LMFDB - Embedded newform 336.2.bs.a.19.14

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [336,2,Mod(19,336)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(336, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([6, 9, 0, 10]))

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

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

chi := DirichletCharacter("336.19");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 336 = 2^{4} \cdot 3 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	336.bs (of order $12$, 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:	$2.68297350792$
Analytic rank:	$0$
Dimension:	$128$
Relative dimension:	$32$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			19.14
Character	$\chi$	$=$	336.19
Dual form			336.2.bs.a.283.14

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.375468 + 1.36346i) q^{2} +(0.258819 - 0.965926i) q^{3} +(-1.71805 - 1.02387i) q^{4} +(2.98722 - 0.800424i) q^{5} +(1.21982 + 0.715563i) q^{6} +(-1.52023 + 2.16539i) q^{7} +(2.04108 - 1.95806i) q^{8} +(-0.866025 - 0.500000i) q^{9} +O(q^{10})$	\(q+(-0.375468 + 1.36346i) q^{2} +(0.258819 - 0.965926i) q^{3} +(-1.71805 - 1.02387i) q^{4} +(2.98722 - 0.800424i) q^{5} +(1.21982 + 0.715563i) q^{6} +(-1.52023 + 2.16539i) q^{7} +(2.04108 - 1.95806i) q^{8} +(-0.866025 - 0.500000i) q^{9} +(-0.0302596 + 4.37349i) q^{10} +(-0.126027 + 0.470339i) q^{11} +(-1.43365 + 1.39451i) q^{12} +(3.47774 - 3.47774i) q^{13} +(-2.38162 - 2.88581i) q^{14} -3.09260i q^{15} +(1.90338 + 3.51812i) q^{16} +(2.71585 - 1.56800i) q^{17} +(1.00689 - 0.993057i) q^{18} +(7.02925 - 1.88348i) q^{19} +(-5.95172 - 1.68336i) q^{20} +(1.69814 + 2.02887i) q^{21} +(-0.593970 - 0.348430i) q^{22} +(-2.23427 + 3.86987i) q^{23} +(-1.36307 - 2.47831i) q^{24} +(3.95269 - 2.28209i) q^{25} +(3.43598 + 6.04753i) q^{26} +(-0.707107 + 0.707107i) q^{27} +(4.82890 - 2.16372i) q^{28} +(-1.84259 - 1.84259i) q^{29} +(4.21664 + 1.16117i) q^{30} +(2.06549 + 3.57754i) q^{31} +(-5.51147 + 1.27424i) q^{32} +(0.421695 + 0.243466i) q^{33} +(1.11819 + 4.29169i) q^{34} +(-2.80804 + 7.68532i) q^{35} +(0.975938 + 1.74572i) q^{36} +(0.247863 + 0.925038i) q^{37} +(-0.0712041 + 10.2913i) q^{38} +(-2.45913 - 4.25934i) q^{39} +(4.52988 - 7.48289i) q^{40} -10.5903 q^{41} +(-3.40388 + 1.55357i) q^{42} +(0.0791459 + 0.0791459i) q^{43} +(0.698087 - 0.679030i) q^{44} +(-2.98722 - 0.800424i) q^{45} +(-4.43752 - 4.49935i) q^{46} +(0.463923 - 0.803538i) q^{47} +(3.89087 - 0.927965i) q^{48} +(-2.37780 - 6.58377i) q^{49} +(1.62743 + 6.24619i) q^{50} +(-0.811655 - 3.02914i) q^{51} +(-9.53567 + 2.41416i) q^{52} +(0.494143 + 0.132405i) q^{53} +(-0.698616 - 1.22961i) q^{54} +1.50588i q^{55} +(1.13705 + 7.39643i) q^{56} -7.27722i q^{57} +(3.20412 - 1.82046i) q^{58} +(-8.37839 - 2.24498i) q^{59} +(-3.16642 + 5.31324i) q^{60} +(3.47221 + 12.9585i) q^{61} +(-5.65335 + 1.47297i) q^{62} +(2.39925 - 1.11517i) q^{63} +(0.332005 - 7.99311i) q^{64} +(7.60511 - 13.1724i) q^{65} +(-0.490289 + 0.483551i) q^{66} +(-7.23899 - 1.93968i) q^{67} +(-6.27139 - 0.0867859i) q^{68} +(3.15974 + 3.15974i) q^{69} +(-9.42430 - 6.71424i) q^{70} +7.13408 q^{71} +(-2.74666 + 0.675190i) q^{72} +(2.30993 + 4.00091i) q^{73} +(-1.35432 - 0.00937034i) q^{74} +(-1.18130 - 4.40866i) q^{75} +(-14.0050 - 3.96113i) q^{76} +(-0.826877 - 0.987922i) q^{77} +(6.73076 - 1.75368i) q^{78} +(-3.17895 - 1.83537i) q^{79} +(8.50180 + 8.98589i) q^{80} +(0.500000 + 0.866025i) q^{81} +(3.97630 - 14.4394i) q^{82} +(-6.06590 - 6.06590i) q^{83} +(-0.840180 - 5.22438i) q^{84} +(6.85779 - 6.85779i) q^{85} +(-0.137629 + 0.0781955i) q^{86} +(-2.25670 + 1.30290i) q^{87} +(0.663722 + 1.20677i) q^{88} +(-6.37228 + 11.0371i) q^{89} +(2.21295 - 3.77243i) q^{90} +(2.24369 + 12.8176i) q^{91} +(7.80083 - 4.36102i) q^{92} +(3.99022 - 1.06918i) q^{93} +(0.921404 + 0.934243i) q^{94} +(19.4904 - 11.2528i) q^{95} +(-0.195653 + 5.65347i) q^{96} -12.9745i q^{97} +(9.86950 - 0.770044i) q^{98} +(0.344312 - 0.344312i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 128 q + 4 q^{4} - 24 q^{8}+O(q^{10}) $ 128 * q + 4 * q^4 - 24 * q^8	$ 128 q + 4 q^{4} - 24 q^{8} + 36 q^{10} - 8 q^{11} - 32 q^{14} - 4 q^{16} + 4 q^{18} + 16 q^{22} + 16 q^{23} - 32 q^{28} + 32 q^{29} - 24 q^{35} - 16 q^{37} + 60 q^{40} - 20 q^{42} - 16 q^{43} - 12 q^{44} - 20 q^{46} - 32 q^{50} - 144 q^{52} - 16 q^{53} - 56 q^{56} - 40 q^{58} - 96 q^{59} - 24 q^{60} - 32 q^{64} - 72 q^{66} + 16 q^{67} - 60 q^{68} + 28 q^{70} + 128 q^{71} - 4 q^{72} - 72 q^{74} + 72 q^{78} - 36 q^{80} + 64 q^{81} - 60 q^{82} + 24 q^{84} - 44 q^{86} - 48 q^{88} - 8 q^{91} + 56 q^{92} + 36 q^{94} + 60 q^{96} + 148 q^{98} - 16 q^{99}+O(q^{100}) $ 128 * q + 4 * q^4 - 24 * q^8 + 36 * q^10 - 8 * q^11 - 32 * q^14 - 4 * q^16 + 4 * q^18 + 16 * q^22 + 16 * q^23 - 32 * q^28 + 32 * q^29 - 24 * q^35 - 16 * q^37 + 60 * q^40 - 20 * q^42 - 16 * q^43 - 12 * q^44 - 20 * q^46 - 32 * q^50 - 144 * q^52 - 16 * q^53 - 56 * q^56 - 40 * q^58 - 96 * q^59 - 24 * q^60 - 32 * q^64 - 72 * q^66 + 16 * q^67 - 60 * q^68 + 28 * q^70 + 128 * q^71 - 4 * q^72 - 72 * q^74 + 72 * q^78 - 36 * q^80 + 64 * q^81 - 60 * q^82 + 24 * q^84 - 44 * q^86 - 48 * q^88 - 8 * q^91 + 56 * q^92 + 36 * q^94 + 60 * q^96 + 148 * q^98 - 16 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/336\mathbb{Z}\right)^\times$.

$n$	$85$	$113$	$127$	$241$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$1$	$-1$	$e\left(\frac{5}{6}\right)$

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 $

$2$	−0.375468	+	1.36346i	−0.265496	+	0.964112i
$2$	−0.375468	+	1.36346i	−0.265496	+	0.964112i
$3$	0.258819	−	0.965926i	0.149429	−	0.557678i
$3$	0.258819	−	0.965926i	0.149429	−	0.557678i
$4$	−1.71805	−	1.02387i	−0.859024	−	0.511935i
$5$	2.98722	−	0.800424i	1.33593	−	0.357960i	0.481005	−	0.876718i	$-0.340272\pi$
$5$	2.98722	−	0.800424i	1.33593	−	0.357960i	0.854922	+	0.518757i	$0.173605\pi$
$6$	1.21982	+	0.715563i	0.497991	+	0.292128i
$7$	−1.52023	+	2.16539i	−0.574593	+	0.818439i
$7$	−1.52023	+	2.16539i	−0.574593	+	0.818439i
$8$	2.04108	−	1.95806i	0.721630	−	0.692279i
$9$	−0.866025	−	0.500000i	−0.288675	−	0.166667i
$10$	−0.0302596	+	4.37349i	−0.00956893	+	1.38302i
$11$	−0.126027	+	0.470339i	−0.0379986	+	0.141813i	−0.982319	−	0.187214i	$-0.940054\pi$
$11$	−0.126027	+	0.470339i	−0.0379986	+	0.141813i	0.944320	+	0.329027i	$0.106721\pi$
$12$	−1.43365	+	1.39451i	−0.413858	+	0.402560i
$13$	3.47774	−	3.47774i	0.964550	−	0.964550i	−0.0348426	−	0.999393i	$-0.511093\pi$
$13$	3.47774	−	3.47774i	0.964550	−	0.964550i	0.999393	+	0.0348426i	$0.0110930\pi$
$14$	−2.38162	−	2.88581i	−0.636515	−	0.771264i
$15$		−	3.09260i		−	0.798506i
$16$	1.90338	+	3.51812i	0.475844	+	0.879530i
$17$	2.71585	−	1.56800i	0.658691	−	0.380295i	−0.133087	−	0.991104i	$-0.542489\pi$
$17$	2.71585	−	1.56800i	0.658691	−	0.380295i	0.791778	+	0.610809i	$0.209156\pi$
$18$	1.00689	−	0.993057i	0.237327	−	0.234066i
$19$	7.02925	−	1.88348i	1.61262	−	0.432101i	0.663799	−	0.747911i	$-0.268943\pi$
$19$	7.02925	−	1.88348i	1.61262	−	0.432101i	0.948822	+	0.315811i	$0.102276\pi$
$20$	−5.95172	−	1.68336i	−1.33085	−	0.376411i
$21$	1.69814	+	2.02887i	0.370564	+	0.442736i
$22$	−0.593970	−	0.348430i	−0.126635	−	0.0742856i
$23$	−2.23427	+	3.86987i	−0.465878	+	0.806924i	−0.999241	−	0.0389627i	$-0.987595\pi$
$23$	−2.23427	+	3.86987i	−0.465878	+	0.806924i	0.533363	+	0.845886i	$0.320928\pi$
$24$	−1.36307	−	2.47831i	−0.278236	−	0.505884i
$25$	3.95269	−	2.28209i	0.790539	−	0.456418i
$26$	3.43598	+	6.04753i	0.673850	+	1.18602i
$27$	−0.707107	+	0.707107i	−0.136083	+	0.136083i
$28$	4.82890	−	2.16372i	0.912577	−	0.408905i
$29$	−1.84259	−	1.84259i	−0.342160	−	0.342160i	0.515019	−	0.857179i	$-0.327785\pi$
$29$	−1.84259	−	1.84259i	−0.342160	−	0.342160i	−0.857179	+	0.515019i	$0.827785\pi$
$30$	4.21664	+	1.16117i	0.769849	+	0.212000i
$31$	2.06549	+	3.57754i	0.370973	+	0.642545i	0.989716	−	0.143049i	$-0.0456908\pi$
$31$	2.06549	+	3.57754i	0.370973	+	0.642545i	−0.618742	+	0.785594i	$0.712357\pi$
$32$	−5.51147	+	1.27424i	−0.974300	+	0.225256i
$33$	0.421695	+	0.243466i	0.0734076	+	0.0423819i
$34$	1.11819	+	4.29169i	0.191768	+	0.736018i
$35$	−2.80804	+	7.68532i	−0.474645	+	1.29906i
$36$	0.975938	+	1.74572i	0.162656	+	0.290954i
$37$	0.247863	+	0.925038i	0.0407485	+	0.152075i	0.983303	−	0.181978i	$-0.0582500\pi$
$37$	0.247863	+	0.925038i	0.0407485	+	0.152075i	−0.942554	+	0.334054i	$0.891583\pi$
$38$	−0.0712041	+	10.2913i	−0.0115508	+	1.66947i
$39$	−2.45913	−	4.25934i	−0.393776	−	0.682040i
$40$	4.52988	−	7.48289i	0.716237	−	1.18315i
$41$	−10.5903			−1.65392			−0.826961	−	0.562260i	$-0.809932\pi$
$41$	−10.5903			−1.65392			−0.826961	+	0.562260i	$0.809932\pi$
$42$	−3.40388	+	1.55357i	−0.525231	+	0.239721i
$43$	0.0791459	+	0.0791459i	0.0120696	+	0.0120696i	0.713116	−	0.701046i	$-0.247283\pi$
$43$	0.0791459	+	0.0791459i	0.0120696	+	0.0120696i	−0.701046	+	0.713116i	$0.747283\pi$
$44$	0.698087	−	0.679030i	0.105241	−	0.102368i
$45$	−2.98722	−	0.800424i	−0.445309	−	0.119320i
$46$	−4.43752	−	4.49935i	−0.654276	−	0.663393i
$47$	0.463923	−	0.803538i	0.0676701	−	0.117208i	−0.830205	−	0.557458i	$-0.811777\pi$
$47$	0.463923	−	0.803538i	0.0676701	−	0.117208i	0.897875	+	0.440250i	$0.145110\pi$
$48$	3.89087	−	0.927965i	0.561599	−	0.133940i
$49$	−2.37780	−	6.58377i	−0.339686	−	0.940539i
$50$	1.62743	+	6.24619i	0.230153	+	0.883345i
$51$	−0.811655	−	3.02914i	−0.113654	−	0.424164i
$52$	−9.53567	+	2.41416i	−1.32236	+	0.334784i
$53$	0.494143	+	0.132405i	0.0678757	+	0.0181872i	0.292597	−	0.956236i	$-0.405481\pi$
$53$	0.494143	+	0.132405i	0.0678757	+	0.0181872i	−0.224721	+	0.974423i	$0.572147\pi$
