i			0.841264i	0.907231	+	0.420632i	$0.138192\pi$
$523$			10062.0i			0.841264i	−0.907231	+	0.420632i	$0.861808\pi$
$524$	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
$528$	2563.08	+	11231.3i	0.211257	+	0.925715i
$529$	−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
$534$	−12152.5	−	2236.64i	−0.984814	−	0.181253i
$535$		−	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
$540$	9374.92	−	3589.96i	0.747097	−	0.286087i
$541$	−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
$546$	−1119.62	−	206.062i	−0.0877566	−	0.0161514i
$547$			15112.4i			1.18128i	0.806936	+	0.590639i	$0.201124\pi$
$547$			15112.4i			1.18128i	−0.806936	+	0.590639i	$0.798876\pi$
$548$	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
$552$	−10343.6	−	4802.66i	−0.797562	−	0.370317i
$553$	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	$-0.209094\pi$
$558$	−8933.12	−	14645.2i	−0.677722	−	1.11108i
$559$			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	$-0.890164\pi$
$563$	−25142.4			−1.88211			−0.941055	+	0.338254i	$0.890164\pi$
$564$	−7163.69	+	3702.65i	−0.534833	+	0.276436i
$565$	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	$0.668826\pi$
$570$	−1658.77	+	9012.73i	−0.121892	+	0.662284i
$571$			4918.69i			0.360492i	0.983622	+	0.180246i	$0.0576893\pi$
$571$			4918.69i			0.360492i	−0.983622	+	0.180246i	$0.942311\pi$
$572$	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
$576$	8920.61	+	10560.6i	0.645299	+	0.763930i
$577$	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
$582$	2048.40	−	11129.7i	0.145891	−	0.792683i
$583$		−	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	$-0.484720\pi$
$587$	1364.86			0.0959687			0.0479844	+	0.998848i	$0.484720\pi$
$588$	10450.7	−	5401.58i	0.732957	−	0.378839i
$589$	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	$-0.351515\pi$
$594$	13158.9	+	3974.87i	0.908951	+	0.274564i
$595$		−	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	$-0.526355\pi$
$599$	−2424.87			−0.165405			−0.0827025	+	0.996574i	$0.526355\pi$
$600$	4798.85	+	2228.16i	0.326520	+	0.151607i
$601$	−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
$606$	21590.1	+	3973.60i	1.44726	+	0.266364i
$607$			19558.6i			1.30784i	0.756565	+	0.653919i	$0.226876\pi$
$607$			19558.6i			1.30784i	−0.756565	+	0.653919i	$0.773124\pi$
$608$	−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
$612$	−2751.38	+	7221.47i	−0.181729	+	0.476978i
$613$	−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	$-0.0890236\pi$
$618$	−19593.3	−	3606.09i	−1.27533	−	0.234722i
$619$		−	19930.4i		−	1.29413i	−0.762433	−	0.647067i	$-0.775995\pi$
$619$		−	19930.4i		−	1.29413i	0.762433	−	0.647067i	$-0.224005\pi$
$620$	−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
$624$	−739.897	−	3242.18i	−0.0474673	−	0.207999i
$625$	−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
$630$	−4516.92	+	2755.18i	−0.285648	+	0.174236i
$631$		−	12199.9i		−	0.769683i	−0.922983	−	0.384842i	$-0.874256\pi$
$631$		−	12199.9i		−	0.769683i	0.922983	−	0.384842i	$-0.125744\pi$
$632$	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
$636$	−10413.8	−	20148.0i	−0.649267	−	1.25617i
$637$	−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	$-0.0693158\pi$
$642$	1714.06	−	9313.15i	0.105372	−	0.572525i
$643$			15979.9i			0.980073i	0.871702	+	0.490036i	$0.163017\pi$
$643$			15979.9i			0.980073i	−0.871702	+	0.490036i	$0.836983\pi$
$644$	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	$-0.315824\pi$
$647$	17999.5			1.09371			0.546856	+	0.837226i	$0.315824\pi$
$648$	16217.9	−	3013.12i	0.983175	−	0.182664i
$649$	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	$0.950233\pi$
$654$	−2835.83	+	15408.1i	−0.169556	+	0.921263i
$655$			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	$-0.442658\pi$
$659$	6062.18			0.358344			0.179172	+	0.983818i	$0.442658\pi$
$660$	−5913.84	−	11441.8i	−0.348782	−	0.674804i
$661$	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
$666$	8475.50	−	5169.79i	0.493122	−	0.300789i
$667$		−	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
$672$	−5631.38	−	4622.95i	−0.323267	−	0.265378i
$673$	−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	$0.798819\pi$
$678$	14996.7	+	2760.11i	0.849477	+	0.156344i
$679$			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	$-0.385025\pi$
$683$	12616.3			0.706805			0.353402	+	0.935471i	$0.385025\pi$
$684$	−5361.23	+	14071.4i	−0.299696	+	0.786601i
$685$	−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
$690$	12539.7	+	2307.90i	0.691852	+	0.127334i
$691$			3028.67i			0.166738i	0.996519	+	0.0833691i	$0.0265681\pi$
$691$			3028.67i			0.166738i	−0.996519	+	0.0833691i	$0.973432\pi$
$692$	−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
$696$	−7528.82	+	16215.0i	−0.410028	+	0.883089i
$697$	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	$-0.157873\pi$
$702$	−3798.65	−	1147.45i	−0.204232	−	0.0616917i
$703$			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
$708$	6396.15	−	3305.94i	0.339523	−	0.175487i
$709$	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
$714$	737.231	−	4005.66i	0.0386417	−	0.209955i
$715$			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	$-0.824415\pi$
$719$	−32839.7			−1.70336			−0.851678	+	0.524065i	$0.824415\pi$
$720$	−12608.6	−	8938.77i	−0.652632	−	0.462678i
$721$	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
$726$	−348.493	+	1893.50i	−0.0178151	+	0.0967965i
$727$			8001.58i			0.408201i	0.978950	+	0.204101i	$0.0654270\pi$
$727$			8001.58i			0.408201i	−0.978950	+	0.204101i	$0.934573\pi$
$728$	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
$732$	−16322.3	+	8436.39i	−0.824164	+	0.425981i
$733$	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
$738$	−4979.69	−	8163.85i	−0.248381	−	0.407203i
$739$		−	19961.4i		−	0.993627i	−0.867857	−	0.496814i	$-0.834503\pi$
$739$		−	19961.4i		−	0.993627i	0.867857	−	0.496814i	$-0.165497\pi$
$740$	−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	$-0.282302\pi$
$743$	25592.8			1.26367			0.631836	+	0.775102i	$0.282302\pi$
$744$	−11122.6	+	23955.1i	−0.548084	+	1.18043i
$745$	−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
$750$	−21977.9	−	4044.99i	−1.07003	−	0.196936i
$751$			5244.02i			0.254803i	0.991851	+	0.127401i	$0.0406637\pi$
$751$			5244.02i			0.254803i	−0.991851	+	0.127401i	$0.959336\pi$
$752$	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
$756$	−8118.92	+	3108.99i	−0.390585	+	0.149567i
$757$	−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	$0.867505\pi$
$762$	26534.9	+	4883.68i	1.26149	+	0.232175i
$763$		−	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
$768$	5902.11	−	20448.7i	0.277310	−	0.960780i

