LMFDB - Embedded newform 1950.2.i.be.601.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1950,2,Mod(451,1950)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1950, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 0, 4]))

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

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

chi := DirichletCharacter("1950.451");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1950 = 2 \cdot 3 \cdot 5^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1950.i (of order $3$, 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:	$15.5708283941$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{3})$
Coefficient field:	$\Q(\sqrt{-3}, \sqrt{11})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} + 11x^{2} + 121 $ x^4 + 11*x^2 + 121
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 390)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			601.1
Root			$-1.65831 + 2.87228i$ of defining polynomial
Character	$\chi$	$=$	1950.601
Dual form			1950.2.i.be.451.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.500000 + 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(0.500000 - 0.866025i) q^{6} +(-2.15831 + 3.73831i) q^{7} -1.00000 q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})$	\(q+(0.500000 + 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(0.500000 - 0.866025i) q^{6} +(-2.15831 + 3.73831i) q^{7} -1.00000 q^{8} +(-0.500000 + 0.866025i) q^{9} +(3.15831 + 5.47036i) q^{11} +1.00000 q^{12} +(-3.50000 + 0.866025i) q^{13} -4.31662 q^{14} +(-0.500000 - 0.866025i) q^{16} +(3.81662 - 6.61059i) q^{17} -1.00000 q^{18} +(-2.15831 + 3.73831i) q^{19} +4.31662 q^{21} +(-3.15831 + 5.47036i) q^{22} +(-0.841688 - 1.45785i) q^{23} +(0.500000 + 0.866025i) q^{24} +(-2.50000 - 2.59808i) q^{26} +1.00000 q^{27} +(-2.15831 - 3.73831i) q^{28} +(-1.50000 - 2.59808i) q^{29} -4.00000 q^{31} +(0.500000 - 0.866025i) q^{32} +(3.15831 - 5.47036i) q^{33} +7.63325 q^{34} +(-0.500000 - 0.866025i) q^{36} +(-3.81662 - 6.61059i) q^{37} -4.31662 q^{38} +(2.50000 + 2.59808i) q^{39} +(0.341688 + 0.591820i) q^{41} +(2.15831 + 3.73831i) q^{42} +(-1.15831 + 2.00626i) q^{43} -6.31662 q^{44} +(0.841688 - 1.45785i) q^{46} -1.68338 q^{47} +(-0.500000 + 0.866025i) q^{48} +(-5.81662 - 10.0747i) q^{49} -7.63325 q^{51} +(1.00000 - 3.46410i) q^{52} -4.68338 q^{53} +(0.500000 + 0.866025i) q^{54} +(2.15831 - 3.73831i) q^{56} +4.31662 q^{57} +(1.50000 - 2.59808i) q^{58} +(2.31662 - 4.01251i) q^{59} +(-0.341688 + 0.591820i) q^{61} +(-2.00000 - 3.46410i) q^{62} +(-2.15831 - 3.73831i) q^{63} +1.00000 q^{64} +6.31662 q^{66} +(3.47494 + 6.01877i) q^{67} +(3.81662 + 6.61059i) q^{68} +(-0.841688 + 1.45785i) q^{69} +(-4.15831 + 7.20241i) q^{71} +(0.500000 - 0.866025i) q^{72} -0.683375 q^{73} +(3.81662 - 6.61059i) q^{74} +(-2.15831 - 3.73831i) q^{76} -27.2665 q^{77} +(-1.00000 + 3.46410i) q^{78} -4.00000 q^{79} +(-0.500000 - 0.866025i) q^{81} +(-0.341688 + 0.591820i) q^{82} -8.31662 q^{83} +(-2.15831 + 3.73831i) q^{84} -2.31662 q^{86} +(-1.50000 + 2.59808i) q^{87} +(-3.15831 - 5.47036i) q^{88} +(5.63325 + 9.75707i) q^{89} +(4.31662 - 14.9532i) q^{91} +1.68338 q^{92} +(2.00000 + 3.46410i) q^{93} +(-0.841688 - 1.45785i) q^{94} -1.00000 q^{96} +(3.00000 - 5.19615i) q^{97} +(5.81662 - 10.0747i) q^{98} -6.31662 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 2 q^{2} - 2 q^{3} - 2 q^{4} + 2 q^{6} - 2 q^{7} - 4 q^{8} - 2 q^{9}+O(q^{10}) $ 4 * q + 2 * q^2 - 2 * q^3 - 2 * q^4 + 2 * q^6 - 2 * q^7 - 4 * q^8 - 2 * q^9	$ 4 q + 2 q^{2} - 2 q^{3} - 2 q^{4} + 2 q^{6} - 2 q^{7} - 4 q^{8} - 2 q^{9} + 6 q^{11} + 4 q^{12} - 14 q^{13} - 4 q^{14} - 2 q^{16} + 2 q^{17} - 4 q^{18} - 2 q^{19} + 4 q^{21} - 6 q^{22} - 10 q^{23} + 2 q^{24} - 10 q^{26} + 4 q^{27} - 2 q^{28} - 6 q^{29} - 16 q^{31} + 2 q^{32} + 6 q^{33} + 4 q^{34} - 2 q^{36} - 2 q^{37} - 4 q^{38} + 10 q^{39} + 8 q^{41} + 2 q^{42} + 2 q^{43} - 12 q^{44} + 10 q^{46} - 20 q^{47} - 2 q^{48} - 10 q^{49} - 4 q^{51} + 4 q^{52} - 32 q^{53} + 2 q^{54} + 2 q^{56} + 4 q^{57} + 6 q^{58} - 4 q^{59} - 8 q^{61} - 8 q^{62} - 2 q^{63} + 4 q^{64} + 12 q^{66} - 6 q^{67} + 2 q^{68} - 10 q^{69} - 10 q^{71} + 2 q^{72} - 16 q^{73} + 2 q^{74} - 2 q^{76} - 56 q^{77} - 4 q^{78} - 16 q^{79} - 2 q^{81} - 8 q^{82} - 20 q^{83} - 2 q^{84} + 4 q^{86} - 6 q^{87} - 6 q^{88} - 4 q^{89} + 4 q^{91} + 20 q^{92} + 8 q^{93} - 10 q^{94} - 4 q^{96} + 12 q^{97} + 10 q^{98} - 12 q^{99}+O(q^{100}) $ 4 * q + 2 * q^2 - 2 * q^3 - 2 * q^4 + 2 * q^6 - 2 * q^7 - 4 * q^8 - 2 * q^9 + 6 * q^11 + 4 * q^12 - 14 * q^13 - 4 * q^14 - 2 * q^16 + 2 * q^17 - 4 * q^18 - 2 * q^19 + 4 * q^21 - 6 * q^22 - 10 * q^23 + 2 * q^24 - 10 * q^26 + 4 * q^27 - 2 * q^28 - 6 * q^29 - 16 * q^31 + 2 * q^32 + 6 * q^33 + 4 * q^34 - 2 * q^36 - 2 * q^37 - 4 * q^38 + 10 * q^39 + 8 * q^41 + 2 * q^42 + 2 * q^43 - 12 * q^44 + 10 * q^46 - 20 * q^47 - 2 * q^48 - 10 * q^49 - 4 * q^51 + 4 * q^52 - 32 * q^53 + 2 * q^54 + 2 * q^56 + 4 * q^57 + 6 * q^58 - 4 * q^59 - 8 * q^61 - 8 * q^62 - 2 * q^63 + 4 * q^64 + 12 * q^66 - 6 * q^67 + 2 * q^68 - 10 * q^69 - 10 * q^71 + 2 * q^72 - 16 * q^73 + 2 * q^74 - 2 * q^76 - 56 * q^77 - 4 * q^78 - 16 * q^79 - 2 * q^81 - 8 * q^82 - 20 * q^83 - 2 * q^84 + 4 * q^86 - 6 * q^87 - 6 * q^88 - 4 * q^89 + 4 * q^91 + 20 * q^92 + 8 * q^93 - 10 * q^94 - 4 * q^96 + 12 * q^97 + 10 * q^98 - 12 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1950\mathbb{Z}\right)^\times$.

$n$	$301$	$1301$	$1327$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$1$	$1$

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 $

$2$	0.500000	+	0.866025i	0.353553	+	0.612372i
$2$	0.500000	+	0.866025i	0.353553	+	0.612372i
$3$	−0.500000	−	0.866025i	−0.288675	−	0.500000i
$3$	−0.500000	−	0.866025i	−0.288675	−	0.500000i
$4$	−0.500000	+	0.866025i	−0.250000	+	0.433013i
$5$		0			0
$5$		0			0
$6$	0.500000	−	0.866025i	0.204124	−	0.353553i
$7$	−2.15831	+	3.73831i	−0.815765	+	1.41295i	0.0930116	+	0.995665i	$0.470351\pi$
$7$	−2.15831	+	3.73831i	−0.815765	+	1.41295i	−0.908777	+	0.417282i	$0.862983\pi$
$8$	−1.00000			−0.353553
$9$	−0.500000	+	0.866025i	−0.166667	+	0.288675i
$10$		0			0
$11$	3.15831	+	5.47036i	0.952267	+	1.64937i	0.740502	+	0.672054i	$0.234588\pi$
$11$	3.15831	+	5.47036i	0.952267	+	1.64937i	0.211765	+	0.977321i	$0.432079\pi$
$12$	1.00000			0.288675
$13$	−3.50000	+	0.866025i	−0.970725	+	0.240192i
$13$	−3.50000	+	0.866025i	−0.970725	+	0.240192i
$14$	−4.31662			−1.15367
$15$		0			0
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	3.81662	−	6.61059i	0.925667	−	1.60330i	0.135183	−	0.990821i	$-0.456838\pi$
$17$	3.81662	−	6.61059i	0.925667	−	1.60330i	0.790484	−	0.612483i	$-0.209829\pi$
$18$	−1.00000			−0.235702
$19$	−2.15831	+	3.73831i	−0.495151	+	0.857626i	−0.999984	−	0.00559033i	$-0.998221\pi$
$19$	−2.15831	+	3.73831i	−0.495151	+	0.857626i	0.504834	+	0.863217i	$0.331554\pi$
$20$		0			0
$21$	4.31662			0.941965
$22$	−3.15831	+	5.47036i	−0.673354	+	1.16628i
$23$	−0.841688	−	1.45785i	−0.175504	−	0.303982i	0.764832	−	0.644230i	$-0.222822\pi$
$23$	−0.841688	−	1.45785i	−0.175504	−	0.303982i	−0.940336	+	0.340248i	$0.889489\pi$
$24$	0.500000	+	0.866025i	0.102062	+	0.176777i
$25$		0			0
$26$	−2.50000	−	2.59808i	−0.490290	−	0.509525i
$27$	1.00000			0.192450
$28$	−2.15831	−	3.73831i	−0.407883	−	0.706474i
$29$	−1.50000	−	2.59808i	−0.278543	−	0.482451i	0.692480	−	0.721437i	$-0.256518\pi$
$29$	−1.50000	−	2.59808i	−0.278543	−	0.482451i	−0.971023	+	0.238987i	$0.923185\pi$
$30$		0			0
$31$	−4.00000			−0.718421			−0.359211	−	0.933257i	$-0.616954\pi$
$31$	−4.00000			−0.718421			−0.359211	+	0.933257i	$0.616954\pi$
$32$	0.500000	−	0.866025i	0.0883883	−	0.153093i
$33$	3.15831	−	5.47036i	0.549792	−	0.952267i
$34$	7.63325			1.30909
$35$		0			0
$36$	−0.500000	−	0.866025i	−0.0833333	−	0.144338i
$37$	−3.81662	−	6.61059i	−0.627449	−	1.08677i	−0.988062	−	0.154058i	$-0.950766\pi$
$37$	−3.81662	−	6.61059i	−0.627449	−	1.08677i	0.360613	−	0.932716i	$-0.382568\pi$
$38$	−4.31662			−0.700249
$39$	2.50000	+	2.59808i	0.400320	+	0.416025i
$40$		0			0
$41$	0.341688	+	0.591820i	0.0533626	+	0.0924268i	0.891473	−	0.453074i	$-0.149673\pi$
