LMFDB - Embedded newform 1470.2.m.e.1273.7

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			1273.7
Root			$0.277956 + 0.213283i$ of defining polynomial
Character	$\chi$	$=$	1470.1273
Dual form			1470.2.m.e.97.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.707107 - 0.707107i) q^{2} +(0.707107 - 0.707107i) q^{3} -1.00000i q^{4} +(1.36519 + 1.77095i) q^{5} -1.00000i q^{6} +(-0.707107 - 0.707107i) q^{8} -1.00000i q^{9} +O(q^{10})$	\(q+(0.707107 - 0.707107i) q^{2} +(0.707107 - 0.707107i) q^{3} -1.00000i q^{4} +(1.36519 + 1.77095i) q^{5} -1.00000i q^{6} +(-0.707107 - 0.707107i) q^{8} -1.00000i q^{9} +(2.21758 + 0.286912i) q^{10} +5.48630 q^{11} +(-0.707107 - 0.707107i) q^{12} +(-2.41668 + 2.41668i) q^{13} +(2.21758 + 0.286912i) q^{15} -1.00000 q^{16} +(-1.49783 - 1.49783i) q^{17} +(-0.707107 - 0.707107i) q^{18} +6.99593 q^{19} +(1.77095 - 1.36519i) q^{20} +(3.87940 - 3.87940i) q^{22} +(-1.24054 - 1.24054i) q^{23} -1.00000 q^{24} +(-1.27250 + 4.83536i) q^{25} +3.41770i q^{26} +(-0.707107 - 0.707107i) q^{27} -0.684610i q^{29} +(1.77095 - 1.36519i) q^{30} +5.57642i q^{31} +(-0.707107 + 0.707107i) q^{32} +(3.87940 - 3.87940i) q^{33} -2.11825 q^{34} -1.00000 q^{36} +(6.92974 - 6.92974i) q^{37} +(4.94687 - 4.94687i) q^{38} +3.41770i q^{39} +(0.286912 - 2.21758i) q^{40} +2.50597i q^{41} +(-1.95305 - 1.95305i) q^{43} -5.48630i q^{44} +(1.77095 - 1.36519i) q^{45} -1.75439 q^{46} +(2.49268 + 2.49268i) q^{47} +(-0.707107 + 0.707107i) q^{48} +(2.51932 + 4.31891i) q^{50} -2.11825 q^{51} +(2.41668 + 2.41668i) q^{52} +(-6.64852 - 6.64852i) q^{53} -1.00000 q^{54} +(7.48985 + 9.71594i) q^{55} +(4.94687 - 4.94687i) q^{57} +(-0.484092 - 0.484092i) q^{58} +10.1603 q^{59} +(0.286912 - 2.21758i) q^{60} -1.17166i q^{61} +(3.94312 + 3.94312i) q^{62} +1.00000i q^{64} +(-7.57904 - 0.980578i) q^{65} -5.48630i q^{66} +(7.03792 - 7.03792i) q^{67} +(-1.49783 + 1.49783i) q^{68} -1.75439 q^{69} -11.9716 q^{71} +(-0.707107 + 0.707107i) q^{72} +(-3.44417 + 3.44417i) q^{73} -9.80013i q^{74} +(2.51932 + 4.31891i) q^{75} -6.99593i q^{76} +(2.41668 + 2.41668i) q^{78} -8.33087i q^{79} +(-1.36519 - 1.77095i) q^{80} -1.00000 q^{81} +(1.77199 + 1.77199i) q^{82} +(-4.05281 + 4.05281i) q^{83} +(0.607749 - 4.69739i) q^{85} -2.76202 q^{86} +(-0.484092 - 0.484092i) q^{87} +(-3.87940 - 3.87940i) q^{88} +7.18356 q^{89} +(0.286912 - 2.21758i) q^{90} +(-1.24054 + 1.24054i) q^{92} +(3.94312 + 3.94312i) q^{93} +3.52518 q^{94} +(9.55079 + 12.3894i) q^{95} +1.00000i q^{96} +(-13.1212 - 13.1212i) q^{97} -5.48630i 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
$5$	1.36519	+	1.77095i	0.610532	+	0.791991i
$5$	1.36519	+	1.77095i	0.610532	+	0.791991i
$6$		−	1.00000i		−	0.408248i
$7$		0			0
$7$		0			0
$8$	−0.707107	−	0.707107i	−0.250000	−	0.250000i
$9$		−	1.00000i		−	0.333333i
$10$	2.21758	+	0.286912i	0.701262	+	0.0907294i
$11$	5.48630			1.65418			0.827091	−	0.562068i	$-0.189994\pi$
$11$	5.48630			1.65418			0.827091	+	0.562068i	$0.189994\pi$
$12$	−0.707107	−	0.707107i	−0.204124	−	0.204124i
$13$	−2.41668	+	2.41668i	−0.670266	+	0.670266i	−0.957777	−	0.287511i	$-0.907172\pi$
$13$	−2.41668	+	2.41668i	−0.670266	+	0.670266i	0.287511	+	0.957777i	$0.407172\pi$
$14$		0			0
$15$	2.21758	+	0.286912i	0.572578	+	0.0740803i
$16$	−1.00000			−0.250000
$17$	−1.49783	−	1.49783i	−0.363276	−	0.363276i	0.501742	−	0.865018i	$-0.332693\pi$
$17$	−1.49783	−	1.49783i	−0.363276	−	0.363276i	−0.865018	+	0.501742i	$0.832693\pi$
$18$	−0.707107	−	0.707107i	−0.166667	−	0.166667i
$19$	6.99593			1.60498			0.802489	−	0.596668i	$-0.203509\pi$
$19$	6.99593			1.60498			0.802489	+	0.596668i	$0.203509\pi$
$20$	1.77095	−	1.36519i	0.395996	−	0.305266i
$21$		0			0
$22$	3.87940	−	3.87940i	0.827091	−	0.827091i
$23$	−1.24054	−	1.24054i	−0.258670	−	0.258670i	0.565843	−	0.824513i	$-0.308551\pi$
$23$	−1.24054	−	1.24054i	−0.258670	−	0.258670i	−0.824513	+	0.565843i	$0.808551\pi$
$24$	−1.00000			−0.204124
$25$	−1.27250	+	4.83536i	−0.254500	+	0.967073i
$26$			3.41770i			0.670266i
$27$	−0.707107	−	0.707107i	−0.136083	−	0.136083i
$28$		0			0
$29$		−	0.684610i		−	0.127129i	−0.997978	−	0.0635644i	$-0.979753\pi$
$29$		−	0.684610i		−	0.127129i	0.997978	−	0.0635644i	$-0.0202468\pi$
$30$	1.77095	−	1.36519i	0.323329	−	0.249249i
$31$			5.57642i			1.00155i	0.865576	+	0.500777i	$0.166952\pi$
$31$			5.57642i			1.00155i	−0.865576	+	0.500777i	$0.833048\pi$
$32$	−0.707107	+	0.707107i	−0.125000	+	0.125000i
$33$	3.87940	−	3.87940i	0.675317	−	0.675317i
$34$	−2.11825			−0.363276
$35$		0			0
$36$	−1.00000			−0.166667
$37$	6.92974	−	6.92974i	1.13924	−	1.13924i	0.150656	−	0.988586i	$-0.451861\pi$
$37$	6.92974	−	6.92974i	1.13924	−	1.13924i	0.988586	−	0.150656i	$-0.0481386\pi$
$38$	4.94687	−	4.94687i	0.802489	−	0.802489i
$39$			3.41770i			0.547270i
$40$	0.286912	−	2.21758i	0.0453647	−	0.350631i
$41$			2.50597i			0.391366i	0.980667	+	0.195683i	$0.0626924\pi$
$41$			2.50597i			0.391366i	−0.980667	+	0.195683i	$0.937308\pi$
$42$		0			0
$43$	−1.95305	−	1.95305i	−0.297837	−	0.297837i	0.542329	−	0.840166i	$-0.317543\pi$
$43$	−1.95305	−	1.95305i	−0.297837	−	0.297837i	−0.840166	+	0.542329i	$0.817543\pi$
$44$		−	5.48630i		−	0.827091i
$45$	1.77095	−	1.36519i	0.263997	−	0.203511i
$46$	−1.75439			−0.258670
$47$	2.49268	+	2.49268i	0.363594	+	0.363594i	0.865134	−	0.501540i	$-0.167233\pi$
$47$	2.49268	+	2.49268i	0.363594	+	0.363594i	−0.501540	+	0.865134i	$0.667233\pi$
$48$	−0.707107	+	0.707107i	−0.102062	+	0.102062i
$49$		0			0
$50$	2.51932	+	4.31891i	0.356286	+	0.610787i
$51$	−2.11825			−0.296614
$52$	2.41668	+	2.41668i	0.335133	+	0.335133i
$53$	−6.64852	−	6.64852i	−0.913244	−	0.913244i	0.0832822	−	0.996526i	$-0.473460\pi$
$53$	−6.64852	−	6.64852i	−0.913244	−	0.913244i	−0.996526	+	0.0832822i	$0.973460\pi$
$54$	−1.00000			−0.136083
$55$	7.48985	+	9.71594i	1.00993	+	1.31010i
$56$		0			0
$57$	4.94687	−	4.94687i	0.655229	−	0.655229i
$58$	−0.484092	−	0.484092i	−0.0635644	−	0.0635644i
$59$	10.1603			1.32276			0.661379	−	0.750052i	$-0.269972\pi$
$59$	10.1603			1.32276			0.661379	+	0.750052i	$0.269972\pi$
$60$	0.286912	−	2.21758i	0.0370401	−	0.286289i
$61$		−	1.17166i		−	0.150016i	−0.997183	−	0.0750079i	$-0.976102\pi$
$61$		−	1.17166i		−	0.150016i	0.997183	−	0.0750079i	$-0.0238982\pi$
$62$	3.94312	+	3.94312i	0.500777	+	0.500777i
$63$		0			0
$64$			1.00000i			0.125000i
$65$	−7.57904	−	0.980578i	−0.940064	−	0.121626i
$66$		−	5.48630i		−	0.675317i
$67$	7.03792	−	7.03792i	0.859819	−	0.859819i	−0.131497	−	0.991317i	$-0.541978\pi$
$67$	7.03792	−	7.03792i	0.859819	−	0.859819i	0.991317	+	0.131497i	$0.0419784\pi$
$68$	−1.49783	+	1.49783i	−0.181638	+	0.181638i
$69$	−1.75439			−0.211204
$70$		0			0
$71$	−11.9716			−1.42077			−0.710383	−	0.703816i	$-0.751478\pi$
$71$	−11.9716			−1.42077			−0.710383	+	0.703816i	$0.751478\pi$
$72$	−0.707107	+	0.707107i	−0.0833333	+	0.0833333i
$73$	−3.44417	+	3.44417i	−0.403109	+	0.403109i	−0.879327	−	0.476218i	$-0.842007\pi$
$73$	−3.44417	+	3.44417i	−0.403109	+	0.403109i	0.476218	+	0.879327i	$0.342007\pi$
$74$		−	9.80013i		−	1.13924i
$75$	2.51932	+	4.31891i	0.290906	+	0.498705i
$76$		−	6.99593i		−	0.802489i
$77$		0			0
$78$	2.41668	+	2.41668i	0.273635	+	0.273635i
$79$		−	8.33087i		−	0.937296i	−0.883385	−	0.468648i	$-0.844741\pi$
$79$		−	8.33087i		−	0.937296i	0.883385	−	0.468648i	$-0.155259\pi$
$80$	−1.36519	−	1.77095i	−0.152633	−	0.197998i
$81$	−1.00000			−0.111111
$82$	1.77199	+	1.77199i	0.195683	+	0.195683i
$83$	−4.05281	+	4.05281i	−0.444854	+	0.444854i	−0.893639	−	0.448786i	$-0.851857\pi$
$83$	−4.05281	+	4.05281i	−0.444854	+	0.444854i	0.448786	+	0.893639i	$0.351857\pi$
$84$		0			0
