LMFDB - Embedded newform 552.2.j.d.323.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [552,2,Mod(323,552)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(552, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([1, 1, 1, 0]))

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

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

chi := DirichletCharacter("552.323");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 552 = 2^{3} \cdot 3 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	552.j (of order $2$, degree $1$, 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:	$4.40774219157$
Analytic rank:	$0$
Dimension:	$42$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			323.8
Character	$\chi$	$=$	552.323
Dual form			552.2.j.d.323.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.30785 + 0.538067i) q^{2} +(-1.71722 - 0.226158i) q^{3} +(1.42097 - 1.40743i) q^{4} +3.49837 q^{5} +(2.36757 - 0.628199i) q^{6} +1.83575i q^{7} +(-1.10113 + 2.60529i) q^{8} +(2.89771 + 0.776727i) q^{9} +O(q^{10})$	\(q+(-1.30785 + 0.538067i) q^{2} +(-1.71722 - 0.226158i) q^{3} +(1.42097 - 1.40743i) q^{4} +3.49837 q^{5} +(2.36757 - 0.628199i) q^{6} +1.83575i q^{7} +(-1.10113 + 2.60529i) q^{8} +(2.89771 + 0.776727i) q^{9} +(-4.57536 + 1.88236i) q^{10} -1.48415i q^{11} +(-2.75842 + 2.09550i) q^{12} +6.77805i q^{13} +(-0.987759 - 2.40090i) q^{14} +(-6.00748 - 0.791185i) q^{15} +(0.0382962 - 3.99982i) q^{16} -4.55269i q^{17} +(-4.20771 + 0.543314i) q^{18} +0.397968 q^{19} +(4.97107 - 4.92370i) q^{20} +(0.415171 - 3.15240i) q^{21} +(0.798571 + 1.94105i) q^{22} +1.00000 q^{23} +(2.48009 - 4.22483i) q^{24} +7.23861 q^{25} +(-3.64705 - 8.86470i) q^{26} +(-4.80034 - 1.98915i) q^{27} +(2.58369 + 2.60855i) q^{28} +0.0571930 q^{29} +(8.28262 - 2.19767i) q^{30} +3.03359i q^{31} +(2.10208 + 5.25178i) q^{32} +(-0.335652 + 2.54861i) q^{33} +(2.44965 + 5.95425i) q^{34} +6.42215i q^{35} +(5.21073 - 2.97461i) q^{36} +9.08955i q^{37} +(-0.520484 + 0.214133i) q^{38} +(1.53291 - 11.6394i) q^{39} +(-3.85216 + 9.11426i) q^{40} +3.30370i q^{41} +(1.15322 + 4.34627i) q^{42} -7.31819 q^{43} +(-2.08883 - 2.10892i) q^{44} +(10.1372 + 2.71728i) q^{45} +(-1.30785 + 0.538067i) q^{46} +9.07796 q^{47} +(-0.970354 + 6.85991i) q^{48} +3.63001 q^{49} +(-9.46704 + 3.89486i) q^{50} +(-1.02963 + 7.81798i) q^{51} +(9.53961 + 9.63139i) q^{52} -1.34170 q^{53} +(7.34845 + 0.0186167i) q^{54} -5.19210i q^{55} +(-4.78266 - 2.02140i) q^{56} +(-0.683399 - 0.0900036i) q^{57} +(-0.0748001 + 0.0307737i) q^{58} +4.89061i q^{59} +(-9.64997 + 7.33085i) q^{60} -6.29061i q^{61} +(-1.63228 - 3.96750i) q^{62} +(-1.42588 + 5.31947i) q^{63} +(-5.57503 - 5.73751i) q^{64} +23.7121i q^{65} +(-0.932340 - 3.51382i) q^{66} +7.37815 q^{67} +(-6.40758 - 6.46922i) q^{68} +(-1.71722 - 0.226158i) q^{69} +(-3.45555 - 8.39924i) q^{70} +11.3688 q^{71} +(-5.21434 + 6.69408i) q^{72} +10.8453 q^{73} +(-4.89079 - 11.8878i) q^{74} +(-12.4303 - 1.63707i) q^{75} +(0.565499 - 0.560111i) q^{76} +2.72453 q^{77} +(4.25797 + 16.0475i) q^{78} +6.29565i q^{79} +(0.133974 - 13.9928i) q^{80} +(7.79339 + 4.50145i) q^{81} +(-1.77761 - 4.32076i) q^{82} +12.3460i q^{83} +(-3.84683 - 5.06378i) q^{84} -15.9270i q^{85} +(9.57113 - 3.93768i) q^{86} +(-0.0982131 - 0.0129347i) q^{87} +(3.86663 + 1.63424i) q^{88} -16.4215i q^{89} +(-14.7201 + 1.90071i) q^{90} -12.4428 q^{91} +(1.42097 - 1.40743i) q^{92} +(0.686071 - 5.20935i) q^{93} +(-11.8727 + 4.88456i) q^{94} +1.39224 q^{95} +(-2.42201 - 9.49389i) q^{96} -13.2603 q^{97} +(-4.74752 + 1.95319i) q^{98} +(1.15278 - 4.30062i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 42 q + 2 q^{3} + 4 q^{4} + 8 q^{5} + 4 q^{6} - 9 q^{8} + 2 q^{9}+O(q^{10}) $ 42 * q + 2 * q^3 + 4 * q^4 + 8 * q^5 + 4 * q^6 - 9 * q^8 + 2 * q^9	$ 42 q + 2 q^{3} + 4 q^{4} + 8 q^{5} + 4 q^{6} - 9 q^{8} + 2 q^{9} - 4 q^{10} - 21 q^{12} - 4 q^{14} - 8 q^{15} - 12 q^{16} - 11 q^{18} + 4 q^{19} - 2 q^{20} + 8 q^{21} + 18 q^{22} + 42 q^{23} + 28 q^{24} + 22 q^{25} + 11 q^{26} - 16 q^{27} + 6 q^{28} + 2 q^{30} - 20 q^{32} + 12 q^{33} + 14 q^{34} - 24 q^{36} - 22 q^{38} + 8 q^{39} + 4 q^{40} - 44 q^{42} + 28 q^{43} + 56 q^{44} - 8 q^{45} + 30 q^{48} - 50 q^{49} + 20 q^{50} + 28 q^{51} - q^{52} + 24 q^{53} + 52 q^{54} - 34 q^{56} - 8 q^{57} - 21 q^{58} - 42 q^{60} - 79 q^{62} - 16 q^{63} + 7 q^{64} - 62 q^{66} - 4 q^{67} + 20 q^{68} + 2 q^{69} - 8 q^{70} + 22 q^{72} + 4 q^{73} + 36 q^{74} - 6 q^{75} + 14 q^{76} + 32 q^{77} + 27 q^{78} - 52 q^{80} + 18 q^{81} + 11 q^{82} - 80 q^{84} - 28 q^{86} - 48 q^{87} - 38 q^{88} - 46 q^{90} - 8 q^{91} + 4 q^{92} - 22 q^{93} + q^{94} - 16 q^{95} + 9 q^{96} + 20 q^{97} + 64 q^{98}+O(q^{100}) $ 42 * q + 2 * q^3 + 4 * q^4 + 8 * q^5 + 4 * q^6 - 9 * q^8 + 2 * q^9 - 4 * q^10 - 21 * q^12 - 4 * q^14 - 8 * q^15 - 12 * q^16 - 11 * q^18 + 4 * q^19 - 2 * q^20 + 8 * q^21 + 18 * q^22 + 42 * q^23 + 28 * q^24 + 22 * q^25 + 11 * q^26 - 16 * q^27 + 6 * q^28 + 2 * q^30 - 20 * q^32 + 12 * q^33 + 14 * q^34 - 24 * q^36 - 22 * q^38 + 8 * q^39 + 4 * q^40 - 44 * q^42 + 28 * q^43 + 56 * q^44 - 8 * q^45 + 30 * q^48 - 50 * q^49 + 20 * q^50 + 28 * q^51 - q^52 + 24 * q^53 + 52 * q^54 - 34 * q^56 - 8 * q^57 - 21 * q^58 - 42 * q^60 - 79 * q^62 - 16 * q^63 + 7 * q^64 - 62 * q^66 - 4 * q^67 + 20 * q^68 + 2 * q^69 - 8 * q^70 + 22 * q^72 + 4 * q^73 + 36 * q^74 - 6 * q^75 + 14 * q^76 + 32 * q^77 + 27 * q^78 - 52 * q^80 + 18 * q^81 + 11 * q^82 - 80 * q^84 - 28 * q^86 - 48 * q^87 - 38 * q^88 - 46 * q^90 - 8 * q^91 + 4 * q^92 - 22 * q^93 + q^94 - 16 * q^95 + 9 * q^96 + 20 * q^97 + 64 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/552\mathbb{Z}\right)^\times$.

$n$	$97$	$185$	$277$	$415$
$\chi(n)$	$1$	$-1$	$-1$	$-1$

Coefficient data

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

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

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

$2$	−1.30785	+	0.538067i	−0.924793	+	0.380471i
$2$	−1.30785	+	0.538067i	−0.924793	+	0.380471i
$3$	−1.71722	−	0.226158i	−0.991439	−	0.130572i
$3$	−1.71722	−	0.226158i	−0.991439	−	0.130572i
$4$	1.42097	−	1.40743i	0.710484	−	0.703714i
$5$	3.49837			1.56452			0.782260	−	0.622952i	$-0.214067\pi$
$5$	3.49837			1.56452			0.782260	+	0.622952i	$0.214067\pi$
$6$	2.36757	−	0.628199i	0.966555	−	0.256461i
$7$			1.83575i			0.693850i	0.937893	+	0.346925i	$0.112774\pi$
$7$			1.83575i			0.693850i	−0.937893	+	0.346925i	$0.887226\pi$
$8$	−1.10113	+	2.60529i	−0.389308	+	0.921108i
$9$	2.89771	+	0.776727i	0.965902	+	0.258909i
$10$	−4.57536	+	1.88236i	−1.44686	+	0.595254i
$11$		−	1.48415i		−	0.447487i	−0.974648	−	0.223744i	$-0.928172\pi$
$11$		−	1.48415i		−	0.447487i	0.974648	−	0.223744i	$-0.0718278\pi$
$12$	−2.75842	+	2.09550i	−0.796287	+	0.604919i
$13$			6.77805i			1.87989i	0.341322	+	0.939946i	$0.389125\pi$
$13$			6.77805i			1.87989i	−0.341322	+	0.939946i	$0.610875\pi$
$14$	−0.987759	−	2.40090i	−0.263990	−	0.641667i
$15$	−6.00748	−	0.791185i	−1.55113	−	0.204283i
$16$	0.0382962	−	3.99982i	0.00957406	−	0.999954i
$17$		−	4.55269i		−	1.10419i	−0.833782	−	0.552094i	$-0.813829\pi$
$17$		−	4.55269i		−	1.10419i	0.833782	−	0.552094i	$-0.186171\pi$
$18$	−4.20771	+	0.543314i	−0.991766	+	0.128060i
$19$	0.397968			0.0913001			0.0456500	−	0.998957i	$-0.485464\pi$
$19$	0.397968			0.0913001			0.0456500	+	0.998957i	$0.485464\pi$
$20$	4.97107	−	4.92370i	1.11157	−	1.10097i
$21$	0.415171	−	3.15240i	0.0905976	−	0.687910i
$22$	0.798571	+	1.94105i	0.170256	+	0.413833i
$23$	1.00000			0.208514
$23$	1.00000			0.208514
$24$	2.48009	−	4.22483i	0.506246	−	0.862389i
$25$	7.23861			1.44772
$26$	−3.64705	−	8.86470i	−0.715245	−	1.73851i
$27$	−4.80034	−	1.98915i	−0.923826	−	0.382813i
$28$	2.58369	+	2.60855i	0.488272	+	0.492969i
$29$	0.0571930			0.0106205			0.00531024	−	0.999986i	$-0.498310\pi$
$29$	0.0571930			0.0106205			0.00531024	+	0.999986i	$0.498310\pi$
$30$	8.28262	−	2.19767i	1.51219	−	0.401239i
$31$			3.03359i			0.544849i	0.962177	+	0.272425i	$0.0878255\pi$
$31$			3.03359i			0.544849i	−0.962177	+	0.272425i	$0.912174\pi$
$32$	2.10208	+	5.25178i	0.371600	+	0.928393i
$33$	−0.335652	+	2.54861i	−0.0584295	+	0.443656i
$34$	2.44965	+	5.95425i	0.420112	+	1.02115i
$35$			6.42215i			1.08554i
$36$	5.21073	−	2.97461i	0.868455	−	0.495768i
$37$			9.08955i			1.49431i	0.664649	+	0.747156i	$0.268581\pi$
$37$			9.08955i			1.49431i	−0.664649	+	0.747156i	$0.731419\pi$
$38$	−0.520484	+	0.214133i	−0.0844336	+	0.0347370i
$39$	1.53291	−	11.6394i	0.245462	−	1.86380i
$40$	−3.85216	+	9.11426i	−0.609079	+	1.44109i
$41$			3.30370i			0.515951i	0.966151	+	0.257975i	$0.0830553\pi$
$41$			3.30370i			0.515951i	−0.966151	+	0.257975i	$0.916945\pi$
$42$	1.15322	+	4.34627i	0.177946	+	0.670644i
$43$	−7.31819			−1.11601			−0.558007	−	0.829836i	$-0.688434\pi$
