LMFDB - Embedded newform 12.4.b.a.11.3

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

$q$-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	$0.130990\pi$
$5$			8.94427i			0.800000i	−0.916515	+	0.400000i	$0.869010\pi$
$6$	2.66025	+	14.4542i	0.181007	+	0.983482i
$7$		−	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	$-0.342536\pi$
$11$	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	$0.0821454\pi$
$17$			35.7771i			0.510425i	−0.966885	+	0.255212i	$0.917855\pi$
$18$	−65.1962	−	39.7676i	−0.853716	−	0.520740i
$19$			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	$-0.644905\pi$
$23$	−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	$-0.838157\pi$
$29$		−	152.053i		−	0.973637i	0.873503	−	0.486818i	$-0.161843\pi$
$30$	−129.282	+	23.7940i	−0.786785	+	0.144806i
$31$		−	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
$36$	−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	$-0.923348\pi$
$41$		−	125.220i		−	0.476977i	0.971145	−	0.238488i	$-0.0766519\pi$
$42$	111.962	−	20.6062i	0.411334	−	0.0757050i
$43$			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	$-0.597329\pi$
$47$	−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	$0.249960\pi$
$53$			545.601i			1.41404i	−0.707195	+	0.707019i	$0.750040\pi$
$54$	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	$-0.765908\pi$
$67$		−	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	$-0.165053\pi$
$71$	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	$0.0193248\pi$
$79$			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	$-0.811196\pi$
$83$	−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	$0.166916\pi$
$89$			840.762i			1.00135i	−0.865634	+	0.500677i	$0.833084\pi$
$90$	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	$-0.736815\pi$
$101$		−	1493.69i		−	1.47156i	0.677218	−	0.735782i	$-0.263185\pi$
$102$	−517.128	+	95.1761i	−0.501993	+	0.0923906i
$103$			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	$-0.405989\pi$
$107$	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	$-0.857853\pi$
$113$		−	1037.54i		−	0.863745i	0.901935	−	0.431872i	$-0.142147\pi$
$114$	−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	$-0.778379\pi$
$127$		−	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	$-0.547984\pi$
$131$	−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	$0.00887852\pi$
$137$			89.4427i			0.0557782i	−0.999611	+	0.0278891i	$0.991121\pi$
$138$	−258.031	−	1401.98i	−0.159167	−	0.864815i
$139$			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
$144$	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	$0.146816\pi$
$149$			1618.91i			0.890111i	−0.895503	+	0.445055i	$0.853184\pi$
$150$	119.711	+	650.438i	0.0651626	+	0.354053i
$151$		−	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
$156$	−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	$0.0195615\pi$
$163$			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	$-0.501022\pi$
$167$	−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	$-0.920991\pi$