$85$	0.607749	−	4.69739i	0.0659197	−	0.509503i
$86$	−2.76202			−0.297837
$87$	−0.484092	−	0.484092i	−0.0519001	−	0.0519001i
$88$	−3.87940	−	3.87940i	−0.413545	−	0.413545i
$89$	7.18356			0.761456			0.380728	−	0.924687i	$-0.375673\pi$
$89$	7.18356			0.761456			0.380728	+	0.924687i	$0.375673\pi$
$90$	0.286912	−	2.21758i	0.0302431	−	0.233754i
$91$		0			0
$92$	−1.24054	+	1.24054i	−0.129335	+	0.129335i
$93$	3.94312	+	3.94312i	0.408883	+	0.408883i
$94$	3.52518			0.363594
$95$	9.55079	+	12.3894i	0.979891	+	1.27113i
$96$			1.00000i			0.102062i
$97$	−13.1212	−	13.1212i	−1.33226	−	1.33226i	−0.903348	−	0.428909i	$-0.858898\pi$
$97$	−13.1212	−	13.1212i	−1.33226	−	1.33226i	−0.428909	−	0.903348i	$-0.641102\pi$
$98$		0			0
$99$		−	5.48630i		−	0.551394i
$100$	4.83536	+	1.27250i	0.483536	+	0.127250i
$101$			8.26766i			0.822663i	0.911486	+	0.411332i	$0.134936\pi$
$101$			8.26766i			0.822663i	−0.911486	+	0.411332i	$0.865064\pi$
$102$	−1.49783	+	1.49783i	−0.148307	+	0.148307i
$103$	−6.58048	+	6.58048i	−0.648394	+	0.648394i	−0.952605	−	0.304211i	$-0.901607\pi$
$103$	−6.58048	+	6.58048i	−0.648394	+	0.648394i	0.304211	+	0.952605i	$0.401607\pi$
$104$	3.41770			0.335133
$105$		0			0
$106$	−9.40242			−0.913244
$107$	−8.67454	+	8.67454i	−0.838600	+	0.838600i	−0.988675	−	0.150075i	$-0.952049\pi$
$107$	−8.67454	+	8.67454i	−0.838600	+	0.838600i	0.150075	+	0.988675i	$0.452049\pi$
$108$	−0.707107	+	0.707107i	−0.0680414	+	0.0680414i
$109$		−	0.336622i		−	0.0322425i	−0.999870	−	0.0161213i	$-0.994868\pi$
$109$		−	0.336622i		−	0.0322425i	0.999870	−	0.0161213i	$-0.00513178\pi$
$110$	12.1663	+	1.57408i	1.16001	+	0.150083i
$111$		−	9.80013i		−	0.930188i
$112$		0			0
$113$	10.1896	+	10.1896i	0.958555	+	0.958555i	0.999175	−	0.0406198i	$-0.0129332\pi$
$113$	10.1896	+	10.1896i	0.958555	+	0.958555i	−0.0406198	+	0.999175i	$0.512933\pi$
$114$		−	6.99593i		−	0.655229i
$115$	0.503355	−	3.89051i	0.0469380	−	0.362792i
$116$	−0.684610			−0.0635644
$117$	2.41668	+	2.41668i	0.223422	+	0.223422i
$118$	7.18441	−	7.18441i	0.661379	−	0.661379i
$119$		0			0
$120$	−1.36519	−	1.77095i	−0.124624	−	0.161665i
$121$	19.0995			1.73632
$122$	−0.828489	−	0.828489i	−0.0750079	−	0.0750079i
$123$	1.77199	+	1.77199i	0.159775	+	0.159775i
$124$	5.57642			0.500777
$125$	−10.3004	+	4.34767i	−0.921294	+	0.388867i
$126$		0			0
$127$	−4.77054	+	4.77054i	−0.423317	+	0.423317i	−0.886344	−	0.463027i	$-0.846763\pi$
$127$	−4.77054	+	4.77054i	−0.423317	+	0.423317i	0.463027	+	0.886344i	$0.346763\pi$
$128$	0.707107	+	0.707107i	0.0625000	+	0.0625000i
$129$	−2.76202			−0.243183
$130$	−6.05256	+	4.66582i	−0.530845	+	0.409219i
$131$		−	18.2091i		−	1.59094i	−0.605996	−	0.795468i	$-0.707225\pi$
$131$		−	18.2091i		−	1.59094i	0.605996	−	0.795468i	$-0.292775\pi$
$132$	−3.87940	−	3.87940i	−0.337658	−	0.337658i
$133$		0			0
$134$		−	9.95313i		−	0.859819i
$135$	0.286912	−	2.21758i	0.0246934	−	0.190859i
$136$			2.11825i			0.181638i
$137$	1.54481	−	1.54481i	0.131982	−	0.131982i	−0.638030	−	0.770012i	$-0.720250\pi$
$137$	1.54481	−	1.54481i	0.131982	−	0.131982i	0.770012	+	0.638030i	$0.220250\pi$
$138$	−1.24054	+	1.24054i	−0.105602	+	0.105602i
$139$	−18.1446			−1.53900			−0.769501	−	0.638645i	$-0.779495\pi$
$139$	−18.1446			−1.53900			−0.769501	+	0.638645i	$0.779495\pi$
$140$		0			0
$141$	3.52518			0.296873
$142$	−8.46519	+	8.46519i	−0.710383	+	0.710383i
$143$	−13.2586	+	13.2586i	−1.10874	+	1.10874i
$144$			1.00000i			0.0833333i
$145$	1.21241	−	0.934623i	0.100685	−	0.0776163i
$146$			4.87079i			0.403109i
$147$		0			0
$148$	−6.92974	−	6.92974i	−0.569621	−	0.569621i
$149$			0.193656i			0.0158649i	0.999969	+	0.00793245i	$0.00252500\pi$
$149$			0.193656i			0.0158649i	−0.999969	+	0.00793245i	$0.997475\pi$
$150$	4.83536	+	1.27250i	0.394806	+	0.103899i
$151$	−21.3227			−1.73522			−0.867610	−	0.497245i	$-0.834345\pi$
$151$	−21.3227			−1.73522			−0.867610	+	0.497245i	$0.834345\pi$
$152$	−4.94687	−	4.94687i	−0.401244	−	0.401244i
$153$	−1.49783	+	1.49783i	−0.121092	+	0.121092i
$154$		0			0
$155$	−9.87553	+	7.61288i	−0.793222	+	0.611481i
$156$	3.41770			0.273635
$157$	−2.60217	−	2.60217i	−0.207676	−	0.207676i	0.595603	−	0.803279i	$-0.296913\pi$
$157$	−2.60217	−	2.60217i	−0.207676	−	0.207676i	−0.803279	+	0.595603i	$0.796913\pi$
$158$	−5.89081	−	5.89081i	−0.468648	−	0.468648i
$159$	−9.40242			−0.745660
$160$	−2.21758	−	0.286912i	−0.175315	−	0.0226824i
$161$		0			0
$162$	−0.707107	+	0.707107i	−0.0555556	+	0.0555556i
$163$	−9.95676	−	9.95676i	−0.779874	−	0.779874i	0.199935	−	0.979809i	$-0.435927\pi$
$163$	−9.95676	−	9.95676i	−0.779874	−	0.779874i	−0.979809	+	0.199935i	$0.935927\pi$
$164$	2.50597			0.195683
$165$	12.1663	+	1.57408i	0.947148	+	0.122542i
$166$			5.73154i			0.444854i
$167$	6.07259	+	6.07259i	0.469911	+	0.469911i	0.901886	−	0.431974i	$-0.142183\pi$
$167$	6.07259	+	6.07259i	0.469911	+	0.469911i	−0.431974	+	0.901886i	$0.642183\pi$
$168$		0			0
$169$			1.31933i			0.101487i
$170$	−2.89181	−	3.75130i	−0.221792	−	0.287711i
$171$		−	6.99593i		−	0.534992i
$172$	−1.95305	+	1.95305i	−0.148918	+	0.148918i
$173$	−2.86311	+	2.86311i	−0.217678	+	0.217678i	−0.807519	−	0.589841i	$-0.799190\pi$
$173$	−2.86311	+	2.86311i	−0.217678	+	0.217678i	0.589841	+	0.807519i	$0.299190\pi$
$174$	−0.684610			−0.0519001
$175$		0			0
$176$	−5.48630			−0.413545
$177$	7.18441	−	7.18441i	0.540014	−	0.540014i
$178$	5.07954	−	5.07954i	0.380728	−	0.380728i
$179$			3.66534i			0.273960i	0.990574	+	0.136980i	$0.0437396\pi$
$179$			3.66534i			0.273960i	−0.990574	+	0.136980i	$0.956260\pi$
$180$	−1.36519	−	1.77095i	−0.101755	−	0.131999i
$181$		−	2.39985i		−	0.178379i	−0.996015	−	0.0891896i	$-0.971572\pi$
$181$		−	2.39985i		−	0.178379i	0.996015	−	0.0891896i	$-0.0284277\pi$
$182$		0			0
$183$	−0.828489	−	0.828489i	−0.0612437	−	0.0612437i
$184$			1.75439i			0.129335i
$185$	21.7326	+	2.81177i	1.59781	+	0.206726i
$186$	5.57642			0.408883
$187$	−8.21752	−	8.21752i	−0.600925	−	0.600925i
$188$	2.49268	−	2.49268i	0.181797	−	0.181797i
$189$		0			0
$190$	15.5141	+	2.00721i	1.12551	+	0.145619i
$191$	8.07532			0.584310			0.292155	−	0.956371i	$-0.405628\pi$
$191$	8.07532			0.584310			0.292155	+	0.956371i	$0.405628\pi$
$192$	0.707107	+	0.707107i	0.0510310	+	0.0510310i
$193$	−1.21801	−	1.21801i	−0.0876740	−	0.0876740i	0.661910	−	0.749584i	$-0.269746\pi$
$193$	−1.21801	−	1.21801i	−0.0876740	−	0.0876740i	−0.749584	+	0.661910i	$0.769746\pi$
$194$	−18.5562			−1.33226
$195$	−6.05256	+	4.66582i	−0.433433	+	0.334126i
$196$		0			0
$197$	6.01174	−	6.01174i	0.428319	−	0.428319i	−0.459737	−	0.888055i	$-0.652056\pi$
$197$	6.01174	−	6.01174i	0.428319	−	0.428319i	0.888055	+	0.459737i	$0.152056\pi$
$198$	−3.87940	−	3.87940i	−0.275697	−	0.275697i
$199$	−11.0179			−0.781041			−0.390520	−	0.920594i	$-0.627705\pi$
$199$	−11.0179			−0.781041			−0.390520	+	0.920594i	$0.627705\pi$
$200$	4.31891	−	2.51932i	0.305393	−	0.178143i
$201$		−	9.95313i		−	0.702040i
$202$	5.84612	+	5.84612i	0.411332	+	0.411332i
$203$		0			0
$204$			2.11825i			0.148307i
$205$	−4.43793	+	3.42113i	−0.309959	+	0.238942i
$206$			9.30620i			0.648394i
$207$	−1.24054	+	1.24054i	−0.0862235	+	0.0862235i
$208$	2.41668	−	2.41668i	0.167566	−	0.167566i
$209$	38.3818			2.65492
$210$		0			0
$211$	10.3323			0.711302			0.355651	−	0.934619i	$-0.384259\pi$
$211$	10.3323			0.711302			0.355651	+	0.934619i	$0.384259\pi$
$212$	−6.64852	+	6.64852i	−0.456622	+	0.456622i
$213$	−8.46519	+	8.46519i	−0.580025	+	0.580025i
$214$			12.2677i			0.838600i
$215$	0.792457	−	6.12502i	0.0540451	−	0.417723i
$216$			1.00000i			0.0680414i
$217$		0			0
$218$	−0.238027	−	0.238027i	−0.0161213	−	0.0161213i
$219$			4.87079i			0.329137i
