LMFDB - Embedded newform 80.2.q.c.69.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [80,2,Mod(29,80)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(80, base_ring=CyclotomicField(4))

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

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

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

chi := DirichletCharacter("80.29");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 80 = 2^{4} \cdot 5 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	80.q (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:	$0.638803216170$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(i)$
Coefficient field:	16.0.534694406811304329216.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 2x^{14} - 2x^{12} + 4x^{10} + 4x^{8} + 16x^{6} - 32x^{4} - 128x^{2} + 256 $ x^16 - 2x^14 - 2x^12 + 4x^10 + 4x^8 + 16x^6 - 32x^4 - 128*x^2 + 256
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{5} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			69.2
Root			$-0.841995 + 1.13624i$ of defining polynomial
Character	$\chi$	$=$	80.69
Dual form			80.2.q.c.29.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.13624 + 0.841995i) q^{2} +(1.86033 + 1.86033i) q^{3} +(0.582088 - 1.91342i) q^{4} +(1.90421 - 1.17216i) q^{5} +(-3.68016 - 0.547394i) q^{6} -3.61392 q^{7} +(0.949697 + 2.66422i) q^{8} +3.92163i q^{9} +O(q^{10})$	\(q+(-1.13624 + 0.841995i) q^{2} +(1.86033 + 1.86033i) q^{3} +(0.582088 - 1.91342i) q^{4} +(1.90421 - 1.17216i) q^{5} +(-3.68016 - 0.547394i) q^{6} -3.61392 q^{7} +(0.949697 + 2.66422i) q^{8} +3.92163i q^{9} +(-1.17669 + 2.93520i) q^{10} +(-0.0947876 - 0.0947876i) q^{11} +(4.64246 - 2.47671i) q^{12} +(-2.59462 - 2.59462i) q^{13} +(4.10628 - 3.04290i) q^{14} +(5.72307 + 1.36185i) q^{15} +(-3.32235 - 2.22756i) q^{16} -1.89939i q^{17} +(-3.30199 - 4.45591i) q^{18} +(-2.16418 + 2.16418i) q^{19} +(-1.13442 - 4.32586i) q^{20} +(-6.72307 - 6.72307i) q^{21} +(0.187512 + 0.0278909i) q^{22} +5.08251 q^{23} +(-3.18958 + 6.72307i) q^{24} +(2.25207 - 4.46410i) q^{25} +(5.13277 + 0.763457i) q^{26} +(-1.71452 + 1.71452i) q^{27} +(-2.10362 + 6.91494i) q^{28} +(1.25896 - 1.25896i) q^{29} +(-7.64946 + 3.27140i) q^{30} -1.27453 q^{31} +(5.65058 - 0.266355i) q^{32} -0.352672i q^{33} +(1.59928 + 2.15817i) q^{34} +(-6.88168 + 4.23610i) q^{35} +(7.50371 + 2.28273i) q^{36} +(-2.25207 + 2.25207i) q^{37} +(0.636801 - 4.28125i) q^{38} -9.65368i q^{39} +(4.93133 + 3.96005i) q^{40} +8.52451i q^{41} +(13.2998 + 1.97824i) q^{42} +(-1.61439 + 1.61439i) q^{43} +(-0.236543 + 0.126194i) q^{44} +(4.59679 + 7.46762i) q^{45} +(-5.77495 + 4.27944i) q^{46} +2.53884i q^{47} +(-2.03666 - 10.3246i) q^{48} +6.06040 q^{49} +(1.19986 + 6.96852i) q^{50} +(3.53349 - 3.53349i) q^{51} +(-6.47489 + 3.45430i) q^{52} +(-5.67100 + 5.67100i) q^{53} +(0.504492 - 3.39174i) q^{54} +(-0.291602 - 0.0693893i) q^{55} +(-3.43213 - 9.62828i) q^{56} -8.05215 q^{57} +(-0.370445 + 2.49053i) q^{58} +(-7.81785 - 7.81785i) q^{59} +(5.93713 - 10.1579i) q^{60} +(3.46410 - 3.46410i) q^{61} +(1.44817 - 1.07315i) q^{62} -14.1724i q^{63} +(-6.19615 + 5.06040i) q^{64} +(-7.98203 - 1.89939i) q^{65} +(0.296948 + 0.400720i) q^{66} +(-6.29856 - 6.29856i) q^{67} +(-3.63434 - 1.10561i) q^{68} +(9.45512 + 9.45512i) q^{69} +(4.25246 - 10.6076i) q^{70} +11.3074i q^{71} +(-10.4481 + 3.72436i) q^{72} +16.1786 q^{73} +(0.662661 - 4.45512i) q^{74} +(12.4943 - 4.11511i) q^{75} +(2.88124 + 5.40072i) q^{76} +(0.342555 + 0.342555i) q^{77} +(8.12835 + 10.9689i) q^{78} +1.13575 q^{79} +(-8.93752 - 0.347416i) q^{80} +5.38573 q^{81} +(-7.17759 - 9.68590i) q^{82} +(3.75489 + 3.75489i) q^{83} +(-16.7775 + 8.95062i) q^{84} +(-2.22640 - 3.61685i) q^{85} +(0.475028 - 3.19364i) q^{86} +4.68417 q^{87} +(0.162516 - 0.342555i) q^{88} -3.98203i q^{89} +(-11.5108 - 4.61454i) q^{90} +(9.37674 + 9.37674i) q^{91} +(2.95847 - 9.72496i) q^{92} +(-2.37103 - 2.37103i) q^{93} +(-2.13769 - 2.88473i) q^{94} +(-1.58429 + 6.65783i) q^{95} +(11.0074 + 10.0164i) q^{96} +10.3042i q^{97} +(-6.88608 + 5.10283i) q^{98} +(0.371721 - 0.371721i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 4 q^{4} - 8 q^{5} - 4 q^{6}+O(q^{10}) $ 16 * q - 4 * q^4 - 8 * q^5 - 4 * q^6	$ 16 q - 4 q^{4} - 8 q^{5} - 4 q^{6} - 12 q^{10} + 8 q^{11} - 4 q^{14} + 16 q^{16} - 8 q^{19} - 4 q^{20} - 16 q^{21} - 32 q^{24} + 32 q^{26} - 16 q^{29} - 36 q^{30} + 16 q^{31} + 48 q^{34} - 24 q^{35} + 60 q^{36} + 24 q^{40} - 8 q^{44} + 8 q^{45} - 28 q^{46} + 16 q^{49} + 24 q^{50} - 16 q^{51} + 40 q^{54} - 56 q^{56} - 24 q^{59} + 48 q^{60} - 16 q^{64} - 72 q^{66} + 32 q^{69} + 20 q^{70} + 48 q^{75} - 88 q^{76} + 16 q^{79} + 16 q^{80} - 16 q^{81} - 80 q^{84} - 28 q^{86} - 84 q^{90} - 16 q^{91} + 12 q^{94} + 32 q^{95} + 56 q^{96} + 88 q^{99}+O(q^{100}) $ 16 * q - 4 * q^4 - 8 * q^5 - 4 * q^6 - 12 * q^10 + 8 * q^11 - 4 * q^14 + 16 * q^16 - 8 * q^19 - 4 * q^20 - 16 * q^21 - 32 * q^24 + 32 * q^26 - 16 * q^29 - 36 * q^30 + 16 * q^31 + 48 * q^34 - 24 * q^35 + 60 * q^36 + 24 * q^40 - 8 * q^44 + 8 * q^45 - 28 * q^46 + 16 * q^49 + 24 * q^50 - 16 * q^51 + 40 * q^54 - 56 * q^56 - 24 * q^59 + 48 * q^60 - 16 * q^64 - 72 * q^66 + 32 * q^69 + 20 * q^70 + 48 * q^75 - 88 * q^76 + 16 * q^79 + 16 * q^80 - 16 * q^81 - 80 * q^84 - 28 * q^86 - 84 * q^90 - 16 * q^91 + 12 * q^94 + 32 * q^95 + 56 * q^96 + 88 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/80\mathbb{Z}\right)^\times$.

$n$	$17$	$21$	$31$
$\chi(n)$	$-1$	$e\left(\frac{1}{4}\right)$	$1$

Coefficient data

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

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

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

$2$	−1.13624	+	0.841995i	−0.803444	+	0.595380i
$2$	−1.13624	+	0.841995i	−0.803444	+	0.595380i
$3$	1.86033	+	1.86033i	1.07406	+	1.07406i	0.997029	+	0.0770310i	$0.0245441\pi$
$3$	1.86033	+	1.86033i	1.07406	+	1.07406i	0.0770310	+	0.997029i	$0.475456\pi$
$4$	0.582088	−	1.91342i	0.291044	−	0.956710i
$5$	1.90421	−	1.17216i	0.851591	−	0.524207i
$5$	1.90421	−	1.17216i	0.851591	−	0.524207i
$6$	−3.68016	−	0.547394i	−1.50242	−	0.223473i
$7$	−3.61392			−1.36593			−0.682966	−	0.730450i	$-0.739310\pi$
$7$	−3.61392			−1.36593			−0.682966	+	0.730450i	$0.739310\pi$
$8$	0.949697	+	2.66422i	0.335768	+	0.941945i
$9$			3.92163i			1.30721i
$10$	−1.17669	+	2.93520i	−0.372102	+	0.928192i
$11$	−0.0947876	−	0.0947876i	−0.0285795	−	0.0285795i	0.692673	−	0.721252i	$-0.256433\pi$
$11$	−0.0947876	−	0.0947876i	−0.0285795	−	0.0285795i	−0.721252	+	0.692673i	$0.756433\pi$
$12$	4.64246	−	2.47671i	1.34016	−	0.714964i
$13$	−2.59462	−	2.59462i	−0.719618	−	0.719618i	0.248909	−	0.968527i	$-0.419928\pi$
$13$	−2.59462	−	2.59462i	−0.719618	−	0.719618i	−0.968527	+	0.248909i	$0.919928\pi$
$14$	4.10628	−	3.04290i	1.09745	−	0.813250i
$15$	5.72307	+	1.36185i	1.47769	+	0.351629i
$16$	−3.32235	−	2.22756i	−0.830587	−	0.556890i
$17$		−	1.89939i		−	0.460671i	−0.973111	−	0.230335i	$-0.926018\pi$
$17$		−	1.89939i		−	0.460671i	0.973111	−	0.230335i	$-0.0739823\pi$
$18$	−3.30199	−	4.45591i	−0.778286	−	1.05027i
$19$	−2.16418	+	2.16418i	−0.496496	+	0.496496i	−0.910345	−	0.413849i	$-0.864184\pi$
$19$	−2.16418	+	2.16418i	−0.496496	+	0.496496i	0.413849	+	0.910345i	$0.364184\pi$
$20$	−1.13442	−	4.32586i	−0.253664	−	0.967292i
$21$	−6.72307	−	6.72307i	−1.46709	−	1.46709i
$22$	0.187512	+	0.0278909i	0.0399777	+	0.00594636i
$23$	5.08251			1.05978			0.529888	−	0.848068i	$-0.322234\pi$
$23$	5.08251			1.05978			0.529888	+	0.848068i	$0.322234\pi$
$24$	−3.18958	+	6.72307i	−0.651069	+	1.37234i
$25$	2.25207	−	4.46410i	0.450413	−	0.892820i
$26$	5.13277	+	0.763457i	1.00662	+	0.149726i
$27$	−1.71452	+	1.71452i	−0.329960	+	0.329960i
$28$	−2.10362	+	6.91494i	−0.397547	+	1.30680i
$29$	1.25896	−	1.25896i	0.233784	−	0.233784i	−0.580486	−	0.814270i	$-0.697137\pi$
$29$	1.25896	−	1.25896i	0.233784	−	0.233784i	0.814270	+	0.580486i	$0.197137\pi$
$30$	−7.64946	+	3.27140i	−1.39659	+	0.597273i
$31$	−1.27453			−0.228912			−0.114456	−	0.993428i	$-0.536512\pi$
$31$	−1.27453			−0.228912			−0.114456	+	0.993428i	$0.536512\pi$
$32$	5.65058	−	0.266355i	0.998891	−	0.0470854i
$33$		−	0.352672i		−	0.0613923i
$34$	1.59928	+	2.15817i	0.274274	+	0.370123i
$35$	−6.88168	+	4.23610i	−1.16322	+	0.716032i
$36$	7.50371	+	2.28273i	1.25062	+	0.380456i
$37$	−2.25207	+	2.25207i	−0.370237	+	0.370237i	−0.867564	−	0.497326i	$-0.834315\pi$
$37$	−2.25207	+	2.25207i	−0.370237	+	0.370237i	0.497326	+	0.867564i	$0.334315\pi$
$38$	0.636801	−	4.28125i	0.103303	−	0.694511i
$39$		−	9.65368i		−	1.54583i
$40$	4.93133	+	3.96005i	0.779712	+	0.626139i
$41$			8.52451i			1.33130i	0.746262	+	0.665652i	$0.231847\pi$
$41$			8.52451i			1.33130i	−0.746262	+	0.665652i	$0.768153\pi$
$42$	13.2998	+	1.97824i	2.05221	+	0.305249i
$43$	−1.61439	+	1.61439i	−0.246192	+	0.246192i	−0.819406	−	0.573214i	$-0.805696\pi$
$43$	−1.61439	+	1.61439i	−0.246192	+	0.246192i	0.573214	+	0.819406i	$0.305696\pi$
$44$	−0.236543	+	0.126194i	−0.0356602	+	0.0190244i
$45$	4.59679	+	7.46762i	0.685249	+	1.11321i
$46$	−5.77495	+	4.27944i	−0.851470	+	0.630970i
$47$			2.53884i			0.370328i	0.982708	+	0.185164i	$0.0592816\pi$
$47$			2.53884i			0.370328i	−0.982708	+	0.185164i	$0.940718\pi$
$48$	−2.03666	−	10.3246i	−0.293967	−	1.49023i
$49$	6.06040			0.865772
$50$	1.19986	+	6.96852i	0.169686	+	0.985498i
