LMFDB - Embedded newform 1470.2.m.e.1273.2

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			1273.2
Root			$0.792206 - 1.03242i$ of defining polynomial
Character	$\chi$	$=$	1470.1273
Dual form			1470.2.m.e.97.2

$q$-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 $\left(\mathbb{Z}/1470\mathbb{Z}\right)^\times$.

$n$	$491$	$1081$	$1177$
$\chi(n)$	$1$	$-1$	$e\left(\frac{3}{4}\right)$

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	−0.222272	−	0.974985i	$-0.571347\pi$
$13$	2.71395	−	2.71395i	0.752713	−	0.752713i	0.974985	+	0.222272i	$0.0713472\pi$
$14$		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	0.490531	−	0.871424i	$-0.336803\pi$
$17$	−1.57046	−	1.57046i	−0.380893	−	0.380893i	−0.871424	+	0.490531i	$0.836803\pi$
$18$	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	0.939428	−	0.342747i	$-0.111357\pi$
$23$	2.86158	+	2.86158i	0.596681	+	0.596681i	−0.342747	+	0.939428i	$0.611357\pi$
$24$	−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	$0.116241\pi$
$29$			3.84628i			0.714236i	−0.934059	+	0.357118i	$0.883759\pi$
$30$	−1.16009	+	1.91159i	−0.211803	+	0.349007i
$31$		−	10.3294i		−	1.85522i	−0.373551	−	0.927610i	$-0.621860\pi$
$31$		−	10.3294i		−	1.85522i	0.373551	−	0.927610i	$-0.378140\pi$
$32$	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	−0.873594	−	0.486655i	$-0.838217\pi$
$37$	−2.35366	+	2.35366i	−0.386939	+	0.386939i	0.486655	+	0.873594i	$0.338217\pi$
$38$	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	$0.379487\pi$
$41$			11.8993i			1.85836i	−0.369622	+	0.929182i	$0.620513\pi$
$42$		0			0
$43$	3.46335	+	3.46335i	0.528155	+	0.528155i	0.920022	−	0.391867i	$-0.128171\pi$
$43$	3.46335	+	3.46335i	0.528155	+	0.528155i	−0.391867	+	0.920022i	$0.628171\pi$
$44$			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	0.314992	−	0.949094i	$-0.397998\pi$
$47$	−4.34719	−	4.34719i	−0.634102	−	0.634102i	−0.949094	+	0.314992i	$0.897998\pi$
$48$	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	0.726764	−	0.686888i	$-0.241024\pi$
$53$	0.290303	+	0.290303i	0.0398762	+	0.0398762i	−0.686888	+	0.726764i	$0.741024\pi$
$54$	−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	$0.143116\pi$
$61$			6.78891i			0.869230i	−0.900616	+	0.434615i	$0.856884\pi$
$62$	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	−0.295474	−	0.955351i	$-0.595478\pi$
$67$	5.40132	−	5.40132i	0.659877	−	0.659877i	0.955351	+	0.295474i	$0.0954776\pi$
$68$	−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	−0.993532	−	0.113553i	$-0.963777\pi$
$73$	−7.51854	+	7.51854i	−0.879979	+	0.879979i	0.113553	+	0.993532i	$0.463777\pi$
$74$		−	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	$0.253082\pi$
$79$			12.6909i			1.42784i	−0.700228	+	0.713920i	$0.746918\pi$
$80$	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	−0.805622	−	0.592430i	$-0.798169\pi$
$83$	−1.94227	+	1.94227i	−0.213191	+	0.213191i	0.592430	+	0.805622i	$0.298169\pi$
$84$		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	0.234293	−	0.972166i	$-0.424722\pi$
$97$	−7.26720	−	7.26720i	−0.737872	−	0.737872i	−0.972166	+	0.234293i	$0.924722\pi$
$98$		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	$0.366069\pi$
$101$			18.3467i			1.82556i	−0.408451	+	0.912780i	$0.633931\pi$
$102$	−1.57046	+	1.57046i	−0.155499	+	0.155499i
