LMFDB - Embedded newform 1470.2.m.e.97.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1470,2,Mod(97,1470)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1470, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([0, 1, 2]))

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

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

chi := DirichletCharacter("1470.97");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1470 = 2 \cdot 3 \cdot 5 \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1470.m (of order $4$, degree $2$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$11.7380090971$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(i)$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 4 x^{15} + 12 x^{14} - 48 x^{13} + 67 x^{12} - 24 x^{11} + 118 x^{10} - 176 x^{9} + 351 x^{8} + \cdots + 4 $ x^16 - 4x^15 + 12x^14 - 48x^13 + 67x^12 - 24x^11 + 118x^10 - 176x^9 + 351x^8 - 180x^7 + 358x^6 - 336x^5 + 390x^4 - 344x^3 + 164x^2 - 40*x + 4
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{4} $
Twist minimal:	no (minimal twist has level 210)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			97.2
Root			$0.792206 + 1.03242i$ of defining polynomial
Character	$\chi$	$=$	1470.97
Dual form			1470.2.m.e.1273.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.707107 - 0.707107i) q^{2} +(-0.707107 - 0.707107i) q^{3} +1.00000i q^{4} +(-1.91159 + 1.16009i) q^{5} +1.00000i q^{6} +(0.707107 - 0.707107i) q^{8} +1.00000i q^{9} +O(q^{10})$	\(q+(-0.707107 - 0.707107i) q^{2} +(-0.707107 - 0.707107i) q^{3} +1.00000i q^{4} +(-1.91159 + 1.16009i) q^{5} +1.00000i q^{6} +(0.707107 - 0.707107i) q^{8} +1.00000i q^{9} +(2.17201 + 0.531389i) q^{10} -1.76606 q^{11} +(0.707107 - 0.707107i) q^{12} +(2.71395 + 2.71395i) q^{13} +(2.17201 + 0.531389i) q^{15} -1.00000 q^{16} +(-1.57046 + 1.57046i) q^{17} +(0.707107 - 0.707107i) q^{18} -1.77399 q^{19} +(-1.16009 - 1.91159i) q^{20} +(1.24879 + 1.24879i) q^{22} +(2.86158 - 2.86158i) q^{23} -1.00000 q^{24} +(2.30836 - 4.43525i) q^{25} -3.83810i q^{26} +(0.707107 - 0.707107i) q^{27} -3.84628i q^{29} +(-1.16009 - 1.91159i) q^{30} +10.3294i q^{31} +(0.707107 + 0.707107i) q^{32} +(1.24879 + 1.24879i) q^{33} +2.22097 q^{34} -1.00000 q^{36} +(-2.35366 - 2.35366i) q^{37} +(1.25440 + 1.25440i) q^{38} -3.83810i q^{39} +(-0.531389 + 2.17201i) q^{40} -11.8993i q^{41} +(3.46335 - 3.46335i) q^{43} -1.76606i q^{44} +(-1.16009 - 1.91159i) q^{45} -4.04689 q^{46} +(-4.34719 + 4.34719i) q^{47} +(0.707107 + 0.707107i) q^{48} +(-4.76846 + 1.50394i) q^{50} +2.22097 q^{51} +(-2.71395 + 2.71395i) q^{52} +(0.290303 - 0.290303i) q^{53} -1.00000 q^{54} +(3.37598 - 2.04879i) q^{55} +(1.25440 + 1.25440i) q^{57} +(-2.71973 + 2.71973i) q^{58} -10.3676 q^{59} +(-0.531389 + 2.17201i) q^{60} -6.78891i q^{61} +(7.30401 - 7.30401i) q^{62} -1.00000i q^{64} +(-8.33639 - 2.03952i) q^{65} -1.76606i q^{66} +(5.40132 + 5.40132i) q^{67} +(-1.57046 - 1.57046i) q^{68} -4.04689 q^{69} -10.7193 q^{71} +(0.707107 + 0.707107i) q^{72} +(-7.51854 - 7.51854i) q^{73} +3.32858i q^{74} +(-4.76846 + 1.50394i) q^{75} -1.77399i q^{76} +(-2.71395 + 2.71395i) q^{78} -12.6909i q^{79} +(1.91159 - 1.16009i) q^{80} -1.00000 q^{81} +(-8.41410 + 8.41410i) q^{82} +(-1.94227 - 1.94227i) q^{83} +(1.18020 - 4.82397i) q^{85} -4.89791 q^{86} +(-2.71973 + 2.71973i) q^{87} +(-1.24879 + 1.24879i) q^{88} +1.11625 q^{89} +(-0.531389 + 2.17201i) q^{90} +(2.86158 + 2.86158i) q^{92} +(7.30401 - 7.30401i) q^{93} +6.14785 q^{94} +(3.39114 - 2.05799i) q^{95} -1.00000i q^{96} +(-7.26720 + 7.26720i) q^{97} -1.76606i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q+O(q^{10}) $ 16 * q	$ 16 q + 4 q^{10} - 8 q^{11} + 16 q^{13} + 4 q^{15} - 16 q^{16} - 24 q^{17} - 16 q^{19} + 8 q^{20} + 4 q^{22} + 8 q^{23} - 16 q^{24} + 16 q^{25} + 8 q^{30} + 4 q^{33} - 16 q^{34} - 16 q^{36} + 16 q^{37} - 8 q^{38} - 24 q^{43} + 8 q^{45} + 8 q^{46} - 24 q^{47} - 16 q^{51} - 16 q^{52} - 16 q^{53} - 16 q^{54} + 56 q^{55} - 8 q^{57} - 36 q^{58} + 16 q^{59} - 8 q^{62} - 32 q^{65} + 48 q^{67} - 24 q^{68} + 8 q^{69} - 32 q^{71} - 56 q^{73} - 16 q^{78} - 16 q^{81} - 24 q^{82} + 16 q^{83} + 8 q^{85} + 16 q^{86} - 36 q^{87} - 4 q^{88} - 32 q^{89} + 8 q^{92} - 8 q^{93} + 16 q^{94} - 24 q^{95} - 44 q^{97}+O(q^{100}) $ 16 * q + 4 * q^10 - 8 * q^11 + 16 * q^13 + 4 * q^15 - 16 * q^16 - 24 * q^17 - 16 * q^19 + 8 * q^20 + 4 * q^22 + 8 * q^23 - 16 * q^24 + 16 * q^25 + 8 * q^30 + 4 * q^33 - 16 * q^34 - 16 * q^36 + 16 * q^37 - 8 * q^38 - 24 * q^43 + 8 * q^45 + 8 * q^46 - 24 * q^47 - 16 * q^51 - 16 * q^52 - 16 * q^53 - 16 * q^54 + 56 * q^55 - 8 * q^57 - 36 * q^58 + 16 * q^59 - 8 * q^62 - 32 * q^65 + 48 * q^67 - 24 * q^68 + 8 * q^69 - 32 * q^71 - 56 * q^73 - 16 * q^78 - 16 * q^81 - 24 * q^82 + 16 * q^83 + 8 * q^85 + 16 * q^86 - 36 * q^87 - 4 * q^88 - 32 * q^89 + 8 * q^92 - 8 * q^93 + 16 * q^94 - 24 * q^95 - 44 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1470\mathbb{Z}\right)^\times$.

$n$	$491$	$1081$	$1177$
$\chi(n)$	$1$	$-1$	$e\left(\frac{1}{4}\right)$

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 $

$2$	−0.707107	−	0.707107i	−0.500000	−	0.500000i
$2$	−0.707107	−	0.707107i	−0.500000	−	0.500000i
$3$	−0.707107	−	0.707107i	−0.408248	−	0.408248i
$3$	−0.707107	−	0.707107i	−0.408248	−	0.408248i
$4$			1.00000i			0.500000i
$5$	−1.91159	+	1.16009i	−0.854890	+	0.518810i
$5$	−1.91159	+	1.16009i	−0.854890	+	0.518810i
$6$			1.00000i			0.408248i
$7$		0			0
$7$		0			0
$8$	0.707107	−	0.707107i	0.250000	−	0.250000i
$9$			1.00000i			0.333333i
$10$	2.17201	+	0.531389i	0.686850	+	0.168040i
$11$	−1.76606			−0.532486			−0.266243	−	0.963906i	$-0.585782\pi$
$11$	−1.76606			−0.532486			−0.266243	+	0.963906i	$0.585782\pi$
$12$	0.707107	−	0.707107i	0.204124	−	0.204124i
$13$	2.71395	+	2.71395i	0.752713	+	0.752713i	0.974985	−	0.222272i	$-0.0713472\pi$
$13$	2.71395	+	2.71395i	0.752713	+	0.752713i	−0.222272	+	0.974985i	$0.571347\pi$
$14$		0			0
$15$	2.17201	+	0.531389i	0.560810	+	0.137204i
$16$	−1.00000			−0.250000
$17$	−1.57046	+	1.57046i	−0.380893	+	0.380893i	−0.871424	−	0.490531i	$-0.836803\pi$
$17$	−1.57046	+	1.57046i	−0.380893	+	0.380893i	0.490531	+	0.871424i	$0.336803\pi$
$18$	0.707107	−	0.707107i	0.166667	−	0.166667i
$19$	−1.77399			−0.406981			−0.203490	−	0.979077i	$-0.565229\pi$
$19$	−1.77399			−0.406981			−0.203490	+	0.979077i	$0.565229\pi$
$20$	−1.16009	−	1.91159i	−0.259405	−	0.427445i
$21$		0			0
$22$	1.24879	+	1.24879i	0.266243	+	0.266243i
$23$	2.86158	−	2.86158i	0.596681	−	0.596681i	−0.342747	−	0.939428i	$-0.611357\pi$
$23$	2.86158	−	2.86158i	0.596681	−	0.596681i	0.939428	+	0.342747i	$0.111357\pi$
$24$	−1.00000			−0.204124
$25$	2.30836	−	4.43525i	0.461673	−	0.887050i
$26$		−	3.83810i		−	0.752713i
$27$	0.707107	−	0.707107i	0.136083	−	0.136083i
$28$		0			0
$29$		−	3.84628i		−	0.714236i	−0.934059	−	0.357118i	$-0.883759\pi$
$29$		−	3.84628i		−	0.714236i	0.934059	−	0.357118i	$-0.116241\pi$
$30$	−1.16009	−	1.91159i	−0.211803	−	0.349007i
$31$			10.3294i			1.85522i	0.373551	+	0.927610i	$0.378140\pi$
$31$			10.3294i			1.85522i	−0.373551	+	0.927610i	$0.621860\pi$
$32$	0.707107	+	0.707107i	0.125000	+	0.125000i
$33$	1.24879	+	1.24879i	0.217387	+	0.217387i
$34$	2.22097			0.380893
$35$		0			0
$36$	−1.00000			−0.166667
$37$	−2.35366	−	2.35366i	−0.386939	−	0.386939i	0.486655	−	0.873594i	$-0.338217\pi$
$37$	−2.35366	−	2.35366i	−0.386939	−	0.386939i	−0.873594	+	0.486655i	$0.838217\pi$
$38$	1.25440	+	1.25440i	0.203490	+	0.203490i
$39$		−	3.83810i		−	0.614588i
$40$	−0.531389	+	2.17201i	−0.0840200	+	0.343425i
$41$		−	11.8993i		−	1.85836i	−0.369622	−	0.929182i	$-0.620513\pi$
$41$		−	11.8993i		−	1.85836i	0.369622	−	0.929182i	$-0.379487\pi$
$42$		0			0
$43$	3.46335	−	3.46335i	0.528155	−	0.528155i	−0.391867	−	0.920022i	$-0.628171\pi$
$43$	3.46335	−	3.46335i	0.528155	−	0.528155i	0.920022	+	0.391867i	$0.128171\pi$
$44$		−	1.76606i		−	0.266243i
$45$	−1.16009	−	1.91159i	−0.172937	−	0.284963i
$46$	−4.04689			−0.596681
$47$	−4.34719	+	4.34719i	−0.634102	+	0.634102i	−0.949094	−	0.314992i	$-0.897998\pi$
$47$	−4.34719	+	4.34719i	−0.634102	+	0.634102i	0.314992	+	0.949094i	$0.397998\pi$
