LMFDB - Embedded newform 735.2.v.a.178.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [735,2,Mod(178,735)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(735, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([0, 9, 2]))

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

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

chi := DirichletCharacter("735.178");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 735 = 3 \cdot 5 \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	735.v (of order $12$, 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:	$5.86900454856$
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			178.6
Character	$\chi$	$=$	735.178
Dual form			735.2.v.a.607.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.228203 + 0.0611467i) q^{2} +(0.258819 + 0.965926i) q^{3} +(-1.68371 - 0.972092i) q^{4} +(-1.18965 - 1.89334i) q^{5} +0.236253i q^{6} +(-0.658899 - 0.658899i) q^{8} +(-0.866025 + 0.500000i) q^{9} +O(q^{10})$	\(q+(0.228203 + 0.0611467i) q^{2} +(0.258819 + 0.965926i) q^{3} +(-1.68371 - 0.972092i) q^{4} +(-1.18965 - 1.89334i) q^{5} +0.236253i q^{6} +(-0.658899 - 0.658899i) q^{8} +(-0.866025 + 0.500000i) q^{9} +(-0.155711 - 0.504808i) q^{10} +(-1.99301 + 3.45200i) q^{11} +(0.503192 - 1.87794i) q^{12} +(0.500437 - 0.500437i) q^{13} +(1.52092 - 1.63915i) q^{15} +(1.83411 + 3.17677i) q^{16} +(2.29273 - 0.614336i) q^{17} +(-0.228203 + 0.0611467i) q^{18} +(3.60925 + 6.25141i) q^{19} +(0.162536 + 4.34429i) q^{20} +(-0.665888 + 0.665888i) q^{22} +(-1.88872 + 7.04878i) q^{23} +(0.465912 - 0.806983i) q^{24} +(-2.16945 + 4.50483i) q^{25} +(0.144801 - 0.0836010i) q^{26} +(-0.707107 - 0.707107i) q^{27} +3.65191i q^{29} +(0.447306 - 0.281059i) q^{30} +(-4.27662 - 2.46911i) q^{31} +(0.706647 + 2.63724i) q^{32} +(-3.85020 - 1.03166i) q^{33} +0.560773 q^{34} +1.94418 q^{36} +(-0.399255 - 0.106980i) q^{37} +(0.441387 + 1.64728i) q^{38} +(0.612908 + 0.353863i) q^{39} +(-0.463657 + 2.03138i) q^{40} -7.63184i q^{41} +(3.65191 + 3.65191i) q^{43} +(6.71132 - 3.87478i) q^{44} +(1.97694 + 1.04485i) q^{45} +(-0.862019 + 1.49306i) q^{46} +(-0.111749 + 0.417052i) q^{47} +(-2.59383 + 2.59383i) q^{48} +(-0.770530 + 0.895358i) q^{50} +(1.18681 + 2.05561i) q^{51} +(-1.32906 + 0.356122i) q^{52} +(-7.37179 + 1.97527i) q^{53} +(-0.118126 - 0.204601i) q^{54} +(8.90678 - 0.333235i) q^{55} +(-5.10425 + 5.10425i) q^{57} +(-0.223302 + 0.833375i) q^{58} +(-3.05480 + 5.29106i) q^{59} +(-4.15419 + 1.28138i) q^{60} +(6.15784 - 3.55523i) q^{61} +(-0.824957 - 0.824957i) q^{62} -6.69141i q^{64} +(-1.54284 - 0.352150i) q^{65} +(-0.815543 - 0.470854i) q^{66} +(0.345596 + 1.28978i) q^{67} +(-4.45750 - 1.19438i) q^{68} -7.29744 q^{69} +1.19297 q^{71} +(0.900073 + 0.241174i) q^{72} +(0.506205 + 1.88918i) q^{73} +(-0.0845694 - 0.0488262i) q^{74} +(-4.91283 - 0.929594i) q^{75} -14.0341i q^{76} +(0.118230 + 0.118230i) q^{78} +(-7.48269 + 4.32013i) q^{79} +(3.83275 - 7.25185i) q^{80} +(0.500000 - 0.866025i) q^{81} +(0.466662 - 1.74161i) q^{82} +(-11.9895 + 11.9895i) q^{83} +(-3.89070 - 3.61007i) q^{85} +(0.610073 + 1.05668i) q^{86} +(-3.52747 + 0.945184i) q^{87} +(3.58771 - 0.961324i) q^{88} +(-3.91290 - 6.77735i) q^{89} +(0.387253 + 0.359321i) q^{90} +(10.0321 - 10.0321i) q^{92} +(1.27810 - 4.76995i) q^{93} +(-0.0510027 + 0.0883393i) q^{94} +(7.54226 - 14.2705i) q^{95} +(-2.36449 + 1.36514i) q^{96} +(7.43671 + 7.43671i) q^{97} -3.98602i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q + 48 q^{8}+O(q^{10}) $ 32 * q + 48 * q^8	$ 32 q + 48 q^{8} + 16 q^{11} + 16 q^{15} + 48 q^{16} - 32 q^{22} + 40 q^{23} + 8 q^{30} - 48 q^{32} - 32 q^{36} - 32 q^{37} - 32 q^{43} - 64 q^{46} - 144 q^{50} + 16 q^{51} - 24 q^{53} + 16 q^{57} - 32 q^{58} - 40 q^{60} - 40 q^{65} + 32 q^{67} + 128 q^{71} - 24 q^{72} - 16 q^{78} + 16 q^{81} + 96 q^{85} - 64 q^{86} + 64 q^{88} - 80 q^{92} - 24 q^{93} + 72 q^{95}+O(q^{100}) $ 32 * q + 48 * q^8 + 16 * q^11 + 16 * q^15 + 48 * q^16 - 32 * q^22 + 40 * q^23 + 8 * q^30 - 48 * q^32 - 32 * q^36 - 32 * q^37 - 32 * q^43 - 64 * q^46 - 144 * q^50 + 16 * q^51 - 24 * q^53 + 16 * q^57 - 32 * q^58 - 40 * q^60 - 40 * q^65 + 32 * q^67 + 128 * q^71 - 24 * q^72 - 16 * q^78 + 16 * q^81 + 96 * q^85 - 64 * q^86 + 64 * q^88 - 80 * q^92 - 24 * q^93 + 72 * q^95

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/735\mathbb{Z}\right)^\times$.

$n$	$346$	$442$	$491$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{3}{4}\right)$	$1$

Coefficient data

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

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

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

$2$	0.228203	+	0.0611467i	0.161364	+	0.0432372i	0.338596	−	0.940932i	$-0.390048\pi$
$2$	0.228203	+	0.0611467i	0.161364	+	0.0432372i	−0.177233	+	0.984169i	$0.556715\pi$
$3$	0.258819	+	0.965926i	0.149429	+	0.557678i
$3$	0.258819	+	0.965926i	0.149429	+	0.557678i
$4$	−1.68371	−	0.972092i	−0.841857	−	0.486046i
$5$	−1.18965	−	1.89334i	−0.532029	−	0.846726i
$5$	−1.18965	−	1.89334i	−0.532029	−	0.846726i
$6$			0.236253i			0.0964497i
$7$		0			0
$7$		0			0
$8$	−0.658899	−	0.658899i	−0.232956	−	0.232956i
$9$	−0.866025	+	0.500000i	−0.288675	+	0.166667i
$10$	−0.155711	−	0.504808i	−0.0492400	−	0.159634i
$11$	−1.99301	+	3.45200i	−0.600915	+	1.04082i	0.391767	+	0.920064i	$0.371864\pi$
$11$	−1.99301	+	3.45200i	−0.600915	+	1.04082i	−0.992683	+	0.120752i	$0.961470\pi$
$12$	0.503192	−	1.87794i	0.145259	−	0.542114i
$13$	0.500437	−	0.500437i	0.138796	−	0.138796i	−0.634295	−	0.773091i	$-0.718709\pi$
$13$	0.500437	−	0.500437i	0.138796	−	0.138796i	0.773091	+	0.634295i	$0.218709\pi$
$14$		0			0
$15$	1.52092	−	1.63915i	0.392699	−	0.423226i
$16$	1.83411	+	3.17677i	0.458528	+	0.794194i
$17$	2.29273	−	0.614336i	0.556070	−	0.148998i	0.0301697	−	0.999545i	$-0.490395\pi$
$17$	2.29273	−	0.614336i	0.556070	−	0.148998i	0.525900	+	0.850546i	$0.323729\pi$
$18$	−0.228203	+	0.0611467i	−0.0537879	+	0.0144124i
$19$	3.60925	+	6.25141i	0.828019	+	1.43417i	0.899590	+	0.436735i	$0.143865\pi$
$19$	3.60925	+	6.25141i	0.828019	+	1.43417i	−0.0715711	+	0.997435i	$0.522801\pi$
$20$	0.162536	+	4.34429i	0.0363441	+	0.971413i
$21$		0			0
$22$	−0.665888	+	0.665888i	−0.141968	+	0.141968i
$23$	−1.88872	+	7.04878i	−0.393824	+	1.46977i	0.429949	+	0.902853i	$0.358532\pi$
$23$	−1.88872	+	7.04878i	−0.393824	+	1.46977i	−0.823773	+	0.566919i	$0.808135\pi$
$24$	0.465912	−	0.806983i	0.0951039	−	0.164725i
$25$	−2.16945	+	4.50483i	−0.433890	+	0.900966i
$26$	0.144801	−	0.0836010i	0.0283978	−	0.0163955i
$27$	−0.707107	−	0.707107i	−0.136083	−	0.136083i
$28$		0			0
$29$			3.65191i			0.678143i	0.940761	+	0.339071i	$0.110113\pi$
$29$			3.65191i			0.678143i	−0.940761	+	0.339071i	$0.889887\pi$
$30$	0.447306	−	0.281059i	0.0816665	−	0.0513141i
$31$	−4.27662	−	2.46911i	−0.768103	−	0.443465i	0.0640944	−	0.997944i	$-0.479584\pi$
$31$	−4.27662	−	2.46911i	−0.768103	−	0.443465i	−0.832198	+	0.554479i	$0.812917\pi$
$32$	0.706647	+	2.63724i	0.124919	+	0.466203i
$33$	−3.85020	−	1.03166i	−0.670234	−	0.179589i
$34$	0.560773			0.0961717
$35$		0			0
$36$	1.94418			0.324031
$37$	−0.399255	−	0.106980i	−0.0656371	−	0.0175874i	0.225851	−	0.974162i	$-0.427484\pi$
$37$	−0.399255	−	0.106980i	−0.0656371	−	0.0175874i	−0.291488	+	0.956574i	$0.594150\pi$
$38$	0.441387	+	1.64728i	0.0716025	+	0.267224i
$39$	0.612908	+	0.353863i	0.0981438	+	0.0566634i
$40$	−0.463657	+	2.03138i	−0.0733106	+	0.321189i
$41$		−	7.63184i		−	1.19189i	−0.803024	−	0.595947i	$-0.796777\pi$
$41$		−	7.63184i		−	1.19189i	0.803024	−	0.595947i	$-0.203223\pi$
$42$		0			0
$43$	3.65191	+	3.65191i	0.556911	+	0.556911i	0.928427	−	0.371516i	$-0.121162\pi$
$43$	3.65191	+	3.65191i	0.556911	+	0.556911i	−0.371516	+	0.928427i	$0.621162\pi$
$44$	6.71132	−	3.87478i	1.01177	−	0.584145i
$45$	1.97694	+	1.04485i	0.294705	+	0.155757i
$46$	−0.862019	+	1.49306i	−0.127098	+	0.220140i
$47$	−0.111749	+	0.417052i	−0.0163002	+	0.0608333i	−0.973597	−	0.228274i	$-0.926692\pi$
$47$	−0.111749	+	0.417052i	−0.0163002	+	0.0608333i	0.957297	+	0.289107i	$0.0933585\pi$
$48$	−2.59383	+	2.59383i	−0.374386	+	0.374386i
$49$		0			0
$50$	−0.770530	+	0.895358i	−0.108969	+	0.126623i
$51$	1.18681	+	2.05561i	0.166186	+	0.287843i
$52$	−1.32906	+	0.356122i	−0.184308	+	0.0493852i
$53$	−7.37179	+	1.97527i	−1.01259	+	0.271324i	−0.726713	−	0.686942i	$-0.758953\pi$
$53$	−7.37179	+	1.97527i	−1.01259	+	0.271324i	−0.285881	+	0.958265i	$0.592286\pi$
$54$	−0.118126	−	0.204601i	−0.0160750	−	0.0278426i
$55$	8.90678	−	0.333235i	1.20099	−	0.0449335i
$56$		0			0
$57$	−5.10425	+	5.10425i	−0.676075	+	0.676075i
$58$	−0.223302	+	0.833375i	−0.0293210	+	0.109428i
$59$	−3.05480	+	5.29106i	−0.397701	+	0.688838i	−0.993442	−	0.114339i	$-0.963525\pi$
$59$	−3.05480	+	5.29106i	−0.397701	+	0.688838i	0.595741	+	0.803176i	$0.296858\pi$
$60$	−4.15419	+	1.28138i	−0.536304	+	0.165426i
