LMFDB - Embedded newform 175.2.k.a.149.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [175,2,Mod(74,175)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(175, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 4]))

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

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

chi := DirichletCharacter("175.74");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 175 = 5^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	175.k (of order $6$, degree $2$, not 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:	$1.39738203537$
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:	$\Z[a_1, \ldots, a_{4}]$
Coefficient ring index:	$ 2^{6} $
Twist minimal:	no (minimal twist has level 35)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			149.3
Root			$0.965926 - 0.258819i$ of defining polynomial
Character	$\chi$	$=$	175.149
Dual form			175.2.k.a.74.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.358719 + 0.207107i) q^{2} +(-2.09077 + 1.20711i) q^{3} +(-0.914214 - 1.58346i) q^{4} -1.00000 q^{6} +(-2.09077 - 1.62132i) q^{7} -1.58579i q^{8} +(1.41421 - 2.44949i) q^{9} +O(q^{10})$	\(q+(0.358719 + 0.207107i) q^{2} +(-2.09077 + 1.20711i) q^{3} +(-0.914214 - 1.58346i) q^{4} -1.00000 q^{6} +(-2.09077 - 1.62132i) q^{7} -1.58579i q^{8} +(1.41421 - 2.44949i) q^{9} +(-2.41421 - 4.18154i) q^{11} +(3.82282 + 2.20711i) q^{12} -0.828427i q^{13} +(-0.414214 - 1.01461i) q^{14} +(-1.50000 + 2.59808i) q^{16} +(-0.717439 + 0.414214i) q^{17} +(1.01461 - 0.585786i) q^{18} +(-1.41421 + 2.44949i) q^{19} +(6.32843 + 0.866025i) q^{21} -2.00000i q^{22} +(-2.09077 - 1.20711i) q^{23} +(1.91421 + 3.31552i) q^{24} +(0.171573 - 0.297173i) q^{26} -0.414214i q^{27} +(-0.655892 + 4.79289i) q^{28} +1.00000 q^{29} +(3.00000 + 5.19615i) q^{31} +(-3.82282 + 2.20711i) q^{32} +(10.0951 + 5.82843i) q^{33} -0.343146 q^{34} -5.17157 q^{36} +(-1.01461 + 0.585786i) q^{38} +(1.00000 + 1.73205i) q^{39} -2.17157 q^{41} +(2.09077 + 1.62132i) q^{42} -6.41421i q^{43} +(-4.41421 + 7.64564i) q^{44} +(-0.500000 - 0.866025i) q^{46} +(-1.73205 - 1.00000i) q^{47} -7.24264i q^{48} +(1.74264 + 6.77962i) q^{49} +(1.00000 - 1.73205i) q^{51} +(-1.31178 + 0.757359i) q^{52} +(5.91359 - 3.41421i) q^{53} +(0.0857864 - 0.148586i) q^{54} +(-2.57107 + 3.31552i) q^{56} -6.82843i q^{57} +(0.358719 + 0.207107i) q^{58} +(-6.24264 - 10.8126i) q^{59} +(5.74264 - 9.94655i) q^{61} +2.48528i q^{62} +(-6.92820 + 2.82843i) q^{63} +4.17157 q^{64} +(2.41421 + 4.18154i) q^{66} +(10.7510 - 6.20711i) q^{67} +(1.31178 + 0.757359i) q^{68} +5.82843 q^{69} -12.4853 q^{71} +(-3.88437 - 2.24264i) q^{72} +(-4.18154 + 2.41421i) q^{73} +5.17157 q^{76} +(-1.73205 + 12.6569i) q^{77} +0.828427i q^{78} +(4.58579 - 7.94282i) q^{79} +(4.74264 + 8.21449i) q^{81} +(-0.778985 - 0.449747i) q^{82} +11.7279i q^{83} +(-4.41421 - 10.8126i) q^{84} +(1.32843 - 2.30090i) q^{86} +(-2.09077 + 1.20711i) q^{87} +(-6.63103 + 3.82843i) q^{88} +(1.32843 - 2.30090i) q^{89} +(-1.34315 + 1.73205i) q^{91} +4.41421i q^{92} +(-12.5446 - 7.24264i) q^{93} +(-0.414214 - 0.717439i) q^{94} +(5.32843 - 9.22911i) q^{96} +0.343146i q^{97} +(-0.778985 + 2.79289i) q^{98} -13.6569 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 4 q^{4} - 8 q^{6}+O(q^{10}) $ 8 * q + 4 * q^4 - 8 * q^6	$ 8 q + 4 q^{4} - 8 q^{6} - 8 q^{11} + 8 q^{14} - 12 q^{16} + 28 q^{21} + 4 q^{24} + 24 q^{26} + 8 q^{29} + 24 q^{31} - 48 q^{34} - 64 q^{36} + 8 q^{39} - 40 q^{41} - 24 q^{44} - 4 q^{46} - 20 q^{49} + 8 q^{51} + 12 q^{54} + 36 q^{56} - 16 q^{59} + 12 q^{61} + 56 q^{64} + 8 q^{66} + 24 q^{69} - 32 q^{71} + 64 q^{76} + 48 q^{79} + 4 q^{81} - 24 q^{84} - 12 q^{86} - 12 q^{89} - 56 q^{91} + 8 q^{94} + 20 q^{96} - 64 q^{99}+O(q^{100}) $ 8 * q + 4 * q^4 - 8 * q^6 - 8 * q^11 + 8 * q^14 - 12 * q^16 + 28 * q^21 + 4 * q^24 + 24 * q^26 + 8 * q^29 + 24 * q^31 - 48 * q^34 - 64 * q^36 + 8 * q^39 - 40 * q^41 - 24 * q^44 - 4 * q^46 - 20 * q^49 + 8 * q^51 + 12 * q^54 + 36 * q^56 - 16 * q^59 + 12 * q^61 + 56 * q^64 + 8 * q^66 + 24 * q^69 - 32 * q^71 + 64 * q^76 + 48 * q^79 + 4 * q^81 - 24 * q^84 - 12 * q^86 - 12 * q^89 - 56 * q^91 + 8 * q^94 + 20 * q^96 - 64 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/175\mathbb{Z}\right)^\times$.

$n$	$101$	$127$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$-1$

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 $

$2$	0.358719	+	0.207107i	0.253653	+	0.146447i	0.621436	−	0.783465i	$-0.286550\pi$
$2$	0.358719	+	0.207107i	0.253653	+	0.146447i	−0.367783	+	0.929912i	$0.619883\pi$
$3$	−2.09077	+	1.20711i	−1.20711	+	0.696923i	−0.962126	−	0.272605i	$-0.912115\pi$
$3$	−2.09077	+	1.20711i	−1.20711	+	0.696923i	−0.244981	+	0.969528i	$0.578782\pi$
$4$	−0.914214	−	1.58346i	−0.457107	−	0.791732i
$5$		0			0
$5$		0			0
$6$	−1.00000			−0.408248
$7$	−2.09077	−	1.62132i	−0.790237	−	0.612801i
$7$	−2.09077	−	1.62132i	−0.790237	−	0.612801i
$8$		−	1.58579i		−	0.560660i
$9$	1.41421	−	2.44949i	0.471405	−	0.816497i
$10$		0			0
$11$	−2.41421	−	4.18154i	−0.727913	−	1.26078i	−0.957764	−	0.287556i	$-0.907157\pi$
$11$	−2.41421	−	4.18154i	−0.727913	−	1.26078i	0.229851	−	0.973226i	$-0.426176\pi$
$12$	3.82282	+	2.20711i	1.10355	+	0.637137i
$13$		−	0.828427i		−	0.229764i	−0.993379	−	0.114882i	$-0.963351\pi$
$13$		−	0.828427i		−	0.229764i	0.993379	−	0.114882i	$-0.0366490\pi$
$14$	−0.414214	−	1.01461i	−0.110703	−	0.271166i
$15$		0			0
$16$	−1.50000	+	2.59808i	−0.375000	+	0.649519i
$17$	−0.717439	+	0.414214i	−0.174005	+	0.100462i	−0.584473	−	0.811413i	$-0.698699\pi$
$17$	−0.717439	+	0.414214i	−0.174005	+	0.100462i	0.410468	+	0.911875i	$0.365365\pi$
$18$	1.01461	−	0.585786i	0.239146	−	0.138071i
$19$	−1.41421	+	2.44949i	−0.324443	+	0.561951i	−0.981399	−	0.191977i	$-0.938510\pi$
$19$	−1.41421	+	2.44949i	−0.324443	+	0.561951i	0.656957	+	0.753928i	$0.271843\pi$
$20$		0			0
$21$	6.32843	+	0.866025i	1.38098	+	0.188982i
$22$		−	2.00000i		−	0.426401i
$23$	−2.09077	−	1.20711i	−0.435956	−	0.251699i	0.265925	−	0.963994i	$-0.414323\pi$
$23$	−2.09077	−	1.20711i	−0.435956	−	0.251699i	−0.701881	+	0.712295i	$0.747656\pi$
$24$	1.91421	+	3.31552i	0.390737	+	0.676777i
$25$		0			0
$26$	0.171573	−	0.297173i	0.0336482	−	0.0582804i
$27$		−	0.414214i		−	0.0797154i
$28$	−0.655892	+	4.79289i	−0.123952	+	0.905772i
$29$	1.00000			0.185695			0.0928477	−	0.995680i	$-0.470403\pi$
$29$	1.00000			0.185695			0.0928477	+	0.995680i	$0.470403\pi$
$30$		0			0
$31$	3.00000	+	5.19615i	0.538816	+	0.933257i	0.998968	+	0.0454165i	$0.0144615\pi$
$31$	3.00000	+	5.19615i	0.538816	+	0.933257i	−0.460152	+	0.887840i	$0.652205\pi$
$32$	−3.82282	+	2.20711i	−0.675786	+	0.390165i
$33$	10.0951	+	5.82843i	1.75734	+	1.01460i
$34$	−0.343146			−0.0588490
$35$		0			0
$36$	−5.17157			−0.861929
$37$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$37$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$38$	−1.01461	+	0.585786i	−0.164592	+	0.0950271i
$39$	1.00000	+	1.73205i	0.160128	+	0.277350i
$40$		0			0
$41$	−2.17157			−0.339143			−0.169571	−	0.985518i	$-0.554238\pi$
$41$	−2.17157			−0.339143			−0.169571	+	0.985518i	$0.554238\pi$
$42$	2.09077	+	1.62132i	0.322613	+	0.250175i
$43$		−	6.41421i		−	0.978158i	−0.872239	−	0.489079i	$-0.837333\pi$
$43$		−	6.41421i		−	0.978158i	0.872239	−	0.489079i	$-0.162667\pi$
$44$	−4.41421	+	7.64564i	−0.665468	+	1.15262i
$45$		0			0
$46$	−0.500000	−	0.866025i	−0.0737210	−	0.127688i
$47$	−1.73205	−	1.00000i	−0.252646	−	0.145865i	0.368329	−	0.929695i	$-0.379930\pi$
$47$	−1.73205	−	1.00000i	−0.252646	−	0.145865i	−0.620975	+	0.783830i	$0.713263\pi$
$48$		−	7.24264i		−	1.04539i
$49$	1.74264	+	6.77962i	0.248949	+	0.968517i
$50$		0			0
$51$	1.00000	−	1.73205i	0.140028	−	0.242536i
$52$	−1.31178	+	0.757359i	−0.181912	+	0.105027i
$53$	5.91359	−	3.41421i	0.812294	−	0.468978i	−0.0354577	−	0.999371i	$-0.511289\pi$
$53$	5.91359	−	3.41421i	0.812294	−	0.468978i	0.847752	+	0.530393i	$0.177956\pi$
$54$	0.0857864	−	0.148586i	0.0116741	−	0.0202201i
$55$		0			0
$56$	−2.57107	+	3.31552i	−0.343573	+	0.443054i
$57$		−	6.82843i		−	0.904447i
