LMFDB - Embedded newform 315.2.bz.a.73.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [315,2,Mod(73,315)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(315, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([0, 9, 2]))

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

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

chi := DirichletCharacter("315.73");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 315 = 3^{2} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	315.bz (of order $12$, degree $4$, 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:	$2.51528766367$
Analytic rank:	$1$
Dimension:	$4$
Coefficient field:	$\Q(\zeta_{12})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{2} + 1 $ x^4 - x^2 + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 35)
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			73.1
Root			$-0.866025 - 0.500000i$ of defining polynomial
Character	$\chi$	$=$	315.73
Dual form			315.2.bz.a.82.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.500000 - 0.133975i) q^{2} +(-1.50000 - 0.866025i) q^{4} +(-0.133975 - 2.23205i) q^{5} +(-2.50000 + 0.866025i) q^{7} +(1.36603 + 1.36603i) q^{8} +O(q^{10})$	\(q+(-0.500000 - 0.133975i) q^{2} +(-1.50000 - 0.866025i) q^{4} +(-0.133975 - 2.23205i) q^{5} +(-2.50000 + 0.866025i) q^{7} +(1.36603 + 1.36603i) q^{8} +(-0.232051 + 1.13397i) q^{10} +(-1.36603 + 2.36603i) q^{11} +(-2.00000 + 2.00000i) q^{13} +(1.36603 - 0.0980762i) q^{14} +(1.23205 + 2.13397i) q^{16} +(-3.73205 + 1.00000i) q^{17} +(0.366025 + 0.633975i) q^{19} +(-1.73205 + 3.46410i) q^{20} +(1.00000 - 1.00000i) q^{22} +(-0.0358984 + 0.133975i) q^{23} +(-4.96410 + 0.598076i) q^{25} +(1.26795 - 0.732051i) q^{26} +(4.50000 + 0.866025i) q^{28} -3.00000i q^{29} +(-6.46410 - 3.73205i) q^{31} +(-1.33013 - 4.96410i) q^{32} +2.00000 q^{34} +(2.26795 + 5.46410i) q^{35} +(-4.73205 - 1.26795i) q^{37} +(-0.0980762 - 0.366025i) q^{38} +(2.86603 - 3.23205i) q^{40} -6.46410i q^{41} +(2.83013 + 2.83013i) q^{43} +(4.09808 - 2.36603i) q^{44} +(0.0358984 - 0.0621778i) q^{46} +(-2.36603 + 8.83013i) q^{47} +(5.50000 - 4.33013i) q^{49} +(2.56218 + 0.366025i) q^{50} +(4.73205 - 1.26795i) q^{52} +(-6.83013 + 1.83013i) q^{53} +(5.46410 + 2.73205i) q^{55} +(-4.59808 - 2.23205i) q^{56} +(-0.401924 + 1.50000i) q^{58} +(4.09808 - 7.09808i) q^{59} +(1.33013 - 0.767949i) q^{61} +(2.73205 + 2.73205i) q^{62} -2.26795i q^{64} +(4.73205 + 4.19615i) q^{65} +(2.86603 + 10.6962i) q^{67} +(6.46410 + 1.73205i) q^{68} +(-0.401924 - 3.03590i) q^{70} -1.26795 q^{71} +(-3.46410 - 12.9282i) q^{73} +(2.19615 + 1.26795i) q^{74} -1.26795i q^{76} +(1.36603 - 7.09808i) q^{77} +(2.83013 - 1.63397i) q^{79} +(4.59808 - 3.03590i) q^{80} +(-0.866025 + 3.23205i) q^{82} +(2.09808 - 2.09808i) q^{83} +(2.73205 + 8.19615i) q^{85} +(-1.03590 - 1.79423i) q^{86} +(-5.09808 + 1.36603i) q^{88} +(0.330127 + 0.571797i) q^{89} +(3.26795 - 6.73205i) q^{91} +(0.169873 - 0.169873i) q^{92} +(2.36603 - 4.09808i) q^{94} +(1.36603 - 0.901924i) q^{95} +(-5.92820 - 5.92820i) q^{97} +(-3.33013 + 1.42820i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 2 q^{2} - 6 q^{4} - 4 q^{5} - 10 q^{7} + 2 q^{8}+O(q^{10}) $ 4 * q - 2 * q^2 - 6 * q^4 - 4 * q^5 - 10 * q^7 + 2 * q^8	$ 4 q - 2 q^{2} - 6 q^{4} - 4 q^{5} - 10 q^{7} + 2 q^{8} + 6 q^{10} - 2 q^{11} - 8 q^{13} + 2 q^{14} - 2 q^{16} - 8 q^{17} - 2 q^{19} + 4 q^{22} - 14 q^{23} - 6 q^{25} + 12 q^{26} + 18 q^{28} - 12 q^{31} + 12 q^{32} + 8 q^{34} + 16 q^{35} - 12 q^{37} + 10 q^{38} + 8 q^{40} - 6 q^{43} + 6 q^{44} + 14 q^{46} - 6 q^{47} + 22 q^{49} - 14 q^{50} + 12 q^{52} - 10 q^{53} + 8 q^{55} - 8 q^{56} - 12 q^{58} + 6 q^{59} - 12 q^{61} + 4 q^{62} + 12 q^{65} + 8 q^{67} + 12 q^{68} - 12 q^{70} - 12 q^{71} - 12 q^{74} + 2 q^{77} - 6 q^{79} + 8 q^{80} - 2 q^{83} + 4 q^{85} - 18 q^{86} - 10 q^{88} - 16 q^{89} + 20 q^{91} + 18 q^{92} + 6 q^{94} + 2 q^{95} + 4 q^{97} + 4 q^{98}+O(q^{100}) $ 4 * q - 2 * q^2 - 6 * q^4 - 4 * q^5 - 10 * q^7 + 2 * q^8 + 6 * q^10 - 2 * q^11 - 8 * q^13 + 2 * q^14 - 2 * q^16 - 8 * q^17 - 2 * q^19 + 4 * q^22 - 14 * q^23 - 6 * q^25 + 12 * q^26 + 18 * q^28 - 12 * q^31 + 12 * q^32 + 8 * q^34 + 16 * q^35 - 12 * q^37 + 10 * q^38 + 8 * q^40 - 6 * q^43 + 6 * q^44 + 14 * q^46 - 6 * q^47 + 22 * q^49 - 14 * q^50 + 12 * q^52 - 10 * q^53 + 8 * q^55 - 8 * q^56 - 12 * q^58 + 6 * q^59 - 12 * q^61 + 4 * q^62 + 12 * q^65 + 8 * q^67 + 12 * q^68 - 12 * q^70 - 12 * q^71 - 12 * q^74 + 2 * q^77 - 6 * q^79 + 8 * q^80 - 2 * q^83 + 4 * q^85 - 18 * q^86 - 10 * q^88 - 16 * q^89 + 20 * q^91 + 18 * q^92 + 6 * q^94 + 2 * q^95 + 4 * q^97 + 4 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/315\mathbb{Z}\right)^\times$.

$n$	$127$	$136$	$281$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$e\left(\frac{1}{6}\right)$	$1$

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	−	0.133975i	−0.353553	−	0.0947343i	0.0776710	−	0.996979i	$-0.475252\pi$
$2$	−0.500000	−	0.133975i	−0.353553	−	0.0947343i	−0.431224	+	0.902245i	$0.641918\pi$
$3$		0			0
$3$		0			0
$4$	−1.50000	−	0.866025i	−0.750000	−	0.433013i
$5$	−0.133975	−	2.23205i	−0.0599153	−	0.998203i
$5$	−0.133975	−	2.23205i	−0.0599153	−	0.998203i
$6$		0			0
$7$	−2.50000	+	0.866025i	−0.944911	+	0.327327i
$7$	−2.50000	+	0.866025i	−0.944911	+	0.327327i
$8$	1.36603	+	1.36603i	0.482963	+	0.482963i
$9$		0			0
$10$	−0.232051	+	1.13397i	−0.0733809	+	0.358594i
$11$	−1.36603	+	2.36603i	−0.411872	+	0.713384i	−0.995094	−	0.0989291i	$-0.968458\pi$
$11$	−1.36603	+	2.36603i	−0.411872	+	0.713384i	0.583222	+	0.812313i	$0.301792\pi$
$12$		0			0
$13$	−2.00000	+	2.00000i	−0.554700	+	0.554700i	−0.927794	−	0.373094i	$-0.878297\pi$
$13$	−2.00000	+	2.00000i	−0.554700	+	0.554700i	0.373094	+	0.927794i	$0.378297\pi$
$14$	1.36603	−	0.0980762i	0.365086	−	0.0262120i
$15$		0			0
$16$	1.23205	+	2.13397i	0.308013	+	0.533494i
$17$	−3.73205	+	1.00000i	−0.905155	+	0.242536i	−0.681229	−	0.732070i	$-0.738554\pi$
$17$	−3.73205	+	1.00000i	−0.905155	+	0.242536i	−0.223926	+	0.974606i	$0.571888\pi$
$18$		0			0
$19$	0.366025	+	0.633975i	0.0839720	+	0.145444i	0.904953	−	0.425512i	$-0.139906\pi$
$19$	0.366025	+	0.633975i	0.0839720	+	0.145444i	−0.820981	+	0.570956i	$0.806573\pi$
$20$	−1.73205	+	3.46410i	−0.387298	+	0.774597i
$21$		0			0
$22$	1.00000	−	1.00000i	0.213201	−	0.213201i
$23$	−0.0358984	+	0.133975i	−0.00748533	+	0.0279356i	−0.969567	−	0.244824i	$-0.921270\pi$
$23$	−0.0358984	+	0.133975i	−0.00748533	+	0.0279356i	0.962082	+	0.272760i	$0.0879364\pi$
$24$		0			0
$25$	−4.96410	+	0.598076i	−0.992820	+	0.119615i
$26$	1.26795	−	0.732051i	0.248665	−	0.143567i
$27$		0			0
$28$	4.50000	+	0.866025i	0.850420	+	0.163663i
$29$		−	3.00000i		−	0.557086i	−0.960424	−	0.278543i	$-0.910149\pi$
$29$		−	3.00000i		−	0.557086i	0.960424	−	0.278543i	$-0.0898515\pi$
$30$		0			0
$31$	−6.46410	−	3.73205i	−1.16099	−	0.670296i	−0.209447	−	0.977820i	$-0.567166\pi$
$31$	−6.46410	−	3.73205i	−1.16099	−	0.670296i	−0.951540	+	0.307524i	$0.900500\pi$
$32$	−1.33013	−	4.96410i	−0.235135	−	0.877537i
$33$		0			0
$34$	2.00000			0.342997
$35$	2.26795	+	5.46410i	0.383353	+	0.923602i
$36$		0			0
$37$	−4.73205	−	1.26795i	−0.777944	−	0.208450i	−0.152066	−	0.988370i	$-0.548593\pi$
$37$	−4.73205	−	1.26795i	−0.777944	−	0.208450i	−0.625878	+	0.779921i	$0.715259\pi$
$38$	−0.0980762	−	0.366025i	−0.0159101	−	0.0593772i
$39$		0			0
$40$	2.86603	−	3.23205i	0.453158	−	0.511032i
$41$		−	6.46410i		−	1.00952i	−0.863259	−	0.504762i	$-0.831580\pi$
$41$		−	6.46410i		−	1.00952i	0.863259	−	0.504762i	$-0.168420\pi$
$42$		0			0
$43$	2.83013	+	2.83013i	0.431590	+	0.431590i	0.889169	−	0.457579i	$-0.151283\pi$
$43$	2.83013	+	2.83013i	0.431590	+	0.431590i	−0.457579	+	0.889169i	$0.651283\pi$
$44$	4.09808	−	2.36603i	0.617808	−	0.356692i
$45$		0			0
$46$	0.0358984	−	0.0621778i	0.00529293	−	0.00916762i
$47$	−2.36603	+	8.83013i	−0.345120	+	1.28801i	0.547351	+	0.836903i	$0.315636\pi$
$47$	−2.36603	+	8.83013i	−0.345120	+	1.28801i	−0.892472	+	0.451103i	$0.851031\pi$
$48$		0			0
$49$	5.50000	−	4.33013i	0.785714	−	0.618590i
$50$	2.56218	+	0.366025i	0.362347	+	0.0517638i
$51$		0			0
