LMFDB - Embedded newform 1122.2.l.g.727.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1122,2,Mod(463,1122)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1122, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([0, 0, 3]))

N = Newforms(chi, 2, names="a")

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

chi := DirichletCharacter("1122.463");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1122 = 2 \cdot 3 \cdot 11 \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1122.l (of order $4$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$8.95921510679$
Analytic rank:	$0$
Dimension:	$20$
Relative dimension:	$10$ over $\Q(i)$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} + 44 x^{18} + 732 x^{16} + 6050 x^{14} + 27262 x^{12} + 69598 x^{10} + 100205 x^{8} + 77682 x^{6} + \cdots + 289 $ x^20 + 44x^18 + 732x^16 + 6050x^14 + 27262x^12 + 69598x^10 + 100205x^8 + 77682x^6 + 29931x^4 + 5170*x^2 + 289
Coefficient ring:	$\Z[a_1, \ldots, a_{17}]$
Coefficient ring index:	$ 2^{12} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			727.2
Root			$-1.68287i$ of defining polynomial
Character	$\chi$	$=$	1122.727
Dual form			1122.2.l.g.463.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000i q^{2} +(-0.707107 - 0.707107i) q^{3} -1.00000 q^{4} +(-2.39327 - 2.39327i) q^{5} +(0.707107 - 0.707107i) q^{6} +(2.34381 - 2.34381i) q^{7} -1.00000i q^{8} +1.00000i q^{9} +O(q^{10})$	\(q+1.00000i q^{2} +(-0.707107 - 0.707107i) q^{3} -1.00000 q^{4} +(-2.39327 - 2.39327i) q^{5} +(0.707107 - 0.707107i) q^{6} +(2.34381 - 2.34381i) q^{7} -1.00000i q^{8} +1.00000i q^{9} +(2.39327 - 2.39327i) q^{10} +(0.707107 - 0.707107i) q^{11} +(0.707107 + 0.707107i) q^{12} +3.51677 q^{13} +(2.34381 + 2.34381i) q^{14} +3.38459i q^{15} +1.00000 q^{16} +(0.493446 + 4.09347i) q^{17} -1.00000 q^{18} -6.61609i q^{19} +(2.39327 + 2.39327i) q^{20} -3.31465 q^{21} +(0.707107 + 0.707107i) q^{22} +(-4.00263 + 4.00263i) q^{23} +(-0.707107 + 0.707107i) q^{24} +6.45547i q^{25} +3.51677i q^{26} +(0.707107 - 0.707107i) q^{27} +(-2.34381 + 2.34381i) q^{28} +(-4.44399 - 4.44399i) q^{29} -3.38459 q^{30} +(-3.28291 - 3.28291i) q^{31} +1.00000i q^{32} -1.00000 q^{33} +(-4.09347 + 0.493446i) q^{34} -11.2187 q^{35} -1.00000i q^{36} +(-4.80137 - 4.80137i) q^{37} +6.61609 q^{38} +(-2.48673 - 2.48673i) q^{39} +(-2.39327 + 2.39327i) q^{40} +(7.83142 - 7.83142i) q^{41} -3.31465i q^{42} -3.36543i q^{43} +(-0.707107 + 0.707107i) q^{44} +(2.39327 - 2.39327i) q^{45} +(-4.00263 - 4.00263i) q^{46} -5.73282 q^{47} +(-0.707107 - 0.707107i) q^{48} -3.98689i q^{49} -6.45547 q^{50} +(2.54560 - 3.24344i) q^{51} -3.51677 q^{52} +7.51780i q^{53} +(0.707107 + 0.707107i) q^{54} -3.38459 q^{55} +(-2.34381 - 2.34381i) q^{56} +(-4.67828 + 4.67828i) q^{57} +(4.44399 - 4.44399i) q^{58} +7.26150i q^{59} -3.38459i q^{60} +(-2.43640 + 2.43640i) q^{61} +(3.28291 - 3.28291i) q^{62} +(2.34381 + 2.34381i) q^{63} -1.00000 q^{64} +(-8.41659 - 8.41659i) q^{65} -1.00000i q^{66} -9.13246 q^{67} +(-0.493446 - 4.09347i) q^{68} +5.66057 q^{69} -11.2187i q^{70} +(1.61357 + 1.61357i) q^{71} +1.00000 q^{72} +(-3.29555 - 3.29555i) q^{73} +(4.80137 - 4.80137i) q^{74} +(4.56471 - 4.56471i) q^{75} +6.61609i q^{76} -3.31465i q^{77} +(2.48673 - 2.48673i) q^{78} +(-0.0452462 + 0.0452462i) q^{79} +(-2.39327 - 2.39327i) q^{80} -1.00000 q^{81} +(7.83142 + 7.83142i) q^{82} -9.64066i q^{83} +3.31465 q^{84} +(8.61583 - 10.9777i) q^{85} +3.36543 q^{86} +6.28476i q^{87} +(-0.707107 - 0.707107i) q^{88} -7.57633 q^{89} +(2.39327 + 2.39327i) q^{90} +(8.24265 - 8.24265i) q^{91} +(4.00263 - 4.00263i) q^{92} +4.64274i q^{93} -5.73282i q^{94} +(-15.8341 + 15.8341i) q^{95} +(0.707107 - 0.707107i) q^{96} +(6.97597 + 6.97597i) q^{97} +3.98689 q^{98} +(0.707107 + 0.707107i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q - 20 q^{4} - 4 q^{5}+O(q^{10}) $ 20 * q - 20 * q^4 - 4 * q^5	$ 20 q - 20 q^{4} - 4 q^{5} + 4 q^{10} + 20 q^{16} - 12 q^{17} - 20 q^{18} + 4 q^{20} + 16 q^{23} + 4 q^{29} - 8 q^{31} - 20 q^{33} + 16 q^{35} - 20 q^{37} + 8 q^{39} - 4 q^{40} + 20 q^{41} + 4 q^{45} + 16 q^{46} - 16 q^{47} - 68 q^{50} + 8 q^{57} - 4 q^{58} - 20 q^{61} + 8 q^{62} - 20 q^{64} + 8 q^{65} - 48 q^{67} + 12 q^{68} - 32 q^{71} + 20 q^{72} + 20 q^{73} + 20 q^{74} - 8 q^{75} - 8 q^{78} - 16 q^{79} - 4 q^{80} - 20 q^{81} + 20 q^{82} - 4 q^{85} - 16 q^{86} + 4 q^{90} + 88 q^{91} - 16 q^{92} - 48 q^{95} + 4 q^{97} + 36 q^{98}+O(q^{100}) $ 20 * q - 20 * q^4 - 4 * q^5 + 4 * q^10 + 20 * q^16 - 12 * q^17 - 20 * q^18 + 4 * q^20 + 16 * q^23 + 4 * q^29 - 8 * q^31 - 20 * q^33 + 16 * q^35 - 20 * q^37 + 8 * q^39 - 4 * q^40 + 20 * q^41 + 4 * q^45 + 16 * q^46 - 16 * q^47 - 68 * q^50 + 8 * q^57 - 4 * q^58 - 20 * q^61 + 8 * q^62 - 20 * q^64 + 8 * q^65 - 48 * q^67 + 12 * q^68 - 32 * q^71 + 20 * q^72 + 20 * q^73 + 20 * q^74 - 8 * q^75 - 8 * q^78 - 16 * q^79 - 4 * q^80 - 20 * q^81 + 20 * q^82 - 4 * q^85 - 16 * q^86 + 4 * q^90 + 88 * q^91 - 16 * q^92 - 48 * q^95 + 4 * q^97 + 36 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1122\mathbb{Z}\right)^\times$.

$n$	$409$	$749$	$1057$
$\chi(n)$	$1$	$1$	$e\left(\frac{1}{4}\right)$

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 $

$2$			1.00000i			0.707107i
$2$			1.00000i			0.707107i
$3$	−0.707107	−	0.707107i	−0.408248	−	0.408248i
$3$	−0.707107	−	0.707107i	−0.408248	−	0.408248i
$4$	−1.00000			−0.500000
$5$	−2.39327	−	2.39327i	−1.07030	−	1.07030i	−0.997334	−	0.0729682i	$-0.976753\pi$
$5$	−2.39327	−	2.39327i	−1.07030	−	1.07030i	−0.0729682	−	0.997334i	$-0.523247\pi$
$6$	0.707107	−	0.707107i	0.288675	−	0.288675i
$7$	2.34381	−	2.34381i	0.885877	−	0.885877i	−0.108247	−	0.994124i	$-0.534524\pi$
$7$	2.34381	−	2.34381i	0.885877	−	0.885877i	0.994124	+	0.108247i	$0.0345238\pi$
$8$		−	1.00000i		−	0.353553i
$9$			1.00000i			0.333333i
$10$	2.39327	−	2.39327i	0.756818	−	0.756818i
$11$	0.707107	−	0.707107i	0.213201	−	0.213201i
$11$	0.707107	−	0.707107i	0.213201	−	0.213201i
$12$	0.707107	+	0.707107i	0.204124	+	0.204124i
$13$	3.51677			0.975377			0.487689	−	0.873018i	$-0.337840\pi$
$13$	3.51677			0.975377			0.487689	+	0.873018i	$0.337840\pi$
$14$	2.34381	+	2.34381i	0.626410	+	0.626410i
$15$			3.38459i			0.873898i
$16$	1.00000			0.250000
$17$	0.493446	+	4.09347i	0.119678	+	0.992813i
$17$	0.493446	+	4.09347i	0.119678	+	0.992813i
$18$	−1.00000			−0.235702
$19$		−	6.61609i		−	1.51784i	−0.651186	−	0.758918i	$-0.725728\pi$
$19$		−	6.61609i		−	1.51784i	0.651186	−	0.758918i	$-0.274272\pi$
$20$	2.39327	+	2.39327i	0.535151	+	0.535151i
$21$	−3.31465			−0.723316
$22$	0.707107	+	0.707107i	0.150756	+	0.150756i
$23$	−4.00263	+	4.00263i	−0.834606	+	0.834606i	−0.988143	−	0.153537i	$-0.950934\pi$
$23$	−4.00263	+	4.00263i	−0.834606	+	0.834606i	0.153537	+	0.988143i	$0.450934\pi$
$24$	−0.707107	+	0.707107i	−0.144338	+	0.144338i
$25$			6.45547i			1.29109i
$26$			3.51677i			0.689696i
$27$	0.707107	−	0.707107i	0.136083	−	0.136083i
$28$	−2.34381	+	2.34381i	−0.442938	+	0.442938i
$29$	−4.44399	−	4.44399i	−0.825229	−	0.825229i	0.161624	−	0.986852i	$-0.448327\pi$
$29$	−4.44399	−	4.44399i	−0.825229	−	0.825229i	−0.986852	+	0.161624i	$0.948327\pi$
$30$	−3.38459			−0.617939
$31$	−3.28291	−	3.28291i	−0.589628	−	0.589628i	0.347903	−	0.937531i	$-0.386894\pi$
$31$	−3.28291	−	3.28291i	−0.589628	−	0.589628i	−0.937531	+	0.347903i	$0.886894\pi$
$32$			1.00000i			0.176777i
$33$	−1.00000			−0.174078
$34$	−4.09347	+	0.493446i	−0.702025	+	0.0846253i
$35$	−11.2187			−1.89631
$36$		−	1.00000i		−	0.166667i
$37$	−4.80137	−	4.80137i	−0.789340	−	0.789340i	0.192046	−	0.981386i	$-0.438488\pi$
$37$	−4.80137	−	4.80137i	−0.789340	−	0.789340i	−0.981386	+	0.192046i	$0.938488\pi$
$38$	6.61609			1.07327
$39$	−2.48673	−	2.48673i	−0.398196	−	0.398196i
$40$	−2.39327	+	2.39327i	−0.378409	+	0.378409i
$41$	7.83142	−	7.83142i	1.22306	−	1.22306i	0.256525	−	0.966538i	$-0.417422\pi$
$41$	7.83142	−	7.83142i	1.22306	−	1.22306i	0.966538	−	0.256525i	$-0.0825776\pi$
$42$		−	3.31465i		−	0.511461i
$43$		−	3.36543i		−	0.513224i	−0.966515	−	0.256612i	$-0.917394\pi$
$43$		−	3.36543i		−	0.513224i	0.966515	−	0.256612i	$-0.0826062\pi$
$44$	−0.707107	+	0.707107i	−0.106600	+	0.106600i
$45$	2.39327	−	2.39327i	0.356767	−	0.356767i
$46$	−4.00263	−	4.00263i	−0.590156	−	0.590156i
$47$	−5.73282			−0.836218			−0.418109	−	0.908397i	$-0.637307\pi$
