LMFDB - Embedded newform 990.2.t.b.131.5

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [990,2,Mod(131,990)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(990, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([5, 0, 3])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("990.131"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 990 = 2 \cdot 3^{2} \cdot 5 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	990.t (of order $6$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [48,24] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(2)] == traces)

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

Self dual:	no
Analytic conductor:	$7.90518980011$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$24$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			131.5
Character	$\chi$	$=$	990.131
Dual form			990.2.t.b.461.5

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.500000 + 0.866025i) q^{2} +(-1.60551 + 0.649887i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(-0.866025 - 0.500000i) q^{5} +(-1.36557 - 1.06546i) q^{6} +(-3.00605 + 1.73554i) q^{7} -1.00000 q^{8} +(2.15529 - 2.08679i) q^{9} -1.00000i q^{10} +(-2.51831 - 2.15827i) q^{11} +(0.239934 - 1.71535i) q^{12} +(2.66134 + 1.53653i) q^{13} +(-3.00605 - 1.73554i) q^{14} +(1.71535 + 0.239934i) q^{15} +(-0.500000 - 0.866025i) q^{16} -0.571778 q^{17} +(2.88486 + 0.823142i) q^{18} -4.19161i q^{19} +(0.866025 - 0.500000i) q^{20} +(3.69832 - 4.74002i) q^{21} +(0.609965 - 3.26005i) q^{22} +(-1.07593 - 0.621187i) q^{23} +(1.60551 - 0.649887i) q^{24} +(0.500000 + 0.866025i) q^{25} +3.07305i q^{26} +(-2.10416 + 4.75106i) q^{27} -3.47109i q^{28} +(1.40673 + 2.43653i) q^{29} +(0.649887 + 1.60551i) q^{30} +(2.98744 - 5.17440i) q^{31} +(0.500000 - 0.866025i) q^{32} +(5.44579 + 1.82850i) q^{33} +(-0.285889 - 0.495174i) q^{34} +3.47109 q^{35} +(0.729570 + 2.90994i) q^{36} +10.7687 q^{37} +(3.63004 - 2.09580i) q^{38} +(-5.27137 - 0.737330i) q^{39} +(0.866025 + 0.500000i) q^{40} +(3.55333 - 6.15455i) q^{41} +(5.95414 + 0.832832i) q^{42} +(-4.72362 + 2.72718i) q^{43} +(3.12827 - 1.10178i) q^{44} +(-2.90994 + 0.729570i) q^{45} -1.24237i q^{46} +(3.51185 - 2.02757i) q^{47} +(1.36557 + 1.06546i) q^{48} +(2.52423 - 4.37210i) q^{49} +(-0.500000 + 0.866025i) q^{50} +(0.917992 - 0.371591i) q^{51} +(-2.66134 + 1.53653i) q^{52} -7.80538i q^{53} +(-5.16661 + 0.553276i) q^{54} +(1.10178 + 3.12827i) q^{55} +(3.00605 - 1.73554i) q^{56} +(2.72407 + 6.72965i) q^{57} +(-1.40673 + 2.43653i) q^{58} +(3.04470 + 1.75786i) q^{59} +(-1.06546 + 1.36557i) q^{60} +(-6.43091 + 3.71288i) q^{61} +5.97489 q^{62} +(-2.85720 + 10.0136i) q^{63} +1.00000 q^{64} +(-1.53653 - 2.66134i) q^{65} +(1.13936 + 5.63044i) q^{66} +(6.88293 - 11.9216i) q^{67} +(0.285889 - 0.495174i) q^{68} +(2.13111 + 0.298088i) q^{69} +(1.73554 + 3.00605i) q^{70} -8.76870i q^{71} +(-2.15529 + 2.08679i) q^{72} +10.7034i q^{73} +(5.38434 + 9.32595i) q^{74} +(-1.36557 - 1.06546i) q^{75} +(3.63004 + 2.09580i) q^{76} +(11.3159 + 2.11724i) q^{77} +(-1.99714 - 4.93380i) q^{78} +(-6.96609 + 4.02187i) q^{79} +1.00000i q^{80} +(0.290583 - 8.99531i) q^{81} +7.10667 q^{82} +(-8.27594 - 14.3343i) q^{83} +(2.25582 + 5.57285i) q^{84} +(0.495174 + 0.285889i) q^{85} +(-4.72362 - 2.72718i) q^{86} +(-3.84199 - 2.99765i) q^{87} +(2.51831 + 2.15827i) q^{88} +2.07911i q^{89} +(-2.08679 - 2.15529i) q^{90} -10.6668 q^{91} +(1.07593 - 0.621187i) q^{92} +(-1.43358 + 10.2490i) q^{93} +(3.51185 + 2.02757i) q^{94} +(-2.09580 + 3.63004i) q^{95} +(-0.239934 + 1.71535i) q^{96} +(5.52201 + 9.56440i) q^{97} +5.04846 q^{98} +(-9.93156 + 0.603475i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q + 24 q^{2} - 2 q^{3} - 24 q^{4} + 2 q^{6} - 48 q^{8} + 10 q^{9} - 12 q^{11} + 4 q^{12} - 24 q^{13} - 4 q^{15} - 24 q^{16} + 12 q^{17} + 8 q^{18} + 16 q^{21} - 6 q^{22} + 36 q^{23} + 2 q^{24} + 24 q^{25}+ \cdots - 44 q^{99}+O(q^{100}) $ 48 * q + 24 * q^2 - 2 * q^3 - 24 * q^4 + 2 * q^6 - 48 * q^8 + 10 * q^9 - 12 * q^11 + 4 * q^12 - 24 * q^13 - 4 * q^15 - 24 * q^16 + 12 * q^17 + 8 * q^18 + 16 * q^21 - 6 * q^22 + 36 * q^23 + 2 * q^24 + 24 * q^25 - 8 * q^27 - 8 * q^30 + 24 * q^32 + 12 * q^33 + 6 * q^34 - 2 * q^36 - 6 * q^38 + 40 * q^39 + 6 * q^41 + 8 * q^42 - 30 * q^43 + 6 * q^44 - 2 * q^48 + 24 * q^49 - 24 * q^50 - 22 * q^51 + 24 * q^52 - 22 * q^54 - 40 * q^57 - 54 * q^59 - 4 * q^60 + 38 * q^63 + 48 * q^64 - 12 * q^66 - 6 * q^67 - 6 * q^68 + 76 * q^69 - 10 * q^72 + 2 * q^75 - 6 * q^76 - 18 * q^77 + 32 * q^78 + 10 * q^81 + 12 * q^82 - 36 * q^83 - 8 * q^84 - 30 * q^86 + 44 * q^87 + 12 * q^88 + 24 * q^91 - 36 * q^92 - 68 * q^93 - 4 * q^96 + 6 * q^97 + 48 * q^98 - 44 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/990\mathbb{Z}\right)^\times$.

$n$	$397$	$541$	$551$
$\chi(n)$	$1$	$-1$	$e\left(\frac{5}{6}\right)$

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 $

$2$	0.500000	+	0.866025i	0.353553	+	0.612372i
$2$	0.500000	+	0.866025i	0.353553	+	0.612372i
$3$	−1.60551	+	0.649887i	−0.926939	+	0.375212i
$3$	−1.60551	+	0.649887i	−0.926939	+	0.375212i
$4$	−0.500000	+	0.866025i	−0.250000	+	0.433013i
$5$	−0.866025	−	0.500000i	−0.387298	−	0.223607i
$5$	−0.866025	−	0.500000i	−0.387298	−	0.223607i
$6$	−1.36557	−	1.06546i	−0.557492	−	0.434974i
$7$	−3.00605	+	1.73554i	−1.13618	+	0.655974i	−0.945482	−	0.325674i	$-0.894409\pi$
$7$	−3.00605	+	1.73554i	−1.13618	+	0.655974i	−0.190699	+	0.981649i	$0.561075\pi$
$8$	−1.00000			−0.353553
$9$	2.15529	−	2.08679i	0.718431	−	0.695598i
$10$		−	1.00000i		−	0.316228i
$11$	−2.51831	−	2.15827i	−0.759298	−	0.650743i
$11$	−2.51831	−	2.15827i	−0.759298	−	0.650743i
$12$	0.239934	−	1.71535i	0.0692630	−	0.495179i
$13$	2.66134	+	1.53653i	0.738123	+	0.426156i	0.821387	−	0.570372i	$-0.193201\pi$
$13$	2.66134	+	1.53653i	0.738123	+	0.426156i	−0.0832632	+	0.996528i	$0.526534\pi$
$14$	−3.00605	−	1.73554i	−0.803401	−	0.463844i
$15$	1.71535	+	0.239934i	0.442902	+	0.0619507i
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	−0.571778			−0.138676			−0.0693382	−	0.997593i	$-0.522089\pi$
$17$	−0.571778			−0.138676			−0.0693382	+	0.997593i	$0.522089\pi$
$18$	2.88486	+	0.823142i	0.679969	+	0.194016i
$19$		−	4.19161i		−	0.961621i	−0.876825	−	0.480810i	$-0.840343\pi$
$19$		−	4.19161i		−	0.961621i	0.876825	−	0.480810i	$-0.159657\pi$
$20$	0.866025	−	0.500000i	0.193649	−	0.111803i
$21$	3.69832	−	4.74002i	0.807040	−	1.03436i
$22$	0.609965	−	3.26005i	0.130045	−	0.695046i
$23$	−1.07593	−	0.621187i	−0.224346	−	0.129526i	0.383615	−	0.923493i	$-0.374679\pi$
$23$	−1.07593	−	0.621187i	−0.224346	−	0.129526i	−0.607961	+	0.793967i	$0.708012\pi$
$24$	1.60551	−	0.649887i	0.327722	−	0.132658i
$25$	0.500000	+	0.866025i	0.100000	+	0.173205i
$26$			3.07305i			0.602675i
$27$	−2.10416	+	4.75106i	−0.404945	+	0.914341i
$28$		−	3.47109i		−	0.655974i
$29$	1.40673	+	2.43653i	0.261224	+	0.452453i	0.966567	−	0.256413i	$-0.0825407\pi$
$29$	1.40673	+	2.43653i	0.261224	+	0.452453i	−0.705344	+	0.708865i	$0.749207\pi$
$30$	0.649887	+	1.60551i	0.118653	+	0.293124i
$31$	2.98744	−	5.17440i	0.536561	−	0.929350i	−0.462525	−	0.886606i	$-0.653057\pi$
$31$	2.98744	−	5.17440i	0.536561	−	0.929350i	0.999086	−	0.0427442i	$-0.0136100\pi$
$32$	0.500000	−	0.866025i	0.0883883	−	0.153093i
$33$	5.44579	+	1.82850i	0.947990	+	0.318301i
$34$	−0.285889	−	0.495174i	−0.0490295	−	0.0849217i
$35$	3.47109			0.586721
$36$	0.729570	+	2.90994i	0.121595	+	0.484989i
$37$	10.7687			1.77036			0.885180	−	0.465250i	$-0.154035\pi$
$37$	10.7687			1.77036			0.885180	+	0.465250i	$0.154035\pi$
$38$	3.63004	−	2.09580i	0.588870	−	0.339984i
$39$	−5.27137	−	0.737330i	−0.844094	−	0.118067i
$40$	0.866025	+	0.500000i	0.136931	+	0.0790569i
$41$	3.55333	−	6.15455i	0.554937	−	0.961180i	−0.442971	−	0.896536i	$-0.646076\pi$
$41$	3.55333	−	6.15455i	0.554937	−	0.961180i	0.997908	−	0.0646439i	$-0.0205911\pi$
$42$	5.95414	+	0.832832i	0.918744	+	0.128509i
$43$	−4.72362	+	2.72718i	−0.720345	+	0.415891i	−0.814880	−	0.579630i	$-0.803197\pi$
$43$	−4.72362	+	2.72718i	−0.720345	+	0.415891i	0.0945347	+	0.995522i	$0.469864\pi$
$44$	3.12827	−	1.10178i	0.471605	−	0.166100i
$45$	−2.90994	+	0.729570i	−0.433788	+	0.108758i
$46$		−	1.24237i		−	0.183178i
$47$	3.51185	−	2.02757i	0.512256	−	0.295751i	−0.221505	−	0.975159i	$-0.571097\pi$
$47$	3.51185	−	2.02757i	0.512256	−	0.295751i	0.733760	+	0.679408i	$0.237763\pi$
$48$	1.36557	+	1.06546i	0.197103	+	0.153787i
$49$	2.52423	−	4.37210i	0.360605	−	0.624586i
$50$	−0.500000	+	0.866025i	−0.0707107	+	0.122474i
$51$	0.917992	−	0.371591i	0.128545	−	0.0520331i
$52$	−2.66134	+	1.53653i	−0.369062	+	0.213078i
$53$		−	7.80538i		−	1.07215i	−0.844170	−	0.536075i	$-0.819906\pi$
$53$		−	7.80538i		−	1.07215i	0.844170	−	0.536075i	$-0.180094\pi$
$54$	−5.16661	+	0.553276i	−0.703087	+	0.0752913i
$55$	1.10178	+	3.12827i	0.148564	+	0.421816i
$56$	3.00605	−	1.73554i	0.401701	−	0.231922i
$57$	2.72407	+	6.72965i	0.360812	+	0.891364i
$58$	−1.40673	+	2.43653i	−0.184713	+	0.319932i
$59$	3.04470	+	1.75786i	0.396386	+	0.228854i	0.684923	−	0.728615i	$-0.259836\pi$