$52$	4.73205	−	1.26795i	0.656217	−	0.175833i
$53$	−6.83013	+	1.83013i	−0.938190	+	0.251387i	−0.695344	−	0.718677i	$-0.744748\pi$
$53$	−6.83013	+	1.83013i	−0.938190	+	0.251387i	−0.242846	+	0.970065i	$0.578081\pi$
$54$		0			0
$55$	5.46410	+	2.73205i	0.736779	+	0.368390i
$56$	−4.59808	−	2.23205i	−0.614444	−	0.298270i
$57$		0			0
$58$	−0.401924	+	1.50000i	−0.0527752	+	0.196960i
$59$	4.09808	−	7.09808i	0.533524	−	0.924091i	−0.465709	−	0.884938i	$-0.654201\pi$
$59$	4.09808	−	7.09808i	0.533524	−	0.924091i	0.999233	−	0.0391530i	$-0.0124660\pi$
$60$		0			0
$61$	1.33013	−	0.767949i	0.170305	−	0.0983258i	−0.412424	−	0.910992i	$-0.635318\pi$
$61$	1.33013	−	0.767949i	0.170305	−	0.0983258i	0.582730	+	0.812666i	$0.301985\pi$
$62$	2.73205	+	2.73205i	0.346971	+	0.346971i
$63$		0			0
$64$		−	2.26795i		−	0.283494i
$65$	4.73205	+	4.19615i	0.586939	+	0.520469i
$66$		0			0
$67$	2.86603	+	10.6962i	0.350141	+	1.30674i	0.886490	+	0.462747i	$0.153136\pi$
$67$	2.86603	+	10.6962i	0.350141	+	1.30674i	−0.536350	+	0.843996i	$0.680197\pi$
$68$	6.46410	+	1.73205i	0.783887	+	0.210042i
$69$		0			0
$70$	−0.401924	−	3.03590i	−0.0480391	−	0.362859i
$71$	−1.26795			−0.150478			−0.0752389	−	0.997166i	$-0.523972\pi$
$71$	−1.26795			−0.150478			−0.0752389	+	0.997166i	$0.523972\pi$
$72$		0			0
$73$	−3.46410	−	12.9282i	−0.405442	−	1.51313i	−0.803238	−	0.595658i	$-0.796891\pi$
$73$	−3.46410	−	12.9282i	−0.405442	−	1.51313i	0.397796	−	0.917474i	$-0.369775\pi$
$74$	2.19615	+	1.26795i	0.255298	+	0.147396i
$75$		0			0
$76$		−	1.26795i		−	0.145444i
$77$	1.36603	−	7.09808i	0.155673	−	0.808901i
$78$		0			0
$79$	2.83013	−	1.63397i	0.318414	−	0.183837i	−0.332271	−	0.943184i	$-0.607815\pi$
$79$	2.83013	−	1.63397i	0.318414	−	0.183837i	0.650686	+	0.759347i	$0.274482\pi$
$80$	4.59808	−	3.03590i	0.514081	−	0.339424i
$81$		0			0
$82$	−0.866025	+	3.23205i	−0.0956365	+	0.356920i
$83$	2.09808	−	2.09808i	0.230294	−	0.230294i	−0.582522	−	0.812815i	$-0.697934\pi$
$83$	2.09808	−	2.09808i	0.230294	−	0.230294i	0.812815	+	0.582522i	$0.197934\pi$
$84$		0			0
$85$	2.73205	+	8.19615i	0.296333	+	0.888998i
$86$	−1.03590	−	1.79423i	−0.111704	−	0.193477i
$87$		0			0
$88$	−5.09808	+	1.36603i	−0.543457	+	0.145619i
$89$	0.330127	+	0.571797i	0.0349934	+	0.0606103i	0.882992	−	0.469389i	$-0.155526\pi$
$89$	0.330127	+	0.571797i	0.0349934	+	0.0606103i	−0.847998	+	0.529999i	$0.822192\pi$
$90$		0			0
$91$	3.26795	−	6.73205i	0.342574	−	0.705711i
$92$	0.169873	−	0.169873i	0.0177105	−	0.0177105i
$93$		0			0
$94$	2.36603	−	4.09808i	0.244037	−	0.422684i
$95$	1.36603	−	0.901924i	0.140151	−	0.0925354i
$96$		0			0
$97$	−5.92820	−	5.92820i	−0.601918	−	0.601918i	0.338903	−	0.940821i	$-0.389944\pi$
$97$	−5.92820	−	5.92820i	−0.601918	−	0.601918i	−0.940821	+	0.338903i	$0.889944\pi$
$98$	−3.33013	+	1.42820i	−0.336394	+	0.144270i
$99$		0			0
$100$	7.96410	+	3.40192i	0.796410	+	0.340192i
$101$	−7.16025	−	4.13397i	−0.712472	−	0.411346i	0.0995037	−	0.995037i	$-0.468274\pi$
$101$	−7.16025	−	4.13397i	−0.712472	−	0.411346i	−0.811976	+	0.583691i	$0.801608\pi$
$102$		0			0
$103$	4.59808	+	1.23205i	0.453062	+	0.121398i	0.478132	−	0.878288i	$-0.341314\pi$
$103$	4.59808	+	1.23205i	0.453062	+	0.121398i	−0.0250698	+	0.999686i	$0.507981\pi$
$104$	−5.46410			−0.535799
$105$		0			0
$106$	3.66025			0.355515
$107$	−12.6962	−	3.40192i	−1.22738	−	0.328876i	−0.413823	−	0.910357i	$-0.635807\pi$
$107$	−12.6962	−	3.40192i	−1.22738	−	0.328876i	−0.813560	+	0.581481i	$0.802474\pi$
$108$		0			0
$109$	−8.76795	−	5.06218i	−0.839817	−	0.484869i	0.0173849	−	0.999849i	$-0.494466\pi$
$109$	−8.76795	−	5.06218i	−0.839817	−	0.484869i	−0.857202	+	0.514980i	$0.827799\pi$
$110$	−2.36603	−	2.09808i	−0.225592	−	0.200044i
$111$		0			0
$112$	−4.92820	−	4.26795i	−0.465671	−	0.403283i
$113$	7.73205	+	7.73205i	0.727370	+	0.727370i	0.970095	−	0.242725i	$-0.0780413\pi$
$113$	7.73205	+	7.73205i	0.727370	+	0.727370i	−0.242725	+	0.970095i	$0.578041\pi$
$114$		0			0
$115$	0.303848	+	0.0621778i	0.0283339	+	0.00579811i
$116$	−2.59808	+	4.50000i	−0.241225	+	0.417815i
$117$		0			0
$118$	−3.00000	+	3.00000i	−0.276172	+	0.276172i
$119$	8.46410	−	5.73205i	0.775903	−	0.525456i
$120$		0			0
$121$	1.76795	+	3.06218i	0.160723	+	0.278380i
$122$	−0.767949	+	0.205771i	−0.0695269	+	0.0186297i
$123$		0			0
$124$	6.46410	+	11.1962i	0.580493	+	1.00544i
$125$	2.00000	+	11.0000i	0.178885	+	0.983870i
$126$		0			0
$127$	0.464102	−	0.464102i	0.0411824	−	0.0411824i	−0.686216	−	0.727398i	$-0.740729\pi$
$127$	0.464102	−	0.464102i	0.0411824	−	0.0411824i	0.727398	+	0.686216i	$0.240729\pi$
$128$	−2.96410	+	11.0622i	−0.261992	+	0.977768i
$129$		0			0
$130$	−1.80385	−	2.73205i	−0.158208	−	0.239617i
$131$	13.3923	−	7.73205i	1.17009	−	0.675552i	0.216390	−	0.976307i	$-0.430572\pi$
$131$	13.3923	−	7.73205i	1.17009	−	0.675552i	0.953702	+	0.300755i	$0.0972385\pi$
$132$		0			0
$133$	−1.46410	−	1.26795i	−0.126954	−	0.109945i
$134$		−	5.73205i		−	0.495174i
$135$		0			0
$136$	−6.46410	−	3.73205i	−0.554292	−	0.320021i
$137$	3.53590	+	13.1962i	0.302092	+	1.12742i	0.935420	+	0.353539i	$0.115022\pi$
$137$	3.53590	+	13.1962i	0.302092	+	1.12742i	−0.633327	+	0.773884i	$0.718311\pi$
$138$		0			0
$139$	−5.66025			−0.480096			−0.240048	−	0.970761i	$-0.577163\pi$
$139$	−5.66025			−0.480096			−0.240048	+	0.970761i	$0.577163\pi$
$140$	1.33013	−	10.1603i	0.112416	−	0.858698i
$141$		0			0
$142$	0.633975	+	0.169873i	0.0532020	+	0.0142554i
$143$	−2.00000	−	7.46410i	−0.167248	−	0.624180i
$144$		0			0
$145$	−6.69615	+	0.401924i	−0.556085	+	0.0333780i
$146$			6.92820i			0.573382i
$147$		0			0
$148$	6.00000	+	6.00000i	0.493197	+	0.493197i
$149$	−0.696152	+	0.401924i	−0.0570310	+	0.0329269i	−0.528244	−	0.849092i	$-0.677150\pi$
$149$	−0.696152	+	0.401924i	−0.0570310	+	0.0329269i	0.471213	+	0.882019i	$0.343816\pi$
$150$		0			0
$151$	−6.92820	+	12.0000i	−0.563809	+	0.976546i	0.433350	+	0.901226i	$0.357331\pi$
$151$	−6.92820	+	12.0000i	−0.563809	+	0.976546i	−0.997159	+	0.0753205i	$0.976002\pi$
$152$	−0.366025	+	1.36603i	−0.0296886	+	0.110799i
$153$		0			0
$154$	−1.63397	+	3.36603i	−0.131669	+	0.271242i
$155$	−7.46410	+	14.9282i	−0.599531	+	1.19906i
$156$		0			0
$157$	−4.63397	+	1.24167i	−0.369831	+	0.0990960i	−0.438948	−	0.898513i	$-0.644649\pi$
$157$	−4.63397	+	1.24167i	−0.369831	+	0.0990960i	0.0691164	+	0.997609i	$0.477982\pi$
$158$	−1.63397	+	0.437822i	−0.129992	+	0.0348313i
$159$		0			0
$160$	−10.9019	+	3.63397i	−0.861873	+	0.287291i
$161$	−0.0262794	−	0.366025i	−0.00207111	−	0.0288468i
$162$		0			0
$163$	−3.63397	+	13.5622i	−0.284635	+	1.06227i	0.664471	+	0.747314i	$0.268657\pi$
$163$	−3.63397	+	13.5622i	−0.284635	+	1.06227i	−0.949106	+	0.314958i	$0.898010\pi$
$164$	−5.59808	+	9.69615i	−0.437136	+	0.757142i
$165$		0			0
$166$	−1.33013	+	0.767949i	−0.103238	+	0.0596044i
$167$	−11.7583	−	11.7583i	−0.909887	−	0.909887i	0.0863757	−	0.996263i	$-0.472471\pi$
$167$	−11.7583	−	11.7583i	−0.909887	−	0.909887i	−0.996263	+	0.0863757i	$0.972471\pi$
$168$		0			0
$169$			5.00000i			0.384615i
$170$	−0.267949	−	4.46410i	−0.0205508	−	0.342381i
$171$		0			0
$172$	−1.79423	−	6.69615i	−0.136809	−	0.510577i
$173$	−19.9282	−	5.33975i	−1.51511	−	0.405973i	−0.596984	−	0.802253i	$-0.703634\pi$
$173$	−19.9282	−	5.33975i	−1.51511	−	0.405973i	−0.918130	+	0.396280i	$0.870301\pi$
$174$		0			0
$175$	11.8923	−	5.79423i	0.898974	−	0.438003i
$176$	−6.73205			−0.507447
$177$		0			0
$178$	−0.0884573	−	0.330127i	−0.00663015	−	0.0247441i
$179$	−6.80385	−	3.92820i	−0.508543	−	0.293608i	0.223691	−	0.974660i	$-0.428189\pi$
$179$	−6.80385	−	3.92820i	−0.508543	−	0.293608i	−0.732235	+	0.681052i	$0.761523\pi$
$180$		0			0
$181$			1.19615i			0.0889093i	0.999011	+	0.0444547i	$0.0141550\pi$
$181$			1.19615i			0.0889093i	−0.999011	+	0.0444547i	$0.985845\pi$
$182$	−2.53590	+	2.92820i	−0.187973	+	0.217053i
$183$		0			0
$184$	−0.232051	+	0.133975i	−0.0171070	+	0.00987674i
$185$	−2.19615	+	10.7321i	−0.161464	+	0.789036i
$186$		0			0
$187$	2.73205	−	10.1962i	0.199787	−	0.745617i
$188$	11.1962	−	11.1962i	0.816563	−	0.816563i
$189$		0			0
$190$	−0.803848	+	0.267949i	−0.0583172	+	0.0194391i
$191$	6.63397	+	11.4904i	0.480018	+	0.831415i	0.999737	−	0.0229220i	$-0.00729695\pi$
