LMFDB - Embedded newform 343.2.g.d.312.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [343,2,Mod(30,343)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("343.30"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(343, base_ring=CyclotomicField(42)) chi = DirichletCharacter(H, H._module([32])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 343 = 7^{3} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	343.g (of order $21$, degree $12$, not minimal)

Newform invariants

comment:select newform

sage:traces = [12,1,0,-1,14] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(5)] == traces)

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

Self dual:	no
Analytic conductor:	$2.73886878933$
Analytic rank:	$0$
Dimension:	$12$
Coefficient field:	$\Q(\zeta_{21})$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - x^{11} + x^{9} - x^{8} + x^{6} - x^{4} + x^{3} - x + 1 $ x^12 - x^11 + x^9 - x^8 + x^6 - x^4 + x^3 - x + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 49)
Sato-Tate group:	$\mathrm{SU}(2)[C_{21}]$

Embedding invariants

Embedding label			312.1
Root			$-0.988831 + 0.149042i$ of defining polynomial
Character	$\chi$	$=$	343.312
Dual form			343.2.g.d.177.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.109562 - 0.101659i) q^{2} +(2.87863 - 0.433884i) q^{3} +(-0.147791 + 1.97213i) q^{4} +(0.802576 - 2.04493i) q^{5} +(0.271281 - 0.340175i) q^{6} +(0.370666 + 0.464800i) q^{8} +(5.23154 - 1.61372i) q^{9} +(-0.119953 - 0.305636i) q^{10} +(-3.27960 - 1.01162i) q^{11} +(0.430241 + 5.74116i) q^{12} +(-0.103718 - 0.454418i) q^{13} +(1.42306 - 6.23482i) q^{15} +(-3.82328 - 0.576267i) q^{16} +(-1.26239 + 0.860686i) q^{17} +(0.409130 - 0.708634i) q^{18} +(2.16885 + 3.75656i) q^{19} +(3.91426 + 1.88501i) q^{20} +(-0.462160 + 0.222565i) q^{22} +(-0.181049 - 0.123437i) q^{23} +(1.26868 + 1.17716i) q^{24} +(0.127648 + 0.118440i) q^{25} +(-0.0575591 - 0.0392431i) q^{26} +(6.49095 - 3.12588i) q^{27} +(-7.82477 - 3.76821i) q^{29} +(-0.477911 - 0.827766i) q^{30} +(-2.04523 + 3.54245i) q^{31} +(-1.45987 + 0.995323i) q^{32} +(-9.87968 - 1.48912i) q^{33} +(-0.0508143 + 0.222632i) q^{34} +(2.40929 + 10.5558i) q^{36} +(0.483324 + 6.44950i) q^{37} +(0.619511 + 0.191094i) q^{38} +(-0.495730 - 1.26310i) q^{39} +(1.24797 - 0.384948i) q^{40} +(-1.77240 - 2.22252i) q^{41} +(2.00772 - 2.51761i) q^{43} +(2.47975 - 6.31829i) q^{44} +(0.898771 - 11.9933i) q^{45} +(-0.0323845 + 0.00488118i) q^{46} +(8.26184 - 7.66586i) q^{47} -11.2559 q^{48} +0.0260258 q^{50} +(-3.26053 + 3.02533i) q^{51} +(0.911500 - 0.137386i) q^{52} +(0.342907 - 4.57578i) q^{53} +(0.393389 - 1.00234i) q^{54} +(-4.70082 + 5.89465i) q^{55} +(7.87324 + 9.87273i) q^{57} +(-1.24037 + 0.382603i) q^{58} +(2.63207 + 6.70640i) q^{59} +(12.0856 + 3.72791i) q^{60} +(-0.358884 - 4.78897i) q^{61} +(0.136041 + 0.596034i) q^{62} +(1.66198 - 7.28160i) q^{64} +(-1.01249 - 0.152609i) q^{65} +(-1.23382 + 0.841205i) q^{66} +(-3.14905 + 5.45432i) q^{67} +(-1.51081 - 2.61681i) q^{68} +(-0.574730 - 0.276775i) q^{69} +(-5.98346 + 2.88148i) q^{71} +(2.68921 + 1.83347i) q^{72} +(-2.69341 - 2.49912i) q^{73} +(0.708603 + 0.657487i) q^{74} +(0.418840 + 0.285561i) q^{75} +(-7.72897 + 3.72208i) q^{76} +(-0.182718 - 0.0879925i) q^{78} +(-1.73277 - 3.00124i) q^{79} +(-4.24690 + 7.35585i) q^{80} +(3.75838 - 2.56242i) q^{81} +(-0.420126 - 0.0633238i) q^{82} +(0.948934 - 4.15755i) q^{83} +(0.746875 + 3.27227i) q^{85} +(-0.0359663 - 0.479937i) q^{86} +(-24.1596 - 7.45224i) q^{87} +(-0.745433 - 1.89933i) q^{88} +(-4.02653 + 1.24202i) q^{89} +(-1.12075 - 1.40537i) q^{90} +(0.270191 - 0.338809i) q^{92} +(-4.35046 + 11.0848i) q^{93} +(0.125882 - 1.67978i) q^{94} +(9.42258 - 1.42023i) q^{95} +(-3.77057 + 3.49858i) q^{96} +7.50450 q^{97} -18.7898 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + q^{2} - q^{4} + 14 q^{5} - 7 q^{6} + 6 q^{8} + 25 q^{9} - 7 q^{10} + 4 q^{11} + 7 q^{12} + 7 q^{13} - 7 q^{15} - 29 q^{16} - 10 q^{18} + 7 q^{19} + 7 q^{20} + 13 q^{22} + q^{23} + 9 q^{25} - 7 q^{26}+ \cdots - 18 q^{99}+O(q^{100}) $ 12 * q + q^2 - q^4 + 14 * q^5 - 7 * q^6 + 6 * q^8 + 25 * q^9 - 7 * q^10 + 4 * q^11 + 7 * q^12 + 7 * q^13 - 7 * q^15 - 29 * q^16 - 10 * q^18 + 7 * q^19 + 7 * q^20 + 13 * q^22 + q^23 + 9 * q^25 - 7 * q^26 + 21 * q^27 - 11 * q^29 - 21 * q^30 + 7 * q^31 - 9 * q^32 - 49 * q^33 - 42 * q^34 - 13 * q^36 + 15 * q^37 + 21 * q^38 + 21 * q^40 + 21 * q^41 + 17 * q^43 - 18 * q^44 + 35 * q^45 + 8 * q^46 + 21 * q^47 - 46 * q^50 + 7 * q^51 - 7 * q^52 - 24 * q^53 - 21 * q^54 - 28 * q^55 + 7 * q^57 + 16 * q^58 - 7 * q^59 + 35 * q^60 + 14 * q^61 + 56 * q^62 + 14 * q^64 + 14 * q^65 - 49 * q^66 - 24 * q^67 - 28 * q^68 - 7 * q^69 - 39 * q^71 + 23 * q^72 - 21 * q^73 - 20 * q^74 - 14 * q^75 - 28 * q^76 + 8 * q^79 - 21 * q^80 + 23 * q^81 + 7 * q^82 - 7 * q^83 + 28 * q^85 - 19 * q^86 - 56 * q^87 + 16 * q^88 - 35 * q^89 - 14 * q^90 + 16 * q^92 - 7 * q^93 + 56 * q^94 - 7 * q^95 + 35 * q^96 - 28 * q^97 - 18 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/343\mathbb{Z}\right)^\times$.

$n$	$3$
$\chi(n)$	$e\left(\frac{20}{21}\right)$

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 $

$2$	0.109562	−	0.101659i	0.0774721	−	0.0718836i	−0.640486	−	0.767970i	$-0.721267\pi$
$2$	0.109562	−	0.101659i	0.0774721	−	0.0718836i	0.717958	+	0.696086i	$0.245077\pi$
$3$	2.87863	−	0.433884i	1.66198	−	0.250503i	0.750207	−	0.661203i	$-0.229954\pi$
$3$	2.87863	−	0.433884i	1.66198	−	0.250503i	0.911771	+	0.410700i	$0.134716\pi$
$4$	−0.147791	+	1.97213i	−0.0738954	+	0.986066i
$5$	0.802576	−	2.04493i	0.358923	−	0.914521i	−0.631365	−	0.775486i	$-0.717505\pi$
$5$	0.802576	−	2.04493i	0.358923	−	0.914521i	0.990288	−	0.139035i	$-0.0443999\pi$
$6$	0.271281	−	0.340175i	0.110750	−	0.138876i
$7$		0			0
$7$		0			0
$8$	0.370666	+	0.464800i	0.131050	+	0.164332i
$9$	5.23154	−	1.61372i	1.74385	−	0.537905i
$10$	−0.119953	−	0.305636i	−0.0379325	−	0.0966505i
$11$	−3.27960	−	1.01162i	−0.988836	−	0.305016i	−0.242184	−	0.970230i	$-0.577864\pi$
$11$	−3.27960	−	1.01162i	−0.988836	−	0.305016i	−0.746652	+	0.665215i	$0.768340\pi$
$12$	0.430241	+	5.74116i	0.124200	+	1.65733i
$13$	−0.103718	−	0.454418i	−0.0287662	−	0.126033i	0.958506	−	0.285072i	$-0.0920175\pi$
$13$	−0.103718	−	0.454418i	−0.0287662	−	0.126033i	−0.987272	+	0.159039i	$0.949160\pi$
$14$		0			0
$15$	1.42306	−	6.23482i	0.367432	−	1.60982i
$16$	−3.82328	−	0.576267i	−0.955821	−	0.144067i
$17$	−1.26239	+	0.860686i	−0.306175	+	0.208747i	−0.706654	−	0.707559i	$-0.749796\pi$
$17$	−1.26239	+	0.860686i	−0.306175	+	0.208747i	0.400479	+	0.916306i	$0.368844\pi$
$18$	0.409130	−	0.708634i	0.0964329	−	0.167027i
$19$	2.16885	+	3.75656i	0.497569	+	0.861815i	0.999996	−	0.00280488i	$-0.000892822\pi$
$19$	2.16885	+	3.75656i	0.497569	+	0.861815i	−0.502427	+	0.864620i	$0.667559\pi$
$20$	3.91426	+	1.88501i	0.875255	+	0.421500i
$21$		0			0
$22$	−0.462160	+	0.222565i	−0.0985328	+	0.0474509i
$23$	−0.181049	−	0.123437i	−0.0377513	−	0.0257384i	0.544297	−	0.838892i	$-0.316796\pi$
$23$	−0.181049	−	0.123437i	−0.0377513	−	0.0257384i	−0.582049	+	0.813154i	$0.697749\pi$
$24$	1.26868	+	1.17716i	0.258968	+	0.240287i
$25$	0.127648	+	0.118440i	0.0255296	+	0.0236880i
$26$	−0.0575591	−	0.0392431i	−0.0112883	−	0.00769621i
$27$	6.49095	−	3.12588i	1.24918	−	0.601575i
$28$		0			0
$29$	−7.82477	−	3.76821i	−1.45302	−	0.699739i	−0.469906	−	0.882717i	$-0.655712\pi$
$29$	−7.82477	−	3.76821i	−1.45302	−	0.699739i	−0.983117	+	0.182978i	$0.941426\pi$
$30$	−0.477911	−	0.827766i	−0.0872542	−	0.151129i
$31$	−2.04523	+	3.54245i	−0.367335	+	0.636242i	−0.989148	−	0.146923i	$-0.953063\pi$
$31$	−2.04523	+	3.54245i	−0.367335	+	0.636242i	0.621813	+	0.783166i	$0.286396\pi$
$32$	−1.45987	+	0.995323i	−0.258071	+	0.175950i
$33$	−9.87968	−	1.48912i	−1.71983	−	0.259223i
$34$	−0.0508143	+	0.222632i	−0.00871458	+	0.0381810i
$35$		0			0
$36$	2.40929	+	10.5558i	0.401548	+	1.75930i
$37$	0.483324	+	6.44950i	0.0794579	+	1.06029i	0.884336	+	0.466852i	$0.154612\pi$
$37$	0.483324	+	6.44950i	0.0794579	+	1.06029i	−0.804878	+	0.593441i	$0.797769\pi$
$38$	0.619511	+	0.191094i	0.100498	+	0.0309995i
$39$	−0.495730	−	1.26310i	−0.0793803	−	0.202258i
$40$	1.24797	−	0.384948i	0.197322	−	0.0608657i
$41$	−1.77240	−	2.22252i	−0.276802	−	0.347099i	0.623925	−	0.781484i	$-0.285537\pi$
$41$	−1.77240	−	2.22252i	−0.276802	−	0.347099i	−0.900727	+	0.434385i	$0.856966\pi$
$42$		0			0
$43$	2.00772	−	2.51761i	0.306175	−	0.383931i	−0.604811	−	0.796369i	$-0.706751\pi$
$43$	2.00772	−	2.51761i	0.306175	−	0.383931i	0.910986	+	0.412438i	$0.135323\pi$
$44$	2.47975	−	6.31829i	0.373836	−	0.952519i
$45$	0.898771	−	11.9933i	0.133981	−	1.78785i
$46$	−0.0323845	+	0.00488118i	−0.00477484	+	0.000719691i
$47$	8.26184	−	7.66586i	1.20511	−	1.11818i	0.215190	−	0.976572i	$-0.430963\pi$
$47$	8.26184	−	7.66586i	1.20511	−	1.11818i	0.989923	−	0.141609i	$-0.0452276\pi$
$48$	−11.2559			−1.62464
$49$		0			0
$50$	0.0260258			0.00368061
$51$	−3.26053	+	3.02533i	−0.456565	+	0.423631i
$52$	0.911500	−	0.137386i	0.126402	−	0.0190521i
$53$	0.342907	−	4.57578i	0.0471019	−	0.628532i	−0.922838	−	0.385188i	$-0.874137\pi$
$53$	0.342907	−	4.57578i	0.0471019	−	0.628532i	0.969940	−	0.243344i	$-0.0782443\pi$