$47$	−5.73282			−0.836218			−0.418109	+	0.908397i	$0.637307\pi$
$48$	−0.707107	−	0.707107i	−0.102062	−	0.102062i
$49$		−	3.98689i		−	0.569556i
$50$	−6.45547			−0.912942
$51$	2.54560	−	3.24344i	0.356456	−	0.454173i
$52$	−3.51677			−0.487689
$53$			7.51780i			1.03265i	0.856393	+	0.516325i	$0.172700\pi$
$53$			7.51780i			1.03265i	−0.856393	+	0.516325i	$0.827300\pi$
$54$	0.707107	+	0.707107i	0.0962250	+	0.0962250i
$55$	−3.38459			−0.456378
$56$	−2.34381	−	2.34381i	−0.313205	−	0.313205i
$57$	−4.67828	+	4.67828i	−0.619654	+	0.619654i
$58$	4.44399	−	4.44399i	0.583525	−	0.583525i
$59$			7.26150i			0.945367i	0.881232	+	0.472684i	$0.156715\pi$
$59$			7.26150i			0.945367i	−0.881232	+	0.472684i	$0.843285\pi$
$60$		−	3.38459i		−	0.436949i
$61$	−2.43640	+	2.43640i	−0.311949	+	0.311949i	−0.845664	−	0.533715i	$-0.820795\pi$
$61$	−2.43640	+	2.43640i	−0.311949	+	0.311949i	0.533715	+	0.845664i	$0.320795\pi$
$62$	3.28291	−	3.28291i	0.416930	−	0.416930i
$63$	2.34381	+	2.34381i	0.295292	+	0.295292i
$64$	−1.00000			−0.125000
$65$	−8.41659	−	8.41659i	−1.04395	−	1.04395i
$66$		−	1.00000i		−	0.123091i
$67$	−9.13246			−1.11571			−0.557854	−	0.829939i	$-0.688375\pi$
$67$	−9.13246			−1.11571			−0.557854	+	0.829939i	$0.688375\pi$
$68$	−0.493446	−	4.09347i	−0.0598391	−	0.496406i
$69$	5.66057			0.681453
$70$		−	11.2187i		−	1.34090i
$71$	1.61357	+	1.61357i	0.191496	+	0.191496i	0.796342	−	0.604846i	$-0.206765\pi$
$71$	1.61357	+	1.61357i	0.191496	+	0.191496i	−0.604846	+	0.796342i	$0.706765\pi$
$72$	1.00000			0.117851
$73$	−3.29555	−	3.29555i	−0.385715	−	0.385715i	0.487441	−	0.873156i	$-0.337930\pi$
$73$	−3.29555	−	3.29555i	−0.385715	−	0.385715i	−0.873156	+	0.487441i	$0.837930\pi$
$74$	4.80137	−	4.80137i	0.558148	−	0.558148i
$75$	4.56471	−	4.56471i	0.527087	−	0.527087i
$76$			6.61609i			0.758918i
$77$		−	3.31465i		−	0.377739i
$78$	2.48673	−	2.48673i	0.281567	−	0.281567i
$79$	−0.0452462	+	0.0452462i	−0.00509059	+	0.00509059i	−0.709647	−	0.704557i	$-0.751146\pi$
$79$	−0.0452462	+	0.0452462i	−0.00509059	+	0.00509059i	0.704557	+	0.709647i	$0.251146\pi$
$80$	−2.39327	−	2.39327i	−0.267576	−	0.267576i
$81$	−1.00000			−0.111111
$82$	7.83142	+	7.83142i	0.864836	+	0.864836i
$83$		−	9.64066i		−	1.05820i	−0.848559	−	0.529100i	$-0.822530\pi$
$83$		−	9.64066i		−	1.05820i	0.848559	−	0.529100i	$-0.177470\pi$
$84$	3.31465			0.361658
$85$	8.61583	−	10.9777i	0.934518	−	1.19070i
$86$	3.36543			0.362904
$87$			6.28476i			0.673797i
$88$	−0.707107	−	0.707107i	−0.0753778	−	0.0753778i
$89$	−7.57633			−0.803090			−0.401545	−	0.915839i	$-0.631527\pi$
$89$	−7.57633			−0.803090			−0.401545	+	0.915839i	$0.631527\pi$
$90$	2.39327	+	2.39327i	0.252273	+	0.252273i
$91$	8.24265	−	8.24265i	0.864064	−	0.864064i
$92$	4.00263	−	4.00263i	0.417303	−	0.417303i
$93$			4.64274i			0.481429i
$94$		−	5.73282i		−	0.591296i
$95$	−15.8341	+	15.8341i	−1.62454	+	1.62454i
$96$	0.707107	−	0.707107i	0.0721688	−	0.0721688i
$97$	6.97597	+	6.97597i	0.708303	+	0.708303i	0.966178	−	0.257875i	$-0.0830224\pi$
$97$	6.97597	+	6.97597i	0.708303	+	0.708303i	−0.257875	+	0.966178i	$0.583022\pi$
$98$	3.98689			0.402737
$99$	0.707107	+	0.707107i	0.0710669	+	0.0710669i
$100$		−	6.45547i		−	0.645547i
$101$	−12.2443			−1.21835			−0.609174	−	0.793036i	$-0.708499\pi$
$101$	−12.2443			−1.21835			−0.609174	+	0.793036i	$0.708499\pi$
$102$	3.24344	+	2.54560i	0.321148	+	0.252052i
$103$	18.4297			1.81594			0.907968	−	0.419040i	$-0.137633\pi$
$103$	18.4297			1.81594			0.907968	+	0.419040i	$0.137633\pi$
$104$		−	3.51677i		−	0.344848i
$105$	7.93284	+	7.93284i	0.774166	+	0.774166i
$106$	−7.51780			−0.730193
$107$	−7.41192	−	7.41192i	−0.716538	−	0.716538i	0.251357	−	0.967895i	$-0.419123\pi$
$107$	−7.41192	−	7.41192i	−0.716538	−	0.716538i	−0.967895	+	0.251357i	$0.919123\pi$
$108$	−0.707107	+	0.707107i	−0.0680414	+	0.0680414i
$109$	−7.89485	+	7.89485i	−0.756189	+	0.756189i	−0.975627	−	0.219437i	$-0.929578\pi$
$109$	−7.89485	+	7.89485i	−0.756189	+	0.756189i	0.219437	+	0.975627i	$0.429578\pi$
$110$		−	3.38459i		−	0.322708i
$111$			6.79016i			0.644494i
$112$	2.34381	−	2.34381i	0.221469	−	0.221469i
$113$	4.39466	−	4.39466i	0.413415	−	0.413415i	−0.469512	−	0.882926i	$-0.655570\pi$
$113$	4.39466	−	4.39466i	0.413415	−	0.413415i	0.882926	+	0.469512i	$0.155570\pi$
$114$	−4.67828	−	4.67828i	−0.438161	−	0.438161i
$115$	19.1587			1.78656
$116$	4.44399	+	4.44399i	0.412614	+	0.412614i
$117$			3.51677i			0.325126i
$118$	−7.26150			−0.668476
$119$	10.7509	+	8.43778i	0.985530	+	0.773490i
$120$	3.38459			0.308970
$121$		−	1.00000i		−	0.0909091i
$122$	−2.43640	−	2.43640i	−0.220581	−	0.220581i
$123$	−11.0753			−0.998626
$124$	3.28291	+	3.28291i	0.294814	+	0.294814i
$125$	3.48334	−	3.48334i	0.311559	−	0.311559i
$126$	−2.34381	+	2.34381i	−0.208803	+	0.208803i
$127$			18.2690i			1.62111i	0.585664	+	0.810554i	$0.300834\pi$
$127$			18.2690i			1.62111i	−0.585664	+	0.810554i	$0.699166\pi$
$128$		−	1.00000i		−	0.0883883i
$129$	−2.37972	+	2.37972i	−0.209523	+	0.209523i
$130$	8.41659	−	8.41659i	0.738183	−	0.738183i
$131$	−1.41544	−	1.41544i	−0.123668	−	0.123668i	0.642564	−	0.766232i	$-0.277871\pi$
$131$	−1.41544	−	1.41544i	−0.123668	−	0.123668i	−0.766232	+	0.642564i	$0.777871\pi$
$132$	1.00000			0.0870388
$133$	−15.5069	−	15.5069i	−1.34462	−	1.34462i
$134$		−	9.13246i		−	0.788925i
$135$	−3.38459			−0.291299
$136$	4.09347	−	0.493446i	0.351012	−	0.0423126i
$137$	−18.0417			−1.54141			−0.770705	−	0.637193i	$-0.780096\pi$
$137$	−18.0417			−1.54141			−0.770705	+	0.637193i	$0.780096\pi$
$138$			5.66057i			0.481860i
$139$	−6.37213	−	6.37213i	−0.540477	−	0.540477i	0.383192	−	0.923669i	$-0.374825\pi$
$139$	−6.37213	−	6.37213i	−0.540477	−	0.540477i	−0.923669	+	0.383192i	$0.874825\pi$
$140$	11.2187			0.948156
$141$	4.05372	+	4.05372i	0.341385	+	0.341385i
$142$	−1.61357	+	1.61357i	−0.135408	+	0.135408i
$143$	2.48673	−	2.48673i	0.207951	−	0.207951i
$144$			1.00000i			0.0833333i
$145$			21.2713i			1.76649i
$146$	3.29555	−	3.29555i	0.272742	−	0.272742i
$147$	−2.81916	+	2.81916i	−0.232520	+	0.232520i
$148$	4.80137	+	4.80137i	0.394670	+	0.394670i
$149$	22.8494			1.87190			0.935949	−	0.352136i	$-0.114545\pi$
$149$	22.8494			1.87190			0.935949	+	0.352136i	$0.114545\pi$
$150$	4.56471	+	4.56471i	0.372707	+	0.372707i
$151$		−	6.66119i		−	0.542080i	−0.962568	−	0.271040i	$-0.912632\pi$
$151$		−	6.66119i		−	0.542080i	0.962568	−	0.271040i	$-0.0873675\pi$
$152$	−6.61609			−0.536636
$153$	−4.09347	+	0.493446i	−0.330938	+	0.0398927i
$154$	3.31465			0.267102
$155$			15.7138i			1.26216i
$156$	2.48673	+	2.48673i	0.199098	+	0.199098i
$157$	−10.2168			−0.815390			−0.407695	−	0.913118i	$-0.633667\pi$
$157$	−10.2168			−0.815390			−0.407695	+	0.913118i	$0.633667\pi$
$158$	−0.0452462	−	0.0452462i	−0.00359959	−	0.00359959i
$159$	5.31589	−	5.31589i	0.421577	−	0.421577i
$160$	2.39327	−	2.39327i	0.189205	−	0.189205i
$161$			18.7628i			1.47872i
$162$		−	1.00000i		−	0.0785674i
$163$	15.5238	−	15.5238i	1.21592	−	1.21592i	0.246866	−	0.969050i	$-0.420599\pi$
$163$	15.5238	−	15.5238i	1.21592	−	1.21592i	0.969050	−	0.246866i	$-0.0794007\pi$
$164$	−7.83142	+	7.83142i	−0.611531	+	0.611531i
$165$	2.39327	+	2.39327i	0.186316	+	0.186316i
$166$	9.64066			0.748261
$167$	4.44355	+	4.44355i	0.343852	+	0.343852i	0.857813	−	0.513961i	$-0.171823\pi$
$167$	4.44355	+	4.44355i	0.343852	+	0.343852i	−0.513961	+	0.857813i	$0.671823\pi$
$168$			3.31465i			0.255731i
$169$	−0.632304			−0.0486387
$170$	10.9777	+	8.61583i	0.841953	+	0.660804i
$171$	6.61609			0.505945
$172$			3.36543i			0.256612i
$173$	0.601723	+	0.601723i	0.0457482	+	0.0457482i	0.729611	−	0.683863i	$-0.239701\pi$
$173$	0.601723	+	0.601723i	0.0457482	+	0.0457482i	−0.683863	+	0.729611i	$0.739701\pi$
$174$	−6.28476			−0.476446
$175$	15.1304	+	15.1304i	1.14375	+	1.14375i
$176$	0.707107	−	0.707107i	0.0533002	−	0.0533002i
$177$	5.13466	−	5.13466i	0.385945	−	0.385945i
$178$		−	7.57633i		−	0.567870i
$179$		−	20.2603i		−	1.51432i	−0.653228	−	0.757162i	$-0.726586\pi$
$179$		−	20.2603i		−	1.51432i	0.653228	−	0.757162i	$-0.273414\pi$
$180$	−2.39327	+	2.39327i	−0.178384	+	0.178384i
$181$	12.6215	−	12.6215i	0.938145	−	0.938145i	−0.0600500	−	0.998195i	$-0.519126\pi$
$181$	12.6215	−	12.6215i	0.938145	−	0.938145i	0.998195	+	0.0600500i	$0.0191260\pi$
$182$	8.24265	+	8.24265i	0.610986	+	0.610986i
$183$	3.44559			0.254705
$184$	4.00263	+	4.00263i	0.295078	+	0.295078i
