LMFDB - Embedded newform 968.2.o.j.565.5

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			565.5
Character	$\chi$	$=$	968.565
Dual form			968.2.o.j.245.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.322293 + 1.37700i) q^{2} +(0.305500 + 0.0992629i) q^{3} +(-1.79225 + 0.887594i) q^{4} +(0.756671 + 1.04147i) q^{5} +(-0.0382245 + 0.452665i) q^{6} +(-1.02182 - 3.14484i) q^{7} +(-1.79985 - 2.18187i) 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} +(4.00112 - 2.42061i) q^{14} +(0.127784 + 0.393278i) q^{15} +(2.42435 - 3.18159i) q^{16} +(2.58719 - 1.87971i) q^{17} +(1.58931 - 3.77587i) q^{18} +(4.48707 + 1.45794i) q^{19} +(-2.28055 - 1.19496i) q^{20} -1.06218i q^{21} -3.47634 q^{23} +(-0.333275 - 0.845219i) q^{24} +(1.03298 - 3.17919i) q^{25} +(4.02270 + 1.69320i) q^{26} +(-1.11337 - 1.53243i) q^{27} +(4.62271 + 4.72940i) q^{28} +(5.88781 - 1.91307i) q^{29} +(-0.500359 + 0.302709i) 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} +(5.71159 + 0.971539i) q^{36} +(-7.46003 + 2.42391i) q^{37} +(-0.561428 + 6.64858i) q^{38} +(0.802018 - 0.582700i) q^{39} +(0.910453 - 3.52544i) q^{40} +(1.60231 - 4.93140i) q^{41} +(1.46262 - 0.342333i) q^{42} +2.37086i q^{43} -3.72915i q^{45} +(-1.12040 - 4.78692i) q^{46} +(0.986855 - 3.03723i) q^{47} +(1.05645 - 0.731327i) q^{48} +(-3.18281 + 2.31245i) q^{49} +(4.71066 + 0.397784i) q^{50} +(0.976972 - 0.317438i) q^{51} +(-1.03505 + 6.08496i) 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} +(4.53189 + 7.49094i) q^{58} +(-13.4517 + 4.37073i) q^{59} +(-0.578092 - 0.591434i) q^{60} +(-9.14936 - 12.5930i) q^{61} +(-1.47014 + 3.49275i) q^{62} +(-2.96003 + 9.11004i) q^{63} +(-1.52109 + 7.85406i) q^{64} +3.97292 q^{65} +4.70162i q^{67} +(-2.96849 + 5.66529i) q^{68} +(-1.06202 - 0.345072i) q^{69} +(5.54852 + 2.33544i) q^{70} +(7.42164 - 5.39214i) q^{71} +(0.502998 + 8.17798i) q^{72} +(-0.290193 - 0.893124i) q^{73} +(-5.74204 - 9.49125i) 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} +(5.14796 + 0.117469i) q^{80} +(2.49747 + 7.68644i) q^{81} +(7.30695 + 0.617023i) q^{82} +(0.751333 + 1.03412i) q^{83} +(0.942784 + 1.90370i) q^{84} +(3.91531 + 1.27216i) q^{85} +(-3.26467 + 0.764112i) q^{86} +1.98862 q^{87} +15.3866 q^{89} +(5.13503 - 1.20188i) q^{90} +(-9.70557 - 3.15353i) q^{91} +(6.23049 - 3.08558i) q^{92} +(0.505936 + 0.696361i) q^{93} +(4.50031 + 0.380021i) q^{94} +(1.87684 + 5.77632i) q^{95} +(1.34752 + 1.21903i) 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 $\left(\mathbb{Z}/968\mathbb{Z}\right)^\times$.

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

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 $

$2$	0.322293	+	1.37700i	0.227896	+	0.973686i
$2$	0.322293	+	1.37700i	0.227896	+	0.973686i
$3$	0.305500	+	0.0992629i	0.176380	+	0.0573095i	0.395876	−	0.918304i	$-0.370441\pi$
$3$	0.305500	+	0.0992629i	0.176380	+	0.0573095i	−0.219495	+	0.975614i	$0.570441\pi$
$4$	−1.79225	+	0.887594i	−0.896127	+	0.443797i
$5$	0.756671	+	1.04147i	0.338393	+	0.465759i	0.943971	−	0.330027i	$-0.107058\pi$
$5$	0.756671	+	1.04147i	0.338393	+	0.465759i	−0.605578	+	0.795786i	$0.707058\pi$
$6$	−0.0382245	+	0.452665i	−0.0156051	+	0.184800i
$7$	−1.02182	−	3.14484i	−0.386212	−	1.18864i	−0.935597	−	0.353070i	$-0.885138\pi$
$7$	−1.02182	−	3.14484i	−0.386212	−	1.18864i	0.549384	−	0.835570i	$-0.314862\pi$
$8$	−1.79985	−	2.18187i	−0.636342	−	0.771407i
$9$	−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	−0.479623	−	0.877475i	$-0.659227\pi$
$13$	1.81401	−	2.49677i	0.503117	−	0.692481i	0.982740	+	0.184994i	$0.0592266\pi$
$14$	4.00112	−	2.42061i	1.06935	−	0.646935i
$15$	0.127784	+	0.393278i	0.0329936	+	0.101544i
$16$	2.42435	−	3.18159i	0.606088	−	0.795398i
$17$	2.58719	−	1.87971i	0.627486	−	0.455896i	−0.228042	−	0.973651i	$-0.573232\pi$
$17$	2.58719	−	1.87971i	0.627486	−	0.455896i	0.855528	+	0.517756i	$0.173232\pi$
$18$	1.58931	−	3.77587i	0.374603	−	0.889981i
$19$	4.48707	+	1.45794i	1.02941	+	0.334474i	0.774555	−	0.632506i	$-0.217974\pi$
$19$	4.48707	+	1.45794i	1.02941	+	0.334474i	0.254850	+	0.966981i	$0.417974\pi$
$20$	−2.28055	−	1.19496i	−0.509946	−	0.267201i
$21$		−	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	$0.618054\pi$
$24$	−0.333275	−	0.845219i	−0.0680294	−	0.172530i
$25$	1.03298	−	3.17919i	0.206596	−	0.635837i
$26$	4.02270	+	1.69320i	0.788916	+	0.332064i
$27$	−1.11337	−	1.53243i	−0.214269	−	0.294916i
$28$	4.62271	+	4.72940i	0.873610	+	0.893772i
$29$	5.88781	−	1.91307i	1.09334	−	0.355247i	0.293803	−	0.955866i	$-0.405079\pi$
$29$	5.88781	−	1.91307i	1.09334	−	0.355247i	0.799536	+	0.600619i	$0.205079\pi$
$30$	−0.500359	+	0.302709i	−0.0913527	+	0.0552668i
$31$	2.16785	+	1.57504i	0.389358	+	0.282885i	0.765192	−	0.643802i	$-0.222644\pi$
$31$	2.16785	+	1.57504i	0.389358	+	0.282885i	−0.375835	+	0.926687i	$0.622644\pi$
$32$	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
$36$	5.71159	+	0.971539i	0.951932	+	0.161923i
$37$	−7.46003	+	2.42391i	−1.22642	+	0.398489i	−0.849417	−	0.527723i	$-0.823046\pi$
$37$	−7.46003	+	2.42391i	−1.22642	+	0.398489i	−0.377005	+	0.926211i	$0.623046\pi$
$38$	−0.561428	+	6.64858i	−0.0910757	+	1.07854i
$39$	0.802018	−	0.582700i	0.128426	−	0.0933067i
$40$	0.910453	−	3.52544i	0.143955	−	0.557421i
$41$	1.60231	−	4.93140i	0.250239	−	0.770155i	−0.744492	−	0.667631i	$-0.767308\pi$
$41$	1.60231	−	4.93140i	0.250239	−	0.770155i	0.994731	−	0.102524i	$-0.0326918\pi$
$42$	1.46262	−	0.342333i	0.225687	−	0.0528231i
$43$			2.37086i			0.361553i	0.983524	+	0.180776i	$0.0578610\pi$
$43$			2.37086i			0.361553i	−0.983524	+	0.180776i	$0.942139\pi$
$44$		0			0
$45$		−	3.72915i		−	0.555908i
$46$	−1.12040	−	4.78692i	−0.165194	−	0.705792i
$47$	0.986855	−	3.03723i	0.143948	−	0.443025i	−0.852927	−	0.522031i	$-0.825175\pi$
$47$	0.986855	−	3.03723i	0.143948	−	0.443025i	0.996874	+	0.0790059i	$0.0251746\pi$
$48$	1.05645	−	0.731327i	0.152486	−	0.105558i
$49$	−3.18281	+	2.31245i	−0.454687	+	0.330350i
$50$	4.71066	+	0.397784i	0.666188	+	0.0562551i
$51$	0.976972	−	0.317438i	0.136803	−	0.0444501i
$52$	−1.03505	+	6.08496i	−0.143536	+	0.843832i
$53$	2.77602	−	3.82086i	0.381315	−	0.524835i	−0.574617	−	0.818422i	$-0.694849\pi$
$53$	2.77602	−	3.82086i	0.381315	−	0.524835i	0.955932	+	0.293587i	$0.0948490\pi$
$54$	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
$58$	4.53189	+	7.49094i	0.595066	+	0.983609i
$59$	−13.4517	+	4.37073i	−1.75127	+	0.569020i	−0.996237	−	0.0866719i	$-0.972377\pi$
$59$	−13.4517	+	4.37073i	−1.75127	+	0.569020i	−0.755028	+	0.655692i	$0.772377\pi$
$60$	−0.578092	−	0.591434i	−0.0746314	−	0.0763538i
$61$	−9.14936	−	12.5930i	−1.17146	−	1.61237i	−0.653355	−	0.757052i	$-0.726639\pi$
$61$	−9.14936	−	12.5930i	−1.17146	−	1.61237i	−0.518101	−	0.855319i	$-0.673361\pi$
$62$	−1.47014	+	3.49275i	−0.186708	+	0.443580i
$63$	−2.96003	+	9.11004i	−0.372929	+	1.14776i
$64$	−1.52109	+	7.85406i	−0.190137	+	0.981758i
$65$	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	$0.907276\pi$
$68$	−2.96849	+	5.66529i	−0.359982	+	0.687017i
$69$	−1.06202	−	0.345072i	−0.127852	−	0.0415418i
$70$	5.54852	+	2.33544i	0.663175	+	0.279138i
$71$	7.42164	−	5.39214i	0.880787	−	0.639929i	−0.0526729	−	0.998612i	$-0.516774\pi$
$71$	7.42164	−	5.39214i	0.880787	−	0.639929i	0.933459	+	0.358683i	$0.116774\pi$
$72$	0.502998	+	8.17798i	0.0592788	+	0.963784i
$73$	−0.290193	−	0.893124i	−0.0339646	−	0.104532i	0.932637	−	0.360816i	$-0.117502\pi$
$73$	−0.290193	−	0.893124i	−0.0339646	−	0.104532i	−0.966602	+	0.256284i	$0.917502\pi$
$74$	−5.74204	−	9.49125i	−0.667499	−	1.10334i
$75$	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	$-0.480864\pi$
$79$	−7.73885	−	5.62261i	−0.870689	−	0.632593i	−0.930772	+	0.365601i	$0.880864\pi$
$80$	5.14796	+	0.117469i	0.575560	+	0.0131334i
$81$	2.49747	+	7.68644i	0.277497	+	0.854048i
$82$	7.30695	+	0.617023i	0.806917	+	0.0681388i