$61$	6.15784	−	3.55523i	0.788431	−	0.455201i	−0.0509788	−	0.998700i	$-0.516234\pi$
$61$	6.15784	−	3.55523i	0.788431	−	0.455201i	0.839410	+	0.543499i	$0.182901\pi$
$62$	−0.824957	−	0.824957i	−0.104770	−	0.104770i
$63$		0			0
$64$		−	6.69141i		−	0.836426i
$65$	−1.54284	−	0.352150i	−0.191366	−	0.0436788i
$66$	−0.815543	−	0.470854i	−0.100386	−	0.0579581i
$67$	0.345596	+	1.28978i	0.0422212	+	0.157572i	0.983818	−	0.179171i	$-0.0573415\pi$
$67$	0.345596	+	1.28978i	0.0422212	+	0.157572i	−0.941597	+	0.336743i	$0.890675\pi$
$68$	−4.45750	−	1.19438i	−0.540551	−	0.144840i
$69$	−7.29744			−0.878508
$70$		0			0
$71$	1.19297			0.141579			0.0707897	−	0.997491i	$-0.477448\pi$
$71$	1.19297			0.141579			0.0707897	+	0.997491i	$0.477448\pi$
$72$	0.900073	+	0.241174i	0.106075	+	0.0284226i
$73$	0.506205	+	1.88918i	0.0592469	+	0.221112i	0.989201	−	0.146562i	$-0.0468208\pi$
$73$	0.506205	+	1.88918i	0.0592469	+	0.221112i	−0.929955	+	0.367674i	$0.880154\pi$
$74$	−0.0845694	−	0.0488262i	−0.00983100	−	0.00567593i
$75$	−4.91283	−	0.929594i	−0.567284	−	0.107340i
$76$		−	14.0341i		−	1.60982i
$77$		0			0
$78$	0.118230	+	0.118230i	0.0133869	+	0.0133869i
$79$	−7.48269	+	4.32013i	−0.841868	+	0.486053i	−0.857899	−	0.513819i	$-0.828230\pi$
$79$	−7.48269	+	4.32013i	−0.841868	+	0.486053i	0.0160304	+	0.999872i	$0.494897\pi$
$80$	3.83275	−	7.25185i	0.428514	−	0.810782i
$81$	0.500000	−	0.866025i	0.0555556	−	0.0962250i
$82$	0.466662	−	1.74161i	0.0515342	−	0.192328i
$83$	−11.9895	+	11.9895i	−1.31602	+	1.31602i	−0.399122	+	0.916898i	$0.630685\pi$
$83$	−11.9895	+	11.9895i	−1.31602	+	1.31602i	−0.916898	+	0.399122i	$0.869315\pi$
$84$		0			0
$85$	−3.89070	−	3.61007i	−0.422006	−	0.391567i
$86$	0.610073	+	1.05668i	0.0657859	+	0.113944i
$87$	−3.52747	+	0.945184i	−0.378185	+	0.101334i
$88$	3.58771	−	0.961324i	0.382451	−	0.102477i
$89$	−3.91290	−	6.77735i	−0.414767	−	0.718397i	0.580637	−	0.814163i	$-0.302804\pi$
$89$	−3.91290	−	6.77735i	−0.414767	−	0.718397i	−0.995404	+	0.0957652i	$0.969470\pi$
$90$	0.387253	+	0.359321i	0.0408201	+	0.0378758i
$91$		0			0
$92$	10.0321	−	10.0321i	1.04592	−	1.04592i
$93$	1.27810	−	4.76995i	0.132533	−	0.494620i
$94$	−0.0510027	+	0.0883393i	−0.00526053	+	0.00911150i
$95$	7.54226	−	14.2705i	0.773820	−	1.46413i
$96$	−2.36449	+	1.36514i	−0.241325	+	0.139329i
$97$	7.43671	+	7.43671i	0.755083	+	0.755083i	0.975423	−	0.220340i	$-0.0707167\pi$
$97$	7.43671	+	7.43671i	0.755083	+	0.755083i	−0.220340	+	0.975423i	$0.570717\pi$
$98$		0			0
$99$		−	3.98602i		−	0.400610i
$100$	8.03184	−	5.47593i	0.803184	−	0.547593i
$101$	−5.47010	−	3.15816i	−0.544295	−	0.314249i	0.202523	−	0.979278i	$-0.435086\pi$
$101$	−5.47010	−	3.15816i	−0.544295	−	0.314249i	−0.746818	+	0.665028i	$0.768419\pi$
$102$	0.145139	+	0.541665i	0.0143709	+	0.0536328i
$103$	17.1313	+	4.59031i	1.68799	+	0.452296i	0.969871	−	0.243620i	$-0.0783351\pi$
$103$	17.1313	+	4.59031i	1.68799	+	0.452296i	0.718122	+	0.695917i	$0.245002\pi$
$104$	−0.659476			−0.0646669
$105$		0			0
$106$	−1.80304			−0.175127
$107$	−10.2181	−	2.73794i	−0.987825	−	0.264687i	−0.271488	−	0.962442i	$-0.587516\pi$
$107$	−10.2181	−	2.73794i	−0.987825	−	0.264687i	−0.716337	+	0.697755i	$0.754183\pi$
$108$	0.503192	+	1.87794i	0.0484197	+	0.180705i
$109$	0.578698	+	0.334112i	0.0554293	+	0.0320021i	0.527459	−	0.849581i	$-0.323145\pi$
$109$	0.578698	+	0.334112i	0.0554293	+	0.0320021i	−0.472029	+	0.881583i	$0.656478\pi$
$110$	2.05293	+	0.468575i	0.195739	+	0.0446769i
$111$		−	0.413339i		−	0.0392324i
$112$		0			0
$113$	−3.39653	−	3.39653i	−0.319518	−	0.319518i	0.529064	−	0.848582i	$-0.322543\pi$
$113$	−3.39653	−	3.39653i	−0.319518	−	0.319518i	−0.848582	+	0.529064i	$0.822543\pi$
$114$	−1.47691	+	0.852695i	−0.138325	+	0.0798622i
$115$	15.5926	−	4.80963i	1.45402	−	0.448500i
$116$	3.54999	−	6.14877i	0.329609	−	0.570899i
$117$	−0.183173	+	0.683610i	−0.0169343	+	0.0631998i
$118$	−1.02064	+	1.02064i	−0.0939578	+	0.0939578i
$119$		0			0
$120$	−2.08217	+	0.0779014i	−0.190075	+	0.00711139i
$121$	−2.44418	−	4.23345i	−0.222199	−	0.384859i
$122$	1.62263	−	0.434781i	0.146906	−	0.0393633i
$123$	7.37179	−	1.97527i	0.664692	−	0.178104i
$124$	4.80040	+	8.31453i	0.431088	+	0.746667i
$125$	11.1101	−	1.25168i	0.993713	−	0.111953i
$126$		0			0
$127$	−5.88837	+	5.88837i	−0.522508	+	0.522508i	−0.918328	−	0.395820i	$-0.870460\pi$
$127$	−5.88837	+	5.88837i	−0.522508	+	0.522508i	0.395820	+	0.918328i	$0.370460\pi$
$128$	1.82245	−	6.80149i	0.161084	−	0.601172i
$129$	−2.58229	+	4.47266i	−0.227358	+	0.393796i
$130$	−0.330548	−	0.174701i	−0.0289910	−	0.0153223i
$131$	−16.2938	+	9.40722i	−1.42359	+	0.821913i	−0.996604	−	0.0823433i	$-0.973760\pi$
$131$	−16.2938	+	9.40722i	−1.42359	+	0.821913i	−0.426991	+	0.904256i	$0.640426\pi$
$132$	5.47977	+	5.47977i	0.476953	+	0.476953i
$133$		0			0
$134$			0.315463i			0.0272519i
$135$	−0.497580	+	2.18000i	−0.0428249	+	0.187625i
$136$	−1.91547	−	1.10590i	−0.164250	−	0.0948297i
$137$	−0.297204	−	1.10918i	−0.0253919	−	0.0947637i	0.952067	−	0.305889i	$-0.0989538\pi$
$137$	−0.297204	−	1.10918i	−0.0253919	−	0.0947637i	−0.977459	+	0.211126i	$0.932287\pi$
$138$	−1.66529	−	0.446214i	−0.141759	−	0.0379843i
$139$	−0.442439			−0.0375272			−0.0187636	−	0.999824i	$-0.505973\pi$
$139$	−0.442439			−0.0375272			−0.0187636	+	0.999824i	$0.505973\pi$
$140$		0			0
$141$	−0.431764			−0.0363611
$142$	0.272239	+	0.0729461i	0.0228458	+	0.00612150i
$143$	0.730131	+	2.72489i	0.0610566	+	0.227866i
$144$	−3.17677	−	1.83411i	−0.264731	−	0.152843i
$145$	6.91430	−	4.34451i	0.574201	−	0.360792i
$146$			0.462070i			0.0382411i
$147$		0			0
$148$	0.568236	+	0.568236i	0.0467087	+	0.0467087i
$149$	2.72031	−	1.57057i	0.222856	−	0.128666i	−0.384416	−	0.923160i	$-0.625597\pi$
$149$	2.72031	−	1.57057i	0.222856	−	0.128666i	0.607272	+	0.794494i	$0.292264\pi$
$150$	−1.06428	−	0.512539i	−0.0868979	−	0.0418486i
$151$	7.36197	−	12.7513i	0.599109	−	1.03769i	−0.393844	−	0.919177i	$-0.628855\pi$
$151$	7.36197	−	12.7513i	0.599109	−	1.03769i	0.992953	−	0.118509i	$-0.0378116\pi$
$152$	1.74091	−	6.49718i	0.141207	−	0.526991i
$153$	−1.67840	+	1.67840i	−0.135690	+	0.135690i
$154$		0			0
$155$	0.412839	+	11.0345i	0.0331601	+	0.886309i
$156$	−0.687974	−	1.19161i	−0.0550820	−	0.0954049i
$157$	10.8805	−	2.91542i	0.868358	−	0.232676i	0.202980	−	0.979183i	$-0.434937\pi$
$157$	10.8805	−	2.91542i	0.868358	−	0.232676i	0.665378	+	0.746507i	$0.268271\pi$
$158$	−1.97173	+	0.528324i	−0.156862	+	0.0420312i
$159$	−3.81592	−	6.60937i	−0.302622	−	0.524157i
$160$	4.15253	−	4.47533i	0.328286	−	0.353806i
$161$		0			0
$162$	0.167056	−	0.167056i	0.0131251	−	0.0131251i
$163$	3.82312	−	14.2681i	0.299450	−	1.11756i	−0.638169	−	0.769897i	$-0.720308\pi$
$163$	3.82312	−	14.2681i	0.299450	−	1.11756i	0.937619	−	0.347666i	$-0.113026\pi$
$164$	−7.41885	+	12.8498i	−0.579315	+	1.00340i
$165$	2.62713	+	8.51705i	0.204521	+	0.663051i
$166$	−3.46916	+	2.00292i	−0.269259	+	0.155457i
$167$	4.63621	+	4.63621i	0.358761	+	0.358761i	0.863356	−	0.504595i	$-0.168358\pi$
$167$	4.63621	+	4.63621i	0.358761	+	0.358761i	−0.504595	+	0.863356i	$0.668358\pi$
$168$		0			0
$169$			12.4991i			0.961471i
$170$	−0.667125	−	1.06173i	−0.0511661	−	0.0814311i
$171$	−6.25141	−	3.60925i	−0.478057	−	0.276006i
$172$	−2.59878	−	9.69876i	−0.198155	−	0.739524i
$173$	3.39499	+	0.909686i	0.258117	+	0.0691621i	0.385557	−	0.922684i	$-0.374009\pi$
$173$	3.39499	+	0.909686i	0.258117	+	0.0691621i	−0.127440	+	0.991846i	$0.540676\pi$
$174$	−0.862773			−0.0654067
$175$		0			0
$176$	−14.6216			−1.10215
$177$	−5.90141	−	1.58128i	−0.443577	−	0.118856i
$178$	−0.478522	−	1.78587i	−0.0358667	−	0.133857i
$179$	19.1486	+	11.0554i	1.43123	+	0.826321i	0.997215	−	0.0745840i	$-0.0237629\pi$
$179$	19.1486	+	11.0554i	1.43123	+	0.826321i	0.434016	+	0.900905i	$0.357096\pi$
$180$	−2.31290	−	3.68100i	−0.172394	−	0.274365i
$181$		−	8.48528i		−	0.630706i	−0.948974	−	0.315353i	$-0.897877\pi$
$181$		−	8.48528i		−	0.630706i	0.948974	−	0.315353i	$-0.102123\pi$
$182$		0			0
$183$	5.02786	+	5.02786i	0.371670	+	0.371670i
$184$	5.88891	−	3.39996i	0.434136	−	0.250649i
$185$	0.272425	+	0.883193i	0.0200291	+	0.0649336i
$186$	0.583333	−	1.01036i	0.0427720	−	0.0740833i
$187$	−2.44876	+	9.13889i	−0.179071	+	0.668302i
$188$	0.593566	−	0.593566i	0.0432903	−	0.0432903i
$189$		0			0
$190$	2.59376	−	2.79539i	0.188171	−	0.202799i
$191$	−7.64492	−	13.2414i	−0.553167	−	0.958113i	−0.998044	−	0.0625216i	$-0.980086\pi$
$191$	−7.64492	−	13.2414i	−0.553167	−	0.958113i	0.444877	−	0.895592i	$-0.353248\pi$
$192$	6.46341	−	1.73186i	0.466456	−	0.124987i
$193$	12.1957	−	3.26783i	0.877866	−	0.235223i	0.208380	−	0.978048i	$-0.433181\pi$
$193$	12.1957	−	3.26783i	0.877866	−	0.235223i	0.669486	+	0.742825i	$0.266514\pi$
$194$	1.24235	+	2.15181i	0.0891952	+	0.154491i
$195$	−0.0591665	−	1.58142i	−0.00423700	−	0.113248i
$196$		0			0
$197$	−2.68715	+	2.68715i	−0.191451	+	0.191451i	−0.796323	−	0.604872i	$-0.793224\pi$
$197$	−2.68715	+	2.68715i	−0.191451	+	0.191451i	0.604872	+	0.796323i	$0.293224\pi$
