LMFDB - Embedded newform 1470.2.m.d.97.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("1470.97");

S:= CuspForms(chi, 2);

N := Newforms(S);

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

Newform invariants

comment: select newform

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

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

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

Embedding invariants

Embedding label			97.4
Root			$2.69978 - 0.355433i$ of defining polynomial
Character	$\chi$	$=$	1470.97
Dual form			1470.2.m.d.1273.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.707107 - 0.707107i) q^{2} +(0.707107 + 0.707107i) q^{3} +1.00000i q^{4} +(1.99671 + 1.00656i) q^{5} -1.00000i q^{6} +(0.707107 - 0.707107i) q^{8} +1.00000i q^{9} +O(q^{10})$	\(q+(-0.707107 - 0.707107i) q^{2} +(0.707107 + 0.707107i) q^{3} +1.00000i q^{4} +(1.99671 + 1.00656i) q^{5} -1.00000i q^{6} +(0.707107 - 0.707107i) q^{8} +1.00000i q^{9} +(-0.700141 - 2.12363i) q^{10} -3.10780 q^{11} +(-0.707107 + 0.707107i) q^{12} +(-3.40812 - 3.40812i) q^{13} +(0.700141 + 2.12363i) q^{15} -1.00000 q^{16} +(-3.76725 + 3.76725i) q^{17} +(0.707107 - 0.707107i) q^{18} -7.23346 q^{19} +(-1.00656 + 1.99671i) q^{20} +(2.19755 + 2.19755i) q^{22} +(-3.72349 + 3.72349i) q^{23} +1.00000 q^{24} +(2.97368 + 4.01961i) q^{25} +4.81981i q^{26} +(-0.707107 + 0.707107i) q^{27} -4.49359i q^{29} +(1.00656 - 1.99671i) q^{30} +9.22503i q^{31} +(0.707107 + 0.707107i) q^{32} +(-2.19755 - 2.19755i) q^{33} +5.32769 q^{34} -1.00000 q^{36} +(-2.54080 - 2.54080i) q^{37} +(5.11483 + 5.11483i) q^{38} -4.81981i q^{39} +(2.12363 - 0.700141i) q^{40} -2.51851i q^{41} +(-3.86848 + 3.86848i) q^{43} -3.10780i q^{44} +(-1.00656 + 1.99671i) q^{45} +5.26581 q^{46} +(2.88813 - 2.88813i) q^{47} +(-0.707107 - 0.707107i) q^{48} +(0.739583 - 4.94500i) q^{50} -5.32769 q^{51} +(3.40812 - 3.40812i) q^{52} +(2.43203 - 2.43203i) q^{53} +1.00000 q^{54} +(-6.20538 - 3.12819i) q^{55} +(-5.11483 - 5.11483i) q^{57} +(-3.17745 + 3.17745i) q^{58} +1.33238 q^{59} +(-2.12363 + 0.700141i) q^{60} +12.5538i q^{61} +(6.52308 - 6.52308i) q^{62} -1.00000i q^{64} +(-3.37454 - 10.2355i) q^{65} +3.10780i q^{66} +(-4.71136 - 4.71136i) q^{67} +(-3.76725 - 3.76725i) q^{68} -5.26581 q^{69} +9.22738 q^{71} +(0.707107 + 0.707107i) q^{72} +(-5.82099 - 5.82099i) q^{73} +3.59323i q^{74} +(-0.739583 + 4.94500i) q^{75} -7.23346i q^{76} +(-3.40812 + 3.40812i) q^{78} -1.91436i q^{79} +(-1.99671 - 1.00656i) q^{80} -1.00000 q^{81} +(-1.78086 + 1.78086i) q^{82} +(8.97250 + 8.97250i) q^{83} +(-11.3140 + 3.73013i) q^{85} +5.47086 q^{86} +(3.17745 - 3.17745i) q^{87} +(-2.19755 + 2.19755i) q^{88} +4.07354 q^{89} +(2.12363 - 0.700141i) q^{90} +(-3.72349 - 3.72349i) q^{92} +(-6.52308 + 6.52308i) q^{93} -4.08444 q^{94} +(-14.4431 - 7.28091i) q^{95} +1.00000i q^{96} +(2.69423 - 2.69423i) q^{97} -3.10780i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q+O(q^{10}) $ 16 * q	$ 16 q - 4 q^{10} - 8 q^{11} - 16 q^{13} + 4 q^{15} - 16 q^{16} + 24 q^{17} + 16 q^{19} - 8 q^{20} + 4 q^{22} + 8 q^{23} + 16 q^{24} + 16 q^{25} + 8 q^{30} - 4 q^{33} + 16 q^{34} - 16 q^{36} + 16 q^{37} + 8 q^{38} - 24 q^{43} - 8 q^{45} + 8 q^{46} + 24 q^{47} - 16 q^{51} + 16 q^{52} - 16 q^{53} + 16 q^{54} - 56 q^{55} - 8 q^{57} - 36 q^{58} - 16 q^{59} + 8 q^{62} - 32 q^{65} + 48 q^{67} + 24 q^{68} - 8 q^{69} - 32 q^{71} + 56 q^{73} - 16 q^{78} - 16 q^{81} + 24 q^{82} - 16 q^{83} + 8 q^{85} + 16 q^{86} + 36 q^{87} - 4 q^{88} + 32 q^{89} + 8 q^{92} - 8 q^{93} - 16 q^{94} - 24 q^{95} + 44 q^{97}+O(q^{100}) $ 16 * q - 4 * q^10 - 8 * q^11 - 16 * q^13 + 4 * q^15 - 16 * q^16 + 24 * q^17 + 16 * q^19 - 8 * q^20 + 4 * q^22 + 8 * q^23 + 16 * q^24 + 16 * q^25 + 8 * q^30 - 4 * q^33 + 16 * q^34 - 16 * q^36 + 16 * q^37 + 8 * q^38 - 24 * q^43 - 8 * q^45 + 8 * q^46 + 24 * q^47 - 16 * q^51 + 16 * q^52 - 16 * q^53 + 16 * q^54 - 56 * q^55 - 8 * q^57 - 36 * q^58 - 16 * q^59 + 8 * q^62 - 32 * q^65 + 48 * q^67 + 24 * q^68 - 8 * q^69 - 32 * q^71 + 56 * q^73 - 16 * q^78 - 16 * q^81 + 24 * q^82 - 16 * q^83 + 8 * q^85 + 16 * q^86 + 36 * q^87 - 4 * q^88 + 32 * q^89 + 8 * q^92 - 8 * q^93 - 16 * q^94 - 24 * q^95 + 44 * q^97

