LMFDB - Embedded newform 390.2.bd.a.223.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [390,2,Mod(7,390)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(390, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([0, 3, 11]))

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

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

chi := DirichletCharacter("390.7");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 390 = 2 \cdot 3 \cdot 5 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	390.bd (of order $12$, degree $4$, 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:	$8$
Relative dimension:	$2$ over $\Q(\zeta_{12})$
Coefficient field:	$\Q(\zeta_{24})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - x^{4} + 1 $ x^8 - x^4 + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			223.1
Root			$-0.965926 + 0.258819i$ of defining polynomial
Character	$\chi$	$=$	390.223
Dual form			390.2.bd.a.7.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.866025 - 0.500000i) q^{2} +(-0.258819 + 0.965926i) q^{3} +(0.500000 - 0.866025i) q^{4} +(-2.12132 + 0.707107i) q^{5} +(0.258819 + 0.965926i) q^{6} +(-1.88366 + 3.26260i) q^{7} -1.00000i q^{8} +(-0.866025 - 0.500000i) q^{9} +O(q^{10})$	\(q+(0.866025 - 0.500000i) q^{2} +(-0.258819 + 0.965926i) q^{3} +(0.500000 - 0.866025i) q^{4} +(-2.12132 + 0.707107i) q^{5} +(0.258819 + 0.965926i) q^{6} +(-1.88366 + 3.26260i) q^{7} -1.00000i q^{8} +(-0.866025 - 0.500000i) q^{9} +(-1.48356 + 1.67303i) q^{10} +(-1.23388 + 4.60488i) q^{11} +(0.707107 + 0.707107i) q^{12} +(-3.53553 - 0.707107i) q^{13} +3.76733i q^{14} +(-0.133975 - 2.23205i) q^{15} +(-0.500000 - 0.866025i) q^{16} +(6.22973 - 1.66925i) q^{17} -1.00000 q^{18} +(-5.43916 + 1.45742i) q^{19} +(-0.448288 + 2.19067i) q^{20} +(-2.66390 - 2.66390i) q^{21} +(1.23388 + 4.60488i) q^{22} +(7.94414 + 2.12863i) q^{23} +(0.965926 + 0.258819i) q^{24} +(4.00000 - 3.00000i) q^{25} +(-3.41542 + 1.15539i) q^{26} +(0.707107 - 0.707107i) q^{27} +(1.88366 + 3.26260i) q^{28} +(-4.61193 + 2.66270i) q^{29} +(-1.23205 - 1.86603i) q^{30} +(-0.648586 + 0.648586i) q^{31} +(-0.866025 - 0.500000i) q^{32} +(-4.12863 - 2.38366i) q^{33} +(4.56048 - 4.56048i) q^{34} +(1.68885 - 8.25297i) q^{35} +(-0.866025 + 0.500000i) q^{36} +(0.423344 + 0.733253i) q^{37} +(-3.98174 + 3.98174i) q^{38} +(1.59808 - 3.23205i) q^{39} +(0.707107 + 2.12132i) q^{40} +(2.23437 + 0.598698i) q^{41} +(-3.63896 - 0.975056i) q^{42} +(0.155395 + 0.579940i) q^{43} +(3.37101 + 3.37101i) q^{44} +(2.19067 + 0.448288i) q^{45} +(7.94414 - 2.12863i) q^{46} -1.59575 q^{47} +(0.965926 - 0.258819i) q^{48} +(-3.59638 - 6.22911i) q^{49} +(1.96410 - 4.59808i) q^{50} +6.44949i q^{51} +(-2.38014 + 2.70831i) q^{52} +(4.92820 + 4.92820i) q^{53} +(0.258819 - 0.965926i) q^{54} +(-0.638701 - 10.6409i) q^{55} +(3.26260 + 1.88366i) q^{56} -5.63103i q^{57} +(-2.66270 + 4.61193i) q^{58} +(-2.86919 - 10.7079i) q^{59} +(-2.00000 - 1.00000i) q^{60} +(-1.30751 + 2.26467i) q^{61} +(-0.237399 + 0.885986i) q^{62} +(3.26260 - 1.88366i) q^{63} -1.00000 q^{64} +(8.00000 - 1.00000i) q^{65} -4.76733 q^{66} +(0.210133 - 0.121320i) q^{67} +(1.66925 - 6.22973i) q^{68} +(-4.11219 + 7.12252i) q^{69} +(-2.66390 - 7.99171i) q^{70} +(2.87075 + 10.7138i) q^{71} +(-0.500000 + 0.866025i) q^{72} -8.62498i q^{73} +(0.733253 + 0.423344i) q^{74} +(1.86250 + 4.64016i) q^{75} +(-1.45742 + 5.43916i) q^{76} +(-12.6997 - 12.6997i) q^{77} +(-0.232051 - 3.59808i) q^{78} +11.7214i q^{79} +(1.67303 + 1.48356i) q^{80} +(0.500000 + 0.866025i) q^{81} +(2.23437 - 0.598698i) q^{82} +14.8983 q^{83} +(-3.63896 + 0.975056i) q^{84} +(-12.0349 + 7.94610i) q^{85} +(0.424546 + 0.424546i) q^{86} +(-1.37832 - 5.14394i) q^{87} +(4.60488 + 1.23388i) q^{88} +(-2.58044 - 0.691426i) q^{89} +(2.12132 - 0.707107i) q^{90} +(8.96676 - 10.2031i) q^{91} +(5.81552 - 5.81552i) q^{92} +(-0.458620 - 0.794353i) q^{93} +(-1.38196 + 0.797877i) q^{94} +(10.5076 - 6.93772i) q^{95} +(0.707107 - 0.707107i) q^{96} +(6.60867 + 3.81552i) q^{97} +(-6.22911 - 3.59638i) q^{98} +(3.37101 - 3.37101i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 4 q^{4} - 4 q^{7}+O(q^{10}) $ 8 * q + 4 * q^4 - 4 * q^7	$ 8 q + 4 q^{4} - 4 q^{7} - 16 q^{11} - 8 q^{15} - 4 q^{16} + 12 q^{17} - 8 q^{18} - 24 q^{19} + 8 q^{21} + 16 q^{22} + 16 q^{23} + 32 q^{25} + 4 q^{28} - 24 q^{29} + 4 q^{30} - 4 q^{31} - 12 q^{33} - 24 q^{35} + 8 q^{37} - 8 q^{39} + 28 q^{41} - 8 q^{42} - 8 q^{43} - 8 q^{44} + 16 q^{46} + 32 q^{47} - 20 q^{49} - 12 q^{50} - 16 q^{53} - 4 q^{55} + 12 q^{56} - 8 q^{58} + 32 q^{59} - 16 q^{60} - 8 q^{61} - 16 q^{62} + 12 q^{63} - 8 q^{64} + 64 q^{65} - 16 q^{66} + 12 q^{68} + 8 q^{70} + 8 q^{71} - 4 q^{72} - 24 q^{74} - 24 q^{76} - 24 q^{77} + 12 q^{78} + 4 q^{81} + 28 q^{82} - 32 q^{83} - 8 q^{84} - 32 q^{85} - 8 q^{86} + 28 q^{87} + 8 q^{88} - 4 q^{89} - 8 q^{91} + 20 q^{92} - 12 q^{94} + 4 q^{95} + 12 q^{97} + 24 q^{98} - 8 q^{99}+O(q^{100}) $ 8 * q + 4 * q^4 - 4 * q^7 - 16 * q^11 - 8 * q^15 - 4 * q^16 + 12 * q^17 - 8 * q^18 - 24 * q^19 + 8 * q^21 + 16 * q^22 + 16 * q^23 + 32 * q^25 + 4 * q^28 - 24 * q^29 + 4 * q^30 - 4 * q^31 - 12 * q^33 - 24 * q^35 + 8 * q^37 - 8 * q^39 + 28 * q^41 - 8 * q^42 - 8 * q^43 - 8 * q^44 + 16 * q^46 + 32 * q^47 - 20 * q^49 - 12 * q^50 - 16 * q^53 - 4 * q^55 + 12 * q^56 - 8 * q^58 + 32 * q^59 - 16 * q^60 - 8 * q^61 - 16 * q^62 + 12 * q^63 - 8 * q^64 + 64 * q^65 - 16 * q^66 + 12 * q^68 + 8 * q^70 + 8 * q^71 - 4 * q^72 - 24 * q^74 - 24 * q^76 - 24 * q^77 + 12 * q^78 + 4 * q^81 + 28 * q^82 - 32 * q^83 - 8 * q^84 - 32 * q^85 - 8 * q^86 + 28 * q^87 + 8 * q^88 - 4 * q^89 - 8 * q^91 + 20 * q^92 - 12 * q^94 + 4 * q^95 + 12 * q^97 + 24 * q^98 - 8 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$131$	$157$	$301$
$\chi(n)$	$1$	$e\left(\frac{3}{4}\right)$	$e\left(\frac{1}{12}\right)$

Coefficient data

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

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

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

$2$	0.866025	−	0.500000i	0.612372	−	0.353553i
$2$	0.866025	−	0.500000i	0.612372	−	0.353553i
$3$	−0.258819	+	0.965926i	−0.149429	+	0.557678i
$3$	−0.258819	+	0.965926i	−0.149429	+	0.557678i
$4$	0.500000	−	0.866025i	0.250000	−	0.433013i
$5$	−2.12132	+	0.707107i	−0.948683	+	0.316228i
$5$	−2.12132	+	0.707107i	−0.948683	+	0.316228i
$6$	0.258819	+	0.965926i	0.105662	+	0.394338i
$7$	−1.88366	+	3.26260i	−0.711958	+	1.23315i	0.252163	+	0.967685i	$0.418858\pi$
$7$	−1.88366	+	3.26260i	−0.711958	+	1.23315i	−0.964121	+	0.265463i	$0.914475\pi$
$8$		−	1.00000i		−	0.353553i
$9$	−0.866025	−	0.500000i	−0.288675	−	0.166667i
$10$	−1.48356	+	1.67303i	−0.469144	+	0.529059i
$11$	−1.23388	+	4.60488i	−0.372027	+	1.38842i	0.485613	+	0.874174i	$0.338597\pi$
$11$	−1.23388	+	4.60488i	−0.372027	+	1.38842i	−0.857640	+	0.514251i	$0.828070\pi$
$12$	0.707107	+	0.707107i	0.204124	+	0.204124i
$13$	−3.53553	−	0.707107i	−0.980581	−	0.196116i
$13$	−3.53553	−	0.707107i	−0.980581	−	0.196116i
$14$			3.76733i			1.00686i
$15$	−0.133975	−	2.23205i	−0.0345921	−	0.576313i
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	6.22973	−	1.66925i	1.51093	−	0.404853i	0.594187	−	0.804327i	$-0.297474\pi$
$17$	6.22973	−	1.66925i	1.51093	−	0.404853i	0.916744	+	0.399474i	$0.130807\pi$
$18$	−1.00000			−0.235702
$19$	−5.43916	+	1.45742i	−1.24783	+	0.334355i	−0.821497	−	0.570213i	$-0.806861\pi$
$19$	−5.43916	+	1.45742i	−1.24783	+	0.334355i	−0.426331	+	0.904567i	$0.640194\pi$
$20$	−0.448288	+	2.19067i	−0.100240	+	0.489849i
$21$	−2.66390	−	2.66390i	−0.581311	−	0.581311i
$22$	1.23388	+	4.60488i	0.263063	+	0.981765i
$23$	7.94414	+	2.12863i	1.65647	+	0.443849i	0.961413	−	0.275108i	$-0.0887135\pi$
$23$	7.94414	+	2.12863i	1.65647	+	0.443849i	0.695055	+	0.718957i	$0.255380\pi$
$24$	0.965926	+	0.258819i	0.197169	+	0.0528312i
$25$	4.00000	−	3.00000i	0.800000	−	0.600000i
$26$	−3.41542	+	1.15539i	−0.669818	+	0.226592i
$27$	0.707107	−	0.707107i	0.136083	−	0.136083i
$28$	1.88366	+	3.26260i	0.355979	+	0.616574i
$29$	−4.61193	+	2.66270i	−0.856414	+	0.494451i	−0.862810	−	0.505528i	$-0.831298\pi$
$29$	−4.61193	+	2.66270i	−0.856414	+	0.494451i	0.00639555	+	0.999980i	$0.497964\pi$
$30$	−1.23205	−	1.86603i	−0.224941	−	0.340688i
$31$	−0.648586	+	0.648586i	−0.116490	+	0.116490i	−0.762949	−	0.646459i	$-0.776249\pi$
$31$	−0.648586	+	0.648586i	−0.116490	+	0.116490i	0.646459	+	0.762949i	$0.276249\pi$
$32$	−0.866025	−	0.500000i	−0.153093	−	0.0883883i
$33$	−4.12863	−	2.38366i	−0.718702	−	0.414943i
$34$	4.56048	−	4.56048i	0.782116	−	0.782116i
$35$	1.68885	−	8.25297i	0.285467	−	1.39501i
$36$	−0.866025	+	0.500000i	−0.144338	+	0.0833333i
$37$	0.423344	+	0.733253i	0.0695973	+	0.120546i	0.898724	−	0.438515i	$-0.144495\pi$
$37$	0.423344	+	0.733253i	0.0695973	+	0.120546i	−0.829127	+	0.559061i	$0.811162\pi$
$38$	−3.98174	+	3.98174i	−0.645923	+	0.645923i
$39$	1.59808	−	3.23205i	0.255897	−	0.517542i
$40$	0.707107	+	2.12132i	0.111803	+	0.335410i
$41$	2.23437	+	0.598698i	0.348950	+	0.0935010i	0.429037	−	0.903287i	$-0.358853\pi$
$41$	2.23437	+	0.598698i	0.348950	+	0.0935010i	−0.0800865	+	0.996788i	$0.525520\pi$
$42$	−3.63896	−	0.975056i	−0.561503	−	0.150454i
$43$	0.155395	+	0.579940i	0.0236974	+	0.0884401i	0.976762	−	0.214328i	$-0.0687560\pi$
$43$	0.155395	+	0.579940i	0.0236974	+	0.0884401i	−0.953064	+	0.302768i	$0.902089\pi$
$44$	3.37101	+	3.37101i	0.508199	+	0.508199i
$45$	2.19067	+	0.448288i	0.326566	+	0.0668268i
$46$	7.94414	−	2.12863i	1.17130	−	0.313849i
$47$	−1.59575			−0.232765			−0.116382	−	0.993204i	$-0.537130\pi$