$198$	0.243732	−	0.909620i	0.0173213	−	0.0646439i
$199$	−0.308318	+	0.534023i	−0.0218561	+	0.0378559i	−0.876747	−	0.480953i	$-0.840291\pi$
$199$	−0.308318	+	0.534023i	−0.0218561	+	0.0378559i	0.854890	+	0.518809i	$0.173624\pi$
$200$	4.39768	−	1.53878i	0.310963	−	0.108808i
$201$	−1.15639	+	0.667639i	−0.0815651	+	0.0470917i
$202$	−1.05518	−	1.05518i	−0.0742422	−	0.0742422i
$203$		0			0
$204$		−	4.61474i		−	0.323097i
$205$	−14.4496	+	9.07924i	−1.00921	+	0.634122i
$206$	3.62871	+	2.09504i	0.252825	+	0.145968i
$207$	−1.88872	−	7.04878i	−0.131275	−	0.489924i
$208$	2.50763	+	0.671919i	0.173873	+	0.0465892i
$209$	−28.7731			−1.99028
$210$		0			0
$211$	9.30849			0.640823			0.320411	−	0.947278i	$-0.396179\pi$
$211$	9.30849			0.640823			0.320411	+	0.947278i	$0.396179\pi$
$212$	14.3321	+	3.84028i	0.984334	+	0.263752i
$213$	0.308763	+	1.15232i	0.0211561	+	0.0789557i
$214$	−2.16439	−	1.24961i	−0.147955	−	0.0854217i
$215$	2.56979	−	11.2588i	0.175258	−	0.767844i
$216$			0.931824i			0.0634026i
$217$		0			0
$218$	0.111631	+	0.111631i	0.00756058	+	0.00756058i
$219$	−1.69380	+	0.977914i	−0.114456	+	0.0660813i
$220$	−15.3204	−	8.09714i	−1.03290	−	0.545909i
$221$	0.839933	−	1.45481i	0.0565000	−	0.0978609i
$222$	0.0252743	−	0.0943250i	0.00169630	−	0.00633068i
$223$	−1.35505	+	1.35505i	−0.0907407	+	0.0907407i	−0.751020	−	0.660279i	$-0.770438\pi$
$223$	−1.35505	+	1.35505i	−0.0907407	+	0.0907407i	0.660279	+	0.751020i	$0.270438\pi$
$224$		0			0
$225$	−0.373614	−	4.98602i	−0.0249076	−	0.332401i
$226$	−0.567410	−	0.982782i	−0.0377435	−	0.0653737i
$227$	−5.67498	+	1.52061i	−0.376662	+	0.100926i	−0.442183	−	0.896925i	$-0.645796\pi$
$227$	−5.67498	+	1.52061i	−0.376662	+	0.100926i	0.0655211	+	0.997851i	$0.479129\pi$
$228$	13.5559	−	3.63229i	0.897761	−	0.240554i
$229$	−6.49500	−	11.2497i	−0.429202	−	0.743399i	0.567601	−	0.823304i	$-0.307872\pi$
$229$	−6.49500	−	11.2497i	−0.429202	−	0.743399i	−0.996802	+	0.0799049i	$0.974538\pi$
$230$	3.85237	−	0.144131i	0.254018	−	0.00950374i
$231$		0			0
$232$	2.40624	−	2.40624i	0.157977	−	0.157977i
$233$	−6.02620	+	22.4901i	−0.394790	+	1.47337i	0.427349	+	0.904087i	$0.359448\pi$
$233$	−6.02620	+	22.4901i	−0.394790	+	1.47337i	−0.822138	+	0.569288i	$0.807219\pi$
$234$	−0.0836010	+	0.144801i	−0.00546517	+	0.00946595i
$235$	0.922563	−	0.284569i	0.0601813	−	0.0185632i
$236$	10.2868	−	5.93909i	0.669614	−	0.386602i
$237$	−6.10959	−	6.10959i	−0.396861	−	0.396861i
$238$		0			0
$239$		−	5.48048i		−	0.354503i	−0.984166	−	0.177251i	$-0.943279\pi$
$239$		−	5.48048i		−	0.354503i	0.984166	−	0.177251i	$-0.0567205\pi$
$240$	7.99674	+	1.82523i	0.516187	+	0.117818i
$241$	−12.6879	−	7.32537i	−0.817300	−	0.471868i	0.0321844	−	0.999482i	$-0.489754\pi$
$241$	−12.6879	−	7.32537i	−0.817300	−	0.471868i	−0.849485	+	0.527613i	$0.823087\pi$
$242$	−0.298908	−	1.11554i	−0.0192145	−	0.0717095i
$243$	0.965926	+	0.258819i	0.0619642	+	0.0166032i
$244$	−13.8241			−0.884995
$245$		0			0
$246$	1.80304			0.114958
$247$	4.93464	+	1.32223i	0.313984	+	0.0841317i
$248$	1.19097	+	4.44475i	0.0756265	+	0.282242i
$249$	−14.6841	−	8.47787i	−0.930567	−	0.537263i
$250$	2.61188	+	0.393707i	0.165190	+	0.0249002i
$251$		−	21.1506i		−	1.33501i	−0.744604	−	0.667507i	$-0.767361\pi$
$251$		−	21.1506i		−	1.33501i	0.744604	−	0.667507i	$-0.232639\pi$
$252$		0			0
$253$	−20.5681	−	20.5681i	−1.29311	−	1.29311i
$254$	−1.70380	+	0.983687i	−0.106906	+	0.0617220i
$255$	2.48007	−	4.69249i	0.155308	−	0.293855i
$256$	−5.85964	+	10.1492i	−0.366227	+	0.634324i
$257$	−3.43788	+	12.8304i	−0.214449	+	0.800336i	0.771910	+	0.635731i	$0.219301\pi$
$257$	−3.43788	+	12.8304i	−0.214449	+	0.800336i	−0.986360	+	0.164604i	$0.947365\pi$
$258$	−0.862773	+	0.862773i	−0.0537139	+	0.0537139i
$259$		0			0
$260$	2.25538	+	2.09271i	0.139873	+	0.129784i
$261$	−1.82596	−	3.16265i	−0.113024	−	0.195763i
$262$	−4.29350	+	1.15044i	−0.265254	+	0.0710745i
$263$	−21.0066	+	5.62869i	−1.29532	+	0.347080i	−0.839679	−	0.543083i	$-0.817257\pi$
$263$	−21.0066	+	5.62869i	−1.29532	+	0.347080i	−0.455642	+	0.890163i	$0.650590\pi$
$264$	1.85714	+	3.21665i	0.114299	+	0.197971i
$265$	12.5097	+	11.6074i	0.768466	+	0.713037i
$266$		0			0
$267$	5.53368	−	5.53368i	0.338656	−	0.338656i
$268$	0.671902	−	2.50757i	0.0410429	−	0.153174i
$269$	11.4926	−	19.9057i	0.700714	−	1.21367i	−0.267501	−	0.963557i	$-0.586198\pi$
$269$	11.4926	−	19.9057i	0.700714	−	1.21367i	0.968216	−	0.250116i	$-0.0804686\pi$
$270$	−0.246849	+	0.467057i	−0.0150228	+	0.0284242i
$271$	−13.6483	+	7.87982i	−0.829072	+	0.478665i	−0.853535	−	0.521036i	$-0.825546\pi$
$271$	−13.6483	+	7.87982i	−0.829072	+	0.478665i	0.0244625	+	0.999701i	$0.492213\pi$
$272$	6.15674	+	6.15674i	0.373307	+	0.373307i
$273$		0			0
$274$		−	0.271291i		−	0.0163893i
$275$	−11.2269	−	16.4671i	−0.677008	−	0.993004i
$276$	12.2868	+	7.09378i	0.739578	+	0.426995i
$277$	1.75975	+	6.56746i	0.105733	+	0.394600i	0.998427	−	0.0560621i	$-0.0178545\pi$
$277$	1.75975	+	6.56746i	0.105733	+	0.394600i	−0.892694	+	0.450662i	$0.851188\pi$
$278$	−0.100966	−	0.0270537i	−0.00605553	−	0.00162257i
$279$	4.93821			0.295643
$280$		0			0
$281$	−9.65658			−0.576063			−0.288032	−	0.957621i	$-0.593001\pi$
$281$	−9.65658			−0.576063			−0.288032	+	0.957621i	$0.593001\pi$
$282$	−0.0985297	−	0.0264009i	−0.00586736	−	0.00157215i
$283$	5.45726	+	20.3668i	0.324400	+	1.21068i	0.914913	+	0.403650i	$0.132259\pi$
$283$	5.45726	+	20.3668i	0.324400	+	1.21068i	−0.590513	+	0.807028i	$0.701075\pi$
$284$	−2.00862	−	1.15968i	−0.119190	−	0.0688141i
$285$	15.7364	+	3.59178i	0.932141	+	0.212759i
$286$			0.666471i			0.0394092i
$287$		0			0
$288$	−1.93060	−	1.93060i	−0.113761	−	0.113761i
$289$	−9.84321	+	5.68298i	−0.579012	+	0.334293i
$290$	1.84351	−	0.568641i	0.108255	−	0.0333917i
$291$	−5.25855	+	9.10807i	−0.308261	+	0.533924i
$292$	0.984157	−	3.67292i	0.0575934	−	0.214942i
$293$	4.79236	−	4.79236i	0.279973	−	0.279973i	−0.553125	−	0.833098i	$-0.686565\pi$
$293$	4.79236	−	4.79236i	0.279973	−	0.279973i	0.833098	+	0.553125i	$0.186565\pi$
$294$		0			0
$295$	13.6519	−	0.510768i	0.794845	−	0.0297381i
$296$	0.192580	+	0.333558i	0.0111935	+	0.0193876i
$297$	3.85020	−	1.03166i	0.223411	−	0.0598629i
$298$	0.716817	−	0.192070i	0.0415241	−	0.0111263i
$299$	2.58229	+	4.47266i	0.149338	+	0.258660i
$300$	7.36814	+	6.34089i	0.425400	+	0.366091i
$301$		0			0
$302$	2.45972	−	2.45972i	0.141541	−	0.141541i
$303$	1.63479	−	6.10111i	0.0939160	−	0.350499i
$304$	−13.2395	+	22.9316i	−0.759340	+	1.31521i
$305$	−14.0570	−	7.42938i	−0.804899	−	0.425405i
$306$	−0.485643	+	0.280386i	−0.0277624	+	0.0160286i
$307$	9.85063	+	9.85063i	0.562205	+	0.562205i	0.929933	−	0.367728i	$-0.119864\pi$
$307$	9.85063	+	9.85063i	0.562205	+	0.562205i	−0.367728	+	0.929933i	$0.619864\pi$
$308$		0			0
$309$			17.7356i			1.00894i
$310$	−0.580510	+	2.54334i	−0.0329707	+	0.144452i
$311$	−23.6480	−	13.6532i	−1.34095	−	0.774200i	−0.354006	−	0.935243i	$-0.615181\pi$
$311$	−23.6480	−	13.6532i	−1.34095	−	0.774200i	−0.986947	+	0.161043i	$0.948514\pi$
$312$	−0.170685	−	0.637004i	−0.00966313	−	0.0360633i
$313$	−25.2824	−	6.77439i	−1.42904	−	0.382911i	−0.540361	−	0.841434i	$-0.681712\pi$
$313$	−25.2824	−	6.77439i	−1.42904	−	0.382911i	−0.888683	+	0.458523i	$0.848379\pi$
$314$	2.66123			0.150182
$315$		0			0
$316$	16.7983			0.944977
$317$	29.8877	+	8.00839i	1.67866	+	0.449796i	0.967425	−	0.253156i	$-0.0814687\pi$
$317$	29.8877	+	8.00839i	1.67866	+	0.449796i	0.711237	+	0.702952i	$0.248135\pi$
$318$	−0.466662	−	1.74161i	−0.0261691	−	0.0976644i
$319$	−12.6064	−	7.27830i	−0.705822	−	0.407506i
$320$	−12.6691	+	7.96046i	−0.708224	+	0.445003i
$321$		−	10.5786i		−	0.590440i
$322$		0			0
$323$	12.1155	+	12.1155i	0.674126	+	0.674126i
$324$	−1.68371	+	0.972092i	−0.0935396	+	0.0540051i
$325$	1.16871	+	3.34006i	0.0648283	+	0.185273i
$326$	1.74489	−	3.02224i	0.0966406	−	0.167386i
$327$	−0.172949	+	0.645454i	−0.00956410	+	0.0356937i
$328$	−5.02861	+	5.02861i	−0.277659	+	0.277659i
$329$		0			0
$330$	0.0787277	+	2.10425i	0.00433382	+	0.115835i
$331$	8.34566	+	14.4551i	0.458719	+	0.794524i	0.998894	−	0.0470286i	$-0.0149752\pi$
$331$	8.34566	+	14.4551i	0.458719	+	0.794524i	−0.540175	+	0.841553i	$0.681642\pi$
$332$	31.8418	−	8.53199i	1.74755	−	0.468254i
$333$	0.399255	−	0.106980i	0.0218790	−	0.00586246i
$334$	0.774506	+	1.34148i	0.0423791	+	0.0734027i
$335$	2.03085	−	2.18872i	0.110957	−	0.119583i
$336$		0			0
$337$	2.54028	−	2.54028i	0.138378	−	0.138378i	−0.634525	−	0.772903i	$-0.718804\pi$
$337$	2.54028	−	2.54028i	0.138378	−	0.138378i	0.772903	+	0.634525i	$0.218804\pi$
$338$	−0.764280	+	2.85233i	−0.0415714	+	0.155146i
$339$	2.40171	−	4.15988i	0.130443	−	0.225934i
$340$	3.04151	+	9.86045i	0.164949	+	0.534758i
$341$	17.0467	−	9.84191i	0.923130	−	0.532969i
$342$	−1.20589	−	1.20589i	−0.0652072	−	0.0652072i
$343$		0			0
$344$		−	4.81248i		−	0.259472i
$345$	8.68142	+	13.8165i	0.467392	+	0.743856i
