LMFDB - Embedded newform 960.2.cn.a.611.90

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [960,2,Mod(11,960)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(960, base_ring=CyclotomicField(16))

chi = DirichletCharacter(H, H._module([8, 5, 8, 0]))

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

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

chi := DirichletCharacter("960.11");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 960 = 2^{6} \cdot 3 \cdot 5 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	960.cn (of order $16$, degree $8$, 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:	$7.66563859404$
Analytic rank:	$0$
Dimension:	$1024$
Relative dimension:	$128$ over $\Q(\zeta_{16})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{16}]$

Embedding invariants

Embedding label			611.90
Character	$\chi$	$=$	960.611
Dual form			960.2.cn.a.11.90

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.831887 - 1.14366i) q^{2} +(-1.72307 + 0.176174i) q^{3} +(-0.615929 - 1.90280i) q^{4} +(-0.831470 - 0.555570i) q^{5} +(-1.23191 + 2.11717i) q^{6} +(-1.53037 - 3.69465i) q^{7} +(-2.68854 - 0.878495i) q^{8} +(2.93793 - 0.607119i) q^{9} +O(q^{10})$	\(q+(0.831887 - 1.14366i) q^{2} +(-1.72307 + 0.176174i) q^{3} +(-0.615929 - 1.90280i) q^{4} +(-0.831470 - 0.555570i) q^{5} +(-1.23191 + 2.11717i) q^{6} +(-1.53037 - 3.69465i) q^{7} +(-2.68854 - 0.878495i) q^{8} +(2.93793 - 0.607119i) q^{9} +(-1.32707 + 0.488749i) q^{10} +(-0.519857 - 2.61350i) q^{11} +(1.39651 + 3.17014i) q^{12} +(2.12901 + 3.18628i) q^{13} +(-5.49853 - 1.32330i) q^{14} +(1.53056 + 0.810802i) q^{15} +(-3.24126 + 2.34397i) q^{16} +(-1.81246 + 1.81246i) q^{17} +(1.74968 - 3.86505i) q^{18} +(-2.62842 - 3.93371i) q^{19} +(-0.545010 + 1.92431i) q^{20} +(3.28784 + 6.09652i) q^{21} +(-3.42142 - 1.57959i) q^{22} +(0.157368 - 0.379920i) q^{23} +(4.78730 + 1.04006i) q^{24} +(0.382683 + 0.923880i) q^{25} +(5.41512 + 0.215761i) q^{26} +(-4.95529 + 1.56369i) q^{27} +(-6.08756 + 5.18763i) q^{28} +(-7.83393 - 1.55827i) q^{29} +(2.20053 - 1.07594i) q^{30} +6.58057 q^{31} +(-0.0156458 + 5.65683i) q^{32} +(1.35618 + 4.41165i) q^{33} +(0.565082 + 3.58060i) q^{34} +(-0.780177 + 3.92222i) q^{35} +(-2.96478 - 5.21633i) q^{36} +(6.24903 + 4.17547i) q^{37} +(-6.68539 - 0.266374i) q^{38} +(-4.22976 - 5.11510i) q^{39} +(1.74737 + 2.22411i) q^{40} +(-0.724580 - 0.300131i) q^{41} +(9.70747 + 1.31143i) q^{42} +(2.05652 + 10.3388i) q^{43} +(-4.65276 + 2.59891i) q^{44} +(-2.78009 - 1.12742i) q^{45} +(-0.303588 - 0.496026i) q^{46} +(3.53608 + 3.53608i) q^{47} +(5.17197 - 4.60985i) q^{48} +(-6.35863 + 6.35863i) q^{49} +(1.37496 + 0.330902i) q^{50} +(2.80368 - 3.44230i) q^{51} +(4.75153 - 6.01359i) q^{52} +(-13.8731 + 2.75954i) q^{53} +(-2.33390 + 6.96799i) q^{54} +(-1.01974 + 2.46186i) q^{55} +(0.868740 + 11.2776i) q^{56} +(5.22197 + 6.31499i) q^{57} +(-8.29907 + 7.66307i) q^{58} +(3.36410 - 5.03474i) q^{59} +(0.600076 - 3.41173i) q^{60} +(-8.78985 - 1.74841i) q^{61} +(5.47429 - 7.52595i) q^{62} +(-6.73921 - 9.92548i) q^{63} +(6.45649 + 4.72374i) q^{64} -3.83211i q^{65} +(6.17363 + 2.11898i) q^{66} +(-0.123698 + 0.621873i) q^{67} +(4.56509 + 2.33239i) q^{68} +(-0.204224 + 0.682351i) q^{69} +(3.83667 + 4.15510i) q^{70} +(-6.97840 + 2.89055i) q^{71} +(-8.43208 - 0.948688i) q^{72} +(-6.92553 - 2.86865i) q^{73} +(9.97381 - 3.67327i) q^{74} +(-0.822153 - 1.52449i) q^{75} +(-5.86613 + 7.42424i) q^{76} +(-8.86038 + 5.92032i) q^{77} +(-9.36863 + 0.582233i) q^{78} +(-12.0007 - 12.0007i) q^{79} +(3.99725 - 0.148195i) q^{80} +(8.26281 - 3.56734i) q^{81} +(-0.946017 + 0.579000i) q^{82} +(1.02021 - 0.681680i) q^{83} +(9.57535 - 10.0111i) q^{84} +(2.51395 - 0.500056i) q^{85} +(13.5349 + 6.24876i) q^{86} +(13.7729 + 1.30486i) q^{87} +(-0.898288 + 7.48319i) q^{88} +(12.8800 - 5.33508i) q^{89} +(-3.60211 + 2.24160i) q^{90} +(8.51401 - 12.7421i) q^{91} +(-0.819837 - 0.0654353i) q^{92} +(-11.3388 + 1.15933i) q^{93} +(6.98569 - 1.10246i) q^{94} +4.73103i q^{95} +(-0.969628 - 9.74986i) q^{96} -6.06601i q^{97} +(1.98247 + 12.5618i) q^{98} +(-3.11401 - 7.36265i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 1024 q+O(q^{10}) $ 1024 * q	$ 1024 q + 80 q^{24} + 80 q^{42} - 96 q^{52} - 288 q^{58} - 96 q^{64} + 256 q^{67} - 112 q^{76} - 48 q^{78} + 32 q^{79} - 112 q^{84} - 160 q^{88} - 144 q^{90} - 16 q^{94} - 272 q^{96}+O(q^{100}) $ 1024 * q + 80 * q^24 + 80 * q^42 - 96 * q^52 - 288 * q^58 - 96 * q^64 + 256 * q^67 - 112 * q^76 - 48 * q^78 + 32 * q^79 - 112 * q^84 - 160 * q^88 - 144 * q^90 - 16 * q^94 - 272 * q^96

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/960\mathbb{Z}\right)^\times$.

$n$	$511$	$577$	$641$	$901$
$\chi(n)$	$-1$	$1$	$-1$	$e\left(\frac{11}{16}\right)$