$54$	−0.698616	−	1.22961i	−0.0950696	−	0.167328i
$55$			1.50588i			0.203053i
$56$	1.13705	+	7.39643i	0.151944	+	0.988389i
$57$		−	7.27722i		−	0.963891i
$58$	3.20412	−	1.82046i	0.420722	−	0.239038i
$59$	−8.37839	−	2.24498i	−1.09077	−	0.292272i	−0.331771	−	0.943360i	$-0.607646\pi$
$59$	−8.37839	−	2.24498i	−1.09077	−	0.292272i	−0.759002	+	0.651088i	$0.774313\pi$
$60$	−3.16642	+	5.31324i	−0.408783	+	0.685936i
$61$	3.47221	+	12.9585i	0.444571	+	1.65916i	0.717068	+	0.697004i	$0.245484\pi$
$61$	3.47221	+	12.9585i	0.444571	+	1.65916i	−0.272497	+	0.962157i	$0.587849\pi$
$62$	−5.65335	+	1.47297i	−0.717977	+	0.187067i
$63$	2.39925	−	1.11517i	0.302277	−	0.140498i
$64$	0.332005	−	7.99311i	0.0415006	−	0.999138i
$65$	7.60511	−	13.1724i	0.943297	−	1.63384i
$66$	−0.490289	+	0.483551i	−0.0603503	+	0.0595210i
$67$	−7.23899	−	1.93968i	−0.884383	−	0.236970i	−0.212086	−	0.977251i	$-0.568026\pi$
$67$	−7.23899	−	1.93968i	−0.884383	−	0.236970i	−0.672297	+	0.740281i	$0.734692\pi$
$68$	−6.27139	−	0.0867859i	−0.760518	−	0.0105243i
$69$	3.15974	+	3.15974i	0.380388	+	0.380388i
$70$	−9.42430	−	6.71424i	−1.12642	−	0.802505i
$71$	7.13408			0.846659			0.423329	−	0.905976i	$-0.360861\pi$
$71$	7.13408			0.846659			0.423329	+	0.905976i	$0.360861\pi$
$72$	−2.74666	+	0.675190i	−0.323696	+	0.0795719i
$73$	2.30993	+	4.00091i	0.270357	+	0.468272i	0.968953	−	0.247244i	$-0.0795250\pi$
$73$	2.30993	+	4.00091i	0.270357	+	0.468272i	−0.698596	+	0.715516i	$0.746192\pi$
$74$	−1.35432	−	0.00937034i	−0.157436	−	0.00108928i
$75$	−1.18130	−	4.40866i	−0.136404	−	0.509068i
$76$	−14.0050	−	3.96113i	−1.60649	−	0.454373i
$77$	−0.826877	−	0.987922i	−0.0942314	−	0.112584i
$78$	6.73076	−	1.75368i	0.762109	−	0.198565i
$79$	−3.17895	−	1.83537i	−0.357660	−	0.206495i	0.310394	−	0.950608i	$-0.399539\pi$
$79$	−3.17895	−	1.83537i	−0.357660	−	0.206495i	−0.668054	+	0.744113i	$0.732872\pi$
$80$	8.50180	+	8.98589i	0.950530	+	1.00465i
$81$	0.500000	+	0.866025i	0.0555556	+	0.0962250i
$82$	3.97630	−	14.4394i	0.439109	−	1.59457i
$83$	−6.06590	−	6.06590i	−0.665819	−	0.665819i	0.290927	−	0.956745i	$-0.406036\pi$
$83$	−6.06590	−	6.06590i	−0.665819	−	0.665819i	−0.956745	+	0.290927i	$0.906036\pi$
$84$	−0.840180	−	5.22438i	−0.0916712	−	0.570026i
$85$	6.85779	−	6.85779i	0.743832	−	0.743832i
$86$	−0.137629	+	0.0781955i	−0.0148409	+	0.00843204i
$87$	−2.25670	+	1.30290i	−0.241943	+	0.139686i
$88$	0.663722	+	1.20677i	0.0707530	+	0.128642i
$89$	−6.37228	+	11.0371i	−0.675461	+	1.16993i	0.300873	+	0.953664i	$0.402722\pi$
$89$	−6.37228	+	11.0371i	−0.675461	+	1.16993i	−0.976334	+	0.216268i	$0.930611\pi$
$90$	2.21295	−	3.77243i	0.233266	−	0.397649i
$91$	2.24369	+	12.8176i	0.235202	+	1.34365i
$92$	7.80083	−	4.36102i	0.813293	−	0.454668i
$93$	3.99022	−	1.06918i	0.413767	−	0.110869i
$94$	0.921404	+	0.934243i	0.0950356	+	0.0963598i
$95$	19.4904	−	11.2528i	1.99967	−	1.15451i
$96$	−0.195653	+	5.65347i	−0.0199687	+	0.577005i
$97$		−	12.9745i		−	1.31736i	−0.752425	−	0.658678i	$-0.771116\pi$
$97$		−	12.9745i		−	1.31736i	0.752425	−	0.658678i	$-0.228884\pi$
$98$	9.86950	−	0.770044i	0.996970	−	0.0777862i
$99$	0.344312	−	0.344312i	0.0346047	−	0.0346047i
$100$	−9.12748	−	0.126310i	−0.912748	−	0.0126310i
$101$	3.46635	−	12.9366i	0.344915	−	1.28724i	−0.547797	−	0.836611i	$-0.684534\pi$
$101$	3.46635	−	12.9366i	0.344915	−	1.28724i	0.892712	−	0.450628i	$-0.148800\pi$
$102$	4.43486	+	0.0306842i	0.439117	+	0.00303819i
$103$	−9.23324	−	5.33081i	−0.909778	−	0.525261i	−0.0294183	−	0.999567i	$-0.509365\pi$
$103$	−9.23324	−	5.33081i	−0.909778	−	0.525261i	−0.880360	+	0.474307i	$0.842699\pi$
$104$	0.288718	−	13.9079i	0.0283112	−	1.36379i
$105$	6.69668	+	4.70146i	0.653529	+	0.458816i
$106$	−0.366064	+	0.624030i	−0.0355552	+	0.0606111i
$107$	−17.1980	+	4.60820i	−1.66260	+	0.445492i	−0.963100	−	0.269144i	$-0.913259\pi$
$107$	−17.1980	+	4.60820i	−1.66260	+	0.445492i	−0.699497	+	0.714635i	$0.746593\pi$
$108$	1.93883	−	0.490857i	0.186564	−	0.0472328i
$109$	−5.28529	+	19.7250i	−0.506239	+	1.88931i	−0.0515242	+	0.998672i	$0.516408\pi$
$109$	−5.28529	+	19.7250i	−0.506239	+	1.88931i	−0.454715	+	0.890637i	$0.650259\pi$
$110$	−2.05321	−	0.565411i	−0.195766	−	0.0539098i
$111$	0.957670			0.0908980
$112$	−10.5117	−	1.22680i	−0.993258	−	0.115922i
$113$	−7.25487			−0.682481			−0.341240	−	0.939976i	$-0.610847\pi$
$113$	−7.25487			−0.682481			−0.341240	+	0.939976i	$0.610847\pi$
$114$	9.92220	+	2.73236i	0.929299	+	0.255909i
$115$	−3.57673	+	13.3485i	−0.333532	+	1.24476i
$116$	1.27908	+	5.05222i	0.118760	+	0.469087i
$117$	−4.75067	+	1.27294i	−0.439200	+	0.117683i
$118$	6.20676	−	10.5807i	0.571379	−	0.974031i
$119$	−0.733397	+	8.26459i	−0.0672304	+	0.757613i
$120$	−6.05550	−	6.31224i	−0.552789	−	0.576226i
$121$	9.32094	+	5.38145i	0.847358	+	0.489223i
$122$	−18.9720	−	0.131265i	−1.71765	−	0.0118842i
$123$	−2.74096	+	10.2294i	−0.247144	+	0.922355i
$124$	0.114321	−	8.26118i	0.0102664	−	0.741876i
$125$	−0.953056	+	0.953056i	−0.0852439	+	0.0852439i
$126$	0.619642	+	3.68999i	0.0552021	+	0.328731i
$127$		−	0.527420i		−	0.0468010i	−0.999726	−	0.0234005i	$-0.992551\pi$
$127$		−	0.527420i		−	0.0468010i	0.999726	−	0.0234005i	$-0.00744928\pi$
$128$	10.7736	+	3.45383i	0.952263	+	0.305278i
$129$	0.0969335	−	0.0559646i	0.00853452	−	0.00492741i
$130$	15.1046	+	15.3151i	1.32476	+	1.34322i
$131$	−19.0490	+	5.10415i	−1.66431	+	0.445952i	−0.963569	−	0.267459i	$-0.913816\pi$
$131$	−19.0490	+	5.10415i	−1.66431	+	0.445952i	−0.700746	+	0.713411i	$0.747149\pi$
$132$	−0.475215	−	0.850047i	−0.0413621	−	0.0739871i
$133$	−6.60761	+	18.0844i	−0.572953	+	1.56811i
$134$	5.36268	−	9.14179i	0.463265	−	0.789730i
$135$	−1.54630	+	2.67827i	−0.133084	+	0.230509i
$136$	2.47303	−	8.51821i	0.212061	−	0.730430i
$137$	9.21727	−	5.32159i	0.787484	−	0.454654i	−0.0515919	−	0.998668i	$-0.516429\pi$
$137$	9.21727	−	5.32159i	0.787484	−	0.454654i	0.839076	+	0.544014i	$0.183096\pi$
$138$	−5.49455	+	3.12180i	−0.467727	+	0.265745i
$139$	1.15349	−	1.15349i	0.0978381	−	0.0978381i	−0.656494	−	0.754332i	$-0.727961\pi$
$139$	1.15349	−	1.15349i	0.0978381	−	0.0978381i	0.754332	+	0.656494i	$0.227961\pi$
$140$	12.6931	−	10.3287i	1.07276	−	0.872933i
$141$	−0.656086	−	0.656086i	−0.0552524	−	0.0552524i
$142$	−2.67862	+	9.72703i	−0.224784	+	0.816274i
$143$	1.19743	+	2.07400i	0.100134	+	0.173437i
$144$	0.110686	−	3.99847i	0.00922383	−	0.333206i
$145$	−6.97906	−	4.02936i	−0.579580	−	0.334620i
$146$	−6.32239	+	1.64728i	−0.523245	+	0.136330i
$147$	−6.97486	+	0.592774i	−0.575276	+	0.0488912i
$148$	0.521279	−	1.84304i	0.0428489	−	0.151497i
$149$	0.869826	+	3.24623i	0.0712589	+	0.265942i	0.992359	−	0.123384i	$-0.0393747\pi$
$149$	0.869826	+	3.24623i	0.0712589	+	0.265942i	−0.921100	+	0.389326i	$0.872708\pi$
$150$	6.45457	+	0.0446583i	0.527013	+	0.00364633i
$151$	−6.36861	−	11.0308i	−0.518270	−	0.897670i	−0.999775	−	0.0212268i	$-0.993243\pi$
$151$	−6.36861	−	11.0308i	−0.518270	−	0.897670i	0.481504	−	0.876444i	$-0.340091\pi$
$152$	10.6593	−	17.6080i	0.864582	−	1.42820i
$153$	−3.13600			−0.253530
$154$	1.65746	−	0.756481i	0.133562	−	0.0609590i
$155$	9.03363	+	9.03363i	0.725599	+	0.725599i
$156$	−0.136109	+	9.83558i	−0.0108974	+	0.787477i
$157$	15.0874	+	4.04266i	1.20411	+	0.322639i	0.804447	−	0.594025i	$-0.202462\pi$
$157$	15.0874	+	4.04266i	1.20411	+	0.322639i	0.399659	+	0.916664i	$0.369129\pi$
$158$	3.69604	−	3.64525i	0.294041	−	0.290000i
$159$	0.255787	−	0.443036i	0.0202852	−	0.0351350i
$160$	−15.4441	+	8.21795i	−1.22096	+	0.649686i
$161$	−4.98316	−	10.7212i	−0.392728	−	0.844945i
$162$	−1.36853	+	0.356566i	−0.107521	+	0.0280144i
$163$	−3.58390	−	13.3753i	−0.280713	−	1.04763i	−0.951916	−	0.306360i	$-0.900889\pi$
$163$	−3.58390	−	13.3753i	−0.280713	−	1.04763i	0.671203	−	0.741274i	$-0.265778\pi$
$164$	18.1946	+	10.8431i	1.42076	+	0.846701i
$165$	1.45457	+	0.389751i	0.113238	+	0.0303421i
$166$	10.5482	−	5.99306i	0.818696	−	0.465152i
$167$			17.4217i			1.34813i	0.738670	+	0.674067i	$0.235454\pi$
$167$			17.4217i			1.34813i	−0.738670	+	0.674067i	$0.764546\pi$
$168$	7.43869	+	0.816032i	0.573907	+	0.0629582i
$169$		−	11.1893i		−	0.860714i
$170$	6.77545	+	11.9252i	0.519653	+	0.914621i
$171$	−7.02925	−	1.88348i	−0.537540	−	0.144034i
$172$	−0.0549412	−	0.217011i	−0.00418923	−	0.0165470i
$173$	−1.13148	−	4.22275i	−0.0860250	−	0.321050i	0.909481	−	0.415745i	$-0.136479\pi$
$173$	−1.13148	−	4.22275i	−0.0860250	−	0.321050i	−0.995506	+	0.0946952i	$0.969812\pi$
$174$	−0.929142	−	3.56612i	−0.0704381	−	0.270347i
$175$	−1.06740	+	12.0284i	−0.0806877	+	0.909262i
$176$	−1.89459	+	0.451855i	−0.142810	+	0.0340599i
$177$	−4.33697	+	7.51186i	−0.325987	+	0.564626i
$178$	−12.6561	−	12.8324i	−0.948614	−	0.961832i
$179$	23.2689	+	6.23489i	1.73920	+	0.466017i	0.982269	−	0.187477i	$-0.0600309\pi$
$179$	23.2689	+	6.23489i	1.73920	+	0.466017i	0.756932	+	0.653494i	$0.226698\pi$
$180$	4.31266	+	4.43370i	0.321447	+	0.330468i
$181$	17.5258	+	17.5258i	1.30268	+	1.30268i	0.926575	+	0.376109i	$0.122738\pi$
$181$	17.5258	+	17.5258i	1.30268	+	1.30268i	0.376109	+	0.926575i	$0.377262\pi$
$182$	−18.3187	−	1.75342i	−1.35787	−	0.129972i
$183$	13.4156			0.991708
$184$	3.01711	+	12.2735i	0.222425	+	0.904818i
$185$	1.48085	+	2.56490i	0.108874	+	0.188575i
$186$	−0.0404197	+	5.84195i	−0.00296371	+	0.428353i
$187$	0.395220	+	1.47498i	0.0289014	+	0.107861i
$188$	−1.61976	+	0.905520i	−0.118133	+	0.0660418i
$189$	−0.456195	−	2.60612i	−0.0331833	−	0.189568i
$190$	8.02469	+	30.7994i	0.582173	+	2.23442i
$191$	14.9461	+	8.62913i	1.08146	+	0.624382i	0.931290	−	0.364278i	$-0.118684\pi$
$191$	14.9461	+	8.62913i	1.08146	+	0.624382i	0.150171	+	0.988660i	$0.452017\pi$
$192$	−7.63482	−	2.38946i	−0.550996	−	0.172444i
