LMFDB - Embedded newform 968.2.k.g.699.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [968,2,Mod(403,968)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(968, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([5, 5, 7]))

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

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

chi := DirichletCharacter("968.403");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 968 = 2^{3} \cdot 11^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	968.k (of order $10$, degree $4$, not minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$7.72951891566$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$8$ over $\Q(\zeta_{10})$
Twist minimal:	no (minimal twist has level 88)
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			699.5
Character	$\chi$	$=$	968.699
Dual form			968.2.k.g.475.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.405150 - 1.35494i) q^{2} +(-0.335106 - 0.243469i) q^{3} +(-1.67171 - 1.09791i) q^{4} +(-2.51626 - 0.817582i) q^{5} +(-0.465653 + 0.355406i) q^{6} +(-2.66220 + 1.93420i) q^{7} +(-2.16488 + 1.82024i) q^{8} +(-0.874032 - 2.68999i) q^{9} +(-2.12723 + 3.07813i) q^{10} +(0.292893 + 0.774923i) q^{12} +(-0.421201 - 1.29632i) q^{13} +(1.54213 + 4.39075i) q^{14} +(0.644157 + 0.886607i) q^{15} +(1.58921 + 3.67075i) q^{16} +(5.22148 + 1.69656i) q^{17} +(-3.99889 + 0.0944070i) q^{18} +(1.33669 - 1.83979i) q^{19} +(3.30882 + 4.12937i) q^{20} +1.36303 q^{21} +6.38741i q^{23} +(1.16864 - 0.0828919i) q^{24} +(1.61803 + 1.17557i) q^{25} +(-1.92709 + 0.0454952i) q^{26} +(-0.746033 + 2.29605i) q^{27} +(6.57398 - 0.310574i) q^{28} +(5.32440 - 3.86840i) q^{29} +(1.46228 - 0.513584i) q^{30} +(-1.04227 + 0.338654i) q^{31} +(5.61750 - 0.666071i) q^{32} +(4.41421 - 6.38741i) q^{34} +(8.28015 - 2.69038i) q^{35} +(-1.49223 + 5.45649i) q^{36} +(2.84345 + 3.91367i) q^{37} +(-1.95124 - 2.55652i) q^{38} +(-0.174467 + 0.536955i) q^{39} +(6.93561 - 2.81023i) q^{40} +(-5.90043 + 8.12124i) q^{41} +(0.552234 - 1.84683i) q^{42} +6.43215i q^{43} +7.48331i q^{45} +(8.65453 + 2.58786i) q^{46} +(0.361160 - 1.61701i) q^{48} +(1.18305 - 3.64105i) q^{49} +(2.24837 - 1.71605i) q^{50} +(-1.33669 - 1.83979i) q^{51} +(-0.719116 + 2.62951i) q^{52} +(-7.11706 + 2.31247i) q^{53} +(2.80875 + 1.94107i) q^{54} +(2.24264 - 9.03316i) q^{56} +(-0.895864 + 0.291084i) q^{57} +(-3.08426 - 8.78150i) q^{58} +(-2.62335 + 1.90598i) q^{59} +(-0.103432 - 2.18937i) q^{60} +(2.03374 - 6.25920i) q^{61} +(0.0365790 + 1.54941i) q^{62} +(7.52983 + 5.47074i) q^{63} +(1.37345 - 7.88122i) q^{64} +3.60625i q^{65} -6.07107 q^{67} +(-6.86612 - 8.56884i) q^{68} +(1.55513 - 2.14046i) q^{69} +(-0.290597 - 12.3091i) q^{70} +(-6.07479 - 1.97382i) q^{71} +(6.78861 + 4.23258i) q^{72} +(-0.553674 - 0.762067i) q^{73} +(6.45480 - 2.26707i) q^{74} +(-0.255998 - 0.787881i) q^{75} +(-4.25447 + 1.60804i) q^{76} +(0.656854 + 0.453939i) q^{78} +(2.87614 + 8.85185i) q^{79} +(-0.997718 - 10.5359i) q^{80} +(-6.05572 + 4.39974i) q^{81} +(8.61321 + 11.2850i) q^{82} +(4.32561 + 1.40548i) q^{83} +(-2.27860 - 1.49648i) q^{84} +(-11.7515 - 8.53797i) q^{85} +(8.71516 + 2.60599i) q^{86} -2.72607 q^{87} -10.6569 q^{89} +(10.1394 + 3.03187i) q^{90} +(3.62867 + 2.63638i) q^{91} +(7.01277 - 10.6779i) q^{92} +(0.431722 + 0.140275i) q^{93} +(-4.86763 + 3.53654i) q^{95} +(-2.04463 - 1.14448i) q^{96} +(2.31308 + 7.11893i) q^{97} +(-4.45408 - 3.07813i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q + 8 q^{3} + 32 q^{12} + 8 q^{14} + 24 q^{16} + 16 q^{25} - 24 q^{26} + 8 q^{27} + 96 q^{34} + 16 q^{36} + 8 q^{38} + 24 q^{42} - 24 q^{48} - 8 q^{49} - 64 q^{56} - 16 q^{58} + 8 q^{59} - 56 q^{60}+ \cdots + 8 q^{97}+O(q^{100}) $ 32 * q + 8 * q^3 + 32 * q^12 + 8 * q^14 + 24 * q^16 + 16 * q^25 - 24 * q^26 + 8 * q^27 + 96 * q^34 + 16 * q^36 + 8 * q^38 + 24 * q^42 - 24 * q^48 - 8 * q^49 - 64 * q^56 - 16 * q^58 + 8 * q^59 - 56 * q^60 + 32 * q^67 + 56 * q^70 - 16 * q^75 - 160 * q^78 - 56 * q^80 + 8 * q^81 + 8 * q^82 - 64 * q^86 - 160 * q^89 - 32 * q^91 + 56 * q^92 + 8 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/968\mathbb{Z}\right)^\times$.

$n$	$485$	$727$	$849$
$\chi(n)$	$-1$	$-1$	$e\left(\frac{9}{10}\right)$

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 $

$2$	0.405150	−	1.35494i	0.286484	−	0.958085i
$2$	0.405150	−	1.35494i	0.286484	−	0.958085i
$3$	−0.335106	−	0.243469i	−0.193473	−	0.140567i	0.486831	−	0.873496i	$-0.338153\pi$
$3$	−0.335106	−	0.243469i	−0.193473	−	0.140567i	−0.680305	+	0.732929i	$0.738153\pi$
$4$	−1.67171	−	1.09791i	−0.835853	−	0.548953i
$5$	−2.51626	−	0.817582i	−1.12531	−	0.365634i	−0.313515	−	0.949583i	$-0.601507\pi$
$5$	−2.51626	−	0.817582i	−1.12531	−	0.365634i	−0.811790	+	0.583949i	$0.801507\pi$
$6$	−0.465653	+	0.355406i	−0.190102	+	0.145094i
$7$	−2.66220	+	1.93420i	−1.00622	+	0.731059i	−0.963412	−	0.268025i	$-0.913629\pi$
$7$	−2.66220	+	1.93420i	−1.00622	+	0.731059i	−0.0428042	+	0.999083i	$0.513629\pi$
$8$	−2.16488	+	1.82024i	−0.765402	+	0.643552i
$9$	−0.874032	−	2.68999i	−0.291344	−	0.896665i
$10$	−2.12723	+	3.07813i	−0.672691	+	0.973390i
$11$		0			0
$11$		0			0
$12$	0.292893	+	0.774923i	0.0845510	+	0.223701i
$13$	−0.421201	−	1.29632i	−0.116820	−	0.359535i	0.875502	−	0.483214i	$-0.160531\pi$
$13$	−0.421201	−	1.29632i	−0.116820	−	0.359535i	−0.992322	+	0.123679i	$0.960531\pi$
$14$	1.54213	+	4.39075i	0.412151	+	1.17348i
$15$	0.644157	+	0.886607i	0.166321	+	0.228921i
$16$	1.58921	+	3.67075i	0.397302	+	0.917688i
$17$	5.22148	+	1.69656i	1.26639	+	0.411476i	0.863769	−	0.503888i	$-0.168098\pi$
$17$	5.22148	+	1.69656i	1.26639	+	0.411476i	0.402625	+	0.915365i	$0.368098\pi$
$18$	−3.99889	+	0.0944070i	−0.942546	+	0.0222519i
$19$	1.33669	−	1.83979i	0.306657	−	0.422077i	−0.627678	−	0.778473i	$-0.715994\pi$
$19$	1.33669	−	1.83979i	0.306657	−	0.422077i	0.934335	+	0.356396i	$0.115994\pi$
$20$	3.30882	+	4.12937i	0.739875	+	0.923356i
$21$	1.36303			0.297439
$22$		0			0
$23$			6.38741i			1.33187i	0.746011	+	0.665933i	$0.231967\pi$
$23$			6.38741i			1.33187i	−0.746011	+	0.665933i	$0.768033\pi$
$24$	1.16864	−	0.0828919i	0.238547	−	0.0169202i
$25$	1.61803	+	1.17557i	0.323607	+	0.235114i
$26$	−1.92709	+	0.0454952i	−0.377933	+	0.00892235i
$27$	−0.746033	+	2.29605i	−0.143574	+	0.441876i
$28$	6.57398	−	0.310574i	1.24237	−	0.0586930i
$29$	5.32440	−	3.86840i	0.988715	−	0.718344i	0.0290761	−	0.999577i	$-0.490743\pi$
$29$	5.32440	−	3.86840i	0.988715	−	0.718344i	0.959639	+	0.281233i	$0.0907435\pi$
$30$	1.46228	−	0.513584i	0.266974	−	0.0937672i
$31$	−1.04227	+	0.338654i	−0.187197	+	0.0608240i	−0.401115	−	0.916028i	$-0.631377\pi$
$31$	−1.04227	+	0.338654i	−0.187197	+	0.0608240i	0.213918	+	0.976852i	$0.431377\pi$
$32$	5.61750	−	0.666071i	0.993044	−	0.117746i
$33$		0			0
$34$	4.41421	−	6.38741i	0.757031	−	1.09543i
$35$	8.28015	−	2.69038i	1.39960	−	0.454758i
$36$	−1.49223	+	5.45649i	−0.248706	+	0.909414i
$37$	2.84345	+	3.91367i	0.467460	+	0.643404i	0.976035	−	0.217614i	$-0.0698275\pi$
$37$	2.84345	+	3.91367i	0.467460	+	0.643404i	−0.508575	+	0.861018i	$0.669827\pi$
$38$	−1.95124	−	2.55652i	−0.316534	−	0.414722i
$39$	−0.174467	+	0.536955i	−0.0279371	+	0.0859816i
$40$	6.93561	−	2.81023i	1.09662	−	0.444336i
$41$	−5.90043	+	8.12124i	−0.921492	+	1.26832i	0.0415954	+	0.999135i	$0.486756\pi$
$41$	−5.90043	+	8.12124i	−0.921492	+	1.26832i	−0.963087	+	0.269190i	$0.913244\pi$
$42$	0.552234	−	1.84683i	0.0852115	−	0.284971i
$43$			6.43215i			0.980894i	0.871471	+	0.490447i	$0.163166\pi$
$43$			6.43215i			0.980894i	−0.871471	+	0.490447i	$0.836834\pi$
$44$		0			0
$45$			7.48331i			1.11555i
$46$	8.65453	+	2.58786i	1.27604	+	0.381559i
$47$		0			0		−0.809017	−	0.587785i	$-0.800000\pi$
$47$		0			0		0.809017	+	0.587785i	$0.200000\pi$
$48$	0.361160	−	1.61701i	0.0521290	−	0.233396i
$49$	1.18305	−	3.64105i	0.169007	−	0.520150i
$50$	2.24837	−	1.71605i	0.317968	−	0.242686i
$51$	−1.33669	−	1.83979i	−0.187174	−	0.257623i
$52$	−0.719116	+	2.62951i	−0.0997234	+	0.364648i
$53$	−7.11706	+	2.31247i	−0.977603	+	0.317642i	−0.753881	−	0.657011i	$-0.771821\pi$
$53$	−7.11706	+	2.31247i	−0.977603	+	0.317642i	−0.223722	+	0.974653i	$0.571821\pi$
$54$	2.80875	+	1.94107i	0.382223	+	0.264147i
$55$		0			0
$56$	2.24264	−	9.03316i	0.299685	−	1.20711i
$57$	−0.895864	+	0.291084i	−0.118660	+	0.0385550i
$58$	−3.08426	−	8.78150i	−0.404983	−	1.15307i
$59$	−2.62335	+	1.90598i	−0.341531	+	0.248137i	−0.745308	−	0.666721i	$-0.767697\pi$
$59$	−2.62335	+	1.90598i	−0.341531	+	0.248137i	0.403776	+	0.914858i	$0.367697\pi$
$60$	−0.103432	−	2.18937i	−0.0133531	−	0.282646i
$61$	2.03374	−	6.25920i	0.260393	−	0.801409i	−0.732325	−	0.680955i	$-0.761565\pi$
$61$	2.03374	−	6.25920i	0.260393	−	0.801409i	0.992719	−	0.120454i	$-0.0384350\pi$
$62$	0.0365790	+	1.54941i	0.00464554	+	0.196776i
$63$	7.52983	+	5.47074i	0.948670	+	0.689249i
$64$	1.37345	−	7.88122i	0.171681	−	0.985153i
$65$			3.60625i			0.447300i
$66$		0			0
$67$	−6.07107			−0.741699			−0.370849	−	0.928693i	$-0.620933\pi$
$67$	−6.07107			−0.741699			−0.370849	+	0.928693i	$0.620933\pi$