$59$	3.04470	+	1.75786i	0.396386	+	0.228854i	−0.288537	+	0.957469i	$0.593169\pi$
$60$	−1.06546	+	1.36557i	−0.137551	+	0.176294i
$61$	−6.43091	+	3.71288i	−0.823393	+	0.475386i	−0.851585	−	0.524216i	$-0.824358\pi$
$61$	−6.43091	+	3.71288i	−0.823393	+	0.475386i	0.0281921	+	0.999603i	$0.491025\pi$
$62$	5.97489			0.758811
$63$	−2.85720	+	10.0136i	−0.359973	+	1.26160i
$64$	1.00000			0.125000
$65$	−1.53653	−	2.66134i	−0.190583	−	0.330099i
$66$	1.13936	+	5.63044i	0.140246	+	0.693059i
$67$	6.88293	−	11.9216i	0.840884	−	1.45645i	−0.0482650	−	0.998835i	$-0.515369\pi$
$67$	6.88293	−	11.9216i	0.840884	−	1.45645i	0.889149	−	0.457619i	$-0.151297\pi$
$68$	0.285889	−	0.495174i	0.0346691	−	0.0600487i
$69$	2.13111	+	0.298088i	0.256555	+	0.0358855i
$70$	1.73554	+	3.00605i	0.207437	+	0.359292i
$71$		−	8.76870i		−	1.04065i	−0.853967	−	0.520326i	$-0.825810\pi$
$71$		−	8.76870i		−	1.04065i	0.853967	−	0.520326i	$-0.174190\pi$
$72$	−2.15529	+	2.08679i	−0.254004	+	0.245931i
$73$			10.7034i			1.25273i	0.779529	+	0.626367i	$0.215459\pi$
$73$			10.7034i			1.25273i	−0.779529	+	0.626367i	$0.784541\pi$
$74$	5.38434	+	9.32595i	0.625916	+	1.08412i
$75$	−1.36557	−	1.06546i	−0.157683	−	0.123029i
$76$	3.63004	+	2.09580i	0.416394	+	0.240405i
$77$	11.3159	+	2.11724i	1.28957	+	0.241282i
$78$	−1.99714	−	4.93380i	−0.226131	−	0.558643i
$79$	−6.96609	+	4.02187i	−0.783746	+	0.452496i	−0.837756	−	0.546044i	$-0.816133\pi$
$79$	−6.96609	+	4.02187i	−0.783746	+	0.452496i	0.0540101	+	0.998540i	$0.482800\pi$
$80$			1.00000i			0.111803i
$81$	0.290583	−	8.99531i	0.0322870	−	0.999479i
$82$	7.10667			0.784800
$83$	−8.27594	−	14.3343i	−0.908402	−	1.57340i	−0.816284	−	0.577651i	$-0.803969\pi$
$83$	−8.27594	−	14.3343i	−0.908402	−	1.57340i	−0.0921188	−	0.995748i	$-0.529364\pi$
$84$	2.25582	+	5.57285i	0.246130	+	0.608048i
$85$	0.495174	+	0.285889i	0.0537092	+	0.0310090i
$86$	−4.72362	−	2.72718i	−0.509361	−	0.294080i
$87$	−3.84199	−	2.99765i	−0.411904	−	0.321381i
$88$	2.51831	+	2.15827i	0.268452	+	0.230073i
$89$			2.07911i			0.220385i	0.993910	+	0.110193i	$0.0351468\pi$
$89$			2.07911i			0.220385i	−0.993910	+	0.110193i	$0.964853\pi$
$90$	−2.08679	−	2.15529i	−0.219967	−	0.227188i
$91$	−10.6668			−1.11819
$92$	1.07593	−	0.621187i	0.112173	−	0.0647632i
$93$	−1.43358	+	10.2490i	−0.148655	+	1.06277i
$94$	3.51185	+	2.02757i	0.362219	+	0.209127i
$95$	−2.09580	+	3.63004i	−0.215025	+	0.372434i
$96$	−0.239934	+	1.71535i	−0.0244882	+	0.175072i
$97$	5.52201	+	9.56440i	0.560675	+	0.971117i	0.997438	+	0.0715406i	$0.0227916\pi$
$97$	5.52201	+	9.56440i	0.560675	+	0.971117i	−0.436763	+	0.899577i	$0.643875\pi$
$98$	5.04846			0.509972
$99$	−9.93156	+	0.603475i	−0.998159	+	0.0606515i
$100$	−1.00000			−0.100000
$101$	−2.88766	−	5.00157i	−0.287333	−	0.497675i	0.685840	−	0.727753i	$-0.259435\pi$
$101$	−2.88766	−	5.00157i	−0.287333	−	0.497675i	−0.973172	+	0.230078i	$0.926102\pi$
$102$	0.780803	+	0.609209i	0.0773111	+	0.0603207i
$103$	6.23938	−	10.8069i	0.614784	−	1.06484i	−0.375638	−	0.926766i	$-0.622577\pi$
$103$	6.23938	−	10.8069i	0.614784	−	1.06484i	0.990422	−	0.138071i	$-0.0440902\pi$
$104$	−2.66134	−	1.53653i	−0.260966	−	0.150669i
$105$	−5.57285	+	2.25582i	−0.543855	+	0.220145i
$106$	6.75965	−	3.90269i	0.656556	−	0.379063i
$107$	2.70777			0.261770			0.130885	−	0.991398i	$-0.458218\pi$
$107$	2.70777			0.261770			0.130885	+	0.991398i	$0.458218\pi$
$108$	−3.06246	−	4.19778i	−0.294685	−	0.403932i
$109$		−	12.6169i		−	1.20848i	−0.796804	−	0.604238i	$-0.793477\pi$
$109$		−	12.6169i		−	1.20848i	0.796804	−	0.604238i	$-0.206523\pi$
$110$	−2.15827	+	2.51831i	−0.205783	+	0.240111i
$111$	−17.2892	+	6.99842i	−1.64101	+	0.664261i
$112$	3.00605	+	1.73554i	0.284045	+	0.163994i
$113$	−15.7790	−	9.11003i	−1.48437	−	0.856999i	−0.484525	−	0.874778i	$-0.661007\pi$
$113$	−15.7790	−	9.11003i	−1.48437	−	0.856999i	−0.999842	+	0.0177782i	$0.994341\pi$
$114$	−4.46601	+	5.72394i	−0.418280	+	0.536096i
$115$	0.621187	+	1.07593i	0.0579260	+	0.100331i
$116$	−2.81346			−0.261224
$117$	8.94239	−	2.24201i	0.826724	−	0.207274i
$118$			3.51572i			0.323648i
$119$	1.71879	−	0.992346i	0.157562	−	0.0909682i
$120$	−1.71535	−	0.239934i	−0.156589	−	0.0219029i
$121$	1.68373	+	10.8704i	0.153066	+	0.988216i
$122$	−6.43091	−	3.71288i	−0.582227	−	0.336149i
$123$	−1.70513	+	12.1904i	−0.153746	+	1.09917i
$124$	2.98744	+	5.17440i	0.268280	+	0.464675i
$125$		−	1.00000i		−	0.0894427i
$126$	−10.1006	+	2.53240i	−0.899837	+	0.225604i
$127$			8.16097i			0.724169i	0.932145	+	0.362085i	$0.117935\pi$
$127$			8.16097i			0.724169i	−0.932145	+	0.362085i	$0.882065\pi$
$128$	0.500000	+	0.866025i	0.0441942	+	0.0765466i
$129$	5.81143	−	7.44832i	0.511668	−	0.655788i
$130$	1.53653	−	2.66134i	0.134762	−	0.233415i
$131$	2.42797	−	4.20538i	0.212133	−	0.367425i	−0.740249	−	0.672333i	$-0.765292\pi$
$131$	2.42797	−	4.20538i	0.212133	−	0.367425i	0.952382	+	0.304908i	$0.0986256\pi$
$132$	−4.30642	+	3.80194i	−0.374826	+	0.330916i
$133$	7.27472	+	12.6002i	0.630799	+	1.09258i
$134$	13.7659			1.18919
$135$	4.19778	−	3.06246i	0.361287	−	0.263574i
$136$	0.571778			0.0490295
$137$	12.0414	−	6.95213i	1.02877	−	0.593960i	0.112138	−	0.993693i	$-0.464230\pi$
$137$	12.0414	−	6.95213i	1.02877	−	0.593960i	0.916632	+	0.399732i	$0.130897\pi$
$138$	0.807403	+	1.99464i	0.0687307	+	0.169795i
$139$	−2.05748	−	1.18789i	−0.174514	−	0.100755i	0.410199	−	0.911996i	$-0.365459\pi$
$139$	−2.05748	−	1.18789i	−0.174514	−	0.100755i	−0.584712	+	0.811241i	$0.698793\pi$
$140$	−1.73554	+	3.00605i	−0.146680	+	0.254058i
$141$	−4.32060	+	5.53757i	−0.363860	+	0.466348i
$142$	7.59391	−	4.38435i	0.637267	−	0.367926i
$143$	−3.38583	−	9.61334i	−0.283137	−	0.803908i
$144$	−2.88486	−	0.823142i	−0.240405	−	0.0685952i
$145$		−	2.81346i		−	0.233645i
$146$	−9.26938	+	5.35168i	−0.767139	+	0.442908i
$147$	−1.21130	+	8.65989i	−0.0999062	+	0.714256i
$148$	−5.38434	+	9.32595i	−0.442590	+	0.766588i
$149$	5.19792	−	9.00307i	0.425831	−	0.737560i	−0.570667	−	0.821182i	$-0.693315\pi$
$149$	5.19792	−	9.00307i	0.425831	−	0.737560i	0.996498	+	0.0836214i	$0.0266486\pi$
$150$	0.239934	−	1.71535i	0.0195905	−	0.140058i
$151$	−1.51253	+	0.873262i	−0.123088	+	0.0710651i	−0.560280	−	0.828303i	$-0.689306\pi$
$151$	−1.51253	+	0.873262i	−0.123088	+	0.0710651i	0.437192	+	0.899368i	$0.355973\pi$
$152$			4.19161i			0.339984i
$153$	−1.23235	+	1.19318i	−0.0996295	+	0.0964631i
$154$	3.82438	+	10.8585i	0.308177	+	0.875004i
$155$	−5.17440	+	2.98744i	−0.415618	+	0.239957i
$156$	3.27423	−	4.19647i	0.262148	−	0.335987i
$157$	−2.92817	+	5.07174i	−0.233693	+	0.404769i	−0.958892	−	0.283771i	$-0.908415\pi$
$157$	−2.92817	+	5.07174i	−0.233693	+	0.404769i	0.725199	+	0.688540i	$0.241748\pi$
$158$	−6.96609	−	4.02187i	−0.554192	−	0.319963i
$159$	5.07261	+	12.5316i	0.402284	+	0.993818i
$160$	−0.866025	+	0.500000i	−0.0684653	+	0.0395285i
$161$	4.31239			0.339864
$162$	7.93546	−	4.24600i	0.623468	−	0.333597i
$163$	−13.0015			−1.01836			−0.509180	−	0.860660i	$-0.670051\pi$
$163$	−13.0015			−1.01836			−0.509180	+	0.860660i	$0.670051\pi$
$164$	3.55333	+	6.15455i	0.277469	+	0.480590i
$165$	−3.80194	−	4.30642i	−0.295980	−	0.335255i
$166$	8.27594	−	14.3343i	0.642338	−	1.11256i
$167$	−10.1133	+	17.5168i	−0.782592	+	1.35549i	0.147836	+	0.989012i	$0.452769\pi$
$167$	−10.1133	+	17.5168i	−0.782592	+	1.35549i	−0.930427	+	0.366476i	$0.880564\pi$
$168$	−3.69832	+	4.74002i	−0.285332	+	0.365701i
$169$	−1.77817	−	3.07989i	−0.136783	−	0.236914i
$170$			0.571778i			0.0438534i
$171$	−8.74702	−	9.03415i	−0.668901	−	0.690858i
$172$		−	5.45436i		−	0.415891i
$173$	−5.97884	−	10.3557i	−0.454563	−	0.787326i	0.544100	−	0.839020i	$-0.316871\pi$
$173$	−5.97884	−	10.3557i	−0.454563	−	0.787326i	−0.998663	+	0.0516941i	$0.983538\pi$
$174$	0.675046	−	4.82608i	0.0511751	−	0.365864i
$175$	−3.00605	−	1.73554i	−0.227236	−	0.131195i
$176$	−0.609965	+	3.26005i	−0.0459779	+	0.245736i
$177$	−6.03069	−	0.843539i	−0.453294	−	0.0634043i
$178$	−1.80056	+	1.03955i	−0.134958	+	0.0779179i
$179$		−	15.7324i		−	1.17589i	−0.808900	−	0.587946i	$-0.799937\pi$
$179$		−	15.7324i		−	1.17589i	0.808900	−	0.587946i	$-0.200063\pi$
$180$	0.823142	−	2.88486i	0.0613534	−	0.215025i
$181$	−15.8181			−1.17575			−0.587874	−	0.808952i	$-0.700035\pi$
$181$	−15.8181			−1.17575			−0.587874	+	0.808952i	$0.700035\pi$
$182$	−5.33342	−	9.23776i	−0.395339	−	0.684748i
$183$	7.91190	−	10.1404i	0.584864	−	0.749601i
$184$	1.07593	+	0.621187i	0.0793184	+	0.0457945i
$185$	−9.32595	−	5.38434i	−0.685657	−	0.395864i
$186$	−9.59271	+	3.88300i	−0.703372	+	0.284715i
$187$	1.43991	+	1.23405i	0.105297	+	0.0902428i
$188$			4.05513i			0.295751i
$189$	−1.92047	−	17.9338i	−0.139694	−	1.30449i
$190$	−4.19161			−0.304091
$191$	2.71000	−	1.56462i	0.196089	−	0.113212i	−0.398741	−	0.917064i	$-0.630553\pi$
$191$	2.71000	−	1.56462i	0.196089	−	0.113212i	0.594830	+	0.803852i	$0.297219\pi$
$192$	−1.60551	+	0.649887i	−0.115867	+	0.0469016i
$193$	−21.1134	−	12.1898i	−1.51977	−	0.877441i	−0.999728	−	0.0233019i	$-0.992582\pi$
$193$	−21.1134	−	12.1898i	−1.51977	−	0.877441i	−0.520044	−	0.854139i	$-0.674085\pi$
$194$	−5.52201	+	9.56440i	−0.396457	+	0.686684i