$47$	−1.59575			−0.232765			−0.116382	+	0.993204i	$0.537130\pi$
$48$	0.965926	−	0.258819i	0.139419	−	0.0373573i
$49$	−3.59638	−	6.22911i	−0.513768	−	0.889872i
$50$	1.96410	−	4.59808i	0.277766	−	0.650266i
$51$			6.44949i			0.903109i
$52$	−2.38014	+	2.70831i	−0.330066	+	0.375575i
$53$	4.92820	+	4.92820i	0.676941	+	0.676941i	0.959307	−	0.282366i	$-0.0911192\pi$
$53$	4.92820	+	4.92820i	0.676941	+	0.676941i	−0.282366	+	0.959307i	$0.591119\pi$
$54$	0.258819	−	0.965926i	0.0352208	−	0.131446i
$55$	−0.638701	−	10.6409i	−0.0861224	−	1.43482i
$56$	3.26260	+	1.88366i	0.435983	+	0.251715i
$57$		−	5.63103i		−	0.745848i
$58$	−2.66270	+	4.61193i	−0.349630	+	0.605576i
$59$	−2.86919	−	10.7079i	−0.373536	−	1.39406i	−0.855472	−	0.517849i	$-0.826733\pi$
$59$	−2.86919	−	10.7079i	−0.373536	−	1.39406i	0.481936	−	0.876206i	$-0.339934\pi$
$60$	−2.00000	−	1.00000i	−0.258199	−	0.129099i
$61$	−1.30751	+	2.26467i	−0.167409	+	0.289961i	−0.937508	−	0.347963i	$-0.886873\pi$
$61$	−1.30751	+	2.26467i	−0.167409	+	0.289961i	0.770099	+	0.637924i	$0.220207\pi$
$62$	−0.237399	+	0.885986i	−0.0301497	+	0.112520i
$63$	3.26260	−	1.88366i	0.411049	−	0.237319i
$64$	−1.00000			−0.125000
$65$	8.00000	−	1.00000i	0.992278	−	0.124035i
$66$	−4.76733			−0.586817
$67$	0.210133	−	0.121320i	0.0256718	−	0.0148216i	−0.487109	−	0.873341i	$-0.661949\pi$
$67$	0.210133	−	0.121320i	0.0256718	−	0.0148216i	0.512781	+	0.858519i	$0.328615\pi$
$68$	1.66925	−	6.22973i	0.202426	−	0.755466i
$69$	−4.11219	+	7.12252i	−0.495050	+	0.857451i
$70$	−2.66390	−	7.99171i	−0.318397	−	0.955192i
$71$	2.87075	+	10.7138i	0.340696	+	1.27149i	0.897561	+	0.440890i	$0.145337\pi$
$71$	2.87075	+	10.7138i	0.340696	+	1.27149i	−0.556865	+	0.830603i	$0.687996\pi$
$72$	−0.500000	+	0.866025i	−0.0589256	+	0.102062i
$73$		−	8.62498i		−	1.00948i	−0.863272	−	0.504739i	$-0.831589\pi$
$73$		−	8.62498i		−	1.00948i	0.863272	−	0.504739i	$-0.168411\pi$
$74$	0.733253	+	0.423344i	0.0852389	+	0.0492127i
$75$	1.86250	+	4.64016i	0.215063	+	0.535800i
$76$	−1.45742	+	5.43916i	−0.167177	+	0.623914i
$77$	−12.6997	−	12.6997i	−1.44726	−	1.44726i
$78$	−0.232051	−	3.59808i	−0.0262746	−	0.407402i
$79$			11.7214i			1.31876i	0.751812	+	0.659378i	$0.229180\pi$
$79$			11.7214i			1.31876i	−0.751812	+	0.659378i	$0.770820\pi$
$80$	1.67303	+	1.48356i	0.187051	+	0.165867i
$81$	0.500000	+	0.866025i	0.0555556	+	0.0962250i
$82$	2.23437	−	0.598698i	0.246745	−	0.0661152i
$83$	14.8983			1.63530			0.817648	−	0.575719i	$-0.195278\pi$
$83$	14.8983			1.63530			0.817648	+	0.575719i	$0.195278\pi$
$84$	−3.63896	+	0.975056i	−0.397043	+	0.106387i
$85$	−12.0349	+	7.94610i	−1.30537	+	0.861875i
$86$	0.424546	+	0.424546i	0.0457799	+	0.0457799i
$87$	−1.37832	−	5.14394i	−0.147771	−	0.551488i
$88$	4.60488	+	1.23388i	0.490882	+	0.131532i
$89$	−2.58044	−	0.691426i	−0.273526	−	0.0732910i	0.119449	−	0.992840i	$-0.461887\pi$
$89$	−2.58044	−	0.691426i	−0.273526	−	0.0732910i	−0.392975	+	0.919549i	$0.628554\pi$
$90$	2.12132	−	0.707107i	0.223607	−	0.0745356i
$91$	8.96676	−	10.2031i	0.939972	−	1.06957i
$92$	5.81552	−	5.81552i	0.606309	−	0.606309i
$93$	−0.458620	−	0.794353i	−0.0475567	−	0.0823706i
$94$	−1.38196	+	0.797877i	−0.142539	+	0.0822947i
$95$	10.5076	−	6.93772i	1.07806	−	0.711795i
$96$	0.707107	−	0.707107i	0.0721688	−	0.0721688i
$97$	6.60867	+	3.81552i	0.671008	+	0.387407i	0.796459	−	0.604693i	$-0.206704\pi$
$97$	6.60867	+	3.81552i	0.671008	+	0.387407i	−0.125450	+	0.992100i	$0.540038\pi$
$98$	−6.22911	−	3.59638i	−0.629235	−	0.363289i
$99$	3.37101	−	3.37101i	0.338799	−	0.338799i
$100$	−0.598076	−	4.96410i	−0.0598076	−	0.496410i
$101$	6.07483	−	3.50731i	0.604468	−	0.348990i	−0.166329	−	0.986070i	$-0.553191\pi$
$101$	6.07483	−	3.50731i	0.604468	−	0.348990i	0.770797	+	0.637080i	$0.219858\pi$
$102$	3.22474	+	5.58542i	0.319297	+	0.553039i
$103$	−1.81722	+	1.81722i	−0.179056	+	0.179056i	−0.790944	−	0.611889i	$-0.790410\pi$
$103$	−1.81722	+	1.81722i	−0.179056	+	0.179056i	0.611889	+	0.790944i	$0.290410\pi$
$104$	−0.707107	+	3.53553i	−0.0693375	+	0.346688i
$105$	7.53465	+	3.76733i	0.735307	+	0.367653i
$106$	6.73205	+	1.80385i	0.653875	+	0.175205i
$107$	8.88865	+	2.38171i	0.859298	+	0.230248i	0.661454	−	0.749985i	$-0.269940\pi$
$107$	8.88865	+	2.38171i	0.859298	+	0.230248i	0.197844	+	0.980234i	$0.436606\pi$
$108$	−0.258819	−	0.965926i	−0.0249049	−	0.0929463i
$109$	−8.59335	−	8.59335i	−0.823094	−	0.823094i	0.163457	−	0.986550i	$-0.447736\pi$
$109$	−8.59335	−	8.59335i	−0.823094	−	0.823094i	−0.986550	+	0.163457i	$0.947736\pi$
$110$	−5.87359	−	8.89595i	−0.560025	−	0.848196i
$111$	−0.817837	+	0.219139i	−0.0776257	+	0.0207997i
$112$	3.76733			0.355979
$113$	−16.2374	+	4.35079i	−1.52748	+	0.409288i	−0.922197	−	0.386720i	$-0.873608\pi$
$113$	−16.2374	+	4.35079i	−1.52748	+	0.409288i	−0.605286	+	0.796008i	$0.706941\pi$
$114$	−2.81552	−	4.87662i	−0.263697	−	0.456737i
$115$	−18.3572	+	1.10186i	−1.71182	+	0.102749i
$116$			5.32540i			0.494451i
$117$	2.70831	+	2.38014i	0.250383	+	0.220044i
$118$	−7.83876	−	7.83876i	−0.721616	−	0.721616i
$119$	−6.28861	+	23.4694i	−0.576476	+	2.15144i
$120$	−2.23205	+	0.133975i	−0.203757	+	0.0122302i
$121$	−10.1562	−	5.86370i	−0.923294	−	0.533064i
$122$			2.61501i			0.236752i
$123$	−1.15660	+	2.00328i	−0.104287	+	0.180630i
$124$	0.237399	+	0.885986i	0.0213191	+	0.0795639i
$125$	−6.36396	+	9.19239i	−0.569210	+	0.822192i
$126$	1.88366	−	3.26260i	0.167810	−	0.290656i
$127$	0.447086	−	1.66855i	0.0396724	−	0.148060i	−0.943249	−	0.332088i	$-0.892247\pi$
$127$	0.447086	−	1.66855i	0.0396724	−	0.148060i	0.982921	+	0.184028i	$0.0589137\pi$
$128$	−0.866025	+	0.500000i	−0.0765466	+	0.0441942i
$129$	−0.600398			−0.0528621
$130$	6.42820	−	4.86603i	0.563791	−	0.426779i
$131$	9.67511			0.845319			0.422659	−	0.906289i	$-0.361097\pi$
$131$	9.67511			0.845319			0.422659	+	0.906289i	$0.361097\pi$
$132$	−4.12863	+	2.38366i	−0.359351	+	0.207471i
$133$	5.49057	−	20.4911i	0.476093	−	1.77680i
$134$	0.121320	−	0.210133i	0.0104805	−	0.0181527i
$135$	−1.00000	+	2.00000i	−0.0860663	+	0.172133i
$136$	−1.66925	−	6.22973i	−0.143137	−	0.534195i
$137$	−9.81489	+	16.9999i	−0.838543	+	1.45240i	0.0525700	+	0.998617i	$0.483259\pi$
$137$	−9.81489	+	16.9999i	−0.838543	+	1.45240i	−0.891113	+	0.453782i	$0.850075\pi$
$138$			8.22438i			0.700106i
$139$	−11.1783	−	6.45377i	−0.948127	−	0.547402i	−0.0556286	−	0.998452i	$-0.517716\pi$
$139$	−11.1783	−	6.45377i	−0.948127	−	0.547402i	−0.892499	+	0.451050i	$0.851050\pi$
$140$	−6.30286	−	5.58907i	−0.532689	−	0.472363i
$141$	0.413012	−	1.54138i	0.0347818	−	0.129808i
$142$	7.84304	+	7.84304i	0.658173	+	0.658173i
$143$	7.61855	−	15.4082i	0.637095	−	1.28850i
$144$			1.00000i			0.0833333i
$145$	7.90057	−	8.90957i	0.656107	−	0.739899i
$146$	−4.31249	−	7.46945i	−0.356904	−	0.618176i
$147$	6.94767	−	1.86162i	0.573034	−	0.153544i
$148$	0.846687			0.0695973
$149$	6.27207	−	1.68060i	0.513828	−	0.137680i	0.00741780	−	0.999972i	$-0.497639\pi$
$149$	6.27207	−	1.68060i	0.513828	−	0.137680i	0.506410	+	0.862293i	$0.330972\pi$
$150$	3.93305	+	3.08725i	0.321132	+	0.252073i
$151$	−0.892927	−	0.892927i	−0.0726654	−	0.0726654i	0.669840	−	0.742505i	$-0.266363\pi$
$151$	−0.892927	−	0.892927i	−0.0726654	−	0.0726654i	−0.742505	+	0.669840i	$0.766363\pi$
$152$	1.45742	+	5.43916i	0.118212	+	0.441174i
$153$	−6.22973	−	1.66925i	−0.503644	−	0.134951i
$154$	−17.3481	−	4.64841i	−1.39795	−	0.374580i
$155$	0.917240	−	1.83448i	0.0736745	−	0.147349i
$156$	−2.00000	−	3.00000i	−0.160128	−	0.240192i
$157$	−9.21305	+	9.21305i	−0.735282	+	0.735282i	−0.971661	−	0.236379i	$-0.924039\pi$
$157$	−9.21305	+	9.21305i	−0.735282	+	0.735282i	0.236379	+	0.971661i	$0.424039\pi$
$158$	5.86068	+	10.1510i	0.466250	+	0.807569i
$159$	−6.03579	+	3.48477i	−0.478669	+	0.276360i
$160$	2.19067	+	0.448288i	0.173188	+	0.0354403i
$161$	−21.9089	+	21.9089i	−1.72667	+	1.72667i
$162$	0.866025	+	0.500000i	0.0680414	+	0.0392837i
$163$	10.5118	+	6.06899i	0.823347	+	0.475360i	0.851569	−	0.524242i	$-0.175651\pi$
$163$	10.5118	+	6.06899i	0.823347	+	0.475360i	−0.0282222	+	0.999602i	$0.508985\pi$
$164$	1.63567	−	1.63567i	0.127725	−	0.127725i
$165$	10.4436	+	2.13713i	0.813037	+	0.166376i
$166$	12.9023	−	7.44913i	1.00141	−	0.578164i
$167$	−1.71441	−	2.96945i	−0.132665	−	0.229783i	0.792038	−	0.610472i	$-0.209020\pi$
$167$	−1.71441	−	2.96945i	−0.132665	−	0.229783i	−0.924703	+	0.380689i	$0.875687\pi$
$168$	−2.66390	+	2.66390i	−0.205525	+	0.205525i
$169$	12.0000	+	5.00000i	0.923077	+	0.384615i
$170$	−6.44949	+	12.8990i	−0.494653	+	0.989307i
$171$	5.43916	+	1.45742i	0.415943	+	0.111452i
$172$	0.579940	+	0.155395i	0.0442200	+	0.0118487i
$173$	−0.909943	−	3.39595i	−0.0691817	−	0.258190i	0.922669	−	0.385592i	$-0.126003\pi$
$173$	−0.909943	−	3.39595i	−0.0691817	−	0.258190i	−0.991851	+	0.127402i	$0.959336\pi$
$174$	−3.76563	−	3.76563i	−0.285471	−	0.285471i
$175$	2.25315	+	18.7014i	0.170322	+	1.41369i
$176$	4.60488	−	1.23388i	0.347106	−	0.0930068i
$177$	11.0857			0.833251
$178$	−2.58044	+	0.691426i	−0.193412	+	0.0518246i
$179$	5.97589	+	10.3506i	0.446659	+	0.773637i	0.998166	−	0.0605338i	$-0.0192803\pi$
$179$	5.97589	+	10.3506i	0.446659	+	0.773637i	−0.551507	+	0.834170i	$0.685947\pi$
$180$	1.48356	−	1.67303i	0.110578	−	0.124700i
$181$			13.9494i			1.03685i	0.855123	+	0.518425i	$0.173481\pi$
$181$			13.9494i			1.03685i	−0.855123	+	0.518425i	$0.826519\pi$
$182$	2.66390	−	13.3195i	0.197462	−	0.987308i
$183$	−1.84909	−	1.84909i	−0.136689	−	0.136689i
$184$	2.12863	−	7.94414i	0.156924	−	0.585650i
$185$	−1.41654	−	1.25611i	−0.104146	−	0.0923514i
$186$	−0.794353	−	0.458620i	−0.0582448	−	0.0336276i
$187$			30.7468i			2.24843i
