LMFDB - Embedded newform 390.2.f.a.259.2

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [390,2,Mod(259,390)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://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);

sage: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")

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:traces = [6,-6] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(2)] == traces)

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			259.2
Root			$1.45161 + 1.45161i$ of defining polynomial
Character	$\chi$	$=$	390.259
Dual form			390.2.f.a.259.5

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q-1.00000 q^{2} -1.00000i q^{3} +1.00000 q^{4} +(-0.311108 - 2.21432i) q^{5} +1.00000i q^{6} -1.52543 q^{7} -1.00000 q^{8} -1.00000 q^{9} +(0.311108 + 2.21432i) q^{10} -2.42864i q^{11} -1.00000i q^{12} +(-3.59210 + 0.311108i) q^{13} +1.52543 q^{14} +(-2.21432 + 0.311108i) q^{15} +1.00000 q^{16} -0.903212i q^{17} +1.00000 q^{18} +4.90321i q^{19} +(-0.311108 - 2.21432i) q^{20} +1.52543i q^{21} +2.42864i q^{22} -2.90321i q^{23} +1.00000i q^{24} +(-4.80642 + 1.37778i) q^{25} +(3.59210 - 0.311108i) q^{26} +1.00000i q^{27} -1.52543 q^{28} -5.95407 q^{29} +(2.21432 - 0.311108i) q^{30} -0.755569i q^{31} -1.00000 q^{32} -2.42864 q^{33} +0.903212i q^{34} +(0.474572 + 3.37778i) q^{35} -1.00000 q^{36} -0.428639 q^{37} -4.90321i q^{38} +(0.311108 + 3.59210i) q^{39} +(0.311108 + 2.21432i) q^{40} -7.80642i q^{41} -1.52543i q^{42} -7.18421i q^{43} -2.42864i q^{44} +(0.311108 + 2.21432i) q^{45} +2.90321i q^{46} -0.949145 q^{47} -1.00000i q^{48} -4.67307 q^{49} +(4.80642 - 1.37778i) q^{50} -0.903212 q^{51} +(-3.59210 + 0.311108i) q^{52} -2.56199i q^{53} -1.00000i q^{54} +(-5.37778 + 0.755569i) q^{55} +1.52543 q^{56} +4.90321 q^{57} +5.95407 q^{58} +2.13335i q^{59} +(-2.21432 + 0.311108i) q^{60} -5.05086 q^{61} +0.755569i q^{62} +1.52543 q^{63} +1.00000 q^{64} +(1.80642 + 7.85728i) q^{65} +2.42864 q^{66} +5.18421 q^{67} -0.903212i q^{68} -2.90321 q^{69} +(-0.474572 - 3.37778i) q^{70} -5.37778i q^{71} +1.00000 q^{72} +8.76986 q^{73} +0.428639 q^{74} +(1.37778 + 4.80642i) q^{75} +4.90321i q^{76} +3.70471i q^{77} +(-0.311108 - 3.59210i) q^{78} +15.0923 q^{79} +(-0.311108 - 2.21432i) q^{80} +1.00000 q^{81} +7.80642i q^{82} +13.2859 q^{83} +1.52543i q^{84} +(-2.00000 + 0.280996i) q^{85} +7.18421i q^{86} +5.95407i q^{87} +2.42864i q^{88} -8.62222i q^{89} +(-0.311108 - 2.21432i) q^{90} +(5.47949 - 0.474572i) q^{91} -2.90321i q^{92} -0.755569 q^{93} +0.949145 q^{94} +(10.8573 - 1.52543i) q^{95} +1.00000i q^{96} +11.1383 q^{97} +4.67307 q^{98} +2.42864i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q - 6 q^{2} + 6 q^{4} - 2 q^{5} + 4 q^{7} - 6 q^{8} - 6 q^{9} + 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}+ \cdots + 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

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
$5$	−0.311108	−	2.21432i	−0.139132	−	0.990274i
$5$	−0.311108	−	2.21432i	−0.139132	−	0.990274i
$6$			1.00000i			0.408248i
$7$	−1.52543			−0.576557			−0.288279	−	0.957547i	$-0.593083\pi$
$7$	−1.52543			−0.576557			−0.288279	+	0.957547i	$0.593083\pi$
$8$	−1.00000			−0.353553
$9$	−1.00000			−0.333333
$10$	0.311108	+	2.21432i	0.0983809	+	0.700229i
$11$		−	2.42864i		−	0.732262i	−0.930563	−	0.366131i	$-0.880682\pi$
$11$		−	2.42864i		−	0.732262i	0.930563	−	0.366131i	$-0.119318\pi$
$12$		−	1.00000i		−	0.288675i
$13$	−3.59210	+	0.311108i	−0.996270	+	0.0862858i
$13$	−3.59210	+	0.311108i	−0.996270	+	0.0862858i
$14$	1.52543			0.407688
$15$	−2.21432	+	0.311108i	−0.571735	+	0.0803277i
$16$	1.00000			0.250000
$17$		−	0.903212i		−	0.219061i	−0.993983	−	0.109531i	$-0.965065\pi$
$17$		−	0.903212i		−	0.219061i	0.993983	−	0.109531i	$-0.0349347\pi$
$18$	1.00000			0.235702
$19$			4.90321i			1.12487i	0.826840	+	0.562437i	$0.190136\pi$
$19$			4.90321i			1.12487i	−0.826840	+	0.562437i	$0.809864\pi$
$20$	−0.311108	−	2.21432i	−0.0695658	−	0.495137i
$21$			1.52543i			0.332876i
$22$			2.42864i			0.517788i
$23$		−	2.90321i		−	0.605362i	−0.953092	−	0.302681i	$-0.902118\pi$
$23$		−	2.90321i		−	0.605362i	0.953092	−	0.302681i	$-0.0978816\pi$
$24$			1.00000i			0.204124i
$25$	−4.80642	+	1.37778i	−0.961285	+	0.275557i
$26$	3.59210	−	0.311108i	0.704470	−	0.0610133i
$27$			1.00000i			0.192450i
$28$	−1.52543			−0.288279
$29$	−5.95407			−1.10564			−0.552821	−	0.833300i	$-0.686449\pi$
$29$	−5.95407			−1.10564			−0.552821	+	0.833300i	$0.686449\pi$
$30$	2.21432	−	0.311108i	0.404278	−	0.0568003i
$31$		−	0.755569i		−	0.135704i	−0.997695	−	0.0678521i	$-0.978385\pi$
$31$		−	0.755569i		−	0.135704i	0.997695	−	0.0678521i	$-0.0216146\pi$
$32$	−1.00000			−0.176777
$33$	−2.42864			−0.422772
$34$			0.903212i			0.154900i
$35$	0.474572	+	3.37778i	0.0802174	+	0.570950i
$36$	−1.00000			−0.166667
$37$	−0.428639			−0.0704679			−0.0352339	−	0.999379i	$-0.511218\pi$
$37$	−0.428639			−0.0704679			−0.0352339	+	0.999379i	$0.511218\pi$
$38$		−	4.90321i		−	0.795406i
$39$	0.311108	+	3.59210i	0.0498171	+	0.575197i
$40$	0.311108	+	2.21432i	0.0491905	+	0.350115i
$41$		−	7.80642i		−	1.21916i	−0.792725	−	0.609579i	$-0.791338\pi$
$41$		−	7.80642i		−	1.21916i	0.792725	−	0.609579i	$-0.208662\pi$
$42$		−	1.52543i		−	0.235379i
$43$		−	7.18421i		−	1.09558i	−0.836615	−	0.547791i	$-0.815469\pi$
$43$		−	7.18421i		−	1.09558i	0.836615	−	0.547791i	$-0.184531\pi$
$44$		−	2.42864i		−	0.366131i
$45$	0.311108	+	2.21432i	0.0463772	+	0.330091i
$46$			2.90321i			0.428055i
$47$	−0.949145			−0.138447			−0.0692235	−	0.997601i	$-0.522052\pi$
$47$	−0.949145			−0.138447			−0.0692235	+	0.997601i	$0.522052\pi$
$48$		−	1.00000i		−	0.144338i
$49$	−4.67307			−0.667582
$50$	4.80642	−	1.37778i	0.679731	−	0.194848i
$51$	−0.903212			−0.126475
$52$	−3.59210	+	0.311108i	−0.498135	+	0.0431429i
$53$		−	2.56199i		−	0.351917i	−0.984398	−	0.175958i	$-0.943698\pi$
$53$		−	2.56199i		−	0.351917i	0.984398	−	0.175958i	$-0.0563024\pi$
$54$		−	1.00000i		−	0.136083i
$55$	−5.37778	+	0.755569i	−0.725140	+	0.101881i
$56$	1.52543			0.203844
$57$	4.90321			0.649446
$58$	5.95407			0.781807
$59$			2.13335i			0.277739i	0.990311	+	0.138869i	$0.0443468\pi$
$59$			2.13335i			0.277739i	−0.990311	+	0.138869i	$0.955653\pi$
$60$	−2.21432	+	0.311108i	−0.285867	+	0.0401638i
$61$	−5.05086			−0.646696			−0.323348	−	0.946280i	$-0.604808\pi$
$61$	−5.05086			−0.646696			−0.323348	+	0.946280i	$0.604808\pi$
$62$			0.755569i			0.0959573i
$63$	1.52543			0.192186
$64$	1.00000			0.125000
$65$	1.80642	+	7.85728i	0.224059	+	0.974576i
$66$	2.42864			0.298945
$67$	5.18421			0.633352			0.316676	−	0.948534i	$-0.397433\pi$
$67$	5.18421			0.633352			0.316676	+	0.948534i	$0.397433\pi$
$68$		−	0.903212i		−	0.109531i
$69$	−2.90321			−0.349506
$70$	−0.474572	−	3.37778i	−0.0567223	−	0.403722i
$71$		−	5.37778i		−	0.638226i	−0.947717	−	0.319113i	$-0.896615\pi$
$71$		−	5.37778i		−	0.638226i	0.947717	−	0.319113i	$-0.103385\pi$
$72$	1.00000			0.117851
$73$	8.76986			1.02643			0.513217	−	0.858259i	$-0.328454\pi$
$73$	8.76986			1.02643			0.513217	+	0.858259i	$0.328454\pi$
$74$	0.428639			0.0498283
$75$	1.37778	+	4.80642i	0.159093	+	0.554998i
$76$			4.90321i			0.562437i