$58$	0.358719	+	0.207107i	0.0471022	+	0.0271945i
$59$	−6.24264	−	10.8126i	−0.812723	−	1.40768i	−0.910952	−	0.412513i	$-0.864651\pi$
$59$	−6.24264	−	10.8126i	−0.812723	−	1.40768i	0.0982291	−	0.995164i	$-0.468682\pi$
$60$		0			0
$61$	5.74264	−	9.94655i	0.735270	−	1.27352i	−0.219335	−	0.975650i	$-0.570389\pi$
$61$	5.74264	−	9.94655i	0.735270	−	1.27352i	0.954605	−	0.297875i	$-0.0962779\pi$
$62$			2.48528i			0.315631i
$63$	−6.92820	+	2.82843i	−0.872872	+	0.356348i
$64$	4.17157			0.521447
$65$		0			0
$66$	2.41421	+	4.18154i	0.297169	+	0.514712i
$67$	10.7510	−	6.20711i	1.31345	−	0.758319i	0.330781	−	0.943707i	$-0.392688\pi$
$67$	10.7510	−	6.20711i	1.31345	−	0.758319i	0.982665	+	0.185389i	$0.0593544\pi$
$68$	1.31178	+	0.757359i	0.159077	+	0.0918433i
$69$	5.82843			0.701660
$70$		0			0
$71$	−12.4853			−1.48173			−0.740865	−	0.671654i	$-0.765584\pi$
$71$	−12.4853			−1.48173			−0.740865	+	0.671654i	$0.765584\pi$
$72$	−3.88437	−	2.24264i	−0.457777	−	0.264298i
$73$	−4.18154	+	2.41421i	−0.489412	+	0.282562i	−0.724331	−	0.689453i	$-0.757851\pi$
$73$	−4.18154	+	2.41421i	−0.489412	+	0.282562i	0.234918	+	0.972015i	$0.424518\pi$
$74$		0			0
$75$		0			0
$76$	5.17157			0.593220
$77$	−1.73205	+	12.6569i	−0.197386	+	1.44238i
$78$			0.828427i			0.0938009i
$79$	4.58579	−	7.94282i	0.515941	−	0.893637i	−0.483887	−	0.875130i	$-0.660776\pi$
$79$	4.58579	−	7.94282i	0.515941	−	0.893637i	0.999829	−	0.0185063i	$-0.00589107\pi$
$80$		0			0
$81$	4.74264	+	8.21449i	0.526960	+	0.912722i
$82$	−0.778985	−	0.449747i	−0.0860246	−	0.0496663i
$83$			11.7279i			1.28731i	0.765317	+	0.643653i	$0.222582\pi$
$83$			11.7279i			1.28731i	−0.765317	+	0.643653i	$0.777418\pi$
$84$	−4.41421	−	10.8126i	−0.481630	−	1.17975i
$85$		0			0
$86$	1.32843	−	2.30090i	0.143248	−	0.248113i
$87$	−2.09077	+	1.20711i	−0.224154	+	0.129415i
$88$	−6.63103	+	3.82843i	−0.706870	+	0.408112i
$89$	1.32843	−	2.30090i	0.140813	−	0.243895i	−0.786990	−	0.616966i	$-0.788362\pi$
$89$	1.32843	−	2.30090i	0.140813	−	0.243895i	0.927803	+	0.373070i	$0.121695\pi$
$90$		0			0
$91$	−1.34315	+	1.73205i	−0.140800	+	0.181568i
$92$			4.41421i			0.460214i
$93$	−12.5446	−	7.24264i	−1.30082	−	0.751027i
$94$	−0.414214	−	0.717439i	−0.0427229	−	0.0739982i
$95$		0			0
$96$	5.32843	−	9.22911i	0.543830	−	0.941942i
$97$			0.343146i			0.0348412i	0.999848	+	0.0174206i	$0.00554543\pi$
$97$			0.343146i			0.0348412i	−0.999848	+	0.0174206i	$0.994455\pi$
$98$	−0.778985	+	2.79289i	−0.0786894	+	0.282125i
$99$	−13.6569			−1.37257
$100$		0			0
$101$	−6.15685	−	10.6640i	−0.612630	−	1.06111i	−0.990795	−	0.135368i	$-0.956778\pi$
$101$	−6.15685	−	10.6640i	−0.612630	−	1.06111i	0.378165	−	0.925738i	$-0.376555\pi$
$102$	0.717439	−	0.414214i	0.0710370	−	0.0410133i
$103$	0.358719	+	0.207107i	0.0353457	+	0.0204068i	0.517569	−	0.855642i	$-0.326837\pi$
$103$	0.358719	+	0.207107i	0.0353457	+	0.0204068i	−0.482223	+	0.876048i	$0.660171\pi$
$104$	−1.31371			−0.128820
$105$		0			0
$106$	2.82843			0.274721
$107$	−2.38794	−	1.37868i	−0.230851	−	0.133282i	0.380113	−	0.924940i	$-0.375885\pi$
$107$	−2.38794	−	1.37868i	−0.230851	−	0.133282i	−0.610965	+	0.791658i	$0.709218\pi$
$108$	−0.655892	+	0.378680i	−0.0631133	+	0.0364385i
$109$	1.74264	+	3.01834i	0.166915	+	0.289105i	0.937334	−	0.348433i	$-0.113286\pi$
$109$	1.74264	+	3.01834i	0.166915	+	0.289105i	−0.770419	+	0.637538i	$0.779953\pi$
$110$		0			0
$111$		0			0
$112$	7.34847	−	3.00000i	0.694365	−	0.283473i
$113$		−	12.4853i		−	1.17452i	−0.809400	−	0.587258i	$-0.800207\pi$
$113$		−	12.4853i		−	1.17452i	0.809400	−	0.587258i	$-0.199793\pi$
$114$	1.41421	−	2.44949i	0.132453	−	0.229416i
$115$		0			0
$116$	−0.914214	−	1.58346i	−0.0848826	−	0.147021i
$117$	−2.02922	−	1.17157i	−0.187602	−	0.108312i
$118$		−	5.17157i		−	0.476082i
$119$	2.17157	+	0.297173i	0.199068	+	0.0272418i
$120$		0			0
$121$	−6.15685	+	10.6640i	−0.559714	+	0.969453i
$122$	4.11999	−	2.37868i	0.373007	−	0.215356i
$123$	4.54026	−	2.62132i	0.409381	−	0.236356i
$124$	5.48528	−	9.50079i	0.492593	−	0.853196i
$125$		0			0
$126$	−3.07107	−	0.420266i	−0.273592	−	0.0374403i
$127$			13.3137i			1.18140i	0.806891	+	0.590700i	$0.201148\pi$
$127$			13.3137i			1.18140i	−0.806891	+	0.590700i	$0.798852\pi$
$128$	9.14207	+	5.27817i	0.808052	+	0.466529i
$129$	7.74264	+	13.4106i	0.681702	+	1.18074i
$130$		0			0
$131$	−1.65685	+	2.86976i	−0.144760	+	0.250732i	−0.929283	−	0.369368i	$-0.879574\pi$
$131$	−1.65685	+	2.86976i	−0.144760	+	0.250732i	0.784523	+	0.620099i	$0.212908\pi$
$132$		−	21.3137i		−	1.85512i
$133$	6.92820	−	2.82843i	0.600751	−	0.245256i
$134$	5.14214			0.444213
$135$		0			0
$136$	0.656854	+	1.13770i	0.0563248	+	0.0975574i
$137$	1.43488	−	0.828427i	0.122590	−	0.0707773i	−0.437451	−	0.899242i	$-0.644119\pi$
$137$	1.43488	−	0.828427i	0.122590	−	0.0707773i	0.560041	+	0.828465i	$0.310785\pi$
$138$	2.09077	+	1.20711i	0.177978	+	0.102756i
$139$	−12.1421			−1.02988			−0.514941	−	0.857225i	$-0.672186\pi$
$139$	−12.1421			−1.02988			−0.514941	+	0.857225i	$0.672186\pi$
$140$		0			0
$141$	4.82843			0.406627
$142$	−4.47871	−	2.58579i	−0.375845	−	0.216994i
$143$	−3.46410	+	2.00000i	−0.289683	+	0.167248i
$144$	4.24264	+	7.34847i	0.353553	+	0.612372i
$145$		0			0
$146$	−2.00000			−0.165521
$147$	−11.8272	−	12.0711i	−0.975490	−	0.995605i
$148$		0			0
$149$	−3.91421	+	6.77962i	−0.320665	+	0.555408i	−0.980625	−	0.195892i	$-0.937240\pi$
$149$	−3.91421	+	6.77962i	−0.320665	+	0.555408i	0.659961	+	0.751300i	$0.270573\pi$
$150$		0			0
$151$	−0.171573	−	0.297173i	−0.0139624	−	0.0241836i	0.858960	−	0.512043i	$-0.171111\pi$
$151$	−0.171573	−	0.297173i	−0.0139624	−	0.0241836i	−0.872922	+	0.487859i	$0.837778\pi$
$152$	3.88437	+	2.24264i	0.315064	+	0.181902i
$153$			2.34315i			0.189432i
$154$	−3.24264	+	4.18154i	−0.261299	+	0.336958i
$155$		0			0
$156$	1.82843	−	3.16693i	0.146391	−	0.253557i
$157$	−4.60181	+	2.65685i	−0.367264	+	0.212040i	−0.672263	−	0.740313i	$-0.734677\pi$
$157$	−4.60181	+	2.65685i	−0.367264	+	0.212040i	0.304998	+	0.952353i	$0.401344\pi$
$158$	3.29002	−	1.89949i	0.261740	−	0.151116i
$159$	−8.24264	+	14.2767i	−0.653684	+	1.13221i
$160$		0			0
$161$	2.41421	+	5.91359i	0.190267	+	0.466056i
$162$			3.92893i			0.308686i
$163$	20.4874	+	11.8284i	1.60470	+	0.926474i	0.990529	+	0.137301i	$0.0438426\pi$
$163$	20.4874	+	11.8284i	1.60470	+	0.926474i	0.614170	+	0.789173i	$0.289491\pi$
$164$	1.98528	+	3.43861i	0.155024	+	0.268510i
$165$		0			0
$166$	−2.42893	+	4.20703i	−0.188522	+	0.326529i
$167$			19.5858i			1.51559i	0.652491	+	0.757797i	$0.273724\pi$
$167$			19.5858i			1.51559i	−0.652491	+	0.757797i	$0.726276\pi$
$168$	1.37333	−	10.0355i	0.105955	−	0.774258i
$169$	12.3137			0.947208
$170$		0			0
$171$	4.00000	+	6.92820i	0.305888	+	0.529813i
$172$	−10.1567	+	5.86396i	−0.774439	+	0.447123i
$173$	−16.7262	−	9.65685i	−1.27167	−	0.734197i	−0.296365	−	0.955075i	$-0.595774\pi$
$173$	−16.7262	−	9.65685i	−1.27167	−	0.734197i	−0.975302	+	0.220878i	$0.929108\pi$
$174$	−1.00000			−0.0758098
$175$		0			0
$176$	14.4853			1.09187
$177$	26.1039	+	15.0711i	1.96209	+	1.13281i
$178$	0.953065	−	0.550253i	0.0714353	−	0.0412432i
$179$	−5.00000	−	8.66025i	−0.373718	−	0.647298i	0.616417	−	0.787420i	$-0.288584\pi$
$179$	−5.00000	−	8.66025i	−0.373718	−	0.647298i	−0.990134	+	0.140122i	$0.955250\pi$
$180$		0			0
$181$	−8.65685			−0.643459			−0.321729	−	0.946832i	$-0.604264\pi$
$181$	−8.65685			−0.643459			−0.321729	+	0.946832i	$0.604264\pi$
$182$	−0.840532	+	0.343146i	−0.0623044	+	0.0254357i
$183$			27.7279i			2.04971i
$184$	−1.91421	+	3.31552i	−0.141118	+	0.244423i
$185$		0			0
$186$	−3.00000	−	5.19615i	−0.219971	−	0.381000i
$187$	3.46410	+	2.00000i	0.253320	+	0.146254i
$188$			3.65685i			0.266704i
$189$	−0.671573	+	0.866025i	−0.0488497	+	0.0629941i
$190$		0			0
$191$	3.58579	−	6.21076i	0.259458	−	0.449395i	−0.706639	−	0.707575i	$-0.749789\pi$
$191$	3.58579	−	6.21076i	0.259458	−	0.449395i	0.966097	+	0.258180i	$0.0831226\pi$
$192$	−8.72180	+	5.03553i	−0.629442	+	0.363408i
$193$	1.73205	−	1.00000i	0.124676	−	0.0719816i	−0.436365	−	0.899770i	$-0.643734\pi$
$193$	1.73205	−	1.00000i	0.124676	−	0.0719816i	0.561041	+	0.827788i	$0.310401\pi$