$41$	0.341688	+	0.591820i	0.0533626	+	0.0924268i	−0.838110	+	0.545501i	$0.816339\pi$
$42$	2.15831	+	3.73831i	0.333035	+	0.576833i
$43$	−1.15831	+	2.00626i	−0.176641	+	0.305951i	−0.940728	−	0.339162i	$-0.889856\pi$
$43$	−1.15831	+	2.00626i	−0.176641	+	0.305951i	0.764087	+	0.645113i	$0.223190\pi$
$44$	−6.31662			−0.952267
$45$		0			0
$46$	0.841688	−	1.45785i	0.124100	−	0.214948i
$47$	−1.68338			−0.245546			−0.122773	−	0.992435i	$-0.539179\pi$
$47$	−1.68338			−0.245546			−0.122773	+	0.992435i	$0.539179\pi$
$48$	−0.500000	+	0.866025i	−0.0721688	+	0.125000i
$49$	−5.81662	−	10.0747i	−0.830946	−	1.43924i
$50$		0			0
$51$	−7.63325			−1.06887
$52$	1.00000	−	3.46410i	0.138675	−	0.480384i
$53$	−4.68338			−0.643311			−0.321656	−	0.946857i	$-0.604239\pi$
$53$	−4.68338			−0.643311			−0.321656	+	0.946857i	$0.604239\pi$
$54$	0.500000	+	0.866025i	0.0680414	+	0.117851i
$55$		0			0
$56$	2.15831	−	3.73831i	0.288417	−	0.499552i
$57$	4.31662			0.571751
$58$	1.50000	−	2.59808i	0.196960	−	0.341144i
$59$	2.31662	−	4.01251i	0.301599	−	0.522385i	−0.674899	−	0.737910i	$-0.735813\pi$
$59$	2.31662	−	4.01251i	0.301599	−	0.522385i	0.976498	+	0.215525i	$0.0691463\pi$
$60$		0			0
$61$	−0.341688	+	0.591820i	−0.0437486	+	0.0757748i	−0.887071	−	0.461634i	$-0.847263\pi$
$61$	−0.341688	+	0.591820i	−0.0437486	+	0.0757748i	0.843322	+	0.537409i	$0.180597\pi$
$62$	−2.00000	−	3.46410i	−0.254000	−	0.439941i
$63$	−2.15831	−	3.73831i	−0.271922	−	0.470982i
$64$	1.00000			0.125000
$65$		0			0
$66$	6.31662			0.777523
$67$	3.47494	+	6.01877i	0.424531	+	0.735310i	0.996377	−	0.0850519i	$-0.0271056\pi$
$67$	3.47494	+	6.01877i	0.424531	+	0.735310i	−0.571845	+	0.820361i	$0.693772\pi$
$68$	3.81662	+	6.61059i	0.462834	+	0.801652i
$69$	−0.841688	+	1.45785i	−0.101327	+	0.175504i
$70$		0			0
$71$	−4.15831	+	7.20241i	−0.493501	+	0.854769i	−0.999972	−	0.00748834i	$-0.997616\pi$
$71$	−4.15831	+	7.20241i	−0.493501	+	0.854769i	0.506471	+	0.862257i	$0.330950\pi$
$72$	0.500000	−	0.866025i	0.0589256	−	0.102062i
$73$	−0.683375			−0.0799830			−0.0399915	−	0.999200i	$-0.512733\pi$
$73$	−0.683375			−0.0799830			−0.0399915	+	0.999200i	$0.512733\pi$
$74$	3.81662	−	6.61059i	0.443674	−	0.768465i
$75$		0			0
$76$	−2.15831	−	3.73831i	−0.247575	−	0.428813i
$77$	−27.2665			−3.10731
$78$	−1.00000	+	3.46410i	−0.113228	+	0.392232i
$79$	−4.00000			−0.450035			−0.225018	−	0.974355i	$-0.572244\pi$
$79$	−4.00000			−0.450035			−0.225018	+	0.974355i	$0.572244\pi$
$80$		0			0
$81$	−0.500000	−	0.866025i	−0.0555556	−	0.0962250i
$82$	−0.341688	+	0.591820i	−0.0377331	+	0.0653556i
$83$	−8.31662			−0.912868			−0.456434	−	0.889757i	$-0.650874\pi$
$83$	−8.31662			−0.912868			−0.456434	+	0.889757i	$0.650874\pi$
$84$	−2.15831	+	3.73831i	−0.235491	+	0.407883i
$85$		0			0
$86$	−2.31662			−0.249808
$87$	−1.50000	+	2.59808i	−0.160817	+	0.278543i
$88$	−3.15831	−	5.47036i	−0.336677	−	0.583142i
$89$	5.63325	+	9.75707i	0.597123	+	1.03425i	0.993243	+	0.116049i	$0.0370230\pi$
$89$	5.63325	+	9.75707i	0.597123	+	1.03425i	−0.396120	+	0.918199i	$0.629644\pi$
$90$		0			0
$91$	4.31662	−	14.9532i	0.452505	−	1.56752i
$92$	1.68338			0.175504
$93$	2.00000	+	3.46410i	0.207390	+	0.359211i
$94$	−0.841688	−	1.45785i	−0.0868134	−	0.150365i
$95$		0			0
$96$	−1.00000			−0.102062
$97$	3.00000	−	5.19615i	0.304604	−	0.527589i	−0.672569	−	0.740034i	$-0.734809\pi$
$97$	3.00000	−	5.19615i	0.304604	−	0.527589i	0.977173	+	0.212445i	$0.0681426\pi$
$98$	5.81662	−	10.0747i	0.587568	−	1.01770i
$99$	−6.31662			−0.634845
$100$		0			0
$101$	0.183375	+	0.317615i	0.0182465	+	0.0316039i	0.875004	−	0.484115i	$-0.160858\pi$
$101$	0.183375	+	0.317615i	0.0182465	+	0.0316039i	−0.856758	+	0.515719i	$0.827525\pi$
$102$	−3.81662	−	6.61059i	−0.377902	−	0.654546i
$103$	−8.31662			−0.819461			−0.409731	−	0.912207i	$-0.634377\pi$
$103$	−8.31662			−0.819461			−0.409731	+	0.912207i	$0.634377\pi$
$104$	3.50000	−	0.866025i	0.343203	−	0.0849208i
$105$		0			0
$106$	−2.34169	−	4.05592i	−0.227445	−	0.393946i
$107$	−5.84169	−	10.1181i	−0.564737	−	0.978154i	−0.997074	−	0.0764414i	$-0.975644\pi$
$107$	−5.84169	−	10.1181i	−0.564737	−	0.978154i	0.432337	−	0.901712i	$-0.357689\pi$
$108$	−0.500000	+	0.866025i	−0.0481125	+	0.0833333i
$109$	−6.00000			−0.574696			−0.287348	−	0.957826i	$-0.592774\pi$
$109$	−6.00000			−0.574696			−0.287348	+	0.957826i	$0.592774\pi$
$110$		0			0
$111$	−3.81662	+	6.61059i	−0.362258	+	0.627449i
$112$	4.31662			0.407883
$113$	−8.13325	+	14.0872i	−0.765112	+	1.32521i	0.175076	+	0.984555i	$0.443983\pi$
$113$	−8.13325	+	14.0872i	−0.765112	+	1.32521i	−0.940187	+	0.340657i	$0.889350\pi$
$114$	2.15831	+	3.73831i	0.202144	+	0.350125i
$115$		0			0
$116$	3.00000			0.278543
$117$	1.00000	−	3.46410i	0.0924500	−	0.320256i
$118$	4.63325			0.426525
$119$	16.4749	+	28.5354i	1.51026	+	2.61584i
$120$		0			0
$121$	−14.4499	+	25.0279i	−1.31362	+	2.27527i
$122$	−0.683375			−0.0618699
$123$	0.341688	−	0.591820i	0.0308089	−	0.0533626i
$124$	2.00000	−	3.46410i	0.179605	−	0.311086i
$125$		0			0
$126$	2.15831	−	3.73831i	0.192278	−	0.333035i
$127$	2.00000	+	3.46410i	0.177471	+	0.307389i	0.941014	−	0.338368i	$-0.109875\pi$
$127$	2.00000	+	3.46410i	0.177471	+	0.307389i	−0.763542	+	0.645758i	$0.776542\pi$
$128$	0.500000	+	0.866025i	0.0441942	+	0.0765466i
$129$	2.31662			0.203967
$130$		0			0
$131$		0			0			−	1.00000i	$-0.5\pi$
$131$		0			0				1.00000i	$0.5\pi$
$132$	3.15831	+	5.47036i	0.274896	+	0.476134i
$133$	−9.31662	−	16.1369i	−0.807854	−	1.39924i
$134$	−3.47494	+	6.01877i	−0.300189	+	0.519942i
$135$		0			0
$136$	−3.81662	+	6.61059i	−0.327273	+	0.566853i
$137$	2.81662	−	4.87854i	0.240640	−	0.416802i	−0.720256	−	0.693708i	$-0.755976\pi$
$137$	2.81662	−	4.87854i	0.240640	−	0.416802i	0.960897	+	0.276906i	$0.0893092\pi$
$138$	−1.68338			−0.143298
$139$	−2.63325	+	4.56092i	−0.223349	+	0.386852i	−0.955823	−	0.293943i	$-0.905032\pi$
$139$	−2.63325	+	4.56092i	−0.223349	+	0.386852i	0.732474	+	0.680795i	$0.238366\pi$
$140$		0			0
$141$	0.841688	+	1.45785i	0.0708829	+	0.122773i
$142$	−8.31662			−0.697916
$143$	−15.7916	−	16.4111i	−1.32056	−	1.37236i
$144$	1.00000			0.0833333
$145$		0			0
$146$	−0.341688	−	0.591820i	−0.0282783	−	0.0489794i
$147$	−5.81662	+	10.0747i	−0.479747	+	0.830946i
$148$	7.63325			0.627449
$149$	1.81662	−	3.14649i	0.148824	−	0.257770i	−0.781969	−	0.623317i	$-0.785785\pi$
$149$	1.81662	−	3.14649i	0.148824	−	0.257770i	0.930793	+	0.365547i	$0.119118\pi$
$150$		0			0
$151$	6.94987			0.565573			0.282786	−	0.959183i	$-0.408741\pi$
$151$	6.94987			0.565573			0.282786	+	0.959183i	$0.408741\pi$
$152$	2.15831	−	3.73831i	0.175062	−	0.303217i
$153$	3.81662	+	6.61059i	0.308556	+	0.534434i
$154$	−13.6332	−	23.6135i	−1.09860	−	1.90283i
$155$		0			0
$156$	−3.50000	+	0.866025i	−0.280224	+	0.0693375i
$157$	−14.2665			−1.13859			−0.569295	−	0.822133i	$-0.692784\pi$
$157$	−14.2665			−1.13859			−0.569295	+	0.822133i	$0.692784\pi$
$158$	−2.00000	−	3.46410i	−0.159111	−	0.275589i
$159$	2.34169	+	4.05592i	0.185708	+	0.321656i
$160$		0			0
$161$	7.26650			0.572680
$162$	0.500000	−	0.866025i	0.0392837	−	0.0680414i
$163$	4.31662	−	7.47661i	0.338104	−	0.585614i	−0.645972	−	0.763361i	$-0.723548\pi$
$163$	4.31662	−	7.47661i	0.338104	−	0.585614i	0.984076	+	0.177748i	$0.0568811\pi$
$164$	−0.683375			−0.0533626
$165$		0			0
$166$	−4.15831	−	7.20241i	−0.322748	−	0.559015i
$167$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$167$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$168$	−4.31662			−0.333035
$169$	11.5000	−	6.06218i	0.884615	−	0.466321i
$170$		0			0
$171$	−2.15831	−	3.73831i	−0.165050	−	0.285875i
$172$	−1.15831	−	2.00626i	−0.0883205	−	0.152976i
$173$	7.63325	−	13.2212i	0.580345	−	1.00519i	−0.415093	−	0.909779i	$-0.636251\pi$
$173$	7.63325	−	13.2212i	0.580345	−	1.00519i	0.995438	−	0.0954084i	$-0.0304157\pi$
$174$	−3.00000			−0.227429
$175$		0			0
$176$	3.15831	−	5.47036i	0.238067	−	0.412344i
$177$	−4.63325			−0.348256
$178$	−5.63325	+	9.75707i	−0.422230	+	0.731324i
$179$	−3.79156	−	6.56718i	−0.283395	−	0.490854i	0.688824	−	0.724929i	$-0.258127\pi$
$179$	−3.79156	−	6.56718i	−0.283395	−	0.490854i	−0.972219	+	0.234075i	$0.924794\pi$
$180$		0			0
$181$	19.9499			1.48286			0.741431	−	0.671029i	$-0.234147\pi$
