LMFDB - Embedded newform 175.2.k.a.74.4

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			74.4
Root			$0.258819 - 0.965926i$ of defining polynomial
Character	$\chi$	$=$	175.74
Dual form			175.2.k.a.149.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(2.09077 - 1.20711i) q^{2} +(-0.358719 - 0.207107i) q^{3} +(1.91421 - 3.31552i) q^{4} -1.00000 q^{6} +(-0.358719 + 2.62132i) q^{7} -4.41421i q^{8} +(-1.41421 - 2.44949i) q^{9} +O(q^{10})$	\(q+(2.09077 - 1.20711i) q^{2} +(-0.358719 - 0.207107i) q^{3} +(1.91421 - 3.31552i) q^{4} -1.00000 q^{6} +(-0.358719 + 2.62132i) q^{7} -4.41421i q^{8} +(-1.41421 - 2.44949i) q^{9} +(0.414214 - 0.717439i) q^{11} +(-1.37333 + 0.792893i) q^{12} +4.82843i q^{13} +(2.41421 + 5.91359i) q^{14} +(-1.50000 - 2.59808i) q^{16} +(-4.18154 - 2.41421i) q^{17} +(-5.91359 - 3.41421i) q^{18} +(1.41421 + 2.44949i) q^{19} +(0.671573 - 0.866025i) q^{21} -2.00000i q^{22} +(-0.358719 + 0.207107i) q^{23} +(-0.914214 + 1.58346i) q^{24} +(5.82843 + 10.0951i) q^{26} +2.41421i q^{27} +(8.00436 + 6.20711i) q^{28} +1.00000 q^{29} +(3.00000 - 5.19615i) q^{31} +(1.37333 + 0.792893i) q^{32} +(-0.297173 + 0.171573i) q^{33} -11.6569 q^{34} -10.8284 q^{36} +(5.91359 + 3.41421i) q^{38} +(1.00000 - 1.73205i) q^{39} -7.82843 q^{41} +(0.358719 - 2.62132i) q^{42} -3.58579i q^{43} +(-1.58579 - 2.74666i) q^{44} +(-0.500000 + 0.866025i) q^{46} +(1.73205 - 1.00000i) q^{47} +1.24264i q^{48} +(-6.74264 - 1.88064i) q^{49} +(1.00000 + 1.73205i) q^{51} +(16.0087 + 9.24264i) q^{52} +(-1.01461 - 0.585786i) q^{53} +(2.91421 + 5.04757i) q^{54} +(11.5711 + 1.58346i) q^{56} -1.17157i q^{57} +(2.09077 - 1.20711i) q^{58} +(2.24264 - 3.88437i) q^{59} +(-2.74264 - 4.75039i) q^{61} -14.4853i q^{62} +(6.92820 - 2.82843i) q^{63} +9.82843 q^{64} +(-0.414214 + 0.717439i) q^{66} +(-8.30153 - 4.79289i) q^{67} +(-16.0087 + 9.24264i) q^{68} +0.171573 q^{69} +4.48528 q^{71} +(-10.8126 + 6.24264i) q^{72} +(-0.717439 - 0.414214i) q^{73} +10.8284 q^{76} +(1.73205 + 1.34315i) q^{77} -4.82843i q^{78} +(7.41421 + 12.8418i) q^{79} +(-3.74264 + 6.48244i) q^{81} +(-16.3674 + 9.44975i) q^{82} -13.7279i q^{83} +(-1.58579 - 3.88437i) q^{84} +(-4.32843 - 7.49706i) q^{86} +(-0.358719 - 0.207107i) q^{87} +(-3.16693 - 1.82843i) q^{88} +(-4.32843 - 7.49706i) q^{89} +(-12.6569 - 1.73205i) q^{91} +1.58579i q^{92} +(-2.15232 + 1.24264i) q^{93} +(2.41421 - 4.18154i) q^{94} +(-0.328427 - 0.568852i) q^{96} +11.6569i q^{97} +(-16.3674 + 4.20711i) q^{98} -2.34315 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 $\left(\mathbb{Z}/175\mathbb{Z}\right)^\times$.

$n$	$101$	$127$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$-1$

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 $

$2$	2.09077	−	1.20711i	1.47840	−	0.853553i	0.478696	−	0.877981i	$-0.341110\pi$
$2$	2.09077	−	1.20711i	1.47840	−	0.853553i	0.999702	+	0.0244272i	$0.00777619\pi$
$3$	−0.358719	−	0.207107i	−0.207107	−	0.119573i	0.392859	−	0.919599i	$-0.371486\pi$
$3$	−0.358719	−	0.207107i	−0.207107	−	0.119573i	−0.599966	+	0.800025i	$0.704819\pi$
$4$	1.91421	−	3.31552i	0.957107	−	1.65776i
$5$		0			0
$5$		0			0
$6$	−1.00000			−0.408248
$7$	−0.358719	+	2.62132i	−0.135583	+	0.990766i
$7$	−0.358719	+	2.62132i	−0.135583	+	0.990766i
$8$		−	4.41421i		−	1.56066i
$9$	−1.41421	−	2.44949i	−0.471405	−	0.816497i
$10$		0			0
$11$	0.414214	−	0.717439i	0.124890	−	0.216316i	−0.796800	−	0.604243i	$-0.793476\pi$
$11$	0.414214	−	0.717439i	0.124890	−	0.216316i	0.921690	+	0.387927i	$0.126809\pi$
$12$	−1.37333	+	0.792893i	−0.396447	+	0.228889i
$13$			4.82843i			1.33916i	0.742738	+	0.669582i	$0.233527\pi$
$13$			4.82843i			1.33916i	−0.742738	+	0.669582i	$0.766473\pi$
$14$	2.41421	+	5.91359i	0.645226	+	1.58047i
$15$		0			0
$16$	−1.50000	−	2.59808i	−0.375000	−	0.649519i
$17$	−4.18154	−	2.41421i	−1.01417	−	0.585533i	−0.101762	−	0.994809i	$-0.532448\pi$
$17$	−4.18154	−	2.41421i	−1.01417	−	0.585533i	−0.912411	+	0.409276i	$0.865781\pi$
$18$	−5.91359	−	3.41421i	−1.39385	−	0.804738i
$19$	1.41421	+	2.44949i	0.324443	+	0.561951i	0.981399	−	0.191977i	$-0.0614899\pi$
$19$	1.41421	+	2.44949i	0.324443	+	0.561951i	−0.656957	+	0.753928i	$0.728157\pi$
$20$		0			0
$21$	0.671573	−	0.866025i	0.146549	−	0.188982i
$22$		−	2.00000i		−	0.426401i
$23$	−0.358719	+	0.207107i	−0.0747982	+	0.0431847i	−0.536933	−	0.843625i	$-0.680417\pi$
$23$	−0.358719	+	0.207107i	−0.0747982	+	0.0431847i	0.462134	+	0.886810i	$0.347084\pi$
$24$	−0.914214	+	1.58346i	−0.186613	+	0.323223i
$25$		0			0
$26$	5.82843	+	10.0951i	1.14305	+	1.97982i
$27$			2.41421i			0.464616i
$28$	8.00436	+	6.20711i	1.51268	+	1.17303i
$29$	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	−0.460152	−	0.887840i	$-0.652205\pi$
$31$	3.00000	−	5.19615i	0.538816	−	0.933257i	0.998968	−	0.0454165i	$-0.0144615\pi$
$32$	1.37333	+	0.792893i	0.242773	+	0.140165i
$33$	−0.297173	+	0.171573i	−0.0517312	+	0.0298670i
$34$	−11.6569			−1.99913
$35$		0			0
$36$	−10.8284			−1.80474
$37$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$37$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$38$	5.91359	+	3.41421i	0.959311	+	0.553859i
$39$	1.00000	−	1.73205i	0.160128	−	0.277350i
$40$		0			0
$41$	−7.82843			−1.22259			−0.611297	−	0.791401i	$-0.709352\pi$
$41$	−7.82843			−1.22259			−0.611297	+	0.791401i	$0.709352\pi$
$42$	0.358719	−	2.62132i	0.0553516	−	0.404479i
$43$		−	3.58579i		−	0.546827i	−0.961897	−	0.273414i	$-0.911847\pi$
$43$		−	3.58579i		−	0.546827i	0.961897	−	0.273414i	$-0.0881528\pi$
$44$	−1.58579	−	2.74666i	−0.239066	−	0.414075i
$45$		0			0
$46$	−0.500000	+	0.866025i	−0.0737210	+	0.127688i
$47$	1.73205	−	1.00000i	0.252646	−	0.145865i	−0.368329	−	0.929695i	$-0.620070\pi$
$47$	1.73205	−	1.00000i	0.252646	−	0.145865i	0.620975	+	0.783830i	$0.286737\pi$
$48$			1.24264i			0.179360i
$49$	−6.74264	−	1.88064i	−0.963234	−	0.268662i
$50$		0			0
$51$	1.00000	+	1.73205i	0.140028	+	0.242536i
$52$	16.0087	+	9.24264i	2.22001	+	1.28172i
$53$	−1.01461	−	0.585786i	−0.139368	−	0.0804640i	0.428695	−	0.903449i	$-0.358974\pi$
$53$	−1.01461	−	0.585786i	−0.139368	−	0.0804640i	−0.568063	+	0.822985i	$0.692307\pi$
$54$	2.91421	+	5.04757i	0.396574	+	0.686887i
$55$		0			0
$56$	11.5711	+	1.58346i	1.54625	+	0.211599i
$57$		−	1.17157i		−	0.155179i
$58$	2.09077	−	1.20711i	0.274532	−	0.158501i
$59$	2.24264	−	3.88437i	0.291967	−	0.505702i	−0.682308	−	0.731065i	$-0.739024\pi$
$59$	2.24264	−	3.88437i	0.291967	−	0.505702i	0.974275	+	0.225363i	$0.0723569\pi$
$60$		0			0
$61$	−2.74264	−	4.75039i	−0.351159	−	0.608226i	0.635294	−	0.772271i	$-0.280879\pi$
$61$	−2.74264	−	4.75039i	−0.351159	−	0.608226i	−0.986453	+	0.164045i	$0.947546\pi$
$62$		−	14.4853i		−	1.83963i
$63$	6.92820	−	2.82843i	0.872872	−	0.356348i
$64$	9.82843			1.22855
$65$		0			0
$66$	−0.414214	+	0.717439i	−0.0509862	+	0.0883106i
$67$	−8.30153	−	4.79289i	−1.01419	−	0.585545i	−0.101777	−	0.994807i	$-0.532453\pi$
$67$	−8.30153	−	4.79289i	−1.01419	−	0.585545i	−0.912417	+	0.409262i	$0.865786\pi$
$68$	−16.0087	+	9.24264i	−1.94134	+	1.12083i
$69$	0.171573			0.0206549
$70$		0			0
$71$	4.48528			0.532305			0.266152	−	0.963931i	$-0.414248\pi$
$71$	4.48528			0.532305			0.266152	+	0.963931i	$0.414248\pi$
$72$	−10.8126	+	6.24264i	−1.27427	+	0.735702i
$73$	−0.717439	−	0.414214i	−0.0839699	−	0.0484800i	0.457427	−	0.889247i	$-0.348771\pi$
$73$	−0.717439	−	0.414214i	−0.0839699	−	0.0484800i	−0.541397	+	0.840767i	$0.682104\pi$
$74$		0			0
$75$		0			0
$76$	10.8284			1.24211
$77$	1.73205	+	1.34315i	0.197386	+	0.153066i
$78$		−	4.82843i		−	0.546712i
$79$	7.41421	+	12.8418i	0.834164	+	1.44481i	0.894709	+	0.446649i	$0.147383\pi$
$79$	7.41421	+	12.8418i	0.834164	+	1.44481i	−0.0605449	+	0.998165i	$0.519284\pi$