$51$	3.53349	−	3.53349i	0.494788	−	0.494788i
$52$	−6.47489	+	3.45430i	−0.897906	+	0.479025i
$53$	−5.67100	+	5.67100i	−0.778971	+	0.778971i	−0.979656	−	0.200684i	$-0.935683\pi$
$53$	−5.67100	+	5.67100i	−0.778971	+	0.778971i	0.200684	+	0.979656i	$0.435683\pi$
$54$	0.504492	−	3.39174i	0.0686527	−	0.461557i
$55$	−0.291602	−	0.0693893i	−0.0393197	−	0.00935646i
$56$	−3.43213	−	9.62828i	−0.458637	−	1.28663i
$57$	−8.05215			−1.06653
$58$	−0.370445	+	2.49053i	−0.0486419	+	0.327023i
$59$	−7.81785	−	7.81785i	−1.01780	−	1.01780i	−0.999839	−	0.0179591i	$-0.994283\pi$
$59$	−7.81785	−	7.81785i	−1.01780	−	1.01780i	−0.0179591	−	0.999839i	$-0.505717\pi$
$60$	5.93713	−	10.1579i	0.766480	−	1.31138i
$61$	3.46410	−	3.46410i	0.443533	−	0.443533i	−0.449665	−	0.893197i	$-0.648457\pi$
$61$	3.46410	−	3.46410i	0.443533	−	0.443533i	0.893197	+	0.449665i	$0.148457\pi$
$62$	1.44817	−	1.07315i	0.183918	−	0.136290i
$63$		−	14.1724i		−	1.78556i
$64$	−6.19615	+	5.06040i	−0.774519	+	0.632551i
$65$	−7.98203	−	1.89939i	−0.990049	−	0.235591i
$66$	0.296948	+	0.400720i	0.0365517	+	0.0493252i
$67$	−6.29856	−	6.29856i	−0.769491	−	0.769491i	0.208526	−	0.978017i	$-0.433134\pi$
$67$	−6.29856	−	6.29856i	−0.769491	−	0.769491i	−0.978017	+	0.208526i	$0.933134\pi$
$68$	−3.63434	−	1.10561i	−0.440728	−	0.134076i
$69$	9.45512	+	9.45512i	1.13826	+	1.13826i
$70$	4.25246	−	10.6076i	0.508267	−	1.26785i
$71$			11.3074i			1.34194i	0.741486	+	0.670968i	$0.234121\pi$
$71$			11.3074i			1.34194i	−0.741486	+	0.670968i	$0.765879\pi$
$72$	−10.4481	+	3.72436i	−1.23132	+	0.438919i
$73$	16.1786			1.89356			0.946779	−	0.321885i	$-0.104316\pi$
$73$	16.1786			1.89356			0.946779	+	0.321885i	$0.104316\pi$
$74$	0.662661	−	4.45512i	0.0770328	−	0.517897i
$75$	12.4943	−	4.11511i	1.44271	−	0.475172i
$76$	2.88124	+	5.40072i	0.330500	+	0.619505i
$77$	0.342555	+	0.342555i	0.0390377	+	0.0390377i
$78$	8.12835	+	10.9689i	0.920354	+	1.24198i
$79$	1.13575			0.127782			0.0638908	−	0.997957i	$-0.479649\pi$
$79$	1.13575			0.127782			0.0638908	+	0.997957i	$0.479649\pi$
$80$	−8.93752	−	0.347416i	−0.999245	−	0.0388423i
$81$	5.38573			0.598414
$82$	−7.17759	−	9.68590i	−0.792633	−	1.06963i
$83$	3.75489	+	3.75489i	0.412153	+	0.412153i	0.882488	−	0.470335i	$-0.155867\pi$
$83$	3.75489	+	3.75489i	0.412153	+	0.412153i	−0.470335	+	0.882488i	$0.655867\pi$
$84$	−16.7775	+	8.95062i	−1.83057	+	0.976593i
$85$	−2.22640	−	3.61685i	−0.241487	−	0.392303i
$86$	0.475028	−	3.19364i	0.0512235	−	0.344379i
$87$	4.68417			0.502196
$88$	0.162516	−	0.342555i	0.0173242	−	0.0365164i
$89$		−	3.98203i		−	0.422094i	−0.977476	−	0.211047i	$-0.932313\pi$
$89$		−	3.98203i		−	0.422094i	0.977476	−	0.211047i	$-0.0676874\pi$
$90$	−11.5108	−	4.61454i	−1.21334	−	0.486415i
$91$	9.37674	+	9.37674i	0.982950	+	0.982950i
$92$	2.95847	−	9.72496i	0.308442	−	1.01390i
$93$	−2.37103	−	2.37103i	−0.245865	−	0.245865i
$94$	−2.13769	−	2.88473i	−0.220486	−	0.297537i
$95$	−1.58429	+	6.65783i	−0.162544	+	0.683079i
$96$	11.0074	+	10.0164i	1.12344	+	1.02230i
$97$			10.3042i			1.04623i	0.852261	+	0.523117i	$0.175231\pi$
$97$			10.3042i			1.04623i	−0.852261	+	0.523117i	$0.824769\pi$
$98$	−6.88608	+	5.10283i	−0.695599	+	0.515464i
$99$	0.371721	−	0.371721i	0.0373594	−	0.0373594i
$100$	−7.23080	−	6.90765i	−0.723080	−	0.690765i
$101$	1.25896	+	1.25896i	0.125272	+	0.125272i	0.766963	−	0.641691i	$-0.221767\pi$
$101$	1.25896	+	1.25896i	0.125272	+	0.125272i	−0.641691	+	0.766963i	$0.721767\pi$
$102$	−1.03972	+	6.99008i	−0.102947	+	0.692121i
$103$	−10.8655			−1.07061			−0.535306	−	0.844658i	$-0.679804\pi$
$103$	−10.8655			−1.07061			−0.535306	+	0.844658i	$0.679804\pi$
$104$	4.44854	−	9.37674i	0.436215	−	0.919465i
$105$	−20.6827	−	4.92163i	−2.01842	−	0.480302i
$106$	1.66867	−	11.2186i	0.162075	−	1.08964i
$107$	9.48167	−	9.48167i	0.916628	−	0.916628i	−0.0801549	−	0.996782i	$-0.525541\pi$
$107$	9.48167	−	9.48167i	0.916628	−	0.916628i	0.996782	+	0.0801549i	$0.0255415\pi$
$108$	2.28260	+	4.27861i	0.219643	+	0.411709i
$109$	−8.57530	+	8.57530i	−0.821365	+	0.821365i	−0.986304	−	0.164939i	$-0.947257\pi$
$109$	−8.57530	+	8.57530i	−0.821365	+	0.821365i	0.164939	+	0.986304i	$0.447257\pi$
$110$	0.389756	−	0.166685i	0.0371618	−	0.0158928i
$111$	−8.37915			−0.795314
$112$	12.0067	+	8.05021i	1.13453	+	0.760674i
$113$			12.5286i			1.17860i	0.807916	+	0.589298i	$0.200595\pi$
$113$			12.5286i			1.17860i	−0.807916	+	0.589298i	$0.799405\pi$
$114$	9.14918	−	6.77987i	0.856900	−	0.634993i
$115$	9.67818	−	5.95753i	0.902495	−	0.555542i
$116$	−1.67610	−	3.14176i	−0.155622	−	0.291705i
$117$	10.1751	−	10.1751i	0.940691	−	0.940691i
$118$	15.4656	+	2.30037i	1.42372	+	0.211767i
$119$			6.86425i			0.629245i
$120$	1.80690	+	16.5409i	0.164946	+	1.50997i
$121$		−	10.9820i		−	0.998366i
$122$	−1.01930	+	6.85281i	−0.0922830	+	0.620424i
$123$	−15.8584	+	15.8584i	−1.42990	+	1.42990i
$124$	−0.741887	+	2.43870i	−0.0666234	+	0.219002i
$125$	−0.944243	−	11.1404i	−0.0844556	−	0.996427i
$126$	11.9331	+	16.1033i	1.06309	+	1.43460i
$127$			2.94200i			0.261061i	0.991444	+	0.130530i	$0.0416680\pi$
$127$			2.94200i			0.261061i	−0.991444	+	0.130530i	$0.958332\pi$
$128$	2.77949	−	10.9670i	0.245674	−	0.969352i
$129$	−6.00658			−0.528850
$130$	10.6688	−	4.56266i	0.935715	−	0.400172i
$131$	6.54333	−	6.54333i	0.571693	−	0.571693i	−0.360908	−	0.932601i	$-0.617533\pi$
$131$	6.54333	−	6.54333i	0.571693	−	0.571693i	0.932601	+	0.360908i	$0.117533\pi$
$132$	−0.674809	−	0.205286i	−0.0587346	−	0.0178679i
$133$	7.82116	−	7.82116i	0.678180	−	0.678180i
$134$	12.4600	+	1.85333i	1.07638	+	0.160103i
$135$	−1.25512	+	5.27453i	−0.108023	+	0.453959i
$136$	5.06040	−	1.80385i	0.433926	−	0.154679i
$137$	1.82513			0.155931			0.0779657	−	0.996956i	$-0.475158\pi$
$137$	1.82513			0.155931			0.0779657	+	0.996956i	$0.475158\pi$
$138$	−18.7045	−	2.78213i	−1.59223	−	0.236831i
$139$	−5.36931	−	5.36931i	−0.455419	−	0.455419i	0.441729	−	0.897148i	$-0.354365\pi$
$139$	−5.36931	−	5.36931i	−0.455419	−	0.455419i	−0.897148	+	0.441729i	$0.854365\pi$
$140$	4.09970	+	15.6333i	0.346488	+	1.32126i
$141$	−4.72307	+	4.72307i	−0.397754	+	0.397754i
$142$	−9.52074	−	12.8479i	−0.798962	−	1.07817i
$143$			0.491875i			0.0411327i
$144$	8.73565	−	13.0290i	0.727971	−	1.08575i
$145$	0.921626	−	3.87305i	0.0765369	−	0.321639i
$146$	−18.3828	+	13.6223i	−1.52137	+	1.12739i
$147$	11.2743	+	11.2743i	0.929891	+	0.929891i
$148$	2.99824	+	5.62005i	0.246454	+	0.461965i
$149$	4.37915	+	4.37915i	0.358754	+	0.358754i	0.863354	−	0.504600i	$-0.168360\pi$
$149$	4.37915	+	4.37915i	0.358754	+	0.358754i	−0.504600	+	0.863354i	$0.668360\pi$
$150$	−10.7316	+	15.1959i	−0.876231	+	1.24074i
$151$		−	12.9610i		−	1.05475i	−0.849631	−	0.527377i	$-0.823176\pi$
$151$		−	12.9610i		−	1.05475i	0.849631	−	0.527377i	$-0.176824\pi$
$152$	−7.82116	−	3.71054i	−0.634380	−	0.300964i
$153$	7.44871			0.602193
$154$	−0.677654	−	0.100795i	−0.0546069	−	0.00812232i
$155$	−2.42697	+	1.49395i	−0.194939	+	0.119997i
$156$	−18.4715	−	5.61929i	−1.47891	−	0.449904i
$157$	9.12723	+	9.12723i	0.728432	+	0.728432i	0.970307	−	0.241875i	$-0.0777624\pi$
$157$	9.12723	+	9.12723i	0.728432	+	0.728432i	−0.241875	+	0.970307i	$0.577762\pi$
$158$	−1.29048	+	0.956294i	−0.102665	+	0.0760787i
$159$	−21.0998			−1.67332
$160$	10.4477	−	7.13060i	0.825964	−	0.563724i
$161$	−18.3678			−1.44758
$162$	−6.11949	+	4.53476i	−0.480792	+	0.356284i
$163$	−6.15099	−	6.15099i	−0.481783	−	0.481783i	0.423918	−	0.905701i	$-0.360654\pi$
$163$	−6.15099	−	6.15099i	−0.481783	−	0.481783i	−0.905701	+	0.423918i	$0.860654\pi$
$164$	16.3110	+	4.96202i	1.27367	+	0.387468i
$165$	−0.413389	−	0.671562i	−0.0321823	−	0.0522811i
$166$	−7.42806	−	1.10486i	−0.576529	−	0.0857539i
$167$	0.710173			0.0549548			0.0274774	−	0.999622i	$-0.491253\pi$
$167$	0.710173			0.0549548			0.0274774	+	0.999622i	$0.491253\pi$
$168$	11.5269	−	24.2966i	0.889317	−	1.87452i
$169$			0.464102i			0.0357001i
$170$	5.57510	+	2.23500i	0.427591	+	0.171417i
$171$	−8.48709	−	8.48709i	−0.649024	−	0.649024i
$172$	2.14928	+	4.02872i	0.163881	+	0.307187i
$173$	−14.1773	−	14.1773i	−1.07788	−	1.07788i	−0.996700	−	0.0811779i	$-0.974132\pi$
$173$	−14.1773	−	14.1773i	−1.07788	−	1.07788i	−0.0811779	−	0.996700i	$-0.525868\pi$
$174$	−5.32235	+	3.94405i	−0.403486	+	0.298997i
$175$	−8.13878	+	16.1329i	−0.615234	+	1.21953i
$176$	0.103772	+	0.526062i	0.00782213	+	0.0396534i
$177$		−	29.0875i		−	2.18635i
$178$	3.35285	+	4.52455i	0.251307	+	0.339129i
$179$	9.00502	−	9.00502i	0.673067	−	0.673067i	−0.285355	−	0.958422i	$-0.592111\pi$
$179$	9.00502	−	9.00502i	0.673067	−	0.673067i	0.958422	+	0.285355i	$0.0921115\pi$
$180$	16.9644	−	4.44877i	1.26445	−	0.331592i
$181$	14.1872	+	14.1872i	1.05452	+	1.05452i	0.998425	+	0.0560986i	$0.0178661\pi$
$181$	14.1872	+	14.1872i	1.05452	+	1.05452i	0.0560986	+	0.998425i	$0.482134\pi$
$182$	−18.5494	−	2.75907i	−1.37497	−	0.204516i
$183$	12.8887			0.952761
$184$	4.82684	+	13.5409i	0.355839	+	0.998250i
$185$	−1.64863	+	6.92820i	−0.121209	+	0.509372i
$186$	4.69047	+	0.697668i	0.343922	+	0.0511555i
$187$	−0.180039	+	0.180039i	−0.0131657	+	0.0131657i
$188$	4.85786	+	1.47783i	0.354296	+	0.107782i
$189$	6.19615	−	6.19615i	0.450704	−	0.450704i
$190$	−3.80572	−	8.89886i	−0.276096	−	0.645591i
$191$	18.9282			1.36960			0.684798	−	0.728733i	$-0.259890\pi$
$191$	18.9282			1.36960			0.684798	+	0.728733i	$0.259890\pi$