$195$	4.19647	+	3.27423i	0.300516	+	0.234472i
$196$	2.52423	+	4.37210i	0.180302	+	0.312293i
$197$	−5.28218			−0.376340			−0.188170	−	0.982136i	$-0.560256\pi$
$197$	−5.28218			−0.376340			−0.188170	+	0.982136i	$0.560256\pi$
$198$	−5.48840	−	8.29924i	−0.390044	−	0.589802i
$199$	16.9828			1.20388			0.601938	−	0.798543i	$-0.294395\pi$
$199$	16.9828			1.20388			0.601938	+	0.798543i	$0.294395\pi$
$200$	−0.500000	−	0.866025i	−0.0353553	−	0.0612372i
$201$	−3.30290	+	23.6133i	−0.232968	+	1.66555i
$202$	2.88766	−	5.00157i	0.203175	−	0.351909i
$203$	−8.45742	−	4.88289i	−0.593595	−	0.342712i
$204$	−0.137189	+	0.980800i	−0.00960515	+	0.0686697i
$205$	−6.15455	+	3.55333i	−0.429853	+	0.248176i
$206$	12.4788			0.869436
$207$	−3.61523	+	0.906398i	−0.251276	+	0.0629990i
$208$		−	3.07305i		−	0.213078i
$209$	−9.04663	+	10.5557i	−0.625768	+	0.730156i
$210$	−4.74002	−	3.69832i	−0.327092	−	0.255209i
$211$	−8.05701	−	4.65172i	−0.554667	−	0.320237i	0.196335	−	0.980537i	$-0.437096\pi$
$211$	−8.05701	−	4.65172i	−0.554667	−	0.320237i	−0.751002	+	0.660300i	$0.770429\pi$
$212$	6.75965	+	3.90269i	0.464255	+	0.268038i
$213$	5.69866	+	14.0782i	0.390466	+	0.964622i
$214$	1.35389	+	2.34500i	0.0925497	+	0.160301i
$215$	5.45436			0.371985
$216$	2.10416	−	4.75106i	0.143170	−	0.323268i
$217$			20.7394i			1.40788i
$218$	10.9265	−	6.30844i	0.740038	−	0.427261i
$219$	−6.95597	−	17.1843i	−0.470041	−	1.16121i
$220$	−3.26005	−	0.609965i	−0.219793	−	0.0411239i
$221$	−1.52170	−	0.878552i	−0.102360	−	0.0590978i
$222$	−14.7054	−	11.4736i	−0.986961	−	0.770061i
$223$	3.34915	+	5.80089i	0.224275	+	0.388456i	0.956102	−	0.293035i	$-0.0946651\pi$
$223$	3.34915	+	5.80089i	0.224275	+	0.388456i	−0.731826	+	0.681491i	$0.761332\pi$
$224$			3.47109i			0.231922i
$225$	2.88486	+	0.823142i	0.192324	+	0.0548762i
$226$		−	18.2201i		−	1.21198i
$227$	3.40726	+	5.90154i	0.226148	+	0.391699i	0.956663	−	0.291197i	$-0.0940535\pi$
$227$	3.40726	+	5.90154i	0.226148	+	0.391699i	−0.730516	+	0.682896i	$0.760720\pi$
$228$	−7.19008	−	1.00571i	−0.476175	−	0.0666047i
$229$	−0.835411	+	1.44697i	−0.0552055	+	0.0956188i	−0.892307	−	0.451428i	$-0.850915\pi$
$229$	−0.835411	+	1.44697i	−0.0552055	+	0.0956188i	0.837102	+	0.547047i	$0.184248\pi$
$230$	−0.621187	+	1.07593i	−0.0409599	+	0.0709445i
$231$	−19.5438	+	3.95483i	−1.28589	+	0.260209i
$232$	−1.40673	−	2.43653i	−0.0923565	−	0.159966i
$233$	−7.96134			−0.521565			−0.260782	−	0.965398i	$-0.583981\pi$
$233$	−7.96134			−0.521565			−0.260782	+	0.965398i	$0.583981\pi$
$234$	6.41283	+	6.62333i	0.419220	+	0.432981i
$235$	−4.05513			−0.264528
$236$	−3.04470	+	1.75786i	−0.198193	+	0.114427i
$237$	8.57033	−	10.9843i	0.556703	−	0.713508i
$238$	1.71879	+	0.992346i	0.111413	+	0.0643242i
$239$	4.82150	−	8.35109i	0.311877	−	0.540187i	−0.666892	−	0.745155i	$-0.732376\pi$
$239$	4.82150	−	8.35109i	0.311877	−	0.540187i	0.978769	+	0.204968i	$0.0657089\pi$
$240$	−0.649887	−	1.60551i	−0.0419500	−	0.103635i
$241$	13.3384	−	7.70092i	0.859201	−	0.496060i	−0.00454362	−	0.999990i	$-0.501446\pi$
$241$	13.3384	−	7.70092i	0.859201	−	0.496060i	0.863745	+	0.503930i	$0.168113\pi$
$242$	−8.57216	+	6.89334i	−0.551039	+	0.443120i
$243$	5.37940	+	14.6309i	0.345089	+	0.938570i
$244$		−	7.42577i		−	0.475386i
$245$	−4.37210	+	2.52423i	−0.279323	+	0.161267i
$246$	−11.4098	+	4.61853i	−0.727462	+	0.294467i
$247$	6.44052	−	11.1553i	0.409800	−	0.709795i
$248$	−2.98744	+	5.17440i	−0.189703	+	0.328575i
$249$	22.6028	+	17.6354i	1.43239	+	1.11760i
$250$	0.866025	−	0.500000i	0.0547723	−	0.0316228i
$251$			15.7928i			0.996831i	0.866938	+	0.498416i	$0.166085\pi$
$251$			15.7928i			0.996831i	−0.866938	+	0.498416i	$0.833915\pi$
$252$	−7.24345	−	7.48122i	−0.456294	−	0.471272i
$253$	1.36882	+	3.88648i	0.0860572	+	0.244341i
$254$	−7.06761	+	4.08049i	−0.443461	+	0.256032i
$255$	−0.980800	−	0.137189i	−0.0614201	−	0.00859110i
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	−12.0217	−	6.94071i	−0.749891	−	0.432950i	0.0757638	−	0.997126i	$-0.475861\pi$
$257$	−12.0217	−	6.94071i	−0.749891	−	0.432950i	−0.825654	+	0.564176i	$0.809194\pi$
$258$	9.35615	+	1.30869i	0.582489	+	0.0814753i
$259$	−32.3712	+	18.6895i	−2.01145	+	1.16131i
$260$	3.07305			0.190583
$261$	8.11646	+	2.31588i	0.502396	+	0.143349i
$262$	4.85595			0.300002
$263$	9.46310	+	16.3906i	0.583520	+	1.01069i	0.995058	+	0.0992938i	$0.0316584\pi$
$263$	9.46310	+	16.3906i	0.583520	+	1.01069i	−0.411538	+	0.911393i	$0.635008\pi$
$264$	−5.44579	−	1.82850i	−0.335165	−	0.112537i
$265$	−3.90269	+	6.75965i	−0.239740	+	0.415242i
$266$	−7.27472	+	12.6002i	−0.446042	+	0.772567i
$267$	−1.35119	−	3.33802i	−0.0826913	−	0.204284i
$268$	6.88293	+	11.9216i	0.420442	+	0.728227i
$269$		−	27.3058i		−	1.66486i	−0.554128	−	0.832431i	$-0.686948\pi$
$269$		−	27.3058i		−	1.66486i	0.554128	−	0.832431i	$-0.313052\pi$
$270$	4.75106	+	2.10416i	0.289140	+	0.128055i
$271$			6.51976i			0.396047i	0.980197	+	0.198024i	$0.0634523\pi$
$271$			6.51976i			0.396047i	−0.980197	+	0.198024i	$0.936548\pi$
$272$	0.285889	+	0.495174i	0.0173346	+	0.0300243i
$273$	17.1257	−	6.93224i	1.03649	−	0.419558i
$274$	12.0414	+	6.95213i	0.727450	+	0.419993i
$275$	0.609965	−	3.26005i	0.0367823	−	0.196589i
$276$	−1.32371	+	1.69655i	−0.0796777	+	0.102120i
$277$	19.2805	−	11.1316i	1.15845	−	0.668834i	0.207522	−	0.978230i	$-0.433460\pi$
$277$	19.2805	−	11.1316i	1.15845	−	0.668834i	0.950933	+	0.309396i	$0.100127\pi$
$278$		−	2.37578i		−	0.142490i
$279$	−4.35909	−	17.3865i	−0.260972	−	1.04090i
$280$	−3.47109			−0.207437
$281$	−11.2677	−	19.5162i	−0.672175	−	1.16424i	−0.977286	−	0.211924i	$-0.932027\pi$
$281$	−11.2677	−	19.5162i	−0.672175	−	1.16424i	0.305112	−	0.952317i	$-0.401306\pi$
$282$	−6.95598	−	0.972964i	−0.414223	−	0.0579392i
$283$	12.0832	+	6.97624i	0.718272	+	0.414695i	0.814116	−	0.580702i	$-0.197222\pi$
$283$	12.0832	+	6.97624i	0.718272	+	0.414695i	−0.0958442	+	0.995396i	$0.530555\pi$
$284$	7.59391	+	4.38435i	0.450616	+	0.260163i
$285$	1.00571	−	7.19008i	0.0595731	−	0.425904i
$286$	6.63248	−	7.73889i	0.392187	−	0.457610i
$287$			24.6679i			1.45610i
$288$	−0.729570	−	2.90994i	−0.0429903	−	0.171470i
$289$	−16.6731			−0.980769
$290$	2.43653	−	1.40673i	0.143078	−	0.0826062i
$291$	−15.0814	−	11.7670i	−0.884087	−	0.689794i
$292$	−9.26938	−	5.35168i	−0.542449	−	0.313183i
$293$	9.14949	−	15.8474i	0.534519	−	0.925814i	−0.464667	−	0.885485i	$-0.653826\pi$
$293$	9.14949	−	15.8474i	0.534519	−	0.925814i	0.999186	−	0.0403288i	$-0.0128405\pi$
$294$	−8.10534	+	3.28093i	−0.472713	+	0.191348i
$295$	−1.75786	−	3.04470i	−0.102346	−	0.177269i
$296$	−10.7687			−0.625916
$297$	15.5530	−	7.42327i	0.902475	−	0.430742i
$298$	10.3958			0.602215
$299$	−1.90894	−	3.30638i	−0.110397	−	0.191213i
$300$	1.60551	−	0.649887i	0.0926939	−	0.0375212i
$301$	9.46629	−	16.3961i	0.545628	−	0.945056i
$302$	−1.51253	−	0.873262i	−0.0870366	−	0.0502506i
$303$	7.88660	+	6.15339i	0.453074	+	0.353503i
$304$	−3.63004	+	2.09580i	−0.208197	+	0.120203i
$305$	7.42577			0.425198
$306$	−1.64950	−	0.470655i	−0.0942957	−	0.0269055i
$307$		−	10.4327i		−	0.595424i	−0.954656	−	0.297712i	$-0.903776\pi$
$307$		−	10.4327i		−	0.595424i	0.954656	−	0.297712i	$-0.0962235\pi$
$308$	−7.49156	+	8.74126i	−0.426871	+	0.498080i
$309$	−2.99408	+	21.4055i	−0.170327	+	1.21771i
$310$	−5.17440	−	2.98744i	−0.293886	−	0.169675i
$311$	13.6444	+	7.87762i	0.773705	+	0.446699i	0.834195	−	0.551470i	$-0.185933\pi$
$311$	13.6444	+	7.87762i	0.773705	+	0.446699i	−0.0604900	+	0.998169i	$0.519266\pi$
$312$	5.27137	+	0.737330i	0.298432	+	0.0417431i
$313$	16.8517	+	29.1880i	0.952515	+	1.64980i	0.739954	+	0.672657i	$0.234847\pi$
$313$	16.8517	+	29.1880i	0.952515	+	1.64980i	0.212561	+	0.977148i	$0.431820\pi$
$314$	−5.85634			−0.330492
$315$	7.48122	−	7.24345i	0.421519	−	0.408122i
$316$		−	8.04375i		−	0.452496i
$317$	19.6982	−	11.3728i	1.10636	−	0.638758i	0.168476	−	0.985706i	$-0.446115\pi$
$317$	19.6982	−	11.3728i	1.10636	−	0.638758i	0.937884	+	0.346948i	$0.112782\pi$
$318$	−8.31635	+	10.6588i	−0.466358	+	0.597716i
$319$	1.71612	−	9.17204i	0.0960840	−	0.513536i
$320$	−0.866025	−	0.500000i	−0.0484123	−	0.0279508i
$321$	−4.34734	+	1.75975i	−0.242645	+	0.0982194i
$322$	2.15620	+	3.73464i	0.120160	+	0.208123i
$323$			2.39667i			0.133354i
$324$	7.64487	+	4.74931i	0.424715	+	0.263850i
$325$			3.07305i			0.170462i
$326$	−6.50077	−	11.2597i	−0.360045	−	0.623615i
$327$	8.19954	+	20.2565i	0.453436	+	1.12018i
$328$	−3.55333	+	6.15455i	−0.196200	+	0.339828i
$329$	−7.03786	+	12.1899i	−0.388010	+	0.672053i
$330$	1.82850	−	5.44579i	0.100656	−	0.299781i
$331$	13.3625	+	23.1445i	0.734469	+	1.27214i	0.954956	+	0.296747i	$0.0959019\pi$
$331$	13.3625	+	23.1445i	0.734469	+	1.27214i	−0.220487	+	0.975390i	$0.570765\pi$
$332$	16.5519			0.908402
$333$	23.2097	−	22.4720i	1.27188	−	1.23146i
$334$	−20.2266			−1.10675
$335$	−11.9216	+	6.88293i	−0.651346	+	0.376055i
$336$	−5.95414	−	0.832832i	−0.324825	−	0.0454347i
$337$	22.7650	+	13.1434i	1.24009	+	0.715967i	0.969113	−	0.246619i	$-0.0793196\pi$
$337$	22.7650	+	13.1434i	1.24009	+	0.715967i	0.270978	+	0.962586i	$0.412653\pi$
