LMFDB - Embedded newform 80.2.q.c.69.7

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			69.7
Root			$0.841995 - 1.13624i$ of defining polynomial
Character	$\chi$	$=$	80.69
Dual form			80.2.q.c.29.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.13624 - 0.841995i) q^{2} +(-1.86033 - 1.86033i) q^{3} +(0.582088 - 1.91342i) q^{4} +(-1.17216 + 1.90421i) q^{5} +(-3.68016 - 0.547394i) q^{6} +3.61392 q^{7} +(-0.949697 - 2.66422i) q^{8} +3.92163i q^{9} +O(q^{10})$	\(q+(1.13624 - 0.841995i) q^{2} +(-1.86033 - 1.86033i) q^{3} +(0.582088 - 1.91342i) q^{4} +(-1.17216 + 1.90421i) q^{5} +(-3.68016 - 0.547394i) q^{6} +3.61392 q^{7} +(-0.949697 - 2.66422i) q^{8} +3.92163i q^{9} +(0.271479 + 3.15060i) 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} +(2.96126 + 3.35126i) 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} +(5.35611 - 6.36619i) q^{30} -1.27453 q^{31} +(-5.65058 + 0.266355i) q^{32} +0.352672i q^{33} +(1.59928 + 2.15817i) q^{34} +(-4.23610 + 6.88168i) q^{35} +(7.50371 + 2.28273i) q^{36} +(2.25207 - 2.25207i) q^{37} +(-0.636801 + 4.28125i) q^{38} -9.65368i q^{39} +(6.18645 + 1.31448i) q^{40} +8.52451i q^{41} +(-13.2998 - 1.97824i) q^{42} +(1.61439 - 1.61439i) q^{43} +(-0.236543 + 0.126194i) q^{44} +(-7.46762 - 4.59679i) q^{45} +(-5.77495 + 4.27944i) q^{46} -2.53884i q^{47} +(2.03666 + 10.3246i) q^{48} +6.06040 q^{49} +(-6.31764 - 3.17607i) 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} +(0.725535 - 11.7433i) 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} +(0.981101 + 11.3860i) q^{70} +11.3074i q^{71} +(10.4481 - 3.72436i) q^{72} -16.1786 q^{73} +(0.662661 - 4.45512i) q^{74} +(-4.11511 + 12.4943i) q^{75} +(2.88124 + 5.40072i) q^{76} +(-0.342555 - 0.342555i) q^{77} +(-8.12835 - 10.9689i) q^{78} +1.13575 q^{79} +(8.13608 - 3.71540i) q^{80} +5.38573 q^{81} +(7.17759 + 9.68590i) q^{82} +(-3.75489 - 3.75489i) q^{83} +(-16.7775 + 8.95062i) q^{84} +(-3.61685 - 2.22640i) q^{85} +(0.475028 - 3.19364i) q^{86} -4.68417 q^{87} +(-0.162516 + 0.342555i) q^{88} -3.98203i q^{89} +(-12.3555 + 1.06464i) 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	$-0.975456\pi$
$3$	−1.86033	−	1.86033i	−1.07406	−	1.07406i	−0.0770310	−	0.997029i	$-0.524544\pi$
$4$	0.582088	−	1.91342i	0.291044	−	0.956710i
$5$	−1.17216	+	1.90421i	−0.524207	+	0.851591i
$5$	−1.17216	+	1.90421i	−0.524207	+	0.851591i
$6$	−3.68016	−	0.547394i	−1.50242	−	0.223473i
$7$	3.61392			1.36593			0.682966	−	0.730450i	$-0.260690\pi$
$7$	3.61392			1.36593			0.682966	+	0.730450i	$0.260690\pi$
$8$	−0.949697	−	2.66422i	−0.335768	−	0.941945i
$9$			3.92163i			1.30721i
$10$	0.271479	+	3.15060i	0.0858491	+	0.996308i
$11$	−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	0.968527	−	0.248909i	$-0.0800720\pi$
$13$	2.59462	+	2.59462i	0.719618	+	0.719618i	−0.248909	+	0.968527i	$0.580072\pi$
$14$	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	$0.0739823\pi$
$17$			1.89939i			0.460671i	−0.973111	+	0.230335i	$0.926018\pi$
$18$	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	$0.364184\pi$
$20$	2.96126	+	3.35126i	0.662157	+	0.749365i
$21$	−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	$-0.677766\pi$
$23$	−5.08251			−1.05978			−0.529888	+	0.848068i	$0.677766\pi$
$24$	−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	$0.197137\pi$
$30$	5.35611	−	6.36619i	0.977887	−	1.16230i
$31$	−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
$35$	−4.23610	+	6.88168i	−0.716032	+	1.16322i
$36$	7.50371	+	2.28273i	1.25062	+	0.380456i
$37$	2.25207	−	2.25207i	0.370237	−	0.370237i	−0.497326	−	0.867564i	$-0.665685\pi$
$37$	2.25207	−	2.25207i	0.370237	−	0.370237i	0.867564	+	0.497326i	$0.165685\pi$
$38$	−0.636801	+	4.28125i	−0.103303	+	0.694511i
$39$		−	9.65368i		−	1.54583i
$40$	6.18645	+	1.31448i	0.978163	+	0.207837i
$41$			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	−0.573214	−	0.819406i	$-0.694304\pi$
$43$	1.61439	−	1.61439i	0.246192	−	0.246192i	0.819406	+	0.573214i	$0.194304\pi$
$44$	−0.236543	+	0.126194i	−0.0356602	+	0.0190244i
$45$	−7.46762	−	4.59679i	−1.11321	−	0.685249i
$46$	−5.77495	+	4.27944i	−0.851470	+	0.630970i
$47$		−	2.53884i		−	0.370328i	−0.982708	−	0.185164i	$-0.940718\pi$
$47$		−	2.53884i		−	0.370328i	0.982708	−	0.185164i	$-0.0592816\pi$
$48$	2.03666	+	10.3246i	0.293967	+	1.49023i
$49$	6.06040			0.865772
$50$	−6.31764	−	3.17607i	−0.893449	−	0.449164i
$51$	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	−0.200684	−	0.979656i	$-0.564317\pi$
$53$	5.67100	−	5.67100i	0.778971	−	0.778971i	0.979656	+	0.200684i	$0.0643166\pi$
$54$	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	$-0.505717\pi$
$60$	0.725535	−	11.7433i	0.0936661	−	1.51606i
$61$	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	0.978017	−	0.208526i	$-0.0668665\pi$
