LMFDB - Embedded newform 968.2.o.d.245.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [968,2,Mod(245,968)]

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([0, 5, 8]))

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

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

chi := DirichletCharacter("968.245");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 968 = 2^{3} \cdot 11^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	968.o (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:	$40$
Relative dimension:	$10$ over $\Q(\zeta_{10})$
Twist minimal:	no (minimal twist has level 88)
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			245.1
Character	$\chi$	$=$	968.245
Dual form			968.2.o.d.565.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.40920 - 0.118997i) q^{2} +(-0.305500 + 0.0992629i) q^{3} +(1.97168 + 0.335382i) q^{4} +(-0.756671 + 1.04147i) q^{5} +(0.442322 - 0.103527i) q^{6} +(1.02182 - 3.14484i) q^{7} +(-2.73858 - 0.707244i) q^{8} +(-2.34357 + 1.70271i) q^{9} +(1.19023 - 1.37759i) q^{10} +(-0.635639 + 0.0932556i) q^{12} +(1.81401 + 2.49677i) q^{13} +(-1.81418 + 4.31012i) q^{14} +(0.127784 - 0.393278i) q^{15} +(3.77504 + 1.32253i) q^{16} +(-2.58719 - 1.87971i) q^{17} +(3.50518 - 2.12057i) q^{18} +(4.48707 - 1.45794i) q^{19} +(-1.84120 + 1.79967i) q^{20} +1.06218i q^{21} -3.47634 q^{23} +(0.906838 - 0.0557763i) q^{24} +(1.03298 + 3.17919i) q^{25} +(-2.25919 - 3.73431i) q^{26} +(1.11337 - 1.53243i) q^{27} +(3.06943 - 5.85793i) q^{28} +(5.88781 + 1.91307i) q^{29} +(-0.226872 + 0.539000i) q^{30} +(2.16785 - 1.57504i) q^{31} +(-5.16240 - 2.31293i) q^{32} +(3.42219 + 2.95675i) q^{34} +(2.50207 + 3.44381i) q^{35} +(-5.19183 + 2.57120i) q^{36} +(7.46003 + 2.42391i) q^{37} +(-6.49667 + 1.52057i) q^{38} +(-0.802018 - 0.582700i) q^{39} +(2.80877 - 2.31699i) q^{40} +(-1.60231 - 4.93140i) q^{41} +(0.126396 - 1.49682i) q^{42} -2.37086i q^{43} -3.72915i q^{45} +(4.89885 + 0.413675i) q^{46} +(0.986855 + 3.03723i) q^{47} +(-1.28455 - 0.0293115i) q^{48} +(-3.18281 - 2.31245i) q^{49} +(-1.07736 - 4.60302i) q^{50} +(0.976972 + 0.317438i) q^{51} +(2.73928 + 5.53122i) q^{52} +(-2.77602 - 3.82086i) q^{53} +(-1.75132 + 2.02701i) q^{54} +(-5.02251 + 7.88972i) q^{56} +(-1.22608 + 0.890800i) q^{57} +(-8.06944 - 3.39652i) q^{58} +(13.4517 + 4.37073i) q^{59} +(0.383847 - 0.732561i) q^{60} +(-9.14936 + 12.5930i) q^{61} +(-3.24236 + 1.96157i) q^{62} +(2.96003 + 9.11004i) q^{63} +(6.99961 + 3.87368i) q^{64} -3.97292 q^{65} +4.70162i q^{67} +(-4.47069 - 4.57387i) q^{68} +(1.06202 - 0.345072i) q^{69} +(-3.11611 - 5.15075i) q^{70} +(7.42164 + 5.39214i) q^{71} +(7.62229 - 3.00551i) q^{72} +(0.290193 - 0.893124i) q^{73} +(-10.2242 - 4.30350i) q^{74} +(-0.631151 - 0.868704i) q^{75} +(9.33604 - 1.36970i) q^{76} +(1.06086 + 0.916578i) q^{78} +(7.73885 - 5.62261i) q^{79} +(-4.23383 + 2.93086i) q^{80} +(2.49747 - 7.68644i) q^{81} +(1.67115 + 7.13999i) q^{82} +(0.751333 - 1.03412i) q^{83} +(-0.356235 + 2.09428i) q^{84} +(3.91531 - 1.27216i) q^{85} +(-0.282126 + 3.34101i) q^{86} -1.98862 q^{87} +15.3866 q^{89} +(-0.443758 + 5.25510i) q^{90} +(9.70557 - 3.15353i) q^{91} +(-6.85423 - 1.16590i) q^{92} +(-0.505936 + 0.696361i) q^{93} +(-1.02925 - 4.39749i) q^{94} +(-1.87684 + 5.77632i) q^{95} +(1.80670 + 0.194164i) q^{96} +(11.2973 - 8.20794i) q^{97} +(4.21004 + 3.63744i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q - 5 q^{2} - q^{4} - 8 q^{6} - 5 q^{8} + 10 q^{9} + 20 q^{10} - 6 q^{12} + 2 q^{14} + 22 q^{15} - 25 q^{16} - 4 q^{17} - 25 q^{18} + 8 q^{20} - 8 q^{23} + 40 q^{24} + 6 q^{25} - 20 q^{26} + 18 q^{28}+ \cdots + 144 q^{98}+O(q^{100}) $ 40 * q - 5 * q^2 - q^4 - 8 * q^6 - 5 * q^8 + 10 * q^9 + 20 * q^10 - 6 * q^12 + 2 * q^14 + 22 * q^15 - 25 * q^16 - 4 * q^17 - 25 * q^18 + 8 * q^20 - 8 * q^23 + 40 * q^24 + 6 * q^25 - 20 * q^26 + 18 * q^28 - 12 * q^30 + 4 * q^31 - 20 * q^32 + 10 * q^34 - 27 * q^36 - 33 * q^38 - 6 * q^39 + 20 * q^40 - 16 * q^41 - 20 * q^42 + 42 * q^46 + 4 * q^47 + 23 * q^48 + 6 * q^49 + 39 * q^50 - 108 * q^54 - 32 * q^56 - 4 * q^57 - 16 * q^58 + 94 * q^60 + 52 * q^62 + 30 * q^63 + 11 * q^64 + 36 * q^65 - 63 * q^68 + 52 * q^70 + 12 * q^71 - 44 * q^72 - 4 * q^73 + 26 * q^74 + 134 * q^76 - 12 * q^78 + 16 * q^79 + 16 * q^80 + 16 * q^81 + 54 * q^82 - 72 * q^84 - 10 * q^86 - 68 * q^87 - 16 * q^89 - 126 * q^90 - 64 * q^92 - 40 * q^94 - 26 * q^95 + 5 * q^96 - 20 * q^97 + 144 * q^98

Character values

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

$n$	$485$	$727$	$849$
$\chi(n)$	$-1$	$1$	$e\left(\frac{4}{5}\right)$

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 $

$2$	−1.40920	−	0.118997i	−0.996454	−	0.0841438i
$2$	−1.40920	−	0.118997i	−0.996454	−	0.0841438i
$3$	−0.305500	+	0.0992629i	−0.176380	+	0.0573095i	−0.395876	−	0.918304i	$-0.629559\pi$
$3$	−0.305500	+	0.0992629i	−0.176380	+	0.0573095i	0.219495	+	0.975614i	$0.429559\pi$
$4$	1.97168	+	0.335382i	0.985840	+	0.167691i
$5$	−0.756671	+	1.04147i	−0.338393	+	0.465759i	−0.943971	−	0.330027i	$-0.892942\pi$
$5$	−0.756671	+	1.04147i	−0.338393	+	0.465759i	0.605578	+	0.795786i	$0.292942\pi$
$6$	0.442322	−	0.103527i	0.180577	−	0.0422649i
$7$	1.02182	−	3.14484i	0.386212	−	1.18864i	−0.549384	−	0.835570i	$-0.685138\pi$
$7$	1.02182	−	3.14484i	0.386212	−	1.18864i	0.935597	−	0.353070i	$-0.114862\pi$
$8$	−2.73858	−	0.707244i	−0.968233	−	0.250048i
$9$	−2.34357	+	1.70271i	−0.781191	+	0.567569i
$10$	1.19023	−	1.37759i	0.376384	−	0.435633i
$11$		0			0
$11$		0			0
$12$	−0.635639	+	0.0932556i	−0.183493	+	0.0269206i
$13$	1.81401	+	2.49677i	0.503117	+	0.692481i	0.982740	−	0.184994i	$-0.0592266\pi$
$13$	1.81401	+	2.49677i	0.503117	+	0.692481i	−0.479623	+	0.877475i	$0.659227\pi$
$14$	−1.81418	+	4.31012i	−0.484859	+	1.15193i
$15$	0.127784	−	0.393278i	0.0329936	−	0.101544i
$16$	3.77504	+	1.32253i	0.943760	+	0.330633i
$17$	−2.58719	−	1.87971i	−0.627486	−	0.455896i	0.228042	−	0.973651i	$-0.426768\pi$
$17$	−2.58719	−	1.87971i	−0.627486	−	0.455896i	−0.855528	+	0.517756i	$0.826768\pi$
$18$	3.50518	−	2.12057i	0.826178	−	0.499823i
$19$	4.48707	−	1.45794i	1.02941	−	0.334474i	0.254850	−	0.966981i	$-0.417974\pi$
$19$	4.48707	−	1.45794i	1.02941	−	0.334474i	0.774555	+	0.632506i	$0.217974\pi$
$20$	−1.84120	+	1.79967i	−0.411705	+	0.402418i
$21$			1.06218i			0.231786i
$22$		0			0
$23$	−3.47634			−0.724867			−0.362433	−	0.932010i	$-0.618054\pi$
$23$	−3.47634			−0.724867			−0.362433	+	0.932010i	$0.618054\pi$
$24$	0.906838	−	0.0557763i	0.185108	−	0.0113853i
$25$	1.03298	+	3.17919i	0.206596	+	0.635837i
$26$	−2.25919	−	3.73431i	−0.443064	−	0.732359i
$27$	1.11337	−	1.53243i	0.214269	−	0.294916i
$28$	3.06943	−	5.85793i	0.580068	−	1.10704i
$29$	5.88781	+	1.91307i	1.09334	+	0.355247i	0.799536	−	0.600619i	$-0.205079\pi$
$29$	5.88781	+	1.91307i	1.09334	+	0.355247i	0.293803	+	0.955866i	$0.405079\pi$
$30$	−0.226872	+	0.539000i	−0.0414209	+	0.0984076i
$31$	2.16785	−	1.57504i	0.389358	−	0.282885i	−0.375835	−	0.926687i	$-0.622644\pi$
$31$	2.16785	−	1.57504i	0.389358	−	0.282885i	0.765192	+	0.643802i	$0.222644\pi$
$32$	−5.16240	−	2.31293i	−0.912592	−	0.408872i
$33$		0			0
$34$	3.42219	+	2.95675i	0.586900	+	0.507078i
$35$	2.50207	+	3.44381i	0.422927	+	0.582110i
$36$	−5.19183	+	2.57120i	−0.865305	+	0.428533i
$37$	7.46003	+	2.42391i	1.22642	+	0.398489i	0.849417	−	0.527723i	$-0.176954\pi$
$37$	7.46003	+	2.42391i	1.22642	+	0.398489i	0.377005	+	0.926211i	$0.376954\pi$
$38$	−6.49667	+	1.52057i	−1.05390	+	0.246670i
$39$	−0.802018	−	0.582700i	−0.128426	−	0.0933067i
$40$	2.80877	−	2.31699i	0.444106	−	0.366348i
$41$	−1.60231	−	4.93140i	−0.250239	−	0.770155i	−0.994731	−	0.102524i	$-0.967308\pi$
$41$	−1.60231	−	4.93140i	−0.250239	−	0.770155i	0.744492	−	0.667631i	$-0.232692\pi$
$42$	0.126396	−	1.49682i	0.0195034	−	0.230964i
$43$		−	2.37086i		−	0.361553i	−0.983524	−	0.180776i	$-0.942139\pi$
$43$		−	2.37086i		−	0.361553i	0.983524	−	0.180776i	$-0.0578610\pi$
$44$		0			0
$45$		−	3.72915i		−	0.555908i
$46$	4.89885	+	0.413675i	0.722296	+	0.0609931i
$47$	0.986855	+	3.03723i	0.143948	+	0.443025i	0.996874	−	0.0790059i	$-0.0251746\pi$
$47$	0.986855	+	3.03723i	0.143948	+	0.443025i	−0.852927	+	0.522031i	$0.825175\pi$
$48$	−1.28455	−	0.0293115i	−0.185409	−	0.00423075i
$49$	−3.18281	−	2.31245i	−0.454687	−	0.330350i
$50$	−1.07736	−	4.60302i	−0.152362	−	0.650966i
$51$	0.976972	+	0.317438i	0.136803	+	0.0444501i
$52$	2.73928	+	5.53122i	0.379870	+	0.767043i
$53$	−2.77602	−	3.82086i	−0.381315	−	0.524835i	0.574617	−	0.818422i	$-0.305151\pi$
$53$	−2.77602	−	3.82086i	−0.381315	−	0.524835i	−0.955932	+	0.293587i	$0.905151\pi$
$54$	−1.75132	+	2.02701i	−0.238324	+	0.275841i
$55$		0			0
$56$	−5.02251	+	7.88972i	−0.671161	+	1.05431i
$57$	−1.22608	+	0.890800i	−0.162398	+	0.117989i
$58$	−8.06944	−	3.39652i	−1.05957	−	0.445985i
$59$	13.4517	+	4.37073i	1.75127	+	0.569020i	0.996237	−	0.0866719i	$-0.0276232\pi$
$59$	13.4517	+	4.37073i	1.75127	+	0.569020i	0.755028	+	0.655692i	$0.227623\pi$
$60$	0.383847	−	0.732561i	0.0495544	−	0.0945733i
$61$	−9.14936	+	12.5930i	−1.17146	+	1.61237i	−0.518101	+	0.855319i	$0.673361\pi$
$61$	−9.14936	+	12.5930i	−1.17146	+	1.61237i	−0.653355	+	0.757052i	$0.726639\pi$
