LMFDB - Embedded newform 1950.2.bc.e.751.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1950,2,Mod(751,1950)]

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, 5]))

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

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

chi := DirichletCharacter("1950.751");

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.bc (of order $6$, 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:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{6})$
Coefficient field:	$\Q(\zeta_{24})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - x^{4} + 1 $ x^8 - x^4 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			751.4
Root			$0.965926 + 0.258819i$ of defining polynomial
Character	$\chi$	$=$	1950.751
Dual form			1950.2.bc.e.901.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.866025 - 0.500000i) q^{2} +(-0.500000 - 0.866025i) q^{3} +(0.500000 - 0.866025i) q^{4} +(-0.866025 - 0.500000i) q^{6} +(0.807007 + 0.465926i) q^{7} -1.00000i q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})$	\(q+(0.866025 - 0.500000i) q^{2} +(-0.500000 - 0.866025i) q^{3} +(0.500000 - 0.866025i) q^{4} +(-0.866025 - 0.500000i) q^{6} +(0.807007 + 0.465926i) q^{7} -1.00000i q^{8} +(-0.500000 + 0.866025i) q^{9} +(1.45680 - 0.841081i) q^{11} -1.00000 q^{12} +(1.86250 + 3.08725i) q^{13} +0.931852 q^{14} +(-0.500000 - 0.866025i) q^{16} +(1.27646 - 2.21089i) q^{17} +1.00000i q^{18} +(2.27646 + 1.31431i) q^{19} -0.931852i q^{21} +(0.841081 - 1.45680i) q^{22} +(3.22853 + 5.59197i) q^{23} +(-0.866025 + 0.500000i) q^{24} +(3.15660 + 1.74238i) q^{26} +1.00000 q^{27} +(0.807007 - 0.465926i) q^{28} +(1.69419 + 2.93443i) q^{29} -9.29493i q^{31} +(-0.866025 - 0.500000i) q^{32} +(-1.45680 - 0.841081i) q^{33} -2.55291i q^{34} +(0.500000 + 0.866025i) q^{36} +(7.93269 - 4.57994i) q^{37} +2.62863 q^{38} +(1.74238 - 3.15660i) q^{39} +(1.01714 - 0.587246i) q^{41} +(-0.465926 - 0.807007i) q^{42} +(-1.47626 + 2.55695i) q^{43} -1.68216i q^{44} +(5.59197 + 3.22853i) q^{46} +3.97934i q^{47} +(-0.500000 + 0.866025i) q^{48} +(-3.06583 - 5.31017i) q^{49} -2.55291 q^{51} +(3.60488 - 0.0693504i) q^{52} -5.36068 q^{53} +(0.866025 - 0.500000i) q^{54} +(0.465926 - 0.807007i) q^{56} -2.62863i q^{57} +(2.93443 + 1.69419i) q^{58} +(-3.44174 - 1.98709i) q^{59} +(4.36188 - 7.55500i) q^{61} +(-4.64747 - 8.04965i) q^{62} +(-0.807007 + 0.465926i) q^{63} -1.00000 q^{64} -1.68216 q^{66} +(4.49598 - 2.59575i) q^{67} +(-1.27646 - 2.21089i) q^{68} +(3.22853 - 5.59197i) q^{69} +(3.40803 + 1.96763i) q^{71} +(0.866025 + 0.500000i) q^{72} +7.26330i q^{73} +(4.57994 - 7.93269i) q^{74} +(2.27646 - 1.31431i) q^{76} +1.56753 q^{77} +(-0.0693504 - 3.60488i) q^{78} -3.68973 q^{79} +(-0.500000 - 0.866025i) q^{81} +(0.587246 - 1.01714i) q^{82} +3.84909i q^{83} +(-0.807007 - 0.465926i) q^{84} +2.95252i q^{86} +(1.69419 - 2.93443i) q^{87} +(-0.841081 - 1.45680i) q^{88} +(11.6628 - 6.73351i) q^{89} +(0.0646242 + 3.35922i) q^{91} +6.45705 q^{92} +(-8.04965 + 4.64747i) q^{93} +(1.98967 + 3.44621i) q^{94} +1.00000i q^{96} +(12.1945 + 7.04052i) q^{97} +(-5.31017 - 3.06583i) q^{98} +1.68216i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 4 q^{3} + 4 q^{4} - 4 q^{9}+O(q^{10}) $ 8 * q - 4 * q^3 + 4 * q^4 - 4 * q^9	$ 8 q - 4 q^{3} + 4 q^{4} - 4 q^{9} - 12 q^{11} - 8 q^{12} - 8 q^{14} - 4 q^{16} + 4 q^{17} + 12 q^{19} + 8 q^{22} + 4 q^{23} + 8 q^{27} + 4 q^{29} + 12 q^{33} + 4 q^{36} - 24 q^{37} + 4 q^{42} - 4 q^{43} + 12 q^{46} - 4 q^{48} - 16 q^{49} - 8 q^{51} - 8 q^{53} - 4 q^{56} + 12 q^{58} - 12 q^{59} - 16 q^{61} + 4 q^{62} - 8 q^{64} - 16 q^{66} + 24 q^{67} - 4 q^{68} + 4 q^{69} + 60 q^{71} + 16 q^{74} + 12 q^{76} - 8 q^{77} - 8 q^{79} - 4 q^{81} - 20 q^{82} + 4 q^{87} - 8 q^{88} + 24 q^{89} + 8 q^{91} + 8 q^{92} - 24 q^{93} + 16 q^{94} + 12 q^{97} + 12 q^{98}+O(q^{100}) $ 8 * q - 4 * q^3 + 4 * q^4 - 4 * q^9 - 12 * q^11 - 8 * q^12 - 8 * q^14 - 4 * q^16 + 4 * q^17 + 12 * q^19 + 8 * q^22 + 4 * q^23 + 8 * q^27 + 4 * q^29 + 12 * q^33 + 4 * q^36 - 24 * q^37 + 4 * q^42 - 4 * q^43 + 12 * q^46 - 4 * q^48 - 16 * q^49 - 8 * q^51 - 8 * q^53 - 4 * q^56 + 12 * q^58 - 12 * q^59 - 16 * q^61 + 4 * q^62 - 8 * q^64 - 16 * q^66 + 24 * q^67 - 4 * q^68 + 4 * q^69 + 60 * q^71 + 16 * q^74 + 12 * q^76 - 8 * q^77 - 8 * q^79 - 4 * q^81 - 20 * q^82 + 4 * q^87 - 8 * q^88 + 24 * q^89 + 8 * q^91 + 8 * q^92 - 24 * q^93 + 16 * q^94 + 12 * q^97 + 12 * q^98

Display 100 coefficients 10 coefficients

Character values

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

$n$	$301$	$1301$	$1327$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$1$	$1$

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 $

$2$	0.866025	−	0.500000i	0.612372	−	0.353553i
$2$	0.866025	−	0.500000i	0.612372	−	0.353553i
$3$	−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
$6$	−0.866025	−	0.500000i	−0.353553	−	0.204124i
$7$	0.807007	+	0.465926i	0.305020	+	0.176103i	0.644696	−	0.764439i	$-0.276984\pi$
$7$	0.807007	+	0.465926i	0.305020	+	0.176103i	−0.339676	+	0.940543i	$0.610317\pi$
$8$		−	1.00000i		−	0.353553i
$9$	−0.500000	+	0.866025i	−0.166667	+	0.288675i
$10$		0			0
$11$	1.45680	−	0.841081i	0.439240	−	0.253596i	−0.264035	−	0.964513i	$-0.585053\pi$
$11$	1.45680	−	0.841081i	0.439240	−	0.253596i	0.703275	+	0.710918i	$0.251720\pi$
$12$	−1.00000			−0.288675
$13$	1.86250	+	3.08725i	0.516565	+	0.856248i
$13$	1.86250	+	3.08725i	0.516565	+	0.856248i
$14$	0.931852			0.249048
$15$		0			0
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	1.27646	−	2.21089i	0.309586	−	0.536219i	−0.668686	−	0.743545i	$-0.733143\pi$
$17$	1.27646	−	2.21089i	0.309586	−	0.536219i	0.978272	+	0.207326i	$0.0664761\pi$
$18$			1.00000i			0.235702i
$19$	2.27646	+	1.31431i	0.522255	+	0.301524i	0.737857	−	0.674957i	$-0.235838\pi$
$19$	2.27646	+	1.31431i	0.522255	+	0.301524i	−0.215602	+	0.976481i	$0.569171\pi$
$20$		0			0
$21$		−	0.931852i		−	0.203347i
$22$	0.841081	−	1.45680i	0.179319	−	0.310590i
$23$	3.22853	+	5.59197i	0.673194	+	1.16601i	0.976993	+	0.213271i	$0.0684116\pi$
$23$	3.22853	+	5.59197i	0.673194	+	1.16601i	−0.303799	+	0.952736i	$0.598255\pi$
$24$	−0.866025	+	0.500000i	−0.176777	+	0.102062i
$25$		0			0
$26$	3.15660	+	1.74238i	0.619060	+	0.341709i
$27$	1.00000			0.192450
$28$	0.807007	−	0.465926i	0.152510	−	0.0880517i
$29$	1.69419	+	2.93443i	0.314604	+	0.544910i	0.979353	−	0.202156i	$-0.0647949\pi$
$29$	1.69419	+	2.93443i	0.314604	+	0.544910i	−0.664749	+	0.747067i	$0.731462\pi$
$30$		0			0
$31$		−	9.29493i		−	1.66942i	−0.550690	−	0.834710i	$-0.685635\pi$
$31$		−	9.29493i		−	1.66942i	0.550690	−	0.834710i	$-0.314365\pi$
$32$	−0.866025	−	0.500000i	−0.153093	−	0.0883883i
$33$	−1.45680	−	0.841081i	−0.253596	−	0.146413i
$34$		−	2.55291i		−	0.437821i
$35$		0			0
$36$	0.500000	+	0.866025i	0.0833333	+	0.144338i
$37$	7.93269	−	4.57994i	1.30413	−	0.752938i	0.323017	−	0.946393i	$-0.395303\pi$
$37$	7.93269	−	4.57994i	1.30413	−	0.752938i	0.981109	+	0.193456i	$0.0619695\pi$
$38$	2.62863			0.426419
$39$	1.74238	−	3.15660i	0.279005	−	0.505460i
$40$		0			0
$41$	1.01714	−	0.587246i	0.158851	−	0.0917124i	−0.418467	−	0.908232i	$-0.637433\pi$
$41$	1.01714	−	0.587246i	0.158851	−	0.0917124i	0.577318	+	0.816519i	$0.304099\pi$
$42$	−0.465926	−	0.807007i	−0.0718939	−	0.124524i
$43$	−1.47626	+	2.55695i	−0.225127	+	0.389932i	−0.956358	−	0.292199i	$-0.905613\pi$
$43$	−1.47626	+	2.55695i	−0.225127	+	0.389932i	0.731230	+	0.682131i	$0.238946\pi$
$44$		−	1.68216i		−	0.253596i
$45$		0			0
$46$	5.59197	+	3.22853i	0.824491	+	0.476020i
$47$			3.97934i			0.580446i	0.956959	+	0.290223i	$0.0937294\pi$
$47$			3.97934i			0.580446i	−0.956959	+	0.290223i	$0.906271\pi$
$48$	−0.500000	+	0.866025i	−0.0721688	+	0.125000i
$49$	−3.06583	−	5.31017i	−0.437975	−	0.758595i
$50$		0			0
$51$	−2.55291			−0.357480
$52$	3.60488	−	0.0693504i	0.499908	−	0.00961716i
$53$	−5.36068			−0.736346			−0.368173	−	0.929757i	$-0.620017\pi$
$53$	−5.36068			−0.736346			−0.368173	+	0.929757i	$0.620017\pi$
$54$	0.866025	−	0.500000i	0.117851	−	0.0680414i
$55$		0			0