$181$	19.9499			1.48286			0.741431	+	0.671029i	$0.234147\pi$
$182$	15.1082	−	3.73831i	1.11989	−	0.277102i
$183$	0.683375			0.0505165
$184$	0.841688	+	1.45785i	0.0620500	+	0.107474i
$185$		0			0
$186$	−2.00000	+	3.46410i	−0.146647	+	0.254000i
$187$	48.2164			3.52593
$188$	0.841688	−	1.45785i	0.0613864	−	0.106324i
$189$	−2.15831	+	3.73831i	−0.156994	+	0.271922i
$190$		0			0
$191$	−6.31662	+	10.9407i	−0.457055	+	0.791642i	−0.998804	−	0.0488981i	$-0.984429\pi$
$191$	−6.31662	+	10.9407i	−0.457055	+	0.791642i	0.541749	+	0.840540i	$0.317762\pi$
$192$	−0.500000	−	0.866025i	−0.0360844	−	0.0625000i
$193$	1.97494	+	3.42069i	0.142159	+	0.246227i	0.928309	−	0.371809i	$-0.121262\pi$
$193$	1.97494	+	3.42069i	0.142159	+	0.246227i	−0.786150	+	0.618035i	$0.787929\pi$
$194$	6.00000			0.430775
$195$		0			0
$196$	11.6332			0.830946
$197$	6.63325	+	11.4891i	0.472599	+	0.818566i	0.999508	−	0.0313555i	$-0.00998241\pi$
$197$	6.63325	+	11.4891i	0.472599	+	0.818566i	−0.526909	+	0.849922i	$0.676649\pi$
$198$	−3.15831	−	5.47036i	−0.224451	−	0.388761i
$199$	11.1583	−	19.3268i	0.790992	−	1.37004i	−0.134362	−	0.990932i	$-0.542898\pi$
$199$	11.1583	−	19.3268i	0.790992	−	1.37004i	0.925353	−	0.379106i	$-0.123768\pi$
$200$		0			0
$201$	3.47494	−	6.01877i	0.245103	−	0.424531i
$202$	−0.183375	+	0.317615i	−0.0129022	+	0.0223473i
$203$	12.9499			0.908903
$204$	3.81662	−	6.61059i	0.267217	−	0.462834i
$205$		0			0
$206$	−4.15831	−	7.20241i	−0.289723	−	0.501816i
$207$	1.68338			0.117003
$208$	2.50000	+	2.59808i	0.173344	+	0.180144i
$209$	−27.2665			−1.88606
$210$		0			0
$211$	−4.31662	−	7.47661i	−0.297169	−	0.514711i	0.678318	−	0.734768i	$-0.262709\pi$
$211$	−4.31662	−	7.47661i	−0.297169	−	0.514711i	−0.975487	+	0.220057i	$0.929376\pi$
$212$	2.34169	−	4.05592i	0.160828	−	0.278562i
$213$	8.31662			0.569846
$214$	5.84169	−	10.1181i	0.399330	−	0.691659i
$215$		0			0
$216$	−1.00000			−0.0680414
$217$	8.63325	−	14.9532i	0.586063	−	1.01509i
$218$	−3.00000	−	5.19615i	−0.203186	−	0.351928i
$219$	0.341688	+	0.591820i	0.0230891	+	0.0399915i
$220$		0			0
$221$	−7.63325	+	26.4424i	−0.513468	+	1.77871i
$222$	−7.63325			−0.512310
$223$	3.68338	+	6.37979i	0.246657	+	0.427223i	0.962596	−	0.270940i	$-0.0873345\pi$
$223$	3.68338	+	6.37979i	0.246657	+	0.427223i	−0.715939	+	0.698163i	$0.754001\pi$
$224$	2.15831	+	3.73831i	0.144208	+	0.249776i
$225$		0			0
$226$	−16.2665			−1.08203
$227$	−14.7916	+	25.6197i	−0.981750	+	1.70044i	−0.326180	+	0.945308i	$0.605762\pi$
$227$	−14.7916	+	25.6197i	−0.981750	+	1.70044i	−0.655571	+	0.755134i	$0.727572\pi$
$228$	−2.15831	+	3.73831i	−0.142938	+	0.247575i
$229$	−12.0000			−0.792982			−0.396491	−	0.918039i	$-0.629772\pi$
$229$	−12.0000			−0.792982			−0.396491	+	0.918039i	$0.629772\pi$
$230$		0			0
$231$	13.6332	+	23.6135i	0.897002	+	1.55365i
$232$	1.50000	+	2.59808i	0.0984798	+	0.170572i
$233$	−11.3668			−0.744661			−0.372330	−	0.928100i	$-0.621441\pi$
$233$	−11.3668			−0.744661			−0.372330	+	0.928100i	$0.621441\pi$
$234$	3.50000	−	0.866025i	0.228802	−	0.0566139i
$235$		0			0
$236$	2.31662	+	4.01251i	0.150799	+	0.261192i
$237$	2.00000	+	3.46410i	0.129914	+	0.225018i
$238$	−16.4749	+	28.5354i	−1.06791	+	1.84968i
$239$	8.31662			0.537958			0.268979	−	0.963146i	$-0.413314\pi$
$239$	8.31662			0.537958			0.268979	+	0.963146i	$0.413314\pi$
$240$		0			0
$241$	12.8166	−	22.1990i	0.825591	−	1.42997i	−0.0758751	−	0.997117i	$-0.524175\pi$
$241$	12.8166	−	22.1990i	0.825591	−	1.42997i	0.901466	−	0.432849i	$-0.142492\pi$
$242$	−28.8997			−1.85775
$243$	−0.500000	+	0.866025i	−0.0320750	+	0.0555556i
$244$	−0.341688	−	0.591820i	−0.0218743	−	0.0378874i
$245$		0			0
$246$	0.683375			0.0435704
$247$	4.31662	−	14.9532i	0.274660	−	0.951451i
$248$	4.00000			0.254000
$249$	4.15831	+	7.20241i	0.263522	+	0.456434i
$250$		0			0
$251$	12.9499	−	22.4298i	0.817389	−	1.41576i	−0.0902110	−	0.995923i	$-0.528754\pi$
$251$	12.9499	−	22.4298i	0.817389	−	1.41576i	0.907600	−	0.419836i	$-0.137913\pi$
$252$	4.31662			0.271922
$253$	5.31662	−	9.20866i	0.334253	−	0.578944i
$254$	−2.00000	+	3.46410i	−0.125491	+	0.217357i
$255$		0			0
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	11.1332	+	19.2834i	0.694473	+	1.20286i	0.970358	+	0.241672i	$0.0776958\pi$
$257$	11.1332	+	19.2834i	0.694473	+	1.20286i	−0.275885	+	0.961191i	$0.588971\pi$
$258$	1.15831	+	2.00626i	0.0721134	+	0.124904i
$259$	32.9499			2.04741
$260$		0			0
$261$	3.00000			0.185695
$262$		0			0
$263$	−7.79156	−	13.4954i	−0.480448	−	0.832161i	0.519300	−	0.854592i	$-0.326193\pi$
$263$	−7.79156	−	13.4954i	−0.480448	−	0.832161i	−0.999748	+	0.0224311i	$0.992859\pi$
$264$	−3.15831	+	5.47036i	−0.194381	+	0.336677i
$265$		0			0
$266$	9.31662	−	16.1369i	0.571239	−	0.989415i
$267$	5.63325	−	9.75707i	0.344749	−	0.597123i
$268$	−6.94987			−0.424531
$269$	−6.31662	+	10.9407i	−0.385131	+	0.667067i	−0.991787	−	0.127897i	$-0.959177\pi$
$269$	−6.31662	+	10.9407i	−0.385131	+	0.667067i	0.606656	+	0.794964i	$0.292511\pi$
$270$		0			0
$271$	8.00000	+	13.8564i	0.485965	+	0.841717i	0.999870	−	0.0161307i	$-0.00513477\pi$
$271$	8.00000	+	13.8564i	0.485965	+	0.841717i	−0.513905	+	0.857847i	$0.671801\pi$
$272$	−7.63325			−0.462834
$273$	−15.1082	+	3.73831i	−0.914389	+	0.226253i
$274$	5.63325			0.340317
$275$		0			0
$276$	−0.841688	−	1.45785i	−0.0506636	−	0.0877520i
$277$	−13.5000	+	23.3827i	−0.811136	+	1.40493i	0.100933	+	0.994893i	$0.467817\pi$
$277$	−13.5000	+	23.3827i	−0.811136	+	1.40493i	−0.912069	+	0.410036i	$0.865516\pi$
$278$	−5.26650			−0.315864
$279$	2.00000	−	3.46410i	0.119737	−	0.207390i
$280$		0			0
$281$	−27.2164			−1.62359			−0.811796	−	0.583941i	$-0.801510\pi$
$281$	−27.2164			−1.62359			−0.811796	+	0.583941i	$0.801510\pi$
$282$	−0.841688	+	1.45785i	−0.0501218	+	0.0868134i
$283$	11.4749	+	19.8752i	0.682114	+	1.18146i	0.974334	+	0.225105i	$0.0722726\pi$
$283$	11.4749	+	19.8752i	0.682114	+	1.18146i	−0.292220	+	0.956351i	$0.594394\pi$
$284$	−4.15831	−	7.20241i	−0.246750	−	0.427384i
$285$		0			0
$286$	6.31662	−	21.8814i	0.373510	−	1.29388i
$287$	−2.94987			−0.174126
$288$	0.500000	+	0.866025i	0.0294628	+	0.0510310i
$289$	−20.6332	−	35.7378i	−1.21372	−	2.10223i
$290$		0			0
$291$	−6.00000			−0.351726
$292$	0.341688	−	0.591820i	0.0199958	−	0.0346337i
$293$	−10.6583	+	18.4607i	−0.622665	+	1.07849i	0.366322	+	0.930488i	$0.380617\pi$
$293$	−10.6583	+	18.4607i	−0.622665	+	1.07849i	−0.988987	+	0.148000i	$0.952717\pi$
$294$	−11.6332			−0.678465
$295$		0			0
$296$	3.81662	+	6.61059i	0.221837	+	0.384233i
$297$	3.15831	+	5.47036i	0.183264	+	0.317422i
$298$	3.63325			0.210468
$299$	4.20844	+	4.37354i	0.243380	+	0.252928i
$300$		0			0
$301$	−5.00000	−	8.66025i	−0.288195	−	0.499169i
$302$	3.47494	+	6.01877i	0.199960	+	0.346341i
$303$	0.183375	−	0.317615i	0.0105346	−	0.0182465i
$304$	4.31662			0.247575
$305$		0			0
$306$	−3.81662	+	6.61059i	−0.218182	+	0.377902i
$307$	−16.2164			−0.925517			−0.462759	−	0.886484i	$-0.653140\pi$
$307$	−16.2164			−0.925517			−0.462759	+	0.886484i	$0.653140\pi$
$308$	13.6332	−	23.6135i	0.776826	−	1.34550i
$309$	4.15831	+	7.20241i	0.236558	+	0.409731i
$310$		0			0
$311$	12.3166			0.698412			0.349206	−	0.937046i	$-0.386451\pi$
$311$	12.3166			0.698412			0.349206	+	0.937046i	$0.386451\pi$
$312$	−2.50000	−	2.59808i	−0.141535	−	0.147087i
$313$	30.0000			1.69570			0.847850	−	0.530236i	$-0.177897\pi$
$313$	30.0000			1.69570			0.847850	+	0.530236i	$0.177897\pi$
$314$	−7.13325	−	12.3552i	−0.402553	−	0.697241i
$315$		0			0
$316$	2.00000	−	3.46410i	0.112509	−	0.194871i
$317$	−3.94987			−0.221847			−0.110924	−	0.993829i	$-0.535381\pi$
$317$	−3.94987			−0.221847			−0.110924	+	0.993829i	$0.535381\pi$
$318$	−2.34169	+	4.05592i	−0.131315	+	0.227445i
$319$	9.47494	−	16.4111i	0.530495	−	0.918844i
$320$		0			0
$321$	−5.84169	+	10.1181i	−0.326051	+	0.564737i
$322$	3.63325	+	6.29297i	0.202473	+	0.350694i
$323$	16.4749	+	28.5354i	0.916690	+	1.58775i
$324$	1.00000			0.0555556
$325$		0			0
$326$	8.63325			0.478151
$327$	3.00000	+	5.19615i	0.165900	+	0.287348i
$328$	−0.341688	−	0.591820i	−0.0188665	−	0.0326778i
$329$	3.63325	−	6.29297i	0.200308	−	0.346943i
$330$		0			0
$331$	−2.63325	+	4.56092i	−0.144736	+	0.250691i	−0.929275	−	0.369390i	$-0.879567\pi$
