LMFDB - Embedded newform 104.2.m.b.83.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [104,2,Mod(83,104)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(104, base_ring=CyclotomicField(4))

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

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

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

chi := DirichletCharacter("104.83");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 104 = 2^{3} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	104.m (of order $4$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$0.830444181021$
Analytic rank:	$0$
Dimension:	$20$
Relative dimension:	$10$ over $\Q(i)$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} - 2 x^{19} + 2 x^{18} - 7 x^{16} + 14 x^{15} - 14 x^{14} + 8 x^{13} + 16 x^{12} - 40 x^{11} + \cdots + 1024 $ x^20 - 2x^19 + 2x^18 - 7x^16 + 14x^15 - 14x^14 + 8x^13 + 16x^12 - 40x^11 + 48x^10 - 80x^9 + 64x^8 + 64x^7 - 224x^6 + 448x^5 - 448x^4 + 512x^2 - 1024*x + 1024
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{6} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			83.8
Root			$-0.813947 + 1.15650i$ of defining polynomial
Character	$\chi$	$=$	104.83
Dual form			104.2.m.b.99.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.15650 + 0.813947i) q^{2} +1.38809 q^{3} +(0.674982 + 1.88266i) q^{4} +(-2.40872 - 2.40872i) q^{5} +(1.60533 + 1.12983i) q^{6} +(-0.127019 + 0.127019i) q^{7} +(-0.751766 + 2.72669i) q^{8} -1.07320 q^{9} +O(q^{10})$	\(q+(1.15650 + 0.813947i) q^{2} +1.38809 q^{3} +(0.674982 + 1.88266i) q^{4} +(-2.40872 - 2.40872i) q^{5} +(1.60533 + 1.12983i) q^{6} +(-0.127019 + 0.127019i) q^{7} +(-0.751766 + 2.72669i) q^{8} -1.07320 q^{9} +(-0.825113 - 4.74625i) q^{10} +(-2.63237 - 2.63237i) q^{11} +(0.936938 + 2.61330i) q^{12} +(1.93837 + 3.04019i) q^{13} +(-0.250285 + 0.0435109i) q^{14} +(-3.34352 - 3.34352i) q^{15} +(-3.08880 + 2.54152i) q^{16} +4.33908i q^{17} +(-1.24115 - 0.873526i) q^{18} +(4.97146 - 4.97146i) q^{19} +(2.90895 - 6.16063i) q^{20} +(-0.176315 + 0.176315i) q^{21} +(-0.901727 - 5.18695i) q^{22} +3.98711 q^{23} +(-1.04352 + 3.78490i) q^{24} +6.60383i q^{25} +(-0.232832 + 5.09370i) q^{26} -5.65398 q^{27} +(-0.324870 - 0.153398i) q^{28} -4.59378i q^{29} +(-1.14533 - 6.58823i) q^{30} +(1.07702 + 1.07702i) q^{31} +(-5.64086 + 0.425150i) q^{32} +(-3.65398 - 3.65398i) q^{33} +(-3.53178 + 5.01815i) q^{34} +0.611907 q^{35} +(-0.724390 - 2.02047i) q^{36} +(-2.45494 + 2.45494i) q^{37} +(9.79599 - 1.70299i) q^{38} +(2.69063 + 4.22006i) q^{39} +(8.37862 - 4.75704i) q^{40} +(0.388093 - 0.388093i) q^{41} +(-0.347419 + 0.0603971i) q^{42} -5.02419i q^{43} +(3.17905 - 6.73266i) q^{44} +(2.58503 + 2.58503i) q^{45} +(4.61110 + 3.24530i) q^{46} +(1.00356 - 1.00356i) q^{47} +(-4.28754 + 3.52787i) q^{48} +6.96773i q^{49} +(-5.37516 + 7.63732i) q^{50} +6.02305i q^{51} +(-4.41527 + 5.70135i) q^{52} -1.83922i q^{53} +(-6.53882 - 4.60204i) q^{54} +12.6813i q^{55} +(-0.250854 - 0.441832i) q^{56} +(6.90084 - 6.90084i) q^{57} +(3.73909 - 5.31271i) q^{58} +(6.28635 + 6.28635i) q^{59} +(4.03789 - 8.55152i) q^{60} +10.5817i q^{61} +(0.368936 + 2.12221i) q^{62} +(0.136317 - 0.136317i) q^{63} +(-6.86970 - 4.09967i) q^{64} +(2.65398 - 11.9919i) q^{65} +(-1.25168 - 7.19997i) q^{66} +(-4.21315 + 4.21315i) q^{67} +(-8.16901 + 2.92880i) q^{68} +5.53449 q^{69} +(0.707670 + 0.498060i) q^{70} +(-2.59715 - 2.59715i) q^{71} +(0.806794 - 2.92628i) q^{72} +(-0.388093 - 0.388093i) q^{73} +(-4.83732 + 0.840947i) q^{74} +9.16673i q^{75} +(12.7152 + 6.00390i) q^{76} +0.668725 q^{77} +(-0.323192 + 7.07053i) q^{78} -15.3812i q^{79} +(13.5618 + 1.31824i) q^{80} -4.62865 q^{81} +(0.764716 - 0.132942i) q^{82} +(-2.46502 + 2.46502i) q^{83} +(-0.450949 - 0.212931i) q^{84} +(10.4516 - 10.4516i) q^{85} +(4.08942 - 5.81047i) q^{86} -6.37660i q^{87} +(9.15660 - 5.19874i) q^{88} +(-11.3583 - 11.3583i) q^{89} +(0.885510 + 5.09366i) q^{90} +(-0.632373 - 0.139953i) q^{91} +(2.69123 + 7.50637i) q^{92} +(1.49500 + 1.49500i) q^{93} +(1.97746 - 0.343772i) q^{94} -23.9497 q^{95} +(-7.83003 + 0.590148i) q^{96} +(3.31375 - 3.31375i) q^{97} +(-5.67136 + 8.05818i) q^{98} +(2.82506 + 2.82506i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q + 2 q^{2} - 4 q^{3} - 4 q^{6} - 4 q^{8} + 16 q^{9}+O(q^{10}) $ 20 * q + 2 * q^2 - 4 * q^3 - 4 * q^6 - 4 * q^8 + 16 * q^9	$ 20 q + 2 q^{2} - 4 q^{3} - 4 q^{6} - 4 q^{8} + 16 q^{9} - 8 q^{11} - 20 q^{14} + 20 q^{16} - 26 q^{18} - 12 q^{19} + 8 q^{20} - 8 q^{22} + 4 q^{24} - 34 q^{26} - 52 q^{27} + 12 q^{28} - 8 q^{32} - 12 q^{33} + 4 q^{34} + 44 q^{35} + 44 q^{40} - 24 q^{41} + 28 q^{42} + 32 q^{44} + 20 q^{46} - 20 q^{48} + 6 q^{50} + 36 q^{52} + 24 q^{54} + 8 q^{57} + 12 q^{58} + 20 q^{59} - 56 q^{60} - 8 q^{65} + 56 q^{66} - 16 q^{67} - 28 q^{68} + 8 q^{70} - 44 q^{72} + 24 q^{73} + 40 q^{74} + 44 q^{76} + 68 q^{78} - 12 q^{80} - 44 q^{81} + 16 q^{83} - 60 q^{84} - 36 q^{86} - 16 q^{89} + 32 q^{91} - 88 q^{92} - 44 q^{94} - 84 q^{96} + 12 q^{97} - 26 q^{98} + 20 q^{99}+O(q^{100}) $ 20 * q + 2 * q^2 - 4 * q^3 - 4 * q^6 - 4 * q^8 + 16 * q^9 - 8 * q^11 - 20 * q^14 + 20 * q^16 - 26 * q^18 - 12 * q^19 + 8 * q^20 - 8 * q^22 + 4 * q^24 - 34 * q^26 - 52 * q^27 + 12 * q^28 - 8 * q^32 - 12 * q^33 + 4 * q^34 + 44 * q^35 + 44 * q^40 - 24 * q^41 + 28 * q^42 + 32 * q^44 + 20 * q^46 - 20 * q^48 + 6 * q^50 + 36 * q^52 + 24 * q^54 + 8 * q^57 + 12 * q^58 + 20 * q^59 - 56 * q^60 - 8 * q^65 + 56 * q^66 - 16 * q^67 - 28 * q^68 + 8 * q^70 - 44 * q^72 + 24 * q^73 + 40 * q^74 + 44 * q^76 + 68 * q^78 - 12 * q^80 - 44 * q^81 + 16 * q^83 - 60 * q^84 - 36 * q^86 - 16 * q^89 + 32 * q^91 - 88 * q^92 - 44 * q^94 - 84 * q^96 + 12 * q^97 - 26 * q^98 + 20 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/104\mathbb{Z}\right)^\times$.

$n$	$41$	$53$	$79$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$-1$	$-1$

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 $

$2$	1.15650	+	0.813947i	0.817769	+	0.575547i
$2$	1.15650	+	0.813947i	0.817769	+	0.575547i
$3$	1.38809			0.801416			0.400708	−	0.916206i	$-0.368764\pi$
$3$	1.38809			0.801416			0.400708	+	0.916206i	$0.368764\pi$
$4$	0.674982	+	1.88266i	0.337491	+	0.941329i
$5$	−2.40872	−	2.40872i	−1.07721	−	1.07721i	−0.996758	−	0.0804522i	$-0.974364\pi$
$5$	−2.40872	−	2.40872i	−1.07721	−	1.07721i	−0.0804522	−	0.996758i	$-0.525636\pi$
$6$	1.60533	+	1.12983i	0.655373	+	0.461252i
$7$	−0.127019	+	0.127019i	−0.0480088	+	0.0480088i	−0.730704	−	0.682695i	$-0.760808\pi$
$7$	−0.127019	+	0.127019i	−0.0480088	+	0.0480088i	0.682695	+	0.730704i	$0.260808\pi$
$8$	−0.751766	+	2.72669i	−0.265789	+	0.964031i
$9$	−1.07320			−0.357733
$10$	−0.825113	−	4.74625i	−0.260924	−	1.50089i
$11$	−2.63237	−	2.63237i	−0.793690	−	0.793690i	0.188402	−	0.982092i	$-0.439669\pi$
$11$	−2.63237	−	2.63237i	−0.793690	−	0.793690i	−0.982092	+	0.188402i	$0.939669\pi$
$12$	0.936938	+	2.61330i	0.270471	+	0.754396i
$13$	1.93837	+	3.04019i	0.537606	+	0.843196i
$13$	1.93837	+	3.04019i	0.537606	+	0.843196i
$14$	−0.250285	+	0.0435109i	−0.0668914	+	0.0116288i
$15$	−3.34352	−	3.34352i	−0.863294	−	0.863294i
$16$	−3.08880	+	2.54152i	−0.772200	+	0.635380i
$17$			4.33908i			1.05238i	0.850366	+	0.526191i	$0.176380\pi$
$17$			4.33908i			1.05238i	−0.850366	+	0.526191i	$0.823620\pi$
$18$	−1.24115	−	0.873526i	−0.292543	−	0.205892i
$19$	4.97146	−	4.97146i	1.14053	−	1.14053i	0.152177	−	0.988353i	$-0.451372\pi$
$19$	4.97146	−	4.97146i	1.14053	−	1.14053i	0.988353	−	0.152177i	$-0.0486284\pi$
$20$	2.90895	−	6.16063i	0.650460	−	1.37756i
$21$	−0.176315	+	0.176315i	−0.0384750	+	0.0384750i
$22$	−0.901727	−	5.18695i	−0.192249	−	1.10586i
$23$	3.98711			0.831371			0.415685	−	0.909508i	$-0.363542\pi$
$23$	3.98711			0.831371			0.415685	+	0.909508i	$0.363542\pi$
$24$	−1.04352	+	3.78490i	−0.213008	+	0.772590i
$25$			6.60383i			1.32077i
$26$	−0.232832	+	5.09370i	−0.0456621	+	0.998957i
$27$	−5.65398			−1.08811
$28$	−0.324870	−	0.153398i	−0.0613946	−	0.0289895i
$29$		−	4.59378i		−	0.853044i	−0.904477	−	0.426522i	$-0.859739\pi$
$29$		−	4.59378i		−	0.853044i	0.904477	−	0.426522i	$-0.140261\pi$
$30$	−1.14533	−	6.58823i	−0.209108	−	1.20284i
$31$	1.07702	+	1.07702i	0.193438	+	0.193438i	0.797180	−	0.603742i	$-0.206324\pi$
$31$	1.07702	+	1.07702i	0.193438	+	0.193438i	−0.603742	+	0.797180i	$0.706324\pi$
$32$	−5.64086	+	0.425150i	−0.997172	+	0.0751566i
$33$	−3.65398	−	3.65398i	−0.636076	−	0.636076i
$34$	−3.53178	+	5.01815i	−0.605696	+	0.860605i
$35$	0.611907			0.103431
$36$	−0.724390	−	2.02047i	−0.120732	−	0.336744i
$37$	−2.45494	+	2.45494i	−0.403590	+	0.403590i	−0.879496	−	0.475906i	$-0.842120\pi$
$37$	−2.45494	+	2.45494i	−0.403590	+	0.403590i	0.475906	+	0.879496i	$0.342120\pi$
$38$	9.79599	−	1.70299i	1.58912	−	0.276261i
$39$	2.69063	+	4.22006i	0.430846	+	0.675751i
$40$	8.37862	−	4.75704i	1.32478	−	0.752153i
$41$	0.388093	−	0.388093i	0.0606099	−	0.0606099i	−0.676152	−	0.736762i	$-0.736354\pi$
$41$	0.388093	−	0.388093i	0.0606099	−	0.0606099i	0.736762	+	0.676152i	$0.236354\pi$
$42$	−0.347419	+	0.0603971i	−0.0536078	+	0.00931948i
$43$		−	5.02419i		−	0.766182i	−0.923711	−	0.383091i	$-0.874860\pi$
$43$		−	5.02419i		−	0.766182i	0.923711	−	0.383091i	$-0.125140\pi$