Display 100 coefficients 10 coefficients

Character values

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

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

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−0.707107	−	0.707107i	−0.500000	−	0.500000i
$2$	−0.707107	−	0.707107i	−0.500000	−	0.500000i
$3$	0.707107	+	0.707107i	0.408248	+	0.408248i
$3$	0.707107	+	0.707107i	0.408248	+	0.408248i
$4$			1.00000i			0.500000i
$5$	1.99671	+	1.00656i	0.892955	+	0.450147i
$5$	1.99671	+	1.00656i	0.892955	+	0.450147i
$6$		−	1.00000i		−	0.408248i
$7$		0			0
$7$		0			0
$8$	0.707107	−	0.707107i	0.250000	−	0.250000i
$9$			1.00000i			0.333333i
$10$	−0.700141	−	2.12363i	−0.221404	−	0.671551i
$11$	−3.10780			−0.937038			−0.468519	−	0.883453i	$-0.655212\pi$
$11$	−3.10780			−0.937038			−0.468519	+	0.883453i	$0.655212\pi$
$12$	−0.707107	+	0.707107i	−0.204124	+	0.204124i
$13$	−3.40812	−	3.40812i	−0.945243	−	0.945243i	0.0533341	−	0.998577i	$-0.483015\pi$
$13$	−3.40812	−	3.40812i	−0.945243	−	0.945243i	−0.998577	+	0.0533341i	$0.983015\pi$
$14$		0			0
$15$	0.700141	+	2.12363i	0.180776	+	0.548319i
$16$	−1.00000			−0.250000
$17$	−3.76725	+	3.76725i	−0.913692	+	0.913692i	−0.996560	−	0.0828688i	$-0.973592\pi$
$17$	−3.76725	+	3.76725i	−0.913692	+	0.913692i	0.0828688	+	0.996560i	$0.473592\pi$
$18$	0.707107	−	0.707107i	0.166667	−	0.166667i
$19$	−7.23346			−1.65947			−0.829735	−	0.558158i	$-0.811508\pi$
$19$	−7.23346			−1.65947			−0.829735	+	0.558158i	$0.811508\pi$
$20$	−1.00656	+	1.99671i	−0.225073	+	0.446477i
$21$		0			0
$22$	2.19755	+	2.19755i	0.468519	+	0.468519i
$23$	−3.72349	+	3.72349i	−0.776401	+	0.776401i	−0.979217	−	0.202816i	$-0.934991\pi$
$23$	−3.72349	+	3.72349i	−0.776401	+	0.776401i	0.202816	+	0.979217i	$0.434991\pi$
$24$	1.00000			0.204124
$25$	2.97368	+	4.01961i	0.594736	+	0.803921i
$26$			4.81981i			0.945243i
$27$	−0.707107	+	0.707107i	−0.136083	+	0.136083i
$28$		0			0
$29$		−	4.49359i		−	0.834438i	−0.908806	−	0.417219i	$-0.863005\pi$
$29$		−	4.49359i		−	0.834438i	0.908806	−	0.417219i	$-0.136995\pi$
$30$	1.00656	−	1.99671i	0.183772	−	0.364547i
$31$			9.22503i			1.65686i	0.560089	+	0.828432i	$0.310767\pi$
$31$			9.22503i			1.65686i	−0.560089	+	0.828432i	$0.689233\pi$
$32$	0.707107	+	0.707107i	0.125000	+	0.125000i
$33$	−2.19755	−	2.19755i	−0.382544	−	0.382544i
$34$	5.32769			0.913692
$35$		0			0
$36$	−1.00000			−0.166667
$37$	−2.54080	−	2.54080i	−0.417705	−	0.417705i	0.466707	−	0.884412i	$-0.345440\pi$
$37$	−2.54080	−	2.54080i	−0.417705	−	0.417705i	−0.884412	+	0.466707i	$0.845440\pi$
$38$	5.11483	+	5.11483i	0.829735	+	0.829735i
$39$		−	4.81981i		−	0.771787i
$40$	2.12363	−	0.700141i	0.335775	−	0.110702i
$41$		−	2.51851i		−	0.393326i	−0.980471	−	0.196663i	$-0.936990\pi$
$41$		−	2.51851i		−	0.393326i	0.980471	−	0.196663i	$-0.0630104\pi$
$42$		0			0
$43$	−3.86848	+	3.86848i	−0.589938	+	0.589938i	−0.937615	−	0.347677i	$-0.886971\pi$
$43$	−3.86848	+	3.86848i	−0.589938	+	0.589938i	0.347677	+	0.937615i	$0.386971\pi$
$44$		−	3.10780i		−	0.468519i
$45$	−1.00656	+	1.99671i	−0.150049	+	0.297652i
$46$	5.26581			0.776401
$47$	2.88813	−	2.88813i	0.421277	−	0.421277i	−0.464366	−	0.885643i	$-0.653718\pi$
$47$	2.88813	−	2.88813i	0.421277	−	0.421277i	0.885643	+	0.464366i	$0.153718\pi$
$48$	−0.707107	−	0.707107i	−0.102062	−	0.102062i
$49$		0			0
$50$	0.739583	−	4.94500i	0.104593	−	0.699328i
$51$	−5.32769			−0.746026
$52$	3.40812	−	3.40812i	0.472621	−	0.472621i
$53$	2.43203	−	2.43203i	0.334066	−	0.334066i	−0.520063	−	0.854128i	$-0.674091\pi$
$53$	2.43203	−	2.43203i	0.334066	−	0.334066i	0.854128	+	0.520063i	$0.174091\pi$
$54$	1.00000			0.136083
$55$	−6.20538	−	3.12819i	−0.836733	−	0.421805i
$56$		0			0
$57$	−5.11483	−	5.11483i	−0.677476	−	0.677476i
$58$	−3.17745	+	3.17745i	−0.417219	+	0.417219i
$59$	1.33238			0.173461			0.0867303	−	0.996232i	$-0.472358\pi$
$59$	1.33238			0.173461			0.0867303	+	0.996232i	$0.472358\pi$
$60$	−2.12363	+	0.700141i	−0.274159	+	0.0903878i
$61$			12.5538i			1.60735i	0.595071	+	0.803673i	$0.297124\pi$
$61$			12.5538i			1.60735i	−0.595071	+	0.803673i	$0.702876\pi$
$62$	6.52308	−	6.52308i	0.828432	−	0.828432i
$63$		0			0
$64$		−	1.00000i		−	0.125000i
$65$	−3.37454	−	10.2355i	−0.418561	−	1.26956i
$66$			3.10780i			0.382544i
$67$	−4.71136	−	4.71136i	−0.575584	−	0.575584i	0.358099	−	0.933684i	$-0.383425\pi$
$67$	−4.71136	−	4.71136i	−0.575584	−	0.575584i	−0.933684	+	0.358099i	$0.883425\pi$
$68$	−3.76725	−	3.76725i	−0.456846	−	0.456846i
$69$	−5.26581			−0.633929
$70$		0			0
$71$	9.22738			1.09509			0.547544	−	0.836777i	$-0.315563\pi$
$71$	9.22738			1.09509			0.547544	+	0.836777i	$0.315563\pi$
$72$	0.707107	+	0.707107i	0.0833333	+	0.0833333i
$73$	−5.82099	−	5.82099i	−0.681296	−	0.681296i	0.278996	−	0.960292i	$-0.409998\pi$
$73$	−5.82099	−	5.82099i	−0.681296	−	0.681296i	−0.960292	+	0.278996i	$0.909998\pi$
$74$			3.59323i			0.417705i
$75$	−0.739583	+	4.94500i	−0.0853997	+	0.570999i
$76$		−	7.23346i		−	0.829735i
$77$		0			0
$78$	−3.40812	+	3.40812i	−0.385894	+	0.385894i
$79$		−	1.91436i		−	0.215383i	−0.994184	−	0.107691i	$-0.965654\pi$
$79$		−	1.91436i		−	0.215383i	0.994184	−	0.107691i	$-0.0343458\pi$
$80$	−1.99671	−	1.00656i	−0.223239	−	0.112537i
$81$	−1.00000			−0.111111
$82$	−1.78086	+	1.78086i	−0.196663	+	0.196663i
$83$	8.97250	+	8.97250i	0.984860	+	0.984860i	0.999887	−	0.0150269i	$-0.00478339\pi$
$83$	8.97250	+	8.97250i	0.984860	+	0.984860i	−0.0150269	+	0.999887i	$0.504783\pi$
$84$		0			0
$85$	−11.3140	+	3.73013i	−1.22718	+	0.404590i
$86$	5.47086			0.589938
$87$	3.17745	−	3.17745i	0.340658	−	0.340658i
$88$	−2.19755	+	2.19755i	−0.234260	+	0.234260i
$89$	4.07354			0.431794			0.215897	−	0.976416i	$-0.430732\pi$
$89$	4.07354			0.431794			0.215897	+	0.976416i	$0.430732\pi$
$90$	2.12363	−	0.700141i	0.223850	−	0.0738013i
$91$		0			0
$92$	−3.72349	−	3.72349i	−0.388201	−	0.388201i
$93$	−6.52308	+	6.52308i	−0.676412	+	0.676412i
$94$	−4.08444			−0.421277
$95$	−14.4431	−	7.28091i	−1.48183	−	0.747005i
$96$			1.00000i			0.102062i
$97$	2.69423	−	2.69423i	0.273558	−	0.273558i	−0.556973	−	0.830531i	$-0.688037\pi$
$97$	2.69423	−	2.69423i	0.273558	−	0.273558i	0.830531	+	0.556973i	$0.188037\pi$
$98$		0			0
$99$		−	3.10780i		−	0.312346i
$100$	−4.01961	+	2.97368i	−0.401961	+	0.297368i
$101$			7.86244i			0.782342i	0.920318	+	0.391171i	$0.127930\pi$
$101$			7.86244i			0.782342i	−0.920318	+	0.391171i	$0.872070\pi$
$102$	3.76725	+	3.76725i	0.373013	+	0.373013i
$103$	8.36587	+	8.36587i	0.824313	+	0.824313i	0.986723	−	0.162410i	$-0.0519267\pi$
$103$	8.36587	+	8.36587i	0.824313	+	0.824313i	−0.162410	+	0.986723i	$0.551927\pi$
$104$	−4.81981			−0.472621
$105$		0			0
$106$	−3.43942			−0.334066
$107$	−1.52895	−	1.52895i	−0.147809	−	0.147809i	0.629329	−	0.777139i	$-0.283330\pi$
$107$	−1.52895	−	1.52895i	−0.147809	−	0.147809i	−0.777139	+	0.629329i	$0.783330\pi$
$108$	−0.707107	−	0.707107i	−0.0680414	−	0.0680414i
$109$			0.565551i			0.0541700i	0.999633	+	0.0270850i	$0.00862248\pi$
$109$			0.565551i			0.0541700i	−0.999633	+	0.0270850i	$0.991378\pi$
$110$	2.17590	+	6.59983i	0.207464	+	0.629269i
$111$		−	3.59323i		−	0.341054i
$112$		0			0
$113$	9.98231	−	9.98231i	0.939057	−	0.939057i	−0.0591899	−	0.998247i	$-0.518852\pi$
$113$	9.98231	−	9.98231i	0.939057	−	0.939057i	0.998247	+	0.0591899i	$0.0188518\pi$
$114$			7.23346i			0.677476i
$115$	−11.1826	+	3.68681i	−1.04279	+	0.343797i
$116$	4.49359			0.417219
$117$	3.40812	−	3.40812i	0.315081	−	0.315081i
$118$	−0.942132	−	0.942132i	−0.0867303	−	0.0867303i
$119$		0			0
$120$	1.99671	+	1.00656i	0.182274	+	0.0918858i
$121$	−1.34155			−0.121959
$122$	8.87686	−	8.87686i	0.803673	−	0.803673i
$123$	1.78086	−	1.78086i	0.160575	−	0.160575i
$124$	−9.22503			−0.828432
$125$	1.89159	+	11.0192i	0.169189	+	0.985584i
$126$		0			0
$127$	−2.14534	−	2.14534i	−0.190368	−	0.190368i	0.605487	−	0.795855i	$-0.292978\pi$
$127$	−2.14534	−	2.14534i	−0.190368	−	0.190368i	−0.795855	+	0.605487i	$0.792978\pi$
$128$	−0.707107	+	0.707107i	−0.0625000	+	0.0625000i
$129$	−5.47086			−0.481682
$130$	−4.85142	+	9.62375i	−0.425498	+	0.844059i
$131$			8.77339i			0.766534i	0.923638	+	0.383267i	$0.125201\pi$
$131$			8.77339i			0.766534i	−0.923638	+	0.383267i	$0.874799\pi$
$132$	2.19755	−	2.19755i	0.191272	−	0.191272i
$133$		0			0
$134$			6.66287i			0.575584i
$135$	−2.12363	+	0.700141i	−0.182773	+	0.0602585i
$136$			5.32769i			0.456846i
$137$	−9.62030	−	9.62030i	−0.821918	−	0.821918i	0.164465	−	0.986383i	$-0.447410\pi$
$137$	−9.62030	−	9.62030i	−0.821918	−	0.821918i	−0.986383	+	0.164465i	$0.947410\pi$
$138$	3.72349	+	3.72349i	0.316965	+	0.316965i
$139$	−10.9145			−0.925753			−0.462876	−	0.886423i	$-0.653183\pi$
$139$	−10.9145			−0.925753			−0.462876	+	0.886423i	$0.653183\pi$
$140$		0			0
$141$	4.08444			0.343972
$142$	−6.52474	−	6.52474i	−0.547544	−	0.547544i
$143$	10.5918	+	10.5918i	0.885729	+	0.885729i
$144$		−	1.00000i		−	0.0833333i
$145$	4.52306	−	8.97238i	0.375620	−	0.745115i
$146$			8.23213i			0.681296i
$147$		0			0
$148$	2.54080	−	2.54080i	0.208852	−	0.208852i
$149$		−	2.09021i		−	0.171237i	−0.996328	−	0.0856183i	$-0.972713\pi$
$149$		−	2.09021i		−	0.171237i	0.996328	−	0.0856183i	$-0.0272866\pi$
$150$	4.01961	−	2.97368i	0.328200	−	0.242800i
$151$	4.04236			0.328963			0.164481	−	0.986380i	$-0.447405\pi$
$151$	4.04236			0.328963			0.164481	+	0.986380i	$0.447405\pi$
$152$	−5.11483	+	5.11483i	−0.414867	+	0.414867i
$153$	−3.76725	−	3.76725i	−0.304564	−	0.304564i
$154$		0			0
$155$	−9.28554	+	18.4197i	−0.745832	+	1.47950i
$156$	4.81981			0.385894
$157$	0.640337	−	0.640337i	0.0511044	−	0.0511044i	−0.681093	−	0.732197i	$-0.738495\pi$
$157$	0.640337	−	0.640337i	0.0511044	−	0.0511044i	0.732197	+	0.681093i	$0.238495\pi$
$158$	−1.35366	+	1.35366i	−0.107691	+	0.107691i
$159$	3.43942			0.272763
$160$	0.700141	+	2.12363i	0.0553510	+	0.167888i
$161$		0			0
$162$	0.707107	+	0.707107i	0.0555556	+	0.0555556i
$163$	−5.21998	+	5.21998i	−0.408860	+	0.408860i	−0.881341	−	0.472481i	$-0.843359\pi$
$163$	−5.21998	+	5.21998i	−0.408860	+	0.408860i	0.472481	+	0.881341i	$0.343359\pi$
$164$	2.51851			0.196663
$165$	−2.17590	−	6.59983i	−0.169394	−	0.513796i
$166$		−	12.6890i		−	0.984860i
$167$	−0.610646	+	0.610646i	−0.0472532	+	0.0472532i	−0.730339	−	0.683085i	$-0.760638\pi$
$167$	−0.610646	+	0.610646i	−0.0472532	+	0.0472532i	0.683085	+	0.730339i	$0.260638\pi$
$168$		0			0
$169$			10.2306i			0.786967i
$170$	10.6378	+	5.36264i	0.815885	+	0.411295i
$171$		−	7.23346i		−	0.553157i
$172$	−3.86848	−	3.86848i	−0.294969	−	0.294969i
$173$	−2.47309	−	2.47309i	−0.188026	−	0.188026i	0.606816	−	0.794842i	$-0.292446\pi$
$173$	−2.47309	−	2.47309i	−0.188026	−	0.188026i	−0.794842	+	0.606816i	$0.792446\pi$
$174$	−4.49359			−0.340658
$175$		0			0
$176$	3.10780			0.234260
$177$	0.942132	+	0.942132i	0.0708150	+	0.0708150i
$178$	−2.88043	−	2.88043i	−0.215897	−	0.215897i
$179$			18.0618i			1.35000i	0.737816	+	0.675002i	$0.235857\pi$
$179$			18.0618i			1.35000i	−0.737816	+	0.675002i	$0.764143\pi$
$180$	−1.99671	−	1.00656i	−0.148826	−	0.0750245i
