LMFDB - Embedded newform 950.2.bb.e.143.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [950,2,Mod(143,950)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(950, base_ring=CyclotomicField(36))

chi = DirichletCharacter(H, H._module([27, 34]))

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

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

chi := DirichletCharacter("950.143");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 950 = 2 \cdot 5^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	950.bb (of order $36$, degree $12$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$7.58578819202$
Analytic rank:	$0$
Dimension:	$120$
Relative dimension:	$10$ over $\Q(\zeta_{36})$
Twist minimal:	no (minimal twist has level 190)
Sato-Tate group:	$\mathrm{SU}(2)[C_{36}]$

Embedding invariants

Embedding label			143.8
Character	$\chi$	$=$	950.143
Dual form			950.2.bb.e.857.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.573576 - 0.819152i) q^{2} +(0.0201525 - 0.230344i) q^{3} +(-0.342020 - 0.939693i) q^{4} +(-0.177128 - 0.148628i) q^{6} +(-1.23887 - 4.62353i) q^{7} +(-0.965926 - 0.258819i) q^{8} +(2.90177 + 0.511661i) q^{9} +O(q^{10})$	\(q+(0.573576 - 0.819152i) q^{2} +(0.0201525 - 0.230344i) q^{3} +(-0.342020 - 0.939693i) q^{4} +(-0.177128 - 0.148628i) q^{6} +(-1.23887 - 4.62353i) q^{7} +(-0.965926 - 0.258819i) q^{8} +(2.90177 + 0.511661i) q^{9} +(0.299320 + 0.518438i) q^{11} +(-0.223345 + 0.0598451i) q^{12} +(-4.00004 + 0.349958i) q^{13} +(-4.49796 - 1.63712i) q^{14} +(-0.766044 + 0.642788i) q^{16} +(-3.44552 - 2.41258i) q^{17} +(2.08352 - 2.08352i) q^{18} +(-4.23509 - 1.03152i) q^{19} +(-1.08997 + 0.192191i) q^{21} +(0.596362 + 0.0521749i) q^{22} +(3.98766 + 1.85948i) q^{23} +(-0.0790832 + 0.217279i) q^{24} +(-2.00766 + 3.47737i) q^{26} +(0.355871 - 1.32813i) q^{27} +(-3.92098 + 2.74550i) q^{28} +(1.07268 - 6.08348i) q^{29} +(4.32894 + 2.49932i) q^{31} +(0.0871557 + 0.996195i) q^{32} +(0.125451 - 0.0584987i) q^{33} +(-3.95254 + 1.43861i) q^{34} +(-0.511661 - 2.90177i) q^{36} +(2.05978 + 2.05978i) q^{37} +(-3.27412 + 2.87752i) q^{38} +0.928436i q^{39} +(-5.43198 - 6.47359i) q^{41} +(-0.467746 + 1.00308i) q^{42} +(0.0474908 + 0.101844i) q^{43} +(0.384799 - 0.458585i) q^{44} +(3.81042 - 2.19995i) q^{46} +(-2.59629 - 3.70788i) q^{47} +(0.132624 + 0.189407i) q^{48} +(-13.7800 + 7.95590i) q^{49} +(-0.625158 + 0.745035i) q^{51} +(1.69695 + 3.63911i) q^{52} +(-2.70861 + 5.80863i) q^{53} +(-0.883820 - 1.05330i) q^{54} +4.78663i q^{56} +(-0.322952 + 0.954738i) q^{57} +(-4.36803 - 4.36803i) q^{58} +(-0.921977 - 5.22879i) q^{59} +(-11.0985 + 4.03952i) q^{61} +(4.53030 - 2.11251i) q^{62} +(-1.22924 - 14.0503i) q^{63} +(0.866025 + 0.500000i) q^{64} +(0.0240363 - 0.136317i) q^{66} +(3.54544 - 2.48254i) q^{67} +(-1.08865 + 4.06288i) q^{68} +(0.508680 - 0.881060i) q^{69} +(0.892149 - 2.45116i) q^{71} +(-2.67047 - 1.24526i) q^{72} +(-5.65032 - 0.494339i) q^{73} +(2.86871 - 0.505832i) q^{74} +(0.479172 + 4.33248i) q^{76} +(2.02619 - 2.02619i) q^{77} +(0.760530 + 0.532529i) q^{78} +(10.9589 - 9.19562i) q^{79} +(8.00776 + 2.91459i) q^{81} +(-8.41851 + 0.736524i) q^{82} +(10.0994 - 2.70613i) q^{83} +(0.553391 + 0.958501i) q^{84} +(0.110666 + 0.0195134i) q^{86} +(-1.37968 - 0.369683i) q^{87} +(-0.154939 - 0.578242i) q^{88} +(-0.184391 - 0.154722i) q^{89} +(6.57357 + 18.0607i) q^{91} +(0.383476 - 4.38316i) q^{92} +(0.662941 - 0.946778i) q^{93} -4.52649 q^{94} +0.231224 q^{96} +(7.30298 - 10.4297i) q^{97} +(-1.38681 + 15.8513i) q^{98} +(0.603294 + 1.65754i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 120 q + 12 q^{7}+O(q^{10}) $ 120 * q + 12 * q^7	$ 120 q + 12 q^{7} - 36 q^{17} - 96 q^{21} - 24 q^{22} - 12 q^{26} + 96 q^{33} - 12 q^{41} + 72 q^{43} + 24 q^{47} + 24 q^{51} - 36 q^{53} - 84 q^{57} + 48 q^{61} + 24 q^{62} - 36 q^{63} - 24 q^{66} + 96 q^{67} + 12 q^{68} + 36 q^{73} + 12 q^{76} - 96 q^{78} + 144 q^{81} - 48 q^{82} - 24 q^{83} + 48 q^{86} - 72 q^{87} + 72 q^{91} - 72 q^{92} - 156 q^{93} - 120 q^{97} - 24 q^{98}+O(q^{100}) $ 120 * q + 12 * q^7 - 36 * q^17 - 96 * q^21 - 24 * q^22 - 12 * q^26 + 96 * q^33 - 12 * q^41 + 72 * q^43 + 24 * q^47 + 24 * q^51 - 36 * q^53 - 84 * q^57 + 48 * q^61 + 24 * q^62 - 36 * q^63 - 24 * q^66 + 96 * q^67 + 12 * q^68 + 36 * q^73 + 12 * q^76 - 96 * q^78 + 144 * q^81 - 48 * q^82 - 24 * q^83 + 48 * q^86 - 72 * q^87 + 72 * q^91 - 72 * q^92 - 156 * q^93 - 120 * q^97 - 24 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/950\mathbb{Z}\right)^\times$.

$n$	$77$	$401$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$e\left(\frac{17}{18}\right)$