$173$		−	1118.03i		−	0.491344i	0.969353	−	0.245672i	$-0.0790086\pi$
$174$	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	$-0.873664\pi$
$197$		−	2137.68i		−	0.773114i	0.922266	−	0.386557i	$-0.126336\pi$
$198$	−2258.46	−	1377.59i	−0.810615	−	0.494450i
$199$		−	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
$204$	−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	$-0.971403\pi$
$211$		−	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
$216$	−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	$-0.977399\pi$
$223$		−	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	$-0.523557\pi$
$227$	−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	$-0.733935\pi$
$233$		−	5277.12i		−	1.48376i	0.670534	−	0.741879i	$-0.266065\pi$
$234$	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	$0.124793\pi$
$257$			3148.38i			0.764166i	−0.924128	+	0.382083i	$0.875207\pi$
$258$	−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	$-0.998387\pi$
$269$		−	44.7214i		−	0.0101365i	0.999987	−	0.00506823i	$-0.00161328\pi$
$270$	1026.31	+	3397.62i	0.231330	+	0.765824i
$271$			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
$276$	−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	$0.201083\pi$
$281$			5563.34i			1.18107i	−0.807012	+	0.590535i	$0.798917\pi$
$282$	−516.062	−	2803.96i	−0.108975	−	0.592104i
$283$		−	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
$288$	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	$0.0207345\pi$
$293$			652.932i			0.130187i	−0.997879	+	0.0650933i	$0.979265\pi$
$294$	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	$0.0462287\pi$
$307$			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	$-0.595939\pi$
$311$	−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	$0.0138764\pi$
$317$			491.935i			0.0871603i	−0.999050	+	0.0435802i	$0.986124\pi$
$318$	−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	$-0.885571\pi$
$331$		−	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
$336$	−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	$-0.773627\pi$
$353$		−	8658.06i		−	1.30544i	0.757597	−	0.652722i	$-0.226373\pi$
$354$	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	$0.189711\pi$
$367$			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
$372$	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	$0.0681897\pi$
$379$			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	$-0.635902\pi$
$383$	−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	$0.211297\pi$
$389$			9454.10i			1.23224i	−0.787652	+	0.616120i	$0.788703\pi$
$390$	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	$-0.966611\pi$
$401$		−	1681.52i		−	0.209405i	0.994504	−	0.104702i	$-0.0333890\pi$
$402$	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	$-0.694545\pi$
$439$		−	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	$-0.552149\pi$
$443$	−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	$0.270951\pi$