$194$	−0.0710678	+	0.123093i	−0.00510237	+	0.00883757i
$195$		0			0
$196$	9.14214	−	8.95743i	0.653010	−	0.639816i
$197$		−	23.6569i		−	1.68548i	−0.538320	−	0.842741i	$-0.680941\pi$
$197$		−	23.6569i		−	1.68548i	0.538320	−	0.842741i	$-0.319059\pi$
$198$	−4.89898	−	2.82843i	−0.348155	−	0.201008i
$199$	0.828427	+	1.43488i	0.0587256	+	0.101716i	0.893894	−	0.448279i	$-0.147963\pi$
$199$	0.828427	+	1.43488i	0.0587256	+	0.101716i	−0.835168	+	0.549995i	$0.814630\pi$
$200$		0			0
$201$	−14.9853	+	25.9553i	−1.05698	+	1.83074i
$202$		−	5.10051i		−	0.358870i
$203$	−2.09077	−	1.62132i	−0.146743	−	0.113794i
$204$	−3.65685			−0.256031
$205$		0			0
$206$	0.0857864	+	0.148586i	0.00597702	+	0.0103525i
$207$	−5.91359	+	3.41421i	−0.411023	+	0.237304i
$208$	2.15232	+	1.24264i	0.149236	+	0.0861616i
$209$	13.6569			0.944664
$210$		0			0
$211$	3.51472			0.241963			0.120982	−	0.992655i	$-0.461396\pi$
$211$	3.51472			0.241963			0.120982	+	0.992655i	$0.461396\pi$
$212$	−10.8126	−	6.24264i	−0.742610	−	0.428746i
$213$	26.1039	−	15.0711i	1.78861	−	1.03265i
$214$	−0.571068	−	0.989118i	−0.0390374	−	0.0676147i
$215$		0			0
$216$	−0.656854			−0.0446933
$217$	2.15232	−	15.7279i	0.146109	−	1.06768i
$218$			1.44365i			0.0977764i
$219$	5.82843	−	10.0951i	0.393849	−	0.682166i
$220$		0			0
$221$	0.343146	+	0.594346i	0.0230825	+	0.0399800i
$222$		0			0
$223$		−	11.6569i		−	0.780601i	−0.920688	−	0.390300i	$-0.872371\pi$
$223$		−	11.6569i		−	0.780601i	0.920688	−	0.390300i	$-0.127629\pi$
$224$	11.5711	+	1.58346i	0.773124	+	0.105800i
$225$		0			0
$226$	2.58579	−	4.47871i	0.172004	−	0.297920i
$227$	23.3572	−	13.4853i	1.55027	−	0.895050i	0.552152	−	0.833743i	$-0.313807\pi$
$227$	23.3572	−	13.4853i	1.55027	−	0.895050i	0.998119	−	0.0613063i	$-0.0195266\pi$
$228$	−10.8126	+	6.24264i	−0.716080	+	0.413429i
$229$	−0.171573	+	0.297173i	−0.0113379	+	0.0196377i	−0.871639	−	0.490149i	$-0.836942\pi$
$229$	−0.171573	+	0.297173i	−0.0113379	+	0.0196377i	0.860301	+	0.509787i	$0.170276\pi$
$230$		0			0
$231$	−11.6569	−	28.5533i	−0.766965	−	1.87867i
$232$		−	1.58579i		−	0.104112i
$233$	−9.67487	−	5.58579i	−0.633822	−	0.365937i	0.148409	−	0.988926i	$-0.452585\pi$
$233$	−9.67487	−	5.58579i	−0.633822	−	0.365937i	−0.782231	+	0.622989i	$0.785918\pi$
$234$	−0.485281	−	0.840532i	−0.0317238	−	0.0549473i
$235$		0			0
$236$	−11.4142	+	19.7700i	−0.743002	+	1.28692i
$237$			22.1421i			1.43829i
$238$	0.717439	+	0.556349i	0.0465047	+	0.0360628i
$239$	−1.31371			−0.0849767			−0.0424884	−	0.999097i	$-0.513529\pi$
$239$	−1.31371			−0.0849767			−0.0424884	+	0.999097i	$0.513529\pi$
$240$		0			0
$241$	−8.17157	−	14.1536i	−0.526377	−	0.911712i	−0.999528	−	0.0307305i	$-0.990217\pi$
$241$	−8.17157	−	14.1536i	−0.526377	−	0.911712i	0.473150	−	0.880982i	$-0.343117\pi$
$242$	−4.41717	+	2.55025i	−0.283946	+	0.163936i
$243$	−18.7554	−	10.8284i	−1.20316	−	0.694644i
$244$	−21.0000			−1.34439
$245$		0			0
$246$	2.17157			0.138454
$247$	2.02922	+	1.17157i	0.129116	+	0.0745454i
$248$	8.23999	−	4.75736i	0.523240	−	0.302093i
$249$	−14.1569	−	24.5204i	−0.897154	−	1.55392i
$250$		0			0
$251$	13.3137			0.840354			0.420177	−	0.907442i	$-0.361968\pi$
$251$	13.3137			0.840354			0.420177	+	0.907442i	$0.361968\pi$
$252$	10.8126	+	8.38478i	0.681128	+	0.528191i
$253$			11.6569i			0.732860i
$254$	−2.75736	+	4.77589i	−0.173012	+	0.299666i
$255$		0			0
$256$	−1.98528	−	3.43861i	−0.124080	−	0.214913i
$257$	−15.2913	−	8.82843i	−0.953844	−	0.550702i	−0.0595711	−	0.998224i	$-0.518973\pi$
$257$	−15.2913	−	8.82843i	−0.953844	−	0.550702i	−0.894273	+	0.447522i	$0.852307\pi$
$258$			6.41421i			0.399331i
$259$		0			0
$260$		0			0
$261$	1.41421	−	2.44949i	0.0875376	−	0.151620i
$262$	−1.18869	+	0.686292i	−0.0734376	+	0.0423992i
$263$	−16.4905	+	9.52082i	−1.01685	+	0.587079i	−0.913190	−	0.407534i	$-0.866389\pi$
$263$	−16.4905	+	9.52082i	−1.01685	+	0.587079i	−0.103660	+	0.994613i	$0.533055\pi$
$264$	9.24264	−	16.0087i	0.568845	−	0.985269i
$265$		0			0
$266$	3.07107	+	0.420266i	0.188299	+	0.0257682i
$267$			6.41421i			0.392543i
$268$	−19.6575	−	11.3492i	−1.20077	−	0.693265i
$269$	−15.2279	−	26.3755i	−0.928463	−	1.60814i	−0.785895	−	0.618360i	$-0.787798\pi$
$269$	−15.2279	−	26.3755i	−0.928463	−	1.60814i	−0.142568	−	0.989785i	$-0.545536\pi$
$270$		0			0
$271$	0.242641	−	0.420266i	0.0147394	−	0.0255293i	−0.858562	−	0.512710i	$-0.828641\pi$
$271$	0.242641	−	0.420266i	0.0147394	−	0.0255293i	0.873301	+	0.487181i	$0.161975\pi$
$272$		−	2.48528i		−	0.150692i
$273$	0.717439	−	5.24264i	0.0434214	−	0.317299i
$274$	0.686292			0.0414604
$275$		0			0
$276$	−5.32843	−	9.22911i	−0.320734	−	0.555527i
$277$	−10.5154	+	6.07107i	−0.631809	+	0.364775i	−0.781452	−	0.623965i	$-0.785521\pi$
$277$	−10.5154	+	6.07107i	−0.631809	+	0.364775i	0.149643	+	0.988740i	$0.452187\pi$
$278$	−4.35562	−	2.51472i	−0.261233	−	0.150823i
$279$	16.9706			1.01600
$280$		0			0
$281$	26.2843			1.56799			0.783994	−	0.620768i	$-0.213179\pi$
$281$	26.2843			1.56799			0.783994	+	0.620768i	$0.213179\pi$
$282$	1.73205	+	1.00000i	0.103142	+	0.0595491i
$283$	−12.1244	+	7.00000i	−0.720718	+	0.416107i	−0.815017	−	0.579437i	$-0.803272\pi$
$283$	−12.1244	+	7.00000i	−0.720718	+	0.416107i	0.0942988	+	0.995544i	$0.469939\pi$
$284$	11.4142	+	19.7700i	0.677309	+	1.17313i
$285$		0			0
$286$	−1.65685			−0.0979718
$287$	4.54026	+	3.52082i	0.268003	+	0.207827i
$288$			12.4853i			0.735702i
$289$	−8.15685	+	14.1281i	−0.479815	+	0.831064i
$290$		0			0
$291$	−0.414214	−	0.717439i	−0.0242816	−	0.0420570i
$292$	7.64564	+	4.41421i	0.447427	+	0.258322i
$293$			16.0000i			0.934730i	0.884064	+	0.467365i	$0.154797\pi$
$293$			16.0000i			0.934730i	−0.884064	+	0.467365i	$0.845203\pi$
$294$	−1.74264	−	6.77962i	−0.101633	−	0.395395i
$295$		0			0
$296$		0			0
$297$	−1.73205	+	1.00000i	−0.100504	+	0.0580259i
$298$	−2.80821	+	1.62132i	−0.162675	+	0.0939206i
$299$	−1.00000	+	1.73205i	−0.0578315	+	0.100167i
$300$		0			0
$301$	−10.3995	+	13.4106i	−0.599417	+	0.772977i
$302$		−	0.142136i		−	0.00817899i
$303$	25.7451	+	14.8640i	1.47902	+	0.853912i
$304$	−4.24264	−	7.34847i	−0.243332	−	0.421464i
$305$		0			0
$306$	−0.485281	+	0.840532i	−0.0277417	+	0.0480500i
$307$		−	13.2426i		−	0.755797i	−0.925847	−	0.377899i	$-0.876647\pi$
$307$		−	13.2426i		−	0.755797i	0.925847	−	0.377899i	$-0.123353\pi$
$308$	21.6251	−	8.82843i	1.23221	−	0.503046i
$309$	−1.00000			−0.0568880
$310$		0			0
$311$	9.41421	+	16.3059i	0.533831	+	0.924623i	0.999219	+	0.0395157i	$0.0125815\pi$
$311$	9.41421	+	16.3059i	0.533831	+	0.924623i	−0.465388	+	0.885107i	$0.654085\pi$
$312$	2.74666	−	1.58579i	0.155499	−	0.0897775i
$313$	−15.2913	−	8.82843i	−0.864314	−	0.499012i	0.00114023	−	0.999999i	$-0.499637\pi$
$313$	−15.2913	−	8.82843i	−0.864314	−	0.499012i	−0.865455	+	0.500987i	$0.832970\pi$
$314$	−2.20101			−0.124210
$315$		0			0
$316$	−16.7696			−0.943361
$317$	−22.3426	−	12.8995i	−1.25488	−	0.724508i	−0.282809	−	0.959176i	$-0.591266\pi$
$317$	−22.3426	−	12.8995i	−1.25488	−	0.724508i	−0.972075	+	0.234668i	$0.924600\pi$
$318$	−5.91359	+	3.41421i	−0.331618	+	0.191460i
$319$	−2.41421	−	4.18154i	−0.135170	−	0.234121i
$320$		0			0
$321$	6.65685			0.371549
$322$	−0.358719	+	2.62132i	−0.0199907	+	0.146080i
$323$		−	2.34315i		−	0.130376i
$324$	8.67157	−	15.0196i	0.481754	−	0.834422i
$325$		0			0
$326$	4.89949	+	8.48617i	0.271358	+	0.470006i
$327$	−7.28692	−	4.20711i	−0.402968	−	0.232654i
$328$			3.44365i			0.190144i
$329$	2.00000	+	4.89898i	0.110264	+	0.270089i
$330$		0			0
$331$	5.48528	−	9.50079i	0.301498	−	0.522210i	−0.674977	−	0.737839i	$-0.735847\pi$
$331$	5.48528	−	9.50079i	0.301498	−	0.522210i	0.976476	+	0.215628i	$0.0691799\pi$
$332$	18.5707	−	10.7218i	1.01920	−	0.588437i
$333$		0			0
$334$	−4.05635	+	7.02580i	−0.221954	+	0.384435i
$335$		0			0
$336$	−11.7426	+	15.1427i	−0.640614	+	0.826102i
$337$			14.8284i			0.807756i	0.914813	+	0.403878i	$0.132338\pi$
$337$			14.8284i			0.807756i	−0.914813	+	0.403878i	$0.867662\pi$
$338$	4.41717	+	2.55025i	0.240262	+	0.138715i
$339$	15.0711	+	26.1039i	0.818548	+	1.41777i
$340$		0			0
$341$	14.4853	−	25.0892i	0.784422	−	1.35866i