$62$	−3.24236	+	1.96157i	−0.411780	+	0.249120i
$63$	2.96003	+	9.11004i	0.372929	+	1.14776i
$64$	6.99961	+	3.87368i	0.874952	+	0.484211i
$65$	−3.97292			−0.492780
$66$		0			0
$67$			4.70162i			0.574395i	0.957871	+	0.287197i	$0.0927236\pi$
$67$			4.70162i			0.574395i	−0.957871	+	0.287197i	$0.907276\pi$
$68$	−4.47069	−	4.57387i	−0.542151	−	0.554664i
$69$	1.06202	−	0.345072i	0.127852	−	0.0415418i
$70$	−3.11611	−	5.15075i	−0.372447	−	0.615632i
$71$	7.42164	+	5.39214i	0.880787	+	0.639929i	0.933459	−	0.358683i	$-0.116774\pi$
$71$	7.42164	+	5.39214i	0.880787	+	0.639929i	−0.0526729	+	0.998612i	$0.516774\pi$
$72$	7.62229	−	3.00551i	0.898295	−	0.354203i
$73$	0.290193	−	0.893124i	0.0339646	−	0.104532i	−0.932637	−	0.360816i	$-0.882498\pi$
$73$	0.290193	−	0.893124i	0.0339646	−	0.104532i	0.966602	+	0.256284i	$0.0824982\pi$
$74$	−10.2242	−	4.30350i	−1.18854	−	0.500271i
$75$	−0.631151	−	0.868704i	−0.0728790	−	0.100309i
$76$	9.33604	−	1.36970i	1.07092	−	0.157116i
$77$		0			0
$78$	1.06086	+	0.916578i	0.120119	+	0.103782i
$79$	7.73885	−	5.62261i	0.870689	−	0.632593i	−0.0600826	−	0.998193i	$-0.519136\pi$
$79$	7.73885	−	5.62261i	0.870689	−	0.632593i	0.930772	+	0.365601i	$0.119136\pi$
$80$	−4.23383	+	2.93086i	−0.473357	+	0.327680i
$81$	2.49747	−	7.68644i	0.277497	−	0.854048i
$82$	1.67115	+	7.13999i	0.184547	+	0.788480i
$83$	0.751333	−	1.03412i	0.0824695	−	0.113510i	−0.765789	−	0.643092i	$-0.777651\pi$
$83$	0.751333	−	1.03412i	0.0824695	−	0.113510i	0.848259	+	0.529582i	$0.177651\pi$
$84$	−0.356235	+	2.09428i	−0.0388685	+	0.228504i
$85$	3.91531	−	1.27216i	0.424675	−	0.137985i
$86$	−0.282126	+	3.34101i	−0.0304224	+	0.360271i
$87$	−1.98862			−0.213203
$88$		0			0
$89$	15.3866			1.63098			0.815489	−	0.578773i	$-0.196468\pi$
$89$	15.3866			1.63098			0.815489	+	0.578773i	$0.196468\pi$
$90$	−0.443758	+	5.25510i	−0.0467762	+	0.553937i
$91$	9.70557	−	3.15353i	1.01742	−	0.330580i
$92$	−6.85423	−	1.16590i	−0.714603	−	0.121554i
$93$	−0.505936	+	0.696361i	−0.0524631	+	0.0722093i
$94$	−1.02925	−	4.39749i	−0.106159	−	0.453566i
$95$	−1.87684	+	5.77632i	−0.192560	+	0.592638i
$96$	1.80670	+	0.194164i	0.184396	+	0.0198168i
$97$	11.2973	−	8.20794i	1.14706	−	0.833390i	0.158975	−	0.987283i	$-0.449181\pi$
$97$	11.2973	−	8.20794i	1.14706	−	0.833390i	0.988088	+	0.153893i	$0.0491811\pi$
$98$	4.21004	+	3.63744i	0.425278	+	0.367437i
$99$		0			0
$100$	0.970465	+	6.61478i	0.0970465	+	0.661478i
$101$	6.47507	+	8.91217i	0.644293	+	0.886794i	0.998835	−	0.0482463i	$-0.0153632\pi$
$101$	6.47507	+	8.91217i	0.644293	+	0.886794i	−0.354542	+	0.935040i	$0.615363\pi$
$102$	−1.33897	−	0.563589i	−0.132578	−	0.0558037i
$103$	−3.36761	+	10.3644i	−0.331820	+	1.02124i	0.636447	+	0.771321i	$0.280404\pi$
$103$	−3.36761	+	10.3644i	−0.331820	+	1.02124i	−0.968267	+	0.249918i	$0.919596\pi$
$104$	−3.20199	−	8.12056i	−0.313981	−	0.796286i
$105$	−1.10623	−	0.803720i	−0.107957	−	0.0784350i
$106$	3.45729	+	5.71469i	0.335801	+	0.555059i
$107$	13.7836	−	4.47858i	1.33251	−	0.432960i	0.445740	−	0.895162i	$-0.352941\pi$
$107$	13.7836	−	4.47858i	1.33251	−	0.432960i	0.886775	+	0.462202i	$0.152941\pi$
$108$	2.70916	−	2.64805i	0.260690	−	0.254809i
$109$		−	1.96781i		−	0.188482i	−0.995549	−	0.0942411i	$-0.969958\pi$
$109$		−	1.96781i		−	0.188482i	0.995549	−	0.0942411i	$-0.0300424\pi$
$110$		0			0
$111$	−2.51964			−0.239154
$112$	8.01657	−	10.5205i	0.757495	−	0.994096i
$113$	−1.96151	−	6.03690i	−0.184523	−	0.567904i	0.815417	−	0.578874i	$-0.196508\pi$
$113$	−1.96151	−	6.03690i	−0.184523	−	0.567904i	−0.999940	+	0.0109706i	$0.996508\pi$
$114$	1.83379	−	1.10941i	0.171751	−	0.103906i
$115$	2.63044	−	3.62050i	0.245290	−	0.337613i
$116$	10.9673	+	5.74662i	1.01829	+	0.533560i
$117$	−8.50255	−	2.76264i	−0.786061	−	0.255407i
$118$	−18.4360	−	7.75994i	−1.69717	−	0.714361i
$119$	−8.55503	+	6.21559i	−0.784239	+	0.569783i
$120$	−0.628089	+	0.986647i	−0.0573364	+	0.0900682i
$121$		0			0
$122$	14.3918	−	16.6573i	1.30297	−	1.50808i
$123$	0.979010	+	1.34749i	0.0882744	+	0.121499i
$124$	4.80255	−	2.37841i	0.431281	−	0.213587i
$125$	−10.2142	−	3.31881i	−0.913590	−	0.296843i
$126$	−3.08720	−	13.1901i	−0.275030	−	1.17507i
$127$	13.5130	+	9.81774i	1.19908	+	0.871183i	0.994194	−	0.107603i	$-0.0343174\pi$
$127$	13.5130	+	9.81774i	1.19908	+	0.871183i	0.204887	+	0.978786i	$0.434317\pi$
$128$	−9.40288	−	6.29172i	−0.831105	−	0.556115i
$129$	0.235339	+	0.724298i	0.0207204	+	0.0637708i
$130$	5.59863	+	0.472767i	0.491033	+	0.0414644i
$131$			9.29813i			0.812381i	0.913788	+	0.406191i	$0.133143\pi$
$131$			9.29813i			0.812381i	−0.913788	+	0.406191i	$0.866857\pi$
$132$		0			0
$133$		−	15.6009i		−	1.35277i
$134$	0.559481	−	6.62552i	0.0483318	−	0.572358i
$135$	0.753517	+	2.31909i	0.0648524	+	0.199595i
$136$	5.75582	+	6.97749i	0.493557	+	0.598315i
$137$	−7.33574	−	5.32973i	−0.626735	−	0.455350i	0.228533	−	0.973536i	$-0.426607\pi$
$137$	−7.33574	−	5.32973i	−0.626735	−	0.455350i	−0.855268	+	0.518187i	$0.826607\pi$
$138$	−1.53766	+	0.359897i	−0.130894	+	0.0306364i
$139$	−0.222080	−	0.0721581i	−0.0188366	−	0.00612037i	0.299584	−	0.954070i	$-0.403152\pi$
$139$	−0.222080	−	0.0721581i	−0.0188366	−	0.00612037i	−0.318420	+	0.947950i	$0.603152\pi$
$140$	3.77829	+	7.62923i	0.319324	+	0.644788i
$141$	−0.602968	−	0.829914i	−0.0507791	−	0.0698914i
$142$	−9.81691	−	8.48174i	−0.823817	−	0.711772i
$143$		0			0
$144$	−11.0990	+	3.32833i	−0.924913	+	0.277361i
$145$	−6.44753	+	4.68441i	−0.535438	+	0.389019i
$146$	−0.515220	+	1.22406i	−0.0426399	+	0.101304i
$147$	1.20189	+	0.390517i	0.0991301	+	0.0322093i
$148$	13.8959	+	7.28114i	1.14223	+	0.598506i
$149$	−1.34601	+	1.85262i	−0.110269	+	0.151773i	−0.860585	−	0.509307i	$-0.829902\pi$
$149$	−1.34601	+	1.85262i	−0.110269	+	0.151773i	0.750315	+	0.661080i	$0.229902\pi$
$150$	0.786043	+	1.29928i	0.0641801	+	0.106086i
$151$	−1.17300	−	3.61013i	−0.0954576	−	0.293788i	0.891915	−	0.452203i	$-0.149362\pi$
$151$	−1.17300	−	3.61013i	−0.0954576	−	0.293788i	−0.987373	+	0.158415i	$0.949362\pi$
$152$	−13.3193	+	0.819222i	−1.08034	+	0.0664477i
$153$	9.26386			0.748939
$154$		0			0
$155$			3.44953i			0.277073i
$156$	−1.38590	−	1.41788i	−0.110960	−	0.113521i
$157$	11.5590	−	3.75574i	0.922507	−	0.299741i	0.191012	−	0.981588i	$-0.438823\pi$
$157$	11.5590	−	3.75574i	0.922507	−	0.299741i	0.731495	+	0.681847i	$0.238823\pi$
$158$	−11.5747	+	7.00246i	−0.920830	+	0.557086i
$159$	1.22734	+	0.891717i	0.0973346	+	0.0707177i
$160$	6.31508	−	3.62635i	0.499251	−	0.286688i
$161$	−3.55220	+	10.9325i	−0.279953	+	0.861606i
$162$	−4.43410	+	10.5345i	−0.348376	+	0.827670i
$163$	4.87169	+	6.70531i	0.381580	+	0.525200i	0.956002	−	0.293359i	$-0.0947731\pi$
$163$	4.87169	+	6.70531i	0.381580	+	0.525200i	−0.574422	+	0.818559i	$0.694773\pi$
$164$	−1.50534	−	10.2605i	−0.117547	−	0.801212i
$165$		0			0
$166$	−1.18183	+	1.36788i	−0.0917282	+	0.106168i
$167$	−7.22356	+	5.24822i	−0.558975	+	0.406119i	−0.831084	−	0.556147i	$-0.812279\pi$
$167$	−7.22356	+	5.24822i	−0.558975	+	0.406119i	0.272108	+	0.962267i	$0.412279\pi$
$168$	0.751220	−	2.90886i	0.0579579	−	0.224423i
$169$	1.07398	−	3.30537i	0.0826139	−	0.254260i
$170$	−5.66883	+	1.32681i	−0.434779	+	0.101762i
$171$	−8.03335	+	11.0570i	−0.614325	+	0.845546i
$172$	0.795143	−	4.67458i	0.0606291	−	0.356433i
$173$	−8.08869	+	2.62818i	−0.614972	+	0.199817i	−0.599907	−	0.800070i	$-0.704796\pi$
$173$	−8.08869	+	2.62818i	−0.614972	+	0.199817i	−0.0150654	+	0.999887i	$0.504796\pi$
$174$	2.80236	+	0.236641i	0.212447	+	0.0179397i
$175$	11.0536			0.835571
$176$		0			0
$177$	−4.54335			−0.341499
$178$	−21.6828	−	1.83097i	−1.62519	−	0.137237i
$179$	2.79940	−	0.909581i	0.209237	−	0.0679853i	−0.202523	−	0.979277i	$-0.564914\pi$
$179$	2.79940	−	0.909581i	0.209237	−	0.0679853i	0.411760	+	0.911292i	$0.364914\pi$
$180$	1.25069	−	7.35268i	0.0932207	−	0.548036i
$181$	−12.5027	+	17.2085i	−0.929318	+	1.27910i	0.0308063	+	0.999525i	$0.490192\pi$
$181$	−12.5027	+	17.2085i	−0.929318	+	1.27910i	−0.960125	+	0.279572i	$0.909808\pi$
$182$	−14.0523	+	3.28901i	−1.04163	+	0.243798i
$183$	1.54511	−	4.75536i	0.114218	−	0.351526i
$184$	9.52023	+	2.45862i	0.701840	+	0.181252i
$185$	−8.16922	+	5.93528i	−0.600613	+	0.436371i
$186$	0.795829	−	0.921105i	0.0583530	−	0.0675387i
$187$		0			0
$188$	0.927131	+	6.31941i	0.0676179	+	0.460890i
$189$	−3.68158	−	5.06726i	−0.267795	−	0.368589i
$190$	3.33221	−	7.91665i	0.241744	−	0.574334i
$191$	−1.59325	+	4.90352i	−0.115283	+	0.354806i	−0.992006	−	0.126190i	$-0.959725\pi$
$191$	−1.59325	+	4.90352i	−0.115283	+	0.354806i	0.876723	+	0.480996i	$0.159725\pi$
$192$	−2.52289	−	0.488608i	−0.182074	−	0.0352623i
$193$	−21.8572	−	15.8802i	−1.57331	−	1.14308i	−0.923894	−	0.382649i	$-0.875012\pi$
$193$	−21.8572	−	15.8802i	−1.57331	−	1.14308i	−0.649419	−	0.760430i	$-0.724988\pi$
$194$	−16.8968	+	10.2223i	−1.21312	+	0.733916i
$195$	1.21373	−	0.394364i	0.0869168	−	0.0282410i
$196$	−5.49993	−	5.62686i	−0.392852	−	0.401919i
$197$			6.68220i			0.476087i	0.971254	+	0.238044i	$0.0765061\pi$
$197$			6.68220i			0.476087i	−0.971254	+	0.238044i	$0.923494\pi$
$198$		0			0
$199$	−14.2586			−1.01076			−0.505382	−	0.862896i	$-0.668648\pi$
$199$	−14.2586			−1.01076			−0.505382	+	0.862896i	$0.668648\pi$
$200$	−0.580436	−	9.43701i	−0.0410430	−	0.667298i