$220$	9.71594	−	7.48985i	0.655049	−	0.504966i
$221$	7.23953			0.486983
$222$	−6.92974	−	6.92974i	−0.465094	−	0.465094i
$223$	3.41183	−	3.41183i	0.228473	−	0.228473i	−0.583582	−	0.812054i	$-0.698349\pi$
$223$	3.41183	−	3.41183i	0.228473	−	0.228473i	0.812054	+	0.583582i	$0.198349\pi$
$224$		0			0
$225$	4.83536	+	1.27250i	0.322358	+	0.0848334i
$226$	14.4102			0.958555
$227$	−12.7942	−	12.7942i	−0.849182	−	0.849182i	0.140849	−	0.990031i	$-0.455017\pi$
$227$	−12.7942	−	12.7942i	−0.849182	−	0.849182i	−0.990031	+	0.140849i	$0.955017\pi$
$228$	−4.94687	−	4.94687i	−0.327615	−	0.327615i
$229$	−9.64749			−0.637524			−0.318762	−	0.947835i	$-0.603267\pi$
$229$	−9.64749			−0.637524			−0.318762	+	0.947835i	$0.603267\pi$
$230$	−2.39508	−	3.10693i	−0.157927	−	0.204865i
$231$		0			0
$232$	−0.484092	+	0.484092i	−0.0317822	+	0.0317822i
$233$	10.2342	+	10.2342i	0.670463	+	0.670463i	0.957823	−	0.287360i	$-0.0927775\pi$
$233$	10.2342	+	10.2342i	0.670463	+	0.670463i	−0.287360	+	0.957823i	$0.592777\pi$
$234$	3.41770			0.223422
$235$	−1.01141	+	7.81738i	−0.0659774	+	0.509949i
$236$		−	10.1603i		−	0.661379i
$237$	−5.89081	−	5.89081i	−0.382649	−	0.382649i
$238$		0			0
$239$			29.9736i			1.93883i	0.245427	+	0.969415i	$0.421072\pi$
$239$			29.9736i			1.93883i	−0.245427	+	0.969415i	$0.578928\pi$
$240$	−2.21758	−	0.286912i	−0.143144	−	0.0185201i
$241$			16.6201i			1.07059i	0.844664	+	0.535296i	$0.179800\pi$
$241$			16.6201i			1.07059i	−0.844664	+	0.535296i	$0.820200\pi$
$242$	13.5054	−	13.5054i	0.868158	−	0.868158i
$243$	−0.707107	+	0.707107i	−0.0453609	+	0.0453609i
$244$	−1.17166			−0.0750079
$245$		0			0
$246$	2.50597			0.159775
$247$	−16.9069	+	16.9069i	−1.07576	+	1.07576i
$248$	3.94312	−	3.94312i	0.250388	−	0.250388i
$249$			5.73154i			0.363222i
$250$	−4.20920	+	10.3577i	−0.266213	+	0.655081i
$251$			10.7660i			0.679546i	0.940508	+	0.339773i	$0.110350\pi$
$251$			10.7660i			0.679546i	−0.940508	+	0.339773i	$0.889650\pi$
$252$		0			0
$253$	−6.80597	−	6.80597i	−0.427888	−	0.427888i
$254$			6.74657i			0.423317i
$255$	−2.89181	−	3.75130i	−0.181092	−	0.234915i
$256$	1.00000			0.0625000
$257$	10.6366	+	10.6366i	0.663495	+	0.663495i	0.956202	−	0.292707i	$-0.0945560\pi$
$257$	10.6366	+	10.6366i	0.663495	+	0.663495i	−0.292707	+	0.956202i	$0.594556\pi$
$258$	−1.95305	+	1.95305i	−0.121591	+	0.121591i
$259$		0			0
$260$	−0.980578	+	7.57904i	−0.0608128	+	0.470032i
$261$	−0.684610			−0.0423763
$262$	−12.8758	−	12.8758i	−0.795468	−	0.795468i
$263$	15.9321	+	15.9321i	0.982418	+	0.982418i	0.999848	−	0.0174300i	$-0.00554843\pi$
$263$	15.9321	+	15.9321i	0.982418	+	0.982418i	−0.0174300	+	0.999848i	$0.505548\pi$
$264$	−5.48630			−0.337658
$265$	2.69766	−	20.8507i	0.165716	−	1.28085i
$266$		0			0
$267$	5.07954	−	5.07954i	0.310863	−	0.310863i
$268$	−7.03792	−	7.03792i	−0.429910	−	0.429910i
$269$	−11.0424			−0.673270			−0.336635	−	0.941635i	$-0.609289\pi$
$269$	−11.0424			−0.673270			−0.336635	+	0.941635i	$0.609289\pi$
$270$	−1.36519	−	1.77095i	−0.0830829	−	0.107776i
$271$		−	5.01640i		−	0.304724i	−0.988325	−	0.152362i	$-0.951312\pi$
$271$		−	5.01640i		−	0.304724i	0.988325	−	0.152362i	$-0.0486880\pi$
$272$	1.49783	+	1.49783i	0.0908190	+	0.0908190i
$273$		0			0
$274$		−	2.18468i		−	0.131982i
$275$	−6.98132	+	26.5283i	−0.420990	+	1.59971i
$276$			1.75439i			0.105602i
$277$	4.47957	−	4.47957i	0.269151	−	0.269151i	−0.559607	−	0.828758i	$-0.689048\pi$
$277$	4.47957	−	4.47957i	0.269151	−	0.269151i	0.828758	+	0.559607i	$0.189048\pi$
$278$	−12.8302	+	12.8302i	−0.769501	+	0.769501i
$279$	5.57642			0.333851
$280$		0			0
$281$	−29.4723			−1.75817			−0.879085	−	0.476665i	$-0.841846\pi$
$281$	−29.4723			−1.75817			−0.879085	+	0.476665i	$0.841846\pi$
$282$	2.49268	−	2.49268i	0.148437	−	0.148437i
$283$	0.0691733	−	0.0691733i	0.00411193	−	0.00411193i	−0.705048	−	0.709160i	$-0.749074\pi$
$283$	0.0691733	−	0.0691733i	0.00411193	−	0.00411193i	0.709160	+	0.705048i	$0.249074\pi$
$284$			11.9716i			0.710383i
$285$	15.5141	+	2.00721i	0.918974	+	0.118897i
$286$			18.7505i			1.10874i
$287$		0			0
$288$	0.707107	+	0.707107i	0.0416667	+	0.0416667i
$289$		−	12.5130i		−	0.736061i
$290$	0.196422	−	1.51818i	0.0115343	−	0.0891506i
$291$	−18.5562			−1.08778
$292$	3.44417	+	3.44417i	0.201555	+	0.201555i
$293$	−14.0076	+	14.0076i	−0.818330	+	0.818330i	−0.985866	−	0.167536i	$-0.946419\pi$
$293$	−14.0076	+	14.0076i	−0.818330	+	0.818330i	0.167536	+	0.985866i	$0.446419\pi$
$294$		0			0
$295$	13.8708	+	17.9933i	0.807587	+	1.04761i
$296$	−9.80013			−0.569621
$297$	−3.87940	−	3.87940i	−0.225106	−	0.225106i
$298$	0.136935	+	0.136935i	0.00793245	+	0.00793245i
$299$	5.99597			0.346756
$300$	4.31891	−	2.51932i	0.249353	−	0.145453i
$301$		0			0
$302$	−15.0775	+	15.0775i	−0.867610	+	0.867610i
$303$	5.84612	+	5.84612i	0.335851	+	0.335851i
$304$	−6.99593			−0.401244
$305$	2.07495	−	1.59954i	0.118811	−	0.0915895i
$306$			2.11825i			0.121092i
$307$	−3.05320	−	3.05320i	−0.174255	−	0.174255i	0.614591	−	0.788846i	$-0.289321\pi$
$307$	−3.05320	−	3.05320i	−0.174255	−	0.174255i	−0.788846	+	0.614591i	$0.789321\pi$
$308$		0			0
$309$			9.30620i			0.529411i
$310$	−1.59994	+	12.3662i	−0.0908704	+	0.702351i
$311$		−	8.44532i		−	0.478890i	−0.970910	−	0.239445i	$-0.923035\pi$
$311$		−	8.44532i		−	0.478890i	0.970910	−	0.239445i	$-0.0769655\pi$
$312$	2.41668	−	2.41668i	0.136817	−	0.136817i
$313$	−13.7247	+	13.7247i	−0.775764	+	0.775764i	−0.979107	−	0.203343i	$-0.934819\pi$
$313$	−13.7247	+	13.7247i	−0.775764	+	0.775764i	0.203343	+	0.979107i	$0.434819\pi$
$314$	−3.68003			−0.207676
$315$		0			0
$316$	−8.33087			−0.468648
$317$	−10.9957	+	10.9957i	−0.617581	+	0.617581i	−0.944910	−	0.327329i	$-0.893851\pi$
$317$	−10.9957	+	10.9957i	−0.617581	+	0.617581i	0.327329	+	0.944910i	$0.393851\pi$
$318$	−6.64852	+	6.64852i	−0.372830	+	0.372830i
$319$		−	3.75597i		−	0.210294i
$320$	−1.77095	+	1.36519i	−0.0989989	+	0.0763166i
$321$			12.2677i			0.684714i
$322$		0			0
$323$	−10.4787	−	10.4787i	−0.583050	−	0.583050i
$324$			1.00000i			0.0555556i
$325$	−8.61029	−	14.7607i	−0.477613	−	0.818779i
$326$	−14.0810			−0.779874
$327$	−0.238027	−	0.238027i	−0.0131629	−	0.0131629i
$328$	1.77199	−	1.77199i	0.0978416	−	0.0978416i
$329$		0			0
$330$	9.71594	−	7.48985i	0.534845	−	0.412303i
$331$	16.1859			0.889659			0.444830	−	0.895615i	$-0.353264\pi$
$331$	16.1859			0.889659			0.444830	+	0.895615i	$0.353264\pi$
$332$	4.05281	+	4.05281i	0.222427	+	0.222427i
$333$	−6.92974	−	6.92974i	−0.379747	−	0.379747i
$334$	8.58794			0.469911
$335$	22.0719	+	2.85567i	1.20592	+	0.156022i
$336$		0			0
$337$	19.2055	−	19.2055i	1.04619	−	1.04619i	0.0473073	−	0.998880i	$-0.484936\pi$
$337$	19.2055	−	19.2055i	1.04619	−	1.04619i	0.998880	−	0.0473073i	$-0.0150640\pi$
$338$	0.932908	+	0.932908i	0.0507435	+	0.0507435i
$339$	14.4102			0.782657
$340$	−4.69739	−	0.607749i	−0.254752	−	0.0329598i
$341$			30.5939i			1.65675i
$342$	−4.94687	−	4.94687i	−0.267496	−	0.267496i
$343$		0			0
$344$			2.76202i			0.148918i
$345$	−2.39508	−	3.10693i	−0.128947	−	0.167271i
$346$			4.04905i			0.217678i
$347$	7.25896	−	7.25896i	0.389681	−	0.389681i	−0.484892	−	0.874574i	$-0.661141\pi$
$347$	7.25896	−	7.25896i	0.389681	−	0.389681i	0.874574	+	0.484892i	$0.161141\pi$
$348$	−0.484092	+	0.484092i	−0.0259501	+	0.0259501i
$349$	6.61441			0.354061			0.177031	−	0.984205i	$-0.443351\pi$
$349$	6.61441			0.354061			0.177031	+	0.984205i	$0.443351\pi$
$350$		0			0
$351$	3.41770			0.182423
$352$	−3.87940	+	3.87940i	−0.206773	+	0.206773i
$353$	−9.63411	+	9.63411i	−0.512772	+	0.512772i	−0.915375	−	0.402603i	$-0.868106\pi$
$353$	−9.63411	+	9.63411i	−0.512772	+	0.512772i	0.402603	+	0.915375i	$0.368106\pi$