Coefficient data

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

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

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

$2$	0.831887	−	1.14366i	0.588233	−	0.808692i
$2$	0.831887	−	1.14366i	0.588233	−	0.808692i
$3$	−1.72307	+	0.176174i	−0.994814	+	0.101714i
$3$	−1.72307	+	0.176174i	−0.994814	+	0.101714i
$4$	−0.615929	−	1.90280i	−0.307965	−	0.951398i
$5$	−0.831470	−	0.555570i	−0.371845	−	0.248459i
$5$	−0.831470	−	0.555570i	−0.371845	−	0.248459i
$6$	−1.23191	+	2.11717i	−0.502927	+	0.864329i
$7$	−1.53037	−	3.69465i	−0.578427	−	1.39645i	−0.894224	−	0.447619i	$-0.852272\pi$
$7$	−1.53037	−	3.69465i	−0.578427	−	1.39645i	0.315798	−	0.948826i	$-0.397728\pi$
$8$	−2.68854	−	0.878495i	−0.950542	−	0.310595i
$9$	2.93793	−	0.607119i	0.979308	−	0.202373i
$10$	−1.32707	+	0.488749i	−0.419657	+	0.154556i
$11$	−0.519857	−	2.61350i	−0.156743	−	0.788000i	−0.976538	−	0.215343i	$-0.930913\pi$
$11$	−0.519857	−	2.61350i	−0.156743	−	0.788000i	0.819796	−	0.572656i	$-0.194087\pi$
$12$	1.39651	+	3.17014i	0.403138	+	0.915139i
$13$	2.12901	+	3.18628i	0.590480	+	0.883715i	0.999586	−	0.0287713i	$-0.00915947\pi$
$13$	2.12901	+	3.18628i	0.590480	+	0.883715i	−0.409106	+	0.912487i	$0.634159\pi$
$14$	−5.49853	−	1.32330i	−1.46954	−	0.353666i
$15$	1.53056	+	0.810802i	0.395188	+	0.209348i
$16$	−3.24126	+	2.34397i	−0.810316	+	0.585994i
$17$	−1.81246	+	1.81246i	−0.439586	+	0.439586i	−0.891873	−	0.452287i	$-0.850608\pi$
$17$	−1.81246	+	1.81246i	−0.439586	+	0.439586i	0.452287	+	0.891873i	$0.350608\pi$
$18$	1.74968	−	3.86505i	0.412404	−	0.911001i
$19$	−2.62842	−	3.93371i	−0.603001	−	0.902455i	0.396880	−	0.917871i	$-0.370093\pi$
$19$	−2.62842	−	3.93371i	−0.603001	−	0.902455i	−0.999881	+	0.0154152i	$0.995093\pi$
$20$	−0.545010	+	1.92431i	−0.121868	+	0.430289i
$21$	3.28784	+	6.09652i	0.717465	+	1.33037i
$22$	−3.42142	−	1.57959i	−0.729450	−	0.336770i
$23$	0.157368	−	0.379920i	0.0328135	−	0.0792187i	−0.906623	−	0.421941i	$-0.861349\pi$
$23$	0.157368	−	0.379920i	0.0328135	−	0.0792187i	0.939437	+	0.342722i	$0.111349\pi$
$24$	4.78730	+	1.04006i	0.977204	+	0.212300i
$25$	0.382683	+	0.923880i	0.0765367	+	0.184776i
$26$	5.41512	+	0.215761i	1.06199	+	0.0423142i
$27$	−4.95529	+	1.56369i	−0.953645	+	0.300933i
$28$	−6.08756	+	5.18763i	−1.15044	+	0.980370i
$29$	−7.83393	−	1.55827i	−1.45472	−	0.289363i	−0.596490	−	0.802621i	$-0.703438\pi$
$29$	−7.83393	−	1.55827i	−1.45472	−	0.289363i	−0.858234	+	0.513258i	$0.828438\pi$
$30$	2.20053	−	1.07594i	0.401760	−	0.196440i
$31$	6.58057			1.18191			0.590953	−	0.806706i	$-0.298752\pi$
$31$	6.58057			1.18191			0.590953	+	0.806706i	$0.298752\pi$
$32$	−0.0156458	+	5.65683i	−0.00276581	+	0.999996i
$33$	1.35618	+	4.41165i	0.236081	+	0.767970i
$34$	0.565082	+	3.58060i	0.0969107	+	0.614068i
$35$	−0.780177	+	3.92222i	−0.131874	+	0.662976i
$36$	−2.96478	−	5.21633i	−0.494130	−	0.869388i
$37$	6.24903	+	4.17547i	1.02733	+	0.686443i	0.950539	−	0.310604i	$-0.100531\pi$
$37$	6.24903	+	4.17547i	1.02733	+	0.686443i	0.0767950	+	0.997047i	$0.475531\pi$
$38$	−6.68539	−	0.266374i	−1.08451	−	0.0432115i
$39$	−4.22976	−	5.11510i	−0.677304	−	0.819072i
$40$	1.74737	+	2.22411i	0.276284	+	0.351663i
$41$	−0.724580	−	0.300131i	−0.113160	−	0.0468726i	0.325385	−	0.945582i	$-0.394506\pi$
$41$	−0.724580	−	0.300131i	−0.113160	−	0.0468726i	−0.438545	+	0.898709i	$0.644506\pi$
$42$	9.70747	+	1.31143i	1.49789	+	0.202359i
$43$	2.05652	+	10.3388i	0.313616	+	1.57665i	0.740315	+	0.672260i	$0.234676\pi$
$43$	2.05652	+	10.3388i	0.313616	+	1.57665i	−0.426699	+	0.904394i	$0.640324\pi$
$44$	−4.65276	+	2.59891i	−0.701430	+	0.391801i
$45$	−2.78009	−	1.12742i	−0.414432	−	0.168066i
$46$	−0.303588	−	0.496026i	−0.0447616	−	0.0731350i
$47$	3.53608	+	3.53608i	0.515790	+	0.515790i	0.916295	−	0.400505i	$-0.131165\pi$
$47$	3.53608	+	3.53608i	0.515790	+	0.515790i	−0.400505	+	0.916295i	$0.631165\pi$
$48$	5.17197	−	4.60985i	0.746509	−	0.665375i
$49$	−6.35863	+	6.35863i	−0.908375	+	0.908375i
$50$	1.37496	+	0.330902i	0.194448	+	0.0467966i
$51$	2.80368	−	3.44230i	0.392594	−	0.482018i
$52$	4.75153	−	6.01359i	0.658918	−	0.833934i
$53$	−13.8731	+	2.75954i	−1.90562	+	0.379052i	−0.999073	−	0.0430464i	$-0.986294\pi$
$53$	−13.8731	+	2.75954i	−1.90562	+	0.379052i	−0.906550	+	0.422098i	$0.861294\pi$
$54$	−2.33390	+	6.96799i	−0.317603	+	0.948224i
$55$	−1.01974	+	2.46186i	−0.137501	+	0.331957i
$56$	0.868740	+	11.2776i	0.116090	+	1.50704i
$57$	5.22197	+	6.31499i	0.691666	+	0.836441i
$58$	−8.29907	+	7.66307i	−1.08972	+	1.00621i
$59$	3.36410	−	5.03474i	0.437969	−	0.655467i	−0.545170	−	0.838325i	$-0.683535\pi$
$59$	3.36410	−	5.03474i	0.437969	−	0.655467i	0.983139	+	0.182858i	$0.0585350\pi$
$60$	0.600076	−	3.41173i	0.0774695	−	0.440453i
$61$	−8.78985	−	1.74841i	−1.12542	−	0.223861i	−0.402925	−	0.915233i	$-0.632007\pi$
$61$	−8.78985	−	1.74841i	−1.12542	−	0.223861i	−0.722499	+	0.691372i	$0.757007\pi$
$62$	5.47429	−	7.52595i	0.695235	−	0.955797i
$63$	−6.73921	−	9.92548i	−0.849061	−	1.25049i
$64$	6.45649	+	4.72374i	0.807062	+	0.590467i
$65$		−	3.83211i		−	0.475314i
$66$	6.17363	+	2.11898i	0.759921	+	0.260829i
$67$	−0.123698	+	0.621873i	−0.0151121	+	0.0759739i	−0.987605	−	0.156957i	$-0.949832\pi$
$67$	−0.123698	+	0.621873i	−0.0151121	+	0.0759739i	0.972493	+	0.232931i	$0.0748316\pi$
$68$	4.56509	+	2.33239i	0.553598	+	0.282844i
$69$	−0.204224	+	0.682351i	−0.0245856	+	0.0821455i
$70$	3.83667	+	4.15510i	0.458570	+	0.496629i
$71$	−6.97840	+	2.89055i	−0.828184	+	0.343045i	−0.756183	−	0.654360i	$-0.772938\pi$
$71$	−6.97840	+	2.89055i	−0.828184	+	0.343045i	−0.0720003	+	0.997405i	$0.522938\pi$
$72$	−8.43208	−	0.948688i	−0.993730	−	0.111804i
$73$	−6.92553	−	2.86865i	−0.810571	−	0.335750i	−0.0613895	−	0.998114i	$-0.519553\pi$
$73$	−6.92553	−	2.86865i	−0.810571	−	0.335750i	−0.749182	+	0.662364i	$0.769553\pi$
$74$	9.97381	−	3.67327i	1.15943	−	0.427009i
$75$	−0.822153	−	1.52449i	−0.0949341	−	0.176033i
$76$	−5.86613	+	7.42424i	−0.672891	+	0.851619i
$77$	−8.86038	+	5.92032i	−1.00973	+	0.674683i
$78$	−9.36863	+	0.582233i	−1.06079	+	0.0659249i
$79$	−12.0007	−	12.0007i	−1.35018	−	1.35018i	−0.885452	−	0.464730i	$-0.846151\pi$
$79$	−12.0007	−	12.0007i	−1.35018	−	1.35018i	−0.464730	−	0.885452i	$-0.653849\pi$
$80$	3.99725	−	0.148195i	0.446907	−	0.0165687i
$81$	8.26281	−	3.56734i	0.918090	−	0.396371i
$82$	−0.946017	+	0.579000i	−0.104470	+	0.0639399i
$83$	1.02021	−	0.681680i	0.111982	−	0.0748241i	−0.498318	−	0.866994i	$-0.666049\pi$
$83$	1.02021	−	0.681680i	0.111982	−	0.0748241i	0.610300	+	0.792170i	$0.291049\pi$
$84$	9.57535	−	10.0111i	1.04476	−	1.09230i
$85$	2.51395	−	0.500056i	0.272677	−	0.0542387i
$86$	13.5349	+	6.24876i	1.45951	+	0.673821i
$87$	13.7729	+	1.30486i	1.47661	+	0.139896i
$88$	−0.898288	+	7.48319i	−0.0957579	+	0.797711i
$89$	12.8800	−	5.33508i	1.36528	−	0.565517i	0.424775	−	0.905299i	$-0.360353\pi$
$89$	12.8800	−	5.33508i	1.36528	−	0.565517i	0.940504	+	0.339782i	$0.110353\pi$
$90$	−3.60211	+	2.24160i	−0.379696	+	0.236286i
$91$	8.51401	−	12.7421i	0.892511	−	1.33574i
$92$	−0.819837	−	0.0654353i	−0.0854739	−	0.00682210i
$93$	−11.3388	+	1.15933i	−1.17578	+	0.120216i
$94$	6.98569	−	1.10246i	0.720519	−	0.113710i
$95$			4.73103i			0.485394i
$96$	−0.969628	−	9.74986i	−0.0989622	−	0.995091i
$97$		−	6.06601i		−	0.615909i	−0.951401	−	0.307955i	$-0.900355\pi$
$97$		−	6.06601i		−	0.615909i	0.951401	−	0.307955i	$-0.0996445\pi$
$98$	1.98247	+	12.5618i	0.200260	+	1.26893i
$99$	−3.11401	−	7.36265i	−0.312970	−	0.739974i
$100$	1.52225	−	1.29721i	0.152225	−	0.129721i
$101$	5.55610	−	8.31530i	0.552853	−	0.827403i	−0.444817	−	0.895621i	$-0.646731\pi$
$101$	5.55610	−	8.31530i	0.552853	−	0.827403i	0.997670	+	0.0682184i	$0.0217315\pi$
$102$	−1.60448	−	6.07007i	−0.158868	−	0.601026i
$103$	10.2047	−	4.22694i	1.00550	−	0.416493i	0.181691	−	0.983356i	$-0.441843\pi$
$103$	10.2047	−	4.22694i	1.00550	−	0.416493i	0.823812	+	0.566863i	$0.191843\pi$
$104$	−2.92478	−	10.4368i	−0.286799	−	1.02341i
$105$	0.653306	−	6.89569i	0.0637562	−	0.672951i
$106$	−8.38490	+	18.1618i	−0.814414	+	1.76403i
$107$	−12.6357	+	2.51340i	−1.22154	+	0.242979i	−0.763414	−	0.645909i	$-0.776478\pi$
$107$	−12.6357	+	2.51340i	−1.22154	+	0.242979i	−0.458124	+	0.888888i	$0.651478\pi$
$108$	6.02750	+	8.46577i	0.579996	+	0.814619i
$109$	−5.04755	+	3.37267i	−0.483468	+	0.323043i	−0.773306	−	0.634033i	$-0.781398\pi$
$109$	−5.04755	+	3.37267i	−0.483468	+	0.323043i	0.289838	+	0.957076i	$0.406398\pi$
$110$	1.96724	+	3.21423i	0.187569	+	0.306464i
$111$	−11.5031	−	6.09370i	−1.09183	−	0.578388i
$112$	13.6205	+	8.38816i	1.28702	+	0.792607i
$113$	6.11758	+	6.11758i	0.575494	+	0.575494i	0.933658	−	0.358165i	$-0.116597\pi$
$113$	6.11758	+	6.11758i	0.575494	+	0.575494i	−0.358165	+	0.933658i	$0.616597\pi$
$114$	11.5663	−	0.718812i	1.08328	−	0.0673229i
$115$	−0.341919	+	0.228463i	−0.0318841	+	0.0213043i
$116$	1.86009	+	15.8661i	0.172705	+	1.47313i
$117$	8.18931	+	8.06850i	0.757102	+	0.745933i
$118$	−2.95949	−	8.03573i	−0.272443	−	0.739749i
$119$	9.47014	+	3.92266i	0.868126	+	0.359590i
$120$	−3.40267	−	3.52446i	−0.310620	−	0.321738i
$121$	3.60255	−	1.49222i	0.327504	−	0.135657i
$122$	−9.31175	+	8.59814i	−0.843046	+	0.778439i
$123$	1.30138	+	0.389494i	0.117341	+	0.0351195i
$124$	−4.05317	−	12.5215i	−0.363985	−	1.12446i
$125$	0.195090	−	0.980785i	0.0174494	−	0.0877241i
$126$	−16.9577	−	0.549486i	−1.51071	−	0.0489521i
$127$		−	10.4529i		−	0.927547i	−0.885954	−	0.463774i	$-0.846495\pi$
$127$		−	10.4529i		−	0.927547i	0.885954	−	0.463774i	$-0.153505\pi$
$128$	10.7734	−	3.45444i	0.952246	−	0.305332i
$129$	−5.36495	−	17.4522i	−0.472357	−	1.53658i
$130$	−4.38264	−	3.18788i	−0.384383	−	0.279596i
$131$	12.5122	+	2.48883i	1.09319	+	0.217450i	0.708582	−	0.705629i	$-0.249335\pi$
$131$	12.5122	+	2.48883i	1.09319	+	0.217450i	0.384612	+	0.923078i	$0.374335\pi$
$132$	7.55916	−	5.29780i	0.657940	−	0.461114i
$133$	−10.5112	+	15.7311i	−0.911438	+	1.36406i
$134$	0.608310	+	0.658797i	0.0525500	+	0.0569114i
$135$	4.98891	+	1.45285i	0.429377	+	0.125041i
$136$	6.46511	−	3.28063i	0.554378	−	0.281312i
$137$	4.77431	−	11.5262i	0.407897	−	0.984750i	−0.577793	−	0.816183i	$-0.696086\pi$
$137$	4.77431	−	11.5262i	0.407897	−	0.984750i	0.985690	−	0.168567i	$-0.0539139\pi$
$138$	0.610489	+	0.801202i	0.0519683	+	0.0682028i
$139$	−11.6971	+	2.32671i	−0.992138	+	0.197349i	−0.664365	−	0.747408i	$-0.731298\pi$
$139$	−11.6971	+	2.32671i	−0.992138	+	0.197349i	−0.327773	+	0.944757i	$0.606298\pi$
$140$	7.94371	−	0.931290i	0.671366	−	0.0787084i
$141$	−6.71586	−	5.46993i	−0.565578	−	0.460651i
$142$	−2.49943	+	10.3855i	−0.209747	+	0.871536i
$143$	7.22056	−	7.22056i	0.603814	−	0.603814i
$144$	−8.09951	+	8.85426i	−0.674960	+	0.737855i
$145$	5.64795	+	5.64795i	0.469036	+	0.469036i
$146$	−9.04202	+	5.53408i	−0.748323	+	0.458004i
$147$	9.83612	−	12.0766i	0.811270	−	0.996059i
$148$	4.09610	−	14.4624i	0.336698	−	1.18880i
$149$	2.16138	+	10.8660i	0.177067	+	0.890176i	0.962511	+	0.271243i	$0.0874348\pi$
$149$	2.16138	+	10.8660i	0.177067	+	0.890176i	−0.785444	+	0.618933i	$0.787565\pi$
$150$	−2.42744	−	0.327936i	−0.198200	−	0.0267758i
$151$	−20.4834	−	8.48448i	−1.66691	−	0.690458i	−0.668339	−	0.743857i	$-0.732994\pi$
