LMFDB - Embedded newform 525.2.bc.e.157.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [525,2,Mod(82,525)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(525, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([0, 3, 10]))

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

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

chi := DirichletCharacter("525.82");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 525 = 3 \cdot 5^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	525.bc (of order $12$, degree $4$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$4.19214610612$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$8$ over $\Q(\zeta_{12})$
Twist minimal:	no (minimal twist has level 105)
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			157.5
Character	$\chi$	$=$	525.157
Dual form			525.2.bc.e.418.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.173702 - 0.648264i) q^{2} +(0.965926 - 0.258819i) q^{3} +(1.34198 + 0.774791i) q^{4} -0.671132i q^{6} +(0.588837 - 2.57939i) q^{7} +(1.68450 - 1.68450i) q^{8} +(0.866025 - 0.500000i) q^{9} +O(q^{10})$	\(q+(0.173702 - 0.648264i) q^{2} +(0.965926 - 0.258819i) q^{3} +(1.34198 + 0.774791i) q^{4} -0.671132i q^{6} +(0.588837 - 2.57939i) q^{7} +(1.68450 - 1.68450i) q^{8} +(0.866025 - 0.500000i) q^{9} +(0.0701413 - 0.121488i) q^{11} +(1.49678 + 0.401061i) q^{12} +(-2.35788 - 2.35788i) q^{13} +(-1.56985 - 0.829767i) q^{14} +(0.750183 + 1.29935i) q^{16} +(1.97494 + 7.37059i) q^{17} +(-0.173702 - 0.648264i) q^{18} +(-3.89475 - 6.74590i) q^{19} +(-0.0988237 - 2.64391i) q^{21} +(-0.0665729 - 0.0665729i) q^{22} +(2.50617 + 0.671527i) q^{23} +(1.19112 - 2.06308i) q^{24} +(-1.93810 + 1.11896i) q^{26} +(0.707107 - 0.707107i) q^{27} +(2.78870 - 3.00526i) q^{28} +5.09095i q^{29} +(2.54499 + 1.46935i) q^{31} +(5.57476 - 1.49375i) q^{32} +(0.0363078 - 0.135503i) q^{33} +5.12114 q^{34} +1.54958 q^{36} +(-1.53657 + 5.73455i) q^{37} +(-5.04965 + 1.35305i) q^{38} +(-2.88780 - 1.66727i) q^{39} -0.261637i q^{41} +(-1.73111 - 0.395187i) q^{42} +(2.11921 - 2.11921i) q^{43} +(0.188256 - 0.108690i) q^{44} +(0.870653 - 1.50802i) q^{46} +(-1.50250 - 0.402594i) q^{47} +(1.06092 + 1.06092i) q^{48} +(-6.30654 - 3.03768i) q^{49} +(3.81530 + 6.60829i) q^{51} +(-1.33736 - 4.99108i) q^{52} +(-0.749137 - 2.79582i) q^{53} +(-0.335566 - 0.581218i) q^{54} +(-3.35309 - 5.33688i) q^{56} +(-5.50801 - 5.50801i) q^{57} +(3.30028 + 0.884307i) q^{58} +(-4.37132 + 7.57134i) q^{59} +(-4.76685 + 2.75214i) q^{61} +(1.39459 - 1.39459i) q^{62} +(-0.779749 - 2.52824i) q^{63} -0.872657i q^{64} +(-0.0815348 - 0.0470741i) q^{66} +(-7.54968 + 2.02293i) q^{67} +(-3.06033 + 11.4213i) q^{68} +2.59458 q^{69} +3.56278 q^{71} +(0.616569 - 2.30107i) q^{72} +(3.16145 - 0.847107i) q^{73} +(3.45060 + 1.99220i) q^{74} -12.0705i q^{76} +(-0.272064 - 0.252459i) q^{77} +(-1.58245 + 1.58245i) q^{78} +(0.113694 - 0.0656415i) q^{79} +(0.500000 - 0.866025i) q^{81} +(-0.169610 - 0.0454469i) q^{82} +(-7.33949 - 7.33949i) q^{83} +(1.91585 - 3.62463i) q^{84} +(-1.00570 - 1.74192i) q^{86} +(1.31763 + 4.91748i) q^{87} +(-0.0864939 - 0.322800i) q^{88} +(2.44220 + 4.23001i) q^{89} +(-7.47030 + 4.69349i) q^{91} +(2.84293 + 2.84293i) q^{92} +(2.83856 + 0.760591i) q^{93} +(-0.521974 + 0.904086i) q^{94} +(4.99820 - 2.88571i) q^{96} +(1.25230 - 1.25230i) q^{97} +(-3.06468 + 3.56065i) q^{98} -0.140283i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q - 8 q^{7} + 24 q^{8}+O(q^{10}) $ 32 * q - 8 * q^7 + 24 * q^8	$ 32 q - 8 q^{7} + 24 q^{8} - 8 q^{11} - 8 q^{21} + 8 q^{22} + 8 q^{23} + 24 q^{26} + 24 q^{28} + 24 q^{31} - 24 q^{32} + 36 q^{33} - 32 q^{36} - 4 q^{37} - 12 q^{38} - 16 q^{42} - 40 q^{43} - 40 q^{46} + 60 q^{47} - 8 q^{51} + 108 q^{52} + 24 q^{53} - 48 q^{56} - 16 q^{57} - 4 q^{58} - 24 q^{61} - 4 q^{63} + 72 q^{66} - 8 q^{67} - 132 q^{68} - 16 q^{71} - 12 q^{72} - 36 q^{73} - 60 q^{77} - 80 q^{78} + 16 q^{81} - 12 q^{82} - 16 q^{86} + 24 q^{87} + 32 q^{88} - 24 q^{91} + 56 q^{92} + 24 q^{93} + 72 q^{98}+O(q^{100}) $ 32 * q - 8 * q^7 + 24 * q^8 - 8 * q^11 - 8 * q^21 + 8 * q^22 + 8 * q^23 + 24 * q^26 + 24 * q^28 + 24 * q^31 - 24 * q^32 + 36 * q^33 - 32 * q^36 - 4 * q^37 - 12 * q^38 - 16 * q^42 - 40 * q^43 - 40 * q^46 + 60 * q^47 - 8 * q^51 + 108 * q^52 + 24 * q^53 - 48 * q^56 - 16 * q^57 - 4 * q^58 - 24 * q^61 - 4 * q^63 + 72 * q^66 - 8 * q^67 - 132 * q^68 - 16 * q^71 - 12 * q^72 - 36 * q^73 - 60 * q^77 - 80 * q^78 + 16 * q^81 - 12 * q^82 - 16 * q^86 + 24 * q^87 + 32 * q^88 - 24 * q^91 + 56 * q^92 + 24 * q^93 + 72 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/525\mathbb{Z}\right)^\times$.

$n$	$127$	$176$	$451$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$1$	$e\left(\frac{1}{6}\right)$

Coefficient data

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

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

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

$2$	0.173702	−	0.648264i	0.122826	−	0.458392i	−0.876927	−	0.480623i	$-0.840410\pi$
$2$	0.173702	−	0.648264i	0.122826	−	0.458392i	0.999753	+	0.0222315i	$0.00707709\pi$
$3$	0.965926	−	0.258819i	0.557678	−	0.149429i
$3$	0.965926	−	0.258819i	0.557678	−	0.149429i
$4$	1.34198	+	0.774791i	0.670988	+	0.387395i
$5$		0			0
$5$		0			0
$6$		−	0.671132i		−	0.273989i
$7$	0.588837	−	2.57939i	0.222559	−	0.974919i
$7$	0.588837	−	2.57939i	0.222559	−	0.974919i
$8$	1.68450	−	1.68450i	0.595560	−	0.595560i
$9$	0.866025	−	0.500000i	0.288675	−	0.166667i
$10$		0			0
$11$	0.0701413	−	0.121488i	0.0211484	−	0.0366301i	−0.855258	−	0.518203i	$-0.826601\pi$
$11$	0.0701413	−	0.121488i	0.0211484	−	0.0366301i	0.876406	+	0.481573i	$0.159934\pi$
$12$	1.49678	+	0.401061i	0.432083	+	0.115776i
$13$	−2.35788	−	2.35788i	−0.653958	−	0.653958i	0.299986	−	0.953944i	$-0.403018\pi$
$13$	−2.35788	−	2.35788i	−0.653958	−	0.653958i	−0.953944	+	0.299986i	$0.903018\pi$
$14$	−1.56985	−	0.829767i	−0.419559	−	0.221765i
$15$		0			0
$16$	0.750183	+	1.29935i	0.187546	+	0.324839i
$17$	1.97494	+	7.37059i	0.478994	+	1.78763i	0.605704	+	0.795690i	$0.292892\pi$
$17$	1.97494	+	7.37059i	0.478994	+	1.78763i	−0.126710	+	0.991940i	$0.540442\pi$
$18$	−0.173702	−	0.648264i	−0.0409419	−	0.152797i
$19$	−3.89475	−	6.74590i	−0.893517	−	1.54762i	−0.835630	−	0.549293i	$-0.814897\pi$
$19$	−3.89475	−	6.74590i	−0.893517	−	1.54762i	−0.0578866	−	0.998323i	$-0.518436\pi$
$20$		0			0
$21$	−0.0988237	−	2.64391i	−0.0215651	−	0.576947i
$22$	−0.0665729	−	0.0665729i	−0.0141934	−	0.0141934i
$23$	2.50617	+	0.671527i	0.522573	+	0.140023i	0.510456	−	0.859904i	$-0.329476\pi$
$23$	2.50617	+	0.671527i	0.522573	+	0.140023i	0.0121164	+	0.999927i	$0.496143\pi$
$24$	1.19112	−	2.06308i	0.243136	−	0.421124i
$25$		0			0
$26$	−1.93810	+	1.11896i	−0.380092	+	0.219446i
$27$	0.707107	−	0.707107i	0.136083	−	0.136083i
$28$	2.78870	−	3.00526i	0.527014	−	0.567941i
$29$			5.09095i			0.945365i	0.881233	+	0.472683i	$0.156714\pi$
$29$			5.09095i			0.945365i	−0.881233	+	0.472683i	$0.843286\pi$
$30$		0			0
$31$	2.54499	+	1.46935i	0.457093	+	0.263903i	0.710821	−	0.703373i	$-0.248324\pi$
$31$	2.54499	+	1.46935i	0.457093	+	0.263903i	−0.253728	+	0.967276i	$0.581657\pi$
$32$	5.57476	−	1.49375i	0.985489	−	0.264061i
$33$	0.0363078	−	0.135503i	0.00632038	−	0.0235880i
$34$	5.12114			0.878268
$35$		0			0
$36$	1.54958			0.258264
$37$	−1.53657	+	5.73455i	−0.252610	+	0.942754i	0.716794	+	0.697285i	$0.245609\pi$
$37$	−1.53657	+	5.73455i	−0.252610	+	0.942754i	−0.969404	+	0.245469i	$0.921058\pi$
$38$	−5.04965	+	1.35305i	−0.819161	+	0.219494i
$39$	−2.88780	−	1.66727i	−0.462418	−	0.266977i
$40$		0			0
$41$		−	0.261637i		−	0.0408609i	−0.999791	−	0.0204304i	$-0.993496\pi$
$41$		−	0.261637i		−	0.0408609i	0.999791	−	0.0204304i	$-0.00650367\pi$
$42$	−1.73111	−	0.395187i	−0.267117	−	0.0609787i
$43$	2.11921	−	2.11921i	0.323177	−	0.323177i	−0.526808	−	0.849984i	$-0.676611\pi$
$43$	2.11921	−	2.11921i	0.323177	−	0.323177i	0.849984	+	0.526808i	$0.176611\pi$
$44$	0.188256	−	0.108690i	0.0283807	−	0.0163856i
$45$		0			0
$46$	0.870653	−	1.50802i	0.128371	−	0.222345i
$47$	−1.50250	−	0.402594i	−0.219162	−	0.0587244i	0.147567	−	0.989052i	$-0.452856\pi$
$47$	−1.50250	−	0.402594i	−0.219162	−	0.0587244i	−0.366729	+	0.930328i	$0.619522\pi$
$48$	1.06092	+	1.06092i	0.153130	+	0.153130i
$49$	−6.30654	−	3.03768i	−0.900935	−	0.433955i
$50$		0			0
$51$	3.81530	+	6.60829i	0.534248	+	0.925345i
$52$	−1.33736	−	4.99108i	−0.185458	−	0.692138i
$53$	−0.749137	−	2.79582i	−0.102902	−	0.384035i	0.895197	−	0.445671i	$-0.147035\pi$
$53$	−0.749137	−	2.79582i	−0.102902	−	0.384035i	−0.998099	+	0.0616360i	$0.980368\pi$
$54$	−0.335566	−	0.581218i	−0.0456648	−	0.0790937i