$185$			22.9819i			1.68967i
$186$	−4.64274			−0.340422
$187$	3.24344	+	2.54560i	0.237184	+	0.186153i
$188$	5.73282			0.418109
$189$		−	3.31465i		−	0.241105i
$190$	−15.8341	−	15.8341i	−1.14873	−	1.14873i
$191$	−12.6910			−0.918292			−0.459146	−	0.888361i	$-0.651844\pi$
$191$	−12.6910			−0.918292			−0.459146	+	0.888361i	$0.651844\pi$
$192$	0.707107	+	0.707107i	0.0510310	+	0.0510310i
$193$	14.1544	−	14.1544i	1.01886	−	1.01886i	0.0190406	−	0.999819i	$-0.493939\pi$
$193$	14.1544	−	14.1544i	1.01886	−	1.01886i	0.999819	−	0.0190406i	$-0.00606117\pi$
$194$	−6.97597	+	6.97597i	−0.500846	+	0.500846i
$195$			11.9028i			0.852381i
$196$			3.98689i			0.284778i
$197$	9.25344	−	9.25344i	0.659280	−	0.659280i	−0.295930	−	0.955210i	$-0.595629\pi$
$197$	9.25344	−	9.25344i	0.659280	−	0.659280i	0.955210	+	0.295930i	$0.0956294\pi$
$198$	−0.707107	+	0.707107i	−0.0502519	+	0.0502519i
$199$	−3.56152	−	3.56152i	−0.252469	−	0.252469i	0.569513	−	0.821982i	$-0.307132\pi$
$199$	−3.56152	−	3.56152i	−0.252469	−	0.252469i	−0.821982	+	0.569513i	$0.807132\pi$
$200$	6.45547			0.456471
$201$	6.45763	+	6.45763i	0.455486	+	0.455486i
$202$		−	12.2443i		−	0.861503i
$203$	−20.8318			−1.46210
$204$	−2.54560	+	3.24344i	−0.178228	+	0.227086i
$205$	−37.4854			−2.61809
$206$			18.4297i			1.28406i
$207$	−4.00263	−	4.00263i	−0.278202	−	0.278202i
$208$	3.51677			0.243844
$209$	−4.67828	−	4.67828i	−0.323604	−	0.323604i
$210$	−7.93284	+	7.93284i	−0.547418	+	0.547418i
$211$	−2.69985	+	2.69985i	−0.185865	+	0.185865i	−0.793906	−	0.608041i	$-0.791956\pi$
$211$	−2.69985	+	2.69985i	−0.185865	+	0.185865i	0.608041	+	0.793906i	$0.291956\pi$
$212$		−	7.51780i		−	0.516325i
$213$		−	2.28194i		−	0.156356i
$214$	7.41192	−	7.41192i	0.506669	−	0.506669i
$215$	−8.05439	+	8.05439i	−0.549305	+	0.549305i
$216$	−0.707107	−	0.707107i	−0.0481125	−	0.0481125i
$217$	−15.3890			−1.04468
$218$	−7.89485	−	7.89485i	−0.534707	−	0.534707i
$219$			4.66061i			0.314935i
$220$	3.38459			0.228189
$221$	1.73534	+	14.3958i	0.116731	+	0.968367i
$222$	−6.79016			−0.455726
$223$		−	4.40601i		−	0.295048i	−0.989058	−	0.147524i	$-0.952870\pi$
$223$		−	4.40601i		−	0.295048i	0.989058	−	0.147524i	$-0.0471304\pi$
$224$	2.34381	+	2.34381i	0.156602	+	0.156602i
$225$	−6.45547			−0.430365
$226$	4.39466	+	4.39466i	0.292328	+	0.292328i
$227$	14.4708	−	14.4708i	0.960463	−	0.960463i	−0.0387848	−	0.999248i	$-0.512349\pi$
$227$	14.4708	−	14.4708i	0.960463	−	0.960463i	0.999248	+	0.0387848i	$0.0123487\pi$
$228$	4.67828	−	4.67828i	0.309827	−	0.309827i
$229$			24.9524i			1.64890i	0.565933	+	0.824451i	$0.308516\pi$
$229$			24.9524i			1.64890i	−0.565933	+	0.824451i	$0.691484\pi$
$230$			19.1587i			1.26329i
$231$	−2.34381	+	2.34381i	−0.154211	+	0.154211i
$232$	−4.44399	+	4.44399i	−0.291762	+	0.291762i
$233$	−8.55964	−	8.55964i	−0.560760	−	0.560760i	0.368763	−	0.929523i	$-0.379781\pi$
$233$	−8.55964	−	8.55964i	−0.560760	−	0.560760i	−0.929523	+	0.368763i	$0.879781\pi$
$234$	−3.51677			−0.229899
$235$	13.7202	+	13.7202i	0.895006	+	0.895006i
$236$		−	7.26150i		−	0.472684i
$237$	0.0639877			0.00415645
$238$	−8.43778	+	10.7509i	−0.546940	+	0.696875i
$239$	10.9971			0.711343			0.355671	−	0.934611i	$-0.384252\pi$
$239$	10.9971			0.711343			0.355671	+	0.934611i	$0.384252\pi$
$240$			3.38459i			0.218475i
$241$	0.0273602	+	0.0273602i	0.00176243	+	0.00176243i	0.707987	−	0.706225i	$-0.249603\pi$
$241$	0.0273602	+	0.0273602i	0.00176243	+	0.00176243i	−0.706225	+	0.707987i	$0.749603\pi$
$242$	1.00000			0.0642824
$243$	0.707107	+	0.707107i	0.0453609	+	0.0453609i
$244$	2.43640	−	2.43640i	0.155974	−	0.155974i
$245$	−9.54171	+	9.54171i	−0.609597	+	0.609597i
$246$		−	11.0753i		−	0.706136i
$247$		−	23.2673i		−	1.48046i
$248$	−3.28291	+	3.28291i	−0.208465	+	0.208465i
$249$	−6.81698	+	6.81698i	−0.432008	+	0.432008i
$250$	3.48334	+	3.48334i	0.220306	+	0.220306i
$251$	8.40722			0.530659			0.265329	−	0.964158i	$-0.414519\pi$
$251$	8.40722			0.530659			0.265329	+	0.964158i	$0.414519\pi$
$252$	−2.34381	−	2.34381i	−0.147646	−	0.147646i
$253$			5.66057i			0.355877i
$254$	−18.2690			−1.14630
$255$	−13.8547	+	1.67011i	−0.867617	+	0.104587i
$256$	1.00000			0.0625000
$257$			16.7748i			1.04638i	0.852215	+	0.523192i	$0.175259\pi$
$257$			16.7748i			1.04638i	−0.852215	+	0.523192i	$0.824741\pi$
$258$	−2.37972	−	2.37972i	−0.148155	−	0.148155i
$259$	−22.5070			−1.39852
$260$	8.41659	+	8.41659i	0.521974	+	0.521974i
$261$	4.44399	−	4.44399i	0.275076	−	0.275076i
$262$	1.41544	−	1.41544i	0.0874465	−	0.0874465i
$263$		−	8.70868i		−	0.537000i	−0.963280	−	0.268500i	$-0.913472\pi$
$263$		−	8.70868i		−	0.537000i	0.963280	−	0.268500i	$-0.0865279\pi$
$264$			1.00000i			0.0615457i
$265$	17.9921	−	17.9921i	1.10525	−	1.10525i
$266$	15.5069	−	15.5069i	0.950787	−	0.950787i
$267$	5.35728	+	5.35728i	0.327860	+	0.327860i
$268$	9.13246			0.557854
$269$	0.243083	+	0.243083i	0.0148210	+	0.0148210i	0.714478	−	0.699657i	$-0.246664\pi$
$269$	0.243083	+	0.243083i	0.0148210	+	0.0148210i	−0.699657	+	0.714478i	$0.746664\pi$
$270$		−	3.38459i		−	0.205980i
$271$	7.81268			0.474587			0.237293	−	0.971438i	$-0.423740\pi$
$271$	7.81268			0.474587			0.237293	+	0.971438i	$0.423740\pi$
$272$	0.493446	+	4.09347i	0.0299196	+	0.248203i
$273$	−11.6569			−0.705506
$274$		−	18.0417i		−	1.08994i
$275$	4.56471	+	4.56471i	0.275262	+	0.275262i
$276$	−5.66057			−0.340727
$277$	14.0839	+	14.0839i	0.846220	+	0.846220i	0.989659	−	0.143440i	$-0.0458163\pi$
$277$	14.0839	+	14.0839i	0.846220	+	0.846220i	−0.143440	+	0.989659i	$0.545816\pi$
$278$	6.37213	−	6.37213i	0.382175	−	0.382175i
$279$	3.28291	−	3.28291i	0.196543	−	0.196543i
$280$			11.2187i			0.670448i
$281$			8.46851i			0.505189i	0.967572	+	0.252595i	$0.0812839\pi$
$281$			8.46851i			0.505189i	−0.967572	+	0.252595i	$0.918716\pi$
$282$	−4.05372	+	4.05372i	−0.241395	+	0.241395i
$283$	19.0755	−	19.0755i	1.13392	−	1.13392i	0.144401	−	0.989519i	$-0.453875\pi$
$283$	19.0755	−	19.0755i	1.13392	−	1.13392i	0.989519	−	0.144401i	$-0.0461254\pi$
$284$	−1.61357	−	1.61357i	−0.0957480	−	0.0957480i
$285$	22.3928			1.32643
$286$	2.48673	+	2.48673i	0.147044	+	0.147044i
$287$		−	36.7107i		−	2.16697i
$288$	−1.00000			−0.0589256
$289$	−16.5130	+	4.03981i	−0.971354	+	0.237636i
$290$	−21.2713			−1.24910
$291$		−	9.86552i		−	0.578327i
$292$	3.29555	+	3.29555i	0.192857	+	0.192857i
$293$	8.32080			0.486106			0.243053	−	0.970013i	$-0.421851\pi$
$293$	8.32080			0.486106			0.243053	+	0.970013i	$0.421851\pi$
$294$	−2.81916	−	2.81916i	−0.164417	−	0.164417i
$295$	17.3787	−	17.3787i	1.01183	−	1.01183i
$296$	−4.80137	+	4.80137i	−0.279074	+	0.279074i
$297$		−	1.00000i		−	0.0580259i
$298$			22.8494i			1.32363i
$299$	−14.0763	+	14.0763i	−0.814056	+	0.814056i
$300$	−4.56471	+	4.56471i	−0.263544	+	0.263544i
$301$	−7.88793	−	7.88793i	−0.454653	−	0.454653i
$302$	6.66119			0.383308
$303$	8.65799	+	8.65799i	0.497389	+	0.497389i
$304$		−	6.61609i		−	0.379459i
$305$	11.6619			0.667759
$306$	−0.493446	−	4.09347i	−0.0282084	−	0.234008i
$307$	27.0791			1.54548			0.772742	−	0.634721i	$-0.218885\pi$
$307$	27.0791			1.54548			0.772742	+	0.634721i	$0.218885\pi$
$308$			3.31465i			0.188870i
$309$	−13.0318	−	13.0318i	−0.741353	−	0.741353i
$310$	−15.7138			−0.892483
$311$	19.3088	+	19.3088i	1.09490	+	1.09490i	0.994997	+	0.0999050i	$0.0318539\pi$
$311$	19.3088	+	19.3088i	1.09490	+	1.09490i	0.0999050	+	0.994997i	$0.468146\pi$
$312$	−2.48673	+	2.48673i	−0.140784	+	0.140784i
$313$	−10.4790	+	10.4790i	−0.592309	+	0.592309i	−0.938255	−	0.345945i	$-0.887558\pi$
$313$	−10.4790	+	10.4790i	−0.592309	+	0.592309i	0.345945	+	0.938255i	$0.387558\pi$
$314$		−	10.2168i		−	0.576568i
$315$		−	11.2187i		−	0.632104i
$316$	0.0452462	−	0.0452462i	0.00254530	−	0.00254530i
$317$	−11.5864	+	11.5864i	−0.650756	+	0.650756i	−0.953175	−	0.302419i	$-0.902206\pi$
$317$	−11.5864	+	11.5864i	−0.650756	+	0.650756i	0.302419	+	0.953175i	$0.402206\pi$
$318$	5.31589	+	5.31589i	0.298100	+	0.298100i
$319$	−6.28476			−0.351879
$320$	2.39327	+	2.39327i	0.133788	+	0.133788i
$321$			10.4820i			0.585051i
$322$	−18.7628			−1.04561
$323$	27.0828	−	3.26468i	1.50693	−	0.181652i
$324$	1.00000			0.0555556
$325$			22.7024i			1.25930i
$326$	15.5238	+	15.5238i	0.859782	+	0.859782i
$327$	11.1650			0.617426
$328$	−7.83142	−	7.83142i	−0.432418	−	0.432418i
$329$	−13.4366	+	13.4366i	−0.740786	+	0.740786i
$330$	−2.39327	+	2.39327i	−0.131745	+	0.131745i