$181$			21.7257i			1.61486i	0.589965	+	0.807429i	$0.299142\pi$
$181$			21.7257i			1.61486i	−0.589965	+	0.807429i	$0.700858\pi$
$182$		0			0
$183$	−8.87686	+	8.87686i	−0.656196	+	0.656196i
$184$			5.26581i			0.388201i
$185$	−2.51577	−	7.63069i	−0.184963	−	0.561020i
$186$	9.22503			0.676412
$187$	11.7079	−	11.7079i	0.856164	−	0.856164i
$188$	2.88813	+	2.88813i	0.210639	+	0.210639i
$189$		0			0
$190$	5.06444	+	15.3612i	0.367413	+	1.11442i
$191$	16.5825			1.19986			0.599932	−	0.800051i	$-0.295194\pi$
$191$	16.5825			1.19986			0.599932	+	0.800051i	$0.295194\pi$
$192$	0.707107	−	0.707107i	0.0510310	−	0.0510310i
$193$	−1.49728	+	1.49728i	−0.107777	+	0.107777i	−0.758939	−	0.651162i	$-0.774282\pi$
$193$	−1.49728	+	1.49728i	−0.107777	+	0.107777i	0.651162	+	0.758939i	$0.274282\pi$
$194$	−3.81022			−0.273558
$195$	4.85142	−	9.62375i	0.347418	−	0.689171i
$196$		0			0
$197$	−1.22531	−	1.22531i	−0.0872995	−	0.0872995i	0.662108	−	0.749408i	$-0.269662\pi$
$197$	−1.22531	−	1.22531i	−0.0872995	−	0.0872995i	−0.749408	+	0.662108i	$0.769662\pi$
$198$	−2.19755	+	2.19755i	−0.156173	+	0.156173i
$199$	−7.87801			−0.558458			−0.279229	−	0.960225i	$-0.590079\pi$
$199$	−7.87801			−0.558458			−0.279229	+	0.960225i	$0.590079\pi$
$200$	4.94500	+	0.739583i	0.349664	+	0.0522964i
$201$		−	6.66287i		−	0.469963i
$202$	5.55958	−	5.55958i	0.391171	−	0.391171i
$203$		0			0
$204$		−	5.32769i		−	0.373013i
$205$	2.53503	−	5.02873i	0.177054	−	0.351222i
$206$		−	11.8311i		−	0.824313i
$207$	−3.72349	−	3.72349i	−0.258800	−	0.258800i
$208$	3.40812	+	3.40812i	0.236311	+	0.236311i
$209$	22.4802			1.55499
$210$		0			0
$211$	−15.9995			−1.10145			−0.550724	−	0.834687i	$-0.685648\pi$
$211$	−15.9995			−1.10145			−0.550724	+	0.834687i	$0.685648\pi$
$212$	2.43203	+	2.43203i	0.167033	+	0.167033i
$213$	6.52474	+	6.52474i	0.447068	+	0.447068i
$214$			2.16226i			0.147809i
$215$	−11.6181	+	3.83037i	−0.792347	+	0.261229i
$216$			1.00000i			0.0680414i
$217$		0			0
$218$	0.399905	−	0.399905i	0.0270850	−	0.0270850i
$219$		−	8.23213i		−	0.556276i
$220$	3.12819	−	6.20538i	0.210902	−	0.418366i
$221$	25.6785			1.72732
$222$	−2.54080	+	2.54080i	−0.170527	+	0.170527i
$223$	−1.20707	−	1.20707i	−0.0808314	−	0.0808314i	0.665535	−	0.746367i	$-0.268203\pi$
$223$	−1.20707	−	1.20707i	−0.0808314	−	0.0808314i	−0.746367	+	0.665535i	$0.768203\pi$
$224$		0			0
$225$	−4.01961	+	2.97368i	−0.267974	+	0.198245i
$226$	−14.1171			−0.939057
$227$	4.81749	−	4.81749i	0.319748	−	0.319748i	−0.528922	−	0.848670i	$-0.677404\pi$
$227$	4.81749	−	4.81749i	0.319748	−	0.319748i	0.848670	+	0.528922i	$0.177404\pi$
$228$	5.11483	−	5.11483i	0.338738	−	0.338738i
$229$	−19.8143			−1.30936			−0.654682	−	0.755904i	$-0.727198\pi$
$229$	−19.8143			−1.30936			−0.654682	+	0.755904i	$0.727198\pi$
$230$	10.5143	+	5.30035i	0.693291	+	0.349495i
$231$		0			0
$232$	−3.17745	−	3.17745i	−0.208610	−	0.208610i
$233$	12.7261	−	12.7261i	0.833714	−	0.833714i	−0.154309	−	0.988023i	$-0.549315\pi$
$233$	12.7261	−	12.7261i	0.833714	−	0.833714i	0.988023	+	0.154309i	$0.0493150\pi$
$234$	−4.81981			−0.315081
$235$	8.67383	−	2.85968i	0.565818	−	0.186545i
$236$			1.33238i			0.0867303i
$237$	1.35366	−	1.35366i	0.0879296	−	0.0879296i
$238$		0			0
$239$		−	26.6409i		−	1.72325i	−0.507542	−	0.861627i	$-0.669446\pi$
$239$		−	26.6409i		−	1.72325i	0.507542	−	0.861627i	$-0.330554\pi$
$240$	−0.700141	−	2.12363i	−0.0451939	−	0.137080i
$241$			14.4248i			0.929185i	0.885525	+	0.464592i	$0.153799\pi$
$241$			14.4248i			0.929185i	−0.885525	+	0.464592i	$0.846201\pi$
$242$	0.948618	+	0.948618i	0.0609795	+	0.0609795i
$243$	−0.707107	−	0.707107i	−0.0453609	−	0.0453609i
$244$	−12.5538			−0.803673
$245$		0			0
$246$	−2.51851			−0.160575
$247$	24.6525	+	24.6525i	1.56860	+	1.56860i
$248$	6.52308	+	6.52308i	0.414216	+	0.414216i
$249$			12.6890i			0.804135i
$250$	6.45416	−	9.12928i	0.408197	−	0.577386i
$251$			26.4573i			1.66997i	0.550271	+	0.834986i	$0.314524\pi$
$251$			26.4573i			1.66997i	−0.550271	+	0.834986i	$0.685476\pi$
$252$		0			0
$253$	11.5719	−	11.5719i	0.727518	−	0.727518i
$254$			3.03397i			0.190368i
$255$	−10.6378	−	5.36264i	−0.666167	−	0.335821i
$256$	1.00000			0.0625000
$257$	7.93021	−	7.93021i	0.494673	−	0.494673i	−0.415102	−	0.909775i	$-0.636254\pi$
$257$	7.93021	−	7.93021i	0.494673	−	0.494673i	0.909775	+	0.415102i	$0.136254\pi$
$258$	3.86848	+	3.86848i	0.240841	+	0.240841i
$259$		0			0
$260$	10.2355	−	3.37454i	0.634778	−	0.209280i
$261$	4.49359			0.278146
$262$	6.20372	−	6.20372i	0.383267	−	0.383267i
$263$	−4.85012	+	4.85012i	−0.299071	+	0.299071i	−0.840650	−	0.541579i	$-0.817827\pi$
$263$	−4.85012	+	4.85012i	−0.299071	+	0.299071i	0.541579	+	0.840650i	$0.317827\pi$
$264$	−3.10780			−0.191272
$265$	7.30405	−	2.40807i	0.448684	−	0.147927i
$266$		0			0
$267$	2.88043	+	2.88043i	0.176279	+	0.176279i
$268$	4.71136	−	4.71136i	0.287792	−	0.287792i
$269$	−8.98064			−0.547559			−0.273780	−	0.961792i	$-0.588274\pi$
$269$	−8.98064			−0.547559			−0.273780	+	0.961792i	$0.588274\pi$
$270$	1.99671	+	1.00656i	0.121516	+	0.0612572i
$271$			8.97179i			0.544998i	0.962156	+	0.272499i	$0.0878501\pi$
$271$			8.97179i			0.544998i	−0.962156	+	0.272499i	$0.912150\pi$
$272$	3.76725	−	3.76725i	0.228423	−	0.228423i
$273$		0			0
$274$			13.6052i			0.821918i
$275$	−9.24161	−	12.4922i	−0.557290	−	0.753305i
$276$		−	5.26581i		−	0.316965i
$277$	−17.4734	−	17.4734i	−1.04988	−	1.04988i	−0.998689	−	0.0511860i	$-0.983700\pi$
$277$	−17.4734	−	17.4734i	−1.04988	−	1.04988i	−0.0511860	−	0.998689i	$-0.516300\pi$
$278$	7.71769	+	7.71769i	0.462876	+	0.462876i
$279$	−9.22503			−0.552288
$280$		0			0
$281$	18.4916			1.10312			0.551558	−	0.834137i	$-0.314034\pi$
$281$	18.4916			1.10312			0.551558	+	0.834137i	$0.314034\pi$
$282$	−2.88813	−	2.88813i	−0.171986	−	0.171986i
$283$	−3.93983	−	3.93983i	−0.234198	−	0.234198i	0.580244	−	0.814443i	$-0.302957\pi$
$283$	−3.93983	−	3.93983i	−0.234198	−	0.234198i	−0.814443	+	0.580244i	$0.802957\pi$
$284$			9.22738i			0.547544i
$285$	−5.06444	−	15.3612i	−0.299992	−	0.909919i
$286$		−	14.9790i		−	0.885729i
$287$		0			0
$288$	−0.707107	+	0.707107i	−0.0416667	+	0.0416667i
$289$		−	11.3843i		−	0.669665i
$290$	−9.54272	+	3.14614i	−0.560368	+	0.184748i
$291$	3.81022			0.223359
$292$	5.82099	−	5.82099i	0.340648	−	0.340648i
$293$	−17.6465	−	17.6465i	−1.03092	−	1.03092i	−0.999507	−	0.0314115i	$-0.990000\pi$
$293$	−17.6465	−	17.6465i	−1.03092	−	1.03092i	−0.0314115	−	0.999507i	$-0.510000\pi$
$294$		0			0
$295$	2.66037	+	1.34112i	0.154892	+	0.0780828i
$296$	−3.59323			−0.208852
$297$	2.19755	−	2.19755i	0.127515	−	0.127515i
$298$	−1.47800	+	1.47800i	−0.0856183	+	0.0856183i
$299$	25.3802			1.46778
$300$	−4.94500	−	0.739583i	−0.285500	−	0.0426998i
$301$		0			0
$302$	−2.85838	−	2.85838i	−0.164481	−	0.164481i
$303$	−5.55958	+	5.55958i	−0.319390	+	0.319390i
$304$	7.23346			0.414867
$305$	−12.6361	+	25.0662i	−0.723542	+	1.43529i
$306$			5.32769i			0.304564i
$307$	−11.4807	+	11.4807i	−0.655239	+	0.655239i	−0.954250	−	0.299011i	$-0.903343\pi$
$307$	−11.4807	+	11.4807i	−0.655239	+	0.655239i	0.299011	+	0.954250i	$0.403343\pi$
$308$		0			0
$309$			11.8311i			0.673049i
$310$	19.5906	−	6.45882i	1.11267	−	0.366836i
$311$			13.1349i			0.744809i	0.928070	+	0.372405i	$0.121467\pi$
$311$			13.1349i			0.744809i	−0.928070	+	0.372405i	$0.878533\pi$
$312$	−3.40812	−	3.40812i	−0.192947	−	0.192947i
$313$	−17.9946	−	17.9946i	−1.01711	−	1.01711i	−0.999851	−	0.0172640i	$-0.994504\pi$
$313$	−17.9946	−	17.9946i	−1.01711	−	1.01711i	−0.0172640	−	0.999851i	$-0.505496\pi$
$314$	−0.905573			−0.0511044
$315$		0			0
$316$	1.91436			0.107691
$317$	13.4535	+	13.4535i	0.755626	+	0.755626i	0.975523	−	0.219897i	$-0.0705722\pi$
$317$	13.4535	+	13.4535i	0.755626	+	0.755626i	−0.219897	+	0.975523i	$0.570572\pi$
$318$	−2.43203	−	2.43203i	−0.136382	−	0.136382i
$319$			13.9652i			0.781901i
$320$	1.00656	−	1.99671i	0.0562684	−	0.111619i
$321$		−	2.16226i		−	0.120686i
$322$		0			0
$323$	27.2502	−	27.2502i	1.51624	−	1.51624i
$324$		−	1.00000i		−	0.0555556i
$325$	3.56465	−	23.8340i	0.197731	−	1.32207i
$326$	7.38217			0.408860
$327$	−0.399905	+	0.399905i	−0.0221148	+	0.0221148i
$328$	−1.78086	−	1.78086i	−0.0983314	−	0.0983314i
$329$		0			0
$330$	−3.12819	+	6.20538i	−0.172201	+	0.341595i
$331$	−20.9381			−1.15086			−0.575430	−	0.817851i	$-0.695165\pi$
$331$	−20.9381			−1.15086			−0.575430	+	0.817851i	$0.695165\pi$
$332$	−8.97250	+	8.97250i	−0.492430	+	0.492430i
$333$	2.54080	−	2.54080i	0.139235	−	0.139235i
$334$	0.863584			0.0472532
$335$	−4.66495	−	14.1495i	−0.254873	−	0.773068i
$336$		0			0
$337$	0.272770	+	0.272770i	0.0148587	+	0.0148587i	0.714497	−	0.699638i	$-0.246656\pi$
$337$	0.272770	+	0.272770i	0.0148587	+	0.0148587i	−0.699638	+	0.714497i	$0.746656\pi$
$338$	7.23411	−	7.23411i	0.393484	−	0.393484i
$339$	14.1171			0.766737
$340$	−3.73013	−	11.3140i	−0.202295	−	0.613590i
$341$		−	28.6696i		−	1.55255i
$342$	−5.11483	+	5.11483i	−0.276578	+	0.276578i
$343$		0			0
$344$			5.47086i			0.294969i
$345$	−10.5143	−	5.30035i	−0.566070	−	0.285361i
$346$			3.49748i			0.188026i
$347$	−10.6964	−	10.6964i	−0.574214	−	0.574214i	0.359089	−	0.933303i	$-0.383087\pi$
$347$	−10.6964	−	10.6964i	−0.574214	−	0.574214i	−0.933303	+	0.359089i	$0.883087\pi$
$348$	3.17745	+	3.17745i	0.170329	+	0.170329i
$349$	15.2733			0.817563			0.408781	−	0.912632i	$-0.365954\pi$
$349$	15.2733			0.817563			0.408781	+	0.912632i	$0.365954\pi$
$350$		0			0
$351$	4.81981			0.257262
$352$	−2.19755	−	2.19755i	−0.117130	−	0.117130i
$353$	−21.2321	−	21.2321i	−1.13007	−	1.13007i	−0.990165	−	0.139903i	$-0.955321\pi$
$353$	−21.2321	−	21.2321i	−1.13007	−	1.13007i	−0.139903	−	0.990165i	$-0.544679\pi$
$354$		−	1.33238i		−	0.0708150i
$355$	18.4244	+	9.28790i	0.977864	+	0.492950i
$356$			4.07354i			0.215897i
$357$		0			0
$358$	12.7716	−	12.7716i	0.675002	−	0.675002i
$359$			11.7244i			0.618792i	0.950933	+	0.309396i	$0.100127\pi$
$359$			11.7244i			0.618792i	−0.950933	+	0.309396i	$0.899873\pi$
$360$	0.700141	+	2.12363i	0.0369006	+	0.111925i
$361$	33.3230			1.75384
$362$	15.3624	−	15.3624i	0.807429	−	0.807429i
$363$	−0.948618	−	0.948618i	−0.0497895	−	0.0497895i
$364$		0			0
$365$	−5.76365	−	17.4820i	−0.301683	−	0.915049i
$366$	12.5538			0.656196
$367$	21.4951	−	21.4951i	1.12204	−	1.12204i	0.130600	−	0.991435i	$-0.458310\pi$
$367$	21.4951	−	21.4951i	1.12204	−	1.12204i	0.991435	−	0.130600i	$-0.0416904\pi$
$368$	3.72349	−	3.72349i	0.194100	−	0.194100i
$369$	2.51851			0.131109
$370$	−3.61680	+	7.17463i	−0.188028	+	0.372991i
$371$		0			0
$372$	−6.52308	−	6.52308i	−0.338206	−	0.338206i
$373$	21.3303	−	21.3303i	1.10444	−	1.10444i	0.110572	−	0.993868i	$-0.464732\pi$
$373$	21.3303	−	21.3303i	1.10444	−	1.10444i	0.993868	−	0.110572i	$-0.0352681\pi$
$374$	−16.5574			−0.856164
$375$	−6.45416	+	9.12928i	−0.333292	+	0.471434i
$376$		−	4.08444i		−	0.210639i
$377$	−15.3147	+	15.3147i	−0.788746	+	0.788746i
$378$		0			0
$379$		−	4.44115i		−	0.228127i	−0.993473	−	0.114063i	$-0.963613\pi$
$379$		−	4.44115i		−	0.228127i	0.993473	−	0.114063i	$-0.0363867\pi$
