LMFDB - Embedded newform 1470.2.n.k.79.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1470,2,Mod(79,1470)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1470, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 3, 2]))

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

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

chi := DirichletCharacter("1470.79");

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.n (of order $6$, degree $2$, not minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$11.7380090971$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(\zeta_{6})$
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} - 18x^{14} + 227x^{12} - 1394x^{10} + 6177x^{8} - 14768x^{6} + 24768x^{4} - 11264x^{2} + 4096 $ x^16 - 18x^14 + 227x^12 - 1394x^10 + 6177x^8 - 14768x^6 + 24768x^4 - 11264*x^2 + 4096
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{4} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			79.8
Root			$1.87108 + 1.08027i$ of defining polynomial
Character	$\chi$	$=$	1470.79
Dual form			1470.2.n.k.949.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.866025 + 0.500000i) q^{2} +(0.866025 - 0.500000i) q^{3} +(0.500000 + 0.866025i) q^{4} +(1.89827 + 1.18176i) q^{5} +1.00000 q^{6} +1.00000i q^{8} +(0.500000 - 0.866025i) q^{9} +O(q^{10})$	\(q+(0.866025 + 0.500000i) q^{2} +(0.866025 - 0.500000i) q^{3} +(0.500000 + 0.866025i) q^{4} +(1.89827 + 1.18176i) q^{5} +1.00000 q^{6} +1.00000i q^{8} +(0.500000 - 0.866025i) q^{9} +(1.05307 + 1.97257i) q^{10} +(1.52773 + 2.64610i) q^{11} +(0.866025 + 0.500000i) q^{12} +1.64124i q^{13} +(2.23483 + 0.0743018i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(2.51741 - 1.45342i) q^{17} +(0.866025 - 0.500000i) q^{18} +(1.10508 - 1.91405i) q^{19} +(-0.0743018 + 2.23483i) q^{20} +3.05545i q^{22} +(-1.55005 - 0.894921i) q^{23} +(0.500000 + 0.866025i) q^{24} +(2.20687 + 4.48662i) q^{25} +(-0.820620 + 1.42135i) q^{26} -1.00000i q^{27} -5.58667 q^{29} +(1.89827 + 1.18176i) q^{30} +(-0.472274 - 0.818002i) q^{31} +(-0.866025 + 0.500000i) q^{32} +(2.64610 + 1.52773i) q^{33} +2.90685 q^{34} +1.00000 q^{36} +(-9.27713 - 5.35615i) q^{37} +(1.91405 - 1.10508i) q^{38} +(0.820620 + 1.42135i) q^{39} +(-1.18176 + 1.89827i) q^{40} +6.67982 q^{41} +10.5021i q^{43} +(-1.52773 + 2.64610i) q^{44} +(1.97257 - 1.05307i) q^{45} +(-0.894921 - 1.55005i) q^{46} +(9.85235 + 5.68826i) q^{47} +1.00000i q^{48} +(-0.332104 + 4.98896i) q^{50} +(1.45342 - 2.51741i) q^{51} +(-1.42135 + 0.820620i) q^{52} +(5.01415 - 2.89492i) q^{53} +(0.500000 - 0.866025i) q^{54} +(-0.227026 + 6.82843i) q^{55} -2.21016i q^{57} +(-4.83820 - 2.79334i) q^{58} +(-2.98896 - 5.17703i) q^{59} +(1.05307 + 1.97257i) q^{60} +(-0.222905 + 0.386083i) q^{61} -0.944547i q^{62} -1.00000 q^{64} +(-1.93956 + 3.11552i) q^{65} +(1.52773 + 2.64610i) q^{66} +(-1.09605 + 0.632805i) q^{67} +(2.51741 + 1.45342i) q^{68} -1.78984 q^{69} -14.8523 q^{71} +(0.866025 + 0.500000i) q^{72} +(6.85577 - 3.95818i) q^{73} +(-5.35615 - 9.27713i) q^{74} +(4.15451 + 2.78209i) q^{75} +2.21016 q^{76} +1.64124i q^{78} +(7.14949 - 12.3833i) q^{79} +(-1.97257 + 1.05307i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(5.78490 + 3.33991i) q^{82} +0.874366i q^{83} +(6.49632 + 0.215984i) q^{85} +(-5.25107 + 9.09513i) q^{86} +(-4.83820 + 2.79334i) q^{87} +(-2.64610 + 1.52773i) q^{88} +(8.75413 - 15.1626i) q^{89} +(2.23483 + 0.0743018i) q^{90} -1.78984i q^{92} +(-0.818002 - 0.472274i) q^{93} +(5.68826 + 9.85235i) q^{94} +(4.35970 - 2.32745i) q^{95} +(-0.500000 + 0.866025i) q^{96} +10.4476i q^{97} +3.05545 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 8 q^{4} - 4 q^{5} + 16 q^{6} + 8 q^{9}+O(q^{10}) $ 16 * q + 8 * q^4 - 4 * q^5 + 16 * q^6 + 8 * q^9	$ 16 q + 8 q^{4} - 4 q^{5} + 16 q^{6} + 8 q^{9} - 8 q^{16} + 24 q^{19} - 8 q^{20} + 8 q^{24} - 4 q^{25} + 32 q^{29} - 4 q^{30} - 32 q^{31} - 16 q^{34} + 16 q^{36} + 48 q^{41} + 4 q^{45} - 8 q^{46} - 8 q^{50} - 8 q^{51} + 8 q^{54} + 40 q^{59} - 24 q^{61} - 16 q^{64} - 28 q^{65} - 16 q^{69} - 80 q^{71} - 16 q^{74} - 4 q^{75} + 48 q^{76} - 16 q^{79} - 4 q^{80} - 8 q^{81} + 56 q^{85} - 8 q^{86} + 88 q^{89} + 24 q^{94} - 24 q^{95} - 8 q^{96}+O(q^{100}) $ 16 * q + 8 * q^4 - 4 * q^5 + 16 * q^6 + 8 * q^9 - 8 * q^16 + 24 * q^19 - 8 * q^20 + 8 * q^24 - 4 * q^25 + 32 * q^29 - 4 * q^30 - 32 * q^31 - 16 * q^34 + 16 * q^36 + 48 * q^41 + 4 * q^45 - 8 * q^46 - 8 * q^50 - 8 * q^51 + 8 * q^54 + 40 * q^59 - 24 * q^61 - 16 * q^64 - 28 * q^65 - 16 * q^69 - 80 * q^71 - 16 * q^74 - 4 * q^75 + 48 * q^76 - 16 * q^79 - 4 * q^80 - 8 * q^81 + 56 * q^85 - 8 * q^86 + 88 * q^89 + 24 * q^94 - 24 * q^95 - 8 * q^96