$55$		0			0
$56$	−3.35309	−	5.33688i	−0.448075	−	0.713170i
$57$	−5.50801	−	5.50801i	−0.729553	−	0.729553i
$58$	3.30028	+	0.884307i	0.433348	+	0.116115i
$59$	−4.37132	+	7.57134i	−0.569097	+	0.985705i	0.427558	+	0.903988i	$0.359374\pi$
$59$	−4.37132	+	7.57134i	−0.569097	+	0.985705i	−0.996656	+	0.0817173i	$0.973960\pi$
$60$		0			0
$61$	−4.76685	+	2.75214i	−0.610332	+	0.352375i	−0.773095	−	0.634290i	$-0.781293\pi$
$61$	−4.76685	+	2.75214i	−0.610332	+	0.352375i	0.162763	+	0.986665i	$0.447959\pi$
$62$	1.39459	−	1.39459i	0.177114	−	0.177114i
$63$	−0.779749	−	2.52824i	−0.0982392	−	0.318528i
$64$		−	0.872657i		−	0.109082i
$65$		0			0
$66$	−0.0815348	−	0.0470741i	−0.0100362	−	0.00579442i
$67$	−7.54968	+	2.02293i	−0.922340	+	0.247140i	−0.688585	−	0.725155i	$-0.741768\pi$
$67$	−7.54968	+	2.02293i	−0.922340	+	0.247140i	−0.233755	+	0.972296i	$0.575101\pi$
$68$	−3.06033	+	11.4213i	−0.371120	+	1.38504i
$69$	2.59458			0.312351
$70$		0			0
$71$	3.56278			0.422824			0.211412	−	0.977397i	$-0.432194\pi$
$71$	3.56278			0.422824			0.211412	+	0.977397i	$0.432194\pi$
$72$	0.616569	−	2.30107i	0.0726633	−	0.271183i
$73$	3.16145	−	0.847107i	0.370019	−	0.0991464i	−0.0690174	−	0.997615i	$-0.521986\pi$
$73$	3.16145	−	0.847107i	0.370019	−	0.0991464i	0.439037	+	0.898469i	$0.355320\pi$
$74$	3.45060	+	1.99220i	0.401124	+	0.231589i
$75$		0			0
$76$		−	12.0705i		−	1.38458i
$77$	−0.272064	−	0.252459i	−0.0310046	−	0.0287704i
$78$	−1.58245	+	1.58245i	−0.179177	+	0.179177i
$79$	0.113694	−	0.0656415i	0.0127916	−	0.00738524i	−0.493591	−	0.869694i	$-0.664316\pi$
$79$	0.113694	−	0.0656415i	0.0127916	−	0.00738524i	0.506382	+	0.862309i	$0.330983\pi$
$80$		0			0
$81$	0.500000	−	0.866025i	0.0555556	−	0.0962250i
$82$	−0.169610	−	0.0454469i	−0.0187303	−	0.00501877i
$83$	−7.33949	−	7.33949i	−0.805613	−	0.805613i	0.178353	−	0.983967i	$-0.442923\pi$
$83$	−7.33949	−	7.33949i	−0.805613	−	0.805613i	−0.983967	+	0.178353i	$0.942923\pi$
$84$	1.91585	−	3.62463i	0.209037	−	0.395479i
$85$		0			0
$86$	−1.00570	−	1.74192i	−0.108447	−	0.187836i
$87$	1.31763	+	4.91748i	0.141265	+	0.527209i
$88$	−0.0864939	−	0.322800i	−0.00922028	−	0.0344106i
$89$	2.44220	+	4.23001i	0.258872	+	0.448380i	0.965940	−	0.258766i	$-0.0833158\pi$
$89$	2.44220	+	4.23001i	0.258872	+	0.448380i	−0.707068	+	0.707146i	$0.749982\pi$
$90$		0			0
$91$	−7.47030	+	4.69349i	−0.783100	+	0.492012i
$92$	2.84293	+	2.84293i	0.296396	+	0.296396i
$93$	2.83856	+	0.760591i	0.294345	+	0.0788696i
$94$	−0.521974	+	0.904086i	−0.0538376	+	0.0932494i
$95$		0			0
$96$	4.99820	−	2.88571i	0.510126	−	0.294522i
$97$	1.25230	−	1.25230i	0.127152	−	0.127152i	−0.640667	−	0.767819i	$-0.721342\pi$
$97$	1.25230	−	1.25230i	0.127152	−	0.127152i	0.767819	+	0.640667i	$0.221342\pi$
$98$	−3.06468	+	3.56065i	−0.309579	+	0.359680i
$99$		−	0.140283i		−	0.0140989i
$100$		0			0
$101$	−6.19787	−	3.57834i	−0.616711	−	0.356058i	0.158876	−	0.987299i	$-0.449213\pi$
$101$	−6.19787	−	3.57834i	−0.616711	−	0.356058i	−0.775587	+	0.631240i	$0.782546\pi$
$102$	4.94664	−	1.32545i	0.489790	−	0.131239i
$103$	−2.25417	+	8.41269i	−0.222110	+	0.828927i	0.761431	+	0.648246i	$0.224497\pi$
$103$	−2.25417	+	8.41269i	−0.222110	+	0.828927i	−0.983542	+	0.180682i	$0.942170\pi$
$104$	−7.94368			−0.778942
$105$		0			0
$106$	−1.94255			−0.188678
$107$	−0.618295	+	2.30751i	−0.0597728	+	0.223075i	−0.989351	−	0.145550i	$-0.953505\pi$
$107$	−0.618295	+	2.30751i	−0.0597728	+	0.223075i	0.929578	+	0.368625i	$0.120171\pi$
$108$	1.49678	−	0.401061i	0.144028	−	0.0385921i
$109$	12.1949	+	7.04071i	1.16806	+	0.674377i	0.953221	−	0.302273i	$-0.0977455\pi$
$109$	12.1949	+	7.04071i	1.16806	+	0.674377i	0.214834	+	0.976650i	$0.431079\pi$
$110$		0			0
$111$			5.93684i			0.563500i
$112$	3.79328	−	1.16991i	0.358431	−	0.110546i
$113$	−4.27451	+	4.27451i	−0.402112	+	0.402112i	−0.878977	−	0.476865i	$-0.841773\pi$
$113$	−4.27451	+	4.27451i	−0.402112	+	0.402112i	0.476865	+	0.878977i	$0.341773\pi$
$114$	−4.52739	+	2.61389i	−0.424029	+	0.244813i
$115$		0			0
$116$	−3.94442	+	6.83193i	−0.366230	+	0.634329i
$117$	−3.22092	−	0.863043i	−0.297774	−	0.0797884i
$118$	4.14892	+	4.14892i	0.381939	+	0.381939i
$119$	20.1746	−	0.754083i	1.84940	−	0.0691267i
$120$		0			0
$121$	5.49016	+	9.50924i	0.499105	+	0.864476i
$122$	0.956104	+	3.56823i	0.0865615	+	0.323052i
$123$	−0.0677167	−	0.252722i	−0.00610581	−	0.0227872i
$124$	2.27688	+	3.94366i	0.204469	+	0.354152i
$125$		0			0
$126$	−1.77441	+	0.0663238i	−0.158077	+	0.00590859i
$127$	1.28415	+	1.28415i	0.113950	+	0.113950i	0.761783	−	0.647833i	$-0.224324\pi$
$127$	1.28415	+	1.28415i	0.113950	+	0.113950i	−0.647833	+	0.761783i	$0.724324\pi$
$128$	10.5838	+	2.83593i	0.935486	+	0.250663i
$129$	1.49851	−	2.59549i	0.131936	−	0.228520i
$130$		0			0
$131$	−14.9253	+	8.61714i	−1.30403	+	0.752883i	−0.981093	−	0.193537i	$-0.938004\pi$
$131$	−14.9253	+	8.61714i	−1.30403	+	0.752883i	−0.322938	+	0.946420i	$0.604671\pi$
$132$	0.153710	−	0.153710i	0.0133788	−	0.0133788i
$133$	−19.6937	+	6.07385i	−1.70766	+	0.526670i
$134$			5.24557i			0.453148i
$135$		0			0
$136$	15.7425	+	9.08895i	1.34991	+	0.779371i
$137$	−11.0794	+	2.96872i	−0.946578	+	0.253635i	−0.698909	−	0.715210i	$-0.746331\pi$
$137$	−11.0794	+	2.96872i	−0.946578	+	0.253635i	−0.247668	+	0.968845i	$0.579664\pi$
$138$	0.450683	−	1.68197i	0.0383647	−	0.143179i
$139$	−7.07812			−0.600358			−0.300179	−	0.953883i	$-0.597046\pi$
$139$	−7.07812			−0.600358			−0.300179	+	0.953883i	$0.597046\pi$
$140$		0			0
$141$	−1.55550			−0.130997
$142$	0.618861	−	2.30962i	0.0519336	−	0.193819i
$143$	−0.451839	+	0.121070i	−0.0377847	+	0.0101244i
$144$	1.29935	+	0.750183i	0.108280	+	0.0625152i
$145$		0			0
$146$		−	2.19660i		−	0.181792i
$147$	−6.87786	−	1.30192i	−0.567277	−	0.107381i
$148$	−6.50511	+	6.50511i	−0.534717	+	0.534717i
$149$	−15.0133	+	8.66791i	−1.22993	+	0.710103i	−0.967016	−	0.254715i	$-0.918018\pi$
$149$	−15.0133	+	8.66791i	−1.22993	+	0.710103i	−0.262919	+	0.964818i	$0.584685\pi$
$150$		0			0
$151$	8.91043	−	15.4333i	0.725120	−	1.25595i	−0.233804	−	0.972284i	$-0.575117\pi$
$151$	8.91043	−	15.4333i	0.725120	−	1.25595i	0.958924	−	0.283662i	$-0.0915493\pi$
$152$	−17.9241	−	4.80276i	−1.45384	−	0.389555i
$153$	5.39564	+	5.39564i	0.436212	+	0.436212i
$154$	−0.210918	+	0.132517i	−0.0169963	+	0.0106785i
$155$		0			0
$156$	−2.58357	−	4.47488i	−0.206851	−	0.358277i
$157$	−4.65977	−	17.3905i	−0.371890	−	1.38791i	−0.857836	−	0.513924i	$-0.828191\pi$
$157$	−4.65977	−	17.3905i	−0.371890	−	1.38791i	0.485946	−	0.873989i	$-0.338475\pi$
$158$	−0.0228041	−	0.0851060i	−0.00181420	−	0.00677067i
$159$	−1.44722	−	2.50666i	−0.114772	−	0.198791i
$160$		0			0
$161$	3.20786	−	6.06898i	0.252815	−	0.478303i
$162$	−0.474562	−	0.474562i	−0.0372851	−	0.0372851i
$163$	10.5053	+	2.81489i	0.822840	+	0.220479i	0.645588	−	0.763686i	$-0.276612\pi$
$163$	10.5053	+	2.81489i	0.822840	+	0.220479i	0.177253	+	0.984165i	$0.443279\pi$
$164$	0.202714	−	0.351111i	0.0158293	−	0.0274172i
$165$		0			0
$166$	−6.03281	+	3.48304i	−0.468237	+	0.270337i
$167$	11.3579	−	11.3579i	0.878901	−	0.878901i	−0.114520	−	0.993421i	$-0.536533\pi$
$167$	11.3579	−	11.3579i	0.878901	−	0.878901i	0.993421	+	0.114520i	$0.0365331\pi$
$168$	−4.62012	−	4.28718i	−0.356450	−	0.330763i
$169$		−	1.88082i		−	0.144678i
$170$		0			0
$171$	−6.74590	−	3.89475i	−0.515872	−	0.297839i
$172$	4.48588	−	1.20199i	0.342045	−	0.0916507i
$173$	0.508623	−	1.89821i	0.0386699	−	0.144318i	−0.943892	−	0.330255i	$-0.892865\pi$
$173$	0.508623	−	1.89821i	0.0386699	−	0.144318i	0.982562	+	0.185937i	$0.0595320\pi$
$174$	3.41670			0.259019
$175$		0			0
$176$	0.210475			0.0158652
$177$	−2.26276	+	8.44474i	−0.170079	+	0.634745i
$178$	3.16638	−	0.848428i	0.237330	−	0.0635924i
$179$	−2.73795	−	1.58076i	−0.204644	−	0.118151i	0.394176	−	0.919035i	$-0.371030\pi$
$179$	−2.73795	−	1.58076i	−0.204644	−	0.118151i	−0.598820	+	0.800884i	$0.704363\pi$
$180$		0			0
$181$			8.71267i			0.647608i	0.946124	+	0.323804i	$0.104962\pi$
$181$			8.71267i			0.647608i	−0.946124	+	0.323804i	$0.895038\pi$
$182$	1.74502	+	5.65800i	0.129349	+	0.419399i
$183$	−3.89211	+	3.89211i	−0.287713	+	0.287713i
$184$	5.35282	−	3.09045i	0.394615	−	0.227831i
$185$		0			0
$186$	0.986128	−	1.70802i	0.0723064	−	0.125238i
$187$	1.03397	+	0.277050i	0.0756110	+	0.0202599i
$188$	−1.70440	−	1.70440i	−0.124306	−	0.124306i
$189$	−1.40754	−	2.24028i	−0.102383	−	0.162956i
$190$		0			0
$191$	9.19085	+	15.9190i	0.665027	+	1.15186i	0.979278	+	0.202520i	$0.0649133\pi$
$191$	9.19085	+	15.9190i	0.665027	+	1.15186i	−0.314251	+	0.949340i	$0.601753\pi$
$192$	−0.225860	−	0.842922i	−0.0163001	−	0.0608326i
$193$	−3.36118	−	12.5441i	−0.241943	−	0.902944i	−0.974895	−	0.222664i	$-0.928525\pi$