$193$	4.44266	+	7.69491i	0.319790	+	0.553892i	0.980444	−	0.196798i	$-0.0630544\pi$
$193$	4.44266	+	7.69491i	0.319790	+	0.553892i	−0.660654	+	0.750690i	$0.729721\pi$
$194$	17.6901	+	4.87149i	1.27008	+	0.349752i
$195$	−10.7552	−	10.7552i	−0.770199	−	0.770199i
$196$	−2.65576	+	13.7458i	−0.189697	+	0.981843i
$197$	−6.37151	+	6.37151i	−0.453952	+	0.453952i	−0.896664	−	0.442712i	$-0.854016\pi$
$197$	−6.37151	+	6.37151i	−0.453952	+	0.453952i	0.442712	+	0.896664i	$0.354016\pi$
$198$	0.340178	+	0.598734i	0.0241754	+	0.0425502i
$199$	12.6313	−	7.29269i	0.895410	−	0.516965i	0.0197020	−	0.999806i	$-0.493728\pi$
$199$	12.6313	−	7.29269i	0.895410	−	0.516965i	0.875708	+	0.482841i	$0.160395\pi$
$200$	3.59929	−	12.3975i	0.254508	−	0.876638i
$201$	−3.74718	+	6.49030i	−0.264305	+	0.457790i
$202$	16.3370	+	9.58350i	1.14947	+	0.674293i
$203$	6.79106	−	1.18876i	0.476639	−	0.0834344i
$204$	−1.70698	+	6.03524i	−0.119513	+	0.422551i
$205$	−31.6355	+	8.47670i	−2.20952	+	0.592038i
$206$	10.7351	−	10.5876i	0.747952	−	0.737673i
$207$	3.86987	−	2.23427i	0.268975	−	0.155293i
$208$	18.8545	+	5.61564i	1.30733	+	0.389375i
$209$			3.54350i			0.245109i
$210$	−8.92465	+	7.36540i	−0.615859	+	0.508261i
$211$	18.2937	−	18.2937i	1.25939	−	1.25939i	0.308003	−	0.951385i	$-0.400339\pi$
$211$	18.2937	−	18.2937i	1.25939	−	1.25939i	0.951385	−	0.308003i	$-0.0996608\pi$
$212$	−0.713395	−	0.733416i	−0.0489962	−	0.0503712i
$213$	1.84643	−	6.89099i	0.126516	−	0.472163i
$214$	0.174211	−	25.1791i	0.0119088	−	1.72121i
$215$	0.299777	+	0.173076i	0.0204446	+	0.0118037i
$216$	−0.0587034	+	2.82782i	−0.00399426	+	0.192409i
$217$	−10.8868	−	0.966090i	−0.739042	−	0.0655824i
$218$	−24.9098	−	14.6124i	−1.68710	−	0.989675i
$219$	4.46244	−	1.19571i	0.301544	−	0.0807984i
$220$	1.54183	−	2.58718i	0.103950	−	0.174428i
$221$	3.99193	−	14.8981i	0.268526	−	1.00215i
$222$	−0.359574	+	1.30575i	−0.0241330	+	0.0876359i
$223$	9.30454			0.623078			0.311539	−	0.950233i	$-0.399156\pi$
$223$	9.30454			0.623078			0.311539	+	0.950233i	$0.399156\pi$
$224$	5.61948	−	13.8716i	0.375467	−	0.926836i
$225$	−4.56418			−0.304278
$226$	2.72397	−	9.89173i	0.181196	−	0.657988i
$227$	−1.38129	+	5.15506i	−0.0916797	+	0.342153i	−0.996495	−	0.0836507i	$-0.973342\pi$
$227$	−1.38129	+	5.15506i	−0.0916797	+	0.342153i	0.904815	+	0.425804i	$0.140009\pi$
$228$	−7.45093	+	12.5026i	−0.493450	+	0.828005i
$229$	−6.10608	+	1.63612i	−0.403501	+	0.108118i	−0.454861	−	0.890562i	$-0.650311\pi$
$229$	−6.10608	+	1.63612i	−0.403501	+	0.108118i	0.0513599	+	0.998680i	$0.483644\pi$
$230$	−16.8572	−	9.88867i	−1.11153	−	0.652039i
$231$	−1.16827	+	0.543009i	−0.0768666	+	0.0357274i
$232$	−7.36875	−	0.152970i	−0.483782	−	0.0100430i
$233$	−9.67912	−	5.58824i	−0.634101	−	0.366098i	0.148238	−	0.988952i	$-0.452640\pi$
$233$	−9.67912	−	5.58824i	−0.634101	−	0.366098i	−0.782338	+	0.622854i	$0.785973\pi$
$234$	0.0481228	−	6.95530i	0.00314589	−	0.454682i
$235$	0.742670	−	2.77168i	0.0484465	−	0.180805i
$236$	12.0959	+	12.4354i	0.787376	+	0.809474i
$237$	−2.59560	+	2.59560i	−0.168602	+	0.168602i
$238$	−10.9931	−	4.10304i	−0.712575	−	0.265961i
$239$			6.93252i			0.448428i	0.974540	+	0.224214i	$0.0719814\pi$
$239$			6.93252i			0.448428i	−0.974540	+	0.224214i	$0.928019\pi$
$240$	10.8801	−	5.88639i	0.702310	−	0.379965i
$241$	−8.40040	+	4.84998i	−0.541118	+	0.312414i	−0.745532	−	0.666470i	$-0.767804\pi$
$241$	−8.40040	+	4.84998i	−0.541118	+	0.312414i	0.204414	+	0.978884i	$0.434471\pi$
$242$	−10.8371	+	10.6882i	−0.696636	+	0.687062i
$243$	0.965926	−	0.258819i	0.0619642	−	0.0166032i
$244$	7.30237	−	25.8183i	0.467486	−	1.65285i
$245$	−12.3728	−	17.7639i	−0.790471	−	1.13490i
$246$	−12.9182	−	7.57801i	−0.823637	−	0.483156i
$247$	17.8956	−	30.9961i	1.13867	−	1.97224i
$248$	11.2209	+	3.25768i	0.712525	+	0.206863i
$249$	−7.42918	+	4.28924i	−0.470805	+	0.271819i
$250$	−0.941613	−	1.65730i	−0.0595528	−	0.104817i
$251$	10.1841	−	10.1841i	0.642812	−	0.642812i	−0.308434	−	0.951246i	$-0.599805\pi$
$251$	10.1841	−	10.1841i	0.642812	−	0.642812i	0.951246	+	0.308434i	$0.0998048\pi$
$252$	−5.26381	−	0.540616i	−0.331589	−	0.0340556i
$253$	−1.53857	−	1.53857i	−0.0967293	−	0.0967293i
$254$	0.719116	+	0.198029i	0.0451214	+	0.0124255i
$255$	−4.84919	−	8.39904i	−0.303668	−	0.525969i
$256$	−8.75431	+	13.3926i	−0.547144	+	0.837038i
$257$	−9.11571	−	5.26296i	−0.568622	−	0.328294i	0.187977	−	0.982174i	$-0.439807\pi$
$257$	−9.11571	−	5.26296i	−0.568622	−	0.328294i	−0.756599	+	0.653879i	$0.773140\pi$
$258$	0.0399101	+	0.153178i	0.00248469	+	0.00953644i
$259$	−2.37988	−	0.869551i	−0.147878	−	0.0540313i
$260$	−26.5528	+	14.8442i	−1.64674	+	0.920600i
$261$	0.674433	+	2.51702i	0.0417464	+	0.155800i
$262$	0.192960	−	27.8889i	0.0119211	−	1.72298i
$263$	−12.9215	−	22.3806i	−0.796772	−	1.38005i	−0.921708	−	0.387884i	$-0.873206\pi$
$263$	−12.9215	−	22.3806i	−0.796772	−	1.38005i	0.124936	−	0.992165i	$-0.460127\pi$
$264$	1.33743	−	0.328771i	0.0823133	−	0.0202345i
$265$	1.58209			0.0971873
$266$	−22.1764	−	15.7993i	−1.35972	−	0.968718i
$267$	9.01177	+	9.01177i	0.551511	+	0.551511i
$268$	10.4509	+	10.7443i	0.638393	+	0.656310i
$269$	3.70529	+	0.992830i	0.225916	+	0.0605339i	0.370001	−	0.929031i	$-0.379357\pi$
$269$	3.70529	+	0.992830i	0.225916	+	0.0605339i	−0.144085	+	0.989565i	$0.546024\pi$
$270$	−3.07113	−	3.11392i	−0.186903	−	0.189507i
$271$	−14.9974	+	25.9763i	−0.911029	+	1.57795i	−0.0984158	+	0.995145i	$0.531378\pi$
$271$	−14.9974	+	25.9763i	−0.911029	+	1.57795i	−0.812613	+	0.582803i	$0.801956\pi$
$272$	10.6857	+	6.57020i	0.647915	+	0.398377i
$273$	12.9616	+	1.15021i	0.784469	+	0.0696136i
$274$	3.79499	+	14.5655i	0.229264	+	0.879932i
$275$	0.575210	+	2.14671i	0.0346865	+	0.129452i
$276$	−2.19342	−	8.66374i	−0.132028	−	0.521496i
$277$	8.69269	+	2.32920i	0.522293	+	0.139948i	0.510327	−	0.859980i	$-0.329524\pi$
$277$	8.69269	+	2.32920i	0.522293	+	0.139948i	0.0119660	+	0.999928i	$0.496191\pi$
$278$	1.13964	+	2.00584i	0.0683513	+	0.120303i
$279$		−	4.13098i		−	0.247316i
$280$	9.31689	+	21.1847i	0.556791	+	1.26603i
$281$		−	16.7358i		−	0.998376i	−0.866494	−	0.499188i	$-0.833632\pi$
$281$		−	16.7358i		−	0.998376i	0.866494	−	0.499188i	$-0.166368\pi$
$282$	1.14089	−	0.648208i	0.0679388	−	0.0386002i
$283$	−17.1643	−	4.59916i	−1.02031	−	0.273392i	−0.290379	−	0.956912i	$-0.593782\pi$
$283$	−17.1643	−	4.59916i	−1.02031	−	0.273392i	−0.729932	+	0.683520i	$0.760448\pi$
$284$	−12.2567	−	7.30437i	−0.727300	−	0.433435i
$285$	−5.82486	−	21.7387i	−0.345035	−	1.28769i
$286$	−3.27742	+	0.853923i	−0.193798	+	0.0504935i
$287$	16.0996	−	22.9320i	0.950331	−	1.35363i
$288$	5.41019	+	1.65221i	0.318799	+	0.0973575i
$289$	−3.58277	+	6.20553i	−0.210751	+	0.365031i
$290$	8.11429	−	8.00278i	0.476488	−	0.469939i
$291$	−12.5324	−	3.35803i	−0.734660	−	0.196851i
$292$	0.127851	−	9.23883i	0.00748189	−	0.540662i
$293$	1.78284	+	1.78284i	0.104154	+	0.104154i	0.757264	−	0.653109i	$-0.226536\pi$
$293$	1.78284	+	1.78284i	0.104154	+	0.104154i	−0.653109	+	0.757264i	$0.726536\pi$
$294$	1.81061	−	9.73251i	0.105597	−	0.567611i
$295$	−26.8251			−1.56181
$296$	2.31719	+	1.40275i	0.134684	+	0.0815329i
$297$	−0.243466	−	0.421695i	−0.0141273	−	0.0244692i
$298$	−4.75270	−	0.0328833i	−0.275317	−	0.00190488i
$299$	5.68818	+	21.2286i	0.328956	+	1.22768i
$300$	−2.48437	+	8.78378i	−0.143435	+	0.507132i
$301$	−0.291701	+	0.0510615i	−0.0168134	+	0.00294314i
$302$	17.4312	−	4.54165i	1.00305	−	0.261343i
$303$	−11.5986	−	6.69647i	−0.666324	−	0.384702i
$304$	20.0056	+	21.1448i	1.14740	+	1.21274i
$305$	20.7445	+	35.9306i	1.18783	+	2.05738i
$306$	1.17747	−	4.27581i	0.0673112	−	0.244432i
$307$	9.82617	+	9.82617i	0.560809	+	0.560809i	0.929537	−	0.368728i	$-0.120207\pi$
$307$	9.82617	+	9.82617i	0.560809	+	0.560809i	−0.368728	+	0.929537i	$0.620207\pi$
$308$	0.409110	+	2.54391i	0.0233112	+	0.144953i
$309$	−7.53891	+	7.53891i	−0.428873	+	0.428873i
$310$	−15.7088	+	8.92516i	−0.892202	+	0.506915i
$311$	0.949948	−	0.548453i	0.0538666	−	0.0310999i	−0.472825	−	0.881156i	$-0.656766\pi$
$311$	0.949948	−	0.548453i	0.0538666	−	0.0310999i	0.526691	+	0.850057i	$0.323432\pi$
$312$	−13.3593	−	3.87852i	−0.756322	−	0.219578i
$313$	−5.82011	+	10.0807i	−0.328972	+	0.569797i	−0.982308	−	0.187271i	$-0.940036\pi$
$313$	−5.82011	+	10.0807i	−0.328972	+	0.569797i	0.653336	+	0.757068i	$0.273369\pi$
$314$	−11.1768	+	19.0532i	−0.630745	+	1.07523i
$315$	6.27449	−	5.25166i	0.353528	−	0.295898i
$316$	3.58241	+	6.40808i	0.201526	+	0.360483i
$317$	−29.4984	+	7.90407i	−1.65679	+	0.443937i	−0.961504	−	0.274791i	$-0.911391\pi$
$317$	−29.4984	+	7.90407i	−1.65679	+	0.443937i	−0.695291	+	0.718728i	$0.744725\pi$
$318$	0.508022	+	0.515101i	0.0284885	+	0.0288854i
$319$	1.09886	−	0.634425i	0.0615241	−	0.0355210i
$320$	−5.40610	−	24.1429i	−0.302210	−	1.34963i
$321$			17.8047i			0.993762i
$322$	16.4889	−	2.76890i	0.918890	−	0.154305i
$323$	16.1371	−	16.1371i	0.897893	−	0.897893i
$324$	0.0276741	−	1.99981i	0.00153745	−	0.111100i
$325$	5.80992	−	21.6829i	0.322276	−	1.20275i
$326$	19.5823	+	0.135487i	1.08456	+	0.00750395i
$327$	17.6849	+	10.2104i	0.977978	+	0.564636i
$328$	−21.6156	+	20.7364i	−1.19352	+	1.14497i
$329$	1.03470	+	2.22614i	0.0570449	+	0.122731i
$330$	−1.07756	+	1.83691i	−0.0593175	+	0.101119i
$331$	9.88524	−	2.64874i	0.543342	−	0.145588i	0.0232996	−	0.999729i	$-0.492583\pi$
$331$	9.88524	−	2.64874i	0.543342	−	0.145588i	0.520042	+	0.854140i	$0.325916\pi$
$332$	4.21081	+	16.6322i	0.231098	+	0.912810i
$333$	0.247863	−	0.925038i	0.0135828	−	0.0506918i
$334$	−23.7538	−	6.54130i	−1.29975	−	0.357924i
$335$	−23.1770			−1.26630
$336$	−3.90562	+	9.83596i	−0.213069	+	0.536596i
$337$	−33.0412			−1.79987			−0.899934	−	0.436025i	$-0.856386\pi$