$103$	6.44872	−	6.44872i	0.635411	−	0.635411i	−0.314009	−	0.949420i	$-0.601672\pi$
$103$	6.44872	−	6.44872i	0.635411	−	0.635411i	0.949420	+	0.314009i	$0.101672\pi$
$104$	3.83810			0.376356
$105$		0			0
$106$	−0.410550			−0.0398762
$107$	−10.4332	+	10.4332i	−1.00861	+	1.00861i	−0.00864811	+	0.999963i	$0.502753\pi$
$107$	−10.4332	+	10.4332i	−1.00861	+	1.00861i	−0.999963	+	0.00864811i	$0.997247\pi$
$108$	0.707107	−	0.707107i	0.0680414	−	0.0680414i
$109$			20.1488i			1.92991i	0.262416	+	0.964955i	$0.415481\pi$
$109$			20.1488i			1.92991i	−0.262416	+	0.964955i	$0.584519\pi$
$110$	−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	0.328600	−	0.944469i	$-0.393423\pi$
$113$	−6.54677	−	6.54677i	−0.615869	−	0.615869i	−0.944469	+	0.328600i	$0.893423\pi$
$114$			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	0.120409	−	0.992724i	$-0.461579\pi$
$127$	12.5444	−	12.5444i	1.11313	−	1.11313i	0.992724	−	0.120409i	$-0.0384206\pi$
$128$	−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	$-0.986657\pi$
$131$		−	0.959275i		−	0.0838122i	0.999122	−	0.0419061i	$-0.0133430\pi$
$132$	−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	−0.285099	−	0.958498i	$-0.592026\pi$
$137$	7.88194	−	7.88194i	0.673399	−	0.673399i	0.958498	+	0.285099i	$0.0920264\pi$
$138$	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	$-0.864252\pi$
$149$		−	10.0986i		−	0.827310i	0.910434	−	0.413655i	$-0.135748\pi$
$150$	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	0.382948	−	0.923770i	$-0.374909\pi$
$157$	−6.77647	−	6.77647i	−0.540821	−	0.540821i	−0.923770	+	0.382948i	$0.874909\pi$
$158$	−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	0.954422	−	0.298462i	$-0.0964735\pi$
$163$	8.37474	+	8.37474i	0.655960	+	0.655960i	−0.298462	+	0.954422i	$0.596473\pi$
$164$	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	0.923085	−	0.384595i	$-0.125659\pi$
$167$	6.95883	+	6.95883i	0.538490	+	0.538490i	−0.384595	+	0.923085i	$0.625659\pi$
$168$		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	−0.900581	−	0.434687i	$-0.856859\pi$
$173$	−6.12788	+	6.12788i	−0.465894	+	0.465894i	0.434687	+	0.900581i	$0.356859\pi$
$174$	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	$0.166317\pi$
$179$			13.3536i			0.998097i	−0.866574	+	0.499049i	$0.833683\pi$
$180$	1.91159	+	1.16009i	0.142482	+	0.0864683i
$181$			8.73922i			0.649581i	0.945786	+	0.324791i	$0.105294\pi$
$181$			8.73922i			0.649581i	−0.945786	+	0.324791i	$0.894706\pi$
$182$		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	0.932163	−	0.362038i	$-0.117919\pi$
$193$	7.92044	+	7.92044i	0.570126	+	0.570126i	−0.362038	+	0.932163i	$0.617919\pi$
$194$	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	−0.972456	−	0.233088i	$-0.925117\pi$
$197$	−10.3775	+	10.3775i	−0.739367	+	0.739367i	0.233088	+	0.972456i	$0.425117\pi$
$198$	−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	−0.533132	−	0.846032i	$-0.678985\pi$
$223$	4.67260	−	4.67260i	0.312901	−	0.312901i	0.846032	+	0.533132i	$0.178985\pi$
$224$		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	0.200304	−	0.979734i	$-0.435807\pi$
$227$	−11.7433	−	11.7433i	−0.779430	−	0.779430i	−0.979734	+	0.200304i	$0.935807\pi$
$228$	−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	0.922456	−	0.386103i	$-0.126179\pi$
$233$	8.18707	+	8.18707i	0.536353	+	0.536353i	−0.386103	+	0.922456i	$0.626179\pi$