Display 100 coefficients 10 coefficients

Character values

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

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

Coefficient data

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

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

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

$2$	0.866025	+	0.500000i	0.612372	+	0.353553i
$2$	0.866025	+	0.500000i	0.612372	+	0.353553i
$3$	0.866025	−	0.500000i	0.500000	−	0.288675i
$3$	0.866025	−	0.500000i	0.500000	−	0.288675i
$4$	0.500000	+	0.866025i	0.250000	+	0.433013i
$5$	1.89827	+	1.18176i	0.848933	+	0.528501i
$5$	1.89827	+	1.18176i	0.848933	+	0.528501i
$6$	1.00000			0.408248
$7$		0			0
$7$		0			0
$8$			1.00000i			0.353553i
$9$	0.500000	−	0.866025i	0.166667	−	0.288675i
$10$	1.05307	+	1.97257i	0.333010	+	0.623782i
$11$	1.52773	+	2.64610i	0.460627	+	0.797829i	0.998992	−	0.0448824i	$-0.0142913\pi$
$11$	1.52773	+	2.64610i	0.460627	+	0.797829i	−0.538365	+	0.842711i	$0.680958\pi$
$12$	0.866025	+	0.500000i	0.250000	+	0.144338i
$13$			1.64124i			0.455198i	0.973755	+	0.227599i	$0.0730875\pi$
$13$			1.64124i			0.455198i	−0.973755	+	0.227599i	$0.926912\pi$
$14$		0			0
$15$	2.23483	+	0.0743018i	0.577031	+	0.0191846i
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	2.51741	−	1.45342i	0.610560	−	0.352507i	−0.162624	−	0.986688i	$-0.551996\pi$
$17$	2.51741	−	1.45342i	0.610560	−	0.352507i	0.773185	+	0.634181i	$0.218663\pi$
$18$	0.866025	−	0.500000i	0.204124	−	0.117851i
$19$	1.10508	−	1.91405i	0.253522	−	0.439114i	−0.710971	−	0.703222i	$-0.751744\pi$
$19$	1.10508	−	1.91405i	0.253522	−	0.439114i	0.964493	+	0.264108i	$0.0850775\pi$
$20$	−0.0743018	+	2.23483i	−0.0166144	+	0.499724i
$21$		0			0
$22$			3.05545i			0.651425i
$23$	−1.55005	−	0.894921i	−0.323208	−	0.186604i	0.329614	−	0.944116i	$-0.393081\pi$
$23$	−1.55005	−	0.894921i	−0.323208	−	0.186604i	−0.652821	+	0.757512i	$0.726415\pi$
$24$	0.500000	+	0.866025i	0.102062	+	0.176777i
$25$	2.20687	+	4.48662i	0.441374	+	0.897323i
$26$	−0.820620	+	1.42135i	−0.160937	+	0.278751i
$27$		−	1.00000i		−	0.192450i
$28$		0			0
$29$	−5.58667			−1.03742			−0.518710	−	0.854951i	$-0.673587\pi$
$29$	−5.58667			−1.03742			−0.518710	+	0.854951i	$0.673587\pi$
$30$	1.89827	+	1.18176i	0.346575	+	0.215760i
$31$	−0.472274	−	0.818002i	−0.0848228	−	0.146917i	0.820493	−	0.571657i	$-0.193699\pi$
$31$	−0.472274	−	0.818002i	−0.0848228	−	0.146917i	−0.905316	+	0.424739i	$0.860366\pi$
$32$	−0.866025	+	0.500000i	−0.153093	+	0.0883883i
$33$	2.64610	+	1.52773i	0.460627	+	0.265943i
$34$	2.90685			0.498521
$35$		0			0
$36$	1.00000			0.166667
$37$	−9.27713	−	5.35615i	−1.52515	−	0.880546i	−0.999556	−	0.0298114i	$-0.990509\pi$
$37$	−9.27713	−	5.35615i	−1.52515	−	0.880546i	−0.525595	−	0.850735i	$-0.676157\pi$
$38$	1.91405	−	1.10508i	0.310500	−	0.179267i
$39$	0.820620	+	1.42135i	0.131404	+	0.227599i
$40$	−1.18176	+	1.89827i	−0.186853	+	0.300143i
$41$	6.67982			1.04321			0.521607	−	0.853186i	$-0.325333\pi$
$41$	6.67982			1.04321			0.521607	+	0.853186i	$0.325333\pi$
$42$		0			0
$43$			10.5021i			1.60156i	0.598957	+	0.800781i	$0.295582\pi$
$43$			10.5021i			1.60156i	−0.598957	+	0.800781i	$0.704418\pi$
$44$	−1.52773	+	2.64610i	−0.230313	+	0.398915i
$45$	1.97257	−	1.05307i	0.294054	−	0.156982i
$46$	−0.894921	−	1.55005i	−0.131949	−	0.228542i
$47$	9.85235	+	5.68826i	1.43711	+	0.829718i	0.997648	−	0.0685421i	$-0.0218347\pi$
$47$	9.85235	+	5.68826i	1.43711	+	0.829718i	0.439465	+	0.898260i	$0.355168\pi$
$48$			1.00000i			0.144338i
$49$		0			0
$50$	−0.332104	+	4.98896i	−0.0469666	+	0.705545i
$51$	1.45342	−	2.51741i	0.203520	−	0.352507i
$52$	−1.42135	+	0.820620i	−0.197106	+	0.113799i
$53$	5.01415	−	2.89492i	0.688747	−	0.397648i	−0.114396	−	0.993435i	$-0.536493\pi$
$53$	5.01415	−	2.89492i	0.688747	−	0.397648i	0.803142	+	0.595787i	$0.203160\pi$
$54$	0.500000	−	0.866025i	0.0680414	−	0.117851i
$55$	−0.227026	+	6.82843i	−0.0306121	+	0.920745i
$56$		0			0
$57$		−	2.21016i		−	0.292742i
$58$	−4.83820	−	2.79334i	−0.635287	−	0.366783i
$59$	−2.98896	−	5.17703i	−0.389129	−	0.673992i	0.603203	−	0.797587i	$-0.293891\pi$
$59$	−2.98896	−	5.17703i	−0.389129	−	0.673992i	−0.992333	+	0.123596i	$0.960557\pi$
$60$	1.05307	+	1.97257i	0.135951	+	0.254658i
$61$	−0.222905	+	0.386083i	−0.0285401	+	0.0494329i	−0.879943	−	0.475080i	$-0.842419\pi$
$61$	−0.222905	+	0.386083i	−0.0285401	+	0.0494329i	0.851403	+	0.524513i	$0.175752\pi$
$62$		−	0.944547i		−	0.119958i
$63$		0			0
$64$	−1.00000			−0.125000
$65$	−1.93956	+	3.11552i	−0.240572	+	0.386432i
$66$	1.52773	+	2.64610i	0.188050	+	0.325712i
$67$	−1.09605	+	0.632805i	−0.133904	+	0.0773094i	−0.565456	−	0.824779i	$-0.691300\pi$
$67$	−1.09605	+	0.632805i	−0.133904	+	0.0773094i	0.431552	+	0.902088i	$0.357966\pi$
$68$	2.51741	+	1.45342i	0.305280	+	0.176254i
$69$	−1.78984			−0.215472
$70$		0			0
$71$	−14.8523			−1.76264			−0.881321	−	0.472518i	$-0.843345\pi$
$71$	−14.8523			−1.76264			−0.881321	+	0.472518i	$0.843345\pi$
$72$	0.866025	+	0.500000i	0.102062	+	0.0589256i
$73$	6.85577	−	3.95818i	0.802407	−	0.463270i	−0.0419049	−	0.999122i	$-0.513343\pi$
$73$	6.85577	−	3.95818i	0.802407	−	0.463270i	0.844312	+	0.535851i	$0.180009\pi$
$74$	−5.35615	−	9.27713i	−0.622640	−	1.07844i
$75$	4.15451	+	2.78209i	0.479722	+	0.321248i
$76$	2.21016			0.253522
$77$		0			0
$78$			1.64124i			0.185834i
$79$	7.14949	−	12.3833i	0.804380	−	1.39323i	−0.112328	−	0.993671i	$-0.535831\pi$
$79$	7.14949	−	12.3833i	0.804380	−	1.39323i	0.916709	−	0.399557i	$-0.130836\pi$
$80$	−1.97257	+	1.05307i	−0.220540	+	0.117737i
$81$	−0.500000	−	0.866025i	−0.0555556	−	0.0962250i
$82$	5.78490	+	3.33991i	0.638835	+	0.368832i
$83$			0.874366i			0.0959741i	0.998848	+	0.0479871i	$0.0152806\pi$
$83$			0.874366i			0.0959741i	−0.998848	+	0.0479871i	$0.984719\pi$
$84$		0			0
$85$	6.49632	+	0.215984i	0.704625	+	0.0234268i
$86$	−5.25107	+	9.09513i	−0.566238	+	0.980753i
$87$	−4.83820	+	2.79334i	−0.518710	+	0.299477i
$88$	−2.64610	+	1.52773i	−0.282075	+	0.162856i
$89$	8.75413	−	15.1626i	0.927935	−	1.60723i	0.141165	−	0.989986i	$-0.454915\pi$
$89$	8.75413	−	15.1626i	0.927935	−	1.60723i	0.786771	−	0.617245i	$-0.211751\pi$
$90$	2.23483	+	0.0743018i	0.235572	+	0.00783210i
$91$		0			0
$92$		−	1.78984i		−	0.186604i
$93$	−0.818002	−	0.472274i	−0.0848228	−	0.0489725i
$94$	5.68826	+	9.85235i	0.586699	+	1.01619i
$95$	4.35970	−	2.32745i	0.447295	−	0.238791i
$96$	−0.500000	+	0.866025i	−0.0510310	+	0.0883883i
$97$			10.4476i			1.06079i	0.847750	+	0.530396i	$0.177957\pi$
$97$			10.4476i			1.06079i	−0.847750	+	0.530396i	$0.822043\pi$
$98$		0			0
$99$	3.05545			0.307085
$100$	−2.78209	+	4.15451i	−0.278209	+	0.415451i
$101$	−7.72747	−	13.3844i	−0.768912	−	1.33179i	−0.938153	−	0.346220i	$-0.887465\pi$
$101$	−7.72747	−	13.3844i	−0.768912	−	1.33179i	0.169242	−	0.985575i	$-0.445868\pi$
$102$	2.51741	−	1.45342i	0.249260	−	0.143910i
$103$	−2.70688	−	1.56282i	−0.266717	−	0.153989i	0.360678	−	0.932690i	$-0.382545\pi$
$103$	−2.70688	−	1.56282i	−0.266717	−	0.153989i	−0.627395	+	0.778701i	$0.715879\pi$
$104$	−1.64124			−0.160937
$105$		0			0
$106$	5.78984			0.562359
$107$	−4.14176	−	2.39124i	−0.400399	−	0.231170i	0.286257	−	0.958153i	$-0.407589\pi$
$107$	−4.14176	−	2.39124i	−0.400399	−	0.231170i	−0.686656	+	0.726982i	$0.740922\pi$
$108$	0.866025	−	0.500000i	0.0833333	−	0.0481125i
$109$	−4.55178	−	7.88391i	−0.435981	−	0.755141i	0.561394	−	0.827549i	$-0.310265\pi$
$109$	−4.55178	−	7.88391i	−0.435981	−	0.755141i	−0.997375	+	0.0724073i	$0.976932\pi$
$110$	−3.61082	+	5.80008i	−0.344279	+	0.553016i
$111$	−10.7123			−1.01677
$112$		0			0
$113$			14.3982i			1.35447i	0.735766	+	0.677236i	$0.236822\pi$
$113$			14.3982i			1.35447i	−0.735766	+	0.677236i	$0.763178\pi$
$114$	1.10508	−	1.91405i	0.103500	−	0.179267i
$115$	−1.88483	−	3.53060i	−0.175761	−	0.329230i
$116$	−2.79334	−	4.83820i	−0.259355	−	0.449216i
$117$	1.42135	+	0.820620i	0.131404	+	0.0758663i
$118$		−	5.97792i		−	0.550312i
$119$		0			0
$120$	−0.0743018	+	2.23483i	−0.00678279	+	0.204011i
$121$	0.832104	−	1.44125i	0.0756458	−	0.131022i
$122$	−0.386083	+	0.222905i	−0.0349544	+	0.0201809i
$123$	5.78490	−	3.33991i	0.521607	−	0.301150i
$124$	0.472274	−	0.818002i	0.0424114	−	0.0734587i
$125$	−1.11289	+	11.1248i	−0.0995396	+	0.995034i
$126$		0			0
$127$			8.45405i			0.750176i	0.926989	+	0.375088i	$0.122387\pi$
$127$			8.45405i			0.750176i	−0.926989	+	0.375088i	$0.877613\pi$
$128$	−0.866025	−	0.500000i	−0.0765466	−	0.0441942i
$129$	5.25107	+	9.09513i	0.462331	+	0.800781i
$130$	−3.23746	+	1.72834i	−0.283944	+	0.151585i
$131$	−4.16053	+	7.20625i	−0.363507	+	0.629613i	−0.988535	−	0.150989i	$-0.951754\pi$
$131$	−4.16053	+	7.20625i	−0.363507	+	0.629613i	0.625028	+	0.780602i	$0.285087\pi$
$132$			3.05545i			0.265943i
$133$		0			0
$134$	−1.26561			−0.109332
$135$	1.18176	−	1.89827i	0.101710	−	0.163377i
$136$	1.45342	+	2.51741i	0.124630	+	0.215866i
$137$	−8.54508	+	4.93351i	−0.730056	+	0.421498i	−0.818443	−	0.574588i	$-0.805162\pi$
$137$	−8.54508	+	4.93351i	−0.730056	+	0.421498i	0.0883869	+	0.996086i	$0.471829\pi$
$138$	−1.55005	−	0.894921i	−0.131949	−	0.0761808i
$139$	−16.9632			−1.43880			−0.719399	−	0.694597i	$-0.755583\pi$
$139$	−16.9632			−1.43880			−0.719399	+	0.694597i	$0.755583\pi$
$140$		0			0
$141$	11.3765			0.958075
$142$	−12.8625	−	7.42614i	−1.07939	−	0.623188i
$143$	−4.34288	+	2.50736i	−0.363170	+	0.209676i
$144$	0.500000	+	0.866025i	0.0416667	+	0.0721688i
$145$	−10.6050	−	6.60213i	−0.880699	−	0.548277i
$146$	7.91636			0.655163
$147$		0			0
$148$		−	10.7123i		−	0.880546i
$149$	4.02405	−	6.96986i	0.329663	−	0.570993i	−0.652782	−	0.757546i	$-0.726398\pi$
$149$	4.02405	−	6.96986i	0.329663	−	0.570993i	0.982445	+	0.186553i	$0.0597316\pi$
$150$	2.20687	+	4.48662i	0.180190	+	0.366331i
$151$	4.98896	+	8.64113i	0.405996	+	0.703205i	0.994437	−	0.105335i	$-0.0335915\pi$