$331$			4.45941i			0.245111i	0.992462	+	0.122556i	$0.0391090\pi$
$331$			4.45941i			0.245111i	−0.992462	+	0.122556i	$0.960891\pi$
$332$			9.64066i			0.529100i
$333$	4.80137	−	4.80137i	0.263113	−	0.263113i
$334$	−4.44355	+	4.44355i	−0.243140	+	0.243140i
$335$	21.8564	+	21.8564i	1.19415	+	1.19415i
$336$	−3.31465			−0.180829
$337$	−18.8234	−	18.8234i	−1.02538	−	1.02538i	−0.999669	−	0.0257089i	$-0.991816\pi$
$337$	−18.8234	−	18.8234i	−1.02538	−	1.02538i	−0.0257089	−	0.999669i	$-0.508184\pi$
$338$		−	0.632304i		−	0.0343928i
$339$	−6.21499			−0.337552
$340$	−8.61583	+	10.9777i	−0.467259	+	0.595351i
$341$	−4.64274			−0.251418
$342$			6.61609i			0.357757i
$343$	7.06215	+	7.06215i	0.381320	+	0.381320i
$344$	−3.36543			−0.181452
$345$	−13.5473	−	13.5473i	−0.729361	−	0.729361i
$346$	−0.601723	+	0.601723i	−0.0323488	+	0.0323488i
$347$	2.77518	−	2.77518i	0.148980	−	0.148980i	−0.628682	−	0.777662i	$-0.716405\pi$
$347$	2.77518	−	2.77518i	0.148980	−	0.148980i	0.777662	+	0.628682i	$0.216405\pi$
$348$		−	6.28476i		−	0.336898i
$349$			26.1806i			1.40142i	0.713448	+	0.700708i	$0.247133\pi$
$349$			26.1806i			1.40142i	−0.713448	+	0.700708i	$0.752867\pi$
$350$	−15.1304	+	15.1304i	−0.808754	+	0.808754i
$351$	2.48673	−	2.48673i	0.132732	−	0.132732i
$352$	0.707107	+	0.707107i	0.0376889	+	0.0376889i
$353$	−27.7054			−1.47461			−0.737304	−	0.675562i	$-0.763901\pi$
$353$	−27.7054			−1.47461			−0.737304	+	0.675562i	$0.763901\pi$
$354$	5.13466	+	5.13466i	0.272904	+	0.272904i
$355$		−	7.72344i		−	0.409917i
$356$	7.57633			0.401545
$357$	−1.63560	−	13.5684i	−0.0865651	−	0.718117i
$358$	20.2603			1.07079
$359$		−	13.9763i		−	0.737641i	−0.929501	−	0.368820i	$-0.879762\pi$
$359$		−	13.9763i		−	0.737641i	0.929501	−	0.368820i	$-0.120238\pi$
$360$	−2.39327	−	2.39327i	−0.126136	−	0.126136i
$361$	−24.7727			−1.30383
$362$	12.6215	+	12.6215i	0.663369	+	0.663369i
$363$	−0.707107	+	0.707107i	−0.0371135	+	0.0371135i
$364$	−8.24265	+	8.24265i	−0.432032	+	0.432032i
$365$			15.7743i			0.825663i
$366$			3.44559i			0.180104i
$367$	3.56450	−	3.56450i	0.186065	−	0.186065i	−0.607927	−	0.793993i	$-0.707999\pi$
$367$	3.56450	−	3.56450i	0.186065	−	0.186065i	0.793993	+	0.607927i	$0.207999\pi$
$368$	−4.00263	+	4.00263i	−0.208652	+	0.208652i
$369$	7.83142	+	7.83142i	0.407688	+	0.407688i
$370$	−22.9819			−1.19477
$371$	17.6203	+	17.6203i	0.914800	+	0.914800i
$372$		−	4.64274i		−	0.240715i
$373$	21.9025			1.13407			0.567035	−	0.823694i	$-0.308091\pi$
$373$	21.9025			1.13407			0.567035	+	0.823694i	$0.308091\pi$
$374$	−2.54560	+	3.24344i	−0.131630	+	0.167714i
$375$	−4.92619			−0.254387
$376$			5.73282i			0.295648i
$377$	−15.6285	−	15.6285i	−0.804910	−	0.804910i
$378$	3.31465			0.170487
$379$	0.873103	+	0.873103i	0.0448483	+	0.0448483i	0.729175	−	0.684327i	$-0.239904\pi$
$379$	0.873103	+	0.873103i	0.0448483	+	0.0448483i	−0.684327	+	0.729175i	$0.739904\pi$
$380$	15.8341	−	15.8341i	0.812272	−	0.812272i
$381$	12.9181	−	12.9181i	0.661814	−	0.661814i
$382$		−	12.6910i		−	0.649330i
$383$			10.9988i			0.562014i	0.959706	+	0.281007i	$0.0906685\pi$
$383$			10.9988i			0.562014i	−0.959706	+	0.281007i	$0.909332\pi$
$384$	−0.707107	+	0.707107i	−0.0360844	+	0.0360844i
$385$	−7.93284	+	7.93284i	−0.404295	+	0.404295i
$386$	14.1544	+	14.1544i	0.720442	+	0.720442i
$387$	3.36543			0.171075
$388$	−6.97597	−	6.97597i	−0.354151	−	0.354151i
$389$		−	7.11651i		−	0.360821i	−0.983591	−	0.180411i	$-0.942257\pi$
$389$		−	7.11651i		−	0.360821i	0.983591	−	0.180411i	$-0.0577426\pi$
$390$	−11.9028			−0.602724
$391$	−18.3597	−	14.4096i	−0.928492	−	0.728723i
$392$	−3.98689			−0.201368
$393$			2.00174i			0.100975i
$394$	9.25344	+	9.25344i	0.466181	+	0.466181i
$395$	0.216573			0.0108969
$396$	−0.707107	−	0.707107i	−0.0355335	−	0.0355335i
$397$	−17.4922	+	17.4922i	−0.877910	+	0.877910i	−0.993318	−	0.115409i	$-0.963182\pi$
$397$	−17.4922	+	17.4922i	−0.877910	+	0.877910i	0.115409	+	0.993318i	$0.463182\pi$
$398$	3.56152	−	3.56152i	0.178523	−	0.178523i
$399$			21.9300i			1.09787i
$400$			6.45547i			0.322774i
$401$	27.0371	−	27.0371i	1.35017	−	1.35017i	0.464698	−	0.885469i	$-0.346163\pi$
$401$	27.0371	−	27.0371i	1.35017	−	1.35017i	0.885469	−	0.464698i	$-0.153837\pi$
$402$	−6.45763	+	6.45763i	−0.322077	+	0.322077i
$403$	−11.5453	−	11.5453i	−0.575110	−	0.575110i
$404$	12.2443			0.609174
$405$	2.39327	+	2.39327i	0.118922	+	0.118922i
$406$		−	20.8318i		−	1.03386i
$407$	−6.79016			−0.336576
$408$	−3.24344	−	2.54560i	−0.160574	−	0.126026i
$409$	11.3501			0.561226			0.280613	−	0.959821i	$-0.409462\pi$
$409$	11.3501			0.561226			0.280613	+	0.959821i	$0.409462\pi$
$410$		−	37.4854i		−	1.85127i
$411$	12.7574	+	12.7574i	0.629278	+	0.629278i
$412$	−18.4297			−0.907968
$413$	17.0196	+	17.0196i	0.837479	+	0.837479i
$414$	4.00263	−	4.00263i	0.196719	−	0.196719i
$415$	−23.0727	+	23.0727i	−1.13259	+	1.13259i
$416$			3.51677i			0.172424i
$417$			9.01156i			0.441298i
$418$	4.67828	−	4.67828i	0.228822	−	0.228822i
$419$	19.7651	−	19.7651i	0.965586	−	0.965586i	−0.0338408	−	0.999427i	$-0.510774\pi$
$419$	19.7651	−	19.7651i	0.965586	−	0.965586i	0.999427	+	0.0338408i	$0.0107739\pi$
$420$	−7.93284	−	7.93284i	−0.387083	−	0.387083i
$421$	−9.32029			−0.454243			−0.227122	−	0.973866i	$-0.572932\pi$
$421$	−9.32029			−0.454243			−0.227122	+	0.973866i	$0.572932\pi$
$422$	−2.69985	−	2.69985i	−0.131426	−	0.131426i
$423$		−	5.73282i		−	0.278739i
$424$	7.51780			0.365097
$425$	−26.4253	+	3.18543i	−1.28182	+	0.154516i
$426$	2.28194			0.110560
$427$			11.4209i			0.552697i
$428$	7.41192	+	7.41192i	0.358269	+	0.358269i
$429$	−3.51677			−0.169791
$430$	−8.05439	−	8.05439i	−0.388417	−	0.388417i
$431$	18.1861	−	18.1861i	0.875992	−	0.875992i	−0.117125	−	0.993117i	$-0.537368\pi$
$431$	18.1861	−	18.1861i	0.875992	−	0.875992i	0.993117	+	0.117125i	$0.0373678\pi$
$432$	0.707107	−	0.707107i	0.0340207	−	0.0340207i
$433$		−	33.0289i		−	1.58727i	−0.608395	−	0.793634i	$-0.708186\pi$
$433$		−	33.0289i		−	1.58727i	0.608395	−	0.793634i	$-0.291814\pi$
$434$		−	15.3890i		−	0.738697i
$435$	15.0411	−	15.0411i	0.721166	−	0.721166i
$436$	7.89485	−	7.89485i	0.378095	−	0.378095i
$437$	26.4818	+	26.4818i	1.26680	+	1.26680i
$438$	−4.66061			−0.222693
$439$	−23.7573	−	23.7573i	−1.13387	−	1.13387i	−0.989527	−	0.144346i	$-0.953892\pi$
$439$	−23.7573	−	23.7573i	−1.13387	−	1.13387i	−0.144346	−	0.989527i	$-0.546108\pi$
$440$			3.38459i			0.161354i
$441$	3.98689			0.189852
$442$	−14.3958	+	1.73534i	−0.684739	+	0.0825416i
$443$	20.6765			0.982371			0.491185	−	0.871055i	$-0.336564\pi$
$443$	20.6765			0.982371			0.491185	+	0.871055i	$0.336564\pi$
$444$		−	6.79016i		−	0.322247i
$445$	18.1322	+	18.1322i	0.859549	+	0.859549i
$446$	4.40601			0.208630
$447$	−16.1570	−	16.1570i	−0.764199	−	0.764199i
$448$	−2.34381	+	2.34381i	−0.110735	+	0.110735i
$449$	−7.51896	+	7.51896i	−0.354842	+	0.354842i	−0.861907	−	0.507066i	$-0.830730\pi$
$449$	−7.51896	+	7.51896i	−0.354842	+	0.354842i	0.507066	+	0.861907i	$0.330730\pi$
$450$		−	6.45547i		−	0.304314i
$451$		−	11.0753i		−	0.521516i
$452$	−4.39466	+	4.39466i	−0.206707	+	0.206707i
$453$	−4.71017	+	4.71017i	−0.221303	+	0.221303i
$454$	14.4708	+	14.4708i	0.679150	+	0.679150i
$455$	−39.4538			−1.84962
$456$	4.67828	+	4.67828i	0.219081	+	0.219081i
$457$			25.5384i			1.19464i	0.802004	+	0.597318i	$0.203767\pi$
$457$			25.5384i			1.19464i	−0.802004	+	0.597318i	$0.796233\pi$
$458$	−24.9524			−1.16595
$459$	3.24344	+	2.54560i	0.151391	+	0.118819i
$460$	−19.1587			−0.893281
$461$		−	34.3772i		−	1.60111i	−0.599261	−	0.800553i	$-0.704539\pi$
$461$		−	34.3772i		−	1.60111i	0.599261	−	0.800553i	$-0.295461\pi$
$462$	−2.34381	−	2.34381i	−0.109044	−	0.109044i
$463$	12.2297			0.568362			0.284181	−	0.958771i	$-0.408278\pi$
$463$	12.2297			0.568362			0.284181	+	0.958771i	$0.408278\pi$
$464$	−4.44399	−	4.44399i	−0.206307	−	0.206307i
$465$	11.1113	−	11.1113i	0.515275	−	0.515275i
$466$	8.55964	−	8.55964i	0.396517	−	0.396517i
$467$			12.1097i			0.560371i	0.959946	+	0.280186i	$0.0903961\pi$
$467$			12.1097i			0.560371i	−0.959946	+	0.280186i	$0.909604\pi$
$468$		−	3.51677i		−	0.162563i
$469$	−21.4048	+	21.4048i	−0.988380	+	0.988380i
$470$	−13.7202	+	13.7202i	−0.632865	+	0.632865i
$471$	7.22438	+	7.22438i	0.332882	+	0.332882i
$472$	7.26150			0.334238
$473$	−2.37972	−	2.37972i	−0.109420	−	0.109420i
$474$			0.0639877i			0.00293905i
$475$	42.7100			1.95967