$201$	−0.466697	−	1.43635i	−0.0329183	−	0.101312i
$202$	−8.06413	−	13.3295i	−0.567390	−	0.937862i
$203$	12.0326	−	16.5614i	0.844522	−	1.16239i
$204$	1.81981	+	0.953544i	0.127412	+	0.0667614i
$205$	6.34831	+	2.06269i	0.443386	+	0.144065i
$206$	5.97897	−	14.2048i	0.416575	−	0.989696i
$207$	8.14706	−	5.91918i	0.566260	−	0.411412i
$208$	3.54591	+	11.8245i	0.245864	+	0.819882i
$209$		0			0
$210$	1.46325	+	1.26424i	0.100974	+	0.0872407i
$211$	−11.3616	−	15.6378i	−0.782162	−	1.07655i	−0.995040	−	0.0994744i	$-0.968284\pi$
$211$	−11.3616	−	15.6378i	−0.782162	−	1.07655i	0.212879	−	0.977079i	$-0.431716\pi$
$212$	−4.19197	−	8.46453i	−0.287906	−	0.581347i
$213$	−2.80255	−	0.910604i	−0.192028	−	0.0623935i
$214$	−19.9568	+	4.67098i	−1.36422	+	0.319302i
$215$	2.46917	+	1.79396i	0.168396	+	0.122347i
$216$	−4.13286	+	3.40925i	−0.281206	+	0.231970i
$217$	−2.73809	−	8.42696i	−0.185873	−	0.572060i
$218$	−0.234164	+	2.77304i	−0.0158596	+	0.187814i
$219$			0.301655i			0.0203839i
$220$		0			0
$221$		−	9.86944i		−	0.663891i
$222$	3.55068	+	0.299831i	0.238306	+	0.0201233i
$223$	−4.22873	−	13.0147i	−0.283176	−	0.871528i	−0.986939	−	0.161093i	$-0.948498\pi$
$223$	−4.22873	−	13.0147i	−0.283176	−	0.871528i	0.703763	−	0.710435i	$-0.251502\pi$
$224$	−12.5489	+	13.8715i	−0.838455	+	0.926832i
$225$	−7.83408	−	5.69180i	−0.522272	−	0.379453i
$226$	2.04578	+	8.74060i	0.136083	+	0.581416i
$227$	−11.3059	−	3.67351i	−0.750399	−	0.243819i	−0.0912459	−	0.995828i	$-0.529085\pi$
$227$	−11.3059	−	3.67351i	−0.750399	−	0.243819i	−0.659153	+	0.752009i	$0.729085\pi$
$228$	−2.71620	+	1.34517i	−0.179885	+	0.0890859i
$229$	−0.127954	−	0.176114i	−0.00845546	−	0.0116379i	0.804768	−	0.593589i	$-0.202290\pi$
$229$	−0.127954	−	0.176114i	−0.00845546	−	0.0116379i	−0.813224	+	0.581951i	$0.802290\pi$
$230$	−4.13765	+	4.78898i	−0.272828	+	0.315776i
$231$		0			0
$232$	−14.7712	−	9.40320i	−0.969778	−	0.617350i
$233$	−2.97642	+	2.16249i	−0.194992	+	0.141670i	−0.680997	−	0.732286i	$-0.738453\pi$
$233$	−2.97642	+	2.16249i	−0.194992	+	0.141670i	0.486006	+	0.873956i	$0.338453\pi$
$234$	11.6530	+	4.90489i	0.761782	+	0.320643i
$235$	−3.90990	−	1.27040i	−0.255054	−	0.0828719i
$236$	25.0566	+	13.1291i	1.63105	+	0.854634i
$237$	−1.80610	+	2.48589i	−0.117319	+	0.161476i
$238$	12.7954	−	7.74098i	0.829401	−	0.501773i
$239$	6.19507	+	19.0665i	0.400726	+	1.23331i	0.924412	+	0.381396i	$0.124556\pi$
$239$	6.19507	+	19.0665i	0.400726	+	1.23331i	−0.523686	+	0.851911i	$0.675444\pi$
$240$	1.00251	−	1.31564i	0.0647118	−	0.0849243i
$241$	−14.4772			−0.932561			−0.466280	−	0.884637i	$-0.654406\pi$
$241$	−14.4772			−0.932561			−0.466280	+	0.884637i	$0.654406\pi$
$242$		0			0
$243$			8.27867i			0.531077i
$244$	−22.2631	+	21.7609i	−1.42525	+	1.39310i
$245$	4.81668	−	1.56503i	0.307726	−	0.0999864i
$246$	−1.21927	−	2.01538i	−0.0777379	−	0.128496i
$247$	11.7798	+	8.55849i	0.749528	+	0.544564i
$248$	−7.05076	+	2.78016i	−0.447724	+	0.176540i
$249$	−0.126882	+	0.390504i	−0.00804084	+	0.0247472i
$250$	13.9990	+	5.89233i	0.885372	+	0.372663i
$251$	−12.7189	−	17.5061i	−0.802809	−	1.10497i	−0.992393	−	0.123108i	$-0.960714\pi$
$251$	−12.7189	−	17.5061i	−0.802809	−	1.10497i	0.189584	−	0.981864i	$-0.439286\pi$
$252$	2.78089	+	18.9548i	0.175180	+	1.19404i
$253$		0			0
$254$	−17.8741	−	15.4431i	−1.12152	−	0.968989i
$255$	−1.06985	+	0.777290i	−0.0669964	+	0.0486758i
$256$	12.5018	+	9.98520i	0.781364	+	0.624075i
$257$	−2.62943	+	8.09254i	−0.164019	+	0.504799i	−0.998963	−	0.0455368i	$-0.985500\pi$
$257$	−2.62943	+	8.09254i	−0.164019	+	0.504799i	0.834944	+	0.550335i	$0.185500\pi$
$258$	−0.245449	−	1.04868i	−0.0152810	−	0.0652882i
$259$	15.2457	−	20.9838i	0.947319	−	1.30387i
$260$	−7.83333	−	1.33245i	−0.485802	−	0.0826347i
$261$	−17.0559	+	5.54180i	−1.05573	+	0.343029i
$262$	1.10645	−	13.1029i	0.0683569	−	0.809500i
$263$	−9.34658			−0.576335			−0.288167	−	0.957580i	$-0.593046\pi$
$263$	−9.34658			−0.576335			−0.288167	+	0.957580i	$0.593046\pi$
$264$		0			0
$265$	6.07983			0.373481
$266$	−1.85647	+	21.9848i	−0.113827	+	1.34797i
$267$	−4.70061	+	1.52732i	−0.287673	+	0.0934705i
$268$	−1.57684	+	9.27009i	−0.0963207	+	0.566261i
$269$	7.18877	−	9.89449i	0.438307	−	0.603278i	−0.531528	−	0.847041i	$-0.678382\pi$
$269$	7.18877	−	9.89449i	0.438307	−	0.603278i	0.969835	+	0.243763i	$0.0783819\pi$
$270$	−0.785890	−	3.35772i	−0.0478277	−	0.204344i
$271$	7.62308	−	23.4614i	0.463069	−	1.42518i	−0.398325	−	0.917244i	$-0.630408\pi$
$271$	7.62308	−	23.4614i	0.463069	−	1.42518i	0.861395	−	0.507936i	$-0.169592\pi$
$272$	−7.28078	−	10.5176i	−0.441462	−	0.637723i
$273$	−2.65202	+	1.92681i	−0.160508	+	0.116616i
$274$	9.70329	+	8.38358i	0.586197	+	0.506471i
$275$		0			0
$276$	2.20970	−	0.324188i	0.133008	−	0.0195138i
$277$	−4.73257	−	6.51382i	−0.284353	−	0.391378i	0.642817	−	0.766020i	$-0.277766\pi$
$277$	−4.73257	−	6.51382i	−0.284353	−	0.391378i	−0.927170	+	0.374642i	$0.877766\pi$
$278$	0.304368	+	0.128112i	0.0182548	+	0.00768365i
$279$	−2.39870	+	7.38243i	−0.143606	+	0.441974i
$280$	−4.41651	−	11.2007i	−0.263937	−	0.669370i
$281$	10.7513	+	7.81131i	0.641371	+	0.465983i	0.860321	−	0.509753i	$-0.170263\pi$
$281$	10.7513	+	7.81131i	0.641371	+	0.465983i	−0.218950	+	0.975736i	$0.570263\pi$
$282$	0.750944	+	1.24127i	0.0447181	+	0.0739163i
$283$	0.328993	−	0.106896i	0.0195566	−	0.00635433i	−0.299222	−	0.954183i	$-0.596727\pi$
$283$	0.328993	−	0.106896i	0.0195566	−	0.00635433i	0.318779	+	0.947829i	$0.396727\pi$
$284$	12.8247	+	13.1206i	0.761004	+	0.778567i
$285$		−	1.95097i		−	0.115565i
$286$		0			0
$287$	−17.1458			−1.01208
$288$	16.0367	−	3.36953i	0.944972	−	0.198552i
$289$	−2.09302	−	6.44164i	−0.123119	−	0.378920i
$290$	9.64328	−	5.83402i	0.566273	−	0.342585i
$291$	−2.63657	+	3.62892i	−0.154558	+	0.212731i
$292$	0.871706	−	1.66363i	0.0510127	−	0.0973565i
$293$	3.64193	+	1.18334i	0.212764	+	0.0691313i	0.413460	−	0.910522i	$-0.364320\pi$
$293$	3.64193	+	1.18334i	0.212764	+	0.0691313i	−0.200696	+	0.979654i	$0.564320\pi$
$294$	−1.64723	−	0.693338i	−0.0960683	−	0.0404363i
$295$	−14.7305	+	10.7023i	−0.857643	+	0.623114i
$296$	−18.7156	−	11.9141i	−1.08782	−	0.692495i
$297$		0			0
$298$	2.11725	−	2.45054i	0.122649	−	0.141956i
$299$	−6.30612	−	8.67964i	−0.364693	−	0.501956i
$300$	−0.953079	−	1.92448i	−0.0550261	−	0.111110i
$301$	−7.45599	−	2.42260i	−0.429756	−	0.139636i
$302$	1.22340	+	5.22698i	0.0703986	+	0.300779i
$303$	−2.86278	−	2.07993i	−0.164462	−	0.119489i
$304$	18.8670	+	0.430517i	1.08210	+	0.0246918i
$305$	−6.19217	−	19.0575i	−0.354563	−	1.09123i
$306$	−13.0546	−	1.10238i	−0.746283	−	0.0630186i
$307$		−	23.7376i		−	1.35478i	−0.735626	−	0.677388i	$-0.763112\pi$
$307$		−	23.7376i		−	1.35478i	0.735626	−	0.677388i	$-0.236888\pi$
$308$		0			0
$309$		−	3.50061i		−	0.199143i
$310$	0.410485	−	4.86107i	0.0233140	−	0.276090i
$311$	2.72596	+	8.38966i	0.154575	+	0.475734i	0.998118	−	0.0613289i	$-0.0195339\pi$
$311$	2.72596	+	8.38966i	0.154575	+	0.475734i	−0.843542	+	0.537063i	$0.819534\pi$
$312$	1.78428	+	2.16299i	0.101015	+	0.122455i
$313$	2.60133	+	1.88998i	0.147036	+	0.106828i	0.658871	−	0.752256i	$-0.271034\pi$
$313$	2.60133	+	1.88998i	0.147036	+	0.106828i	−0.511835	+	0.859084i	$0.671034\pi$
$314$	−16.7358	+	3.91709i	−0.944457	+	0.221054i
$315$	−11.7276	−	3.81052i	−0.660774	−	0.214699i
$316$	17.1443	−	8.49051i	0.964440	−	0.477628i
$317$	5.42855	+	7.47176i	0.304898	+	0.419656i	0.933782	−	0.357844i	$-0.116488\pi$
$317$	5.42855	+	7.47176i	0.304898	+	0.419656i	−0.628884	+	0.777499i	$0.716488\pi$
$318$	−1.62346	−	1.40266i	−0.0910390	−	0.0786571i
$319$		0			0
$320$	−9.33072	+	4.35877i	−0.521603	+	0.243663i
$321$	−3.76634	+	2.73641i	−0.210217	+	0.152731i
$322$	6.30670	−	14.9834i	0.351459	−	0.834994i
$323$	−14.3494	−	4.66241i	−0.798423	−	0.259423i
$324$	7.50211	−	14.3176i	0.416784	−	0.795421i
$325$	−6.06387	+	8.34620i	−0.336363	+	0.462964i
$326$	−6.06727	−	10.0288i	−0.336035	−	0.555445i
$327$	0.195331	+	0.601166i	0.0108018	+	0.0332446i
$328$	0.900344	+	14.6382i	0.0497132	+	0.808262i
$329$	10.5600			0.582191
$330$		0			0
$331$			4.00167i			0.219952i	0.993934	+	0.109976i	$0.0350774\pi$
$331$			4.00167i			0.219952i	−0.993934	+	0.109976i	$0.964923\pi$
$332$	1.82821	−	1.78697i	0.100336	−	0.0980728i
$333$	−21.6103	+	7.02163i	−1.18424	+	0.384783i
$334$	10.8039	−	6.53620i	0.591166	−	0.357645i
$335$	−4.89659	−	3.55758i	−0.267529	−	0.194371i
$336$	−1.40476	+	4.00977i	−0.0766362	+	0.218751i
$337$	−0.728908	+	2.24335i	−0.0397061	+	0.122203i	−0.968945	−	0.247277i	$-0.920464\pi$
$337$	−0.728908	+	2.24335i	−0.0397061	+	0.122203i	0.929239	+	0.369480i	$0.120464\pi$
$338$	−1.90678	+	4.53013i	−0.103715	+	0.246406i
$339$	1.19848	+	1.64957i	0.0650926	+	0.0895922i
$340$	8.14639	−	1.19517i	0.441800	−	0.0648172i
$341$		0			0
$342$	12.6363	−	14.6255i	0.683294	−	0.790856i
$343$	8.20160	−	5.95881i	0.442845	−	0.321746i
$344$	−1.67678	+	6.49278i	−0.0904057	+	0.350067i
$345$	−0.444220	+	1.36717i	−0.0239160	+	0.0736058i
$346$	11.7113	−	2.74109i	0.629604	−	0.147362i
$347$	14.0591	−	19.3506i	0.754730	−	1.03880i	−0.242904	−	0.970050i	$-0.578100\pi$
$347$	14.0591	−	19.3506i	0.754730	−	1.03880i	0.997634	−	0.0687465i	$-0.0219000\pi$