$151$	4.98896	+	8.64113i	0.405996	+	0.703205i	−0.588441	+	0.808540i	$0.700258\pi$
$152$	1.91405	+	1.10508i	0.155250	+	0.0896337i
$153$		−	2.90685i		−	0.235005i
$154$		0			0
$155$	0.0701816	−	2.11091i	0.00563712	−	0.169552i
$156$	−0.820620	+	1.42135i	−0.0657022	+	0.113799i
$157$	10.9705	−	6.33381i	0.875540	−	0.505493i	0.00635459	−	0.999980i	$-0.497977\pi$
$157$	10.9705	−	6.33381i	0.875540	−	0.505493i	0.869185	+	0.494487i	$0.164644\pi$
$158$	12.3833	−	7.14949i	0.985161	−	0.568783i
$159$	2.89492	−	5.01415i	0.229582	−	0.397648i
$160$	−2.23483	−	0.0743018i	−0.176679	−	0.00587407i
$161$		0			0
$162$		−	1.00000i		−	0.0785674i
$163$	20.4075	+	11.7823i	1.59844	+	0.922861i	0.991788	+	0.127894i	$0.0408218\pi$
$163$	20.4075	+	11.7823i	1.59844	+	0.922861i	0.606654	+	0.794966i	$0.292512\pi$
$164$	3.33991	+	5.78490i	0.260803	+	0.451725i
$165$	3.21760	+	6.02710i	0.250490	+	0.469209i
$166$	−0.437183	+	0.757223i	−0.0339320	+	0.0587719i
$167$		−	18.0818i		−	1.39921i	−0.714528	−	0.699607i	$-0.753358\pi$
$167$		−	18.0818i		−	1.39921i	0.714528	−	0.699607i	$-0.246642\pi$
$168$		0			0
$169$	10.3063			0.792795
$170$	5.51799	+	3.43521i	0.423210	+	0.263469i
$171$	−1.10508	−	1.91405i	−0.0845075	−	0.146371i
$172$	−9.09513	+	5.25107i	−0.693497	+	0.400391i
$173$	1.67874	+	0.969223i	0.127633	+	0.0736887i	0.562457	−	0.826827i	$-0.309856\pi$
$173$	1.67874	+	0.969223i	0.127633	+	0.0736887i	−0.434824	+	0.900515i	$0.643190\pi$
$174$	−5.58667			−0.423525
$175$		0			0
$176$	−3.05545			−0.230313
$177$	−5.17703	−	2.98896i	−0.389129	−	0.224664i
$178$	15.1626	−	8.75413i	1.13648	−	0.656149i
$179$	−12.2232	−	21.1711i	−0.913602	−	1.58241i	−0.808935	−	0.587898i	$-0.799956\pi$
$179$	−12.2232	−	21.1711i	−0.913602	−	1.58241i	−0.104667	−	0.994507i	$-0.533378\pi$
$180$	1.89827	+	1.18176i	0.141489	+	0.0880835i
$181$	−16.9788			−1.26202			−0.631012	−	0.775773i	$-0.717360\pi$
$181$	−16.9788			−1.26202			−0.631012	+	0.775773i	$0.717360\pi$
$182$		0			0
$183$			0.445811i			0.0329553i
$184$	0.894921	−	1.55005i	0.0659745	−	0.114271i
$185$	−11.2808	−	21.1308i	−0.829381	−	1.55357i
$186$	−0.472274	−	0.818002i	−0.0346288	−	0.0599788i
$187$	7.69181	+	4.44087i	0.562481	+	0.324749i
$188$			11.3765i			0.829718i
$189$		0			0
$190$	4.93933	+	0.164219i	0.358337	+	0.0119137i
$191$	−0.370689	+	0.642051i	−0.0268221	+	0.0464572i	−0.879125	−	0.476592i	$-0.841872\pi$
$191$	−0.370689	+	0.642051i	−0.0268221	+	0.0464572i	0.852303	+	0.523049i	$0.175205\pi$
$192$	−0.866025	+	0.500000i	−0.0625000	+	0.0360844i
$193$	−5.29220	+	3.05545i	−0.380941	+	0.219936i	−0.678228	−	0.734852i	$-0.737252\pi$
$193$	−5.29220	+	3.05545i	−0.380941	+	0.219936i	0.297287	+	0.954788i	$0.403918\pi$
$194$	−5.22379	+	9.04787i	−0.375046	+	0.649599i
$195$	−0.121947	+	3.66790i	−0.00873281	+	0.262663i
$196$		0			0
$197$		−	20.6832i		−	1.47362i	−0.676100	−	0.736810i	$-0.736331\pi$
$197$		−	20.6832i		−	1.47362i	0.676100	−	0.736810i	$-0.263669\pi$
$198$	2.64610	+	1.52773i	0.188050	+	0.108571i
$199$	6.03509	+	10.4531i	0.427816	+	0.740999i	0.996679	−	0.0814331i	$-0.0259497\pi$
$199$	6.03509	+	10.4531i	0.427816	+	0.740999i	−0.568863	+	0.822433i	$0.692616\pi$
$200$	−4.48662	+	2.20687i	−0.317252	+	0.156049i
$201$	−0.632805	+	1.09605i	−0.0446346	+	0.0773094i
$202$		−	15.4549i		−	1.08741i
$203$		0			0
$204$	2.90685			0.203520
$205$	12.6801	+	7.89397i	0.885618	+	0.551339i
$206$	−1.56282	−	2.70688i	−0.108887	−	0.188597i
$207$	−1.55005	+	0.894921i	−0.107736	+	0.0622013i
$208$	−1.42135	−	0.820620i	−0.0985532	−	0.0568997i
$209$	6.75303			0.467117
$210$		0			0
$211$	2.95153			0.203192			0.101596	−	0.994826i	$-0.467605\pi$
$211$	2.95153			0.203192			0.101596	+	0.994826i	$0.467605\pi$
$212$	5.01415	+	2.89492i	0.344373	+	0.198824i
$213$	−12.8625	+	7.42614i	−0.881321	+	0.508831i
$214$	−2.39124	−	4.14176i	−0.163462	−	0.283125i
$215$	−12.4111	+	19.9359i	−0.846427	+	1.35962i
$216$	1.00000			0.0680414
$217$		0			0
$218$		−	9.10355i		−	0.616570i
$219$	3.95818	−	6.85577i	0.267469	−	0.463270i
$220$	−6.02710	+	3.21760i	−0.406347	+	0.216931i
$221$	2.38542	+	4.13166i	0.160461	+	0.277926i
$222$	−9.27713	−	5.35615i	−0.622640	−	0.359481i
$223$		−	11.7678i		−	0.788027i	−0.919105	−	0.394014i	$-0.871086\pi$
$223$		−	11.7678i		−	0.788027i	0.919105	−	0.394014i	$-0.128914\pi$
$224$		0			0
$225$	4.98896	+	0.332104i	0.332597	+	0.0221403i
$226$	−7.19912	+	12.4692i	−0.478878	+	0.829441i
$227$	−11.4632	+	6.61827i	−0.760838	+	0.439270i	−0.829597	−	0.558363i	$-0.811430\pi$
$227$	−11.4632	+	6.61827i	−0.760838	+	0.439270i	0.0687586	+	0.997633i	$0.478096\pi$
$228$	1.91405	−	1.10508i	0.126761	−	0.0731856i
$229$	12.6224	−	21.8626i	0.834111	−	1.44472i	−0.0606412	−	0.998160i	$-0.519315\pi$
$229$	12.6224	−	21.8626i	0.834111	−	1.44472i	0.894752	−	0.446563i	$-0.147352\pi$
$230$	0.132989	−	4.00000i	0.00876900	−	0.263752i
$231$		0			0
$232$		−	5.58667i		−	0.366783i
$233$	−2.88249	−	1.66421i	−0.188838	−	0.109026i	0.402600	−	0.915376i	$-0.368106\pi$
$233$	−2.88249	−	1.66421i	−0.188838	−	0.109026i	−0.591439	+	0.806350i	$0.701440\pi$
$234$	0.820620	+	1.42135i	0.0536456	+	0.0929169i
$235$	11.9803	+	22.4410i	0.781506	+	1.46389i
$236$	2.98896	−	5.17703i	0.194565	−	0.336996i
$237$		−	14.2990i		−	0.928819i
$238$		0			0
$239$	−24.8713			−1.60879			−0.804396	−	0.594094i	$-0.797511\pi$
$239$	−24.8713			−1.60879			−0.804396	+	0.594094i	$0.797511\pi$
$240$	−1.18176	+	1.89827i	−0.0762825	+	0.122533i
$241$	−5.17677	−	8.96643i	−0.333465	−	0.577579i	0.649724	−	0.760171i	$-0.274885\pi$
$241$	−5.17677	−	8.96643i	−0.333465	−	0.577579i	−0.983189	+	0.182592i	$0.941551\pi$
$242$	1.44125	−	0.832104i	0.0926469	−	0.0534897i
$243$	−0.866025	−	0.500000i	−0.0555556	−	0.0320750i
$244$	−0.445811			−0.0285401
$245$		0			0
$246$	6.67982			0.425890
$247$	3.14142	+	1.81370i	0.199884	+	0.115403i
$248$	0.818002	−	0.472274i	0.0519432	−	0.0299894i
$249$	0.437183	+	0.757223i	0.0277053	+	0.0479871i
$250$	−6.52619	+	9.07793i	−0.412753	+	0.574139i
$251$	16.5502			1.04464			0.522321	−	0.852749i	$-0.325066\pi$
$251$	16.5502			1.04464			0.522321	+	0.852749i	$0.325066\pi$
$252$		0			0
$253$		−	5.46878i		−	0.343819i
$254$	−4.22703	+	7.32142i	−0.265227	+	0.459387i
$255$	5.73397	−	3.06111i	0.359075	−	0.191694i
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	−21.1783	−	12.2273i	−1.32106	−	0.762717i	−0.337166	−	0.941445i	$-0.609468\pi$
$257$	−21.1783	−	12.2273i	−1.32106	−	0.762717i	−0.983899	+	0.178728i	$0.942802\pi$
$258$			10.5021i			0.653835i
$259$		0			0
$260$	−3.66790	−	0.121947i	−0.227473	−	0.00756283i
$261$	−2.79334	+	4.83820i	−0.172903	+	0.299477i
$262$	−7.20625	+	4.16053i	−0.445204	+	0.257038i
$263$	−10.8332	+	6.25457i	−0.668006	+	0.385673i	−0.795321	−	0.606189i	$-0.792697\pi$
$263$	−10.8332	+	6.25457i	−0.668006	+	0.385673i	0.127315	+	0.991862i	$0.459364\pi$
$264$	−1.52773	+	2.64610i	−0.0940251	+	0.162856i
$265$	12.9393	+	0.430196i	0.794857	+	0.0264267i
$266$		0			0
$267$		−	17.5083i		−	1.07149i
$268$	−1.09605	−	0.632805i	−0.0669519	−	0.0386547i
$269$	−9.48330	−	16.4256i	−0.578207	−	1.00148i	−0.995685	−	0.0927970i	$-0.970419\pi$
$269$	−9.48330	−	16.4256i	−0.578207	−	1.00148i	0.417478	−	0.908687i	$-0.362914\pi$
$270$	1.97257	−	1.05307i	0.120047	−	0.0640878i
$271$	−9.83192	+	17.0294i	−0.597247	+	1.03446i	0.395979	+	0.918260i	$0.370405\pi$
$271$	−9.83192	+	17.0294i	−0.597247	+	1.03446i	−0.993226	+	0.116202i	$0.962928\pi$
$272$			2.90685i			0.176254i
$273$		0			0
$274$	−9.86701			−0.596088
$275$	−8.50054	+	12.6939i	−0.512602	+	0.765472i
$276$	−0.894921	−	1.55005i	−0.0538679	−	0.0933020i
$277$	5.31737	−	3.06999i	0.319490	−	0.184458i	−0.331675	−	0.943394i	$-0.607614\pi$
$277$	5.31737	−	3.06999i	0.319490	−	0.184458i	0.651165	+	0.758936i	$0.274280\pi$
$278$	−14.6906	−	8.48159i	−0.881081	−	0.508692i
$279$	−0.944547			−0.0565486
$280$		0			0
$281$	−12.1330			−0.723793			−0.361897	−	0.932218i	$-0.617871\pi$
$281$	−12.1330			−0.723793			−0.361897	+	0.932218i	$0.617871\pi$
$282$	9.85235	+	5.68826i	0.586699	+	0.338731i
$283$	−15.0838	+	8.70862i	−0.896637	+	0.517674i	−0.876108	−	0.482116i	$-0.839869\pi$
$283$	−15.0838	+	8.70862i	−0.896637	+	0.517674i	−0.0205295	+	0.999789i	$0.506535\pi$
$284$	−7.42614	−	12.8625i	−0.440660	−	0.763246i
$285$	2.61188	−	4.19548i	0.154715	−	0.248519i
$286$	−5.01473			−0.296527
$287$		0			0
$288$			1.00000i			0.0589256i
$289$	−4.27511	+	7.40471i	−0.251477	+	0.435571i
$290$	−5.88315	−	11.0201i	−0.345471	−	0.647124i
$291$	5.22379	+	9.04787i	0.306224	+	0.530396i
$292$	6.85577	+	3.95818i	0.401204	+	0.231635i
$293$		−	23.7521i		−	1.38762i	−0.720160	−	0.693808i	$-0.755932\pi$
$293$		−	23.7521i		−	1.38762i	0.720160	−	0.693808i	$-0.244068\pi$
$294$		0			0
$295$	0.444170	−	13.3596i	0.0258606	−	0.777829i
$296$	5.35615	−	9.27713i	0.311320	−	0.539222i
$297$	2.64610	−	1.52773i	0.153542	−	0.0886477i
$298$	6.96986	−	4.02405i	0.403753	−	0.233107i
$299$	1.46878	−	2.54400i	0.0849417	−	0.147123i
$300$	−0.332104	+	4.98896i	−0.0191740	+	0.288038i
$301$		0			0
$302$			9.97792i			0.574165i
$303$	−13.3844	−	7.72747i	−0.768912	−	0.443931i
$304$	1.10508	+	1.91405i	0.0633806	+	0.109778i
$305$	−0.879394	+	0.469470i	−0.0503540	+	0.0268818i
$306$	1.45342	−	2.51741i	0.0830868	−	0.143910i
$307$			7.90812i			0.451340i	0.974204	+	0.225670i	$0.0724572\pi$
$307$			7.90812i			0.451340i	−0.974204	+	0.225670i	$0.927543\pi$
$308$		0			0
$309$	−3.12563			−0.177811
$310$	1.11623	−	1.79301i	0.0633977	−	0.101836i
$311$	5.03858	+	8.72708i	0.285712	+	0.494868i	0.972782	−	0.231724i	$-0.0744366\pi$
$311$	5.03858	+	8.72708i	0.285712	+	0.494868i	−0.687070	+	0.726592i	$0.741103\pi$
$312$	−1.42135	+	0.820620i	−0.0804684	+	0.0464584i
$313$	−17.6534	−	10.1922i	−0.997829	−	0.576097i	−0.0902238	−	0.995922i	$-0.528758\pi$
$313$	−17.6534	−	10.1922i	−0.997829	−	0.576097i	−0.907605	+	0.419825i	$0.862092\pi$
$314$	12.6676			0.714875
$315$		0			0
$316$	14.2990			0.804380
$317$	−0.278048	−	0.160531i	−0.0156168	−	0.00901634i	0.492171	−	0.870498i	$-0.336203\pi$