$476$	−10.7509	−	8.43778i	−0.492765	−	0.386745i
$477$	−7.51780			−0.344216
$478$			10.9971i			0.502995i
$479$	−7.12547	−	7.12547i	−0.325571	−	0.325571i	0.525328	−	0.850900i	$-0.323942\pi$
$479$	−7.12547	−	7.12547i	−0.325571	−	0.325571i	−0.850900	+	0.525328i	$0.823942\pi$
$480$	−3.38459			−0.154485
$481$	−16.8853	−	16.8853i	−0.769905	−	0.769905i
$482$	−0.0273602	+	0.0273602i	−0.00124622	+	0.00124622i
$483$	13.2673	−	13.2673i	0.603684	−	0.603684i
$484$			1.00000i			0.0454545i
$485$		−	33.3908i		−	1.51620i
$486$	−0.707107	+	0.707107i	−0.0320750	+	0.0320750i
$487$	−3.78996	+	3.78996i	−0.171739	+	0.171739i	−0.787743	−	0.616004i	$-0.788751\pi$
$487$	−3.78996	+	3.78996i	−0.171739	+	0.171739i	0.616004	+	0.787743i	$0.288751\pi$
$488$	2.43640	+	2.43640i	0.110291	+	0.110291i
$489$	−21.9539			−0.992791
$490$	−9.54171	−	9.54171i	−0.431050	−	0.431050i
$491$		−	33.0313i		−	1.49068i	−0.666685	−	0.745340i	$-0.732287\pi$
$491$		−	33.0313i		−	1.49068i	0.666685	−	0.745340i	$-0.267713\pi$
$492$	11.0753			0.499313
$493$	15.9985	−	20.3842i	0.720536	−	0.918060i
$494$	23.2673			1.04685
$495$		−	3.38459i		−	0.152126i
$496$	−3.28291	−	3.28291i	−0.147407	−	0.147407i
$497$	7.56383			0.339284
$498$	−6.81698	−	6.81698i	−0.305476	−	0.305476i
$499$	14.6255	−	14.6255i	0.654725	−	0.654725i	−0.299402	−	0.954127i	$-0.596787\pi$
$499$	14.6255	−	14.6255i	0.654725	−	0.654725i	0.954127	+	0.299402i	$0.0967871\pi$
$500$	−3.48334	+	3.48334i	−0.155780	+	0.155780i
$501$		−	6.28413i		−	0.280754i
$502$			8.40722i			0.375232i
$503$	−25.8126	+	25.8126i	−1.15093	+	1.15093i	−0.164561	+	0.986367i	$0.552621\pi$
$503$	−25.8126	+	25.8126i	−1.15093	+	1.15093i	−0.986367	+	0.164561i	$0.947379\pi$
$504$	2.34381	−	2.34381i	0.104402	−	0.104402i
$505$	29.3038	+	29.3038i	1.30400	+	1.30400i
$506$	−5.66057			−0.251643
$507$	0.447106	+	0.447106i	0.0198567	+	0.0198567i
$508$		−	18.2690i		−	0.810554i
$509$	−12.4979			−0.553960			−0.276980	−	0.960876i	$-0.589334\pi$
$509$	−12.4979			−0.553960			−0.276980	+	0.960876i	$0.589334\pi$
$510$	−1.67011	−	13.8547i	−0.0739539	−	0.613498i
$511$	−15.4483			−0.683392
$512$			1.00000i			0.0441942i
$513$	−4.67828	−	4.67828i	−0.206551	−	0.206551i
$514$	−16.7748			−0.739906
$515$	−44.1073	−	44.1073i	−1.94360	−	1.94360i
$516$	2.37972	−	2.37972i	0.104761	−	0.104761i
$517$	−4.05372	+	4.05372i	−0.178282	+	0.178282i
$518$		−	22.5070i		−	0.988901i
$519$		−	0.850965i		−	0.0373532i
$520$	−8.41659	+	8.41659i	−0.369092	+	0.369092i
$521$	0.325063	−	0.325063i	0.0142413	−	0.0142413i	−0.699950	−	0.714192i	$-0.746795\pi$
$521$	0.325063	−	0.325063i	0.0142413	−	0.0142413i	0.714192	+	0.699950i	$0.246795\pi$
$522$	4.44399	+	4.44399i	0.194508	+	0.194508i
$523$	41.0895			1.79672			0.898359	−	0.439262i	$-0.144760\pi$
$523$	41.0895			1.79672			0.898359	+	0.439262i	$0.144760\pi$
$524$	1.41544	+	1.41544i	0.0618340	+	0.0618340i
$525$		−	21.3976i		−	0.933869i
$526$	8.70868			0.379716
$527$	11.8186	−	15.0584i	0.514825	−	0.655956i
$528$	−1.00000			−0.0435194
$529$		−	9.04211i		−	0.393135i
$530$	17.9921	+	17.9921i	0.781528	+	0.781528i
$531$	−7.26150			−0.315122
$532$	15.5069	+	15.5069i	0.672308	+	0.672308i
$533$	27.5413	−	27.5413i	1.19295	−	1.19295i
$534$	−5.35728	+	5.35728i	−0.231832	+	0.231832i
$535$			35.4775i			1.53382i
$536$			9.13246i			0.394462i
$537$	−14.3262	+	14.3262i	−0.618220	+	0.618220i
$538$	−0.243083	+	0.243083i	−0.0104800	+	0.0104800i
$539$	−2.81916	−	2.81916i	−0.121430	−	0.121430i
$540$	3.38459			0.145650
$541$	−5.91057	−	5.91057i	−0.254115	−	0.254115i	0.568540	−	0.822655i	$-0.307508\pi$
$541$	−5.91057	−	5.91057i	−0.254115	−	0.254115i	−0.822655	+	0.568540i	$0.807508\pi$
$542$			7.81268i			0.335583i
$543$	−17.8494			−0.765992
$544$	−4.09347	+	0.493446i	−0.175506	+	0.0211563i
$545$	37.7890			1.61870
$546$		−	11.6569i		−	0.498868i
$547$	2.41717	+	2.41717i	0.103351	+	0.103351i	0.756891	−	0.653541i	$-0.226717\pi$
$547$	2.41717	+	2.41717i	0.103351	+	0.103351i	−0.653541	+	0.756891i	$0.726717\pi$
$548$	18.0417			0.770705
$549$	−2.43640	−	2.43640i	−0.103983	−	0.103983i
$550$	−4.56471	+	4.56471i	−0.194640	+	0.194640i
$551$	−29.4019	+	29.4019i	−1.25256	+	1.25256i
$552$		−	5.66057i		−	0.240930i
$553$			0.212097i			0.00901928i
$554$	−14.0839	+	14.0839i	−0.598368	+	0.598368i
$555$	16.2507	−	16.2507i	0.689803	−	0.689803i
$556$	6.37213	+	6.37213i	0.270239	+	0.270239i
$557$	35.5918			1.50807			0.754037	−	0.656832i	$-0.228104\pi$
$557$	35.5918			1.50807			0.754037	+	0.656832i	$0.228104\pi$
$558$	3.28291	+	3.28291i	0.138977	+	0.138977i
$559$		−	11.8355i		−	0.500587i
$560$	−11.2187			−0.474078
$561$	−0.493446	−	4.09347i	−0.0208333	−	0.172827i
$562$	−8.46851			−0.357223
$563$		−	18.6826i		−	0.787379i	−0.919243	−	0.393689i	$-0.871199\pi$
$563$		−	18.6826i		−	0.787379i	0.919243	−	0.393689i	$-0.128801\pi$
$564$	−4.05372	−	4.05372i	−0.170692	−	0.170692i
$565$	−21.0352			−0.884958
$566$	19.0755	+	19.0755i	0.801803	+	0.801803i
$567$	−2.34381	+	2.34381i	−0.0984308	+	0.0984308i
$568$	1.61357	−	1.61357i	0.0677041	−	0.0677041i
$569$		−	12.2237i		−	0.512445i	−0.966618	−	0.256222i	$-0.917522\pi$
$569$		−	12.2237i		−	0.512445i	0.966618	−	0.256222i	$-0.0824779\pi$
$570$			22.3928i			0.937931i
$571$	4.94472	−	4.94472i	0.206930	−	0.206930i	−0.596031	−	0.802961i	$-0.703257\pi$
$571$	4.94472	−	4.94472i	0.206930	−	0.206930i	0.802961	+	0.596031i	$0.203257\pi$
$572$	−2.48673	+	2.48673i	−0.103976	+	0.103976i
$573$	8.97392	+	8.97392i	0.374891	+	0.374891i
$574$	36.7107			1.53228
$575$	−25.8389	−	25.8389i	−1.07756	−	1.07756i
$576$		−	1.00000i		−	0.0416667i
$577$	−1.19237			−0.0496391			−0.0248195	−	0.999692i	$-0.507901\pi$
$577$	−1.19237			−0.0496391			−0.0248195	+	0.999692i	$0.507901\pi$
$578$	−4.03981	−	16.5130i	−0.168034	−	0.686851i
$579$	−20.0174			−0.831895
$580$		−	21.2713i		−	0.883244i
$581$	−22.5959	−	22.5959i	−0.937435	−	0.937435i
$582$	9.86552			0.408939
$583$	5.31589	+	5.31589i	0.220162	+	0.220162i
$584$	−3.29555	+	3.29555i	−0.136371	+	0.136371i
$585$	8.41659	−	8.41659i	0.347983	−	0.347983i
$586$			8.32080i			0.343729i
$587$		−	45.8530i		−	1.89255i	−0.323357	−	0.946277i	$-0.604811\pi$
$587$		−	45.8530i		−	1.89255i	0.323357	−	0.946277i	$-0.395189\pi$
$588$	2.81916	−	2.81916i	0.116260	−	0.116260i
$589$	−21.7200	+	21.7200i	−0.894959	+	0.894959i
$590$	17.3787	+	17.3787i	0.715471	+	0.715471i
$591$	−13.0863			−0.538300
$592$	−4.80137	−	4.80137i	−0.197335	−	0.197335i
$593$		−	48.3426i		−	1.98519i	−0.121466	−	0.992596i	$-0.538759\pi$
$593$		−	48.3426i		−	1.98519i	0.121466	−	0.992596i	$-0.461241\pi$
$594$	1.00000			0.0410305
$595$	−5.53584	−	45.9236i	−0.226947	−	1.88268i
$596$	−22.8494			−0.935949
$597$			5.03675i			0.206140i
$598$	−14.0763	−	14.0763i	−0.575625	−	0.575625i
$599$	13.6723			0.558633			0.279317	−	0.960199i	$-0.409892\pi$
$599$	13.6723			0.558633			0.279317	+	0.960199i	$0.409892\pi$
$600$	−4.56471	−	4.56471i	−0.186353	−	0.186353i
$601$	−12.6718	+	12.6718i	−0.516894	+	0.516894i	−0.916630	−	0.399736i	$-0.869102\pi$
$601$	−12.6718	+	12.6718i	−0.516894	+	0.516894i	0.399736	+	0.916630i	$0.369102\pi$
$602$	7.88793	−	7.88793i	0.321488	−	0.321488i
$603$		−	9.13246i		−	0.371903i
$604$			6.66119i			0.271040i
$605$	−2.39327	+	2.39327i	−0.0973002	+	0.0973002i
$606$	−8.65799	+	8.65799i	−0.351707	+	0.351707i
$607$	3.08388	+	3.08388i	0.125171	+	0.125171i	0.766917	−	0.641746i	$-0.221790\pi$
$607$	3.08388	+	3.08388i	0.125171	+	0.125171i	−0.641746	+	0.766917i	$0.721790\pi$
$608$	6.61609			0.268318
$609$	14.7303	+	14.7303i	0.596901	+	0.596901i
$610$			11.6619i			0.472177i
$611$	−20.1610			−0.815628
$612$	4.09347	−	0.493446i	0.165469	−	0.0199464i
$613$	−9.99299			−0.403613			−0.201806	−	0.979425i	$-0.564681\pi$
$613$	−9.99299			−0.403613			−0.201806	+	0.979425i	$0.564681\pi$
$614$			27.0791i			1.09282i
$615$	26.5062	+	26.5062i	1.06883	+	1.06883i
$616$	−3.31465			−0.133551
$617$	6.23120	+	6.23120i	0.250859	+	0.250859i	0.821323	−	0.570464i	$-0.193237\pi$
$617$	6.23120	+	6.23120i	0.250859	+	0.250859i	−0.570464	+	0.821323i	$0.693237\pi$
$618$	13.0318	−	13.0318i	0.524215	−	0.524215i
$619$	−13.8805	+	13.8805i	−0.557904	+	0.557904i	−0.928710	−	0.370806i	$-0.879081\pi$
$619$	−13.8805	+	13.8805i	−0.557904	+	0.557904i	0.370806	+	0.928710i	$0.379081\pi$
$620$		−	15.7138i		−	0.631080i
$621$			5.66057i			0.227151i
$622$	−19.3088	+	19.3088i	−0.774213	+	0.774213i
$623$	−17.7575	+	17.7575i	−0.711439	+	0.711439i