$77$			3.70471i			0.422191i
$78$	−0.311108	−	3.59210i	−0.0352260	−	0.406726i
$79$	15.0923			1.69802			0.849011	−	0.528376i	$-0.177199\pi$
$79$	15.0923			1.69802			0.849011	+	0.528376i	$0.177199\pi$
$80$	−0.311108	−	2.21432i	−0.0347829	−	0.247568i
$81$	1.00000			0.111111
$82$			7.80642i			0.862075i
$83$	13.2859			1.45832			0.729160	−	0.684344i	$-0.239911\pi$
$83$	13.2859			1.45832			0.729160	+	0.684344i	$0.239911\pi$
$84$			1.52543i			0.166438i
$85$	−2.00000	+	0.280996i	−0.216930	+	0.0304783i
$86$			7.18421i			0.774693i
$87$			5.95407i			0.638343i
$88$			2.42864i			0.258894i
$89$		−	8.62222i		−	0.913953i	−0.889479	−	0.456977i	$-0.848932\pi$
$89$		−	8.62222i		−	0.913953i	0.889479	−	0.456977i	$-0.151068\pi$
$90$	−0.311108	−	2.21432i	−0.0327936	−	0.233410i
$91$	5.47949	−	0.474572i	0.574407	−	0.0497487i
$92$		−	2.90321i		−	0.302681i
$93$	−0.755569			−0.0783488
$94$	0.949145			0.0978968
$95$	10.8573	−	1.52543i	1.11393	−	0.156506i
$96$			1.00000i			0.102062i
$97$	11.1383			1.13092			0.565460	−	0.824776i	$-0.308699\pi$
$97$	11.1383			1.13092			0.565460	+	0.824776i	$0.308699\pi$
$98$	4.67307			0.472051
$99$			2.42864i			0.244087i
$100$	−4.80642	+	1.37778i	−0.480642	+	0.137778i
$101$	−11.7605			−1.17021			−0.585106	−	0.810957i	$-0.698947\pi$
$101$	−11.7605			−1.17021			−0.585106	+	0.810957i	$0.698947\pi$
$102$	0.903212			0.0894313
$103$		−	18.8573i		−	1.85806i	−0.370001	−	0.929031i	$-0.620643\pi$
$103$		−	18.8573i		−	1.85806i	0.370001	−	0.929031i	$-0.379357\pi$
$104$	3.59210	−	0.311108i	0.352235	−	0.0305066i
$105$	3.37778	−	0.474572i	0.329638	−	0.0463135i
$106$			2.56199i			0.248843i
$107$			15.5210i			1.50047i	0.661171	+	0.750235i	$0.270060\pi$
$107$			15.5210i			1.50047i	−0.661171	+	0.750235i	$0.729940\pi$
$108$			1.00000i			0.0962250i
$109$			11.1985i			1.07262i	0.844021	+	0.536311i	$0.180183\pi$
$109$			11.1985i			1.07262i	−0.844021	+	0.536311i	$0.819817\pi$
$110$	5.37778	−	0.755569i	0.512752	−	0.0720407i
$111$			0.428639i			0.0406847i
$112$	−1.52543			−0.144139
$113$		−	10.7096i		−	1.00748i	−0.863856	−	0.503739i	$-0.831957\pi$
$113$		−	10.7096i		−	1.00748i	0.863856	−	0.503739i	$-0.168043\pi$
$114$	−4.90321			−0.459228
$115$	−6.42864	+	0.903212i	−0.599474	+	0.0842249i
$116$	−5.95407			−0.552821
$117$	3.59210	−	0.311108i	0.332090	−	0.0287619i
$118$		−	2.13335i		−	0.196391i
$119$			1.37778i			0.126301i
$120$	2.21432	−	0.311108i	0.202139	−	0.0284001i
$121$	5.10171			0.463792
$122$	5.05086			0.457283
$123$	−7.80642			−0.703882
$124$		−	0.755569i		−	0.0678521i
$125$	4.54617	+	10.2143i	0.406622	+	0.913597i
$126$	−1.52543			−0.135896
$127$		−	7.53972i		−	0.669042i	−0.942388	−	0.334521i	$-0.891426\pi$
$127$		−	7.53972i		−	0.669042i	0.942388	−	0.334521i	$-0.108574\pi$
$128$	−1.00000			−0.0883883
$129$	−7.18421			−0.632534
$130$	−1.80642	−	7.85728i	−0.158434	−	0.689129i
$131$	15.0049			1.31099			0.655493	−	0.755201i	$-0.272461\pi$
$131$	15.0049			1.31099			0.655493	+	0.755201i	$0.272461\pi$
$132$	−2.42864			−0.211386
$133$		−	7.47949i		−	0.648554i
$134$	−5.18421			−0.447847
$135$	2.21432	−	0.311108i	0.190578	−	0.0267759i
$136$			0.903212i			0.0774498i
$137$	−20.6637			−1.76542			−0.882710	−	0.469919i	$-0.844283\pi$
$137$	−20.6637			−1.76542			−0.882710	+	0.469919i	$0.844283\pi$
$138$	2.90321			0.247138
$139$	13.4193			1.13821			0.569104	−	0.822266i	$-0.307290\pi$
$139$	13.4193			1.13821			0.569104	+	0.822266i	$0.307290\pi$
$140$	0.474572	+	3.37778i	0.0401087	+	0.285475i
$141$			0.949145i			0.0799324i
$142$			5.37778i			0.451294i
$143$	0.755569	+	8.72393i	0.0631838	+	0.729531i
$144$	−1.00000			−0.0833333
$145$	1.85236	+	13.1842i	0.153830	+	1.09489i
$146$	−8.76986			−0.725799
$147$			4.67307i			0.385428i
$148$	−0.428639			−0.0352339
$149$		−	0.133353i		−	0.0109247i	−0.999985	−	0.00546236i	$-0.998261\pi$
$149$		−	0.133353i		−	0.0109247i	0.999985	−	0.00546236i	$-0.00173873\pi$
$150$	−1.37778	−	4.80642i	−0.112496	−	0.392443i
$151$		−	17.5210i		−	1.42584i	−0.701247	−	0.712919i	$-0.747373\pi$
$151$		−	17.5210i		−	1.42584i	0.701247	−	0.712919i	$-0.252627\pi$
$152$		−	4.90321i		−	0.397703i
$153$			0.903212i			0.0730204i
$154$		−	3.70471i		−	0.298534i
$155$	−1.67307	+	0.235063i	−0.134384	+	0.0188807i
$156$	0.311108	+	3.59210i	0.0249086	+	0.287598i
$157$			2.38715i			0.190515i	0.995453	+	0.0952577i	$0.0303675\pi$
$157$			2.38715i			0.190515i	−0.995453	+	0.0952577i	$0.969632\pi$
$158$	−15.0923			−1.20068
$159$	−2.56199			−0.203179
$160$	0.311108	+	2.21432i	0.0245952	+	0.175057i
$161$			4.42864i			0.349026i
$162$	−1.00000			−0.0785674
$163$	−11.2859			−0.883981			−0.441991	−	0.897020i	$-0.645728\pi$
$163$	−11.2859			−0.883981			−0.441991	+	0.897020i	$0.645728\pi$
$164$		−	7.80642i		−	0.609579i
$165$	0.755569	+	5.37778i	0.0588209	+	0.418660i
$166$	−13.2859			−1.03119
$167$	−5.80642			−0.449315			−0.224657	−	0.974438i	$-0.572126\pi$
$167$	−5.80642			−0.449315			−0.224657	+	0.974438i	$0.572126\pi$
$168$		−	1.52543i		−	0.117689i
$169$	12.8064	−	2.23506i	0.985110	−	0.171928i
$170$	2.00000	−	0.280996i	0.153393	−	0.0215514i
$171$		−	4.90321i		−	0.374958i
$172$		−	7.18421i		−	0.547791i
$173$		−	9.61285i		−	0.730851i	−0.930841	−	0.365426i	$-0.880923\pi$
$173$		−	9.61285i		−	0.730851i	0.930841	−	0.365426i	$-0.119077\pi$
$174$		−	5.95407i		−	0.451377i
$175$	7.33185	−	2.10171i	0.554236	−	0.158874i
$176$		−	2.42864i		−	0.183066i
$177$	2.13335			0.160353
$178$			8.62222i			0.646262i
$179$	−20.1289			−1.50451			−0.752253	−	0.658875i	$-0.771033\pi$
$179$	−20.1289			−1.50451			−0.752253	+	0.658875i	$0.771033\pi$
$180$	0.311108	+	2.21432i	0.0231886	+	0.165046i
$181$	−18.4701			−1.37287			−0.686437	−	0.727189i	$-0.740826\pi$
$181$	−18.4701			−1.37287			−0.686437	+	0.727189i	$0.740826\pi$
$182$	−5.47949	+	0.474572i	−0.406167	+	0.0351776i
$183$			5.05086i			0.373370i
$184$			2.90321i			0.214028i
$185$	0.133353	+	0.949145i	0.00980431	+	0.0697825i
$186$	0.755569			0.0554010
$187$	−2.19358			−0.160410
$188$	−0.949145			−0.0692235
$189$		−	1.52543i		−	0.110959i
$190$	−10.8573	+	1.52543i	−0.787670	+	0.110666i
$191$	8.29529			0.600226			0.300113	−	0.953904i	$-0.402976\pi$
$191$	8.29529			0.600226			0.300113	+	0.953904i	$0.402976\pi$
$192$		−	1.00000i		−	0.0721688i
$193$	−23.1383			−1.66553			−0.832765	−	0.553627i	$-0.813243\pi$
$193$	−23.1383			−1.66553			−0.832765	+	0.553627i	$0.813243\pi$
$194$	−11.1383			−0.799682
$195$	7.85728	−	1.80642i	0.562671	−	0.129361i
$196$	−4.67307			−0.333791
$197$	−4.36842			−0.311237			−0.155618	−	0.987817i	$-0.549737\pi$
$197$	−4.36842			−0.311237			−0.155618	+	0.987817i	$0.549737\pi$
$198$		−	2.42864i		−	0.172596i
$199$	11.7462			0.832666			0.416333	−	0.909212i	$-0.363315\pi$
$199$	11.7462			0.832666			0.416333	+	0.909212i	$0.363315\pi$
$200$	4.80642	−	1.37778i	0.339865	−	0.0974241i
$201$		−	5.18421i		−	0.365666i
$202$	11.7605			0.827465
$203$	9.08250			0.637466
$204$	−0.903212			−0.0632375
$205$	−17.2859	+	2.42864i	−1.20730	+	0.169624i
$206$			18.8573i			1.31385i
$207$			2.90321i			0.201787i
$208$	−3.59210	+	0.311108i	−0.249068	+	0.0215714i
$209$	11.9081			0.823703
$210$	−3.37778	+	0.474572i	−0.233089	+	0.0327486i
$211$	−7.31756			−0.503762			−0.251881	−	0.967758i	$-0.581049\pi$