$338$	1.77817	−	3.07989i	0.0967199	−	0.167524i
$339$	31.2538	+	4.37161i	1.69747	+	0.237433i
$340$	−0.495174	+	0.285889i	−0.0268546	+	0.0155045i
$341$	−18.6911	+	6.58301i	−1.01218	+	0.356490i
$342$	3.45029	−	12.0922i	0.186570	−	0.653872i
$343$		−	6.77395i		−	0.365759i
$344$	4.72362	−	2.72718i	0.254680	−	0.147040i
$345$	−1.69655	−	1.32371i	−0.0913392	−	0.0712659i
$346$	5.97884	−	10.3557i	0.321425	−	0.556724i
$347$	−6.86855	+	11.8967i	−0.368723	+	0.638648i	−0.989366	−	0.145446i	$-0.953538\pi$
$347$	−6.86855	+	11.8967i	−0.368723	+	0.638648i	0.620643	+	0.784093i	$0.286872\pi$
$348$	4.51703	−	1.82843i	0.242138	−	0.0980143i
$349$	19.1383	−	11.0495i	1.02445	−	0.591468i	0.109062	−	0.994035i	$-0.465215\pi$
$349$	19.1383	−	11.0495i	1.02445	−	0.591468i	0.915390	+	0.402567i	$0.131882\pi$
$350$		−	3.47109i		−	0.185538i
$351$	−12.9000	+	9.41109i	−0.688551	+	0.502327i
$352$	−3.12827	+	1.10178i	−0.166737	+	0.0587251i
$353$	−22.4212	+	12.9449i	−1.19336	+	0.688985i	−0.959066	−	0.283181i	$-0.908610\pi$
$353$	−22.4212	+	12.9449i	−1.19336	+	0.688985i	−0.234291	+	0.972166i	$0.575277\pi$
$354$	−2.28482	−	5.64450i	−0.121437	−	0.300002i
$355$	−4.38435	+	7.59391i	−0.232697	+	0.403043i
$356$	−1.80056	−	1.03955i	−0.0954296	−	0.0550963i
$357$	−2.11462	+	2.71024i	−0.111918	+	0.143441i
$358$	13.6246	−	7.86619i	0.720084	−	0.415741i
$359$	−7.88211			−0.416002			−0.208001	−	0.978129i	$-0.566696\pi$
$359$	−7.88211			−0.416002			−0.208001	+	0.978129i	$0.566696\pi$
$360$	2.90994	−	0.729570i	0.153367	−	0.0384517i
$361$	1.43042			0.0752855
$362$	−7.90904	−	13.6989i	−0.415690	−	0.719996i
$363$	−9.76775	−	16.3582i	−0.512674	−	0.858584i
$364$	5.33342	−	9.23776i	0.279547	−	0.484190i
$365$	5.35168	−	9.26938i	0.280120	−	0.485182i
$366$	12.7378	+	1.78169i	0.665816	+	0.0931307i
$367$	−5.02343	−	8.70084i	−0.262221	−	0.454180i	0.704611	−	0.709594i	$-0.251122\pi$
$367$	−5.02343	−	8.70084i	−0.262221	−	0.454180i	−0.966832	+	0.255414i	$0.917788\pi$
$368$			1.24237i			0.0647632i
$369$	−5.18481	−	20.6799i	−0.269910	−	1.07655i
$370$		−	10.7687i		−	0.559837i
$371$	13.5466	+	23.4634i	0.703303	+	1.21816i
$372$	−8.15913	−	6.36603i	−0.423031	−	0.330063i
$373$	22.9222	+	13.2341i	1.18687	+	0.685238i	0.957593	−	0.288124i	$-0.0930316\pi$
$373$	22.9222	+	13.2341i	1.18687	+	0.685238i	0.229274	+	0.973362i	$0.426365\pi$
$374$	−0.348765	+	1.86403i	−0.0180342	+	0.0963865i
$375$	0.649887	+	1.60551i	0.0335600	+	0.0829079i
$376$	−3.51185	+	2.02757i	−0.181110	+	0.104564i
$377$			8.64592i			0.445288i
$378$	14.5709	−	10.6301i	0.749445	−	0.546752i
$379$	19.3457			0.993721			0.496860	−	0.867830i	$-0.334486\pi$
$379$	19.3457			0.993721			0.496860	+	0.867830i	$0.334486\pi$
$380$	−2.09580	−	3.63004i	−0.107512	−	0.186217i
$381$	−5.30371	−	13.1025i	−0.271717	−	0.671261i
$382$	2.71000	+	1.56462i	0.138656	+	0.0800529i
$383$	−11.4329	−	6.60081i	−0.584196	−	0.337286i	0.178603	−	0.983921i	$-0.442842\pi$
$383$	−11.4329	−	6.60081i	−0.584196	−	0.337286i	−0.762799	+	0.646635i	$0.776176\pi$
$384$	−1.36557	−	1.06546i	−0.0696865	−	0.0543718i
$385$	−8.74126	−	7.49156i	−0.445496	−	0.381805i
$386$		−	24.3796i		−	1.24089i
$387$	−4.48972	+	15.7351i	−0.228225	+	0.799860i
$388$	−11.0440			−0.560675
$389$	18.7302	−	10.8139i	0.949659	−	0.548286i	0.0566838	−	0.998392i	$-0.481947\pi$
$389$	18.7302	−	10.8139i	0.949659	−	0.548286i	0.892975	+	0.450107i	$0.148614\pi$
$390$	−0.737330	+	5.27137i	−0.0373361	+	0.266926i
$391$	0.615191	+	0.355181i	0.0311116	+	0.0179623i
$392$	−2.52423	+	4.37210i	−0.127493	+	0.220824i
$393$	−1.16511	+	8.32966i	−0.0587719	+	0.420176i
$394$	−2.64109	−	4.57451i	−0.133056	−	0.230460i
$395$	8.04375			0.404725
$396$	4.44315	−	8.90272i	0.223277	−	0.447378i
$397$	−21.7580			−1.09200			−0.546001	−	0.837785i	$-0.683850\pi$
$397$	−21.7580			−1.09200			−0.546001	+	0.837785i	$0.683850\pi$
$398$	8.49138	+	14.7075i	0.425634	+	0.737220i
$399$	−19.8683	−	15.5019i	−0.994659	−	0.776067i
$400$	0.500000	−	0.866025i	0.0250000	−	0.0433013i
$401$	−2.75480	−	1.59048i	−0.137568	−	0.0794249i	0.429636	−	0.903002i	$-0.358642\pi$
$401$	−2.75480	−	1.59048i	−0.137568	−	0.0794249i	−0.567204	+	0.823577i	$0.691975\pi$
$402$	−22.1012	+	8.94625i	−1.10231	+	0.446198i
$403$	15.9012	−	9.18057i	0.792096	−	0.457317i
$404$	5.77531			0.287333
$405$	−4.74931	+	7.64487i	−0.235995	+	0.379877i
$406$		−	9.76579i		−	0.484668i
$407$	−27.1188	−	23.2417i	−1.34423	−	1.15205i
$408$	−0.917992	+	0.371591i	−0.0454474	+	0.0183965i
$409$	9.14331	+	5.27889i	0.452108	+	0.261024i	0.708720	−	0.705490i	$-0.249273\pi$
$409$	9.14331	+	5.27889i	0.452108	+	0.261024i	−0.256612	+	0.966514i	$0.582606\pi$
$410$	−6.15455	−	3.55333i	−0.303952	−	0.175487i
$411$	−14.8145	+	18.9873i	−0.730745	+	0.936572i
$412$	6.23938	+	10.8069i	0.307392	+	0.532419i
$413$	−12.2034			−0.600488
$414$	−2.59258	−	2.67768i	−0.127418	−	0.131601i
$415$			16.5519i			0.812500i
$416$	2.66134	−	1.53653i	0.130483	−	0.0753344i
$417$	4.07530	+	0.570030i	0.199568	+	0.0279145i
$418$	−13.6649	−	2.55674i	−0.668370	−	0.125054i
$419$	28.3276	+	16.3549i	1.38389	+	0.798991i	0.992618	−	0.121283i	$-0.0387009\pi$
$419$	28.3276	+	16.3549i	1.38389	+	0.798991i	0.391275	+	0.920274i	$0.372034\pi$
$420$	0.832832	−	5.95414i	0.0406381	−	0.290532i
$421$	−14.4327	−	24.9982i	−0.703408	−	1.21834i	−0.967263	−	0.253776i	$-0.918327\pi$
$421$	−14.4327	−	24.9982i	−0.703408	−	1.21834i	0.263855	−	0.964562i	$-0.415006\pi$
$422$		−	9.30343i		−	0.452884i
$423$	3.33795	−	11.6985i	0.162297	−	0.568801i
$424$			7.80538i			0.379063i
$425$	−0.285889	−	0.495174i	−0.0138676	−	0.0240195i
$426$	−9.34274	+	11.9743i	−0.452657	+	0.580156i
$427$	12.8878	−	22.3223i	0.623682	−	1.08025i
$428$	−1.35389	+	2.34500i	−0.0654425	+	0.113350i
$429$	11.6836	+	13.2339i	0.564087	+	0.638937i
$430$	2.72718	+	4.72362i	0.131516	+	0.227793i
$431$	−18.2579			−0.879451			−0.439726	−	0.898132i	$-0.644924\pi$
$431$	−18.2579			−0.879451			−0.439726	+	0.898132i	$0.644924\pi$
$432$	5.16661	−	0.553276i	0.248579	−	0.0266195i
$433$	−1.76891			−0.0850085			−0.0425043	−	0.999096i	$-0.513534\pi$
$433$	−1.76891			−0.0850085			−0.0425043	+	0.999096i	$0.513534\pi$
$434$	−17.9608	+	10.3697i	−0.862147	+	0.497761i
$435$	1.82843	+	4.51703i	0.0876667	+	0.216575i
$436$	10.9265	+	6.30844i	0.523286	+	0.302119i
$437$	−2.60377	+	4.50987i	−0.124555	+	0.215736i
$438$	11.4041	−	14.6162i	0.544907	−	0.698389i
$439$	−17.1678	+	9.91186i	−0.819376	+	0.473067i	−0.850201	−	0.526458i	$-0.823520\pi$
$439$	−17.1678	+	9.91186i	−0.819376	+	0.473067i	0.0308250	+	0.999525i	$0.490187\pi$
$440$	−1.10178	−	3.12827i	−0.0525253	−	0.149134i
$441$	−3.68321	−	14.6907i	−0.175391	−	0.699558i
$442$		−	1.75710i		−	0.0835769i
$443$	3.88455	−	2.24275i	0.184561	−	0.106556i	−0.404873	−	0.914373i	$-0.632684\pi$
$443$	3.88455	−	2.24275i	0.184561	−	0.106556i	0.589434	+	0.807817i	$0.299351\pi$
$444$	2.58377	−	18.4721i	0.122620	−	0.876645i
$445$	1.03955	−	1.80056i	0.0492796	−	0.0853548i
$446$	−3.34915	+	5.80089i	−0.158587	+	0.274680i
$447$	−2.49432	+	17.8325i	−0.117977	+	0.843450i
$448$	−3.00605	+	1.73554i	−0.142023	+	0.0819968i
$449$			28.8727i			1.36259i	0.732011	+	0.681293i	$0.238582\pi$
$449$			28.8727i			1.36259i	−0.732011	+	0.681293i	$0.761418\pi$
$450$	0.729570	+	2.90994i	0.0343922	+	0.137176i
$451$	−22.2316	+	7.82999i	−1.04684	+	0.368700i
$452$	15.7790	−	9.11003i	0.742183	−	0.428500i
$453$	1.86086	−	2.38500i	0.0874309	−	0.112057i
$454$	−3.40726	+	5.90154i	−0.159911	+	0.276973i
$455$	9.23776	+	5.33342i	0.433073	+	0.250035i
$456$	−2.72407	−	6.72965i	−0.127566	−	0.315145i
$457$	−2.48854	+	1.43676i	−0.116409	+	0.0672087i	−0.557074	−	0.830463i	$-0.688076\pi$
$457$	−2.48854	+	1.43676i	−0.116409	+	0.0672087i	0.440665	+	0.897672i	$0.354743\pi$
$458$	−1.67082			−0.0780724
$459$	1.20311	−	2.71655i	0.0561563	−	0.126798i
$460$	−1.24237			−0.0579260
$461$	17.9951	+	31.1684i	0.838114	+	1.45166i	0.891470	+	0.453080i	$0.149675\pi$
$461$	17.9951	+	31.1684i	0.838114	+	1.45166i	−0.0533562	+	0.998576i	$0.516992\pi$
$462$	−13.1969	−	14.9480i	−0.613974	−	0.695443i
$463$	−18.7516	+	32.4788i	−0.871462	+	1.50942i	−0.0109775	+	0.999940i	$0.503494\pi$
$463$	−18.7516	+	32.4788i	−0.871462	+	1.50942i	−0.860484	+	0.509477i	$0.829839\pi$
$464$	1.40673	−	2.43653i	0.0653059	−	0.113113i
$465$	6.36603	−	8.15913i	0.295218	−	0.378371i
$466$	−3.98067	−	6.89472i	−0.184401	−	0.319392i
$467$		−	20.4378i		−	0.945750i	−0.881130	−	0.472875i	$-0.843216\pi$
$467$		−	20.4378i		−	0.945750i	0.881130	−	0.472875i	$-0.156784\pi$
$468$	−2.52956	+	8.86534i	−0.116929	+	0.409800i
$469$			47.7825i			2.20639i
$470$	−2.02757	−	3.51185i	−0.0935247	−	0.161989i
$471$	1.40514	−	10.0457i	0.0647452	−	0.462881i
$472$	−3.04470	−	1.75786i	−0.140144	−	0.0809120i
$473$	17.7815	+	3.32697i	0.817595	+	0.152974i
$474$	13.7979	+	1.92997i	0.633756	+	0.0886464i
$475$	3.63004	−	2.09580i	0.166558	−	0.0961621i
$476$			1.98469i			0.0909682i
$477$	−16.2882	−	16.8229i	−0.745786	−	0.770267i
$478$	9.64301			0.441061
$479$	5.45440	+	9.44730i	0.249218	+	0.431658i	0.963309	−	0.268395i	$-0.0864931\pi$
$479$	5.45440	+	9.44730i	0.249218	+	0.431658i	−0.714091	+	0.700053i	$0.753160\pi$