$56$	0.465926	−	0.807007i	0.0622620	−	0.107841i
$57$		−	2.62863i		−	0.348170i
$58$	2.93443	+	1.69419i	0.385310	+	0.222459i
$59$	−3.44174	−	1.98709i	−0.448076	−	0.258697i	0.258941	−	0.965893i	$-0.416626\pi$
$59$	−3.44174	−	1.98709i	−0.448076	−	0.258697i	−0.707017	+	0.707196i	$0.749960\pi$
$60$		0			0
$61$	4.36188	−	7.55500i	0.558481	−	0.967318i	−0.439142	−	0.898418i	$-0.644718\pi$
$61$	4.36188	−	7.55500i	0.558481	−	0.967318i	0.997624	−	0.0689005i	$-0.0219491\pi$
$62$	−4.64747	−	8.04965i	−0.590229	−	1.02231i
$63$	−0.807007	+	0.465926i	−0.101673	+	0.0587011i
$64$	−1.00000			−0.125000
$65$		0			0
$66$	−1.68216			−0.207060
$67$	4.49598	−	2.59575i	0.549271	−	0.317122i	−0.199557	−	0.979886i	$-0.563950\pi$
$67$	4.49598	−	2.59575i	0.549271	−	0.317122i	0.748828	+	0.662764i	$0.230617\pi$
$68$	−1.27646	−	2.21089i	−0.154793	−	0.268110i
$69$	3.22853	−	5.59197i	0.388669	−	0.673194i
$70$		0			0
$71$	3.40803	+	1.96763i	0.404458	+	0.233514i	0.688406	−	0.725326i	$-0.258311\pi$
$71$	3.40803	+	1.96763i	0.404458	+	0.233514i	−0.283947	+	0.958840i	$0.591644\pi$
$72$	0.866025	+	0.500000i	0.102062	+	0.0589256i
$73$			7.26330i			0.850106i	0.905169	+	0.425053i	$0.139744\pi$
$73$			7.26330i			0.850106i	−0.905169	+	0.425053i	$0.860256\pi$
$74$	4.57994	−	7.93269i	0.532407	−	0.922156i
$75$		0			0
$76$	2.27646	−	1.31431i	0.261128	−	0.150762i
$77$	1.56753			0.178636
$78$	−0.0693504	−	3.60488i	−0.00785238	−	0.408173i
$79$	−3.68973			−0.415127			−0.207563	−	0.978222i	$-0.566553\pi$
$79$	−3.68973			−0.415127			−0.207563	+	0.978222i	$0.566553\pi$
$80$		0			0
$81$	−0.500000	−	0.866025i	−0.0555556	−	0.0962250i
$82$	0.587246	−	1.01714i	0.0648505	−	0.112324i
$83$			3.84909i			0.422493i	0.977433	+	0.211246i	$0.0677522\pi$
$83$			3.84909i			0.422493i	−0.977433	+	0.211246i	$0.932248\pi$
$84$	−0.807007	−	0.465926i	−0.0880517	−	0.0508367i
$85$		0			0
$86$			2.95252i			0.318378i
$87$	1.69419	−	2.93443i	0.181637	−	0.314604i
$88$	−0.841081	−	1.45680i	−0.0896596	−	0.155295i
$89$	11.6628	−	6.73351i	1.23625	−	0.713751i	0.267926	−	0.963439i	$-0.413662\pi$
$89$	11.6628	−	6.73351i	1.23625	−	0.713751i	0.968326	+	0.249689i	$0.0803283\pi$
$90$		0			0
$91$	0.0646242	+	3.35922i	0.00677446	+	0.352142i
$92$	6.45705			0.673194
$93$	−8.04965	+	4.64747i	−0.834710	+	0.481920i
$94$	1.98967	+	3.44621i	0.205219	+	0.355449i
$95$		0			0
$96$			1.00000i			0.102062i
$97$	12.1945	+	7.04052i	1.23817	+	0.714856i	0.968719	−	0.248159i	$-0.0798254\pi$
$97$	12.1945	+	7.04052i	1.23817	+	0.714856i	0.269448	+	0.963015i	$0.413159\pi$
$98$	−5.31017	−	3.06583i	−0.536408	−	0.309695i
$99$			1.68216i			0.169064i
$100$		0			0
$101$	−5.65892	−	9.80153i	−0.563083	−	0.975289i	−0.997225	−	0.0744445i	$-0.976282\pi$
$101$	−5.65892	−	9.80153i	−0.563083	−	0.975289i	0.434142	−	0.900845i	$-0.357052\pi$
$102$	−2.21089	+	1.27646i	−0.218911	+	0.126388i
$103$	−0.725003			−0.0714366			−0.0357183	−	0.999362i	$-0.511372\pi$
$103$	−0.725003			−0.0714366			−0.0357183	+	0.999362i	$0.511372\pi$
$104$	3.08725	−	1.86250i	0.302729	−	0.182633i
$105$		0			0
$106$	−4.64248	+	2.68034i	−0.450918	+	0.260337i
$107$	−8.60867	−	14.9106i	−0.832231	−	1.44147i	−0.896265	−	0.443519i	$-0.853730\pi$
$107$	−8.60867	−	14.9106i	−0.832231	−	1.44147i	0.0640338	−	0.997948i	$-0.479603\pi$
$108$	0.500000	−	0.866025i	0.0481125	−	0.0833333i
$109$		−	10.2816i		−	0.984795i	−0.870370	−	0.492398i	$-0.836121\pi$
$109$		−	10.2816i		−	0.984795i	0.870370	−	0.492398i	$-0.163879\pi$
$110$		0			0
$111$	−7.93269	−	4.57994i	−0.752938	−	0.434709i
$112$		−	0.931852i		−	0.0880517i
$113$	−4.82843	+	8.36308i	−0.454220	+	0.786732i	−0.998643	−	0.0520785i	$-0.983415\pi$
$113$	−4.82843	+	8.36308i	−0.454220	+	0.786732i	0.544423	+	0.838811i	$0.316749\pi$
$114$	−1.31431	−	2.27646i	−0.123097	−	0.213210i
$115$		0			0
$116$	3.38839			0.314604
$117$	−3.60488	+	0.0693504i	−0.333272	+	0.00641144i
$118$	−3.97418			−0.365853
$119$	2.06022	−	1.18947i	0.188860	−	0.109038i
$120$		0			0
$121$	−4.08516	+	7.07571i	−0.371379	+	0.643247i
$122$		−	8.72376i		−	0.789812i
$123$	−1.01714	−	0.587246i	−0.0917124	−	0.0529502i
$124$	−8.04965	−	4.64747i	−0.722880	−	0.417355i
$125$		0			0
$126$	−0.465926	+	0.807007i	−0.0415080	+	0.0718939i
$127$	0.338502	+	0.586302i	0.0300372	+	0.0520259i	0.880653	−	0.473761i	$-0.157104\pi$
$127$	0.338502	+	0.586302i	0.0300372	+	0.0520259i	−0.850616	+	0.525787i	$0.823771\pi$
$128$	−0.866025	+	0.500000i	−0.0765466	+	0.0441942i
$129$	2.95252			0.259955
$130$		0			0
$131$	1.86710			0.163130			0.0815648	−	0.996668i	$-0.474008\pi$
$131$	1.86710			0.163130			0.0815648	+	0.996668i	$0.474008\pi$
$132$	−1.45680	+	0.841081i	−0.126798	+	0.0732067i
$133$	1.22474	+	2.12132i	0.106199	+	0.183942i
$134$	2.59575	−	4.49598i	0.224239	−	0.388393i
$135$		0			0
$136$	−2.21089	−	1.27646i	−0.189582	−	0.109455i
$137$	−6.31212	−	3.64431i	−0.539281	−	0.311354i	0.205506	−	0.978656i	$-0.434116\pi$
$137$	−6.31212	−	3.64431i	−0.539281	−	0.311354i	−0.744788	+	0.667302i	$0.767449\pi$
$138$		−	6.45705i		−	0.549661i
$139$	−2.35569	+	4.08018i	−0.199807	+	0.346076i	−0.948466	−	0.316879i	$-0.897365\pi$
$139$	−2.35569	+	4.08018i	−0.199807	+	0.346076i	0.748659	+	0.662956i	$0.230698\pi$
$140$		0			0
$141$	3.44621	−	1.98967i	0.290223	−	0.167560i
$142$	3.93525			0.330239
$143$	5.30991	+	2.93097i	0.444037	+	0.245100i
$144$	1.00000			0.0833333
$145$		0			0
$146$	3.63165	+	6.29021i	0.300558	+	0.520581i
$147$	−3.06583	+	5.31017i	−0.252865	+	0.437975i
$148$		−	9.15988i		−	0.752938i
$149$	−2.60016	−	1.50120i	−0.213013	−	0.122983i	0.389698	−	0.920943i	$-0.372579\pi$
$149$	−2.60016	−	1.50120i	−0.213013	−	0.122983i	−0.602711	+	0.797960i	$0.705913\pi$
$150$		0			0
$151$		−	12.4200i		−	1.01073i	−0.862907	−	0.505363i	$-0.831358\pi$
$151$		−	12.4200i		−	1.01073i	0.862907	−	0.505363i	$-0.168642\pi$
$152$	1.31431	−	2.27646i	0.106605	−	0.184645i
$153$	1.27646	+	2.21089i	0.103195	+	0.178740i
$154$	1.35752	−	0.783763i	0.109392	−	0.0631574i
$155$		0			0
$156$	−1.86250	−	3.08725i	−0.149119	−	0.247178i
$157$	22.5217			1.79743			0.898714	−	0.438535i	$-0.144502\pi$
$157$	22.5217			1.79743			0.898714	+	0.438535i	$0.144502\pi$
$158$	−3.19540	+	1.84486i	−0.254212	+	0.146769i
$159$	2.68034	+	4.64248i	0.212565	+	0.368173i
$160$		0			0
$161$			6.01702i			0.474207i
$162$	−0.866025	−	0.500000i	−0.0680414	−	0.0392837i
$163$	2.40313	+	1.38745i	0.188227	+	0.108673i	0.591152	−	0.806560i	$-0.298673\pi$
$163$	2.40313	+	1.38745i	0.188227	+	0.108673i	−0.402925	+	0.915233i	$0.632006\pi$
$164$		−	1.17449i		−	0.0917124i
$165$		0			0
$166$	1.92455	+	3.33341i	0.149374	+	0.258723i
$167$	−19.2296	+	11.1022i	−1.48803	+	0.859114i	−0.999907	−	0.0136615i	$-0.995651\pi$
$167$	−19.2296	+	11.1022i	−1.48803	+	0.859114i	−0.488122	+	0.872775i	$0.662318\pi$
$168$	−0.931852			−0.0718939
$169$	−6.06218	+	11.5000i	−0.466321	+	0.884615i
$170$		0			0
$171$	−2.27646	+	1.31431i	−0.174085	+	0.100508i
$172$	1.47626	+	2.55695i	0.112564	+	0.194966i
$173$	−0.475314	+	0.823267i	−0.0361374	+	0.0625919i	−0.883528	−	0.468377i	$-0.844839\pi$
$173$	−0.475314	+	0.823267i	−0.0361374	+	0.0625919i	0.847391	+	0.530969i	$0.178172\pi$
$174$		−	3.38839i		−	0.256873i
$175$		0			0
$176$	−1.45680	−	0.841081i	−0.109810	−	0.0633989i
$177$			3.97418i			0.298717i
$178$	6.73351	−	11.6628i	0.504698	−	0.874162i
$179$	4.94156	+	8.55904i	0.369350	+	0.639732i	0.989464	−	0.144779i	$-0.0462471\pi$
$179$	4.94156	+	8.55904i	0.369350	+	0.639732i	−0.620114	+	0.784511i	$0.712914\pi$
$180$		0			0
$181$	14.3015			1.06302			0.531511	−	0.847051i	$-0.321624\pi$
$181$	14.3015			1.06302			0.531511	+	0.847051i	$0.321624\pi$
$182$	1.73557	+	2.87686i	0.128649	+	0.213247i
$183$	−8.72376			−0.644879
$184$	5.59197	−	3.22853i	0.412246	−	0.238010i
$185$		0			0
$186$	−4.64747	+	8.04965i	−0.340769	+	0.590229i
$187$		−	4.29442i		−	0.314039i
$188$	3.44621	+	1.98967i	0.251340	+	0.145111i
$189$	0.807007	+	0.465926i	0.0587011	+	0.0338911i
$190$		0			0
$191$	0.0573183	−	0.0992782i	0.00414741	−	0.00718352i	−0.863944	−	0.503587i	$-0.832013\pi$
$191$	0.0573183	−	0.0992782i	0.00414741	−	0.00718352i	0.868092	+	0.496404i	$0.165347\pi$