$44$	3.17905	−	6.73266i	0.479260	−	1.01499i
$45$	2.58503	+	2.58503i	0.385354	+	0.385354i
$46$	4.61110	+	3.24530i	0.679869	+	0.478493i
$47$	1.00356	−	1.00356i	0.146384	−	0.146384i	−0.630116	−	0.776501i	$-0.716993\pi$
$47$	1.00356	−	1.00356i	0.146384	−	0.146384i	0.776501	+	0.630116i	$0.216993\pi$
$48$	−4.28754	+	3.52787i	−0.618853	+	0.509204i
$49$			6.96773i			0.995390i
$50$	−5.37516	+	7.63732i	−0.760163	+	1.08008i
$51$			6.02305i			0.843396i
$52$	−4.41527	+	5.70135i	−0.612288	+	0.790635i
$53$		−	1.83922i		−	0.252636i	−0.991990	−	0.126318i	$-0.959684\pi$
$53$		−	1.83922i		−	0.252636i	0.991990	−	0.126318i	$-0.0403161\pi$
$54$	−6.53882	−	4.60204i	−0.889821	−	0.626258i
$55$			12.6813i			1.70994i
$56$	−0.250854	−	0.441832i	−0.0335218	−	0.0590422i
$57$	6.90084	−	6.90084i	0.914039	−	0.914039i
$58$	3.73909	−	5.31271i	0.490967	−	0.697593i
$59$	6.28635	+	6.28635i	0.818413	+	0.818413i	0.985878	−	0.167465i	$-0.0535581\pi$
$59$	6.28635	+	6.28635i	0.818413	+	0.818413i	−0.167465	+	0.985878i	$0.553558\pi$
$60$	4.03789	−	8.55152i	0.521289	−	1.10400i
$61$			10.5817i			1.35485i	0.735592	+	0.677425i	$0.236904\pi$
$61$			10.5817i			1.35485i	−0.735592	+	0.677425i	$0.763096\pi$
$62$	0.368936	+	2.12221i	0.0468549	+	0.269521i
$63$	0.136317	−	0.136317i	0.0171743	−	0.0171743i
$64$	−6.86970	−	4.09967i	−0.858712	−	0.512459i
$65$	2.65398	−	11.9919i	0.329185	−	1.48741i
$66$	−1.25168	−	7.19997i	−0.154071	−	0.886254i
$67$	−4.21315	+	4.21315i	−0.514718	+	0.514718i	−0.915969	−	0.401250i	$-0.868576\pi$
$67$	−4.21315	+	4.21315i	−0.514718	+	0.514718i	0.401250	+	0.915969i	$0.368576\pi$
$68$	−8.16901	+	2.92880i	−0.990638	+	0.355170i
$69$	5.53449			0.666274
$70$	0.707670	+	0.498060i	0.0845828	+	0.0595295i
$71$	−2.59715	−	2.59715i	−0.308225	−	0.308225i	0.535995	−	0.844221i	$-0.319936\pi$
$71$	−2.59715	−	2.59715i	−0.308225	−	0.308225i	−0.844221	+	0.535995i	$0.819936\pi$
$72$	0.806794	−	2.92628i	0.0950816	−	0.344866i
$73$	−0.388093	−	0.388093i	−0.0454228	−	0.0454228i	0.684031	−	0.729453i	$-0.260225\pi$
$73$	−0.388093	−	0.388093i	−0.0454228	−	0.0454228i	−0.729453	+	0.684031i	$0.760225\pi$
$74$	−4.83732	+	0.840947i	−0.562328	+	0.0977581i
$75$			9.16673i			1.05848i
$76$	12.7152	+	6.00390i	1.45853	+	0.688695i
$77$	0.668725			0.0762082
$78$	−0.323192	+	7.07053i	−0.0365943	+	0.800580i
$79$		−	15.3812i		−	1.73052i	−0.501323	−	0.865260i	$-0.667153\pi$
$79$		−	15.3812i		−	1.73052i	0.501323	−	0.865260i	$-0.332847\pi$
$80$	13.5618	+	1.31824i	1.51626	+	0.147383i
$81$	−4.62865			−0.514294
$82$	0.764716	−	0.132942i	0.0844487	−	0.0146810i
$83$	−2.46502	+	2.46502i	−0.270571	+	0.270571i	−0.829330	−	0.558759i	$-0.811278\pi$
$83$	−2.46502	+	2.46502i	−0.270571	+	0.270571i	0.558759	+	0.829330i	$0.311278\pi$
$84$	−0.450949	−	0.212931i	−0.0492026	−	0.0232327i
$85$	10.4516	−	10.4516i	1.13364	−	1.13364i
$86$	4.08942	−	5.81047i	0.440974	−	0.626559i
$87$		−	6.37660i		−	0.683643i
$88$	9.15660	−	5.19874i	0.976097	−	0.554188i
$89$	−11.3583	−	11.3583i	−1.20397	−	1.20397i	−0.972947	−	0.231027i	$-0.925791\pi$
$89$	−11.3583	−	11.3583i	−1.20397	−	1.20397i	−0.231027	−	0.972947i	$-0.574209\pi$
$90$	0.885510	+	5.09366i	0.0933409	+	0.536919i
$91$	−0.632373	−	0.139953i	−0.0662907	−	0.0146710i
$92$	2.69123	+	7.50637i	0.280580	+	0.782593i
$93$	1.49500	+	1.49500i	0.155025	+	0.155025i
$94$	1.97746	−	0.343772i	0.203960	−	0.0354574i
$95$	−23.9497			−2.45718
$96$	−7.83003	+	0.590148i	−0.799149	+	0.0602317i
$97$	3.31375	−	3.31375i	0.336461	−	0.336461i	−0.518573	−	0.855034i	$-0.673536\pi$
$97$	3.31375	−	3.31375i	0.336461	−	0.336461i	0.855034	+	0.518573i	$0.173536\pi$
$98$	−5.67136	+	8.05818i	−0.572894	+	0.813999i
$99$	2.82506	+	2.82506i	0.283929	+	0.283929i
$100$	−12.4327	+	4.45747i	−1.24327	+	0.445747i
$101$	−19.0522			−1.89577			−0.947884	−	0.318617i	$-0.896782\pi$
$101$	−19.0522			−1.89577			−0.947884	+	0.318617i	$0.896782\pi$
$102$	−4.90244	+	6.96565i	−0.485414	+	0.689703i
$103$	13.3555			1.31596			0.657978	−	0.753037i	$-0.271412\pi$
$103$	13.3555			1.31596			0.657978	+	0.753037i	$0.271412\pi$
$104$	−9.74685	+	2.99981i	−0.955757	+	0.294156i
$105$	0.849384			0.0828914
$106$	1.49703	−	2.12706i	0.145404	−	0.206598i
$107$	−1.78249			−0.172320			−0.0861601	−	0.996281i	$-0.527460\pi$
$107$	−1.78249			−0.172320			−0.0861601	+	0.996281i	$0.527460\pi$
$108$	−3.81633	−	10.6445i	−0.367227	−	1.02427i
$109$	−10.3367	−	10.3367i	−0.990079	−	0.990079i	0.00987275	−	0.999951i	$-0.496857\pi$
$109$	−10.3367	−	10.3367i	−0.990079	−	0.990079i	−0.999951	+	0.00987275i	$0.996857\pi$
$110$	−10.3219	+	14.6659i	−0.984153	+	1.39834i
$111$	−3.40768	+	3.40768i	−0.323443	+	0.323443i
$112$	0.0695149	−	0.715160i	0.00656854	−	0.0675762i
$113$	11.9787			1.12686			0.563429	−	0.826164i	$-0.309482\pi$
$113$	11.9787			1.12686			0.563429	+	0.826164i	$0.309482\pi$
$114$	13.5977	−	2.36390i	1.27354	−	0.221400i
$115$	−9.60383	−	9.60383i	−0.895562	−	0.895562i
$116$	8.64852	−	3.10072i	0.802995	−	0.287895i
$117$	−2.08025	−	3.26273i	−0.192319	−	0.301639i
$118$	2.15341	+	12.3869i	0.198237	+	1.14031i
$119$	−0.551148	−	0.551148i	−0.0505236	−	0.0505236i
$120$	11.6303	−	6.60321i	1.06170	−	0.602788i
$121$			2.85877i			0.259888i
$122$	−8.61295	+	12.2377i	−0.779780	+	1.10795i
$123$	0.538709	−	0.538709i	0.0485737	−	0.0485737i
$124$	−1.30069	+	2.75463i	−0.116805	+	0.247373i
$125$	3.86317	−	3.86317i	0.345532	−	0.345532i
$126$	0.268605	−	0.0466958i	0.0239293	−	0.00415999i
$127$	1.46123			0.129663			0.0648316	−	0.997896i	$-0.479349\pi$
$127$	1.46123			0.129663			0.0648316	+	0.997896i	$0.479349\pi$
$128$	−4.60789	−	10.3328i	−0.407284	−	0.913302i
$129$		−	6.97404i		−	0.614030i
$130$	12.8301	−	11.7085i	1.12527	−	1.02690i
$131$	3.75944			0.328464			0.164232	−	0.986422i	$-0.447485\pi$
$131$	3.75944			0.328464			0.164232	+	0.986422i	$0.447485\pi$
$132$	4.41282	−	9.34556i	0.384087	−	0.813426i
$133$			1.26294i			0.109511i
$134$	−8.30179	+	1.44323i	−0.717165	+	0.124676i
$135$	13.6188	+	13.6188i	1.17212	+	1.17212i
$136$	−11.8313	−	3.26198i	−1.01453	−	0.279712i
$137$	6.09739	+	6.09739i	0.520935	+	0.520935i	0.917854	−	0.396919i	$-0.129921\pi$
$137$	6.09739	+	6.09739i	0.520935	+	0.520935i	−0.396919	+	0.917854i	$0.629921\pi$
$138$	6.40063	+	4.50477i	0.544858	+	0.383472i
$139$	19.3362			1.64007			0.820036	−	0.572311i	$-0.193953\pi$
$139$	19.3362			1.64007			0.820036	+	0.572311i	$0.193953\pi$
$140$	0.413026	+	1.15201i	0.0349071	+	0.0973628i
$141$	1.39303	−	1.39303i	0.117315	−	0.117315i
$142$	−0.889662	−	5.11755i	−0.0746588	−	0.429455i
$143$	2.90041	−	13.1054i	0.242544	−	1.09593i
$144$	3.31489	−	2.72756i	0.276241	−	0.227296i
$145$	−11.0651	+	11.0651i	−0.918908	+	0.918908i
$146$	−0.132942	−	0.764716i	−0.0110024	−	0.0632883i
$147$			9.67186i			0.797721i
$148$	−6.27885	−	2.96477i	−0.516118	−	0.243703i
$149$	5.83926	+	5.83926i	0.478371	+	0.478371i	0.904610	−	0.426240i	$-0.140162\pi$
$149$	5.83926	+	5.83926i	0.478371	+	0.478371i	−0.426240	+	0.904610i	$0.640162\pi$
$150$	−7.46123	+	10.6013i	−0.609206	+	0.865594i
$151$	−13.5924	+	13.5924i	−1.10613	+	1.10613i	−0.112479	+	0.993654i	$0.535879\pi$
$151$	−13.5924	+	13.5924i	−1.10613	+	1.10613i	−0.993654	+	0.112479i	$0.964121\pi$
$152$	9.81826	+	17.2930i	0.796366	+	1.40265i
$153$		−	4.65670i		−	0.376472i
$154$	0.773380	+	0.544306i	0.0623207	+	0.0438614i
$155$		−	5.18847i		−	0.416748i
$156$	−6.12880	+	7.91400i	−0.490697	+	0.633627i
$157$			3.22500i			0.257383i	0.991685	+	0.128691i	$0.0410777\pi$
$157$			3.22500i			0.257383i	−0.991685	+	0.128691i	$0.958922\pi$
$158$	12.5195	−	17.7884i	0.995996	−	1.41517i
$159$		−	2.55301i		−	0.202467i
$160$	14.6113	+	12.5632i	1.15512	+	0.993205i
$161$	−0.506441	+	0.506441i	−0.0399131	+	0.0399131i
$162$	−5.35303	−	3.76747i	−0.420574	−	0.296001i
$163$	−12.2685	−	12.2685i	−0.960941	−	0.960941i	0.0383247	−	0.999265i	$-0.487798\pi$
$163$	−12.2685	−	12.2685i	−0.960941	−	0.960941i	−0.999265	+	0.0383247i	$0.987798\pi$
$164$	0.992601	+	0.468690i	0.0775091	+	0.0365985i
$165$			17.6028i			1.37038i
$166$	−4.85718	+	0.844398i	−0.376990	+	0.0655380i
$167$	7.73367	−	7.73367i	0.598450	−	0.598450i	−0.341450	−	0.939900i	$-0.610918\pi$
$167$	7.73367	−	7.73367i	0.598450	−	0.598450i	0.939900	+	0.341450i	$0.110918\pi$
$168$	−0.348208	−	0.613303i	−0.0268649	−	0.0473174i
$169$	−5.48548	+	11.7860i	−0.421960	+	0.906614i
$170$	20.5944	−	3.58023i	1.57951	−	0.274591i
$171$	−5.33536	+	5.33536i	−0.408005	+	0.408005i
$172$	9.45883	−	3.39124i	0.721229	−	0.258579i
$173$	13.2073			1.00413			0.502066	−	0.864829i	$-0.332573\pi$
$173$	13.2073			1.00413			0.502066	+	0.864829i	$0.332573\pi$
$174$	5.19021	−	7.37453i	0.393469	−	0.559062i
$175$	−0.838814	−	0.838814i	−0.0634084	−	0.0634084i
$176$	14.8211	+	1.44064i	1.11718	+	0.108592i
$177$	8.72604	+	8.72604i	0.655889	+	0.655889i
$178$	−3.89081	−	22.3809i	−0.291629	−	1.67752i
$179$			5.24686i			0.392169i	0.980587	+	0.196085i	$0.0628227\pi$
$179$			5.24686i			0.392169i	−0.980587	+	0.196085i	$0.937177\pi$
$180$	−3.12188	+	6.61158i	−0.232691	+	0.492798i
$181$	−3.49698			−0.259928			−0.129964	−	0.991519i	$-0.541486\pi$
$181$	−3.49698			−0.259928			−0.129964	+	0.991519i	$0.541486\pi$
$182$	−0.617425	−	0.676573i	−0.0457666	−	0.0501509i
$183$			14.6884i			1.08580i
$184$	−2.99738	+	10.8716i	−0.220970	+	0.801467i
$185$	11.8265			0.869502