$54$	0.393389	−	1.00234i	0.0535335	−	0.136401i
$55$	−4.70082	+	5.89465i	−0.633859	+	0.794834i
$56$		0			0
$57$	7.87324	+	9.87273i	1.04284	+	1.30767i
$58$	−1.24037	+	0.382603i	−0.162868	+	0.0502383i
$59$	2.63207	+	6.70640i	0.342666	+	0.873099i	0.993495	+	0.113874i	$0.0363262\pi$
$59$	2.63207	+	6.70640i	0.342666	+	0.873099i	−0.650829	+	0.759224i	$0.725579\pi$
$60$	12.0856	+	3.72791i	1.56024	+	0.481271i
$61$	−0.358884	−	4.78897i	−0.0459504	−	0.613165i	−0.971881	−	0.235472i	$-0.924336\pi$
$61$	−0.358884	−	4.78897i	−0.0459504	−	0.613165i	0.925931	−	0.377693i	$-0.123283\pi$
$62$	0.136041	+	0.596034i	0.0172772	+	0.0756963i
$63$		0			0
$64$	1.66198	−	7.28160i	0.207747	−	0.910200i
$65$	−1.01249	−	0.152609i	−0.125584	−	0.0189288i
$66$	−1.23382	+	0.841205i	−0.151873	+	0.103545i
$67$	−3.14905	+	5.45432i	−0.384718	+	0.666351i	−0.991730	−	0.128341i	$-0.959035\pi$
$67$	−3.14905	+	5.45432i	−0.384718	+	0.666351i	0.607012	+	0.794693i	$0.292368\pi$
$68$	−1.51081	−	2.61681i	−0.183213	−	0.317335i
$69$	−0.574730	−	0.276775i	−0.0691894	−	0.0333198i
$70$		0			0
$71$	−5.98346	+	2.88148i	−0.710106	+	0.341969i	−0.753825	−	0.657075i	$-0.771793\pi$
$71$	−5.98346	+	2.88148i	−0.710106	+	0.341969i	0.0437196	+	0.999044i	$0.486079\pi$
$72$	2.68921	+	1.83347i	0.316926	+	0.216077i
$73$	−2.69341	−	2.49912i	−0.315240	−	0.292500i	0.506643	−	0.862156i	$-0.330886\pi$
$73$	−2.69341	−	2.49912i	−0.315240	−	0.292500i	−0.821884	+	0.569656i	$0.807077\pi$
$74$	0.708603	+	0.657487i	0.0823734	+	0.0764313i
$75$	0.418840	+	0.285561i	0.0483635	+	0.0329737i
$76$	−7.72897	+	3.72208i	−0.886574	+	0.426952i
$77$		0			0
$78$	−0.182718	−	0.0879925i	−0.0206888	−	0.00996318i
$79$	−1.73277	−	3.00124i	−0.194952	−	0.337666i	0.751933	−	0.659239i	$-0.229122\pi$
$79$	−1.73277	−	3.00124i	−0.194952	−	0.337666i	−0.946885	+	0.321573i	$0.895788\pi$
$80$	−4.24690	+	7.35585i	−0.474818	+	0.822409i
$81$	3.75838	−	2.56242i	0.417598	−	0.284714i
$82$	−0.420126	−	0.0633238i	−0.0463952	−	0.00699295i
$83$	0.948934	−	4.15755i	0.104159	−	0.456351i	−0.895771	−	0.444516i	$-0.853376\pi$
$83$	0.948934	−	4.15755i	0.104159	−	0.456351i	0.999930	−	0.0118347i	$-0.00376719\pi$
$84$		0			0
$85$	0.746875	+	3.27227i	0.0810100	+	0.354928i
$86$	−0.0359663	−	0.479937i	−0.00387835	−	0.0517529i
$87$	−24.1596	−	7.45224i	−2.59018	−	0.798964i
$88$	−0.745433	−	1.89933i	−0.0794635	−	0.202470i
$89$	−4.02653	+	1.24202i	−0.426811	+	0.131654i	−0.500716	−	0.865612i	$-0.666930\pi$
$89$	−4.02653	+	1.24202i	−0.426811	+	0.131654i	0.0739052	+	0.997265i	$0.476454\pi$
$90$	−1.12075	−	1.40537i	−0.118137	−	0.148140i
$91$		0			0
$92$	0.270191	−	0.338809i	0.0281694	−	0.0353233i
$93$	−4.35046	+	11.0848i	−0.451122	+	1.14944i
$94$	0.125882	−	1.67978i	0.0129837	−	0.173256i
$95$	9.42258	−	1.42023i	0.966736	−	0.145712i
$96$	−3.77057	+	3.49858i	−0.384833	+	0.357072i
$97$	7.50450			0.761966			0.380983	−	0.924582i	$-0.375586\pi$
$97$	7.50450			0.761966			0.380983	+	0.924582i	$0.375586\pi$
$98$		0			0
$99$	−18.7898			−1.88845
$100$	−0.252444	+	0.234234i	−0.0252444	+	0.0234234i
$101$	12.2776	−	1.85055i	1.22167	−	0.184137i	0.493628	−	0.869673i	$-0.335670\pi$
$101$	12.2776	−	1.85055i	1.22167	−	0.184137i	0.728038	+	0.685536i	$0.240432\pi$
$102$	−0.0496792	+	0.662922i	−0.00491897	+	0.0656391i
$103$	−0.807400	+	2.05722i	−0.0795554	+	0.202704i	−0.965118	−	0.261817i	$-0.915678\pi$
$103$	−0.807400	+	2.05722i	−0.0795554	+	0.202704i	0.885562	+	0.464521i	$0.153774\pi$
$104$	0.172769	−	0.216645i	0.0169414	−	0.0212438i
$105$		0			0
$106$	−0.427598	−	0.536191i	−0.0415320	−	0.0520795i
$107$	−13.5265	+	4.17237i	−1.30766	+	0.403358i	−0.868784	−	0.495191i	$-0.835098\pi$
$107$	−13.5265	+	4.17237i	−1.30766	+	0.403358i	−0.438872	+	0.898550i	$0.644622\pi$
$108$	5.20534	+	13.2630i	0.500884	+	1.27623i
$109$	−12.2291	−	3.77217i	−1.17133	−	0.361308i	−0.352762	−	0.935713i	$-0.614757\pi$
$109$	−12.2291	−	3.77217i	−1.17133	−	0.361308i	−0.818571	+	0.574405i	$0.805234\pi$
$110$	0.0842104	+	1.12371i	0.00802915	+	0.107142i
$111$	4.18965	+	18.3560i	0.397664	+	1.74228i
$112$		0			0
$113$	−2.27119	+	9.95071i	−0.213655	+	0.936084i	0.748404	+	0.663243i	$0.230820\pi$
$113$	−2.27119	+	9.95071i	−0.213655	+	0.936084i	−0.962059	+	0.272841i	$0.912037\pi$
$114$	1.86626	+	0.281293i	0.174791	+	0.0263455i
$115$	−0.397726	+	0.271165i	−0.0370881	+	0.0252862i
$116$	8.58783	−	14.8746i	0.797360	−	1.38107i
$117$	−1.27591	−	2.20993i	−0.117957	−	0.204308i
$118$	0.970139	+	0.467194i	0.0893085	+	0.0430087i
$119$		0			0
$120$	3.42543	−	1.64960i	0.312697	−	0.150587i
$121$	0.643766	+	0.438912i	0.0585242	+	0.0399011i
$122$	−0.526161	−	0.488206i	−0.0476364	−	0.0442001i
$123$	−6.06640	−	5.62879i	−0.546989	−	0.507531i
$124$	−6.68390	−	4.55701i	−0.600232	−	0.409231i
$125$	10.2408	−	4.93172i	0.915967	−	0.441107i
$126$		0			0
$127$	2.61806	+	1.26079i	0.232315	+	0.111877i	0.546420	−	0.837511i	$-0.315990\pi$
$127$	2.61806	+	1.26079i	0.232315	+	0.111877i	−0.314105	+	0.949388i	$0.601704\pi$
$128$	−2.32504	−	4.02708i	−0.205506	−	0.355947i
$129$	4.68715	−	8.11838i	0.412680	−	0.714783i
$130$	−0.126445	+	0.0862087i	−0.0110900	+	0.00756100i
$131$	20.6650	+	3.11475i	1.80551	+	0.272137i	0.963574	−	0.267440i	$-0.0861777\pi$
$131$	20.6650	+	3.11475i	1.80551	+	0.272137i	0.841936	+	0.539577i	$0.181416\pi$
$132$	4.39687	−	19.2640i	0.382699	−	1.67671i
$133$		0			0
$134$	0.209463	+	0.917715i	0.0180948	+	0.0792785i
$135$	−1.18272	−	15.7823i	−0.101792	−	1.35832i
$136$	−0.867973	−	0.267734i	−0.0744281	−	0.0229580i
$137$	4.69174	+	11.9544i	0.400843	+	1.02133i	0.978719	+	0.205206i	$0.0657864\pi$
$137$	4.69174	+	11.9544i	0.400843	+	1.02133i	−0.577876	+	0.816124i	$0.696118\pi$
$138$	−0.0911053	+	0.0281023i	−0.00775539	+	0.00239222i
$139$	−12.4426	−	15.6026i	−1.05537	−	1.32339i	−0.944120	−	0.329602i	$-0.893085\pi$
$139$	−12.4426	−	15.6026i	−1.05537	−	1.32339i	−0.111252	−	0.993792i	$-0.535486\pi$
$140$		0			0
$141$	20.4567	−	25.6519i	1.72276	−	2.16028i
$142$	−0.362632	+	0.923972i	−0.0304314	+	0.0775380i
$143$	−0.119546	+	1.59523i	−0.00999694	+	0.133400i
$144$	−20.9316	+	3.15493i	−1.74430	+	0.262911i
$145$	−13.9857	+	12.9768i	−1.16145	+	1.07767i
$146$	−0.549154			−0.0454483
$147$		0			0
$148$	−12.7907			−1.05139
$149$	9.35856	−	8.68348i	0.766683	−	0.711378i	−0.196417	−	0.980520i	$-0.562931\pi$
$149$	9.35856	−	8.68348i	0.766683	−	0.711378i	0.963100	+	0.269142i	$0.0867401\pi$
$150$	0.0749187	−	0.0112922i	0.00611709	−	0.000922003i
$151$	−0.498015	+	6.64555i	−0.0405279	+	0.540807i	0.939578	+	0.342334i	$0.111217\pi$
$151$	−0.498015	+	6.64555i	−0.0405279	+	0.540807i	−0.980106	+	0.198474i	$0.936402\pi$
$152$	−0.942132	+	2.40051i	−0.0764170	+	0.194707i
$153$	−5.21536	+	6.53986i	−0.421637	+	0.528716i
$154$		0			0
$155$	5.60260	+	7.02544i	0.450012	+	0.564297i
$156$	2.56426	−	0.790970i	0.205305	−	0.0633283i
$157$	−2.93891	−	7.48823i	−0.234551	−	0.597626i	0.764335	−	0.644819i	$-0.223067\pi$
$157$	−2.93891	−	7.48823i	−0.234551	−	0.597626i	−0.998886	+	0.0471937i	$0.984972\pi$
$158$	−0.494948	−	0.152671i	−0.0393760	−	0.0121459i
$159$	−0.998253	−	13.3208i	−0.0791666	−	1.05641i
$160$	0.863709	+	3.78416i	0.0682822	+	0.299164i
$161$		0			0
$162$	0.151284	−	0.662817i	0.0118860	−	0.0520758i
$163$	24.2979	+	3.66231i	1.90315	+	0.286854i	0.992102	−	0.125435i	$-0.0400326\pi$
$163$	24.2979	+	3.66231i	1.90315	+	0.286854i	0.911053	+	0.412289i	$0.135271\pi$
$164$	4.64504	−	3.16694i	0.362717	−	0.247296i
$165$	−10.9743	+	19.0081i	−0.854352	+	1.47978i
$166$	−0.318684	−	0.551978i	−0.0247347	−	0.0428418i
$167$	7.50517	+	3.61430i	0.580768	+	0.279683i	0.701114	−	0.713049i	$-0.252686\pi$
$167$	7.50517	+	3.61430i	0.580768	+	0.279683i	−0.120346	+	0.992732i	$0.538401\pi$
$168$		0			0
$169$	11.5169	−	5.54623i	0.885912	−	0.426633i
$170$	0.414484	+	0.282591i	0.0317895	+	0.0216737i
$171$	17.4085	+	16.1527i	1.33126	+	1.23523i
$172$	4.66833	+	4.33158i	0.355957	+	0.330280i
$173$	8.89580	+	6.06506i	0.676336	+	0.461118i	0.852144	−	0.523307i	$-0.175302\pi$
$173$	8.89580	+	6.06506i	0.676336	+	0.461118i	−0.175809	+	0.984424i	$0.556254\pi$
$174$	−3.40456	+	1.63955i	−0.258099	+	0.124294i
$175$		0			0
$176$	11.9559	+	5.75765i	0.901208	+	0.433999i
$177$	10.4865	+	18.1632i	0.788217	+	1.36523i
$178$	−0.314893	+	0.545410i	−0.0236022	+	0.0408802i
$179$	6.84139	−	4.66438i	0.511350	−	0.348632i	−0.279996	−	0.960001i	$-0.590333\pi$
$179$	6.84139	−	4.66438i	0.511350	−	0.348632i	0.791346	+	0.611369i	$0.209381\pi$
$180$	23.5195	+	3.54499i	1.75304	+	0.264228i
$181$	−1.41369	+	6.19379i	−0.105079	+	0.460381i	0.894824	+	0.446420i	$0.147301\pi$
$181$	−1.41369	+	6.19379i	−0.105079	+	0.460381i	−0.999903	+	0.0139610i	$0.995556\pi$
$182$		0			0
$183$	−3.11095	−	13.6300i	−0.229968	−	1.00756i
$184$	−0.00973507	−	0.129905i	−0.000717679	−	0.00957676i
$185$	13.5767	+	4.18785i	0.998178	+	0.307897i
$186$	0.650220	+	1.65673i	0.0476765	+	0.121478i
$187$	5.01083	−	1.54564i	0.366429	−	0.113028i
$188$	13.8971	+	17.4264i	1.01355	+	1.27095i
$189$		0			0
$190$	0.887979	−	1.11349i	0.0644208	−	0.0807811i
$191$	8.11936	−	20.6878i	0.587496	−	1.49692i	−0.259728	−	0.965682i	$-0.583633\pi$
$191$	8.11936	−	20.6878i	0.587496	−	1.49692i	0.847225	−	0.531235i	$-0.178272\pi$