$192$	0.500000	+	0.866025i	0.0360844	+	0.0625000i
$193$	−7.49706	+	4.32843i	−0.539650	+	0.311567i	−0.744937	−	0.667135i	$-0.767521\pi$
$193$	−7.49706	+	4.32843i	−0.539650	+	0.311567i	0.205287	+	0.978702i	$0.434187\pi$
$194$	14.0810			1.01096
$195$		0			0
$196$	−6.13165			−0.437975
$197$	−17.7363	+	10.2401i	−1.26366	+	0.729574i	−0.973781	−	0.227489i	$-0.926948\pi$
$197$	−17.7363	+	10.2401i	−1.26366	+	0.729574i	−0.289879	+	0.957063i	$0.593615\pi$
$198$	0.841081	+	1.45680i	0.0597731	+	0.103530i
$199$	0.955336	−	1.65469i	0.0677220	−	0.117298i	−0.830176	−	0.557501i	$-0.811760\pi$
$199$	0.955336	−	1.65469i	0.0677220	−	0.117298i	0.897898	+	0.440203i	$0.145094\pi$
$200$		0			0
$201$	−4.49598	−	2.59575i	−0.317122	−	0.183090i
$202$	−9.80153	−	5.65892i	−0.689634	−	0.398160i
$203$			3.15748i			0.221611i
$204$	−1.27646	+	2.21089i	−0.0893699	+	0.154793i
$205$		0			0
$206$	−0.627871	+	0.362501i	−0.0437458	+	0.0252567i
$207$	−6.45705			−0.448796
$208$	1.74238	−	3.15660i	0.120813	−	0.218871i
$209$	4.42178			0.305861
$210$		0			0
$211$	−0.620118	−	1.07408i	−0.0426907	−	0.0739425i	0.843891	−	0.536515i	$-0.180260\pi$
$211$	−0.620118	−	1.07408i	−0.0426907	−	0.0739425i	−0.886581	+	0.462573i	$0.846926\pi$
$212$	−2.68034	+	4.64248i	−0.184086	+	0.318847i
$213$		−	3.93525i		−	0.269639i
$214$	−14.9106	−	8.60867i	−1.01927	−	0.588476i
$215$		0			0
$216$		−	1.00000i		−	0.0680414i
$217$	4.33075	−	7.50108i	0.293990	−	0.509206i
$218$	−5.14078	−	8.90410i	−0.348178	−	0.603062i
$219$	6.29021	−	3.63165i	0.425053	−	0.245404i
$220$		0			0
$221$	9.20296	−	0.177046i	0.619058	−	0.0119094i
$222$	−9.15988			−0.614771
$223$	−12.7984	+	7.38915i	−0.857043	+	0.494814i	−0.863021	−	0.505168i	$-0.831430\pi$
$223$	−12.7984	+	7.38915i	−0.857043	+	0.494814i	0.00597823	+	0.999982i	$0.498097\pi$
$224$	−0.465926	−	0.807007i	−0.0311310	−	0.0539204i
$225$		0			0
$226$			9.65685i			0.642364i
$227$	−8.28423	−	4.78290i	−0.549843	−	0.317452i	0.199215	−	0.979956i	$-0.436161\pi$
$227$	−8.28423	−	4.78290i	−0.549843	−	0.317452i	−0.749059	+	0.662503i	$0.769494\pi$
$228$	−2.27646	−	1.31431i	−0.150762	−	0.0870425i
$229$		−	15.1478i		−	1.00099i	−0.865739	−	0.500497i	$-0.833151\pi$
$229$		−	15.1478i		−	1.00099i	0.865739	−	0.500497i	$-0.166849\pi$
$230$		0			0
$231$	−0.783763	−	1.35752i	−0.0515678	−	0.0893181i
$232$	2.93443	−	1.69419i	0.192655	−	0.111229i
$233$	18.7413			1.22778			0.613891	−	0.789391i	$-0.289603\pi$
$233$	18.7413			1.22778			0.613891	+	0.789391i	$0.289603\pi$
$234$	−3.08725	+	1.86250i	−0.201820	+	0.121756i
$235$		0			0
$236$	−3.44174	+	1.98709i	−0.224038	+	0.129348i
$237$	1.84486	+	3.19540i	0.119837	+	0.207563i
$238$	1.18947	−	2.06022i	0.0771018	−	0.133544i
$239$		−	4.62330i		−	0.299057i	−0.988757	−	0.149528i	$-0.952224\pi$
$239$		−	4.62330i		−	0.299057i	0.988757	−	0.149528i	$-0.0477755\pi$
$240$		0			0
$241$	15.2373	+	8.79725i	0.981520	+	0.566681i	0.902729	−	0.430210i	$-0.141561\pi$
$241$	15.2373	+	8.79725i	0.981520	+	0.566681i	0.0787915	+	0.996891i	$0.474894\pi$
$242$			8.17033i			0.525209i
$243$	−0.500000	+	0.866025i	−0.0320750	+	0.0555556i
$244$	−4.36188	−	7.55500i	−0.279241	−	0.483659i
$245$		0			0
$246$	−1.17449			−0.0748829
$247$	0.182296	+	9.47589i	0.0115992	+	0.602937i
$248$	−9.29493			−0.590229
$249$	3.33341	−	1.92455i	0.211246	−	0.121963i
$250$		0			0
$251$	−13.2599	+	22.9668i	−0.836958	+	1.44965i	0.0554676	+	0.998460i	$0.482335\pi$
$251$	−13.2599	+	22.9668i	−0.836958	+	1.44965i	−0.892426	+	0.451194i	$0.850998\pi$
$252$			0.931852i			0.0587011i
$253$	9.40661	+	5.43091i	0.591388	+	0.341438i
$254$	0.586302	+	0.338502i	0.0367879	+	0.0212395i
$255$		0			0
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	−0.912132	−	1.57986i	−0.0568972	−	0.0985489i	0.836174	−	0.548464i	$-0.184787\pi$
$257$	−0.912132	−	1.57986i	−0.0568972	−	0.0985489i	−0.893071	+	0.449916i	$0.851454\pi$
$258$	2.55695	−	1.47626i	0.159189	−	0.0919078i
$259$	8.53565			0.530379
$260$		0			0
$261$	−3.38839			−0.209736
$262$	1.61696	−	0.933552i	0.0998960	−	0.0576750i
$263$	−6.06828	−	10.5106i	−0.374186	−	0.648110i	0.616019	−	0.787732i	$-0.288745\pi$
$263$	−6.06828	−	10.5106i	−0.374186	−	0.648110i	−0.990205	+	0.139622i	$0.955411\pi$
$264$	−0.841081	+	1.45680i	−0.0517650	+	0.0896596i
$265$		0			0
$266$	2.12132	+	1.22474i	0.130066	+	0.0750939i
$267$	−11.6628	−	6.73351i	−0.713751	−	0.412084i
$268$		−	5.19151i		−	0.317122i
$269$	−11.7655	+	20.3784i	−0.717355	+	1.24250i	0.244689	+	0.969602i	$0.421314\pi$
$269$	−11.7655	+	20.3784i	−0.717355	+	1.24250i	−0.962044	+	0.272894i	$0.912019\pi$
$270$		0			0
$271$	10.9872	−	6.34349i	0.667427	−	0.385339i	−0.127674	−	0.991816i	$-0.540751\pi$
$271$	10.9872	−	6.34349i	0.667427	−	0.385339i	0.795101	+	0.606477i	$0.207418\pi$
$272$	−2.55291			−0.154793
$273$	2.87686	−	1.73557i	0.174115	−	0.105042i
$274$	−7.28861			−0.440321
$275$		0			0
$276$	−3.22853	−	5.59197i	−0.194334	−	0.336597i
$277$	−6.41177	+	11.1055i	−0.385246	+	0.667265i	−0.991803	−	0.127774i	$-0.959217\pi$
$277$	−6.41177	+	11.1055i	−0.385246	+	0.667265i	0.606558	+	0.795040i	$0.292550\pi$
$278$			4.71139i			0.282570i
$279$	8.04965	+	4.64747i	0.481920	+	0.278237i
$280$		0			0
$281$		−	5.16720i		−	0.308249i	−0.988051	−	0.154125i	$-0.950744\pi$
$281$		−	5.16720i		−	0.308249i	0.988051	−	0.154125i	$-0.0492557\pi$
$282$	1.98967	−	3.44621i	0.118483	−	0.205219i
$283$	6.48124	+	11.2258i	0.385270	+	0.667307i	0.991807	−	0.127749i	$-0.0407750\pi$
$283$	6.48124	+	11.2258i	0.385270	+	0.667307i	−0.606537	+	0.795055i	$0.707442\pi$
$284$	3.40803	−	1.96763i	0.202229	−	0.116757i
$285$		0			0
$286$	6.06400	−	0.116659i	0.358572	−	0.00689817i
$287$	1.09445			0.0646035
$288$	0.866025	−	0.500000i	0.0510310	−	0.0294628i
$289$	5.24131	+	9.07822i	0.308313	+	0.534013i
$290$		0			0
$291$		−	14.0810i		−	0.825445i
$292$	6.29021	+	3.63165i	0.368107	+	0.212526i
$293$	11.6657	+	6.73521i	0.681519	+	0.393475i	0.800427	−	0.599430i	$-0.204606\pi$
$293$	11.6657	+	6.73521i	0.681519	+	0.393475i	−0.118908	+	0.992905i	$0.537939\pi$
$294$			6.13165i			0.357605i
$295$		0			0
$296$	−4.57994	−	7.93269i	−0.266204	−	0.461078i
$297$	1.45680	−	0.841081i	0.0845319	−	0.0488045i
$298$	−3.00240			−0.173925
$299$	−11.2507	+	20.3823i	−0.650642	+	1.17874i
$300$		0			0
$301$	−2.38270	+	1.37565i	−0.137337	+	0.0792913i
$302$	−6.21001	−	10.7561i	−0.357346	−	0.618941i
$303$	−5.65892	+	9.80153i	−0.325096	+	0.563083i
$304$		−	2.62863i		−	0.150762i
$305$		0			0
$306$	2.21089	+	1.27646i	0.126388	+	0.0729702i
$307$			21.4620i			1.22490i	0.790510	+	0.612450i	$0.209816\pi$
$307$			21.4620i			1.22490i	−0.790510	+	0.612450i	$0.790184\pi$
$308$	0.783763	−	1.35752i	0.0446590	−	0.0773517i
$309$	0.362501	+	0.627871i	0.0206220	+	0.0357183i
$310$		0			0
$311$	−14.7562			−0.836745			−0.418372	−	0.908276i	$-0.637399\pi$
$311$	−14.7562			−0.836745			−0.418372	+	0.908276i	$0.637399\pi$
$312$	−3.15660	−	1.74238i	−0.178707	−	0.0986430i
$313$	1.40441			0.0793819			0.0396910	−	0.999212i	$-0.487363\pi$
$313$	1.40441			0.0793819			0.0396910	+	0.999212i	$0.487363\pi$
$314$	19.5044	−	11.2609i	1.10070	−	0.635487i
$315$		0			0
$316$	−1.84486	+	3.19540i	−0.103782	+	0.179755i
$317$			33.1421i			1.86144i	0.365729	+	0.930722i	$0.380820\pi$
$317$			33.1421i			1.86144i	−0.365729	+	0.930722i	$0.619180\pi$
$318$	4.64248	+	2.68034i	0.260337	+	0.150306i
$319$	4.93619	+	2.84991i	0.276374	+	0.159564i
$320$		0			0
$321$	−8.60867	+	14.9106i	−0.480489	+	0.832231i
$322$	3.00851	+	5.21089i	0.167658	+	0.290391i
$323$	5.81160	−	3.35533i	0.323366	−	0.186695i
$324$	−1.00000			−0.0555556
$325$		0			0
$326$	2.77489			0.153687
$327$	−8.90410	+	5.14078i	−0.492398	+	0.284286i
$328$	−0.587246	−	1.01714i	−0.0324252	−	0.0561622i
$329$	−1.85408	+	3.21135i	−0.102218	+	0.177048i
$330$		0			0
$331$	−6.05268	−	3.49452i	−0.332686	−	0.192076i	0.324347	−	0.945938i	$-0.394855\pi$
$331$	−6.05268	−	3.49452i	−0.332686	−	0.192076i	−0.657033	+	0.753862i	$0.728189\pi$
$332$	3.33341	+	1.92455i	0.182945	+	0.105623i
$333$			9.15988i			0.501958i
$334$	−11.1022	+	19.2296i	−0.607485	+	1.05220i
$335$		0			0