$43$	−7.31819			−1.11601			−0.558007	+	0.829836i	$0.688434\pi$
$44$	−2.08883	−	2.10892i	−0.314903	−	0.317932i
$45$	10.1372	+	2.71728i	1.51117	+	0.405068i
$46$	−1.30785	+	0.538067i	−0.192833	+	0.0793337i
$47$	9.07796			1.32416			0.662079	−	0.749434i	$-0.269674\pi$
$47$	9.07796			1.32416			0.662079	+	0.749434i	$0.269674\pi$
$48$	−0.970354	+	6.85991i	−0.140059	+	0.990143i
$49$	3.63001			0.518573
$50$	−9.46704	+	3.89486i	−1.33884	+	0.550816i
$51$	−1.02963	+	7.81798i	−0.144177	+	1.09474i
$52$	9.53961	+	9.63139i	1.32291	+	1.33563i
$53$	−1.34170			−0.184296			−0.0921482	−	0.995745i	$-0.529373\pi$
$53$	−1.34170			−0.184296			−0.0921482	+	0.995745i	$0.529373\pi$
$54$	7.34845	+	0.0186167i	0.999997	+	0.00253341i
$55$		−	5.19210i		−	0.700102i
$56$	−4.78266	−	2.02140i	−0.639110	−	0.270121i
$57$	−0.683399	−	0.0900036i	−0.0905184	−	0.0119213i
$58$	−0.0748001	+	0.0307737i	−0.00982174	+	0.00404078i
$59$			4.89061i			0.636703i	0.947973	+	0.318351i	$0.103129\pi$
$59$			4.89061i			0.636703i	−0.947973	+	0.318351i	$0.896871\pi$
$60$	−9.64997	+	7.33085i	−1.24581	+	0.946408i
$61$		−	6.29061i		−	0.805430i	−0.915325	−	0.402715i	$-0.868067\pi$
$61$		−	6.29061i		−	0.805430i	0.915325	−	0.402715i	$-0.131933\pi$
$62$	−1.63228	−	3.96750i	−0.207299	−	0.503872i
$63$	−1.42588	+	5.31947i	−0.179644	+	0.670191i
$64$	−5.57503	−	5.73751i	−0.696879	−	0.717188i
$65$			23.7121i			2.94113i
$66$	−0.932340	−	3.51382i	−0.114763	−	0.432521i
$67$	7.37815			0.901385			0.450692	−	0.892679i	$-0.351177\pi$
$67$	7.37815			0.901385			0.450692	+	0.892679i	$0.351177\pi$
$68$	−6.40758	−	6.46922i	−0.777033	−	0.784508i
$69$	−1.71722	−	0.226158i	−0.206729	−	0.0272262i
$70$	−3.45555	−	8.39924i	−0.413017	−	1.00390i
$71$	11.3688			1.34923			0.674617	−	0.738168i	$-0.264309\pi$
$71$	11.3688			1.34923			0.674617	+	0.738168i	$0.264309\pi$
$72$	−5.21434	+	6.69408i	−0.614516	+	0.788904i
$73$	10.8453			1.26935			0.634675	−	0.772779i	$-0.281134\pi$
$73$	10.8453			1.26935			0.634675	+	0.772779i	$0.281134\pi$
$74$	−4.89079	−	11.8878i	−0.568542	−	1.38193i
$75$	−12.4303	−	1.63707i	−1.43533	−	0.189032i
$76$	0.565499	−	0.560111i	0.0648672	−	0.0642491i
$77$	2.72453			0.310489
$78$	4.25797	+	16.0475i	0.482120	+	1.81702i
$79$			6.29565i			0.708316i	0.935186	+	0.354158i	$0.115232\pi$
$79$			6.29565i			0.708316i	−0.935186	+	0.354158i	$0.884768\pi$
$80$	0.133974	−	13.9928i	0.0149788	−	1.56445i
$81$	7.79339	+	4.50145i	0.865932	+	0.500161i
$82$	−1.77761	−	4.32076i	−0.196304	−	0.477148i
$83$			12.3460i			1.35515i	0.735452	+	0.677577i	$0.236970\pi$
$83$			12.3460i			1.35515i	−0.735452	+	0.677577i	$0.763030\pi$
$84$	−3.84683	−	5.06378i	−0.419723	−	0.552503i
$85$		−	15.9270i		−	1.72752i
$86$	9.57113	−	3.93768i	1.03208	−	0.424611i
$87$	−0.0982131	−	0.0129347i	−0.0105296	−	0.00138674i
$88$	3.86663	+	1.63424i	0.412184	+	0.174210i
$89$		−	16.4215i		−	1.74068i	−0.492454	−	0.870339i	$-0.663900\pi$
$89$		−	16.4215i		−	1.74068i	0.492454	−	0.870339i	$-0.336100\pi$
$90$	−14.7201	+	1.90071i	−1.55164	+	0.200353i
$91$	−12.4428			−1.30436
$92$	1.42097	−	1.40743i	0.148146	−	0.146734i
$93$	0.686071	−	5.20935i	0.0711423	−	0.540184i
$94$	−11.8727	+	4.88456i	−1.22457	+	0.503803i
$95$	1.39224			0.142841
$96$	−2.42201	−	9.49389i	−0.247196	−	0.968966i
$97$	−13.2603			−1.34638			−0.673192	−	0.739468i	$-0.735077\pi$
$97$	−13.2603			−1.34638			−0.673192	+	0.739468i	$0.735077\pi$
$98$	−4.74752	+	1.95319i	−0.479572	+	0.197302i
$99$	1.15278	−	4.30062i	0.115859	−	0.432229i
$100$	10.2858	−	10.1878i	1.02858	−	1.01878i
$101$	−9.99270			−0.994311			−0.497155	−	0.867662i	$-0.665622\pi$
$101$	−9.99270			−0.994311			−0.497155	+	0.867662i	$0.665622\pi$
$102$	−2.85999	−	10.7788i	−0.283182	−	1.06726i
$103$			8.33372i			0.821146i	0.911828	+	0.410573i	$0.134671\pi$
$103$			8.33372i			0.821146i	−0.911828	+	0.410573i	$0.865329\pi$
$104$	−17.6588	−	7.46350i	−1.73158	−	0.731857i
$105$	1.45242	−	11.0283i	0.141742	−	1.07625i
$106$	1.75475	−	0.721924i	0.170436	−	0.0701194i
$107$		−	5.27006i		−	0.509476i	−0.967010	−	0.254738i	$-0.918011\pi$
$107$		−	5.27006i		−	0.509476i	0.967010	−	0.254738i	$-0.0819892\pi$
$108$	−9.62072	+	3.92961i	−0.925754	+	0.378127i
$109$		−	0.584317i		−	0.0559674i	−0.999608	−	0.0279837i	$-0.991091\pi$
$109$		−	0.584317i		−	0.0559674i	0.999608	−	0.0279837i	$-0.00890865\pi$
$110$	2.79370	+	6.79051i	0.266369	+	0.647450i
$111$	2.05567	−	15.6088i	0.195116	−	1.48152i
$112$	7.34268	+	0.0703025i	0.693818	+	0.00664296i
$113$		−	18.2683i		−	1.71853i	−0.511528	−	0.859266i	$-0.670921\pi$
$113$		−	18.2683i		−	1.71853i	0.511528	−	0.859266i	$-0.329079\pi$
$114$	0.942215	−	0.250003i	0.0882465	−	0.0234149i
$115$	3.49837			0.326225
$116$	0.0812694	−	0.0804950i	0.00754567	−	0.00747377i
$117$	−5.26470	+	19.6408i	−0.486721	+	1.81579i
$118$	−2.63147	−	6.39620i	−0.242247	−	0.588818i
$119$	8.35761			0.766141
$120$	8.67627	−	14.7800i	0.792032	−	1.34922i
$121$	8.79731			0.799755
$122$	3.38477	+	8.22720i	0.306443	+	0.744856i
$123$	0.747158	−	5.67318i	0.0673689	−	0.511534i
$124$	4.26956	+	4.31063i	0.383418	+	0.387106i
$125$	7.83147			0.700468
$126$	−0.997390	−	7.72432i	−0.0888546	−	0.688137i
$127$		−	21.3335i		−	1.89304i	−0.322645	−	0.946520i	$-0.604572\pi$
$127$		−	21.3335i		−	1.89304i	0.322645	−	0.946520i	$-0.395428\pi$
$128$	10.3785	+	4.50408i	0.917338	+	0.398108i
$129$	12.5670	+	1.65507i	1.10646	+	0.145721i
$130$	−12.7587	−	31.0120i	−1.11901	−	2.71994i
$131$			7.38296i			0.645052i	0.946561	+	0.322526i	$0.104532\pi$
$131$			7.38296i			0.645052i	−0.946561	+	0.322526i	$0.895468\pi$
$132$	3.11003	+	4.09390i	0.270694	+	0.356328i
$133$			0.730571i			0.0633485i
$134$	−9.64955	+	3.96994i	−0.833594	+	0.342951i
$135$	−16.7934	−	6.95880i	−1.44534	−	0.598918i
$136$	11.8611	+	5.01309i	1.01708	+	0.429869i
$137$			9.89626i			0.845494i	0.906248	+	0.422747i	$0.138934\pi$
$137$			9.89626i			0.845494i	−0.906248	+	0.422747i	$0.861066\pi$
$138$	2.36757	−	0.628199i	0.201541	−	0.0534759i
$139$	−4.54971			−0.385902			−0.192951	−	0.981208i	$-0.561806\pi$
$139$	−4.54971			−0.385902			−0.192951	+	0.981208i	$0.561806\pi$
$140$	9.03871	+	9.12566i	0.763910	+	0.771259i
$141$	−15.5889	−	2.05305i	−1.31282	−	0.172898i
$142$	−14.8688	+	6.11720i	−1.24776	+	0.513344i
$143$	10.0596			0.841228
$144$	3.21774	−	11.5605i	0.268145	−	0.963379i
$145$	0.200082			0.0166159
$146$	−14.1841	+	5.83552i	−1.17389	+	0.482951i
$147$	−6.23353	−	0.820956i	−0.514133	−	0.0677113i
$148$	12.7929	+	12.9159i	1.05157	+	1.06168i
$149$	−5.78896			−0.474250			−0.237125	−	0.971479i	$-0.576205\pi$
$149$	−5.78896			−0.474250			−0.237125	+	0.971479i	$0.576205\pi$
$150$	17.1379	−	4.54729i	1.39930	−	0.371284i
$151$		−	3.76214i		−	0.306159i	−0.988214	−	0.153079i	$-0.951081\pi$
$151$		−	3.76214i		−	0.306159i	0.988214	−	0.153079i	$-0.0489190\pi$
$152$	−0.438213	+	1.03682i	−0.0355438	+	0.0840972i
$153$	3.53620	−	13.1923i	0.285885	−	1.06654i
$154$	−3.56329	+	1.46598i	−0.287138	+	0.118132i
$155$			10.6126i			0.852427i
$156$	−14.2034	−	18.6967i	−1.13718	−	1.49693i
$157$			7.07465i			0.564619i	0.959323	+	0.282309i	$0.0911005\pi$
$157$			7.07465i			0.564619i	−0.959323	+	0.282309i	$0.908900\pi$
$158$	−3.38748	−	8.23379i	−0.269494	−	0.655045i
$159$	2.30399	+	0.303436i	0.182719	+	0.0240640i
$160$	7.35387	+	18.3727i	0.581375	+	1.45249i
$161$			1.83575i			0.144678i
$162$	−12.6147	−	1.69388i	−0.991105	−	0.133084i
$163$	19.3880			1.51858			0.759291	−	0.650751i	$-0.225546\pi$
$163$	19.3880			1.51858			0.759291	+	0.650751i	$0.225546\pi$
$164$	4.64971	+	4.69445i	0.363082	+	0.366575i
$165$	−1.17423	+	8.91599i	−0.0914141	+	0.694109i
$166$	−6.64300	−	16.1468i	−0.515597	−	1.25324i
$167$	−22.4698			−1.73876			−0.869382	−	0.494141i	$-0.835483\pi$
$167$	−22.4698			−1.73876			−0.869382	+	0.494141i	$0.835483\pi$
$168$	7.75574	+	4.55283i	0.598368	+	0.351259i
$169$	−32.9420			−2.53400
$170$	8.56979	+	20.8302i	0.657273	+	1.59760i
$171$	1.15319	+	0.309112i	0.0881869	+	0.0236384i
$172$	−10.3989	+	10.2998i	−0.792909	+	0.785354i
$173$	10.4676			0.795841			0.397920	−	0.917420i	$-0.369732\pi$
$173$	10.4676			0.795841			0.397920	+	0.917420i	$0.369732\pi$
$174$	0.135408	−	0.0359286i	0.0102653	−	0.00272374i
$175$			13.2883i			1.00450i
$176$	−5.93632	−	0.0568373i	−0.447467	−	0.00428427i
$177$	1.10605	−	8.39826i	0.0831358	−	0.631252i
$178$	8.83588	+	21.4770i	0.662277	+	1.60977i
$179$		−	22.5561i		−	1.68592i	−0.537976	−	0.842960i	$-0.680811\pi$
$179$		−	22.5561i		−	1.68592i	0.537976	−	0.842960i	$-0.319189\pi$
$180$	18.2291	−	10.4063i	1.35872	−	0.775638i
$181$			2.84476i			0.211449i	0.994395	+	0.105725i	$0.0337162\pi$
$181$			2.84476i			0.211449i	−0.994395	+	0.105725i	$0.966284\pi$
$182$	16.2734	−	6.69508i	1.20627	−	0.496272i
$183$	−1.42267	+	10.8024i	−0.105167	+	0.798534i
$184$	−1.10113	+	2.60529i	−0.0811762	+	0.192064i