$192$	1.62485	−	21.6821i	0.117264	−	1.56477i
$193$	6.56004	−	0.988768i	0.472202	−	0.0711730i	0.0913697	−	0.995817i	$-0.470876\pi$
$193$	6.56004	−	0.988768i	0.472202	−	0.0711730i	0.380833	+	0.924644i	$0.375637\pi$
$194$	0.822208	−	0.762898i	0.0590311	−	0.0547729i
$195$	−2.98081			−0.213460
$196$		0			0
$197$	−10.0402			−0.715332			−0.357666	−	0.933850i	$-0.616427\pi$
$197$	−10.0402			−0.715332			−0.357666	+	0.933850i	$0.616427\pi$
$198$	−2.05865	+	1.91015i	−0.146302	+	0.135748i
$199$	17.2003	−	2.59252i	1.21929	−	0.183779i	0.492302	−	0.870424i	$-0.336156\pi$
$199$	17.2003	−	2.59252i	1.21929	−	0.183779i	0.726993	+	0.686645i	$0.240917\pi$
$200$	−0.00773620	+	0.103232i	−0.000547032	+	0.00729964i
$201$	−6.69842	+	17.0673i	−0.472470	+	1.20383i
$202$	1.15703	−	1.45088i	0.0814086	−	0.102083i
$203$		0			0
$204$	−5.48447	−	6.87731i	−0.383990	−	0.481508i
$205$	−5.96738	+	1.84069i	−0.416780	+	0.128560i
$206$	0.120674	+	0.307473i	0.00840776	+	0.0214226i
$207$	−1.14636	−	0.353604i	−0.0796773	−	0.0245772i
$208$	0.134677	+	1.79714i	0.00933815	+	0.124609i
$209$	−3.31274	−	14.5141i	−0.229147	−	1.00396i
$210$		0			0
$211$	−1.44188	+	6.31729i	−0.0992632	+	0.434900i	0.900737	+	0.434366i	$0.143027\pi$
$211$	−1.44188	+	6.31729i	−0.0992632	+	0.434900i	−1.00000		0.000534816i	$0.999830\pi$
$212$	8.97336	+	1.35252i	0.616293	+	0.0928912i
$213$	−15.9739	+	10.8908i	−1.09452	+	0.746228i
$214$	−1.05783	+	1.83222i	−0.0723120	+	0.125248i
$215$	−3.53698	−	6.12623i	−0.241220	−	0.417805i
$216$	3.85888	+	1.85834i	0.262564	+	0.126444i
$217$		0			0
$218$	−1.72332	+	0.829906i	−0.116718	+	0.0562083i
$219$	−8.83767	−	6.02542i	−0.597195	−	0.407160i
$220$	−10.9303	−	10.1418i	−0.736920	−	0.683761i
$221$	0.522043	+	0.484385i	0.0351164	+	0.0325833i
$222$	2.32508	+	1.58521i	0.156049	+	0.106392i
$223$	13.7827	−	6.63738i	0.922956	−	0.444472i	0.0888303	−	0.996047i	$-0.471687\pi$
$223$	13.7827	−	6.63738i	0.922956	−	0.444472i	0.834125	+	0.551575i	$0.185973\pi$
$224$		0			0
$225$	0.858924	+	0.413636i	0.0572616	+	0.0275757i
$226$	0.762741	+	1.32111i	0.0507368	+	0.0878787i
$227$	−9.30113	+	16.1100i	−0.617338	+	1.06926i	0.372632	+	0.927979i	$0.378456\pi$
$227$	−9.30113	+	16.1100i	−0.617338	+	1.06926i	−0.989969	+	0.141281i	$0.954878\pi$
$228$	−20.6339	+	14.0680i	−1.36651	+	0.931674i
$229$	−18.4731	−	2.78437i	−1.22074	−	0.183997i	−0.493109	−	0.869967i	$-0.664140\pi$
$229$	−18.4731	−	2.78437i	−1.22074	−	0.183997i	−0.727629	+	0.685971i	$0.759378\pi$
$230$	−0.0160094	+	0.0701416i	−0.00105563	+	0.00462500i
$231$		0			0
$232$	−1.14891	−	5.03370i	−0.0754296	−	0.330479i
$233$	−0.581603	−	7.76095i	−0.0381021	−	0.508437i	−0.983306	−	0.181957i	$-0.941757\pi$
$233$	−0.581603	−	7.76095i	−0.0381021	−	0.508437i	0.945204	−	0.326479i	$-0.105862\pi$
$234$	−0.364450	−	0.112418i	−0.0238248	−	0.00734899i
$235$	−9.04541	−	23.0473i	−0.590057	−	1.50344i
$236$	−13.6149	+	4.19964i	−0.886254	+	0.273373i
$237$	−6.29019	−	7.88765i	−0.408592	−	0.512358i
$238$		0			0
$239$	−3.84245	+	4.81828i	−0.248547	+	0.311668i	−0.890417	−	0.455145i	$-0.849587\pi$
$239$	−3.84245	+	4.81828i	−0.248547	+	0.311668i	0.641870	+	0.766813i	$0.278159\pi$
$240$	−9.03368	+	23.0174i	−0.583121	+	1.48577i
$241$	−0.257401	+	3.43478i	−0.0165807	+	0.221254i	0.982758	+	0.184896i	$0.0591947\pi$
$241$	−0.257401	+	3.43478i	−0.0165807	+	0.221254i	−0.999339	+	0.0363581i	$0.988424\pi$
$242$	0.115152	−	0.0173563i	0.00740222	−	0.00111571i
$243$	−6.13642	+	5.69376i	−0.393651	+	0.365255i
$244$	9.49752			0.608017
$245$		0			0
$246$	−1.23686			−0.0788595
$247$	1.48210	−	1.37519i	0.0943037	−	0.0875011i
$248$	−2.40463	+	0.362439i	−0.152694	+	0.0230149i
$249$	0.927737	−	12.3798i	0.0587929	−	0.784537i
$250$	0.620653	−	1.58140i	0.0392536	−	0.100016i
$251$	5.83985	−	7.32294i	0.368608	−	0.462220i	−0.562589	−	0.826737i	$-0.690194\pi$
$251$	5.83985	−	7.32294i	0.368608	−	0.462220i	0.931197	+	0.364517i	$0.118766\pi$
$252$		0			0
$253$	0.468896	+	0.587977i	0.0294792	+	0.0369658i
$254$	0.415010	−	0.128014i	0.0260400	−	0.00803229i
$255$	3.56976	+	9.09561i	0.223547	+	0.569589i
$256$	13.6100	+	4.19811i	0.850622	+	0.262382i
$257$	−0.462303	−	6.16900i	−0.0288376	−	0.384812i	−0.992885	−	0.119080i	$-0.962006\pi$
$257$	−0.462303	−	6.16900i	−0.0288376	−	0.384812i	0.964047	−	0.265732i	$-0.0856135\pi$
$258$	−0.311770	−	1.36596i	−0.0194100	−	0.0850407i
$259$		0			0
$260$	0.450602	−	1.97422i	0.0279452	−	0.122436i
$261$	−47.0164	−	7.08658i	−2.91024	−	0.438648i
$262$	2.58074	−	1.75952i	0.159439	−	0.108704i
$263$	11.0880	−	19.2050i	0.683715	−	1.18423i	−0.290123	−	0.956989i	$-0.593696\pi$
$263$	11.0880	−	19.2050i	0.683715	−	1.18423i	0.973839	−	0.227241i	$-0.0729704\pi$
$264$	−2.96992	−	5.14405i	−0.182786	−	0.316594i
$265$	−9.08194	−	4.37363i	−0.557899	−	0.268670i
$266$		0			0
$267$	−11.0520	+	5.32236i	−0.676371	+	0.325723i
$268$	−10.2912	−	7.01645i	−0.628637	−	0.428598i
$269$	−8.74924	−	8.11811i	−0.533450	−	0.494970i	0.366825	−	0.930290i	$-0.380445\pi$
$269$	−8.74924	−	8.11811i	−0.533450	−	0.494970i	−0.900276	+	0.435320i	$0.856635\pi$
$270$	−1.73399	−	1.60891i	−0.105527	−	0.0979150i
$271$	12.2680	+	8.36419i	0.745228	+	0.508088i	0.875398	−	0.483404i	$-0.160600\pi$
$271$	12.2680	+	8.36419i	0.745228	+	0.508088i	−0.130169	+	0.991492i	$0.541552\pi$
$272$	5.32247	−	2.56317i	0.322722	−	0.155415i
$273$		0			0
$274$	1.72930	+	0.832788i	0.104471	+	0.0503106i
$275$	−0.298818	−	0.517567i	−0.0180194	−	0.0312105i
$276$	0.630777	−	1.09254i	0.0379683	−	0.0657631i
$277$	−2.06395	+	1.40718i	−0.124011	+	0.0845493i	−0.623737	−	0.781634i	$-0.714386\pi$
$277$	−2.06395	+	1.40718i	−0.124011	+	0.0845493i	0.499726	+	0.866184i	$0.333434\pi$
$278$	−2.94938	−	0.444548i	−0.176892	−	0.0266622i
$279$	−4.98321	+	21.8329i	−0.298337	+	1.30710i
$280$		0			0
$281$	2.47839	+	10.8585i	0.147848	+	0.647766i	0.993481	+	0.114000i	$0.0363665\pi$
$281$	2.47839	+	10.8585i	0.147848	+	0.647766i	−0.845632	+	0.533766i	$0.820776\pi$
$282$	−0.366460	−	4.89007i	−0.0218224	−	0.291200i
$283$	−4.35012	−	1.34183i	−0.258588	−	0.0797637i	0.162751	−	0.986667i	$-0.447963\pi$
$283$	−4.35012	−	1.34183i	−0.258588	−	0.0797637i	−0.421338	+	0.906904i	$0.638440\pi$
$284$	−4.79836	−	12.2260i	−0.284730	−	0.725481i
$285$	26.5079	−	8.17661i	1.57019	−	0.484340i
$286$	0.149071	+	0.186930i	0.00881478	+	0.0110534i
$287$		0			0
$288$	−6.03120	+	7.56289i	−0.355392	+	0.445648i
$289$	−5.35794	+	13.6518i	−0.315173	+	0.803047i
$290$	−0.213094	+	2.84354i	−0.0125133	+	0.166978i
$291$	21.6027	−	3.25608i	1.26637	−	0.190875i
$292$	5.32666	−	4.94242i	0.311719	−	0.289233i
$293$	−26.1249			−1.52623			−0.763116	−	0.646262i	$-0.776331\pi$
$293$	−26.1249			−1.52623			−0.763116	+	0.646262i	$0.776331\pi$
$294$		0			0
$295$	15.8266			0.921457
$296$	−2.81858	+	2.61526i	−0.163827	+	0.152009i
$297$	−24.4499	+	3.68523i	−1.41873	+	0.213839i
$298$	0.142592	−	1.90276i	0.00826014	−	0.110224i
$299$	−0.0373140	+	0.0950744i	−0.00215792	+	0.00549829i
$300$	−0.625064	+	0.783805i	−0.0360881	+	0.0452530i
$301$		0			0
$302$	0.621015	+	0.778728i	0.0357354	+	0.0448108i
$303$	34.5397	−	10.6541i	1.98426	−	0.612062i
$304$	−6.12735	−	15.6122i	−0.351428	−	0.895424i
$305$	−10.0811	−	3.10962i	−0.577245	−	0.178056i
$306$	0.0934278	+	1.24671i	0.00534091	+	0.0712695i
$307$	−0.488612	−	2.14075i	−0.0278866	−	0.122179i	0.959069	−	0.283173i	$-0.0913871\pi$
$307$	−0.488612	−	2.14075i	−0.0278866	−	0.122179i	−0.986955	+	0.160994i	$0.948530\pi$
$308$		0			0
$309$	−1.43161	+	6.27229i	−0.0814415	+	0.356818i
$310$	1.32803	+	0.200168i	0.0754270	+	0.0113688i
$311$	13.2189	−	9.01249i	0.749575	−	0.511051i	−0.127245	−	0.991871i	$-0.540613\pi$
$311$	13.2189	−	9.01249i	0.749575	−	0.511051i	0.876819	+	0.480820i	$0.159661\pi$
$312$	0.403339	−	0.698603i	0.0228346	−	0.0395506i
$313$	−0.458062	−	0.793387i	−0.0258912	−	0.0448449i	0.852789	−	0.522255i	$-0.174909\pi$
$313$	−0.458062	−	0.793387i	−0.0258912	−	0.0448449i	−0.878681	+	0.477410i	$0.841576\pi$
$314$	−1.08324	−	0.521660i	−0.0611306	−	0.0294390i
$315$		0			0
$316$	6.17493	−	2.97369i	0.347367	−	0.167283i
$317$	8.89509	+	6.06457i	0.499598	+	0.340620i	0.786757	−	0.617263i	$-0.211758\pi$
$317$	8.89509	+	6.06457i	0.499598	+	0.340620i	−0.287159	+	0.957883i	$0.592711\pi$
$318$	−1.46354	−	1.35797i	−0.0820714	−	0.0761511i
$319$	21.8501	+	20.2739i	1.22337	+	1.13512i
$320$	−13.5565	−	9.24266i	−0.757831	−	0.516681i
$321$	−37.1275	+	17.8796i	−2.07225	+	0.997944i
$322$		0			0
$323$	−5.97117	−	2.87556i	−0.332245	−	0.160001i
$324$	4.49798	+	7.79073i	0.249888	+	0.432818i
$325$	0.0405818	−	0.0702898i	0.00225107	−	0.00389898i
$326$	3.03443	−	2.06884i	0.168061	−	0.114582i
$327$	−36.8397	−	5.55269i	−2.03724	−	0.307064i
$328$	0.376059	−	1.64762i	0.0207644	−	0.0909748i
$329$		0			0
$330$	0.729970	+	3.19821i	0.0401835	+	0.176056i
$331$	2.46620	+	32.9091i	0.135554	+	1.80885i	0.487817	+	0.872946i	$0.337793\pi$
$331$	2.46620	+	32.9091i	0.135554	+	1.80885i	−0.352262	+	0.935901i	$0.614588\pi$
$332$	8.05900	+	2.48587i	0.442295	+	0.136430i
$333$	12.9362	+	32.9609i	0.708899	+	1.80625i
$334$	1.18971	−	0.366976i	0.0650979	−	0.0200800i
$335$	8.62635	+	10.8171i	0.471308	+	0.591001i
$336$		0			0
$337$	−11.7365	+	14.7171i	−0.639328	+	0.801692i	−0.990919	−	0.134462i	$-0.957069\pi$