$192$	−20.9409	−	2.11286i	−1.51128	−	0.152483i
$193$		−	21.3880i		−	1.53954i	−0.638319	−	0.769772i	$-0.720370\pi$
$193$		−	21.3880i		−	1.53954i	0.638319	−	0.769772i	$-0.279630\pi$
$194$	−8.67610	−	11.7081i	−0.622908	−	0.840591i
$195$	−11.3157	−	18.3827i	−0.810333	−	1.31641i
$196$	3.52769	−	11.5961i	0.251978	−	0.828292i
$197$	−6.39341	+	6.39341i	−0.455511	+	0.455511i	−0.897179	−	0.441667i	$-0.854387\pi$
$197$	−6.39341	+	6.39341i	−0.455511	+	0.455511i	0.441667	+	0.897179i	$0.354387\pi$
$198$	−0.109378	+	0.735353i	−0.00777313	+	0.0522593i
$199$			5.85641i			0.415150i	0.978219	+	0.207575i	$0.0665570\pi$
$199$			5.85641i			0.415150i	−0.978219	+	0.207575i	$0.933443\pi$
$200$	14.0321	+	1.76046i	0.992222	+	0.124483i
$201$		−	23.4347i		−	1.65296i
$202$	−2.49053	−	0.370445i	−0.175233	−	0.0260645i
$203$	−4.54979	+	4.54979i	−0.319333	+	0.319333i
$204$	−4.70425	−	8.81785i	−0.329363	−	0.617373i
$205$	9.99212	+	16.2325i	0.697880	+	1.13373i
$206$	12.3459	−	9.14872i	0.860177	−	0.637421i
$207$			19.9317i			1.38535i
$208$	2.84056	+	14.3999i	0.196957	+	0.998453i
$209$	0.410274			0.0283793
$210$	27.6445	−	11.8226i	1.90765	−	0.815835i
$211$	−19.2640	+	19.2640i	−1.32619	+	1.32619i	−0.417520	+	0.908668i	$0.637100\pi$
$211$	−19.2640	+	19.2640i	−1.32619	+	1.32619i	−0.908668	+	0.417520i	$0.862900\pi$
$212$	7.54997	+	14.1520i	0.518534	+	0.971965i
$213$	−21.0354	+	21.0354i	−1.44132	+	1.44132i
$214$	−2.78994	+	18.7570i	−0.190717	+	1.28220i
$215$	−1.18181	+	4.96647i	−0.0805991	+	0.338710i
$216$	−6.19615	−	2.93960i	−0.421595	−	0.200014i
$217$	4.60603			0.312678
$218$	2.52325	−	16.9640i	0.170896	−	1.14895i
$219$	30.0974	+	30.0974i	2.03379	+	2.03379i
$220$	−0.302509	+	0.517567i	−0.0203952	+	0.0348944i
$221$	−4.92820	+	4.92820i	−0.331507	+	0.331507i
$222$	9.52074	−	7.05520i	0.638990	−	0.473514i
$223$		−	20.1117i		−	1.34678i	−0.739287	−	0.673390i	$-0.764837\pi$
$223$		−	20.1117i		−	1.34678i	0.739287	−	0.673390i	$-0.235163\pi$
$224$	−20.4207	+	0.962586i	−1.36442	+	0.0643155i
$225$	17.5065	+	8.83176i	1.16710	+	0.588784i
$226$	−10.5491	−	14.2356i	−0.701713	−	0.946935i
$227$	−4.21430	−	4.21430i	−0.279713	−	0.279713i	0.553282	−	0.832994i	$-0.313375\pi$
$227$	−4.21430	−	4.21430i	−0.279713	−	0.279713i	−0.832994	+	0.553282i	$0.813375\pi$
$228$	−4.68706	+	15.4071i	−0.310408	+	1.02036i
$229$	−18.0304	−	18.0304i	−1.19148	−	1.19148i	−0.976651	−	0.214833i	$-0.931079\pi$
$229$	−18.0304	−	18.0304i	−1.19148	−	1.19148i	−0.214833	−	0.976651i	$-0.568921\pi$
$230$	−5.98054	+	14.9182i	−0.394345	+	0.983675i
$231$			1.27453i			0.0838577i
$232$	4.54979	+	2.15853i	0.298709	+	0.141714i
$233$	4.57839			0.299941			0.149970	−	0.988691i	$-0.452082\pi$
$233$	4.57839			0.299941			0.149970	+	0.988691i	$0.452082\pi$
$234$	−2.99399	+	20.1288i	−0.195723	+	1.31586i
$235$	2.97593	+	4.83449i	0.194128	+	0.315367i
$236$	−19.5095	+	10.4081i	−1.26996	+	0.677513i
$237$	2.11286	+	2.11286i	0.137245	+	0.137245i
$238$	−5.77967	−	7.79945i	−0.374640	−	0.505563i
$239$	18.3104			1.18440			0.592200	−	0.805791i	$-0.298259\pi$
$239$	18.3104			1.18440			0.592200	+	0.805791i	$0.298259\pi$
$240$	−15.9804	−	17.2730i	−1.03153	−	1.11497i
$241$	−9.31393			−0.599963			−0.299982	−	0.953945i	$-0.596981\pi$
$241$	−9.31393			−0.599963			−0.299982	+	0.953945i	$0.596981\pi$
$242$	9.24682	+	12.4782i	0.594408	+	0.802131i
$243$	15.1628	+	15.1628i	0.972693	+	0.972693i
$244$	−4.61186	−	8.64469i	−0.295244	−	0.553420i
$245$	11.5403	−	7.10379i	0.737283	−	0.453844i
$246$	4.66626	−	31.3716i	0.297510	−	2.00018i
$247$	11.2304			0.714575
$248$	−1.21041	−	3.39562i	−0.0768613	−	0.215622i
$249$			13.9706i			0.885353i
$250$	10.4530	+	11.8631i	0.661109	+	0.750290i
$251$	−14.2156	−	14.2156i	−0.897281	−	0.897281i	0.0979143	−	0.995195i	$-0.468783\pi$
$251$	−14.2156	−	14.2156i	−0.897281	−	0.897281i	−0.995195	+	0.0979143i	$0.968783\pi$
$252$	−27.1178	−	8.24961i	−1.70826	−	0.519677i
$253$	−0.481758	−	0.481758i	−0.0302879	−	0.0302879i
$254$	−2.47715	−	3.34283i	−0.155430	−	0.209748i
$255$	2.58669	−	10.8704i	0.161985	−	0.680728i
$256$	6.07597	+	14.8014i	0.379748	+	0.925090i
$257$			17.1347i			1.06883i	0.845222	+	0.534416i	$0.179468\pi$
$257$			17.1347i			1.06883i	−0.845222	+	0.534416i	$0.820532\pi$
$258$	6.82492	−	5.05751i	0.424901	−	0.314867i
$259$	8.13878	−	8.13878i	0.505719	−	0.505719i
$260$	−8.28058	+	14.1674i	−0.513540	+	0.878622i
$261$	4.93719	+	4.93719i	0.305604	+	0.305604i
$262$	−1.92535	+	12.9442i	−0.118948	+	0.799698i
$263$	5.11593			0.315462			0.157731	−	0.987482i	$-0.449582\pi$
$263$	5.11593			0.315462			0.157731	+	0.987482i	$0.449582\pi$
$264$	0.939595	−	0.334931i	0.0578281	−	0.0206136i
$265$	−4.15146	+	17.4461i	−0.255022	+	1.07171i
$266$	−2.30135	+	15.4721i	−0.141105	+	0.948655i
$267$	7.40788	−	7.40788i	0.453355	−	0.453355i
$268$	−15.7181	+	8.38546i	−0.960136	+	0.512224i
$269$	19.1506	−	19.1506i	1.16763	−	1.16763i	0.184870	−	0.982763i	$-0.440814\pi$
$269$	19.1506	−	19.1506i	1.16763	−	1.16763i	0.982763	−	0.184870i	$-0.0591864\pi$
$270$	−3.01501	−	7.04994i	−0.183487	−	0.429046i
$271$	4.72066			0.286760			0.143380	−	0.989668i	$-0.454203\pi$
$271$	4.72066			0.286760			0.143380	+	0.989668i	$0.454203\pi$
$272$	−4.23101	+	6.31044i	−0.256543	+	0.382627i
$273$			34.8876i			2.11149i
$274$	−2.07379	+	1.53675i	−0.125282	+	0.0928385i
$275$	−0.636609	+	0.209674i	−0.0383890	+	0.0126438i
$276$	23.5953	−	12.5879i	1.42027	−	0.757702i
$277$	12.8887	−	12.8887i	0.774408	−	0.774408i	−0.204466	−	0.978874i	$-0.565546\pi$
$277$	12.8887	−	12.8887i	0.774408	−	0.774408i	0.978874	+	0.204466i	$0.0655457\pi$
$278$	10.6218	+	1.57990i	0.637052	+	0.0947561i
$279$		−	4.99822i		−	0.299235i
$280$	−17.8214	−	14.3113i	−1.06503	−	0.855263i
$281$			16.4934i			0.983913i	0.870620	+	0.491956i	$0.163718\pi$
$281$			16.4934i			0.983913i	−0.870620	+	0.491956i	$0.836282\pi$
$282$	1.38974	−	9.34334i	0.0827581	−	0.556388i
$283$	7.69771	−	7.69771i	0.457581	−	0.457581i	−0.440279	−	0.897861i	$-0.645121\pi$
$283$	7.69771	−	7.69771i	0.457581	−	0.457581i	0.897861	+	0.440279i	$0.145121\pi$
$284$	21.6357	+	6.58188i	1.28384	+	0.390563i
$285$	−15.3330	+	9.43844i	−0.908250	+	0.559085i
$286$	−0.414157	−	0.558889i	−0.0244896	−	0.0330478i
$287$		−	30.8069i		−	1.81847i
$288$	1.04455	+	22.1595i	0.0615504	+	1.30576i
$289$	13.3923			0.787783
$290$	2.21390	+	5.17672i	0.130005	+	0.303988i
$291$	−19.1692	+	19.1692i	−1.12372	+	1.12372i
$292$	9.41735	−	30.9564i	0.551109	−	1.81158i
$293$	5.75538	−	5.75538i	0.336233	−	0.336233i	−0.518715	−	0.854947i	$-0.673589\pi$
$293$	5.75538	−	5.75538i	0.336233	−	0.336233i	0.854947	+	0.518715i	$0.173589\pi$
$294$	−22.3033	−	3.31743i	−1.30075	−	0.193476i
$295$	−24.0507	−	5.72307i	−1.40028	−	0.333210i
$296$	−8.13878	−	3.86122i	−0.473057	−	0.224429i
$297$	0.325031			0.0188602
$298$	−8.66299	−	1.28855i	−0.501834	−	0.0746436i
$299$	−13.1872	−	13.1872i	−0.762634	−	0.762634i
$300$	−0.601165	−	26.3021i	−0.0347083	−	1.51855i
$301$	5.83427	−	5.83427i	0.336282	−	0.336282i
$302$	10.9131	+	14.7269i	0.627980	+	0.847435i
$303$			4.68417i			0.269098i
$304$	12.0110	−	2.36931i	0.688877	−	0.135889i
$305$	2.53590	−	10.6569i	0.145205	−	0.610212i
$306$	−8.46353	+	6.27178i	−0.483828	+	0.358534i
$307$	−9.60547	−	9.60547i	−0.548213	−	0.548213i	0.377711	−	0.925924i	$-0.376711\pi$
$307$	−9.60547	−	9.60547i	−0.548213	−	0.548213i	−0.925924	+	0.377711i	$0.876711\pi$
$308$	0.854848	−	0.456053i	0.0487095	−	0.0259861i
$309$	−20.2134	−	20.2134i	−1.14990	−	1.14990i
$310$	1.49972	−	3.74099i	0.0851786	−	0.212474i
$311$		−	20.3415i		−	1.15346i	−0.816934	−	0.576731i	$-0.804328\pi$
$311$		−	20.3415i		−	1.15346i	0.816934	−	0.576731i	$-0.195672\pi$
$312$	25.7195	−	9.16806i	1.45608	−	0.519039i
$313$	−25.6414			−1.44934			−0.724669	−	0.689097i	$-0.758007\pi$
$313$	−25.6414			−1.44934			−0.724669	+	0.689097i	$0.758007\pi$
$314$	−18.0558	−	2.68565i	−1.01895	−	0.151560i
$315$	−16.6124	−	26.9874i	−0.936003	−	1.52057i
$316$	0.661106	−	2.17316i	0.0371901	−	0.122250i
$317$	−0.945994	−	0.945994i	−0.0531323	−	0.0531323i	0.680041	−	0.733174i	$-0.261962\pi$
$317$	−0.945994	−	0.945994i	−0.0531323	−	0.0531323i	−0.733174	+	0.680041i	$0.761962\pi$
$318$	23.9745	−	17.7659i	1.34442	−	0.996264i
$319$	−0.238668			−0.0133629
$320$	−5.86718	+	16.8990i	−0.327985	+	0.944683i
$321$	35.2780			1.96903
$322$	20.8702	−	15.4656i	1.16305	−	0.861862i
$323$	4.11062	+	4.11062i	0.228721	+	0.228721i
$324$	3.13497	−	10.3052i	0.174165	−	0.572509i
$325$	−17.4259	+	5.73939i	−0.966615	+	0.318364i
$326$	12.1681	+	1.80990i	0.673929	+	0.100241i
$327$	−31.9057			−1.76439
$328$	−22.7112	+	8.09570i	−1.25401	+	0.447010i
$329$		−	9.17515i		−	0.505843i
$330$	1.03516	+	0.414986i	0.0569838	+	0.0228442i
$331$	6.16418	+	6.16418i	0.338814	+	0.338814i	0.855921	−	0.517107i	$-0.172991\pi$
$331$	6.16418	+	6.16418i	0.338814	+	0.338814i	−0.517107	+	0.855921i	$0.672991\pi$
$332$	9.37036	−	4.99900i	0.514265	−	0.274356i
$333$	−8.83176	−	8.83176i	−0.483977	−	0.483977i
$334$	−0.806928	+	0.597962i	−0.0441531	+	0.0327190i
$335$	−19.3767	−	4.61086i	−1.05866	−	0.251918i
$336$	7.36033	+	37.3124i	0.401539	+	2.03556i
$337$			28.2333i			1.53797i	0.639269	+	0.768983i	$0.279237\pi$
$337$			28.2333i			1.53797i	−0.639269	+	0.768983i	$0.720763\pi$
$338$	−0.390771	−	0.527331i	−0.0212552	−	0.0286830i
$339$	−23.3074	+	23.3074i	−1.26588	+	1.26588i
$340$	−8.21652	+	2.15471i	−0.445603	+	0.116855i