$151$	−20.4834	−	8.48448i	−1.66691	−	0.690458i	−0.998573	+	0.0533994i	$0.982994\pi$
$152$	3.61087	+	12.8850i	0.292880	+	1.04511i
$153$	−4.22449	+	6.42525i	−0.341530	+	0.519451i
$154$	−0.599986	+	15.0583i	−0.0483482	+	1.21343i
$155$	−5.47155	−	3.65597i	−0.439485	−	0.293655i
$156$	−7.12776	+	11.1989i	−0.570678	+	0.896630i
$157$	2.62154	−	13.1794i	0.209222	−	1.05183i	−0.723250	−	0.690587i	$-0.757352\pi$
$157$	2.62154	−	13.1794i	0.209222	−	1.05183i	0.932472	−	0.361243i	$-0.117648\pi$
$158$	−23.7079	+	3.74153i	−1.88610	+	0.297660i
$159$	23.4182	−	7.19896i	1.85718	−	0.570915i
$160$	3.15578	−	4.69479i	0.249486	−	0.371156i
$161$	−1.64450			−0.129605
$162$	2.79389	−	12.4175i	0.219508	−	0.975611i
$163$	−7.06124	−	1.40457i	−0.553079	−	0.110014i	−0.0893646	−	0.995999i	$-0.528484\pi$
$163$	−7.06124	−	1.40457i	−0.553079	−	0.110014i	−0.463714	+	0.885985i	$0.653484\pi$
$164$	−0.124798	+	1.56359i	−0.00974506	+	0.122096i
$165$	1.32336	−	4.42161i	0.103023	−	0.344222i
$166$	0.0690839	−	1.73385i	0.00536195	−	0.134573i
$167$	−8.04625	−	19.4254i	−0.622638	−	1.50318i	−0.848595	−	0.529043i	$-0.822551\pi$
$167$	−8.04625	−	19.4254i	−0.622638	−	1.50318i	0.225957	−	0.974137i	$-0.427449\pi$
$168$	−3.48372	−	19.2791i	−0.268775	−	1.48741i
$169$	−0.644841	+	1.55678i	−0.0496031	+	0.119753i
$170$	1.51943	−	3.29111i	0.116535	−	0.252416i
$171$	−10.1103	−	9.96119i	−0.773157	−	0.761751i
$172$	18.4060	−	10.2811i	1.40344	−	0.783927i
$173$	−5.49247	−	8.22007i	−0.417585	−	0.624960i	0.561725	−	0.827324i	$-0.310138\pi$
$173$	−5.49247	−	8.22007i	−0.417585	−	0.624960i	−0.979310	+	0.202364i	$0.935138\pi$
$174$	12.9498	−	14.6661i	0.981724	−	1.11183i
$175$	2.82776	−	2.82776i	0.213759	−	0.213759i
$176$	7.81097	+	7.25250i	0.588774	+	0.546678i
$177$	−4.90959	+	9.26786i	−0.369027	+	0.696615i
$178$	4.61318	−	19.1686i	0.345773	−	1.43675i
$179$	0.194311	+	0.290807i	0.0145235	+	0.0217360i	0.838660	−	0.544655i	$-0.183339\pi$
$179$	0.194311	+	0.290807i	0.0145235	+	0.0217360i	−0.824137	+	0.566391i	$0.808339\pi$
$180$	−0.432914	+	5.98436i	−0.0322675	+	0.446048i
$181$	0.631934	+	3.17695i	0.0469713	+	0.236141i	0.997138	−	0.0756012i	$-0.0240876\pi$
$181$	0.631934	+	3.17695i	0.0469713	+	0.236141i	−0.950167	+	0.311742i	$0.899088\pi$
$182$	−7.49000	−	20.3372i	−0.555195	−	1.50749i
$183$	15.4535	+	1.46409i	1.14236	+	0.108228i
$184$	−0.756847	+	0.883182i	−0.0557955	+	0.0651091i
$185$	−2.87611	−	6.94355i	−0.211456	−	0.510500i
$186$	−8.10669	+	13.9322i	−0.594412	+	1.02156i
$187$	5.67908	+	3.79464i	0.415296	+	0.277492i
$188$	4.55046	−	8.90640i	0.331876	−	0.649566i
$189$	13.3607	+	15.9150i	0.971850	+	1.15765i
$190$	5.41071	+	3.93568i	0.392534	+	0.285525i
$191$	−15.0633			−1.08994			−0.544971	−	0.838455i	$-0.683459\pi$
$191$	−15.0633			−1.08994			−0.544971	+	0.838455i	$0.683459\pi$
$192$	−11.9572	−	7.00185i	−0.862935	−	0.505315i
$193$	12.4821			0.898478			0.449239	−	0.893412i	$-0.351695\pi$
$193$	12.4821			0.898478			0.449239	+	0.893412i	$0.351695\pi$
$194$	−6.93746	−	5.04623i	−0.498081	−	0.362298i
$195$	0.675118	+	6.60298i	0.0483462	+	0.472849i
$196$	16.0156	+	8.18270i	1.14397	+	0.584479i
$197$	0.171637	+	0.114684i	0.0122286	+	0.00817090i	0.561670	−	0.827362i	$-0.310159\pi$
$197$	0.171637	+	0.114684i	0.0122286	+	0.00817090i	−0.549441	+	0.835533i	$0.685159\pi$
$198$	−11.0109	−	2.56352i	−0.782510	−	0.182181i
$199$	2.33282	+	5.63193i	0.165369	+	0.399237i	0.984741	−	0.174026i	$-0.0556775\pi$
$199$	2.33282	+	5.63193i	0.165369	+	0.399237i	−0.819372	+	0.573262i	$0.805678\pi$
$200$	−0.217236	−	2.82007i	−0.0153609	−	0.199409i
$201$	0.103583	−	1.09332i	0.00730615	−	0.0771169i
$202$	−4.88785	−	13.2717i	−0.343908	−	0.933793i
$203$	6.23159	+	31.3283i	0.437372	+	2.19882i
$204$	−8.27686	−	3.21462i	−0.579496	−	0.225069i
$205$	0.435723	+	0.652105i	0.0304322	+	0.0455450i
$206$	3.65499	−	15.1871i	0.254655	−	1.05814i
$207$	0.231679	−	1.21172i	0.0161028	−	0.0842201i
$208$	−14.3692	−	5.33724i	−0.996327	−	0.370071i
$209$	−8.91435	+	8.91435i	−0.616618	+	0.616618i
$210$	−7.34287	−	6.48360i	−0.506706	−	0.447411i
$211$	−11.3350	−	16.9640i	−0.780334	−	1.16785i	−0.982089	−	0.188416i	$-0.939665\pi$
$211$	−11.3350	−	16.9640i	−0.780334	−	1.16785i	0.201756	−	0.979436i	$-0.435335\pi$
$212$	13.7957	+	24.6981i	0.947494	+	1.69627i
$213$	11.5150	−	6.21002i	0.788996	−	0.425504i
$214$	−7.63699	+	16.5418i	−0.522054	+	1.13078i
$215$	4.03400	−	9.73895i	0.275117	−	0.664191i
$216$	14.6962	+	0.149141i	0.999949	+	0.0101478i
$217$	−10.0707	−	24.3129i	−0.683646	−	1.65047i
$218$	−0.341798	+	8.57838i	−0.0231495	+	0.581001i
$219$	12.4385	+	3.72278i	0.840518	+	0.251562i
$220$	5.31251	+	0.424018i	0.358169	+	0.0285873i
$221$	−9.63374	−	1.91627i	−0.648036	−	0.128902i
$222$	−16.5384	+	8.08642i	−1.10999	+	0.542725i
$223$	−20.5232			−1.37434			−0.687168	−	0.726498i	$-0.741147\pi$
$223$	−20.5232			−1.37434			−0.687168	+	0.726498i	$0.741147\pi$
$224$	20.9239	−	8.59926i	1.39804	−	0.574562i
$225$	1.68520	+	2.48195i	0.112347	+	0.165464i
$226$	12.0856	−	1.90732i	0.803921	−	0.126873i
$227$	−4.13598	+	20.7930i	−0.274515	+	1.38008i	0.559726	+	0.828678i	$0.310906\pi$
$227$	−4.13598	+	20.7930i	−0.274515	+	1.38008i	−0.834240	+	0.551401i	$0.814094\pi$
$228$	8.79978	−	13.8259i	0.582780	−	0.915644i
$229$	14.0325	+	9.37625i	0.927297	+	0.619600i	0.924823	−	0.380397i	$-0.124213\pi$
$229$	14.0325	+	9.37625i	0.927297	+	0.619600i	0.00247357	+	0.999997i	$0.499213\pi$
$230$	−0.0231532	+	0.581095i	−0.00152668	+	0.0383163i
$231$	14.2240	−	11.7621i	0.935873	−	0.773888i
$232$	19.6929	+	11.0715i	1.29290	+	0.726881i
$233$	−13.4786	−	5.58301i	−0.883011	−	0.365755i	−0.105347	−	0.994435i	$-0.533595\pi$
$233$	−13.4786	−	5.58301i	−0.883011	−	0.365755i	−0.777664	+	0.628680i	$0.783595\pi$
$234$	16.0402	−	2.65374i	1.04858	−	0.173480i
$235$	−0.975601	−	4.90468i	−0.0636412	−	0.319946i
$236$	−11.6521	−	3.30016i	−0.758489	−	0.214822i
$237$	22.7922	+	18.5638i	1.48051	+	1.20585i
$238$	12.3643	−	7.56744i	0.801457	−	0.490524i
$239$	8.83587	+	8.83587i	0.571545	+	0.571545i	0.932560	−	0.361015i	$-0.117570\pi$
$239$	8.83587	+	8.83587i	0.571545	+	0.571545i	−0.361015	+	0.932560i	$0.617570\pi$
$240$	−6.86143	+	0.959562i	−0.442903	+	0.0619395i
$241$	−2.45694	+	2.45694i	−0.158265	+	0.158265i	−0.781798	−	0.623532i	$-0.785697\pi$
$241$	−2.45694	+	2.45694i	−0.158265	+	0.158265i	0.623532	+	0.781798i	$0.285697\pi$
$242$	1.29031	−	5.36146i	0.0829443	−	0.344648i
$243$	−13.6089	+	7.60247i	−0.873012	+	0.487698i
$244$	2.08706	+	17.8022i	0.133610	+	1.13967i
$245$	8.81967	−	1.75434i	0.563468	−	0.112081i
$246$	1.52805	−	1.16432i	0.0974247	−	0.0742344i
$247$	6.93799	−	16.7498i	0.441454	−	1.06576i
$248$	−17.6921	−	5.78100i	−1.12345	−	0.367094i
$249$	−1.63779	+	1.35431i	−0.103791	+	0.0858262i
$250$	−0.959395	−	1.03902i	−0.0606774	−	0.0657134i
$251$	1.04078	−	1.55764i	0.0656937	−	0.0983176i	−0.797168	−	0.603757i	$-0.793670\pi$
$251$	1.04078	−	1.55764i	0.0656937	−	0.0983176i	0.862862	+	0.505440i	$0.168670\pi$
$252$	−14.7353	+	18.9367i	−0.928235	+	1.19290i
$253$	−1.07473	−	0.213777i	−0.0675676	−	0.0134400i
$254$	−11.9546	−	8.69565i	−0.750100	−	0.545614i
$255$	−4.24362	+	1.30452i	−0.265746	+	0.0816925i
$256$	5.01156	−	15.1949i	0.313223	−	0.949680i
$257$			20.4881i			1.27801i	0.769203	+	0.639005i	$0.220654\pi$
$257$			20.4881i			1.27801i	−0.769203	+	0.639005i	$0.779346\pi$
$258$	−24.4224	−	8.38253i	−1.52047	−	0.521874i
$259$	5.86354	−	29.4780i	0.364342	−	1.83167i
$260$	−7.29172	+	2.36031i	−0.452213	+	0.146380i
$261$	−23.9615	+	0.178062i	−1.48318	+	0.0110217i
$262$	13.2551	−	12.2393i	0.818902	−	0.756145i
$263$	−16.0545	+	6.65000i	−0.989965	+	0.410057i	−0.818108	−	0.575065i	$-0.804977\pi$
$263$	−16.0545	+	6.65000i	−0.989965	+	0.410057i	−0.171857	+	0.985122i	$0.554977\pi$
$264$	0.229469	−	13.0523i	0.0141228	−	0.803313i
$265$	13.0682	+	5.41303i	0.802774	+	0.332520i
$266$	9.24698	+	25.1078i	0.566969	+	1.53946i
$267$	−21.2532	+	11.4618i	−1.30068	+	0.701452i
$268$	1.25949	−	0.147657i	0.0769354	−	0.00901960i
$269$	7.02472	−	4.69377i	0.428305	−	0.286184i	−0.322674	−	0.946510i	$-0.604582\pi$
$269$	7.02472	−	4.69377i	0.428305	−	0.286184i	0.750979	+	0.660326i	$0.229582\pi$
$270$	5.81177	−	4.49703i	0.353693	−	0.273681i
$271$	−11.2864	−	11.2864i	−0.685600	−	0.685600i	0.275656	−	0.961256i	$-0.411105\pi$
$271$	−11.2864	−	11.2864i	−0.685600	−	0.685600i	−0.961256	+	0.275656i	$0.911105\pi$
$272$	1.62630	−	10.1230i	0.0986087	−	0.613798i
$273$	−12.4254	+	23.4555i	−0.752019	+	1.41959i
$274$	−9.21041	−	15.0487i	−0.556421	−	0.909125i
$275$	2.21562	−	1.48043i	0.133607	−	0.0892732i
$276$	1.42416	−	0.0316845i	0.0857245	−	0.00190718i
$277$	−15.1495	+	3.01343i	−0.910248	+	0.181060i	−0.627938	−	0.778264i	$-0.716101\pi$
$277$	−15.1495	+	3.01343i	−0.910248	+	0.181060i	−0.282310	+	0.959323i	$0.591101\pi$
$278$	−7.06973	+	15.3131i	−0.424014	+	0.918421i
$279$	19.3332	−	3.99519i	1.15745	−	0.239186i
$280$	5.54318	−	9.85965i	0.331269	−	0.589227i
$281$	−0.127649	+	0.0528739i	−0.00761489	+	0.00315419i	−0.386488	−	0.922295i	$-0.626312\pi$
$281$	−0.127649	+	0.0528739i	−0.00761489	+	0.00315419i	0.378873	+	0.925449i	$0.376312\pi$
$282$	−11.8426	+	3.13032i	−0.705216	+	0.186408i
$283$	5.69258	−	8.51955i	0.338389	−	0.506435i	−0.622779	−	0.782397i	$-0.713997\pi$
$283$	5.69258	−	8.51955i	0.338389	−	0.506435i	0.961168	+	0.275963i	$0.0889966\pi$
$284$	9.79832	+	11.4981i	0.581423	+	0.682286i
$285$	−0.833485	−	8.15189i	−0.0493714	−	0.482877i
$286$	−2.25120	−	14.2646i	−0.133116	−	0.843482i
$287$			3.13638i			0.185135i
$288$	3.38841	+	16.6289i	0.199664	+	0.979864i
$289$			10.4300i			0.613528i
$290$	11.1578	−	1.76090i	0.655209	−	0.103403i
$291$	1.06867	+	10.4521i	0.0626467	+	0.612715i
$292$	−1.19281	+	14.9447i	−0.0698042	+	0.874575i
$293$	−4.43182	+	6.63269i	−0.258910	+	0.387486i	−0.938037	−	0.346535i	$-0.887358\pi$
$293$	−4.43182	+	6.63269i	−0.258910	+	0.387486i	0.679127	+	0.734020i	$0.262358\pi$
$294$	−5.62899	−	21.2955i	−0.328289	−	1.24198i
$295$	−5.59430	+	2.31723i	−0.325713	+	0.134915i
$296$	−13.1326	−	16.7157i	−0.763319	−	0.971578i
$297$	6.66275	+	12.1377i	0.386612	+	0.704303i
$298$	14.2250	+	6.56738i	0.824035	+	0.380438i
$299$	1.54557	−	0.307433i	0.0893825	−	0.0177793i
$300$	−2.39440	+	2.50337i	−0.138241	+	0.144532i
$301$	35.0510	−	23.4203i	2.02031	−	1.34993i
$302$	−26.7432	+	16.3679i	−1.53890	+	0.941868i
$303$	−8.10860	+	15.3067i	−0.465827	+	0.879345i
$304$	17.7399	+	6.58924i	1.01745	+	0.377919i
$305$	6.33713	+	6.33713i	0.362863	+	0.362863i
$306$	3.83402	+	10.1765i	0.219176	+	0.581750i
$307$	−11.0786	+	7.40246i	−0.632287	+	0.422481i	−0.829988	−	0.557782i	$-0.811653\pi$
$307$	−11.0786	+	7.40246i	−0.632287	+	0.422481i	0.197701	+	0.980262i	$0.436653\pi$
$308$	16.7225	+	13.2130i	0.952854	+	0.752880i
$309$	−16.8388	+	9.08112i	−0.957925	+	0.516607i
$310$	−8.73290	+	3.21625i	−0.495995	+	0.182671i
$311$	6.12917	+	2.53878i	0.347553	+	0.143961i	0.549630	−	0.835409i	$-0.314769\pi$
$311$	6.12917	+	2.53878i	0.347553	+	0.143961i	−0.202076	+	0.979370i	$0.564769\pi$
$312$	6.87829	+	17.4680i	0.389406	+	0.988930i
$313$	−5.36304	+	2.22145i	−0.303137	+	0.125564i	−0.529067	−	0.848580i	$-0.677458\pi$
$313$	−5.36304	+	2.22145i	−0.303137	+	0.125564i	0.225930	+	0.974144i	$0.427458\pi$
$314$	−12.8920	−	13.9619i	−0.727535	−	0.787917i