$337$	−11.7365	+	14.7171i	−0.639328	+	0.801692i	0.351591	+	0.936154i	$0.385641\pi$
$338$	0.697988	−	1.77845i	0.0379656	−	0.0967347i
$339$	−2.22045	+	29.6299i	−0.120598	+	1.60927i
$340$	−6.56373	+	0.989324i	−0.355968	+	0.0536536i
$341$	10.2912	−	9.54880i	0.557298	−	0.517097i
$342$	3.54937			0.191928
$343$		0			0
$344$	1.91438			0.103216
$345$	−1.02725	+	0.953150i	−0.0553053	+	0.0513159i
$346$	1.59121	−	0.239836i	0.0855439	−	0.0128937i
$347$	−2.40314	+	32.0677i	−0.129007	+	1.72148i	0.439024	+	0.898476i	$0.355324\pi$
$347$	−2.40314	+	32.0677i	−0.129007	+	1.72148i	−0.568031	+	0.823007i	$0.692295\pi$
$348$	18.2674	−	46.5445i	0.979234	−	2.49505i
$349$	−6.40434	+	8.03078i	−0.342816	+	0.429878i	−0.923114	−	0.384526i	$-0.874365\pi$
$349$	−6.40434	+	8.03078i	−0.342816	+	0.429878i	0.580298	+	0.814404i	$0.302936\pi$
$350$		0			0
$351$	−2.09368	−	2.62539i	−0.111752	−	0.140133i
$352$	5.79468	−	1.78742i	0.308858	−	0.0952700i
$353$	−10.0068	−	25.4968i	−0.532607	−	1.35706i	−0.903581	−	0.428417i	$-0.859072\pi$
$353$	−10.0068	−	25.4968i	−0.532607	−	1.35706i	0.370975	−	0.928643i	$-0.379024\pi$
$354$	2.99538	+	0.923952i	0.159203	+	0.0491075i
$355$	1.09025	+	14.5484i	0.0578644	+	0.772147i
$356$	−1.85434	−	8.12440i	−0.0982799	−	0.430592i
$357$		0			0
$358$	0.275382	−	1.20653i	0.0145544	−	0.0637669i
$359$	4.67270	+	0.704297i	0.246616	+	0.0371714i	0.271187	−	0.962527i	$-0.412584\pi$
$359$	4.67270	+	0.704297i	0.246616	+	0.0371714i	−0.0245710	+	0.999698i	$0.507822\pi$
$360$	5.90762	−	4.02775i	0.311359	−	0.212281i
$361$	0.0921558	−	0.159619i	0.00485030	−	0.00840097i
$362$	0.474766	+	0.822319i	0.0249531	+	0.0432201i
$363$	2.04360	+	0.984146i	0.107261	+	0.0516543i
$364$		0			0
$365$	−7.27220	+	3.50211i	−0.380644	+	0.183309i
$366$	−1.72645	−	1.17707i	−0.0902429	−	0.0615265i
$367$	2.37827	+	2.20671i	0.124145	+	0.115190i	0.739802	−	0.672824i	$-0.234919\pi$
$367$	2.37827	+	2.20671i	0.124145	+	0.115190i	−0.615657	+	0.788014i	$0.711109\pi$
$368$	0.621068	+	0.576267i	0.0323754	+	0.0300400i
$369$	−12.8589	−	8.76704i	−0.669407	−	0.456394i
$370$	1.91322	−	0.921359i	0.0994637	−	0.0478992i
$371$		0			0
$372$	−21.2177	−	10.2179i	−1.10009	−	0.529774i
$373$	−17.7184	−	30.6892i	−0.917424	−	1.58903i	−0.803313	−	0.595557i	$-0.796931\pi$
$373$	−17.7184	−	30.6892i	−0.917424	−	1.58903i	−0.114111	−	0.993468i	$-0.536402\pi$
$374$	0.391870	−	0.678738i	0.0202631	−	0.0350967i
$375$	27.3398	−	18.6399i	1.41182	−	0.962562i
$376$	6.62548	+	0.998630i	0.341683	+	0.0515004i
$377$	−0.900772	+	3.94654i	−0.0463921	+	0.203257i
$378$		0			0
$379$	5.47579	+	23.9910i	0.281272	+	1.23233i	0.896164	+	0.443723i	$0.146343\pi$
$379$	5.47579	+	23.9910i	0.281272	+	1.23233i	−0.614892	+	0.788611i	$0.710800\pi$
$380$	1.40830	+	18.7925i	0.0722443	+	0.964033i
$381$	8.08345	+	2.49341i	0.414128	+	0.127741i
$382$	−1.21352	−	3.09200i	−0.0620892	−	0.158201i
$383$	−4.86286	+	1.49999i	−0.248480	+	0.0766460i	−0.416493	−	0.909139i	$-0.636741\pi$
$383$	−4.86286	+	1.49999i	−0.248480	+	0.0766460i	0.168013	+	0.985785i	$0.446265\pi$
$384$	−8.44020	−	10.5837i	−0.430712	−	0.540096i
$385$		0			0
$386$	0.618215	−	0.775217i	0.0314663	−	0.0394575i
$387$	6.44079	−	16.4109i	0.327404	−	0.834211i
$388$	−1.10910	+	14.7999i	−0.0563058	+	0.751349i
$389$	−14.9686	+	2.25615i	−0.758936	+	0.114391i	−0.517099	−	0.855926i	$-0.672988\pi$
$389$	−14.9686	+	2.25615i	−0.758936	+	0.114391i	−0.241837	+	0.970317i	$0.577750\pi$
$390$	−0.326584	+	0.303025i	−0.0165372	+	0.0153443i
$391$	0.334795			0.0169313
$392$		0			0
$393$	60.8384			3.06889
$394$	−1.10002	+	1.02067i	−0.0554182	+	0.0514206i
$395$	−7.52801	+	1.13466i	−0.378775	+	0.0570912i
$396$	2.77696	−	37.0560i	0.139548	−	1.86213i
$397$	2.60679	−	6.64199i	0.130831	−	0.333352i	−0.850415	−	0.526113i	$-0.823649\pi$
$397$	2.60679	−	6.64199i	0.130831	−	0.333352i	0.981246	+	0.192761i	$0.0617441\pi$
$398$	1.62094	−	2.03260i	0.0812506	−	0.101885i
$399$		0			0
$400$	−0.419781	−	0.526389i	−0.0209891	−	0.0263194i
$401$	−27.5103	+	8.48580i	−1.37380	+	0.423760i	−0.891807	−	0.452416i	$-0.850562\pi$
$401$	−27.5103	+	8.48580i	−1.37380	+	0.423760i	−0.481991	+	0.876176i	$0.660086\pi$
$402$	1.00115	+	2.55088i	0.0499327	+	0.127226i
$403$	1.82188	+	0.561975i	0.0907542	+	0.0279939i
$404$	1.83501	+	24.4865i	0.0912953	+	1.21825i
$405$	−2.22359	−	9.74217i	−0.110491	−	0.484092i
$406$		0			0
$407$	4.93936	−	21.6407i	0.244835	−	1.07269i
$408$	−2.61474	−	0.394109i	−0.129449	−	0.0195113i
$409$	−24.2046	+	16.5024i	−1.19684	+	0.815990i	−0.986838	−	0.161711i	$-0.948299\pi$
$409$	−24.2046	+	16.5024i	−1.19684	+	0.815990i	−0.210000	+	0.977701i	$0.567346\pi$
$410$	−0.466676	+	0.808306i	−0.0230475	+	0.0399194i
$411$	18.6926	+	32.3765i	0.922038	+	1.59702i
$412$	−3.93778	−	1.89634i	−0.194001	−	0.0934258i
$413$		0			0
$414$	−0.161544	+	0.0777956i	−0.00793946	+	0.00382344i
$415$	−7.74031	−	5.27726i	−0.379957	−	0.259050i
$416$	0.603707	+	0.560158i	0.0295992	+	0.0274640i
$417$	−42.5875	−	39.5154i	−2.08552	−	1.93508i
$418$	−1.83843	−	1.25342i	−0.0899208	−	0.0613069i
$419$	19.5831	−	9.43072i	0.956697	−	0.460721i	0.110668	−	0.993857i	$-0.464701\pi$
$419$	19.5831	−	9.43072i	0.956697	−	0.460721i	0.846029	+	0.533136i	$0.178987\pi$
$420$		0			0
$421$	−3.60206	−	1.73466i	−0.175554	−	0.0845423i	0.344043	−	0.938954i	$-0.388203\pi$
$421$	−3.60206	−	1.73466i	−0.175554	−	0.0845423i	−0.519597	+	0.854412i	$0.673918\pi$
$422$	0.484233	+	0.838715i	0.0235721	+	0.0408280i
$423$	30.8516	−	53.4365i	1.50006	−	2.59817i
$424$	2.25393	−	1.53670i	0.109460	−	0.0746289i
$425$	−0.263082	−	0.0396532i	−0.0127613	−	0.00192346i
$426$	−0.642988	+	2.81711i	−0.0311529	+	0.136490i
$427$		0			0
$428$	−6.22937	−	27.2927i	−0.301108	−	1.31924i
$429$	0.348016	+	4.64395i	0.0168024	+	0.224212i
$430$	−1.01030	−	0.311637i	−0.0487211	−	0.0150285i
$431$	3.12111	+	7.95247i	0.150339	+	0.383057i	0.986126	−	0.165996i	$-0.0530838\pi$
$431$	3.12111	+	7.95247i	0.150339	+	0.383057i	−0.835788	+	0.549053i	$0.814989\pi$
$432$	−26.6181	+	8.21059i	−1.28066	+	0.395032i
$433$	15.9991	+	20.0623i	0.768868	+	0.964131i	0.999961	−	0.00880118i	$-0.00280154\pi$
$433$	15.9991	+	20.0623i	0.768868	+	0.964131i	−0.231093	+	0.972932i	$0.574230\pi$
$434$		0			0
$435$	−34.6292	+	43.4237i	−1.66034	+	2.08200i
$436$	9.24656	−	23.5599i	0.442830	−	1.12831i
$437$	0.0710307	−	0.947838i	0.00339786	−	0.0453412i
$438$	−1.58081	+	0.238269i	−0.0755341	+	0.0113849i
$439$	12.0236	−	11.1563i	0.573855	−	0.532460i	−0.338977	−	0.940795i	$-0.610081\pi$
$439$	12.0236	−	11.1563i	0.573855	−	0.532460i	0.912832	+	0.408335i	$0.133890\pi$
$440$	−4.48227			−0.213684
$441$		0			0
$442$	0.106438			0.00506275
$443$	−17.5883	+	16.3196i	−0.835647	+	0.775367i	−0.976694	−	0.214636i	$-0.931143\pi$
$443$	−17.5883	+	16.3196i	−0.835647	+	0.775367i	0.141048	+	0.990003i	$0.454953\pi$
$444$	−36.8197	+	5.54968i	−1.74739	+	0.263376i
$445$	−0.691751	+	9.23078i	−0.0327922	+	0.437581i
$446$	0.835310	−	2.12833i	0.0395531	−	0.100780i
$447$	23.1722	−	29.0571i	1.09601	−	1.37435i
$448$		0			0
$449$	−18.0813	−	22.6732i	−0.853309	−	1.07002i	−0.996766	−	0.0803595i	$-0.974393\pi$
$449$	−18.0813	−	22.6732i	−0.853309	−	1.07002i	0.143457	−	0.989657i	$-0.454178\pi$
$450$	0.136155	−	0.0419983i	0.00641842	−	0.00197982i
$451$	3.56441	+	9.08197i	0.167842	+	0.427653i
$452$	−19.2885	−	5.94970i	−0.907253	−	0.279850i
$453$	1.44980	+	19.3462i	0.0681173	+	0.908963i
$454$	0.618675	+	2.71059i	0.0290358	+	0.127214i
$455$		0			0
$456$	−1.67051	+	7.31897i	−0.0782286	+	0.342742i
$457$	−0.959121	−	0.144564i	−0.0448658	−	0.00676243i	0.126571	−	0.991958i	$-0.459603\pi$
$457$	−0.959121	−	0.144564i	−0.0448658	−	0.00676243i	−0.171437	+	0.985195i	$0.554841\pi$
$458$	−2.30701	+	1.57289i	−0.107799	+	0.0734964i
$459$	−5.50374	+	9.53276i	−0.256893	+	0.444951i
$460$	−0.475992	−	0.824443i	−0.0221933	−	0.0384398i
$461$	−18.6091	−	8.96165i	−0.866710	−	0.417386i	−0.0529575	−	0.998597i	$-0.516865\pi$
$461$	−18.6091	−	8.96165i	−0.866710	−	0.417386i	−0.813753	+	0.581211i	$0.802579\pi$
$462$		0			0
$463$	−11.6576	+	5.61401i	−0.541776	+	0.260905i	−0.684696	−	0.728829i	$-0.740065\pi$
$463$	−11.6576	+	5.61401i	−0.541776	+	0.260905i	0.142920	+	0.989734i	$0.454351\pi$
$464$	27.7448	+	18.9161i	1.28802	+	0.878157i
$465$	19.1760	+	17.7928i	0.889268	+	0.825120i
$466$	−0.852690	−	0.791181i	−0.0395001	−	0.0366507i
$467$	−14.8209	−	10.1047i	−0.685831	−	0.467592i	0.169597	−	0.985514i	$-0.445754\pi$
$467$	−14.8209	−	10.1047i	−0.685831	−	0.467592i	−0.855428	+	0.517922i	$0.826706\pi$
$468$	4.54685	−	2.18965i	0.210178	−	0.101216i
$469$		0			0
$470$	−3.33399	−	1.60557i	−0.153786	−	0.0740593i
$471$	−11.7091	−	20.2807i	−0.539525	−	0.934485i
$472$	−2.14152	+	3.70922i	−0.0985714	+	0.170731i
$473$	−9.13140	+	6.22568i	−0.419862	+	0.286257i
$474$	−1.49101	−	0.224734i	−0.0684846	−	0.0103224i
$475$	−0.168078	+	0.736396i	−0.00771193	+	0.0337882i
$476$		0			0
$477$	−5.59008	−	24.4917i	−0.255952	−	1.12140i
$478$	0.0688335	+	0.918519i	0.00314837	+	0.0420121i
$479$	−8.90872	−	2.74798i	−0.407050	−	0.125558i	0.0844670	−	0.996426i	$-0.473081\pi$
$479$	−8.90872	−	2.74798i	−0.407050	−	0.125558i	−0.491517	+	0.870868i	$0.663557\pi$
$480$	4.12818	+	10.5184i	0.188425	+	0.480099i