$341$	0.120809	+	0.120809i	0.00654219	+	0.00654219i
$342$	16.7895	+	2.49729i	0.907871	+	0.135038i
$343$	3.39562			0.183346
$344$	−5.83427	−	2.76791i	−0.314563	−	0.149236i
$345$	29.0875	+	6.92163i	1.56602	+	0.372648i
$346$	28.0460	+	4.17161i	1.50776	+	0.224267i
$347$	−13.0548	+	13.0548i	−0.700816	+	0.700816i	−0.964586	−	0.263770i	$-0.915034\pi$
$347$	−13.0548	+	13.0548i	−0.700816	+	0.700816i	0.263770	+	0.964586i	$0.415034\pi$
$348$	2.72660	−	8.96278i	0.146161	−	0.480455i
$349$	−20.3080	+	20.3080i	−1.08706	+	1.08706i	−0.0912314	+	0.995830i	$0.529080\pi$
$349$	−20.3080	+	20.3080i	−1.08706	+	1.08706i	−0.995830	+	0.0912314i	$0.970920\pi$
$350$	−4.33621	−	25.1837i	−0.231780	−	1.34612i
$351$	8.89708			0.474891
$352$	−0.560852	−	0.510358i	−0.0298935	−	0.0272022i
$353$		−	18.6814i		−	0.994310i	−0.867662	−	0.497155i	$-0.834378\pi$
$353$		−	18.6814i		−	0.994310i	0.867662	−	0.497155i	$-0.165622\pi$
$354$	24.4915	+	33.0504i	1.30171	+	1.75661i
$355$	13.2541	+	21.5316i	0.703453	+	1.14278i
$356$	−7.61929	−	2.31789i	−0.403822	−	0.122848i
$357$	−12.7697	+	12.7697i	−0.675847	+	0.675847i
$358$	−2.64969	+	17.8141i	−0.140041	+	0.941502i
$359$			16.4072i			0.865937i	0.901409	+	0.432968i	$0.142534\pi$
$359$			16.4072i			0.865937i	−0.901409	+	0.432968i	$0.857466\pi$
$360$	−15.5298	+	19.3388i	−0.818494	+	1.01925i
$361$			9.63268i			0.506983i
$362$	−28.0656	−	4.17452i	−1.47509	−	0.219408i
$363$	20.4302	−	20.4302i	1.07231	−	1.07231i
$364$	23.3997	−	12.4835i	1.22648	−	0.654316i
$365$	30.8075	−	18.9639i	1.61254	−	0.992617i
$366$	−14.6447	+	10.8522i	−0.765490	+	0.567255i
$367$			3.58049i			0.186900i	0.995624	+	0.0934500i	$0.0297895\pi$
$367$			3.58049i			0.186900i	−0.995624	+	0.0934500i	$0.970210\pi$
$368$	−16.8858	−	11.3216i	−0.880235	−	0.590178i
$369$	−33.4299			−1.74029
$370$	−3.96028	−	9.26025i	−0.205885	−	0.481417i
$371$	20.4945	−	20.4945i	1.06402	−	1.06402i
$372$	−5.91694	+	3.15663i	−0.306779	+	0.163664i
$373$	−8.72985	+	8.72985i	−0.452015	+	0.452015i	−0.896023	−	0.444008i	$-0.853556\pi$
$373$	−8.72985	+	8.72985i	−0.452015	+	0.452015i	0.444008	+	0.896023i	$0.353556\pi$
$374$	0.0529758	−	0.356160i	0.00273931	−	0.0184166i
$375$	18.9682	−	22.4814i	0.979512	−	1.16093i
$376$	−6.76403	+	2.41113i	−0.348828	+	0.124344i
$377$	−6.53307			−0.336470
$378$	−1.82319	+	12.2575i	−0.0937750	+	0.630455i
$379$	6.11276	+	6.11276i	0.313991	+	0.313991i	0.846454	−	0.532462i	$-0.178733\pi$
$379$	6.11276	+	6.11276i	0.313991	+	0.313991i	−0.532462	+	0.846454i	$0.678733\pi$
$380$	11.8170	+	6.90685i	0.606200	+	0.354314i
$381$	−5.47309	+	5.47309i	−0.280395	+	0.280395i
$382$	−21.5070	+	15.9375i	−1.10039	+	0.815431i
$383$			7.31434i			0.373745i	0.982384	+	0.186873i	$0.0598351\pi$
$383$			7.31434i			0.373745i	−0.982384	+	0.186873i	$0.940165\pi$
$384$	25.5729	−	15.2314i	1.30501	−	0.777273i
$385$	1.05383	+	0.250767i	0.0537080	+	0.0127803i
$386$	18.0086	+	24.3020i	0.916615	+	1.23694i
$387$	−6.33103	−	6.33103i	−0.321824	−	0.321824i
$388$	19.7163	+	5.99796i	1.00094	+	0.304501i
$389$	−9.74166	−	9.74166i	−0.493922	−	0.493922i	0.415618	−	0.909539i	$-0.363565\pi$
$389$	−9.74166	−	9.74166i	−0.493922	−	0.493922i	−0.909539	+	0.415618i	$0.863565\pi$
$390$	28.3355	+	11.3594i	1.43482	+	0.575205i
$391$		−	9.65368i		−	0.488207i
$392$	5.75555	+	16.1463i	0.290699	+	0.815509i
$393$	24.3454			1.22807
$394$	1.88124	−	12.6477i	0.0947753	−	0.637180i
$395$	2.16271	−	1.33128i	0.108818	−	0.0669841i
$396$	−0.494884	−	0.927634i	−0.0248689	−	0.0466154i
$397$	−8.04203	−	8.04203i	−0.403618	−	0.403618i	0.475888	−	0.879506i	$-0.342127\pi$
$397$	−8.04203	−	8.04203i	−0.403618	−	0.403618i	−0.879506	+	0.475888i	$0.842127\pi$
$398$	−4.93107	−	6.65429i	−0.247172	−	0.333549i
$399$	29.0998			1.45681
$400$	−17.4262	+	9.81468i	−0.871309	+	0.490734i
$401$	−6.77627			−0.338391			−0.169195	−	0.985583i	$-0.554117\pi$
$401$	−6.77627			−0.338391			−0.169195	+	0.985583i	$0.554117\pi$
$402$	19.7319	+	26.6275i	0.984140	+	1.32806i
$403$	3.30691	+	3.30691i	0.164729	+	0.164729i
$404$	3.14176	−	1.67610i	0.156308	−	0.0833890i
$405$	10.2556	−	6.31295i	0.509604	−	0.313693i
$406$	1.33876	−	9.00057i	0.0664415	−	0.446691i
$407$	0.426936			0.0211624
$408$	12.7697	+	6.05826i	0.632197	+	0.299928i
$409$		−	16.2601i		−	0.804010i	−0.915637	−	0.402005i	$-0.868313\pi$
$409$		−	16.2601i		−	0.804010i	0.915637	−	0.402005i	$-0.131687\pi$
$410$	−25.0211	−	10.0307i	−1.23571	−	0.495381i
$411$	3.39534	+	3.39534i	0.167480	+	0.167480i
$412$	−6.32470	+	20.7903i	−0.311595	+	1.02426i
$413$	28.2531	+	28.2531i	1.39024	+	1.39024i
$414$	−16.7824	−	22.6472i	−0.824809	−	1.11305i
$415$	11.5515	+	2.74877i	0.567039	+	0.134932i
$416$	−15.3522	−	13.9700i	−0.752703	−	0.684936i
$417$		−	19.9773i		−	0.978295i
$418$	−0.466171	+	0.345449i	−0.0228011	+	0.0168965i
$419$	−10.1408	+	10.1408i	−0.495409	+	0.495409i	−0.910005	−	0.414596i	$-0.863923\pi$
$419$	−10.1408	+	10.1408i	−0.495409	+	0.495409i	0.414596	+	0.910005i	$0.363923\pi$
$420$	−21.4563	+	36.7098i	−1.04696	+	1.79126i
$421$	−13.5849	−	13.5849i	−0.662088	−	0.662088i	0.293784	−	0.955872i	$-0.405085\pi$
$421$	−13.5849	−	13.5849i	−0.662088	−	0.662088i	−0.955872	+	0.293784i	$0.905085\pi$
$422$	5.66835	−	38.1087i	0.275931	−	1.85510i
$423$	−9.95637			−0.484095
$424$	−20.4945	−	9.72307i	−0.995302	−	0.472194i
$425$	−8.47908	−	4.27756i	−0.411296	−	0.207492i
$426$	6.18958	−	41.6129i	0.299886	−	2.01615i
$427$	−12.5190	+	12.5190i	−0.605836	+	0.605836i
$428$	−12.6232	−	23.6616i	−0.610167	−	1.14373i
$429$	−0.915049	+	0.915049i	−0.0441790	+	0.0441790i
$430$	−2.83892	−	6.63819i	−0.136905	−	0.320122i
$431$	1.37612			0.0662853			0.0331427	−	0.999451i	$-0.489448\pi$
$431$	1.37612			0.0662853			0.0331427	+	0.999451i	$0.489448\pi$
$432$	9.51545	−	1.87704i	0.457812	−	0.0903092i
$433$		−	19.9307i		−	0.957810i	−0.877867	−	0.478905i	$-0.841034\pi$
$433$		−	19.9307i		−	0.957810i	0.877867	−	0.478905i	$-0.158966\pi$
$434$	−5.23357	+	3.87826i	−0.251219	+	0.186162i
$435$	8.91966	−	5.49061i	0.427665	−	0.263255i
$436$	11.4166	+	21.3997i	0.546754	+	1.02486i
$437$	−10.9994	+	10.9994i	−0.526175	+	0.526175i
$438$	−59.5398	−	8.85604i	−2.84492	−	0.423158i
$439$			25.4133i			1.21291i	0.795117	+	0.606455i	$0.207409\pi$
$439$			25.4133i			1.21291i	−0.795117	+	0.606455i	$0.792591\pi$
$440$	−0.0920653	−	0.842792i	−0.00438904	−	0.0401785i
$441$			23.7666i			1.13174i
$442$	1.45010	−	9.74915i	0.0689745	−	0.463720i
$443$	−24.7208	+	24.7208i	−1.17452	+	1.17452i	−0.193402	+	0.981120i	$0.561952\pi$
$443$	−24.7208	+	24.7208i	−1.17452	+	1.17452i	−0.981120	+	0.193402i	$0.938048\pi$
$444$	−4.87741	+	16.0328i	−0.231471	+	0.760884i
$445$	−4.66759	−	7.58264i	−0.221265	−	0.359452i
$446$	16.9340	+	22.8518i	0.801847	+	1.08206i
$447$			16.2933i			0.770646i
$448$	22.3924	−	18.2879i	1.05794	−	0.864022i
$449$	5.62743			0.265575			0.132787	−	0.991145i	$-0.457607\pi$
$449$	5.62743			0.265575			0.132787	+	0.991145i	$0.457607\pi$
$450$	−27.3279	+	4.70541i	−1.28825	+	0.221815i
$451$	0.808017	−	0.808017i	0.0380481	−	0.0380481i
$452$	23.9725	+	7.29278i	1.12757	+	0.343023i
$453$	24.1117	−	24.1117i	1.13287	−	1.13287i
$454$	8.33687	+	1.24004i	0.391269	+	0.0581980i
$455$	28.8464	+	6.86425i	1.35234	+	0.321801i
$456$	−7.64710	−	21.4527i	−0.358108	−	1.00462i
$457$	−26.6040			−1.24448			−0.622241	−	0.782825i	$-0.713778\pi$
$457$	−26.6040			−1.24448			−0.622241	+	0.782825i	$0.713778\pi$
$458$	35.6684	+	5.30538i	1.66668	+	0.247904i
$459$	3.25656	+	3.25656i	0.152003	+	0.152003i
$460$	−5.76569	−	21.9862i	−0.268827	−	1.02511i
$461$	11.9468	−	11.9468i	0.556418	−	0.556418i	−0.371868	−	0.928286i	$-0.621283\pi$
$461$	11.9468	−	11.9468i	0.556418	−	0.556418i	0.928286	+	0.371868i	$0.121283\pi$
$462$	−1.07315	−	1.44817i	−0.0499272	−	0.0673749i
$463$		−	0.530134i		−	0.0246374i	−0.999924	−	0.0123187i	$-0.996079\pi$
$463$		−	0.530134i		−	0.0246374i	0.999924	−	0.0123187i	$-0.00392127\pi$
$464$	−6.98713	+	1.37830i	−0.324369	+	0.0639859i
$465$	−7.29420	−	1.73572i	−0.338260	−	0.0804920i
$466$	−5.20216	+	3.85499i	−0.240985	+	0.178579i
$467$	11.4219	+	11.4219i	0.528542	+	0.528542i	0.920138	−	0.391595i	$-0.128077\pi$
$467$	11.4219	+	11.4219i	0.528542	+	0.528542i	−0.391595	+	0.920138i	$0.628077\pi$
$468$	−13.5465	−	25.3921i	−0.626185	−	1.17375i
$469$	22.7625	+	22.7625i	1.05107	+	1.05107i
$470$	−7.45200	−	2.98743i	−0.343735	−	0.137800i
$471$			33.9592i			1.56476i
$472$	13.4039	−	28.2531i	0.616965	−	1.30045i
$473$	0.306048			0.0140721
$474$	−4.17974	−	0.621701i	−0.191982	−	0.0285557i
$475$	4.78724	+	14.5350i	0.219654	+	0.666910i
$476$	13.1342	+	3.99560i	0.602005	+	0.183138i
$477$	−22.2395	−	22.2395i	−1.01828	−	1.01828i
$478$	−20.8050	+	15.4173i	−0.951599	+	0.705169i
$479$	6.37434			0.291251			0.145625	−	0.989340i	$-0.453481\pi$
$479$	6.37434			0.291251			0.145625	+	0.989340i	$0.453481\pi$
$480$	32.7014	+	6.17089i	1.49261	+	0.281661i
$481$	11.6865			0.532859
$482$	10.5829	−	7.84228i	0.482037	−	0.357206i
$483$	−34.1700	−	34.1700i	−1.55479	−	1.55479i
$484$	−21.0132	−	6.39251i	−0.955147	−	0.290569i
$485$	12.0782	+	19.6214i	0.548444	+	0.890963i
$486$	−29.9956	−	4.46159i	−1.36063	−	0.202382i
$487$	31.3203			1.41926			0.709629	−	0.704575i	$-0.248862\pi$
$487$	31.3203			1.41926			0.709629	+	0.704575i	$0.248862\pi$
$488$	12.5190	+	5.93929i	0.566708	+	0.268859i
$489$		−	22.8857i		−	1.03493i