$342$			3.31371i			0.179185i
$343$	7.34847	−	17.0000i	0.396780	−	0.917914i
$344$	−10.1716			−0.548414
$345$		0			0
$346$	−4.00000	−	6.92820i	−0.215041	−	0.372463i
$347$	19.1141	−	11.0355i	1.02610	−	0.592418i	0.110234	−	0.993906i	$-0.464840\pi$
$347$	19.1141	−	11.0355i	1.02610	−	0.592418i	0.915865	+	0.401487i	$0.131507\pi$
$348$	3.82282	+	2.20711i	0.204925	+	0.118313i
$349$	26.6569			1.42691			0.713454	−	0.700702i	$-0.247130\pi$
$349$	26.6569			1.42691			0.713454	+	0.700702i	$0.247130\pi$
$350$		0			0
$351$	−0.343146			−0.0183158
$352$	18.4582	+	10.6569i	0.983826	+	0.568012i
$353$	18.3351	−	10.5858i	0.975880	−	0.563425i	0.0748562	−	0.997194i	$-0.476150\pi$
$353$	18.3351	−	10.5858i	0.975880	−	0.563425i	0.901024	+	0.433770i	$0.142817\pi$
$354$	6.24264	+	10.8126i	0.331793	+	0.574682i
$355$		0			0
$356$	−4.85786			−0.257466
$357$	−4.89898	+	2.00000i	−0.259281	+	0.105851i
$358$		−	4.14214i		−	0.218919i
$359$	−5.00000	+	8.66025i	−0.263890	+	0.457071i	−0.967272	−	0.253741i	$-0.918339\pi$
$359$	−5.00000	+	8.66025i	−0.263890	+	0.457071i	0.703382	+	0.710812i	$0.251672\pi$
$360$		0			0
$361$	5.50000	+	9.52628i	0.289474	+	0.501383i
$362$	−3.10538	−	1.79289i	−0.163215	−	0.0942324i
$363$		−	29.7279i		−	1.56031i
$364$	3.97056	+	0.543359i	0.208114	+	0.0284798i
$365$		0			0
$366$	−5.74264	+	9.94655i	−0.300173	+	0.519914i
$367$	−9.73641	+	5.62132i	−0.508237	+	0.293431i	−0.732108	−	0.681188i	$-0.761464\pi$
$367$	−9.73641	+	5.62132i	−0.508237	+	0.293431i	0.223872	+	0.974619i	$0.428130\pi$
$368$	6.27231	−	3.62132i	0.326967	−	0.188774i
$369$	−3.07107	+	5.31925i	−0.159873	+	0.276909i
$370$		0			0
$371$	−17.8995	−	2.44949i	−0.929295	−	0.127171i
$372$			26.4853i			1.37320i
$373$	11.2328	+	6.48528i	0.581614	+	0.335795i	0.761775	−	0.647842i	$-0.224328\pi$
$373$	11.2328	+	6.48528i	0.581614	+	0.335795i	−0.180160	+	0.983637i	$0.557662\pi$
$374$	0.828427	+	1.43488i	0.0428369	+	0.0741958i
$375$		0			0
$376$	−1.58579	+	2.74666i	−0.0817807	+	0.141648i
$377$		−	0.828427i		−	0.0426662i
$378$	−0.420266	+	0.171573i	−0.0216162	+	0.00882476i
$379$	−21.1716			−1.08751			−0.543755	−	0.839244i	$-0.682998\pi$
$379$	−21.1716			−1.08751			−0.543755	+	0.839244i	$0.682998\pi$
$380$		0			0
$381$	−16.0711	−	27.8359i	−0.823346	−	1.42608i
$382$	2.57258	−	1.48528i	0.131625	−	0.0759936i
$383$	14.6354	+	8.44975i	0.747834	+	0.431762i	0.824911	−	0.565263i	$-0.191225\pi$
$383$	14.6354	+	8.44975i	0.747834	+	0.431762i	−0.0770770	+	0.997025i	$0.524559\pi$
$384$	−25.4853			−1.30054
$385$		0			0
$386$	0.828427			0.0421658
$387$	−15.7116	−	9.07107i	−0.798663	−	0.461108i
$388$	0.543359	−	0.313708i	0.0275849	−	0.0159261i
$389$	6.17157	+	10.6895i	0.312911	+	0.541978i	0.978991	−	0.203902i	$-0.0653625\pi$
$389$	6.17157	+	10.6895i	0.312911	+	0.541978i	−0.666080	+	0.745880i	$0.732029\pi$
$390$		0			0
$391$	2.00000			0.101144
$392$	10.7510	−	2.76346i	0.543009	−	0.139576i
$393$		−	8.00000i		−	0.403547i
$394$	4.89949	−	8.48617i	0.246833	−	0.427527i
$395$		0			0
$396$	12.4853	+	21.6251i	0.627409	+	1.08670i
$397$	−24.7921	−	14.3137i	−1.24428	−	0.718384i	−0.274316	−	0.961640i	$-0.588451\pi$
$397$	−24.7921	−	14.3137i	−1.24428	−	0.718384i	−0.969962	+	0.243255i	$0.921785\pi$
$398$			0.686292i			0.0344007i
$399$	−11.0711	+	14.2767i	−0.554247	+	0.714728i
$400$		0			0
$401$	−3.84315	+	6.65652i	−0.191918	+	0.332411i	−0.945886	−	0.324500i	$-0.894804\pi$
$401$	−3.84315	+	6.65652i	−0.191918	+	0.332411i	0.753968	+	0.656911i	$0.228137\pi$
$402$	−10.7510	+	6.20711i	−0.536212	+	0.309582i
$403$	4.30463	−	2.48528i	0.214429	−	0.123801i
$404$	−11.2574	+	19.4983i	−0.560075	+	0.970078i
$405$		0			0
$406$	−0.414214	−	1.01461i	−0.0205571	−	0.0503543i
$407$		0			0
$408$	−2.74666	−	1.58579i	−0.135980	−	0.0785081i
$409$	12.3995	+	21.4766i	0.613116	+	1.06195i	0.990712	+	0.135977i	$0.0434173\pi$
$409$	12.3995	+	21.4766i	0.613116	+	1.06195i	−0.377596	+	0.925970i	$0.623249\pi$
$410$		0			0
$411$	−2.00000	+	3.46410i	−0.0986527	+	0.170872i
$412$		−	0.757359i		−	0.0373124i
$413$	−4.47871	+	32.7279i	−0.220383	+	1.61044i
$414$	−2.82843			−0.139010
$415$		0			0
$416$	1.82843	+	3.16693i	0.0896460	+	0.155271i
$417$	25.3864	−	14.6569i	1.24318	−	0.717749i
$418$	4.89898	+	2.82843i	0.239617	+	0.138343i
$419$	23.3137			1.13895			0.569475	−	0.822009i	$-0.307147\pi$
$419$	23.3137			1.13895			0.569475	+	0.822009i	$0.307147\pi$
$420$		0			0
$421$	−3.48528			−0.169862			−0.0849311	−	0.996387i	$-0.527067\pi$
$421$	−3.48528			−0.169862			−0.0849311	+	0.996387i	$0.527067\pi$
$422$	1.26080	+	0.727922i	0.0613747	+	0.0354347i
$423$	−4.89898	+	2.82843i	−0.238197	+	0.137523i
$424$	−5.41421	−	9.37769i	−0.262937	−	0.455421i
$425$		0			0
$426$	12.4853			0.604914
$427$	−28.1331	+	11.4853i	−1.36146	+	0.555812i
$428$			5.04163i			0.243696i
$429$	4.82843	−	8.36308i	0.233119	−	0.403773i
$430$		0			0
$431$	10.8995	+	18.8785i	0.525010	+	0.909344i	0.999576	+	0.0291242i	$0.00927183\pi$
$431$	10.8995	+	18.8785i	0.525010	+	0.909344i	−0.474566	+	0.880220i	$0.657395\pi$
$432$	1.07616	+	0.621320i	0.0517767	+	0.0298933i
$433$			31.7990i			1.52816i	0.645120	+	0.764081i	$0.276807\pi$
$433$			31.7990i			1.52816i	−0.645120	+	0.764081i	$0.723193\pi$
$434$	4.02944	−	5.19615i	0.193419	−	0.249423i
$435$		0			0
$436$	3.18629	−	5.51882i	0.152596	−	0.264303i
$437$	5.91359	−	3.41421i	0.282885	−	0.163324i
$438$	4.18154	−	2.41421i	0.199802	−	0.115356i
$439$	16.9706	−	29.3939i	0.809961	−	1.40289i	−0.102930	−	0.994689i	$-0.532822\pi$
$439$	16.9706	−	29.3939i	0.809961	−	1.40289i	0.912890	−	0.408205i	$-0.133845\pi$
$440$		0			0
$441$	19.0711	+	5.31925i	0.908146	+	0.253297i
$442$			0.284271i			0.0135214i
$443$	−10.5769	−	6.10660i	−0.502526	−	0.290133i	0.227230	−	0.973841i	$-0.427033\pi$
$443$	−10.5769	−	6.10660i	−0.502526	−	0.290133i	−0.729756	+	0.683708i	$0.760366\pi$
$444$		0			0
$445$		0			0
$446$	2.41421	−	4.18154i	0.114316	−	0.198002i
$447$		−	18.8995i		−	0.893915i
$448$	−8.72180	−	6.76346i	−0.412066	−	0.319543i
$449$	1.82843			0.0862888			0.0431444	−	0.999069i	$-0.486262\pi$
$449$	1.82843			0.0862888			0.0431444	+	0.999069i	$0.486262\pi$
$450$		0			0
$451$	5.24264	+	9.08052i	0.246866	+	0.427585i
$452$	−19.7700	+	11.4142i	−0.929902	+	0.536879i
$453$	0.717439	+	0.414214i	0.0337082	+	0.0194615i
$454$	11.1716			0.524308
$455$		0			0
$456$	−10.8284			−0.507088
$457$	27.9590	+	16.1421i	1.30787	+	0.755097i	0.981740	−	0.190229i	$-0.0609230\pi$
$457$	27.9590	+	16.1421i	1.30787	+	0.755097i	0.326127	+	0.945326i	$0.394256\pi$
$458$	−0.123093	+	0.0710678i	−0.00575176	+	0.00332078i
$459$	0.171573	+	0.297173i	0.00800834	+	0.0138708i
$460$		0			0
$461$	18.6863			0.870307			0.435154	−	0.900356i	$-0.356694\pi$
$461$	18.6863			0.870307			0.435154	+	0.900356i	$0.356694\pi$
$462$	1.73205	−	12.6569i	0.0805823	−	0.588850i
$463$		−	11.0416i		−	0.513148i	−0.966525	−	0.256574i	$-0.917406\pi$
$463$		−	11.0416i		−	0.513148i	0.966525	−	0.256574i	$-0.0825937\pi$
$464$	−1.50000	+	2.59808i	−0.0696358	+	0.120613i
$465$		0			0
$466$	−2.31371	−	4.00746i	−0.107180	−	0.185642i
$467$	19.8315	+	11.4497i	0.917694	+	0.529831i	0.882899	−	0.469563i	$-0.155589\pi$
$467$	19.8315	+	11.4497i	0.917694	+	0.529831i	0.0347956	+	0.999394i	$0.488922\pi$
$468$			4.28427i			0.198041i
$469$	−32.5416	−	4.45322i	−1.50263	−	0.205631i
$470$		0			0
$471$	6.41421	−	11.1097i	0.295551	−	0.511910i
$472$	−17.1464	+	9.89949i	−0.789228	+	0.455661i
$473$	−26.8213	+	15.4853i	−1.23324	+	0.712014i
$474$	−4.58579	+	7.94282i	−0.210632	+	0.364826i
$475$		0			0
$476$	−1.51472	−	3.71029i	−0.0694270	−	0.170061i
$477$		−	19.3137i		−	0.884314i
$478$	−0.471253	−	0.272078i	−0.0215546	−	0.0124446i
$479$	−12.1716	−	21.0818i	−0.556133	−	0.963251i	−0.997814	−	0.0660791i	$-0.978951\pi$
$479$	−12.1716	−	21.0818i	−0.556133	−	0.963251i	0.441681	−	0.897172i	$-0.354382\pi$
$480$		0			0
$481$		0			0
$482$		−	6.76955i		−	0.308345i
$483$	−12.1859	−	9.44975i	−0.554478	−	0.429978i
$484$	22.5147			1.02340
$485$		0			0
$486$	−4.48528	−	7.76874i	−0.203456	−	0.352397i
$487$	13.5592	−	7.82843i	0.614428	−	0.354740i	−0.160269	−	0.987073i	$-0.551236\pi$
$487$	13.5592	−	7.82843i	0.614428	−	0.354740i	0.774696	+	0.632334i	$0.217903\pi$