$48$	0.707107	+	0.707107i	0.102062	+	0.102062i
$49$		0			0
$50$	−4.76846	+	1.50394i	−0.674362	+	0.212689i
$51$	2.22097			0.310998
$52$	−2.71395	+	2.71395i	−0.376356	+	0.376356i
$53$	0.290303	−	0.290303i	0.0398762	−	0.0398762i	−0.686888	−	0.726764i	$-0.741024\pi$
$53$	0.290303	−	0.290303i	0.0398762	−	0.0398762i	0.726764	+	0.686888i	$0.241024\pi$
$54$	−1.00000			−0.136083
$55$	3.37598	−	2.04879i	0.455217	−	0.276259i
$56$		0			0
$57$	1.25440	+	1.25440i	0.166149	+	0.166149i
$58$	−2.71973	+	2.71973i	−0.357118	+	0.357118i
$59$	−10.3676			−1.34974			−0.674872	−	0.737935i	$-0.735801\pi$
$59$	−10.3676			−1.34974			−0.674872	+	0.737935i	$0.735801\pi$
$60$	−0.531389	+	2.17201i	−0.0686020	+	0.280405i
$61$		−	6.78891i		−	0.869230i	−0.900616	−	0.434615i	$-0.856884\pi$
$61$		−	6.78891i		−	0.869230i	0.900616	−	0.434615i	$-0.143116\pi$
$62$	7.30401	−	7.30401i	0.927610	−	0.927610i
$63$		0			0
$64$		−	1.00000i		−	0.125000i
$65$	−8.33639	−	2.03952i	−1.03400	−	0.252972i
$66$		−	1.76606i		−	0.217387i
$67$	5.40132	+	5.40132i	0.659877	+	0.659877i	0.955351	−	0.295474i	$-0.0954776\pi$
$67$	5.40132	+	5.40132i	0.659877	+	0.659877i	−0.295474	+	0.955351i	$0.595478\pi$
$68$	−1.57046	−	1.57046i	−0.190447	−	0.190447i
$69$	−4.04689			−0.487188
$70$		0			0
$71$	−10.7193			−1.27214			−0.636072	−	0.771629i	$-0.719442\pi$
$71$	−10.7193			−1.27214			−0.636072	+	0.771629i	$0.719442\pi$
$72$	0.707107	+	0.707107i	0.0833333	+	0.0833333i
$73$	−7.51854	−	7.51854i	−0.879979	−	0.879979i	0.113553	−	0.993532i	$-0.463777\pi$
$73$	−7.51854	−	7.51854i	−0.879979	−	0.879979i	−0.993532	+	0.113553i	$0.963777\pi$
$74$			3.32858i			0.386939i
$75$	−4.76846	+	1.50394i	−0.550614	+	0.173660i
$76$		−	1.77399i		−	0.203490i
$77$		0			0
$78$	−2.71395	+	2.71395i	−0.307294	+	0.307294i
$79$		−	12.6909i		−	1.42784i	−0.700228	−	0.713920i	$-0.746918\pi$
$79$		−	12.6909i		−	1.42784i	0.700228	−	0.713920i	$-0.253082\pi$
$80$	1.91159	−	1.16009i	0.213722	−	0.129702i
$81$	−1.00000			−0.111111
$82$	−8.41410	+	8.41410i	−0.929182	+	0.929182i
$83$	−1.94227	−	1.94227i	−0.213191	−	0.213191i	0.592430	−	0.805622i	$-0.298169\pi$
$83$	−1.94227	−	1.94227i	−0.213191	−	0.213191i	−0.805622	+	0.592430i	$0.798169\pi$
$84$		0			0
$85$	1.18020	−	4.82397i	0.128011	−	0.523233i
$86$	−4.89791			−0.528155
$87$	−2.71973	+	2.71973i	−0.291586	+	0.291586i
$88$	−1.24879	+	1.24879i	−0.133122	+	0.133122i
$89$	1.11625			0.118323			0.0591614	−	0.998248i	$-0.481157\pi$
$89$	1.11625			0.118323			0.0591614	+	0.998248i	$0.481157\pi$
$90$	−0.531389	+	2.17201i	−0.0560133	+	0.228950i
$91$		0			0
$92$	2.86158	+	2.86158i	0.298341	+	0.298341i
$93$	7.30401	−	7.30401i	0.757390	−	0.757390i
$94$	6.14785			0.634102
$95$	3.39114	−	2.05799i	0.347924	−	0.211146i
$96$		−	1.00000i		−	0.102062i
$97$	−7.26720	+	7.26720i	−0.737872	+	0.737872i	−0.972166	−	0.234293i	$-0.924722\pi$
$97$	−7.26720	+	7.26720i	−0.737872	+	0.737872i	0.234293	+	0.972166i	$0.424722\pi$
$98$		0			0
$99$		−	1.76606i		−	0.177495i
$100$	4.43525	+	2.30836i	0.443525	+	0.230836i
$101$		−	18.3467i		−	1.82556i	−0.408451	−	0.912780i	$-0.633931\pi$
$101$		−	18.3467i		−	1.82556i	0.408451	−	0.912780i	$-0.366069\pi$
$102$	−1.57046	−	1.57046i	−0.155499	−	0.155499i
$103$	6.44872	+	6.44872i	0.635411	+	0.635411i	0.949420	−	0.314009i	$-0.101672\pi$
$103$	6.44872	+	6.44872i	0.635411	+	0.635411i	−0.314009	+	0.949420i	$0.601672\pi$
$104$	3.83810			0.376356
$105$		0			0
$106$	−0.410550			−0.0398762
$107$	−10.4332	−	10.4332i	−1.00861	−	1.00861i	−0.999963	−	0.00864811i	$-0.997247\pi$
$107$	−10.4332	−	10.4332i	−1.00861	−	1.00861i	−0.00864811	−	0.999963i	$-0.502753\pi$
$108$	0.707107	+	0.707107i	0.0680414	+	0.0680414i
$109$		−	20.1488i		−	1.92991i	−0.262416	−	0.964955i	$-0.584519\pi$
$109$		−	20.1488i		−	1.92991i	0.262416	−	0.964955i	$-0.415481\pi$
$110$	−3.83589	−	0.938463i	−0.365738	−	0.0894790i
$111$			3.32858i			0.315935i
$112$		0			0
$113$	−6.54677	+	6.54677i	−0.615869	+	0.615869i	−0.944469	−	0.328600i	$-0.893423\pi$
$113$	−6.54677	+	6.54677i	−0.615869	+	0.615869i	0.328600	+	0.944469i	$0.393423\pi$
$114$		−	1.77399i		−	0.166149i
$115$	−2.15047	+	8.78988i	−0.200533	+	0.819661i
$116$	3.84628			0.357118
$117$	−2.71395	+	2.71395i	−0.250904	+	0.250904i
$118$	7.33099	+	7.33099i	0.674872	+	0.674872i
$119$		0			0
$120$	1.91159	−	1.16009i	0.174504	−	0.105902i
$121$	−7.88104			−0.716459
$122$	−4.80048	+	4.80048i	−0.434615	+	0.434615i
$123$	−8.41410	+	8.41410i	−0.758674	+	0.758674i
$124$	−10.3294			−0.927610
$125$	0.732658	+	11.1563i	0.0655309	+	0.997851i
$126$		0			0
$127$	12.5444	+	12.5444i	1.11313	+	1.11313i	0.992724	+	0.120409i	$0.0384206\pi$
$127$	12.5444	+	12.5444i	1.11313	+	1.11313i	0.120409	+	0.992724i	$0.461579\pi$
$128$	−0.707107	+	0.707107i	−0.0625000	+	0.0625000i
$129$	−4.89791			−0.431237
$130$	4.45255	+	7.33688i	0.390515	+	0.643487i
$131$			0.959275i			0.0838122i	0.999122	+	0.0419061i	$0.0133430\pi$
$131$			0.959275i			0.0838122i	−0.999122	+	0.0419061i	$0.986657\pi$
$132$	−1.24879	+	1.24879i	−0.108693	+	0.108693i
$133$		0			0
$134$		−	7.63862i		−	0.659877i
$135$	−0.531389	+	2.17201i	−0.0457347	+	0.186937i
$136$			2.22097i			0.190447i
$137$	7.88194	+	7.88194i	0.673399	+	0.673399i	0.958498	−	0.285099i	$-0.0920264\pi$
$137$	7.88194	+	7.88194i	0.673399	+	0.673399i	−0.285099	+	0.958498i	$0.592026\pi$
$138$	2.86158	+	2.86158i	0.243594	+	0.243594i
$139$	−13.5695			−1.15095			−0.575477	−	0.817818i	$-0.695184\pi$
$139$	−13.5695			−1.15095			−0.575477	+	0.817818i	$0.695184\pi$
$140$		0			0
$141$	6.14785			0.517742
$142$	7.57968	+	7.57968i	0.636072	+	0.636072i
$143$	−4.79298	−	4.79298i	−0.400809	−	0.400809i
$144$		−	1.00000i		−	0.0833333i
$145$	4.46205	+	7.35252i	0.370553	+	0.610593i
$146$			10.6328i			0.879979i
$147$		0			0
$148$	2.35366	−	2.35366i	0.193470	−	0.193470i
$149$			10.0986i			0.827310i	0.910434	+	0.413655i	$0.135748\pi$
$149$			10.0986i			0.827310i	−0.910434	+	0.413655i	$0.864252\pi$
$150$	4.43525	+	2.30836i	0.362137	+	0.188477i
$151$	−14.3099			−1.16453			−0.582263	−	0.813001i	$-0.697833\pi$
$151$	−14.3099			−1.16453			−0.582263	+	0.813001i	$0.697833\pi$
$152$	−1.25440	+	1.25440i	−0.101745	+	0.101745i
$153$	−1.57046	−	1.57046i	−0.126964	−	0.126964i
$154$		0			0
$155$	−11.9831	−	19.7456i	−0.962506	−	1.58601i
$156$	3.83810			0.307294
$157$	−6.77647	+	6.77647i	−0.540821	+	0.540821i	−0.923770	−	0.382948i	$-0.874909\pi$
$157$	−6.77647	+	6.77647i	−0.540821	+	0.540821i	0.382948	+	0.923770i	$0.374909\pi$
$158$	−8.97383	+	8.97383i	−0.713920	+	0.713920i
$159$	−0.410550			−0.0325588
$160$	−2.17201	−	0.531389i	−0.171712	−	0.0420100i
$161$		0			0
$162$	0.707107	+	0.707107i	0.0555556	+	0.0555556i
$163$	8.37474	−	8.37474i	0.655960	−	0.655960i	−0.298462	−	0.954422i	$-0.596473\pi$
$163$	8.37474	−	8.37474i	0.655960	−	0.655960i	0.954422	+	0.298462i	$0.0964735\pi$
$164$	11.8993			0.929182
$165$	−3.83589	−	0.938463i	−0.298624	−	0.0730593i
$166$			2.74678i			0.213191i
$167$	6.95883	−	6.95883i	0.538490	−	0.538490i	−0.384595	−	0.923085i	$-0.625659\pi$
$167$	6.95883	−	6.95883i	0.538490	−	0.538490i	0.923085	+	0.384595i	$0.125659\pi$
$168$		0			0
$169$			1.73100i			0.133154i
$170$	−4.24559	+	2.57653i	−0.325622	+	0.197611i
$171$		−	1.77399i		−	0.135660i
$172$	3.46335	+	3.46335i	0.264078	+	0.264078i
$173$	−6.12788	−	6.12788i	−0.465894	−	0.465894i	0.434687	−	0.900581i	$-0.356859\pi$
$173$	−6.12788	−	6.12788i	−0.465894	−	0.465894i	−0.900581	+	0.434687i	$0.856859\pi$
$174$	3.84628			0.291586
$175$		0			0
$176$	1.76606			0.133122
$177$	7.33099	+	7.33099i	0.551031	+	0.551031i
$178$	−0.789311	−	0.789311i	−0.0591614	−	0.0591614i
$179$		−	13.3536i		−	0.998097i	−0.866574	−	0.499049i	$-0.833683\pi$
$179$		−	13.3536i		−	0.998097i	0.866574	−	0.499049i	$-0.166317\pi$
$180$	1.91159	−	1.16009i	0.142482	−	0.0864683i
$181$		−	8.73922i		−	0.649581i	−0.945786	−	0.324791i	$-0.894706\pi$
$181$		−	8.73922i		−	0.649581i	0.945786	−	0.324791i	$-0.105294\pi$
$182$		0			0
$183$	−4.80048	+	4.80048i	−0.354862	+	0.354862i
$184$		−	4.04689i		−	0.298341i
$185$	7.22970	+	1.76877i	0.531538	+	0.130043i
$186$	−10.3294			−0.757390
$187$	2.77353	−	2.77353i	0.202820	−	0.202820i