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 $

$2$	0.573576	−	0.819152i	0.405580	−	0.579228i
$2$	0.573576	−	0.819152i	0.405580	−	0.579228i
$3$	0.0201525	−	0.230344i	0.0116350	−	0.132989i	−0.988155	−	0.153456i	$-0.950960\pi$
$3$	0.0201525	−	0.230344i	0.0116350	−	0.132989i	0.999791	+	0.0204668i	$0.00651525\pi$
$4$	−0.342020	−	0.939693i	−0.171010	−	0.469846i
$5$		0			0
$5$		0			0
$6$	−0.177128	−	0.148628i	−0.0723120	−	0.0606770i
$7$	−1.23887	−	4.62353i	−0.468249	−	1.74753i	−0.645887	−	0.763433i	$-0.723512\pi$
$7$	−1.23887	−	4.62353i	−0.468249	−	1.74753i	0.177638	−	0.984096i	$-0.443155\pi$
$8$	−0.965926	−	0.258819i	−0.341506	−	0.0915064i
$9$	2.90177	+	0.511661i	0.967257	+	0.170554i
$10$		0			0
$11$	0.299320	+	0.518438i	0.0902484	+	0.156315i	0.907616	−	0.419802i	$-0.137901\pi$
$11$	0.299320	+	0.518438i	0.0902484	+	0.156315i	−0.817367	+	0.576117i	$0.804567\pi$
$12$	−0.223345	+	0.0598451i	−0.0644741	+	0.0172758i
$13$	−4.00004	+	0.349958i	−1.10941	+	0.0970608i	−0.627099	−	0.778939i	$-0.715758\pi$
$13$	−4.00004	+	0.349958i	−1.10941	+	0.0970608i	−0.482311	+	0.876000i	$0.660202\pi$
$14$	−4.49796	−	1.63712i	−1.20213	−	0.437540i
$15$		0			0
$16$	−0.766044	+	0.642788i	−0.191511	+	0.160697i
$17$	−3.44552	−	2.41258i	−0.835661	−	0.585136i	0.0755188	−	0.997144i	$-0.475939\pi$
$17$	−3.44552	−	2.41258i	−0.835661	−	0.585136i	−0.911180	+	0.412008i	$0.864828\pi$
$18$	2.08352	−	2.08352i	0.491089	−	0.491089i
$19$	−4.23509	−	1.03152i	−0.971596	−	0.236647i
$19$	−4.23509	−	1.03152i	−0.971596	−	0.236647i
$20$		0			0
$21$	−1.08997	+	0.192191i	−0.237850	+	0.0419394i
$22$	0.596362	+	0.0521749i	0.127145	+	0.0111237i
$23$	3.98766	+	1.85948i	0.831485	+	0.387728i	0.791273	−	0.611463i	$-0.209419\pi$
$23$	3.98766	+	1.85948i	0.831485	+	0.387728i	0.0402123	+	0.999191i	$0.487197\pi$
$24$	−0.0790832	+	0.217279i	−0.0161428	+	0.0443519i
$25$		0			0
$26$	−2.00766	+	3.47737i	−0.393734	+	0.681967i
$27$	0.355871	−	1.32813i	0.0684874	−	0.255598i
$28$	−3.92098	+	2.74550i	−0.740995	+	0.518850i
$29$	1.07268	−	6.08348i	0.199192	−	1.12967i	−0.707129	−	0.707085i	$-0.750010\pi$
$29$	1.07268	−	6.08348i	0.199192	−	1.12967i	0.906321	−	0.422590i	$-0.138879\pi$
$30$		0			0
$31$	4.32894	+	2.49932i	0.777501	+	0.448890i	0.835544	−	0.549424i	$-0.185153\pi$
$31$	4.32894	+	2.49932i	0.777501	+	0.448890i	−0.0580429	+	0.998314i	$0.518486\pi$
$32$	0.0871557	+	0.996195i	0.0154071	+	0.176104i
$33$	0.125451	−	0.0584987i	0.0218382	−	0.0101833i
$34$	−3.95254	+	1.43861i	−0.677855	+	0.246719i
$35$		0			0
$36$	−0.511661	−	2.90177i	−0.0852768	−	0.483629i
$37$	2.05978	+	2.05978i	0.338626	+	0.338626i	0.855850	−	0.517224i	$-0.173035\pi$
$37$	2.05978	+	2.05978i	0.338626	+	0.338626i	−0.517224	+	0.855850i	$0.673035\pi$
$38$	−3.27412	+	2.87752i	−0.531132	+	0.466796i
$39$			0.928436i			0.148669i
$40$		0			0
$41$	−5.43198	−	6.47359i	−0.848333	−	1.01100i	−0.999746	−	0.0225337i	$-0.992827\pi$
$41$	−5.43198	−	6.47359i	−0.848333	−	1.01100i	0.151413	−	0.988471i	$-0.451618\pi$
$42$	−0.467746	+	1.00308i	−0.0721748	+	0.154779i
$43$	0.0474908	+	0.101844i	0.00724229	+	0.0155311i	0.909896	−	0.414837i	$-0.136161\pi$
$43$	0.0474908	+	0.101844i	0.00724229	+	0.0155311i	−0.902653	+	0.430368i	$0.858384\pi$
$44$	0.384799	−	0.458585i	0.0580106	−	0.0691343i
$45$		0			0
$46$	3.81042	−	2.19995i	0.561816	−	0.324365i
$47$	−2.59629	−	3.70788i	−0.378707	−	0.540850i	0.583874	−	0.811845i	$-0.301536\pi$
$47$	−2.59629	−	3.70788i	−0.378707	−	0.540850i	−0.962581	+	0.270994i	$0.912648\pi$
$48$	0.132624	+	0.189407i	0.0191427	+	0.0273386i
$49$	−13.7800	+	7.95590i	−1.96858	+	1.13656i
$50$		0			0
$51$	−0.625158	+	0.745035i	−0.0875397	+	0.104326i
$52$	1.69695	+	3.63911i	0.235324	+	0.504654i
$53$	−2.70861	+	5.80863i	−0.372056	+	0.797877i	0.627754	+	0.778411i	$0.283974\pi$
$53$	−2.70861	+	5.80863i	−0.372056	+	0.797877i	−0.999811	+	0.0194655i	$0.993804\pi$
$54$	−0.883820	−	1.05330i	−0.120273	−	0.143335i
$55$		0			0
$56$			4.78663i			0.639640i
$57$	−0.322952	+	0.954738i	−0.0427761	+	0.126458i
$58$	−4.36803	−	4.36803i	−0.573551	−	0.573551i
$59$	−0.921977	−	5.22879i	−0.120031	−	0.680731i	−0.984136	−	0.177418i	$-0.943226\pi$
$59$	−0.921977	−	5.22879i	−0.120031	−	0.680731i	0.864104	−	0.503313i	$-0.167886\pi$
$60$		0			0
$61$	−11.0985	+	4.03952i	−1.42102	+	0.517208i	−0.934343	−	0.356376i	$-0.884012\pi$
$61$	−11.0985	+	4.03952i	−1.42102	+	0.517208i	−0.486674	+	0.873584i	$0.661790\pi$
$62$	4.53030	−	2.11251i	0.575349	−	0.268289i
$63$	−1.22924	−	14.0503i	−0.154870	−	1.77017i
$64$	0.866025	+	0.500000i	0.108253	+	0.0625000i
$65$		0			0
$66$	0.0240363	−	0.136317i	0.00295867	−	0.0167794i
$67$	3.54544	−	2.48254i	0.433144	−	0.303291i	−0.336595	−	0.941650i	$-0.609275\pi$
$67$	3.54544	−	2.48254i	0.433144	−	0.303291i	0.769739	+	0.638359i	$0.220386\pi$
$68$	−1.08865	+	4.06288i	−0.132018	+	0.492697i
$69$	0.508680	−	0.881060i	0.0612379	−	0.106067i
$70$		0			0
$71$	0.892149	−	2.45116i	0.105879	−	0.290899i	−0.875428	−	0.483348i	$-0.839421\pi$
$71$	0.892149	−	2.45116i	0.105879	−	0.290899i	0.981307	+	0.192449i	$0.0616429\pi$
$72$	−2.67047	−	1.24526i	−0.314718	−	0.146755i
$73$	−5.65032	−	0.494339i	−0.661319	−	0.0578579i	−0.248445	−	0.968646i	$-0.579920\pi$
$73$	−5.65032	−	0.494339i	−0.661319	−	0.0578579i	−0.412874	+	0.910788i	$0.635475\pi$
$74$	2.86871	−	0.505832i	0.333481	−	0.0588018i
$75$		0			0
$76$	0.479172	+	4.33248i	0.0549648	+	0.496970i
$77$	2.02619	−	2.02619i	0.230906	−	0.230906i
$78$	0.760530	+	0.532529i	0.0861131	+	0.0602970i
$79$	10.9589	−	9.19562i	1.23297	−	1.03459i	0.234934	−	0.972011i	$-0.424512\pi$
$79$	10.9589	−	9.19562i	1.23297	−	1.03459i	0.998040	−	0.0625773i	$-0.0199320\pi$
$80$		0			0
$81$	8.00776	+	2.91459i	0.889751	+	0.323843i
$82$	−8.41851	+	0.736524i	−0.929669	+	0.0813355i
$83$	10.0994	−	2.70613i	1.10856	−	0.297037i	0.342312	−	0.939586i	$-0.388790\pi$
$83$	10.0994	−	2.70613i	1.10856	−	0.297037i	0.766244	+	0.642550i	$0.222123\pi$
$84$	0.553391	+	0.958501i	0.0603799	+	0.104581i
$85$		0			0
$86$	0.110666	+	0.0195134i	0.0119334	+	0.00210418i
$87$	−1.37968	−	0.369683i	−0.147917	−	0.0396342i
$88$	−0.154939	−	0.578242i	−0.0165166	−	0.0616408i
$89$	−0.184391	−	0.154722i	−0.0195454	−	0.0164005i	0.632963	−	0.774182i	$-0.281839\pi$
$89$	−0.184391	−	0.154722i	−0.0195454	−	0.0164005i	−0.652508	+	0.757782i	$0.726283\pi$
$90$		0			0
$91$	6.57357	+	18.0607i	0.689097	+	1.89328i
$92$	0.383476	−	4.38316i	0.0399802	−	0.456976i
$93$	0.662941	−	0.946778i	0.0687438	−	0.0981763i
$94$	−4.52649			−0.466872
$95$		0			0
$96$	0.231224			0.0235992
$97$	7.30298	−	10.4297i	0.741505	−	1.05898i	−0.254268	−	0.967134i	$-0.581835\pi$
$97$	7.30298	−	10.4297i	0.741505	−	1.05898i	0.995773	−	0.0918452i	$-0.0292765\pi$
$98$	−1.38681	+	15.8513i	−0.140089	+	1.60122i
$99$	0.603294	+	1.65754i	0.0606334	+	0.166589i
$100$		0			0
$101$	−7.46146	−	6.26091i	−0.742443	−	0.622984i	0.191050	−	0.981580i	$-0.438811\pi$
$101$	−7.46146	−	6.26091i	−0.742443	−	0.622984i	−0.933493	+	0.358597i	$0.883255\pi$
$102$	0.251721	+	0.939434i	0.0249241	+	0.0930179i
$103$	14.8802	+	3.98714i	1.46619	+	0.392865i	0.901623	−	0.432522i	$-0.142376\pi$
$103$	14.8802	+	3.98714i	1.46619	+	0.392865i	0.564568	+	0.825387i	$0.309043\pi$
$104$	3.95431	+	0.697252i	0.387752	+	0.0683712i
$105$		0			0
$106$	3.20456	+	5.55046i	0.311254	+	0.539108i
$107$	−4.64140	+	1.24366i	−0.448701	+	0.120229i	−0.476092	−	0.879396i	$-0.657947\pi$
$107$	−4.64140	+	1.24366i	−0.448701	+	0.120229i	0.0273903	+	0.999625i	$0.491280\pi$
$108$	−1.36975	+	0.119837i	−0.131804	+	0.0115314i
$109$	10.1368	+	3.68949i	0.970929	+	0.353389i	0.778307	−	0.627884i	$-0.216079\pi$
$109$	10.1368	+	3.68949i	0.970929	+	0.353389i	0.192622	+	0.981273i	$0.438301\pi$
$110$		0			0
$111$	0.515967	−	0.432948i	0.0489734	−	0.0410936i
$112$	3.92098	+	2.74550i	0.370497	+	0.259425i
$113$	12.1135	−	12.1135i	1.13954	−	1.13954i	0.151009	−	0.988532i	$-0.451748\pi$
$113$	12.1135	−	12.1135i	1.13954	−	1.13954i	0.988532	−	0.151009i	$-0.0482523\pi$
$114$	0.596838	+	0.812162i	0.0558990	+	0.0760660i
$115$		0			0
$116$	−6.08348	+	1.07268i	−0.564837	+	0.0995961i
$117$	−11.7862	−	1.03116i	−1.08964	−	0.0953311i
$118$	−4.81200	−	2.24387i	−0.442981	−	0.206565i
$119$	−6.88607	+	18.9193i	−0.631245	+	1.73433i
$120$		0			0
$121$	5.32081	−	9.21592i	0.483710	−	0.837811i
$122$	−3.05685	+	11.4083i	−0.276754	+	1.03286i
$123$	−1.60062	+	1.12077i	−0.144323	+	0.101056i
$124$	0.868003	−	4.92269i	0.0779490	−	0.442071i
$125$		0			0
$126$	−12.2144	−	7.05199i	−1.08814	−	0.628241i
$127$	1.78877	+	20.4457i	0.158728	+	1.81426i	0.491086	+	0.871111i	$0.336600\pi$
$127$	1.78877	+	20.4457i	0.158728	+	1.81426i	−0.332359	+	0.943153i	$0.607845\pi$
$128$	0.906308	−	0.422618i	0.0801070	−	0.0373545i
$129$	0.0244163	−	0.00888680i	0.00214973	−	0.000782439i
$130$		0			0
$131$	0.0837874	+	0.475182i	0.00732054	+	0.0415169i	0.988249	−	0.152851i	$-0.0488455\pi$
$131$	0.0837874	+	0.475182i	0.00732054	+	0.0415169i	−0.980929	+	0.194368i	$0.937734\pi$
$132$	−0.0978776	−	0.0978776i	−0.00851915	−	0.00851915i
$133$	0.477455	+	20.8590i	0.0414006	+	1.80870i
$134$		−	4.32818i		−	0.373898i
$135$		0			0
$136$	2.70370	+	3.22214i	0.231840	+	0.276296i
$137$	−2.02288	+	4.33808i	−0.172826	+	0.370627i	−0.973573	−	0.228376i	$-0.926658\pi$
$137$	−2.02288	+	4.33808i	−0.172826	+	0.370627i	0.800747	+	0.599003i	$0.204436\pi$
$138$	−0.429955	−	0.922042i	−0.0366002	−	0.0784894i
$139$	5.63689	−	6.71778i	0.478114	−	0.569795i	−0.472039	−	0.881578i	$-0.656482\pi$
$139$	5.63689	−	6.71778i	0.478114	−	0.569795i	0.950153	+	0.311783i	$0.100926\pi$
$140$		0			0
$141$	−0.906409	+	0.523316i	−0.0763334	+	0.0440711i
$142$	−1.49616	−	2.13673i	−0.125555	−	0.179311i
$143$	−1.37872	−	1.96902i	−0.115295	−	0.164658i
$144$	−2.55177	+	1.47327i	−0.212648	+	0.122772i
$145$		0			0
$146$	−3.64583	+	4.34493i	−0.301731	+	0.359589i
$147$	1.55489	+	3.33448i	0.128245	+	0.275023i
$148$	1.23107	−	2.64005i	0.101194	−	0.217011i
$149$	5.69021	+	6.78132i	0.466160	+	0.555548i	0.946989	−	0.321267i	$-0.104109\pi$
$149$	5.69021	+	6.78132i	0.466160	+	0.555548i	−0.480829	+	0.876814i	$0.659664\pi$
$150$		0			0
$151$		−	7.83363i		−	0.637491i	−0.947840	−	0.318746i	$-0.896738\pi$
$151$		−	7.83363i		−	0.637491i	0.947840	−	0.318746i	$-0.103262\pi$
