LMFDB - Embedded newform 390.2.f.a.259.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [390,2,Mod(259,390)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(390, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("390.259");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 390 = 2 \cdot 3 \cdot 5 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	390.f (of order $2$, degree $1$, 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:	$3.11416567883$
Analytic rank:	$0$
Dimension:	$6$
Coefficient field:	6.0.350464.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - 2x^{5} + 2x^{4} + 2x^{3} + 4x^{2} - 4x + 2 $ x^6 - 2x^5 + 2x^4 + 2x^3 + 4x^2 - 4*x + 2
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			259.3
Root			$0.403032 + 0.403032i$ of defining polynomial
Character	$\chi$	$=$	390.259
Dual form			390.2.f.a.259.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} -1.00000i q^{3} +1.00000 q^{4} +(1.48119 + 1.67513i) q^{5} +1.00000i q^{6} +4.15633 q^{7} -1.00000 q^{8} -1.00000 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} -1.00000i q^{3} +1.00000 q^{4} +(1.48119 + 1.67513i) q^{5} +1.00000i q^{6} +4.15633 q^{7} -1.00000 q^{8} -1.00000 q^{9} +(-1.48119 - 1.67513i) q^{10} +5.35026i q^{11} -1.00000i q^{12} +(-3.28726 - 1.48119i) q^{13} -4.15633 q^{14} +(1.67513 - 1.48119i) q^{15} +1.00000 q^{16} +1.19394i q^{17} +1.00000 q^{18} +2.80606i q^{19} +(1.48119 + 1.67513i) q^{20} -4.15633i q^{21} -5.35026i q^{22} -0.806063i q^{23} +1.00000i q^{24} +(-0.612127 + 4.96239i) q^{25} +(3.28726 + 1.48119i) q^{26} +1.00000i q^{27} +4.15633 q^{28} +7.50659 q^{29} +(-1.67513 + 1.48119i) q^{30} -7.92478i q^{31} -1.00000 q^{32} +5.35026 q^{33} -1.19394i q^{34} +(6.15633 + 6.96239i) q^{35} -1.00000 q^{36} +7.35026 q^{37} -2.80606i q^{38} +(-1.48119 + 3.28726i) q^{39} +(-1.48119 - 1.67513i) q^{40} -3.61213i q^{41} +4.15633i q^{42} -6.57452i q^{43} +5.35026i q^{44} +(-1.48119 - 1.67513i) q^{45} +0.806063i q^{46} -12.3127 q^{47} -1.00000i q^{48} +10.2750 q^{49} +(0.612127 - 4.96239i) q^{50} +1.19394 q^{51} +(-3.28726 - 1.48119i) q^{52} -5.53690i q^{53} -1.00000i q^{54} +(-8.96239 + 7.92478i) q^{55} -4.15633 q^{56} +2.80606 q^{57} -7.50659 q^{58} +12.8872i q^{59} +(1.67513 - 1.48119i) q^{60} +6.31265 q^{61} +7.92478i q^{62} -4.15633 q^{63} +1.00000 q^{64} +(-2.38787 - 7.70052i) q^{65} -5.35026 q^{66} +4.57452 q^{67} +1.19394i q^{68} -0.806063 q^{69} +(-6.15633 - 6.96239i) q^{70} -8.96239i q^{71} +1.00000 q^{72} -4.08110 q^{73} -7.35026 q^{74} +(4.96239 + 0.612127i) q^{75} +2.80606i q^{76} +22.2374i q^{77} +(1.48119 - 3.28726i) q^{78} -12.4387 q^{79} +(1.48119 + 1.67513i) q^{80} +1.00000 q^{81} +3.61213i q^{82} -10.0508 q^{83} -4.15633i q^{84} +(-2.00000 + 1.76845i) q^{85} +6.57452i q^{86} -7.50659i q^{87} -5.35026i q^{88} -5.03761i q^{89} +(1.48119 + 1.67513i) q^{90} +(-13.6629 - 6.15633i) q^{91} -0.806063i q^{92} -7.92478 q^{93} +12.3127 q^{94} +(-4.70052 + 4.15633i) q^{95} +1.00000i q^{96} -2.93207 q^{97} -10.2750 q^{98} -5.35026i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q - 6 q^{2} + 6 q^{4} - 2 q^{5} + 4 q^{7} - 6 q^{8} - 6 q^{9}+O(q^{10}) $ 6 * q - 6 * q^2 + 6 * q^4 - 2 * q^5 + 4 * q^7 - 6 * q^8 - 6 * q^9	$ 6 q - 6 q^{2} + 6 q^{4} - 2 q^{5} + 4 q^{7} - 6 q^{8} - 6 q^{9} + 2 q^{10} - 8 q^{13} - 4 q^{14} + 6 q^{16} + 6 q^{18} - 2 q^{20} - 2 q^{25} + 8 q^{26} + 4 q^{28} + 4 q^{29} - 6 q^{32} + 12 q^{33} + 16 q^{35} - 6 q^{36} + 24 q^{37} + 2 q^{39} + 2 q^{40} + 2 q^{45} - 32 q^{47} - 2 q^{49} + 2 q^{50} + 8 q^{51} - 8 q^{52} - 32 q^{55} - 4 q^{56} + 16 q^{57} - 4 q^{58} - 4 q^{61} - 4 q^{63} + 6 q^{64} - 16 q^{65} - 12 q^{66} + 4 q^{67} - 4 q^{69} - 16 q^{70} + 6 q^{72} + 40 q^{73} - 24 q^{74} + 8 q^{75} - 2 q^{78} - 16 q^{79} - 2 q^{80} + 6 q^{81} - 12 q^{85} - 2 q^{90} - 20 q^{91} - 4 q^{93} + 32 q^{94} + 12 q^{95} + 2 q^{98}+O(q^{100}) $ 6 * q - 6 * q^2 + 6 * q^4 - 2 * q^5 + 4 * q^7 - 6 * q^8 - 6 * q^9 + 2 * q^10 - 8 * q^13 - 4 * q^14 + 6 * q^16 + 6 * q^18 - 2 * q^20 - 2 * q^25 + 8 * q^26 + 4 * q^28 + 4 * q^29 - 6 * q^32 + 12 * q^33 + 16 * q^35 - 6 * q^36 + 24 * q^37 + 2 * q^39 + 2 * q^40 + 2 * q^45 - 32 * q^47 - 2 * q^49 + 2 * q^50 + 8 * q^51 - 8 * q^52 - 32 * q^55 - 4 * q^56 + 16 * q^57 - 4 * q^58 - 4 * q^61 - 4 * q^63 + 6 * q^64 - 16 * q^65 - 12 * q^66 + 4 * q^67 - 4 * q^69 - 16 * q^70 + 6 * q^72 + 40 * q^73 - 24 * q^74 + 8 * q^75 - 2 * q^78 - 16 * q^79 - 2 * q^80 + 6 * q^81 - 12 * q^85 - 2 * q^90 - 20 * q^91 - 4 * q^93 + 32 * q^94 + 12 * q^95 + 2 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/390\mathbb{Z}\right)^\times$.

$n$	$131$	$157$	$301$
$\chi(n)$	$1$	$-1$	$-1$

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 $

$2$	−1.00000			−0.707107
$2$	−1.00000			−0.707107
$3$		−	1.00000i		−	0.577350i
$3$		−	1.00000i		−	0.577350i
$4$	1.00000			0.500000
$5$	1.48119	+	1.67513i	0.662410	+	0.749141i
$5$	1.48119	+	1.67513i	0.662410	+	0.749141i
$6$			1.00000i			0.408248i
$7$	4.15633			1.57094			0.785472	−	0.618898i	$-0.212420\pi$
$7$	4.15633			1.57094			0.785472	+	0.618898i	$0.212420\pi$
$8$	−1.00000			−0.353553
$9$	−1.00000			−0.333333
$10$	−1.48119	−	1.67513i	−0.468395	−	0.529723i
$11$			5.35026i			1.61316i	0.591122	+	0.806582i	$0.298685\pi$
$11$			5.35026i			1.61316i	−0.591122	+	0.806582i	$0.701315\pi$
$12$		−	1.00000i		−	0.288675i
$13$	−3.28726	−	1.48119i	−0.911721	−	0.410809i
$13$	−3.28726	−	1.48119i	−0.911721	−	0.410809i
$14$	−4.15633			−1.11082
$15$	1.67513	−	1.48119i	0.432517	−	0.382443i
$16$	1.00000			0.250000
$17$			1.19394i			0.289572i	0.989463	+	0.144786i	$0.0462494\pi$
$17$			1.19394i			0.289572i	−0.989463	+	0.144786i	$0.953751\pi$
$18$	1.00000			0.235702
$19$			2.80606i			0.643755i	0.946781	+	0.321878i	$0.104314\pi$
$19$			2.80606i			0.643755i	−0.946781	+	0.321878i	$0.895686\pi$
$20$	1.48119	+	1.67513i	0.331205	+	0.374571i
$21$		−	4.15633i		−	0.906985i
$22$		−	5.35026i		−	1.14068i
$23$		−	0.806063i		−	0.168076i	−0.996463	−	0.0840379i	$-0.973218\pi$
$23$		−	0.806063i		−	0.168076i	0.996463	−	0.0840379i	$-0.0267817\pi$
$24$			1.00000i			0.204124i
$25$	−0.612127	+	4.96239i	−0.122425	+	0.992478i
$26$	3.28726	+	1.48119i	0.644684	+	0.290486i
$27$			1.00000i			0.192450i
$28$	4.15633			0.785472
$29$	7.50659			1.39394			0.696969	−	0.717101i	$-0.254531\pi$
$29$	7.50659			1.39394			0.696969	+	0.717101i	$0.254531\pi$
$30$	−1.67513	+	1.48119i	−0.305836	+	0.270428i
$31$		−	7.92478i		−	1.42333i	−0.702518	−	0.711666i	$-0.747941\pi$
$31$		−	7.92478i		−	1.42333i	0.702518	−	0.711666i	$-0.252059\pi$
$32$	−1.00000			−0.176777
$33$	5.35026			0.931361
$34$		−	1.19394i		−	0.204758i
$35$	6.15633	+	6.96239i	1.04061	+	1.17686i
$36$	−1.00000			−0.166667
$37$	7.35026			1.20838			0.604188	−	0.796842i	$-0.293498\pi$
$37$	7.35026			1.20838			0.604188	+	0.796842i	$0.293498\pi$
$38$		−	2.80606i		−	0.455204i
$39$	−1.48119	+	3.28726i	−0.237181	+	0.526383i
$40$	−1.48119	−	1.67513i	−0.234197	−	0.264861i
$41$		−	3.61213i		−	0.564119i	−0.959397	−	0.282060i	$-0.908982\pi$
$41$		−	3.61213i		−	0.564119i	0.959397	−	0.282060i	$-0.0910176\pi$
$42$			4.15633i			0.641335i
$43$		−	6.57452i		−	1.00260i	−0.865272	−	0.501302i	$-0.832855\pi$
$43$		−	6.57452i		−	1.00260i	0.865272	−	0.501302i	$-0.167145\pi$
$44$			5.35026i			0.806582i
$45$	−1.48119	−	1.67513i	−0.220803	−	0.249714i
$46$			0.806063i			0.118848i
$47$	−12.3127			−1.79598			−0.897992	−	0.440011i	$-0.854974\pi$
$47$	−12.3127			−1.79598			−0.897992	+	0.440011i	$0.854974\pi$
$48$		−	1.00000i		−	0.144338i
$49$	10.2750			1.46786