$234$	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	$-0.814371\pi$
$239$		−	17.0264i		−	1.10135i	0.834721	−	0.550673i	$-0.185629\pi$
$240$	−2.17201	+	0.531389i	−0.140203	+	0.0343010i
$241$			18.9216i			1.21885i	0.792844	+	0.609424i	$0.208599\pi$
$241$			18.9216i			1.21885i	−0.792844	+	0.609424i	$0.791401\pi$
$242$	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	$0.194179\pi$
$251$			18.1527i			1.14579i	−0.819629	+	0.572894i	$0.805821\pi$
$252$		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	0.997968	+	0.0637239i	$0.0202977\pi$
$257$	17.0202	+	17.0202i	1.06169	+	1.06169i	0.0637239	+	0.997968i	$0.479702\pi$
$258$	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	0.943465	−	0.331473i	$-0.107546\pi$
$263$	9.92483	+	9.92483i	0.611991	+	0.611991i	−0.331473	+	0.943465i	$0.607546\pi$
$264$	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	$-0.881657\pi$
$271$		−	11.9606i		−	0.726556i	0.931681	−	0.363278i	$-0.118343\pi$
$272$	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	−0.755493	−	0.655156i	$-0.772603\pi$
$277$	−1.66994	+	1.66994i	−0.100337	+	0.100337i	0.655156	+	0.755493i	$0.272603\pi$
$278$	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	−0.999874	−	0.0158433i	$-0.994957\pi$
$283$	−16.5540	+	16.5540i	−0.984031	+	0.984031i	0.0158433	+	0.999874i	$0.494957\pi$
$284$			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	−0.995827	−	0.0912620i	$-0.970910\pi$
$293$	−15.4837	+	15.4837i	−0.904565	+	0.904565i	0.0912620	+	0.995827i	$0.470910\pi$
$294$		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	0.765050	−	0.643971i	$-0.222714\pi$
$307$	2.12149	+	2.12149i	0.121080	+	0.121080i	−0.643971	+	0.765050i	$0.722714\pi$
$308$		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	$0.140031\pi$
$311$			15.0205i			0.851737i	−0.904785	+	0.425868i	$0.859969\pi$
$312$	−2.71395	+	2.71395i	−0.153647	+	0.153647i
$313$	−9.41740	+	9.41740i	−0.532303	+	0.532303i	−0.921257	−	0.388954i	$-0.872836\pi$
$313$	−9.41740	+	9.41740i	−0.532303	+	0.532303i	0.388954	+	0.921257i	$0.372836\pi$
$314$	9.58338			0.540821
$315$		0			0
$316$	12.6909			0.713920
$317$	9.82998	−	9.82998i	0.552107	−	0.552107i	−0.374942	−	0.927048i	$-0.622337\pi$
$317$	9.82998	−	9.82998i	0.552107	−	0.552107i	0.927048	+	0.374942i	$0.122337\pi$
$318$	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	−0.394155	−	0.919044i	$-0.628963\pi$
$337$	9.63568	−	9.63568i	0.524889	−	0.524889i	0.919044	+	0.394155i	$0.128963\pi$
$338$	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	0.413359	−	0.910568i	$-0.364355\pi$
$347$	24.6620	−	24.6620i	1.32393	−	1.32393i	0.910568	−	0.413359i	$-0.135645\pi$
$348$	−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	−0.585855	−	0.810416i	$-0.699241\pi$
$353$	4.21912	−	4.21912i	0.224561	−	0.224561i	0.810416	+	0.585855i	$0.199241\pi$
$354$			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	$-0.848910\pi$
$359$		−	17.3193i		−	0.914076i	0.889447	−	0.457038i	$-0.151090\pi$
$360$	−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	0.801050	−	0.598598i	$-0.204275\pi$
$367$	3.87842	+	3.87842i	0.202452	+	0.202452i	−0.598598	+	0.801050i	$0.704275\pi$
$368$	−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	0.990312	+	0.138857i	$0.0443428\pi$
$373$	21.8079	+	21.8079i	1.12917	+	1.12917i	0.138857	+	0.990312i	$0.455657\pi$