$188$	−4.34719	−	4.34719i	−0.317051	−	0.317051i
$189$		0			0
$190$	−3.85312	−	0.942678i	−0.279535	−	0.0683891i
$191$	−10.8759			−0.786955			−0.393477	−	0.919334i	$-0.628728\pi$
$191$	−10.8759			−0.786955			−0.393477	+	0.919334i	$0.628728\pi$
$192$	−0.707107	+	0.707107i	−0.0510310	+	0.0510310i
$193$	7.92044	−	7.92044i	0.570126	−	0.570126i	−0.362038	−	0.932163i	$-0.617919\pi$
$193$	7.92044	−	7.92044i	0.570126	−	0.570126i	0.932163	+	0.362038i	$0.117919\pi$
$194$	10.2774			0.737872
$195$	4.45255	+	7.33688i	0.318854	+	0.525405i
$196$		0			0
$197$	−10.3775	−	10.3775i	−0.739367	−	0.739367i	0.233088	−	0.972456i	$-0.425117\pi$
$197$	−10.3775	−	10.3775i	−0.739367	−	0.739367i	−0.972456	+	0.233088i	$0.925117\pi$
$198$	−1.24879	+	1.24879i	−0.0887477	+	0.0887477i
$199$	18.5630			1.31590			0.657949	−	0.753062i	$-0.271424\pi$
$199$	18.5630			1.31590			0.657949	+	0.753062i	$0.271424\pi$
$200$	−1.50394	−	4.76846i	−0.106344	−	0.337181i
$201$		−	7.63862i		−	0.538787i
$202$	−12.9730	+	12.9730i	−0.912780	+	0.912780i
$203$		0			0
$204$			2.22097i			0.155499i
$205$	13.8043	+	22.7467i	0.964138	+	1.58870i
$206$		−	9.11987i		−	0.635411i
$207$	2.86158	+	2.86158i	0.198894	+	0.198894i
$208$	−2.71395	−	2.71395i	−0.188178	−	0.188178i
$209$	3.13296			0.216712
$210$		0			0
$211$	−0.453133			−0.0311950			−0.0155975	−	0.999878i	$-0.504965\pi$
$211$	−0.453133			−0.0311950			−0.0155975	+	0.999878i	$0.504965\pi$
$212$	0.290303	+	0.290303i	0.0199381	+	0.0199381i
$213$	7.57968	+	7.57968i	0.519351	+	0.519351i
$214$			14.7547i			1.00861i
$215$	−2.60270	+	10.6383i	−0.177502	+	0.725527i
$216$		−	1.00000i		−	0.0680414i
$217$		0			0
$218$	−14.2474	+	14.2474i	−0.964955	+	0.964955i
$219$			10.6328i			0.718500i
$220$	2.04879	+	3.37598i	0.138130	+	0.227608i
$221$	−8.52430			−0.573407
$222$	2.35366	−	2.35366i	0.157967	−	0.157967i
$223$	4.67260	+	4.67260i	0.312901	+	0.312901i	0.846032	−	0.533132i	$-0.178985\pi$
$223$	4.67260	+	4.67260i	0.312901	+	0.312901i	−0.533132	+	0.846032i	$0.678985\pi$
$224$		0			0
$225$	4.43525	+	2.30836i	0.295683	+	0.153891i
$226$	9.25854			0.615869
$227$	−11.7433	+	11.7433i	−0.779430	+	0.779430i	−0.979734	−	0.200304i	$-0.935807\pi$
$227$	−11.7433	+	11.7433i	−0.779430	+	0.779430i	0.200304	+	0.979734i	$0.435807\pi$
$228$	−1.25440	+	1.25440i	−0.0830746	+	0.0830746i
$229$	13.5415			0.894847			0.447423	−	0.894322i	$-0.352342\pi$
$229$	13.5415			0.894847			0.447423	+	0.894322i	$0.352342\pi$
$230$	7.73600	−	4.69477i	0.510097	−	0.309564i
$231$		0			0
$232$	−2.71973	−	2.71973i	−0.178559	−	0.178559i
$233$	8.18707	−	8.18707i	0.536353	−	0.536353i	−0.386103	−	0.922456i	$-0.626179\pi$
$233$	8.18707	−	8.18707i	0.536353	−	0.536353i	0.922456	+	0.386103i	$0.126179\pi$
$234$	3.83810			0.250904
$235$	3.26690	−	13.3532i	0.213109	−	0.871066i
$236$		−	10.3676i		−	0.674872i
$237$	−8.97383	+	8.97383i	−0.582913	+	0.582913i
$238$		0			0
$239$			17.0264i			1.10135i	0.834721	+	0.550673i	$0.185629\pi$
$239$			17.0264i			1.10135i	−0.834721	+	0.550673i	$0.814371\pi$
$240$	−2.17201	−	0.531389i	−0.140203	−	0.0343010i
$241$		−	18.9216i		−	1.21885i	−0.792844	−	0.609424i	$-0.791401\pi$
$241$		−	18.9216i		−	1.21885i	0.792844	−	0.609424i	$-0.208599\pi$
$242$	5.57274	+	5.57274i	0.358229	+	0.358229i
$243$	0.707107	+	0.707107i	0.0453609	+	0.0453609i
$244$	6.78891			0.434615
$245$		0			0
$246$	11.8993			0.758674
$247$	−4.81451	−	4.81451i	−0.306340	−	0.306340i
$248$	7.30401	+	7.30401i	0.463805	+	0.463805i
$249$			2.74678i			0.174070i
$250$	7.37063	−	8.40677i	0.466160	−	0.531691i
$251$		−	18.1527i		−	1.14579i	−0.819629	−	0.572894i	$-0.805821\pi$
$251$		−	18.1527i		−	1.14579i	0.819629	−	0.572894i	$-0.194179\pi$
$252$		0			0
$253$	−5.05372	+	5.05372i	−0.317725	+	0.317725i
$254$		−	17.7404i		−	1.11313i
$255$	−4.24559	+	2.57653i	−0.265869	+	0.161349i
$256$	1.00000			0.0625000
$257$	17.0202	−	17.0202i	1.06169	−	1.06169i	0.0637239	−	0.997968i	$-0.479702\pi$
$257$	17.0202	−	17.0202i	1.06169	−	1.06169i	0.997968	−	0.0637239i	$-0.0202977\pi$
$258$	3.46335	+	3.46335i	0.215619	+	0.215619i
$259$		0			0
$260$	2.03952	−	8.33639i	0.126486	−	0.517001i
$261$	3.84628			0.238079
$262$	0.678310	−	0.678310i	0.0419061	−	0.0419061i
$263$	9.92483	−	9.92483i	0.611991	−	0.611991i	−0.331473	−	0.943465i	$-0.607546\pi$
$263$	9.92483	−	9.92483i	0.611991	−	0.611991i	0.943465	+	0.331473i	$0.107546\pi$
$264$	1.76606			0.108693
$265$	−0.218162	+	0.891719i	−0.0134016	+	0.0547779i
$266$		0			0
$267$	−0.789311	−	0.789311i	−0.0483051	−	0.0483051i
$268$	−5.40132	+	5.40132i	−0.329938	+	0.329938i
$269$	26.5525			1.61893			0.809466	−	0.587166i	$-0.199756\pi$
$269$	26.5525			1.61893			0.809466	+	0.587166i	$0.199756\pi$
$270$	1.91159	−	1.16009i	0.116336	−	0.0706011i
$271$			11.9606i			0.726556i	0.931681	+	0.363278i	$0.118343\pi$
$271$			11.9606i			0.726556i	−0.931681	+	0.363278i	$0.881657\pi$
$272$	1.57046	−	1.57046i	0.0952233	−	0.0952233i
$273$		0			0
$274$		−	11.1467i		−	0.673399i
$275$	−4.07670	+	7.83291i	−0.245834	+	0.472342i
$276$		−	4.04689i		−	0.243594i
$277$	−1.66994	−	1.66994i	−0.100337	−	0.100337i	0.655156	−	0.755493i	$-0.272603\pi$
$277$	−1.66994	−	1.66994i	−0.100337	−	0.100337i	−0.755493	+	0.655156i	$0.772603\pi$
$278$	9.59512	+	9.59512i	0.575477	+	0.575477i
$279$	−10.3294			−0.618406
$280$		0			0
$281$	−11.0306			−0.658033			−0.329017	−	0.944324i	$-0.606717\pi$
$281$	−11.0306			−0.658033			−0.329017	+	0.944324i	$0.606717\pi$
$282$	−4.34719	−	4.34719i	−0.258871	−	0.258871i
$283$	−16.5540	−	16.5540i	−0.984031	−	0.984031i	0.0158433	−	0.999874i	$-0.494957\pi$
$283$	−16.5540	−	16.5540i	−0.984031	−	0.984031i	−0.999874	+	0.0158433i	$0.994957\pi$
$284$		−	10.7193i		−	0.636072i
$285$	−3.85312	−	0.942678i	−0.228239	−	0.0558394i
$286$			6.77830i			0.400809i
$287$		0			0
$288$	−0.707107	+	0.707107i	−0.0416667	+	0.0416667i
$289$			12.0673i			0.709841i
$290$	2.04387	−	8.35416i	0.120020	−	0.490573i
$291$	10.2774			0.602470
$292$	7.51854	−	7.51854i	0.439990	−	0.439990i
$293$	−15.4837	−	15.4837i	−0.904565	−	0.904565i	0.0912620	−	0.995827i	$-0.470910\pi$
$293$	−15.4837	−	15.4837i	−0.904565	−	0.904565i	−0.995827	+	0.0912620i	$0.970910\pi$
$294$		0			0
$295$	19.8186	−	12.0274i	1.15388	−	0.700261i
$296$	−3.32858			−0.193470
$297$	−1.24879	+	1.24879i	−0.0724622	+	0.0724622i
$298$	7.14079	−	7.14079i	0.413655	−	0.413655i
$299$	15.5324			0.898260
$300$	−1.50394	−	4.76846i	−0.0868298	−	0.275307i
$301$		0			0
$302$	10.1186	+	10.1186i	0.582263	+	0.582263i
$303$	−12.9730	+	12.9730i	−0.745282	+	0.745282i
$304$	1.77399			0.101745
$305$	7.87577	+	12.9776i	0.450965	+	0.743096i
$306$			2.22097i			0.126964i
$307$	2.12149	−	2.12149i	0.121080	−	0.121080i	−0.643971	−	0.765050i	$-0.722714\pi$
$307$	2.12149	−	2.12149i	0.121080	−	0.121080i	0.765050	+	0.643971i	$0.222714\pi$
$308$		0			0
$309$		−	9.11987i		−	0.518811i
$310$	−5.48894	+	22.4356i	−0.311751	+	1.27426i
$311$		−	15.0205i		−	0.851737i	−0.904785	−	0.425868i	$-0.859969\pi$
$311$		−	15.0205i		−	0.851737i	0.904785	−	0.425868i	$-0.140031\pi$
$312$	−2.71395	−	2.71395i	−0.153647	−	0.153647i
$313$	−9.41740	−	9.41740i	−0.532303	−	0.532303i	0.388954	−	0.921257i	$-0.372836\pi$
$313$	−9.41740	−	9.41740i	−0.532303	−	0.532303i	−0.921257	+	0.388954i	$0.872836\pi$
$314$	9.58338			0.540821
$315$		0			0
$316$	12.6909			0.713920
$317$	9.82998	+	9.82998i	0.552107	+	0.552107i	0.927048	−	0.374942i	$-0.122337\pi$
$317$	9.82998	+	9.82998i	0.552107	+	0.552107i	−0.374942	+	0.927048i	$0.622337\pi$
$318$	0.290303	+	0.290303i	0.0162794	+	0.0162794i
$319$			6.79275i			0.380321i
$320$	1.16009	+	1.91159i	0.0648512	+	0.106861i
$321$			14.7547i			0.823527i
$322$		0			0
$323$	2.78598	−	2.78598i	0.155016	−	0.155016i
$324$		−	1.00000i		−	0.0555556i
$325$	18.3018	−	5.77225i	1.01520	−	0.320187i
$326$	−11.8437			−0.655960
$327$	−14.2474	+	14.2474i	−0.787882	+	0.787882i
$328$	−8.41410	−	8.41410i	−0.464591	−	0.464591i
$329$		0			0
$330$	2.04879	+	3.37598i	0.112782	+	0.185842i
$331$	−18.6326			−1.02414			−0.512071	−	0.858943i	$-0.671121\pi$
$331$	−18.6326			−1.02414			−0.512071	+	0.858943i	$0.671121\pi$
$332$	1.94227	−	1.94227i	0.106596	−	0.106596i
$333$	2.35366	−	2.35366i	0.128980	−	0.128980i
$334$	−9.84127			−0.538490