$490$	−7.13122	+	17.7885i	−0.322156	+	0.803602i
$491$	14.0893	+	14.0893i	0.635843	+	0.635843i	0.949527	−	0.313684i	$-0.101563\pi$
$491$	14.0893	+	14.0893i	0.635843	+	0.635843i	−0.313684	+	0.949527i	$0.601563\pi$
$492$	21.1127	+	39.5747i	0.951835	+	1.78416i
$493$	−2.39127	−	2.39127i	−0.107697	−	0.107697i
$494$	−12.7605	+	9.45597i	−0.574121	+	0.425444i
$495$	0.272119	−	1.14356i	0.0122308	−	0.0513990i
$496$	4.23442	+	2.83908i	0.190131	+	0.127479i
$497$		−	40.8639i		−	1.83299i
$498$	−11.7632	−	15.8740i	−0.527122	−	0.711332i
$499$	−2.30233	+	2.30233i	−0.103067	+	0.103067i	−0.756760	−	0.653693i	$-0.773219\pi$
$499$	−2.30233	+	2.30233i	−0.103067	+	0.103067i	0.653693	+	0.756760i	$0.273219\pi$
$500$	−21.8659	−	4.67796i	−0.977872	−	0.209205i
$501$	1.32115	+	1.32115i	0.0590248	+	0.0590248i
$502$	28.1218	+	4.18288i	1.25514	+	0.186691i
$503$	−14.7556			−0.657921			−0.328961	−	0.944344i	$-0.606698\pi$
$503$	−14.7556			−0.657921			−0.328961	+	0.944344i	$0.606698\pi$
$504$	37.7585	−	13.4595i	1.68190	−	0.599534i
$505$	3.87305	+	0.921626i	0.172348	+	0.0410118i
$506$	0.953032	+	0.141756i	0.0423674	+	0.00630180i
$507$	−0.863380	+	0.863380i	−0.0383441	+	0.0383441i
$508$	5.62929	+	1.71251i	0.249759	+	0.0759802i
$509$	−8.03042	+	8.03042i	−0.355942	+	0.355942i	−0.862315	−	0.506373i	$-0.830986\pi$
$509$	−8.03042	+	8.03042i	−0.355942	+	0.355942i	0.506373	+	0.862315i	$0.330986\pi$
$510$	6.21368	+	14.5293i	0.275146	+	0.643370i
$511$	−58.4680			−2.58647
$512$	−19.3665	−	11.7021i	−0.855887	−	0.517163i
$513$		−	7.42107i		−	0.327648i
$514$	−14.4273	−	19.4691i	−0.636361	−	0.858746i
$515$	−20.6903	+	12.7362i	−0.911723	+	0.561223i
$516$	−3.49636	+	11.4931i	−0.153919	+	0.505956i
$517$	0.240650	−	0.240650i	0.0105838	−	0.0105838i
$518$	−2.39480	+	16.1004i	−0.105222	+	0.707412i
$519$		−	52.7487i		−	2.31541i
$520$	−2.52010	−	23.0697i	−0.110514	−	1.01168i
$521$			13.7417i			0.602033i	0.953619	+	0.301017i	$0.0973259\pi$
$521$			13.7417i			0.602033i	−0.953619	+	0.301017i	$0.902674\pi$
$522$	−9.76692	−	1.45275i	−0.427487	−	0.0635851i
$523$	6.77116	−	6.77116i	0.296082	−	0.296082i	−0.543395	−	0.839477i	$-0.682861\pi$
$523$	6.77116	−	6.77116i	0.296082	−	0.296082i	0.839477	+	0.543395i	$0.182861\pi$
$524$	−8.71133	−	16.3289i	−0.380556	−	0.713332i
$525$	−45.1532	+	14.8717i	−1.97065	+	0.649053i
$526$	−5.81294	+	4.30759i	−0.253456	+	0.187820i
$527$			2.42083i			0.105453i
$528$	−0.785597	+	1.17170i	−0.0341887	+	0.0509916i
$529$	2.83186			0.123124
$530$	−9.97250	−	23.3185i	−0.433178	−	1.01289i
$531$	30.6587	−	30.6587i	1.33047	−	1.33047i
$532$	−10.4125	−	19.5178i	−0.451441	−	0.846202i
$533$	22.1179	−	22.1179i	0.958030	−	0.958030i
$534$	−2.17974	+	14.6545i	−0.0943265	+	0.634163i
$535$	6.94106	−	29.1692i	0.300088	−	1.26109i
$536$	10.7990	−	22.7625i	0.466447	−	0.983189i
$537$	33.5046			1.44583
$538$	−5.63499	+	37.8844i	−0.242942	+	1.63331i
$539$	−0.574451	−	0.574451i	−0.0247434	−	0.0247434i
$540$	9.36179	+	5.47181i	0.402867	+	0.235469i
$541$	7.82599	−	7.82599i	0.336465	−	0.336465i	−0.518570	−	0.855035i	$-0.673535\pi$
$541$	7.82599	−	7.82599i	0.336465	−	0.336465i	0.855035	+	0.518570i	$0.173535\pi$
$542$	−5.36381	+	3.97477i	−0.230395	+	0.170731i
$543$			52.7855i			2.26524i
$544$	−0.505913	−	10.7327i	−0.0216909	−	0.460160i
$545$	−6.27756	+	26.3809i	−0.268901	+	1.13003i
$546$	−29.3752	−	39.6407i	−1.25714	−	1.69647i
$547$	16.1263	+	16.1263i	0.689511	+	0.689511i	0.962124	−	0.272613i	$-0.0878878\pi$
$547$	16.1263	+	16.1263i	0.689511	+	0.689511i	−0.272613	+	0.962124i	$0.587888\pi$
$548$	1.06239	−	3.49224i	0.0453829	−	0.149181i
$549$	13.5849	+	13.5849i	0.579790	+	0.579790i
$550$	0.546798	−	0.774262i	0.0233155	−	0.0330146i
$551$			5.44924i			0.232146i
$552$	−16.2110	+	34.1700i	−0.689987	+	1.45437i
$553$	−4.10450			−0.174541
$554$	−3.79246	+	25.4969i	−0.161126	+	1.08326i
$555$	−15.9557	+	9.82174i	−0.677282	+	0.416909i
$556$	−13.3992	+	7.14833i	−0.568251	+	0.303157i
$557$	13.7333	+	13.7333i	0.581897	+	0.581897i	0.935424	−	0.353527i	$-0.115018\pi$
$557$	13.7333	+	13.7333i	0.581897	+	0.581897i	−0.353527	+	0.935424i	$0.615018\pi$
$558$	4.20847	+	5.67918i	0.178159	+	0.240419i
$559$	8.37745			0.354328
$560$	32.2995	+	1.25553i	1.36490	+	0.0530559i
$561$	−0.669862			−0.0282816
$562$	−13.8873	−	18.7405i	−0.585802	−	0.790519i
$563$	−13.2023	−	13.2023i	−0.556412	−	0.556412i	0.371872	−	0.928284i	$-0.378716\pi$
$563$	−13.2023	−	13.2023i	−0.556412	−	0.556412i	−0.928284	+	0.371872i	$0.878716\pi$
$564$	6.28796	+	11.7864i	0.264771	+	0.496299i
$565$	14.6856	+	23.8572i	0.617828	+	1.00368i
$566$	−2.26502	+	15.2279i	−0.0952060	+	0.640076i
$567$	−19.4636			−0.817393
$568$	−30.1253	+	10.7386i	−1.26403	+	0.450580i
$569$		−	7.32481i		−	0.307072i	−0.988143	−	0.153536i	$-0.950934\pi$
$569$		−	7.32481i		−	0.307072i	0.988143	−	0.153536i	$-0.0490661\pi$
$570$	9.47489	−	23.6347i	0.396860	−	0.989947i
$571$	−22.1916	−	22.1916i	−0.928688	−	0.928688i	0.0689332	−	0.997621i	$-0.478040\pi$
$571$	−22.1916	−	22.1916i	−0.928688	−	0.928688i	−0.997621	+	0.0689332i	$0.978040\pi$
$572$	0.941164	+	0.286315i	0.0393520	+	0.0119714i
$573$	35.2126	+	35.2126i	1.47103	+	1.47103i
$574$	25.9392	+	35.0040i	1.08268	+	1.46104i
$575$	11.4461	−	22.6888i	0.477337	−	0.946189i
$576$	−19.8450	−	24.2990i	−0.826876	−	1.01246i
$577$			9.39473i			0.391108i	0.980693	+	0.195554i	$0.0626504\pi$
$577$			9.39473i			0.391108i	−0.980693	+	0.195554i	$0.937350\pi$
$578$	−15.2169	+	11.2763i	−0.632939	+	0.469030i
$579$	39.7887	−	39.7887i	1.65356	−	1.65356i
$580$	−6.87430	−	4.01791i	−0.285440	−	0.166835i
$581$	−13.5699	−	13.5699i	−0.562973	−	0.562973i
$582$	5.64046	−	37.9212i	0.233805	−	1.57188i
$583$	1.07508			0.0445253
$584$	15.3647	+	43.1033i	0.635797	+	1.78363i
$585$	7.44871	−	31.3025i	0.307966	−	1.29420i
$586$	−1.69350	+	11.3855i	−0.0699578	+	0.470331i
$587$	10.7246	−	10.7246i	0.442650	−	0.442650i	−0.450252	−	0.892902i	$-0.648666\pi$
$587$	10.7246	−	10.7246i	0.442650	−	0.442650i	0.892902	+	0.450252i	$0.148666\pi$
$588$	28.1352	−	15.0099i	1.16027	−	0.618996i
$589$	2.75830	−	2.75830i	0.113654	−	0.113654i
$590$	32.1462	−	13.7478i	1.32344	−	0.565987i
$591$	−23.7876			−0.978493
$592$	12.4987	−	2.46553i	0.513695	−	0.101333i
$593$			38.2253i			1.56973i	0.619670	+	0.784863i	$0.287267\pi$
$593$			38.2253i			1.56973i	−0.619670	+	0.784863i	$0.712733\pi$
$594$	−0.369314	+	0.273675i	−0.0151531	+	0.0112290i
$595$	8.04603	+	13.0710i	0.329855	+	0.535859i
$596$	10.9282	−	5.83010i	0.447637	−	0.238810i
$597$	−10.8948	+	10.8948i	−0.445896	+	0.445896i
$598$	26.0873	+	3.88027i	1.06679	+	0.158676i
$599$			41.5801i			1.69892i	0.527656	+	0.849458i	$0.323071\pi$
$599$			41.5801i			1.69892i	−0.527656	+	0.849458i	$0.676929\pi$
$600$	22.8293	+	29.3794i	0.932003	+	1.19941i
$601$		−	23.1081i		−	0.942599i	−0.881973	−	0.471299i	$-0.843785\pi$
$601$		−	23.1081i		−	0.942599i	0.881973	−	0.471299i	$-0.156215\pi$
$602$	−1.71671	+	11.5416i	−0.0699679	+	0.470399i
$603$	24.7006	−	24.7006i	1.00589	−	1.00589i
$604$	−24.7999	−	7.54447i	−1.00909	−	0.306980i
$605$	−12.8727	−	20.9121i	−0.523351	−	0.850199i
$606$	−3.94405	−	5.32235i	−0.160216	−	0.216206i
$607$		−	15.1150i		−	0.613500i	−0.951790	−	0.306750i	$-0.900759\pi$
$607$		−	15.1150i		−	0.613500i	0.951790	−	0.306750i	$-0.0992415\pi$
$608$	−11.6524	+	12.8053i	−0.472568	+	0.519323i
$609$	−16.9282			−0.685965
$610$	6.09165	+	14.2440i	0.246644	+	0.576723i
$611$	6.58732	−	6.58732i	0.266494	−	0.266494i
$612$	4.33581	−	14.2525i	0.175265	−	0.576123i
$613$	1.18710	−	1.18710i	0.0479466	−	0.0479466i	−0.682727	−	0.730674i	$-0.739206\pi$
$613$	1.18710	−	1.18710i	0.0479466	−	0.0479466i	0.730674	+	0.682727i	$0.239206\pi$
$614$	19.0019	+	2.82637i	0.766854	+	0.114063i
$615$	−11.6091	+	48.7863i	−0.468125	+	1.96725i
$616$	−0.587318	+	1.23796i	−0.0236637	+	0.0498790i
$617$	−5.23711			−0.210838			−0.105419	−	0.994428i	$-0.533618\pi$
$617$	−5.23711			−0.210838			−0.105419	+	0.994428i	$0.533618\pi$
$618$	39.9869	+	5.94772i	1.60851	+	0.239252i
$619$	−6.52847	−	6.52847i	−0.262401	−	0.262401i	0.563628	−	0.826029i	$-0.309405\pi$
$619$	−6.52847	−	6.52847i	−0.262401	−	0.262401i	−0.826029	+	0.563628i	$0.809405\pi$
$620$	1.44585	+	5.51343i	0.0580666	+	0.221425i
$621$	−8.71408	+	8.71408i	−0.349684	+	0.349684i
$622$	17.1275	+	23.1129i	0.686748	+	0.926741i
$623$			14.3907i			0.576553i
$624$	−21.5041	+	32.0729i	−0.860854	+	1.28394i
$625$	−14.8564	−	20.1069i	−0.594256	−	0.804276i
$626$	29.1348	−	21.5899i	1.16446	−	0.862907i
$627$	0.763244	+	0.763244i	0.0304810	+	0.0304810i
$628$	22.7771	−	12.1514i	0.908904	−	0.484892i
$629$	4.27756	+	4.27756i	0.170557	+	0.170557i
$630$	41.5989	+	16.6766i	1.65734	+	0.664411i
$631$			21.7193i			0.864633i	0.901722	+	0.432316i	$0.142304\pi$
$631$			21.7193i			0.864633i	−0.901722	+	0.432316i	$0.857696\pi$
$632$	1.07862	+	3.02588i	0.0429050	+	0.120363i
$633$	−71.6746			−2.84881
$634$	1.87140	+	0.278355i	0.0743227	+	0.0110549i
$635$	3.44851	+	5.60221i	0.136850	+	0.222317i
$636$	−12.2820	+	40.3728i	−0.487011	+	1.60088i
$637$	−15.7244	−	15.7244i	−0.623025	−	0.623025i
$638$	0.271185	−	0.200958i	0.0107363	−	0.00795599i
$639$	−44.3432			−1.75419
$640$	−7.56234	−	24.1415i	−0.298928	−	0.954276i
$641$	−45.3927			−1.79291			−0.896453	−	0.443139i	$-0.853865\pi$
$641$	−45.3927			−1.79291			−0.896453	+	0.443139i	$0.853865\pi$
$642$	−40.0843	+	29.7039i	−1.58200	+	1.17232i