$50$	0.612127	−	4.96239i	0.0865678	−	0.701788i
$51$	1.19394			0.167185
$52$	−3.28726	−	1.48119i	−0.455861	−	0.205405i
$53$		−	5.53690i		−	0.760552i	−0.924873	−	0.380276i	$-0.875829\pi$
$53$		−	5.53690i		−	0.760552i	0.924873	−	0.380276i	$-0.124171\pi$
$54$		−	1.00000i		−	0.136083i
$55$	−8.96239	+	7.92478i	−1.20849	+	1.06858i
$56$	−4.15633			−0.555412
$57$	2.80606			0.371672
$58$	−7.50659			−0.985663
$59$			12.8872i			1.67777i	0.544312	+	0.838883i	$0.316791\pi$
$59$			12.8872i			1.67777i	−0.544312	+	0.838883i	$0.683209\pi$
$60$	1.67513	−	1.48119i	0.216258	−	0.191221i
$61$	6.31265			0.808252			0.404126	−	0.914703i	$-0.367576\pi$
$61$	6.31265			0.808252			0.404126	+	0.914703i	$0.367576\pi$
$62$			7.92478i			1.00645i
$63$	−4.15633			−0.523648
$64$	1.00000			0.125000
$65$	−2.38787	−	7.70052i	−0.296179	−	0.955132i
$66$	−5.35026			−0.658572
$67$	4.57452			0.558866			0.279433	−	0.960165i	$-0.409854\pi$
$67$	4.57452			0.558866			0.279433	+	0.960165i	$0.409854\pi$
$68$			1.19394i			0.144786i
$69$	−0.806063			−0.0970386
$70$	−6.15633	−	6.96239i	−0.735822	−	0.832165i
$71$		−	8.96239i		−	1.06364i	−0.846857	−	0.531820i	$-0.821508\pi$
$71$		−	8.96239i		−	1.06364i	0.846857	−	0.531820i	$-0.178492\pi$
$72$	1.00000			0.117851
$73$	−4.08110			−0.477657			−0.238828	−	0.971062i	$-0.576763\pi$
$73$	−4.08110			−0.477657			−0.238828	+	0.971062i	$0.576763\pi$
$74$	−7.35026			−0.854451
$75$	4.96239	+	0.612127i	0.573007	+	0.0706823i
$76$			2.80606i			0.321878i
$77$			22.2374i			2.53419i
$78$	1.48119	−	3.28726i	0.167712	−	0.372209i
$79$	−12.4387			−1.39946			−0.699729	−	0.714408i	$-0.746696\pi$
$79$	−12.4387			−1.39946			−0.699729	+	0.714408i	$0.746696\pi$
$80$	1.48119	+	1.67513i	0.165603	+	0.187285i
$81$	1.00000			0.111111
$82$			3.61213i			0.398893i
$83$	−10.0508			−1.10322			−0.551609	−	0.834103i	$-0.685986\pi$
$83$	−10.0508			−1.10322			−0.551609	+	0.834103i	$0.685986\pi$
$84$		−	4.15633i		−	0.453492i
$85$	−2.00000	+	1.76845i	−0.216930	+	0.191816i
$86$			6.57452i			0.708948i
$87$		−	7.50659i		−	0.804791i
$88$		−	5.35026i		−	0.570340i
$89$		−	5.03761i		−	0.533986i	−0.963699	−	0.266993i	$-0.913970\pi$
$89$		−	5.03761i		−	0.533986i	0.963699	−	0.266993i	$-0.0860300\pi$
$90$	1.48119	+	1.67513i	0.156132	+	0.176574i
$91$	−13.6629	−	6.15633i	−1.43226	−	0.645358i
$92$		−	0.806063i		−	0.0840379i
$93$	−7.92478			−0.821761
$94$	12.3127			1.26995
$95$	−4.70052	+	4.15633i	−0.482264	+	0.426430i
$96$			1.00000i			0.102062i
$97$	−2.93207			−0.297707			−0.148853	−	0.988859i	$-0.547558\pi$
$97$	−2.93207			−0.297707			−0.148853	+	0.988859i	$0.547558\pi$
$98$	−10.2750			−1.03794
$99$		−	5.35026i		−	0.537722i
$100$	−0.612127	+	4.96239i	−0.0612127	+	0.496239i
$101$	5.89446			0.586521			0.293260	−	0.956033i	$-0.405260\pi$
$101$	5.89446			0.586521			0.293260	+	0.956033i	$0.405260\pi$
$102$	−1.19394			−0.118217
$103$		−	3.29948i		−	0.325107i	−0.986700	−	0.162554i	$-0.948027\pi$
$103$		−	3.29948i		−	0.325107i	0.986700	−	0.162554i	$-0.0519730\pi$
$104$	3.28726	+	1.48119i	0.322342	+	0.145243i
$105$	6.96239	−	6.15633i	0.679460	−	0.600796i
$106$			5.53690i			0.537792i
$107$		−	19.7889i		−	1.91307i	−0.291622	−	0.956534i	$-0.594195\pi$
$107$		−	19.7889i		−	1.91307i	0.291622	−	0.956534i	$-0.405805\pi$
$108$			1.00000i			0.0962250i
$109$		−	9.43136i		−	0.903361i	−0.892180	−	0.451680i	$-0.850825\pi$
$109$		−	9.43136i		−	0.903361i	0.892180	−	0.451680i	$-0.149175\pi$
$110$	8.96239	−	7.92478i	0.854530	−	0.755598i
$111$		−	7.35026i		−	0.697656i
$112$	4.15633			0.392736
$113$		−	4.41819i		−	0.415628i	−0.978168	−	0.207814i	$-0.933365\pi$
$113$		−	4.41819i		−	0.415628i	0.978168	−	0.207814i	$-0.0666349\pi$
$114$	−2.80606			−0.262812
$115$	1.35026	−	1.19394i	0.125913	−	0.111335i
$116$	7.50659			0.696969
$117$	3.28726	+	1.48119i	0.303907	+	0.136936i
$118$		−	12.8872i		−	1.18636i
$119$			4.96239i			0.454901i
$120$	−1.67513	+	1.48119i	−0.152918	+	0.135214i
$121$	−17.6253			−1.60230
$122$	−6.31265			−0.571521
$123$	−3.61213			−0.325695
$124$		−	7.92478i		−	0.711666i
$125$	−9.21933	+	6.32487i	−0.824602	+	0.565713i
$126$	4.15633			0.370275
$127$			18.1622i			1.61164i	0.592164	+	0.805818i	$0.298274\pi$
$127$			18.1622i			1.61164i	−0.592164	+	0.805818i	$0.701726\pi$
$128$	−1.00000			−0.0883883
$129$	−6.57452			−0.578854
$130$	2.38787	+	7.70052i	0.209430	+	0.675381i
$131$	−9.81924			−0.857911			−0.428955	−	0.903326i	$-0.641118\pi$
$131$	−9.81924			−0.857911			−0.428955	+	0.903326i	$0.641118\pi$
$132$	5.35026			0.465681
$133$			11.6629i			1.01130i
$134$	−4.57452			−0.395178
$135$	−1.67513	+	1.48119i	−0.144172	+	0.127481i
$136$		−	1.19394i		−	0.102379i
$137$	−0.911603			−0.0778835			−0.0389418	−	0.999241i	$-0.512399\pi$
$137$	−0.911603			−0.0778835			−0.0389418	+	0.999241i	$0.512399\pi$
$138$	0.806063			0.0686167
$139$	0.836381			0.0709409			0.0354704	−	0.999371i	$-0.488707\pi$
$139$	0.836381			0.0709409			0.0354704	+	0.999371i	$0.488707\pi$
$140$	6.15633	+	6.96239i	0.520304	+	0.588429i
$141$			12.3127i			1.03691i
$142$			8.96239i			0.752107i
$143$	7.92478	−	17.5877i	0.662703	−	1.47076i
$144$	−1.00000			−0.0833333
$145$	11.1187	+	12.5745i	0.923359	+	1.04426i
$146$	4.08110			0.337754
$147$		−	10.2750i		−	0.847471i
$148$	7.35026			0.604188
$149$		−	10.8872i		−	0.891911i	−0.895055	−	0.445956i	$-0.852864\pi$
$149$		−	10.8872i		−	0.891911i	0.895055	−	0.445956i	$-0.147136\pi$
$150$	−4.96239	−	0.612127i	−0.405177	−	0.0499799i
$151$			17.7889i			1.44764i	0.689988	+	0.723821i	$0.257616\pi$
$151$			17.7889i			1.44764i	−0.689988	+	0.723821i	$0.742384\pi$
$152$		−	2.80606i		−	0.227602i
$153$		−	1.19394i		−	0.0965241i
$154$		−	22.2374i		−	1.79194i
$155$	13.2750	−	11.7381i	1.06628	−	0.942830i
$156$	−1.48119	+	3.28726i	−0.118590	+	0.263191i
$157$			10.7757i			0.859998i	0.902829	+	0.429999i	$0.141486\pi$
$157$			10.7757i			0.859998i	−0.902829	+	0.429999i	$0.858514\pi$
$158$	12.4387			0.989567
$159$	−5.53690			−0.439105
$160$	−1.48119	−	1.67513i	−0.117099	−	0.132431i
$161$		−	3.35026i		−	0.264038i
$162$	−1.00000			−0.0785674
$163$	12.0508			0.943890			0.471945	−	0.881628i	$-0.343552\pi$
$163$	12.0508			0.943890			0.471945	+	0.881628i	$0.343552\pi$
$164$		−	3.61213i		−	0.282060i
$165$	7.92478	+	8.96239i	0.616943	+	0.697721i
$166$	10.0508			0.780092
$167$	−1.61213			−0.124750			−0.0623751	−	0.998053i	$-0.519867\pi$
$167$	−1.61213			−0.124750			−0.0623751	+	0.998053i	$0.519867\pi$
$168$			4.15633i			0.320667i
$169$	8.61213	+	9.73813i	0.662471	+	0.749087i
$170$	2.00000	−	1.76845i	0.153393	−	0.135634i
$171$		−	2.80606i		−	0.214585i
$172$		−	6.57452i		−	0.501302i
$173$		−	1.22425i		−	0.0930783i	−0.998916	−	0.0465391i	$-0.985181\pi$
$173$		−	1.22425i		−	0.0930783i	0.998916	−	0.0465391i	$-0.0148192\pi$
$174$			7.50659i			0.569073i
$175$	−2.54420	+	20.6253i	−0.192323	+	1.55913i
$176$			5.35026i			0.403291i
$177$	12.8872			0.968659
$178$			5.03761i			0.377585i
$179$	−1.25457			−0.0937710			−0.0468855	−	0.998900i	$-0.514930\pi$
$179$	−1.25457			−0.0937710			−0.0468855	+	0.998900i	$0.514930\pi$
$180$	−1.48119	−	1.67513i	−0.110402	−	0.124857i
$181$	5.47627			0.407048			0.203524	−	0.979070i	$-0.434761\pi$
$181$	5.47627			0.407048			0.203524	+	0.979070i	$0.434761\pi$
$182$	13.6629	+	6.15633i	1.01276	+	0.456337i
$183$		−	6.31265i		−	0.466645i
$184$			0.806063i			0.0594238i
$185$	10.8872	+	12.3127i	0.800440	+	0.905244i
$186$	7.92478			0.581073
$187$	−6.38787			−0.467128
$188$	−12.3127			−0.897992
$189$			4.15633i			0.302328i
$190$	4.70052	−	4.15633i	0.341012	−	0.301532i