$449$			14310.8i			1.50416i	−0.659069	+	0.752082i	$0.729049\pi$
$450$	−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	$-0.936736\pi$
$461$		−	3908.65i		−	0.394889i	0.980314	−	0.197445i	$-0.0632642\pi$
$462$	3878.46	−	713.821i	0.390568	−	0.0718830i
$463$			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	$-0.470786\pi$
$467$	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	$0.150415\pi$
$487$			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	$-0.602610\pi$
$491$	−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	$0.0187017\pi$
$499$			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	$-0.385535\pi$
$503$	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	$-0.781890\pi$
$509$		−	14534.4i		−	1.26567i	0.774285	−	0.632837i	$-0.218110\pi$
$510$	−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	$-0.871313\pi$
$521$		−	9355.71i		−	0.786720i	0.919385	−	0.393360i	$-0.128687\pi$
$522$	−6046.77	+	9913.25i	−0.507011	+	0.831209i
$523$		−	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
$528$	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	$-0.798876\pi$
$547$		−	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
$552$	−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	$0.209094\pi$
$557$			16055.0i			1.22131i	−0.791896	+	0.610656i	$0.790906\pi$
$558$	−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	$-0.668826\pi$
$569$		−	23416.1i		−	1.72523i	0.505864	−	0.862613i	$-0.331174\pi$
$570$	−1658.77	−	9012.73i	−0.121892	−	0.662284i
$571$		−	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
$576$	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	$0.351515\pi$
$593$			25795.3i			1.78632i	−0.449743	+	0.893158i	$0.648485\pi$
$594$	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	$-0.773124\pi$
$607$		−	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
$612$	−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	$0.0890236\pi$
$617$			8461.28i			0.552088i	−0.961145	+	0.276044i	$0.910976\pi$
$618$	−19593.3	+	3606.09i	−1.27533	+	0.234722i
$619$			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
$624$	−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	$0.125744\pi$
$631$			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
$636$	−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	$0.0693158\pi$
$641$			7012.31i			0.432090i	−0.976383	+	0.216045i	$0.930684\pi$
$642$	1714.06	+	9313.15i	0.105372	+	0.572525i
$643$		−	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	$-0.315824\pi$
$647$	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	$-0.950233\pi$
$653$		−	5196.62i		−	0.311423i	0.987803	−	0.155712i	$-0.0497671\pi$
$654$	−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	$-0.798819\pi$
$677$		−	20813.3i		−	1.18157i	0.806830	−	0.590784i	$-0.201181\pi$
$678$	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	$-0.973432\pi$
$691$		−	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
$696$	−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	$0.157873\pi$
