LMFDB - Embedded newform 731.2.m.b.87.14

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [731,2,Mod(87,731)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(731, base_ring=CyclotomicField(8))

chi = DirichletCharacter(H, H._module([7, 0]))

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

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

chi := DirichletCharacter("731.87");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 731 = 17 \cdot 43 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	731.m (of order $8$, degree $4$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$5.83706438776$
Analytic rank:	$0$
Dimension:	$116$
Relative dimension:	$29$ over $\Q(\zeta_{8})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{8}]$

Embedding invariants

Embedding label			87.14
Character	$\chi$	$=$	731.87
Dual form			731.2.m.b.689.14

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.292872 - 0.292872i) q^{2} +(2.84462 - 1.17828i) q^{3} -1.82845i q^{4} +(0.0154981 + 0.0374157i) q^{5} +(-1.17820 - 0.488025i) q^{6} +(-0.341796 + 0.825169i) q^{7} +(-1.12125 + 1.12125i) q^{8} +(4.58219 - 4.58219i) q^{9} +O(q^{10})$	\(q+(-0.292872 - 0.292872i) q^{2} +(2.84462 - 1.17828i) q^{3} -1.82845i q^{4} +(0.0154981 + 0.0374157i) q^{5} +(-1.17820 - 0.488025i) q^{6} +(-0.341796 + 0.825169i) q^{7} +(-1.12125 + 1.12125i) q^{8} +(4.58219 - 4.58219i) q^{9} +(0.00641907 - 0.0154970i) q^{10} +(2.69934 + 1.11811i) q^{11} +(-2.15443 - 5.20124i) q^{12} -4.69807i q^{13} +(0.341772 - 0.141567i) q^{14} +(0.0881723 + 0.0881723i) q^{15} -3.00014 q^{16} +(-0.147431 + 4.12047i) q^{17} -2.68399 q^{18} +(1.40993 + 1.40993i) q^{19} +(0.0684128 - 0.0283375i) q^{20} +2.75002i q^{21} +(-0.463101 - 1.11803i) q^{22} +(-7.48176 - 3.09905i) q^{23} +(-1.86838 + 4.51067i) q^{24} +(3.53437 - 3.53437i) q^{25} +(-1.37594 + 1.37594i) q^{26} +(4.10064 - 9.89981i) q^{27} +(1.50878 + 0.624958i) q^{28} +(0.652501 + 1.57528i) q^{29} -0.0516465i q^{30} +(6.85556 - 2.83967i) q^{31} +(3.12115 + 3.12115i) q^{32} +8.99604 q^{33} +(1.24995 - 1.16359i) q^{34} -0.0361715 q^{35} +(-8.37831 - 8.37831i) q^{36} +(-8.16961 + 3.38396i) q^{37} -0.825860i q^{38} +(-5.53564 - 13.3642i) q^{39} +(-0.0593295 - 0.0245751i) q^{40} +(-0.849335 + 2.05048i) q^{41} +(0.805406 - 0.805406i) q^{42} +(0.707107 - 0.707107i) q^{43} +(2.04440 - 4.93562i) q^{44} +(0.242461 + 0.100431i) q^{45} +(1.28358 + 3.09883i) q^{46} +13.0421i q^{47} +(-8.53424 + 3.53500i) q^{48} +(4.38567 + 4.38567i) q^{49} -2.07024 q^{50} +(4.43568 + 11.8949i) q^{51} -8.59020 q^{52} +(-9.03159 - 9.03159i) q^{53} +(-4.10035 + 1.69842i) q^{54} +0.118326i q^{55} +(-0.541981 - 1.30846i) q^{56} +(5.67201 + 2.34942i) q^{57} +(0.270256 - 0.652455i) q^{58} +(-1.17907 + 1.17907i) q^{59} +(0.161219 - 0.161219i) q^{60} +(-5.00659 + 12.0870i) q^{61} +(-2.83947 - 1.17615i) q^{62} +(2.21491 + 5.34725i) q^{63} +4.17207i q^{64} +(0.175782 - 0.0728112i) q^{65} +(-2.63469 - 2.63469i) q^{66} -4.59166 q^{67} +(7.53408 + 0.269570i) q^{68} -24.9343 q^{69} +(0.0105936 + 0.0105936i) q^{70} +(12.1537 - 5.03422i) q^{71} +10.2755i q^{72} +(-3.38853 - 8.18063i) q^{73} +(3.38372 + 1.40158i) q^{74} +(5.88946 - 14.2184i) q^{75} +(2.57799 - 2.57799i) q^{76} +(-1.84525 + 1.84525i) q^{77} +(-2.29278 + 5.53525i) q^{78} +(7.47640 + 3.09683i) q^{79} +(-0.0464964 - 0.112252i) q^{80} -13.5523i q^{81} +(0.849275 - 0.351781i) q^{82} +(8.05520 + 8.05520i) q^{83} +5.02828 q^{84} +(-0.156455 + 0.0583432i) q^{85} -0.414184 q^{86} +(3.71223 + 3.71223i) q^{87} +(-4.28031 + 1.77296i) q^{88} +9.27657i q^{89} +(-0.0415968 - 0.100424i) q^{90} +(3.87671 + 1.60578i) q^{91} +(-5.66646 + 13.6800i) q^{92} +(16.1555 - 16.1555i) q^{93} +(3.81968 - 3.81968i) q^{94} +(-0.0309023 + 0.0746048i) q^{95} +(12.5561 + 5.20090i) q^{96} +(1.77021 + 4.27367i) q^{97} -2.56888i q^{98} +(17.4923 - 7.24553i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 116 q - 8 q^{6}+O(q^{10}) $ 116 * q - 8 * q^6	$ 116 q - 8 q^{6} - 8 q^{10} + 8 q^{14} + 4 q^{15} - 68 q^{16} - 4 q^{17} - 44 q^{18} + 12 q^{19} + 8 q^{20} - 16 q^{22} - 28 q^{23} - 12 q^{24} - 4 q^{25} - 8 q^{26} + 24 q^{28} + 80 q^{33} + 32 q^{34} - 112 q^{35} + 160 q^{36} - 20 q^{37} + 8 q^{39} - 112 q^{40} + 8 q^{41} + 4 q^{42} + 32 q^{44} - 52 q^{45} - 40 q^{46} + 40 q^{48} + 8 q^{49} + 100 q^{50} - 32 q^{51} - 152 q^{52} + 28 q^{53} - 36 q^{54} + 124 q^{56} - 104 q^{57} - 32 q^{58} - 36 q^{59} - 24 q^{60} + 52 q^{61} - 68 q^{62} + 20 q^{63} + 20 q^{65} - 60 q^{66} + 64 q^{67} - 128 q^{69} + 188 q^{70} + 52 q^{73} - 104 q^{74} + 36 q^{75} - 112 q^{76} + 28 q^{77} + 56 q^{78} - 108 q^{79} - 44 q^{80} + 52 q^{82} - 52 q^{83} + 120 q^{84} + 12 q^{85} - 20 q^{86} + 56 q^{87} + 36 q^{88} + 144 q^{90} - 16 q^{92} - 176 q^{93} - 8 q^{94} + 164 q^{95} - 164 q^{96} - 8 q^{97} - 24 q^{99}+O(q^{100}) $ 116 * q - 8 * q^6 - 8 * q^10 + 8 * q^14 + 4 * q^15 - 68 * q^16 - 4 * q^17 - 44 * q^18 + 12 * q^19 + 8 * q^20 - 16 * q^22 - 28 * q^23 - 12 * q^24 - 4 * q^25 - 8 * q^26 + 24 * q^28 + 80 * q^33 + 32 * q^34 - 112 * q^35 + 160 * q^36 - 20 * q^37 + 8 * q^39 - 112 * q^40 + 8 * q^41 + 4 * q^42 + 32 * q^44 - 52 * q^45 - 40 * q^46 + 40 * q^48 + 8 * q^49 + 100 * q^50 - 32 * q^51 - 152 * q^52 + 28 * q^53 - 36 * q^54 + 124 * q^56 - 104 * q^57 - 32 * q^58 - 36 * q^59 - 24 * q^60 + 52 * q^61 - 68 * q^62 + 20 * q^63 + 20 * q^65 - 60 * q^66 + 64 * q^67 - 128 * q^69 + 188 * q^70 + 52 * q^73 - 104 * q^74 + 36 * q^75 - 112 * q^76 + 28 * q^77 + 56 * q^78 - 108 * q^79 - 44 * q^80 + 52 * q^82 - 52 * q^83 + 120 * q^84 + 12 * q^85 - 20 * q^86 + 56 * q^87 + 36 * q^88 + 144 * q^90 - 16 * q^92 - 176 * q^93 - 8 * q^94 + 164 * q^95 - 164 * q^96 - 8 * q^97 - 24 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/731\mathbb{Z}\right)^\times$.

$n$	$173$	$562$
$\chi(n)$	$e\left(\frac{7}{8}\right)$	$1$

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 $

$2$	−0.292872	−	0.292872i	−0.207092	−	0.207092i	0.595938	−	0.803030i	$-0.296780\pi$
$2$	−0.292872	−	0.292872i	−0.207092	−	0.207092i	−0.803030	+	0.595938i	$0.796780\pi$
$3$	2.84462	−	1.17828i	1.64234	−	0.680280i	0.645809	−	0.763499i	$-0.276520\pi$
$3$	2.84462	−	1.17828i	1.64234	−	0.680280i	0.996531	+	0.0832189i	$0.0265201\pi$
$4$		−	1.82845i		−	0.914226i
$5$	0.0154981	+	0.0374157i	0.00693096	+	0.0167328i	0.927307	−	0.374301i	$-0.122117\pi$
$5$	0.0154981	+	0.0374157i	0.00693096	+	0.0167328i	−0.920376	+	0.391034i	$0.872117\pi$
$6$	−1.17820	−	0.488025i	−0.480996	−	0.199235i
$7$	−0.341796	+	0.825169i	−0.129187	+	0.311885i	−0.975217	−	0.221250i	$-0.928986\pi$
$7$	−0.341796	+	0.825169i	−0.129187	+	0.311885i	0.846030	+	0.533135i	$0.178986\pi$
$8$	−1.12125	+	1.12125i	−0.396421	+	0.396421i
$9$	4.58219	−	4.58219i	1.52740	−	1.52740i
$10$	0.00641907	−	0.0154970i	0.00202989	−	0.00490058i
$11$	2.69934	+	1.11811i	0.813883	+	0.337121i	0.750502	−	0.660868i	$-0.229812\pi$
$11$	2.69934	+	1.11811i	0.813883	+	0.337121i	0.0633808	+	0.997989i	$0.479812\pi$
$12$	−2.15443	−	5.20124i	−0.621929	−	1.50147i
$13$		−	4.69807i		−	1.30301i	−0.758644	−	0.651506i	$-0.774138\pi$
$13$		−	4.69807i		−	1.30301i	0.758644	−	0.651506i	$-0.225862\pi$
$14$	0.341772	−	0.141567i	0.0913424	−	0.0378353i
$15$	0.0881723	+	0.0881723i	0.0227660	+	0.0227660i
$16$	−3.00014			−0.750034
$17$	−0.147431	+	4.12047i	−0.0357573	+	0.999361i
$17$	−0.147431	+	4.12047i	−0.0357573	+	0.999361i
$18$	−2.68399			−0.632623
$19$	1.40993	+	1.40993i	0.323460	+	0.323460i	0.850093	−	0.526633i	$-0.176546\pi$
$19$	1.40993	+	1.40993i	0.323460	+	0.323460i	−0.526633	+	0.850093i	$0.676546\pi$
$20$	0.0684128	−	0.0283375i	0.0152976	−	0.00633646i
$21$			2.75002i			0.600104i
$22$	−0.463101	−	1.11803i	−0.0987336	−	0.238364i
$23$	−7.48176	−	3.09905i	−1.56006	−	0.646196i	−0.574957	−	0.818184i	$-0.694981\pi$
$23$	−7.48176	−	3.09905i	−1.56006	−	0.646196i	−0.985099	+	0.171988i	$0.944981\pi$
$24$	−1.86838	+	4.51067i	−0.381381	+	0.920736i
$25$	3.53437	−	3.53437i	0.706875	−	0.706875i
$26$	−1.37594	+	1.37594i	−0.269843	+	0.269843i
$27$	4.10064	−	9.89981i	0.789168	−	1.90522i
$28$	1.50878	+	0.624958i	0.285133	+	0.118106i
$29$	0.652501	+	1.57528i	0.121166	+	0.292521i	0.972812	−	0.231597i	$-0.0743950\pi$
$29$	0.652501	+	1.57528i	0.121166	+	0.292521i	−0.851646	+	0.524118i	$0.824395\pi$
$30$		−	0.0516465i		−	0.00942932i
$31$	6.85556	−	2.83967i	1.23130	−	0.510019i	0.330312	−	0.943872i	$-0.392846\pi$
$31$	6.85556	−	2.83967i	1.23130	−	0.510019i	0.900984	+	0.433853i	$0.142846\pi$
$32$	3.12115	+	3.12115i	0.551747	+	0.551747i
$33$	8.99604			1.56601
$34$	1.24995	−	1.16359i	0.214365	−	0.199555i
$35$	−0.0361715			−0.00611410
$36$	−8.37831	−	8.37831i	−1.39638	−	1.39638i
$37$	−8.16961	+	3.38396i	−1.34308	+	0.556320i	−0.934356	−	0.356340i	$-0.884024\pi$
$37$	−8.16961	+	3.38396i	−1.34308	+	0.556320i	−0.408719	+	0.912660i	$0.634024\pi$
$38$		−	0.825860i		−	0.133972i
$39$	−5.53564	−	13.3642i	−0.886412	−	2.13999i
$40$	−0.0593295	−	0.0245751i	−0.00938082	−	0.00388566i
$41$	−0.849335	+	2.05048i	−0.132644	+	0.320230i	−0.976221	−	0.216777i	$-0.930445\pi$
$41$	−0.849335	+	2.05048i	−0.132644	+	0.320230i	0.843577	+	0.537008i	$0.180445\pi$
$42$	0.805406	−	0.805406i	0.124277	−	0.124277i
$43$	0.707107	−	0.707107i	0.107833	−	0.107833i
$43$	0.707107	−	0.707107i	0.107833	−	0.107833i
$44$	2.04440	−	4.93562i	0.308205	−	0.744073i