$191$	−10.2374			−0.740754			−0.370377	−	0.928881i	$-0.620772\pi$
$191$	−10.2374			−0.740754			−0.370377	+	0.928881i	$0.620772\pi$
$192$		−	1.00000i		−	0.0721688i
$193$	−9.06793			−0.652724			−0.326362	−	0.945245i	$-0.605823\pi$
$193$	−9.06793			−0.652724			−0.326362	+	0.945245i	$0.605823\pi$
$194$	2.93207			0.210510
$195$	−7.70052	+	2.38787i	−0.551446	+	0.170999i
$196$	10.2750			0.733931
$197$	−3.14903			−0.224359			−0.112180	−	0.993688i	$-0.535783\pi$
$197$	−3.14903			−0.224359			−0.112180	+	0.993688i	$0.535783\pi$
$198$			5.35026i			0.380227i
$199$	14.1114			1.00033			0.500166	−	0.865930i	$-0.333272\pi$
$199$	14.1114			1.00033			0.500166	+	0.865930i	$0.333272\pi$
$200$	0.612127	−	4.96239i	0.0432839	−	0.350894i
$201$		−	4.57452i		−	0.322661i
$202$	−5.89446			−0.414733
$203$	31.1998			2.18980
$204$	1.19394			0.0835923
$205$	6.05079	−	5.35026i	0.422605	−	0.373678i
$206$			3.29948i			0.229885i
$207$			0.806063i			0.0560253i
$208$	−3.28726	−	1.48119i	−0.227930	−	0.102702i
$209$	−15.0132			−1.03848
$210$	−6.96239	+	6.15633i	−0.480450	+	0.424827i
$211$	−17.4617			−1.20211			−0.601056	−	0.799207i	$-0.705253\pi$
$211$	−17.4617			−1.20211			−0.601056	+	0.799207i	$0.705253\pi$
$212$		−	5.53690i		−	0.380276i
$213$	−8.96239			−0.614093
$214$			19.7889i			1.35274i
$215$	11.0132	−	9.73813i	0.751092	−	0.664135i
$216$		−	1.00000i		−	0.0680414i
$217$		−	32.9380i		−	2.23597i
$218$			9.43136i			0.638773i
$219$			4.08110i			0.275775i
$220$	−8.96239	+	7.92478i	−0.604244	+	0.534288i
$221$	1.76845	−	3.92478i	0.118959	−	0.264009i
$222$			7.35026i			0.493317i
$223$	−19.6326			−1.31470			−0.657348	−	0.753587i	$-0.728322\pi$
$223$	−19.6326			−1.31470			−0.657348	+	0.753587i	$0.728322\pi$
$224$	−4.15633			−0.277706
$225$	0.612127	−	4.96239i	0.0408085	−	0.330826i
$226$			4.41819i			0.293894i
$227$	4.77575			0.316977			0.158489	−	0.987361i	$-0.449338\pi$
$227$	4.77575			0.316977			0.158489	+	0.987361i	$0.449338\pi$
$228$	2.80606			0.185836
$229$		−	19.5672i		−	1.29304i	−0.762898	−	0.646519i	$-0.776224\pi$
$229$		−	19.5672i		−	1.29304i	0.762898	−	0.646519i	$-0.223776\pi$
$230$	−1.35026	+	1.19394i	−0.0890336	+	0.0787258i
$231$	22.2374			1.46312
$232$	−7.50659			−0.492832
$233$		−	2.74543i		−	0.179859i	−0.995948	−	0.0899295i	$-0.971336\pi$
$233$		−	2.74543i		−	0.179859i	0.995948	−	0.0899295i	$-0.0286642\pi$
$234$	−3.28726	−	1.48119i	−0.214895	−	0.0968287i
$235$	−18.2374	−	20.6253i	−1.18968	−	1.34545i
$236$			12.8872i			0.838883i
$237$			12.4387i			0.807978i
$238$		−	4.96239i		−	0.321664i
$239$			5.29948i			0.342795i	0.985202	+	0.171397i	$0.0548282\pi$
$239$			5.29948i			0.342795i	−0.985202	+	0.171397i	$0.945172\pi$
$240$	1.67513	−	1.48119i	0.108129	−	0.0956107i
$241$			12.9380i			0.833407i	0.909043	+	0.416703i	$0.136815\pi$
$241$			12.9380i			0.833407i	−0.909043	+	0.416703i	$0.863185\pi$
$242$	17.6253			1.13300
$243$		−	1.00000i		−	0.0641500i
$244$	6.31265			0.404126
$245$	15.2193	+	17.2120i	0.972327	+	1.09964i
$246$	3.61213			0.230301
$247$	4.15633	−	9.22425i	0.264461	−	0.586925i
$248$			7.92478i			0.503224i
$249$			10.0508i			0.636943i
$250$	9.21933	−	6.32487i	0.583082	−	0.400020i
$251$	8.10554			0.511617			0.255809	−	0.966727i	$-0.417658\pi$
$251$	8.10554			0.511617			0.255809	+	0.966727i	$0.417658\pi$
$252$	−4.15633			−0.261824
$253$	4.31265			0.271134
$254$		−	18.1622i		−	1.13960i
$255$	1.76845	+	2.00000i	0.110745	+	0.125245i
$256$	1.00000			0.0625000
$257$			12.0567i			0.752074i	0.926605	+	0.376037i	$0.122713\pi$
$257$			12.0567i			0.752074i	−0.926605	+	0.376037i	$0.877287\pi$
$258$	6.57452			0.409311
$259$	30.5501			1.89829
$260$	−2.38787	−	7.70052i	−0.148090	−	0.477566i
$261$	−7.50659			−0.464646
$262$	9.81924			0.606635
$263$		−	4.28233i		−	0.264060i	−0.991246	−	0.132030i	$-0.957850\pi$
$263$		−	4.28233i		−	0.264060i	0.991246	−	0.132030i	$-0.0421495\pi$
$264$	−5.35026			−0.329286
$265$	9.27504	−	8.20123i	0.569761	−	0.503798i
$266$		−	11.6629i		−	0.715099i
$267$	−5.03761			−0.308297
$268$	4.57452			0.279433
$269$	−19.8799			−1.21210			−0.606049	−	0.795428i	$-0.707246\pi$
$269$	−19.8799			−1.21210			−0.606049	+	0.795428i	$0.707246\pi$
$270$	1.67513	−	1.48119i	0.101945	−	0.0901426i
$271$		−	5.01317i		−	0.304529i	−0.988340	−	0.152264i	$-0.951344\pi$
$271$		−	5.01317i		−	0.304529i	0.988340	−	0.152264i	$-0.0486565\pi$
$272$			1.19394i			0.0723930i
$273$	−6.15633	+	13.6629i	−0.372598	+	0.826917i
$274$	0.911603			0.0550720
$275$	−26.5501	−	3.27504i	−1.60103	−	0.197492i
$276$	−0.806063			−0.0485193
$277$		−	8.55008i		−	0.513724i	−0.966448	−	0.256862i	$-0.917311\pi$
$277$		−	8.55008i		−	0.513724i	0.966448	−	0.256862i	$-0.0826887\pi$
$278$	−0.836381			−0.0501628
$279$			7.92478i			0.474444i
$280$	−6.15633	−	6.96239i	−0.367911	−	0.416082i
$281$		−	25.5125i		−	1.52195i	−0.648783	−	0.760973i	$-0.724722\pi$
$281$		−	25.5125i		−	1.52195i	0.648783	−	0.760973i	$-0.275278\pi$
$282$		−	12.3127i		−	0.733208i
$283$			23.7235i			1.41022i	0.709099	+	0.705109i	$0.249102\pi$
$283$			23.7235i			1.41022i	−0.709099	+	0.705109i	$0.750898\pi$
$284$		−	8.96239i		−	0.531820i
$285$	4.15633	+	4.70052i	0.246199	+	0.278435i
$286$	−7.92478	+	17.5877i	−0.468602	+	1.03998i
$287$		−	15.0132i		−	0.886200i
$288$	1.00000			0.0589256
$289$	15.5745			0.916148
$290$	−11.1187	−	12.5745i	−0.652913	−	0.738401i
$291$			2.93207i			0.171881i
$292$	−4.08110			−0.238828
$293$	23.9248			1.39770			0.698850	−	0.715268i	$-0.253695\pi$
$293$	23.9248			1.39770			0.698850	+	0.715268i	$0.253695\pi$
$294$			10.2750i			0.599252i
$295$	−21.5877	+	19.0884i	−1.25688	+	1.11137i
$296$	−7.35026			−0.427225
$297$	−5.35026			−0.310454
$298$			10.8872i			0.630677i
$299$	−1.19394	+	2.64974i	−0.0690471	+	0.153238i
$300$	4.96239	+	0.612127i	0.286504	+	0.0353412i
$301$		−	27.3258i		−	1.57503i
$302$		−	17.7889i		−	1.02364i
$303$		−	5.89446i		−	0.338628i
$304$			2.80606i			0.160939i
$305$	9.35026	+	10.5745i	0.535394	+	0.605495i
$306$			1.19394i			0.0682528i
$307$	−33.5125			−1.91266			−0.956329	−	0.292293i	$-0.905582\pi$
$307$	−33.5125			−1.91266			−0.956329	+	0.292293i	$0.905582\pi$
$308$			22.2374i			1.26710i
$309$	−3.29948			−0.187701
$310$	−13.2750	+	11.7381i	−0.753972	+	0.666681i
$311$	−5.76257			−0.326766			−0.163383	−	0.986563i	$-0.552241\pi$
$311$	−5.76257			−0.326766			−0.163383	+	0.986563i	$0.552241\pi$
$312$	1.48119	−	3.28726i	0.0838561	−	0.186104i
$313$		−	12.6253i		−	0.713624i	−0.934176	−	0.356812i	$-0.883864\pi$
$313$		−	12.6253i		−	0.713624i	0.934176	−	0.356812i	$-0.116136\pi$
$314$		−	10.7757i		−	0.608111i
$315$	−6.15633	−	6.96239i	−0.346870	−	0.392286i
$316$	−12.4387			−0.699729
$317$	3.73813			0.209955			0.104977	−	0.994475i	$-0.466523\pi$
$317$	3.73813			0.209955			0.104977	+	0.994475i	$0.466523\pi$
$318$	5.53690			0.310494
$319$			40.1622i			2.24865i
$320$	1.48119	+	1.67513i	0.0828013	+	0.0936427i
$321$	−19.7889			−1.10451
$322$			3.35026i			0.186703i
$323$	−3.35026			−0.186414
$324$	1.00000			0.0555556
$325$	9.36248	−	15.4060i	0.519337	−	0.854570i
$326$	−12.0508			−0.667431
$327$	−9.43136			−0.521556
$328$			3.61213i			0.199446i
$329$	−51.1754			−2.82139
$330$	−7.92478	−	8.96239i	−0.436245	−	0.493363i
$331$			1.81924i			0.0999943i	0.998749	+	0.0499972i	$0.0159212\pi$
$331$			1.81924i			0.0999943i	−0.998749	+	0.0499972i	$0.984079\pi$
$332$	−10.0508			−0.551609
$333$	−7.35026			−0.402792
$334$	1.61213			0.0882117
$335$	6.77575	+	7.66291i	0.370199	+	0.418670i
$336$		−	4.15633i		−	0.226746i
$337$			8.83638i			0.481348i	0.970606	+	0.240674i	$0.0773685\pi$