$643$	20.5408	+	20.5408i	0.810049	+	0.810049i	0.984641	−	0.174592i	$-0.0558607\pi$
$643$	20.5408	+	20.5408i	0.810049	+	0.810049i	−0.174592	+	0.984641i	$0.555861\pi$
$644$	−10.6917	+	35.1452i	−0.421310	+	1.38492i
$645$	−11.4378	+	7.04069i	−0.450363	+	0.277227i
$646$	−8.13178	−	1.20954i	−0.319941	−	0.0475885i
$647$	−31.7472			−1.24811			−0.624056	−	0.781379i	$-0.714516\pi$
$647$	−31.7472			−1.24811			−0.624056	+	0.781379i	$0.714516\pi$
$648$	5.11481	+	14.3488i	0.200929	+	0.563673i
$649$			1.48207i			0.0581764i
$650$	14.9675	−	21.1939i	0.587073	−	0.831291i
$651$	8.56873	+	8.56873i	0.335835	+	0.335835i
$652$	−15.3498	+	8.18900i	−0.601146	+	0.320706i
$653$	−4.30078	−	4.30078i	−0.168302	−	0.168302i	0.617930	−	0.786233i	$-0.287971\pi$
$653$	−4.30078	−	4.30078i	−0.168302	−	0.168302i	−0.786233	+	0.617930i	$0.787971\pi$
$654$	36.2526	−	26.8645i	1.41759	−	1.05048i
$655$	4.79005	−	20.1297i	0.187163	−	0.786534i
$656$	18.9888	−	28.3214i	0.741389	−	1.10576i
$657$			63.4463i			2.47527i
$658$	7.72543	+	10.4252i	0.301169	+	0.406416i
$659$	−18.2156	+	18.2156i	−0.709579	+	0.709579i	−0.966447	−	0.256868i	$-0.917310\pi$
$659$	−18.2156	+	18.2156i	−0.709579	+	0.709579i	0.256868	+	0.966447i	$0.417310\pi$
$660$	−1.52561	+	0.400077i	−0.0593843	+	0.0155730i
$661$	−19.7679	−	19.7679i	−0.768883	−	0.768883i	0.209027	−	0.977910i	$-0.432970\pi$
$661$	−19.7679	−	19.7679i	−0.768883	−	0.768883i	−0.977910	+	0.209027i	$0.932970\pi$
$662$	−12.1942	−	1.81379i	−0.473941	−	0.0704948i
$663$	−18.3361			−0.712116
$664$	−6.43785	+	13.5699i	−0.249837	+	0.526613i
$665$	5.72549	−	24.0608i	0.222025	−	0.933039i
$666$	17.4713	+	2.59871i	0.676999	+	0.100698i
$667$	6.39869	−	6.39869i	0.247758	−	0.247758i
$668$	0.413383	−	1.35886i	0.0159943	−	0.0525758i
$669$	37.4144	−	37.4144i	1.44652	−	1.44652i
$670$	25.8990	−	11.0761i	1.00056	−	0.427906i
$671$	−0.656708			−0.0253519
$672$	−39.7799	−	36.1985i	−1.53454	−	1.39639i
$673$			8.43246i			0.325047i	0.986705	+	0.162524i	$0.0519634\pi$
$673$			8.43246i			0.325047i	−0.986705	+	0.162524i	$0.948037\pi$
$674$	−23.7723	−	32.0798i	−0.915675	−	1.23567i
$675$	3.79259	+	11.5150i	0.145977	+	0.443214i
$676$	0.888021	+	0.270148i	0.0341547	+	0.0103903i
$677$	20.8693	−	20.8693i	0.802073	−	0.802073i	−0.181346	−	0.983419i	$-0.558046\pi$
$677$	20.8693	−	20.8693i	0.802073	−	0.802073i	0.983419	+	0.181346i	$0.0580455\pi$
$678$	6.85810	−	46.1075i	0.263384	−	1.77075i
$679$		−	37.2386i		−	1.42909i
$680$	7.52169	−	9.36653i	0.288444	−	0.359190i
$681$		−	15.6799i		−	0.600856i
$682$	−0.238989	−	0.0355477i	−0.00915137	−	0.00136119i
$683$	16.4398	−	16.4398i	0.629051	−	0.629051i	−0.318778	−	0.947829i	$-0.603272\pi$
$683$	16.4398	−	16.4398i	0.629051	−	0.629051i	0.947829	+	0.318778i	$0.103272\pi$
$684$	−21.1796	+	11.2991i	−0.809822	+	0.432033i
$685$	3.47544	−	2.13935i	0.132790	−	0.0817404i
$686$	−3.85824	+	2.85910i	−0.147308	+	0.109161i
$687$		−	67.0849i		−	2.55945i
$688$	8.95970	−	1.76741i	0.341585	−	0.0673820i
$689$	29.4282			1.12112
$690$	−38.8784	+	16.6269i	−1.48008	+	0.632976i
$691$	17.4076	−	17.4076i	0.662216	−	0.662216i	−0.293686	−	0.955902i	$-0.594882\pi$
$691$	17.4076	−	17.4076i	0.662216	−	0.662216i	0.955902	+	0.293686i	$0.0948821\pi$
$692$	−35.3795	+	18.8746i	−1.34493	+	0.717506i
$693$	−1.34337	+	1.34337i	−0.0510304	+	0.0510304i
$694$	3.84131	−	25.8254i	0.145814	−	0.980318i
$695$	−16.5180	−	3.93061i	−0.626565	−	0.149097i
$696$	4.44854	+	12.4797i	0.168621	+	0.473040i
$697$	16.1914			0.613293
$698$	5.97554	−	40.1740i	0.226178	−	1.52061i
$699$	8.51731	+	8.51731i	0.322154	+	0.322154i
$700$	26.1315	+	24.9637i	0.987678	+	0.943538i
$701$	−25.3888	+	25.3888i	−0.958920	+	0.958920i	−0.999189	−	0.0402687i	$-0.987179\pi$
$701$	−25.3888	+	25.3888i	−0.958920	+	0.958920i	0.0402687	+	0.999189i	$0.487179\pi$
$702$	−10.1092	+	7.49130i	−0.381548	+	0.282741i
$703$		−	9.74773i		−	0.367643i
$704$	1.06698	+	0.107655i	0.0402134	+	0.00405739i
$705$	−3.45752	+	14.5299i	−0.130218	+	0.547229i
$706$	15.7296	+	21.2266i	0.591993	+	0.798873i
$707$	−4.54979	−	4.54979i	−0.171113	−	0.171113i
$708$	−55.6566	−	16.9315i	−2.09170	−	0.636325i
$709$	17.6201	+	17.6201i	0.661738	+	0.661738i	0.955790	−	0.294051i	$-0.0950036\pi$
$709$	17.6201	+	17.6201i	0.661738	+	0.661738i	−0.294051	+	0.955790i	$0.595004\pi$
$710$	−33.1893	−	13.3053i	−1.24557	−	0.499338i
$711$			4.45398i			0.167037i
$712$	10.6090	−	3.78172i	0.397590	−	0.141726i
$713$	−6.47779			−0.242595
$714$	3.75745	−	25.2616i	0.140619	−	0.945391i
$715$	0.576559	+	0.936636i	0.0215621	+	0.0350282i
$716$	−11.9887	−	22.4721i	−0.448037	−	0.839822i
$717$	34.0633	+	34.0633i	1.27212	+	1.27212i
$718$	−13.8148	−	18.6425i	−0.515562	−	0.695732i
$719$	−42.6068			−1.58896			−0.794482	−	0.607287i	$-0.792258\pi$
$719$	−42.6068			−1.58896			−0.794482	+	0.607287i	$0.792258\pi$
$720$	1.36243	−	35.0496i	0.0507750	−	1.30622i
$721$	39.2671			1.46238
$722$	−8.11067	−	10.9450i	−0.301848	−	0.407332i
$723$	−17.3269	−	17.3269i	−0.644396	−	0.644396i
$724$	35.4042	−	18.8878i	1.31579	−	0.701960i
$725$	−2.78488	−	8.45542i	−0.103428	−	0.314026i
$726$	−6.01150	+	40.4157i	−0.223108	+	1.49997i
$727$	50.5830			1.87602			0.938010	−	0.346609i	$-0.112667\pi$
$727$	50.5830			1.87602			0.938010	+	0.346609i	$0.112667\pi$
$728$	−16.0767	+	33.8868i	−0.595841	+	1.25593i
$729$			40.2583i			1.49105i
$730$	−19.0372	+	47.4873i	−0.704597	+	1.75758i
$731$	3.06636	+	3.06636i	0.113413	+	0.113413i
$732$	7.50237	−	24.6615i	0.277296	−	0.911516i
$733$	−6.17299	−	6.17299i	−0.228005	−	0.228005i	0.583854	−	0.811859i	$-0.301544\pi$
$733$	−6.17299	−	6.17299i	−0.228005	−	0.228005i	−0.811859	+	0.583854i	$0.801544\pi$
$734$	−3.01475	−	4.06830i	−0.111277	−	0.150164i
$735$	34.6841	+	8.25338i	1.27934	+	0.304431i
$736$	28.7191	−	1.35375i	1.05860	−	0.0499000i
$737$			1.19405i			0.0439834i
$738$	37.9845	−	28.1478i	1.39823	−	1.03614i
$739$	22.8974	−	22.8974i	0.842293	−	0.842293i	−0.146864	−	0.989157i	$-0.546918\pi$
$739$	22.8974	−	22.8974i	0.842293	−	0.842293i	0.989157	+	0.146864i	$0.0469178\pi$
$740$	12.2969	+	7.18734i	0.452043	+	0.264212i
$741$	20.8923	+	20.8923i	0.767497	+	0.767497i
$742$	−6.03043	+	40.5430i	−0.221384	+	1.48838i
$743$	11.8975			0.436478			0.218239	−	0.975895i	$-0.429969\pi$
$743$	11.8975			0.436478			0.218239	+	0.975895i	$0.429969\pi$
$744$	4.06520	−	8.56873i	0.149037	−	0.314145i
$745$	13.4719	+	3.20576i	0.493573	+	0.117450i
$746$	2.56873	−	17.2697i	0.0940477	−	0.632289i
$747$	−14.7253	+	14.7253i	−0.538770	+	0.538770i
$748$	0.239691	+	0.449288i	0.00876398	+	0.0164276i
$749$	−34.2660	+	34.2660i	−1.25205	+	1.25205i
$750$	−2.62321	+	41.5154i	−0.0957862	+	1.51593i
$751$	23.4102			0.854250			0.427125	−	0.904193i	$-0.359526\pi$
$751$	23.4102			0.854250			0.427125	+	0.904193i	$0.359526\pi$
$752$	5.65541	−	8.43490i	0.206232	−	0.307589i
$753$		−	52.8913i		−	1.92747i
$754$	7.42314	−	5.50081i	0.270335	−	0.200328i
$755$	−15.1924	−	24.6806i	−0.552910	−	0.898218i
$756$	−8.24913	−	15.4625i	−0.300018	−	0.562367i
$757$	11.3218	−	11.3218i	0.411496	−	0.411496i	−0.470763	−	0.882260i	$-0.656021\pi$
$757$	11.3218	−	11.3218i	0.411496	−	0.411496i	0.882260	+	0.470763i	$0.156021\pi$
$758$	−12.0925	−	1.79866i	−0.439219	−	0.0653301i
$759$		−	1.79246i		−	0.0650620i
$760$	−19.2425	+	2.10202i	−0.697999	+	0.0762484i
$761$		−	8.53590i		−	0.309426i	−0.987959	−	0.154713i	$-0.950555\pi$
$761$		−	8.53590i		−	0.309426i	0.987959	−	0.154713i	$-0.0494453\pi$
$762$	1.61043	−	10.8271i	0.0583399	−	0.392223i
$763$	30.9904	−	30.9904i	1.12193	−	1.12193i
$764$	11.0179	−	36.2176i	0.398613	−	1.31031i
$765$	14.1839	−	8.73111i	0.512821	−	0.315674i
$766$	−6.15864	−	8.31085i	−0.222521	−	0.300283i
$767$			40.5687i			1.46485i
$768$	−16.2322	+	38.8388i	−0.585730	+	1.40147i
$769$	−17.8384			−0.643270			−0.321635	−	0.946864i	$-0.604232\pi$
$769$	−17.8384			−0.643270			−0.321635	+	0.946864i	$0.604232\pi$
$770$	−1.40855	+	0.602385i	−0.0507605	+	0.0217085i
$771$	−31.8761	+	31.8761i	−1.14799	+	1.14799i
$772$	−40.9243	−	12.4497i	−1.47290	−	0.448076i
$773$	−23.9457	+	23.9457i	−0.861267	+	0.861267i	−0.991485	−	0.130219i	$-0.958432\pi$
$773$	−23.9457	+	23.9457i	−0.861267	+	0.861267i	0.130219	+	0.991485i	$0.458432\pi$
$774$	12.5243	+	1.86288i	0.450176	+	0.0669599i
$775$	−2.87032	+	5.68962i	−0.103105	+	0.204377i
$776$	−27.4527	+	9.78588i	−0.985495	+	0.351293i
$777$	30.2816			1.08635
$778$	19.2713	+	2.86645i	0.690910	+	0.102767i
$779$	−18.4485	−	18.4485i	−0.660988	−	0.660988i
$780$	−41.7605	+	10.9513i	−1.49527	+	0.392120i
$781$	1.07180	−	1.07180i	0.0383519	−	0.0383519i
$782$	8.12835	+	10.9689i	0.290669	+	0.392247i
$783$			4.31705i			0.154279i
$784$	−20.1348	−	13.4999i	−0.719099	−	0.482139i
$785$	28.0788	+	6.68160i	1.00218	+	0.238476i
$786$	−27.6623	+	20.4987i	−0.986682	+	0.731166i
$787$	−32.3914	−	32.3914i	−1.15463	−	1.15463i	−0.985614	−	0.169014i	$-0.945942\pi$
$787$	−32.3914	−	32.3914i	−1.15463	−	1.15463i	−0.169014	−	0.985614i	$-0.554058\pi$
$788$	8.51174	+	15.9548i	0.303218	+	0.568366i
$789$	9.51731	+	9.51731i	0.338825	+	0.338825i
$790$	−1.33642	+	3.33365i	−0.0475478	+	0.118606i
$791$		−	45.2775i		−	1.60988i
$792$	1.34337	+	0.637326i	0.0477346	+	0.0226464i
$793$	−17.9761			−0.638348
$794$	15.9090	+	2.36634i	0.564591	+	0.0839782i
$795$	−40.1786	+	24.7324i	−1.42499	+	0.877169i
$796$	11.2058	+	3.40895i	0.397178	+	0.120827i
$797$	−1.92658	−	1.92658i	−0.0682428	−	0.0682428i	0.672162	−	0.740404i	$-0.265366\pi$