$45$	0.242461	+	0.100431i	0.0361440	+	0.0149713i
$46$	1.28358	+	3.09883i	0.189253	+	0.456897i
$47$			13.0421i			1.90239i	0.308595	+	0.951194i	$0.400141\pi$
$47$			13.0421i			1.90239i	−0.308595	+	0.951194i	$0.599859\pi$
$48$	−8.53424	+	3.53500i	−1.23181	+	0.510233i
$49$	4.38567	+	4.38567i	0.626524	+	0.626524i
$50$	−2.07024			−0.292776
$51$	4.43568	+	11.8949i	0.621119	+	1.66562i
$52$	−8.59020			−1.19125
$53$	−9.03159	−	9.03159i	−1.24058	−	1.24058i	−0.959759	−	0.280825i	$-0.909392\pi$
$53$	−9.03159	−	9.03159i	−1.24058	−	1.24058i	−0.280825	−	0.959759i	$-0.590608\pi$
$54$	−4.10035	+	1.69842i	−0.557986	+	0.231126i
$55$			0.118326i			0.0159551i
$56$	−0.541981	−	1.30846i	−0.0724253	−	0.174850i
$57$	5.67201	+	2.34942i	0.751276	+	0.311189i
$58$	0.270256	−	0.652455i	0.0354863	−	0.0856715i
$59$	−1.17907	+	1.17907i	−0.153502	+	0.153502i	−0.779680	−	0.626178i	$-0.784618\pi$
$59$	−1.17907	+	1.17907i	−0.153502	+	0.153502i	0.626178	+	0.779680i	$0.284618\pi$
$60$	0.161219	−	0.161219i	0.0208133	−	0.0208133i
$61$	−5.00659	+	12.0870i	−0.641029	+	1.54758i	0.184266	+	0.982876i	$0.441009\pi$
$61$	−5.00659	+	12.0870i	−0.641029	+	1.54758i	−0.825294	+	0.564703i	$0.808991\pi$
$62$	−2.83947	−	1.17615i	−0.360613	−	0.149371i
$63$	2.21491	+	5.34725i	0.279052	+	0.673691i
$64$			4.17207i			0.521509i
$65$	0.175782	−	0.0728112i	0.0218031	−	0.00903112i
$66$	−2.63469	−	2.63469i	−0.324308	−	0.324308i
$67$	−4.59166			−0.560960			−0.280480	−	0.959860i	$-0.590494\pi$
$67$	−4.59166			−0.560960			−0.280480	+	0.959860i	$0.590494\pi$
$68$	7.53408	+	0.269570i	0.913641	+	0.0326902i
$69$	−24.9343			−3.00174
$70$	0.0105936	+	0.0105936i	0.00126618	+	0.00126618i
$71$	12.1537	−	5.03422i	1.44238	−	0.597452i	0.482004	−	0.876169i	$-0.339909\pi$
$71$	12.1537	−	5.03422i	1.44238	−	0.597452i	0.960373	+	0.278716i	$0.0899089\pi$
$72$			10.2755i			1.21098i
$73$	−3.38853	−	8.18063i	−0.396597	−	0.957470i	−0.988467	−	0.151437i	$-0.951610\pi$
$73$	−3.38853	−	8.18063i	−0.396597	−	0.957470i	0.591870	−	0.806034i	$-0.298390\pi$
$74$	3.38372	+	1.40158i	0.393350	+	0.162931i
$75$	5.88946	−	14.2184i	0.680057	−	1.64180i
$76$	2.57799	−	2.57799i	0.295716	−	0.295716i
$77$	−1.84525	+	1.84525i	−0.210286	+	0.210286i
$78$	−2.29278	+	5.53525i	−0.259606	+	0.626744i
$79$	7.47640	+	3.09683i	0.841161	+	0.348420i	0.761311	−	0.648387i	$-0.224556\pi$
$79$	7.47640	+	3.09683i	0.841161	+	0.348420i	0.0798498	+	0.996807i	$0.474556\pi$
$80$	−0.0464964	−	0.112252i	−0.00519846	−	0.0125502i
$81$		−	13.5523i		−	1.50581i
$82$	0.849275	−	0.351781i	0.0937867	−	0.0388477i
$83$	8.05520	+	8.05520i	0.884173	+	0.884173i	0.993956	−	0.109782i	$-0.0350154\pi$
$83$	8.05520	+	8.05520i	0.884173	+	0.884173i	−0.109782	+	0.993956i	$0.535015\pi$
$84$	5.02828			0.548631
$85$	−0.156455	+	0.0583432i	−0.0169700	+	0.00632821i
$86$	−0.414184			−0.0446626
$87$	3.71223	+	3.71223i	0.397993	+	0.397993i
$88$	−4.28031	+	1.77296i	−0.456282	+	0.188998i
$89$			9.27657i			0.983314i	0.870789	+	0.491657i	$0.163609\pi$
$89$			9.27657i			0.983314i	−0.870789	+	0.491657i	$0.836391\pi$
$90$	−0.0415968	−	0.100424i	−0.00438469	−	0.0105856i
$91$	3.87671	+	1.60578i	0.406389	+	0.168332i
$92$	−5.66646	+	13.6800i	−0.590769	+	1.42624i
$93$	16.1555	−	16.1555i	1.67525	−	1.67525i
$94$	3.81968	−	3.81968i	0.393969	−	0.393969i
$95$	−0.0309023	+	0.0746048i	−0.00317051	+	0.00765430i
$96$	12.5561	+	5.20090i	1.28150	+	0.530814i
$97$	1.77021	+	4.27367i	0.179738	+	0.433926i	0.987912	−	0.155019i	$-0.0495438\pi$
$97$	1.77021	+	4.27367i	0.179738	+	0.433926i	−0.808174	+	0.588944i	$0.799544\pi$
$98$		−	2.56888i		−	0.259496i
$99$	17.4923	−	7.24553i	1.75804	−	0.728203i
$100$	−6.46243	−	6.46243i	−0.646243	−	0.646243i
$101$	12.3457			1.22844			0.614221	−	0.789134i	$-0.289470\pi$
$101$	12.3457			1.22844			0.614221	+	0.789134i	$0.289470\pi$
$102$	2.18459	−	4.78277i	0.216307	−	0.473565i
$103$	−9.61616			−0.947508			−0.473754	−	0.880657i	$-0.657101\pi$
$103$	−9.61616			−0.947508			−0.473754	+	0.880657i	$0.657101\pi$
$104$	5.26771	+	5.26771i	0.516541	+	0.516541i
$105$	−0.102894	+	0.0426201i	−0.0100414	+	0.00415930i
$106$			5.29021i			0.513830i
$107$	−4.55613	−	10.9995i	−0.440458	−	1.06336i	−0.975788	−	0.218716i	$-0.929813\pi$
$107$	−4.55613	−	10.9995i	−0.440458	−	1.06336i	0.535331	−	0.844642i	$-0.320187\pi$
$108$	−18.1013	−	7.49781i	−1.74180	−	0.721477i
$109$	6.22672	−	15.0326i	0.596412	−	1.43986i	−0.280803	−	0.959766i	$-0.590601\pi$
$109$	6.22672	−	15.0326i	0.596412	−	1.43986i	0.877214	−	0.480099i	$-0.159399\pi$
$110$	0.0346546	−	0.0346546i	0.00330418	−	0.00330418i
$111$	−19.2522	+	19.2522i	−1.82733	+	1.82733i
$112$	1.02544	−	2.47562i	0.0968946	−	0.233924i
$113$	−1.03520	−	0.428792i	−0.0973831	−	0.0403374i	0.333460	−	0.942764i	$-0.391784\pi$
$113$	−1.03520	−	0.428792i	−0.0973831	−	0.0403374i	−0.430843	+	0.902427i	$0.641784\pi$
$114$	−0.973094	−	2.34926i	−0.0911386	−	0.220028i
$115$		−	0.327965i		−	0.0305829i
$116$	2.88032	−	1.19307i	0.267431	−	0.110773i
$117$	−21.5275	−	21.5275i	−1.99021	−	1.99021i
$118$	0.690637			0.0635782
$119$	−3.34969	−	1.53002i	−0.307066	−	0.140256i
$120$	−0.197726			−0.0180498
$121$	−1.74187	−	1.74187i	−0.158352	−	0.158352i
$122$	5.00624	−	2.07365i	0.453244	−	0.187740i
$123$			6.83357i			0.616162i
$124$	−5.19219	−	12.5351i	−0.466273	−	1.12568i
$125$	0.374096	+	0.154956i	0.0334602	+	0.0138596i
$126$	0.917379	−	2.21475i	0.0817266	−	0.197305i
$127$	5.91283	−	5.91283i	0.524679	−	0.524679i	−0.394302	−	0.918981i	$-0.629014\pi$
$127$	5.91283	−	5.91283i	0.524679	−	0.524679i	0.918981	+	0.394302i	$0.129014\pi$
$128$	7.46419	−	7.46419i	0.659748	−	0.659748i
$129$	1.17828	−	2.84462i	0.103742	−	0.250455i
$130$	−0.0728061	−	0.0301573i	−0.00638552	−	0.00264497i
$131$	6.92651	+	16.7221i	0.605172	+	1.46102i	0.868194	+	0.496225i	$0.165281\pi$
$131$	6.92651	+	16.7221i	0.605172	+	1.46102i	−0.263022	+	0.964790i	$0.584719\pi$
$132$		−	16.4488i		−	1.43169i
$133$	−1.64534	+	0.681523i	−0.142669	+	0.0590955i
$134$	1.34477	+	1.34477i	0.116170	+	0.116170i
$135$	0.433961			0.0373494
$136$	−4.45476	−	4.78537i	−0.381993	−	0.410342i
$137$	6.63874			0.567186			0.283593	−	0.958945i	$-0.408474\pi$
$137$	6.63874			0.567186			0.283593	+	0.958945i	$0.408474\pi$
$138$	7.30257	+	7.30257i	0.621636	+	0.621636i
$139$	−2.32836	+	0.964439i	−0.197489	+	0.0818026i	−0.479236	−	0.877686i	$-0.659086\pi$
$139$	−2.32836	+	0.964439i	−0.197489	+	0.0818026i	0.281747	+	0.959489i	$0.409086\pi$
$140$			0.0661378i			0.00558967i
$141$	15.3672	+	37.0998i	1.29416	+	3.12437i
$142$	−5.03387	−	2.08510i	−0.422433	−	0.174977i
$143$	5.25294	−	12.6817i	0.439273	−	1.06050i
$144$	−13.7472	+	13.7472i	−1.14560	+	1.14560i
$145$	−0.0488276	+	0.0488276i	−0.00405491	+	0.00405491i
$146$	−1.40347	+	3.38829i	−0.116152	+	0.280417i
$147$	17.6431	+	7.30801i	1.45518	+	0.602754i
$148$	6.18741	+	14.9377i	0.508602	+	1.22787i
$149$			15.1764i			1.24330i	0.783295	+	0.621650i	$0.213537\pi$
$149$			15.1764i			1.24330i	−0.783295	+	0.621650i	$0.786463\pi$
$150$	−5.88905	+	2.43932i	−0.480839	+	0.199170i
$151$	−7.01588	−	7.01588i	−0.570944	−	0.570944i	0.361448	−	0.932392i	$-0.382282\pi$
$151$	−7.01588	−	7.01588i	−0.570944	−	0.570944i	−0.932392	+	0.361448i	$0.882282\pi$
$152$	−3.16176			−0.256453
$153$	18.2052	+	19.5563i	1.47180	+	1.58103i
$154$	1.08085			0.0870971
$155$	0.212496	+	0.212496i	0.0170681	+	0.0170681i
$156$	−24.4358	+	10.1217i	−1.95643	+	0.810381i
$157$			12.9856i			1.03636i	0.855270	+	0.518182i	$0.173391\pi$
$157$			12.9856i			1.03636i	−0.855270	+	0.518182i	$0.826609\pi$
$158$	−1.28266	−	3.09661i	−0.102043	−	0.246353i
$159$	−36.3331	−	15.0497i	−2.88141	−	1.19352i
$160$	−0.0684083	+	0.165152i	−0.00540815	+	0.0130564i
$161$	5.11448	−	5.11448i	0.403077	−	0.403077i
$162$	−3.96909	+	3.96909i	−0.311842	+	0.311842i
$163$	3.26076	−	7.87218i	0.255403	−	0.616596i	−0.743221	−	0.669046i	$-0.766703\pi$
$163$	3.26076	−	7.87218i	0.255403	−	0.616596i	0.998624	+	0.0524497i	$0.0167029\pi$
$164$	3.74919	+	1.55297i	0.292763	+	0.121266i
$165$	0.139422	+	0.336593i	0.0108540	+	0.0262038i
$166$		−	4.71829i		−	0.366211i
$167$	12.1494	−	5.03243i	0.940146	−	0.389421i	0.140627	−	0.990063i	$-0.455088\pi$
$167$	12.1494	−	5.03243i	0.940146	−	0.389421i	0.799518	+	0.600642i	$0.205088\pi$
$168$	−3.08346	−	3.08346i	−0.237894	−	0.237894i
$169$	−9.07191			−0.697839
$170$	0.0629086	+	0.0287343i	0.00482487	+	0.00220382i
$171$	12.9211			0.988104
$172$	−1.29291	−	1.29291i	−0.0985835	−	0.0985835i
$173$	12.5852	−	5.21295i	0.956833	−	0.396333i	0.151038	−	0.988528i	$-0.451738\pi$
$173$	12.5852	−	5.21295i	0.956833	−	0.396333i	0.805795	+	0.592195i	$0.201738\pi$
$174$		−	2.17442i		−	0.164842i
$175$	1.70842	+	4.12449i	0.129144	+	0.311782i
$176$	−8.09840	−	3.35447i	−0.610440	−	0.252853i
$177$	−1.96474	+	4.74329i	−0.147679	+	0.356528i
$178$	2.71685	−	2.71685i	0.203637	−	0.203637i
$179$	−2.63252	+	2.63252i	−0.196764	+	0.196764i	−0.798611	−	0.601847i	$-0.794432\pi$
$179$	−2.63252	+	2.63252i	−0.196764	+	0.196764i	0.601847	+	0.798611i	$0.294432\pi$
$180$	0.183633	−	0.443328i	0.0136872	−	0.0330437i
$181$	−18.5247	−	7.67319i	−1.37693	−	0.570344i	−0.433272	−	0.901263i	$-0.642641\pi$
$181$	−18.5247	−	7.67319i	−1.37693	−	0.570344i	−0.943659	+	0.330920i	$0.892641\pi$
$182$	−0.665091	−	1.60567i	−0.0492998	−	0.119020i
$183$			40.2820i			2.97773i
$184$	11.8637	−	4.91411i	0.874605	−	0.362273i
$185$	−0.253227	−	0.253227i	−0.0186176	−	0.0186176i