$374$	−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	$-0.892332\pi$
$379$		−	12.9203i		−	0.663670i	0.943337	−	0.331835i	$-0.107668\pi$
$380$	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	−0.728279	−	0.685281i	$-0.759679\pi$
$383$	−0.841477	+	0.841477i	−0.0429975	+	0.0429975i	0.685281	+	0.728279i	$0.259679\pi$
$384$	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	$-0.922340\pi$
$389$		−	9.52874i		−	0.483126i	0.970385	−	0.241563i	$-0.0776601\pi$
$390$	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	0.999920	+	0.0126858i	$0.00403813\pi$
$397$	20.1760	+	20.1760i	1.01261	+	1.01261i	0.0126858	+	0.999920i	$0.495962\pi$
$398$	−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	−0.374025	−	0.927419i	$-0.622023\pi$
$433$	11.5154	−	11.5154i	0.553393	−	0.553393i	0.927419	+	0.374025i	$0.122023\pi$
$434$		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	−0.994044	−	0.108982i	$-0.965241\pi$
$443$	−23.2160	−	23.2160i	−1.10303	−	1.10303i	−0.108982	−	0.994044i	$-0.534759\pi$
$444$	−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	$-0.938476\pi$
$449$		−	8.14032i		−	0.384165i	0.981379	−	0.192083i	$-0.0615242\pi$
$450$	−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	−0.627548	−	0.778578i	$-0.715941\pi$
$457$	3.22864	−	3.22864i	0.151030	−	0.151030i	0.778578	+	0.627548i	$0.215941\pi$
$458$	−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	$-0.943751\pi$
$461$		−	7.54894i		−	0.351589i	0.984427	−	0.175795i	$-0.0562495\pi$
$462$		0			0
$463$	−8.87647	−	8.87647i	−0.412525	−	0.412525i	0.470092	−	0.882617i	$-0.344221\pi$
$463$	−8.87647	−	8.87647i	−0.412525	−	0.412525i	−0.882617	+	0.470092i	$0.844221\pi$
$464$		−	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	0.493297	−	0.869861i	$-0.335792\pi$
$467$	−8.13763	−	8.13763i	−0.376565	−	0.376565i	−0.869861	+	0.493297i	$0.835792\pi$
$468$	−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	−0.911261	−	0.411830i	$-0.864890\pi$
$487$	−11.0215	+	11.0215i	−0.499431	+	0.499431i	0.411830	+	0.911261i	$0.364890\pi$
$488$	−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	$0.133371\pi$
$499$			18.1765i			0.813692i	−0.913497	+	0.406846i	$0.866629\pi$
$500$	−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	−0.782722	−	0.622371i	$-0.786169\pi$
$503$	−3.59630	+	3.59630i	−0.160351	+	0.160351i	0.622371	+	0.782722i	$0.286169\pi$
$504$		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	$0.0372405\pi$
$521$			5.32872i			0.233455i	−0.993164	+	0.116728i	$0.962760\pi$
$522$	−2.71973	+	2.71973i	−0.119039	+	0.119039i
$523$	4.33196	−	4.33196i	0.189424	−	0.189424i	−0.606023	−	0.795447i	$-0.707236\pi$
$523$	4.33196	−	4.33196i	0.189424	−	0.189424i	0.795447	+	0.606023i	$0.207236\pi$
$524$	−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	−0.949079	−	0.315037i	$-0.897983\pi$
$547$	−14.8290	+	14.8290i	−0.634042	+	0.634042i	0.315037	+	0.949079i	$0.397983\pi$
$548$	−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	−0.706506	−	0.707707i	$-0.749729\pi$
$557$	0.0283655	−	0.0283655i	0.00120188	−	0.00120188i	0.707707	+	0.706506i	$0.249729\pi$
$558$	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	−0.883279	−	0.468848i	$-0.844669\pi$
$563$	−9.83345	+	9.83345i	−0.414430	+	0.414430i	0.468848	+	0.883279i	$0.344669\pi$