$380$	7.28091	−	14.4431i	0.373503	−	0.740916i
$381$		−	3.03397i		−	0.155435i
$382$	−11.7256	−	11.7256i	−0.599932	−	0.599932i
$383$	−15.7414	−	15.7414i	−0.804350	−	0.804350i	0.179422	−	0.983772i	$-0.442577\pi$
$383$	−15.7414	−	15.7414i	−0.804350	−	0.804350i	−0.983772	+	0.179422i	$0.942577\pi$
$384$	−1.00000			−0.0510310
$385$		0			0
$386$	2.11748			0.107777
$387$	−3.86848	−	3.86848i	−0.196646	−	0.196646i
$388$	2.69423	+	2.69423i	0.136779	+	0.136779i
$389$		−	12.6880i		−	0.643307i	−0.946857	−	0.321653i	$-0.895761\pi$
$389$		−	12.6880i		−	0.643307i	0.946857	−	0.321653i	$-0.104239\pi$
$390$	−10.2355	+	3.37454i	−0.518294	+	0.170877i
$391$		−	28.0546i		−	1.41878i
$392$		0			0
$393$	−6.20372	+	6.20372i	−0.312936	+	0.312936i
$394$			1.73285i			0.0872995i
$395$	1.92692	−	3.82242i	0.0969538	−	0.192327i
$396$	3.10780			0.156173
$397$	−15.3969	+	15.3969i	−0.772748	+	0.772748i	−0.978586	−	0.205838i	$-0.934008\pi$
$397$	−15.3969	+	15.3969i	−0.772748	+	0.772748i	0.205838	+	0.978586i	$0.434008\pi$
$398$	5.57060	+	5.57060i	0.279229	+	0.279229i
$399$		0			0
$400$	−2.97368	−	4.01961i	−0.148684	−	0.200980i
$401$	26.3077			1.31374			0.656872	−	0.754002i	$-0.271879\pi$
$401$	26.3077			1.31374			0.656872	+	0.754002i	$0.271879\pi$
$402$	−4.71136	+	4.71136i	−0.234981	+	0.234981i
$403$	31.4400	−	31.4400i	1.56614	−	1.56614i
$404$	−7.86244			−0.391171
$405$	−1.99671	−	1.00656i	−0.0992172	−	0.0500163i
$406$		0			0
$407$	7.89630	+	7.89630i	0.391405	+	0.391405i
$408$	−3.76725	+	3.76725i	−0.186507	+	0.186507i
$409$	2.34651			0.116027			0.0580137	−	0.998316i	$-0.481523\pi$
$409$	2.34651			0.116027			0.0580137	+	0.998316i	$0.481523\pi$
$410$	−5.34839	+	1.76331i	−0.264138	+	0.0870838i
$411$		−	13.6052i		−	0.671093i
$412$	−8.36587	+	8.36587i	−0.412157	+	0.412157i
$413$		0			0
$414$			5.26581i			0.258800i
$415$	8.88411	+	26.9468i	0.436104	+	1.32277i
$416$		−	4.81981i		−	0.236311i
$417$	−7.71769	−	7.71769i	−0.377937	−	0.377937i
$418$	−15.8959	−	15.8959i	−0.777494	−	0.777494i
$419$	−1.03087			−0.0503614			−0.0251807	−	0.999683i	$-0.508016\pi$
$419$	−1.03087			−0.0503614			−0.0251807	+	0.999683i	$0.508016\pi$
$420$		0			0
$421$	28.6945			1.39849			0.699243	−	0.714884i	$-0.253521\pi$
$421$	28.6945			1.39849			0.699243	+	0.714884i	$0.253521\pi$
$422$	11.3133	+	11.3133i	0.550724	+	0.550724i
$423$	2.88813	+	2.88813i	0.140426	+	0.140426i
$424$		−	3.43942i		−	0.167033i
$425$	−26.3454	−	3.94027i	−1.27794	−	0.191131i
$426$		−	9.22738i		−	0.447068i
$427$		0			0
$428$	1.52895	−	1.52895i	0.0739047	−	0.0739047i
$429$			14.9790i			0.723194i
$430$	10.9237	+	5.50674i	0.526788	+	0.265559i
$431$	−24.2775			−1.16941			−0.584704	−	0.811247i	$-0.698789\pi$
$431$	−24.2775			−1.16941			−0.584704	+	0.811247i	$0.698789\pi$
$432$	0.707107	−	0.707107i	0.0340207	−	0.0340207i
$433$	19.1704	+	19.1704i	0.921271	+	0.921271i	0.997119	−	0.0758481i	$-0.0241664\pi$
$433$	19.1704	+	19.1704i	0.921271	+	0.921271i	−0.0758481	+	0.997119i	$0.524166\pi$
$434$		0			0
$435$	9.54272	−	3.14614i	0.457538	−	0.150846i
$436$	−0.565551			−0.0270850
$437$	26.9337	−	26.9337i	1.28841	−	1.28841i
$438$	−5.82099	+	5.82099i	−0.278138	+	0.278138i
$439$	14.5989			0.696769			0.348385	−	0.937352i	$-0.386730\pi$
$439$	14.5989			0.696769			0.348385	+	0.937352i	$0.386730\pi$
$440$	−6.59983	+	2.17590i	−0.314634	+	0.103732i
$441$		0			0
$442$	−18.1574	−	18.1574i	−0.863660	−	0.863660i
$443$	−16.0790	+	16.0790i	−0.763938	+	0.763938i	−0.977032	−	0.213094i	$-0.931646\pi$
$443$	−16.0790	+	16.0790i	−0.763938	+	0.763938i	0.213094	+	0.977032i	$0.431646\pi$
$444$	3.59323			0.170527
$445$	8.13367	+	4.10026i	0.385573	+	0.194371i
$446$			1.70706i			0.0808314i
$447$	1.47800	−	1.47800i	0.0699071	−	0.0699071i
$448$		0			0
$449$			41.8564i			1.97532i	0.156600	+	0.987662i	$0.449947\pi$
$449$			41.8564i			1.97532i	−0.156600	+	0.987662i	$0.550053\pi$
$450$	4.94500	+	0.739583i	0.233109	+	0.0348643i
$451$			7.82705i			0.368561i
$452$	9.98231	+	9.98231i	0.469528	+	0.469528i
$453$	2.85838	+	2.85838i	0.134298	+	0.134298i
$454$	−6.81296			−0.319748
$455$		0			0
$456$	−7.23346			−0.338738
$457$	18.7798	+	18.7798i	0.878480	+	0.878480i	0.993377	−	0.114897i	$-0.0366539\pi$
$457$	18.7798	+	18.7798i	0.878480	+	0.878480i	−0.114897	+	0.993377i	$0.536654\pi$
$458$	14.0108	+	14.0108i	0.654682	+	0.654682i
$459$		−	5.32769i		−	0.248675i
$460$	−3.68681	−	11.1826i	−0.171898	−	0.521393i
$461$			16.5608i			0.771313i	0.922642	+	0.385656i	$0.126025\pi$
$461$			16.5608i			0.771313i	−0.922642	+	0.385656i	$0.873975\pi$
$462$		0			0
$463$	−19.0305	+	19.0305i	−0.884424	+	0.884424i	−0.993981	−	0.109557i	$-0.965057\pi$
$463$	−19.0305	+	19.0305i	−0.884424	+	0.884424i	0.109557	+	0.993981i	$0.465057\pi$
$464$			4.49359i			0.208610i
$465$	−19.5906	+	6.45882i	−0.908490	+	0.299521i
$466$	−17.9974			−0.833714
$467$	9.62124	−	9.62124i	0.445218	−	0.445218i	−0.448543	−	0.893761i	$-0.648057\pi$
$467$	9.62124	−	9.62124i	0.445218	−	0.445218i	0.893761	+	0.448543i	$0.148057\pi$
$468$	3.40812	+	3.40812i	0.157540	+	0.157540i
$469$		0			0
$470$	−8.15542	−	4.11123i	−0.376182	−	0.189637i
$471$	0.905573			0.0417266
$472$	0.942132	−	0.942132i	0.0433652	−	0.0433652i
$473$	12.0225	−	12.0225i	0.552795	−	0.552795i
$474$	−1.91436			−0.0879296
$475$	−21.5100	−	29.0757i	−0.986946	−	1.33408i
$476$		0			0
$477$	2.43203	+	2.43203i	0.111355	+	0.111355i
$478$	−18.8379	+	18.8379i	−0.861627	+	0.861627i
$479$	1.32529			0.0605539			0.0302769	−	0.999542i	$-0.490361\pi$
$479$	1.32529			0.0605539			0.0302769	+	0.999542i	$0.490361\pi$
$480$	−1.00656	+	1.99671i	−0.0459429	+	0.0911368i
$481$			17.3187i			0.789664i
$482$	10.1999	−	10.1999i	0.464592	−	0.464592i
$483$		0			0
$484$		−	1.34155i		−	0.0609795i
$485$	8.09149	−	2.66769i	0.367416	−	0.121133i
$486$			1.00000i			0.0453609i
$487$	22.6570	+	22.6570i	1.02669	+	1.02669i	0.999634	+	0.0270532i	$0.00861234\pi$
$487$	22.6570	+	22.6570i	1.02669	+	1.02669i	0.0270532	+	0.999634i	$0.491388\pi$
$488$	8.87686	+	8.87686i	0.401837	+	0.401837i
$489$	−7.38217			−0.333833
$490$		0			0
$491$	−22.3460			−1.00846			−0.504231	−	0.863569i	$-0.668224\pi$
$491$	−22.3460			−1.00846			−0.504231	+	0.863569i	$0.668224\pi$
$492$	1.78086	+	1.78086i	0.0802873	+	0.0802873i
$493$	16.9285	+	16.9285i	0.762419	+	0.762419i
$494$		−	34.8639i		−	1.56860i
$495$	3.12819	−	6.20538i	0.140602	−	0.278911i
$496$		−	9.22503i		−	0.414216i
$497$		0			0
$498$	8.97250	−	8.97250i	0.402067	−	0.402067i
$499$		−	10.8523i		−	0.485817i	−0.970049	−	0.242908i	$-0.921899\pi$
$499$		−	10.8523i		−	0.485817i	0.970049	−	0.242908i	$-0.0781014\pi$
$500$	−11.0192	+	1.89159i	−0.492792	+	0.0845947i
$501$	−0.863584			−0.0385821
$502$	18.7082	−	18.7082i	0.834986	−	0.834986i
$503$	2.64043	+	2.64043i	0.117731	+	0.117731i	0.763518	−	0.645787i	$-0.223471\pi$
$503$	2.64043	+	2.64043i	0.117731	+	0.117731i	−0.645787	+	0.763518i	$0.723471\pi$
$504$		0			0
$505$	−7.91401	+	15.6990i	−0.352169	+	0.698596i
$506$	−16.3651			−0.727518
$507$	−7.23411	+	7.23411i	−0.321278	+	0.321278i
$508$	2.14534	−	2.14534i	0.0951842	−	0.0951842i
$509$	−17.4093			−0.771653			−0.385827	−	0.922571i	$-0.626084\pi$
$509$	−17.4093			−0.771653			−0.385827	+	0.922571i	$0.626084\pi$
$510$	3.73013	+	11.3140i	0.165173	+	0.500994i
$511$		0			0
$512$	−0.707107	−	0.707107i	−0.0312500	−	0.0312500i
$513$	5.11483	−	5.11483i	0.225825	−	0.225825i
$514$	−11.2150			−0.494673
$515$	8.28345	+	25.1249i	0.365012	+	1.10714i
$516$		−	5.47086i		−	0.240841i
$517$	−8.97575	+	8.97575i	−0.394753	+	0.394753i
$518$		0			0
$519$		−	3.49748i		−	0.153522i
$520$	−9.62375	−	4.85142i	−0.422029	−	0.212749i
$521$		−	7.09577i		−	0.310871i	−0.987846	−	0.155436i	$-0.950322\pi$
$521$		−	7.09577i		−	0.310871i	0.987846	−	0.155436i	$-0.0496781\pi$
$522$	−3.17745	−	3.17745i	−0.139073	−	0.139073i
$523$	2.49227	+	2.49227i	0.108979	+	0.108979i	0.759494	−	0.650515i	$-0.225447\pi$
$523$	2.49227	+	2.49227i	0.108979	+	0.108979i	−0.650515	+	0.759494i	$0.725447\pi$
$524$	−8.77339			−0.383267
$525$		0			0
$526$	6.85911			0.299071
$527$	−34.7530	−	34.7530i	−1.51386	−	1.51386i
$528$	2.19755	+	2.19755i	0.0956361	+	0.0956361i
$529$		−	4.72876i		−	0.205598i
$530$	−6.86751	−	3.46198i	−0.298305	−	0.150379i
$531$			1.33238i			0.0578202i
$532$		0			0
$533$	−8.58340	+	8.58340i	−0.371788	+	0.371788i
$534$		−	4.07354i		−	0.176279i
$535$	−1.51389	−	4.59185i	−0.0654511	−	0.198523i
$536$	−6.66287			−0.287792
$537$	−12.7716	+	12.7716i	−0.551137	+	0.551137i
$538$	6.35027	+	6.35027i	0.273780	+	0.273780i
$539$		0			0
$540$	−0.700141	−	2.12363i	−0.0301293	−	0.0913865i
$541$	20.3951			0.876853			0.438426	−	0.898767i	$-0.355536\pi$
$541$	20.3951			0.876853			0.438426	+	0.898767i	$0.355536\pi$
$542$	6.34402	−	6.34402i	0.272499	−	0.272499i
$543$	−15.3624	+	15.3624i	−0.659263	+	0.659263i
$544$	−5.32769			−0.228423
$545$	−0.569261	+	1.12924i	−0.0243845	+	0.0483713i
$546$		0			0
$547$	−8.79499	−	8.79499i	−0.376047	−	0.376047i	0.493627	−	0.869674i	$-0.335671\pi$
$547$	−8.79499	−	8.79499i	−0.376047	−	0.376047i	−0.869674	+	0.493627i	$0.835671\pi$
$548$	9.62030	−	9.62030i	0.410959	−	0.410959i
$549$	−12.5538			−0.535782
$550$	−2.29848	+	15.3681i	−0.0980075	+	0.655298i
$551$			32.5042i			1.38473i
$552$	−3.72349	+	3.72349i	−0.158482	+	0.158482i
$553$		0			0
$554$			24.7111i			1.04988i
$555$	3.61680	−	7.17463i	0.153525	−	0.304546i
$556$		−	10.9145i		−	0.462876i
$557$	−12.7022	−	12.7022i	−0.538210	−	0.538210i	0.384793	−	0.923003i	$-0.374273\pi$
$557$	−12.7022	−	12.7022i	−0.538210	−	0.538210i	−0.923003	+	0.384793i	$0.874273\pi$
$558$	6.52308	+	6.52308i	0.276144	+	0.276144i
$559$	26.3685			1.11527
$560$		0			0
$561$	16.5574			0.699055
$562$	−13.0755	−	13.0755i	−0.551558	−	0.551558i
$563$	30.7771	+	30.7771i	1.29710	+	1.29710i	0.930300	+	0.366799i	$0.119546\pi$
$563$	30.7771	+	30.7771i	1.29710	+	1.29710i	0.366799	+	0.930300i	$0.380454\pi$
$564$			4.08444i			0.171986i
$565$	29.9795	−	9.88397i	1.26125	−	0.415822i
$566$			5.57176i			0.234198i
$567$		0			0
$568$	6.52474	−	6.52474i	0.273772	−	0.273772i
$569$		−	18.1826i		−	0.762255i	−0.924522	−	0.381128i	$-0.875536\pi$
$569$		−	18.1826i		−	0.762255i	0.924522	−	0.381128i	$-0.124464\pi$
$570$	−7.28091	+	14.4431i	−0.304964	+	0.604955i
$571$	−27.3134			−1.14303			−0.571516	−	0.820591i	$-0.693644\pi$
$571$	−27.3134			−1.14303			−0.571516	+	0.820591i	$0.693644\pi$
$572$	−10.5918	+	10.5918i	−0.442864	+	0.442864i
$573$	11.7256	+	11.7256i	0.489843	+	0.489843i
$574$		0			0
$575$	−26.0394	−	3.89450i	−1.08592	−	0.162412i
$576$	1.00000			0.0416667
$577$	17.5022	−	17.5022i	0.728625	−	0.728625i	−0.241721	−	0.970346i	$-0.577712\pi$
$577$	17.5022	−	17.5022i	0.728625	−	0.728625i	0.970346	+	0.241721i	$0.0777119\pi$
$578$	−8.04992	+	8.04992i	−0.334832	+	0.334832i
$579$	−2.11748			−0.0879995
$580$	8.97238	+	4.52306i	0.372558	+	0.187810i
$581$		0			0
$582$	−2.69423	−	2.69423i	−0.111679	−	0.111679i
$583$	−7.55829	+	7.55829i	−0.313032	+	0.313032i
$584$	−8.23213			−0.340648
$585$	10.2355	−	3.37454i	0.423186	−	0.139520i
$586$			24.9559i			1.03092i