$191$	6.63397	+	11.4904i	0.480018	+	0.831415i	−0.519720	+	0.854337i	$0.673964\pi$
$192$		0			0
$193$	−7.83013	+	2.09808i	−0.563625	+	0.151023i	−0.529371	−	0.848390i	$-0.677572\pi$
$193$	−7.83013	+	2.09808i	−0.563625	+	0.151023i	−0.0342537	+	0.999413i	$0.510905\pi$
$194$	2.16987	+	3.75833i	0.155788	+	0.269832i
$195$		0			0
$196$	−12.0000	+	1.73205i	−0.857143	+	0.123718i
$197$	10.1244	−	10.1244i	0.721330	−	0.721330i	−0.247546	−	0.968876i	$-0.579624\pi$
$197$	10.1244	−	10.1244i	0.721330	−	0.721330i	0.968876	+	0.247546i	$0.0796240\pi$
$198$		0			0
$199$	−5.53590	+	9.58846i	−0.392429	+	0.679708i	−0.992769	−	0.120037i	$-0.961699\pi$
$199$	−5.53590	+	9.58846i	−0.392429	+	0.679708i	0.600340	+	0.799745i	$0.295032\pi$
$200$	−7.59808	−	5.96410i	−0.537265	−	0.421726i
$201$		0			0
$202$	3.02628	+	3.02628i	0.212928	+	0.212928i
$203$	2.59808	+	7.50000i	0.182349	+	0.526397i
$204$		0			0
$205$	−14.4282	+	0.866025i	−1.00771	+	0.0604858i
$206$	−2.13397	−	1.23205i	−0.148681	−	0.0858410i
$207$		0			0
$208$	−6.73205	−	1.80385i	−0.466784	−	0.125074i
$209$	−2.00000			−0.138343
$210$		0			0
$211$	−0.196152			−0.0135037			−0.00675184	−	0.999977i	$-0.502149\pi$
$211$	−0.196152			−0.0135037			−0.00675184	+	0.999977i	$0.502149\pi$
$212$	11.8301	+	3.16987i	0.812496	+	0.217708i
$213$		0			0
$214$	5.89230	+	3.40192i	0.402790	+	0.232551i
$215$	5.93782	−	6.69615i	0.404956	−	0.456674i
$216$		0			0
$217$	19.3923	+	3.73205i	1.31644	+	0.253348i
$218$	3.70577	+	3.70577i	0.250987	+	0.250987i
$219$		0			0
$220$	−5.83013	−	8.83013i	−0.393067	−	0.595327i
$221$	5.46410	−	9.46410i	0.367555	−	0.636624i
$222$		0			0
$223$	18.1244	−	18.1244i	1.21370	−	1.21370i	0.243895	−	0.969802i	$-0.421575\pi$
$223$	18.1244	−	18.1244i	1.21370	−	1.21370i	0.969802	−	0.243895i	$-0.0784252\pi$
$224$	7.62436	+	11.2583i	0.509424	+	0.752229i
$225$		0			0
$226$	−2.83013	−	4.90192i	−0.188257	−	0.326071i
$227$	19.0263	−	5.09808i	1.26282	−	0.338371i	0.435543	−	0.900168i	$-0.356556\pi$
$227$	19.0263	−	5.09808i	1.26282	−	0.338371i	0.827275	+	0.561797i	$0.189890\pi$
$228$		0			0
$229$	−9.19615	−	15.9282i	−0.607699	−	1.05257i	−0.991619	−	0.129199i	$-0.958759\pi$
$229$	−9.19615	−	15.9282i	−0.607699	−	1.05257i	0.383920	−	0.923366i	$-0.374574\pi$
$230$	−0.143594	−	0.0717968i	−0.00946828	−	0.00473414i
$231$		0			0
$232$	4.09808	−	4.09808i	0.269052	−	0.269052i
$233$	1.73205	−	6.46410i	0.113470	−	0.423477i	−0.885698	−	0.464263i	$-0.846319\pi$
$233$	1.73205	−	6.46410i	0.113470	−	0.423477i	0.999168	+	0.0407854i	$0.0129860\pi$
$234$		0			0
$235$	20.0263	+	4.09808i	1.30637	+	0.267329i
$236$	−12.2942	+	7.09808i	−0.800286	+	0.462045i
$237$		0			0
$238$	−5.00000	+	1.73205i	−0.324102	+	0.112272i
$239$			2.39230i			0.154745i	0.997002	+	0.0773727i	$0.0246531\pi$
$239$			2.39230i			0.154745i	−0.997002	+	0.0773727i	$0.975347\pi$
$240$		0			0
$241$	21.4641	+	12.3923i	1.38262	+	0.798259i	0.992470	−	0.122491i	$-0.0390882\pi$
$241$	21.4641	+	12.3923i	1.38262	+	0.798259i	0.390155	+	0.920749i	$0.372422\pi$
$242$	−0.473721	−	1.76795i	−0.0304519	−	0.113648i
$243$		0			0
$244$	−2.66025			−0.170305
$245$	−10.4019	−	11.6962i	−0.664555	−	0.747240i
$246$		0			0
$247$	−2.00000	−	0.535898i	−0.127257	−	0.0340984i
$248$	−3.73205	−	13.9282i	−0.236985	−	0.884442i
$249$		0			0
$250$	0.473721	−	5.76795i	0.0299607	−	0.364797i
$251$			21.8564i			1.37956i	0.724017	+	0.689782i	$0.242294\pi$
$251$			21.8564i			1.37956i	−0.724017	+	0.689782i	$0.757706\pi$
$252$		0			0
$253$	−0.267949	−	0.267949i	−0.0168458	−	0.0168458i
$254$	−0.294229	+	0.169873i	−0.0184615	+	0.0106588i
$255$		0			0
$256$	0.696152	−	1.20577i	0.0435095	−	0.0753607i
$257$	0.732051	−	2.73205i	0.0456641	−	0.170421i	−0.939328	−	0.343020i	$-0.888550\pi$
$257$	0.732051	−	2.73205i	0.0456641	−	0.170421i	0.984992	+	0.172600i	$0.0552167\pi$
$258$		0			0
$259$	12.9282	−	0.928203i	0.803319	−	0.0576757i
$260$	−3.46410	−	10.3923i	−0.214834	−	0.644503i
$261$		0			0
$262$	−7.73205	+	2.07180i	−0.477688	+	0.127996i
$263$	15.1603	−	4.06218i	0.934821	−	0.250485i	0.240912	−	0.970547i	$-0.422553\pi$
$263$	15.1603	−	4.06218i	0.934821	−	0.250485i	0.693909	+	0.720062i	$0.255887\pi$
$264$		0			0
$265$	5.00000	+	15.0000i	0.307148	+	0.921443i
$266$	0.562178	+	0.830127i	0.0344693	+	0.0508984i
$267$		0			0
$268$	4.96410	−	18.5263i	0.303231	−	1.13167i
$269$	−11.4282	+	19.7942i	−0.696790	+	1.20688i	0.272784	+	0.962075i	$0.412056\pi$
$269$	−11.4282	+	19.7942i	−0.696790	+	1.20688i	−0.969574	+	0.244800i	$0.921278\pi$
$270$		0			0
$271$	18.4186	−	10.6340i	1.11885	−	0.645968i	0.177742	−	0.984077i	$-0.443121\pi$
$271$	18.4186	−	10.6340i	1.11885	−	0.645968i	0.941107	+	0.338109i	$0.109787\pi$
$272$	−6.73205	−	6.73205i	−0.408191	−	0.408191i
$273$		0			0
$274$		−	7.07180i		−	0.427223i
$275$	5.36603	−	12.5622i	0.323584	−	0.757528i
$276$		0			0
$277$	−1.39230	−	5.19615i	−0.0836555	−	0.312207i	0.911401	−	0.411520i	$-0.135002\pi$
$277$	−1.39230	−	5.19615i	−0.0836555	−	0.312207i	−0.995056	+	0.0993135i	$0.968335\pi$
$278$	2.83013	+	0.758330i	0.169740	+	0.0454816i
$279$		0			0
$280$	−4.36603	+	10.5622i	−0.260920	+	0.631211i
$281$	0.928203			0.0553720			0.0276860	−	0.999617i	$-0.491186\pi$
$281$	0.928203			0.0553720			0.0276860	+	0.999617i	$0.491186\pi$
$282$		0			0
$283$	−0.509619	−	1.90192i	−0.0302937	−	0.113058i	0.949123	−	0.314904i	$-0.101972\pi$
$283$	−0.509619	−	1.90192i	−0.0302937	−	0.113058i	−0.979417	+	0.201847i	$0.935306\pi$
$284$	1.90192	+	1.09808i	0.112858	+	0.0651588i
$285$		0			0
$286$			4.00000i			0.236525i
$287$	5.59808	+	16.1603i	0.330444	+	0.953910i
$288$		0			0
$289$	−1.79423	+	1.03590i	−0.105543	+	0.0609352i
$290$	3.40192	+	0.696152i	0.199768	+	0.0408795i
$291$		0			0
$292$	−6.00000	+	22.3923i	−0.351123	+	1.31041i
$293$	2.39230	−	2.39230i	0.139760	−	0.139760i	−0.633765	−	0.773525i	$-0.718492\pi$
$293$	2.39230	−	2.39230i	0.139760	−	0.139760i	0.773525	+	0.633765i	$0.218492\pi$
$294$		0			0
$295$	−16.3923	−	8.19615i	−0.954397	−	0.477198i
$296$	−4.73205	−	8.19615i	−0.275045	−	0.476392i
$297$		0			0
$298$	0.401924	−	0.107695i	0.0232828	−	0.00623861i
$299$	−0.196152	−	0.339746i	−0.0113438	−	0.0196480i
$300$		0			0
$301$	−9.52628	−	4.62436i	−0.549086	−	0.266543i
$302$	5.07180	−	5.07180i	0.291849	−	0.291849i
$303$		0			0
$304$	−0.901924	+	1.56218i	−0.0517289	+	0.0895970i
$305$	−1.89230	−	2.86603i	−0.108353	−	0.164108i
$306$		0			0
$307$	6.29423	+	6.29423i	0.359231	+	0.359231i	0.863529	−	0.504299i	$-0.168249\pi$
$307$	6.29423	+	6.29423i	0.359231	+	0.359231i	−0.504299	+	0.863529i	$0.668249\pi$
$308$	−8.19615	+	9.46410i	−0.467019	+	0.539267i
$309$		0			0
$310$	5.73205	−	6.46410i	0.325559	−	0.367136i
$311$	13.2224	+	7.63397i	0.749775	+	0.432883i	0.825613	−	0.564237i	$-0.190830\pi$
$311$	13.2224	+	7.63397i	0.749775	+	0.432883i	−0.0758374	+	0.997120i	$0.524163\pi$
$312$		0			0
$313$	−5.19615	−	1.39230i	−0.293704	−	0.0786977i	0.108958	−	0.994046i	$-0.465248\pi$
$313$	−5.19615	−	1.39230i	−0.293704	−	0.0786977i	−0.402662	+	0.915349i	$0.631915\pi$
$314$	2.48334			0.140143
$315$		0			0
$316$	−5.66025			−0.318414
$317$	−9.19615	−	2.46410i	−0.516507	−	0.138398i	−0.00885679	−	0.999961i	$-0.502819\pi$
$317$	−9.19615	−	2.46410i	−0.516507	−	0.138398i	−0.507651	+	0.861563i	$0.669486\pi$
$318$		0			0
$319$	7.09808	+	4.09808i	0.397416	+	0.229448i
$320$	−5.06218	+	0.303848i	−0.282984	+	0.0169856i
$321$		0			0
$322$	−0.0358984	+	0.186533i	−0.00200054	+	0.0103951i
$323$	−2.00000	−	2.00000i	−0.111283	−	0.111283i
$324$		0			0
$325$	8.73205	−	11.1244i	0.484367	−	0.617068i
$326$	3.63397	−	6.29423i	0.201267	−	0.348605i
$327$		0			0
$328$	8.83013	−	8.83013i	0.487562	−	0.487562i
$329$	−1.73205	−	24.1244i	−0.0954911	−	1.33002i
$330$		0			0
$331$	0.928203	+	1.60770i	0.0510187	+	0.0883669i	0.890407	−	0.455165i	$-0.150420\pi$
$331$	0.928203	+	1.60770i	0.0510187	+	0.0883669i	−0.839388	+	0.543532i	$0.817087\pi$
$332$	−4.96410	+	1.33013i	−0.272440	+	0.0730002i
$333$		0			0
$334$	4.30385	+	7.45448i	0.235496	+	0.407891i
$335$	23.4904	−	7.83013i	1.28342	−	0.427806i
$336$		0			0
$337$	9.53590	−	9.53590i	0.519453	−	0.519453i	−0.397953	−	0.917406i	$-0.630279\pi$