$488$	−15.7731	−	9.10660i	−0.714015	−	0.412236i
$489$	−57.1127			−2.58273
$490$		0			0
$491$	−13.3137			−0.600839			−0.300420	−	0.953807i	$-0.597127\pi$
$491$	−13.3137			−0.600839			−0.300420	+	0.953807i	$0.597127\pi$
$492$	−8.30153	−	4.79289i	−0.374262	−	0.216080i
$493$	−0.717439	+	0.414214i	−0.0323118	+	0.0186552i
$494$	0.485281	+	0.840532i	0.0218338	+	0.0378173i
$495$		0			0
$496$	−18.0000			−0.808224
$497$	26.1039	+	20.2426i	1.17092	+	0.908007i
$498$		−	11.7279i		−	0.525541i
$499$	2.41421	−	4.18154i	0.108075	−	0.187191i	−0.806915	−	0.590667i	$-0.798865\pi$
$499$	2.41421	−	4.18154i	0.108075	−	0.187191i	0.914990	+	0.403476i	$0.132198\pi$
$500$		0			0
$501$	−23.6421	−	40.9494i	−1.05625	−	1.82948i
$502$	4.77589	+	2.75736i	0.213158	+	0.123067i
$503$		−	37.8701i		−	1.68854i	−0.535916	−	0.844271i	$-0.680034\pi$
$503$		−	37.8701i		−	1.68854i	0.535916	−	0.844271i	$-0.319966\pi$
$504$	4.48528	+	10.9867i	0.199790	+	0.489384i
$505$		0			0
$506$	−2.41421	+	4.18154i	−0.107325	+	0.185892i
$507$	−25.7451	+	14.8640i	−1.14338	+	0.660132i
$508$	21.0818	−	12.1716i	0.935353	−	0.540026i
$509$	12.3284	−	21.3535i	0.546448	−	0.946476i	−0.452066	−	0.891984i	$-0.649313\pi$
$509$	12.3284	−	21.3535i	0.546448	−	0.946476i	0.998514	−	0.0544912i	$-0.0173537\pi$
$510$		0			0
$511$	12.6569	+	1.73205i	0.559906	+	0.0766214i
$512$		−	22.7574i		−	1.00574i
$513$	1.01461	+	0.585786i	0.0447962	+	0.0258631i
$514$	−3.65685	−	6.33386i	−0.161297	−	0.279374i
$515$		0			0
$516$	14.1569	−	24.5204i	0.623221	−	1.07945i
$517$			9.65685i			0.424708i
$518$		0			0
$519$	46.6274			2.04672
$520$		0			0
$521$	9.48528	+	16.4290i	0.415558	+	0.719767i	0.995487	−	0.0948999i	$-0.0302531\pi$
$521$	9.48528	+	16.4290i	0.415558	+	0.719767i	−0.579929	+	0.814667i	$0.696920\pi$
$522$	1.01461	−	0.585786i	0.0444084	−	0.0256392i
$523$	21.0818	+	12.1716i	0.921842	+	0.532226i	0.884222	−	0.467066i	$-0.154689\pi$
$523$	21.0818	+	12.1716i	0.921842	+	0.532226i	0.0376197	+	0.999292i	$0.488022\pi$
$524$	6.05887			0.264683
$525$		0			0
$526$	−7.88730			−0.343903
$527$	−4.30463	−	2.48528i	−0.187513	−	0.108261i
$528$	−30.2854	+	17.4853i	−1.31800	+	0.760949i
$529$	−8.58579	−	14.8710i	−0.373295	−	0.646566i
$530$		0			0
$531$	−35.3137			−1.53248
$532$	−10.8126	−	8.38478i	−0.468784	−	0.363526i
$533$			1.79899i			0.0779229i
$534$	−1.32843	+	2.30090i	−0.0574867	+	0.0995698i
$535$		0			0
$536$	−9.84315	−	17.0488i	−0.425159	−	0.736397i
$537$	20.9077	+	12.0711i	0.902234	+	0.520905i
$538$		−	12.6152i		−	0.543881i
$539$	24.1421	−	23.6544i	1.03988	−	1.01887i
$540$		0			0
$541$	−9.32843	+	16.1573i	−0.401060	+	0.694657i	−0.993854	−	0.110697i	$-0.964692\pi$
$541$	−9.32843	+	16.1573i	−0.401060	+	0.694657i	0.592794	+	0.805354i	$0.298025\pi$
$542$	0.174080	−	0.100505i	0.00747737	−	0.00431706i
$543$	18.0995	−	10.4497i	0.776724	−	0.448442i
$544$	1.82843	−	3.16693i	0.0783932	−	0.135781i
$545$		0			0
$546$	1.34315	−	1.73205i	0.0574813	−	0.0741249i
$547$			5.10051i			0.218082i	0.994037	+	0.109041i	$0.0347780\pi$
$547$			5.10051i			0.218082i	−0.994037	+	0.109041i	$0.965222\pi$
$548$	−2.62357	−	1.51472i	−0.112073	−	0.0647056i
$549$	−16.2426	−	28.1331i	−0.693219	−	1.20069i
$550$		0			0
$551$	−1.41421	+	2.44949i	−0.0602475	+	0.104352i
$552$		−	9.24264i		−	0.393393i
$553$	−22.4657	+	9.17157i	−0.955338	+	0.390015i
$554$	−5.02944			−0.213680
$555$		0			0
$556$	11.1005	+	19.2266i	0.470766	+	0.815391i
$557$	−29.6910	+	17.1421i	−1.25805	+	0.726336i	−0.972695	−	0.232086i	$-0.925445\pi$
$557$	−29.6910	+	17.1421i	−1.25805	+	0.726336i	−0.285355	+	0.958422i	$0.592111\pi$
$558$	6.08767	+	3.51472i	0.257712	+	0.148790i
$559$	−5.31371			−0.224746
$560$		0			0
$561$	−9.65685			−0.407713
$562$	9.42868	+	5.44365i	0.397725	+	0.229627i
$563$	−14.0920	+	8.13604i	−0.593908	+	0.342893i	−0.766641	−	0.642076i	$-0.778074\pi$
$563$	−14.0920	+	8.13604i	−0.593908	+	0.342893i	0.172733	+	0.984969i	$0.444740\pi$
$564$	−4.41421	−	7.64564i	−0.185872	−	0.321940i
$565$		0			0
$566$	−5.79899			−0.243750
$567$	3.40256	−	24.8640i	0.142894	−	1.04419i
$568$			19.7990i			0.830747i
$569$	−1.82843	+	3.16693i	−0.0766517	+	0.132765i	−0.901803	−	0.432147i	$-0.857756\pi$
$569$	−1.82843	+	3.16693i	−0.0766517	+	0.132765i	0.825152	+	0.564911i	$0.191090\pi$
$570$		0			0
$571$	−7.41421	−	12.8418i	−0.310275	−	0.537412i	0.668147	−	0.744030i	$-0.267088\pi$
$571$	−7.41421	−	12.8418i	−0.310275	−	0.537412i	−0.978422	+	0.206617i	$0.933755\pi$
$572$	6.33386	+	3.65685i	0.264832	+	0.152901i
$573$			17.3137i			0.723291i
$574$	0.899495	+	2.20330i	0.0375442	+	0.0919641i
$575$		0			0
$576$	5.89949	−	10.2182i	0.245812	−	0.425759i
$577$	20.7336	−	11.9706i	0.863152	−	0.498341i	−0.00191453	−	0.999998i	$-0.500609\pi$
$577$	20.7336	−	11.9706i	0.863152	−	0.498341i	0.865067	+	0.501657i	$0.167276\pi$
$578$	−5.85204	+	3.37868i	−0.243413	+	0.140535i
$579$	−2.41421	+	4.18154i	−0.100331	+	0.173779i
$580$		0			0
$581$	19.0147	−	24.5204i	0.788863	−	1.01728i
$582$		−	0.343146i		−	0.0142238i
$583$	−28.5533	−	16.4853i	−1.18256	−	0.682751i
$584$	3.82843	+	6.63103i	0.158421	+	0.274394i
$585$		0			0
$586$	−3.31371	+	5.73951i	−0.136888	+	0.237097i
$587$			22.2843i			0.919770i	0.887978	+	0.459885i	$0.152109\pi$
$587$			22.2843i			0.919770i	−0.887978	+	0.459885i	$0.847891\pi$
$588$	−8.30153	+	29.7635i	−0.342350	+	1.22742i
$589$	−16.9706			−0.699260
$590$		0			0
$591$	28.5563	+	49.4610i	1.17465	+	2.03456i
$592$		0			0
$593$	37.9310	+	21.8995i	1.55764	+	0.899304i	0.997482	+	0.0709193i	$0.0225933\pi$
$593$	37.9310	+	21.8995i	1.55764	+	0.899304i	0.560159	+	0.828385i	$0.310740\pi$
$594$	−0.828427			−0.0339908
$595$		0			0
$596$	14.3137			0.586312
$597$	−3.46410	−	2.00000i	−0.141776	−	0.0818546i
$598$	−0.717439	+	0.414214i	−0.0293383	+	0.0169385i
$599$	8.82843	+	15.2913i	0.360720	+	0.624785i	0.988079	−	0.153945i	$-0.0491977\pi$
$599$	8.82843	+	15.2913i	0.360720	+	0.624785i	−0.627360	+	0.778730i	$0.715864\pi$
$600$		0			0
$601$	8.34315			0.340324			0.170162	−	0.985416i	$-0.445571\pi$
$601$	8.34315			0.340324			0.170162	+	0.985416i	$0.445571\pi$
$602$	−6.50794	+	2.65685i	−0.265244	+	0.108285i
$603$		−	35.1127i		−	1.42990i
$604$	−0.313708	+	0.543359i	−0.0127646	+	0.0221090i
$605$		0			0
$606$	6.15685	+	10.6640i	0.250105	+	0.433195i
$607$	3.64874	+	2.10660i	0.148098	+	0.0855043i	0.572218	−	0.820102i	$-0.306083\pi$
$607$	3.64874	+	2.10660i	0.148098	+	0.0855043i	−0.424120	+	0.905606i	$0.639417\pi$
$608$		−	12.4853i		−	0.506345i
$609$	6.32843	+	0.866025i	0.256441	+	0.0350931i
$610$		0			0
$611$	−0.828427	+	1.43488i	−0.0335146	+	0.0580489i
$612$	3.71029	−	2.14214i	0.149979	−	0.0865907i
$613$	13.3852	−	7.72792i	0.540621	−	0.312128i	−0.204709	−	0.978823i	$-0.565625\pi$
$613$	13.3852	−	7.72792i	0.540621	−	0.312128i	0.745331	+	0.666695i	$0.232292\pi$
$614$	2.74264	−	4.75039i	0.110684	−	0.191710i
$615$		0			0
$616$	20.0711	+	2.74666i	0.808686	+	0.110666i
$617$		−	11.3137i		−	0.455473i	−0.973723	−	0.227736i	$-0.926868\pi$
$617$		−	11.3137i		−	0.455473i	0.973723	−	0.227736i	$-0.0731324\pi$
$618$	−0.358719	−	0.207107i	−0.0144298	−	0.00833106i
$619$	21.2426	+	36.7933i	0.853814	+	1.47885i	0.877741	+	0.479135i	$0.159050\pi$
$619$	21.2426	+	36.7933i	0.853814	+	1.47885i	−0.0239273	+	0.999714i	$0.507617\pi$
$620$		0			0
$621$	−0.500000	+	0.866025i	−0.0200643	+	0.0347524i
$622$			7.79899i			0.312711i
$623$	−6.50794	+	2.65685i	−0.260735	+	0.106445i
$624$	−6.00000			−0.240192
$625$		0			0
$626$	−3.65685	−	6.33386i	−0.146157	−	0.253152i
$627$	−28.5533	+	16.4853i	−1.14031	+	0.658359i
$628$	8.41407	+	4.85786i	0.335758	+	0.193850i
$629$		0			0
$630$		0			0
$631$	8.14214			0.324133			0.162067	−	0.986780i	$-0.448184\pi$
$631$	8.14214			0.324133			0.162067	+	0.986780i	$0.448184\pi$
$632$	−12.5956	−	7.27208i	−0.501026	−	0.289268i
$633$	−7.34847	+	4.24264i	−0.292075	+	0.168630i
$634$	−5.34315	−	9.25460i	−0.212203	−	0.367547i
$635$		0			0
$636$	30.1421			1.19521
$637$	5.61642	−	1.44365i	0.222531	−	0.0571995i
$638$		−	2.00000i		−	0.0791808i
$639$	−17.6569	+	30.5826i	−0.698494	+	1.20983i
$640$		0			0