$80$		0			0
$81$	−3.74264	+	6.48244i	−0.415849	+	0.720272i
$82$	−16.3674	+	9.44975i	−1.80748	+	1.04355i
$83$		−	13.7279i		−	1.50684i	−0.657542	−	0.753418i	$-0.728404\pi$
$83$		−	13.7279i		−	1.50684i	0.657542	−	0.753418i	$-0.271596\pi$
$84$	−1.58579	−	3.88437i	−0.173023	−	0.423819i
$85$		0			0
$86$	−4.32843	−	7.49706i	−0.466746	−	0.808428i
$87$	−0.358719	−	0.207107i	−0.0384588	−	0.0222042i
$88$	−3.16693	−	1.82843i	−0.337596	−	0.194911i
$89$	−4.32843	−	7.49706i	−0.458812	−	0.794686i	0.540086	−	0.841610i	$-0.318392\pi$
$89$	−4.32843	−	7.49706i	−0.458812	−	0.794686i	−0.998898	+	0.0469234i	$0.985058\pi$
$90$		0			0
$91$	−12.6569	−	1.73205i	−1.32680	−	0.181568i
$92$			1.58579i			0.165330i
$93$	−2.15232	+	1.24264i	−0.223185	+	0.128856i
$94$	2.41421	−	4.18154i	0.249007	−	0.431293i
$95$		0			0
$96$	−0.328427	−	0.568852i	−0.0335200	−	0.0580583i
$97$			11.6569i			1.18357i	0.806094	+	0.591787i	$0.201577\pi$
$97$			11.6569i			1.18357i	−0.806094	+	0.591787i	$0.798423\pi$
$98$	−16.3674	+	4.20711i	−1.65336	+	0.424982i
$99$	−2.34315			−0.235495
$100$		0			0
$101$	5.15685	−	8.93193i	0.513126	−	0.888761i	−0.486758	−	0.873537i	$-0.661821\pi$
$101$	5.15685	−	8.93193i	0.513126	−	0.888761i	0.999884	−	0.0152237i	$-0.00484604\pi$
$102$	4.18154	+	2.41421i	0.414034	+	0.239043i
$103$	2.09077	−	1.20711i	0.206010	−	0.118940i	−0.393446	−	0.919348i	$-0.628717\pi$
$103$	2.09077	−	1.20711i	0.206010	−	0.118940i	0.599456	+	0.800408i	$0.295384\pi$
$104$	21.3137			2.08998
$105$		0			0
$106$	−2.82843			−0.274721
$107$	9.73641	−	5.62132i	0.941255	−	0.543434i	0.0509012	−	0.998704i	$-0.483791\pi$
$107$	9.73641	−	5.62132i	0.941255	−	0.543434i	0.890353	+	0.455270i	$0.150457\pi$
$108$	8.00436	+	4.62132i	0.770220	+	0.444687i
$109$	−6.74264	+	11.6786i	−0.645828	+	1.11861i	0.338282	+	0.941045i	$0.390154\pi$
$109$	−6.74264	+	11.6786i	−0.645828	+	1.11861i	−0.984110	+	0.177562i	$0.943179\pi$
$110$		0			0
$111$		0			0
$112$	7.34847	−	3.00000i	0.694365	−	0.283473i
$113$			4.48528i			0.421940i	0.977493	+	0.210970i	$0.0676622\pi$
$113$			4.48528i			0.421940i	−0.977493	+	0.210970i	$0.932338\pi$
$114$	−1.41421	−	2.44949i	−0.132453	−	0.229416i
$115$		0			0
$116$	1.91421	−	3.31552i	0.177730	−	0.307838i
$117$	11.8272	−	6.82843i	1.09342	−	0.631288i
$118$		−	10.8284i		−	0.996838i
$119$	7.82843	−	10.0951i	0.717631	−	0.925419i
$120$		0			0
$121$	5.15685	+	8.93193i	0.468805	+	0.811994i
$122$	−11.4685	−	6.62132i	−1.03831	−	0.599466i
$123$	2.80821	+	1.62132i	0.253208	+	0.146190i
$124$	−11.4853	−	19.8931i	−1.03141	−	1.78645i
$125$		0			0
$126$	11.0711	−	14.2767i	0.986289	−	1.27187i
$127$		−	9.31371i		−	0.826458i	−0.910627	−	0.413229i	$-0.864401\pi$
$127$		−	9.31371i		−	0.826458i	0.910627	−	0.413229i	$-0.135599\pi$
$128$	17.8023	−	10.2782i	1.57352	−	0.908471i
$129$	−0.742641	+	1.28629i	−0.0653859	+	0.113252i
$130$		0			0
$131$	9.65685	+	16.7262i	0.843723	+	1.46137i	0.886725	+	0.462297i	$0.152974\pi$
$131$	9.65685	+	16.7262i	0.843723	+	1.46137i	−0.0430021	+	0.999075i	$0.513692\pi$
$132$			1.31371i			0.114344i
$133$	−6.92820	+	2.82843i	−0.600751	+	0.245256i
$134$	−23.1421			−1.99918
$135$		0			0
$136$	−10.6569	+	18.4582i	−0.913818	+	1.58278i
$137$	8.36308	+	4.82843i	0.714506	+	0.412520i	0.812727	−	0.582644i	$-0.197982\pi$
$137$	8.36308	+	4.82843i	0.714506	+	0.412520i	−0.0982211	+	0.995165i	$0.531315\pi$
$138$	0.358719	−	0.207107i	0.0305362	−	0.0176301i
$139$	16.1421			1.36916			0.684579	−	0.728939i	$-0.259986\pi$
$139$	16.1421			1.36916			0.684579	+	0.728939i	$0.259986\pi$
$140$		0			0
$141$	−0.828427			−0.0697661
$142$	9.37769	−	5.41421i	0.786959	−	0.454351i
$143$	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
$147$	2.02922	+	2.07107i	0.167368	+	0.170819i
$148$		0			0
$149$	−1.08579	−	1.88064i	−0.0889511	−	0.154068i	0.818117	−	0.575052i	$-0.195018\pi$
$149$	−1.08579	−	1.88064i	−0.0889511	−	0.154068i	−0.907068	+	0.420984i	$0.861685\pi$
$150$		0			0
$151$	−5.82843	+	10.0951i	−0.474311	+	0.821530i	−0.999567	−	0.0294137i	$-0.990636\pi$
$151$	−5.82843	+	10.0951i	−0.474311	+	0.821530i	0.525257	+	0.850944i	$0.323969\pi$
$152$	10.8126	−	6.24264i	0.877015	−	0.506345i
$153$			13.6569i			1.10409i
$154$	5.24264	+	0.717439i	0.422464	+	0.0578129i
$155$		0			0
$156$	−3.82843	−	6.63103i	−0.306519	−	0.530907i
$157$	−14.9941	−	8.65685i	−1.19666	−	0.690892i	−0.236851	−	0.971546i	$-0.576115\pi$
$157$	−14.9941	−	8.65685i	−1.19666	−	0.690892i	−0.959809	+	0.280654i	$0.909449\pi$
$158$	31.0028	+	17.8995i	2.46645	+	1.42401i
$159$	0.242641	+	0.420266i	0.0192427	+	0.0333293i
$160$		0			0
$161$	−0.414214	−	1.01461i	−0.0326446	−	0.0799626i
$162$			18.0711i			1.41980i
$163$	−10.6895	+	6.17157i	−0.837265	+	0.483395i	−0.856333	−	0.516423i	$-0.827263\pi$
$163$	−10.6895	+	6.17157i	−0.837265	+	0.483395i	0.0190689	+	0.999818i	$0.493930\pi$
$164$	−14.9853	+	25.9553i	−1.17015	+	2.02677i
$165$		0			0
$166$	−16.5711	−	28.7019i	−1.28616	−	2.22770i
$167$			22.4142i			1.73446i	0.497904	+	0.867232i	$0.334103\pi$
$167$			22.4142i			1.73446i	−0.497904	+	0.867232i	$0.665897\pi$
$168$	−3.82282	−	2.96447i	−0.294937	−	0.228714i
$169$	−10.3137			−0.793362
$170$		0			0
$171$	4.00000	−	6.92820i	0.305888	−	0.529813i
$172$	−11.8887	−	6.86396i	−0.906507	−	0.523372i
$173$	−2.86976	+	1.65685i	−0.218183	+	0.125968i	−0.605109	−	0.796143i	$-0.706870\pi$
$173$	−2.86976	+	1.65685i	−0.218183	+	0.125968i	0.386925	+	0.922111i	$0.373537\pi$
$174$	−1.00000			−0.0758098
$175$		0			0
$176$	−2.48528			−0.187335
$177$	−1.60896	+	0.928932i	−0.120937	+	0.0698228i
$178$	−18.0995	−	10.4497i	−1.35661	−	0.783242i
$179$	−5.00000	+	8.66025i	−0.373718	+	0.647298i	−0.990134	−	0.140122i	$-0.955250\pi$
$179$	−5.00000	+	8.66025i	−0.373718	+	0.647298i	0.616417	+	0.787420i	$0.288584\pi$
$180$		0			0
$181$	2.65685			0.197482			0.0987412	−	0.995113i	$-0.468518\pi$
$181$	2.65685			0.197482			0.0987412	+	0.995113i	$0.468518\pi$
$182$	−28.5533	+	11.6569i	−2.11651	+	0.864064i
$183$			2.27208i			0.167957i
$184$	0.914214	+	1.58346i	0.0673967	+	0.116735i
$185$		0			0
$186$	−3.00000	+	5.19615i	−0.219971	+	0.381000i
$187$	−3.46410	+	2.00000i	−0.253320	+	0.146254i
$188$		−	7.65685i		−	0.558433i
$189$	−6.32843	−	0.866025i	−0.460325	−	0.0629941i
$190$		0			0
$191$	6.41421	+	11.1097i	0.464116	+	0.803873i	0.999161	−	0.0409507i	$-0.0130387\pi$
$191$	6.41421	+	11.1097i	0.464116	+	0.803873i	−0.535045	+	0.844824i	$0.679705\pi$
$192$	−3.52565	−	2.03553i	−0.254442	−	0.146902i
$193$	−1.73205	−	1.00000i	−0.124676	−	0.0719816i	0.436365	−	0.899770i	$-0.356266\pi$
$193$	−1.73205	−	1.00000i	−0.124676	−	0.0719816i	−0.561041	+	0.827788i	$0.689599\pi$
$194$	14.0711	+	24.3718i	1.01024	+	1.74979i
$195$		0			0
$196$	−19.1421	+	18.7554i	−1.36730	+	1.33967i
$197$		−	12.3431i		−	0.879413i	−0.898142	−	0.439706i	$-0.855083\pi$
$197$		−	12.3431i		−	0.879413i	0.898142	−	0.439706i	$-0.144917\pi$
$198$	−4.89898	+	2.82843i	−0.348155	+	0.201008i
$199$	−4.82843	+	8.36308i	−0.342278	+	0.592843i	−0.984855	−	0.173378i	$-0.944532\pi$
$199$	−4.82843	+	8.36308i	−0.342278	+	0.592843i	0.642577	+	0.766221i	$0.277865\pi$
$200$		0			0
$201$	1.98528	+	3.43861i	0.140031	+	0.242541i
$202$		−	24.8995i		−	1.75192i
$203$	−0.358719	+	2.62132i	−0.0251772	+	0.183981i
$204$	7.65685			0.536087
$205$		0			0
$206$	2.91421	−	5.04757i	0.203043	−	0.351681i
$207$	1.01461	+	0.585786i	0.0705204	+	0.0407150i
$208$	12.5446	−	7.24264i	0.869813	−	0.502187i
$209$	2.34315			0.162079
$210$		0			0
$211$	20.4853			1.41026			0.705132	−	0.709076i	$-0.250888\pi$
$211$	20.4853			1.41026			0.705132	+	0.709076i	$0.250888\pi$
$212$	−3.88437	+	2.24264i	−0.266779	+	0.154025i
$213$	−1.60896	−	0.928932i	−0.110244	−	0.0636494i
$214$	13.5711	−	23.5058i	0.927699	−	1.60682i