$68$	−6.86612	−	8.56884i	−0.832639	−	1.03912i
$69$	1.55513	−	2.14046i	0.187216	−	0.257681i
$70$	−0.290597	−	12.3091i	−0.0347329	−	1.47122i
$71$	−6.07479	−	1.97382i	−0.720945	−	0.234249i	−0.0745119	−	0.997220i	$-0.523740\pi$
$71$	−6.07479	−	1.97382i	−0.720945	−	0.234249i	−0.646433	+	0.762971i	$0.723740\pi$
$72$	6.78861	+	4.23258i	0.800046	+	0.498814i
$73$	−0.553674	−	0.762067i	−0.0648027	−	0.0891932i	0.775386	−	0.631488i	$-0.217556\pi$
$73$	−0.553674	−	0.762067i	−0.0648027	−	0.0891932i	−0.840188	+	0.542295i	$0.817556\pi$
$74$	6.45480	−	2.26707i	0.750355	−	0.263541i
$75$	−0.255998	−	0.787881i	−0.0295601	−	0.0909767i
$76$	−4.25447	+	1.60804i	−0.488021	+	0.184455i
$77$		0			0
$78$	0.656854	+	0.453939i	0.0743741	+	0.0513985i
$79$	2.87614	+	8.85185i	0.323591	+	0.995911i	0.972073	+	0.234680i	$0.0754044\pi$
$79$	2.87614	+	8.85185i	0.323591	+	0.995911i	−0.648482	+	0.761230i	$0.724596\pi$
$80$	−0.997718	−	10.5359i	−0.111548	−	1.17795i
$81$	−6.05572	+	4.39974i	−0.672858	+	0.488860i
$82$	8.61321	+	11.2850i	0.951170	+	1.24622i
$83$	4.32561	+	1.40548i	0.474798	+	0.154271i	0.536634	−	0.843815i	$-0.319696\pi$
$83$	4.32561	+	1.40548i	0.474798	+	0.154271i	−0.0618362	+	0.998086i	$0.519696\pi$
$84$	−2.27860	−	1.49648i	−0.248615	−	0.163280i
$85$	−11.7515	−	8.53797i	−1.27463	−	0.926073i
$86$	8.71516	+	2.60599i	0.939780	+	0.281011i
$87$	−2.72607			−0.292265
$88$		0			0
$89$	−10.6569			−1.12962			−0.564812	−	0.825220i	$-0.691051\pi$
$89$	−10.6569			−1.12962			−0.564812	+	0.825220i	$0.691051\pi$
$90$	10.1394	+	3.03187i	1.06879	+	0.319587i
$91$	3.62867	+	2.63638i	0.380388	+	0.276368i
$92$	7.01277	−	10.6779i	0.731132	−	1.11325i
$93$	0.431722	+	0.140275i	0.0447675	+	0.0145458i
$94$		0			0
$95$	−4.86763	+	3.53654i	−0.499409	+	0.362842i
$96$	−2.04463	−	1.14448i	−0.208679	−	0.116808i
$97$	2.31308	+	7.11893i	0.234858	+	0.722817i	0.997140	+	0.0755731i	$0.0240786\pi$
$97$	2.31308	+	7.11893i	0.234858	+	0.722817i	−0.762283	+	0.647244i	$0.775921\pi$
$98$	−4.45408	−	3.07813i	−0.449930	−	0.310938i
$99$		0			0
$100$	−1.41421	−	3.74166i	−0.141421	−	0.374166i
$101$	−5.33108	−	16.4074i	−0.530462	−	1.63259i	−0.753255	−	0.657729i	$-0.771517\pi$
$101$	−5.33108	−	16.4074i	−0.530462	−	1.63259i	0.222792	−	0.974866i	$-0.428483\pi$
$102$	−3.03436	+	1.06574i	−0.300447	+	0.105524i
$103$	10.6191	+	14.6160i	1.04633	+	1.44015i	0.891946	+	0.452143i	$0.149340\pi$
$103$	10.6191	+	14.6160i	1.04633	+	1.44015i	0.154387	+	0.988010i	$0.450660\pi$
$104$	3.27147	+	2.03970i	0.320794	+	0.200009i
$105$	−3.42975	−	1.11439i	−0.334709	−	0.108754i
$106$	0.249777	+	10.5801i	0.0242605	+	1.02763i
$107$	5.11741	−	7.04351i	0.494719	−	0.680922i	−0.486531	−	0.873663i	$-0.661738\pi$
$107$	5.11741	−	7.04351i	0.494719	−	0.680922i	0.981250	+	0.192741i	$0.0617378\pi$
$108$	3.76800	−	3.01926i	0.362576	−	0.290528i
$109$	2.72607			0.261110			0.130555	−	0.991441i	$-0.458324\pi$
$109$	2.72607			0.261110			0.130555	+	0.991441i	$0.458324\pi$
$110$		0			0
$111$		−	2.00378i		−	0.190191i
$112$	−11.3308	−	6.69842i	−1.07066	−	0.632941i
$113$	−4.99291	−	3.62756i	−0.469693	−	0.341252i	0.327629	−	0.944807i	$-0.393751\pi$
$113$	−4.99291	−	3.62756i	−0.469693	−	0.341252i	−0.797322	+	0.603555i	$0.793751\pi$
$114$	0.0314409	+	1.33177i	0.00294471	+	0.124732i
$115$	5.22223	−	16.0724i	0.486976	−	1.49876i
$116$	−13.1480	+	0.621149i	−1.22076	+	0.0576722i
$117$	−3.11896	+	2.26606i	−0.288348	+	0.209497i
$118$	1.51963	+	4.32668i	0.139893	+	0.398303i
$119$	−17.1821	+	5.58280i	−1.57508	+	0.511774i
$120$	−3.00836	−	0.746879i	−0.274625	−	0.0681804i
$121$		0			0
$122$	−7.65685	−	5.29150i	−0.693219	−	0.479070i
$123$	3.95453	−	1.28491i	0.356568	−	0.115856i
$124$	2.11418	+	0.578183i	0.189859	+	0.0519223i
$125$	4.66540	+	6.42137i	0.417286	+	0.574345i
$126$	10.4632	−	7.98597i	0.932138	−	0.711447i
$127$	0.174467	−	0.536955i	0.0154815	−	0.0476470i	−0.943017	−	0.332744i	$-0.892026\pi$
$127$	0.174467	−	0.536955i	0.0154815	−	0.0476470i	0.958499	+	0.285097i	$0.0920257\pi$
$128$	−10.1221	−	5.05401i	−0.894676	−	0.446716i
$129$	1.56603	−	2.15545i	0.137881	−	0.189777i
$130$	4.88624	+	1.46107i	0.428552	+	0.128145i
$131$		−	6.82233i		−	0.596070i	−0.954555	−	0.298035i	$-0.903669\pi$
$131$		−	6.82233i		−	0.596070i	0.954555	−	0.298035i	$-0.0963311\pi$
$132$		0			0
$133$			7.48331i			0.648886i
$134$	−2.45969	+	8.22591i	−0.212485	+	0.710611i
$135$	3.75442	−	5.16752i	0.323129	−	0.444749i
$136$	−14.3920	+	5.83149i	−1.23411	+	0.500046i
$137$	−2.67512	+	8.23316i	−0.228551	+	0.703406i	0.769361	+	0.638814i	$0.220575\pi$
$137$	−2.67512	+	8.23316i	−0.228551	+	0.703406i	−0.997912	+	0.0645922i	$0.979425\pi$
$138$	−2.27012	−	2.97431i	−0.193246	−	0.253190i
$139$	11.5715	+	15.9268i	0.981483	+	1.35090i	0.936027	+	0.351929i	$0.114474\pi$
$139$	11.5715	+	15.9268i	0.981483	+	1.35090i	0.0454561	+	0.998966i	$0.485526\pi$
$140$	−16.7958	−	4.59329i	−1.41950	−	0.388203i
$141$		0			0
$142$	−5.13560	+	7.43126i	−0.430970	+	0.623617i
$143$		0			0
$144$	8.48528	−	7.48331i	0.707107	−	0.623610i
$145$	−16.5603	+	5.38077i	−1.37526	+	0.446848i
$146$	−1.25687	+	0.441442i	−0.104020	+	0.0365340i
$147$	−1.28293	+	0.932102i	−0.105814	+	0.0768785i
$148$	−0.456572	−	9.66435i	−0.0375300	−	0.794405i
$149$	−6.52242	+	20.0739i	−0.534337	+	1.64452i	0.210740	+	0.977542i	$0.432413\pi$
$149$	−6.52242	+	20.0739i	−0.534337	+	1.64452i	−0.745077	+	0.666978i	$0.767587\pi$
$150$	−1.17125	+	0.0276512i	−0.0956319	+	0.00225771i
$151$	10.6488	+	7.73680i	0.866586	+	0.629612i	0.929669	−	0.368396i	$-0.120093\pi$
$151$	10.6488	+	7.73680i	0.866586	+	0.629612i	−0.0630824	+	0.998008i	$0.520093\pi$
$152$	0.455092	+	6.41603i	0.0369128	+	0.520409i
$153$		−	15.5286i		−	1.25541i
$154$		0			0
$155$	2.89949			0.232893
$156$	0.881183	−	0.706082i	0.0705511	−	0.0565318i
$157$	−0.266819	+	0.367244i	−0.0212945	+	0.0293093i	−0.819531	−	0.573034i	$-0.805766\pi$
$157$	−0.266819	+	0.367244i	−0.0212945	+	0.0293093i	0.798237	+	0.602343i	$0.205766\pi$
$158$	13.1590	−	0.310661i	1.04687	−	0.0247149i
$159$	2.94798	+	0.957857i	0.233790	+	0.0759630i
$160$	−14.6797	−	2.91676i	−1.16053	−	0.230590i
$161$	−12.3545	−	17.0045i	−0.973673	−	1.34015i
$162$	3.50789	+	9.98767i	0.275606	+	0.784706i
$163$	−3.96420	−	12.2006i	−0.310500	−	0.955622i	−0.977567	−	0.210624i	$-0.932451\pi$
$163$	−3.96420	−	12.2006i	−0.310500	−	0.955622i	0.667067	−	0.744998i	$-0.267549\pi$
$164$	18.7801	−	7.09822i	1.46648	−	0.554278i
$165$		0			0
$166$	3.65685	−	5.29150i	0.283827	−	0.410700i
$167$	6.76915	+	20.8333i	0.523813	+	1.61213i	0.766652	+	0.642063i	$0.221921\pi$
$167$	6.76915	+	20.8333i	0.523813	+	1.61213i	−0.242840	+	0.970066i	$0.578079\pi$
$168$	−2.95081	+	2.48105i	−0.227660	+	0.191417i
$169$	9.01418	−	6.54918i	0.693398	−	0.503783i
$170$	−16.3295	+	12.4634i	−1.25242	+	0.955899i
$171$	−6.11734	−	1.98764i	−0.467805	−	0.151999i
$172$	7.06189	−	10.7527i	0.538464	−	0.819884i
$173$	−4.41087	−	3.20469i	−0.335353	−	0.243648i	0.407346	−	0.913274i	$-0.366454\pi$
$173$	−4.41087	−	3.20469i	−0.335353	−	0.243648i	−0.742698	+	0.669626i	$0.766454\pi$
$174$	−1.10447	+	3.69365i	−0.0837295	+	0.280015i
$175$	−6.58132			−0.497501
$176$		0			0
$177$	1.34315			0.100957
$178$	−4.31762	+	14.4394i	−0.323620	+	1.08228i
$179$	−7.87005	−	5.71793i	−0.588235	−	0.427378i	0.253448	−	0.967349i	$-0.418435\pi$
$179$	−7.87005	−	5.71793i	−0.588235	−	0.427378i	−0.841684	+	0.539971i	$0.818435\pi$
$180$	8.21597	−	12.5099i	0.612382	−	0.932434i
$181$	2.51626	+	0.817582i	0.187032	+	0.0607704i	0.401036	−	0.916063i	$-0.368650\pi$
$181$	2.51626	+	0.817582i	0.187032	+	0.0607704i	−0.214003	+	0.976833i	$0.568650\pi$
$182$	5.04229	−	3.84849i	0.373759	−	0.285269i
$183$	−2.20544	+	1.60234i	−0.163031	+	0.118449i
$184$	−11.6266	−	13.8280i	−0.857126	−	1.01941i
$185$	−3.95511	−	12.1726i	−0.290785	−	0.894945i
$186$	0.364976	−	0.528123i	0.0267613	−	0.0387239i
$187$		0			0
$188$		0			0
$189$	−2.45494	−	7.55553i	−0.178571	−	0.549584i
$190$	2.81967	+	8.02817i	0.204560	+	0.582425i
$191$	−9.97496	−	13.7294i	−0.721763	−	0.993421i	−0.999463	−	0.0327535i	$-0.989572\pi$
$191$	−9.97496	−	13.7294i	−0.721763	−	0.993421i	0.277701	−	0.960668i	$-0.410428\pi$
$192$	−2.37908	+	2.30665i	−0.171695	+	0.166468i
$193$	−12.2347	−	3.97529i	−0.880672	−	0.286148i	−0.166435	−	0.986052i	$-0.553226\pi$
$193$	−12.2347	−	3.97529i	−0.880672	−	0.286148i	−0.714236	+	0.699905i	$0.753226\pi$
$194$	10.5828	−	0.249843i	0.759803	−	0.0179377i
$195$	0.878009	−	1.20848i	0.0628755	−	0.0865408i
$196$	−5.97524	+	4.78789i	−0.426803	+	0.341992i
$197$	10.4366			0.743574			0.371787	−	0.928318i	$-0.378745\pi$
$197$	10.4366			0.743574			0.371787	+	0.928318i	$0.378745\pi$
$198$		0			0
$199$			21.1660i			1.50042i	0.661200	+	0.750209i	$0.270047\pi$
$199$			21.1660i			1.50042i	−0.661200	+	0.750209i	$0.729953\pi$
$200$	−5.64268	+	0.400237i	−0.398998	+	0.0283010i
$201$	2.03445	+	1.47811i	0.143499	+	0.104258i
$202$	−24.3908	+	0.575827i	−1.71613	+	0.0405150i
$203$	−6.69234	+	20.5969i	−0.469710	+	1.44562i
$204$	0.214632	+	4.54315i	0.0150272	+	0.318084i
$205$	21.4868	−	15.6111i	1.50070	−	1.09032i
$206$	24.1060	−	8.46657i	1.67955	−	0.589894i