$624$	−2.48673	−	2.48673i	−0.0995490	−	0.0995490i
$625$	15.6042			0.624169
$626$	−10.4790	−	10.4790i	−0.418826	−	0.418826i
$627$			6.61609i			0.264221i
$628$	10.2168			0.407695
$629$	17.2851	−	22.0235i	0.689200	−	0.878134i
$630$	11.2187			0.446965
$631$		−	14.8741i		−	0.592127i	−0.955168	−	0.296064i	$-0.904326\pi$
$631$		−	14.8741i		−	0.592127i	0.955168	−	0.296064i	$-0.0956740\pi$
$632$	0.0452462	+	0.0452462i	0.00179980	+	0.00179980i
$633$	3.81816			0.151758
$634$	−11.5864	−	11.5864i	−0.460154	−	0.460154i
$635$	43.7225	−	43.7225i	1.73508	−	1.73508i
$636$	−5.31589	+	5.31589i	−0.210789	+	0.210789i
$637$		−	14.0210i		−	0.555532i
$638$		−	6.28476i		−	0.248816i
$639$	−1.61357	+	1.61357i	−0.0638320	+	0.0638320i
$640$	−2.39327	+	2.39327i	−0.0946023	+	0.0946023i
$641$	−30.5891	−	30.5891i	−1.20820	−	1.20820i	−0.971610	−	0.236588i	$-0.923971\pi$
$641$	−30.5891	−	30.5891i	−1.20820	−	1.20820i	−0.236588	−	0.971610i	$-0.576029\pi$
$642$	−10.4820			−0.413693
$643$	31.1379	+	31.1379i	1.22796	+	1.22796i	0.964735	+	0.263222i	$0.0847853\pi$
$643$	31.1379	+	31.1379i	1.22796	+	1.22796i	0.263222	+	0.964735i	$0.415215\pi$
$644$		−	18.7628i		−	0.739358i
$645$	11.3906			0.448505
$646$	3.26468	+	27.0828i	0.128447	+	1.06556i
$647$	21.0854			0.828952			0.414476	−	0.910060i	$-0.363965\pi$
$647$	21.0854			0.828952			0.414476	+	0.910060i	$0.363965\pi$
$648$			1.00000i			0.0392837i
$649$	5.13466	+	5.13466i	0.201553	+	0.201553i
$650$	−22.7024			−0.890463
$651$	10.8817	+	10.8817i	0.426487	+	0.426487i
$652$	−15.5238	+	15.5238i	−0.607958	+	0.607958i
$653$	2.86233	−	2.86233i	0.112012	−	0.112012i	−0.648879	−	0.760891i	$-0.724762\pi$
$653$	2.86233	−	2.86233i	0.112012	−	0.112012i	0.760891	+	0.648879i	$0.224762\pi$
$654$			11.1650i			0.436586i
$655$			6.77508i			0.264724i
$656$	7.83142	−	7.83142i	0.305766	−	0.305766i
$657$	3.29555	−	3.29555i	0.128572	−	0.128572i
$658$	−13.4366	−	13.4366i	−0.523815	−	0.523815i
$659$	−36.7868			−1.43301			−0.716505	−	0.697582i	$-0.754259\pi$
$659$	−36.7868			−1.43301			−0.716505	+	0.697582i	$0.754259\pi$
$660$	−2.39327	−	2.39327i	−0.0931579	−	0.0931579i
$661$		−	14.5496i		−	0.565912i	−0.959133	−	0.282956i	$-0.908685\pi$
$661$		−	14.5496i		−	0.565912i	0.959133	−	0.282956i	$-0.0913151\pi$
$662$	−4.45941			−0.173320
$663$	8.95231	−	11.4064i	0.347679	−	0.442990i
$664$	−9.64066			−0.374130
$665$			74.2242i			2.87829i
$666$	4.80137	+	4.80137i	0.186049	+	0.186049i
$667$	35.5753			1.37748
$668$	−4.44355	−	4.44355i	−0.171926	−	0.171926i
$669$	−3.11552	+	3.11552i	−0.120453	+	0.120453i
$670$	−21.8564	+	21.8564i	−0.844388	+	0.844388i
$671$			3.44559i			0.133015i
$672$		−	3.31465i		−	0.127865i
$673$	15.8238	−	15.8238i	0.609962	−	0.609962i	−0.332974	−	0.942936i	$-0.608052\pi$
$673$	15.8238	−	15.8238i	0.609962	−	0.609962i	0.942936	+	0.332974i	$0.108052\pi$
$674$	18.8234	−	18.8234i	0.725052	−	0.725052i
$675$	4.56471	+	4.56471i	0.175696	+	0.175696i
$676$	0.632304			0.0243194
$677$	24.1162	+	24.1162i	0.926862	+	0.926862i	0.997502	−	0.0706396i	$-0.0225040\pi$
$677$	24.1162	+	24.1162i	0.926862	+	0.926862i	−0.0706396	+	0.997502i	$0.522504\pi$
$678$		−	6.21499i		−	0.238685i
$679$	32.7007			1.25494
$680$	−10.9777	−	8.61583i	−0.420977	−	0.330402i
$681$	−20.4648			−0.784215
$682$		−	4.64274i		−	0.177780i
$683$	−21.5974	−	21.5974i	−0.826402	−	0.826402i	0.160615	−	0.987017i	$-0.448652\pi$
$683$	−21.5974	−	21.5974i	−0.826402	−	0.826402i	−0.987017	+	0.160615i	$0.948652\pi$
$684$	−6.61609			−0.252973
$685$	43.1787	+	43.1787i	1.64977	+	1.64977i
$686$	−7.06215	+	7.06215i	−0.269634	+	0.269634i
$687$	17.6440	−	17.6440i	0.673162	−	0.673162i
$688$		−	3.36543i		−	0.128306i
$689$			26.4384i			1.00722i
$690$	13.5473	−	13.5473i	0.515736	−	0.515736i
$691$	−16.9064	+	16.9064i	−0.643151	+	0.643151i	−0.951329	−	0.308178i	$-0.900281\pi$
$691$	−16.9064	+	16.9064i	−0.643151	+	0.643151i	0.308178	+	0.951329i	$0.400281\pi$
$692$	−0.601723	−	0.601723i	−0.0228741	−	0.0228741i
$693$	3.31465			0.125913
$694$	2.77518	+	2.77518i	0.105345	+	0.105345i
$695$			30.5005i			1.15695i
$696$	6.28476			0.238223
$697$	35.9221	+	28.1933i	1.36065	+	1.06790i
$698$	−26.1806			−0.990951
$699$			12.1052i			0.457859i
$700$	−15.1304	−	15.1304i	−0.571876	−	0.571876i
$701$	−27.4345			−1.03619			−0.518093	−	0.855324i	$-0.673358\pi$
$701$	−27.4345			−1.03619			−0.518093	+	0.855324i	$0.673358\pi$
$702$	2.48673	+	2.48673i	0.0938557	+	0.0938557i
$703$	−31.7663	+	31.7663i	−1.19809	+	1.19809i
$704$	−0.707107	+	0.707107i	−0.0266501	+	0.0266501i
$705$		−	19.4033i		−	0.730770i
$706$		−	27.7054i		−	1.04270i
$707$	−28.6982	+	28.6982i	−1.07931	+	1.07931i
$708$	−5.13466	+	5.13466i	−0.192972	+	0.192972i
$709$	−12.9348	−	12.9348i	−0.485775	−	0.485775i	0.421195	−	0.906970i	$-0.361611\pi$
$709$	−12.9348	−	12.9348i	−0.485775	−	0.485775i	−0.906970	+	0.421195i	$0.861611\pi$
$710$	7.72344			0.289855
$711$	−0.0452462	−	0.0452462i	−0.00169686	−	0.00169686i
$712$			7.57633i			0.283935i
$713$	26.2806			0.984215
$714$	13.5684	−	1.63560i	0.507785	−	0.0612108i
$715$	−11.9028			−0.445141
$716$			20.2603i			0.757162i
$717$	−7.77612	−	7.77612i	−0.290404	−	0.290404i
$718$	13.9763			0.521591
$719$	13.5813	+	13.5813i	0.506496	+	0.506496i	0.913449	−	0.406953i	$-0.133409\pi$
$719$	13.5813	+	13.5813i	0.506496	+	0.506496i	−0.406953	+	0.913449i	$0.633409\pi$
$720$	2.39327	−	2.39327i	0.0891919	−	0.0891919i
$721$	43.1958	−	43.1958i	1.60870	−	1.60870i
$722$		−	24.7727i		−	0.921944i
$723$		−	0.0386932i		−	0.00143901i
$724$	−12.6215	+	12.6215i	−0.469073	+	0.469073i
$725$	28.6881	−	28.6881i	1.06545	−	1.06545i
$726$	−0.707107	−	0.707107i	−0.0262432	−	0.0262432i
$727$	−6.92225			−0.256732			−0.128366	−	0.991727i	$-0.540973\pi$
$727$	−6.92225			−0.256732			−0.128366	+	0.991727i	$0.540973\pi$
$728$	−8.24265	−	8.24265i	−0.305493	−	0.305493i
$729$		−	1.00000i		−	0.0370370i
$730$	−15.7743			−0.583832
$731$	13.7763	−	1.66066i	0.509535	−	0.0614217i
$732$	−3.44559			−0.127353
$733$		−	15.5767i		−	0.575338i	−0.957730	−	0.287669i	$-0.907120\pi$
$733$		−	15.5767i		−	0.575338i	0.957730	−	0.287669i	$-0.0928803\pi$
$734$	3.56450	+	3.56450i	0.131568	+	0.131568i
$735$	13.4940			0.497734
$736$	−4.00263	−	4.00263i	−0.147539	−	0.147539i
$737$	−6.45763	+	6.45763i	−0.237870	+	0.237870i
$738$	−7.83142	+	7.83142i	−0.288279	+	0.288279i
$739$		−	0.638462i		−	0.0234862i	−0.999931	−	0.0117431i	$-0.996262\pi$
$739$		−	0.638462i		−	0.0234862i	0.999931	−	0.0117431i	$-0.00373803\pi$
$740$		−	22.9819i		−	0.844833i
$741$	−16.4525	+	16.4525i	−0.604396	+	0.604396i
$742$	−17.6203	+	17.6203i	−0.646861	+	0.646861i
$743$	17.4775	+	17.4775i	0.641187	+	0.641187i	0.950847	−	0.309660i	$-0.100215\pi$
$743$	17.4775	+	17.4775i	0.641187	+	0.641187i	−0.309660	+	0.950847i	$0.600215\pi$
$744$	4.64274			0.170211
$745$	−54.6848	−	54.6848i	−2.00350	−	2.00350i
$746$			21.9025i			0.801908i
$747$	9.64066			0.352733
$748$	−3.24344	−	2.54560i	−0.118592	−	0.0930764i
$749$	−34.7443			−1.26953
$750$		−	4.92619i		−	0.179879i
$751$	−6.33953	−	6.33953i	−0.231333	−	0.231333i	0.581916	−	0.813249i	$-0.302303\pi$
$751$	−6.33953	−	6.33953i	−0.231333	−	0.231333i	−0.813249	+	0.581916i	$0.802303\pi$
$752$	−5.73282			−0.209055
$753$	−5.94480	−	5.94480i	−0.216641	−	0.216641i
$754$	15.6285	−	15.6285i	0.569157	−	0.569157i
$755$	−15.9420	+	15.9420i	−0.580189	+	0.580189i
$756$			3.31465i			0.120553i
$757$			10.6539i			0.387224i	0.981078	+	0.193612i	$0.0620203\pi$
$757$			10.6539i			0.387224i	−0.981078	+	0.193612i	$0.937980\pi$
$758$	−0.873103	+	0.873103i	−0.0317125	+	0.0317125i
$759$	4.00263	−	4.00263i	0.145286	−	0.145286i
$760$	15.8341	+	15.8341i	0.574363	+	0.574363i
$761$	−20.7937			−0.753769			−0.376885	−	0.926260i	$-0.623005\pi$
$761$	−20.7937			−0.753769			−0.376885	+	0.926260i	$0.623005\pi$
$762$	12.9181	+	12.9181i	0.467973	+	0.467973i
$763$			37.0080i			1.33978i
$764$	12.6910			0.459146
$765$	10.9777	+	8.61583i	0.396901	+	0.311506i
$766$	−10.9988			−0.397404
$767$			25.5371i			0.922090i
$768$	−0.707107	−	0.707107i	−0.0255155	−	0.0255155i
$769$	1.37941			0.0497429			0.0248715	−	0.999691i	$-0.492082\pi$
$769$	1.37941			0.0497429			0.0248715	+	0.999691i	$0.492082\pi$
$770$	−7.93284	−	7.93284i	−0.285880	−	0.285880i
$771$	11.8616	−	11.8616i	0.427185	−	0.427185i
$772$	−14.1544	+	14.1544i	−0.509430	+	0.509430i
$773$			5.97717i			0.214984i	0.994206	+	0.107492i	$0.0342820\pi$