$193$	−3.36118	−	12.5441i	−0.241943	−	0.902944i	0.732952	−	0.680280i	$-0.238142\pi$
$194$	−0.594296	−	1.02935i	−0.0426680	−	0.0739031i
$195$		0			0
$196$	−6.10967	−	8.96275i	−0.436405	−	0.640196i
$197$	12.3248	+	12.3248i	0.878103	+	0.878103i	0.993338	−	0.115235i	$-0.0367622\pi$
$197$	12.3248	+	12.3248i	0.878103	+	0.878103i	−0.115235	+	0.993338i	$0.536762\pi$
$198$	−0.0909402	−	0.0243674i	−0.00646284	−	0.00173171i
$199$	2.25915	−	3.91296i	0.160147	−	0.277382i	−0.774775	−	0.632238i	$-0.782137\pi$
$199$	2.25915	−	3.91296i	0.160147	−	0.277382i	0.934921	+	0.354856i	$0.115470\pi$
$200$		0			0
$201$	−6.76886	+	3.90800i	−0.477438	+	0.275649i
$202$	−3.39629	+	3.39629i	−0.238962	+	0.238962i
$203$	13.1316	+	2.99774i	0.921654	+	0.210400i
$204$			11.8242i			0.827861i
$205$		0			0
$206$	5.06209	+	2.92260i	0.352693	+	0.203627i
$207$	2.50617	−	0.671527i	0.174191	−	0.0466743i
$208$	1.29488	−	4.83256i	0.0897838	−	0.335078i
$209$	−1.09273			−0.0755858
$210$		0			0
$211$	−3.09996			−0.213410			−0.106705	−	0.994291i	$-0.534030\pi$
$211$	−3.09996			−0.213410			−0.106705	+	0.994291i	$0.534030\pi$
$212$	1.16085	−	4.33235i	0.0797274	−	0.297547i
$213$	3.44138	−	0.922114i	0.235799	−	0.0631822i
$214$	1.38847	+	0.801636i	0.0949142	+	0.0547987i
$215$		0			0
$216$		−	2.38224i		−	0.162091i
$217$	5.28861	−	5.69932i	0.359014	−	0.386895i
$218$	6.68251	−	6.68251i	0.452596	−	0.452596i
$219$	2.83448	−	1.63649i	0.191536	−	0.110583i
$220$		0			0
$221$	12.7223	−	22.0356i	0.855793	−	1.48228i
$222$	3.84864	+	1.03124i	0.258304	+	0.0692123i
$223$	1.52444	+	1.52444i	0.102084	+	0.102084i	0.756304	−	0.654220i	$-0.227003\pi$
$223$	1.52444	+	1.52444i	0.102084	+	0.102084i	−0.654220	+	0.756304i	$0.727003\pi$
$224$	−0.570353	−	15.2591i	−0.0381083	−	1.01954i
$225$		0			0
$226$	2.02852	+	3.51350i	0.134935	+	0.233715i
$227$	−1.00293	−	3.74300i	−0.0665671	−	0.248432i	0.924622	−	0.380886i	$-0.124381\pi$
$227$	−1.00293	−	3.74300i	−0.0665671	−	0.248432i	−0.991189	+	0.132454i	$0.957714\pi$
$228$	−3.12406	−	11.6592i	−0.206896	−	0.772147i
$229$	−5.85880	−	10.1477i	−0.387160	−	0.670581i	0.604906	−	0.796297i	$-0.293211\pi$
$229$	−5.85880	−	10.1477i	−0.387160	−	0.670581i	−0.992066	+	0.125716i	$0.959877\pi$
$230$		0			0
$231$	−0.328135	−	0.173441i	−0.0215897	−	0.0114116i
$232$	8.57569	+	8.57569i	0.563021	+	0.563021i
$233$	−5.73648	−	1.53709i	−0.375809	−	0.100698i	0.0659698	−	0.997822i	$-0.478986\pi$
$233$	−5.73648	−	1.53709i	−0.375809	−	0.100698i	−0.441779	+	0.897124i	$0.645653\pi$
$234$	−1.11896	+	1.93810i	−0.0731487	+	0.126697i
$235$		0			0
$236$	−11.7324	+	6.77371i	−0.763715	+	0.440931i
$237$	0.0928311	−	0.0928311i	0.00603003	−	0.00603003i
$238$	3.01551	−	13.2094i	0.195467	−	0.856240i
$239$		−	27.8506i		−	1.80150i	−0.434335	−	0.900751i	$-0.643017\pi$
$239$		−	27.8506i		−	1.80150i	0.434335	−	0.900751i	$-0.356983\pi$
$240$		0			0
$241$	−13.3046	−	7.68141i	−0.857024	−	0.494803i	0.00599067	−	0.999982i	$-0.498093\pi$
$241$	−13.3046	−	7.68141i	−0.857024	−	0.494803i	−0.863015	+	0.505179i	$0.831426\pi$
$242$	7.11815	−	1.90730i	0.457572	−	0.122606i
$243$	0.258819	−	0.965926i	0.0166032	−	0.0619642i
$244$	−8.52933			−0.546034
$245$		0			0
$246$	−0.175593			−0.0111954
$247$	−6.72267	+	25.0894i	−0.427753	+	1.59640i
$248$	6.76214	−	1.81191i	0.429396	−	0.115056i
$249$	−8.98900	−	5.18980i	−0.569655	−	0.328890i
$250$		0			0
$251$		−	18.3280i		−	1.15685i	−0.815735	−	0.578426i	$-0.803667\pi$
$251$		−	18.3280i		−	1.15685i	0.815735	−	0.578426i	$-0.196333\pi$
$252$	0.912450	−	3.99698i	0.0574790	−	0.251786i
$253$	0.257369	−	0.257369i	0.0161806	−	0.0161806i
$254$	1.05553	−	0.609408i	0.0662296	−	0.0382377i
$255$		0			0
$256$	4.54951	−	7.87999i	0.284345	−	0.492499i
$257$	−8.52285	−	2.28369i	−0.531641	−	0.142453i	−0.0169949	−	0.999856i	$-0.505410\pi$
$257$	−8.52285	−	2.28369i	−0.531641	−	0.142453i	−0.514646	+	0.857403i	$0.672077\pi$
$258$	−1.42227	−	1.42227i	−0.0885467	−	0.0885467i
$259$	13.8869	+	7.34012i	0.862888	+	0.456093i
$260$		0			0
$261$	2.54547	+	4.40889i	0.157561	+	0.272903i
$262$	2.99362	+	11.1724i	0.184947	+	0.690231i
$263$	−0.158138	−	0.590180i	−0.00975122	−	0.0363920i	0.960879	−	0.276969i	$-0.0893300\pi$
$263$	−0.158138	−	0.590180i	−0.00975122	−	0.0363920i	−0.970630	+	0.240577i	$0.922663\pi$
$264$	−0.167093	−	0.289414i	−0.0102839	−	0.0178122i
$265$		0			0
$266$	0.516629	+	13.8218i	0.0316765	+	0.847467i
$267$	3.45379	+	3.45379i	0.211368	+	0.211368i
$268$	−11.6988	−	3.13470i	−0.714621	−	0.191482i
$269$	2.98048	−	5.16233i	0.181723	−	0.314753i	−0.760745	−	0.649051i	$-0.775166\pi$
$269$	2.98048	−	5.16233i	0.181723	−	0.314753i	0.942467	+	0.334298i	$0.108499\pi$
$270$		0			0
$271$	10.5427	−	6.08684i	0.640424	−	0.369749i	−0.144354	−	0.989526i	$-0.546110\pi$
$271$	10.5427	−	6.08684i	0.640424	−	0.369749i	0.784778	+	0.619777i	$0.212777\pi$
$272$	−8.09544	+	8.09544i	−0.490858	+	0.490858i
$273$	−6.00099	+	6.46702i	−0.363197	+	0.391402i
$274$			7.69805i			0.465056i
$275$		0			0
$276$	3.48187	+	2.01026i	0.209584	+	0.121003i
$277$	24.3943	−	6.53642i	1.46571	−	0.392736i	0.564252	−	0.825603i	$-0.309165\pi$
$277$	24.3943	−	6.53642i	1.46571	−	0.392736i	0.901458	+	0.432867i	$0.142498\pi$
$278$	−1.22948	+	4.58849i	−0.0737394	+	0.275199i
$279$	2.93870			0.175935
$280$		0			0
$281$	29.0002			1.73001			0.865003	−	0.501766i	$-0.167316\pi$
$281$	29.0002			1.73001			0.865003	+	0.501766i	$0.167316\pi$
$282$	−0.270194	+	1.00838i	−0.0160898	+	0.0600480i
$283$	17.6534	−	4.73021i	1.04938	−	0.281182i	0.307387	−	0.951585i	$-0.400545\pi$
$283$	17.6534	−	4.73021i	1.04938	−	0.281182i	0.741997	+	0.670403i	$0.233879\pi$
$284$	4.78116	+	2.76041i	0.283710	+	0.163800i
$285$		0			0
$286$			0.313941i			0.0185637i
$287$	−0.674866	−	0.154062i	−0.0398361	−	0.00909397i
$288$	4.08101	−	4.08101i	0.240476	−	0.240476i
$289$	−35.7027	+	20.6130i	−2.10016	+	1.21253i
$290$		0			0
$291$	0.885513	−	1.53375i	0.0519097	−	0.0899102i
$292$	4.89892	+	1.31266i	0.286688	+	0.0768177i
$293$	−17.8951	−	17.8951i	−1.04544	−	1.04544i	−0.998917	−	0.0465260i	$-0.985185\pi$
$293$	−17.8951	−	17.8951i	−1.04544	−	1.04544i	−0.0465260	−	0.998917i	$-0.514815\pi$
$294$	−2.03869	+	4.23252i	−0.118899	+	0.246846i
$295$		0			0
$296$	7.07148	+	12.2482i	0.411022	+	0.711910i
$297$	−0.0363078	−	0.135503i	−0.00210679	−	0.00786266i
$298$	3.01126	+	11.2382i	0.174438	+	0.651011i
$299$	−4.32587	−	7.49263i	−0.250171	−	0.433310i
$300$		0			0
$301$	−4.21841	−	6.71415i	−0.243145	−	0.386997i
$302$	−8.45711	−	8.45711i	−0.486652	−	0.486652i
$303$	−6.91283	−	1.85229i	−0.397132	−	0.106411i
$304$	5.84355	−	10.1213i	0.335150	−	0.580497i
$305$		0			0
$306$	4.43504	−	2.56057i	0.253534	−	0.146378i
$307$	−10.5679	+	10.5679i	−0.603143	+	0.603143i	−0.941145	−	0.338002i	$-0.890249\pi$
$307$	−10.5679	+	10.5679i	−0.603143	+	0.603143i	0.338002	+	0.941145i	$0.390249\pi$
$308$	−0.169501	−	0.549587i	−0.00965824	−	0.0313156i
$309$			8.70946i			0.495464i
$310$		0			0
$311$	14.0122	+	8.08997i	0.794562	+	0.458740i	0.841566	−	0.540154i	$-0.181634\pi$
$311$	14.0122	+	8.08997i	0.794562	+	0.458740i	−0.0470044	+	0.998895i	$0.514967\pi$
$312$	−7.67300	+	2.05598i	−0.434398	+	0.116397i
$313$	2.90722	−	10.8499i	0.164326	−	0.613272i	−0.833800	−	0.552067i	$-0.813839\pi$
$313$	2.90722	−	10.8499i	0.164326	−	0.613272i	0.998125	−	0.0612045i	$-0.0194942\pi$
$314$	−12.0830			−0.681886
$315$		0			0
$316$	0.203434			0.0114440
$317$	3.36067	−	12.5422i	0.188754	−	0.704441i	−0.805041	−	0.593219i	$-0.797857\pi$
$317$	3.36067	−	12.5422i	0.188754	−	0.704441i	0.993796	−	0.111222i	$-0.0354764\pi$
$318$	−1.87636	+	0.502770i	−0.105221	+	0.0281939i
$319$	0.618491	+	0.357086i	0.0346288	+	0.0199930i
$320$		0			0
$321$			2.38891i			0.133336i
$322$	−3.37709	−	3.13373i	−0.188198	−	0.174636i
$323$	42.0293	−	42.0293i	2.33858	−	2.33858i
$324$	1.34198	−	0.774791i	0.0745543	−	0.0430439i
$325$		0			0
$326$	3.64959	−	6.32127i	0.202132	−	0.350103i
$327$	13.6016	+	3.64454i	0.752170	+	0.201543i
$328$	−0.440728	−	0.440728i	−0.0243351	−	0.0243351i
$329$	−1.92318	+	3.63848i	−0.106028	+	0.200596i
$330$		0			0
$331$	−11.3176	−	19.6027i	−0.622071	−	1.07746i	−0.989099	−	0.147249i	$-0.952958\pi$
$331$	−11.3176	−	19.6027i	−0.622071	−	1.07746i	0.367028	−	0.930210i	$-0.380375\pi$
$332$	−4.16286	−	15.5360i	−0.228466	−	0.852648i
$333$	1.53657	+	5.73455i	0.0842034	+	0.314251i
$334$	−5.39003	−	9.33581i	−0.294929	−	0.510833i
$335$		0			0
$336$	3.36123	−	2.11182i	0.183370	−	0.115209i
$337$	−14.8328	−	14.8328i	−0.807992	−	0.807992i	0.176338	−	0.984330i	$-0.443575\pi$
$337$	−14.8328	−	14.8328i	−0.807992	−	0.807992i	−0.984330	+	0.176338i	$0.943575\pi$
$338$	−1.21927	−	0.326702i	−0.0663194	−	0.0177702i