$337$	9.53590	−	9.53590i	0.519453	−	0.519453i	0.917406	+	0.397953i	$0.130279\pi$
$338$	0.669873	−	2.50000i	0.0364363	−	0.135982i
$339$		0			0
$340$	3.00000	−	14.6603i	0.162698	−	0.795064i
$341$	17.6603	−	10.1962i	0.956356	−	0.552153i
$342$		0			0
$343$	−10.0000	+	15.5885i	−0.539949	+	0.841698i
$344$			7.73205i			0.416884i
$345$		0			0
$346$	9.24871	+	5.33975i	0.497214	+	0.287067i
$347$	7.79423	+	29.0885i	0.418416	+	1.56155i	0.777893	+	0.628396i	$0.216288\pi$
$347$	7.79423	+	29.0885i	0.418416	+	1.56155i	−0.359477	+	0.933154i	$0.617045\pi$
$348$		0			0
$349$	6.26795			0.335516			0.167758	−	0.985828i	$-0.446347\pi$
$349$	6.26795			0.335516			0.167758	+	0.985828i	$0.446347\pi$
$350$	−6.72243	+	1.30385i	−0.359329	+	0.0696936i
$351$		0			0
$352$	13.5622	+	3.63397i	0.722867	+	0.193691i
$353$	−3.63397	−	13.5622i	−0.193417	−	0.721842i	−0.992671	−	0.120849i	$-0.961438\pi$
$353$	−3.63397	−	13.5622i	−0.193417	−	0.721842i	0.799254	−	0.600993i	$-0.205228\pi$
$354$		0			0
$355$	0.169873	+	2.83013i	0.00901592	+	0.150208i
$356$		−	1.14359i		−	0.0606103i
$357$		0			0
$358$	2.87564	+	2.87564i	0.151983	+	0.151983i
$359$	−29.6603	+	17.1244i	−1.56541	+	0.903789i	−0.568715	+	0.822535i	$0.692559\pi$
$359$	−29.6603	+	17.1244i	−1.56541	+	0.903789i	−0.996693	+	0.0812542i	$0.974107\pi$
$360$		0			0
$361$	9.23205	−	15.9904i	0.485897	−	0.841599i
$362$	0.160254	−	0.598076i	0.00842277	−	0.0314342i
$363$		0			0
$364$	−10.7321	+	7.26795i	−0.562512	+	0.380944i
$365$	−28.3923	+	9.46410i	−1.48612	+	0.495374i
$366$		0			0
$367$	0.500000	−	0.133975i	0.0260998	−	0.00699342i	−0.245746	−	0.969334i	$-0.579033\pi$
$367$	0.500000	−	0.133975i	0.0260998	−	0.00699342i	0.271845	+	0.962341i	$0.412366\pi$
$368$	−0.330127	+	0.0884573i	−0.0172091	+	0.00461115i
$369$		0			0
$370$	2.53590	−	5.07180i	0.131835	−	0.263670i
$371$	15.4904	−	10.4904i	0.804221	−	0.544633i
$372$		0			0
$373$	2.07180	−	7.73205i	0.107274	−	0.400350i	−0.891320	−	0.453376i	$-0.850220\pi$
$373$	2.07180	−	7.73205i	0.107274	−	0.400350i	0.998593	+	0.0530251i	$0.0168863\pi$
$374$	−2.73205	+	4.73205i	−0.141271	+	0.244689i
$375$		0			0
$376$	−15.2942	+	8.83013i	−0.788740	+	0.455379i
$377$	6.00000	+	6.00000i	0.309016	+	0.309016i
$378$		0			0
$379$		−	2.33975i		−	0.120185i	−0.998193	−	0.0600923i	$-0.980860\pi$
$379$		−	2.33975i		−	0.120185i	0.998193	−	0.0600923i	$-0.0191395\pi$
$380$	−2.83013	+	0.169873i	−0.145182	+	0.00871430i
$381$		0			0
$382$	−1.77757	−	6.63397i	−0.0909483	−	0.339424i
$383$	−30.5526	−	8.18653i	−1.56116	−	0.418312i	−0.628131	−	0.778107i	$-0.716180\pi$
$383$	−30.5526	−	8.18653i	−1.56116	−	0.418312i	−0.933031	+	0.359795i	$0.882847\pi$
$384$		0			0
$385$	−16.0263	−	2.09808i	−0.816775	−	0.106928i
$386$	4.19615			0.213579
$387$		0			0
$388$	3.75833	+	14.0263i	0.190800	+	0.712076i
$389$	4.26795	+	2.46410i	0.216394	+	0.124935i	0.604279	−	0.796773i	$-0.293461\pi$
$389$	4.26795	+	2.46410i	0.216394	+	0.124935i	−0.387886	+	0.921707i	$0.626794\pi$
$390$		0			0
$391$		−	0.535898i		−	0.0271015i
$392$	13.4282	+	1.59808i	0.678227	+	0.0807150i
$393$		0			0
$394$	−6.41858	+	3.70577i	−0.323364	+	0.186694i
$395$	−4.02628	−	6.09808i	−0.202584	−	0.306828i
$396$		0			0
$397$	−0.973721	+	3.63397i	−0.0488696	+	0.182384i	−0.986046	−	0.166471i	$-0.946763\pi$
$397$	−0.973721	+	3.63397i	−0.0488696	+	0.182384i	0.937177	+	0.348855i	$0.113429\pi$
$398$	4.05256	−	4.05256i	0.203136	−	0.203136i
$399$		0			0
$400$	−7.39230	−	9.85641i	−0.369615	−	0.492820i
$401$	5.50000	+	9.52628i	0.274657	+	0.475720i	0.970049	−	0.242911i	$-0.0781024\pi$
$401$	5.50000	+	9.52628i	0.274657	+	0.475720i	−0.695392	+	0.718631i	$0.744769\pi$
$402$		0			0
$403$	20.3923	−	5.46410i	1.01581	−	0.272186i
$404$	7.16025	+	12.4019i	0.356236	+	0.617019i
$405$		0			0
$406$	−0.294229	−	4.09808i	−0.0146023	−	0.203384i
$407$	9.46410	−	9.46410i	0.469118	−	0.469118i
$408$		0			0
$409$	−10.4282	+	18.0622i	−0.515641	+	0.893117i	0.484194	+	0.874961i	$0.339113\pi$
$409$	−10.4282	+	18.0622i	−0.515641	+	0.893117i	−0.999835	+	0.0181564i	$0.994220\pi$
$410$	7.33013	+	1.50000i	0.362009	+	0.0740797i
$411$		0			0
$412$	−5.83013	−	5.83013i	−0.287230	−	0.287230i
$413$	−4.09808	+	21.2942i	−0.201653	+	1.04782i
$414$		0			0
$415$	−4.96410	−	4.40192i	−0.243678	−	0.216082i
$416$	12.5885	+	7.26795i	0.617200	+	0.356341i
$417$		0			0
$418$	1.00000	+	0.267949i	0.0489116	+	0.0131058i
$419$	−23.8564			−1.16546			−0.582731	−	0.812665i	$-0.698016\pi$
$419$	−23.8564			−1.16546			−0.582731	+	0.812665i	$0.698016\pi$
$420$		0			0
$421$	−17.3397			−0.845088			−0.422544	−	0.906343i	$-0.638863\pi$
$421$	−17.3397			−0.845088			−0.422544	+	0.906343i	$0.638863\pi$
$422$	0.0980762	+	0.0262794i	0.00477428	+	0.00127926i
$423$		0			0
$424$	−11.8301	−	6.83013i	−0.574522	−	0.331700i
$425$	17.9282	−	7.19615i	0.869646	−	0.349065i
$426$		0			0
$427$	−2.66025	+	3.07180i	−0.128739	+	0.148655i
$428$	16.0981	+	16.0981i	0.778130	+	0.778130i
$429$		0			0
$430$	−3.86603	+	2.55256i	−0.186436	+	0.123095i
$431$	3.09808	−	5.36603i	0.149229	−	0.258472i	−0.781714	−	0.623637i	$-0.785654\pi$
$431$	3.09808	−	5.36603i	0.149229	−	0.258472i	0.930943	+	0.365165i	$0.118987\pi$
$432$		0			0
$433$	−17.5359	+	17.5359i	−0.842721	+	0.842721i	−0.989212	−	0.146491i	$-0.953202\pi$
$433$	−17.5359	+	17.5359i	−0.842721	+	0.842721i	0.146491	+	0.989212i	$0.453202\pi$
$434$	−9.19615	−	4.46410i	−0.441429	−	0.214284i
$435$		0			0
$436$	8.76795	+	15.1865i	0.419909	+	0.727303i
$437$	−0.0980762	+	0.0262794i	−0.00469162	+	0.00125712i
$438$		0			0
$439$	1.66025	+	2.87564i	0.0792396	+	0.137247i	0.902922	−	0.429804i	$-0.141417\pi$
$439$	1.66025	+	2.87564i	0.0792396	+	0.137247i	−0.823682	+	0.567051i	$0.808084\pi$
$440$	3.73205	+	11.1962i	0.177919	+	0.533756i
$441$		0			0
$442$	−4.00000	+	4.00000i	−0.190261	+	0.190261i
$443$	3.50000	−	13.0622i	0.166290	−	0.620603i	−0.831582	−	0.555402i	$-0.812564\pi$
$443$	3.50000	−	13.0622i	0.166290	−	0.620603i	0.997872	−	0.0652010i	$-0.0207689\pi$
$444$		0			0
$445$	1.23205	−	0.813467i	0.0584048	−	0.0385620i
$446$	−11.4904	+	6.63397i	−0.544085	+	0.314128i
$447$		0			0
$448$	1.96410	+	5.66987i	0.0927951	+	0.267876i
$449$		−	33.0526i		−	1.55985i	−0.625875	−	0.779923i	$-0.715258\pi$
$449$		−	33.0526i		−	1.55985i	0.625875	−	0.779923i	$-0.284742\pi$
$450$		0			0
$451$	15.2942	+	8.83013i	0.720177	+	0.415794i
$452$	−4.90192	−	18.2942i	−0.230567	−	0.860488i
$453$		0			0
$454$	−10.1962			−0.478529
$455$	−15.4641	−	6.39230i	−0.724968	−	0.299676i
$456$		0			0
$457$	−11.7321	−	3.14359i	−0.548802	−	0.147051i	−0.0262453	−	0.999656i	$-0.508355\pi$
$457$	−11.7321	−	3.14359i	−0.548802	−	0.147051i	−0.522557	+	0.852604i	$0.675022\pi$
$458$	2.46410	+	9.19615i	0.115140	+	0.429708i
$459$		0			0
$460$	−0.401924	−	0.356406i	−0.0187398	−	0.0166175i
$461$		−	5.60770i		−	0.261176i	−0.991437	−	0.130588i	$-0.958313\pi$
$461$		−	5.60770i		−	0.261176i	0.991437	−	0.130588i	$-0.0416866\pi$
$462$		0			0
$463$	−4.75833	−	4.75833i	−0.221138	−	0.221138i	0.587839	−	0.808978i	$-0.299979\pi$
$463$	−4.75833	−	4.75833i	−0.221138	−	0.221138i	−0.808978	+	0.587839i	$0.799979\pi$
$464$	6.40192	−	3.69615i	0.297202	−	0.171590i
$465$		0			0
$466$	−1.73205	+	3.00000i	−0.0802357	+	0.138972i
$467$	−3.64359	+	13.5981i	−0.168605	+	0.629244i	0.828947	+	0.559327i	$0.188940\pi$
$467$	−3.64359	+	13.5981i	−0.168605	+	0.629244i	−0.997553	+	0.0699173i	$0.977726\pi$
$468$		0			0
$469$	−16.4282	−	24.2583i	−0.758584	−	1.12015i
$470$	−9.46410	−	4.73205i	−0.436546	−	0.218273i
$471$		0			0
$472$	15.2942	−	4.09808i	0.703974	−	0.188629i
$473$	−10.5622	+	2.83013i	−0.485649	+	0.130129i
$474$		0			0
$475$	−2.19615	−	2.92820i	−0.100766	−	0.134355i
$476$	−17.6603	+	1.26795i	−0.809456	+	0.0581164i
$477$		0			0
$478$	0.320508	−	1.19615i	0.0146597	−	0.0547107i
$479$	−6.53590	+	11.3205i	−0.298633	+	0.517247i	−0.975823	−	0.218560i	$-0.929864\pi$
$479$	−6.53590	+	11.3205i	−0.298633	+	0.517247i	0.677191	+	0.735808i	$0.263197\pi$
$480$		0			0
$481$	12.0000	−	6.92820i	0.547153	−	0.315899i
$482$	−9.07180	−	9.07180i	−0.413209	−	0.413209i
$483$		0			0
$484$		−	6.12436i		−	0.278380i
$485$	−12.4378	+	14.0263i	−0.564772	+	0.636901i
$486$		0			0