$186$	0.512117	+	2.94582i	0.0375503	+	0.215998i
$187$	11.4221	−	11.4221i	0.835266	−	0.835266i
$188$	2.56674	+	1.21197i	0.187199	+	0.0883923i
$189$	0.718165	−	0.718165i	0.0522388	−	0.0522388i
$190$	−27.6978	−	19.4937i	−2.00941	−	1.41422i
$191$		−	9.17512i		−	0.663888i	−0.943299	−	0.331944i	$-0.892295\pi$
$191$		−	9.17512i		−	0.663888i	0.943299	−	0.331944i	$-0.107705\pi$
$192$	−9.53577	−	5.69072i	−0.688185	−	0.410692i
$193$	0.0825862	+	0.0825862i	0.00594469	+	0.00594469i	0.710073	−	0.704128i	$-0.248662\pi$
$193$	0.0825862	+	0.0825862i	0.00594469	+	0.00594469i	−0.704128	+	0.710073i	$0.748662\pi$
$194$	6.52957	−	1.13514i	0.468796	−	0.0814980i
$195$	3.68397	−	16.6459i	0.263814	−	1.19204i
$196$	−13.1179	+	4.70309i	−0.936990	+	0.335935i
$197$	8.65184	+	8.65184i	0.616418	+	0.616418i	0.944611	−	0.328193i	$-0.106439\pi$
$197$	8.65184	+	8.65184i	0.616418	+	0.616418i	−0.328193	+	0.944611i	$0.606439\pi$
$198$	0.967732	+	5.56663i	0.0687737	+	0.395603i
$199$	16.3536			1.15927			0.579637	−	0.814875i	$-0.303194\pi$
$199$	16.3536			1.15927			0.579637	+	0.814875i	$0.303194\pi$
$200$	−18.0066	−	4.96453i	−1.27326	−	0.351046i
$201$	−5.84824	+	5.84824i	−0.412503	+	0.412503i
$202$	−22.0339	−	15.5075i	−1.55030	−	1.09110i
$203$	0.583499	+	0.583499i	0.0409536	+	0.0409536i
$204$	−11.3393	+	4.06545i	−0.793913	+	0.284638i
$205$	−1.86961			−0.130579
$206$	15.4456	+	10.8707i	1.07615	+	0.757394i
$207$	−4.27897			−0.297409
$208$	−13.7139	−	4.46413i	−0.950889	−	0.309532i
$209$	−26.1734			−1.81046
$210$	0.982312	+	0.691353i	0.0677860	+	0.0477079i
$211$	−12.7723			−0.879283			−0.439642	−	0.898173i	$-0.644895\pi$
$211$	−12.7723			−0.879283			−0.439642	+	0.898173i	$0.644895\pi$
$212$	3.46262	−	1.24144i	0.237814	−	0.0852626i
$213$	−3.60509	−	3.60509i	−0.247017	−	0.247017i
$214$	−2.06145	−	1.45085i	−0.140918	−	0.0991784i
$215$	−12.1018	+	12.1018i	−0.825339	+	0.825339i
$216$	4.25047	−	15.4167i	0.289208	−	1.04897i
$217$	−0.273605			−0.0185735
$218$	−3.54087	−	20.3680i	−0.239818	−	1.37949i
$219$	−0.538709	−	0.538709i	−0.0364026	−	0.0364026i
$220$	−23.8745	+	8.55964i	−1.60962	+	0.577090i
$221$	−13.1916	+	8.41073i	−0.887365	+	0.565767i
$222$	−6.71466	+	1.16731i	−0.450658	+	0.0783448i
$223$	−12.8482	−	12.8482i	−0.860380	−	0.860380i	0.131002	−	0.991382i	$-0.458181\pi$
$223$	−12.8482	−	12.8482i	−0.860380	−	0.860380i	−0.991382	+	0.131002i	$0.958181\pi$
$224$	0.662496	−	0.770500i	0.0442649	−	0.0514812i
$225$		−	7.08722i		−	0.472481i
$226$	13.8533	+	9.75000i	0.921510	+	0.648560i
$227$	−10.2863	+	10.2863i	−0.682729	+	0.682729i	−0.960614	−	0.277885i	$-0.910366\pi$
$227$	−10.2863	+	10.2863i	−0.682729	+	0.682729i	0.277885	+	0.960614i	$0.410366\pi$
$228$	17.6499	+	8.33398i	1.16889	+	0.551931i
$229$	−2.44653	+	2.44653i	−0.161671	+	0.161671i	−0.783307	−	0.621635i	$-0.786469\pi$
$229$	−2.44653	+	2.44653i	−0.161671	+	0.161671i	0.621635	+	0.783307i	$0.286469\pi$
$230$	−3.28982	−	18.9238i	−0.216924	−	1.24780i
$231$	0.928252			0.0610745
$232$	12.5258	+	3.45345i	0.822361	+	0.226730i
$233$		−	6.36599i		−	0.417050i	−0.978017	−	0.208525i	$-0.933134\pi$
$233$		−	6.36599i		−	0.417050i	0.978017	−	0.208525i	$-0.0668663\pi$
$234$	0.249875	−	5.46655i	0.0163348	−	0.357360i
$235$	−4.83458			−0.315373
$236$	−7.59187	+	16.0782i	−0.494189	+	1.04660i
$237$		−	21.3505i		−	1.38687i
$238$	−0.188797	−	1.08601i	−0.0122379	−	0.0703954i
$239$	12.2196	+	12.2196i	0.790418	+	0.790418i	0.981562	−	0.191144i	$-0.0612197\pi$
$239$	12.2196	+	12.2196i	0.790418	+	0.790418i	−0.191144	+	0.981562i	$0.561220\pi$
$240$	18.8251	+	1.82984i	1.21515	+	0.118115i
$241$	10.9752	+	10.9752i	0.706973	+	0.706973i	0.965898	−	0.258924i	$-0.0833680\pi$
$241$	10.9752	+	10.9752i	0.706973	+	0.706973i	−0.258924	+	0.965898i	$0.583368\pi$
$242$	−2.32689	+	3.30617i	−0.149578	+	0.212529i
$243$	10.5369			0.675945
$244$	−19.9217	+	7.14247i	−1.27536	+	0.457250i
$245$	16.7833	−	16.7833i	1.07225	−	1.07225i
$246$	1.06150	−	0.184536i	0.0676785	−	0.0117656i
$247$	24.7507	+	5.47766i	1.57485	+	0.348535i
$248$	−3.74637	+	2.12703i	−0.237894	+	0.135067i
$249$	−3.42167	+	3.42167i	−0.216839	+	0.216839i
$250$	7.61216	−	1.32334i	0.481436	−	0.0836953i
$251$			0.692187i			0.0436905i	0.999761	+	0.0218452i	$0.00695411\pi$
$251$			0.692187i			0.0436905i	−0.999761	+	0.0218452i	$0.993046\pi$
$252$	0.348650	+	0.164627i	0.0219629	+	0.0103705i
$253$	−10.4956	−	10.4956i	−0.659851	−	0.659851i
$254$	1.68991	+	1.18936i	0.106034	+	0.0746273i
$255$	14.5078	−	14.5078i	0.908515	−	0.908515i
$256$	3.08135	−	15.7005i	0.192584	−	0.981280i
$257$			16.5622i			1.03312i	0.856251	+	0.516560i	$0.172788\pi$
$257$			16.5622i			1.03312i	−0.856251	+	0.516560i	$0.827212\pi$
$258$	5.67650	−	8.06547i	0.353403	−	0.502134i
$259$		−	0.623650i		−	0.0387517i
$260$	24.3681	−	3.09780i	1.51124	−	0.192118i
$261$			4.93004i			0.305162i
$262$	4.34779	+	3.05999i	0.268608	+	0.189047i
$263$			3.54818i			0.218790i	0.993998	+	0.109395i	$0.0348914\pi$
$263$			3.54818i			0.218790i	−0.993998	+	0.109395i	$0.965109\pi$
$264$	12.7102	−	7.21633i	0.782259	−	0.444135i
$265$	−4.43016	+	4.43016i	−0.272143	+	0.272143i
$266$	−1.02797	+	1.46059i	−0.0630287	+	0.0895547i
$267$	−15.7663	−	15.7663i	−0.964884	−	0.964884i
$268$	−10.7757	−	5.08812i	−0.658232	−	0.310806i
$269$			12.6310i			0.770127i	0.922890	+	0.385063i	$0.125820\pi$
$269$			12.6310i			0.770127i	−0.922890	+	0.385063i	$0.874180\pi$
$270$	4.66517	+	26.8352i	0.283913	+	1.63314i
$271$	−15.0265	+	15.0265i	−0.912795	+	0.912795i	−0.996491	−	0.0836966i	$-0.973327\pi$
$271$	−15.0265	+	15.0265i	−0.912795	+	0.912795i	0.0836966	+	0.996491i	$0.473327\pi$
$272$	−11.0279	−	13.4026i	−0.668663	−	0.812649i
$273$	−0.877792	−	0.194267i	−0.0531264	−	0.0117576i
$274$	2.08868	+	12.0146i	0.126182	+	0.725827i
$275$	17.3837	−	17.3837i	1.04828	−	1.04828i
$276$	3.73568	+	10.4195i	0.224861	+	0.627183i
$277$	11.4437			0.687585			0.343793	−	0.939046i	$-0.388288\pi$
$277$	11.4437			0.687585			0.343793	+	0.939046i	$0.388288\pi$
$278$	22.3623	+	15.7386i	1.34120	+	0.943939i
$279$	−1.15586	−	1.15586i	−0.0691993	−	0.0691993i
$280$	−0.460011	+	1.66848i	−0.0274909	+	0.0997109i
$281$	0.709295	+	0.709295i	0.0423130	+	0.0423130i	0.727947	−	0.685634i	$-0.240475\pi$
$281$	0.709295	+	0.709295i	0.0423130	+	0.0423130i	−0.685634	+	0.727947i	$0.740475\pi$
$282$	2.74490	−	0.477188i	0.163456	−	0.0284161i
$283$		−	4.12466i		−	0.245185i	−0.992457	−	0.122593i	$-0.960879\pi$
$283$		−	4.12466i		−	0.245185i	0.992457	−	0.122593i	$-0.0391209\pi$
$284$	3.13652	−	6.64258i	0.186118	−	0.394165i
$285$	−33.2443			−1.96922
$286$	14.0214	−	12.7956i	0.829104	−	0.756621i
$287$			0.0985906i			0.00581962i
$288$	6.05376	−	0.456270i	0.356721	−	0.0268860i
$289$	−1.82764			−0.107508
$290$	−21.8032	+	3.79039i	−1.28033	+	0.222579i
$291$	4.59980	−	4.59980i	0.269645	−	0.269645i
$292$	0.468690	−	0.992601i	0.0274280	−	0.0580876i
$293$	−3.00083	+	3.00083i	−0.175310	+	0.175310i	−0.789308	−	0.613998i	$-0.789560\pi$
$293$	−3.00083	+	3.00083i	−0.175310	+	0.175310i	0.613998	+	0.789308i	$0.289560\pi$
$294$	−7.87238	+	11.1855i	−0.459126	+	0.652352i
$295$		−	30.2841i		−	1.76321i
$296$	−4.84832	−	8.53940i	−0.281803	−	0.496343i
$297$	14.8834	+	14.8834i	0.863621	+	0.863621i
$298$	2.00026	+	11.5059i	0.115872	+	0.666522i
$299$	7.72848	+	12.1216i	0.446950	+	0.701009i
$300$	−17.2578	+	6.18738i	−0.996380	+	0.357228i
$301$	0.638169	+	0.638169i	0.0367835	+	0.0367835i
$302$	−26.7831	+	4.65611i	−1.54119	+	0.267929i
$303$	−26.4463			−1.51930
$304$	−2.72077	+	27.9909i	−0.156047	+	1.60539i
$305$	25.4883	−	25.4883i	1.45946	−	1.45946i
$306$	3.79030	−	5.38547i	0.216677	−	0.307867i
$307$	−2.76089	−	2.76089i	−0.157572	−	0.157572i	0.623918	−	0.781490i	$-0.285540\pi$
$307$	−2.76089	−	2.76089i	−0.157572	−	0.157572i	−0.781490	+	0.623918i	$0.785540\pi$
$308$	0.451377	+	1.25898i	0.0257196	+	0.0717370i
$309$	18.5387			1.05463
$310$	4.22313	−	6.00046i	0.239858	−	0.340803i
$311$	−4.27897			−0.242638			−0.121319	−	0.992614i	$-0.538712\pi$
$311$	−4.27897			−0.242638			−0.121319	+	0.992614i	$0.538712\pi$
$312$	−13.5295	+	4.16402i	−0.765959	+	0.235741i
$313$	−3.68528			−0.208304			−0.104152	−	0.994561i	$-0.533213\pi$
$313$	−3.68528			−0.208304			−0.104152	+	0.994561i	$0.533213\pi$
$314$	−2.62498	+	3.72971i	−0.148136	+	0.210480i
$315$	−0.656698			−0.0370007
$316$	28.9575	−	10.3820i	1.62899	−	0.584035i
$317$	2.94735	+	2.94735i	0.165540	+	0.165540i	0.785016	−	0.619476i	$-0.212655\pi$
$317$	2.94735	+	2.94735i	0.165540	+	0.165540i	−0.619476	+	0.785016i	$0.712655\pi$
$318$	2.07801	−	2.95255i	0.116529	−	0.165571i
$319$	−12.0925	+	12.0925i	−0.677053	+	0.677053i
$320$	6.67221	+	26.4221i	0.372988	+	1.47704i
$321$	−2.47427			−0.138100
$322$	−0.997914	+	0.173483i	−0.0556116	+	0.00966782i
$323$	21.5716	+	21.5716i	1.20027	+	1.20027i
$324$	−3.12426	−	8.71416i	−0.173570	−	0.484120i
$325$	−20.0769	+	12.8006i	−1.11366	+	0.710051i
$326$	−4.20260	−	24.1744i	−0.232760	−	1.33889i
$327$	−14.3483	−	14.3483i	−0.793464	−	0.793464i
$328$	0.766454	+	1.34996i	0.0423204	+	0.0745393i
$329$			0.254943i			0.0140555i
$330$	−14.3277	+	20.3576i	−0.788716	+	1.12065i
$331$	8.72345	−	8.72345i	0.479484	−	0.479484i	−0.425482	−	0.904967i	$-0.639896\pi$
$331$	8.72345	−	8.72345i	0.479484	−	0.479484i	0.904967	+	0.425482i	$0.139896\pi$