$481$	2.88064	−	0.888559i	0.131346	−	0.0405148i
$482$	0.320974	+	0.402489i	0.0146200	+	0.0183329i
$483$		0			0
$484$	−0.960735	+	1.20472i	−0.0436698	+	0.0547602i
$485$	6.02293	−	15.3462i	0.273487	−	0.696834i
$486$	−0.0934978	+	1.24764i	−0.00424115	+	0.0565942i
$487$	−0.388846	+	0.0586091i	−0.0176203	+	0.00265583i	−0.157846	−	0.987464i	$-0.550455\pi$
$487$	−0.388846	+	0.0586091i	−0.0176203	+	0.00265583i	0.140226	+	0.990119i	$0.455217\pi$
$488$	2.09289	−	1.94192i	0.0947407	−	0.0879065i
$489$	71.5336			3.23486
$490$		0			0
$491$	25.1698			1.13590			0.567948	−	0.823065i	$-0.307738\pi$
$491$	25.1698			1.13590			0.567948	+	0.823065i	$0.307738\pi$
$492$	11.9973	−	11.1318i	0.540879	−	0.501863i
$493$	13.1212	−	1.97770i	0.590948	−	0.0890711i
$494$	0.0225821	−	0.301337i	0.00101602	−	0.0135578i
$495$	−15.0803	+	38.4239i	−0.677807	+	1.72703i
$496$	9.86090	−	12.3652i	0.442767	−	0.555213i
$497$		0			0
$498$	−1.15687	−	1.45067i	−0.0518405	−	0.0650060i
$499$	2.31812	−	0.715045i	0.103773	−	0.0320098i	−0.242434	−	0.970168i	$-0.577946\pi$
$499$	2.31812	−	0.715045i	0.103773	−	0.0320098i	0.346207	+	0.938158i	$0.387470\pi$
$500$	8.21251	+	20.9251i	0.367274	+	0.935800i
$501$	23.1728	+	7.14786i	1.03528	+	0.319343i
$502$	−0.104615	−	1.39599i	−0.00466919	−	0.0623060i
$503$	−3.94989	−	17.3056i	−0.176117	−	0.771618i	−0.983400	−	0.181453i	$-0.941920\pi$
$503$	−3.94989	−	17.3056i	−0.176117	−	0.771618i	0.807283	−	0.590165i	$-0.200937\pi$
$504$		0			0
$505$	6.06946	−	26.5920i	0.270087	−	1.18333i
$506$	0.111146	+	0.0167526i	0.00494105	+	0.000744744i
$507$	30.7464	−	20.9625i	1.36549	−	0.930978i
$508$	−2.87337	+	4.97682i	−0.127485	+	0.220811i
$509$	13.1109	+	22.7087i	0.581130	+	1.00655i	0.995346	+	0.0963683i	$0.0307227\pi$
$509$	13.1109	+	22.7087i	0.581130	+	1.00655i	−0.414215	+	0.910179i	$0.635944\pi$
$510$	1.31576	+	0.633636i	0.0582628	+	0.0280579i
$511$		0			0
$512$	10.2970	−	4.95880i	0.455070	−	0.219150i
$513$	25.8205	+	17.6041i	1.14000	+	0.777240i
$514$	−0.677783	−	0.628891i	−0.0298957	−	0.0277392i
$515$	3.55887	+	3.30215i	0.156823	+	0.145510i
$516$	15.3178	+	10.4435i	0.674328	+	0.459749i
$517$	−34.8505	+	16.7831i	−1.53272	+	0.738120i
$518$		0			0
$519$	28.2393	+	13.5993i	1.23957	+	0.596944i
$520$	−0.304364	−	0.527174i	−0.0133473	−	0.0231181i
$521$	−2.37745	+	4.11786i	−0.104158	+	0.180407i	−0.913394	−	0.407077i	$-0.866548\pi$
$521$	−2.37745	+	4.11786i	−0.104158	+	0.180407i	0.809236	+	0.587484i	$0.199881\pi$
$522$	−5.87163	+	4.00321i	−0.256994	+	0.175216i
$523$	0.389809	+	0.0587543i	0.0170452	+	0.00256915i	0.157559	−	0.987510i	$-0.449637\pi$
$523$	0.389809	+	0.0587543i	0.0170452	+	0.00256915i	−0.140514	+	0.990079i	$0.544876\pi$
$524$	−9.19680	+	40.2938i	−0.401764	+	1.76024i
$525$		0			0
$526$	−0.737530	−	3.23133i	−0.0321578	−	0.140893i
$527$	−0.467044	−	6.23226i	−0.0203447	−	0.271482i
$528$	36.9147	+	11.3867i	1.60651	+	0.495541i
$529$	−8.38530	−	21.3654i	−0.364578	−	0.928930i
$530$	−1.43965	+	0.444075i	−0.0625346	+	0.0192894i
$531$	24.5920	+	30.8374i	1.06720	+	1.33823i
$532$		0			0
$533$	−0.826122	+	1.03592i	−0.0357833	+	0.0448709i
$534$	−0.669815	+	1.70666i	−0.0289857	+	0.0738544i
$535$	−2.32383	+	31.0094i	−0.100468	+	1.34065i
$536$	−3.70242	+	0.558050i	−0.159920	+	0.0241041i
$537$	17.6700	−	16.3954i	0.762518	−	0.707514i
$538$	−1.78386			−0.0769077
$539$		0			0
$540$	31.2996			1.34692
$541$	11.6410	−	10.8013i	0.500487	−	0.464384i	−0.389070	−	0.921208i	$-0.627204\pi$
$541$	11.6410	−	10.8013i	0.500487	−	0.464384i	0.889557	+	0.456824i	$0.151013\pi$
$542$	2.19440	−	0.330753i	0.0942576	−	0.0142070i
$543$	−1.38211	+	18.4430i	−0.0593121	+	0.791466i
$544$	0.986272	−	2.51298i	0.0422861	−	0.107743i
$545$	−17.5286	+	21.9802i	−0.750842	+	0.941526i
$546$		0			0
$547$	−21.5460	−	27.0178i	−0.921239	−	1.15520i	−0.987535	−	0.157397i	$-0.949690\pi$
$547$	−21.5460	−	27.0178i	−0.921239	−	1.15520i	0.0662966	−	0.997800i	$-0.478882\pi$
$548$	−24.2690	+	7.48599i	−1.03672	+	0.319786i
$549$	−9.60556	−	24.4746i	−0.409955	−	1.04455i
$550$	−0.0853543	−	0.0263283i	−0.00363952	−	0.00112264i
$551$	−2.81525	−	37.5669i	−0.119934	−	1.60040i
$552$	−0.0843876	−	0.369726i	−0.00359177	−	0.0157366i
$553$		0			0
$554$	−0.0830789	+	0.363993i	−0.00352969	+	0.0154646i
$555$	40.8993	+	6.16458i	1.73608	+	0.261672i
$556$	32.6093	−	22.2326i	1.38294	−	0.942873i
$557$	−13.2184	+	22.8950i	−0.560084	+	0.970093i	0.437405	+	0.899265i	$0.355898\pi$
$557$	−13.2184	+	22.8950i	−0.560084	+	0.970093i	−0.997489	+	0.0708285i	$0.977436\pi$
$558$	1.67353	+	2.89864i	0.0708462	+	0.122709i
$559$	−1.35228	−	0.651224i	−0.0571954	−	0.0275439i
$560$		0			0
$561$	13.7537	−	6.62344i	0.580682	−	0.279642i
$562$	1.37540	+	0.937734i	0.0580179	+	0.0395559i
$563$	−30.3648	−	28.1745i	−1.27973	−	1.18741i	−0.971749	−	0.236018i	$-0.924158\pi$
$563$	−30.3648	−	28.1745i	−1.27973	−	1.18741i	−0.307977	−	0.951394i	$-0.599652\pi$
$564$	47.5655	+	44.1344i	2.00287	+	1.85839i
$565$	18.5257	+	12.6306i	0.779383	+	0.531374i
$566$	−0.613017	+	0.295213i	−0.0257670	+	0.0124087i
$567$		0			0
$568$	−3.55718	−	1.71305i	−0.149256	−	0.0718778i
$569$	14.2483	+	24.6788i	0.597321	+	1.03459i	0.993215	+	0.116294i	$0.0371015\pi$
$569$	14.2483	+	24.6788i	0.597321	+	1.03459i	−0.395894	+	0.918296i	$0.629565\pi$
$570$	2.07304	−	3.59061i	0.0868300	−	0.150394i
$571$	−24.0432	+	16.3924i	−1.00618	+	0.686000i	−0.949945	−	0.312417i	$-0.898861\pi$
$571$	−24.0432	+	16.3924i	−1.00618	+	0.686000i	−0.0562327	+	0.998418i	$0.517909\pi$
$572$	−3.12834	−	0.471521i	−0.130802	−	0.0197153i
$573$	14.3965	−	63.0754i	0.601424	−	2.63501i
$574$		0			0
$575$	−0.00849063	−	0.0371999i	−0.000354084	−	0.00155134i
$576$	−3.05573	−	40.7759i	−0.127322	−	1.69900i
$577$	38.3623	+	11.8332i	1.59704	+	0.492622i	0.960421	−	0.278554i	$-0.0898551\pi$
$577$	38.3623	+	11.8332i	1.59704	+	0.492622i	0.636622	+	0.771176i	$0.280331\pi$
$578$	0.800799	+	2.04040i	0.0333088	+	0.0848695i
$579$	18.4549	−	5.69259i	0.766961	−	0.236576i
$580$	−23.5251	−	29.4995i	−0.976825	−	1.22490i
$581$		0			0
$582$	2.03582	−	2.55284i	0.0843876	−	0.105819i
$583$	−5.75356	+	14.6598i	−0.238288	+	0.607148i
$584$	0.163237	−	2.17824i	0.00675478	−	0.0901362i
$585$	−5.54317	+	0.835498i	−0.229182	+	0.0345436i
$586$	−2.86229	+	2.65582i	−0.118240	+	0.109711i
$587$	−23.9240			−0.987449			−0.493724	−	0.869618i	$-0.664365\pi$
$587$	−23.9240			−0.987449			−0.493724	+	0.869618i	$0.664365\pi$
$588$		0			0
$589$	−17.7432			−0.731097
$590$	1.73399	−	1.60891i	0.0713872	−	0.0662377i
$591$	−28.9019	+	4.35626i	−1.18887	+	0.179193i
$592$	1.86876	−	24.9368i	0.0768054	−	1.02490i
$593$	−10.3241	+	26.3054i	−0.423960	+	1.08023i	0.546176	+	0.837670i	$0.316083\pi$
$593$	−10.3241	+	26.3054i	−0.423960	+	1.08023i	−0.970136	+	0.242562i	$0.922012\pi$
$594$	−2.30415	+	2.88931i	−0.0945404	+	0.118550i
$595$		0			0
$596$	15.7419	+	19.7397i	0.644811	+	0.808568i
$597$	48.3884	−	14.9258i	1.98040	−	0.610874i
$598$	0.00557695	+	0.0142098i	0.000228058	+	0.000581083i
$599$	−4.51079	−	1.39139i	−0.184306	−	0.0568508i	0.201228	−	0.979544i	$-0.435507\pi$
$599$	−4.51079	−	1.39139i	−0.184306	−	0.0568508i	−0.385534	+	0.922694i	$0.625983\pi$
$600$	0.0225212	+	0.300525i	0.000919425	+	0.0122689i
$601$	7.41533	+	32.4887i	0.302478	+	1.32524i	0.866374	+	0.499396i	$0.166445\pi$
$601$	7.41533	+	32.4887i	0.302478	+	1.32524i	−0.563896	+	0.825846i	$0.690698\pi$
$602$		0			0
$603$	−7.67267	+	33.6162i	−0.312455	+	1.36896i
$604$	−13.0323	−	1.96430i	−0.530277	−	0.0799264i
$605$	1.41422	−	0.964196i	0.0574960	−	0.0392001i
$606$	2.70116	−	4.67855i	0.109727	−	0.190053i
$607$	−16.8576	−	29.1983i	−0.684230	−	1.18512i	−0.973678	−	0.227927i	$-0.926805\pi$
$607$	−16.8576	−	29.1983i	−0.684230	−	1.18512i	0.289448	−	0.957194i	$-0.406528\pi$
$608$	−6.90524	−	3.32539i	−0.280044	−	0.134862i
$609$		0			0
$610$	−1.42063	+	0.684140i	−0.0575197	+	0.0277000i
$611$	−4.34040	−	2.95924i	−0.175594	−	0.119718i
$612$	−12.1267	−	11.2519i	−0.490192	−	0.454832i
$613$	−26.4593	−	24.5506i	−1.06868	−	0.991590i	−0.0686976	−	0.997638i	$-0.521884\pi$
$613$	−26.4593	−	24.5506i	−1.06868	−	0.991590i	−0.999982	+	0.00604802i	$0.998075\pi$
$614$	−0.271159	−	0.184873i	−0.0109431	−	0.00746088i
$615$	−16.3792	+	7.88782i	−0.660475	+	0.318068i
$616$		0			0
$617$	2.28017	+	1.09807i	0.0917961	+	0.0442067i	0.479218	−	0.877696i	$-0.340920\pi$
$617$	2.28017	+	1.09807i	0.0917961	+	0.0442067i	−0.387422	+	0.921902i	$0.626634\pi$
$618$	0.480783	+	0.832741i	0.0193399	+	0.0334978i
$619$	−1.34133	+	2.32325i	−0.0539126	+	0.0933794i	−0.891722	−	0.452583i	$-0.850503\pi$
$619$	−1.34133	+	2.32325i	−0.0539126	+	0.0933794i	0.837810	+	0.545963i	$0.183836\pi$
$620$	−14.6831	+	10.0108i	−0.589688	+	0.402042i
$621$	−1.56103	−	0.235287i	−0.0626419	−	0.00944175i
$622$	0.532091	−	2.33124i	0.0213349	−	0.0934743i
$623$		0			0
$624$	1.16743	+	5.11486i	0.0467347	+	0.204758i
$625$	−1.80092	−	24.0316i	−0.0720369	−	0.961265i
$626$	−0.130841	−	0.0403591i	−0.00522946	−	0.00161307i
$627$	−15.8336	−	40.3433i	−0.632333	−	1.61116i
$628$	15.2021	−	4.68923i	0.606631	−	0.187121i
$629$	−6.16114	−	7.72583i	−0.245661	−	0.308049i
$630$		0			0
$631$	10.5445	−	13.2224i	0.419772	−	0.526377i	−0.526315	−	0.850289i	$-0.676427\pi$