$339$	−3.02254	+	5.23519i	−0.164162	+	0.284336i
$340$		0			0
$341$	0.357018	−	0.206124i	0.0193336	−	0.0111622i
$342$	−3.69660	+	3.69660i	−0.199889	+	0.199889i
$343$	−11.5489	+	14.4784i	−0.623582	+	0.781758i
$344$		−	7.13961i		−	0.384942i
$345$		0			0
$346$	−1.14219	−	0.659444i	−0.0614045	−	0.0354519i
$347$	1.14992	−	0.308119i	0.0617307	−	0.0165407i	−0.227822	−	0.973703i	$-0.573160\pi$
$347$	1.14992	−	0.308119i	0.0617307	−	0.0165407i	0.289552	+	0.957162i	$0.406494\pi$
$348$	−2.04178	+	7.62003i	−0.109451	+	0.408477i
$349$	30.1708			1.61501			0.807504	−	0.589862i	$-0.200818\pi$
$349$	30.1708			1.61501			0.807504	+	0.589862i	$0.200818\pi$
$350$		0			0
$351$	−3.33454			−0.177985
$352$	0.209548	−	0.782043i	0.0111689	−	0.0416830i
$353$	−20.9922	+	5.62484i	−1.11730	+	0.299380i	−0.769791	−	0.638296i	$-0.779639\pi$
$353$	−20.9922	+	5.62484i	−1.11730	+	0.299380i	−0.347510	+	0.937676i	$0.612973\pi$
$354$	5.08137	+	2.93373i	0.270072	+	0.155926i
$355$		0			0
$356$			7.56877i			0.401144i
$357$	19.2920	−	5.94995i	1.02104	−	0.314905i
$358$	−1.50033	+	1.50033i	−0.0792951	+	0.0792951i
$359$	29.2159	−	16.8678i	1.54196	−	0.890249i	0.543242	−	0.839576i	$-0.317197\pi$
$359$	29.2159	−	16.8678i	1.54196	−	0.890249i	0.998715	−	0.0506728i	$-0.0161366\pi$
$360$		0			0
$361$	−20.8381	+	36.0927i	−1.09674	+	1.89962i
$362$	5.64811	+	1.51341i	0.296858	+	0.0795429i
$363$	7.76426	+	7.76426i	0.407518	+	0.407518i
$364$	−13.6614	+	0.510636i	−0.716054	+	0.0267646i
$365$		0			0
$366$	1.84705	+	3.19918i	0.0965469	+	0.167224i
$367$	4.25805	+	15.8913i	0.222269	+	0.829518i	0.983480	+	0.181014i	$0.0579381\pi$
$367$	4.25805	+	15.8913i	0.222269	+	0.829518i	−0.761212	+	0.648503i	$0.775395\pi$
$368$	1.00754	+	3.76017i	0.0525214	+	0.196013i
$369$	−0.130819	−	0.226585i	−0.00681015	−	0.0117955i
$370$		0			0
$371$	−7.65263	+	0.286039i	−0.397305	+	0.0148504i
$372$	3.21999	+	3.21999i	0.166949	+	0.166949i
$373$	11.6913	+	3.13267i	0.605351	+	0.162203i	0.548460	−	0.836177i	$-0.315214\pi$
$373$	11.6913	+	3.13267i	0.605351	+	0.162203i	0.0568914	+	0.998380i	$0.481881\pi$
$374$	0.359203	−	0.622159i	0.0185740	−	0.0321711i
$375$		0			0
$376$	−3.20913	+	1.85279i	−0.165498	+	0.0955504i
$377$	12.0038	−	12.0038i	0.618229	−	0.618229i
$378$	−1.69678	+	0.523315i	−0.0872731	+	0.0269164i
$379$			19.9826i			1.02644i	0.858257	+	0.513219i	$0.171547\pi$
$379$			19.9826i			1.02644i	−0.858257	+	0.513219i	$0.828453\pi$
$380$		0			0
$381$	1.57275	+	0.908030i	0.0805746	+	0.0465198i
$382$	11.9162	−	3.19294i	0.609686	−	0.163365i
$383$	−6.84545	+	25.5476i	−0.349786	+	1.30542i	0.537134	+	0.843497i	$0.319507\pi$
$383$	−6.84545	+	25.5476i	−0.349786	+	1.30542i	−0.886920	+	0.461923i	$0.847160\pi$
$384$	10.9572			0.559156
$385$		0			0
$386$	−8.71573			−0.443619
$387$	0.775685	−	2.89490i	0.0394303	−	0.147156i
$388$	2.65084	−	0.710290i	0.134576	−	0.0360595i
$389$	−10.7399	−	6.20070i	−0.544536	−	0.314388i	0.202379	−	0.979307i	$-0.435133\pi$
$389$	−10.7399	−	6.20070i	−0.544536	−	0.314388i	−0.746915	+	0.664919i	$0.768466\pi$
$390$		0			0
$391$			19.7982i			1.00124i
$392$	−15.7403	+	5.50639i	−0.795006	+	0.278114i
$393$	−12.1865	+	12.1865i	−0.614726	+	0.614726i
$394$	10.1305	−	5.84887i	0.510369	−	0.294662i
$395$		0			0
$396$	0.108690	−	0.188256i	0.00546186	−	0.00946022i
$397$	−9.31864	−	2.49692i	−0.467689	−	0.125317i	0.0172754	−	0.999851i	$-0.494501\pi$
$397$	−9.31864	−	2.49692i	−0.467689	−	0.125317i	−0.484964	+	0.874534i	$0.661167\pi$
$398$	−2.14421	−	2.14421i	−0.107480	−	0.107480i
$399$	−17.4506	+	10.9640i	−0.873624	+	0.548887i
$400$		0			0
$401$	−17.8020	−	30.8340i	−0.888990	−	1.53978i	−0.841071	−	0.540924i	$-0.818074\pi$
$401$	−17.8020	−	30.8340i	−0.888990	−	1.53978i	−0.0479187	−	0.998851i	$-0.515259\pi$
$402$	1.35765	+	5.06683i	0.0677136	+	0.252711i
$403$	−2.53622	−	9.46532i	−0.126338	−	0.471501i
$404$	−5.54493	−	9.60411i	−0.275871	−	0.477822i
$405$		0			0
$406$	4.22430	−	7.99200i	0.209648	−	0.396636i
$407$	0.588904	+	0.588904i	0.0291909	+	0.0291909i
$408$	17.5585	+	4.70479i	0.869275	+	0.232922i
$409$	0.897110	−	1.55384i	0.0443592	−	0.0768325i	−0.842993	−	0.537924i	$-0.819209\pi$
$409$	0.897110	−	1.55384i	0.0443592	−	0.0768325i	0.887353	+	0.461092i	$0.152542\pi$
$410$		0			0
$411$	−9.93353	+	5.73512i	−0.489985	+	0.282893i
$412$	−9.54313	+	9.54313i	−0.470156	+	0.470156i
$413$	16.9555	+	15.7336i	0.834325	+	0.774201i
$414$		−	1.74131i		−	0.0855805i
$415$		0			0
$416$	−16.6667	−	9.62253i	−0.817153	−	0.471783i
$417$	−6.83694	+	1.83195i	−0.334806	+	0.0897111i
$418$	−0.189809	+	0.708378i	−0.00928388	+	0.0346479i
$419$	37.3453			1.82444			0.912219	−	0.409703i	$-0.134368\pi$
$419$	37.3453			1.82444			0.912219	+	0.409703i	$0.134368\pi$
$420$		0			0
$421$	−0.951407			−0.0463687			−0.0231844	−	0.999731i	$-0.507380\pi$
$421$	−0.951407			−0.0463687			−0.0231844	+	0.999731i	$0.507380\pi$
$422$	−0.538468	+	2.00959i	−0.0262122	+	0.0978253i
$423$	−1.50250	+	0.402594i	−0.0730541	+	0.0195748i
$424$	−5.97147	−	3.44763i	−0.290000	−	0.167432i
$425$		0			0
$426$		−	2.39109i		−	0.115849i
$427$	4.29196	+	13.9161i	0.207702	+	0.673449i
$428$	−2.61757	+	2.61757i	−0.126525	+	0.126525i
$429$	−0.405108	+	0.233889i	−0.0195588	+	0.0112923i
$430$		0			0
$431$	−0.775727	+	1.34360i	−0.0373654	+	0.0647189i	−0.884103	−	0.467291i	$-0.845230\pi$
$431$	−0.775727	+	1.34360i	−0.0373654	+	0.0647189i	0.846738	+	0.532010i	$0.178563\pi$
$432$	1.44924	+	0.388323i	0.0697267	+	0.0186832i
$433$	9.22281	+	9.22281i	0.443220	+	0.443220i	0.893093	−	0.449873i	$-0.148531\pi$
$433$	9.22281	+	9.22281i	0.443220	+	0.443220i	−0.449873	+	0.893093i	$0.648531\pi$
$434$	−2.77602	−	4.41840i	−0.133253	−	0.212090i
$435$		0			0
$436$	10.9101	+	18.8969i	0.522501	+	0.904999i
$437$	−5.23085	−	19.5218i	−0.250226	−	0.933855i
$438$	−0.568521	−	2.12175i	−0.0271650	−	0.101381i
$439$	−6.81704	−	11.8075i	−0.325360	−	0.563540i	0.656225	−	0.754565i	$-0.272152\pi$
$439$	−6.81704	−	11.8075i	−0.325360	−	0.563540i	−0.981585	+	0.191025i	$0.938819\pi$
$440$		0			0
$441$	−6.98047	+	0.522561i	−0.332403	+	0.0248838i
$442$	−12.0750	−	12.0750i	−0.574350	−	0.574350i
$443$	−6.52796	−	1.74916i	−0.310153	−	0.0831052i	0.100385	−	0.994949i	$-0.467992\pi$
$443$	−6.52796	−	1.74916i	−0.310153	−	0.0831052i	−0.410538	+	0.911843i	$0.634659\pi$
$444$	−4.59981	+	7.96710i	−0.218297	+	0.378102i
$445$		0			0
$446$	1.25303	−	0.723440i	0.0593329	−	0.0342559i
$447$	−12.2583	+	12.2583i	−0.579797	+	0.579797i
$448$	−2.25093	−	0.513852i	−0.106346	−	0.0242772i
$449$		−	7.45668i		−	0.351903i	−0.984399	−	0.175951i	$-0.943700\pi$
$449$		−	7.45668i		−	0.351903i	0.984399	−	0.175951i	$-0.0563001\pi$
$450$		0			0
$451$	−0.0317859	−	0.0183516i	−0.00149674	−	0.000864143i
$452$	−9.04815	+	2.42444i	−0.425589	+	0.114036i
$453$	4.61238	−	17.2136i	0.216708	−	0.808767i
$454$	−2.60066			−0.122055
$455$		0			0
$456$	−18.5564			−0.868985
$457$	9.87800	−	36.8652i	0.462073	−	1.72448i	−0.204342	−	0.978900i	$-0.565505\pi$
$457$	9.87800	−	36.8652i	0.462073	−	1.72448i	0.666415	−	0.745581i	$-0.267828\pi$
$458$	−7.59610	+	2.03537i	−0.354942	+	0.0951065i
$459$	6.60829	+	3.81530i	0.308448	+	0.178083i
$460$		0			0
$461$			7.86072i			0.366110i	0.983103	+	0.183055i	$0.0585987\pi$
$461$			7.86072i			0.366110i	−0.983103	+	0.183055i	$0.941401\pi$
$462$	−0.169433	+	0.182591i	−0.00788275	+	0.00849491i
$463$	−10.4981	+	10.4981i	−0.487887	+	0.487887i	−0.907639	−	0.419752i	$-0.862117\pi$
$463$	−10.4981	+	10.4981i	−0.487887	+	0.487887i	0.419752	+	0.907639i	$0.362117\pi$
$464$	−6.61494	+	3.81914i	−0.307091	+	0.177299i
$465$		0			0
$466$	−1.99287	+	3.45176i	−0.0923181	+	0.159900i
$467$	13.0548	+	3.49803i	0.604105	+	0.161869i	0.547892	−	0.836549i	$-0.315431\pi$
$467$	13.0548	+	3.49803i	0.604105	+	0.161869i	0.0562135	+	0.998419i	$0.482097\pi$
$468$	−3.65372	−	3.65372i	−0.168893	−	0.168893i
$469$	0.772406	+	20.6648i	0.0356664	+	0.954210i
$470$		0			0
$471$	−9.00198	−	15.5919i	−0.414790	−	0.718437i
$472$	5.39044	+	20.1174i	0.248115	+	0.925977i
$473$	−0.108815	−	0.406104i	−0.00500333	−	0.0186727i
$474$	−0.0440541	−	0.0763040i	−0.00202347	−	0.00350476i
$475$		0			0
$476$	27.6581	+	14.6191i	1.26770	+	0.670065i
$477$	−2.04668	−	2.04668i	−0.0937110	−	0.0937110i
$478$	−18.0545	−	4.83769i	−0.825794	−	0.221271i
$479$	−13.4819	+	23.3514i	−0.616005	+	1.06695i	0.374202	+	0.927347i	$0.377917\pi$
$479$	−13.4819	+	23.3514i	−0.616005	+	1.06695i	−0.990207	+	0.139605i	$0.955417\pi$
$480$		0			0
$481$	17.1444	−	9.89832i	0.781717	−	0.451325i
$482$	−7.29061	+	7.29061i	−0.332078	+	0.332078i
$483$	1.52778	−	6.69244i	0.0695166	−	0.304517i
$484$			17.0149i			0.773405i
$485$		0			0
$486$	−0.581218	−	0.335566i	−0.0263646	−	0.0152216i