$185$			31.7986i			2.33788i
$186$	1.90570	+	7.18223i	0.139733	+	0.526626i
$187$	−6.75686			−0.494110
$188$	12.8995	−	12.7766i	0.940792	−	0.931828i
$189$	3.65159	−	8.81224i	0.265614	−	0.640996i
$190$	−1.82085	+	0.749118i	−0.132098	+	0.0543467i
$191$	−4.26548			−0.308639			−0.154320	−	0.988021i	$-0.549319\pi$
$191$	−4.26548			−0.308639			−0.154320	+	0.988021i	$0.549319\pi$
$192$	8.27599	+	11.1134i	0.597268	+	0.802042i
$193$	−8.79066			−0.632765			−0.316383	−	0.948632i	$-0.602468\pi$
$193$	−8.79066			−0.632765			−0.316383	+	0.948632i	$0.602468\pi$
$194$	17.3426	−	7.13496i	1.24513	−	0.512260i
$195$	5.36269	−	40.7190i	0.384030	−	2.91595i
$196$	5.15812	−	5.10897i	0.368437	−	0.364927i
$197$	−9.28630			−0.661622			−0.330811	−	0.943697i	$-0.607322\pi$
$197$	−9.28630			−0.661622			−0.330811	+	0.943697i	$0.607322\pi$
$198$	0.806358	+	6.24486i	0.0573053	+	0.443803i
$199$			3.73492i			0.264761i	0.991199	+	0.132381i	$0.0422621\pi$
$199$			3.73492i			0.264761i	−0.991199	+	0.132381i	$0.957738\pi$
$200$	−7.97063	+	18.8586i	−0.563609	+	1.33351i
$201$	−12.6699	−	1.66863i	−0.893668	−	0.117696i
$202$	13.0690	−	5.37674i	0.919532	−	0.378306i
$203$			0.104992i			0.00736901i
$204$	9.54017	+	12.5582i	0.667945	+	0.879251i
$205$			11.5576i			0.807215i
$206$	−4.48410	−	10.8993i	−0.312422	−	0.759390i
$207$	2.89771	+	0.776727i	0.201404	+	0.0539863i
$208$	27.1110	+	0.259574i	1.87981	+	0.0179982i
$209$		−	0.590643i		−	0.0408556i
$210$	4.03439	+	15.2049i	0.278399	+	1.04923i
$211$	−1.83633			−0.126418			−0.0632090	−	0.998000i	$-0.520133\pi$
$211$	−1.83633			−0.126418			−0.0632090	+	0.998000i	$0.520133\pi$
$212$	−1.90651	+	1.88834i	−0.130940	+	0.129692i
$213$	−19.5228	−	2.57116i	−1.33768	−	0.176173i
$214$	2.83564	+	6.89247i	0.193841	+	0.471159i
$215$	−25.6017			−1.74602
$216$	10.4681	−	10.3160i	0.712264	−	0.701911i
$217$	−5.56893			−0.378043
$218$	0.314402	+	0.764201i	0.0212940	+	0.0517582i
$219$	−18.6238	−	2.45276i	−1.25848	−	0.165742i
$220$	−7.30750	−	7.37780i	−0.492672	−	0.497411i
$221$	30.8583			2.07576
$222$	5.71005	+	21.5201i	0.383233	+	1.44433i
$223$		−	10.6636i		−	0.714090i	−0.934087	−	0.357045i	$-0.883784\pi$
$223$		−	10.6636i		−	0.714090i	0.934087	−	0.357045i	$-0.116216\pi$
$224$	−9.64098	+	3.85891i	−0.644165	+	0.257834i
$225$	20.9753	+	5.62242i	1.39836	+	0.374828i
$226$	9.82955	+	23.8922i	0.653852	+	1.58929i
$227$			3.35272i			0.222528i	0.993791	+	0.111264i	$0.0354899\pi$
$227$			3.35272i			0.222528i	−0.993791	+	0.111264i	$0.964510\pi$
$228$	−1.09776	+	0.833942i	−0.0727010	+	0.0552292i
$229$		−	23.5299i		−	1.55490i	−0.628944	−	0.777451i	$-0.716512\pi$
$229$		−	23.5299i		−	1.55490i	0.628944	−	0.777451i	$-0.283488\pi$
$230$	−4.57536	+	1.88236i	−0.301690	+	0.124119i
$231$	−4.67862	−	0.616174i	−0.307831	−	0.0405413i
$232$	−0.0629768	+	0.149004i	−0.00413463	+	0.00978260i
$233$		−	15.8187i		−	1.03632i	−0.855284	−	0.518160i	$-0.826617\pi$
$233$		−	15.8187i		−	1.03632i	0.855284	−	0.518160i	$-0.173383\pi$
$234$	−3.68261	−	28.5201i	−0.240740	−	1.86441i
$235$	31.7581			2.07167
$236$	6.88317	+	6.94939i	0.448056	+	0.452367i
$237$	1.42381	−	10.8110i	0.0924865	−	0.702252i
$238$	−10.9305	+	4.49696i	−0.708522	+	0.291494i
$239$	−6.78491			−0.438879			−0.219440	−	0.975626i	$-0.570423\pi$
$239$	−6.78491			−0.438879			−0.219440	+	0.975626i	$0.570423\pi$
$240$	−3.39466	+	23.9985i	−0.219124	+	1.54910i
$241$	−6.22915			−0.401255			−0.200628	−	0.979668i	$-0.564298\pi$
$241$	−6.22915			−0.401255			−0.200628	+	0.979668i	$0.564298\pi$
$242$	−11.5056	+	4.73354i	−0.739608	+	0.304284i
$243$	−12.3649	−	9.49253i	−0.793211	−	0.608946i
$244$	−8.85357	−	8.93875i	−0.566792	−	0.572245i
$245$	12.6991			0.811317
$246$	2.07538	+	7.82172i	0.132321	+	0.498695i
$247$			2.69745i			0.171634i
$248$	−7.90337	−	3.34037i	−0.501865	−	0.212114i
$249$	2.79216	−	21.2009i	0.176946	−	1.34355i
$250$	−10.2424	+	4.21386i	−0.647788	+	0.266508i
$251$		−	7.62900i		−	0.481538i	−0.970582	−	0.240769i	$-0.922600\pi$
$251$		−	7.62900i		−	0.481538i	0.970582	−	0.240769i	$-0.0773997\pi$
$252$	5.46064	+	9.56562i	0.343988	+	0.602577i
$253$		−	1.48415i		−	0.0933075i
$254$	11.4788	+	27.9011i	0.720247	+	1.75067i
$255$	−3.60202	+	27.3502i	−0.225567	+	1.71274i
$256$	−15.9971	−	0.306356i	−0.999817	−	0.0191472i
$257$		−	10.8201i		−	0.674937i	−0.941337	−	0.337468i	$-0.890429\pi$
$257$		−	10.8201i		−	0.674937i	0.941337	−	0.337468i	$-0.109571\pi$
$258$	−17.3263	+	4.59728i	−1.07869	+	0.286214i
$259$	−16.6862			−1.03683
$260$	33.3731	+	33.6942i	2.06971	+	2.08962i
$261$	0.165728	+	0.0444234i	0.0102583	+	0.00274974i
$262$	−3.97253	−	9.65583i	−0.245424	−	0.596539i
$263$	−17.9040			−1.10401			−0.552004	−	0.833841i	$-0.686137\pi$
$263$	−17.9040			−1.10401			−0.552004	+	0.833841i	$0.686137\pi$
$264$	−6.27027	−	3.68082i	−0.385908	−	0.226539i
$265$	−4.69376			−0.288335
$266$	−0.393096	−	0.955480i	−0.0241023	−	0.0585843i
$267$	−3.71386	+	28.1994i	−0.227284	+	1.72578i
$268$	10.4841	−	10.3842i	0.640419	−	0.634317i
$269$	−19.9736			−1.21781			−0.608905	−	0.793243i	$-0.708391\pi$
$269$	−19.9736			−1.21781			−0.608905	+	0.793243i	$0.708391\pi$
$270$	25.7076	+	0.0651280i	1.56451	+	0.00396357i
$271$			2.74931i			0.167009i	0.996507	+	0.0835045i	$0.0266113\pi$
$271$			2.74931i			0.167009i	−0.996507	+	0.0835045i	$0.973389\pi$
$272$	−18.2099	−	0.174351i	−1.10414	−	0.0105716i
$273$	21.3671	+	2.81405i	1.29320	+	0.170314i
$274$	−5.32485	−	12.9429i	−0.321686	−	0.781907i
$275$		−	10.7432i		−	0.647837i
$276$	−2.75842	+	2.09550i	−0.166037	+	0.126134i
$277$			6.32916i			0.380282i	0.981757	+	0.190141i	$0.0608946\pi$
$277$			6.32916i			0.380282i	−0.981757	+	0.190141i	$0.939105\pi$
$278$	5.95036	−	2.44805i	0.356879	−	0.146824i
$279$	−2.35627	+	8.79045i	−0.141066	+	0.526271i
$280$	−16.7315	−	7.07161i	−0.999901	−	0.422609i
$281$			23.6899i			1.41322i	0.707604	+	0.706609i	$0.249776\pi$
$281$			23.6899i			1.41322i	−0.707604	+	0.706609i	$0.750224\pi$
$282$	21.4927	−	5.70277i	1.27987	−	0.339595i
$283$	−10.5607			−0.627770			−0.313885	−	0.949461i	$-0.601631\pi$
$283$	−10.5607			−0.627770			−0.313885	+	0.949461i	$0.601631\pi$
$284$	16.1548	−	16.0008i	0.958609	−	0.949474i
$285$	−2.39078	−	0.314866i	−0.141618	−	0.0186511i
$286$	−13.1565	+	5.41275i	−0.777962	+	0.320063i
$287$	−6.06477			−0.357992
$288$	2.01202	+	16.8509i	0.118559	+	0.992947i
$289$	−3.72696			−0.219233
$290$	−0.261679	+	0.107658i	−0.0153663	+	0.00632188i
$291$	22.7710	+	2.99893i	1.33486	+	0.175801i
$292$	15.4109	−	15.2640i	0.901852	−	0.893259i
$293$	−3.10037			−0.181125			−0.0905627	−	0.995891i	$-0.528867\pi$
$293$	−3.10037			−0.181125			−0.0905627	+	0.995891i	$0.528867\pi$
$294$	8.59428	−	2.28037i	0.501229	−	0.132994i
$295$			17.1092i			0.996134i
$296$	−23.6809	−	10.0088i	−1.37642	−	0.581747i
$297$	−2.95220	+	7.12441i	−0.171304	+	0.413400i
$298$	7.57112	−	3.11485i	0.438583	−	0.180439i
$299$			6.77805i			0.391985i
$300$	−19.9671	+	15.1685i	−1.15280	+	0.875755i
$301$		−	13.4344i		−	0.774345i
$302$	2.02428	+	4.92033i	0.116485	+	0.283133i
$303$	17.1597	+	2.25993i	0.985798	+	0.129830i
$304$	0.0152407	−	1.59180i	0.000874112	−	0.0912959i
$305$		−	22.0069i		−	1.26011i
$306$	2.47354	+	19.1564i	0.141403	+	1.09510i
$307$	22.1946			1.26671			0.633356	−	0.773860i	$-0.281677\pi$
$307$	22.1946			1.26671			0.633356	+	0.773860i	$0.281677\pi$
$308$	3.87147	−	3.83458i	0.220597	−	0.218495i
$309$	1.88474	−	14.3108i	0.107219	−	0.814116i
$310$	−5.71031	−	13.8798i	−0.324324	−	0.788318i
$311$	22.6209			1.28271			0.641357	−	0.767242i	$-0.278372\pi$
$311$	22.6209			1.28271			0.641357	+	0.767242i	$0.278372\pi$
$312$	28.6361	+	16.8102i	1.62120	+	0.951688i
$313$	31.8167			1.79838			0.899192	−	0.437555i	$-0.144155\pi$
$313$	31.8167			1.79838			0.899192	+	0.437555i	$0.144155\pi$
$314$	−3.80664	−	9.25262i	−0.214821	−	0.522155i
$315$	−4.98826	+	18.6095i	−0.281057	+	1.04853i
$316$	8.86067	+	8.94591i	0.498452	+	0.503247i
$317$	−5.60860			−0.315010			−0.157505	−	0.987518i	$-0.550345\pi$
$317$	−5.60860			−0.315010			−0.157505	+	0.987518i	$0.550345\pi$
$318$	−3.17656	+	0.842854i	−0.178133	+	0.0472649i
$319$		−	0.0848828i		−	0.00475253i
$320$	−19.5035	−	20.0719i	−1.09028	−	1.12206i
$321$	−1.19187	+	9.04986i	−0.0665235	+	0.505114i
$322$	−0.987759	−	2.40090i	−0.0550457	−	0.133797i
$323$		−	1.81182i		−	0.100813i
$324$	17.4096	−	4.57221i	0.967201	−	0.254012i
$325$			49.0636i			2.72156i
$326$	−25.3566	+	10.4320i	−1.40437	+	0.577777i
$327$	−0.132148	+	1.00340i	−0.00730780	+	0.0554882i
$328$	−8.60708	−	3.63779i	−0.475246	−	0.200864i
$329$			16.6649i			0.918766i
$330$	−3.26167	−	12.2926i	−0.179549	−	0.676687i
$331$	17.1064			0.940255			0.470128	−	0.882598i	$-0.344208\pi$
$331$	17.1064			0.940255			0.470128	+	0.882598i	$0.344208\pi$
$332$	17.3762	+	17.5433i	0.953641	+	0.962815i