$348$	−3.92093	−	0.666948i	−0.210184	−	0.0357521i
$349$	2.01885	−	0.655963i	0.108066	−	0.0351129i	−0.254485	−	0.967077i	$-0.581906\pi$
$349$	2.01885	−	0.655963i	0.108066	−	0.0351129i	0.362551	+	0.931964i	$0.381906\pi$
$350$	−15.5767	−	1.31535i	−0.832608	−	0.0703082i
$351$	5.84580			0.312026
$352$		0			0
$353$	5.11533			0.272262			0.136131	−	0.990691i	$-0.456533\pi$
$353$	5.11533			0.272262			0.136131	+	0.990691i	$0.456533\pi$
$354$	6.40248	+	0.540647i	0.340288	+	0.0287351i
$355$	−11.2315	+	3.64933i	−0.596105	+	0.193686i
$356$	30.3375	+	5.16039i	1.60788	+	0.273500i
$357$	1.99658	−	2.74806i	0.105670	−	0.145443i
$358$	−4.05315	+	0.948659i	−0.214216	+	0.0501382i
$359$	−8.95267	+	27.5535i	−0.472504	+	1.45422i	0.376790	+	0.926299i	$0.377028\pi$
$359$	−8.95267	+	27.5535i	−0.472504	+	1.45422i	−0.849294	+	0.527919i	$0.822972\pi$
$360$	−2.63742	+	10.2126i	−0.139004	+	0.538249i
$361$	2.63692	−	1.91584i	0.138785	−	0.100833i
$362$	19.6665	−	22.7624i	1.03365	−	1.19636i
$363$		0			0
$364$	20.1939	−	2.96268i	1.05845	−	0.155287i
$365$	0.710579	+	0.978028i	0.0371934	+	0.0511923i
$366$	−2.74324	+	6.51738i	−0.143392	+	0.340669i
$367$	9.17609	−	28.2411i	0.478988	−	1.47417i	−0.361515	−	0.932366i	$-0.617740\pi$
$367$	9.17609	−	28.2411i	0.478988	−	1.47417i	0.840503	−	0.541807i	$-0.182260\pi$
$368$	−13.1233	−	4.59756i	−0.684100	−	0.239665i
$369$	12.1519	+	8.82884i	0.632600	+	0.459611i
$370$	12.2183	−	7.39187i	0.635201	−	0.384285i
$371$	−14.8526	+	4.82590i	−0.771109	+	0.250548i
$372$	−1.23109	+	1.20332i	−0.0638290	+	0.0623892i
$373$		−	4.07522i		−	0.211007i	−0.994419	−	0.105504i	$-0.966355\pi$
$373$		−	4.07522i		−	0.211007i	0.994419	−	0.105504i	$-0.0336454\pi$
$374$		0			0
$375$	3.44988			0.178151
$376$	−0.554518	−	9.01563i	−0.0285971	−	0.464945i
$377$	5.90407	+	18.1709i	0.304075	+	0.935847i
$378$	4.58508	+	7.57887i	0.235831	+	0.389815i
$379$	−17.1222	+	23.5667i	−0.879507	+	1.21054i	0.0970499	+	0.995280i	$0.469059\pi$
$379$	−17.1222	+	23.5667i	−0.879507	+	1.21054i	−0.976557	+	0.215258i	$0.930941\pi$
$380$	−5.63780	+	10.7596i	−0.289213	+	0.551956i
$381$	−5.10274	−	1.65798i	−0.261421	−	0.0849410i
$382$	2.82871	−	6.72043i	0.144729	−	0.343847i
$383$	15.2236	−	11.0606i	0.777889	−	0.565170i	−0.126456	−	0.991972i	$-0.540360\pi$
$383$	15.2236	−	11.0606i	0.777889	−	0.565170i	0.904345	+	0.426803i	$0.140360\pi$
$384$	3.49712	+	0.988764i	0.178461	+	0.0504576i
$385$		0			0
$386$	28.9114	+	24.9792i	1.47155	+	1.27141i
$387$	4.03688	+	5.55629i	0.205206	+	0.282442i
$388$	25.0274	−	12.3945i	1.27057	−	0.629237i
$389$	−25.6888	−	8.34679i	−1.30247	−	0.423199i	−0.426032	−	0.904708i	$-0.640089\pi$
$389$	−25.6888	−	8.34679i	−1.30247	−	0.423199i	−0.876441	+	0.481509i	$0.840089\pi$
$390$	−1.75731	+	0.411307i	−0.0889849	+	0.0208273i
$391$	8.99396	+	6.53449i	0.454844	+	0.330464i
$392$	7.08091	+	8.58384i	0.357640	+	0.433549i
$393$	−0.922959	−	2.84058i	−0.0465571	−	0.143288i
$394$	0.795164	−	9.41655i	0.0400598	−	0.474399i
$395$			12.3142i			0.619596i
$396$		0			0
$397$			28.1281i			1.41171i	0.708358	+	0.705854i	$0.249436\pi$
$397$			28.1281i			1.41171i	−0.708358	+	0.705854i	$0.750564\pi$
$398$	20.0932	+	1.69673i	1.00718	+	0.0850495i
$399$	1.54859	+	4.76608i	0.0775266	+	0.238602i
$400$	−0.305030	+	13.3677i	−0.0152515	+	0.668385i
$401$	6.74146	+	4.89796i	0.336653	+	0.244592i	0.743248	−	0.669016i	$-0.233284\pi$
$401$	6.74146	+	4.89796i	0.336653	+	0.244592i	−0.406596	+	0.913608i	$0.633284\pi$
$402$	0.486747	+	2.07963i	0.0242767	+	0.103723i
$403$	7.86502	+	2.55550i	0.391785	+	0.127299i
$404$	9.77778	+	19.7436i	0.486463	+	0.982279i
$405$	6.11541	+	8.41714i	0.303877	+	0.418251i
$406$	−18.9271	+	21.9065i	−0.939335	+	1.08720i
$407$		0			0
$408$	−2.45101	−	1.56028i	−0.121343	−	0.0772456i
$409$	3.35559	−	2.43798i	0.165923	−	0.120550i	−0.501725	−	0.865027i	$-0.667301\pi$
$409$	3.35559	−	2.43798i	0.165923	−	0.120550i	0.667648	+	0.744477i	$0.267301\pi$
$410$	−8.70058	−	3.66218i	−0.429691	−	0.180862i
$411$	2.77011	+	0.900065i	0.136640	+	0.0443969i
$412$	−10.1159	+	19.3059i	−0.498374	+	0.951134i
$413$	27.4905	−	37.8375i	1.35272	−	1.86186i
$414$	−12.1852	+	7.37183i	−0.598869	+	0.362306i
$415$	0.508492	+	1.56498i	0.0249609	+	0.0768218i
$416$	−3.58980	−	17.0850i	−0.176005	−	0.837662i
$417$	0.0750080			0.00367316
$418$		0			0
$419$			7.25457i			0.354409i	0.984174	+	0.177204i	$0.0567054\pi$
$419$			7.25457i			0.354409i	−0.984174	+	0.177204i	$0.943295\pi$
$420$	−1.91157	−	1.95569i	−0.0932750	−	0.0954277i
$421$	−33.4753	+	10.8768i	−1.63149	+	0.530102i	−0.974613	−	0.223897i	$-0.928122\pi$
$421$	−33.4753	+	10.8768i	−1.63149	+	0.530102i	−0.656875	+	0.754000i	$0.728122\pi$
$422$	14.1498	+	23.3888i	0.688802	+	1.13855i
$423$	−7.48427	−	5.43764i	−0.363898	−	0.264387i
$424$	4.90006	+	12.4270i	0.237968	+	0.603510i
$425$	3.30341	−	10.1669i	0.160239	−	0.493165i
$426$	3.84099	+	1.61672i	0.186097	+	0.0783302i
$427$	30.2541	+	41.6412i	1.46410	+	2.01516i
$428$	28.6789	−	4.20753i	1.38625	−	0.203379i
$429$		0			0
$430$	−3.26608	−	2.82187i	−0.157504	−	0.136083i
$431$	10.9280	−	7.93969i	0.526385	−	0.382441i	−0.292619	−	0.956229i	$-0.594527\pi$
$431$	10.9280	−	7.93969i	0.526385	−	0.382441i	0.819004	+	0.573788i	$0.194527\pi$
$432$	6.22971	−	4.31250i	0.299727	−	0.207485i
$433$	4.49738	−	13.8415i	0.216130	−	0.665181i	−0.782941	−	0.622096i	$-0.786281\pi$
$433$	4.49738	−	13.8415i	0.216130	−	0.665181i	0.999071	−	0.0430848i	$-0.0137186\pi$
$434$	2.85572	+	12.2011i	0.137079	+	0.585671i
$435$	1.50473	−	2.07109i	0.0721464	−	0.0993010i
$436$	0.659968	−	3.87989i	0.0316067	−	0.185813i
$437$	−15.5986	+	5.06829i	−0.746182	+	0.242449i
$438$	0.0358961	−	0.425091i	0.00171518	−	0.0203116i
$439$	−8.11893			−0.387495			−0.193748	−	0.981051i	$-0.562064\pi$
$439$	−8.11893			−0.387495			−0.193748	+	0.981051i	$0.562064\pi$
$440$		0			0
$441$	11.3966			0.542694
$442$	−1.17444	+	13.9080i	−0.0558623	+	0.661536i
$443$	3.86328	−	1.25526i	0.183550	−	0.0596390i	−0.215800	−	0.976438i	$-0.569236\pi$
$443$	3.86328	−	1.25526i	0.183550	−	0.0596390i	0.399350	+	0.916799i	$0.369236\pi$
$444$	−4.96793	−	0.845043i	−0.235768	−	0.0401039i
$445$	−11.6426	+	16.0247i	−0.551912	+	0.759642i
$446$	4.41040	+	18.8435i	0.208839	+	0.892264i
$447$	0.227309	−	0.699584i	0.0107513	−	0.0330892i
$448$	19.3345	−	18.0545i	0.913469	−	0.852994i
$449$	6.70425	−	4.87092i	0.316393	−	0.229873i	−0.418242	−	0.908336i	$-0.637354\pi$
$449$	6.70425	−	4.87092i	0.316393	−	0.229873i	0.734635	+	0.678463i	$0.237354\pi$
$450$	10.3625	+	8.95310i	0.488491	+	0.422053i
$451$		0			0
$452$	−1.84280	−	12.5607i	−0.0866780	−	0.590805i
$453$	0.716705	+	0.986459i	0.0336737	+	0.0463479i
$454$	15.4951	+	6.52207i	0.727222	+	0.306096i
$455$	−4.05962	+	12.4942i	−0.190318	+	0.585738i
$456$	3.98773	−	1.57239i	0.186743	−	0.0736338i
$457$	−7.95132	−	5.77697i	−0.371947	−	0.270235i	0.386071	−	0.922469i	$-0.373832\pi$
$457$	−7.95132	−	5.77697i	−0.371947	−	0.270235i	−0.758018	+	0.652234i	$0.773832\pi$
$458$	0.159356	+	0.263406i	0.00744621	+	0.0123081i
$459$	−5.76103	+	1.87187i	−0.268902	+	0.0873714i
$460$	6.40064	−	6.25626i	0.298431	−	0.291699i
$461$			24.4759i			1.13996i	0.821660	+	0.569978i	$0.193048\pi$
$461$			24.4759i			1.13996i	−0.821660	+	0.569978i	$0.806952\pi$
$462$		0			0
$463$	20.2431			0.940778			0.470389	−	0.882459i	$-0.344114\pi$
$463$	20.2431			0.940778			0.470389	+	0.882459i	$0.344114\pi$
$464$	19.6966	+	15.0087i	0.914393	+	0.696762i
$465$	−0.342411	−	1.05383i	−0.0158789	−	0.0488703i
$466$	4.45169	−	2.69320i	0.206221	−	0.124760i
$467$	14.3336	−	19.7285i	0.663279	−	0.912925i	−0.336306	−	0.941753i	$-0.609178\pi$
$467$	14.3336	−	19.7285i	0.663279	−	0.912925i	0.999584	+	0.0288281i	$0.00917753\pi$
$468$	−15.8378	−	8.29865i	−0.732100	−	0.383605i
$469$	14.7859	+	4.80422i	0.682748	+	0.221838i
$470$	5.35865	+	2.25552i	0.247176	+	0.104039i
$471$	−3.15846	+	2.29476i	−0.145534	+	0.105737i
$472$	−33.7474	−	21.4832i	−1.55335	−	0.988846i
$473$		0			0
$474$	2.84097	−	3.28819i	0.130490	−	0.151031i
$475$	9.27012	+	12.7592i	0.425342	+	0.585433i
$476$	−18.9524	+	9.38596i	−0.868681	+	0.430205i
$477$	13.0116	+	4.22773i	0.595760	+	0.193574i
$478$	−6.46122	−	27.6056i	−0.295529	−	1.26265i
$479$	−1.39875	−	1.01625i	−0.0639103	−	0.0464336i	0.555371	−	0.831602i	$-0.312576\pi$
$479$	−1.39875	−	1.01625i	−0.0639103	−	0.0464336i	−0.619282	+	0.785169i	$0.712576\pi$
$480$	−1.56929	+	1.73470i	−0.0716281	+	0.0791780i
$481$	7.48063	+	23.0230i	0.341088	+	1.04976i
$482$	20.4013	+	1.72275i	0.929253	+	0.0784692i
$483$		−	3.69250i		−	0.168014i
$484$		0			0
$485$			17.9764i			0.816268i
$486$	0.985140	−	11.6663i	0.0446868	−	0.529193i
$487$	−0.820437	−	2.52505i	−0.0371775	−	0.114421i	0.930745	−	0.365668i	$-0.119159\pi$
$487$	−0.820437	−	2.52505i	−0.0371775	−	0.114421i	−0.967923	+	0.251247i	$0.919159\pi$
$488$	33.9626	−	28.0161i	1.53741	−	1.26823i
$489$	−2.15389	−	1.56489i	−0.0974023	−	0.0707669i
$490$	−6.97389	+	1.63227i	−0.315048	+	0.0737385i
$491$	27.8745	+	9.05697i	1.25796	+	0.408735i	0.860766	−	0.509000i	$-0.169985\pi$
$491$	27.8745	+	9.05697i	1.25796	+	0.408735i	0.397192	+	0.917736i	$0.369985\pi$
$492$	1.47837	+	2.98516i	0.0666501	+	0.134582i
$493$	−11.6369	−	16.0168i	−0.524100	−	0.721361i
$494$	−15.5816	−	13.4624i	−0.701048	−	0.605701i