$337$	−33.0412			−1.79987			−0.899934	+	0.436025i	$0.856386\pi$
$338$	15.2561	+	4.20121i	0.829825	+	0.228516i
$339$	−1.87770	+	7.00767i	−0.101983	+	0.380604i
$340$	−18.8035	+	4.76052i	−1.01976	+	0.258176i
$341$	−1.94296	+	0.520616i	−0.105217	+	0.0281929i
$342$	5.20731	−	8.87692i	0.281579	−	0.480009i
$343$	17.8712	+	4.85999i	0.964955	+	0.262415i
$344$	0.316515	+	0.00657062i	0.0170654	+	0.000354264i
$345$	11.9680	+	6.90971i	0.644333	+	0.372006i
$346$	6.18238	+	0.0427751i	0.332367	+	0.00229960i
$347$	3.19579	−	11.9269i	0.171559	−	0.640267i	−0.825553	−	0.564325i	$-0.809137\pi$
$347$	3.19579	−	11.9269i	0.171559	−	0.640267i	0.997112	−	0.0759428i	$-0.0241966\pi$
$348$	5.21112	+	0.0721135i	0.279345	+	0.00386569i
$349$	11.2223	−	11.2223i	0.600718	−	0.600718i	−0.339785	−	0.940503i	$-0.610354\pi$
$349$	11.2223	−	11.2223i	0.600718	−	0.600718i	0.940503	+	0.339785i	$0.110354\pi$
$350$	−15.9995	−	5.97164i	−0.855209	−	0.319197i
$351$			4.91826i			0.262517i
$352$	0.0952695	−	2.75285i	0.00507788	−	0.146727i
$353$	13.0680	−	7.54480i	0.695539	−	0.401569i	−0.110145	−	0.993916i	$-0.535132\pi$
$353$	13.0680	−	7.54480i	0.695539	−	0.401569i	0.805684	+	0.592346i	$0.201798\pi$
$354$	−8.61373	−	8.73375i	−0.457814	−	0.464194i
$355$	21.3111	−	5.71028i	1.13107	−	0.303070i
$356$	22.2485	−	12.4379i	1.17917	−	0.659208i
$357$	7.79316	+	2.84744i	0.412458	+	0.150702i
$358$	−17.2378	+	29.3852i	−0.911044	+	1.55306i
$359$	3.54609	−	6.14200i	0.187155	−	0.324163i	−0.757145	−	0.653246i	$-0.773407\pi$
$359$	3.54609	−	6.14200i	0.187155	−	0.324163i	0.944301	+	0.329084i	$0.106740\pi$
$360$	−7.66443	+	4.21543i	−0.403951	+	0.222173i
$361$	29.4084	−	16.9789i	1.54781	−	0.893629i
$362$	−30.4762	+	17.3154i	−1.60179	+	0.910077i
$363$	7.61052	−	7.61052i	0.399449	−	0.399449i
$364$	9.26881	−	24.3185i	0.485817	−	1.27464i
$365$	10.1027	+	10.1027i	0.528799	+	0.528799i
$366$	−5.03712	+	18.2916i	−0.263294	+	0.956118i
$367$	−11.1656	−	19.3394i	−0.582841	−	1.00951i	−0.995141	−	0.0984616i	$-0.968608\pi$
$367$	−11.1656	−	19.3394i	−0.582841	−	1.00951i	0.412300	−	0.911048i	$-0.364725\pi$
$368$	−17.8673	−	0.494605i	−0.931399	−	0.0257830i
$369$	9.17144	+	5.29513i	0.477446	+	0.275654i
$370$	−4.05315	+	1.05604i	−0.210713	+	0.0549008i
$371$	−1.03792	+	0.868724i	−0.0538860	+	0.0451019i
$372$	−7.95010	−	2.24858i	−0.412193	−	0.116583i
$373$	−1.87748	−	7.00685i	−0.0972123	−	0.362801i	0.900133	−	0.435615i	$-0.143469\pi$
$373$	−1.87748	−	7.00685i	−0.0972123	−	0.362801i	−0.997346	+	0.0728134i	$0.976802\pi$
$374$	−2.15947	−	0.0149411i	−0.111664	−	0.000772586i
$375$	0.673913	+	1.16725i	0.0348007	+	0.0602766i
$376$	−0.626472	−	2.54847i	−0.0323078	−	0.131427i
$377$	−12.8160			−0.660060
$378$	3.72463	+	0.356512i	0.191575	+	0.0183370i
$379$	−0.254449	−	0.254449i	−0.0130701	−	0.0130701i	0.700542	−	0.713612i	$-0.252942\pi$
$379$	−0.254449	−	0.254449i	−0.0130701	−	0.0130701i	−0.713612	+	0.700542i	$0.752942\pi$
$380$	−45.0067	−	0.622821i	−2.30880	−	0.0319500i
$381$	−0.509449	−	0.136506i	−0.0260998	−	0.00699343i
$382$	−17.3773	+	17.1385i	−0.889098	+	0.876879i
$383$	2.03560	−	3.52576i	0.104014	−	0.180158i	−0.809321	−	0.587367i	$-0.800165\pi$
$383$	2.03560	−	3.52576i	0.104014	−	0.180158i	0.913335	+	0.407209i	$0.133498\pi$
$384$	6.12456	−	9.51261i	0.312543	−	0.485438i
$385$	−3.26082	−	2.28929i	−0.166187	−	0.116673i
$386$	−12.1598	+	3.16820i	−0.618917	+	0.161257i
$387$	−0.0289694	−	0.108115i	−0.00147260	−	0.00549581i
$388$	−13.2842	+	22.2907i	−0.674401	+	1.13164i
$389$	6.89087	+	1.84640i	0.349381	+	0.0936164i	0.429242	−	0.903190i	$-0.358781\pi$
$389$	6.89087	+	1.84640i	0.349381	+	0.0936164i	−0.0798606	+	0.996806i	$0.525448\pi$
$390$	18.7026	−	10.6261i	0.947043	−	0.538074i
$391$			14.0133i			0.708684i
$392$	−17.7447	−	8.78212i	−0.896243	−	0.443564i
$393$			19.7209i			0.994789i
$394$	−6.29501	−	11.0796i	−0.317138	−	0.558182i
$395$	−10.9653	−	2.93814i	−0.551724	−	0.147834i
$396$	−0.944077	+	0.239014i	−0.0474416	+	0.0120109i
$397$	−6.35245	−	23.7077i	−0.318820	−	1.18985i	−0.920380	−	0.391025i	$-0.872121\pi$
$397$	−6.35245	−	23.7077i	−0.318820	−	1.18985i	0.601560	−	0.798828i	$-0.294546\pi$
$398$	5.20065	+	19.9605i	0.260685	+	1.00053i
$399$	15.7580	+	11.0630i	0.788886	+	0.553845i
$400$	15.5521	+	9.56237i	0.777606	+	0.478118i
$401$	7.79003	−	13.4927i	0.389016	−	0.673795i	−0.603302	−	0.797513i	$-0.706149\pi$
$401$	7.79003	−	13.4927i	0.389016	−	0.673795i	0.992317	+	0.123718i	$0.0394818\pi$
$402$	−7.44232	−	7.54602i	−0.371189	−	0.376361i
$403$	19.6250	+	5.25849i	0.977589	+	0.261944i
$404$	−19.2007	+	18.6766i	−0.955273	+	0.929195i
$405$	2.18680	+	2.18680i	0.108663	+	0.108663i
$406$	−0.929003	+	9.70569i	−0.0461056	+	0.481685i
$407$	−0.466320			−0.0231146
$408$	−7.58789	−	4.59344i	−0.375656	−	0.227409i
$409$	0.0716712	+	0.124138i	0.00354391	+	0.00613824i	0.867792	−	0.496928i	$-0.165539\pi$
$409$	0.0716712	+	0.124138i	0.00354391	+	0.00613824i	−0.864248	+	0.503066i	$0.832205\pi$
$410$	0.320457	−	46.3164i	0.0158262	−	2.28741i
$411$	−2.75466	−	10.2805i	−0.135877	−	0.507101i
$412$	10.4051	+	18.6122i	0.512622	+	0.916959i
$413$	17.5983	−	14.7296i	0.865957	−	0.724795i
$414$	1.59333	+	6.11531i	0.0783078	+	0.300551i
$415$	−22.9755	−	13.2649i	−1.12782	−	0.651148i
$416$	−14.7360	+	23.5989i	−0.722490	+	1.15703i
$417$	−0.815644	−	1.41274i	−0.0399422	−	0.0691820i
$418$	−4.83143	−	1.33047i	−0.236313	−	0.0650755i
$419$	−4.81101	−	4.81101i	−0.235033	−	0.235033i	0.579756	−	0.814790i	$-0.303148\pi$
$419$	−4.81101	−	4.81101i	−0.235033	−	0.235033i	−0.814790	+	0.579756i	$0.803148\pi$
$420$	−6.69152	−	14.9339i	−0.326513	−	0.728698i
$421$	−6.23817	+	6.23817i	−0.304030	+	0.304030i	−0.842588	−	0.538558i	$-0.818969\pi$
$421$	−6.23817	+	6.23817i	−0.304030	+	0.304030i	0.538558	+	0.842588i	$0.318969\pi$
$422$	18.0740	+	31.8114i	0.879829	+	1.54855i
$423$	−0.803538	+	0.463923i	−0.0390694	+	0.0225567i
$424$	1.26784	−	0.697311i	0.0615718	−	0.0338644i
$425$	7.15662	−	12.3956i	0.347147	−	0.601276i
$426$	8.70231	+	5.10488i	0.421628	+	0.247332i
$427$	−33.3386	−	12.1812i	−1.61337	−	0.589488i
$428$	34.2653	+	9.69146i	1.65627	+	0.468454i
$429$	2.31325	−	0.619834i	0.111685	−	0.0299259i
$430$	−0.348539	+	0.343749i	−0.0168080	+	0.0165770i
$431$	−24.2541	+	14.0031i	−1.16828	+	0.674505i	−0.953274	−	0.302108i	$-0.902310\pi$
$431$	−24.2541	+	14.0031i	−1.16828	+	0.674505i	−0.215003	+	0.976613i	$0.568976\pi$
$432$	−3.83358	−	1.14179i	−0.184443	−	0.0549346i
$433$		−	29.3694i		−	1.41140i	−0.708509	−	0.705702i	$-0.750632\pi$
$433$		−	29.3694i		−	1.41140i	0.708509	−	0.705702i	$-0.249368\pi$
$434$	5.40486	−	14.4809i	0.259441	−	0.695108i
$435$	−5.69838	+	5.69838i	−0.273216	+	0.273216i
$436$	29.2762	−	28.4770i	1.40208	−	1.36380i
$437$	−8.41642	+	31.4105i	−0.402612	+	1.50257i
$438$	−0.0452031	+	6.53331i	−0.00215989	+	0.312174i
$439$	3.95503	+	2.28344i	0.188763	+	0.108983i	0.591404	−	0.806376i	$-0.298574\pi$
$439$	3.95503	+	2.28344i	0.188763	+	0.108983i	−0.402640	+	0.915358i	$0.631907\pi$
$440$	2.94861	+	3.07363i	0.140569	+	0.146529i
$441$	−1.23265	+	6.89061i	−0.0586976	+	0.328125i
$442$	18.8141	+	11.0366i	0.894896	+	0.524957i
$443$	19.4737	−	5.21796i	0.925222	−	0.247913i	0.235406	−	0.971897i	$-0.424358\pi$
$443$	19.4737	−	5.21796i	0.925222	−	0.247913i	0.689816	+	0.723985i	$0.257691\pi$
$444$	−1.64532	−	0.980531i	−0.0780836	−	0.0465339i
$445$	−10.2011	+	38.0709i	−0.483576	+	1.80473i
$446$	−3.49356	+	12.6864i	−0.165425	+	0.600717i
$447$	3.36075			0.158958
$448$	16.8034	+	12.8703i	0.793888	+	0.608064i
$449$	−3.45383			−0.162996			−0.0814982	−	0.996673i	$-0.525971\pi$
$449$	−3.45383			−0.162996			−0.0814982	+	0.996673i	$0.525971\pi$
$450$	1.71370	−	6.22307i	0.0807847	−	0.293359i
$451$	1.33466	−	4.98102i	0.0628467	−	0.234547i
$452$	12.4642	+	7.42805i	0.586267	+	0.349386i
$453$	−12.3032	+	3.29664i	−0.578055	+	0.154889i
$454$	−6.51009	−	3.81890i	−0.305534	−	0.179230i
$455$	16.9619	+	36.4931i	0.795186	+	1.71082i
$456$	−14.2492	−	14.8534i	−0.667281	−	0.695573i
$457$	−3.97361	−	2.29417i	−0.185878	−	0.107317i	0.404174	−	0.914682i	$-0.367559\pi$
$457$	−3.97361	−	2.29417i	−0.185878	−	0.107317i	−0.590051	+	0.807366i	$0.700893\pi$
$458$	0.0618526	−	8.93971i	0.00289018	−	0.417725i
$459$	−0.811655	+	3.02914i	−0.0378848	+	0.141388i
$460$	19.8122	−	19.2713i	0.923747	−	0.898529i
$461$	13.1818	−	13.1818i	0.613939	−	0.613939i	−0.330031	−	0.943970i	$-0.607059\pi$
$461$	13.1818	−	13.1818i	0.613939	−	0.613939i	0.943970	+	0.330031i	$0.107059\pi$
$462$	−0.301723	−	1.79677i	−0.0140374	−	0.0835934i
$463$		−	17.8141i		−	0.827892i	−0.910301	−	0.413946i	$-0.864150\pi$
$463$		−	17.8141i		−	0.827892i	0.910301	−	0.413946i	$-0.135850\pi$
$464$	2.97530	−	9.98957i	0.138125	−	0.463754i
$465$	11.0639	−	6.38774i	0.513076	−	0.296224i
$466$	11.2535	−	11.0989i	0.521311	−	0.514146i
$467$	−1.33113	+	0.356676i	−0.0615975	+	0.0165050i	−0.289486	−	0.957182i	$-0.593484\pi$
$467$	−1.33113	+	0.356676i	−0.0615975	+	0.0165050i	0.227889	+	0.973687i	$0.426818\pi$
$468$	9.46521	+	2.67711i	0.437530	+	0.123749i
$469$	15.2051	−	12.7264i	0.702106	−	0.587653i
$470$	3.50023	+	2.05328i	0.161454	+	0.0947107i
$471$	7.80981	−	13.5270i	0.359857	−	0.623291i
$472$	−21.4968	+	11.8232i	−0.989469	+	0.544207i
$473$	−0.0471999	+	0.0272509i	−0.00217026	+	0.00125300i
$474$	−2.56443	−	4.51356i	−0.117788	−	0.207315i
$475$	23.4862	−	23.4862i	1.07762	−	1.07762i
$476$	9.72188	−	13.4481i	0.445602	−	0.616390i
$477$	−0.361737	−	0.361737i	−0.0165628	−	0.0165628i
$478$	−9.45222	−	2.60294i	−0.432334	−	0.119056i
$479$	3.51472	+	6.08767i	0.160592	+	0.278153i	0.935081	−	0.354434i	$-0.115326\pi$
$479$	3.51472	+	6.08767i	0.160592	+	0.278153i	−0.774489	+	0.632587i	$0.781993\pi$