$336$	−0.807007	+	0.465926i	−0.0440259	+	0.0254183i
$337$	35.3229			1.92416			0.962082	−	0.272761i	$-0.0879369\pi$
$337$	35.3229			1.92416			0.962082	+	0.272761i	$0.0879369\pi$
$338$	0.500000	+	12.9904i	0.0271964	+	0.706584i
$339$	9.65685			0.524488
$340$		0			0
$341$	−7.81779	−	13.5408i	−0.423357	−	0.733276i
$342$	−1.31431	+	2.27646i	−0.0710699	+	0.123097i
$343$		−	12.2368i		−	0.660723i
$344$	2.55695	+	1.47626i	0.137862	+	0.0795945i
$345$		0			0
$346$			0.950627i			0.0511060i
$347$	1.80920	−	3.13363i	0.0971232	−	0.168222i	−0.813370	−	0.581747i	$-0.802369\pi$
$347$	1.80920	−	3.13363i	0.0971232	−	0.168222i	0.910493	+	0.413525i	$0.135703\pi$
$348$	−1.69419	−	2.93443i	−0.0908184	−	0.157302i
$349$	−25.1956	+	14.5467i	−1.34869	+	0.778667i	−0.988064	−	0.154043i	$-0.950771\pi$
$349$	−25.1956	+	14.5467i	−1.34869	+	0.778667i	−0.360627	+	0.932710i	$0.617437\pi$
$350$		0			0
$351$	1.86250	+	3.08725i	0.0994130	+	0.164785i
$352$	−1.68216			−0.0896596
$353$	8.30867	−	4.79701i	0.442226	−	0.255319i	−0.262315	−	0.964982i	$-0.584486\pi$
$353$	8.30867	−	4.79701i	0.442226	−	0.255319i	0.704541	+	0.709663i	$0.251153\pi$
$354$	1.98709	+	3.44174i	0.105613	+	0.182926i
$355$		0			0
$356$		−	13.4670i		−	0.713751i
$357$	−2.06022	−	1.18947i	−0.109038	−	0.0629534i
$358$	8.55904	+	4.94156i	0.452359	+	0.261170i
$359$			6.31495i			0.333290i	0.986017	+	0.166645i	$0.0532935\pi$
$359$			6.31495i			0.333290i	−0.986017	+	0.166645i	$0.946707\pi$
$360$		0			0
$361$	−6.04516	−	10.4705i	−0.318166	−	0.551080i
$362$	12.3855	−	7.15075i	0.650965	−	0.375835i
$363$	8.17033			0.428831
$364$	2.94148	+	1.62364i	0.154175	+	0.0851020i
$365$		0			0
$366$	−7.55500	+	4.36188i	−0.394906	+	0.227999i
$367$	−17.4472	−	30.2194i	−0.910735	−	1.57744i	−0.813028	−	0.582224i	$-0.802182\pi$
$367$	−17.4472	−	30.2194i	−0.910735	−	1.57744i	−0.0977071	−	0.995215i	$-0.531151\pi$
$368$	3.22853	−	5.59197i	0.168299	−	0.291502i
$369$			1.17449i			0.0611416i
$370$		0			0
$371$	−4.32611	−	2.49768i	−0.224600	−	0.129673i
$372$			9.29493i			0.481920i
$373$	2.40608	−	4.16745i	0.124582	−	0.215782i	−0.796987	−	0.603996i	$-0.793574\pi$
$373$	2.40608	−	4.16745i	0.124582	−	0.215782i	0.921569	+	0.388213i	$0.126908\pi$
$374$	−2.14721	−	3.71907i	−0.111030	−	0.192309i
$375$		0			0
$376$	3.97934			0.205219
$377$	−5.90387	+	10.6958i	−0.304065	+	0.550861i
$378$	0.931852			0.0479293
$379$	−24.0847	+	13.9053i	−1.23715	+	0.714267i	−0.968510	−	0.248974i	$-0.919907\pi$
$379$	−24.0847	+	13.9053i	−1.23715	+	0.714267i	−0.268637	+	0.963241i	$0.586573\pi$
$380$		0			0
$381$	0.338502	−	0.586302i	0.0173420	−	0.0300372i
$382$		−	0.114637i		−	0.00586532i
$383$	0.697788	+	0.402868i	0.0356553	+	0.0205856i	0.517722	−	0.855549i	$-0.326780\pi$
$383$	0.697788	+	0.402868i	0.0356553	+	0.0205856i	−0.482066	+	0.876135i	$0.660114\pi$
$384$	0.866025	+	0.500000i	0.0441942	+	0.0255155i
$385$		0			0
$386$	−4.32843	+	7.49706i	−0.220311	+	0.381590i
$387$	−1.47626	−	2.55695i	−0.0750424	−	0.129977i
$388$	12.1945	−	7.04052i	0.619084	−	0.357428i
$389$	−27.5013			−1.39437			−0.697186	−	0.716891i	$-0.745565\pi$
$389$	−27.5013			−1.39437			−0.697186	+	0.716891i	$0.745565\pi$
$390$		0			0
$391$	16.4843			0.833647
$392$	−5.31017	+	3.06583i	−0.268204	+	0.154848i
$393$	−0.933552	−	1.61696i	−0.0470914	−	0.0815648i
$394$	−10.2401	+	17.7363i	−0.515887	+	0.893542i
$395$		0			0
$396$	1.45680	+	0.841081i	0.0732067	+	0.0422659i
$397$	0.994360	+	0.574094i	0.0499055	+	0.0288130i	0.524745	−	0.851259i	$-0.324161\pi$
$397$	0.994360	+	0.574094i	0.0499055	+	0.0288130i	−0.474840	+	0.880072i	$0.657494\pi$
$398$		−	1.91067i		−	0.0957733i
$399$	1.22474	−	2.12132i	0.0613139	−	0.106199i
$400$		0			0
$401$	11.8647	−	6.85009i	0.592495	−	0.342077i	−0.173589	−	0.984818i	$-0.555536\pi$
$401$	11.8647	−	6.85009i	0.592495	−	0.342077i	0.766083	+	0.642741i	$0.222203\pi$
$402$	−5.19151			−0.258929
$403$	28.6957	−	17.3118i	1.42944	−	0.862363i
$404$	−11.3178			−0.563083
$405$		0			0
$406$	1.57874	+	2.73445i	0.0783515	+	0.135709i
$407$	7.70420	−	13.3441i	0.381883	−	0.661441i
$408$			2.55291i			0.126388i
$409$	−6.63613	−	3.83137i	−0.328136	−	0.189449i	0.326878	−	0.945067i	$-0.394004\pi$
$409$	−6.63613	−	3.83137i	−0.328136	−	0.189449i	−0.655013	+	0.755618i	$0.727337\pi$
$410$		0			0
$411$			7.28861i			0.359521i
$412$	−0.362501	+	0.627871i	−0.0178592	+	0.0309330i
$413$	−1.85167	−	3.20719i	−0.0911148	−	0.157815i
$414$	−5.59197	+	3.22853i	−0.274830	+	0.158673i
$415$		0			0
$416$	−0.0693504	−	3.60488i	−0.00340018	−	0.176744i
$417$	4.71139			0.230718
$418$	3.82937	−	2.21089i	0.187301	−	0.108138i
$419$	19.5013	+	33.7773i	0.952701	+	1.65013i	0.739543	+	0.673110i	$0.235042\pi$
$419$	19.5013	+	33.7773i	0.952701	+	1.65013i	0.213159	+	0.977018i	$0.431625\pi$
$420$		0			0
$421$			32.7923i			1.59820i	0.601198	+	0.799100i	$0.294690\pi$
$421$			32.7923i			1.59820i	−0.601198	+	0.799100i	$0.705310\pi$
$422$	−1.07408	−	0.620118i	−0.0522852	−	0.0301869i
$423$	−3.44621	−	1.98967i	−0.167560	−	0.0967410i
$424$			5.36068i			0.260337i
$425$		0			0
$426$	−1.96763	−	3.40803i	−0.0953318	−	0.165119i
$427$	7.04014	−	4.06462i	0.340696	−	0.196701i
$428$	−17.2173			−0.832231
$429$	−0.116659	−	6.06400i	−0.00563233	−	0.292773i
$430$		0			0
$431$	−28.6031	+	16.5140i	−1.37776	+	0.795452i	−0.991890	−	0.127100i	$-0.959433\pi$
$431$	−28.6031	+	16.5140i	−1.37776	+	0.795452i	−0.385873	+	0.922552i	$0.626100\pi$
$432$	−0.500000	−	0.866025i	−0.0240563	−	0.0416667i
$433$	4.49706	−	7.78913i	0.216115	−	0.374322i	−0.737502	−	0.675345i	$-0.763995\pi$
$433$	4.49706	−	7.78913i	0.216115	−	0.374322i	0.953617	+	0.301023i	$0.0973282\pi$
$434$		−	8.66150i		−	0.415765i
$435$		0			0
$436$	−8.90410	−	5.14078i	−0.426429	−	0.246199i
$437$			16.9732i			0.811937i
$438$	3.63165	−	6.29021i	0.173527	−	0.300558i
$439$	3.65685	+	6.33386i	0.174532	+	0.302299i	0.939999	−	0.341176i	$-0.110825\pi$
$439$	3.65685	+	6.33386i	0.174532	+	0.302299i	−0.765467	+	0.643475i	$0.777492\pi$
$440$		0			0
$441$	6.13165			0.291983
$442$	7.88147	−	4.75481i	0.374884	−	0.226163i
$443$	−27.5200			−1.30752			−0.653758	−	0.756703i	$-0.726809\pi$
$443$	−27.5200			−1.30752			−0.653758	+	0.756703i	$0.726809\pi$
$444$	−7.93269	+	4.57994i	−0.376469	+	0.217354i
$445$		0			0
$446$	−7.38915	+	12.7984i	−0.349886	+	0.606021i
$447$			3.00240i			0.142009i
$448$	−0.807007	−	0.465926i	−0.0381275	−	0.0220129i
$449$	8.88390	+	5.12912i	0.419257	+	0.242058i	0.694760	−	0.719242i	$-0.255511\pi$
$449$	8.88390	+	5.12912i	0.419257	+	0.242058i	−0.275502	+	0.961300i	$0.588844\pi$
$450$		0			0
$451$	0.987844	−	1.71100i	0.0465157	−	0.0805676i
$452$	4.82843	+	8.36308i	0.227110	+	0.393366i
$453$	−10.7561	+	6.21001i	−0.505363	+	0.291772i
$454$	−9.56580			−0.448945
$455$		0			0
$456$	−2.62863			−0.123097
$457$	−12.7653	+	7.37005i	−0.597135	+	0.344756i	−0.767914	−	0.640553i	$-0.778705\pi$
$457$	−12.7653	+	7.37005i	−0.597135	+	0.344756i	0.170778	+	0.985309i	$0.445372\pi$
$458$	−7.57389	−	13.1184i	−0.353905	−	0.612981i
$459$	1.27646	−	2.21089i	0.0595799	−	0.103195i
$460$		0			0
$461$	17.1993	+	9.93003i	0.801052	+	0.462487i	0.843839	−	0.536597i	$-0.180290\pi$
$461$	17.1993	+	9.93003i	0.801052	+	0.462487i	−0.0427870	+	0.999084i	$0.513624\pi$
$462$	−1.35752	−	0.783763i	−0.0631574	−	0.0364640i
$463$		−	32.1533i		−	1.49429i	−0.664662	−	0.747144i	$-0.731424\pi$
$463$		−	32.1533i		−	1.49429i	0.664662	−	0.747144i	$-0.268576\pi$
$464$	1.69419	−	2.93443i	0.0786510	−	0.136228i
$465$		0			0
$466$	16.2304	−	9.37064i	0.751860	−	0.434087i
$467$	−22.2754			−1.03078			−0.515392	−	0.856955i	$-0.672354\pi$
$467$	−22.2754			−1.03078			−0.515392	+	0.856955i	$0.672354\pi$
$468$	−1.74238	+	3.15660i	−0.0805417	+	0.145914i
$469$	4.83772			0.223385
$470$		0			0
$471$	−11.2609	−	19.5044i	−0.518873	−	0.898714i
$472$	−1.98709	+	3.44174i	−0.0914631	+	0.158419i
$473$			4.96661i			0.228365i
$474$	3.19540	+	1.84486i	0.146769	+	0.0847374i
$475$		0			0
$476$		−	2.37894i		−	0.109038i
$477$	2.68034	−	4.64248i	0.122724	−	0.212565i
$478$	−2.31165	−	4.00390i	−0.105732	−	0.183134i
$479$	−19.0007	+	10.9700i	−0.868163	+	0.501234i	−0.866737	−	0.498765i	$-0.833787\pi$