$337$			8.83638i			0.481348i	−0.970606	+	0.240674i	$0.922631\pi$
$338$	−8.61213	−	9.73813i	−0.468438	−	0.529685i
$339$	−4.41819			−0.239963
$340$	−2.00000	+	1.76845i	−0.108465	+	0.0959078i
$341$	42.3996			2.29607
$342$			2.80606i			0.151735i
$343$	13.6121			0.734986
$344$			6.57452i			0.354474i
$345$	−1.19394	−	1.35026i	−0.0642794	−	0.0726956i
$346$			1.22425i			0.0658163i
$347$		−	2.13586i		−	0.114659i	−0.998355	−	0.0573294i	$-0.981741\pi$
$347$		−	2.13586i		−	0.114659i	0.998355	−	0.0573294i	$-0.0182585\pi$
$348$		−	7.50659i		−	0.402395i
$349$		−	16.4934i		−	0.882872i	−0.897293	−	0.441436i	$-0.854469\pi$
$349$		−	16.4934i		−	0.882872i	0.897293	−	0.441436i	$-0.145531\pi$
$350$	2.54420	−	20.6253i	0.135993	−	1.10247i
$351$	1.48119	−	3.28726i	0.0790603	−	0.175461i
$352$		−	5.35026i		−	0.285170i
$353$	−3.86414			−0.205668			−0.102834	−	0.994699i	$-0.532791\pi$
$353$	−3.86414			−0.205668			−0.102834	+	0.994699i	$0.532791\pi$
$354$	−12.8872			−0.684945
$355$	15.0132	−	13.2750i	0.796817	−	0.704566i
$356$		−	5.03761i		−	0.266993i
$357$	4.96239			0.262637
$358$	1.25457			0.0663061
$359$		−	18.5139i		−	0.977125i	−0.872529	−	0.488563i	$-0.837521\pi$
$359$		−	18.5139i		−	0.977125i	0.872529	−	0.488563i	$-0.162479\pi$
$360$	1.48119	+	1.67513i	0.0780658	+	0.0882871i
$361$	11.1260			0.585579
$362$	−5.47627			−0.287826
$363$			17.6253i			0.925088i
$364$	−13.6629	−	6.15633i	−0.716131	−	0.322679i
$365$	−6.04491	−	6.83638i	−0.316405	−	0.357833i
$366$			6.31265i			0.329968i
$367$			23.7137i			1.23784i	0.785452	+	0.618922i	$0.212430\pi$
$367$			23.7137i			1.23784i	−0.785452	+	0.618922i	$0.787570\pi$
$368$		−	0.806063i		−	0.0420190i
$369$			3.61213i			0.188040i
$370$	−10.8872	−	12.3127i	−0.565997	−	0.640104i
$371$		−	23.0132i		−	1.19478i
$372$	−7.92478			−0.410881
$373$			11.1490i			0.577275i	0.957438	+	0.288637i	$0.0932022\pi$
$373$			11.1490i			0.577275i	−0.957438	+	0.288637i	$0.906798\pi$
$374$	6.38787			0.330309
$375$	6.32487	+	9.21933i	0.326615	+	0.476084i
$376$	12.3127			0.634976
$377$	−24.6761	−	11.1187i	−1.27088	−	0.572643i
$378$		−	4.15633i		−	0.213778i
$379$		−	38.7572i		−	1.99082i	−0.0956865	−	0.995412i	$-0.530505\pi$
$379$		−	38.7572i		−	1.99082i	0.0956865	−	0.995412i	$-0.469495\pi$
$380$	−4.70052	+	4.15633i	−0.241132	+	0.213215i
$381$	18.1622			0.930478
$382$	10.2374			0.523792
$383$	−1.76257			−0.0900632			−0.0450316	−	0.998986i	$-0.514339\pi$
$383$	−1.76257			−0.0900632			−0.0450316	+	0.998986i	$0.514339\pi$
$384$			1.00000i			0.0510310i
$385$	−37.2506	+	32.9380i	−1.89847	+	1.67867i
$386$	9.06793			0.461545
$387$			6.57452i			0.334201i
$388$	−2.93207			−0.148853
$389$	34.0567			1.72674			0.863371	−	0.504570i	$-0.168349\pi$
$389$	34.0567			1.72674			0.863371	+	0.504570i	$0.168349\pi$
$390$	7.70052	−	2.38787i	0.389931	−	0.120915i
$391$	0.962389			0.0486701
$392$	−10.2750			−0.518968
$393$			9.81924i			0.495315i
$394$	3.14903			0.158646
$395$	−18.4241	−	20.8364i	−0.927016	−	1.04839i
$396$		−	5.35026i		−	0.268861i
$397$	15.8134			0.793650			0.396825	−	0.917894i	$-0.370112\pi$
$397$	15.8134			0.793650			0.396825	+	0.917894i	$0.370112\pi$
$398$	−14.1114			−0.707342
$399$	11.6629			0.583876
$400$	−0.612127	+	4.96239i	−0.0306063	+	0.248119i
$401$			25.0132i			1.24910i	0.780986	+	0.624549i	$0.214717\pi$
$401$			25.0132i			1.24910i	−0.780986	+	0.624549i	$0.785283\pi$
$402$			4.57452i			0.228156i
$403$	−11.7381	+	26.0508i	−0.584718	+	1.29768i
$404$	5.89446			0.293260
$405$	1.48119	+	1.67513i	0.0736011	+	0.0832379i
$406$	−31.1998			−1.54842
$407$			39.3258i			1.94931i
$408$	−1.19394			−0.0591087
$409$		−	34.0263i		−	1.68249i	−0.540651	−	0.841247i	$-0.681822\pi$
$409$		−	34.0263i		−	1.68249i	0.540651	−	0.841247i	$-0.318178\pi$
$410$	−6.05079	+	5.35026i	−0.298827	+	0.264231i
$411$			0.911603i			0.0449661i
$412$		−	3.29948i		−	0.162554i
$413$			53.5633i			2.63568i
$414$		−	0.806063i		−	0.0396159i
$415$	−14.8872	−	16.8364i	−0.730782	−	0.826465i
$416$	3.28726	+	1.48119i	0.161171	+	0.0726215i
$417$		−	0.836381i		−	0.0409577i
$418$	15.0132			0.734318
$419$	−3.73226			−0.182333			−0.0911663	−	0.995836i	$-0.529059\pi$
$419$	−3.73226			−0.182333			−0.0911663	+	0.995836i	$0.529059\pi$
$420$	6.96239	−	6.15633i	0.339730	−	0.300398i
$421$			16.9683i			0.826983i	0.910508	+	0.413491i	$0.135691\pi$
$421$			16.9683i			0.826983i	−0.910508	+	0.413491i	$0.864309\pi$
$422$	17.4617			0.850021
$423$	12.3127			0.598662
$424$			5.53690i			0.268896i
$425$	−5.92478	−	0.730841i	−0.287394	−	0.0354510i
$426$	8.96239			0.434229
$427$	26.2374			1.26972
$428$		−	19.7889i		−	0.956534i
$429$	−17.5877	−	7.92478i	−0.849142	−	0.382612i
$430$	−11.0132	+	9.73813i	−0.531102	+	0.469615i
$431$		−	20.9986i		−	1.01147i	−0.862690	−	0.505733i	$-0.831222\pi$
$431$		−	20.9986i		−	1.01147i	0.862690	−	0.505733i	$-0.168778\pi$
$432$			1.00000i			0.0481125i
$433$		−	17.3404i		−	0.833327i	−0.909061	−	0.416664i	$-0.863199\pi$
$433$		−	17.3404i		−	0.833327i	0.909061	−	0.416664i	$-0.136801\pi$
$434$			32.9380i			1.58107i
$435$	12.5745	−	11.1187i	0.602902	−	0.533102i
$436$		−	9.43136i		−	0.451680i
$437$	2.26187			0.108200
$438$		−	4.08110i		−	0.195003i
$439$	13.7743			0.657413			0.328706	−	0.944432i	$-0.393387\pi$
$439$	13.7743			0.657413			0.328706	+	0.944432i	$0.393387\pi$
$440$	8.96239	−	7.92478i	0.427265	−	0.377799i
$441$	−10.2750			−0.489288
$442$	−1.76845	+	3.92478i	−0.0841167	+	0.186683i
$443$			9.61213i			0.456686i	0.973581	+	0.228343i	$0.0733307\pi$
$443$			9.61213i			0.456686i	−0.973581	+	0.228343i	$0.926669\pi$
$444$		−	7.35026i		−	0.348828i
$445$	8.43866	−	7.46168i	0.400031	−	0.353718i
$446$	19.6326			0.929630
$447$	−10.8872			−0.514945
$448$	4.15633			0.196368
$449$			25.6629i			1.21111i	0.795804	+	0.605554i	$0.207048\pi$
$449$			25.6629i			1.21111i	−0.795804	+	0.605554i	$0.792952\pi$
$450$	−0.612127	+	4.96239i	−0.0288559	+	0.233929i
$451$	19.3258			0.910018
$452$		−	4.41819i		−	0.207814i
$453$	17.7889			0.835796
$454$	−4.77575			−0.224137
$455$	−9.92478	−	32.0059i	−0.465281	−	1.50046i
$456$	−2.80606			−0.131406
$457$	−22.9321			−1.07272			−0.536359	−	0.843990i	$-0.680201\pi$
$457$	−22.9321			−1.07272			−0.536359	+	0.843990i	$0.680201\pi$
$458$			19.5672i			0.914316i
$459$	−1.19394			−0.0557282
$460$	1.35026	−	1.19394i	0.0629563	−	0.0556676i
$461$			22.7367i			1.05895i	0.848324	+	0.529477i	$0.177612\pi$
$461$			22.7367i			1.05895i	−0.848324	+	0.529477i	$0.822388\pi$
$462$	−22.2374			−1.03458
$463$	5.08252			0.236205			0.118102	−	0.993001i	$-0.462319\pi$
$463$	5.08252			0.236205			0.118102	+	0.993001i	$0.462319\pi$
$464$	7.50659			0.348485
$465$	−11.7381	−	13.2750i	−0.544343	−	0.615615i
$466$			2.74543i			0.127180i
$467$			16.4631i			0.761821i	0.924612	+	0.380911i	$0.124389\pi$
$467$			16.4631i			0.761821i	−0.924612	+	0.380911i	$0.875611\pi$
$468$	3.28726	+	1.48119i	0.151954	+	0.0684682i
$469$	19.0132			0.877947
$470$	18.2374	+	20.6253i	0.841230	+	0.951374i
$471$	10.7757			0.496520
$472$		−	12.8872i		−	0.593180i
$473$	35.1754			1.61737
$474$		−	12.4387i		−	0.571327i
$475$	−13.9248	−	1.71767i	−0.638913	−	0.0788120i
$476$			4.96239i			0.227451i
$477$			5.53690i			0.253517i
$478$		−	5.29948i		−	0.242392i
$479$		−	8.15045i		−	0.372403i	−0.982512	−	0.186202i	$-0.940382\pi$
$479$		−	8.15045i		−	0.372403i	0.982512	−	0.186202i	$-0.0596178\pi$
$480$	−1.67513	+	1.48119i	−0.0764589	+	0.0676070i
$481$	−24.1622	−	10.8872i	−1.10170	−	0.496412i
$482$		−	12.9380i		−	0.589308i
$483$	−3.35026			−0.152442
$484$	−17.6253			−0.801150
$485$	−4.34297	−	4.91160i	−0.197204	−	0.223024i