$480$	3.94071	+	17.0448i	0.179868	+	0.777984i
$481$	4.07904	+	2.35504i	0.185988	+	0.107380i
$482$	−3.45867	−	13.2746i	−0.157538	−	0.604643i
$483$	−11.6456	+	2.03853i	−0.529892	+	0.0927561i
$484$	−10.5039	−	18.7890i	−0.477451	−	0.854047i
$485$	−10.3851	−	38.7576i	−0.471561	−	1.75989i
$486$	−0.00978452	+	1.41418i	−0.000443835	+	0.0641485i
$487$	2.47602	+	4.28860i	0.112199	+	0.194335i	0.916657	−	0.399675i	$-0.130877\pi$
$487$	2.47602	+	4.28860i	0.112199	+	0.194335i	−0.804457	+	0.594010i	$0.797544\pi$
$488$	32.4605	+	19.6504i	1.46942	+	0.889534i
$489$	−13.8471			−0.626188
$490$	28.8660	−	10.2001i	1.30403	−	0.460792i
$491$	11.0483	+	11.0483i	0.498602	+	0.498602i	0.911002	−	0.412401i	$-0.135310\pi$
$491$	11.0483	+	11.0483i	0.498602	+	0.498602i	−0.412401	+	0.911002i	$0.635310\pi$
$492$	15.1827	−	14.7682i	0.684489	−	0.665803i
$493$	−7.89336	−	2.11502i	−0.355499	−	0.0952557i
$494$	35.5428	+	36.0380i	1.59914	+	1.62143i
$495$	0.752942	−	1.30413i	0.0338422	−	0.0586164i
$496$	−8.65479	+	14.0760i	−0.388611	+	0.632033i
$497$	−10.8454	+	15.4480i	−0.486484	+	0.692939i
$498$	−3.05879	−	11.7399i	−0.137068	−	0.526076i
$499$	1.74368	+	6.50750i	0.0780578	+	0.291316i	0.993909	−	0.110202i	$-0.0351496\pi$
$499$	1.74368	+	6.50750i	0.0780578	+	0.291316i	−0.915851	+	0.401517i	$0.868483\pi$
$500$	2.61320	−	0.661590i	0.116866	−	0.0295872i
$501$	16.8281	+	4.50907i	0.751824	+	0.201451i
$502$	10.0618	+	17.7093i	0.449079	+	0.790407i
$503$		−	3.17333i		−	0.141492i	−0.997494	−	0.0707459i	$-0.977462\pi$
$503$		−	3.17333i		−	0.141492i	0.997494	−	0.0707459i	$-0.0225379\pi$
$504$	2.71350	−	6.97402i	0.120869	−	0.310647i
$505$		−	41.4190i		−	1.84312i
$506$	2.67547	−	1.52010i	0.118939	−	0.0675767i
$507$	−10.8080	−	2.89600i	−0.480001	−	0.128616i
$508$	−0.540010	+	0.906133i	−0.0239591	+	0.0402031i
$509$	5.45721	+	20.3666i	0.241886	+	0.902733i	0.974923	+	0.222543i	$0.0714358\pi$
$509$	5.45721	+	20.3666i	0.241886	+	0.902733i	−0.733036	+	0.680189i	$0.761897\pi$
$510$	13.2725	−	3.45811i	0.587715	−	0.153128i
$511$	−12.1751	−	1.08042i	−0.538597	−	0.0477950i
$512$	−14.9733	−	16.9646i	−0.661734	−	0.749739i
$513$	−3.63861	+	6.30226i	−0.160649	+	0.278251i
$514$	10.5985	−	10.4528i	0.467479	−	0.461055i
$515$	−31.8486	−	8.53382i	−1.40342	−	0.376045i
$516$	−0.223837	−	0.00309754i	−0.00985387	−	0.000136362i
$517$	0.319469	+	0.319469i	0.0140502	+	0.0140502i
$518$	2.07916	−	2.91838i	0.0913533	−	0.128226i
$519$	−4.37171			−0.191897
$520$	−10.2698	−	41.7772i	−0.450360	−	1.83205i
$521$	17.2956	+	29.9568i	0.757732	+	1.31243i	0.944005	+	0.329933i	$0.107026\pi$
$521$	17.2956	+	29.9568i	0.757732	+	1.31243i	−0.186272	+	0.982498i	$0.559641\pi$
$522$	−3.68508	−	0.0254966i	−0.161292	−	0.00111596i
$523$	3.43510	+	12.8200i	0.150207	+	0.560578i	0.999468	+	0.0326063i	$0.0103808\pi$
$523$	3.43510	+	12.8200i	0.150207	+	0.560578i	−0.849262	+	0.527972i	$0.822953\pi$
$524$	37.9530	+	10.7345i	1.65798	+	0.468938i
$525$	11.3423	+	4.14421i	0.495018	+	0.180868i
$526$	35.3667	−	9.21470i	1.54206	−	0.401780i
$527$	11.2191	+	6.47737i	0.488713	+	0.282159i
$528$	−0.0538964	+	1.94698i	−0.00234554	+	0.0847314i
$529$	1.51607	+	2.62591i	0.0659160	+	0.114170i
$530$	−0.594025	+	2.15712i	−0.0258028	+	0.0936994i
$531$	6.13341	+	6.13341i	0.266167	+	0.266167i
$532$	29.8683	−	24.3045i	1.29495	−	1.05373i
$533$	−36.8301	+	36.8301i	−1.59529	+	1.59529i
$534$	−15.6708	+	8.90356i	−0.678143	+	0.385295i
$535$	−47.6859	+	27.5314i	−2.06164	+	1.19029i
$536$	−18.5734	+	10.2153i	−0.802247	+	0.441235i
$537$	12.0449	−	20.8623i	0.519775	−	0.900277i
$538$	−2.74490	+	4.67924i	−0.118341	+	0.201737i
$539$	3.39628	−	0.288640i	0.146288	−	0.0124326i
$540$	5.39882	−	3.01819i	0.232328	−	0.129882i
$541$	9.90361	−	2.65367i	0.425790	−	0.114090i	−0.0395595	−	0.999217i	$-0.512595\pi$
$541$	9.90361	−	2.65367i	0.425790	−	0.114090i	0.465349	+	0.885127i	$0.345929\pi$
$542$	−29.7866	−	30.2017i	−1.27944	−	1.29727i
$543$	21.4647	−	12.3926i	0.921137	−	0.531819i
$544$	−12.9703	+	12.1026i	−0.556098	+	0.518896i
$545$			63.1533i			2.70519i
$546$	−6.43491	+	17.2407i	−0.275389	+	0.737834i
$547$	−4.53345	+	4.53345i	−0.193836	+	0.193836i	−0.797352	−	0.603515i	$-0.793766\pi$
$547$	−4.53345	+	4.53345i	−0.193836	+	0.193836i	0.603515	+	0.797352i	$0.293766\pi$
$548$	−21.2843	−	0.294541i	−0.909221	−	0.0125822i
$549$	3.47221	−	12.9585i	0.148190	−	0.553053i
$550$	−3.14293	−	0.0217455i	−0.134015	−	0.000927231i
$551$	−16.4225	−	9.48152i	−0.699621	−	0.403926i
$552$	12.6362	+	0.262318i	0.537833	+	0.0111650i
$553$	8.80701	−	4.09347i	0.374512	−	0.174072i
$554$	−6.43959	+	10.9776i	−0.273592	+	0.466393i
$555$	2.86077	−	0.766542i	0.121433	−	0.0325379i
$556$	−3.16279	+	0.800730i	−0.134132	+	0.0339585i
$557$	−0.375690	+	1.40209i	−0.0159185	+	0.0594087i	−0.973428	−	0.228992i	$-0.926457\pi$
$557$	−0.375690	+	1.40209i	−0.0159185	+	0.0594087i	0.957510	+	0.288401i	$0.0931236\pi$
$558$	5.63243	+	1.55105i	0.238440	+	0.0656612i
$559$	0.550497			0.0232835
$560$	−32.3826	+	4.74906i	−1.36842	+	0.200684i
$561$	1.52701			0.0644706
$562$	22.8186	+	6.28376i	0.962546	+	0.265065i
$563$	−5.79415	+	21.6241i	−0.244194	+	0.911345i	0.729592	+	0.683882i	$0.239710\pi$
$563$	−5.79415	+	21.6241i	−0.244194	+	0.911345i	−0.973787	+	0.227463i	$0.926957\pi$
$564$	0.455440	+	1.79894i	0.0191775	+	0.0757488i
$565$	−21.6719	+	5.80697i	−0.911744	+	0.244301i
$566$	12.7154	−	21.6760i	0.534468	−	0.911110i
$567$	−2.63540	−	0.233864i	−0.110676	−	0.00982138i
$568$	14.5612	−	13.9689i	0.610975	−	0.586124i
$569$	−12.4299	−	7.17640i	−0.521088	−	0.300850i	0.216292	−	0.976329i	$-0.430604\pi$
$569$	−12.4299	−	7.17640i	−0.521088	−	0.300850i	−0.737380	+	0.675478i	$0.763937\pi$
$570$	31.8269	+	0.220206i	1.33308	+	0.00922340i
$571$	8.79010	−	32.8051i	0.367854	−	1.37285i	−0.495656	−	0.868519i	$-0.665072\pi$
$571$	8.79010	−	32.8051i	0.367854	−	1.37285i	0.863510	−	0.504331i	$-0.168261\pi$
$572$	0.0662755	−	4.78925i	0.00277112	−	0.200249i
$573$	12.2034	−	12.2034i	0.509806	−	0.509806i
$574$	25.2220	+	30.5614i	1.05275	+	1.27561i
$575$			20.3952i			0.850539i
$576$	−4.28408	+	6.75623i	−0.178503	+	0.281510i
$577$	19.6290	−	11.3328i	0.817164	−	0.471790i	−0.0322734	−	0.999479i	$-0.510275\pi$
$577$	19.6290	−	11.3328i	0.817164	−	0.471790i	0.849438	+	0.527689i	$0.176941\pi$
$578$	−7.11579	−	7.21494i	−0.295978	−	0.300102i
$579$	8.58256	−	2.29969i	0.356679	−	0.0955719i
$580$	7.86482	+	14.0683i	0.326569	+	0.584154i
$581$	22.3566	−	3.91346i	0.927507	−	0.162357i
$582$	9.28404	−	15.8265i	0.384836	−	0.656031i
$583$	−0.124551	+	0.215728i	−0.00515836	+	0.00893455i
$584$	12.5488	+	3.64320i	0.519272	+	0.150757i
$585$	−13.1724	+	7.60511i	−0.544613	+	0.314432i
$586$	−3.10022	+	1.76143i	−0.128069	+	0.0727639i
$587$	−0.304714	+	0.304714i	−0.0125769	+	0.0125769i	−0.713367	−	0.700790i	$-0.752831\pi$
$587$	−0.304714	+	0.304714i	−0.0125769	+	0.0125769i	0.700790	+	0.713367i	$0.252831\pi$
$588$	12.5901	+	6.12294i	0.519205	+	0.252506i
$589$	21.2571	+	21.2571i	0.875883	+	0.875883i
$590$	10.0719	−	36.5749i	0.414655	−	1.50576i
$591$	4.50534	+	7.80348i	0.185325	+	0.320992i
$592$	−2.78262	+	2.63271i	−0.114365	+	0.108204i
$593$	5.06391	+	2.92365i	0.207950	+	0.120060i	0.600358	−	0.799731i	$-0.295025\pi$
$593$	5.06391	+	2.92365i	0.207950	+	0.120060i	−0.392408	+	0.919791i	$0.628358\pi$
$594$	0.666378	−	0.173623i	0.0273418	−	0.00712383i
$595$	4.42435	+	25.2752i	0.181381	+	1.03618i
$596$	1.82932	−	6.46777i	0.0749319	−	0.264930i
$597$	−3.77498	−	14.0884i	−0.154499	−	0.576600i
$598$	−31.0801	−	0.215039i	−1.27096	−	0.00879359i
$599$	−0.314227	−	0.544257i	−0.0128390	−	0.0222378i	0.859535	−	0.511078i	$-0.170754\pi$
$599$	−0.314227	−	0.544257i	−0.0128390	−	0.0222378i	−0.872374	+	0.488840i	$0.837420\pi$
$600$	−11.0435	−	6.68537i	−0.450850	−	0.272929i
$601$	−0.723489			−0.0295117			−0.0147559	−	0.999891i	$-0.504697\pi$
$601$	−0.723489			−0.0295117			−0.0147559	+	0.999891i	$0.504697\pi$
$602$	0.0399041	−	0.416895i	0.00162637	−	0.0169914i
$603$	5.29931	+	5.29931i	0.215804	+	0.215804i
$604$	−0.352492	+	25.4720i	−0.0143427	+	1.03644i
$605$	32.1512	+	8.61488i	1.30713	+	0.350245i
$606$	13.4853	−	13.3000i	0.547802	−	0.540274i
$607$	−12.4643	+	21.5889i	−0.505912	+	0.876265i	0.494065	+	0.869425i	$0.335511\pi$
$607$	−12.4643	+	21.5889i	−0.505912	+	0.876265i	−0.999977	+	0.00684015i	$0.997823\pi$
$608$	−36.3415	+	19.3377i	−1.47384	+	0.784248i
$609$	0.609406	−	6.86734i	0.0246944	−	0.278279i
$610$	−56.7788	+	14.7936i	−2.29891	+	0.598974i
$611$	−1.18109	−	4.40789i	−0.0477819	−	0.178324i
$612$	5.38779	+	3.21085i	0.217789	+	0.129791i
$613$	−46.9212	−	12.5725i	−1.89513	−	0.507798i	−0.997789	−	0.0664585i	$-0.978830\pi$
$613$	−46.9212	−	12.5725i	−1.89513	−	0.507798i	−0.897340	−	0.441340i	$-0.854503\pi$
$614$	−17.0870	+	9.70818i	−0.689575	+	0.391790i
$615$			32.7514i			1.32067i
$616$	−3.62213	−	0.397352i	−0.145940	−	0.0160098i
$617$			16.2331i			0.653519i	0.945107	+	0.326760i	$0.105957\pi$
$617$			16.2331i			0.653519i	−0.945107	+	0.326760i	$0.894043\pi$
$618$	−7.44838	−	13.1096i	−0.299618	−	0.527346i
$619$	25.2247	+	6.75893i	1.01386	+	0.271664i	0.727243	−	0.686380i	$-0.240801\pi$
$619$	25.2247	+	6.75893i	1.01386	+	0.271664i	0.286621	+	0.958044i	$0.407468\pi$
$620$	−6.27094	−	24.7695i	−0.251847	−	0.994766i
$621$	−1.15654	−	4.31628i	−0.0464105	−	0.173206i
$622$	0.391119	+	1.50114i	0.0156824	+	0.0601904i
$623$	−14.2123	−	30.5774i	−0.569404	−	1.22506i
$624$	10.3042	−	16.7586i	0.412498	−	0.670882i
$625$	−13.4946	+	23.3733i	−0.539783	+	0.934932i
$626$	−11.5594	−	11.7205i	−0.462007	−	0.468445i
$627$	3.42276	+	0.917126i	0.136692	+	0.0366265i
$628$	−21.7817	−	22.3930i	−0.869185	−	0.893579i
$629$	2.12362	+	2.12362i	0.0846742	+	0.0846742i