$317$	−0.278048	−	0.160531i	−0.0156168	−	0.00901634i	−0.507788	+	0.861482i	$0.669537\pi$
$318$	5.01415	−	2.89492i	0.281180	−	0.162339i
$319$	−8.53491	−	14.7829i	−0.477863	−	0.827683i
$320$	−1.89827	−	1.18176i	−0.106117	−	0.0660626i
$321$	−4.78249			−0.266932
$322$		0			0
$323$		−	6.42459i		−	0.357474i
$324$	0.500000	−	0.866025i	0.0277778	−	0.0481125i
$325$	−7.36361	+	3.62200i	−0.408460	+	0.200912i
$326$	11.7823	+	20.4075i	0.652561	+	1.13027i
$327$	−7.88391	−	4.55178i	−0.435981	−	0.251714i
$328$			6.67982i			0.368832i
$329$		0			0
$330$	−0.227026	+	6.82843i	−0.0124973	+	0.375893i
$331$	8.30419	−	14.3833i	0.456440	−	0.790577i	−0.542330	−	0.840166i	$-0.682458\pi$
$331$	8.30419	−	14.3833i	0.456440	−	0.790577i	0.998770	+	0.0495887i	$0.0157910\pi$
$332$	−0.757223	+	0.437183i	−0.0415580	+	0.0239935i
$333$	−9.27713	+	5.35615i	−0.508384	+	0.293515i
$334$	9.04092	−	15.6593i	0.494697	−	0.856840i
$335$	−2.82843	−	0.0940371i	−0.154533	−	0.00513780i
$336$		0			0
$337$			1.91118i			0.104108i	0.998644	+	0.0520542i	$0.0165769\pi$
$337$			1.91118i			0.104108i	−0.998644	+	0.0520542i	$0.983423\pi$
$338$	8.92555	+	5.15317i	0.485486	+	0.280295i
$339$	7.19912	+	12.4692i	0.391002	+	0.677236i
$340$	3.06111	+	5.73397i	0.166012	+	0.310968i
$341$	1.44301	−	2.49937i	0.0781434	−	0.135348i
$342$		−	2.21016i		−	0.119512i
$343$		0			0
$344$	−10.5021			−0.566238
$345$	−3.39761	−	2.11517i	−0.182921	−	0.113877i
$346$	0.969223	+	1.67874i	0.0521058	+	0.0902498i
$347$	6.84864	−	3.95406i	0.367654	−	0.212265i	−0.304779	−	0.952423i	$-0.598583\pi$
$347$	6.84864	−	3.95406i	0.367654	−	0.212265i	0.672433	+	0.740158i	$0.265249\pi$
$348$	−4.83820	−	2.79334i	−0.259355	−	0.149739i
$349$	23.5273			1.25939			0.629693	−	0.776844i	$-0.283181\pi$
$349$	23.5273			1.25939			0.629693	+	0.776844i	$0.283181\pi$
$350$		0			0
$351$	1.64124			0.0876029
$352$	−2.64610	−	1.52773i	−0.141038	−	0.0814281i
$353$	−19.8942	+	11.4859i	−1.05886	+	0.611333i	−0.925117	−	0.379683i	$-0.876033\pi$
$353$	−19.8942	+	11.4859i	−1.05886	+	0.611333i	−0.133743	+	0.991016i	$0.542700\pi$
$354$	−2.98896	−	5.17703i	−0.158861	−	0.275156i
$355$	−28.1937	−	17.5519i	−1.49636	−	0.931558i
$356$	17.5083			0.927935
$357$		0			0
$358$		−	24.4463i		−	1.29203i
$359$	5.51319	−	9.54913i	0.290975	−	0.503984i	−0.683065	−	0.730357i	$-0.739354\pi$
$359$	5.51319	−	9.54913i	0.290975	−	0.503984i	0.974041	+	0.226373i	$0.0726870\pi$
$360$	1.05307	+	1.97257i	0.0555016	+	0.103964i
$361$	7.05760	+	12.2241i	0.371453	+	0.643375i
$362$	−14.7041	−	8.48940i	−0.772829	−	0.446193i
$363$		−	1.66421i		−	0.0873483i
$364$		0			0
$365$	17.6918	+	0.588200i	0.926029	+	0.0307878i
$366$	−0.222905	+	0.386083i	−0.0116515	+	0.0201809i
$367$	−8.78552	+	5.07232i	−0.458600	+	0.264773i	−0.711456	−	0.702731i	$-0.751964\pi$
$367$	−8.78552	+	5.07232i	−0.458600	+	0.264773i	0.252855	+	0.967504i	$0.418630\pi$
$368$	1.55005	−	0.894921i	0.0808019	−	0.0466510i
$369$	3.33991	−	5.78490i	0.173869	−	0.301150i
$370$	0.795944	−	23.9402i	0.0413791	−	1.24459i
$371$		0			0
$372$		−	0.944547i		−	0.0489725i
$373$	22.9515	+	13.2511i	1.18839	+	0.686115i	0.957939	−	0.286970i	$-0.0926482\pi$
$373$	22.9515	+	13.2511i	1.18839	+	0.686115i	0.230446	+	0.973085i	$0.425981\pi$
$374$	4.44087	+	7.69181i	0.229632	+	0.397734i
$375$	4.59862	+	10.1908i	0.237472	+	0.526251i
$376$	−5.68826	+	9.85235i	−0.293349	+	0.508096i
$377$		−	9.16907i		−	0.472231i
$378$		0			0
$379$	−29.4142			−1.51091			−0.755453	−	0.655203i	$-0.772583\pi$
$379$	−29.4142			−1.51091			−0.755453	+	0.655203i	$0.772583\pi$
$380$	4.19548	+	2.61188i	0.215223	+	0.133987i
$381$	4.22703	+	7.32142i	0.216557	+	0.375088i
$382$	−0.642051	+	0.370689i	−0.0328502	+	0.0189661i
$383$	−3.15449	−	1.82125i	−0.161187	−	0.0930613i	0.417237	−	0.908798i	$-0.362999\pi$
$383$	−3.15449	−	1.82125i	−0.161187	−	0.0930613i	−0.578424	+	0.815737i	$0.696332\pi$
$384$	−1.00000			−0.0510310
$385$		0			0
$386$	−6.11091			−0.311037
$387$	9.09513	+	5.25107i	0.462331	+	0.266927i
$388$	−9.04787	+	5.22379i	−0.459336	+	0.265198i
$389$	−11.8969	−	20.6060i	−0.603196	−	1.04477i	−0.992334	−	0.123587i	$-0.960560\pi$
$389$	−11.8969	−	20.6060i	−0.603196	−	1.04477i	0.389138	−	0.921180i	$-0.372773\pi$
$390$	−1.93956	+	3.11552i	−0.0982133	+	0.157760i
$391$	−5.20280			−0.263117
$392$		0			0
$393$			8.32106i			0.419742i
$394$	10.3416	−	17.9122i	0.521003	−	0.902404i
$395$	28.2058	−	15.0578i	1.41919	−	0.757641i
$396$	1.52773	+	2.64610i	0.0767711	+	0.132972i
$397$	8.45353	+	4.88065i	0.424270	+	0.244953i	0.696903	−	0.717166i	$-0.254561\pi$
$397$	8.45353	+	4.88065i	0.424270	+	0.244953i	−0.272632	+	0.962118i	$0.587894\pi$
$398$			12.0702i			0.605024i
$399$		0			0
$400$	−4.98896	−	0.332104i	−0.249448	−	0.0166052i
$401$	−4.98896	+	8.64113i	−0.249137	+	0.431517i	−0.963287	−	0.268475i	$-0.913480\pi$
$401$	−4.98896	+	8.64113i	−0.249137	+	0.431517i	0.714150	+	0.699993i	$0.246814\pi$
$402$	−1.09605	+	0.632805i	−0.0546660	+	0.0315614i
$403$	1.34254	−	0.775114i	0.0668765	−	0.0386112i
$404$	7.72747	−	13.3844i	0.384456	−	0.665897i
$405$	0.0743018	−	2.23483i	0.00369209	−	0.111050i
$406$		0			0
$407$		−	32.7309i		−	1.62241i
$408$	2.51741	+	1.45342i	0.124630	+	0.0719552i
$409$	17.5919	+	30.4700i	0.869862	+	1.50665i	0.862137	+	0.506675i	$0.169126\pi$
$409$	17.5919	+	30.4700i	0.869862	+	1.50665i	0.00772514	+	0.999970i	$0.497541\pi$
$410$	7.03432	+	13.1764i	0.347400	+	0.650738i
$411$	−4.93351	+	8.54508i	−0.243352	+	0.421498i
$412$		−	3.12563i		−	0.153989i
$413$		0			0
$414$	−1.78984			−0.0879660
$415$	−1.03329	+	1.65978i	−0.0507224	+	0.0814756i
$416$	−0.820620	−	1.42135i	−0.0402342	−	0.0696877i
$417$	−14.6906	+	8.48159i	−0.719399	+	0.415345i
$418$	5.84830	+	3.37652i	0.286050	+	0.165151i
$419$	−18.6274			−0.910009			−0.455004	−	0.890489i	$-0.650362\pi$
$419$	−18.6274			−0.910009			−0.455004	+	0.890489i	$0.650362\pi$
$420$		0			0
$421$	31.6464			1.54235			0.771176	−	0.636622i	$-0.219669\pi$
$421$	31.6464			1.54235			0.771176	+	0.636622i	$0.219669\pi$
$422$	2.55610	+	1.47577i	0.124429	+	0.0718392i
$423$	9.85235	−	5.68826i	0.479038	−	0.276573i
$424$	2.89492	+	5.01415i	0.140590	+	0.243509i
$425$	12.0765	+	8.08712i	0.585798	+	0.392283i
$426$	−14.8523			−0.719595
$427$		0			0
$428$		−	4.78249i		−	0.231170i
$429$	−2.50736	+	4.34288i	−0.121057	+	0.209676i
$430$	−20.7163	+	11.0595i	−0.999027	+	0.533336i
$431$	7.40229	+	12.8211i	0.356556	+	0.617572i	0.987383	−	0.158351i	$-0.0506177\pi$
$431$	7.40229	+	12.8211i	0.356556	+	0.617572i	−0.630827	+	0.775923i	$0.717284\pi$
$432$	0.866025	+	0.500000i	0.0416667	+	0.0240563i
$433$			4.24731i			0.204113i	0.994779	+	0.102056i	$0.0325422\pi$
$433$			4.24731i			0.204113i	−0.994779	+	0.102056i	$0.967458\pi$
$434$		0			0
$435$	−12.4853	−	0.415100i	−0.598623	−	0.0199025i
$436$	4.55178	−	7.88391i	0.217991	−	0.377571i
$437$	−3.42585	+	1.97792i	−0.163881	+	0.0946166i
$438$	6.85577	−	3.95818i	0.327581	−	0.189129i
$439$	−1.11440	+	1.93020i	−0.0531874	+	0.0921232i	−0.891393	−	0.453231i	$-0.850271\pi$
$439$	−1.11440	+	1.93020i	−0.0531874	+	0.0921232i	0.838206	+	0.545354i	$0.183605\pi$
$440$	−6.82843	−	0.227026i	−0.325532	−	0.0108230i
$441$		0			0
$442$			4.77083i			0.226925i
$443$	4.02020	+	2.32106i	0.191005	+	0.110277i	0.592453	−	0.805605i	$-0.298160\pi$
$443$	4.02020	+	2.32106i	0.191005	+	0.110277i	−0.401448	+	0.915882i	$0.631493\pi$
$444$	−5.35615	−	9.27713i	−0.254192	−	0.440273i
$445$	34.5363	−	18.4374i	1.63718	−	0.874017i
$446$	5.88388	−	10.1912i	0.278610	−	0.482566i
$447$		−	8.04810i		−	0.380662i
$448$		0			0
$449$	3.69059			0.174170			0.0870849	−	0.996201i	$-0.472245\pi$
$449$	3.69059			0.174170			0.0870849	+	0.996201i	$0.472245\pi$
$450$	4.15451	+	2.78209i	0.195846	+	0.131149i
$451$	10.2049	+	17.6755i	0.480532	+	0.832306i
$452$	−12.4692	+	7.19912i	−0.586503	+	0.338618i
$453$	8.64113	+	4.98896i	0.405996	+	0.234402i
$454$	−13.2365			−0.621222
$455$		0			0
$456$	2.21016			0.103500
$457$	−2.36401	−	1.36486i	−0.110584	−	0.0638455i	0.443688	−	0.896181i	$-0.353670\pi$
$457$	−2.36401	−	1.36486i	−0.110584	−	0.0638455i	−0.554272	+	0.832336i	$0.687003\pi$
$458$	21.8626	−	12.6224i	1.02157	−	0.589806i
$459$	−1.45342	−	2.51741i	−0.0678400	−	0.117502i
$460$	2.11517	−	3.39761i	0.0986204	−	0.158414i
$461$	11.8072			0.549918			0.274959	−	0.961456i	$-0.411336\pi$
$461$	11.8072			0.549918			0.274959	+	0.961456i	$0.411336\pi$
$462$		0			0
$463$			2.40561i			0.111798i	0.998436	+	0.0558990i	$0.0178025\pi$
$463$			2.40561i			0.111798i	−0.998436	+	0.0558990i	$0.982198\pi$
$464$	2.79334	−	4.83820i	0.129677	−	0.224608i
$465$	−0.994674	−	1.86319i	−0.0461269	−	0.0864033i
$466$	−1.66421	−	2.88249i	−0.0770930	−	0.133529i
$467$	−12.6969	−	7.33058i	−0.587544	−	0.339219i	0.176582	−	0.984286i	$-0.443496\pi$
$467$	−12.6969	−	7.33058i	−0.587544	−	0.339219i	−0.764126	+	0.645067i	$0.776829\pi$
$468$			1.64124i			0.0758663i
$469$		0			0
$470$	−0.845296	+	25.4246i	−0.0389906	+	1.17275i
$471$	6.33381	−	10.9705i	0.291847	−	0.505493i
$472$	5.17703	−	2.98896i	0.238292	−	0.137578i
$473$	−27.7897	+	16.0444i	−1.27777	+	0.737723i
$474$	7.14949	−	12.3833i	0.328387	−	0.568783i
$475$	11.0264	+	0.734003i	0.505925	+	0.0336783i
$476$		0			0
$477$		−	5.78984i		−	0.265099i
$478$	−21.5392	−	12.4357i	−0.985179	−	0.568794i
$479$	5.94669	+	10.3000i	0.271711	+	0.470617i	0.969300	−	0.245881i	$-0.0790772\pi$
$479$	5.94669	+	10.3000i	0.271711	+	0.470617i	−0.697589	+	0.716498i	$0.745744\pi$
$480$	−1.97257	+	1.05307i	−0.0900352	+	0.0480658i
$481$	8.79073	−	15.2260i	0.400823	−	0.694245i
$482$		−	10.3535i		−	0.471591i
$483$		0			0
$484$	1.66421			0.0756458
$485$	−12.3466	+	19.8323i	−0.560629	+	0.900541i
$486$	−0.500000	−	0.866025i	−0.0226805	−	0.0392837i
$487$	30.7454	−	17.7509i	1.39321	−	0.804370i	0.399540	−	0.916716i	$-0.369170\pi$
$487$	30.7454	−	17.7509i	1.39321	−	0.804370i	0.993669	+	0.112346i	$0.0358365\pi$
$488$	−0.386083	−	0.222905i	−0.0174772	−	0.0100905i