$335$	−16.5912	−	4.05908i	−0.906472	−	0.221771i
$336$		0			0
$337$	9.63568	+	9.63568i	0.524889	+	0.524889i	0.919044	−	0.394155i	$-0.128963\pi$
$337$	9.63568	+	9.63568i	0.524889	+	0.524889i	−0.394155	+	0.919044i	$0.628963\pi$
$338$	1.22400	−	1.22400i	0.0665768	−	0.0665768i
$339$	9.25854			0.502855
$340$	4.82397	+	1.18020i	0.261616	+	0.0640053i
$341$		−	18.2423i		−	0.987879i
$342$	−1.25440	+	1.25440i	−0.0678301	+	0.0678301i
$343$		0			0
$344$		−	4.89791i		−	0.264078i
$345$	7.73600	−	4.69477i	0.416492	−	0.252758i
$346$			8.66613i			0.465894i
$347$	24.6620	+	24.6620i	1.32393	+	1.32393i	0.910568	+	0.413359i	$0.135645\pi$
$347$	24.6620	+	24.6620i	1.32393	+	1.32393i	0.413359	+	0.910568i	$0.364355\pi$
$348$	−2.71973	−	2.71973i	−0.145793	−	0.145793i
$349$	−1.49727			−0.0801469			−0.0400735	−	0.999197i	$-0.512759\pi$
$349$	−1.49727			−0.0801469			−0.0400735	+	0.999197i	$0.512759\pi$
$350$		0			0
$351$	3.83810			0.204863
$352$	−1.24879	−	1.24879i	−0.0665608	−	0.0665608i
$353$	4.21912	+	4.21912i	0.224561	+	0.224561i	0.810416	−	0.585855i	$-0.199241\pi$
$353$	4.21912	+	4.21912i	0.224561	+	0.224561i	−0.585855	+	0.810416i	$0.699241\pi$
$354$		−	10.3676i		−	0.551031i
$355$	20.4909	−	12.4354i	1.08754	−	0.660001i
$356$			1.11625i			0.0591614i
$357$		0			0
$358$	−9.44244	+	9.44244i	−0.499049	+	0.499049i
$359$			17.3193i			0.914076i	0.889447	+	0.457038i	$0.151090\pi$
$359$			17.3193i			0.914076i	−0.889447	+	0.457038i	$0.848910\pi$
$360$	−2.17201	−	0.531389i	−0.114475	−	0.0280067i
$361$	−15.8530			−0.834367
$362$	−6.17956	+	6.17956i	−0.324791	+	0.324791i
$363$	5.57274	+	5.57274i	0.292493	+	0.292493i
$364$		0			0
$365$	23.0946	+	5.65017i	1.20883	+	0.295743i
$366$	6.78891			0.354862
$367$	3.87842	−	3.87842i	0.202452	−	0.202452i	−0.598598	−	0.801050i	$-0.704275\pi$
$367$	3.87842	−	3.87842i	0.202452	−	0.202452i	0.801050	+	0.598598i	$0.204275\pi$
$368$	−2.86158	+	2.86158i	−0.149170	+	0.149170i
$369$	11.8993			0.619455
$370$	−3.86146	−	6.36288i	−0.200748	−	0.330790i
$371$		0			0
$372$	7.30401	+	7.30401i	0.378695	+	0.378695i
$373$	21.8079	−	21.8079i	1.12917	−	1.12917i	0.138857	−	0.990312i	$-0.455657\pi$
$373$	21.8079	−	21.8079i	1.12917	−	1.12917i	0.990312	−	0.138857i	$-0.0443428\pi$
$374$	−3.92236			−0.202820
$375$	7.37063	−	8.40677i	0.380618	−	0.434124i
$376$			6.14785i			0.317051i
$377$	10.4386	−	10.4386i	0.537615	−	0.537615i
$378$		0			0
$379$			12.9203i			0.663670i	0.943337	+	0.331835i	$0.107668\pi$
$379$			12.9203i			0.663670i	−0.943337	+	0.331835i	$0.892332\pi$
$380$	2.05799	+	3.39114i	0.105573	+	0.173962i
$381$		−	17.7404i		−	0.908870i
$382$	7.69044	+	7.69044i	0.393477	+	0.393477i
$383$	−0.841477	−	0.841477i	−0.0429975	−	0.0429975i	0.685281	−	0.728279i	$-0.259679\pi$
$383$	−0.841477	−	0.841477i	−0.0429975	−	0.0429975i	−0.728279	+	0.685281i	$0.759679\pi$
$384$	1.00000			0.0510310
$385$		0			0
$386$	−11.2012			−0.570126
$387$	3.46335	+	3.46335i	0.176052	+	0.176052i
$388$	−7.26720	−	7.26720i	−0.368936	−	0.368936i
$389$			9.52874i			0.483126i	0.970385	+	0.241563i	$0.0776601\pi$
$389$			9.52874i			0.483126i	−0.970385	+	0.241563i	$0.922340\pi$
$390$	2.03952	−	8.33639i	0.103275	−	0.422129i
$391$			8.98802i			0.454544i
$392$		0			0
$393$	0.678310	−	0.678310i	0.0342162	−	0.0342162i
$394$			14.6760i			0.739367i
$395$	14.7227	+	24.2598i	0.740777	+	1.22065i
$396$	1.76606			0.0887477
$397$	20.1760	−	20.1760i	1.01261	−	1.01261i	0.0126858	−	0.999920i	$-0.495962\pi$
$397$	20.1760	−	20.1760i	1.01261	−	1.01261i	0.999920	−	0.0126858i	$-0.00403813\pi$
$398$	−13.1260	−	13.1260i	−0.657949	−	0.657949i
$399$		0			0
$400$	−2.30836	+	4.43525i	−0.115418	+	0.221763i
$401$	39.2300			1.95905			0.979526	−	0.201320i	$-0.0645230\pi$
$401$	39.2300			1.95905			0.979526	+	0.201320i	$0.0645230\pi$
$402$	−5.40132	+	5.40132i	−0.269394	+	0.269394i
$403$	−28.0335	+	28.0335i	−1.39645	+	1.39645i
$404$	18.3467			0.912780
$405$	1.91159	−	1.16009i	0.0949877	−	0.0576455i
$406$		0			0
$407$	4.15670	+	4.15670i	0.206040	+	0.206040i
$408$	1.57046	−	1.57046i	0.0777495	−	0.0777495i
$409$	−8.65825			−0.428123			−0.214061	−	0.976820i	$-0.568669\pi$
$409$	−8.65825			−0.428123			−0.214061	+	0.976820i	$0.568669\pi$
$410$	6.32318	−	25.8455i	0.312280	−	1.27642i
$411$		−	11.1467i		−	0.549828i
$412$	−6.44872	+	6.44872i	−0.317706	+	0.317706i
$413$		0			0
$414$		−	4.04689i		−	0.198894i
$415$	5.96603	+	1.45961i	0.292861	+	0.0716493i
$416$			3.83810i			0.188178i
$417$	9.59512	+	9.59512i	0.469875	+	0.469875i
$418$	−2.21534	−	2.21534i	−0.108356	−	0.108356i
$419$	4.29623			0.209884			0.104942	−	0.994478i	$-0.466534\pi$
$419$	4.29623			0.209884			0.104942	+	0.994478i	$0.466534\pi$
$420$		0			0
$421$	−18.8346			−0.917945			−0.458972	−	0.888451i	$-0.651782\pi$
$421$	−18.8346			−0.917945			−0.458972	+	0.888451i	$0.651782\pi$
$422$	0.320413	+	0.320413i	0.0155975	+	0.0155975i
$423$	−4.34719	−	4.34719i	−0.211367	−	0.211367i
$424$		−	0.410550i		−	0.0199381i
$425$	3.34020	+	10.5906i	0.162023	+	0.513720i
$426$		−	10.7193i		−	0.519351i
$427$		0			0
$428$	10.4332	−	10.4332i	0.504305	−	0.504305i
$429$			6.77830i			0.327259i
$430$	9.36281	−	5.68204i	0.451515	−	0.274012i
$431$	6.92462			0.333547			0.166774	−	0.985995i	$-0.446665\pi$
$431$	6.92462			0.333547			0.166774	+	0.985995i	$0.446665\pi$
$432$	−0.707107	+	0.707107i	−0.0340207	+	0.0340207i
$433$	11.5154	+	11.5154i	0.553393	+	0.553393i	0.927419	−	0.374025i	$-0.122023\pi$
$433$	11.5154	+	11.5154i	0.553393	+	0.553393i	−0.374025	+	0.927419i	$0.622023\pi$
$434$		0			0
$435$	2.04387	−	8.35416i	0.0979961	−	0.400551i
$436$	20.1488			0.964955
$437$	−5.07642	+	5.07642i	−0.242838	+	0.242838i
$438$	7.51854	−	7.51854i	0.359250	−	0.359250i
$439$	−18.2239			−0.869778			−0.434889	−	0.900484i	$-0.643212\pi$
$439$	−18.2239			−0.869778			−0.434889	+	0.900484i	$0.643212\pi$
$440$	0.938463	−	3.83589i	0.0447395	−	0.182869i
$441$		0			0
$442$	6.02759	+	6.02759i	0.286703	+	0.286703i
$443$	−23.2160	+	23.2160i	−1.10303	+	1.10303i	−0.108982	+	0.994044i	$0.534759\pi$
$443$	−23.2160	+	23.2160i	−1.10303	+	1.10303i	−0.994044	+	0.108982i	$0.965241\pi$
$444$	−3.32858			−0.157967
$445$	−2.13382	+	1.29496i	−0.101153	+	0.0613870i
$446$		−	6.60806i		−	0.312901i
$447$	7.14079	−	7.14079i	0.337748	−	0.337748i
$448$		0			0
$449$			8.14032i			0.384165i	0.981379	+	0.192083i	$0.0615242\pi$
$449$			8.14032i			0.384165i	−0.981379	+	0.192083i	$0.938476\pi$
$450$	−1.50394	−	4.76846i	−0.0708962	−	0.224787i
$451$			21.0149i			0.989553i
$452$	−6.54677	−	6.54677i	−0.307934	−	0.307934i
$453$	10.1186	+	10.1186i	0.475416	+	0.475416i
$454$	16.6075			0.779430
$455$		0			0
$456$	1.77399			0.0830746
$457$	3.22864	+	3.22864i	0.151030	+	0.151030i	0.778578	−	0.627548i	$-0.215941\pi$
$457$	3.22864	+	3.22864i	0.151030	+	0.151030i	−0.627548	+	0.778578i	$0.715941\pi$
$458$	−9.57528	−	9.57528i	−0.447423	−	0.447423i
$459$			2.22097i			0.103666i
$460$	−8.78988	−	2.15047i	−0.409830	−	0.100266i
$461$			7.54894i			0.351589i	0.984427	+	0.175795i	$0.0562495\pi$
$461$			7.54894i			0.351589i	−0.984427	+	0.175795i	$0.943751\pi$
$462$		0			0
$463$	−8.87647	+	8.87647i	−0.412525	+	0.412525i	−0.882617	−	0.470092i	$-0.844221\pi$
$463$	−8.87647	+	8.87647i	−0.412525	+	0.412525i	0.470092	+	0.882617i	$0.344221\pi$
$464$			3.84628i			0.178559i
$465$	−5.48894	+	22.4356i	−0.254544	+	1.04043i
$466$	−11.5783			−0.536353
$467$	−8.13763	+	8.13763i	−0.376565	+	0.376565i	−0.869861	−	0.493297i	$-0.835792\pi$
$467$	−8.13763	+	8.13763i	−0.376565	+	0.376565i	0.493297	+	0.869861i	$0.335792\pi$
$468$	−2.71395	−	2.71395i	−0.125452	−	0.125452i
$469$		0			0
$470$	−11.7522	+	7.13208i	−0.542088	+	0.328979i
$471$	9.58338			0.441579
$472$	−7.33099	+	7.33099i	−0.337436	+	0.337436i
$473$	−6.11647	+	6.11647i	−0.281235	+	0.281235i
$474$	12.6909			0.582913
$475$	−4.09501	+	7.86808i	−0.187892	+	0.361012i
$476$		0			0
$477$	0.290303	+	0.290303i	0.0132921	+	0.0132921i
$478$	12.0395	−	12.0395i	0.550673	−	0.550673i
$479$	−12.3476			−0.564175			−0.282088	−	0.959389i	$-0.591027\pi$
$479$	−12.3476			−0.564175			−0.282088	+	0.959389i	$0.591027\pi$
$480$	1.16009	+	1.91159i	0.0529508	+	0.0872518i
$481$		−	12.7754i		−	0.582509i