$354$		−	10.1603i		−	0.540014i
$355$	−16.3435	−	21.2010i	−0.867423	−	1.12523i
$356$		−	7.18356i		−	0.380728i
$357$		0			0
$358$	2.59178	+	2.59178i	0.136980	+	0.136980i
$359$			17.2964i			0.912871i	0.889757	+	0.456435i	$0.150874\pi$
$359$			17.2964i			0.912871i	−0.889757	+	0.456435i	$0.849126\pi$
$360$	−2.21758	−	0.286912i	−0.116877	−	0.0151216i
$361$	29.9431			1.57595
$362$	−1.69695	−	1.69695i	−0.0891896	−	0.0891896i
$363$	13.5054	−	13.5054i	0.708848	−	0.708848i
$364$		0			0
$365$	−10.8014	−	1.39749i	−0.565370	−	0.0731477i
$366$	−1.17166			−0.0612437
$367$	−18.3007	−	18.3007i	−0.955288	−	0.955288i	0.0437539	−	0.999042i	$-0.486068\pi$
$367$	−18.3007	−	18.3007i	−0.955288	−	0.955288i	−0.999042	+	0.0437539i	$0.986068\pi$
$368$	1.24054	+	1.24054i	0.0646676	+	0.0646676i
$369$	2.50597			0.130455
$370$	17.3555	−	13.3791i	0.902270	−	0.695544i
$371$		0			0
$372$	3.94312	−	3.94312i	0.204441	−	0.204441i
$373$	6.48161	+	6.48161i	0.335605	+	0.335605i	0.854710	−	0.519105i	$-0.173735\pi$
$373$	6.48161	+	6.48161i	0.335605	+	0.335605i	−0.519105	+	0.854710i	$0.673735\pi$
$374$	−11.6213			−0.600925
$375$	−4.20920	+	10.3577i	−0.217362	+	0.534871i
$376$		−	3.52518i		−	0.181797i
$377$	1.65448	+	1.65448i	0.0852101	+	0.0852101i
$378$		0			0
$379$			18.6871i			0.959891i	0.877298	+	0.479946i	$0.159344\pi$
$379$			18.6871i			0.959891i	−0.877298	+	0.479946i	$0.840656\pi$
$380$	12.3894	−	9.55079i	0.635564	−	0.489945i
$381$			6.74657i			0.345637i
$382$	5.71012	−	5.71012i	0.292155	−	0.292155i
$383$	−14.0300	+	14.0300i	−0.716900	+	0.716900i	−0.967969	−	0.251069i	$-0.919218\pi$
$383$	−14.0300	+	14.0300i	−0.716900	+	0.716900i	0.251069	+	0.967969i	$0.419218\pi$
$384$	1.00000			0.0510310
$385$		0			0
$386$	−1.72252			−0.0876740
$387$	−1.95305	+	1.95305i	−0.0992789	+	0.0992789i
$388$	−13.1212	+	13.1212i	−0.666128	+	0.666128i
$389$		−	5.12717i		−	0.259958i	−0.991517	−	0.129979i	$-0.958509\pi$
$389$		−	5.12717i		−	0.259958i	0.991517	−	0.129979i	$-0.0414910\pi$
$390$	−0.980578	+	7.57904i	−0.0496535	+	0.383779i
$391$			3.71623i			0.187938i
$392$		0			0
$393$	−12.8758	−	12.8758i	−0.649497	−	0.649497i
$394$		−	8.50188i		−	0.428319i
$395$	14.7535	−	11.3732i	0.742330	−	0.572249i
$396$	−5.48630			−0.275697
$397$	−18.6630	−	18.6630i	−0.936668	−	0.936668i	0.0614422	−	0.998111i	$-0.480430\pi$
$397$	−18.6630	−	18.6630i	−0.936668	−	0.936668i	−0.998111	+	0.0614422i	$0.980430\pi$
$398$	−7.79086	+	7.79086i	−0.390520	+	0.390520i
$399$		0			0
$400$	1.27250	−	4.83536i	0.0636251	−	0.241768i
$401$	−17.2294			−0.860396			−0.430198	−	0.902735i	$-0.641556\pi$
$401$	−17.2294			−0.860396			−0.430198	+	0.902735i	$0.641556\pi$
$402$	−7.03792	−	7.03792i	−0.351020	−	0.351020i
$403$	−13.4764	−	13.4764i	−0.671307	−	0.671307i
$404$	8.26766			0.411332
$405$	−1.36519	−	1.77095i	−0.0678369	−	0.0879990i
$406$		0			0
$407$	38.0186	−	38.0186i	1.88451	−	1.88451i
$408$	1.49783	+	1.49783i	0.0741534	+	0.0741534i
$409$	35.7138			1.76593			0.882967	−	0.469436i	$-0.155543\pi$
$409$	35.7138			1.76593			0.882967	+	0.469436i	$0.155543\pi$
$410$	−0.718991	+	5.55719i	−0.0355084	+	0.274450i
$411$		−	2.18468i		−	0.107763i
$412$	6.58048	+	6.58048i	0.324197	+	0.324197i
$413$		0			0
$414$			1.75439i			0.0862235i
$415$	−12.7102	−	1.64445i	−0.623918	−	0.0807227i
$416$		−	3.41770i		−	0.167566i
$417$	−12.8302	+	12.8302i	−0.628295	+	0.628295i
$418$	27.1400	−	27.1400i	1.32746	−	1.32746i
$419$	14.0414			0.685966			0.342983	−	0.939342i	$-0.388563\pi$
$419$	14.0414			0.685966			0.342983	+	0.939342i	$0.388563\pi$
$420$		0			0
$421$	24.4332			1.19080			0.595401	−	0.803429i	$-0.296993\pi$
$421$	24.4332			1.19080			0.595401	+	0.803429i	$0.296993\pi$
$422$	7.30601	−	7.30601i	0.355651	−	0.355651i
$423$	2.49268	−	2.49268i	0.121198	−	0.121198i
$424$			9.40242i			0.456622i
$425$	9.14852	−	5.33655i	0.443768	−	0.258861i
$426$			11.9716i			0.580025i
$427$		0			0
$428$	8.67454	+	8.67454i	0.419300	+	0.419300i
$429$			18.7505i			0.905284i
$430$	−3.77069	−	4.89140i	−0.181839	−	0.235884i
$431$	−38.7771			−1.86783			−0.933914	−	0.357498i	$-0.883630\pi$
$431$	−38.7771			−1.86783			−0.933914	+	0.357498i	$0.883630\pi$
$432$	0.707107	+	0.707107i	0.0340207	+	0.0340207i
$433$	−7.85700	+	7.85700i	−0.377583	+	0.377583i	−0.870230	−	0.492646i	$-0.836030\pi$
$433$	−7.85700	+	7.85700i	−0.377583	+	0.377583i	0.492646	+	0.870230i	$0.336030\pi$
$434$		0			0
$435$	0.196422	−	1.51818i	0.00941774	−	0.0727911i
$436$	−0.336622			−0.0161213
$437$	−8.67874	−	8.67874i	−0.415160	−	0.415160i
$438$	3.44417	+	3.44417i	0.164569	+	0.164569i
$439$	−21.1279			−1.00838			−0.504190	−	0.863593i	$-0.668209\pi$
$439$	−21.1279			−1.00838			−0.504190	+	0.863593i	$0.668209\pi$
$440$	1.57408	−	12.1663i	0.0750415	−	0.580007i
$441$		0			0
$442$	5.11912	−	5.11912i	0.243492	−	0.243492i
$443$	4.74580	+	4.74580i	0.225480	+	0.225480i	0.810801	−	0.585321i	$-0.199032\pi$
$443$	4.74580	+	4.74580i	0.225480	+	0.225480i	−0.585321	+	0.810801i	$0.699032\pi$
$444$	−9.80013			−0.465094
$445$	9.80694	+	12.7217i	0.464894	+	0.603066i
$446$		−	4.82505i		−	0.228473i
$447$	0.136935	+	0.136935i	0.00647682	+	0.00647682i
$448$		0			0
$449$		−	8.28979i		−	0.391219i	−0.980682	−	0.195610i	$-0.937331\pi$
$449$		−	8.28979i		−	0.391219i	0.980682	−	0.195610i	$-0.0626685\pi$
$450$	4.31891	−	2.51932i	0.203596	−	0.118762i
$451$			13.7485i			0.647391i
$452$	10.1896	−	10.1896i	0.479277	−	0.479277i
$453$	−15.0775	+	15.0775i	−0.708401	+	0.708401i
$454$	−18.0938			−0.849182
$455$		0			0
$456$	−6.99593			−0.327615
$457$	15.6143	−	15.6143i	0.730407	−	0.730407i	−0.240293	−	0.970700i	$-0.577244\pi$
$457$	15.6143	−	15.6143i	0.730407	−	0.730407i	0.970700	+	0.240293i	$0.0772436\pi$
$458$	−6.82181	+	6.82181i	−0.318762	+	0.318762i
$459$			2.11825i			0.0988712i
$460$	−3.89051	−	0.503355i	−0.181396	−	0.0234690i
$461$		−	19.0130i		−	0.885524i	−0.896639	−	0.442762i	$-0.853999\pi$
$461$		−	19.0130i		−	0.885524i	0.896639	−	0.442762i	$-0.146001\pi$
$462$		0			0
$463$	−16.6091	−	16.6091i	−0.771891	−	0.771891i	0.206546	−	0.978437i	$-0.433778\pi$
$463$	−16.6091	−	16.6091i	−0.771891	−	0.771891i	−0.978437	+	0.206546i	$0.933778\pi$
$464$			0.684610i			0.0317822i
$465$	−1.59994	+	12.3662i	−0.0741954	+	0.573468i
$466$	14.4733			0.670463
$467$	−11.3062	−	11.3062i	−0.523190	−	0.523190i	0.395343	−	0.918533i	$-0.370626\pi$
$467$	−11.3062	−	11.3062i	−0.523190	−	0.523190i	−0.918533	+	0.395343i	$0.870626\pi$
$468$	2.41668	−	2.41668i	0.111711	−	0.111711i
$469$		0			0
$470$	4.81254	+	6.24290i	0.221986	+	0.287963i
$471$	−3.68003			−0.169567
$472$	−7.18441	−	7.18441i	−0.330689	−	0.330689i
$473$	−10.7150	−	10.7150i	−0.492676	−	0.492676i
$474$	−8.33087			−0.382649
$475$	−8.90234	+	33.8279i	−0.408467	+	1.55213i
$476$		0			0
$477$	−6.64852	+	6.64852i	−0.304415	+	0.304415i
$478$	21.1945	+	21.1945i	0.969415	+	0.969415i
$479$	−9.01051			−0.411701			−0.205850	−	0.978583i	$-0.565996\pi$
$479$	−9.01051			−0.411701			−0.205850	+	0.978583i	$0.565996\pi$
$480$	−1.77095	+	1.36519i	−0.0808323	+	0.0623122i
$481$			33.4939i			1.52719i
$482$	11.7522	+	11.7522i	0.535296	+	0.535296i
$483$		0			0
$484$		−	19.0995i		−	0.868158i
$485$	5.32399	−	41.1499i	0.241750	−	1.86852i
$486$			1.00000i			0.0453609i
$487$	6.60446	−	6.60446i	0.299277	−	0.299277i	−0.541454	−	0.840731i	$-0.682126\pi$
$487$	6.60446	−	6.60446i	0.299277	−	0.299277i	0.840731	+	0.541454i	$0.182126\pi$
$488$	−0.828489	+	0.828489i	−0.0375039	+	0.0375039i
$489$	−14.0810			−0.636764
$490$		0			0
$491$	2.08535			0.0941107			0.0470554	−	0.998892i	$-0.485016\pi$
$491$	2.08535			0.0941107			0.0470554	+	0.998892i	$0.485016\pi$
$492$	1.77199	−	1.77199i	0.0798873	−	0.0798873i