$479$	−19.0007	+	10.9700i	−0.868163	+	0.501234i	−0.00142578	+	0.999999i	$0.500454\pi$
$480$		0			0
$481$	28.9140	+	15.9600i	1.31837	+	0.727714i
$482$	17.5945			0.801408
$483$	5.21089	−	3.00851i	0.237104	−	0.136892i
$484$	4.08516	+	7.07571i	0.185689	+	0.321623i
$485$		0			0
$486$			1.00000i			0.0453609i
$487$	7.84015	+	4.52651i	0.355271	+	0.205116i	0.667004	−	0.745054i	$-0.267576\pi$
$487$	7.84015	+	4.52651i	0.355271	+	0.205116i	−0.311733	+	0.950170i	$0.600910\pi$
$488$	−7.55500	−	4.36188i	−0.341999	−	0.197453i
$489$		−	2.77489i		−	0.125485i
$490$		0			0
$491$	−15.1000	−	26.1540i	−0.681455	−	1.18031i	−0.974537	−	0.224227i	$-0.928014\pi$
$491$	−15.1000	−	26.1540i	−0.681455	−	1.18031i	0.293082	−	0.956087i	$-0.405319\pi$
$492$	−1.01714	+	0.587246i	−0.0458562	+	0.0264751i
$493$	8.65027			0.389588
$494$	4.89582	+	8.11522i	0.220273	+	0.365121i
$495$		0			0
$496$	−8.04965	+	4.64747i	−0.361440	+	0.208677i
$497$	1.83354	+	3.17578i	0.0822453	+	0.142453i
$498$	1.92455	−	3.33341i	0.0862410	−	0.149374i
$499$		−	9.04336i		−	0.404836i	−0.979299	−	0.202418i	$-0.935120\pi$
$499$		−	9.04336i		−	0.404836i	0.979299	−	0.202418i	$-0.0648800\pi$
$500$		0			0
$501$	19.2296	+	11.1022i	0.859114	+	0.496010i
$502$			26.5198i			1.18364i
$503$	15.5446	−	26.9241i	0.693101	−	1.20049i	−0.277715	−	0.960663i	$-0.589577\pi$
$503$	15.5446	−	26.9241i	0.693101	−	1.20049i	0.970817	−	0.239823i	$-0.0770894\pi$
$504$	0.465926	+	0.807007i	0.0207540	+	0.0359470i
$505$		0			0
$506$	10.8618			0.482867
$507$	12.9904	−	0.500000i	0.576923	−	0.0222058i
$508$	0.677003			0.0300372
$509$	−22.5466	+	13.0173i	−0.999361	+	0.576981i	−0.908059	−	0.418842i	$-0.862436\pi$
$509$	−22.5466	+	13.0173i	−0.999361	+	0.576981i	−0.0913018	+	0.995823i	$0.529103\pi$
$510$		0			0
$511$	−3.38416	+	5.86154i	−0.149706	+	0.259299i
$512$			1.00000i			0.0441942i
$513$	2.27646	+	1.31431i	0.100508	+	0.0580283i
$514$	−1.57986	−	0.912132i	−0.0696846	−	0.0402324i
$515$		0			0
$516$	1.47626	−	2.55695i	0.0649886	−	0.112564i
$517$	3.34695	+	5.79708i	0.147198	+	0.254955i
$518$	7.39209	−	4.26782i	0.324790	−	0.187517i
$519$	0.950627			0.0417279
$520$		0			0
$521$	−24.8332			−1.08796			−0.543982	−	0.839097i	$-0.683084\pi$
$521$	−24.8332			−1.08796			−0.543982	+	0.839097i	$0.683084\pi$
$522$	−2.93443	+	1.69419i	−0.128437	+	0.0741529i
$523$	4.20445	+	7.28231i	0.183848	+	0.318433i	0.943188	−	0.332261i	$-0.107811\pi$
$523$	4.20445	+	7.28231i	0.183848	+	0.318433i	−0.759340	+	0.650694i	$0.774478\pi$
$524$	0.933552	−	1.61696i	0.0407824	−	0.0706372i
$525$		0			0
$526$	−10.5106	−	6.06828i	−0.458283	−	0.264590i
$527$	−20.5501	−	11.8646i	−0.895175	−	0.516829i
$528$			1.68216i			0.0732067i
$529$	−9.34677	+	16.1891i	−0.406381	+	0.703873i
$530$		0			0
$531$	3.44174	−	1.98709i	0.149359	−	0.0862323i
$532$	2.44949			0.106199
$533$	3.70740	+	2.04642i	0.160585	+	0.0886401i
$534$	−13.4670			−0.582775
$535$		0			0
$536$	−2.59575	−	4.49598i	−0.112120	−	0.194197i
$537$	4.94156	−	8.55904i	0.213244	−	0.369350i
$538$			23.5310i			1.01449i
$539$	−8.93256	−	5.15722i	−0.384753	−	0.222137i
$540$		0			0
$541$		−	15.7195i		−	0.675833i	−0.941176	−	0.337916i	$-0.890278\pi$
$541$		−	15.7195i		−	0.675833i	0.941176	−	0.337916i	$-0.109722\pi$
$542$	6.34349	−	10.9872i	0.272476	−	0.471942i
$543$	−7.15075	−	12.3855i	−0.306868	−	0.531511i
$544$	−2.21089	+	1.27646i	−0.0947911	+	0.0547276i
$545$		0			0
$546$	1.62364	−	2.94148i	0.0694855	−	0.125884i
$547$	23.0313			0.984745			0.492373	−	0.870385i	$-0.336130\pi$
$547$	23.0313			0.984745			0.492373	+	0.870385i	$0.336130\pi$
$548$	−6.31212	+	3.64431i	−0.269641	+	0.155677i
$549$	4.36188	+	7.55500i	0.186160	+	0.322439i
$550$		0			0
$551$			8.90681i			0.379443i
$552$	−5.59197	−	3.22853i	−0.238010	−	0.137415i
$553$	−2.97764	−	1.71914i	−0.126622	−	0.0731052i
$554$			12.8235i			0.544820i
$555$		0			0
$556$	2.35569	+	4.08018i	0.0999036	+	0.173038i
$557$	35.2097	−	20.3283i	1.49188	−	0.861339i	0.491925	−	0.870637i	$-0.336293\pi$
$557$	35.2097	−	20.3283i	1.49188	−	0.861339i	0.999957	+	0.00929877i	$0.00295993\pi$
$558$	9.29493			0.393486
$559$	−10.6435	+	0.204758i	−0.450171	+	0.00866034i
$560$		0			0
$561$	−3.71907	+	2.14721i	−0.157019	+	0.0906552i
$562$	−2.58360	−	4.47492i	−0.108982	−	0.188763i
$563$	1.71770	−	2.97514i	0.0723923	−	0.125387i	−0.827557	−	0.561382i	$-0.810270\pi$
$563$	1.71770	−	2.97514i	0.0723923	−	0.125387i	0.899949	+	0.435995i	$0.143603\pi$
$564$		−	3.97934i		−	0.167560i
$565$		0			0
$566$	11.2258	+	6.48124i	0.471857	+	0.272427i
$567$		−	0.931852i		−	0.0391341i
$568$	1.96763	−	3.40803i	0.0825597	−	0.142998i
$569$	−11.0320	−	19.1079i	−0.462484	−	0.801046i	0.536600	−	0.843837i	$-0.319708\pi$
$569$	−11.0320	−	19.1079i	−0.462484	−	0.801046i	−0.999084	+	0.0427908i	$0.986375\pi$
$570$		0			0
$571$	4.56829			0.191177			0.0955885	−	0.995421i	$-0.469527\pi$
$571$	4.56829			0.191177			0.0955885	+	0.995421i	$0.469527\pi$
$572$	5.19325	−	3.13303i	0.217141	−	0.130999i
$573$	−0.114637			−0.00478901
$574$	0.947824	−	0.547226i	0.0395614	−	0.0228408i
$575$		0			0
$576$	0.500000	−	0.866025i	0.0208333	−	0.0360844i
$577$			4.42655i			0.184280i	0.995746	+	0.0921398i	$0.0293707\pi$
$577$			4.42655i			0.184280i	−0.995746	+	0.0921398i	$0.970629\pi$
$578$	9.07822	+	5.24131i	0.377604	+	0.218010i
$579$	7.49706	+	4.32843i	0.311567	+	0.179883i
$580$		0			0
$581$	−1.79339	+	3.10624i	−0.0744024	+	0.128869i
$582$	−7.04052	−	12.1945i	−0.291839	−	0.505480i
$583$	−7.80941	+	4.50877i	−0.323433	+	0.186734i
$584$	7.26330			0.300558
$585$		0			0
$586$	13.4704			0.556458
$587$	−37.3725	+	21.5770i	−1.54253	+	0.890580i	−0.543852	+	0.839181i	$0.683035\pi$
$587$	−37.3725	+	21.5770i	−1.54253	+	0.890580i	−0.998678	+	0.0513987i	$0.983632\pi$
$588$	3.06583	+	5.31017i	0.126433	+	0.218988i
$589$	12.2165	−	21.1595i	0.503370	−	0.871863i
$590$		0			0
$591$	17.7363	+	10.2401i	0.729574	+	0.421220i
$592$	−7.93269	−	4.57994i	−0.326032	−	0.188234i
$593$		−	28.8372i		−	1.18420i	−0.805864	−	0.592101i	$-0.798299\pi$
$593$		−	28.8372i		−	1.18420i	0.805864	−	0.592101i	$-0.201701\pi$
$594$	0.841081	−	1.45680i	0.0345100	−	0.0597731i
$595$		0			0
$596$	−2.60016	+	1.50120i	−0.106507	+	0.0614916i
$597$	−1.91067			−0.0781986
$598$	0.447799	+	23.2769i	0.0183119	+	0.951864i
$599$	−28.1704			−1.15101			−0.575505	−	0.817798i	$-0.695194\pi$
$599$	−28.1704			−1.15101			−0.575505	+	0.817798i	$0.695194\pi$
$600$		0			0
$601$	7.31925	+	12.6773i	0.298558	+	0.517118i	0.975806	−	0.218637i	$-0.0701610\pi$
$601$	7.31925	+	12.6773i	0.298558	+	0.517118i	−0.677248	+	0.735755i	$0.736828\pi$
$602$	−1.37565	+	2.38270i	−0.0560674	+	0.0971117i
$603$			5.19151i			0.211415i
$604$	−10.7561	−	6.21001i	−0.437657	−	0.252682i
$605$		0			0
$606$			11.3178i			0.459756i
$607$	6.50853	−	11.2731i	0.264173	−	0.457561i	−0.703174	−	0.711018i	$-0.748234\pi$
$607$	6.50853	−	11.2731i	0.264173	−	0.457561i	0.967347	+	0.253457i	$0.0815677\pi$
$608$	−1.31431	−	2.27646i	−0.0533024	−	0.0923225i
$609$	2.73445	−	1.57874i	0.110806	−	0.0639737i
$610$		0			0
$611$	−12.2852	+	7.41152i	−0.497006	+	0.299838i
$612$	2.55291			0.103195
$613$	−23.5813	+	13.6146i	−0.952438	+	0.549890i	−0.893837	−	0.448391i	$-0.851997\pi$
$613$	−23.5813	+	13.6146i	−0.952438	+	0.549890i	−0.0586006	+	0.998282i	$0.518664\pi$
$614$	10.7310	+	18.5866i	0.433067	+	0.750094i
$615$		0			0
$616$		−	1.56753i		−	0.0631574i
$617$	20.3825	+	11.7678i	0.820569	+	0.473755i	0.850613	−	0.525793i	$-0.176231\pi$
$617$	20.3825	+	11.7678i	0.820569	+	0.473755i	−0.0300439	+	0.999549i	$0.509565\pi$
$618$	0.627871	+	0.362501i	0.0252567	+	0.0145819i
$619$		−	23.0280i		−	0.925573i	−0.886470	−	0.462786i	$-0.846850\pi$
$619$		−	23.0280i		−	0.925573i	0.886470	−	0.462786i	$-0.153150\pi$
$620$		0			0
$621$	3.22853	+	5.59197i	0.129556	+	0.224398i
$622$	−12.7792	+	7.37808i	−0.512399	+	0.295834i
$623$	12.5493			0.502776
$624$	−3.60488	+	0.0693504i	−0.144311	+	0.00277624i
$625$		0			0
$626$	1.21625	−	0.702205i	0.0486113	−	0.0280658i
$627$	−2.21089	−	3.82937i	−0.0882944	−	0.152930i
$628$	11.2609	−	19.5044i	0.449357	−	0.778309i
$629$		−	23.3844i		−	0.932397i