$315$	0.0891503	+	11.9968i	0.00502305	+	0.675945i
$316$	−15.4433	+	30.2264i	−0.868752	+	1.70037i
$317$	−2.54258	+	12.7824i	−0.142806	+	0.717933i	0.841331	+	0.540520i	$0.181773\pi$
$317$	−2.54258	+	12.7824i	−0.142806	+	0.717933i	−0.984137	+	0.177412i	$0.943227\pi$
$318$	11.2481	−	32.7713i	0.630763	−	1.83772i
$319$			21.2840i			1.19168i
$320$	−2.74401	−	7.51468i	−0.153395	−	0.420083i
$321$	21.3294	−	6.55683i	1.19049	−	0.365967i
$322$	−1.36804	+	1.88075i	−0.0762378	+	0.104810i
$323$	11.8936	+	2.36578i	0.661778	+	0.131636i
$324$	−11.8772	−	13.5252i	−0.659846	−	0.751401i
$325$	−2.12901	+	3.18628i	−0.118096	+	0.176743i
$326$	−7.48050	+	6.90724i	−0.414307	+	0.382556i
$327$	8.10310	−	6.70058i	0.448103	−	0.370543i
$328$	1.68440	+	1.44345i	0.0930054	+	0.0797014i
$329$	7.65304	−	18.4761i	0.421926	−	1.01862i
$330$	−3.95594	−	5.19175i	−0.217767	−	0.285797i
$331$	−5.23461	+	1.04123i	−0.287720	+	0.0572311i	−0.336840	−	0.941562i	$-0.609358\pi$
$331$	−5.23461	+	1.04123i	−0.287720	+	0.0572311i	0.0491202	+	0.998793i	$0.484358\pi$
$332$	−1.92547	−	1.52138i	−0.105674	−	0.0834964i
$333$	20.8942	+	8.47331i	1.14499	+	0.464335i
$334$	−28.9096	−	6.95751i	−1.58187	−	0.380698i
$335$	0.448345	−	0.448345i	0.0244957	−	0.0244957i
$336$	−24.9468	−	12.0538i	−1.36096	−	0.657589i
$337$	2.81400	+	2.81400i	0.153288	+	0.153288i	0.779585	−	0.626297i	$-0.215430\pi$
$337$	2.81400	+	2.81400i	0.153288	+	0.153288i	−0.626297	+	0.779585i	$0.715430\pi$
$338$	1.24400	+	2.03255i	0.0676647	+	0.110556i
$339$	−11.6188	−	9.46325i	−0.631045	−	0.513973i
$340$	−2.49992	−	4.47554i	−0.135577	−	0.242720i
$341$	−3.42096	−	17.1983i	−0.185255	−	0.931341i
$342$	−19.8029	+	3.27624i	−1.07082	+	0.177159i
$343$	7.36143	+	3.04920i	0.397480	+	0.164641i
$344$	3.55356	−	29.6029i	0.191595	−	1.59608i
$345$	0.548900	−	0.453894i	0.0295518	−	0.0244368i
$346$	−13.9701	−	0.556627i	−0.751037	−	0.0299244i
$347$	−8.86303	−	5.92208i	−0.475792	−	0.317914i	0.294449	−	0.955667i	$-0.404864\pi$
$347$	−8.86303	−	5.92208i	−0.475792	−	0.317914i	−0.770241	+	0.637753i	$0.779864\pi$
$348$	−6.00025	−	27.0107i	−0.321647	−	1.44793i
$349$	0.280506	−	1.41020i	0.0150152	−	0.0754863i	−0.972551	−	0.232689i	$-0.925248\pi$
$349$	0.280506	−	1.41020i	0.0150152	−	0.0754863i	0.987566	+	0.157203i	$0.0502476\pi$
$350$	−0.881628	−	5.58638i	−0.0471250	−	0.298605i
$351$	−15.5322	−	12.4598i	−0.829047	−	0.665056i
$352$	14.7923	−	2.89986i	0.788430	−	0.154563i
$353$	23.3031			1.24030			0.620148	−	0.784485i	$-0.287072\pi$
$353$	23.3031			1.24030			0.620148	+	0.784485i	$0.287072\pi$
$354$	6.51509	+	13.3247i	0.346273	+	0.708201i
$355$	7.40823	+	1.47359i	0.393188	+	0.0782100i
$356$	−18.0847	−	21.2220i	−0.958489	−	1.12476i
$357$	−17.0088	−	5.09062i	−0.900199	−	0.269424i
$358$	0.494231	+	0.0196922i	0.0261209	+	0.00104076i
$359$	4.26567	+	10.2982i	0.225134	+	0.543520i	0.995573	−	0.0939929i	$-0.0299631\pi$
$359$	4.26567	+	10.2982i	0.225134	+	0.543520i	−0.770439	+	0.637513i	$0.779963\pi$
$360$	6.48396	+	5.47342i	0.341735	+	0.288474i
$361$	−1.29450	+	3.12520i	−0.0681316	+	0.164484i
$362$	4.15905	+	1.92014i	0.218595	+	0.100920i
$363$	−5.94454	+	3.20588i	−0.312008	+	0.168265i
$364$	−29.4897	−	8.35218i	−1.54568	−	0.437773i
$365$	4.16463	+	6.23281i	0.217987	+	0.326240i
$366$	14.5300	−	16.4557i	0.759495	−	0.860151i
$367$	−15.5181	+	15.5181i	−0.810037	+	0.810037i	−0.984639	−	0.174602i	$-0.944136\pi$
$367$	−15.5181	+	15.5181i	−0.810037	+	0.810037i	0.174602	+	0.984639i	$0.444136\pi$
$368$	0.380452	+	1.60029i	0.0198324	+	0.0834207i
$369$	−2.31098	−	0.441856i	−0.120305	−	0.0230021i
$370$	−10.3337	−	2.48694i	−0.537223	−	0.129290i
$371$	31.4266	+	47.0332i	1.63159	+	2.44184i
$372$	9.18984	+	20.8613i	0.476471	+	1.08161i
$373$	1.20049	+	6.03525i	0.0621588	+	0.312493i	0.999339	−	0.0363522i	$-0.0115738\pi$
$373$	1.20049	+	6.03525i	0.0621588	+	0.312493i	−0.937180	+	0.348845i	$0.886574\pi$
$374$	9.06414	−	3.33824i	0.468696	−	0.172616i
$375$	−0.163365	+	1.72433i	−0.00843614	+	0.0890440i
$376$	−6.40046	−	12.6133i	−0.330078	−	0.650481i
$377$	−11.7134	−	28.2787i	−0.603271	−	1.45642i
$378$	29.3160	−	2.04070i	1.50785	−	0.104962i
$379$	6.39024	+	4.26982i	0.328245	+	0.219326i	0.708762	−	0.705448i	$-0.249254\pi$
$379$	6.39024	+	4.26982i	0.328245	+	0.219326i	−0.380517	+	0.924774i	$0.624254\pi$
$380$	9.00219	−	2.91398i	0.461803	−	0.149484i
$381$	1.84153	+	18.0111i	0.0943446	+	0.922737i
$382$	−12.5309	+	17.2273i	−0.641139	+	0.881426i
$383$	−15.0433			−0.768678			−0.384339	−	0.923192i	$-0.625571\pi$
$383$	−15.0433			−0.768678			−0.384339	+	0.923192i	$0.625571\pi$
$384$	−17.9548	+	7.85023i	−0.916251	+	0.400605i
$385$	10.6563			0.543095
$386$	10.3837	−	14.2753i	0.528514	−	0.726592i
$387$	12.3188	+	29.1261i	0.626199	+	1.48056i
$388$	−11.5424	+	3.73623i	−0.585975	+	0.189678i
$389$	−10.7626	−	7.19136i	−0.545687	−	0.364616i	0.251963	−	0.967737i	$-0.418924\pi$
$389$	−10.7626	−	7.19136i	−0.545687	−	0.364616i	−0.797650	+	0.603121i	$0.793924\pi$
$390$	8.11321	+	4.72083i	0.410828	+	0.239048i
$391$	0.403366	+	0.973812i	0.0203991	+	0.0492478i
$392$	22.6814	−	11.5094i	1.14559	−	0.581313i
$393$	−21.9978	−	2.08410i	−1.10964	−	0.105129i
$394$	0.273942	−	0.100891i	0.0138010	−	0.00508279i
$395$	3.31098	+	16.6454i	0.166594	+	0.837522i
$396$	−12.0916	+	10.4602i	−0.607626	+	0.525644i
$397$	−17.2070	−	25.7520i	−0.863592	−	1.29246i	−0.954989	−	0.296643i	$-0.904133\pi$
$397$	−17.2070	−	25.7520i	−0.863592	−	1.29246i	0.0913961	−	0.995815i	$-0.470867\pi$
$398$	8.38167	+	2.01717i	0.420135	+	0.101111i
$399$	15.3401	−	28.9576i	0.767966	−	1.44969i
$400$	−3.40593	−	2.09754i	−0.170296	−	0.104877i
$401$	20.5543	−	20.5543i	1.02643	−	1.02643i	0.0267926	−	0.999641i	$-0.491471\pi$
$401$	20.5543	−	20.5543i	1.02643	−	1.02643i	0.999641	−	0.0267926i	$-0.00852937\pi$
$402$	−1.16422	−	1.02798i	−0.0580661	−	0.0512711i
$403$	14.0101	+	20.9676i	0.697891	+	1.04447i
$404$	−19.2445	−	5.45049i	−0.957448	−	0.271172i
$405$	−8.85219	−	1.62444i	−0.439869	−	0.0807189i
$406$	41.0130	+	18.9348i	2.03544	+	0.939717i
$407$	7.66398	−	18.5025i	0.379889	−	0.917134i
$408$	−10.5619	+	6.79174i	−0.522890	+	0.336241i
$409$	1.73134	+	4.17981i	0.0856090	+	0.206678i	0.960886	−	0.276943i	$-0.0893212\pi$
$409$	1.73134	+	4.17981i	0.0856090	+	0.206678i	−0.875277	+	0.483621i	$0.839321\pi$
$410$	1.10826	+	0.0441577i	0.0547330	+	0.00218079i
$411$	−6.19584	+	20.7015i	−0.305618	+	1.02113i
$412$	−14.3284	−	16.8140i	−0.705910	−	0.828369i
$413$	−23.7499	−	4.72415i	−1.16866	−	0.232460i
$414$	−1.19307	−	1.27297i	−0.0586359	−	0.0625632i
$415$	−1.22699			−0.0602307
$416$	−18.0576	+	11.9936i	−0.885345	+	0.588033i
$417$	19.7451	−	6.06980i	0.966920	−	0.297239i
$418$	2.77928	+	17.6107i	0.135939	+	0.861369i
$419$	−2.18148	+	10.9670i	−0.106572	+	0.535774i	0.890206	+	0.455559i	$0.150561\pi$
$419$	−2.18148	+	10.9670i	−0.106572	+	0.535774i	−0.996778	+	0.0802148i	$0.974439\pi$
$420$	−13.5235	+	3.00415i	−0.659878	+	0.146588i
$421$	−31.3909	−	20.9747i	−1.52990	−	1.02225i	−0.982692	−	0.185248i	$-0.940691\pi$
$421$	−31.3909	−	20.9747i	−1.52990	−	1.02225i	−0.547206	−	0.836998i	$-0.684309\pi$
$422$	−28.8306	−	1.14873i	−1.40345	−	0.0559192i
$423$	12.5355	+	8.24191i	0.609499	+	0.400735i
$424$	39.7227	+	4.76835i	1.92911	+	0.231572i
$425$	−2.36809	−	0.980896i	−0.114869	−	0.0475804i
$426$	2.47702	−	18.3353i	0.120012	−	0.888350i
$427$	6.99199	+	35.1511i	0.338366	+	1.70108i
$428$	12.5652	+	22.4951i	0.607360	+	1.08734i
$429$	−11.1694	+	13.7136i	−0.539266	+	0.662099i
$430$	−7.78224	−	12.7152i	−0.375293	−	0.613183i
$431$	7.26035	+	7.26035i	0.349719	+	0.349719i	0.860005	−	0.510286i	$-0.170460\pi$
$431$	7.26035	+	7.26035i	0.349719	+	0.349719i	−0.510286	+	0.860005i	$0.670460\pi$
$432$	12.3961	−	16.6834i	0.596409	−	0.802681i
$433$	−8.48094	+	8.48094i	−0.407568	+	0.407568i	−0.880890	−	0.473322i	$-0.843055\pi$
$433$	−8.48094	+	8.48094i	−0.407568	+	0.407568i	0.473322	+	0.880890i	$0.343055\pi$
$434$	−36.1834	−	8.70805i	−1.73686	−	0.418000i
$435$	−10.7268	−	8.73678i	−0.514312	−	0.418896i
$436$	9.52644	+	7.52714i	0.456234	+	0.360485i
$437$	−1.90812	+	0.379549i	−0.0912779	+	0.0181563i
$438$	14.6050	−	11.1286i	0.697856	−	0.531743i
$439$	10.2537	−	24.7545i	0.489380	−	1.18147i	−0.465653	−	0.884968i	$-0.654180\pi$
$439$	10.2537	−	24.7545i	0.489380	−	1.18147i	0.955033	−	0.296501i	$-0.0958197\pi$
$440$	4.90434	−	5.72298i	0.233805	−	0.272832i
$441$	−14.8207	+	22.5416i	−0.705749	+	1.07341i
$442$	−10.2057	+	9.42363i	−0.485438	+	0.448236i
$443$	8.89410	−	13.3110i	0.422572	−	0.632423i	−0.557708	−	0.830037i	$-0.688319\pi$
$443$	8.89410	−	13.3110i	0.422572	−	0.632423i	0.980280	+	0.197614i	$0.0633192\pi$
$444$	−4.50996	+	25.6414i	−0.214033	+	1.21689i
$445$	−13.6733	−	2.71980i	−0.648179	−	0.128931i
$446$	−17.0730	+	23.4716i	−0.808430	+	1.11141i
$447$	−5.63851	−	18.3421i	−0.266692	−	0.867549i
$448$	7.57170	−	31.0835i	0.357729	−	1.46856i
$449$		−	4.68780i		−	0.221231i	−0.993863	−	0.110615i	$-0.964718\pi$
$449$		−	4.68780i		−	0.221231i	0.993863	−	0.110615i	$-0.0352822\pi$
$450$	4.24042	+	0.137404i	0.199895	+	0.00647728i
$451$	−0.407714	+	2.04971i	−0.0191985	+	0.0965173i
$452$	7.87251	−	15.4085i	0.370292	−	0.724755i
$453$	36.7890	+	11.0107i	1.72850	+	0.517328i
$454$	20.3395	+	22.0276i	0.954580	+	1.03381i
$455$	−14.1583	+	5.86455i	−0.663751	+	0.274935i
$456$	−8.49178	−	21.5656i	−0.397664	−	1.00990i
$457$	24.0720	+	9.97094i	1.12604	+	0.466421i	0.866433	−	0.499294i	$-0.166407\pi$
$457$	24.0720	+	9.97094i	1.12604	+	0.466421i	0.259607	+	0.965714i	$0.416407\pi$
$458$	22.3968	−	8.24853i	1.04653	−	0.385428i
$459$	6.14712	−	11.8154i	0.286923	−	0.551495i
$460$	0.645316	+	0.509884i	0.0300880	+	0.0237735i
$461$	29.9097	−	19.9850i	1.39303	−	0.930795i	0.393097	−	0.919497i	$-0.371404\pi$
$461$	29.9097	−	19.9850i	1.39303	−	0.930795i	0.999936	−	0.0112977i	$-0.00359624\pi$
$462$	−1.61907	−	26.0522i	−0.0753258	−	1.21206i
$463$	5.45569	+	5.45569i	0.253548	+	0.253548i	0.822423	−	0.568876i	$-0.192622\pi$
$463$	5.45569	+	5.45569i	0.253548	+	0.253548i	−0.568876	+	0.822423i	$0.692622\pi$
$464$	29.0443	−	13.3118i	1.34835	−	0.617984i
$465$	10.0719	+	5.33554i	0.467075	+	0.247430i
$466$	−17.5977	+	10.7705i	−0.815199	+	0.498935i
$467$	29.4196	−	19.6575i	1.36138	−	0.909643i	0.361634	−	0.932320i	$-0.382219\pi$
$467$	29.4196	−	19.6575i	1.36138	−	0.909643i	0.999743	+	0.0226773i	$0.00721902\pi$
$468$	10.3087	−	20.5522i	0.476518	−	0.950026i
$469$	2.48690	−	0.494676i	0.114835	−	0.0228420i
$470$	−6.42089	−	2.96438i	−0.296173	−	0.136737i
$471$	−2.19523	+	23.1708i	−0.101151	+	1.06766i
$472$	−13.4675	+	10.5807i	−0.619893	+	0.487018i
$473$	25.9514	−	10.7494i	1.19325	−	0.494258i
$474$	40.1912	−	10.6236i	1.84604	−	0.487959i
$475$	2.62842	−	3.93371i	0.120600	−	0.180491i
$476$	1.63108	−	20.4358i	0.0747606	−	0.936674i
$477$	−39.0829	+	16.5300i	−1.78948	+	0.756856i
$478$	17.4557	−	2.75481i	0.798405	−	0.126002i
$479$		−	9.63326i		−	0.440155i	−0.975482	−	0.220077i	$-0.929369\pi$
$479$		−	9.63326i		−	0.440155i	0.975482	−	0.220077i	$-0.0706310\pi$
$480$	−4.61052	+	8.64541i	−0.210440	+	0.394607i
$481$			28.8008i			1.31320i
$482$	0.766016	+	4.85381i	0.0348911	+	0.221085i
$483$	2.83359	−	0.289718i	0.128933	−	0.0131826i
$484$	−5.05831	−	5.93581i	−0.229923	−	0.269809i