$207$	17.1821	−	5.58280i	1.19424	−	0.388031i
$208$	4.08910	−	3.60625i	0.283528	−	0.250049i
$209$		0			0
$210$	−2.89949	+	4.19560i	−0.200084	+	0.289524i
$211$	−8.65123	+	2.81095i	−0.595575	+	0.193514i	−0.591266	−	0.806477i	$-0.701372\pi$
$211$	−8.65123	+	2.81095i	−0.595575	+	0.193514i	−0.00430905	+	0.999991i	$0.501372\pi$
$212$	14.4365	+	3.94808i	0.991503	+	0.271155i
$213$	1.55513	+	2.14046i	0.106556	+	0.146662i
$214$	−7.47020	−	9.78745i	−0.510652	−	0.669056i
$215$	5.25881	−	16.1850i	0.358648	−	1.10381i
$216$	−2.56430	−	6.32865i	−0.174478	−	0.430610i
$217$	2.11970	−	2.91752i	0.143895	−	0.198054i
$218$	1.10447	−	3.69365i	0.0748040	−	0.250166i
$219$			0.390175i			0.0263656i
$220$		0			0
$221$		−	7.48331i		−	0.503382i
$222$	−2.71500	−	0.811833i	−0.182219	−	0.0544867i
$223$	−2.46611	+	3.39431i	−0.165143	+	0.227300i	−0.883566	−	0.468307i	$-0.844864\pi$
$223$	−2.46611	+	3.39431i	−0.165143	+	0.227300i	0.718423	+	0.695606i	$0.244864\pi$
$224$	−13.6666	+	12.6386i	−0.913138	+	0.844451i
$225$	1.74806	−	5.37999i	0.116538	−	0.358666i
$226$	−6.93799	+	5.29537i	−0.461508	+	0.352243i
$227$	7.79079	+	10.7231i	0.517093	+	0.711717i	0.985095	−	0.172010i	$-0.0550262\pi$
$227$	7.79079	+	10.7231i	0.517093	+	0.711717i	−0.468002	+	0.883727i	$0.655026\pi$
$228$	1.81720	+	0.496967i	0.120347	+	0.0329124i
$229$	9.63331	−	3.13005i	0.636587	−	0.206840i	0.0270964	−	0.999633i	$-0.491374\pi$
$229$	9.63331	−	3.13005i	0.636587	−	0.206840i	0.609491	+	0.792793i	$0.291374\pi$
$230$	−19.6613	−	13.5875i	−1.29643	−	0.895934i
$231$		0			0
$232$	−4.48528	+	18.0663i	−0.294473	+	1.18611i
$233$	−7.90907	+	2.56981i	−0.518140	+	0.168354i	−0.556401	−	0.830914i	$-0.687818\pi$
$233$	−7.90907	+	2.56981i	−0.518140	+	0.168354i	0.0382609	+	0.999268i	$0.487818\pi$
$234$	1.80672	+	5.14408i	0.118109	+	0.336279i
$235$		0			0
$236$	6.47806	−	0.306043i	0.421686	−	0.0199217i
$237$	1.19134	−	3.66656i	0.0773856	−	0.238168i
$238$	0.603016	+	25.5425i	0.0390877	+	1.65568i
$239$	4.41087	+	3.20469i	0.285316	+	0.207294i	0.721233	−	0.692693i	$-0.243576\pi$
$239$	4.41087	+	3.20469i	0.285316	+	0.207294i	−0.435917	+	0.899987i	$0.643576\pi$
$240$	−2.23081	+	3.77354i	−0.143998	+	0.243581i
$241$		−	4.54822i		−	0.292977i	−0.989212	−	0.146488i	$-0.953203\pi$
$241$		−	4.54822i		−	0.292977i	0.989212	−	0.146488i	$-0.0467971\pi$
$242$		0			0
$243$	10.3431			0.663513
$244$	−10.2718	+	8.23070i	−0.657586	+	0.526917i
$245$	−5.95372	+	8.19459i	−0.380369	+	0.523533i
$246$	−0.138787	−	5.87872i	−0.00884872	−	0.374814i
$247$	−2.94798	−	0.957857i	−0.187576	−	0.0609470i
$248$	1.63996	−	2.63033i	0.104138	−	0.167026i
$249$	−1.10735	−	1.52413i	−0.0701754	−	0.0965881i
$250$	10.5907	−	3.71970i	0.669817	−	0.235255i
$251$	5.69030	+	17.5130i	0.359169	+	1.10541i	0.953553	+	0.301227i	$0.0973960\pi$
$251$	5.69030	+	17.5130i	0.359169	+	1.10541i	−0.594384	+	0.804182i	$0.702604\pi$
$252$	−6.58132	−	17.4125i	−0.414584	−	1.09689i
$253$		0			0
$254$	−0.656854	−	0.453939i	−0.0412147	−	0.0284827i
$255$	1.85927	+	5.72225i	0.116432	+	0.358341i
$256$	−10.9488	+	11.6672i	−0.684302	+	0.729199i
$257$	−5.24670	+	3.81195i	−0.327280	+	0.237783i	−0.739276	−	0.673403i	$-0.764832\pi$
$257$	−5.24670	+	3.81195i	−0.327280	+	0.237783i	0.411995	+	0.911186i	$0.364832\pi$
$258$	−2.28602	−	2.99515i	−0.142322	−	0.186470i
$259$	−15.1396	−	4.91917i	−0.940732	−	0.305662i
$260$	3.95932	−	6.02860i	0.245547	−	0.373878i
$261$	−15.0597	−	10.9415i	−0.932170	−	0.677261i
$262$	−9.24382	−	2.76407i	−0.571085	−	0.170765i
$263$	−19.1794			−1.18265			−0.591325	−	0.806433i	$-0.701395\pi$
$263$	−19.1794			−1.18265			−0.591325	+	0.806433i	$0.701395\pi$
$264$		0			0
$265$	19.7990			1.21624
$266$	10.1394	+	3.03187i	0.621688	+	0.185896i
$267$	3.57117	+	2.59461i	0.218552	+	0.158788i
$268$	10.1490	+	6.66546i	0.619952	+	0.407158i
$269$	−13.0130	−	4.22819i	−0.793418	−	0.257797i	−0.115859	−	0.993266i	$-0.536962\pi$
$269$	−13.0130	−	4.22819i	−0.793418	−	0.257797i	−0.677559	+	0.735469i	$0.736962\pi$
$270$	−5.48056	−	7.18063i	−0.333536	−	0.436999i
$271$	−10.1920	+	7.40494i	−0.619122	+	0.449818i	−0.852615	−	0.522540i	$-0.824984\pi$
$271$	−10.1920	+	7.40494i	−0.619122	+	0.449818i	0.233493	+	0.972359i	$0.424984\pi$
$272$	2.07036	+	21.8629i	0.125534	+	1.32563i
$273$	−0.574112	−	1.76693i	−0.0347468	−	0.106940i
$274$	10.0716	+	6.96028i	0.608447	+	0.420486i
$275$		0			0
$276$	−4.94975	+	1.87083i	−0.297940	+	0.112611i
$277$	−1.19134	−	3.66656i	−0.0715805	−	0.220302i	0.908866	−	0.417088i	$-0.136949\pi$
$277$	−1.19134	−	3.66656i	−0.0715805	−	0.220302i	−0.980446	+	0.196786i	$0.936949\pi$
$278$	26.2680	−	9.22591i	1.57545	−	0.553334i
$279$	1.82195	+	2.50770i	0.109077	+	0.150132i
$280$	−13.0284	+	20.8962i	−0.778597	+	1.24879i
$281$	−6.11734	−	1.98764i	−0.364930	−	0.118573i	0.120812	−	0.992675i	$-0.461450\pi$
$281$	−6.11734	−	1.98764i	−0.364930	−	0.118573i	−0.485741	+	0.874103i	$0.661450\pi$
$282$		0			0
$283$	1.10735	−	1.52413i	0.0658250	−	0.0906004i	−0.774835	−	0.632163i	$-0.782167\pi$
$283$	1.10735	−	1.52413i	0.0658250	−	0.0906004i	0.840660	+	0.541563i	$0.182167\pi$
$284$	7.98820	+	9.96919i	0.474012	+	0.591562i
$285$	2.49221			0.147626
$286$		0			0
$287$		−	33.0329i		−	1.94987i
$288$	−6.70161	−	14.5289i	−0.394896	−	0.856123i
$289$	10.6322	+	7.72475i	0.625424	+	0.454397i
$290$	0.581193	+	24.6182i	0.0341289	+	1.44563i
$291$	0.958109	−	2.94876i	0.0561653	−	0.172859i
$292$	0.0889034	+	1.88183i	0.00520268	+	0.110126i
$293$	−11.7515	+	8.53797i	−0.686531	+	0.498794i	−0.875518	−	0.483186i	$-0.839480\pi$
$293$	−11.7515	+	8.53797i	−0.686531	+	0.498794i	0.188987	+	0.981980i	$0.439480\pi$
$294$	0.743161	+	2.11593i	0.0433420	+	0.123403i
$295$	8.15932	−	2.65113i	0.475054	−	0.154354i
$296$	−13.2796	−	3.29688i	−0.771859	−	0.191627i
$297$		0			0
$298$	24.5563	+	16.9704i	1.42251	+	0.983070i
$299$	8.28015	−	2.69038i	0.478853	−	0.155589i
$300$	−0.437065	+	1.59817i	−0.0252340	+	0.0922703i
$301$	−12.4411	−	17.1237i	−0.717091	−	0.986991i
$302$	14.7972	−	11.2939i	0.851485	−	0.649889i
$303$	−2.20821	+	6.79616i	−0.126858	+	0.390429i
$304$	8.87770	+	1.98284i	0.509171	+	0.113723i
$305$	−10.2348	+	14.0870i	−0.586044	+	0.806621i
$306$	−21.0403	−	6.29141i	−1.20279	−	0.359656i
$307$			22.3509i			1.27563i	0.770188	+	0.637817i	$0.220162\pi$
$307$			22.3509i			1.27563i	−0.770188	+	0.637817i	$0.779838\pi$
$308$		0			0
$309$		−	7.48331i		−	0.425711i
$310$	1.17473	−	3.92863i	0.0667202	−	0.223131i
$311$	−8.79716	+	12.1083i	−0.498841	+	0.686596i	−0.981988	−	0.188943i	$-0.939494\pi$
$311$	−8.79716	+	12.1083i	−0.498841	+	0.686596i	0.483147	+	0.875539i	$0.339494\pi$
$312$	−0.599686	−	1.48002i	−0.0339505	−	0.0837895i
$313$	2.41912	−	7.44528i	0.136737	−	0.420832i	−0.859120	−	0.511775i	$-0.828988\pi$
$313$	2.41912	−	7.44528i	0.136737	−	0.420832i	0.995856	+	0.0909431i	$0.0289881\pi$
$314$	0.389491	+	0.510312i	0.0219803	+	0.0287986i
$315$	−14.4742	−	19.9221i	−0.815530	−	1.12248i
$316$	4.91043	−	17.9554i	0.276233	−	1.01007i
$317$	−14.6658	+	4.76522i	−0.823715	+	0.267641i	−0.690396	−	0.723432i	$-0.742564\pi$
$317$	−14.6658	+	4.76522i	−0.823715	+	0.267641i	−0.133319	+	0.991073i	$0.542564\pi$
$318$	2.49221	−	3.60625i	0.139756	−	0.202229i
$319$		0			0
$320$	−9.89949	+	18.7083i	−0.553399	+	1.04583i
$321$	−3.42975	+	1.11439i	−0.191430	+	0.0621994i
$322$	−28.0455	+	9.85021i	−1.56292	+	0.548931i
$323$	10.1008	−	7.33866i	0.562024	−	0.408334i
$324$	14.9539	−	0.706466i	0.830771	−	0.0392481i
$325$	0.842402	−	2.59265i	0.0467281	−	0.143814i
$326$	−18.1371	+	0.428186i	−1.00452	+	0.0237150i
$327$	−0.913522	−	0.663713i	−0.0505179	−	0.0367034i
$328$	−2.00887	−	28.3217i	−0.110921	−	1.56381i
$329$		0			0
$330$		0			0
$331$	−18.0711			−0.993276			−0.496638	−	0.867958i	$-0.665432\pi$
$331$	−18.0711			−0.993276			−0.496638	+	0.867958i	$0.665432\pi$
$332$	−5.68808	−	7.09866i	−0.312174	−	0.389589i
$333$	8.04249	−	11.0695i	0.440726	−	0.606607i
$334$	30.9703	−	0.731157i	1.69462	−	0.0400071i
$335$	15.2764	+	4.96360i	0.834638	+	0.271190i
$336$	2.16615	+	5.00336i	0.118173	+	0.272956i
$337$	11.2472	+	15.4804i	0.612673	+	0.843272i	0.996794	−	0.0800109i	$-0.0254955\pi$
$337$	11.2472	+	15.4804i	0.612673	+	0.843272i	−0.384121	+	0.923283i	$0.625496\pi$
$338$	−5.22163	−	14.8670i	−0.284019	−	0.808660i
$339$	0.789955	+	2.43123i	0.0429045	+	0.132046i
$340$	10.2712	+	27.1750i	0.557034	+	1.47377i
$341$		0			0
$342$	−5.17157	+	7.48331i	−0.279647	+	0.404651i
$343$	−3.22507	−	9.92576i	−0.174138	−	0.535941i
$344$	−11.7081	−	13.9249i	−0.631257	−	0.750778i
$345$	−5.66312	+	4.11450i	−0.304892	+	0.221517i
$346$	−6.12921	+	4.67808i	−0.329509	+	0.251495i
$347$	3.95453	+	1.28491i	0.212291	+	0.0689774i	0.413232	−	0.910626i	$-0.364400\pi$
$347$	3.95453	+	1.28491i	0.212291	+	0.0689774i	−0.200941	+	0.979603i	$0.564400\pi$
$348$	4.55719	+	2.99297i	0.244291	+	0.160440i
$349$	11.7515	+	8.53797i	0.629044	+	0.457027i	0.856069	−	0.516862i	$-0.172900\pi$
$349$	11.7515	+	8.53797i	0.629044	+	0.457027i	−0.227025	+	0.973889i	$0.572900\pi$
$350$	−2.66642	+	8.91727i	−0.142526	+	0.476648i
$351$	3.29066			0.175642
$352$		0			0
$353$	1.82843			0.0973174			0.0486587	−	0.998815i	$-0.484505\pi$