$83$	0.751333	+	1.03412i	0.0824695	+	0.113510i	0.848259	−	0.529582i	$-0.177651\pi$
$83$	0.751333	+	1.03412i	0.0824695	+	0.113510i	−0.765789	+	0.643092i	$0.777651\pi$
$84$	0.942784	+	1.90370i	0.102866	+	0.207710i
$85$	3.91531	+	1.27216i	0.424675	+	0.137985i
$86$	−3.26467	+	0.764112i	−0.352039	+	0.0823963i
$87$	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	$0.196468\pi$
$90$	5.13503	−	1.20188i	0.541280	−	0.126689i
$91$	−9.70557	−	3.15353i	−1.01742	−	0.330580i
$92$	6.23049	−	3.08558i	0.649573	−	0.321694i
$93$	0.505936	+	0.696361i	0.0524631	+	0.0722093i
$94$	4.50031	+	0.380021i	0.464172	+	0.0391962i
$95$	1.87684	+	5.77632i	0.192560	+	0.592638i
$96$	1.34752	+	1.21903i	0.137531	+	0.124417i
$97$	11.2973	+	8.20794i	1.14706	+	0.833390i	0.988088	−	0.153893i	$-0.0491811\pi$
$97$	11.2973	+	8.20794i	1.14706	+	0.833390i	0.158975	+	0.987283i	$0.449181\pi$
$98$	−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	−0.354542	−	0.935040i	$-0.615363\pi$
$101$	6.47507	−	8.91217i	0.644293	−	0.886794i	0.998835	+	0.0482463i	$0.0153632\pi$
$102$	0.751983	+	1.24298i	0.0744574	+	0.123074i
$103$	−3.36761	−	10.3644i	−0.331820	−	1.02124i	−0.968267	−	0.249918i	$-0.919596\pi$
$103$	−3.36761	−	10.3644i	−0.331820	−	1.02124i	0.636447	−	0.771321i	$-0.280404\pi$
$104$	−8.71258	+	0.535879i	−0.854339	+	0.0525472i
$105$	1.10623	−	0.803720i	0.107957	−	0.0784350i
$106$	6.15601	+	2.59114i	0.597925	+	0.251673i
$107$	13.7836	+	4.47858i	1.33251	+	0.432960i	0.886775	−	0.462202i	$-0.152941\pi$
$107$	13.7836	+	4.47858i	1.33251	+	0.432960i	0.445740	+	0.895162i	$0.352941\pi$
$108$	3.35562	+	1.75828i	0.322895	+	0.169190i
$109$			1.96781i			0.188482i	0.995549	+	0.0942411i	$0.0300424\pi$
$109$			1.96781i			0.188482i	−0.995549	+	0.0942411i	$0.969958\pi$
$110$		0			0
$111$	−2.51964			−0.239154
$112$	−12.4829	−	4.37319i	−1.17952	−	0.413228i
$113$	−1.96151	+	6.03690i	−0.184523	+	0.567904i	−0.999940	−	0.0109706i	$-0.996508\pi$
$113$	−1.96151	+	6.03690i	−0.184523	+	0.567904i	0.815417	+	0.578874i	$0.196508\pi$
$114$	−0.831474	+	1.97541i	−0.0778747	+	0.185014i
$115$	−2.63044	−	3.62050i	−0.245290	−	0.337613i
$116$	−8.85443	+	8.65469i	−0.822113	+	0.803568i
$117$	−8.50255	+	2.76264i	−0.786061	+	0.255407i
$118$	−10.3539	−	17.1144i	−0.953153	−	1.57550i
$119$	−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
$124$	−5.28333	−	0.898693i	−0.474457	−	0.0807050i
$125$	10.2142	−	3.31881i	0.913590	−	0.296843i
$126$	−13.4985	−	1.13986i	−1.20254	−	0.101547i
$127$	−13.5130	+	9.81774i	−1.19908	+	0.871183i	−0.994194	−	0.107603i	$-0.965683\pi$
$127$	−13.5130	+	9.81774i	−1.19908	+	0.871183i	−0.204887	+	0.978786i	$0.565683\pi$
$128$	−11.3053	+	0.436764i	−0.999255	+	0.0386048i
$129$	−0.235339	+	0.724298i	−0.0207204	+	0.0637708i
$130$	1.28044	+	5.47071i	0.112302	+	0.479813i
$131$		−	9.29813i		−	0.812381i	−0.913788	−	0.406191i	$-0.866857\pi$
$131$		−	9.29813i		−	0.812381i	0.913788	−	0.406191i	$-0.133143\pi$
$132$		0			0
$133$		−	15.6009i		−	1.35277i
$134$	−6.47413	+	1.51530i	−0.559280	+	0.130902i
$135$	0.753517	−	2.31909i	0.0648524	−	0.199595i
$136$	−8.75782	−	2.26173i	−0.750977	−	0.193942i
$137$	−7.33574	+	5.32973i	−0.626735	+	0.455350i	−0.855268	−	0.518187i	$-0.826607\pi$
$137$	−7.33574	+	5.32973i	−0.626735	+	0.455350i	0.228533	+	0.973536i	$0.426607\pi$
$138$	0.132881	−	1.57362i	0.0113116	−	0.133955i
$139$	−0.222080	+	0.0721581i	−0.0188366	+	0.00612037i	−0.318420	−	0.947950i	$-0.603152\pi$
$139$	−0.222080	+	0.0721581i	−0.0188366	+	0.00612037i	0.299584	+	0.954070i	$0.403152\pi$
$140$	−1.42765	+	8.39300i	−0.120658	+	0.709338i
$141$	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
$146$	1.13630	−	0.687444i	0.0940411	−	0.0568933i
$147$	−1.20189	+	0.390517i	−0.0991301	+	0.0322093i
$148$	11.2188	−	10.9658i	0.922182	−	0.901379i
$149$	−1.34601	−	1.85262i	−0.110269	−	0.151773i	0.750315	−	0.661080i	$-0.229902\pi$
$149$	−1.34601	−	1.85262i	−0.110269	−	0.151773i	−0.860585	+	0.509307i	$0.829902\pi$
$150$	1.39962	+	0.589117i	0.114279	+	0.0481012i
$151$	1.17300	−	3.61013i	0.0954576	−	0.293788i	−0.891915	−	0.452203i	$-0.850638\pi$
$151$	1.17300	−	3.61013i	0.0954576	−	0.293788i	0.987373	+	0.158415i	$0.0506383\pi$
$152$	−4.89502	−	12.4143i	−0.397039	−	1.00693i
$153$	−9.26386			−0.748939
$154$		0			0
$155$			3.44953i			0.277073i
$156$	−0.920219	+	1.75621i	−0.0736765	+	0.140610i
$157$	−11.5590	−	3.75574i	−0.922507	−	0.299741i	−0.191012	−	0.981588i	$-0.561177\pi$
$157$	−11.5590	−	3.75574i	−0.922507	−	0.299741i	−0.731495	+	0.681847i	$0.761177\pi$
$158$	5.24815	−	12.4685i	0.417520	−	0.991943i
$159$	1.22734	−	0.891717i	0.0973346	−	0.0707177i
$160$	1.49740	+	7.12660i	0.118380	+	0.563407i
$161$	3.55220	+	10.9325i	0.279953	+	0.861606i
$162$	−9.77930	+	5.91630i	−0.768334	+	0.464829i
$163$	−4.87169	+	6.70531i	−0.381580	+	0.525200i	−0.956002	−	0.293359i	$-0.905227\pi$
$163$	−4.87169	+	6.70531i	−0.381580	+	0.525200i	0.574422	+	0.818559i	$0.305227\pi$
$164$	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	$-0.187721\pi$
$167$	7.22356	+	5.24822i	0.558975	+	0.406119i	−0.272108	+	0.962267i	$0.587721\pi$
$168$	−2.31753	+	1.91176i	−0.178802	+	0.147496i
$169$	1.07398	+	3.30537i	0.0826139	+	0.254260i
$170$	−0.489888	+	5.80138i	−0.0375727	+	0.444946i
$171$	−8.03335	−	11.0570i	−0.614325	−	0.845546i
$172$	−2.10436	−	4.24918i	−0.160456	−	0.323997i
$173$	−8.08869	−	2.62818i	−0.614972	−	0.199817i	−0.0150654	−	0.999887i	$-0.504796\pi$
$173$	−8.08869	−	2.62818i	−0.614972	−	0.199817i	−0.599907	+	0.800070i	$0.704796\pi$
$174$	0.640919	+	2.73833i	0.0485880	+	0.207592i
$175$	−11.0536			−0.835571
$176$		0			0
$177$	−4.54335			−0.341499
$178$	4.95900	+	21.1873i	0.371692	+	1.58806i
$179$	−2.79940	−	0.909581i	−0.209237	−	0.0679853i	0.202523	−	0.979277i	$-0.435086\pi$
$179$	−2.79940	−	0.909581i	−0.209237	−	0.0679853i	−0.411760	+	0.911292i	$0.635086\pi$
$180$	3.30997	+	6.68358i	0.246711	+	0.498164i
$181$	12.5027	+	17.2085i	0.929318	+	1.27910i	0.960125	+	0.279572i	$0.0901925\pi$
$181$	12.5027	+	17.2085i	0.929318	+	1.27910i	−0.0308063	+	0.999525i	$0.509808\pi$
$182$	1.21437	−	14.3809i	0.0900153	−	1.06598i
$183$	−1.54511	−	4.75536i	−0.114218	−	0.351526i
$184$	6.25688	+	7.58491i	0.461264	+	0.559167i
$185$	−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
$190$	−7.34910	+	4.44608i	−0.533160	+	0.322552i
$191$	−1.59325	−	4.90352i	−0.115283	−	0.354806i	0.876723	−	0.480996i	$-0.159725\pi$
$191$	−1.59325	−	4.90352i	−0.115283	−	0.354806i	−0.992006	+	0.126190i	$0.959725\pi$
$192$	−1.24431	+	2.24843i	−0.0898004	+	0.162266i
$193$	21.8572	−	15.8802i	1.57331	−	1.14308i	0.649419	−	0.760430i	$-0.275012\pi$
$193$	21.8572	−	15.8802i	1.57331	−	1.14308i	0.923894	−	0.382649i	$-0.124988\pi$
$194$	−7.66130	+	18.2017i	−0.550049	+	1.30680i
$195$	1.21373	+	0.394364i	0.0869168	+	0.0282410i
$196$	3.65189	−	6.96954i	0.260849	−	0.497824i
$197$		−	6.68220i		−	0.476087i	−0.971254	−	0.238044i	$-0.923494\pi$
$197$		−	6.68220i		−	0.476087i	0.971254	−	0.238044i	$-0.0765061\pi$
$198$		0			0
$199$	−14.2586			−1.01076			−0.505382	−	0.862896i	$-0.668648\pi$
$199$	−14.2586			−1.01076			−0.505382	+	0.862896i	$0.668648\pi$
$200$	−8.79577	+	3.46823i	−0.621955	+	0.245241i
$201$	−0.466697	+	1.43635i	−0.0329183	+	0.101312i
$202$	14.3589	+	6.04384i	1.01029	+	0.425243i
$203$	−12.0326	−	16.5614i	−0.844522	−	1.16239i
$204$	−1.46923	+	1.43608i	−0.102866	+	0.100546i
$205$	6.34831	−	2.06269i	0.443386	−	0.144065i
$206$	13.1865	−	7.97758i	0.918745	−	0.555824i
$207$	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	0.212879	+	0.977079i	$0.431716\pi$
$211$	−11.3616	+	15.6378i	−0.782162	+	1.07655i	−0.995040	+	0.0994744i	$0.968284\pi$
$212$	−1.58395	+	9.31193i	−0.108786	+	0.639546i
$213$	2.80255	−	0.910604i	0.192028	−	0.0623935i
$214$	−1.72463	+	20.4235i	−0.117893	+	1.39612i
$215$	−2.46917	+	1.79396i	−0.168396	+	0.122347i
$216$	−1.33965	+	5.18737i	−0.0911517	+	0.352956i