$482$	−13.3796	+	13.3796i	−0.609424	+	0.609424i
$483$		0			0
$484$		−	7.88104i		−	0.358229i
$485$	5.46128	−	22.3226i	0.247984	−	1.01361i
$486$		−	1.00000i		−	0.0453609i
$487$	−11.0215	−	11.0215i	−0.499431	−	0.499431i	0.411830	−	0.911261i	$-0.364890\pi$
$487$	−11.0215	−	11.0215i	−0.499431	−	0.499431i	−0.911261	+	0.411830i	$0.864890\pi$
$488$	−4.80048	−	4.80048i	−0.217308	−	0.217308i
$489$	−11.8437			−0.535589
$490$		0			0
$491$	−2.67474			−0.120709			−0.0603547	−	0.998177i	$-0.519223\pi$
$491$	−2.67474			−0.120709			−0.0603547	+	0.998177i	$0.519223\pi$
$492$	−8.41410	−	8.41410i	−0.379337	−	0.379337i
$493$	6.04044	+	6.04044i	0.272048	+	0.272048i
$494$			6.80874i			0.306340i
$495$	2.04879	+	3.37598i	0.0920863	+	0.151739i
$496$		−	10.3294i		−	0.463805i
$497$		0			0
$498$	1.94227	−	1.94227i	0.0870350	−	0.0870350i
$499$		−	18.1765i		−	0.813692i	−0.913497	−	0.406846i	$-0.866629\pi$
$499$		−	18.1765i		−	0.813692i	0.913497	−	0.406846i	$-0.133371\pi$
$500$	−11.1563	+	0.732658i	−0.498925	+	0.0327655i
$501$	−9.84127			−0.439675
$502$	−12.8359	+	12.8359i	−0.572894	+	0.572894i
$503$	−3.59630	−	3.59630i	−0.160351	−	0.160351i	0.622371	−	0.782722i	$-0.286169\pi$
$503$	−3.59630	−	3.59630i	−0.160351	−	0.160351i	−0.782722	+	0.622371i	$0.786169\pi$
$504$		0			0
$505$	21.2838	+	35.0713i	0.947119	+	1.56065i
$506$	7.14704			0.317725
$507$	1.22400	−	1.22400i	0.0543598	−	0.0543598i
$508$	−12.5444	+	12.5444i	−0.556567	+	0.556567i
$509$	−4.81258			−0.213314			−0.106657	−	0.994296i	$-0.534015\pi$
$509$	−4.81258			−0.213314			−0.106657	+	0.994296i	$0.534015\pi$
$510$	4.82397	+	1.18020i	0.213609	+	0.0522601i
$511$		0			0
$512$	−0.707107	−	0.707107i	−0.0312500	−	0.0312500i
$513$	−1.25440	+	1.25440i	−0.0553831	+	0.0553831i
$514$	−24.0702			−1.06169
$515$	−19.8084	−	4.84620i	−0.872864	−	0.213549i
$516$		−	4.89791i		−	0.215619i
$517$	7.67738	−	7.67738i	0.337651	−	0.337651i
$518$		0			0
$519$			8.66613i			0.380401i
$520$	−7.33688	+	4.45255i	−0.321743	+	0.195257i
$521$		−	5.32872i		−	0.233455i	−0.993164	−	0.116728i	$-0.962760\pi$
$521$		−	5.32872i		−	0.233455i	0.993164	−	0.116728i	$-0.0372405\pi$
$522$	−2.71973	−	2.71973i	−0.119039	−	0.119039i
$523$	4.33196	+	4.33196i	0.189424	+	0.189424i	0.795447	−	0.606023i	$-0.207236\pi$
$523$	4.33196	+	4.33196i	0.189424	+	0.189424i	−0.606023	+	0.795447i	$0.707236\pi$
$524$	−0.959275			−0.0419061
$525$		0			0
$526$	−14.0358			−0.611991
$527$	−16.2220	−	16.2220i	−0.706641	−	0.706641i
$528$	−1.24879	−	1.24879i	−0.0543466	−	0.0543466i
$529$			6.62268i			0.287943i
$530$	0.784804	−	0.476277i	0.0340897	−	0.0206881i
$531$		−	10.3676i		−	0.449915i
$532$		0			0
$533$	32.2942	−	32.2942i	1.39881	−	1.39881i
$534$			1.11625i			0.0483051i
$535$	32.0474	+	7.84049i	1.38553	+	0.338974i
$536$	7.63862			0.329938
$537$	−9.44244	+	9.44244i	−0.407472	+	0.407472i
$538$	−18.7754	−	18.7754i	−0.809466	−	0.809466i
$539$		0			0
$540$	−2.17201	−	0.531389i	−0.0934684	−	0.0228673i
$541$	−13.6248			−0.585775			−0.292887	−	0.956147i	$-0.594616\pi$
$541$	−13.6248			−0.585775			−0.292887	+	0.956147i	$0.594616\pi$
$542$	8.45744	−	8.45744i	0.363278	−	0.363278i
$543$	−6.17956	+	6.17956i	−0.265190	+	0.265190i
$544$	−2.22097			−0.0952233
$545$	23.3746	+	38.5164i	1.00126	+	1.64986i
$546$		0			0
$547$	−14.8290	−	14.8290i	−0.634042	−	0.634042i	0.315037	−	0.949079i	$-0.397983\pi$
$547$	−14.8290	−	14.8290i	−0.634042	−	0.634042i	−0.949079	+	0.315037i	$0.897983\pi$
$548$	−7.88194	+	7.88194i	−0.336700	+	0.336700i
$549$	6.78891			0.289743
$550$	8.42136	−	2.65604i	0.359088	−	0.113254i
$551$			6.82326i			0.290681i
$552$	−2.86158	+	2.86158i	−0.121797	+	0.121797i
$553$		0			0
$554$			2.36165i			0.100337i
$555$	−3.86146	−	6.36288i	−0.163910	−	0.270089i
$556$		−	13.5695i		−	0.575477i
$557$	0.0283655	+	0.0283655i	0.00120188	+	0.00120188i	0.707707	−	0.706506i	$-0.249729\pi$
$557$	0.0283655	+	0.0283655i	0.00120188	+	0.00120188i	−0.706506	+	0.707707i	$0.749729\pi$
$558$	7.30401	+	7.30401i	0.309203	+	0.309203i
$559$	18.7987			0.795099
$560$		0			0
$561$	−3.92236			−0.165602
$562$	7.79984	+	7.79984i	0.329017	+	0.329017i
$563$	−9.83345	−	9.83345i	−0.414430	−	0.414430i	0.468848	−	0.883279i	$-0.344669\pi$
$563$	−9.83345	−	9.83345i	−0.414430	−	0.414430i	−0.883279	+	0.468848i	$0.844669\pi$
$564$			6.14785i			0.258871i
$565$	4.91989	−	20.1096i	0.206981	−	0.846018i
$566$			23.4108i			0.984031i
$567$		0			0
$568$	−7.57968	+	7.57968i	−0.318036	+	0.318036i
$569$			19.8397i			0.831722i	0.909428	+	0.415861i	$0.136520\pi$
$569$			19.8397i			0.831722i	−0.909428	+	0.415861i	$0.863480\pi$
$570$	2.05799	+	3.39114i	0.0861998	+	0.142039i
$571$	−5.88908			−0.246450			−0.123225	−	0.992379i	$-0.539324\pi$
$571$	−5.88908			−0.246450			−0.123225	+	0.992379i	$0.539324\pi$
$572$	4.79298	−	4.79298i	0.200405	−	0.200405i
$573$	7.69044	+	7.69044i	0.321273	+	0.321273i
$574$		0			0
$575$	−6.08626	−	19.2974i	−0.253815	−	0.804758i
$576$	1.00000			0.0416667
$577$	10.5453	−	10.5453i	0.439005	−	0.439005i	−0.452672	−	0.891677i	$-0.649529\pi$
$577$	10.5453	−	10.5453i	0.439005	−	0.439005i	0.891677	+	0.452672i	$0.149529\pi$
$578$	8.53286	−	8.53286i	0.354920	−	0.354920i
$579$	−11.2012			−0.465506
$580$	−7.35252	+	4.46205i	−0.305297	+	0.185276i
$581$		0			0
$582$	−7.26720	−	7.26720i	−0.301235	−	0.301235i
$583$	−0.512691	+	0.512691i	−0.0212335	+	0.0212335i
$584$	−10.6328			−0.439990
$585$	2.03952	−	8.33639i	0.0843239	−	0.344667i
$586$			21.8972i			0.904565i
$587$	−4.86057	+	4.86057i	−0.200617	+	0.200617i	−0.800264	−	0.599647i	$-0.795308\pi$
$587$	−4.86057	+	4.86057i	−0.200617	+	0.200617i	0.599647	+	0.800264i	$0.295308\pi$
$588$		0			0
$589$		−	18.3243i		−	0.755039i
$590$	−22.5185	−	5.50922i	−0.927072	−	0.226811i
$591$			14.6760i			0.603691i
$592$	2.35366	+	2.35366i	0.0967348	+	0.0967348i
$593$	−14.9862	−	14.9862i	−0.615409	−	0.615409i	0.328941	−	0.944350i	$-0.393308\pi$
$593$	−14.9862	−	14.9862i	−0.615409	−	0.615409i	−0.944350	+	0.328941i	$0.893308\pi$
$594$	1.76606			0.0724622
$595$		0			0
$596$	−10.0986			−0.413655
$597$	−13.1260	−	13.1260i	−0.537213	−	0.537213i
$598$	−10.9830	−	10.9830i	−0.449130	−	0.449130i
$599$		−	11.5942i		−	0.473728i	−0.971543	−	0.236864i	$-0.923880\pi$
$599$		−	11.5942i		−	0.473728i	0.971543	−	0.236864i	$-0.0761196\pi$
$600$	−2.30836	+	4.43525i	−0.0942386	+	0.181068i
$601$		−	15.3561i		−	0.626387i	−0.949689	−	0.313193i	$-0.898601\pi$
$601$		−	15.3561i		−	0.626387i	0.949689	−	0.313193i	$-0.101399\pi$
$602$		0			0
$603$	−5.40132	+	5.40132i	−0.219959	+	0.219959i
$604$		−	14.3099i		−	0.582263i
$605$	15.0653	−	9.14275i	0.612493	−	0.371706i
$606$	18.3467			0.745282
$607$	−15.9479	+	15.9479i	−0.647306	+	0.647306i	−0.952341	−	0.305035i	$-0.901332\pi$
$607$	−15.9479	+	15.9479i	−0.647306	+	0.647306i	0.305035	+	0.952341i	$0.401332\pi$
$608$	−1.25440	−	1.25440i	−0.0508726	−	0.0508726i
$609$		0			0
$610$	3.60755	−	14.7456i	0.146065	−	0.597031i
$611$	−23.5961			−0.954594
$612$	1.57046	−	1.57046i	0.0634822	−	0.0634822i
$613$	−3.38354	+	3.38354i	−0.136660	+	0.136660i	−0.772127	−	0.635468i	$-0.780807\pi$
$613$	−3.38354	+	3.38354i	−0.136660	+	0.136660i	0.635468	+	0.772127i	$0.280807\pi$
$614$	−3.00024			−0.121080
$615$	6.32318	−	25.8455i	0.254975	−	1.04219i
$616$		0			0
$617$	17.3498	+	17.3498i	0.698475	+	0.698475i	0.964082	−	0.265606i	$-0.0855722\pi$
$617$	17.3498	+	17.3498i	0.698475	+	0.698475i	−0.265606	+	0.964082i	$0.585572\pi$
$618$	−6.44872	+	6.44872i	−0.259406	+	0.259406i
$619$	−20.9603			−0.842464			−0.421232	−	0.906953i	$-0.638402\pi$
$619$	−20.9603			−0.842464			−0.421232	+	0.906953i	$0.638402\pi$
$620$	19.7456	−	11.9831i	0.793004	−	0.481253i
$621$		−	4.04689i		−	0.162396i
$622$	−10.6211	+	10.6211i	−0.425868	+	0.425868i
$623$		0			0
$624$			3.83810i			0.153647i
$625$	−14.3429	−	20.4764i	−0.573716	−	0.819054i
$626$			13.3182i			0.532303i
$627$	−2.21534	−	2.21534i	−0.0884722	−	0.0884722i
$628$	−6.77647	−	6.77647i	−0.270411	−	0.270411i
$629$	7.39267			0.294765
$630$		0			0
$631$	−48.7823			−1.94199			−0.970996	−	0.239095i	$-0.923149\pi$
$631$	−48.7823			−1.94199			−0.970996	+	0.239095i	$0.923149\pi$
$632$	−8.97383	−	8.97383i	−0.356960	−	0.356960i