$188$	−0.797877	+	1.38196i	−0.0581912	+	0.100790i
$189$	0.975056	+	3.63896i	0.0709249	+	0.264695i
$190$	5.63103	−	11.2621i	0.408518	−	0.817036i
$191$	−2.56823	+	4.44831i	−0.185831	+	0.321868i	−0.943856	−	0.330357i	$-0.892831\pi$
$191$	−2.56823	+	4.44831i	−0.185831	+	0.321868i	0.758025	+	0.652225i	$0.226164\pi$
$192$	0.258819	−	0.965926i	0.0186787	−	0.0697097i
$193$	22.7936	−	13.1599i	1.64072	−	0.947269i	0.660139	−	0.751143i	$-0.270497\pi$
$193$	22.7936	−	13.1599i	1.64072	−	0.947269i	0.980579	−	0.196126i	$-0.0628360\pi$
$194$	7.63103			0.547876
$195$	−1.10463	+	7.98623i	−0.0791039	+	0.571905i
$196$	−7.19275			−0.513768
$197$	6.85337	−	3.95680i	0.488282	−	0.281910i	−0.235579	−	0.971855i	$-0.575699\pi$
$197$	6.85337	−	3.95680i	0.488282	−	0.281910i	0.723862	+	0.689945i	$0.242365\pi$
$198$	1.23388	−	4.60488i	0.0876877	−	0.327255i
$199$	−13.4242	+	23.2514i	−0.951615	+	1.64825i	−0.209684	+	0.977769i	$0.567244\pi$
$199$	−13.4242	+	23.2514i	−0.951615	+	1.64825i	−0.741931	+	0.670476i	$0.766090\pi$
$200$	−3.00000	−	4.00000i	−0.212132	−	0.282843i
$201$	0.0628000	+	0.234373i	0.00442957	+	0.0165314i
$202$	3.50731	−	6.07483i	0.246773	−	0.427424i
$203$		−	20.0625i		−	1.40811i
$204$	5.58542	+	3.22474i	0.391058	+	0.225777i
$205$	−5.16316	+	0.309909i	−0.360611	+	0.0216450i
$206$	−0.665147	+	2.48236i	−0.0463430	+	0.172954i
$207$	−5.81552	−	5.81552i	−0.404206	−	0.404206i
$208$	1.15539	+	3.41542i	0.0801122	+	0.236816i
$209$		−	26.8450i		−	1.85690i
$210$	8.40887	−	0.504726i	0.580267	−	0.0348294i
$211$	4.97041	+	8.60901i	0.342177	+	0.592668i	0.984837	−	0.173484i	$-0.0555023\pi$
$211$	4.97041	+	8.60901i	0.342177	+	0.592668i	−0.642660	+	0.766152i	$0.722169\pi$
$212$	6.73205	−	1.80385i	0.462359	−	0.123889i
$213$	−11.0917			−0.759993
$214$	8.88865	−	2.38171i	0.607615	−	0.162810i
$215$	−0.739721	−	1.12036i	−0.0504486	−	0.0764078i
$216$	−0.707107	−	0.707107i	−0.0481125	−	0.0481125i
$217$	−0.894360	−	3.33780i	−0.0607131	−	0.226584i
$218$	−11.7387	−	3.14538i	−0.795047	−	0.213032i
$219$	8.33109	+	2.23231i	0.562963	+	0.150845i
$220$	−9.53465	−	4.76733i	−0.642826	−	0.321413i
$221$	−23.2058	+	1.49661i	−1.56099	+	0.100673i
$222$	−0.598698	+	0.598698i	−0.0401820	+	0.0401820i
$223$	3.33610	+	5.77829i	0.223402	+	0.386943i	0.955839	−	0.293892i	$-0.0949505\pi$
$223$	3.33610	+	5.77829i	0.223402	+	0.386943i	−0.732437	+	0.680835i	$0.761617\pi$
$224$	3.26260	−	1.88366i	0.217992	−	0.125858i
$225$	−4.96410	+	0.598076i	−0.330940	+	0.0398717i
$226$	−11.8866	+	11.8866i	−0.790684	+	0.790684i
$227$	12.2418	+	7.06778i	0.812514	+	0.469105i	0.847828	−	0.530271i	$-0.177910\pi$
$227$	12.2418	+	7.06778i	0.812514	+	0.469105i	−0.0353140	+	0.999376i	$0.511243\pi$
$228$	−4.87662	−	2.81552i	−0.322962	−	0.186462i
$229$	1.24213	−	1.24213i	0.0820819	−	0.0820819i	−0.664874	−	0.746956i	$-0.731515\pi$
$229$	1.24213	−	1.24213i	0.0820819	−	0.0820819i	0.746956	+	0.664874i	$0.231515\pi$
$230$	−15.3469	+	10.1329i	−1.01194	+	0.668141i
$231$	15.5539	−	8.98004i	1.02337	−	0.590843i
$232$	2.66270	+	4.61193i	0.174815	+	0.302788i
$233$	−5.51745	+	5.51745i	−0.361460	+	0.361460i	−0.864350	−	0.502890i	$-0.832270\pi$
$233$	−5.51745	+	5.51745i	−0.361460	+	0.361460i	0.502890	+	0.864350i	$0.332270\pi$
$234$	3.53553	+	0.707107i	0.231125	+	0.0462250i
$235$	3.38511	−	1.12837i	0.220820	−	0.0736066i
$236$	−10.7079	−	2.86919i	−0.697028	−	0.186768i
$237$	−11.3220	−	3.03371i	−0.735440	−	0.197061i
$238$	6.28861	+	23.4694i	0.407630	+	1.52130i
$239$	−1.65029	−	1.65029i	−0.106748	−	0.106748i	0.651715	−	0.758464i	$-0.274050\pi$
$239$	−1.65029	−	1.65029i	−0.106748	−	0.106748i	−0.758464	+	0.651715i	$0.774050\pi$
$240$	−1.86603	+	1.23205i	−0.120451	+	0.0795285i
$241$	6.90957	−	1.85141i	0.445084	−	0.119260i	−0.0293140	−	0.999570i	$-0.509332\pi$
$241$	6.90957	−	1.85141i	0.445084	−	0.119260i	0.474398	+	0.880310i	$0.342666\pi$
$242$	−11.7274			−0.753866
$243$	−0.965926	+	0.258819i	−0.0619642	+	0.0166032i
$244$	1.30751	+	2.26467i	0.0837044	+	0.144980i
$245$	12.0337	+	10.6709i	0.768806	+	0.681739i
$246$			2.31319i			0.147484i
$247$	20.2609	−	1.30669i	1.28917	−	0.0831424i
$248$	0.648586	+	0.648586i	0.0411853	+	0.0411853i
$249$	−3.85595	+	14.3906i	−0.244361	+	0.911968i
$250$	−0.915158	+	11.1428i	−0.0578797	+	0.704734i
$251$	−20.8609	−	12.0440i	−1.31673	−	0.760213i	−0.333527	−	0.942741i	$-0.608239\pi$
$251$	−20.8609	−	12.0440i	−1.31673	−	0.760213i	−0.983201	+	0.182527i	$0.941572\pi$
$252$		−	3.76733i		−	0.237319i
$253$	−19.6042	+	33.9554i	−1.23250	+	2.13476i
$254$	−0.447086	−	1.66855i	−0.0280527	−	0.104694i
$255$	−4.56048	−	13.6814i	−0.285588	−	0.856765i
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	4.47418	−	16.6979i	0.279091	−	1.04158i	−0.673958	−	0.738769i	$-0.735407\pi$
$257$	4.47418	−	16.6979i	0.279091	−	1.04158i	0.953050	−	0.302814i	$-0.0979261\pi$
$258$	−0.519960	+	0.300199i	−0.0323713	+	0.0186896i
$259$	−3.18975			−0.198201
$260$	3.13397	−	7.42820i	0.194361	−	0.460678i
$261$	5.32540			0.329634
$262$	8.37889	−	4.83756i	0.517650	−	0.298865i
$263$	5.27659	−	19.6925i	0.325369	−	1.21429i	−0.588572	−	0.808445i	$-0.700310\pi$
$263$	5.27659	−	19.6925i	0.325369	−	1.21429i	0.913941	−	0.405847i	$-0.133024\pi$
$264$	−2.38366	+	4.12863i	−0.146704	+	0.254099i
$265$	−13.9391	−	6.96953i	−0.856270	−	0.428135i
$266$	−5.49057	−	20.4911i	−0.336648	−	1.25639i
$267$	1.33573	−	2.31356i	0.0817455	−	0.141587i
$268$		−	0.242641i		−	0.0148216i
$269$	−4.36637	−	2.52092i	−0.266222	−	0.153703i	0.360948	−	0.932586i	$-0.382453\pi$
$269$	−4.36637	−	2.52092i	−0.266222	−	0.153703i	−0.627170	+	0.778883i	$0.715787\pi$
$270$	0.133975	+	2.23205i	0.00815343	+	0.135838i
$271$	7.30501	−	27.2627i	0.443748	−	1.65609i	−0.275475	−	0.961308i	$-0.588835\pi$
$271$	7.30501	−	27.2627i	0.443748	−	1.65609i	0.719222	−	0.694780i	$-0.244498\pi$
$272$	−4.56048	−	4.56048i	−0.276520	−	0.276520i
$273$	7.53465	+	11.3020i	0.456018	+	0.684027i
$274$			19.6298i			1.18588i
$275$	8.87915	+	22.1212i	0.535433	+	1.33396i
$276$	4.11219	+	7.12252i	0.247525	+	0.428725i
$277$	−13.3041	+	3.56481i	−0.799364	+	0.214189i	−0.635305	−	0.772262i	$-0.719125\pi$
$277$	−13.3041	+	3.56481i	−0.799364	+	0.214189i	−0.164059	+	0.986451i	$0.552459\pi$
$278$	−12.9075			−0.774143
$279$	0.885986	−	0.237399i	0.0530426	−	0.0142127i
$280$	−8.25297	−	1.68885i	−0.493209	−	0.100928i
$281$	12.8092	+	12.8092i	0.764131	+	0.764131i	0.977066	−	0.212935i	$-0.0683023\pi$
$281$	12.8092	+	12.8092i	0.764131	+	0.764131i	−0.212935	+	0.977066i	$0.568302\pi$
$282$	−0.413012	−	1.54138i	−0.0245945	−	0.0917878i
$283$	25.7974	+	6.91239i	1.53350	+	0.410899i	0.924158	−	0.382012i	$-0.124769\pi$
$283$	25.7974	+	6.91239i	1.53350	+	0.410899i	0.609338	+	0.792911i	$0.291435\pi$
$284$	10.7138	+	2.87075i	0.635747	+	0.170348i
$285$	3.98174	+	11.9452i	0.235858	+	0.707574i
$286$	−1.10626	−	17.1532i	−0.0654146	−	1.01429i
$287$	−6.16212	+	6.16212i	−0.363738	+	0.363738i
$288$	0.500000	+	0.866025i	0.0294628	+	0.0510310i
$289$	21.3007	−	12.2980i	1.25298	−	0.723409i
$290$	2.38731	−	11.6662i	0.140188	−	0.685063i
$291$	−5.39595	+	5.39595i	−0.316316	+	0.316316i
$292$	−7.46945	−	4.31249i	−0.437116	−	0.252369i
$293$	−13.7458	−	7.93613i	−0.803037	−	0.463634i	0.0414949	−	0.999139i	$-0.486788\pi$
$293$	−13.7458	−	7.93613i	−0.803037	−	0.463634i	−0.844532	+	0.535505i	$0.820121\pi$
$294$	5.08604	−	5.08604i	0.296624	−	0.296624i
$295$	13.6581	+	20.6862i	0.795207	+	1.20439i
$296$	0.733253	−	0.423344i	0.0426195	−	0.0246064i
$297$	2.38366	+	4.12863i	0.138314	+	0.239567i
$298$	4.59147	−	4.59147i	0.265977	−	0.265977i
$299$	−26.5816	−	13.1432i	−1.53725	−	0.760090i
$300$	4.94975	+	0.707107i	0.285774	+	0.0408248i
$301$	−2.18482	−	0.585422i	−0.125931	−	0.0337432i
$302$	−1.21976	−	0.326834i	−0.0701894	−	0.0188072i
$303$	1.81552	+	6.77559i	0.104299	+	0.389248i
$304$	3.98174	+	3.98174i	0.228368	+	0.228368i
$305$	1.17228	−	5.72863i	0.0671244	−	0.328020i
$306$	−6.22973	+	1.66925i	−0.356130	+	0.0954247i
$307$	−23.1192			−1.31948			−0.659741	−	0.751493i	$-0.729334\pi$
$307$	−23.1192			−1.31948			−0.659741	+	0.751493i	$0.729334\pi$
$308$	−17.3481	+	4.64841i	−0.988500	+	0.264868i
$309$	−1.28497	−	2.22562i	−0.0730991	−	0.126611i
$310$	−0.122887	−	2.04733i	−0.00697950	−	0.116280i
$311$		−	0.741339i		−	0.0420375i	−0.999779	−	0.0210187i	$-0.993309\pi$
$311$		−	0.741339i		−	0.0420375i	0.999779	−	0.0210187i	$-0.00669097\pi$
$312$	−3.23205	−	1.59808i	−0.182979	−	0.0904732i
$313$	−4.37769	−	4.37769i	−0.247442	−	0.247442i	0.572478	−	0.819920i	$-0.305982\pi$
$313$	−4.37769	−	4.37769i	−0.247442	−	0.247442i	−0.819920	+	0.572478i	$0.805982\pi$
$314$	−3.37221	+	12.5853i	−0.190305	+	0.710228i
$315$	−5.58907	+	6.30286i	−0.314908	+	0.355126i
$316$	10.1510	+	5.86068i	0.571038	+	0.329689i
$317$		−	2.85765i		−	0.160502i	−0.996775	−	0.0802508i	$-0.974428\pi$
$317$		−	2.85765i		−	0.160502i	0.996775	−	0.0802508i	$-0.0255721\pi$
$318$	−3.48477	+	6.03579i	−0.195416	+	0.338470i
$319$	−6.57088	−	24.5229i	−0.367899	−	1.37302i
$320$	2.12132	−	0.707107i	0.118585	−	0.0395285i
$321$	−4.60110	+	7.96934i	−0.256808	+	0.444805i
$322$	−8.01923	+	29.9282i	−0.446894	+	1.66783i
$323$	−31.4517	+	18.1586i	−1.75002	+	1.01037i
$324$	1.00000			0.0555556
$325$	−16.2635	+	7.77817i	−0.902134	+	0.431455i
$326$	12.1380			0.672260
$327$	10.5247	−	6.07642i	0.582015	−	0.336027i
$328$	0.598698	−	2.23437i	0.0330576	−	0.123373i
$329$	3.00586	−	5.20631i	0.165719	−	0.287033i
$330$	10.1130	−	3.37101i	0.556704	−	0.185568i
$331$	−4.92001	−	18.3617i	−0.270428	−	1.00925i	−0.958844	−	0.283935i	$-0.908360\pi$
$331$	−4.92001	−	18.3617i	−0.270428	−	1.00925i	0.688415	−	0.725317i	$-0.258307\pi$