$487$	1.87031	−	0.501148i	0.0847518	−	0.0227092i	−0.216194	−	0.976350i	$-0.569364\pi$
$487$	1.87031	−	0.501148i	0.0847518	−	0.0227092i	0.300946	+	0.953641i	$0.402698\pi$
$488$	−3.39377	+	12.6657i	−0.153629	+	0.573350i
$489$	10.8759			0.491826
$490$		0			0
$491$	23.5074			1.06087			0.530436	−	0.847725i	$-0.322028\pi$
$491$	23.5074			1.06087			0.530436	+	0.847725i	$0.322028\pi$
$492$	0.104933	−	0.391614i	0.00473073	−	0.0176553i
$493$	−37.5233	+	10.0543i	−1.68996	+	0.452824i
$494$	15.0968	+	8.71613i	0.679237	+	0.392157i
$495$		0			0
$496$			4.40912i			0.197975i
$497$	2.09789	−	9.18980i	0.0941034	−	0.412219i
$498$	−4.92577	+	4.92577i	−0.220729	+	0.220729i
$499$	6.07971	−	3.51012i	0.272165	−	0.157135i	−0.357706	−	0.933834i	$-0.616441\pi$
$499$	6.07971	−	3.51012i	0.272165	−	0.157135i	0.629871	+	0.776700i	$0.283108\pi$
$500$		0			0
$501$	8.03125	−	13.9105i	0.358810	−	0.621477i
$502$	−11.8814	−	3.18360i	−0.530292	−	0.142091i
$503$	21.3755	+	21.3755i	0.953087	+	0.953087i	0.998948	−	0.0458611i	$-0.0146032\pi$
$503$	21.3755	+	21.3755i	0.953087	+	0.953087i	−0.0458611	+	0.998948i	$0.514603\pi$
$504$	−5.57230	−	2.94533i	−0.248210	−	0.131195i
$505$		0			0
$506$	−0.122138	−	0.211548i	−0.00542968	−	0.00940447i
$507$	−0.486792	−	1.81673i	−0.0216192	−	0.0806839i
$508$	0.728351	+	2.71824i	0.0323154	+	0.120603i
$509$	20.5791	+	35.6441i	0.912155	+	1.57990i	0.811015	+	0.585026i	$0.198916\pi$
$509$	20.5791	+	35.6441i	0.912155	+	1.57990i	0.101140	+	0.994872i	$0.467751\pi$
$510$		0			0
$511$	−0.323447	−	8.65343i	−0.0143085	−	0.382805i
$512$	11.1777	+	11.1777i	0.493991	+	0.493991i
$513$	−7.52408	−	2.01607i	−0.332196	−	0.0890117i
$514$	−2.96087	+	5.12838i	−0.130598	+	0.226203i
$515$		0			0
$516$	4.02193	−	2.32206i	0.177055	−	0.102223i
$517$	−0.154298	+	0.154298i	−0.00678602	+	0.00678602i
$518$	7.17051	−	7.72736i	0.315054	−	0.339521i
$519$		−	1.96517i		−	0.0862613i
$520$		0			0
$521$	−13.4350	−	7.75669i	−0.588597	−	0.339827i	0.175945	−	0.984400i	$-0.443702\pi$
$521$	−13.4350	−	7.75669i	−0.588597	−	0.339827i	−0.764543	+	0.644573i	$0.777035\pi$
$522$	3.30028	−	0.884307i	0.144449	−	0.0387051i
$523$	1.10376	−	4.11930i	0.0482641	−	0.180124i	−0.937586	−	0.347754i	$-0.886945\pi$
$523$	1.10376	−	4.11930i	0.0482641	−	0.180124i	0.985850	+	0.167629i	$0.0536112\pi$
$524$	−26.7059			−1.16665
$525$		0			0
$526$	−0.410061			−0.0178795
$527$	−5.80376	+	21.6599i	−0.252816	+	0.943521i
$528$	0.203303	−	0.0544750i	0.00884765	−	0.00237072i
$529$	−14.0886	−	8.13408i	−0.612549	−	0.353656i
$530$		0			0
$531$			8.74263i			0.379398i
$532$	−31.1345	−	7.10753i	−1.34985	−	0.308150i
$533$	−0.616909	+	0.616909i	−0.0267213	+	0.0267213i
$534$	2.83890	−	1.63904i	0.122851	−	0.0709281i
$535$		0			0
$536$	−9.30979	+	16.1250i	−0.402122	+	0.696495i
$537$	−3.05378	−	0.818259i	−0.131781	−	0.0353105i
$538$	−2.82884	−	2.82884i	−0.121960	−	0.121960i
$539$	−0.811392	+	0.553104i	−0.0349491	+	0.0238239i
$540$		0			0
$541$	8.04749	+	13.9387i	0.345989	+	0.599270i	0.985533	−	0.169484i	$-0.0542103\pi$
$541$	8.04749	+	13.9387i	0.345989	+	0.599270i	−0.639544	+	0.768754i	$0.720877\pi$
$542$	−2.11459	−	7.89176i	−0.0908294	−	0.338980i
$543$	2.25500	+	8.41579i	0.0967715	+	0.361156i
$544$	22.0197	+	38.1392i	0.944086	+	1.63521i
$545$		0			0
$546$	3.14995	+	5.01356i	0.134806	+	0.214561i
$547$	−26.4927	−	26.4927i	−1.13275	−	1.13275i	−0.989719	−	0.143028i	$-0.954316\pi$
$547$	−26.4927	−	26.4927i	−1.13275	−	1.13275i	−0.143028	−	0.989719i	$-0.545684\pi$
$548$	−17.1684	−	4.60027i	−0.733400	−	0.196514i
$549$	−2.75214	+	4.76685i	−0.117458	+	0.203444i
$550$		0			0
$551$	34.3430	−	19.8280i	1.46306	−	0.844699i
$552$	4.37056	−	4.37056i	0.186023	−	0.186023i
$553$	−0.102368	−	0.331915i	−0.00435312	−	0.0141144i
$554$		−	16.9493i		−	0.720107i
$555$		0			0
$556$	−9.49867	−	5.48406i	−0.402833	−	0.232576i
$557$	−28.2477	+	7.56894i	−1.19689	+	0.320706i	−0.801607	−	0.597852i	$-0.796021\pi$
$557$	−28.2477	+	7.56894i	−1.19689	+	0.320706i	−0.395286	+	0.918558i	$0.629354\pi$
$558$	0.510457	−	1.90505i	0.0216094	−	0.0806473i
$559$	−9.99368			−0.422688
$560$		0			0
$561$	1.07044			0.0451940
$562$	5.03739	−	18.7998i	0.212489	−	0.793021i
$563$	5.13597	−	1.37618i	0.216455	−	0.0579990i	−0.148962	−	0.988843i	$-0.547593\pi$
$563$	5.13597	−	1.37618i	0.216455	−	0.0579990i	0.365417	+	0.930844i	$0.380926\pi$
$564$	−2.08745	−	1.20519i	−0.0878975	−	0.0507477i
$565$		0			0
$566$		−	12.2657i		−	0.515566i
$567$	−1.93940	−	1.79964i	−0.0814472	−	0.0755780i
$568$	6.00149	−	6.00149i	0.251817	−	0.251817i
$569$	−19.9960	+	11.5447i	−0.838275	+	0.483979i	−0.856678	−	0.515852i	$-0.827475\pi$
$569$	−19.9960	+	11.5447i	−0.838275	+	0.483979i	0.0184022	+	0.999831i	$0.494142\pi$
$570$		0			0
$571$	−3.99620	+	6.92162i	−0.167236	+	0.289661i	−0.937447	−	0.348128i	$-0.886817\pi$
$571$	−3.99620	+	6.92162i	−0.167236	+	0.289661i	0.770211	+	0.637789i	$0.220151\pi$
$572$	−0.700162	−	0.187608i	−0.0292752	−	0.00784428i
$573$	12.9978	+	12.9978i	0.542992	+	0.542992i
$574$	−0.217098	+	0.410730i	−0.00906150	+	0.0171436i
$575$		0			0
$576$	−0.436328	−	0.755743i	−0.0181804	−	0.0314893i
$577$	5.23782	+	19.5478i	0.218053	+	0.813787i	0.985069	+	0.172158i	$0.0550741\pi$
$577$	5.23782	+	19.5478i	0.218053	+	0.813787i	−0.767016	+	0.641628i	$0.778259\pi$
$578$	7.16102	+	26.7253i	0.297859	+	1.11163i
$579$	−6.49330	−	11.2467i	−0.269852	−	0.467398i
$580$		0			0
$581$	−23.2532	+	14.6097i	−0.964705	+	0.606111i
$582$	−0.840462	−	0.840462i	−0.0348383	−	0.0348383i
$583$	−0.392205	−	0.105091i	−0.0162435	−	0.00435242i
$584$	3.89850	−	6.75240i	0.161321	−	0.279416i
$585$		0			0
$586$	−14.7092	+	8.49234i	−0.607630	+	0.350815i
$587$	22.7486	−	22.7486i	0.938935	−	0.938935i	−0.0593051	−	0.998240i	$-0.518888\pi$
$587$	22.7486	−	22.7486i	0.938935	−	0.938935i	0.998240	+	0.0593051i	$0.0188885\pi$
$588$	−8.22121	−	7.07605i	−0.339037	−	0.291812i
$589$		−	22.8910i		−	0.943206i
$590$		0			0
$591$	15.0947	+	8.71492i	0.620913	+	0.358484i
$592$	−8.60391	+	2.30541i	−0.353619	+	0.0947518i
$593$	−0.696488	+	2.59933i	−0.0286013	+	0.106742i	−0.978751	−	0.205053i	$-0.934263\pi$
$593$	−0.696488	+	2.59933i	−0.0286013	+	0.106742i	0.950150	+	0.311794i	$0.100930\pi$
$594$	−0.0941482			−0.00386295
$595$		0			0
$596$	−26.8633			−1.10036
$597$	1.16942	−	4.36433i	0.0478612	−	0.178620i
$598$	−5.60861	+	1.50282i	−0.229353	+	0.0614550i
$599$	14.6440	+	8.45472i	0.598338	+	0.345450i	0.768387	−	0.639985i	$-0.221059\pi$
$599$	14.6440	+	8.45472i	0.598338	+	0.345450i	−0.170050	+	0.985435i	$0.554393\pi$
$600$		0			0
$601$		−	35.5747i		−	1.45112i	−0.688157	−	0.725562i	$-0.741580\pi$
$601$		−	35.5747i		−	1.45112i	0.688157	−	0.725562i	$-0.258420\pi$
$602$	−5.08529	+	1.56838i	−0.207261	+	0.0639226i
$603$	−5.52675	+	5.52675i	−0.225067	+	0.225067i
$604$	23.9152	−	13.8074i	0.973095	−	0.561817i
$605$		0			0
$606$	−2.40154	+	4.15959i	−0.0975560	+	0.168972i
$607$	30.1121	+	8.06852i	1.22221	+	0.327491i	0.811543	−	0.584293i	$-0.198628\pi$
$607$	30.1121	+	8.06852i	1.22221	+	0.327491i	0.410670	+	0.911784i	$0.365295\pi$
$608$	−31.7890	−	31.7890i	−1.28922	−	1.28922i
$609$	13.4600	−	0.503106i	0.545426	−	0.0203869i
$610$		0			0
$611$	2.59345	+	4.49198i	0.104920	+	0.181726i
$612$	3.06033	+	11.4213i	0.123707	+	0.461680i
$613$	6.54182	+	24.4144i	0.264221	+	0.986088i	0.962725	+	0.270481i	$0.0871829\pi$
$613$	6.54182	+	24.4144i	0.264221	+	0.986088i	−0.698504	+	0.715606i	$0.746150\pi$
$614$	5.01514	+	8.68647i	0.202394	+	0.350557i
$615$		0			0
$616$	−0.883558	+	0.0330256i	−0.0355996	+	0.00133064i
$617$	21.4018	+	21.4018i	0.861605	+	0.861605i	0.991525	−	0.129919i	$-0.0414719\pi$
$617$	21.4018	+	21.4018i	0.861605	+	0.861605i	−0.129919	+	0.991525i	$0.541472\pi$
$618$	5.64603	+	1.51285i	0.227117	+	0.0608557i
$619$	11.5675	−	20.0354i	0.464935	−	0.805292i	−0.534263	−	0.845318i	$-0.679411\pi$
$619$	11.5675	−	20.0354i	0.464935	−	0.805292i	0.999199	+	0.0400264i	$0.0127442\pi$
$620$		0			0
$621$	2.24697	−	1.29729i	0.0901679	−	0.0520584i
$622$	7.67839	−	7.67839i	0.307875	−	0.307875i
$623$	12.3489	−	3.80860i	0.494749	−	0.152588i
$624$		−	5.00303i		−	0.200282i
$625$		0			0
$626$	−6.52860	−	3.76929i	−0.260935	−	0.150651i
$627$	−1.05550	+	0.282820i	−0.0421525	+	0.0112947i
$628$	7.22069	−	26.9480i	0.288137	−	1.07534i
$629$	−45.3016			−1.80629
$630$		0			0
$631$	4.26570			0.169815			0.0849075	−	0.996389i	$-0.472941\pi$
$631$	4.26570			0.169815			0.0849075	+	0.996389i	$0.472941\pi$
$632$	0.0809450	−	0.302091i	0.00321982	−	0.0120165i
$633$	−2.99433	+	0.802328i	−0.119014	+	0.0318897i
$634$	−7.54691	−	4.35721i	−0.299726	−	0.173047i
$635$		0			0
$636$		−	4.48517i		−	0.177849i
$637$	7.70757	+	22.0325i	0.305385	+	0.872961i