$630$	4.80457	+	10.5269i	0.191419	+	0.419400i
$631$	−35.0364			−1.39478			−0.697389	−	0.716692i	$-0.745655\pi$
$631$	−35.0364			−1.39478			−0.697389	+	0.716692i	$0.745655\pi$
$632$	−10.0822	+	2.47844i	−0.401050	+	0.0985871i
$633$	−12.9356	−	22.4051i	−0.514143	−	0.890522i
$634$	0.298809	−	43.1876i	0.0118672	−	1.71520i
$635$	−0.422160	−	1.57552i	−0.0167529	−	0.0625226i
$636$	−0.893066	+	0.499264i	−0.0354124	+	0.0197971i
$637$	−31.1660	−	14.6273i	−1.23484	−	0.579553i
$638$	0.452428	+	1.73645i	0.0179118	+	0.0687468i
$639$	−6.17829	−	3.56704i	−0.244409	−	0.141110i
$640$	34.9478	+	1.69389i	1.38143	+	0.0669568i
$641$	−15.9878	−	27.6917i	−0.631481	−	1.09376i	−0.987249	−	0.159183i	$-0.949114\pi$
$641$	−15.9878	−	27.6917i	−0.631481	−	1.09376i	0.355768	−	0.934574i	$-0.384219\pi$
$642$	−24.2760	−	6.68510i	−0.958098	−	0.263840i
$643$	3.83965	+	3.83965i	0.151421	+	0.151421i	0.778752	−	0.627331i	$-0.215853\pi$
$643$	3.83965	+	3.83965i	0.151421	+	0.151421i	−0.627331	+	0.778752i	$0.715853\pi$
$644$	−2.41577	+	23.5216i	−0.0951945	+	0.926880i
$645$	0.244766	−	0.244766i	0.00963767	−	0.00963767i
$646$	15.9433	+	28.0613i	0.627282	+	1.10406i
$647$	5.53072	−	3.19316i	0.217435	−	0.125536i	−0.387327	−	0.921942i	$-0.626602\pi$
$647$	5.53072	−	3.19316i	0.217435	−	0.125536i	0.604762	+	0.796406i	$0.293268\pi$
$648$	2.71627	+	0.788596i	0.106705	+	0.0309790i
$649$	2.11181	−	3.65776i	0.0828957	−	0.143580i
$650$	27.3824	+	16.0628i	1.07402	+	0.630036i
$651$	−3.75088	+	10.2658i	−0.147008	+	0.402347i
$652$	−7.53726	+	26.6488i	−0.295182	+	1.04365i
$653$	−13.0859	+	3.50636i	−0.512091	+	0.137214i	−0.505606	−	0.862765i	$-0.668731\pi$
$653$	−13.0859	+	3.50636i	−0.512091	+	0.137214i	−0.00648534	+	0.999979i	$0.502064\pi$
$654$	−20.5616	+	20.2790i	−0.804021	+	0.792972i
$655$	−52.8180	+	30.4945i	−2.06377	+	1.19152i
$656$	−20.1573	−	37.2578i	−0.787009	−	1.45467i
$657$		−	4.61986i		−	0.180238i
$658$	−3.42374	+	0.574932i	−0.133471	+	0.0224132i
$659$	0.566220	−	0.566220i	0.0220568	−	0.0220568i	−0.695992	−	0.718049i	$-0.745035\pi$
$659$	0.566220	−	0.566220i	0.0220568	−	0.0220568i	0.718049	+	0.695992i	$0.245035\pi$
$660$	−2.09997	−	2.15891i	−0.0817412	−	0.0840353i
$661$	11.9113	−	44.4536i	0.463296	−	1.72904i	−0.199182	−	0.979963i	$-0.563828\pi$
$661$	11.9113	−	44.4536i	0.463296	−	1.72904i	0.662478	−	0.749082i	$-0.269505\pi$
$662$	−0.100134	+	14.4727i	−0.00389183	+	0.562496i
$663$	−13.3573	−	7.71182i	−0.518753	−	0.299502i
$664$	−24.2584	−	0.503585i	−0.941407	−	0.0195429i
$665$	−5.26324	+	59.3110i	−0.204100	+	2.29998i
$666$	1.16819	+	0.685274i	0.0452664	+	0.0265538i
$667$	11.2474	−	3.01373i	0.435501	−	0.116692i
$668$	17.8376	−	29.9314i	0.690157	−	1.15808i
$669$	2.40819	−	8.98750i	0.0931061	−	0.347477i
$670$	8.70223	−	31.6010i	0.336196	−	1.22085i
$671$	−6.53247			−0.252183
$672$	−11.9445	−	9.01824i	−0.460770	−	0.347886i
$673$	10.2038			0.393327			0.196664	−	0.980471i	$-0.436989\pi$
$673$	10.2038			0.393327			0.196664	+	0.980471i	$0.436989\pi$
$674$	12.4059	−	45.0504i	0.477858	−	1.73527i
$675$	−1.18130	+	4.40866i	−0.0454681	+	0.169689i
$676$	−11.4564	+	19.2237i	−0.440630	+	0.739374i
$677$	20.1848	−	5.40849i	0.775763	−	0.207865i	0.150847	−	0.988557i	$-0.451800\pi$
$677$	20.1848	−	5.40849i	0.775763	−	0.207865i	0.624916	+	0.780692i	$0.285133\pi$
$678$	−8.84966	−	5.19132i	−0.339869	−	0.199371i
$679$	28.0947	+	19.7241i	1.07818	+	0.756943i
$680$	0.569327	−	27.4253i	0.0218327	−	1.05171i
$681$	4.62190	+	2.66846i	0.177112	+	0.102255i
$682$	0.0196816	−	2.84463i	0.000753648	−	0.108926i
$683$	4.92114	−	18.3659i	0.188302	−	0.702753i	−0.805597	−	0.592463i	$-0.798156\pi$
$683$	4.92114	−	18.3659i	0.188302	−	0.702753i	0.993900	−	0.110290i	$-0.0351778\pi$
$684$	10.1481	+	10.4330i	0.388024	+	0.398914i
$685$	23.2745	−	23.2745i	0.889273	−	0.889273i
$686$	−13.3365	+	22.5419i	−0.509189	+	0.860655i
$687$			6.32148i			0.241180i
$688$	−0.127800	+	0.429089i	−0.00487233	+	0.0163589i
$689$	2.17897	−	1.25803i	0.0830120	−	0.0479270i
$690$	−13.9147	+	13.7235i	−0.529723	+	0.522444i
$691$	19.7036	−	5.27956i	0.749560	−	0.200844i	0.136237	−	0.990676i	$-0.456499\pi$
$691$	19.7036	−	5.27956i	0.749560	−	0.200844i	0.613323	+	0.789832i	$0.289832\pi$
$692$	−2.37961	+	8.41337i	−0.0904591	+	0.319829i
$693$	0.222136	+	1.26900i	0.00843823	+	0.0482055i
$694$	15.0619	+	8.83549i	0.571741	+	0.335390i
$695$	2.52246	−	4.36903i	0.0956824	−	0.165727i
$696$	−2.05493	+	7.07808i	−0.0778920	+	0.268294i
$697$	−28.7616	+	16.6055i	−1.08942	+	0.628978i
$698$	11.0876	+	19.5148i	0.419671	+	0.738648i
$699$	−7.90297	+	7.90297i	−0.298918	+	0.298918i
$700$	14.1494	−	19.5725i	0.534796	−	0.739771i
$701$	−19.2645	−	19.2645i	−0.727611	−	0.727611i	0.242533	−	0.970143i	$-0.422022\pi$
$701$	−19.2645	−	19.2645i	−0.727611	−	0.727611i	−0.970143	+	0.242533i	$0.922022\pi$
$702$	−6.70585	−	1.84665i	−0.253096	−	0.0696972i
$703$	3.48459	+	6.03548i	0.131424	+	0.227633i
$704$	3.71763	+	1.16350i	0.140114	+	0.0438512i
$705$	−2.48502	−	1.43473i	−0.0935914	−	0.0540350i
$706$	5.38043	+	20.6505i	0.202495	+	0.777192i
$707$	22.7431	+	27.1726i	0.855341	+	1.02193i
$708$	15.1423	−	8.46523i	0.569082	−	0.318143i
$709$	5.76320	+	21.5086i	0.216442	+	0.807771i	0.985654	+	0.168778i	$0.0539821\pi$
$709$	5.76320	+	21.5086i	0.216442	+	0.807771i	−0.769213	+	0.638993i	$0.779351\pi$
$710$	−0.215874	+	31.2008i	−0.00810162	+	1.17095i
$711$	1.83537	+	3.17895i	0.0688316	+	0.119220i
$712$	8.60501	+	35.0049i	0.322486	+	1.31187i
$713$	−18.4595			−0.691313
$714$	−6.80845	+	9.55654i	−0.254800	+	0.357645i
$715$	5.23706	+	5.23706i	0.195855	+	0.195855i
$716$	−33.5934	−	34.5362i	−1.25544	−	1.29068i
$717$	6.69630	+	1.79427i	0.250078	+	0.0670082i
$718$	7.04294	+	7.14107i	0.262840	+	0.266502i
$719$	−5.58987	+	9.68193i	−0.208467	+	0.361075i	−0.951232	−	0.308477i	$-0.900181\pi$
$719$	−5.58987	+	9.68193i	−0.208467	+	0.361075i	0.742765	+	0.669552i	$0.233514\pi$
$720$	−2.86983	−	12.0329i	−0.106952	−	0.448440i
$721$	25.5799	−	11.8895i	0.952646	−	0.442787i
$722$	12.1082	+	46.4722i	0.450621	+	1.72952i
$723$	2.51053	+	9.36943i	0.0933677	+	0.348453i
$724$	−12.1660	−	48.0544i	−0.452147	−	1.78593i
$725$	−11.4881	−	3.07823i	−0.426658	−	0.114323i
$726$	7.51914	+	13.2341i	0.279061	+	0.491165i
$727$		−	29.6716i		−	1.10046i	−0.835014	−	0.550229i	$-0.814540\pi$
$727$		−	29.6716i		−	1.10046i	0.835014	−	0.550229i	$-0.185460\pi$
$728$	29.6772	+	21.7685i	1.09991	+	0.806793i
$729$		−	1.00000i		−	0.0370370i
$730$	−17.5679	+	9.98139i	−0.650216	+	0.369428i
$731$	0.339049	+	0.0908479i	0.0125402	+	0.00336013i
$732$	−23.0486	−	13.7358i	−0.851901	−	0.507691i
$733$	5.71370	+	21.3238i	0.211040	+	0.787613i	0.987523	+	0.157474i	$0.0503351\pi$
$733$	5.71370	+	21.3238i	0.211040	+	0.787613i	−0.776483	+	0.630138i	$0.782998\pi$
$734$	30.5609	−	7.96255i	1.12802	−	0.293903i
$735$	−20.3610	+	7.35359i	−0.751026	+	0.271241i
$736$	7.38298	−	24.1757i	0.272140	−	0.891127i
$737$	1.82462	−	3.16033i	0.0672106	−	0.116412i
$738$	−10.6633	+	10.5167i	−0.392521	+	0.387126i
$739$	4.64179	+	1.24376i	0.170751	+	0.0457526i	0.343182	−	0.939269i	$-0.388495\pi$
$739$	4.64179	+	1.24376i	0.170751	+	0.0457526i	−0.172431	+	0.985022i	$0.555162\pi$
$740$	0.0819622	−	5.92282i	0.00301299	−	0.217727i
$741$	−25.3082	−	25.3082i	−0.929721	−	0.929721i
$742$	−0.794765	−	1.74134i	−0.0291767	−	0.0639265i
$743$	19.4674			0.714190			0.357095	−	0.934068i	$-0.383767\pi$
$743$	19.4674			0.714190			0.357095	+	0.934068i	$0.383767\pi$
$744$	6.05085	−	9.99537i	0.221835	−	0.366448i
$745$	5.19673	+	9.00099i	0.190393	+	0.329771i
$746$	10.2585	+	0.0709772i	0.375590	+	0.00259866i
$747$	2.22027	+	8.28617i	0.0812355	+	0.303175i
$748$	0.831184	−	2.93874i	0.0303911	−	0.107451i
$749$	16.1664	−	44.2459i	0.590709	−	1.61671i
$750$	−1.84453	+	0.480588i	−0.0673528	+	0.0175486i
$751$	26.1899	+	15.1208i	0.955684	+	0.551764i	0.894842	−	0.446383i	$-0.147288\pi$
$751$	26.1899	+	15.1208i	0.955684	+	0.551764i	0.0608417	+	0.998147i	$0.480622\pi$
$752$	3.70996	+	0.102699i	0.135288	+	0.00374507i
$753$	−7.20122	−	12.4729i	−0.262427	−	0.454537i
$754$	4.81201	−	17.4742i	0.175243	−	0.636372i
$755$	−27.8537	−	27.8537i	−1.01370	−	1.01370i
$756$	−1.88457	+	4.94453i	−0.0685412	+	0.179831i
$757$	−6.26750	+	6.26750i	−0.227796	+	0.227796i	−0.811771	−	0.583975i	$-0.801496\pi$
$757$	−6.26750	+	6.26750i	−0.227796	+	0.227796i	0.583975	+	0.811771i	$0.301496\pi$
$758$	0.442468	−	0.251393i	0.0160712	−	0.00913102i
$759$	−1.88436	+	1.08794i	−0.0683980	+	0.0394896i
$760$	17.7478	−	61.1311i	0.643779	−	2.21746i
$761$	22.0610	−	38.2108i	0.799712	−	1.38514i	−0.120092	−	0.992763i	$-0.538319\pi$
$761$	22.0610	−	38.2108i	0.799712	−	1.38514i	0.919804	−	0.392379i	$-0.128348\pi$
$762$	0.377402	−	0.643359i	0.0136718	−	0.0233064i
$763$	−34.6773	−	41.4312i	−1.25540	−	1.49991i
$764$	−16.8430	−	30.1281i	−0.609358	−	1.09000i
$765$	−9.36792	+	2.51013i	−0.338698	+	0.0907538i
$766$	4.04293	+	4.09927i	0.146077	+	0.148113i
$767$	−36.9453	+	21.3304i	−1.33402	+	0.770195i
$768$	10.6705	+	11.9223i	0.385038	+	0.430208i
$769$			50.4135i			1.81796i	0.416843	+	0.908978i	$0.363136\pi$
$769$			50.4135i			1.81796i	−0.416843	+	0.908978i	$0.636864\pi$
$770$	4.34569	−	3.58645i	0.156608	−	0.129247i
$771$	−7.44295	+	7.44295i	−0.268051	+	0.268051i
$772$	0.245894	−	17.7689i	0.00884990	−	0.639518i
$773$	−2.75705	+	10.2894i	−0.0991641	+	0.370085i	−0.997618	−	0.0689828i	$-0.978025\pi$
$773$	−2.75705	+	10.2894i	−0.0991641	+	0.370085i	0.898454	+	0.439068i	$0.144691\pi$
$774$	0.158288	+	0.00109517i	0.00568954	+	3.93652e-5i
$775$	16.3285	+	9.42727i	0.586537	+	0.338638i
$776$	−25.4047	−	26.4819i	−0.911977	−	0.950644i
$777$	−1.45588	+	2.07373i	−0.0522294	+	0.0743945i