$332$	7.44913	−	12.9023i	0.408824	−	0.708104i
$333$		−	0.846687i		−	0.0463982i
$334$	−2.96945	−	1.71441i	−0.162481	−	0.0938085i
$335$	−0.359973	+	0.405946i	−0.0196674	+	0.0221792i
$336$	−0.975056	+	3.63896i	−0.0531937	+	0.198521i
$337$	−16.8591	−	16.8591i	−0.918371	−	0.918371i	0.0785395	−	0.996911i	$-0.474974\pi$
$337$	−16.8591	−	16.8591i	−0.918371	−	0.918371i	−0.996911	+	0.0785395i	$0.974974\pi$
$338$	12.8923	−	1.66987i	0.701249	−	0.0908291i
$339$		−	16.8102i		−	0.913003i
$340$	0.864068	+	14.3956i	0.0468607	+	0.780710i
$341$	−2.18639	−	3.78694i	−0.118400	−	0.205074i
$342$	5.43916	−	1.45742i	0.294116	−	0.0788081i
$343$	0.726162			0.0392091
$344$	0.579940	−	0.155395i	0.0312683	−	0.00837831i
$345$	3.68689	−	18.0169i	0.198495	−	0.969998i
$346$	−2.48601	−	2.48601i	−0.133649	−	0.133649i
$347$	−6.63859	−	24.7756i	−0.356378	−	1.33002i	−0.878741	−	0.477299i	$-0.841616\pi$
$347$	−6.63859	−	24.7756i	−0.356378	−	1.33002i	0.522363	−	0.852723i	$-0.325051\pi$
$348$	−5.14394	−	1.37832i	−0.275744	−	0.0738854i
$349$	15.7613	+	4.22322i	0.843682	+	0.226064i	0.654674	−	0.755912i	$-0.272806\pi$
$349$	15.7613	+	4.22322i	0.843682	+	0.226064i	0.189008	+	0.981976i	$0.439473\pi$
$350$	11.3020	+	15.0693i	0.604116	+	0.805488i
$351$	−3.00000	+	2.00000i	−0.160128	+	0.106752i
$352$	3.37101	−	3.37101i	0.179675	−	0.179675i
$353$	6.25725	+	10.8379i	0.333040	+	0.576842i	0.983106	−	0.183035i	$-0.0585923\pi$
$353$	6.25725	+	10.8379i	0.333040	+	0.576842i	−0.650066	+	0.759877i	$0.725259\pi$
$354$	9.60048	−	5.54284i	0.510260	−	0.294599i
$355$	−13.6656	−	20.6975i	−0.725294	−	1.09851i
$356$	−1.88901	+	1.88901i	−0.100117	+	0.100117i
$357$	−21.0421	−	12.1487i	−1.11367	−	0.642976i
$358$	10.3506	+	5.97589i	0.547044	+	0.315836i
$359$	10.4293	−	10.4293i	0.550440	−	0.550440i	−0.376128	−	0.926568i	$-0.622745\pi$
$359$	10.4293	−	10.4293i	0.550440	−	0.550440i	0.926568	+	0.376128i	$0.122745\pi$
$360$	0.448288	−	2.19067i	0.0236268	−	0.115458i
$361$	11.0059	−	6.35425i	0.579257	−	0.334434i
$362$	6.97469	+	12.0805i	0.366582	+	0.634938i
$363$	8.29253	−	8.29253i	0.435245	−	0.435245i
$364$	−4.35275	−	12.8670i	−0.228146	−	0.674413i
$365$	6.09878	+	18.2963i	0.319225	+	0.957674i
$366$	−2.52591	−	0.676814i	−0.132031	−	0.0353777i
$367$	0.658579	+	0.176466i	0.0343775	+	0.00921143i	0.275967	−	0.961167i	$-0.411002\pi$
$367$	0.658579	+	0.176466i	0.0343775	+	0.00921143i	−0.241589	+	0.970379i	$0.577669\pi$
$368$	−2.12863	−	7.94414i	−0.110962	−	0.414117i
$369$	−1.63567	−	1.63567i	−0.0851498	−	0.0851498i
$370$	−1.85481	−	0.379560i	−0.0964272	−	0.0197324i
$371$	−25.3618	+	6.79568i	−1.31672	+	0.352814i
$372$	−0.917240			−0.0475567
$373$	26.8845	−	7.20367i	1.39203	−	0.372992i	0.516551	−	0.856256i	$-0.327216\pi$
$373$	26.8845	−	7.20367i	1.39203	−	0.372992i	0.875474	+	0.483264i	$0.160549\pi$
$374$	15.3734	+	26.6275i	0.794940	+	1.37688i
$375$	−7.23205	−	8.52628i	−0.373461	−	0.440295i
$376$			1.59575i			0.0822947i
$377$	18.1885	−	6.15294i	0.936753	−	0.316892i
$378$	2.66390	+	2.66390i	0.137016	+	0.137016i
$379$	4.78711	−	17.8657i	0.245897	−	0.917702i	−0.727033	−	0.686603i	$-0.759101\pi$
$379$	4.78711	−	17.8657i	0.245897	−	0.917702i	0.972930	−	0.231099i	$-0.0742321\pi$
$380$	−0.754415	−	12.5687i	−0.0387007	−	0.644763i
$381$	1.49598	+	0.863703i	0.0766413	+	0.0442489i
$382$			5.13646i			0.262804i
$383$	2.08871	−	3.61774i	0.106728	−	0.184858i	−0.807715	−	0.589573i	$-0.799296\pi$
$383$	2.08871	−	3.61774i	0.106728	−	0.184858i	0.914443	+	0.404715i	$0.132629\pi$
$384$	−0.258819	−	0.965926i	−0.0132078	−	0.0492922i
$385$	35.9202	+	17.9601i	1.83066	+	0.915330i
$386$	13.1599	−	22.7936i	0.669820	−	1.16016i
$387$	0.155395	−	0.579940i	0.00789915	−	0.0294800i
$388$	6.60867	−	3.81552i	0.335504	−	0.193703i
$389$	22.9853			1.16540			0.582701	−	0.812687i	$-0.301996\pi$
$389$	22.9853			1.16540			0.582701	+	0.812687i	$0.301996\pi$
$390$	3.03648	+	7.46859i	0.153758	+	0.378187i
$391$	53.0431			2.68250
$392$	−6.22911	+	3.59638i	−0.314617	+	0.181644i
$393$	−2.50410	+	9.34544i	−0.126315	+	0.471415i
$394$	3.95680	−	6.85337i	0.199340	−	0.345268i
$395$	−8.28825	−	24.8647i	−0.417027	−	1.25108i
$396$	−1.23388	−	4.60488i	−0.0620046	−	0.231404i
$397$	4.59795	−	7.96389i	0.230765	−	0.399696i	−0.727269	−	0.686353i	$-0.759211\pi$
$397$	4.59795	−	7.96389i	0.230765	−	0.399696i	0.958033	+	0.286657i	$0.0925439\pi$
$398$			26.8484i			1.34579i
$399$	18.3718	+	10.6070i	0.919741	+	0.531012i
$400$	−4.59808	−	1.96410i	−0.229904	−	0.0982051i
$401$	8.89506	−	33.1968i	0.444198	−	1.65777i	−0.273846	−	0.961773i	$-0.588296\pi$
$401$	8.89506	−	33.1968i	0.444198	−	1.65777i	0.718045	−	0.695997i	$-0.245037\pi$
$402$	0.171573	+	0.171573i	0.00855728	+	0.00855728i
$403$	2.75172	−	1.83448i	0.137073	−	0.0913819i
$404$		−	7.01461i		−	0.348990i
$405$	−1.67303	−	1.48356i	−0.0831337	−	0.0737189i
$406$	−10.0313	−	17.3747i	−0.497843	−	0.862290i
$407$	−3.89890	+	1.04471i	−0.193261	+	0.0517842i
$408$	6.44949			0.319297
$409$	−28.9225	+	7.74977i	−1.43013	+	0.383202i	−0.889065	−	0.457781i	$-0.848644\pi$
$409$	−28.9225	+	7.74977i	−1.43013	+	0.383202i	−0.541062	+	0.840982i	$0.681978\pi$
$410$	−4.31648	+	2.84997i	−0.213176	+	0.140750i
$411$	−13.8804	−	13.8804i	−0.684667	−	0.684667i
$412$	0.665147	+	2.48236i	0.0327694	+	0.122297i
$413$	40.3403	+	10.8092i	1.98502	+	0.531884i
$414$	−7.94414	−	2.12863i	−0.390433	−	0.104616i
$415$	−31.6040	+	10.5347i	−1.55138	+	0.517126i
$416$	2.70831	+	2.38014i	0.132786	+	0.116696i
$417$	9.12701	−	9.12701i	0.446952	−	0.446952i
$418$	−13.4225	−	23.2484i	−0.656515	−	1.13712i
$419$	8.15884	−	4.71051i	0.398585	−	0.230123i	−0.287288	−	0.957844i	$-0.592754\pi$
$419$	8.15884	−	4.71051i	0.398585	−	0.230123i	0.685873	+	0.727721i	$0.259420\pi$
$420$	7.02993	−	4.64154i	0.343025	−	0.226484i
$421$	5.85201	−	5.85201i	0.285210	−	0.285210i	−0.549973	−	0.835182i	$-0.685362\pi$
$421$	5.85201	−	5.85201i	0.285210	−	0.285210i	0.835182	+	0.549973i	$0.185362\pi$
$422$	8.60901	+	4.97041i	0.419080	+	0.241956i
$423$	1.38196	+	0.797877i	0.0671934	+	0.0387941i
$424$	4.92820	−	4.92820i	0.239335	−	0.239335i
$425$	19.9112	−	25.3662i	0.965833	−	1.23044i
$426$	−9.60572	+	5.54587i	−0.465399	+	0.268698i
$427$	−4.92580	−	8.53173i	−0.238376	−	0.412880i
$428$	6.50694	−	6.50694i	0.314525	−	0.314525i
$429$	12.9114	+	11.3469i	0.623368	+	0.547834i
$430$	−1.20080	−	0.600398i	−0.0579076	−	0.0289538i
$431$	−11.6094	−	3.11072i	−0.559204	−	0.149838i	−0.0318632	−	0.999492i	$-0.510144\pi$
$431$	−11.6094	−	3.11072i	−0.559204	−	0.149838i	−0.527340	+	0.849654i	$0.676811\pi$
$432$	−0.965926	−	0.258819i	−0.0464731	−	0.0124524i
$433$	−6.88020	−	25.6773i	−0.330641	−	1.23397i	−0.908518	−	0.417846i	$-0.862785\pi$
$433$	−6.88020	−	25.6773i	−0.330641	−	1.23397i	0.577876	−	0.816124i	$-0.303882\pi$
$434$	−2.44344	−	2.44344i	−0.117289	−	0.117289i
$435$	6.56116	+	9.93733i	0.314584	+	0.476459i
$436$	−11.7387	+	3.14538i	−0.562183	+	0.150637i
$437$	−46.3117			−2.21539
$438$	8.33109	−	2.23231i	0.398075	−	0.106664i
$439$	−3.87367	−	6.70939i	−0.184880	−	0.320222i	0.758656	−	0.651492i	$-0.225856\pi$
$439$	−3.87367	−	6.70939i	−0.184880	−	0.320222i	−0.943536	+	0.331270i	$0.892523\pi$
$440$	−10.6409	+	0.638701i	−0.507286	+	0.0304489i
$441$			7.19275i			0.342512i
$442$	−19.3485	+	12.8990i	−0.920313	+	0.613542i
$443$	−0.124604	−	0.124604i	−0.00592013	−	0.00592013i	0.704141	−	0.710061i	$-0.251333\pi$
$443$	−0.124604	−	0.124604i	−0.00592013	−	0.00592013i	−0.710061	+	0.704141i	$0.751333\pi$
$444$	−0.219139	+	0.817837i	−0.0103999	+	0.0388128i
$445$	5.96285	−	0.357909i	0.282666	−	0.0169665i
$446$	5.77829	+	3.33610i	0.273610	+	0.157969i
$447$			6.49333i			0.307124i
$448$	1.88366	−	3.26260i	0.0889947	−	0.154143i
$449$	1.67611	+	6.25533i	0.0791005	+	0.295207i	0.994132	−	0.108176i	$-0.0345009\pi$
$449$	1.67611	+	6.25533i	0.0791005	+	0.295207i	−0.915031	+	0.403383i	$0.867834\pi$
$450$	−4.00000	+	3.00000i	−0.188562	+	0.141421i
$451$	−5.51387	+	9.55031i	−0.259638	+	0.449707i
$452$	−4.35079	+	16.2374i	−0.204644	+	0.763742i
$453$	1.09361	−	0.631395i	0.0513822	−	0.0296655i
$454$	14.1356			0.663415
$455$	−11.8067	+	27.9845i	−0.553507	+	1.31193i
$456$	−5.63103			−0.263697
$457$	29.6505	−	17.1187i	1.38699	−	0.800780i	0.394016	−	0.919104i	$-0.371085\pi$
$457$	29.6505	−	17.1187i	1.38699	−	0.800780i	0.992975	+	0.118324i	$0.0377521\pi$
$458$	0.454649	−	1.69677i	0.0212444	−	0.0792851i
$459$	3.22474	−	5.58542i	0.150518	−	0.260705i
$460$	−8.22438	+	16.4488i	−0.383464	+	0.766927i
$461$	0.718392	+	2.68108i	0.0334589	+	0.124870i	0.980635	−	0.195843i	$-0.0627442\pi$
$461$	0.718392	+	2.68108i	0.0334589	+	0.124870i	−0.947176	+	0.320713i	$0.896078\pi$
$462$	8.98004	−	15.5539i	0.417789	−	0.723632i
$463$			6.58403i			0.305986i	0.988227	+	0.152993i	$0.0488911\pi$
$463$			6.58403i			0.305986i	−0.988227	+	0.152993i	$0.951109\pi$
$464$	4.61193	+	2.66270i	0.214104	+	0.123613i
$465$	1.53457	+	1.36078i	0.0711641	+	0.0631048i
$466$	−2.01953	+	7.53698i	−0.0935528	+	0.349144i
$467$	7.69161	+	7.69161i	0.355925	+	0.355925i	0.862309	−	0.506383i	$-0.169018\pi$
$467$	7.69161	+	7.69161i	0.355925	+	0.355925i	−0.506383	+	0.862309i	$0.669018\pi$
$468$	3.41542	−	1.15539i	0.157878	−	0.0534081i
$469$			0.914107i			0.0422095i
$470$	2.36740	−	2.66975i	0.109200	−	0.123146i
$471$	−6.51461	−	11.2836i	−0.300177	−	0.519923i
$472$	−10.7079	+	2.86919i	−0.492873	+	0.132065i
$473$	−2.86230			−0.131608
$474$	−11.3220	+	3.03371i	−0.520035	+	0.139343i
$475$	−17.3844	+	22.1471i	−0.797650	+	1.01618i
$476$	17.1808	+	17.1808i	0.787481	+	0.787481i
$477$	−1.80385	−	6.73205i	−0.0825925	−	0.308239i