$485$	−3.37009	+	5.04370i	−0.153028	+	0.229023i
$486$	−2.62642	+	21.8884i	−0.119137	+	0.992878i
$487$	33.0636	−	13.6954i	1.49825	−	0.620597i	0.525158	−	0.851004i	$-0.324006\pi$
$487$	33.0636	−	13.6954i	1.49825	−	0.620597i	0.973094	+	0.230408i	$0.0740061\pi$
$488$	22.0959	+	12.4225i	1.00023	+	0.562340i
$489$	12.4144	+	1.17616i	0.561401	+	0.0531878i
$490$	5.33059	−	11.5461i	0.240812	−	0.521601i
$491$	−11.3877	+	2.26515i	−0.513919	+	0.102225i	−0.445235	−	0.895414i	$-0.646880\pi$
$491$	−11.3877	+	2.26515i	−0.513919	+	0.102225i	−0.0686837	+	0.997638i	$0.521880\pi$
$492$	−0.0604284	−	2.71615i	−0.00272432	−	0.122454i
$493$	17.0230	−	11.3744i	0.766676	−	0.512277i
$494$	−13.3845	−	21.8686i	−0.602197	−	0.983917i
$495$	−1.50127	+	7.85187i	−0.0674769	+	0.352915i
$496$	−21.3294	+	15.4247i	−0.957716	+	0.692589i
$497$	21.3591	+	21.3591i	0.958087	+	0.958087i
$498$	0.186423	+	2.99972i	0.00835383	+	0.134420i
$499$	31.1292	−	20.7998i	1.39353	−	0.931129i	0.393603	−	0.919281i	$-0.371229\pi$
$499$	31.1292	−	20.7998i	1.39353	−	0.931129i	0.999930	−	0.0118479i	$-0.00377138\pi$
$500$	−1.98640	+	0.232877i	−0.0888343	+	0.0104146i
$501$	17.2865	+	32.0537i	0.772303	+	1.43205i
$502$	−0.915605	−	2.48609i	−0.0408654	−	0.110960i
$503$	−36.8119	−	15.2480i	−1.64136	−	0.679875i	−0.644929	−	0.764243i	$-0.723113\pi$
$503$	−36.8119	−	15.2480i	−1.64136	−	0.679875i	−0.996435	+	0.0843677i	$0.973113\pi$
$504$	9.39916	+	32.6054i	0.418672	+	1.45236i
$505$	−9.23946	+	3.82711i	−0.411151	+	0.170304i
$506$	−1.13854	+	1.05129i	−0.0506143	+	0.0467355i
$507$	0.836840	−	2.79605i	0.0371654	−	0.124177i
$508$	−19.8898	+	6.43826i	−0.882467	+	0.285652i
$509$	−4.31697	+	21.7029i	−0.191346	+	0.961962i	0.759077	+	0.651001i	$0.225651\pi$
$509$	−4.31697	+	21.7029i	−0.191346	+	0.961962i	−0.950423	+	0.310961i	$0.899349\pi$
$510$	−2.03827	+	5.93848i	−0.0902562	+	0.262960i
$511$			29.9775i			1.32613i
$512$	−13.2088	−	18.3720i	−0.583750	−	0.811933i
$513$	19.1757	+	15.3826i	0.846628	+	0.679159i
$514$	23.4314	+	17.0437i	1.03352	+	0.751767i
$515$	−10.8333	−	2.15488i	−0.477372	−	0.0949552i
$516$	−29.9035	+	20.9577i	−1.31643	+	0.922611i
$517$	7.40328	−	11.0798i	0.325596	−	0.487288i
$518$	−28.8351	−	31.2283i	−1.26694	−	1.37209i
$519$	10.9121	+	13.1961i	0.478987	+	0.579245i
$520$	−3.36649	+	10.3028i	−0.147630	+	0.451807i
$521$	9.57846	−	23.1245i	0.419640	−	1.01310i	−0.562812	−	0.826585i	$-0.690281\pi$
$521$	9.57846	−	23.1245i	0.419640	−	1.01310i	0.982452	−	0.186516i	$-0.0597195\pi$
$522$	−19.7296	+	27.5521i	−0.863543	+	1.20592i
$523$	9.35382	−	1.86059i	0.409014	−	0.0813580i	0.0137049	−	0.999906i	$-0.495637\pi$
$523$	9.35382	−	1.86059i	0.409014	−	0.0813580i	0.395309	+	0.918548i	$0.370637\pi$
$524$	−2.97089	−	25.3410i	−0.129784	−	1.10703i
$525$	−4.37425	+	5.37060i	−0.190908	+	0.234392i
$526$	−5.75019	+	23.8930i	−0.250720	+	1.04179i
$527$	−11.9270	+	11.9270i	−0.519549	+	0.519549i
$528$	−14.7365	−	11.1205i	−0.641325	−	0.483956i
$529$	16.1439	+	16.1439i	0.701908	+	0.701908i
$530$	17.0620	−	10.4426i	0.741124	−	0.453598i
$531$	6.82680	−	16.8341i	0.296258	−	0.730537i
$532$	36.4073	+	10.3114i	1.57846	+	0.447057i
$533$	−0.586333	−	2.94770i	−0.0253969	−	0.127679i
$534$	−4.57182	+	33.8415i	−0.197842	+	1.46446i
$535$	11.9026	+	4.93020i	0.514593	+	0.213151i
$536$	0.878880	−	1.56326i	0.0379618	−	0.0675226i
$537$	−0.386044	−	0.466848i	−0.0166590	−	0.0201460i
$538$	0.475683	−	11.9386i	0.0205081	−	0.514709i
$539$	19.9238	+	13.3127i	0.858181	+	0.573418i
$540$	−0.308348	−	10.3877i	−0.0132692	−	0.447017i
$541$	8.61286	−	43.2998i	0.370296	−	1.86160i	−0.123963	−	0.992287i	$-0.539560\pi$
$541$	8.61286	−	43.2998i	0.370296	−	1.86160i	0.494259	−	0.869315i	$-0.335440\pi$
$542$	−22.2968	+	3.51883i	−0.957732	+	0.151147i
$543$	−1.64856	−	5.36277i	−0.0707465	−	0.230138i
$544$	−10.2244	−	10.2811i	−0.438369	−	0.440800i
$545$	6.07064			0.260038
$546$	16.4886	+	33.7228i	0.705649	+	1.44320i
$547$	0.367230	+	0.0730466i	0.0157016	+	0.00312325i	0.202935	−	0.979192i	$-0.434952\pi$
$547$	0.367230	+	0.0730466i	0.0157016	+	0.00312325i	−0.187233	+	0.982315i	$0.559952\pi$
$548$	−24.8726	−	1.98521i	−1.06251	−	0.0848040i
$549$	−26.8854	+	0.199789i	−1.14744	+	0.00852680i
$550$	0.150032	−	3.76547i	0.00639738	−	0.160560i
$551$	14.4611	+	34.9122i	0.616064	+	1.48731i
$552$	1.14851	−	1.65512i	0.0488836	−	0.0704466i
$553$	−25.9728	+	62.7038i	−1.10447	+	2.66644i
$554$	−9.15635	+	19.8328i	−0.389016	+	0.842615i
$555$	6.17901	+	11.4575i	0.262284	+	0.486344i
$556$	11.6319	+	20.8242i	0.493300	+	0.883142i
$557$	5.58006	+	8.35115i	0.236435	+	0.353849i	0.930645	−	0.365922i	$-0.119246\pi$
$557$	5.58006	+	8.35115i	0.236435	+	0.353849i	−0.694211	+	0.719772i	$0.744246\pi$
$558$	11.5139	−	25.4342i	0.487422	−	1.07672i
$559$	−28.5640	+	28.5640i	−1.20813	+	1.20813i
$560$	−6.66482	−	14.5416i	−0.281640	−	0.614497i
$561$	−10.4540	−	5.53792i	−0.441367	−	0.233811i
$562$	−0.0457195	+	0.189972i	−0.00192856	+	0.00801350i
$563$	0.159428	+	0.238600i	0.00671907	+	0.0100558i	0.834814	−	0.550532i	$-0.185575\pi$
$563$	0.159428	+	0.238600i	0.00671907	+	0.0100558i	−0.828095	+	0.560588i	$0.810575\pi$
$564$	−6.27167	+	16.1480i	−0.264085	+	0.679954i
$565$	−1.68784	−	8.48533i	−0.0710079	−	0.356981i
$566$	−5.00791	−	13.5977i	−0.210498	−	0.571554i
$567$	−25.8253	−	25.0688i	−1.08456	−	1.05279i
$568$	21.3010	−	1.64086i	0.893772	−	0.0688492i
$569$	10.0631	+	24.2944i	0.421865	+	1.01847i	0.981797	+	0.189934i	$0.0608273\pi$
$569$	10.0631	+	24.2944i	0.421865	+	1.01847i	−0.559932	+	0.828539i	$0.689173\pi$
$570$	−10.0164	−	5.82823i	−0.419540	−	0.244118i
$571$	−25.0098	−	16.7110i	−1.04663	−	0.699333i	−0.0915823	−	0.995798i	$-0.529192\pi$
$571$	−25.0098	−	16.7110i	−1.04663	−	0.699333i	−0.955044	+	0.296464i	$0.904192\pi$
$572$	−18.1866	−	9.29190i	−0.760421	−	0.388514i
$573$	25.9551	−	2.65376i	1.08429	−	0.110862i
$574$	3.58696	+	2.60911i	0.149717	+	0.108902i
$575$	0.411222			0.0171491
$576$	21.8366	+	9.95813i	0.909857	+	0.414922i
$577$	10.4729			0.435992			0.217996	−	0.975950i	$-0.430048\pi$
$577$	10.4729			0.435992			0.217996	+	0.975950i	$0.430048\pi$
$578$	11.9284	+	8.67656i	0.496155	+	0.360897i
$579$	−21.5074	+	2.19901i	−0.893818	+	0.0913879i
$580$	7.26815	−	14.2256i	0.301794	−	0.590687i
$581$	−4.07986	−	2.72608i	−0.169261	−	0.113097i
$582$	12.8427	+	7.47279i	0.532349	+	0.309757i
$583$	14.4241	+	34.8229i	0.597386	+	1.44222i
$584$	16.0995	+	13.7965i	0.666200	+	0.570904i
$585$	−2.32655	−	11.2584i	−0.0961909	−	0.465480i
$586$	3.89879	+	10.5862i	0.161057	+	0.437310i
$587$	−6.32636	−	31.8048i	−0.261117	−	1.31272i	−0.859345	−	0.511397i	$-0.829128\pi$
$587$	−6.32636	−	31.8048i	−0.261117	−	1.31272i	0.598228	−	0.801326i	$-0.295872\pi$
$588$	−29.0376	−	11.2778i	−1.19749	−	0.465089i
$589$	−17.2965	−	25.8861i	−0.712691	−	1.06662i
$590$	−2.00369	+	8.32567i	−0.0824905	+	0.342762i
$591$	−0.315946	−	0.167371i	−0.0129963	−	0.00688470i
$592$	−30.0419	+	1.11378i	−1.23472	+	0.0457762i
$593$	−2.12596	+	2.12596i	−0.0873026	+	0.0873026i	−0.749409	−	0.662107i	$-0.769662\pi$
$593$	−2.12596	+	2.12596i	−0.0873026	+	0.0873026i	0.662107	+	0.749409i	$0.269662\pi$
$594$	19.4241	+	2.47728i	0.796982	+	0.101644i
$595$	−5.69482	−	8.52290i	−0.233465	−	0.349405i
$596$	19.3445	−	10.8053i	0.792381	−	0.442604i
$597$	−5.01181	−	9.29321i	−0.205120	−	0.380346i
$598$	0.934138	−	2.02336i	0.0381997	−	0.0827412i
$599$	10.6654	−	25.7485i	0.435775	−	1.05205i	−0.541618	−	0.840625i	$-0.682188\pi$
$599$	10.6654	−	25.7485i	0.435775	−	1.05205i	0.977393	−	0.211430i	$-0.0678120\pi$
$600$	0.871136	+	4.82090i	0.0355640	+	0.196813i
$601$	−6.84468	−	16.5245i	−0.279200	−	0.674049i	0.720614	−	0.693337i	$-0.243860\pi$
$601$	−6.84468	−	16.5245i	−0.279200	−	0.674049i	−0.999814	+	0.0192877i	$0.993860\pi$
$602$	2.37350	−	59.5696i	0.0967366	−	2.42788i
$603$	0.0141349	+	1.90212i	0.000575618	+	0.0774601i
$604$	−3.52794	+	44.2015i	−0.143550	+	1.79853i
$605$	−3.82444	−	0.760729i	−0.155486	−	0.0309280i
$606$	10.7602	+	22.0069i	0.437104	+	0.893970i
$607$	−13.3084			−0.540170			−0.270085	−	0.962837i	$-0.587052\pi$
$607$	−13.3084			−0.540170			−0.270085	+	0.962837i	$0.587052\pi$
$608$	22.2935	−	14.8070i	0.904120	−	0.600503i
$609$	−16.2567	−	52.8830i	−0.658754	−	2.14293i
$610$	12.5193	−	1.97576i	0.506892	−	0.0799964i
$611$	−3.73861	+	18.7953i	−0.151248	+	0.760375i
$612$	14.8279	+	4.08085i	0.599383	+	0.164958i
$613$	−37.8947	−	25.3204i	−1.53055	−	1.02268i	−0.982505	−	0.186235i	$-0.940372\pi$
$613$	−37.8947	−	25.3204i	−1.53055	−	1.02268i	−0.548047	−	0.836448i	$-0.684628\pi$
$614$	−0.750191	+	18.8281i	−0.0302752	+	0.759842i
$615$	−0.865663	−	1.04686i	−0.0349069	−	0.0422134i
$616$	29.0225	−	8.13321i	1.16935	−	0.327696i
$617$	−27.4418	−	11.3668i	−1.10476	−	0.457608i	−0.245632	−	0.969363i	$-0.578996\pi$
$617$	−27.4418	−	11.3668i	−1.10476	−	0.457608i	−0.859132	+	0.511755i	$0.828996\pi$
$618$	−3.62222	+	26.8124i	−0.145707	+	1.07855i
$619$	2.62525	+	13.1980i	0.105518	+	0.530474i	0.996999	+	0.0774158i	$0.0246669\pi$
$619$	2.62525	+	13.1980i	0.105518	+	0.530474i	−0.891481	+	0.453058i	$0.850333\pi$
$620$	−3.58648	+	12.6631i	−0.144036	+	0.508560i
$621$	−0.185725	+	2.12869i	−0.00745288	+	0.0854212i
$622$	8.00229	−	4.89772i	0.320862	−	0.196381i
$623$	−39.4224	−	39.4224i	−1.57943	−	1.57943i
$624$	25.6994	+	6.66494i	1.02880	+	0.266811i
$625$	−0.707107	+	0.707107i	−0.0282843	+	0.0282843i
$626$	−1.92086	+	7.98150i	−0.0767730	+	0.319005i
$627$	13.7896	−	16.9305i	0.550702	−	0.676139i
$628$	−26.6924	+	3.12931i	−1.06514	+	0.124873i
$629$	−18.8940	+	3.75825i	−0.753353	+	0.149851i
$630$	13.7945	+	9.87805i	0.549586	+	0.393551i
$631$	−5.79808	+	13.9978i	−0.230818	+	0.557243i	−0.996274	−	0.0862446i	$-0.972513\pi$
$631$	−5.79808	+	13.9978i	−0.230818	+	0.557243i	0.765456	+	0.643488i	$0.222513\pi$
$632$	21.7218	+	42.8069i	0.864046	+	1.70277i
$633$	22.5196	+	27.2332i	0.895073	+	1.08242i
$634$	12.5036	+	13.5414i	0.496583	+	0.537797i
$635$	−5.80734	+	8.69129i	−0.230457	+	0.344903i
$636$	−28.1221	−	40.1260i	−1.11511	−	1.59110i
$637$	−33.7979	−	6.72283i	−1.33912	−	0.266368i
$638$	24.3418	+	17.7059i	0.963700	+	0.700984i
$639$	−18.7471	+	12.7289i	−0.741624	+	0.503549i
$640$	−10.8770	−	3.11314i	−0.429950	−	0.123058i
$641$			22.1086i			0.873236i	0.899647	+	0.436618i	$0.143824\pi$
$641$			22.1086i			0.873236i	−0.899647	+	0.436618i	$0.856176\pi$
$642$	10.2448	−	29.8481i	0.404330	−	1.17801i
$643$	8.26126	−	41.5321i	0.325792	−	1.63787i	−0.376814	−	0.926289i	$-0.622980\pi$
$643$	8.26126	−	41.5321i	0.325792	−	1.63787i	0.702606	−	0.711579i	$-0.252020\pi$
$644$	1.01290	+	3.12915i	0.0399137	+	0.123306i
$645$	−5.23511	+	17.4915i	−0.206132	+	0.688729i
$646$	12.5998	−	11.6342i	0.495732	−	0.457742i
$647$	22.5213	−	9.32864i	0.885405	−	0.366747i	0.106814	−	0.994279i	$-0.465935\pi$
$647$	22.5213	−	9.32864i	0.885405	−	0.366747i	0.778591	+	0.627532i	$0.215935\pi$
$648$	−25.3488	+	2.33210i	−0.995795	+	0.0916137i
$649$	−14.9071	−	6.17474i	−0.585156	−	0.242380i
$650$	1.87294	+	5.08549i	0.0734628	+	0.199469i
$651$	21.6358	+	40.1186i	0.847976	+	1.57237i
$652$	1.67662	+	14.3012i	0.0656614	+	0.560079i
$653$	−6.88068	+	4.59752i	−0.269262	+	0.179915i	−0.682870	−	0.730540i	$-0.739268\pi$
$653$	−6.88068	+	4.59752i	−0.269262	+	0.179915i	0.413608	+	0.910455i	$0.364268\pi$