$67$	6.29856	+	6.29856i	0.769491	+	0.769491i	−0.208526	+	0.978017i	$0.566866\pi$
$68$	3.63434	+	1.10561i	0.440728	+	0.134076i
$69$	9.45512	+	9.45512i	1.13826	+	1.13826i
$70$	0.981101	+	11.3860i	0.117264	+	1.36089i
$71$			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	$-0.895684\pi$
$73$	−16.1786			−1.89356			−0.946779	+	0.321885i	$0.895684\pi$
$74$	0.662661	−	4.45512i	0.0770328	−	0.517897i
$75$	−4.11511	+	12.4943i	−0.475172	+	1.44271i
$76$	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	$0.479649\pi$
$80$	8.13608	−	3.71540i	0.909642	−	0.415394i
$81$	5.38573			0.598414
$82$	7.17759	+	9.68590i	0.792633	+	1.06963i
$83$	−3.75489	−	3.75489i	−0.412153	−	0.412153i	0.470335	−	0.882488i	$-0.344133\pi$
$83$	−3.75489	−	3.75489i	−0.412153	−	0.412153i	−0.882488	+	0.470335i	$0.844133\pi$
$84$	−16.7775	+	8.95062i	−1.83057	+	0.976593i
$85$	−3.61685	−	2.22640i	−0.392303	−	0.241487i
$86$	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	$-0.0676874\pi$
$90$	−12.3555	+	1.06464i	−1.30238	+	0.112223i
$91$	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	$-0.824769\pi$
$97$		−	10.3042i		−	1.04623i	0.852261	−	0.523117i	$-0.175231\pi$
$98$	6.88608	−	5.10283i	0.695599	−	0.515464i
$99$	0.371721	−	0.371721i	0.0373594	−	0.0373594i
$100$	−9.85260	+	1.71064i	−0.985260	+	0.171064i
$101$	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	$-0.320196\pi$
$103$	10.8655			1.07061			0.535306	+	0.844658i	$0.320196\pi$
$104$	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	−0.996782	−	0.0801549i	$-0.974459\pi$
$107$	−9.48167	+	9.48167i	−0.916628	+	0.916628i	0.0801549	+	0.996782i	$0.474459\pi$
$108$	−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	$0.447257\pi$
$110$	0.272905	−	0.324371i	0.0260205	−	0.0309275i
$111$	−8.37915			−0.795314
$112$	−12.0067	−	8.05021i	−1.13453	−	0.760674i
$113$		−	12.5286i		−	1.17860i	−0.807916	−	0.589298i	$-0.799405\pi$
$113$		−	12.5286i		−	1.17860i	0.807916	−	0.589298i	$-0.200595\pi$
$114$	9.14918	−	6.77987i	0.856900	−	0.634993i
$115$	5.95753	−	9.67818i	0.555542	−	0.902495i
$116$	−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
$120$	−9.06346	−	13.9542i	−0.827376	−	1.27384i
$121$		−	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
$125$	11.1404	+	0.944243i	0.996427	+	0.0844556i
$126$	11.9331	+	16.1033i	1.06309	+	1.43460i
$127$		−	2.94200i		−	0.261061i	−0.991444	−	0.130530i	$-0.958332\pi$
$127$		−	2.94200i		−	0.261061i	0.991444	−	0.130530i	$-0.0416680\pi$
$128$	−2.77949	+	10.9670i	−0.245674	+	0.969352i
$129$	−6.00658			−0.528850
$130$	−7.47023	+	8.87900i	−0.655183	+	0.778740i
$131$	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	$-0.524842\pi$
$137$	−1.82513			−0.155931			−0.0779657	+	0.996956i	$0.524842\pi$
$138$	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	$0.854365\pi$
$140$	10.7017	+	12.1112i	0.904462	+	1.02358i
$141$	−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	$0.668360\pi$
$150$	5.84435	+	17.6614i	0.477189	+	1.44205i
$151$		−	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
$155$	1.49395	−	2.42697i	0.119997	−	0.194939i
$156$	−18.4715	−	5.61929i	−1.47891	−	0.449904i
$157$	−9.12723	−	9.12723i	−0.728432	−	0.728432i	0.241875	−	0.970307i	$-0.422238\pi$
$157$	−9.12723	−	9.12723i	−0.728432	−	0.728432i	−0.970307	+	0.241875i	$0.922238\pi$
$158$	1.29048	−	0.956294i	0.102665	−	0.0760787i
$159$	−21.0998			−1.67332
$160$	6.11621	−	11.0721i	0.483529	−	0.875329i
$161$	−18.3678			−1.44758
$162$	6.11949	−	4.53476i	0.480792	−	0.356284i
$163$	6.15099	+	6.15099i	0.481783	+	0.481783i	0.905701	−	0.423918i	$-0.139346\pi$
$163$	6.15099	+	6.15099i	0.481783	+	0.481783i	−0.423918	+	0.905701i	$0.639346\pi$
$164$	16.3110	+	4.96202i	1.27367	+	0.387468i
$165$	−0.671562	−	0.413389i	−0.0522811	−	0.0321823i
$166$	−7.42806	−	1.10486i	−0.576529	−	0.0857539i
$167$	−0.710173			−0.0549548			−0.0274774	−	0.999622i	$-0.508747\pi$
$167$	−0.710173			−0.0549548			−0.0274774	+	0.999622i	$0.508747\pi$
$168$	−11.5269	+	24.2966i	−0.889317	+	1.87452i
$169$			0.464102i			0.0357001i
$170$	−5.98423	+	0.515645i	−0.458970	+	0.0395481i
$171$	−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	$0.0258682\pi$
$173$	14.1773	+	14.1773i	1.07788	+	1.07788i	0.0811779	+	0.996700i	$0.474132\pi$
$174$	−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	$0.0921115\pi$
$180$	−13.1424	+	11.6129i	−0.979576	+	0.865578i
$181$	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
$190$	−7.40599	−	6.23093i	−0.537287	−	0.452040i
$191$	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	$0.279630\pi$
$193$			21.3880i			1.53954i	−0.638319	+	0.769772i	$0.720370\pi$
$194$	−8.67610	−	11.7081i	−0.622908	−	0.840591i
$195$	18.3827	+	11.3157i	1.31641	+	0.810333i
$196$	3.52769	−	11.5961i	0.251978	−	0.828292i