$478$	−2.25433	−	0.604047i	−0.103111	−	0.0276285i
$479$	−3.50425	−	0.938960i	−0.160113	−	0.0429022i	0.177872	−	0.984054i	$-0.443079\pi$
$479$	−3.50425	−	0.938960i	−0.160113	−	0.0429022i	−0.337985	+	0.941151i	$0.609745\pi$
$480$	−1.00000	+	2.00000i	−0.0456435	+	0.0912871i
$481$	−0.978258	−	2.89179i	−0.0446047	−	0.131854i
$482$	5.05816	−	5.05816i	0.230393	−	0.230393i
$483$	−15.4920	−	26.8329i	−0.704909	−	1.22094i
$484$	−10.1562	+	5.86370i	−0.461647	+	0.266532i
$485$	−16.7171	−	3.42090i	−0.759083	−	0.155335i
$486$	−0.707107	+	0.707107i	−0.0320750	+	0.0320750i
$487$	12.6787	+	7.32005i	0.574527	+	0.331703i	0.758955	−	0.651143i	$-0.225710\pi$
$487$	12.6787	+	7.32005i	0.574527	+	0.331703i	−0.184428	+	0.982846i	$0.559043\pi$
$488$	2.26467	+	1.30751i	0.102517	+	0.0591880i
$489$	−8.58284	+	8.58284i	−0.388130	+	0.388130i
$490$	15.7570	+	3.22442i	0.711827	+	0.145665i
$491$	10.7938	−	6.23179i	0.487117	−	0.281237i	−0.236261	−	0.971690i	$-0.575922\pi$
$491$	10.7938	−	6.23179i	0.487117	−	0.281237i	0.723377	+	0.690453i	$0.242589\pi$
$492$	1.15660	+	2.00328i	0.0521434	+	0.0903150i
$493$	−24.2864	+	24.2864i	−1.09380	+	1.09380i
$494$	16.8931	−	11.2621i	0.760056	−	0.506704i
$495$	−4.76733	+	9.53465i	−0.214275	+	0.428551i
$496$	0.885986	+	0.237399i	0.0397819	+	0.0106595i
$497$	−40.3624	−	10.8151i	−1.81050	−	0.485122i
$498$	3.85595	+	14.3906i	0.172789	+	0.644858i
$499$	5.87367	+	5.87367i	0.262942	+	0.262942i	0.826248	−	0.563306i	$-0.190471\pi$
$499$	5.87367	+	5.87367i	0.262942	+	0.262942i	−0.563306	+	0.826248i	$0.690471\pi$
$500$	4.77886	+	10.1075i	0.213717	+	0.452023i
$501$	3.31199	−	0.887445i	0.147969	−	0.0396481i
$502$	−24.0881			−1.07510
$503$	−34.4830	+	9.23970i	−1.53752	+	0.411978i	−0.925464	−	0.378835i	$-0.876325\pi$
$503$	−34.4830	+	9.23970i	−1.53752	+	0.411978i	−0.612058	+	0.790813i	$0.709658\pi$
$504$	−1.88366	−	3.26260i	−0.0839050	−	0.145328i
$505$	−10.4066	+	11.7357i	−0.463089	+	0.522231i
$506$			39.2083i			1.74302i
$507$	−7.93546	+	10.2970i	−0.352426	+	0.457306i
$508$	−1.22146	−	1.22146i	−0.0541936	−	0.0541936i
$509$	−3.53272	+	13.1843i	−0.156585	+	0.584384i	0.842379	+	0.538885i	$0.181154\pi$
$509$	−3.53272	+	13.1843i	−0.156585	+	0.584384i	−0.998964	+	0.0454987i	$0.985512\pi$
$510$	−10.7902	−	9.56823i	−0.477798	−	0.423688i
$511$	28.1399	+	16.2466i	1.24483	+	0.718705i
$512$			1.00000i			0.0441942i
$513$	−2.81552	+	4.87662i	−0.124308	+	0.215308i
$514$	−4.47418	−	16.6979i	−0.197347	−	0.736511i
$515$	2.56993	−	5.13986i	0.113245	−	0.226489i
$516$	−0.300199	+	0.519960i	−0.0132155	+	0.0228900i
$517$	1.96896	−	7.34826i	0.0865948	−	0.323176i
$518$	−2.76240	+	1.59487i	−0.121373	+	0.0700747i
$519$	3.51575			0.154324
$520$	−1.00000	−	8.00000i	−0.0438529	−	0.350823i
$521$	1.33953			0.0586860			0.0293430	−	0.999569i	$-0.490658\pi$
$521$	1.33953			0.0586860			0.0293430	+	0.999569i	$0.490658\pi$
$522$	4.61193	−	2.66270i	0.201859	−	0.116543i
$523$	−4.55775	+	17.0098i	−0.199297	+	0.743785i	0.791816	+	0.610760i	$0.209136\pi$
$523$	−4.55775	+	17.0098i	−0.199297	+	0.743785i	−0.991113	+	0.133025i	$0.957531\pi$
$524$	4.83756	−	8.37889i	0.211330	−	0.366034i
$525$	−18.6473	−	2.66390i	−0.813836	−	0.116262i
$526$	−5.27659	−	19.6925i	−0.230070	−	0.858634i
$527$	−2.95786	+	5.12317i	−0.128847	+	0.223169i
$528$			4.76733i			0.207471i
$529$	38.6597	+	22.3202i	1.68086	+	0.970444i
$530$	−15.5563	+	0.933740i	−0.675725	+	0.0405591i
$531$	−2.86919	+	10.7079i	−0.124512	+	0.464685i
$532$	−15.0005	−	15.0005i	−0.650355	−	0.650355i
$533$	−7.47636	−	3.69666i	−0.323837	−	0.160120i
$534$		−	2.67147i		−	0.115606i
$535$	−20.5398	+	1.23286i	−0.888013	+	0.0533013i
$536$	−0.121320	−	0.210133i	−0.00524024	−	0.00907636i
$537$	−11.5445	+	3.09335i	−0.498184	+	0.133488i
$538$	−5.04184			−0.217369
$539$	33.1218	−	8.87496i	1.42666	−	0.382271i
$540$	1.23205	+	1.86603i	0.0530190	+	0.0803009i
$541$	−5.55631	−	5.55631i	−0.238885	−	0.238885i	0.577504	−	0.816388i	$-0.304027\pi$
$541$	−5.55631	−	5.55631i	−0.238885	−	0.238885i	−0.816388	+	0.577504i	$0.804027\pi$
$542$	−7.30501	−	27.2627i	−0.313777	−	1.17103i
$543$	−13.4741	−	3.61037i	−0.578228	−	0.154936i
$544$	−6.22973	−	1.66925i	−0.267097	−	0.0715685i
$545$	24.3057	+	12.1528i	1.04114	+	0.520570i
$546$	12.1762	+	6.02048i	0.521093	+	0.257653i
$547$	−9.03455	+	9.03455i	−0.386289	+	0.386289i	−0.873362	−	0.487072i	$-0.838065\pi$
$547$	−9.03455	+	9.03455i	−0.386289	+	0.386289i	0.487072	+	0.873362i	$0.338065\pi$
$548$	9.81489	+	16.9999i	0.419271	+	0.726199i
$549$	2.26467	−	1.30751i	0.0966536	−	0.0558030i
$550$	18.7502	+	14.7179i	0.799509	+	0.627574i
$551$	21.2044	−	21.2044i	0.903336	−	0.903336i
$552$	7.12252	+	4.11219i	0.303155	+	0.175026i
$553$	−38.2421	−	22.0791i	−1.62622	−	0.938898i
$554$	−9.73925	+	9.73925i	−0.413781	+	0.413781i
$555$	1.57994	−	1.04316i	0.0670647	−	0.0442798i
$556$	−11.1783	+	6.45377i	−0.474064	+	0.273701i
$557$	7.98126	+	13.8239i	0.338177	+	0.585739i	0.984090	−	0.177672i	$-0.0568565\pi$
$557$	7.98126	+	13.8239i	0.338177	+	0.585739i	−0.645913	+	0.763411i	$0.723523\pi$
$558$	0.648586	−	0.648586i	0.0274569	−	0.0274569i
$559$	−0.139323	−	2.16028i	−0.00589273	−	0.0913701i
$560$	−7.99171	+	2.66390i	−0.337711	+	0.112570i
$561$	−29.6992	−	7.95786i	−1.25390	−	0.335981i
$562$	17.4977	+	4.68848i	0.738094	+	0.197772i
$563$	9.00277	+	33.5988i	0.379421	+	1.41602i	0.846776	+	0.531950i	$0.178541\pi$
$563$	9.00277	+	33.5988i	0.379421	+	1.41602i	−0.467354	+	0.884070i	$0.654793\pi$
$564$	−1.12837	−	1.12837i	−0.0475129	−	0.0475129i
$565$	31.3682	−	20.7110i	1.31967	−	0.871317i
$566$	25.7974	−	6.91239i	1.08435	−	0.290549i
$567$	−3.76733			−0.158213
$568$	10.7138	−	2.87075i	0.449541	−	0.120454i
$569$	−2.52761	−	4.37794i	−0.105963	−	0.183533i	0.808168	−	0.588951i	$-0.200459\pi$
$569$	−2.52761	−	4.37794i	−0.105963	−	0.183533i	−0.914131	+	0.405419i	$0.867126\pi$
$570$	9.42090	+	8.35399i	0.394598	+	0.349910i
$571$			5.67855i			0.237640i	0.992916	+	0.118820i	$0.0379111\pi$
$571$			5.67855i			0.237640i	−0.992916	+	0.118820i	$0.962089\pi$
$572$	−9.53465	−	14.3020i	−0.398664	−	0.597996i
$573$	−3.63203	−	3.63203i	−0.151730	−	0.151730i
$574$	−2.25549	+	8.41761i	−0.0941424	+	0.351344i
$575$	38.1624	−	15.3179i	1.59148	−	0.638801i
$576$	0.866025	+	0.500000i	0.0360844	+	0.0208333i
$577$		−	27.7859i		−	1.15674i	−0.815774	−	0.578370i	$-0.803689\pi$
$577$		−	27.7859i		−	1.15674i	0.815774	−	0.578370i	$-0.196311\pi$
$578$	12.2980	−	21.3007i	0.511528	−	0.885992i
$579$	6.81206	+	25.4229i	0.283099	+	1.05654i
$580$	−3.76563	−	11.2969i	−0.156359	−	0.469077i
$581$	−28.0633	+	48.6070i	−1.16426	+	2.01656i
$582$	−1.97506	+	7.37101i	−0.0818687	+	0.305538i
$583$	−28.7746	+	16.6130i	−1.19172	+	0.688041i
$584$	−8.62498			−0.356904
$585$	−7.42820	−	3.13397i	−0.307118	−	0.129574i
$586$	−15.8723			−0.655677
$587$	−10.1521	+	5.86130i	−0.419021	+	0.241922i	−0.694658	−	0.719340i	$-0.744444\pi$
$587$	−10.1521	+	5.86130i	−0.419021	+	0.241922i	0.275638	+	0.961262i	$0.411111\pi$
$588$	1.86162	−	6.94767i	0.0767720	−	0.286517i
$589$	2.58250	−	4.47303i	0.106410	−	0.184308i
$590$	22.1714	+	11.0857i	0.912780	+	0.456390i
$591$	2.04819	+	7.64394i	0.0842512	+	0.314430i
$592$	0.423344	−	0.733253i	0.0173993	−	0.0301365i
$593$			42.8515i			1.75970i	0.475249	+	0.879851i	$0.342358\pi$
$593$			42.8515i			1.75970i	−0.475249	+	0.879851i	$0.657642\pi$
$594$	4.12863	+	2.38366i	0.169400	+	0.0978029i
$595$	−3.25523	−	54.2329i	−0.133451	−	2.22333i
$596$	1.68060	−	6.27207i	0.0688399	−	0.256914i
$597$	−18.9847	−	18.9847i	−0.776990	−	0.776990i
$598$	−29.5919	+	1.90847i	−1.21010	+	0.0780433i
$599$			3.31997i			0.135650i	0.997697	+	0.0678252i	$0.0216060\pi$
$599$			3.31997i			0.135650i	−0.997697	+	0.0678252i	$0.978394\pi$
$600$	4.64016	−	1.86250i	0.189434	−	0.0760363i
$601$	4.74604	+	8.22038i	0.193595	+	0.335316i	0.946439	−	0.322883i	$-0.104652\pi$
$601$	4.74604	+	8.22038i	0.193595	+	0.335316i	−0.752844	+	0.658199i	$0.771319\pi$
$602$	−2.18482	+	0.585422i	−0.0890468	+	0.0238600i
$603$	−0.242641			−0.00988109
$604$	−1.21976	+	0.326834i	−0.0496314	+	0.0132987i
$605$	25.6909	+	5.25725i	1.04448	+	0.213738i
$606$	4.96008	+	4.96008i	0.201489	+	0.201489i
$607$	9.01513	+	33.6449i	0.365913	+	1.36560i	0.866179	+	0.499733i	$0.166569\pi$
$607$	9.01513	+	33.6449i	0.365913	+	1.36560i	−0.500267	+	0.865871i	$0.666765\pi$
$608$	5.43916	+	1.45742i	0.220587	+	0.0591061i
$609$	19.3789	+	5.19256i	0.785273	+	0.210413i
$610$	−1.84909	−	5.54727i	−0.0748675	−	0.224603i
$611$	5.64184	+	1.12837i	0.228245	+	0.0456489i
$612$	−4.56048	+	4.56048i	−0.184346	+	0.184346i
$613$	2.68008	+	4.64204i	0.108247	+	0.187490i	0.915060	−	0.403317i	$-0.132143\pi$
$613$	2.68008	+	4.64204i	0.108247	+	0.187490i	−0.806813	+	0.590807i	$0.798809\pi$
$614$	−20.0218	+	11.5596i	−0.808015	+	0.466507i
$615$	1.03698	−	5.06744i	0.0418149	−	0.204339i
$616$	−12.6997	+	12.6997i	−0.511685	+	0.511685i
$617$	11.4000	+	6.58176i	0.458945	+	0.264972i	0.711600	−	0.702584i	$-0.247971\pi$
$617$	11.4000	+	6.58176i	0.458945	+	0.264972i	−0.252656	+	0.967556i	$0.581304\pi$
$618$	−2.22562	−	1.28497i	−0.0895278	−	0.0516889i
$619$	16.7286	−	16.7286i	0.672378	−	0.672378i	−0.285886	−	0.958264i	$-0.592288\pi$
$619$	16.7286	−	16.7286i	0.672378	−	0.672378i	0.958264	+	0.285886i	$0.0922878\pi$
$620$	−1.13009	−	1.71159i	−0.0453853	−	0.0687392i
$621$	7.12252	−	4.11219i	0.285817	−	0.165017i
$622$	−0.370670	−	0.642019i	−0.0148625	−	0.0257426i
$623$	7.11653	−	7.11653i	0.285118	−	0.285118i
$624$	−3.59808	+	0.232051i	−0.144038	+	0.00928947i
$625$	7.00000	−	24.0000i	0.280000	−	0.960000i
$626$	−5.98004	−	1.60235i	−0.239010	−	0.0640427i
$627$	25.9302	+	6.94799i	1.03555	+	0.277476i