$333$	−7.06010	+	26.3388i	−0.386891	+	1.44336i
$334$	29.3872	−	12.0903i	1.60800	−	0.661549i
$335$	25.8115			1.41023
$336$	−12.5931	−	1.78133i	−0.687011	−	0.0971796i
$337$	−14.0119			−0.763274			−0.381637	−	0.924312i	$-0.624640\pi$
$337$	−14.0119			−0.763274			−0.381637	+	0.924312i	$0.624640\pi$
$338$	43.0833	−	17.7250i	2.34342	−	0.964113i
$339$	−4.13151	+	31.3707i	−0.224393	+	1.70382i
$340$	−22.4161	−	22.6317i	−1.21568	−	1.22738i
$341$	4.50230			0.243813
$342$	−1.67453	+	0.216221i	−0.0905483	+	0.0116919i
$343$			19.5141i			1.05366i
$344$	8.05826	−	19.0660i	0.434472	−	1.02797i
$345$	−6.00748	−	0.791185i	−0.323432	−	0.0425960i
$346$	−13.6902	+	5.63230i	−0.735988	+	0.302794i
$347$		−	14.6542i		−	0.786681i	−0.919393	−	0.393340i	$-0.871319\pi$
$347$		−	14.6542i		−	0.786681i	0.919393	−	0.393340i	$-0.128681\pi$
$348$	−0.157762	+	0.119848i	−0.00845694	+	0.00642453i
$349$		−	1.85884i		−	0.0995015i	−0.998762	−	0.0497507i	$-0.984157\pi$
$349$		−	1.85884i		−	0.0995015i	0.998762	−	0.0497507i	$-0.0158427\pi$
$350$	−7.15000	−	17.3792i	−0.382183	−	0.928955i
$351$	13.4826	−	32.5370i	0.719647	−	1.73669i
$352$	7.79442	−	3.11980i	0.415444	−	0.166286i
$353$		−	13.6060i		−	0.724173i	−0.932144	−	0.362087i	$-0.882064\pi$
$353$		−	13.6060i		−	0.724173i	0.932144	−	0.362087i	$-0.117936\pi$
$354$	3.07227	+	11.5788i	0.163290	+	0.615408i
$355$	39.7725			2.11090
$356$	−23.1121	−	23.3344i	−1.22494	−	1.23672i
$357$	−14.3519	−	1.89014i	−0.759582	−	0.100037i
$358$	12.1367	+	29.5001i	0.641444	+	1.55913i
$359$	−13.1810			−0.695666			−0.347833	−	0.937557i	$-0.613082\pi$
$359$	−13.1810			−0.695666			−0.347833	+	0.937557i	$0.613082\pi$
$360$	−18.2417	+	23.4184i	−0.961422	+	1.23426i
$361$	−18.8416			−0.991664
$362$	−1.53067	−	3.72053i	−0.0804504	−	0.195547i
$363$	−15.1069	−	1.98958i	−0.792908	−	0.104426i
$364$	−17.6809	+	17.5124i	−0.926729	+	0.917898i
$365$	37.9410			1.98592
$366$	−3.95175	−	14.8934i	−0.206562	−	0.778492i
$367$		−	37.4124i		−	1.95291i	−0.215715	−	0.976456i	$-0.569208\pi$
$367$		−	37.4124i		−	1.95291i	0.215715	−	0.976456i	$-0.430792\pi$
$368$	0.0382962	−	3.99982i	0.00199633	−	0.208505i
$369$	−2.56607	+	9.57314i	−0.133584	+	0.498358i
$370$	−17.1098	−	41.5880i	−0.889496	−	2.16205i
$371$		−	2.46303i		−	0.127874i
$372$	−6.35690	−	8.36791i	−0.329590	−	0.433856i
$373$		−	11.9834i		−	0.620478i	−0.950659	−	0.310239i	$-0.899591\pi$
$373$		−	11.9834i		−	0.620478i	0.950659	−	0.310239i	$-0.100409\pi$
$374$	8.83699	−	3.63564i	0.456950	−	0.187995i
$375$	−13.4484	−	1.77115i	−0.694471	−	0.0914618i
$376$	−9.99600	+	23.6507i	−0.515504	+	1.21969i
$377$			0.387657i			0.0199654i
$378$	−0.0341756	+	13.4899i	−0.00175780	+	0.693847i
$379$	1.20081			0.0616815			0.0308408	−	0.999524i	$-0.490182\pi$
$379$	1.20081			0.0616815			0.0308408	+	0.999524i	$0.490182\pi$
$380$	1.97833	−	1.95948i	0.101486	−	0.100519i
$381$	−4.82474	+	36.6343i	−0.247179	+	1.87683i
$382$	5.57863	−	2.29511i	0.285427	−	0.117428i
$383$	−8.82522			−0.450948			−0.225474	−	0.974249i	$-0.572393\pi$
$383$	−8.82522			−0.450948			−0.225474	+	0.974249i	$0.572393\pi$
$384$	−16.8036	−	10.0817i	−0.857503	−	0.514479i
$385$	9.53141			0.485766
$386$	11.4969	−	4.72997i	0.585177	−	0.240749i
$387$	−21.2060	−	5.68424i	−1.07796	−	0.288946i
$388$	−18.8425	+	18.6630i	−0.956584	+	0.947469i
$389$	−30.1120			−1.52674			−0.763369	−	0.645963i	$-0.776456\pi$
$389$	−30.1120			−1.52674			−0.763369	+	0.645963i	$0.776456\pi$
$390$	14.8959	+	56.1400i	0.754286	+	2.84276i
$391$		−	4.55269i		−	0.230239i
$392$	−3.99710	+	9.45721i	−0.201884	+	0.477661i
$393$	1.66972	−	12.6782i	0.0842260	−	0.639529i
$394$	12.1451	−	4.99666i	0.611863	−	0.251728i
$395$			22.0245i			1.10817i
$396$	−4.41475	−	7.73349i	−0.221850	−	0.388623i
$397$		−	21.4698i		−	1.07754i	−0.842453	−	0.538770i	$-0.818889\pi$
$397$		−	21.4698i		−	1.07754i	0.842453	−	0.538770i	$-0.181111\pi$
$398$	−2.00964	−	4.88473i	−0.100734	−	0.244849i
$399$	0.165224	−	1.25455i	0.00827157	−	0.0628062i
$400$	0.277211	−	28.9531i	0.0138606	−	1.44765i
$401$		−	6.28511i		−	0.313863i	−0.987609	−	0.156932i	$-0.949840\pi$
$401$		−	6.28511i		−	0.313863i	0.987609	−	0.156932i	$-0.0501603\pi$
$402$	17.4683	−	4.63495i	0.871238	−	0.231170i
$403$	−20.5618			−1.02426
$404$	−14.1993	+	14.0640i	−0.706442	+	0.699710i
$405$	27.2642	+	15.7478i	1.35477	+	0.782512i
$406$	−0.0564929	−	0.137315i	−0.00280370	−	0.00681481i
$407$	13.4902			0.668686
$408$	−19.2343	−	11.2911i	−0.952240	−	0.558991i
$409$	28.1063			1.38977			0.694883	−	0.719123i	$-0.255456\pi$
$409$	28.1063			1.38977			0.694883	+	0.719123i	$0.255456\pi$
$410$	−6.21874	−	15.1156i	−0.307122	−	0.746507i
$411$	2.23812	−	16.9941i	0.110398	−	0.838256i
$412$	11.7291	+	11.8419i	0.577851	+	0.583411i
$413$	−8.97795			−0.441776
$414$	−4.20771	+	0.543314i	−0.206798	+	0.0267024i
$415$			43.1911i			2.12017i
$416$	−35.5969	+	14.2480i	−1.74528	+	0.698567i
$417$	7.81287	+	1.02895i	0.382598	+	0.0503881i
$418$	0.317805	+	0.772475i	0.0155444	+	0.0377830i
$419$		−	23.5289i		−	1.14946i	−0.818342	−	0.574731i	$-0.805107\pi$
$419$		−	23.5289i		−	1.14946i	0.818342	−	0.574731i	$-0.194893\pi$
$420$	−13.4576	−	17.7150i	−0.656665	−	0.864402i
$421$		−	11.8398i		−	0.577037i	−0.957474	−	0.288519i	$-0.906837\pi$
$421$		−	11.8398i		−	0.577037i	0.957474	−	0.288519i	$-0.0931627\pi$
$422$	2.40165	−	0.988067i	0.116910	−	0.0480984i
$423$	26.3053	+	7.05110i	1.27901	+	0.342836i
$424$	1.47738	−	3.49551i	0.0717480	−	0.169757i
$425$		−	32.9551i		−	1.59856i
$426$	26.9165	−	7.14190i	1.30411	−	0.346026i
$427$	11.5480			0.558847
$428$	−7.41722	−	7.48858i	−0.358525	−	0.361974i
$429$	−17.2746	−	2.27507i	−0.834026	−	0.109841i
$430$	33.4834	−	13.7755i	1.61471	−	0.664312i
$431$	38.1707			1.83862			0.919310	−	0.393535i	$-0.128748\pi$
$431$	38.1707			1.83862			0.919310	+	0.393535i	$0.128748\pi$
$432$	−8.14008	+	19.1243i	−0.391640	+	0.920119i
$433$	−22.4335			−1.07809			−0.539043	−	0.842278i	$-0.681214\pi$
$433$	−22.4335			−1.07809			−0.539043	+	0.842278i	$0.681214\pi$
$434$	7.28335	−	2.99646i	0.349612	−	0.143835i
$435$	−0.343586	−	0.0452502i	−0.0164737	−	0.00216958i
$436$	−0.822383	−	0.830295i	−0.0393850	−	0.0397639i
$437$	0.397968			0.0190374
$438$	25.6770	−	6.81303i	1.22690	−	0.325539i
$439$		−	19.1642i		−	0.914657i	−0.889298	−	0.457329i	$-0.848806\pi$
$439$		−	19.1642i		−	0.914657i	0.889298	−	0.457329i	$-0.151194\pi$
$440$	13.5269	+	5.71717i	0.644870	+	0.272555i
$441$	10.5187	+	2.81953i	0.500890	+	0.134263i
$442$	−40.3582	+	16.6039i	−1.91965	+	0.789765i
$443$		−	32.0444i		−	1.52248i	−0.648472	−	0.761239i	$-0.724591\pi$
$443$		−	32.0444i		−	1.52248i	0.648472	−	0.761239i	$-0.275409\pi$
$444$	−19.0472	−	25.0728i	−0.903938	−	1.18990i
$445$		−	57.4486i		−	2.72332i
$446$	5.73776	+	13.9465i	0.271691	+	0.660386i
$447$	9.94094	+	1.30922i	0.470190	+	0.0619240i
$448$	10.5327	−	10.2344i	0.497621	−	0.483529i
$449$			27.7362i			1.30895i	0.756083	+	0.654476i	$0.227111\pi$
$449$			27.7362i			1.30895i	−0.756083	+	0.654476i	$0.772889\pi$
$450$	−30.4579	+	3.93283i	−1.43580	+	0.185396i
$451$	4.90317			0.230881
$452$	−25.7112	−	25.9586i	−1.20935	−	1.22099i
$453$	−0.850839	+	6.46043i	−0.0399759	+	0.303538i
$454$	−1.80399	−	4.38487i	−0.0846653	−	0.205792i
$455$	−43.5297			−2.04070
$456$	0.986995	−	1.68134i	0.0462203	−	0.0787362i
$457$	−5.94455			−0.278074			−0.139037	−	0.990287i	$-0.544401\pi$
$457$	−5.94455			−0.278074			−0.139037	+	0.990287i	$0.544401\pi$
$458$	12.6607	+	30.7737i	0.591595	+	1.43796i
$459$	−9.05599	+	21.8544i	−0.422697	+	1.02008i
$460$	4.97107	−	4.92370i	0.231777	−	0.229569i
$461$	28.9618			1.34888			0.674442	−	0.738328i	$-0.264384\pi$
$461$	28.9618			1.34888			0.674442	+	0.738328i	$0.264384\pi$
$462$	6.45050	−	1.71155i	0.300104	−	0.0796284i
$463$			10.5305i			0.489392i	0.969600	+	0.244696i	$0.0786881\pi$
$463$			10.5305i			0.489392i	−0.969600	+	0.244696i	$0.921312\pi$
$464$	0.00219028	−	0.228762i	0.000101681	−	0.0106200i
$465$	2.40013	−	18.2242i	0.111303	−	0.845129i
$466$	8.51154	+	20.6886i	0.394289	+	0.958381i
$467$			10.7287i			0.496466i	0.968700	+	0.248233i	$0.0798499\pi$
$467$			10.7287i			0.496466i	−0.968700	+	0.248233i	$0.920150\pi$
$468$	20.1620	+	35.3186i	0.931990	+	1.63260i
$469$			13.5445i			0.625426i
$470$	−41.5350	+	17.0880i	−1.91587	+	0.788210i
$471$	1.59999	−	12.1488i	0.0737236	−	0.559785i
$472$	−12.7414	−	5.38518i	−0.586472	−	0.247873i
$473$			10.8613i			0.499402i
$474$	3.95492	+	14.9054i	0.181656	+	0.684626i
$475$	2.88073			0.132177
$476$	11.8759	−	11.7627i	0.544331	−	0.539144i
$477$	−3.88785	−	1.04213i	−0.178012	−	0.0477160i
$478$	8.87368	−	3.65074i	0.405872	−	0.166981i
$479$	26.1074			1.19288			0.596439	−	0.802659i	$-0.296582\pi$
$479$	26.1074			1.19288			0.596439	+	0.802659i	$0.296582\pi$
$480$	−8.47310	−	33.2131i	−0.386742	−	1.51597i
$481$	−61.6094			−2.80915