$186$	−9.46302			−0.693863
$187$	−5.00508	+	10.9577i	−0.366008	+	0.801308i
$188$	23.8469			1.73921
$189$	6.76744	+	6.76744i	0.492259	+	0.492259i
$190$	0.0309002	−	0.0127993i	0.00224173	−	0.000928556i
$191$			13.6572i			0.988203i	0.869404	+	0.494102i	$0.164503\pi$
$191$			13.6572i			0.988203i	−0.869404	+	0.494102i	$0.835497\pi$
$192$	4.91587	+	11.8680i	0.354772	+	0.856496i
$193$	8.53061	+	3.53349i	0.614046	+	0.254346i	0.667958	−	0.744199i	$-0.267169\pi$
$193$	8.53061	+	3.53349i	0.614046	+	0.254346i	−0.0539111	+	0.998546i	$0.517169\pi$
$194$	0.733194	−	1.77009i	0.0526403	−	0.127085i
$195$	0.414240	−	0.414240i	0.0296644	−	0.0296644i
$196$	8.01898	−	8.01898i	0.572784	−	0.572784i
$197$	0.0126681	−	0.0305835i	0.000902565	−	0.00217898i	−0.923428	−	0.383773i	$-0.874625\pi$
$197$	0.0126681	−	0.0305835i	0.000902565	−	0.00217898i	0.924330	+	0.381594i	$0.124625\pi$
$198$	−7.24502	−	3.00099i	−0.514881	−	0.213271i
$199$	−3.72147	−	8.98442i	−0.263808	−	0.636889i	0.735360	−	0.677677i	$-0.237013\pi$
$199$	−3.72147	−	8.98442i	−0.263808	−	0.636889i	−0.999168	+	0.0407880i	$0.987013\pi$
$200$			7.92582i			0.560440i
$201$	−13.0615	+	5.41025i	−0.921288	+	0.381610i
$202$	−3.61571	−	3.61571i	−0.254401	−	0.254401i
$203$	−1.52289			−0.106886
$204$	21.7492	−	8.11042i	1.52275	−	0.567843i
$205$	−0.0898831			−0.00627771
$206$	2.81631	+	2.81631i	0.196221	+	0.196221i
$207$	−48.4833	+	20.0824i	−3.36982	+	1.39582i
$208$			14.0949i			0.977303i
$209$	2.22944	+	5.38234i	0.154213	+	0.372304i
$210$	0.0426171	+	0.0176526i	0.00294086	+	0.00121814i
$211$	−8.04053	+	19.4116i	−0.553533	+	1.33635i	0.361276	+	0.932459i	$0.382341\pi$
$211$	−8.04053	+	19.4116i	−0.553533	+	1.33635i	−0.914809	+	0.403887i	$0.867659\pi$
$212$	−16.5138	+	16.5138i	−1.13417	+	1.13417i
$213$	28.6409	−	28.6409i	1.96244	−	1.96244i
$214$	−1.88708	+	4.55581i	−0.128998	+	0.311429i
$215$	0.0374157	+	0.0154981i	0.00255173	+	0.00105696i
$216$	6.50231	+	15.6980i	0.442426	+	1.06811i
$217$			6.62759i			0.449910i
$218$	−6.22628	+	2.57901i	−0.421697	+	0.174673i
$219$	−19.2781	−	19.2781i	−1.30270	−	1.30270i
$220$	0.216354			0.0145866
$221$	19.3583	+	0.692642i	1.30218	+	0.0465921i
$222$	11.2769			0.756853
$223$	−7.93922	−	7.93922i	−0.531649	−	0.531649i	0.389414	−	0.921063i	$-0.372678\pi$
$223$	−7.93922	−	7.93922i	−0.531649	−	0.531649i	−0.921063	+	0.389414i	$0.872678\pi$
$224$	−3.64228	+	1.50868i	−0.243360	+	0.100803i
$225$		−	32.3903i		−	2.15935i
$226$	0.177599	+	0.428762i	0.0118137	+	0.0285208i
$227$	−17.1702	−	7.11211i	−1.13962	−	0.472047i	−0.268582	−	0.963257i	$-0.586555\pi$
$227$	−17.1702	−	7.11211i	−1.13962	−	0.472047i	−0.871041	+	0.491209i	$0.836555\pi$
$228$	4.29580	−	10.3710i	0.284497	−	0.686836i
$229$	−9.04457	+	9.04457i	−0.597682	+	0.597682i	−0.939695	−	0.342013i	$-0.888891\pi$
$229$	−9.04457	+	9.04457i	−0.597682	+	0.597682i	0.342013	+	0.939695i	$0.388891\pi$
$230$	−0.0960519	+	0.0960519i	−0.00633348	+	0.00633348i
$231$	−3.07481	+	7.42326i	−0.202308	+	0.488414i
$232$	−2.49789	−	1.03466i	−0.163995	−	0.0679288i
$233$	2.12851	+	5.13867i	0.139443	+	0.336645i	0.978138	−	0.207956i	$-0.0666810\pi$
$233$	2.12851	+	5.13867i	0.139443	+	0.336645i	−0.838695	+	0.544601i	$0.816681\pi$
$234$			12.6096i			0.824315i
$235$	−0.487980	+	0.202128i	−0.0318323	+	0.0131854i
$236$	2.15588	+	2.15588i	0.140336	+	0.140336i
$237$	24.9164			1.61850
$238$	0.532933	+	1.42913i	0.0345449	+	0.0926369i
$239$	−26.3355			−1.70350			−0.851751	−	0.523947i	$-0.824459\pi$
$239$	−26.3355			−1.70350			−0.851751	+	0.523947i	$0.824459\pi$
$240$	−0.264529	−	0.264529i	−0.0170753	−	0.0170753i
$241$	10.6098	−	4.39471i	0.683436	−	0.283088i	−0.0138266	−	0.999904i	$-0.504401\pi$
$241$	10.6098	−	4.39471i	0.683436	−	0.283088i	0.697262	+	0.716816i	$0.254401\pi$
$242$			1.02029i			0.0655870i
$243$	−3.66648	−	8.85167i	−0.235205	−	0.567835i
$244$	22.1005	+	9.15431i	1.41484	+	0.586045i
$245$	−0.0961234	+	0.232062i	−0.00614110	+	0.0148259i
$246$	2.00137	−	2.00137i	0.127602	−	0.127602i
$247$	6.62396	−	6.62396i	0.421473	−	0.421473i
$248$	−4.50282	+	10.8708i	−0.285929	+	0.690294i
$249$	32.4052	+	13.4227i	2.05360	+	0.850629i
$250$	−0.0641802	−	0.154945i	−0.00405911	−	0.00979956i
$251$		−	1.49685i		−	0.0944801i	−0.998884	−	0.0472400i	$-0.984957\pi$
$251$		−	1.49685i		−	0.0944801i	0.998884	−	0.0472400i	$-0.0150426\pi$
$252$	9.77719	−	4.04985i	0.615905	−	0.255116i
$253$	−16.7308	−	16.7308i	−1.05186	−	1.05186i
$254$	−3.46341			−0.217314
$255$	−0.376311	+	0.350312i	−0.0235655	+	0.0219374i
$256$	3.97204			0.248252
$257$	−21.0810	−	21.0810i	−1.31500	−	1.31500i	−0.917684	−	0.397311i	$-0.869943\pi$
$257$	−21.0810	−	21.0810i	−1.31500	−	1.31500i	−0.397311	−	0.917684i	$-0.630057\pi$
$258$	−1.17820	+	0.488025i	−0.0733513	+	0.0303831i
$259$		−	7.89793i		−	0.490754i
$260$	−0.133132	−	0.321409i	−0.00825648	−	0.0199329i
$261$	10.2081	+	4.22833i	0.631865	+	0.261727i
$262$	2.86885	−	6.92602i	0.177238	−	0.427891i
$263$	−8.38873	+	8.38873i	−0.517271	+	0.517271i	−0.916745	−	0.399474i	$-0.869193\pi$
$263$	−8.38873	+	8.38873i	−0.517271	+	0.517271i	0.399474	+	0.916745i	$0.369193\pi$
$264$	−10.0868	+	10.0868i	−0.620799	+	0.620799i
$265$	0.197951	−	0.477896i	0.0121600	−	0.0293569i
$266$	0.681474	+	0.282276i	0.0417839	+	0.0173074i
$267$	10.9304	+	26.3883i	0.668929	+	1.61494i
$268$			8.39562i			0.512844i
$269$	−5.22390	+	2.16381i	−0.318507	+	0.131930i	−0.536209	−	0.844085i	$-0.680144\pi$
$269$	−5.22390	+	2.16381i	−0.318507	+	0.131930i	0.217702	+	0.976015i	$0.430144\pi$
$270$	−0.127095	−	0.127095i	−0.00773476	−	0.00773476i
$271$	−8.53140			−0.518245			−0.259123	−	0.965844i	$-0.583433\pi$
$271$	−8.53140			−0.518245			−0.259123	+	0.965844i	$0.583433\pi$
$272$	0.442313	−	12.3620i	0.0268192	−	0.749555i
$273$	12.9198			0.781943
$274$	−1.94430	−	1.94430i	−0.117460	−	0.117460i
$275$	13.4923	−	5.58869i	0.813616	−	0.337011i
$276$			45.5912i			2.74427i
$277$	1.95625	+	4.72280i	0.117540	+	0.283765i	0.971690	−	0.236261i	$-0.0759221\pi$
$277$	1.95625	+	4.72280i	0.117540	+	0.283765i	−0.854150	+	0.520027i	$0.825922\pi$
$278$	0.964371	+	0.399455i	0.0578391	+	0.0239577i
$279$	18.4016	−	44.4254i	1.10167	−	2.65968i
$280$	0.0405572	−	0.0405572i	0.00242376	−	0.00242376i
$281$	−5.32962	+	5.32962i	−0.317939	+	0.317939i	−0.847975	−	0.530036i	$-0.822178\pi$
$281$	−5.32962	+	5.32962i	−0.317939	+	0.317939i	0.530036	+	0.847975i	$0.322178\pi$
$282$	6.36487	−	15.3662i	0.379023	−	0.915041i
$283$	9.00565	+	3.73026i	0.535330	+	0.221741i	0.633936	−	0.773385i	$-0.281438\pi$
$283$	9.00565	+	3.73026i	0.535330	+	0.221741i	−0.0986056	+	0.995127i	$0.531438\pi$
$284$	−9.20483	−	22.2224i	−0.546206	−	1.31866i
$285$			0.248634i			0.0147278i
$286$	−5.25257	+	2.17569i	−0.310591	+	0.128651i
$287$	−1.40169	−	1.40169i	−0.0827391	−	0.0827391i
$288$	28.6034			1.68547
$289$	−16.9565	−	1.21497i	−0.997443	−	0.0714688i
$290$	0.0286005			0.00167948
$291$	10.0712	+	10.0712i	0.590382	+	0.590382i
$292$	−14.9579	+	6.19576i	−0.875344	+	0.362579i
$293$		−	17.5372i		−	1.02453i	−0.858827	−	0.512266i	$-0.828806\pi$
$293$		−	17.5372i		−	1.02453i	0.858827	−	0.512266i	$-0.171194\pi$
$294$	−3.02686	−	7.30749i	−0.176530	−	0.426181i
$295$	−0.0623893	−	0.0258425i	−0.00363245	−	0.00150461i
$296$	5.36590	−	12.9544i	0.311886	−	0.752960i
$297$	22.1381	−	22.1381i	1.28458	−	1.28458i
$298$	4.44476	−	4.44476i	0.257478	−	0.257478i
$299$	−14.5596	+	35.1499i	−0.842001	+	2.03277i
$300$	−25.9977	−	10.7686i	−1.50098	−	0.621725i
$301$	0.341796	+	0.825169i	0.0197008	+	0.0475620i
$302$			4.10952i			0.236476i
$303$	35.1188	−	14.5467i	2.01752	−	0.835685i
$304$	−4.22999	−	4.22999i	−0.242606	−	0.242606i
$305$	−0.529836			−0.0303383
$306$	0.395704	−	11.0593i	0.0226209	−	0.632219i
$307$	−0.543141			−0.0309987			−0.0154993	−	0.999880i	$-0.504934\pi$
$307$	−0.543141			−0.0309987			−0.0154993	+	0.999880i	$0.504934\pi$
$308$	3.37395	+	3.37395i	0.192249	+	0.192249i
$309$	−27.3543	+	11.3305i	−1.55613	+	0.644571i
$310$		−	0.124469i		−	0.00706935i
$311$	−2.51193	−	6.06432i	−0.142438	−	0.343876i	0.836520	−	0.547936i	$-0.184586\pi$
$311$	−2.51193	−	6.06432i	−0.142438	−	0.343876i	−0.978958	+	0.204060i	$0.934586\pi$
$312$	21.1914	+	8.77778i	1.19973	+	0.496944i
$313$	−11.4182	+	27.5659i	−0.645393	+	1.55812i	0.173912	+	0.984761i	$0.444359\pi$
$313$	−11.4182	+	27.5659i	−0.645393	+	1.55812i	−0.819306	+	0.573357i	$0.805641\pi$
$314$	3.80313	−	3.80313i	0.214623	−	0.214623i
$315$	−0.165745	+	0.165745i	−0.00933865	+	0.00933865i
$316$	5.66240	−	13.6702i	0.318535	−	0.769011i
$317$	2.24234	+	0.928806i	0.125942	+	0.0521670i	0.444765	−	0.895648i	$-0.353287\pi$
$317$	2.24234	+	0.928806i	0.125942	+	0.0521670i	−0.318822	+	0.947814i	$0.603287\pi$
$318$	6.23334	+	15.0486i	0.349548	+	0.843884i
$319$			4.98178i			0.278926i
$320$	−0.156101	+	0.0646592i	−0.00872632	+	0.00361456i
$321$	−25.9209	−	25.9209i	−1.44676	−	1.44676i
$322$	−2.99578			−0.166948
$323$	−6.01744	+	5.60171i	−0.334820	+	0.311687i
$324$	−24.7797			−1.37665
$325$	−16.6048	−	16.6048i	−0.921066	−	0.921066i
$326$	−3.26053	+	1.35056i	−0.180584	+	0.0748004i
$327$		−	50.0989i		−	2.77048i
$328$	−1.34678	−	3.25141i	−0.0743633	−	0.179529i
$329$	−10.7619	−	4.45774i	−0.593325	−	0.245763i
$330$	0.0577462	−	0.139412i	0.00317882	−	0.00767436i
$331$	−8.84202	+	8.84202i	−0.486002	+	0.486002i	−0.907042	−	0.421040i	$-0.861665\pi$