$628$	3.37221	+	12.5853i	0.134566	+	0.502207i
$629$	3.86130	+	3.86130i	0.153960	+	0.153960i
$630$	−1.68885	+	8.25297i	−0.0672853	+	0.328806i
$631$	−28.3414	+	7.59405i	−1.12825	+	0.302315i	−0.774219	−	0.632918i	$-0.781857\pi$
$631$	−28.3414	+	7.59405i	−1.12825	+	0.302315i	−0.354034	+	0.935232i	$0.615190\pi$
$632$	11.7214			0.466250
$633$	−9.60210	+	2.57287i	−0.381649	+	0.102263i
$634$	−1.42883	−	2.47480i	−0.0567459	−	0.0982868i
$635$	0.231429	+	3.85566i	0.00918396	+	0.153007i
$636$			6.96953i			0.276360i
$637$	8.31047	+	24.5662i	0.329273	+	0.973350i
$638$	−17.9520	−	17.9520i	−0.710726	−	0.710726i
$639$	2.87075	−	10.7138i	0.113565	−	0.423831i
$640$	1.48356	−	1.67303i	0.0586430	−	0.0661324i
$641$	23.1304	+	13.3543i	0.913595	+	0.527464i	0.881586	−	0.472023i	$-0.156476\pi$
$641$	23.1304	+	13.3543i	0.913595	+	0.527464i	0.0320091	+	0.999488i	$0.489809\pi$
$642$			9.20220i			0.363182i
$643$	3.07118	−	5.31945i	0.121116	−	0.209778i	−0.799092	−	0.601208i	$-0.794686\pi$
$643$	3.07118	−	5.31945i	0.121116	−	0.209778i	0.920208	+	0.391430i	$0.128019\pi$
$644$	8.01923	+	29.9282i	0.316002	+	1.17934i
$645$	1.27364	−	0.424546i	0.0501494	−	0.0167165i
$646$	−18.1586	+	31.4517i	−0.714442	+	1.23745i
$647$	−9.33732	+	34.8473i	−0.367088	+	1.36999i	0.497481	+	0.867475i	$0.334259\pi$
$647$	−9.33732	+	34.8473i	−0.367088	+	1.36999i	−0.864568	+	0.502515i	$0.832408\pi$
$648$	0.866025	−	0.500000i	0.0340207	−	0.0196419i
$649$	52.8491			2.07451
$650$	−10.1955	+	14.8678i	−0.399900	+	0.583164i
$651$	3.45554			0.135433
$652$	10.5118	−	6.06899i	0.411674	−	0.237680i
$653$	−1.47392	+	5.50074i	−0.0576789	+	0.215261i	−0.988750	−	0.149577i	$-0.952209\pi$
$653$	−1.47392	+	5.50074i	−0.0576789	+	0.215261i	0.931071	+	0.364838i	$0.118875\pi$
$654$	6.07642	−	10.5247i	0.237607	−	0.411547i
$655$	−20.5240	+	6.84134i	−0.801940	+	0.267313i
$656$	−0.598698	−	2.23437i	−0.0233752	−	0.0872376i
$657$	−4.31249	+	7.46945i	−0.168246	+	0.291411i
$658$		−	6.01173i		−	0.234362i
$659$	−18.8057	−	10.8575i	−0.732567	−	0.422948i	0.0867934	−	0.996226i	$-0.472338\pi$
$659$	−18.8057	−	10.8575i	−0.732567	−	0.422948i	−0.819361	+	0.573278i	$0.805671\pi$
$660$	7.07263	−	7.97589i	0.275302	−	0.310461i
$661$	0.0273480	−	0.102064i	0.00106372	−	0.00396984i	−0.965392	−	0.260803i	$-0.916013\pi$
$661$	0.0273480	−	0.102064i	0.00106372	−	0.00396984i	0.966456	+	0.256834i	$0.0826792\pi$
$662$	−13.4417	−	13.4417i	−0.522427	−	0.522427i
$663$	4.56048	−	22.8024i	0.177114	−	0.885571i
$664$		−	14.8983i		−	0.578164i
$665$	2.84213	+	47.3506i	0.110213	+	1.83618i
$666$	−0.423344	−	0.733253i	−0.0164042	−	0.0284130i
$667$	−42.3057	+	11.3358i	−1.63808	+	0.438923i
$668$	−3.42883			−0.132665
$669$	−6.44485	+	1.72689i	−0.249172	+	0.0667655i
$670$	−0.108773	+	0.531546i	−0.00420226	+	0.0205354i
$671$	−8.81522	−	8.81522i	−0.340308	−	0.340308i
$672$	0.975056	+	3.63896i	0.0376136	+	0.140376i
$673$	−3.87370	−	1.03795i	−0.149320	−	0.0400102i	0.183385	−	0.983041i	$-0.441295\pi$
$673$	−3.87370	−	1.03795i	−0.149320	−	0.0400102i	−0.332705	+	0.943031i	$0.607961\pi$
$674$	−23.0299	−	6.17084i	−0.887079	−	0.237692i
$675$	0.707107	−	4.94975i	0.0272166	−	0.190516i
$676$	10.3301	−	7.89230i	0.397313	−	0.303550i
$677$	28.6174	−	28.6174i	1.09986	−	1.09986i	0.105430	−	0.994427i	$-0.466378\pi$
$677$	28.6174	−	28.6174i	1.09986	−	1.09986i	0.994427	−	0.105430i	$-0.0336218\pi$
$678$	−8.40508	−	14.5580i	−0.322795	−	0.559098i
$679$	−24.8970	+	14.3743i	−0.955459	+	0.551635i
$680$	7.94610	+	12.0349i	0.304719	+	0.461518i
$681$	−9.99536	+	9.99536i	−0.383023	+	0.383023i
$682$	−3.78694	−	2.18639i	−0.145009	−	0.0837212i
$683$	7.42899	+	4.28913i	0.284262	+	0.164119i	0.635351	−	0.772223i	$-0.280855\pi$
$683$	7.42899	+	4.28913i	0.284262	+	0.164119i	−0.351089	+	0.936342i	$0.614189\pi$
$684$	3.98174	−	3.98174i	0.152246	−	0.152246i
$685$	8.79979	−	43.0024i	0.336223	−	1.64304i
$686$	0.628875	−	0.363081i	0.0240106	−	0.0138625i
$687$	0.878315	+	1.52129i	0.0335098	+	0.0580407i
$688$	0.424546	−	0.424546i	0.0161857	−	0.0161857i
$689$	−13.9391	−	20.9086i	−0.531036	−	0.796554i
$690$	−5.81552	−	17.4465i	−0.221393	−	0.664179i
$691$	−35.5575	−	9.52761i	−1.35267	−	0.362447i	−0.491551	−	0.870849i	$-0.663570\pi$
$691$	−35.5575	−	9.52761i	−1.35267	−	0.362447i	−0.861120	+	0.508401i	$0.830237\pi$
$692$	−3.39595	−	0.909943i	−0.129095	−	0.0345908i
$693$	4.64841	+	17.3481i	0.176579	+	0.659000i
$694$	−18.1370	−	18.1370i	−0.688470	−	0.688470i
$695$	28.2762	+	5.78629i	1.07258	+	0.219487i
$696$	−5.14394	+	1.37832i	−0.194981	+	0.0522449i
$697$	14.9189			0.565094
$698$	15.7613	−	4.22322i	0.596573	−	0.159851i
$699$	−3.90143	−	6.75747i	−0.147565	−	0.255591i
$700$	17.3225	+	7.39941i	0.654727	+	0.279672i
$701$		−	34.6799i		−	1.30984i	−0.755697	−	0.654922i	$-0.772702\pi$
$701$		−	34.6799i		−	1.30984i	0.755697	−	0.654922i	$-0.227298\pi$
$702$	−1.59808	+	3.23205i	−0.0603155	+	0.121986i
$703$	−3.37129	−	3.37129i	−0.127151	−	0.127151i
$704$	1.23388	−	4.60488i	0.0465034	−	0.173553i
$705$	0.213791	+	3.56180i	0.00805182	+	0.134145i
$706$	10.8379	+	6.25725i	0.407889	+	0.235495i
$707$			26.4263i			0.993865i
$708$	5.54284	−	9.60048i	0.208313	−	0.360808i
$709$	2.19073	+	8.17590i	0.0822744	+	0.307052i	0.994784	−	0.102003i	$-0.0325250\pi$
$709$	2.19073	+	8.17590i	0.0822744	+	0.307052i	−0.912510	+	0.409055i	$0.865858\pi$
$710$	−22.1835	−	11.0917i	−0.832531	−	0.416265i
$711$	5.86068	−	10.1510i	0.219793	−	0.380692i
$712$	−0.691426	+	2.58044i	−0.0259123	+	0.0967060i
$713$	−6.53306	+	3.77186i	−0.244665	+	0.141257i
$714$	−24.2973			−0.909305
$715$	−5.26612	+	38.0729i	−0.196942	+	1.42385i
$716$	11.9518			0.446659
$717$	2.02118	−	1.16693i	0.0754823	−	0.0435798i
$718$	3.81740	−	14.2467i	0.142464	−	0.531684i
$719$	−4.78248	+	8.28350i	−0.178356	+	0.308922i	−0.941318	−	0.337522i	$-0.890411\pi$
$719$	−4.78248	+	8.28350i	−0.178356	+	0.308922i	0.762961	+	0.646444i	$0.223745\pi$
$720$	−0.707107	−	2.12132i	−0.0263523	−	0.0790569i
$721$	−2.50583	−	9.35187i	−0.0933218	−	0.348282i
$722$	6.35425	−	11.0059i	0.236481	−	0.409597i
$723$			7.15331i			0.266035i
$724$	12.0805	+	6.97469i	0.448969	+	0.259212i
$725$	−10.4596	+	24.4866i	−0.388461	+	0.909409i
$726$	3.03528	−	11.3278i	0.112650	−	0.420414i
$727$	−7.48455	−	7.48455i	−0.277587	−	0.277587i	0.554558	−	0.832145i	$-0.312887\pi$
$727$	−7.48455	−	7.48455i	−0.277587	−	0.277587i	−0.832145	+	0.554558i	$0.812887\pi$
$728$	−10.2031	−	8.96676i	−0.378151	−	0.332330i
$729$		−	1.00000i		−	0.0370370i
$730$	14.4299	+	12.7957i	0.534073	+	0.473590i
$731$	1.93613	+	3.35348i	0.0716104	+	0.124033i
$732$	−2.52591	+	0.676814i	−0.0933602	+	0.0250158i
$733$	36.8257			1.36019			0.680094	−	0.733125i	$-0.261939\pi$
$733$	36.8257			1.36019			0.680094	+	0.733125i	$0.261939\pi$
$734$	0.658579	−	0.176466i	0.0243086	−	0.00651347i
$735$	−13.4219	+	8.86184i	−0.495073	+	0.326874i
$736$	−5.81552	−	5.81552i	−0.214363	−	0.214363i
$737$	0.299388	+	1.11733i	0.0110281	+	0.0411575i
$738$	−2.23437	−	0.598698i	−0.0822484	−	0.0220384i
$739$	−21.2470	−	5.69313i	−0.781585	−	0.209425i	−0.154102	−	0.988055i	$-0.549248\pi$
$739$	−21.2470	−	5.69313i	−0.781585	−	0.209425i	−0.627483	+	0.778630i	$0.715915\pi$
$740$	−1.79610	+	0.598698i	−0.0660258	+	0.0220086i
$741$	−3.98174	+	19.9087i	−0.146273	+	0.731364i
$742$	−18.5662	+	18.5662i	−0.681585	+	0.681585i
$743$	−6.59391	−	11.4210i	−0.241907	−	0.418996i	0.719350	−	0.694647i	$-0.244440\pi$
$743$	−6.59391	−	11.4210i	−0.241907	−	0.418996i	−0.961258	+	0.275652i	$0.911106\pi$
$744$	−0.794353	+	0.458620i	−0.0291224	+	0.0168138i
$745$	−12.1167	+	8.00011i	−0.443922	+	0.293101i
$746$	19.6808	−	19.6808i	0.720565	−	0.720565i
$747$	−12.9023	−	7.44913i	−0.472069	−	0.272549i
$748$	26.6275	+	15.3734i	0.973599	+	0.562108i
$749$	−24.5138	+	24.5138i	−0.895714	+	0.895714i
$750$	−10.5263	−	3.76795i	−0.384365	−	0.137586i
$751$	−28.7550	+	16.6017i	−1.04929	+	0.605806i	−0.922449	−	0.386118i	$-0.873816\pi$
$751$	−28.7550	+	16.6017i	−1.04929	+	0.605806i	−0.126837	+	0.991924i	$0.540482\pi$
$752$	0.797877	+	1.38196i	0.0290956	+	0.0503950i
$753$	17.0328	−	17.0328i	0.620711	−	0.620711i
$754$	12.6752	−	14.4228i	0.461603	−	0.525248i
$755$	2.52558	+	1.26279i	0.0919152	+	0.0459576i
$756$	3.63896	+	0.975056i	0.132348	+	0.0354624i
$757$	9.01801	+	2.41637i	0.327765	+	0.0878244i	0.418949	−	0.908010i	$-0.362399\pi$
$757$	9.01801	+	2.41637i	0.327765	+	0.0878244i	−0.0911841	+	0.995834i	$0.529065\pi$
$758$	−4.78711	−	17.8657i	−0.173876	−	0.648913i
$759$	−27.7245	−	27.7245i	−1.00633	−	1.00633i
$760$	−6.93772	−	10.5076i	−0.251657	−	0.381152i
$761$	45.4241	−	12.1714i	1.64662	−	0.441211i	0.687959	−	0.725750i	$-0.258507\pi$
$761$	45.4241	−	12.1714i	1.64662	−	0.441211i	0.958665	+	0.284538i	$0.0918403\pi$
$762$	1.72741			0.0625773
$763$	44.2237	−	11.8497i	1.60100	−	0.428988i
$764$	2.56823	+	4.44831i	0.0929153	+	0.160934i
$765$	14.3956	−	0.864068i	0.520474	−	0.0312404i
$766$		−	4.17741i		−	0.150936i
$767$	2.57244	+	39.8871i	0.0928855	+	1.44024i
$768$	−0.707107	−	0.707107i	−0.0255155	−	0.0255155i
$769$	−9.14127	+	34.1157i	−0.329643	+	1.23024i	0.579919	+	0.814674i	$0.303084\pi$
$769$	−9.14127	+	34.1157i	−0.329643	+	1.23024i	−0.909562	+	0.415569i	$0.863582\pi$
$770$	40.0878	−	2.40619i	1.44466	−	0.0867132i
$771$	14.9709	+	8.64344i	0.539163	+	0.311286i
$772$		−	26.3198i		−	0.947269i
$773$	−0.577494	+	1.00025i	−0.0207710	+	0.0359764i	−0.876224	−	0.481904i	$-0.839945\pi$
$773$	−0.577494	+	1.00025i	−0.0207710	+	0.0359764i	0.855453	+	0.517880i	$0.173279\pi$
$774$	−0.155395	−	0.579940i	−0.00558554	−	0.0208455i
$775$	−0.648586	+	4.54011i	−0.0232979	+	0.163085i