$482$	8.14683	−	3.35170i	0.371078	−	0.152666i
$483$	0.415171	−	3.15240i	0.0188909	−	0.143439i
$484$	12.5007	−	12.3816i	0.568213	−	0.562799i
$485$	−46.3896			−2.10644
$486$	21.2792	+	5.76168i	0.965243	+	0.261355i
$487$		−	8.52059i		−	0.386105i	−0.981188	−	0.193052i	$-0.938161\pi$
$487$		−	8.52059i		−	0.386105i	0.981188	−	0.193052i	$-0.0618387\pi$
$488$	16.3888	+	6.92676i	0.741888	+	0.313560i
$489$	−33.2934	−	4.38474i	−1.50558	−	0.198285i
$490$	−16.6086	+	6.83298i	−0.750300	+	0.308683i
$491$			4.75511i			0.214595i	0.994227	+	0.107298i	$0.0342198\pi$
$491$			4.75511i			0.214595i	−0.994227	+	0.107298i	$0.965780\pi$
$492$	−6.92291	−	9.11298i	−0.312109	−	0.410845i
$493$		−	0.260382i		−	0.0117270i
$494$	−1.45141	−	3.52787i	−0.0653019	−	0.158726i
$495$	4.03284	−	15.0452i	0.181263	−	0.676230i
$496$	12.1338	+	0.116175i	0.544824	+	0.00521642i
$497$			20.8704i			0.936166i
$498$	7.75578	+	29.2301i	0.347545	+	1.30983i
$499$	−20.4668			−0.916221			−0.458110	−	0.888895i	$-0.651474\pi$
$499$	−20.4668			−0.916221			−0.458110	+	0.888895i	$0.651474\pi$
$500$	11.1283	−	11.0222i	0.497671	−	0.492929i
$501$	38.5856	+	5.08172i	1.72388	+	0.227035i
$502$	4.10492	+	9.97763i	0.183211	+	0.445323i
$503$	−29.0443			−1.29502			−0.647511	−	0.762056i	$-0.724190\pi$
$503$	−29.0443			−1.29502			−0.647511	+	0.762056i	$0.724190\pi$
$504$	−12.2887	−	9.57225i	−0.547381	−	0.426382i
$505$	−34.9582			−1.55562
$506$	0.798571	+	1.94105i	0.0355008	+	0.0862901i
$507$	56.5687	+	7.45009i	2.51230	+	0.330870i
$508$	−30.0253	−	30.3142i	−1.33216	−	1.34497i
$509$	5.05888			0.224231			0.112116	−	0.993695i	$-0.464237\pi$
$509$	5.05888			0.224231			0.112116	+	0.993695i	$0.464237\pi$
$510$	−10.0053	−	37.7082i	−0.443043	−	1.66975i
$511$			19.9094i			0.880738i
$512$	21.0867	−	8.20683i	0.931908	−	0.362694i
$513$	−1.91038	−	0.791619i	−0.0843454	−	0.0349508i
$514$	5.82192	+	14.1511i	0.256794	+	0.624177i
$515$			29.1544i			1.28470i
$516$	20.1866	−	15.3353i	0.888666	−	0.675098i
$517$		−	13.4730i		−	0.592543i
$518$	21.8231	−	8.97828i	0.958851	−	0.394483i
$519$	−17.9753	−	2.36734i	−0.789027	−	0.103915i
$520$	−61.7769	−	26.1101i	−2.70910	−	1.14500i
$521$		−	8.08682i		−	0.354290i	−0.984185	−	0.177145i	$-0.943314\pi$
$521$		−	8.08682i		−	0.354290i	0.984185	−	0.177145i	$-0.0566862\pi$
$522$	−0.240652	+	0.0310737i	−0.0105330	+	0.00136006i
$523$	−12.3602			−0.540476			−0.270238	−	0.962794i	$-0.587102\pi$
$523$	−12.3602			−0.540476			−0.270238	+	0.962794i	$0.587102\pi$
$524$	10.3910	+	10.4909i	0.453932	+	0.458299i
$525$	3.00526	−	22.8190i	0.131160	−	0.995901i
$526$	23.4158	−	9.63356i	1.02098	−	0.420043i
$527$	13.8110			0.601616
$528$	10.1811	+	1.44015i	0.443076	+	0.0626744i
$529$	1.00000			0.0434783
$530$	6.13875	−	2.52556i	0.266650	−	0.109703i
$531$	−3.79867	+	14.1715i	−0.164848	+	0.614992i
$532$	1.02823	+	1.03812i	0.0445792	+	0.0450081i
$533$	−22.3926			−0.969932
$534$	−10.3160	−	38.8790i	−0.446416	−	1.68246i
$535$		−	18.4366i		−	0.797084i
$536$	−8.12429	+	19.2222i	−0.350916	+	0.830273i
$537$	−5.10124	+	38.7338i	−0.220135	+	1.67149i
$538$	26.1225	−	10.7471i	1.12622	−	0.463341i
$539$		−	5.38747i		−	0.232055i
$540$	−33.6568	+	13.7472i	−1.44836	+	0.591587i
$541$		−	20.6048i		−	0.885869i	−0.896554	−	0.442935i	$-0.853937\pi$
$541$		−	20.6048i		−	0.885869i	0.896554	−	0.442935i	$-0.146063\pi$
$542$	−1.47932	−	3.59570i	−0.0635421	−	0.154449i
$543$	0.643366	−	4.88509i	0.0276095	−	0.209639i
$544$	23.9097	−	9.57013i	1.02512	−	0.410316i
$545$		−	2.04416i		−	0.0875621i
$546$	−29.4592	+	7.81658i	−1.26074	+	0.334519i
$547$	−2.24560			−0.0960148			−0.0480074	−	0.998847i	$-0.515287\pi$
$547$	−2.24560			−0.0960148			−0.0480074	+	0.998847i	$0.515287\pi$
$548$	13.9283	+	14.0623i	0.594986	+	0.600710i
$549$	4.88609	−	18.2283i	0.208533	−	0.777966i
$550$	5.78054	+	14.0505i	0.246483	+	0.599115i
$551$	0.0227610			0.000969650
$552$	2.48009	−	4.22483i	0.105560	−	0.179821i
$553$	−11.5573			−0.491465
$554$	−3.40551	−	8.27762i	−0.144686	−	0.351682i
$555$	7.19151	−	54.6053i	0.305263	−	2.31787i
$556$	−6.46499	+	6.40339i	−0.274177	+	0.271564i
$557$	−15.4155			−0.653177			−0.326589	−	0.945167i	$-0.605899\pi$
$557$	−15.4155			−0.653177			−0.326589	+	0.945167i	$0.605899\pi$
$558$	−1.64819	−	12.7645i	−0.0697735	−	0.540363i
$559$		−	49.6030i		−	2.09799i
$560$	25.6874	+	0.245944i	1.08549	+	0.0103930i
$561$	11.6030	+	1.52812i	0.489880	+	0.0645172i
$562$	−12.7467	−	30.9829i	−0.537689	−	1.30693i
$563$			23.5763i			0.993620i	0.867859	+	0.496810i	$0.165496\pi$
$563$			23.5763i			0.993620i	−0.867859	+	0.496810i	$0.834504\pi$
$564$	−25.0408	+	19.0229i	−1.05441	+	0.801008i
$565$		−	63.9091i		−	2.68868i
$566$	13.8119	−	5.68238i	0.580557	−	0.238848i
$567$	−8.26356	+	14.3067i	−0.347037	+	0.600827i
$568$	−12.5186	+	29.6191i	−0.525267	+	1.24279i
$569$		−	30.0352i		−	1.25914i	−0.776943	−	0.629570i	$-0.783231\pi$
$569$		−	30.0352i		−	1.25914i	0.776943	−	0.629570i	$-0.216769\pi$
$570$	3.29622	−	0.874604i	0.138063	−	0.0366331i
$571$	20.7993			0.870423			0.435212	−	0.900328i	$-0.356674\pi$
$571$	20.7993			0.870423			0.435212	+	0.900328i	$0.356674\pi$
$572$	14.2944	−	14.1582i	0.597679	−	0.591984i
$573$	7.32478	+	0.964672i	0.305997	+	0.0402998i
$574$	7.93184	−	3.26326i	0.331069	−	0.136206i
$575$	7.23861			0.301871
$576$	−11.6983	−	20.9559i	−0.487430	−	0.873162i
$577$	−22.2543			−0.926459			−0.463230	−	0.886238i	$-0.653310\pi$
$577$	−22.2543			−0.926459			−0.463230	+	0.886238i	$0.653310\pi$
$578$	4.87432	−	2.00536i	0.202745	−	0.0834118i
$579$	15.0955	+	1.98808i	0.627348	+	0.0826217i
$580$	0.284311	−	0.281601i	0.0118054	−	0.0116929i
$581$	−22.6643			−0.940274
$582$	−31.3947	+	8.33014i	−1.30135	+	0.345295i
$583$			1.99128i			0.0824703i
$584$	−11.9421	+	28.2552i	−0.494168	+	1.16921i
$585$	−18.4179	+	68.7108i	−0.761485	+	2.84084i
$586$	4.05483	−	1.66821i	0.167503	−	0.0689129i
$587$			42.9955i			1.77461i	0.461181	+	0.887306i	$0.347426\pi$
$587$			42.9955i			1.77461i	−0.461181	+	0.887306i	$0.652574\pi$
$588$	−10.0131	+	7.60669i	−0.412932	+	0.313695i
$589$			1.20727i			0.0497447i
$590$	−9.20588	−	22.3763i	−0.379000	−	0.921217i
$591$	15.9466	+	2.10017i	0.655957	+	0.0863896i
$592$	36.3565	+	0.348095i	1.49424	+	0.0143066i
$593$		−	13.8567i		−	0.569028i	−0.958672	−	0.284514i	$-0.908168\pi$
$593$		−	13.8567i		−	0.569028i	0.958672	−	0.284514i	$-0.0918322\pi$
$594$	0.0276299	−	10.9062i	0.00113367	−	0.447486i
$595$	29.2380			1.19864
$596$	−8.22593	+	8.14755i	−0.336947	+	0.333737i
$597$	0.844682	−	6.41369i	0.0345705	−	0.262495i
$598$	−3.64705	−	8.86470i	−0.149139	−	0.362505i
$599$	−31.7274			−1.29635			−0.648174	−	0.761492i	$-0.724467\pi$
$599$	−31.7274			−1.29635			−0.648174	+	0.761492i	$0.724467\pi$
$600$	17.9524	−	30.5819i	0.732903	−	1.24850i
$601$	40.5341			1.65342			0.826710	−	0.562628i	$-0.190210\pi$
$601$	40.5341			1.65342			0.826710	+	0.562628i	$0.190210\pi$
$602$	7.22861	+	17.5702i	0.294616	+	0.716109i
$603$	21.3797	+	5.73081i	0.870649	+	0.233377i
$604$	−5.29494	−	5.34588i	−0.215448	−	0.217521i
$605$	30.7763			1.25123
$606$	−23.6584	+	6.27741i	−0.961056	+	0.255002i
$607$			35.7346i			1.45042i	0.688526	+	0.725211i	$0.258258\pi$
$607$			35.7346i			1.45042i	−0.688526	+	0.725211i	$0.741742\pi$
$608$	0.836562	+	2.09004i	0.0339271	+	0.0847623i
$609$	0.0237449	−	0.180295i	0.000962190	−	0.00730593i
$610$	11.8412	+	28.7818i	0.479436	+	1.16534i
$611$			61.5309i			2.48927i
$612$	−13.5424	−	23.7228i	−0.547421	−	0.958939i
$613$			13.2676i			0.535872i	0.963437	+	0.267936i	$0.0863415\pi$
$613$			13.2676i			0.535872i	−0.963437	+	0.267936i	$0.913658\pi$
$614$	−29.0273	+	11.9422i	−1.17145	+	0.481947i
$615$	2.61384	−	19.8469i	0.105400	−	0.800304i
$616$	−3.00006	+	7.09818i	−0.120876	+	0.285994i
$617$			15.4046i			0.620165i	0.950710	+	0.310083i	$0.100357\pi$
$617$			15.4046i			0.620165i	−0.950710	+	0.310083i	$0.899643\pi$
$618$	5.23523	+	19.7306i	0.210592	+	0.793682i
$619$	29.4960			1.18554			0.592772	−	0.805371i	$-0.298034\pi$
$619$	29.4960			1.18554			0.592772	+	0.805371i	$0.298034\pi$
$620$	14.9365	+	15.0802i	0.599864	+	0.605635i
$621$	−4.80034	−	1.98915i	−0.192631	−	0.0798220i
$622$	−29.5849	+	12.1716i	−1.18625	+	0.488036i
$623$	30.1459			1.20777
$624$	−46.4968	−	6.57711i	−1.86136	−	0.263295i
$625$	−8.79562			−0.351825
$626$	−41.6116	+	17.1195i	−1.66313	+	0.684233i
$627$	−0.133579	+	1.01426i	−0.00533462	+	0.0405058i
$628$	9.95706	+	10.0528i	0.397330	+	0.401152i
$629$	41.3819			1.65000
$630$	−3.48924	−	27.0225i	−0.139015	−	1.07660i
$631$			45.7384i			1.82082i	0.413710	+	0.910409i	$0.364233\pi$
$631$			45.7384i			1.82082i	−0.413710	+	0.910409i	$0.635767\pi$
$632$	−16.4020	−	6.93232i	−0.652435	−	0.275753i
$633$	3.15338	+	0.415300i	0.125336	+	0.0165067i
$634$	7.33524	−	3.01780i	0.291319	−	0.119852i
$635$		−	74.6324i		−	2.96170i