$215$		0			0
$216$	10.6569			0.725107
$217$	12.5446	+	9.72792i	0.851584	+	0.660374i
$218$			32.5563i			2.20499i
$219$	0.171573	+	0.297173i	0.0115938	+	0.0200811i
$220$		0			0
$221$	11.6569	−	20.1903i	0.784125	−	1.35814i
$222$		0			0
$223$		−	0.343146i		−	0.0229787i	−0.999934	−	0.0114894i	$-0.996343\pi$
$223$		−	0.343146i		−	0.0229787i	0.999934	−	0.0114894i	$-0.00365726\pi$
$224$	−2.57107	+	3.31552i	−0.171787	+	0.221527i
$225$		0			0
$226$	5.41421	+	9.37769i	0.360148	+	0.623795i
$227$	6.03668	+	3.48528i	0.400669	+	0.231326i	0.686773	−	0.726872i	$-0.259027\pi$
$227$	6.03668	+	3.48528i	0.400669	+	0.231326i	−0.286104	+	0.958199i	$0.592360\pi$
$228$	−3.88437	−	2.24264i	−0.257249	−	0.148523i
$229$	−5.82843	−	10.0951i	−0.385153	−	0.667105i	0.606637	−	0.794979i	$-0.292518\pi$
$229$	−5.82843	−	10.0951i	−0.385153	−	0.667105i	−0.991790	+	0.127874i	$0.959185\pi$
$230$		0			0
$231$	−0.343146	−	0.840532i	−0.0225773	−	0.0553029i
$232$		−	4.41421i		−	0.289807i
$233$	14.5738	−	8.41421i	0.954764	−	0.551233i	0.0602067	−	0.998186i	$-0.480824\pi$
$233$	14.5738	−	8.41421i	0.954764	−	0.551233i	0.894558	+	0.446952i	$0.147491\pi$
$234$	16.4853	−	28.5533i	1.07768	−	1.86659i
$235$		0			0
$236$	−8.58579	−	14.8710i	−0.558887	−	0.968021i
$237$		−	6.14214i		−	0.398975i
$238$	4.18154	−	30.5563i	0.271049	−	1.98067i
$239$	21.3137			1.37867			0.689335	−	0.724443i	$-0.257903\pi$
$239$	21.3137			1.37867			0.689335	+	0.724443i	$0.257903\pi$
$240$		0			0
$241$	−13.8284	+	23.9515i	−0.890767	+	1.54285i	−0.0518100	+	0.998657i	$0.516499\pi$
$241$	−13.8284	+	23.9515i	−0.890767	+	1.54285i	−0.838957	+	0.544197i	$0.816834\pi$
$242$	21.5636	+	12.4497i	1.38616	+	0.800300i
$243$	8.95743	−	5.17157i	0.574619	−	0.331757i
$244$	−21.0000			−1.34439
$245$		0			0
$246$	7.82843			0.499122
$247$	−11.8272	+	6.82843i	−0.752546	+	0.434482i
$248$	−22.9369	−	13.2426i	−1.45650	−	0.840909i
$249$	−2.84315	+	4.92447i	−0.180177	+	0.312076i
$250$		0			0
$251$	−9.31371			−0.587876			−0.293938	−	0.955824i	$-0.594966\pi$
$251$	−9.31371			−0.587876			−0.293938	+	0.955824i	$0.594966\pi$
$252$	3.88437	−	28.3848i	0.244692	−	1.78807i
$253$			0.343146i			0.0215734i
$254$	−11.2426	−	19.4728i	−0.705426	−	1.22183i
$255$		0			0
$256$	14.9853	−	25.9553i	0.936580	−	1.62220i
$257$	5.49333	−	3.17157i	0.342664	−	0.197837i	−0.318785	−	0.947827i	$-0.603275\pi$
$257$	5.49333	−	3.17157i	0.342664	−	0.197837i	0.661450	+	0.749990i	$0.269942\pi$
$258$			3.58579i			0.223241i
$259$		0			0
$260$		0			0
$261$	−1.41421	−	2.44949i	−0.0875376	−	0.151620i
$262$	40.3805	+	23.3137i	2.49472	+	1.44033i
$263$	−25.1508	−	14.5208i	−1.55086	−	0.895392i	−0.998072	−	0.0620729i	$-0.980229\pi$
$263$	−25.1508	−	14.5208i	−1.55086	−	0.895392i	−0.552793	−	0.833319i	$-0.686438\pi$
$264$	0.757359	+	1.31178i	0.0466122	+	0.0807348i
$265$		0			0
$266$	−11.0711	+	14.2767i	−0.678811	+	0.875359i
$267$			3.58579i			0.219447i
$268$	−31.7818	+	18.3492i	−1.94138	+	1.12086i
$269$	10.2279	−	17.7153i	0.623607	−	1.08012i	−0.365201	−	0.930929i	$-0.619000\pi$
$269$	10.2279	−	17.7153i	0.623607	−	1.08012i	0.988808	−	0.149191i	$-0.0476669\pi$
$270$		0			0
$271$	−8.24264	−	14.2767i	−0.500705	−	0.867246i	−1.00000		0.000813982i	$-0.999741\pi$
$271$	−8.24264	−	14.2767i	−0.500705	−	0.867246i	0.499295	−	0.866432i	$-0.333592\pi$
$272$			14.4853i			0.878299i
$273$	4.18154	+	3.24264i	0.253078	+	0.196254i
$274$	23.3137			1.40843
$275$		0			0
$276$	0.328427	−	0.568852i	0.0197690	−	0.0342409i
$277$	−13.9795	−	8.07107i	−0.839947	−	0.484943i	0.0172994	−	0.999850i	$-0.494493\pi$
$277$	−13.9795	−	8.07107i	−0.839947	−	0.484943i	−0.857246	+	0.514907i	$0.827826\pi$
$278$	33.7495	−	19.4853i	2.02416	−	1.16865i
$279$	−16.9706			−1.01600
$280$		0			0
$281$	−30.2843			−1.80661			−0.903304	−	0.429001i	$-0.858866\pi$
$281$	−30.2843			−1.80661			−0.903304	+	0.429001i	$0.858866\pi$
$282$	−1.73205	+	1.00000i	−0.103142	+	0.0595491i
$283$	12.1244	+	7.00000i	0.720718	+	0.416107i	0.815017	−	0.579437i	$-0.196728\pi$
$283$	12.1244	+	7.00000i	0.720718	+	0.416107i	−0.0942988	+	0.995544i	$0.530061\pi$
$284$	8.58579	−	14.8710i	0.509473	−	0.882433i
$285$		0			0
$286$	9.65685			0.571022
$287$	2.80821	−	20.5208i	0.165763	−	1.21131i
$288$		−	4.48528i		−	0.264298i
$289$	3.15685	+	5.46783i	0.185697	+	0.321637i
$290$		0			0
$291$	2.41421	−	4.18154i	0.141524	−	0.245126i
$292$	−2.74666	+	1.58579i	−0.160736	+	0.0928011i
$293$			16.0000i			0.934730i	0.884064	+	0.467365i	$0.154797\pi$
$293$			16.0000i			0.934730i	−0.884064	+	0.467365i	$0.845203\pi$
$294$	6.74264	+	1.88064i	0.393239	+	0.109681i
$295$		0			0
$296$		0			0
$297$	1.73205	+	1.00000i	0.100504	+	0.0580259i
$298$	−4.54026	−	2.62132i	−0.263010	−	0.151849i
$299$	−1.00000	−	1.73205i	−0.0578315	−	0.100167i
$300$		0			0
$301$	9.39949	+	1.28629i	0.541778	+	0.0741406i
$302$			28.1421i			1.61940i
$303$	−3.69973	+	2.13604i	−0.212544	+	0.122712i
$304$	4.24264	−	7.34847i	0.243332	−	0.421464i
$305$		0			0
$306$	16.4853	+	28.5533i	0.942401	+	1.63229i
$307$		−	4.75736i		−	0.271517i	−0.990742	−	0.135758i	$-0.956653\pi$
$307$		−	4.75736i		−	0.271517i	0.990742	−	0.135758i	$-0.0433471\pi$
$308$	7.76874	−	3.17157i	0.442665	−	0.180717i
$309$	−1.00000			−0.0568880
$310$		0			0
$311$	6.58579	−	11.4069i	0.373446	−	0.646827i	−0.616647	−	0.787239i	$-0.711510\pi$
$311$	6.58579	−	11.4069i	0.373446	−	0.646827i	0.990093	+	0.140413i	$0.0448429\pi$
$312$	−7.64564	−	4.41421i	−0.432849	−	0.249906i
$313$	5.49333	−	3.17157i	0.310501	−	0.179268i	−0.336650	−	0.941630i	$-0.609294\pi$
$313$	5.49333	−	3.17157i	0.310501	−	0.179268i	0.647151	+	0.762362i	$0.275960\pi$
$314$	−41.7990			−2.35885
$315$		0			0
$316$	56.7696			3.19354
$317$	−11.9503	+	6.89949i	−0.671194	+	0.387514i	−0.796529	−	0.604600i	$-0.793333\pi$
$317$	−11.9503	+	6.89949i	−0.671194	+	0.387514i	0.125335	+	0.992115i	$0.460000\pi$
$318$	1.01461	+	0.585786i	0.0568966	+	0.0328493i
$319$	0.414214	−	0.717439i	0.0231915	−	0.0401689i
$320$		0			0
$321$	−4.65685			−0.259920
$322$	−2.09077	−	1.62132i	−0.116514	−	0.0903527i
$323$		−	13.6569i		−	0.759888i
$324$	14.3284	+	24.8176i	0.796024	+	1.37875i
$325$		0			0
$326$	−14.8995	+	25.8067i	−0.825207	+	1.42930i
$327$	4.83743	−	2.79289i	0.267511	−	0.154447i
$328$			34.5563i			1.90806i
$329$	2.00000	+	4.89898i	0.110264	+	0.270089i
$330$		0			0
$331$	−11.4853	−	19.8931i	−0.631288	−	1.09342i	−0.987289	−	0.158937i	$-0.949193\pi$
$331$	−11.4853	−	19.8931i	−0.631288	−	1.09342i	0.356001	−	0.934486i	$-0.384140\pi$
$332$	−45.5151	−	26.2782i	−2.49797	−	1.44220i
$333$		0			0
$334$	27.0563	+	46.8630i	1.48046	+	2.56423i
$335$		0			0
$336$	−3.25736	−	0.445759i	−0.177704	−	0.0243182i
$337$			9.17157i			0.499607i	0.968296	+	0.249804i	$0.0803661\pi$
$337$			9.17157i			0.499607i	−0.968296	+	0.249804i	$0.919634\pi$
$338$	−21.5636	+	12.4497i	−1.17290	+	0.677177i
$339$	0.928932	−	1.60896i	0.0504527	−	0.0873866i
$340$		0			0
$341$	−2.48528	−	4.30463i	−0.134586	−	0.233109i
$342$		−	19.3137i		−	1.04437i
$343$	7.34847	−	17.0000i	0.396780	−	0.917914i
$344$	−15.8284			−0.853412
$345$		0			0
$346$	−4.00000	+	6.92820i	−0.215041	+	0.372463i
$347$	−6.86666	−	3.96447i	−0.368621	−	0.212824i	0.304235	−	0.952597i	$-0.401599\pi$
$347$	−6.86666	−	3.96447i	−0.368621	−	0.212824i	−0.672856	+	0.739773i	$0.734933\pi$
$348$	−1.37333	+	0.792893i	−0.0736183	+	0.0425035i
$349$	15.3431			0.821300			0.410650	−	0.911793i	$-0.365302\pi$
$349$	15.3431			0.821300			0.410650	+	0.911793i	$0.365302\pi$
$350$		0			0
$351$	−11.6569			−0.622197
$352$	1.13770	−	0.656854i	0.0606399	−	0.0350104i
$353$	−23.2341	−	13.4142i	−1.23663	−	0.713967i	−0.268223	−	0.963357i	$-0.586436\pi$
$353$	−23.2341	−	13.4142i	−1.23663	−	0.713967i	−0.968403	+	0.249390i	$0.919770\pi$