$217$	2.73809	−	8.42696i	0.185873	−	0.572060i
$218$	−2.70967	+	0.634212i	−0.183522	+	0.0429542i
$219$		−	0.301655i		−	0.0203839i
$220$		0			0
$221$		−	9.86944i		−	0.663891i
$222$	−0.812064	−	3.46955i	−0.0545021	−	0.232861i
$223$	−4.22873	+	13.0147i	−0.283176	+	0.871528i	0.703763	+	0.710435i	$0.251502\pi$
$223$	−4.22873	+	13.0147i	−0.283176	+	0.871528i	−0.986939	+	0.161093i	$0.948498\pi$
$224$	1.99874	−	18.5983i	0.133547	−	1.24265i
$225$	−7.83408	+	5.69180i	−0.522272	+	0.379453i
$226$	−8.94499	−	0.755344i	−0.595012	−	0.0502448i
$227$	−11.3059	+	3.67351i	−0.750399	+	0.243819i	−0.659153	−	0.752009i	$-0.729085\pi$
$227$	−11.3059	+	3.67351i	−0.750399	+	0.243819i	−0.0912459	+	0.995828i	$0.529085\pi$
$228$	−2.98812	−	0.508278i	−0.197893	−	0.0336615i
$229$	0.127954	−	0.176114i	0.00845546	−	0.0116379i	−0.804768	−	0.593589i	$-0.797710\pi$
$229$	0.127954	−	0.176114i	0.00845546	−	0.0116379i	0.813224	+	0.581951i	$0.197710\pi$
$230$	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	$-0.261547\pi$
$233$	2.97642	+	2.16249i	0.194992	+	0.141670i	−0.486006	+	0.873956i	$0.661547\pi$
$234$	−6.54447	−	10.8176i	−0.427825	−	0.707170i
$235$	3.90990	−	1.27040i	0.255054	−	0.0828719i
$236$	20.2295	−	19.7731i	1.31683	−	1.28712i
$237$	−1.80610	−	2.48589i	−0.117319	−	0.161476i
$238$	5.80164	−	13.7835i	0.376065	−	0.893453i
$239$	−6.19507	+	19.0665i	−0.400726	+	1.23331i	0.523686	+	0.851911i	$0.324556\pi$
$239$	−6.19507	+	19.0665i	−0.400726	+	1.23331i	−0.924412	+	0.381396i	$0.875444\pi$
$240$	1.56104	+	0.546888i	0.100765	+	0.0353015i
$241$	14.4772			0.932561			0.466280	−	0.884637i	$-0.345594\pi$
$241$	14.4772			0.932561			0.466280	+	0.884637i	$0.345594\pi$
$242$		0			0
$243$			8.27867i			0.531077i
$244$	27.5755	+	14.4490i	1.76534	+	0.925001i
$245$	−4.81668	−	1.56503i	−0.307726	−	0.0999864i
$246$	2.17102	+	0.913809i	0.138419	+	0.0582624i
$247$	11.7798	−	8.55849i	0.749528	−	0.544564i
$248$	−0.465282	−	7.56479i	−0.0295455	−	0.480365i
$249$	0.126882	+	0.390504i	0.00804084	+	0.0247472i
$250$	7.86198	+	12.9954i	0.497235	+	0.821900i
$251$	12.7189	−	17.5061i	0.802809	−	1.10497i	−0.189584	−	0.981864i	$-0.560714\pi$
$251$	12.7189	−	17.5061i	0.802809	−	1.10497i	0.992393	−	0.123108i	$-0.0392861\pi$
$252$	−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
$256$	−4.24503	−	15.4266i	−0.265315	−	0.964162i
$257$	−2.62943	−	8.09254i	−0.164019	−	0.504799i	0.834944	−	0.550335i	$-0.185500\pi$
$257$	−2.62943	−	8.09254i	−0.164019	−	0.504799i	−0.998963	+	0.0455368i	$0.985500\pi$
$258$	−1.07321	−	0.0906250i	−0.0668148	−	0.00564207i
$259$	15.2457	+	20.9838i	0.947319	+	1.30387i
$260$	−7.12049	+	3.52634i	−0.441594	+	0.218695i
$261$	−17.0559	−	5.54180i	−1.05573	−	0.343029i
$262$	12.8035	−	2.99672i	0.791004	−	0.185138i
$263$	9.34658			0.576335			0.288167	−	0.957580i	$-0.406954\pi$
$263$	9.34658			0.576335			0.288167	+	0.957580i	$0.406954\pi$
$264$		0			0
$265$	6.07983			0.373481
$266$	21.4824	−	5.02806i	1.31717	−	0.308290i
$267$	4.70061	+	1.52732i	0.287673	+	0.0934705i
$268$	−4.17313	−	8.42651i	−0.254915	−	0.514731i
$269$	−7.18877	−	9.89449i	−0.438307	−	0.603278i	0.531528	−	0.847041i	$-0.321618\pi$
$269$	−7.18877	−	9.89449i	−0.438307	−	0.603278i	−0.969835	+	0.243763i	$0.921618\pi$
$270$	3.43623	+	0.290167i	0.209123	+	0.0176590i
$271$	−7.62308	−	23.4614i	−0.463069	−	1.42518i	−0.861395	−	0.507936i	$-0.830408\pi$
$271$	−7.62308	−	23.4614i	−0.463069	−	1.42518i	0.398325	−	0.917244i	$-0.369592\pi$
$272$	0.291813	−	12.7885i	0.0176938	−	0.775414i
$273$	−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	−0.927170	−	0.374642i	$-0.877766\pi$
$277$	−4.73257	+	6.51382i	−0.284353	+	0.391378i	0.642817	+	0.766020i	$0.277766\pi$
$278$	−0.170936	−	0.282548i	−0.0102521	−	0.0169461i
$279$	−2.39870	−	7.38243i	−0.143606	−	0.441974i
$280$	−12.0173	+	0.739139i	−0.718170	+	0.0441720i
$281$	−10.7513	+	7.81131i	−0.641371	+	0.465983i	−0.860321	−	0.509753i	$-0.829737\pi$
$281$	−10.7513	+	7.81131i	−0.641371	+	0.465983i	0.218950	+	0.975736i	$0.429737\pi$
$282$	1.33712	+	0.562811i	0.0796246	+	0.0335149i
$283$	0.328993	+	0.106896i	0.0195566	+	0.00635433i	0.318779	−	0.947829i	$-0.396727\pi$
$283$	0.328993	+	0.106896i	0.0195566	+	0.00635433i	−0.299222	+	0.954183i	$0.596727\pi$
$284$	−8.51544	+	16.2515i	−0.505298	+	0.964348i
$285$			1.95097i			0.115565i
$286$		0			0
$287$	−17.1458			−1.01208
$288$	−8.16023	−	14.2106i	−0.480846	−	0.837366i
$289$	−2.09302	+	6.44164i	−0.123119	+	0.378920i
$290$	−4.37243	+	10.3880i	−0.256758	+	0.610004i
$291$	2.63657	+	3.62892i	0.154558	+	0.212731i
$292$	1.31283	+	1.34313i	0.0768277	+	0.0786008i
$293$	3.64193	−	1.18334i	0.212764	−	0.0691313i	−0.200696	−	0.979654i	$-0.564320\pi$
$293$	3.64193	−	1.18334i	0.212764	−	0.0691313i	0.413460	+	0.910522i	$0.364320\pi$
$294$	−0.925102	−	1.52914i	−0.0539531	−	0.0891812i
$295$	−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
$300$	−0.360125	+	2.11715i	−0.0207918	+	0.122233i
$301$	7.45599	−	2.42260i	0.429756	−	0.139636i
$302$	5.34920	+	0.451704i	0.307812	+	0.0259927i
$303$	2.86278	−	2.07993i	0.164462	−	0.119489i
$304$	15.5168	−	10.7415i	0.889950	−	0.616066i
$305$	6.19217	−	19.0575i	0.354563	−	1.09123i
$306$	−2.98568	−	12.7563i	−0.170680	−	0.729231i
$307$			23.7376i			1.35478i	0.735626	+	0.677388i	$0.236888\pi$
$307$			23.7376i			1.35478i	−0.735626	+	0.677388i	$0.763112\pi$
$308$		0			0
$309$		−	3.50061i		−	0.199143i
$310$	−4.75000	+	1.11176i	−0.269782	+	0.0631437i
$311$	2.72596	−	8.38966i	0.154575	−	0.475734i	−0.843542	−	0.537063i	$-0.819534\pi$
$311$	2.72596	−	8.38966i	0.154575	−	0.475734i	0.998118	+	0.0613289i	$0.0195339\pi$
$312$	−2.71489	−	0.701125i	−0.153700	−	0.0396934i
$313$	2.60133	−	1.88998i	0.147036	−	0.106828i	−0.511835	−	0.859084i	$-0.671034\pi$
$313$	2.60133	−	1.88998i	0.147036	−	0.106828i	0.658871	+	0.752256i	$0.271034\pi$
$314$	1.44627	−	17.1272i	0.0816179	−	0.966541i
$315$	−11.7276	+	3.81052i	−0.660774	+	0.214699i
$316$	18.8606	+	3.20818i	1.06099	+	0.180474i
$317$	−5.42855	+	7.47176i	−0.304898	+	0.419656i	−0.933782	−	0.357844i	$-0.883512\pi$
$317$	−5.42855	+	7.47176i	−0.304898	+	0.419656i	0.628884	+	0.777499i	$0.283512\pi$
$318$	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
$322$	−13.9093	+	8.41486i	−0.775133	+	0.468942i
$323$	14.3494	−	4.66241i	0.798423	−	0.259423i
$324$	−11.2985	−	11.5593i	−0.627697	−	0.642184i
$325$	−6.06387	−	8.34620i	−0.336363	−	0.462964i
$326$	−10.8033	−	4.54724i	−0.598340	−	0.251848i
$327$	−0.195331	+	0.601166i	−0.0108018	+	0.0332446i
$328$	−13.6436	+	5.37974i	−0.753340	+	0.297047i
$329$	−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	$0.964923\pi$
$332$	−2.26446	−	1.18653i	−0.124278	−	0.0651193i
$333$	21.6103	+	7.02163i	1.18424	+	0.384783i
$334$	−4.89869	+	11.6383i	−0.268045	+	0.636819i
$335$	−4.89659	+	3.55758i	−0.267529	+	0.194371i
$336$	−3.37942	−	2.57510i	−0.184362	−	0.140483i
$337$	0.728908	+	2.24335i	0.0397061	+	0.122203i	0.968945	−	0.247277i	$-0.0795358\pi$
$337$	0.728908	+	2.24335i	0.0397061	+	0.122203i	−0.929239	+	0.369480i	$0.879536\pi$
$338$	−4.20536	+	2.54417i	−0.228741	+	0.138385i
$339$	−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
$344$	5.17290	−	4.26719i	0.278904	−	0.230071i
$345$	−0.444220	−	1.36717i	−0.0239160	−	0.0736058i
$346$	1.01207	−	11.9852i	0.0544091	−	0.644327i
$347$	14.0591	+	19.3506i	0.754730	+	1.03880i	0.997634	+	0.0687465i	$0.0219000\pi$
$347$	14.0591	+	19.3506i	0.754730	+	1.03880i	−0.242904	+	0.970050i	$0.578100\pi$
$348$	−3.56412	+	1.76509i	−0.191057	+	0.0946188i
$349$	2.01885	+	0.655963i	0.108066	+	0.0351129i	0.362551	−	0.931964i	$-0.381906\pi$
$349$	2.01885	+	0.655963i	0.108066	+	0.0351129i	−0.254485	+	0.967077i	$0.581906\pi$
$350$	−3.56249	−	15.2208i	−0.190423	−	0.813584i
$351$	−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	$0.456533\pi$
$354$	−1.46429	−	6.25619i	−0.0778262	−	0.332513i