$636$	3.70096	−	2.81153i	0.146753	−	0.111484i
$637$			24.6044i			0.974861i
$638$	0.0456727	+	0.111014i	0.00180820	+	0.00439510i
$639$	32.9436	+	8.83049i	1.30323	+	0.349329i
$640$	36.3078	+	15.7570i	1.43519	+	0.622848i
$641$			25.1457i			0.993193i	0.867981	+	0.496597i	$0.165417\pi$
$641$			25.1457i			0.993193i	−0.867981	+	0.496597i	$0.834583\pi$
$642$	−3.31065	−	12.4772i	−0.130661	−	0.492436i
$643$	−40.2658			−1.58793			−0.793963	−	0.607966i	$-0.791986\pi$
$643$	−40.2658			−1.58793			−0.793963	+	0.607966i	$0.791986\pi$
$644$	2.58369	+	2.60855i	0.101812	+	0.102791i
$645$	43.9639	+	5.79004i	1.73108	+	0.227983i
$646$	0.974882	+	2.36960i	0.0383562	+	0.0932307i
$647$	15.9572			0.627344			0.313672	−	0.949531i	$-0.398441\pi$
$647$	15.9572			0.627344			0.313672	+	0.949531i	$0.398441\pi$
$648$	−20.3091	+	15.3473i	−0.797817	+	0.602900i
$649$	7.25838			0.284916
$650$	−26.3995	−	64.1681i	−1.03547	−	2.51688i
$651$	9.56308	+	1.25946i	0.374807	+	0.0493620i
$652$	27.5497	−	27.2871i	1.07893	−	1.06865i
$653$	−3.01578			−0.118017			−0.0590083	−	0.998257i	$-0.518794\pi$
$653$	−3.01578			−0.118017			−0.0590083	+	0.998257i	$0.518794\pi$
$654$	−0.367067	−	1.38341i	−0.0143535	−	0.0540955i
$655$			25.8283i			1.00920i
$656$	13.2142	+	0.126519i	0.515927	+	0.00493974i
$657$	31.4266	+	8.42386i	1.22607	+	0.328646i
$658$	−8.96684	−	21.7953i	−0.349564	−	0.849668i
$659$		−	26.3106i		−	1.02492i	−0.858713	−	0.512458i	$-0.828735\pi$
$659$		−	26.3106i		−	1.02492i	0.858713	−	0.512458i	$-0.171265\pi$
$660$	10.8801	+	14.3220i	0.423506	+	0.557482i
$661$			40.9689i			1.59350i	0.604306	+	0.796752i	$0.293450\pi$
$661$			40.9689i			1.59350i	−0.604306	+	0.796752i	$0.706550\pi$
$662$	−22.3727	+	9.20442i	−0.869542	+	0.357740i
$663$	−52.9906	−	6.97886i	−2.05799	−	0.271037i
$664$	−32.1650	−	13.5946i	−1.24824	−	0.527572i
$665$			2.55581i			0.0991100i
$666$	−4.93847	−	38.2462i	−0.191362	−	1.48201i
$667$	0.0571930			0.00221452
$668$	−31.9288	+	31.6246i	−1.23536	+	1.22359i
$669$	−2.41167	+	18.3118i	−0.0932405	+	0.707977i
$670$	−33.7577	+	13.8883i	−1.30417	+	0.536553i
$671$	−9.33619			−0.360420
$672$	17.4284	−	4.44622i	0.672316	−	0.171517i
$673$	0.596803			0.0230051			0.0115025	−	0.999934i	$-0.496339\pi$
$673$	0.596803			0.0230051			0.0115025	+	0.999934i	$0.496339\pi$
$674$	18.3255	−	7.53932i	0.705870	−	0.290404i
$675$	−34.7478	−	14.3987i	−1.33744	−	0.554206i
$676$	−46.8095	+	46.3634i	−1.80036	+	1.78321i
$677$	0.318263			0.0122318			0.00611592	−	0.999981i	$-0.498053\pi$
$677$	0.318263			0.0122318			0.00611592	+	0.999981i	$0.498053\pi$
$678$	−11.4761	−	43.2513i	−0.440737	−	1.66106i
$679$		−	24.3427i		−	0.934188i
$680$	41.4944	+	17.5377i	1.59124	+	0.672539i
$681$	0.758244	−	5.75736i	0.0290560	−	0.220623i
$682$	−5.88835	+	2.42254i	−0.225476	+	0.0927638i
$683$		−	43.9030i		−	1.67990i	−0.542663	−	0.839950i	$-0.682584\pi$
$683$		−	43.9030i		−	1.67990i	0.542663	−	0.839950i	$-0.317416\pi$
$684$	2.07370	−	1.18380i	0.0792900	−	0.0452636i
$685$			34.6208i			1.32279i
$686$	−10.4999	−	25.5216i	−0.400887	−	0.974418i
$687$	−5.32148	+	40.4061i	−0.203027	+	1.54159i
$688$	−0.280259	+	29.2714i	−0.0106848	+	1.11596i
$689$		−	9.09410i		−	0.346458i
$690$	8.28262	−	2.19767i	0.315314	−	0.0836640i
$691$	31.3526			1.19271			0.596355	−	0.802721i	$-0.296615\pi$
$691$	31.3526			1.19271			0.596355	+	0.802721i	$0.296615\pi$
$692$	14.8742	−	14.7325i	0.565432	−	0.560044i
$693$	7.89488	+	2.11622i	0.299902	+	0.0803884i
$694$	7.88497	+	19.1656i	0.299309	+	0.727517i
$695$	−15.9166			−0.603751
$696$	0.141844	−	0.241631i	0.00537657	−	0.00915898i
$697$	15.0407			0.569707
$698$	1.00018	+	2.43109i	0.0378574	+	0.0920182i
$699$	−3.57753	+	27.1643i	−0.135315	+	1.02745i
$700$	18.7023	+	18.8822i	0.706881	+	0.713681i
$701$	−0.606957			−0.0229245			−0.0114622	−	0.999934i	$-0.503649\pi$
$701$	−0.606957			−0.0229245			−0.0114622	+	0.999934i	$0.503649\pi$
$702$	−0.126185	+	49.8081i	−0.00476254	+	1.87989i
$703$			3.61735i			0.136431i
$704$	−8.51531	+	8.27417i	−0.320933	+	0.311845i
$705$	−54.5357	−	7.18235i	−2.05393	−	0.270503i
$706$	7.32093	+	17.7946i	0.275527	+	0.669710i
$707$		−	18.3441i		−	0.689902i
$708$	−10.2483	−	13.4903i	−0.385154	−	0.506998i
$709$			1.59438i			0.0598780i	0.999552	+	0.0299390i	$0.00953131\pi$
$709$			1.59438i			0.0598780i	−0.999552	+	0.0299390i	$0.990469\pi$
$710$	−52.0166	+	21.4003i	−1.95215	+	0.803137i
$711$	−4.89000	+	18.2429i	−0.183389	+	0.684164i
$712$	42.7828	+	18.0822i	1.60335	+	0.677659i
$713$			3.03359i			0.113609i
$714$	19.7872	−	5.25025i	0.740517	−	0.196486i
$715$	35.1923			1.31612
$716$	−31.7460	−	32.0514i	−1.18640	−	1.19782i
$717$	11.6512	+	1.53446i	0.435122	+	0.0573055i
$718$	17.2388	−	7.09226i	0.643347	−	0.264681i
$719$	23.8694			0.890177			0.445088	−	0.895487i	$-0.353172\pi$
$719$	23.8694			0.890177			0.445088	+	0.895487i	$0.353172\pi$
$720$	11.2568	−	40.4431i	0.419518	−	1.50722i
$721$	−15.2987			−0.569752
$722$	24.6421	−	10.1381i	0.917084	−	0.377299i
$723$	10.6968	+	1.40877i	0.397820	+	0.0523929i
$724$	4.00380	+	4.04231i	0.148800	+	0.150231i
$725$	0.413998			0.0153755
$726$	20.8282	−	5.52646i	0.773007	−	0.205106i
$727$			16.3323i			0.605732i	0.953033	+	0.302866i	$0.0979434\pi$
$727$			16.3323i			0.605732i	−0.953033	+	0.302866i	$0.902057\pi$
$728$	13.7012	−	32.4171i	0.507798	−	1.20146i
$729$	19.0865	+	19.0972i	0.706909	+	0.707305i
$730$	−49.6213	+	20.4148i	−1.83657	+	0.755586i
$731$			33.3174i			1.23229i
$732$	13.1820	+	17.3521i	0.487220	+	0.641353i
$733$			30.4643i			1.12522i	0.826721	+	0.562612i	$0.190204\pi$
$733$			30.4643i			1.12522i	−0.826721	+	0.562612i	$0.809796\pi$
$734$	20.1304	+	48.9300i	0.743027	+	1.80604i
$735$	−21.8072	−	2.87201i	−0.804371	−	0.105936i
$736$	2.10208	+	5.25178i	0.0774839	+	0.193583i
$737$		−	10.9503i		−	0.403358i
$738$	−1.79494	−	13.9010i	−0.0660728	−	0.511703i
$739$	−5.14542			−0.189277			−0.0946387	−	0.995512i	$-0.530170\pi$
$739$	−5.14542			−0.189277			−0.0946387	+	0.995512i	$0.530170\pi$
$740$	44.7542	+	45.1848i	1.64520	+	1.66103i
$741$	0.610049	−	4.63211i	0.0224107	−	0.170165i
$742$	1.32527	+	3.22128i	0.0486523	+	0.118257i
$743$	−35.6747			−1.30878			−0.654388	−	0.756159i	$-0.727074\pi$
$743$	−35.6747			−1.30878			−0.654388	+	0.756159i	$0.727074\pi$
$744$	12.8164	+	7.52357i	0.469872	+	0.275828i
$745$	−20.2519			−0.741974
$746$	6.44788	+	15.6726i	0.236074	+	0.573813i
$747$	−9.58951	+	35.7752i	−0.350862	+	1.30895i
$748$	−9.60127	+	9.50979i	−0.351057	+	0.347712i
$749$	9.67453			0.353499
$750$	18.5415	−	4.91973i	0.677041	−	0.179643i
$751$		−	17.8117i		−	0.649958i	−0.945721	−	0.324979i	$-0.894643\pi$
$751$		−	17.8117i		−	0.649958i	0.945721	−	0.324979i	$-0.105357\pi$
$752$	0.347652	−	36.3102i	0.0126776	−	1.32410i
$753$	−1.72536	+	13.1007i	−0.0628756	+	0.477416i
$754$	−0.208586	−	0.506999i	−0.00759624	−	0.0184638i
$755$		−	13.1614i		−	0.478991i
$756$	−7.21380	−	17.6613i	−0.262363	−	0.642334i
$757$		−	44.3720i		−	1.61273i	−0.591419	−	0.806365i	$-0.701432\pi$
$757$		−	44.3720i		−	1.61273i	0.591419	−	0.806365i	$-0.298568\pi$
$758$	−1.57049	+	0.646117i	−0.0570426	+	0.0234680i
$759$	−0.335652	+	2.54861i	−0.0121834	+	0.0925087i
$760$	−1.53303	+	3.62718i	−0.0556090	+	0.131572i
$761$			5.71269i			0.207085i	0.994625	+	0.103542i	$0.0330178\pi$
$761$			5.71269i			0.207085i	−0.994625	+	0.103542i	$0.966982\pi$
$762$	−13.4017	−	50.5084i	−0.485491	−	1.82973i
$763$	1.07266			0.0388329
$764$	−6.06111	+	6.00335i	−0.219283	+	0.217194i
$765$	12.3709	−	46.1517i	0.447272	−	1.66862i
$766$	11.5421	−	4.74856i	0.417033	−	0.171573i
$767$	−33.1488			−1.19693
$768$	27.4012	+	4.14395i	0.988757	+	0.149532i
$769$	−22.6419			−0.816486			−0.408243	−	0.912873i	$-0.633858\pi$
$769$	−22.6419			−0.816486			−0.408243	+	0.912873i	$0.633858\pi$
$770$	−12.4657	+	5.12854i	−0.449233	+	0.184820i
$771$	−2.44704	+	18.5805i	−0.0881282	+	0.669159i
$772$	−12.4912	+	12.3722i	−0.449570	+	0.445286i
$773$	−22.9307			−0.824760			−0.412380	−	0.911012i	$-0.635302\pi$
$773$	−22.9307			−0.824760			−0.412380	+	0.911012i	$0.635302\pi$
$774$	30.7928	−	3.97607i	1.10682	−	0.142917i
$775$			21.9590i			0.788789i
$776$	14.6013	−	34.5470i	0.524157	−	1.24016i
$777$	28.6539	+	3.77371i	1.02795	+	0.135381i
$778$	39.3821	−	16.2023i	1.41192	−	0.580880i
$779$			1.31476i			0.0471063i
$780$	−49.6889	−	65.4080i	−1.77915	−	2.34198i
$781$		−	16.8730i		−	0.603765i
$782$	2.44965	+	5.95425i	0.0875994	+	0.212924i
$783$	−0.274546	−	0.113766i	−0.00981147	−	0.00406565i
$784$	0.139016	−	14.5194i	0.00496484	−	0.518549i
$785$			24.7498i			0.883357i
$786$	4.63797	+	17.4796i	0.165431	+	0.623478i
$787$	12.3839			0.441437			0.220718	−	0.975338i	$-0.429160\pi$
$787$	12.3839			0.441437			0.220718	+	0.975338i	$0.429160\pi$
$788$	−13.1955	+	13.0698i	−0.470071	+	0.465592i
$789$	30.7452	+	4.04914i	1.09456	+	0.144153i