$630$		0			0
$631$	−14.3378	−	8.27792i	−0.570778	−	0.329539i	0.186682	−	0.982420i	$-0.440227\pi$
$631$	−14.3378	−	8.27792i	−0.570778	−	0.329539i	−0.757460	+	0.652882i	$0.773560\pi$
$632$			3.68973i			0.146769i
$633$	−0.620118	+	1.07408i	−0.0246475	+	0.0426907i
$634$	16.5710	+	28.7019i	0.658119	+	1.13990i
$635$		0			0
$636$	5.36068			0.212565
$637$	10.6837	−	19.3552i	0.423303	−	0.766879i
$638$	5.69982			0.225658
$639$	−3.40803	+	1.96763i	−0.134819	+	0.0778381i
$640$		0			0
$641$	−0.390454	+	0.676286i	−0.0154220	+	0.0267117i	−0.873633	−	0.486585i	$-0.838243\pi$
$641$	−0.390454	+	0.676286i	−0.0154220	+	0.0267117i	0.858211	+	0.513296i	$0.171576\pi$
$642$			17.2173i			0.679514i
$643$	−21.2597	−	12.2743i	−0.838399	−	0.484050i	0.0183207	−	0.999832i	$-0.494168\pi$
$643$	−21.2597	−	12.2743i	−0.838399	−	0.484050i	−0.856720	+	0.515782i	$0.827501\pi$
$644$	5.21089	+	3.00851i	0.205338	+	0.118552i
$645$		0			0
$646$	3.35533	−	5.81160i	0.132014	−	0.228654i
$647$	1.58200	+	2.74011i	0.0621950	+	0.107725i	0.895446	−	0.445170i	$-0.146857\pi$
$647$	1.58200	+	2.74011i	0.0621950	+	0.107725i	−0.833251	+	0.552894i	$0.813523\pi$
$648$	−0.866025	+	0.500000i	−0.0340207	+	0.0196419i
$649$	−6.68521			−0.262417
$650$		0			0
$651$	−8.66150			−0.339471
$652$	2.40313	−	1.38745i	0.0941137	−	0.0543366i
$653$	−16.1443	−	27.9627i	−0.631774	−	1.09426i	−0.987189	−	0.159556i	$-0.948994\pi$
$653$	−16.1443	−	27.9627i	−0.631774	−	1.09426i	0.355415	−	0.934709i	$-0.384340\pi$
$654$	−5.14078	+	8.90410i	−0.201021	+	0.348178i
$655$		0			0
$656$	−1.01714	−	0.587246i	−0.0397127	−	0.0229281i
$657$	−6.29021	−	3.63165i	−0.245404	−	0.141684i
$658$			3.70815i			0.144559i
$659$	−17.6775	+	30.6184i	−0.688619	+	1.19272i	0.283666	+	0.958923i	$0.408449\pi$
$659$	−17.6775	+	30.6184i	−0.688619	+	1.19272i	−0.972285	+	0.233799i	$0.924884\pi$
$660$		0			0
$661$	16.9243	−	9.77124i	0.658279	−	0.380057i	−0.133342	−	0.991070i	$-0.542571\pi$
$661$	16.9243	−	9.77124i	0.658279	−	0.380057i	0.791621	+	0.611013i	$0.209238\pi$
$662$	−6.98904			−0.271637
$663$	−4.75481	−	7.88147i	−0.184661	−	0.306091i
$664$	3.84909			0.149374
$665$		0			0
$666$	4.57994	+	7.93269i	0.177469	+	0.307385i
$667$	−10.9395	+	18.9478i	−0.423579	+	0.733661i
$668$			22.2044i			0.859114i
$669$	12.7984	+	7.38915i	0.494814	+	0.285681i
$670$		0			0
$671$		−	14.6748i		−	0.566514i
$672$	−0.465926	+	0.807007i	−0.0179735	+	0.0311310i
$673$	−1.25806	−	2.17903i	−0.0484948	−	0.0839954i	0.840759	−	0.541409i	$-0.182109\pi$
$673$	−1.25806	−	2.17903i	−0.0484948	−	0.0839954i	−0.889254	+	0.457414i	$0.848776\pi$
$674$	30.5906	−	17.6615i	1.17830	−	0.680295i
$675$		0			0
$676$	6.92820	+	11.0000i	0.266469	+	0.423077i
$677$	41.0114			1.57620			0.788098	−	0.615550i	$-0.211066\pi$
$677$	41.0114			1.57620			0.788098	+	0.615550i	$0.211066\pi$
$678$	8.36308	−	4.82843i	0.321182	−	0.185435i
$679$	6.56072	+	11.3635i	0.251777	+	0.436091i
$680$		0			0
$681$			9.56580i			0.366562i
$682$	−13.5408	−	7.81779i	−0.518505	−	0.299359i
$683$	−20.9177	−	12.0769i	−0.800395	−	0.462108i	0.0432142	−	0.999066i	$-0.486240\pi$
$683$	−20.9177	−	12.0769i	−0.800395	−	0.462108i	−0.843609	+	0.536958i	$0.819574\pi$
$684$			2.62863i			0.100508i
$685$		0			0
$686$	−6.11838	−	10.5973i	−0.233601	−	0.404608i
$687$	−13.1184	+	7.57389i	−0.500497	+	0.288962i
$688$	2.95252			0.112564
$689$	−9.98427	−	16.5497i	−0.380370	−	0.630494i
$690$		0			0
$691$	−35.7340	+	20.6310i	−1.35939	+	0.784841i	−0.989541	−	0.144252i	$-0.953922\pi$
$691$	−35.7340	+	20.6310i	−1.35939	+	0.784841i	−0.369844	+	0.929094i	$0.620589\pi$
$692$	0.475314	+	0.823267i	0.0180687	+	0.0312959i
$693$	−0.783763	+	1.35752i	−0.0297727	+	0.0515678i
$694$		−	3.61841i		−	0.137353i
$695$		0			0
$696$	−2.93443	−	1.69419i	−0.111229	−	0.0642183i
$697$		−	2.99838i		−	0.113572i
$698$	−14.5467	+	25.1956i	−0.550601	+	0.953669i
$699$	−9.37064	−	16.2304i	−0.354430	−	0.613891i
$700$		0			0
$701$	27.2880			1.03065			0.515327	−	0.856994i	$-0.327671\pi$
$701$	27.2880			1.03065			0.515327	+	0.856994i	$0.327671\pi$
$702$	3.15660	+	1.74238i	0.119138	+	0.0657620i
$703$	24.0779			0.908115
$704$	−1.45680	+	0.841081i	−0.0549051	+	0.0316994i
$705$		0			0
$706$	4.79701	−	8.30867i	0.180538	−	0.312701i
$707$		−	10.5465i		−	0.396644i
$708$	3.44174	+	1.98709i	0.129348	+	0.0746793i
$709$	2.18928	+	1.26398i	0.0822200	+	0.0474697i	0.540546	−	0.841314i	$-0.318218\pi$
$709$	2.18928	+	1.26398i	0.0822200	+	0.0474697i	−0.458326	+	0.888784i	$0.651551\pi$
$710$		0			0
$711$	1.84486	−	3.19540i	0.0691878	−	0.119837i
$712$	−6.73351	−	11.6628i	−0.252349	−	0.437081i
$713$	51.9770	−	30.0089i	1.94655	−	1.12384i
$714$	−2.37894			−0.0890295
$715$		0			0
$716$	9.88312			0.369350
$717$	−4.00390	+	2.31165i	−0.149528	+	0.0863302i
$718$	3.15748	+	5.46891i	0.117836	+	0.204098i
$719$	26.6943	−	46.2359i	0.995530	−	1.72431i	0.415968	−	0.909379i	$-0.363443\pi$
$719$	26.6943	−	46.2359i	0.995530	−	1.72431i	0.579562	−	0.814928i	$-0.303224\pi$
$720$		0			0
$721$	−0.585082	−	0.337797i	−0.0217896	−	0.0125802i
$722$	−10.4705	−	6.04516i	−0.389673	−	0.224978i
$723$		−	17.5945i		−	0.654347i
$724$	7.15075	−	12.3855i	0.265756	−	0.460302i
$725$		0			0
$726$	7.07571	−	4.08516i	0.262604	−	0.151615i
$727$	−2.09614			−0.0777417			−0.0388709	−	0.999244i	$-0.512376\pi$
$727$	−2.09614			−0.0777417			−0.0388709	+	0.999244i	$0.512376\pi$
$728$	3.35922	−	0.0646242i	0.124501	−	0.00239513i
$729$	1.00000			0.0370370
$730$		0			0
$731$	3.76876	+	6.52768i	0.139393	+	0.241435i
$732$	−4.36188	+	7.55500i	−0.161220	+	0.279241i
$733$			16.7827i			0.619883i	0.950756	+	0.309942i	$0.100310\pi$
$733$			16.7827i			0.619883i	−0.950756	+	0.309942i	$0.899690\pi$
$734$	−30.2194	−	17.4472i	−1.11542	−	0.643987i
$735$		0			0
$736$		−	6.45705i		−	0.238010i
$737$	4.36648	−	7.56297i	0.160841	−	0.278585i
$738$	0.587246	+	1.01714i	0.0216168	+	0.0374414i
$739$	8.24563	−	4.76062i	0.303321	−	0.175122i	−0.340613	−	0.940204i	$-0.610635\pi$
$739$	8.24563	−	4.76062i	0.303321	−	0.175122i	0.643934	+	0.765081i	$0.277301\pi$
$740$		0			0
$741$	8.11522	−	4.89582i	0.298120	−	0.179852i
$742$	−4.99536			−0.183385
$743$	−28.2034	+	16.2832i	−1.03468	+	0.597374i	−0.918323	−	0.395833i	$-0.870456\pi$
$743$	−28.2034	+	16.2832i	−1.03468	+	0.597374i	−0.116360	+	0.993207i	$0.537123\pi$
$744$	4.64747	+	8.04965i	0.170384	+	0.295114i
$745$		0			0
$746$		−	4.81216i		−	0.176186i
$747$	−3.33341	−	1.92455i	−0.121963	−	0.0704154i
$748$	−3.71907	−	2.14721i	−0.135983	−	0.0785097i
$749$		−	16.0440i		−	0.586235i
$750$		0			0
$751$	−7.38117	−	12.7846i	−0.269343	−	0.466515i	0.699350	−	0.714780i	$-0.253473\pi$
$751$	−7.38117	−	12.7846i	−0.269343	−	0.466515i	−0.968692	+	0.248265i	$0.920140\pi$
$752$	3.44621	−	1.98967i	0.125670	−	0.0725557i
$753$	26.5198			0.966436
$754$	0.234986	+	12.2148i	0.00855769	+	0.444835i
$755$		0			0
$756$	0.807007	−	0.465926i	0.0293506	−	0.0169456i
$757$	−17.5781	−	30.4462i	−0.638888	−	1.10659i	−0.985677	−	0.168643i	$-0.946061\pi$
$757$	−17.5781	−	30.4462i	−0.638888	−	1.10659i	0.346789	−	0.937943i	$-0.387272\pi$
$758$	−13.9053	+	24.0847i	−0.505063	+	0.874795i
$759$		−	10.8618i		−	0.394259i
$760$		0			0
$761$	−36.2215	−	20.9125i	−1.31303	−	0.758076i	−0.330431	−	0.943830i	$-0.607194\pi$
$761$	−36.2215	−	20.9125i	−1.31303	−	0.758076i	−0.982596	+	0.185754i	$0.940527\pi$
$762$		−	0.677003i		−	0.0245252i
$763$	4.79045	−	8.29730i	0.173426	−	0.300382i
$764$	−0.0573183	−	0.0992782i	−0.00207370	−	0.00359176i
$765$		0			0
$766$	0.805736			0.0291124
$767$	−0.275611	−	14.3264i	−0.00995172	−	0.517298i
$768$	1.00000			0.0360844
$769$	39.4957	−	22.8028i	1.42425	−	0.822291i	0.427591	−	0.903972i	$-0.359362\pi$
$769$	39.4957	−	22.8028i	1.42425	−	0.822291i	0.996659	+	0.0816812i	$0.0260289\pi$
$770$		0			0
$771$	−0.912132	+	1.57986i	−0.0328496	+	0.0568972i
$772$			8.65685i			0.311567i
$773$	−10.9424	−	6.31759i	−0.393570	−	0.227228i	0.290136	−	0.956986i	$-0.406300\pi$
$773$	−10.9424	−	6.31759i	−0.393570	−	0.227228i	−0.683706	+	0.729758i	$0.739633\pi$
$774$	−2.55695	−	1.47626i	−0.0919078	−	0.0530630i
$775$		0			0
$776$	7.04052	−	12.1945i	0.252740	−	0.437758i