$197$	6.39341	−	6.39341i	0.455511	−	0.455511i	−0.441667	−	0.897179i	$-0.645613\pi$
$197$	6.39341	−	6.39341i	0.455511	−	0.455511i	0.897179	+	0.441667i	$0.145613\pi$
$198$	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	$0.933443\pi$
$200$	−9.75458	+	10.2395i	−0.689753	+	0.724045i
$201$		−	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
$205$	−16.2325	−	9.99212i	−1.13373	−	0.697880i
$206$	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
$210$	19.3565	−	23.0069i	1.33573	−	1.58763i
$211$	−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
$220$	0.0369675	−	0.598348i	0.00249235	−	0.0403406i
$221$	−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	$0.235163\pi$
$223$			20.1117i			1.34678i	−0.739287	+	0.673390i	$0.764837\pi$
$224$	−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	0.832994	−	0.553282i	$-0.186625\pi$
$227$	4.21430	+	4.21430i	0.279713	+	0.279713i	−0.553282	+	0.832994i	$0.686625\pi$
$228$	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	$-0.568921\pi$
$230$	−1.37979	−	16.0130i	−0.0909807	−	1.05586i
$231$			1.27453i			0.0838577i
$232$	−4.54979	−	2.15853i	−0.298709	−	0.141714i
$233$	−4.57839			−0.299941			−0.149970	−	0.988691i	$-0.547918\pi$
$233$	−4.57839			−0.299941			−0.149970	+	0.988691i	$0.547918\pi$
$234$	−2.99399	+	20.1288i	−0.195723	+	1.31586i
$235$	4.83449	+	2.97593i	0.315367	+	0.194128i
$236$	−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	$0.298259\pi$
$240$	−22.0476	−	8.22392i	−1.42317	−	0.530852i
$241$	−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
$245$	−7.10379	+	11.5403i	−0.453844	+	0.737283i
$246$	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
$250$	13.4532	−	8.30727i	0.850857	−	0.525398i
$251$	−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	$-0.820532\pi$
$257$		−	17.1347i		−	1.06883i	0.845222	−	0.534416i	$-0.179468\pi$
$258$	−6.82492	+	5.05751i	−0.424901	+	0.314867i
$259$	8.13878	−	8.13878i	0.505719	−	0.505719i
$260$	−1.01191	+	16.3786i	−0.0627561	+	1.01576i
$261$	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	$-0.550418\pi$
$263$	−5.11593			−0.315462			−0.157731	+	0.987482i	$0.550418\pi$
$264$	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	$-0.0591864\pi$
$270$	5.86724	+	4.93633i	0.357069	+	0.300415i
$271$	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
$275$	−0.209674	+	0.636609i	−0.0126438	+	0.0383890i
$276$	23.5953	−	12.5879i	1.42027	−	0.757702i
$277$	−12.8887	+	12.8887i	−0.774408	+	0.774408i	−0.978874	−	0.204466i	$-0.934454\pi$
$277$	−12.8887	+	12.8887i	−0.774408	+	0.774408i	0.204466	+	0.978874i	$0.434454\pi$
$278$	−10.6218	−	1.57990i	−0.637052	−	0.0947561i
$279$		−	4.99822i		−	0.299235i
$280$	22.3573	+	4.75041i	1.33611	+	0.283892i
$281$			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	−0.897861	−	0.440279i	$-0.854879\pi$
$283$	−7.69771	+	7.69771i	−0.457581	+	0.457581i	0.440279	+	0.897861i	$0.354879\pi$
$284$	21.6357	+	6.58188i	1.28384	+	0.390563i
$285$	−9.43844	+	15.3330i	−0.559085	+	0.908250i
$286$	−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
$290$	4.30828	+	3.62472i	0.252991	+	0.212851i
$291$	−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	−0.854947	−	0.518715i	$-0.826411\pi$
$293$	−5.75538	+	5.75538i	−0.336233	+	0.336233i	0.518715	+	0.854947i	$0.326411\pi$
$294$	−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
$300$	21.5114	+	15.1467i	1.24196	+	0.874495i
$301$	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	0.925924	−	0.377711i	$-0.123289\pi$
$307$	9.60547	+	9.60547i	0.548213	+	0.548213i	−0.377711	+	0.925924i	$0.623289\pi$
$308$	−0.854848	+	0.456053i	−0.0487095	+	0.0259861i
$309$	−20.2134	−	20.2134i	−1.14990	−	1.14990i
$310$	−0.346007	−	4.01553i	−0.0196519	−	0.228067i
$311$		−	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	$-0.241993\pi$
$313$	25.6414			1.44934			0.724669	+	0.689097i	$0.241993\pi$
$314$	−18.0558	−	2.68565i	−1.01895	−	0.151560i
$315$	−26.9874	−	16.6124i	−1.52057	−	0.936003i
$316$	0.661106	−	2.17316i	0.0371901	−	0.122250i
$317$	0.945994	+	0.945994i	0.0531323	+	0.0531323i	0.733174	−	0.680041i	$-0.238038\pi$
$317$	0.945994	+	0.945994i	0.0531323	+	0.0531323i	−0.680041	+	0.733174i	$0.738038\pi$
$318$	−23.9745	+	17.7659i	−1.34442	+	0.996264i
$319$	−0.238668			−0.0133629
$320$	−2.37319	−	17.7304i	−0.132665	−	0.991161i
$321$	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
$325$	5.73939	−	17.4259i	0.318364	−	0.966615i
$326$	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
$330$	−1.11113	+	0.0957428i	−0.0611656	+	0.00527047i
$331$	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	$-0.720763\pi$
$337$		−	28.2333i		−	1.53797i	0.639269	−	0.768983i	$-0.279237\pi$
$338$	0.390771	+	0.527331i	0.0212552	+	0.0286830i