$489$	23.5646			1.06563
$490$		0			0
$491$	−0.978284			−0.0441493			−0.0220747	−	0.999756i	$-0.507027\pi$
$491$	−0.978284			−0.0441493			−0.0220747	+	0.999756i	$0.507027\pi$
$492$	5.78490	+	3.33991i	0.260803	+	0.150575i
$493$	−14.0639	+	8.11981i	−0.633407	+	0.365698i
$494$	1.81370	+	3.14142i	0.0816021	+	0.141339i
$495$	5.80008	+	3.61082i	0.260694	+	0.162294i
$496$	0.944547			0.0424114
$497$		0			0
$498$			0.874366i			0.0391813i
$499$	5.86701	−	10.1620i	0.262644	−	0.454912i	−0.704300	−	0.709902i	$-0.748739\pi$
$499$	5.86701	−	10.1620i	0.262644	−	0.454912i	0.966944	+	0.254991i	$0.0820724\pi$
$500$	−10.1908	+	4.59862i	−0.455747	+	0.205657i
$501$	−9.04092	−	15.6593i	−0.403918	−	0.699607i
$502$	14.3329	+	8.27512i	0.639710	+	0.369337i
$503$			17.3618i			0.774125i	0.922054	+	0.387062i	$0.126510\pi$
$503$			17.3618i			0.774125i	−0.922054	+	0.387062i	$0.873490\pi$
$504$		0			0
$505$	1.14833	−	34.5392i	0.0511000	−	1.53697i
$506$	2.73439	−	4.73610i	0.121558	−	0.210545i
$507$	8.92555	−	5.15317i	0.396397	−	0.228860i
$508$	−7.32142	+	4.22703i	−0.324836	+	0.187544i
$509$	12.9147	−	22.3688i	0.572432	−	0.991481i	−0.423883	−	0.905717i	$-0.639333\pi$
$509$	12.9147	−	22.3688i	0.572432	−	0.991481i	0.996315	−	0.0857647i	$-0.0273333\pi$
$510$	6.49632	+	0.215984i	0.287662	+	0.00956394i
$511$		0			0
$512$		−	1.00000i		−	0.0441942i
$513$	−1.91405	−	1.10508i	−0.0845075	−	0.0487904i
$514$	−12.2273	−	21.1783i	−0.539322	−	0.934134i
$515$	−3.29151	−	6.16554i	−0.145041	−	0.271686i
$516$	−5.25107	+	9.09513i	−0.231166	+	0.400391i
$517$			34.7604i			1.52876i
$518$		0			0
$519$	1.93845			0.0850884
$520$	−3.11552	−	1.93956i	−0.136624	−	0.0850552i
$521$	12.3733	+	21.4312i	0.542083	+	0.938916i	0.998784	+	0.0492955i	$0.0156976\pi$
$521$	12.3733	+	21.4312i	0.542083	+	0.938916i	−0.456701	+	0.889620i	$0.650969\pi$
$522$	−4.83820	+	2.79334i	−0.211762	+	0.122261i
$523$	1.39927	+	0.807871i	0.0611860	+	0.0353258i	0.530281	−	0.847822i	$-0.322086\pi$
$523$	1.39927	+	0.807871i	0.0611860	+	0.0353258i	−0.469095	+	0.883148i	$0.655420\pi$
$524$	−8.32106			−0.363507
$525$		0			0
$526$	−12.5091			−0.545424
$527$	−2.37781	−	1.37283i	−0.103579	−	0.0598013i
$528$	−2.64610	+	1.52773i	−0.115157	+	0.0664858i
$529$	−9.89823	−	17.1442i	−0.430358	−	0.745402i
$530$	10.9907	+	6.84223i	0.477405	+	0.297207i
$531$	−5.97792			−0.259420
$532$		0			0
$533$			10.9632i			0.474868i
$534$	8.75413	−	15.1626i	0.378828	−	0.656149i
$535$	−5.03629	−	9.43381i	−0.217738	−	0.407859i
$536$	−0.632805	−	1.09605i	−0.0273330	−	0.0473422i
$537$	−21.1711	−	12.2232i	−0.913602	−	0.527469i
$538$		−	18.9666i		−	0.817708i
$539$		0			0
$540$	2.23483	+	0.0743018i	0.0961719	+	0.00319744i
$541$	−12.3765	+	21.4368i	−0.532108	+	0.921638i	0.467189	+	0.884157i	$0.345267\pi$
$541$	−12.3765	+	21.4368i	−0.532108	+	0.921638i	−0.999297	+	0.0374808i	$0.988067\pi$
$542$	−17.0294	+	9.83192i	−0.731475	+	0.422317i
$543$	−14.7041	+	8.48940i	−0.631012	+	0.364315i
$544$	−1.45342	+	2.51741i	−0.0623151	+	0.107933i
$545$	0.676410	−	20.3449i	0.0289742	−	0.871481i
$546$		0			0
$547$			44.0524i			1.88354i	0.336253	+	0.941772i	$0.390840\pi$
$547$			44.0524i			1.88354i	−0.336253	+	0.941772i	$0.609160\pi$
$548$	−8.54508	−	4.93351i	−0.365028	−	0.210749i
$549$	0.222905	+	0.386083i	0.00951337	+	0.0164776i
$550$	−13.7086	+	6.74298i	−0.584539	+	0.287522i
$551$	−6.17371	+	10.6932i	−0.263009	+	0.455545i
$552$		−	1.78984i		−	0.0761808i
$553$		0			0
$554$	6.13998			0.260863
$555$	−20.3349	−	12.6594i	−0.863167	−	0.537362i
$556$	−8.48159	−	14.6906i	−0.359700	−	0.623018i
$557$	1.79249	−	1.03490i	0.0759504	−	0.0438500i	−0.461544	−	0.887117i	$-0.652704\pi$
$557$	1.79249	−	1.03490i	0.0759504	−	0.0438500i	0.537494	+	0.843267i	$0.319371\pi$
$558$	−0.818002	−	0.472274i	−0.0346288	−	0.0199929i
$559$	−17.2365			−0.729028
$560$		0			0
$561$	8.88174			0.374987
$562$	−10.5075	−	6.06649i	−0.443231	−	0.255900i
$563$	8.52596	−	4.92246i	0.359326	−	0.207457i	−0.309459	−	0.950913i	$-0.600148\pi$
$563$	8.52596	−	4.92246i	0.359326	−	0.207457i	0.668785	+	0.743456i	$0.266815\pi$
$564$	5.68826	+	9.85235i	0.239519	+	0.414859i
$565$	−17.0153	+	27.3318i	−0.715839	+	1.14986i
$566$	−17.4172			−0.732101
$567$		0			0
$568$		−	14.8523i		−	0.623188i
$569$	6.87805	−	11.9131i	0.288343	−	0.499425i	−0.685071	−	0.728476i	$-0.740229\pi$
$569$	6.87805	−	11.9131i	0.288343	−	0.499425i	0.973414	+	0.229051i	$0.0735623\pi$
$570$	4.35970	−	2.32745i	0.182608	−	0.0974861i
$571$	−9.60354	−	16.6338i	−0.401896	−	0.696104i	0.592059	−	0.805895i	$-0.298315\pi$
$571$	−9.60354	−	16.6338i	−0.401896	−	0.696104i	−0.993955	+	0.109791i	$0.964982\pi$
$572$	−4.34288	−	2.50736i	−0.181585	−	0.104838i
$573$			0.741377i			0.0309715i
$574$		0			0
$575$	0.594414	−	8.92945i	0.0247888	−	0.372384i
$576$	−0.500000	+	0.866025i	−0.0208333	+	0.0360844i
$577$	32.3090	−	18.6536i	1.34504	−	0.776560i	0.357500	−	0.933913i	$-0.383629\pi$
$577$	32.3090	−	18.6536i	1.34504	−	0.776560i	0.987542	+	0.157353i	$0.0502960\pi$
$578$	−7.40471	+	4.27511i	−0.307996	+	0.177821i
$579$	−3.05545	+	5.29220i	−0.126980	+	0.219936i
$580$	0.415100	−	12.4853i	0.0172361	−	0.518423i
$581$		0			0
$582$			10.4476i			0.433066i
$583$	15.3205	+	8.84530i	0.634510	+	0.366335i
$584$	3.95818	+	6.85577i	0.163791	+	0.283694i
$585$	1.72834	+	3.23746i	0.0714580	+	0.133853i
$586$	11.8761	−	20.5700i	0.490596	−	0.849737i
$587$			19.5459i			0.806748i	0.915035	+	0.403374i	$0.132163\pi$
$587$			19.5459i			0.806748i	−0.915035	+	0.403374i	$0.867837\pi$
$588$		0			0
$589$	−2.08760			−0.0860180
$590$	7.06449	−	11.3477i	0.290840	−	0.467178i
$591$	−10.3416	−	17.9122i	−0.425397	−	0.736810i
$592$	9.27713	−	5.35615i	0.381288	−	0.220137i
$593$	25.0648	+	14.4712i	1.02929	+	0.594260i	0.916781	−	0.399391i	$-0.130778\pi$
$593$	25.0648	+	14.4712i	1.02929	+	0.594260i	0.112508	+	0.993651i	$0.464112\pi$
$594$	3.05545			0.125367
$595$		0			0
$596$	8.04810			0.329663
$597$	10.4531	+	6.03509i	0.427816	+	0.247000i
$598$	2.54400	−	1.46878i	0.104032	−	0.0600629i
$599$	−4.86585	−	8.42790i	−0.198813	−	0.344355i	0.749331	−	0.662196i	$-0.230375\pi$
$599$	−4.86585	−	8.42790i	−0.198813	−	0.344355i	−0.948144	+	0.317841i	$0.897042\pi$
$600$	−2.78209	+	4.15451i	−0.113578	+	0.169607i
$601$	33.4038			1.36257			0.681284	−	0.732019i	$-0.261422\pi$
$601$	33.4038			1.36257			0.681284	+	0.732019i	$0.261422\pi$
$602$		0			0
$603$			1.26561i			0.0515396i
$604$	−4.98896	+	8.64113i	−0.202998	+	0.351603i
$605$	3.28277	−	1.75253i	0.133464	−	0.0712504i
$606$	−7.72747	−	13.3844i	−0.313907	−	0.543703i
$607$	37.4433	+	21.6179i	1.51978	+	0.877444i	0.999728	+	0.0233069i	$0.00741949\pi$
$607$	37.4433	+	21.6179i	1.51978	+	0.877444i	0.520049	+	0.854137i	$0.325914\pi$
$608$			2.21016i			0.0896337i
$609$		0			0
$610$	−0.996313	−	0.0331245i	−0.0403395	−	0.00134117i
$611$	−9.33579	+	16.1701i	−0.377686	+	0.654171i
$612$	2.51741	−	1.45342i	0.101760	−	0.0587512i
$613$	−1.55038	+	0.895115i	−0.0626195	+	0.0361534i	−0.530983	−	0.847383i	$-0.678177\pi$
$613$	−1.55038	+	0.895115i	−0.0626195	+	0.0361534i	0.468363	+	0.883536i	$0.344844\pi$
$614$	−3.95406	+	6.84864i	−0.159573	+	0.276388i
$615$	14.9283	+	0.496323i	0.601967	+	0.0200137i
$616$		0			0
$617$			38.2665i			1.54055i	0.637712	+	0.770275i	$0.279881\pi$
$617$			38.2665i			1.54055i	−0.637712	+	0.770275i	$0.720119\pi$
$618$	−2.70688	−	1.56282i	−0.108887	−	0.0628657i
$619$	0.0664943	+	0.115171i	0.00267263	+	0.00462913i	0.867359	−	0.497684i	$-0.165816\pi$
$619$	0.0664943	+	0.115171i	0.00267263	+	0.00462913i	−0.864686	+	0.502313i	$0.832483\pi$
$620$	1.86319	−	0.994674i	0.0748275	−	0.0399471i
$621$	−0.894921	+	1.55005i	−0.0359120	+	0.0622013i
$622$			10.0772i			0.404058i
$623$		0			0
$624$	−1.64124			−0.0657022
$625$	−15.2595	+	19.8027i	−0.610379	+	0.792110i
$626$	−10.1922	−	17.6534i	−0.407362	−	0.705572i
$627$	5.84830	−	3.37652i	0.233558	−	0.134845i
$628$	10.9705	+	6.33381i	0.437770	+	0.252747i
$629$	−31.1391			−1.24160
$630$		0			0
$631$	−25.1850			−1.00260			−0.501299	−	0.865274i	$-0.667145\pi$
$631$	−25.1850			−1.00260			−0.501299	+	0.865274i	$0.667145\pi$
$632$	12.3833	+	7.14949i	0.492580	+	0.284391i
$633$	2.55610	−	1.47577i	0.101596	−	0.0586565i
$634$	−0.160531	−	0.278048i	−0.00637551	−	0.0110427i
$635$	−9.99069	+	16.0481i	−0.396469	+	0.636849i
$636$	5.78984			0.229582
$637$		0			0
$638$		−	17.0698i		−	0.675800i
$639$	−7.42614	+	12.8625i	−0.293774	+	0.508831i
$640$	−1.05307	−	1.97257i	−0.0416262	−	0.0779728i
$641$	12.2953	+	21.2961i	0.485635	+	0.841144i	0.999864	−	0.0165088i	$-0.00525514\pi$
$641$	12.2953	+	21.2961i	0.485635	+	0.841144i	−0.514229	+	0.857653i	$0.671922\pi$
$642$	−4.14176	−	2.39124i	−0.163462	−	0.0943749i
$643$			9.15126i			0.360891i	0.983585	+	0.180445i	$0.0577539\pi$
$643$			9.15126i			0.360891i	−0.983585	+	0.180445i	$0.942246\pi$
$644$		0			0
$645$	−0.780329	+	23.4706i	−0.0307254	+	0.924152i
$646$	3.21230	−	5.56386i	0.126386	−	0.218907i
$647$	27.6494	−	15.9634i	1.08701	−	0.627585i	0.154231	−	0.988035i	$-0.450710\pi$
$647$	27.6494	−	15.9634i	1.08701	−	0.627585i	0.932779	+	0.360450i	$0.117377\pi$
$648$	0.866025	−	0.500000i	0.0340207	−	0.0196419i
$649$	9.13262	−	15.8182i	0.358487	−	0.620917i
$650$	−8.18807	−	0.545062i	−0.321163	−	0.0213791i
$651$		0			0
$652$			23.5646i			0.922861i
$653$	−2.65215	−	1.53122i	−0.103787	−	0.0599213i	0.447208	−	0.894430i	$-0.352418\pi$
$653$	−2.65215	−	1.53122i	−0.103787	−	0.0599213i	−0.550995	+	0.834509i	$0.685752\pi$
$654$	−4.55178	−	7.88391i	−0.177989	−	0.308285i
$655$	−16.4139	+	8.76266i	−0.641344	+	0.342385i
$656$	−3.33991	+	5.78490i	−0.130402	+	0.225862i
$657$		−	7.91636i		−	0.308847i
$658$		0			0
$659$	9.16636			0.357071			0.178535	−	0.983934i	$-0.442864\pi$
$659$	9.16636			0.357071			0.178535	+	0.983934i	$0.442864\pi$
$660$	−3.61082	+	5.80008i	−0.140551	+	0.225768i
$661$	−15.7091	−	27.2089i	−0.611012	−	1.05830i	−0.991070	−	0.133341i	$-0.957429\pi$