$211$	−7.31756			−0.503762			−0.251881	+	0.967758i	$0.581049\pi$
$212$		−	2.56199i		−	0.175958i
$213$	−5.37778			−0.368480
$214$		−	15.5210i		−	1.06099i
$215$	−15.9081	+	2.23506i	−1.08493	+	0.152430i
$216$		−	1.00000i		−	0.0680414i
$217$			1.15257i			0.0782412i
$218$		−	11.1985i		−	0.758458i
$219$		−	8.76986i		−	0.592612i
$220$	−5.37778	+	0.755569i	−0.362570	+	0.0509404i
$221$	0.280996	+	3.24443i	0.0189019	+	0.218244i
$222$		−	0.428639i		−	0.0287684i
$223$	9.99555			0.669352			0.334676	−	0.942333i	$-0.391373\pi$
$223$	9.99555			0.669352			0.334676	+	0.942333i	$0.391373\pi$
$224$	1.52543			0.101922
$225$	4.80642	−	1.37778i	0.320428	−	0.0918523i
$226$			10.7096i			0.712394i
$227$	−3.61285			−0.239793			−0.119897	−	0.992786i	$-0.538256\pi$
$227$	−3.61285			−0.239793			−0.119897	+	0.992786i	$0.538256\pi$
$228$	4.90321			0.324723
$229$		−	27.0781i		−	1.78937i	−0.446700	−	0.894684i	$-0.647401\pi$
$229$		−	27.0781i		−	1.78937i	0.446700	−	0.894684i	$-0.352599\pi$
$230$	6.42864	−	0.903212i	0.423892	−	0.0595560i
$231$	3.70471			0.243752
$232$	5.95407			0.390904
$233$			16.1289i			1.05664i	0.849045	+	0.528320i	$0.177178\pi$
$233$			16.1289i			1.05664i	−0.849045	+	0.528320i	$0.822822\pi$
$234$	−3.59210	+	0.311108i	−0.234823	+	0.0203378i
$235$	0.295286	+	2.10171i	0.0192624	+	0.137100i
$236$			2.13335i			0.138869i
$237$		−	15.0923i		−	0.980353i
$238$		−	1.37778i		−	0.0893085i
$239$			20.8573i			1.34915i	0.738209	+	0.674573i	$0.235672\pi$
$239$			20.8573i			1.34915i	−0.738209	+	0.674573i	$0.764328\pi$
$240$	−2.21432	+	0.311108i	−0.142934	+	0.0200819i
$241$		−	21.1526i		−	1.36256i	−0.732025	−	0.681278i	$-0.761424\pi$
$241$		−	21.1526i		−	1.36256i	0.732025	−	0.681278i	$-0.238576\pi$
$242$	−5.10171			−0.327950
$243$		−	1.00000i		−	0.0641500i
$244$	−5.05086			−0.323348
$245$	1.45383	+	10.3477i	0.0928817	+	0.661089i
$246$	7.80642			0.497719
$247$	−1.52543	−	17.6128i	−0.0970606	−	1.12068i
$248$			0.755569i			0.0479787i
$249$		−	13.2859i		−	0.841961i
$250$	−4.54617	−	10.2143i	−0.287525	−	0.646010i
$251$	25.7605			1.62599			0.812994	−	0.582272i	$-0.197836\pi$
$251$	25.7605			1.62599			0.812994	+	0.582272i	$0.197836\pi$
$252$	1.52543			0.0960929
$253$	−7.05086			−0.443283
$254$			7.53972i			0.473084i
$255$	0.280996	+	2.00000i	0.0175967	+	0.125245i
$256$	1.00000			0.0625000
$257$		−	31.3002i		−	1.95245i	−0.216752	−	0.976227i	$-0.569546\pi$
$257$		−	31.3002i		−	1.95245i	0.216752	−	0.976227i	$-0.430454\pi$
$258$	7.18421			0.447269
$259$	0.653858			0.0406288
$260$	1.80642	+	7.85728i	0.112030	+	0.487288i
$261$	5.95407			0.368547
$262$	−15.0049			−0.927007
$263$			17.5669i			1.08322i	0.840629	+	0.541611i	$0.182185\pi$
$263$			17.5669i			1.08322i	−0.840629	+	0.541611i	$0.817815\pi$
$264$	2.42864			0.149472
$265$	−5.67307	+	0.797056i	−0.348494	+	0.0489628i
$266$			7.47949i			0.458597i
$267$	−8.62222			−0.527671
$268$	5.18421			0.316676
$269$	−16.0272			−0.977195			−0.488598	−	0.872509i	$-0.662491\pi$
$269$	−16.0272			−0.977195			−0.488598	+	0.872509i	$0.662491\pi$
$270$	−2.21432	+	0.311108i	−0.134759	+	0.0189334i
$271$			21.9081i			1.33082i	0.746476	+	0.665412i	$0.231744\pi$
$271$			21.9081i			1.33082i	−0.746476	+	0.665412i	$0.768256\pi$
$272$		−	0.903212i		−	0.0547653i
$273$	−0.474572	−	5.47949i	−0.0287224	−	0.331634i
$274$	20.6637			1.24834
$275$	3.34614	+	11.6731i	0.201780	+	0.703913i
$276$	−2.90321			−0.174753
$277$			21.3461i			1.28257i	0.767305	+	0.641283i	$0.221597\pi$
$277$			21.3461i			1.28257i	−0.767305	+	0.641283i	$0.778403\pi$
$278$	−13.4193			−0.804834
$279$			0.755569i			0.0452347i
$280$	−0.474572	−	3.37778i	−0.0283611	−	0.201861i
$281$			7.96836i			0.475352i	0.971344	+	0.237676i	$0.0763857\pi$
$281$			7.96836i			0.475352i	−0.971344	+	0.237676i	$0.923614\pi$
$282$		−	0.949145i		−	0.0565208i
$283$			25.5526i			1.51895i	0.650539	+	0.759473i	$0.274543\pi$
$283$			25.5526i			1.51895i	−0.650539	+	0.759473i	$0.725457\pi$
$284$		−	5.37778i		−	0.319113i
$285$	−1.52543	−	10.8573i	−0.0903585	−	0.643130i
$286$	−0.755569	−	8.72393i	−0.0446777	−	0.515857i
$287$			11.9081i			0.702915i
$288$	1.00000			0.0589256
$289$	16.1842			0.952012
$290$	−1.85236	−	13.1842i	−0.108774	−	0.774203i
$291$		−	11.1383i		−	0.652937i
$292$	8.76986			0.513217
$293$	16.7556			0.978871			0.489435	−	0.872040i	$-0.337203\pi$
$293$	16.7556			0.978871			0.489435	+	0.872040i	$0.337203\pi$
$294$		−	4.67307i		−	0.272539i
$295$	4.72393	−	0.663703i	0.275038	−	0.0386423i
$296$	0.428639			0.0249142
$297$	2.42864			0.140924
$298$			0.133353i			0.00772494i
$299$	0.903212	+	10.4286i	0.0522341	+	0.603104i
$300$	1.37778	+	4.80642i	0.0795464	+	0.277499i
$301$			10.9590i			0.631666i
$302$			17.5210i			1.00822i
$303$			11.7605i			0.675623i
$304$			4.90321i			0.281218i
$305$	1.57136	+	11.1842i	0.0899758	+	0.640406i
$306$		−	0.903212i		−	0.0516332i
$307$	−0.0316429			−0.00180595			−0.000902976	−	1.00000i	$-0.500287\pi$
$307$	−0.0316429			−0.00180595			−0.000902976		1.00000i	$0.500287\pi$
$308$			3.70471i			0.211096i
$309$	−18.8573			−1.07275
$310$	1.67307	−	0.235063i	0.0950240	−	0.0133507i
$311$	−24.2953			−1.37766			−0.688830	−	0.724923i	$-0.741875\pi$
$311$	−24.2953			−1.37766			−0.688830	+	0.724923i	$0.741875\pi$
$312$	−0.311108	−	3.59210i	−0.0176130	−	0.203363i
$313$			10.1017i			0.570982i	0.958381	+	0.285491i	$0.0921567\pi$
$313$			10.1017i			0.570982i	−0.958381	+	0.285491i	$0.907843\pi$
$314$		−	2.38715i		−	0.134715i
$315$	−0.474572	−	3.37778i	−0.0267391	−	0.190317i
$316$	15.0923			0.849011
$317$	−8.23506			−0.462527			−0.231264	−	0.972891i	$-0.574286\pi$
$317$	−8.23506			−0.462527			−0.231264	+	0.972891i	$0.574286\pi$
$318$	2.56199			0.143669
$319$			14.4603i			0.809620i
$320$	−0.311108	−	2.21432i	−0.0173915	−	0.123784i
$321$	15.5210			0.866297
$322$		−	4.42864i		−	0.246798i
$323$	4.42864			0.246416
$324$	1.00000			0.0555556
$325$	16.8365	−	6.44446i	0.933923	−	0.357474i
$326$	11.2859			0.625069
$327$	11.1985			0.619278
$328$			7.80642i			0.431038i
$329$	1.44785			0.0798227
$330$	−0.755569	−	5.37778i	−0.0415927	−	0.296037i
$331$		−	23.0049i		−	1.26446i	−0.774779	−	0.632232i	$-0.782139\pi$
$331$		−	23.0049i		−	1.26446i	0.774779	−	0.632232i	$-0.217861\pi$
$332$	13.2859			0.729160
$333$	0.428639			0.0234893
$334$	5.80642			0.317713
$335$	−1.61285	−	11.4795i	−0.0881193	−	0.627192i
$336$			1.52543i			0.0832189i
$337$			21.4193i			1.16678i	0.812191	+	0.583391i	$0.198274\pi$
$337$			21.4193i			1.16678i	−0.812191	+	0.583391i	$0.801726\pi$
$338$	−12.8064	+	2.23506i	−0.696578	+	0.121571i
$339$	−10.7096			−0.581668
$340$	−2.00000	+	0.280996i	−0.108465	+	0.0152392i
$341$	−1.83500			−0.0993710
$342$			4.90321i			0.265135i
$343$	17.8064			0.961457
$344$			7.18421i			0.387347i
$345$	0.903212	+	6.42864i	0.0486273	+	0.346106i
$346$			9.61285i			0.516790i
$347$		−	30.2766i		−	1.62533i	−0.582731	−	0.812665i	$-0.698016\pi$
$347$		−	30.2766i		−	1.62533i	0.582731	−	0.812665i	$-0.301984\pi$
$348$			5.95407i			0.319171i
$349$		−	29.9541i		−	1.60340i	−0.597724	−	0.801702i	$-0.703928\pi$
$349$		−	29.9541i		−	1.60340i	0.597724	−	0.801702i	$-0.296072\pi$
$350$	−7.33185	+	2.10171i	−0.391904	+	0.112341i
$351$	−0.311108	−	3.59210i	−0.0166057	−	0.191732i