$487$	7.29423	+	27.2224i	0.330533	+	1.23357i	0.908631	+	0.417599i	$0.137128\pi$
$487$	7.29423	+	27.2224i	0.330533	+	1.23357i	−0.578098	+	0.815967i	$0.696205\pi$
$488$	2.86603	+	0.767949i	0.129739	+	0.0347634i
$489$		0			0
$490$	3.63397	+	7.24167i	0.164166	+	0.327145i
$491$	−37.7128			−1.70196			−0.850978	−	0.525202i	$-0.823990\pi$
$491$	−37.7128			−1.70196			−0.850978	+	0.525202i	$0.823990\pi$
$492$		0			0
$493$	3.00000	+	11.1962i	0.135113	+	0.504249i
$494$	0.928203	+	0.535898i	0.0417618	+	0.0241112i
$495$		0			0
$496$		−	18.3923i		−	0.825839i
$497$	3.16987	−	1.09808i	0.142188	−	0.0492554i
$498$		0			0
$499$	−9.97372	+	5.75833i	−0.446485	+	0.257778i	−0.706345	−	0.707868i	$-0.749657\pi$
$499$	−9.97372	+	5.75833i	−0.446485	+	0.257778i	0.259860	+	0.965646i	$0.416324\pi$
$500$	6.52628	−	18.2321i	0.291864	−	0.815362i
$501$		0			0
$502$	2.92820	−	10.9282i	0.130692	−	0.487750i
$503$	17.6340	−	17.6340i	0.786260	−	0.786260i	−0.194619	−	0.980879i	$-0.562347\pi$
$503$	17.6340	−	17.6340i	0.786260	−	0.786260i	0.980879	+	0.194619i	$0.0623470\pi$
$504$		0			0
$505$	−8.26795	+	16.5359i	−0.367919	+	0.735838i
$506$	0.0980762	+	0.169873i	0.00436002	+	0.00755178i
$507$		0			0
$508$	−1.09808	+	0.294229i	−0.0487193	+	0.0130543i
$509$	19.4545	+	33.6962i	0.862305	+	1.49356i	0.869699	+	0.493583i	$0.164313\pi$
$509$	19.4545	+	33.6962i	0.862305	+	1.49356i	−0.00739389	+	0.999973i	$0.502354\pi$
$510$		0			0
$511$	19.8564	+	29.3205i	0.878396	+	1.29706i
$512$	15.6865	−	15.6865i	0.693253	−	0.693253i
$513$		0			0
$514$	−0.732051	+	1.26795i	−0.0322894	+	0.0559268i
$515$	2.13397	−	10.4282i	0.0940342	−	0.459522i
$516$		0			0
$517$	−17.6603	−	17.6603i	−0.776697	−	0.776697i
$518$	−6.58846	−	1.26795i	−0.289480	−	0.0557105i
$519$		0			0
$520$	0.732051	+	12.1962i	0.0321026	+	0.534837i
$521$	20.6603	+	11.9282i	0.905142	+	0.522584i	0.878865	−	0.477071i	$-0.158301\pi$
$521$	20.6603	+	11.9282i	0.905142	+	0.522584i	0.0262772	+	0.999655i	$0.491635\pi$
$522$		0			0
$523$	−42.8827	−	11.4904i	−1.87513	−	0.502439i	−0.999822	−	0.0188717i	$-0.993993\pi$
$523$	−42.8827	−	11.4904i	−1.87513	−	0.502439i	−0.875307	−	0.483568i	$-0.839341\pi$
$524$	−26.7846			−1.17009
$525$		0			0
$526$	−8.12436			−0.354239
$527$	27.8564	+	7.46410i	1.21344	+	0.325141i
$528$		0			0
$529$	19.9019	+	11.4904i	0.865301	+	0.499582i
$530$	−0.490381	−	8.16987i	−0.0213008	−	0.354877i
$531$		0			0
$532$	1.09808	+	3.16987i	0.0476076	+	0.137431i
$533$	12.9282	+	12.9282i	0.559983	+	0.559983i
$534$		0			0
$535$	−5.89230	+	28.7942i	−0.254747	+	1.24488i
$536$	−10.6962	+	18.5263i	−0.462003	+	0.800213i
$537$		0			0
$538$	8.36603	−	8.36603i	0.360685	−	0.360685i
$539$	2.73205	+	18.9282i	0.117678	+	0.815295i
$540$		0			0
$541$	−18.3564	−	31.7942i	−0.789204	−	1.36694i	−0.926455	−	0.376404i	$-0.877160\pi$
$541$	−18.3564	−	31.7942i	−0.789204	−	1.36694i	0.137252	−	0.990536i	$-0.456173\pi$
$542$	−10.6340	+	2.84936i	−0.456768	+	0.122391i
$543$		0			0
$544$	9.92820	+	17.1962i	0.425668	+	0.737279i
$545$	−10.1244	+	20.2487i	−0.433680	+	0.867359i
$546$		0			0
$547$	−16.7583	+	16.7583i	−0.716534	+	0.716534i	−0.967894	−	0.251359i	$-0.919122\pi$
$547$	−16.7583	+	16.7583i	−0.716534	+	0.716534i	0.251359	+	0.967894i	$0.419122\pi$
$548$	6.12436	−	22.8564i	0.261620	−	0.976377i
$549$		0			0
$550$	−4.36603	+	5.56218i	−0.186168	+	0.237172i
$551$	1.90192	−	1.09808i	0.0810247	−	0.0467796i
$552$		0			0
$553$	−5.66025	+	6.53590i	−0.240698	+	0.277935i
$554$			2.78461i			0.118307i
$555$		0			0
$556$	8.49038	+	4.90192i	0.360072	+	0.207888i
$557$	−8.36603	−	31.2224i	−0.354480	−	1.32294i	−0.881138	−	0.472860i	$-0.843222\pi$
$557$	−8.36603	−	31.2224i	−0.354480	−	1.32294i	0.526658	−	0.850077i	$-0.323445\pi$
$558$		0			0
$559$	−11.3205			−0.478806
$560$	−8.86603	+	11.5718i	−0.374658	+	0.488998i
$561$		0			0
$562$	−0.464102	−	0.124356i	−0.0195769	−	0.00524563i
$563$	6.35641	+	23.7224i	0.267891	+	0.999781i	0.960457	+	0.278427i	$0.0898132\pi$
$563$	6.35641	+	23.7224i	0.267891	+	0.999781i	−0.692567	+	0.721354i	$0.743520\pi$
$564$		0			0
$565$	16.2224	−	18.2942i	0.682483	−	0.769644i
$566$			1.01924i			0.0428418i
$567$		0			0
$568$	−1.73205	−	1.73205i	−0.0726752	−	0.0726752i
$569$	25.0526	−	14.4641i	1.05026	−	0.606367i	0.127536	−	0.991834i	$-0.459293\pi$
$569$	25.0526	−	14.4641i	1.05026	−	0.606367i	0.922722	+	0.385467i	$0.125960\pi$
$570$		0			0
$571$	9.02628	−	15.6340i	0.377738	−	0.654261i	−0.612995	−	0.790087i	$-0.710035\pi$
$571$	9.02628	−	15.6340i	0.377738	−	0.654261i	0.990733	+	0.135826i	$0.0433687\pi$
$572$	−3.46410	+	12.9282i	−0.144841	+	0.540555i
$573$		0			0
$574$	−0.633975	−	8.83013i	−0.0264616	−	0.368562i
$575$	0.0980762	−	0.686533i	0.00409006	−	0.0286304i
$576$		0			0
$577$	5.63397	−	1.50962i	0.234545	−	0.0628463i	−0.139632	−	0.990204i	$-0.544592\pi$
$577$	5.63397	−	1.50962i	0.234545	−	0.0628463i	0.374177	+	0.927357i	$0.377925\pi$
$578$	1.03590	−	0.277568i	0.0430877	−	0.0115453i
$579$		0			0
$580$	10.3923	+	5.19615i	0.431517	+	0.215758i
$581$	−3.42820	+	7.06218i	−0.142226	+	0.292989i
$582$		0			0
$583$	5.00000	−	18.6603i	0.207079	−	0.772829i
$584$	12.9282	−	22.3923i	0.534973	−	0.926600i
$585$		0			0
$586$	−1.51666	+	0.875644i	−0.0626527	+	0.0361725i
$587$	−15.7846	−	15.7846i	−0.651501	−	0.651501i	0.301854	−	0.953354i	$-0.402395\pi$
$587$	−15.7846	−	15.7846i	−0.651501	−	0.651501i	−0.953354	+	0.301854i	$0.902395\pi$
$588$		0			0
$589$		−	5.46410i		−	0.225144i
$590$	7.09808	+	6.29423i	0.292223	+	0.259129i
$591$		0			0
$592$	−3.12436	−	11.6603i	−0.128410	−	0.479233i
$593$	−20.7583	−	5.56218i	−0.852442	−	0.228411i	−0.193962	−	0.981009i	$-0.562134\pi$
$593$	−20.7583	−	5.56218i	−0.852442	−	0.228411i	−0.658481	+	0.752598i	$0.728801\pi$
$594$		0			0
$595$	−13.9282	−	18.1244i	−0.571001	−	0.743026i
$596$	1.39230			0.0570310
$597$		0			0
$598$	0.0525589	+	0.196152i	0.00214929	+	0.00802127i
$599$	15.3397	+	8.85641i	0.626765	+	0.361863i	0.779498	−	0.626405i	$-0.215474\pi$
$599$	15.3397	+	8.85641i	0.626765	+	0.361863i	−0.152733	+	0.988267i	$0.548807\pi$
$600$		0			0
$601$			41.1769i			1.67964i	0.542864	+	0.839821i	$0.317340\pi$
$601$			41.1769i			1.67964i	−0.542864	+	0.839821i	$0.682660\pi$
$602$	4.14359	+	3.58846i	0.168880	+	0.146255i
$603$		0			0
$604$	20.7846	−	12.0000i	0.845714	−	0.488273i
$605$	6.59808	−	4.35641i	0.268250	−	0.177113i
$606$		0			0
$607$	3.40192	−	12.6962i	0.138080	−	0.515321i	−0.861886	−	0.507101i	$-0.830717\pi$
$607$	3.40192	−	12.6962i	0.138080	−	0.515321i	0.999966	−	0.00821951i	$-0.00261638\pi$
$608$	2.66025	−	2.66025i	0.107888	−	0.107888i
$609$		0			0
$610$	0.562178	+	1.68653i	0.0227619	+	0.0682857i
$611$	−12.9282	−	22.3923i	−0.523019	−	0.905896i
$612$		0			0
$613$	24.3923	−	6.53590i	0.985196	−	0.263982i	0.269965	−	0.962870i	$-0.412988\pi$
$613$	24.3923	−	6.53590i	0.985196	−	0.263982i	0.715231	+	0.698888i	$0.246321\pi$
$614$	−2.30385	−	3.99038i	−0.0929757	−	0.161039i
$615$		0			0
$616$	11.5622	−	7.83013i	0.465853	−	0.315485i
$617$	−33.9090	+	33.9090i	−1.36512	+	1.36512i	−0.497874	+	0.867249i	$0.665886\pi$
$617$	−33.9090	+	33.9090i	−1.36512	+	1.36512i	−0.867249	+	0.497874i	$0.834114\pi$
$618$		0			0
$619$	5.09808	−	8.83013i	0.204909	−	0.354913i	−0.745195	−	0.666847i	$-0.767643\pi$
$619$	5.09808	−	8.83013i	0.204909	−	0.354913i	0.950104	+	0.311934i	$0.100977\pi$
$620$	24.1244	−	15.9282i	0.968857	−	0.639692i
$621$		0			0
$622$	−5.58846	−	5.58846i	−0.224077	−	0.224077i
$623$	−1.32051	−	1.14359i	−0.0529050	−	0.0458171i
$624$		0			0
$625$	24.2846	−	5.93782i	0.971384	−	0.237513i
$626$	2.41154	+	1.39230i	0.0963846	+	0.0556477i
$627$		0			0
$628$	8.02628	+	2.15064i	0.320283	+	0.0858197i
$629$	18.9282			0.754717
$630$		0			0
$631$	−4.58846			−0.182664			−0.0913318	−	0.995821i	$-0.529112\pi$
$631$	−4.58846			−0.182664			−0.0913318	+	0.995821i	$0.529112\pi$
$632$	6.09808	+	1.63397i	0.242568	+	0.0649960i
$633$		0			0
$634$	4.26795	+	2.46410i	0.169502	+	0.0978620i
$635$	−1.09808	−	0.973721i	−0.0435758	−	0.0386409i
$636$		0			0
$637$	−2.33975	+	19.6603i	−0.0927041	+	0.778968i
$638$	−3.00000	−	3.00000i	−0.118771	−	0.118771i
$639$		0			0
$640$	25.0885	+	5.13397i	0.991708	+	0.202938i