$346$	0.719122	+	0.415185i	0.0386602	+	0.0223205i
$347$	5.01382	+	18.7118i	0.269156	+	1.00450i	0.959657	+	0.281173i	$0.0907233\pi$
$347$	5.01382	+	18.7118i	0.269156	+	1.00450i	−0.690501	+	0.723331i	$0.742610\pi$
$348$	6.85806	+	1.83761i	0.367631	+	0.0985063i
$349$	0.508601			0.0272248			0.0136124	−	0.999907i	$-0.495667\pi$
$349$	0.508601			0.0272248			0.0136124	+	0.999907i	$0.495667\pi$
$350$		0			0
$351$	−0.707725			−0.0377756
$352$	−10.5121	−	2.81671i	−0.560297	−	0.150131i
$353$	3.99763	+	14.9193i	0.212772	+	0.794077i	0.986939	+	0.161095i	$0.0515025\pi$
$353$	3.99763	+	14.9193i	0.212772	+	0.794077i	−0.774167	+	0.632982i	$0.781831\pi$
$354$	−1.25003	−	0.721704i	−0.0664382	−	0.0383581i
$355$	−1.41922	−	2.25869i	−0.0753244	−	0.119879i
$356$			15.2148i			0.806383i
$357$		0			0
$358$	3.69375	+	3.69375i	0.195221	+	0.195221i
$359$	13.8443	−	7.99301i	0.730674	−	0.421855i	−0.0879945	−	0.996121i	$-0.528046\pi$
$359$	13.8443	−	7.99301i	0.730674	−	0.421855i	0.818669	+	0.574266i	$0.194712\pi$
$360$	−0.614151	−	1.99105i	−0.0323686	−	0.104938i
$361$	−16.5534	+	28.6713i	−0.871231	+	1.50902i
$362$	0.518847	−	1.93636i	0.0272700	−	0.101773i
$363$	3.45660	−	3.45660i	0.181424	−	0.181424i
$364$		0			0
$365$	2.97465	−	3.20589i	0.155701	−	0.167804i
$366$	0.839933	+	1.45481i	0.0439040	+	0.0760440i
$367$	−0.560120	+	0.150084i	−0.0292380	+	0.00783431i	−0.273408	−	0.961898i	$-0.588151\pi$
$367$	−0.560120	+	0.150084i	−0.0292380	+	0.00783431i	0.244170	+	0.969732i	$0.421484\pi$
$368$	−25.8565	+	6.92823i	−1.34786	+	0.361159i
$369$	3.81592	+	6.60937i	0.198649	+	0.344070i
$370$	0.00816384	+	0.218205i	0.000424418	+	0.0113439i
$371$		0			0
$372$	−6.78879	+	6.78879i	−0.351982	+	0.351982i
$373$	−1.26094	+	4.70591i	−0.0652892	+	0.243663i	−0.990856	−	0.134921i	$-0.956922\pi$
$373$	−1.26094	+	4.70591i	−0.0652892	+	0.243663i	0.925567	+	0.378583i	$0.123589\pi$
$374$	−1.11763	+	1.93578i	−0.0577911	+	0.100097i
$375$	4.08452	+	10.4075i	0.210924	+	0.537443i
$376$	0.348426	−	0.201164i	0.0179687	−	0.0103742i
$377$	1.82755	+	1.82755i	0.0941237	+	0.0941237i
$378$		0			0
$379$			12.9179i			0.663547i	0.943359	+	0.331773i	$0.107647\pi$
$379$			12.9179i			0.663547i	−0.943359	+	0.331773i	$0.892353\pi$
$380$	−26.5713	+	16.6957i	−1.36308	+	0.856472i
$381$	−7.21175	−	4.16371i	−0.369469	−	0.213313i
$382$	−0.934923	−	3.48918i	−0.0478348	−	0.178522i
$383$	13.7654	+	3.68844i	0.703381	+	0.188470i	0.592744	−	0.805391i	$-0.298044\pi$
$383$	13.7654	+	3.68844i	0.703381	+	0.188470i	0.110636	+	0.993861i	$0.464711\pi$
$384$	7.04142			0.359331
$385$		0			0
$386$	2.98291			0.151826
$387$	−4.98860	−	1.33669i	−0.253585	−	0.0679479i
$388$	−5.29212	−	19.7504i	−0.268666	−	1.00268i
$389$	21.0704	+	12.1650i	1.06831	+	0.616791i	0.927720	−	0.373277i	$-0.121766\pi$
$389$	21.0704	+	12.1650i	1.06831	+	0.616791i	0.140593	+	0.990068i	$0.455099\pi$
$390$	0.0831964	−	0.364501i	0.00421281	−	0.0184572i
$391$			17.3213i			0.875976i
$392$		0			0
$393$	−13.3038	−	13.3038i	−0.671089	−	0.671089i
$394$	−0.777524	+	0.448904i	−0.0391711	+	0.0226154i
$395$	17.0813	+	9.02780i	0.859452	+	0.454238i
$396$	−3.87478	+	6.71132i	−0.194715	+	0.337256i
$397$	2.49129	−	9.29762i	0.125034	−	0.466634i	−0.874807	−	0.484472i	$-0.839012\pi$
$397$	2.49129	−	9.29762i	0.125034	−	0.466634i	0.999841	+	0.0178380i	$0.00567832\pi$
$398$	−0.103013	+	0.103013i	−0.00516356	+	0.00516356i
$399$		0			0
$400$	−18.2898	+	1.37050i	−0.914492	+	0.0685249i
$401$	4.41545	+	7.64778i	0.220497	+	0.381912i	0.954959	−	0.296738i	$-0.0958987\pi$
$401$	4.41545	+	7.64778i	0.220497	+	0.381912i	−0.734462	+	0.678650i	$0.762565\pi$
$402$	−0.304714	+	0.0816479i	−0.0151978	+	0.00407223i
$403$	−3.37581	+	0.904546i	−0.168161	+	0.0450587i
$404$	6.14006	+	10.6349i	0.305479	+	0.529105i
$405$	−2.23450	+	0.0836010i	−0.111033	+	0.00415417i
$406$		0			0
$407$	1.16501	−	1.16501i	0.0577476	−	0.0577476i
$408$	0.572453	−	2.13643i	0.0283407	−	0.105769i
$409$	11.5992	−	20.0905i	0.573546	−	0.993410i	−0.422652	−	0.906292i	$-0.638901\pi$
$409$	11.5992	−	20.0905i	0.573546	−	0.993410i	0.996198	−	0.0871183i	$-0.0277658\pi$
$410$	−3.85261	+	1.18836i	−0.190267	+	0.0586888i
$411$	0.994464	−	0.574154i	0.0490533	−	0.0283209i
$412$	−24.3819	−	24.3819i	−1.20121	−	1.20121i
$413$		0			0
$414$		−	1.72404i		−	0.0847319i
$415$	36.9635	+	8.43683i	1.81447	+	0.414148i
$416$	1.67341	+	0.966143i	0.0820456	+	0.0473690i
$417$	−0.114512	−	0.427364i	−0.00560766	−	0.0209281i
$418$	−6.56610	−	1.75938i	−0.321158	−	0.0860541i
$419$	13.0393			0.637009			0.318505	−	0.947921i	$-0.396819\pi$
$419$	13.0393			0.637009			0.318505	+	0.947921i	$0.396819\pi$
$420$		0			0
$421$	−31.3549			−1.52814			−0.764071	−	0.645132i	$-0.776802\pi$
$421$	−31.3549			−1.52814			−0.764071	+	0.645132i	$0.776802\pi$
$422$	2.12422	+	0.569183i	0.103405	+	0.0277074i
$423$	−0.111749	−	0.417052i	−0.00543341	−	0.0202778i
$424$	6.15877	+	3.55577i	0.299096	+	0.172683i
$425$	−2.20650	+	11.6611i	−0.107031	+	0.565649i
$426$			0.281842i			0.0136553i
$427$		0			0
$428$	14.5429	+	14.5429i	0.702957	+	0.702957i
$429$	−2.44307	+	1.41050i	−0.117952	+	0.0680998i
$430$	1.27487	−	2.41215i	0.0614798	−	0.116324i
$431$	11.2779	−	19.5339i	0.543238	−	0.940915i	−0.455478	−	0.890247i	$-0.650532\pi$
$431$	11.2779	−	19.5339i	0.543238	−	0.940915i	0.998716	−	0.0506681i	$-0.0161351\pi$
$432$	0.949406	−	3.54323i	0.0456783	−	0.170474i
$433$	−19.9639	+	19.9639i	−0.959405	+	0.959405i	−0.999208	−	0.0398028i	$-0.987327\pi$
$433$	−19.9639	+	19.9639i	−0.959405	+	0.959405i	0.0398028	+	0.999208i	$0.487327\pi$
$434$		0			0
$435$	5.98602	+	5.55426i	0.287008	+	0.266306i
$436$	−0.649575	−	1.12510i	−0.0311090	−	0.0538824i
$437$	−50.8816	+	13.6337i	−2.43400	+	0.652188i
$438$	−0.446325	+	0.119592i	−0.0213262	+	0.00571435i
$439$	−15.0972	−	26.1490i	−0.720548	−	1.24803i	−0.960780	−	0.277310i	$-0.910557\pi$
$439$	−15.0972	−	26.1490i	−0.720548	−	1.24803i	0.240232	−	0.970715i	$-0.422776\pi$
$440$	−6.08824	−	5.64910i	−0.290246	−	0.269310i
$441$		0			0
$442$	0.280632	−	0.280632i	0.0133483	−	0.0133483i
$443$	−4.66400	+	17.4063i	−0.221593	+	0.826997i	0.762148	+	0.647403i	$0.224145\pi$
$443$	−4.66400	+	17.4063i	−0.221593	+	0.826997i	−0.983741	+	0.179594i	$0.942522\pi$
$444$	−0.401803	+	0.695944i	−0.0190687	+	0.0330280i
$445$	−8.17681	+	15.4711i	−0.387618	+	0.733402i
$446$	−0.392082	+	0.226369i	−0.0185656	+	0.0107189i
$447$	2.22112	+	2.22112i	0.105056	+	0.105056i
$448$		0			0
$449$		−	30.4170i		−	1.43547i	−0.696318	−	0.717734i	$-0.745180\pi$
$449$		−	30.4170i		−	1.43547i	0.696318	−	0.717734i	$-0.254820\pi$
$450$	0.219619	−	1.16067i	0.0103529	−	0.0547144i
$451$	26.3451	+	15.2103i	1.24054	+	0.716227i
$452$	2.41704	+	9.02051i	0.113688	+	0.424289i
$453$	14.2222	+	3.81084i	0.668219	+	0.179049i
$454$	−1.38802			−0.0651432
$455$		0			0
$456$	6.72637			0.314991
$457$	−1.79696	−	0.481493i	−0.0840581	−	0.0225233i	0.216545	−	0.976273i	$-0.430521\pi$
$457$	−1.79696	−	0.481493i	−0.0840581	−	0.0225233i	−0.300603	+	0.953749i	$0.597188\pi$
$458$	−0.794295	−	2.96435i	−0.0371150	−	0.138515i
$459$	−2.05561	−	1.18681i	−0.0959476	−	0.0553954i
$460$	−30.9289	−	7.05945i	−1.44207	−	0.329148i
$461$			1.29957i			0.0605272i	0.999542	+	0.0302636i	$0.00963467\pi$
$461$			1.29957i			0.0605272i	−0.999542	+	0.0302636i	$0.990365\pi$
$462$		0			0
$463$	16.5240	+	16.5240i	0.767934	+	0.767934i	0.977742	−	0.209809i	$-0.0672841\pi$
$463$	16.5240	+	16.5240i	0.767934	+	0.767934i	−0.209809	+	0.977742i	$0.567284\pi$
$464$	−11.6013	+	6.69801i	−0.538577	+	0.310947i
$465$	−10.5516	+	3.25470i	−0.489320	+	0.150933i
$466$	−2.75039	+	4.76381i	−0.127409	+	0.220679i
$467$	7.35742	−	27.4583i	0.340461	−	1.27062i	−0.557365	−	0.830267i	$-0.688188\pi$
$467$	7.35742	−	27.4583i	0.340461	−	1.27062i	0.897826	−	0.440350i	$-0.145146\pi$
$468$	0.972943	−	0.972943i	0.0449743	−	0.0449743i
$469$		0			0
$470$	0.227932	−	0.00852775i	0.0105137	−	0.000393356i
$471$	5.63216	+	9.75519i	0.259516	+	0.449495i
$472$	5.49908	−	1.47347i	0.253116	−	0.0678221i
$473$	−19.8847	+	5.32808i	−0.914298	+	0.244986i
$474$	−1.02064	−	1.76781i	−0.0468797	−	0.0811980i
$475$	−35.9916	+	2.69693i	−1.65141	+	0.123744i
$476$		0			0
$477$	5.39653	−	5.39653i	0.247090	−	0.247090i
$478$	0.335113	−	1.25066i	0.0153277	−	0.0572038i
$479$	5.54182	−	9.59872i	0.253212	−	0.438577i	−0.711196	−	0.702994i	$-0.751846\pi$
$479$	5.54182	−	9.59872i	0.253212	−	0.438577i	0.964408	+	0.264417i	$0.0851795\pi$
$480$	5.39759	+	2.85273i	0.246365	+	0.130209i
$481$	−0.253339	+	0.146265i	−0.0115513	+	0.00666912i
$482$	−2.44749	−	2.44749i	−0.111480	−	0.111480i
$483$		0			0
$484$			9.50389i			0.431995i
$485$	5.23309	−	22.9273i	0.237623	−	1.04107i
$486$	0.204601	+	0.118126i	0.00928088	+	0.00535832i
$487$	−4.99695	−	18.6489i	−0.226433	−	0.845060i	−0.981825	−	0.189787i	$-0.939220\pi$
$487$	−4.99695	−	18.6489i	−0.226433	−	0.845060i	0.755392	−	0.655273i	$-0.227446\pi$
$488$	−6.39994	−	1.71486i	−0.289712	−	0.0776280i