$354$	−2.24264	+	3.88437i	−0.119195	+	0.206452i
$355$		0			0
$356$	−33.1421			−1.75653
$357$	−4.89898	+	2.00000i	−0.259281	+	0.105851i
$358$			24.1421i			1.27595i
$359$	−5.00000	−	8.66025i	−0.263890	−	0.457071i	0.703382	−	0.710812i	$-0.251672\pi$
$359$	−5.00000	−	8.66025i	−0.263890	−	0.457071i	−0.967272	+	0.253741i	$0.918339\pi$
$360$		0			0
$361$	5.50000	−	9.52628i	0.289474	−	0.501383i
$362$	5.55487	−	3.20711i	0.291958	−	0.168562i
$363$		−	4.27208i		−	0.224226i
$364$	−29.9706	+	38.6485i	−1.57088	+	2.02573i
$365$		0			0
$366$	2.74264	+	4.75039i	0.143360	+	0.248307i
$367$	2.38794	+	1.37868i	0.124650	+	0.0719665i	0.561028	−	0.827797i	$-0.310406\pi$
$367$	2.38794	+	1.37868i	0.124650	+	0.0719665i	−0.436379	+	0.899763i	$0.643739\pi$
$368$	1.07616	+	0.621320i	0.0560986	+	0.0323886i
$369$	11.0711	+	19.1757i	0.576337	+	0.998245i
$370$		0			0
$371$	1.89949	−	2.44949i	0.0986169	−	0.127171i
$372$			9.51472i			0.493315i
$373$	18.1610	−	10.4853i	0.940343	−	0.542907i	0.0502752	−	0.998735i	$-0.483990\pi$
$373$	18.1610	−	10.4853i	0.940343	−	0.542907i	0.890068	+	0.455828i	$0.150657\pi$
$374$	−4.82843	+	8.36308i	−0.249672	+	0.432445i
$375$		0			0
$376$	−4.41421	−	7.64564i	−0.227646	−	0.394294i
$377$			4.82843i			0.248677i
$378$	−14.2767	+	5.82843i	−0.734313	+	0.299782i
$379$	−26.8284			−1.37808			−0.689042	−	0.724722i	$-0.741968\pi$
$379$	−26.8284			−1.37808			−0.689042	+	0.724722i	$0.741968\pi$
$380$		0			0
$381$	−1.92893	+	3.34101i	−0.0988222	+	0.171165i
$382$	26.8213	+	15.4853i	1.37230	+	0.792296i
$383$	2.51104	−	1.44975i	0.128308	−	0.0740786i	−0.434472	−	0.900685i	$-0.643065\pi$
$383$	2.51104	−	1.44975i	0.128308	−	0.0740786i	0.562780	+	0.826607i	$0.309732\pi$
$384$	−8.51472			−0.434515
$385$		0			0
$386$	−4.82843			−0.245760
$387$	−8.78335	+	5.07107i	−0.446483	+	0.257777i
$388$	38.6485	+	22.3137i	1.96208	+	1.13281i
$389$	11.8284	−	20.4874i	0.599725	−	1.03875i	−0.393136	−	0.919480i	$-0.628610\pi$
$389$	11.8284	−	20.4874i	0.599725	−	1.03875i	0.992861	−	0.119274i	$-0.0380567\pi$
$390$		0			0
$391$	2.00000			0.101144
$392$	−8.30153	+	29.7635i	−0.419291	+	1.50328i
$393$		−	8.00000i		−	0.403547i
$394$	−14.8995	−	25.8067i	−0.750626	−	1.30012i
$395$		0			0
$396$	−4.48528	+	7.76874i	−0.225394	+	0.390394i
$397$	−14.3998	+	8.31371i	−0.722704	+	0.417253i	−0.815747	−	0.578409i	$-0.803674\pi$
$397$	−14.3998	+	8.31371i	−0.722704	+	0.417253i	0.0930434	+	0.995662i	$0.470340\pi$
$398$			23.3137i			1.16861i
$399$	3.07107	+	0.420266i	0.153746	+	0.0210396i
$400$		0			0
$401$	−15.1569	−	26.2524i	−0.756897	−	1.31098i	−0.944426	−	0.328725i	$-0.893381\pi$
$401$	−15.1569	−	26.2524i	−0.756897	−	1.31098i	0.187528	−	0.982259i	$-0.439952\pi$
$402$	8.30153	+	4.79289i	0.414043	+	0.239048i
$403$	25.0892	+	14.4853i	1.24978	+	0.721563i
$404$	−19.7426	−	34.1953i	−0.982233	−	1.70128i
$405$		0			0
$406$	2.41421	+	5.91359i	0.119815	+	0.293487i
$407$		0			0
$408$	7.64564	−	4.41421i	0.378516	−	0.218536i
$409$	−7.39949	+	12.8163i	−0.365881	+	0.633725i	−0.988917	−	0.148468i	$-0.952566\pi$
$409$	−7.39949	+	12.8163i	−0.365881	+	0.633725i	0.623036	+	0.782193i	$0.285899\pi$
$410$		0			0
$411$	−2.00000	−	3.46410i	−0.0986527	−	0.170872i
$412$		−	9.24264i		−	0.455352i
$413$	9.37769	+	7.27208i	0.461446	+	0.357836i
$414$	2.82843			0.139010
$415$		0			0
$416$	−3.82843	+	6.63103i	−0.187704	+	0.325113i
$417$	−5.79050	−	3.34315i	−0.283562	−	0.163715i
$418$	4.89898	−	2.82843i	0.239617	−	0.138343i
$419$	0.686292			0.0335275			0.0167638	−	0.999859i	$-0.494664\pi$
$419$	0.686292			0.0335275			0.0167638	+	0.999859i	$0.494664\pi$
$420$		0			0
$421$	13.4853			0.657232			0.328616	−	0.944464i	$-0.393418\pi$
$421$	13.4853			0.657232			0.328616	+	0.944464i	$0.393418\pi$
$422$	42.8300	−	24.7279i	2.08493	−	1.20374i
$423$	−4.89898	−	2.82843i	−0.238197	−	0.137523i
$424$	−2.58579	+	4.47871i	−0.125577	+	0.217506i
$425$		0			0
$426$	−4.48528			−0.217313
$427$	13.4361	−	5.48528i	0.650220	−	0.265451i
$428$		−	43.0416i		−	2.08050i
$429$	−0.828427	−	1.43488i	−0.0399968	−	0.0692766i
$430$		0			0
$431$	−8.89949	+	15.4144i	−0.428674	+	0.742484i	−0.996756	−	0.0804875i	$-0.974352\pi$
$431$	−8.89949	+	15.4144i	−0.428674	+	0.742484i	0.568082	+	0.822972i	$0.307686\pi$
$432$	6.27231	−	3.62132i	0.301777	−	0.174231i
$433$		−	7.79899i		−	0.374796i	−0.982284	−	0.187398i	$-0.939995\pi$
$433$		−	7.79899i		−	0.374796i	0.982284	−	0.187398i	$-0.0600053\pi$
$434$	37.9706	+	5.19615i	1.82265	+	0.249423i
$435$		0			0
$436$	25.8137	+	44.7107i	1.23625	+	2.14125i
$437$	−1.01461	−	0.585786i	−0.0485355	−	0.0280220i
$438$	0.717439	+	0.414214i	0.0342806	+	0.0197919i
$439$	−16.9706	−	29.3939i	−0.809961	−	1.40289i	−0.912890	−	0.408205i	$-0.866155\pi$
$439$	−16.9706	−	29.3939i	−0.809961	−	1.40289i	0.102930	−	0.994689i	$-0.467178\pi$
$440$		0			0
$441$	4.92893	+	19.1757i	0.234711	+	0.913126i
$442$		−	56.2843i		−	2.67717i
$443$	−26.1654	+	15.1066i	−1.24316	+	0.717736i	−0.969735	−	0.244158i	$-0.921488\pi$
$443$	−26.1654	+	15.1066i	−1.24316	+	0.717736i	−0.273420	+	0.961895i	$0.588155\pi$
$444$		0			0
$445$		0			0
$446$	−0.414214	−	0.717439i	−0.0196136	−	0.0339717i
$447$			0.899495i			0.0425447i
$448$	−3.52565	+	25.7635i	−0.166571	+	1.21721i
$449$	−3.82843			−0.180675			−0.0903373	−	0.995911i	$-0.528795\pi$
$449$	−3.82843			−0.180675			−0.0903373	+	0.995911i	$0.528795\pi$
$450$		0			0
$451$	−3.24264	+	5.61642i	−0.152690	+	0.264467i
$452$	14.8710	+	8.58579i	0.699474	+	0.403841i
$453$	4.18154	−	2.41421i	0.196466	−	0.113430i
$454$	16.8284			0.789797
$455$		0			0
$456$	−5.17157			−0.242181
$457$	21.0308	−	12.1421i	0.983779	−	0.567985i	0.0803702	−	0.996765i	$-0.474390\pi$
$457$	21.0308	−	12.1421i	0.983779	−	0.567985i	0.903409	+	0.428780i	$0.141056\pi$
$458$	−24.3718	−	14.0711i	−1.13882	−	0.657498i
$459$	5.82843	−	10.0951i	0.272048	−	0.471200i
$460$		0			0
$461$	41.3137			1.92417			0.962086	−	0.272748i	$-0.0879324\pi$
$461$	41.3137			1.92417			0.962086	+	0.272748i	$0.0879324\pi$
$462$	−1.73205	−	1.34315i	−0.0805823	−	0.0624888i
$463$			37.0416i			1.72147i	0.509053	+	0.860735i	$0.329996\pi$
$463$			37.0416i			1.72147i	−0.509053	+	0.860735i	$0.670004\pi$
$464$	−1.50000	−	2.59808i	−0.0696358	−	0.120613i
$465$		0			0
$466$	20.3137	−	35.1844i	0.941014	−	1.62988i
$467$	−2.68512	+	1.55025i	−0.124252	+	0.0717371i	−0.560838	−	0.827926i	$-0.689521\pi$
$467$	−2.68512	+	1.55025i	−0.124252	+	0.0717371i	0.436586	+	0.899663i	$0.356188\pi$
$468$		−	52.2843i		−	2.41684i
$469$	15.5416	−	20.0417i	0.717646	−	0.925439i
$470$		0			0
$471$	3.58579	+	6.21076i	0.165224	+	0.286177i
$472$	−17.1464	−	9.89949i	−0.789228	−	0.455661i
$473$	−2.57258	−	1.48528i	−0.118287	−	0.0682933i
$474$	−7.41421	−	12.8418i	−0.340546	−	0.589843i
$475$		0			0
$476$	−18.4853	−	45.2795i	−0.847271	−	2.07538i
$477$			3.31371i			0.151724i
$478$	44.5621	−	25.7279i	2.03822	−	1.17677i
$479$	−17.8284	+	30.8797i	−0.814602	+	1.41093i	0.0950120	+	0.995476i	$0.469711\pi$
$479$	−17.8284	+	30.8797i	−0.814602	+	1.41093i	−0.909614	+	0.415455i	$0.863622\pi$
$480$		0			0
$481$		0			0
$482$			66.7696i			3.04127i
$483$	−0.0615465	+	0.449747i	−0.00280046	+	0.0204642i
$484$	39.4853			1.79479
$485$		0			0
$486$	12.4853	−	21.6251i	0.566344	−	0.980936i
$487$	−3.76127	−	2.17157i	−0.170440	−	0.0984034i	0.412353	−	0.911024i	$-0.364707\pi$
$487$	−3.76127	−	2.17157i	−0.170440	−	0.0984034i	−0.582793	+	0.812621i	$0.698040\pi$
$488$	−20.9692	+	12.1066i	−0.949233	+	0.548040i
$489$	5.11270			0.231204
$490$		0			0
$491$	9.31371			0.420322			0.210161	−	0.977667i	$-0.432601\pi$
$491$	9.31371			0.420322			0.210161	+	0.977667i	$0.432601\pi$
$492$	10.7510	−	6.20711i	0.484694	−	0.279838i
$493$	−4.18154	−	2.41421i	−0.188327	−	0.108731i