$797$	−1.92658	−	1.92658i	−0.0682428	−	0.0682428i	−0.740404	+	0.672162i	$0.765366\pi$
$798$	−33.0644	+	24.5019i	−1.17047	+	0.867358i
$799$	4.82225			0.170599
$800$	11.5364	−	25.8246i	0.407875	−	0.913038i
$801$	15.6160			0.551765
$802$	7.69948	−	5.70559i	0.271878	−	0.201471i
$803$	−1.53353	−	1.53353i	−0.0541170	−	0.0541170i
$804$	−44.8405	−	13.6411i	−1.58140	−	0.481084i
$805$	−34.9761	+	21.5300i	−1.23275	+	0.758833i
$806$	−6.54185	−	0.973046i	−0.230427	−	0.0342741i
$807$	71.2527			2.50822
$808$	−2.15853	+	4.54979i	−0.0759367	+	0.160061i
$809$			49.8993i			1.75437i	0.480157	+	0.877183i	$0.340580\pi$
$809$			49.8993i			1.75437i	−0.480157	+	0.877183i	$0.659420\pi$
$810$	−6.33734	+	15.8082i	−0.222671	+	0.555443i
$811$	22.9363	+	22.9363i	0.805401	+	0.805401i	0.983934	−	0.178533i	$-0.0571351\pi$
$811$	22.9363	+	22.9363i	0.805401	+	0.805401i	−0.178533	+	0.983934i	$0.557135\pi$
$812$	6.05728	+	11.3540i	0.212569	+	0.398449i
$813$	8.78196	+	8.78196i	0.307997	+	0.307997i
$814$	−0.485102	+	0.359478i	−0.0170028	+	0.0125997i
$815$	−18.9228	−	4.50284i	−0.662836	−	0.157727i
$816$	−19.6105	+	3.86842i	−0.686506	+	0.135422i
$817$		−	6.98764i		−	0.244467i
$818$	13.6909	+	18.4754i	0.478692	+	0.645977i
$819$	−36.7721	+	36.7721i	−1.28492	+	1.28492i
$820$	36.8758	−	9.67036i	1.28776	−	0.337704i
$821$	10.7321	+	10.7321i	0.374551	+	0.374551i	0.869132	−	0.494581i	$-0.164678\pi$
$821$	10.7321	+	10.7321i	0.374551	+	0.374551i	−0.494581	+	0.869132i	$0.664678\pi$
$822$	−6.71678	−	0.999064i	−0.234274	−	0.0348464i
$823$	8.56875			0.298688			0.149344	−	0.988785i	$-0.452284\pi$
$823$	8.56875			0.298688			0.149344	+	0.988785i	$0.452284\pi$
$824$	−10.3190	−	28.9482i	−0.359478	−	1.00846i
$825$	−1.57436	−	0.794239i	−0.0548123	−	0.0276519i
$826$	−55.8913	−	8.31336i	−1.94471	−	0.289259i
$827$	10.0841	−	10.0841i	0.350660	−	0.350660i	−0.509695	−	0.860355i	$-0.670242\pi$
$827$	10.0841	−	10.0841i	0.350660	−	0.350660i	0.860355	+	0.509695i	$0.170242\pi$
$828$	38.1377	+	11.6020i	1.32538	+	0.403197i
$829$	0.656708	−	0.656708i	0.0228084	−	0.0228084i	−0.695611	−	0.718419i	$-0.744866\pi$
$829$	0.656708	−	0.656708i	0.0228084	−	0.0228084i	0.718419	+	0.695611i	$0.244866\pi$
$830$	−15.4397	+	6.60301i	−0.535920	+	0.229194i
$831$	47.9544			1.66352
$832$	29.2065	+	2.94683i	1.01255	+	0.102163i
$833$		−	11.5111i		−	0.398836i
$834$	16.8208	+	22.6991i	0.582458	+	0.786005i
$835$	1.35232	−	0.832439i	0.0467990	−	0.0288077i
$836$	0.238816	−	0.785027i	0.00825962	−	0.0271507i
$837$	2.18521	−	2.18521i	0.0755318	−	0.0755318i
$838$	2.98388	−	20.0608i	0.103077	−	0.692990i
$839$		−	5.41206i		−	0.186845i	−0.995627	−	0.0934225i	$-0.970219\pi$
$839$		−	5.41206i		−	0.186845i	0.995627	−	0.0934225i	$-0.0297807\pi$
$840$	−6.52998	−	59.7773i	−0.225306	−	2.06251i
$841$			25.8300i			0.890690i
$842$	26.8742	+	3.99731i	0.926145	+	0.137756i
$843$	−30.6831	+	30.6831i	−1.05678	+	1.05678i
$844$	25.6467	+	48.0734i	0.882797	+	1.65476i
$845$	0.544003	+	0.883749i	0.0187143	+	0.0304019i
$846$	11.3128	−	8.38322i	0.388943	−	0.288221i
$847$			39.6882i			1.36370i
$848$	31.4735	−	6.20854i	1.08080	−	0.213202i
$849$	28.6405			0.982939
$850$	13.2360	−	2.27901i	0.453990	−	0.0781694i
$851$	−11.4461	+	11.4461i	−0.392368	+	0.392368i
$852$	28.0050	+	52.4939i	0.959436	+	1.79841i
$853$	−17.0301	+	17.0301i	−0.583098	+	0.583098i	−0.935753	−	0.352655i	$-0.885279\pi$
$853$	−17.0301	+	17.0301i	−0.583098	+	0.583098i	0.352655	+	0.935753i	$0.385279\pi$
$854$	3.68366	−	24.7655i	0.126052	−	0.847458i
$855$	−26.1095	−	6.21298i	−0.892926	−	0.212480i
$856$	34.2660	+	16.2566i	1.17119	+	0.555638i
$857$	53.1079			1.81413			0.907066	−	0.420988i	$-0.138317\pi$
$857$	53.1079			1.81413			0.907066	+	0.420988i	$0.138317\pi$
$858$	0.269250	−	1.81018i	0.00919203	−	0.0617986i
$859$	−10.7609	−	10.7609i	−0.367158	−	0.367158i	0.499282	−	0.866440i	$-0.333597\pi$
$859$	−10.7609	−	10.7609i	−0.367158	−	0.367158i	−0.866440	+	0.499282i	$0.833597\pi$
$860$	8.81502	+	5.15223i	0.300590	+	0.175690i
$861$	57.3108	−	57.3108i	1.95315	−	1.95315i
$862$	−1.56360	+	1.15869i	−0.0532566	+	0.0394650i
$863$			21.2106i			0.722016i	0.932563	+	0.361008i	$0.117567\pi$
$863$			21.2106i			0.722016i	−0.932563	+	0.361008i	$0.882433\pi$
$864$	−9.23139	+	10.1447i	−0.314058	+	0.345131i
$865$	−43.6146	−	10.3785i	−1.48294	−	0.352879i
$866$	16.7816	+	22.6461i	0.570261	+	0.769546i
$867$	24.9141	+	24.9141i	0.846126	+	0.846126i
$868$	2.68112	−	8.81327i	0.0910031	−	0.299142i
$869$	−0.107655	−	0.107655i	−0.00365194	−	0.00365194i
$870$	−5.51182	+	13.7490i	−0.186868	+	0.466134i
$871$			32.6847i			1.10748i
$872$	−30.9904	−	14.7026i	−1.04947	−	0.497892i
$873$	−40.4093			−1.36765
$874$	3.23654	−	21.7595i	0.109478	−	0.736026i
$875$	3.41242	+	40.2605i	0.115361	+	1.36105i
$876$	75.1083	−	40.0696i	2.53767	−	1.35383i
$877$	−25.6041	−	25.6041i	−0.864589	−	0.864589i	0.127278	−	0.991867i	$-0.459376\pi$
$877$	−25.6041	−	25.6041i	−0.864589	−	0.864589i	−0.991867	+	0.127278i	$0.959376\pi$
$878$	−21.3979	−	28.8756i	−0.722143	−	0.974506i
$879$	21.4138			0.722268
$880$	0.814235	+	0.880097i	0.0274479	+	0.0296681i
$881$	−13.0675			−0.440255			−0.220128	−	0.975471i	$-0.570647\pi$
$881$	−13.0675			−0.440255			−0.220128	+	0.975471i	$0.570647\pi$
$882$	−20.0114	−	27.0046i	−0.673819	−	0.909293i
$883$	−12.1957	−	12.1957i	−0.410419	−	0.410419i	0.471466	−	0.881884i	$-0.343725\pi$
$883$	−12.1957	−	12.1957i	−0.410419	−	0.410419i	−0.881884	+	0.471466i	$0.843725\pi$
$884$	6.56107	+	12.2984i	0.220673	+	0.413639i
$885$	−34.0953	−	55.3889i	−1.14610	−	1.86188i
$886$	7.27401	−	48.9036i	0.244375	−	1.64295i
$887$	−36.3716			−1.22124			−0.610619	−	0.791924i	$-0.709079\pi$
$887$	−36.3716			−1.22124			−0.610619	+	0.791924i	$0.709079\pi$
$888$	−7.95765	−	22.3239i	−0.267041	−	0.749141i
$889$		−	10.6322i		−	0.356591i
$890$	11.6881	+	4.68562i	0.391785	+	0.157062i
$891$	−0.510500	−	0.510500i	−0.0171024	−	0.0171024i
$892$	−38.4822	−	11.7068i	−1.28848	−	0.391973i
$893$	−5.49449	−	5.49449i	−0.183866	−	0.183866i
$894$	−13.7189	−	18.5131i	−0.458828	−	0.619171i
$895$	6.59213	−	27.7028i	0.220351	−	0.926004i
$896$	−10.0448	+	39.6337i	−0.335575	+	1.32407i
$897$		−	49.0649i		−	1.63823i
$898$	−6.39411	+	4.73827i	−0.213374	+	0.158118i
$899$	−1.60458	+	1.60458i	−0.0535159	+	0.0535159i
$900$	27.0892	−	28.3565i	0.902974	−	0.945216i
$901$	10.7715	+	10.7715i	0.358849	+	0.358849i
$902$	−0.237756	+	1.59845i	−0.00791641	+	0.0532225i
$903$	21.7073			0.722373
$904$	−33.3791	+	11.8984i	−1.11017	+	0.395735i
$905$	43.6451	+	10.3857i	1.45081	+	0.345233i
$906$	−7.09479	+	47.6987i	−0.235709	+	1.58468i
$907$	−35.4831	+	35.4831i	−1.17820	+	1.17820i	−0.197996	+	0.980203i	$0.563443\pi$
$907$	−35.4831	+	35.4831i	−1.17820	+	1.17820i	−0.980203	+	0.197996i	$0.936557\pi$
$908$	−10.5168	+	5.61062i	−0.349012	+	0.186195i
$909$	−4.93719	+	4.93719i	−0.163756	+	0.163756i
$910$	−38.5561	+	16.4891i	−1.27812	+	0.546608i
$911$	22.6536			0.750547			0.375274	−	0.926914i	$-0.377549\pi$
$911$	22.6536			0.750547			0.375274	+	0.926914i	$0.377549\pi$
$912$	26.7520	+	17.9366i	0.885848	+	0.593941i
$913$		−	0.711834i		−	0.0235583i
$914$	30.2286	−	22.4004i	0.999872	−	0.740941i
$915$	24.5429	−	15.1077i	0.811363	−	0.499445i
$916$	−44.9951	+	24.0045i	−1.48668	+	0.793129i
$917$	−23.6470	+	23.6470i	−0.780894	+	0.780894i
$918$	−6.44224	−	0.958229i	−0.212626	−	0.0316263i
$919$		−	19.9532i		−	0.658195i	−0.944296	−	0.329097i	$-0.893256\pi$
$919$		−	19.9532i		−	0.658195i	0.944296	−	0.329097i	$-0.106744\pi$
$920$	25.0635	+	20.1270i	0.826319	+	0.663567i
$921$		−	35.7386i		−	1.17763i
$922$	−3.51530	+	23.6336i	−0.115770	+	0.778331i
$923$	29.3383	−	29.3383i	0.965681	−	0.965681i
$924$	2.43870	+	0.741887i	0.0802275	+	0.0244063i
$925$	4.98165	+	15.1252i	0.163796	+	0.497315i
$926$	0.446370	+	0.602360i	0.0146686	+	0.0197948i
$927$		−	42.6105i		−	1.39951i
$928$	6.77855	−	7.44921i	0.222517	−	0.244532i
$929$	11.0293			0.361859			0.180929	−	0.983496i	$-0.442089\pi$
$929$	11.0293			0.361859			0.180929	+	0.983496i	$0.442089\pi$
$930$	9.74944	−	4.16949i	0.319697	−	0.136723i
$931$	−13.1158	+	13.1158i	−0.429853	+	0.429853i
$932$	2.66503	−	8.76039i	0.0872960	−	0.286956i
$933$	37.8418	−	37.8418i	1.23889	−	1.23889i
$934$	−22.5952	−	3.36085i	−0.739338	−	0.109970i
$935$	−0.131798	+	0.553868i	−0.00431024	+	0.0181134i
$936$	36.7721	+	17.4455i	1.20193	+	0.570224i
$937$	−36.6851			−1.19845			−0.599225	−	0.800581i	$-0.704524\pi$
$937$	−36.6851			−1.19845			−0.599225	+	0.800581i	$0.704524\pi$
$938$	−45.0295	−	6.69777i	−1.47027	−	0.218690i
$939$	−47.7014	−	47.7014i	−1.55668	−	1.55668i
$940$	10.9827	−	2.88011i	0.358215	−	0.0939387i
$941$	−26.8618	+	26.8618i	−0.875671	+	0.875671i	−0.993083	−	0.117412i	$-0.962540\pi$
$941$	−26.8618	+	26.8618i	−0.875671	+	0.875671i	0.117412	+	0.993083i	$0.462540\pi$
$942$	−28.5935	−	38.5859i	−0.931627	−	1.25720i
$943$			43.3258i			1.41088i
$944$	8.55889	+	43.3883i	0.278568	+	1.41217i
$945$	4.53590	−	19.0617i	0.147553	−	0.620077i
$946$	−0.347744	+	0.257691i	−0.0113061	+	0.00837825i
$947$	42.0944	+	42.0944i	1.36788	+	1.36788i	0.863451	+	0.504433i	$0.168299\pi$
$947$	42.0944	+	42.0944i	1.36788	+	1.36788i	0.504433	+	0.863451i	$0.331701\pi$
$948$	5.27266	−	2.81292i	0.171248	−	0.0913593i
$949$	−41.9772	−	41.9772i	−1.36264	−	1.36264i
$950$	−17.6778	−	12.4844i	−0.573545	−	0.405048i