$489$	14.7714			0.667986
$490$		0			0
$491$	32.1155			1.44935			0.724677	−	0.689089i	$-0.241989\pi$
$491$	32.1155			1.44935			0.724677	+	0.689089i	$0.241989\pi$
$492$	−14.3321	−	3.84028i	−0.646142	−	0.173133i
$493$	2.24350	+	8.37286i	0.101042	+	0.377095i
$494$	1.04525	+	0.603474i	0.0470279	+	0.0271516i
$495$	−7.54688	+	4.74198i	−0.339207	+	0.213136i
$496$		−	18.1145i		−	0.813364i
$497$		0			0
$498$	−2.83255	−	2.83255i	−0.126930	−	0.126930i
$499$	−3.70166	+	2.13715i	−0.165709	+	0.0956722i	−0.580561	−	0.814217i	$-0.697167\pi$
$499$	−3.70166	+	2.13715i	−0.165709	+	0.0956722i	0.414852	+	0.909889i	$0.363833\pi$
$500$	−19.9229	−	8.69253i	−0.890979	−	0.388742i
$501$	−3.27830	+	5.67818i	−0.146463	+	0.253682i
$502$	1.29329	−	4.82662i	0.0577223	−	0.215423i
$503$	17.5637	−	17.5637i	0.783128	−	0.783128i	−0.197229	−	0.980357i	$-0.563194\pi$
$503$	17.5637	−	17.5637i	0.783128	−	0.783128i	0.980357	+	0.197229i	$0.0631943\pi$
$504$		0			0
$505$	0.528051	+	14.1139i	0.0234980	+	0.628059i
$506$	−3.43603	−	5.95138i	−0.152750	−	0.264571i
$507$	−12.0732	+	3.23501i	−0.536191	+	0.143672i
$508$	15.6384	−	4.19029i	0.693840	−	0.185914i
$509$	13.9581	+	24.1762i	0.618682	+	1.07159i	0.989726	+	0.142974i	$0.0456666\pi$
$509$	13.9581	+	24.1762i	0.618682	+	1.07159i	−0.371044	+	0.928615i	$0.621000\pi$
$510$	0.852889	−	0.919189i	0.0377666	−	0.0407024i
$511$		0			0
$512$	−11.9158	+	11.9158i	−0.526611	+	0.526611i
$513$	1.86829	−	6.97254i	0.0824868	−	0.307845i
$514$	−1.56907	+	2.71771i	−0.0692086	+	0.119873i
$515$	−11.6893	−	37.8961i	−0.515090	−	1.66990i
$516$	8.69567	−	5.02045i	0.382806	−	0.221013i
$517$	−1.21695	−	1.21695i	−0.0535212	−	0.0535212i
$518$		0			0
$519$			3.51476i			0.154281i
$520$	0.784547	+	1.24861i	0.0344047	+	0.0547552i
$521$	24.9975	+	14.4323i	1.09516	+	0.632292i	0.934946	−	0.354790i	$-0.115448\pi$
$521$	24.9975	+	14.4323i	1.09516	+	0.632292i	0.160216	+	0.987082i	$0.448781\pi$
$522$	−0.223302	−	0.833375i	−0.00977367	−	0.0364758i
$523$	4.84539	+	1.29832i	0.211874	+	0.0567715i	0.363195	−	0.931713i	$-0.381686\pi$
$523$	4.84539	+	1.29832i	0.211874	+	0.0567715i	−0.151321	+	0.988485i	$0.548353\pi$
$524$	36.5788			1.59795
$525$		0			0
$526$	−5.13793			−0.224024
$527$	−11.3220	−	3.03372i	−0.493195	−	0.132151i
$528$	−3.78435	−	14.1234i	−0.164693	−	0.614642i
$529$	−26.1995	−	15.1263i	−1.13911	−	0.657665i
$530$	2.14499	+	3.41377i	0.0931726	+	0.148285i
$531$		−	6.10959i		−	0.265134i
$532$		0			0
$533$	−3.81926	−	3.81926i	−0.165430	−	0.165430i
$534$	1.60117	−	0.924434i	0.0692892	−	0.0400042i
$535$	6.97219	+	22.6036i	0.301434	+	0.977239i
$536$	0.622122	−	1.07755i	0.0268716	−	0.0465430i
$537$	−5.72271	+	21.3574i	−0.246953	+	0.921642i
$538$	3.83980	−	3.83980i	0.165546	−	0.165546i
$539$		0			0
$540$	2.95695	−	3.18681i	0.127247	−	0.137138i
$541$	2.04349	+	3.53943i	0.0878565	+	0.152172i	0.906605	−	0.421981i	$-0.138665\pi$
$541$	2.04349	+	3.53943i	0.0878565	+	0.152172i	−0.818748	+	0.574153i	$0.805332\pi$
$542$	−3.59639	+	0.963650i	−0.154478	+	0.0413923i
$543$	8.19615	−	2.19615i	0.351731	−	0.0942459i
$544$	3.24031	+	5.61238i	0.138927	+	0.240629i
$545$	−0.0558641	−	1.49315i	−0.00239296	−	0.0639594i
$546$		0			0
$547$	28.2200	−	28.2200i	1.20660	−	1.20660i	0.234482	−	0.972121i	$-0.424661\pi$
$547$	28.2200	−	28.2200i	1.20660	−	1.20660i	0.972121	−	0.234482i	$-0.0753392\pi$
$548$	−0.577820	+	2.15645i	−0.0246832	+	0.0921191i
$549$	−3.55523	+	6.15784i	−0.151734	+	0.262810i
$550$	−1.55510	−	4.44433i	−0.0663097	−	0.189507i
$551$	−22.8296	+	13.1807i	−0.972572	+	0.561515i
$552$	4.80827	+	4.80827i	0.204654	+	0.204654i
$553$		0			0
$554$			1.60631i			0.0682457i
$555$	−0.782590	+	0.491730i	−0.0332191	+	0.0208728i
$556$	0.744941	+	0.430092i	0.0315925	+	0.0182400i
$557$	10.3079	+	38.4695i	0.436758	+	1.63000i	0.736823	+	0.676086i	$0.236325\pi$
$557$	10.3079	+	38.4695i	0.436758	+	1.63000i	−0.300065	+	0.953919i	$0.597008\pi$
$558$	1.12691	+	0.301955i	0.0477060	+	0.0127828i
$559$	3.65510			0.154594
$560$		0			0
$561$	−9.46128			−0.399455
$562$	−2.20366	−	0.590468i	−0.0929556	−	0.0249074i
$563$	−10.0161	−	37.3806i	−0.422129	−	1.57541i	−0.770114	−	0.637906i	$-0.779801\pi$
$563$	−10.0161	−	37.3806i	−0.422129	−	1.57541i	0.347985	−	0.937500i	$-0.386866\pi$
$564$	0.726967	+	0.419715i	0.0306108	+	0.0176732i
$565$	−2.39008	+	10.4715i	−0.100552	+	0.440537i
$566$			4.98144i			0.209386i
$567$		0			0
$568$	−0.786047	−	0.786047i	−0.0329818	−	0.0329818i
$569$	15.3951	−	8.88837i	0.645396	−	0.372620i	−0.141294	−	0.989968i	$-0.545126\pi$
$569$	15.3951	−	8.88837i	0.645396	−	0.372620i	0.786690	+	0.617348i	$0.211793\pi$
$570$	3.37145	+	1.78188i	0.141215	+	0.0746347i
$571$	8.44331	−	14.6242i	0.353342	−	0.612005i	−0.633491	−	0.773750i	$-0.718379\pi$
$571$	8.44331	−	14.6242i	0.353342	−	0.612005i	0.986833	+	0.161744i	$0.0517120\pi$
$572$	1.41951	−	5.29768i	0.0593527	−	0.221507i
$573$	10.8116	−	10.8116i	0.451659	−	0.451659i
$574$		0			0
$575$	−27.6561	−	23.8003i	−1.15334	−	0.992543i
$576$	3.34571	+	5.79493i	0.139404	+	0.241456i
$577$	−5.32309	+	1.42632i	−0.221603	+	0.0593784i	−0.367912	−	0.929861i	$-0.619927\pi$
$577$	−5.32309	+	1.42632i	−0.221603	+	0.0593784i	0.146309	+	0.989239i	$0.453261\pi$
$578$	−2.59374	+	0.694991i	−0.107885	+	0.0289078i
$579$	6.31296	+	10.9344i	0.262358	+	0.454417i
$580$	−15.8650	+	0.593566i	−0.658756	+	0.0246465i
$581$		0			0
$582$	−1.75694	+	1.75694i	−0.0728276	+	0.0728276i
$583$	7.87345	−	29.3841i	0.326085	−	1.21697i
$584$	0.911244	−	1.57832i	0.0377075	−	0.0653114i
$585$	1.51222	−	0.466451i	0.0625225	−	0.0192854i
$586$	1.38667	−	0.800592i	0.0572826	−	0.0330721i
$587$	−15.1058	−	15.1058i	−0.623484	−	0.623484i	0.322937	−	0.946420i	$-0.395330\pi$
$587$	−15.1058	−	15.1058i	−0.623484	−	0.623484i	−0.946420	+	0.322937i	$0.895330\pi$
$588$		0			0
$589$		−	35.6465i		−	1.46879i
$590$	3.14663	+	0.718211i	0.129545	+	0.0295683i
$591$	−3.29107	−	1.90010i	−0.135377	−	0.0781597i
$592$	−0.392426	−	1.46456i	−0.0161286	−	0.0601928i
$593$	4.68590	+	1.25558i	0.192427	+	0.0515606i	0.353745	−	0.935342i	$-0.384908\pi$
$593$	4.68590	+	1.25558i	0.192427	+	0.0515606i	−0.161318	+	0.986902i	$0.551575\pi$
$594$	0.941708			0.0386388
$595$		0			0
$596$	−6.10696			−0.250151
$597$	−0.595625	−	0.159597i	−0.0243773	−	0.00653188i
$598$	0.315797	+	1.17857i	0.0129139	+	0.0481953i
$599$	8.74769	+	5.05048i	0.357421	+	0.206357i	0.667949	−	0.744207i	$-0.267173\pi$
$599$	8.74769	+	5.05048i	0.357421	+	0.206357i	−0.310528	+	0.950564i	$0.600506\pi$
$600$	2.62455	+	3.84957i	0.107147	+	0.157158i
$601$			38.4063i			1.56663i	0.621628	+	0.783313i	$0.286472\pi$
$601$			38.4063i			1.56663i	−0.621628	+	0.783313i	$0.713528\pi$
$602$		0			0
$603$	−0.944185	−	0.944185i	−0.0384502	−	0.0384502i
$604$	−24.7909	+	14.3130i	−1.00873	+	0.582389i
$605$	−5.10762	+	9.66400i	−0.207654	+	0.392898i
$606$	0.746125	−	1.29233i	0.0303093	−	0.0524972i
$607$	3.76752	−	14.0606i	0.152919	−	0.570702i	−0.846356	−	0.532618i	$-0.821208\pi$
$607$	3.76752	−	14.0606i	0.152919	−	0.570702i	0.999275	−	0.0380833i	$-0.0121252\pi$
$608$	−13.9360	+	13.9360i	−0.565180	+	0.565180i
$609$		0			0
$610$	−2.75355	−	2.55494i	−0.111488	−	0.103447i
$611$	0.152785	+	0.264632i	0.00618103	+	0.0107059i
$612$	4.45750	−	1.19438i	0.180184	−	0.0482801i
$613$	19.6919	−	5.27642i	0.795347	−	0.213113i	0.161807	−	0.986822i	$-0.448268\pi$
$613$	19.6919	−	5.27642i	0.795347	−	0.213113i	0.633540	+	0.773710i	$0.281601\pi$
$614$	1.64560	+	2.85027i	0.0664112	+	0.115028i
$615$	−12.5097	−	11.6074i	−0.504440	−	0.468056i
$616$		0			0
$617$	−25.4196	+	25.4196i	−1.02336	+	1.02336i	−0.0236346	+	0.999721i	$0.507524\pi$
$617$	−25.4196	+	25.4196i	−1.02336	+	1.02336i	−0.999721	+	0.0236346i	$0.992476\pi$
$618$	−1.08447	+	4.04731i	−0.0436239	+	0.162807i
$619$	5.59953	−	9.69868i	0.225064	−	0.389823i	−0.731274	−	0.682083i	$-0.761074\pi$
$619$	5.59953	−	9.69868i	0.225064	−	0.389823i	0.956339	+	0.292261i	$0.0944075\pi$
$620$	10.0314	−	18.9802i	0.402871	−	0.762262i
$621$	6.31977	−	3.64872i	0.253603	−	0.146418i
$622$	−4.56168	−	4.56168i	−0.182907	−	0.182907i
$623$		0			0
$624$			2.59609i			0.103927i
$625$	−15.5870	−	19.5460i	−0.623478	−	0.781841i
$626$	−5.35527	−	3.09186i	−0.214040	−	0.123576i
$627$	−7.44703	−	27.7927i	−0.297406	−	1.10993i
$628$	−21.1537	−	5.66812i	−0.844124	−	0.226182i
$629$	−0.981107			−0.0391193
$630$		0			0
$631$	21.2015			0.844020			0.422010	−	0.906591i	$-0.361325\pi$
$631$	21.2015			0.844020			0.422010	+	0.906591i	$0.361325\pi$
$632$	7.77687	+	2.08381i	0.309347	+	0.0828894i
$633$	2.40921	+	8.99131i	0.0957577	+	0.357373i
$634$	6.33077	+	3.65507i	0.251427	+	0.145161i
$635$	18.1538	+	4.14355i	0.720411	+	0.164432i
$636$			14.8377i			0.588353i
$637$		0			0
$638$	−2.43176	−	2.43176i	−0.0962745	−	0.0962745i
$639$	−1.03314	+	0.596485i	−0.0408705	+	0.0235966i
$640$	−15.0456	+	4.64089i	−0.594729	+	0.183447i
$641$	14.9484	−	25.8915i	0.590428	−	1.02265i	−0.403746	−	0.914871i	$-0.632292\pi$