$494$	−16.4853	+	28.5533i	−0.741708	+	1.28468i
$495$		0			0
$496$	−18.0000			−0.808224
$497$	−1.60896	+	11.7574i	−0.0721716	+	0.527390i
$498$			13.7279i			0.615163i
$499$	−0.414214	−	0.717439i	−0.0185427	−	0.0321170i	0.856605	−	0.515973i	$-0.172569\pi$
$499$	−0.414214	−	0.717439i	−0.0185427	−	0.0321170i	−0.875148	+	0.483856i	$0.839236\pi$
$500$		0			0
$501$	4.64214	−	8.04041i	0.207395	−	0.359219i
$502$	−19.4728	+	11.2426i	−0.869115	+	0.501784i
$503$			15.8701i			0.707611i	0.935319	+	0.353805i	$0.115113\pi$
$503$			15.8701i			0.707611i	−0.935319	+	0.353805i	$0.884887\pi$
$504$	−12.4853	−	30.5826i	−0.556139	−	1.36226i
$505$		0			0
$506$	0.414214	+	0.717439i	0.0184140	+	0.0318941i
$507$	3.69973	+	2.13604i	0.164311	+	0.0948648i
$508$	−30.8797	−	17.8284i	−1.37007	−	0.791009i
$509$	6.67157	+	11.5555i	0.295712	+	0.512189i	0.975150	−	0.221544i	$-0.0711097\pi$
$509$	6.67157	+	11.5555i	0.295712	+	0.512189i	−0.679438	+	0.733733i	$0.737776\pi$
$510$		0			0
$511$	1.34315	−	1.73205i	0.0594173	−	0.0766214i
$512$		−	31.2426i		−	1.38074i
$513$	−5.91359	+	3.41421i	−0.261091	+	0.150741i
$514$	7.65685	−	13.2621i	0.337729	−	0.584964i
$515$		0			0
$516$	2.84315	+	4.92447i	0.125163	+	0.216788i
$517$		−	1.65685i		−	0.0728684i
$518$		0			0
$519$	1.37258			0.0602497
$520$		0			0
$521$	−7.48528	+	12.9649i	−0.327936	+	0.568002i	−0.982102	−	0.188349i	$-0.939686\pi$
$521$	−7.48528	+	12.9649i	−0.327936	+	0.568002i	0.654166	+	0.756351i	$0.273020\pi$
$522$	−5.91359	−	3.41421i	−0.258831	−	0.149436i
$523$	−30.8797	+	17.8284i	−1.35028	+	0.779583i	−0.988288	−	0.152600i	$-0.951235\pi$
$523$	−30.8797	+	17.8284i	−1.35028	+	0.779583i	−0.361989	+	0.932182i	$0.617902\pi$
$524$	73.9411			3.23013
$525$		0			0
$526$	−70.1127			−3.05706
$527$	−25.0892	+	14.4853i	−1.09290	+	0.630989i
$528$	0.891519	+	0.514719i	0.0387984	+	0.0224003i
$529$	−11.4142	+	19.7700i	−0.496270	+	0.859565i
$530$		0			0
$531$	−12.6863			−0.550538
$532$	−3.88437	+	28.3848i	−0.168409	+	1.23064i
$533$		−	37.7990i		−	1.63726i
$534$	4.32843	+	7.49706i	0.187309	+	0.324429i
$535$		0			0
$536$	−21.1569	+	36.6447i	−0.913837	+	1.58281i
$537$	3.58719	−	2.07107i	0.154799	−	0.0893732i
$538$		−	49.3848i		−	2.12913i
$539$	−4.14214	+	4.05845i	−0.178414	+	0.174810i
$540$		0			0
$541$	−3.67157	−	6.35935i	−0.157853	−	0.273410i	0.776241	−	0.630436i	$-0.217124\pi$
$541$	−3.67157	−	6.35935i	−0.157853	−	0.273410i	−0.934094	+	0.357026i	$0.883791\pi$
$542$	−34.4669	−	19.8995i	−1.48048	−	0.854756i
$543$	−0.953065	−	0.550253i	−0.0408999	−	0.0236136i
$544$	−3.82843	−	6.63103i	−0.164142	−	0.284303i
$545$		0			0
$546$	12.6569	+	1.73205i	0.541663	+	0.0741249i
$547$			24.8995i			1.06463i	0.846548	+	0.532313i	$0.178677\pi$
$547$			24.8995i			1.06463i	−0.846548	+	0.532313i	$0.821323\pi$
$548$	32.0174	−	18.4853i	1.36772	−	0.789652i
$549$	−7.75736	+	13.4361i	−0.331076	+	0.573441i
$550$		0			0
$551$	1.41421	+	2.44949i	0.0602475	+	0.104352i
$552$		−	0.757359i		−	0.0322354i
$553$	−36.3221	+	14.8284i	−1.54457	+	0.630569i
$554$	−38.9706			−1.65570
$555$		0			0
$556$	30.8995	−	53.5195i	1.31043	−	2.26973i
$557$	−19.2987	−	11.1421i	−0.817714	−	0.472107i	0.0319135	−	0.999491i	$-0.489840\pi$
$557$	−19.2987	−	11.1421i	−0.817714	−	0.472107i	−0.849628	+	0.527383i	$0.823173\pi$
$558$	−35.4815	+	20.4853i	−1.50205	+	0.867211i
$559$	17.3137			0.732292
$560$		0			0
$561$	1.65685			0.0699524
$562$	−63.3175	+	36.5563i	−2.67089	+	1.54204i
$563$	36.1374	+	20.8640i	1.52301	+	0.879311i	0.999630	+	0.0272129i	$0.00866320\pi$
$563$	36.1374	+	20.8640i	1.52301	+	0.879311i	0.523382	+	0.852098i	$0.324670\pi$
$564$	−1.58579	+	2.74666i	−0.0667737	+	0.115655i
$565$		0			0
$566$	33.7990			1.42068
$567$	−15.6500	−	12.1360i	−0.657238	−	0.509666i
$568$		−	19.7990i		−	0.830747i
$569$	3.82843	+	6.63103i	0.160496	+	0.277987i	0.935047	−	0.354525i	$-0.115357\pi$
$569$	3.82843	+	6.63103i	0.160496	+	0.277987i	−0.774551	+	0.632512i	$0.782024\pi$
$570$		0			0
$571$	−4.58579	+	7.94282i	−0.191909	+	0.332396i	−0.945883	−	0.324508i	$-0.894801\pi$
$571$	−4.58579	+	7.94282i	−0.191909	+	0.332396i	0.753974	+	0.656905i	$0.228135\pi$
$572$	13.2621	−	7.65685i	0.554515	−	0.320149i
$573$		−	5.31371i		−	0.221983i
$574$	−18.8995	−	46.2941i	−0.788850	−	1.93228i
$575$		0			0
$576$	−13.8995	−	24.0746i	−0.579146	−	1.00311i
$577$	38.0541	+	21.9706i	1.58421	+	0.914646i	0.994234	+	0.107228i	$0.0341976\pi$
$577$	38.0541	+	21.9706i	1.58421	+	0.914646i	0.589980	+	0.807418i	$0.299136\pi$
$578$	13.2005	+	7.62132i	0.549069	+	0.317005i
$579$	0.414214	+	0.717439i	0.0172141	+	0.0298157i
$580$		0			0
$581$	35.9853	+	4.92447i	1.49292	+	0.204302i
$582$		−	11.6569i		−	0.483192i
$583$	−0.840532	+	0.485281i	−0.0348113	+	0.0200983i
$584$	−1.82843	+	3.16693i	−0.0756609	+	0.131048i
$585$		0			0
$586$	19.3137	+	33.4523i	0.797842	+	1.38190i
$587$		−	34.2843i		−	1.41506i	−0.706682	−	0.707532i	$-0.749809\pi$
$587$		−	34.2843i		−	1.41506i	0.706682	−	0.707532i	$-0.250191\pi$
$588$	10.7510	−	2.76346i	0.443365	−	0.113963i
$589$	16.9706			0.699260
$590$		0			0
$591$	−2.55635	+	4.42773i	−0.105154	+	0.182132i
$592$		0			0
$593$	−3.63818	+	2.10051i	−0.149402	+	0.0862574i	−0.572838	−	0.819669i	$-0.694157\pi$
$593$	−3.63818	+	2.10051i	−0.149402	+	0.0862574i	0.423435	+	0.905926i	$0.360824\pi$
$594$	4.82843			0.198113
$595$		0			0
$596$	−8.31371			−0.340543
$597$	3.46410	−	2.00000i	0.141776	−	0.0818546i
$598$	−4.18154	−	2.41421i	−0.170996	−	0.0987245i
$599$	3.17157	−	5.49333i	0.129587	−	0.224451i	−0.793930	−	0.608010i	$-0.791968\pi$
$599$	3.17157	−	5.49333i	0.129587	−	0.224451i	0.923517	+	0.383558i	$0.125302\pi$
$600$		0			0
$601$	19.6569			0.801820			0.400910	−	0.916117i	$-0.368694\pi$
$601$	19.6569			0.801820			0.400910	+	0.916117i	$0.368694\pi$
$602$	21.2049	−	8.65685i	0.864246	−	0.352827i
$603$			27.1127i			1.10411i
$604$	22.3137	+	38.6485i	0.907932	+	1.57258i
$605$		0			0
$606$	−5.15685	+	8.93193i	−0.209483	+	0.362835i
$607$	33.0936	−	19.1066i	1.34323	−	0.775513i	0.355948	−	0.934506i	$-0.384158\pi$
$607$	33.0936	−	19.1066i	1.34323	−	0.775513i	0.987280	+	0.158993i	$0.0508246\pi$
$608$			4.48528i			0.181902i
$609$	0.671573	−	0.866025i	0.0272135	−	0.0350931i
$610$		0			0
$611$	4.82843	+	8.36308i	0.195337	+	0.338334i
$612$	45.2795	+	26.1421i	1.83032	+	1.05673i
$613$	30.7057	+	17.7279i	1.24019	+	0.716024i	0.969133	−	0.246539i	$-0.0792934\pi$
$613$	30.7057	+	17.7279i	1.24019	+	0.716024i	0.271057	+	0.962563i	$0.412627\pi$
$614$	−5.74264	−	9.94655i	−0.231754	−	0.401410i
$615$		0			0
$616$	5.92893	−	7.64564i	0.238883	−	0.308052i
$617$			11.3137i			0.455473i	0.973723	+	0.227736i	$0.0731324\pi$
$617$			11.3137i			0.455473i	−0.973723	+	0.227736i	$0.926868\pi$
$618$	−2.09077	+	1.20711i	−0.0841031	+	0.0485570i
$619$	12.7574	−	22.0964i	0.512762	−	0.888129i	−0.487129	−	0.873330i	$-0.661956\pi$
$619$	12.7574	−	22.0964i	0.512762	−	0.888129i	0.999890	−	0.0147990i	$-0.00471084\pi$
$620$		0			0
$621$	−0.500000	−	0.866025i	−0.0200643	−	0.0347524i
$622$		−	31.7990i		−	1.27502i
$623$	21.2049	−	8.65685i	0.849555	−	0.346830i
$624$	−6.00000			−0.240192
$625$		0			0
$626$	7.65685	−	13.2621i	0.306029	−	0.530059i
$627$	−0.840532	−	0.485281i	−0.0335676	−	0.0193803i
$628$	−57.4039	+	33.1421i	−2.29066	+	1.32252i
$629$		0			0
$630$		0			0
$631$	−20.1421			−0.801846			−0.400923	−	0.916112i	$-0.631310\pi$
$631$	−20.1421			−0.801846			−0.400923	+	0.916112i	$0.631310\pi$
$632$	56.6864	−	32.7279i	2.25486	−	1.30185i
$633$	−7.34847	−	4.24264i	−0.292075	−	0.168630i
$634$	−16.6569	+	28.8505i	−0.661528	+	1.14580i
$635$		0			0
$636$	1.85786			0.0736691
$637$	9.08052	−	32.5563i	0.359783	−	1.28993i
$638$		−	2.00000i		−	0.0791808i
$639$	−6.34315	−	10.9867i	−0.250931	−	0.434625i