$332$	−6.30462	−	2.97694i	−0.346011	−	0.163381i
$333$	2.63464	−	2.63464i	0.144377	−	0.144377i
$334$	15.2388	−	2.64919i	0.833829	−	0.144957i
$335$	20.2966			1.10892
$336$	0.0964932	−	0.992708i	0.00526413	−	0.0541566i
$337$		−	7.00939i		−	0.381826i	−0.981607	−	0.190913i	$-0.938855\pi$
$337$		−	7.00939i		−	0.381826i	0.981607	−	0.190913i	$-0.0611448\pi$
$338$	−15.9371	+	9.16560i	−0.866865	+	0.498543i
$339$	16.6275			0.903082
$340$	26.7315	+	12.6222i	1.44972	+	0.684533i
$341$		−	5.67023i		−	0.307060i
$342$	−10.5130	+	1.82764i	−0.568480	+	0.0988276i
$343$	−1.77417	−	1.77417i	−0.0957963	−	0.0957963i
$344$	13.6994	+	3.77702i	0.738623	+	0.203643i
$345$	−13.3310	−	13.3310i	−0.717717	−	0.717717i
$346$	15.2742	+	10.7500i	0.821148	+	0.577925i
$347$	−33.5948			−1.80346			−0.901730	−	0.432299i	$-0.857703\pi$
$347$	−33.5948			−1.80346			−0.901730	+	0.432299i	$0.857703\pi$
$348$	12.0049	−	4.30409i	0.643533	−	0.230723i
$349$	14.5137	−	14.5137i	0.776901	−	0.776901i	−0.202401	−	0.979303i	$-0.564875\pi$
$349$	14.5137	−	14.5137i	0.776901	−	0.776901i	0.979303	+	0.202401i	$0.0648745\pi$
$350$	−0.287338	−	1.65284i	−0.0153589	−	0.0883479i
$351$	−10.9595	−	17.1892i	−0.584973	−	0.917489i
$352$	15.9680	+	13.7297i	0.851097	+	0.731794i
$353$	−5.02174	+	5.02174i	−0.267280	+	0.267280i	−0.828003	−	0.560723i	$-0.810523\pi$
$353$	−5.02174	+	5.02174i	−0.267280	+	0.267280i	0.560723	+	0.828003i	$0.310523\pi$
$354$	2.98913	+	17.1942i	0.158870	+	0.913861i
$355$			12.5116i			0.664047i
$356$	13.7171	−	29.0504i	0.727005	−	1.53967i
$357$	−0.765044	−	0.765044i	−0.0404904	−	0.0404904i
$358$	−4.27067	+	6.06800i	−0.225712	+	0.320704i
$359$	−15.4781	+	15.4781i	−0.816903	+	0.816903i	−0.985658	−	0.168755i	$-0.946025\pi$
$359$	−15.4781	+	15.4781i	−0.816903	+	0.816903i	0.168755	+	0.985658i	$0.446025\pi$
$360$	−8.99192	+	5.10524i	−0.473916	+	0.269070i
$361$		−	30.4307i		−	1.60162i
$362$	−4.04425	−	2.84635i	−0.212561	−	0.149601i
$363$			3.96824i			0.208279i
$364$	−0.163357	−	1.28501i	−0.00856224	−	0.0673527i
$365$			1.86961i			0.0978599i
$366$	−11.9556	+	16.9871i	−0.624928	+	0.887931i
$367$		−	29.4166i		−	1.53553i	−0.640729	−	0.767767i	$-0.721368\pi$
$367$		−	29.4166i		−	1.53553i	0.640729	−	0.767767i	$-0.278632\pi$
$368$	−12.3154	+	10.1333i	−0.641984	+	0.528236i
$369$	−0.416501	+	0.416501i	−0.0216822	+	0.0216822i
$370$	13.6773	+	9.62614i	0.711051	+	0.500439i
$371$	0.233617	+	0.233617i	0.0121288	+	0.0121288i
$372$	−1.80548	+	3.82368i	−0.0936097	+	0.198248i
$373$		−	2.12493i		−	0.110025i	−0.998486	−	0.0550123i	$-0.982480\pi$
$373$		−	2.12493i		−	0.110025i	0.998486	−	0.0550123i	$-0.0175198\pi$
$374$	22.5066	−	3.91267i	1.16379	−	0.202319i
$375$	5.36244	−	5.36244i	0.276915	−	0.276915i
$376$	1.98196	+	3.49084i	0.102212	+	0.180026i
$377$	13.9660	−	8.90443i	0.719284	−	0.458601i
$378$	1.41510	−	0.246009i	0.0727851	−	0.0126534i
$379$	−9.31054	+	9.31054i	−0.478250	+	0.478250i	−0.904572	−	0.426321i	$-0.859809\pi$
$379$	−9.31054	+	9.31054i	−0.478250	+	0.478250i	0.426321	+	0.904572i	$0.359809\pi$
$380$	−16.1656	−	45.0890i	−0.829277	−	2.31302i
$381$	2.02832			0.103914
$382$	7.46805	−	10.6110i	0.382099	−	0.542907i
$383$	24.0746	+	24.0746i	1.23015	+	1.23015i	0.963904	+	0.266249i	$0.0857842\pi$
$383$	24.0746	+	24.0746i	1.23015	+	1.23015i	0.266249	+	0.963904i	$0.414216\pi$
$384$	−6.39618	−	14.3429i	−0.326403	−	0.731934i
$385$	−1.61077	−	1.61077i	−0.0820923	−	0.0820923i
$386$	0.0282902	+	0.162732i	0.00143993	+	0.00828282i
$387$			5.39195i			0.274088i
$388$	8.47539	+	4.00194i	0.430273	+	0.203168i
$389$	−20.8431			−1.05679			−0.528394	−	0.848999i	$-0.677206\pi$
$389$	−20.8431			−1.05679			−0.528394	+	0.848999i	$0.677206\pi$
$390$	17.8094	−	16.2524i	0.901813	−	0.822973i
$391$			17.3004i			0.874920i
$392$	−18.9989	−	5.23810i	−0.959587	−	0.264564i
$393$	5.21846			0.263236
$394$	2.96371	+	17.0480i	0.149310	+	0.858865i
$395$	−37.0490	+	37.0490i	−1.86414	+	1.86414i
$396$	−3.41175	+	7.22548i	−0.171447	+	0.363094i
$397$	16.7224	−	16.7224i	0.839273	−	0.839273i	−0.149490	−	0.988763i	$-0.547763\pi$
$397$	16.7224	−	16.7224i	0.839273	−	0.839273i	0.988763	+	0.149490i	$0.0477633\pi$
$398$	18.9129	+	13.3109i	0.948018	+	0.667217i
$399$			1.75308i			0.0877638i
$400$	−16.7838	−	20.3979i	−0.839188	−	1.01989i
$401$	−19.8319	−	19.8319i	−0.990359	−	0.990359i	0.00959526	−	0.999954i	$-0.496946\pi$
$401$	−19.8319	−	19.8319i	−0.990359	−	0.990359i	−0.999954	+	0.00959526i	$0.996946\pi$
$402$	−11.5237	+	2.00333i	−0.574747	+	0.0999172i
$403$	−1.18668	+	5.36200i	−0.0591129	+	0.267100i
$404$	−12.8599	−	35.8688i	−0.639804	−	1.78454i
$405$	11.1491	+	11.1491i	0.554003	+	0.554003i
$406$	0.199879	+	1.14975i	0.00991985	+	0.0570613i
$407$	12.9246			0.640650
$408$	−16.4230	−	4.52792i	−0.813060	−	0.224166i
$409$	−10.6165	+	10.6165i	−0.524954	+	0.524954i	−0.919064	−	0.394109i	$-0.871053\pi$
$409$	−10.6165	+	10.6165i	−0.524954	+	0.524954i	0.394109	+	0.919064i	$0.371053\pi$
$410$	−2.16220	−	1.52176i	−0.106784	−	0.0751545i
$411$	8.46374	+	8.46374i	0.417485	+	0.417485i
$412$	9.01472	+	25.1438i	0.444123	+	1.23875i
$413$	−1.59698			−0.0785821
$414$	−4.94862	−	3.48285i	−0.243212	−	0.171173i
$415$	11.8750			0.582923
$416$	−12.2266	−	16.3252i	−0.599457	−	0.800407i
$417$	26.8404			1.31438
$418$	−30.2696	−	21.3038i	−1.48053	−	1.04200i
$419$	19.6570			0.960308			0.480154	−	0.877184i	$-0.340581\pi$
$419$	19.6570			0.960308			0.480154	+	0.877184i	$0.340581\pi$
$420$	0.573319	+	1.59910i	0.0279751	+	0.0780281i
$421$	−2.77602	−	2.77602i	−0.135295	−	0.135295i	0.636216	−	0.771511i	$-0.280499\pi$
$421$	−2.77602	−	2.77602i	−0.135295	−	0.135295i	−0.771511	+	0.636216i	$0.780499\pi$
$422$	−14.7712	−	10.3960i	−0.719050	−	0.506069i
$423$	−1.07702	+	1.07702i	−0.0523665	+	0.0523665i
$424$	5.01499	+	1.38266i	0.243549	+	0.0671481i
$425$	−28.6546			−1.38995
$426$	−1.23493	−	7.10363i	−0.0598327	−	0.344172i
$427$	−1.34408	−	1.34408i	−0.0650447	−	0.0650447i
$428$	−1.20315	−	3.35582i	−0.0581565	−	0.162210i
$429$	4.02603	−	18.1915i	0.194379	−	0.878295i
$430$	−23.8460	+	4.14552i	−1.14996	+	0.199915i
$431$	24.6412	+	24.6412i	1.18692	+	1.18692i	0.977914	+	0.209009i	$0.0670238\pi$
$431$	24.6412	+	24.6412i	1.18692	+	1.18692i	0.209009	+	0.977914i	$0.432976\pi$
$432$	17.4640	−	14.3697i	0.840237	−	0.691362i
$433$		−	1.73076i		−	0.0831752i	−0.999135	−	0.0415876i	$-0.986758\pi$
$433$		−	1.73076i		−	0.0831752i	0.999135	−	0.0415876i	$-0.0132416\pi$
$434$	−0.316424	−	0.222700i	−0.0151888	−	0.0106899i
$435$	−15.3594	+	15.3594i	−0.736427	+	0.736427i
$436$	12.4834	−	26.4376i	0.597847	−	1.26613i
$437$	19.8218	−	19.8218i	0.948204	−	0.948204i
$438$	−0.184536	−	1.06150i	−0.00881748	−	0.0507203i
$439$	−25.0521			−1.19567			−0.597836	−	0.801618i	$-0.703973\pi$
$439$	−25.0521			−1.19567			−0.597836	+	0.801618i	$0.703973\pi$
$440$	−34.5779	−	9.53336i	−1.64844	−	0.454485i
$441$		−	7.47776i		−	0.356084i
$442$	−22.1020	−	1.01028i	−1.05128	−	0.0480539i
$443$	−11.4098			−0.542098			−0.271049	−	0.962566i	$-0.587370\pi$
$443$	−11.4098			−0.542098			−0.271049	+	0.962566i	$0.587370\pi$
$444$	−8.71563	−	4.11538i	−0.413625	−	0.195307i
$445$			54.7177i			2.59387i
$446$	−4.40119	−	25.3167i	−0.208403	−	1.19878i
$447$	8.10543	+	8.10543i	0.383374	+	0.383374i
$448$	1.39332	−	0.351847i	0.0658283	−	0.0166232i
$449$	−1.05015	−	1.05015i	−0.0495596	−	0.0495596i	0.681893	−	0.731452i	$-0.261157\pi$
$449$	−1.05015	−	1.05015i	−0.0495596	−	0.0495596i	−0.731452	+	0.681893i	$0.761157\pi$
$450$	5.76862	−	8.19637i	0.271935	−	0.386380i
$451$	−2.04321			−0.0962110
$452$	8.08539	+	22.5517i	0.380305	+	1.06074i
$453$	−18.8675	+	18.8675i	−0.886473	+	0.886473i
$454$	−20.2687	+	3.52362i	−0.951257	+	0.165372i
$455$	1.18610	+	1.86031i	0.0556052	+	0.0872128i
$456$	13.6286	+	24.0043i	0.638220	+	1.12410i
$457$	26.4630	−	26.4630i	1.23789	−	1.23789i	0.277025	−	0.960863i	$-0.410652\pi$
$457$	26.4630	−	26.4630i	1.23789	−	1.23789i	0.960863	−	0.277025i	$-0.0893484\pi$
$458$	−4.82075	+	0.838066i	−0.225259	+	0.0391602i
$459$		−	24.5331i		−	1.14511i
$460$	11.5983	−	24.5631i	0.540774	−	1.14526i
$461$	15.0134	+	15.0134i	0.699243	+	0.699243i	0.964247	−	0.265004i	$-0.0853734\pi$
$461$	15.0134	+	15.0134i	0.699243	+	0.699243i	−0.265004	+	0.964247i	$0.585373\pi$
$462$	1.07352	+	0.755547i	0.0499448	+	0.0351512i
$463$	−4.90869	+	4.90869i	−0.228126	+	0.228126i	−0.811909	−	0.583783i	$-0.801572\pi$
$463$	−4.90869	+	4.90869i	−0.228126	+	0.228126i	0.583783	+	0.811909i	$0.301572\pi$
$464$	11.6752	+	14.1893i	0.542007	+	0.658720i
$465$		−	7.20207i		−	0.333988i
$466$	5.18158	−	7.36227i	0.240032	−	0.341050i
$467$			15.5284i			0.718566i	0.933229	+	0.359283i	$0.116979\pi$
$467$			15.5284i			0.718566i	−0.933229	+	0.359283i	$0.883021\pi$
$468$	4.73846	−	6.11868i	0.219035	−	0.282836i
$469$		−	1.07030i		−	0.0494220i
$470$	−5.59119	−	3.93509i	−0.257902	−	0.181512i
$471$			4.47660i			0.206271i
$472$	−21.8668	+	12.4151i	−1.00650	+	0.571450i
$473$	−13.2255	+	13.2255i	−0.608111	+	0.608111i
$474$	17.3782	−	24.6919i	0.798207	−	1.13414i
$475$	32.8306	+	32.8306i	1.50637	+	1.50637i
$476$	0.665607	−	1.40964i	0.0305081	−	0.0646106i
$477$			1.97385i			0.0903764i
$478$	4.18585	+	24.0780i	0.191456	+	1.10130i
$479$	−13.9271	+	13.9271i	−0.636345	+	0.636345i	−0.949652	−	0.313307i	$-0.898563\pi$