$152$	3.82380	+	2.09249i	0.310151	+	0.169724i
$153$	−8.76369	−	8.76369i	−0.708502	−	0.708502i
$154$	−0.497583	−	2.82194i	−0.0400964	−	0.227398i
$155$		0			0
$156$	0.872444	−	0.317544i	0.0698515	−	0.0254239i
$157$	−10.7103	+	4.99430i	−0.854776	+	0.398588i	−0.800065	−	0.599914i	$-0.795202\pi$
$157$	−10.7103	+	4.99430i	−0.854776	+	0.398588i	−0.0547109	+	0.998502i	$0.517424\pi$
$158$	−1.24684	−	14.2514i	−0.0991930	−	1.13378i
$159$	1.28340	+	0.740970i	0.101780	+	0.0587627i
$160$		0			0
$161$	3.65715	−	20.7407i	0.288224	−	1.63460i
$162$	6.98055	−	4.88783i	0.548444	−	0.384025i
$163$	3.11846	−	11.6382i	0.244256	−	0.911577i	−0.729500	−	0.683981i	$-0.760247\pi$
$163$	3.11846	−	11.6382i	0.244256	−	0.911577i	0.973756	−	0.227595i	$-0.0730864\pi$
$164$	−4.22533	+	7.31849i	−0.329943	+	0.571478i
$165$		0			0
$166$	3.57606	−	9.82514i	0.277556	−	0.762578i
$167$	13.5331	+	6.31059i	1.04722	+	0.488328i	0.868561	−	0.495582i	$-0.165045\pi$
$167$	13.5331	+	6.31059i	1.04722	+	0.488328i	0.178662	+	0.983910i	$0.442823\pi$
$168$	1.10257	+	0.0964624i	0.0850651	+	0.00744223i
$169$	3.07532	−	0.542261i	0.236563	−	0.0417124i
$170$		0			0
$171$	−11.7615	−	5.16017i	−0.899422	−	0.394608i
$172$	0.0794596	−	0.0794596i	0.00605874	−	0.00605874i
$173$	15.9551	+	11.1719i	1.21304	+	0.849383i	0.992044	−	0.125891i	$-0.0401789\pi$
$173$	15.9551	+	11.1719i	1.21304	+	0.849383i	0.221000	+	0.975274i	$0.429068\pi$
$174$	−1.09418	+	0.918123i	−0.0829493	+	0.0696027i
$175$		0			0
$176$	−0.562538	−	0.204747i	−0.0424029	−	0.0154334i
$177$	−1.22300	+	0.106999i	−0.0919263	+	0.00804251i
$178$	−0.232503	+	0.0622991i	−0.0174269	+	0.00466951i
$179$	4.87857	+	8.44994i	0.364642	+	0.631578i	0.988719	−	0.149785i	$-0.0478581\pi$
$179$	4.87857	+	8.44994i	0.364642	+	0.631578i	−0.624077	+	0.781363i	$0.714525\pi$
$180$		0			0
$181$	13.2188	+	2.33083i	0.982544	+	0.173249i	0.641771	−	0.766897i	$-0.278200\pi$
$181$	13.2188	+	2.33083i	0.982544	+	0.173249i	0.340773	+	0.940146i	$0.389311\pi$
$182$	18.5649	+	4.97446i	1.37612	+	0.368731i
$183$	0.706817	+	2.63788i	0.0522494	+	0.194997i
$184$	−3.37052	−	2.82820i	−0.248478	−	0.208498i
$185$		0			0
$186$	−0.395308	−	1.08610i	−0.0289854	−	0.0796366i
$187$	0.219458	−	2.50842i	0.0160484	−	0.183434i
$188$	−2.59629	+	3.70788i	−0.189354	+	0.270425i
$189$	−6.58152			−0.478735
$190$		0			0
$191$	6.39643			0.462830			0.231415	−	0.972855i	$-0.425665\pi$
$191$	6.39643			0.462830			0.231415	+	0.972855i	$0.425665\pi$
$192$	0.132624	−	0.189407i	0.00957135	−	0.0136693i
$193$	0.504830	−	5.77023i	0.0363384	−	0.415350i	−0.956138	−	0.292916i	$-0.905374\pi$
$193$	0.504830	−	5.77023i	0.0363384	−	0.415350i	0.992477	−	0.122434i	$-0.0390701\pi$
$194$	−4.35472	−	11.9645i	−0.312651	−	0.859001i
$195$		0			0
$196$	12.1892	+	10.2279i	0.870654	+	0.730565i
$197$	0.151671	+	0.566044i	0.0108061	+	0.0403290i	0.971118	−	0.238598i	$-0.0766879\pi$
$197$	0.151671	+	0.566044i	0.0108061	+	0.0403290i	−0.960312	+	0.278927i	$0.910021\pi$
$198$	1.70381	+	0.456535i	0.121085	+	0.0324445i
$199$	26.0886	+	4.60012i	1.84937	+	0.326094i	0.984429	−	0.175782i	$-0.0562453\pi$
$199$	26.0886	+	4.60012i	1.84937	+	0.326094i	0.864940	+	0.501875i	$0.167356\pi$
$200$		0			0
$201$	−0.500389	−	0.866699i	−0.0352947	−	0.0611322i
$202$	−9.40835	+	2.52096i	−0.661969	+	0.177374i
$203$	−29.4561	+	2.57707i	−2.06741	+	0.180875i
$204$	0.913921	+	0.332640i	0.0639872	+	0.0232894i
$205$		0			0
$206$	11.8010	−	9.90223i	0.822216	−	0.689921i
$207$	10.6199	+	7.43611i	0.738131	+	0.516845i
$208$	2.83926	−	2.83926i	0.196867	−	0.196867i
$209$	−0.732867	−	2.50438i	−0.0506935	−	0.173232i
$210$		0			0
$211$	−1.83562	+	0.323670i	−0.126370	+	0.0222824i	−0.236475	−	0.971638i	$-0.575992\pi$
$211$	−1.83562	+	0.323670i	−0.126370	+	0.0222824i	0.110106	+	0.993920i	$0.464881\pi$
$212$	6.38473	+	0.558591i	0.438505	+	0.0383642i
$213$	−0.546631	−	0.254898i	−0.0374545	−	0.0174653i
$214$	−1.64345	+	4.51535i	−0.112344	+	0.308663i
$215$		0			0
$216$	−0.687490	+	1.19077i	−0.0467778	+	0.0810215i
$217$	6.19266	−	23.1113i	0.420385	−	1.56890i
$218$	8.83648	−	6.18737i	0.598482	−	0.419061i
$219$	−0.227736	+	1.29155i	−0.0153889	+	0.0872751i
$220$		0			0
$221$	14.6265	+	8.44462i	0.983885	+	0.568046i
$222$	−0.0587035	−	0.670984i	−0.00393992	−	0.0450335i
$223$	6.71804	−	3.13268i	0.449874	−	0.209779i	−0.184458	−	0.982840i	$-0.559053\pi$
$223$	6.71804	−	3.13268i	0.449874	−	0.209779i	0.634332	+	0.773061i	$0.281275\pi$
$224$	4.49796	−	1.63712i	0.300533	−	0.109385i
$225$		0			0
$226$	−2.97478	−	16.8708i	−0.197879	−	1.12223i
$227$	−9.49571	−	9.49571i	−0.630253	−	0.630253i	0.317879	−	0.948131i	$-0.397029\pi$
$227$	−9.49571	−	9.49571i	−0.630253	−	0.630253i	−0.948131	+	0.317879i	$0.897029\pi$
$228$	1.00762	−	0.0230640i	0.0667310	−	0.00152745i
$229$		−	15.2402i		−	1.00710i	−0.863966	−	0.503551i	$-0.832027\pi$
$229$		−	15.2402i		−	1.00710i	0.863966	−	0.503551i	$-0.167973\pi$
$230$		0			0
$231$	−0.425888	−	0.507554i	−0.0280214	−	0.0333946i
$232$	−2.61065	+	5.59856i	−0.171398	+	0.367564i
$233$	5.65600	+	12.1293i	0.370537	+	0.794620i	0.999847	+	0.0174654i	$0.00555969\pi$
$233$	5.65600	+	12.1293i	0.370537	+	0.794620i	−0.629310	+	0.777154i	$0.716663\pi$
$234$	−7.60499	+	9.06328i	−0.497154	+	0.592485i
$235$		0			0
$236$	−4.59812	+	2.65473i	−0.299312	+	0.172808i
$237$	−1.89731	−	2.70963i	−0.123243	−	0.176010i
$238$	11.5481	+	16.4924i	0.748554	+	1.06905i
$239$	1.39169	−	0.803494i	0.0900210	−	0.0519737i	−0.454314	−	0.890842i	$-0.650115\pi$
$239$	1.39169	−	0.803494i	0.0900210	−	0.0519737i	0.544335	+	0.838868i	$0.316782\pi$
$240$		0			0
$241$	−1.81684	+	2.16522i	−0.117033	+	0.139474i	−0.821380	−	0.570381i	$-0.806795\pi$
$241$	−1.81684	+	2.16522i	−0.117033	+	0.139474i	0.704347	+	0.709856i	$0.251240\pi$
$242$	−4.49735	−	9.64459i	−0.289100	−	0.619978i
$243$	2.57601	−	5.52427i	0.165251	−	0.354382i
$244$	7.59182	+	9.04758i	0.486016	+	0.579212i
$245$		0			0
$246$			1.95399i			0.124582i
$247$	17.3015	+	2.64402i	1.10087	+	0.168235i
$248$	−3.53457	−	3.53457i	−0.224445	−	0.224445i
$249$	−0.419812	−	2.38087i	−0.0266045	−	0.150882i
$250$		0			0
$251$	−21.9511	+	7.98956i	−1.38554	+	0.504297i	−0.923854	−	0.382745i	$-0.874979\pi$
$251$	−21.9511	+	7.98956i	−1.38554	+	0.504297i	−0.461689	+	0.887042i	$0.652756\pi$
$252$	−12.7825	+	5.96060i	−0.805224	+	0.375482i
$253$	0.229564	+	2.62393i	0.0144326	+	0.164965i
$254$	17.7741	+	10.2619i	1.11525	+	0.643889i
$255$		0			0
$256$	0.173648	−	0.984808i	0.0108530	−	0.0615505i
$257$	−0.0264397	+	0.0185133i	−0.00164926	+	0.00115483i	−0.574401	−	0.818574i	$-0.694765\pi$
$257$	−0.0264397	+	0.0185133i	−0.00164926	+	0.00115483i	0.572752	+	0.819729i	$0.305876\pi$
$258$	0.00672497	−	0.0250979i	0.000418678	−	0.00156253i
$259$	6.97165	−	12.0753i	0.433197	−	0.750320i
$260$		0			0
$261$	6.22536	−	17.1040i	0.385340	−	1.05871i
$262$	0.437305	+	0.203919i	0.0270168	+	0.0125981i
$263$	−26.3765	−	2.30764i	−1.62644	−	0.142295i	−0.762882	−	0.646538i	$-0.776216\pi$
$263$	−26.3765	−	2.30764i	−1.62644	−	0.142295i	−0.863562	+	0.504242i	$0.831772\pi$
$264$	−0.136317	+	0.0240363i	−0.00838972	+	0.00147933i
$265$		0			0
$266$	17.3605	+	11.5731i	1.06444	+	0.709592i
$267$	−0.0393553	+	0.0393553i	−0.00240850	+	0.00240850i
$268$	−3.54544	−	2.48254i	−0.216572	−	0.151645i
$269$	−8.17614	+	6.86060i	−0.498508	+	0.418298i	−0.857064	−	0.515210i	$-0.827714\pi$
$269$	−8.17614	+	6.86060i	−0.498508	+	0.418298i	0.358556	+	0.933508i	$0.383269\pi$
$270$		0			0
$271$	−2.24462	−	0.816973i	−0.136351	−	0.0496276i	0.272943	−	0.962030i	$-0.412003\pi$
$271$	−2.24462	−	0.816973i	−0.136351	−	0.0496276i	−0.409294	+	0.912402i	$0.634225\pi$
$272$	4.19020	−	0.366595i	0.254068	−	0.0222281i
$273$	4.29265	−	1.15021i	0.259803	−	0.0696140i
$274$	2.39327	+	4.14526i	0.144583	+	0.250425i
$275$		0			0
$276$	−1.00190	−	0.176663i	−0.0603076	−	0.0106339i
$277$	−17.7898	−	4.76677i	−1.06889	−	0.286407i	−0.318851	−	0.947805i	$-0.603297\pi$
$277$	−17.7898	−	4.76677i	−1.06889	−	0.286407i	−0.750036	+	0.661397i	$0.769964\pi$
$278$	−2.26970	−	8.47063i	−0.136127	−	0.508034i
$279$	11.2828	+	9.46739i	0.675484	+	0.566798i
$280$		0			0
$281$	−0.760406	−	2.08920i	−0.0453620	−	0.124631i	0.914943	−	0.403583i	$-0.132235\pi$
$281$	−0.760406	−	2.08920i	−0.0453620	−	0.124631i	−0.960305	+	0.278952i	$0.910013\pi$
$282$	−0.0912199	+	1.04265i	−0.00543207	+	0.0620888i
$283$	3.04018	−	4.34183i	0.180720	−	0.258095i	−0.718563	−	0.695462i	$-0.755200\pi$
$283$	3.04018	−	4.34183i	0.180720	−	0.258095i	0.899283	+	0.437367i	$0.144089\pi$
$284$	−2.60847			−0.154784
$285$		0			0
$286$	−2.40373			−0.142135
$287$	−23.2013	+	33.1349i	−1.36953	+	1.95589i
$288$	−0.256807	+	2.93532i	−0.0151325	+	0.172966i
$289$	0.236730	+	0.650410i	0.0139253	+	0.0382594i
$290$		0			0
$291$	−2.25525	−	1.89238i	−0.132205	−	0.110933i
$292$	1.46800	+	5.47863i	0.0859079	+	0.320613i
$293$	−24.1149	−	6.46156i	−1.40881	−	0.377489i	−0.527308	−	0.849674i	$-0.676798\pi$
$293$	−24.1149	−	6.46156i	−1.40881	−	0.377489i	−0.881499	+	0.472186i	$0.843465\pi$
$294$	3.62329	+	0.638884i	0.211315	+	0.0372605i
$295$		0			0
$296$	−1.45648	−	2.52271i	−0.0846565	−	0.146629i
$297$	0.795071	−	0.213039i	0.0461347	−	0.0123618i
$298$	8.81870	−	0.771537i	0.510854	−	0.0446939i
$299$	−16.6015	−	6.04246i	−0.960091	−	0.349445i
$300$		0			0
$301$	0.412046	−	0.345747i	0.0237499	−	0.0199285i
$302$	−6.41693	−	4.49318i	−0.369253	−	0.258554i
$303$	−1.59253	+	1.59253i	−0.0914884	+	0.0914884i
$304$	3.90731	−	1.93207i	0.224100	−	0.110812i
$305$		0			0
$306$	−12.2054	+	2.15215i	−0.697739	+	0.123030i
$307$	13.6350	+	1.19291i	0.778190	+	0.0680828i	0.469328	−	0.883024i	$-0.344496\pi$
$307$	13.6350	+	1.19291i	0.778190	+	0.0680828i	0.308862	+	0.951107i	$0.400052\pi$
$308$	−2.59700	−	1.21100i	−0.147978	−	0.0690031i
$309$	1.21829	−	3.34721i	0.0693059	−	0.190416i
$310$		0			0
$311$	−9.25408	+	16.0285i	−0.524751	+	0.908895i	0.474834	+	0.880075i	$0.342508\pi$
$311$	−9.25408	+	16.0285i	−0.524751	+	0.908895i	−0.999585	+	0.0288194i	$0.990825\pi$
$312$	0.240297	−	0.896800i	0.0136041	−	0.0507713i
$313$	−4.37753	+	3.06518i	−0.247433	+	0.173254i	−0.690713	−	0.723129i	$-0.742703\pi$
$313$	−4.37753	+	3.06518i	−0.247433	+	0.173254i	0.443281	+	0.896383i	$0.353814\pi$
$314$	−2.05209	+	11.6380i	−0.115806	+	0.656769i