$331$	−8.84202	+	8.84202i	−0.486002	+	0.486002i	0.421040	+	0.907042i	$0.361665\pi$
$332$	14.7285	−	14.7285i	0.808334	−	0.808334i
$333$	−21.9287	+	52.9406i	−1.20169	+	2.90113i
$334$	−5.03207	−	2.08435i	−0.275343	−	0.114051i
$335$	−0.0711620	−	0.171800i	−0.00388799	−	0.00938645i
$336$		−	8.25044i		−	0.450099i
$337$	11.7352	−	4.86088i	0.639257	−	0.264789i	−0.0394235	−	0.999223i	$-0.512552\pi$
$337$	11.7352	−	4.86088i	0.639257	−	0.264789i	0.678680	+	0.734434i	$0.262552\pi$
$338$	2.65691	+	2.65691i	0.144517	+	0.144517i
$339$	−3.44997			−0.187377
$340$	0.106678	+	0.286071i	0.00578541	+	0.0155144i
$341$	21.6806			1.17407
$342$	−3.78424	−	3.78424i	−0.204629	−	0.204629i
$343$	−10.8941	+	4.51249i	−0.588227	+	0.243651i
$344$			1.58568i			0.0854944i
$345$	−0.386434	−	0.932935i	−0.0208049	−	0.0502275i
$346$	−5.21258	−	2.15912i	−0.280230	−	0.116075i
$347$	4.14037	−	9.99573i	0.222266	−	0.536599i	−0.772931	−	0.634491i	$-0.781210\pi$
$347$	4.14037	−	9.99573i	0.222266	−	0.536599i	0.995197	+	0.0978919i	$0.0312099\pi$
$348$	6.78763	−	6.78763i	0.363855	−	0.363855i
$349$	13.2133	−	13.2133i	0.707291	−	0.707291i	−0.258674	−	0.965965i	$-0.583286\pi$
$349$	13.2133	−	13.2133i	0.707291	−	0.707291i	0.965965	+	0.258674i	$0.0832856\pi$
$350$	0.707601	−	1.70830i	0.0378229	−	0.0913125i
$351$	−46.5100	−	19.2651i	−2.48252	−	1.02829i
$352$	4.93529	+	11.9148i	0.263052	+	0.635063i
$353$			17.7684i			0.945716i	0.881139	+	0.472858i	$0.156778\pi$
$353$			17.7684i			0.945716i	−0.881139	+	0.472858i	$0.843222\pi$
$354$	1.96460	−	0.813763i	0.104417	−	0.0432510i
$355$	0.376718	+	0.376718i	0.0199941	+	0.0199941i
$356$	16.9618			0.898971
$357$	−11.3314	−	0.405438i	−0.599720	−	0.0214581i
$358$	1.54199			0.0814964
$359$	8.41551	+	8.41551i	0.444153	+	0.444153i	0.893405	−	0.449252i	$-0.148309\pi$
$359$	8.41551	+	8.41551i	0.444153	+	0.444153i	−0.449252	+	0.893405i	$0.648309\pi$
$360$	−0.384467	+	0.159251i	−0.0202632	+	0.00839328i
$361$		−	15.0242i		−	0.790747i
$362$	3.17811	+	7.67264i	0.167038	+	0.403265i
$363$	−7.00738	−	2.90255i	−0.367792	−	0.152344i
$364$	2.93610	−	7.08837i	0.153893	−	0.371532i
$365$	0.253568	−	0.253568i	0.0132724	−	0.0132724i
$366$	11.7975	−	11.7975i	0.616665	−	0.616665i
$367$	12.5564	−	30.3139i	0.655440	−	1.58237i	−0.149332	−	0.988787i	$-0.547712\pi$
$367$	12.5564	−	30.3139i	0.655440	−	1.58237i	0.804772	−	0.593584i	$-0.202288\pi$
$368$	22.4463	+	9.29757i	1.17010	+	0.484669i
$369$	5.50385	+	13.2875i	0.286519	+	0.691718i
$370$			0.148326i			0.00771112i
$371$	10.5396	−	4.36562i	0.547186	−	0.226652i
$372$	−29.5396	−	29.5396i	−1.53156	−	1.53156i
$373$	−12.3327			−0.638562			−0.319281	−	0.947660i	$-0.603441\pi$
$373$	−12.3327			−0.638562			−0.319281	+	0.947660i	$0.603441\pi$
$374$	4.67507	−	1.74336i	0.241742	−	0.0901472i
$375$	1.24674			0.0643814
$376$	−14.6234	−	14.6234i	−0.754146	−	0.754146i
$377$	7.40077	−	3.06550i	0.381159	−	0.157881i
$378$		−	3.96399i		−	0.203886i
$379$	−8.22473	−	19.8563i	−0.422476	−	1.01995i	−0.981615	−	0.190874i	$-0.938868\pi$
$379$	−8.22473	−	19.8563i	−0.422476	−	1.01995i	0.559138	−	0.829074i	$-0.311132\pi$
$380$	0.136411	+	0.0565034i	0.00699775	+	0.00289856i
$381$	9.85278	−	23.7867i	0.504773	−	1.21863i
$382$	3.99983	−	3.99983i	0.204649	−	0.204649i
$383$	−0.926758	+	0.926758i	−0.0473551	+	0.0473551i	−0.730388	−	0.683033i	$-0.760661\pi$
$383$	−0.926758	+	0.926758i	−0.0473551	+	0.0473551i	0.683033	+	0.730388i	$0.260661\pi$
$384$	12.4379	−	30.0277i	0.634717	−	1.53234i
$385$	−0.0976393	−	0.0404435i	−0.00497616	−	0.00206119i
$386$	−1.46352	−	3.53324i	−0.0744911	−	0.179837i
$387$		−	6.48019i		−	0.329407i
$388$	7.81420	−	3.23675i	0.396706	−	0.164321i
$389$	2.08443	+	2.08443i	0.105685	+	0.105685i	0.757972	−	0.652287i	$-0.226190\pi$
$389$	2.08443	+	2.08443i	0.105685	+	0.105685i	−0.652287	+	0.757972i	$0.726190\pi$
$390$	−0.242639			−0.0122865
$391$	13.8726	−	30.3715i	0.701566	−	1.53595i
$392$	−9.83484			−0.496735
$393$	39.4066	+	39.4066i	1.98780	+	1.98780i
$394$	−0.0126672	+	0.00524693i	−0.000638165	+	0.000264336i
$395$			0.327730i			0.0164899i
$396$	−13.2481	−	31.9838i	−0.665742	−	1.60724i
$397$	−20.2280	−	8.37871i	−1.01521	−	0.420515i	−0.187860	−	0.982196i	$-0.560155\pi$
$397$	−20.2280	−	8.37871i	−1.01521	−	0.420515i	−0.827354	+	0.561680i	$0.810155\pi$
$398$	−1.54137	+	3.72121i	−0.0772621	+	0.186527i
$399$	−3.87734	+	3.87734i	−0.194110	+	0.194110i
$400$	−10.6036	+	10.6036i	−0.530180	+	0.530180i
$401$	13.7378	−	33.1659i	0.686031	−	1.65623i	−0.0665972	−	0.997780i	$-0.521214\pi$
$401$	13.7378	−	33.1659i	0.686031	−	1.65623i	0.752628	−	0.658446i	$-0.228786\pi$
$402$	5.40987	+	2.24084i	0.269820	+	0.111763i
$403$	−13.3410	−	32.2080i	−0.664561	−	1.60439i
$404$		−	22.5735i		−	1.12307i
$405$	0.507069	−	0.210035i	0.0251965	−	0.0104367i
$406$	0.446013	+	0.446013i	0.0221353	+	0.0221353i
$407$	−25.8362			−1.28065
$408$	−18.3106	−	8.36361i	−0.906510	−	0.414060i
$409$	−25.2906			−1.25054			−0.625270	−	0.780408i	$-0.715011\pi$
$409$	−25.2906			−1.25054			−0.625270	+	0.780408i	$0.715011\pi$
$410$	0.0263243	+	0.0263243i	0.00130006	+	0.00130006i
$411$	18.8847	−	7.82229i	0.931512	−	0.385845i
$412$			17.5827i			0.866236i
$413$	−0.569932	−	1.37594i	−0.0280445	−	0.0677055i
$414$	20.0810	+	8.31782i	0.986927	+	0.408799i
$415$	−0.176551	+	0.426232i	−0.00866654	+	0.0209229i
$416$	14.6634	−	14.6634i	0.718933	−	0.718933i
$417$	−5.48692	+	5.48692i	−0.268696	+	0.268696i
$418$	0.923398	−	2.22928i	0.0451649	−	0.109038i
$419$	4.23973	+	1.75615i	0.207124	+	0.0857936i	0.483834	−	0.875160i	$-0.339244\pi$
$419$	4.23973	+	1.75615i	0.207124	+	0.0857936i	−0.276709	+	0.960954i	$0.589244\pi$
$420$	0.0779288	+	0.188137i	0.00380254	+	0.00918014i
$421$			7.09936i			0.346002i	0.984922	+	0.173001i	$0.0553463\pi$
$421$			7.09936i			0.346002i	−0.984922	+	0.173001i	$0.944654\pi$
$422$	8.03996	−	3.33026i	0.391379	−	0.162115i
$423$	59.7614	+	59.7614i	2.90570	+	2.90570i
$424$	20.2533			0.983587
$425$	14.0422	+	15.0844i	0.681147	+	0.731699i
$426$	−16.7763			−0.812812
$427$	−8.26257	−	8.26257i	−0.399854	−	0.399854i
$428$	−20.1120	+	8.33066i	−0.972150	+	0.402678i
$429$		−	42.2641i		−	2.04053i
$430$	−0.00641907	−	0.0154970i	−0.000309555	−	0.000747332i
$431$	−6.29400	−	2.60706i	−0.303171	−	0.125578i	0.225912	−	0.974148i	$-0.427464\pi$
$431$	−6.29400	−	2.60706i	−0.303171	−	0.125578i	−0.529083	+	0.848570i	$0.677464\pi$
$432$	−12.3025	+	29.7008i	−0.591903	+	1.42898i
$433$	−11.5724	+	11.5724i	−0.556132	+	0.556132i	−0.928204	−	0.372072i	$-0.878648\pi$
$433$	−11.5724	+	11.5724i	−0.556132	+	0.556132i	0.372072	+	0.928204i	$0.378648\pi$
$434$	1.94104	−	1.94104i	0.0931728	−	0.0931728i
$435$	−0.0813633	+	0.196428i	−0.00390107	+	0.00941802i
$436$	−27.4864	−	11.3853i	−1.31636	−	0.545255i
$437$	−6.17933	−	14.9182i	−0.295597	−	0.713635i
$438$			11.2921i			0.539556i
$439$	−24.7599	+	10.2559i	−1.18172	+	0.489486i	−0.885052	−	0.465493i	$-0.845877\pi$
$439$	−24.7599	+	10.2559i	−1.18172	+	0.489486i	−0.296673	+	0.954979i	$0.595877\pi$
$440$	−0.132673	−	0.132673i	−0.00632495	−	0.00632495i
$441$	40.1919			1.91390
$442$	−5.46665	−	5.87236i	−0.260022	−	0.279320i
$443$	1.57907			0.0750239			0.0375119	−	0.999296i	$-0.488057\pi$
$443$	1.57907			0.0750239			0.0375119	+	0.999296i	$0.488057\pi$
$444$	35.2016	+	35.2016i	1.67060	+	1.67060i
$445$	−0.347090	+	0.143769i	−0.0164536	+	0.00681531i
$446$			4.65036i			0.220201i
$447$	17.8821	+	43.1711i	0.845792	+	2.04192i
$448$	−3.44267	−	1.42600i	−0.162651	−	0.0673722i
$449$	5.31454	−	12.8304i	0.250809	−	0.605505i	−0.747461	−	0.664305i	$-0.768727\pi$
$449$	5.31454	−	12.8304i	0.250809	−	0.605505i	0.998270	+	0.0588000i	$0.0187274\pi$
$450$	−9.48623	+	9.48623i	−0.447185	+	0.447185i
$451$	−4.58529	+	4.58529i	−0.215913	+	0.215913i
$452$	−0.784026	+	1.89281i	−0.0368775	+	0.0890301i
$453$	−28.2242	−	11.6908i	−1.32609	−	0.549283i
$454$	2.94572	+	7.11161i	0.138250	+	0.333764i
$455$			0.169936i			0.00796674i
$456$	−8.99401	+	3.72544i	−0.421183	+	0.174460i
$457$	0.452441	+	0.452441i	0.0211643	+	0.0211643i	0.717610	−	0.696445i	$-0.245236\pi$
$457$	0.452441	+	0.452441i	0.0211643	+	0.0211643i	−0.696445	+	0.717610i	$0.745236\pi$
$458$	5.29781			0.247551
$459$	40.1873	+	18.3561i	1.87578	+	0.856788i
$460$	−0.599668			−0.0279597
$461$	2.84225	+	2.84225i	0.132377	+	0.132377i	0.770191	−	0.637814i	$-0.220161\pi$
$461$	2.84225	+	2.84225i	0.132377	+	0.132377i	−0.637814	+	0.770191i	$0.720161\pi$
$462$	3.07460	−	1.27354i	0.143043	−	0.0592504i
$463$		−	35.3942i		−	1.64491i	−0.568832	−	0.822454i	$-0.692604\pi$
$463$		−	35.3942i		−	1.64491i	0.568832	−	0.822454i	$-0.307396\pi$
$464$	−1.95759	−	4.72604i	−0.0908789	−	0.219401i
$465$	0.854851	+	0.354091i	0.0396428	+	0.0164206i
$466$	0.881594	−	2.12836i	0.0408391	−	0.0985942i
$467$	10.4883	−	10.4883i	0.485342	−	0.485342i	−0.421490	−	0.906833i	$-0.638493\pi$
$467$	10.4883	−	10.4883i	0.485342	−	0.485342i	0.906833	+	0.421490i	$0.138493\pi$
$468$	−39.3619	+	39.3619i	−1.81950	+	1.81950i
$469$	1.56941	−	3.78889i	0.0724687	−	0.174955i
$470$	0.202114	+	0.0837182i	0.00932281	+	0.00386163i
$471$	15.3007	+	36.9391i	0.705018	+	1.70206i
$472$		−	2.64407i		−	0.121703i
$473$	2.69934	−	1.11811i	0.124116	−	0.0514105i
$474$	−7.29734	−	7.29734i	−0.335178	−	0.335178i
$475$	9.96645			0.457292
$476$	−2.79756	+	6.12475i	−0.128226	+	0.280727i
$477$	−82.7688			−3.78972
$478$	7.71294	+	7.71294i	0.352782	+	0.352782i