$331$	−2.63325	+	4.56092i	−0.144736	+	0.250691i	0.784538	+	0.620081i	$0.212900\pi$
$332$	4.15831	−	7.20241i	0.228217	−	0.395284i
$333$	7.63325			0.418300
$334$		0			0
$335$		0			0
$336$	−2.15831	−	3.73831i	−0.117746	−	0.203941i
$337$	−4.68338			−0.255120			−0.127560	−	0.991831i	$-0.540714\pi$
$337$	−4.68338			−0.255120			−0.127560	+	0.991831i	$0.540714\pi$
$338$	11.0000	+	6.92820i	0.598321	+	0.376845i
$339$	16.2665			0.883475
$340$		0			0
$341$	−12.6332	−	21.8814i	−0.684129	−	1.18495i
$342$	2.15831	−	3.73831i	0.116708	−	0.202144i
$343$	20.0000			1.07990
$344$	1.15831	−	2.00626i	0.0624520	−	0.108170i
$345$		0			0
$346$	15.2665			0.820732
$347$	0.791562	−	1.37103i	0.0424933	−	0.0736005i	−0.843997	−	0.536349i	$-0.819803\pi$
$347$	0.791562	−	1.37103i	0.0424933	−	0.0736005i	0.886490	+	0.462748i	$0.153137\pi$
$348$	−1.50000	−	2.59808i	−0.0804084	−	0.139272i
$349$	−0.366750	−	0.635230i	−0.0196317	−	0.0340031i	0.856043	−	0.516905i	$-0.172916\pi$
$349$	−0.366750	−	0.635230i	−0.0196317	−	0.0340031i	−0.875674	+	0.482902i	$0.839583\pi$
$350$		0			0
$351$	−3.50000	+	0.866025i	−0.186816	+	0.0462250i
$352$	6.31662			0.336677
$353$	10.1834	+	17.6381i	0.542006	+	0.938783i	0.998789	+	0.0492041i	$0.0156685\pi$
$353$	10.1834	+	17.6381i	0.542006	+	0.938783i	−0.456782	+	0.889578i	$0.650998\pi$
$354$	−2.31662	−	4.01251i	−0.123127	−	0.213263i
$355$		0			0
$356$	−11.2665			−0.597123
$357$	16.4749	−	28.5354i	0.871946	−	1.51026i
$358$	3.79156	−	6.56718i	0.200390	−	0.347086i
$359$	−16.3166			−0.861159			−0.430579	−	0.902553i	$-0.641691\pi$
$359$	−16.3166			−0.861159			−0.430579	+	0.902553i	$0.641691\pi$
$360$		0			0
$361$	0.183375	+	0.317615i	0.00965133	+	0.0167166i
$362$	9.97494	+	17.2771i	0.524271	+	0.908064i
$363$	28.8997			1.51684
$364$	10.7916	+	11.2149i	0.565632	+	0.587822i
$365$		0			0
$366$	0.341688	+	0.591820i	0.0178603	+	0.0309349i
$367$	−9.84169	−	17.0463i	−0.513732	−	0.889810i	−0.999873	−	0.0159295i	$-0.994929\pi$
$367$	−9.84169	−	17.0463i	−0.513732	−	0.889810i	0.486141	−	0.873880i	$-0.338404\pi$
$368$	−0.841688	+	1.45785i	−0.0438760	+	0.0759955i
$369$	−0.683375			−0.0355751
$370$		0			0
$371$	10.1082	−	17.5079i	0.524791	−	0.908965i
$372$	−4.00000			−0.207390
$373$	0.500000	−	0.866025i	0.0258890	−	0.0448411i	−0.852791	−	0.522253i	$-0.825092\pi$
$373$	0.500000	−	0.866025i	0.0258890	−	0.0448411i	0.878680	+	0.477412i	$0.158425\pi$
$374$	24.1082	+	41.7566i	1.24660	+	2.15918i
$375$		0			0
$376$	1.68338			0.0868134
$377$	7.50000	+	7.79423i	0.386270	+	0.401423i
$378$	−4.31662			−0.222023
$379$	6.94987	+	12.0375i	0.356991	+	0.618327i	0.987457	−	0.157891i	$-0.0504693\pi$
$379$	6.94987	+	12.0375i	0.356991	+	0.618327i	−0.630466	+	0.776217i	$0.717136\pi$
$380$		0			0
$381$	2.00000	−	3.46410i	0.102463	−	0.177471i
$382$	−12.6332			−0.646373
$383$	3.36675	−	5.83138i	0.172033	−	0.297970i	−0.767098	−	0.641530i	$-0.778300\pi$
$383$	3.36675	−	5.83138i	0.172033	−	0.297970i	0.939130	+	0.343561i	$0.111633\pi$
$384$	0.500000	−	0.866025i	0.0255155	−	0.0441942i
$385$		0			0
$386$	−1.97494	+	3.42069i	−0.100522	+	0.174109i
$387$	−1.15831	−	2.00626i	−0.0588803	−	0.101984i
$388$	3.00000	+	5.19615i	0.152302	+	0.263795i
$389$	−15.6332			−0.792637			−0.396319	−	0.918113i	$-0.629712\pi$
$389$	−15.6332			−0.792637			−0.396319	+	0.918113i	$0.629712\pi$
$390$		0			0
$391$	−12.8496			−0.649833
$392$	5.81662	+	10.0747i	0.293784	+	0.508849i
$393$		0			0
$394$	−6.63325	+	11.4891i	−0.334178	+	0.578814i
$395$		0			0
$396$	3.15831	−	5.47036i	0.158711	−	0.274896i
$397$	−8.94987	+	15.5016i	−0.449181	+	0.778005i	−0.998333	−	0.0577179i	$-0.981618\pi$
$397$	−8.94987	+	15.5016i	−0.449181	+	0.778005i	0.549152	+	0.835723i	$0.314951\pi$
$398$	22.3166			1.11863
$399$	−9.31662	+	16.1369i	−0.466415	+	0.807854i
$400$		0			0
$401$	5.34169	+	9.25207i	0.266751	+	0.462027i	0.968021	−	0.250869i	$-0.0807165\pi$
$401$	5.34169	+	9.25207i	0.266751	+	0.462027i	−0.701270	+	0.712896i	$0.747383\pi$
$402$	6.94987			0.346628
$403$	14.0000	−	3.46410i	0.697390	−	0.172559i
$404$	−0.366750			−0.0182465
$405$		0			0
$406$	6.47494	+	11.2149i	0.321346	+	0.556587i
$407$	24.1082	−	41.7566i	1.19500	−	2.06980i
$408$	7.63325			0.377902
$409$	10.5000	−	18.1865i	0.519192	−	0.899266i	−0.480560	−	0.876962i	$-0.659566\pi$
$409$	10.5000	−	18.1865i	0.519192	−	0.899266i	0.999751	−	0.0223042i	$-0.00710022\pi$
$410$		0			0
$411$	−5.63325			−0.277868
$412$	4.15831	−	7.20241i	0.204865	−	0.354837i
$413$	10.0000	+	17.3205i	0.492068	+	0.852286i
$414$	0.841688	+	1.45785i	0.0413667	+	0.0716492i
$415$		0			0
$416$	−1.00000	+	3.46410i	−0.0490290	+	0.169842i
$417$	5.26650			0.257902
$418$	−13.6332	−	23.6135i	−0.666824	−	1.15497i
$419$	19.5831	+	33.9190i	0.956698	+	1.65705i	0.730433	+	0.682984i	$0.239318\pi$
$419$	19.5831	+	33.9190i	0.956698	+	1.65705i	0.226265	+	0.974066i	$0.427348\pi$
$420$		0			0
$421$	−37.9499			−1.84956			−0.924782	−	0.380498i	$-0.875753\pi$
$421$	−37.9499			−1.84956			−0.924782	+	0.380498i	$0.875753\pi$
$422$	4.31662	−	7.47661i	0.210130	−	0.363956i
$423$	0.841688	−	1.45785i	0.0409243	−	0.0708829i
$424$	4.68338			0.227445
$425$		0			0
$426$	4.15831	+	7.20241i	0.201471	+	0.348958i
$427$	−1.47494	−	2.55467i	−0.0713772	−	0.123629i
$428$	11.6834			0.564737
$429$	−6.31662	+	21.8814i	−0.304970	+	1.05645i
$430$		0			0
$431$	6.47494	+	11.2149i	0.311887	+	0.540204i	0.978771	−	0.204958i	$-0.0657057\pi$
$431$	6.47494	+	11.2149i	0.311887	+	0.540204i	−0.666884	+	0.745161i	$0.732372\pi$
$432$	−0.500000	−	0.866025i	−0.0240563	−	0.0416667i
$433$	−4.29156	+	7.43320i	−0.206239	+	0.357217i	−0.950527	−	0.310642i	$-0.899456\pi$
$433$	−4.29156	+	7.43320i	−0.206239	+	0.357217i	0.744288	+	0.667859i	$0.232789\pi$
$434$	17.2665			0.828818
$435$		0			0
$436$	3.00000	−	5.19615i	0.143674	−	0.248851i
$437$	7.26650			0.347604
$438$	−0.341688	+	0.591820i	−0.0163265	+	0.0282783i
$439$	19.1583	+	33.1832i	0.914376	+	1.58375i	0.807812	+	0.589441i	$0.200652\pi$
$439$	19.1583	+	33.1832i	0.914376	+	1.58375i	0.106565	+	0.994306i	$0.466015\pi$
$440$		0			0
$441$	11.6332			0.553964
$442$	−26.7164	+	6.61059i	−1.27077	+	0.314434i
$443$	13.2665			0.630310			0.315155	−	0.949040i	$-0.397943\pi$
$443$	13.2665			0.630310			0.315155	+	0.949040i	$0.397943\pi$
$444$	−3.81662	−	6.61059i	−0.181129	−	0.313725i
$445$		0			0
$446$	−3.68338	+	6.37979i	−0.174413	+	0.302092i
$447$	−3.63325			−0.171847
$448$	−2.15831	+	3.73831i	−0.101971	+	0.176618i
$449$	−8.26650	+	14.3180i	−0.390120	+	0.675708i	−0.992465	−	0.122528i	$-0.960900\pi$
$449$	−8.26650	+	14.3180i	−0.390120	+	0.675708i	0.602345	+	0.798236i	$0.294233\pi$
$450$		0			0
$451$	−2.15831	+	3.73831i	−0.101631	+	0.176030i
$452$	−8.13325	−	14.0872i	−0.382556	−	0.662606i
$453$	−3.47494	−	6.01877i	−0.163267	−	0.282786i
$454$	−29.5831			−1.38840
$455$		0			0
$456$	−4.31662			−0.202144
$457$	7.97494	+	13.8130i	0.373052	+	0.646145i	0.990033	−	0.140833i	$-0.0449780\pi$
$457$	7.97494	+	13.8130i	0.373052	+	0.646145i	−0.616982	+	0.786978i	$0.711645\pi$
$458$	−6.00000	−	10.3923i	−0.280362	−	0.485601i
$459$	3.81662	−	6.61059i	0.178145	−	0.308556i
$460$		0			0
$461$	−4.81662	+	8.34264i	−0.224333	+	0.388555i	−0.956119	−	0.292979i	$-0.905354\pi$
$461$	−4.81662	+	8.34264i	−0.224333	+	0.388555i	0.731786	+	0.681534i	$0.238687\pi$
$462$	−13.6332	+	23.6135i	−0.634276	+	1.09860i
$463$	−8.94987			−0.415936			−0.207968	−	0.978136i	$-0.566685\pi$
$463$	−8.94987			−0.415936			−0.207968	+	0.978136i	$0.566685\pi$
$464$	−1.50000	+	2.59808i	−0.0696358	+	0.120613i
$465$		0			0
$466$	−5.68338	−	9.84389i	−0.263277	−	0.456010i
$467$	33.5831			1.55404			0.777021	−	0.629475i	$-0.216730\pi$
$467$	33.5831			1.55404			0.777021	+	0.629475i	$0.216730\pi$
$468$	2.50000	+	2.59808i	0.115563	+	0.120096i
$469$	−30.0000			−1.38527
$470$		0			0
$471$	7.13325	+	12.3552i	0.328683	+	0.569295i
$472$	−2.31662	+	4.01251i	−0.106631	+	0.184691i
$473$	−14.6332			−0.672838
$474$	−2.00000	+	3.46410i	−0.0918630	+	0.159111i
$475$		0			0
$476$	−32.9499			−1.51026
$477$	2.34169	−	4.05592i	0.107219	−	0.185708i
$478$	4.15831	+	7.20241i	0.190197	+	0.329430i
$479$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$479$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$480$		0			0