$339$	−23.3074	+	23.3074i	−1.26588	+	1.26588i
$340$	−6.36536	+	5.62459i	−0.345210	+	0.305036i
$341$	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	−0.263770	−	0.964586i	$-0.584966\pi$
$347$	13.0548	−	13.0548i	0.700816	−	0.700816i	0.964586	+	0.263770i	$0.0849659\pi$
$348$	−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	$0.970920\pi$
$350$	−22.8314	−	11.4781i	−1.22039	−	0.613528i
$351$	8.89708			0.474891
$352$	0.560852	+	0.510358i	0.0298935	+	0.0272022i
$353$			18.6814i			0.994310i	0.867662	+	0.497155i	$0.165622\pi$
$353$			18.6814i			0.994310i	−0.867662	+	0.497155i	$0.834378\pi$
$354$	24.4915	+	33.0504i	1.30171	+	1.75661i
$355$	−21.5316	−	13.2541i	−1.14278	−	0.703453i
$356$	−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	$0.857466\pi$
$360$	−5.15489	+	24.2609i	−0.271686	+	1.27866i
$361$			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
$365$	18.9639	−	30.8075i	0.992617	−	1.61254i
$366$	−14.6447	+	10.8522i	−0.765490	+	0.567255i
$367$		−	3.58049i		−	0.186900i	−0.995624	−	0.0934500i	$-0.970210\pi$
$367$		−	3.58049i		−	0.186900i	0.995624	−	0.0934500i	$-0.0297895\pi$
$368$	16.8858	+	11.3216i	0.880235	+	0.590178i
$369$	−33.4299			−1.74029
$370$	7.70675	+	6.48398i	0.400655	+	0.337086i
$371$	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	−0.444008	−	0.896023i	$-0.646444\pi$
$373$	8.72985	−	8.72985i	0.452015	−	0.452015i	0.896023	+	0.444008i	$0.146444\pi$
$374$	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	$0.678733\pi$
$380$	−13.6614	−	0.844038i	−0.700815	−	0.0432982i
$381$	−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	$-0.940165\pi$
$383$		−	7.31434i		−	0.373745i	0.982384	−	0.186873i	$-0.0598351\pi$
$384$	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	$0.863565\pi$
$390$	30.4149	−	2.62077i	1.54012	−	0.132708i
$391$		−	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
$395$	−1.33128	+	2.16271i	−0.0669841	+	0.108818i
$396$	−0.494884	−	0.927634i	−0.0248689	−	0.0466154i
$397$	8.04203	+	8.04203i	0.403618	+	0.403618i	0.879506	−	0.475888i	$-0.157873\pi$
$397$	8.04203	+	8.04203i	0.403618	+	0.403618i	−0.475888	+	0.879506i	$0.657873\pi$
$398$	4.93107	+	6.65429i	0.247172	+	0.333549i
$399$	29.0998			1.45681
$400$	−2.46191	+	19.8479i	−0.123095	+	0.992395i
$401$	−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
$405$	−6.31295	+	10.2556i	−0.313693	+	0.509604i
$406$	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	$-0.131687\pi$
$410$	−26.8573	+	2.31422i	−1.32639	+	0.114291i
$411$	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	$0.363923\pi$
$420$	2.62202	−	42.4395i	0.127942	−	2.07083i
$421$	−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
$430$	5.52457	+	4.64802i	0.266418	+	0.224148i
$431$	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	$0.158966\pi$
$433$			19.9307i			0.957810i	−0.877867	+	0.478905i	$0.841034\pi$
$434$	−5.23357	+	3.87826i	−0.251219	+	0.186162i
$435$	5.49061	−	8.91966i	0.263255	−	0.427665i
$436$	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	$0.792591\pi$
$440$	−0.461802	−	0.710995i	−0.0220156	−	0.0338953i
$441$			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	$-0.438048\pi$
$443$	24.7208	−	24.7208i	1.17452	−	1.17452i	0.981120	−	0.193402i	$-0.0619522\pi$
$444$	−4.87741	+	16.0328i	−0.231471	+	0.760884i
$445$	7.58264	+	4.66759i	0.359452	+	0.221265i
$446$	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	$0.457607\pi$
$450$	12.4554	−	24.7754i	0.587151	−	1.16792i
$451$	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	$-0.286222\pi$
$457$	26.6040			1.24448			0.622241	+	0.782825i	$0.286222\pi$
$458$	−35.6684	−	5.30538i	−1.66668	−	0.247904i
$459$	3.25656	+	3.25656i	0.152003	+	0.152003i
$460$	−15.0506	−	17.0328i	−0.701738	−	0.794159i
$461$	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	$0.00392127\pi$
$463$			0.530134i			0.0246374i	−0.999924	+	0.0123187i	$0.996079\pi$
$464$	−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	0.391595	−	0.920138i	$-0.371923\pi$
$467$	−11.4219	−	11.4219i	−0.528542	−	0.528542i	−0.920138	+	0.391595i	$0.871923\pi$
$468$	13.5465	+	25.3921i	0.626185	+	1.17375i
$469$	22.7625	+	22.7625i	1.05107	+	1.05107i
$470$	7.99887	−	0.689240i	0.368960	−	0.0317923i
$471$			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
$475$	14.5350	+	4.78724i	0.666910	+	0.219654i
$476$	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	$0.453481\pi$
$480$	−31.9759	+	9.21963i	−1.45949	+	0.420817i
$481$	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
$485$	19.6214	+	12.0782i	0.890963	+	0.548444i
$486$	−29.9956	−	4.46159i	−1.36063	−	0.202382i
$487$	−31.3203			−1.41926			−0.709629	−	0.704575i	$-0.751138\pi$
$487$	−31.3203			−1.41926			−0.709629	+	0.704575i	$0.751138\pi$
$488$	−12.5190	−	5.93929i	−0.566708	−	0.268859i