$631$	10.5445	−	13.2224i	0.419772	−	0.526377i	0.946087	+	0.323912i	$0.104998\pi$
$632$	0.752700	−	1.91785i	0.0299408	−	0.0762880i
$633$	−1.40967	+	18.8108i	−0.0560294	+	0.747661i
$634$	1.59108	−	0.239817i	0.0631899	−	0.00952435i
$635$	4.67941	−	4.34186i	0.185697	−	0.172302i
$636$	26.4178			1.04754
$637$		0			0
$638$	4.45496			0.176374
$639$	−26.6528	+	24.7302i	−1.05437	+	0.978311i
$640$	−10.1011	+	1.52250i	−0.399282	+	0.0601820i
$641$	−0.681070	+	9.08824i	−0.0269006	+	0.358964i	0.967468	+	0.252992i	$0.0814145\pi$
$641$	−0.681070	+	9.08824i	−0.0269006	+	0.358964i	−0.994369	+	0.105972i	$0.966205\pi$
$642$	−2.25014	+	5.73326i	−0.0888059	+	0.226274i
$643$	23.7264	−	29.7520i	0.935679	−	1.17330i	−0.0489769	−	0.998800i	$-0.515596\pi$
$643$	23.7264	−	29.7520i	0.935679	−	1.17330i	0.984656	−	0.174505i	$-0.0558325\pi$
$644$		0			0
$645$	−12.8397	−	16.1005i	−0.505564	−	0.633957i
$646$	−0.946539	+	0.291969i	−0.0372411	+	0.0114874i
$647$	−8.85663	−	22.5663i	−0.348190	−	0.887174i	−0.992482	−	0.122394i	$-0.960943\pi$
$647$	−8.85663	−	22.5663i	−0.348190	−	0.887174i	0.644291	−	0.764780i	$-0.277152\pi$
$648$	2.58412	+	0.797096i	0.101514	+	0.0313129i
$649$	−1.84778	−	24.6570i	−0.0725318	−	0.967870i
$650$	−0.00269934	−	0.0118266i	−0.000105877	−	0.000463877i
$651$		0			0
$652$	−10.8136	+	47.3773i	−0.423492	+	1.85544i
$653$	−25.8055	−	3.88956i	−1.00985	−	0.152210i	−0.376778	−	0.926304i	$-0.622968\pi$
$653$	−25.8055	−	3.88956i	−1.00985	−	0.152210i	−0.633071	+	0.774093i	$0.718206\pi$
$654$	−4.60071	+	3.13671i	−0.179902	+	0.122655i
$655$	22.9547	−	39.7587i	0.896914	−	1.55350i
$656$	5.49562	+	9.51869i	0.214568	+	0.371643i
$657$	−18.1236	−	8.72786i	−0.707068	−	0.340506i
$658$		0			0
$659$	35.4630	−	17.0781i	1.38144	−	0.665268i	0.412136	−	0.911122i	$-0.364783\pi$
$659$	35.4630	−	17.0781i	1.38144	−	0.665268i	0.969307	+	0.245855i	$0.0790687\pi$
$660$	−35.8646	−	24.4521i	−1.39603	−	0.951796i
$661$	13.5704	+	12.5915i	0.527828	+	0.489753i	0.898477	−	0.439020i	$-0.144674\pi$
$661$	13.5704	+	12.5915i	0.527828	+	0.489753i	−0.370649	+	0.928773i	$0.620865\pi$
$662$	3.61570	+	3.35488i	0.140528	+	0.130391i
$663$	1.71294	+	1.16786i	0.0665250	+	0.0453559i
$664$	2.28417	−	1.10000i	0.0886430	−	0.0426882i
$665$		0			0
$666$	4.76808	+	2.29619i	0.184759	+	0.0889754i
$667$	0.951528	+	1.64810i	0.0368433	+	0.0638145i
$668$	−8.23707	+	14.2670i	−0.318702	+	0.552008i
$669$	36.7954	−	25.0866i	1.42259	−	0.969906i
$670$	2.04477	+	0.308200i	0.0789965	+	0.0119068i
$671$	−3.66764	+	16.0690i	−0.141588	+	0.620335i
$672$		0			0
$673$	−7.07769	−	31.0094i	−0.272825	−	1.19532i	−0.906662	−	0.421857i	$-0.861378\pi$
$673$	−7.07769	−	31.0094i	−0.272825	−	1.19532i	0.633838	−	0.773466i	$-0.281479\pi$
$674$	0.210247	+	2.80555i	0.00809842	+	0.108066i
$675$	1.19879	+	0.369776i	0.0461413	+	0.0142327i
$676$	9.23580	+	23.5324i	0.355223	+	0.905094i
$677$	−35.9465	+	11.0880i	−1.38154	+	0.426148i	−0.894436	−	0.447197i	$-0.852422\pi$
$677$	−35.9465	+	11.0880i	−1.38154	+	0.426148i	−0.487102	+	0.873345i	$0.661946\pi$
$678$	2.76886	+	3.47204i	0.106337	+	0.133343i
$679$		0			0
$680$	−1.24411	+	1.56007i	−0.0477095	+	0.0598259i
$681$	−19.7846	+	50.4105i	−0.758149	+	1.93173i
$682$	0.156802	−	2.09237i	0.00600425	−	0.0801211i
$683$	14.3846	−	2.16813i	0.550413	−	0.0829613i	0.132053	−	0.991243i	$-0.457843\pi$
$683$	14.3846	−	2.16813i	0.550413	−	0.0829613i	0.418360	+	0.908281i	$0.362605\pi$
$684$	−34.4281	+	31.9446i	−1.31639	+	1.22143i
$685$	28.2113			1.07790
$686$		0			0
$687$	−54.3854			−2.07493
$688$	−9.12691	+	8.46854i	−0.347960	+	0.322860i
$689$	−2.11488	+	0.318767i	−0.0805705	+	0.0121441i
$690$	−0.0156518	+	0.208858i	−0.000595852	+	0.00795109i
$691$	6.96378	−	17.7434i	0.264915	−	0.674992i	−0.735081	−	0.677980i	$-0.762856\pi$
$691$	6.96378	−	17.7434i	0.264915	−	0.674992i	0.999996	+	0.00298766i	$0.000951003\pi$
$692$	−13.2758	+	16.6473i	−0.504671	+	0.632837i
$693$		0			0
$694$	2.99667	+	3.75770i	0.113752	+	0.142640i
$695$	−41.8924	+	12.9221i	−1.58907	+	0.490163i
$696$	−5.49133	−	13.9917i	−0.208148	−	0.530353i
$697$	4.15036	+	1.28022i	0.157206	+	0.0484916i
$698$	0.114727	+	1.53093i	0.00434248	+	0.0579464i
$699$	−5.04157	−	22.0886i	−0.190690	−	0.835466i
$700$		0			0
$701$	−3.63929	+	15.9448i	−0.137454	+	0.602225i	0.858535	+	0.512754i	$0.171375\pi$
$701$	−3.63929	+	15.9448i	−0.137454	+	0.602225i	−0.995989	+	0.0894711i	$0.971482\pi$
$702$	−0.496282	−	0.0748025i	−0.0187310	−	0.00282324i
$703$	−23.1797	+	15.8037i	−0.874239	+	0.596046i
$704$	−12.8168	+	22.1994i	−0.483053	+	0.836673i
$705$	−36.0382	−	62.4201i	−1.35728	−	2.35088i
$706$	−3.68834	−	1.77621i	−0.138812	−	0.0668486i
$707$		0			0
$708$	−37.3701	+	17.9965i	−1.40445	+	0.676350i
$709$	−7.49143	−	5.10757i	−0.281347	−	0.191819i	0.414422	−	0.910085i	$-0.363984\pi$
$709$	−7.49143	−	5.10757i	−0.281347	−	0.191819i	−0.695769	+	0.718266i	$0.744936\pi$
$710$	1.59842	+	1.48311i	0.0599875	+	0.0556603i
$711$	−13.9082	−	12.9049i	−0.521598	−	0.483972i
$712$	−2.06979	−	1.41116i	−0.0775686	−	0.0528854i
$713$	0.807556	−	0.388898i	0.0302432	−	0.0145644i
$714$		0			0
$715$	3.16619	+	1.52476i	0.118409	+	0.0570227i
$716$	8.18768	+	14.1815i	0.305988	+	0.529987i
$717$	−8.97041	+	15.5372i	−0.335006	+	0.580248i
$718$	0.583549	−	0.397857i	0.0217779	−	0.0148479i
$719$	37.5757	+	5.66362i	1.40134	+	0.211217i	0.805836	−	0.592139i	$-0.201716\pi$
$719$	37.5757	+	5.66362i	1.40134	+	0.211217i	0.595499	+	0.803356i	$0.296954\pi$
$720$	−10.3476	+	45.3357i	−0.385632	+	1.68956i
$721$		0			0
$722$	−0.00612984	−	0.0268566i	−0.000228129	−	0.000999498i
$723$	0.749333	+	9.99915i	0.0278680	+	0.371872i
$724$	−12.0060	−	3.70337i	−0.446201	−	0.137635i
$725$	−0.552509	−	1.40777i	−0.0205197	−	0.0522832i
$726$	0.323948	−	0.0999248i	0.0120228	−	0.00370856i
$727$	9.93554	+	12.4588i	0.368489	+	0.462070i	0.931160	−	0.364610i	$-0.118798\pi$
$727$	9.93554	+	12.4588i	0.368489	+	0.462070i	−0.562671	+	0.826681i	$0.690226\pi$
$728$		0			0
$729$	−23.7024	+	29.7219i	−0.877867	+	1.10081i
$730$	−0.440738	+	1.12298i	−0.0163124	+	0.0415634i
$731$	−0.367671	+	4.90623i	−0.0135988	+	0.181463i
$732$	27.3399	−	4.12082i	1.01051	−	0.152310i
$733$	−28.8768	+	26.7937i	−1.06659	+	0.989650i	−0.999967	−	0.00812872i	$-0.997413\pi$
$733$	−28.8768	+	26.7937i	−1.06659	+	0.989650i	−0.0666216	+	0.997778i	$0.521222\pi$
$734$	0.484900			0.0178980
$735$		0			0
$736$	0.387168			0.0142712
$737$	15.8453	−	14.7023i	0.583671	−	0.541567i
$738$	−2.30009	+	0.346683i	−0.0846676	+	0.0127616i
$739$	−1.28528	+	17.1508i	−0.0472797	+	0.630904i	0.922355	+	0.386344i	$0.126262\pi$
$739$	−1.28528	+	17.1508i	−0.0472797	+	0.630904i	−0.969634	+	0.244559i	$0.921357\pi$
$740$	−10.2655	+	26.1561i	−0.377368	+	0.961517i
$741$	3.66975	−	4.60172i	0.134811	−	0.169048i
$742$		0			0
$743$	−12.1490	−	15.2344i	−0.445704	−	0.558896i	0.507332	−	0.861750i	$-0.330632\pi$
$743$	−12.1490	−	15.2344i	−0.445704	−	0.558896i	−0.953037	+	0.302855i	$0.902060\pi$
$744$	−6.76478	+	2.08666i	−0.248009	+	0.0765006i
$745$	−10.2461	−	26.1068i	−0.375390	−	0.956478i
$746$	−5.06109	−	1.56114i	−0.185300	−	0.0571574i
$747$	−1.74472	−	23.2817i	−0.0638361	−	0.851833i
$748$	2.30765	+	10.1105i	0.0843759	+	0.369675i
$749$		0			0
$750$	1.10049	−	4.82156i	0.0401842	−	0.176058i
$751$	34.9847	+	5.27309i	1.27661	+	0.192418i	0.752135	−	0.659009i	$-0.229024\pi$
$751$	34.9847	+	5.27309i	1.27661	+	0.192418i	0.524473	+	0.851427i	$0.324262\pi$
$752$	−36.0049	+	24.5477i	−1.31296	+	0.895164i
$753$	13.6335	−	23.6139i	0.496831	−	0.860537i
$754$	0.302510	+	0.523963i	0.0110168	+	0.0190816i
$755$	13.1900	+	6.35197i	0.480033	+	0.231172i
$756$		0			0
$757$	−19.5973	+	9.43757i	−0.712276	+	0.343014i	−0.754686	−	0.656086i	$-0.772211\pi$
$757$	−19.5973	+	9.43757i	−0.712276	+	0.343014i	0.0424098	+	0.999100i	$0.486497\pi$
$758$	3.03883	+	2.07184i	0.110375	+	0.0752526i
$759$	1.60489	+	1.48912i	0.0582539	+	0.0540517i
$760$	4.15275	+	3.85319i	0.150636	+	0.139770i
$761$	−10.3120	−	7.03058i	−0.373808	−	0.254858i	0.361814	−	0.932250i	$-0.382158\pi$
$761$	−10.3120	−	7.03058i	−0.373808	−	0.254858i	−0.735622	+	0.677392i	$0.763110\pi$
$762$	1.13912	−	0.548570i	0.0412658	−	0.0198726i
$763$		0			0
$764$	39.5991	+	19.0699i	1.43264	+	0.689925i
$765$	9.18783	+	15.9138i	0.332187	+	0.575364i
$766$	−0.380297	+	0.658694i	−0.0137407	+	0.0237996i
$767$	2.77451	−	1.89163i	0.100182	−	0.0683028i
$768$	40.9995	+	6.17968i	1.47944	+	0.222990i
$769$	4.89228	−	21.4345i	0.176420	−	0.772947i	−0.806844	−	0.590764i	$-0.798826\pi$
$769$	4.89228	−	21.4345i	0.176420	−	0.772947i	0.983265	−	0.182183i	$-0.0583164\pi$
$770$		0			0
$771$	−4.00743	−	17.5577i	−0.144324	−	0.632324i
$772$	0.980465	+	13.0834i	0.0352877	+	0.470882i
$773$	−18.8456	−	5.81308i	−0.677828	−	0.209082i	−0.0633203	−	0.997993i	$-0.520169\pi$
$773$	−18.8456	−	5.81308i	−0.677828	−	0.209082i	−0.614507	+	0.788911i	$0.710645\pi$
$774$	−0.962641	−	2.45277i	−0.0346014	−	0.0881630i
$775$	−0.680637	+	0.209949i	−0.0244492	+	0.00754158i
$776$	2.78166	+	3.48809i	0.0998558	+	0.125215i
$777$		0			0
$778$	−1.41063	+	1.76887i	−0.0505735	+	0.0634172i
$779$	4.50496	−	11.4784i	0.161407	−	0.411258i
$780$	0.440536	−	5.87855i	0.0157737	−	0.210486i
$781$	22.5383	−	3.39710i	0.806484	−	0.121558i