$641$	14.9484	−	25.8915i	0.590428	−	1.02265i	0.994175	−	0.107781i	$-0.0343745\pi$
$642$	0.646846	−	2.41406i	0.0255290	−	0.0952755i
$643$	11.2813	−	11.2813i	0.444891	−	0.444891i	−0.448761	−	0.893652i	$-0.648134\pi$
$643$	11.2813	−	11.2813i	0.444891	−	0.444891i	0.893652	+	0.448761i	$0.148134\pi$
$644$		0			0
$645$	11.5403	−	0.431764i	0.454398	−	0.0170007i
$646$	2.02397	+	3.50562i	0.0796320	+	0.137927i
$647$	35.8439	−	9.60434i	1.40917	−	0.377586i	0.527540	−	0.849530i	$-0.323114\pi$
$647$	35.8439	−	9.60434i	1.40917	−	0.377586i	0.881628	+	0.471944i	$0.156448\pi$
$648$	−0.900073	+	0.241174i	−0.0353582	+	0.00947420i
$649$	−12.1765	−	21.0903i	−0.477969	−	0.827866i
$650$	0.0624689	+	0.833673i	0.00245023	+	0.0326993i
$651$		0			0
$652$	−20.3069	+	20.3069i	−0.795281	+	0.795281i
$653$	−0.723414	+	2.69982i	−0.0283094	+	0.105652i	−0.978635	−	0.205606i	$-0.934084\pi$
$653$	−0.723414	+	2.69982i	−0.0283094	+	0.105652i	0.950326	+	0.311258i	$0.100750\pi$
$654$	−0.0789348	+	0.136719i	−0.00308659	+	0.00534614i
$655$	37.1950	+	19.6583i	1.45333	+	0.768113i
$656$	24.2446	−	13.9976i	0.946594	−	0.546516i
$657$	−1.38298	−	1.38298i	−0.0539552	−	0.0539552i
$658$		0			0
$659$			15.1044i			0.588385i	0.955746	+	0.294193i	$0.0950507\pi$
$659$			15.1044i			0.588385i	−0.955746	+	0.294193i	$0.904949\pi$
$660$	3.85603	−	16.8941i	0.150096	−	0.657601i
$661$	−0.953098	−	0.550272i	−0.0370712	−	0.0214031i	0.481350	−	0.876529i	$-0.340147\pi$
$661$	−0.953098	−	0.550272i	−0.0370712	−	0.0214031i	−0.518421	+	0.855125i	$0.673480\pi$
$662$	1.02062	+	3.80900i	0.0396675	+	0.148041i
$663$	1.62263	+	0.434781i	0.0630176	+	0.0168855i
$664$	15.7998			0.613150
$665$		0			0
$666$	0.0976524			0.00378395
$667$	−25.7415	−	6.89742i	−0.996716	−	0.267069i
$668$	−3.29923	−	12.3129i	−0.127651	−	0.476399i
$669$	−1.65959	−	0.958163i	−0.0641633	−	0.0370447i
$670$	0.597278	−	0.375292i	0.0230749	−	0.0144988i
$671$			28.3425i			1.09415i
$672$		0			0
$673$	−11.4381	−	11.4381i	−0.440906	−	0.440906i	0.451411	−	0.892316i	$-0.350921\pi$
$673$	−11.4381	−	11.4381i	−0.440906	−	0.440906i	−0.892316	+	0.451411i	$0.850921\pi$
$674$	0.735028	−	0.424369i	0.0283122	−	0.0163461i
$675$	4.71943	−	1.65136i	0.181651	−	0.0635609i
$676$	12.1503	−	21.0449i	0.467319	−	0.809421i
$677$	−9.00447	+	33.6052i	−0.346070	+	1.29155i	0.545287	+	0.838249i	$0.316421\pi$
$677$	−9.00447	+	33.6052i	−0.346070	+	1.29155i	−0.891357	+	0.453302i	$0.850246\pi$
$678$	0.802438	−	0.802438i	0.0308175	−	0.0308175i
$679$		0			0
$680$	0.184908	+	4.94226i	0.00709089	+	0.189527i
$681$	−2.93759	−	5.08805i	−0.112569	−	0.194974i
$682$	4.49190	−	1.20360i	0.172004	−	0.0460882i
$683$	18.9404	−	5.07507i	0.724736	−	0.194192i	0.122452	−	0.992474i	$-0.460924\pi$
$683$	18.9404	−	5.07507i	0.724736	−	0.194192i	0.602284	+	0.798282i	$0.294258\pi$
$684$	7.01705	+	12.1539i	0.268304	+	0.464715i
$685$	−1.74648	+	1.88225i	−0.0667297	+	0.0719170i
$686$		0			0
$687$	9.18531	−	9.18531i	0.350442	−	0.350442i
$688$	−4.90328	+	18.2993i	−0.186936	+	0.697655i
$689$	−2.70062	+	4.67762i	−0.102886	+	0.178203i
$690$	1.13629	+	3.68380i	0.0432577	+	0.140240i
$691$	10.7439	−	6.20301i	0.408718	−	0.235974i	−0.281521	−	0.959555i	$-0.590839\pi$
$691$	10.7439	−	6.20301i	0.408718	−	0.235974i	0.690239	+	0.723582i	$0.257505\pi$
$692$	−4.83190	−	4.83190i	−0.183681	−	0.183681i
$693$		0			0
$694$			4.57667i			0.173728i
$695$	0.526349	+	0.837687i	0.0199656	+	0.0317753i
$696$	2.94703	+	1.70147i	0.111707	+	0.0644940i
$697$	−4.68852	−	17.4978i	−0.177590	−	0.662776i
$698$	0.116064	+	0.0310993i	0.00439309	+	0.00117713i
$699$	−23.2835			−0.880661
$700$		0			0
$701$	1.45193			0.0548388			0.0274194	−	0.999624i	$-0.491271\pi$
$701$	1.45193			0.0548388			0.0274194	+	0.999624i	$0.491271\pi$
$702$	−0.161505	−	0.0432751i	−0.00609560	−	0.00163331i
$703$	−0.772235	−	2.88202i	−0.0291254	−	0.108697i
$704$	23.0987	+	13.3361i	0.870566	+	0.502622i
$705$	0.513649	+	0.817475i	0.0193452	+	0.0307879i
$706$			3.64907i			0.137335i
$707$		0			0
$708$	8.39914	+	8.39914i	0.315659	+	0.315659i
$709$	42.0269	−	24.2642i	1.57835	−	0.911262i	0.583262	−	0.812284i	$-0.301776\pi$
$709$	42.0269	−	24.2642i	1.57835	−	0.911262i	0.995090	−	0.0989781i	$-0.0315574\pi$
$710$	−0.185758	−	0.602220i	−0.00697137	−	0.0226009i
$711$	4.32013	−	7.48269i	0.162018	−	0.280623i
$712$	−1.88738	+	7.04380i	−0.0707325	+	0.263977i
$713$	25.4815	−	25.4815i	0.954290	−	0.954290i
$714$		0			0
$715$	4.29052	−	4.62405i	0.160457	−	0.172930i
$716$	−21.4938	−	37.2283i	−0.803261	−	1.39129i
$717$	5.29373	−	1.41845i	0.197698	−	0.0529730i
$718$	3.64805	−	0.977492i	0.136144	−	0.0364797i
$719$	−21.7936	−	37.7476i	−0.812764	−	1.40775i	−0.910922	−	0.412578i	$-0.864628\pi$
$719$	−21.7936	−	37.7476i	−0.812764	−	1.40775i	0.0981578	−	0.995171i	$-0.468705\pi$
$720$	0.306667	+	8.19666i	0.0114288	+	0.305472i
$721$		0			0
$722$	−5.53068	+	5.53068i	−0.205831	+	0.205831i
$723$	3.79189	−	14.1515i	0.141022	−	0.526301i
$724$	−8.24848	+	14.2868i	−0.306552	+	0.530964i
$725$	−16.4512	−	7.92264i	−0.610983	−	0.294240i
$726$	1.00016	−	0.577445i	0.0371196	−	0.0214310i
$727$	10.4498	+	10.4498i	0.387563	+	0.387563i	0.873817	−	0.486254i	$-0.161637\pi$
$727$	10.4498	+	10.4498i	0.387563	+	0.387563i	−0.486254	+	0.873817i	$0.661637\pi$
$728$		0			0
$729$			1.00000i			0.0370370i
$730$	0.874853	−	0.549702i	0.0323798	−	0.0203454i
$731$	10.6164	+	6.12936i	0.392660	+	0.226703i
$732$	−3.57793	−	13.3530i	−0.132244	−	0.493542i
$733$	−25.7752	−	6.90644i	−0.952028	−	0.255095i	−0.250806	−	0.968037i	$-0.580695\pi$
$733$	−25.7752	−	6.90644i	−0.952028	−	0.255095i	−0.701223	+	0.712942i	$0.747362\pi$
$734$	−0.136998			−0.00505669
$735$		0			0
$736$	−19.9240			−0.734409
$737$	−5.14109	−	1.37755i	−0.189375	−	0.0507428i
$738$	0.466662	+	1.74161i	0.0171781	+	0.0641094i
$739$	18.1596	+	10.4845i	0.668013	+	0.385677i	0.795323	−	0.606186i	$-0.207301\pi$
$739$	18.1596	+	10.4845i	0.668013	+	0.385677i	−0.127311	+	0.991863i	$0.540634\pi$
$740$	0.399859	−	1.75187i	0.0146991	−	0.0643999i
$741$			5.10872i			0.187673i
$742$		0			0
$743$	9.18724	+	9.18724i	0.337047	+	0.337047i	0.855255	−	0.518208i	$-0.173401\pi$
$743$	9.18724	+	9.18724i	0.337047	+	0.337047i	−0.518208	+	0.855255i	$0.673401\pi$
$744$	−3.98506	+	2.30077i	−0.146099	+	0.0843504i
$745$	−6.20984	−	3.28203i	−0.227511	−	0.120244i
$746$	−0.575501	+	0.996797i	−0.0210706	+	0.0364953i
$747$	4.38847	−	16.3780i	0.160566	−	0.599239i
$748$	13.0069	−	13.0069i	0.475578	−	0.475578i
$749$		0			0
$750$	0.295712	+	2.62478i	0.0107979	+	0.0958434i
$751$	−5.59843	−	9.69676i	−0.204290	−	0.353840i	0.745617	−	0.666375i	$-0.232155\pi$
$751$	−5.59843	−	9.69676i	−0.204290	−	0.353840i	−0.949906	+	0.312535i	$0.898822\pi$
$752$	−1.52984	+	0.409919i	−0.0557875	+	0.0149482i
$753$	20.4299	−	5.47418i	0.744507	−	0.199490i
$754$	0.305303	+	0.528801i	0.0111185	+	0.0192578i
$755$	−32.9007	+	1.23094i	−1.19738	+	0.0447984i
$756$		0			0
$757$	−13.9324	+	13.9324i	−0.506383	+	0.506383i	−0.913414	−	0.407031i	$-0.866564\pi$
$757$	−13.9324	+	13.9324i	−0.506383	+	0.506383i	0.407031	+	0.913414i	$0.366564\pi$
$758$	−0.789886	+	2.94789i	−0.0286899	+	0.107072i
$759$	14.5439	−	25.1907i	0.527909	−	0.914365i
$760$	−14.3724	+	4.43325i	−0.521343	+	0.160811i
$761$	7.61085	−	4.39412i	0.275893	−	0.159287i	−0.355670	−	0.934612i	$-0.615747\pi$
$761$	7.61085	−	4.39412i	0.275893	−	0.159287i	0.631563	+	0.775325i	$0.282414\pi$
$762$	−1.39114	−	1.39114i	−0.0503958	−	0.0503958i
$763$		0			0
$764$			29.7263i			1.07546i
$765$	5.17449	+	1.18106i	0.187084	+	0.0427014i
$766$	2.91577	+	1.68342i	0.105351	+	0.0608245i
$767$	1.11911	+	4.17658i	0.0404088	+	0.150808i
$768$	−11.3199	−	3.03317i	−0.408473	−	0.109450i
$769$	−11.2183			−0.404543			−0.202271	−	0.979330i	$-0.564832\pi$
$769$	−11.2183			−0.404543			−0.202271	+	0.979330i	$0.564832\pi$
$770$		0			0
$771$	−13.2830			−0.478374
$772$	−23.7107	−	6.35326i	−0.853366	−	0.228659i
$773$	7.87192	+	29.3784i	0.283133	+	1.05667i	0.950193	+	0.311663i	$0.100886\pi$
$773$	7.87192	+	29.3784i	0.283133	+	1.05667i	−0.667059	+	0.745005i	$0.732447\pi$
$774$	−1.05668	−	0.610073i	−0.0379815	−	0.0219286i
$775$	20.4008	−	13.9088i	0.732819	−	0.499620i
$776$		−	9.80008i		−	0.351802i
$777$		0			0
$778$	4.06447	+	4.06447i	0.145718	+	0.145718i
$779$	47.7097	−	27.5452i	1.70938	−	0.986910i
$780$	−1.43766	+	2.72017i	−0.0514766	+	0.0973976i
$781$	−2.37760	+	4.11813i	−0.0850773	+	0.147358i
$782$	−1.05914	+	3.95276i	−0.0378748	+	0.141351i
$783$	2.58229	−	2.58229i	0.0922835	−	0.0922835i
$784$		0			0
$785$	−18.4639	−	17.1321i	−0.659004	−	0.611471i
$786$	−2.22248	−	3.84945i	−0.0792733	−	0.137305i
$787$	−51.1813	+	13.7140i	−1.82442	+	0.488851i	−0.997317	−	0.0732040i	$-0.976678\pi$
$787$	−51.1813	+	13.7140i	−1.82442	+	0.488851i	−0.827100	+	0.562055i	$0.810011\pi$
$788$	7.13654	−	1.91223i	0.254229	−	0.0681204i
$789$	−10.8738	−	18.8340i	−0.387118	−	0.670507i
$790$	3.34597	+	3.10463i	0.119044	+	0.110458i
$791$		0			0
$792$	−2.62639	+	2.62639i	−0.0933246	+	0.0933246i