$701$			17664.9i			0.951777i	−0.879506	+	0.475888i	$0.842127\pi$
$702$	−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	$-0.934573\pi$
$727$		−	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
$732$	−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	$0.165497\pi$
$739$			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	$-0.282302\pi$
$743$	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	$-0.959336\pi$
$751$		−	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
$756$	−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	$-0.867505\pi$
$761$		−	16976.2i		−	0.808657i	0.914614	−	0.404328i	$-0.132495\pi$
$762$	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
$769$	−29566.0			−1.38645			−0.693223	−	0.720723i	$-0.743810\pi$
$769$	−29566.0			−1.38645			−0.693223	+	0.720723i	$0.743810\pi$
$770$	4156.92	−	5366.56i	0.194552	−	0.251166i
$771$	−12193.6	−	10906.3i	−0.569576	−	0.509444i
$772$	380.000	+	1471.73i	0.0177157	+	0.0686125i
$773$		−	21457.3i		−	0.998403i	−0.866486	−	0.499202i	$-0.833627\pi$
$773$		−	21457.3i		−	0.998403i	0.866486	−	0.499202i	$-0.166373\pi$
$774$	8933.12	−	14645.2i	0.414850	−	0.680118i
$775$		−	10108.5i		−	0.468526i
$776$	−16004.1	−	6887.09i	−0.740355	−	0.318598i
$777$	−3900.00	−	3488.27i	−0.180067	−	0.161056i
$778$	21140.0	+	16375.0i	0.974172	+	0.754590i
$779$	8729.54			0.401499
$780$	1707.18	−	3302.96i	0.0783677	−	0.151622i
$781$	36000.0			1.64940
$782$	−7759.59	−	6010.55i	−0.354837	−	0.274855i
$783$	12366.8	−	17381.9i	0.564438	−	0.793334i
$784$	−15848.0	+	8768.43i	−0.721939	+	0.399437i
$785$		−	6529.32i		−	0.296868i
$786$	−1198.00	−	6509.19i	−0.0543655	−	0.295388i
$787$		−	3896.22i		−	0.176474i	−0.996099	−	0.0882372i	$-0.971877\pi$
$787$		−	3896.22i		−	0.176474i	0.996099	−	0.0882372i	$-0.0281233\pi$
$788$	−16558.4	+	4275.36i	−0.748564	+	0.193279i
$789$	−14736.0	+	16475.3i	−0.664912	+	0.743394i
$790$	−1320.00	+	1704.11i	−0.0594475	+	0.0767463i
$791$	−8036.72			−0.361255
$792$	−6153.84	+	20249.1i	−0.276095	+	0.908487i
$793$	4420.00			0.197930
$794$	−18307.8	+	23635.2i	−0.818286	+	1.05640i
$795$	16904.8	−	18900.2i	0.754154	−	0.843169i
$796$	−1980.00	+	511.234i	−0.0881649	+	0.0227641i
$797$			30759.4i			1.36707i	0.729919	+	0.683533i	$0.239558\pi$
$797$			30759.4i			1.36707i	−0.729919	+	0.683533i	$0.760442\pi$
$798$	1436.54	+	7805.25i	0.0637254	+	0.346244i
$799$		−	6940.39i		−	0.307301i
$800$	−1247.08	+	8049.84i	−0.0551135	+	0.355756i
$801$	22560.0	−	2522.28i	0.995154	−	0.111262i
$802$	−3760.00	−	2912.48i	−0.165549	−	0.128234i
$803$	14202.8			0.624168
$804$	14045.4	−	27174.2i	0.616097	−	1.19199i
$805$	−6720.00			−0.294222
$806$	5022.95	+	3890.76i	0.219511	+	0.170032i
$807$	173.205	+	154.919i	0.00755528	+	0.00675764i
$808$	−13360.0	+	31045.8i	−0.581687	+	1.35172i
$809$		−	10429.0i		−	0.453232i	−0.973984	−	0.226616i	$-0.927234\pi$
$809$		−	10429.0i		−	0.453232i	0.973984	−	0.226616i	$-0.0727663\pi$
$810$	−16714.2	−	7794.83i	−0.725031	−	0.338126i