$641$	5.33013	−	9.23205i	0.210527	−	0.364644i	−0.741352	−	0.671116i	$-0.765815\pi$
$641$	5.33013	−	9.23205i	0.210527	−	0.364644i	0.951880	+	0.306472i	$0.0991486\pi$
$642$		0			0
$643$	17.5359	−	17.5359i	0.691548	−	0.691548i	−0.271024	−	0.962573i	$-0.587362\pi$
$643$	17.5359	−	17.5359i	0.691548	−	0.691548i	0.962573	+	0.271024i	$0.0873623\pi$
$644$	−0.277568	+	0.571797i	−0.0109377	+	0.0225319i
$645$		0			0
$646$	0.732051	+	1.26795i	0.0288022	+	0.0498868i
$647$	−39.5526	+	10.5981i	−1.55497	+	0.416653i	−0.931067	−	0.364847i	$-0.881121\pi$
$647$	−39.5526	+	10.5981i	−1.55497	+	0.416653i	−0.623904	+	0.781501i	$0.714454\pi$
$648$		0			0
$649$	11.1962	+	19.3923i	0.439487	+	0.761215i
$650$	−5.85641	+	4.39230i	−0.229707	+	0.172280i
$651$		0			0
$652$	17.1962	−	17.1962i	0.673453	−	0.673453i
$653$	5.26795	−	19.6603i	0.206151	−	0.769365i	−0.782945	−	0.622091i	$-0.786283\pi$
$653$	5.26795	−	19.6603i	0.206151	−	0.769365i	0.989096	−	0.147274i	$-0.0470500\pi$
$654$		0			0
$655$	−19.0526	−	28.8564i	−0.744445	−	1.12751i
$656$	13.7942	−	7.96410i	0.538574	−	0.310946i
$657$		0			0
$658$	−2.36603	+	12.2942i	−0.0922373	+	0.479279i
$659$		−	27.6603i		−	1.07749i	−0.842469	−	0.538745i	$-0.818899\pi$
$659$		−	27.6603i		−	1.07749i	0.842469	−	0.538745i	$-0.181101\pi$
$660$		0			0
$661$	−41.7224	−	24.0885i	−1.62281	−	0.936932i	−0.986163	−	0.165781i	$-0.946985\pi$
$661$	−41.7224	−	24.0885i	−1.62281	−	0.936932i	−0.636652	−	0.771151i	$-0.719681\pi$
$662$	−0.248711	−	0.928203i	−0.00966644	−	0.0360756i
$663$		0			0
$664$	5.73205			0.222447
$665$	−2.63397	+	3.43782i	−0.102141	+	0.133313i
$666$		0			0
$667$	0.401924	+	0.107695i	0.0155626	+	0.00416997i
$668$	7.45448	+	27.8205i	0.288423	+	1.07641i
$669$		0			0
$670$	−12.7942	+	0.767949i	−0.494284	+	0.0296685i
$671$			4.19615i			0.161991i
$672$		0			0
$673$	4.39230	+	4.39230i	0.169311	+	0.169311i	0.786676	−	0.617366i	$-0.211800\pi$
$673$	4.39230	+	4.39230i	0.169311	+	0.169311i	−0.617366	+	0.786676i	$0.711800\pi$
$674$	−6.04552	+	3.49038i	−0.232865	+	0.134444i
$675$		0			0
$676$	4.33013	−	7.50000i	0.166543	−	0.288462i
$677$	6.92820	−	25.8564i	0.266272	−	0.993742i	−0.695194	−	0.718822i	$-0.744682\pi$
$677$	6.92820	−	25.8564i	0.266272	−	0.993742i	0.961467	−	0.274921i	$-0.0886516\pi$
$678$		0			0
$679$	19.9545	+	9.68653i	0.765783	+	0.371735i
$680$	−7.46410	+	14.9282i	−0.286235	+	0.572470i
$681$		0			0
$682$	−10.1962	+	2.73205i	−0.390431	+	0.104616i
$683$	−17.0622	+	4.57180i	−0.652866	+	0.174935i	−0.570024	−	0.821628i	$-0.693066\pi$
$683$	−17.0622	+	4.57180i	−0.652866	+	0.174935i	−0.0828417	+	0.996563i	$0.526400\pi$
$684$		0			0
$685$	28.9808	−	9.66025i	1.10730	−	0.369099i
$686$	7.08846	−	6.45448i	0.270639	−	0.246433i
$687$		0			0
$688$	−2.55256	+	9.52628i	−0.0973154	+	0.363186i
$689$	10.0000	−	17.3205i	0.380970	−	0.659859i
$690$		0			0
$691$	−44.0263	+	25.4186i	−1.67484	+	0.966969i	−0.709971	+	0.704231i	$0.751292\pi$
$691$	−44.0263	+	25.4186i	−1.67484	+	0.966969i	−0.964867	+	0.262738i	$0.915375\pi$
$692$	25.2679	+	25.2679i	0.960543	+	0.960543i
$693$		0			0
$694$		−	15.5885i		−	0.591730i
$695$	0.758330	+	12.6340i	0.0287651	+	0.479234i
$696$		0			0
$697$	6.46410	+	24.1244i	0.244845	+	0.913775i
$698$	−3.13397	−	0.839746i	−0.118623	−	0.0317849i
$699$		0			0
$700$	−22.8564	−	1.60770i	−0.863891	−	0.0607652i
$701$	20.2679			0.765510			0.382755	−	0.923850i	$-0.374975\pi$
$701$	20.2679			0.765510			0.382755	+	0.923850i	$0.374975\pi$
$702$		0			0
$703$	−0.928203	−	3.46410i	−0.0350078	−	0.130651i
$704$	5.36603	+	3.09808i	0.202240	+	0.116763i
$705$		0			0
$706$			7.26795i			0.273533i
$707$	21.4808	+	4.13397i	0.807867	+	0.155474i
$708$		0			0
$709$	18.9904	−	10.9641i	0.713199	−	0.411765i	−0.0990456	−	0.995083i	$-0.531579\pi$
$709$	18.9904	−	10.9641i	0.713199	−	0.411765i	0.812244	+	0.583317i	$0.198246\pi$
$710$	0.294229	−	1.43782i	0.0110422	−	0.0539605i
$711$		0			0
$712$	−0.330127	+	1.23205i	−0.0123720	+	0.0461731i
$713$	0.732051	−	0.732051i	0.0274155	−	0.0274155i
$714$		0			0
$715$	−16.3923	+	5.46410i	−0.613037	+	0.204346i
$716$	6.80385	+	11.7846i	0.254272	+	0.440412i
$717$		0			0
$718$	17.1244	−	4.58846i	0.639075	−	0.171240i
$719$	−19.2942	−	33.4186i	−0.719553	−	1.24630i	−0.961177	−	0.275933i	$-0.911013\pi$
$719$	−19.2942	−	33.4186i	−0.719553	−	1.24630i	0.241624	−	0.970370i	$-0.422320\pi$
$720$		0			0
$721$	−12.5622	+	0.901924i	−0.467840	+	0.0335894i
$722$	−6.75833	+	6.75833i	−0.251519	+	0.251519i
$723$		0			0
$724$	1.03590	−	1.79423i	0.0384989	−	0.0666820i
$725$	1.79423	+	14.8923i	0.0666360	+	0.553086i
$726$		0			0
$727$	−10.0981	−	10.0981i	−0.374517	−	0.374517i	0.494602	−	0.869119i	$-0.335314\pi$
$727$	−10.0981	−	10.0981i	−0.374517	−	0.374517i	−0.869119	+	0.494602i	$0.835314\pi$
$728$	13.6603	−	4.73205i	0.506283	−	0.175381i
$729$		0			0
$730$	15.4641	−	0.928203i	0.572352	−	0.0343543i
$731$	−13.3923	−	7.73205i	−0.495332	−	0.285980i
$732$		0			0
$733$	−4.36603	−	1.16987i	−0.161263	−	0.0432102i	0.177284	−	0.984160i	$-0.443269\pi$
$733$	−4.36603	−	1.16987i	−0.161263	−	0.0432102i	−0.338547	+	0.940949i	$0.609935\pi$
$734$	−0.267949			−0.00989019
$735$		0			0
$736$	0.712813			0.0262746
$737$	−29.2224	−	7.83013i	−1.07642	−	0.288426i
$738$		0			0
$739$	−19.5622	−	11.2942i	−0.719606	−	0.415465i	0.0950014	−	0.995477i	$-0.469714\pi$
$739$	−19.5622	−	11.2942i	−0.719606	−	0.415465i	−0.814608	+	0.580012i	$0.803048\pi$
$740$	12.5885	−	14.1962i	0.462761	−	0.521861i
$741$		0			0
$742$	−9.15064	+	3.16987i	−0.335930	+	0.116370i
$743$	6.16987	+	6.16987i	0.226351	+	0.226351i	0.811166	−	0.584816i	$-0.198833\pi$
$743$	6.16987	+	6.16987i	0.226351	+	0.226351i	−0.584816	+	0.811166i	$0.698833\pi$
$744$		0			0
$745$	0.990381	+	1.50000i	0.0362848	+	0.0549557i
$746$	−2.07180	+	3.58846i	−0.0758539	+	0.131383i
$747$		0			0
$748$	−12.9282	+	12.9282i	−0.472702	+	0.472702i
$749$	34.6865	−	2.49038i	1.26742	−	0.0909965i
$750$		0			0
$751$	3.19615	+	5.53590i	0.116629	+	0.202008i	0.918430	−	0.395584i	$-0.129458\pi$
$751$	3.19615	+	5.53590i	0.116629	+	0.202008i	−0.801801	+	0.597592i	$0.796124\pi$
$752$	−21.7583	+	5.83013i	−0.793445	+	0.212603i
$753$		0			0
$754$	−2.19615	−	3.80385i	−0.0799792	−	0.138528i
$755$	27.7128	+	13.8564i	1.00857	+	0.504286i
$756$		0			0
$757$	12.7321	−	12.7321i	0.462754	−	0.462754i	−0.436803	−	0.899557i	$-0.643889\pi$
$757$	12.7321	−	12.7321i	0.462754	−	0.462754i	0.899557	+	0.436803i	$0.143889\pi$
$758$	−0.313467	+	1.16987i	−0.0113856	+	0.0424917i
$759$		0			0
$760$	3.09808	+	0.633975i	0.112379	+	0.0229967i
$761$	−24.9282	+	14.3923i	−0.903647	+	0.521721i	−0.878382	−	0.477960i	$-0.841376\pi$
$761$	−24.9282	+	14.3923i	−0.903647	+	0.521721i	−0.0252651	+	0.999681i	$0.508043\pi$
$762$		0			0
$763$	26.3038	+	5.06218i	0.952263	+	0.183263i
$764$		−	22.9808i		−	0.831415i
$765$		0			0
$766$	14.1795	+	8.18653i	0.512326	+	0.295791i
$767$	6.00000	+	22.3923i	0.216647	+	0.808539i
$768$		0			0
$769$	15.1769			0.547294			0.273647	−	0.961830i	$-0.411770\pi$
$769$	15.1769			0.547294			0.273647	+	0.961830i	$0.411770\pi$
$770$	7.73205	+	3.19615i	0.278644	+	0.115181i
$771$		0			0
$772$	13.5622	+	3.63397i	0.488113	+	0.130790i
$773$	−4.07180	−	15.1962i	−0.146452	−	0.546568i	−0.999686	−	0.0250395i	$-0.992029\pi$
$773$	−4.07180	−	15.1962i	−0.146452	−	0.546568i	0.853234	−	0.521528i	$-0.174638\pi$
$774$		0			0
$775$	34.3205	+	14.6603i	1.23283	+	0.526612i
$776$		−	16.1962i		−	0.581408i
$777$		0			0
$778$	−1.80385	−	1.80385i	−0.0646711	−	0.0646711i
$779$	4.09808	−	2.36603i	0.146829	−	0.0847717i
$780$		0			0
$781$	1.73205	−	3.00000i	0.0619777	−	0.107348i
$782$	−0.0717968	+	0.267949i	−0.00256745	+	0.00958184i
$783$		0			0
$784$	16.0167	+	6.40192i	0.572024	+	0.228640i
$785$	3.39230	+	10.1769i	0.121077	+	0.363230i
$786$		0			0
$787$	31.1865	−	8.35641i	1.11168	−	0.297874i	0.344168	−	0.938908i	$-0.388161\pi$
$787$	31.1865	−	8.35641i	1.11168	−	0.297874i	0.767512	+	0.641034i	$0.221494\pi$
$788$	−23.9545	+	6.41858i	−0.853343	+	0.228653i
$789$		0			0
$790$	1.19615	+	3.58846i	0.0425572	+	0.127672i
$791$	−26.0263	−	12.6340i	−0.925388	−	0.449212i
$792$		0			0
$793$	−1.12436	+	4.19615i	−0.0399270	+	0.149010i
$794$	0.973721	−	1.68653i	0.0345560	−	0.0598528i