$352$			2.42864i			0.129447i
$353$	24.2766			1.29211			0.646055	−	0.763291i	$-0.276418\pi$
$353$	24.2766			1.29211			0.646055	+	0.763291i	$0.276418\pi$
$354$	−2.13335			−0.113386
$355$	−11.9081	+	1.67307i	−0.632018	+	0.0887974i
$356$		−	8.62222i		−	0.456977i
$357$	1.37778			0.0729201
$358$	20.1289			1.06385
$359$			1.84791i			0.0975290i	0.998810	+	0.0487645i	$0.0155284\pi$
$359$			1.84791i			0.0975290i	−0.998810	+	0.0487645i	$0.984472\pi$
$360$	−0.311108	−	2.21432i	−0.0163968	−	0.116705i
$361$	−5.04149			−0.265341
$362$	18.4701			0.970768
$363$		−	5.10171i		−	0.267770i
$364$	5.47949	−	0.474572i	0.287204	−	0.0248744i
$365$	−2.72837	−	19.4193i	−0.142809	−	1.01645i
$366$		−	5.05086i		−	0.264012i
$367$		−	18.7654i		−	0.979547i	−0.871850	−	0.489773i	$-0.837080\pi$
$367$		−	18.7654i		−	0.979547i	0.871850	−	0.489773i	$-0.162920\pi$
$368$		−	2.90321i		−	0.151340i
$369$			7.80642i			0.406386i
$370$	−0.133353	−	0.949145i	−0.00693270	−	0.0493437i
$371$			3.90813i			0.202900i
$372$	−0.755569			−0.0391744
$373$			12.3684i			0.640412i	0.947348	+	0.320206i	$0.103752\pi$
$373$			12.3684i			0.640412i	−0.947348	+	0.320206i	$0.896248\pi$
$374$	2.19358			0.113427
$375$	10.2143	−	4.54617i	0.527465	−	0.234763i
$376$	0.949145			0.0489484
$377$	21.3876	−	1.85236i	1.10152	−	0.0954012i
$378$			1.52543i			0.0784595i
$379$			20.1575i			1.03542i	0.855556	+	0.517710i	$0.173215\pi$
$379$			20.1575i			1.03542i	−0.855556	+	0.517710i	$0.826785\pi$
$380$	10.8573	−	1.52543i	0.556967	−	0.0782528i
$381$	−7.53972			−0.386271
$382$	−8.29529			−0.424424
$383$	−20.2953			−1.03704			−0.518520	−	0.855065i	$-0.673517\pi$
$383$	−20.2953			−1.03704			−0.518520	+	0.855065i	$0.673517\pi$
$384$			1.00000i			0.0510310i
$385$	8.20342	−	1.15257i	0.418085	−	0.0587402i
$386$	23.1383			1.17771
$387$			7.18421i			0.365194i
$388$	11.1383			0.565460
$389$	−9.30021			−0.471539			−0.235770	−	0.971809i	$-0.575761\pi$
$389$	−9.30021			−0.471539			−0.235770	+	0.971809i	$0.575761\pi$
$390$	−7.85728	+	1.80642i	−0.397869	+	0.0914718i
$391$	−2.62222			−0.132611
$392$	4.67307			0.236026
$393$		−	15.0049i		−	0.756898i
$394$	4.36842			0.220078
$395$	−4.69535	−	33.4193i	−0.236248	−	1.68151i
$396$			2.42864i			0.122044i
$397$	11.0094			0.552544			0.276272	−	0.961079i	$-0.410901\pi$
$397$	11.0094			0.552544			0.276272	+	0.961079i	$0.410901\pi$
$398$	−11.7462			−0.588784
$399$	−7.47949			−0.374443
$400$	−4.80642	+	1.37778i	−0.240321	+	0.0688892i
$401$		−	1.90813i		−	0.0952877i	−0.998864	−	0.0476438i	$-0.984829\pi$
$401$		−	1.90813i		−	0.0952877i	0.998864	−	0.0476438i	$-0.0151712\pi$
$402$			5.18421i			0.258565i
$403$	0.235063	+	2.71408i	0.0117093	+	0.135198i
$404$	−11.7605			−0.585106
$405$	−0.311108	−	2.21432i	−0.0154591	−	0.110030i
$406$	−9.08250			−0.450757
$407$			1.04101i			0.0516010i
$408$	0.903212			0.0447157
$409$			19.8163i			0.979851i	0.871764	+	0.489926i	$0.162976\pi$
$409$			19.8163i			0.979851i	−0.871764	+	0.489926i	$0.837024\pi$
$410$	17.2859	−	2.42864i	0.853691	−	0.119942i
$411$			20.6637i			1.01927i
$412$		−	18.8573i		−	0.929031i
$413$		−	3.25428i		−	0.160132i
$414$		−	2.90321i		−	0.142685i
$415$	−4.13335	−	29.4193i	−0.202898	−	1.44414i
$416$	3.59210	−	0.311108i	0.176117	−	0.0152533i
$417$		−	13.4193i		−	0.657145i
$418$	−11.9081			−0.582446
$419$	−11.7792			−0.575453			−0.287726	−	0.957713i	$-0.592899\pi$
$419$	−11.7792			−0.575453			−0.287726	+	0.957713i	$0.592899\pi$
$420$	3.37778	−	0.474572i	0.164819	−	0.0231568i
$421$		−	6.63651i		−	0.323443i	−0.986836	−	0.161722i	$-0.948295\pi$
$421$		−	6.63651i		−	0.323443i	0.986836	−	0.161722i	$-0.0517047\pi$
$422$	7.31756			0.356213
$423$	0.949145			0.0461490
$424$			2.56199i			0.124421i
$425$	1.24443	+	4.34122i	0.0603638	+	0.210580i
$426$	5.37778			0.260555
$427$	7.70471			0.372857
$428$			15.5210i			0.750235i
$429$	8.72393	−	0.755569i	0.421195	−	0.0364792i
$430$	15.9081	−	2.23506i	0.767158	−	0.107784i
$431$		−	7.87955i		−	0.379545i	−0.981828	−	0.189772i	$-0.939225\pi$
$431$		−	7.87955i		−	0.379545i	0.981828	−	0.189772i	$-0.0607750\pi$
$432$			1.00000i			0.0481125i
$433$			34.7467i			1.66982i	0.550387	+	0.834909i	$0.314480\pi$
$433$			34.7467i			1.66982i	−0.550387	+	0.834909i	$0.685520\pi$
$434$		−	1.15257i		−	0.0553249i
$435$	13.1842	−	1.85236i	0.632134	−	0.0888137i
$436$			11.1985i			0.536311i
$437$	14.2351			0.680955
$438$			8.76986i			0.419040i
$439$	−7.73329			−0.369090			−0.184545	−	0.982824i	$-0.559081\pi$
$439$	−7.73329			−0.369090			−0.184545	+	0.982824i	$0.559081\pi$
$440$	5.37778	−	0.755569i	0.256376	−	0.0360203i
$441$	4.67307			0.222527
$442$	−0.280996	−	3.24443i	−0.0133656	−	0.154322i
$443$			13.8064i			0.655963i	0.944684	+	0.327981i	$0.106368\pi$
$443$			13.8064i			0.655963i	−0.944684	+	0.327981i	$0.893632\pi$
$444$			0.428639i			0.0203423i
$445$	−19.0923	+	2.68244i	−0.905064	+	0.127160i
$446$	−9.99555			−0.473303
$447$	−0.133353			−0.00630738
$448$	−1.52543			−0.0720697
$449$			6.52051i			0.307722i	0.988093	+	0.153861i	$0.0491707\pi$
$449$			6.52051i			0.307722i	−0.988093	+	0.153861i	$0.950829\pi$
$450$	−4.80642	+	1.37778i	−0.226577	+	0.0649494i
$451$	−18.9590			−0.892744
$452$		−	10.7096i		−	0.503739i
$453$	−17.5210			−0.823208
$454$	3.61285			0.169559
$455$	−2.75557	−	11.9857i	−0.129183	−	0.561899i
$456$	−4.90321			−0.229614
$457$	−8.86172			−0.414534			−0.207267	−	0.978284i	$-0.566457\pi$
$457$	−8.86172			−0.414534			−0.207267	+	0.978284i	$0.566457\pi$
$458$			27.0781i			1.26527i
$459$	0.903212			0.0421583
$460$	−6.42864	+	0.903212i	−0.299737	+	0.0421125i
$461$		−	2.35551i		−	0.109707i	−0.998494	−	0.0548535i	$-0.982531\pi$
$461$		−	2.35551i		−	0.109707i	0.998494	−	0.0548535i	$-0.0174692\pi$
$462$	−3.70471			−0.172359
$463$	5.35059			0.248663			0.124331	−	0.992241i	$-0.460321\pi$
$463$	5.35059			0.248663			0.124331	+	0.992241i	$0.460321\pi$
$464$	−5.95407			−0.276411
$465$	0.235063	+	1.67307i	0.0109008	+	0.0775868i
$466$		−	16.1289i		−	0.747157i
$467$			19.4380i			0.899484i	0.893159	+	0.449742i	$0.148484\pi$
$467$			19.4380i			0.899484i	−0.893159	+	0.449742i	$0.851516\pi$
$468$	3.59210	−	0.311108i	0.166045	−	0.0143810i
$469$	−7.90813			−0.365164
$470$	−0.295286	−	2.10171i	−0.0136205	−	0.0969447i
$471$	2.38715			0.109994
$472$		−	2.13335i		−	0.0981955i
$473$	−17.4479			−0.802253
$474$			15.0923i			0.693214i
$475$	−6.75557	−	23.5669i	−0.309967	−	1.08132i
$476$			1.37778i			0.0631506i
$477$			2.56199i			0.117306i
$478$		−	20.8573i		−	0.953990i
$479$		−	22.4889i		−	1.02754i	−0.857927	−	0.513771i	$-0.828248\pi$
$479$		−	22.4889i		−	1.02754i	0.857927	−	0.513771i	$-0.171752\pi$
$480$	2.21432	−	0.311108i	0.101069	−	0.0142001i
$481$	1.53972	−	0.133353i	0.0702051	−	0.00608038i
$482$			21.1526i			0.963473i
$483$	4.42864			0.201510
$484$	5.10171			0.231896
$485$	−3.46520	−	24.6637i	−0.157347	−	1.11992i
$486$			1.00000i			0.0453609i
$487$	−29.5165			−1.33752			−0.668761	−	0.743477i	$-0.733175\pi$
$487$	−29.5165			−1.33752			−0.668761	+	0.743477i	$0.733175\pi$
$488$	5.05086			0.228641
$489$			11.2859i			0.510367i
$490$	−1.45383	−	10.3477i	−0.0656773	−	0.467460i
$491$	−24.7828			−1.11843			−0.559215	−	0.829022i	$-0.688897\pi$