$353$	1.82843			0.0973174			0.0486587	+	0.998815i	$0.484505\pi$
$354$	0.544176	−	1.81988i	0.0289226	−	0.0967254i
$355$	13.6720	+	9.93327i	0.725633	+	0.527203i
$356$	17.8151	+	11.7002i	0.944200	+	0.620110i
$357$	7.11706	+	2.31247i	0.376675	+	0.122389i
$358$	−10.9360	+	8.34681i	−0.577985	+	0.441142i
$359$	2.66220	−	1.93420i	0.140505	−	0.102083i	−0.515312	−	0.857003i	$-0.672324\pi$
$359$	2.66220	−	1.93420i	0.140505	−	0.102083i	0.655818	+	0.754919i	$0.272324\pi$
$360$	−13.6214	−	16.2005i	−0.717913	−	0.853842i
$361$	4.27322	+	13.1516i	0.224906	+	0.692190i
$362$	2.12723	−	3.07813i	0.111805	−	0.161783i
$363$		0			0
$364$	−3.17157	−	8.39119i	−0.166236	−	0.439818i
$365$	0.770135	+	2.37023i	0.0403107	+	0.124064i
$366$	1.27754	+	3.63742i	0.0667782	+	0.190131i
$367$	−13.0852	−	18.0103i	−0.683043	−	0.940128i	0.316922	−	0.948452i	$-0.397351\pi$
$367$	−13.0852	−	18.0103i	−0.683043	−	0.940128i	−0.999965	+	0.00832319i	$0.997351\pi$
$368$	−23.4466	+	10.1509i	−1.22224	+	0.529153i
$369$	27.0032	+	8.77389i	1.40573	+	0.456750i
$370$	−18.0955	+	0.427203i	−0.940738	+	0.0222092i
$371$	14.4742	−	19.9221i	0.751464	−	1.03430i
$372$	−0.567704	−	0.708488i	−0.0294341	−	0.0367334i
$373$	0.233860			0.0121088			0.00605440	−	0.999982i	$-0.498073\pi$
$373$	0.233860			0.0121088			0.00605440	+	0.999982i	$0.498073\pi$
$374$		0			0
$375$		−	3.28772i		−	0.169777i
$376$		0			0
$377$	−7.25734	−	5.27276i	−0.373772	−	0.271561i
$378$	−11.2319	+	0.265166i	−0.577705	+	0.0136387i
$379$	−4.96623	+	15.2845i	−0.255098	+	0.785112i	0.738712	+	0.674021i	$0.235434\pi$
$379$	−4.96623	+	15.2845i	−0.255098	+	0.785112i	−0.993810	+	0.111091i	$0.964566\pi$
$380$	12.0200	−	0.567863i	0.616615	−	0.0291307i
$381$	−0.189197	+	0.137459i	−0.00969283	+	0.00704226i
$382$	−22.6438	+	7.95299i	−1.15856	+	0.406910i
$383$	6.93823	−	2.25437i	0.354527	−	0.115193i	−0.126338	−	0.991987i	$-0.540323\pi$
$383$	6.93823	−	2.25437i	0.354527	−	0.115193i	0.480865	+	0.876794i	$0.340323\pi$
$384$	2.16148	+	4.15804i	0.110303	+	0.212189i
$385$		0			0
$386$	−10.3431	+	14.9666i	−0.526452	+	0.761781i
$387$	17.3025	−	5.62191i	0.879533	−	0.285778i
$388$	3.94912	−	14.4403i	0.200486	−	0.733095i
$389$	−19.1495	−	26.3570i	−0.970916	−	1.33635i	−0.941583	−	0.336782i	$-0.890661\pi$
$389$	−19.1495	−	26.3570i	−0.970916	−	1.33635i	−0.0293336	−	0.999570i	$-0.509339\pi$
$390$	−1.28168	−	1.67926i	−0.0649005	−	0.0850327i
$391$	−10.8366	+	33.3517i	−0.548032	+	1.68667i
$392$	4.06642	+	10.0359i	0.205385	+	0.506889i
$393$	−1.66102	+	2.28620i	−0.0837875	+	0.115324i
$394$	4.22837	−	14.1409i	0.213022	−	0.712407i
$395$		−	24.6250i		−	1.23902i
$396$		0			0
$397$		−	22.4499i		−	1.12673i	−0.826208	−	0.563365i	$-0.809506\pi$
$397$		−	22.4499i		−	1.12673i	0.826208	−	0.563365i	$-0.190494\pi$
$398$	28.6786	+	8.57541i	1.43753	+	0.429846i
$399$	1.82195	−	2.50770i	0.0912117	−	0.125542i
$400$	−1.74383	+	7.80763i	−0.0871917	+	0.390381i
$401$	−1.49207	+	4.59211i	−0.0745102	+	0.229319i	−0.981375	−	0.192104i	$-0.938469\pi$
$401$	−1.49207	+	4.59211i	−0.0745102	+	0.229319i	0.906864	+	0.421422i	$0.138469\pi$
$402$	2.82701	−	2.15769i	0.140998	−	0.107616i
$403$	0.878009	+	1.20848i	0.0437367	+	0.0601985i
$404$	−9.10174	+	33.2813i	−0.452829	+	1.65581i
$405$	18.8349	−	6.11983i	0.935914	−	0.304097i
$406$	25.1961	+	17.4125i	1.25046	+	0.864169i
$407$		0			0
$408$	6.24264	+	1.54985i	0.309057	+	0.0767288i
$409$	1.79173	−	0.582168i	0.0885952	−	0.0287863i	−0.264384	−	0.964417i	$-0.585169\pi$
$409$	1.79173	−	0.582168i	0.0885952	−	0.0287863i	0.352979	+	0.935631i	$0.385169\pi$
$410$	−12.4466	−	35.4380i	−0.614695	−	1.75016i
$411$	2.90096	−	2.10767i	0.143094	−	0.103964i
$412$	−1.70511	−	36.0924i	−0.0840048	−	1.77814i
$413$	3.29734	−	10.1482i	0.162252	−	0.499359i
$414$	−0.603016	−	25.5425i	−0.0296366	−	1.25535i
$415$	−9.73527	−	7.07309i	−0.477886	−	0.347204i
$416$	−3.22954	−	7.00155i	−0.158341	−	0.343279i
$417$		−	8.15447i		−	0.399326i
$418$		0			0
$419$	16.1421			0.788595			0.394297	−	0.918983i	$-0.370988\pi$
$419$	16.1421			0.788595			0.394297	+	0.918983i	$0.370988\pi$
$420$	4.51004	+	5.62848i	0.220067	+	0.274642i
$421$	4.39858	−	6.05413i	0.214374	−	0.295060i	−0.688265	−	0.725460i	$-0.741627\pi$
$421$	4.39858	−	6.05413i	0.214374	−	0.295060i	0.902639	+	0.430399i	$0.141627\pi$
$422$	0.303620	+	12.8607i	0.0147800	+	0.626050i
$423$		0			0
$424$	11.1983	−	17.9610i	0.543840	−	0.872263i
$425$	6.45410	+	8.88331i	0.313070	+	0.430904i
$426$	3.53025	−	1.23990i	0.171041	−	0.0600734i
$427$	6.69234	+	20.5969i	0.323865	+	0.996753i
$428$	−16.2879	+	6.15626i	−0.787307	+	0.297574i
$429$		0			0
$430$	−19.7990	−	13.6827i	−0.954792	−	0.659838i
$431$	−0.667935	−	2.05569i	−0.0321733	−	0.0990192i	0.933680	−	0.358108i	$-0.116578\pi$
$431$	−0.667935	−	2.05569i	−0.0321733	−	0.0990192i	−0.965854	+	0.259088i	$0.916578\pi$
$432$	−9.61384	+	0.910405i	−0.462546	+	0.0438019i
$433$	14.0309	−	10.1940i	0.674282	−	0.489895i	−0.197174	−	0.980369i	$-0.563176\pi$
$433$	14.0309	−	10.1940i	0.674282	−	0.489895i	0.871456	+	0.490474i	$0.163176\pi$
$434$	−3.09426	−	4.05409i	−0.148529	−	0.194603i
$435$	6.85950	+	2.22879i	0.328888	+	0.106862i
$436$	−4.55719	−	2.99297i	−0.218250	−	0.143337i
$437$	11.7515	+	8.53797i	0.562151	+	0.408427i
$438$	0.528663	+	0.158080i	0.0252605	+	0.00755334i
$439$	34.5035			1.64676			0.823380	−	0.567490i	$-0.192085\pi$
$439$	34.5035			1.64676			0.823380	+	0.567490i	$0.192085\pi$
$440$		0			0
$441$	−10.8284			−0.515639
$442$	−10.1394	−	3.03187i	−0.482283	−	0.144211i
$443$	−21.3695	−	15.5259i	−1.01530	−	0.737657i	−0.0499842	−	0.998750i	$-0.515917\pi$
$443$	−21.3695	−	15.5259i	−1.01530	−	0.737657i	−0.965314	+	0.261093i	$0.915917\pi$
$444$	−2.19997	+	3.34974i	−0.104406	+	0.158972i
$445$	26.8154	+	8.71285i	1.27117	+	0.413029i
$446$	3.59993	+	4.71663i	0.170462	+	0.223339i
$447$	7.07307	−	5.13889i	0.334545	−	0.243061i
$448$	11.5875	+	23.6379i	0.547456	+	1.11679i
$449$	4.93518	+	15.1889i	0.232905	+	0.716809i	0.997392	+	0.0721698i	$0.0229923\pi$
$449$	4.93518	+	15.1889i	0.232905	+	0.716809i	−0.764487	+	0.644639i	$0.777008\pi$
$450$	−6.58132	−	4.54822i	−0.310246	−	0.214405i
$451$		0			0
$452$	4.36396	+	11.5460i	0.205263	+	0.543076i
$453$	−1.68480	−	5.18529i	−0.0791590	−	0.243626i
$454$	17.6856	−	6.21156i	0.830024	−	0.291523i
$455$	−6.97521	−	9.60056i	−0.327003	−	0.450081i
$456$	1.40960	−	2.26085i	0.0660105	−	0.105874i
$457$	21.6281	+	7.02738i	1.01172	+	0.328727i	0.767539	−	0.641003i	$-0.221481\pi$
$457$	21.6281	+	7.02738i	1.01172	+	0.328727i	0.244180	+	0.969730i	$0.421481\pi$
$458$	−0.338087	−	14.3207i	−0.0157978	−	0.669161i
$459$	−7.79079	+	10.7231i	−0.363643	+	0.500511i
$460$	−26.3760	+	21.1348i	−1.22979	+	0.985414i
$461$	−3.85525			−0.179557			−0.0897783	−	0.995962i	$-0.528616\pi$
$461$	−3.85525			−0.179557			−0.0897783	+	0.995962i	$0.528616\pi$
$462$		0			0
$463$		−	22.2619i		−	1.03460i	−0.855804	−	0.517300i	$-0.826937\pi$
$463$		−	22.2619i		−	1.03460i	0.855804	−	0.517300i	$-0.173063\pi$
$464$	22.6615	+	13.3968i	1.05203	+	0.621933i
$465$	−0.971638	−	0.705936i	−0.0450586	−	0.0327370i
$466$	0.277573	+	11.7574i	0.0128583	+	0.544653i
$467$	11.1466	−	34.3056i	0.515802	−	1.58747i	−0.266016	−	0.963969i	$-0.585708\pi$
$467$	11.1466	−	34.3056i	0.515802	−	1.58747i	0.781818	−	0.623506i	$-0.214292\pi$
$468$	7.70190	−	0.363861i	0.356020	−	0.0168195i
$469$	16.1624	−	11.7427i	0.746310	−	0.542226i
$470$		0			0
$471$	0.178825	−	0.0581038i	0.00823982	−	0.00267728i
$472$	2.20992	−	8.90135i	0.101720	−	0.409718i
$473$		0			0
$474$	−4.48528	−	3.09969i	−0.206016	−	0.142373i
$475$	4.32561	−	1.40548i	0.198473	−	0.0644877i
$476$	34.8528	+	9.53150i	1.59748	+	0.436876i
$477$	12.4411	+	17.1237i	0.569637	+	0.784039i
$478$	6.12921	−	4.67808i	0.280344	−	0.213970i
$479$	8.45395	−	26.0186i	0.386271	−	1.18882i	−0.549283	−	0.835636i	$-0.685099\pi$
$479$	8.45395	−	26.0186i	0.386271	−	1.18882i	0.935554	−	0.353184i	$-0.114901\pi$
$480$	4.20910	+	4.55146i	0.192118	+	0.207745i
$481$	3.87572	−	5.33447i	0.176718	−	0.243231i
$482$	−6.16255	−	1.84271i	−0.280696	−	0.0839332i
$483$			8.70626i			0.396149i
$484$		0			0
$485$		−	19.8042i		−	0.899262i
$486$	4.19053	−	14.0143i	0.190086	−	0.635702i
$487$	15.6619	−	21.5567i	0.709706	−	0.976827i	−0.290097	−	0.956997i	$-0.593688\pi$
$487$	15.6619	−	21.5567i	0.709706	−	0.976827i	0.999803	−	0.0198298i	$-0.00631245\pi$
$488$	6.99045	+	17.2523i	0.316443	+	0.780977i
$489$	−1.64203	+	5.05364i	−0.0742550	+	0.228533i
$490$	8.69100	+	11.3869i	0.392619	+	0.514410i
$491$	−15.1229	−	20.8149i	−0.682487	−	0.939362i	0.317474	−	0.948267i	$-0.397166\pi$
$491$	−15.1229	−	20.8149i	−0.682487	−	0.939362i	−0.999960	+	0.00890465i	$0.997166\pi$
$492$	−8.02153	−	2.19372i	−0.361638	−	0.0989004i
$493$	34.3642	−	11.1656i	1.54768	−	0.502873i
$494$	−2.49221	+	3.60625i	−0.112130	+	0.162253i
$495$		0			0
$496$	−2.89949	−	3.28772i	−0.130191	−	0.147623i
$497$	19.9900	−	6.49516i	0.896676	−	0.291348i
$498$	−2.51375	+	0.882884i	−0.112644	+	0.0395630i
$499$	−14.9549	+	10.8654i	−0.669474	+	0.486401i	−0.869849	−	0.493318i	$-0.835784\pi$
$499$	−14.9549	+	10.8654i	−0.669474	+	0.486401i	0.200375	+	0.979719i	$0.435784\pi$