$778$	−5.10480	+	8.70216i	−0.183016	+	0.311988i
$779$	−74.4416	+	19.9466i	−2.66715	+	0.714660i
$780$	7.46605	+	29.4900i	0.267327	+	1.05591i
$781$	−0.899087	+	3.35544i	−0.0321719	+	0.120067i
$782$	−19.1066	−	5.26155i	−0.683251	−	0.188153i
$783$	2.60581			0.0931240
$784$	18.6366	−	20.8968i	0.665594	−	0.746314i
$785$	48.3052			1.72409
$786$	−26.8887	−	7.40457i	−0.959088	−	0.264112i
$787$	−3.75786	+	14.0245i	−0.133953	+	0.499920i	−1.00000		4.27807e-5i	$-0.999986\pi$
$787$	−3.75786	+	14.0245i	−0.133953	+	0.499920i	0.866047	+	0.499963i	$0.166653\pi$
$788$	17.4702	−	4.42296i	0.622349	−	0.157561i
$789$	−24.9624	+	6.68864i	−0.888683	+	0.238122i
$790$	8.12316	−	13.8476i	0.289009	−	0.492674i
$791$	11.0291	−	15.7096i	0.392149	−	0.558569i
$792$	0.0285845	−	1.37695i	0.00101571	−	0.0489279i
$793$	57.1415	+	32.9907i	2.02915	+	1.17153i
$794$	34.7096	+	0.240151i	1.23180	+	0.00852263i
$795$	0.409476	−	1.52819i	0.0145226	−	0.0541992i
$796$	−29.1680	−	0.403638i	−1.03383	−	0.0143066i
$797$	−0.0125839	+	0.0125839i	−0.000445746	+	0.000445746i	−0.707330	−	0.706884i	$-0.750100\pi$
$797$	−0.0125839	+	0.0125839i	−0.000445746	+	0.000445746i	0.706884	+	0.707330i	$0.250100\pi$
$798$	−21.0006	+	17.3316i	−0.743415	+	0.613531i
$799$		−	2.90972i		−	0.102939i
$800$	−18.8772	+	17.6143i	−0.667411	+	0.622761i
$801$	11.0371	−	6.37228i	0.389977	−	0.225154i
$802$	15.4719	+	15.6875i	0.546332	+	0.553944i
$803$	−2.17290	+	0.582227i	−0.0766800	+	0.0205463i
$804$	13.0831	−	7.31402i	0.461404	−	0.257946i
$805$	−23.4673	−	28.0378i	−0.827113	−	0.988204i
$806$	−14.5383	+	24.7835i	−0.512089	+	0.872960i
$807$	1.91800	−	3.32207i	0.0675168	−	0.116943i
$808$	−18.2555	−	33.1919i	−0.642227	−	1.16769i
$809$	−1.94015	+	1.12015i	−0.0682122	+	0.0393823i	−0.533718	−	0.845662i	$-0.679206\pi$
$809$	−1.94015	+	1.12015i	−0.0682122	+	0.0393823i	0.465506	+	0.885045i	$0.345872\pi$
$810$	−3.80269	+	2.16054i	−0.133613	+	0.0759137i
$811$	−20.6026	+	20.6026i	−0.723455	+	0.723455i	−0.969307	−	0.245852i	$-0.920932\pi$
$811$	−20.6026	+	20.6026i	−0.723455	+	0.723455i	0.245852	+	0.969307i	$0.420932\pi$
$812$	−12.8845	−	4.91083i	−0.452158	−	0.172336i
$813$	21.2096	+	21.2096i	0.743852	+	0.743852i
$814$	0.175088	−	0.635808i	0.00613683	−	0.0222851i
$815$	−21.4118	−	37.0863i	−0.750023	−	1.29908i
$816$	9.11198	−	8.62109i	0.318983	−	0.301799i
$817$	0.705406	+	0.407266i	0.0246790	+	0.0142484i
$818$	−0.196168	+	0.0511110i	−0.00685884	+	0.00178705i
$819$	4.46571	−	12.2222i	0.156045	−	0.427079i
$820$	63.0303	+	17.8273i	2.20111	+	0.622555i
$821$	−5.70794	−	21.3023i	−0.199208	−	0.743456i	−0.991137	−	0.132842i	$-0.957590\pi$
$821$	−5.70794	−	21.3023i	−0.199208	−	0.743456i	0.791929	−	0.610613i	$-0.209077\pi$
$822$	15.0514	+	0.104138i	0.524977	+	0.00363224i
$823$	−27.1622	−	47.0462i	−0.946814	−	1.63993i	−0.752079	−	0.659073i	$-0.770949\pi$
$823$	−27.1622	−	47.0462i	−0.946814	−	1.63993i	−0.194735	−	0.980856i	$-0.562385\pi$
$824$	−29.2838	+	7.19862i	−1.02015	+	0.250776i
$825$	2.22244			0.0773754
$826$	13.4756	+	29.5251i	0.468875	+	1.02731i
$827$	−13.3803	−	13.3803i	−0.465279	−	0.465279i	0.435102	−	0.900381i	$-0.356712\pi$
$827$	−13.3803	−	13.3803i	−0.465279	−	0.465279i	−0.900381	+	0.435102i	$0.856712\pi$
$828$	−8.93623	−	0.123663i	−0.310555	−	0.00429759i
$829$	19.0323	+	5.09968i	0.661018	+	0.177119i	0.573705	−	0.819062i	$-0.305505\pi$
$829$	19.0323	+	5.09968i	0.661018	+	0.177119i	0.0873126	+	0.996181i	$0.472172\pi$
$830$	26.7127	−	26.3456i	0.927212	−	0.914469i
$831$	4.49967	−	7.79365i	0.156092	−	0.270359i
$832$	−26.6433	−	28.9525i	−0.923690	−	1.00375i
$833$	−16.7811	−	14.1522i	−0.581431	−	0.490343i
$834$	2.23246	−	0.581661i	0.0773037	−	0.0201413i
$835$	13.9448	+	52.0426i	0.482579	+	1.80101i
$836$	3.62809	−	6.08791i	0.125480	−	0.210555i
$837$	−3.99022	−	1.06918i	−0.137922	−	0.0369562i
$838$	8.36601	−	4.75324i	0.288999	−	0.164198i
$839$			19.4753i			0.672362i	0.941797	+	0.336181i	$0.109135\pi$
$839$			19.4753i			0.672362i	−0.941797	+	0.336181i	$0.890865\pi$
$840$	22.8742	−	3.51643i	0.789235	−	0.121329i
$841$		−	22.2098i		−	0.765854i
$842$	−6.16327	−	10.8477i	−0.212400	−	0.373838i
$843$	−16.1656	−	4.33155i	−0.556772	−	0.149187i
$844$	−50.1598	+	12.6991i	−1.72657	+	0.437119i
$845$	−8.95617	−	33.4249i	−0.308102	−	1.14985i
$846$	−0.330838	−	1.26978i	−0.0113744	−	0.0436560i
$847$	−25.8229	+	12.0024i	−0.887285	+	0.412408i
$848$	0.474723	+	1.99047i	0.0163021	+	0.0683530i
$849$	−8.88489	+	15.3891i	−0.304929	+	0.528152i
$850$	14.2139	+	14.4119i	0.487532	+	0.494325i
$851$	−4.13357	−	1.10759i	−0.141697	−	0.0379676i
$852$	−10.2277	+	9.94854i	−0.350397	+	0.340831i
$853$	2.31491	+	2.31491i	0.0792609	+	0.0792609i	0.745626	−	0.666365i	$-0.232151\pi$
$853$	2.31491	+	2.31491i	0.0792609	+	0.0792609i	−0.666365	+	0.745626i	$0.732151\pi$
$854$	29.1261	−	40.8823i	0.996675	−	1.39896i
$855$	−22.5055			−0.769673
$856$	−26.0794	+	43.0805i	−0.891376	+	1.47246i
$857$	−13.9462	−	24.1555i	−0.476393	−	0.825137i	0.523241	−	0.852185i	$-0.324723\pi$
$857$	−13.9462	−	24.1555i	−0.476393	−	0.825137i	−0.999634	+	0.0270478i	$0.991389\pi$
$858$	−0.0234325	+	3.38675i	−0.000799972	+	0.115622i
$859$	3.17886	+	11.8637i	0.108461	+	0.404783i	0.998715	−	0.0506824i	$-0.0161396\pi$
$859$	3.17886	+	11.8637i	0.108461	+	0.404783i	−0.890254	+	0.455465i	$0.849473\pi$
$860$	−0.337823	−	0.604285i	−0.0115197	−	0.0206060i
$861$	−17.9837	−	21.4863i	−0.612884	−	0.732251i
$862$	−9.98604	−	38.3272i	−0.340126	−	1.30543i
$863$	0.770725	+	0.444979i	0.0262358	+	0.0151472i	0.513061	−	0.858352i	$-0.328512\pi$
$863$	0.770725	+	0.444979i	0.0262358	+	0.0151472i	−0.486825	+	0.873500i	$0.661845\pi$
$864$	2.99618	−	4.79822i	0.101932	−	0.163239i
$865$	−6.75998	−	11.7086i	−0.229846	−	0.398105i
$866$	40.0440	+	11.0273i	1.36075	+	0.374722i
$867$	5.06680	+	5.06680i	0.172077	+	0.172077i
$868$	17.7148	+	12.8064i	0.601281	+	0.434679i
$869$	1.26388	−	1.26388i	0.0428742	−	0.0428742i
$870$	−5.62996	−	9.90907i	−0.190873	−	0.335949i
$871$	−31.9210	+	18.4296i	−1.08160	+	0.624463i
$872$	27.8350	+	50.6091i	0.942611	+	1.71384i
$873$	−6.48723	+	11.2362i	−0.219559	+	0.380288i
$874$	−39.6669	−	23.2691i	−1.34175	−	0.787089i
$875$	−0.614871	−	3.51260i	−0.0207864	−	0.118748i
$876$	−8.89093	−	2.51468i	−0.300397	−	0.0849631i
$877$	34.6123	−	9.27435i	1.16878	−	0.313173i	0.378310	−	0.925679i	$-0.376505\pi$
$877$	34.6123	−	9.27435i	1.16878	−	0.313173i	0.790466	+	0.612506i	$0.209839\pi$
$878$	−4.59837	+	4.53517i	−0.155187	+	0.153055i
$879$	2.18352	−	1.26066i	0.0736483	−	0.0425209i
$880$	−5.29788	+	2.86627i	−0.178591	+	0.0966218i
$881$			7.07074i			0.238219i	0.992881	+	0.119110i	$0.0380040\pi$
$881$			7.07074i			0.238219i	−0.992881	+	0.119110i	$0.961996\pi$
$882$	−8.93226	−	4.26787i	−0.300765	−	0.143707i
$883$	24.5956	−	24.5956i	0.827709	−	0.827709i	−0.159490	−	0.987200i	$-0.550985\pi$
$883$	24.5956	−	24.5956i	0.827709	−	0.827709i	0.987200	+	0.159490i	$0.0509851\pi$
$884$	−22.1121	+	21.5084i	−0.743709	+	0.723406i
$885$	−6.94283	+	25.9110i	−0.233381	+	0.870989i
$886$	−0.197262	+	28.5108i	−0.00662715	+	0.957838i
$887$	−23.7641	−	13.7202i	−0.797921	−	0.460680i	0.0448228	−	0.998995i	$-0.485728\pi$
$887$	−23.7641	−	13.7202i	−0.797921	−	0.460680i	−0.842744	+	0.538315i	$0.819061\pi$
$888$	1.95468	−	1.87518i	0.0655948	−	0.0629268i
$889$	1.14207	+	0.801800i	0.0383037	+	0.0268915i
$890$	−48.0779	−	28.2031i	−1.61158	−	0.945371i
$891$	−0.470339	+	0.126027i	−0.0157570	+	0.00422207i
$892$	−15.9856	−	9.52665i	−0.535239	−	0.318976i
$893$	1.74758	−	6.52206i	0.0584806	−	0.218253i
$894$	−1.26185	+	4.58225i	−0.0422027	+	0.153253i
$895$	74.5000			2.49026
$896$	−23.8573	+	18.0785i	−0.797015	+	0.603959i
$897$	21.9775			0.733806
$898$	1.29680	−	4.70917i	0.0432749	−	0.157147i
$899$	2.78607	−	10.3978i	0.0929207	−	0.346785i
$900$	7.84148	+	4.67313i	0.261383	+	0.155771i
$901$	1.54963	−	0.415222i	0.0516256	−	0.0138330i
$902$	6.29030	+	3.68997i	0.209444	+	0.122862i
$903$	−0.0261762	+	0.294977i	−0.000871090	+	0.00981624i
$904$	−14.8078	+	14.2055i	−0.492499	+	0.472467i
$905$	66.3816	+	38.3255i	2.20660	+	1.27398i
$906$	0.124628	−	18.0127i	0.00414047	−	0.598433i
$907$	−7.95829	+	29.7007i	−0.264251	+	0.986197i	0.698457	+	0.715652i	$0.253870\pi$
$907$	−7.95829	+	29.7007i	−0.264251	+	0.986197i	−0.962707	+	0.270545i	$0.912796\pi$
$908$	7.65124	−	7.44237i	0.253915	−	0.246984i
$909$	−9.47024	+	9.47024i	−0.314108	+	0.314108i
$910$	−56.1256	+	9.42489i	−1.86054	+	0.312432i
$911$		−	17.5572i		−	0.581697i	−0.956769	−	0.290849i	$-0.906062\pi$
$911$		−	17.5572i		−	0.581697i	0.956769	−	0.290849i	$-0.0939376\pi$
$912$	25.6021	−	13.8513i	0.847771	−	0.458662i
$913$	3.61750	−	2.08856i	0.119722	−	0.0691214i
$914$	4.61997	−	4.55648i	0.152815	−	0.150715i
$915$	40.0753	−	10.7382i	1.32485	−	0.354992i
$916$	12.1657	+	3.44091i	0.401967	+	0.113691i
$917$	17.9063	−	49.0078i	0.591319	−	1.61838i
$918$	−3.82536	−	2.24400i	−0.126256	−	0.0740632i
$919$	3.63110	−	6.28925i	0.119779	−	0.207463i	−0.799901	−	0.600132i	$-0.795115\pi$
$919$	3.63110	−	6.28925i	0.119779	−	0.207463i	0.919680	+	0.392669i	$0.128448\pi$
$920$	18.8368	+	34.2488i	0.621032	+	1.12915i
$921$	12.0345	−	6.94815i	0.396552	−	0.228949i
$922$	13.0236	+	22.9223i	0.428908	+	0.754904i
$923$	24.8104	−	24.8104i	0.816645	−	0.816645i
$924$	2.56312	+	0.263243i	0.0843203	+	0.00866005i
$925$	3.09075	+	3.09075i	0.101623	+	0.101623i
$926$	24.2888	+	6.68863i	0.798181	+	0.219802i
$927$	5.33081	+	9.23324i	0.175087	+	0.303259i
$928$	12.5033	+	7.80746i	0.410439	+	0.256292i
$929$	22.9247	+	13.2356i	0.752134	+	0.434245i	0.826465	−	0.562989i	$-0.190349\pi$
$929$	22.9247	+	13.2356i	0.752134	+	0.434245i	−0.0743302	+	0.997234i	$0.523682\pi$