$633$	0.320413	+	0.320413i	0.0127353	+	0.0127353i
$634$		−	13.9017i		−	0.552107i
$635$	−38.5324	−	9.42707i	−1.52911	−	0.374102i
$636$		−	0.410550i		−	0.0162794i
$637$		0			0
$638$	4.80320	−	4.80320i	0.190160	−	0.190160i
$639$		−	10.7193i		−	0.424048i
$640$	0.531389	−	2.17201i	0.0210050	−	0.0858562i
$641$	12.0639			0.476496			0.238248	−	0.971204i	$-0.423427\pi$
$641$	12.0639			0.476496			0.238248	+	0.971204i	$0.423427\pi$
$642$	10.4332	−	10.4332i	0.411764	−	0.411764i
$643$	15.5935	+	15.5935i	0.614947	+	0.614947i	0.944231	−	0.329284i	$-0.106807\pi$
$643$	15.5935	+	15.5935i	0.614947	+	0.614947i	−0.329284	+	0.944231i	$0.606807\pi$
$644$		0			0
$645$	9.36281	−	5.68204i	0.368660	−	0.223730i
$646$	−3.93998			−0.155016
$647$	−4.63554	+	4.63554i	−0.182242	+	0.182242i	−0.792332	−	0.610090i	$-0.791133\pi$
$647$	−4.63554	+	4.63554i	−0.182242	+	0.182242i	0.610090	+	0.792332i	$0.291133\pi$
$648$	−0.707107	+	0.707107i	−0.0277778	+	0.0277778i
$649$	18.3097			0.718720
$650$	−17.0229	−	8.85973i	−0.667694	−	0.347507i
$651$		0			0
$652$	8.37474	+	8.37474i	0.327980	+	0.327980i
$653$	−16.3274	+	16.3274i	−0.638942	+	0.638942i	−0.950294	−	0.311353i	$-0.899218\pi$
$653$	−16.3274	+	16.3274i	−0.638942	+	0.638942i	0.311353	+	0.950294i	$0.399218\pi$
$654$	20.1488			0.787882
$655$	−1.11285	−	1.83374i	−0.0434826	−	0.0716502i
$656$			11.8993i			0.464591i
$657$	7.51854	−	7.51854i	0.293326	−	0.293326i
$658$		0			0
$659$			8.89429i			0.346472i	0.984880	+	0.173236i	$0.0554224\pi$
$659$			8.89429i			0.346472i	−0.984880	+	0.173236i	$0.944578\pi$
$660$	0.938463	−	3.83589i	0.0365296	−	0.149312i
$661$		−	8.36057i		−	0.325188i	−0.986693	−	0.162594i	$-0.948014\pi$
$661$		−	8.36057i		−	0.325188i	0.986693	−	0.162594i	$-0.0519861\pi$
$662$	13.1752	+	13.1752i	0.512071	+	0.512071i
$663$	6.02759	+	6.02759i	0.234092	+	0.234092i
$664$	−2.74678			−0.106596
$665$		0			0
$666$	−3.32858			−0.128980
$667$	−11.0065	−	11.0065i	−0.426172	−	0.426172i
$668$	6.95883	+	6.95883i	0.269245	+	0.269245i
$669$		−	6.60806i		−	0.255482i
$670$	8.86152	+	14.6019i	0.342350	+	0.564122i
$671$			11.9896i			0.462853i
$672$		0			0
$673$	−11.1305	+	11.1305i	−0.429048	+	0.429048i	−0.888304	−	0.459256i	$-0.848116\pi$
$673$	−11.1305	+	11.1305i	−0.429048	+	0.429048i	0.459256	+	0.888304i	$0.348116\pi$
$674$		−	13.6269i		−	0.524889i
$675$	−1.50394	−	4.76846i	−0.0578865	−	0.183538i
$676$	−1.73100			−0.0665768
$677$	−30.6974	+	30.6974i	−1.17980	+	1.17980i	−0.200003	+	0.979795i	$0.564095\pi$
$677$	−30.6974	+	30.6974i	−1.17980	+	1.17980i	−0.979795	+	0.200003i	$0.935905\pi$
$678$	−6.54677	−	6.54677i	−0.251427	−	0.251427i
$679$		0			0
$680$	−2.57653	−	4.24559i	−0.0988056	−	0.162811i
$681$	16.6075			0.636402
$682$	−12.8993	+	12.8993i	−0.493939	+	0.493939i
$683$	−12.6456	+	12.6456i	−0.483869	+	0.483869i	−0.906365	−	0.422496i	$-0.861154\pi$
$683$	−12.6456	+	12.6456i	−0.483869	+	0.483869i	0.422496	+	0.906365i	$0.361154\pi$
$684$	1.77399			0.0678301
$685$	−24.2108	−	5.92326i	−0.925048	−	0.226316i
$686$		0			0
$687$	−9.57528	−	9.57528i	−0.365320	−	0.365320i
$688$	−3.46335	+	3.46335i	−0.132039	+	0.132039i
$689$	1.57573			0.0600306
$690$	−8.78988	−	2.15047i	−0.334625	−	0.0818671i
$691$			35.2835i			1.34225i	0.741346	+	0.671123i	$0.234188\pi$
$691$			35.2835i			1.34225i	−0.741346	+	0.671123i	$0.765812\pi$
$692$	6.12788	−	6.12788i	0.232947	−	0.232947i
$693$		0			0
$694$		−	34.8774i		−	1.32393i
$695$	25.9394	−	15.7419i	0.983939	−	0.597126i
$696$			3.84628i			0.145793i
$697$	18.6875	+	18.6875i	0.707839	+	0.707839i
$698$	1.05873	+	1.05873i	0.0400735	+	0.0400735i
$699$	−11.5783			−0.437930
$700$		0			0
$701$	−14.9862			−0.566020			−0.283010	−	0.959117i	$-0.591333\pi$
$701$	−14.9862			−0.566020			−0.283010	+	0.959117i	$0.591333\pi$
$702$	−2.71395	−	2.71395i	−0.102431	−	0.102431i
$703$	4.17537	+	4.17537i	0.157477	+	0.157477i
$704$			1.76606i			0.0665608i
$705$	−11.7522	+	7.13208i	−0.442613	+	0.268610i
$706$		−	5.96674i		−	0.224561i
$707$		0			0
$708$	−7.33099	+	7.33099i	−0.275515	+	0.275515i
$709$			8.30928i			0.312061i	0.987752	+	0.156031i	$0.0498699\pi$
$709$			8.30928i			0.312061i	−0.987752	+	0.156031i	$0.950130\pi$
$710$	−23.2824	−	5.69611i	−0.873772	−	0.213771i
$711$	12.6909			0.475946
$712$	0.789311	−	0.789311i	0.0295807	−	0.0295807i
$713$	29.5585	+	29.5585i	1.10697	+	1.10697i
$714$		0			0
$715$	14.7225	+	3.60191i	0.550591	+	0.134704i
$716$	13.3536			0.499049
$717$	12.0395	−	12.0395i	0.449623	−	0.449623i
$718$	12.2466	−	12.2466i	0.457038	−	0.457038i
$719$	−14.1536			−0.527839			−0.263920	−	0.964545i	$-0.585015\pi$
$719$	−14.1536			−0.527839			−0.263920	+	0.964545i	$0.585015\pi$
$720$	1.16009	+	1.91159i	0.0432341	+	0.0712408i
$721$		0			0
$722$	11.2097	+	11.2097i	0.417183	+	0.417183i
$723$	−13.3796	+	13.3796i	−0.497593	+	0.497593i
$724$	8.73922			0.324791
$725$	−17.0592	−	8.87862i	−0.633564	−	0.329744i
$726$		−	7.88104i		−	0.292493i
$727$	19.9622	−	19.9622i	0.740357	−	0.740357i	−0.232290	−	0.972647i	$-0.574622\pi$
$727$	19.9622	−	19.9622i	0.740357	−	0.740357i	0.972647	+	0.232290i	$0.0746217\pi$
$728$		0			0
$729$		−	1.00000i		−	0.0370370i
$730$	−12.3351	−	20.3256i	−0.456542	−	0.752285i
$731$			10.8781i			0.402342i
$732$	−4.80048	−	4.80048i	−0.177431	−	0.177431i
$733$	−32.8171	−	32.8171i	−1.21213	−	1.21213i	−0.970325	−	0.241803i	$-0.922261\pi$
$733$	−32.8171	−	32.8171i	−1.21213	−	1.21213i	−0.241803	−	0.970325i	$-0.577739\pi$
$734$	−5.48491			−0.202452
$735$		0			0
$736$	4.04689			0.149170
$737$	−9.53904	−	9.53904i	−0.351375	−	0.351375i
$738$	−8.41410	−	8.41410i	−0.309727	−	0.309727i
$739$		−	17.4849i		−	0.643193i	−0.946877	−	0.321597i	$-0.895780\pi$
$739$		−	17.4849i		−	0.643193i	0.946877	−	0.321597i	$-0.104220\pi$
$740$	−1.76877	+	7.22970i	−0.0650213	+	0.265769i
$741$			6.80874i			0.250125i
$742$		0			0
$743$	−12.2427	+	12.2427i	−0.449143	+	0.449143i	−0.895069	−	0.445927i	$-0.852874\pi$
$743$	−12.2427	+	12.2427i	−0.449143	+	0.449143i	0.445927	+	0.895069i	$0.352874\pi$
$744$		−	10.3294i		−	0.378695i
$745$	−11.7153	−	19.3044i	−0.429216	−	0.707259i
$746$	−30.8410			−1.12917
$747$	1.94227	−	1.94227i	0.0710638	−	0.0710638i
$748$	2.77353	+	2.77353i	0.101410	+	0.101410i
$749$		0			0
$750$	−11.1563	+	0.732658i	−0.407371	+	0.0267529i
$751$	−24.9464			−0.910308			−0.455154	−	0.890413i	$-0.650416\pi$
$751$	−24.9464			−0.910308			−0.455154	+	0.890413i	$0.650416\pi$
$752$	4.34719	−	4.34719i	0.158526	−	0.158526i
$753$	−12.8359	+	12.8359i	−0.467766	+	0.467766i
$754$	−14.7624			−0.537615
$755$	27.3547	−	16.6009i	0.995541	−	0.604167i
$756$		0			0
$757$	−32.4637	−	32.4637i	−1.17991	−	1.17991i	−0.979765	−	0.200149i	$-0.935857\pi$
$757$	−32.4637	−	32.4637i	−1.17991	−	1.17991i	−0.200149	−	0.979765i	$-0.564143\pi$
$758$	9.13602	−	9.13602i	0.331835	−	0.331835i
$759$	7.14704			0.259421
$760$	0.942678	−	3.85312i	0.0341945	−	0.139767i
$761$			32.9956i			1.19609i	0.801463	+	0.598045i	$0.204055\pi$
$761$			32.9956i			1.19609i	−0.801463	+	0.598045i	$0.795945\pi$
$762$	−12.5444	+	12.5444i	−0.454435	+	0.454435i
$763$		0			0
$764$		−	10.8759i		−	0.393477i
$765$	4.82397	+	1.18020i	0.174411	+	0.0426702i
$766$			1.19003i			0.0429975i
$767$	−28.1371	−	28.1371i	−1.01597	−	1.01597i
$768$	−0.707107	−	0.707107i	−0.0255155	−	0.0255155i
$769$	10.0980			0.364144			0.182072	−	0.983285i	$-0.441720\pi$
$769$	10.0980			0.364144			0.182072	+	0.983285i	$0.441720\pi$
$770$		0			0
$771$	−24.0702			−0.866867
$772$	7.92044	+	7.92044i	0.285063	+	0.285063i
$773$	8.36265	+	8.36265i	0.300783	+	0.300783i	0.841320	−	0.540537i	$-0.181779\pi$
$773$	8.36265	+	8.36265i	0.300783	+	0.300783i	−0.540537	+	0.841320i	$0.681779\pi$
$774$		−	4.89791i		−	0.176052i
$775$	45.8136	+	23.8441i	1.64567	+	0.856504i
$776$			10.2774i			0.368936i
$777$		0			0
$778$	6.73784	−	6.73784i	0.241563	−	0.241563i
$779$			21.1093i			0.756319i
$780$	−7.33688	+	4.45255i	−0.262702	+	0.159427i
$781$	18.9309			0.677399
$782$	6.35549	−	6.35549i	0.227272	−	0.227272i
$783$	−2.71973	−	2.71973i	−0.0971953	−	0.0971953i
$784$		0			0
$785$	5.09250	−	20.8152i	0.181759	−	0.742926i
$786$	−0.959275			−0.0342162
$787$	−6.20178	+	6.20178i	−0.221070	+	0.221070i	−0.808949	−	0.587879i	$-0.799963\pi$