$500$	−0.749123	−	15.8568i	−0.0335018	−	0.709139i
$501$	2.80387	−	8.62944i	0.125268	−	0.385535i
$502$	26.0344	−	0.614628i	1.16197	−	0.0274322i
$503$	−3.11896	−	2.26606i	−0.139068	−	0.101038i	0.516076	−	0.856543i	$-0.327392\pi$
$503$	−3.11896	−	2.26606i	−0.139068	−	0.101038i	−0.655144	+	0.755504i	$0.727392\pi$
$504$	−26.2593	+	1.86258i	−1.16968	+	0.0829660i
$505$			45.6438i			2.03112i
$506$		0			0
$507$	−4.61522			−0.204969
$508$	−0.881183	+	0.706082i	−0.0390962	+	0.0313273i
$509$	−20.9714	+	28.8647i	−0.929542	+	1.27940i	0.0304965	+	0.999535i	$0.490291\pi$
$509$	−20.9714	+	28.8647i	−0.929542	+	1.27940i	−0.960038	+	0.279869i	$0.909709\pi$
$510$	8.50657	−	0.200826i	0.376677	−	0.00889271i
$511$	2.94798	+	0.957857i	0.130411	+	0.0423731i
$512$	11.3724	+	19.5619i	0.502592	+	0.864524i
$513$	3.22705	+	4.44165i	0.142478	+	0.196104i
$514$	3.03925	+	8.65336i	0.134056	+	0.381683i
$515$	−14.7707	−	45.4595i	−0.650875	−	2.00319i
$516$	−4.98442	+	1.88393i	−0.219427	+	0.0829356i
$517$		0			0
$518$	−12.7990	+	18.5203i	−0.562355	+	0.813733i
$519$	0.697869	+	2.14782i	0.0306330	+	0.0942788i
$520$	−6.56425	−	7.80712i	−0.287861	−	0.342365i
$521$	16.2715	−	11.8219i	0.712868	−	0.517929i	−0.171230	−	0.985231i	$-0.554774\pi$
$521$	16.2715	−	11.8219i	0.712868	−	0.517929i	0.884098	+	0.467302i	$0.154774\pi$
$522$	−20.9264	+	15.9719i	−0.915926	+	0.699073i
$523$	16.1892	+	5.26019i	0.707905	+	0.230012i	0.640771	−	0.767732i	$-0.278615\pi$
$523$	16.1892	+	5.26019i	0.707905	+	0.230012i	0.0671335	+	0.997744i	$0.478615\pi$
$524$	−7.49027	+	11.4049i	−0.327214	+	0.498227i
$525$	2.20544	+	1.60234i	0.0962532	+	0.0699320i
$526$	−7.77052	+	25.9868i	−0.338811	+	1.13308i
$527$	−6.01673			−0.262093
$528$		0			0
$529$	−17.7990			−0.773869
$530$	8.02156	−	26.8264i	0.348434	−	1.16526i
$531$	7.41996	+	5.39092i	0.321999	+	0.233946i
$532$	8.21597	−	12.5099i	0.356208	−	0.542373i
$533$	13.0130	+	4.22819i	0.563656	+	0.183143i
$534$	4.96239	−	3.78751i	0.214744	−	0.163902i
$535$	−18.6354	+	13.5394i	−0.805678	+	0.585359i
$536$	13.1432	−	11.0508i	0.567698	−	0.477322i
$537$	1.24516	+	3.83222i	0.0537328	+	0.165373i
$538$	−11.0011	+	15.9188i	−0.474293	+	0.686307i
$539$		0			0
$540$	−11.9497	+	4.51658i	−0.514235	+	0.194363i
$541$	5.33108	+	16.4074i	0.229201	+	0.705408i	0.997838	+	0.0657228i	$0.0209353\pi$
$541$	5.33108	+	16.4074i	0.229201	+	0.705408i	−0.768637	+	0.639685i	$0.779065\pi$
$542$	5.90393	+	16.8097i	0.253595	+	0.722037i
$543$	−0.644157	−	0.886607i	−0.0276434	−	0.0380479i
$544$	30.4617	+	6.05256i	1.30603	+	0.259501i
$545$	−6.85950	−	2.22879i	−0.293829	−	0.0954707i
$546$	−2.62669	+	0.0620116i	−0.112412	+	0.00265385i
$547$	−24.2504	+	33.3778i	−1.03687	+	1.42713i	−0.137210	+	0.990542i	$0.543813\pi$
$547$	−24.2504	+	33.3778i	−1.03687	+	1.42713i	−0.899661	+	0.436589i	$0.856187\pi$
$548$	13.5112	−	10.8264i	0.577171	−	0.462481i
$549$	−18.6148			−0.794459
$550$		0			0
$551$		−	14.9666i		−	0.637600i
$552$	0.529464	+	7.46456i	0.0225355	+	0.317713i
$553$	−24.7781	−	18.0023i	−1.05367	−	0.765538i
$554$	−5.45062	+	0.128680i	−0.231575	+	0.00546709i
$555$	−1.63826	+	5.04204i	−0.0695402	+	0.214023i
$556$	−1.85804	−	39.3294i	−0.0787983	−	1.66794i
$557$	−19.2813	+	14.0087i	−0.816977	+	0.593568i	−0.915845	−	0.401532i	$-0.868478\pi$
$557$	−19.2813	+	14.0087i	−0.816977	+	0.593568i	0.0988682	+	0.995101i	$0.468478\pi$
$558$	4.13594	−	1.45263i	0.175088	−	0.0614949i
$559$	8.33815	−	2.70923i	0.352666	−	0.114588i
$560$	23.0346	+	26.1188i	0.973390	+	1.10372i
$561$		0			0
$562$	−5.17157	+	7.48331i	−0.218150	+	0.315665i
$563$	−11.1851	+	3.63426i	−0.471396	+	0.153166i	−0.535075	−	0.844805i	$-0.679717\pi$
$563$	−11.1851	+	3.63426i	−0.471396	+	0.153166i	0.0636788	+	0.997970i	$0.479717\pi$
$564$		0			0
$565$	9.59762	+	13.2100i	0.403775	+	0.555749i
$566$	−1.61646	−	2.11789i	−0.0679450	−	0.0890216i
$567$	7.61155	−	23.4259i	0.319655	−	0.983797i
$568$	16.7440	−	6.78449i	0.702564	−	0.284671i
$569$	−1.56603	+	2.15545i	−0.0656513	+	0.0903612i	−0.840580	−	0.541687i	$-0.817786\pi$
$569$	−1.56603	+	2.15545i	−0.0656513	+	0.0903612i	0.774929	+	0.632049i	$0.217786\pi$
$570$	1.00972	−	3.37679i	0.0422925	−	0.141438i
$571$			21.9607i			0.919028i	0.888170	+	0.459514i	$0.151976\pi$
$571$			21.9607i			0.919028i	−0.888170	+	0.459514i	$0.848024\pi$
$572$		0			0
$573$			7.02938i			0.293656i
$574$	−44.7576	−	13.3833i	−1.86814	−	0.558608i
$575$	−7.50885	+	10.3350i	−0.313141	+	0.431001i
$576$	−22.4009	+	3.19387i	−0.933370	+	0.133078i
$577$	−9.77341	+	30.0795i	−0.406872	+	1.25222i	0.512449	+	0.858717i	$0.328738\pi$
$577$	−9.77341	+	30.0795i	−0.406872	+	1.25222i	−0.919322	+	0.393507i	$0.871262\pi$
$578$	14.7742	−	11.2763i	0.614525	−	0.469032i
$579$	3.13205	+	4.31090i	0.130164	+	0.179155i
$580$	33.5915	+	9.18657i	1.39481	+	0.381452i
$581$	−14.2341	+	4.62494i	−0.590530	+	0.191875i
$582$	−3.60720	−	2.49287i	−0.149523	−	0.103333i
$583$		0			0
$584$	2.58579	+	0.641967i	0.107001	+	0.0265648i
$585$	9.70080	−	3.15198i	0.401079	−	0.130318i
$586$	6.80729	+	19.3817i	0.281206	+	0.800651i
$587$	24.5005	−	17.8006i	1.01124	−	0.734711i	0.0467739	−	0.998906i	$-0.485106\pi$
$587$	24.5005	−	17.8006i	1.01124	−	0.734711i	0.964470	+	0.264194i	$0.0851060\pi$
$588$	3.16804	−	0.149668i	0.130648	−	0.00617219i
$589$	−0.770135	+	2.37023i	−0.0317329	+	0.0976637i
$590$	−0.286356	−	12.1295i	−0.0117891	−	0.499362i
$591$	−3.49735	−	2.54097i	−0.143862	−	0.104522i
$592$	−9.84728	+	16.6572i	−0.404721	+	0.684608i
$593$		−	1.88393i		−	0.0773639i	−0.999252	−	0.0386819i	$-0.987684\pi$
$593$		−	1.88393i		−	0.0773639i	0.999252	−	0.0386819i	$-0.0123159\pi$
$594$		0			0
$595$	47.7990			1.95957
$596$	32.9428	−	26.3967i	1.34939	−	1.08125i
$597$	5.15326	−	7.09285i	0.210909	−	0.290291i
$598$	−0.290597	−	12.3091i	−0.0118834	−	0.503356i
$599$		0			0		0.309017	−	0.951057i	$-0.400000\pi$
$599$		0			0		−0.309017	+	0.951057i	$0.600000\pi$
$600$	1.98834	+	1.23969i	0.0811736	+	0.0506103i
$601$	−19.2673	−	26.5192i	−0.785930	−	1.08174i	−0.994603	−	0.103754i	$-0.966915\pi$
$601$	−19.2673	−	26.5192i	−0.785930	−	1.08174i	0.208673	−	0.977985i	$-0.433085\pi$
$602$	−28.2420	+	9.91921i	−1.15106	+	0.404277i
$603$	5.30631	+	16.3311i	0.216090	+	0.665055i
$604$	−9.30739	−	24.6250i	−0.378712	−	1.00198i
$605$		0			0
$606$	8.31371	+	5.74544i	0.337721	+	0.233393i
$607$	−8.97735	−	27.6295i	−0.364380	−	1.12145i	−0.950369	−	0.311126i	$-0.899294\pi$
$607$	−8.97735	−	27.6295i	−0.364380	−	1.12145i	0.585989	−	0.810319i	$-0.300706\pi$
$608$	6.28342	−	11.2254i	0.254826	−	0.455249i
$609$	7.25734	−	5.27276i	0.294082	−	0.213663i
$610$	14.9404	+	19.5749i	0.604919	+	0.792564i
$611$		0			0
$612$	−17.0489	+	25.9593i	−0.689162	+	1.04934i
$613$	21.6760	+	15.7485i	0.875484	+	0.636077i	0.932053	−	0.362322i	$-0.118016\pi$
$613$	21.6760	+	15.7485i	0.875484	+	0.636077i	−0.0565685	+	0.998399i	$0.518016\pi$
$614$	30.2841	+	9.05547i	1.22217	+	0.365449i
$615$	−11.0011			−0.443609
$616$		0			0
$617$	33.1127			1.33307			0.666534	−	0.745475i	$-0.267777\pi$
$617$	33.1127			1.33307			0.666534	+	0.745475i	$0.267777\pi$
$618$	−10.1394	−	3.03187i	−0.407867	−	0.121960i
$619$	−25.5058	−	18.5311i	−1.02516	−	0.744826i	−0.0578297	−	0.998326i	$-0.518418\pi$
$619$	−25.5058	−	18.5311i	−1.02516	−	0.744826i	−0.967335	+	0.253501i	$0.918418\pi$
$620$	−4.84711	−	3.18337i	−0.194664	−	0.127847i
$621$	−14.6658	−	4.76522i	−0.588520	−	0.191222i
$622$	12.8418	+	16.8253i	0.514907	+	0.674632i
$623$	28.3707	−	20.6125i	1.13665	−	0.825822i
$624$	−2.24829	+	0.212907i	−0.0900037	+	0.00852311i
$625$	−9.57953	−	29.4828i	−0.383181	−	1.17931i
$626$	−9.10777	−	6.29420i	−0.364020	−	0.251567i
$627$		0			0
$628$	0.849242	−	0.320983i	0.0338885	−	0.0128086i
$629$	8.20722	+	25.2592i	0.327243	+	1.00715i
$630$	−32.8574	+	11.5402i	−1.30907	+	0.459774i
$631$	6.86469	+	9.44844i	0.273279	+	0.376136i	0.923493	−	0.383615i	$-0.125321\pi$
$631$	6.86469	+	9.44844i	0.273279	+	0.376136i	−0.650214	+	0.759751i	$0.725321\pi$
$632$	−22.3390	−	13.9280i	−0.888598	−	0.554025i
$633$	3.58346	+	1.16434i	0.142430	+	0.0462782i
$634$	0.514706	+	21.8019i	0.0204416	+	0.865864i
$635$	−0.878009	+	1.20848i	−0.0348427	+	0.0479569i
$636$	−3.87652	−	4.83786i	−0.153714	−	0.191834i
$637$	−5.21828			−0.206756
$638$		0			0
$639$			18.0663i			0.714693i
$640$	21.3378	+	20.9929i	0.843449	+	0.829815i
$641$	14.4235	+	10.4793i	0.569694	+	0.413907i	0.834994	−	0.550259i	$-0.185471\pi$
$641$	14.4235	+	10.4793i	0.569694	+	0.413907i	−0.265300	+	0.964166i	$0.585471\pi$
$642$	0.120369	+	5.09859i	0.00475059	+	0.201225i
$643$	0.190115	−	0.585112i	0.00749739	−	0.0230746i	−0.947238	−	0.320532i	$-0.896138\pi$
$643$	0.190115	−	0.585112i	0.00749739	−	0.0230746i	0.954735	+	0.297457i	$0.0961385\pi$
$644$	1.98377	+	41.9907i	0.0781713	+	1.65467i
$645$	−5.70279	+	4.14332i	−0.224547	+	0.163143i
$646$	−5.85108	−	16.6592i	−0.230208	−	0.655448i
$647$	−22.3934	+	7.27607i	−0.880377	+	0.286052i	−0.714114	−	0.700030i	$-0.753170\pi$
$647$	−22.3934	+	7.27607i	−0.880377	+	0.286052i	−0.166263	+	0.986081i	$0.553170\pi$
$648$	5.10135	−	20.5478i	0.200400	−	0.807193i
$649$		0			0