$654$	−0.922345	−	14.8413i	−0.0360666	−	0.580342i
$655$	−9.02077	−	9.02077i	−0.352471	−	0.352471i
$656$	3.05205	−	0.725595i	0.119163	−	0.0283297i
$657$	−22.0883	−	4.22325i	−0.861746	−	0.164765i
$658$	−14.7639	−	24.1225i	−0.575558	−	0.940392i
$659$	−2.96129	+	1.97867i	−0.115356	+	0.0770782i	−0.611910	−	0.790928i	$-0.709598\pi$
$659$	−2.96129	+	1.97867i	−0.115356	+	0.0770782i	0.496554	+	0.868006i	$0.334598\pi$
$660$	−9.22851	+	0.205314i	−0.359219	+	0.00799184i
$661$	−10.9271	+	2.17354i	−0.425016	+	0.0845409i	−0.402964	−	0.915216i	$-0.632020\pi$
$661$	−10.9271	+	2.17354i	−0.425016	+	0.0845409i	−0.0220520	+	0.999757i	$0.507020\pi$
$662$	−3.16379	+	6.85281i	−0.122964	+	0.266342i
$663$	16.9372	+	1.60465i	0.657786	+	0.0623194i
$664$	−3.34172	+	0.936478i	−0.129684	+	0.0363424i
$665$	17.4795	−	7.24025i	0.677826	−	0.280765i
$666$	27.0722	−	16.8471i	1.04903	−	0.652811i
$667$	−1.82482	+	2.73104i	−0.0706575	+	0.105746i
$668$	−32.0066	+	27.2750i	−1.23837	+	1.05530i
$669$	35.3629	−	3.61566i	1.36721	−	0.139789i
$670$	−0.139783	−	0.885728i	−0.00540030	−	0.0342187i
$671$			23.8812i			0.921923i
$672$	−34.5384	+	18.5034i	−1.33235	+	0.713783i
$673$			34.5110i			1.33030i	0.746709	+	0.665151i	$0.231633\pi$
$673$			34.5110i			1.33030i	−0.746709	+	0.665151i	$0.768367\pi$
$674$	5.55920	−	0.877339i	0.214132	−	0.0337938i
$675$	−3.34097	−	3.97969i	−0.128594	−	0.153178i
$676$	3.35942	+	0.268132i	0.129208	+	0.0103128i
$677$	5.38227	−	8.05514i	0.206857	−	0.309584i	−0.713505	−	0.700650i	$-0.752894\pi$
$677$	5.38227	−	8.05514i	0.206857	−	0.309584i	0.920363	+	0.391066i	$0.127894\pi$
$678$	−20.4883	+	5.41560i	−0.786847	+	0.207985i
$679$	−22.4117	+	9.28325i	−0.860084	+	0.356258i
$680$	−7.19816	−	0.864074i	−0.276037	−	0.0331357i
$681$	3.46339	−	36.5564i	0.132718	−	1.40084i
$682$	−22.5149	−	10.3946i	−0.862141	−	0.398031i
$683$	29.1352	−	5.79535i	1.11483	−	0.221753i	0.396893	−	0.917865i	$-0.370088\pi$
$683$	29.1352	−	5.79535i	1.11483	−	0.221753i	0.717933	+	0.696112i	$0.245088\pi$
$684$	−12.7268	+	25.3733i	−0.486623	+	0.970172i
$685$	−10.3733	+	6.93122i	−0.396344	+	0.264828i
$686$	9.61113	−	5.88240i	0.366955	−	0.224591i
$687$	−25.8309	−	13.6837i	−0.985510	−	0.522067i
$688$	−30.8996	−	28.6904i	−1.17804	−	1.09381i
$689$	−38.3287	−	38.3287i	−1.46021	−	1.46021i
$690$	−0.0624792	−	1.00534i	−0.00237854	−	0.0382728i
$691$	−9.22698	+	6.16527i	−0.351011	+	0.234538i	−0.718558	−	0.695467i	$-0.755198\pi$
$691$	−9.22698	+	6.16527i	−0.351011	+	0.234538i	0.367547	+	0.930005i	$0.380198\pi$
$692$	−12.2581	+	15.5140i	−0.465984	+	0.589755i
$693$	−22.4368	+	22.7728i	−0.852304	+	0.865066i
$694$	−14.1459	+	5.20981i	−0.536971	+	0.197762i
$695$	11.0185	+	4.56400i	0.417954	+	0.173122i
$696$	−35.8827	−	15.6076i	−1.36013	−	0.591605i
$697$	1.85725	−	0.769297i	0.0703483	−	0.0291392i
$698$	−1.37944	−	1.49393i	−0.0522127	−	0.0565461i
$699$	24.2081	+	7.24533i	0.915634	+	0.274044i
$700$	−7.12235	−	3.63895i	−0.269200	−	0.137539i
$701$	9.57241	−	48.1238i	0.361545	−	1.81761i	−0.188027	−	0.982164i	$-0.560209\pi$
$701$	9.57241	−	48.1238i	0.361545	−	1.81761i	0.549572	−	0.835446i	$-0.314791\pi$
$702$	−27.1709	+	7.39844i	−1.02550	+	0.279236i
$703$		−	35.5568i		−	1.34105i
$704$	8.98903	−	19.3297i	0.338787	−	0.728516i
$705$	2.54510	+	8.27922i	0.0958541	+	0.311813i
$706$	19.3855	−	26.6508i	0.729583	−	1.00302i
$707$	−39.2250	−	7.80234i	−1.47521	−	0.293437i
$708$	20.6588	+	3.63360i	0.776405	+	0.136559i
$709$	−27.7652	+	41.5536i	−1.04275	+	1.56058i	−0.234162	+	0.972198i	$0.575235\pi$
$709$	−27.7652	+	41.5536i	−1.04275	+	1.56058i	−0.808583	+	0.588382i	$0.799765\pi$
$710$	7.84810	−	7.24666i	0.294534	−	0.271962i
$711$	−42.5430	−	27.9713i	−1.59549	−	1.04900i
$712$	−39.3153	+	3.02854i	−1.47340	+	0.113499i
$713$	1.03557	−	2.50009i	0.0387824	−	0.0936290i
$714$	−19.9713	+	15.2175i	−0.747407	+	0.569499i
$715$	−10.0152	+	1.99215i	−0.374548	+	0.0745022i
$716$	0.433665	−	0.548852i	0.0162068	−	0.0205115i
$717$	−16.7815	−	13.6682i	−0.626715	−	0.510447i
$718$	15.3263	+	3.68848i	0.571971	+	0.137653i
$719$	−2.67110	+	2.67110i	−0.0996151	+	0.0996151i	−0.755158	−	0.655543i	$-0.772440\pi$
$719$	−2.67110	+	2.67110i	−0.0996151	+	0.0996151i	0.655543	+	0.755158i	$0.272440\pi$
$720$	11.6537	−	2.86220i	0.434306	−	0.106668i
$721$	−31.2341	−	31.2341i	−1.16322	−	1.16322i
$722$	2.49730	+	4.08028i	0.0929398	+	0.151852i
$723$	3.80063	−	4.66632i	0.141347	−	0.173542i
$724$	5.65585	−	3.15922i	0.210198	−	0.117411i
$725$	−1.55827	−	7.83393i	−0.0578725	−	0.290945i
$726$	−1.27874	+	9.46548i	−0.0474586	+	0.351297i
$727$	1.02001	+	0.422503i	0.0378301	+	0.0156698i	0.401518	−	0.915851i	$-0.368483\pi$
$727$	1.02001	+	0.422503i	0.0378301	+	0.0156698i	−0.363688	+	0.931521i	$0.618483\pi$
$728$	−34.0841	+	26.7782i	−1.26324	+	0.992465i
$729$	22.1097	−	15.4971i	0.818879	−	0.573967i
$730$	10.5927	+	0.422058i	0.392055	+	0.0156211i
$731$	−22.4660	−	15.0113i	−0.830936	−	0.555214i
$732$	−6.73242	−	30.3067i	−0.248837	−	1.12017i
$733$	0.166341	−	0.836254i	0.00614395	−	0.0308877i	−0.977592	−	0.210510i	$-0.932488\pi$
$733$	0.166341	−	0.836254i	0.00614395	−	0.0308877i	0.983736	+	0.179622i	$0.0574875\pi$
$734$	4.83817	+	30.6567i	0.178580	+	1.13156i
$735$	−14.8878	+	4.57665i	−0.549145	+	0.168812i
$736$	2.14668	+	0.896148i	0.0791277	+	0.0330324i
$737$	1.68957			0.0622361
$738$	−2.42781	+	2.27541i	−0.0893687	+	0.0837588i
$739$	−15.6953	−	3.12198i	−0.577360	−	0.114844i	−0.102232	−	0.994761i	$-0.532598\pi$
$739$	−15.6953	−	3.12198i	−0.577360	−	0.114844i	−0.475128	+	0.879917i	$0.657598\pi$
$740$	−11.4407	+	9.74939i	−0.420568	+	0.358395i
$741$	−9.00375	+	30.0833i	−0.330761	+	1.10514i
$742$	79.9336	+	3.18488i	2.93445	+	0.116921i
$743$	6.50126	+	15.6954i	0.238508	+	0.575809i	0.997129	−	0.0757229i	$-0.0241265\pi$
$743$	6.50126	+	15.6954i	0.238508	+	0.575809i	−0.758621	+	0.651532i	$0.774126\pi$
$744$	31.5032	+	6.84416i	1.15496	+	0.250919i
$745$	4.23970	−	10.2355i	0.155330	−	0.375001i
$746$	7.90095	+	3.64769i	0.289275	+	0.133551i
$747$	2.58343	−	2.62211i	0.0945227	−	0.0959381i
$748$	3.72251	−	13.1434i	0.136109	−	0.480569i
$749$	28.6234	+	42.8380i	1.04588	+	1.56527i
$750$	1.83615	+	1.62128i	0.0670467	+	0.0592008i
$751$	−3.34000	+	3.34000i	−0.121878	+	0.121878i	−0.765415	−	0.643537i	$-0.777466\pi$
$751$	−3.34000	+	3.34000i	−0.121878	+	0.121878i	0.643537	+	0.765415i	$0.277466\pi$
$752$	−19.7498	−	3.17288i	−0.720202	−	0.115703i
$753$	−1.51893	+	2.86729i	−0.0553527	+	0.104490i
$754$	−42.0855	−	10.1285i	−1.53266	−	0.368856i
$755$	12.3176	+	18.4345i	0.448282	+	0.670901i
$756$	22.0537	−	35.2253i	0.802086	−	1.28113i
$757$	−5.01258	−	25.1999i	−0.182185	−	0.915907i	−0.958398	−	0.285436i	$-0.907862\pi$
$757$	−5.01258	−	25.1999i	−0.182185	−	0.915907i	0.776212	−	0.630471i	$-0.217138\pi$
$758$	10.1992	−	3.75627i	0.370452	−	0.136434i
$759$	1.88949	+	0.179013i	0.0685842	+	0.00649775i
$760$	4.15619	−	12.7196i	0.150761	−	0.461388i
$761$	11.2443	+	27.1462i	0.407606	+	0.984049i	0.985766	+	0.168125i	$0.0537712\pi$
$761$	11.2443	+	27.1462i	0.407606	+	0.984049i	−0.578159	+	0.815924i	$0.696229\pi$
$762$	22.1306	+	12.8771i	0.801706	+	0.466488i
$763$	20.1855	+	13.4875i	0.730763	+	0.488280i
$764$	9.27792	+	28.6624i	0.335663	+	1.03697i
$765$	7.08221	−	2.99540i	0.256058	−	0.108299i
$766$	−12.5143	+	17.2045i	−0.452162	+	0.621624i
$767$	23.2043			0.837858
$768$	−5.95832	+	27.0647i	−0.215002	+	0.976614i
$769$	−5.26826			−0.189978			−0.0949892	−	0.995478i	$-0.530282\pi$
$769$	−5.26826			−0.189978			−0.0949892	+	0.995478i	$0.530282\pi$
$770$	8.86483	−	12.1872i	0.319466	−	0.439196i
$771$	−3.60946	−	35.3023i	−0.129992	−	1.27138i
$772$	−7.68806	−	23.7508i	−0.276699	−	0.854810i
$773$	11.2106	+	7.49066i	0.403216	+	0.269420i	0.740599	−	0.671947i	$-0.234542\pi$
$773$	11.2106	+	7.49066i	0.403216	+	0.269420i	−0.337383	+	0.941367i	$0.609542\pi$
$774$	43.5583	+	10.1411i	1.56567	+	0.364514i
$775$	2.51828	+	6.07966i	0.0904591	+	0.218388i
$776$	−5.32895	+	16.3087i	−0.191298	+	0.585448i
$777$	−4.91002	+	51.8256i	−0.176146	+	1.85923i
$778$	−17.1778	+	6.32642i	−0.615853	+	0.226813i
$779$	0.723874	+	3.63916i	0.0259355	+	0.130386i
$780$	12.1483	−	5.35158i	0.434979	−	0.191617i
$781$	11.1822	+	16.7354i	0.400131	+	0.598839i
$782$	1.44927	+	0.348786i	0.0518257	+	0.0124726i
$783$	41.2560	−	4.52821i	1.47437	−	0.161825i
$784$	5.70552	−	35.5144i	0.203768	−	1.26837i
$785$	−9.50181	+	9.50181i	−0.339134	+	0.339134i
$786$	−20.6832	+	23.4243i	−0.737744	+	0.835518i
$787$	15.5638	+	23.2928i	0.554788	+	0.830299i	0.997805	−	0.0662141i	$-0.0210920\pi$
$787$	15.5638	+	23.2928i	0.554788	+	0.830299i	−0.443017	+	0.896513i	$0.646092\pi$
$788$	0.112504	−	0.397227i	0.00400780	−	0.0141506i
$789$	26.4915	−	14.2868i	0.943122	−	0.508623i
$790$	21.7911	+	10.0605i	0.775293	+	0.357935i
$791$	13.2401	−	31.9645i	0.470765	−	1.13653i
$792$	1.90408	+	22.5304i	0.0676587	+	0.800584i
$793$	−13.1427	−	31.7293i	−0.466711	−	1.12674i
$794$	−43.7659	−	1.74381i	−1.55319	−	0.0618856i
$795$	−23.4711	−	7.02474i	−0.832433	−	0.249142i
$796$	9.27956	−	7.90775i	0.328905	−	0.280283i
$797$	−10.3378	−	2.05631i	−0.366182	−	0.0728382i	0.00856967	−	0.999963i	$-0.497272\pi$
$797$	−10.3378	−	2.05631i	−0.366182	−	0.0728382i	−0.374752	+	0.927125i	$0.622272\pi$
$798$	−20.3565	−	41.6334i	−0.720613	−	1.47381i
$799$	−12.8180			−0.453468
$800$	−5.23222	+	2.15032i	−0.184987	+	0.0760253i
$801$	34.6015	−	23.4938i	1.22258	−	0.830111i
$802$	−6.40835	−	40.6061i	−0.226287	−	1.43385i
$803$	−3.89692	+	19.5911i	−0.137519	+	0.691356i
$804$	−2.14417	+	0.476312i	−0.0756189	+	0.0167982i
$805$	1.36735	+	0.913635i	0.0481928	+	0.0322014i
$806$	35.6346	+	1.41983i	1.25518	+	0.0500114i
$807$	−11.2771	+	9.32525i	−0.396974	+	0.328264i
$808$	−22.2427	+	17.4750i	−0.782497	+	0.614768i
$809$	−4.71003	−	1.95096i	−0.165596	−	0.0685921i	0.298346	−	0.954458i	$-0.403565\pi$
$809$	−4.71003	−	1.95096i	−0.165596	−	0.0685921i	−0.463941	+	0.885866i	$0.653565\pi$
$810$	−9.22182	+	8.77257i	−0.324022	+	0.308237i
$811$	9.35547	+	47.0331i	0.328515	+	1.65156i	0.693436	+	0.720518i	$0.256096\pi$
$811$	9.35547	+	47.0331i	0.328515	+	1.65156i	−0.364921	+	0.931038i	$0.618904\pi$
$812$	55.7732	−	31.1535i	1.95725	−	1.09327i
$813$	21.4356	+	17.4589i	0.751780	+	0.612309i
$814$	−14.7850	−	24.1570i	−0.518215	−	0.846702i
$815$	5.09087	+	5.09087i	0.178325	+	0.178325i
$816$	−1.01881	+	17.7292i	−0.0356654	+	0.620645i
$817$	35.2645	−	35.2645i	1.23375	−	1.23375i
$818$	6.22057	+	1.49707i	0.217497	+	0.0523437i
$819$	17.2775	−	42.6044i	0.603726	−	1.48872i
$820$	0.972448	−	1.23074i	0.0339594	−	0.0429794i
$821$	35.4018	−	7.04186i	1.23553	−	0.245763i	0.466239	−	0.884659i	$-0.345609\pi$
$821$	35.4018	−	7.04186i	1.23553	−	0.245763i	0.769293	+	0.638896i	$0.220609\pi$
$822$	18.5213	+	24.3073i	0.646006	+	0.847814i
$823$	−17.2339	+	41.6064i	−0.600737	+	1.45031i	0.272088	+	0.962272i	$0.412286\pi$
$823$	−17.2339	+	41.6064i	−0.600737	+	1.45031i	−0.872824	+	0.488034i	$0.837714\pi$
$824$	−31.1492	+	2.39949i	−1.08513	+	0.0835902i
$825$	−3.55685	+	2.94121i	−0.123834	+	0.102400i
$826$	−25.1601	+	23.2319i	−0.875431	+	0.808342i
$827$	10.3405	−	15.4756i	0.359573	−	0.538140i	−0.606943	−	0.794746i	$-0.707604\pi$
$827$	10.3405	−	15.4756i	0.359573	−	0.538140i	0.966516	+	0.256606i	$0.0826042\pi$