$790$	−11.8507	−	28.8049i	−0.421628	−	1.02483i
$791$	33.5360			1.19240
$792$	9.93499	+	7.73885i	0.353025	+	0.274988i
$793$	42.6381			1.51412
$794$	11.5522	+	28.0794i	0.409972	+	0.996501i
$795$	8.06023	+	1.06153i	0.285867	+	0.0376486i
$796$	5.25663	+	5.30720i	0.186316	+	0.188109i
$797$	24.6146			0.871892			0.435946	−	0.899973i	$-0.356414\pi$
$797$	24.6146			0.871892			0.435946	+	0.899973i	$0.356414\pi$
$798$	0.458944	+	1.72967i	0.0162464	+	0.0612298i
$799$		−	41.3291i		−	1.46212i
$800$	15.2162	+	38.0156i	0.537972	+	1.34405i
$801$	12.7550	−	47.5847i	0.450677	−	1.68132i
$802$	3.38181	+	8.22001i	0.119416	+	0.290259i
$803$		−	16.0961i		−	0.568018i
$804$	−20.3520	+	15.4609i	−0.717761	+	0.545265i
$805$			6.42215i			0.226351i
$806$	26.8919	−	11.0636i	0.947226	−	0.389700i
$807$	34.2991	+	4.51718i	1.20738	+	0.159012i
$808$	11.0032	−	26.0338i	0.387093	−	0.915867i
$809$		−	44.8118i		−	1.57550i	−0.615997	−	0.787749i	$-0.711246\pi$
$809$		−	44.8118i		−	1.57550i	0.615997	−	0.787749i	$-0.288754\pi$
$810$	−44.1309	−	5.92582i	−1.55060	−	0.208212i
$811$	9.84923			0.345853			0.172927	−	0.984935i	$-0.444678\pi$
$811$	9.84923			0.345853			0.172927	+	0.984935i	$0.444678\pi$
$812$	0.147769	+	0.149191i	0.00518568	+	0.00523556i
$813$	0.621780	−	4.72118i	0.0218068	−	0.165579i
$814$	−17.6433	+	7.25865i	−0.618396	+	0.254415i
$815$	67.8263			2.37585
$816$	31.2310	+	4.41772i	1.09331	+	0.154651i
$817$	−2.91240			−0.101892
$818$	−36.7589	+	15.1231i	−1.28525	+	0.528766i
$819$	−36.0557	−	9.66469i	−1.25989	−	0.337712i
$820$	16.2664	+	16.4229i	0.568048	+	0.573513i
$821$	−0.934045			−0.0325984			−0.0162992	−	0.999867i	$-0.505188\pi$
$821$	−0.934045			−0.0325984			−0.0162992	+	0.999867i	$0.505188\pi$
$822$	6.21682	+	23.4300i	0.216837	+	0.817216i
$823$		−	0.533620i		−	0.0186008i	−0.999957	−	0.00930042i	$-0.997040\pi$
$823$		−	0.533620i		−	0.0186008i	0.999957	−	0.00930042i	$-0.00296046\pi$
$824$	−21.7117	−	9.17649i	−0.756364	−	0.319678i
$825$	−2.42965	+	18.4484i	−0.0845896	+	0.642290i
$826$	11.7418	−	4.83074i	0.408551	−	0.168083i
$827$		−	22.4084i		−	0.779216i	−0.920981	−	0.389608i	$-0.872610\pi$
$827$		−	22.4084i		−	0.779216i	0.920981	−	0.389608i	$-0.127390\pi$
$828$	5.21073	−	2.97461i	0.181085	−	0.103375i
$829$			9.92771i			0.344804i	0.985027	+	0.172402i	$0.0551528\pi$
$829$			9.92771i			0.344804i	−0.985027	+	0.172402i	$0.944847\pi$
$830$	−23.2397	−	56.4876i	−0.806661	−	1.96071i
$831$	1.43139	−	10.8686i	0.0496544	−	0.377027i
$832$	38.8891	−	37.7879i	1.34824	−	1.31006i
$833$		−	16.5263i		−	0.572602i
$834$	−10.7717	+	2.85813i	−0.372995	+	0.0989688i
$835$	−78.6076			−2.72033
$836$	−0.831287	−	0.839284i	−0.0287507	−	0.0290272i
$837$	6.03428	−	14.5623i	0.208575	−	0.503346i
$838$	12.6601	+	30.7724i	0.437337	+	1.06301i
$839$	−7.41997			−0.256166			−0.128083	−	0.991763i	$-0.540882\pi$
$839$	−7.41997			−0.256166			−0.128083	+	0.991763i	$0.540882\pi$
$840$	27.1325	+	15.9275i	0.936159	+	0.549551i
$841$	−28.9967			−0.999887
$842$	6.37061	+	15.4848i	0.219546	+	0.533640i
$843$	5.35765	−	40.6807i	0.184527	−	1.40112i
$844$	−2.60936	+	2.58450i	−0.0898179	+	0.0889621i
$845$	−115.243			−3.96449
$846$	−38.1974	+	4.93218i	−1.31325	+	0.169572i
$847$			16.1497i			0.554910i
$848$	−0.0513820	+	5.36655i	−0.00176446	+	0.184288i
$849$	18.1351	+	2.38839i	0.622396	+	0.0819695i
$850$	17.7321	+	43.1005i	0.608205	+	1.47833i
$851$			9.08955i			0.311586i
$852$	−31.3600	+	23.8234i	−1.07438	+	0.816178i
$853$			16.7758i			0.574392i	0.957872	+	0.287196i	$0.0927232\pi$
$853$			16.7758i			0.574392i	−0.957872	+	0.287196i	$0.907277\pi$
$854$	−15.1031	+	6.21360i	−0.516818	+	0.212625i
$855$	4.03430	+	1.08139i	0.137970	+	0.0369828i
$856$	13.7300	+	5.80301i	0.469282	+	0.198343i
$857$		−	33.5867i		−	1.14730i	−0.819100	−	0.573650i	$-0.805527\pi$
$857$		−	33.5867i		−	1.14730i	0.819100	−	0.573650i	$-0.194473\pi$
$858$	23.8168	−	6.31945i	0.813093	−	0.215742i
$859$	14.2245			0.485332			0.242666	−	0.970110i	$-0.421978\pi$
$859$	14.2245			0.485332			0.242666	+	0.970110i	$0.421978\pi$
$860$	−36.3792	+	36.0326i	−1.24052	+	1.22870i
$861$	10.4146	+	1.37160i	0.354927	+	0.0467439i
$862$	−49.9218	+	20.5384i	−1.70034	+	0.699541i
$863$	−4.22578			−0.143847			−0.0719237	−	0.997410i	$-0.522914\pi$
$863$	−4.22578			−0.143847			−0.0719237	+	0.997410i	$0.522914\pi$
$864$	0.355881	−	29.3917i	0.0121073	−	0.999927i
$865$	36.6197			1.24511
$866$	29.3398	−	12.0708i	0.997007	−	0.410181i
$867$	6.40002	+	0.842882i	0.217356	+	0.0286258i
$868$	−7.91326	+	7.83786i	−0.268594	+	0.266034i
$869$	9.34367			0.316962
$870$	0.473708	−	0.125692i	0.0160602	−	0.00426134i
$871$			50.0095i			1.69451i
$872$	1.52231	+	0.643407i	0.0515520	+	0.0217885i
$873$	−38.4246	−	10.2997i	−1.30047	−	0.348591i
$874$	−0.520484	+	0.214133i	−0.0176056	+	0.00724317i
$875$			14.3767i			0.486020i
$876$	−29.9160	+	22.7264i	−1.01077	+	0.767854i
$877$		−	6.03973i		−	0.203947i	−0.994787	−	0.101974i	$-0.967484\pi$
$877$		−	6.03973i		−	0.203947i	0.994787	−	0.101974i	$-0.0325157\pi$
$878$	10.3116	+	25.0640i	0.348001	+	0.845869i
$879$	5.32402	+	0.701173i	0.179575	+	0.0236500i
$880$	−20.7674	−	0.198838i	−0.700070	−	0.00670282i
$881$			50.7576i			1.71007i	0.518573	+	0.855033i	$0.326463\pi$
$881$			50.7576i			1.71007i	−0.518573	+	0.855033i	$0.673537\pi$
$882$	−15.2740	+	1.97223i	−0.514303	+	0.0664085i
$883$	35.1212			1.18192			0.590961	−	0.806700i	$-0.298749\pi$
$883$	35.1212			1.18192			0.590961	+	0.806700i	$0.298749\pi$
$884$	43.8487	−	43.4309i	1.47479	−	1.46074i
$885$	3.86937	−	29.3802i	0.130068	−	0.987605i
$886$	17.2421	+	41.9095i	0.579259	+	1.40798i
$887$	22.6297			0.759833			0.379916	−	0.925021i	$-0.375953\pi$
$887$	22.6297			0.759833			0.379916	+	0.925021i	$0.375953\pi$
$888$	38.4018	+	22.5429i	1.28868	+	0.756489i
$889$	39.1630			1.31349
$890$	30.9112	+	75.1344i	1.03615	+	2.51851i
$891$	6.68082	−	11.5665i	0.223816	−	0.387494i
$892$	−15.0083	−	15.1527i	−0.502515	−	0.507349i
$893$	3.61274			0.120896
$894$	−13.7058	+	3.63662i	−0.458389	+	0.121627i
$895$		−	78.9095i		−	2.63765i
$896$	−8.26839	+	19.0524i	−0.276227	+	0.636495i
$897$	1.53291	−	11.6394i	0.0511824	−	0.388629i
$898$	−14.9239	−	36.2749i	−0.498018	−	1.21051i
$899$			0.173500i			0.00578656i
$900$	37.7184	−	21.5320i	1.25728	−	0.717733i
$901$			6.10833i			0.203498i
$902$	−6.41264	+	2.63824i	−0.213517	+	0.0878437i
$903$	−3.03830	+	23.0698i	−0.101108	+	0.767716i
$904$	47.5940	+	20.1157i	1.58295	+	0.669038i
$905$			9.95203i			0.330817i
$906$	−2.36337	−	8.90711i	−0.0785178	−	0.295919i
$907$	−33.3651			−1.10787			−0.553935	−	0.832560i	$-0.686875\pi$
$907$	−33.3651			−1.10787			−0.553935	+	0.832560i	$0.686875\pi$
$908$	4.71871	+	4.76410i	0.156596	+	0.158102i
$909$	−28.9559	−	7.76160i	−0.960406	−	0.257436i
$910$	56.9305	−	23.4219i	1.88723	−	0.776428i
$911$	−10.5367			−0.349096			−0.174548	−	0.984649i	$-0.555846\pi$
$911$	−10.5367			−0.349096			−0.174548	+	0.984649i	$0.555846\pi$
$912$	−0.386170	+	2.73002i	−0.0127874	+	0.0904001i
$913$	18.3233			0.606414
$914$	7.77461	−	3.19857i	0.257161	−	0.105799i
$915$	−4.97703	+	37.7907i	−0.164536	+	1.24932i
$916$	−33.1167	−	33.4353i	−1.09421	−	1.10473i
$917$	−13.5533			−0.447569
$918$	0.0847559	−	33.4552i	0.00279736	−	1.10419i
$919$		−	35.3828i		−	1.16717i	−0.812052	−	0.583585i	$-0.801650\pi$
$919$		−	35.3828i		−	1.16717i	0.812052	−	0.583585i	$-0.198350\pi$
$920$	−3.85216	+	9.11426i	−0.127002	+	0.300488i
$921$	−38.1131	−	5.01949i	−1.25587	−	0.165398i
$922$	−37.8778	+	15.5834i	−1.24744	+	0.513211i
$923$			77.0586i			2.53642i
$924$	−7.51539	+	5.70926i	−0.247238	+	0.187821i
$925$			65.7956i			2.16335i
$926$	−5.66609	−	13.7723i	−0.186199	−	0.452586i
$927$	−6.47303	+	24.1487i	−0.212602	+	0.793146i
$928$	0.120225	+	0.300365i	0.00394656	+	0.00985998i
$929$		−	34.3275i		−	1.12625i	−0.826372	−	0.563124i	$-0.809599\pi$
$929$		−	34.3275i		−	1.12625i	0.826372	−	0.563124i	$-0.190401\pi$
$930$	6.66685	+	25.1261i	0.218614	+	0.823917i
$931$	1.44463			0.0473457
$932$	−22.2637	−	22.4779i	−0.729272	−	0.736288i
$933$	−38.8452	−	5.11590i	−1.27173	−	0.167487i
$934$	−5.77278	−	14.0316i	−0.188891	−	0.459129i
$935$	−23.6380			−0.773045
$936$	−45.3728	−	35.3431i	−1.48306	−	1.15522i
$937$	13.5318			0.442065			0.221033	−	0.975266i	$-0.429057\pi$
$937$	13.5318			0.442065			0.221033	+	0.975266i	$0.429057\pi$
$938$	−7.28784	−	17.7142i	−0.237956	−	0.578389i
$939$	−54.6363	−	7.19559i	−1.78299	−	0.234819i
$940$	45.1272	−	44.6972i	1.47189	−	1.45786i
$941$	24.9448			0.813176			0.406588	−	0.913612i	$-0.366718\pi$
$941$	24.9448			0.813176			0.406588	+	0.913612i	$0.366718\pi$
$942$	4.44429	+	16.7497i	0.144803	+	0.545735i
$943$			3.30370i			0.107583i
$944$	19.5615	+	0.187292i	0.636673	+	0.00609583i
$945$	12.7746	−	30.8285i	0.415559	−	1.00285i