$587$	25.7187	−	25.7187i	1.06153	−	1.06153i	0.0635463	−	0.997979i	$-0.479759\pi$
$587$	25.7187	−	25.7187i	1.06153	−	1.06153i	0.997979	−	0.0635463i	$-0.0202411\pi$
$588$		0			0
$589$		−	66.7289i		−	2.74952i
$590$	−0.932851	−	2.82947i	−0.0384049	−	0.116488i
$591$		−	1.73285i		−	0.0712798i
$592$	2.54080	+	2.54080i	0.104426	+	0.104426i
$593$	19.5784	+	19.5784i	0.803988	+	0.803988i	0.983716	−	0.179728i	$-0.0575218\pi$
$593$	19.5784	+	19.5784i	0.803988	+	0.803988i	−0.179728	+	0.983716i	$0.557522\pi$
$594$	−3.10780			−0.127515
$595$		0			0
$596$	2.09021			0.0856183
$597$	−5.57060	−	5.57060i	−0.227989	−	0.227989i
$598$	−17.9465	−	17.9465i	−0.733888	−	0.733888i
$599$			21.9587i			0.897207i	0.893731	+	0.448603i	$0.148078\pi$
$599$			21.9587i			0.897207i	−0.893731	+	0.448603i	$0.851922\pi$
$600$	2.97368	+	4.01961i	0.121400	+	0.164100i
$601$		−	7.04092i		−	0.287205i	−0.989635	−	0.143603i	$-0.954131\pi$
$601$		−	7.04092i		−	0.287205i	0.989635	−	0.143603i	$-0.0458687\pi$
$602$		0			0
$603$	4.71136	−	4.71136i	0.191861	−	0.191861i
$604$			4.04236i			0.164481i
$605$	−2.67868	−	1.35035i	−0.108904	−	0.0548994i
$606$	7.86244			0.319390
$607$	−16.6691	+	16.6691i	−0.676576	+	0.676576i	−0.959224	−	0.282647i	$-0.908787\pi$
$607$	−16.6691	+	16.6691i	−0.676576	+	0.676576i	0.282647	+	0.959224i	$0.408787\pi$
$608$	−5.11483	−	5.11483i	−0.207434	−	0.207434i
$609$		0			0
$610$	26.6596	−	8.78941i	1.07941	−	0.355873i
$611$	−19.6862			−0.796419
$612$	3.76725	−	3.76725i	0.152282	−	0.152282i
$613$	−9.85213	+	9.85213i	−0.397924	+	0.397924i	−0.877500	−	0.479576i	$-0.840790\pi$
$613$	−9.85213	+	9.85213i	−0.397924	+	0.397924i	0.479576	+	0.877500i	$0.340790\pi$
$614$	16.2362			0.655239
$615$	5.34839	−	1.76331i	0.215668	−	0.0711036i
$616$		0			0
$617$	9.68360	+	9.68360i	0.389847	+	0.389847i	0.874633	−	0.484786i	$-0.161102\pi$
$617$	9.68360	+	9.68360i	0.389847	+	0.389847i	−0.484786	+	0.874633i	$0.661102\pi$
$618$	8.36587	−	8.36587i	0.336525	−	0.336525i
$619$	12.4190			0.499162			0.249581	−	0.968354i	$-0.419707\pi$
$619$	12.4190			0.499162			0.249581	+	0.968354i	$0.419707\pi$
$620$	−18.4197	−	9.28554i	−0.739752	−	0.372916i
$621$		−	5.26581i		−	0.211310i
$622$	9.28775	−	9.28775i	0.372405	−	0.372405i
$623$		0			0
$624$			4.81981i			0.192947i
$625$	−7.31447	+	23.9060i	−0.292579	+	0.956241i
$626$			25.4482i			1.01711i
$627$	15.8959	+	15.8959i	0.634821	+	0.634821i
$628$	0.640337	+	0.640337i	0.0255522	+	0.0255522i
$629$	19.1436			0.763306
$630$		0			0
$631$	−0.546516			−0.0217565			−0.0108782	−	0.999941i	$-0.503463\pi$
$631$	−0.546516			−0.0217565			−0.0108782	+	0.999941i	$0.503463\pi$
$632$	−1.35366	−	1.35366i	−0.0538457	−	0.0538457i
$633$	−11.3133	−	11.3133i	−0.449665	−	0.449665i
$634$		−	19.0262i		−	0.755626i
$635$	−2.12421	−	6.44304i	−0.0842966	−	0.255684i
$636$			3.43942i			0.136382i
$637$		0			0
$638$	9.87488	−	9.87488i	0.390950	−	0.390950i
$639$			9.22738i			0.365029i
$640$	−2.12363	+	0.700141i	−0.0839438	+	0.0276755i
$641$	8.75118			0.345651			0.172825	−	0.984952i	$-0.444710\pi$
$641$	8.75118			0.345651			0.172825	+	0.984952i	$0.444710\pi$
$642$	−1.52895	+	1.52895i	−0.0603429	+	0.0603429i
$643$	10.2080	+	10.2080i	0.402565	+	0.402565i	0.879136	−	0.476571i	$-0.158121\pi$
$643$	10.2080	+	10.2080i	0.402565	+	0.402565i	−0.476571	+	0.879136i	$0.658121\pi$
$644$		0			0
$645$	−10.9237	−	5.50674i	−0.430120	−	0.216828i
$646$	−38.5377			−1.51624
$647$	−16.9715	+	16.9715i	−0.667219	+	0.667219i	−0.957071	−	0.289852i	$-0.906394\pi$
$647$	−16.9715	+	16.9715i	−0.667219	+	0.667219i	0.289852	+	0.957071i	$0.406394\pi$
$648$	−0.707107	+	0.707107i	−0.0277778	+	0.0277778i
$649$	−4.14077			−0.162539
$650$	−19.3737	+	14.3326i	−0.759901	+	0.562169i
$651$		0			0
$652$	−5.21998	−	5.21998i	−0.204430	−	0.204430i
$653$	−26.5386	+	26.5386i	−1.03854	+	1.03854i	−0.0393104	+	0.999227i	$0.512516\pi$
$653$	−26.5386	+	26.5386i	−1.03854	+	1.03854i	−0.999227	+	0.0393104i	$0.987484\pi$
$654$	0.565551			0.0221148
$655$	−8.83093	+	17.5179i	−0.345053	+	0.684480i
$656$			2.51851i			0.0983314i
$657$	5.82099	−	5.82099i	0.227099	−	0.227099i
$658$		0			0
$659$			30.4591i			1.18652i	0.805011	+	0.593259i	$0.202159\pi$
$659$			30.4591i			1.18652i	−0.805011	+	0.593259i	$0.797841\pi$
$660$	6.59983	−	2.17590i	0.256898	−	0.0846968i
$661$			27.5737i			1.07249i	0.844062	+	0.536246i	$0.180158\pi$
$661$			27.5737i			1.07249i	−0.844062	+	0.536246i	$0.819842\pi$
$662$	14.8054	+	14.8054i	0.575430	+	0.575430i
$663$	18.1574	+	18.1574i	0.705176	+	0.705176i
$664$	12.6890			0.492430
$665$		0			0
$666$	−3.59323			−0.139235
$667$	16.7318	+	16.7318i	0.647859	+	0.647859i
$668$	−0.610646	−	0.610646i	−0.0236266	−	0.0236266i
$669$		−	1.70706i		−	0.0659986i
$670$	−6.70657	+	13.3038i	−0.259097	+	0.513971i
$671$		−	39.0147i		−	1.50615i
$672$		0			0
$673$	−8.77420	+	8.77420i	−0.338221	+	0.338221i	−0.855697	−	0.517477i	$-0.826871\pi$
$673$	−8.77420	+	8.77420i	−0.338221	+	0.338221i	0.517477	+	0.855697i	$0.326871\pi$
$674$		−	0.385754i		−	0.0148587i
$675$	−4.94500	−	0.739583i	−0.190333	−	0.0284666i
$676$	−10.2306			−0.393484
$677$	−20.9822	+	20.9822i	−0.806412	+	0.806412i	−0.984089	−	0.177677i	$-0.943142\pi$
$677$	−20.9822	+	20.9822i	−0.806412	+	0.806412i	0.177677	+	0.984089i	$0.443142\pi$
$678$	−9.98231	−	9.98231i	−0.383368	−	0.383368i
$679$		0			0
$680$	−5.36264	+	10.6378i	−0.205648	+	0.407943i
$681$	6.81296			0.261073
$682$	−20.2725	+	20.2725i	−0.776273	+	0.776273i
$683$	29.5234	−	29.5234i	1.12968	−	1.12968i	0.139451	−	0.990229i	$-0.455466\pi$
$683$	29.5234	−	29.5234i	1.12968	−	1.12968i	0.990229	−	0.139451i	$-0.0445337\pi$
$684$	7.23346			0.276578
$685$	−9.52552	−	28.8923i	−0.363952	−	1.10392i
$686$		0			0
$687$	−14.0108	−	14.0108i	−0.534546	−	0.534546i
$688$	3.86848	−	3.86848i	0.147485	−	0.147485i
$689$	−16.5773			−0.631546
$690$	3.68681	+	11.1826i	0.140354	+	0.425716i
$691$			45.1068i			1.71594i	0.513697	+	0.857972i	$0.328276\pi$
$691$			45.1068i			1.71594i	−0.513697	+	0.857972i	$0.671724\pi$
$692$	2.47309	−	2.47309i	0.0940129	−	0.0940129i
$693$		0			0
$694$			15.1270i			0.574214i
$695$	−21.7930	−	10.9860i	−0.826655	−	0.416725i
$696$		−	4.49359i		−	0.170329i
$697$	9.48786	+	9.48786i	0.359378	+	0.359378i
$698$	−10.7999	−	10.7999i	−0.408781	−	0.408781i
$699$	17.9974			0.680725
$700$		0			0
$701$	−2.29359			−0.0866278			−0.0433139	−	0.999062i	$-0.513792\pi$
$701$	−2.29359			−0.0866278			−0.0433139	+	0.999062i	$0.513792\pi$
$702$	−3.40812	−	3.40812i	−0.128631	−	0.128631i
$703$	18.3788	+	18.3788i	0.693168	+	0.693168i
$704$			3.10780i			0.117130i
$705$	8.15542	+	4.11123i	0.307151	+	0.154838i
$706$			30.0267i			1.13007i
$707$		0			0
$708$	−0.942132	+	0.942132i	−0.0354075	+	0.0354075i
$709$		−	48.2598i		−	1.81243i	−0.422812	−	0.906217i	$-0.638957\pi$
$709$		−	48.2598i		−	1.81243i	0.422812	−	0.906217i	$-0.361043\pi$
$710$	−6.46046	−	19.5955i	−0.242457	−	0.735407i
$711$	1.91436			0.0717942
$712$	2.88043	−	2.88043i	0.107949	−	0.107949i
$713$	−34.3493	−	34.3493i	−1.28639	−	1.28639i
$714$		0			0
$715$	10.4874	+	31.8099i	0.392207	+	1.18962i
$716$	−18.0618			−0.675002
$717$	18.8379	−	18.8379i	0.703516	−	0.703516i
$718$	8.29043	−	8.29043i	0.309396	−	0.309396i
$719$	25.0470			0.934096			0.467048	−	0.884232i	$-0.345318\pi$
$719$	25.0470			0.934096			0.467048	+	0.884232i	$0.345318\pi$
$720$	1.00656	−	1.99671i	0.0375122	−	0.0744129i
$721$		0			0
$722$	−23.5629	−	23.5629i	−0.876920	−	0.876920i
$723$	−10.1999	+	10.1999i	−0.379338	+	0.379338i
$724$	−21.7257			−0.807429
$725$	18.0625	−	13.3625i	0.670823	−	0.496270i
$726$			1.34155i			0.0497895i
$727$	−17.1495	+	17.1495i	−0.636039	+	0.636039i	−0.949576	−	0.313537i	$-0.898486\pi$
$727$	−17.1495	+	17.1495i	−0.636039	+	0.636039i	0.313537	+	0.949576i	$0.398486\pi$
$728$		0			0
$729$		−	1.00000i		−	0.0370370i
$730$	−8.28612	+	16.4372i	−0.306683	+	0.608366i
$731$		−	29.1471i		−	1.07804i
$732$	−8.87686	−	8.87686i	−0.328098	−	0.328098i
$733$	−5.25687	−	5.25687i	−0.194167	−	0.194167i	0.603327	−	0.797494i	$-0.293841\pi$
$733$	−5.25687	−	5.25687i	−0.194167	−	0.194167i	−0.797494	+	0.603327i	$0.793841\pi$
$734$	−30.3987			−1.12204
$735$		0			0
$736$	−5.26581			−0.194100
$737$	14.6420	+	14.6420i	0.539345	+	0.539345i
$738$	−1.78086	−	1.78086i	−0.0655543	−	0.0655543i
$739$			8.35457i			0.307328i	0.988123	+	0.153664i	$0.0491073\pi$
$739$			8.35457i			0.307328i	−0.988123	+	0.153664i	$0.950893\pi$
$740$	7.63069	−	2.51577i	0.280510	−	0.0924814i
$741$			34.8639i			1.28076i
$742$		0			0
$743$	−20.5565	+	20.5565i	−0.754146	+	0.754146i	−0.975250	−	0.221104i	$-0.929034\pi$
$743$	−20.5565	+	20.5565i	−0.754146	+	0.754146i	0.221104	+	0.975250i	$0.429034\pi$
$744$			9.22503i			0.338206i
$745$	2.10392	−	4.17354i	0.0770816	−	0.152907i
$746$	−30.1656			−1.10444
$747$	−8.97250	+	8.97250i	−0.328287	+	0.328287i
$748$	11.7079	+	11.7079i	0.428082	+	0.428082i
$749$		0			0
$750$	11.0192	−	1.89159i	0.402363	−	0.0690712i
$751$	−34.6297			−1.26366			−0.631828	−	0.775109i	$-0.717695\pi$
$751$	−34.6297			−1.26366			−0.631828	+	0.775109i	$0.717695\pi$
$752$	−2.88813	+	2.88813i	−0.105319	+	0.105319i
$753$	−18.7082	+	18.7082i	−0.681763	+	0.681763i
$754$	21.6582			0.788746
$755$	8.07141	+	4.06887i	0.293749	+	0.148082i
$756$		0			0
$757$	−24.7332	−	24.7332i	−0.898945	−	0.898945i	0.0963983	−	0.995343i	$-0.469268\pi$
$757$	−24.7332	−	24.7332i	−0.898945	−	0.898945i	−0.995343	+	0.0963983i	$0.969268\pi$
$758$	−3.14037	+	3.14037i	−0.114063	+	0.114063i
$759$	16.3651			0.594016
$760$	−15.3612	+	5.06444i	−0.557209	+	0.183707i
$761$		−	37.5984i		−	1.36294i	−0.731845	−	0.681471i	$-0.761341\pi$
$761$		−	37.5984i		−	1.36294i	0.731845	−	0.681471i	$-0.238659\pi$
$762$	−2.14534	+	2.14534i	−0.0777176	+	0.0777176i
$763$		0			0
$764$			16.5825i			0.599932i
$765$	−3.73013	−	11.3140i	−0.134863	−	0.409060i
$766$			22.2618i			0.804350i
$767$	−4.54090	−	4.54090i	−0.163962	−	0.163962i
$768$	0.707107	+	0.707107i	0.0255155	+	0.0255155i
$769$	23.9494			0.863638			0.431819	−	0.901960i	$-0.357872\pi$
$769$	23.9494			0.863638			0.431819	+	0.901960i	$0.357872\pi$
$770$		0			0
$771$	11.2150			0.403899
$772$	−1.49728	−	1.49728i	−0.0538884	−	0.0538884i
$773$	0.0264874	+	0.0264874i	0.000952685	+	0.000952685i	0.707583	−	0.706630i	$-0.249786\pi$
$773$	0.0264874	+	0.0264874i	0.000952685	+	0.000952685i	−0.706630	+	0.707583i	$0.749786\pi$
$774$			5.47086i			0.196646i
$775$	−37.0810	+	27.4323i	−1.33199	+	0.985396i
$776$		−	3.81022i		−	0.136779i
$777$		0			0
$778$	−8.97176	+	8.97176i	−0.321653	+	0.321653i
$779$			18.2176i			0.652712i
$780$	9.62375	+	4.85142i	0.344586	+	0.173709i
$781$	−28.6769			−1.02614
$782$	−19.8376	+	19.8376i	−0.709391	+	0.709391i
$783$	3.17745	+	3.17745i	0.113553	+	0.113553i
$784$		0			0
$785$	1.92310	−	0.634028i	0.0686384	−	0.0226294i
$786$	8.77339			0.312936
$787$	−18.4576	+	18.4576i	−0.657942	+	0.657942i	−0.954893	−	0.296951i	$-0.904030\pi$
$787$	−18.4576	+	18.4576i	−0.657942	+	0.657942i	0.296951	+	0.954893i	$0.404030\pi$
$788$	1.22531	−	1.22531i	0.0436498	−	0.0436498i
$789$	−6.85911			−0.244191
$790$	−4.06540	+	1.34032i	−0.144640	+	0.0476866i