$355$	11.2315	+	3.64933i	0.596105	+	0.193686i
$356$	−27.5767	+	13.6571i	−1.46156	+	0.723823i
$357$	−1.99658	−	2.74806i	−0.105670	−	0.145443i
$358$	0.350265	−	4.14793i	0.0185121	−	0.219225i
$359$	8.95267	+	27.5535i	0.472504	+	1.45422i	0.849294	+	0.527919i	$0.177028\pi$
$359$	8.95267	+	27.5535i	0.472504	+	1.45422i	−0.376790	+	0.926299i	$0.622972\pi$
$360$	−8.13650	+	6.71190i	−0.428831	+	0.353748i
$361$	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
$366$	6.05015	−	3.66023i	0.316246	−	0.191324i
$367$	9.17609	+	28.2411i	0.478988	+	1.47417i	0.840503	+	0.541807i	$0.182260\pi$
$367$	9.17609	+	28.2411i	0.478988	+	1.47417i	−0.361515	+	0.932366i	$0.617740\pi$
$368$	−8.42787	+	11.0603i	−0.439333	+	0.576557i
$369$	−12.1519	+	8.82884i	−0.632600	+	0.459611i
$370$	5.54000	−	13.1619i	0.288011	−	0.684255i
$371$	−14.8526	−	4.82590i	−0.771109	−	0.250548i
$372$	−1.52485	−	0.798990i	−0.0790599	−	0.0414257i
$373$			4.07522i			0.211007i	0.994419	+	0.105504i	$0.0336454\pi$
$373$			4.07522i			0.211007i	−0.994419	+	0.105504i	$0.966355\pi$
$374$		0			0
$375$	3.44988			0.178151
$376$	−8.40301	+	3.31336i	−0.433352	+	0.170873i
$377$	5.90407	−	18.1709i	0.304075	−	0.935847i
$378$	−8.16416	−	3.43639i	−0.419919	−	0.176749i
$379$	17.1222	+	23.5667i	0.879507	+	1.21054i	0.976557	+	0.215258i	$0.0690594\pi$
$379$	17.1222	+	23.5667i	0.879507	+	1.21054i	−0.0970499	+	0.995280i	$0.530941\pi$
$380$	−8.49081	−	8.68677i	−0.435569	−	0.445622i
$381$	−5.10274	+	1.65798i	−0.261421	+	0.0849410i
$382$	6.23865	−	3.77427i	0.319197	−	0.193109i
$383$	15.2236	+	11.0606i	0.777889	+	0.565170i	0.904345	−	0.426803i	$-0.140360\pi$
$383$	15.2236	+	11.0606i	0.777889	+	0.565170i	−0.126456	+	0.991972i	$0.540360\pi$
$384$	−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
$388$	−27.5329	−	4.68333i	−1.39777	−	0.237760i
$389$	25.6888	−	8.34679i	1.30247	−	0.423199i	0.426032	−	0.904708i	$-0.359911\pi$
$389$	25.6888	−	8.34679i	1.30247	−	0.423199i	0.876441	+	0.481509i	$0.159911\pi$
$390$	−0.151863	+	1.79840i	−0.00768988	+	0.0910656i
$391$	−8.99396	+	6.53449i	−0.454844	+	0.330464i
$392$	10.7740	+	2.78242i	0.544171	+	0.140533i
$393$	0.922959	−	2.84058i	0.0465571	−	0.143288i
$394$	9.20139	−	2.15363i	0.463559	−	0.108498i
$395$		−	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	$0.750564\pi$
$398$	−4.59544	−	19.6340i	−0.230348	−	0.984166i
$399$	1.54859	−	4.76608i	0.0775266	−	0.238602i
$400$	−7.61056	−	10.9940i	−0.380528	−	0.549699i
$401$	6.74146	−	4.89796i	0.336653	−	0.244592i	−0.406596	−	0.913608i	$-0.633284\pi$
$401$	6.74146	−	4.89796i	0.336653	−	0.244592i	0.743248	+	0.669016i	$0.233284\pi$
$402$	−2.12826	−	0.179717i	−0.106148	−	0.00896348i
$403$	7.86502	−	2.55550i	0.391785	−	0.127299i
$404$	−3.69458	+	21.7201i	−0.183812	+	1.08062i
$405$	−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	$-0.332699\pi$
$409$	−3.35559	−	2.43798i	−0.165923	−	0.120550i	−0.667648	+	0.744477i	$0.732699\pi$
$410$	4.88634	+	8.07683i	0.241319	+	0.398886i
$411$	−2.77011	+	0.900065i	−0.136640	+	0.0443969i
$412$	15.2350	+	15.5866i	0.750576	+	0.767898i
$413$	27.4905	+	37.8375i	1.35272	+	1.86186i
$414$	−5.52497	+	13.1262i	−0.271538	+	0.645118i
$415$	−0.508492	+	1.56498i	−0.0249609	+	0.0768218i
$416$	15.1395	−	8.69367i	0.742276	−	0.426242i
$417$	−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	$0.943295\pi$
$420$	−1.26926	+	2.42235i	−0.0619336	+	0.118199i
$421$	33.4753	+	10.8768i	1.63149	+	0.530102i	0.974613	−	0.223897i	$-0.0718780\pi$
$421$	33.4753	+	10.8768i	1.63149	+	0.530102i	0.656875	+	0.754000i	$0.271878\pi$
$422$	−25.1950	−	10.6049i	−1.22648	−	0.516238i
$423$	−7.48427	+	5.43764i	−0.363898	+	0.264387i
$424$	−13.3330	+	0.820065i	−0.647509	+	0.0398259i
$425$	−3.30341	−	10.1669i	−0.160239	−	0.493165i
$426$	2.15714	+	3.56563i	0.104514	+	0.172755i
$427$	−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	$-0.405473\pi$
$431$	−10.9280	−	7.93969i	−0.526385	−	0.382441i	−0.819004	+	0.573788i	$0.805473\pi$
$432$	−7.57477	−	0.172845i	−0.364441	−	0.00831599i
$433$	4.49738	+	13.8415i	0.216130	+	0.665181i	0.999071	+	0.0430848i	$0.0137186\pi$
$433$	4.49738	+	13.8415i	0.216130	+	0.665181i	−0.782941	+	0.622096i	$0.786281\pi$
$434$	12.4864	+	1.05439i	0.599366	+	0.0506124i
$435$	1.50473	+	2.07109i	0.0721464	+	0.0993010i
$436$	−1.74662	−	3.52682i	−0.0836478	−	0.168904i
$437$	−15.5986	−	5.06829i	−0.746182	−	0.242449i
$438$	0.415378	−	0.0972212i	0.0198475	−	0.00464541i
$439$	8.11893			0.387495			0.193748	−	0.981051i	$-0.437936\pi$
$439$	8.11893			0.387495			0.193748	+	0.981051i	$0.437936\pi$
$440$		0			0
$441$	11.3966			0.542694
$442$	13.5902	−	3.18085i	0.646421	−	0.151298i
$443$	−3.86328	−	1.25526i	−0.183550	−	0.0596390i	0.215800	−	0.976438i	$-0.430764\pi$
$443$	−3.86328	−	1.25526i	−0.183550	−	0.0596390i	−0.399350	+	0.916799i	$0.630764\pi$
$444$	4.51584	−	2.23642i	0.214312	−	0.106136i
$445$	11.6426	+	16.0247i	0.551912	+	0.759642i
$446$	−19.2841	−	1.62841i	−0.913129	−	0.0771076i
$447$	−0.227309	−	0.699584i	−0.0107513	−	0.0330892i
$448$	26.2541	−	3.24185i	1.24039	−	0.153163i
$449$	6.70425	+	4.87092i	0.316393	+	0.229873i	0.734635	−	0.678463i	$-0.237354\pi$
$449$	6.70425	+	4.87092i	0.316393	+	0.229873i	−0.418242	+	0.908336i	$0.637354\pi$
$450$	−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
$454$	−8.70223	−	14.3843i	−0.408416	−	0.675087i
$455$	−4.05962	−	12.4942i	−0.190318	−	0.585738i
$456$	−0.263152	−	4.27845i	−0.0123232	−	0.200357i
$457$	7.95132	−	5.77697i	0.371947	−	0.270235i	−0.386071	−	0.922469i	$-0.626168\pi$
$457$	7.95132	−	5.77697i	0.371947	−	0.270235i	0.758018	+	0.652234i	$0.226168\pi$
$458$	0.283748	+	0.119433i	0.0132587	+	0.00558072i
$459$	−5.76103	−	1.87187i	−0.268902	−	0.0873714i
$460$	7.92796	+	4.15408i	0.369643	+	0.193685i
$461$		−	24.4759i		−	1.13996i	−0.821660	−	0.569978i	$-0.806952\pi$
$461$		−	24.4759i		−	1.13996i	0.821660	−	0.569978i	$-0.193048\pi$
$462$		0			0
$463$	20.2431			0.940778			0.470389	−	0.882459i	$-0.344114\pi$
$463$	20.2431			0.940778			0.470389	+	0.882459i	$0.344114\pi$
$464$	8.18753	−	23.3705i	0.380097	−	1.08495i
$465$	−0.342411	+	1.05383i	−0.0158789	+	0.0488703i
$466$	−2.01847	+	4.79548i	−0.0935040	+	0.222146i
$467$	−14.3336	−	19.7285i	−0.663279	−	0.912925i	0.336306	−	0.941753i	$-0.390822\pi$
$467$	−14.3336	−	19.7285i	−0.663279	−	0.912925i	−0.999584	+	0.0288281i	$0.990822\pi$
$468$	12.7866	−	12.4982i	0.591062	−	0.577728i
$469$	14.7859	−	4.80422i	0.682748	−	0.221838i
$470$	3.00948	+	4.97448i	0.138817	+	0.229456i
$471$	−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
$476$	20.8497	+	3.54653i	0.955645	+	0.162555i
$477$	−13.0116	+	4.22773i	−0.595760	+	0.193574i
$478$	−28.2511	−	2.38562i	−1.29218	−	0.109116i
$479$	1.39875	−	1.01625i	0.0639103	−	0.0464336i	−0.555371	−	0.831602i	$-0.687424\pi$
$479$	1.39875	−	1.01625i	0.0639103	−	0.0464336i	0.619282	+	0.785169i	$0.287424\pi$
$480$	−0.249952	+	2.32581i	−0.0114087	+	0.106158i
$481$	−7.48063	+	23.0230i	−0.341088	+	1.04976i
$482$	4.66591	+	19.9351i	0.212526	+	0.908021i
$483$			3.69250i			0.168014i
$484$		0			0
$485$			17.9764i			0.816268i
$486$	−11.3997	+	2.66816i	−0.517102	+	0.121030i
$487$	−0.820437	+	2.52505i	−0.0371775	+	0.114421i	−0.967923	−	0.251247i	$-0.919159\pi$
$487$	−0.820437	+	2.52505i	−0.0371775	+	0.114421i	0.930745	+	0.365668i	$0.119159\pi$
$488$	−11.0088	+	42.6282i	−0.498347	+	1.92969i
$489$	−2.15389	+	1.56489i	−0.0974023	+	0.0707669i
$490$	0.602669	−	7.13696i	0.0272258	−	0.322415i
$491$	27.8745	−	9.05697i	1.25796	−	0.408735i	0.397192	−	0.917736i	$-0.369985\pi$
$491$	27.8745	−	9.05697i	1.25796	−	0.408735i	0.860766	+	0.509000i	$0.169985\pi$
$492$	−0.558609	+	3.28401i	−0.0251840	+	0.148055i
$493$	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
$498$	−0.496830	+	0.300573i	−0.0222635	+	0.0134690i
$499$	−7.66065	+	2.48910i	−0.342938	+	0.111427i	−0.475422	−	0.879758i	$-0.657705\pi$