$828$	−2.44835	+	0.305495i	−0.0850859	+	0.0106167i
$829$	31.7381	+	6.31311i	1.10231	+	0.219263i	0.712528	−	0.701644i	$-0.247550\pi$
$829$	31.7381	+	6.31311i	1.10231	+	0.219263i	0.389783	+	0.920907i	$0.372550\pi$
$830$	−1.02072	+	1.40326i	−0.0354296	+	0.0487080i
$831$	25.5728	−	7.86130i	0.887111	−	0.272706i
$832$	−1.30525	+	30.6291i	−0.0452513	+	1.06187i
$833$		−	23.0495i		−	0.798618i
$834$	9.48384	−	27.6311i	0.328399	−	0.956786i
$835$	−4.10194	+	20.6219i	−0.141954	+	0.713649i
$836$	22.4528	+	11.4716i	0.776546	+	0.396753i
$837$	−32.6086	+	10.2900i	−1.12712	+	0.355674i
$838$	10.7278	+	11.6182i	0.370587	+	0.401344i
$839$	−0.394324	+	0.163335i	−0.0136136	+	0.00563893i	−0.389480	−	0.921035i	$-0.627345\pi$
$839$	−0.394324	+	0.163335i	−0.0136136	+	0.00563893i	0.375866	+	0.926674i	$0.377345\pi$
$840$	−7.81427	+	17.9654i	−0.269618	+	0.619866i
$841$	32.1497	+	13.3169i	1.10861	+	0.459202i
$842$	−50.1017	+	18.4520i	−1.72662	+	0.635898i
$843$	0.210633	−	0.113594i	0.00725458	−	0.00391238i
$844$	−25.2975	+	32.0168i	−0.870776	+	1.10206i
$845$	1.40107	−	0.936164i	0.0481982	−	0.0322050i
$846$	19.8541	−	7.48011i	0.682599	−	0.257171i
$847$	−11.0265	−	11.0265i	−0.378874	−	0.378874i
$848$	38.4982	−	41.4627i	1.32203	−	1.42383i
$849$	−8.30778	+	15.6827i	−0.285122	+	0.538227i
$850$	−3.09180	+	1.89231i	−0.106048	+	0.0649055i
$851$	2.56974	−	1.71705i	0.0880895	−	0.0588595i
$852$	−18.9088	−	18.0858i	−0.647806	−	0.619609i
$853$	45.9820	−	9.14639i	1.57439	−	0.313166i	0.670827	−	0.741614i	$-0.265939\pi$
$853$	45.9820	−	9.14639i	1.57439	−	0.313166i	0.903567	+	0.428447i	$0.140939\pi$
$854$	46.0175	+	21.2452i	1.57469	+	0.726997i
$855$	2.87230	+	13.8994i	0.0982307	+	0.475350i
$856$	36.1796	+	4.34303i	1.23659	+	0.148442i
$857$	20.3192	−	8.41650i	0.694091	−	0.287502i	−0.00761221	−	0.999971i	$-0.502423\pi$
$857$	20.3192	−	8.41650i	0.694091	−	0.287502i	0.701704	+	0.712469i	$0.252423\pi$
$858$	6.39202	+	24.1822i	0.218220	+	0.825568i
$859$	11.7926	−	17.6489i	0.402358	−	0.602171i	−0.573862	−	0.818952i	$-0.694556\pi$
$859$	11.7926	−	17.6489i	0.402358	−	0.602171i	0.976220	+	0.216780i	$0.0695556\pi$
$860$	−21.0159	−	1.67738i	−0.716636	−	0.0571983i
$861$	−0.552548	−	5.40419i	−0.0188308	−	0.184174i
$862$	14.3432	−	2.26360i	0.488531	−	0.0770987i
$863$		−	28.8732i		−	0.982855i	−0.870918	−	0.491428i	$-0.836475\pi$
$863$		−	28.8732i		−	0.982855i	0.870918	−	0.491428i	$-0.163525\pi$
$864$	−8.76802	−	28.0557i	−0.298294	−	0.954474i
$865$			9.88619i			0.336141i
$866$	2.64416	+	16.7545i	0.0898521	+	0.569342i
$867$	−1.83749	−	17.9716i	−0.0624045	−	0.610346i
$868$	−40.0596	+	34.1376i	−1.35971	+	1.15870i
$869$	−25.1251	+	37.6024i	−0.852312	+	1.27557i
$870$	−18.9154	+	4.99986i	−0.641293	+	0.169511i
$871$	−2.24482	+	0.929833i	−0.0760627	+	0.0315062i
$872$	16.5334	−	4.63330i	0.559892	−	0.156903i
$873$	−3.68279	−	17.8215i	−0.124644	−	0.603165i
$874$	−1.15327	+	2.49799i	−0.0390098	+	0.0844958i
$875$	−3.92222	+	0.780177i	−0.132595	+	0.0263748i
$876$	−0.577574	−	25.9610i	−0.0195144	−	0.877139i
$877$	26.8580	−	17.9459i	0.906929	−	0.605991i	−0.0122094	−	0.999925i	$-0.503886\pi$
$877$	26.8580	−	17.9459i	0.906929	−	0.605991i	0.919138	+	0.393935i	$0.128886\pi$
$878$	−19.7809	−	32.3197i	−0.667574	−	1.09074i
$879$	6.46782	−	12.2093i	0.218154	−	0.411811i
$880$	−2.46531	−	10.3698i	−0.0831056	−	0.349565i
$881$	−15.2532	−	15.2532i	−0.513892	−	0.513892i	0.401825	−	0.915717i	$-0.368376\pi$
$881$	−15.2532	−	15.2532i	−0.513892	−	0.513892i	−0.915717	+	0.401825i	$0.868376\pi$
$882$	13.4508	+	35.7020i	0.452914	+	1.20215i
$883$	−24.1335	+	16.1255i	−0.812156	+	0.542665i	−0.890884	−	0.454231i	$-0.849914\pi$
$883$	−24.1335	+	16.1255i	−0.812156	+	0.542665i	0.0787280	+	0.996896i	$0.474914\pi$
$884$	2.28743	+	19.5113i	0.0769347	+	0.656237i
$885$	9.23112	−	4.97832i	0.310301	−	0.167344i
$886$	−7.82437	−	21.2451i	−0.262865	−	0.713742i
$887$	31.5782	+	13.0801i	1.06029	+	0.439188i	0.843555	−	0.537042i	$-0.180458\pi$
$887$	31.5782	+	13.0801i	1.06029	+	0.439188i	0.216738	+	0.976230i	$0.430458\pi$
$888$	25.5733	+	26.4886i	0.858184	+	0.888899i
$889$	−38.6199	+	15.9969i	−1.29527	+	0.536518i
$890$	−14.4852	+	13.3751i	−0.485545	+	0.448336i
$891$	−13.6187	−	19.7403i	−0.456245	−	0.661326i
$892$	12.6409	+	39.0515i	0.423247	+	1.30754i
$893$	4.61560	−	23.2042i	0.154455	−	0.776499i
$894$	−25.6677	−	8.80996i	−0.858457	−	0.294649i
$895$		−	0.349751i		−	0.0116909i
$896$	−29.2503	−	34.5175i	−0.977184	−	1.15315i
$897$	−2.60896	+	0.802016i	−0.0871105	+	0.0267785i
$898$	−5.36126	−	3.89972i	−0.178908	−	0.130135i
$899$	−51.5517	−	10.2543i	−1.71935	−	0.341999i
$900$	3.68469	−	4.73530i	0.122823	−	0.157843i
$901$	20.1430	−	30.1461i	0.671059	−	1.00431i
$902$	2.00501	+	2.17142i	0.0667596	+	0.0723003i
$903$	−56.2692	+	46.5299i	−1.87252	+	1.54842i
$904$	−11.0731	−	21.8216i	−0.368286	−	0.725777i
$905$	1.23958	−	2.99262i	0.0412051	−	0.0994780i
$906$	43.1968	−	32.9145i	1.43512	−	1.09351i
$907$	28.3828	−	5.64568i	0.942434	−	0.187462i	0.300118	−	0.953902i	$-0.402974\pi$
$907$	28.3828	−	5.64568i	0.942434	−	0.187462i	0.642316	+	0.766440i	$0.277974\pi$
$908$	42.1123	−	4.93708i	1.39754	−	0.163843i
$909$	11.2750	−	27.8029i	0.373969	−	0.922165i
$910$	−5.07102	+	21.0709i	−0.168103	+	0.698495i
$911$	0.570164	−	0.570164i	0.0188904	−	0.0188904i	−0.697599	−	0.716489i	$-0.745748\pi$
$911$	0.570164	−	0.570164i	0.0188904	−	0.0188904i	0.716489	+	0.697599i	$0.245748\pi$
$912$	−31.7280	−	8.22839i	−1.05062	−	0.272469i
$913$	−2.31193	−	2.31193i	−0.0765138	−	0.0765138i
$914$	31.4285	−	19.2355i	1.03956	−	0.636255i
$915$	−12.0357	−	9.80286i	−0.397889	−	0.324073i
$916$	9.19803	−	32.4762i	0.303911	−	1.07304i
$917$	−9.95295	−	50.0369i	−0.328675	−	1.65236i
$918$	−8.39911	−	16.8593i	−0.277212	−	0.556440i
$919$	8.39365	+	3.47676i	0.276881	+	0.114688i	0.516803	−	0.856104i	$-0.327122\pi$
$919$	8.39365	+	3.47676i	0.276881	+	0.114688i	−0.239922	+	0.970792i	$0.577122\pi$
$920$	1.11997	−	0.313857i	0.0369242	−	0.0103476i
$921$	17.7850	−	14.7067i	0.586035	−	0.484602i
$922$	2.02535	−	50.8319i	0.0667014	−	1.67406i
$923$	−24.0671	−	16.0812i	−0.792180	−	0.529318i
$924$	−31.1418	−	19.8208i	−1.02449	−	0.652057i
$925$	−1.46623	+	7.37123i	−0.0482093	+	0.242365i
$926$	10.7780	−	1.70096i	0.354187	−	0.0558969i
$927$	27.4145	−	18.6139i	0.900411	−	0.611362i
$928$	8.93741	−	44.2908i	0.293385	−	1.45392i
$929$	40.2052			1.31909			0.659546	−	0.751665i	$-0.270749\pi$
$929$	40.2052			1.31909			0.659546	+	0.751665i	$0.270749\pi$
$930$	14.4808	−	7.08033i	0.474843	−	0.232173i
$931$	41.7262	+	8.29985i	1.36752	+	0.272017i
$932$	−2.32148	+	29.0857i	−0.0760425	+	0.952734i
$933$	−11.0082	−	3.29470i	−0.360394	−	0.107864i
$934$	1.99217	−	49.9990i	0.0651856	−	1.63602i
$935$	−2.61379	−	6.31026i	−0.0854802	−	0.206367i
$936$	−14.9292	−	28.8867i	−0.487975	−	0.944193i
$937$	9.97041	−	24.0707i	0.325719	−	0.786355i	−0.673182	−	0.739477i	$-0.735073\pi$
$937$	9.97041	−	24.0707i	0.325719	−	0.786355i	0.998901	−	0.0468780i	$-0.0149272\pi$
$938$	1.50308	−	3.25569i	0.0490773	−	0.106302i
$939$	8.84953	−	4.77253i	0.288793	−	0.155746i
$940$	−8.73170	+	4.87730i	−0.284797	+	0.159080i
$941$	−25.4390	−	38.0722i	−0.829288	−	1.24112i	−0.968042	−	0.250790i	$-0.919310\pi$
$941$	−25.4390	−	38.0722i	−0.829288	−	1.24112i	0.138754	−	0.990327i	$-0.455690\pi$
$942$	24.6734	+	21.7861i	0.803904	+	0.709830i
$943$	−0.228051	+	0.228051i	−0.00742637	+	0.00742637i
$944$	0.897355	+	24.2043i	0.0292064	+	0.787782i
$945$	−2.26714	−	20.6557i	−0.0737501	−	0.671929i
$946$	9.29490	−	38.6219i	0.302203	−	1.25571i
$947$	10.5015	+	15.7166i	0.341253	+	0.510722i	0.961912	−	0.273359i	$-0.0881347\pi$
$947$	10.5015	+	15.7166i	0.341253	+	0.510722i	−0.620659	+	0.784081i	$0.713135\pi$
$948$	21.2847	−	54.8029i	0.691295	−	1.77991i
$949$	−5.60416	−	28.1740i	−0.181919	−	0.914568i
$950$	−2.31229	−	6.27843i	−0.0750206	−	0.203699i
$951$	2.12911	−	22.4729i	0.0690412	−	0.728735i
$952$	−22.0148	−	18.8657i	−0.713504	−	0.611441i
$953$	−9.57772	−	23.1227i	−0.310253	−	0.749016i	−0.999695	−	0.0246763i	$-0.992145\pi$
$953$	−9.57772	−	23.1227i	−0.310253	−	0.749016i	0.689443	−	0.724340i	$-0.257855\pi$
$954$	−13.6078	+	58.4487i	−0.440569	+	1.89235i
$955$	12.5247	+	8.36871i	0.405289	+	0.270805i
$956$	11.3706	−	22.2551i	0.367751	−	0.719782i
$957$	−3.74969	−	36.6738i	−0.121210	−	1.18550i
$958$	−11.0172	−	8.01378i	−0.355950	−	0.258914i
$959$	−49.8917			−1.61109
$960$	6.05201	+	12.4649i	0.195328	+	0.402302i
$961$	12.3039			0.396901
$962$	32.9384	+	23.9590i	1.06198	+	0.772468i
$963$	−35.5968	+	15.0555i	−1.14709	+	0.485158i
$964$	6.18836	+	3.16175i	0.199314	+	0.101833i
$965$	−10.3785	−	6.93466i	−0.334094	−	0.223235i
$966$	2.02588	−	3.48168i	0.0651817	−	0.112021i
$967$	−3.50982	−	8.47344i	−0.112868	−	0.272488i	0.857344	−	0.514743i	$-0.172113\pi$
$967$	−3.50982	−	8.47344i	−0.112868	−	0.272488i	−0.970212	+	0.242256i	$0.922113\pi$
$968$	−10.9965	+	0.847085i	−0.353441	+	0.0272263i
$969$	−20.9103	−	1.98106i	−0.671735	−	0.0636410i
$970$	2.96476	+	8.05003i	0.0951926	+	0.258471i
$971$	0.582473	+	2.92829i	0.0186924	+	0.0939732i	0.989005	−	0.147880i	$-0.0472448\pi$
$971$	0.582473	+	2.92829i	0.0186924	+	0.0939732i	−0.970313	+	0.241853i	$0.922245\pi$
$972$	22.8481	+	21.2124i	0.732852	+	0.680388i
$973$	26.4973	+	39.6561i	0.849466	+	1.27132i
$974$	11.8422	−	49.2066i	0.379450	−	1.57668i
$975$	3.10708	−	5.86525i	0.0995062	−	0.187838i
$976$	32.5884	−	14.9361i	1.04313	−	0.478094i
$977$	−30.3707	+	30.3707i	−0.971644	+	0.971644i	−0.999609	−	0.0279652i	$-0.991097\pi$
$977$	−30.3707	+	30.3707i	−0.971644	+	0.971644i	0.0279652	+	0.999609i	$0.491097\pi$
$978$	11.6725	−	13.2195i	0.373247	−	0.422713i
$979$	−20.6390	−	30.8884i	−0.659625	−	0.987198i
$980$	−8.77045	−	15.7015i	−0.280162	−	0.501565i
$981$	−12.7817	+	12.9731i	−0.408089	+	0.414200i
$982$	−6.88269	+	14.9080i	−0.219636	+	0.475734i
$983$	1.49913	−	3.61922i	0.0478148	−	0.115435i	−0.898167	−	0.439653i	$-0.855101\pi$
$983$	1.49913	−	3.61922i	0.0478148	−	0.115435i	0.945982	+	0.324218i	$0.105101\pi$
$984$	−3.15663	−	2.19042i	−0.100630	−	0.0698281i
$985$	−0.0789958	−	0.190713i	−0.00251701	−	0.00607661i
$986$	1.15272	−	28.9307i	0.0367101	−	0.921342i
$987$	−9.93170	+	33.1838i	−0.316129	+	1.05625i
$988$	−36.1447	−	2.88489i	−1.14992	−	0.0917806i
$989$	4.25155	+	0.845685i	0.135191	+	0.0268912i
$990$	7.73101	+	8.24881i	0.245708	+	0.262164i
$991$	22.1624			0.704013			0.352007	−	0.935998i	$-0.385499\pi$
$991$	22.1624			0.704013			0.352007	+	0.935998i	$0.385499\pi$
$992$	−0.102958	+	37.2252i	−0.00326892	+	1.18190i
$993$	8.83615	−	2.71631i	0.280407	−	0.0861994i
$994$	42.1960	−	6.65926i	1.33838	−	0.211219i
$995$	1.18926	−	5.97882i	0.0377021	−	0.189541i
$996$	3.58575	+	2.28222i	0.113619	+	0.0723149i
$997$	−2.43551	−	1.62736i	−0.0771335	−	0.0515389i	0.516406	−	0.856344i	$-0.327270\pi$
$997$	−2.43551	−	1.62736i	−0.0771335	−	0.0515389i	−0.593539	+	0.804805i	$0.702270\pi$
$998$	2.10793	−	52.9044i	0.0667253	−	1.67466i
$999$	−37.4949	−	10.9191i	−1.18629	−	0.345464i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	960.2.cn.a.611.90	yes	1024
3.2	odd	2	inner	960.2.cn.a.611.39	yes	1024
64.11	odd	16	inner	960.2.cn.a.11.39	✓	1024
192.11	even	16	inner	960.2.cn.a.11.90	yes	1024