$489$		−	22.8857i		−	1.03493i
$490$	1.64527	+	19.0939i	0.0743257	+	0.862576i
$491$	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	$0.273219\pi$
$500$	8.29143	−	20.7666i	0.370804	−	0.928711i
$501$	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	$-0.393302\pi$
$503$	14.7556			0.657921			0.328961	+	0.944344i	$0.393302\pi$
$504$	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	$0.330986\pi$
$510$	12.0919	+	10.1734i	0.535438	+	0.450484i
$511$	−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
$515$	−12.7362	+	20.6903i	−0.561223	+	0.911723i
$516$	−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
$520$	12.6409	+	19.4621i	0.554341	+	0.853467i
$521$			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	−0.839477	−	0.543395i	$-0.817139\pi$
$523$	−6.77116	+	6.77116i	−0.296082	+	0.296082i	0.543395	+	0.839477i	$0.317139\pi$
$524$	−8.71133	−	16.3289i	−0.380556	−	0.713332i
$525$	−14.8717	+	45.1532i	−0.649053	+	1.97065i
$526$	−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
$530$	19.4066	+	16.3275i	0.842970	+	0.709222i
$531$	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
$540$	10.8230	+	0.668672i	0.465746	+	0.0287750i
$541$	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	0.272613	−	0.962124i	$-0.412112\pi$
$547$	−16.1263	−	16.1263i	−0.689511	−	0.689511i	−0.962124	+	0.272613i	$0.912112\pi$
$548$	−1.06239	+	3.49224i	−0.0453829	+	0.149181i
$549$	13.5849	+	13.5849i	0.579790	+	0.579790i
$550$	0.297782	+	0.899886i	0.0126975	+	0.0383713i
$551$			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
$555$	9.82174	−	15.9557i	0.416909	−	0.677282i
$556$	−13.3992	+	7.14833i	−0.568251	+	0.303157i
$557$	−13.7333	−	13.7333i	−0.581897	−	0.581897i	0.353527	−	0.935424i	$-0.384982\pi$
$557$	−13.7333	−	13.7333i	−0.581897	−	0.581897i	−0.935424	+	0.353527i	$0.884982\pi$
$558$	−4.20847	−	5.67918i	−0.178159	−	0.240419i
$559$	8.37745			0.354328
$560$	29.4031	−	13.4271i	1.24251	−	0.567400i
$561$	−0.669862			−0.0282816
$562$	13.8873	+	18.7405i	0.585802	+	0.790519i
$563$	13.2023	+	13.2023i	0.556412	+	0.556412i	0.928284	−	0.371872i	$-0.121284\pi$
$563$	13.2023	+	13.2023i	0.556412	+	0.556412i	−0.371872	+	0.928284i	$0.621284\pi$
$564$	6.28796	+	11.7864i	0.264771	+	0.496299i
$565$	23.8572	+	14.6856i	1.00368	+	0.617828i
$566$	−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	$-0.0490661\pi$
$570$	2.18599	+	25.3691i	0.0915609	+	1.06260i
$571$	−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	$-0.937350\pi$
$577$		−	9.39473i		−	0.391108i	0.980693	−	0.195554i	$-0.0626504\pi$
$578$	15.2169	−	11.2763i	0.632939	−	0.469030i
$579$	39.7887	−	39.7887i	1.65356	−	1.65356i
$580$	7.94724	+	0.491001i	0.329991	+	0.0203877i
$581$	−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	−0.892902	−	0.450252i	$-0.851334\pi$
$587$	−10.7246	+	10.7246i	−0.442650	+	0.442650i	0.450252	+	0.892902i	$0.351334\pi$
$588$	−28.1352	+	15.0099i	−1.16027	+	0.618996i
$589$	2.75830	−	2.75830i	0.113654	−	0.113654i
$590$	22.5086	−	26.7533i	0.926663	−	1.10142i
$591$	−23.7876			−0.978493
$592$	−12.4987	+	2.46553i	−0.513695	+	0.101333i
$593$		−	38.2253i		−	1.56973i	−0.619670	−	0.784863i	$-0.712733\pi$
$593$		−	38.2253i		−	1.56973i	0.619670	−	0.784863i	$-0.287267\pi$
$594$	−0.369314	+	0.273675i	−0.0151531	+	0.0112290i
$595$	−13.0710	−	8.04603i	−0.535859	−	0.329855i
$596$	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	$0.676929\pi$
$600$	37.1956	−	0.902194i	1.51850	−	0.0368319i
$601$		−	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
$605$	20.9121	+	12.8727i	0.850199	+	0.523351i
$606$	−3.94405	−	5.32235i	−0.160216	−	0.216206i
$607$			15.1150i			0.613500i	0.951790	+	0.306750i	$0.0992415\pi$
$607$			15.1150i			0.613500i	−0.951790	+	0.306750i	$0.900759\pi$
$608$	11.6524	−	12.8053i	0.472568	−	0.519323i
$609$	−16.9282			−0.685965
$610$	11.8544	+	9.97358i	0.479972	+	0.403818i
$611$	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	−0.730674	−	0.682727i	$-0.760794\pi$
$613$	−1.18710	+	1.18710i	−0.0479466	+	0.0479466i	0.682727	+	0.730674i	$0.260794\pi$
$614$	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	$-0.466382\pi$
$617$	5.23711			0.210838			0.105419	+	0.994428i	$0.466382\pi$
$618$	−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	$0.809405\pi$
$620$	−3.77420	−	4.27127i	−0.151576	−	0.171538i
$621$	−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
$630$	−44.6517	+	3.84751i	−1.77897	+	0.153289i
$631$			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
$635$	5.60221	+	3.44851i	0.222317	+	0.136850i
$636$	−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
$640$	−17.6254	−	18.1478i	−0.696707	−	0.717356i
$641$	−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	0.174592	−	0.984641i	$-0.444139\pi$