$499$	−7.66065	+	2.48910i	−0.342938	+	0.111427i	0.132484	+	0.991185i	$0.457705\pi$
$500$	−15.3608	+	15.0143i	−0.686954	+	0.671458i
$501$	1.68584	+	2.32036i	0.0753179	+	0.103666i
$502$	28.2050	+	11.8718i	1.25885	+	0.529866i
$503$	9.28221	−	28.5677i	0.413873	−	1.27377i	−0.499382	−	0.866382i	$-0.666439\pi$
$503$	9.28221	−	28.5677i	0.413873	−	1.27377i	0.913255	−	0.407389i	$-0.133561\pi$
$504$	25.2045	−	9.93829i	1.12270	−	0.442687i
$505$	14.1812			0.631057
$506$		0			0
$507$			1.11640i			0.0495810i
$508$	15.5045	−	29.5899i	0.687900	−	1.31284i
$509$	−2.63101	−	0.854869i	−0.116618	−	0.0378914i	0.250127	−	0.968213i	$-0.419528\pi$
$509$	−2.63101	−	0.854869i	−0.116618	−	0.0378914i	−0.366745	+	0.930322i	$0.619528\pi$
$510$	−0.725523	+	1.72369i	−0.0321267	+	0.0763265i
$511$	−2.51221	+	1.82523i	−0.111134	+	0.0807433i
$512$	19.8743	−	10.8173i	0.878326	−	0.478061i
$513$	−2.76161	−	8.49935i	−0.121928	−	0.375255i
$514$	10.2960	−	6.22889i	0.454136	−	0.274744i
$515$	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
$520$	−7.15065	−	8.66839i	−0.313577	−	0.380134i
$521$	3.71389	+	11.4302i	0.162709	+	0.500766i	0.998860	−	0.0477328i	$-0.0151996\pi$
$521$	3.71389	+	11.4302i	0.162709	+	0.500766i	−0.836151	+	0.548499i	$0.815200\pi$
$522$	2.13406	−	25.2721i	0.0934051	−	1.10613i
$523$	−3.13009	−	4.30819i	−0.136869	−	0.188384i	0.735080	−	0.677980i	$-0.237144\pi$
$523$	−3.13009	−	4.30819i	−0.136869	−	0.188384i	−0.871950	+	0.489596i	$0.837144\pi$
$524$	8.25297	+	16.6646i	0.360532	+	0.727997i
$525$	−3.37686	−	1.09721i	−0.147378	−	0.0478862i
$526$	3.01234	+	12.8702i	0.131344	+	0.561169i
$527$	8.56925			0.373283
$528$		0			0
$529$	−10.9151			−0.474568
$530$	1.95949	+	8.37193i	0.0851147	+	0.363653i
$531$	38.9672	+	12.6612i	1.69103	+	0.549449i
$532$	13.8473	+	27.9608i	0.600356	+	1.21225i
$533$	−9.40598	−	12.9462i	−0.407418	−	0.560763i
$534$	−0.588146	+	6.96498i	−0.0254516	+	0.301404i
$535$	5.76538	+	17.7440i	0.249259	+	0.767141i
$536$	10.2583	−	8.46221i	0.443092	−	0.365512i
$537$	−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	−0.668485	−	0.743726i	$-0.733057\pi$
$541$	5.70817	−	7.85662i	0.245413	−	0.337782i	0.913898	+	0.405943i	$0.133057\pi$
$542$	29.8495	−	18.0584i	1.28215	−	0.775676i
$543$	2.11141	+	6.49825i	0.0906092	+	0.278867i
$544$	17.7037	−	3.71980i	0.759042	−	0.159485i
$545$	−2.04941	+	1.48899i	−0.0877872	+	0.0637811i
$546$	1.79848	−	4.27283i	0.0769680	−	0.182860i
$547$	−19.6515	−	6.38515i	−0.840236	−	0.273009i	−0.142885	−	0.989739i	$-0.545638\pi$
$547$	−19.6515	−	6.38515i	−0.840236	−	0.273009i	−0.697351	+	0.716730i	$0.745638\pi$
$548$	8.41688	−	16.0634i	0.359551	−	0.686194i
$549$			45.0914i			1.92445i
$550$		0			0
$551$	29.2082			1.24431
$552$	1.15858	+	2.93827i	0.0493123	+	0.125061i
$553$	−9.77449	+	30.0828i	−0.415654	+	1.27925i
$554$	−10.4948	−	4.41739i	−0.445882	−	0.187677i
$555$	−1.90654	−	2.62413i	−0.0809282	−	0.111388i
$556$	0.333976	−	0.326443i	0.0141638	−	0.0138442i
$557$	−25.2473	+	8.20335i	−1.06976	+	0.347587i	−0.790395	−	0.612597i	$-0.790125\pi$
$557$	−25.2473	+	8.20335i	−1.06976	+	0.347587i	−0.279368	+	0.960184i	$0.590125\pi$
$558$	9.39252	−	5.68231i	0.397617	−	0.240551i
$559$	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	−0.943501	−	0.331371i	$-0.892489\pi$
$563$	−7.99123	+	10.9990i	−0.336790	+	0.463552i	0.606710	+	0.794923i	$0.292489\pi$
$564$	−0.344045	+	2.02261i	−0.0144869	+	0.0851672i
$565$	−7.77145	+	2.52510i	−0.326948	+	0.106232i
$566$	−0.0411640	+	0.487475i	−0.00173025	+	0.0204901i
$567$	21.6207	−	15.7083i	0.907983	−	0.659688i
$568$	−25.1228	−	6.48801i	−1.05413	−	0.272231i
$569$	−7.56071	+	23.2695i	−0.316961	+	0.975507i	0.657978	+	0.753037i	$0.271412\pi$
$569$	−7.56071	+	23.2695i	−0.316961	+	0.975507i	−0.974940	+	0.222470i	$0.928588\pi$
$570$	−2.68648	+	0.628783i	−0.112524	+	0.0263368i
$571$			12.1063i			0.506634i	0.967383	+	0.253317i	$0.0815216\pi$
$571$			12.1063i			0.506634i	−0.967383	+	0.253317i	$0.918478\pi$
$572$		0			0
$573$		−	1.65617i		−	0.0691877i
$574$	−5.52596	−	23.6097i	−0.230649	−	0.985450i
$575$	−3.59099	+	11.0519i	−0.149755	+	0.460897i
$576$	16.9380	−	15.8166i	0.705748	−	0.659025i
$577$	1.88795	−	1.37168i	0.0785964	−	0.0571036i	−0.547793	−	0.836614i	$-0.684532\pi$
$577$	1.88795	−	1.37168i	0.0785964	−	0.0571036i	0.626390	+	0.779510i	$0.284532\pi$
$578$	−9.54470	−	0.805986i	−0.397007	−	0.0335246i
$579$	8.25368	−	2.68178i	0.343011	−	0.111451i
$580$	−15.7135	−	2.67285i	−0.652466	−	0.110984i
$581$	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
$586$	2.80322	+	4.63356i	0.115800	+	0.191411i
$587$	23.0193	−	7.47941i	0.950106	−	0.308708i	0.207348	−	0.978267i	$-0.433517\pi$
$587$	23.0193	−	7.47941i	0.950106	−	0.308708i	0.742759	+	0.669559i	$0.233517\pi$
$588$	1.80747	−	1.76670i	0.0745388	−	0.0728573i
$589$	7.43100	+	10.2279i	0.306189	+	0.421433i
$590$	9.98957	−	23.7332i	0.411264	−	0.977079i
$591$	0.663295	−	2.04141i	0.0272843	−	0.0839725i
$592$	−10.3739	+	29.6112i	−0.426363	+	1.21701i
$593$	−27.1495			−1.11490			−0.557448	−	0.830212i	$-0.688220\pi$
$593$	−27.1495			−1.11490			−0.557448	+	0.830212i	$0.688220\pi$
$594$		0			0
$595$		−	13.6130i		−	0.558077i
$596$	4.05676	+	2.12566i	0.166172	+	0.0870704i
$597$	−4.35599	−	1.41535i	−0.178279	−	0.0579263i
$598$	−13.9843	−	5.88614i	−0.571859	−	0.240702i
$599$	−5.67813	+	4.12540i	−0.232002	+	0.168559i	−0.697713	−	0.716378i	$-0.745799\pi$
$599$	−5.67813	+	4.12540i	−0.232002	+	0.168559i	0.465711	+	0.884937i	$0.345799\pi$
$600$	−3.03137	+	0.186449i	−0.123755	+	0.00761173i
$601$	0.870194	+	2.67818i	0.0354960	+	0.109245i	0.967235	−	0.253884i	$-0.0817082\pi$
$601$	0.870194	+	2.67818i	0.0354960	+	0.109245i	−0.931739	+	0.363130i	$0.881708\pi$
$602$	5.73893	+	9.48610i	0.233901	+	0.386625i
$603$	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	$-0.0374554\pi$
$607$	29.2769	+	21.2709i	1.18831	+	0.863360i	0.195228	+	0.980758i	$0.437455\pi$
$608$	19.7920	+	17.9047i	0.802670	+	0.726133i
$609$	−2.03202	−	6.25391i	−0.0823415	−	0.253421i
$610$	28.2379	+	2.38450i	1.14332	+	0.0965457i
$611$	−5.79310	−	7.97352i	−0.234364	−	0.322574i
$612$	16.6032	−	8.22255i	0.671145	−	0.332377i
$613$	29.6824	+	9.64440i	1.19886	+	0.389534i	0.839342	−	0.543604i	$-0.182940\pi$
$613$	29.6824	+	9.64440i	1.19886	+	0.389534i	0.359520	+	0.933137i	$0.382940\pi$
$614$	−32.6866	+	7.65046i	−1.31913	+	0.308747i
$615$	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	$0.745539\pi$
$618$	4.82034	−	1.12822i	0.193903	−	0.0453838i
$619$	15.1194	+	4.91259i	0.607700	+	0.197454i	0.596672	−	0.802485i	$-0.296489\pi$
$619$	15.1194	+	4.91259i	0.607700	+	0.197454i	0.0110283	+	0.999939i	$0.496489\pi$
$620$	−3.06179	−	6.18244i	−0.122964	−	0.248293i
$621$	3.87047	+	5.32724i	0.155316	+	0.213775i
$622$	12.4311	+	1.04972i	0.498442	+	0.0420901i
$623$	−15.7224	−	48.3885i	−0.629904	−	1.93864i
$624$	0.0904607	−	3.96436i	0.00362132	−	0.158702i
$625$	−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
$630$	−9.02681	−	14.9208i	−0.359637	−	0.594458i
$631$	−4.51514	−	13.8962i	−0.179745	−	0.553198i	0.820073	−	0.572259i	$-0.193933\pi$
$631$	−4.51514	−	13.8962i	−0.179745	−	0.553198i	−0.999818	+	0.0190601i	$0.993933\pi$
$632$	1.66098	+	27.0050i	0.0660702	+	1.07420i
$633$	−5.02321	+	3.64958i	−0.199655	+	0.145058i
$634$	−12.0382	−	5.06701i	−0.478098	−	0.201237i
$635$	−20.4497	−	6.64452i	−0.811522	−	0.263680i
$636$	−1.40823	+	2.68757i	−0.0558399	+	0.106569i
$637$			12.1416i			0.481066i
$638$		0			0
$639$	−26.5744			−1.05127
$640$	−9.00925	−	11.4436i	−0.356122	−	0.452348i
$641$	9.15575	−	28.1785i	0.361630	−	1.11298i	−0.590434	−	0.807086i	$-0.701043\pi$
$641$	9.15575	−	28.1785i	0.361630	−	1.11298i	0.952064	−	0.305898i	$-0.0989565\pi$
$642$	−2.55417	+	6.06818i	−0.100805	+	0.239492i
$643$	17.3594	+	23.8931i	0.684586	+	0.942252i	0.999977	−	0.00670979i	$-0.00213581\pi$
$643$	17.3594	+	23.8931i	0.684586	+	0.942252i	−0.315391	+	0.948962i	$0.602136\pi$