$661$	−15.7091	−	27.2089i	−0.611012	−	1.05830i	0.380058	−	0.924963i	$-0.375904\pi$
$662$	14.3833	−	8.30419i	0.559022	−	0.322752i
$663$	4.13166	+	2.38542i	0.160461	+	0.0926419i
$664$	−0.874366			−0.0339320
$665$		0			0
$666$	−10.7123			−0.415093
$667$	8.65962	+	4.99963i	0.335302	+	0.193587i
$668$	15.6593	−	9.04092i	0.605878	−	0.349804i
$669$	−5.88388	−	10.1912i	−0.227484	−	0.394014i
$670$	−2.40247	−	1.49565i	−0.0928156	−	0.0577821i
$671$	−1.36215			−0.0525854
$672$		0			0
$673$			6.45100i			0.248668i	0.992240	+	0.124334i	$0.0396794\pi$
$673$			6.45100i			0.248668i	−0.992240	+	0.124334i	$0.960321\pi$
$674$	−0.955589	+	1.65513i	−0.0368079	+	0.0637532i
$675$	4.48662	−	2.20687i	0.172690	−	0.0849424i
$676$	5.15317	+	8.92555i	0.198199	+	0.343290i
$677$	−5.20814	−	3.00692i	−0.200165	−	0.115565i	0.396567	−	0.918006i	$-0.370201\pi$
$677$	−5.20814	−	3.00692i	−0.200165	−	0.115565i	−0.596732	+	0.802440i	$0.703535\pi$
$678$			14.3982i			0.552961i
$679$		0			0
$680$	−0.215984	+	6.49632i	−0.00828261	+	0.249123i
$681$	−6.61827	+	11.4632i	−0.253613	+	0.439270i
$682$	2.49937	−	1.44301i	0.0957057	−	0.0552557i
$683$	7.72675	−	4.46104i	0.295656	−	0.170697i	−0.344834	−	0.938664i	$-0.612065\pi$
$683$	7.72675	−	4.46104i	0.295656	−	0.170697i	0.640490	+	0.767967i	$0.278731\pi$
$684$	1.10508	−	1.91405i	0.0422537	−	0.0731856i
$685$	−22.0511	−	0.733137i	−0.842530	−	0.0280117i
$686$		0			0
$687$		−	25.2448i		−	0.963148i
$688$	−9.09513	−	5.25107i	−0.346749	−	0.200195i
$689$	4.75126	+	8.22942i	0.181009	+	0.313516i
$690$	−1.88483	−	3.53060i	−0.0717542	−	0.134407i
$691$	−23.8290	+	41.2731i	−0.906499	+	1.57010i	−0.0876076	+	0.996155i	$0.527922\pi$
$691$	−23.8290	+	41.2731i	−0.906499	+	1.57010i	−0.818892	+	0.573948i	$0.805411\pi$
$692$			1.93845i			0.0736887i
$693$		0			0
$694$	7.90812			0.300188
$695$	−32.2007	−	20.0465i	−1.22144	−	0.760406i
$696$	−2.79334	−	4.83820i	−0.105881	−	0.183392i
$697$	16.8158	−	9.70862i	0.636945	−	0.367740i
$698$	20.3752	+	11.7636i	0.771214	+	0.445260i
$699$	−3.32842			−0.125892
$700$		0			0
$701$	31.0788			1.17383			0.586914	−	0.809649i	$-0.300343\pi$
$701$	31.0788			1.17383			0.586914	+	0.809649i	$0.300343\pi$
$702$	1.42135	+	0.820620i	0.0536456	+	0.0309723i
$703$	−20.5039	+	11.8379i	−0.773320	+	0.446476i
$704$	−1.52773	−	2.64610i	−0.0575784	−	0.0997286i
$705$	21.5957	+	13.4444i	0.813342	+	0.506344i
$706$	−22.9718			−0.864556
$707$		0			0
$708$		−	5.97792i		−	0.224664i
$709$	−6.09074	+	10.5495i	−0.228742	+	0.396194i	−0.957436	−	0.288647i	$-0.906795\pi$
$709$	−6.09074	+	10.5495i	−0.228742	+	0.396194i	0.728693	+	0.684840i	$0.240128\pi$
$710$	−15.6405	−	29.2972i	−0.586977	−	1.09950i
$711$	−7.14949	−	12.3833i	−0.268127	−	0.464409i
$712$	15.1626	+	8.75413i	0.568242	+	0.328075i
$713$			1.69059i			0.0633131i
$714$		0			0
$715$	−11.2071	−	0.372603i	−0.419121	−	0.0139346i
$716$	12.2232	−	21.1711i	0.456801	−	0.791203i
$717$	−21.5392	+	12.4357i	−0.804396	+	0.464418i
$718$	9.54913	−	5.51319i	0.356370	−	0.205750i
$719$	−15.9948	+	27.7038i	−0.596505	+	1.03318i	0.396828	+	0.917893i	$0.370111\pi$
$719$	−15.9948	+	27.7038i	−0.596505	+	1.03318i	−0.993333	+	0.115284i	$0.963222\pi$
$720$	−0.0743018	+	2.23483i	−0.00276906	+	0.0832873i
$721$		0			0
$722$			14.1152i			0.525314i
$723$	−8.96643	−	5.17677i	−0.333465	−	0.192526i
$724$	−8.48940	−	14.7041i	−0.315506	−	0.546473i
$725$	−12.3291	−	25.0653i	−0.457890	−	0.930900i
$726$	0.832104	−	1.44125i	0.0308823	−	0.0534897i
$727$			22.9992i			0.852995i	0.904489	+	0.426497i	$0.140253\pi$
$727$			22.9992i			0.852995i	−0.904489	+	0.426497i	$0.859747\pi$
$728$		0			0
$729$	−1.00000			−0.0370370
$730$	15.0274	+	9.35527i	0.556189	+	0.346254i
$731$	15.2641	+	26.4382i	0.564562	+	0.977851i
$732$	−0.386083	+	0.222905i	−0.0142701	+	0.00823882i
$733$	15.2422	+	8.80006i	0.562982	+	0.325038i	0.754341	−	0.656482i	$-0.227956\pi$
$733$	15.2422	+	8.80006i	0.562982	+	0.325038i	−0.191360	+	0.981520i	$0.561290\pi$
$734$	−10.1446			−0.374446
$735$		0			0
$736$	1.78984			0.0659745
$737$	−3.34893	−	1.93351i	−0.123359	−	0.0712216i
$738$	5.78490	−	3.33991i	0.212945	−	0.122944i
$739$	−0.0870500	−	0.150775i	−0.00320218	−	0.00554635i	0.864420	−	0.502771i	$-0.167686\pi$
$739$	−0.0870500	−	0.150775i	−0.00320218	−	0.00554635i	−0.867622	+	0.497224i	$0.834353\pi$
$740$	12.6594	−	20.3349i	0.465369	−	0.747525i
$741$	3.62740			0.133256
$742$		0			0
$743$			53.6360i			1.96771i	0.178957	+	0.983857i	$0.442728\pi$
$743$			53.6360i			1.96771i	−0.178957	+	0.983857i	$0.557272\pi$
$744$	0.472274	−	0.818002i	0.0173144	−	0.0299894i
$745$	15.8755	−	8.47521i	0.581632	−	0.310508i
$746$	13.2511	+	22.9515i	0.485156	+	0.840315i
$747$	0.757223	+	0.437183i	0.0277053	+	0.0159957i
$748$			8.88174i			0.324749i
$749$		0			0
$750$	−1.11289	+	11.1248i	−0.0406369	+	0.406221i
$751$	−14.5466	+	25.1954i	−0.530812	+	0.919393i	0.468542	+	0.883441i	$0.344779\pi$
$751$	−14.5466	+	25.1954i	−0.530812	+	0.919393i	−0.999354	+	0.0359513i	$0.988554\pi$
$752$	−9.85235	+	5.68826i	−0.359278	+	0.207429i
$753$	14.3329	−	8.27512i	0.522321	−	0.301562i
$754$	4.58453	−	7.94064i	0.166959	−	0.289181i
$755$	−0.741377	+	22.2990i	−0.0269815	+	0.811543i
$756$		0			0
$757$			34.0842i			1.23881i	0.785072	+	0.619405i	$0.212626\pi$
$757$			34.0842i			1.23881i	−0.785072	+	0.619405i	$0.787374\pi$
$758$	−25.4734	−	14.7071i	−0.925237	−	0.534186i
$759$	−2.73439	−	4.73610i	−0.0992521	−	0.171910i
$760$	2.32745	+	4.35970i	0.0844254	+	0.158143i
$761$	3.81479	−	6.60741i	0.138286	−	0.239519i	−0.788562	−	0.614955i	$-0.789174\pi$
$761$	3.81479	−	6.60741i	0.138286	−	0.239519i	0.926848	+	0.375437i	$0.122507\pi$
$762$			8.45405i			0.306258i
$763$		0			0
$764$	−0.741377			−0.0268221
$765$	3.43521	−	5.51799i	0.124200	−	0.199503i
$766$	−1.82125	−	3.15449i	−0.0658043	−	0.113976i
$767$	8.49674	−	4.90560i	0.306800	−	0.177131i
$768$	−0.866025	−	0.500000i	−0.0312500	−	0.0180422i
$769$	37.8241			1.36397			0.681986	−	0.731365i	$-0.261117\pi$
$769$	37.8241			1.36397			0.681986	+	0.731365i	$0.261117\pi$
$770$		0			0
$771$	−24.4546			−0.880710
$772$	−5.29220	−	3.05545i	−0.190470	−	0.109968i
$773$	−21.8541	+	12.6174i	−0.786036	+	0.453818i	−0.838565	−	0.544801i	$-0.816605\pi$
$773$	−21.8541	+	12.6174i	−0.786036	+	0.453818i	0.0525292	+	0.998619i	$0.483272\pi$
$774$	5.25107	+	9.09513i	0.188746	+	0.326918i
$775$	2.62782	−	3.92413i	0.0943939	−	0.140959i
$776$	−10.4476			−0.375046
$777$		0			0
$778$		−	23.7938i		−	0.853048i
$779$	7.38173	−	12.7855i	0.264478	−	0.458089i
$780$	−3.23746	+	1.72834i	−0.115920	+	0.0618845i
$781$	−22.6902	−	39.3006i	−0.811920	−	1.40629i
$782$	−4.50576	−	2.60140i	−0.161126	−	0.0930259i
$783$			5.58667i			0.199651i
$784$		0			0
$785$	28.3100	+	0.941227i	1.01043	+	0.0335938i
$786$	−4.16053	+	7.20625i	−0.148401	+	0.257038i
$787$	19.6755	−	11.3596i	0.701355	−	0.404928i	−0.106497	−	0.994313i	$-0.533963\pi$
$787$	19.6755	−	11.3596i	0.701355	−	0.404928i	0.807852	+	0.589385i	$0.200630\pi$
$788$	17.9122	−	10.3416i	0.638096	−	0.368405i
$789$	−6.25457	+	10.8332i	−0.222669	+	0.385673i
$790$	31.9558	+	1.06244i	1.13694	+	0.0377999i
$791$		0			0
$792$			3.05545i			0.108571i
$793$	−0.633655	−	0.365841i	−0.0225018	−	0.0129914i
$794$	4.88065	+	8.45353i	0.173208	+	0.300004i
$795$	11.4209	−	6.09711i	0.405057	−	0.216242i
$796$	−6.03509	+	10.4531i	−0.213908	+	0.370500i
$797$			10.1057i			0.357963i	0.983852	+	0.178981i	$0.0572802\pi$
$797$			10.1057i			0.357963i	−0.983852	+	0.178981i	$0.942720\pi$
$798$		0			0
$799$	33.0698			1.16993
$800$	−4.15451	−	2.78209i	−0.146884	−	0.0983617i
$801$	−8.75413	−	15.1626i	−0.309312	−	0.535744i
$802$	−8.64113	+	4.98896i	−0.305129	+	0.176166i
$803$	20.9475	+	12.0940i	0.739221	+	0.426789i
$804$	−1.26561			−0.0446346
$805$		0			0
$806$	1.55023			0.0546045
$807$	−16.4256	−	9.48330i	−0.578207	−	0.333828i
$808$	13.3844	−	7.72747i	0.470860	−	0.271851i
$809$	23.1590	+	40.1126i	0.814227	+	1.41028i	0.909881	+	0.414868i	$0.136172\pi$
$809$	23.1590	+	40.1126i	0.814227	+	1.41028i	−0.0956543	+	0.995415i	$0.530494\pi$
$810$	1.18176	−	1.89827i	0.0415229	−	0.0666985i
$811$	−42.0012			−1.47486			−0.737431	−	0.675422i	$-0.763961\pi$
$811$	−42.0012			−1.47486			−0.737431	+	0.675422i	$0.763961\pi$
$812$		0			0
$813$			19.6638i			0.689641i
$814$	16.3655	−	28.3458i	0.573610	−	0.993521i
$815$	24.8151	+	46.4829i	0.869237	+	1.62822i
$816$	1.45342	+	2.51741i	0.0508800	+	0.0881268i
$817$	20.1017	+	11.6057i	0.703268	+	0.406032i
$818$			35.1837i			1.23017i
$819$		0			0
$820$	−0.496323	+	14.9283i	−0.0173323	+	0.521319i
$821$	−8.44903	+	14.6341i	−0.294873	+	0.510735i	−0.974955	−	0.222401i	$-0.928611\pi$
$821$	−8.44903	+	14.6341i	−0.294873	+	0.510735i	0.680082	+	0.733136i	$0.261944\pi$
$822$	−8.54508	+	4.93351i	−0.298044	+	0.172076i
$823$	−39.1791	+	22.6200i	−1.36570	+	0.788485i	−0.990375	−	0.138410i	$-0.955801\pi$
$823$	−39.1791	+	22.6200i	−1.36570	+	0.788485i	−0.375321	+	0.926895i	$0.622468\pi$
$824$	1.56282	−	2.70688i	0.0544433	−	0.0942986i
$825$	−1.01473	+	15.2435i	−0.0353283	+	0.530711i
$826$		0			0
$827$		−	34.5452i		−	1.20125i	−0.799529	−	0.600627i	$-0.794918\pi$
$827$		−	34.5452i		−	1.20125i	0.799529	−	0.600627i	$-0.205082\pi$
$828$	−1.55005	−	0.894921i	−0.0538679	−	0.0311007i
$829$	−4.99802	−	8.65682i	−0.173588	−	0.300664i	0.766083	−	0.642741i	$-0.222203\pi$
$829$	−4.99802	−	8.65682i	−0.173588	−	0.300664i	−0.939672	+	0.342077i	$0.888870\pi$
$830$	−1.72475	+	0.920768i	−0.0598670	+	0.0319603i
$831$	3.06999	−	5.31737i	0.106497	−	0.184458i
$832$		−	1.64124i		−	0.0568997i
$833$		0			0
$834$	−16.9632			−0.587387
$835$	21.3685	−	34.3242i	0.739486	−	1.18784i
$836$	3.37652	+	5.84830i	0.116779	+	0.202268i
$837$	−0.818002	+	0.472274i	−0.0282743	+	0.0163242i
$838$	−16.1318	−	9.31371i	−0.557264	−	0.321737i
$839$	−32.3180			−1.11574			−0.557871	−	0.829928i	$-0.688382\pi$
$839$	−32.3180			−1.11574			−0.557871	+	0.829928i	$0.688382\pi$
$840$		0			0
$841$	2.21091			0.0762383