$776$	3.81552	−	6.60867i	0.136969	−	0.237237i
$777$	0.825568	−	3.08106i	0.0296171	−	0.110532i
$778$	19.9059	−	11.4927i	0.713660	−	0.412032i
$779$	−13.0257			−0.466693
$780$	6.36396	+	4.94975i	0.227866	+	0.177229i
$781$	−52.8779			−1.89212
$782$	45.9366	−	26.5215i	1.64269	−	0.948408i
$783$	−1.37832	+	5.14394i	−0.0492570	+	0.183829i
$784$	−3.59638	+	6.22911i	−0.128442	+	0.222468i
$785$	13.0292	−	26.0584i	0.465033	−	0.930066i
$786$	2.50410	+	9.34544i	0.0893184	+	0.333341i
$787$	10.5734	−	18.3137i	0.376901	−	0.652812i	−0.613708	−	0.789533i	$-0.710323\pi$
$787$	10.5734	−	18.3137i	0.376901	−	0.652812i	0.990610	+	0.136721i	$0.0436563\pi$
$788$		−	7.91359i		−	0.281910i
$789$	17.6558	+	10.1936i	0.628564	+	0.362901i
$790$	−19.6102	−	17.3894i	−0.697700	−	0.618686i
$791$	16.3909	−	61.1715i	0.582792	−	2.17501i
$792$	−3.37101	−	3.37101i	−0.119784	−	0.119784i
$793$	6.22409	−	7.08226i	0.221024	−	0.251498i
$794$		−	9.19590i		−	0.326350i
$795$	10.3397	−	11.6603i	0.366713	−	0.413547i
$796$	13.4242	+	23.2514i	0.475807	+	0.824123i
$797$	33.8743	−	9.07659i	1.19989	−	0.321509i	0.397102	−	0.917775i	$-0.370016\pi$
$797$	33.8743	−	9.07659i	1.19989	−	0.321509i	0.802788	+	0.596265i	$0.203349\pi$
$798$	21.2139			0.750965
$799$	−9.94112	+	2.66371i	−0.351691	+	0.0942354i
$800$	−4.96410	+	0.598076i	−0.175507	+	0.0211452i
$801$	1.88901	+	1.88901i	0.0667450	+	0.0667450i
$802$	−8.89506	−	33.1968i	−0.314096	−	1.17222i
$803$	39.7170	+	10.6421i	1.40158	+	0.375553i
$804$	0.234373	+	0.0628000i	0.00826570	+	0.00221479i
$805$	30.9839	−	61.9679i	1.09204	−	2.18408i
$806$	1.46582	−	2.96457i	0.0516313	−	0.104422i
$807$	3.56512	−	3.56512i	0.125498	−	0.125498i
$808$	−3.50731	−	6.07483i	−0.123387	−	0.213712i
$809$	8.78457	−	5.07177i	0.308849	−	0.178314i	−0.337562	−	0.941303i	$-0.609602\pi$
$809$	8.78457	−	5.07177i	0.308849	−	0.178314i	0.646411	+	0.762989i	$0.276269\pi$
$810$	−2.19067	−	0.448288i	−0.0769723	−	0.0157512i
$811$	24.4656	−	24.4656i	0.859104	−	0.859104i	−0.132129	−	0.991233i	$-0.542181\pi$
$811$	24.4656	−	24.4656i	0.859104	−	0.859104i	0.991233	+	0.132129i	$0.0421812\pi$
$812$	−17.3747	−	10.0313i	−0.609731	−	0.352028i
$813$	24.4430	+	14.1122i	0.857255	+	0.494936i
$814$	−2.85419	+	2.85419i	−0.100039	+	0.100039i
$815$	−26.5903	−	5.44130i	−0.931418	−	0.190601i
$816$	5.58542	−	3.22474i	0.195529	−	0.112889i
$817$	−1.69043	−	2.92791i	−0.0591407	−	0.102435i
$818$	−21.1728	+	21.1728i	−0.740288	+	0.740288i
$819$	−12.8670	+	4.35275i	−0.449609	+	0.152097i
$820$	−2.31319	+	4.62639i	−0.0807802	+	0.161560i
$821$	−27.5021	−	7.36916i	−0.959830	−	0.257186i	−0.255301	−	0.966862i	$-0.582175\pi$
$821$	−27.5021	−	7.36916i	−0.959830	−	0.257186i	−0.704528	+	0.709676i	$0.748841\pi$
$822$	−18.9609	−	5.08056i	−0.661338	−	0.177205i
$823$	−10.8844	−	40.6210i	−0.379405	−	1.41596i	−0.846800	−	0.531911i	$-0.821474\pi$
$823$	−10.8844	−	40.6210i	−0.379405	−	1.41596i	0.467395	−	0.884049i	$-0.345193\pi$
$824$	1.81722	+	1.81722i	0.0633057	+	0.0633057i
$825$	−23.6655	+	2.85122i	−0.823927	+	0.0992669i
$826$	40.3403	−	10.8092i	1.40362	−	0.376099i
$827$	17.7939			0.618754			0.309377	−	0.950939i	$-0.399880\pi$
$827$	17.7939			0.618754			0.309377	+	0.950939i	$0.399880\pi$
$828$	−7.94414	+	2.12863i	−0.276078	+	0.0739749i
$829$	−7.73081	−	13.3901i	−0.268502	−	0.465059i	0.699973	−	0.714169i	$-0.253195\pi$
$829$	−7.73081	−	13.3901i	−0.268502	−	0.465059i	−0.968475	+	0.249110i	$0.919862\pi$
$830$	−22.1025	+	24.9253i	−0.767189	+	0.865168i
$831$		−	13.7734i		−	0.477793i
$832$	3.53553	+	0.707107i	0.122573	+	0.0245145i
$833$	−32.8024	−	32.8024i	−1.13654	−	1.13654i
$834$	3.34072	−	12.4677i	0.115680	−	0.431722i
$835$	5.73654	+	5.08688i	0.198521	+	0.176039i
$836$	−23.2484	−	13.4225i	−0.804063	−	0.464226i
$837$			0.917240i			0.0317044i
$838$	4.71051	−	8.15884i	0.162722	−	0.281842i
$839$	3.25771	+	12.1579i	0.112469	+	0.419738i	0.999085	−	0.0427669i	$-0.0136173\pi$
$839$	3.25771	+	12.1579i	0.112469	+	0.419738i	−0.886617	+	0.462505i	$0.846951\pi$
$840$	3.76733	−	7.53465i	0.129985	−	0.259970i
$841$	−0.320053	+	0.554347i	−0.0110363	+	0.0191154i
$842$	2.14198	−	7.99400i	0.0738177	−	0.275491i
$843$	−15.6880	+	9.05745i	−0.540322	+	0.311955i
$844$	9.94082			0.342177
$845$	−28.9914	−	2.12132i	−0.997334	−	0.0729756i
$846$	1.59575			0.0548632
$847$	38.2618	−	22.0905i	1.31469	−	0.759038i
$848$	1.80385	−	6.73205i	0.0619444	−	0.231180i
$849$	−13.3537	+	23.1293i	−0.458298	+	0.793796i
$850$	4.56048	−	31.9233i	0.156423	−	1.09496i
$851$	1.80228	+	6.72620i	0.0617814	+	0.230571i
$852$	−5.54587	+	9.60572i	−0.189998	+	0.329087i
$853$			31.5185i			1.07917i	0.841930	+	0.539586i	$0.181419\pi$
$853$			31.5185i			1.07917i	−0.841930	+	0.539586i	$0.818581\pi$
$854$	−8.53173	−	4.92580i	−0.291950	−	0.168557i
$855$	−12.5687	+	0.754415i	−0.429842	+	0.0258004i
$856$	2.38171	−	8.88865i	0.0814050	−	0.303808i
$857$	8.12000	+	8.12000i	0.277374	+	0.277374i	0.832060	−	0.554686i	$-0.187162\pi$
$857$	8.12000	+	8.12000i	0.277374	+	0.277374i	−0.554686	+	0.832060i	$0.687162\pi$
$858$	16.8550	+	3.37101i	0.575422	+	0.115084i
$859$			42.4263i			1.44757i	0.690027	+	0.723784i	$0.257599\pi$
$859$			42.4263i			1.44757i	−0.690027	+	0.723784i	$0.742401\pi$
$860$	−1.34012	+	0.0804381i	−0.0456977	+	0.00274292i
$861$	−4.35728	−	7.54703i	−0.148496	−	0.257202i
$862$	−11.6094	+	3.11072i	−0.395417	+	0.105952i
$863$	16.8826			0.574691			0.287345	−	0.957827i	$-0.407227\pi$
$863$	16.8826			0.574691			0.287345	+	0.957827i	$0.407227\pi$
$864$	−0.965926	+	0.258819i	−0.0328615	+	0.00880520i
$865$	4.33158	+	6.56048i	0.147278	+	0.223063i
$866$	−18.7971	−	18.7971i	−0.638750	−	0.638750i
$867$	6.36589	+	23.7578i	0.216197	+	0.806858i
$868$	−3.33780	−	0.894360i	−0.113292	−	0.0303566i
$869$	−53.9755	−	14.4627i	−1.83099	−	0.490613i
$870$	10.6508	+	5.32540i	0.361096	+	0.180548i
$871$	−0.828719	+	0.280346i	−0.0280801	+	0.00949915i
$872$	−8.59335	+	8.59335i	−0.291008	+	0.291008i
$873$	−3.81552	−	6.60867i	−0.129136	−	0.223669i
$874$	−40.1071	+	23.1559i	−1.35664	+	0.783259i
$875$	−18.0035	−	38.0784i	−0.608630	−	1.28729i
$876$	6.09878	−	6.09878i	0.206059	−	0.206059i
$877$	45.2458	+	26.1227i	1.52784	+	0.882100i	0.999452	+	0.0330982i	$0.0105374\pi$
$877$	45.2458	+	26.1227i	1.52784	+	0.882100i	0.528390	+	0.849002i	$0.322796\pi$
$878$	−6.70939	−	3.87367i	−0.226431	−	0.130730i
$879$	11.2234	−	11.2234i	0.378555	−	0.378555i
$880$	−8.89595	+	5.87359i	−0.299883	+	0.197999i
$881$	13.1929	−	7.61693i	0.444481	−	0.256621i	−0.261016	−	0.965335i	$-0.584057\pi$
$881$	13.1929	−	7.61693i	0.444481	−	0.256621i	0.705496	+	0.708714i	$0.250724\pi$
$882$	3.59638	+	6.22911i	0.121096	+	0.209745i
$883$	−33.1772	+	33.1772i	−1.11650	+	1.11650i	−0.124251	+	0.992251i	$0.539653\pi$
$883$	−33.1772	+	33.1772i	−1.11650	+	1.11650i	−0.992251	+	0.124251i	$0.960347\pi$
$884$	−10.3068	+	20.8451i	−0.346654	+	0.701096i
$885$	−23.5163	+	7.83876i	−0.790491	+	0.263497i
$886$	−0.170213	−	0.0456083i	−0.00571840	−	0.00153224i
$887$	27.9495	+	7.48904i	0.938451	+	0.251457i	0.695455	−	0.718570i	$-0.255203\pi$
$887$	27.9495	+	7.48904i	0.938451	+	0.251457i	0.242996	+	0.970027i	$0.421870\pi$
$888$	0.219139	+	0.817837i	0.00735382	+	0.0274448i
$889$	4.60164	+	4.60164i	0.154334	+	0.154334i
$890$	4.98502	−	3.29138i	0.167098	−	0.110327i
$891$	−4.60488	+	1.23388i	−0.154269	+	0.0413364i
$892$	6.67220			0.223402
$893$	8.67956	−	2.32568i	0.290450	−	0.0778259i
$894$	3.24666	+	5.62338i	0.108585	+	0.188074i
$895$	−19.9957	−	17.7312i	−0.668384	−	0.592690i
$896$		−	3.76733i		−	0.125858i
$897$	19.5752	−	22.2742i	0.653596	−	0.743713i
$898$	4.57922	+	4.57922i	0.152811	+	0.152811i
$899$	1.26425	−	4.71823i	0.0421649	−	0.157362i
$900$	−1.96410	+	4.59808i	−0.0654701	+	0.153269i
$901$	38.9278	+	22.4750i	1.29687	+	0.748750i
$902$			11.0277i			0.367184i
$903$	1.13095	−	1.95886i	0.0376356	−	0.0651868i
$904$	4.35079	+	16.2374i	0.144705	+	0.540047i
$905$	−9.86370	−	29.5911i	−0.327881	−	0.983642i
$906$	0.631395	−	1.09361i	0.0209767	−	0.0363327i
$907$	−6.95307	+	25.9492i	−0.230873	+	0.861630i	0.749093	+	0.662465i	$0.230490\pi$
$907$	−6.95307	+	25.9492i	−0.230873	+	0.861630i	−0.979966	+	0.199165i	$0.936177\pi$
$908$	12.2418	−	7.06778i	0.406257	−	0.234553i
$909$	−7.01461			−0.232660
$910$	3.76733	+	30.1386i	0.124886	+	0.999085i
$911$	−38.0646			−1.26114			−0.630568	−	0.776134i	$-0.717178\pi$
$911$	−38.0646			−1.26114			−0.630568	+	0.776134i	$0.717178\pi$
$912$	−4.87662	+	2.81552i	−0.161481	+	0.0932310i
$913$	−18.3826	+	68.6047i	−0.608375	+	2.27048i
$914$	17.1187	−	29.6505i	0.566237	−	0.980751i
$915$	5.23002	+	2.61501i	0.172899	+	0.0864496i
$916$	−0.454649	−	1.69677i	−0.0150220	−	0.0560630i
$917$	−18.2247	+	31.5660i	−0.601831	+	1.04240i
$918$		−	6.44949i		−	0.212865i
$919$	23.8444	+	13.7666i	0.786556	+	0.454118i	0.838749	−	0.544519i	$-0.183288\pi$
$919$	23.8444	+	13.7666i	0.786556	+	0.454118i	−0.0521929	+	0.998637i	$0.516621\pi$
$920$	1.10186	+	18.3572i	0.0363272	+	0.605220i
$921$	5.98369	−	22.3314i	0.197169	−	0.735846i
$922$	1.96268	+	1.96268i	0.0646376	+	0.0646376i
$923$	−2.57385	−	39.9089i	−0.0847192	−	1.31362i
$924$		−	17.9601i		−	0.590843i
$925$	3.89313	+	1.66298i	0.128005	+	0.0546784i
$926$	3.29201	+	5.70193i	0.108182	+	0.187377i
$927$	2.48236	−	0.665147i	0.0815315	−	0.0218463i
$928$	5.32540			0.174815
$929$	37.6349	−	10.0842i	1.23476	−	0.330853i	0.418330	−	0.908295i	$-0.362616\pi$
$929$	37.6349	−	10.0842i	1.23476	−	0.330853i	0.816432	+	0.577442i	$0.195949\pi$
$930$	2.00937	+	0.411187i	0.0658898	+	0.0134834i
$931$	28.6397	+	28.6397i	0.938627	+	0.938627i
$932$	2.01953	+	7.53698i	0.0661518	+	0.246882i
$933$	0.716079	+	0.191873i	0.0234434	+	0.00628163i