$493$	−1.02543	+	1.02543i	−0.0461829	+	0.0461829i
$494$			23.9100i			1.07576i
$495$	9.71594	−	7.48985i	0.436699	−	0.336644i
$496$		−	5.57642i		−	0.250388i
$497$		0			0
$498$	4.05281	+	4.05281i	0.181611	+	0.181611i
$499$			13.4246i			0.600966i	0.953787	+	0.300483i	$0.0971479\pi$
$499$			13.4246i			0.600966i	−0.953787	+	0.300483i	$0.902852\pi$
$500$	4.34767	+	10.3004i	0.194434	+	0.460647i
$501$	8.58794			0.383681
$502$	7.61273	+	7.61273i	0.339773	+	0.339773i
$503$	−7.19669	+	7.19669i	−0.320885	+	0.320885i	−0.849106	−	0.528222i	$-0.822859\pi$
$503$	−7.19669	+	7.19669i	−0.320885	+	0.320885i	0.528222	+	0.849106i	$0.322859\pi$
$504$		0			0
$505$	−14.6416	+	11.2869i	−0.651542	+	0.502263i
$506$	−9.62510			−0.427888
$507$	0.932908	+	0.932908i	0.0414319	+	0.0414319i
$508$	4.77054	+	4.77054i	0.211659	+	0.211659i
$509$	−4.28156			−0.189777			−0.0948884	−	0.995488i	$-0.530249\pi$
$509$	−4.28156			−0.189777			−0.0948884	+	0.995488i	$0.530249\pi$
$510$	−4.69739	−	0.607749i	−0.208004	−	0.0269116i
$511$		0			0
$512$	0.707107	−	0.707107i	0.0312500	−	0.0312500i
$513$	−4.94687	−	4.94687i	−0.218410	−	0.218410i
$514$	15.0425			0.663495
$515$	−20.6373	−	2.67006i	−0.909388	−	0.117657i
$516$			2.76202i			0.121591i
$517$	13.6756	+	13.6756i	0.601451	+	0.601451i
$518$		0			0
$519$			4.04905i			0.177733i
$520$	4.66582	+	6.05256i	0.204610	+	0.265422i
$521$		−	14.5754i		−	0.638558i	−0.947661	−	0.319279i	$-0.896559\pi$
$521$		−	14.5754i		−	0.638558i	0.947661	−	0.319279i	$-0.103441\pi$
$522$	−0.484092	+	0.484092i	−0.0211881	+	0.0211881i
$523$	26.9324	−	26.9324i	1.17767	−	1.17767i	0.197336	−	0.980336i	$-0.436771\pi$
$523$	26.9324	−	26.9324i	1.17767	−	1.17767i	0.980336	−	0.197336i	$-0.0632290\pi$
$524$	−18.2091			−0.795468
$525$		0			0
$526$	22.5315			0.982418
$527$	8.35250	−	8.35250i	0.363841	−	0.363841i
$528$	−3.87940	+	3.87940i	−0.168829	+	0.168829i
$529$		−	19.9221i		−	0.866179i
$530$	−12.8361	−	16.6512i	−0.557565	−	0.723281i
$531$		−	10.1603i		−	0.440919i
$532$		0			0
$533$	−6.05612	−	6.05612i	−0.262319	−	0.262319i
$534$		−	7.18356i		−	0.310863i
$535$	−27.2046	−	3.51973i	−1.17616	−	0.152171i
$536$	−9.95313			−0.429910
$537$	2.59178	+	2.59178i	0.111844	+	0.111844i
$538$	−7.80819	+	7.80819i	−0.336635	+	0.336635i
$539$		0			0
$540$	−2.21758	−	0.286912i	−0.0954296	−	0.0123467i
$541$	16.8603			0.724882			0.362441	−	0.932007i	$-0.381944\pi$
$541$	16.8603			0.724882			0.362441	+	0.932007i	$0.381944\pi$
$542$	−3.54713	−	3.54713i	−0.152362	−	0.152362i
$543$	−1.69695	−	1.69695i	−0.0728230	−	0.0728230i
$544$	2.11825			0.0908190
$545$	0.596139	−	0.459553i	0.0255358	−	0.0196851i
$546$		0			0
$547$	−2.04444	+	2.04444i	−0.0874141	+	0.0874141i	−0.749462	−	0.662048i	$-0.769688\pi$
$547$	−2.04444	+	2.04444i	−0.0874141	+	0.0874141i	0.662048	+	0.749462i	$0.269688\pi$
$548$	−1.54481	−	1.54481i	−0.0659908	−	0.0659908i
$549$	−1.17166			−0.0500052
$550$	13.8218	+	23.6948i	0.589362	+	1.01035i
$551$		−	4.78948i		−	0.204039i
$552$	1.24054	+	1.24054i	0.0528009	+	0.0528009i
$553$		0			0
$554$		−	6.33506i		−	0.269151i
$555$	17.3555	−	13.3791i	0.736700	−	0.567910i
$556$			18.1446i			0.769501i
$557$	2.95885	−	2.95885i	0.125371	−	0.125371i	−0.641637	−	0.767008i	$-0.721745\pi$
$557$	2.95885	−	2.95885i	0.125371	−	0.125371i	0.767008	+	0.641637i	$0.221745\pi$
$558$	3.94312	−	3.94312i	0.166926	−	0.166926i
$559$	9.43977			0.399260
$560$		0			0
$561$	−11.6213			−0.490653
$562$	−20.8401	+	20.8401i	−0.879085	+	0.879085i
$563$	−17.7096	+	17.7096i	−0.746372	+	0.746372i	−0.973796	−	0.227424i	$-0.926970\pi$
$563$	−17.7096	+	17.7096i	−0.746372	+	0.746372i	0.227424	+	0.973796i	$0.426970\pi$
$564$		−	3.52518i		−	0.148437i
$565$	−4.13447	+	31.9559i	−0.173938	+	1.34440i
$566$		−	0.0978259i		−	0.00411193i
$567$		0			0
$568$	8.46519	+	8.46519i	0.355191	+	0.355191i
$569$			2.30741i			0.0967316i	0.998830	+	0.0483658i	$0.0154013\pi$
$569$			2.30741i			0.0967316i	−0.998830	+	0.0483658i	$0.984599\pi$
$570$	12.3894	−	9.55079i	0.518936	−	0.400039i
$571$	15.8865			0.664830			0.332415	−	0.943133i	$-0.392137\pi$
$571$	15.8865			0.664830			0.332415	+	0.943133i	$0.392137\pi$
$572$	13.2586	+	13.2586i	0.554371	+	0.554371i
$573$	5.71012	−	5.71012i	0.238544	−	0.238544i
$574$		0			0
$575$	7.57705	−	4.41987i	0.315985	−	0.184321i
$576$	1.00000			0.0416667
$577$	2.82904	+	2.82904i	0.117774	+	0.117774i	0.763538	−	0.645763i	$-0.223461\pi$
$577$	2.82904	+	2.82904i	0.117774	+	0.117774i	−0.645763	+	0.763538i	$0.723461\pi$
$578$	−8.84805	−	8.84805i	−0.368030	−	0.368030i
$579$	−1.72252			−0.0715855
$580$	−0.934623	−	1.21241i	−0.0388081	−	0.0503425i
$581$		0			0
$582$	−13.1212	+	13.1212i	−0.543891	+	0.543891i
$583$	−36.4757	−	36.4757i	−1.51067	−	1.51067i
$584$	4.87079			0.201555
$585$	−0.980578	+	7.57904i	−0.0405419	+	0.313355i
$586$			19.8097i			0.818330i
$587$	−5.31785	−	5.31785i	−0.219491	−	0.219491i	0.588793	−	0.808284i	$-0.299603\pi$
$587$	−5.31785	−	5.31785i	−0.219491	−	0.219491i	−0.808284	+	0.588793i	$0.799603\pi$
$588$		0			0
$589$			39.0122i			1.60747i
$590$	22.5313	+	2.91511i	0.927600	+	0.120013i
$591$		−	8.50188i		−	0.349721i
$592$	−6.92974	+	6.92974i	−0.284811	+	0.284811i
$593$	12.5171	−	12.5171i	0.514014	−	0.514014i	−0.401740	−	0.915754i	$-0.631594\pi$
$593$	12.5171	−	12.5171i	0.514014	−	0.514014i	0.915754	+	0.401740i	$0.131594\pi$
$594$	−5.48630			−0.225106
$595$		0			0
$596$	0.193656			0.00793245
$597$	−7.79086	+	7.79086i	−0.318858	+	0.318858i
$598$	4.23979	−	4.23979i	0.173378	−	0.173378i
$599$		−	31.2892i		−	1.27844i	−0.769024	−	0.639220i	$-0.779257\pi$
$599$		−	31.2892i		−	1.27844i	0.769024	−	0.639220i	$-0.220743\pi$
$600$	1.27250	−	4.83536i	0.0519497	−	0.197403i
$601$		−	47.5637i		−	1.94016i	−0.242776	−	0.970082i	$-0.578058\pi$
$601$		−	47.5637i		−	1.94016i	0.242776	−	0.970082i	$-0.421942\pi$
$602$		0			0
$603$	−7.03792	−	7.03792i	−0.286606	−	0.286606i
$604$			21.3227i			0.867610i
$605$	26.0745	+	33.8242i	1.06008	+	1.37515i
$606$	8.26766			0.335851
$607$	−17.3556	−	17.3556i	−0.704443	−	0.704443i	0.260918	−	0.965361i	$-0.415975\pi$
$607$	−17.3556	−	17.3556i	−0.704443	−	0.704443i	−0.965361	+	0.260918i	$0.915975\pi$
$608$	−4.94687	+	4.94687i	−0.200622	+	0.200622i
$609$		0			0
$610$	0.336163	−	2.59826i	0.0136108	−	0.105200i
$611$	−12.0480			−0.487410
$612$	1.49783	+	1.49783i	0.0605460	+	0.0605460i
$613$	−19.6837	−	19.6837i	−0.795016	−	0.795016i	0.187289	−	0.982305i	$-0.440030\pi$
$613$	−19.6837	−	19.6837i	−0.795016	−	0.795016i	−0.982305	+	0.187289i	$0.940030\pi$
$614$	−4.31788			−0.174255
$615$	−0.718991	+	5.55719i	−0.0289925	+	0.224088i
$616$		0			0
$617$	−24.4884	+	24.4884i	−0.985865	+	0.985865i	−0.999901	−	0.0140365i	$-0.995532\pi$
$617$	−24.4884	+	24.4884i	−0.985865	+	0.985865i	0.0140365	+	0.999901i	$0.495532\pi$
$618$	6.58048	+	6.58048i	0.264706	+	0.264706i
$619$	31.8275			1.27925			0.639627	−	0.768686i	$-0.279089\pi$
$619$	31.8275			1.27925			0.639627	+	0.768686i	$0.279089\pi$
$620$	7.61288	+	9.87553i	0.305741	+	0.396611i
$621$			1.75439i			0.0704012i
$622$	−5.97174	−	5.97174i	−0.239445	−	0.239445i
$623$		0			0
$624$		−	3.41770i		−	0.136817i
$625$	−21.7615	−	12.3060i	−0.870459	−	0.492241i
$626$			19.4096i			0.775764i
$627$	27.1400	−	27.1400i	1.08387	−	1.08387i
$628$	−2.60217	+	2.60217i	−0.103838	+	0.103838i
$629$	−20.7591			−0.827719
$630$		0			0
$631$	−34.9471			−1.39122			−0.695610	−	0.718419i	$-0.744866\pi$
$631$	−34.9471			−1.39122			−0.695610	+	0.718419i	$0.744866\pi$
$632$	−5.89081	+	5.89081i	−0.234324	+	0.234324i
$633$	7.30601	−	7.30601i	0.290388	−	0.290388i
$634$			15.5503i			0.617581i
$635$	−14.9611	−	1.93567i	−0.593713	−	0.0768147i
$636$			9.40242i			0.372830i