$842$	27.4066	+	15.8232i	0.944494	+	0.545304i
$843$	−10.5075	+	6.06649i	−0.361897	+	0.208941i
$844$	1.47577	+	2.55610i	0.0507980	+	0.0879847i
$845$	19.5642	+	12.1797i	0.673030	+	0.418993i
$846$	11.3765			0.391133
$847$		0			0
$848$			5.78984i			0.198824i
$849$	−8.70862	+	15.0838i	−0.298879	+	0.517674i
$850$	6.41503	+	13.0419i	0.220034	+	0.447334i
$851$	9.58667	+	16.6046i	0.328627	+	0.569199i
$852$	−12.8625	−	7.42614i	−0.440660	−	0.254415i
$853$		−	13.7577i		−	0.471056i	−0.971868	−	0.235528i	$-0.924318\pi$
$853$		−	13.7577i		−	0.471056i	0.971868	−	0.235528i	$-0.0756820\pi$
$854$		0			0
$855$	0.164219	−	4.93933i	0.00561616	−	0.168922i
$856$	2.39124	−	4.14176i	0.0817310	−	0.141562i
$857$	−6.45804	+	3.72855i	−0.220602	+	0.127365i	−0.606229	−	0.795290i	$-0.707319\pi$
$857$	−6.45804	+	3.72855i	−0.220602	+	0.127365i	0.385627	+	0.922655i	$0.373985\pi$
$858$	−4.34288	+	2.50736i	−0.148264	+	0.0856000i
$859$	−16.9430	+	29.3462i	−0.578088	+	1.00128i	0.417610	+	0.908626i	$0.362868\pi$
$859$	−16.9430	+	29.3462i	−0.578088	+	1.00128i	−0.995699	+	0.0926521i	$0.970466\pi$
$860$	−23.4706	−	0.780329i	−0.800339	−	0.0266090i
$861$		0			0
$862$			14.8046i			0.504246i
$863$	−35.7532	−	20.6421i	−1.21705	−	0.702666i	−0.252767	−	0.967527i	$-0.581341\pi$
$863$	−35.7532	−	20.6421i	−1.21705	−	0.702666i	−0.964287	+	0.264861i	$0.914674\pi$
$864$	0.500000	+	0.866025i	0.0170103	+	0.0294628i
$865$	2.04132	+	3.82373i	0.0694069	+	0.130011i
$866$	−2.12365	+	3.67828i	−0.0721647	+	0.124993i
$867$			8.55023i			0.290381i
$868$		0			0
$869$	43.6899			1.48208
$870$	−10.6050	−	6.60213i	−0.359544	−	0.223833i
$871$	−1.03858	−	1.79888i	−0.0351911	−	0.0609528i
$872$	7.88391	−	4.55178i	0.266983	−	0.154143i
$873$	9.04787	+	5.22379i	0.306224	+	0.176799i
$874$	−3.95583			−0.133808
$875$		0			0
$876$	7.91636			0.267469
$877$	−23.2041	−	13.3969i	−0.783546	−	0.452380i	0.0541396	−	0.998533i	$-0.482758\pi$
$877$	−23.2041	−	13.3969i	−0.783546	−	0.452380i	−0.837685	+	0.546153i	$0.816092\pi$
$878$	−1.93020	+	1.11440i	−0.0651410	+	0.0376091i
$879$	−11.8761	−	20.5700i	−0.400570	−	0.693808i
$880$	−5.80008	−	3.61082i	−0.195521	−	0.121721i
$881$	31.0247			1.04525			0.522625	−	0.852563i	$-0.324953\pi$
$881$	31.0247			1.04525			0.522625	+	0.852563i	$0.324953\pi$
$882$		0			0
$883$			39.6123i			1.33306i	0.745478	+	0.666530i	$0.232221\pi$
$883$			39.6123i			1.33306i	−0.745478	+	0.666530i	$0.767779\pi$
$884$	−2.38542	+	4.13166i	−0.0802303	+	0.138963i
$885$	−6.29516	−	11.7919i	−0.211610	−	0.396380i
$886$	2.32106	+	4.02020i	0.0779776	+	0.135061i
$887$	−10.2583	−	5.92266i	−0.344441	−	0.198863i	0.317793	−	0.948160i	$-0.397058\pi$
$887$	−10.2583	−	5.92266i	−0.344441	−	0.198863i	−0.662234	+	0.749297i	$0.730392\pi$
$888$		−	10.7123i		−	0.359481i
$889$		0			0
$890$	39.1280	+	1.30089i	1.31157	+	0.0436061i
$891$	1.52773	−	2.64610i	0.0511808	−	0.0886477i
$892$	10.1912	−	5.88388i	0.341226	−	0.197007i
$893$	21.7752	−	12.5719i	0.728681	−	0.420704i
$894$	4.02405	−	6.96986i	0.134584	−	0.233107i
$895$	1.81641	−	54.6335i	0.0607158	−	1.82620i
$896$		0			0
$897$		−	2.93756i		−	0.0980823i
$898$	3.19615	+	1.84530i	0.106657	+	0.0615783i
$899$	2.63844	+	4.56991i	0.0879968	+	0.152415i
$900$	2.20687	+	4.48662i	0.0735623	+	0.149554i
$901$	8.41510	−	14.5754i	0.280348	−	0.485576i
$902$			20.4099i			0.679575i
$903$		0			0
$904$	−14.3982			−0.478878
$905$	−32.2304	−	20.0649i	−1.07137	−	0.666981i
$906$	4.98896	+	8.64113i	0.165747	+	0.287082i
$907$	−14.7093	+	8.49244i	−0.488416	+	0.281987i	−0.723917	−	0.689887i	$-0.757660\pi$
$907$	−14.7093	+	8.49244i	−0.488416	+	0.281987i	0.235501	+	0.971874i	$0.424327\pi$
$908$	−11.4632	−	6.61827i	−0.380419	−	0.219635i
$909$	−15.4549			−0.512608
$910$		0			0
$911$	15.5723			0.515934			0.257967	−	0.966154i	$-0.416947\pi$
$911$	15.5723			0.515934			0.257967	+	0.966154i	$0.416947\pi$
$912$	1.91405	+	1.10508i	0.0633806	+	0.0365928i
$913$	−2.31366	+	1.33579i	−0.0765709	+	0.0442082i
$914$	−1.36486	−	2.36401i	−0.0451456	−	0.0781945i
$915$	−0.526843	+	0.846270i	−0.0174169	+	0.0279768i
$916$	25.2448			0.834111
$917$		0			0
$918$		−	2.90685i		−	0.0959403i
$919$	−18.4816	+	32.0111i	−0.609652	+	1.05595i	0.381646	+	0.924308i	$0.375357\pi$
$919$	−18.4816	+	32.0111i	−0.609652	+	1.05595i	−0.991298	+	0.131639i	$0.957976\pi$
$920$	3.53060	−	1.88483i	0.116400	−	0.0621410i
$921$	3.95406	+	6.84864i	0.130291	+	0.225670i
$922$	10.2254	+	5.90362i	0.336754	+	0.194425i
$923$		−	24.3761i		−	0.802351i
$924$		0			0
$925$	3.55760	−	53.4433i	0.116973	−	1.75720i
$926$	−1.20280	+	2.08332i	−0.0395266	+	0.0684620i
$927$	−2.70688	+	1.56282i	−0.0889056	+	0.0513296i
$928$	4.83820	−	2.79334i	0.158822	−	0.0916958i
$929$	16.9916	−	29.4302i	0.557475	−	0.965575i	−0.440232	−	0.897884i	$-0.645104\pi$
$929$	16.9916	−	29.4302i	0.557475	−	0.965575i	0.997706	−	0.0676903i	$-0.0215630\pi$
$930$	0.0701816	−	2.11091i	0.00230134	−	0.0692193i
$931$		0			0
$932$		−	3.32842i		−	0.109026i
$933$	8.72708	+	5.03858i	0.285712	+	0.164956i
$934$	−7.33058	−	12.6969i	−0.239864	−	0.415456i
$935$	9.35309	+	17.5199i	0.305879	+	0.572961i
$936$	−0.820620	+	1.42135i	−0.0268228	+	0.0464584i
$937$			43.1719i			1.41037i	0.709026	+	0.705183i	$0.249135\pi$
$937$			43.1719i			1.41037i	−0.709026	+	0.705183i	$0.750865\pi$
$938$		0			0
$939$	−20.3844			−0.665219
$940$	−13.4444	+	21.5957i	−0.438506	+	0.704375i
$941$	16.5593	+	28.6816i	0.539818	+	0.934992i	0.998913	+	0.0466053i	$0.0148403\pi$
$941$	16.5593	+	28.6816i	0.539818	+	0.934992i	−0.459095	+	0.888387i	$0.651826\pi$
$942$	10.9705	−	6.33381i	0.357438	−	0.206367i
$943$	−10.3541	−	5.97792i	−0.337174	−	0.194668i
$944$	5.97792			0.194565
$945$		0			0
$946$	−32.0888			−1.04330
$947$	36.5816	+	21.1204i	1.18874	+	0.686321i	0.958021	−	0.286698i	$-0.0925577\pi$
$947$	36.5816	+	21.1204i	1.18874	+	0.686321i	0.230723	+	0.973020i	$0.425891\pi$
$948$	12.3833	−	7.14949i	0.402190	−	0.232205i
$949$	6.49632	+	11.2520i	0.210880	+	0.365254i
$950$	9.18213	+	6.14886i	0.297908	+	0.199495i
$951$	−0.321063			−0.0104112
$952$		0			0
$953$		−	16.2358i		−	0.525929i	−0.964806	−	0.262964i	$-0.915300\pi$
$953$		−	16.2358i		−	0.525929i	0.964806	−	0.262964i	$-0.0847002\pi$
$954$	2.89492	−	5.01415i	0.0937265	−	0.162339i
$955$	−1.46242	+	0.780722i	−0.0473228	+	0.0252636i
$956$	−12.4357	−	21.5392i	−0.402198	−	0.696627i
$957$	−14.7829	−	8.53491i	−0.477863	−	0.275894i
$958$			11.8934i			0.384257i
$959$		0			0
$960$	−2.23483	−	0.0743018i	−0.0721289	−	0.00239808i
$961$	15.0539	−	26.0741i	0.485610	−	0.841101i
$962$	15.2260	−	8.79073i	0.490906	−	0.283424i
$963$	−4.14176	+	2.39124i	−0.133466	+	0.0770568i
$964$	5.17677	−	8.96643i	0.166733	−	0.288789i
$965$	−13.6569	−	0.454051i	−0.439630	−	0.0146164i
$966$		0			0
$967$			56.9706i			1.83205i	0.401121	+	0.916025i	$0.368621\pi$
$967$			56.9706i			1.83205i	−0.401121	+	0.916025i	$0.631379\pi$
$968$	1.44125	+	0.832104i	0.0463234	+	0.0267448i
$969$	−3.21230	−	5.56386i	−0.103194	−	0.178737i
$970$	−20.6086	+	11.0020i	−0.661703	+	0.353254i
$971$	24.1997	−	41.9152i	0.776606	−	1.34512i	−0.157281	−	0.987554i	$-0.550273\pi$
$971$	24.1997	−	41.9152i	0.776606	−	1.34512i	0.933887	−	0.357568i	$-0.116394\pi$
$972$		−	1.00000i		−	0.0320750i
$973$		0			0
$974$	35.5018			1.13755
$975$	−4.56608	+	6.81855i	−0.146231	+	0.218368i
$976$	−0.222905	−	0.386083i	−0.00713503	−	0.0123582i
$977$	−33.9829	+	19.6200i	−1.08721	+	0.627701i	−0.932832	−	0.360311i	$-0.882671\pi$
$977$	−33.9829	+	19.6200i	−1.08721	+	0.627701i	−0.154377	+	0.988012i	$0.549337\pi$
$978$	20.4075	+	11.7823i	0.652561	+	0.376756i
$979$	53.4956			1.70973
$980$		0			0
$981$	−9.10355			−0.290654
$982$	−0.847219	−	0.489142i	−0.0270358	−	0.0156091i
$983$	10.2583	−	5.92266i	0.327190	−	0.188903i	−0.327403	−	0.944885i	$-0.606173\pi$
$983$	10.2583	−	5.92266i	0.327190	−	0.188903i	0.654593	+	0.755981i	$0.272840\pi$
$984$	3.33991	+	5.78490i	0.106472	+	0.184416i
$985$	24.4427	−	39.2624i	0.778809	−	1.25100i
$986$	−16.2396			−0.517175
$987$		0			0
$988$			3.62740i			0.115403i
$989$	9.39860	−	16.2789i	0.298858	−	0.517637i
$990$	3.21760	+	6.02710i	0.102262	+	0.191554i
$991$	−3.07601	−	5.32780i	−0.0977126	−	0.169243i	0.813025	−	0.582229i	$-0.197819\pi$
$991$	−3.07601	−	5.32780i	−0.0977126	−	0.169243i	−0.910738	+	0.412986i	$0.864486\pi$
$992$	0.818002	+	0.472274i	0.0259716	+	0.0149947i
$993$		−	16.6084i		−	0.527051i
$994$		0			0
$995$	−0.896836	+	26.9748i	−0.0284316	+	0.855160i
$996$	−0.437183	+	0.757223i	−0.0138527	+	0.0239935i
$997$	43.0945	−	24.8806i	1.36482	−	0.787978i	0.374557	−	0.927204i	$-0.377795\pi$
$997$	43.0945	−	24.8806i	1.36482	−	0.787978i	0.990261	+	0.139226i	$0.0444614\pi$
$998$	10.1620	−	5.86701i	0.321671	−	0.185717i
$999$	−5.35615	+	9.27713i	−0.169461	+	0.293515i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1470.2.n.k.79.8		16
5.4	even	2	inner	1470.2.n.k.79.1		16
7.2	even	3		1470.2.g.k.589.2	yes	8
7.3	odd	6		1470.2.n.l.949.4		16
7.4	even	3	inner	1470.2.n.k.949.1		16
7.5	odd	6		1470.2.g.j.589.3	✓	8
7.6	odd	2		1470.2.n.l.79.5		16
35.2	odd	12		7350.2.a.du.1.1		4
35.4	even	6	inner	1470.2.n.k.949.8		16
35.9	even	6		1470.2.g.k.589.6	yes	8
35.12	even	12		7350.2.a.dt.1.1		4
35.19	odd	6		1470.2.g.j.589.7	yes	8
35.23	odd	12		7350.2.a.dr.1.1		4
35.24	odd	6		1470.2.n.l.949.5		16
35.33	even	12		7350.2.a.ds.1.1		4
35.34	odd	2		1470.2.n.l.79.4		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1470.2.g.j.589.3	✓	8	7.5	odd	6
1470.2.g.j.589.7	yes	8	35.19	odd	6
1470.2.g.k.589.2	yes	8	7.2	even	3
1470.2.g.k.589.6	yes	8	35.9	even	6
1470.2.n.k.79.1		16	5.4	even	2	inner
1470.2.n.k.79.8		16	1.1	even	1	trivial
1470.2.n.k.949.1		16	7.4	even	3	inner
1470.2.n.k.949.8		16	35.4	even	6	inner
1470.2.n.l.79.4		16	35.34	odd	2
1470.2.n.l.79.5		16	7.6	odd	2
1470.2.n.l.949.4		16	7.3	odd	6
1470.2.n.l.949.5		16	35.24	odd	6
7350.2.a.dr.1.1		4	35.23	odd	12
7350.2.a.ds.1.1		4	35.33	even	12
7350.2.a.dt.1.1		4	35.12	even	12
7350.2.a.du.1.1		4	35.2	odd	12