$777$	−4.26782	−	7.39209i	−0.153107	−	0.265190i
$778$	−23.8168	+	13.7507i	−0.853875	+	0.492985i
$779$	3.08730			0.110614
$780$		0			0
$781$	6.61973			0.236873
$782$	14.2758	−	8.24215i	0.510502	−	0.294739i
$783$	1.69419	+	2.93443i	0.0605456	+	0.104868i
$784$	−3.06583	+	5.31017i	−0.109494	+	0.189649i
$785$		0			0
$786$	−1.61696	−	0.933552i	−0.0576750	−	0.0332987i
$787$	−45.1559	−	26.0708i	−1.60963	−	0.929323i	−0.989451	−	0.144865i	$-0.953725\pi$
$787$	−45.1559	−	26.0708i	−1.60963	−	0.929323i	−0.620182	−	0.784458i	$-0.712941\pi$
$788$			20.4801i			0.729574i
$789$	−6.06828	+	10.5106i	−0.216037	+	0.374186i
$790$		0			0
$791$	−7.79315	+	4.49938i	−0.277093	+	0.159979i
$792$	1.68216			0.0597731
$793$	31.4481	−	0.604996i	1.11676	−	0.0214840i
$794$	1.14819			0.0407477
$795$		0			0
$796$	−0.955336	−	1.65469i	−0.0338610	−	0.0586489i
$797$	−21.3956	+	37.0582i	−0.757870	+	1.31267i	0.186065	+	0.982537i	$0.440426\pi$
$797$	−21.3956	+	37.0582i	−0.757870	+	1.31267i	−0.943935	+	0.330132i	$0.892907\pi$
$798$		−	2.44949i		−	0.0867110i
$799$	8.79787	+	5.07945i	0.311246	+	0.179698i
$800$		0			0
$801$			13.4670i			0.475834i
$802$	6.85009	−	11.8647i	0.241885	−	0.418957i
$803$	6.10903	+	10.5812i	0.215583	+	0.373401i
$804$	−4.49598	+	2.59575i	−0.158561	+	0.0915452i
$805$		0			0
$806$	16.1953	−	29.3404i	0.570456	−	1.03347i
$807$	23.5310			0.828331
$808$	−9.80153	+	5.65892i	−0.344817	+	0.199080i
$809$	−24.3918	−	42.2478i	−0.857569	−	1.48535i	−0.874241	−	0.485492i	$-0.838640\pi$
$809$	−24.3918	−	42.2478i	−0.857569	−	1.48535i	0.0166719	−	0.999861i	$-0.494693\pi$
$810$		0			0
$811$			7.87402i			0.276494i	0.990398	+	0.138247i	$0.0441468\pi$
$811$			7.87402i			0.276494i	−0.990398	+	0.138247i	$0.955853\pi$
$812$	2.73445	+	1.57874i	0.0959606	+	0.0554029i
$813$	−10.9872	−	6.34349i	−0.385339	−	0.222476i
$814$		−	15.4084i		−	0.540064i
$815$		0			0
$816$	1.27646	+	2.21089i	0.0446849	+	0.0773966i
$817$	−6.72128	+	3.88053i	−0.235148	+	0.135763i
$818$	−7.66274			−0.267922
$819$	−2.94148	−	1.62364i	−0.102784	−	0.0567347i
$820$		0			0
$821$	−24.6790	+	14.2484i	−0.861304	+	0.497274i	−0.864449	−	0.502721i	$-0.832332\pi$
$821$	−24.6790	+	14.2484i	−0.861304	+	0.497274i	0.00314470	+	0.999995i	$0.498999\pi$
$822$	3.64431	+	6.31212i	0.127110	+	0.220161i
$823$	−23.1164	+	40.0387i	−0.805786	+	1.39566i	0.109973	+	0.993935i	$0.464924\pi$
$823$	−23.1164	+	40.0387i	−0.805786	+	1.39566i	−0.915759	+	0.401728i	$0.868410\pi$
$824$			0.725003i			0.0252567i
$825$		0			0
$826$	−3.20719	−	1.85167i	−0.111592	−	0.0644279i
$827$			9.53716i			0.331640i	0.986156	+	0.165820i	$0.0530270\pi$
$827$			9.53716i			0.331640i	−0.986156	+	0.165820i	$0.946973\pi$
$828$	−3.22853	+	5.59197i	−0.112199	+	0.194334i
$829$	6.64904	+	11.5165i	0.230931	+	0.399984i	0.958082	−	0.286493i	$-0.0924896\pi$
$829$	6.64904	+	11.5165i	0.230931	+	0.399984i	−0.727152	+	0.686477i	$0.759156\pi$
$830$		0			0
$831$	12.8235			0.444843
$832$	−1.86250	−	3.08725i	−0.0645706	−	0.107031i
$833$	−15.6536			−0.542365
$834$	4.08018	−	2.35569i	0.141285	−	0.0815710i
$835$		0			0
$836$	2.21089	−	3.82937i	0.0764652	−	0.132442i
$837$		−	9.29493i		−	0.321280i
$838$	33.7773	+	19.5013i	1.16682	+	0.673662i
$839$	42.8848	+	24.7595i	1.48055	+	0.854794i	0.999757	−	0.0220420i	$-0.00701677\pi$
$839$	42.8848	+	24.7595i	1.48055	+	0.854794i	0.480790	+	0.876836i	$0.340350\pi$
$840$		0			0
$841$	8.75941	−	15.1717i	0.302049	−	0.523163i
$842$	16.3962	+	28.3990i	0.565049	+	0.978694i
$843$	−4.47492	+	2.58360i	−0.154125	+	0.0889838i
$844$	−1.24024			−0.0426907
$845$		0			0
$846$	−3.97934			−0.136812
$847$	−6.59351	+	3.80677i	−0.226556	+	0.130802i
$848$	2.68034	+	4.64248i	0.0920432	+	0.159424i
$849$	6.48124	−	11.2258i	0.222436	−	0.385270i
$850$		0			0
$851$	51.2218	+	29.5729i	1.75586	+	1.01375i
$852$	−3.40803	−	1.96763i	−0.116757	−	0.0674097i
$853$		−	6.87904i		−	0.235534i	−0.993041	−	0.117767i	$-0.962426\pi$
$853$		−	6.87904i		−	0.235534i	0.993041	−	0.117767i	$-0.0375736\pi$
$854$	4.06462	−	7.04014i	0.139089	−	0.240908i
$855$		0			0
$856$	−14.9106	+	8.60867i	−0.509635	+	0.294238i
$857$	25.1526			0.859198			0.429599	−	0.903020i	$-0.358655\pi$
$857$	25.1526			0.859198			0.429599	+	0.903020i	$0.358655\pi$
$858$	−3.13303	−	5.19325i	−0.106960	−	0.177295i
$859$	52.3171			1.78504			0.892518	−	0.451012i	$-0.148937\pi$
$859$	52.3171			1.78504			0.892518	+	0.451012i	$0.148937\pi$
$860$		0			0
$861$	−0.547226	−	0.947824i	−0.0186494	−	0.0323017i
$862$	−16.5140	+	28.6031i	−0.562469	+	0.974225i
$863$		−	29.9308i		−	1.01886i	−0.860513	−	0.509428i	$-0.829857\pi$
$863$		−	29.9308i		−	1.01886i	0.860513	−	0.509428i	$-0.170143\pi$
$864$	−0.866025	−	0.500000i	−0.0294628	−	0.0170103i
$865$		0			0
$866$		−	8.99411i		−	0.305632i
$867$	5.24131	−	9.07822i	0.178004	−	0.308313i
$868$	−4.33075	−	7.50108i	−0.146995	−	0.254603i
$869$	−5.37518	+	3.10336i	−0.182340	+	0.105274i
$870$		0			0
$871$	16.3875	+	9.04560i	0.555269	+	0.306498i
$872$	−10.2816			−0.348178
$873$	−12.1945	+	7.04052i	−0.412722	+	0.238285i
$874$	8.48659	+	14.6992i	0.287063	+	0.497208i
$875$		0			0
$876$		−	7.26330i		−	0.245404i
$877$	13.6363	+	7.87295i	0.460467	+	0.265851i	0.712240	−	0.701936i	$-0.247681\pi$
$877$	13.6363	+	7.87295i	0.460467	+	0.265851i	−0.251774	+	0.967786i	$0.581014\pi$
$878$	6.33386	+	3.65685i	0.213757	+	0.123413i
$879$		−	13.4704i		−	0.454346i
$880$		0			0
$881$	7.56434	+	13.1018i	0.254849	+	0.441412i	0.964855	−	0.262785i	$-0.0846409\pi$
$881$	7.56434	+	13.1018i	0.254849	+	0.441412i	−0.710005	+	0.704196i	$0.751308\pi$
$882$	5.31017	−	3.06583i	0.178803	−	0.103232i
$883$	−54.8263			−1.84505			−0.922525	−	0.385936i	$-0.873878\pi$
$883$	−54.8263			−1.84505			−0.922525	+	0.385936i	$0.873878\pi$
$884$	4.44815	−	8.05852i	0.149608	−	0.271037i
$885$		0			0
$886$	−23.8331	+	13.7600i	−0.800687	+	0.462277i
$887$	−23.3928	−	40.5176i	−0.785454	−	1.36045i	−0.928727	−	0.370763i	$-0.879096\pi$
$887$	−23.3928	−	40.5176i	−0.785454	−	1.36045i	0.143273	−	0.989683i	$-0.454237\pi$
$888$	−4.57994	+	7.93269i	−0.153693	+	0.266204i
$889$			0.630866i			0.0211586i
$890$		0			0
$891$	−1.45680	−	0.841081i	−0.0488045	−	0.0281773i
$892$			14.7783i			0.494814i
$893$	−5.23009	+	9.05879i	−0.175018	+	0.303141i
$894$	1.50120	+	2.60016i	0.0502077	+	0.0869623i
$895$		0			0
$896$	−0.931852			−0.0311310
$897$	23.2769	−	0.447799i	0.777194	−	0.0149516i
$898$	10.2582			0.342322
$899$	27.2753	−	15.7474i	0.909684	−	0.525206i
$900$		0			0
$901$	−6.84267	+	11.8519i	−0.227963	+	0.394843i
$902$		−	1.97569i		−	0.0657832i
$903$	2.38270	+	1.37565i	0.0792913	+	0.0457789i
$904$	8.36308	+	4.82843i	0.278152	+	0.160591i
$905$		0			0
$906$	−6.21001	+	10.7561i	−0.206314	+	0.357346i
$907$	−14.5536	−	25.2077i	−0.483246	−	0.837006i	0.516569	−	0.856246i	$-0.327209\pi$
$907$	−14.5536	−	25.2077i	−0.483246	−	0.837006i	−0.999815	+	0.0192392i	$0.993876\pi$
$908$	−8.28423	+	4.78290i	−0.274922	+	0.158726i
$909$	11.3178			0.375389
$910$		0			0
$911$	−6.59919			−0.218641			−0.109320	−	0.994007i	$-0.534867\pi$
$911$	−6.59919			−0.218641			−0.109320	+	0.994007i	$0.534867\pi$
$912$	−2.27646	+	1.31431i	−0.0753810	+	0.0435213i
$913$	3.23740	+	5.60734i	0.107142	+	0.185576i
$914$	−7.37005	+	12.7653i	−0.243780	+	0.422238i
$915$		0			0
$916$	−13.1184	−	7.57389i	−0.433443	−	0.250248i
$917$	1.50677	+	0.869932i	0.0497578	+	0.0287277i
$918$		−	2.55291i		−	0.0842587i
$919$	16.9793	−	29.4089i	0.560094	−	0.970111i	−0.437394	−	0.899270i	$-0.644098\pi$
$919$	16.9793	−	29.4089i	0.560094	−	0.970111i	0.997488	−	0.0708412i	$-0.0225684\pi$
$920$		0			0
$921$	18.5866	−	10.7310i	0.612450	−	0.353598i
$922$	19.8601			0.654056
$923$	0.272911	+	14.1861i	0.00898298	+	0.466942i
$924$	−1.56753			−0.0515678
$925$		0			0
$926$	−16.0766	−	27.8455i	−0.528311	−	0.915061i
$927$	0.362501	−	0.627871i	0.0119061	−	0.0206220i
$928$		−	3.38839i		−	0.111229i
$929$	0.599403	+	0.346065i	0.0196658	+	0.0113540i	0.509801	−	0.860293i	$-0.329719\pi$
$929$	0.599403	+	0.346065i	0.0196658	+	0.0113540i	−0.490135	+	0.871647i	$0.663052\pi$
$930$		0			0
$931$		−	16.1178i		−	0.528240i