$481$	19.0831	+	19.8318i	0.870116	+	0.904251i
$482$	25.6332			1.16756
$483$	−3.63325	−	6.29297i	−0.165319	−	0.286340i
$484$	−14.4499	−	25.0279i	−0.656812	−	1.13763i
$485$		0			0
$486$	−1.00000			−0.0453609
$487$	−2.15831	+	3.73831i	−0.0978025	+	0.169399i	−0.910775	−	0.412903i	$-0.864515\pi$
$487$	−2.15831	+	3.73831i	−0.0978025	+	0.169399i	0.812972	+	0.582302i	$0.197848\pi$
$488$	0.341688	−	0.591820i	0.0154675	−	0.0267904i
$489$	−8.63325			−0.390409
$490$		0			0
$491$	19.7916	+	34.2800i	0.893181	+	1.54703i	0.836040	+	0.548668i	$0.184865\pi$
$491$	19.7916	+	34.2800i	0.893181	+	1.54703i	0.0571405	+	0.998366i	$0.481802\pi$
$492$	0.341688	+	0.591820i	0.0154045	+	0.0266813i
$493$	−22.8997			−1.03135
$494$	15.1082	−	3.73831i	0.679749	−	0.168194i
$495$		0			0
$496$	2.00000	+	3.46410i	0.0898027	+	0.155543i
$497$	−17.9499	−	31.0901i	−0.805162	−	1.39458i
$498$	−4.15831	+	7.20241i	−0.186338	+	0.322748i
$499$	−41.8997			−1.87569			−0.937845	−	0.347054i	$-0.887182\pi$
$499$	−41.8997			−1.87569			−0.937845	+	0.347054i	$0.887182\pi$
$500$		0			0
$501$		0			0
$502$	25.8997			1.15596
$503$	−9.15831	+	15.8627i	−0.408349	+	0.707281i	−0.994705	−	0.102772i	$-0.967229\pi$
$503$	−9.15831	+	15.8627i	−0.408349	+	0.707281i	0.586356	+	0.810054i	$0.300562\pi$
$504$	2.15831	+	3.73831i	0.0961389	+	0.166517i
$505$		0			0
$506$	10.6332			0.472706
$507$	−11.0000	−	6.92820i	−0.488527	−	0.307692i
$508$	−4.00000			−0.177471
$509$	−18.0831	−	31.3209i	−0.801520	−	1.38827i	−0.918615	−	0.395153i	$-0.870691\pi$
$509$	−18.0831	−	31.3209i	−0.801520	−	1.38827i	0.117095	−	0.993121i	$-0.462642\pi$
$510$		0			0
$511$	1.47494	−	2.55467i	0.0652474	−	0.113012i
$512$	−1.00000			−0.0441942
$513$	−2.15831	+	3.73831i	−0.0952918	+	0.165050i
$514$	−11.1332	+	19.2834i	−0.491067	+	0.850552i
$515$		0			0
$516$	−1.15831	+	2.00626i	−0.0509919	+	0.0883205i
$517$	−5.31662	−	9.20866i	−0.233825	−	0.404997i
$518$	16.4749	+	28.5354i	0.723867	+	1.25377i
$519$	−15.2665			−0.670125
$520$		0			0
$521$	−20.0501			−0.878412			−0.439206	−	0.898386i	$-0.644740\pi$
$521$	−20.0501			−0.878412			−0.439206	+	0.898386i	$0.644740\pi$
$522$	1.50000	+	2.59808i	0.0656532	+	0.113715i
$523$	12.4248	+	21.5204i	0.543299	+	0.941022i	0.998712	+	0.0507412i	$0.0161584\pi$
$523$	12.4248	+	21.5204i	0.543299	+	0.941022i	−0.455413	+	0.890280i	$0.650508\pi$
$524$		0			0
$525$		0			0
$526$	7.79156	−	13.4954i	0.339728	−	0.588427i
$527$	−15.2665	+	26.4424i	−0.665019	+	1.15185i
$528$	−6.31662			−0.274896
$529$	10.0831	−	17.4645i	0.438397	−	0.759325i
$530$		0			0
$531$	2.31662	+	4.01251i	0.100533	+	0.174128i
$532$	18.6332			0.807854
$533$	−1.70844	−	1.77546i	−0.0740007	−	0.0769037i
$534$	11.2665			0.487549
$535$		0			0
$536$	−3.47494	−	6.01877i	−0.150094	−	0.259971i
$537$	−3.79156	+	6.56718i	−0.163618	+	0.283395i
$538$	−12.6332			−0.544658
$539$	36.7414	−	63.6380i	1.58257	−	2.74108i
$540$		0			0
$541$	25.2164			1.08414			0.542068	−	0.840334i	$-0.317641\pi$
$541$	25.2164			1.08414			0.542068	+	0.840334i	$0.317641\pi$
$542$	−8.00000	+	13.8564i	−0.343629	+	0.595184i
$543$	−9.97494	−	17.2771i	−0.428066	−	0.741431i
$544$	−3.81662	−	6.61059i	−0.163636	−	0.283427i
$545$		0			0
$546$	−10.7916	−	11.2149i	−0.461836	−	0.479954i
$547$	−30.9499			−1.32332			−0.661661	−	0.749804i	$-0.730148\pi$
$547$	−30.9499			−1.32332			−0.661661	+	0.749804i	$0.730148\pi$
$548$	2.81662	+	4.87854i	0.120320	+	0.208401i
$549$	−0.341688	−	0.591820i	−0.0145829	−	0.0252583i
$550$		0			0
$551$	12.9499			0.551683
$552$	0.841688	−	1.45785i	0.0358246	−	0.0620500i
$553$	8.63325	−	14.9532i	0.367123	−	0.635876i
$554$	−27.0000			−1.14712
$555$		0			0
$556$	−2.63325	−	4.56092i	−0.111675	−	0.193426i
$557$	19.6583	+	34.0492i	0.832949	+	1.44271i	0.895689	+	0.444681i	$0.146683\pi$
$557$	19.6583	+	34.0492i	0.832949	+	1.44271i	−0.0627397	+	0.998030i	$0.519984\pi$
$558$	4.00000			0.169334
$559$	2.31662	−	8.02502i	0.0979828	−	0.339422i
$560$		0			0
$561$	−24.1082	−	41.7566i	−1.01785	−	1.76297i
$562$	−13.6082	−	23.5701i	−0.574027	−	0.994243i
$563$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$563$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$564$	−1.68338			−0.0708829
$565$		0			0
$566$	−11.4749	+	19.8752i	−0.482328	+	0.835416i
$567$	4.31662			0.181281
$568$	4.15831	−	7.20241i	0.174479	−	0.302206i
$569$	21.2665	+	36.8347i	0.891538	+	1.54419i	0.838032	+	0.545622i	$0.183706\pi$
$569$	21.2665	+	36.8347i	0.891538	+	1.54419i	0.0535064	+	0.998568i	$0.482960\pi$
$570$		0			0
$571$	−28.9499			−1.21151			−0.605757	−	0.795650i	$-0.707130\pi$
$571$	−28.9499			−1.21151			−0.605757	+	0.795650i	$0.707130\pi$
$572$	22.1082	−	5.47036i	0.924390	−	0.228727i
$573$	12.6332			0.527762
$574$	−1.47494	−	2.55467i	−0.0615627	−	0.106630i
$575$		0			0
$576$	−0.500000	+	0.866025i	−0.0208333	+	0.0360844i
$577$	24.0501			1.00122			0.500610	−	0.865673i	$-0.333109\pi$
$577$	24.0501			1.00122			0.500610	+	0.865673i	$0.333109\pi$
$578$	20.6332	−	35.7378i	0.858230	−	1.48650i
$579$	1.97494	−	3.42069i	0.0820756	−	0.142159i
$580$		0			0
$581$	17.9499	−	31.0901i	0.744686	−	1.28983i
$582$	−3.00000	−	5.19615i	−0.124354	−	0.215387i
$583$	−14.7916	−	25.6197i	−0.612604	−	1.06106i
$584$	0.683375			0.0282783
$585$		0			0
$586$	−21.3166			−0.880582
$587$	−9.26650	−	16.0500i	−0.382469	−	0.662456i	0.608945	−	0.793212i	$-0.291593\pi$
$587$	−9.26650	−	16.0500i	−0.382469	−	0.662456i	−0.991415	+	0.130756i	$0.958260\pi$
$588$	−5.81662	−	10.0747i	−0.239874	−	0.415473i
$589$	8.63325	−	14.9532i	0.355727	−	0.616137i
$590$		0			0
$591$	6.63325	−	11.4891i	0.272855	−	0.472599i
$592$	−3.81662	+	6.61059i	−0.156862	+	0.271693i
$593$	4.36675			0.179321			0.0896605	−	0.995972i	$-0.471422\pi$
$593$	4.36675			0.179321			0.0896605	+	0.995972i	$0.471422\pi$
$594$	−3.15831	+	5.47036i	−0.129587	+	0.224451i
$595$		0			0
$596$	1.81662	+	3.14649i	0.0744119	+	0.128885i
$597$	−22.3166			−0.913359
$598$	−1.68338	+	5.83138i	−0.0688383	+	0.238463i
$599$	−25.2665			−1.03236			−0.516181	−	0.856480i	$-0.672647\pi$
$599$	−25.2665			−1.03236			−0.516181	+	0.856480i	$0.672647\pi$
$600$		0			0
$601$	−16.5000	−	28.5788i	−0.673049	−	1.16576i	−0.977035	−	0.213079i	$-0.931651\pi$
$601$	−16.5000	−	28.5788i	−0.673049	−	1.16576i	0.303986	−	0.952676i	$-0.401682\pi$
$602$	5.00000	−	8.66025i	0.203785	−	0.352966i
$603$	−6.94987			−0.283021
$604$	−3.47494	+	6.01877i	−0.141393	+	0.244900i
$605$		0			0
$606$	0.366750			0.0148982
$607$	−12.9499	+	22.4298i	−0.525619	+	0.910399i	0.473936	+	0.880560i	$0.342833\pi$
$607$	−12.9499	+	22.4298i	−0.525619	+	0.910399i	−0.999555	+	0.0298396i	$0.990500\pi$
$608$	2.15831	+	3.73831i	0.0875311	+	0.151608i
$609$	−6.47494	−	11.2149i	−0.262378	−	0.454451i
$610$		0			0
$611$	5.89181	−	1.45785i	0.238357	−	0.0589781i
$612$	−7.63325			−0.308556
$613$	17.4499	+	30.2241i	0.704794	+	1.22074i	0.966766	+	0.255663i	$0.0822938\pi$
$613$	17.4499	+	30.2241i	0.704794	+	1.22074i	−0.261972	+	0.965075i	$0.584373\pi$
$614$	−8.10819	−	14.0438i	−0.327220	−	0.566761i
$615$		0			0
$616$	27.2665			1.09860
$617$	2.13325	−	3.69490i	0.0858814	−	0.148751i	−0.819885	−	0.572528i	$-0.805963\pi$
$617$	2.13325	−	3.69490i	0.0858814	−	0.148751i	0.905766	+	0.423777i	$0.139296\pi$
$618$	−4.15831	+	7.20241i	−0.167272	+	0.289723i
$619$	−35.1662			−1.41345			−0.706725	−	0.707488i	$-0.749828\pi$
$619$	−35.1662			−1.41345			−0.706725	+	0.707488i	$0.749828\pi$
$620$		0			0
$621$	−0.841688	−	1.45785i	−0.0337758	−	0.0585013i
$622$	6.15831	+	10.6665i	0.246926	+	0.427688i
$623$	−48.6332			−1.94845
$624$	1.00000	−	3.46410i	0.0400320	−	0.138675i
$625$		0			0
$626$	15.0000	+	25.9808i	0.599521	+	1.03840i
$627$	13.6332	+	23.6135i	0.544460	+	0.943032i
$628$	7.13325	−	12.3552i	0.284648	−	0.493024i
$629$	−58.2665			−2.32324
$630$		0			0
$631$	10.0000	−	17.3205i	0.398094	−	0.689519i	−0.595397	−	0.803432i	$-0.703005\pi$
$631$	10.0000	−	17.3205i	0.398094	−	0.689519i	0.993491	+	0.113913i	$0.0363385\pi$
$632$	4.00000			0.159111
$633$	−4.31662	+	7.47661i	−0.171570	+	0.297169i
$634$	−1.97494	−	3.42069i	−0.0784348	−	0.135853i
$635$		0			0
$636$	−4.68338			−0.185708
$637$	29.0831	+	30.2241i	1.15232	+	1.19752i