$641$	−7.25736	−	12.5701i	−0.286648	−	0.496490i	0.686359	−	0.727263i	$-0.259208\pi$
$641$	−7.25736	−	12.5701i	−0.286648	−	0.496490i	−0.973008	+	0.230773i	$0.925875\pi$
$642$	2.38794	+	1.37868i	0.0942446	+	0.0544121i
$643$			30.2843i			1.19430i	0.802131	+	0.597148i	$0.203699\pi$
$643$			30.2843i			1.19430i	−0.802131	+	0.597148i	$0.796301\pi$
$644$	7.15685	−	9.22911i	0.282020	−	0.363678i
$645$		0			0
$646$	0.485281	−	0.840532i	0.0190931	−	0.0330703i
$647$	14.7585	−	8.52082i	0.580216	−	0.334988i	−0.181003	−	0.983482i	$-0.557934\pi$
$647$	14.7585	−	8.52082i	0.580216	−	0.334988i	0.761219	+	0.648495i	$0.224601\pi$
$648$	13.0264	−	7.52082i	0.511727	−	0.295446i
$649$	−30.1421	+	52.2077i	−1.18318	+	2.04933i
$650$		0			0
$651$	14.4853	+	35.4815i	0.567723	+	1.39063i
$652$		−	43.2548i		−	1.69399i
$653$	−21.5020	−	12.4142i	−0.841440	−	0.485806i	0.0163133	−	0.999867i	$-0.494807\pi$
$653$	−21.5020	−	12.4142i	−0.841440	−	0.485806i	−0.857754	+	0.514061i	$0.828140\pi$
$654$	−1.74264	−	3.01834i	−0.0681426	−	0.118027i
$655$		0			0
$656$	3.25736	−	5.64191i	0.127179	−	0.220280i
$657$			13.6569i			0.532805i
$658$	−0.297173	+	2.17157i	−0.0115850	+	0.0846567i
$659$	−26.8284			−1.04509			−0.522544	−	0.852613i	$-0.675017\pi$
$659$	−26.8284			−1.04509			−0.522544	+	0.852613i	$0.675017\pi$
$660$		0			0
$661$	−13.0858	−	22.6652i	−0.508978	−	0.881576i	−0.999946	−	0.0103982i	$-0.996690\pi$
$661$	−13.0858	−	22.6652i	−0.508978	−	0.881576i	0.490968	−	0.871178i	$-0.336643\pi$
$662$	3.93535	−	2.27208i	0.152952	−	0.0883068i
$663$	−1.43488	−	0.828427i	−0.0557260	−	0.0321734i
$664$	18.5980			0.721742
$665$		0			0
$666$		0			0
$667$	−2.09077	−	1.20711i	−0.0809549	−	0.0467394i
$668$	31.0134	−	17.9056i	1.19994	−	0.692788i
$669$	14.0711	+	24.3718i	0.544019	+	0.942268i
$670$		0			0
$671$	−55.4558			−2.14085
$672$	−26.1039	+	10.6569i	−1.00698	+	0.411097i
$673$		−	18.3431i		−	0.707076i	−0.935420	−	0.353538i	$-0.884978\pi$
$673$		−	18.3431i		−	0.707076i	0.935420	−	0.353538i	$-0.115022\pi$
$674$	−3.07107	+	5.31925i	−0.118293	+	0.204890i
$675$		0			0
$676$	−11.2574	−	19.4983i	−0.432975	−	0.749935i
$677$	−0.123093	−	0.0710678i	−0.00473085	−	0.00273136i	0.497633	−	0.867388i	$-0.334203\pi$
$677$	−0.123093	−	0.0710678i	−0.00473085	−	0.00273136i	−0.502364	+	0.864656i	$0.667536\pi$
$678$			12.4853i			0.479494i
$679$	0.556349	−	0.717439i	0.0213507	−	0.0275328i
$680$		0			0
$681$	−32.5563	+	56.3893i	−1.24756	+	2.16084i
$682$	10.3923	−	6.00000i	0.397942	−	0.229752i
$683$	37.4492	−	21.6213i	1.43295	−	0.827317i	0.435610	−	0.900136i	$-0.356533\pi$
$683$	37.4492	−	21.6213i	1.43295	−	0.827317i	0.997345	+	0.0728189i	$0.0231995\pi$
$684$	7.31371	−	12.6677i	0.279647	−	0.484362i
$685$		0			0
$686$	6.15685	−	4.57631i	0.235070	−	0.174724i
$687$		−	0.828427i		−	0.0316065i
$688$	16.6646	+	9.62132i	0.635333	+	0.366809i
$689$	−2.82843	−	4.89898i	−0.107754	−	0.186636i
$690$		0			0
$691$	2.41421	−	4.18154i	0.0918410	−	0.159073i	−0.816445	−	0.577423i	$-0.804058\pi$
$691$	2.41421	−	4.18154i	0.0918410	−	0.159073i	0.908286	+	0.418350i	$0.137392\pi$
$692$			35.3137i			1.34243i
$693$	28.5533	+	22.1421i	1.08465	+	0.841110i
$694$	9.14214			0.347031
$695$		0			0
$696$	1.91421	+	3.31552i	0.0725581	+	0.125674i
$697$	1.55797	−	0.899495i	0.0590124	−	0.0340708i
$698$	9.56233	+	5.52082i	0.361940	+	0.208966i
$699$	26.9706			1.02012
$700$		0			0
$701$	−42.7990			−1.61650			−0.808248	−	0.588843i	$-0.799584\pi$
$701$	−42.7990			−1.61650			−0.808248	+	0.588843i	$0.799584\pi$
$702$	−0.123093	−	0.0710678i	−0.00464585	−	0.00268228i
$703$		0			0
$704$	−10.0711	−	17.4436i	−0.379568	−	0.657430i
$705$		0			0
$706$	8.76955			0.330046
$707$	−4.41717	+	32.2782i	−0.166125	+	1.21395i
$708$		−	55.1127i		−	2.07126i
$709$	19.1569	−	33.1806i	0.719451	−	1.24613i	−0.241767	−	0.970334i	$-0.577727\pi$
$709$	19.1569	−	33.1806i	0.719451	−	1.24613i	0.961218	−	0.275791i	$-0.0889397\pi$
$710$		0			0
$711$	−12.9706	−	22.4657i	−0.486434	−	0.842529i
$712$	−3.64874	−	2.10660i	−0.136742	−	0.0789482i
$713$		−	14.4853i		−	0.542478i
$714$	−2.17157	−	0.297173i	−0.0812691	−	0.0111214i
$715$		0			0
$716$	−9.14214	+	15.8346i	−0.341658	+	0.591768i
$717$	2.74666	−	1.58579i	0.102576	−	0.0592223i
$718$	−3.58719	+	2.07107i	−0.133873	+	0.0772916i
$719$	−20.5563	+	35.6046i	−0.766622	+	1.32783i	0.172762	+	0.984964i	$0.444731\pi$
$719$	−20.5563	+	35.6046i	−0.766622	+	1.32783i	−0.939385	+	0.342865i	$0.888602\pi$
$720$		0			0
$721$	−0.414214	−	1.01461i	−0.0154261	−	0.0377861i
$722$			4.55635i			0.169570i
$723$	34.1698	+	19.7279i	1.27079	+	0.733689i
$724$	7.91421	+	13.7078i	0.294129	+	0.509447i
$725$		0			0
$726$	6.15685	−	10.6640i	0.228502	−	0.395778i
$727$		−	40.4142i		−	1.49888i	−0.662072	−	0.749440i	$-0.730323\pi$
$727$		−	40.4142i		−	1.49888i	0.662072	−	0.749440i	$-0.269677\pi$
$728$	2.74666	+	2.12994i	0.101798	+	0.0789409i
$729$	23.8284			0.882534
$730$		0			0
$731$	2.65685	+	4.60181i	0.0982673	+	0.170204i
$732$	43.9062	−	25.3492i	1.62282	−	0.936935i
$733$	−19.0526	−	11.0000i	−0.703722	−	0.406294i	0.105010	−	0.994471i	$-0.466513\pi$
$733$	−19.0526	−	11.0000i	−0.703722	−	0.406294i	−0.808732	+	0.588177i	$0.799846\pi$
$734$	−4.65685			−0.171888
$735$		0			0
$736$	10.6569			0.392817
$737$	−51.9105	−	29.9706i	−1.91215	−	1.10398i
$738$	−2.20330	+	1.27208i	−0.0811047	+	0.0468258i
$739$	20.5563	+	35.6046i	0.756178	+	1.30974i	0.944787	+	0.327686i	$0.106269\pi$
$739$	20.5563	+	35.6046i	0.756178	+	1.30974i	−0.188609	+	0.982052i	$0.560398\pi$
$740$		0			0
$741$	−5.65685			−0.207810
$742$	−5.91359	−	4.58579i	−0.217095	−	0.168350i
$743$			1.92893i			0.0707657i	0.999374	+	0.0353828i	$0.0112651\pi$
$743$			1.92893i			0.0707657i	−0.999374	+	0.0353828i	$0.988735\pi$
$744$	−11.4853	+	19.8931i	−0.421071	+	0.729316i
$745$		0			0
$746$	2.68629	+	4.65279i	0.0983521	+	0.170351i
$747$	28.7274	+	16.5858i	1.05108	+	0.606842i
$748$		−	7.31371i		−	0.267416i
$749$	2.75736	+	6.75412i	0.100752	+	0.246790i
$750$		0			0
$751$	20.8284	−	36.0759i	0.760040	−	1.31643i	−0.182789	−	0.983152i	$-0.558513\pi$
$751$	20.8284	−	36.0759i	0.760040	−	1.31643i	0.942829	−	0.333276i	$-0.108154\pi$
$752$	5.19615	−	3.00000i	0.189484	−	0.109399i
$753$	−27.8359	+	16.0711i	−1.01440	+	0.585662i
$754$	0.171573	−	0.297173i	0.00624832	−	0.0108224i
$755$		0			0
$756$	1.98528	+	0.271680i	0.0722040	+	0.00988089i
$757$			19.4558i			0.707135i	0.935409	+	0.353567i	$0.115031\pi$
$757$			19.4558i			0.707135i	−0.935409	+	0.353567i	$0.884969\pi$
$758$	−7.59466	−	4.38478i	−0.275850	−	0.159262i
$759$	−14.0711	−	24.3718i	−0.510747	−	0.884640i
$760$		0			0
$761$	6.65685	−	11.5300i	0.241311	−	0.417963i	−0.719777	−	0.694205i	$-0.755756\pi$
$761$	6.65685	−	11.5300i	0.241311	−	0.417963i	0.961088	+	0.276243i	$0.0890894\pi$
$762$		−	13.3137i		−	0.482305i
$763$	1.25024	−	9.13604i	0.0452617	−	0.330747i
$764$	−13.1127			−0.474401
$765$		0			0
$766$	3.50000	+	6.06218i	0.126460	+	0.219035i
$767$	−8.95743	+	5.17157i	−0.323434	+	0.186735i
$768$	8.30153	+	4.79289i	0.299556	+	0.172949i
$769$	−44.6274			−1.60931			−0.804653	−	0.593745i	$-0.797649\pi$
$769$	−44.6274			−1.60931			−0.804653	+	0.593745i	$0.797649\pi$
$770$		0			0
$771$	42.6274			1.53519
$772$	−3.16693	−	1.82843i	−0.113980	−	0.0658065i
$773$	−21.7482	+	12.5563i	−0.782230	+	0.451620i	−0.837220	−	0.546866i	$-0.815821\pi$
$773$	−21.7482	+	12.5563i	−0.782230	+	0.451620i	0.0549903	+	0.998487i	$0.482487\pi$
$774$	−3.75736	−	6.50794i	−0.135055	−	0.233923i
$775$		0			0
$776$	0.544156			0.0195341
$777$		0			0
$778$			5.11270i			0.183299i
$779$	3.07107	−	5.31925i	0.110032	−	0.190582i
$780$		0			0
$781$	30.1421	+	52.2077i	1.07857	+	1.86814i
$782$	0.717439	+	0.414214i	0.0256556	+	0.0148122i
$783$		−	0.414214i		−	0.0148028i
$784$	−20.2279	−	5.64191i	−0.722426	−	0.201497i
$785$		0			0
$786$	1.65685	−	2.86976i	0.0590980	−	0.102361i
$787$	−24.7305	+	14.2782i	−0.881548	+	0.508962i	−0.871168	−	0.490984i	$-0.836637\pi$
$787$	−24.7305	+	14.2782i	−0.881548	+	0.508962i	−0.0103795	+	0.999946i	$0.503304\pi$
$788$	−37.4598	+	21.6274i	−1.33445	+	0.770445i
$789$	22.9853	−	39.8117i	0.818298	−	1.41733i
$790$		0			0
$791$	−20.2426	+	26.1039i	−0.719745	+	0.928146i