$479$	−13.9271	+	13.9271i	−0.636345	+	0.636345i	0.313307	+	0.949652i	$0.398563\pi$
$480$	20.2818	+	17.4388i	0.925734	+	0.795970i
$481$	−12.2220	−	2.70491i	−0.557277	−	0.123333i
$482$	3.75958	+	21.6260i	0.171244	+	0.985037i
$483$	−0.702987	+	0.702987i	−0.0319870	+	0.0319870i
$484$	−5.38209	+	1.92962i	−0.244640	+	0.0877100i
$485$	−15.9638			−0.724878
$486$	12.1860	+	8.57650i	0.552767	+	0.389038i
$487$	−10.2416	−	10.2416i	−0.464092	−	0.464092i	0.435902	−	0.899994i	$-0.356429\pi$
$487$	−10.2416	−	10.2416i	−0.464092	−	0.464092i	−0.899994	+	0.435902i	$0.856429\pi$
$488$	−28.8531	−	7.95497i	−1.30612	−	0.360105i
$489$	−17.0298	−	17.0298i	−0.770113	−	0.770113i
$490$	33.0706	−	5.74917i	1.49398	−	0.259721i
$491$		−	38.4981i		−	1.73740i	−0.495341	−	0.868698i	$-0.664957\pi$
$491$		−	38.4981i		−	1.73740i	0.495341	−	0.868698i	$-0.335043\pi$
$492$	1.37782	+	0.650585i	0.0621170	+	0.0293306i
$493$	19.9328			0.897728
$494$	24.1656	+	26.4806i	1.08726	+	1.19142i
$495$		−	13.6095i		−	0.611703i
$496$	−6.06396	−	0.589429i	−0.272280	−	0.0264662i
$497$	0.659778			0.0295951
$498$	−6.74221	+	1.17210i	−0.302126	+	0.0525232i
$499$	7.83831	−	7.83831i	0.350891	−	0.350891i	−0.509550	−	0.860441i	$-0.670188\pi$
$499$	7.83831	−	7.83831i	0.350891	−	0.350891i	0.860441	+	0.509550i	$0.170188\pi$
$500$	9.88059	+	4.66545i	0.441873	+	0.208645i
$501$	10.7351	−	10.7351i	0.479607	−	0.479607i
$502$	−0.563404	+	0.800514i	−0.0251459	+	0.0357287i
$503$		−	30.2373i		−	1.34822i	−0.738633	−	0.674108i	$-0.764528\pi$
$503$		−	30.2373i		−	1.34822i	0.738633	−	0.674108i	$-0.235472\pi$
$504$	0.269216	+	0.474173i	0.0119918	+	0.0211213i
$505$	45.8914	+	45.8914i	2.04214	+	2.04214i
$506$	−3.59529	−	20.6810i	−0.159830	−	0.919381i
$507$	−7.61436	+	16.3600i	−0.338165	+	0.726575i
$508$	0.986304	+	2.75100i	0.0437602	+	0.122056i
$509$	8.49635	+	8.49635i	0.376594	+	0.376594i	0.869872	−	0.493278i	$-0.164201\pi$
$509$	8.49635	+	8.49635i	0.376594	+	0.376594i	−0.493278	+	0.869872i	$0.664201\pi$
$510$	28.5869	−	4.96970i	1.26585	−	0.220062i
$511$	0.0985906			0.00436139
$512$	16.3429	−	15.6495i	0.722263	−	0.691619i
$513$	−28.1085	+	28.1085i	−1.24102	+	1.24102i
$514$	−13.4807	+	19.1541i	−0.594609	+	0.844853i
$515$	−32.1696	−	32.1696i	−1.41756	−	1.41756i
$516$	13.1297	−	4.70735i	0.578004	−	0.207230i
$517$	−5.28349			−0.232368
$518$	0.507617	−	0.721251i	0.0223034	−	0.0316899i
$519$	18.3329			0.804727
$520$	30.7031	+	16.2517i	1.34642	+	0.712684i
$521$	22.8258			1.00002			0.500008	−	0.866021i	$-0.333330\pi$
$521$	22.8258			1.00002			0.500008	+	0.866021i	$0.333330\pi$
$522$	−4.01279	+	5.70159i	−0.175635	+	0.249552i
$523$	29.2368			1.27844			0.639219	−	0.769025i	$-0.279258\pi$
$523$	29.2368			1.27844			0.639219	+	0.769025i	$0.279258\pi$
$524$	2.53756	+	7.07774i	0.110854	+	0.309193i
$525$	−1.16435	−	1.16435i	−0.0508165	−	0.0508165i
$526$	−2.88803	+	4.10347i	−0.125924	+	0.178920i
$527$	−4.67328	+	4.67328i	−0.203571	+	0.203571i
$528$	20.5731	+	1.99974i	0.895327	+	0.0870276i
$529$	−7.10292			−0.308822
$530$	−8.72940	+	1.51757i	−0.379181	+	0.0659188i
$531$	−6.74650	−	6.74650i	−0.292773	−	0.292773i
$532$	−2.37769	+	0.852464i	−0.103086	+	0.0369590i
$533$	1.93214	+	0.427609i	0.0836903	+	0.0185218i
$534$	−5.40080	−	31.0667i	−0.233716	−	1.34439i
$535$	4.29352	+	4.29352i	0.185625	+	0.185625i
$536$	−8.32066	−	14.6553i	−0.359398	−	0.633011i
$537$			7.28313i			0.314290i
$538$	−10.2810	+	14.6078i	−0.443244	+	0.629785i
$539$	18.3417	−	18.3417i	0.790032	−	0.790032i
$540$	−16.4471	+	34.8321i	−0.707771	+	1.49893i
$541$	−4.53575	+	4.53575i	−0.195007	+	0.195007i	−0.797856	−	0.602849i	$-0.794032\pi$
$541$	−4.53575	+	4.53575i	−0.195007	+	0.195007i	0.602849	+	0.797856i	$0.294032\pi$
$542$	−29.6089	+	5.14737i	−1.27181	+	0.221099i
$543$	−4.85413			−0.208311
$544$	−1.84476	−	24.4761i	−0.0790935	−	1.04941i
$545$			49.7965i			2.13305i
$546$	−0.857043	−	0.939146i	−0.0366780	−	0.0401917i
$547$	−11.5183			−0.492488			−0.246244	−	0.969208i	$-0.579197\pi$
$547$	−11.5183			−0.492488			−0.246244	+	0.969208i	$0.579197\pi$
$548$	−7.36367	+	15.5949i	−0.314560	+	0.666182i
$549$		−	11.3563i		−	0.484674i
$550$	34.2537	−	5.95485i	1.46058	−	0.253916i
$551$	−22.8378	−	22.8378i	−0.972923	−	0.972923i
$552$	−4.16064	+	15.0908i	−0.177089	+	0.642309i
$553$	1.95371	+	1.95371i	0.0830803	+	0.0830803i
$554$	13.2346	+	9.31456i	0.562286	+	0.395738i
$555$	16.4163			0.696832
$556$	13.0516	+	36.4034i	0.553510	+	1.54385i
$557$	−21.7184	+	21.7184i	−0.920237	+	0.920237i	−0.997046	−	0.0768092i	$-0.975527\pi$
$557$	−21.7184	+	21.7184i	−0.920237	+	0.920237i	0.0768092	+	0.997046i	$0.475527\pi$
$558$	−0.395942	−	2.27755i	−0.0167615	−	0.0964164i
$559$	15.2745	−	9.73871i	0.646042	−	0.411904i
$560$	−1.89006	+	1.55517i	−0.0798695	+	0.0657181i
$561$	15.8549	−	15.8549i	0.669395	−	0.669395i
$562$	0.242971	+	1.39763i	0.0102491	+	0.0589554i
$563$		−	22.2920i		−	0.939494i	−0.882801	−	0.469747i	$-0.844345\pi$
$563$		−	22.2920i		−	0.939494i	0.882801	−	0.469747i	$-0.155655\pi$
$564$	3.56288	+	1.68233i	0.150024	+	0.0708390i
$565$	−28.8532	−	28.8532i	−1.21386	−	1.21386i
$566$	3.35725	−	4.77016i	0.141116	−	0.200505i
$567$	0.587928	−	0.587928i	0.0246907	−	0.0246907i
$568$	9.03409	−	5.12918i	0.379062	−	0.215216i
$569$			9.56035i			0.400791i	0.979715	+	0.200395i	$0.0642226\pi$
$569$			9.56035i			0.400791i	−0.979715	+	0.200395i	$0.935777\pi$
$570$	−38.4471	−	27.0591i	−1.61037	−	1.13338i
$571$		−	13.1869i		−	0.551854i	−0.961179	−	0.275927i	$-0.911015\pi$
$571$		−	13.1869i		−	0.551854i	0.961179	−	0.275927i	$-0.0889848\pi$
$572$	26.6307	−	3.38544i	1.11349	−	0.141552i
$573$		−	12.7359i		−	0.532050i
$574$	−0.0802475	+	0.114020i	−0.00334946	+	0.00475910i
$575$			26.3302i			1.09805i
$576$	7.37255	+	4.39976i	0.307189	+	0.183323i
$577$	21.0017	−	21.0017i	0.874313	−	0.874313i	−0.118626	−	0.992939i	$-0.537849\pi$
$577$	21.0017	−	21.0017i	0.874313	−	0.874313i	0.992939	+	0.118626i	$0.0378489\pi$
$578$	−2.11367	−	1.48760i	−0.0879170	−	0.0618762i
$579$	0.114637	+	0.114637i	0.00476416	+	0.00476416i
$580$	−28.3006	−	13.3631i	−1.17512	−	0.554871i
$581$		−	0.626209i		−	0.0259795i
$582$	9.06366	−	1.57567i	0.375701	−	0.0653138i
$583$	−4.84152	+	4.84152i	−0.200515	+	0.200515i
$584$	1.34996	−	0.766454i	0.0558619	−	0.0317161i
$585$	−2.84824	+	12.8697i	−0.117760	+	0.532097i
$586$	−5.91297	+	1.02794i	−0.244263	+	0.0424639i
$587$	17.6365	−	17.6365i	0.727938	−	0.727938i	−0.242271	−	0.970209i	$-0.577892\pi$
$587$	17.6365	−	17.6365i	0.727938	−	0.727938i	0.970209	+	0.242271i	$0.0778922\pi$
$588$	−18.2088	+	6.52833i	−0.750918	+	0.269224i
$589$	10.7087			0.441245
$590$	24.6496	−	35.0235i	1.01481	−	1.44190i
$591$	12.0096	+	12.0096i	0.494007	+	0.494007i
$592$	1.34353	−	13.8221i	0.0552189	−	0.568084i
$593$	−8.59997	−	8.59997i	−0.353158	−	0.353158i	0.508125	−	0.861283i	$-0.330339\pi$
$593$	−8.59997	−	8.59997i	−0.353158	−	0.353158i	−0.861283	+	0.508125i	$0.830339\pi$
$594$	5.09834	+	29.3269i	0.209188	+	1.20330i
$595$			2.65512i			0.108849i
$596$	−7.05193	+	14.9347i	−0.288858	+	0.611750i
$597$	22.7003			0.929061
$598$	−0.928327	+	20.3092i	−0.0379621	+	0.830504i
$599$		−	30.9851i		−	1.26602i	−0.774145	−	0.633009i	$-0.781820\pi$
$599$		−	30.9851i		−	1.26602i	0.774145	−	0.633009i	$-0.218180\pi$
$600$	−24.9948	−	6.89123i	−1.02041	−	0.281333i
$601$	−27.5087			−1.12210			−0.561052	−	0.827781i	$-0.689603\pi$
$601$	−27.5087			−1.12210			−0.561052	+	0.827781i	$0.689603\pi$
$602$	0.218607	+	1.25748i	0.00890975	+	0.0512510i
$603$	4.52155	−	4.52155i	0.184132	−	0.184132i
$604$	−34.7644	−	16.4152i	−1.41455	−	0.667925i
$605$	6.88597	−	6.88597i	0.279954	−	0.279954i
$606$	−30.5851	−	21.5258i	−1.24243	−	0.874427i
$607$			24.3086i			0.986655i	0.869844	+	0.493328i	$0.164220\pi$
$607$			24.3086i			0.986655i	−0.869844	+	0.493328i	$0.835780\pi$
$608$	−25.9296	+	30.1569i	−1.05159	+	1.22302i
$609$	0.809951	+	0.809951i	0.0328209	+	0.0328209i
$610$	50.2234	−	8.73111i	2.03349	−	0.353512i
$611$	4.99628	+	1.10574i	0.202128	+	0.0447336i
$612$	8.76697	−	3.14319i	0.354384	−	0.127056i
$613$	−18.8428	−	18.8428i	−0.761053	−	0.761053i	0.215460	−	0.976513i	$-0.430875\pi$
$613$	−18.8428	−	18.8428i	−0.761053	−	0.761053i	−0.976513	+	0.215460i	$0.930875\pi$
$614$	−0.945751	−	5.44018i	−0.0381674	−	0.219548i
$615$	−2.59519			−0.104648
$616$	−0.502725	+	1.82341i	−0.0202553	+	0.0734671i
$617$	−17.2326	+	17.2326i	−0.693759	+	0.693759i	−0.963057	−	0.269298i	$-0.913208\pi$
$617$	−17.2326	+	17.2326i	−0.693759	+	0.693759i	0.269298	+	0.963057i	$0.413208\pi$
$618$	21.4400	+	15.0895i	0.862441	+	0.606988i
$619$	3.52674	+	3.52674i	0.141752	+	0.141752i	0.774422	−	0.632670i	$-0.218041\pi$
$619$	3.52674	+	3.52674i	0.141752	+	0.141752i	−0.632670	+	0.774422i	$0.718041\pi$
$620$	9.76811	−	3.50212i	0.392297	−	0.140649i
$621$	−22.5431			−0.904622
$622$	−4.94862	−	3.48285i	−0.198422	−	0.139650i
$623$	2.88544			0.115603
$624$	−19.0362	−	6.19663i	−0.762057	−	0.248064i
$625$	14.4086			0.576344
$626$	−4.26202	−	2.99962i	−0.170345	−	0.119889i
$627$	−36.3312			−1.45093
$628$	−6.07157	+	2.17682i	−0.242282	+	0.0868644i
$629$	−10.6522	−	10.6522i	−0.424730	−	0.424730i
$630$	−0.759471	−	0.534517i	−0.0302580	−	0.0212957i
$631$	6.65131	−	6.65131i	0.264784	−	0.264784i	−0.562210	−	0.826994i	$-0.690049\pi$