$644$	−16.0701	−	16.4410i	−0.633251	−	0.647866i
$645$	−0.932407	+	0.302957i	−0.0367135	+	0.0119289i
$646$	11.0449	+	18.2565i	0.434554	+	0.718291i
$647$	−5.81487	−	4.22475i	−0.228606	−	0.166092i	0.467586	−	0.883948i	$-0.345124\pi$
$647$	−5.81487	−	4.22475i	−0.228606	−	0.166092i	−0.696192	+	0.717855i	$0.745124\pi$
$648$	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
$652$	2.77972	−	16.3417i	0.108862	−	0.639991i
$653$	−27.1028	+	8.80623i	−1.06061	+	0.344614i	−0.786825	−	0.617176i	$-0.788277\pi$
$653$	−27.1028	+	8.80623i	−1.06061	+	0.344614i	−0.273788	+	0.961790i	$0.588277\pi$
$654$	−0.890759	−	0.0752186i	−0.0348314	−	0.00294128i
$655$	9.68370	−	7.03562i	0.378373	−	0.274904i
$656$	−11.8051	−	17.0533i	−0.460913	−	0.665821i
$657$	−0.840637	+	2.58722i	−0.0327964	+	0.100937i
$658$	−3.40341	−	14.5411i	−0.132679	−	0.566871i
$659$		−	26.9704i		−	1.05062i	−0.850912	−	0.525308i	$-0.823950\pi$
$659$		−	26.9704i		−	1.05062i	0.850912	−	0.525308i	$-0.176050\pi$
$660$		0			0
$661$			40.1424i			1.56136i	0.624931	+	0.780680i	$0.285127\pi$
$661$			40.1424i			1.56136i	−0.624931	+	0.780680i	$0.714873\pi$
$662$	−5.51030	+	1.28971i	−0.214164	+	0.0501260i
$663$	0.979670	−	3.01511i	0.0380472	−	0.117097i
$664$	0.904030	−	3.50057i	0.0350832	−	0.135848i
$665$	16.2478	−	11.8047i	0.630064	−	0.457769i
$666$	−2.70391	+	32.0205i	−0.104775	+	1.24077i
$667$	−20.4680	+	6.65047i	−0.792525	+	0.257507i
$668$	−17.6047	−	2.99456i	−0.681148	−	0.115863i
$669$	−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	$-0.176787\pi$
$673$	15.8453	+	11.5123i	0.610793	+	0.443767i	−0.238900	+	0.971044i	$0.576787\pi$
$674$	−2.85417	+	1.72672i	−0.109938	+	0.0665108i
$675$	−6.02197	+	1.95666i	−0.231786	+	0.0753117i
$676$	−4.85868	−	4.97081i	−0.186872	−	0.191185i
$677$	8.37755	+	11.5307i	0.321975	+	0.443161i	0.939069	−	0.343729i	$-0.111690\pi$
$677$	8.37755	+	11.5307i	0.321975	+	0.443161i	−0.617094	+	0.786890i	$0.711690\pi$
$678$	−2.65772	−	1.11866i	−0.102069	−	0.0429620i
$679$	14.2689	−	43.9152i	0.547590	−	1.68531i
$680$	−4.27127	−	10.8324i	−0.163796	−	0.415403i
$681$	−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	$-0.0693367\pi$
$684$	24.2119	+	12.6865i	0.925765	+	0.485081i
$685$	−11.1015	−	3.60709i	−0.424166	−	0.137820i
$686$	5.56196	−	13.2141i	0.212357	−	0.504516i
$687$	0.0565716	−	0.0411017i	0.00215834	−	0.00156813i
$688$	7.54311	+	5.74780i	0.287578	+	0.219133i
$689$	−4.50409	−	13.8622i	−0.171592	−	0.528107i
$690$	1.73942	−	1.05232i	0.0662186	−	0.0400611i
$691$	5.04537	−	6.94436i	0.191935	−	0.264176i	−0.702194	−	0.711986i	$-0.747796\pi$
$691$	5.04537	−	6.94436i	0.191935	−	0.264176i	0.894129	+	0.447810i	$0.147796\pi$
$692$	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
$696$	−3.57922	−	4.33891i	−0.135670	−	0.164466i
$697$	−5.12410	−	15.7703i	−0.194089	−	0.597344i
$698$	−0.252601	+	2.99136i	−0.00956107	+	0.113225i
$699$	0.694640	+	0.956090i	0.0262737	+	0.0361626i
$700$	19.8108	−	9.81109i	0.748778	−	0.370824i
$701$	24.3811	+	7.92191i	0.920862	+	0.299206i	0.730821	−	0.682570i	$-0.239138\pi$
$701$	24.3811	+	7.92191i	0.920862	+	0.299206i	0.190042	+	0.981776i	$0.439138\pi$
$702$	−1.88406	−	8.04967i	−0.0711093	−	0.303815i
$703$	−37.0076			−1.39577
$704$		0			0
$705$	1.32058			0.0497358
$706$	1.64864	+	7.04381i	0.0620472	+	0.265097i
$707$	−34.6438	−	11.2564i	−1.30291	−	0.423342i
$708$	8.14284	−	4.03265i	0.306027	−	0.151556i
$709$	−17.5131	−	24.1047i	−0.657718	−	0.905271i	0.341685	−	0.939814i	$-0.389002\pi$
$709$	−17.5131	−	24.1047i	−0.657718	−	0.905271i	−0.999403	+	0.0345436i	$0.989002\pi$
$710$	−1.40530	+	16.6419i	−0.0527398	+	0.624559i
$711$	8.56293	+	26.3540i	0.321135	+	0.988352i
$712$	−27.6936	−	33.5715i	−1.03786	−	1.25815i
$713$	−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
$718$	−35.0558	+	21.2081i	−1.30827	+	0.791480i
$719$	13.4629	+	41.4347i	0.502083	+	1.54525i	0.805620	+	0.592433i	$0.201832\pi$
$719$	13.4629	+	41.4347i	0.502083	+	1.54525i	−0.303537	+	0.952820i	$0.598168\pi$
$720$	−11.8646	−	9.04076i	−0.442168	−	0.336929i
$721$	−29.1534	+	21.1812i	−1.08573	+	0.788830i
$722$	−1.78824	+	4.24850i	−0.0665515	+	0.158113i
$723$	4.42279	+	1.43705i	0.164485	+	0.0534446i
$724$	−37.6822	−	19.7447i	−1.40045	−	0.733805i
$725$		−	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	$0.102280\pi$
$728$	10.5880	+	26.8521i	0.392416	+	0.995206i
$729$	6.67066	−	20.5302i	0.247061	−	0.760377i
$730$	1.57576	+	0.663255i	0.0583214	+	0.0245482i
$731$	4.45652	+	6.13387i	0.164830	+	0.226869i
$732$	6.99006	+	7.15138i	0.258360	+	0.264323i
$733$	16.5329	−	5.37186i	0.610656	−	0.198414i	0.0126687	−	0.999920i	$-0.495967\pi$
$733$	16.5329	−	5.37186i	0.610656	−	0.198414i	0.597987	+	0.801506i	$0.295967\pi$
$734$	−35.9306	+	21.7374i	−1.32622	+	0.802341i
$735$	−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	−0.681749	−	0.731586i	$-0.738781\pi$
$739$	6.10843	−	8.40753i	0.224702	−	0.309276i	0.906452	+	0.422310i	$0.138781\pi$
$740$	19.9094	+	3.38659i	0.731885	+	0.124493i
$741$	4.44825	−	1.44533i	0.163411	−	0.0530954i
$742$	1.85838	−	22.0074i	0.0682231	−	0.807916i
$743$	10.1596	−	7.38138i	0.372720	−	0.270797i	−0.385618	−	0.922658i	$-0.626012\pi$
$743$	10.1596	−	7.38138i	0.372720	−	0.270797i	0.758338	+	0.651862i	$0.226012\pi$
$744$	0.608760	−	2.35723i	0.0223182	−	0.0864202i
$745$	0.910960	−	2.80365i	0.0333750	−	0.102718i
$746$	−5.61158	+	1.31342i	−0.205455	+	0.0480876i
$747$		−	3.70284i		−	0.135480i
$748$		0			0
$749$		−	47.9237i		−	1.75109i
$750$	1.11187	+	4.75049i	0.0405999	+	0.173463i
$751$	12.5674	−	38.6784i	0.458590	−	1.41139i	−0.408278	−	0.912857i	$-0.633871\pi$
$751$	12.5674	−	38.6784i	0.458590	−	1.41139i	0.866868	−	0.498537i	$-0.166129\pi$
$752$	−7.27073	−	10.5031i	−0.265136	−	0.383008i
$753$	5.62332	−	4.08558i	0.204925	−	0.148887i
$754$	26.9241	+	2.27356i	0.980518	+	0.0827982i
$755$	4.64741	−	1.51004i	0.169137	−	0.0549559i
$756$	2.10065	−	12.3496i	0.0764001	−	0.449149i
$757$	−21.1584	+	29.1220i	−0.769014	+	1.05846i	0.227396	+	0.973802i	$0.426979\pi$
$757$	−21.1584	+	29.1220i	−0.769014	+	1.05846i	−0.996410	+	0.0846546i	$0.973021\pi$
$758$	−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	$-0.160821\pi$
$761$	18.9007	+	13.7321i	0.685149	+	0.497790i	−0.189913	+	0.981801i	$0.560821\pi$
$762$	−3.92762	−	6.49212i	−0.142283	−	0.235185i
$763$	6.18846	−	2.01075i	0.224037	−	0.0727941i
$764$	7.20784	+	7.37419i	0.260771	+	0.266789i
$765$	−7.00969	−	9.64802i	−0.253436	−	0.348825i
$766$	−10.3240	+	24.5276i	−0.373020	+	0.886219i
$767$	−13.4889	+	41.5145i	−0.487055	+	1.49900i
$768$	0.234431	−	5.13420i	0.00845930	−	0.185264i
$769$	8.08790			0.291657			0.145829	−	0.989310i	$-0.453415\pi$
$769$	8.08790			0.291657			0.145829	+	0.989310i	$0.453415\pi$
$770$		0			0
$771$		−	2.73327i		−	0.0984365i
$772$	−25.0785	+	47.8616i	−0.902594	+	1.72258i
$773$	−26.5593	−	8.62964i	−0.955271	−	0.310387i	−0.210416	−	0.977612i	$-0.567482\pi$
$773$	−26.5593	−	8.62964i	−0.955271	−	0.310387i	−0.744856	+	0.667226i	$0.767482\pi$
$774$	8.95206	+	3.76803i	0.321775	+	0.135439i
$775$	7.24668	−	5.26502i	0.260308	−	0.189125i
$776$	−2.42471	−	39.4222i	−0.0870421	−	1.41517i
$777$	2.57463	+	7.92389i	0.0923643	+	0.284268i
$778$	19.7728	+	32.6833i	0.708891	+	1.17175i
$779$	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
$784$	−0.358993	+	15.7326i	−0.0128212	+	0.561878i
$785$	−4.83486	−	14.8802i	−0.172563	−	0.531096i
$786$	4.20894	+	0.355416i	0.150128	+	0.0126773i
$787$	−19.4090	−	26.7141i	−0.691855	−	0.952256i	−1.00000		0.000916708i	$-0.999708\pi$
$787$	−19.4090	−	26.7141i	−0.691855	−	0.952256i	0.308145	−	0.951339i	$-0.400292\pi$
$788$	5.93109	+	11.9762i	0.211286	+	0.426635i
$789$	2.85538	+	0.927769i	0.101654	+	0.0330294i
$790$	16.9567	−	3.96879i	0.603292	−	0.141203i
$791$	20.9894			0.746298
$792$		0			0
$793$	−48.0390			−1.70591