$787$	−6.20178	+	6.20178i	−0.221070	+	0.221070i	0.587879	+	0.808949i	$0.299963\pi$
$788$	10.3775	−	10.3775i	0.369684	−	0.369684i
$789$	−14.0358			−0.499689
$790$	6.74381	−	27.5648i	0.239934	−	0.980711i
$791$		0			0
$792$	−1.24879	−	1.24879i	−0.0443738	−	0.0443738i
$793$	18.4247	−	18.4247i	0.654281	−	0.654281i
$794$	−28.5332			−1.01261
$795$	0.784804	−	0.476277i	0.0278341	−	0.0168918i
$796$			18.5630i			0.657949i
$797$	−26.4972	+	26.4972i	−0.938580	+	0.938580i	−0.998220	−	0.0596400i	$-0.981005\pi$
$797$	−26.4972	+	26.4972i	−0.938580	+	0.938580i	0.0596400	+	0.998220i	$0.481005\pi$
$798$		0			0
$799$		−	13.6542i		−	0.483051i
$800$	4.76846	−	1.50394i	0.168590	−	0.0531722i
$801$			1.11625i			0.0394409i
$802$	−27.7398	−	27.7398i	−0.979526	−	0.979526i
$803$	13.2782	+	13.2782i	0.468577	+	0.468577i
$804$	7.63862			0.269394
$805$		0			0
$806$	39.6453			1.39645
$807$	−18.7754	−	18.7754i	−0.660927	−	0.660927i
$808$	−12.9730	−	12.9730i	−0.456390	−	0.456390i
$809$			39.2866i			1.38124i	0.723216	+	0.690622i	$0.242663\pi$
$809$			39.2866i			1.38124i	−0.723216	+	0.690622i	$0.757337\pi$
$810$	−2.17201	−	0.531389i	−0.0763166	−	0.0186711i
$811$		−	9.61165i		−	0.337511i	−0.985658	−	0.168755i	$-0.946025\pi$
$811$		−	9.61165i		−	0.337511i	0.985658	−	0.168755i	$-0.0539748\pi$
$812$		0			0
$813$	8.45744	−	8.45744i	0.296615	−	0.296615i
$814$		−	5.87846i		−	0.206040i
$815$	−6.29360	+	25.7246i	−0.220455	+	0.901092i
$816$	−2.22097			−0.0777495
$817$	−6.14394	+	6.14394i	−0.214949	+	0.214949i
$818$	6.12230	+	6.12230i	0.214061	+	0.214061i
$819$		0			0
$820$	−22.7467	+	13.8043i	−0.794348	+	0.482069i
$821$	51.8714			1.81032			0.905162	−	0.425067i	$-0.139750\pi$
$821$	51.8714			1.81032			0.905162	+	0.425067i	$0.139750\pi$
$822$	−7.88194	+	7.88194i	−0.274914	+	0.274914i
$823$	7.35640	−	7.35640i	0.256428	−	0.256428i	−0.567172	−	0.823600i	$-0.691962\pi$
$823$	7.35640	−	7.35640i	0.256428	−	0.256428i	0.823600	+	0.567172i	$0.191962\pi$
$824$	9.11987			0.317706
$825$	8.42136	−	2.65604i	0.293194	−	0.0924713i
$826$		0			0
$827$	7.55951	+	7.55951i	0.262870	+	0.262870i	0.826219	−	0.563349i	$-0.190487\pi$
$827$	7.55951	+	7.55951i	0.262870	+	0.262870i	−0.563349	+	0.826219i	$0.690487\pi$
$828$	−2.86158	+	2.86158i	−0.0994469	+	0.0994469i
$829$	−32.3051			−1.12200			−0.561001	−	0.827815i	$-0.689583\pi$
$829$	−32.3051			−1.12200			−0.561001	+	0.827815i	$0.689583\pi$
$830$	−3.18652	−	5.25072i	−0.110606	−	0.182255i
$831$			2.36165i			0.0819248i
$832$	2.71395	−	2.71395i	0.0940891	−	0.0940891i
$833$		0			0
$834$		−	13.5695i		−	0.469875i
$835$	−5.22954	+	21.3753i	−0.180976	+	0.739724i
$836$			3.13296i			0.108356i
$837$	7.30401	+	7.30401i	0.252463	+	0.252463i
$838$	−3.03789	−	3.03789i	−0.104942	−	0.104942i
$839$	−24.7218			−0.853490			−0.426745	−	0.904372i	$-0.640340\pi$
$839$	−24.7218			−0.853490			−0.426745	+	0.904372i	$0.640340\pi$
$840$		0			0
$841$	14.2061			0.489866
$842$	13.3181	+	13.3181i	0.458972	+	0.458972i
$843$	7.79984	+	7.79984i	0.268641	+	0.268641i
$844$		−	0.453133i		−	0.0155975i
$845$	−2.00812	−	3.30896i	−0.0690814	−	0.113832i
$846$			6.14785i			0.211367i
$847$		0			0
$848$	−0.290303	+	0.290303i	−0.00996904	+	0.00996904i
$849$			23.4108i			0.803458i
$850$	5.12681	−	9.85056i	0.175848	−	0.337872i
$851$	−13.4704			−0.461759
$852$	−7.57968	+	7.57968i	−0.259675	+	0.259675i
$853$	−28.0435	−	28.0435i	−0.960191	−	0.960191i	0.0390463	−	0.999237i	$-0.487568\pi$
$853$	−28.0435	−	28.0435i	−0.960191	−	0.960191i	−0.999237	+	0.0390463i	$0.987568\pi$
$854$		0			0
$855$	2.05799	+	3.39114i	0.0703819	+	0.115975i
$856$	−14.7547			−0.504305
$857$	−33.6436	+	33.6436i	−1.14924	+	1.14924i	−0.162540	+	0.986702i	$0.551969\pi$
$857$	−33.6436	+	33.6436i	−1.14924	+	1.14924i	−0.986702	+	0.162540i	$0.948031\pi$
$858$	4.79298	−	4.79298i	0.163630	−	0.163630i
$859$	−53.7120			−1.83263			−0.916315	−	0.400457i	$-0.868851\pi$
$859$	−53.7120			−1.83263			−0.916315	+	0.400457i	$0.868851\pi$
$860$	−10.6383	−	2.60270i	−0.362763	−	0.0887512i
$861$		0			0
$862$	−4.89645	−	4.89645i	−0.166774	−	0.166774i
$863$	28.2674	−	28.2674i	0.962232	−	0.962232i	−0.0370799	−	0.999312i	$-0.511806\pi$
$863$	28.2674	−	28.2674i	0.962232	−	0.962232i	0.999312	+	0.0370799i	$0.0118056\pi$
$864$	1.00000			0.0340207
$865$	18.8229	+	4.60509i	0.639998	+	0.156578i
$866$		−	16.2852i		−	0.553393i
$867$	8.53286	−	8.53286i	0.289791	−	0.289791i
$868$		0			0
$869$			22.4129i			0.760305i
$870$	−7.35252	+	4.46205i	−0.249274	+	0.151278i
$871$			29.3178i			0.993395i
$872$	−14.2474	−	14.2474i	−0.482477	−	0.482477i
$873$	−7.26720	−	7.26720i	−0.245957	−	0.245957i
$874$	7.17914			0.242838
$875$		0			0
$876$	−10.6328			−0.359250
$877$	−5.37896	−	5.37896i	−0.181635	−	0.181635i	0.610433	−	0.792068i	$-0.290995\pi$
$877$	−5.37896	−	5.37896i	−0.181635	−	0.181635i	−0.792068	+	0.610433i	$0.790995\pi$
$878$	12.8862	+	12.8862i	0.434889	+	0.434889i
$879$			21.8972i			0.738574i
$880$	−3.37598	+	2.04879i	−0.113804	+	0.0690648i
$881$			37.1659i			1.25215i	0.779763	+	0.626075i	$0.215340\pi$
$881$			37.1659i			1.25215i	−0.779763	+	0.626075i	$0.784660\pi$
$882$		0			0
$883$	25.7803	−	25.7803i	0.867577	−	0.867577i	−0.124627	−	0.992204i	$-0.539773\pi$
$883$	25.7803	−	25.7803i	0.867577	−	0.867577i	0.992204	+	0.124627i	$0.0397734\pi$
$884$		−	8.52430i		−	0.286703i
$885$	−22.5185	−	5.50922i	−0.756951	−	0.185190i
$886$	32.8324			1.10303
$887$	10.5420	−	10.5420i	0.353965	−	0.353965i	−0.507617	−	0.861583i	$-0.669474\pi$
$887$	10.5420	−	10.5420i	0.353965	−	0.353965i	0.861583	+	0.507617i	$0.169474\pi$
$888$	2.35366	+	2.35366i	0.0789837	+	0.0789837i
$889$		0			0
$890$	2.42452	+	0.593166i	0.0812700	+	0.0198830i
$891$	1.76606			0.0591651
$892$	−4.67260	+	4.67260i	−0.156450	+	0.156450i
$893$	7.71186	−	7.71186i	0.258068	−	0.258068i
$894$	−10.0986			−0.337748
$895$	15.4915	+	25.5267i	0.517823	+	0.853263i
$896$		0			0
$897$	−10.9830	−	10.9830i	−0.366713	−	0.366713i
$898$	5.75608	−	5.75608i	0.192083	−	0.192083i
$899$	39.7299			1.32507
$900$	−2.30836	+	4.43525i	−0.0769455	+	0.147842i
$901$			0.911820i			0.0303771i
$902$	14.8598	−	14.8598i	0.494777	−	0.494777i
$903$		0			0
$904$			9.25854i			0.307934i
$905$	10.1383	+	16.7058i	0.337009	+	0.555320i
$906$		−	14.3099i		−	0.475416i
$907$	15.2119	+	15.2119i	0.505103	+	0.505103i	0.913019	−	0.407916i	$-0.133744\pi$
$907$	15.2119	+	15.2119i	0.505103	+	0.505103i	−0.407916	+	0.913019i	$0.633744\pi$
$908$	−11.7433	−	11.7433i	−0.389715	−	0.389715i
$909$	18.3467			0.608520
$910$		0			0
$911$	23.6120			0.782301			0.391151	−	0.920327i	$-0.372077\pi$
$911$	23.6120			0.782301			0.391151	+	0.920327i	$0.372077\pi$
$912$	−1.25440	−	1.25440i	−0.0415373	−	0.0415373i
$913$	3.43015	+	3.43015i	0.113521	+	0.113521i
$914$		−	4.56599i		−	0.151030i
$915$	3.60755	−	14.7456i	0.119262	−	0.487473i
$916$			13.5415i			0.447423i
$917$		0			0
$918$	1.57046	−	1.57046i	0.0518330	−	0.0518330i
$919$		−	44.2136i		−	1.45847i	−0.684262	−	0.729236i	$-0.739876\pi$
$919$		−	44.2136i		−	1.45847i	0.684262	−	0.729236i	$-0.260124\pi$
$920$	4.69477	+	7.73600i	0.154782	+	0.255048i
$921$	−3.00024			−0.0988612
$922$	5.33791	−	5.33791i	0.175795	−	0.175795i
$923$	−29.0915	−	29.0915i	−0.957560	−	0.957560i
$924$		0			0
$925$	−15.8722	+	5.00597i	−0.521874	+	0.164595i
$926$	12.5532			0.412525
$927$	−6.44872	+	6.44872i	−0.211804	+	0.211804i
$928$	2.71973	−	2.71973i	0.0892796	−	0.0892796i
$929$	0.776448			0.0254744			0.0127372	−	0.999919i	$-0.495946\pi$
$929$	0.776448			0.0254744			0.0127372	+	0.999919i	$0.495946\pi$
$930$	19.7456	−	11.9831i	0.647485	−	0.392941i
$931$		0			0
$932$	8.18707	+	8.18707i	0.268177	+	0.268177i
$933$	−10.6211	+	10.6211i	−0.347720	+	0.347720i
$934$	11.5084			0.376565
$935$	−2.08430	+	8.51940i	−0.0681639	+	0.278614i
$936$			3.83810i			0.125452i
$937$	0.494892	−	0.494892i	0.0161674	−	0.0161674i	−0.698977	−	0.715144i	$-0.746361\pi$
$937$	0.494892	−	0.494892i	0.0161674	−	0.0161674i	0.715144	+	0.698977i	$0.246361\pi$
$938$		0			0
$939$			13.3182i			0.434624i
$940$	13.3532	+	3.26690i	0.435533	+	0.106555i
$941$		−	18.4494i		−	0.601434i	−0.953713	−	0.300717i	$-0.902774\pi$
$941$		−	18.4494i		−	0.601434i	0.953713	−	0.300717i	$-0.0972260\pi$