$631$	6.65131	−	6.65131i	0.264784	−	0.264784i	0.826994	+	0.562210i	$0.190049\pi$
$632$	41.9398	+	11.5631i	1.66828	+	0.459954i
$633$	−17.7292			−0.704671
$634$	1.00962	+	5.80759i	0.0400973	+	0.230649i
$635$	−3.51969	−	3.51969i	−0.139675	−	0.139675i
$636$	4.80644	−	1.72324i	0.190588	−	0.0683308i
$637$	−21.1832	+	13.5060i	−0.839309	+	0.535128i
$638$	−23.8277	+	4.14234i	−0.943348	+	0.163997i
$639$	2.78726	+	2.78726i	0.110262	+	0.110262i
$640$	−13.7898	+	35.9880i	−0.545088	+	1.42255i
$641$			27.4814i			1.08545i	0.839910	+	0.542725i	$0.182607\pi$
$641$			27.4814i			1.08545i	−0.839910	+	0.542725i	$0.817393\pi$
$642$	−2.86149	−	2.01392i	−0.112934	−	0.0794831i
$643$	−8.78571	+	8.78571i	−0.346475	+	0.346475i	−0.858795	−	0.512320i	$-0.828786\pi$
$643$	−8.78571	+	8.78571i	−0.346475	+	0.346475i	0.512320	+	0.858795i	$0.328786\pi$
$644$	−1.29529	−	0.611616i	−0.0510417	−	0.0241011i
$645$	−16.7985	+	16.7985i	−0.661440	+	0.661440i
$646$	7.38940	+	42.5056i	0.290732	+	1.67236i
$647$	5.55484			0.218383			0.109192	−	0.994021i	$-0.465174\pi$
$647$	5.55484			0.218383			0.109192	+	0.994021i	$0.465174\pi$
$648$	3.47966	−	12.6209i	0.136694	−	0.495796i
$649$		−	33.0960i		−	1.29913i
$650$	−33.6379	−	1.53758i	−1.31939	−	0.0603089i
$651$	−0.379789			−0.0148851
$652$	14.8163	−	31.3783i	0.580252	−	1.22887i
$653$		−	20.7670i		−	0.812675i	−0.913723	−	0.406338i	$-0.866806\pi$
$653$		−	20.7670i		−	0.812675i	0.913723	−	0.406338i	$-0.133194\pi$
$654$	−4.91506	−	28.2726i	−0.192194	−	1.10555i
$655$	−9.05543	−	9.05543i	−0.353825	−	0.353825i
$656$	−0.212395	+	2.18509i	−0.00829262	+	0.0853133i
$657$	0.416501	+	0.416501i	0.0162492	+	0.0162492i
$658$	−0.207510	+	0.294842i	−0.00808958	+	0.0114941i
$659$	−42.9802			−1.67427			−0.837135	−	0.546997i	$-0.815771\pi$
$659$	−42.9802			−1.67427			−0.837135	+	0.546997i	$0.815771\pi$
$660$	−33.1400	+	11.8816i	−1.28997	+	0.462489i
$661$	24.6988	−	24.6988i	0.960674	−	0.960674i	−0.0385817	−	0.999255i	$-0.512284\pi$
$661$	24.6988	−	24.6988i	0.960674	−	0.960674i	0.999255	+	0.0385817i	$0.0122840\pi$
$662$	17.1891	−	2.98824i	0.668073	−	0.116141i
$663$	−18.3112	+	11.6749i	−0.711148	+	0.453414i
$664$	−4.86822	−	8.57445i	−0.188924	−	0.332753i
$665$	3.04207	−	3.04207i	0.117966	−	0.117966i
$666$	5.19141	−	0.902503i	0.201163	−	0.0349713i
$667$		−	18.3159i		−	0.709196i
$668$	19.7799	+	9.33977i	0.765309	+	0.361366i
$669$	−17.8345	−	17.8345i	−0.689522	−	0.689522i
$670$	23.4730	+	16.5203i	0.906840	+	0.638236i
$671$	27.8550	−	27.8550i	1.07533	−	1.07533i
$672$	0.919605	−	1.06953i	0.0354745	−	0.0412578i
$673$		−	0.630317i		−	0.0242969i	−0.999926	−	0.0121485i	$-0.996133\pi$
$673$		−	0.630317i		−	0.0242969i	0.999926	−	0.0121485i	$-0.00386707\pi$
$674$	5.70527	−	8.10635i	0.219759	−	0.312245i
$675$		−	37.3379i		−	1.43714i
$676$	−25.8916	−	2.37195i	−0.995830	−	0.0912289i
$677$			19.4398i			0.747132i	0.927604	+	0.373566i	$0.121865\pi$
$677$			19.4398i			0.747132i	−0.927604	+	0.373566i	$0.878135\pi$
$678$	19.2297	+	13.5339i	0.738512	+	0.519766i
$679$			0.841822i			0.0323062i
$680$	20.6412	+	36.3555i	0.791553	+	1.39417i
$681$	−14.2784	+	14.2784i	−0.547150	+	0.547150i
$682$	4.61527	−	6.55762i	0.176728	−	0.251104i
$683$	23.5885	+	23.5885i	0.902590	+	0.902590i	0.995660	−	0.0930695i	$-0.0296679\pi$
$683$	23.5885	+	23.5885i	0.902590	+	0.902590i	−0.0930695	+	0.995660i	$0.529668\pi$
$684$	−13.6459	−	6.44338i	−0.521765	−	0.246369i
$685$		−	29.3738i		−	1.12231i
$686$	−0.607748	−	3.49591i	−0.0232039	−	0.133475i
$687$	−3.39601	+	3.39601i	−0.129566	+	0.129566i
$688$	12.7691	+	15.5187i	0.486817	+	0.591645i
$689$	5.59158	−	3.56508i	0.213022	−	0.135819i
$690$	−4.56657	−	26.2680i	−0.173847	−	1.00001i
$691$	10.6764	−	10.6764i	0.406149	−	0.406149i	−0.474244	−	0.880393i	$-0.657279\pi$
$691$	10.6764	−	10.6764i	0.406149	−	0.406149i	0.880393	+	0.474244i	$0.157279\pi$
$692$	8.91469	+	24.8648i	0.338886	+	0.945218i
$693$	−0.717674			−0.0272622
$694$	−38.8523	−	27.3443i	−1.47481	−	1.03798i
$695$	−46.5754	−	46.5754i	−1.76670	−	1.76670i
$696$	17.3870	+	4.79371i	0.659053	+	0.181705i
$697$	1.68397	+	1.68397i	0.0637848	+	0.0637848i
$698$	28.5985	−	4.97172i	1.08247	−	0.188182i
$699$		−	8.83659i		−	0.334230i
$700$	1.01302	−	2.14538i	0.0382884	−	0.0810879i
$701$	28.6855			1.08344			0.541718	−	0.840560i	$-0.317774\pi$
$701$	28.6855			1.08344			0.541718	+	0.840560i	$0.317774\pi$
$702$	1.31643	−	28.7997i	0.0496853	−	1.08697i
$703$			24.4092i			0.920612i
$704$	7.29174	+	28.8755i	0.274818	+	1.08828i
$705$	−6.71085			−0.252745
$706$	−9.89507	+	1.72021i	−0.372406	+	0.0647410i
$707$	2.42000	−	2.42000i	0.0910135	−	0.0910135i
$708$	−10.5382	+	22.3181i	−0.396051	+	0.838764i
$709$	−32.5813	+	32.5813i	−1.22362	+	1.22362i	−0.257279	+	0.966337i	$0.582826\pi$
$709$	−32.5813	+	32.5813i	−1.22362	+	1.22362i	−0.966337	+	0.257279i	$0.917174\pi$
$710$	−10.1838	+	14.4697i	−0.382191	+	0.543037i
$711$			16.5071i			0.619064i
$712$	39.5093	−	22.4317i	1.48067	−	0.840665i
$713$	4.29420	+	4.29420i	0.160819	+	0.160819i
$714$	−0.262068	−	1.50748i	−0.00980765	−	0.0564159i
$715$	−38.5535	+	24.5809i	−1.44182	+	0.919275i
$716$	−9.87805	+	3.54154i	−0.369160	+	0.132354i
$717$	16.9619	+	16.9619i	0.633454	+	0.633454i
$718$	−30.4988	+	5.30207i	−1.13820	+	0.197872i
$719$	13.6202			0.507948			0.253974	−	0.967211i	$-0.418262\pi$
$719$	13.6202			0.507948			0.253974	+	0.967211i	$0.418262\pi$
$720$	−14.5545	−	1.41473i	−0.542416	−	0.0527239i
$721$	−1.69641	+	1.69641i	−0.0631775	+	0.0631775i
$722$	24.7690	−	35.1931i	0.921807	−	1.30975i
$723$	15.2346	+	15.2346i	0.566580	+	0.566580i
$724$	−2.36040	−	6.58361i	−0.0877234	−	0.244678i
$725$	30.3366			1.12667
$726$	−3.22994	+	4.58927i	−0.119874	+	0.170324i
$727$	−6.72700			−0.249491			−0.124745	−	0.992189i	$-0.539811\pi$
$727$	−6.72700			−0.249491			−0.124745	+	0.992189i	$0.539811\pi$
$728$	0.857004	−	1.61907i	0.0317627	−	0.0600069i
$729$	28.5122			1.05601
$730$	−1.52176	+	2.16220i	−0.0563230	+	0.0800267i
$731$	21.8004			0.806316
$732$	−27.6532	+	9.91441i	−1.02209	+	0.366447i
$733$	14.0245	+	14.0245i	0.518008	+	0.518008i	0.916968	−	0.398961i	$-0.130629\pi$
$733$	14.0245	+	14.0245i	0.518008	+	0.518008i	−0.398961	+	0.916968i	$0.630629\pi$
$734$	23.9435	−	34.0203i	0.883772	−	1.25571i
$735$	23.2968	−	23.2968i	0.859314	−	0.859314i
$736$	−22.4907	+	1.69512i	−0.829020	+	0.0624830i
$737$	22.1812			0.817054
$738$	−0.820692	+	0.142673i	−0.0302101	+	0.00525188i
$739$	23.8579	+	23.8579i	0.877627	+	0.877627i	0.993289	−	0.115661i	$-0.0368987\pi$
$739$	23.8579	+	23.8579i	0.877627	+	0.877627i	−0.115661	+	0.993289i	$0.536899\pi$
$740$	7.98268	+	22.2653i	0.293449	+	0.818487i
$741$	34.3562	+	7.60350i	1.26211	+	0.279322i
$742$	0.0800261	+	0.460329i	0.00293785	+	0.0168992i
$743$	−17.6669	−	17.6669i	−0.648137	−	0.648137i	0.304406	−	0.952542i	$-0.401542\pi$
$743$	−17.6669	−	17.6669i	−0.648137	−	0.648137i	−0.952542	+	0.304406i	$0.901542\pi$
$744$	−5.20030	+	2.95252i	−0.190652	+	0.108245i
$745$		−	28.1302i		−	1.03061i
$746$	1.72958	−	2.45748i	0.0633243	−	0.0899747i
$747$	2.64545	−	2.64545i	0.0967920	−	0.0967920i
$748$	29.2136	+	13.7942i	1.06815	+	0.504365i
$749$	0.226411	−	0.226411i	0.00827289	−	0.00827289i
$750$	10.5664	−	1.83692i	0.385830	−	0.0670748i
$751$	21.8413			0.797002			0.398501	−	0.917168i	$-0.369531\pi$
$751$	21.8413			0.797002			0.398501	+	0.917168i	$0.369531\pi$
$752$	−0.549227	+	5.65036i	−0.0200282	+	0.206048i
$753$			0.960820i			0.0350142i
$754$	23.3994	+	1.06958i	0.852154	+	0.0389517i
$755$	65.4804			2.38308
$756$	1.83681	+	0.867310i	0.0668040	+	0.0315438i
$757$			4.18475i			0.152097i	0.997104	+	0.0760486i	$0.0242304\pi$
$757$			4.18475i			0.152097i	−0.997104	+	0.0760486i	$0.975770\pi$
$758$	−18.3459	+	3.18935i	−0.666354	+	0.115843i
$759$	−14.5688	−	14.5688i	−0.528815	−	0.528815i
$760$	18.0045	−	65.3033i	0.653093	−	2.36880i
$761$	7.52046	+	7.52046i	0.272617	+	0.272617i	0.830153	−	0.557536i	$-0.188253\pi$
$761$	7.52046	+	7.52046i	0.272617	+	0.272617i	−0.557536	+	0.830153i	$0.688253\pi$
$762$	2.34575	+	1.65095i	0.0849777	+	0.0598075i
$763$	2.62593			0.0950650
$764$	17.2736	−	6.19304i	0.624937	−	0.224056i
$765$	−11.2167	+	11.2167i	−0.405539	+	0.405539i
$766$	8.24681	+	47.4376i	0.297970	+	1.71399i
$767$	−6.92644	+	31.2969i	−0.250099	+	1.13007i
$768$	4.27720	−	21.7937i	0.154340	−	0.786414i
$769$	−9.42965	+	9.42965i	−0.340042	+	0.340042i	−0.856383	−	0.516341i	$-0.827294\pi$
$769$	−9.42965	+	9.42965i	−0.340042	+	0.340042i	0.516341	+	0.856383i	$0.327294\pi$
$770$	−0.551773	−	3.17393i	−0.0198845	−	0.114381i
$771$			22.9898i			0.827959i
$772$	−0.0997373	+	0.211226i	−0.00358963	+	0.00760218i
$773$	22.5741	+	22.5741i	0.811933	+	0.811933i	0.984924	−	0.172990i	$-0.0553429\pi$
$773$	22.5741	+	22.5741i	0.811933	+	0.811933i	−0.172990	+	0.984924i	$0.555343\pi$
$774$	−4.38876	+	6.23579i	−0.157751	+	0.224141i
$775$	−7.11245	+	7.11245i	−0.255487	+	0.255487i
$776$	6.54442	+	11.5268i	0.234931	+	0.413786i
$777$		−	0.865684i		−	0.0310562i
$778$	−24.1051	−	16.9652i	−0.864208	−	0.608231i
$779$		−	3.85877i		−	0.138255i
$780$	33.8251	−	4.30004i	1.21113	−	0.153966i
$781$			13.6733i			0.489271i
$782$	−14.0816	+	20.0079i	−0.503558	+	0.715482i
$783$			25.9731i			0.928204i
$784$	−17.7086	−	21.5219i	−0.632451	−	0.768640i