$951$		−	3.51971i		−	0.114135i
$952$	−18.2879	+	6.51896i	−0.592714	+	0.211281i
$953$	−5.32619			−0.172532			−0.0862661	−	0.996272i	$-0.527494\pi$
$953$	−5.32619			−0.172532			−0.0862661	+	0.996272i	$0.527494\pi$
$954$	43.9951	+	6.54390i	1.42439	+	0.211866i
$955$	36.0434	−	22.1870i	1.16634	−	0.717953i
$956$	10.6583	−	35.0354i	0.344713	−	1.13313i
$957$	−0.444001	−	0.444001i	−0.0143525	−	0.0143525i
$958$	−7.24278	+	5.36716i	−0.234004	+	0.173405i
$959$	−6.59587			−0.212992
$960$	−42.3525	+	20.5228i	−1.36692	+	0.662370i
$961$	−29.3756			−0.947599
$962$	−13.2787	+	9.83998i	−0.428122	+	0.317254i
$963$	37.1836	+	37.1836i	1.19822	+	1.19822i
$964$	−5.42153	+	17.8215i	−0.174616	+	0.573990i
$965$	−25.0703	−	40.7274i	−0.807041	−	1.31106i
$966$	67.5964	+	10.0544i	2.17488	+	0.323495i
$967$	−29.9668			−0.963667			−0.481833	−	0.876263i	$-0.660029\pi$
$967$	−29.9668			−0.963667			−0.481833	+	0.876263i	$0.660029\pi$
$968$	29.2586	−	10.4296i	0.940406	−	0.335220i
$969$			15.2942i			0.491320i
$970$	−30.2449	−	12.1249i	−0.971106	−	0.389306i
$971$	0.750872	+	0.750872i	0.0240966	+	0.0240966i	0.719052	−	0.694956i	$-0.244576\pi$
$971$	0.750872	+	0.750872i	0.0240966	+	0.0240966i	−0.694956	+	0.719052i	$0.744576\pi$
$972$	37.8388	−	20.1867i	1.21368	−	0.647488i
$973$	19.4043	+	19.4043i	0.622072	+	0.622072i
$974$	−35.5874	+	26.3715i	−1.14029	+	0.844999i
$975$	−43.0950	−	21.7407i	−1.38014	−	0.696260i
$976$	−19.2254	+	3.79246i	−0.615391	+	0.121394i
$977$		−	26.2513i		−	0.839854i	−0.907558	−	0.419927i	$-0.862056\pi$
$977$		−	26.2513i		−	0.839854i	0.907558	−	0.419927i	$-0.137944\pi$
$978$	19.2696	+	26.0037i	0.616175	+	0.831505i
$979$	−0.377447	+	0.377447i	−0.0120633	+	0.0120633i
$980$	−6.87504	−	26.2165i	−0.219615	−	0.837455i
$981$	−33.6291	−	33.6291i	−1.07370	−	1.07370i
$982$	−27.8721	−	4.14574i	−0.889433	−	0.132296i
$983$	−13.0227			−0.415360			−0.207680	−	0.978197i	$-0.566591\pi$
$983$	−13.0227			−0.415360			−0.207680	+	0.978197i	$0.566591\pi$
$984$	−57.3108	−	27.1896i	−1.82700	−	0.866771i
$985$	−4.68030	+	19.6685i	−0.149127	+	0.626692i
$986$	4.73050	+	0.703622i	0.150650	+	0.0224079i
$987$	17.0688	−	17.0688i	0.543305	−	0.543305i
$988$	6.53710	−	21.4885i	0.207973	−	0.683641i
$989$	−8.20514	+	8.20514i	−0.260908	+	0.260908i
$990$	0.653676	+	1.52848i	0.0207752	+	0.0485782i
$991$	44.7487			1.42149			0.710744	−	0.703451i	$-0.248358\pi$
$991$	44.7487			1.42149			0.710744	+	0.703451i	$0.248358\pi$
$992$	−7.20181	+	0.339477i	−0.228658	+	0.0107784i
$993$			22.9348i			0.727813i
$994$	34.4072	+	46.4312i	1.09133	+	1.47271i
$995$	6.86467	+	11.1519i	0.217625	+	0.353538i
$996$	26.7317	+	8.13215i	0.847026	+	0.257677i
$997$	21.2387	−	21.2387i	0.672637	−	0.672637i	−0.285686	−	0.958323i	$-0.592222\pi$
$997$	21.2387	−	21.2387i	0.672637	−	0.672637i	0.958323	+	0.285686i	$0.0922215\pi$
$998$	0.677452	−	4.55456i	0.0214444	−	0.144172i
$999$		−	7.72244i		−	0.244327i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	80.2.q.c.69.2	yes	16
3.2	odd	2		720.2.bm.f.469.7		16
4.3	odd	2		320.2.q.c.49.2		16
5.2	odd	4		400.2.l.i.101.3		16
5.3	odd	4		400.2.l.i.101.6		16
5.4	even	2	inner	80.2.q.c.69.7	yes	16
8.3	odd	2		640.2.q.f.609.7		16
8.5	even	2		640.2.q.e.609.2		16
15.14	odd	2		720.2.bm.f.469.2		16
16.3	odd	4		320.2.q.c.209.7		16
16.5	even	4		640.2.q.e.289.7		16
16.11	odd	4		640.2.q.f.289.2		16
16.13	even	4	inner	80.2.q.c.29.7	yes	16
20.3	even	4		1600.2.l.h.1201.7		16
20.7	even	4		1600.2.l.h.1201.2		16
20.19	odd	2		320.2.q.c.49.7		16
40.19	odd	2		640.2.q.f.609.2		16
40.29	even	2		640.2.q.e.609.7		16
48.29	odd	4		720.2.bm.f.109.2		16
80.3	even	4		1600.2.l.h.401.7		16
80.13	odd	4		400.2.l.i.301.6		16
80.19	odd	4		320.2.q.c.209.2		16
80.29	even	4	inner	80.2.q.c.29.2	✓	16
80.59	odd	4		640.2.q.f.289.7		16
80.67	even	4		1600.2.l.h.401.2		16
80.69	even	4		640.2.q.e.289.2		16
80.77	odd	4		400.2.l.i.301.3		16
240.29	odd	4		720.2.bm.f.109.7		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
80.2.q.c.29.2	✓	16	80.29	even	4	inner
80.2.q.c.29.7	yes	16	16.13	even	4	inner
80.2.q.c.69.2	yes	16	1.1	even	1	trivial
80.2.q.c.69.7	yes	16	5.4	even	2	inner
320.2.q.c.49.2		16	4.3	odd	2
320.2.q.c.49.7		16	20.19	odd	2
320.2.q.c.209.2		16	80.19	odd	4
320.2.q.c.209.7		16	16.3	odd	4
400.2.l.i.101.3		16	5.2	odd	4
400.2.l.i.101.6		16	5.3	odd	4
400.2.l.i.301.3		16	80.77	odd	4
400.2.l.i.301.6		16	80.13	odd	4
640.2.q.e.289.2		16	80.69	even	4
640.2.q.e.289.7		16	16.5	even	4
640.2.q.e.609.2		16	8.5	even	2
640.2.q.e.609.7		16	40.29	even	2
640.2.q.f.289.2		16	16.11	odd	4
640.2.q.f.289.7		16	80.59	odd	4
640.2.q.f.609.2		16	40.19	odd	2
640.2.q.f.609.7		16	8.3	odd	2
720.2.bm.f.109.2		16	48.29	odd	4
720.2.bm.f.109.7		16	240.29	odd	4
720.2.bm.f.469.2		16	15.14	odd	2
720.2.bm.f.469.7		16	3.2	odd	2
1600.2.l.h.401.2		16	80.67	even	4
1600.2.l.h.401.7		16	80.3	even	4
1600.2.l.h.1201.2		16	20.7	even	4
1600.2.l.h.1201.7		16	20.3	even	4

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:	\( N \)	\(=\)	\( 80 = 2^{4} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	80.q (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.13624 + 0.841995i) q^{2} +(1.86033 + 1.86033i) q^{3} +(0.582088 - 1.91342i) q^{4} +(1.90421 - 1.17216i) q^{5} +(-3.68016 - 0.547394i) q^{6} -3.61392 q^{7} +(0.949697 + 2.66422i) q^{8} +3.92163i q^{9} +O(q^{10})\)	\(q+(-1.13624 + 0.841995i) q^{2} +(1.86033 + 1.86033i) q^{3} +(0.582088 - 1.91342i) q^{4} +(1.90421 - 1.17216i) q^{5} +(-3.68016 - 0.547394i) q^{6} -3.61392 q^{7} +(0.949697 + 2.66422i) q^{8} +3.92163i q^{9} +(-1.17669 + 2.93520i) q^{10} +(-0.0947876 - 0.0947876i) q^{11} +(4.64246 - 2.47671i) q^{12} +(-2.59462 - 2.59462i) q^{13} +(4.10628 - 3.04290i) q^{14} +(5.72307 + 1.36185i) q^{15} +(-3.32235 - 2.22756i) q^{16} -1.89939i q^{17} +(-3.30199 - 4.45591i) q^{18} +(-2.16418 + 2.16418i) q^{19} +(-1.13442 - 4.32586i) q^{20} +(-6.72307 - 6.72307i) q^{21} +(0.187512 + 0.0278909i) q^{22} +5.08251 q^{23} +(-3.18958 + 6.72307i) q^{24} +(2.25207 - 4.46410i) q^{25} +(5.13277 + 0.763457i) q^{26} +(-1.71452 + 1.71452i) q^{27} +(-2.10362 + 6.91494i) q^{28} +(1.25896 - 1.25896i) q^{29} +(-7.64946 + 3.27140i) q^{30} -1.27453 q^{31} +(5.65058 - 0.266355i) q^{32} -0.352672i q^{33} +(1.59928 + 2.15817i) q^{34} +(-6.88168 + 4.23610i) q^{35} +(7.50371 + 2.28273i) q^{36} +(-2.25207 + 2.25207i) q^{37} +(0.636801 - 4.28125i) q^{38} -9.65368i q^{39} +(4.93133 + 3.96005i) q^{40} +8.52451i q^{41} +(13.2998 + 1.97824i) q^{42} +(-1.61439 + 1.61439i) q^{43} +(-0.236543 + 0.126194i) q^{44} +(4.59679 + 7.46762i) q^{45} +(-5.77495 + 4.27944i) q^{46} +2.53884i q^{47} +(-2.03666 - 10.3246i) q^{48} +6.06040 q^{49} +(1.19986 + 6.96852i) q^{50} +(3.53349 - 3.53349i) q^{51} +(-6.47489 + 3.45430i) q^{52} +(-5.67100 + 5.67100i) q^{53} +(0.504492 - 3.39174i) q^{54} +(-0.291602 - 0.0693893i) q^{55} +(-3.43213 - 9.62828i) q^{56} -8.05215 q^{57} +(-0.370445 + 2.49053i) q^{58} +(-7.81785 - 7.81785i) q^{59} +(5.93713 - 10.1579i) q^{60} +(3.46410 - 3.46410i) q^{61} +(1.44817 - 1.07315i) q^{62} -14.1724i q^{63} +(-6.19615 + 5.06040i) q^{64} +(-7.98203 - 1.89939i) q^{65} +(0.296948 + 0.400720i) q^{66} +(-6.29856 - 6.29856i) q^{67} +(-3.63434 - 1.10561i) q^{68} +(9.45512 + 9.45512i) q^{69} +(4.25246 - 10.6076i) q^{70} +11.3074i q^{71} +(-10.4481 + 3.72436i) q^{72} +16.1786 q^{73} +(0.662661 - 4.45512i) q^{74} +(12.4943 - 4.11511i) q^{75} +(2.88124 + 5.40072i) q^{76} +(0.342555 + 0.342555i) q^{77} +(8.12835 + 10.9689i) q^{78} +1.13575 q^{79} +(-8.93752 - 0.347416i) q^{80} +5.38573 q^{81} +(-7.17759 - 9.68590i) q^{82} +(3.75489 + 3.75489i) q^{83} +(-16.7775 + 8.95062i) q^{84} +(-2.22640 - 3.61685i) q^{85} +(0.475028 - 3.19364i) q^{86} +4.68417 q^{87} +(0.162516 - 0.342555i) q^{88} -3.98203i q^{89} +(-11.5108 - 4.61454i) q^{90} +(9.37674 + 9.37674i) q^{91} +(2.95847 - 9.72496i) q^{92} +(-2.37103 - 2.37103i) q^{93} +(-2.13769 - 2.88473i) q^{94} +(-1.58429 + 6.65783i) q^{95} +(11.0074 + 10.0164i) q^{96} +10.3042i q^{97} +(-6.88608 + 5.10283i) q^{98} +(0.371721 - 0.371721i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 4 q^{4} - 8 q^{5} - 4 q^{6}+O(q^{10}) \) 16 * q - 4 * q^4 - 8 * q^5 - 4 * q^6	\( 16 q - 4 q^{4} - 8 q^{5} - 4 q^{6} - 12 q^{10} + 8 q^{11} - 4 q^{14} + 16 q^{16} - 8 q^{19} - 4 q^{20} - 16 q^{21} - 32 q^{24} + 32 q^{26} - 16 q^{29} - 36 q^{30} + 16 q^{31} + 48 q^{34} - 24 q^{35} + 60 q^{36} + 24 q^{40} - 8 q^{44} + 8 q^{45} - 28 q^{46} + 16 q^{49} + 24 q^{50} - 16 q^{51} + 40 q^{54} - 56 q^{56} - 24 q^{59} + 48 q^{60} - 16 q^{64} - 72 q^{66} + 32 q^{69} + 20 q^{70} + 48 q^{75} - 88 q^{76} + 16 q^{79} + 16 q^{80} - 16 q^{81} - 80 q^{84} - 28 q^{86} - 84 q^{90} - 16 q^{91} + 12 q^{94} + 32 q^{95} + 56 q^{96} + 88 q^{99}+O(q^{100}) \) 16 * q - 4 * q^4 - 8 * q^5 - 4 * q^6 - 12 * q^10 + 8 * q^11 - 4 * q^14 + 16 * q^16 - 8 * q^19 - 4 * q^20 - 16 * q^21 - 32 * q^24 + 32 * q^26 - 16 * q^29 - 36 * q^30 + 16 * q^31 + 48 * q^34 - 24 * q^35 + 60 * q^36 + 24 * q^40 - 8 * q^44 + 8 * q^45 - 28 * q^46 + 16 * q^49 + 24 * q^50 - 16 * q^51 + 40 * q^54 - 56 * q^56 - 24 * q^59 + 48 * q^60 - 16 * q^64 - 72 * q^66 + 32 * q^69 + 20 * q^70 + 48 * q^75 - 88 * q^76 + 16 * q^79 + 16 * q^80 - 16 * q^81 - 80 * q^84 - 28 * q^86 - 84 * q^90 - 16 * q^91 + 12 * q^94 + 32 * q^95 + 56 * q^96 + 88 * q^99

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