$486$			1.00000i			0.0453609i
$487$	35.4215			1.60510			0.802551	−	0.596583i	$-0.203476\pi$
$487$	35.4215			1.60510			0.802551	+	0.596583i	$0.203476\pi$
$488$	−6.31265			−0.285760
$489$		−	12.0508i		−	0.544955i
$490$	−15.2193	−	17.2120i	−0.687539	−	0.777560i
$491$	−35.8046			−1.61584			−0.807921	−	0.589291i	$-0.799407\pi$
$491$	−35.8046			−1.61584			−0.807921	+	0.589291i	$0.799407\pi$
$492$	−3.61213			−0.162847
$493$			8.96239i			0.403646i
$494$	−4.15633	+	9.22425i	−0.187002	+	0.415019i
$495$	8.96239	−	7.92478i	0.402829	−	0.356192i
$496$		−	7.92478i		−	0.355833i
$497$		−	37.2506i		−	1.67092i
$498$		−	10.0508i		−	0.450386i
$499$			29.1939i			1.30690i	0.756970	+	0.653450i	$0.226679\pi$
$499$			29.1939i			1.30690i	−0.756970	+	0.653450i	$0.773321\pi$
$500$	−9.21933	+	6.32487i	−0.412301	+	0.282857i
$501$			1.61213i			0.0720245i
$502$	−8.10554			−0.361768
$503$		−	0.806063i		−	0.0359406i	−0.999839	−	0.0179703i	$-0.994280\pi$
$503$		−	0.806063i		−	0.0359406i	0.999839	−	0.0179703i	$-0.00572043\pi$
$504$	4.15633			0.185137
$505$	8.73084	+	9.87399i	0.388517	+	0.439387i
$506$	−4.31265			−0.191721
$507$	9.73813	−	8.61213i	0.432486	−	0.382478i
$508$			18.1622i			0.805818i
$509$			11.9149i			0.528120i	0.964506	+	0.264060i	$0.0850617\pi$
$509$			11.9149i			0.528120i	−0.964506	+	0.264060i	$0.914938\pi$
$510$	−1.76845	−	2.00000i	−0.0783084	−	0.0885615i
$511$	−16.9624			−0.750372
$512$	−1.00000			−0.0441942
$513$	−2.80606			−0.123891
$514$		−	12.0567i		−	0.531797i
$515$	5.52705	−	4.88717i	0.243551	−	0.215354i
$516$	−6.57452			−0.289427
$517$		−	65.8759i		−	2.89722i
$518$	−30.5501			−1.34229
$519$	−1.22425			−0.0537388
$520$	2.38787	+	7.70052i	0.104715	+	0.337690i
$521$	16.4485			0.720622			0.360311	−	0.932832i	$-0.382671\pi$
$521$	16.4485			0.720622			0.360311	+	0.932832i	$0.382671\pi$
$522$	7.50659			0.328554
$523$		−	6.07522i		−	0.265651i	−0.991139	−	0.132825i	$-0.957595\pi$
$523$		−	6.07522i		−	0.265651i	0.991139	−	0.132825i	$-0.0424050\pi$
$524$	−9.81924			−0.428955
$525$	20.6253	+	2.54420i	0.900162	+	0.111038i
$526$			4.28233i			0.186719i
$527$	9.46168			0.412157
$528$	5.35026			0.232840
$529$	22.3503			0.971751
$530$	−9.27504	+	8.20123i	−0.402882	+	0.356239i
$531$		−	12.8872i		−	0.559255i
$532$			11.6629i			0.505651i
$533$	−5.35026	+	11.8740i	−0.231746	+	0.514320i
$534$	5.03761			0.217999
$535$	33.1490	−	29.3112i	1.43316	−	1.26724i
$536$	−4.57452			−0.197589
$537$			1.25457i			0.0541387i
$538$	19.8799			0.857082
$539$			54.9741i			2.36790i
$540$	−1.67513	+	1.48119i	−0.0720862	+	0.0637405i
$541$			6.10554i			0.262498i	0.991349	+	0.131249i	$0.0418987\pi$
$541$			6.10554i			0.262498i	−0.991349	+	0.131249i	$0.958101\pi$
$542$			5.01317i			0.215334i
$543$		−	5.47627i		−	0.235009i
$544$		−	1.19394i		−	0.0511896i
$545$	15.7988	−	13.9697i	0.676745	−	0.598395i
$546$	6.15633	−	13.6629i	0.263466	−	0.584719i
$547$			0.775746i			0.0331685i	0.999862	+	0.0165843i	$0.00527918\pi$
$547$			0.775746i			0.0331685i	−0.999862	+	0.0165843i	$0.994721\pi$
$548$	−0.911603			−0.0389418
$549$	−6.31265			−0.269417
$550$	26.5501	+	3.27504i	1.13210	+	0.139648i
$551$			21.0640i			0.897355i
$552$	0.806063			0.0343083
$553$	−51.6991			−2.19847
$554$			8.55008i			0.363258i
$555$	12.3127	−	10.8872i	0.522643	−	0.462134i
$556$	0.836381			0.0354704
$557$	5.13918			0.217754			0.108877	−	0.994055i	$-0.465275\pi$
$557$	5.13918			0.217754			0.108877	+	0.994055i	$0.465275\pi$
$558$		−	7.92478i		−	0.335483i
$559$	−9.73813	+	21.6121i	−0.411879	+	0.914096i
$560$	6.15633	+	6.96239i	0.260152	+	0.294215i
$561$			6.38787i			0.269696i
$562$			25.5125i			1.07618i
$563$			30.3390i			1.27864i	0.768942	+	0.639318i	$0.220783\pi$
$563$			30.3390i			1.27864i	−0.768942	+	0.639318i	$0.779217\pi$
$564$			12.3127i			0.518456i
$565$	7.40105	−	6.54420i	0.311364	−	0.275316i
$566$		−	23.7235i		−	0.997175i
$567$	4.15633			0.174549
$568$			8.96239i			0.376053i
$569$	−7.25060			−0.303961			−0.151981	−	0.988383i	$-0.548565\pi$
$569$	−7.25060			−0.303961			−0.151981	+	0.988383i	$0.548565\pi$
$570$	−4.15633	−	4.70052i	−0.174089	−	0.196883i
$571$	16.3127			0.682663			0.341332	−	0.939943i	$-0.389122\pi$
$571$	16.3127			0.682663			0.341332	+	0.939943i	$0.389122\pi$
$572$	7.92478	−	17.5877i	0.331352	−	0.735378i
$573$			10.2374i			0.427675i
$574$			15.0132i			0.626638i
$575$	4.00000	+	0.493413i	0.166812	+	0.0205767i
$576$	−1.00000			−0.0416667
$577$	4.85685			0.202193			0.101097	−	0.994877i	$-0.467765\pi$
$577$	4.85685			0.202193			0.101097	+	0.994877i	$0.467765\pi$
$578$	−15.5745			−0.647814
$579$			9.06793i			0.376850i
$580$	11.1187	+	12.5745i	0.461679	+	0.522128i
$581$	−41.7743			−1.73309
$582$		−	2.93207i		−	0.121538i
$583$	29.6239			1.22690
$584$	4.08110			0.168877
$585$	2.38787	+	7.70052i	0.0987264	+	0.318377i
$586$	−23.9248			−0.988323
$587$	18.8218			0.776859			0.388429	−	0.921479i	$-0.373018\pi$
$587$	18.8218			0.776859			0.388429	+	0.921479i	$0.373018\pi$
$588$		−	10.2750i		−	0.423735i
$589$	22.2374			0.916277
$590$	21.5877	−	19.0884i	0.888751	−	0.785857i
$591$			3.14903i			0.129534i
$592$	7.35026			0.302094
$593$	5.59754			0.229863			0.114932	−	0.993373i	$-0.463335\pi$
$593$	5.59754			0.229863			0.114932	+	0.993373i	$0.463335\pi$
$594$	5.35026			0.219524
$595$	−8.31265	+	7.35026i	−0.340785	+	0.301331i
$596$		−	10.8872i		−	0.445956i
$597$		−	14.1114i		−	0.577542i
$598$	1.19394	−	2.64974i	0.0488237	−	0.108356i
$599$	47.9511			1.95923			0.979615	−	0.200885i	$-0.0643816\pi$
$599$	47.9511			1.95923			0.979615	+	0.200885i	$0.0643816\pi$
$600$	−4.96239	−	0.612127i	−0.202589	−	0.0249900i
$601$	−1.97556			−0.0805849			−0.0402924	−	0.999188i	$-0.512829\pi$
$601$	−1.97556			−0.0805849			−0.0402924	+	0.999188i	$0.512829\pi$
$602$			27.3258i			1.11372i
$603$	−4.57452			−0.186289
$604$			17.7889i			0.723821i
$605$	−26.1065	−	29.5247i	−1.06138	−	1.20035i
$606$			5.89446i			0.239446i
$607$			18.1622i			0.737181i	0.929592	+	0.368591i	$0.120160\pi$
$607$			18.1622i			0.737181i	−0.929592	+	0.368591i	$0.879840\pi$
$608$		−	2.80606i		−	0.113801i
$609$		−	31.1998i		−	1.26428i
$610$	−9.35026	−	10.5745i	−0.378581	−	0.428150i
$611$	40.4749	+	18.2374i	1.63744	+	0.737807i
$612$		−	1.19394i		−	0.0482620i
$613$	30.6761			1.23900			0.619498	−	0.784998i	$-0.287336\pi$
$613$	30.6761			1.23900			0.619498	+	0.784998i	$0.287336\pi$
$614$	33.5125			1.35245
$615$	−5.35026	−	6.05079i	−0.215743	−	0.243991i
$616$		−	22.2374i		−	0.895971i
$617$	−37.3258			−1.50268			−0.751341	−	0.659915i	$-0.770592\pi$
$617$	−37.3258			−1.50268			−0.751341	+	0.659915i	$0.770592\pi$
$618$	3.29948			0.132724
$619$			17.9814i			0.722735i	0.932423	+	0.361368i	$0.117690\pi$
$619$			17.9814i			0.722735i	−0.932423	+	0.361368i	$0.882310\pi$
$620$	13.2750	−	11.7381i	0.533138	−	0.471415i
$621$	0.806063			0.0323462
$622$	5.76257			0.231058
$623$		−	20.9380i		−	0.838861i
$624$	−1.48119	+	3.28726i	−0.0592952	+	0.131596i
$625$	−24.2506	−	6.07522i	−0.970024	−	0.243009i
$626$			12.6253i			0.504609i
$627$			15.0132i			0.599568i
$628$			10.7757i			0.429999i
$629$			8.77575i			0.349912i
$630$	6.15633	+	6.96239i	0.245274	+	0.277388i
$631$		−	32.2374i		−	1.28335i	−0.766976	−	0.641676i	$-0.778239\pi$
$631$		−	32.2374i		−	1.28335i	0.766976	−	0.641676i	$-0.221761\pi$
$632$	12.4387			0.494783
$633$			17.4617i			0.694040i
$634$	−3.73813			−0.148460
$635$	−30.4241	+	26.9018i	−1.20734	+	1.06756i
$636$	−5.53690			−0.219553
$637$	−33.7767	−	15.2193i	−1.33828	−	0.603012i
$638$		−	40.1622i		−	1.59004i
$639$			8.96239i			0.354547i