$794$	−38.7323	+	9.06548i	−1.37456	+	0.321722i
$795$	1.85739	+	0.603502i	0.0658748	+	0.0214040i
$796$	25.5550	−	12.6558i	0.905772	−	0.448574i
$797$	−15.2250	−	20.9553i	−0.539295	−	0.742277i	0.449216	−	0.893423i	$-0.351703\pi$
$797$	−15.2250	−	20.9553i	−0.539295	−	0.742277i	−0.988511	+	0.151147i	$0.951703\pi$
$798$	7.06198	+	0.596337i	0.249991	+	0.0211101i
$799$	−3.15591	−	9.71288i	−0.111648	−	0.343617i
$800$	12.6859	−	14.0230i	0.448514	−	0.495789i
$801$	−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
$806$	6.05376	+	10.0065i	0.213235	+	0.352464i
$807$	−1.21401	−	3.73634i	−0.0427352	−	0.131526i
$808$	−31.0993	+	1.91280i	−1.09407	+	0.0672922i
$809$	5.27690	−	3.83389i	0.185526	−	0.134792i	−0.491146	−	0.871077i	$-0.663422\pi$
$809$	5.27690	−	3.83389i	0.185526	−	0.134792i	0.676671	+	0.736285i	$0.263422\pi$
$810$	−13.5614	−	5.70813i	−0.476497	−	0.200563i
$811$	24.3226	+	7.90289i	0.854082	+	0.277508i	0.703155	−	0.711037i	$-0.251774\pi$
$811$	24.3226	+	7.90289i	0.854082	+	0.277508i	0.150927	+	0.988545i	$0.451774\pi$
$812$	36.2653	+	19.0023i	1.27266	+	0.666848i
$813$		−	7.92416i		−	0.277912i
$814$		0			0
$815$	−10.6696			−0.373741
$816$	1.35857	−	3.87791i	0.0475594	−	0.135754i
$817$	−3.45657	+	10.6382i	−0.120930	+	0.372184i
$818$	2.27561	−	5.40639i	0.0795650	−	0.189030i
$819$	17.3762	+	23.9163i	0.607173	+	0.835702i
$820$	−9.54696	+	9.33160i	−0.333394	+	0.325874i
$821$	13.4191	−	4.36011i	0.468328	−	0.152169i	−0.0653399	−	0.997863i	$-0.520813\pi$
$821$	13.4191	−	4.36011i	0.468328	−	0.152169i	0.533668	+	0.845694i	$0.320813\pi$
$822$	−2.13218	−	3.52436i	−0.0743682	−	0.122926i
$823$	−18.5470	−	13.4752i	−0.646508	−	0.469716i	0.215572	−	0.976488i	$-0.430839\pi$
$823$	−18.5470	−	13.4752i	−0.646508	−	0.469716i	−0.862080	+	0.506772i	$0.830839\pi$
$824$	−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	−0.150281	−	0.988643i	$-0.548018\pi$
$827$	24.0533	−	33.1065i	0.836414	−	1.15122i	0.986695	−	0.162582i	$-0.0519821\pi$
$828$	−19.8554	−	3.37740i	−0.690024	−	0.117373i
$829$	−2.43906	+	0.792499i	−0.0847121	+	0.0275246i	−0.351066	−	0.936351i	$-0.614181\pi$
$829$	−2.43906	+	0.792499i	−0.0847121	+	0.0275246i	0.266354	+	0.963875i	$0.414181\pi$
$830$	−2.31886	−	0.195812i	−0.0804887	−	0.00679674i
$831$	−2.09238	+	1.52020i	−0.0725839	+	0.0527353i
$832$	16.8505	+	18.0452i	0.584187	+	0.625605i
$833$	−3.88782	+	11.9655i	−0.134705	+	0.414580i
$834$	−0.0241746	−	0.103286i	−0.000837096	−	0.00357650i
$835$			11.4943i			0.397776i
$836$		0			0
$837$		−	5.07568i		−	0.175441i
$838$	−9.98953	+	2.33810i	−0.345083	+	0.0807682i
$839$	−12.9894	+	39.9771i	−0.448443	+	1.38016i	0.430221	+	0.902723i	$0.358436\pi$
$839$	−12.9894	+	39.9771i	−0.448443	+	1.38016i	−0.878664	+	0.477441i	$0.841564\pi$
$840$	−3.74465	−	0.967064i	−0.129203	−	0.0333669i
$841$	7.54500	−	5.48177i	0.260173	−	0.189026i
$842$	−4.18847	+	49.6010i	−0.144344	+	1.70936i
$843$	−4.05991	+	1.31914i	−0.139831	+	0.0454337i
$844$	6.48274	−	38.1114i	0.223145	−	1.31185i
$845$	−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
$850$	12.9351	−	7.82551i	0.443670	−	0.268413i
$851$	25.9336	−	8.42634i	0.888993	−	0.288851i
$852$	−4.21464	+	4.11956i	−0.144391	+	0.141134i
$853$	−12.0073	−	16.5267i	−0.411124	−	0.565863i	0.552368	−	0.833600i	$-0.313724\pi$
$853$	−12.0073	−	16.5267i	−0.411124	−	0.565863i	−0.963492	+	0.267737i	$0.913724\pi$
$854$	−67.0905	−	28.2392i	−2.29579	−	0.966325i
$855$	5.43686	−	16.7329i	0.185937	−	0.572255i
$856$	−15.0368	−	38.1348i	−0.513947	−	1.30342i
$857$	51.9575			1.77483			0.887417	−	0.460968i	$-0.152498\pi$
$857$	51.9575			1.77483			0.887417	+	0.460968i	$0.152498\pi$
$858$		0			0
$859$		−	44.6566i		−	1.52366i	−0.647775	−	0.761832i	$-0.724300\pi$
$859$		−	44.6566i		−	1.52366i	0.647775	−	0.761832i	$-0.275700\pi$
$860$	2.83308	−	5.40686i	0.0966072	−	0.184372i
$861$	−5.23803	−	1.70194i	−0.178512	−	0.0580019i
$862$	7.41091	−	17.6068i	0.252417	−	0.599690i
$863$	−40.8122	+	29.6518i	−1.38926	+	1.00936i	−0.393319	+	0.919402i	$0.628673\pi$
$863$	−40.8122	+	29.6518i	−1.38926	+	1.00936i	−0.995946	+	0.0899581i	$0.971327\pi$
$864$	−2.20329	−	10.4862i	−0.0749574	−	0.356746i
$865$	−3.38332	−	10.4128i	−0.115036	−	0.354045i
$866$	−17.6103	+	10.6539i	−0.598422	+	0.362035i
$867$	−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
$872$	4.29350	−	3.54176i	0.145396	−	0.119939i
$873$	−12.5003	−	38.4718i	−0.423069	−	1.30207i
$874$	1.95171	−	23.1127i	0.0660177	−	0.781800i
$875$	−20.8743	−	28.7310i	−0.705679	−	0.971284i
$876$	0.267747	+	0.540642i	0.00904633	+	0.0182666i
$877$	−17.1577	−	5.57487i	−0.579374	−	0.188250i	0.00464624	−	0.999989i	$-0.498521\pi$
$877$	−17.1577	−	5.57487i	−0.579374	−	0.188250i	−0.584020	+	0.811739i	$0.698521\pi$
$878$	2.61667	+	11.1798i	0.0883085	+	0.377299i
$879$	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	$0.478690\pi$
$882$	3.67303	+	15.6931i	0.123678	+	0.528413i
$883$	−47.0907	−	15.3007i	−1.58473	−	0.514910i	−0.621460	−	0.783446i	$-0.713460\pi$
$883$	−47.0907	−	15.3007i	−1.58473	−	0.514910i	−0.963270	+	0.268536i	$0.913460\pi$
$884$	8.76007	+	17.6886i	0.294633	+	0.594931i
$885$	−3.43782	−	4.73176i	−0.115561	−	0.159056i
$886$	0.483378	−	5.72429i	0.0162394	−	0.192311i
$887$	10.3361	+	31.8112i	0.347051	+	1.06811i	0.960476	+	0.278362i	$0.0897913\pi$
$887$	10.3361	+	31.8112i	0.347051	+	1.06811i	−0.613425	+	0.789753i	$0.710209\pi$
$888$	4.53498	+	5.49753i	0.152184	+	0.184485i
$889$	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
$894$	0.890067	−	0.538475i	0.0297683	−	0.0180093i
$895$	−1.17093	−	3.60374i	−0.0391398	−	0.120460i
$896$	12.9255	+	35.1070i	0.431812	+	1.17284i
$897$	−2.78809	+	2.02566i	−0.0930915	+	0.0676349i
$898$	−4.54652	+	10.8016i	−0.151719	+	0.360454i
$899$	15.7770	+	5.12627i	0.526194	+	0.170971i
$900$	8.98867	−	17.1546i	0.299622	−	0.571821i
$901$		−	15.1034i		−	0.503167i
$902$		0			0
$903$	2.51828			0.0838030
$904$	16.7021	−	6.58575i	0.555505	−	0.219039i
$905$	−8.46167	+	26.0423i	−0.281275	+	0.865676i
$906$	1.58934	+	0.668973i	0.0528024	+	0.0222251i
$907$	4.08489	+	5.62236i	0.135636	+	0.186688i	0.871432	−	0.490516i	$-0.163192\pi$
$907$	4.08489	+	5.62236i	0.135636	+	0.186688i	−0.735796	+	0.677204i	$0.763192\pi$
$908$	17.0025	−	16.6189i	0.564246	−	0.551518i
$909$	−30.3496	+	9.86118i	−1.00663	+	0.327075i
$910$	15.8961	−	9.61689i	0.526952	−	0.318797i
$911$	34.3244	+	24.9382i	1.13722	+	0.826238i	0.986729	−	0.162374i	$-0.0519150\pi$
$911$	34.3244	+	24.9382i	1.13722	+	0.826238i	0.150489	+	0.988612i	$0.451915\pi$
$912$	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
$916$	−0.0730088	+	0.429212i	−0.00241228	+	0.0141816i
$917$	−29.2412	+	9.50103i	−0.965628	+	0.313752i
$918$	0.720827	−	8.53622i	0.0237908	−	0.281737i
$919$	−2.60869	+	1.89533i	−0.0860528	+	0.0625210i	−0.629980	−	0.776612i	$-0.716937\pi$
$919$	−2.60869	+	1.89533i	−0.0860528	+	0.0625210i	0.543927	+	0.839133i	$0.316937\pi$
$920$	−3.16504	+	12.2556i	−0.104348	+	0.404056i
$921$	−2.35626	+	7.25183i	−0.0776415	+	0.238956i
$922$	33.7033	−	7.88840i	1.10996	−	0.259791i
$923$		−	28.3116i		−	0.931886i
$924$		0			0
$925$			26.2207i			0.862131i
$926$	6.52422	+	27.8748i	0.214399	+	0.916022i
$927$	−9.75535	+	30.0239i	−0.320408	+	0.986113i
$928$	34.8200	+	3.74207i	1.14302	+	0.122839i
$929$	19.3523	−	14.0602i	0.634927	−	0.461301i	−0.223177	−	0.974778i	$-0.571643\pi$
$929$	19.3523	−	14.0602i	0.634927	−	0.461301i	0.858104	+	0.513477i	$0.171643\pi$
$930$	−1.56148	−	0.131857i	−0.0512030	−	0.00432375i
$931$	−17.6529	+	5.73578i	−0.578551	+	0.187983i
$932$	−7.25391	−	1.23389i	−0.237610	−	0.0404173i
$933$	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	$-0.429383\pi$
$937$	−19.5822	−	14.2273i	−0.639721	−	0.464785i	−0.859754	+	0.510708i	$0.829383\pi$
$938$	11.3808	+	18.8118i	0.371596	+	0.614226i
$939$	0.982312	−	0.319173i	0.0320565	−	0.0104158i
$940$	−5.87993	+	5.74729i	−0.191782	+	0.187456i