$491$	−24.7828			−1.11843			−0.559215	+	0.829022i	$0.688897\pi$
$492$	−7.80642			−0.351941
$493$			5.37778i			0.242203i
$494$	1.52543	+	17.6128i	0.0686322	+	0.792439i
$495$	5.37778	−	0.755569i	0.241713	−	0.0339603i
$496$		−	0.755569i		−	0.0339260i
$497$			8.20342i			0.367974i
$498$			13.2859i			0.595356i
$499$			27.0968i			1.21302i	0.795076	+	0.606509i	$0.207431\pi$
$499$			27.0968i			1.21302i	−0.795076	+	0.606509i	$0.792569\pi$
$500$	4.54617	+	10.2143i	0.203311	+	0.456798i
$501$			5.80642i			0.259412i
$502$	−25.7605			−1.14975
$503$		−	2.90321i		−	0.129448i	−0.997903	−	0.0647239i	$-0.979383\pi$
$503$		−	2.90321i		−	0.129448i	0.997903	−	0.0647239i	$-0.0206167\pi$
$504$	−1.52543			−0.0679479
$505$	3.65878	+	26.0415i	0.162814	+	1.15883i
$506$	7.05086			0.313449
$507$	−2.23506	−	12.8064i	−0.0992626	−	0.568753i
$508$		−	7.53972i		−	0.334521i
$509$		−	39.5625i		−	1.75358i	−0.480877	−	0.876788i	$-0.659682\pi$
$509$		−	39.5625i		−	1.75358i	0.480877	−	0.876788i	$-0.340318\pi$
$510$	−0.280996	−	2.00000i	−0.0124427	−	0.0885615i
$511$	−13.3778			−0.591798
$512$	−1.00000			−0.0441942
$513$	−4.90321			−0.216482
$514$			31.3002i			1.38059i
$515$	−41.7560	+	5.86665i	−1.83999	+	0.258515i
$516$	−7.18421			−0.316267
$517$			2.30513i			0.101380i
$518$	−0.653858			−0.0287289
$519$	−9.61285			−0.421957
$520$	−1.80642	−	7.85728i	−0.0792169	−	0.344564i
$521$	33.2257			1.45564			0.727822	−	0.685766i	$-0.240533\pi$
$521$	33.2257			1.45564			0.727822	+	0.685766i	$0.240533\pi$
$522$	−5.95407			−0.260602
$523$		−	13.2444i		−	0.579139i	−0.957157	−	0.289569i	$-0.906488\pi$
$523$		−	13.2444i		−	0.579139i	0.957157	−	0.289569i	$-0.0935121\pi$
$524$	15.0049			0.655493
$525$	−2.10171	−	7.33185i	−0.0917262	−	0.319988i
$526$		−	17.5669i		−	0.765954i
$527$	−0.682439			−0.0297275
$528$	−2.42864			−0.105693
$529$	14.5714			0.633537
$530$	5.67307	−	0.797056i	0.246422	−	0.0346219i
$531$		−	2.13335i		−	0.0925796i
$532$		−	7.47949i		−	0.324277i
$533$	2.42864	+	28.0415i	0.105196	+	1.21461i
$534$	8.62222			0.373120
$535$	34.3684	−	4.82870i	1.48588	−	0.208763i
$536$	−5.18421			−0.223924
$537$			20.1289i			0.868626i
$538$	16.0272			0.690982
$539$			11.3492i			0.488845i
$540$	2.21432	−	0.311108i	0.0952891	−	0.0133879i
$541$			23.7605i			1.02154i	0.859716	+	0.510772i	$0.170640\pi$
$541$			23.7605i			1.02154i	−0.859716	+	0.510772i	$0.829360\pi$
$542$		−	21.9081i		−	0.941035i
$543$			18.4701i			0.792629i
$544$			0.903212i			0.0387249i
$545$	24.7971	−	3.48394i	1.06219	−	0.149236i
$546$	0.474572	+	5.47949i	0.0203098	+	0.234501i
$547$		−	7.61285i		−	0.325502i	−0.986667	−	0.162751i	$-0.947963\pi$
$547$		−	7.61285i		−	0.325502i	0.986667	−	0.162751i	$-0.0520367\pi$
$548$	−20.6637			−0.882710
$549$	5.05086			0.215565
$550$	−3.34614	−	11.6731i	−0.142680	−	0.497741i
$551$		−	29.1941i		−	1.24371i
$552$	2.90321			0.123569
$553$	−23.0223			−0.979007
$554$		−	21.3461i		−	0.906911i
$555$	0.949145	−	0.133353i	0.0402890	−	0.00566052i
$556$	13.4193			0.569104
$557$	−37.9496			−1.60798			−0.803989	−	0.594645i	$-0.797293\pi$
$557$	−37.9496			−1.60798			−0.803989	+	0.594645i	$0.797293\pi$
$558$		−	0.755569i		−	0.0319858i
$559$	2.23506	+	25.8064i	0.0945331	+	1.09150i
$560$	0.474572	+	3.37778i	0.0200543	+	0.142737i
$561$			2.19358i			0.0926129i
$562$		−	7.96836i		−	0.336125i
$563$		−	34.8671i		−	1.46947i	−0.678352	−	0.734737i	$-0.737306\pi$
$563$		−	34.8671i		−	1.46947i	0.678352	−	0.734737i	$-0.262694\pi$
$564$			0.949145i			0.0399662i
$565$	−23.7146	+	3.33185i	−0.997679	+	0.140172i
$566$		−	25.5526i		−	1.07406i
$567$	−1.52543			−0.0640619
$568$			5.37778i			0.225647i
$569$	38.2034			1.60157			0.800785	−	0.598951i	$-0.204416\pi$
$569$	38.2034			1.60157			0.800785	+	0.598951i	$0.204416\pi$
$570$	1.52543	+	10.8573i	0.0638931	+	0.454761i
$571$	4.94914			0.207115			0.103558	−	0.994623i	$-0.466977\pi$
$571$	4.94914			0.207115			0.103558	+	0.994623i	$0.466977\pi$
$572$	0.755569	+	8.72393i	0.0315919	+	0.364766i
$573$		−	8.29529i		−	0.346541i
$574$		−	11.9081i		−	0.497036i
$575$	4.00000	+	13.9541i	0.166812	+	0.581925i
$576$	−1.00000			−0.0416667
$577$	−16.3827			−0.682021			−0.341010	−	0.940059i	$-0.610769\pi$
$577$	−16.3827			−0.682021			−0.341010	+	0.940059i	$0.610769\pi$
$578$	−16.1842			−0.673174
$579$			23.1383i			0.961594i
$580$	1.85236	+	13.1842i	0.0769149	+	0.547444i
$581$	−20.2667			−0.840805
$582$			11.1383i			0.461696i
$583$	−6.22216			−0.257695
$584$	−8.76986			−0.362899
$585$	−1.80642	−	7.85728i	−0.0746864	−	0.324859i
$586$	−16.7556			−0.692166
$587$	45.2070			1.86589			0.932945	−	0.360018i	$-0.117229\pi$
$587$	45.2070			1.86589			0.932945	+	0.360018i	$0.117229\pi$
$588$			4.67307i			0.192714i
$589$	3.70471			0.152650
$590$	−4.72393	+	0.663703i	−0.194481	+	0.0273242i
$591$			4.36842i			0.179693i
$592$	−0.428639			−0.0176170
$593$	23.5941			0.968894			0.484447	−	0.874821i	$-0.339021\pi$
$593$	23.5941			0.968894			0.484447	+	0.874821i	$0.339021\pi$
$594$	−2.42864			−0.0996483
$595$	3.05086	−	0.428639i	0.125073	−	0.0175725i
$596$		−	0.133353i		−	0.00546236i
$597$		−	11.7462i		−	0.480740i
$598$	−0.903212	−	10.4286i	−0.0369351	−	0.426459i
$599$	−13.0607			−0.533646			−0.266823	−	0.963746i	$-0.585974\pi$
$599$	−13.0607			−0.533646			−0.266823	+	0.963746i	$0.585974\pi$
$600$	−1.37778	−	4.80642i	−0.0562478	−	0.196221i
$601$	28.5303			1.16378			0.581889	−	0.813268i	$-0.302314\pi$
$601$	28.5303			1.16378			0.581889	+	0.813268i	$0.302314\pi$
$602$		−	10.9590i		−	0.446655i
$603$	−5.18421			−0.211117
$604$		−	17.5210i		−	0.712919i
$605$	−1.58718	−	11.2968i	−0.0645281	−	0.459281i
$606$		−	11.7605i		−	0.477737i
$607$		−	7.53972i		−	0.306028i	−0.988224	−	0.153014i	$-0.951102\pi$
$607$		−	7.53972i		−	0.306028i	0.988224	−	0.153014i	$-0.0488979\pi$
$608$		−	4.90321i		−	0.198852i
$609$		−	9.08250i		−	0.368041i
$610$	−1.57136	−	11.1842i	−0.0636225	−	0.452835i
$611$	3.40943	−	0.295286i	0.137931	−	0.0119460i
$612$			0.903212i			0.0365102i
$613$	−15.3876			−0.621500			−0.310750	−	0.950492i	$-0.600580\pi$
$613$	−15.3876			−0.621500			−0.310750	+	0.950492i	$0.600580\pi$
$614$	0.0316429			0.00127700
$615$	2.42864	+	17.2859i	0.0979322	+	0.697036i
$616$		−	3.70471i		−	0.149267i
$617$	0.958989			0.0386075			0.0193037	−	0.999814i	$-0.493855\pi$
$617$	0.958989			0.0386075			0.0193037	+	0.999814i	$0.493855\pi$
$618$	18.8573			0.758551
$619$		−	32.5446i		−	1.30808i	−0.756460	−	0.654040i	$-0.773073\pi$
$619$		−	32.5446i		−	1.30808i	0.756460	−	0.654040i	$-0.226927\pi$
$620$	−1.67307	+	0.235063i	−0.0671921	+	0.00944037i
$621$	2.90321			0.116502
$622$	24.2953			0.974152
$623$			13.1526i			0.526946i
$624$	0.311108	+	3.59210i	0.0124543	+	0.143799i
$625$	21.2034	−	13.2444i	0.848137	−	0.529777i
$626$		−	10.1017i		−	0.403746i
$627$		−	11.9081i		−	0.475565i
$628$			2.38715i			0.0952577i
$629$			0.387152i			0.0154368i
$630$	0.474572	+	3.37778i	0.0189074	+	0.134574i
$631$		−	13.7047i		−	0.545576i	−0.962074	−	0.272788i	$-0.912054\pi$
$631$		−	13.7047i		−	0.545576i	0.962074	−	0.272788i	$-0.0879458\pi$
$632$	−15.0923			−0.600341
$633$			7.31756i			0.290847i
$634$	8.23506			0.327056
$635$	−16.6953	+	2.34567i	−0.662535	+	0.0930849i
$636$	−2.56199			−0.101590
$637$	16.7862	−	1.45383i	0.665092	−	0.0576028i