$638$	18.9499			0.750233
$639$	−4.15831	−	7.20241i	−0.164500	−	0.284923i
$640$		0			0
$641$	−6.60819	+	11.4457i	−0.261008	+	0.452079i	−0.966510	−	0.256629i	$-0.917388\pi$
$641$	−6.60819	+	11.4457i	−0.261008	+	0.452079i	0.705502	+	0.708708i	$0.250721\pi$
$642$	−11.6834			−0.461106
$643$	−7.36675	+	12.7596i	−0.290516	+	0.503189i	−0.973932	−	0.226841i	$-0.927160\pi$
$643$	−7.36675	+	12.7596i	−0.290516	+	0.503189i	0.683416	+	0.730030i	$0.260494\pi$
$644$	−3.63325	+	6.29297i	−0.143170	+	0.247978i
$645$		0			0
$646$	−16.4749	+	28.5354i	−0.648198	+	1.12271i
$647$	−18.9499	−	32.8221i	−0.744996	−	1.29037i	−0.950196	−	0.311652i	$-0.899118\pi$
$647$	−18.9499	−	32.8221i	−0.744996	−	1.29037i	0.205200	−	0.978720i	$-0.434216\pi$
$648$	0.500000	+	0.866025i	0.0196419	+	0.0340207i
$649$	29.2665			1.14881
$650$		0			0
$651$	−17.2665			−0.676727
$652$	4.31662	+	7.47661i	0.169052	+	0.292807i
$653$	13.6332	+	23.6135i	0.533510	+	0.924067i	0.999234	+	0.0391367i	$0.0124608\pi$
$653$	13.6332	+	23.6135i	0.533510	+	0.924067i	−0.465724	+	0.884930i	$0.654206\pi$
$654$	−3.00000	+	5.19615i	−0.117309	+	0.203186i
$655$		0			0
$656$	0.341688	−	0.591820i	0.0133407	−	0.0231067i
$657$	0.341688	−	0.591820i	0.0133305	−	0.0230891i
$658$	7.26650			0.283278
$659$	−14.3166	+	24.7971i	−0.557697	+	0.965959i	0.439992	+	0.898002i	$0.354981\pi$
$659$	−14.3166	+	24.7971i	−0.557697	+	0.965959i	−0.997688	+	0.0679569i	$0.978352\pi$
$660$		0			0
$661$	5.97494	+	10.3489i	0.232398	+	0.402525i	0.958513	−	0.285048i	$-0.0920094\pi$
$661$	5.97494	+	10.3489i	0.232398	+	0.402525i	−0.726115	+	0.687573i	$0.758676\pi$
$662$	−5.26650			−0.204688
$663$	26.7164	−	6.61059i	1.03758	−	0.256734i
$664$	8.31662			0.322748
$665$		0			0
$666$	3.81662	+	6.61059i	0.147891	+	0.256155i
$667$	−2.52506	+	4.37354i	−0.0977708	+	0.169344i
$668$		0			0
$669$	3.68338	−	6.37979i	0.142408	−	0.246657i
$670$		0			0
$671$	−4.31662			−0.166641
$672$	2.15831	−	3.73831i	0.0832587	−	0.144208i
$673$	−18.9248	−	32.7787i	−0.729498	−	1.26353i	−0.957096	−	0.289772i	$-0.906420\pi$
$673$	−18.9248	−	32.7787i	−0.729498	−	1.26353i	0.227598	−	0.973755i	$-0.426913\pi$
$674$	−2.34169	−	4.05592i	−0.0901984	−	0.156228i
$675$		0			0
$676$	−0.500000	+	12.9904i	−0.0192308	+	0.499630i
$677$	27.2665			1.04794			0.523968	−	0.851738i	$-0.324451\pi$
$677$	27.2665			1.04794			0.523968	+	0.851738i	$0.324451\pi$
$678$	8.13325	+	14.0872i	0.312356	+	0.541016i
$679$	12.9499	+	22.4298i	0.496971	+	0.860778i
$680$		0			0
$681$	29.5831			1.13363
$682$	12.6332	−	21.8814i	0.483752	−	0.837883i
$683$	−0.633250	+	1.09682i	−0.0242306	+	0.0419687i	−0.877886	−	0.478869i	$-0.841047\pi$
$683$	−0.633250	+	1.09682i	−0.0242306	+	0.0419687i	0.853656	+	0.520838i	$0.174380\pi$
$684$	4.31662			0.165050
$685$		0			0
$686$	10.0000	+	17.3205i	0.381802	+	0.661300i
$687$	6.00000	+	10.3923i	0.228914	+	0.396491i
$688$	2.31662			0.0883205
$689$	16.3918	−	4.05592i	0.624478	−	0.154518i
$690$		0			0
$691$	17.4248	+	30.1807i	0.662871	+	1.14813i	0.979858	+	0.199696i	$0.0639956\pi$
$691$	17.4248	+	30.1807i	0.662871	+	1.14813i	−0.316987	+	0.948430i	$0.602671\pi$
$692$	7.63325	+	13.2212i	0.290173	+	0.502594i
$693$	13.6332	−	23.6135i	0.517884	−	0.897002i
$694$	1.58312			0.0600946
$695$		0			0
$696$	1.50000	−	2.59808i	0.0568574	−	0.0984798i
$697$	5.21637			0.197584
$698$	0.366750	−	0.635230i	0.0138817	−	0.0240438i
$699$	5.68338	+	9.84389i	0.214965	+	0.372330i
$700$		0			0
$701$	−15.3668			−0.580394			−0.290197	−	0.956967i	$-0.593721\pi$
$701$	−15.3668			−0.580394			−0.290197	+	0.956967i	$0.593721\pi$
$702$	−2.50000	−	2.59808i	−0.0943564	−	0.0980581i
$703$	32.9499			1.24273
$704$	3.15831	+	5.47036i	0.119033	+	0.206172i
$705$		0			0
$706$	−10.1834	+	17.6381i	−0.383256	+	0.663820i
$707$	−1.58312			−0.0595395
$708$	2.31662	−	4.01251i	0.0870641	−	0.150799i
$709$	0.974937	−	1.68864i	0.0366145	−	0.0634182i	−0.847137	−	0.531374i	$-0.821676\pi$
$709$	0.974937	−	1.68864i	0.0366145	−	0.0634182i	0.883752	+	0.467956i	$0.155009\pi$
$710$		0			0
$711$	2.00000	−	3.46410i	0.0750059	−	0.129914i
$712$	−5.63325	−	9.75707i	−0.211115	−	0.365662i
$713$	3.36675	+	5.83138i	0.126086	+	0.218387i
$714$	32.9499			1.23312
$715$		0			0
$716$	7.58312			0.283395
$717$	−4.15831	−	7.20241i	−0.155295	−	0.268979i
$718$	−8.15831	−	14.1306i	−0.304466	−	0.527350i
$719$	12.3166	−	21.3330i	0.459333	−	0.795587i	−0.539593	−	0.841926i	$-0.681422\pi$
$719$	12.3166	−	21.3330i	0.459333	−	0.795587i	0.998926	+	0.0463385i	$0.0147553\pi$
$720$		0			0
$721$	17.9499	−	31.0901i	0.668488	−	1.15786i
$722$	−0.183375	+	0.317615i	−0.00682452	+	0.0118204i
$723$	−25.6332			−0.953311
$724$	−9.97494	+	17.2771i	−0.370716	+	0.642098i
$725$		0			0
$726$	14.4499	+	25.0279i	0.536285	+	0.928873i
$727$	14.8496			0.550742			0.275371	−	0.961338i	$-0.411199\pi$
$727$	14.8496			0.550742			0.275371	+	0.961338i	$0.411199\pi$
$728$	−4.31662	+	14.9532i	−0.159985	+	0.554203i
$729$	1.00000			0.0370370
$730$		0			0
$731$	8.84169	+	15.3143i	0.327022	+	0.566418i
$732$	−0.341688	+	0.591820i	−0.0126291	+	0.0218743i
$733$	−1.00000			−0.0369358			−0.0184679	−	0.999829i	$-0.505879\pi$
$733$	−1.00000			−0.0369358			−0.0184679	+	0.999829i	$0.505879\pi$
$734$	9.84169	−	17.0463i	0.363263	−	0.629191i
$735$		0			0
$736$	−1.68338			−0.0620500
$737$	−21.9499	+	38.0183i	−0.808534	+	1.40042i
$738$	−0.341688	−	0.591820i	−0.0125777	−	0.0217852i
$739$	8.00000	+	13.8564i	0.294285	+	0.509716i	0.974818	−	0.223001i	$-0.0715853\pi$
$739$	8.00000	+	13.8564i	0.294285	+	0.509716i	−0.680534	+	0.732717i	$0.738252\pi$
$740$		0			0
$741$	−15.1082	+	3.73831i	−0.555013	+	0.137330i
$742$	20.2164			0.742166
$743$	0.316625	+	0.548410i	0.0116158	+	0.0201192i	0.871775	−	0.489907i	$-0.162969\pi$
$743$	0.316625	+	0.548410i	0.0116158	+	0.0201192i	−0.860159	+	0.510026i	$0.829636\pi$
$744$	−2.00000	−	3.46410i	−0.0733236	−	0.127000i
$745$		0			0
$746$	1.00000			0.0366126
$747$	4.15831	−	7.20241i	0.152145	−	0.263522i
$748$	−24.1082	+	41.7566i	−0.881483	+	1.52677i
$749$	50.4327			1.84277
$750$		0			0
$751$	−12.4248	−	21.5204i	−0.453388	−	0.785291i	0.545206	−	0.838302i	$-0.316451\pi$
$751$	−12.4248	−	21.5204i	−0.453388	−	0.785291i	−0.998594	+	0.0530113i	$0.983118\pi$
$752$	0.841688	+	1.45785i	0.0306932	+	0.0531622i
$753$	−25.8997			−0.943839
$754$	−3.00000	+	10.3923i	−0.109254	+	0.378465i
$755$		0			0
$756$	−2.15831	−	3.73831i	−0.0784971	−	0.135961i
$757$	−1.05013	−	1.81887i	−0.0381675	−	0.0661080i	0.846311	−	0.532690i	$-0.178819\pi$
$757$	−1.05013	−	1.81887i	−0.0381675	−	0.0661080i	−0.884478	+	0.466582i	$0.845485\pi$
$758$	−6.94987	+	12.0375i	−0.252431	+	0.437223i
$759$	−10.6332			−0.385963
$760$		0			0
$761$	−9.63325	+	16.6853i	−0.349205	+	0.604841i	−0.986108	−	0.166103i	$-0.946882\pi$
$761$	−9.63325	+	16.6853i	−0.349205	+	0.604841i	0.636903	+	0.770944i	$0.280215\pi$
$762$	4.00000			0.144905
$763$	12.9499	−	22.4298i	0.468817	−	0.812015i
$764$	−6.31662	−	10.9407i	−0.228527	−	0.395821i
$765$		0			0
$766$	6.73350			0.243291
$767$	−4.63325	+	16.0500i	−0.167297	+	0.579534i
$768$	1.00000			0.0360844
$769$	4.94987	+	8.57343i	0.178497	+	0.309166i	0.941366	−	0.337387i	$-0.109543\pi$
$769$	4.94987	+	8.57343i	0.178497	+	0.309166i	−0.762869	+	0.646553i	$0.776210\pi$
$770$		0			0
$771$	11.1332	−	19.2834i	0.400954	−	0.694473i
$772$	−3.94987			−0.142159
$773$	9.63325	−	16.6853i	0.346484	−	0.600128i	−0.639138	−	0.769092i	$-0.720709\pi$
$773$	9.63325	−	16.6853i	0.346484	−	0.600128i	0.985622	+	0.168964i	$0.0540422\pi$
$774$	1.15831	−	2.00626i	0.0416347	−	0.0721134i
$775$		0			0
$776$	−3.00000	+	5.19615i	−0.107694	+	0.186531i
$777$	−16.4749	−	28.5354i	−0.591035	−	1.02370i
$778$	−7.81662	−	13.5388i	−0.280240	−	0.485389i
$779$	−2.94987			−0.105690
$780$		0			0
$781$	−52.5330			−1.87978
$782$	−6.42481	−	11.1281i	−0.229751	−	0.397940i
$783$	−1.50000	−	2.59808i	−0.0536056	−	0.0928477i
$784$	−5.81662	+	10.0747i	−0.207737	+	0.359810i
$785$		0			0
$786$		0			0
$787$	−3.68338	+	6.37979i	−0.131298	+	0.227415i	−0.924177	−	0.381964i	$-0.875248\pi$
$787$	−3.68338	+	6.37979i	−0.131298	+	0.227415i	0.792879	+	0.609379i	$0.208581\pi$
$788$	−13.2665			−0.472599
$789$	−7.79156	+	13.4954i	−0.277387	+	0.480448i