$782$	0.0366809	−	0.0340349i	0.00131171	−	0.00121708i
$783$	−62.5691			−2.23604
$784$		0			0
$785$	−17.6716			−0.630727
$786$	6.66558	−	6.18475i	0.237753	−	0.220603i
$787$	−15.2188	+	2.29386i	−0.542490	+	0.0817672i	−0.414570	−	0.910017i	$-0.636068\pi$
$787$	−15.2188	+	2.29386i	−0.542490	+	0.0817672i	−0.127920	+	0.991785i	$0.540830\pi$
$788$	1.48384	−	19.8005i	0.0528597	−	0.705364i
$789$	23.5855	−	60.0950i	0.839667	−	2.13944i
$790$	−0.709436	+	0.889604i	−0.0252406	+	0.0316507i
$791$		0			0
$792$	−6.96475	−	8.73352i	−0.247482	−	0.310332i
$793$	−2.13897	+	0.659785i	−0.0759571	+	0.0234296i
$794$	−0.389611	−	0.992714i	−0.0138268	−	0.0352301i
$795$	−28.0412	−	8.64956i	−0.994519	−	0.306768i
$796$	2.57075	+	34.3043i	0.0911180	+	1.21589i
$797$	−4.92695	−	21.5864i	−0.174522	−	0.764629i	−0.984100	−	0.177617i	$-0.943161\pi$
$797$	−4.92695	−	21.5864i	−0.174522	−	0.764629i	0.809578	−	0.587012i	$-0.199696\pi$
$798$		0			0
$799$	−3.83179	+	16.7882i	−0.135559	+	0.593923i
$800$	−0.304235	−	0.0458561i	−0.0107563	−	0.00162126i
$801$	−19.0607	+	12.9953i	−0.673476	+	0.459168i
$802$	−2.15143	+	3.72638i	−0.0759695	+	0.131583i
$803$	6.30515	+	10.9208i	0.222504	+	0.385388i
$804$	−32.6690	−	15.7326i	−1.15215	−	0.554844i
$805$		0			0
$806$	0.256738	−	0.123639i	0.00904322	−	0.00435498i
$807$	−28.7081	−	19.5729i	−1.01057	−	0.688998i
$808$	5.41102	+	5.02070i	0.190359	+	0.176627i
$809$	13.6431	+	12.6590i	0.479667	+	0.445066i	0.882573	−	0.470176i	$-0.155809\pi$
$809$	13.6431	+	12.6590i	0.479667	+	0.445066i	−0.402906	+	0.915241i	$0.632000\pi$
$810$	−1.23400	−	0.841325i	−0.0433583	−	0.0295612i
$811$	−28.7892	+	13.8641i	−1.01092	+	0.486835i	−0.864632	−	0.502406i	$-0.832448\pi$
$811$	−28.7892	+	13.8641i	−1.01092	+	0.486835i	−0.146292	+	0.989241i	$0.546734\pi$
$812$		0			0
$813$	38.9441	+	18.7545i	1.36583	+	0.657749i
$814$	−1.65880	−	2.87313i	−0.0581410	−	0.100703i
$815$	26.9900	−	46.7481i	0.945420	−	1.63752i
$816$	14.2093	−	9.68775i	0.497426	−	0.339139i
$817$	13.8120	+	2.08182i	0.483221	+	0.0728338i
$818$	−0.974289	+	4.26864i	−0.0340652	+	0.149249i
$819$		0			0
$820$	−2.74816	−	12.0405i	−0.0959701	−	0.420472i
$821$	−1.25307	−	16.7211i	−0.0437324	−	0.583569i	−0.975427	−	0.220325i	$-0.929288\pi$
$821$	−1.25307	−	16.7211i	−0.0437324	−	0.583569i	0.931694	−	0.363244i	$-0.118331\pi$
$822$	5.33936	+	1.64697i	0.186231	+	0.0574448i
$823$	17.7420	+	45.2058i	0.618447	+	1.57578i	0.804963	+	0.593325i	$0.202185\pi$
$823$	17.7420	+	45.2058i	0.618447	+	1.57578i	−0.186516	+	0.982452i	$0.559720\pi$
$824$	−1.25547	+	0.387262i	−0.0437365	+	0.0134909i
$825$	−1.08475	−	1.36023i	−0.0377661	−	0.0473572i
$826$		0			0
$827$	27.7978	−	34.8574i	0.966625	−	1.21211i	−0.0106085	−	0.999944i	$-0.503377\pi$
$827$	27.7978	−	34.8574i	0.966625	−	1.21211i	0.977234	−	0.212166i	$-0.0680517\pi$
$828$	0.866775	−	2.20851i	0.0301225	−	0.0767509i
$829$	3.14121	−	41.9165i	0.109099	−	1.45582i	−0.627038	−	0.778989i	$-0.715733\pi$
$829$	3.14121	−	41.9165i	0.109099	−	1.45582i	0.736137	−	0.676833i	$-0.236648\pi$
$830$	−1.38452	+	0.208683i	−0.0480575	+	0.00724351i
$831$	−5.33081	+	4.94627i	−0.184924	+	0.171584i
$832$	−3.48126			−0.120691
$833$		0			0
$834$	−8.68306			−0.300670
$835$	13.4145	−	12.4468i	0.464227	−	0.430739i
$836$	29.1133	−	4.38812i	1.00690	−	0.151766i
$837$	−2.20225	+	29.3870i	−0.0761209	+	1.01576i
$838$	1.18685	−	3.02404i	0.0409990	−	0.104464i
$839$	−14.7280	+	18.4683i	−0.508466	+	0.637596i	−0.968116	−	0.250504i	$-0.919404\pi$
$839$	−14.7280	+	18.4683i	−0.508466	+	0.637596i	0.459650	+	0.888100i	$0.347975\pi$
$840$		0			0
$841$	28.9464	+	36.2976i	0.998150	+	1.25164i
$842$	−0.570993	+	0.176128i	−0.0196777	+	0.00606978i
$843$	11.8457	+	30.1824i	0.407988	+	1.03954i
$844$	−12.2454	−	3.77722i	−0.421505	−	0.130017i
$845$	−2.09849	−	28.0024i	−0.0721903	−	0.963313i
$846$	−2.05213	−	8.99095i	−0.0705536	−	0.309115i
$847$		0			0
$848$	−3.94790	+	17.2969i	−0.135572	+	0.593978i
$849$	−13.1046	−	1.97520i	−0.449748	−	0.0677886i
$850$	−0.0328548	+	0.0224001i	−0.00112691	+	0.000768316i
$851$	0.708603	−	1.22734i	0.0242906	−	0.0420725i
$852$	−19.1174	−	33.1123i	−0.654950	−	1.13441i
$853$	41.7615	+	20.1113i	1.42989	+	0.688597i	0.978976	−	0.203973i	$-0.0653855\pi$
$853$	41.7615	+	20.1113i	1.42989	+	0.688597i	0.450909	+	0.892570i	$0.351100\pi$
$854$		0			0
$855$	47.0028	−	22.6353i	1.60746	−	0.774112i
$856$	−6.95313	−	4.74057i	−0.237653	−	0.162029i
$857$	13.4724	+	12.5005i	0.460208	+	0.427011i	0.875898	−	0.482496i	$-0.160270\pi$
$857$	13.4724	+	12.5005i	0.460208	+	0.427011i	−0.415690	+	0.909506i	$0.636460\pi$
$858$	0.510227	+	0.473422i	0.0174189	+	0.0161624i
$859$	1.71855	+	1.17169i	0.0586361	+	0.0399774i	0.592283	−	0.805730i	$-0.298227\pi$
$859$	1.71855	+	1.17169i	0.0586361	+	0.0399774i	−0.533647	+	0.845707i	$0.679179\pi$
$860$	12.6045	−	6.06999i	0.429808	−	0.206985i
$861$		0			0
$862$	1.15039	+	0.554000i	0.0391826	+	0.0188693i
$863$	25.1040	+	43.4815i	0.854552	+	1.48013i	0.877060	+	0.480380i	$0.159501\pi$
$863$	25.1040	+	43.4815i	0.854552	+	1.48013i	−0.0225085	+	0.999747i	$0.507165\pi$
$864$	−6.36469	+	11.0240i	−0.216531	+	0.375043i
$865$	19.5422	−	13.3236i	0.664454	−	0.453017i
$866$	3.79240	+	0.571612i	0.128871	+	0.0194242i
$867$	−9.50023	+	41.6232i	−0.322645	+	1.41360i
$868$		0			0
$869$	2.64666	+	11.5958i	0.0897818	+	0.393360i
$870$	0.620346	+	8.27795i	0.0210317	+	0.280649i
$871$	2.80515	+	0.865275i	0.0950489	+	0.0293187i
$872$	−2.77960	−	7.08229i	−0.0941290	−	0.239837i
$873$	39.2601	−	12.1101i	1.32875	−	0.409866i
$874$	−0.0885738	−	0.111068i	−0.00299605	−	0.00375693i
$875$		0			0
$876$	13.1891	−	16.5386i	0.445617	−	0.558786i
$877$	−1.18424	+	3.01740i	−0.0399890	+	0.101890i	−0.949473	−	0.313848i	$-0.898382\pi$
$877$	−1.18424	+	3.01740i	−0.0399890	+	0.101890i	0.909484	+	0.415739i	$0.136477\pi$
$878$	0.183198	−	2.44461i	0.00618263	−	0.0825015i
$879$	−75.2038	+	11.3352i	−2.53656	+	0.382325i
$880$	21.3695	−	19.8280i	0.720365	−	0.668401i
$881$	−47.0450			−1.58499			−0.792494	−	0.609880i	$-0.791218\pi$
$881$	−47.0450			−1.58499			−0.792494	+	0.609880i	$0.791218\pi$
$882$		0			0
$883$	20.9572			0.705266			0.352633	−	0.935762i	$-0.385286\pi$
$883$	20.9572			0.705266			0.352633	+	0.935762i	$0.385286\pi$
$884$	−1.03243	+	0.957951i	−0.0347242	+	0.0322194i
$885$	45.5588	−	6.86688i	1.53144	−	0.230828i
$886$	−0.267985	+	3.57601i	−0.00900314	+	0.120139i
$887$	−13.0428	+	33.2325i	−0.437934	+	1.11584i	0.526185	+	0.850370i	$0.323622\pi$
$887$	−13.0428	+	33.2325i	−0.437934	+	1.11584i	−0.964120	+	0.265468i	$0.914473\pi$
$888$	−6.97893	+	8.75131i	−0.234198	+	0.293675i
$889$		0			0
$890$	0.862600	+	1.08167i	0.0289144	+	0.0362575i
$891$	−14.9182	+	4.60165i	−0.499778	+	0.154161i
$892$	11.0528	+	28.1622i	0.370077	+	0.942940i
$893$	46.7160	+	14.4100i	1.56329	+	0.482212i
$894$	−0.415106	−	5.53921i	−0.0138832	−	0.185259i
$895$	−4.04760	−	17.7337i	−0.135296	−	0.592772i
$896$		0			0
$897$	−0.0661618	+	0.289874i	−0.00220908	+	0.00967861i
$898$	−4.28596	−	0.646004i	−0.143024	−	0.0215574i
$899$	29.3521	−	20.0120i	0.978949	−	0.667436i
$900$	−0.942685	+	1.63278i	−0.0314228	+	0.0544260i
$901$	3.50542	+	6.07157i	0.116783	+	0.202273i
$902$	1.31379	+	0.632686i	0.0437443	+	0.0210661i
$903$		0			0
$904$	−5.46695	+	2.63274i	−0.181828	+	0.0875637i
$905$	11.5313	+	7.86189i	0.383313	+	0.261338i
$906$	2.12555	+	1.97222i	0.0706167	+	0.0655227i
$907$	−20.2424	−	18.7822i	−0.672137	−	0.623652i	0.268415	−	0.963303i	$-0.413500\pi$
$907$	−20.2424	−	18.7822i	−0.672137	−	0.623652i	−0.940551	+	0.339652i	$0.889691\pi$
$908$	−30.3965	−	20.7240i	−1.00874	−	0.687749i
$909$	61.2445	−	29.4938i	2.03135	−	0.978247i
$910$		0			0
$911$	−32.8752	−	15.8319i	−1.08920	−	0.524533i	−0.198955	−	0.980009i	$-0.563755\pi$
$911$	−32.8752	−	15.8319i	−1.08920	−	0.524533i	−0.890248	+	0.455476i	$0.849469\pi$
$912$	−24.4123	−	42.2833i	−0.808372	−	1.40014i
$913$	−7.31800	+	12.6751i	−0.242190	+	0.419486i
$914$	−0.119779	+	0.0816643i	−0.00396195	+	0.00270121i
$915$	−30.3691	−	4.57741i	−1.00397	−	0.151324i
$916$	8.22131	−	36.0199i	0.271640	−	1.19013i
$917$		0			0
$918$	0.366087	+	1.60393i	0.0120827	+	0.0529376i
$919$	−0.243462	−	3.24877i	−0.00803106	−	0.107167i	0.991748	−	0.128206i	$-0.0409217\pi$
$919$	−0.243462	−	3.24877i	−0.00803106	−	0.107167i	−0.999779	+	0.0210386i	$0.993303\pi$
$920$	−0.273461	−	0.0843515i	−0.00901574	−	0.00278099i
$921$	−2.33537	−	5.95043i	−0.0769531	−	0.196073i
$922$	−2.94988	+	0.909917i	−0.0971490	+	0.0299665i
$923$	1.92999	+	2.42013i	0.0635263	+	0.0796594i
$924$		0			0
$925$	−0.702184	+	0.880511i	−0.0230877	+	0.0289510i
$926$	−0.706519	+	1.80018i	−0.0232177	+	0.0591577i
$927$	−0.904173	+	12.0653i	−0.0296969	+	0.396278i
$928$	15.1737	−	2.28707i	0.498102	−	0.0750768i
$929$	−36.0167	+	33.4186i	−1.18167	+	1.09643i	−0.188223	+	0.982126i	$0.560273\pi$
$929$	−36.0167	+	33.4186i	−1.18167	+	1.09643i	−0.993446	+	0.114302i	$0.963537\pi$
$930$	3.90976			0.128206
$931$		0			0
$932$	15.3916			0.504168
$933$	34.1419	−	31.6791i	1.11776	−	1.03713i
$934$	−2.65105	+	0.399581i	−0.0867450	+	0.0130747i
$935$	0.860854	−	11.4873i	0.0281529	−	0.375675i
$936$	0.554243	−	1.41219i	0.0181160	−	0.0461588i
$937$	20.6062	−	25.8394i	0.673177	−	0.844137i	−0.321529	−	0.946900i	$-0.604197\pi$