$637$		0			0
$638$	−2.65587	−	2.65587i	−0.105147	−	0.105147i
$639$			11.9716i			0.473589i
$640$	−0.286912	+	2.21758i	−0.0113412	+	0.0876577i
$641$	−11.2298			−0.443549			−0.221774	−	0.975098i	$-0.571185\pi$
$641$	−11.2298			−0.443549			−0.221774	+	0.975098i	$0.571185\pi$
$642$	8.67454	+	8.67454i	0.342357	+	0.342357i
$643$	9.89036	−	9.89036i	0.390038	−	0.390038i	−0.484663	−	0.874701i	$-0.661058\pi$
$643$	9.89036	−	9.89036i	0.390038	−	0.390038i	0.874701	+	0.484663i	$0.161058\pi$
$644$		0			0
$645$	−3.77069	−	4.89140i	−0.148471	−	0.192599i
$646$	−14.8191			−0.583050
$647$	11.0962	+	11.0962i	0.436235	+	0.436235i	0.890743	−	0.454508i	$-0.150185\pi$
$647$	11.0962	+	11.0962i	0.436235	+	0.436235i	−0.454508	+	0.890743i	$0.650185\pi$
$648$	0.707107	+	0.707107i	0.0277778	+	0.0277778i
$649$	55.7424			2.18808
$650$	−16.5258	−	4.34903i	−0.648196	−	0.170583i
$651$		0			0
$652$	−9.95676	+	9.95676i	−0.389937	+	0.389937i
$653$	11.2769	+	11.2769i	0.441297	+	0.441297i	0.892448	−	0.451151i	$-0.148986\pi$
$653$	11.2769	+	11.2769i	0.441297	+	0.441297i	−0.451151	+	0.892448i	$0.648986\pi$
$654$	−0.336622			−0.0131629
$655$	32.2473	−	24.8589i	1.26001	−	0.971318i
$656$		−	2.50597i		−	0.0978416i
$657$	3.44417	+	3.44417i	0.134370	+	0.134370i
$658$		0			0
$659$			10.4778i			0.408157i	0.978955	+	0.204078i	$0.0654198\pi$
$659$			10.4778i			0.408157i	−0.978955	+	0.204078i	$0.934580\pi$
$660$	1.57408	−	12.1663i	0.0612711	−	0.473574i
$661$		−	24.2215i		−	0.942106i	−0.882105	−	0.471053i	$-0.843874\pi$
$661$		−	24.2215i		−	0.942106i	0.882105	−	0.471053i	$-0.156126\pi$
$662$	11.4452	−	11.4452i	0.444830	−	0.444830i
$663$	5.11912	−	5.11912i	0.198810	−	0.198810i
$664$	5.73154			0.222427
$665$		0			0
$666$	−9.80013			−0.379747
$667$	−0.849286	+	0.849286i	−0.0328845	+	0.0328845i
$668$	6.07259	−	6.07259i	0.234956	−	0.234956i
$669$		−	4.82505i		−	0.186547i
$670$	17.6265	−	13.5879i	0.680969	−	0.524948i
$671$		−	6.42808i		−	0.248153i
$672$		0			0
$673$	−1.16725	−	1.16725i	−0.0449943	−	0.0449943i	0.684252	−	0.729246i	$-0.260129\pi$
$673$	−1.16725	−	1.16725i	−0.0449943	−	0.0449943i	−0.729246	+	0.684252i	$0.760129\pi$
$674$		−	27.1606i		−	1.04619i
$675$	4.31891	−	2.51932i	0.166235	−	0.0969688i
$676$	1.31933			0.0507435
$677$	9.07752	+	9.07752i	0.348877	+	0.348877i	0.859691	−	0.510814i	$-0.170656\pi$
$677$	9.07752	+	9.07752i	0.348877	+	0.348877i	−0.510814	+	0.859691i	$0.670656\pi$
$678$	10.1896	−	10.1896i	0.391328	−	0.391328i
$679$		0			0
$680$	−3.75130	+	2.89181i	−0.143856	+	0.110896i
$681$	−18.0938			−0.693354
$682$	21.6331	+	21.6331i	0.828376	+	0.828376i
$683$	15.1075	+	15.1075i	0.578073	+	0.578073i	0.934372	−	0.356299i	$-0.115962\pi$
$683$	15.1075	+	15.1075i	0.578073	+	0.578073i	−0.356299	+	0.934372i	$0.615962\pi$
$684$	−6.99593			−0.267496
$685$	4.84472	+	0.626811i	0.185107	+	0.0239492i
$686$		0			0
$687$	−6.82181	+	6.82181i	−0.260268	+	0.260268i
$688$	1.95305	+	1.95305i	0.0744592	+	0.0744592i
$689$	32.1346			1.22423
$690$	−3.89051	−	0.503355i	−0.148109	−	0.0191624i
$691$			42.7386i			1.62585i	0.582365	+	0.812927i	$0.302127\pi$
$691$			42.7386i			1.62585i	−0.582365	+	0.812927i	$0.697873\pi$
$692$	2.86311	+	2.86311i	0.108839	+	0.108839i
$693$		0			0
$694$		−	10.2657i		−	0.389681i
$695$	−24.7708	−	32.1331i	−0.939611	−	1.21888i
$696$			0.684610i			0.0259501i
$697$	3.75350	−	3.75350i	0.142174	−	0.142174i
$698$	4.67709	−	4.67709i	0.177031	−	0.177031i
$699$	14.4733			0.547431
$700$		0			0
$701$	44.5959			1.68436			0.842182	−	0.539194i	$-0.181271\pi$
$701$	44.5959			1.68436			0.842182	+	0.539194i	$0.181271\pi$
$702$	2.41668	−	2.41668i	0.0912116	−	0.0912116i
$703$	48.4800	−	48.4800i	1.82846	−	1.82846i
$704$			5.48630i			0.206773i
$705$	4.81254	+	6.24290i	0.181251	+	0.235121i
$706$			13.6247i			0.512772i
$707$		0			0
$708$	−7.18441	−	7.18441i	−0.270007	−	0.270007i
$709$		−	41.4249i		−	1.55575i	−0.628422	−	0.777873i	$-0.716299\pi$
$709$		−	41.4249i		−	1.55575i	0.628422	−	0.777873i	$-0.283701\pi$
$710$	−26.5480	−	3.43479i	−0.996329	−	0.128905i
$711$	−8.33087			−0.312432
$712$	−5.07954	−	5.07954i	−0.190364	−	0.190364i
$713$	6.91777	−	6.91777i	0.259072	−	0.259072i
$714$		0			0
$715$	−41.5809	−	5.37974i	−1.55504	−	0.201191i
$716$	3.66534			0.136980
$717$	21.1945	+	21.1945i	0.791524	+	0.791524i
$718$	12.2304	+	12.2304i	0.456435	+	0.456435i
$719$	23.5677			0.878928			0.439464	−	0.898260i	$-0.355168\pi$
$719$	23.5677			0.878928			0.439464	+	0.898260i	$0.355168\pi$
$720$	−1.77095	+	1.36519i	−0.0659993	+	0.0508777i
$721$		0			0
$722$	21.1730	−	21.1730i	0.787976	−	0.787976i
$723$	11.7522	+	11.7522i	0.437068	+	0.437068i
$724$	−2.39985			−0.0891896
$725$	3.31034	+	0.871167i	0.122943	+	0.0323543i
$726$		−	19.0995i		−	0.708848i
$727$	3.38556	+	3.38556i	0.125563	+	0.125563i	0.767096	−	0.641532i	$-0.221701\pi$
$727$	3.38556	+	3.38556i	0.125563	+	0.125563i	−0.641532	+	0.767096i	$0.721701\pi$
$728$		0			0
$729$			1.00000i			0.0370370i
$730$	−8.62590	+	6.64956i	−0.319259	+	0.246111i
$731$			5.85065i			0.216394i
$732$	−0.828489	+	0.828489i	−0.0306218	+	0.0306218i
$733$	27.7720	−	27.7720i	1.02578	−	1.02578i	0.0261249	−	0.999659i	$-0.491683\pi$
$733$	27.7720	−	27.7720i	1.02578	−	1.02578i	0.999659	−	0.0261249i	$-0.00831677\pi$
$734$	−25.8811			−0.955288
$735$		0			0
$736$	1.75439			0.0646676
$737$	38.6122	−	38.6122i	1.42230	−	1.42230i
$738$	1.77199	−	1.77199i	0.0652277	−	0.0652277i
$739$			44.5958i			1.64048i	0.572016	+	0.820242i	$0.306161\pi$
$739$			44.5958i			1.64048i	−0.572016	+	0.820242i	$0.693839\pi$
$740$	2.81177	−	21.7326i	0.103363	−	0.798907i
$741$			23.9100i			0.878356i
$742$		0			0
$743$	24.7787	+	24.7787i	0.909041	+	0.909041i	0.996195	−	0.0871537i	$-0.0277771\pi$
$743$	24.7787	+	24.7787i	0.909041	+	0.909041i	−0.0871537	+	0.996195i	$0.527777\pi$
$744$		−	5.57642i		−	0.204441i
$745$	−0.342954	+	0.264377i	−0.0125649	+	0.00968604i
$746$	9.16638			0.335605
$747$	4.05281	+	4.05281i	0.148285	+	0.148285i
$748$	−8.21752	+	8.21752i	−0.300462	+	0.300462i
$749$		0			0
$750$	4.34767	+	10.3004i	0.158754	+	0.376117i
$751$	5.09462			0.185905			0.0929526	−	0.995671i	$-0.470369\pi$
$751$	5.09462			0.185905			0.0929526	+	0.995671i	$0.470369\pi$
$752$	−2.49268	−	2.49268i	−0.0908985	−	0.0908985i
$753$	7.61273	+	7.61273i	0.277423	+	0.277423i
$754$	2.33979			0.0852101
$755$	−29.1096	−	37.7614i	−1.05941	−	1.37428i
$756$		0			0
$757$	18.2623	−	18.2623i	0.663754	−	0.663754i	−0.292509	−	0.956263i	$-0.594490\pi$
$757$	18.2623	−	18.2623i	0.663754	−	0.663754i	0.956263	+	0.292509i	$0.0944900\pi$
$758$	13.2138	+	13.2138i	0.479946	+	0.479946i
$759$	−9.62510			−0.349369
$760$	2.00721	−	15.5141i	0.0728093	−	0.562755i
$761$		−	28.1315i		−	1.01976i	−0.860244	−	0.509882i	$-0.829689\pi$
$761$		−	28.1315i		−	1.01976i	0.860244	−	0.509882i	$-0.170311\pi$
$762$	4.77054	+	4.77054i	0.172819	+	0.172819i
$763$		0			0
$764$		−	8.07532i		−	0.292155i
$765$	−4.69739	−	0.607749i	−0.169834	−	0.0219732i
$766$			19.8414i			0.716900i
$767$	−24.5542	+	24.5542i	−0.886600	+	0.886600i
$768$	0.707107	−	0.707107i	0.0255155	−	0.0255155i
$769$	−3.03517			−0.109451			−0.0547256	−	0.998501i	$-0.517428\pi$
$769$	−3.03517			−0.109451			−0.0547256	+	0.998501i	$0.517428\pi$
$770$		0			0
$771$	15.0425			0.541742
$772$	−1.21801	+	1.21801i	−0.0438370	+	0.0438370i
$773$	34.3021	−	34.3021i	1.23376	−	1.23376i	0.271253	−	0.962508i	$-0.412562\pi$
$773$	34.3021	−	34.3021i	1.23376	−	1.23376i	0.962508	−	0.271253i	$-0.0874379\pi$
$774$			2.76202i			0.0992789i
$775$	−26.9640	−	7.09600i	−0.968575	−	0.254896i
$776$			18.5562i			0.666128i
$777$		0			0
$778$	−3.62546	−	3.62546i	−0.129979	−	0.129979i
$779$			17.5316i			0.628134i