$638$		−	14.4603i		−	0.572488i
$639$			5.37778i			0.212742i
$640$	0.311108	+	2.21432i	0.0122976	+	0.0875287i
$641$	−3.68598			−0.145587			−0.0727937	−	0.997347i	$-0.523191\pi$
$641$	−3.68598			−0.145587			−0.0727937	+	0.997347i	$0.523191\pi$
$642$	−15.5210			−0.612564
$643$	−28.4099			−1.12038			−0.560189	−	0.828365i	$-0.689271\pi$
$643$	−28.4099			−1.12038			−0.560189	+	0.828365i	$0.689271\pi$
$644$			4.42864i			0.174513i
$645$	2.23506	+	15.9081i	0.0880055	+	0.626382i
$646$	−4.42864			−0.174242
$647$		−	18.7828i		−	0.738427i	−0.929345	−	0.369213i	$-0.879627\pi$
$647$		−	18.7828i		−	0.738427i	0.929345	−	0.369213i	$-0.120373\pi$
$648$	−1.00000			−0.0392837
$649$	5.18115			0.203378
$650$	−16.8365	+	6.44446i	−0.660383	+	0.252773i
$651$	1.15257			0.0451726
$652$	−11.2859			−0.441991
$653$		−	3.60300i		−	0.140996i	−0.997512	−	0.0704982i	$-0.977541\pi$
$653$		−	3.60300i		−	0.140996i	0.997512	−	0.0704982i	$-0.0224589\pi$
$654$	−11.1985			−0.437896
$655$	−4.66815	−	33.2257i	−0.182400	−	1.29824i
$656$		−	7.80642i		−	0.304790i
$657$	−8.76986			−0.342145
$658$	−1.44785			−0.0564431
$659$	3.36349			0.131023			0.0655116	−	0.997852i	$-0.479132\pi$
$659$	3.36349			0.131023			0.0655116	+	0.997852i	$0.479132\pi$
$660$	0.755569	+	5.37778i	0.0294105	+	0.209330i
$661$			33.1512i			1.28943i	0.764422	+	0.644716i	$0.223024\pi$
$661$			33.1512i			1.28943i	−0.764422	+	0.644716i	$0.776976\pi$
$662$			23.0049i			0.894112i
$663$	3.24443	−	0.280996i	0.126003	−	0.0109130i
$664$	−13.2859			−0.515594
$665$	−16.5620	+	2.32693i	−0.642247	+	0.0902344i
$666$	−0.428639			−0.0166094
$667$			17.2859i			0.669313i
$668$	−5.80642			−0.224657
$669$		−	9.99555i		−	0.386450i
$670$	1.61285	+	11.4795i	0.0623097	+	0.443492i
$671$			12.2667i			0.473551i
$672$		−	1.52543i		−	0.0588446i
$673$			26.3970i			1.01753i	0.860906	+	0.508765i	$0.169898\pi$
$673$			26.3970i			1.01753i	−0.860906	+	0.508765i	$0.830102\pi$
$674$		−	21.4193i		−	0.825040i
$675$	−1.37778	−	4.80642i	−0.0530309	−	0.184999i
$676$	12.8064	−	2.23506i	0.492555	−	0.0859640i
$677$			20.6637i			0.794171i	0.917782	+	0.397085i	$0.129978\pi$
$677$			20.6637i			0.794171i	−0.917782	+	0.397085i	$0.870022\pi$
$678$	10.7096			0.411301
$679$	−16.9906			−0.652041
$680$	2.00000	−	0.280996i	0.0766965	−	0.0107757i
$681$			3.61285i			0.138445i
$682$	1.83500			0.0702659
$683$	5.08250			0.194476			0.0972382	−	0.995261i	$-0.468999\pi$
$683$	5.08250			0.194476			0.0972382	+	0.995261i	$0.468999\pi$
$684$		−	4.90321i		−	0.187479i
$685$	6.42864	+	45.7560i	0.245626	+	1.74825i
$686$	−17.8064			−0.679852
$687$	−27.0781			−1.03309
$688$		−	7.18421i		−	0.273895i
$689$	0.797056	+	9.20294i	0.0303654	+	0.350604i
$690$	−0.903212	−	6.42864i	−0.0343847	−	0.244734i
$691$			15.4839i			0.589037i	0.955646	+	0.294518i	$0.0951592\pi$
$691$			15.4839i			0.589037i	−0.955646	+	0.294518i	$0.904841\pi$
$692$		−	9.61285i		−	0.365426i
$693$		−	3.70471i		−	0.140730i
$694$			30.2766i			1.14928i
$695$	−4.17484	−	29.7146i	−0.158361	−	1.12714i
$696$		−	5.95407i		−	0.225688i
$697$	−7.05086			−0.267070
$698$			29.9541i			1.13378i
$699$	16.1289			0.610051
$700$	7.33185	−	2.10171i	0.277118	−	0.0794372i
$701$	10.6909			0.403790			0.201895	−	0.979407i	$-0.435290\pi$
$701$	10.6909			0.403790			0.201895	+	0.979407i	$0.435290\pi$
$702$	0.311108	+	3.59210i	0.0117420	+	0.135575i
$703$		−	2.10171i		−	0.0792675i
$704$		−	2.42864i		−	0.0915328i
$705$	2.10171	−	0.295286i	0.0791550	−	0.0111211i
$706$	−24.2766			−0.913660
$707$	17.9398			0.674695
$708$	2.13335			0.0801763
$709$		−	22.6909i		−	0.852175i	−0.904682	−	0.426087i	$-0.859892\pi$
$709$		−	22.6909i		−	0.852175i	0.904682	−	0.426087i	$-0.140108\pi$
$710$	11.9081	−	1.67307i	0.446904	−	0.0627892i
$711$	−15.0923			−0.566007
$712$			8.62222i			0.323131i
$713$	−2.19358			−0.0821501
$714$	−1.37778			−0.0515623
$715$	19.0825	−	4.38715i	0.713645	−	0.164070i
$716$	−20.1289			−0.752253
$717$	20.8573			0.778929
$718$		−	1.84791i		−	0.0689634i
$719$	−7.87955			−0.293858			−0.146929	−	0.989147i	$-0.546939\pi$
$719$	−7.87955			−0.293858			−0.146929	+	0.989147i	$0.546939\pi$
$720$	0.311108	+	2.21432i	0.0115943	+	0.0825228i
$721$			28.7654i			1.07128i
$722$	5.04149			0.187625
$723$	−21.1526			−0.786672
$724$	−18.4701			−0.686437
$725$	28.6178	−	8.20342i	1.06284	−	0.304667i
$726$			5.10171i			0.189342i
$727$		−	2.47013i		−	0.0916119i	−0.998950	−	0.0458060i	$-0.985414\pi$
$727$		−	2.47013i		−	0.0916119i	0.998950	−	0.0458060i	$-0.0145856\pi$
$728$	−5.47949	+	0.474572i	−0.203084	+	0.0175888i
$729$	−1.00000			−0.0370370
$730$	2.72837	+	19.4193i	0.100982	+	0.718739i
$731$	−6.48886			−0.239999
$732$			5.05086i			0.186685i
$733$	−9.84791			−0.363741			−0.181870	−	0.983323i	$-0.558215\pi$
$733$	−9.84791			−0.363741			−0.181870	+	0.983323i	$0.558215\pi$
$734$			18.7654i			0.692644i
$735$	10.3477	−	1.45383i	0.381680	−	0.0536253i
$736$			2.90321i			0.107014i
$737$		−	12.5906i		−	0.463780i
$738$		−	7.80642i		−	0.287358i
$739$		−	3.87109i		−	0.142400i	−0.997462	−	0.0712002i	$-0.977317\pi$
$739$		−	3.87109i		−	0.142400i	0.997462	−	0.0712002i	$-0.0226829\pi$
$740$	0.133353	+	0.949145i	0.00490216	+	0.0348913i
$741$	−17.6128	+	1.52543i	−0.647024	+	0.0560380i
$742$		−	3.90813i		−	0.143472i
$743$	29.0607			1.06613			0.533067	−	0.846073i	$-0.321039\pi$
$743$	29.0607			1.06613			0.533067	+	0.846073i	$0.321039\pi$
$744$	0.755569			0.0277005
$745$	−0.295286	+	0.0414872i	−0.0108185	+	0.00151997i
$746$		−	12.3684i		−	0.452840i
$747$	−13.2859			−0.486106
$748$	−2.19358			−0.0802051
$749$		−	23.6761i		−	0.865107i
$750$	−10.2143	+	4.54617i	−0.372974	+	0.166003i
$751$	29.5941			1.07990			0.539952	−	0.841696i	$-0.318442\pi$
$751$	29.5941			1.07990			0.539952	+	0.841696i	$0.318442\pi$
$752$	−0.949145			−0.0346118
$753$		−	25.7605i		−	0.938764i
$754$	−21.3876	+	1.85236i	−0.778891	+	0.0674589i
$755$	−38.7971	+	5.45091i	−1.41197	+	0.198379i
$756$		−	1.52543i		−	0.0554793i
$757$			0.0316429i			0.00115008i	1.00000		0.000575040i	$0.000183041\pi$
$757$			0.0316429i			0.00115008i	−1.00000		0.000575040i	$0.999817\pi$
$758$		−	20.1575i		−	0.732153i
$759$			7.05086i			0.255930i
$760$	−10.8573	+	1.52543i	−0.393835	+	0.0553331i
$761$		−	18.8859i		−	0.684612i	−0.939589	−	0.342306i	$-0.888792\pi$
$761$		−	18.8859i		−	0.684612i	0.939589	−	0.342306i	$-0.111208\pi$
$762$	7.53972			0.273135
$763$		−	17.0825i		−	0.618428i
$764$	8.29529			0.300113
$765$	2.00000	−	0.280996i	0.0723102	−	0.0101594i
$766$	20.2953			0.733299
$767$	−0.663703	−	7.66323i	−0.0239649	−	0.276703i
$768$		−	1.00000i		−	0.0360844i
$769$		−	14.2854i		−	0.515146i	−0.966259	−	0.257573i	$-0.917077\pi$
$769$		−	14.2854i		−	0.515146i	0.966259	−	0.257573i	$-0.0829228\pi$
$770$	−8.20342	+	1.15257i	−0.295631	+	0.0415356i
$771$	−31.3002			−1.12725
$772$	−23.1383			−0.832765
$773$	26.4701			0.952064			0.476032	−	0.879428i	$-0.342075\pi$
$773$	26.4701			0.952064			0.476032	+	0.879428i	$0.342075\pi$
$774$		−	7.18421i		−	0.258231i
$775$	1.04101	+	3.63158i	0.0373942	+	0.130450i
$776$	−11.1383			−0.399841
$777$		−	0.653858i		−	0.0234570i
$778$	9.30021			0.333429
$779$	38.2766			1.37140
$780$	7.85728	−	1.80642i	0.281336	−	0.0646803i