$315$		0			0
$316$	−12.3892	−	7.15293i	−0.696949	−	0.402383i
$317$	0.0257602	+	0.294441i	0.00144684	+	0.0165374i	0.996884	−	0.0788840i	$-0.0251357\pi$
$317$	0.0257602	+	0.294441i	0.00144684	+	0.0165374i	−0.995437	+	0.0954215i	$0.969580\pi$
$318$	1.34309	−	0.626295i	0.0753169	−	0.0351209i
$319$	3.47498	−	1.26479i	0.194562	−	0.0708147i
$320$		0			0
$321$	0.192934	+	1.09418i	0.0107685	+	0.0610712i
$322$	−14.8921	−	14.8921i	−0.829907	−	0.829907i
$323$	12.1035	+	13.7716i	0.673454	+	0.766273i
$324$		−	8.52168i		−	0.473427i
$325$		0			0
$326$	−7.74481	−	9.22991i	−0.428945	−	0.511197i
$327$	1.05413	−	2.26059i	0.0582937	−	0.125011i
$328$	3.57141	+	7.65891i	0.197198	+	0.422892i
$329$	−13.9270	+	16.5976i	−0.767822	+	0.915055i
$330$		0			0
$331$	−0.00538229	+	0.00310747i	−0.000295838	+	0.000170802i	−0.500148	−	0.865940i	$-0.666721\pi$
$331$	−0.00538229	+	0.00310747i	−0.000295838	+	0.000170802i	0.499852	+	0.866111i	$0.333388\pi$
$332$	−5.99714	−	8.56480i	−0.329136	−	0.470054i
$333$	4.92310	+	7.03092i	0.269784	+	0.385292i
$334$	12.9316	−	7.46607i	0.707586	−	0.408525i
$335$		0			0
$336$	0.711426	−	0.847844i	0.0388114	−	0.0462537i
$337$	−8.58022	−	18.4003i	−0.467394	−	1.00233i	−0.988831	−	0.149040i	$-0.952382\pi$
$337$	−8.58022	−	18.4003i	−0.467394	−	1.00233i	0.521437	−	0.853290i	$-0.325396\pi$
$338$	1.31973	−	2.83018i	0.0717841	−	0.153941i
$339$	−2.54615	−	3.03438i	−0.138288	−	0.164805i
$340$		0			0
$341$			2.99238i			0.162047i
$342$	−10.9731	+	6.67468i	−0.593355	+	0.360925i
$343$	30.1634	+	30.1634i	1.62867	+	1.62867i
$344$	−0.0195134	−	0.110666i	−0.00105209	−	0.00596670i
$345$		0			0
$346$	18.3029	−	6.66173i	0.983973	−	0.358137i
$347$	23.5457	−	10.9795i	1.26400	−	0.589413i	0.329091	−	0.944298i	$-0.393258\pi$
$347$	23.5457	−	10.9795i	1.26400	−	0.589413i	0.934910	+	0.354885i	$0.115480\pi$
$348$	0.124489	+	1.42291i	0.00667328	+	0.0762760i
$349$	13.4502	+	7.76546i	0.719971	+	0.415675i	0.814742	−	0.579824i	$-0.196879\pi$
$349$	13.4502	+	7.76546i	0.719971	+	0.415675i	−0.0947710	+	0.995499i	$0.530212\pi$
$350$		0			0
$351$	−0.958708	+	5.43710i	−0.0511720	+	0.290211i
$352$	−0.490377	+	0.343366i	−0.0261372	+	0.0183015i
$353$	6.52730	−	24.3602i	0.347413	−	1.29656i	−0.542355	−	0.840150i	$-0.682467\pi$
$353$	6.52730	−	24.3602i	0.347413	−	1.29656i	0.889768	−	0.456414i	$-0.150866\pi$
$354$	−0.613836	+	1.06319i	−0.0326250	+	0.0565082i
$355$		0			0
$356$	−0.0823260	+	0.226189i	−0.00436327	+	0.0119880i
$357$	4.21918	+	1.96744i	0.223303	+	0.104128i
$358$	9.72002	+	0.850392i	0.513719	+	0.0449446i
$359$	−23.6492	+	4.17000i	−1.24816	+	0.220084i	−0.758409	−	0.651779i	$-0.774023\pi$
$359$	−23.6492	+	4.17000i	−1.24816	+	0.220084i	−0.489750	+	0.871863i	$0.662912\pi$
$360$		0			0
$361$	16.8719	+	8.73717i	0.887996	+	0.459851i
$362$	9.49128	−	9.49128i	0.498851	−	0.498851i
$363$	−2.01560	−	1.41134i	−0.105792	−	0.0740762i
$364$	14.7232	−	12.3543i	0.771707	−	0.647539i
$365$		0			0
$366$	2.56623	+	0.934033i	0.134139	+	0.0488227i
$367$	17.2937	−	1.51300i	0.902725	−	0.0789782i	0.373666	−	0.927563i	$-0.378101\pi$
$367$	17.2937	−	1.51300i	0.902725	−	0.0789782i	0.529059	+	0.848585i	$0.322545\pi$
$368$	−4.24998	+	1.13878i	−0.221545	+	0.0593629i
$369$	−12.4501	−	21.5642i	−0.648126	−	1.12259i
$370$		0			0
$371$	30.2120	+	5.32719i	1.56853	+	0.276574i
$372$	−1.11642	−	0.299144i	−0.0578836	−	0.0155099i
$373$	−1.56812	−	5.85232i	−0.0811944	−	0.303022i	0.913372	−	0.407126i	$-0.133469\pi$
$373$	−1.56812	−	5.85232i	−0.0811944	−	0.303022i	−0.994566	+	0.104104i	$0.966802\pi$
$374$	−1.92890	−	1.61854i	−0.0997412	−	0.0836928i
$375$		0			0
$376$	1.54815	+	4.25351i	0.0798398	+	0.219358i
$377$	−2.16181	+	24.7096i	−0.111339	+	1.27261i
$378$	−3.77500	+	5.39126i	−0.194165	+	0.277297i
$379$	−23.0274			−1.18284			−0.591419	−	0.806364i	$-0.701432\pi$
$379$	−23.0274			−1.18284			−0.591419	+	0.806364i	$0.701432\pi$
$380$		0			0
$381$	4.74559			0.243124
$382$	3.66884	−	5.23965i	0.187714	−	0.268084i
$383$	1.08093	−	12.3551i	0.0552329	−	0.631315i	−0.917246	−	0.398322i	$-0.869593\pi$
$383$	1.08093	−	12.3551i	0.0552329	−	0.631315i	0.972478	−	0.232993i	$-0.0748519\pi$
$384$	−0.0790832	−	0.217279i	−0.00403570	−	0.0110880i
$385$		0			0
$386$	−4.43714	−	3.72320i	−0.225844	−	0.189506i
$387$	0.0856978	+	0.319828i	0.00435626	+	0.0162578i
$388$	−12.2985	−	3.29538i	−0.624362	−	0.167297i
$389$	−24.3101	−	4.28652i	−1.23257	−	0.217335i	−0.480841	−	0.876808i	$-0.659669\pi$
$389$	−24.3101	−	4.28652i	−1.23257	−	0.217335i	−0.751729	+	0.659472i	$0.770780\pi$
$390$		0			0
$391$	−9.25344	−	16.0274i	−0.467966	−	0.810542i
$392$	15.3696	−	4.11828i	0.776283	−	0.208005i
$393$	0.111144	−	0.00972382i	0.00560646	−	0.000490502i
$394$	0.550671	+	0.200428i	0.0277424	+	0.0100974i
$395$		0			0
$396$	1.35124	−	1.13382i	0.0679022	−	0.0569767i
$397$	1.13384	+	0.793926i	0.0569060	+	0.0398460i	0.601683	−	0.798735i	$-0.294497\pi$
$397$	1.13384	+	0.793926i	0.0569060	+	0.0398460i	−0.544777	+	0.838581i	$0.683386\pi$
$398$	18.7320	−	18.7320i	0.938949	−	0.938949i
$399$	4.81436	+	0.310381i	0.241019	+	0.0155385i
$400$		0			0
$401$	−2.87396	+	0.506756i	−0.143519	+	0.0253062i	−0.244946	−	0.969537i	$-0.578770\pi$
$401$	−2.87396	+	0.506756i	−0.143519	+	0.0253062i	0.101427	+	0.994843i	$0.467659\pi$
$402$	−0.996970	−	0.0872235i	−0.0497243	−	0.00435031i
$403$	−18.1906	−	8.48241i	−0.906137	−	0.422539i
$404$	−3.33136	+	9.15284i	−0.165741	+	0.455371i
$405$		0			0
$406$	−14.7843	+	25.6072i	−0.733732	+	1.27086i
$407$	−0.451334	+	1.68440i	−0.0223718	+	0.0834927i
$408$	0.796686	−	0.557845i	0.0394418	−	0.0276175i
$409$	−0.561877	+	3.18656i	−0.0277830	+	0.157565i	−0.995543	−	0.0943090i	$-0.969936\pi$
$409$	−0.561877	+	3.18656i	−0.0277830	+	0.157565i	0.967760	+	0.251874i	$0.0810470\pi$
$410$		0			0
$411$	0.958483	+	0.553381i	0.0472785	+	0.0272962i
$412$	−1.34265	−	15.3465i	−0.0661474	−	0.756068i
$413$	−23.0333	+	10.7406i	−1.13339	+	0.528510i
$414$	12.1826	−	4.43411i	0.598742	−	0.217924i
$415$		0			0
$416$	−0.697252	−	3.95431i	−0.0341856	−	0.193876i
$417$	−1.43380	−	1.43380i	−0.0702136	−	0.0702136i
$418$	−2.47183	−	0.836126i	−0.120901	−	0.0408963i
$419$		−	7.65112i		−	0.373782i	−0.982381	−	0.186891i	$-0.940159\pi$
$419$		−	7.65112i		−	0.373782i	0.982381	−	0.186891i	$-0.0598410\pi$
$420$		0			0
$421$	9.03107	+	10.7628i	0.440147	+	0.524547i	0.939821	−	0.341666i	$-0.110991\pi$
$421$	9.03107	+	10.7628i	0.440147	+	0.524547i	−0.499674	+	0.866214i	$0.666547\pi$
$422$	−0.787736	+	1.68930i	−0.0383464	+	0.0822341i
$423$	−5.63665	−	12.0878i	−0.274063	−	0.587731i
$424$	4.11970	−	4.90967i	0.200070	−	0.238435i
$425$		0			0
$426$	−0.522335	+	0.301570i	−0.0253072	+	0.0146111i
$427$	32.4264	+	46.3098i	1.56923	+	2.24109i
$428$	2.75611	+	3.93613i	0.133222	+	0.190260i
$429$	−0.481336	+	0.277900i	−0.0232391	+	0.0134171i
$430$		0			0
$431$	0.638750	−	0.761232i	0.0307675	−	0.0366673i	−0.750441	−	0.660937i	$-0.770159\pi$
$431$	0.638750	−	0.761232i	0.0307675	−	0.0366673i	0.781209	+	0.624270i	$0.214603\pi$
$432$	0.581092	+	1.24615i	0.0279578	+	0.0599557i
$433$	0.270008	−	0.579035i	0.0129758	−	0.0278266i	−0.899713	−	0.436482i	$-0.856224\pi$
$433$	0.270008	−	0.579035i	0.0129758	−	0.0278266i	0.912689	+	0.408655i	$0.134002\pi$
$434$	−15.3797	−	18.3288i	−0.738250	−	0.879812i
$435$		0			0
$436$		−	10.7873i		−	0.516620i
$437$	−14.9700	−	11.9884i	−0.716113	−	0.573483i
$438$	0.927354	+	0.927354i	0.0443107	+	0.0443107i
$439$	−5.17808	−	29.3663i	−0.247136	−	1.40158i	−0.815479	−	0.578787i	$-0.803526\pi$
$439$	−5.17808	−	29.3663i	−0.247136	−	1.40158i	0.568343	−	0.822792i	$-0.307585\pi$
$440$		0			0
$441$	−44.0572	+	16.0355i	−2.09796	+	0.763596i
$442$	15.3068	−	7.13770i	0.728072	−	0.339506i
$443$	1.97868	+	22.6164i	0.0940098	+	1.07454i	0.885901	+	0.463874i	$0.153541\pi$
$443$	1.97868	+	22.6164i	0.0940098	+	1.07454i	−0.791891	+	0.610662i	$0.790903\pi$
$444$	−0.583309	−	0.336774i	−0.0276826	−	0.0159826i
$445$		0			0
$446$	1.28717	−	7.29993i	0.0609495	−	0.345662i
$447$	1.67671	−	1.17404i	0.0793056	−	0.0555304i
$448$	1.23887	−	4.62353i	0.0585311	−	0.218441i
$449$	−7.86562	+	13.6237i	−0.371202	+	0.642940i	−0.989751	−	0.142806i	$-0.954387\pi$
$449$	−7.86562	+	13.6237i	−0.371202	+	0.642940i	0.618549	+	0.785746i	$0.287721\pi$
$450$		0			0
$451$	1.73025	−	4.75382i	0.0814742	−	0.223849i
$452$	−15.5260	−	7.23990i	−0.730282	−	0.340536i
$453$	−1.80443	−	0.157867i	−0.0847794	−	0.00741723i
$454$	−13.2249	+	2.33192i	−0.620678	+	0.109442i
$455$		0			0
$456$	0.559052	−	0.838620i	0.0261800	−	0.0392720i
$457$	−1.54830	+	1.54830i	−0.0724266	+	0.0724266i	−0.742392	−	0.669966i	$-0.766309\pi$
$457$	−1.54830	+	1.54830i	−0.0724266	+	0.0724266i	0.669966	+	0.742392i	$0.266309\pi$
$458$	−12.4840	−	8.74143i	−0.583341	−	0.408460i
$459$	−4.43038	+	3.71753i	−0.206792	+	0.173519i
$460$		0			0
$461$	−10.8534	−	3.95030i	−0.505492	−	0.183984i	0.0766708	−	0.997056i	$-0.475571\pi$
$461$	−10.8534	−	3.95030i	−0.505492	−	0.183984i	−0.582162	+	0.813073i	$0.697793\pi$
$462$	−0.660043	+	0.0577463i	−0.0307080	+	0.00268660i
$463$	−23.7104	+	6.35320i	−1.10192	+	0.295258i	−0.763545	−	0.645754i	$-0.776543\pi$
$463$	−23.7104	+	6.35320i	−1.10192	+	0.295258i	−0.338373	+	0.941012i	$0.609876\pi$
$464$	3.08867	+	5.34973i	0.143388	+	0.248355i
$465$		0			0
$466$	13.1799	+	2.32398i	0.610548	+	0.107656i
$467$	−6.15448	−	1.64909i	−0.284795	−	0.0763107i	0.113593	−	0.993527i	$-0.463764\pi$
$467$	−6.15448	−	1.64909i	−0.284795	−	0.0763107i	−0.398389	+	0.917217i	$0.630431\pi$
$468$	3.06216	+	11.4281i	0.141548	+	0.528265i
$469$	−15.8704	−	13.3169i	−0.732829	−	0.614917i
$470$		0			0
$471$	0.934566	+	2.56770i	0.0430625	+	0.118313i
$472$	−0.462750	+	5.28925i	−0.0212998	+	0.243458i
$473$	−0.0385850	+	0.0551051i	−0.00177414	+	0.00253374i
$474$	−3.30785			−0.151935
$475$		0			0
$476$	20.1335			0.922819
$477$	−10.8318	+	15.4694i	−0.495955	+	0.708297i
$478$	0.140058	−	1.60087i	0.00640611	−	0.0732222i
$479$	13.9310	+	38.2750i	0.636522	+	1.74883i	0.662384	+	0.749165i	$0.269545\pi$
$479$	13.9310	+	38.2750i	0.636522	+	1.74883i	−0.0258616	+	0.999666i	$0.508233\pi$
$480$		0			0
$481$	−8.96003	−	7.51836i	−0.408542	−	0.342808i
$482$	0.731551	+	2.73019i	0.0333212	+	0.124357i
$483$	−4.70380	−	1.26038i	−0.214030	−	0.0573492i