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
960.2.cn.a.11.39	✓	1024	64.11	odd	16	inner
960.2.cn.a.11.90	yes	1024	192.11	even	16	inner
960.2.cn.a.611.39	yes	1024	3.2	odd	2	inner
960.2.cn.a.611.90	yes	1024	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 960 = 2^{6} \cdot 3 \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	960.cn (of order \(16\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(0.831887 - 1.14366i) q^{2} +(-1.72307 + 0.176174i) q^{3} +(-0.615929 - 1.90280i) q^{4} +(-0.831470 - 0.555570i) q^{5} +(-1.23191 + 2.11717i) q^{6} +(-1.53037 - 3.69465i) q^{7} +(-2.68854 - 0.878495i) q^{8} +(2.93793 - 0.607119i) q^{9} +O(q^{10})\)	\(q+(0.831887 - 1.14366i) q^{2} +(-1.72307 + 0.176174i) q^{3} +(-0.615929 - 1.90280i) q^{4} +(-0.831470 - 0.555570i) q^{5} +(-1.23191 + 2.11717i) q^{6} +(-1.53037 - 3.69465i) q^{7} +(-2.68854 - 0.878495i) q^{8} +(2.93793 - 0.607119i) q^{9} +(-1.32707 + 0.488749i) q^{10} +(-0.519857 - 2.61350i) q^{11} +(1.39651 + 3.17014i) q^{12} +(2.12901 + 3.18628i) q^{13} +(-5.49853 - 1.32330i) q^{14} +(1.53056 + 0.810802i) q^{15} +(-3.24126 + 2.34397i) q^{16} +(-1.81246 + 1.81246i) q^{17} +(1.74968 - 3.86505i) q^{18} +(-2.62842 - 3.93371i) q^{19} +(-0.545010 + 1.92431i) q^{20} +(3.28784 + 6.09652i) q^{21} +(-3.42142 - 1.57959i) q^{22} +(0.157368 - 0.379920i) q^{23} +(4.78730 + 1.04006i) q^{24} +(0.382683 + 0.923880i) q^{25} +(5.41512 + 0.215761i) q^{26} +(-4.95529 + 1.56369i) q^{27} +(-6.08756 + 5.18763i) q^{28} +(-7.83393 - 1.55827i) q^{29} +(2.20053 - 1.07594i) q^{30} +6.58057 q^{31} +(-0.0156458 + 5.65683i) q^{32} +(1.35618 + 4.41165i) q^{33} +(0.565082 + 3.58060i) q^{34} +(-0.780177 + 3.92222i) q^{35} +(-2.96478 - 5.21633i) q^{36} +(6.24903 + 4.17547i) q^{37} +(-6.68539 - 0.266374i) q^{38} +(-4.22976 - 5.11510i) q^{39} +(1.74737 + 2.22411i) q^{40} +(-0.724580 - 0.300131i) q^{41} +(9.70747 + 1.31143i) q^{42} +(2.05652 + 10.3388i) q^{43} +(-4.65276 + 2.59891i) q^{44} +(-2.78009 - 1.12742i) q^{45} +(-0.303588 - 0.496026i) q^{46} +(3.53608 + 3.53608i) q^{47} +(5.17197 - 4.60985i) q^{48} +(-6.35863 + 6.35863i) q^{49} +(1.37496 + 0.330902i) q^{50} +(2.80368 - 3.44230i) q^{51} +(4.75153 - 6.01359i) q^{52} +(-13.8731 + 2.75954i) q^{53} +(-2.33390 + 6.96799i) q^{54} +(-1.01974 + 2.46186i) q^{55} +(0.868740 + 11.2776i) q^{56} +(5.22197 + 6.31499i) q^{57} +(-8.29907 + 7.66307i) q^{58} +(3.36410 - 5.03474i) q^{59} +(0.600076 - 3.41173i) q^{60} +(-8.78985 - 1.74841i) q^{61} +(5.47429 - 7.52595i) q^{62} +(-6.73921 - 9.92548i) q^{63} +(6.45649 + 4.72374i) q^{64} -3.83211i q^{65} +(6.17363 + 2.11898i) q^{66} +(-0.123698 + 0.621873i) q^{67} +(4.56509 + 2.33239i) q^{68} +(-0.204224 + 0.682351i) q^{69} +(3.83667 + 4.15510i) q^{70} +(-6.97840 + 2.89055i) q^{71} +(-8.43208 - 0.948688i) q^{72} +(-6.92553 - 2.86865i) q^{73} +(9.97381 - 3.67327i) q^{74} +(-0.822153 - 1.52449i) q^{75} +(-5.86613 + 7.42424i) q^{76} +(-8.86038 + 5.92032i) q^{77} +(-9.36863 + 0.582233i) q^{78} +(-12.0007 - 12.0007i) q^{79} +(3.99725 - 0.148195i) q^{80} +(8.26281 - 3.56734i) q^{81} +(-0.946017 + 0.579000i) q^{82} +(1.02021 - 0.681680i) q^{83} +(9.57535 - 10.0111i) q^{84} +(2.51395 - 0.500056i) q^{85} +(13.5349 + 6.24876i) q^{86} +(13.7729 + 1.30486i) q^{87} +(-0.898288 + 7.48319i) q^{88} +(12.8800 - 5.33508i) q^{89} +(-3.60211 + 2.24160i) q^{90} +(8.51401 - 12.7421i) q^{91} +(-0.819837 - 0.0654353i) q^{92} +(-11.3388 + 1.15933i) q^{93} +(6.98569 - 1.10246i) q^{94} +4.73103i q^{95} +(-0.969628 - 9.74986i) q^{96} -6.06601i q^{97} +(1.98247 + 12.5618i) q^{98} +(-3.11401 - 7.36265i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 1024 q+O(q^{10}) \) 1024 * q	\( 1024 q + 80 q^{24} + 80 q^{42} - 96 q^{52} - 288 q^{58} - 96 q^{64} + 256 q^{67} - 112 q^{76} - 48 q^{78} + 32 q^{79} - 112 q^{84} - 160 q^{88} - 144 q^{90} - 16 q^{94} - 272 q^{96}+O(q^{100}) \) 1024 * q + 80 * q^24 + 80 * q^42 - 96 * q^52 - 288 * q^58 - 96 * q^64 + 256 * q^67 - 112 * q^76 - 48 * q^78 + 32 * q^79 - 112 * q^84 - 160 * q^88 - 144 * q^90 - 16 * q^94 - 272 * q^96

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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