$781$	−13.0607			−0.467349
$782$	2.62222			0.0937702
$783$		−	5.95407i		−	0.212781i
$784$	−4.67307			−0.166895
$785$	5.28592	−	0.742662i	0.188663	−	0.0265067i
$786$			15.0049i			0.535208i
$787$	22.1619			0.789988			0.394994	−	0.918684i	$-0.370747\pi$
$787$	22.1619			0.789988			0.394994	+	0.918684i	$0.370747\pi$
$788$	−4.36842			−0.155618
$789$	17.5669			0.625399
$790$	4.69535	+	33.4193i	0.167053	+	1.18900i
$791$			16.3368i			0.580869i
$792$		−	2.42864i		−	0.0862979i
$793$	18.1432	−	1.57136i	0.644284	−	0.0558006i
$794$	−11.0094			−0.390708
$795$	0.797056	+	5.67307i	0.0282687	+	0.201203i
$796$	11.7462			0.416333
$797$		−	51.1437i		−	1.81160i	−0.423704	−	0.905801i	$-0.639270\pi$
$797$		−	51.1437i		−	1.81160i	0.423704	−	0.905801i	$-0.360730\pi$
$798$	7.47949			0.264771
$799$			0.857279i			0.0303283i
$800$	4.80642	−	1.37778i	0.169933	−	0.0487120i
$801$			8.62222i			0.304651i
$802$			1.90813i			0.0673786i
$803$		−	21.2988i		−	0.751619i
$804$		−	5.18421i		−	0.182833i
$805$	9.80642	−	1.37778i	0.345631	−	0.0485605i
$806$	−0.235063	−	2.71408i	−0.00827975	−	0.0955994i
$807$			16.0272i			0.564184i
$808$	11.7605			0.413733
$809$	−13.7047			−0.481832			−0.240916	−	0.970546i	$-0.577448\pi$
$809$	−13.7047			−0.481832			−0.240916	+	0.970546i	$0.577448\pi$
$810$	0.311108	+	2.21432i	0.0109312	+	0.0778033i
$811$			5.66862i			0.199052i	0.995035	+	0.0995262i	$0.0317327\pi$
$811$			5.66862i			0.199052i	−0.995035	+	0.0995262i	$0.968267\pi$
$812$	9.08250			0.318733
$813$	21.9081			0.768352
$814$		−	1.04101i		−	0.0364874i
$815$	3.51114	+	24.9906i	0.122990	+	0.875384i
$816$	−0.903212			−0.0316187
$817$	35.2257			1.23239
$818$		−	19.8163i		−	0.692860i
$819$	−5.47949	+	0.474572i	−0.191469	+	0.0165829i
$820$	−17.2859	+	2.42864i	−0.603650	+	0.0848118i
$821$			44.4830i			1.55247i	0.630445	+	0.776234i	$0.282873\pi$
$821$			44.4830i			1.55247i	−0.630445	+	0.776234i	$0.717127\pi$
$822$		−	20.6637i		−	0.720729i
$823$		−	14.0000i		−	0.488009i	−0.969774	−	0.244005i	$-0.921539\pi$
$823$		−	14.0000i		−	0.488009i	0.969774	−	0.244005i	$-0.0784612\pi$
$824$			18.8573i			0.656924i
$825$	11.6731	−	3.34614i	0.406404	−	0.116498i
$826$			3.25428i			0.113231i
$827$	26.4099			0.918362			0.459181	−	0.888343i	$-0.348143\pi$
$827$	26.4099			0.918362			0.459181	+	0.888343i	$0.348143\pi$
$828$			2.90321i			0.100894i
$829$	16.6923			0.579747			0.289873	−	0.957065i	$-0.406387\pi$
$829$	16.6923			0.579747			0.289873	+	0.957065i	$0.406387\pi$
$830$	4.13335	+	29.4193i	0.143471	+	1.02116i
$831$	21.3461			0.740489
$832$	−3.59210	+	0.311108i	−0.124534	+	0.0107857i
$833$			4.22077i			0.146241i
$834$			13.4193i			0.464671i
$835$	1.80642	+	12.8573i	0.0625139	+	0.444944i
$836$	11.9081			0.411851
$837$	0.755569			0.0261163
$838$	11.7792			0.406907
$839$			36.4701i			1.25909i	0.776965	+	0.629544i	$0.216758\pi$
$839$			36.4701i			1.25909i	−0.776965	+	0.629544i	$0.783242\pi$
$840$	−3.37778	+	0.474572i	−0.116545	+	0.0163743i
$841$	6.45091			0.222445
$842$			6.63651i			0.228709i
$843$	7.96836			0.274445
$844$	−7.31756			−0.251881
$845$	−8.93332	−	27.6622i	−0.307316	−	0.951608i
$846$	−0.949145			−0.0326323
$847$	−7.78229			−0.267403
$848$		−	2.56199i		−	0.0879792i
$849$	25.5526			0.876964
$850$	−1.24443	−	4.34122i	−0.0426836	−	0.148903i
$851$			1.24443i			0.0426586i
$852$	−5.37778			−0.184240
$853$	53.3975			1.82829			0.914147	−	0.405382i	$-0.132862\pi$
$853$	53.3975			1.82829			0.914147	+	0.405382i	$0.132862\pi$
$854$	−7.70471			−0.263650
$855$	−10.8573	+	1.52543i	−0.371311	+	0.0521685i
$856$		−	15.5210i		−	0.530496i
$857$			36.3323i			1.24109i	0.784171	+	0.620544i	$0.213088\pi$
$857$			36.3323i			1.24109i	−0.784171	+	0.620544i	$0.786912\pi$
$858$	−8.72393	+	0.755569i	−0.297830	+	0.0257947i
$859$	−10.0731			−0.343691			−0.171845	−	0.985124i	$-0.554973\pi$
$859$	−10.0731			−0.343691			−0.171845	+	0.985124i	$0.554973\pi$
$860$	−15.9081	+	2.23506i	−0.542463	+	0.0762150i
$861$	11.9081			0.405828
$862$			7.87955i			0.268379i
$863$	0.0285802			0.000972881			0.000486441	−	1.00000i	$-0.499845\pi$
$863$	0.0285802			0.000972881			0.000486441		1.00000i	$0.499845\pi$
$864$		−	1.00000i		−	0.0340207i
$865$	−21.2859	+	2.99063i	−0.723743	+	0.101685i
$866$		−	34.7467i		−	1.18074i
$867$		−	16.1842i		−	0.549645i
$868$			1.15257i			0.0391206i
$869$		−	36.6539i		−	1.24340i
$870$	−13.1842	+	1.85236i	−0.446987	+	0.0628008i
$871$	−18.6222	+	1.61285i	−0.630990	+	0.0546493i
$872$		−	11.1985i		−	0.379229i
$873$	−11.1383			−0.376974
$874$	−14.2351			−0.481508
$875$	−6.93485	−	15.5812i	−0.234441	−	0.526741i
$876$		−	8.76986i		−	0.296306i
$877$	5.25734			0.177528			0.0887638	−	0.996053i	$-0.471708\pi$
$877$	5.25734			0.177528			0.0887638	+	0.996053i	$0.471708\pi$
$878$	7.73329			0.260986
$879$		−	16.7556i		−	0.565151i
$880$	−5.37778	+	0.755569i	−0.181285	+	0.0254702i
$881$	34.8484			1.17407			0.587036	−	0.809561i	$-0.300295\pi$
$881$	34.8484			1.17407			0.587036	+	0.809561i	$0.300295\pi$
$882$	−4.67307			−0.157350
$883$		−	4.47013i		−	0.150432i	−0.997167	−	0.0752159i	$-0.976035\pi$
$883$		−	4.47013i		−	0.150432i	0.997167	−	0.0752159i	$-0.0239646\pi$
$884$	0.280996	+	3.24443i	0.00945093	+	0.109122i
$885$	−0.663703	−	4.72393i	−0.0223101	−	0.158793i
$886$		−	13.8064i		−	0.463836i
$887$			51.0781i			1.71503i	0.514456	+	0.857517i	$0.327994\pi$
$887$			51.0781i			1.71503i	−0.514456	+	0.857517i	$0.672006\pi$
$888$		−	0.428639i		−	0.0143842i
$889$			11.5013i			0.385741i
$890$	19.0923	−	2.68244i	0.639977	−	0.0899155i
$891$		−	2.42864i		−	0.0813625i
$892$	9.99555			0.334676
$893$		−	4.65386i		−	0.155735i
$894$	0.133353			0.00445999
$895$	6.26226	+	44.5718i	0.209324	+	1.48987i
$896$	1.52543			0.0509610
$897$	10.4286	−	0.903212i	0.348202	−	0.0301574i
$898$		−	6.52051i		−	0.217592i
$899$			4.49871i			0.150040i
$900$	4.80642	−	1.37778i	0.160214	−	0.0459261i
$901$	−2.31402			−0.0770913
$902$	18.9590			0.631265
$903$	10.9590			0.364692
$904$			10.7096i			0.356197i
$905$	5.74620	+	40.8988i	0.191010	+	1.35952i
$906$	17.5210			0.582096
$907$			33.4893i			1.11200i	0.831184	+	0.555998i	$0.187664\pi$
$907$			33.4893i			1.11200i	−0.831184	+	0.555998i	$0.812336\pi$
$908$	−3.61285			−0.119897
$909$	11.7605			0.390071
$910$	2.75557	+	11.9857i	0.0913462	+	0.397322i
$911$	−18.1847			−0.602485			−0.301243	−	0.953547i	$-0.597401\pi$
$911$	−18.1847			−0.602485			−0.301243	+	0.953547i	$0.597401\pi$
$912$	4.90321			0.162362
$913$		−	32.2667i		−	1.06787i
$914$	8.86172			0.293120
$915$	11.1842	−	1.57136i	0.369739	−	0.0519476i
$916$		−	27.0781i		−	0.894684i
$917$	−22.8889			−0.755859
$918$	−0.903212			−0.0298104
$919$	−46.3684			−1.52955			−0.764776	−	0.644296i	$-0.777151\pi$
$919$	−46.3684			−1.52955			−0.764776	+	0.644296i	$0.777151\pi$
$920$	6.42864	−	0.903212i	0.211946	−	0.0297780i
$921$			0.0316429i			0.00104267i
$922$			2.35551i			0.0775746i
$923$	1.67307	+	19.3176i	0.0550698	+	0.635845i
$924$	3.70471			0.121876
$925$	2.06022	−	0.590573i	0.0677397	−	0.0194179i
$926$	−5.35059			−0.175831
$927$			18.8573i			0.619354i
$928$	5.95407			0.195452
$929$		−	41.8292i		−	1.37237i	−0.727427	−	0.686185i	$-0.759284\pi$
$929$		−	41.8292i		−	1.37237i	0.727427	−	0.686185i	$-0.240716\pi$