$811$			8156.50i			0.353161i	0.984286	+	0.176580i	$0.0565036\pi$
$811$			8156.50i			0.353161i	−0.984286	+	0.176580i	$0.943496\pi$
$812$	2355.59	+	9123.16i	0.101804	+	0.394286i
$813$	−33930.0	−	30347.9i	−1.46369	−	1.30916i
$814$	−7800.00	+	10069.8i	−0.335860	+	0.433593i
$815$	−2286.31			−0.0982648
$816$	11599.6	+	2647.14i	0.497631	+	0.113564i
$817$	−15660.0			−0.670592
$818$	−6190.35	+	7991.71i	−0.264597	+	0.341593i
$819$	2078.46	−	232.379i	0.0886780	−	0.00991450i
$820$	−2240.00	−	8675.48i	−0.0953954	−	0.369465i
$821$			35750.3i			1.51972i	0.650085	+	0.759861i	$0.274733\pi$
$821$			35750.3i			1.51972i	−0.650085	+	0.759861i	$0.725267\pi$
$822$	−1292.82	+	237.940i	−0.0548568	+	0.0100963i
$823$			20875.4i			0.884168i	0.896974	+	0.442084i	$0.145761\pi$
$823$			20875.4i			0.884168i	−0.896974	+	0.442084i	$0.854239\pi$
$824$	12124.4	−	28174.5i	0.512587	−	1.19115i
$825$	−5400.00	+	6037.38i	−0.227883	+	0.254781i
$826$	−3000.00	−	2323.79i	−0.126372	−	0.0978874i
$827$	−12907.2			−0.542719			−0.271360	−	0.962478i	$-0.587473\pi$
$827$	−12907.2			−0.542719			−0.271360	+	0.962478i	$0.587473\pi$
$828$	19578.0	−	7459.25i	0.821719	−	0.313076i
$829$	−14074.0			−0.589638			−0.294819	−	0.955553i	$-0.595259\pi$
$829$	−14074.0			−0.589638			−0.294819	+	0.955553i	$0.595259\pi$
$830$	−25080.1	−	19427.0i	−1.04885	−	0.812433i
$831$	−21997.0	+	24593.4i	−0.918254	+	1.02664i
$832$	−3520.00	−	3718.06i	−0.146676	−	0.154929i
$833$			10124.9i			0.421138i
$834$	−28326.3	+	5213.38i	−1.17609	+	0.216456i
$835$		−	123.935i		−	0.00513648i
$836$	18706.1	−	4829.91i	0.773882	−	0.199816i
$837$	18270.0	−	25679.0i	0.754485	−	1.06045i
$838$	26580.0	−	34314.6i	1.09569	−	1.41453i
$839$	−16697.0			−0.687060			−0.343530	−	0.939142i	$-0.611623\pi$
$839$	−16697.0			−0.687060			−0.343530	+	0.939142i	$0.611623\pi$
$840$	7388.31	−	3430.47i	0.303477	−	0.140908i
$841$	1269.00			0.0520317
$842$	6093.35	−	7866.49i	0.249395	−	0.321968i
$843$	−21546.7	−	19272.0i	−0.880318	−	0.787380i
$844$	−4260.00	+	1099.93i	−0.173738	+	0.0448591i
$845$		−	18756.1i		−	0.763587i
$846$	12647.4	+	7714.50i	0.513979	+	0.313511i
$847$			1014.72i			0.0411644i
$848$	−16904.8	−	30553.6i	−0.684568	−	1.23728i
$849$	26250.0	+	23478.7i	1.06113	+	0.949102i
$850$	3600.00	+	2788.55i	0.145269	+	0.112525i
$851$	12609.3			0.507923
$852$	38376.9	+	19835.6i	1.54316	+	0.797603i
$853$	23630.0			0.948506			0.474253	−	0.880389i	$-0.342718\pi$
$853$	23630.0			0.948506			0.474253	+	0.880389i	$0.342718\pi$
$854$	7655.66	+	5930.05i	0.306758	+	0.237614i
$855$	1870.61	+	16731.3i	0.0748230	+	0.669237i
$856$	−13392.0	−	5763.00i	−0.534730	−	0.230111i
$857$			31322.8i			1.24850i	0.781223	+	0.624252i	$0.214596\pi$
$857$			31322.8i			1.24850i	−0.781223	+	0.624252i	$0.785404\pi$
$858$	−921.539	−	5007.07i	−0.0366676	−	0.199229i
$859$			13671.6i			0.543038i	0.962433	+	0.271519i	$0.0875261\pi$
$859$			13671.6i			0.543038i	−0.962433	+	0.271519i	$0.912474\pi$
$860$	4018.36	+	15563.0i	0.159331	+	0.617087i
$861$	3360.00	−	3756.59i	0.132995	−	0.148693i