$640$		0			0
$641$	−15.7426	+	27.2671i	−0.621797	+	1.07698i	0.367354	+	0.930081i	$0.380264\pi$
$641$	−15.7426	+	27.2671i	−0.621797	+	1.07698i	−0.989151	+	0.146903i	$0.953070\pi$
$642$	−9.73641	+	5.62132i	−0.384266	+	0.221856i
$643$		−	26.2843i		−	1.03655i	−0.855214	−	0.518275i	$-0.826574\pi$
$643$		−	26.2843i		−	1.03655i	0.855214	−	0.518275i	$-0.173426\pi$
$644$	−4.15685	−	0.568852i	−0.163803	−	0.0224159i
$645$		0			0
$646$	−16.4853	−	28.5533i	−0.648605	−	1.12342i
$647$	26.8828	+	15.5208i	1.05687	+	0.610186i	0.924566	−	0.381022i	$-0.124428\pi$
$647$	26.8828	+	15.5208i	1.05687	+	0.610186i	0.132308	+	0.991209i	$0.457761\pi$
$648$	28.6149	+	16.5208i	1.12410	+	0.648999i
$649$	−1.85786	−	3.21792i	−0.0729276	−	0.126314i
$650$		0			0
$651$	−2.48528	−	6.08767i	−0.0974059	−	0.238595i
$652$			47.2548i			1.85064i
$653$	16.6031	−	9.58579i	0.649728	−	0.375121i	−0.138624	−	0.990345i	$-0.544268\pi$
$653$	16.6031	−	9.58579i	0.649728	−	0.375121i	0.788352	+	0.615224i	$0.210935\pi$
$654$	6.74264	−	11.6786i	0.263658	−	0.456669i
$655$		0			0
$656$	11.7426	+	20.3389i	0.458473	+	0.794099i
$657$			2.34315i			0.0914148i
$658$	10.0951	+	7.82843i	0.393549	+	0.305184i
$659$	−21.1716			−0.824727			−0.412364	−	0.911019i	$-0.635297\pi$
$659$	−21.1716			−0.824727			−0.412364	+	0.911019i	$0.635297\pi$
$660$		0			0
$661$	−15.9142	+	27.5642i	−0.618991	+	1.07212i	0.370679	+	0.928761i	$0.379125\pi$
$661$	−15.9142	+	27.5642i	−0.618991	+	1.07212i	−0.989670	+	0.143363i	$0.954208\pi$
$662$	−48.0262	−	27.7279i	−1.86659	−	1.07768i
$663$	−8.36308	+	4.82843i	−0.324795	+	0.187521i
$664$	−60.5980			−2.35166
$665$		0			0
$666$		0			0
$667$	−0.358719	+	0.207107i	−0.0138897	+	0.00801921i
$668$	74.3147	+	42.9056i	2.87532	+	1.66007i
$669$	−0.0710678	+	0.123093i	−0.00274764	+	0.00475905i
$670$		0			0
$671$	−4.54416			−0.175425
$672$	1.60896	−	0.656854i	0.0620669	−	0.0253387i
$673$		−	29.6569i		−	1.14319i	−0.820537	−	0.571594i	$-0.806325\pi$
$673$		−	29.6569i		−	1.14319i	0.820537	−	0.571594i	$-0.193675\pi$
$674$	11.0711	+	19.1757i	0.426442	+	0.738619i
$675$		0			0
$676$	−19.7426	+	34.1953i	−0.759332	+	1.31520i
$677$	−24.3718	+	14.0711i	−0.936685	+	0.540795i	−0.888919	−	0.458064i	$-0.848543\pi$
$677$	−24.3718	+	14.0711i	−0.936685	+	0.540795i	−0.0477651	+	0.998859i	$0.515210\pi$
$678$		−	4.48528i		−	0.172256i
$679$	−30.5563	−	4.18154i	−1.17265	−	0.160473i
$680$		0			0
$681$	−1.44365	−	2.50048i	−0.0553208	−	0.0958185i
$682$	−10.3923	−	6.00000i	−0.397942	−	0.229752i
$683$	−30.1008	−	17.3787i	−1.15177	−	0.664977i	−0.202455	−	0.979292i	$-0.564892\pi$
$683$	−30.1008	−	17.3787i	−1.15177	−	0.664977i	−0.949319	+	0.314315i	$0.898225\pi$
$684$	−15.3137	−	26.5241i	−0.585534	−	1.01418i
$685$		0			0
$686$	−5.15685	−	44.4135i	−0.196890	−	1.69571i
$687$			4.82843i			0.184216i
$688$	−9.31615	+	5.37868i	−0.355175	+	0.205060i
$689$	2.82843	−	4.89898i	0.107754	−	0.186636i
$690$		0			0
$691$	−0.414214	−	0.717439i	−0.0157574	−	0.0272927i	0.858039	−	0.513584i	$-0.171683\pi$
$691$	−0.414214	−	0.717439i	−0.0157574	−	0.0272927i	−0.873797	+	0.486292i	$0.838349\pi$
$692$			12.6863i			0.482260i
$693$	0.840532	−	6.14214i	0.0319292	−	0.233320i
$694$	−19.1421			−0.726626
$695$		0			0
$696$	−0.914214	+	1.58346i	−0.0346532	+	0.0600211i
$697$	32.7349	+	18.8995i	1.23992	+	0.715869i
$698$	32.0790	−	18.5208i	1.21421	−	0.701023i
$699$	−6.97056			−0.263651
$700$		0			0
$701$	−3.20101			−0.120900			−0.0604502	−	0.998171i	$-0.519254\pi$
$701$	−3.20101			−0.120900			−0.0604502	+	0.998171i	$0.519254\pi$
$702$	−24.3718	+	14.0711i	−0.919854	+	0.531078i
$703$		0			0
$704$	4.07107	−	7.05130i	0.153434	−	0.265756i
$705$		0			0
$706$	−64.7696			−2.43763
$707$	21.5636	+	16.7218i	0.810982	+	0.628889i
$708$			7.11270i			0.267312i
$709$	7.84315	+	13.5847i	0.294556	+	0.510185i	0.974881	−	0.222725i	$-0.0714951\pi$
$709$	7.84315	+	13.5847i	0.294556	+	0.510185i	−0.680326	+	0.732910i	$0.738162\pi$
$710$		0			0
$711$	20.9706	−	36.3221i	0.786458	−	1.36218i
$712$	−33.0936	+	19.1066i	−1.24024	+	0.716050i
$713$			2.48528i			0.0930745i
$714$	−7.82843	+	10.0951i	−0.292972	+	0.377801i
$715$		0			0
$716$	19.1421	+	33.1552i	0.715375	+	1.23907i
$717$	−7.64564	−	4.41421i	−0.285532	−	0.164852i
$718$	−20.9077	−	12.0711i	−0.780269	−	0.450488i
$719$	10.5563	+	18.2841i	0.393685	+	0.681883i	0.992932	−	0.118681i	$-0.0378666\pi$
$719$	10.5563	+	18.2841i	0.393685	+	0.681883i	−0.599247	+	0.800564i	$0.704533\pi$
$720$		0			0
$721$	2.41421	+	5.91359i	0.0899100	+	0.220234i
$722$		−	26.5563i		−	0.988325i
$723$	9.92105	−	5.72792i	0.368968	−	0.213024i
$724$	5.08579	−	8.80884i	0.189012	−	0.327378i
$725$		0			0
$726$	−5.15685	−	8.93193i	−0.191389	−	0.331495i
$727$		−	37.5858i		−	1.39398i	−0.717081	−	0.696990i	$-0.754522\pi$
$727$		−	37.5858i		−	1.39398i	0.717081	−	0.696990i	$-0.245478\pi$
$728$	−7.64564	+	55.8701i	−0.283366	+	2.07068i
$729$	18.1716			0.673021
$730$		0			0
$731$	−8.65685	+	14.9941i	−0.320185	+	0.554577i
$732$	7.53311	+	4.34924i	0.278432	+	0.160753i
$733$	19.0526	−	11.0000i	0.703722	−	0.406294i	−0.105010	−	0.994471i	$-0.533487\pi$
$733$	19.0526	−	11.0000i	0.703722	−	0.406294i	0.808732	+	0.588177i	$0.200154\pi$
$734$	6.65685			0.245709
$735$		0			0
$736$	−0.656854			−0.0242120
$737$	−6.87722	+	3.97056i	−0.253326	+	0.146258i
$738$	46.2941	+	26.7279i	1.70411	+	0.983868i
$739$	−10.5563	+	18.2841i	−0.388322	+	0.672593i	−0.992224	−	0.124466i	$-0.960278\pi$
$739$	−10.5563	+	18.2841i	−0.388322	+	0.672593i	0.603902	+	0.797058i	$0.293612\pi$
$740$		0			0
$741$	5.65685			0.207810
$742$	1.01461	−	7.41421i	0.0372476	−	0.272184i
$743$			16.0711i			0.589590i	0.955560	+	0.294795i	$0.0952514\pi$
$743$			16.0711i			0.589590i	−0.955560	+	0.294795i	$0.904749\pi$
$744$	5.48528	+	9.50079i	0.201100	+	0.348316i
$745$		0			0
$746$	25.3137	−	43.8446i	0.926801	−	1.60527i
$747$	−33.6264	+	19.4142i	−1.23033	+	0.710329i
$748$			15.3137i			0.559925i
$749$	11.2426	+	27.5387i	0.410797	+	1.00624i
$750$		0			0
$751$	15.1716	+	26.2779i	0.553619	+	0.958895i	0.998010	+	0.0630625i	$0.0200868\pi$
$751$	15.1716	+	26.2779i	0.553619	+	0.958895i	−0.444391	+	0.895833i	$0.646580\pi$
$752$	−5.19615	−	3.00000i	−0.189484	−	0.109399i
$753$	3.34101	+	1.92893i	0.121753	+	0.0702942i
$754$	5.82843	+	10.0951i	0.212259	+	0.367643i
$755$		0			0
$756$	−14.9853	+	19.3242i	−0.545009	+	0.702816i
$757$		−	31.4558i		−	1.14328i	−0.820504	−	0.571641i	$-0.806307\pi$
$757$		−	31.4558i		−	1.14328i	0.820504	−	0.571641i	$-0.193693\pi$
$758$	−56.0921	+	32.3848i	−2.03736	+	1.17627i
$759$	0.0710678	−	0.123093i	0.00257960	−	0.00446800i
$760$		0			0
$761$	−4.65685	−	8.06591i	−0.168811	−	0.292389i	0.769191	−	0.639019i	$-0.220659\pi$
$761$	−4.65685	−	8.06591i	−0.168811	−	0.292389i	−0.938002	+	0.346630i	$0.887326\pi$
$762$			9.31371i			0.337400i
$763$	−28.1946	−	21.8640i	−1.02071	−	0.791529i
$764$	49.1127			1.77684
$765$		0			0
$766$	3.50000	−	6.06218i	0.126460	−	0.219035i
$767$	18.7554	+	10.8284i	0.677218	+	0.390992i
$768$	−10.7510	+	6.20711i	−0.387944	+	0.223980i
$769$	0.627417			0.0226252			0.0113126	−	0.999936i	$-0.496399\pi$
$769$	0.627417			0.0226252			0.0113126	+	0.999936i	$0.496399\pi$
$770$		0			0
$771$	−2.62742			−0.0946241
$772$	−6.63103	+	3.82843i	−0.238656	+	0.137788i
$773$	−32.1405	−	18.5563i	−1.15601	−	0.667425i	−0.205669	−	0.978622i	$-0.565937\pi$
$773$	−32.1405	−	18.5563i	−1.15601	−	0.667425i	−0.950346	+	0.311196i	$0.899270\pi$
$774$	−12.2426	+	21.2049i	−0.440053	+	0.762194i
$775$		0			0
$776$	51.4558			1.84716
$777$		0			0
$778$		−	57.1127i		−	2.04759i
$779$	−11.0711	−	19.1757i	−0.396662	−	0.687039i
$780$		0			0
$781$	1.85786	−	3.21792i	0.0664796	−	0.115146i
$782$	4.18154	−	2.41421i	0.149532	−	0.0863321i