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 1470 = 2 \cdot 3 \cdot 5 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1470.n (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.866025 + 0.500000i) q^{2} +(0.866025 - 0.500000i) q^{3} +(0.500000 + 0.866025i) q^{4} +(1.89827 + 1.18176i) q^{5} +1.00000 q^{6} +1.00000i q^{8} +(0.500000 - 0.866025i) q^{9} +O(q^{10})\)	\(q+(0.866025 + 0.500000i) q^{2} +(0.866025 - 0.500000i) q^{3} +(0.500000 + 0.866025i) q^{4} +(1.89827 + 1.18176i) q^{5} +1.00000 q^{6} +1.00000i q^{8} +(0.500000 - 0.866025i) q^{9} +(1.05307 + 1.97257i) q^{10} +(1.52773 + 2.64610i) q^{11} +(0.866025 + 0.500000i) q^{12} +1.64124i q^{13} +(2.23483 + 0.0743018i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(2.51741 - 1.45342i) q^{17} +(0.866025 - 0.500000i) q^{18} +(1.10508 - 1.91405i) q^{19} +(-0.0743018 + 2.23483i) q^{20} +3.05545i q^{22} +(-1.55005 - 0.894921i) q^{23} +(0.500000 + 0.866025i) q^{24} +(2.20687 + 4.48662i) q^{25} +(-0.820620 + 1.42135i) q^{26} -1.00000i q^{27} -5.58667 q^{29} +(1.89827 + 1.18176i) q^{30} +(-0.472274 - 0.818002i) q^{31} +(-0.866025 + 0.500000i) q^{32} +(2.64610 + 1.52773i) q^{33} +2.90685 q^{34} +1.00000 q^{36} +(-9.27713 - 5.35615i) q^{37} +(1.91405 - 1.10508i) q^{38} +(0.820620 + 1.42135i) q^{39} +(-1.18176 + 1.89827i) q^{40} +6.67982 q^{41} +10.5021i q^{43} +(-1.52773 + 2.64610i) q^{44} +(1.97257 - 1.05307i) q^{45} +(-0.894921 - 1.55005i) q^{46} +(9.85235 + 5.68826i) q^{47} +1.00000i q^{48} +(-0.332104 + 4.98896i) q^{50} +(1.45342 - 2.51741i) q^{51} +(-1.42135 + 0.820620i) q^{52} +(5.01415 - 2.89492i) q^{53} +(0.500000 - 0.866025i) q^{54} +(-0.227026 + 6.82843i) q^{55} -2.21016i q^{57} +(-4.83820 - 2.79334i) q^{58} +(-2.98896 - 5.17703i) q^{59} +(1.05307 + 1.97257i) q^{60} +(-0.222905 + 0.386083i) q^{61} -0.944547i q^{62} -1.00000 q^{64} +(-1.93956 + 3.11552i) q^{65} +(1.52773 + 2.64610i) q^{66} +(-1.09605 + 0.632805i) q^{67} +(2.51741 + 1.45342i) q^{68} -1.78984 q^{69} -14.8523 q^{71} +(0.866025 + 0.500000i) q^{72} +(6.85577 - 3.95818i) q^{73} +(-5.35615 - 9.27713i) q^{74} +(4.15451 + 2.78209i) q^{75} +2.21016 q^{76} +1.64124i q^{78} +(7.14949 - 12.3833i) q^{79} +(-1.97257 + 1.05307i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(5.78490 + 3.33991i) q^{82} +0.874366i q^{83} +(6.49632 + 0.215984i) q^{85} +(-5.25107 + 9.09513i) q^{86} +(-4.83820 + 2.79334i) q^{87} +(-2.64610 + 1.52773i) q^{88} +(8.75413 - 15.1626i) q^{89} +(2.23483 + 0.0743018i) q^{90} -1.78984i q^{92} +(-0.818002 - 0.472274i) q^{93} +(5.68826 + 9.85235i) q^{94} +(4.35970 - 2.32745i) q^{95} +(-0.500000 + 0.866025i) q^{96} +10.4476i q^{97} +3.05545 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 8 q^{4} - 4 q^{5} + 16 q^{6} + 8 q^{9}+O(q^{10}) \) 16 * q + 8 * q^4 - 4 * q^5 + 16 * q^6 + 8 * q^9	\( 16 q + 8 q^{4} - 4 q^{5} + 16 q^{6} + 8 q^{9} - 8 q^{16} + 24 q^{19} - 8 q^{20} + 8 q^{24} - 4 q^{25} + 32 q^{29} - 4 q^{30} - 32 q^{31} - 16 q^{34} + 16 q^{36} + 48 q^{41} + 4 q^{45} - 8 q^{46} - 8 q^{50} - 8 q^{51} + 8 q^{54} + 40 q^{59} - 24 q^{61} - 16 q^{64} - 28 q^{65} - 16 q^{69} - 80 q^{71} - 16 q^{74} - 4 q^{75} + 48 q^{76} - 16 q^{79} - 4 q^{80} - 8 q^{81} + 56 q^{85} - 8 q^{86} + 88 q^{89} + 24 q^{94} - 24 q^{95} - 8 q^{96}+O(q^{100}) \) 16 * q + 8 * q^4 - 4 * q^5 + 16 * q^6 + 8 * q^9 - 8 * q^16 + 24 * q^19 - 8 * q^20 + 8 * q^24 - 4 * q^25 + 32 * q^29 - 4 * q^30 - 32 * q^31 - 16 * q^34 + 16 * q^36 + 48 * q^41 + 4 * q^45 - 8 * q^46 - 8 * q^50 - 8 * q^51 + 8 * q^54 + 40 * q^59 - 24 * q^61 - 16 * q^64 - 28 * q^65 - 16 * q^69 - 80 * q^71 - 16 * q^74 - 4 * q^75 + 48 * q^76 - 16 * q^79 - 4 * q^80 - 8 * q^81 + 56 * q^85 - 8 * q^86 + 88 * q^89 + 24 * q^94 - 24 * q^95 - 8 * q^96

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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