$862$	22320.0	−	28815.0i	0.881928	−	1.13856i
$863$	25107.8			0.990359			0.495179	−	0.868791i	$-0.335102\pi$
$863$	25107.8			0.990359			0.495179	+	0.868791i	$0.335102\pi$
$864$	−17717.2	+	18195.4i	−0.697630	+	0.716458i
$865$	10000.0			0.393075
$866$	25028.1	−	32311.2i	0.982091	−	1.26787i
$867$	−12585.1	+	14070.5i	−0.492978	+	0.551166i
$868$	3480.00	+	13478.0i	0.136082	+	0.527042i
$869$			2951.61i			0.115220i
$870$	3617.95	+	19657.7i	0.140988	+	0.766043i
$871$			7358.67i			0.286267i
$872$	22156.4	+	9534.59i	0.860447	+	0.370278i
$873$	−2310.00	−	20661.3i	−0.0895552	−	0.801006i
$874$	−15120.0	−	11711.9i	−0.585173	−	0.453273i
$875$	11777.9			0.455048
$876$	15140.6	+	7825.61i	0.583964	+	0.301830i
$877$	41750.0			1.60752			0.803761	−	0.594952i	$-0.202829\pi$
$877$	41750.0			1.60752			0.803761	+	0.594952i	$0.202829\pi$
$878$	−33688.4	−	26094.9i	−1.29491	−	1.00303i
$879$	−2528.79	−	2261.82i	−0.0970354	−	0.0867911i
$880$	−9600.00	−	17351.0i	−0.367745	−	0.664660i
$881$			2397.06i			0.0916676i	0.998949	+	0.0458338i	$0.0145945\pi$
$881$			2397.06i			0.0916676i	−0.998949	+	0.0458338i	$0.985406\pi$
$882$	−18450.5	−	11254.2i	−0.704378	−	0.429648i
$883$		−	43431.6i		−	1.65526i	−0.561277	−	0.827628i	$-0.689690\pi$
$883$		−	43431.6i		−	1.65526i	0.561277	−	0.827628i	$-0.310310\pi$
$884$	−2771.28	+	715.542i	−0.105439	+	0.0272243i
$885$	−6000.00	−	5366.56i	−0.227896	−	0.203836i
$886$	−5268.00	+	6800.96i	−0.199754	+	0.257881i
$887$	6387.80			0.241805			0.120903	−	0.992664i	$-0.461421\pi$
$887$	6387.80			0.241805			0.120903	+	0.992664i	$0.461421\pi$
$888$	−13863.3	+	6436.90i	−0.523900	+	0.243252i
$889$	−14220.0			−0.536472
$890$	−13025.0	+	16815.2i	−0.490561	+	0.633312i
$891$	−24629.8	+	5577.10i	−0.926070	+	0.209697i
$892$	−3660.00	+	945.008i	−0.137383	+	0.0354722i
$893$		−	13523.7i		−	0.506780i
$894$	−23400.0	+	4306.72i	−0.875408	+	0.161117i
$895$			12083.7i			0.451300i
$896$	−1108.51	−	11162.5i	−0.0413313	−	0.416196i
$897$	−3360.00	+	3756.59i	−0.125069	+	0.139832i
$898$	32000.0	+	24787.1i	1.18915	+	0.921109i
$899$	−34156.0			−1.26715
$900$	−9083.07	+	3460.66i	−0.336410	+	0.128173i
$901$	−19520.0			−0.721760
$902$	−9699.48	−	7513.19i	−0.358046	−	0.277341i
$903$	−6027.54	+	6738.99i	−0.222131	+	0.248349i
$904$	−9280.00	+	21564.8i	−0.341425	+	0.793400i
$905$			11287.7i			0.414602i
$906$	8173.19	−	1504.26i	0.299709	−	0.0551606i
$907$		−	37327.8i		−	1.36654i	−0.730167	−	0.683269i	$-0.760558\pi$
$907$		−	37327.8i		−	1.36654i	0.730167	−	0.683269i	$-0.239442\pi$
$908$	1011.52	+	3917.59i	0.0369696	+	0.143183i
$909$	−40080.0	+	4481.08i	−1.46245	+	0.163507i
$910$	−1200.00	+	1549.19i	−0.0437139	+	0.0564344i
$911$	50853.0			1.84944			0.924718	−	0.380654i	$-0.124301\pi$
$911$	50853.0			1.84944			0.924718	+	0.380654i	$0.124301\pi$
$912$	22602.5	+	5158.10i	0.820660	+	0.187282i
$913$	−43440.0			−1.57465
$914$	−5940.93	+	7669.71i	−0.214999	+	0.277562i
$915$	15311.3	+	13694.9i	0.553199	+	0.494796i
$916$	−8188.00	−	31712.0i	−0.295348	−	1.14388i