$480$	1.06546	−	1.36557i	0.0486316	−	0.0623295i
$481$	28.6591	+	16.5464i	1.30674	+	0.754449i
$482$	13.3384	+	7.70092i	0.607547	+	0.350767i
$483$	−6.92357	+	2.80257i	−0.315033	+	0.127521i
$484$	−10.2559	−	3.97704i	−0.466177	−	0.180774i
$485$		−	11.0440i		−	0.501483i
$486$	−9.98100	+	11.9741i	−0.452747	+	0.543157i
$487$	−28.0743			−1.27217			−0.636083	−	0.771621i	$-0.719446\pi$
$487$	−28.0743			−1.27217			−0.636083	+	0.771621i	$0.719446\pi$
$488$	6.43091	−	3.71288i	0.291113	−	0.168074i
$489$	20.8741	−	8.44954i	0.943957	−	0.382101i
$490$	−4.37210	−	2.52423i	−0.197511	−	0.114033i
$491$	2.26883	−	3.92974i	0.102391	−	0.177346i	−0.810278	−	0.586045i	$-0.800684\pi$
$491$	2.26883	−	3.92974i	0.102391	−	0.177346i	0.912669	+	0.408699i	$0.134017\pi$
$492$	−9.70466	−	7.57190i	−0.437520	−	0.341368i
$493$	−0.804338	−	1.39315i	−0.0362256	−	0.0627445i
$494$	12.8810			0.579545
$495$	8.90272	+	4.44315i	0.400147	+	0.199705i
$496$	−5.97489			−0.268280
$497$	15.2185	+	26.3592i	0.682642	+	1.18237i
$498$	−3.97136	+	28.3923i	−0.177961	+	1.27229i
$499$	1.10495	−	1.91384i	0.0494645	−	0.0856751i	−0.840233	−	0.542225i	$-0.817582\pi$
$499$	1.10495	−	1.91384i	0.0494645	−	0.0856751i	0.889698	+	0.456550i	$0.150915\pi$
$500$	0.866025	+	0.500000i	0.0387298	+	0.0223607i
$501$	4.85305	−	34.6958i	0.216818	−	1.55009i
$502$	−13.6769	+	7.89639i	−0.610432	+	0.352433i
$503$	25.7799			1.14947			0.574735	−	0.818339i	$-0.305105\pi$
$503$	25.7799			1.14947			0.574735	+	0.818339i	$0.305105\pi$
$504$	2.85720	−	10.0136i	0.127270	−	0.446042i
$505$			5.77531i			0.256998i
$506$	−2.68138	+	3.12868i	−0.119202	+	0.139087i
$507$	4.85644	+	3.78916i	0.215682	+	0.168283i
$508$	−7.06761	−	4.08049i	−0.313574	−	0.181042i
$509$	27.5723	+	15.9189i	1.22212	+	0.705591i	0.965370	−	0.260886i	$-0.0840147\pi$
$509$	27.5723	+	15.9189i	1.22212	+	0.705591i	0.256751	+	0.966478i	$0.417348\pi$
$510$	−0.371591	−	0.917992i	−0.0164543	−	0.0406494i
$511$	−18.5762	−	32.1749i	−0.821761	−	1.42333i
$512$	−1.00000			−0.0441942
$513$	19.9146	+	8.81979i	0.879249	+	0.389403i
$514$		−	13.8814i		−	0.612283i
$515$	−10.8069	+	6.23938i	−0.476210	+	0.274940i
$516$	3.54472	+	8.75701i	0.156048	+	0.385506i
$517$	−13.2199	−	2.47349i	−0.581413	−	0.108784i
$518$	−32.3712	−	18.6895i	−1.42231	−	0.821170i
$519$	16.3291	+	12.7405i	0.716767	+	0.559246i
$520$	1.53653	+	2.66134i	0.0673811	+	0.116708i
$521$			25.9716i			1.13784i	0.822394	+	0.568918i	$0.192638\pi$
$521$			25.9716i			1.13784i	−0.822394	+	0.568918i	$0.807362\pi$
$522$	2.05262	+	8.18700i	0.0898406	+	0.358335i
$523$		−	36.9966i		−	1.61775i	−0.587982	−	0.808874i	$-0.700077\pi$
$523$		−	36.9966i		−	1.61775i	0.587982	−	0.808874i	$-0.299923\pi$
$524$	2.42797	+	4.20538i	0.106067	+	0.183713i
$525$	5.95414	+	0.832832i	0.259860	+	0.0363478i
$526$	−9.46310	+	16.3906i	−0.412611	+	0.714663i
$527$	−1.70815	+	2.95861i	−0.0744083	+	0.128879i
$528$	−1.13936	−	5.63044i	−0.0495844	−	0.245033i
$529$	−10.7283	−	18.5819i	−0.466446	−	0.807908i
$530$	−7.80538			−0.339044
$531$	10.2305	−	2.56496i	0.443966	−	0.111310i
$532$	−14.5494			−0.630799
$533$	18.9133	−	10.9196i	0.819225	−	0.472980i
$534$	2.21522	−	2.83917i	0.0958619	−	0.122863i
$535$	−2.34500	−	1.35389i	−0.101383	−	0.0585336i
$536$	−6.88293	+	11.9216i	−0.297297	+	0.514934i
$537$	10.2243	+	25.2584i	0.441210	+	1.08998i
$538$	23.6475	−	13.6529i	1.01952	−	0.588618i
$539$	−15.7930	+	5.56230i	−0.680251	+	0.239585i
$540$	0.553276	+	5.16661i	0.0238092	+	0.222336i
$541$		−	22.6737i		−	0.974820i	−0.873173	−	0.487410i	$-0.837942\pi$
$541$		−	22.6737i		−	0.974820i	0.873173	−	0.487410i	$-0.162058\pi$
$542$	−5.64628	+	3.25988i	−0.242528	+	0.140024i
$543$	25.3960	−	10.2800i	1.08985	−	0.441155i
$544$	−0.285889	+	0.495174i	−0.0122574	+	0.0212304i
$545$	−6.30844	+	10.9265i	−0.270224	+	0.468041i
$546$	14.5663	+	11.3651i	0.623382	+	0.486383i
$547$	2.99932	−	1.73166i	0.128241	−	0.0740402i	−0.434507	−	0.900669i	$-0.643077\pi$
$547$	2.99932	−	1.73166i	0.128241	−	0.0740402i	0.562748	+	0.826628i	$0.309744\pi$
$548$			13.9043i			0.593960i
$549$	−6.11247	+	21.4223i	−0.260874	+	0.914283i
$550$	3.12827	−	1.10178i	0.133390	−	0.0469801i
$551$	10.2130	−	5.89647i	0.435088	−	0.251198i
$552$	−2.13111	−	0.298088i	−0.0907060	−	0.0126875i
$553$	13.9603	−	24.1799i	0.593652	−	1.02823i
$554$	19.2805	+	11.1316i	0.819151	+	0.472937i
$555$	18.4721	+	2.58377i	0.784095	+	0.109675i
$556$	2.05748	−	1.18789i	0.0872568	−	0.0503777i
$557$	18.4034			0.779777			0.389889	−	0.920862i	$-0.372514\pi$
$557$	18.4034			0.779777			0.389889	+	0.920862i	$0.372514\pi$
$558$	12.8776	−	12.4684i	0.545154	−	0.527828i
$559$	−16.7615			−0.708938
$560$	−1.73554	−	3.00605i	−0.0733402	−	0.127029i
$561$	−3.11378	−	1.04550i	−0.131464	−	0.0441409i
$562$	11.2677	−	19.5162i	0.475299	−	0.823242i
$563$	5.59054	−	9.68309i	0.235613	−	0.408094i	−0.723838	−	0.689970i	$-0.757624\pi$
$563$	5.59054	−	9.68309i	0.235613	−	0.408094i	0.959451	+	0.281877i	$0.0909569\pi$
$564$	−2.63538	−	6.51054i	−0.110969	−	0.274143i
$565$	9.11003	+	15.7790i	0.383262	+	0.663829i
$566$			13.9525i			0.586467i
$567$	14.7383	+	27.5447i	0.618948	+	1.15677i
$568$			8.76870i			0.367926i
$569$	−17.9961	−	31.1702i	−0.754437	−	1.30672i	−0.945654	−	0.325175i	$-0.894577\pi$
$569$	−17.9961	−	31.1702i	−0.754437	−	1.30672i	0.191217	−	0.981548i	$-0.438756\pi$
$570$	6.72965	−	2.72407i	0.281874	−	0.114099i
$571$	15.7409	+	9.08804i	0.658738	+	0.380322i	0.791796	−	0.610786i	$-0.209146\pi$
$571$	15.7409	+	9.08804i	0.658738	+	0.380322i	−0.133058	+	0.991108i	$0.542480\pi$
$572$	10.0183	+	1.87446i	0.418887	+	0.0783749i
$573$	−3.33409	+	4.27320i	−0.139284	+	0.178515i
$574$	−21.3630	+	12.3339i	−0.891675	+	0.514809i
$575$		−	1.24237i		−	0.0518106i
$576$	2.15529	−	2.08679i	0.0898039	−	0.0869497i
$577$	27.1402			1.12986			0.564931	−	0.825138i	$-0.308903\pi$
$577$	27.1402			1.12986			0.564931	+	0.825138i	$0.308903\pi$
$578$	−8.33654	−	14.4393i	−0.346754	−	0.600596i
$579$	41.8196	+	5.84950i	1.73796	+	0.243097i
$580$	2.43653	+	1.40673i	0.101171	+	0.0584114i
$581$	49.7558	+	28.7265i	2.06422	+	1.19178i
$582$	2.64983	−	18.9444i	0.109839	−	0.785269i
$583$	−16.8461	+	19.6563i	−0.697695	+	0.814082i
$584$		−	10.7034i		−	0.442908i
$585$	−8.86534	−	2.52956i	−0.366537	−	0.104584i
$586$	18.2990			0.755924
$587$	−11.3113	+	6.53058i	−0.466867	+	0.269546i	−0.714927	−	0.699199i	$-0.753540\pi$
$587$	−11.3113	+	6.53058i	−0.466867	+	0.269546i	0.248060	+	0.968745i	$0.420207\pi$
$588$	−6.89404	−	5.37896i	−0.284305	−	0.221825i
$589$	−21.6891	−	12.5222i	−0.893682	−	0.515968i
$590$	1.75786	−	3.04470i	0.0723699	−	0.125348i
$591$	8.48057	−	3.43282i	0.348844	−	0.141207i
$592$	−5.38434	−	9.32595i	−0.221295	−	0.383294i
$593$	−39.1945			−1.60953			−0.804763	−	0.593596i	$-0.797708\pi$
$593$	−39.1945			−1.60953			−0.804763	+	0.593596i	$0.797708\pi$
$594$	14.2052	+	9.75764i	0.582848	+	0.400361i
$595$	−1.98469			−0.0813645
$596$	5.19792	+	9.00307i	0.212915	+	0.368780i
$597$	−27.2659	+	11.0369i	−1.11592	+	0.451709i
$598$	1.90894	−	3.30638i	0.0780624	−	0.135208i
$599$	−20.6589	−	11.9274i	−0.844100	−	0.487341i	0.0145556	−	0.999894i	$-0.495367\pi$
$599$	−20.6589	−	11.9274i	−0.844100	−	0.487341i	−0.858656	+	0.512553i	$0.828700\pi$
$600$	1.36557	+	1.06546i	0.0557492	+	0.0434974i
$601$	−7.31857	+	4.22538i	−0.298531	+	0.172357i	−0.641783	−	0.766887i	$-0.721805\pi$
$601$	−7.31857	+	4.22538i	−0.298531	+	0.172357i	0.343252	+	0.939243i	$0.388471\pi$
$602$	18.9326			0.771635
$603$	−10.0432	−	40.0578i	−0.408989	−	1.63128i
$604$		−	1.74652i		−	0.0710651i
$605$	3.97704	−	10.2559i	0.161690	−	0.416961i
$606$	−1.38569	+	9.90670i	−0.0562900	+	0.402432i
$607$	−22.6122	−	13.0552i	−0.917803	−	0.529894i	−0.0348693	−	0.999392i	$-0.511101\pi$
$607$	−22.6122	−	13.0552i	−0.917803	−	0.529894i	−0.882933	+	0.469498i	$0.844435\pi$
$608$	−3.63004	−	2.09580i	−0.147218	−	0.0849961i
$609$	16.7518	+	2.34314i	0.678816	+	0.0949490i
$610$	3.71288	+	6.43091i	0.150330	+	0.260380i
$611$	12.4616			0.504144
$612$	−0.417152	−	1.66384i	−0.0168624	−	0.0672566i
$613$		−	45.5602i		−	1.84016i	−0.391730	−	0.920080i	$-0.628123\pi$
$613$		−	45.5602i		−	1.84016i	0.391730	−	0.920080i	$-0.371877\pi$
$614$	9.03496	−	5.21634i	0.364621	−	0.210514i
$615$	7.57190	−	9.70466i	0.305329	−	0.391330i
$616$	−11.3159	−	2.11724i	−0.455932	−	0.0853062i
$617$	1.07441	+	0.620312i	0.0432542	+	0.0249728i	0.521471	−	0.853269i	$-0.325383\pi$
$617$	1.07441	+	0.620312i	0.0432542	+	0.0249728i	−0.478217	+	0.878242i	$0.658717\pi$
$618$	−20.0347	+	8.10978i	−0.805914	+	0.326223i
$619$	12.9009	+	22.3450i	0.518532	+	0.898123i	0.999768	+	0.0215325i	$0.00685452\pi$
$619$	12.9009	+	22.3450i	0.518532	+	0.898123i	−0.481236	+	0.876591i	$0.659812\pi$
$620$		−	5.97489i		−	0.239957i
$621$	5.21521	−	3.80472i	0.209279	−	0.152678i
$622$			15.7552i			0.631727i
$623$	−3.60839	−	6.24991i	−0.144567	−	0.250397i
$624$	1.99714	+	4.93380i	0.0799495	+	0.197510i
$625$	−0.500000	+	0.866025i	−0.0200000	+	0.0346410i
$626$	−16.8517	+	29.1880i	−0.673530	+	1.16659i
$627$	7.66437	−	22.8266i	0.306085	−	0.911606i
$628$	−2.92817	−	5.07174i	−0.116847	−	0.202384i