$643$	−20.5408	−	20.5408i	−0.810049	−	0.810049i	−0.984641	+	0.174592i	$0.944139\pi$
$644$	−10.6917	+	35.1452i	−0.421310	+	1.38492i
$645$	7.04069	−	11.4378i	0.277227	−	0.450363i
$646$	−8.13178	−	1.20954i	−0.319941	−	0.0475885i
$647$	31.7472			1.24811			0.624056	−	0.781379i	$-0.285484\pi$
$647$	31.7472			1.24811			0.624056	+	0.781379i	$0.285484\pi$
$648$	−5.11481	−	14.3488i	−0.200929	−	0.563673i
$649$			1.48207i			0.0581764i
$650$	−8.15118	−	24.6326i	−0.319716	−	0.966169i
$651$	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	0.786233	−	0.617930i	$-0.212029\pi$
$653$	4.30078	+	4.30078i	0.168302	+	0.168302i	−0.617930	+	0.786233i	$0.712029\pi$
$654$	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	$0.417310\pi$
$660$	−1.18189	+	1.04435i	−0.0460052	+	0.0406513i
$661$	−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
$670$	−18.1343	+	21.5542i	−0.700590	+	0.832710i
$671$	−0.656708			−0.0253519
$672$	39.7799	+	36.1985i	1.53454	+	1.39639i
$673$		−	8.43246i		−	0.325047i	−0.986705	−	0.162524i	$-0.948037\pi$
$673$		−	8.43246i		−	0.325047i	0.986705	−	0.162524i	$-0.0519634\pi$
$674$	−23.7723	−	32.0798i	−0.915675	−	1.23567i
$675$	−11.5150	−	3.79259i	−0.443214	−	0.145977i
$676$	0.888021	+	0.270148i	0.0341547	+	0.0103903i
$677$	−20.8693	+	20.8693i	−0.802073	+	0.802073i	−0.983419	−	0.181346i	$-0.941954\pi$
$677$	−20.8693	+	20.8693i	−0.802073	+	0.802073i	0.181346	+	0.983419i	$0.441954\pi$
$678$	−6.85810	+	46.1075i	−0.263384	+	1.77075i
$679$		−	37.2386i		−	1.42909i
$680$	−2.49671	+	11.7505i	−0.0957444	+	0.450611i
$681$		−	15.6799i		−	0.600856i
$682$	0.238989	+	0.0355477i	0.00915137	+	0.00136119i
$683$	−16.4398	+	16.4398i	−0.629051	+	0.629051i	−0.947829	−	0.318778i	$-0.896728\pi$
$683$	−16.4398	+	16.4398i	−0.629051	+	0.629051i	0.318778	+	0.947829i	$0.396728\pi$
$684$	−21.1796	+	11.2991i	−0.809822	+	0.432033i
$685$	2.13935	−	3.47544i	0.0817404	−	0.132790i
$686$	−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
$690$	−27.2225	+	32.3562i	−1.03634	+	1.23178i
$691$	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
$700$	−35.6065	+	6.18212i	−1.34580	+	0.233662i
$701$	−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	$0.595004\pi$
$710$	−35.6250	+	3.06970i	−1.33698	+	0.115204i
$711$			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
$715$	0.936636	+	0.576559i	0.0350282	+	0.0215621i
$716$	−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	$0.792258\pi$
$720$	14.5704	+	31.9067i	0.543007	+	1.18909i
$721$	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
$725$	−8.45542	−	2.78488i	−0.314026	−	0.103428i
$726$	−6.01150	+	40.4157i	−0.223108	+	1.49997i
$727$	−50.5830			−1.87602			−0.938010	−	0.346609i	$-0.887333\pi$
$727$	−50.5830			−1.87602			−0.938010	+	0.346609i	$0.887333\pi$
$728$	16.0767	−	33.8868i	0.595841	−	1.25593i
$729$			40.2583i			1.49105i
$730$	−4.39213	−	50.9722i	−0.162560	−	1.88657i
$731$	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	0.811859	−	0.583854i	$-0.198456\pi$
$733$	6.17299	+	6.17299i	0.228005	+	0.228005i	−0.583854	+	0.811859i	$0.698456\pi$
$734$	−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	$0.0469178\pi$
$740$	14.2162	+	0.878314i	0.522598	+	0.0322875i
$741$	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	$-0.570031\pi$
$743$	−11.8975			−0.436478			−0.218239	+	0.975895i	$0.570031\pi$
$744$	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
$750$	−40.4816	−	9.57315i	−1.47818	−	0.349562i
$751$	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
$755$	24.6806	+	15.1924i	0.898218	+	0.552910i
$756$	−8.24913	−	15.4625i	−0.300018	−	0.562367i
$757$	−11.3218	+	11.3218i	−0.411496	+	0.411496i	−0.882260	−	0.470763i	$-0.843979\pi$
$757$	−11.3218	+	11.3218i	−0.411496	+	0.411496i	0.470763	+	0.882260i	$0.343979\pi$
$758$	12.0925	+	1.79866i	0.439219	+	0.0653301i
$759$		−	1.79246i		−	0.0650620i
$760$	−16.2333	+	10.5438i	−0.588845	+	0.382464i
$761$		−	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
$765$	8.73111	−	14.1839i	0.315674	−	0.512821i
$766$	−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	$0.604232\pi$
$770$	0.986257	−	1.17225i	0.0355422	−	0.0422449i
$771$	−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	−0.130219	−	0.991485i	$-0.541568\pi$
$773$	23.9457	−	23.9457i	0.861267	−	0.861267i	0.991485	+	0.130219i	$0.0415679\pi$
$774$	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
$780$	32.3520	−	28.5870i	1.15839	−	1.02358i
$781$	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	$0.0540582\pi$
$787$	32.3914	+	32.3914i	1.15463	+	1.15463i	0.169014	+	0.985614i	$0.445942\pi$
$788$	−8.51174	−	15.9548i	−0.303218	−	0.568366i
$789$	9.51731	+	9.51731i	0.338825	+	0.338825i
$790$	0.308331	+	3.57829i	0.0109699	+	0.127310i
$791$		−	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