$479$	−7.76995	+	3.21842i	−0.355018	+	0.147053i	−0.553063	−	0.833140i	$-0.686541\pi$
$479$	−7.76995	+	3.21842i	−0.355018	+	0.147053i	0.198044	+	0.980193i	$0.436541\pi$
$480$			0.550399i			0.0251222i
$481$	15.8981	+	38.3814i	0.724891	+	1.75004i
$482$	−4.39440	−	1.82022i	−0.200159	−	0.0829088i
$483$	8.52245	−	20.5750i	0.387785	−	0.936196i
$484$	−3.18493	+	3.18493i	−0.144770	+	0.144770i
$485$	−0.132468	+	0.132468i	−0.00601504	+	0.00601504i
$486$	−1.51860	+	3.66622i	−0.0688850	+	0.166303i
$487$	−0.195422	−	0.0809465i	−0.00885542	−	0.00366803i	0.378251	−	0.925703i	$-0.376526\pi$
$487$	−0.195422	−	0.0809465i	−0.00885542	−	0.00366803i	−0.387107	+	0.922035i	$0.626526\pi$
$488$	−7.93888	−	19.1661i	−0.359376	−	0.867610i
$489$		−	26.2354i		−	1.18641i
$490$	0.0961166	−	0.0398128i	0.00434211	−	0.00179856i
$491$	−15.2164	−	15.2164i	−0.686706	−	0.686706i	0.274797	−	0.961502i	$-0.411389\pi$
$491$	−15.2164	−	15.2164i	−0.686706	−	0.686706i	−0.961502	+	0.274797i	$0.911389\pi$
$492$	12.4949			0.563312
$493$	−6.58708	+	2.45636i	−0.296667	+	0.110629i
$494$	−3.87995			−0.174567
$495$	0.542194	+	0.542194i	0.0243698	+	0.0243698i
$496$	−20.5676	+	8.51939i	−0.923514	+	0.382532i
$497$			11.7495i			0.527039i
$498$	−5.55947	−	13.4217i	−0.249126	−	0.601443i
$499$	−5.01103	−	2.07564i	−0.224324	−	0.0929182i	0.267691	−	0.963505i	$-0.413739\pi$
$499$	−5.01103	−	2.07564i	−0.224324	−	0.0929182i	−0.492015	+	0.870587i	$0.663739\pi$
$500$	0.283329	−	0.684016i	0.0126708	−	0.0305901i
$501$	28.6307	−	28.6307i	1.27912	−	1.27912i
$502$	−0.438385	+	0.438385i	−0.0195661	+	0.0195661i
$503$	−6.35785	+	15.3492i	−0.283483	+	0.684387i	−0.999912	−	0.0132723i	$-0.995775\pi$
$503$	−6.35785	+	15.3492i	−0.283483	+	0.684387i	0.716429	+	0.697660i	$0.245775\pi$
$504$	−8.47906	−	3.51214i	−0.377687	−	0.156443i
$505$	0.191335	+	0.461923i	0.00851429	+	0.0205553i
$506$			9.79998i			0.435662i
$507$	−25.8061	+	10.6892i	−1.14609	+	0.474726i
$508$	−10.8113	−	10.8113i	−0.479675	−	0.479675i
$509$	−9.32182			−0.413183			−0.206591	−	0.978427i	$-0.566237\pi$
$509$	−9.32182			−0.413183			−0.206591	+	0.978427i	$0.566237\pi$
$510$	0.212808	+	0.00761429i	0.00942329	+	0.000337167i
$511$	7.90859			0.349855
$512$	−16.0917	−	16.0917i	−0.711159	−	0.711159i
$513$	19.7397	−	8.17644i	0.871527	−	0.360998i
$514$			12.3481i			0.544650i
$515$	−0.149032	−	0.359796i	−0.00656714	−	0.0158545i
$516$	−5.20124	−	2.15443i	−0.228972	−	0.0948433i
$517$	−14.5824	+	35.2051i	−0.641335	+	1.54832i
$518$	−2.31309	+	2.31309i	−0.101631	+	0.101631i
$519$	29.6577	−	29.6577i	1.30183	−	1.30183i
$520$	−0.115456	+	0.278735i	−0.00506306	+	0.0122233i
$521$	−23.6575	−	9.79927i	−1.03646	−	0.429314i	−0.201417	−	0.979506i	$-0.564555\pi$
$521$	−23.6575	−	9.79927i	−1.03646	−	0.429314i	−0.835038	+	0.550192i	$0.814555\pi$
$522$	−1.75131	−	4.22803i	−0.0766526	−	0.185056i
$523$			20.8848i			0.913229i	0.889665	+	0.456614i	$0.150938\pi$
$523$			20.8848i			0.913229i	−0.889665	+	0.456614i	$0.849062\pi$
$524$	30.5755	−	12.6648i	1.33570	−	0.553264i
$525$	9.71961	+	9.71961i	0.424198	+	0.424198i
$526$	4.91366			0.214246
$527$	10.6900	+	28.6668i	0.465665	+	1.24875i
$528$	−26.9894			−1.17456
$529$	30.1092	+	30.1092i	1.30910	+	1.30910i
$530$	−0.197937	+	0.0819882i	−0.00859783	+	0.00356134i
$531$			10.8055i			0.468918i
$532$	1.24613	+	3.00843i	0.0540266	+	0.130432i
$533$	9.63329	+	3.99024i	0.417264	+	0.172836i
$534$	4.52719	−	10.9296i	0.195911	−	0.472971i
$535$	0.340942	−	0.340942i	0.0147402	−	0.0147402i
$536$	5.14839	−	5.14839i	0.222376	−	0.222376i
$537$	−4.38667	+	10.5904i	−0.189299	+	0.457008i
$538$	2.16366	+	0.896216i	0.0932819	+	0.0386386i
$539$	6.93479	+	16.7421i	0.298703	+	0.721132i
$540$		−	0.793476i		−	0.0341458i
$541$	−17.4084	+	7.21078i	−0.748444	+	0.310016i	−0.724107	−	0.689688i	$-0.757748\pi$
$541$	−17.4084	+	7.21078i	−0.748444	+	0.310016i	−0.0243377	+	0.999704i	$0.507748\pi$
$542$	2.49861	+	2.49861i	0.107325	+	0.107325i
$543$	−61.7369			−2.64938
$544$	−13.3208	+	12.4005i	−0.571123	+	0.531665i
$545$	0.658959			0.0282267
$546$	−3.78386	−	3.78386i	−0.161934	−	0.161934i
$547$	1.79984	−	0.745519i	0.0769557	−	0.0318761i	−0.343874	−	0.939016i	$-0.611739\pi$
$547$	1.79984	−	0.745519i	0.0769557	−	0.0318761i	0.420829	+	0.907140i	$0.361739\pi$
$548$		−	12.1386i		−	0.518536i
$549$	32.4437	+	78.3260i	1.38466	+	3.34287i
$550$	−5.58830	−	2.31475i	−0.238286	−	0.0987012i
$551$	−1.30105	+	3.14101i	−0.0554266	+	0.133812i
$552$	27.9575	−	27.9575i	1.18995	−	1.18995i
$553$	−5.11081	+	5.11081i	−0.217334	+	0.217334i
$554$	0.810247	−	1.95611i	0.0344241	−	0.0831071i
$555$	−1.01871	−	0.421961i	−0.0432416	−	0.0179113i
$556$	1.76343	+	4.25730i	0.0747861	+	0.180550i
$557$			29.6187i			1.25498i	0.778623	+	0.627492i	$0.215918\pi$
$557$			29.6187i			1.25498i	−0.778623	+	0.627492i	$0.784082\pi$
$558$	−18.4003	+	7.62165i	−0.778946	+	0.322650i
$559$	−3.32204	−	3.32204i	−0.140507	−	0.140507i
$560$	0.108519			0.00458578
$561$	−1.32630	+	37.0679i	−0.0559962	+	1.56501i
$562$	3.12180			0.131685
$563$	−1.57002	−	1.57002i	−0.0661686	−	0.0661686i	0.673248	−	0.739417i	$-0.264899\pi$
$563$	−1.57002	−	1.57002i	−0.0661686	−	0.0661686i	−0.739417	+	0.673248i	$0.764899\pi$
$564$	67.8352	−	28.0983i	2.85638	−	1.18315i
$565$		−	0.0453781i		−	0.00190907i
$566$	−1.54502	−	3.73000i	−0.0649419	−	0.156784i
$567$	11.1829	+	4.63212i	0.469639	+	0.194531i
$568$	−7.98269	+	19.2719i	−0.334946	+	0.808632i
$569$	−3.95272	+	3.95272i	−0.165707	+	0.165707i	−0.785089	−	0.619383i	$-0.787383\pi$
$569$	−3.95272	+	3.95272i	−0.165707	+	0.165707i	0.619383	+	0.785089i	$0.287383\pi$
$570$	0.0728180	−	0.0728180i	0.00305001	−	0.00305001i
$571$	16.6511	−	40.1993i	0.696826	−	1.68229i	−0.0337276	−	0.999431i	$-0.510738\pi$
$571$	16.6511	−	40.1993i	0.696826	−	1.68229i	0.730553	−	0.682855i	$-0.239262\pi$
$572$	−23.1879	−	9.60475i	−0.969535	−	0.401595i
$573$	16.0920	+	38.8496i	0.672255	+	1.62297i
$574$			0.821033i			0.0342692i
$575$	−37.3966	+	15.4902i	−1.55954	+	0.645984i
$576$	19.1172	+	19.1172i	0.796551	+	0.796551i
$577$	19.0384			0.792578			0.396289	−	0.918126i	$-0.370298\pi$
$577$	19.0384			0.792578			0.396289	+	0.918126i	$0.370298\pi$
$578$	4.61027	+	5.32193i	0.191762	+	0.221363i
$579$	28.4298			1.18150
$580$	0.0892789	+	0.0892789i	0.00370710	+	0.00370710i
$581$	−9.40014	+	3.89367i	−0.389984	+	0.161537i
$582$		−	5.89913i		−	0.244527i
$583$	−14.2811	−	34.4776i	−0.591463	−	1.42792i
$584$	12.9719	+	5.37314i	0.536781	+	0.222342i
$585$	0.471831	−	1.13910i	0.0195078	−	0.0470960i
$586$	−5.13615	+	5.13615i	−0.212172	+	0.212172i
$587$	7.61625	−	7.61625i	0.314356	−	0.314356i	−0.532238	−	0.846595i	$-0.678649\pi$
$587$	7.61625	−	7.61625i	0.314356	−	0.314356i	0.846595	+	0.532238i	$0.178649\pi$
$588$	13.3623	−	32.2595i	0.551053	−	1.33036i
$589$	13.6696	+	5.66214i	0.563246	+	0.233304i
$590$	0.0107036	+	0.0258407i	0.000440658	+	0.00106384i
$591$		−	0.101925i		−	0.00419263i
$592$	24.5099	−	10.1524i	1.00735	−	0.417259i
$593$	33.4366	+	33.4366i	1.37308	+	1.37308i	0.855843	+	0.517235i	$0.173039\pi$
$593$	33.4366	+	33.4366i	1.37308	+	1.37308i	0.517235	+	0.855843i	$0.326961\pi$
$594$	−12.9673			−0.532053
$595$	0.00533280	−	0.149044i	0.000218623	−	0.00611019i
$596$	27.7493			1.13666
$597$	−21.1723	−	21.1723i	−0.866525	−	0.866525i
$598$	14.5585	−	6.03034i	0.595343	−	0.246599i
$599$		−	22.7748i		−	0.930555i	−0.885165	−	0.465277i	$-0.845955\pi$
$599$		−	22.7748i		−	0.930555i	0.885165	−	0.465277i	$-0.154045\pi$
$600$	9.33883	+	22.5459i	0.381256	+	0.920434i
$601$	−18.2545	−	7.56127i	−0.744618	−	0.308431i	−0.0220744	−	0.999756i	$-0.507027\pi$
$601$	−18.2545	−	7.56127i	−0.744618	−	0.308431i	−0.722543	+	0.691326i	$0.757027\pi$
$602$	0.141567	−	0.341772i	0.00576983	−	0.0139296i
$603$	−21.0398	+	21.0398i	−0.856808	+	0.856808i
$604$	−12.8282	+	12.8282i	−0.521972	+	0.521972i
$605$	0.0381777	−	0.0921692i	0.00155215	−	0.00374721i
$606$	−14.5456	−	6.02500i	−0.590876	−	0.244749i
$607$	−15.1998	−	36.6957i	−0.616942	−	1.48943i	−0.855237	−	0.518238i	$-0.826588\pi$
$607$	−15.1998	−	36.6957i	−0.616942	−	1.48943i	0.238294	−	0.971193i	$-0.423412\pi$
$608$			8.80122i			0.356937i
$609$	−4.33204	+	1.79439i	−0.175543	+	0.0727124i
$610$	0.155174	+	0.155174i	0.00628283	+	0.00628283i
$611$	61.2728			2.47883
$612$	35.7578	−	33.2873i	1.44542	−	1.34556i
$613$	20.5064			0.828244			0.414122	−	0.910221i	$-0.364089\pi$
$613$	20.5064			0.828244			0.414122	+	0.910221i	$0.364089\pi$
$614$	0.159071	+	0.159071i	0.00641958	+	0.00641958i
$615$	−0.255683	+	0.105907i	−0.0103101	+	0.00427060i
$616$		−	4.13797i		−	0.166724i
$617$	−2.31472	−	5.58822i	−0.0931869	−	0.224973i	0.870413	−	0.492323i	$-0.163852\pi$
$617$	−2.31472	−	5.58822i	−0.0931869	−	0.224973i	−0.963600	+	0.267350i	$0.913852\pi$
$618$	11.3297	+	4.69292i	0.455748	+	0.188777i
$619$	1.63666	−	3.95125i	0.0657830	−	0.158814i	−0.887569	−	0.460674i	$-0.847608\pi$
$619$	1.63666	−	3.95125i	0.0657830	−	0.158814i	0.953352	+	0.301860i	$0.0976076\pi$
$620$	0.388539	−	0.388539i	0.0156041	−	0.0156041i
$621$	−61.3600	+	61.3600i	−2.46229	+	2.46229i
$622$	−1.04040	+	2.51175i	−0.0417162	+	0.100712i
$623$	−7.65474	−	3.17070i	−0.306681	−	0.127031i
$624$	16.6077	+	40.0945i	0.664840	+	1.60507i
$625$		−	24.9754i		−	0.999016i
$626$	11.4174	−	4.72923i	0.456330	−	0.189018i
$627$	12.6838	+	12.6838i	0.506542	+	0.506542i
$628$	23.7436			0.947471