$484$	−10.4800	−	1.84790i	−0.476362	−	0.0839954i
$485$		0			0
$486$	−3.04768	−	5.27873i	−0.138245	−	0.239448i
$487$	−10.2868	+	2.75634i	−0.466139	+	0.124901i	−0.484241	−	0.874935i	$-0.660904\pi$
$487$	−10.2868	+	2.75634i	−0.466139	+	0.124901i	0.0181023	+	0.999836i	$0.494238\pi$
$488$	11.7658	−	1.02938i	0.532614	−	0.0465977i
$489$	−2.61795	−	0.952856i	−0.118388	−	0.0430896i
$490$		0			0
$491$	−4.72266	+	3.96278i	−0.213131	+	0.178838i	−0.743103	−	0.669177i	$-0.766647\pi$
$491$	−4.72266	+	3.96278i	−0.213131	+	0.178838i	0.529972	+	0.848015i	$0.322202\pi$
$492$	1.60062	+	1.12077i	0.0721614	+	0.0505280i
$493$	−18.3728	+	18.3728i	−0.827471	+	0.827471i
$494$	12.0896	−	12.6560i	0.543936	−	0.569420i
$495$		0			0
$496$	−4.92269	+	0.868003i	−0.221035	+	0.0389745i
$497$	−12.4383	−	1.08821i	−0.557932	−	0.0488128i
$498$	−2.19109	−	1.02172i	−0.0981852	−	0.0457845i
$499$	−1.31402	+	3.61025i	−0.0588238	+	0.161617i	−0.965624	−	0.259945i	$-0.916296\pi$
$499$	−1.31402	+	3.61025i	−0.0588238	+	0.161617i	0.906800	+	0.421562i	$0.138518\pi$
$500$		0			0
$501$	1.72633	−	2.99009i	0.0771268	−	0.133588i
$502$	−6.04599	+	22.5639i	−0.269846	+	1.00708i
$503$	22.9936	−	16.1003i	1.02524	−	0.717877i	0.0652331	−	0.997870i	$-0.479221\pi$
$503$	22.9936	−	16.1003i	1.02524	−	0.717877i	0.960002	+	0.279993i	$0.0903320\pi$
$504$	−2.44913	+	13.8897i	−0.109093	+	0.618696i
$505$		0			0
$506$	2.28107	+	1.31698i	0.101406	+	0.0585468i
$507$	−0.0629313	−	0.719308i	−0.00279488	−	0.0319456i
$508$	18.6009	−	8.67374i	0.825281	−	0.384835i
$509$	34.7369	−	12.6432i	1.53969	−	0.560400i	0.573717	−	0.819053i	$-0.305501\pi$
$509$	34.7369	−	12.6432i	1.53969	−	0.560400i	0.965970	+	0.258653i	$0.0832787\pi$
$510$		0			0
$511$	4.71442	+	26.7368i	0.208554	+	1.18277i
$512$	−0.707107	−	0.707107i	−0.0312500	−	0.0312500i
$513$	−2.87714	+	5.25765i	−0.127029	+	0.232131i
$514$			0.0322769i			0.00142367i
$515$		0			0
$516$	−0.0167017	−	0.0199043i	−0.000735253	−	0.000876240i
$517$	1.14518	−	2.45586i	0.0503652	−	0.108008i
$518$	−5.89269	−	12.6369i	−0.258910	−	0.555235i
$519$	2.89491	−	3.45002i	0.127072	−	0.151439i
$520$		0			0
$521$	−38.8623	+	22.4372i	−1.70259	+	0.982989i	−0.759463	+	0.650551i	$0.774538\pi$
$521$	−38.8623	+	22.4372i	−1.70259	+	0.982989i	−0.943125	+	0.332438i	$0.892129\pi$
$522$	−10.4401	−	14.9100i	−0.456950	−	0.652592i
$523$	24.2172	+	34.5857i	1.05894	+	1.51233i	0.844475	+	0.535596i	$0.179913\pi$
$523$	24.2172	+	34.5857i	1.05894	+	1.51233i	0.214468	+	0.976731i	$0.431198\pi$
$524$	0.417868	−	0.241256i	0.0182547	−	0.0105393i
$525$		0			0
$526$	−17.0192	+	20.2827i	−0.742074	+	0.884370i
$527$	−8.88566	−	19.0554i	−0.387066	−	0.830065i
$528$	−0.0584987	+	0.125451i	−0.00254583	+	0.00545955i
$529$	−2.34032	−	2.78908i	−0.101753	−	0.121264i
$530$		0			0
$531$		−	15.6445i		−	0.678913i
$532$	19.4377	−	7.58285i	0.842732	−	0.328758i
$533$	23.9936	+	23.9936i	1.03928	+	1.03928i
$534$	0.00966469	+	0.0548112i	0.000418232	+	0.00237191i
$535$		0			0
$536$	−4.06716	+	1.48033i	−0.175675	+	0.0639403i
$537$	2.04471	−	0.953462i	0.0882356	−	0.0411449i
$538$	0.930230	+	10.6326i	0.0401051	+	0.458403i
$539$	−8.24928	−	4.76272i	−0.355322	−	0.205145i
$540$		0			0
$541$	−7.38662	+	41.8916i	−0.317576	+	1.80106i	0.239824	+	0.970816i	$0.422910\pi$
$541$	−7.38662	+	41.8916i	−0.317576	+	1.80106i	−0.557400	+	0.830244i	$0.688201\pi$
$542$	−1.95668	+	1.37009i	−0.0840468	+	0.0588502i
$543$	0.803282	−	2.99789i	0.0344722	−	0.128652i
$544$	2.10310	−	3.64268i	0.0901698	−	0.156179i
$545$		0			0
$546$	1.51996	−	4.17607i	0.0650485	−	0.178719i
$547$	−21.9634	−	10.2417i	−0.939089	−	0.437904i	−0.108067	−	0.994144i	$-0.534466\pi$
$547$	−21.9634	−	10.2417i	−0.939089	−	0.437904i	−0.831022	+	0.556239i	$0.812244\pi$
$548$	4.76832	+	0.417174i	0.203693	+	0.0178208i
$549$	−34.2722	+	6.04311i	−1.46270	+	0.257913i
$550$		0			0
$551$	−10.8182	+	24.6576i	−0.460869	+	1.05045i
$552$	−0.719383	+	0.719383i	−0.0306190	+	0.0306190i
$553$	−56.0929	−	39.2767i	−2.38531	−	1.67021i
$554$	−14.1085	+	11.8385i	−0.599414	+	0.502968i
$555$		0			0
$556$	−8.24058	−	2.99932i	−0.349478	−	0.127200i
$557$	−16.2559	+	1.42221i	−0.688784	+	0.0602608i	−0.426174	−	0.904641i	$-0.640139\pi$
$557$	−16.2559	+	1.42221i	−0.688784	+	0.0602608i	−0.262610	+	0.964902i	$0.584583\pi$
$558$	14.2268	−	3.81205i	0.602268	−	0.161377i
$559$	−0.225606	−	0.390762i	−0.00954213	−	0.0165275i
$560$		0			0
$561$	−0.573377	−	0.101102i	−0.0242080	−	0.00426852i
$562$	−2.14752	−	0.575427i	−0.0905878	−	0.0242729i
$563$	−3.50466	−	13.0796i	−0.147704	−	0.551237i	−0.999620	−	0.0275598i	$-0.991226\pi$
$563$	−3.50466	−	13.0796i	−0.147704	−	0.551237i	0.851917	−	0.523678i	$-0.175440\pi$
$564$	0.801766	+	0.672762i	0.0337604	+	0.0283284i
$565$		0			0
$566$	−1.81284	−	4.98074i	−0.0761994	−	0.209356i
$567$	3.55509	−	40.6349i	0.149300	−	1.70650i
$568$	−1.49616	+	2.13673i	−0.0627774	+	0.0896554i
$569$	28.9040			1.21172			0.605860	−	0.795571i	$-0.292829\pi$
$569$	28.9040			1.21172			0.605860	+	0.795571i	$0.292829\pi$
$570$		0			0
$571$	21.7075			0.908432			0.454216	−	0.890891i	$-0.349919\pi$
$571$	21.7075			0.908432			0.454216	+	0.890891i	$0.349919\pi$
$572$	−1.37872	+	1.96902i	−0.0576473	+	0.0823289i
$573$	0.128904	−	1.47338i	0.00538504	−	0.0615513i
$574$	13.8348	+	38.0108i	0.577453	+	1.58654i
$575$		0			0
$576$	2.25718	+	1.89400i	0.0940491	+	0.0789165i
$577$	−1.88629	−	7.03971i	−0.0785271	−	0.293067i	0.915483	−	0.402357i	$-0.131809\pi$
$577$	−1.88629	−	7.03971i	−0.0785271	−	0.293067i	−0.994010	+	0.109290i	$0.965142\pi$
$578$	0.668567	+	0.179142i	0.0278087	+	0.00745133i
$579$	−1.31896	−	0.232569i	−0.0548142	−	0.00966523i
$580$		0			0
$581$	−25.0238	−	43.3424i	−1.03816	−	1.79815i
$582$	−2.84371	+	0.761969i	−0.117875	+	0.0315846i
$583$	−3.82215	+	0.334395i	−0.158297	+	0.0138492i
$584$	5.32984	+	1.93990i	0.220550	+	0.0802738i
$585$		0			0
$586$	−19.1247	+	16.0476i	−0.790035	+	0.662918i
$587$	−9.71118	−	6.79984i	−0.400823	−	0.280659i	0.355734	−	0.934587i	$-0.384231\pi$
$587$	−9.71118	−	6.79984i	−0.400823	−	0.280659i	−0.756557	+	0.653928i	$0.773120\pi$
$588$	2.60158	−	2.60158i	0.107287	−	0.107287i
$589$	−15.7554	−	15.0502i	−0.649188	−	0.620134i
$590$		0			0
$591$	0.133441	−	0.0235293i	0.00548905	−	0.000967867i
$592$	−2.90188	−	0.253882i	−0.119267	−	0.0104345i
$593$	−20.6405	−	9.62483i	−0.847605	−	0.395245i	−0.0502363	−	0.998737i	$-0.515997\pi$
$593$	−20.6405	−	9.62483i	−0.847605	−	0.395245i	−0.797368	+	0.603493i	$0.793775\pi$
$594$	0.281523	−	0.773478i	0.0115510	−	0.0317362i
$595$		0			0
$596$	4.42620	−	7.66640i	0.181304	−	0.314028i
$597$	1.58536	−	5.91663i	0.0648844	−	0.242152i
$598$	−14.4719	+	10.1334i	−0.591802	+	0.414384i
$599$	2.89695	−	16.4294i	0.118366	−	0.671287i	−0.866662	−	0.498895i	$-0.833739\pi$
$599$	2.89695	−	16.4294i	0.118366	−	0.671287i	0.985028	−	0.172392i	$-0.0551497\pi$
$600$		0			0
$601$	32.7469	+	18.9064i	1.33577	+	0.771210i	0.986178	−	0.165690i	$-0.0529852\pi$
$601$	32.7469	+	18.9064i	1.33577	+	0.771210i	0.349597	+	0.936900i	$0.386319\pi$
$602$	−0.0468800	−	0.535841i	−0.00191068	−	0.0218392i
$603$	11.5583	−	5.38971i	0.470689	−	0.219486i
$604$	−7.36120	+	2.67926i	−0.299523	+	0.109017i
$605$		0			0
$606$	0.391086	+	2.21796i	0.0158868	+	0.0900984i
$607$	4.35886	+	4.35886i	0.176920	+	0.176920i	0.790012	−	0.613091i	$-0.210074\pi$
$607$	4.35886	+	4.35886i	0.176920	+	0.176920i	−0.613091	+	0.790012i	$0.710074\pi$
$608$	0.658484	−	4.30887i	0.0267051	−	0.174748i
$609$			6.83696i			0.277048i
$610$		0			0
$611$	11.6828	+	13.9231i	0.472637	+	0.563267i
$612$	−5.23782	+	11.2325i	−0.211726	+	0.454048i
$613$	8.84666	+	18.9717i	0.357313	+	0.766261i	1.00000		0.000131554i	$4.18750e-5\pi$
$613$	8.84666	+	18.9717i	0.357313	+	0.766261i	−0.642687	+	0.766129i	$0.722180\pi$
$614$	8.79788	−	10.4849i	0.355054	−	0.423136i
$615$		0			0
$616$	−2.48157	+	1.43273i	−0.0999852	+	0.0577265i
$617$	−11.8979	−	16.9919i	−0.478990	−	0.684069i	0.504832	−	0.863218i	$-0.331555\pi$
$617$	−11.8979	−	16.9919i	−0.478990	−	0.684069i	−0.983822	+	0.179149i	$0.942666\pi$
$618$	−2.04310	−	2.91785i	−0.0821854	−	0.117373i
$619$	22.1318	−	12.7778i	0.889552	−	0.513583i	0.0157561	−	0.999876i	$-0.494984\pi$
$619$	22.1318	−	12.7778i	0.889552	−	0.513583i	0.873796	+	0.486293i	$0.161651\pi$
$620$		0			0
$621$	3.88872	−	4.63439i	0.156049	−	0.185972i
$622$	7.82189	+	16.7741i	0.313629	+	0.672580i
$623$	−0.486926	+	1.04422i	−0.0195083	+	0.0418357i
$624$	−0.596787	−	0.711223i	−0.0238906	−	0.0284717i
$625$		0			0
$626$			5.34398i			0.213588i
$627$	−0.591638	+	0.118342i	−0.0236278	+	0.00472612i
$628$	8.35625	+	8.35625i	0.333451	+	0.333451i
$629$	−2.12763	−	12.0664i	−0.0848342	−	0.481119i
$630$		0			0
$631$	8.15256	−	2.96729i	0.324548	−	0.118126i	−0.174608	−	0.984638i	$-0.555866\pi$
$631$	8.15256	−	2.96729i	0.324548	−	0.118126i	0.499156	+	0.866512i	$0.333643\pi$
$632$	−12.9655	+	6.04591i	−0.515740	+	0.240494i
$633$	0.0375630	+	0.429347i	0.00149300	+	0.0170650i
$634$	0.255967	+	0.147783i	0.0101658	+	0.00586920i
$635$		0			0
$636$	0.257336	−	1.45943i	0.0102040	−	0.0578700i
$637$	52.3364	−	36.6463i	2.07364	−	1.45198i
$638$	0.957113	−	3.57199i	0.0378925	−	0.141417i
$639$	3.84298	−	6.65623i	0.152026	−	0.263316i
$640$		0			0
$641$	9.60234	−	26.3822i	0.379270	−	1.04203i	−0.592390	−	0.805651i	$-0.701816\pi$
$641$	9.60234	−	26.3822i	0.379270	−	1.04203i	0.971660	−	0.236384i	$-0.0759622\pi$
$642$	1.00696	+	0.469555i	0.0397417	+	0.0185318i
$643$	14.9655	+	1.30931i	0.590181	+	0.0516342i	0.378335	−	0.925669i	$-0.376497\pi$
$643$	14.9655	+	1.30931i	0.590181	+	0.0516342i	0.211846	+	0.977303i	$0.432052\pi$
$644$	−20.7407	+	3.65715i	−0.817299	+	0.144112i
$645$		0			0
$646$	18.2233	−	2.01549i	0.716986	−	0.0792985i
$647$	5.91154	−	5.91154i	0.232407	−	0.232407i	−0.581290	−	0.813696i	$-0.697452\pi$
$647$	5.91154	−	5.91154i	0.232407	−	0.232407i	0.813696	+	0.581290i	$0.197452\pi$
$648$	−6.98055	−	4.88783i	−0.274222	−	0.192012i
$649$	2.43484	−	2.04307i	0.0955757	−	0.0801975i
$650$		0			0
$651$	−5.19875	−	1.89219i	−0.203755	−	0.0741608i
$652$	−12.0029	+	1.05012i	−0.470071	+	0.0411259i
$653$	−46.5416	+	12.4708i	−1.82131	+	0.488019i	−0.996950	−	0.0780431i	$-0.975133\pi$
$653$	−46.5416	+	12.4708i	−1.82131	+	0.488019i	−0.824362	+	0.566062i	$0.808466\pi$