$495$		0			0
$496$	10.2668	−	3.07877i	0.460991	−	0.138241i
$497$	24.5410	−	17.8301i	1.10082	−	0.799789i
$498$	0.225271	−	0.535198i	0.0100946	−	0.0239828i
$499$	7.66065	+	2.48910i	0.342938	+	0.111427i	0.475422	−	0.879758i	$-0.342295\pi$
$499$	7.66065	+	2.48910i	0.342938	+	0.111427i	−0.132484	+	0.991185i	$0.542295\pi$
$500$	−19.0261	−	9.96930i	−0.850875	−	0.445840i
$501$	1.68584	−	2.32036i	0.0753179	−	0.103666i
$502$	15.8403	+	26.1830i	0.706986	+	1.16860i
$503$	−9.28221	−	28.5677i	−0.413873	−	1.27377i	−0.913255	−	0.407389i	$-0.866439\pi$
$503$	−9.28221	−	28.5677i	−0.413873	−	1.27377i	0.499382	−	0.866382i	$-0.333561\pi$
$504$	−1.66325	−	27.0420i	−0.0740873	−	1.20455i
$505$	−14.1812			−0.631057
$506$		0			0
$507$			1.11640i			0.0495810i
$508$	23.3505	+	23.8894i	1.03601	+	1.05992i
$509$	2.63101	−	0.854869i	0.116618	−	0.0378914i	−0.250127	−	0.968213i	$-0.580472\pi$
$509$	2.63101	−	0.854869i	0.116618	−	0.0378914i	0.366745	+	0.930322i	$0.380472\pi$
$510$	1.60012	−	0.968046i	0.0708546	−	0.0428658i
$511$	−2.51221	−	1.82523i	−0.111134	−	0.0807433i
$512$	−16.4293	−	15.5588i	−0.726081	−	0.687609i
$513$	2.76161	−	8.49935i	0.121928	−	0.375255i
$514$	4.66837	−	11.0911i	0.205913	−	0.489207i
$515$	−8.24606	−	11.3497i	−0.363365	−	0.500129i
$516$	0.221096	+	1.50701i	0.00973321	+	0.0663425i
$517$		0			0
$518$	−23.9812	+	27.7562i	−1.05367	+	1.21954i
$519$	2.21022	−	1.60582i	0.0970177	−	0.0704875i
$520$	10.8802	+	2.80982i	0.477126	+	0.123219i
$521$	3.71389	−	11.4302i	0.162709	−	0.500766i	−0.836151	−	0.548499i	$-0.815200\pi$
$521$	3.71389	−	11.4302i	0.162709	−	0.500766i	0.998860	+	0.0477328i	$0.0151996\pi$
$522$	24.6946	−	5.77989i	1.08085	−	0.252979i
$523$	−3.13009	+	4.30819i	−0.136869	+	0.188384i	−0.871950	−	0.489596i	$-0.837144\pi$
$523$	−3.13009	+	4.30819i	−0.136869	+	0.188384i	0.735080	+	0.677980i	$0.237144\pi$
$524$	−3.11842	+	18.3329i	−0.136229	+	0.800877i
$525$	−3.37686	+	1.09721i	−0.147378	+	0.0478862i
$526$	13.1712	+	1.11222i	0.574291	+	0.0484950i
$527$	−8.56925			−0.373283
$528$		0			0
$529$	−10.9151			−0.474568
$530$	−8.56769	−	0.723484i	−0.372157	−	0.0314261i
$531$	−38.9672	+	12.6612i	−1.69103	+	0.549449i
$532$	5.23226	−	30.7600i	0.226847	−	1.33361i
$533$	9.40598	−	12.9462i	0.407418	−	0.560763i
$534$	6.80583	−	1.59294i	0.294517	−	0.0689331i
$535$	−5.76538	+	17.7440i	−0.249259	+	0.767141i
$536$	3.32519	−	12.8758i	0.143627	−	0.556148i
$537$	−0.764930	+	0.555754i	−0.0330092	+	0.0239826i
$538$	−11.3078	+	13.0879i	−0.487515	+	0.564257i
$539$		0			0
$540$	0.707915	+	4.82521i	0.0304638	+	0.207644i
$541$	5.70817	+	7.85662i	0.245413	+	0.337782i	0.913898	−	0.405943i	$-0.133057\pi$
$541$	5.70817	+	7.85662i	0.245413	+	0.337782i	−0.668485	+	0.743726i	$0.733057\pi$
$542$	−13.5343	+	32.1547i	−0.581347	+	1.38116i
$543$	2.11141	−	6.49825i	0.0906092	−	0.278867i
$544$	9.00850	+	15.6878i	0.386236	+	0.672608i
$545$	2.04941	+	1.48899i	0.0877872	+	0.0637811i
$546$	3.96651	−	2.39967i	0.169751	−	0.102696i
$547$	−19.6515	+	6.38515i	−0.840236	+	0.273009i	−0.697351	−	0.716730i	$-0.745638\pi$
$547$	−19.6515	+	6.38515i	−0.840236	+	0.273009i	−0.142885	+	0.989739i	$0.545638\pi$
$548$	−12.6762	−	12.9688i	−0.541502	−	0.553999i
$549$		−	45.0914i		−	1.92445i
$550$		0			0
$551$	29.2082			1.24431
$552$	−3.15248	+	0.193897i	−0.134178	+	0.00825282i
$553$	−9.77449	−	30.0828i	−0.415654	−	1.27925i
$554$	5.89400	+	9.74243i	0.250412	+	0.413916i
$555$	1.90654	−	2.62413i	0.0809282	−	0.111388i
$556$	−0.413670	−	0.216754i	−0.0175435	−	0.00919243i
$557$	−25.2473	−	8.20335i	−1.06976	−	0.347587i	−0.279368	−	0.960184i	$-0.590125\pi$
$557$	−25.2473	−	8.20335i	−1.06976	−	0.347587i	−0.790395	+	0.612597i	$0.790125\pi$
$558$	4.25873	−	10.1179i	0.180286	−	0.428323i
$559$	5.91950	−	4.30077i	0.250368	−	0.181903i
$560$	4.89088	+	16.3096i	0.206677	+	0.689205i
$561$		0			0
$562$	−14.2212	−	12.2871i	−0.599887	−	0.518298i
$563$	−7.99123	−	10.9990i	−0.336790	−	0.463552i	0.606710	−	0.794923i	$-0.292489\pi$
$563$	−7.99123	−	10.9990i	−0.336790	−	0.463552i	−0.943501	+	0.331371i	$0.892489\pi$
$564$	−0.910521	−	1.83855i	−0.0383399	−	0.0774169i
$565$	7.77145	+	2.52510i	0.326948	+	0.106232i
$566$	−0.476337	+	0.111489i	−0.0200219	+	0.00468622i
$567$	−21.6207	−	15.7083i	−0.907983	−	0.659688i
$568$	−16.5112	−	20.0157i	−0.692794	−	0.839840i
$569$	7.56071	+	23.2695i	0.316961	+	0.975507i	0.974940	+	0.222470i	$0.0714119\pi$
$569$	7.56071	+	23.2695i	0.316961	+	0.975507i	−0.657978	+	0.753037i	$0.728588\pi$
$570$	−0.232160	+	2.74930i	−0.00972411	+	0.115155i
$571$		−	12.1063i		−	0.506634i	−0.967383	−	0.253317i	$-0.918478\pi$
$571$		−	12.1063i		−	0.506634i	0.967383	−	0.253317i	$-0.0815216\pi$
$572$		0			0
$573$		−	1.65617i		−	0.0691877i
$574$	24.1618	+	2.04030i	1.00849	+	0.0851605i
$575$	−3.59099	−	11.0519i	−0.149755	−	0.460897i
$576$	−22.9999	+	2.84002i	−0.958327	+	0.118334i
$577$	1.88795	+	1.37168i	0.0785964	+	0.0571036i	0.626390	−	0.779510i	$-0.284532\pi$
$577$	1.88795	+	1.37168i	0.0785964	+	0.0571036i	−0.547793	+	0.836614i	$0.684532\pi$
$578$	2.18294	+	9.32661i	0.0907982	+	0.387936i
$579$	8.25368	+	2.68178i	0.343011	+	0.111451i
$580$	−14.2835	+	7.07376i	−0.593091	+	0.293722i
$581$	−2.48442	−	3.41951i	−0.103071	−	0.141865i
$582$	4.14728	−	4.80013i	0.171910	−	0.198972i
$583$		0			0
$584$	−1.42637	+	2.24065i	−0.0590238	+	0.0927188i
$585$	9.31083	−	6.76472i	0.384956	−	0.279687i
$586$	−4.99139	−	2.10094i	−0.206193	−	0.0867889i
$587$	−23.0193	−	7.47941i	−0.950106	−	0.308708i	−0.207348	−	0.978267i	$-0.566483\pi$
$587$	−23.0193	−	7.47941i	−0.950106	−	0.308708i	−0.742759	+	0.669559i	$0.766483\pi$
$588$	2.23877	+	1.17307i	0.0923252	+	0.0483764i
$589$	7.43100	−	10.2279i	0.306189	−	0.421433i
$590$	22.0317	−	13.3288i	0.907033	−	0.548739i
$591$	−0.663295	−	2.04141i	−0.0272843	−	0.0839725i
$592$	24.9562	+	19.0165i	1.02569	+	0.781572i
$593$	27.1495			1.11490			0.557448	−	0.830212i	$-0.311780\pi$
$593$	27.1495			1.11490			0.557448	+	0.830212i	$0.311780\pi$
$594$		0			0
$595$		−	13.6130i		−	0.558077i
$596$	−3.27523	+	3.20135i	−0.134159	+	0.131132i
$597$	4.35599	−	1.41535i	0.178279	−	0.0579263i
$598$	7.85373	+	12.9817i	0.321163	+	0.530863i
$599$	−5.67813	−	4.12540i	−0.232002	−	0.168559i	0.465711	−	0.884937i	$-0.345799\pi$
$599$	−5.67813	−	4.12540i	−0.232002	−	0.168559i	−0.697713	+	0.716378i	$0.745799\pi$
$600$	1.11407	+	2.82539i	0.0454817	+	0.115346i
$601$	−0.870194	+	2.67818i	−0.0354960	+	0.109245i	−0.967235	−	0.253884i	$-0.918292\pi$
$601$	−0.870194	+	2.67818i	−0.0354960	+	0.109245i	0.931739	+	0.363130i	$0.118292\pi$
$602$	10.2187	+	4.30116i	0.416482	+	0.175302i
$603$	−8.00548	−	11.0186i	−0.326008	−	0.448712i
$604$	−1.10201	−	7.51143i	−0.0448403	−	0.305636i
$605$		0			0
$606$	3.78672	+	3.27170i	0.153825	+	0.132904i
$607$	−29.2769	+	21.2709i	−1.18831	+	0.863360i	−0.993085	−	0.117398i	$-0.962545\pi$
$607$	−29.2769	+	21.2709i	−1.18831	+	0.863360i	−0.195228	+	0.980758i	$0.562545\pi$
$608$	−26.5362	−	2.85181i	−1.07618	−	0.115656i
$609$	−2.03202	+	6.25391i	−0.0823415	+	0.253421i
$610$	6.45820	+	27.5927i	0.261485	+	1.11720i
$611$	−5.79310	+	7.97352i	−0.234364	+	0.322574i
$612$	18.2654	+	3.10693i	0.738334	+	0.125590i
$613$	29.6824	−	9.64440i	1.19886	−	0.389534i	0.359520	−	0.933137i	$-0.382940\pi$
$613$	29.6824	−	9.64440i	1.19886	−	0.389534i	0.839342	+	0.543604i	$0.182940\pi$
$614$	−2.82471	+	33.4510i	−0.113996	+	1.34997i
$615$	−2.14416			−0.0864608
$616$		0			0
$617$	−34.6326			−1.39426			−0.697129	−	0.716946i	$-0.745539\pi$
$617$	−34.6326			−1.39426			−0.697129	+	0.716946i	$0.745539\pi$
$618$	−0.416564	+	4.93306i	−0.0167567	+	0.198437i
$619$	−15.1194	+	4.91259i	−0.607700	+	0.197454i	−0.596672	−	0.802485i	$-0.703511\pi$
$619$	−15.1194	+	4.91259i	−0.607700	+	0.197454i	−0.0110283	+	0.999939i	$0.503511\pi$
$620$	−1.15691	+	6.80137i	−0.0464626	+	0.273150i
$621$	−3.87047	+	5.32724i	−0.155316	+	0.213775i
$622$	−2.84308	−	12.1471i	−0.113997	−	0.487053i
$623$	15.7224	−	48.3885i	0.629904	−	1.93864i
$624$	−2.25701	−	3.26041i	−0.0903527	−	0.130521i
$625$	−2.33663	+	1.69766i	−0.0934653	+	0.0679065i
$626$	−3.44089	−	2.97291i	−0.137526	−	0.118821i
$627$		0			0
$628$	24.0502	−	3.52844i	0.959708	−	0.140800i
$629$	−14.7443	−	20.2938i	−0.587894	−	0.809166i
$630$	16.0730	+	6.76533i	0.640366	+	0.269537i
$631$	−4.51514	+	13.8962i	−0.179745	+	0.553198i	−0.999818	−	0.0190601i	$-0.993933\pi$
$631$	−4.51514	+	13.8962i	−0.179745	+	0.553198i	0.820073	+	0.572259i	$0.193933\pi$
$632$	−25.1700	+	9.92469i	−1.00121	+	0.394783i
$633$	5.02321	+	3.64958i	0.199655	+	0.145058i
$634$	−6.76078	−	11.1752i	−0.268505	−	0.443823i
$635$	−20.4497	+	6.64452i	−0.811522	+	0.263680i
$636$	2.12086	+	2.16981i	0.0840976	+	0.0860385i
$637$		−	12.1416i		−	0.481066i
$638$		0			0
$639$	−26.5744			−1.05127
$640$	13.6675	−	5.03204i	0.540256	−	0.198909i
$641$	9.15575	+	28.1785i	0.361630	+	1.11298i	0.952064	+	0.305898i	$0.0989565\pi$
$641$	9.15575	+	28.1785i	0.361630	+	1.11298i	−0.590434	+	0.807086i	$0.701043\pi$
$642$	5.63315	−	3.40796i	0.222323	−	0.134501i
$643$	−17.3594	+	23.8931i	−0.684586	+	0.942252i	−0.999977	−	0.00670979i	$-0.997864\pi$
$643$	−17.3594	+	23.8931i	−0.684586	+	0.942252i	0.315391	+	0.948962i	$0.397864\pi$