$793$	1.30244	−	4.86079i	0.0462511	−	0.172612i
$794$	1.13704	−	1.96941i	0.0403520	−	0.0698916i
$795$	−7.97414	+	15.0877i	−0.282814	+	0.535105i
$796$	1.03824	−	0.599428i	0.0367994	−	0.0212462i
$797$	6.96365	+	6.96365i	0.246665	+	0.246665i	0.819601	−	0.572935i	$-0.194195\pi$
$797$	6.96365	+	6.96365i	0.246665	+	0.246665i	−0.572935	+	0.819601i	$0.694195\pi$
$798$		0			0
$799$			1.02484i			0.0362563i
$800$	−13.4134	−	2.53805i	−0.474234	−	0.0897336i
$801$	6.77735	+	3.91290i	0.239466	+	0.138256i
$802$	0.539980	+	2.01523i	0.0190674	+	0.0711604i
$803$	−7.53033	−	2.01775i	−0.265740	−	0.0712047i
$804$	2.59603			0.0915549
$805$		0			0
$806$	−0.825679			−0.0290833
$807$	22.2019	+	5.94899i	0.781545	+	0.209414i
$808$	1.52333	+	5.68516i	0.0535907	+	0.200003i
$809$	−36.5817	−	21.1205i	−1.28614	−	0.742556i	−0.308180	−	0.951328i	$-0.599720\pi$
$809$	−36.5817	−	21.1205i	−1.28614	−	0.742556i	−0.977964	+	0.208772i	$0.933053\pi$
$810$	−0.515032	−	0.117555i	−0.0180964	−	0.00413045i
$811$			34.9480i			1.22719i	0.789620	+	0.613596i	$0.210277\pi$
$811$			34.9480i			1.22719i	−0.789620	+	0.613596i	$0.789723\pi$
$812$		0			0
$813$	−11.1438	−	11.1438i	−0.390828	−	0.390828i
$814$	0.337096	−	0.194622i	0.0118152	−	0.00682151i
$815$	−31.5625	+	9.73561i	−1.10559	+	0.341023i
$816$	−4.35347	+	7.54044i	−0.152402	+	0.263968i
$817$	−9.64891	+	36.0102i	−0.337573	+	1.25984i
$818$	3.87544	−	3.87544i	0.135502	−	0.135502i
$819$		0			0
$820$	33.1549	−	1.24045i	1.15782	−	0.0433183i
$821$	2.06708	+	3.58030i	0.0721418	+	0.124953i	0.899840	−	0.436221i	$-0.143683\pi$
$821$	2.06708	+	3.58030i	0.0721418	+	0.124953i	−0.827698	+	0.561174i	$0.810350\pi$
$822$	0.262047	−	0.0702153i	0.00913994	−	0.00244904i
$823$	7.81506	−	2.09404i	0.272416	−	0.0729936i	−0.120025	−	0.992771i	$-0.538297\pi$
$823$	7.81506	−	2.09404i	0.272416	−	0.0729936i	0.392441	+	0.919777i	$0.371631\pi$
$824$	−8.26322	−	14.3123i	−0.287863	−	0.498593i
$825$	13.0003	−	15.1064i	0.452611	−	0.525936i
$826$		0			0
$827$	17.0630	−	17.0630i	0.593339	−	0.593339i	−0.345193	−	0.938532i	$-0.612187\pi$
$827$	17.0630	−	17.0630i	0.593339	−	0.593339i	0.938532	+	0.345193i	$0.112187\pi$
$828$	−3.67201	+	13.7041i	−0.127611	+	0.476252i
$829$	18.8573	−	32.6618i	0.654940	−	1.13439i	−0.326968	−	0.945035i	$-0.606027\pi$
$829$	18.8573	−	32.6618i	0.654940	−	1.13439i	0.981909	−	0.189355i	$-0.0606396\pi$
$830$	7.91929	+	4.18550i	0.274883	+	0.145281i
$831$	−5.88822	+	3.39957i	−0.204260	+	0.117930i
$832$	−3.34863	−	3.34863i	−0.116093	−	0.116093i
$833$		0			0
$834$		−	0.104527i		−	0.00361949i
$835$	3.26243	−	14.2934i	0.112901	−	0.494643i
$836$	48.4457	+	27.9701i	1.67553	+	0.967367i
$837$	1.27810	+	4.76995i	0.0441777	+	0.164873i
$838$	2.97559	+	0.797307i	0.102790	+	0.0275425i
$839$	22.3652			0.772133			0.386066	−	0.922471i	$-0.373834\pi$
$839$	22.3652			0.772133			0.386066	+	0.922471i	$0.373834\pi$
$840$		0			0
$841$	15.6636			0.540123
$842$	−7.15526	−	1.91725i	−0.246587	−	0.0660727i
$843$	−2.49931	−	9.32754i	−0.0860807	−	0.321258i
$844$	−15.6728	−	9.04871i	−0.539481	−	0.311470i
$845$	23.6651	−	14.8696i	0.814103	−	0.511530i
$846$		−	0.102005i		−	0.00350702i
$847$		0			0
$848$	−19.7957	−	19.7957i	−0.679786	−	0.679786i
$849$	−18.2603	+	10.5426i	−0.626693	+	0.361822i
$850$	−1.21657	+	2.52618i	−0.0417280	+	0.0866474i
$851$	1.50816	−	2.61220i	0.0516989	−	0.0895452i
$852$	0.600293	−	2.24032i	0.0205657	−	0.0767522i
$853$	24.1276	−	24.1276i	0.826114	−	0.826114i	−0.160863	−	0.986977i	$-0.551428\pi$
$853$	24.1276	−	24.1276i	0.826114	−	0.826114i	0.986977	+	0.160863i	$0.0514276\pi$
$854$		0			0
$855$	0.603474	+	16.1298i	0.0206384	+	0.551627i
$856$	4.92870	+	8.53675i	0.168459	+	0.291780i
$857$	2.09134	−	0.560372i	0.0714387	−	0.0191419i	−0.222923	−	0.974836i	$-0.571560\pi$
$857$	2.09134	−	0.560372i	0.0714387	−	0.0191419i	0.294361	+	0.955694i	$0.404893\pi$
$858$	−0.643761	+	0.172495i	−0.0219777	+	0.00588889i
$859$	20.9047	+	36.2081i	0.713261	+	1.23540i	0.963627	+	0.267253i	$0.0861158\pi$
$859$	20.9047	+	36.2081i	0.713261	+	1.23540i	−0.250366	+	0.968151i	$0.580551\pi$
$860$	−15.2714	+	16.4585i	−0.520750	+	0.561231i
$861$		0			0
$862$	3.76808	−	3.76808i	0.128341	−	0.128341i
$863$	−5.14806	+	19.2128i	−0.175242	+	0.654011i	0.821268	+	0.570542i	$0.193267\pi$
$863$	−5.14806	+	19.2128i	−0.175242	+	0.654011i	−0.996510	+	0.0834696i	$0.973400\pi$
$864$	1.36514	−	2.36449i	0.0464429	−	0.0804415i
$865$	−2.31652	−	7.51008i	−0.0787641	−	0.255350i
$866$	−5.77654	+	3.33509i	−0.196295	+	0.113331i
$867$	−8.03695	−	8.03695i	−0.272949	−	0.272949i
$868$		0			0
$869$		−	34.4403i		−	1.16831i
$870$	1.02640	+	1.63352i	0.0347983	+	0.0553816i
$871$	0.818403	+	0.472505i	0.0277305	+	0.0160102i
$872$	−0.161158	−	0.601450i	−0.00545750	−	0.0203677i
$873$	−10.1587	−	2.72202i	−0.343821	−	0.0921265i
$874$	−12.4450			−0.420958
$875$		0			0
$876$	3.80249			0.128474
$877$	53.8001	+	14.4157i	1.81670	+	0.486783i	0.996371	−	0.0851110i	$-0.0271245\pi$
$877$	53.8001	+	14.4157i	1.81670	+	0.486783i	0.820328	+	0.571894i	$0.193791\pi$
$878$	−1.84628	−	6.89042i	−0.0623090	−	0.232540i
$879$	5.86942	+	3.38871i	0.197971	+	0.114298i
$880$	17.3947	+	27.6837i	0.586374	+	0.933216i
$881$			25.7205i			0.866546i	0.901263	+	0.433273i	$0.142641\pi$
$881$			25.7205i			0.866546i	−0.901263	+	0.433273i	$0.857359\pi$
$882$		0			0
$883$	−25.0968	−	25.0968i	−0.844574	−	0.844574i	0.144876	−	0.989450i	$-0.453722\pi$
$883$	−25.0968	−	25.0968i	−0.844574	−	0.844574i	−0.989450	+	0.144876i	$0.953722\pi$
$884$	−2.82841	+	1.63299i	−0.0951298	+	0.0549232i
$885$	4.02674	+	13.0545i	0.135357	+	0.438823i
$886$	−2.12867	+	3.68697i	−0.0715142	+	0.123866i
$887$	−13.8704	+	51.7651i	−0.465723	+	1.73810i	0.188760	+	0.982023i	$0.439553\pi$
$887$	−13.8704	+	51.7651i	−0.465723	+	1.73810i	−0.654482	+	0.756077i	$0.727113\pi$
$888$	−0.272349	+	0.272349i	−0.00913942	+	0.00913942i
$889$		0			0
$890$	−2.81198	+	3.03057i	−0.0942577	+	0.101585i
$891$	1.99301	+	3.45200i	0.0667684	+	0.115646i
$892$	3.59874	−	0.964280i	0.120495	−	0.0322865i
$893$	−3.01049	+	0.806659i	−0.100742	+	0.0269938i
$894$	0.371052	+	0.642680i	0.0124098	+	0.0214944i
$895$	−1.84849	−	49.4068i	−0.0617882	−	1.65149i
$896$		0			0
$897$	−3.65191	+	3.65191i	−0.121934	+	0.121934i
$898$	1.85990	−	6.94124i	0.0620656	−	0.231632i
$899$	9.01695	−	15.6178i	0.300732	−	0.520883i
$900$	−4.21782	+	8.75822i	−0.140594	+	0.291941i
$901$	−15.6881	+	9.05752i	−0.522646	+	0.301750i
$902$	5.08195	+	5.08195i	0.169211	+	0.169211i
$903$		0			0
$904$			4.47594i			0.148867i
$905$	−16.0655	+	10.0945i	−0.534035	+	0.335554i
$906$	3.01253	+	1.73929i	0.100085	+	0.0577839i
$907$	−11.1989	−	41.7950i	−0.371855	−	1.38778i	−0.857886	−	0.513840i	$-0.828222\pi$
$907$	−11.1989	−	41.7950i	−0.371855	−	1.38778i	0.486031	−	0.873942i	$-0.338444\pi$
$908$	11.0332	+	2.95634i	0.366150	+	0.0981096i
$909$	6.31633			0.209499
$910$		0			0
$911$	20.7843			0.688614			0.344307	−	0.938857i	$-0.388114\pi$
$911$	20.7843			0.688614			0.344307	+	0.938857i	$0.388114\pi$
$912$	−25.5768	−	6.85329i	−0.846933	−	0.226935i
$913$	−17.4925	−	65.2830i	−0.578918	−	2.16055i
$914$	−0.380628	−	0.219756i	−0.0125901	−	0.00726888i
$915$	3.53803	−	15.5008i	0.116964	−	0.512442i
$916$			25.2550i			0.834447i
$917$		0			0
$918$	−0.396526	−	0.396526i	−0.0130873	−	0.0130873i
$919$	−41.2267	+	23.8023i	−1.35994	+	0.785164i	−0.989616	−	0.143737i	$-0.954088\pi$
$919$	−41.2267	+	23.8023i	−1.35994	+	0.785164i	−0.370328	+	0.928901i	$0.620755\pi$
$920$	−13.4430	−	7.10492i	−0.443204	−	0.234242i
$921$	−6.96544	+	12.0645i	−0.229519	+	0.397539i
$922$	−0.0794646	+	0.296566i	−0.00261703	+	0.00976688i
$923$	0.597007	−	0.597007i	0.0196507	−	0.0196507i
$924$		0			0
$925$	1.34809	−	1.56649i	0.0443249	−	0.0515057i
$926$	2.76043	+	4.78120i	0.0907132	+	0.157120i
$927$	−17.1313	+	4.59031i	−0.562664	+	0.150765i
$928$	−9.63098	+	2.58061i	−0.316152	+	0.0847128i
$929$	−20.3266	−	35.2067i	−0.666895	−	1.15510i	−0.978768	−	0.204972i	$-0.934290\pi$
$929$	−20.3266	−	35.2067i	−0.666895	−	1.15510i	0.311873	−	0.950124i	$-0.399044\pi$
$930$	−2.60692	+	0.0975344i	−0.0854843	+	0.00319828i
$931$		0			0
$932$	32.0088	−	32.0088i	1.04848	−	1.04848i
$933$	7.06740	−	26.3759i	0.231376	−	0.863508i
$934$	3.35797	−	5.81617i	0.109876	−	0.190311i
$935$	20.2162	−	6.23578i	0.661140	−	0.203932i
$936$	0.571123	−	0.329738i	0.0186677	−	0.0107778i
$937$	−8.25994	−	8.25994i	−0.269841	−	0.269841i	0.559195	−	0.829036i	$-0.311110\pi$
$937$	−8.25994	−	8.25994i	−0.269841	−	0.269841i	−0.829036	+	0.559195i	$0.811110\pi$
$938$		0			0
$939$		−	26.1742i		−	0.854163i
$940$	−1.82996	−	0.417683i	−0.0596867	−	0.0136233i
$941$	−24.9263	−	14.3912i	−0.812575	−	0.469140i	0.0352744	−	0.999378i	$-0.488769\pi$
$941$	−24.9263	−	14.3912i	−0.812575	−	0.469140i	−0.847849	+	0.530237i	$0.822103\pi$
$942$	0.688776	+	2.57055i	0.0224415	+	0.0837529i
$943$	53.7952	+	14.4144i	1.75181	+	0.469397i
$944$	−22.4113			−0.729427
$945$		0			0