$638$	0.338919	−	0.338919i	0.0134179	−	0.0134179i
$639$	3.08545	−	1.78139i	0.122059	−	0.0704706i
$640$		0			0
$641$	−18.6834	+	32.3607i	−0.737952	+	1.27817i	0.215464	+	0.976512i	$0.430874\pi$
$641$	−18.6834	+	32.3607i	−0.737952	+	1.27817i	−0.953416	+	0.301658i	$0.902460\pi$
$642$	1.54864	+	0.414957i	0.0611200	+	0.0163771i
$643$	25.7896	+	25.7896i	1.01704	+	1.01704i	0.999852	+	0.0171915i	$0.00547251\pi$
$643$	25.7896	+	25.7896i	1.01704	+	1.01704i	0.0171915	+	0.999852i	$0.494527\pi$
$644$	9.00706	−	5.65902i	0.354928	−	0.222997i
$645$		0			0
$646$	−19.9455	−	34.5467i	−0.784747	−	1.35922i
$647$	0.309677	+	1.15573i	0.0121746	+	0.0454364i	0.971746	−	0.236029i	$-0.0758461\pi$
$647$	0.309677	+	1.15573i	0.0121746	+	0.0454364i	−0.959571	+	0.281466i	$0.909179\pi$
$648$	−0.616569	−	2.30107i	−0.0242211	−	0.0903944i
$649$	0.613220	+	1.06213i	0.0240710	+	0.0416922i
$650$		0			0
$651$	3.63331	−	6.87391i	0.142401	−	0.269410i
$652$	11.9169	+	11.9169i	0.466704	+	0.466704i
$653$	−14.2472	−	3.81751i	−0.557534	−	0.149391i	−0.0309610	−	0.999521i	$-0.509857\pi$
$653$	−14.2472	−	3.81751i	−0.557534	−	0.149391i	−0.526573	+	0.850130i	$0.676523\pi$
$654$	4.72525	−	8.18437i	0.184772	−	0.320034i
$655$		0			0
$656$	0.339960	−	0.196276i	0.0132732	−	0.00766328i
$657$	2.31434	−	2.31434i	0.0902910	−	0.0902910i
$658$	2.02464	+	1.87874i	0.0789286	+	0.0732408i
$659$		−	34.8964i		−	1.35937i	−0.733504	−	0.679685i	$-0.762116\pi$
$659$		−	34.8964i		−	1.35937i	0.733504	−	0.679685i	$-0.237884\pi$
$660$		0			0
$661$	−11.2246	−	6.48055i	−0.436588	−	0.252064i	0.265561	−	0.964094i	$-0.414443\pi$
$661$	−11.2246	−	6.48055i	−0.436588	−	0.252064i	−0.702149	+	0.712030i	$0.747776\pi$
$662$	−14.6736	+	3.93177i	−0.570305	+	0.152813i
$663$	6.58553	−	24.5775i	0.255761	−	0.954513i
$664$	−24.7267			−0.959582
$665$		0			0
$666$	3.98440			0.154393
$667$	−3.41871	+	12.7588i	−0.132373	+	0.494022i
$668$	24.0420	−	6.44204i	0.930214	−	0.249250i
$669$	1.86705	+	1.07794i	0.0721841	+	0.0416755i
$670$		0			0
$671$			0.772155i			0.0298087i
$672$	−4.50026	−	14.5915i	−0.173601	−	0.562881i
$673$	−10.1193	+	10.1193i	−0.390070	+	0.390070i	−0.874713	−	0.484642i	$-0.838950\pi$
$673$	−10.1193	+	10.1193i	−0.390070	+	0.390070i	0.484642	+	0.874713i	$0.338950\pi$
$674$	−12.1920	+	7.03907i	−0.469619	+	0.271135i
$675$		0			0
$676$	1.45724	−	2.52402i	0.0560478	−	0.0970776i
$677$	−22.6039	−	6.05670i	−0.868739	−	0.232778i	−0.203196	−	0.979138i	$-0.565133\pi$
$677$	−22.6039	−	6.05670i	−0.868739	−	0.232778i	−0.665542	+	0.746360i	$0.731800\pi$
$678$	2.86876	+	2.86876i	0.110174	+	0.110174i
$679$	−2.49278	−	3.96759i	−0.0956642	−	0.152262i
$680$		0			0
$681$	−1.93752	−	3.35588i	−0.0742459	−	0.128598i
$682$	−0.0716083	−	0.267246i	−0.00274202	−	0.0102334i
$683$	−6.44776	−	24.0634i	−0.246717	−	0.920759i	−0.972513	−	0.232849i	$-0.925195\pi$
$683$	−6.44776	−	24.0634i	−0.246717	−	0.920759i	0.725796	−	0.687910i	$-0.241472\pi$
$684$	−6.03523	−	10.4533i	−0.230763	−	0.399693i
$685$		0			0
$686$	7.37973	+	10.0017i	0.281760	+	0.381865i
$687$	−8.28559	−	8.28559i	−0.316115	−	0.316115i
$688$	4.34340	+	1.16381i	0.165591	+	0.0443699i
$689$	−4.82582	+	8.35857i	−0.183849	+	0.318436i
$690$		0			0
$691$	16.3532	−	9.44154i	0.622106	−	0.359173i	−0.155582	−	0.987823i	$-0.549725\pi$
$691$	16.3532	−	9.44154i	0.622106	−	0.359173i	0.777689	+	0.628650i	$0.216392\pi$
$692$	2.15327	−	2.15327i	0.0818552	−	0.0818552i
$693$	−0.361844	−	0.0826036i	−0.0137453	−	0.00313785i
$694$		−	0.798970i		−	0.0303285i
$695$		0			0
$696$	10.5030	+	6.06393i	0.398116	+	0.229852i
$697$	1.92842	−	0.516719i	0.0730442	−	0.0195721i
$698$	5.24073	−	19.5587i	0.198365	−	0.740307i
$699$	−5.93884			−0.224628
$700$		0			0
$701$	−16.3668			−0.618165			−0.309082	−	0.951035i	$-0.600022\pi$
$701$	−16.3668			−0.618165			−0.309082	+	0.951035i	$0.600022\pi$
$702$	−0.579216	+	2.16166i	−0.0218611	+	0.0815868i
$703$	44.6692	−	11.9691i	1.68473	−	0.451423i
$704$	−0.106018	−	0.0612093i	−0.00399569	−	0.00230691i
$705$		0			0
$706$			14.5855i			0.548933i
$707$	−12.8795	+	13.8797i	−0.484383	+	0.522000i
$708$	−9.57948	+	9.57948i	−0.360019	+	0.360019i
$709$	11.8938	−	6.86691i	0.446683	−	0.257892i	−0.259745	−	0.965677i	$-0.583639\pi$
$709$	11.8938	−	6.86691i	0.446683	−	0.257892i	0.706428	+	0.707785i	$0.250305\pi$
$710$		0			0
$711$	0.0656415	−	0.113694i	0.00246175	−	0.00426387i
$712$	11.2393	+	3.01157i	0.421211	+	0.112863i
$713$	5.39147	+	5.39147i	0.201912	+	0.201912i
$714$	−0.506090	−	13.5398i	−0.0189399	−	0.506714i
$715$		0			0
$716$	−2.44951	−	4.24267i	−0.0915424	−	0.158556i
$717$	−7.20825	−	26.9016i	−0.269197	−	1.00466i
$718$	−5.85994	−	21.8696i	−0.218691	−	0.816166i
$719$	13.8487	+	23.9867i	0.516469	+	0.894551i	0.999817	+	0.0191228i	$0.00608736\pi$
$719$	13.8487	+	23.9867i	0.516469	+	0.894551i	−0.483348	+	0.875428i	$0.660579\pi$
$720$		0			0
$721$	20.3723	+	10.7681i	0.758704	+	0.401025i
$722$	19.7780	+	19.7780i	0.736060	+	0.736060i
$723$	−14.8393	−	3.97619i	−0.551881	−	0.147876i
$724$	−6.75050	+	11.6922i	−0.250880	+	0.434537i
$725$		0			0
$726$	6.38196	−	3.68462i	0.236857	−	0.136749i
$727$	17.2596	−	17.2596i	0.640123	−	0.640123i	−0.310463	−	0.950586i	$-0.600484\pi$
$727$	17.2596	−	17.2596i	0.640123	−	0.640123i	0.950586	+	0.310463i	$0.100484\pi$
$728$	−4.67753	+	20.4899i	−0.173361	+	0.759405i
$729$		−	1.00000i		−	0.0370370i
$730$		0			0
$731$	19.8051	+	11.4345i	0.732520	+	0.422921i
$732$	−8.23870	+	2.20755i	−0.304511	+	0.0815935i
$733$	0.849397	−	3.16999i	0.0313732	−	0.117086i	−0.948463	−	0.316886i	$-0.897363\pi$
$733$	0.849397	−	3.16999i	0.0313732	−	0.117086i	0.979837	+	0.199800i	$0.0640293\pi$
$734$	11.0414			0.407545
$735$		0			0
$736$	14.9744			0.551964
$737$	−0.283782	+	1.05909i	−0.0104532	+	0.0390120i
$738$	−0.169610	+	0.0454469i	−0.00624344	+	0.00167292i
$739$	−20.6790	−	11.9390i	−0.760689	−	0.439184i	0.0688540	−	0.997627i	$-0.478066\pi$
$739$	−20.6790	−	11.9390i	−0.760689	−	0.439184i	−0.829543	+	0.558443i	$0.811399\pi$
$740$		0			0
$741$			25.9744i			0.954194i
$742$	−1.14385	+	5.01061i	−0.0419919	+	0.183945i
$743$	−15.0559	+	15.0559i	−0.552348	+	0.552348i	−0.927118	−	0.374770i	$-0.877722\pi$
$743$	−15.0559	+	15.0559i	−0.552348	+	0.552348i	0.374770	+	0.927118i	$0.377722\pi$
$744$	6.06277	−	3.50034i	0.222272	−	0.128329i
$745$		0			0
$746$	4.06159	−	7.03488i	0.148705	−	0.257565i
$747$	−10.0259	−	2.68644i	−0.366829	−	0.0982916i
$748$	1.17290	+	1.17290i	0.0428855	+	0.0428855i
$749$	5.58789	+	2.95357i	0.204177	+	0.107921i
$750$		0			0
$751$	−10.1965	−	17.6608i	−0.372074	−	0.644451i	0.617810	−	0.786327i	$-0.288020\pi$
$751$	−10.1965	−	17.6608i	−0.372074	−	0.644451i	−0.989884	+	0.141876i	$0.954687\pi$
$752$	−0.604038	−	2.25430i	−0.0220270	−	0.0822059i
$753$	−4.74363	−	17.7035i	−0.172868	−	0.645150i
$754$	−5.69657	−	9.86674i	−0.207457	−	0.359326i
$755$		0			0
$756$	−0.153135	−	4.09695i	−0.00556948	−	0.149004i
$757$	30.2269	+	30.2269i	1.09862	+	1.09862i	0.994573	+	0.104043i	$0.0331780\pi$
$757$	30.2269	+	30.2269i	1.09862	+	1.09862i	0.104043	+	0.994573i	$0.466822\pi$
$758$	12.9540	+	3.47102i	0.470511	+	0.126073i
$759$	0.181987	−	0.315211i	0.00660572	−	0.0114414i
$760$		0			0
$761$	9.10874	−	5.25893i	0.330192	−	0.190636i	−0.325735	−	0.945461i	$-0.605612\pi$
$761$	9.10874	−	5.25893i	0.330192	−	0.190636i	0.655926	+	0.754825i	$0.272278\pi$
$762$	0.861833	−	0.861833i	0.0312209	−	0.0312209i
$763$	25.3415	−	27.3095i	0.917425	−	0.988671i
$764$			28.4840i			1.03051i
$765$		0			0
$766$	15.3725	+	8.87532i	0.555431	+	0.320678i
$767$	28.1593	−	7.54527i	1.01677	−	0.272444i
$768$	2.35500	−	8.78899i	0.0849788	−	0.317145i
$769$	48.0351			1.73219			0.866095	−	0.499879i	$-0.166622\pi$
$769$	48.0351			1.73219			0.866095	+	0.499879i	$0.166622\pi$
$770$		0			0
$771$	−8.82350			−0.317771
$772$	5.20842	−	19.4381i	0.187455	−	0.699592i
$773$	−36.4607	+	9.76962i	−1.31140	+	0.351389i	−0.845750	−	0.533579i	$-0.820847\pi$
$773$	−36.4607	+	9.76962i	−1.31140	+	0.351389i	−0.465651	+	0.884968i	$0.654180\pi$
$774$	−1.74192	−	1.00570i	−0.0626120	−	0.0361490i
$775$		0			0
$776$		−	4.21901i		−	0.151453i
$777$	15.3134	+	3.49583i	0.549367	+	0.125412i
$778$	−5.88524	+	5.88524i	−0.210996	+	0.210996i
$779$	−1.76498	+	1.01901i	−0.0632370	+	0.0365099i
$780$		0			0
$781$	0.249898	−	0.432836i	0.00894205	−	0.0154881i
$782$	12.8344	+	3.43898i	0.458959	+	0.122978i
$783$	3.59984	+	3.59984i	0.128648	+	0.128648i
$784$	−0.784032	−	10.4733i	−0.0280011	−	0.374045i
$785$		0			0
$786$	5.78324	+	10.0169i	0.206281	+	0.357290i
$787$	−10.6558	−	39.7678i	−0.379837	−	1.41757i	−0.846148	−	0.532949i	$-0.821084\pi$
$787$	−10.6558	−	39.7678i	−0.379837	−	1.41757i	0.466311	−	0.884621i	$-0.345583\pi$
$788$	6.99043	+	26.0887i	0.249024	+	0.929370i