$773$			5.97717i			0.214984i	−0.994206	+	0.107492i	$0.965718\pi$
$774$			3.36543i			0.120968i
$775$	21.1927	−	21.1927i	0.761266	−	0.761266i
$776$	6.97597	−	6.97597i	0.250423	−	0.250423i
$777$	15.9149	+	15.9149i	0.570942	+	0.570942i
$778$	7.11651			0.255139
$779$	−51.8134	−	51.8134i	−1.85641	−	1.85641i
$780$		−	11.9028i		−	0.426190i
$781$	2.28194			0.0816542
$782$	14.4096	−	18.3597i	0.515285	−	0.656543i
$783$	−6.28476			−0.224599
$784$		−	3.98689i		−	0.142389i
$785$	24.4516	+	24.4516i	0.872714	+	0.872714i
$786$	−2.00174			−0.0713998
$787$	−10.3217	−	10.3217i	−0.367930	−	0.367930i	0.498792	−	0.866722i	$-0.333777\pi$
$787$	−10.3217	−	10.3217i	−0.367930	−	0.367930i	−0.866722	+	0.498792i	$0.833777\pi$
$788$	−9.25344	+	9.25344i	−0.329640	+	0.329640i
$789$	−6.15796	+	6.15796i	−0.219229	+	0.219229i
$790$			0.216573i			0.00770530i
$791$		−	20.6005i		−	0.732469i
$792$	0.707107	−	0.707107i	0.0251259	−	0.0251259i
$793$	−8.56826	+	8.56826i	−0.304268	+	0.304268i
$794$	−17.4922	−	17.4922i	−0.620776	−	0.620776i
$795$	−25.4447			−0.902430
$796$	3.56152	+	3.56152i	0.126235	+	0.126235i
$797$		−	34.4623i		−	1.22072i	−0.792125	−	0.610359i	$-0.791025\pi$
$797$		−	34.4623i		−	1.22072i	0.792125	−	0.610359i	$-0.208975\pi$
$798$	−21.9300			−0.776314
$799$	−2.82884	−	23.4671i	−0.100077	−	0.830208i
$800$	−6.45547			−0.228235
$801$		−	7.57633i		−	0.267697i
$802$	27.0371	+	27.0371i	0.954712	+	0.954712i
$803$	−4.66061			−0.164469
$804$	−6.45763	−	6.45763i	−0.227743	−	0.227743i
$805$	44.9045	−	44.9045i	1.58267	−	1.58267i
$806$	11.5453	−	11.5453i	0.406664	−	0.406664i
$807$		−	0.343771i		−	0.0121013i
$808$			12.2443i			0.430751i
$809$	−23.4750	+	23.4750i	−0.825338	+	0.825338i	−0.986868	−	0.161530i	$-0.948357\pi$
$809$	−23.4750	+	23.4750i	−0.825338	+	0.825338i	0.161530	+	0.986868i	$0.448357\pi$
$810$	−2.39327	+	2.39327i	−0.0840909	+	0.0840909i
$811$	22.7961	+	22.7961i	0.800480	+	0.800480i	0.983171	−	0.182690i	$-0.0584805\pi$
$811$	22.7961	+	22.7961i	0.800480	+	0.800480i	−0.182690	+	0.983171i	$0.558481\pi$
$812$	20.8318			0.731051
$813$	−5.52440	−	5.52440i	−0.193749	−	0.193749i
$814$		−	6.79016i		−	0.237995i
$815$	−74.3051			−2.60279
$816$	2.54560	−	3.24344i	0.0891139	−	0.113543i
$817$	−22.2660			−0.778989
$818$			11.3501i			0.396847i
$819$	8.24265	+	8.24265i	0.288021	+	0.288021i
$820$	37.4854			1.30905
$821$	−8.85309	−	8.85309i	−0.308975	−	0.308975i	0.535537	−	0.844512i	$-0.320109\pi$
$821$	−8.85309	−	8.85309i	−0.308975	−	0.308975i	−0.844512	+	0.535537i	$0.820109\pi$
$822$	−12.7574	+	12.7574i	−0.444967	+	0.444967i
$823$	−14.6131	+	14.6131i	−0.509379	+	0.509379i	−0.914336	−	0.404957i	$-0.867287\pi$
$823$	−14.6131	+	14.6131i	−0.509379	+	0.509379i	0.404957	+	0.914336i	$0.367287\pi$
$824$		−	18.4297i		−	0.642030i
$825$		−	6.45547i		−	0.224751i
$826$	−17.0196	+	17.0196i	−0.592187	+	0.592187i
$827$	−23.6308	+	23.6308i	−0.821725	+	0.821725i	−0.986355	−	0.164630i	$-0.947357\pi$
$827$	−23.6308	+	23.6308i	−0.821725	+	0.821725i	0.164630	+	0.986355i	$0.447357\pi$
$828$	4.00263	+	4.00263i	0.139101	+	0.139101i
$829$	−23.0987			−0.802252			−0.401126	−	0.916023i	$-0.631381\pi$
$829$	−23.0987			−0.802252			−0.401126	+	0.916023i	$0.631381\pi$
$830$	−23.0727	−	23.0727i	−0.800865	−	0.800865i
$831$		−	19.9176i		−	0.690935i
$832$	−3.51677			−0.121922
$833$	16.3202	−	1.96732i	0.565462	−	0.0681635i
$834$	−9.01156			−0.312045
$835$		−	21.2692i		−	0.736051i
$836$	4.67828	+	4.67828i	0.161802	+	0.161802i
$837$	−4.64274			−0.160476
$838$	19.7651	+	19.7651i	0.682773	+	0.682773i
$839$	5.49837	−	5.49837i	0.189825	−	0.189825i	−0.605796	−	0.795620i	$-0.707145\pi$
$839$	5.49837	−	5.49837i	0.189825	−	0.189825i	0.795620	+	0.605796i	$0.207145\pi$
$840$	7.93284	−	7.93284i	0.273709	−	0.273709i
$841$			10.4982i			0.362005i
$842$		−	9.32029i		−	0.321199i
$843$	5.98814	−	5.98814i	0.206243	−	0.206243i
$844$	2.69985	−	2.69985i	0.0929325	−	0.0929325i
$845$	1.51327	+	1.51327i	0.0520582	+	0.0520582i
$846$	5.73282			0.197099
$847$	−2.34381	−	2.34381i	−0.0805343	−	0.0805343i
$848$			7.51780i			0.258162i
$849$	−26.9768			−0.925842
$850$	−3.18543	−	26.4253i	−0.109259	−	0.906380i
$851$	38.4362			1.31758
$852$			2.28194i			0.0781779i
$853$	−8.41690	−	8.41690i	−0.288189	−	0.288189i	0.548175	−	0.836364i	$-0.315323\pi$
$853$	−8.41690	−	8.41690i	−0.288189	−	0.288189i	−0.836364	+	0.548175i	$0.815323\pi$
$854$	−11.4209			−0.390816
$855$	−15.8341	−	15.8341i	−0.541514	−	0.541514i
$856$	−7.41192	+	7.41192i	−0.253334	+	0.253334i
$857$	37.0146	−	37.0146i	1.26440	−	1.26440i	0.315455	−	0.948940i	$-0.397843\pi$
$857$	37.0146	−	37.0146i	1.26440	−	1.26440i	0.948940	−	0.315455i	$-0.102157\pi$
$858$		−	3.51677i		−	0.120061i
$859$			30.6915i			1.04718i	0.851970	+	0.523590i	$0.175408\pi$
$859$			30.6915i			1.04718i	−0.851970	+	0.523590i	$0.824592\pi$
$860$	8.05439	−	8.05439i	0.274652	−	0.274652i
$861$	−25.9584	+	25.9584i	−0.884660	+	0.884660i
$862$	18.1861	+	18.1861i	0.619420	+	0.619420i
$863$	−12.4057			−0.422296			−0.211148	−	0.977454i	$-0.567720\pi$
$863$	−12.4057			−0.422296			−0.211148	+	0.977454i	$0.567720\pi$
$864$	0.707107	+	0.707107i	0.0240563	+	0.0240563i
$865$		−	2.88017i		−	0.0979288i
$866$	33.0289			1.12237
$867$	14.5331	+	8.81989i	0.493568	+	0.299539i
$868$	15.3890			0.522338
$869$			0.0639877i			0.00217064i
$870$	15.0411	+	15.0411i	0.509941	+	0.509941i
$871$	−32.1168			−1.08824
$872$	7.89485	+	7.89485i	0.267353	+	0.267353i
$873$	−6.97597	+	6.97597i	−0.236101	+	0.236101i
$874$	−26.4818	+	26.4818i	−0.895760	+	0.895760i
$875$		−	16.3286i		−	0.552006i
$876$		−	4.66061i		−	0.157467i
$877$	2.14167	−	2.14167i	0.0723191	−	0.0723191i	−0.670022	−	0.742341i	$-0.733715\pi$
$877$	2.14167	−	2.14167i	0.0723191	−	0.0723191i	0.742341	+	0.670022i	$0.233715\pi$
$878$	23.7573	−	23.7573i	0.801769	−	0.801769i
$879$	−5.88369	−	5.88369i	−0.198452	−	0.198452i
$880$	−3.38459			−0.114095
$881$	37.7280	+	37.7280i	1.27109	+	1.27109i	0.945518	+	0.325570i	$0.105556\pi$
$881$	37.7280	+	37.7280i	1.27109	+	1.27109i	0.325570	+	0.945518i	$0.394444\pi$
$882$			3.98689i			0.134246i
$883$	−8.86623			−0.298372			−0.149186	−	0.988809i	$-0.547665\pi$
$883$	−8.86623			−0.298372			−0.149186	+	0.988809i	$0.547665\pi$
$884$	−1.73534	−	14.3958i	−0.0583657	−	0.484184i
$885$	−24.5772			−0.826155
$886$			20.6765i			0.694641i
$887$	18.2671	+	18.2671i	0.613348	+	0.613348i	0.943817	−	0.330469i	$-0.107207\pi$
$887$	18.2671	+	18.2671i	0.613348	+	0.613348i	−0.330469	+	0.943817i	$0.607207\pi$
$888$	6.79016			0.227863
$889$	42.8190	+	42.8190i	1.43610	+	1.43610i
$890$	−18.1322	+	18.1322i	−0.607793	+	0.607793i
$891$	−0.707107	+	0.707107i	−0.0236890	+	0.0236890i
$892$			4.40601i			0.147524i
$893$			37.9289i			1.26924i
$894$	16.1570	−	16.1570i	0.540370	−	0.540370i
$895$	−48.4883	+	48.4883i	−1.62078	+	1.62078i
$896$	−2.34381	−	2.34381i	−0.0783012	−	0.0783012i
$897$	19.9070			0.664674
$898$	−7.51896	−	7.51896i	−0.250911	−	0.250911i
$899$			29.1785i			0.973156i
$900$	6.45547			0.215182
$901$	−30.7739	+	3.70963i	−1.02523	+	0.123586i
$902$	11.0753			0.368767
$903$			11.1552i			0.371223i
$904$	−4.39466	−	4.39466i	−0.146164	−	0.146164i
$905$	−60.4131			−2.00820
$906$	−4.71017	−	4.71017i	−0.156485	−	0.156485i
$907$	8.67343	−	8.67343i	0.287997	−	0.287997i	−0.548291	−	0.836288i	$-0.684721\pi$
$907$	8.67343	−	8.67343i	0.287997	−	0.287997i	0.836288	+	0.548291i	$0.184721\pi$
$908$	−14.4708	+	14.4708i	−0.480231	+	0.480231i
$909$		−	12.2443i		−	0.406116i
$910$		−	39.4538i		−	1.30788i
$911$	14.3991	−	14.3991i	0.477065	−	0.477065i	−0.427127	−	0.904192i	$-0.640474\pi$
$911$	14.3991	−	14.3991i	0.477065	−	0.477065i	0.904192	+	0.427127i	$0.140474\pi$
$912$	−4.67828	+	4.67828i	−0.154913	+	0.154913i
$913$	−6.81698	−	6.81698i	−0.225609	−	0.225609i
$914$	−25.5384			−0.844736
$915$	−8.24622	−	8.24622i	−0.272612	−	0.272612i
$916$		−	24.9524i		−	0.824451i
$917$	−6.63507			−0.219109
$918$	−2.54560	+	3.24344i	−0.0840174	+	0.107049i
$919$	−46.4180			−1.53119			−0.765595	−	0.643323i	$-0.777555\pi$
$919$	−46.4180			−1.53119			−0.765595	+	0.643323i	$0.777555\pi$
$920$		−	19.1587i		−	0.631645i
$921$	−19.1478	−	19.1478i	−0.630941	−	0.630941i
$922$	34.3772			1.13215
$923$	5.67458	+	5.67458i	0.186781	+	0.186781i
$924$	2.34381	−	2.34381i	0.0771057	−	0.0771057i
$925$	30.9951	−	30.9951i	1.01911	−	1.01911i
$926$			12.2297i			0.401893i
$927$			18.4297i			0.605312i