$937$	20.6062	−	25.8394i	0.673177	−	0.844137i	0.994706	+	0.102763i	$0.0327682\pi$
$938$		0			0
$939$	−1.66283	−	2.08512i	−0.0542644	−	0.0680454i
$940$	46.7892	−	14.4325i	1.52609	−	0.470738i
$941$	−6.89526	−	17.5688i	−0.224779	−	0.572728i	0.773343	−	0.633988i	$-0.218583\pi$
$941$	−6.89526	−	17.5688i	−0.224779	−	0.572728i	−0.998122	+	0.0612605i	$0.980488\pi$
$942$	−3.34458	−	1.03167i	−0.108972	−	0.0336135i
$943$	0.0465498	+	0.621164i	0.00151587	+	0.0202279i
$944$	−6.19846	−	27.1572i	−0.201743	−	0.883893i
$945$		0			0
$946$	−0.367560	+	1.61039i	−0.0119504	+	0.0523581i
$947$	−5.44333	−	0.820450i	−0.176884	−	0.0266610i	0.0600027	−	0.998198i	$-0.480889\pi$
$947$	−5.44333	−	0.820450i	−0.176884	−	0.0266610i	−0.236887	+	0.971537i	$0.576127\pi$
$948$	16.4851	−	11.2394i	0.535412	−	0.365037i
$949$	−0.856290	+	1.48314i	−0.0277964	+	0.0481447i
$950$	0.0564462	+	0.0977677i	0.00183136	+	0.00317200i
$951$	28.2370	+	13.5982i	0.915648	+	0.440953i
$952$		0			0
$953$	−22.6943	+	10.9290i	−0.735140	+	0.354025i	−0.763703	−	0.645567i	$-0.776621\pi$
$953$	−22.6943	+	10.9290i	−0.735140	+	0.354025i	0.0285637	+	0.999592i	$0.490907\pi$
$954$	−3.10226	−	2.11508i	−0.100439	−	0.0684784i
$955$	−35.7887	−	33.2071i	−1.15810	−	1.07456i
$956$	−8.93440	−	8.28991i	−0.288959	−	0.268115i
$957$	71.6949	+	48.8807i	2.31757	+	1.58009i
$958$	−1.25541	+	0.604576i	−0.0405606	+	0.0195329i
$959$		0			0
$960$	−43.0344	−	20.7243i	−1.38893	−	0.668873i
$961$	7.13405	+	12.3565i	0.230131	+	0.398598i
$962$	0.225279	−	0.390195i	0.00726328	−	0.0125804i
$963$	−64.0314	+	43.6559i	−2.06338	+	1.40679i
$964$	−6.73580	−	1.01526i	−0.216946	−	0.0326993i
$965$	3.24297	−	14.2084i	0.104395	−	0.457384i
$966$		0			0
$967$	4.88076	+	21.3840i	0.156955	+	0.687664i	0.990762	+	0.135609i	$0.0432990\pi$
$967$	4.88076	+	21.3840i	0.156955	+	0.687664i	−0.833808	+	0.552055i	$0.813844\pi$
$968$	0.0346155	+	0.461912i	0.00111259	+	0.0148464i
$969$	−18.4364	−	5.68689i	−0.592264	−	0.182689i
$970$	−0.900188	−	2.29364i	−0.0289033	−	0.0736444i
$971$	5.39894	−	1.66535i	0.173260	−	0.0534437i	−0.206911	−	0.978360i	$-0.566341\pi$
$971$	5.39894	−	1.66535i	0.173260	−	0.0534437i	0.380171	+	0.924916i	$0.375865\pi$
$972$	−10.3219	−	12.9433i	−0.331077	−	0.415157i
$973$		0			0
$974$	−0.0366446	+	0.0459509i	−0.00117417	+	0.00147236i
$975$	0.0863225	−	0.219946i	0.00276453	−	0.00704391i
$976$	−1.38761	+	18.5164i	−0.0444164	+	0.592696i
$977$	4.10160	−	0.618216i	0.131222	−	0.0197785i	−0.0831030	−	0.996541i	$-0.526483\pi$
$977$	4.10160	−	0.618216i	0.131222	−	0.0197785i	0.214325	+	0.976762i	$0.431245\pi$
$978$	7.83737	−	7.27201i	0.250611	−	0.232533i
$979$	14.4619			0.462203
$980$		0			0
$981$	−70.0641			−2.23697
$982$	2.75765	−	2.55873i	0.0880002	−	0.0816523i
$983$	−19.4655	+	2.93395i	−0.620853	+	0.0935786i	−0.451934	−	0.892051i	$-0.649266\pi$
$983$	−19.4655	+	2.93395i	−0.620853	+	0.0935786i	−0.168919	+	0.985630i	$0.554028\pi$
$984$	0.367659	−	4.90607i	0.0117205	−	0.156400i
$985$	−8.05799	+	20.5314i	−0.256749	+	0.654186i
$986$	1.23653	−	1.55056i	0.0393792	−	0.0493800i
$987$		0			0
$988$	2.49301	+	3.12614i	0.0793132	+	0.0994556i
$989$	−0.674262	+	0.207982i	−0.0214403	+	0.00661345i
$990$	2.25390	+	5.74284i	0.0716336	+	0.182519i
$991$	−12.7523	−	3.93355i	−0.405089	−	0.124953i	0.0855132	−	0.996337i	$-0.472747\pi$
$991$	−12.7523	−	3.93355i	−0.405089	−	0.124953i	−0.490602	+	0.871384i	$0.663223\pi$
$992$	−0.540104	−	7.20718i	−0.0171483	−	0.228828i
$993$	21.3780	+	93.6631i	0.678410	+	2.97231i
$994$		0			0
$995$	8.50299	−	37.2540i	0.269563	−	1.18103i
$996$	24.2775	+	3.65924i	0.769261	+	0.115947i
$997$	40.3598	−	27.5168i	1.27821	−	0.871467i	0.282080	−	0.959391i	$-0.408976\pi$
$997$	40.3598	−	27.5168i	1.27821	−	0.871467i	0.996127	+	0.0879241i	$0.0280233\pi$
$998$	0.181287	−	0.313999i	0.00573855	−	0.00993946i
$999$	23.2976	+	40.3526i	0.737103	+	1.27670i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	343.2.g.d.312.1		12
7.2	even	3		343.2.g.b.128.1		12
7.3	odd	6		343.2.e.b.246.1		12
7.4	even	3		49.2.e.b.36.1	yes	12
7.5	odd	6		343.2.g.c.128.1		12
7.6	odd	2		343.2.g.a.312.1		12
21.11	odd	6		441.2.u.b.379.2		12
28.11	odd	6		784.2.u.b.673.2		12
49.3	odd	42		2401.2.a.d.1.4		6
49.9	even	21	inner	343.2.g.d.177.1		12
49.15	even	7		343.2.g.b.67.1		12
49.24	odd	42		343.2.e.b.99.1		12
49.25	even	21		49.2.e.b.15.1	✓	12
49.34	odd	14		343.2.g.c.67.1		12
49.40	odd	42		343.2.g.a.177.1		12
49.46	even	21		2401.2.a.c.1.4		6
147.74	odd	42		441.2.u.b.64.2		12
196.123	odd	42		784.2.u.b.113.2		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
49.2.e.b.15.1	✓	12	49.25	even	21
49.2.e.b.36.1	yes	12	7.4	even	3
343.2.e.b.99.1		12	49.24	odd	42
343.2.e.b.246.1		12	7.3	odd	6
343.2.g.a.177.1		12	49.40	odd	42
343.2.g.a.312.1		12	7.6	odd	2
343.2.g.b.67.1		12	49.15	even	7
343.2.g.b.128.1		12	7.2	even	3
343.2.g.c.67.1		12	49.34	odd	14
343.2.g.c.128.1		12	7.5	odd	6
343.2.g.d.177.1		12	49.9	even	21	inner
343.2.g.d.312.1		12	1.1	even	1	trivial
441.2.u.b.64.2		12	147.74	odd	42
441.2.u.b.379.2		12	21.11	odd	6
784.2.u.b.113.2		12	196.123	odd	42
784.2.u.b.673.2		12	28.11	odd	6
2401.2.a.c.1.4		6	49.46	even	21
2401.2.a.d.1.4		6	49.3	odd	42

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 343 = 7^{3} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	343.g (of order \(21\), degree \(12\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.109562 - 0.101659i) q^{2} +(2.87863 - 0.433884i) q^{3} +(-0.147791 + 1.97213i) q^{4} +(0.802576 - 2.04493i) q^{5} +(0.271281 - 0.340175i) q^{6} +(0.370666 + 0.464800i) q^{8} +(5.23154 - 1.61372i) q^{9} +(-0.119953 - 0.305636i) q^{10} +(-3.27960 - 1.01162i) q^{11} +(0.430241 + 5.74116i) q^{12} +(-0.103718 - 0.454418i) q^{13} +(1.42306 - 6.23482i) q^{15} +(-3.82328 - 0.576267i) q^{16} +(-1.26239 + 0.860686i) q^{17} +(0.409130 - 0.708634i) q^{18} +(2.16885 + 3.75656i) q^{19} +(3.91426 + 1.88501i) q^{20} +(-0.462160 + 0.222565i) q^{22} +(-0.181049 - 0.123437i) q^{23} +(1.26868 + 1.17716i) q^{24} +(0.127648 + 0.118440i) q^{25} +(-0.0575591 - 0.0392431i) q^{26} +(6.49095 - 3.12588i) q^{27} +(-7.82477 - 3.76821i) q^{29} +(-0.477911 - 0.827766i) q^{30} +(-2.04523 + 3.54245i) q^{31} +(-1.45987 + 0.995323i) q^{32} +(-9.87968 - 1.48912i) q^{33} +(-0.0508143 + 0.222632i) q^{34} +(2.40929 + 10.5558i) q^{36} +(0.483324 + 6.44950i) q^{37} +(0.619511 + 0.191094i) q^{38} +(-0.495730 - 1.26310i) q^{39} +(1.24797 - 0.384948i) q^{40} +(-1.77240 - 2.22252i) q^{41} +(2.00772 - 2.51761i) q^{43} +(2.47975 - 6.31829i) q^{44} +(0.898771 - 11.9933i) q^{45} +(-0.0323845 + 0.00488118i) q^{46} +(8.26184 - 7.66586i) q^{47} -11.2559 q^{48} +0.0260258 q^{50} +(-3.26053 + 3.02533i) q^{51} +(0.911500 - 0.137386i) q^{52} +(0.342907 - 4.57578i) q^{53} +(0.393389 - 1.00234i) q^{54} +(-4.70082 + 5.89465i) q^{55} +(7.87324 + 9.87273i) q^{57} +(-1.24037 + 0.382603i) q^{58} +(2.63207 + 6.70640i) q^{59} +(12.0856 + 3.72791i) q^{60} +(-0.358884 - 4.78897i) q^{61} +(0.136041 + 0.596034i) q^{62} +(1.66198 - 7.28160i) q^{64} +(-1.01249 - 0.152609i) q^{65} +(-1.23382 + 0.841205i) q^{66} +(-3.14905 + 5.45432i) q^{67} +(-1.51081 - 2.61681i) q^{68} +(-0.574730 - 0.276775i) q^{69} +(-5.98346 + 2.88148i) q^{71} +(2.68921 + 1.83347i) q^{72} +(-2.69341 - 2.49912i) q^{73} +(0.708603 + 0.657487i) q^{74} +(0.418840 + 0.285561i) q^{75} +(-7.72897 + 3.72208i) q^{76} +(-0.182718 - 0.0879925i) q^{78} +(-1.73277 - 3.00124i) q^{79} +(-4.24690 + 7.35585i) q^{80} +(3.75838 - 2.56242i) q^{81} +(-0.420126 - 0.0633238i) q^{82} +(0.948934 - 4.15755i) q^{83} +(0.746875 + 3.27227i) q^{85} +(-0.0359663 - 0.479937i) q^{86} +(-24.1596 - 7.45224i) q^{87} +(-0.745433 - 1.89933i) q^{88} +(-4.02653 + 1.24202i) q^{89} +(-1.12075 - 1.40537i) q^{90} +(0.270191 - 0.338809i) q^{92} +(-4.35046 + 11.0848i) q^{93} +(0.125882 - 1.67978i) q^{94} +(9.42258 - 1.42023i) q^{95} +(-3.77057 + 3.49858i) q^{96} +7.50450 q^{97} -18.7898 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + q^{2} - q^{4} + 14 q^{5} - 7 q^{6} + 6 q^{8} + 25 q^{9} - 7 q^{10} + 4 q^{11} + 7 q^{12} + 7 q^{13} - 7 q^{15} - 29 q^{16} - 10 q^{18} + 7 q^{19} + 7 q^{20} + 13 q^{22} + q^{23} + 9 q^{25} - 7 q^{26}+ \cdots - 18 q^{99}+O(q^{100}) \) 12 * q + q^2 - q^4 + 14 * q^5 - 7 * q^6 + 6 * q^8 + 25 * q^9 - 7 * q^10 + 4 * q^11 + 7 * q^12 + 7 * q^13 - 7 * q^15 - 29 * q^16 - 10 * q^18 + 7 * q^19 + 7 * q^20 + 13 * q^22 + q^23 + 9 * q^25 - 7 * q^26 + 21 * q^27 - 11 * q^29 - 21 * q^30 + 7 * q^31 - 9 * q^32 - 49 * q^33 - 42 * q^34 - 13 * q^36 + 15 * q^37 + 21 * q^38 + 21 * q^40 + 21 * q^41 + 17 * q^43 - 18 * q^44 + 35 * q^45 + 8 * q^46 + 21 * q^47 - 46 * q^50 + 7 * q^51 - 7 * q^52 - 24 * q^53 - 21 * q^54 - 28 * q^55 + 7 * q^57 + 16 * q^58 - 7 * q^59 + 35 * q^60 + 14 * q^61 + 56 * q^62 + 14 * q^64 + 14 * q^65 - 49 * q^66 - 24 * q^67 - 28 * q^68 - 7 * q^69 - 39 * q^71 + 23 * q^72 - 21 * q^73 - 20 * q^74 - 14 * q^75 - 28 * q^76 + 8 * q^79 - 21 * q^80 + 23 * q^81 + 7 * q^82 - 7 * q^83 + 28 * q^85 - 19 * q^86 - 56 * q^87 + 16 * q^88 - 35 * q^89 - 14 * q^90 + 16 * q^92 - 7 * q^93 + 56 * q^94 - 7 * q^95 + 35 * q^96 - 28 * q^97 - 18 * q^99

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