$791$		0			0
$792$	−2.19755	−	2.19755i	−0.0780865	−	0.0780865i
$793$	42.7848	−	42.7848i	1.51933	−	1.51933i
$794$	21.7745			0.772748
$795$	6.86751	+	3.46198i	0.243565	+	0.122784i
$796$		−	7.87801i		−	0.279229i
$797$	−0.973551	+	0.973551i	−0.0344850	+	0.0344850i	−0.724139	−	0.689654i	$-0.757763\pi$
$797$	−0.973551	+	0.973551i	−0.0344850	+	0.0344850i	0.689654	+	0.724139i	$0.257763\pi$
$798$		0			0
$799$			21.7606i			0.769835i
$800$	−0.739583	+	4.94500i	−0.0261482	+	0.174832i
$801$			4.07354i			0.143931i
$802$	−18.6024	−	18.6024i	−0.656872	−	0.656872i
$803$	18.0905	+	18.0905i	0.638400	+	0.638400i
$804$	6.66287			0.234981
$805$		0			0
$806$	−44.4629			−1.56614
$807$	−6.35027	−	6.35027i	−0.223540	−	0.223540i
$808$	5.55958	+	5.55958i	0.195585	+	0.195585i
$809$			40.1730i			1.41241i	0.708009	+	0.706203i	$0.249593\pi$
$809$			40.1730i			1.41241i	−0.708009	+	0.706203i	$0.750407\pi$
$810$	0.700141	+	2.12363i	0.0246004	+	0.0746167i
$811$			24.5727i			0.862866i	0.902145	+	0.431433i	$0.141992\pi$
$811$			24.5727i			0.862866i	−0.902145	+	0.431433i	$0.858008\pi$
$812$		0			0
$813$	−6.34402	+	6.34402i	−0.222494	+	0.222494i
$814$		−	11.1671i		−	0.391405i
$815$	−15.6770	+	5.16855i	−0.549141	+	0.181047i
$816$	5.32769			0.186507
$817$	27.9825	−	27.9825i	0.978984	−	0.978984i
$818$	−1.65923	−	1.65923i	−0.0580137	−	0.0580137i
$819$		0			0
$820$	5.02873	+	2.53503i	0.175611	+	0.0885271i
$821$	−49.0817			−1.71296			−0.856482	−	0.516177i	$-0.827355\pi$
$821$	−49.0817			−1.71296			−0.856482	+	0.516177i	$0.827355\pi$
$822$	−9.62030	+	9.62030i	−0.335547	+	0.335547i
$823$	20.7131	−	20.7131i	0.722014	−	0.722014i	−0.247001	−	0.969015i	$-0.579445\pi$
$823$	20.7131	−	20.7131i	0.722014	−	0.722014i	0.969015	+	0.247001i	$0.0794452\pi$
$824$	11.8311			0.412157
$825$	2.29848	−	15.3681i	0.0800228	−	0.535048i
$826$		0			0
$827$	14.8882	+	14.8882i	0.517712	+	0.517712i	0.916879	−	0.399166i	$-0.130700\pi$
$827$	14.8882	+	14.8882i	0.517712	+	0.517712i	−0.399166	+	0.916879i	$0.630700\pi$
$828$	3.72349	−	3.72349i	0.129400	−	0.129400i
$829$	−36.7688			−1.27703			−0.638516	−	0.769609i	$-0.720451\pi$
$829$	−36.7688			−1.27703			−0.638516	+	0.769609i	$0.720451\pi$
$830$	12.7723	−	25.3363i	0.443332	−	0.879435i
$831$		−	24.7111i		−	0.857219i
$832$	−3.40812	+	3.40812i	−0.118155	+	0.118155i
$833$		0			0
$834$			10.9145i			0.377937i
$835$	−1.83393	+	0.604630i	−0.0634659	+	0.0209241i
$836$			22.4802i			0.777494i
$837$	−6.52308	−	6.52308i	−0.225471	−	0.225471i
$838$	0.728937	+	0.728937i	0.0251807	+	0.0251807i
$839$	11.6715			0.402944			0.201472	−	0.979494i	$-0.435427\pi$
$839$	11.6715			0.402944			0.201472	+	0.979494i	$0.435427\pi$
$840$		0			0
$841$	8.80767			0.303713
$842$	−20.2901	−	20.2901i	−0.699243	−	0.699243i
$843$	13.0755	+	13.0755i	0.450345	+	0.450345i
$844$		−	15.9995i		−	0.550724i
$845$	−10.2977	+	20.4275i	−0.354251	+	0.702726i
$846$		−	4.08444i		−	0.140426i
$847$		0			0
$848$	−2.43203	+	2.43203i	−0.0835164	+	0.0835164i
$849$		−	5.57176i		−	0.191222i
$850$	15.8428	+	21.4152i	0.543405	+	0.734536i
$851$	18.9213			0.648613
$852$	−6.52474	+	6.52474i	−0.223534	+	0.223534i
$853$	19.6499	+	19.6499i	0.672801	+	0.672801i	0.958361	−	0.285560i	$-0.0921795\pi$
$853$	19.6499	+	19.6499i	0.672801	+	0.672801i	−0.285560	+	0.958361i	$0.592179\pi$
$854$		0			0
$855$	7.28091	−	14.4431i	0.249002	−	0.493944i
$856$	−2.16226			−0.0739047
$857$	−39.6746	+	39.6746i	−1.35526	+	1.35526i	−0.475596	+	0.879664i	$0.657767\pi$
$857$	−39.6746	+	39.6746i	−1.35526	+	1.35526i	−0.879664	+	0.475596i	$0.842233\pi$
$858$	10.5918	−	10.5918i	0.361597	−	0.361597i
$859$	−19.0290			−0.649261			−0.324630	−	0.945841i	$-0.605240\pi$
$859$	−19.0290			−0.649261			−0.324630	+	0.945841i	$0.605240\pi$
$860$	−3.83037	−	11.6181i	−0.130615	−	0.396173i
$861$		0			0
$862$	17.1668	+	17.1668i	0.584704	+	0.584704i
$863$	−14.5855	+	14.5855i	−0.496495	+	0.496495i	−0.910345	−	0.413850i	$-0.864184\pi$
$863$	−14.5855	+	14.5855i	−0.496495	+	0.496495i	0.413850	+	0.910345i	$0.364184\pi$
$864$	−1.00000			−0.0340207
$865$	−2.44873	−	7.42736i	−0.0832593	−	0.252538i
$866$		−	27.1111i		−	0.921271i
$867$	8.04992	−	8.04992i	0.273389	−	0.273389i
$868$		0			0
$869$			5.94947i			0.201822i
$870$	−8.97238	−	4.52306i	−0.304192	−	0.153346i
$871$			32.1138i			1.08813i
$872$	0.399905	+	0.399905i	0.0135425	+	0.0135425i
$873$	2.69423	+	2.69423i	0.0911859	+	0.0911859i
$874$	−38.0900			−1.28841
$875$		0			0
$876$	8.23213			0.278138
$877$	−20.1153	−	20.1153i	−0.679245	−	0.679245i	0.280585	−	0.959829i	$-0.409472\pi$
$877$	−20.1153	−	20.1153i	−0.679245	−	0.679245i	−0.959829	+	0.280585i	$0.909472\pi$
$878$	−10.3230	−	10.3230i	−0.348385	−	0.348385i
$879$		−	24.9559i		−	0.841741i
$880$	6.20538	+	3.12819i	0.209183	+	0.105451i
$881$		−	17.6227i		−	0.593724i	−0.954920	−	0.296862i	$-0.904060\pi$
$881$		−	17.6227i		−	0.593724i	0.954920	−	0.296862i	$-0.0959401\pi$
$882$		0			0
$883$	−4.03577	+	4.03577i	−0.135814	+	0.135814i	−0.771746	−	0.635931i	$-0.780616\pi$
$883$	−4.03577	+	4.03577i	−0.135814	+	0.135814i	0.635931	+	0.771746i	$0.280616\pi$
$884$			25.6785i			0.863660i
$885$	0.932851	+	2.82947i	0.0313574	+	0.0951117i
$886$	22.7392			0.763938
$887$	−10.5767	+	10.5767i	−0.355130	+	0.355130i	−0.862014	−	0.506884i	$-0.830797\pi$
$887$	−10.5767	+	10.5767i	−0.355130	+	0.355130i	0.506884	+	0.862014i	$0.330797\pi$
$888$	−2.54080	−	2.54080i	−0.0852636	−	0.0852636i
$889$		0			0
$890$	−2.85205	−	8.65069i	−0.0956010	−	0.289972i
$891$	3.10780			0.104115
$892$	1.20707	−	1.20707i	0.0404157	−	0.0404157i
$893$	−20.8912	+	20.8912i	−0.699097	+	0.699097i
$894$	−2.09021			−0.0699071
$895$	−18.1803	+	36.0642i	−0.607700	+	1.20549i
$896$		0			0
$897$	17.9465	+	17.9465i	0.599217	+	0.599217i
$898$	29.5969	−	29.5969i	0.987662	−	0.987662i
$899$	41.4535			1.38255
$900$	−2.97368	−	4.01961i	−0.0991226	−	0.133987i
$901$			18.3242i			0.610466i
$902$	5.53456	−	5.53456i	0.184281	−	0.184281i
$903$		0			0
$904$		−	14.1171i		−	0.469528i
$905$	−21.8682	+	43.3798i	−0.726923	+	1.44199i
$906$		−	4.04236i		−	0.134298i
$907$	−12.3104	−	12.3104i	−0.408761	−	0.408761i	0.472545	−	0.881306i	$-0.343335\pi$
$907$	−12.3104	−	12.3104i	−0.408761	−	0.408761i	−0.881306	+	0.472545i	$0.843335\pi$
$908$	4.81749	+	4.81749i	0.159874	+	0.159874i
$909$	−7.86244			−0.260781
$910$		0			0
$911$	9.74129			0.322743			0.161372	−	0.986894i	$-0.448408\pi$
$911$	9.74129			0.322743			0.161372	+	0.986894i	$0.448408\pi$
$912$	5.11483	+	5.11483i	0.169369	+	0.169369i
$913$	−27.8848	−	27.8848i	−0.922852	−	0.922852i
$914$		−	26.5586i		−	0.878480i
$915$	−26.6596	+	8.78941i	−0.881338	+	0.290569i
$916$		−	19.8143i		−	0.654682i
$917$		0			0
$918$	−3.76725	+	3.76725i	−0.124338	+	0.124338i
$919$			23.1175i			0.762575i	0.924456	+	0.381288i	$0.124519\pi$
$919$			23.1175i			0.762575i	−0.924456	+	0.381288i	$0.875481\pi$
$920$	−5.30035	+	10.5143i	−0.174747	+	0.346646i
$921$	−16.2362			−0.535001
$922$	11.7102	−	11.7102i	0.385656	−	0.385656i
$923$	−31.4480	−	31.4480i	−1.03512	−	1.03512i
$924$		0			0
$925$	2.65749	−	17.7685i	0.0873778	−	0.584225i
$926$	26.9132			0.884424
$927$	−8.36587	+	8.36587i	−0.274771	+	0.274771i
$928$	3.17745	−	3.17745i	0.104305	−	0.104305i
$929$	−18.3779			−0.602958			−0.301479	−	0.953473i	$-0.597480\pi$
$929$	−18.3779			−0.602958			−0.301479	+	0.953473i	$0.597480\pi$
$930$	18.4197	+	9.28554i	0.604005	+	0.304485i
$931$		0			0
$932$	12.7261	+	12.7261i	0.416857	+	0.416857i
$933$	−9.28775	+	9.28775i	−0.304067	+	0.304067i
$934$	−13.6065			−0.445218
$935$	35.1618	−	11.5925i	1.14992	−	0.379116i
$936$		−	4.81981i		−	0.157540i
$937$	12.6455	−	12.6455i	0.413111	−	0.413111i	−0.469710	−	0.882821i	$-0.655642\pi$
$937$	12.6455	−	12.6455i	0.413111	−	0.413111i	0.882821	+	0.469710i	$0.155642\pi$
$938$		0			0
$939$		−	25.4482i		−	0.830471i
$940$	2.85968	+	8.67383i	0.0932725	+	0.282909i
$941$		−	51.6202i		−	1.68277i	−0.540436	−	0.841385i	$-0.681741\pi$
$941$		−	51.6202i		−	1.68277i	0.540436	−	0.841385i	$-0.318259\pi$
$942$	−0.640337	−	0.640337i	−0.0208633	−	0.0208633i
$943$	9.37766	+	9.37766i	0.305379	+	0.305379i
$944$	−1.33238			−0.0433652
$945$		0			0
$946$	−17.0024			−0.552795
$947$	36.9153	+	36.9153i	1.19959	+	1.19959i	0.974290	+	0.225297i	$0.0723352\pi$
$947$	36.9153	+	36.9153i	1.19959	+	1.19959i	0.225297	+	0.974290i	$0.427665\pi$
$948$	1.35366	+	1.35366i	0.0439648	+	0.0439648i
$949$			39.6773i			1.28798i
$950$	−5.34974	+	35.7695i	−0.173569	+	1.16051i
$951$			19.0262i			0.616966i
$952$		0			0
$953$	0.900242	−	0.900242i	0.0291617	−	0.0291617i	−0.692376	−	0.721537i	$-0.743436\pi$
$953$	0.900242	−	0.900242i	0.0291617	−	0.0291617i	0.721537	+	0.692376i	$0.243436\pi$
$954$		−	3.43942i		−	0.111355i
$955$	33.1103	+	16.6912i	1.07142	+	0.540115i
$956$	26.6409			0.861627
$957$	−9.87488	+	9.87488i	−0.319210	+	0.319210i
$958$	−0.937119	−	0.937119i	−0.0302769	−	0.0302769i
$959$		0			0
$960$	2.12363	−	0.700141i	0.0685399	−	0.0225969i
$961$	−54.1012			−1.74520
$962$	12.2462	−	12.2462i	0.394832	−	0.394832i
$963$	1.52895	−	1.52895i	0.0492698	−	0.0492698i
$964$	−14.4248			−0.464592
$965$	−4.49674	+	1.48253i	−0.144755	+	0.0477244i
$966$		0			0
$967$	39.5119	+	39.5119i	1.27062	+	1.27062i	0.945765	+	0.324852i	$0.105314\pi$
$967$	39.5119	+	39.5119i	1.27062	+	1.27062i	0.324852	+	0.945765i	$0.394686\pi$
$968$	−0.948618	+	0.948618i	−0.0304897	+	0.0304897i
$969$	38.5377			1.23801
$970$	−7.60789	−	3.83521i	−0.244275	−	0.123141i
$971$		−	0.110632i		−	0.00355034i	−0.999998	−	0.00177517i	$-0.999435\pi$
$971$		−	0.110632i		−	0.00355034i	0.999998	−	0.00177517i	$-0.000565055\pi$
$972$	0.707107	−	0.707107i	0.0226805	−	0.0226805i
$973$		0			0
$974$		−	32.0419i		−	1.02669i
$975$	19.3737	−	14.3326i	0.620456	−	0.459009i
$976$		−	12.5538i		−	0.401837i
$977$	5.61031	+	5.61031i	0.179490	+	0.179490i	0.791133	−	0.611644i	$-0.209491\pi$
$977$	5.61031	+	5.61031i	0.179490	+	0.179490i	−0.611644	+	0.791133i	$0.709491\pi$
$978$	5.21998	+	5.21998i	0.166917	+	0.166917i
$979$	−12.6598			−0.404608
$980$		0			0
$981$	−0.565551			−0.0180567
$982$	15.8010	+	15.8010i	0.504231	+	0.504231i
$983$	−23.5138	−	23.5138i	−0.749973	−	0.749973i	0.224501	−	0.974474i	$-0.427925\pi$
$983$	−23.5138	−	23.5138i	−0.749973	−	0.749973i	−0.974474	+	0.224501i	$0.927925\pi$
$984$		−	2.51851i		−	0.0802873i
$985$	−1.21324	−	3.67992i	−0.0386569	−	0.117252i
$986$		−	23.9404i		−	0.762419i
$987$		0			0
$988$	−24.6525	+	24.6525i	−0.784301	+	0.784301i
$989$		−	28.8085i		−	0.916057i
$990$	−6.59983	+	2.17590i	−0.209756	+	0.0691546i
$991$	−14.3373			−0.455439			−0.227720	−	0.973727i	$-0.573127\pi$
$991$	−14.3373			−0.455439			−0.227720	+	0.973727i	$0.573127\pi$
$992$	−6.52308	+	6.52308i	−0.207108	+	0.207108i
$993$	−14.8054	−	14.8054i	−0.469837	−	0.469837i
$994$		0			0
$995$	−15.7301	−	7.92969i	−0.498677	−	0.251388i
$996$	−12.6890			−0.402067
$997$	21.5103	−	21.5103i	0.681239	−	0.681239i	−0.279040	−	0.960279i	$-0.590016\pi$
$997$	21.5103	−	21.5103i	0.681239	−	0.681239i	0.960279	+	0.279040i	$0.0900163\pi$
$998$	−7.67375	+	7.67375i	−0.242908	+	0.242908i
$999$	3.59323			0.113685