$917$			3488.27i			0.125619i
$918$	4105.23	+	13590.5i	0.147596	+	0.488619i
$919$		−	14198.4i		−	0.509642i	−0.966988	−	0.254821i	$-0.917984\pi$
$919$		−	14198.4i		−	0.509642i	0.966988	−	0.254821i	$-0.0820165\pi$
$920$	−7759.59	+	18031.7i	−0.278072	+	0.646180i
$921$	−6030.00	−	5393.40i	−0.215739	−	0.192962i
$922$	−8740.00	−	6769.97i	−0.312187	−	0.241819i
$923$	−10392.3			−0.370603
$924$	5121.54	−	9908.88i	0.182344	−	0.352790i
$925$	−5850.00			−0.207943
$926$	40651.2	+	31488.3i	1.44264	+	1.11746i
$927$	36373.1	−	4066.63i	1.28873	−	0.144084i
$928$	27200.0	+	4213.81i	0.962159	+	0.149057i
$929$			10232.2i			0.361366i	0.983541	+	0.180683i	$0.0578308\pi$
$929$			10232.2i			0.361366i	−0.983541	+	0.180683i	$0.942169\pi$
$930$	5344.93	+	29041.0i	0.188459	+	1.02397i
$931$			19729.0i			0.694512i
$932$	−40876.4	+	10554.2i	−1.43664	+	0.370940i
$933$	11280.0	−	12611.4i	0.395810	−	0.442529i
$934$	3204.00	−	4136.35i	0.112246	−	0.144909i
$935$	−11085.1			−0.387724
$936$	1776.46	−	5845.42i	0.0620358	−	0.204128i
$937$	37850.0			1.31964			0.659822	−	0.751422i	$-0.270632\pi$
$937$	37850.0			1.31964			0.659822	+	0.751422i	$0.270632\pi$
$938$	−9872.69	+	12745.6i	−0.343662	+	0.443665i
$939$	24352.6	−	27227.1i	0.846345	−	0.946243i
$940$	−13440.0	+	3470.19i	−0.466345	+	0.120410i
$941$		−	13997.8i		−	0.484925i	−0.970161	−	0.242463i	$-0.922045\pi$
$941$		−	13997.8i		−	0.484925i	0.970161	−	0.242463i	$-0.0779552\pi$
$942$	−1941.99	−	10551.5i	−0.0671691	−	0.364955i
$943$			12145.7i			0.419425i
$944$	−9699.48	+	5366.56i	−0.334419	+	0.185028i
$945$	7920.00	+	5634.89i	0.272632	+	0.193971i
$946$	17400.0	+	13478.0i	0.598016	+	0.463221i
$947$	−7738.80			−0.265552			−0.132776	−	0.991146i	$-0.542389\pi$
$947$	−7738.80			−0.265552			−0.132776	+	0.991146i	$0.542389\pi$
$948$	−1626.31	+	3146.49i	−0.0557173	+	0.107799i
$949$	−4100.00			−0.140244
$950$	7014.81	+	5433.65i	0.239569	+	0.185569i
$951$	−1905.26	−	1704.11i	−0.0649655	−	0.0581069i
$952$	−5760.00	−	2478.71i	−0.196095	−	0.0843860i
$953$		−	44882.4i		−	1.52558i	−0.646644	−	0.762792i	$-0.723828\pi$
$953$		−	44882.4i		−	1.52558i	0.646644	−	0.762792i	$-0.276172\pi$
$954$	21697.2	−	35571.1i	0.736345	−	1.20719i
$955$		−	24787.1i		−	0.839886i
$956$	−11362.3	−	44005.8i	−0.384395	−	1.48876i
$957$	20400.0	+	18246.3i	0.689068	+	0.616321i
$958$	−26400.0	+	34082.3i	−0.890340	+	1.14942i
$959$	692.820			0.0233288
$960$	−673.638	−	23786.1i	−0.0226475	−	0.799679i
$961$	−20669.0			−0.693800
$962$	2251.67	−	2906.89i	0.0754643	−	0.0974240i
$963$	−1932.97	−	17289.0i	−0.0646823	−	0.578536i
$964$	2396.00	+	9279.67i	0.0800518	+	0.310039i
$965$		−	1699.41i		−	0.0566902i
$966$	−10859.7	+	1998.70i	−0.361703	+	0.0665705i
$967$			15856.0i			0.527295i	0.964619	+	0.263648i	$0.0849256\pi$
$967$			15856.0i			0.527295i	−0.964619	+	0.263648i	$0.915074\pi$
$968$	2722.78	+	1171.70i	0.0904066	+	0.0389048i
$969$	8640.00	−	9659.81i	0.286436	−	0.320246i
$970$	15400.0	+	11928.8i	0.509757	+	0.394856i
$971$	−40426.1			−1.33608			−0.668040	−	0.744125i	$-0.732867\pi$