$780$	4.66582	+	6.05256i	0.167063	+	0.216716i
$781$	−65.6797			−2.35020
$782$	2.62777	+	2.62777i	0.0939688	+	0.0939688i
$783$	−0.484092	+	0.484092i	−0.0173000	+	0.0173000i
$784$		0			0
$785$	1.05584	−	8.16078i	0.0376847	−	0.291271i
$786$	−18.2091			−0.649497
$787$	−26.8578	−	26.8578i	−0.957376	−	0.957376i	0.0417518	−	0.999128i	$-0.486706\pi$
$787$	−26.8578	−	26.8578i	−0.957376	−	0.957376i	−0.999128	+	0.0417518i	$0.986706\pi$
$788$	−6.01174	−	6.01174i	−0.214159	−	0.214159i
$789$	22.5315			0.802141
$790$	2.39022	−	18.4744i	0.0850403	−	0.657290i
$791$		0			0
$792$	−3.87940	+	3.87940i	−0.137848	+	0.137848i
$793$	2.83153	+	2.83153i	0.100550	+	0.100550i
$794$	−26.3934			−0.936668
$795$	−12.8361	−	16.6512i	−0.455250	−	0.590557i
$796$			11.0179i			0.390520i
$797$	−34.4058	−	34.4058i	−1.21871	−	1.21871i	−0.968082	−	0.250632i	$-0.919362\pi$
$797$	−34.4058	−	34.4058i	−1.21871	−	1.21871i	−0.250632	−	0.968082i	$-0.580638\pi$
$798$		0			0
$799$		−	7.46719i		−	0.264170i
$800$	−2.51932	−	4.31891i	−0.0890715	−	0.152697i
$801$		−	7.18356i		−	0.253819i
$802$	−12.1830	+	12.1830i	−0.430198	+	0.430198i
$803$	−18.8957	+	18.8957i	−0.666816	+	0.666816i
$804$	−9.95313			−0.351020
$805$		0			0
$806$	−19.0585			−0.671307
$807$	−7.80819	+	7.80819i	−0.274861	+	0.274861i
$808$	5.84612	−	5.84612i	0.205666	−	0.205666i
$809$			38.8636i			1.36637i	0.730244	+	0.683186i	$0.239406\pi$
$809$			38.8636i			1.36637i	−0.730244	+	0.683186i	$0.760594\pi$
$810$	−2.21758	−	0.286912i	−0.0779180	−	0.0100810i
$811$		−	15.3545i		−	0.539168i	−0.962977	−	0.269584i	$-0.913114\pi$
$811$		−	15.3545i		−	0.539168i	0.962977	−	0.269584i	$-0.0868862\pi$
$812$		0			0
$813$	−3.54713	−	3.54713i	−0.124403	−	0.124403i
$814$		−	53.7665i		−	1.88451i
$815$	4.04000	−	31.2258i	0.141515	−	1.09379i
$816$	2.11825			0.0741534
$817$	−13.6634	−	13.6634i	−0.478021	−	0.478021i
$818$	25.2535	−	25.2535i	0.882967	−	0.882967i
$819$		0			0
$820$	3.42113	+	4.43793i	0.119471	+	0.154979i
$821$	23.9122			0.834542			0.417271	−	0.908782i	$-0.362987\pi$
$821$	23.9122			0.834542			0.417271	+	0.908782i	$0.362987\pi$
$822$	−1.54481	−	1.54481i	−0.0538813	−	0.0538813i
$823$	−20.0196	−	20.0196i	−0.697840	−	0.697840i	0.266105	−	0.963944i	$-0.414263\pi$
$823$	−20.0196	−	20.0196i	−0.697840	−	0.697840i	−0.963944	+	0.266105i	$0.914263\pi$
$824$	9.30620			0.324197
$825$	13.8218	+	23.6948i	0.481212	+	0.824949i
$826$		0			0
$827$	20.7600	−	20.7600i	0.721898	−	0.721898i	−0.247094	−	0.968992i	$-0.579476\pi$
$827$	20.7600	−	20.7600i	0.721898	−	0.721898i	0.968992	+	0.247094i	$0.0794757\pi$
$828$	1.24054	+	1.24054i	0.0431117	+	0.0431117i
$829$	8.28212			0.287650			0.143825	−	0.989603i	$-0.454060\pi$
$829$	8.28212			0.287650			0.143825	+	0.989603i	$0.454060\pi$
$830$	−10.1502	+	7.82465i	−0.352320	+	0.271598i
$831$		−	6.33506i		−	0.219761i
$832$	−2.41668	−	2.41668i	−0.0837832	−	0.0837832i
$833$		0			0
$834$			18.1446i			0.628295i
$835$	−2.46398	+	19.0445i	−0.0852696	+	0.659062i
$836$		−	38.3818i		−	1.32746i
$837$	3.94312	−	3.94312i	0.136294	−	0.136294i
$838$	9.92875	−	9.92875i	0.342983	−	0.342983i
$839$	−8.03334			−0.277342			−0.138671	−	0.990339i	$-0.544283\pi$
$839$	−8.03334			−0.277342			−0.138671	+	0.990339i	$0.544283\pi$
$840$		0			0
$841$	28.5313			0.983838
$842$	17.2769	−	17.2769i	0.595401	−	0.595401i
$843$	−20.8401	+	20.8401i	−0.717770	+	0.717770i
$844$		−	10.3323i		−	0.355651i
$845$	−2.33647	+	1.80114i	−0.0803769	+	0.0619611i
$846$		−	3.52518i		−	0.121198i
$847$		0			0
$848$	6.64852	+	6.64852i	0.228311	+	0.228311i
$849$		−	0.0978259i		−	0.00335738i
$850$	2.69547	−	10.2425i	0.0924539	−	0.351314i
$851$	−17.1932			−0.589377
$852$	8.46519	+	8.46519i	0.290013	+	0.290013i
$853$	−23.8654	+	23.8654i	−0.817136	+	0.817136i	−0.985692	−	0.168556i	$-0.946089\pi$
$853$	−23.8654	+	23.8654i	−0.817136	+	0.817136i	0.168556	+	0.985692i	$0.446089\pi$
$854$		0			0
$855$	12.3894	−	9.55079i	0.423709	−	0.326630i
$856$	12.2677			0.419300
$857$	16.9824	+	16.9824i	0.580107	+	0.580107i	0.934933	−	0.354826i	$-0.115460\pi$
$857$	16.9824	+	16.9824i	0.580107	+	0.580107i	−0.354826	+	0.934933i	$0.615460\pi$
$858$	13.2586	+	13.2586i	0.452642	+	0.452642i
$859$	−6.52841			−0.222747			−0.111373	−	0.993779i	$-0.535525\pi$
$859$	−6.52841			−0.222747			−0.111373	+	0.993779i	$0.535525\pi$
$860$	−6.12502	−	0.792457i	−0.208862	−	0.0270226i
$861$		0			0
$862$	−27.4196	+	27.4196i	−0.933914	+	0.933914i
$863$	−11.7091	−	11.7091i	−0.398582	−	0.398582i	0.479151	−	0.877733i	$-0.340945\pi$
$863$	−11.7091	−	11.7091i	−0.398582	−	0.398582i	−0.877733	+	0.479151i	$0.840945\pi$
$864$	1.00000			0.0340207
$865$	−8.97910	−	1.16172i	−0.305299	−	0.0394996i
$866$			11.1115i			0.377583i
$867$	−8.84805	−	8.84805i	−0.300496	−	0.300496i
$868$		0			0
$869$		−	45.7056i		−	1.55046i
$870$	−0.934623	−	1.21241i	−0.0316867	−	0.0411044i
$871$			34.0168i			1.15262i
$872$	−0.238027	+	0.238027i	−0.00806063	+	0.00806063i
$873$	−13.1212	+	13.1212i	−0.444086	+	0.444086i
$874$	−12.2736			−0.415160
$875$		0			0
$876$	4.87079			0.164569
$877$	26.1379	−	26.1379i	0.882613	−	0.882613i	−0.111186	−	0.993800i	$-0.535465\pi$
$877$	26.1379	−	26.1379i	0.882613	−	0.882613i	0.993800	+	0.111186i	$0.0354651\pi$
$878$	−14.9397	+	14.9397i	−0.504190	+	0.504190i
$879$			19.8097i			0.668164i
$880$	−7.48985	−	9.71594i	−0.252483	−	0.327524i
$881$			17.4940i			0.589386i	0.955592	+	0.294693i	$0.0952174\pi$
$881$			17.4940i			0.589386i	−0.955592	+	0.294693i	$0.904783\pi$
$882$		0			0
$883$	−14.0857	−	14.0857i	−0.474022	−	0.474022i	0.429191	−	0.903214i	$-0.358799\pi$
$883$	−14.0857	−	14.0857i	−0.474022	−	0.474022i	−0.903214	+	0.429191i	$0.858799\pi$
$884$		−	7.23953i		−	0.243492i
$885$	22.5313	+	2.91511i	0.757382	+	0.0979902i
$886$	6.71158			0.225480
$887$	29.0011	+	29.0011i	0.973763	+	0.973763i	0.999664	−	0.0259017i	$-0.00824569\pi$
$887$	29.0011	+	29.0011i	0.973763	+	0.973763i	−0.0259017	+	0.999664i	$0.508246\pi$
$888$	−6.92974	+	6.92974i	−0.232547	+	0.232547i
$889$		0			0
$890$	15.9302	+	2.06105i	0.533980	+	0.0690865i
$891$	−5.48630			−0.183798
$892$	−3.41183	−	3.41183i	−0.114236	−	0.114236i
$893$	17.4386	+	17.4386i	0.583560	+	0.583560i
$894$	0.193656			0.00647682
$895$	−6.49112	+	5.00389i	−0.216974	+	0.167262i
$896$		0			0
$897$	4.23979	−	4.23979i	0.141563	−	0.141563i
$898$	−5.86176	−	5.86176i	−0.195610	−	0.195610i
$899$	3.81767			0.127326
$900$	1.27250	−	4.83536i	0.0424167	−	0.161179i
$901$			19.9166i			0.663519i
$902$	9.72165	+	9.72165i	0.323695	+	0.323695i
$903$		0			0
$904$		−	14.4102i		−	0.479277i
$905$	4.25000	−	3.27625i	0.141275	−	0.108906i
$906$			21.3227i			0.708401i
$907$	14.1293	−	14.1293i	0.469156	−	0.469156i	−0.432485	−	0.901641i	$-0.642363\pi$
$907$	14.1293	−	14.1293i	0.469156	−	0.469156i	0.901641	+	0.432485i	$0.142363\pi$
$908$	−12.7942	+	12.7942i	−0.424591	+	0.424591i
$909$	8.26766			0.274221
$910$		0			0
$911$	−21.3131			−0.706136			−0.353068	−	0.935598i	$-0.614862\pi$
$911$	−21.3131			−0.706136			−0.353068	+	0.935598i	$0.614862\pi$
$912$	−4.94687	+	4.94687i	−0.163807	+	0.163807i
$913$	−22.2349	+	22.2349i	−0.735869	+	0.735869i
$914$		−	22.0820i		−	0.730407i
$915$	0.336163	−	2.59826i	0.0111132	−	0.0858957i
$916$			9.64749i			0.318762i
$917$		0			0
$918$	1.49783	+	1.49783i	0.0494356	+	0.0494356i
$919$			13.1648i			0.434266i	0.976142	+	0.217133i	$0.0696705\pi$
$919$			13.1648i			0.434266i	−0.976142	+	0.217133i	$0.930330\pi$
$920$	−3.10693	+	2.39508i	−0.102432	+	0.0789634i
$921$	−4.31788			−0.142279
$922$	−13.4442	−	13.4442i	−0.442762	−	0.442762i
$923$	28.9315	−	28.9315i	0.952291	−	0.952291i
$924$		0			0
$925$	24.6897	+	42.3259i	0.811793	+	1.39167i