$640$	−1.48119	−	1.67513i	−0.0585493	−	0.0662154i
$641$	−12.6107			−0.498093			−0.249047	−	0.968492i	$-0.580117\pi$
$641$	−12.6107			−0.498093			−0.249047	+	0.968492i	$0.580117\pi$
$642$	19.7889			0.781006
$643$	−11.0230			−0.434706			−0.217353	−	0.976093i	$-0.569742\pi$
$643$	−11.0230			−0.434706			−0.217353	+	0.976093i	$0.569742\pi$
$644$		−	3.35026i		−	0.132019i
$645$	−9.73813	−	11.0132i	−0.383439	−	0.433643i
$646$	3.35026			0.131814
$647$		−	29.8046i		−	1.17174i	−0.810404	−	0.585871i	$-0.800753\pi$
$647$		−	29.8046i		−	1.17174i	0.810404	−	0.585871i	$-0.199247\pi$
$648$	−1.00000			−0.0392837
$649$	−68.9497			−2.70651
$650$	−9.36248	+	15.4060i	−0.367227	+	0.604272i
$651$	−32.9380			−1.29094
$652$	12.0508			0.471945
$653$		−	44.8627i		−	1.75561i	−0.479014	−	0.877807i	$-0.659006\pi$
$653$		−	44.8627i		−	1.75561i	0.479014	−	0.877807i	$-0.340994\pi$
$654$	9.43136			0.368796
$655$	−14.5442	−	16.4485i	−0.568289	−	0.642696i
$656$		−	3.61213i		−	0.141030i
$657$	4.08110			0.159219
$658$	51.1754			1.99502
$659$	26.9683			1.05053			0.525267	−	0.850937i	$-0.323965\pi$
$659$	26.9683			1.05053			0.525267	+	0.850937i	$0.323965\pi$
$660$	7.92478	+	8.96239i	0.308472	+	0.348861i
$661$			42.9537i			1.67070i	0.549715	+	0.835352i	$0.314736\pi$
$661$			42.9537i			1.67070i	−0.549715	+	0.835352i	$0.685264\pi$
$662$		−	1.81924i		−	0.0707067i
$663$	−3.92478	−	1.76845i	−0.152426	−	0.0686810i
$664$	10.0508			0.390046
$665$	−19.5369	+	17.2750i	−0.757609	+	0.669897i
$666$	7.35026			0.284817
$667$		−	6.05079i		−	0.234287i
$668$	−1.61213			−0.0623751
$669$			19.6326i			0.759040i
$670$	−6.77575	−	7.66291i	−0.261770	−	0.296044i
$671$			33.7743i			1.30384i
$672$			4.15633i			0.160334i
$673$		−	14.8627i		−	0.572916i	−0.958093	−	0.286458i	$-0.907522\pi$
$673$		−	14.8627i		−	0.572916i	0.958093	−	0.286458i	$-0.0924779\pi$
$674$		−	8.83638i		−	0.340365i
$675$	−4.96239	−	0.612127i	−0.191002	−	0.0235608i
$676$	8.61213	+	9.73813i	0.331236	+	0.374544i
$677$			0.911603i			0.0350358i	0.999847	+	0.0175179i	$0.00557640\pi$
$677$			0.911603i			0.0350358i	−0.999847	+	0.0175179i	$0.994424\pi$
$678$	4.41819			0.169680
$679$	−12.1866			−0.467680
$680$	2.00000	−	1.76845i	0.0766965	−	0.0678170i
$681$		−	4.77575i		−	0.183007i
$682$	−42.3996			−1.62357
$683$	27.1998			1.04077			0.520386	−	0.853931i	$-0.325788\pi$
$683$	27.1998			1.04077			0.520386	+	0.853931i	$0.325788\pi$
$684$		−	2.80606i		−	0.107293i
$685$	−1.35026	−	1.52705i	−0.0515908	−	0.0583458i
$686$	−13.6121			−0.519713
$687$	−19.5672			−0.746536
$688$		−	6.57452i		−	0.250651i
$689$	−8.20123	+	18.2012i	−0.312442	+	0.693412i
$690$	1.19394	+	1.35026i	0.0454524	+	0.0514036i
$691$			25.9697i			0.987933i	0.869481	+	0.493967i	$0.164454\pi$
$691$			25.9697i			0.987933i	−0.869481	+	0.493967i	$0.835546\pi$
$692$		−	1.22425i		−	0.0465391i
$693$		−	22.2374i		−	0.844730i
$694$			2.13586i			0.0810760i
$695$	1.23884	+	1.40105i	0.0469920	+	0.0531447i
$696$			7.50659i			0.284536i
$697$	4.31265			0.163353
$698$			16.4934i			0.624285i
$699$	−2.74543			−0.103842
$700$	−2.54420	+	20.6253i	−0.0961617	+	0.779563i
$701$	−5.20853			−0.196723			−0.0983616	−	0.995151i	$-0.531360\pi$
$701$	−5.20853			−0.196723			−0.0983616	+	0.995151i	$0.531360\pi$
$702$	−1.48119	+	3.28726i	−0.0559041	+	0.124070i
$703$			20.6253i			0.777898i
$704$			5.35026i			0.201646i
$705$	−20.6253	+	18.2374i	−0.776794	+	0.686861i
$706$	3.86414			0.145429
$707$	24.4993			0.921391
$708$	12.8872			0.484329
$709$		−	6.79147i		−	0.255059i	−0.991835	−	0.127530i	$-0.959295\pi$
$709$		−	6.79147i		−	0.255059i	0.991835	−	0.127530i	$-0.0407048\pi$
$710$	−15.0132	+	13.2750i	−0.563434	+	0.498203i
$711$	12.4387			0.466486
$712$			5.03761i			0.188792i
$713$	−6.38787			−0.239228
$714$	−4.96239			−0.185713
$715$	41.1998	−	12.7757i	1.54079	−	0.477786i
$716$	−1.25457			−0.0468855
$717$	5.29948			0.197913
$718$			18.5139i			0.690932i
$719$	−20.9986			−0.783115			−0.391558	−	0.920154i	$-0.628064\pi$
$719$	−20.9986			−0.783115			−0.391558	+	0.920154i	$0.628064\pi$
$720$	−1.48119	−	1.67513i	−0.0552009	−	0.0624284i
$721$		−	13.7137i		−	0.510725i
$722$	−11.1260			−0.414067
$723$	12.9380			0.481168
$724$	5.47627			0.203524
$725$	−4.59498	+	37.2506i	−0.170653	+	1.38345i
$726$		−	17.6253i		−	0.654136i
$727$			21.4763i			0.796511i	0.917275	+	0.398255i	$0.130384\pi$
$727$			21.4763i			0.796511i	−0.917275	+	0.398255i	$0.869616\pi$
$728$	13.6629	+	6.15633i	0.506381	+	0.228169i
$729$	−1.00000			−0.0370370
$730$	6.04491	+	6.83638i	0.223732	+	0.253026i
$731$	7.84955			0.290326
$732$		−	6.31265i		−	0.233322i
$733$	10.5139			0.388339			0.194170	−	0.980968i	$-0.437799\pi$
$733$	10.5139			0.388339			0.194170	+	0.980968i	$0.437799\pi$
$734$		−	23.7137i		−	0.875289i
$735$	17.2120	−	15.2193i	0.634875	−	0.561373i
$736$			0.806063i			0.0297119i
$737$			24.4749i			0.901543i
$738$		−	3.61213i		−	0.132964i
$739$		−	22.7454i		−	0.836704i	−0.908285	−	0.418352i	$-0.862608\pi$
$739$		−	22.7454i		−	0.836704i	0.908285	−	0.418352i	$-0.137392\pi$
$740$	10.8872	+	12.3127i	0.400220	+	0.452622i
$741$	−9.22425	−	4.15633i	−0.338861	−	0.152686i
$742$			23.0132i			0.844840i
$743$	−31.9511			−1.17217			−0.586087	−	0.810248i	$-0.699332\pi$
$743$	−31.9511			−1.17217			−0.586087	+	0.810248i	$0.699332\pi$
$744$	7.92478			0.290536
$745$	18.2374	−	16.1260i	0.668168	−	0.590811i
$746$		−	11.1490i		−	0.408195i
$747$	10.0508			0.367739
$748$	−6.38787			−0.233564
$749$		−	82.2492i		−	3.00532i
$750$	−6.32487	−	9.21933i	−0.230952	−	0.336642i
$751$	11.5975			0.423200			0.211600	−	0.977356i	$-0.432133\pi$
$751$	11.5975			0.423200			0.211600	+	0.977356i	$0.432133\pi$
$752$	−12.3127			−0.448996
$753$		−	8.10554i		−	0.295382i
$754$	24.6761	+	11.1187i	0.898650	+	0.404920i
$755$	−29.7988	+	26.3488i	−1.08449	+	0.958933i
$756$			4.15633i			0.151164i
$757$			33.5125i			1.21803i	0.793158	+	0.609016i	$0.208435\pi$
$757$			33.5125i			1.21803i	−0.793158	+	0.609016i	$0.791565\pi$
$758$			38.7572i			1.40772i
$759$		−	4.31265i		−	0.156539i
$760$	4.70052	−	4.15633i	0.170506	−	0.150766i
$761$			36.7123i			1.33082i	0.746478	+	0.665410i	$0.231743\pi$
$761$			36.7123i			1.33082i	−0.746478	+	0.665410i	$0.768257\pi$
$762$	−18.1622			−0.657947
$763$		−	39.1998i		−	1.41913i
$764$	−10.2374			−0.370377
$765$	2.00000	−	1.76845i	0.0723102	−	0.0639385i
$766$	1.76257			0.0636843
$767$	19.0884	−	42.3634i	0.689242	−	1.52966i
$768$		−	1.00000i		−	0.0360844i
$769$		−	45.4010i		−	1.63720i	−0.574361	−	0.818602i	$-0.694750\pi$
$769$		−	45.4010i		−	1.63720i	0.574361	−	0.818602i	$-0.305250\pi$
$770$	37.2506	−	32.9380i	1.34242	−	1.18700i
$771$	12.0567			0.434210
$772$	−9.06793			−0.326362
$773$	2.52373			0.0907723			0.0453861	−	0.998970i	$-0.485548\pi$
$773$	2.52373			0.0907723			0.0453861	+	0.998970i	$0.485548\pi$
$774$		−	6.57452i		−	0.236316i
$775$	39.3258	+	4.85097i	1.41263	+	0.174252i
$776$	2.93207			0.105255
$777$		−	30.5501i		−	1.09598i
$778$	−34.0567			−1.22099
$779$	10.1359			0.363155
$780$	−7.70052	+	2.38787i	−0.275723	+	0.0854996i
$781$	47.9511			1.71583
$782$	−0.962389			−0.0344149
$783$			7.50659i			0.268264i
$784$	10.2750			0.366966
$785$	−18.0508	+	15.9610i	−0.644260	+	0.569672i
$786$		−	9.81924i		−	0.350241i
$787$	−7.12459			−0.253964			−0.126982	−	0.991905i	$-0.540529\pi$
$787$	−7.12459			−0.253964			−0.126982	+	0.991905i	$0.540529\pi$
$788$	−3.14903			−0.112180
$789$	−4.28233			−0.152455
$790$	18.4241	+	20.8364i	0.655499	+	0.741325i
$791$		−	18.3634i		−	0.652929i
$792$			5.35026i			0.190113i
$793$	−20.7513	−	9.35026i	−0.736901	−	0.332038i