$795$		0			0
$796$	16.6077	−	9.58846i	0.588644	−	0.339854i
$797$	−22.5359	−	22.5359i	−0.798262	−	0.798262i	0.184559	−	0.982821i	$-0.440914\pi$
$797$	−22.5359	−	22.5359i	−0.798262	−	0.798262i	−0.982821	+	0.184559i	$0.940914\pi$
$798$		0			0
$799$		−	35.3205i		−	1.24955i
$800$	9.57180	+	23.8468i	0.338414	+	0.843111i
$801$		0			0
$802$	−1.47372	−	5.50000i	−0.0520389	−	0.194212i
$803$	35.3205	+	9.46410i	1.24643	+	0.333981i
$804$		0			0
$805$	−0.813467	+	0.107695i	−0.0286709	+	0.00379576i
$806$	−10.9282			−0.384930
$807$		0			0
$808$	−4.13397	−	15.4282i	−0.145433	−	0.542762i
$809$	3.99038	+	2.30385i	0.140294	+	0.0809990i	0.568504	−	0.822680i	$-0.307522\pi$
$809$	3.99038	+	2.30385i	0.140294	+	0.0809990i	−0.428210	+	0.903679i	$0.640856\pi$
$810$		0			0
$811$		−	42.9282i		−	1.50741i	−0.657211	−	0.753707i	$-0.728264\pi$
$811$		−	42.9282i		−	1.50741i	0.657211	−	0.753707i	$-0.271736\pi$
$812$	2.59808	−	13.5000i	0.0911746	−	0.473757i
$813$		0			0
$814$	−6.00000	+	3.46410i	−0.210300	+	0.121417i
$815$	30.7583	+	6.29423i	1.07742	+	0.220477i
$816$		0			0
$817$	−0.758330	+	2.83013i	−0.0265306	+	0.0990136i
$818$	7.63397	−	7.63397i	0.266916	−	0.266916i
$819$		0			0
$820$	22.3923	+	11.1962i	0.781973	+	0.390987i
$821$	−24.6603	−	42.7128i	−0.860649	−	1.49069i	−0.871304	−	0.490744i	$-0.836725\pi$
$821$	−24.6603	−	42.7128i	−0.860649	−	1.49069i	0.0106549	−	0.999943i	$-0.496608\pi$
$822$		0			0
$823$	−53.3827	+	14.3038i	−1.86080	+	0.498601i	−0.999947	−	0.0102479i	$-0.996738\pi$
$823$	−53.3827	+	14.3038i	−1.86080	+	0.498601i	−0.860856	+	0.508849i	$0.830071\pi$
$824$	4.59808	+	7.96410i	0.160182	+	0.277443i
$825$		0			0
$826$	4.90192	−	10.0981i	0.170560	−	0.351357i
$827$	33.2224	−	33.2224i	1.15526	−	1.15526i	0.169774	−	0.985483i	$-0.445696\pi$
$827$	33.2224	−	33.2224i	1.15526	−	1.15526i	0.985483	−	0.169774i	$-0.0543038\pi$
$828$		0			0
$829$	−7.26795	+	12.5885i	−0.252426	+	0.437215i	−0.964193	−	0.265200i	$-0.914562\pi$
$829$	−7.26795	+	12.5885i	−0.252426	+	0.437215i	0.711767	+	0.702416i	$0.247895\pi$
$830$	1.89230	+	2.86603i	0.0656829	+	0.0994812i
$831$		0			0
$832$	4.53590	+	4.53590i	0.157254	+	0.157254i
$833$	−16.1962	+	21.6603i	−0.561163	+	0.750483i
$834$		0			0
$835$	−24.6699	+	27.8205i	−0.853736	+	0.962768i
$836$	3.00000	+	1.73205i	0.103757	+	0.0599042i
$837$		0			0
$838$	11.9282	+	3.19615i	0.412053	+	0.110409i
$839$	−6.87564			−0.237374			−0.118687	−	0.992932i	$-0.537868\pi$
$839$	−6.87564			−0.237374			−0.118687	+	0.992932i	$0.537868\pi$
$840$		0			0
$841$	20.0000			0.689655
$842$	8.66987	+	2.32309i	0.298784	+	0.0800588i
$843$		0			0
$844$	0.294229	+	0.169873i	0.0101278	+	0.00584727i
$845$	11.1603	−	0.669873i	0.383924	−	0.0230443i
$846$		0			0
$847$	−7.07180	−	6.12436i	−0.242990	−	0.210435i
$848$	−12.3205	−	12.3205i	−0.423088	−	0.423088i
$849$		0			0
$850$	−9.92820	+	1.19615i	−0.340535	+	0.0410277i
$851$	0.339746	−	0.588457i	0.0116463	−	0.0201721i
$852$		0			0
$853$	−18.1244	+	18.1244i	−0.620566	+	0.620566i	−0.945676	−	0.325110i	$-0.894599\pi$
$853$	−18.1244	+	18.1244i	−0.620566	+	0.620566i	0.325110	+	0.945676i	$0.394599\pi$
$854$	1.74167	−	1.17949i	0.0595987	−	0.0403614i
$855$		0			0
$856$	−12.6962	−	21.9904i	−0.433946	−	0.751616i
$857$	11.0981	−	2.97372i	0.379103	−	0.101580i	−0.0642351	−	0.997935i	$-0.520461\pi$
$857$	11.0981	−	2.97372i	0.379103	−	0.101580i	0.443338	+	0.896354i	$0.353794\pi$
$858$		0			0
$859$	−17.4641	−	30.2487i	−0.595867	−	1.03207i	−0.993424	−	0.114495i	$-0.963475\pi$
$859$	−17.4641	−	30.2487i	−0.595867	−	1.03207i	0.397556	−	0.917578i	$-0.369858\pi$
$860$	−14.7058	+	4.90192i	−0.501463	+	0.167154i
$861$		0			0
$862$	−2.26795	+	2.26795i	−0.0772467	+	0.0772467i
$863$	−13.3827	+	49.9449i	−0.455552	+	1.70014i	0.230908	+	0.972976i	$0.425830\pi$
$863$	−13.3827	+	49.9449i	−0.455552	+	1.70014i	−0.686460	+	0.727167i	$0.740836\pi$
$864$		0			0
$865$	−9.24871	+	45.1962i	−0.314466	+	1.53672i
$866$	11.1173	−	6.41858i	0.377782	−	0.218112i
$867$		0			0
$868$	−25.8564	−	22.3923i	−0.877624	−	0.760044i
$869$			8.92820i			0.302869i
$870$		0			0
$871$	−27.1244	−	15.6603i	−0.919074	−	0.530627i
$872$	−5.06218	−	18.8923i	−0.171427	−	0.639774i
$873$		0			0
$874$	0.0525589			0.00177783
$875$	−14.5263	−	25.7679i	−0.491078	−	0.871116i
$876$		0			0
$877$	−39.1506	−	10.4904i	−1.32202	−	0.354235i	−0.472288	−	0.881444i	$-0.656572\pi$
$877$	−39.1506	−	10.4904i	−1.32202	−	0.354235i	−0.849735	+	0.527209i	$0.823238\pi$
$878$	−0.444864	−	1.66025i	−0.0150134	−	0.0560309i
$879$		0			0
$880$	0.901924	+	15.0263i	0.0304038	+	0.506536i
$881$			25.1436i			0.847109i	0.905871	+	0.423555i	$0.139218\pi$
$881$			25.1436i			0.847109i	−0.905871	+	0.423555i	$0.860782\pi$
$882$		0			0
$883$	8.07180	+	8.07180i	0.271638	+	0.271638i	0.829759	−	0.558122i	$-0.188478\pi$
$883$	8.07180	+	8.07180i	0.271638	+	0.271638i	−0.558122	+	0.829759i	$0.688478\pi$
$884$	−16.3923	+	9.46410i	−0.551333	+	0.318312i
$885$		0			0
$886$	−3.50000	+	6.06218i	−0.117585	+	0.203663i
$887$	−2.91858	+	10.8923i	−0.0979965	+	0.365728i	−0.997457	−	0.0712748i	$-0.977293\pi$
$887$	−2.91858	+	10.8923i	−0.0979965	+	0.365728i	0.899460	+	0.437003i	$0.143960\pi$
$888$		0			0
$889$	−0.758330	+	1.56218i	−0.0254336	+	0.0523938i
$890$	−0.725009	+	0.241670i	−0.0243024	+	0.00810079i
$891$		0			0
$892$	−42.8827	+	11.4904i	−1.43582	+	0.384726i
$893$	−6.46410	+	1.73205i	−0.216313	+	0.0579609i
$894$		0			0
$895$	−7.85641	+	15.7128i	−0.262611	+	0.525221i
$896$	−2.16987	−	30.2224i	−0.0724904	−	1.00966i
$897$		0			0
$898$	−4.42820	+	16.5263i	−0.147771	+	0.551489i
$899$	−11.1962	+	19.3923i	−0.373413	+	0.646770i
$900$		0			0
$901$	23.6603	−	13.6603i	0.788237	−	0.455089i
$902$	−6.46410	−	6.46410i	−0.215231	−	0.215231i
$903$		0			0
$904$			21.1244i			0.702586i
$905$	2.66987	−	0.160254i	0.0887496	−	0.00532702i
$906$		0			0
$907$	−8.69615	−	32.4545i	−0.288751	−	1.07763i	−0.946055	−	0.324007i	$-0.894970\pi$
$907$	−8.69615	−	32.4545i	−0.288751	−	1.07763i	0.657304	−	0.753626i	$-0.271697\pi$
$908$	−32.9545	−	8.83013i	−1.09363	−	0.293038i
$909$		0			0
$910$	6.87564	+	5.26795i	0.227925	+	0.174631i
$911$	7.51666			0.249038			0.124519	−	0.992217i	$-0.460261\pi$
$911$	7.51666			0.249038			0.124519	+	0.992217i	$0.460261\pi$
$912$		0			0
$913$	2.09808	+	7.83013i	0.0694362	+	0.259139i
$914$	5.44486	+	3.14359i	0.180100	+	0.103981i
$915$		0			0
$916$			31.8564i			1.05257i
$917$	−26.7846	+	30.9282i	−0.884506	+	1.02134i
$918$		0			0
$919$	−48.6673	+	28.0981i	−1.60539	+	0.926870i	−0.615002	+	0.788526i	$0.710845\pi$
$919$	−48.6673	+	28.0981i	−1.60539	+	0.926870i	−0.990384	+	0.138344i	$0.955822\pi$
$920$	0.330127	+	0.500000i	0.0108840	+	0.0164845i
$921$		0			0
$922$	−0.751289	+	2.80385i	−0.0247424	+	0.0923398i
$923$	2.53590	−	2.53590i	0.0834701	−	0.0834701i
$924$		0			0
$925$	24.2487	+	3.46410i	0.797293	+	0.113899i
$926$	1.74167	+	3.01666i	0.0572348	+	0.0991336i
$927$		0			0
$928$	−14.8923	+	3.99038i	−0.488864	+	0.130991i
$929$	18.1603	+	31.4545i	0.595819	+	1.03199i	0.993431	+	0.114435i	$0.0365056\pi$
$929$	18.1603	+	31.4545i	0.595819	+	1.03199i	−0.397612	+	0.917554i	$0.630161\pi$
$930$		0			0
$931$	4.75833	+	1.90192i	0.155948	+	0.0623330i
$932$	−8.19615	+	8.19615i	−0.268474	+	0.268474i
$933$		0			0
$934$	3.64359	−	6.31089i	0.119222	−	0.206499i
$935$	−23.1244	−	4.73205i	−0.756247	−	0.154755i
$936$		0			0
$937$	17.0718	+	17.0718i	0.557711	+	0.557711i	0.928655	−	0.370944i	$-0.120966\pi$
$937$	17.0718	+	17.0718i	0.557711	+	0.557711i	−0.370944	+	0.928655i	$0.620966\pi$
$938$	4.96410	+	14.3301i	0.162084	+	0.467895i
$939$		0			0
$940$	−26.4904	−	23.4904i	−0.864021	−	0.766172i
$941$	−35.1962	−	20.3205i	−1.14736	−	0.662430i	−0.199119	−	0.979975i	$-0.563808\pi$
$941$	−35.1962	−	20.3205i	−1.14736	−	0.662430i	−0.948243	+	0.317546i	$0.897141\pi$
$942$		0			0
$943$	0.866025	+	0.232051i	0.0282017	+	0.00755661i
$944$	20.1962			0.657329
$945$		0			0
$946$	5.66025			0.184031
$947$	1.30385	+	0.349365i	0.0423694	+	0.0113528i	0.279941	−	0.960017i	$-0.409685\pi$
$947$	1.30385	+	0.349365i	0.0423694	+	0.0113528i	−0.237572	+	0.971370i	$0.576352\pi$
$948$		0			0
$949$	32.7846	+	18.9282i	1.06423	+	0.614435i