$564$		−	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	$-0.863480\pi$
$569$		−	19.8397i		−	0.831722i	0.909428	−	0.415861i	$-0.136520\pi$
$570$	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	0.891677	−	0.452672i	$-0.149529\pi$
$577$	10.5453	+	10.5453i	0.439005	+	0.439005i	−0.452672	+	0.891677i	$0.649529\pi$
$578$	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	0.599647	−	0.800264i	$-0.295308\pi$
$587$	−4.86057	−	4.86057i	−0.200617	−	0.200617i	−0.800264	+	0.599647i	$0.795308\pi$
$588$		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	−0.944350	−	0.328941i	$-0.893308\pi$
$593$	−14.9862	+	14.9862i	−0.615409	+	0.615409i	0.328941	+	0.944350i	$0.393308\pi$
$594$	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	$0.0761196\pi$
$599$			11.5942i			0.473728i	−0.971543	+	0.236864i	$0.923880\pi$
$600$	−2.30836	−	4.43525i	−0.0942386	−	0.181068i
$601$			15.3561i			0.626387i	0.949689	+	0.313193i	$0.101399\pi$
$601$			15.3561i			0.626387i	−0.949689	+	0.313193i	$0.898601\pi$
$602$		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	0.305035	−	0.952341i	$-0.401332\pi$
$607$	−15.9479	−	15.9479i	−0.647306	−	0.647306i	−0.952341	+	0.305035i	$0.901332\pi$
$608$	−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	0.635468	−	0.772127i	$-0.280807\pi$
$613$	−3.38354	−	3.38354i	−0.136660	−	0.136660i	−0.772127	+	0.635468i	$0.780807\pi$
$614$	−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	−0.265606	−	0.964082i	$-0.585572\pi$
$617$	17.3498	−	17.3498i	0.698475	−	0.698475i	0.964082	+	0.265606i	$0.0855722\pi$
$618$	−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	−0.329284	−	0.944231i	$-0.606807\pi$
$643$	15.5935	−	15.5935i	0.614947	−	0.614947i	0.944231	+	0.329284i	$0.106807\pi$
$644$		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	0.610090	−	0.792332i	$-0.291133\pi$
$647$	−4.63554	−	4.63554i	−0.182242	−	0.182242i	−0.792332	+	0.610090i	$0.791133\pi$
$648$	−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	0.311353	−	0.950294i	$-0.399218\pi$
$653$	−16.3274	−	16.3274i	−0.638942	−	0.638942i	−0.950294	+	0.311353i	$0.899218\pi$
$654$	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	$-0.944578\pi$
$659$		−	8.89429i		−	0.346472i	0.984880	−	0.173236i	$-0.0554224\pi$
$660$	0.938463	+	3.83589i	0.0365296	+	0.149312i
$661$			8.36057i			0.325188i	0.986693	+	0.162594i	$0.0519861\pi$
$661$			8.36057i			0.325188i	−0.986693	+	0.162594i	$0.948014\pi$
$662$	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	0.459256	−	0.888304i	$-0.348116\pi$
$673$	−11.1305	−	11.1305i	−0.429048	−	0.429048i	−0.888304	+	0.459256i	$0.848116\pi$
$674$			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	−0.979795	−	0.200003i	$-0.935905\pi$
$677$	−30.6974	−	30.6974i	−1.17980	−	1.17980i	−0.200003	−	0.979795i	$-0.564095\pi$
$678$	−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	0.422496	−	0.906365i	$-0.361154\pi$
$683$	−12.6456	−	12.6456i	−0.483869	−	0.483869i	−0.906365	+	0.422496i	$0.861154\pi$
$684$	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	$-0.765812\pi$
$691$		−	35.2835i		−	1.34225i	0.741346	−	0.671123i	$-0.234188\pi$
$692$	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	$-0.950130\pi$
$709$		−	8.30928i		−	0.312061i	0.987752	−	0.156031i	$-0.0498699\pi$
$710$	−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	0.972647	−	0.232290i	$-0.0746217\pi$