$644$	−10.6704	+	20.3641i	−0.420472	+	0.802459i
$645$	−0.932407	−	0.302957i	−0.0367135	−	0.0119289i
$646$	19.6664	+	8.27780i	0.773763	+	0.325686i
$647$	−5.81487	+	4.22475i	−0.228606	+	0.166092i	−0.696192	−	0.717855i	$-0.745124\pi$
$647$	−5.81487	+	4.22475i	−0.228606	+	0.166092i	0.467586	+	0.883948i	$0.345124\pi$
$648$	−12.2757	+	19.2836i	−0.482235	+	0.757530i
$649$		0			0
$650$	9.53837	−	11.0399i	0.374126	−	0.433019i
$651$	1.67297	+	2.30265i	0.0655689	+	0.0902478i
$652$	7.35658	+	14.8546i	0.288106	+	0.581751i
$653$	27.1028	+	8.80623i	1.06061	+	0.344614i	0.786825	−	0.617176i	$-0.211723\pi$
$653$	27.1028	+	8.80623i	1.06061	+	0.344614i	0.273788	+	0.961790i	$0.411723\pi$
$654$	−0.203723	−	0.870406i	−0.00796618	−	0.0340356i
$655$	−9.68370	−	7.03562i	−0.378373	−	0.274904i
$656$	0.473148	−	20.7353i	0.0184733	−	0.809578i
$657$	0.840637	+	2.58722i	0.0327964	+	0.100937i
$658$	−14.8811	−	1.25661i	−0.580127	−	0.0489878i
$659$			26.9704i			1.05062i	0.850912	+	0.525308i	$0.176050\pi$
$659$			26.9704i			1.05062i	−0.850912	+	0.525308i	$0.823950\pi$
$660$		0			0
$661$			40.1424i			1.56136i	0.624931	+	0.780680i	$0.285127\pi$
$661$			40.1424i			1.56136i	−0.624931	+	0.780680i	$0.714873\pi$
$662$	0.476188	−	5.63915i	0.0185076	−	0.219172i
$663$	0.979670	+	3.01511i	0.0380472	+	0.117097i
$664$	−2.78896	+	2.30065i	−0.108233	+	0.0892824i
$665$	16.2478	+	11.8047i	0.630064	+	0.457769i
$666$	31.2888	−	7.32329i	1.21242	−	0.283772i
$667$	−20.4680	−	6.65047i	−0.792525	−	0.257507i
$668$	−16.0027	+	7.92516i	−0.619163	+	0.306634i
$669$	2.58375	+	3.55623i	0.0998936	+	0.137492i
$670$	6.47692	+	5.59602i	0.250225	+	0.216193i
$671$		0			0
$672$	2.45674	−	5.48339i	0.0947709	−	0.211526i
$673$	−15.8453	+	11.5123i	−0.610793	+	0.443767i	−0.849693	−	0.527277i	$-0.823213\pi$
$673$	−15.8453	+	11.5123i	−0.610793	+	0.443767i	0.238900	+	0.971044i	$0.423213\pi$
$674$	1.29413	−	3.07458i	0.0498479	−	0.118428i
$675$	6.02197	+	1.95666i	0.231786	+	0.0753117i
$676$	3.22611	−	6.15694i	0.124081	−	0.236806i
$677$	8.37755	−	11.5307i	0.321975	−	0.443161i	−0.617094	−	0.786890i	$-0.711690\pi$
$677$	8.37755	−	11.5307i	0.321975	−	0.443161i	0.939069	+	0.343729i	$0.111690\pi$
$678$	−1.49260	−	2.46718i	−0.0573231	−	0.0947516i
$679$	−14.2689	−	43.9152i	−0.547590	−	1.68531i
$680$	−11.6221	+	0.714832i	−0.445687	+	0.0274126i
$681$	3.81859			0.146329
$682$		0			0
$683$		−	11.2957i		−	0.432218i	−0.976369	−	0.216109i	$-0.930663\pi$
$683$		−	11.2957i		−	0.432218i	0.976369	−	0.216109i	$-0.0693367\pi$
$684$	−19.5475	+	19.1065i	−0.747417	+	0.730556i
$685$	11.1015	−	3.60709i	0.424166	−	0.137820i
$686$	−12.2668	+	7.42118i	−0.468347	+	0.283342i
$687$	0.0565716	+	0.0411017i	0.00215834	+	0.00156813i
$688$	3.13553	−	8.95009i	0.119541	−	0.341219i
$689$	4.50409	−	13.8622i	0.171592	−	0.528107i
$690$	0.788683	−	1.87375i	0.0300246	−	0.0713324i
$691$	−5.04537	−	6.94436i	−0.191935	−	0.264176i	0.702194	−	0.711986i	$-0.252204\pi$
$691$	−5.04537	−	6.94436i	−0.191935	−	0.264176i	−0.894129	+	0.447810i	$0.852204\pi$
$692$	−16.8298	+	2.46912i	−0.639771	+	0.0938619i
$693$		0			0
$694$	−22.1147	+	25.5959i	−0.839462	+	0.971607i
$695$	0.243192	−	0.176689i	0.00922479	−	0.00670220i
$696$	5.44600	+	1.40644i	0.206430	+	0.0533110i
$697$	−5.12410	+	15.7703i	−0.194089	+	0.597344i
$698$	−2.92301	+	0.684144i	−0.110638	+	0.0258952i
$699$	0.694640	−	0.956090i	0.0262737	−	0.0361626i
$700$	21.7941	+	3.70716i	0.823739	+	0.140118i
$701$	24.3811	−	7.92191i	0.920862	−	0.299206i	0.190042	−	0.981776i	$-0.439138\pi$
$701$	24.3811	−	7.92191i	0.920862	−	0.299206i	0.730821	+	0.682570i	$0.239138\pi$
$702$	−8.23789	−	0.695635i	−0.310919	−	0.0262550i
$703$	37.0076			1.39577
$704$		0			0
$705$	1.32058			0.0497358
$706$	−7.20852	−	0.608711i	−0.271296	−	0.0229091i
$707$	34.6438	−	11.2564i	1.30291	−	0.423342i
$708$	−8.95803	−	1.52376i	−0.336663	−	0.0572663i
$709$	17.5131	−	24.1047i	0.657718	−	0.905271i	−0.341685	−	0.939814i	$-0.610998\pi$
$709$	17.5131	−	24.1047i	0.657718	−	0.905271i	0.999403	+	0.0345436i	$0.0109978\pi$
$710$	16.2616	−	3.80611i	0.610288	−	0.142841i
$711$	−8.56293	+	26.3540i	−0.321135	+	0.988352i
$712$	−42.1374	−	10.8821i	−1.57917	−	0.407823i
$713$	−7.53619	+	5.47536i	−0.282232	+	0.205054i
$714$	−3.14059	+	3.63498i	−0.117534	+	0.136036i
$715$		0			0
$716$	5.82458	−	0.854534i	0.217675	−	0.0319354i
$717$	−3.78519	−	5.20986i	−0.141360	−	0.194566i
$718$	15.8949	−	37.7630i	0.593192	−	1.40930i
$719$	13.4629	−	41.4347i	0.502083	−	1.54525i	−0.303537	−	0.952820i	$-0.598168\pi$
$719$	13.4629	−	41.4347i	0.502083	−	1.54525i	0.805620	−	0.592433i	$-0.201832\pi$
$720$	4.93191	−	14.0777i	0.183801	−	0.524644i
$721$	29.1534	+	21.1812i	1.08573	+	0.788830i
$722$	−3.94392	+	2.38601i	−0.146778	+	0.0887979i
$723$	4.42279	−	1.43705i	0.164485	−	0.0534446i
$724$	−30.4227	+	29.7365i	−1.13065	+	1.10515i
$725$			20.6946i			0.768578i
$726$		0			0
$727$	51.1659			1.89764			0.948819	−	0.315820i	$-0.102280\pi$
$727$	51.1659			1.89764			0.948819	+	0.315820i	$0.102280\pi$
$728$	−28.8098	+	1.77198i	−1.06776	+	0.0656740i
$729$	6.67066	+	20.5302i	0.247061	+	0.760377i
$730$	−0.884964	−	1.46279i	−0.0327540	−	0.0541404i
$731$	−4.45652	+	6.13387i	−0.164830	+	0.226869i
$732$	4.64132	−	8.85784i	0.171548	−	0.327395i
$733$	16.5329	+	5.37186i	0.610656	+	0.198414i	0.597987	−	0.801506i	$-0.295967\pi$
$733$	16.5329	+	5.37186i	0.610656	+	0.198414i	0.0126687	+	0.999920i	$0.495967\pi$
$734$	−16.2915	+	38.7054i	−0.601332	+	1.42864i
$735$	−1.31615	+	0.956236i	−0.0485468	+	0.0352713i
$736$	17.9463	+	8.04052i	0.661508	+	0.296377i
$737$		0			0
$738$	−16.0738	−	13.8876i	−0.591683	−	0.511210i
$739$	6.10843	+	8.40753i	0.224702	+	0.309276i	0.906452	−	0.422310i	$-0.138781\pi$
$739$	6.10843	+	8.40753i	0.224702	+	0.309276i	−0.681749	+	0.731586i	$0.738781\pi$
$740$	−18.0977	+	8.96267i	−0.665283	+	0.329474i
$741$	−4.44825	−	1.44533i	−0.163411	−	0.0530954i
$742$	21.5045	−	5.03323i	0.789456	−	0.184776i
$743$	−10.1596	−	7.38138i	−0.372720	−	0.270797i	0.385618	−	0.922658i	$-0.373988\pi$
$743$	−10.1596	−	7.38138i	−0.372720	−	0.270797i	−0.758338	+	0.651862i	$0.773988\pi$
$744$	1.87804	−	1.54922i	0.0688523	−	0.0567971i
$745$	−0.910960	−	2.80365i	−0.0333750	−	0.102718i
$746$	−0.484941	+	5.74280i	−0.0177549	+	0.210259i
$747$			3.70284i			0.135480i
$748$		0			0
$749$		−	47.9237i		−	1.75109i
$750$	−4.86157	−	0.410527i	−0.177519	−	0.0149903i
$751$	12.5674	+	38.6784i	0.458590	+	1.41139i	0.866868	+	0.498537i	$0.166129\pi$
$751$	12.5674	+	38.6784i	0.458590	+	1.41139i	−0.408278	+	0.912857i	$0.633871\pi$
$752$	−0.291410	+	12.7708i	−0.0106266	+	0.465703i
$753$	5.62332	+	4.08558i	0.204925	+	0.148887i
$754$	−6.15772	−	26.3089i	−0.224251	−	0.958114i
$755$	4.64741	+	1.51004i	0.169137	+	0.0549559i
$756$	−5.55943	−	11.2257i	−0.202194	−	0.408276i
$757$	21.1584	+	29.1220i	0.769014	+	1.05846i	0.996410	+	0.0846546i	$0.0269787\pi$
$757$	21.1584	+	29.1220i	0.769014	+	1.05846i	−0.227396	+	0.973802i	$0.573021\pi$
$758$	26.9329	−	31.1726i	0.978247	−	1.13224i
$759$		0			0
$760$	9.22514	−	14.4915i	0.334631	−	0.525663i
$761$	−18.9007	+	13.7321i	−0.685149	+	0.497790i	−0.875062	−	0.484011i	$-0.839179\pi$
$761$	−18.9007	+	13.7321i	−0.685149	+	0.497790i	0.189913	+	0.981801i	$0.439179\pi$
$762$	6.99348	+	2.94364i	0.253347	+	0.106637i
$763$	−6.18846	−	2.01075i	−0.224037	−	0.0727941i
$764$	−4.78593	+	9.13381i	−0.173149	+	0.330450i
$765$	−7.00969	+	9.64802i	−0.253436	+	0.348825i
$766$	−22.7692	+	13.7750i	−0.822686	+	0.497711i
$767$	13.4889	+	41.5145i	0.487055	+	1.49900i
$768$	−4.81047	−	1.80951i	−0.173583	−	0.0652951i
$769$	−8.08790			−0.291657			−0.145829	−	0.989310i	$-0.546585\pi$
$769$	−8.08790			−0.291657			−0.145829	+	0.989310i	$0.546585\pi$
$770$		0			0
$771$		−	2.73327i		−	0.0984365i
$772$	−37.7694	−	38.6411i	−1.35935	−	1.39072i
$773$	26.5593	−	8.62964i	0.955271	−	0.310387i	0.210416	−	0.977612i	$-0.432518\pi$
$773$	26.5593	−	8.62964i	0.955271	−	0.310387i	0.744856	+	0.667226i	$0.232518\pi$
$774$	−5.02758	−	8.31029i	−0.180713	−	0.298707i
$775$	7.24668	+	5.26502i	0.260308	+	0.189125i
$776$	−36.7434	+	14.4882i	−1.31901	+	0.520094i
$777$	−2.57463	+	7.92389i	−0.0923643	+	0.284268i
$778$	35.2073	+	14.8192i	1.26224	+	0.531293i
$779$	−14.3794	−	19.7915i	−0.515194	−	0.709103i
$780$	2.52534	−	0.370497i	0.0904218	−	0.0132659i
$781$		0			0
$782$	−11.8967	−	10.2787i	−0.425425	−	0.367564i
$783$	9.48697	−	6.89269i	0.339037	−	0.246325i
$784$	−8.95695	−	12.9389i	−0.319891	−	0.462105i
$785$	−4.83486	+	14.8802i	−0.172563	+	0.531096i
$786$	0.962612	+	4.11277i	0.0343352	+	0.146697i
$787$	−19.4090	+	26.7141i	−0.691855	+	0.952256i	0.308145	+	0.951339i	$0.400292\pi$
$787$	−19.4090	+	26.7141i	−0.691855	+	0.952256i	−1.00000		0.000916708i	$0.999708\pi$
$788$	−2.24109	+	13.1752i	−0.0798355	+	0.469346i
$789$	2.85538	−	0.927769i	0.101654	−	0.0330294i
$790$	1.46536	−	17.3532i	0.0521352	−	0.617399i
$791$	−20.9894			−0.746298
$792$		0			0
$793$	−48.0390			−1.70591
$794$	3.34717	−	39.6380i	0.118786	−	1.40670i
$795$	−1.85739	+	0.603502i	−0.0658748	+	0.0214040i
$796$	−28.1133	−	4.78206i	−0.996451	−	0.169496i
$797$	15.2250	−	20.9553i	0.539295	−	0.742277i	−0.449216	−	0.893423i	$-0.648297\pi$
$797$	15.2250	−	20.9553i	0.539295	−	0.742277i	0.988511	+	0.151147i	$0.0482966\pi$