$785$	7.76811	−	7.76811i	0.277256	−	0.277256i
$786$	6.03514	+	4.24754i	0.215266	+	0.151505i
$787$	−28.3997	−	28.3997i	−1.01234	−	1.01234i	−0.999923	−	0.0124163i	$-0.996048\pi$
$787$	−28.3997	−	28.3997i	−1.01234	−	1.01234i	−0.0124163	−	0.999923i	$-0.503952\pi$
$788$	−10.4486	+	22.1283i	−0.372217	+	0.788288i
$789$			4.92521i			0.175342i
$790$	−73.0030	+	12.6912i	−2.59733	+	0.451534i
$791$	−1.52152	+	1.52152i	−0.0540992	+	0.0540992i
$792$	−9.82685	+	5.57928i	−0.349182	+	0.198251i
$793$	−32.1704	+	20.5112i	−1.14240	+	0.728375i
$794$	32.9506	−	5.72830i	1.16937	−	0.203290i
$795$	−6.14948	+	6.14948i	−0.218099	+	0.218099i
$796$	11.0384	+	30.7882i	0.391245	+	1.09126i
$797$	−49.1622			−1.74142			−0.870708	−	0.491800i	$-0.836339\pi$
$797$	−49.1622			−1.74142			−0.870708	+	0.491800i	$0.836339\pi$
$798$	−1.42691	+	2.02744i	−0.0505122	+	0.0717705i
$799$	4.35453	+	4.35453i	0.154052	+	0.154052i
$800$	−2.80762	−	37.2512i	−0.0992643	−	1.31703i
$801$	12.1897	+	12.1897i	0.430701	+	0.430701i
$802$	−6.79348	−	39.0777i	−0.239886	−	1.37988i
$803$			2.04321i			0.0721033i
$804$	−14.9577	−	7.06278i	−0.527517	−	0.249085i
$805$	2.43974			0.0859897
$806$	−5.73678	+	5.23525i	−0.202069	+	0.184404i
$807$			17.5330i			0.617192i
$808$	14.3228	−	51.9495i	0.503875	−	1.82758i
$809$	11.8224			0.415652			0.207826	−	0.978166i	$-0.433361\pi$
$809$	11.8224			0.415652			0.207826	+	0.978166i	$0.433361\pi$
$810$	3.81916	+	21.9687i	0.134192	+	0.771902i
$811$	−24.6297	+	24.6297i	−0.864866	+	0.864866i	−0.991899	−	0.127033i	$-0.959455\pi$
$811$	−24.6297	+	24.6297i	−0.864866	+	0.864866i	0.127033	+	0.991899i	$0.459455\pi$
$812$	−0.704678	+	1.49238i	−0.0247293	+	0.0523723i
$813$	−20.8582	+	20.8582i	−0.731528	+	0.731528i
$814$	14.9473	+	10.5200i	0.523904	+	0.368724i
$815$			59.1025i			2.07027i
$816$	−15.3077	−	18.6040i	−0.535877	−	0.651270i
$817$	−24.9775	−	24.9775i	−0.873853	−	0.873853i
$818$	−20.9193	+	3.63673i	−0.731427	+	0.127155i
$819$	0.678661	+	0.150197i	0.0237144	+	0.00524831i
$820$	−1.26195	−	3.51984i	−0.0440693	−	0.122918i
$821$	−25.0256	−	25.0256i	−0.873400	−	0.873400i	0.119441	−	0.992841i	$-0.461890\pi$
$821$	−25.0256	−	25.0256i	−0.873400	−	0.873400i	−0.992841	+	0.119441i	$0.961890\pi$
$822$	2.89928	+	16.6773i	0.101124	+	0.581689i
$823$	32.0560			1.11740			0.558702	−	0.829369i	$-0.311300\pi$
$823$	32.0560			1.11740			0.558702	+	0.829369i	$0.311300\pi$
$824$	−10.0402	+	36.4163i	−0.349767	+	1.26862i
$825$	24.1302	−	24.1302i	0.840107	−	0.840107i
$826$	−1.84690	−	1.29985i	−0.0642620	−	0.0452277i
$827$	−12.2989	−	12.2989i	−0.427674	−	0.427674i	0.460162	−	0.887835i	$-0.347792\pi$
$827$	−12.2989	−	12.2989i	−0.427674	−	0.427674i	−0.887835	+	0.460162i	$0.847792\pi$
$828$	−2.88823	−	8.05583i	−0.100373	−	0.279959i
$829$	44.2580			1.53714			0.768572	−	0.639763i	$-0.220967\pi$
$829$	44.2580			1.53714			0.768572	+	0.639763i	$0.220967\pi$
$830$	13.7335	+	9.66565i	0.476696	+	0.335500i
$831$	15.8849			0.551042
$832$	−0.852217	−	28.8318i	−0.0295453	−	0.999563i
$833$	−30.2336			−1.04753
$834$	31.0409	+	21.8467i	1.07486	+	0.756488i
$835$	−37.2564			−1.28931
$836$	−17.6666	−	49.2756i	−0.611012	−	1.70423i
$837$	−6.08944	−	6.08944i	−0.210482	−	0.210482i
$838$	22.7333	+	15.9998i	0.785310	+	0.552702i
$839$	11.5850	−	11.5850i	0.399960	−	0.399960i	−0.478259	−	0.878219i	$-0.658732\pi$
$839$	11.5850	−	11.5850i	0.399960	−	0.399960i	0.878219	+	0.478259i	$0.158732\pi$
$840$	−0.638538	+	2.31601i	−0.0220317	+	0.0799099i
$841$	7.89716			0.272316
$842$	−0.950934	−	5.47000i	−0.0327713	−	0.188509i
$843$	0.984567	+	0.984567i	0.0339103	+	0.0339103i
$844$	−8.62109	−	24.0459i	−0.296750	−	0.827694i
$845$	41.6021	−	15.1761i	1.43115	−	0.522075i
$846$	−2.12221	+	0.368936i	−0.0729630	+	0.0126843i
$847$	−0.363119	−	0.363119i	−0.0124769	−	0.0124769i
$848$	4.67442	+	5.68098i	0.160520	+	0.195086i
$849$		−	5.72541i		−	0.196495i
$850$	−33.1390	−	23.3233i	−1.13666	−	0.799982i
$851$	−9.78812	+	9.78812i	−0.335533	+	0.335533i
$852$	4.35378	−	9.22052i	0.149158	−	0.315890i
$853$	15.7316	−	15.7316i	0.538640	−	0.538640i	−0.384490	−	0.923129i	$-0.625623\pi$
$853$	15.7316	−	15.7316i	0.538640	−	0.538640i	0.923129	+	0.384490i	$0.125623\pi$
$854$	−0.460419	−	2.64844i	−0.0157552	−	0.0906278i
$855$	25.7027			0.879015
$856$	1.34002	−	4.86031i	0.0458009	−	0.166122i
$857$			5.28481i			0.180526i	0.995918	+	0.0902628i	$0.0287707\pi$
$857$			5.28481i			0.180526i	−0.995918	+	0.0902628i	$0.971229\pi$
$858$	19.4630	−	17.7615i	0.664457	−	0.606368i
$859$	−25.4764			−0.869242			−0.434621	−	0.900613i	$-0.643118\pi$
$859$	−25.4764			−0.869242			−0.434621	+	0.900613i	$0.643118\pi$
$860$	−30.9522	−	14.6151i	−1.05546	−	0.498371i
$861$			0.136853i			0.00466393i
$862$	8.44090	+	48.5541i	0.287498	+	1.65376i
$863$	12.9386	+	12.9386i	0.440434	+	0.440434i	0.892158	−	0.451724i	$-0.149191\pi$
$863$	12.9386	+	12.9386i	0.440434	+	0.440434i	−0.451724	+	0.892158i	$0.649191\pi$
$864$	31.8933	−	2.40379i	1.08503	−	0.0817785i
$865$	−31.8126	−	31.8126i	−1.08166	−	1.08166i
$866$	1.40875	−	2.00163i	0.0478712	−	0.0680181i
$867$	−2.53694			−0.0861589
$868$	−0.184678	−	0.515104i	−0.00626839	−	0.0174838i
$869$	−40.4891	+	40.4891i	−1.37350	+	1.37350i
$870$	−30.2649	+	5.26141i	−1.02608	+	0.178379i
$871$	−20.9754	−	4.64214i	−0.710724	−	0.157293i
$872$	35.9559	−	20.4143i	1.21762	−	0.691314i
$873$	−3.55632	+	3.55632i	−0.120363	+	0.120363i
$874$	39.0577	−	6.79000i	1.32115	−	0.229675i
$875$			0.981394i			0.0331772i
$876$	0.650585	−	1.37782i	0.0219812	−	0.0465523i
$877$	16.5941	+	16.5941i	0.560342	+	0.560342i	0.929404	−	0.369063i	$-0.120321\pi$
$877$	16.5941	+	16.5941i	0.560342	+	0.560342i	−0.369063	+	0.929404i	$0.620321\pi$
$878$	−28.9728	−	20.3911i	−0.977783	−	0.688166i
$879$	−4.16543	+	4.16543i	−0.140496	+	0.140496i
$880$	−32.2297	−	39.1699i	−1.08646	−	1.32042i
$881$		−	2.69158i		−	0.0906818i	−0.998972	−	0.0453409i	$-0.985563\pi$
$881$		−	2.69158i		−	0.0906818i	0.998972	−	0.0453409i	$-0.0144374\pi$
$882$	6.08650	−	8.64803i	0.204943	−	0.291194i
$883$			48.9980i			1.64892i	0.565924	+	0.824458i	$0.308520\pi$
$883$			48.9980i			1.64892i	−0.565924	+	0.824458i	$0.691480\pi$
$884$	−24.7386	−	19.1582i	−0.832050	−	0.644361i
$885$		−	42.0371i		−	1.41306i
$886$	−13.1955	−	9.28699i	−0.443310	−	0.312003i
$887$		−	18.5664i		−	0.623399i	−0.950181	−	0.311699i	$-0.899102\pi$
$887$		−	18.5664i		−	0.623399i	0.950181	−	0.311699i	$-0.100898\pi$
$888$	−6.72992	−	11.8535i	−0.225841	−	0.397777i
$889$	−0.185605	+	0.185605i	−0.00622498	+	0.00622498i
$890$	−44.5373	+	63.2810i	−1.49289	+	2.12118i
$891$	12.1843	+	12.1843i	0.408190	+	0.408190i
$892$	15.5165	−	32.8611i	0.519530	−	1.10027i
$893$		−	9.97831i		−	0.333911i
$894$	2.77654	+	15.9713i	0.0928614	+	0.534161i
$895$	12.6382	−	12.6382i	0.422449	−	0.422449i
$896$	1.89776	+	0.727179i	0.0633997	+	0.0242933i
$897$	10.7279	+	16.8259i	0.358193	+	0.561800i
$898$	−0.359732	−	2.06926i	−0.0120044	−	0.0690522i
$899$	4.94759	−	4.94759i	0.165011	−	0.165011i
$900$	13.3428	−	4.78375i	0.444760	−	0.159458i
$901$	7.98054			0.265870
$902$	−2.36297	−	1.66306i	−0.0786783	−	0.0553739i
$903$	0.885838	+	0.885838i	0.0294789	+	0.0294789i
$904$	−9.00516	+	32.6622i	−0.299507	+	1.08633i
$905$	8.42322	+	8.42322i	0.279997	+	0.279997i
$906$	−37.1774	+	6.46312i	−1.23514	+	0.214723i
$907$			4.12839i			0.137081i	0.997648	+	0.0685404i	$0.0218342\pi$
$907$			4.12839i			0.137081i	−0.997648	+	0.0685404i	$0.978166\pi$
$908$	−26.3088	−	12.4226i	−0.873087	−	0.412258i
$909$	20.4468			0.678178
$910$	−0.142471	+	3.11687i	−0.00472288	+	0.103323i
$911$		−	14.8565i		−	0.492218i	−0.969242	−	0.246109i	$-0.920848\pi$
$911$		−	14.8565i		−	0.492218i	0.969242	−	0.246109i	$-0.0791522\pi$
$912$	−3.77668	+	38.8539i	−0.125058	+	1.28658i
$913$	12.9777			0.429498
$914$	52.1439	−	9.06498i	1.72477	−	0.299843i
$915$	35.3802	−	35.3802i	1.16963	−	1.16963i
$916$	−6.25734	−	2.95461i	−0.206748	−	0.0976231i
$917$	−0.477522	+	0.477522i	−0.0157692	+	0.0157692i
$918$	19.9686	−	28.3725i	0.659062	−	0.936432i
$919$			3.47888i			0.114758i	0.998352	+	0.0573788i	$0.0182743\pi$
$919$			3.47888i			0.114758i	−0.998352	+	0.0573788i	$0.981726\pi$
$920$	33.4065	−	18.9668i	1.10138	−	0.625318i
$921$	−3.83237	−	3.83237i	−0.126281	−	0.126281i
$922$	5.14288	+	29.5831i	0.169372	+	0.974266i
$923$	2.86160	−	12.9301i	0.0941907	−	0.425598i
$924$	0.626553	+	1.74758i	0.0206121	+	0.0574912i
$925$	−16.2120	−	16.2120i	−0.533047	−	0.533047i
$926$	−9.67230	+	1.68148i	−0.317852	+	0.0552570i
$927$	−14.3331			−0.470761
$928$	1.95305	+	25.9129i	0.0641119	+	0.850631i
$929$	8.41692	−	8.41692i	0.276150	−	0.276150i	−0.555420	−	0.831570i	$-0.687442\pi$
$929$	8.41692	−	8.41692i	0.276150	−	0.276150i	0.831570	+	0.555420i	$0.187442\pi$
$930$	5.86210	−	8.32919i	0.192226	−	0.273125i
$931$	34.6398	+	34.6398i	1.13527	+	1.13527i
$932$	11.9850	−	4.29693i	0.392581	−	0.140751i
$933$	−5.93960			−0.194454
$934$	−12.6392	+	17.9585i	−0.413569	+	0.587621i
$935$	−55.0251			−1.79951
$936$	10.4603	−	3.21940i	0.341906	−	0.105229i
$937$	−22.6059			−0.738503			−0.369251	−	0.929330i	$-0.620386\pi$
$937$	−22.6059			−0.738503			−0.369251	+	0.929330i	$0.620386\pi$
$938$	0.871170	−	1.23781i	0.0284447	−	0.0404158i
$939$	−5.11550			−0.166938
$940$	−3.26326	−	9.10186i	−0.106436	−	0.296870i