$930$	−0.235063	−	1.67307i	−0.00770803	−	0.0548622i
$931$		−	22.9131i		−	0.750945i
$932$			16.1289i			0.528320i
$933$			24.2953i			0.795392i
$934$		−	19.4380i		−	0.636031i
$935$	0.682439	+	4.85728i	0.0223181	+	0.158850i
$936$	−3.59210	+	0.311108i	−0.117412	+	0.0101689i
$937$			21.8894i			0.715095i	0.933895	+	0.357548i	$0.116387\pi$
$937$			21.8894i			0.715095i	−0.933895	+	0.357548i	$0.883613\pi$
$938$	7.90813			0.258210
$939$	10.1017			0.329657
$940$	0.295286	+	2.10171i	0.00963118	+	0.0685502i
$941$			38.2262i			1.24614i	0.782167	+	0.623069i	$0.214114\pi$
$941$			38.2262i			1.24614i	−0.782167	+	0.623069i	$0.785886\pi$
$942$	−2.38715			−0.0777776
$943$	−22.6637			−0.738032
$944$			2.13335i			0.0694347i
$945$	−3.37778	+	0.474572i	−0.109879	+	0.0154378i
$946$	17.4479			0.567279
$947$	15.1842			0.493420			0.246710	−	0.969089i	$-0.420650\pi$
$947$	15.1842			0.493420			0.246710	+	0.969089i	$0.420650\pi$
$948$		−	15.0923i		−	0.490176i
$949$	−31.5022	+	2.72837i	−1.02261	+	0.0885667i
$950$	6.75557	+	23.5669i	0.219180	+	0.764612i
$951$			8.23506i			0.267040i
$952$		−	1.37778i		−	0.0446542i
$953$		−	57.5482i		−	1.86417i	−0.362242	−	0.932084i	$-0.617989\pi$
$953$		−	57.5482i		−	1.86417i	0.362242	−	0.932084i	$-0.382011\pi$
$954$		−	2.56199i		−	0.0829476i
$955$	−2.58073	−	18.3684i	−0.0835104	−	0.594388i
$956$			20.8573i			0.674573i
$957$	14.4603			0.467435
$958$			22.4889i			0.726582i
$959$	31.5210			1.01787
$960$	−2.21432	+	0.311108i	−0.0714669	+	0.0100410i
$961$	30.4291			0.981584
$962$	−1.53972	+	0.133353i	−0.0496425	+	0.00429948i
$963$		−	15.5210i		−	0.500157i
$964$		−	21.1526i		−	0.681278i
$965$	7.19850	+	51.2355i	0.231728	+	1.64933i
$966$	−4.42864			−0.142489
$967$	32.6878			1.05117			0.525585	−	0.850741i	$-0.323846\pi$
$967$	32.6878			1.05117			0.525585	+	0.850741i	$0.323846\pi$
$968$	−5.10171			−0.163975
$969$		−	4.42864i		−	0.142268i
$970$	3.46520	+	24.6637i	0.111261	+	0.791904i
$971$	26.5892			0.853288			0.426644	−	0.904420i	$-0.359696\pi$
$971$	26.5892			0.853288			0.426644	+	0.904420i	$0.359696\pi$
$972$		−	1.00000i		−	0.0320750i
$973$	−20.4701			−0.656242
$974$	29.5165			0.945771
$975$	−6.44446	−	16.8365i	−0.206388	−	0.539201i
$976$	−5.05086			−0.161674
$977$	−33.0420			−1.05711			−0.528553	−	0.848900i	$-0.677265\pi$
$977$	−33.0420			−1.05711			−0.528553	+	0.848900i	$0.677265\pi$
$978$		−	11.2859i		−	0.360884i
$979$	−20.9403			−0.669253
$980$	1.45383	+	10.3477i	0.0464409	+	0.330544i
$981$		−	11.1985i		−	0.357541i
$982$	24.7828			0.790850
$983$	−36.7368			−1.17172			−0.585861	−	0.810411i	$-0.699244\pi$
$983$	−36.7368			−1.17172			−0.585861	+	0.810411i	$0.699244\pi$
$984$	7.80642			0.248860
$985$	1.35905	+	9.67307i	0.0433029	+	0.308210i
$986$		−	5.37778i		−	0.171264i
$987$		−	1.44785i		−	0.0460856i
$988$	−1.52543	−	17.6128i	−0.0485303	−	0.560339i
$989$	−20.8573			−0.663223
$990$	−5.37778	+	0.755569i	−0.170917	+	0.0240136i
$991$	47.0923			1.49594			0.747969	−	0.663734i	$-0.231029\pi$
$991$	47.0923			1.49594			0.747969	+	0.663734i	$0.231029\pi$
$992$			0.755569i			0.0239893i
$993$	−23.0049			−0.730039
$994$		−	8.20342i		−	0.260197i
$995$	−3.65433	−	26.0098i	−0.115850	−	0.824567i
$996$		−	13.2859i		−	0.420980i
$997$		−	15.0607i		−	0.476977i	−0.971145	−	0.238489i	$-0.923348\pi$
$997$		−	15.0607i		−	0.476977i	0.971145	−	0.238489i	$-0.0766520\pi$
$998$		−	27.0968i		−	0.857734i
$999$		−	0.428639i		−	0.0135616i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	390.2.f.a.259.2	✓	6
3.2	odd	2		1170.2.f.d.649.4		6
4.3	odd	2		3120.2.r.g.2209.5		6
5.2	odd	4		1950.2.b.l.1351.1		6
5.3	odd	4		1950.2.b.m.1351.6		6
5.4	even	2		390.2.f.b.259.5	yes	6
13.12	even	2		390.2.f.b.259.2	yes	6
15.14	odd	2		1170.2.f.c.649.4		6
20.19	odd	2		3120.2.r.h.2209.2		6
39.38	odd	2		1170.2.f.c.649.3		6
52.51	odd	2		3120.2.r.h.2209.5		6
65.12	odd	4		1950.2.b.l.1351.6		6
65.38	odd	4		1950.2.b.m.1351.1		6
65.64	even	2	inner	390.2.f.a.259.5	yes	6
195.194	odd	2		1170.2.f.d.649.3		6
260.259	odd	2		3120.2.r.g.2209.2		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
390.2.f.a.259.2	✓	6	1.1	even	1	trivial
390.2.f.a.259.5	yes	6	65.64	even	2	inner
390.2.f.b.259.2	yes	6	13.12	even	2
390.2.f.b.259.5	yes	6	5.4	even	2
1170.2.f.c.649.3		6	39.38	odd	2
1170.2.f.c.649.4		6	15.14	odd	2
1170.2.f.d.649.3		6	195.194	odd	2
1170.2.f.d.649.4		6	3.2	odd	2
1950.2.b.l.1351.1		6	5.2	odd	4
1950.2.b.l.1351.6		6	65.12	odd	4
1950.2.b.m.1351.1		6	65.38	odd	4
1950.2.b.m.1351.6		6	5.3	odd	4
3120.2.r.g.2209.2		6	260.259	odd	2
3120.2.r.g.2209.5		6	4.3	odd	2
3120.2.r.h.2209.2		6	20.19	odd	2
3120.2.r.h.2209.5		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 $\F_{q}$
Belyi maps

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

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} -1.00000i q^{3} +1.00000 q^{4} +(-0.311108 - 2.21432i) q^{5} +1.00000i q^{6} -1.52543 q^{7} -1.00000 q^{8} -1.00000 q^{9} +(0.311108 + 2.21432i) q^{10} -2.42864i q^{11} -1.00000i q^{12} +(-3.59210 + 0.311108i) q^{13} +1.52543 q^{14} +(-2.21432 + 0.311108i) q^{15} +1.00000 q^{16} -0.903212i q^{17} +1.00000 q^{18} +4.90321i q^{19} +(-0.311108 - 2.21432i) q^{20} +1.52543i q^{21} +2.42864i q^{22} -2.90321i q^{23} +1.00000i q^{24} +(-4.80642 + 1.37778i) q^{25} +(3.59210 - 0.311108i) q^{26} +1.00000i q^{27} -1.52543 q^{28} -5.95407 q^{29} +(2.21432 - 0.311108i) q^{30} -0.755569i q^{31} -1.00000 q^{32} -2.42864 q^{33} +0.903212i q^{34} +(0.474572 + 3.37778i) q^{35} -1.00000 q^{36} -0.428639 q^{37} -4.90321i q^{38} +(0.311108 + 3.59210i) q^{39} +(0.311108 + 2.21432i) q^{40} -7.80642i q^{41} -1.52543i q^{42} -7.18421i q^{43} -2.42864i q^{44} +(0.311108 + 2.21432i) q^{45} +2.90321i q^{46} -0.949145 q^{47} -1.00000i q^{48} -4.67307 q^{49} +(4.80642 - 1.37778i) q^{50} -0.903212 q^{51} +(-3.59210 + 0.311108i) q^{52} -2.56199i q^{53} -1.00000i q^{54} +(-5.37778 + 0.755569i) q^{55} +1.52543 q^{56} +4.90321 q^{57} +5.95407 q^{58} +2.13335i q^{59} +(-2.21432 + 0.311108i) q^{60} -5.05086 q^{61} +0.755569i q^{62} +1.52543 q^{63} +1.00000 q^{64} +(1.80642 + 7.85728i) q^{65} +2.42864 q^{66} +5.18421 q^{67} -0.903212i q^{68} -2.90321 q^{69} +(-0.474572 - 3.37778i) q^{70} -5.37778i q^{71} +1.00000 q^{72} +8.76986 q^{73} +0.428639 q^{74} +(1.37778 + 4.80642i) q^{75} +4.90321i q^{76} +3.70471i q^{77} +(-0.311108 - 3.59210i) q^{78} +15.0923 q^{79} +(-0.311108 - 2.21432i) q^{80} +1.00000 q^{81} +7.80642i q^{82} +13.2859 q^{83} +1.52543i q^{84} +(-2.00000 + 0.280996i) q^{85} +7.18421i q^{86} +5.95407i q^{87} +2.42864i q^{88} -8.62222i q^{89} +(-0.311108 - 2.21432i) q^{90} +(5.47949 - 0.474572i) q^{91} -2.90321i q^{92} -0.755569 q^{93} +0.949145 q^{94} +(10.8573 - 1.52543i) q^{95} +1.00000i q^{96} +11.1383 q^{97} +4.67307 q^{98} +2.42864i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - 6 q^{2} + 6 q^{4} - 2 q^{5} + 4 q^{7} - 6 q^{8} - 6 q^{9} + 2 q^{10} - 8 q^{13} - 4 q^{14} + 6 q^{16} + 6 q^{18} - 2 q^{20} - 2 q^{25} + 8 q^{26} + 4 q^{28} + 4 q^{29} - 6 q^{32} + 12 q^{33} + 16 q^{35}+ \cdots + 2 q^{98}+O(q^{100}) \) 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

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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