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1470.2.m.d.97.4		16
5.3	odd	4		1470.2.m.e.1273.1		16
7.2	even	3		210.2.u.a.157.1	yes	16
7.3	odd	6		210.2.u.b.187.4	yes	16
7.6	odd	2		1470.2.m.e.97.1		16
21.2	odd	6		630.2.bv.a.577.4		16
21.17	even	6		630.2.bv.b.397.1		16
35.2	odd	12		1050.2.bc.g.493.2		16
35.3	even	12		210.2.u.a.103.1	✓	16
35.9	even	6		1050.2.bc.h.157.4		16
35.13	even	4	inner	1470.2.m.d.1273.4		16
35.17	even	12		1050.2.bc.h.943.4		16
35.23	odd	12		210.2.u.b.73.4	yes	16
35.24	odd	6		1050.2.bc.g.607.2		16
105.23	even	12		630.2.bv.b.73.1		16
105.38	odd	12		630.2.bv.a.523.4		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
210.2.u.a.103.1	✓	16	35.3	even	12
210.2.u.a.157.1	yes	16	7.2	even	3
210.2.u.b.73.4	yes	16	35.23	odd	12
210.2.u.b.187.4	yes	16	7.3	odd	6
630.2.bv.a.523.4		16	105.38	odd	12
630.2.bv.a.577.4		16	21.2	odd	6
630.2.bv.b.73.1		16	105.23	even	12
630.2.bv.b.397.1		16	21.17	even	6
1050.2.bc.g.493.2		16	35.2	odd	12
1050.2.bc.g.607.2		16	35.24	odd	6
1050.2.bc.h.157.4		16	35.9	even	6
1050.2.bc.h.943.4		16	35.17	even	12
1470.2.m.d.97.4		16	1.1	even	1	trivial
1470.2.m.d.1273.4		16	35.13	even	4	inner
1470.2.m.e.97.1		16	7.6	odd	2
1470.2.m.e.1273.1		16	5.3	odd	4