$629$	−6.15729			−0.245507
$630$	10.0136	+	2.85720i	0.398952	+	0.113834i
$631$	8.79823			0.350252			0.175126	−	0.984546i	$-0.443967\pi$
$631$	8.79823			0.350252			0.175126	+	0.984546i	$0.443967\pi$
$632$	6.96609	−	4.02187i	0.277096	−	0.159982i
$633$	15.9587	+	2.23221i	0.634300	+	0.0887223i
$634$	19.6982	+	11.3728i	0.782315	+	0.451670i
$635$	4.08049	−	7.06761i	0.161929	−	0.280470i
$636$	−13.3890	−	1.87277i	−0.530907	−	0.0742603i
$637$	13.4357	−	7.75710i	0.532341	−	0.307347i
$638$	8.80128	−	3.09982i	0.348446	−	0.122723i
$639$	−18.2985	−	18.8991i	−0.723876	−	0.747638i
$640$		−	1.00000i		−	0.0395285i
$641$	7.93446	−	4.58096i	0.313392	−	0.180937i	−0.335051	−	0.942200i	$-0.608754\pi$
$641$	7.93446	−	4.58096i	0.313392	−	0.180937i	0.648444	+	0.761263i	$0.275420\pi$
$642$	−3.69765	−	2.88503i	−0.145935	−	0.113863i
$643$	−17.3477	+	30.0470i	−0.684125	+	1.18494i	0.289586	+	0.957152i	$0.406482\pi$
$643$	−17.3477	+	30.0470i	−0.684125	+	1.18494i	−0.973711	+	0.227787i	$0.926851\pi$
$644$	−2.15620	+	3.73464i	−0.0849660	+	0.147165i
$645$	−8.75701	+	3.54472i	−0.344807	+	0.139573i
$646$	−2.07558	+	1.19833i	−0.0816624	+	0.0471478i
$647$			3.91478i			0.153906i	0.997035	+	0.0769529i	$0.0245191\pi$
$647$			3.91478i			0.153906i	−0.997035	+	0.0769529i	$0.975481\pi$
$648$	−0.290583	+	8.99531i	−0.0114152	+	0.353369i
$649$	−3.87355	−	10.9981i	−0.152050	−	0.431714i
$650$	−2.66134	+	1.53653i	−0.104386	+	0.0602675i
$651$	−13.4782	−	33.2972i	−0.528254	−	1.30502i
$652$	6.50077	−	11.2597i	0.254590	−	0.440963i
$653$	−37.2106	−	21.4836i	−1.45616	−	0.840717i	−0.457344	−	0.889290i	$-0.651199\pi$
$653$	−37.2106	−	21.4836i	−1.45616	−	0.840717i	−0.998820	+	0.0485733i	$0.984533\pi$
$654$	−13.4428	+	17.2292i	−0.525656	+	0.673716i
$655$	−4.20538	+	2.42797i	−0.164318	+	0.0948688i
$656$	−7.10667			−0.277469
$657$	22.3357	+	23.0689i	0.871399	+	0.900003i
$658$	−14.0757			−0.548729
$659$	20.8627	+	36.1352i	0.812694	+	1.40763i	0.910972	+	0.412468i	$0.135333\pi$
$659$	20.8627	+	36.1352i	0.812694	+	1.40763i	−0.0982785	+	0.995159i	$0.531334\pi$
$660$	5.63044	−	1.13936i	0.219165	−	0.0443496i
$661$	9.67067	−	16.7501i	0.376145	−	0.651503i	−0.614352	−	0.789032i	$-0.710583\pi$
$661$	9.67067	−	16.7501i	0.376145	−	0.651503i	0.990498	+	0.137529i	$0.0439160\pi$
$662$	−13.3625	+	23.1445i	−0.519348	+	0.899537i
$663$	3.01405	+	0.421589i	0.117056	+	0.0163732i
$664$	8.27594	+	14.3343i	0.321169	+	0.556281i
$665$		−	14.5494i		−	0.564203i
$666$	31.0662	+	8.86415i	1.20379	+	0.343479i
$667$		−	3.49537i		−	0.135341i
$668$	−10.1133	−	17.5168i	−0.391296	−	0.677744i
$669$	−9.14700	−	7.13679i	−0.353643	−	0.275924i
$670$	−11.9216	−	6.88293i	−0.460571	−	0.265911i
$671$	24.2084	+	4.52946i	0.934555	+	0.174858i
$672$	−2.25582	−	5.57285i	−0.0870200	−	0.214977i
$673$	−17.0207	+	9.82691i	−0.656100	+	0.378799i	−0.790789	−	0.612088i	$-0.790330\pi$
$673$	−17.0207	+	9.82691i	−0.656100	+	0.378799i	0.134689	+	0.990888i	$0.456996\pi$
$674$			26.2868i			1.01253i
$675$	−5.16661	+	0.553276i	−0.198863	+	0.0212956i
$676$	3.55635			0.136783
$677$	1.63242	+	2.82743i	0.0627389	+	0.108667i	0.895689	−	0.444682i	$-0.146683\pi$
$677$	1.63242	+	2.82743i	0.0627389	+	0.108667i	−0.832950	+	0.553348i	$0.813350\pi$
$678$	11.8410	+	29.2524i	0.454750	+	1.12343i
$679$	−33.1989	−	19.1674i	−1.27406	−	0.735577i
$680$	−0.495174	−	0.285889i	−0.0189891	−	0.0109633i
$681$	−9.30571	−	7.26063i	−0.356595	−	0.278228i
$682$	−15.0466	−	12.8954i	−0.576164	−	0.493791i
$683$		−	22.1856i		−	0.848907i	−0.905450	−	0.424454i	$-0.860466\pi$
$683$		−	22.1856i		−	0.848907i	0.905450	−	0.424454i	$-0.139534\pi$
$684$	12.1973	−	3.05807i	0.466376	−	0.116928i
$685$	−13.9043			−0.531254
$686$	5.86642	−	3.38698i	0.223981	−	0.129315i
$687$	0.400887	−	2.86605i	0.0152948	−	0.109347i
$688$	4.72362	+	2.72718i	0.180086	+	0.103973i
$689$	11.9932	−	20.7728i	0.456903	−	0.791380i
$690$	0.298088	−	2.13111i	0.0113480	−	0.0811299i
$691$	−18.1067	−	31.3618i	−0.688813	−	1.19306i	−0.972222	−	0.234060i	$-0.924799\pi$
$691$	−18.1067	−	31.3618i	−0.688813	−	1.19306i	0.283409	−	0.958999i	$-0.408535\pi$
$692$	11.9577			0.454563
$693$	28.8074	−	19.0507i	1.09430	−	0.723678i
$694$	−13.7371			−0.521454
$695$	1.18789	+	2.05748i	0.0450592	+	0.0780448i
$696$	3.84199	+	2.99765i	0.145630	+	0.113626i
$697$	−2.03172	+	3.51904i	−0.0769568	+	0.133293i
$698$	19.1383	+	11.0495i	0.724397	+	0.418231i
$699$	12.7820	−	5.17397i	0.483459	−	0.195698i
$700$	3.00605	−	1.73554i	0.113618	−	0.0655974i
$701$	−28.8668			−1.09028			−0.545142	−	0.838344i	$-0.683524\pi$
$701$	−28.8668			−1.09028			−0.545142	+	0.838344i	$0.683524\pi$
$702$	−14.6002	−	6.46618i	−0.551051	−	0.244050i
$703$		−	45.1381i		−	1.70241i
$704$	−2.51831	−	2.15827i	−0.0949122	−	0.0813429i
$705$	6.51054	−	2.63538i	0.245201	−	0.0992541i
$706$	−22.4212	−	12.9449i	−0.843831	−	0.487186i
$707$	17.3609	+	10.0233i	0.652924	+	0.376966i
$708$	3.74587	−	4.80096i	0.140778	−	0.180431i
$709$	−8.64860	−	14.9798i	−0.324805	−	0.562579i	0.656668	−	0.754180i	$-0.271965\pi$
$709$	−8.64860	−	14.9798i	−0.324805	−	0.562579i	−0.981473	+	0.191601i	$0.938632\pi$
$710$	−8.76870			−0.329083
$711$	−6.62115	+	23.2051i	−0.248312	+	0.870260i
$712$		−	2.07911i		−	0.0779179i
$713$	−6.42854	+	3.71152i	−0.240751	+	0.138998i
$714$	−3.40445	−	0.476195i	−0.127408	−	0.0178212i
$715$	−1.87446	+	10.0183i	−0.0701007	+	0.374664i
$716$	13.6246	+	7.86619i	0.509176	+	0.293973i
$717$	−2.31369	+	16.5412i	−0.0864062	+	0.617741i
$718$	−3.94106	−	6.82611i	−0.147079	−	0.254748i
$719$			18.8232i			0.701988i	0.936378	+	0.350994i	$0.114156\pi$
$719$			18.8232i			0.701988i	−0.936378	+	0.350994i	$0.885844\pi$
$720$	2.08679	+	2.15529i	0.0777702	+	0.0803231i
$721$			43.3149i			1.61313i
$722$	0.715212	+	1.23878i	0.0266175	+	0.0461028i
$723$	−16.4101	+	21.0323i	−0.610299	+	0.782200i
$724$	7.90904	−	13.6989i	0.293937	−	0.509114i
$725$	−1.40673	+	2.43653i	−0.0522447	+	0.0904905i
$726$	9.28275	−	16.6382i	0.344515	−	0.617502i
$727$	11.2973	+	19.5676i	0.418995	+	0.725720i	0.995839	−	0.0911341i	$-0.0290492\pi$
$727$	11.2973	+	19.5676i	0.418995	+	0.725720i	−0.576844	+	0.816855i	$0.695716\pi$
$728$	10.6668			0.395339
$729$	−18.1451	−	19.9939i	−0.672039	−	0.740515i
$730$	10.7034			0.396149
$731$	2.70086	−	1.55934i	0.0998949	−	0.0576744i
$732$	4.82591	+	11.9221i	0.178371	+	0.440654i
$733$	−8.90985	−	5.14411i	−0.329093	−	0.190002i	0.326345	−	0.945251i	$-0.394183\pi$
$733$	−8.90985	−	5.14411i	−0.329093	−	0.190002i	−0.655438	+	0.755249i	$0.727516\pi$
$734$	5.02343	−	8.70084i	0.185418	−	0.321154i
$735$	5.37896	−	6.89404i	0.198406	−	0.254290i
$736$	−1.07593	+	0.621187i	−0.0396592	+	0.0228973i
$737$	−43.0633	+	15.1670i	−1.58626	+	0.558682i
$738$	15.3170	−	14.8301i	0.563825	−	0.545905i
$739$		−	48.3124i		−	1.77720i	−0.458681	−	0.888601i	$-0.651678\pi$
$739$		−	48.3124i		−	1.77720i	0.458681	−	0.888601i	$-0.348322\pi$
$740$	9.32595	−	5.38434i	0.342829	−	0.197932i
$741$	−3.09060	+	22.0955i	−0.113536	+	0.811699i
$742$	−13.5466	+	23.4634i	−0.497311	+	0.861367i
$743$	19.3398	−	33.4975i	0.709509	−	1.22891i	−0.255531	−	0.966801i	$-0.582250\pi$
$743$	19.3398	−	33.4975i	0.709509	−	1.22891i	0.965040	−	0.262104i	$-0.0844165\pi$
$744$	1.43358	−	10.2490i	0.0525575	−	0.375748i
$745$	−9.00307	+	5.19792i	−0.329847	+	0.190437i
$746$			26.4683i			0.969073i
$747$	−47.7499	−	13.6246i	−1.74708	−	0.498496i
$748$	−1.78868	+	0.629974i	−0.0654005	+	0.0230341i
$749$	−8.13970	+	4.69946i	−0.297418	+	0.171714i
$750$	−1.06546	+	1.36557i	−0.0389053	+	0.0498636i
$751$	19.7238	−	34.1626i	0.719731	−	1.24661i	−0.241375	−	0.970432i	$-0.577598\pi$
$751$	19.7238	−	34.1626i	0.719731	−	1.24661i	0.961106	−	0.276179i	$-0.0890682\pi$
$752$	−3.51185	−	2.02757i	−0.128064	−	0.0739377i
$753$	−10.2635	−	25.3554i	−0.374023	−	0.924002i
$754$	−7.48759	+	4.32296i	−0.272682	+	0.157433i
$755$	1.74652			0.0635625
$756$	16.4913	+	7.30371i	0.599784	+	0.265633i
$757$	−30.7776			−1.11863			−0.559316	−	0.828954i	$-0.688936\pi$
$757$	−30.7776			−1.11863			−0.559316	+	0.828954i	$0.688936\pi$
$758$	9.67284	+	16.7539i	0.351333	+	0.608527i
$759$	−4.72343	−	5.35019i	−0.171450	−	0.194199i
$760$	2.09580	−	3.63004i	0.0760228	−	0.131675i
$761$	2.59838	−	4.50053i	0.0941913	−	0.163144i	−0.815079	−	0.579349i	$-0.803307\pi$
$761$	2.59838	−	4.50053i	0.0941913	−	0.163144i	0.909271	+	0.416205i	$0.136640\pi$
$762$	8.69523	−	11.1444i	0.314995	−	0.403719i
$763$	21.8971	+	37.9270i	0.792730	+	1.37305i
$764$			3.12924i			0.113212i
$765$	1.66384	−	0.417152i	0.0601562	−	0.0150822i
$766$		−	13.2016i		−	0.476994i
$767$	5.40199	+	9.35652i	0.195055	+	0.337844i
$768$	0.239934	−	1.71535i	0.00865787	−	0.0618974i
$769$	33.0089	+	19.0577i	1.19033	+	0.687238i	0.958382	−	0.285489i	$-0.0921561\pi$
$769$	33.0089	+	19.0577i	1.19033	+	0.687238i	0.231950	+	0.972728i	$0.425489\pi$
$770$	2.11724	−	11.3159i	0.0763002	−	0.407798i
$771$	23.8115	+	3.33062i	0.857551	+	0.119949i
$772$	21.1134	−	12.1898i	0.759886	−	0.438721i
$773$		−	10.7047i		−	0.385021i	−0.981295	−	0.192511i	$-0.938337\pi$
$773$		−	10.7047i		−	0.385021i	0.981295	−	0.192511i	$-0.0616630\pi$
$774$	−15.8718	+	3.97934i	−0.570502	+	0.143034i