$783$			2.41421i			0.0862770i
$784$	5.22792	+	20.3389i	0.186712	+	0.726388i
$785$		0			0
$786$	−9.65685	−	16.7262i	−0.344449	−	0.596602i
$787$	−2.21386	−	1.27817i	−0.0789157	−	0.0455620i	0.460023	−	0.887907i	$-0.347841\pi$
$787$	−2.21386	−	1.27817i	−0.0789157	−	0.0455620i	−0.538939	+	0.842345i	$0.681175\pi$
$788$	−40.9239	−	23.6274i	−1.45785	−	0.841692i
$789$	6.01472	+	10.4178i	0.214130	+	0.370883i
$790$		0			0
$791$	−11.7574	−	1.60896i	−0.418044	−	0.0572080i
$792$			10.3431i			0.367528i
$793$	22.9369	−	13.2426i	0.814514	−	0.470260i
$794$	−20.0711	+	34.7641i	−0.712296	+	1.23373i
$795$		0			0
$796$	18.4853	+	32.0174i	0.655193	+	1.13483i
$797$		−	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
$799$	−9.65685			−0.341635
$800$		0			0
$801$	−12.2426	+	21.2049i	−0.432572	+	0.749237i
$802$	−63.3790	−	36.5919i	−2.23799	−	1.29210i
$803$	−0.594346	+	0.343146i	−0.0209740	+	0.0121094i
$804$	15.2010			0.536098
$805$		0			0
$806$	69.9411			2.46357
$807$	−7.33791	+	4.23654i	−0.258307	+	0.149133i
$808$	−39.4275	−	22.7635i	−1.38705	−	0.800816i
$809$	17.8137	−	30.8542i	0.626297	−	1.08478i	−0.361992	−	0.932181i	$-0.617903\pi$
$809$	17.8137	−	30.8542i	0.626297	−	1.08478i	0.988289	−	0.152596i	$-0.0487634\pi$
$810$		0			0
$811$	−20.6274			−0.724327			−0.362163	−	0.932115i	$-0.617962\pi$
$811$	−20.6274			−0.724327			−0.362163	+	0.932115i	$0.617962\pi$
$812$	8.00436	+	6.20711i	0.280898	+	0.217827i
$813$			6.82843i			0.239483i
$814$		0			0
$815$		0			0
$816$	3.00000	−	5.19615i	0.105021	−	0.181902i
$817$	8.78335	−	5.07107i	0.307290	−	0.177414i
$818$			35.7279i			1.24920i
$819$	13.6569	+	33.4523i	0.477209	+	1.16892i
$820$		0			0
$821$	−23.9706	−	41.5182i	−0.836578	−	1.44900i	−0.892739	−	0.450575i	$-0.851219\pi$
$821$	−23.9706	−	41.5182i	−0.836578	−	1.44900i	0.0561604	−	0.998422i	$-0.482114\pi$
$822$	−8.36308	−	4.82843i	−0.291696	−	0.168411i
$823$	1.79360	+	1.03553i	0.0625209	+	0.0360964i	0.530935	−	0.847413i	$-0.321841\pi$
$823$	1.79360	+	1.03553i	0.0625209	+	0.0360964i	−0.468414	+	0.883509i	$0.655174\pi$
$824$	−5.32843	−	9.22911i	−0.185625	−	0.321511i
$825$		0			0
$826$	28.3848	+	3.88437i	0.987633	+	0.135154i
$827$		−	26.2132i		−	0.911522i	−0.890102	−	0.455761i	$-0.849367\pi$
$827$		−	26.2132i		−	0.911522i	0.890102	−	0.455761i	$-0.150633\pi$
$828$	3.88437	−	2.24264i	0.134991	−	0.0779372i
$829$	14.6569	−	25.3864i	0.509054	−	0.881707i	−0.490891	−	0.871221i	$-0.663329\pi$
$829$	14.6569	−	25.3864i	0.509054	−	0.881707i	0.999945	−	0.0104859i	$-0.00333784\pi$
$830$		0			0
$831$	3.34315	+	5.79050i	0.115972	+	0.200870i
$832$			47.4558i			1.64524i
$833$	23.6544	+	24.1421i	0.819575	+	0.836475i
$834$	−16.1421			−0.558956
$835$		0			0
$836$	4.48528	−	7.76874i	0.155127	−	0.268687i
$837$	12.5446	+	7.24264i	0.433606	+	0.250342i
$838$	1.43488	−	0.828427i	0.0495670	−	0.0286175i
$839$	−15.1716			−0.523781			−0.261890	−	0.965098i	$-0.584346\pi$
$839$	−15.1716			−0.523781			−0.261890	+	0.965098i	$0.584346\pi$
$840$		0			0
$841$	−28.0000			−0.965517
$842$	28.1946	−	16.2782i	0.971651	−	0.560983i
$843$	10.8636	+	6.27208i	0.374161	+	0.216022i
$844$	39.2132	−	67.9193i	1.34977	−	2.33788i
$845$		0			0
$846$	−13.6569			−0.469532
$847$	−25.2633	+	10.3137i	−0.868058	+	0.354383i
$848$			3.51472i			0.120696i
$849$	−2.89949	−	5.02207i	−0.0995104	−	0.172357i
$850$		0			0
$851$		0			0
$852$	−6.15978	+	3.55635i	−0.211030	+	0.121839i
$853$		−	2.54416i		−	0.0871102i	−0.999051	−	0.0435551i	$-0.986132\pi$
$853$		−	2.54416i		−	0.0871102i	0.999051	−	0.0435551i	$-0.0138684\pi$
$854$	21.4706	−	27.6873i	0.734708	−	0.947441i
$855$		0			0
$856$	−24.8137	−	42.9786i	−0.848115	−	1.46898i
$857$	−29.6910	−	17.1421i	−1.01423	−	0.585564i	−0.101800	−	0.994805i	$-0.532460\pi$
$857$	−29.6910	−	17.1421i	−1.01423	−	0.585564i	−0.912426	+	0.409241i	$0.865794\pi$
$858$	−3.46410	−	2.00000i	−0.118262	−	0.0682789i
$859$	0.686292	+	1.18869i	0.0234160	+	0.0405576i	0.877496	−	0.479584i	$-0.159212\pi$
$859$	0.686292	+	1.18869i	0.0234160	+	0.0405576i	−0.854080	+	0.520142i	$0.825879\pi$
$860$		0			0
$861$	−5.25736	+	6.77962i	−0.179170	+	0.231049i
$862$			42.9706i			1.46358i
$863$	−12.6062	+	7.27817i	−0.429119	+	0.247752i	−0.698971	−	0.715150i	$-0.746358\pi$
$863$	−12.6062	+	7.27817i	−0.429119	+	0.247752i	0.269852	+	0.962902i	$0.413025\pi$
$864$	−1.91421	+	3.31552i	−0.0651229	+	0.112796i
$865$		0			0
$866$	−9.41421	−	16.3059i	−0.319908	−	0.554097i
$867$		−	2.61522i		−	0.0888177i
$868$	56.2662	−	22.9706i	1.90980	−	0.779672i
$869$	12.2843			0.416715
$870$		0			0
$871$	23.1421	−	40.0834i	0.784141	−	1.35817i
$872$	51.5518	+	29.7635i	1.74576	+	1.00792i
$873$	28.5533	−	16.4853i	0.966384	−	0.557942i
$874$	−2.82843			−0.0956730
$875$		0			0
$876$	1.31371			0.0443861
$877$	21.7992	−	12.5858i	0.736107	−	0.424992i	−0.0845449	−	0.996420i	$-0.526944\pi$
$877$	21.7992	−	12.5858i	0.736107	−	0.424992i	0.820652	+	0.571428i	$0.193610\pi$
$878$	−70.9631	−	40.9706i	−2.39489	−	1.38269i
$879$	3.31371	−	5.73951i	0.111769	−	0.193589i
$880$		0			0
$881$	1.82843			0.0616013			0.0308006	−	0.999526i	$-0.490194\pi$
$881$	1.82843			0.0616013			0.0308006	+	0.999526i	$0.490194\pi$
$882$	33.4523	+	34.1421i	1.12640	+	1.14963i
$883$		−	18.2843i		−	0.615315i	−0.951497	−	0.307657i	$-0.900455\pi$
$883$		−	18.2843i		−	0.615315i	0.951497	−	0.307657i	$-0.0995450\pi$
$884$	−44.6274	−	77.2970i	−1.50098	−	2.59978i
$885$		0			0
$886$	−36.4706	+	63.1689i	−1.22525	+	2.12220i
$887$	25.9192	−	14.9645i	0.870282	−	0.502458i	0.00284012	−	0.999996i	$-0.499096\pi$
$887$	25.9192	−	14.9645i	0.870282	−	0.502458i	0.867442	+	0.497538i	$0.165763\pi$
$888$		0			0
$889$	24.4142	+	3.34101i	0.818826	+	0.112054i
$890$		0			0
$891$	3.10051	+	5.37023i	0.103871	+	0.179910i
$892$	−1.13770	−	0.656854i	−0.0380932	−	0.0219931i
$893$	4.89898	+	2.82843i	0.163938	+	0.0946497i
$894$	1.08579	+	1.88064i	0.0363141	+	0.0628979i
$895$		0			0
$896$	20.5563	+	50.3526i	0.686739	+	1.68216i
$897$			0.828427i			0.0276604i
$898$	−8.00436	+	4.62132i	−0.267109	+	0.154215i
$899$	3.00000	−	5.19615i	0.100056	−	0.173301i
$900$		0			0
$901$	2.82843	+	4.89898i	0.0942286	+	0.163209i
$902$			15.6569i			0.521316i
$903$	−3.10538	−	2.40812i	−0.103341	−	0.0801371i
$904$	19.7990			0.658505
$905$		0			0
$906$	5.82843	−	10.0951i	0.193637	−	0.335388i
$907$	12.3090	+	7.10660i	0.408713	+	0.235971i	0.690237	−	0.723584i	$-0.257506\pi$
$907$	12.3090	+	7.10660i	0.408713	+	0.235971i	−0.281523	+	0.959554i	$0.590840\pi$
$908$	23.1110	−	13.3431i	0.766966	−	0.442808i
$909$	−29.1716			−0.967560
$910$		0			0
$911$	−10.2010			−0.337975			−0.168987	−	0.985618i	$-0.554050\pi$
$911$	−10.2010			−0.337975			−0.168987	+	0.985618i	$0.554050\pi$
$912$	−3.04384	+	1.75736i	−0.100791	+	0.0581920i
$913$	−9.84895	−	5.68629i	−0.325953	−	0.188189i
$914$	29.3137	−	50.7728i	0.969611	−	1.67942i
$915$		0			0
$916$	−44.6274			−1.47453
$917$	−47.3087	+	19.3137i	−1.56227	+	0.637795i
$918$		−	28.1421i		−	0.928829i
$919$	−21.5563	−	37.3367i	−0.711078	−	1.23162i	−0.964453	−	0.264256i	$-0.914874\pi$
$919$	−21.5563	−	37.3367i	−0.711078	−	1.23162i	0.253374	−	0.967368i	$-0.418460\pi$
$920$		0			0
$921$	−0.985281	+	1.70656i	−0.0324661	+	0.0562330i
$922$	86.3775	−	49.8701i	2.84469	−	1.64238i
$923$			21.6569i			0.712844i
$924$	−3.44365	−	0.471253i	−0.113288	−	0.0155031i
$925$		0			0
$926$	44.7132	+	77.4455i	1.46937	+	2.54502i
$927$	−5.91359	−	3.41421i	−0.194228	−	0.112137i
$928$	1.37333	+	0.792893i	0.0450818	+	0.0260280i
$929$	2.74264	+	4.75039i	0.0899831	+	0.155855i	0.907504	−	0.420044i	$-0.137985\pi$
$929$	2.74264	+	4.75039i	0.0899831	+	0.155855i	−0.817521	+	0.575899i	$0.804652\pi$
$930$		0			0
$931$	−4.92893	−	19.1757i	−0.161539	−	0.628457i
$932$		−	64.4264i		−	2.11036i