$654$	−1.24715	−	2.16012i	−0.0487672	−	0.0844673i
$655$		0			0
$656$	8.32228	+	1.46744i	0.324931	+	0.0572940i
$657$	−16.1430	−	4.32550i	−0.629798	−	0.168754i
$658$	5.60773	+	20.9283i	0.218612	+	0.815872i
$659$	23.4421	+	19.6702i	0.913174	+	0.766244i	0.972720	−	0.231982i	$-0.0745210\pi$
$659$	23.4421	+	19.6702i	0.913174	+	0.766244i	−0.0595463	+	0.998226i	$0.518965\pi$
$660$		0			0
$661$	6.99514	+	19.2190i	0.272079	+	0.747532i	0.998200	+	0.0599652i	$0.0190990\pi$
$661$	6.99514	+	19.2190i	0.272079	+	0.747532i	−0.726121	+	0.687567i	$0.758679\pi$
$662$	−0.000541667		0.00619129i	−2.10525e−5		0.000240631i
$663$	2.23993	−	3.19895i	0.0869915	−	0.124237i
$664$	−10.4557			−0.405760
$665$		0			0
$666$	8.58317			0.332591
$667$	15.5896	−	22.2643i	0.603632	−	0.862075i
$668$	1.30142	−	14.8753i	0.0503535	−	0.575543i
$669$	−0.586207	−	1.61059i	−0.0226641	−	0.0622690i
$670$		0			0
$671$	−5.41624	−	4.54477i	−0.209092	−	0.175449i
$672$	−0.286456	−	1.06907i	−0.0110503	−	0.0412402i
$673$	−5.14271	−	1.37799i	−0.198237	−	0.0531175i	0.158334	−	0.987386i	$-0.449388\pi$
$673$	−5.14271	−	1.37799i	−0.198237	−	0.0531175i	−0.356571	+	0.934268i	$0.616054\pi$
$674$	−19.9941	−	3.52550i	−0.770143	−	0.135797i
$675$		0			0
$676$	−1.56138	−	2.70439i	−0.0600530	−	0.104015i
$677$	43.1368	−	11.5585i	1.65788	−	0.444228i	0.696078	−	0.717966i	$-0.254927\pi$
$677$	43.1368	−	11.5585i	1.65788	−	0.444228i	0.961805	+	0.273737i	$0.0882599\pi$
$678$	−3.94603	+	0.345233i	−0.151547	+	0.0132586i
$679$	−57.2696	−	20.8444i	−2.19781	−	0.799936i
$680$		0			0
$681$	−2.37864	+	1.99592i	−0.0911497	+	0.0764837i
$682$	2.45122	+	1.71636i	0.0938619	+	0.0657228i
$683$	7.51469	−	7.51469i	0.287542	−	0.287542i	−0.548566	−	0.836107i	$-0.684826\pi$
$683$	7.51469	−	7.51469i	0.287542	−	0.287542i	0.836107	+	0.548566i	$0.184826\pi$
$684$	−0.826313	+	12.8170i	−0.0315949	+	0.490072i
$685$		0			0
$686$	42.0095	−	7.40740i	1.60393	−	0.282816i
$687$	−3.51049	−	0.307128i	−0.133933	−	0.0117177i
$688$	−0.101844	−	0.0474908i	−0.00388278	−	0.00181057i
$689$	8.80176	−	24.1826i	0.335320	−	0.921285i
$690$		0			0
$691$	−4.21378	+	7.29848i	−0.160300	+	0.277647i	−0.934976	−	0.354710i	$-0.884579\pi$
$691$	−4.21378	+	7.29848i	−0.160300	+	0.277647i	0.774676	+	0.632358i	$0.217913\pi$
$692$	5.04117	−	18.8139i	0.191637	−	0.715197i
$693$	6.91627	−	4.84282i	0.262727	−	0.183964i
$694$	4.51135	−	25.5851i	0.171248	−	0.971198i
$695$		0			0
$696$	1.23698	+	0.714173i	0.0468877	+	0.0270706i
$697$	3.09797	+	35.4100i	0.117344	+	1.34125i
$698$	14.0758	−	6.56365i	0.532777	−	0.248438i
$699$	2.90790	−	1.05839i	0.109987	−	0.0400320i
$700$		0			0
$701$	−4.33246	−	24.5706i	−0.163635	−	0.928020i	−0.950461	−	0.310845i	$-0.899388\pi$
$701$	−4.33246	−	24.5706i	−0.163635	−	0.928020i	0.786826	−	0.617175i	$-0.211723\pi$
$702$	3.90392	+	3.90392i	0.147344	+	0.147344i
$703$	−6.59864	−	10.8481i	−0.248872	−	0.409142i
$704$			0.598640i			0.0225621i
$705$		0			0
$706$	−16.2108	−	19.3193i	−0.610102	−	0.727091i
$707$	−19.7037	+	42.2547i	−0.741034	+	1.58915i
$708$	0.518837	+	1.11265i	0.0194991	+	0.0418159i
$709$	−30.4957	+	36.3434i	−1.14529	+	1.36490i	−0.224674	+	0.974434i	$0.572132\pi$
$709$	−30.4957	+	36.3434i	−1.14529	+	1.36490i	−0.920616	+	0.390469i	$0.872313\pi$
$710$		0			0
$711$	36.5053	−	21.0763i	1.36906	−	0.790425i
$712$	0.138063	+	0.197174i	0.00517412	+	0.00738941i
$713$	12.6149	+	18.0160i	0.472433	+	0.674705i
$714$	4.03165	−	2.32767i	0.150881	−	0.0871110i
$715$		0			0
$716$	6.27177	−	7.47441i	0.234387	−	0.279332i
$717$	−0.157034	−	0.336760i	−0.00586453	−	0.0125765i
$718$	−10.1488	+	21.7641i	−0.378749	+	0.812230i
$719$	−31.3291	−	37.3366i	−1.16838	−	1.39242i	−0.903745	−	0.428071i	$-0.859193\pi$
$719$	−31.3291	−	37.3366i	−1.16838	−	1.39242i	−0.264634	−	0.964349i	$-0.585251\pi$
$720$		0			0
$721$		−	73.7386i		−	2.74617i
$722$	16.8344	−	8.80924i	0.626512	−	0.327846i
$723$	0.462132	+	0.462132i	0.0171869	+	0.0171869i
$724$	−2.33083	−	13.2188i	−0.0866245	−	0.491272i
$725$		0			0
$726$	−2.31220	+	0.841574i	−0.0858140	+	0.0312337i
$727$	−13.9842	+	6.52095i	−0.518646	+	0.241849i	−0.664272	−	0.747491i	$-0.731258\pi$
$727$	−13.9842	+	6.52095i	−0.518646	+	0.241849i	0.145626	+	0.989340i	$0.453481\pi$
$728$	−1.67512	−	19.1467i	−0.0620840	−	0.709623i
$729$	20.9194	+	12.0778i	0.774793	+	0.447327i
$730$		0			0
$731$	0.0820771	−	0.465483i	0.00303573	−	0.0172165i
$732$	2.23705	−	1.56640i	0.0826836	−	0.0578957i
$733$	−7.41449	+	27.6713i	−0.273860	+	1.02206i	0.682741	+	0.730661i	$0.260788\pi$
$733$	−7.41449	+	27.6713i	−0.273860	+	1.02206i	−0.956601	+	0.291400i	$0.905879\pi$
$734$	8.67989	−	15.0340i	0.320381	−	0.554915i
$735$		0			0
$736$	−1.50485	+	4.13455i	−0.0554697	+	0.152402i
$737$	2.34826	+	1.09501i	0.0864994	+	0.0403354i
$738$	−24.8054	−	2.17019i	−0.913101	−	0.0798860i
$739$	21.5847	−	3.80597i	0.794008	−	0.140005i	0.238091	−	0.971243i	$-0.423478\pi$
$739$	21.5847	−	3.80597i	0.794008	−	0.140005i	0.555917	+	0.831238i	$0.312367\pi$
$740$		0			0
$741$	0.957702	−	3.93201i	0.0351821	−	0.144446i
$742$	21.6927	−	21.6927i	0.796363	−	0.796363i
$743$	−15.0508	−	10.5387i	−0.552160	−	0.386627i	0.263938	−	0.964540i	$-0.414979\pi$
$743$	−15.0508	−	10.5387i	−0.552160	−	0.386627i	−0.816099	+	0.577913i	$0.803867\pi$
$744$	−0.885396	+	0.742935i	−0.0324602	+	0.0272373i
$745$		0			0
$746$	−5.69338	−	2.07222i	−0.208449	−	0.0758694i
$747$	30.6908	−	2.68510i	1.12292	−	0.0982427i
$748$	−2.43220	+	0.651707i	−0.0889302	+	0.0238288i
$749$	11.5002	+	19.9189i	0.420208	+	0.727822i
$750$		0			0
$751$	48.7977	+	8.60436i	1.78065	+	0.313978i	0.964545	−	0.263919i	$-0.0850151\pi$
$751$	48.7977	+	8.60436i	1.78065	+	0.313978i	0.816110	+	0.577896i	$0.196126\pi$
$752$	4.37225	+	1.17154i	0.159440	+	0.0427217i
$753$	1.39798	+	5.21732i	0.0509451	+	0.190130i
$754$	19.0009	+	15.9437i	0.691973	+	0.580634i
$755$		0			0
$756$	2.25101	+	6.18460i	0.0818685	+	0.224932i
$757$	−3.54967	+	40.5730i	−0.129015	+	1.47465i	0.605385	+	0.795933i	$0.293019\pi$
$757$	−3.54967	+	40.5730i	−0.129015	+	1.47465i	−0.734400	+	0.678717i	$0.762536\pi$
$758$	−13.2080	+	18.8630i	−0.479735	+	0.685133i
$759$	0.609033			0.0221065
$760$		0			0
$761$	14.2916			0.518069			0.259035	−	0.965868i	$-0.416596\pi$
$761$	14.2916			0.518069			0.259035	+	0.965868i	$0.416596\pi$
$762$	2.72196	−	3.88736i	0.0986062	−	0.140824i
$763$	4.50029	−	51.4385i	0.162921	−	1.86220i
$764$	−2.18771	−	6.01068i	−0.0791486	−	0.217459i
$765$		0			0
$766$	−9.50069	−	7.97203i	−0.343274	−	0.288041i
$767$	5.51780	+	20.5927i	0.199236	+	0.743559i
$768$	−0.223345	−	0.0598451i	−0.00805927	−	0.00215947i
$769$	21.6621	+	3.81962i	0.781156	+	0.137739i	0.549985	−	0.835174i	$-0.314633\pi$
$769$	21.6621	+	3.81962i	0.781156	+	0.137739i	0.231171	+	0.972913i	$0.425744\pi$
$770$		0			0
$771$	0.00373159	+	0.00646330i	0.000134390	+	0.000232770i
$772$	−5.59490	+	1.49915i	−0.201365	+	0.0539556i
$773$	33.8827	−	2.96435i	1.21868	−	0.106620i	0.540388	−	0.841416i	$-0.318277\pi$
$773$	33.8827	−	2.96435i	1.21868	−	0.106620i	0.678289	+	0.734795i	$0.262722\pi$
$774$	0.311142	+	0.113247i	0.0111838	+	0.00407056i
$775$		0			0
$776$	−9.75355	+	8.18420i	−0.350132	+	0.293796i
$777$	−2.64096	−	1.84922i	−0.0947440	−	0.0663405i
$778$	−17.4550	+	17.4550i	−0.625792	+	0.625792i
$779$	16.3273	+	33.0194i	0.584985	+	1.18304i
$780$		0			0
$781$	1.53781	−	0.271158i	0.0550272	−	0.00970279i
$782$	−18.4364	−	1.61298i	−0.659286	−	0.0576801i
$783$	−7.69791	−	3.58960i	−0.275101	−	0.128282i
$784$	5.44216	−	14.9522i	0.194363	−	0.534008i
$785$		0			0
$786$	0.0557842	−	0.0966210i	0.00198976	−	0.00344636i
$787$	−3.32809	+	12.4206i	−0.118634	+	0.442746i	−0.999533	−	0.0305570i	$-0.990272\pi$
$787$	−3.32809	+	12.4206i	−0.118634	+	0.442746i	0.880899	+	0.473303i	$0.156939\pi$
$788$	0.480033	−	0.336123i	0.0171005	−	0.0119739i
$789$	−1.06310	+	6.02916i	−0.0378475	+	0.214644i
$790$		0			0
$791$	−71.0141	−	41.0000i	−2.52497	−	1.45779i
$792$	−0.153735	−	1.75720i	−0.00546275	−	0.0624395i
$793$	42.9807	−	20.0422i	1.52629	−	0.711721i
$794$	1.30069	−	0.473413i	0.0461599	−	0.0168008i
$795$		0			0
$796$	−4.60012	−	26.0886i	−0.163047	−	0.924685i
$797$	−8.55912	−	8.55912i	−0.303180	−	0.303180i	0.539077	−	0.842257i	$-0.318773\pi$
$797$	−8.55912	−	8.55912i	−0.303180	−	0.303180i	−0.842257	+	0.539077i	$0.818773\pi$
$798$	3.01565	−	3.76566i	0.106753	−	0.133303i
$799$			19.0393i			0.673563i
$800$		0			0
$801$	−0.455895	−	0.543314i	−0.0161082	−	0.0191971i
$802$	−1.23332	+	2.64487i	−0.0435502	+	0.0933936i
$803$	−1.43497	−	3.07730i	−0.0506390	−	0.108596i
$804$	−0.643288	+	0.766640i	−0.0226870	+	0.0270373i
$805$		0			0
$806$	−17.3821	+	10.0355i	−0.612257	+	0.353487i
$807$	1.41553	+	2.02158i	0.0498289	+	0.0711630i
$808$	5.58677	+	7.97874i	0.196542	+	0.280691i
$809$	−38.8223	+	22.4141i	−1.36492	+	0.788036i	−0.990274	−	0.139132i	$-0.955569\pi$
$809$	−38.8223	+	22.4141i	−1.36492	+	0.788036i	−0.374645	+	0.927168i	$0.622235\pi$
$810$		0			0
$811$	−21.5092	+	25.6336i	−0.755289	+	0.900118i	−0.997540	−	0.0700953i	$-0.977670\pi$
$811$	−21.5092	+	25.6336i	−0.755289	+	0.900118i	0.242251	+	0.970213i	$0.422114\pi$
$812$	12.4962	+	26.7982i	0.438532	+	0.940434i
$813$	−0.233419	+	0.500569i	−0.00818637	+	0.0175557i
$814$	1.12091	+	1.33584i	0.0392877	+	0.0468213i
$815$		0			0
$816$		−	0.972574i		−	0.0340469i
$817$	−0.0960731	−	0.480308i	−0.00336117	−	0.0168038i
$818$	2.28800	+	2.28800i	0.0799980	+	0.0799980i
$819$	9.83402	+	55.7715i	0.343629	+	1.94881i
$820$		0			0
$821$	8.87927	−	3.23179i	0.309889	−	0.112790i	−0.182394	−	0.983225i	$-0.558385\pi$
$821$	8.87927	−	3.23179i	0.309889	−	0.112790i	0.492283	+	0.870435i	$0.336163\pi$
$822$	1.00307	−	0.467737i	0.0349859	−	0.0163142i
$823$	2.41976	+	27.6580i	0.0843475	+	0.964096i	0.913973	+	0.405775i	$0.132998\pi$
$823$	2.41976	+	27.6580i	0.0843475	+	0.964096i	−0.829625	+	0.558320i	$0.811446\pi$
$824$	−13.3412	−	7.70257i	−0.464764	−	0.268332i
$825$		0			0
$826$	−4.41316	+	25.0283i	−0.153554	+	0.870845i
$827$	−30.1869	+	21.1371i	−1.04970	+	0.735008i	−0.965226	−	0.261418i	$-0.915810\pi$
$827$	−30.1869	+	21.1371i	−1.04970	+	0.735008i	−0.0844745	+	0.996426i	$0.526921\pi$
$828$	3.35545	−	12.5227i	0.116610	−	0.435194i
$829$	−10.6927	+	18.5203i	−0.371374	+	0.643238i	−0.989777	−	0.142623i	$-0.954446\pi$