$928$	4.44399	−	4.44399i	0.145881	−	0.145881i
$929$	−30.1517	+	30.1517i	−0.989246	+	0.989246i	−0.999943	−	0.0106969i	$-0.996595\pi$
$929$	−30.1517	+	30.1517i	−0.989246	+	0.989246i	0.0106969	+	0.999943i	$0.496595\pi$
$930$	11.1113	+	11.1113i	0.364354	+	0.364354i
$931$	−26.3776			−0.864492
$932$	8.55964	+	8.55964i	0.280380	+	0.280380i
$933$		−	27.3068i		−	0.893984i
$934$	−12.1097			−0.396242
$935$	−1.67011	−	13.8547i	−0.0546186	−	0.453098i
$936$	3.51677			0.114949
$937$			27.4903i			0.898071i	0.893514	+	0.449035i	$0.148232\pi$
$937$			27.4903i			0.898071i	−0.893514	+	0.449035i	$0.851768\pi$
$938$	−21.4048	−	21.4048i	−0.698890	−	0.698890i
$939$	14.8196			0.483619
$940$	−13.7202	−	13.7202i	−0.447503	−	0.447503i
$941$	1.11209	−	1.11209i	0.0362531	−	0.0362531i	−0.688748	−	0.725001i	$-0.741839\pi$
$941$	1.11209	−	1.11209i	0.0362531	−	0.0362531i	0.725001	+	0.688748i	$0.241839\pi$
$942$	−7.22438	+	7.22438i	−0.235383	+	0.235383i
$943$			62.6926i			2.04155i
$944$			7.26150i			0.236342i
$945$	−7.93284	+	7.93284i	−0.258055	+	0.258055i
$946$	2.37972	−	2.37972i	0.0773714	−	0.0773714i
$947$	−13.3253	−	13.3253i	−0.433013	−	0.433013i	0.456639	−	0.889652i	$-0.349053\pi$
$947$	−13.3253	−	13.3253i	−0.433013	−	0.433013i	−0.889652	+	0.456639i	$0.849053\pi$
$948$	−0.0639877			−0.00207823
$949$	−11.5897	−	11.5897i	−0.376217	−	0.376217i
$950$			42.7100i			1.38570i
$951$	16.3856			0.531340
$952$	8.43778	−	10.7509i	0.273470	−	0.348438i
$953$	45.9580			1.48873			0.744363	−	0.667775i	$-0.232753\pi$
$953$	45.9580			1.48873			0.744363	+	0.667775i	$0.232753\pi$
$954$		−	7.51780i		−	0.243398i
$955$	30.3731	+	30.3731i	0.982850	+	0.982850i
$956$	−10.9971			−0.355671
$957$	4.44399	+	4.44399i	0.143654	+	0.143654i
$958$	7.12547	−	7.12547i	0.230214	−	0.230214i
$959$	−42.2864	+	42.2864i	−1.36550	+	1.36550i
$960$		−	3.38459i		−	0.109237i
$961$		−	9.44500i		−	0.304677i
$962$	16.8853	−	16.8853i	0.544405	−	0.544405i
$963$	7.41192	−	7.41192i	0.238846	−	0.238846i
$964$	−0.0273602	−	0.0273602i	−0.000881213	−	0.000881213i
$965$	−67.7508			−2.18098
$966$	13.2673	+	13.2673i	0.426869	+	0.426869i
$967$			46.3513i			1.49056i	0.666753	+	0.745278i	$0.267683\pi$
$967$			46.3513i			1.49056i	−0.666753	+	0.745278i	$0.732317\pi$
$968$	−1.00000			−0.0321412
$969$	−21.4589	−	16.8419i	−0.689359	−	0.541041i
$970$	33.3908			1.07211
$971$			56.1605i			1.80228i	0.433532	+	0.901138i	$0.357267\pi$
$971$			56.1605i			1.80228i	−0.433532	+	0.901138i	$0.642733\pi$
$972$	−0.707107	−	0.707107i	−0.0226805	−	0.0226805i
$973$	−29.8701			−0.957593
$974$	−3.78996	−	3.78996i	−0.121438	−	0.121438i
$975$	16.0530	−	16.0530i	0.514109	−	0.514109i
$976$	−2.43640	+	2.43640i	−0.0779872	+	0.0779872i
$977$			1.06303i			0.0340094i	0.999855	+	0.0170047i	$0.00541303\pi$
$977$			1.06303i			0.0340094i	−0.999855	+	0.0170047i	$0.994587\pi$
$978$		−	21.9539i		−	0.702009i
$979$	−5.35728	+	5.35728i	−0.171219	+	0.171219i
$980$	9.54171	−	9.54171i	0.304799	−	0.304799i
$981$	−7.89485	−	7.89485i	−0.252063	−	0.252063i
$982$	33.0313			1.05407
$983$	−7.56604	−	7.56604i	−0.241319	−	0.241319i	0.576077	−	0.817396i	$-0.304583\pi$
$983$	−7.56604	−	7.56604i	−0.241319	−	0.241319i	−0.817396	+	0.576077i	$0.804583\pi$
$984$			11.0753i			0.353068i
$985$	−44.2919			−1.41126
$986$	20.3842	+	15.9985i	0.649166	+	0.509496i
$987$	19.0023			0.604850
$988$			23.2673i			0.740231i
$989$	13.4706	+	13.4706i	0.428340	+	0.428340i
$990$	3.38459			0.107569
$991$	−16.7629	−	16.7629i	−0.532490	−	0.532490i	0.388822	−	0.921313i	$-0.372882\pi$
$991$	−16.7629	−	16.7629i	−0.532490	−	0.532490i	−0.921313	+	0.388822i	$0.872882\pi$
$992$	3.28291	−	3.28291i	0.104233	−	0.104233i
$993$	3.15328	−	3.15328i	0.100066	−	0.100066i
$994$			7.56383i			0.239910i
$995$			17.0473i			0.540437i
$996$	6.81698	−	6.81698i	0.216004	−	0.216004i
$997$	−25.8984	+	25.8984i	−0.820210	+	0.820210i	−0.986138	−	0.165928i	$-0.946938\pi$
$997$	−25.8984	+	25.8984i	−0.820210	+	0.820210i	0.165928	+	0.986138i	$0.446938\pi$
$998$	14.6255	+	14.6255i	0.462961	+	0.462961i
$999$	−6.79016			−0.214831

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1122.2.l.g.727.2	yes	20
17.4	even	4	inner	1122.2.l.g.463.2	✓	20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1122.2.l.g.463.2	✓	20	17.4	even	4	inner
1122.2.l.g.727.2	yes	20	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 1122 = 2 \cdot 3 \cdot 11 \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1122.l (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+1.00000i q^{2} +(-0.707107 - 0.707107i) q^{3} -1.00000 q^{4} +(-2.39327 - 2.39327i) q^{5} +(0.707107 - 0.707107i) q^{6} +(2.34381 - 2.34381i) q^{7} -1.00000i q^{8} +1.00000i q^{9} +O(q^{10})\)	\(q+1.00000i q^{2} +(-0.707107 - 0.707107i) q^{3} -1.00000 q^{4} +(-2.39327 - 2.39327i) q^{5} +(0.707107 - 0.707107i) q^{6} +(2.34381 - 2.34381i) q^{7} -1.00000i q^{8} +1.00000i q^{9} +(2.39327 - 2.39327i) q^{10} +(0.707107 - 0.707107i) q^{11} +(0.707107 + 0.707107i) q^{12} +3.51677 q^{13} +(2.34381 + 2.34381i) q^{14} +3.38459i q^{15} +1.00000 q^{16} +(0.493446 + 4.09347i) q^{17} -1.00000 q^{18} -6.61609i q^{19} +(2.39327 + 2.39327i) q^{20} -3.31465 q^{21} +(0.707107 + 0.707107i) q^{22} +(-4.00263 + 4.00263i) q^{23} +(-0.707107 + 0.707107i) q^{24} +6.45547i q^{25} +3.51677i q^{26} +(0.707107 - 0.707107i) q^{27} +(-2.34381 + 2.34381i) q^{28} +(-4.44399 - 4.44399i) q^{29} -3.38459 q^{30} +(-3.28291 - 3.28291i) q^{31} +1.00000i q^{32} -1.00000 q^{33} +(-4.09347 + 0.493446i) q^{34} -11.2187 q^{35} -1.00000i q^{36} +(-4.80137 - 4.80137i) q^{37} +6.61609 q^{38} +(-2.48673 - 2.48673i) q^{39} +(-2.39327 + 2.39327i) q^{40} +(7.83142 - 7.83142i) q^{41} -3.31465i q^{42} -3.36543i q^{43} +(-0.707107 + 0.707107i) q^{44} +(2.39327 - 2.39327i) q^{45} +(-4.00263 - 4.00263i) q^{46} -5.73282 q^{47} +(-0.707107 - 0.707107i) q^{48} -3.98689i q^{49} -6.45547 q^{50} +(2.54560 - 3.24344i) q^{51} -3.51677 q^{52} +7.51780i q^{53} +(0.707107 + 0.707107i) q^{54} -3.38459 q^{55} +(-2.34381 - 2.34381i) q^{56} +(-4.67828 + 4.67828i) q^{57} +(4.44399 - 4.44399i) q^{58} +7.26150i q^{59} -3.38459i q^{60} +(-2.43640 + 2.43640i) q^{61} +(3.28291 - 3.28291i) q^{62} +(2.34381 + 2.34381i) q^{63} -1.00000 q^{64} +(-8.41659 - 8.41659i) q^{65} -1.00000i q^{66} -9.13246 q^{67} +(-0.493446 - 4.09347i) q^{68} +5.66057 q^{69} -11.2187i q^{70} +(1.61357 + 1.61357i) q^{71} +1.00000 q^{72} +(-3.29555 - 3.29555i) q^{73} +(4.80137 - 4.80137i) q^{74} +(4.56471 - 4.56471i) q^{75} +6.61609i q^{76} -3.31465i q^{77} +(2.48673 - 2.48673i) q^{78} +(-0.0452462 + 0.0452462i) q^{79} +(-2.39327 - 2.39327i) q^{80} -1.00000 q^{81} +(7.83142 + 7.83142i) q^{82} -9.64066i q^{83} +3.31465 q^{84} +(8.61583 - 10.9777i) q^{85} +3.36543 q^{86} +6.28476i q^{87} +(-0.707107 - 0.707107i) q^{88} -7.57633 q^{89} +(2.39327 + 2.39327i) q^{90} +(8.24265 - 8.24265i) q^{91} +(4.00263 - 4.00263i) q^{92} +4.64274i q^{93} -5.73282i q^{94} +(-15.8341 + 15.8341i) q^{95} +(0.707107 - 0.707107i) q^{96} +(6.97597 + 6.97597i) q^{97} +3.98689 q^{98} +(0.707107 + 0.707107i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q - 20 q^{4} - 4 q^{5}+O(q^{10}) \) 20 * q - 20 * q^4 - 4 * q^5	\( 20 q - 20 q^{4} - 4 q^{5} + 4 q^{10} + 20 q^{16} - 12 q^{17} - 20 q^{18} + 4 q^{20} + 16 q^{23} + 4 q^{29} - 8 q^{31} - 20 q^{33} + 16 q^{35} - 20 q^{37} + 8 q^{39} - 4 q^{40} + 20 q^{41} + 4 q^{45} + 16 q^{46} - 16 q^{47} - 68 q^{50} + 8 q^{57} - 4 q^{58} - 20 q^{61} + 8 q^{62} - 20 q^{64} + 8 q^{65} - 48 q^{67} + 12 q^{68} - 32 q^{71} + 20 q^{72} + 20 q^{73} + 20 q^{74} - 8 q^{75} - 8 q^{78} - 16 q^{79} - 4 q^{80} - 20 q^{81} + 20 q^{82} - 4 q^{85} - 16 q^{86} + 4 q^{90} + 88 q^{91} - 16 q^{92} - 48 q^{95} + 4 q^{97} + 36 q^{98}+O(q^{100}) \) 20 * q - 20 * q^4 - 4 * q^5 + 4 * q^10 + 20 * q^16 - 12 * q^17 - 20 * q^18 + 4 * q^20 + 16 * q^23 + 4 * q^29 - 8 * q^31 - 20 * q^33 + 16 * q^35 - 20 * q^37 + 8 * q^39 - 4 * q^40 + 20 * q^41 + 4 * q^45 + 16 * q^46 - 16 * q^47 - 68 * q^50 + 8 * q^57 - 4 * q^58 - 20 * q^61 + 8 * q^62 - 20 * q^64 + 8 * q^65 - 48 * q^67 + 12 * q^68 - 32 * q^71 + 20 * q^72 + 20 * q^73 + 20 * q^74 - 8 * q^75 - 8 * q^78 - 16 * q^79 - 4 * q^80 - 20 * q^81 + 20 * q^82 - 4 * q^85 - 16 * q^86 + 4 * q^90 + 88 * q^91 - 16 * q^92 - 48 * q^95 + 4 * q^97 + 36 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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