$933$	−4.72490	+	2.72792i	−0.154686	+	0.0893082i
$934$	−3.74264	+	6.48244i	−0.122463	+	0.212112i
$935$		0			0
$936$	−30.1421	−	52.2077i	−0.985227	−	1.70646i
$937$			34.6274i			1.13123i	0.824670	+	0.565614i	$0.191361\pi$
$937$			34.6274i			1.13123i	−0.824670	+	0.565614i	$0.808639\pi$
$938$	8.30153	−	60.6630i	0.271055	−	1.98072i
$939$	−2.62742			−0.0857425
$940$		0			0
$941$	23.1421	−	40.0834i	0.754412	−	1.30668i	−0.191254	−	0.981541i	$-0.561255\pi$
$941$	23.1421	−	40.0834i	0.754412	−	1.30668i	0.945666	−	0.325139i	$-0.105411\pi$
$942$	14.9941	+	8.65685i	0.488535	+	0.282056i
$943$	2.80821	−	1.62132i	0.0914479	−	0.0527975i
$944$	−13.4558			−0.437950
$945$		0			0
$946$	−7.17157			−0.233168
$947$	28.7380	−	16.5919i	0.933859	−	0.539164i	0.0458290	−	0.998949i	$-0.485407\pi$
$947$	28.7380	−	16.5919i	0.933859	−	0.539164i	0.888030	+	0.459786i	$0.152074\pi$
$948$	−20.3643	−	11.7574i	−0.661403	−	0.381861i
$949$	2.00000	−	3.46410i	0.0649227	−	0.112449i
$950$		0			0
$951$	5.71573			0.185345
$952$	−44.5621	−	34.5563i	−1.44426	−	1.11998i
$953$			13.6569i			0.442389i	0.975230	+	0.221194i	$0.0709955\pi$
$953$			13.6569i			0.442389i	−0.975230	+	0.221194i	$0.929004\pi$
$954$	4.00000	+	6.92820i	0.129505	+	0.224309i
$955$		0			0
$956$	40.7990	−	70.6659i	1.31953	−	2.28550i
$957$	−0.297173	+	0.171573i	−0.00960624	+	0.00554616i
$958$			86.0833i			2.78122i
$959$	−15.6569	+	20.1903i	−0.505586	+	0.651978i
$960$		0			0
$961$	−2.50000	−	4.33013i	−0.0806452	−	0.139682i
$962$		0			0
$963$	−27.5387	−	15.8995i	−0.887423	−	0.512354i
$964$	52.9411	+	91.6967i	1.70512	+	2.95335i
$965$		0			0
$966$	0.414214	+	1.01461i	0.0133271	+	0.0326446i
$967$			37.5269i			1.20678i	0.797445	+	0.603392i	$0.206185\pi$
$967$			37.5269i			1.20678i	−0.797445	+	0.603392i	$0.793815\pi$
$968$	39.4275	−	22.7635i	1.26725	−	0.731645i
$969$	−2.82843	+	4.89898i	−0.0908622	+	0.157378i
$970$		0			0
$971$	12.0000	+	20.7846i	0.385098	+	0.667010i	0.991783	−	0.127933i	$-0.0408342\pi$
$971$	12.0000	+	20.7846i	0.385098	+	0.667010i	−0.606685	+	0.794943i	$0.707501\pi$
$972$		−	39.5980i		−	1.27011i
$973$	−5.79050	+	42.3137i	−0.185635	+	1.35652i
$974$	−10.4853			−0.335970
$975$		0			0
$976$	−8.22792	+	14.2512i	−0.263369	+	0.456169i
$977$	1.13770	+	0.656854i	0.0363984	+	0.0210146i	0.518089	−	0.855327i	$-0.326644\pi$
$977$	1.13770	+	0.656854i	0.0363984	+	0.0210146i	−0.481690	+	0.876341i	$0.659977\pi$
$978$	10.6895	−	6.17157i	0.341812	−	0.197345i
$979$	−7.17157			−0.229204
$980$		0			0
$981$	38.1421			1.21778
$982$	19.4728	−	11.2426i	0.621403	−	0.358767i
$983$	24.4334	+	14.1066i	0.779303	+	0.449931i	0.836183	−	0.548450i	$-0.184782\pi$
$983$	24.4334	+	14.1066i	0.779303	+	0.449931i	−0.0568803	+	0.998381i	$0.518115\pi$
$984$	7.15685	−	12.3960i	0.228152	−	0.395171i
$985$		0			0
$986$	−11.6569			−0.371230
$987$	0.297173	−	2.17157i	0.00945912	−	0.0691219i
$988$			52.2843i			1.66338i
$989$	0.742641	+	1.28629i	0.0236146	+	0.0409017i
$990$		0			0
$991$	2.17157	−	3.76127i	0.0689823	−	0.119481i	−0.829471	−	0.558549i	$-0.811358\pi$
$991$	2.17157	−	3.76127i	0.0689823	−	0.119481i	0.898454	+	0.439069i	$0.144691\pi$
$992$	8.23999	−	4.75736i	0.261620	−	0.151046i
$993$			9.51472i			0.301940i
$994$	10.8284	+	26.5241i	0.343457	+	0.841294i
$995$		0			0
$996$	10.8848	+	18.8530i	0.344897	+	0.597380i
$997$	−28.9736	−	16.7279i	−0.917603	−	0.529779i	−0.0347337	−	0.999397i	$-0.511058\pi$
$997$	−28.9736	−	16.7279i	−0.917603	−	0.529779i	−0.882870	+	0.469618i	$0.844392\pi$
$998$	−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.74.4		8
5.2	odd	4		175.2.e.c.151.2		4
5.3	odd	4		35.2.e.a.11.1	✓	4
5.4	even	2	inner	175.2.k.a.74.1		8
7.2	even	3	inner	175.2.k.a.149.1		8
7.3	odd	6		1225.2.b.h.99.4		4
7.4	even	3		1225.2.b.g.99.4		4
15.8	even	4		315.2.j.e.46.2		4
20.3	even	4		560.2.q.k.81.1		4
35.2	odd	12		175.2.e.c.51.2		4
35.3	even	12		245.2.a.g.1.2		2
35.4	even	6		1225.2.b.g.99.1		4
35.9	even	6	inner	175.2.k.a.149.4		8
35.13	even	4		245.2.e.e.116.1		4
35.17	even	12		1225.2.a.m.1.1		2
35.18	odd	12		245.2.a.h.1.2		2
35.23	odd	12		35.2.e.a.16.1	yes	4
35.24	odd	6		1225.2.b.h.99.1		4
35.32	odd	12		1225.2.a.k.1.1		2
35.33	even	12		245.2.e.e.226.1		4
105.23	even	12		315.2.j.e.226.2		4
105.38	odd	12		2205.2.a.q.1.1		2
105.53	even	12		2205.2.a.n.1.1		2
140.3	odd	12		3920.2.a.bv.1.1		2
140.23	even	12		560.2.q.k.401.1		4
140.123	even	12		3920.2.a.bq.1.2		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
35.2.e.a.11.1	✓	4	5.3	odd	4
35.2.e.a.16.1	yes	4	35.23	odd	12
175.2.e.c.51.2		4	35.2	odd	12
175.2.e.c.151.2		4	5.2	odd	4
175.2.k.a.74.1		8	5.4	even	2	inner
175.2.k.a.74.4		8	1.1	even	1	trivial
175.2.k.a.149.1		8	7.2	even	3	inner
175.2.k.a.149.4		8	35.9	even	6	inner
245.2.a.g.1.2		2	35.3	even	12
245.2.a.h.1.2		2	35.18	odd	12
245.2.e.e.116.1		4	35.13	even	4
245.2.e.e.226.1		4	35.33	even	12
315.2.j.e.46.2		4	15.8	even	4
315.2.j.e.226.2		4	105.23	even	12
560.2.q.k.81.1		4	20.3	even	4
560.2.q.k.401.1		4	140.23	even	12
1225.2.a.k.1.1		2	35.32	odd	12
1225.2.a.m.1.1		2	35.17	even	12
1225.2.b.g.99.1		4	35.4	even	6
1225.2.b.g.99.4		4	7.4	even	3
1225.2.b.h.99.1		4	35.24	odd	6
1225.2.b.h.99.4		4	7.3	odd	6
2205.2.a.n.1.1		2	105.53	even	12
2205.2.a.q.1.1		2	105.38	odd	12
3920.2.a.bq.1.2		2	140.123	even	12
3920.2.a.bv.1.1		2	140.3	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)

\(f(q)\)	\(=\)	\(q+(2.09077 - 1.20711i) q^{2} +(-0.358719 - 0.207107i) q^{3} +(1.91421 - 3.31552i) q^{4} -1.00000 q^{6} +(-0.358719 + 2.62132i) q^{7} -4.41421i q^{8} +(-1.41421 - 2.44949i) q^{9} +O(q^{10})\)	\(q+(2.09077 - 1.20711i) q^{2} +(-0.358719 - 0.207107i) q^{3} +(1.91421 - 3.31552i) q^{4} -1.00000 q^{6} +(-0.358719 + 2.62132i) q^{7} -4.41421i q^{8} +(-1.41421 - 2.44949i) q^{9} +(0.414214 - 0.717439i) q^{11} +(-1.37333 + 0.792893i) q^{12} +4.82843i q^{13} +(2.41421 + 5.91359i) q^{14} +(-1.50000 - 2.59808i) q^{16} +(-4.18154 - 2.41421i) q^{17} +(-5.91359 - 3.41421i) q^{18} +(1.41421 + 2.44949i) q^{19} +(0.671573 - 0.866025i) q^{21} -2.00000i q^{22} +(-0.358719 + 0.207107i) q^{23} +(-0.914214 + 1.58346i) q^{24} +(5.82843 + 10.0951i) q^{26} +2.41421i q^{27} +(8.00436 + 6.20711i) q^{28} +1.00000 q^{29} +(3.00000 - 5.19615i) q^{31} +(1.37333 + 0.792893i) q^{32} +(-0.297173 + 0.171573i) q^{33} -11.6569 q^{34} -10.8284 q^{36} +(5.91359 + 3.41421i) q^{38} +(1.00000 - 1.73205i) q^{39} -7.82843 q^{41} +(0.358719 - 2.62132i) q^{42} -3.58579i q^{43} +(-1.58579 - 2.74666i) q^{44} +(-0.500000 + 0.866025i) q^{46} +(1.73205 - 1.00000i) q^{47} +1.24264i q^{48} +(-6.74264 - 1.88064i) q^{49} +(1.00000 + 1.73205i) q^{51} +(16.0087 + 9.24264i) q^{52} +(-1.01461 - 0.585786i) q^{53} +(2.91421 + 5.04757i) q^{54} +(11.5711 + 1.58346i) q^{56} -1.17157i q^{57} +(2.09077 - 1.20711i) q^{58} +(2.24264 - 3.88437i) q^{59} +(-2.74264 - 4.75039i) q^{61} -14.4853i q^{62} +(6.92820 - 2.82843i) q^{63} +9.82843 q^{64} +(-0.414214 + 0.717439i) q^{66} +(-8.30153 - 4.79289i) q^{67} +(-16.0087 + 9.24264i) q^{68} +0.171573 q^{69} +4.48528 q^{71} +(-10.8126 + 6.24264i) q^{72} +(-0.717439 - 0.414214i) q^{73} +10.8284 q^{76} +(1.73205 + 1.34315i) q^{77} -4.82843i q^{78} +(7.41421 + 12.8418i) q^{79} +(-3.74264 + 6.48244i) q^{81} +(-16.3674 + 9.44975i) q^{82} -13.7279i q^{83} +(-1.58579 - 3.88437i) q^{84} +(-4.32843 - 7.49706i) q^{86} +(-0.358719 - 0.207107i) q^{87} +(-3.16693 - 1.82843i) q^{88} +(-4.32843 - 7.49706i) q^{89} +(-12.6569 - 1.73205i) q^{91} +1.58579i q^{92} +(-2.15232 + 1.24264i) q^{93} +(2.41421 - 4.18154i) q^{94} +(-0.328427 - 0.568852i) q^{96} +11.6569i q^{97} +(-16.3674 + 4.20711i) q^{98} -2.34315 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

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