$794$	−15.8134			−0.561195
$795$	−8.20123	−	9.27504i	−0.290868	−	0.328952i
$796$	14.1114			0.500166
$797$			42.2031i			1.49491i	0.664311	+	0.747456i	$0.268725\pi$
$797$			42.2031i			1.49491i	−0.664311	+	0.747456i	$0.731275\pi$
$798$	−11.6629			−0.412863
$799$		−	14.7005i		−	0.520067i
$800$	0.612127	−	4.96239i	0.0216420	−	0.175447i
$801$			5.03761i			0.177995i
$802$		−	25.0132i		−	0.883246i
$803$		−	21.8350i		−	0.770539i
$804$		−	4.57452i		−	0.161331i
$805$	5.61213	−	4.96239i	0.197801	−	0.174901i
$806$	11.7381	−	26.0508i	0.413458	−	0.917600i
$807$			19.8799i			0.699805i
$808$	−5.89446			−0.207366
$809$	−32.2374			−1.13341			−0.566704	−	0.823922i	$-0.691782\pi$
$809$	−32.2374			−1.13341			−0.566704	+	0.823922i	$0.691782\pi$
$810$	−1.48119	−	1.67513i	−0.0520439	−	0.0588581i
$811$		−	38.9076i		−	1.36623i	−0.730310	−	0.683116i	$-0.760624\pi$
$811$		−	38.9076i		−	1.36623i	0.730310	−	0.683116i	$-0.239376\pi$
$812$	31.1998			1.09490
$813$	−5.01317			−0.175820
$814$		−	39.3258i		−	1.37837i
$815$	17.8496	+	20.1866i	0.625243	+	0.707107i
$816$	1.19394			0.0417961
$817$	18.4485			0.645432
$818$			34.0263i			1.18970i
$819$	13.6629	+	6.15633i	0.477421	+	0.215119i
$820$	6.05079	−	5.35026i	0.211303	−	0.186839i
$821$			44.4095i			1.54990i	0.632022	+	0.774951i	$0.282225\pi$
$821$			44.4095i			1.54990i	−0.632022	+	0.774951i	$0.717775\pi$
$822$		−	0.911603i		−	0.0317958i
$823$		−	14.0000i		−	0.488009i	−0.969774	−	0.244005i	$-0.921539\pi$
$823$		−	14.0000i		−	0.488009i	0.969774	−	0.244005i	$-0.0784612\pi$
$824$			3.29948i			0.114943i
$825$	−3.27504	+	26.5501i	−0.114022	+	0.924355i
$826$		−	53.5633i		−	1.86370i
$827$	9.02302			0.313761			0.156881	−	0.987618i	$-0.449856\pi$
$827$	9.02302			0.313761			0.156881	+	0.987618i	$0.449856\pi$
$828$			0.806063i			0.0280126i
$829$	−43.1002			−1.49693			−0.748465	−	0.663174i	$-0.769209\pi$
$829$	−43.1002			−1.49693			−0.748465	+	0.663174i	$0.769209\pi$
$830$	14.8872	+	16.8364i	0.516741	+	0.584399i
$831$	−8.55008			−0.296599
$832$	−3.28726	−	1.48119i	−0.113965	−	0.0513512i
$833$			12.2677i			0.425052i
$834$			0.836381i			0.0289615i
$835$	−2.38787	−	2.70052i	−0.0826358	−	0.0934555i
$836$	−15.0132			−0.519241
$837$	7.92478			0.273920
$838$	3.73226			0.128929
$839$			12.5237i			0.432367i	0.976353	+	0.216184i	$0.0693610\pi$
$839$			12.5237i			0.432367i	−0.976353	+	0.216184i	$0.930639\pi$
$840$	−6.96239	+	6.15633i	−0.240225	+	0.212413i
$841$	27.3488			0.943064
$842$		−	16.9683i		−	0.584765i
$843$	−25.5125			−0.878696
$844$	−17.4617			−0.601056
$845$	−3.55642	+	28.8505i	−0.122344	+	0.992488i
$846$	−12.3127			−0.423318
$847$	−73.2565			−2.51712
$848$		−	5.53690i		−	0.190138i
$849$	23.7235			0.814190
$850$	5.92478	+	0.730841i	0.203218	+	0.0250676i
$851$		−	5.92478i		−	0.203099i
$852$	−8.96239			−0.307046
$853$	−42.3146			−1.44882			−0.724411	−	0.689368i	$-0.757888\pi$
$853$	−42.3146			−1.44882			−0.724411	+	0.689368i	$0.757888\pi$
$854$	−26.2374			−0.897826
$855$	4.70052	−	4.15633i	0.160755	−	0.142143i
$856$			19.7889i			0.676371i
$857$		−	27.9960i		−	0.956326i	−0.878271	−	0.478163i	$-0.841303\pi$
$857$		−	27.9960i		−	0.956326i	0.878271	−	0.478163i	$-0.158697\pi$
$858$	17.5877	+	7.92478i	0.600434	+	0.270547i
$859$	−27.3865			−0.934414			−0.467207	−	0.884148i	$-0.654740\pi$
$859$	−27.3865			−0.934414			−0.467207	+	0.884148i	$0.654740\pi$
$860$	11.0132	−	9.73813i	0.375546	−	0.332068i
$861$	−15.0132			−0.511648
$862$			20.9986i			0.715215i
$863$	−40.0118			−1.36202			−0.681008	−	0.732276i	$-0.738458\pi$
$863$	−40.0118			−1.36202			−0.681008	+	0.732276i	$0.738458\pi$
$864$		−	1.00000i		−	0.0340207i
$865$	2.05079	−	1.81336i	0.0697288	−	0.0616560i
$866$			17.3404i			0.589251i
$867$		−	15.5745i		−	0.528938i
$868$		−	32.9380i		−	1.11799i
$869$		−	66.5501i		−	2.25756i
$870$	−12.5745	+	11.1187i	−0.426316	+	0.376960i
$871$	−15.0376	−	6.77575i	−0.509530	−	0.229587i
$872$			9.43136i			0.319386i
$873$	2.93207			0.0992356
$874$	−2.26187			−0.0765087
$875$	−38.3185	+	26.2882i	−1.29540	+	0.888704i
$876$			4.08110i			0.137888i
$877$	21.9610			0.741569			0.370785	−	0.928719i	$-0.379089\pi$
$877$	21.9610			0.741569			0.370785	+	0.928719i	$0.379089\pi$
$878$	−13.7743			−0.464861
$879$		−	23.9248i		−	0.806963i
$880$	−8.96239	+	7.92478i	−0.302122	+	0.267144i
$881$	−39.9657			−1.34648			−0.673240	−	0.739424i	$-0.735098\pi$
$881$	−39.9657			−1.34648			−0.673240	+	0.739424i	$0.735098\pi$
$882$	10.2750			0.345979
$883$			19.4763i			0.655429i	0.944777	+	0.327714i	$0.106278\pi$
$883$			19.4763i			0.655429i	−0.944777	+	0.327714i	$0.893722\pi$
$884$	1.76845	−	3.92478i	0.0594795	−	0.132005i
$885$	19.0884	+	21.5877i	0.641649	+	0.725662i
$886$		−	9.61213i		−	0.322926i
$887$			43.5672i			1.46284i	0.681925	+	0.731422i	$0.261143\pi$
$887$			43.5672i			1.46284i	−0.681925	+	0.731422i	$0.738857\pi$
$888$			7.35026i			0.246659i
$889$			75.4880i			2.53179i
$890$	−8.43866	+	7.46168i	−0.282864	+	0.250116i
$891$			5.35026i			0.179241i
$892$	−19.6326			−0.657348
$893$		−	34.5501i		−	1.15617i
$894$	10.8872			0.364121
$895$	−1.85826	−	2.10157i	−0.0621149	−	0.0702478i
$896$	−4.15633			−0.138853
$897$	2.64974	+	1.19394i	0.0884722	+	0.0398644i
$898$		−	25.6629i		−	0.856382i
$899$		−	59.4880i		−	1.98404i
$900$	0.612127	−	4.96239i	0.0204042	−	0.165413i
$901$	6.61071			0.220235
$902$	−19.3258			−0.643480
$903$	−27.3258			−0.909346
$904$			4.41819i			0.146947i
$905$	8.11142	+	9.17347i	0.269633	+	0.304936i
$906$	−17.7889			−0.590997
$907$		−	35.3014i		−	1.17216i	−0.810252	−	0.586082i	$-0.800670\pi$
$907$		−	35.3014i		−	1.17216i	0.810252	−	0.586082i	$-0.199330\pi$
$908$	4.77575			0.158489
$909$	−5.89446			−0.195507
$910$	9.92478	+	32.0059i	0.329003	+	1.06098i
$911$	36.8773			1.22180			0.610900	−	0.791708i	$-0.290808\pi$
$911$	36.8773			1.22180			0.610900	+	0.791708i	$0.290808\pi$
$912$	2.80606			0.0929180
$913$		−	53.7743i		−	1.77967i
$914$	22.9321			0.758526
$915$	10.5745	−	9.35026i	0.349583	−	0.309110i
$916$		−	19.5672i		−	0.646519i
$917$	−40.8119			−1.34773
$918$	1.19394			0.0394058
$919$	−45.1490			−1.48933			−0.744665	−	0.667439i	$-0.767391\pi$
$919$	−45.1490			−1.48933			−0.744665	+	0.667439i	$0.767391\pi$
$920$	−1.35026	+	1.19394i	−0.0445168	+	0.0393629i
$921$			33.5125i			1.10427i
$922$		−	22.7367i		−	0.748794i
$923$	−13.2750	+	29.4617i	−0.436953	+	0.969743i
$924$	22.2374			0.731558
$925$	−4.49929	+	36.4749i	−0.147936	+	1.19929i
$926$	−5.08252			−0.167022
$927$			3.29948i			0.108369i
$928$	−7.50659			−0.246416
$929$		−	11.8594i		−	0.389094i	−0.980893	−	0.194547i	$-0.937676\pi$
$929$		−	11.8594i		−	0.389094i	0.980893	−	0.194547i	$-0.0623237\pi$
$930$	11.7381	+	13.2750i	0.384909	+	0.435306i
$931$			28.8324i			0.944944i
$932$		−	2.74543i		−	0.0899295i
$933$			5.76257i			0.188658i
$934$		−	16.4631i		−	0.538689i
$935$	−9.46168	−	10.7005i	−0.309430	−	0.349945i
$936$	−3.28726	−	1.48119i	−0.107447	−	0.0484144i
$937$		−	14.6399i		−	0.478264i	−0.970987	−	0.239132i	$-0.923137\pi$
$937$		−	14.6399i		−	0.478264i	0.970987	−	0.239132i	$-0.0768629\pi$
$938$	−19.0132			−0.620802
$939$	−12.6253			−0.412011
$940$	−18.2374	−	20.6253i	−0.594839	−	0.672723i
$941$		−	33.0033i		−	1.07588i	−0.842984	−	0.537939i	$-0.819203\pi$
$941$		−	33.0033i		−	1.07588i	0.842984	−	0.537939i	$-0.180797\pi$
$942$	−10.7757			−0.351093
$943$	−2.91160			−0.0948149
$944$			12.8872i			0.419442i
$945$	−6.96239	+	6.15633i	−0.226487	+	0.200265i
$946$	−35.1754			−1.14365
$947$	14.5745			0.473608			0.236804	−	0.971557i	$-0.423900\pi$
$947$	14.5745			0.473608			0.236804	+	0.971557i	$0.423900\pi$