$930$	4.55530	+	17.4836i	0.149374	+	0.573309i
$931$	−29.1146	−	41.8005i	−0.954192	−	1.36995i
$932$	10.9076	+	19.5110i	0.357289	+	0.639106i
$933$	−0.283900	−	1.05953i	−0.00929447	−	0.0346874i
$934$	0.0134839	−	1.94887i	0.000441208	−	0.0637689i
$935$	2.36122	+	4.08976i	0.0772202	+	0.133749i
$936$	−7.20401	+	11.9003i	−0.235470	+	0.388973i
$937$	−39.5704			−1.29271			−0.646355	−	0.763037i	$-0.723707\pi$
$937$	−39.5704			−1.29271			−0.646355	+	0.763037i	$0.723707\pi$
$938$	11.6430	+	25.5099i	0.380157	+	0.832928i
$939$	8.23088	+	8.23088i	0.268605	+	0.268605i
$940$	−4.11379	+	4.00149i	−0.134177	+	0.130514i
$941$	−54.6605	−	14.6462i	−1.78188	−	0.477454i	−0.790956	−	0.611873i	$-0.790416\pi$
$941$	−54.6605	−	14.6462i	−1.78188	−	0.477454i	−0.990925	+	0.134419i	$0.957083\pi$
$942$	15.5112	+	15.7273i	0.505381	+	0.512424i
$943$	23.6615	−	40.9829i	0.770525	−	1.33459i
$944$	−8.04912	−	33.7492i	−0.261977	−	1.09844i
$945$	−3.44876	−	7.41993i	−0.112188	−	0.241370i
$946$	−0.0194335	−	0.0745871i	−0.000631836	−	0.00242503i
$947$	10.5259	+	39.2831i	0.342045	+	1.27653i	0.896027	+	0.443999i	$0.146441\pi$
$947$	10.5259	+	39.2831i	0.342045	+	1.27653i	−0.553983	+	0.832528i	$0.686893\pi$
$948$	7.11692	−	1.80181i	0.231147	−	0.0585199i
$949$	21.9474	+	5.88080i	0.712444	+	0.190899i
$950$	23.2042	+	40.8408i	0.752844	+	1.32505i
$951$			30.5390i			0.990294i
$952$	14.6856	+	18.3047i	0.475964	+	0.593259i
$953$		−	4.64014i		−	0.150309i	−0.997172	−	0.0751544i	$-0.976055\pi$
$953$		−	4.64014i		−	0.150309i	0.997172	−	0.0751544i	$-0.0239450\pi$
$954$	0.629035	−	0.357394i	0.0203658	−	0.0115711i
$955$	51.5543	+	13.8139i	1.66826	+	0.447008i
$956$	7.09801	−	11.9104i	0.229566	−	0.385210i
$957$	−0.328403	−	1.22562i	−0.0106157	−	0.0396185i
$958$	−9.61997	+	2.50646i	−0.310807	+	0.0809799i
$959$	−2.48906	+	28.0490i	−0.0803760	+	0.905749i
$960$	−24.7195	−	1.02676i	−0.797818	−	0.0331385i
$961$	6.96749	−	12.0680i	0.224758	−	0.389292i
$962$	−4.74255	+	4.67737i	−0.152906	+	0.150804i
$963$	17.1980	+	4.60820i	0.554199	+	0.148497i
$964$	19.3980	+	0.268438i	0.624769	+	0.00864580i
$965$	19.4304	+	19.4304i	0.625487	+	0.625487i
$966$	1.59309	−	16.6437i	0.0512568	−	0.535502i
$967$	18.9813			0.610396			0.305198	−	0.952289i	$-0.401277\pi$
$967$	18.9813			0.610396			0.305198	+	0.952289i	$0.401277\pi$
$968$	29.5620	−	7.26700i	0.950158	−	0.233570i
$969$	−11.4107	−	19.7638i	−0.366563	−	0.634906i
$970$	56.7437	+	0.392602i	1.82193	+	0.0126057i
$971$	−8.07053	−	30.1196i	−0.258996	−	0.966585i	−0.965824	−	0.259200i	$-0.916541\pi$
$971$	−8.07053	−	30.1196i	−0.258996	−	0.966585i	0.706828	−	0.707385i	$-0.250125\pi$
$972$	−1.92450	−	0.544320i	−0.0617285	−	0.0174591i
$973$	0.744185	+	4.25134i	0.0238575	+	0.136292i
$974$	−6.77700	+	1.76573i	−0.217149	+	0.0565776i
$975$	−19.4404	−	11.2239i	−0.622590	−	0.359453i
$976$	−38.9805	+	36.8805i	−1.24773	+	1.18052i
$977$	28.0849	+	48.6445i	0.898516	+	1.55628i	0.829391	+	0.558668i	$0.188687\pi$
$977$	28.0849	+	48.6445i	0.898516	+	1.55628i	0.0691248	+	0.997608i	$0.477979\pi$
$978$	5.19915	−	18.8800i	0.166250	−	0.603716i
$979$	−4.38811	−	4.38811i	−0.140245	−	0.140245i
$980$	3.06913	+	43.1875i	0.0980399	+	1.37957i
$981$	14.4397	−	14.4397i	0.461023	−	0.461023i
$982$	−19.2122	+	10.9156i	−0.613084	+	0.348331i
$983$	48.2310	−	27.8462i	1.53833	−	0.888155i	0.539392	−	0.842055i	$-0.318654\pi$
$983$	48.2310	−	27.8462i	1.53833	−	0.888155i	0.998937	−	0.0460998i	$-0.0146792\pi$
$984$	14.4353	+	26.2460i	0.460180	+	0.836692i
$985$	−13.9332	+	24.1330i	−0.443949	+	0.768943i
$986$	5.84745	−	9.96816i	0.186221	−	0.317451i
$987$	2.41808	−	0.423279i	0.0769684	−	0.0134731i
$988$	−62.4816	+	34.9300i	−1.98780	+	1.11127i
$989$	−0.483117	+	0.129451i	−0.0153622	+	0.00411630i
$990$	1.49543	+	1.51627i	0.0475279	+	0.0481901i
$991$	3.60658	−	2.08226i	0.114567	−	0.0661452i	−0.441622	−	0.897201i	$-0.645597\pi$
$991$	3.60658	−	2.08226i	0.114567	−	0.0661452i	0.556188	+	0.831056i	$0.312263\pi$
$992$	−15.9425	−	17.0856i	−0.506176	−	0.542467i
$993$		−	10.2340i		−	0.324765i
$994$	−16.9907	−	20.5876i	−0.538911	−	0.652998i
$995$	31.8953	−	31.8953i	1.01115	−	1.01115i
$996$	17.1553	+	0.237402i	0.543587	+	0.00752236i
$997$	1.22514	−	4.57228i	0.0388006	−	0.144806i	−0.943808	−	0.330494i	$-0.892785\pi$
$997$	1.22514	−	4.57228i	0.0388006	−	0.144806i	0.982609	+	0.185688i	$0.0594514\pi$
$998$	−9.52742	−	0.0659189i	−0.301585	−	0.00208663i
$999$	−0.829367	−	0.478835i	−0.0262400	−	0.0151497i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	336.2.bs.a.19.14	✓	128
7.3	odd	6	inner	336.2.bs.a.115.8	yes	128
16.11	odd	4	inner	336.2.bs.a.187.8	yes	128
112.59	even	12	inner	336.2.bs.a.283.14	yes	128

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
336.2.bs.a.19.14	✓	128	1.1	even	1	trivial
336.2.bs.a.115.8	yes	128	7.3	odd	6	inner
336.2.bs.a.187.8	yes	128	16.11	odd	4	inner
336.2.bs.a.283.14	yes	128	112.59	even	12	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:	\( N \)	\(=\)	\( 336 = 2^{4} \cdot 3 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	336.bs (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.375468 + 1.36346i) q^{2} +(0.258819 - 0.965926i) q^{3} +(-1.71805 - 1.02387i) q^{4} +(2.98722 - 0.800424i) q^{5} +(1.21982 + 0.715563i) q^{6} +(-1.52023 + 2.16539i) q^{7} +(2.04108 - 1.95806i) q^{8} +(-0.866025 - 0.500000i) q^{9} +O(q^{10})\)	\(q+(-0.375468 + 1.36346i) q^{2} +(0.258819 - 0.965926i) q^{3} +(-1.71805 - 1.02387i) q^{4} +(2.98722 - 0.800424i) q^{5} +(1.21982 + 0.715563i) q^{6} +(-1.52023 + 2.16539i) q^{7} +(2.04108 - 1.95806i) q^{8} +(-0.866025 - 0.500000i) q^{9} +(-0.0302596 + 4.37349i) q^{10} +(-0.126027 + 0.470339i) q^{11} +(-1.43365 + 1.39451i) q^{12} +(3.47774 - 3.47774i) q^{13} +(-2.38162 - 2.88581i) q^{14} -3.09260i q^{15} +(1.90338 + 3.51812i) q^{16} +(2.71585 - 1.56800i) q^{17} +(1.00689 - 0.993057i) q^{18} +(7.02925 - 1.88348i) q^{19} +(-5.95172 - 1.68336i) q^{20} +(1.69814 + 2.02887i) q^{21} +(-0.593970 - 0.348430i) q^{22} +(-2.23427 + 3.86987i) q^{23} +(-1.36307 - 2.47831i) q^{24} +(3.95269 - 2.28209i) q^{25} +(3.43598 + 6.04753i) q^{26} +(-0.707107 + 0.707107i) q^{27} +(4.82890 - 2.16372i) q^{28} +(-1.84259 - 1.84259i) q^{29} +(4.21664 + 1.16117i) q^{30} +(2.06549 + 3.57754i) q^{31} +(-5.51147 + 1.27424i) q^{32} +(0.421695 + 0.243466i) q^{33} +(1.11819 + 4.29169i) q^{34} +(-2.80804 + 7.68532i) q^{35} +(0.975938 + 1.74572i) q^{36} +(0.247863 + 0.925038i) q^{37} +(-0.0712041 + 10.2913i) q^{38} +(-2.45913 - 4.25934i) q^{39} +(4.52988 - 7.48289i) q^{40} -10.5903 q^{41} +(-3.40388 + 1.55357i) q^{42} +(0.0791459 + 0.0791459i) q^{43} +(0.698087 - 0.679030i) q^{44} +(-2.98722 - 0.800424i) q^{45} +(-4.43752 - 4.49935i) q^{46} +(0.463923 - 0.803538i) q^{47} +(3.89087 - 0.927965i) q^{48} +(-2.37780 - 6.58377i) q^{49} +(1.62743 + 6.24619i) q^{50} +(-0.811655 - 3.02914i) q^{51} +(-9.53567 + 2.41416i) q^{52} +(0.494143 + 0.132405i) q^{53} +(-0.698616 - 1.22961i) q^{54} +1.50588i q^{55} +(1.13705 + 7.39643i) q^{56} -7.27722i q^{57} +(3.20412 - 1.82046i) q^{58} +(-8.37839 - 2.24498i) q^{59} +(-3.16642 + 5.31324i) q^{60} +(3.47221 + 12.9585i) q^{61} +(-5.65335 + 1.47297i) q^{62} +(2.39925 - 1.11517i) q^{63} +(0.332005 - 7.99311i) q^{64} +(7.60511 - 13.1724i) q^{65} +(-0.490289 + 0.483551i) q^{66} +(-7.23899 - 1.93968i) q^{67} +(-6.27139 - 0.0867859i) q^{68} +(3.15974 + 3.15974i) q^{69} +(-9.42430 - 6.71424i) q^{70} +7.13408 q^{71} +(-2.74666 + 0.675190i) q^{72} +(2.30993 + 4.00091i) q^{73} +(-1.35432 - 0.00937034i) q^{74} +(-1.18130 - 4.40866i) q^{75} +(-14.0050 - 3.96113i) q^{76} +(-0.826877 - 0.987922i) q^{77} +(6.73076 - 1.75368i) q^{78} +(-3.17895 - 1.83537i) q^{79} +(8.50180 + 8.98589i) q^{80} +(0.500000 + 0.866025i) q^{81} +(3.97630 - 14.4394i) q^{82} +(-6.06590 - 6.06590i) q^{83} +(-0.840180 - 5.22438i) q^{84} +(6.85779 - 6.85779i) q^{85} +(-0.137629 + 0.0781955i) q^{86} +(-2.25670 + 1.30290i) q^{87} +(0.663722 + 1.20677i) q^{88} +(-6.37228 + 11.0371i) q^{89} +(2.21295 - 3.77243i) q^{90} +(2.24369 + 12.8176i) q^{91} +(7.80083 - 4.36102i) q^{92} +(3.99022 - 1.06918i) q^{93} +(0.921404 + 0.934243i) q^{94} +(19.4904 - 11.2528i) q^{95} +(-0.195653 + 5.65347i) q^{96} -12.9745i q^{97} +(9.86950 - 0.770044i) q^{98} +(0.344312 - 0.344312i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 128 q + 4 q^{4} - 24 q^{8}+O(q^{10}) \) 128 * q + 4 * q^4 - 24 * q^8	\( 128 q + 4 q^{4} - 24 q^{8} + 36 q^{10} - 8 q^{11} - 32 q^{14} - 4 q^{16} + 4 q^{18} + 16 q^{22} + 16 q^{23} - 32 q^{28} + 32 q^{29} - 24 q^{35} - 16 q^{37} + 60 q^{40} - 20 q^{42} - 16 q^{43} - 12 q^{44} - 20 q^{46} - 32 q^{50} - 144 q^{52} - 16 q^{53} - 56 q^{56} - 40 q^{58} - 96 q^{59} - 24 q^{60} - 32 q^{64} - 72 q^{66} + 16 q^{67} - 60 q^{68} + 28 q^{70} + 128 q^{71} - 4 q^{72} - 72 q^{74} + 72 q^{78} - 36 q^{80} + 64 q^{81} - 60 q^{82} + 24 q^{84} - 44 q^{86} - 48 q^{88} - 8 q^{91} + 56 q^{92} + 36 q^{94} + 60 q^{96} + 148 q^{98} - 16 q^{99}+O(q^{100}) \) 128 * q + 4 * q^4 - 24 * q^8 + 36 * q^10 - 8 * q^11 - 32 * q^14 - 4 * q^16 + 4 * q^18 + 16 * q^22 + 16 * q^23 - 32 * q^28 + 32 * q^29 - 24 * q^35 - 16 * q^37 + 60 * q^40 - 20 * q^42 - 16 * q^43 - 12 * q^44 - 20 * q^46 - 32 * q^50 - 144 * q^52 - 16 * q^53 - 56 * q^56 - 40 * q^58 - 96 * q^59 - 24 * q^60 - 32 * q^64 - 72 * q^66 + 16 * q^67 - 60 * q^68 + 28 * q^70 + 128 * q^71 - 4 * q^72 - 72 * q^74 + 72 * q^78 - 36 * q^80 + 64 * q^81 - 60 * q^82 + 24 * q^84 - 44 * q^86 - 48 * q^88 - 8 * q^91 + 56 * q^92 + 36 * q^94 + 60 * q^96 + 148 * q^98 - 16 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

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Database

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