$789$	−0.305499	−	0.529141i	−0.0108761	−	0.0188379i
$790$		0			0
$791$	8.50866	+	13.5426i	0.302533	+	0.481521i
$792$	−0.236306	−	0.236306i	−0.00839676	−	0.00839676i
$793$	17.7289	+	4.75043i	0.629570	+	0.168693i
$794$	−3.23733	+	5.60722i	−0.114889	+	0.198993i
$795$		0			0
$796$	6.06344	−	3.50073i	0.214913	−	0.124080i
$797$	10.2622	−	10.2622i	0.363506	−	0.363506i	−0.501596	−	0.865102i	$-0.667254\pi$
$797$	10.2622	−	10.2622i	0.363506	−	0.363506i	0.865102	+	0.501596i	$0.167254\pi$
$798$	4.07636	+	13.2171i	0.144302	+	0.467880i
$799$		−	11.8694i		−	0.419910i
$800$		0			0
$801$	4.23001	+	2.44220i	0.149460	+	0.0862908i
$802$	−23.0808	+	6.18448i	−0.815012	+	0.218382i
$803$	0.118834	−	0.443496i	0.00419358	−	0.0156506i
$804$	−12.1115			−0.427141
$805$		0			0
$806$	−6.57657			−0.231650
$807$	1.54281	−	5.75784i	0.0543094	−	0.202685i
$808$	−16.4680	+	4.41259i	−0.579342	+	0.155234i
$809$	−17.4947	−	10.1005i	−0.615080	−	0.355116i	0.159871	−	0.987138i	$-0.448892\pi$
$809$	−17.4947	−	10.1005i	−0.615080	−	0.355116i	−0.774951	+	0.632022i	$0.782225\pi$
$810$		0			0
$811$			34.3867i			1.20748i	0.797181	+	0.603740i	$0.206324\pi$
$811$			34.3867i			1.20748i	−0.797181	+	0.603740i	$0.793676\pi$
$812$	15.2996	+	14.1971i	0.536912	+	0.498221i
$813$	8.60809	−	8.60809i	0.301899	−	0.301899i
$814$	0.484059	−	0.279471i	0.0169663	−	0.00979547i
$815$		0			0
$816$	−5.72434	+	9.91484i	−0.200392	+	0.347089i
$817$	−22.5498	−	6.04220i	−0.788917	−	0.211390i
$818$	−0.851469	−	0.851469i	−0.0297709	−	0.0297709i
$819$	−4.12273	+	7.79983i	−0.144060	+	0.272548i
$820$		0			0
$821$	−20.1949	−	34.9787i	−0.704808	−	1.22076i	−0.966761	−	0.255683i	$-0.917700\pi$
$821$	−20.1949	−	34.9787i	−0.704808	−	1.22076i	0.261952	−	0.965081i	$-0.415634\pi$
$822$	1.99240	+	7.43575i	0.0694930	+	0.259352i
$823$	−5.96476	−	22.2608i	−0.207918	−	0.775962i	−0.988540	−	0.150958i	$-0.951764\pi$
$823$	−5.96476	−	22.2608i	−0.207918	−	0.775962i	0.780622	−	0.625004i	$-0.214903\pi$
$824$	10.3740	+	17.9683i	0.361396	+	0.625956i
$825$		0			0
$826$	13.1447	−	8.25867i	0.457364	−	0.287356i
$827$	−23.8349	−	23.8349i	−0.828821	−	0.828821i	0.158533	−	0.987354i	$-0.449324\pi$
$827$	−23.8349	−	23.8349i	−0.828821	−	0.828821i	−0.987354	+	0.158533i	$0.949324\pi$
$828$	3.88352	+	1.04059i	0.134962	+	0.0361628i
$829$	8.84585	−	15.3215i	0.307229	−	0.532136i	−0.670526	−	0.741886i	$-0.733932\pi$
$829$	8.84585	−	15.3215i	0.307229	−	0.532136i	0.977755	+	0.209750i	$0.0672649\pi$
$830$		0			0
$831$	21.8713	−	12.6274i	0.758707	−	0.438040i
$832$	−2.05762	+	2.05762i	−0.0713351	+	0.0713351i
$833$	9.93444	−	52.4822i	0.344208	−	1.81840i
$834$			4.75035i			0.164491i
$835$		0			0
$836$	−1.46642	−	0.846638i	−0.0507172	−	0.0292816i
$837$	2.83856	−	0.760591i	0.0981151	−	0.0262899i
$838$	6.48695	−	24.2096i	0.224088	−	0.836307i
$839$	−13.3297			−0.460193			−0.230096	−	0.973168i	$-0.573904\pi$
$839$	−13.3297			−0.460193			−0.230096	+	0.973168i	$0.573904\pi$
$840$		0			0
$841$	3.08226			0.106285
$842$	−0.165261	+	0.616763i	−0.00569527	+	0.0212551i
$843$	28.0120	−	7.50580i	0.964786	−	0.258514i
$844$	−4.16007	−	2.40182i	−0.143195	−	0.0826740i
$845$		0			0
$846$			1.04395i			0.0358917i
$847$	27.7609	−	8.56190i	0.953875	−	0.294190i
$848$	3.07077	−	3.07077i	0.105451	−	0.105451i
$849$	15.8276	−	9.13806i	0.543201	−	0.313618i
$850$		0			0
$851$	−7.70180	+	13.3399i	−0.264014	+	0.457286i
$852$	5.33270	+	1.42889i	0.182695	+	0.0489530i
$853$	−16.2606	−	16.2606i	−0.556753	−	0.556753i	0.371628	−	0.928382i	$-0.378800\pi$
$853$	−16.2606	−	16.2606i	−0.556753	−	0.556753i	−0.928382	+	0.371628i	$0.878800\pi$
$854$	9.76685	−	0.365065i	0.334215	−	0.0124923i
$855$		0			0
$856$	2.84547	+	4.92850i	0.0972563	+	0.168453i
$857$	11.3108	+	42.2126i	0.386371	+	1.44196i	0.835995	+	0.548738i	$0.184891\pi$
$857$	11.3108	+	42.2126i	0.386371	+	1.44196i	−0.449624	+	0.893218i	$0.648442\pi$
$858$	0.0812540	+	0.303244i	0.00277397	+	0.0103526i
$859$	0.0254784	+	0.0441300i	0.000869313	+	0.00150570i	0.866460	−	0.499247i	$-0.166390\pi$
$859$	0.0254784	+	0.0441300i	0.000869313	+	0.00150570i	−0.865590	+	0.500753i	$0.833057\pi$
$860$		0			0
$861$	−0.691744	+	0.0258560i	−0.0235746	+	0.000881169i
$862$	0.736261	+	0.736261i	0.0250772	+	0.0250772i
$863$	−35.8249	−	9.59926i	−1.21950	−	0.326763i	−0.409014	−	0.912528i	$-0.634127\pi$
$863$	−35.8249	−	9.59926i	−1.21950	−	0.326763i	−0.810481	+	0.585765i	$0.800794\pi$
$864$	2.88571	−	4.99820i	0.0981739	−	0.170042i
$865$		0			0
$866$	7.58083	−	4.37680i	0.257607	−	0.148730i
$867$	−29.1511	+	29.1511i	−0.990025	+	0.990025i
$868$	11.5130	−	3.55078i	0.390776	−	0.120521i
$869$		−	0.0184167i		−	0.000624745i
$870$		0			0
$871$	22.5710	+	13.0314i	0.764791	+	0.441552i
$872$	32.4023	−	8.68216i	1.09728	−	0.294015i
$873$	0.458375	−	1.71068i	0.0155136	−	0.0578977i
$874$	−13.5639			−0.458806
$875$		0			0
$876$	5.07174			0.171358
$877$	−5.05561	+	18.8678i	−0.170716	+	0.637120i	0.826526	+	0.562899i	$0.190314\pi$
$877$	−5.05561	+	18.8678i	−0.170716	+	0.637120i	−0.997242	+	0.0742215i	$0.976353\pi$
$878$	−8.83849	+	2.36827i	−0.298285	+	0.0799251i
$879$	−21.9169	−	12.6537i	−0.739240	−	0.426800i
$880$		0			0
$881$		−	49.4902i		−	1.66737i	−0.552244	−	0.833683i	$-0.686228\pi$
$881$		−	49.4902i		−	1.66737i	0.552244	−	0.833683i	$-0.313772\pi$
$882$	−0.873763	+	4.61596i	−0.0294211	+	0.155427i
$883$	−8.41740	+	8.41740i	−0.283268	+	0.283268i	−0.834411	−	0.551143i	$-0.814192\pi$
$883$	−8.41740	+	8.41740i	−0.283268	+	0.283268i	0.551143	+	0.834411i	$0.314192\pi$
$884$	34.1460	−	19.7142i	1.14845	−	0.663060i
$885$		0			0
$886$	−2.26784	+	3.92801i	−0.0761895	+	0.131964i
$887$	38.4239	+	10.2956i	1.29015	+	0.345694i	0.837716	−	0.546106i	$-0.183890\pi$
$887$	38.4239	+	10.2956i	1.29015	+	0.345694i	0.452431	+	0.891800i	$0.350557\pi$
$888$	10.0006	+	10.0006i	0.335598	+	0.335598i
$889$	4.06848	−	2.55617i	0.136452	−	0.0857312i
$890$		0			0
$891$	−0.0701413	−	0.121488i	−0.00234982	−	0.00407001i
$892$	0.864639	+	3.22688i	0.0289503	+	0.108044i
$893$	3.13600	+	11.7037i	0.104942	+	0.391650i
$894$	5.81732	+	10.0759i	0.194560	+	0.336988i
$895$		0			0
$896$	13.5471	−	25.6299i	0.452577	−	0.856236i
$897$	−6.11770	−	6.11770i	−0.204264	−	0.204264i
$898$	−4.83390	−	1.29524i	−0.161309	−	0.0432227i
$899$	−7.48038	+	12.9564i	−0.249485	+	0.432120i
$900$		0			0
$901$	19.1273	−	11.0432i	0.637223	−	0.367901i
$902$	−0.0174179	+	0.0174179i	−0.000579954	+	0.000579954i
$903$	−5.81242	−	5.39356i	−0.193425	−	0.179487i
$904$			14.4008i			0.478964i
$905$		0			0
$906$	−10.3578	−	5.98008i	−0.344115	−	0.198675i
$907$	−19.8798	+	5.32678i	−0.660098	+	0.176873i	−0.573290	−	0.819352i	$-0.694333\pi$
$907$	−19.8798	+	5.32678i	−0.660098	+	0.176873i	−0.0868077	+	0.996225i	$0.527667\pi$
$908$	1.55413	−	5.80009i	0.0515756	−	0.192483i
$909$	−7.15669			−0.237372
$910$		0			0
$911$	−44.1582			−1.46303			−0.731513	−	0.681827i	$-0.761186\pi$
$911$	−44.1582			−1.46303			−0.731513	+	0.681827i	$0.761186\pi$
$912$	3.02484	−	11.2889i	0.100163	−	0.373812i
$913$	−1.40646	+	0.376861i	−0.0465471	+	0.0124723i
$914$	−22.1825	−	12.8071i	−0.733733	−	0.423621i
$915$		0			0
$916$		−	18.1574i		−	0.599936i
$917$	13.4384	+	43.5724i	0.443775	+	1.43889i
$918$	3.62119	−	3.62119i	0.119517	−	0.119517i
$919$	−9.87855	+	5.70339i	−0.325863	+	0.188137i	−0.654003	−	0.756492i	$-0.726912\pi$
$919$	−9.87855	+	5.70339i	−0.325863	+	0.188137i	0.328140	+	0.944629i	$0.393578\pi$
$920$		0			0
$921$	−7.47265	+	12.9430i	−0.246232	+	0.426487i
$922$	5.09582	+	1.36542i	0.167822	+	0.0449678i
$923$	−8.40059	−	8.40059i	−0.276509	−	0.276509i
$924$	−0.305969	−	0.486990i	−0.0100657	−	0.0160208i
$925$		0			0
$926$	4.98199	+	8.62907i	0.163718	+	0.283569i
$927$	2.25417	+	8.41269i	0.0740368	+	0.276309i
$928$	7.60462	+	28.3808i	0.249634	+	0.931646i
$929$	9.30040	+	16.1088i	0.305136	+	0.528511i	0.977292	−	0.211899i	$-0.0679647\pi$
$929$	9.30040	+	16.1088i	0.305136	+	0.528511i	−0.672155	+	0.740410i	$0.734631\pi$
$930$		0			0
$931$	4.07049	+	54.3743i	0.133405	+	1.78205i
$932$	−6.50731	−	6.50731i	−0.213154	−	0.213154i
$933$	15.6286	+	4.18768i	0.511658	+	0.137098i
$934$	4.53529	−	7.85536i	0.148399	−	0.257035i
$935$		0			0
$936$	−6.87943	+	3.97184i	−0.224861	+	0.129824i
$937$	−11.7066	+	11.7066i	−0.382439	+	0.382439i	−0.871980	−	0.489541i	$-0.837164\pi$
$937$	−11.7066	+	11.7066i	−0.382439	+	0.382439i	0.489541	+	0.871980i	$0.337164\pi$
$938$	13.5304	+	3.08879i	0.441783	+	0.100852i
$939$		−	11.2326i		−	0.366563i
$940$		0			0
$941$	−23.0147	−	13.2875i	−0.750258	−	0.433162i	0.0755293	−	0.997144i	$-0.475935\pi$
$941$	−23.0147	−	13.2875i	−0.750258	−	0.433162i	−0.825787	+	0.563982i	$0.809269\pi$
$942$	−11.6713	+	3.12732i	−0.380272	+	0.101894i