$941$	−1.32063	−	1.81770i	−0.0430514	−	0.0592552i	0.786949	−	0.617019i	$-0.211660\pi$
$941$	−1.32063	−	1.81770i	−0.0430514	−	0.0592552i	−0.830000	+	0.557763i	$0.811660\pi$
$942$	2.14193	−	5.08878i	0.0697878	−	0.165802i
$943$	−5.57017	+	17.1432i	−0.181390	+	0.558260i
$944$	−18.7058	+	53.3941i	−0.608823	+	1.73783i
$945$	−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	$-0.143132\pi$
$948$	5.44346	+	2.85226i	0.176795	+	0.0926370i
$949$	−2.75634	−	0.895590i	−0.0894747	−	0.0290721i
$950$	20.5571	+	8.65274i	0.666961	+	0.280732i
$951$	−2.40009	+	1.74377i	−0.0778283	+	0.0565455i
$952$	1.83615	+	29.8531i	0.0595101	+	0.967544i
$953$	10.5020	+	32.3219i	0.340194	+	1.04701i	0.964107	+	0.265515i	$0.0855420\pi$
$953$	10.5020	+	32.3219i	0.340194	+	1.04701i	−0.623913	+	0.781494i	$0.714458\pi$
$954$	−10.0151	−	16.5544i	−0.324252	−	0.535968i
$955$	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
$960$	−3.28320	+	0.405409i	−0.105965	+	0.0130845i
$961$	−7.36069	−	22.6539i	−0.237441	−	0.730770i
$962$	−34.1136	−	2.88067i	−1.09987	−	0.0928765i
$963$	−24.6773	−	33.9654i	−0.795214	−	1.09452i
$964$	−25.9469	+	12.8499i	−0.835693	+	0.413868i
$965$	33.0774	+	10.7475i	1.06480	+	0.345974i
$966$	−5.08456	+	1.19007i	−0.163593	+	0.0382897i
$967$	3.94526			0.126871			0.0634356	−	0.997986i	$-0.479794\pi$
$967$	3.94526			0.126871			0.0634356	+	0.997986i	$0.479794\pi$
$968$		0			0
$969$	4.84655			0.155694
$970$	−24.7535	+	5.79368i	−0.794788	+	0.186024i
$971$	−15.9164	−	5.17155i	−0.510781	−	0.165963i	0.0422763	−	0.999106i	$-0.486539\pi$
$971$	−15.9164	−	5.17155i	−0.510781	−	0.165963i	−0.553058	+	0.833143i	$0.686539\pi$
$972$	−7.34810	−	14.8375i	−0.235690	−	0.475912i
$973$	0.453852	+	0.624674i	0.0145498	+	0.0200261i
$974$	−3.74141	−	0.315937i	−0.119882	−	0.0101233i
$975$	−1.02404	−	3.15168i	−0.0327956	−	0.100935i
$976$	−62.2471	−	1.42038i	−1.99248	−	0.0454654i
$977$	−5.54903	−	4.03161i	−0.177529	−	0.128983i	0.495472	−	0.868624i	$-0.334995\pi$
$977$	−5.54903	−	4.03161i	−0.177529	−	0.128983i	−0.673001	+	0.739641i	$0.734995\pi$
$978$	−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
$982$	21.4552	+	35.4642i	0.684663	+	1.13171i
$983$	0.536936	+	1.65252i	0.0171256	+	0.0527072i	0.959254	−	0.282545i	$-0.0911786\pi$
$983$	0.536936	+	1.65252i	0.0171256	+	0.0527072i	−0.942129	+	0.335252i	$0.891179\pi$
$984$	−4.70212	+	0.289210i	−0.149898	+	0.00921968i
$985$	6.95930	−	5.05623i	0.221742	−	0.161105i
$986$	25.8056	+	10.8619i	0.821819	+	0.345913i
$987$	−3.22608	−	1.04822i	−0.102687	−	0.0333651i
$988$	−13.5158	+	25.7946i	−0.429996	+	0.820637i
$989$		−	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	$0.410004\pi$
$992$	7.54837	+	13.1450i	0.239661	+	0.417356i
$993$	−0.397218	+	1.22251i	−0.0126053	+	0.0387952i
$994$	16.6426	−	39.5395i	0.527872	−	1.25412i
$995$	−10.7890	−	14.8498i	−0.342036	−	0.470772i
$996$	−0.574014	−	0.587262i	−0.0181883	−	0.0186081i
$997$	−47.5930	+	15.4639i	−1.50728	+	0.489747i	−0.942133	−	0.335240i	$-0.891183\pi$
$997$	−47.5930	+	15.4639i	−1.50728	+	0.489747i	−0.565152	+	0.824987i	$0.691183\pi$
$998$	−5.89646	−	9.74649i	−0.186649	−	0.308520i
$999$	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.j.565.5		40
8.5	even	2	inner	968.2.o.j.565.10		40
11.2	odd	10		968.2.o.i.269.4		40
11.3	even	5	inner	968.2.o.j.245.10		40
11.4	even	5		88.2.o.a.53.2	yes	40
11.5	even	5		968.2.c.h.485.5		20
11.6	odd	10		968.2.c.i.485.16		20
11.7	odd	10		968.2.o.i.493.9		40
11.8	odd	10		968.2.o.d.245.1		40
11.9	even	5		88.2.o.a.5.7	yes	40
11.10	odd	2		968.2.o.d.565.6		40
33.20	odd	10		792.2.br.b.181.4		40
33.26	odd	10		792.2.br.b.757.9		40
44.15	odd	10		352.2.w.a.273.6		40
44.27	odd	10		3872.2.c.h.1937.10		20
44.31	odd	10		352.2.w.a.49.5		40
44.39	even	10		3872.2.c.i.1937.10		20
88.5	even	10		968.2.c.h.485.6		20
88.13	odd	10		968.2.o.i.269.9		40
88.21	odd	2		968.2.o.d.565.1		40
88.27	odd	10		3872.2.c.h.1937.11		20
88.29	odd	10		968.2.o.i.493.4		40
88.37	even	10		88.2.o.a.53.7	yes	40
88.53	even	10		88.2.o.a.5.2	✓	40
88.59	odd	10		352.2.w.a.273.5		40
88.61	odd	10		968.2.c.i.485.15		20
88.69	even	10	inner	968.2.o.j.245.5		40
88.75	odd	10		352.2.w.a.49.6		40
88.83	even	10		3872.2.c.i.1937.11		20
88.85	odd	10		968.2.o.d.245.6		40
264.53	odd	10		792.2.br.b.181.9		40
264.125	odd	10		792.2.br.b.757.4		40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
88.2.o.a.5.2	✓	40	88.53	even	10
88.2.o.a.5.7	yes	40	11.9	even	5
88.2.o.a.53.2	yes	40	11.4	even	5
88.2.o.a.53.7	yes	40	88.37	even	10
352.2.w.a.49.5		40	44.31	odd	10
352.2.w.a.49.6		40	88.75	odd	10
352.2.w.a.273.5		40	88.59	odd	10
352.2.w.a.273.6		40	44.15	odd	10
792.2.br.b.181.4		40	33.20	odd	10
792.2.br.b.181.9		40	264.53	odd	10
792.2.br.b.757.4		40	264.125	odd	10
792.2.br.b.757.9		40	33.26	odd	10
968.2.c.h.485.5		20	11.5	even	5
968.2.c.h.485.6		20	88.5	even	10
968.2.c.i.485.15		20	88.61	odd	10
968.2.c.i.485.16		20	11.6	odd	10
968.2.o.d.245.1		40	11.8	odd	10
968.2.o.d.245.6		40	88.85	odd	10
968.2.o.d.565.1		40	88.21	odd	2
968.2.o.d.565.6		40	11.10	odd	2
968.2.o.i.269.4		40	11.2	odd	10
968.2.o.i.269.9		40	88.13	odd	10
968.2.o.i.493.4		40	88.29	odd	10
968.2.o.i.493.9		40	11.7	odd	10
968.2.o.j.245.5		40	88.69	even	10	inner
968.2.o.j.245.10		40	11.3	even	5	inner
968.2.o.j.565.5		40	1.1	even	1	trivial
968.2.o.j.565.10		40	8.5	even	2	inner
3872.2.c.h.1937.10		20	44.27	odd	10
3872.2.c.h.1937.11		20	88.27	odd	10
3872.2.c.i.1937.10		20	44.39	even	10
3872.2.c.i.1937.11		20	88.83	even	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+(0.322293 + 1.37700i) q^{2} +(0.305500 + 0.0992629i) q^{3} +(-1.79225 + 0.887594i) q^{4} +(0.756671 + 1.04147i) q^{5} +(-0.0382245 + 0.452665i) q^{6} +(-1.02182 - 3.14484i) q^{7} +(-1.79985 - 2.18187i) 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} +(4.00112 - 2.42061i) q^{14} +(0.127784 + 0.393278i) q^{15} +(2.42435 - 3.18159i) q^{16} +(2.58719 - 1.87971i) q^{17} +(1.58931 - 3.77587i) q^{18} +(4.48707 + 1.45794i) q^{19} +(-2.28055 - 1.19496i) q^{20} -1.06218i q^{21} -3.47634 q^{23} +(-0.333275 - 0.845219i) q^{24} +(1.03298 - 3.17919i) q^{25} +(4.02270 + 1.69320i) q^{26} +(-1.11337 - 1.53243i) q^{27} +(4.62271 + 4.72940i) q^{28} +(5.88781 - 1.91307i) q^{29} +(-0.500359 + 0.302709i) 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} +(5.71159 + 0.971539i) q^{36} +(-7.46003 + 2.42391i) q^{37} +(-0.561428 + 6.64858i) q^{38} +(0.802018 - 0.582700i) q^{39} +(0.910453 - 3.52544i) q^{40} +(1.60231 - 4.93140i) q^{41} +(1.46262 - 0.342333i) q^{42} +2.37086i q^{43} -3.72915i q^{45} +(-1.12040 - 4.78692i) q^{46} +(0.986855 - 3.03723i) q^{47} +(1.05645 - 0.731327i) q^{48} +(-3.18281 + 2.31245i) q^{49} +(4.71066 + 0.397784i) q^{50} +(0.976972 - 0.317438i) q^{51} +(-1.03505 + 6.08496i) 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} +(4.53189 + 7.49094i) q^{58} +(-13.4517 + 4.37073i) q^{59} +(-0.578092 - 0.591434i) q^{60} +(-9.14936 - 12.5930i) q^{61} +(-1.47014 + 3.49275i) q^{62} +(-2.96003 + 9.11004i) q^{63} +(-1.52109 + 7.85406i) q^{64} +3.97292 q^{65} +4.70162i q^{67} +(-2.96849 + 5.66529i) q^{68} +(-1.06202 - 0.345072i) q^{69} +(5.54852 + 2.33544i) q^{70} +(7.42164 - 5.39214i) q^{71} +(0.502998 + 8.17798i) q^{72} +(-0.290193 - 0.893124i) q^{73} +(-5.74204 - 9.49125i) 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} +(5.14796 + 0.117469i) q^{80} +(2.49747 + 7.68644i) q^{81} +(7.30695 + 0.617023i) q^{82} +(0.751333 + 1.03412i) q^{83} +(0.942784 + 1.90370i) q^{84} +(3.91531 + 1.27216i) q^{85} +(-3.26467 + 0.764112i) q^{86} +1.98862 q^{87} +15.3866 q^{89} +(5.13503 - 1.20188i) q^{90} +(-9.70557 - 3.15353i) q^{91} +(6.23049 - 3.08558i) q^{92} +(0.505936 + 0.696361i) q^{93} +(4.50031 + 0.380021i) q^{94} +(1.87684 + 5.77632i) q^{95} +(1.34752 + 1.21903i) 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

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more