$650$	−3.17157	−	2.19181i	−0.124399	−	0.0859699i
$651$	−1.42065	+	0.461597i	−0.0556796	+	0.0180914i
$652$	−6.76807	+	24.7481i	−0.265058	+	0.969210i
$653$	−21.5051	−	29.5992i	−0.841558	−	1.15830i	−0.985660	−	0.168742i	$-0.946030\pi$
$653$	−21.5051	−	29.5992i	−0.841558	−	1.15830i	0.144103	−	0.989563i	$-0.453970\pi$
$654$	−1.26940	+	0.968861i	−0.0496375	+	0.0378855i
$655$	−5.57781	+	17.1667i	−0.217943	+	0.670760i
$656$	−39.1881	−	8.75266i	−1.53004	−	0.341734i
$657$	−1.56603	+	2.15545i	−0.0610965	+	0.0840922i
$658$		0			0
$659$		−	10.9804i		−	0.427735i	−0.976863	−	0.213867i	$-0.931394\pi$
$659$		−	10.9804i		−	0.427735i	0.976863	−	0.213867i	$-0.0686060\pi$
$660$		0			0
$661$			12.3209i			0.479227i	0.970868	+	0.239613i	$0.0770207\pi$
$661$			12.3209i			0.479227i	−0.970868	+	0.239613i	$0.922979\pi$
$662$	−7.32149	+	24.4852i	−0.284558	+	0.951642i
$663$	−1.82195	+	2.50770i	−0.0707588	+	0.0973911i
$664$	−11.9228	+	4.83096i	−0.462693	+	0.187478i
$665$	6.11822	−	18.8300i	0.237255	−	0.730194i
$666$	−11.7401	−	15.3819i	−0.454920	−	0.596036i
$667$	24.7091	+	34.0091i	0.956738	+	1.31684i
$668$	11.5570	−	42.2591i	0.447152	−	1.63505i
$669$	1.65282	−	0.537032i	0.0639015	−	0.0207629i
$670$	12.9146	−	18.6875i	0.498934	−	0.721962i
$671$		0			0
$672$	7.65685	−	0.907878i	0.295370	−	0.0350222i
$673$	36.3966	−	11.8260i	1.40299	−	0.455858i	0.492831	−	0.870125i	$-0.335962\pi$
$673$	36.3966	−	11.8260i	1.40299	−	0.455858i	0.910156	+	0.414267i	$0.135962\pi$
$674$	25.5318	−	8.96732i	0.983447	−	0.345408i
$675$	−3.90628	+	2.83808i	−0.150353	+	0.109238i
$676$	−22.2594	+	1.05160i	−0.856132	+	0.0404462i
$677$	−0.770135	+	2.37023i	−0.0295987	+	0.0910954i	−0.964765	−	0.263115i	$-0.915250\pi$
$677$	−0.770135	+	2.37023i	−0.0295987	+	0.0910954i	0.935166	+	0.354210i	$0.115250\pi$
$678$	3.61422	−	0.0853256i	0.138803	−	0.00327691i
$679$	−19.9273	−	14.4780i	−0.764740	−	0.555616i
$680$	40.9818	−	2.90686i	1.57158	−	0.111473i
$681$		−	5.49019i		−	0.210384i
$682$		0			0
$683$	−36.4264			−1.39382			−0.696909	−	0.717160i	$-0.745442\pi$
$683$	−36.4264			−1.39382			−0.696909	+	0.717160i	$0.745442\pi$
$684$	8.04415	+	10.0390i	0.307576	+	0.383851i
$685$	13.4626	−	18.5296i	0.514378	−	0.707981i
$686$	−14.7554	+	0.348350i	−0.563364	+	0.0133001i
$687$	−3.99025	−	1.29651i	−0.152238	−	0.0494650i
$688$	−23.6108	+	10.2220i	−0.900155	+	0.389711i
$689$	5.99542	+	8.25199i	0.228407	+	0.314376i
$690$	3.28047	+	9.34016i	0.124885	+	0.355574i
$691$	−2.70617	−	8.32874i	−0.102948	−	0.316840i	0.886296	−	0.463120i	$-0.153270\pi$
$691$	−2.70617	−	8.32874i	−0.102948	−	0.316840i	−0.989243	+	0.146280i	$0.953270\pi$
$692$	3.85525	+	10.2000i	0.146554	+	0.387747i
$693$		0			0
$694$	3.34315	−	4.83756i	0.126904	−	0.183631i
$695$	−16.0954	−	49.5367i	−0.610535	−	1.87903i
$696$	5.90163	−	4.96210i	0.223701	−	0.188088i
$697$	−44.5871	+	32.3944i	−1.68886	+	1.22703i
$698$	16.3295	−	12.4634i	0.618082	−	0.471746i
$699$	3.27604	+	1.06445i	0.123911	+	0.0402612i
$700$	11.0020	+	7.22566i	0.415838	+	0.273104i
$701$	−21.1084	−	15.3361i	−0.797253	−	0.579238i	0.112854	−	0.993612i	$-0.464001\pi$
$701$	−21.1084	−	15.3361i	−0.797253	−	0.579238i	−0.910107	+	0.414374i	$0.864001\pi$
$702$	1.33321	−	4.45863i	0.0503188	−	0.168280i
$703$	11.0011			0.414916
$704$		0			0
$705$		0			0
$706$	0.740787	−	2.47740i	0.0278799	−	0.0932383i
$707$	45.9275	+	33.3683i	1.72728	+	1.25494i
$708$	−2.24535	−	1.47465i	−0.0843853	−	0.0554206i
$709$	−43.9975	−	14.2957i	−1.65236	−	0.536885i	−0.673111	−	0.739542i	$-0.735042\pi$
$709$	−43.9975	−	14.2957i	−1.65236	−	0.536885i	−0.979250	+	0.202657i	$0.935042\pi$
$710$	18.9982	−	14.5002i	0.712988	−	0.544183i
$711$	21.2976	−	15.4736i	0.798722	−	0.580305i
$712$	23.0709	−	19.3980i	0.864617	−	0.726972i
$713$	−2.16312	−	6.65740i	−0.0810094	−	0.249321i
$714$	6.01673	−	8.70626i	0.225170	−	0.325824i
$715$		0			0
$716$	6.87868	+	18.1993i	0.257068	+	0.680139i
$717$	−0.697869	−	2.14782i	−0.0260624	−	0.0802118i
$718$	−1.54213	−	4.39075i	−0.0575517	−	0.163861i
$719$	2.99975	+	4.12880i	0.111872	+	0.153978i	0.861281	−	0.508129i	$-0.169663\pi$
$719$	2.99975	+	4.12880i	0.111872	+	0.153978i	−0.749410	+	0.662107i	$0.769663\pi$
$720$	−27.4694	+	11.8925i	−1.02372	+	0.443209i
$721$	−56.5404	−	18.3711i	−2.10567	−	0.684175i
$722$	19.5509	−	0.461564i	0.727609	−	0.0171776i
$723$	−1.10735	+	1.52413i	−0.0411827	+	0.0566832i
$724$	−3.30882	−	4.12937i	−0.122971	−	0.153467i
$725$	13.1626			0.488848
$726$		0			0
$727$			8.57922i			0.318186i	0.987264	+	0.159093i	$0.0508569\pi$
$727$			8.57922i			0.318186i	−0.987264	+	0.159093i	$0.949143\pi$
$728$	−12.6545	+	0.897588i	−0.469007	+	0.0332668i
$729$	14.7011	+	10.6810i	0.544486	+	0.395592i
$730$	3.52354	−	0.0831847i	0.130412	−	0.00307881i
$731$	−10.9125	+	33.5853i	−0.403615	+	1.24220i
$732$	5.44607	−	0.257288i	0.201292	−	0.00950965i
$733$	−22.2111	+	16.1373i	−0.820386	+	0.596045i	−0.916823	−	0.399294i	$-0.869255\pi$
$733$	−22.2111	+	16.1373i	−0.820386	+	0.596045i	0.0964371	+	0.995339i	$0.469255\pi$
$734$	−29.7043	+	10.4328i	−1.09640	+	0.385081i
$735$	3.99025	−	1.29651i	0.147183	−	0.0478225i
$736$	4.25447	+	35.8813i	0.156822	+	1.32260i
$737$		0			0
$738$	22.8284	−	33.0329i	0.840326	−	1.21596i
$739$	−45.3553	+	14.7368i	−1.66842	+	0.542103i	−0.982611	−	0.185678i	$-0.940552\pi$
$739$	−45.3553	+	14.7368i	−1.66842	+	0.542103i	−0.685810	+	0.727781i	$0.740552\pi$
$740$	−6.75254	+	24.6913i	−0.248228	+	0.907670i
$741$	0.754677	+	1.03872i	0.0277238	+	0.0381585i
$742$	−21.1289	−	27.6831i	−0.775666	−	1.01628i
$743$	−7.78602	+	23.9629i	−0.285641	+	0.879114i	0.700564	+	0.713589i	$0.252932\pi$
$743$	−7.78602	+	23.9629i	−0.285641	+	0.879114i	−0.986206	+	0.165524i	$0.947068\pi$
$744$	−1.18996	+	0.482159i	−0.0436261	+	0.0176768i
$745$	32.8242	−	45.1786i	1.20258	−	1.65522i
$746$	0.0947483	−	0.316865i	0.00346898	−	0.0116013i
$747$		−	12.8643i		−	0.470680i
$748$		0			0
$749$			28.6493i			1.04682i
$750$	−4.45465	−	1.33202i	−0.162661	−	0.0486385i
$751$	−4.28806	+	5.90201i	−0.156474	+	0.215367i	−0.880055	−	0.474871i	$-0.842495\pi$
$751$	−4.28806	+	5.90201i	−0.156474	+	0.215367i	0.723582	+	0.690239i	$0.242495\pi$
$752$		0			0
$753$	2.35700	−	7.25410i	0.0858939	−	0.264354i
$754$	−10.0846	+	7.69697i	−0.367258	+	0.280307i
$755$	−20.4696	−	28.1741i	−0.744967	−	1.02536i
$756$	−4.19131	+	15.3259i	−0.152437	+	0.557398i
$757$	−27.2471	+	8.85313i	−0.990314	+	0.321772i	−0.758988	−	0.651104i	$-0.774306\pi$
$757$	−27.2471	+	8.85313i	−0.990314	+	0.321772i	−0.231325	+	0.972876i	$0.574306\pi$
$758$	18.6975	+	12.9214i	0.679122	+	0.469328i
$759$		0			0
$760$	4.10051	−	16.5165i	0.148741	−	0.599116i
$761$	7.01320	−	2.27873i	0.254228	−	0.0826038i	−0.179130	−	0.983825i	$-0.557328\pi$
$761$	7.01320	−	2.27873i	0.254228	−	0.0826038i	0.433359	+	0.901222i	$0.357328\pi$
$762$	0.109596	+	0.312041i	0.00397023	+	0.0113041i
$763$	−7.25734	+	5.27276i	−0.262733	+	0.190887i
$764$	1.60168	+	33.9030i	0.0579467	+	1.22657i
$765$	−12.6959	+	39.0740i	−0.459021	+	1.41272i
$766$	−0.243501	−	10.3142i	−0.00879806	−	0.372668i
$767$	3.57572	+	2.59791i	0.129112	+	0.0938052i
$768$	6.50961	−	1.24404i	0.234895	−	0.0448904i
$769$			2.82590i			0.101905i	0.998701	+	0.0509523i	$0.0162256\pi$
$769$			2.82590i			0.101905i	−0.998701	+	0.0509523i	$0.983774\pi$
$770$		0			0
$771$	2.68629			0.0967444
$772$	16.0883	+	20.0780i	0.579031	+	0.722624i
$773$	−5.15326	+	7.09285i	−0.185350	+	0.255112i	−0.891573	−	0.452877i	$-0.850398\pi$
$773$	−5.15326	+	7.09285i	−0.185350	+	0.255112i	0.706223	+	0.707989i	$0.250398\pi$
$774$	−0.607240	−	25.7214i	−0.0218268	−	0.924538i
$775$	−2.08454	−	0.677307i	−0.0748788	−	0.0243296i
$776$	−17.9657	−	11.2013i	−0.644931	−	0.402103i
$777$	3.87572	+	5.33447i	0.139041	+	0.191373i
$778$	−43.4704	+	15.2678i	−1.55849	+	0.547376i
$779$	7.05437	+	21.7111i	0.252749	+	0.777882i
$780$	−2.79457	+	1.05625i	−0.100062	+	0.0378197i
$781$		0			0
$782$	40.7990	+	28.1954i	1.45897	+	1.00826i
$783$	4.90988	+	15.1111i	0.175465	+	0.540025i
$784$	15.2455	−	1.44371i	0.544482	−	0.0515610i
$785$	0.971638	−	0.705936i	0.0346792	−	0.0251959i
$786$	2.42470	+	3.17684i	0.0864860	+	0.113314i
$787$	31.3289	+	10.1794i	1.11675	+	0.362855i	0.808528	−	0.588458i	$-0.200265\pi$
$787$	31.3289	+	10.1794i	1.11675	+	0.362855i	0.308226	+	0.951313i	$0.400265\pi$
$788$	−17.4469	−	11.4584i	−0.621519	−	0.408187i
$789$	6.42711	+	4.66957i	0.228811	+	0.166241i
$790$	−33.3654	−	9.97683i	−1.18709	−	0.354960i
$791$	20.3085			0.722088
$792$		0			0
$793$	−8.97056			−0.318554
$794$	−30.4183	−	9.09560i	−1.07950	−	0.322791i
$795$	−6.63476	−	4.82043i	−0.235311	−	0.170963i
$796$	23.2383	−	35.3834i	0.823659	−	1.25413i
$797$	41.9130	+	13.6183i	1.48463	+	0.482387i	0.935493	−	0.353344i	$-0.114955\pi$
$797$	41.9130	+	13.6183i	1.48463	+	0.482387i	0.549140	+	0.835731i	$0.314955\pi$
$798$	−2.65961	−	3.48463i	−0.0941493	−	0.123354i
$799$		0			0
$800$	9.87233	+	5.52605i	0.349039	+	0.195375i
$801$	9.31443	+	28.6669i	0.329109	+	1.01289i
$802$	5.61750	+	3.88215i	0.198361	+	0.137083i
$803$		0			0
$804$	−1.77817	−	4.70461i	−0.0627114	−	0.165919i
$805$	17.1846	+	52.8887i	0.605677	+	1.86408i