$926$	−23.4888			−0.771891
$927$	6.58048	+	6.58048i	0.216131	+	0.216131i
$928$	0.484092	+	0.484092i	0.0158911	+	0.0158911i
$929$	−5.19844			−0.170555			−0.0852777	−	0.996357i	$-0.527178\pi$
$929$	−5.19844			−0.170555			−0.0852777	+	0.996357i	$0.527178\pi$
$930$	7.61288	+	9.87553i	0.249636	+	0.323831i
$931$		0			0
$932$	10.2342	−	10.2342i	0.335232	−	0.335232i
$933$	−5.97174	−	5.97174i	−0.195506	−	0.195506i
$934$	−15.9894			−0.523190
$935$	3.33429	−	25.7713i	0.109043	−	0.842811i
$936$		−	3.41770i		−	0.111711i
$937$	−3.54515	−	3.54515i	−0.115815	−	0.115815i	0.646824	−	0.762639i	$-0.276097\pi$
$937$	−3.54515	−	3.54515i	−0.115815	−	0.115815i	−0.762639	+	0.646824i	$0.776097\pi$
$938$		0			0
$939$			19.4096i			0.633409i
$940$	7.81738	+	1.01141i	0.254975	+	0.0329887i
$941$			10.2591i			0.334437i	0.985920	+	0.167219i	$0.0534786\pi$
$941$			10.2591i			0.334437i	−0.985920	+	0.167219i	$0.946521\pi$
$942$	−2.60217	+	2.60217i	−0.0847834	+	0.0847834i
$943$	3.10875	−	3.10875i	0.101235	−	0.101235i
$944$	−10.1603			−0.330689
$945$		0			0
$946$	−15.1533			−0.492676
$947$	19.8496	−	19.8496i	0.645025	−	0.645025i	−0.306761	−	0.951786i	$-0.599245\pi$
$947$	19.8496	−	19.8496i	0.645025	−	0.645025i	0.951786	+	0.306761i	$0.0992454\pi$
$948$	−5.89081	+	5.89081i	−0.191325	+	0.191325i
$949$		−	16.6469i		−	0.540381i
$950$	17.6250	+	30.2148i	0.571831	+	0.980298i
$951$			15.5503i			0.504253i
$952$		0			0
$953$	−29.6648	−	29.6648i	−0.960937	−	0.960937i	0.0383279	−	0.999265i	$-0.487797\pi$
$953$	−29.6648	−	29.6648i	−0.960937	−	0.960937i	−0.999265	+	0.0383279i	$0.987797\pi$
$954$			9.40242i			0.304415i
$955$	11.0244	+	14.3010i	0.356740	+	0.462768i
$956$	29.9736			0.969415
$957$	−2.65587	−	2.65587i	−0.0858522	−	0.0858522i
$958$	−6.37140	+	6.37140i	−0.205850	+	0.205850i
$959$		0			0
$960$	−0.286912	+	2.21758i	−0.00926003	+	0.0715722i
$961$	−0.0964085			−0.00310995
$962$	23.6838	+	23.6838i	0.763595	+	0.763595i
$963$	8.67454	+	8.67454i	0.279533	+	0.279533i
$964$	16.6201			0.535296
$965$	0.494211	−	3.81984i	0.0159092	−	0.122965i
$966$		0			0
$967$	−3.20889	+	3.20889i	−0.103191	+	0.103191i	−0.756817	−	0.653626i	$-0.773247\pi$
$967$	−3.20889	+	3.20889i	−0.103191	+	0.103191i	0.653626	+	0.756817i	$0.273247\pi$
$968$	−13.5054	−	13.5054i	−0.434079	−	0.434079i
$969$	−14.8191			−0.476058
$970$	−25.3328	−	32.8620i	−0.813386	−	1.05514i
$971$		−	59.0859i		−	1.89616i	−0.318036	−	0.948079i	$-0.603023\pi$
$971$		−	59.0859i		−	1.89616i	0.318036	−	0.948079i	$-0.396977\pi$
$972$	0.707107	+	0.707107i	0.0226805	+	0.0226805i
$973$		0			0
$974$		−	9.34012i		−	0.299277i
$975$	−16.5258	−	4.34903i	−0.529250	−	0.139280i
$976$			1.17166i			0.0375039i
$977$	−8.36251	+	8.36251i	−0.267540	+	0.267540i	−0.828108	−	0.560568i	$-0.810583\pi$
$977$	−8.36251	+	8.36251i	−0.267540	+	0.267540i	0.560568	+	0.828108i	$0.310583\pi$
$978$	−9.95676	+	9.95676i	−0.318382	+	0.318382i
$979$	39.4112			1.25959
$980$		0			0
$981$	−0.336622			−0.0107475
$982$	1.47457	−	1.47457i	0.0470554	−	0.0470554i
$983$	26.8714	−	26.8714i	0.857064	−	0.857064i	−0.133927	−	0.990991i	$-0.542759\pi$
$983$	26.8714	−	26.8714i	0.857064	−	0.857064i	0.990991	+	0.133927i	$0.0427587\pi$
$984$		−	2.50597i		−	0.0798873i
$985$	18.8536	+	2.43929i	0.600727	+	0.0777222i
$986$			1.45017i			0.0461829i
$987$		0			0
$988$	16.9069	+	16.9069i	0.537881	+	0.537881i
$989$			4.84566i			0.154083i
$990$	1.57408	−	12.1663i	0.0500276	−	0.386671i
$991$	8.01259			0.254528			0.127264	−	0.991869i	$-0.459380\pi$
$991$	8.01259			0.254528			0.127264	+	0.991869i	$0.459380\pi$
$992$	−3.94312	−	3.94312i	−0.125194	−	0.125194i
$993$	11.4452	−	11.4452i	0.363202	−	0.363202i
$994$		0			0
$995$	−15.0416	−	19.5122i	−0.476851	−	0.618577i
$996$	5.73154			0.181611
$997$	30.0935	+	30.0935i	0.953072	+	0.953072i	0.998947	−	0.0458749i	$-0.0146076\pi$
$997$	30.0935	+	30.0935i	0.953072	+	0.953072i	−0.0458749	+	0.998947i	$0.514608\pi$
$998$	9.49260	+	9.49260i	0.300483	+	0.300483i
$999$	−9.80013			−0.310063

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1470.2.m.e.1273.7		16
5.2	odd	4		1470.2.m.d.97.6		16
7.4	even	3		210.2.u.b.103.3	yes	16
7.5	odd	6		210.2.u.a.73.1	✓	16
7.6	odd	2		1470.2.m.d.1273.6		16
21.5	even	6		630.2.bv.a.73.4		16
21.11	odd	6		630.2.bv.b.523.2		16
35.4	even	6		1050.2.bc.g.943.2		16
35.12	even	12		210.2.u.b.157.3	yes	16
35.18	odd	12		1050.2.bc.h.607.3		16
35.19	odd	6		1050.2.bc.h.493.3		16
35.27	even	4	inner	1470.2.m.e.97.7		16
35.32	odd	12		210.2.u.a.187.1	yes	16
35.33	even	12		1050.2.bc.g.157.2		16
105.32	even	12		630.2.bv.a.397.4		16
105.47	odd	12		630.2.bv.b.577.2		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
210.2.u.a.73.1	✓	16	7.5	odd	6
210.2.u.a.187.1	yes	16	35.32	odd	12
210.2.u.b.103.3	yes	16	7.4	even	3
210.2.u.b.157.3	yes	16	35.12	even	12
630.2.bv.a.73.4		16	21.5	even	6
630.2.bv.a.397.4		16	105.32	even	12
630.2.bv.b.523.2		16	21.11	odd	6
630.2.bv.b.577.2		16	105.47	odd	12
1050.2.bc.g.157.2		16	35.33	even	12
1050.2.bc.g.943.2		16	35.4	even	6
1050.2.bc.h.493.3		16	35.19	odd	6
1050.2.bc.h.607.3		16	35.18	odd	12
1470.2.m.d.97.6		16	5.2	odd	4
1470.2.m.d.1273.6		16	7.6	odd	2
1470.2.m.e.97.7		16	35.27	even	4	inner
1470.2.m.e.1273.7		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)

\(f(q)\)	\(=\)	\(q+(0.707107 - 0.707107i) q^{2} +(0.707107 - 0.707107i) q^{3} -1.00000i q^{4} +(1.36519 + 1.77095i) q^{5} -1.00000i q^{6} +(-0.707107 - 0.707107i) q^{8} -1.00000i q^{9} +O(q^{10})\)	\(q+(0.707107 - 0.707107i) q^{2} +(0.707107 - 0.707107i) q^{3} -1.00000i q^{4} +(1.36519 + 1.77095i) q^{5} -1.00000i q^{6} +(-0.707107 - 0.707107i) q^{8} -1.00000i q^{9} +(2.21758 + 0.286912i) q^{10} +5.48630 q^{11} +(-0.707107 - 0.707107i) q^{12} +(-2.41668 + 2.41668i) q^{13} +(2.21758 + 0.286912i) q^{15} -1.00000 q^{16} +(-1.49783 - 1.49783i) q^{17} +(-0.707107 - 0.707107i) q^{18} +6.99593 q^{19} +(1.77095 - 1.36519i) q^{20} +(3.87940 - 3.87940i) q^{22} +(-1.24054 - 1.24054i) q^{23} -1.00000 q^{24} +(-1.27250 + 4.83536i) q^{25} +3.41770i q^{26} +(-0.707107 - 0.707107i) q^{27} -0.684610i q^{29} +(1.77095 - 1.36519i) q^{30} +5.57642i q^{31} +(-0.707107 + 0.707107i) q^{32} +(3.87940 - 3.87940i) q^{33} -2.11825 q^{34} -1.00000 q^{36} +(6.92974 - 6.92974i) q^{37} +(4.94687 - 4.94687i) q^{38} +3.41770i q^{39} +(0.286912 - 2.21758i) q^{40} +2.50597i q^{41} +(-1.95305 - 1.95305i) q^{43} -5.48630i q^{44} +(1.77095 - 1.36519i) q^{45} -1.75439 q^{46} +(2.49268 + 2.49268i) q^{47} +(-0.707107 + 0.707107i) q^{48} +(2.51932 + 4.31891i) q^{50} -2.11825 q^{51} +(2.41668 + 2.41668i) q^{52} +(-6.64852 - 6.64852i) q^{53} -1.00000 q^{54} +(7.48985 + 9.71594i) q^{55} +(4.94687 - 4.94687i) q^{57} +(-0.484092 - 0.484092i) q^{58} +10.1603 q^{59} +(0.286912 - 2.21758i) q^{60} -1.17166i q^{61} +(3.94312 + 3.94312i) q^{62} +1.00000i q^{64} +(-7.57904 - 0.980578i) q^{65} -5.48630i q^{66} +(7.03792 - 7.03792i) q^{67} +(-1.49783 + 1.49783i) q^{68} -1.75439 q^{69} -11.9716 q^{71} +(-0.707107 + 0.707107i) q^{72} +(-3.44417 + 3.44417i) q^{73} -9.80013i q^{74} +(2.51932 + 4.31891i) q^{75} -6.99593i q^{76} +(2.41668 + 2.41668i) q^{78} -8.33087i q^{79} +(-1.36519 - 1.77095i) q^{80} -1.00000 q^{81} +(1.77199 + 1.77199i) q^{82} +(-4.05281 + 4.05281i) q^{83} +(0.607749 - 4.69739i) q^{85} -2.76202 q^{86} +(-0.484092 - 0.484092i) q^{87} +(-3.87940 - 3.87940i) q^{88} +7.18356 q^{89} +(0.286912 - 2.21758i) q^{90} +(-1.24054 + 1.24054i) q^{92} +(3.94312 + 3.94312i) q^{93} +3.52518 q^{94} +(9.55079 + 12.3894i) q^{95} +1.00000i q^{96} +(-13.1212 - 13.1212i) q^{97} -5.48630i 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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