$790$		0			0
$791$	−35.1082	−	60.8092i	−1.24830	−	2.16212i
$792$	6.31662			0.224451
$793$	0.683375	−	2.36728i	0.0242674	−	0.0840646i
$794$	−17.8997			−0.635238
$795$		0			0
$796$	11.1583	+	19.3268i	0.395496	+	0.685019i
$797$	−19.2665	+	33.3706i	−0.682454	+	1.18205i	0.291775	+	0.956487i	$0.405754\pi$
$797$	−19.2665	+	33.3706i	−0.682454	+	1.18205i	−0.974230	+	0.225559i	$0.927579\pi$
$798$	−18.6332			−0.659610
$799$	−6.42481	+	11.1281i	−0.227293	+	0.393684i
$800$		0			0
$801$	−11.2665			−0.398082
$802$	−5.34169	+	9.25207i	−0.188622	+	0.326702i
$803$	−2.15831	−	3.73831i	−0.0761652	−	0.131922i
$804$	3.47494	+	6.01877i	0.122552	+	0.212266i
$805$		0			0
$806$	10.0000	+	10.3923i	0.352235	+	0.366053i
$807$	12.6332			0.444711
$808$	−0.183375	−	0.317615i	−0.00645112	−	0.0111737i
$809$	−3.70844	−	6.42320i	−0.130382	−	0.225828i	0.793442	−	0.608646i	$-0.208287\pi$
$809$	−3.70844	−	6.42320i	−0.130382	−	0.225828i	−0.923824	+	0.382818i	$0.874954\pi$
$810$		0			0
$811$	−4.00000			−0.140459			−0.0702295	−	0.997531i	$-0.522373\pi$
$811$	−4.00000			−0.140459			−0.0702295	+	0.997531i	$0.522373\pi$
$812$	−6.47494	+	11.2149i	−0.227226	+	0.393567i
$813$	8.00000	−	13.8564i	0.280572	−	0.485965i
$814$	48.2164			1.68998
$815$		0			0
$816$	3.81662	+	6.61059i	0.133609	+	0.231417i
$817$	−5.00000	−	8.66025i	−0.174928	−	0.302984i
$818$	21.0000			0.734248
$819$	10.7916	+	11.2149i	0.377088	+	0.391881i
$820$		0			0
$821$	−15.5831	−	26.9908i	−0.543855	−	0.941984i	−0.998678	−	0.0514024i	$-0.983631\pi$
$821$	−15.5831	−	26.9908i	−0.543855	−	0.941984i	0.454823	−	0.890582i	$-0.349702\pi$
$822$	−2.81662	−	4.87854i	−0.0982411	−	0.170159i
$823$	−3.05013	+	5.28297i	−0.106321	+	0.184153i	−0.914277	−	0.405090i	$-0.867240\pi$
$823$	−3.05013	+	5.28297i	−0.106321	+	0.184153i	0.807956	+	0.589242i	$0.200574\pi$
$824$	8.31662			0.289723
$825$		0			0
$826$	−10.0000	+	17.3205i	−0.347945	+	0.602658i
$827$	1.26650			0.0440405			0.0220202	−	0.999758i	$-0.492990\pi$
$827$	1.26650			0.0440405			0.0220202	+	0.999758i	$0.492990\pi$
$828$	−0.841688	+	1.45785i	−0.0292507	+	0.0506636i
$829$	17.6583	+	30.5851i	0.613299	+	1.06226i	0.990680	+	0.136207i	$0.0434911\pi$
$829$	17.6583	+	30.5851i	0.613299	+	1.06226i	−0.377382	+	0.926058i	$0.623176\pi$
$830$		0			0
$831$	27.0000			0.936620
$832$	−3.50000	+	0.866025i	−0.121341	+	0.0300240i
$833$	−88.7995			−3.07672
$834$	2.63325	+	4.56092i	0.0911820	+	0.157932i
$835$		0			0
$836$	13.6332	−	23.6135i	0.471516	−	0.816689i
$837$	−4.00000			−0.138260
$838$	−19.5831	+	33.9190i	−0.676488	+	1.17171i
$839$	13.6834	−	23.7003i	0.472403	−	0.818225i	−0.527099	−	0.849804i	$-0.676720\pi$
$839$	13.6834	−	23.7003i	0.472403	−	0.818225i	0.999501	+	0.0315788i	$0.0100535\pi$
$840$		0			0
$841$	10.0000	−	17.3205i	0.344828	−	0.597259i
$842$	−18.9749	−	32.8656i	−0.653920	−	1.13262i
$843$	13.6082	+	23.5701i	0.468691	+	0.811796i
$844$	8.63325			0.297169
$845$		0			0
$846$	1.68338			0.0578756
$847$	−62.3747	−	108.036i	−2.14322	−	3.71217i
$848$	2.34169	+	4.05592i	0.0804139	+	0.139281i
$849$	11.4749	−	19.8752i	0.393819	−	0.682114i
$850$		0			0
$851$	−6.42481	+	11.1281i	−0.220240	+	0.381466i
$852$	−4.15831	+	7.20241i	−0.142461	+	0.246750i
$853$	44.8997			1.53734			0.768669	−	0.639647i	$-0.220919\pi$
$853$	44.8997			1.53734			0.768669	+	0.639647i	$0.220919\pi$
$854$	1.47494	−	2.55467i	0.0504713	−	0.0874189i
$855$		0			0
$856$	5.84169	+	10.1181i	0.199665	+	0.345830i
$857$	0.266499			0.00910344			0.00455172	−	0.999990i	$-0.498551\pi$
$857$	0.266499			0.00910344			0.00455172	+	0.999990i	$0.498551\pi$
$858$	−22.1082	+	5.47036i	−0.754761	+	0.186755i
$859$	26.8496			0.916097			0.458049	−	0.888927i	$-0.348549\pi$
$859$	26.8496			0.916097			0.458049	+	0.888927i	$0.348549\pi$
$860$		0			0
$861$	1.47494	+	2.55467i	0.0502657	+	0.0870628i
$862$	−6.47494	+	11.2149i	−0.220537	+	0.381982i
$863$	33.4829			1.13977			0.569885	−	0.821724i	$-0.306988\pi$
$863$	33.4829			1.13977			0.569885	+	0.821724i	$0.306988\pi$
$864$	0.500000	−	0.866025i	0.0170103	−	0.0294628i
$865$		0			0
$866$	−8.58312			−0.291666
$867$	−20.6332	+	35.7378i	−0.700742	+	1.21372i
$868$	8.63325	+	14.9532i	0.293032	+	0.507546i
$869$	−12.6332	−	21.8814i	−0.428554	−	0.742277i
$870$		0			0
$871$	−17.3747	−	18.0563i	−0.588719	−	0.611814i
$872$	6.00000			0.203186
$873$	3.00000	+	5.19615i	0.101535	+	0.175863i
$874$	3.63325	+	6.29297i	0.122897	+	0.212863i
$875$		0			0
$876$	−0.683375			−0.0230891
$877$	19.1332	−	33.1398i	0.646084	−	1.11905i	−0.337966	−	0.941158i	$-0.609739\pi$
$877$	19.1332	−	33.1398i	0.646084	−	1.11905i	0.984050	−	0.177892i	$-0.0569277\pi$
$878$	−19.1583	+	33.1832i	−0.646562	+	1.11988i
$879$	21.3166			0.718992
$880$		0			0
$881$	−22.6583	−	39.2453i	−0.763378	−	1.32221i	−0.941100	−	0.338129i	$-0.890206\pi$
$881$	−22.6583	−	39.2453i	−0.763378	−	1.32221i	0.177722	−	0.984081i	$-0.443127\pi$
$882$	5.81662	+	10.0747i	0.195856	+	0.339232i
$883$	−27.3668			−0.920964			−0.460482	−	0.887669i	$-0.652323\pi$
$883$	−27.3668			−0.920964			−0.460482	+	0.887669i	$0.652323\pi$
$884$	−19.0831	−	19.8318i	−0.641835	−	0.667014i
$885$		0			0
$886$	6.63325	+	11.4891i	0.222848	+	0.385985i
$887$	−20.6332	−	35.7378i	−0.692797	−	1.19996i	−0.970918	−	0.239413i	$-0.923045\pi$
$887$	−20.6332	−	35.7378i	−0.692797	−	1.19996i	0.278121	−	0.960546i	$-0.410288\pi$
$888$	3.81662	−	6.61059i	0.128078	−	0.221837i
$889$	−17.2665			−0.579100
$890$		0			0
$891$	3.15831	−	5.47036i	0.105807	−	0.183264i
$892$	−7.36675			−0.246657
$893$	3.63325	−	6.29297i	0.121582	−	0.210586i
$894$	−1.81662	−	3.14649i	−0.0607570	−	0.105234i
$895$		0			0
$896$	−4.31662			−0.144208
$897$	1.68338	−	5.83138i	0.0562063	−	0.194704i
$898$	−16.5330			−0.551713
$899$	6.00000	+	10.3923i	0.200111	+	0.346603i
$900$		0			0
$901$	−17.8747	+	30.9599i	−0.595492	+	1.03142i
$902$	−4.31662			−0.143728
$903$	−5.00000	+	8.66025i	−0.166390	+	0.288195i
$904$	8.13325	−	14.0872i	0.270508	−	0.468533i
$905$		0			0
$906$	3.47494	−	6.01877i	0.115447	−	0.199960i
$907$	13.3668	+	23.1519i	0.443836	+	0.768746i	0.997970	−	0.0636811i	$-0.0202841\pi$
$907$	13.3668	+	23.1519i	0.443836	+	0.768746i	−0.554135	+	0.832427i	$0.686951\pi$
$908$	−14.7916	−	25.6197i	−0.490875	−	0.850221i
$909$	−0.366750			−0.0121643
$910$		0			0
$911$	19.1662			0.635006			0.317503	−	0.948257i	$-0.397156\pi$
$911$	19.1662			0.635006			0.317503	+	0.948257i	$0.397156\pi$
$912$	−2.15831	−	3.73831i	−0.0714689	−	0.123788i
$913$	−26.2665	−	45.4949i	−0.869294	−	1.50566i
$914$	−7.97494	+	13.8130i	−0.263787	+	0.456893i
$915$		0			0
$916$	6.00000	−	10.3923i	0.198246	−	0.343371i
$917$		0			0
$918$	7.63325			0.251935
$919$	−5.05013	+	8.74707i	−0.166588	+	0.288539i	−0.937218	−	0.348744i	$-0.886608\pi$
$919$	−5.05013	+	8.74707i	−0.166588	+	0.288539i	0.770630	+	0.637283i	$0.219942\pi$
$920$		0			0
$921$	8.10819	+	14.0438i	0.267174	+	0.462759i
$922$	−9.63325			−0.317254
$923$	8.31662	−	28.8096i	0.273745	−	0.948281i
$924$	−27.2665			−0.897002
$925$		0			0
$926$	−4.47494	−	7.75082i	−0.147056	−	0.254708i
$927$	4.15831	−	7.20241i	0.136577	−	0.236558i
$928$	−3.00000			−0.0984798
$929$	7.70844	−	13.3514i	0.252906	−	0.438045i	−0.711419	−	0.702768i	$-0.751947\pi$
$929$	7.70844	−	13.3514i	0.252906	−	0.438045i	0.964325	+	0.264723i	$0.0852804\pi$
$930$		0			0
$931$	50.2164			1.64578
$932$	5.68338	−	9.84389i	0.186165	−	0.322447i
$933$	−6.15831	−	10.6665i	−0.201614	−	0.349206i
$934$	16.7916	+	29.0838i	0.549437	+	0.951652i
$935$		0			0
$936$	−1.00000	+	3.46410i	−0.0326860	+	0.113228i
$937$	13.2164			0.431760			0.215880	−	0.976420i	$-0.430738\pi$
$937$	13.2164			0.431760			0.215880	+	0.976420i	$0.430738\pi$
$938$	−15.0000	−	25.9808i	−0.489767	−	0.848302i
$939$	−15.0000	−	25.9808i	−0.489506	−	0.847850i
$940$		0			0
$941$	36.6332			1.19421			0.597105	−	0.802163i	$-0.296318\pi$
$941$	36.6332			1.19421			0.597105	+	0.802163i	$0.296318\pi$
$942$	−7.13325	+	12.3552i	−0.232414	+	0.402553i
$943$	0.575188	−	0.996256i	0.0187307	−	0.0324425i
$944$	−4.63325			−0.150799
$945$		0			0
$946$	−7.31662	−	12.6728i	−0.237884	−	0.412027i
$947$	−2.73350	−	4.73456i	−0.0888268	−	0.153853i	0.818189	−	0.574950i	$-0.194978\pi$
$947$	−2.73350	−	4.73456i	−0.0888268	−	0.153853i	−0.907015	+	0.421097i	$0.861645\pi$