$946$	−4.86353			−0.158127
$947$	−5.83206	−	1.56270i	−0.189516	−	0.0507808i	0.162812	−	0.986657i	$-0.447943\pi$
$947$	−5.83206	−	1.56270i	−0.189516	−	0.0507808i	−0.352329	+	0.935876i	$0.614610\pi$
$948$	4.34771	+	16.2259i	0.141207	+	0.526992i
$949$	1.19874	+	0.692094i	0.0389128	+	0.0224663i
$950$	−8.37828	−	1.58532i	−0.271827	−	0.0514346i
$951$			30.9421i			1.00336i
$952$		0			0
$953$	31.8382	+	31.8382i	1.03134	+	1.03134i	0.999493	+	0.0318472i	$0.0101390\pi$
$953$	31.8382	+	31.8382i	1.03134	+	1.03134i	0.0318472	+	0.999493i	$0.489861\pi$
$954$	1.56148	−	0.901521i	0.0505548	−	0.0291878i
$955$	−15.9756	+	30.2271i	−0.516959	+	0.978125i
$956$	−5.32753	+	9.22755i	−0.172305	+	0.298440i
$957$	3.76752	−	14.0606i	0.121787	−	0.454514i
$958$	1.85159	−	1.85159i	0.0598221	−	0.0598221i
$959$		0			0
$960$	−10.9682	−	10.1771i	−0.353998	−	0.328464i
$961$	−3.30703	−	5.72794i	−0.106678	−	0.184772i
$962$	−0.0667562	+	0.0178873i	−0.00215231	+	0.000576708i
$963$	10.2181	−	2.73794i	0.329275	−	0.0882290i
$964$	14.2419	+	24.6676i	0.458700	+	0.794491i
$965$	−20.6957	−	19.2030i	−0.666220	−	0.618166i
$966$		0			0
$967$	−17.5518	+	17.5518i	−0.564429	+	0.564429i	−0.930562	−	0.366134i	$-0.880681\pi$
$967$	−17.5518	+	17.5518i	−0.564429	+	0.564429i	0.366134	+	0.930562i	$0.380681\pi$
$968$	−1.17895	+	4.39989i	−0.0378928	+	0.141418i
$969$	−8.56697	+	14.8384i	−0.275211	+	0.476679i
$970$	2.59613	−	4.91208i	0.0833568	−	0.157717i
$971$	−0.0805953	+	0.0465317i	−0.00258643	+	0.00149327i	−0.501293	−	0.865278i	$-0.667142\pi$
$971$	−0.0805953	+	0.0465317i	−0.00258643	+	0.00149327i	0.498706	+	0.866771i	$0.333809\pi$
$972$	−1.37475	−	1.37475i	−0.0440950	−	0.0440950i
$973$		0			0
$974$		−	4.56126i		−	0.146152i
$975$	−2.92377	+	1.99336i	−0.0936354	+	0.0638385i
$976$	22.5883	+	13.0414i	0.723035	+	0.417445i
$977$	1.90257	+	7.10049i	0.0608686	+	0.227165i	0.989659	−	0.143441i	$-0.0458168\pi$
$977$	1.90257	+	7.10049i	0.0608686	+	0.227165i	−0.928790	+	0.370606i	$0.879150\pi$
$978$	3.37087	+	0.903223i	0.107789	+	0.0288819i
$979$	31.1938			0.996959
$980$		0			0
$981$	−0.668223			−0.0213347
$982$	7.32884	+	1.96376i	0.233873	+	0.0626660i
$983$	−11.1249	−	41.5189i	−0.354831	−	1.32425i	−0.880697	−	0.473679i	$-0.842926\pi$
$983$	−11.1249	−	41.5189i	−0.354831	−	1.32425i	0.525867	−	0.850567i	$-0.323741\pi$
$984$	−6.15877	−	3.55577i	−0.196334	−	0.113354i
$985$	8.28445	+	1.89090i	0.263965	+	0.0602492i
$986$			2.04789i			0.0652181i
$987$		0			0
$988$	−7.02319	−	7.02319i	−0.223437	−	0.223437i
$989$	−32.6389	+	18.8441i	−1.03786	+	0.599208i
$990$	−2.01217	+	0.620666i	−0.0639511	+	0.0197260i
$991$	−17.1324	+	29.6742i	−0.544228	+	0.942631i	0.454427	+	0.890784i	$0.349844\pi$
$991$	−17.1324	+	29.6742i	−0.544228	+	0.942631i	−0.998655	+	0.0518468i	$0.983489\pi$
$992$	3.48957	−	13.0233i	0.110794	−	0.413489i
$993$	−11.8025	+	11.8025i	−0.374542	+	0.374542i
$994$		0			0
$995$	1.37788	−	0.0515514i	0.0436817	−	0.00163429i
$996$	16.4825	+	28.5486i	0.522269	+	0.904597i
$997$	28.9336	−	7.75273i	0.916336	−	0.245532i	0.230318	−	0.973116i	$-0.426023\pi$
$997$	28.9336	−	7.75273i	0.916336	−	0.245532i	0.686019	+	0.727584i	$0.259357\pi$
$998$	−0.975408	+	0.261360i	−0.0308760	+	0.00827320i
$999$	0.206669	+	0.357962i	0.00653873	+	0.0113254i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	735.2.v.a.178.6		32
5.2	odd	4	inner	735.2.v.a.472.4		32
7.2	even	3	inner	735.2.v.a.313.3		32
7.3	odd	6		105.2.m.a.13.3	✓	16
7.4	even	3		105.2.m.a.13.4	yes	16
7.5	odd	6	inner	735.2.v.a.313.4		32
7.6	odd	2	inner	735.2.v.a.178.5		32
21.11	odd	6		315.2.p.e.118.5		16
21.17	even	6		315.2.p.e.118.6		16
28.3	even	6		1680.2.cz.d.433.5		16
28.11	odd	6		1680.2.cz.d.433.4		16
35.2	odd	12	inner	735.2.v.a.607.5		32
35.3	even	12		525.2.m.b.307.5		16
35.4	even	6		525.2.m.b.118.5		16
35.12	even	12	inner	735.2.v.a.607.6		32
35.17	even	12		105.2.m.a.97.4	yes	16
35.18	odd	12		525.2.m.b.307.6		16
35.24	odd	6		525.2.m.b.118.6		16
35.27	even	4	inner	735.2.v.a.472.3		32
35.32	odd	12		105.2.m.a.97.3	yes	16
105.17	odd	12		315.2.p.e.307.5		16
105.32	even	12		315.2.p.e.307.6		16
140.67	even	12		1680.2.cz.d.97.5		16
140.87	odd	12		1680.2.cz.d.97.4		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
105.2.m.a.13.3	✓	16	7.3	odd	6
105.2.m.a.13.4	yes	16	7.4	even	3
105.2.m.a.97.3	yes	16	35.32	odd	12
105.2.m.a.97.4	yes	16	35.17	even	12
315.2.p.e.118.5		16	21.11	odd	6
315.2.p.e.118.6		16	21.17	even	6
315.2.p.e.307.5		16	105.17	odd	12
315.2.p.e.307.6		16	105.32	even	12
525.2.m.b.118.5		16	35.4	even	6
525.2.m.b.118.6		16	35.24	odd	6
525.2.m.b.307.5		16	35.3	even	12
525.2.m.b.307.6		16	35.18	odd	12
735.2.v.a.178.5		32	7.6	odd	2	inner
735.2.v.a.178.6		32	1.1	even	1	trivial
735.2.v.a.313.3		32	7.2	even	3	inner
735.2.v.a.313.4		32	7.5	odd	6	inner
735.2.v.a.472.3		32	35.27	even	4	inner
735.2.v.a.472.4		32	5.2	odd	4	inner
735.2.v.a.607.5		32	35.2	odd	12	inner
735.2.v.a.607.6		32	35.12	even	12	inner
1680.2.cz.d.97.4		16	140.87	odd	12
1680.2.cz.d.97.5		16	140.67	even	12
1680.2.cz.d.433.4		16	28.11	odd	6
1680.2.cz.d.433.5		16	28.3	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:	\( N \)	\(=\)	\( 735 = 3 \cdot 5 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	735.v (of order \(12\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.228203 + 0.0611467i) q^{2} +(0.258819 + 0.965926i) q^{3} +(-1.68371 - 0.972092i) q^{4} +(-1.18965 - 1.89334i) q^{5} +0.236253i q^{6} +(-0.658899 - 0.658899i) q^{8} +(-0.866025 + 0.500000i) q^{9} +O(q^{10})\)	\(q+(0.228203 + 0.0611467i) q^{2} +(0.258819 + 0.965926i) q^{3} +(-1.68371 - 0.972092i) q^{4} +(-1.18965 - 1.89334i) q^{5} +0.236253i q^{6} +(-0.658899 - 0.658899i) q^{8} +(-0.866025 + 0.500000i) q^{9} +(-0.155711 - 0.504808i) q^{10} +(-1.99301 + 3.45200i) q^{11} +(0.503192 - 1.87794i) q^{12} +(0.500437 - 0.500437i) q^{13} +(1.52092 - 1.63915i) q^{15} +(1.83411 + 3.17677i) q^{16} +(2.29273 - 0.614336i) q^{17} +(-0.228203 + 0.0611467i) q^{18} +(3.60925 + 6.25141i) q^{19} +(0.162536 + 4.34429i) q^{20} +(-0.665888 + 0.665888i) q^{22} +(-1.88872 + 7.04878i) q^{23} +(0.465912 - 0.806983i) q^{24} +(-2.16945 + 4.50483i) q^{25} +(0.144801 - 0.0836010i) q^{26} +(-0.707107 - 0.707107i) q^{27} +3.65191i q^{29} +(0.447306 - 0.281059i) q^{30} +(-4.27662 - 2.46911i) q^{31} +(0.706647 + 2.63724i) q^{32} +(-3.85020 - 1.03166i) q^{33} +0.560773 q^{34} +1.94418 q^{36} +(-0.399255 - 0.106980i) q^{37} +(0.441387 + 1.64728i) q^{38} +(0.612908 + 0.353863i) q^{39} +(-0.463657 + 2.03138i) q^{40} -7.63184i q^{41} +(3.65191 + 3.65191i) q^{43} +(6.71132 - 3.87478i) q^{44} +(1.97694 + 1.04485i) q^{45} +(-0.862019 + 1.49306i) q^{46} +(-0.111749 + 0.417052i) q^{47} +(-2.59383 + 2.59383i) q^{48} +(-0.770530 + 0.895358i) q^{50} +(1.18681 + 2.05561i) q^{51} +(-1.32906 + 0.356122i) q^{52} +(-7.37179 + 1.97527i) q^{53} +(-0.118126 - 0.204601i) q^{54} +(8.90678 - 0.333235i) q^{55} +(-5.10425 + 5.10425i) q^{57} +(-0.223302 + 0.833375i) q^{58} +(-3.05480 + 5.29106i) q^{59} +(-4.15419 + 1.28138i) q^{60} +(6.15784 - 3.55523i) q^{61} +(-0.824957 - 0.824957i) q^{62} -6.69141i q^{64} +(-1.54284 - 0.352150i) q^{65} +(-0.815543 - 0.470854i) q^{66} +(0.345596 + 1.28978i) q^{67} +(-4.45750 - 1.19438i) q^{68} -7.29744 q^{69} +1.19297 q^{71} +(0.900073 + 0.241174i) q^{72} +(0.506205 + 1.88918i) q^{73} +(-0.0845694 - 0.0488262i) q^{74} +(-4.91283 - 0.929594i) q^{75} -14.0341i q^{76} +(0.118230 + 0.118230i) q^{78} +(-7.48269 + 4.32013i) q^{79} +(3.83275 - 7.25185i) q^{80} +(0.500000 - 0.866025i) q^{81} +(0.466662 - 1.74161i) q^{82} +(-11.9895 + 11.9895i) q^{83} +(-3.89070 - 3.61007i) q^{85} +(0.610073 + 1.05668i) q^{86} +(-3.52747 + 0.945184i) q^{87} +(3.58771 - 0.961324i) q^{88} +(-3.91290 - 6.77735i) q^{89} +(0.387253 + 0.359321i) q^{90} +(10.0321 - 10.0321i) q^{92} +(1.27810 - 4.76995i) q^{93} +(-0.0510027 + 0.0883393i) q^{94} +(7.54226 - 14.2705i) q^{95} +(-2.36449 + 1.36514i) q^{96} +(7.43671 + 7.43671i) q^{97} -3.98602i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q + 48 q^{8}+O(q^{10}) \) 32 * q + 48 * q^8	\( 32 q + 48 q^{8} + 16 q^{11} + 16 q^{15} + 48 q^{16} - 32 q^{22} + 40 q^{23} + 8 q^{30} - 48 q^{32} - 32 q^{36} - 32 q^{37} - 32 q^{43} - 64 q^{46} - 144 q^{50} + 16 q^{51} - 24 q^{53} + 16 q^{57} - 32 q^{58} - 40 q^{60} - 40 q^{65} + 32 q^{67} + 128 q^{71} - 24 q^{72} - 16 q^{78} + 16 q^{81} + 96 q^{85} - 64 q^{86} + 64 q^{88} - 80 q^{92} - 24 q^{93} + 72 q^{95}+O(q^{100}) \) 32 * q + 48 * q^8 + 16 * q^11 + 16 * q^15 + 48 * q^16 - 32 * q^22 + 40 * q^23 + 8 * q^30 - 48 * q^32 - 32 * q^36 - 32 * q^37 - 32 * q^43 - 64 * q^46 - 144 * q^50 + 16 * q^51 - 24 * q^53 + 16 * q^57 - 32 * q^58 - 40 * q^60 - 40 * q^65 + 32 * q^67 + 128 * q^71 - 24 * q^72 - 16 * q^78 + 16 * q^81 + 96 * q^85 - 64 * q^86 + 64 * q^88 - 80 * q^92 - 24 * q^93 + 72 * q^95

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

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