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)

\(f(q)\)	\(=\)	\(q+(1.73205 + 2.23607i) q^{2} +(-3.46410 - 3.87298i) q^{3} +(-2.00000 + 7.74597i) q^{4} -8.94427i q^{5} +(2.66025 - 14.4542i) q^{6} +7.74597i q^{7} +(-20.7846 + 8.94427i) q^{8} +(-3.00000 + 26.8328i) q^{9} +O(q^{10})\)	\(q+(1.73205 + 2.23607i) q^{2} +(-3.46410 - 3.87298i) q^{3} +(-2.00000 + 7.74597i) q^{4} -8.94427i q^{5} +(2.66025 - 14.4542i) 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} +(36.9282 - 19.0868i) 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} +(-65.1962 + 39.7676i) 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} +(106.641 + 49.5146i) 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} +(-129.282 - 23.7940i) 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} +(-201.846 - 76.9035i) 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} +(111.962 + 20.6062i) 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} +(73.9897 + 324.218i) 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} +(379.865 + 114.745i) 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} +(-170.718 - 330.296i) 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} +(92.1539 - 500.707i) 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} +(-177.646 - 584.542i) 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} +(-26.6025 + 144.542i) 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} +(147.846 + 286.045i) 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} +(355.692 + 583.132i) 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} +(-596.820 + 727.009i) 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

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