$629$	−12.7391	−	34.1615i	−0.507939	−	1.36211i
$630$	0.0970840			0.00386792
$631$	13.4430	+	13.4430i	0.535156	+	0.535156i	0.922102	−	0.386946i	$-0.126470\pi$
$631$	13.4430	+	13.4430i	0.535156	+	0.535156i	−0.386946	+	0.922102i	$0.626470\pi$
$632$	−11.8552	+	4.91059i	−0.471575	+	0.195333i
$633$			64.6924i			2.57129i
$634$	−0.384697	−	0.928741i	−0.0152783	−	0.0368850i
$635$	0.312871	+	0.129595i	0.0124159	+	0.00514283i
$636$	−27.5176	+	66.4334i	−1.09114	+	2.63425i
$637$	20.6042	−	20.6042i	0.816368	−	0.816368i
$638$	1.45903	−	1.45903i	0.0577634	−	0.0577634i
$639$	32.6227	−	78.7582i	1.29054	−	3.11563i
$640$	0.394959	+	0.163597i	0.0156121	+	0.00646675i
$641$	−12.5108	−	30.2037i	−0.494146	−	1.19297i	−0.952592	−	0.304251i	$-0.901594\pi$
$641$	−12.5108	−	30.2037i	−0.494146	−	1.19297i	0.458446	−	0.888722i	$-0.348406\pi$
$642$			15.1830i			0.599226i
$643$	15.7017	−	6.50386i	0.619215	−	0.256487i	−0.0509478	−	0.998701i	$-0.516224\pi$
$643$	15.7017	−	6.50386i	0.619215	−	0.256487i	0.670163	+	0.742214i	$0.266224\pi$
$644$	−9.35158	−	9.35158i	−0.368504	−	0.368504i
$645$	0.124695			0.00490984
$646$	3.40293	+	0.121757i	0.133887	+	0.00479048i
$647$	−18.4363			−0.724804			−0.362402	−	0.932022i	$-0.618043\pi$
$647$	−18.4363			−0.724804			−0.362402	+	0.932022i	$0.618043\pi$
$648$	15.1955	+	15.1955i	0.596935	+	0.596935i
$649$	−4.50105	+	1.86440i	−0.176682	+	0.0731840i
$650$			9.72615i			0.381491i
$651$	7.80915	+	18.8530i	0.306065	+	0.738905i
$652$	−14.3939	−	5.96214i	−0.563708	−	0.233496i
$653$	0.106368	−	0.256794i	0.00416249	−	0.0100491i	−0.921785	−	0.387702i	$-0.873269\pi$
$653$	0.106368	−	0.256794i	0.00416249	−	0.0100491i	0.925947	+	0.377653i	$0.123269\pi$
$654$	−14.6726	+	14.6726i	−0.573744	+	0.573744i
$655$	−0.518321	+	0.518321i	−0.0202525	+	0.0202525i
$656$	2.54812	−	6.15171i	0.0994874	−	0.240184i
$657$	−53.0120	−	21.9583i	−2.06820	−	0.856675i
$658$	1.84633	+	4.45743i	0.0719773	+	0.173769i
$659$			3.49899i			0.136301i	0.997675	+	0.0681506i	$0.0217099\pi$
$659$			3.49899i			0.136301i	−0.997675	+	0.0681506i	$0.978290\pi$
$660$	0.615445	−	0.254926i	0.0239562	−	0.00992296i
$661$	33.9221	+	33.9221i	1.31942	+	1.31942i	0.914236	+	0.405182i	$0.132792\pi$
$661$	33.9221	+	33.9221i	1.31942	+	1.31942i	0.405182	+	0.914236i	$0.367208\pi$
$662$	5.17917			0.201294
$663$	55.8830	−	20.8391i	2.17032	−	0.809325i
$664$	−18.0638			−0.701010
$665$	−0.0509993	−	0.0509993i	−0.00197767	−	0.00197767i
$666$	21.9272	−	9.08253i	0.849660	−	0.351941i
$667$		−	13.8080i		−	0.534647i
$668$	−9.20155	−	22.2145i	−0.356019	−	0.859505i
$669$	−31.9386	−	13.2294i	−1.23482	−	0.511479i
$670$	−0.0294742	+	0.0711569i	−0.00113869	+	0.00274903i
$671$	−27.0290	+	27.0290i	−1.04344	+	1.04344i
$672$	−8.58324	+	8.58324i	−0.331106	+	0.331106i
$673$	12.7467	−	30.7733i	0.491350	−	1.18622i	−0.462683	−	0.886524i	$-0.653113\pi$
$673$	12.7467	−	30.7733i	0.491350	−	1.18622i	0.954033	−	0.299701i	$-0.0968869\pi$
$674$	−4.86053	−	2.01330i	−0.187221	−	0.0775494i
$675$	−20.4965	−	49.4828i	−0.788909	−	1.90459i
$676$			16.5875i			0.637982i
$677$	8.68106	−	3.59581i	0.333640	−	0.138198i	−0.209573	−	0.977793i	$-0.567207\pi$
$677$	8.68106	−	3.59581i	0.333640	−	0.138198i	0.543213	+	0.839595i	$0.317207\pi$
$678$	1.01040	+	1.01040i	0.0388043	+	0.0388043i
$679$	−4.13155			−0.158555
$680$	0.110008	−	0.240842i	0.00421861	−	0.00923588i
$681$	−57.2226			−2.19277
$682$	−6.34964	−	6.34964i	−0.243140	−	0.243140i
$683$	−20.3691	+	8.43716i	−0.779402	+	0.322839i	−0.736674	−	0.676248i	$-0.763605\pi$
$683$	−20.3691	+	8.43716i	−0.779402	+	0.322839i	−0.0427279	+	0.999087i	$0.513605\pi$
$684$		−	23.6257i		−	0.903350i
$685$	0.102888	+	0.248393i	0.00393114	+	0.00949062i
$686$	4.51217	+	1.86900i	0.172275	+	0.0713588i
$687$	−15.0713	+	36.3854i	−0.575007	+	1.38819i
$688$	−2.12142	+	2.12142i	−0.0808783	+	0.0808783i
$689$	−42.4311	+	42.4311i	−1.61650	+	1.61650i
$690$	−0.160055	+	0.386407i	−0.00609319	+	0.0147103i
$691$	23.5572	+	9.75769i	0.896156	+	0.371200i	0.782741	−	0.622348i	$-0.213821\pi$
$691$	23.5572	+	9.75769i	0.896156	+	0.371200i	0.113415	+	0.993548i	$0.463821\pi$
$692$	−9.53162	−	23.0114i	−0.362338	−	0.874761i
$693$			16.9106i			0.642380i
$694$	−4.14007	+	1.71487i	−0.157155	+	0.0650957i
$695$	−0.0721704	−	0.0721704i	−0.00273758	−	0.00273758i
$696$	−8.32466			−0.315545
$697$	−8.32370	−	3.80196i	−0.315283	−	0.144010i
$698$	−7.73961			−0.292949
$699$	12.1096	+	12.1096i	0.458026	+	0.458026i
$700$	7.54143	−	3.12376i	0.285039	−	0.118067i
$701$			17.2014i			0.649688i	0.945768	+	0.324844i	$0.105312\pi$
$701$			17.2014i			0.649688i	−0.945768	+	0.324844i	$0.894688\pi$
$702$	7.97930	+	19.2637i	0.301159	+	0.727063i
$703$	−16.2897	−	6.74743i	−0.614379	−	0.254484i
$704$	−4.66482	+	11.2619i	−0.175812	+	0.424448i
$705$	−1.14995	+	1.14995i	−0.0433097	+	0.0433097i
$706$	5.20387	−	5.20387i	0.195850	−	0.195850i
$707$	−4.21971	+	10.1873i	−0.158699	+	0.383132i
$708$	8.67288	+	3.59242i	0.325947	+	0.135012i
$709$	10.0704	+	24.3122i	0.378204	+	0.913064i	0.992303	+	0.123835i	$0.0395195\pi$
$709$	10.0704	+	24.3122i	0.378204	+	0.913064i	−0.614099	+	0.789229i	$0.710481\pi$
$710$		−	0.220661i		−	0.00828125i
$711$	48.4485	−	20.0680i	1.81696	−	0.752610i
$712$	−10.4013	−	10.4013i	−0.389806	−	0.389806i
$713$	−60.0920			−2.25046
$714$	3.19991	+	3.43739i	0.119754	+	0.128641i
$715$	0.555906			0.0207897
$716$	4.81343	+	4.81343i	0.179886	+	0.179886i
$717$	−74.9144	+	31.0306i	−2.79773	+	1.15886i
$718$		−	4.92934i		−	0.183961i
$719$	−8.67298	−	20.9384i	−0.323448	−	0.780872i	−0.999049	−	0.0436046i	$-0.986116\pi$
$719$	−8.67298	−	20.9384i	−0.323448	−	0.780872i	0.675601	−	0.737267i	$-0.263884\pi$
$720$	−0.727416	−	0.301306i	−0.0271092	−	0.0112290i
$721$	3.28677	−	7.93496i	0.122406	−	0.295513i
$722$	−4.40017	+	4.40017i	−0.163757	+	0.163757i
$723$	25.0026	−	25.0026i	0.929855	−	0.929855i
$724$	−14.0301	+	33.8715i	−0.521423	+	1.25883i
$725$	7.87380	+	3.26143i	0.292425	+	0.121127i
$726$	1.20219	+	2.90235i	0.0446175	+	0.107716i
$727$		−	49.9110i		−	1.85109i	−0.378632	−	0.925547i	$-0.623605\pi$
$727$		−	49.9110i		−	1.85109i	0.378632	−	0.925547i	$-0.376395\pi$
$728$	−6.14723	+	2.54627i	−0.227832	+	0.0943709i
$729$	7.88929	+	7.88929i	0.292196	+	0.292196i
$730$	−0.148526			−0.00549721
$731$	2.80936	+	3.01786i	0.103908	+	0.111620i
$732$	73.6537			2.72232
$733$	−28.6720	−	28.6720i	−1.05902	−	1.05902i	−0.998145	−	0.0608786i	$-0.980610\pi$
$733$	−28.6720	−	28.6720i	−1.05902	−	1.05902i	−0.0608786	−	0.998145i	$-0.519390\pi$
$734$	−12.5555	+	5.20067i	−0.463433	+	0.191960i
$735$			0.773389i			0.0285269i
$736$	−13.6791	−	33.0243i	−0.504219	−	1.21729i
$737$	−12.3945	−	5.13395i	−0.456556	−	0.189112i
$738$	2.27961	−	5.50346i	0.0839135	−	0.202585i
$739$	−14.4305	+	14.4305i	−0.530835	+	0.530835i	−0.920821	−	0.389986i	$-0.872480\pi$
$739$	−14.4305	+	14.4305i	−0.530835	+	0.530835i	0.389986	+	0.920821i	$0.372480\pi$
$740$	−0.463013	+	0.463013i	−0.0170207	+	0.0170207i
$741$	11.0378	−	26.6475i	0.405482	−	0.978921i
$742$	−4.36532	−	1.80817i	−0.160256	−	0.0663801i
$743$	−8.28523	−	20.0023i	−0.303955	−	0.733813i	−0.999877	−	0.0156954i	$-0.995004\pi$
$743$	−8.28523	−	20.0023i	−0.303955	−	0.733813i	0.695921	−	0.718118i	$-0.254996\pi$
$744$			36.2287i			1.32821i
$745$	−0.567837	+	0.235206i	−0.0208039	+	0.00861727i
$746$	3.61191	+	3.61191i	0.132241	+	0.132241i
$747$	73.8209			2.70096
$748$	20.0357	+	9.15155i	0.732576	+	0.334614i
$749$	10.6337			0.388547
$750$	−0.365136	−	0.365136i	−0.0133329	−	0.0133329i
$751$	10.0406	−	4.15895i	0.366387	−	0.151762i	−0.191891	−	0.981416i	$-0.561462\pi$
$751$	10.0406	−	4.15895i	0.366387	−	0.151762i	0.558278	+	0.829654i	$0.311462\pi$
$752$		−	39.1281i		−	1.42686i
$753$	−1.76370	−	4.25795i	−0.0642729	−	0.155168i
$754$	−3.06528	−	1.26968i	−0.111631	−	0.0462390i
$755$	0.153771	−	0.371237i	0.00559631	−	0.0135107i
$756$	12.3739	−	12.3739i	0.450035	−	0.450035i
$757$	−15.3269	+	15.3269i	−0.557065	+	0.557065i	−0.928471	−	0.371405i	$-0.878876\pi$
$757$	−15.3269	+	15.3269i	−0.557065	+	0.557065i	0.371405	+	0.928471i	$0.378876\pi$
$758$	−3.40656	+	8.22415i	−0.123732	+	0.298715i
$759$	−67.3063	−	27.8792i	−2.44306	−	1.01195i
$760$	−0.0490014	−	0.118300i	−0.00177747	−	0.00429118i
$761$			29.8082i			1.08055i	0.841490	+	0.540273i	$0.181679\pi$
$761$			29.8082i			1.08055i	−0.841490	+	0.540273i	$0.818321\pi$
$762$	−9.85208	+	4.08087i	−0.356903	+	0.147834i
$763$	10.2762	+	10.2762i	0.372023	+	0.372023i
$764$	24.9716			0.903441
$765$	−0.449568	+	0.984246i	−0.0162542	+	0.0355855i
$766$	0.542844			0.0196137
$767$	5.53938	+	5.53938i	0.200015	+	0.200015i
$768$	11.2989	−	4.68017i	0.407715	−	0.168881i
$769$			19.6136i			0.707284i	0.935381	+	0.353642i	$0.115057\pi$
$769$			19.6136i			0.707284i	−0.935381	+	0.353642i	$0.884943\pi$
$770$	0.0167511	+	0.0404407i	0.000603667	+	0.00145738i
$771$	−84.8066	−	35.1280i	−3.05423	−	1.26511i
$772$	6.46082	−	15.5978i	0.232530	−	0.561377i
$773$	9.37401	−	9.37401i	0.337160	−	0.337160i	−0.518138	−	0.855297i	$-0.673374\pi$
$773$	9.37401	−	9.37401i	0.337160	−	0.337160i	0.855297	+	0.518138i	$0.173374\pi$
$774$	−1.89787	+	1.89787i	−0.0682175	+	0.0682175i
$775$	14.1937	−	34.2666i	0.509852	−	1.23089i
$776$	−6.77669	−	2.80700i	−0.243269	−	0.100765i
$777$	−9.30597	−	22.4666i	−0.333850	−	0.805985i
$778$		−	1.22094i		−	0.0437730i
$779$	−4.08853	+	1.69353i	−0.146487	+	0.0606768i