$775$	5.97489			0.214624
$776$	−5.52201	−	9.56440i	−0.198228	−	0.343342i
$777$	39.8260	−	51.0437i	1.42875	−	1.83118i
$778$	18.7302	+	10.8139i	0.671510	+	0.387697i
$779$	−25.7975	−	14.8942i	−0.924290	−	0.533639i
$780$	−4.93380	+	1.99714i	−0.176658	+	0.0715090i
$781$	−18.9252	+	22.0823i	−0.677198	+	0.790165i
$782$			0.710362i			0.0254025i
$783$	−14.5361	+	1.55662i	−0.519477	+	0.0556291i
$784$	−5.04846			−0.180302
$785$	5.07174	−	2.92817i	0.181018	−	0.104511i
$786$	−7.79625	+	3.15582i	−0.278083	+	0.112564i
$787$	26.8560	+	15.5053i	0.957312	+	0.552705i	0.895345	−	0.445374i	$-0.146929\pi$
$787$	26.8560	+	15.5053i	0.957312	+	0.552705i	0.0619675	+	0.998078i	$0.480262\pi$
$788$	2.64109	−	4.57451i	0.0940850	−	0.162960i
$789$	−25.8451	−	20.1652i	−0.920109	−	0.717900i
$790$	4.02187	+	6.96609i	0.143092	+	0.247842i
$791$	63.2435			2.24868
$792$	9.93156	−	0.603475i	0.352902	−	0.0214435i
$793$	−22.8198			−0.810354
$794$	−10.8790	−	18.8430i	−0.386081	−	0.668712i
$795$	1.87277	−	13.3890i	0.0664205	−	0.474858i
$796$	−8.49138	+	14.7075i	−0.300969	+	0.521294i
$797$	2.55509	+	1.47518i	0.0905058	+	0.0522535i	0.544570	−	0.838716i	$-0.316693\pi$
$797$	2.55509	+	1.47518i	0.0905058	+	0.0522535i	−0.454064	+	0.890969i	$0.650026\pi$
$798$	3.49091	−	24.9574i	0.123577	−	0.883483i
$799$	−2.00800	+	1.15932i	−0.0710378	+	0.0410137i
$800$	1.00000			0.0353553
$801$	4.33867	+	4.48109i	0.153299	+	0.158332i
$802$		−	3.18096i		−	0.112324i
$803$	23.1008	−	26.9543i	0.815208	−	0.951198i
$804$	−18.7983	−	14.6670i	−0.662963	−	0.517266i
$805$	−3.73464	−	2.15620i	−0.131629	−	0.0759959i
$806$	15.9012	+	9.18057i	0.560096	+	0.323372i
$807$	17.7457	+	43.8396i	0.624677	+	1.54323i
$808$	2.88766	+	5.00157i	0.101587	+	0.175955i
$809$	−17.6214			−0.619536			−0.309768	−	0.950812i	$-0.600251\pi$
$809$	−17.6214			−0.619536			−0.309768	+	0.950812i	$0.600251\pi$
$810$	−8.99531	−	0.290583i	−0.316063	−	0.0102100i
$811$			25.9697i			0.911921i	0.890000	+	0.455960i	$0.150704\pi$
$811$			25.9697i			0.911921i	−0.890000	+	0.455960i	$0.849296\pi$
$812$	8.45742	−	4.88289i	0.296797	−	0.171356i
$813$	−4.23711	−	10.4675i	−0.148602	−	0.367112i
$814$	6.56852	−	35.1064i	0.230226	−	1.23048i
$815$	11.2597	+	6.50077i	0.394409	+	0.227712i
$816$	−0.780803	−	0.609209i	−0.0273336	−	0.0213266i
$817$	11.4313	+	19.7996i	0.399930	+	0.692699i
$818$			10.5578i			0.369144i
$819$	−22.9902	+	22.2595i	−0.803342	+	0.777810i
$820$		−	7.10667i		−	0.248176i
$821$	−13.4454	−	23.2882i	−0.469249	−	0.812764i	0.530133	−	0.847915i	$-0.322142\pi$
$821$	−13.4454	−	23.2882i	−0.469249	−	0.812764i	−0.999382	+	0.0351511i	$0.988809\pi$
$822$	−23.8507	−	3.33610i	−0.831888	−	0.116360i
$823$	−15.4771	+	26.8071i	−0.539497	+	0.934436i	0.459435	+	0.888212i	$0.348052\pi$
$823$	−15.4771	+	26.8071i	−0.539497	+	0.934436i	−0.998931	+	0.0462239i	$0.985281\pi$
$824$	−6.23938	+	10.8069i	−0.217359	+	0.376477i
$825$	1.13936	+	5.63044i	0.0396675	+	0.196027i
$826$	−6.10168	−	10.5684i	−0.212305	−	0.367722i
$827$	1.36826			0.0475792			0.0237896	−	0.999717i	$-0.492427\pi$
$827$	1.36826			0.0475792			0.0237896	+	0.999717i	$0.492427\pi$
$828$	1.02265	−	3.58408i	0.0355396	−	0.124555i
$829$	−25.3254			−0.879587			−0.439793	−	0.898099i	$-0.644948\pi$
$829$	−25.3254			−0.879587			−0.439793	+	0.898099i	$0.644948\pi$
$830$	−14.3343	+	8.27594i	−0.497553	+	0.287262i
$831$	−23.7207	+	30.4020i	−0.822862	+	1.05463i
$832$	2.66134	+	1.53653i	0.0922654	+	0.0532695i
$833$	−1.44330	+	2.49987i	−0.0500074	+	0.0866153i
$834$	1.54399	+	3.81433i	0.0534639	+	0.132079i
$835$	17.5168	−	10.1133i	0.606193	−	0.349986i
$836$	−4.61823	−	13.1125i	−0.159725	−	0.453505i
$837$	18.2978	+	25.0813i	0.632466	+	0.866935i
$838$			32.7099i			1.12994i
$839$	−20.8961	+	12.0644i	−0.721415	+	0.416509i	−0.815273	−	0.579076i	$-0.803413\pi$
$839$	−20.8961	+	12.0644i	−0.721415	+	0.416509i	0.0938582	+	0.995586i	$0.470080\pi$
$840$	5.57285	−	2.25582i	0.192282	−	0.0778331i
$841$	10.5422	−	18.2596i	0.363524	−	0.629643i
$842$	14.4327	−	24.9982i	0.497385	−	0.861496i
$843$	30.7737	+	24.0107i	1.05990	+	0.826971i
$844$	8.05701	−	4.65172i	0.277334	−	0.160119i
$845$			3.55635i			0.122342i
$846$	11.8002	−	2.95850i	0.405698	−	0.101715i
$847$	−23.9274	−	29.7547i	−0.822155	−	1.02238i
$848$	−6.75965	+	3.90269i	−0.232127	+	0.134019i
$849$	−23.9334	−	3.34768i	−0.821393	−	0.114892i
$850$	0.285889	−	0.495174i	0.00980591	−	0.0169843i
$851$	−11.5863	−	6.68936i	−0.397174	−	0.229308i
$852$	−15.0414	−	2.10391i	−0.515310	−	0.0720787i
$853$	−40.2188	+	23.2204i	−1.37707	+	0.795050i	−0.991805	−	0.127758i	$-0.959222\pi$
$853$	−40.2188	+	23.2204i	−1.37707	+	0.795050i	−0.385261	+	0.922808i	$0.625889\pi$
$854$	25.7755			0.882020
$855$	3.05807	+	12.1973i	0.104584	+	0.417139i
$856$	−2.70777			−0.0925497
$857$	20.8420	+	36.0995i	0.711951	+	1.23313i	0.964124	+	0.265452i	$0.0855213\pi$
$857$	20.8420	+	36.0995i	0.711951	+	1.23313i	−0.252173	+	0.967682i	$0.581145\pi$
$858$	−5.61908	+	16.7352i	−0.191832	+	0.571330i
$859$	−2.96389	+	5.13360i	−0.101127	+	0.175156i	−0.912149	−	0.409859i	$-0.865578\pi$
$859$	−2.96389	+	5.13360i	−0.101127	+	0.175156i	0.811023	+	0.585015i	$0.198911\pi$
$860$	−2.72718	+	4.72362i	−0.0929961	+	0.161074i
$861$	−16.0313	−	39.6044i	−0.546346	−	1.34971i
$862$	−9.12894	−	15.8118i	−0.310933	−	0.538552i
$863$			23.6512i			0.805095i	0.915399	+	0.402547i	$0.131875\pi$
$863$			23.6512i			0.805095i	−0.915399	+	0.402547i	$0.868125\pi$
$864$	3.06246	+	4.19778i	0.104187	+	0.142811i
$865$			11.9577i			0.406574i
$866$	−0.884457	−	1.53192i	−0.0300551	−	0.0520569i
$867$	26.7687	−	10.8356i	0.909113	−	0.367997i
$868$	−17.9608	−	10.3697i	−0.609630	−	0.351970i
$869$	26.2230	+	4.90641i	0.889556	+	0.166438i
$870$	−2.99765	+	3.84199i	−0.101630	+	0.130256i
$871$	36.6357	−	21.1516i	1.24135	−	0.716695i
$872$			12.6169i			0.427261i
$873$	31.8605	+	9.09079i	1.07831	+	0.307677i
$874$	−5.20754			−0.176148
$875$	1.73554	+	3.00605i	0.0586721	+	0.101623i
$876$	18.3600	+	2.56810i	0.620328	+	0.0867680i
$877$	−21.8959	−	12.6416i	−0.739372	−	0.426877i	0.0824688	−	0.996594i	$-0.473720\pi$
$877$	−21.8959	−	12.6416i	−0.739372	−	0.426877i	−0.821841	+	0.569717i	$0.807053\pi$
$878$	−17.1678	−	9.91186i	−0.579387	−	0.334509i
$879$	−4.39055	+	31.3892i	−0.148089	+	1.05873i
$880$	2.15827	−	2.51831i	0.0727553	−	0.0848921i
$881$		−	11.2617i		−	0.379416i	−0.981841	−	0.189708i	$-0.939246\pi$
$881$		−	11.2617i		−	0.379416i	0.981841	−	0.189708i	$-0.0607542\pi$
$882$	10.8809	−	10.5351i	0.366380	−	0.354735i
$883$	11.5801			0.389702			0.194851	−	0.980833i	$-0.437578\pi$
$883$	11.5801			0.389702			0.194851	+	0.980833i	$0.437578\pi$
$884$	1.52170	−	0.878552i	0.0511802	−	0.0295489i
$885$	4.80096	+	3.74587i	0.161382	+	0.125916i
$886$	3.88455	+	2.24275i	0.130504	+	0.0753466i
$887$	6.01768	−	10.4229i	0.202054	−	0.349968i	−0.747136	−	0.664671i	$-0.768572\pi$
$887$	6.01768	−	10.4229i	0.202054	−	0.349968i	0.949190	+	0.314703i	$0.101905\pi$
$888$	17.2892	−	6.99842i	0.580186	−	0.234852i
$889$	−14.1637	−	24.5323i	−0.475036	−	0.822787i
$890$	2.07911			0.0696919
$891$	−20.1461	+	22.0258i	−0.674920	+	0.737891i
$892$	−6.69829			−0.224275
$893$	−8.49876	−	14.7203i	−0.284400	−	0.492596i
$894$	−16.6906	+	6.75613i	−0.558217	+	0.225959i
$895$	−7.86619	+	13.6246i	−0.262938	+	0.455421i
$896$	−3.00605	−	1.73554i	−0.100425	−	0.0579805i
$897$	5.21359	+	4.06782i	0.174077	+	0.135820i
$898$	−25.0045	+	14.4363i	−0.834410	+	0.481747i
$899$	16.8101			0.560649
$900$	−2.15529	+	2.08679i	−0.0718431	+	0.0695598i
$901$			4.46294i			0.148682i
$902$	−17.8968	−	15.3381i	−0.595897	−	0.510703i
$903$	−4.54257	+	32.4760i	−0.151167	+	1.08074i
$904$	15.7790	+	9.11003i	0.524803	+	0.302995i
$905$	13.6989	+	7.90904i	0.455365	+	0.262905i
$906$	2.99590	+	0.419051i	0.0995323	+	0.0139220i
$907$	−17.3659	−	30.0786i	−0.576625	−	0.998744i	−0.995863	−	0.0908673i	$-0.971036\pi$
$907$	−17.3659	−	30.0786i	−0.576625	−	0.998744i	0.419238	−	0.907876i	$-0.362297\pi$
$908$	−6.81451			−0.226148
$909$	−16.6610	−	4.75391i	−0.552610	−	0.157677i
$910$			10.6668i			0.353602i
$911$	15.3275	−	8.84932i	0.507822	−	0.293191i	−0.224116	−	0.974562i	$-0.571949\pi$
$911$	15.3275	−	8.84932i	0.507822	−	0.293191i	0.731938	+	0.681371i	$0.238616\pi$
$912$	4.46601	−	5.72394i	0.147884	−	0.189539i
$913$	−10.0961	+	53.9600i	−0.334131	+	1.78582i
$914$	−2.48854	−	1.43676i	−0.0823135	−	0.0475237i
$915$	−11.9221	+	4.82591i	−0.394133	+	0.159540i
$916$	−0.835411	−	1.44697i	−0.0276028	−	0.0478094i
$917$			16.8554i			0.556616i
$918$	2.95415	−	0.316351i	0.0975016	−	0.0104411i
$919$		−	27.7821i		−	0.916448i	−0.888837	−	0.458224i	$-0.848486\pi$
$919$		−	27.7821i		−	0.916448i	0.888837	−	0.458224i	$-0.151514\pi$
$920$	−0.621187	−	1.07593i	−0.0204799	−	0.0354723i
$921$	6.78006	+	16.7497i	0.223411	+	0.551922i
$922$	−17.9951	+	31.1684i	−0.592636	+	1.02648i
$923$	13.4733	−	23.3365i	0.443480	−	0.768130i
$924$	6.34690	−	18.9028i	0.208798	−	0.621857i
$925$	5.38434	+	9.32595i	0.177036	+	0.306635i
$926$	−37.5033			−1.23243
$927$	−9.10412	−	36.3124i	−0.299018	−	1.19265i
$928$	2.81346			0.0923565