$948$			12.4387i			0.403989i
$949$	13.4156	+	6.04491i	0.435490	+	0.196226i
$950$	13.9248	+	1.71767i	0.451779	+	0.0557285i
$951$		−	3.73813i		−	0.121217i
$952$		−	4.96239i		−	0.160832i
$953$		−	26.0910i		−	0.845169i	−0.906324	−	0.422584i	$-0.861123\pi$
$953$		−	26.0910i		−	0.845169i	0.906324	−	0.422584i	$-0.138877\pi$
$954$		−	5.53690i		−	0.179264i
$955$	−15.1636	−	17.1490i	−0.490683	−	0.554930i
$956$			5.29948i			0.171397i
$957$	40.1622			1.29826
$958$			8.15045i			0.263329i
$959$	−3.78892			−0.122351
$960$	1.67513	−	1.48119i	0.0540646	−	0.0478053i
$961$	−31.8021			−1.02587
$962$	24.1622	+	10.8872i	0.779021	+	0.351016i
$963$			19.7889i			0.637689i
$964$			12.9380i			0.416703i
$965$	−13.4314	−	15.1900i	−0.432371	−	0.488982i
$966$	3.35026			0.107793
$967$	−56.7328			−1.82440			−0.912201	−	0.409743i	$-0.865618\pi$
$967$	−56.7328			−1.82440			−0.912201	+	0.409743i	$0.865618\pi$
$968$	17.6253			0.566499
$969$			3.35026i			0.107626i
$970$	4.34297	+	4.91160i	0.139444	+	0.157702i
$971$	33.4168			1.07240			0.536198	−	0.844092i	$-0.319860\pi$
$971$	33.4168			1.07240			0.536198	+	0.844092i	$0.319860\pi$
$972$		−	1.00000i		−	0.0320750i
$973$	3.47627			0.111444
$974$	−35.4215			−1.13498
$975$	−15.4060	−	9.36248i	−0.493386	−	0.299839i
$976$	6.31265			0.202063
$977$	37.5778			1.20222			0.601111	−	0.799166i	$-0.294725\pi$
$977$	37.5778			1.20222			0.601111	+	0.799166i	$0.294725\pi$
$978$			12.0508i			0.385342i
$979$	26.9525			0.861407
$980$	15.2193	+	17.2120i	0.486164	+	0.549818i
$981$			9.43136i			0.301120i
$982$	35.8046			1.14257
$983$	−34.2981			−1.09394			−0.546969	−	0.837153i	$-0.684219\pi$
$983$	−34.2981			−1.09394			−0.546969	+	0.837153i	$0.684219\pi$
$984$	3.61213			0.115150
$985$	−4.66433	−	5.27504i	−0.148618	−	0.168077i
$986$		−	8.96239i		−	0.285421i
$987$			51.1754i			1.62893i
$988$	4.15633	−	9.22425i	0.132230	−	0.293463i
$989$	−5.29948			−0.168514
$990$	−8.96239	+	7.92478i	−0.284843	+	0.251866i
$991$	19.5613			0.621386			0.310693	−	0.950510i	$-0.399439\pi$
$991$	19.5613			0.621386			0.310693	+	0.950510i	$0.399439\pi$
$992$			7.92478i			0.251612i
$993$	1.81924			0.0577317
$994$			37.2506i			1.18152i
$995$	20.9018	+	23.6385i	0.662630	+	0.749390i
$996$			10.0508i			0.318471i
$997$			45.9511i			1.45529i	0.685956	+	0.727643i	$0.259384\pi$
$997$			45.9511i			1.45529i	−0.685956	+	0.727643i	$0.740616\pi$
$998$		−	29.1939i		−	0.924118i
$999$			7.35026i			0.232552i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	390.2.f.a.259.3	✓	6
3.2	odd	2		1170.2.f.d.649.1		6
4.3	odd	2		3120.2.r.g.2209.6		6
5.2	odd	4		1950.2.b.l.1351.3		6
5.3	odd	4		1950.2.b.m.1351.4		6
5.4	even	2		390.2.f.b.259.4	yes	6
13.12	even	2		390.2.f.b.259.1	yes	6
15.14	odd	2		1170.2.f.c.649.5		6
20.19	odd	2		3120.2.r.h.2209.1		6
39.38	odd	2		1170.2.f.c.649.6		6
52.51	odd	2		3120.2.r.h.2209.4		6
65.12	odd	4		1950.2.b.l.1351.4		6
65.38	odd	4		1950.2.b.m.1351.3		6
65.64	even	2	inner	390.2.f.a.259.6	yes	6
195.194	odd	2		1170.2.f.d.649.2		6
260.259	odd	2		3120.2.r.g.2209.3		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
390.2.f.a.259.3	✓	6	1.1	even	1	trivial
390.2.f.a.259.6	yes	6	65.64	even	2	inner
390.2.f.b.259.1	yes	6	13.12	even	2
390.2.f.b.259.4	yes	6	5.4	even	2
1170.2.f.c.649.5		6	15.14	odd	2
1170.2.f.c.649.6		6	39.38	odd	2
1170.2.f.d.649.1		6	3.2	odd	2
1170.2.f.d.649.2		6	195.194	odd	2
1950.2.b.l.1351.3		6	5.2	odd	4
1950.2.b.l.1351.4		6	65.12	odd	4
1950.2.b.m.1351.3		6	65.38	odd	4
1950.2.b.m.1351.4		6	5.3	odd	4
3120.2.r.g.2209.3		6	260.259	odd	2
3120.2.r.g.2209.6		6	4.3	odd	2
3120.2.r.h.2209.1		6	20.19	odd	2
3120.2.r.h.2209.4		6	52.51	odd	2

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:	\( N \)	\(=\)	\( 390 = 2 \cdot 3 \cdot 5 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	390.f (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} -1.00000i q^{3} +1.00000 q^{4} +(1.48119 + 1.67513i) q^{5} +1.00000i q^{6} +4.15633 q^{7} -1.00000 q^{8} -1.00000 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} -1.00000i q^{3} +1.00000 q^{4} +(1.48119 + 1.67513i) q^{5} +1.00000i q^{6} +4.15633 q^{7} -1.00000 q^{8} -1.00000 q^{9} +(-1.48119 - 1.67513i) q^{10} +5.35026i q^{11} -1.00000i q^{12} +(-3.28726 - 1.48119i) q^{13} -4.15633 q^{14} +(1.67513 - 1.48119i) q^{15} +1.00000 q^{16} +1.19394i q^{17} +1.00000 q^{18} +2.80606i q^{19} +(1.48119 + 1.67513i) q^{20} -4.15633i q^{21} -5.35026i q^{22} -0.806063i q^{23} +1.00000i q^{24} +(-0.612127 + 4.96239i) q^{25} +(3.28726 + 1.48119i) q^{26} +1.00000i q^{27} +4.15633 q^{28} +7.50659 q^{29} +(-1.67513 + 1.48119i) q^{30} -7.92478i q^{31} -1.00000 q^{32} +5.35026 q^{33} -1.19394i q^{34} +(6.15633 + 6.96239i) q^{35} -1.00000 q^{36} +7.35026 q^{37} -2.80606i q^{38} +(-1.48119 + 3.28726i) q^{39} +(-1.48119 - 1.67513i) q^{40} -3.61213i q^{41} +4.15633i q^{42} -6.57452i q^{43} +5.35026i q^{44} +(-1.48119 - 1.67513i) q^{45} +0.806063i q^{46} -12.3127 q^{47} -1.00000i q^{48} +10.2750 q^{49} +(0.612127 - 4.96239i) q^{50} +1.19394 q^{51} +(-3.28726 - 1.48119i) q^{52} -5.53690i q^{53} -1.00000i q^{54} +(-8.96239 + 7.92478i) q^{55} -4.15633 q^{56} +2.80606 q^{57} -7.50659 q^{58} +12.8872i q^{59} +(1.67513 - 1.48119i) q^{60} +6.31265 q^{61} +7.92478i q^{62} -4.15633 q^{63} +1.00000 q^{64} +(-2.38787 - 7.70052i) q^{65} -5.35026 q^{66} +4.57452 q^{67} +1.19394i q^{68} -0.806063 q^{69} +(-6.15633 - 6.96239i) q^{70} -8.96239i q^{71} +1.00000 q^{72} -4.08110 q^{73} -7.35026 q^{74} +(4.96239 + 0.612127i) q^{75} +2.80606i q^{76} +22.2374i q^{77} +(1.48119 - 3.28726i) q^{78} -12.4387 q^{79} +(1.48119 + 1.67513i) q^{80} +1.00000 q^{81} +3.61213i q^{82} -10.0508 q^{83} -4.15633i q^{84} +(-2.00000 + 1.76845i) q^{85} +6.57452i q^{86} -7.50659i q^{87} -5.35026i q^{88} -5.03761i q^{89} +(1.48119 + 1.67513i) q^{90} +(-13.6629 - 6.15633i) q^{91} -0.806063i q^{92} -7.92478 q^{93} +12.3127 q^{94} +(-4.70052 + 4.15633i) q^{95} +1.00000i q^{96} -2.93207 q^{97} -10.2750 q^{98} -5.35026i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - 6 q^{2} + 6 q^{4} - 2 q^{5} + 4 q^{7} - 6 q^{8} - 6 q^{9}+O(q^{10}) \) 6 * q - 6 * q^2 + 6 * q^4 - 2 * q^5 + 4 * q^7 - 6 * q^8 - 6 * q^9	\( 6 q - 6 q^{2} + 6 q^{4} - 2 q^{5} + 4 q^{7} - 6 q^{8} - 6 q^{9} + 2 q^{10} - 8 q^{13} - 4 q^{14} + 6 q^{16} + 6 q^{18} - 2 q^{20} - 2 q^{25} + 8 q^{26} + 4 q^{28} + 4 q^{29} - 6 q^{32} + 12 q^{33} + 16 q^{35} - 6 q^{36} + 24 q^{37} + 2 q^{39} + 2 q^{40} + 2 q^{45} - 32 q^{47} - 2 q^{49} + 2 q^{50} + 8 q^{51} - 8 q^{52} - 32 q^{55} - 4 q^{56} + 16 q^{57} - 4 q^{58} - 4 q^{61} - 4 q^{63} + 6 q^{64} - 16 q^{65} - 12 q^{66} + 4 q^{67} - 4 q^{69} - 16 q^{70} + 6 q^{72} + 40 q^{73} - 24 q^{74} + 8 q^{75} - 2 q^{78} - 16 q^{79} - 2 q^{80} + 6 q^{81} - 12 q^{85} - 2 q^{90} - 20 q^{91} - 4 q^{93} + 32 q^{94} + 12 q^{95} + 2 q^{98}+O(q^{100}) \) 6 * q - 6 * q^2 + 6 * q^4 - 2 * q^5 + 4 * q^7 - 6 * q^8 - 6 * q^9 + 2 * q^10 - 8 * q^13 - 4 * q^14 + 6 * q^16 + 6 * q^18 - 2 * q^20 - 2 * q^25 + 8 * q^26 + 4 * q^28 + 4 * q^29 - 6 * q^32 + 12 * q^33 + 16 * q^35 - 6 * q^36 + 24 * q^37 + 2 * q^39 + 2 * q^40 + 2 * q^45 - 32 * q^47 - 2 * q^49 + 2 * q^50 + 8 * q^51 - 8 * q^52 - 32 * q^55 - 4 * q^56 + 16 * q^57 - 4 * q^58 - 4 * q^61 - 4 * q^63 + 6 * q^64 - 16 * q^65 - 12 * q^66 + 4 * q^67 - 4 * q^69 - 16 * q^70 + 6 * q^72 + 40 * q^73 - 24 * q^74 + 8 * q^75 - 2 * q^78 - 16 * q^79 - 2 * q^80 + 6 * q^81 - 12 * q^85 - 2 * q^90 - 20 * q^91 - 4 * q^93 + 32 * q^94 + 12 * q^95 + 2 * q^98

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