$829$	−10.6927	+	18.5203i	−0.371374	+	0.643238i	0.618403	+	0.785861i	$0.287780\pi$
$830$		0			0
$831$	−1.45650	+	4.00171i	−0.0505256	+	0.138818i
$832$	−3.63911	−	1.69695i	−0.126163	−	0.0588310i
$833$	66.6736	+	5.83319i	2.31010	+	0.202108i
$834$	−1.99690	+	0.352107i	−0.0691469	+	0.0121925i
$835$		0			0
$836$	−2.10270	+	1.54522i	−0.0727233	+	0.0534425i
$837$	4.85996	−	4.85996i	0.167985	−	0.167985i
$838$	−6.26743	−	4.38850i	−0.216505	−	0.151598i
$839$	−0.733023	+	0.615079i	−0.0253068	+	0.0212349i	−0.655353	−	0.755322i	$-0.727480\pi$
$839$	−0.733023	+	0.615079i	−0.0253068	+	0.0212349i	0.630047	+	0.776557i	$0.283036\pi$
$840$		0			0
$841$	−8.60705	−	3.13271i	−0.296795	−	0.108025i
$842$	13.9964	−	1.22453i	0.482347	−	0.0421999i
$843$	−0.496558	+	0.133052i	−0.0171024	+	0.00458257i
$844$	0.931971	+	1.61422i	0.0320798	+	0.0555638i
$845$		0			0
$846$	−13.1348	−	2.31603i	−0.451585	−	0.0796266i
$847$	−49.2019	−	13.1836i	−1.69060	−	0.452994i
$848$	−1.65880	−	6.19073i	−0.0569635	−	0.212591i
$849$	−0.938846	−	0.787785i	−0.0322211	−	0.0270367i
$850$		0			0
$851$	4.38359	+	12.0438i	0.150268	+	0.412857i
$852$	−0.0525671	+	0.600845i	−0.00180092	+	0.0205846i
$853$	5.59683	−	7.99310i	0.191632	−	0.273679i	−0.711826	−	0.702356i	$-0.752131\pi$
$853$	5.59683	−	7.99310i	0.191632	−	0.273679i	0.903458	+	0.428677i	$0.141020\pi$
$854$	56.5338			1.93455
$855$		0			0
$856$	4.80513			0.164236
$857$	−25.8402	+	36.9036i	−0.882684	+	1.26060i	0.0818496	+	0.996645i	$0.473917\pi$
$857$	−25.8402	+	36.9036i	−0.882684	+	1.26060i	−0.964534	+	0.263959i	$0.914972\pi$
$858$	−0.0484411	+	0.553684i	−0.00165375	+	0.0189025i
$859$	1.49786	+	4.11533i	0.0511062	+	0.140413i	0.962619	−	0.270858i	$-0.0873073\pi$
$859$	1.49786	+	4.11533i	0.0511062	+	0.140413i	−0.911513	+	0.411271i	$0.865085\pi$
$860$		0			0
$861$	7.16485	+	6.01202i	0.244177	+	0.204889i
$862$	−0.257193	−	0.959858i	−0.00876004	−	0.0326929i
$863$	5.43411	+	1.45606i	0.184979	+	0.0495650i	0.350119	−	0.936705i	$-0.386141\pi$
$863$	5.43411	+	1.45606i	0.184979	+	0.0495650i	−0.165140	+	0.986270i	$0.552808\pi$
$864$	1.35409	+	0.238763i	0.0460671	+	0.00812287i
$865$		0			0
$866$	−0.319447	−	0.553299i	−0.0108553	−	0.0188019i
$867$	0.154589	−	0.0414219i	0.00525010	−	0.00140676i
$868$	−23.8355	+	2.08534i	−0.809031	+	0.0707811i
$869$	8.04758	+	2.92908i	0.272996	+	0.0993622i
$870$		0			0
$871$	−13.3131	+	11.1710i	−0.451097	+	0.378515i
$872$	−8.83648	−	6.18737i	−0.299241	−	0.209531i
$873$	26.5281	−	26.5281i	0.897838	−	0.897838i
$874$	−18.4068	+	5.38644i	−0.622618	+	0.182199i
$875$		0			0
$876$	1.29155	−	0.227736i	0.0436375	−	0.00769447i
$877$	40.6680	+	3.55799i	1.37326	+	0.120145i	0.749777	−	0.661691i	$-0.230161\pi$
$877$	40.6680	+	3.55799i	1.37326	+	0.120145i	0.623485	+	0.781836i	$0.285716\pi$
$878$	−27.0255	−	12.6022i	−0.912067	−	0.425304i
$879$	−1.97436	+	5.42450i	−0.0665934	+	0.182964i
$880$		0			0
$881$	1.17452	−	2.03433i	0.0395707	−	0.0685384i	−0.845562	−	0.533878i	$-0.820734\pi$
$881$	1.17452	−	2.03433i	0.0395707	−	0.0685384i	0.885132	+	0.465339i	$0.154068\pi$
$882$	−12.1347	+	45.2872i	−0.408595	+	1.52490i
$883$	6.17577	−	4.32432i	0.207831	−	0.145525i	−0.465027	−	0.885297i	$-0.653955\pi$
$883$	6.17577	−	4.32432i	0.207831	−	0.145525i	0.672858	+	0.739772i	$0.265066\pi$
$884$	2.93278	−	16.6326i	0.0986402	−	0.559417i
$885$		0			0
$886$	19.6612	+	11.3514i	0.660530	+	0.381357i
$887$	−1.72099	−	19.6710i	−0.0577853	−	0.660489i	−0.968756	−	0.248017i	$-0.920221\pi$
$887$	−1.72099	−	19.6710i	−0.0577853	−	0.660489i	0.910970	−	0.412472i	$-0.135335\pi$
$888$	−0.610441	+	0.284653i	−0.0204851	+	0.00955234i
$889$	92.3153	−	33.6000i	3.09616	−	1.12691i
$890$		0			0
$891$	0.885852	+	5.02392i	0.0296772	+	0.168308i
$892$	−5.24146	−	5.24146i	−0.175497	−	0.175497i
$893$	7.17074	+	18.3813i	0.239960	+	0.615108i
$894$		−	2.04688i		−	0.0684580i
$895$		0			0
$896$	−3.07679	−	3.66677i	−0.102788	−	0.122498i
$897$	−1.72641	+	3.70229i	−0.0576430	+	0.123616i
$898$	6.64831	+	14.2574i	0.221857	+	0.475774i
$899$	19.8481	−	23.6541i	0.661972	−	0.788908i
$900$		0			0
$901$	23.3464	−	13.4790i	0.777780	−	0.449051i
$902$	−2.90167	−	4.14402i	−0.0966151	−	0.137981i
$903$	−0.0713370	−	0.101880i	−0.00237395	−	0.00339035i
$904$	−14.8359	+	8.56553i	−0.493436	+	0.284885i
$905$		0			0
$906$	−1.16429	+	1.38755i	−0.0386811	+	0.0460983i
$907$	−7.33485	−	15.7296i	−0.243550	−	0.522294i	0.746094	−	0.665841i	$-0.231927\pi$
$907$	−7.33485	−	15.7296i	−0.243550	−	0.522294i	−0.989644	+	0.143547i	$0.954149\pi$
$908$	−5.67533	+	12.1708i	−0.188342	+	0.403901i
$909$	−18.4480	−	21.9855i	−0.611881	−	0.729212i
$910$		0			0
$911$		−	3.60599i		−	0.119472i	−0.998214	−	0.0597358i	$-0.980974\pi$
$911$		−	3.60599i		−	0.119472i	0.998214	−	0.0597358i	$-0.0190258\pi$
$912$	−0.366298	−	0.938962i	−0.0121293	−	0.0310921i
$913$	4.42592	+	4.42592i	0.146477	+	0.146477i
$914$	0.380226	+	2.15637i	0.0125768	+	0.0713263i
$915$		0			0
$916$	−14.3211	+	5.21246i	−0.473183	+	0.172224i
$917$	2.09322	−	0.976083i	0.0691241	−	0.0322331i
$918$	0.504060	+	5.76144i	0.0166365	+	0.190156i
$919$	16.7346	+	9.66173i	0.552023	+	0.318711i	0.749938	−	0.661508i	$-0.230083\pi$
$919$	16.7346	+	9.66173i	0.552023	+	0.318711i	−0.197914	+	0.980219i	$0.563417\pi$
$920$		0			0
$921$	0.549557	−	3.11669i	0.0181085	−	0.102699i
$922$	−9.46113	+	6.62476i	−0.311586	+	0.218175i
$923$	−2.71083	+	10.1169i	−0.0892280	+	0.333003i
$924$	−0.331282	+	0.573797i	−0.0108984	+	0.0188765i
$925$		0			0
$926$	−8.39552	+	23.0665i	−0.275894	+	0.758012i
$927$	41.1389	+	19.1834i	1.35118	+	0.630065i
$928$	6.15383	+	0.538390i	0.202009	+	0.0176735i
$929$	27.8004	−	4.90196i	0.912101	−	0.160828i	0.302144	−	0.953262i	$-0.402298\pi$
$929$	27.8004	−	4.90196i	0.912101	−	0.160828i	0.609957	+	0.792434i	$0.291187\pi$
$930$		0			0
$931$	66.5663	−	19.4795i	2.18162	−	0.638416i
$932$	9.46338	−	9.46338i	0.309983	−	0.309983i
$933$	3.50558	+	2.45463i	0.114768	+	0.0803611i
$934$	−4.88092	+	4.09558i	−0.159709	+	0.134011i
$935$		0			0
$936$	11.1178	+	4.04653i	0.363395	+	0.132265i
$937$	−15.1395	+	1.32453i	−0.494585	+	0.0432706i	−0.331720	−	0.943378i	$-0.607629\pi$
$937$	−15.1395	+	1.32453i	−0.494585	+	0.0432706i	−0.162865	+	0.986648i	$0.552073\pi$
$938$	−20.0115	+	5.36206i	−0.653397	+	0.175077i
$939$	0.617827	+	1.07011i	0.0201620	+	0.0349216i
$940$		0			0
$941$	−9.12878	−	1.60965i	−0.297590	−	0.0524731i	0.0228598	−	0.999739i	$-0.492723\pi$
$941$	−9.12878	−	1.60965i	−0.297590	−	0.0524731i	−0.320450	+	0.947266i	$0.603834\pi$
$942$	2.63938	+	0.707220i	0.0859957	+	0.0230425i
$943$	−9.62343	−	35.9151i	−0.313382	−	1.16956i
$944$	4.06728	+	3.41285i	0.132379	+	0.111079i
$945$		0			0
$946$	0.0230080	+	0.0632140i	0.000748055	+	0.00205526i
$947$	2.69314	−	30.7827i	0.0875153	−	1.00030i	−0.817783	−	0.575527i	$-0.804797\pi$
$947$	2.69314	−	30.7827i	0.0875153	−	1.00030i	0.905298	−	0.424777i	$-0.139648\pi$
$948$	−1.89731	+	2.70963i	−0.0616216	+	0.0880048i
$949$	22.7745			0.739290
$950$		0			0
$951$	0.0683417			0.00221613
$952$	11.5481	−	16.4924i	0.374277	−	0.534523i
$953$	−2.10373	+	24.0458i	−0.0681466	+	0.778919i	0.882837	+	0.469679i	$0.155630\pi$
$953$	−2.10373	+	24.0458i	−0.0681466	+	0.778919i	−0.950984	+	0.309240i	$0.899925\pi$
$954$	6.45894	+	17.7458i	0.209116	+	0.574542i
$955$		0			0
$956$	−1.23102	−	1.03295i	−0.0398141	−	0.0334080i
$957$	−0.221307	−	0.825929i	−0.00715384	−	0.0266985i
$958$	39.3435	+	10.5421i	1.27113	+	0.340599i
$959$	22.5633	+	3.97852i	0.728607	+	0.128473i
$960$		0			0
$961$	−3.00684	−	5.20799i	−0.0969947	−	0.168000i
$962$	−11.2979	+	3.02727i	−0.364260	+	0.0976032i
$963$	−14.1046	+	1.23399i	−0.454515	+	0.0397649i
$964$	2.65604	+	0.966719i	0.0855452	+	0.0311359i
$965$		0			0
$966$	−3.73043	+	3.13020i	−0.120025	+	0.100713i
$967$	9.51131	+	6.65989i	0.305863	+	0.214168i	0.716423	−	0.697666i	$-0.245778\pi$
$967$	9.51131	+	6.65989i	0.305863	+	0.214168i	−0.410560	+	0.911833i	$0.634667\pi$
$968$	−7.52477	+	7.52477i	−0.241855	+	0.241855i
$969$	3.41612	−	2.51042i	0.109742	−	0.0806464i
$970$		0			0
$971$	−34.2596	+	6.04090i	−1.09944	+	0.193862i	−0.693799	−	0.720169i	$-0.744064\pi$
$971$	−34.2596	+	6.04090i	−1.09944	+	0.193862i	−0.405645	+	0.914031i	$0.632953\pi$
$972$	−6.07216	−	0.531245i	−0.194765	−	0.0170397i
$973$	−38.0432	−	17.7398i	−1.21961	−	0.568713i
$974$	−3.64240	+	10.0074i	−0.116710	+	0.320658i
$975$		0			0
$976$	5.90539	−	10.2284i	0.189027	−	0.327404i
$977$	−0.822582	+	3.06992i	−0.0263167	+	0.0982154i	−0.977835	−	0.209377i	$-0.932857\pi$
$977$	−0.822582	+	3.06992i	−0.0263167	+	0.0982154i	0.951518	+	0.307592i	$0.0995232\pi$
$978$	−2.28213	+	1.59796i	−0.0729744	+	0.0510972i
$979$	0.0250220	−	0.141907i	0.000799706	−	0.00453536i
$980$		0			0
$981$	27.5269	+	15.8927i	0.878866	+	0.507413i
$982$	0.537315	+	6.14154i	0.0171464	+	0.195984i
$983$	27.6241	−	12.8813i	0.881072	−	0.410850i	0.0712030	−	0.997462i	$-0.477316\pi$
$983$	27.6241	−	12.8813i	0.881072	−	0.410850i	0.809869	+	0.586611i	$0.199538\pi$
$984$	1.83615	−	0.668305i	0.0585345	−	0.0213048i
$985$		0			0
$986$	4.51192	+	25.5884i	0.143689	+	0.814900i
$987$	3.54249	+	3.54249i	0.112759	+	0.112759i
$988$	−3.43289	−	17.1624i	−0.109215	−	0.546008i
$989$			0.494429i			0.0157219i
$990$		0			0
$991$	26.9127	+	32.0734i	0.854912	+	1.01884i	0.999569	+	0.0293621i	$0.00934758\pi$
$991$	26.9127	+	32.0734i	0.854912	+	1.01884i	−0.144657	+	0.989482i	$0.546208\pi$
$992$	−2.11251	+	4.53030i	−0.0670724	+	0.143837i
$993$	0.000607319		0.00130240i	1.92727e−5		4.13304e-5i
$994$	−8.02570	+	9.56466i	−0.254560	+	0.303373i
$995$		0			0
$996$	−2.09371	+	1.20880i	−0.0663416	+	0.0383023i
$997$	−7.09538	−	10.1333i	−0.224713	−	0.320923i	0.690926	−	0.722926i	$-0.257203\pi$
$997$	−7.09538	−	10.1333i	−0.224713	−	0.320923i	−0.915639	+	0.402002i	$0.868314\pi$
$998$	2.20365	+	3.14714i	0.0697554	+	0.0996210i
$999$	3.46867	−	2.00264i	0.109744	−	0.0633606i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	950.2.bb.e.143.8		120
5.2	odd	4	inner	950.2.bb.e.257.8		120
5.3	odd	4		190.2.r.a.67.3	✓	120
5.4	even	2		190.2.r.a.143.3	yes	120
19.2	odd	18	inner	950.2.bb.e.743.8		120
95.2	even	36	inner	950.2.bb.e.857.8		120
95.59	odd	18		190.2.r.a.173.3	yes	120
95.78	even	36		190.2.r.a.97.3	yes	120