$727$	19.9622	+	19.9622i	0.740357	+	0.740357i	−0.232290	+	0.972647i	$0.574622\pi$
$728$		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	−0.241803	+	0.970325i	$0.577739\pi$
$733$	−32.8171	+	32.8171i	−1.21213	+	1.21213i	−0.970325	+	0.241803i	$0.922261\pi$
$734$	−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	$0.104220\pi$
$739$			17.4849i			0.643193i	−0.946877	+	0.321597i	$0.895780\pi$
$740$	−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	0.445927	−	0.895069i	$-0.352874\pi$
$743$	−12.2427	−	12.2427i	−0.449143	−	0.449143i	−0.895069	+	0.445927i	$0.852874\pi$
$744$			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	−0.200149	+	0.979765i	$0.564143\pi$
$757$	−32.4637	+	32.4637i	−1.17991	+	1.17991i	−0.979765	+	0.200149i	$0.935857\pi$
$758$	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	$-0.795945\pi$
$761$		−	32.9956i		−	1.19609i	0.801463	−	0.598045i	$-0.204055\pi$
$762$	−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	−0.540537	−	0.841320i	$-0.681779\pi$
$773$	8.36265	−	8.36265i	0.300783	−	0.300783i	0.841320	+	0.540537i	$0.181779\pi$
$774$			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	0.587879	−	0.808949i	$-0.299963\pi$
$787$	−6.20178	−	6.20178i	−0.221070	−	0.221070i	−0.808949	+	0.587879i	$0.799963\pi$
$788$	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	0.0596400	−	0.998220i	$-0.481005\pi$
$797$	−26.4972	−	26.4972i	−0.938580	−	0.938580i	−0.998220	+	0.0596400i	$0.981005\pi$
$798$		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	$-0.757337\pi$
$809$		−	39.2866i		−	1.38124i	0.723216	−	0.690622i	$-0.242663\pi$
$810$	−2.17201	+	0.531389i	−0.0763166	+	0.0186711i
$811$			9.61165i			0.337511i	0.985658	+	0.168755i	$0.0539748\pi$
$811$			9.61165i			0.337511i	−0.985658	+	0.168755i	$0.946025\pi$
$812$		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	0.823600	−	0.567172i	$-0.191962\pi$
$823$	7.35640	+	7.35640i	0.256428	+	0.256428i	−0.567172	+	0.823600i	$0.691962\pi$
$824$	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	−0.563349	−	0.826219i	$-0.690487\pi$
$827$	7.55951	−	7.55951i	0.262870	−	0.262870i	0.826219	+	0.563349i	$0.190487\pi$
$828$	−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	−0.999237	−	0.0390463i	$-0.987568\pi$
$853$	−28.0435	+	28.0435i	−0.960191	+	0.960191i	0.0390463	+	0.999237i	$0.487568\pi$
$854$		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	−0.986702	−	0.162540i	$-0.948031\pi$
$857$	−33.6436	−	33.6436i	−1.14924	−	1.14924i	−0.162540	−	0.986702i	$-0.551969\pi$
$858$	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	0.999312	−	0.0370799i	$-0.0118056\pi$
$863$	28.2674	+	28.2674i	0.962232	+	0.962232i	−0.0370799	+	0.999312i	$0.511806\pi$
$864$	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	−0.792068	−	0.610433i	$-0.790995\pi$
$877$	−5.37896	+	5.37896i	−0.181635	+	0.181635i	0.610433	+	0.792068i	$0.290995\pi$
$878$	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	$-0.784660\pi$
$881$		−	37.1659i		−	1.25215i	0.779763	−	0.626075i	$-0.215340\pi$
$882$		0			0
$883$	25.7803	+	25.7803i	0.867577	+	0.867577i	0.992204	−	0.124627i	$-0.0397734\pi$
$883$	25.7803	+	25.7803i	0.867577	+	0.867577i	−0.124627	+	0.992204i	$0.539773\pi$
$884$			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	0.861583	−	0.507617i	$-0.169474\pi$