$971$	−40426.1			−1.33608			−0.668040	+	0.744125i	$0.732867\pi$
$972$	−29328.9	−	7625.42i	−0.967823	−	0.251631i
$973$	15180.0			0.500153
$974$	21875.8	+	16944.9i	0.719657	+	0.557444i
$975$	1558.85	−	1742.84i	0.0512031	−	0.0572468i
$976$	24752.0	−	13694.9i	0.811775	−	0.449141i
$977$		−	6404.10i		−	0.209709i	−0.994488	−	0.104854i	$-0.966562\pi$
$977$		−	6404.10i		−	0.209709i	0.994488	−	0.104854i	$-0.0334376\pi$
$978$	−3694.73	+	680.006i	−0.120802	+	0.0222333i
$979$			29124.8i			0.950801i
$980$	19606.8	−	5062.46i	0.639099	−	0.165015i
$981$	3198.00	+	28603.8i	0.104082	+	0.930936i
$982$	−11940.0	+	15414.5i	−0.388005	+	0.500912i
$983$	25953.0			0.842089			0.421045	−	0.907040i	$-0.361664\pi$
$983$	25953.0			0.842089			0.421045	+	0.907040i	$0.361664\pi$
$984$	−6200.21	−	13353.6i	−0.200869	−	0.432618i
$985$	19120.0			0.618491
$986$	9422.36	−	12164.2i	0.304330	−	0.392888i
$987$	−5819.69	−	5205.29i	−0.187683	−	0.167868i
$988$	−5400.00	+	1394.27i	−0.173883	+	0.0448965i
$989$		−	21788.2i		−	0.700532i
$990$	12321.5	−	20200.3i	0.395560	−	0.648492i
$991$			48358.1i			1.55010i	0.631903	+	0.775048i	$0.282274\pi$
$991$			48358.1i			1.55010i	−0.631903	+	0.775048i	$0.717726\pi$
$992$	40183.6	+	6225.21i	1.28612	+	0.199245i
$993$	16410.0	+	14677.6i	0.524427	+	0.469061i
$994$	−18000.0	−	13942.7i	−0.574372	−	0.444906i
$995$	2286.31			0.0728450
$996$	−46308.1	−	23935.0i	−1.47322	−	0.761455i
$997$	−18370.0			−0.583534			−0.291767	−	0.956489i	$-0.594243\pi$
$997$	−18370.0			−0.583534			−0.291767	+	0.956489i	$0.594243\pi$
$998$	2927.17	+	2267.37i	0.0928435	+	0.0719163i
$999$	−14861.0	−	10573.2i	−0.470652	−	0.334858i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	12.4.b.a.11.3	yes	4
3.2	odd	2	inner	12.4.b.a.11.2	yes	4
4.3	odd	2	inner	12.4.b.a.11.1	✓	4
8.3	odd	2		192.4.c.b.191.2		4
8.5	even	2		192.4.c.b.191.3		4
12.11	even	2	inner	12.4.b.a.11.4	yes	4
16.3	odd	4		768.4.f.c.383.8		8
16.5	even	4		768.4.f.c.383.7		8
16.11	odd	4		768.4.f.c.383.1		8
16.13	even	4		768.4.f.c.383.2		8
24.5	odd	2		192.4.c.b.191.1		4
24.11	even	2		192.4.c.b.191.4		4
48.5	odd	4		768.4.f.c.383.6		8
48.11	even	4		768.4.f.c.383.4		8
48.29	odd	4		768.4.f.c.383.3		8
48.35	even	4		768.4.f.c.383.5		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
12.4.b.a.11.1	✓	4	4.3	odd	2	inner
12.4.b.a.11.2	yes	4	3.2	odd	2	inner
12.4.b.a.11.3	yes	4	1.1	even	1	trivial
12.4.b.a.11.4	yes	4	12.11	even	2	inner
192.4.c.b.191.1		4	24.5	odd	2
192.4.c.b.191.2		4	8.3	odd	2
192.4.c.b.191.3		4	8.5	even	2
192.4.c.b.191.4		4	24.11	even	2
768.4.f.c.383.1		8	16.11	odd	4
768.4.f.c.383.2		8	16.13	even	4
768.4.f.c.383.3		8	48.29	odd	4
768.4.f.c.383.4		8	48.11	even	4
768.4.f.c.383.5		8	48.35	even	4
768.4.f.c.383.6		8	48.5	odd	4
768.4.f.c.383.7		8	16.5	even	4
768.4.f.c.383.8		8	16.3	odd	4

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 12 = 2^{2} \cdot 3 \)
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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