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
190.2.r.a.67.3	✓	120	5.3	odd	4
190.2.r.a.97.3	yes	120	95.78	even	36
190.2.r.a.143.3	yes	120	5.4	even	2
190.2.r.a.173.3	yes	120	95.59	odd	18
950.2.bb.e.143.8		120	1.1	even	1	trivial
950.2.bb.e.257.8		120	5.2	odd	4	inner
950.2.bb.e.743.8		120	19.2	odd	18	inner
950.2.bb.e.857.8		120	95.2	even	36	inner

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:	\( N \)	\(=\)	\( 950 = 2 \cdot 5^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	950.bb (of order \(36\), degree \(12\), minimal)

\(f(q)\)	\(=\)	\(q+(0.573576 - 0.819152i) q^{2} +(0.0201525 - 0.230344i) q^{3} +(-0.342020 - 0.939693i) q^{4} +(-0.177128 - 0.148628i) q^{6} +(-1.23887 - 4.62353i) q^{7} +(-0.965926 - 0.258819i) q^{8} +(2.90177 + 0.511661i) q^{9} +O(q^{10})\)	\(q+(0.573576 - 0.819152i) q^{2} +(0.0201525 - 0.230344i) q^{3} +(-0.342020 - 0.939693i) q^{4} +(-0.177128 - 0.148628i) q^{6} +(-1.23887 - 4.62353i) q^{7} +(-0.965926 - 0.258819i) q^{8} +(2.90177 + 0.511661i) q^{9} +(0.299320 + 0.518438i) q^{11} +(-0.223345 + 0.0598451i) q^{12} +(-4.00004 + 0.349958i) q^{13} +(-4.49796 - 1.63712i) q^{14} +(-0.766044 + 0.642788i) q^{16} +(-3.44552 - 2.41258i) q^{17} +(2.08352 - 2.08352i) q^{18} +(-4.23509 - 1.03152i) q^{19} +(-1.08997 + 0.192191i) q^{21} +(0.596362 + 0.0521749i) q^{22} +(3.98766 + 1.85948i) q^{23} +(-0.0790832 + 0.217279i) q^{24} +(-2.00766 + 3.47737i) q^{26} +(0.355871 - 1.32813i) q^{27} +(-3.92098 + 2.74550i) q^{28} +(1.07268 - 6.08348i) q^{29} +(4.32894 + 2.49932i) q^{31} +(0.0871557 + 0.996195i) q^{32} +(0.125451 - 0.0584987i) q^{33} +(-3.95254 + 1.43861i) q^{34} +(-0.511661 - 2.90177i) q^{36} +(2.05978 + 2.05978i) q^{37} +(-3.27412 + 2.87752i) q^{38} +0.928436i q^{39} +(-5.43198 - 6.47359i) q^{41} +(-0.467746 + 1.00308i) q^{42} +(0.0474908 + 0.101844i) q^{43} +(0.384799 - 0.458585i) q^{44} +(3.81042 - 2.19995i) q^{46} +(-2.59629 - 3.70788i) q^{47} +(0.132624 + 0.189407i) q^{48} +(-13.7800 + 7.95590i) q^{49} +(-0.625158 + 0.745035i) q^{51} +(1.69695 + 3.63911i) q^{52} +(-2.70861 + 5.80863i) q^{53} +(-0.883820 - 1.05330i) q^{54} +4.78663i q^{56} +(-0.322952 + 0.954738i) q^{57} +(-4.36803 - 4.36803i) q^{58} +(-0.921977 - 5.22879i) q^{59} +(-11.0985 + 4.03952i) q^{61} +(4.53030 - 2.11251i) q^{62} +(-1.22924 - 14.0503i) q^{63} +(0.866025 + 0.500000i) q^{64} +(0.0240363 - 0.136317i) q^{66} +(3.54544 - 2.48254i) q^{67} +(-1.08865 + 4.06288i) q^{68} +(0.508680 - 0.881060i) q^{69} +(0.892149 - 2.45116i) q^{71} +(-2.67047 - 1.24526i) q^{72} +(-5.65032 - 0.494339i) q^{73} +(2.86871 - 0.505832i) q^{74} +(0.479172 + 4.33248i) q^{76} +(2.02619 - 2.02619i) q^{77} +(0.760530 + 0.532529i) q^{78} +(10.9589 - 9.19562i) q^{79} +(8.00776 + 2.91459i) q^{81} +(-8.41851 + 0.736524i) q^{82} +(10.0994 - 2.70613i) q^{83} +(0.553391 + 0.958501i) q^{84} +(0.110666 + 0.0195134i) q^{86} +(-1.37968 - 0.369683i) q^{87} +(-0.154939 - 0.578242i) q^{88} +(-0.184391 - 0.154722i) q^{89} +(6.57357 + 18.0607i) q^{91} +(0.383476 - 4.38316i) q^{92} +(0.662941 - 0.946778i) q^{93} -4.52649 q^{94} +0.231224 q^{96} +(7.30298 - 10.4297i) q^{97} +(-1.38681 + 15.8513i) q^{98} +(0.603294 + 1.65754i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 120 q + 12 q^{7}+O(q^{10}) \) 120 * q + 12 * q^7	\( 120 q + 12 q^{7} - 36 q^{17} - 96 q^{21} - 24 q^{22} - 12 q^{26} + 96 q^{33} - 12 q^{41} + 72 q^{43} + 24 q^{47} + 24 q^{51} - 36 q^{53} - 84 q^{57} + 48 q^{61} + 24 q^{62} - 36 q^{63} - 24 q^{66} + 96 q^{67} + 12 q^{68} + 36 q^{73} + 12 q^{76} - 96 q^{78} + 144 q^{81} - 48 q^{82} - 24 q^{83} + 48 q^{86} - 72 q^{87} + 72 q^{91} - 72 q^{92} - 156 q^{93} - 120 q^{97} - 24 q^{98}+O(q^{100}) \) 120 * q + 12 * q^7 - 36 * q^17 - 96 * q^21 - 24 * q^22 - 12 * q^26 + 96 * q^33 - 12 * q^41 + 72 * q^43 + 24 * q^47 + 24 * q^51 - 36 * q^53 - 84 * q^57 + 48 * q^61 + 24 * q^62 - 36 * q^63 - 24 * q^66 + 96 * q^67 + 12 * q^68 + 36 * q^73 + 12 * q^76 - 96 * q^78 + 144 * q^81 - 48 * q^82 - 24 * q^83 + 48 * q^86 - 72 * q^87 + 72 * q^91 - 72 * q^92 - 156 * q^93 - 120 * q^97 - 24 * q^98

Introduction

L-functions

Modular forms

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