$942$	−6.77647	−	6.77647i	−0.220789	−	0.220789i
$943$	−34.0509	−	34.0509i	−1.10885	−	1.10885i
$944$	10.3676			0.337436
$945$		0			0
$946$	8.64999			0.281235
$947$	−7.30923	−	7.30923i	−0.237518	−	0.237518i	0.578304	−	0.815822i	$-0.303715\pi$
$947$	−7.30923	−	7.30923i	−0.237518	−	0.237518i	−0.815822	+	0.578304i	$0.803715\pi$
$948$	−8.97383	−	8.97383i	−0.291457	−	0.291457i
$949$		−	40.8098i		−	1.32474i
$950$	8.45919	−	2.66797i	0.274452	−	0.0865602i
$951$		−	13.9017i		−	0.450793i
$952$		0			0
$953$	11.1833	−	11.1833i	0.362263	−	0.362263i	−0.502383	−	0.864645i	$-0.667543\pi$
$953$	11.1833	−	11.1833i	0.362263	−	0.362263i	0.864645	+	0.502383i	$0.167543\pi$
$954$		−	0.410550i		−	0.0132921i
$955$	20.7903	−	12.6171i	0.672759	−	0.408280i
$956$	−17.0264			−0.550673
$957$	4.80320	−	4.80320i	0.155265	−	0.155265i
$958$	8.73106	+	8.73106i	0.282088	+	0.282088i
$959$		0			0
$960$	0.531389	−	2.17201i	0.0171505	−	0.0701013i
$961$	−75.6970			−2.44184
$962$	−9.03358	+	9.03358i	−0.291254	+	0.291254i
$963$	10.4332	−	10.4332i	0.336204	−	0.336204i
$964$	18.9216			0.609424
$965$	−5.95219	+	24.3291i	−0.191608	+	0.783181i
$966$		0			0
$967$	−3.47333	−	3.47333i	−0.111695	−	0.111695i	0.649051	−	0.760745i	$-0.275166\pi$
$967$	−3.47333	−	3.47333i	−0.111695	−	0.111695i	−0.760745	+	0.649051i	$0.775166\pi$
$968$	−5.57274	+	5.57274i	−0.179115	+	0.179115i
$969$	−3.93998			−0.126570
$970$	−19.6461	+	11.9227i	−0.630800	+	0.382815i
$971$			36.4108i			1.16848i	0.811582	+	0.584238i	$0.198607\pi$
$971$			36.4108i			1.16848i	−0.811582	+	0.584238i	$0.801393\pi$
$972$	−0.707107	+	0.707107i	−0.0226805	+	0.0226805i
$973$		0			0
$974$			15.5867i			0.499431i
$975$	−17.0229	−	8.85973i	−0.545170	−	0.283738i
$976$			6.78891i			0.217308i
$977$	−17.0532	−	17.0532i	−0.545581	−	0.545581i	0.379578	−	0.925160i	$-0.376069\pi$
$977$	−17.0532	−	17.0532i	−0.545581	−	0.545581i	−0.925160	+	0.379578i	$0.876069\pi$
$978$	8.37474	+	8.37474i	0.267795	+	0.267795i
$979$	−1.97137			−0.0630052
$980$		0			0
$981$	20.1488			0.643303
$982$	1.89133	+	1.89133i	0.0603547	+	0.0603547i
$983$	18.0903	+	18.0903i	0.576991	+	0.576991i	0.934073	−	0.357082i	$-0.116228\pi$
$983$	18.0903	+	18.0903i	0.576991	+	0.576991i	−0.357082	+	0.934073i	$0.616228\pi$
$984$			11.8993i			0.379337i
$985$	31.8765	+	7.79868i	1.01567	+	0.248487i
$986$		−	8.54248i		−	0.272048i
$987$		0			0
$988$	4.81451	−	4.81451i	0.153170	−	0.153170i
$989$		−	19.8213i		−	0.630281i
$990$	0.938463	−	3.83589i	0.0298263	−	0.121913i
$991$	26.2349			0.833378			0.416689	−	0.909049i	$-0.363190\pi$
$991$	26.2349			0.833378			0.416689	+	0.909049i	$0.363190\pi$
$992$	−7.30401	+	7.30401i	−0.231902	+	0.231902i
$993$	13.1752	+	13.1752i	0.418104	+	0.418104i
$994$		0			0
$995$	−35.4849	+	21.5349i	−1.12495	+	0.682701i
$996$	−2.74678			−0.0870350
$997$	26.3868	−	26.3868i	0.835677	−	0.835677i	−0.152609	−	0.988287i	$-0.548768\pi$
$997$	26.3868	−	26.3868i	0.835677	−	0.835677i	0.988287	+	0.152609i	$0.0487677\pi$
$998$	−12.8527	+	12.8527i	−0.406846	+	0.406846i
$999$	−3.32858			−0.105312

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1470.2.m.e.97.2		16
5.3	odd	4		1470.2.m.d.1273.3		16
7.2	even	3		210.2.u.b.157.2	yes	16
7.3	odd	6		210.2.u.a.187.3	yes	16
7.6	odd	2		1470.2.m.d.97.3		16
21.2	odd	6		630.2.bv.b.577.3		16
21.17	even	6		630.2.bv.a.397.2		16
35.2	odd	12		1050.2.bc.h.493.1		16
35.3	even	12		210.2.u.b.103.2	yes	16
35.9	even	6		1050.2.bc.g.157.4		16
35.13	even	4	inner	1470.2.m.e.1273.2		16
35.17	even	12		1050.2.bc.g.943.4		16
35.23	odd	12		210.2.u.a.73.3	✓	16
35.24	odd	6		1050.2.bc.h.607.1		16
105.23	even	12		630.2.bv.a.73.2		16
105.38	odd	12		630.2.bv.b.523.3		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
210.2.u.a.73.3	✓	16	35.23	odd	12
210.2.u.a.187.3	yes	16	7.3	odd	6
210.2.u.b.103.2	yes	16	35.3	even	12
210.2.u.b.157.2	yes	16	7.2	even	3
630.2.bv.a.73.2		16	105.23	even	12
630.2.bv.a.397.2		16	21.17	even	6
630.2.bv.b.523.3		16	105.38	odd	12
630.2.bv.b.577.3		16	21.2	odd	6
1050.2.bc.g.157.4		16	35.9	even	6
1050.2.bc.g.943.4		16	35.17	even	12
1050.2.bc.h.493.1		16	35.2	odd	12
1050.2.bc.h.607.1		16	35.24	odd	6
1470.2.m.d.97.3		16	7.6	odd	2
1470.2.m.d.1273.3		16	5.3	odd	4
1470.2.m.e.97.2		16	1.1	even	1	trivial
1470.2.m.e.1273.2		16	35.13	even	4	inner

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:	\( N \)	\(=\)	\( 1470 = 2 \cdot 3 \cdot 5 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1470.m (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.707107 - 0.707107i) q^{2} +(-0.707107 - 0.707107i) q^{3} +1.00000i q^{4} +(-1.91159 + 1.16009i) q^{5} +1.00000i q^{6} +(0.707107 - 0.707107i) q^{8} +1.00000i q^{9} +O(q^{10})\)	\(q+(-0.707107 - 0.707107i) q^{2} +(-0.707107 - 0.707107i) q^{3} +1.00000i q^{4} +(-1.91159 + 1.16009i) q^{5} +1.00000i q^{6} +(0.707107 - 0.707107i) q^{8} +1.00000i q^{9} +(2.17201 + 0.531389i) q^{10} -1.76606 q^{11} +(0.707107 - 0.707107i) q^{12} +(2.71395 + 2.71395i) q^{13} +(2.17201 + 0.531389i) q^{15} -1.00000 q^{16} +(-1.57046 + 1.57046i) q^{17} +(0.707107 - 0.707107i) q^{18} -1.77399 q^{19} +(-1.16009 - 1.91159i) q^{20} +(1.24879 + 1.24879i) q^{22} +(2.86158 - 2.86158i) q^{23} -1.00000 q^{24} +(2.30836 - 4.43525i) q^{25} -3.83810i q^{26} +(0.707107 - 0.707107i) q^{27} -3.84628i q^{29} +(-1.16009 - 1.91159i) q^{30} +10.3294i q^{31} +(0.707107 + 0.707107i) q^{32} +(1.24879 + 1.24879i) q^{33} +2.22097 q^{34} -1.00000 q^{36} +(-2.35366 - 2.35366i) q^{37} +(1.25440 + 1.25440i) q^{38} -3.83810i q^{39} +(-0.531389 + 2.17201i) q^{40} -11.8993i q^{41} +(3.46335 - 3.46335i) q^{43} -1.76606i q^{44} +(-1.16009 - 1.91159i) q^{45} -4.04689 q^{46} +(-4.34719 + 4.34719i) q^{47} +(0.707107 + 0.707107i) q^{48} +(-4.76846 + 1.50394i) q^{50} +2.22097 q^{51} +(-2.71395 + 2.71395i) q^{52} +(0.290303 - 0.290303i) q^{53} -1.00000 q^{54} +(3.37598 - 2.04879i) q^{55} +(1.25440 + 1.25440i) q^{57} +(-2.71973 + 2.71973i) q^{58} -10.3676 q^{59} +(-0.531389 + 2.17201i) q^{60} -6.78891i q^{61} +(7.30401 - 7.30401i) q^{62} -1.00000i q^{64} +(-8.33639 - 2.03952i) q^{65} -1.76606i q^{66} +(5.40132 + 5.40132i) q^{67} +(-1.57046 - 1.57046i) q^{68} -4.04689 q^{69} -10.7193 q^{71} +(0.707107 + 0.707107i) q^{72} +(-7.51854 - 7.51854i) q^{73} +3.32858i q^{74} +(-4.76846 + 1.50394i) q^{75} -1.77399i q^{76} +(-2.71395 + 2.71395i) q^{78} -12.6909i q^{79} +(1.91159 - 1.16009i) q^{80} -1.00000 q^{81} +(-8.41410 + 8.41410i) q^{82} +(-1.94227 - 1.94227i) q^{83} +(1.18020 - 4.82397i) q^{85} -4.89791 q^{86} +(-2.71973 + 2.71973i) q^{87} +(-1.24879 + 1.24879i) q^{88} +1.11625 q^{89} +(-0.531389 + 2.17201i) q^{90} +(2.86158 + 2.86158i) q^{92} +(7.30401 - 7.30401i) q^{93} +6.14785 q^{94} +(3.39114 - 2.05799i) q^{95} -1.00000i q^{96} +(-7.26720 + 7.26720i) q^{97} -1.76606i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q+O(q^{10}) \) 16 * q	\( 16 q + 4 q^{10} - 8 q^{11} + 16 q^{13} + 4 q^{15} - 16 q^{16} - 24 q^{17} - 16 q^{19} + 8 q^{20} + 4 q^{22} + 8 q^{23} - 16 q^{24} + 16 q^{25} + 8 q^{30} + 4 q^{33} - 16 q^{34} - 16 q^{36} + 16 q^{37} - 8 q^{38} - 24 q^{43} + 8 q^{45} + 8 q^{46} - 24 q^{47} - 16 q^{51} - 16 q^{52} - 16 q^{53} - 16 q^{54} + 56 q^{55} - 8 q^{57} - 36 q^{58} + 16 q^{59} - 8 q^{62} - 32 q^{65} + 48 q^{67} - 24 q^{68} + 8 q^{69} - 32 q^{71} - 56 q^{73} - 16 q^{78} - 16 q^{81} - 24 q^{82} + 16 q^{83} + 8 q^{85} + 16 q^{86} - 36 q^{87} - 4 q^{88} - 32 q^{89} + 8 q^{92} - 8 q^{93} + 16 q^{94} - 24 q^{95} - 44 q^{97}+O(q^{100}) \) 16 * q + 4 * q^10 - 8 * q^11 + 16 * q^13 + 4 * q^15 - 16 * q^16 - 24 * q^17 - 16 * q^19 + 8 * q^20 + 4 * q^22 + 8 * q^23 - 16 * q^24 + 16 * q^25 + 8 * q^30 + 4 * q^33 - 16 * q^34 - 16 * q^36 + 16 * q^37 - 8 * q^38 - 24 * q^43 + 8 * q^45 + 8 * q^46 - 24 * q^47 - 16 * q^51 - 16 * q^52 - 16 * q^53 - 16 * q^54 + 56 * q^55 - 8 * q^57 - 36 * q^58 + 16 * q^59 - 8 * q^62 - 32 * q^65 + 48 * q^67 - 24 * q^68 + 8 * q^69 - 32 * q^71 - 56 * q^73 - 16 * q^78 - 16 * q^81 - 24 * q^82 + 16 * q^83 + 8 * q^85 + 16 * q^86 - 36 * q^87 - 4 * q^88 - 32 * q^89 + 8 * q^92 - 8 * q^93 + 16 * q^94 - 24 * q^95 - 44 * q^97

Introduction

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