$948$	−4.00000			−0.129914
$949$	2.39181	−	0.591820i	0.0776415	−	0.0192113i
$950$		0			0
$951$	1.97494	+	3.42069i	0.0640417	+	0.110924i
$952$	−16.4749	−	28.5354i	−0.533956	−	0.924839i
$953$	3.00000	−	5.19615i	0.0971795	−	0.168320i	−0.813337	−	0.581793i	$-0.802351\pi$
$953$	3.00000	−	5.19615i	0.0971795	−	0.168320i	0.910516	+	0.413473i	$0.135685\pi$
$954$	4.68338			0.151630
$955$		0			0
$956$	−4.15831	+	7.20241i	−0.134489	+	0.232943i
$957$	−18.9499			−0.612562
$958$		0			0
$959$	12.1583	+	21.0588i	0.392612	+	0.680025i
$960$		0			0
$961$	−15.0000			−0.483871
$962$	−7.63325	+	26.4424i	−0.246106	+	0.852536i
$963$	11.6834			0.376492
$964$	12.8166	+	22.1990i	0.412796	+	0.714983i
$965$		0			0
$966$	3.63325	−	6.29297i	0.116898	−	0.202473i
$967$	−22.8496			−0.734794			−0.367397	−	0.930064i	$-0.619751\pi$
$967$	−22.8496			−0.734794			−0.367397	+	0.930064i	$0.619751\pi$
$968$	14.4499	−	25.0279i	0.464437	−	0.804428i
$969$	16.4749	−	28.5354i	0.529251	−	0.916690i
$970$		0			0
$971$	5.36675	−	9.29548i	0.172227	−	0.298306i	−0.766971	−	0.641682i	$-0.778237\pi$
$971$	5.36675	−	9.29548i	0.172227	−	0.298306i	0.939198	+	0.343375i	$0.111570\pi$
$972$	−0.500000	−	0.866025i	−0.0160375	−	0.0277778i
$973$	−11.3668	−	19.6878i	−0.364401	−	0.631162i
$974$	−4.31662			−0.138314
$975$		0			0
$976$	0.683375			0.0218743
$977$	19.1834	+	33.2266i	0.613731	+	1.06301i	0.990606	+	0.136748i	$0.0436652\pi$
$977$	19.1834	+	33.2266i	0.613731	+	1.06301i	−0.376875	+	0.926264i	$0.623001\pi$
$978$	−4.31662	−	7.47661i	−0.138030	−	0.239076i
$979$	−35.5831	+	61.6318i	−1.13724	+	1.96976i
$980$		0			0
$981$	3.00000	−	5.19615i	0.0957826	−	0.165900i
$982$	−19.7916	+	34.2800i	−0.631574	+	1.09392i
$983$	−36.0000			−1.14822			−0.574111	−	0.818778i	$-0.694652\pi$
$983$	−36.0000			−1.14822			−0.574111	+	0.818778i	$0.694652\pi$
$984$	−0.341688	+	0.591820i	−0.0108926	+	0.0188665i
$985$		0			0
$986$	−11.4499	−	19.8318i	−0.364638	−	0.631572i
$987$	−7.26650			−0.231295
$988$	10.7916	+	11.2149i	0.343325	+	0.356794i
$989$	3.89975			0.124005
$990$		0			0
$991$	−5.15831	−	8.93446i	−0.163859	−	0.283812i	0.772390	−	0.635148i	$-0.219061\pi$
$991$	−5.15831	−	8.93446i	−0.163859	−	0.283812i	−0.936250	+	0.351336i	$0.885728\pi$
$992$	−2.00000	+	3.46410i	−0.0635001	+	0.109985i
$993$	5.26650			0.167127
$994$	17.9499	−	31.0901i	0.569335	−	0.986118i
$995$		0			0
$996$	−8.31662			−0.263522
$997$	15.1834	−	26.2984i	0.480862	−	0.832878i	−0.518897	−	0.854837i	$-0.673657\pi$
$997$	15.1834	−	26.2984i	0.480862	−	0.832878i	0.999759	+	0.0219591i	$0.00699035\pi$
$998$	−20.9499	−	36.2862i	−0.663157	−	1.14862i
$999$	−3.81662	−	6.61059i	−0.120753	−	0.209150i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1950.2.i.be.601.1		4
5.2	odd	4		390.2.y.g.289.1	yes	8
5.3	odd	4		390.2.y.g.289.4	yes	8
5.4	even	2		1950.2.i.bb.601.2		4
13.9	even	3	inner	1950.2.i.be.451.1		4
15.2	even	4		1170.2.bp.g.289.4		8
15.8	even	4		1170.2.bp.g.289.1		8
65.9	even	6		1950.2.i.bb.451.2		4
65.22	odd	12		390.2.y.g.139.3	yes	8
65.48	odd	12		390.2.y.g.139.2	✓	8
195.113	even	12		1170.2.bp.g.919.3		8
195.152	even	12		1170.2.bp.g.919.2		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
390.2.y.g.139.2	✓	8	65.48	odd	12
390.2.y.g.139.3	yes	8	65.22	odd	12
390.2.y.g.289.1	yes	8	5.2	odd	4
390.2.y.g.289.4	yes	8	5.3	odd	4
1170.2.bp.g.289.1		8	15.8	even	4
1170.2.bp.g.289.4		8	15.2	even	4
1170.2.bp.g.919.2		8	195.152	even	12
1170.2.bp.g.919.3		8	195.113	even	12
1950.2.i.bb.451.2		4	65.9	even	6
1950.2.i.bb.601.2		4	5.4	even	2
1950.2.i.be.451.1		4	13.9	even	3	inner
1950.2.i.be.601.1		4	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:	\( N \)	\(=\)	\( 1950 = 2 \cdot 3 \cdot 5^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1950.i (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.500000 + 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(0.500000 - 0.866025i) q^{6} +(-2.15831 + 3.73831i) q^{7} -1.00000 q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})\)	\(q+(0.500000 + 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(0.500000 - 0.866025i) q^{6} +(-2.15831 + 3.73831i) q^{7} -1.00000 q^{8} +(-0.500000 + 0.866025i) q^{9} +(3.15831 + 5.47036i) q^{11} +1.00000 q^{12} +(-3.50000 + 0.866025i) q^{13} -4.31662 q^{14} +(-0.500000 - 0.866025i) q^{16} +(3.81662 - 6.61059i) q^{17} -1.00000 q^{18} +(-2.15831 + 3.73831i) q^{19} +4.31662 q^{21} +(-3.15831 + 5.47036i) q^{22} +(-0.841688 - 1.45785i) q^{23} +(0.500000 + 0.866025i) q^{24} +(-2.50000 - 2.59808i) q^{26} +1.00000 q^{27} +(-2.15831 - 3.73831i) q^{28} +(-1.50000 - 2.59808i) q^{29} -4.00000 q^{31} +(0.500000 - 0.866025i) q^{32} +(3.15831 - 5.47036i) q^{33} +7.63325 q^{34} +(-0.500000 - 0.866025i) q^{36} +(-3.81662 - 6.61059i) q^{37} -4.31662 q^{38} +(2.50000 + 2.59808i) q^{39} +(0.341688 + 0.591820i) q^{41} +(2.15831 + 3.73831i) q^{42} +(-1.15831 + 2.00626i) q^{43} -6.31662 q^{44} +(0.841688 - 1.45785i) q^{46} -1.68338 q^{47} +(-0.500000 + 0.866025i) q^{48} +(-5.81662 - 10.0747i) q^{49} -7.63325 q^{51} +(1.00000 - 3.46410i) q^{52} -4.68338 q^{53} +(0.500000 + 0.866025i) q^{54} +(2.15831 - 3.73831i) q^{56} +4.31662 q^{57} +(1.50000 - 2.59808i) q^{58} +(2.31662 - 4.01251i) q^{59} +(-0.341688 + 0.591820i) q^{61} +(-2.00000 - 3.46410i) q^{62} +(-2.15831 - 3.73831i) q^{63} +1.00000 q^{64} +6.31662 q^{66} +(3.47494 + 6.01877i) q^{67} +(3.81662 + 6.61059i) q^{68} +(-0.841688 + 1.45785i) q^{69} +(-4.15831 + 7.20241i) q^{71} +(0.500000 - 0.866025i) q^{72} -0.683375 q^{73} +(3.81662 - 6.61059i) q^{74} +(-2.15831 - 3.73831i) q^{76} -27.2665 q^{77} +(-1.00000 + 3.46410i) q^{78} -4.00000 q^{79} +(-0.500000 - 0.866025i) q^{81} +(-0.341688 + 0.591820i) q^{82} -8.31662 q^{83} +(-2.15831 + 3.73831i) q^{84} -2.31662 q^{86} +(-1.50000 + 2.59808i) q^{87} +(-3.15831 - 5.47036i) q^{88} +(5.63325 + 9.75707i) q^{89} +(4.31662 - 14.9532i) q^{91} +1.68338 q^{92} +(2.00000 + 3.46410i) q^{93} +(-0.841688 - 1.45785i) q^{94} -1.00000 q^{96} +(3.00000 - 5.19615i) q^{97} +(5.81662 - 10.0747i) q^{98} -6.31662 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 2 q^{2} - 2 q^{3} - 2 q^{4} + 2 q^{6} - 2 q^{7} - 4 q^{8} - 2 q^{9}+O(q^{10}) \) 4 * q + 2 * q^2 - 2 * q^3 - 2 * q^4 + 2 * q^6 - 2 * q^7 - 4 * q^8 - 2 * q^9	\( 4 q + 2 q^{2} - 2 q^{3} - 2 q^{4} + 2 q^{6} - 2 q^{7} - 4 q^{8} - 2 q^{9} + 6 q^{11} + 4 q^{12} - 14 q^{13} - 4 q^{14} - 2 q^{16} + 2 q^{17} - 4 q^{18} - 2 q^{19} + 4 q^{21} - 6 q^{22} - 10 q^{23} + 2 q^{24} - 10 q^{26} + 4 q^{27} - 2 q^{28} - 6 q^{29} - 16 q^{31} + 2 q^{32} + 6 q^{33} + 4 q^{34} - 2 q^{36} - 2 q^{37} - 4 q^{38} + 10 q^{39} + 8 q^{41} + 2 q^{42} + 2 q^{43} - 12 q^{44} + 10 q^{46} - 20 q^{47} - 2 q^{48} - 10 q^{49} - 4 q^{51} + 4 q^{52} - 32 q^{53} + 2 q^{54} + 2 q^{56} + 4 q^{57} + 6 q^{58} - 4 q^{59} - 8 q^{61} - 8 q^{62} - 2 q^{63} + 4 q^{64} + 12 q^{66} - 6 q^{67} + 2 q^{68} - 10 q^{69} - 10 q^{71} + 2 q^{72} - 16 q^{73} + 2 q^{74} - 2 q^{76} - 56 q^{77} - 4 q^{78} - 16 q^{79} - 2 q^{81} - 8 q^{82} - 20 q^{83} - 2 q^{84} + 4 q^{86} - 6 q^{87} - 6 q^{88} - 4 q^{89} + 4 q^{91} + 20 q^{92} + 8 q^{93} - 10 q^{94} - 4 q^{96} + 12 q^{97} + 10 q^{98} - 12 q^{99}+O(q^{100}) \) 4 * q + 2 * q^2 - 2 * q^3 - 2 * q^4 + 2 * q^6 - 2 * q^7 - 4 * q^8 - 2 * q^9 + 6 * q^11 + 4 * q^12 - 14 * q^13 - 4 * q^14 - 2 * q^16 + 2 * q^17 - 4 * q^18 - 2 * q^19 + 4 * q^21 - 6 * q^22 - 10 * q^23 + 2 * q^24 - 10 * q^26 + 4 * q^27 - 2 * q^28 - 6 * q^29 - 16 * q^31 + 2 * q^32 + 6 * q^33 + 4 * q^34 - 2 * q^36 - 2 * q^37 - 4 * q^38 + 10 * q^39 + 8 * q^41 + 2 * q^42 + 2 * q^43 - 12 * q^44 + 10 * q^46 - 20 * q^47 - 2 * q^48 - 10 * q^49 - 4 * q^51 + 4 * q^52 - 32 * q^53 + 2 * q^54 + 2 * q^56 + 4 * q^57 + 6 * q^58 - 4 * q^59 - 8 * q^61 - 8 * q^62 - 2 * q^63 + 4 * q^64 + 12 * q^66 - 6 * q^67 + 2 * q^68 - 10 * q^69 - 10 * q^71 + 2 * q^72 - 16 * q^73 + 2 * q^74 - 2 * q^76 - 56 * q^77 - 4 * q^78 - 16 * q^79 - 2 * q^81 - 8 * q^82 - 20 * q^83 - 2 * q^84 + 4 * q^86 - 6 * q^87 - 6 * q^88 - 4 * q^89 + 4 * q^91 + 20 * q^92 + 8 * q^93 - 10 * q^94 - 4 * q^96 + 12 * q^97 + 10 * q^98 - 12 * q^99

Introduction

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