$929$	−42.3109	+	24.4282i	−1.38818	+	0.801464i	−0.993110	−	0.117189i	$-0.962612\pi$
$929$	−42.3109	+	24.4282i	−1.38818	+	0.801464i	−0.395066	+	0.918653i	$0.629278\pi$
$930$	10.2490	+	1.43358i	0.336079	+	0.0470089i
$931$	−18.3261	−	10.5806i	−0.600614	−	0.346765i
$932$	3.98067	−	6.89472i	0.130391	−	0.225844i
$933$	−27.0258	−	3.78021i	−0.884784	−	0.123759i
$934$	17.6997	−	10.2189i	0.579151	−	0.334373i
$935$	−0.629974	−	1.78868i	−0.0206023	−	0.0584960i
$936$	−8.94239	+	2.24201i	−0.292291	+	0.0732823i
$937$			14.3729i			0.469543i	0.972051	+	0.234771i	$0.0754342\pi$
$937$			14.3729i			0.469543i	−0.972051	+	0.234771i	$0.924566\pi$
$938$	−41.3809	+	23.8913i	−1.35113	+	0.780077i
$939$	−46.0244	−	35.9098i	−1.50195	−	1.17187i
$940$	2.02757	−	3.51185i	0.0661319	−	0.114544i
$941$	5.20369	−	9.01306i	0.169636	−	0.293817i	−0.768656	−	0.639662i	$-0.779074\pi$
$941$	5.20369	−	9.01306i	0.169636	−	0.293817i	0.938292	+	0.345845i	$0.112408\pi$
$942$	9.40239	−	3.80596i	0.306346	−	0.124005i
$943$	−7.64626	+	4.41457i	−0.248996	+	0.143758i
$944$		−	3.51572i		−	0.114427i
$945$	−7.30371	+	16.4913i	−0.237590	+	0.536463i
$946$	6.00951	+	17.0627i	0.195386	+	0.554757i
$947$	1.44019	−	0.831492i	0.0467998	−	0.0270199i	−0.476418	−	0.879219i	$-0.658065\pi$
$947$	1.44019	−	0.831492i	0.0467998	−	0.0270199i	0.523217	+	0.852199i	$0.324732\pi$
$948$	5.22753	+	12.9143i	0.169782	+	0.419436i
$949$	−16.4460	+	28.4853i	−0.533860	+	0.924672i
$950$	3.63004	+	2.09580i	0.117774	+	0.0679969i
$951$	−24.2345	+	31.0606i	−0.785859	+	1.00721i
$952$	−1.71879	+	0.992346i	−0.0557064	+	0.0321621i
$953$	−35.9503			−1.16455			−0.582273	−	0.812993i	$-0.697837\pi$
$953$	−35.9503			−1.16455			−0.582273	+	0.812993i	$0.697837\pi$
$954$	6.42494	−	22.5174i	0.208015	−	0.729029i
$955$	−3.12924			−0.101260
$956$	4.82150	+	8.35109i	0.155939	+	0.270094i
$957$	3.20556	+	15.8410i	0.103621	+	0.512068i
$958$	−5.45440	+	9.44730i	−0.176224	+	0.305228i
$959$	−24.1315	+	41.7969i	−0.779246	+	1.34969i
$960$	1.71535	+	0.239934i	0.0553627	+	0.00774383i
$961$	−2.34963	−	4.06968i	−0.0757945	−	0.131280i
$962$			33.0927i			1.06695i
$963$	5.83604	−	5.65056i	0.188064	−	0.182087i
$964$			15.4018i			0.496060i
$965$	12.1898	+	21.1134i	0.392404	+	0.679663i
$966$	−5.88888	−	4.59470i	−0.189472	−	0.147832i
$967$	−37.5394	−	21.6734i	−1.20718	−	0.696969i	−0.245042	−	0.969513i	$-0.578802\pi$
$967$	−37.5394	−	21.6734i	−1.20718	−	0.696969i	−0.962143	+	0.272544i	$0.912135\pi$
$968$	−1.68373	−	10.8704i	−0.0541170	−	0.349387i
$969$	−1.55756	−	3.84786i	−0.0500362	−	0.123611i
$970$	9.56440	−	5.52201i	0.307094	−	0.177301i
$971$			42.6186i			1.36770i	0.729624	+	0.683848i	$0.239695\pi$
$971$			42.6186i			1.36770i	−0.729624	+	0.683848i	$0.760305\pi$
$972$	−15.3604	−	2.65673i	−0.492685	−	0.0852147i
$973$	8.24654			0.264372
$974$	−14.0371	−	24.3130i	−0.449779	−	0.779039i
$975$	−1.99714	−	4.93380i	−0.0639596	−	0.158008i
$976$	6.43091	+	3.71288i	0.205848	+	0.118847i
$977$	−22.3348	−	12.8950i	−0.714554	−	0.412548i	0.0981909	−	0.995168i	$-0.468694\pi$
$977$	−22.3348	−	12.8950i	−0.714554	−	0.412548i	−0.812745	+	0.582620i	$0.802028\pi$
$978$	17.7545	+	13.8527i	0.567728	+	0.442960i
$979$	4.48728	−	5.23583i	0.143414	−	0.167338i
$980$		−	5.04846i		−	0.161267i
$981$	−26.3288	−	27.1931i	−0.840614	−	0.868208i
$982$	4.53767			0.144803
$983$	−28.3895	+	16.3907i	−0.905485	+	0.522782i	−0.878976	−	0.476867i	$-0.841772\pi$
$983$	−28.3895	+	16.3907i	−0.905485	+	0.522782i	−0.0265091	+	0.999649i	$0.508439\pi$
$984$	1.70513	−	12.1904i	0.0543576	−	0.388617i
$985$	4.57451	+	2.64109i	0.145756	+	0.0841522i
$986$	0.804338	−	1.39315i	0.0256153	−	0.0443671i
$987$	3.37725	−	24.1448i	0.107499	−	0.768538i
$988$	6.44052	+	11.1553i	0.204900	+	0.354897i
$989$	6.77636			0.215476
$990$	0.603475	+	9.93156i	0.0191797	+	0.315646i
$991$	11.8177			0.375402			0.187701	−	0.982226i	$-0.439896\pi$
$991$	11.8177			0.375402			0.187701	+	0.982226i	$0.439896\pi$
$992$	−2.98744	−	5.17440i	−0.0948514	−	0.164287i
$993$	−36.4949	−	28.4745i	−1.15813	−	0.903611i
$994$	−15.2185	+	26.3592i	−0.482700	+	0.836062i
$995$	−14.7075	−	8.49138i	−0.466259	−	0.269195i
$996$	−26.5741	+	10.7569i	−0.842034	+	0.340844i
$997$	23.4599	−	13.5446i	0.742981	−	0.428961i	−0.0801709	−	0.996781i	$-0.525547\pi$
$997$	23.4599	−	13.5446i	0.742981	−	0.428961i	0.823152	+	0.567821i	$0.192213\pi$
$998$	2.20991			0.0699534
$999$	−22.6590	+	51.1626i	−0.716898	+	1.61871i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	990.2.t.b.131.5	yes	48
3.2	odd	2		2970.2.t.a.2771.23		48
9.2	odd	6		990.2.t.a.461.5	yes	48
9.7	even	3		2970.2.t.b.791.23		48
11.10	odd	2		990.2.t.a.131.5	✓	48
33.32	even	2		2970.2.t.b.2771.23		48
99.43	odd	6		2970.2.t.a.791.23		48
99.65	even	6	inner	990.2.t.b.461.5	yes	48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
990.2.t.a.131.5	✓	48	11.10	odd	2
990.2.t.a.461.5	yes	48	9.2	odd	6
990.2.t.b.131.5	yes	48	1.1	even	1	trivial
990.2.t.b.461.5	yes	48	99.65	even	6	inner
2970.2.t.a.791.23		48	99.43	odd	6
2970.2.t.a.2771.23		48	3.2	odd	2
2970.2.t.b.791.23		48	9.7	even	3
2970.2.t.b.2771.23		48	33.32	even	2

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 990 = 2 \cdot 3^{2} \cdot 5 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	990.t (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.500000 + 0.866025i) q^{2} +(-1.60551 + 0.649887i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(-0.866025 - 0.500000i) q^{5} +(-1.36557 - 1.06546i) q^{6} +(-3.00605 + 1.73554i) q^{7} -1.00000 q^{8} +(2.15529 - 2.08679i) q^{9} -1.00000i q^{10} +(-2.51831 - 2.15827i) q^{11} +(0.239934 - 1.71535i) q^{12} +(2.66134 + 1.53653i) q^{13} +(-3.00605 - 1.73554i) q^{14} +(1.71535 + 0.239934i) q^{15} +(-0.500000 - 0.866025i) q^{16} -0.571778 q^{17} +(2.88486 + 0.823142i) q^{18} -4.19161i q^{19} +(0.866025 - 0.500000i) q^{20} +(3.69832 - 4.74002i) q^{21} +(0.609965 - 3.26005i) q^{22} +(-1.07593 - 0.621187i) q^{23} +(1.60551 - 0.649887i) q^{24} +(0.500000 + 0.866025i) q^{25} +3.07305i q^{26} +(-2.10416 + 4.75106i) q^{27} -3.47109i q^{28} +(1.40673 + 2.43653i) q^{29} +(0.649887 + 1.60551i) q^{30} +(2.98744 - 5.17440i) q^{31} +(0.500000 - 0.866025i) q^{32} +(5.44579 + 1.82850i) q^{33} +(-0.285889 - 0.495174i) q^{34} +3.47109 q^{35} +(0.729570 + 2.90994i) q^{36} +10.7687 q^{37} +(3.63004 - 2.09580i) q^{38} +(-5.27137 - 0.737330i) q^{39} +(0.866025 + 0.500000i) q^{40} +(3.55333 - 6.15455i) q^{41} +(5.95414 + 0.832832i) q^{42} +(-4.72362 + 2.72718i) q^{43} +(3.12827 - 1.10178i) q^{44} +(-2.90994 + 0.729570i) q^{45} -1.24237i q^{46} +(3.51185 - 2.02757i) q^{47} +(1.36557 + 1.06546i) q^{48} +(2.52423 - 4.37210i) q^{49} +(-0.500000 + 0.866025i) q^{50} +(0.917992 - 0.371591i) q^{51} +(-2.66134 + 1.53653i) q^{52} -7.80538i q^{53} +(-5.16661 + 0.553276i) q^{54} +(1.10178 + 3.12827i) q^{55} +(3.00605 - 1.73554i) q^{56} +(2.72407 + 6.72965i) q^{57} +(-1.40673 + 2.43653i) q^{58} +(3.04470 + 1.75786i) q^{59} +(-1.06546 + 1.36557i) q^{60} +(-6.43091 + 3.71288i) q^{61} +5.97489 q^{62} +(-2.85720 + 10.0136i) q^{63} +1.00000 q^{64} +(-1.53653 - 2.66134i) q^{65} +(1.13936 + 5.63044i) q^{66} +(6.88293 - 11.9216i) q^{67} +(0.285889 - 0.495174i) q^{68} +(2.13111 + 0.298088i) q^{69} +(1.73554 + 3.00605i) q^{70} -8.76870i q^{71} +(-2.15529 + 2.08679i) q^{72} +10.7034i q^{73} +(5.38434 + 9.32595i) q^{74} +(-1.36557 - 1.06546i) q^{75} +(3.63004 + 2.09580i) q^{76} +(11.3159 + 2.11724i) q^{77} +(-1.99714 - 4.93380i) q^{78} +(-6.96609 + 4.02187i) q^{79} +1.00000i q^{80} +(0.290583 - 8.99531i) q^{81} +7.10667 q^{82} +(-8.27594 - 14.3343i) q^{83} +(2.25582 + 5.57285i) q^{84} +(0.495174 + 0.285889i) q^{85} +(-4.72362 - 2.72718i) q^{86} +(-3.84199 - 2.99765i) q^{87} +(2.51831 + 2.15827i) q^{88} +2.07911i q^{89} +(-2.08679 - 2.15529i) q^{90} -10.6668 q^{91} +(1.07593 - 0.621187i) q^{92} +(-1.43358 + 10.2490i) q^{93} +(3.51185 + 2.02757i) q^{94} +(-2.09580 + 3.63004i) q^{95} +(-0.239934 + 1.71535i) q^{96} +(5.52201 + 9.56440i) q^{97} +5.04846 q^{98} +(-9.93156 + 0.603475i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q + 24 q^{2} - 2 q^{3} - 24 q^{4} + 2 q^{6} - 48 q^{8} + 10 q^{9} - 12 q^{11} + 4 q^{12} - 24 q^{13} - 4 q^{15} - 24 q^{16} + 12 q^{17} + 8 q^{18} + 16 q^{21} - 6 q^{22} + 36 q^{23} + 2 q^{24} + 24 q^{25}+ \cdots - 44 q^{99}+O(q^{100}) \) 48 * q + 24 * q^2 - 2 * q^3 - 24 * q^4 + 2 * q^6 - 48 * q^8 + 10 * q^9 - 12 * q^11 + 4 * q^12 - 24 * q^13 - 4 * q^15 - 24 * q^16 + 12 * q^17 + 8 * q^18 + 16 * q^21 - 6 * q^22 + 36 * q^23 + 2 * q^24 + 24 * q^25 - 8 * q^27 - 8 * q^30 + 24 * q^32 + 12 * q^33 + 6 * q^34 - 2 * q^36 - 6 * q^38 + 40 * q^39 + 6 * q^41 + 8 * q^42 - 30 * q^43 + 6 * q^44 - 2 * q^48 + 24 * q^49 - 24 * q^50 - 22 * q^51 + 24 * q^52 - 22 * q^54 - 40 * q^57 - 54 * q^59 - 4 * q^60 + 38 * q^63 + 48 * q^64 - 12 * q^66 - 6 * q^67 - 6 * q^68 + 76 * q^69 - 10 * q^72 + 2 * q^75 - 6 * q^76 - 18 * q^77 + 32 * q^78 + 10 * q^81 + 12 * q^82 - 36 * q^83 - 8 * q^84 - 30 * q^86 + 44 * q^87 + 12 * q^88 + 24 * q^91 - 36 * q^92 - 68 * q^93 - 4 * q^96 + 6 * q^97 + 48 * q^98 - 44 * q^99

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