$946$	−5.84409	−	14.2050i	−0.190008	−	0.461843i
$947$		−	19.8058i		−	0.643602i	−0.946807	−	0.321801i	$-0.895712\pi$
$947$		−	19.8058i		−	0.643602i	0.946807	−	0.321801i	$-0.104288\pi$
$948$	−13.1925	−	17.3660i	−0.428474	−	0.564022i
$949$			73.5102i			2.38624i
$950$	−3.76758	+	1.55003i	−0.122236	+	0.0502895i
$951$	9.63122	+	1.26843i	0.312314	+	0.0411317i
$952$	−9.20280	+	21.7740i	−0.298265	+	0.705699i
$953$			2.99094i			0.0968862i	0.998826	+	0.0484431i	$0.0154260\pi$
$953$			2.99094i			0.0968862i	−0.998826	+	0.0484431i	$0.984574\pi$
$954$	5.64547	−	0.728963i	0.182779	−	0.0236010i
$955$	−14.9222			−0.482872
$956$	−9.64114	+	9.54927i	−0.311817	+	0.308845i
$957$	−0.0191969	+	0.145763i	−0.000620549	+	0.00471184i
$958$	−34.1447	+	14.0475i	−1.10316	+	0.453855i
$959$	−18.1671			−0.586646
$960$	28.9525	+	38.8789i	0.934437	+	1.25481i
$961$	21.7973			0.703140
$962$	80.5761	−	33.1500i	2.59788	−	1.06880i
$963$	4.09340	−	15.2711i	0.131908	−	0.492103i
$964$	−8.85143	+	8.76708i	−0.285085	+	0.282369i
$965$	−30.7530			−0.989974
$966$	1.15322	+	4.34627i	0.0371042	+	0.139839i
$967$		−	47.2836i		−	1.52054i	−0.649608	−	0.760269i	$-0.725067\pi$
$967$		−	47.2836i		−	1.52054i	0.649608	−	0.760269i	$-0.274933\pi$
$968$	−9.68696	+	22.9195i	−0.311351	+	0.736661i
$969$	−0.409758	+	3.11130i	−0.0131633	+	0.0999494i
$970$	60.6709	−	24.9607i	1.94802	−	0.801441i
$971$		−	46.8564i		−	1.50369i	−0.659339	−	0.751846i	$-0.729164\pi$
$971$		−	46.8564i		−	1.50369i	0.659339	−	0.751846i	$-0.270836\pi$
$972$	−30.9302	+	3.91418i	−0.992088	+	0.125547i
$973$		−	8.35215i		−	0.267758i
$974$	4.58465	+	11.1437i	0.146902	+	0.357067i
$975$	11.0961	−	84.2532i	0.355361	−	2.69826i
$976$	−25.1613	−	0.240907i	−0.805393	−	0.00771123i
$977$		−	13.1675i		−	0.421267i	−0.977565	−	0.210633i	$-0.932447\pi$
$977$		−	13.1675i		−	0.421267i	0.977565	−	0.210633i	$-0.0675527\pi$
$978$	45.9023	−	12.1795i	1.46779	−	0.389458i
$979$	−24.3720			−0.778931
$980$	18.0450	−	17.8731i	0.576427	−	0.570935i
$981$	0.453855	−	1.69318i	0.0144905	−	0.0540590i
$982$	−2.55857	−	6.21900i	−0.0816472	−	0.198456i
$983$	35.2112			1.12306			0.561531	−	0.827455i	$-0.310212\pi$
$983$	35.2112			1.12306			0.561531	+	0.827455i	$0.310212\pi$
$984$	13.9575	+	8.19346i	0.444950	+	0.261198i
$985$	−32.4869			−1.03512
$986$	0.140103	+	0.340542i	0.00446179	+	0.0108451i
$987$	3.76890	−	28.6174i	0.119966	−	0.910900i
$988$	3.79646	+	3.83298i	0.120781	+	0.121943i
$989$	−7.31819			−0.232705
$990$	2.82094	+	21.8468i	0.0896553	+	0.694338i
$991$			44.9220i			1.42700i	0.700658	+	0.713498i	$0.252890\pi$
$991$			44.9220i			1.42700i	−0.700658	+	0.713498i	$0.747110\pi$
$992$	−15.9318	+	6.37686i	−0.505834	+	0.202466i
$993$	−29.3756	−	3.86876i	−0.932206	−	0.122771i
$994$	−11.2297	−	27.2955i	−0.356184	−	0.865759i
$995$			13.0661i			0.414224i
$996$	−25.8712	−	34.0556i	−0.819759	−	1.07909i
$997$			14.1137i			0.446985i	0.974706	+	0.223493i	$0.0717459\pi$
$997$			14.1137i			0.446985i	−0.974706	+	0.223493i	$0.928254\pi$
$998$	26.7676	−	11.0125i	0.847314	−	0.348595i
$999$	18.0805	−	43.6329i	0.572042	−	1.38048i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	552.2.j.d.323.8	yes	42
3.2	odd	2		552.2.j.c.323.35	✓	42
4.3	odd	2		2208.2.j.d.47.40		42
8.3	odd	2		552.2.j.c.323.36	yes	42
8.5	even	2		2208.2.j.c.47.40		42
12.11	even	2		2208.2.j.c.47.39		42
24.5	odd	2		2208.2.j.d.47.39		42
24.11	even	2	inner	552.2.j.d.323.7	yes	42

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
552.2.j.c.323.35	✓	42	3.2	odd	2
552.2.j.c.323.36	yes	42	8.3	odd	2
552.2.j.d.323.7	yes	42	24.11	even	2	inner
552.2.j.d.323.8	yes	42	1.1	even	1	trivial
2208.2.j.c.47.39		42	12.11	even	2
2208.2.j.c.47.40		42	8.5	even	2
2208.2.j.d.47.39		42	24.5	odd	2
2208.2.j.d.47.40		42	4.3	odd	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 $\F_{q}$

Level:	\( N \)	\(=\)	\( 552 = 2^{3} \cdot 3 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	552.j (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.30785 + 0.538067i) q^{2} +(-1.71722 - 0.226158i) q^{3} +(1.42097 - 1.40743i) q^{4} +3.49837 q^{5} +(2.36757 - 0.628199i) q^{6} +1.83575i q^{7} +(-1.10113 + 2.60529i) q^{8} +(2.89771 + 0.776727i) q^{9} +O(q^{10})\)	\(q+(-1.30785 + 0.538067i) q^{2} +(-1.71722 - 0.226158i) q^{3} +(1.42097 - 1.40743i) q^{4} +3.49837 q^{5} +(2.36757 - 0.628199i) q^{6} +1.83575i q^{7} +(-1.10113 + 2.60529i) q^{8} +(2.89771 + 0.776727i) q^{9} +(-4.57536 + 1.88236i) q^{10} -1.48415i q^{11} +(-2.75842 + 2.09550i) q^{12} +6.77805i q^{13} +(-0.987759 - 2.40090i) q^{14} +(-6.00748 - 0.791185i) q^{15} +(0.0382962 - 3.99982i) q^{16} -4.55269i q^{17} +(-4.20771 + 0.543314i) q^{18} +0.397968 q^{19} +(4.97107 - 4.92370i) q^{20} +(0.415171 - 3.15240i) q^{21} +(0.798571 + 1.94105i) q^{22} +1.00000 q^{23} +(2.48009 - 4.22483i) q^{24} +7.23861 q^{25} +(-3.64705 - 8.86470i) q^{26} +(-4.80034 - 1.98915i) q^{27} +(2.58369 + 2.60855i) q^{28} +0.0571930 q^{29} +(8.28262 - 2.19767i) q^{30} +3.03359i q^{31} +(2.10208 + 5.25178i) q^{32} +(-0.335652 + 2.54861i) q^{33} +(2.44965 + 5.95425i) q^{34} +6.42215i q^{35} +(5.21073 - 2.97461i) q^{36} +9.08955i q^{37} +(-0.520484 + 0.214133i) q^{38} +(1.53291 - 11.6394i) q^{39} +(-3.85216 + 9.11426i) q^{40} +3.30370i q^{41} +(1.15322 + 4.34627i) q^{42} -7.31819 q^{43} +(-2.08883 - 2.10892i) q^{44} +(10.1372 + 2.71728i) q^{45} +(-1.30785 + 0.538067i) q^{46} +9.07796 q^{47} +(-0.970354 + 6.85991i) q^{48} +3.63001 q^{49} +(-9.46704 + 3.89486i) q^{50} +(-1.02963 + 7.81798i) q^{51} +(9.53961 + 9.63139i) q^{52} -1.34170 q^{53} +(7.34845 + 0.0186167i) q^{54} -5.19210i q^{55} +(-4.78266 - 2.02140i) q^{56} +(-0.683399 - 0.0900036i) q^{57} +(-0.0748001 + 0.0307737i) q^{58} +4.89061i q^{59} +(-9.64997 + 7.33085i) q^{60} -6.29061i q^{61} +(-1.63228 - 3.96750i) q^{62} +(-1.42588 + 5.31947i) q^{63} +(-5.57503 - 5.73751i) q^{64} +23.7121i q^{65} +(-0.932340 - 3.51382i) q^{66} +7.37815 q^{67} +(-6.40758 - 6.46922i) q^{68} +(-1.71722 - 0.226158i) q^{69} +(-3.45555 - 8.39924i) q^{70} +11.3688 q^{71} +(-5.21434 + 6.69408i) q^{72} +10.8453 q^{73} +(-4.89079 - 11.8878i) q^{74} +(-12.4303 - 1.63707i) q^{75} +(0.565499 - 0.560111i) q^{76} +2.72453 q^{77} +(4.25797 + 16.0475i) q^{78} +6.29565i q^{79} +(0.133974 - 13.9928i) q^{80} +(7.79339 + 4.50145i) q^{81} +(-1.77761 - 4.32076i) q^{82} +12.3460i q^{83} +(-3.84683 - 5.06378i) q^{84} -15.9270i q^{85} +(9.57113 - 3.93768i) q^{86} +(-0.0982131 - 0.0129347i) q^{87} +(3.86663 + 1.63424i) q^{88} -16.4215i q^{89} +(-14.7201 + 1.90071i) q^{90} -12.4428 q^{91} +(1.42097 - 1.40743i) q^{92} +(0.686071 - 5.20935i) q^{93} +(-11.8727 + 4.88456i) q^{94} +1.39224 q^{95} +(-2.42201 - 9.49389i) q^{96} -13.2603 q^{97} +(-4.74752 + 1.95319i) q^{98} +(1.15278 - 4.30062i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 42 q + 2 q^{3} + 4 q^{4} + 8 q^{5} + 4 q^{6} - 9 q^{8} + 2 q^{9}+O(q^{10}) \) 42 * q + 2 * q^3 + 4 * q^4 + 8 * q^5 + 4 * q^6 - 9 * q^8 + 2 * q^9	\( 42 q + 2 q^{3} + 4 q^{4} + 8 q^{5} + 4 q^{6} - 9 q^{8} + 2 q^{9} - 4 q^{10} - 21 q^{12} - 4 q^{14} - 8 q^{15} - 12 q^{16} - 11 q^{18} + 4 q^{19} - 2 q^{20} + 8 q^{21} + 18 q^{22} + 42 q^{23} + 28 q^{24} + 22 q^{25} + 11 q^{26} - 16 q^{27} + 6 q^{28} + 2 q^{30} - 20 q^{32} + 12 q^{33} + 14 q^{34} - 24 q^{36} - 22 q^{38} + 8 q^{39} + 4 q^{40} - 44 q^{42} + 28 q^{43} + 56 q^{44} - 8 q^{45} + 30 q^{48} - 50 q^{49} + 20 q^{50} + 28 q^{51} - q^{52} + 24 q^{53} + 52 q^{54} - 34 q^{56} - 8 q^{57} - 21 q^{58} - 42 q^{60} - 79 q^{62} - 16 q^{63} + 7 q^{64} - 62 q^{66} - 4 q^{67} + 20 q^{68} + 2 q^{69} - 8 q^{70} + 22 q^{72} + 4 q^{73} + 36 q^{74} - 6 q^{75} + 14 q^{76} + 32 q^{77} + 27 q^{78} - 52 q^{80} + 18 q^{81} + 11 q^{82} - 80 q^{84} - 28 q^{86} - 48 q^{87} - 38 q^{88} - 46 q^{90} - 8 q^{91} + 4 q^{92} - 22 q^{93} + q^{94} - 16 q^{95} + 9 q^{96} + 20 q^{97} + 64 q^{98}+O(q^{100}) \) 42 * q + 2 * q^3 + 4 * q^4 + 8 * q^5 + 4 * q^6 - 9 * q^8 + 2 * q^9 - 4 * q^10 - 21 * q^12 - 4 * q^14 - 8 * q^15 - 12 * q^16 - 11 * q^18 + 4 * q^19 - 2 * q^20 + 8 * q^21 + 18 * q^22 + 42 * q^23 + 28 * q^24 + 22 * q^25 + 11 * q^26 - 16 * q^27 + 6 * q^28 + 2 * q^30 - 20 * q^32 + 12 * q^33 + 14 * q^34 - 24 * q^36 - 22 * q^38 + 8 * q^39 + 4 * q^40 - 44 * q^42 + 28 * q^43 + 56 * q^44 - 8 * q^45 + 30 * q^48 - 50 * q^49 + 20 * q^50 + 28 * q^51 - q^52 + 24 * q^53 + 52 * q^54 - 34 * q^56 - 8 * q^57 - 21 * q^58 - 42 * q^60 - 79 * q^62 - 16 * q^63 + 7 * q^64 - 62 * q^66 - 4 * q^67 + 20 * q^68 + 2 * q^69 - 8 * q^70 + 22 * q^72 + 4 * q^73 + 36 * q^74 - 6 * q^75 + 14 * q^76 + 32 * q^77 + 27 * q^78 - 52 * q^80 + 18 * q^81 + 11 * q^82 - 80 * q^84 - 28 * q^86 - 48 * q^87 - 38 * q^88 - 46 * q^90 - 8 * q^91 + 4 * q^92 - 22 * q^93 + q^94 - 16 * q^95 + 9 * q^96 + 20 * q^97 + 64 * q^98

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