$932$	9.37064	−	16.2304i	0.306946	−	0.531646i
$933$	7.37808	+	12.7792i	0.241547	+	0.418372i
$934$	−19.2911	+	11.1377i	−0.631224	+	0.364437i
$935$		0			0
$936$	0.0693504	+	3.60488i	0.00226679	+	0.117829i
$937$	22.0269			0.719589			0.359795	−	0.933032i	$-0.382847\pi$
$937$	22.0269			0.719589			0.359795	+	0.933032i	$0.382847\pi$
$938$	4.18958	−	2.41886i	0.136795	−	0.0789785i
$939$	−0.702205	−	1.21625i	−0.0229156	−	0.0396910i
$940$		0			0
$941$		−	15.7015i		−	0.511855i	−0.966696	−	0.255928i	$-0.917619\pi$
$941$		−	15.7015i		−	0.511855i	0.966696	−	0.255928i	$-0.0823809\pi$
$942$	−19.5044	−	11.2609i	−0.635487	−	0.366899i
$943$	6.56773	+	3.79188i	0.213875	+	0.123481i
$944$			3.97418i			0.129348i
$945$		0			0
$946$	2.48331	+	4.30121i	0.0807392	+	0.139844i
$947$	22.6839	−	13.0966i	0.737129	−	0.425581i	−0.0838957	−	0.996475i	$-0.526736\pi$
$947$	22.6839	−	13.0966i	0.737129	−	0.425581i	0.821024	+	0.570893i	$0.193403\pi$
$948$	3.68973			0.119837
$949$	−22.4236	+	13.5279i	−0.727901	+	0.439135i
$950$		0			0
$951$	28.7019	−	16.5710i	0.930722	−	0.537352i
$952$	−1.18947	−	2.06022i	−0.0385509	−	0.0667721i
$953$	11.2248	−	19.4420i	0.363608	−	0.629788i	−0.624943	−	0.780670i	$-0.714878\pi$
$953$	11.2248	−	19.4420i	0.363608	−	0.629788i	0.988552	+	0.150882i	$0.0482113\pi$
$954$		−	5.36068i		−	0.173558i
$955$		0			0
$956$	−4.00390	−	2.31165i	−0.129495	−	0.0747641i
$957$		−	5.69982i		−	0.184249i
$958$	−10.9700	+	19.0007i	−0.354426	+	0.613884i
$959$	−3.39595	−	5.88196i	−0.109661	−	0.189939i
$960$		0			0
$961$	−55.3958			−1.78696
$962$	33.0203	−	0.635241i	1.06462	−	0.0204810i
$963$	17.2173			0.554821
$964$	15.2373	−	8.79725i	0.490760	−	0.283341i
$965$		0			0
$966$	3.00851	−	5.21089i	0.0967972	−	0.167658i
$967$			36.7073i			1.18043i	0.807248	+	0.590213i	$0.200956\pi$
$967$			36.7073i			1.18043i	−0.807248	+	0.590213i	$0.799044\pi$
$968$	7.07571	+	4.08516i	0.227422	+	0.131302i
$969$	−5.81160	−	3.35533i	−0.186695	−	0.107789i
$970$		0			0
$971$	−12.8673	+	22.2869i	−0.412932	+	0.715219i	−0.995209	−	0.0977711i	$-0.968829\pi$
$971$	−12.8673	+	22.2869i	−0.412932	+	0.715219i	0.582277	+	0.812991i	$0.302162\pi$
$972$	0.500000	+	0.866025i	0.0160375	+	0.0277778i
$973$	−3.80212	+	2.19516i	−0.121890	+	0.0703735i
$974$	9.05302			0.290078
$975$		0			0
$976$	−8.72376			−0.279241
$977$	−26.5140	+	15.3079i	−0.848258	+	0.489742i	−0.860063	−	0.510188i	$-0.829576\pi$
$977$	−26.5140	+	15.3079i	−0.848258	+	0.489742i	0.0118045	+	0.999930i	$0.496242\pi$
$978$	−1.38745	−	2.40313i	−0.0443656	−	0.0768435i
$979$	11.3269	−	19.6187i	0.362008	−	0.627016i
$980$		0			0
$981$	8.90410	+	5.14078i	0.284286	+	0.164133i
$982$	−26.1540	−	15.1000i	−0.834609	−	0.481861i
$983$			61.1797i			1.95133i	0.219266	+	0.975665i	$0.429634\pi$
$983$			61.1797i			1.95133i	−0.219266	+	0.975665i	$0.570366\pi$
$984$	−0.587246	+	1.01714i	−0.0187207	+	0.0324252i
$985$		0			0
$986$	7.49135	−	4.32513i	0.238573	−	0.137740i
$987$	3.70815			0.118032
$988$	8.29751	+	4.58007i	0.263979	+	0.145712i
$989$	−19.0646			−0.606218
$990$		0			0
$991$	−25.3797	−	43.9589i	−0.806212	−	1.39640i	−0.915470	−	0.402387i	$-0.868181\pi$
$991$	−25.3797	−	43.9589i	−0.806212	−	1.39640i	0.109258	−	0.994013i	$-0.465153\pi$
$992$	−4.64747	+	8.04965i	−0.147557	+	0.255577i
$993$			6.98904i			0.221790i
$994$	3.17578	+	1.83354i	0.100730	+	0.0581562i
$995$		0			0
$996$		−	3.84909i		−	0.121963i
$997$	−24.6109	+	42.6273i	−0.779434	+	1.35002i	0.152834	+	0.988252i	$0.451160\pi$
$997$	−24.6109	+	42.6273i	−0.779434	+	1.35002i	−0.932268	+	0.361768i	$0.882173\pi$
$998$	−4.52168	−	7.83178i	−0.143131	−	0.247911i
$999$	7.93269	−	4.57994i	0.250979	−	0.144903i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1950.2.bc.e.751.4	✓	8
5.2	odd	4		1950.2.y.l.49.1		8
5.3	odd	4		1950.2.y.i.49.4		8
5.4	even	2		1950.2.bc.f.751.1	yes	8
13.4	even	6	inner	1950.2.bc.e.901.4	yes	8
65.4	even	6		1950.2.bc.f.901.1	yes	8
65.17	odd	12		1950.2.y.i.199.4		8
65.43	odd	12		1950.2.y.l.199.1		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1950.2.y.i.49.4		8	5.3	odd	4
1950.2.y.i.199.4		8	65.17	odd	12
1950.2.y.l.49.1		8	5.2	odd	4
1950.2.y.l.199.1		8	65.43	odd	12
1950.2.bc.e.751.4	✓	8	1.1	even	1	trivial
1950.2.bc.e.901.4	yes	8	13.4	even	6	inner
1950.2.bc.f.751.1	yes	8	5.4	even	2
1950.2.bc.f.901.1	yes	8	65.4	even	6

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.bc (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.866025 - 0.500000i) q^{2} +(-0.500000 - 0.866025i) q^{3} +(0.500000 - 0.866025i) q^{4} +(-0.866025 - 0.500000i) q^{6} +(0.807007 + 0.465926i) q^{7} -1.00000i q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})\)	\(q+(0.866025 - 0.500000i) q^{2} +(-0.500000 - 0.866025i) q^{3} +(0.500000 - 0.866025i) q^{4} +(-0.866025 - 0.500000i) q^{6} +(0.807007 + 0.465926i) q^{7} -1.00000i q^{8} +(-0.500000 + 0.866025i) q^{9} +(1.45680 - 0.841081i) q^{11} -1.00000 q^{12} +(1.86250 + 3.08725i) q^{13} +0.931852 q^{14} +(-0.500000 - 0.866025i) q^{16} +(1.27646 - 2.21089i) q^{17} +1.00000i q^{18} +(2.27646 + 1.31431i) q^{19} -0.931852i q^{21} +(0.841081 - 1.45680i) q^{22} +(3.22853 + 5.59197i) q^{23} +(-0.866025 + 0.500000i) q^{24} +(3.15660 + 1.74238i) q^{26} +1.00000 q^{27} +(0.807007 - 0.465926i) q^{28} +(1.69419 + 2.93443i) q^{29} -9.29493i q^{31} +(-0.866025 - 0.500000i) q^{32} +(-1.45680 - 0.841081i) q^{33} -2.55291i q^{34} +(0.500000 + 0.866025i) q^{36} +(7.93269 - 4.57994i) q^{37} +2.62863 q^{38} +(1.74238 - 3.15660i) q^{39} +(1.01714 - 0.587246i) q^{41} +(-0.465926 - 0.807007i) q^{42} +(-1.47626 + 2.55695i) q^{43} -1.68216i q^{44} +(5.59197 + 3.22853i) q^{46} +3.97934i q^{47} +(-0.500000 + 0.866025i) q^{48} +(-3.06583 - 5.31017i) q^{49} -2.55291 q^{51} +(3.60488 - 0.0693504i) q^{52} -5.36068 q^{53} +(0.866025 - 0.500000i) q^{54} +(0.465926 - 0.807007i) q^{56} -2.62863i q^{57} +(2.93443 + 1.69419i) q^{58} +(-3.44174 - 1.98709i) q^{59} +(4.36188 - 7.55500i) q^{61} +(-4.64747 - 8.04965i) q^{62} +(-0.807007 + 0.465926i) q^{63} -1.00000 q^{64} -1.68216 q^{66} +(4.49598 - 2.59575i) q^{67} +(-1.27646 - 2.21089i) q^{68} +(3.22853 - 5.59197i) q^{69} +(3.40803 + 1.96763i) q^{71} +(0.866025 + 0.500000i) q^{72} +7.26330i q^{73} +(4.57994 - 7.93269i) q^{74} +(2.27646 - 1.31431i) q^{76} +1.56753 q^{77} +(-0.0693504 - 3.60488i) q^{78} -3.68973 q^{79} +(-0.500000 - 0.866025i) q^{81} +(0.587246 - 1.01714i) q^{82} +3.84909i q^{83} +(-0.807007 - 0.465926i) q^{84} +2.95252i q^{86} +(1.69419 - 2.93443i) q^{87} +(-0.841081 - 1.45680i) q^{88} +(11.6628 - 6.73351i) q^{89} +(0.0646242 + 3.35922i) q^{91} +6.45705 q^{92} +(-8.04965 + 4.64747i) q^{93} +(1.98967 + 3.44621i) q^{94} +1.00000i q^{96} +(12.1945 + 7.04052i) q^{97} +(-5.31017 - 3.06583i) q^{98} +1.68216i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 4 q^{3} + 4 q^{4} - 4 q^{9}+O(q^{10}) \) 8 * q - 4 * q^3 + 4 * q^4 - 4 * q^9	\( 8 q - 4 q^{3} + 4 q^{4} - 4 q^{9} - 12 q^{11} - 8 q^{12} - 8 q^{14} - 4 q^{16} + 4 q^{17} + 12 q^{19} + 8 q^{22} + 4 q^{23} + 8 q^{27} + 4 q^{29} + 12 q^{33} + 4 q^{36} - 24 q^{37} + 4 q^{42} - 4 q^{43} + 12 q^{46} - 4 q^{48} - 16 q^{49} - 8 q^{51} - 8 q^{53} - 4 q^{56} + 12 q^{58} - 12 q^{59} - 16 q^{61} + 4 q^{62} - 8 q^{64} - 16 q^{66} + 24 q^{67} - 4 q^{68} + 4 q^{69} + 60 q^{71} + 16 q^{74} + 12 q^{76} - 8 q^{77} - 8 q^{79} - 4 q^{81} - 20 q^{82} + 4 q^{87} - 8 q^{88} + 24 q^{89} + 8 q^{91} + 8 q^{92} - 24 q^{93} + 16 q^{94} + 12 q^{97} + 12 q^{98}+O(q^{100}) \) 8 * q - 4 * q^3 + 4 * q^4 - 4 * q^9 - 12 * q^11 - 8 * q^12 - 8 * q^14 - 4 * q^16 + 4 * q^17 + 12 * q^19 + 8 * q^22 + 4 * q^23 + 8 * q^27 + 4 * q^29 + 12 * q^33 + 4 * q^36 - 24 * q^37 + 4 * q^42 - 4 * q^43 + 12 * q^46 - 4 * q^48 - 16 * q^49 - 8 * q^51 - 8 * q^53 - 4 * q^56 + 12 * q^58 - 12 * q^59 - 16 * q^61 + 4 * q^62 - 8 * q^64 - 16 * q^66 + 24 * q^67 - 4 * q^68 + 4 * q^69 + 60 * q^71 + 16 * q^74 + 12 * q^76 - 8 * q^77 - 8 * q^79 - 4 * q^81 - 20 * q^82 + 4 * q^87 - 8 * q^88 + 24 * q^89 + 8 * q^91 + 8 * q^92 - 24 * q^93 + 16 * q^94 + 12 * q^97 + 12 * q^98

Introduction

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