$950$	0.705771	+	1.75833i	0.0228982	+	0.0570478i
$951$		0			0
$952$	19.3923	+	3.73205i	0.628508	+	0.120956i
$953$	37.8564	+	37.8564i	1.22629	+	1.22629i	0.965357	+	0.260932i	$0.0840299\pi$
$953$	37.8564	+	37.8564i	1.22629	+	1.22629i	0.260932	+	0.965357i	$0.415970\pi$
$954$		0			0
$955$	24.7583	−	16.3468i	0.801161	−	0.528970i
$956$	2.07180	−	3.58846i	0.0670067	−	0.116059i
$957$		0			0
$958$	4.78461	−	4.78461i	0.154584	−	0.154584i
$959$	−20.2679	−	29.9282i	−0.654486	−	0.966432i
$960$		0			0
$961$	12.3564	+	21.4019i	0.398594	+	0.690385i
$962$	−6.92820	+	1.85641i	−0.223374	+	0.0598529i
$963$		0			0
$964$	−21.4641	−	37.1769i	−0.691312	−	1.19739i
$965$	5.73205	+	17.1962i	0.184521	+	0.553564i
$966$		0			0
$967$	−13.5622	+	13.5622i	−0.436130	+	0.436130i	−0.890707	−	0.454577i	$-0.849790\pi$
$967$	−13.5622	+	13.5622i	−0.436130	+	0.436130i	0.454577	+	0.890707i	$0.349790\pi$
$968$	−1.76795	+	6.59808i	−0.0568240	+	0.212070i
$969$		0			0
$970$	8.09808	−	5.34679i	0.260014	−	0.171675i
$971$	−29.0718	+	16.7846i	−0.932958	+	0.538644i	−0.887746	−	0.460334i	$-0.847730\pi$
$971$	−29.0718	+	16.7846i	−0.932958	+	0.538644i	−0.0452124	+	0.998977i	$0.514396\pi$
$972$		0			0
$973$	14.1506	−	4.90192i	0.453649	−	0.157148i
$974$		−	14.5885i		−	0.467444i
$975$		0			0
$976$	3.27757	+	1.89230i	0.104912	+	0.0605712i
$977$	0.150635	+	0.562178i	0.00481924	+	0.0179857i	0.968294	−	0.249815i	$-0.0803698\pi$
$977$	0.150635	+	0.562178i	0.00481924	+	0.0179857i	−0.963474	+	0.267801i	$0.913703\pi$
$978$		0			0
$979$	−1.80385			−0.0576512
$980$	5.47372	+	26.5526i	0.174852	+	0.848190i
$981$		0			0
$982$	18.8564	+	5.05256i	0.601732	+	0.161234i
$983$	−14.5000	−	54.1147i	−0.462478	−	1.72599i	−0.665118	−	0.746739i	$-0.731619\pi$
$983$	−14.5000	−	54.1147i	−0.462478	−	1.72599i	0.202639	−	0.979253i	$-0.435048\pi$
$984$		0			0
$985$	−23.9545	−	21.2417i	−0.763253	−	0.676816i
$986$		−	6.00000i		−	0.191079i
$987$		0			0
$988$	2.53590	+	2.53590i	0.0806777	+	0.0806777i
$989$	−0.480762	+	0.277568i	−0.0152873	+	0.00882615i
$990$		0			0
$991$	−15.8564	+	27.4641i	−0.503695	+	0.872426i	0.496296	+	0.868154i	$0.334693\pi$
$991$	−15.8564	+	27.4641i	−0.503695	+	0.872426i	−0.999991	+	0.00427229i	$0.998640\pi$
$992$	−9.92820	+	37.0526i	−0.315221	+	1.17642i
$993$		0			0
$994$	−1.73205	+	0.124356i	−0.0549373	+	0.00394432i
$995$	22.1436	+	11.0718i	0.701999	+	0.351000i
$996$		0			0
$997$	−39.8827	+	10.6865i	−1.26310	+	0.338446i	−0.827382	−	0.561639i	$-0.810171\pi$
$997$	−39.8827	+	10.6865i	−1.26310	+	0.338446i	−0.435715	+	0.900085i	$0.643504\pi$
$998$	5.75833	−	1.54294i	0.182277	−	0.0488409i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	315.2.bz.a.73.1		4
3.2	odd	2		35.2.k.b.3.1	yes	4
5.2	odd	4		315.2.bz.b.262.1		4
7.5	odd	6		315.2.bz.b.208.1		4
12.11	even	2		560.2.ci.b.353.1		4
15.2	even	4		35.2.k.a.17.1	✓	4
15.8	even	4		175.2.o.b.157.1		4
15.14	odd	2		175.2.o.a.143.1		4
21.2	odd	6		245.2.l.a.68.1		4
21.5	even	6		35.2.k.a.33.1	yes	4
21.11	odd	6		245.2.f.b.48.1		4
21.17	even	6		245.2.f.a.48.1		4
21.20	even	2		245.2.l.b.178.1		4
35.12	even	12	inner	315.2.bz.a.82.1		4
60.47	odd	4		560.2.ci.a.17.1		4
84.47	odd	6		560.2.ci.a.33.1		4
105.2	even	12		245.2.l.b.117.1		4
105.17	odd	12		245.2.f.b.97.1		4
105.32	even	12		245.2.f.a.97.1		4
105.47	odd	12		35.2.k.b.12.1	yes	4
105.62	odd	4		245.2.l.a.227.1		4
105.68	odd	12		175.2.o.a.82.1		4
105.89	even	6		175.2.o.b.68.1		4
420.47	even	12		560.2.ci.b.257.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
35.2.k.a.17.1	✓	4	15.2	even	4
35.2.k.a.33.1	yes	4	21.5	even	6
35.2.k.b.3.1	yes	4	3.2	odd	2
35.2.k.b.12.1	yes	4	105.47	odd	12
175.2.o.a.82.1		4	105.68	odd	12
175.2.o.a.143.1		4	15.14	odd	2
175.2.o.b.68.1		4	105.89	even	6
175.2.o.b.157.1		4	15.8	even	4
245.2.f.a.48.1		4	21.17	even	6
245.2.f.a.97.1		4	105.32	even	12
245.2.f.b.48.1		4	21.11	odd	6
245.2.f.b.97.1		4	105.17	odd	12
245.2.l.a.68.1		4	21.2	odd	6
245.2.l.a.227.1		4	105.62	odd	4
245.2.l.b.117.1		4	105.2	even	12
245.2.l.b.178.1		4	21.20	even	2
315.2.bz.a.73.1		4	1.1	even	1	trivial
315.2.bz.a.82.1		4	35.12	even	12	inner
315.2.bz.b.208.1		4	7.5	odd	6
315.2.bz.b.262.1		4	5.2	odd	4
560.2.ci.a.17.1		4	60.47	odd	4
560.2.ci.a.33.1		4	84.47	odd	6
560.2.ci.b.257.1		4	420.47	even	12
560.2.ci.b.353.1		4	12.11	even	2

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:	\( N \)	\(=\)	\( 315 = 3^{2} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	315.bz (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.500000 - 0.133975i) q^{2} +(-1.50000 - 0.866025i) q^{4} +(-0.133975 - 2.23205i) q^{5} +(-2.50000 + 0.866025i) q^{7} +(1.36603 + 1.36603i) q^{8} +O(q^{10})\)	\(q+(-0.500000 - 0.133975i) q^{2} +(-1.50000 - 0.866025i) q^{4} +(-0.133975 - 2.23205i) q^{5} +(-2.50000 + 0.866025i) q^{7} +(1.36603 + 1.36603i) q^{8} +(-0.232051 + 1.13397i) q^{10} +(-1.36603 + 2.36603i) q^{11} +(-2.00000 + 2.00000i) q^{13} +(1.36603 - 0.0980762i) q^{14} +(1.23205 + 2.13397i) q^{16} +(-3.73205 + 1.00000i) q^{17} +(0.366025 + 0.633975i) q^{19} +(-1.73205 + 3.46410i) q^{20} +(1.00000 - 1.00000i) q^{22} +(-0.0358984 + 0.133975i) q^{23} +(-4.96410 + 0.598076i) q^{25} +(1.26795 - 0.732051i) q^{26} +(4.50000 + 0.866025i) q^{28} -3.00000i q^{29} +(-6.46410 - 3.73205i) q^{31} +(-1.33013 - 4.96410i) q^{32} +2.00000 q^{34} +(2.26795 + 5.46410i) q^{35} +(-4.73205 - 1.26795i) q^{37} +(-0.0980762 - 0.366025i) q^{38} +(2.86603 - 3.23205i) q^{40} -6.46410i q^{41} +(2.83013 + 2.83013i) q^{43} +(4.09808 - 2.36603i) q^{44} +(0.0358984 - 0.0621778i) q^{46} +(-2.36603 + 8.83013i) q^{47} +(5.50000 - 4.33013i) q^{49} +(2.56218 + 0.366025i) q^{50} +(4.73205 - 1.26795i) q^{52} +(-6.83013 + 1.83013i) q^{53} +(5.46410 + 2.73205i) q^{55} +(-4.59808 - 2.23205i) q^{56} +(-0.401924 + 1.50000i) q^{58} +(4.09808 - 7.09808i) q^{59} +(1.33013 - 0.767949i) q^{61} +(2.73205 + 2.73205i) q^{62} -2.26795i q^{64} +(4.73205 + 4.19615i) q^{65} +(2.86603 + 10.6962i) q^{67} +(6.46410 + 1.73205i) q^{68} +(-0.401924 - 3.03590i) q^{70} -1.26795 q^{71} +(-3.46410 - 12.9282i) q^{73} +(2.19615 + 1.26795i) q^{74} -1.26795i q^{76} +(1.36603 - 7.09808i) q^{77} +(2.83013 - 1.63397i) q^{79} +(4.59808 - 3.03590i) q^{80} +(-0.866025 + 3.23205i) q^{82} +(2.09808 - 2.09808i) q^{83} +(2.73205 + 8.19615i) q^{85} +(-1.03590 - 1.79423i) q^{86} +(-5.09808 + 1.36603i) q^{88} +(0.330127 + 0.571797i) q^{89} +(3.26795 - 6.73205i) q^{91} +(0.169873 - 0.169873i) q^{92} +(2.36603 - 4.09808i) q^{94} +(1.36603 - 0.901924i) q^{95} +(-5.92820 - 5.92820i) q^{97} +(-3.33013 + 1.42820i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 2 q^{2} - 6 q^{4} - 4 q^{5} - 10 q^{7} + 2 q^{8}+O(q^{10}) \) 4 * q - 2 * q^2 - 6 * q^4 - 4 * q^5 - 10 * q^7 + 2 * q^8	\( 4 q - 2 q^{2} - 6 q^{4} - 4 q^{5} - 10 q^{7} + 2 q^{8} + 6 q^{10} - 2 q^{11} - 8 q^{13} + 2 q^{14} - 2 q^{16} - 8 q^{17} - 2 q^{19} + 4 q^{22} - 14 q^{23} - 6 q^{25} + 12 q^{26} + 18 q^{28} - 12 q^{31} + 12 q^{32} + 8 q^{34} + 16 q^{35} - 12 q^{37} + 10 q^{38} + 8 q^{40} - 6 q^{43} + 6 q^{44} + 14 q^{46} - 6 q^{47} + 22 q^{49} - 14 q^{50} + 12 q^{52} - 10 q^{53} + 8 q^{55} - 8 q^{56} - 12 q^{58} + 6 q^{59} - 12 q^{61} + 4 q^{62} + 12 q^{65} + 8 q^{67} + 12 q^{68} - 12 q^{70} - 12 q^{71} - 12 q^{74} + 2 q^{77} - 6 q^{79} + 8 q^{80} - 2 q^{83} + 4 q^{85} - 18 q^{86} - 10 q^{88} - 16 q^{89} + 20 q^{91} + 18 q^{92} + 6 q^{94} + 2 q^{95} + 4 q^{97} + 4 q^{98}+O(q^{100}) \) 4 * q - 2 * q^2 - 6 * q^4 - 4 * q^5 - 10 * q^7 + 2 * q^8 + 6 * q^10 - 2 * q^11 - 8 * q^13 + 2 * q^14 - 2 * q^16 - 8 * q^17 - 2 * q^19 + 4 * q^22 - 14 * q^23 - 6 * q^25 + 12 * q^26 + 18 * q^28 - 12 * q^31 + 12 * q^32 + 8 * q^34 + 16 * q^35 - 12 * q^37 + 10 * q^38 + 8 * q^40 - 6 * q^43 + 6 * q^44 + 14 * q^46 - 6 * q^47 + 22 * q^49 - 14 * q^50 + 12 * q^52 - 10 * q^53 + 8 * q^55 - 8 * q^56 - 12 * q^58 + 6 * q^59 - 12 * q^61 + 4 * q^62 + 12 * q^65 + 8 * q^67 + 12 * q^68 - 12 * q^70 - 12 * q^71 - 12 * q^74 + 2 * q^77 - 6 * q^79 + 8 * q^80 - 2 * q^83 + 4 * q^85 - 18 * q^86 - 10 * q^88 - 16 * q^89 + 20 * q^91 + 18 * q^92 + 6 * q^94 + 2 * q^95 + 4 * q^97 + 4 * q^98

Introduction

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