$934$	10.5069	+	2.81533i	0.343798	+	0.0921203i
$935$	−21.7413	−	65.2239i	−0.711016	−	2.13305i
$936$	2.38014	−	2.70831i	0.0777973	−	0.0885238i
$937$	21.9091	−	21.9091i	0.715739	−	0.715739i	−0.251990	−	0.967730i	$-0.581085\pi$
$937$	21.9091	−	21.9091i	0.715739	−	0.715739i	0.967730	+	0.251990i	$0.0810851\pi$
$938$	0.457053	+	0.791640i	0.0149233	+	0.0258480i
$939$	5.36156	−	3.09550i	0.174968	−	0.101018i
$940$	0.715357	−	3.49577i	0.0233324	−	0.114020i
$941$	−8.31518	+	8.31518i	−0.271067	+	0.271067i	−0.829530	−	0.558462i	$-0.811391\pi$
$941$	−8.31518	+	8.31518i	−0.271067	+	0.271067i	0.558462	+	0.829530i	$0.311391\pi$
$942$	−11.2836	−	6.51461i	−0.367641	−	0.212258i
$943$	16.4758	+	9.51229i	0.536525	+	0.309763i
$944$	−7.83876	+	7.83876i	−0.255130	+	0.255130i
$945$	−4.64154	−	7.02993i	−0.150989	−	0.228684i
$946$	−2.47882	+	1.43115i	−0.0805934	+	0.0465306i
$947$	24.2758	+	42.0469i	0.788857	+	1.36634i	0.926668	+	0.375882i	$0.122660\pi$
$947$	24.2758	+	42.0469i	0.788857	+	1.36634i	−0.137811	+	0.990459i	$0.544007\pi$
$948$	−8.28825	+	8.28825i	−0.269190	+	0.269190i
$949$	−6.09878	+	30.4939i	−0.197975	+	0.989874i
$950$	−3.98174	+	27.8722i	−0.129185	+	0.904293i
$951$	2.76028	+	0.739614i	0.0895082	+	0.0239836i
$952$	23.4694	+	6.28861i	0.760648	+	0.203815i
$953$	−12.6389	−	47.1690i	−0.409414	−	1.52795i	−0.795767	−	0.605602i	$-0.792932\pi$
$953$	−12.6389	−	47.1690i	−0.409414	−	1.52795i	0.386354	−	0.922351i	$-0.373734\pi$
$954$	−4.92820	−	4.92820i	−0.159556	−	0.159556i
$955$	2.30261	−	11.2523i	0.0745108	−	0.364116i
$956$	−2.25433	+	0.604047i	−0.0729103	+	0.0195363i
$957$	25.3879			0.820675
$958$	−3.50425	+	0.938960i	−0.113217	+	0.0303364i
$959$	−36.9759	−	64.0442i	−1.19401	−	2.06809i
$960$	0.133975	+	2.23205i	0.00432401	+	0.0720391i
$961$			30.1587i			0.972860i
$962$	−2.29309	−	2.01523i	−0.0739322	−	0.0649738i
$963$	−6.50694	−	6.50694i	−0.209683	−	0.209683i
$964$	1.85141	−	6.90957i	0.0596300	−	0.222542i
$965$	−39.0470	+	44.0338i	−1.25697	+	1.41750i
$966$	−26.8329	−	15.4920i	−0.863333	−	0.498446i
$967$		−	22.1480i		−	0.712231i	−0.934442	−	0.356115i	$-0.884101\pi$
$967$		−	22.1480i		−	0.712231i	0.934442	−	0.356115i	$-0.115899\pi$
$968$	−5.86370	+	10.1562i	−0.188467	+	0.326434i
$969$	−9.39960	−	35.0798i	−0.301959	−	1.12693i
$970$	−16.1879	+	5.39595i	−0.519761	+	0.173254i
$971$	−11.8487	+	20.5226i	−0.380244	+	0.658601i	−0.991097	−	0.133142i	$-0.957493\pi$
$971$	−11.8487	+	20.5226i	−0.380244	+	0.658601i	0.610853	+	0.791744i	$0.290827\pi$
$972$	−0.258819	+	0.965926i	−0.00830162	+	0.0309821i
$973$	42.1121	−	24.3135i	1.35005	−	0.779454i
$974$	14.6401			0.469099
$975$	−3.30385	−	17.7224i	−0.105808	−	0.567572i
$976$	2.61501			0.0837044
$977$	2.30600	−	1.33137i	0.0737756	−	0.0425943i	−0.462658	−	0.886537i	$-0.653104\pi$
$977$	2.30600	−	1.33137i	0.0737756	−	0.0425943i	0.536434	+	0.843942i	$0.319771\pi$
$978$	−3.14154	+	11.7244i	−0.100455	+	0.374904i
$979$	6.36788	−	11.0295i	0.203518	−	0.352504i
$980$	15.2581	−	5.08604i	0.487403	−	0.162468i
$981$	3.14538	+	11.7387i	0.100424	+	0.374789i
$982$	6.23179	−	10.7938i	0.198865	−	0.344443i
$983$			43.2729i			1.38019i	0.723719	+	0.690095i	$0.242431\pi$
$983$			43.2729i			1.38019i	−0.723719	+	0.690095i	$0.757569\pi$
$984$	2.00328	+	1.15660i	0.0638624	+	0.0368710i
$985$	−11.7403	+	13.2397i	−0.374078	+	0.421852i
$986$	−8.88943	+	33.1758i	−0.283097	+	1.05653i
$987$	4.25093	+	4.25093i	0.135309	+	0.135309i
$988$	8.99882	−	18.1998i	0.286290	−	0.579012i
$989$			4.93790i			0.157016i
$990$	0.638701	+	10.6409i	0.0202992	+	0.338191i
$991$	−25.5956	−	44.3329i	−0.813072	−	1.40828i	−0.910704	−	0.413059i	$-0.864460\pi$
$991$	−25.5956	−	44.3329i	−0.813072	−	1.40828i	0.0976325	−	0.995223i	$-0.468873\pi$
$992$	0.885986	−	0.237399i	0.0281301	−	0.00753743i
$993$	19.0095			0.603247
$994$	−40.3624	+	10.8151i	−1.28022	+	0.343033i
$995$	12.0358	−	58.8159i	0.381560	−	1.86459i
$996$	10.5347	+	10.5347i	0.333803	+	0.333803i
$997$	−13.0996	−	48.8882i	−0.414867	−	1.54831i	−0.785101	−	0.619367i	$-0.787389\pi$
$997$	−13.0996	−	48.8882i	−0.414867	−	1.54831i	0.370234	−	0.928939i	$-0.379278\pi$
$998$	8.02358	+	2.14991i	0.253982	+	0.0680543i
$999$	0.817837	+	0.219139i	0.0258752	+	0.00693325i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	390.2.bd.a.223.1	yes	8
5.2	odd	4		390.2.bn.a.67.2	yes	8
13.7	odd	12		390.2.bn.a.163.2	yes	8
65.7	even	12	inner	390.2.bd.a.7.1	✓	8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
390.2.bd.a.7.1	✓	8	65.7	even	12	inner
390.2.bd.a.223.1	yes	8	1.1	even	1	trivial
390.2.bn.a.67.2	yes	8	5.2	odd	4
390.2.bn.a.163.2	yes	8	13.7	odd	12

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 390 = 2 \cdot 3 \cdot 5 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	390.bd (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.866025 - 0.500000i) q^{2} +(-0.258819 + 0.965926i) q^{3} +(0.500000 - 0.866025i) q^{4} +(-2.12132 + 0.707107i) q^{5} +(0.258819 + 0.965926i) q^{6} +(-1.88366 + 3.26260i) q^{7} -1.00000i q^{8} +(-0.866025 - 0.500000i) q^{9} +O(q^{10})\)	\(q+(0.866025 - 0.500000i) q^{2} +(-0.258819 + 0.965926i) q^{3} +(0.500000 - 0.866025i) q^{4} +(-2.12132 + 0.707107i) q^{5} +(0.258819 + 0.965926i) q^{6} +(-1.88366 + 3.26260i) q^{7} -1.00000i q^{8} +(-0.866025 - 0.500000i) q^{9} +(-1.48356 + 1.67303i) q^{10} +(-1.23388 + 4.60488i) q^{11} +(0.707107 + 0.707107i) q^{12} +(-3.53553 - 0.707107i) q^{13} +3.76733i q^{14} +(-0.133975 - 2.23205i) q^{15} +(-0.500000 - 0.866025i) q^{16} +(6.22973 - 1.66925i) q^{17} -1.00000 q^{18} +(-5.43916 + 1.45742i) q^{19} +(-0.448288 + 2.19067i) q^{20} +(-2.66390 - 2.66390i) q^{21} +(1.23388 + 4.60488i) q^{22} +(7.94414 + 2.12863i) q^{23} +(0.965926 + 0.258819i) q^{24} +(4.00000 - 3.00000i) q^{25} +(-3.41542 + 1.15539i) q^{26} +(0.707107 - 0.707107i) q^{27} +(1.88366 + 3.26260i) q^{28} +(-4.61193 + 2.66270i) q^{29} +(-1.23205 - 1.86603i) q^{30} +(-0.648586 + 0.648586i) q^{31} +(-0.866025 - 0.500000i) q^{32} +(-4.12863 - 2.38366i) q^{33} +(4.56048 - 4.56048i) q^{34} +(1.68885 - 8.25297i) q^{35} +(-0.866025 + 0.500000i) q^{36} +(0.423344 + 0.733253i) q^{37} +(-3.98174 + 3.98174i) q^{38} +(1.59808 - 3.23205i) q^{39} +(0.707107 + 2.12132i) q^{40} +(2.23437 + 0.598698i) q^{41} +(-3.63896 - 0.975056i) q^{42} +(0.155395 + 0.579940i) q^{43} +(3.37101 + 3.37101i) q^{44} +(2.19067 + 0.448288i) q^{45} +(7.94414 - 2.12863i) q^{46} -1.59575 q^{47} +(0.965926 - 0.258819i) q^{48} +(-3.59638 - 6.22911i) q^{49} +(1.96410 - 4.59808i) q^{50} +6.44949i q^{51} +(-2.38014 + 2.70831i) q^{52} +(4.92820 + 4.92820i) q^{53} +(0.258819 - 0.965926i) q^{54} +(-0.638701 - 10.6409i) q^{55} +(3.26260 + 1.88366i) q^{56} -5.63103i q^{57} +(-2.66270 + 4.61193i) q^{58} +(-2.86919 - 10.7079i) q^{59} +(-2.00000 - 1.00000i) q^{60} +(-1.30751 + 2.26467i) q^{61} +(-0.237399 + 0.885986i) q^{62} +(3.26260 - 1.88366i) q^{63} -1.00000 q^{64} +(8.00000 - 1.00000i) q^{65} -4.76733 q^{66} +(0.210133 - 0.121320i) q^{67} +(1.66925 - 6.22973i) q^{68} +(-4.11219 + 7.12252i) q^{69} +(-2.66390 - 7.99171i) q^{70} +(2.87075 + 10.7138i) q^{71} +(-0.500000 + 0.866025i) q^{72} -8.62498i q^{73} +(0.733253 + 0.423344i) q^{74} +(1.86250 + 4.64016i) q^{75} +(-1.45742 + 5.43916i) q^{76} +(-12.6997 - 12.6997i) q^{77} +(-0.232051 - 3.59808i) q^{78} +11.7214i q^{79} +(1.67303 + 1.48356i) q^{80} +(0.500000 + 0.866025i) q^{81} +(2.23437 - 0.598698i) q^{82} +14.8983 q^{83} +(-3.63896 + 0.975056i) q^{84} +(-12.0349 + 7.94610i) q^{85} +(0.424546 + 0.424546i) q^{86} +(-1.37832 - 5.14394i) q^{87} +(4.60488 + 1.23388i) q^{88} +(-2.58044 - 0.691426i) q^{89} +(2.12132 - 0.707107i) q^{90} +(8.96676 - 10.2031i) q^{91} +(5.81552 - 5.81552i) q^{92} +(-0.458620 - 0.794353i) q^{93} +(-1.38196 + 0.797877i) q^{94} +(10.5076 - 6.93772i) q^{95} +(0.707107 - 0.707107i) q^{96} +(6.60867 + 3.81552i) q^{97} +(-6.22911 - 3.59638i) q^{98} +(3.37101 - 3.37101i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 4 q^{4} - 4 q^{7}+O(q^{10}) \) 8 * q + 4 * q^4 - 4 * q^7	\( 8 q + 4 q^{4} - 4 q^{7} - 16 q^{11} - 8 q^{15} - 4 q^{16} + 12 q^{17} - 8 q^{18} - 24 q^{19} + 8 q^{21} + 16 q^{22} + 16 q^{23} + 32 q^{25} + 4 q^{28} - 24 q^{29} + 4 q^{30} - 4 q^{31} - 12 q^{33} - 24 q^{35} + 8 q^{37} - 8 q^{39} + 28 q^{41} - 8 q^{42} - 8 q^{43} - 8 q^{44} + 16 q^{46} + 32 q^{47} - 20 q^{49} - 12 q^{50} - 16 q^{53} - 4 q^{55} + 12 q^{56} - 8 q^{58} + 32 q^{59} - 16 q^{60} - 8 q^{61} - 16 q^{62} + 12 q^{63} - 8 q^{64} + 64 q^{65} - 16 q^{66} + 12 q^{68} + 8 q^{70} + 8 q^{71} - 4 q^{72} - 24 q^{74} - 24 q^{76} - 24 q^{77} + 12 q^{78} + 4 q^{81} + 28 q^{82} - 32 q^{83} - 8 q^{84} - 32 q^{85} - 8 q^{86} + 28 q^{87} + 8 q^{88} - 4 q^{89} - 8 q^{91} + 20 q^{92} - 12 q^{94} + 4 q^{95} + 12 q^{97} + 24 q^{98} - 8 q^{99}+O(q^{100}) \) 8 * q + 4 * q^4 - 4 * q^7 - 16 * q^11 - 8 * q^15 - 4 * q^16 + 12 * q^17 - 8 * q^18 - 24 * q^19 + 8 * q^21 + 16 * q^22 + 16 * q^23 + 32 * q^25 + 4 * q^28 - 24 * q^29 + 4 * q^30 - 4 * q^31 - 12 * q^33 - 24 * q^35 + 8 * q^37 - 8 * q^39 + 28 * q^41 - 8 * q^42 - 8 * q^43 - 8 * q^44 + 16 * q^46 + 32 * q^47 - 20 * q^49 - 12 * q^50 - 16 * q^53 - 4 * q^55 + 12 * q^56 - 8 * q^58 + 32 * q^59 - 16 * q^60 - 8 * q^61 - 16 * q^62 + 12 * q^63 - 8 * q^64 + 64 * q^65 - 16 * q^66 + 12 * q^68 + 8 * q^70 + 8 * q^71 - 4 * q^72 - 24 * q^74 - 24 * q^76 - 24 * q^77 + 12 * q^78 + 4 * q^81 + 28 * q^82 - 32 * q^83 - 8 * q^84 - 32 * q^85 - 8 * q^86 + 28 * q^87 + 8 * q^88 - 4 * q^89 - 8 * q^91 + 20 * q^92 - 12 * q^94 + 4 * q^95 + 12 * q^97 + 24 * q^98 - 8 * q^99

Introduction

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