$792$			21.6569i			0.769543i
$793$	−8.23999	−	4.75736i	−0.292611	−	0.168939i
$794$	−5.92893	−	10.2692i	−0.210410	−	0.364441i
$795$		0			0
$796$	1.51472	−	2.62357i	0.0536878	−	0.0929900i
$797$		−	8.00000i		−	0.283375i	−0.989911	−	0.141687i	$-0.954747\pi$
$797$		−	8.00000i		−	0.283375i	0.989911	−	0.141687i	$-0.0452527\pi$
$798$	−6.92820	+	2.82843i	−0.245256	+	0.100125i
$799$	1.65685			0.0586153
$800$		0			0
$801$	−3.75736	−	6.50794i	−0.132760	−	0.229947i
$802$	−2.75722	+	1.59188i	−0.0973609	+	0.0562113i
$803$	20.1903	+	11.6569i	0.712499	+	0.411361i
$804$	54.7990			1.93261
$805$		0			0
$806$	2.05887			0.0725208
$807$	63.6762	+	36.7635i	2.24151	+	1.29413i
$808$	−16.9108	+	9.76346i	−0.594920	+	0.343477i
$809$	−4.81371	−	8.33759i	−0.169241	−	0.293134i	0.768912	−	0.639354i	$-0.220798\pi$
$809$	−4.81371	−	8.33759i	−0.169241	−	0.293134i	−0.938153	+	0.346220i	$0.887465\pi$
$810$		0			0
$811$	24.6274			0.864786			0.432393	−	0.901685i	$-0.357669\pi$
$811$	24.6274			0.864786			0.432393	+	0.901685i	$0.357669\pi$
$812$	−0.655892	+	4.79289i	−0.0230173	+	0.168198i
$813$			1.17157i			0.0410889i
$814$		0			0
$815$		0			0
$816$	3.00000	+	5.19615i	0.105021	+	0.181902i
$817$	15.7116	+	9.07107i	0.549678	+	0.317356i
$818$			10.2721i			0.359155i
$819$	2.34315	+	5.73951i	0.0818761	+	0.200555i
$820$		0			0
$821$	9.97056	−	17.2695i	0.347975	−	0.602710i	−0.637915	−	0.770107i	$-0.720203\pi$
$821$	9.97056	−	17.2695i	0.347975	−	0.602710i	0.985890	+	0.167397i	$0.0535361\pi$
$822$	−1.43488	+	0.828427i	−0.0500471	+	0.0288947i
$823$	10.4539	−	6.03553i	0.364398	−	0.210385i	−0.306610	−	0.951835i	$-0.599195\pi$
$823$	10.4539	−	6.03553i	0.364398	−	0.210385i	0.671008	+	0.741450i	$0.265861\pi$
$824$	0.328427	−	0.568852i	0.0114413	−	0.0198169i
$825$		0			0
$826$	−8.38478	+	10.8126i	−0.291744	+	0.376217i
$827$			16.2132i			0.563788i	0.959446	+	0.281894i	$0.0909627\pi$
$827$			16.2132i			0.563788i	−0.959446	+	0.281894i	$0.909037\pi$
$828$	10.8126	+	6.24264i	0.375763	+	0.216947i
$829$	3.34315	+	5.79050i	0.116112	+	0.201112i	0.918224	−	0.396062i	$-0.129623\pi$
$829$	3.34315	+	5.79050i	0.116112	+	0.201112i	−0.802112	+	0.597174i	$0.796290\pi$
$830$		0			0
$831$	14.6569	−	25.3864i	0.508441	−	0.880645i
$832$		−	3.45584i		−	0.119810i
$833$	−4.05845	−	4.14214i	−0.140617	−	0.143516i
$834$	12.1421			0.420448
$835$		0			0
$836$	−12.4853	−	21.6251i	−0.431812	−	0.747921i
$837$	2.15232	−	1.24264i	0.0743950	−	0.0429519i
$838$	8.36308	+	4.82843i	0.288898	+	0.166795i
$839$	−20.8284			−0.719077			−0.359539	−	0.933130i	$-0.617066\pi$
$839$	−20.8284			−0.719077			−0.359539	+	0.933130i	$0.617066\pi$
$840$		0			0
$841$	−28.0000			−0.965517
$842$	−1.25024	−	0.721825i	−0.0430861	−	0.0248757i
$843$	−54.9544	+	31.7279i	−1.89273	+	1.09277i
$844$	−3.21320	−	5.56543i	−0.110603	−	0.191570i
$845$		0			0
$846$	−2.34315			−0.0805590
$847$	30.1623	−	12.3137i	1.03639	−	0.423104i
$848$			20.4853i			0.703467i
$849$	16.8995	−	29.2708i	0.579989	−	1.00457i
$850$		0			0
$851$		0			0
$852$	−47.7290	−	27.5563i	−1.63517	−	0.944065i
$853$		−	53.4558i		−	1.83029i	−0.403121	−	0.915147i	$-0.632075\pi$
$853$		−	53.4558i		−	1.83029i	0.403121	−	0.915147i	$-0.367925\pi$
$854$	−12.4706	−	1.70656i	−0.426734	−	0.0583972i
$855$		0			0
$856$	−2.18629	+	3.78677i	−0.0747259	+	0.129429i
$857$	−19.2987	+	11.1421i	−0.659233	+	0.380608i	−0.791985	−	0.610541i	$-0.790952\pi$
$857$	−19.2987	+	11.1421i	−0.659233	+	0.380608i	0.132752	+	0.991149i	$0.457619\pi$
$858$	3.46410	−	2.00000i	0.118262	−	0.0682789i
$859$	23.3137	−	40.3805i	0.795453	−	1.37777i	−0.127097	−	0.991890i	$-0.540566\pi$
$859$	23.3137	−	40.3805i	0.795453	−	1.37777i	0.922551	−	0.385876i	$-0.126101\pi$
$860$		0			0
$861$	−13.7426	−	1.88064i	−0.468348	−	0.0640919i
$862$			9.02944i			0.307544i
$863$	−14.3382	−	8.27817i	−0.488079	−	0.281792i	0.235698	−	0.971826i	$-0.424262\pi$
$863$	−14.3382	−	8.27817i	−0.488079	−	0.281792i	−0.723777	+	0.690034i	$0.757596\pi$
$864$	0.914214	+	1.58346i	0.0311022	+	0.0538706i
$865$		0			0
$866$	−6.58579	+	11.4069i	−0.223794	+	0.387623i
$867$		−	39.3848i		−	1.33758i
$868$	−26.8723	+	10.9706i	−0.912105	+	0.372365i
$869$	−44.2843			−1.50224
$870$		0			0
$871$	−5.14214	−	8.90644i	−0.174235	−	0.301783i
$872$	4.78645	−	2.76346i	0.162090	−	0.0935824i
$873$	0.840532	+	0.485281i	0.0284477	+	0.0164243i
$874$	2.82843			0.0956730
$875$		0			0
$876$	−21.3137			−0.720123
$877$	−26.6982	−	15.4142i	−0.901534	−	0.520501i	−0.0238366	−	0.999716i	$-0.507588\pi$
$877$	−26.6982	−	15.4142i	−0.901534	−	0.520501i	−0.877698	+	0.479215i	$0.840921\pi$
$878$	12.1753	−	7.02944i	0.410898	−	0.237232i
$879$	−19.3137	−	33.4523i	−0.651435	−	1.12832i
$880$		0			0
$881$	−3.82843			−0.128983			−0.0644915	−	0.997918i	$-0.520543\pi$
$881$	−3.82843			−0.128983			−0.0644915	+	0.997918i	$0.520543\pi$
$882$	5.73951	+	5.85786i	0.193259	+	0.197245i
$883$			38.2843i			1.28837i	0.764870	+	0.644184i	$0.222803\pi$
$883$			38.2843i			1.28837i	−0.764870	+	0.644184i	$0.777197\pi$
$884$	0.627417	−	1.08672i	0.0211023	−	0.0365503i
$885$		0			0
$886$	−2.52944	−	4.38111i	−0.0849781	−	0.147186i
$887$	−38.1667	−	22.0355i	−1.28151	−	0.739881i	−0.304387	−	0.952549i	$-0.598451\pi$
$887$	−38.1667	−	22.0355i	−1.28151	−	0.739881i	−0.977125	+	0.212668i	$0.931785\pi$
$888$		0			0
$889$	21.5858	−	27.8359i	0.723964	−	0.933586i
$890$		0			0
$891$	22.8995	−	39.6631i	0.767162	−	1.32876i
$892$	−18.4582	+	10.6569i	−0.618027	+	0.356818i
$893$	4.89898	−	2.82843i	0.163938	−	0.0946497i
$894$	3.91421	−	6.77962i	0.130911	−	0.226744i
$895$		0			0
$896$	−10.5563	−	25.8577i	−0.352663	−	0.863844i
$897$		−	4.82843i		−	0.161216i
$898$	0.655892	+	0.378680i	0.0218874	+	0.0126367i
$899$	3.00000	+	5.19615i	0.100056	+	0.173301i
$900$		0			0
$901$	−2.82843	+	4.89898i	−0.0942286	+	0.163209i
$902$			4.34315i			0.144611i
$903$	5.55487	−	40.5919i	0.184855	−	1.35081i
$904$	−19.7990			−0.658505
$905$		0			0
$906$	0.171573	+	0.297173i	0.00570013	+	0.00987291i
$907$	24.4334	−	14.1066i	0.811296	−	0.468402i	−0.0361097	−	0.999348i	$-0.511497\pi$
$907$	24.4334	−	14.1066i	0.811296	−	0.468402i	0.847406	+	0.530946i	$0.178163\pi$
$908$	−42.7069	−	24.6569i	−1.41728	−	0.818266i
$909$	−34.8284			−1.15519
$910$		0			0
$911$	−49.7990			−1.64991			−0.824957	−	0.565195i	$-0.808801\pi$
$911$	−49.7990			−1.64991			−0.824957	+	0.565195i	$0.808801\pi$
$912$	17.7408	+	10.2426i	0.587456	+	0.339168i
$913$	49.0408	−	28.3137i	1.62301	−	0.937047i
$914$	6.68629	+	11.5810i	0.221163	+	0.383065i
$915$		0			0
$916$	0.627417			0.0207304
$917$	8.11689	−	3.31371i	0.268043	−	0.109428i
$918$			0.142136i			0.00469117i
$919$	9.55635	−	16.5521i	0.315235	−	0.546003i	−0.664253	−	0.747508i	$-0.731250\pi$
$919$	9.55635	−	16.5521i	0.315235	−	0.546003i	0.979487	+	0.201505i	$0.0645834\pi$
$920$		0			0
$921$	15.9853	+	27.6873i	0.526733	+	0.912328i
$922$	6.70314	+	3.87006i	0.220756	+	0.127454i
$923$			10.3431i			0.340449i
$924$	−34.5563	+	44.5621i	−1.13682	+	1.46598i
$925$		0			0
$926$	2.28680	−	3.96085i	0.0751488	−	0.130162i
$927$	1.01461	−	0.585786i	0.0333242	−	0.0192398i
$928$	−3.82282	+	2.20711i	−0.125490	+	0.0724518i
$929$	−5.74264	+	9.94655i	−0.188410	+	0.326336i	−0.944720	−	0.327877i	$-0.893667\pi$
$929$	−5.74264	+	9.94655i	−0.188410	+	0.326336i	0.756310	+	0.654213i	$0.227000\pi$
$930$		0			0
$931$	−19.0711	−	5.31925i	−0.625029	−	0.174331i
$932$			20.4264i			0.669089i
$933$	−39.3659	−	22.7279i	−1.28878	−	0.744079i
$934$	4.74264	+	8.21449i	0.155184	+	0.268786i
$935$		0			0
$936$	−1.85786	+	3.21792i	−0.0607262	+	0.105181i
$937$		−	10.6274i		−	0.347183i	−0.984818	−	0.173591i	$-0.944463\pi$
$937$		−	10.6274i		−	0.347183i	0.984818	−	0.173591i	$-0.0555372\pi$
$938$	−10.7510	−	8.33705i	−0.351033	−	0.272214i
$939$	42.6274			1.39109
$940$		0			0
$941$	−5.14214	−	8.90644i	−0.167629	−	0.290342i	0.769957	−	0.638096i	$-0.220278\pi$
$941$	−5.14214	−	8.90644i	−0.167629	−	0.290342i	−0.937586	+	0.347754i	$0.886944\pi$
$942$	4.60181	−	2.65685i	0.149935	−	0.0865650i
$943$	4.54026	+	2.62132i	0.147851	+	0.0853619i
$944$	37.4558			1.21908
$945$		0			0
$946$	−12.8284			−0.417088