$795$	24.7324	−	40.1786i	0.877169	−	1.42499i
$796$	11.2058	+	3.40895i	0.397178	+	0.120827i
$797$	1.92658	+	1.92658i	0.0682428	+	0.0682428i	0.740404	−	0.672162i	$-0.234634\pi$
$797$	1.92658	+	1.92658i	0.0682428	+	0.0682428i	−0.672162	+	0.740404i	$0.734634\pi$
$798$	33.0644	−	24.5019i	1.17047	−	0.867358i
$799$	4.82225			0.170599
$800$	13.9145	+	24.6249i	0.491952	+	0.870622i
$801$	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
$805$	21.5300	−	34.9761i	0.758833	−	1.23275i
$806$	−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	$0.659420\pi$
$810$	1.46211	+	16.9683i	0.0513733	+	0.596205i
$811$	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
$820$	−28.5679	+	25.2433i	−0.997633	+	0.881533i
$821$	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	$-0.547716\pi$
$823$	−8.56875			−0.298688			−0.149344	+	0.988785i	$0.547716\pi$
$824$	−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	−0.860355	−	0.509695i	$-0.829758\pi$
$827$	−10.0841	+	10.0841i	−0.350660	+	0.350660i	0.509695	+	0.860355i	$0.329758\pi$
$828$	−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	$0.244866\pi$
$830$	10.8108	−	12.8495i	0.375248	−	0.446014i
$831$	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
$835$	0.832439	−	1.35232i	0.0288077	−	0.0467990i
$836$	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	$-0.0297807\pi$
$840$	−32.7546	−	50.4292i	−1.13014	−	1.73997i
$841$			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
$845$	−0.883749	−	0.544003i	−0.0304019	−	0.0187143i
$846$	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
$850$	6.03260	−	11.9997i	0.206917	−	0.411586i
$851$	−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	−0.352655	−	0.935753i	$-0.614721\pi$
$853$	17.0301	−	17.0301i	0.583098	−	0.583098i	0.935753	+	0.352655i	$0.114721\pi$
$854$	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	$-0.861683\pi$
$857$	−53.1079			−1.81413			−0.907066	+	0.420988i	$0.861683\pi$
$858$	−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	$0.833597\pi$
$860$	10.1909	+	0.629618i	0.347505	+	0.0214698i
$861$	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	$-0.882433\pi$
$863$		−	21.2106i		−	0.722016i	0.932563	−	0.361008i	$-0.117567\pi$
$864$	−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
$870$	−1.27165	−	14.7580i	−0.0431130	−	0.500342i
$871$			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
$875$	40.2605	+	3.41242i	1.36105	+	0.115361i
$876$	75.1083	−	40.0696i	2.53767	−	1.35383i
$877$	25.6041	+	25.6041i	0.864589	+	0.864589i	0.991867	−	0.127278i	$-0.0406241\pi$
$877$	25.6041	+	25.6041i	0.864589	+	0.864589i	−0.127278	+	0.991867i	$0.540624\pi$
$878$	21.3979	+	28.8756i	0.722143	+	0.974506i
$879$	21.4138			0.722268
$880$	−1.12337	−	0.419026i	−0.0378689	−	0.0141254i
$881$	−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	0.881884	−	0.471466i	$-0.156275\pi$
$883$	12.1957	+	12.1957i	0.410419	+	0.410419i	−0.471466	+	0.881884i	$0.656275\pi$
$884$	6.56107	+	12.2984i	0.220673	+	0.413639i
$885$	−55.3889	−	34.0953i	−1.86188	−	1.14610i
$886$	7.27401	−	48.9036i	0.244375	−	1.64295i
$887$	36.3716			1.22124			0.610619	−	0.791924i	$-0.290921\pi$
$887$	36.3716			1.22124			0.610619	+	0.791924i	$0.290921\pi$
$888$	7.95765	+	22.3239i	0.267041	+	0.749141i
$889$		−	10.6322i		−	0.356591i
$890$	12.5458	−	1.08104i	0.420536	−	0.0362364i
$891$	−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
$900$	−6.70850	−	38.6382i	−0.223617	−	1.28794i
$901$	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	$-0.436557\pi$
$907$	35.4831	−	35.4831i	1.17820	−	1.17820i	0.980203	−	0.197996i	$-0.0634432\pi$
$908$	10.5168	−	5.61062i	0.349012	−	0.186195i
$909$	−4.93719	+	4.93719i	−0.163756	+	0.163756i
$910$	−26.9968	+	32.0880i	−0.894936	+	1.06371i
$911$	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
$915$	15.1077	−	24.5429i	0.499445	−	0.811363i
$916$	−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	$-0.106744\pi$
$920$	−31.4427	−	6.68084i	−1.03663	−	0.220261i
$921$		−	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
$925$	−15.1252	−	4.98165i	−0.497315	−	0.163796i
$926$	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	$0.442089\pi$
$930$	−6.82650	+	8.11387i	−0.223850	+	0.266064i
$931$	−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	$-0.295476\pi$
$937$	36.6851			1.19845			0.599225	+	0.800581i	$0.295476\pi$
$938$	45.0295	+	6.69777i	1.47027	+	0.218690i
$939$	−47.7014	−	47.7014i	−1.55668	−	1.55668i
$940$	8.50831	−	7.51815i	0.277510	−	0.245215i
$941$	−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	$-0.831701\pi$
$947$	−42.0944	−	42.0944i	−1.36788	−	1.36788i	−0.504433	−	0.863451i	$-0.668299\pi$
$948$	−5.27266	+	2.81292i	−0.171248	+	0.0913593i