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)

\(f(q)\)	\(=\)	\(q+(-0.707107 - 0.707107i) q^{2} +(0.707107 + 0.707107i) q^{3} +1.00000i q^{4} +(1.99671 + 1.00656i) q^{5} -1.00000i q^{6} +(0.707107 - 0.707107i) q^{8} +1.00000i q^{9} +O(q^{10})\)	\(q+(-0.707107 - 0.707107i) q^{2} +(0.707107 + 0.707107i) q^{3} +1.00000i q^{4} +(1.99671 + 1.00656i) q^{5} -1.00000i q^{6} +(0.707107 - 0.707107i) q^{8} +1.00000i q^{9} +(-0.700141 - 2.12363i) q^{10} -3.10780 q^{11} +(-0.707107 + 0.707107i) q^{12} +(-3.40812 - 3.40812i) q^{13} +(0.700141 + 2.12363i) q^{15} -1.00000 q^{16} +(-3.76725 + 3.76725i) q^{17} +(0.707107 - 0.707107i) q^{18} -7.23346 q^{19} +(-1.00656 + 1.99671i) q^{20} +(2.19755 + 2.19755i) q^{22} +(-3.72349 + 3.72349i) q^{23} +1.00000 q^{24} +(2.97368 + 4.01961i) q^{25} +4.81981i q^{26} +(-0.707107 + 0.707107i) q^{27} -4.49359i q^{29} +(1.00656 - 1.99671i) q^{30} +9.22503i q^{31} +(0.707107 + 0.707107i) q^{32} +(-2.19755 - 2.19755i) q^{33} +5.32769 q^{34} -1.00000 q^{36} +(-2.54080 - 2.54080i) q^{37} +(5.11483 + 5.11483i) q^{38} -4.81981i q^{39} +(2.12363 - 0.700141i) q^{40} -2.51851i q^{41} +(-3.86848 + 3.86848i) q^{43} -3.10780i q^{44} +(-1.00656 + 1.99671i) q^{45} +5.26581 q^{46} +(2.88813 - 2.88813i) q^{47} +(-0.707107 - 0.707107i) q^{48} +(0.739583 - 4.94500i) q^{50} -5.32769 q^{51} +(3.40812 - 3.40812i) q^{52} +(2.43203 - 2.43203i) q^{53} +1.00000 q^{54} +(-6.20538 - 3.12819i) q^{55} +(-5.11483 - 5.11483i) q^{57} +(-3.17745 + 3.17745i) q^{58} +1.33238 q^{59} +(-2.12363 + 0.700141i) q^{60} +12.5538i q^{61} +(6.52308 - 6.52308i) q^{62} -1.00000i q^{64} +(-3.37454 - 10.2355i) q^{65} +3.10780i q^{66} +(-4.71136 - 4.71136i) q^{67} +(-3.76725 - 3.76725i) q^{68} -5.26581 q^{69} +9.22738 q^{71} +(0.707107 + 0.707107i) q^{72} +(-5.82099 - 5.82099i) q^{73} +3.59323i q^{74} +(-0.739583 + 4.94500i) q^{75} -7.23346i q^{76} +(-3.40812 + 3.40812i) q^{78} -1.91436i q^{79} +(-1.99671 - 1.00656i) q^{80} -1.00000 q^{81} +(-1.78086 + 1.78086i) q^{82} +(8.97250 + 8.97250i) q^{83} +(-11.3140 + 3.73013i) q^{85} +5.47086 q^{86} +(3.17745 - 3.17745i) q^{87} +(-2.19755 + 2.19755i) q^{88} +4.07354 q^{89} +(2.12363 - 0.700141i) q^{90} +(-3.72349 - 3.72349i) q^{92} +(-6.52308 + 6.52308i) q^{93} -4.08444 q^{94} +(-14.4431 - 7.28091i) q^{95} +1.00000i q^{96} +(2.69423 - 2.69423i) q^{97} -3.10780i 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

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more