$780$	−0.757418	−	0.757418i	−0.0271199	−	0.0271199i
$781$	38.4358			1.37534
$782$	−12.9579	+	4.83208i	−0.463372	+	0.172795i
$783$	18.2706			0.652938
$784$	−13.1576	−	13.1576i	−0.469915	−	0.469915i
$785$	−0.485866	+	0.201252i	−0.0173413	+	0.00718300i
$786$		−	23.0822i		−	0.823315i
$787$	−7.89945	−	19.0710i	−0.281585	−	0.679807i	0.718288	−	0.695746i	$-0.244926\pi$
$787$	−7.89945	−	19.0710i	−0.281585	−	0.679807i	−0.999873	+	0.0159395i	$0.994926\pi$
$788$	−0.0559205	−	0.0231630i	−0.00199208	−	0.000825148i
$789$	−13.9785	+	33.7470i	−0.497646	+	1.20142i
$790$	0.0959831	−	0.0959831i	0.00341493	−	0.00341493i
$791$	0.707652	−	0.707652i	0.0251612	−	0.0251612i
$792$	−11.4891	+	27.7372i	−0.408248	+	0.985599i
$793$	56.7856	+	23.5213i	2.01651	+	0.835268i
$794$	3.47033	+	8.37812i	0.123157	+	0.297328i
$795$		−	1.59267i		−	0.0564863i
$796$	−16.4276	+	6.80453i	−0.582260	+	0.241180i
$797$	20.3341	+	20.3341i	0.720269	+	0.720269i	0.968660	−	0.248391i	$-0.0799017\pi$
$797$	20.3341	+	20.3341i	0.720269	+	0.720269i	−0.248391	+	0.968660i	$0.579902\pi$
$798$	2.27113			0.0803973
$799$	−53.7396	−	1.92281i	−1.90117	−	0.0680242i
$800$	22.0627			0.780033
$801$	42.5070	+	42.5070i	1.50191	+	1.50191i
$802$	−13.7368	+	5.68996i	−0.485063	+	0.200920i
$803$		−	25.8711i		−	0.912970i
$804$	9.89239	+	23.8823i	0.348878	+	0.842265i
$805$	0.270627	+	0.112097i	0.00953834	+	0.00395091i
$806$	−5.52562	+	13.3400i	−0.194632	+	0.469882i
$807$	−12.3104	+	12.3104i	−0.433347	+	0.433347i
$808$	−13.8426	+	13.8426i	−0.486981	+	0.486981i
$809$	2.90668	−	7.01735i	0.102193	−	0.246717i	−0.864510	−	0.502615i	$-0.832371\pi$
$809$	2.90668	−	7.01735i	0.102193	−	0.246717i	0.966704	+	0.255898i	$0.0823713\pi$
$810$	−0.210020	−	0.0869931i	−0.00737935	−	0.00305663i
$811$	−3.31901	−	8.01279i	−0.116546	−	0.281367i	0.854832	−	0.518904i	$-0.173660\pi$
$811$	−3.31901	−	8.01279i	−0.116546	−	0.281367i	−0.971378	+	0.237537i	$0.923660\pi$
$812$			2.78453i			0.0977180i
$813$	−24.2686	+	10.0524i	−0.851135	+	0.352552i
$814$	7.56671	+	7.56671i	0.265213	+	0.265213i
$815$	0.345079			0.0120876
$816$	−13.3076	−	35.6863i	−0.465861	−	1.24927i
$817$	1.99394			0.0697593
$818$	7.40693	+	7.40693i	0.258977	+	0.258977i
$819$	25.1218	−	10.4058i	0.877827	−	0.363608i
$820$			0.164347i			0.00573924i
$821$	−11.2306	−	27.1131i	−0.391951	−	0.946254i	−0.989515	−	0.144432i	$-0.953864\pi$
$821$	−11.2306	−	27.1131i	−0.391951	−	0.946254i	0.597563	−	0.801822i	$-0.296136\pi$
$822$	−7.82174	−	3.23987i	−0.272814	−	0.113003i
$823$	−0.301373	+	0.727580i	−0.0105052	+	0.0253618i	−0.929045	−	0.369966i	$-0.879369\pi$
$823$	−0.301373	+	0.727580i	−0.0105052	+	0.0253618i	0.918540	+	0.395328i	$0.129369\pi$
$824$	10.7821	−	10.7821i	0.375612	−	0.375612i
$825$	31.7954	−	31.7954i	1.10697	−	1.10697i
$826$	−0.236057	+	0.569892i	−0.00821347	+	0.0198291i
$827$	−9.04902	−	3.74823i	−0.314665	−	0.130339i	0.219761	−	0.975554i	$-0.429472\pi$
$827$	−9.04902	−	3.74823i	−0.314665	−	0.130339i	−0.534426	+	0.845215i	$0.679472\pi$
$828$	36.7197	+	88.6493i	1.27610	+	3.08078i
$829$			36.1626i			1.25598i	0.778221	+	0.627990i	$0.216122\pi$
$829$			36.1626i			1.25598i	−0.778221	+	0.627990i	$0.783878\pi$
$830$	0.176538	−	0.0731246i	0.00612774	−	0.00253819i
$831$	11.1295	+	11.1295i	0.386080	+	0.386080i
$832$	19.6007			0.679533
$833$	−18.7176	+	17.4244i	−0.648526	+	0.603721i
$834$	3.21394			0.111289
$835$	0.376584	+	0.376584i	0.0130322	+	0.0130322i
$836$	9.84135	−	4.07642i	0.340370	−	0.140986i
$837$		−	79.5132i		−	2.74838i
$838$	−0.727370	−	1.75603i	−0.0251266	−	0.0606610i
$839$	−32.6181	−	13.5108i	−1.12610	−	0.466446i	−0.259647	−	0.965704i	$-0.583606\pi$
$839$	−32.6181	−	13.5108i	−1.12610	−	0.466446i	−0.866454	+	0.499257i	$0.833606\pi$
$840$	0.0675821	−	0.163158i	0.00233180	−	0.00562947i
$841$	18.4504	−	18.4504i	0.636219	−	0.636219i
$842$	2.07921	−	2.07921i	0.0716542	−	0.0716542i
$843$	−8.88096	+	21.4405i	−0.305876	+	0.738451i
$844$	35.4931	+	14.7017i	1.22172	+	0.506054i
$845$	−0.140597	−	0.339432i	−0.00483669	−	0.0116768i
$846$		−	35.0049i		−	1.20349i
$847$	2.03271	−	0.841975i	0.0698446	−	0.0289306i
$848$	27.0960	+	27.0960i	0.930481	+	0.930481i
$849$	30.0129			1.03004
$850$	0.305218	−	8.53037i	0.0104689	−	0.292589i
$851$	71.6101			2.45476
$852$	−52.3685	−	52.3685i	−1.79411	−	1.79411i
$853$	37.5774	−	15.5651i	1.28663	−	0.532938i	0.368648	−	0.929569i	$-0.379821\pi$
$853$	37.5774	−	15.5651i	1.28663	−	0.532938i	0.917978	+	0.396631i	$0.129821\pi$
$854$			4.83976i			0.165613i
$855$	0.200253	+	0.483454i	0.00684851	+	0.0165338i
$856$	17.4417	+	7.22458i	0.596144	+	0.246931i
$857$	2.22702	−	5.37651i	0.0760737	−	0.183658i	−0.881268	−	0.472617i	$-0.843309\pi$
$857$	2.22702	−	5.37651i	0.0760737	−	0.183658i	0.957341	+	0.288959i	$0.0933092\pi$
$858$	−12.3780	+	12.3780i	−0.422577	+	0.422577i
$859$	2.62567	−	2.62567i	0.0895868	−	0.0895868i	−0.660893	−	0.750480i	$-0.729822\pi$
$859$	2.62567	−	2.62567i	0.0895868	−	0.0895868i	0.750480	+	0.660893i	$0.229822\pi$
$860$	0.0283375	−	0.0684128i	0.000966302	−	0.00233286i
$861$	−5.63885	−	2.33569i	−0.192172	−	0.0796001i
$862$	1.07980	+	2.60688i	0.0367782	+	0.0887905i
$863$		−	49.2793i		−	1.67749i	−0.544528	−	0.838743i	$-0.683291\pi$
$863$		−	49.2793i		−	1.67749i	0.544528	−	0.838743i	$-0.316709\pi$
$864$	43.6975	−	18.1001i	1.48662	−	0.615778i
$865$	0.390093	+	0.390093i	0.0132635	+	0.0132635i
$866$	6.77845			0.230341
$867$	−49.6664	+	16.5234i	−1.68676	+	0.561164i
$868$	12.1182			0.411319
$869$	16.7188	+	16.7188i	0.567147	+	0.567147i
$870$	0.0813575	−	0.0336994i	0.00275828	−	0.00114252i
$871$			21.5719i			0.730938i
$872$	9.87361	+	23.8370i	0.334363	+	0.807223i
$873$	27.6942	+	11.4713i	0.937307	+	0.388245i
$874$	−2.55938	+	6.17889i	−0.0865723	+	0.209004i
$875$	−0.255729	+	0.255729i	−0.00864522	+	0.00864522i
$876$	−35.2491	+	35.2491i	−1.19096	+	1.19096i
$877$	−8.99119	+	21.7067i	−0.303611	+	0.732982i	0.696273	+	0.717777i	$0.254840\pi$
$877$	−8.99119	+	21.7067i	−0.303611	+	0.732982i	−0.999884	+	0.0152052i	$0.995160\pi$
$878$	10.2552	+	4.24782i	0.346095	+	0.143357i
$879$	−20.6637	−	49.8865i	−0.696968	−	1.68263i
$880$		−	0.354996i		−	0.0119669i
$881$	−37.0956	+	15.3655i	−1.24978	+	0.517677i	−0.906759	−	0.421649i	$-0.861451\pi$
$881$	−37.0956	+	15.3655i	−1.24978	+	0.517677i	−0.343025	+	0.939326i	$0.611451\pi$
$882$	−11.7711	−	11.7711i	−0.396354	−	0.396354i
$883$	−17.2068			−0.579054			−0.289527	−	0.957170i	$-0.593498\pi$
$883$	−17.2068			−0.579054			−0.289527	+	0.957170i	$0.593498\pi$
$884$	1.26646	−	35.3957i	0.0425957	−	1.19048i
$885$	−0.207923			−0.00698927
$886$	−0.462466	−	0.462466i	−0.0155369	−	0.0155369i
$887$	19.9594	−	8.26745i	0.670171	−	0.277594i	−0.0215404	−	0.999768i	$-0.506857\pi$
$887$	19.9594	−	8.26745i	0.670171	−	0.277594i	0.691711	+	0.722174i	$0.256857\pi$
$888$		−	43.1729i		−	1.44879i
$889$	2.85810	+	6.90007i	0.0958577	+	0.231421i
$890$	0.143759	+	0.0595469i	0.00481881	+	0.00199602i
$891$	15.1529	−	36.5823i	0.507641	−	1.22555i
$892$	−14.5165	+	14.5165i	−0.486047	+	0.486047i
$893$	−18.3885	+	18.3885i	−0.615347	+	0.615347i
$894$	7.40647	−	17.8808i	0.247709	−	0.598023i
$895$	−0.139297	−	0.0576986i	−0.00465617	−	0.00192865i
$896$	3.60799	+	8.71046i	0.120534	+	0.290996i
$897$			117.143i			3.91130i
$898$	−5.31416	+	2.20120i	−0.177336	+	0.0734549i
$899$	8.94652	+	8.94652i	0.298383	+	0.298383i
$900$	−59.2241			−1.97414
$901$	38.5459	−	35.8828i	1.28415	−	1.19543i
$902$	2.68581			0.0894278
$903$	1.94456	+	1.94456i	0.0647109	+	0.0647109i
$904$	1.64149	−	0.679929i	0.0545953	−	0.0226141i
$905$		−	0.812035i		−	0.0269930i
$906$	4.84216	+	11.6900i	0.160870	+	0.388374i
$907$	−6.84803	−	2.83655i	−0.227385	−	0.0941860i	0.266082	−	0.963950i	$-0.414271\pi$
$907$	−6.84803	−	2.83655i	−0.227385	−	0.0941860i	−0.493467	+	0.869764i	$0.664271\pi$
$908$	−13.0042	+	31.3948i	−0.431558	+	1.04187i
$909$	56.5703	−	56.5703i	1.87632	−	1.87632i
$910$	0.0497697	−	0.0497697i	0.00164985	−	0.00164985i
$911$	−16.7698	+	40.4859i	−0.555609	+	1.34136i	0.357603	+	0.933874i	$0.383594\pi$
$911$	−16.7698	+	40.4859i	−0.555609	+	1.34136i	−0.913212	+	0.407485i	$0.866406\pi$
$912$	−17.0168	−	7.04859i	−0.563483	−	0.233402i
$913$	12.7372	+	30.7503i	0.421540	+	1.01769i
$914$		−	0.265015i		−	0.00876592i
$915$	−1.50718	+	0.624295i	−0.0498259	+	0.0206385i
$916$	16.5376	+	16.5376i	0.546416	+	0.546416i
$917$	−16.1660			−0.533849
$918$	−6.39376	−	17.1457i	−0.211026	−	0.565894i
$919$	24.8394			0.819376			0.409688	−	0.912226i	$-0.365638\pi$
$919$	24.8394			0.819376			0.409688	+	0.912226i	$0.365638\pi$
$920$	0.367730	+	0.367730i	0.0121237	+	0.0121237i
$921$	−1.54503	+	0.639971i	−0.0509104	+	0.0210878i
$922$		−	1.66483i		−	0.0548284i
$923$	−23.6512	−	57.0990i	−0.778487	−	1.87943i
$924$	13.5731	+	5.62215i	0.446521	+	0.184955i
$925$	−16.9143	+	40.8346i	−0.556137	+	1.34263i
$926$	−10.3660	+	10.3660i	−0.340647	+	0.340647i
$927$	−44.0630	+	44.0630i	−1.44722	+	1.44722i
$928$	−2.88012	+	6.95323i	−0.0945447	+	0.228251i
$929$	3.14565	+	1.30297i	0.103206	+	0.0427491i	0.433689	−	0.901063i	$-0.357212\pi$
$929$	3.14565	+	1.30297i	0.103206	+	0.0427491i	−0.330483	+	0.943812i	$0.607212\pi$
$930$	−0.146659	−	0.354066i	−0.00480913	−	0.0116103i
$931$			12.3670i			0.405311i
$932$	9.39581	−	3.89187i	0.307770	−	0.127482i
$933$	−14.2909	−	14.2909i	−0.467864	−	0.467864i
$934$	−6.14349			−0.201021
$935$	−0.487560	−	0.0174450i	−0.0159449	−	0.000570512i