$949$	−41.9772	−	41.9772i	−1.36264	−	1.36264i
$950$	20.5461	−	6.79892i	0.666602	−	0.220586i
$951$		−	3.51971i		−	0.114135i
$952$	18.2879	−	6.51896i	0.592714	−	0.211281i
$953$	5.32619			0.172532			0.0862661	−	0.996272i	$-0.472506\pi$
$953$	5.32619			0.172532			0.0862661	+	0.996272i	$0.472506\pi$
$954$	43.9951	+	6.54390i	1.42439	+	0.211866i
$955$	−22.1870	+	36.0434i	−0.717953	+	1.16634i
$956$	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
$960$	−28.5695	+	37.3993i	−0.922075	+	1.20706i
$961$	−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
$965$	−40.7274	−	25.0703i	−1.31106	−	0.807041i
$966$	67.5964	+	10.0544i	2.17488	+	0.323495i
$967$	29.9668			0.963667			0.481833	−	0.876263i	$-0.339971\pi$
$967$	29.9668			0.963667			0.481833	+	0.876263i	$0.339971\pi$
$968$	−29.2586	+	10.4296i	−0.940406	+	0.335220i
$969$			15.2942i			0.491320i
$970$	32.4645	−	2.79737i	1.04237	−	0.0898182i
$971$	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	$0.137944\pi$
$977$			26.2513i			0.839854i	−0.907558	+	0.419927i	$0.862056\pi$
$978$	−19.2696	−	26.0037i	−0.616175	−	0.831505i
$979$	−0.377447	+	0.377447i	−0.0120633	+	0.0120633i
$980$	17.9464	+	20.3100i	0.573277	+	0.648779i
$981$	−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	$-0.433409\pi$
$983$	13.0227			0.415360			0.207680	+	0.978197i	$0.433409\pi$
$984$	−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
$990$	1.27206	+	1.07023i	0.0404288	+	0.0340142i
$991$	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
$995$	−11.1519	−	6.86467i	−0.353538	−	0.217625i
$996$	26.7317	+	8.13215i	0.847026	+	0.257677i
$997$	−21.2387	+	21.2387i	−0.672637	+	0.672637i	−0.958323	−	0.285686i	$-0.907778\pi$
$997$	−21.2387	+	21.2387i	−0.672637	+	0.672637i	0.285686	+	0.958323i	$0.407778\pi$
$998$	−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.69.7	yes	16
3.2	odd	2		720.2.bm.f.469.2		16
4.3	odd	2		320.2.q.c.49.7		16
5.2	odd	4		400.2.l.i.101.6		16
5.3	odd	4		400.2.l.i.101.3		16
5.4	even	2	inner	80.2.q.c.69.2	yes	16
8.3	odd	2		640.2.q.f.609.2		16
8.5	even	2		640.2.q.e.609.7		16
15.14	odd	2		720.2.bm.f.469.7		16
16.3	odd	4		320.2.q.c.209.2		16
16.5	even	4		640.2.q.e.289.2		16
16.11	odd	4		640.2.q.f.289.7		16
16.13	even	4	inner	80.2.q.c.29.2	✓	16
20.3	even	4		1600.2.l.h.1201.2		16
20.7	even	4		1600.2.l.h.1201.7		16
20.19	odd	2		320.2.q.c.49.2		16
40.19	odd	2		640.2.q.f.609.7		16
40.29	even	2		640.2.q.e.609.2		16
48.29	odd	4		720.2.bm.f.109.7		16
80.3	even	4		1600.2.l.h.401.2		16
80.13	odd	4		400.2.l.i.301.3		16
80.19	odd	4		320.2.q.c.209.7		16
80.29	even	4	inner	80.2.q.c.29.7	yes	16
80.59	odd	4		640.2.q.f.289.2		16
80.67	even	4		1600.2.l.h.401.7		16
80.69	even	4		640.2.q.e.289.7		16
80.77	odd	4		400.2.l.i.301.6		16
240.29	odd	4		720.2.bm.f.109.2		16

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

\(f(q)\)	\(=\)	\(q+(1.13624 - 0.841995i) q^{2} +(-1.86033 - 1.86033i) q^{3} +(0.582088 - 1.91342i) q^{4} +(-1.17216 + 1.90421i) q^{5} +(-3.68016 - 0.547394i) q^{6} +3.61392 q^{7} +(-0.949697 - 2.66422i) q^{8} +3.92163i q^{9} +O(q^{10})\)	\(q+(1.13624 - 0.841995i) q^{2} +(-1.86033 - 1.86033i) q^{3} +(0.582088 - 1.91342i) q^{4} +(-1.17216 + 1.90421i) q^{5} +(-3.68016 - 0.547394i) q^{6} +3.61392 q^{7} +(-0.949697 - 2.66422i) q^{8} +3.92163i q^{9} +(0.271479 + 3.15060i) 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} +(2.96126 + 3.35126i) 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} +(5.35611 - 6.36619i) q^{30} -1.27453 q^{31} +(-5.65058 + 0.266355i) q^{32} +0.352672i q^{33} +(1.59928 + 2.15817i) q^{34} +(-4.23610 + 6.88168i) q^{35} +(7.50371 + 2.28273i) q^{36} +(2.25207 - 2.25207i) q^{37} +(-0.636801 + 4.28125i) q^{38} -9.65368i q^{39} +(6.18645 + 1.31448i) q^{40} +8.52451i q^{41} +(-13.2998 - 1.97824i) q^{42} +(1.61439 - 1.61439i) q^{43} +(-0.236543 + 0.126194i) q^{44} +(-7.46762 - 4.59679i) q^{45} +(-5.77495 + 4.27944i) q^{46} -2.53884i q^{47} +(2.03666 + 10.3246i) q^{48} +6.06040 q^{49} +(-6.31764 - 3.17607i) 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} +(0.725535 - 11.7433i) 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} +(0.981101 + 11.3860i) q^{70} +11.3074i q^{71} +(10.4481 - 3.72436i) q^{72} -16.1786 q^{73} +(0.662661 - 4.45512i) q^{74} +(-4.11511 + 12.4943i) q^{75} +(2.88124 + 5.40072i) q^{76} +(-0.342555 - 0.342555i) q^{77} +(-8.12835 - 10.9689i) q^{78} +1.13575 q^{79} +(8.13608 - 3.71540i) q^{80} +5.38573 q^{81} +(7.17759 + 9.68590i) q^{82} +(-3.75489 - 3.75489i) q^{83} +(-16.7775 + 8.95062i) q^{84} +(-3.61685 - 2.22640i) q^{85} +(0.475028 - 3.19364i) q^{86} -4.68417 q^{87} +(-0.162516 + 0.342555i) q^{88} -3.98203i q^{89} +(-12.3555 + 1.06464i) 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

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more