$947$	37.3982	+	21.5919i	1.21528	+	0.701642i	0.963905	−	0.266248i	$-0.0857840\pi$
$947$	37.3982	+	21.5919i	1.21528	+	0.701642i	0.251375	+	0.967890i	$0.419117\pi$
$948$	35.0613	−	20.2426i	1.13874	−	0.657450i
$949$	2.00000	+	3.46410i	0.0649227	+	0.112449i
$950$		0			0
$951$	62.2843			2.01971
$952$	0.471253	−	3.44365i	0.0152734	−	0.111609i
$953$			2.34315i			0.0759019i	0.999280	+	0.0379510i	$0.0120831\pi$
$953$			2.34315i			0.0759019i	−0.999280	+	0.0379510i	$0.987917\pi$
$954$	4.00000	−	6.92820i	0.129505	−	0.224309i
$955$		0			0
$956$	1.20101	+	2.08021i	0.0388434	+	0.0672788i
$957$	10.0951	+	5.82843i	0.326329	+	0.188406i
$958$		−	10.0833i		−	0.325775i
$959$	−4.34315	−	0.594346i	−0.140247	−	0.0191924i
$960$		0			0
$961$	−2.50000	+	4.33013i	−0.0806452	+	0.139682i
$962$		0			0
$963$	−6.75412	+	3.89949i	−0.217649	+	0.125659i
$964$	−14.9411	+	25.8788i	−0.481221	+	0.833500i
$965$		0			0
$966$	−2.41421	−	5.91359i	−0.0776760	−	0.190267i
$967$		−	27.5269i		−	0.885206i	−0.896718	−	0.442603i	$-0.854055\pi$
$967$		−	27.5269i		−	0.885206i	0.896718	−	0.442603i	$-0.145945\pi$
$968$	16.9108	+	9.76346i	0.543534	+	0.313809i
$969$	2.82843	+	4.89898i	0.0908622	+	0.157378i
$970$		0			0
$971$	12.0000	−	20.7846i	0.385098	−	0.667010i	−0.606685	−	0.794943i	$-0.707501\pi$
$971$	12.0000	−	20.7846i	0.385098	−	0.667010i	0.991783	+	0.127933i	$0.0408342\pi$
$972$			39.5980i			1.27011i
$973$	25.3864	+	19.6863i	0.813851	+	0.631114i
$974$	6.48528			0.207802
$975$		0			0
$976$	17.2279	+	29.8396i	0.551452	+	0.955143i
$977$	18.4582	−	10.6569i	0.590531	−	0.340943i	−0.174777	−	0.984608i	$-0.555920\pi$
$977$	18.4582	−	10.6569i	0.590531	−	0.340943i	0.765307	+	0.643665i	$0.222587\pi$
$978$	−20.4874	−	11.8284i	−0.655116	−	0.378231i
$979$	−12.8284			−0.409998
$980$		0			0
$981$	9.85786			0.314737
$982$	−4.77589	−	2.75736i	−0.152405	−	0.0879909i
$983$	12.3090	−	7.10660i	0.392596	−	0.226665i	−0.290688	−	0.956818i	$-0.593884\pi$
$983$	12.3090	−	7.10660i	0.392596	−	0.226665i	0.683284	+	0.730152i	$0.260551\pi$
$984$	−4.15685	−	7.19988i	−0.132516	−	0.229524i
$985$		0			0
$986$	−0.343146			−0.0109280
$987$	−10.0951	−	7.82843i	−0.321332	−	0.249182i
$988$		−	4.28427i		−	0.136301i
$989$	−7.74264	+	13.4106i	−0.246202	+	0.426434i
$990$		0			0
$991$	7.82843	+	13.5592i	0.248678	+	0.430723i	0.963159	−	0.268931i	$-0.0866705\pi$
$991$	7.82843	+	13.5592i	0.248678	+	0.430723i	−0.714481	+	0.699655i	$0.753337\pi$
$992$	−22.9369	−	13.2426i	−0.728248	−	0.420454i
$993$			26.4853i			0.840485i
$994$	5.17157	+	12.6677i	0.164032	+	0.401796i
$995$		0			0
$996$	−25.8848	+	44.8337i	−0.820191	+	1.42061i
$997$	−15.1172	+	8.72792i	−0.478767	+	0.276416i	−0.719902	−	0.694075i	$-0.755813\pi$
$997$	−15.1172	+	8.72792i	−0.478767	+	0.276416i	0.241136	+	0.970491i	$0.422480\pi$
$998$	1.73205	−	1.00000i	0.0548271	−	0.0316544i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	175.2.k.a.149.3		8
5.2	odd	4		175.2.e.c.51.1		4
5.3	odd	4		35.2.e.a.16.2	yes	4
5.4	even	2	inner	175.2.k.a.149.2		8
7.2	even	3		1225.2.b.g.99.2		4
7.4	even	3	inner	175.2.k.a.74.2		8
7.5	odd	6		1225.2.b.h.99.2		4
15.8	even	4		315.2.j.e.226.1		4
20.3	even	4		560.2.q.k.401.2		4
35.2	odd	12		1225.2.a.k.1.2		2
35.3	even	12		245.2.e.e.116.2		4
35.4	even	6	inner	175.2.k.a.74.3		8
35.9	even	6		1225.2.b.g.99.3		4
35.12	even	12		1225.2.a.m.1.2		2
35.13	even	4		245.2.e.e.226.2		4
35.18	odd	12		35.2.e.a.11.2	✓	4
35.19	odd	6		1225.2.b.h.99.3		4
35.23	odd	12		245.2.a.h.1.1		2
35.32	odd	12		175.2.e.c.151.1		4
35.33	even	12		245.2.a.g.1.1		2
105.23	even	12		2205.2.a.n.1.2		2
105.53	even	12		315.2.j.e.46.1		4
105.68	odd	12		2205.2.a.q.1.2		2
140.23	even	12		3920.2.a.bq.1.1		2
140.103	odd	12		3920.2.a.bv.1.2		2
140.123	even	12		560.2.q.k.81.2		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
35.2.e.a.11.2	✓	4	35.18	odd	12
35.2.e.a.16.2	yes	4	5.3	odd	4
175.2.e.c.51.1		4	5.2	odd	4
175.2.e.c.151.1		4	35.32	odd	12
175.2.k.a.74.2		8	7.4	even	3	inner
175.2.k.a.74.3		8	35.4	even	6	inner
175.2.k.a.149.2		8	5.4	even	2	inner
175.2.k.a.149.3		8	1.1	even	1	trivial
245.2.a.g.1.1		2	35.33	even	12
245.2.a.h.1.1		2	35.23	odd	12
245.2.e.e.116.2		4	35.3	even	12
245.2.e.e.226.2		4	35.13	even	4
315.2.j.e.46.1		4	105.53	even	12
315.2.j.e.226.1		4	15.8	even	4
560.2.q.k.81.2		4	140.123	even	12
560.2.q.k.401.2		4	20.3	even	4
1225.2.a.k.1.2		2	35.2	odd	12
1225.2.a.m.1.2		2	35.12	even	12
1225.2.b.g.99.2		4	7.2	even	3
1225.2.b.g.99.3		4	35.9	even	6
1225.2.b.h.99.2		4	7.5	odd	6
1225.2.b.h.99.3		4	35.19	odd	6
2205.2.a.n.1.2		2	105.23	even	12
2205.2.a.q.1.2		2	105.68	odd	12
3920.2.a.bq.1.1		2	140.23	even	12
3920.2.a.bv.1.2		2	140.103	odd	12

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:	\( N \)	\(=\)	\( 175 = 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	175.k (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.358719 + 0.207107i) q^{2} +(-2.09077 + 1.20711i) q^{3} +(-0.914214 - 1.58346i) q^{4} -1.00000 q^{6} +(-2.09077 - 1.62132i) q^{7} -1.58579i q^{8} +(1.41421 - 2.44949i) q^{9} +O(q^{10})\)	\(q+(0.358719 + 0.207107i) q^{2} +(-2.09077 + 1.20711i) q^{3} +(-0.914214 - 1.58346i) q^{4} -1.00000 q^{6} +(-2.09077 - 1.62132i) q^{7} -1.58579i q^{8} +(1.41421 - 2.44949i) q^{9} +(-2.41421 - 4.18154i) q^{11} +(3.82282 + 2.20711i) q^{12} -0.828427i q^{13} +(-0.414214 - 1.01461i) q^{14} +(-1.50000 + 2.59808i) q^{16} +(-0.717439 + 0.414214i) q^{17} +(1.01461 - 0.585786i) q^{18} +(-1.41421 + 2.44949i) q^{19} +(6.32843 + 0.866025i) q^{21} -2.00000i q^{22} +(-2.09077 - 1.20711i) q^{23} +(1.91421 + 3.31552i) q^{24} +(0.171573 - 0.297173i) q^{26} -0.414214i q^{27} +(-0.655892 + 4.79289i) q^{28} +1.00000 q^{29} +(3.00000 + 5.19615i) q^{31} +(-3.82282 + 2.20711i) q^{32} +(10.0951 + 5.82843i) q^{33} -0.343146 q^{34} -5.17157 q^{36} +(-1.01461 + 0.585786i) q^{38} +(1.00000 + 1.73205i) q^{39} -2.17157 q^{41} +(2.09077 + 1.62132i) q^{42} -6.41421i q^{43} +(-4.41421 + 7.64564i) q^{44} +(-0.500000 - 0.866025i) q^{46} +(-1.73205 - 1.00000i) q^{47} -7.24264i q^{48} +(1.74264 + 6.77962i) q^{49} +(1.00000 - 1.73205i) q^{51} +(-1.31178 + 0.757359i) q^{52} +(5.91359 - 3.41421i) q^{53} +(0.0857864 - 0.148586i) q^{54} +(-2.57107 + 3.31552i) q^{56} -6.82843i q^{57} +(0.358719 + 0.207107i) q^{58} +(-6.24264 - 10.8126i) q^{59} +(5.74264 - 9.94655i) q^{61} +2.48528i q^{62} +(-6.92820 + 2.82843i) q^{63} +4.17157 q^{64} +(2.41421 + 4.18154i) q^{66} +(10.7510 - 6.20711i) q^{67} +(1.31178 + 0.757359i) q^{68} +5.82843 q^{69} -12.4853 q^{71} +(-3.88437 - 2.24264i) q^{72} +(-4.18154 + 2.41421i) q^{73} +5.17157 q^{76} +(-1.73205 + 12.6569i) q^{77} +0.828427i q^{78} +(4.58579 - 7.94282i) q^{79} +(4.74264 + 8.21449i) q^{81} +(-0.778985 - 0.449747i) q^{82} +11.7279i q^{83} +(-4.41421 - 10.8126i) q^{84} +(1.32843 - 2.30090i) q^{86} +(-2.09077 + 1.20711i) q^{87} +(-6.63103 + 3.82843i) q^{88} +(1.32843 - 2.30090i) q^{89} +(-1.34315 + 1.73205i) q^{91} +4.41421i q^{92} +(-12.5446 - 7.24264i) q^{93} +(-0.414214 - 0.717439i) q^{94} +(5.32843 - 9.22911i) q^{96} +0.343146i q^{97} +(-0.778985 + 2.79289i) q^{98} -13.6569 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 4 q^{4} - 8 q^{6}+O(q^{10}) \) 8 * q + 4 * q^4 - 8 * q^6	\( 8 q + 4 q^{4} - 8 q^{6} - 8 q^{11} + 8 q^{14} - 12 q^{16} + 28 q^{21} + 4 q^{24} + 24 q^{26} + 8 q^{29} + 24 q^{31} - 48 q^{34} - 64 q^{36} + 8 q^{39} - 40 q^{41} - 24 q^{44} - 4 q^{46} - 20 q^{49} + 8 q^{51} + 12 q^{54} + 36 q^{56} - 16 q^{59} + 12 q^{61} + 56 q^{64} + 8 q^{66} + 24 q^{69} - 32 q^{71} + 64 q^{76} + 48 q^{79} + 4 q^{81} - 24 q^{84} - 12 q^{86} - 12 q^{89} - 56 q^{91} + 8 q^{94} + 20 q^{96} - 64 q^{99}+O(q^{100}) \) 8 * q + 4 * q^4 - 8 * q^6 - 8 * q^11 + 8 * q^14 - 12 * q^16 + 28 * q^21 + 4 * q^24 + 24 * q^26 + 8 * q^29 + 24 * q^31 - 48 * q^34 - 64 * q^36 + 8 * q^39 - 40 * q^41 - 24 * q^44 - 4 * q^46 - 20 * q^49 + 8 * q^51 + 12 * q^54 + 36 * q^56 - 16 * q^59 + 12 * q^61 + 56 * q^64 + 8 * q^66 + 24 * q^69 - 32 * q^71 + 64 * q^76 + 48 * q^79 + 4 * q^81 - 24 * q^84 - 12 * q^86 - 12 * q^89 - 56 * q^91 + 8 * q^94 + 20 * q^96 - 64 * q^99

Introduction

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