$798$	−1.61512	−	6.90062i	−0.0571747	−	0.244279i
$799$	3.15591	−	9.71288i	0.111648	−	0.343617i
$800$	2.02057	−	18.8014i	0.0714379	−	0.664731i
$801$	−36.0596	+	26.1989i	−1.27411	+	0.925692i
$802$	−8.91721	−	7.70441i	−0.314878	−	0.272052i
$803$		0			0
$804$	−0.438453	−	2.98853i	−0.0154630	−	0.105397i
$805$	−8.69805	−	11.9718i	−0.306566	−	0.421952i
$806$	−10.7793	−	4.53712i	−0.379684	−	0.159813i
$807$	−1.21401	+	3.73634i	−0.0427352	+	0.131526i
$808$	−11.4294	−	28.9861i	−0.402085	−	1.01973i
$809$	−5.27690	−	3.83389i	−0.185526	−	0.134792i	0.491146	−	0.871077i	$-0.336578\pi$
$809$	−5.27690	−	3.83389i	−0.185526	−	0.134792i	−0.676671	+	0.736285i	$0.736578\pi$
$810$	−7.61621	−	12.5891i	−0.267606	−	0.442337i
$811$	24.3226	−	7.90289i	0.854082	−	0.277508i	0.150927	−	0.988545i	$-0.451774\pi$
$811$	24.3226	−	7.90289i	0.854082	−	0.277508i	0.703155	+	0.711037i	$0.251774\pi$
$812$	29.2788	−	28.6183i	1.02748	−	1.00431i
$813$			7.92416i			0.277912i
$814$		0			0
$815$	−10.6696			−0.373741
$816$	3.26829	+	2.49041i	0.114413	+	0.0871819i
$817$	−3.45657	−	10.6382i	−0.120930	−	0.372184i
$818$	−5.01881	+	3.03629i	−0.175478	+	0.106161i
$819$	−17.3762	+	23.9163i	−0.607173	+	0.835702i
$820$	11.8251	+	6.19608i	0.412949	+	0.216376i
$821$	13.4191	+	4.36011i	0.468328	+	0.152169i	0.533668	−	0.845694i	$-0.320813\pi$
$821$	13.4191	+	4.36011i	0.468328	+	0.152169i	−0.0653399	+	0.997863i	$0.520813\pi$
$822$	−3.79653	−	1.59801i	−0.132419	−	0.0557369i
$823$	−18.5470	+	13.4752i	−0.646508	+	0.469716i	−0.862080	−	0.506772i	$-0.830839\pi$
$823$	−18.5470	+	13.4752i	−0.646508	+	0.469716i	0.215572	+	0.976488i	$0.430839\pi$
$824$	16.5526	−	26.0021i	0.576639	−	0.905826i
$825$		0			0
$826$	−43.2422	+	50.0492i	−1.50459	+	1.74143i
$827$	24.0533	+	33.1065i	0.836414	+	1.15122i	0.986695	+	0.162582i	$0.0519821\pi$
$827$	24.0533	+	33.1065i	0.836414	+	1.15122i	−0.150281	+	0.988643i	$0.548018\pi$
$828$	18.0486	−	8.93836i	0.627231	−	0.310629i
$829$	2.43906	+	0.792499i	0.0847121	+	0.0275246i	0.351066	−	0.936351i	$-0.385819\pi$
$829$	2.43906	+	0.792499i	0.0847121	+	0.0275246i	−0.266354	+	0.963875i	$0.585819\pi$
$830$	−0.530338	−	2.26587i	−0.0184083	−	0.0786496i
$831$	2.09238	+	1.52020i	0.0725839	+	0.0527353i
$832$	3.02567	+	24.5034i	0.104896	+	0.849501i
$833$	3.88782	+	11.9655i	0.134705	+	0.414580i
$834$	−0.105701	−	0.00892575i	−0.00366013	−	0.000309074i
$835$		−	11.4943i		−	0.397776i
$836$		0			0
$837$		−	5.07568i		−	0.175441i
$838$	0.863274	−	10.2231i	0.0298213	−	0.353152i
$839$	−12.9894	−	39.9771i	−0.448443	−	1.38016i	−0.878664	−	0.477441i	$-0.841564\pi$
$839$	−12.9894	−	39.9771i	−0.448443	−	1.38016i	0.430221	−	0.902723i	$-0.358436\pi$
$840$	2.46106	+	2.98342i	0.0849146	+	0.102938i
$841$	7.54500	+	5.48177i	0.260173	+	0.189026i
$842$	48.4677	−	11.3441i	1.67031	−	0.390943i
$843$	−4.05991	−	1.31914i	−0.139831	−	0.0454337i
$844$	−17.1567	−	34.6433i	−0.590558	−	1.19247i
$845$	2.62979	+	3.61960i	0.0904676	+	0.124518i
$846$	9.89975	+	8.55332i	0.340361	+	0.294069i
$847$		0			0
$848$	−5.42637	−	18.0953i	−0.186342	−	0.621394i
$849$	−0.0898965	+	0.0653136i	−0.00308524	+	0.00224156i
$850$	−5.86500	+	13.9340i	−0.201168	+	0.477933i
$851$	−25.9336	−	8.42634i	−0.888993	−	0.288851i
$852$	−5.22033	−	2.73534i	−0.178846	−	0.0937113i
$853$	−12.0073	+	16.5267i	−0.411124	+	0.565863i	−0.963492	−	0.267737i	$-0.913724\pi$
$853$	−12.0073	+	16.5267i	−0.411124	+	0.565863i	0.552368	+	0.833600i	$0.313724\pi$
$854$	−37.6788	−	62.2808i	−1.28934	−	2.13121i
$855$	−5.43686	−	16.7329i	−0.185937	−	0.572255i
$856$	−40.9150	+	2.51653i	−1.39845	+	0.0860133i
$857$	−51.9575			−1.77483			−0.887417	−	0.460968i	$-0.847502\pi$
$857$	−51.9575			−1.77483			−0.887417	+	0.460968i	$0.847502\pi$
$858$		0			0
$859$		−	44.6566i		−	1.52366i	−0.647775	−	0.761832i	$-0.724300\pi$
$859$		−	44.6566i		−	1.52366i	0.647775	−	0.761832i	$-0.275700\pi$
$860$	4.26676	+	4.36523i	0.145495	+	0.148853i
$861$	5.23803	−	1.70194i	0.178512	−	0.0580019i
$862$	−16.3446	+	9.88819i	−0.556699	+	0.336793i
$863$	−40.8122	−	29.6518i	−1.38926	−	1.00936i	−0.995946	−	0.0899581i	$-0.971327\pi$
$863$	−40.8122	−	29.6518i	−1.38926	−	1.00936i	−0.393319	−	0.919402i	$-0.628673\pi$
$864$	−9.29208	+	5.33585i	−0.316123	+	0.181529i
$865$	3.38332	−	10.4128i	0.115036	−	0.354045i
$866$	−7.98480	+	18.9703i	−0.271335	+	0.644636i
$867$	1.27883	+	1.76016i	0.0434314	+	0.0597782i
$868$	−2.57238	−	17.5336i	−0.0873122	−	0.595128i
$869$		0			0
$870$	−2.36692	+	2.73951i	−0.0802461	+	0.0928782i
$871$	−11.7389	+	8.52880i	−0.397757	+	0.288988i
$872$	−1.39172	+	5.38900i	−0.0471297	+	0.182495i
$873$	−12.5003	+	38.4718i	−0.423069	+	1.30207i
$874$	22.5846	−	5.28603i	0.763936	−	0.178803i
$875$	−20.8743	+	28.7310i	−0.705679	+	0.971284i
$876$	−0.101169	+	0.594766i	−0.00341820	+	0.0200953i
$877$	−17.1577	+	5.57487i	−0.579374	+	0.188250i	−0.584020	−	0.811739i	$-0.698521\pi$
$877$	−17.1577	+	5.57487i	−0.579374	+	0.188250i	0.00464624	+	0.999989i	$0.498521\pi$
$878$	11.4412	+	0.966131i	0.386121	+	0.0326054i
$879$	−1.23007			−0.0414893
$880$		0			0
$881$	3.97122			0.133794			0.0668969	−	0.997760i	$-0.478690\pi$
$881$	3.97122			0.133794			0.0668969	+	0.997760i	$0.478690\pi$
$882$	−16.0600	−	1.35616i	−0.540769	−	0.0456643i
$883$	47.0907	−	15.3007i	1.58473	−	0.514910i	0.621460	−	0.783446i	$-0.286540\pi$
$883$	47.0907	−	15.3007i	1.58473	−	0.514910i	0.963270	+	0.268536i	$0.0865398\pi$
$884$	3.31003	−	19.4594i	0.111328	−	0.654490i
$885$	3.43782	−	4.73176i	0.115561	−	0.159056i
$886$	−5.59350	+	1.30918i	−0.187917	+	0.0439829i
$887$	−10.3361	+	31.8112i	−0.347051	+	1.06811i	0.613425	+	0.789753i	$0.289791\pi$
$887$	−10.3361	+	31.8112i	−0.347051	+	1.06811i	−0.960476	+	0.278362i	$0.910209\pi$
$888$	6.90024	+	1.78200i	0.231557	+	0.0598001i
$889$	44.6831	−	32.4642i	1.49862	−	1.08881i
$890$	18.3136	−	21.1965i	0.613874	−	0.710508i
$891$		0			0
$892$	−3.97281	−	27.0790i	−0.133019	−	0.906673i
$893$	8.85618	+	12.1895i	0.296361	+	0.407905i
$894$	−0.403572	+	0.958804i	−0.0134975	+	0.0320672i
$895$	−1.17093	+	3.60374i	−0.0391398	+	0.120460i
$896$	−29.3946	+	23.1416i	−0.982004	+	0.773106i
$897$	2.78809	+	2.02566i	0.0930915	+	0.0676349i
$898$	−10.0272	+	6.06631i	−0.334613	+	0.202435i
$899$	15.7770	−	5.12627i	0.526194	−	0.170971i
$900$	−13.5374	−	13.8498i	−0.451246	−	0.461660i
$901$			15.1034i			0.503167i
$902$		0			0
$903$	2.51828			0.0838030
$904$	1.10218	+	17.9198i	0.0366580	+	0.596003i
$905$	−8.46167	−	26.0423i	−0.281275	−	0.865676i
$906$	−0.892593	−	1.47540i	−0.0296544	−	0.0490170i
$907$	−4.08489	+	5.62236i	−0.135636	+	0.186688i	−0.871432	−	0.490516i	$-0.836808\pi$
$907$	−4.08489	+	5.62236i	−0.135636	+	0.186688i	0.735796	+	0.677204i	$0.236808\pi$
$908$	−21.0596	−	11.0348i	−0.698886	−	0.366202i
$909$	−30.3496	−	9.86118i	−1.00663	−	0.327075i
$910$	7.20759	−	17.1237i	0.238929	−	0.567647i
$911$	34.3244	−	24.9382i	1.13722	−	0.826238i	0.150489	−	0.988612i	$-0.451915\pi$
$911$	34.3244	−	24.9382i	1.13722	−	0.826238i	0.986729	+	0.162374i	$0.0519150\pi$
$912$	−5.80661	+	1.74128i	−0.192276	+	0.0576594i
$913$		0			0
$914$	10.5175	+	9.08708i	0.347889	+	0.300574i
$915$	3.78342	+	5.20742i	0.125076	+	0.172152i
$916$	−0.193219	−	0.390154i	−0.00638415	−	0.0128910i
$917$	29.2412	+	9.50103i	0.965628	+	0.313752i
$918$	8.34118	−	1.95229i	0.275300	−	0.0644352i
$919$	2.60869	+	1.89533i	0.0860528	+	0.0625210i	0.629980	−	0.776612i	$-0.283063\pi$
$919$	2.60869	+	1.89533i	0.0860528	+	0.0625210i	−0.543927	+	0.839133i	$0.683063\pi$
$920$	−9.76425	+	8.05464i	−0.321918	+	0.265554i
$921$	2.35626	+	7.25183i	0.0776415	+	0.238956i
$922$	2.91256	−	34.4914i	0.0959202	−	1.13591i
$923$			28.3116i			0.931886i
$924$		0			0
$925$			26.2207i			0.862131i
$926$	−28.5266	−	2.40888i	−0.937442	−	0.0791607i
$927$	−9.75535	−	30.0239i	−0.320408	−	0.986113i
$928$	−25.9705	−	23.4941i	−0.852522	−	0.771231i
$929$	19.3523	+	14.0602i	0.634927	+	0.461301i	0.858104	−	0.513477i	$-0.171643\pi$
$929$	19.3523	+	14.0602i	0.634927	+	0.461301i	−0.223177	+	0.974778i	$0.571643\pi$
$930$	0.357121	+	1.52580i	0.0117105	+	0.0500331i
$931$	−17.6529	−	5.73578i	−0.578551	−	0.187983i
$932$	−6.59380	+	3.26551i	−0.215987	+	0.106965i
$933$	−1.66556	−	2.29245i	−0.0545281	−	0.0750515i
$934$	−22.5465	+	26.0957i	−0.737743	+	0.853876i
$935$		0			0
$936$	21.3310	+	13.5791i	0.697226	+	0.443846i
$937$	19.5822	−	14.2273i	0.639721	−	0.464785i	−0.220033	−	0.975492i	$-0.570617\pi$
$937$	19.5822	−	14.2273i	0.639721	−	0.464785i	0.859754	+	0.510708i	$0.170617\pi$
$938$	−20.2645	−	8.52958i	−0.661661	−	0.278501i
$939$	−0.982312	−	0.319173i	−0.0320565	−	0.0104158i
$940$	−7.28299	−	3.81613i	−0.237545	−	0.124469i
$941$	−1.32063	+	1.81770i	−0.0430514	+	0.0592552i	−0.830000	−	0.557763i	$-0.811660\pi$
$941$	−1.32063	+	1.81770i	−0.0430514	+	0.0592552i	0.786949	+	0.617019i	$0.211660\pi$
$942$	4.72397	−	2.85792i	0.153915	−	0.0931160i
$943$	5.57017	+	17.1432i	0.181390	+	0.558260i
$944$	45.0003	+	34.2900i	1.46464	+	1.11604i
$945$	8.06313			0.262294
$946$		0			0
$947$		−	26.7519i		−	0.869321i	−0.900594	−	0.434660i	$-0.856868\pi$
$947$		−	26.7519i		−	0.869321i	0.900594	−	0.434660i	$-0.143132\pi$
$948$	−4.39478	+	4.29564i	−0.142736	+	0.139516i
$949$	2.75634	−	0.895590i	0.0894747	−	0.0290721i