$941$	−24.2984	−	24.2984i	−0.792105	−	0.792105i	0.189731	−	0.981836i	$-0.439238\pi$
$941$	−24.2984	−	24.2984i	−0.792105	−	0.792105i	−0.981836	+	0.189731i	$0.939238\pi$
$942$	−3.64371	+	5.17718i	−0.118719	+	0.168682i
$943$	1.54737	−	1.54737i	0.0503893	−	0.0503893i
$944$	−35.3942	−	3.44038i	−1.15198	−	0.111975i
$945$	−3.45971			−0.112544
$946$	−26.0602	+	4.53045i	−0.847290	+	0.147298i
$947$	11.1576	+	11.1576i	0.362572	+	0.362572i	0.864759	−	0.502187i	$-0.167471\pi$
$947$	11.1576	+	11.1576i	0.362572	+	0.362572i	−0.502187	+	0.864759i	$0.667471\pi$
$948$	40.1958	−	14.4112i	1.30550	−	0.468055i
$949$	0.427609	−	1.93214i	0.0138808	−	0.0627199i
$950$	11.2462	+	64.6910i	0.364876	+	2.09885i
$951$	4.09119	+	4.09119i	0.132666	+	0.132666i
$952$	1.91714	−	1.08848i	0.0621350	−	0.0352777i
$953$		−	59.6199i		−	1.93128i	−0.259888	−	0.965639i	$-0.583686\pi$
$953$		−	59.6199i		−	1.93128i	0.259888	−	0.965639i	$-0.416314\pi$
$954$	−1.60661	+	2.28276i	−0.0520159	+	0.0739070i
$955$	−22.1003	+	22.1003i	−0.715147	+	0.715147i
$956$	−14.7573	+	31.2533i	−0.477284	+	1.01080i
$957$	−16.7856	+	16.7856i	−0.542601	+	0.542601i
$958$	−27.4426	+	4.77076i	−0.886629	+	0.154136i
$959$	−1.54897			−0.0500189
$960$	9.26164	+	36.6763i	0.298918	+	1.18372i
$961$		−	28.6801i		−	0.925163i
$962$	−11.9331	−	13.0763i	−0.384740	−	0.421597i
$963$	1.91297			0.0616446
$964$	−13.2545	+	28.0706i	−0.426897	+	0.904092i
$965$		−	0.397854i		−	0.0128074i
$966$	−1.38520	+	0.240810i	−0.0445680	+	0.00774794i
$967$	−15.0331	−	15.0331i	−0.483433	−	0.483433i	0.422793	−	0.906226i	$-0.361050\pi$
$967$	−15.0331	−	15.0331i	−0.483433	−	0.483433i	−0.906226	+	0.422793i	$0.861050\pi$
$968$	−7.79499	−	2.14913i	−0.250540	−	0.0690756i
$969$	29.9433	+	29.9433i	0.961918	+	0.961918i
$970$	−18.4621	−	12.9937i	−0.592783	−	0.417202i
$971$	−11.8204			−0.379336			−0.189668	−	0.981848i	$-0.560741\pi$
$971$	−11.8204			−0.379336			−0.189668	+	0.981848i	$0.560741\pi$
$972$	7.11224	+	19.8374i	0.228125	+	0.636286i
$973$	−2.45607	+	2.45607i	−0.0787379	+	0.0787379i
$974$	−3.50830	−	20.1806i	−0.112413	−	0.646627i
$975$	−27.8686	+	17.7685i	−0.892508	+	0.569046i
$976$	−26.8936	−	32.6848i	−0.860844	−	1.04621i
$977$	3.25802	−	3.25802i	0.104233	−	0.104233i	−0.653067	−	0.757300i	$-0.726518\pi$
$977$	3.25802	−	3.25802i	0.104233	−	0.104233i	0.757300	+	0.653067i	$0.226518\pi$
$978$	−5.83360	−	33.5562i	−0.186538	−	1.07301i
$979$			59.7984i			1.91117i
$980$	42.9256	+	20.2688i	1.37121	+	0.647462i
$981$	11.0934	+	11.0934i	0.354184	+	0.354184i
$982$	31.3354	−	44.5231i	0.999954	−	1.42079i
$983$	26.9767	−	26.9767i	0.860422	−	0.860422i	−0.130965	−	0.991387i	$-0.541808\pi$
$983$	26.9767	−	26.9767i	0.860422	−	0.860422i	0.991387	+	0.130965i	$0.0418076\pi$
$984$	1.06391	+	1.87388i	0.0339162	+	0.0597370i
$985$		−	41.6797i		−	1.32802i
$986$	23.0523	+	16.2242i	0.734134	+	0.516685i
$987$			0.353885i			0.0112643i
$988$	6.39369	+	50.2943i	0.203410	+	1.60008i
$989$		−	20.0320i		−	0.636981i
$990$	11.0774	−	15.7394i	0.352064	−	0.500231i
$991$		−	51.6574i		−	1.64095i	−0.571681	−	0.820476i	$-0.693709\pi$
$991$		−	51.6574i		−	1.64095i	0.571681	−	0.820476i	$-0.306291\pi$
$992$	−6.53320	−	5.61741i	−0.207429	−	0.178353i
$993$	12.1090	−	12.1090i	0.384266	−	0.384266i
$994$	0.763032	+	0.537024i	0.0242019	+	0.0170334i
$995$	−39.3911	−	39.3911i	−1.24878	−	1.24878i
$996$	−8.75140	−	4.13227i	−0.277299	−	0.130936i
$997$		−	25.6944i		−	0.813749i	−0.913484	−	0.406874i	$-0.866619\pi$
$997$		−	25.6944i		−	0.813749i	0.913484	−	0.406874i	$-0.133381\pi$
$998$	15.4450	−	2.68503i	0.488902	−	0.0849933i
$999$	13.8802	−	13.8802i	0.439149	−	0.439149i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	104.2.m.b.83.8	yes	20
3.2	odd	2		936.2.w.h.811.3		20
4.3	odd	2		416.2.u.b.239.3		20
8.3	odd	2	inner	104.2.m.b.83.3	✓	20
8.5	even	2		416.2.u.b.239.4		20
13.8	odd	4	inner	104.2.m.b.99.3	yes	20
24.11	even	2		936.2.w.h.811.8		20
39.8	even	4		936.2.w.h.307.8		20
52.47	even	4		416.2.u.b.47.4		20
104.21	odd	4		416.2.u.b.47.3		20
104.99	even	4	inner	104.2.m.b.99.8	yes	20
312.203	odd	4		936.2.w.h.307.3		20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
104.2.m.b.83.3	✓	20	8.3	odd	2	inner
104.2.m.b.83.8	yes	20	1.1	even	1	trivial
104.2.m.b.99.3	yes	20	13.8	odd	4	inner
104.2.m.b.99.8	yes	20	104.99	even	4	inner
416.2.u.b.47.3		20	104.21	odd	4
416.2.u.b.47.4		20	52.47	even	4
416.2.u.b.239.3		20	4.3	odd	2
416.2.u.b.239.4		20	8.5	even	2
936.2.w.h.307.3		20	312.203	odd	4
936.2.w.h.307.8		20	39.8	even	4
936.2.w.h.811.3		20	3.2	odd	2
936.2.w.h.811.8		20	24.11	even	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 104 = 2^{3} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	104.m (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.15650 + 0.813947i) q^{2} +1.38809 q^{3} +(0.674982 + 1.88266i) q^{4} +(-2.40872 - 2.40872i) q^{5} +(1.60533 + 1.12983i) q^{6} +(-0.127019 + 0.127019i) q^{7} +(-0.751766 + 2.72669i) q^{8} -1.07320 q^{9} +O(q^{10})\)	\(q+(1.15650 + 0.813947i) q^{2} +1.38809 q^{3} +(0.674982 + 1.88266i) q^{4} +(-2.40872 - 2.40872i) q^{5} +(1.60533 + 1.12983i) q^{6} +(-0.127019 + 0.127019i) q^{7} +(-0.751766 + 2.72669i) q^{8} -1.07320 q^{9} +(-0.825113 - 4.74625i) q^{10} +(-2.63237 - 2.63237i) q^{11} +(0.936938 + 2.61330i) q^{12} +(1.93837 + 3.04019i) q^{13} +(-0.250285 + 0.0435109i) q^{14} +(-3.34352 - 3.34352i) q^{15} +(-3.08880 + 2.54152i) q^{16} +4.33908i q^{17} +(-1.24115 - 0.873526i) q^{18} +(4.97146 - 4.97146i) q^{19} +(2.90895 - 6.16063i) q^{20} +(-0.176315 + 0.176315i) q^{21} +(-0.901727 - 5.18695i) q^{22} +3.98711 q^{23} +(-1.04352 + 3.78490i) q^{24} +6.60383i q^{25} +(-0.232832 + 5.09370i) q^{26} -5.65398 q^{27} +(-0.324870 - 0.153398i) q^{28} -4.59378i q^{29} +(-1.14533 - 6.58823i) q^{30} +(1.07702 + 1.07702i) q^{31} +(-5.64086 + 0.425150i) q^{32} +(-3.65398 - 3.65398i) q^{33} +(-3.53178 + 5.01815i) q^{34} +0.611907 q^{35} +(-0.724390 - 2.02047i) q^{36} +(-2.45494 + 2.45494i) q^{37} +(9.79599 - 1.70299i) q^{38} +(2.69063 + 4.22006i) q^{39} +(8.37862 - 4.75704i) q^{40} +(0.388093 - 0.388093i) q^{41} +(-0.347419 + 0.0603971i) q^{42} -5.02419i q^{43} +(3.17905 - 6.73266i) q^{44} +(2.58503 + 2.58503i) q^{45} +(4.61110 + 3.24530i) q^{46} +(1.00356 - 1.00356i) q^{47} +(-4.28754 + 3.52787i) q^{48} +6.96773i q^{49} +(-5.37516 + 7.63732i) q^{50} +6.02305i q^{51} +(-4.41527 + 5.70135i) q^{52} -1.83922i q^{53} +(-6.53882 - 4.60204i) q^{54} +12.6813i q^{55} +(-0.250854 - 0.441832i) q^{56} +(6.90084 - 6.90084i) q^{57} +(3.73909 - 5.31271i) q^{58} +(6.28635 + 6.28635i) q^{59} +(4.03789 - 8.55152i) q^{60} +10.5817i q^{61} +(0.368936 + 2.12221i) q^{62} +(0.136317 - 0.136317i) q^{63} +(-6.86970 - 4.09967i) q^{64} +(2.65398 - 11.9919i) q^{65} +(-1.25168 - 7.19997i) q^{66} +(-4.21315 + 4.21315i) q^{67} +(-8.16901 + 2.92880i) q^{68} +5.53449 q^{69} +(0.707670 + 0.498060i) q^{70} +(-2.59715 - 2.59715i) q^{71} +(0.806794 - 2.92628i) q^{72} +(-0.388093 - 0.388093i) q^{73} +(-4.83732 + 0.840947i) q^{74} +9.16673i q^{75} +(12.7152 + 6.00390i) q^{76} +0.668725 q^{77} +(-0.323192 + 7.07053i) q^{78} -15.3812i q^{79} +(13.5618 + 1.31824i) q^{80} -4.62865 q^{81} +(0.764716 - 0.132942i) q^{82} +(-2.46502 + 2.46502i) q^{83} +(-0.450949 - 0.212931i) q^{84} +(10.4516 - 10.4516i) q^{85} +(4.08942 - 5.81047i) q^{86} -6.37660i q^{87} +(9.15660 - 5.19874i) q^{88} +(-11.3583 - 11.3583i) q^{89} +(0.885510 + 5.09366i) q^{90} +(-0.632373 - 0.139953i) q^{91} +(2.69123 + 7.50637i) q^{92} +(1.49500 + 1.49500i) q^{93} +(1.97746 - 0.343772i) q^{94} -23.9497 q^{95} +(-7.83003 + 0.590148i) q^{96} +(3.31375 - 3.31375i) q^{97} +(-5.67136 + 8.05818i) q^{98} +(2.82506 + 2.82506i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q + 2 q^{2} - 4 q^{3} - 4 q^{6} - 4 q^{8} + 16 q^{9}+O(q^{10}) \) 20 * q + 2 * q^2 - 4 * q^3 - 4 * q^6 - 4 * q^8 + 16 * q^9	\( 20 q + 2 q^{2} - 4 q^{3} - 4 q^{6} - 4 q^{8} + 16 q^{9} - 8 q^{11} - 20 q^{14} + 20 q^{16} - 26 q^{18} - 12 q^{19} + 8 q^{20} - 8 q^{22} + 4 q^{24} - 34 q^{26} - 52 q^{27} + 12 q^{28} - 8 q^{32} - 12 q^{33} + 4 q^{34} + 44 q^{35} + 44 q^{40} - 24 q^{41} + 28 q^{42} + 32 q^{44} + 20 q^{46} - 20 q^{48} + 6 q^{50} + 36 q^{52} + 24 q^{54} + 8 q^{57} + 12 q^{58} + 20 q^{59} - 56 q^{60} - 8 q^{65} + 56 q^{66} - 16 q^{67} - 28 q^{68} + 8 q^{70} - 44 q^{72} + 24 q^{73} + 40 q^{74} + 44 q^{76} + 68 q^{78} - 12 q^{80} - 44 q^{81} + 16 q^{83} - 60 q^{84} - 36 q^{86} - 16 q^{89} + 32 q^{91} - 88 q^{92} - 44 q^{94} - 84 q^{96} + 12 q^{97} - 26 q^{98} + 20 q^{99}+O(q^{100}) \) 20 * q + 2 * q^2 - 4 * q^3 - 4 * q^6 - 4 * q^8 + 16 * q^9 - 8 * q^11 - 20 * q^14 + 20 * q^16 - 26 * q^18 - 12 * q^19 + 8 * q^20 - 8 * q^22 + 4 * q^24 - 34 * q^26 - 52 * q^27 + 12 * q^28 - 8 * q^32 - 12 * q^33 + 4 * q^34 + 44 * q^35 + 44 * q^40 - 24 * q^41 + 28 * q^42 + 32 * q^44 + 20 * q^46 - 20 * q^48 + 6 * q^50 + 36 * q^52 + 24 * q^54 + 8 * q^57 + 12 * q^58 + 20 * q^59 - 56 * q^60 - 8 * q^65 + 56 * q^66 - 16 * q^67 - 28 * q^68 + 8 * q^70 - 44 * q^72 + 24 * q^73 + 40 * q^74 + 44 * q^76 + 68 * q^78 - 12 * q^80 - 44 * q^81 + 16 * q^83 - 60 * q^84 - 36 * q^86 - 16 * q^89 + 32 * q^91 - 88 * q^92 - 44 * q^94 - 84 * q^96 + 12 * q^97 - 26 * q^98 + 20 * q^99

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