$936$	48.2752			1.57793
$937$	10.4524	+	10.4524i	0.341464	+	0.341464i	0.856917	−	0.515454i	$-0.172377\pi$
$937$	10.4524	+	10.4524i	0.341464	+	0.341464i	−0.515454	+	0.856917i	$0.672377\pi$
$938$	−1.56930	+	0.650025i	−0.0512395	+	0.0212241i
$939$			91.8683i			2.99801i
$940$	0.369581	+	0.892248i	0.0120544	+	0.0291019i
$941$	−36.6004	−	15.1604i	−1.19314	−	0.494214i	−0.304363	−	0.952556i	$-0.598444\pi$
$941$	−36.6004	−	15.1604i	−1.19314	−	0.494214i	−0.888776	+	0.458342i	$0.848444\pi$
$942$	6.33730	−	15.2996i	0.206480	−	0.498488i
$943$	12.7090	−	12.7090i	0.413863	−	0.413863i
$944$	3.53738	−	3.53738i	0.115132	−	0.115132i
$945$	−0.148326	+	0.358091i	−0.00482505	+	0.0116487i
$946$	−1.11803	−	0.463101i	−0.0363502	−	0.0150567i
$947$	−7.74143	−	18.6895i	−0.251563	−	0.607326i	0.746768	−	0.665085i	$-0.231605\pi$
$947$	−7.74143	−	18.6895i	−0.251563	−	0.607326i	−0.998331	+	0.0577588i	$0.981605\pi$
$948$		−	45.5585i		−	1.47967i
$949$	−38.4332	+	15.9196i	−1.24759	+	0.516771i
$950$	−2.91890	−	2.91890i	−0.0947016	−	0.0947016i
$951$	7.47298			0.242328
$952$	5.47136	−	2.04031i	0.177328	−	0.0661268i
$953$	−31.6953			−1.02671			−0.513356	−	0.858175i	$-0.671598\pi$
$953$	−31.6953			−1.02671			−0.513356	+	0.858175i	$0.671598\pi$
$954$	24.2407	+	24.2407i	0.784822	+	0.784822i
$955$	−0.510995	+	0.211661i	−0.0165354	+	0.00684920i
$956$			48.1532i			1.55739i
$957$	5.86992	+	14.1713i	0.189748	+	0.458091i
$958$	3.21819	+	1.33302i	0.103975	+	0.0430679i
$959$	−2.26910	+	5.47808i	−0.0732730	+	0.176897i
$960$	−0.367862	+	0.367862i	−0.0118727	+	0.0118727i
$961$	17.0147	−	17.0147i	0.548862	−	0.548862i
$962$	6.58474	−	15.8970i	0.212301	−	0.512539i
$963$	−71.2786	−	29.5246i	−2.29692	−	0.951416i
$964$	−8.03552	−	19.3995i	−0.258807	−	0.624814i
$965$			0.373941i			0.0120376i
$966$	−8.52185	+	3.52987i	−0.274186	+	0.113572i
$967$	−29.4360	−	29.4360i	−0.946597	−	0.946597i	0.0520479	−	0.998645i	$-0.483425\pi$
$967$	−29.4360	−	29.4360i	−0.946597	−	0.946597i	−0.998645	+	0.0520479i	$0.983425\pi$
$968$	3.90615			0.125548
$969$	−10.5170	+	23.0250i	−0.337853	+	0.739668i
$970$	0.0775922			0.00249134
$971$	11.7993	+	11.7993i	0.378658	+	0.378658i	0.870618	−	0.491960i	$-0.163719\pi$
$971$	11.7993	+	11.7993i	0.378658	+	0.378658i	−0.491960	+	0.870618i	$0.663719\pi$
$972$	−16.1848	+	6.70398i	−0.519129	+	0.215030i
$973$		−	2.25093i		−	0.0721616i
$974$	0.0335268	+	0.0809407i	0.00107427	+	0.00259351i
$975$	−66.7992	−	27.6691i	−2.13929	−	0.886122i
$976$	15.0205	−	36.2626i	0.480793	−	1.16074i
$977$	−8.54624	+	8.54624i	−0.273418	+	0.273418i	−0.830475	−	0.557056i	$-0.811931\pi$
$977$	−8.54624	+	8.54624i	−0.273418	+	0.273418i	0.557056	+	0.830475i	$0.311931\pi$
$978$	−7.68363	+	7.68363i	−0.245695	+	0.245695i
$979$	−10.3722	+	25.0407i	−0.331496	+	0.800303i
$980$	0.424315	+	0.175757i	0.0135542	+	0.00561435i
$981$	−40.3503	−	97.4143i	−1.28829	−	3.11020i
$982$			8.91292i			0.284423i
$983$	4.32337	−	1.79080i	0.137894	−	0.0571176i	−0.312669	−	0.949862i	$-0.601223\pi$
$983$	4.32337	−	1.79080i	0.137894	−	0.0571176i	0.450563	+	0.892744i	$0.351223\pi$
$984$	−7.66213	−	7.66213i	−0.244260	−	0.244260i
$985$	0.00134064			4.27162e−5
$986$	2.64857	+	1.20977i	0.0843478	+	0.0385270i
$987$	−35.8661			−1.14163
$988$	−12.1116	−	12.1116i	−0.385321	−	0.385321i
$989$	−7.48176	+	3.09905i	−0.237906	+	0.0985440i
$990$		−	0.317587i		−	0.0100936i
$991$	11.4119	+	27.5507i	0.362510	+	0.875177i	0.994932	+	0.100553i	$0.0320610\pi$
$991$	11.4119	+	27.5507i	0.362510	+	0.875177i	−0.632422	+	0.774624i	$0.717939\pi$
$992$	30.2603	+	12.5342i	0.960766	+	0.397962i
$993$	−14.7338	+	35.5705i	−0.467563	+	1.12880i
$994$	3.44111	−	3.44111i	0.109146	−	0.109146i
$995$	0.278483	−	0.278483i	0.00882850	−	0.00882850i
$996$	24.5427	−	59.2514i	0.777666	−	1.87745i
$997$	39.1149	+	16.2019i	1.23878	+	0.513120i	0.903334	−	0.428938i	$-0.141112\pi$
$997$	39.1149	+	16.2019i	1.23878	+	0.513120i	0.335448	+	0.942059i	$0.391112\pi$
$998$	0.859695	+	2.07549i	0.0272132	+	0.0656984i
$999$			94.7539i			2.99788i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	731.2.m.b.87.14	✓	116
17.9	even	8	inner	731.2.m.b.689.14	yes	116

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
731.2.m.b.87.14	✓	116	1.1	even	1	trivial
731.2.m.b.689.14	yes	116	17.9	even	8	inner

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:	\( N \)	\(=\)	\( 731 = 17 \cdot 43 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	731.m (of order \(8\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.292872 - 0.292872i) q^{2} +(2.84462 - 1.17828i) q^{3} -1.82845i q^{4} +(0.0154981 + 0.0374157i) q^{5} +(-1.17820 - 0.488025i) q^{6} +(-0.341796 + 0.825169i) q^{7} +(-1.12125 + 1.12125i) q^{8} +(4.58219 - 4.58219i) q^{9} +O(q^{10})\)	\(q+(-0.292872 - 0.292872i) q^{2} +(2.84462 - 1.17828i) q^{3} -1.82845i q^{4} +(0.0154981 + 0.0374157i) q^{5} +(-1.17820 - 0.488025i) q^{6} +(-0.341796 + 0.825169i) q^{7} +(-1.12125 + 1.12125i) q^{8} +(4.58219 - 4.58219i) q^{9} +(0.00641907 - 0.0154970i) q^{10} +(2.69934 + 1.11811i) q^{11} +(-2.15443 - 5.20124i) q^{12} -4.69807i q^{13} +(0.341772 - 0.141567i) q^{14} +(0.0881723 + 0.0881723i) q^{15} -3.00014 q^{16} +(-0.147431 + 4.12047i) q^{17} -2.68399 q^{18} +(1.40993 + 1.40993i) q^{19} +(0.0684128 - 0.0283375i) q^{20} +2.75002i q^{21} +(-0.463101 - 1.11803i) q^{22} +(-7.48176 - 3.09905i) q^{23} +(-1.86838 + 4.51067i) q^{24} +(3.53437 - 3.53437i) q^{25} +(-1.37594 + 1.37594i) q^{26} +(4.10064 - 9.89981i) q^{27} +(1.50878 + 0.624958i) q^{28} +(0.652501 + 1.57528i) q^{29} -0.0516465i q^{30} +(6.85556 - 2.83967i) q^{31} +(3.12115 + 3.12115i) q^{32} +8.99604 q^{33} +(1.24995 - 1.16359i) q^{34} -0.0361715 q^{35} +(-8.37831 - 8.37831i) q^{36} +(-8.16961 + 3.38396i) q^{37} -0.825860i q^{38} +(-5.53564 - 13.3642i) q^{39} +(-0.0593295 - 0.0245751i) q^{40} +(-0.849335 + 2.05048i) q^{41} +(0.805406 - 0.805406i) q^{42} +(0.707107 - 0.707107i) q^{43} +(2.04440 - 4.93562i) q^{44} +(0.242461 + 0.100431i) q^{45} +(1.28358 + 3.09883i) q^{46} +13.0421i q^{47} +(-8.53424 + 3.53500i) q^{48} +(4.38567 + 4.38567i) q^{49} -2.07024 q^{50} +(4.43568 + 11.8949i) q^{51} -8.59020 q^{52} +(-9.03159 - 9.03159i) q^{53} +(-4.10035 + 1.69842i) q^{54} +0.118326i q^{55} +(-0.541981 - 1.30846i) q^{56} +(5.67201 + 2.34942i) q^{57} +(0.270256 - 0.652455i) q^{58} +(-1.17907 + 1.17907i) q^{59} +(0.161219 - 0.161219i) q^{60} +(-5.00659 + 12.0870i) q^{61} +(-2.83947 - 1.17615i) q^{62} +(2.21491 + 5.34725i) q^{63} +4.17207i q^{64} +(0.175782 - 0.0728112i) q^{65} +(-2.63469 - 2.63469i) q^{66} -4.59166 q^{67} +(7.53408 + 0.269570i) q^{68} -24.9343 q^{69} +(0.0105936 + 0.0105936i) q^{70} +(12.1537 - 5.03422i) q^{71} +10.2755i q^{72} +(-3.38853 - 8.18063i) q^{73} +(3.38372 + 1.40158i) q^{74} +(5.88946 - 14.2184i) q^{75} +(2.57799 - 2.57799i) q^{76} +(-1.84525 + 1.84525i) q^{77} +(-2.29278 + 5.53525i) q^{78} +(7.47640 + 3.09683i) q^{79} +(-0.0464964 - 0.112252i) q^{80} -13.5523i q^{81} +(0.849275 - 0.351781i) q^{82} +(8.05520 + 8.05520i) q^{83} +5.02828 q^{84} +(-0.156455 + 0.0583432i) q^{85} -0.414184 q^{86} +(3.71223 + 3.71223i) q^{87} +(-4.28031 + 1.77296i) q^{88} +9.27657i q^{89} +(-0.0415968 - 0.100424i) q^{90} +(3.87671 + 1.60578i) q^{91} +(-5.66646 + 13.6800i) q^{92} +(16.1555 - 16.1555i) q^{93} +(3.81968 - 3.81968i) q^{94} +(-0.0309023 + 0.0746048i) q^{95} +(12.5561 + 5.20090i) q^{96} +(1.77021 + 4.27367i) q^{97} -2.56888i q^{98} +(17.4923 - 7.24553i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 116 q - 8 q^{6}+O(q^{10}) \) 116 * q - 8 * q^6	\( 116 q - 8 q^{6} - 8 q^{10} + 8 q^{14} + 4 q^{15} - 68 q^{16} - 4 q^{17} - 44 q^{18} + 12 q^{19} + 8 q^{20} - 16 q^{22} - 28 q^{23} - 12 q^{24} - 4 q^{25} - 8 q^{26} + 24 q^{28} + 80 q^{33} + 32 q^{34} - 112 q^{35} + 160 q^{36} - 20 q^{37} + 8 q^{39} - 112 q^{40} + 8 q^{41} + 4 q^{42} + 32 q^{44} - 52 q^{45} - 40 q^{46} + 40 q^{48} + 8 q^{49} + 100 q^{50} - 32 q^{51} - 152 q^{52} + 28 q^{53} - 36 q^{54} + 124 q^{56} - 104 q^{57} - 32 q^{58} - 36 q^{59} - 24 q^{60} + 52 q^{61} - 68 q^{62} + 20 q^{63} + 20 q^{65} - 60 q^{66} + 64 q^{67} - 128 q^{69} + 188 q^{70} + 52 q^{73} - 104 q^{74} + 36 q^{75} - 112 q^{76} + 28 q^{77} + 56 q^{78} - 108 q^{79} - 44 q^{80} + 52 q^{82} - 52 q^{83} + 120 q^{84} + 12 q^{85} - 20 q^{86} + 56 q^{87} + 36 q^{88} + 144 q^{90} - 16 q^{92} - 176 q^{93} - 8 q^{94} + 164 q^{95} - 164 q^{96} - 8 q^{97} - 24 q^{99}+O(q^{100}) \) 116 * q - 8 * q^6 - 8 * q^10 + 8 * q^14 + 4 * q^15 - 68 * q^16 - 4 * q^17 - 44 * q^18 + 12 * q^19 + 8 * q^20 - 16 * q^22 - 28 * q^23 - 12 * q^24 - 4 * q^25 - 8 * q^26 + 24 * q^28 + 80 * q^33 + 32 * q^34 - 112 * q^35 + 160 * q^36 - 20 * q^37 + 8 * q^39 - 112 * q^40 + 8 * q^41 + 4 * q^42 + 32 * q^44 - 52 * q^45 - 40 * q^46 + 40 * q^48 + 8 * q^49 + 100 * q^50 - 32 * q^51 - 152 * q^52 + 28 * q^53 - 36 * q^54 + 124 * q^56 - 104 * q^57 - 32 * q^58 - 36 * q^59 - 24 * q^60 + 52 * q^61 - 68 * q^62 + 20 * q^63 + 20 * q^65 - 60 * q^66 + 64 * q^67 - 128 * q^69 + 188 * q^70 + 52 * q^73 - 104 * q^74 + 36 * q^75 - 112 * q^76 + 28 * q^77 + 56 * q^78 - 108 * q^79 - 44 * q^80 + 52 * q^82 - 52 * q^83 + 120 * q^84 + 12 * q^85 - 20 * q^86 + 56 * q^87 + 36 * q^88 + 144 * q^90 - 16 * q^92 - 176 * q^93 - 8 * q^94 + 164 * q^95 - 164 * q^96 - 8 * q^97 - 24 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more