$806$	1.99313	−	0.700033i	0.0702051	−	0.0246576i
$807$	3.33131	+	4.58515i	0.117268	+	0.161405i
$808$	41.4065	+	25.8162i	1.45668	+	0.908211i
$809$	0.895864	+	0.291084i	0.0314969	+	0.0102340i	0.324723	−	0.945809i	$-0.394729\pi$
$809$	0.895864	+	0.291084i	0.0314969	+	0.0102340i	−0.293226	+	0.956043i	$0.594729\pi$
$810$	−0.661022	−	27.9996i	−0.0232260	−	0.983804i
$811$	−3.32205	+	4.57240i	−0.116653	+	0.160559i	−0.863350	−	0.504605i	$-0.831638\pi$
$811$	−3.32205	+	4.57240i	−0.116653	+	0.160559i	0.746698	+	0.665164i	$0.231638\pi$
$812$	33.8011	−	27.0844i	1.18618	−	0.950477i
$813$	5.21828			0.183013
$814$		0			0
$815$			33.9408i			1.18890i
$816$	4.62915	−	7.83046i	0.162053	−	0.274121i
$817$	11.8338	+	8.59778i	0.414013	+	0.300798i
$818$	−0.0628817	−	2.66354i	−0.00219861	−	0.0931286i
$819$	3.92028	−	12.0654i	0.136986	−	0.421599i
$820$	−53.0591	+	2.50667i	−1.85290	+	0.0875366i
$821$	−17.2651	+	12.5438i	−0.602556	+	0.437783i	−0.846785	−	0.531935i	$-0.821465\pi$
$821$	−17.2651	+	12.5438i	−0.602556	+	0.437783i	0.244229	+	0.969718i	$0.421465\pi$
$822$	−1.68044	−	4.78454i	−0.0586120	−	0.166880i
$823$	34.1854	−	11.1075i	1.19163	−	0.387183i	0.354953	−	0.934884i	$-0.384497\pi$
$823$	34.1854	−	11.1075i	1.19163	−	0.387183i	0.836674	+	0.547701i	$0.184497\pi$
$824$	−49.5937	−	12.3125i	−1.72768	−	0.428927i
$825$		0			0
$826$	−12.4142	−	8.57922i	−0.431946	−	0.298509i
$827$	−48.2602	+	15.6807i	−1.67817	+	0.545271i	−0.984556	−	0.175072i	$-0.943984\pi$
$827$	−48.2602	+	15.6807i	−1.67817	+	0.545271i	−0.693617	+	0.720344i	$0.743984\pi$
$828$	−34.8528	−	9.53150i	−1.21122	−	0.331243i
$829$	24.6153	+	33.8801i	0.854925	+	1.17670i	0.982756	+	0.184908i	$0.0591986\pi$
$829$	24.6153	+	33.8801i	0.854925	+	1.17670i	−0.127831	+	0.991796i	$0.540801\pi$
$830$	−13.5278	+	10.3250i	−0.469558	+	0.358386i
$831$	−0.493468	+	1.51874i	−0.0171182	+	0.0526844i
$832$	−10.7951	+	1.53915i	−0.374253	+	0.0533603i
$833$	12.3545	−	17.0045i	0.428059	−	0.589173i
$834$	−11.0488	−	3.30378i	−0.382588	−	0.114401i
$835$		−	57.9563i		−	2.00566i
$836$		0			0
$837$		−	2.64575i		−	0.0914505i
$838$	6.53999	−	21.8716i	0.225920	−	0.755541i
$839$	−31.9679	+	44.0000i	−1.10365	+	1.51905i	−0.273203	+	0.961956i	$0.588083\pi$
$839$	−31.9679	+	44.0000i	−1.10365	+	1.51905i	−0.830451	+	0.557092i	$0.811917\pi$
$840$	9.45347	−	3.83044i	0.326176	−	0.132163i
$841$	4.42318	−	13.6131i	0.152523	−	0.469419i
$842$	−6.42088	−	8.41263i	−0.221278	−	0.289918i
$843$	1.56603	+	2.15545i	0.0539368	+	0.0742377i
$844$	17.5485	+	4.79914i	0.604043	+	0.165193i
$845$	−28.0365	+	9.10961i	−0.964485	+	0.313380i
$846$		0			0
$847$		0			0
$848$	−19.7990	−	22.4499i	−0.679900	−	0.770934i
$849$	−0.742158	+	0.241142i	−0.0254708	+	0.00827596i
$850$	14.6512	−	5.14583i	0.502532	−	0.176500i
$851$	−24.9982	+	18.1623i	−0.856928	+	0.622595i
$852$	−0.249708	−	5.28561i	−0.00855485	−	0.181082i
$853$	17.9547	−	55.2589i	0.614758	−	1.89203i	0.209579	−	0.977792i	$-0.432791\pi$
$853$	17.9547	−	55.2589i	0.614758	−	1.89203i	0.405179	−	0.914237i	$-0.367209\pi$
$854$	30.6189	−	0.722860i	1.04776	−	0.0247358i
$855$	13.7678	+	10.0029i	0.470847	+	0.342090i
$856$	1.74229	+	24.5633i	0.0595501	+	0.839557i
$857$		−	21.9607i		−	0.750165i	−0.926992	−	0.375082i	$-0.877614\pi$
$857$		−	21.9607i		−	0.750165i	0.926992	−	0.375082i	$-0.122386\pi$
$858$		0			0
$859$	−49.2426			−1.68014			−0.840069	−	0.542480i	$-0.817485\pi$
$859$	−49.2426			−1.68014			−0.840069	+	0.542480i	$0.817485\pi$
$860$	−26.5607	+	21.2828i	−0.905714	+	0.725739i
$861$	−8.04249	+	11.0695i	−0.274087	+	0.377249i
$862$	−3.05595	+	0.0721457i	−0.104086	+	0.00245729i
$863$	−14.2341	−	4.62494i	−0.484535	−	0.157435i	0.0565554	−	0.998399i	$-0.481988\pi$
$863$	−14.2341	−	4.62494i	−0.484535	−	0.157435i	−0.541090	+	0.840965i	$0.681988\pi$
$864$	−2.66151	+	13.3950i	−0.0905463	+	0.455707i
$865$	8.47881	+	11.6701i	0.288288	+	0.396794i
$866$	−8.12767	−	23.1411i	−0.276189	−	0.786367i
$867$	−1.68218	−	5.17722i	−0.0571298	−	0.175828i
$868$	−6.74668	+	2.55000i	−0.228997	+	0.0865528i
$869$		0			0
$870$	5.79899	−	8.39119i	0.196604	−	0.284488i
$871$	2.55714	+	7.87007i	0.0866454	+	0.266667i
$872$	−5.90163	+	4.96210i	−0.199854	+	0.168038i
$873$	17.1282	−	12.4443i	0.579700	−	0.421177i
$874$	16.3295	−	12.4634i	0.552355	−	0.421581i
$875$	−24.8404	−	8.07115i	−0.839760	−	0.272855i
$876$	0.428376	−	0.652259i	0.0144735	−	0.0220378i
$877$	23.6922	+	17.2134i	0.800029	+	0.581255i	0.910923	−	0.412577i	$-0.135371\pi$
$877$	23.6922	+	17.2134i	0.800029	+	0.581255i	−0.110893	+	0.993832i	$0.535371\pi$
$878$	13.9791	−	46.7500i	0.471771	−	1.57774i
$879$	6.01673			0.202939
$880$		0			0
$881$	6.51472			0.219486			0.109743	−	0.993960i	$-0.464997\pi$
$881$	6.51472			0.219486			0.109743	+	0.993960i	$0.464997\pi$
$882$	−4.38714	+	14.6718i	−0.147723	+	0.494026i
$883$	3.51368	+	2.55284i	0.118245	+	0.0859098i	0.645336	−	0.763899i	$-0.276717\pi$
$883$	3.51368	+	2.55284i	0.118245	+	0.0859098i	−0.527091	+	0.849809i	$0.676717\pi$
$884$	−8.21597	+	12.5099i	−0.276333	+	0.420754i
$885$	−3.37970	−	1.09813i	−0.113607	−	0.0369133i
$886$	−29.6945	+	22.6641i	−0.997605	+	0.761414i
$887$	37.6492	−	27.3537i	1.26414	−	0.918448i	0.265182	−	0.964198i	$-0.414568\pi$
$887$	37.6492	−	27.3537i	1.26414	−	0.918448i	0.998953	+	0.0457503i	$0.0145679\pi$
$888$	3.64737	+	4.33796i	0.122398	+	0.145572i
$889$	0.574112	+	1.76693i	0.0192551	+	0.0592611i
$890$	22.6696	−	32.8032i	0.759888	−	1.09956i
$891$		0			0
$892$	7.84924	−	2.96673i	0.262812	−	0.0993336i
$893$		0			0
$894$	−4.09721	−	11.6656i	−0.137031	−	0.390156i
$895$	15.1282	+	20.8222i	0.505681	+	0.696010i
$896$	36.7225	−	6.12339i	1.22681	−	0.204568i
$897$	−3.42975	−	1.11439i	−0.114516	−	0.0372085i
$898$	22.5795	−	0.533064i	0.753488	−	0.0177886i
$899$	−4.23940	+	5.83504i	−0.141392	+	0.194609i
$900$	−8.82897	+	7.07455i	−0.294299	+	0.235818i
$901$	−41.0848			−1.36873
$902$		0			0
$903$			8.76725i			0.291756i
$904$	17.4121	−	1.23505i	0.579118	−	0.0410770i
$905$	−5.66312	−	4.11450i	−0.188248	−	0.136771i
$906$	−7.70834	+	0.181981i	−0.256093	+	0.00604591i
$907$	−10.3566	+	31.8744i	−0.343886	+	1.05837i	0.618292	+	0.785949i	$0.287825\pi$
$907$	−10.3566	+	31.8744i	−0.343886	+	1.05837i	−0.962178	+	0.272423i	$0.912175\pi$
$908$	−1.25097	−	26.4794i	−0.0415148	−	0.878751i
$909$	−39.4762	+	28.6811i	−1.30934	+	0.951293i
$910$	−15.8342	+	5.56131i	−0.524897	+	0.184355i
$911$	−42.7023	+	13.8748i	−1.41479	+	0.459694i	−0.913943	−	0.405842i	$-0.866978\pi$
$911$	−42.7023	+	13.8748i	−1.41479	+	0.459694i	−0.500848	+	0.865535i	$0.666978\pi$
$912$	−2.49221	−	2.82590i	−0.0825253	−	0.0935749i
$913$		0			0
$914$	18.2843	−	26.4575i	0.604790	−	0.875137i
$915$	6.85950	−	2.22879i	0.226768	−	0.0736814i
$916$	−19.5406	−	5.34393i	−0.645639	−	0.176569i
$917$	13.1957	+	18.1624i	0.435762	+	0.599775i
$918$	11.3727	+	14.9005i	0.375354	+	0.491789i
$919$	7.29255	−	22.4442i	0.240559	−	0.740365i	−0.755776	−	0.654830i	$-0.772740\pi$
$919$	7.29255	−	22.4442i	0.240559	−	0.740365i	0.996335	−	0.0855346i	$-0.0272598\pi$
$920$	17.9501	+	44.3005i	0.591796	+	1.46055i
$921$	5.44175	−	7.48992i	0.179312	−	0.246801i
$922$	−1.56195	+	5.22361i	−0.0514402	+	0.172031i
$923$			8.70626i			0.286570i
$924$		0			0
$925$			9.67513i			0.318116i
$926$	−30.1635	−	9.01942i	−0.991234	−	0.296396i
$927$	30.0354	−	41.3402i	0.986492	−	1.35779i
$928$	27.3332	−	25.2772i	0.897256	−	0.829764i
$929$	10.6565	−	32.7975i	0.349630	−	1.07605i	−0.609429	−	0.792841i	$-0.708601\pi$
$929$	10.6565	−	32.7975i	0.349630	−	1.07605i	0.959058	−	0.283209i	$-0.0913989\pi$
$930$	−1.35016	+	1.03050i	−0.0442734	+	0.0337913i
$931$	−5.11741	−	7.04351i	−0.167716	−	0.230842i
$932$	16.0431	+	4.38743i	0.525508	+	0.143715i
$933$	5.89596	−	1.91571i	0.193025	−	0.0627177i
$934$	−41.9659	−	29.0018i	−1.37317	−	0.948969i
$935$		0			0
$936$	2.62742	−	10.5830i	0.0858798	−	0.345916i
$937$	−20.7322	+	6.73630i	−0.677291	+	0.220065i	−0.627409	−	0.778690i	$-0.715885\pi$
$937$	−20.7322	+	6.73630i	−0.677291	+	0.220065i	−0.0498823	+	0.998755i	$0.515885\pi$
$938$	−9.36237	−	26.6565i	−0.305692	−	0.870367i
$939$	−2.62335	+	1.90598i	−0.0856098	+	0.0621992i
$940$		0			0
$941$	−4.56094	+	14.0371i	−0.148683	+	0.457598i	−0.997466	−	0.0711426i	$-0.977335\pi$
$941$	−4.56094	+	14.0371i	−0.148683	+	0.457598i	0.848784	+	0.528740i	$0.177335\pi$
$942$	−0.00627597	−	0.265837i	−0.000204482	−	0.00866145i
$943$	−51.8737	−	37.6884i	−1.68924	−	1.22730i
$944$	−11.1654	−	6.60068i	−0.363403	−	0.214834i
$945$			21.0188i			0.683741i
$946$		0			0
$947$	24.4142			0.793355			0.396678	−	0.917958i	$-0.370163\pi$
$947$	24.4142			0.793355			0.396678	+	0.917958i	$0.370163\pi$
$948$	−6.01710	+	4.82143i	−0.195426	+	0.156593i
$949$	−0.754677	+	1.03872i	−0.0244979	+	0.0337184i
$950$	−0.151810	−	6.43036i	−0.00492537	−	0.208628i
$951$	6.07479	+	1.97382i	0.196988	+	0.0640054i
$952$	27.0352	−	43.3617i	0.876216	−	1.40536i
$953$	21.4820	+	29.5674i	0.695870	+	0.957783i	0.999987	+	0.00514842i	$0.00163880\pi$
$953$	21.4820	+	29.5674i	0.695870	+	0.957783i	−0.304116	+	0.952635i	$0.598361\pi$
$954$	28.2420	−	9.91921i	0.914368	−	0.321146i