$887$	10.5420	+	10.5420i	0.353965	+	0.353965i	−0.507617	+	0.861583i	$0.669474\pi$
$888$	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	−0.407916	−	0.913019i	$-0.633744\pi$
$907$	15.2119	−	15.2119i	0.505103	−	0.505103i	0.913019	+	0.407916i	$0.133744\pi$
$908$	−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	$0.260124\pi$
$919$			44.2136i			1.45847i	−0.684262	+	0.729236i	$0.739876\pi$
$920$	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	0.715144	−	0.698977i	$-0.246361\pi$
$937$	0.494892	+	0.494892i	0.0161674	+	0.0161674i	−0.698977	+	0.715144i	$0.746361\pi$
$938$		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	$0.0972260\pi$
$941$			18.4494i			0.601434i	−0.953713	+	0.300717i	$0.902774\pi$
$942$	−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	−0.815822	−	0.578304i	$-0.803715\pi$
$947$	−7.30923	+	7.30923i	−0.237518	+	0.237518i	0.578304	+	0.815822i	$0.303715\pi$
$948$	−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	0.864645	−	0.502383i	$-0.167543\pi$
$953$	11.1833	+	11.1833i	0.362263	+	0.362263i	−0.502383	+	0.864645i	$0.667543\pi$
$954$			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	−0.760745	−	0.649051i	$-0.775166\pi$
$967$	−3.47333	+	3.47333i	−0.111695	+	0.111695i	0.649051	+	0.760745i	$0.275166\pi$
$968$	−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	$-0.801393\pi$
$971$		−	36.4108i		−	1.16848i	0.811582	−	0.584238i	$-0.198607\pi$
$972$	−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	−0.925160	−	0.379578i	$-0.876069\pi$
$977$	−17.0532	+	17.0532i	−0.545581	+	0.545581i	0.379578	+	0.925160i	$0.376069\pi$
$978$	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	−0.357082	−	0.934073i	$-0.616228\pi$
$983$	18.0903	−	18.0903i	0.576991	−	0.576991i	0.934073	+	0.357082i	$0.116228\pi$
$984$		−	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	0.988287	−	0.152609i	$-0.0487677\pi$
$997$	26.3868	+	26.3868i	0.835677	+	0.835677i	−0.152609	+	0.988287i	$0.548768\pi$
$998$	−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.1273.2		16
5.2	odd	4		1470.2.m.d.97.3		16
7.4	even	3		210.2.u.b.103.2	yes	16
7.5	odd	6		210.2.u.a.73.3	✓	16
7.6	odd	2		1470.2.m.d.1273.3		16
21.5	even	6		630.2.bv.a.73.2		16
21.11	odd	6		630.2.bv.b.523.3		16
35.4	even	6		1050.2.bc.g.943.4		16
35.12	even	12		210.2.u.b.157.2	yes	16
35.18	odd	12		1050.2.bc.h.607.1		16
35.19	odd	6		1050.2.bc.h.493.1		16
35.27	even	4	inner	1470.2.m.e.97.2		16
35.32	odd	12		210.2.u.a.187.3	yes	16
35.33	even	12		1050.2.bc.g.157.4		16
105.32	even	12		630.2.bv.a.397.2		16
105.47	odd	12		630.2.bv.b.577.3		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
210.2.u.a.73.3	✓	16	7.5	odd	6
210.2.u.a.187.3	yes	16	35.32	odd	12
210.2.u.b.103.2	yes	16	7.4	even	3
210.2.u.b.157.2	yes	16	35.12	even	12
630.2.bv.a.73.2		16	21.5	even	6
630.2.bv.a.397.2		16	105.32	even	12
630.2.bv.b.523.3		16	21.11	odd	6
630.2.bv.b.577.3		16	105.47	odd	12
1050.2.bc.g.157.4		16	35.33	even	12
1050.2.bc.g.943.4		16	35.4	even	6
1050.2.bc.h.493.1		16	35.19	odd	6
1050.2.bc.h.607.1		16	35.18	odd	12
1470.2.m.d.97.3		16	5.2	odd	4
1470.2.m.d.1273.3		16	7.6	odd	2
1470.2.m.e.97.2		16	35.27	even	4	inner
1470.2.m.e.1273.2		16	1.1	even	1	trivial

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

L-functions

Modular forms

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