$943$	0.175696	−	0.655708i	0.00572146	−	0.0213528i
$944$	−13.1171			−0.426927
$945$		0			0
$946$	−0.282164			−0.00917394
$947$	2.18054	−	8.13788i	0.0708580	−	0.264446i	−0.921404	−	0.388606i	$-0.872957\pi$
$947$	2.18054	−	8.13788i	0.0708580	−	0.264446i	0.992262	+	0.124160i	$0.0396236\pi$
$948$	0.196502	−	0.0526525i	0.00638208	−	0.00171007i
$949$	−9.45168	−	5.45693i	−0.306815	−	0.177140i
$950$		0			0
$951$		−	12.9847i		−	0.421056i
$952$	32.7137	−	35.2542i	1.06026	−	1.14260i
$953$	18.8223	−	18.8223i	0.609715	−	0.609715i	−0.333156	−	0.942872i	$-0.608114\pi$
$953$	18.8223	−	18.8223i	0.609715	−	0.609715i	0.942872	+	0.333156i	$0.108114\pi$
$954$	−1.68230	+	0.971277i	−0.0544665	+	0.0314463i
$955$		0			0
$956$	21.5784	−	37.3748i	0.697894	−	1.20879i
$957$	0.689837	+	0.184841i	0.0222993	+	0.00597507i
$958$	12.7960	+	12.7960i	0.413421	+	0.413421i
$959$	1.13353	+	30.3262i	0.0366037	+	0.979285i
$960$		0			0
$961$	−11.1820	−	19.3678i	−0.360711	−	0.624769i
$962$	−3.43871	−	12.8335i	−0.110869	−	0.413767i
$963$	0.618295	+	2.30751i	0.0199243	+	0.0743584i
$964$	−11.9030	−	20.6165i	−0.383369	−	0.664014i
$965$		0			0
$966$	−4.07309	−	2.15290i	−0.131050	−	0.0692683i
$967$	−17.0481	−	17.0481i	−0.548230	−	0.548230i	0.377699	−	0.925929i	$-0.376715\pi$
$967$	−17.0481	−	17.0481i	−0.548230	−	0.548230i	−0.925929	+	0.377699i	$0.876715\pi$
$968$	25.2664	+	6.77012i	0.812094	+	0.217600i
$969$	29.7192	−	51.4752i	0.954719	−	1.65362i
$970$		0			0
$971$	−43.2583	+	24.9752i	−1.38822	+	0.801492i	−0.993115	−	0.117143i	$-0.962627\pi$
$971$	−43.2583	+	24.9752i	−1.38822	+	0.801492i	−0.395109	+	0.918634i	$0.629293\pi$
$972$	1.09572	−	1.09572i	0.0351452	−	0.0351452i
$973$	−4.16785	+	18.2573i	−0.133615	+	0.585301i
$974$		−	1.29950i		−	0.0416388i
$975$		0			0
$976$	−7.15201	−	4.12922i	−0.228930	−	0.132173i
$977$	−46.6738	+	12.5062i	−1.49323	+	0.400109i	−0.910825	−	0.412792i	$-0.864554\pi$
$977$	−46.6738	+	12.5062i	−1.49323	+	0.400109i	−0.582402	+	0.812901i	$0.697887\pi$
$978$	1.88917	−	7.05046i	0.0604089	−	0.225449i
$979$	0.685196			0.0218990
$980$		0			0
$981$	14.0814			0.449585
$982$	4.08327	−	15.2390i	0.130302	−	0.486295i
$983$	10.5089	−	2.81584i	0.335180	−	0.0898113i	−0.0873035	−	0.996182i	$-0.527825\pi$
$983$	10.5089	−	2.81584i	0.335180	−	0.0898113i	0.422484	+	0.906370i	$0.361158\pi$
$984$	−0.539779	−	0.311641i	−0.0172075	−	0.00993477i
$985$		0			0
$986$			26.0714i			0.830284i
$987$	−0.915938	+	4.01226i	−0.0291546	+	0.127712i
$988$	−28.4607	+	28.4607i	−0.905455	+	0.905455i
$989$	6.73421	−	3.88800i	0.214135	−	0.123631i
$990$		0			0
$991$	8.46610	−	14.6637i	0.268935	−	0.465809i	−0.699652	−	0.714483i	$-0.746662\pi$
$991$	8.46610	−	14.6637i	0.268935	−	0.465809i	0.968587	+	0.248675i	$0.0799951\pi$
$992$	16.3825	+	4.38969i	0.520146	+	0.139373i
$993$	−16.0055	−	16.0055i	−0.507919	−	0.507919i
$994$	−5.59301	−	2.95627i	−0.177400	−	0.0937673i
$995$		0			0
$996$	−8.04202	−	13.9292i	−0.254821	−	0.441363i
$997$	−2.43829	−	9.09981i	−0.0772213	−	0.288194i	0.916507	−	0.400020i	$-0.130997\pi$
$997$	−2.43829	−	9.09981i	−0.0772213	−	0.288194i	−0.993728	+	0.111826i	$0.964330\pi$
$998$	−1.21943	−	4.55097i	−0.0386004	−	0.144059i
$999$	2.96842	+	5.14145i	0.0939166	+	0.162668i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	525.2.bc.e.157.5		32
5.2	odd	4		105.2.u.a.73.5	yes	32
5.3	odd	4	inner	525.2.bc.e.493.4		32
5.4	even	2		105.2.u.a.52.4	✓	32
7.5	odd	6	inner	525.2.bc.e.82.4		32
15.2	even	4		315.2.bz.d.73.4		32
15.14	odd	2		315.2.bz.d.262.5		32
35.2	odd	12		735.2.v.b.313.4		32
35.4	even	6		735.2.m.c.97.8		32
35.9	even	6		735.2.v.b.607.5		32
35.12	even	12		105.2.u.a.103.4	yes	32
35.17	even	12		735.2.m.c.538.8		32
35.19	odd	6		105.2.u.a.82.5	yes	32
35.24	odd	6		735.2.m.c.97.7		32
35.27	even	4		735.2.v.b.178.5		32
35.32	odd	12		735.2.m.c.538.7		32
35.33	even	12	inner	525.2.bc.e.418.5		32
35.34	odd	2		735.2.v.b.472.4		32
105.47	odd	12		315.2.bz.d.208.5		32
105.89	even	6		315.2.bz.d.82.4		32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
105.2.u.a.52.4	✓	32	5.4	even	2
105.2.u.a.73.5	yes	32	5.2	odd	4
105.2.u.a.82.5	yes	32	35.19	odd	6
105.2.u.a.103.4	yes	32	35.12	even	12
315.2.bz.d.73.4		32	15.2	even	4
315.2.bz.d.82.4		32	105.89	even	6
315.2.bz.d.208.5		32	105.47	odd	12
315.2.bz.d.262.5		32	15.14	odd	2
525.2.bc.e.82.4		32	7.5	odd	6	inner
525.2.bc.e.157.5		32	1.1	even	1	trivial
525.2.bc.e.418.5		32	35.33	even	12	inner
525.2.bc.e.493.4		32	5.3	odd	4	inner
735.2.m.c.97.7		32	35.24	odd	6
735.2.m.c.97.8		32	35.4	even	6
735.2.m.c.538.7		32	35.32	odd	12
735.2.m.c.538.8		32	35.17	even	12
735.2.v.b.178.5		32	35.27	even	4
735.2.v.b.313.4		32	35.2	odd	12
735.2.v.b.472.4		32	35.34	odd	2
735.2.v.b.607.5		32	35.9	even	6

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:	\( N \)	\(=\)	\( 525 = 3 \cdot 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	525.bc (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.173702 - 0.648264i) q^{2} +(0.965926 - 0.258819i) q^{3} +(1.34198 + 0.774791i) q^{4} -0.671132i q^{6} +(0.588837 - 2.57939i) q^{7} +(1.68450 - 1.68450i) q^{8} +(0.866025 - 0.500000i) q^{9} +O(q^{10})\)	\(q+(0.173702 - 0.648264i) q^{2} +(0.965926 - 0.258819i) q^{3} +(1.34198 + 0.774791i) q^{4} -0.671132i q^{6} +(0.588837 - 2.57939i) q^{7} +(1.68450 - 1.68450i) q^{8} +(0.866025 - 0.500000i) q^{9} +(0.0701413 - 0.121488i) q^{11} +(1.49678 + 0.401061i) q^{12} +(-2.35788 - 2.35788i) q^{13} +(-1.56985 - 0.829767i) q^{14} +(0.750183 + 1.29935i) q^{16} +(1.97494 + 7.37059i) q^{17} +(-0.173702 - 0.648264i) q^{18} +(-3.89475 - 6.74590i) q^{19} +(-0.0988237 - 2.64391i) q^{21} +(-0.0665729 - 0.0665729i) q^{22} +(2.50617 + 0.671527i) q^{23} +(1.19112 - 2.06308i) q^{24} +(-1.93810 + 1.11896i) q^{26} +(0.707107 - 0.707107i) q^{27} +(2.78870 - 3.00526i) q^{28} +5.09095i q^{29} +(2.54499 + 1.46935i) q^{31} +(5.57476 - 1.49375i) q^{32} +(0.0363078 - 0.135503i) q^{33} +5.12114 q^{34} +1.54958 q^{36} +(-1.53657 + 5.73455i) q^{37} +(-5.04965 + 1.35305i) q^{38} +(-2.88780 - 1.66727i) q^{39} -0.261637i q^{41} +(-1.73111 - 0.395187i) q^{42} +(2.11921 - 2.11921i) q^{43} +(0.188256 - 0.108690i) q^{44} +(0.870653 - 1.50802i) q^{46} +(-1.50250 - 0.402594i) q^{47} +(1.06092 + 1.06092i) q^{48} +(-6.30654 - 3.03768i) q^{49} +(3.81530 + 6.60829i) q^{51} +(-1.33736 - 4.99108i) q^{52} +(-0.749137 - 2.79582i) q^{53} +(-0.335566 - 0.581218i) q^{54} +(-3.35309 - 5.33688i) q^{56} +(-5.50801 - 5.50801i) q^{57} +(3.30028 + 0.884307i) q^{58} +(-4.37132 + 7.57134i) q^{59} +(-4.76685 + 2.75214i) q^{61} +(1.39459 - 1.39459i) q^{62} +(-0.779749 - 2.52824i) q^{63} -0.872657i q^{64} +(-0.0815348 - 0.0470741i) q^{66} +(-7.54968 + 2.02293i) q^{67} +(-3.06033 + 11.4213i) q^{68} +2.59458 q^{69} +3.56278 q^{71} +(0.616569 - 2.30107i) q^{72} +(3.16145 - 0.847107i) q^{73} +(3.45060 + 1.99220i) q^{74} -12.0705i q^{76} +(-0.272064 - 0.252459i) q^{77} +(-1.58245 + 1.58245i) q^{78} +(0.113694 - 0.0656415i) q^{79} +(0.500000 - 0.866025i) q^{81} +(-0.169610 - 0.0454469i) q^{82} +(-7.33949 - 7.33949i) q^{83} +(1.91585 - 3.62463i) q^{84} +(-1.00570 - 1.74192i) q^{86} +(1.31763 + 4.91748i) q^{87} +(-0.0864939 - 0.322800i) q^{88} +(2.44220 + 4.23001i) q^{89} +(-7.47030 + 4.69349i) q^{91} +(2.84293 + 2.84293i) q^{92} +(2.83856 + 0.760591i) q^{93} +(-0.521974 + 0.904086i) q^{94} +(4.99820 - 2.88571i) q^{96} +(1.25230 - 1.25230i) q^{97} +(-3.06468 + 3.56065i) q^{98} -0.140283i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q - 8 q^{7} + 24 q^{8}+O(q^{10}) \) 32 * q - 8 * q^7 + 24 * q^8	\( 32 q - 8 q^{7} + 24 q^{8} - 8 q^{11} - 8 q^{21} + 8 q^{22} + 8 q^{23} + 24 q^{26} + 24 q^{28} + 24 q^{31} - 24 q^{32} + 36 q^{33} - 32 q^{36} - 4 q^{37} - 12 q^{38} - 16 q^{42} - 40 q^{43} - 40 q^{46} + 60 q^{47} - 8 q^{51} + 108 q^{52} + 24 q^{53} - 48 q^{56} - 16 q^{57} - 4 q^{58} - 24 q^{61} - 4 q^{63} + 72 q^{66} - 8 q^{67} - 132 q^{68} - 16 q^{71} - 12 q^{72} - 36 q^{73} - 60 q^{77} - 80 q^{78} + 16 q^{81} - 12 q^{82} - 16 q^{86} + 24 q^{87} + 32 q^{88} - 24 q^{91} + 56 q^{92} + 24 q^{93} + 72 q^{98}+O(q^{100}) \) 32 * q - 8 * q^7 + 24 * q^8 - 8 * q^11 - 8 * q^21 + 8 * q^22 + 8 * q^23 + 24 * q^26 + 24 * q^28 + 24 * q^31 - 24 * q^32 + 36 * q^33 - 32 * q^36 - 4 * q^37 - 12 * q^38 - 16 * q^42 - 40 * q^43 - 40 * q^46 + 60 * q^47 - 8 * q^51 + 108 * q^52 + 24 * q^53 - 48 * q^56 - 16 * q^57 - 4 * q^58 - 24 * q^61 - 4 * q^63 + 72 * q^66 - 8 * q^67 - 132 * q^68 - 16 * q^71 - 12 * q^72 - 36 * q^73 - 60 * q^77 - 80 * q^78 + 16 * q^81 - 12 * q^82 - 16 * q^86 + 24 * q^87 + 32 * q^88 - 24 * q^91 + 56 * q^92 + 24 * q^93 + 72 * q^98

Introduction

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