$950$	−11.5451	−	19.0834i	−0.374573	−	0.619147i
$951$	−2.40009	−	1.74377i	−0.0778283	−	0.0565455i
$952$	27.8246	−	10.9714i	0.901799	−	0.355585i
$953$	−10.5020	+	32.3219i	−0.340194	+	1.04701i	0.623913	+	0.781494i	$0.285542\pi$
$953$	−10.5020	+	32.3219i	−0.340194	+	1.04701i	−0.964107	+	0.265515i	$0.914458\pi$
$954$	−17.8328	−	7.50605i	−0.577359	−	0.243017i
$955$	−3.90129	−	5.36967i	−0.126243	−	0.173758i
$956$	5.82015	+	39.6707i	0.188237	+	1.28304i
$957$		0			0
$958$	1.85018	+	1.59854i	0.0597766	+	0.0516466i
$959$	−24.2570	+	17.6237i	−0.783299	+	0.569100i
$960$	2.41787	−	2.25780i	0.0780364	−	0.0728701i
$961$	−7.36069	+	22.6539i	−0.237441	+	0.730770i
$962$	−7.80202	−	33.3342i	−0.251547	−	1.07474i
$963$	−24.6773	+	33.9654i	−0.795214	+	1.09452i
$964$	−28.5445	−	4.85540i	−0.919355	−	0.156382i
$965$	33.0774	−	10.7475i	1.06480	−	0.345974i
$966$	−0.439397	+	5.20346i	−0.0141374	+	0.167419i
$967$	−3.94526			−0.126871			−0.0634356	−	0.997986i	$-0.520206\pi$
$967$	−3.94526			−0.126871			−0.0634356	+	0.997986i	$0.520206\pi$
$968$		0			0
$969$	4.84655			0.155694
$970$	2.13915	−	25.3324i	0.0686839	−	0.813373i
$971$	15.9164	−	5.17155i	0.510781	−	0.165963i	−0.0422763	−	0.999106i	$-0.513461\pi$
$971$	15.9164	−	5.17155i	0.510781	−	0.165963i	0.553058	+	0.833143i	$0.313461\pi$
$972$	−2.77651	+	16.3229i	−0.0890567	+	0.523557i
$973$	−0.453852	+	0.624674i	−0.0145498	+	0.0200261i
$974$	0.855685	+	3.65592i	0.0274179	+	0.117143i
$975$	1.02404	−	3.15168i	0.0327956	−	0.100935i
$976$	−51.1939	+	35.4388i	−1.63868	+	1.13437i
$977$	−5.54903	+	4.03161i	−0.177529	+	0.128983i	−0.673001	−	0.739641i	$-0.734995\pi$
$977$	−5.54903	+	4.03161i	−0.177529	+	0.128983i	0.495472	+	0.868624i	$0.334995\pi$
$978$	2.84904	+	2.46155i	0.0911023	+	0.0787117i
$979$		0			0
$980$	10.0218	−	1.47032i	0.320136	−	0.0469676i
$981$	3.35060	+	4.61171i	0.106977	+	0.147241i
$982$	−38.2029	−	16.0801i	−1.21910	−	0.513135i
$983$	0.536936	−	1.65252i	0.0171256	−	0.0527072i	−0.942129	−	0.335252i	$-0.891179\pi$
$983$	0.536936	−	1.65252i	0.0171256	−	0.0527072i	0.959254	+	0.282545i	$0.0911786\pi$
$984$	−1.72809	−	4.38261i	−0.0550895	−	0.139713i
$985$	−6.95930	−	5.05623i	−0.221742	−	0.161105i
$986$	14.4927	+	23.9556i	0.461543	+	0.762903i
$987$	−3.22608	+	1.04822i	−0.102687	+	0.0333651i
$988$	20.3555	+	20.8253i	0.647596	+	0.662541i
$989$			8.24192i			0.262078i
$990$		0			0
$991$	17.5645			0.557956			0.278978	−	0.960298i	$-0.410004\pi$
$991$	17.5645			0.557956			0.278978	+	0.960298i	$0.410004\pi$
$992$	−14.8343	+	3.11688i	−0.470988	+	0.0989612i
$993$	−0.397218	−	1.22251i	−0.0126053	−	0.0387952i
$994$	−36.7049	+	22.2058i	−1.16421	+	0.704326i
$995$	10.7890	−	14.8498i	0.342036	−	0.470772i
$996$	−0.381139	+	0.727394i	−0.0120768	+	0.0230484i
$997$	−47.5930	−	15.4639i	−1.50728	−	0.489747i	−0.565152	−	0.824987i	$-0.691183\pi$
$997$	−47.5930	−	15.4639i	−1.50728	−	0.489747i	−0.942133	+	0.335240i	$0.891183\pi$
$998$	−10.4992	−	4.41923i	−0.332346	−	0.139888i
$999$	12.0203	−	8.73324i	0.380305	−	0.276308i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	968.2.o.d.245.1		40
8.5	even	2	inner	968.2.o.d.245.6		40
11.2	odd	10		968.2.c.h.485.5		20
11.3	even	5		968.2.o.i.269.4		40
11.4	even	5	inner	968.2.o.d.565.6		40
11.5	even	5		968.2.o.i.493.9		40
11.6	odd	10		88.2.o.a.53.2	yes	40
11.7	odd	10		968.2.o.j.565.5		40
11.8	odd	10		88.2.o.a.5.7	yes	40
11.9	even	5		968.2.c.i.485.16		20
11.10	odd	2		968.2.o.j.245.10		40
33.8	even	10		792.2.br.b.181.4		40
33.17	even	10		792.2.br.b.757.9		40
44.19	even	10		352.2.w.a.49.5		40
44.31	odd	10		3872.2.c.i.1937.10		20
44.35	even	10		3872.2.c.h.1937.10		20
44.39	even	10		352.2.w.a.273.6		40
88.5	even	10		968.2.o.i.493.4		40
88.13	odd	10		968.2.c.h.485.6		20
88.19	even	10		352.2.w.a.49.6		40
88.21	odd	2		968.2.o.j.245.5		40
88.29	odd	10		968.2.o.j.565.10		40
88.35	even	10		3872.2.c.h.1937.11		20
88.37	even	10	inner	968.2.o.d.565.1		40
88.53	even	10		968.2.c.i.485.15		20
88.61	odd	10		88.2.o.a.53.7	yes	40
88.69	even	10		968.2.o.i.269.9		40
88.75	odd	10		3872.2.c.i.1937.11		20
88.83	even	10		352.2.w.a.273.5		40
88.85	odd	10		88.2.o.a.5.2	✓	40
264.149	even	10		792.2.br.b.757.4		40
264.173	even	10		792.2.br.b.181.9		40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
88.2.o.a.5.2	✓	40	88.85	odd	10
88.2.o.a.5.7	yes	40	11.8	odd	10
88.2.o.a.53.2	yes	40	11.6	odd	10
88.2.o.a.53.7	yes	40	88.61	odd	10
352.2.w.a.49.5		40	44.19	even	10
352.2.w.a.49.6		40	88.19	even	10
352.2.w.a.273.5		40	88.83	even	10
352.2.w.a.273.6		40	44.39	even	10
792.2.br.b.181.4		40	33.8	even	10
792.2.br.b.181.9		40	264.173	even	10
792.2.br.b.757.4		40	264.149	even	10
792.2.br.b.757.9		40	33.17	even	10
968.2.c.h.485.5		20	11.2	odd	10
968.2.c.h.485.6		20	88.13	odd	10
968.2.c.i.485.15		20	88.53	even	10
968.2.c.i.485.16		20	11.9	even	5
968.2.o.d.245.1		40	1.1	even	1	trivial
968.2.o.d.245.6		40	8.5	even	2	inner
968.2.o.d.565.1		40	88.37	even	10	inner
968.2.o.d.565.6		40	11.4	even	5	inner
968.2.o.i.269.4		40	11.3	even	5
968.2.o.i.269.9		40	88.69	even	10
968.2.o.i.493.4		40	88.5	even	10
968.2.o.i.493.9		40	11.5	even	5
968.2.o.j.245.5		40	88.21	odd	2
968.2.o.j.245.10		40	11.10	odd	2
968.2.o.j.565.5		40	11.7	odd	10
968.2.o.j.565.10		40	88.29	odd	10
3872.2.c.h.1937.10		20	44.35	even	10
3872.2.c.h.1937.11		20	88.35	even	10
3872.2.c.i.1937.10		20	44.31	odd	10
3872.2.c.i.1937.11		20	88.75	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.o (of order \(10\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.40920 - 0.118997i) q^{2} +(-0.305500 + 0.0992629i) q^{3} +(1.97168 + 0.335382i) q^{4} +(-0.756671 + 1.04147i) q^{5} +(0.442322 - 0.103527i) q^{6} +(1.02182 - 3.14484i) q^{7} +(-2.73858 - 0.707244i) q^{8} +(-2.34357 + 1.70271i) q^{9} +(1.19023 - 1.37759i) q^{10} +(-0.635639 + 0.0932556i) q^{12} +(1.81401 + 2.49677i) q^{13} +(-1.81418 + 4.31012i) q^{14} +(0.127784 - 0.393278i) q^{15} +(3.77504 + 1.32253i) q^{16} +(-2.58719 - 1.87971i) q^{17} +(3.50518 - 2.12057i) q^{18} +(4.48707 - 1.45794i) q^{19} +(-1.84120 + 1.79967i) q^{20} +1.06218i q^{21} -3.47634 q^{23} +(0.906838 - 0.0557763i) q^{24} +(1.03298 + 3.17919i) q^{25} +(-2.25919 - 3.73431i) q^{26} +(1.11337 - 1.53243i) q^{27} +(3.06943 - 5.85793i) q^{28} +(5.88781 + 1.91307i) q^{29} +(-0.226872 + 0.539000i) q^{30} +(2.16785 - 1.57504i) q^{31} +(-5.16240 - 2.31293i) q^{32} +(3.42219 + 2.95675i) q^{34} +(2.50207 + 3.44381i) q^{35} +(-5.19183 + 2.57120i) q^{36} +(7.46003 + 2.42391i) q^{37} +(-6.49667 + 1.52057i) q^{38} +(-0.802018 - 0.582700i) q^{39} +(2.80877 - 2.31699i) q^{40} +(-1.60231 - 4.93140i) q^{41} +(0.126396 - 1.49682i) q^{42} -2.37086i q^{43} -3.72915i q^{45} +(4.89885 + 0.413675i) q^{46} +(0.986855 + 3.03723i) q^{47} +(-1.28455 - 0.0293115i) q^{48} +(-3.18281 - 2.31245i) q^{49} +(-1.07736 - 4.60302i) q^{50} +(0.976972 + 0.317438i) q^{51} +(2.73928 + 5.53122i) q^{52} +(-2.77602 - 3.82086i) q^{53} +(-1.75132 + 2.02701i) q^{54} +(-5.02251 + 7.88972i) q^{56} +(-1.22608 + 0.890800i) q^{57} +(-8.06944 - 3.39652i) q^{58} +(13.4517 + 4.37073i) q^{59} +(0.383847 - 0.732561i) q^{60} +(-9.14936 + 12.5930i) q^{61} +(-3.24236 + 1.96157i) q^{62} +(2.96003 + 9.11004i) q^{63} +(6.99961 + 3.87368i) q^{64} -3.97292 q^{65} +4.70162i q^{67} +(-4.47069 - 4.57387i) q^{68} +(1.06202 - 0.345072i) q^{69} +(-3.11611 - 5.15075i) q^{70} +(7.42164 + 5.39214i) q^{71} +(7.62229 - 3.00551i) q^{72} +(0.290193 - 0.893124i) q^{73} +(-10.2242 - 4.30350i) q^{74} +(-0.631151 - 0.868704i) q^{75} +(9.33604 - 1.36970i) q^{76} +(1.06086 + 0.916578i) q^{78} +(7.73885 - 5.62261i) q^{79} +(-4.23383 + 2.93086i) q^{80} +(2.49747 - 7.68644i) q^{81} +(1.67115 + 7.13999i) q^{82} +(0.751333 - 1.03412i) q^{83} +(-0.356235 + 2.09428i) q^{84} +(3.91531 - 1.27216i) q^{85} +(-0.282126 + 3.34101i) q^{86} -1.98862 q^{87} +15.3866 q^{89} +(-0.443758 + 5.25510i) q^{90} +(9.70557 - 3.15353i) q^{91} +(-6.85423 - 1.16590i) q^{92} +(-0.505936 + 0.696361i) q^{93} +(-1.02925 - 4.39749i) q^{94} +(-1.87684 + 5.77632i) q^{95} +(1.80670 + 0.194164i) q^{96} +(11.2973 - 8.20794i) q^{97} +(4.21004 + 3.63744i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q - 5 q^{2} - q^{4} - 8 q^{6} - 5 q^{8} + 10 q^{9} + 20 q^{10} - 6 q^{12} + 2 q^{14} + 22 q^{15} - 25 q^{16} - 4 q^{17} - 25 q^{18} + 8 q^{20} - 8 q^{23} + 40 q^{24} + 6 q^{25} - 20 q^{26} + 18 q^{28}+ \cdots + 144 q^{98}+O(q^{100}) \) 40 * q - 5 * q^2 - q^4 - 8 * q^6 - 5 * q^8 + 10 * q^9 + 20 * q^10 - 6 * q^12 + 2 * q^14 + 22 * q^15 - 25 * q^16 - 4 * q^17 - 25 * q^18 + 8 * q^20 - 8 * q^23 + 40 * q^24 + 6 * q^25 - 20 * q^26 + 18 * q^28 - 12 * q^30 + 4 * q^31 - 20 * q^32 + 10 * q^34 - 27 * q^36 - 33 * q^38 - 6 * q^39 + 20 * q^40 - 16 * q^41 - 20 * q^42 + 42 * q^46 + 4 * q^47 + 23 * q^48 + 6 * q^49 + 39 * q^50 - 108 * q^54 - 32 * q^56 - 4 * q^57 - 16 * q^58 + 94 * q^60 + 52 * q^62 + 30 * q^63 + 11 * q^64 + 36 * q^65 - 63 * q^68 + 52 * q^70 + 12 * q^71 - 44 * q^72 - 4 * q^73 + 26 * q^74 + 134 * q^76 - 12 * q^78 + 16 * q^79 + 16 * q^80 + 16 * q^81 + 54 * q^82 - 72 * q^84 - 10 * q^86 - 68 * q^87 - 16 * q^89 - 126 * q^90 - 64 * q^92 - 40 * q^94 - 26 * q^95 + 5 * q^96 - 20 * q^97 + 144 * q^98

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