$955$	13.8747	+	42.7020i	0.448975	+	1.38180i
$956$	−3.85525	−	10.2000i	−0.124688	−	0.329892i
$957$		0			0
$958$	−31.8284	−	21.9960i	−1.02833	−	0.710659i
$959$	−8.80289	−	27.0925i	−0.284260	−	0.874863i
$960$	7.87226	−	3.85904i	0.254076	−	0.124550i
$961$	−24.1079	+	17.5154i	−0.777674	+	0.565013i
$962$	−5.65762	−	7.41262i	−0.182409	−	0.238992i
$963$	−23.4198	−	7.60955i	−0.754692	−	0.245214i
$964$	−4.99351	+	7.60329i	−0.160830	+	0.244885i
$965$	27.5355	+	20.0057i	0.886399	+	0.644007i
$966$	11.7964	+	3.52734i	0.379544	+	0.113490i
$967$	−3.85525			−0.123976			−0.0619882	−	0.998077i	$-0.519744\pi$
$967$	−3.85525			−0.123976			−0.0619882	+	0.998077i	$0.519744\pi$
$968$		0			0
$969$	−5.17157			−0.166135
$970$	−26.8334	−	8.02367i	−0.861569	−	0.257624i
$971$	−26.5686	−	19.3032i	−0.852628	−	0.619470i	0.0732417	−	0.997314i	$-0.476666\pi$
$971$	−26.5686	−	19.3032i	−0.852628	−	0.619470i	−0.925869	+	0.377844i	$0.876666\pi$
$972$	−17.2907	−	11.3558i	−0.554600	−	0.364237i
$973$	−61.6113	−	20.0187i	−1.97517	−	0.641771i
$974$	−22.8626	−	29.9545i	−0.732564	−	0.959805i
$975$	−0.913522	+	0.663713i	−0.0292561	+	0.0212558i
$976$	26.2080	−	2.48183i	0.838898	−	0.0794414i
$977$	−14.0996	−	43.3943i	−0.451088	−	1.38831i	−0.875667	−	0.482915i	$-0.839578\pi$
$977$	−14.0996	−	43.3943i	−0.451088	−	1.38831i	0.424580	−	0.905391i	$-0.360422\pi$
$978$	6.18209	+	4.27232i	0.197681	+	0.136614i
$979$		0			0
$980$	18.9497	−	7.16233i	0.605327	−	0.228792i
$981$	−2.38267	−	7.33311i	−0.0760729	−	0.234128i
$982$	−34.3299	+	12.0574i	−1.09551	+	0.384768i
$983$	−10.5086	−	14.4638i	−0.335172	−	0.461325i	0.607851	−	0.794051i	$-0.292032\pi$
$983$	−10.5086	−	14.4638i	−0.335172	−	0.461325i	−0.943024	+	0.332726i	$0.892032\pi$
$984$	−6.22227	+	9.97988i	−0.198359	+	0.318147i
$985$	−26.2611	−	8.53275i	−0.836748	−	0.271876i
$986$	−1.20603	−	51.0850i	−0.0384079	−	1.62688i
$987$		0			0
$988$	3.87652	+	4.83786i	0.123329	+	0.153913i
$989$	−41.0848			−1.30642
$990$		0			0
$991$			29.9333i			0.950861i	0.879753	+	0.475431i	$0.157708\pi$
$991$			29.9333i			0.950861i	−0.879753	+	0.475431i	$0.842292\pi$
$992$	−5.62938	+	2.59661i	−0.178733	+	0.0824425i
$993$	6.05572	+	4.39974i	0.192172	+	0.139621i
$994$	−0.701563	−	29.7168i	−0.0222522	−	0.942558i
$995$	17.3050	−	53.2592i	0.548604	−	1.68843i
$996$	0.177807	+	3.76367i	0.00563403	+	0.119256i
$997$	44.9898	−	32.6870i	1.42484	−	1.03521i	0.433893	−	0.900964i	$-0.357140\pi$
$997$	44.9898	−	32.6870i	1.42484	−	1.03521i	0.990948	−	0.134243i	$-0.0428604\pi$
$998$	8.66292	+	24.6651i	0.274220	+	0.780759i
$999$	−11.1073	+	3.60898i	−0.351420	+	0.114183i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	968.2.k.g.699.5		32
8.3	odd	2	inner	968.2.k.g.699.7		32
11.2	odd	10	inner	968.2.k.g.475.7		32
11.3	even	5		88.2.g.b.43.1	✓	8
11.4	even	5	inner	968.2.k.g.723.8		32
11.5	even	5	inner	968.2.k.g.403.6		32
11.6	odd	10	inner	968.2.k.g.403.3		32
11.7	odd	10	inner	968.2.k.g.723.1		32
11.8	odd	10		88.2.g.b.43.8	yes	8
11.9	even	5	inner	968.2.k.g.475.2		32
11.10	odd	2	inner	968.2.k.g.699.4		32
33.8	even	10		792.2.h.g.307.1		8
33.14	odd	10		792.2.h.g.307.8		8
44.3	odd	10		352.2.g.b.175.1		8
44.19	even	10		352.2.g.b.175.2		8
88.3	odd	10		88.2.g.b.43.7	yes	8
88.19	even	10		88.2.g.b.43.2	yes	8
88.27	odd	10	inner	968.2.k.g.403.1		32
88.35	even	10	inner	968.2.k.g.475.5		32
88.43	even	2	inner	968.2.k.g.699.2		32
88.51	even	10	inner	968.2.k.g.723.6		32
88.59	odd	10	inner	968.2.k.g.723.3		32
88.69	even	10		352.2.g.b.175.4		8
88.75	odd	10	inner	968.2.k.g.475.4		32
88.83	even	10	inner	968.2.k.g.403.8		32
88.85	odd	10		352.2.g.b.175.3		8
132.47	even	10		3168.2.h.g.2287.5		8
132.107	odd	10		3168.2.h.g.2287.8		8
176.3	odd	20		2816.2.e.o.2815.6		16
176.19	even	20		2816.2.e.o.2815.5		16
176.69	even	20		2816.2.e.o.2815.7		16
176.85	odd	20		2816.2.e.o.2815.8		16
176.91	odd	20		2816.2.e.o.2815.12		16
176.107	even	20		2816.2.e.o.2815.11		16
176.157	even	20		2816.2.e.o.2815.9		16
176.173	odd	20		2816.2.e.o.2815.10		16
264.107	odd	10		792.2.h.g.307.7		8
264.173	even	10		3168.2.h.g.2287.1		8
264.179	even	10		792.2.h.g.307.2		8
264.245	odd	10		3168.2.h.g.2287.4		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
88.2.g.b.43.1	✓	8	11.3	even	5
88.2.g.b.43.2	yes	8	88.19	even	10
88.2.g.b.43.7	yes	8	88.3	odd	10
88.2.g.b.43.8	yes	8	11.8	odd	10
352.2.g.b.175.1		8	44.3	odd	10
352.2.g.b.175.2		8	44.19	even	10
352.2.g.b.175.3		8	88.85	odd	10
352.2.g.b.175.4		8	88.69	even	10
792.2.h.g.307.1		8	33.8	even	10
792.2.h.g.307.2		8	264.179	even	10
792.2.h.g.307.7		8	264.107	odd	10
792.2.h.g.307.8		8	33.14	odd	10
968.2.k.g.403.1		32	88.27	odd	10	inner
968.2.k.g.403.3		32	11.6	odd	10	inner
968.2.k.g.403.6		32	11.5	even	5	inner
968.2.k.g.403.8		32	88.83	even	10	inner
968.2.k.g.475.2		32	11.9	even	5	inner
968.2.k.g.475.4		32	88.75	odd	10	inner
968.2.k.g.475.5		32	88.35	even	10	inner
968.2.k.g.475.7		32	11.2	odd	10	inner
968.2.k.g.699.2		32	88.43	even	2	inner
968.2.k.g.699.4		32	11.10	odd	2	inner
968.2.k.g.699.5		32	1.1	even	1	trivial
968.2.k.g.699.7		32	8.3	odd	2	inner
968.2.k.g.723.1		32	11.7	odd	10	inner
968.2.k.g.723.3		32	88.59	odd	10	inner
968.2.k.g.723.6		32	88.51	even	10	inner
968.2.k.g.723.8		32	11.4	even	5	inner
2816.2.e.o.2815.5		16	176.19	even	20
2816.2.e.o.2815.6		16	176.3	odd	20
2816.2.e.o.2815.7		16	176.69	even	20
2816.2.e.o.2815.8		16	176.85	odd	20
2816.2.e.o.2815.9		16	176.157	even	20
2816.2.e.o.2815.10		16	176.173	odd	20
2816.2.e.o.2815.11		16	176.107	even	20
2816.2.e.o.2815.12		16	176.91	odd	20
3168.2.h.g.2287.1		8	264.173	even	10
3168.2.h.g.2287.4		8	264.245	odd	10
3168.2.h.g.2287.5		8	132.47	even	10
3168.2.h.g.2287.8		8	132.107	odd	10

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:	\( N \)	\(=\)	\( 968 = 2^{3} \cdot 11^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	968.k (of order \(10\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.405150 - 1.35494i) q^{2} +(-0.335106 - 0.243469i) q^{3} +(-1.67171 - 1.09791i) q^{4} +(-2.51626 - 0.817582i) q^{5} +(-0.465653 + 0.355406i) q^{6} +(-2.66220 + 1.93420i) q^{7} +(-2.16488 + 1.82024i) q^{8} +(-0.874032 - 2.68999i) q^{9} +(-2.12723 + 3.07813i) q^{10} +(0.292893 + 0.774923i) q^{12} +(-0.421201 - 1.29632i) q^{13} +(1.54213 + 4.39075i) q^{14} +(0.644157 + 0.886607i) q^{15} +(1.58921 + 3.67075i) q^{16} +(5.22148 + 1.69656i) q^{17} +(-3.99889 + 0.0944070i) q^{18} +(1.33669 - 1.83979i) q^{19} +(3.30882 + 4.12937i) q^{20} +1.36303 q^{21} +6.38741i q^{23} +(1.16864 - 0.0828919i) q^{24} +(1.61803 + 1.17557i) q^{25} +(-1.92709 + 0.0454952i) q^{26} +(-0.746033 + 2.29605i) q^{27} +(6.57398 - 0.310574i) q^{28} +(5.32440 - 3.86840i) q^{29} +(1.46228 - 0.513584i) q^{30} +(-1.04227 + 0.338654i) q^{31} +(5.61750 - 0.666071i) q^{32} +(4.41421 - 6.38741i) q^{34} +(8.28015 - 2.69038i) q^{35} +(-1.49223 + 5.45649i) q^{36} +(2.84345 + 3.91367i) q^{37} +(-1.95124 - 2.55652i) q^{38} +(-0.174467 + 0.536955i) q^{39} +(6.93561 - 2.81023i) q^{40} +(-5.90043 + 8.12124i) q^{41} +(0.552234 - 1.84683i) q^{42} +6.43215i q^{43} +7.48331i q^{45} +(8.65453 + 2.58786i) q^{46} +(0.361160 - 1.61701i) q^{48} +(1.18305 - 3.64105i) q^{49} +(2.24837 - 1.71605i) q^{50} +(-1.33669 - 1.83979i) q^{51} +(-0.719116 + 2.62951i) q^{52} +(-7.11706 + 2.31247i) q^{53} +(2.80875 + 1.94107i) q^{54} +(2.24264 - 9.03316i) q^{56} +(-0.895864 + 0.291084i) q^{57} +(-3.08426 - 8.78150i) q^{58} +(-2.62335 + 1.90598i) q^{59} +(-0.103432 - 2.18937i) q^{60} +(2.03374 - 6.25920i) q^{61} +(0.0365790 + 1.54941i) q^{62} +(7.52983 + 5.47074i) q^{63} +(1.37345 - 7.88122i) q^{64} +3.60625i q^{65} -6.07107 q^{67} +(-6.86612 - 8.56884i) q^{68} +(1.55513 - 2.14046i) q^{69} +(-0.290597 - 12.3091i) q^{70} +(-6.07479 - 1.97382i) q^{71} +(6.78861 + 4.23258i) q^{72} +(-0.553674 - 0.762067i) q^{73} +(6.45480 - 2.26707i) q^{74} +(-0.255998 - 0.787881i) q^{75} +(-4.25447 + 1.60804i) q^{76} +(0.656854 + 0.453939i) q^{78} +(2.87614 + 8.85185i) q^{79} +(-0.997718 - 10.5359i) q^{80} +(-6.05572 + 4.39974i) q^{81} +(8.61321 + 11.2850i) q^{82} +(4.32561 + 1.40548i) q^{83} +(-2.27860 - 1.49648i) q^{84} +(-11.7515 - 8.53797i) q^{85} +(8.71516 + 2.60599i) q^{86} -2.72607 q^{87} -10.6569 q^{89} +(10.1394 + 3.03187i) q^{90} +(3.62867 + 2.63638i) q^{91} +(7.01277 - 10.6779i) q^{92} +(0.431722 + 0.140275i) q^{93} +(-4.86763 + 3.53654i) q^{95} +(-2.04463 - 1.14448i) q^{96} +(2.31308 + 7.11893i) q^{97} +(-4.45408 - 3.07813i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q + 8 q^{3} + 32 q^{12} + 8 q^{14} + 24 q^{16} + 16 q^{25} - 24 q^{26} + 8 q^{27} + 96 q^{34} + 16 q^{36} + 8 q^{38} + 24 q^{42} - 24 q^{48} - 8 q^{49} - 64 q^{56} - 16 q^{58} + 8 q^{59} - 56 q^{60}+ \cdots + 8 q^{97}+O(q^{100}) \) 32 * q + 8 * q^3 + 32 * q^12 + 8 * q^14 + 24 * q^16 + 16 * q^25 - 24 * q^26 + 8 * q^27 + 96 * q^34 + 16 * q^36 + 8 * q^38 + 24 * q^42 - 24 * q^48 - 8 * q^49 - 64 * q^56 - 16 * q^58 + 8 * q^59 - 56 * q^60 + 32 * q^67 + 56 * q^70 - 16 * q^75 - 160 * q^78 - 56 * q^80 + 8 * q^81 + 8 * q^82 - 64 * q^86 - 160 * q^89 - 32 * q^91 + 56 * q^92 + 8 * q^97

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